LMFDB - Embedded newform 18.11.d.a.5.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [18,11,Mod(5,18)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			5.9
Root			$0.500000 + 42.2052i$ of defining polynomial
Character	$\chi$	$=$	18.5
Dual form			18.11.d.a.11.9

$q$-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} +(223.765 - 94.7529i) q^{3} +(256.000 - 443.405i) q^{4} +(3162.64 + 1825.95i) q^{5} +(3312.88 - 4388.38i) q^{6} +(5852.43 + 10136.7i) q^{7} -11585.2i q^{8} +(41092.8 - 42404.8i) q^{9} +82633.0 q^{10} +(-131578. + 75966.4i) q^{11} +(15270.0 - 123475. i) q^{12} +(106294. - 184107. i) q^{13} +(229368. + 132425. i) q^{14} +(880702. + 108915. i) q^{15} +(-131072. - 227023. i) q^{16} -1.52035e6i q^{17} +(325495. - 1.29587e6i) q^{18} +340971. q^{19} +(1.61927e6 - 934886. i) q^{20} +(2.27005e6 + 1.71371e6i) q^{21} +(-1.71892e6 + 2.97726e6i) q^{22} +(1.03573e6 + 597980. i) q^{23} +(-1.09773e6 - 2.59237e6i) q^{24} +(1.78537e6 + 3.09235e6i) q^{25} -4.81032e6i q^{26} +(5.17716e6 - 1.33824e7i) q^{27} +5.99289e6 q^{28} +(-3.07705e7 + 1.77654e7i) q^{29} +(1.84904e7 - 7.82972e6i) q^{30} +(-2.43253e7 + 4.21326e7i) q^{31} +(-5.13695e6 - 2.96582e6i) q^{32} +(-2.22445e7 + 2.94660e7i) q^{33} +(-1.72008e7 - 2.97926e7i) q^{34} +4.27450e7i q^{35} +(-8.28275e6 - 2.90764e7i) q^{36} -1.18848e8 q^{37} +(6.68164e6 - 3.85765e6i) q^{38} +(6.34027e6 - 5.12683e7i) q^{39} +(2.11541e7 - 3.66399e7i) q^{40} +(1.77670e8 + 1.02578e8i) q^{41} +(6.38722e7 + 7.89897e6i) q^{42} +(-4.42750e7 - 7.66865e7i) q^{43} +7.77896e7i q^{44} +(2.07391e8 - 5.90777e7i) q^{45} +2.70615e7 q^{46} +(2.02503e8 - 1.16915e8i) q^{47} +(-5.08405e7 - 3.83805e7i) q^{48} +(7.27357e7 - 1.25982e8i) q^{49} +(6.99720e7 + 4.03983e7i) q^{50} +(-1.44057e8 - 3.40201e8i) q^{51} +(-5.44226e7 - 9.42626e7i) q^{52} +7.02997e8i q^{53} +(-4.99532e7 - 3.20813e8i) q^{54} -5.54843e8 q^{55} +(1.17436e8 - 6.78018e7i) q^{56} +(7.62975e7 - 3.23080e7i) q^{57} +(-4.01985e8 + 6.96258e8i) q^{58} +(-4.55962e7 - 2.63250e7i) q^{59} +(2.73753e8 - 3.62626e8i) q^{60} +(-4.28509e8 - 7.42200e8i) q^{61} +1.10084e9i q^{62} +(6.70338e8 + 1.68374e8i) q^{63} -1.34218e8 q^{64} +(6.72339e8 - 3.88175e8i) q^{65} +(-1.02531e8 + 8.29081e8i) q^{66} +(-2.39467e7 + 4.14769e7i) q^{67} +(-6.74130e8 - 3.89209e8i) q^{68} +(2.88421e8 + 3.56686e7i) q^{69} +(4.83604e8 + 8.37627e8i) q^{70} -2.22381e8i q^{71} +(-4.91270e8 - 4.76070e8i) q^{72} -3.05274e9 q^{73} +(-2.32894e9 + 1.34461e9i) q^{74} +(6.92513e8 + 5.22792e8i) q^{75} +(8.72886e7 - 1.51188e8i) q^{76} +(-1.54010e9 - 8.89177e8i) q^{77} +(-4.55792e8 - 1.07638e9i) q^{78} +(2.49610e9 + 4.32338e9i) q^{79} -9.57323e8i q^{80} +(-1.09551e8 - 3.48506e9i) q^{81} +4.64215e9 q^{82} +(4.86087e9 - 2.80643e9i) q^{83} +(1.34100e9 - 5.67844e8i) q^{84} +(2.77608e9 - 4.80831e9i) q^{85} +(-1.73522e9 - 1.00183e9i) q^{86} +(-5.20205e9 + 6.89087e9i) q^{87} +(8.80089e8 + 1.52436e9i) q^{88} -3.85676e9i q^{89} +(3.39562e9 - 3.50404e9i) q^{90} +2.48832e9 q^{91} +(5.30295e8 - 3.06166e8i) q^{92} +(-1.45097e9 + 1.17327e10i) q^{93} +(2.64548e9 - 4.58211e9i) q^{94} +(1.07837e9 + 6.22596e8i) q^{95} +(-1.43049e9 - 1.76907e8i) q^{96} +(-4.68129e9 - 8.10823e9i) q^{97} -3.29164e9i q^{98} +(-2.18555e9 + 8.70120e9i) 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 $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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
$3$	223.765	−	94.7529i	0.920845	−	0.389930i
$3$	223.765	−	94.7529i	0.920845	−	0.389930i
$4$	256.000	−	443.405i	0.250000	−	0.433013i
$5$	3162.64	+	1825.95i	1.01204	+	0.584304i	0.911789	−	0.410658i	$-0.134701\pi$
$5$	3162.64	+	1825.95i	1.01204	+	0.584304i	0.100255	+	0.994962i	$0.468034\pi$
$6$	3312.88	−	4388.38i	0.426039	−	0.564350i
$7$	5852.43	+	10136.7i	0.348214	+	0.603124i	0.985932	−	0.167145i	$-0.0534549\pi$
$7$	5852.43	+	10136.7i	0.348214	+	0.603124i	−0.637718	+	0.770270i	$0.720122\pi$
$8$		−	11585.2i		−	0.353553i
$9$	41092.8	−	42404.8i	0.695910	−	0.718129i
$10$	82633.0			0.826330
$11$	−131578.	+	75966.4i	−0.816994	+	0.471692i	−0.849379	−	0.527784i	$-0.823023\pi$
$11$	−131578.	+	75966.4i	−0.816994	+	0.471692i	0.0323847	+	0.999475i	$0.489690\pi$
$12$	15270.0	−	123475.i	0.0613667	−	0.496220i
$13$	106294.	−	184107.i	0.286281	−	0.495853i	−0.686638	−	0.726999i	$-0.740914\pi$
$13$	106294.	−	184107.i	0.286281	−	0.495853i	0.972919	+	0.231146i	$0.0742477\pi$
$14$	229368.	+	132425.i	0.426473	+	0.246224i
$15$	880702.	+	108915.i	1.15977	+	0.143427i
$16$	−131072.	−	227023.i	−0.125000	−	0.216506i
$17$		−	1.52035e6i		−	1.07078i	−0.844606	−	0.535388i	$-0.820165\pi$
$17$		−	1.52035e6i		−	1.07078i	0.844606	−	0.535388i	$-0.179835\pi$
$18$	325495.	−	1.29587e6i	0.172259	−	0.685804i
$19$	340971.			0.137705			0.0688524	−	0.997627i	$-0.478066\pi$
$19$	340971.			0.137705			0.0688524	+	0.997627i	$0.478066\pi$
$20$	1.61927e6	−	934886.i	0.506022	−	0.292152i
$21$	2.27005e6	+	1.71371e6i	0.555827	+	0.419605i
$22$	−1.71892e6	+	2.97726e6i	−0.333536	+	0.577702i
$23$	1.03573e6	+	597980.i	0.160919	+	0.0929068i	0.578297	−	0.815826i	$-0.303717\pi$
$23$	1.03573e6	+	597980.i	0.160919	+	0.0929068i	−0.417378	+	0.908733i	$0.637051\pi$
$24$	−1.09773e6	−	2.59237e6i	−0.137861	−	0.325568i
$25$	1.78537e6	+	3.09235e6i	0.182822	+	0.316657i
$26$		−	4.81032e6i		−	0.404862i
$27$	5.17716e6	−	1.33824e7i	0.360805	−	0.932641i
$28$	5.99289e6			0.348214
$29$	−3.07705e7	+	1.77654e7i	−1.50019	+	0.866133i	−0.500186	+	0.865918i	$0.666735\pi$
$29$	−3.07705e7	+	1.77654e7i	−1.50019	+	0.866133i	−1.00000		0.000214283i	$0.999932\pi$
$30$	1.84904e7	−	7.82972e6i	0.760922	−	0.322211i
$31$	−2.43253e7	+	4.21326e7i	−0.849669	+	1.47167i	0.0318356	+	0.999493i	$0.489865\pi$
$31$	−2.43253e7	+	4.21326e7i	−0.849669	+	1.47167i	−0.881504	+	0.472176i	$0.843469\pi$
$32$	−5.13695e6	−	2.96582e6i	−0.153093	−	0.0883883i
$33$	−2.22445e7	+	2.94660e7i	−0.568398	+	0.752925i
$34$	−1.72008e7	−	2.97926e7i	−0.378576	−	0.655714i
$35$			4.27450e7i			0.813851i
$36$	−8.28275e6	−	2.90764e7i	−0.136982	−	0.480870i
$37$	−1.18848e8			−1.71389			−0.856947	−	0.515405i	$-0.827641\pi$
$37$	−1.18848e8			−1.71389			−0.856947	+	0.515405i	$0.827641\pi$
$38$	6.68164e6	−	3.85765e6i	0.0843267	−	0.0486860i
$39$	6.34027e6	−	5.12683e7i	0.0702724	−	0.568233i
$40$	2.11541e7	−	3.66399e7i	0.206583	−	0.357812i
$41$	1.77670e8	+	1.02578e8i	1.53354	+	0.885390i	0.999195	+	0.0401237i	$0.0127752\pi$
$41$	1.77670e8	+	1.02578e8i	1.53354	+	0.885390i	0.534346	+	0.845266i	$0.320558\pi$
$42$	6.38722e7	+	7.89897e6i	0.488726	+	0.0604399i
$43$	−4.42750e7	−	7.66865e7i	−0.301173	−	0.521647i	0.675229	−	0.737608i	$-0.264045\pi$
$43$	−4.42750e7	−	7.66865e7i	−0.301173	−	0.521647i	−0.976402	+	0.215961i	$0.930712\pi$
$44$			7.77896e7i			0.471692i
$45$	2.07391e8	−	5.90777e7i	1.12390	−	0.320155i
$46$	2.70615e7			0.131390
$47$	2.02503e8	−	1.16915e8i	0.882961	−	0.509778i	0.0113273	−	0.999936i	$-0.496394\pi$
$47$	2.02503e8	−	1.16915e8i	0.882961	−	0.509778i	0.871634	+	0.490158i	$0.163061\pi$
$48$	−5.08405e7	−	3.83805e7i	−0.199528	−	0.150628i
$49$	7.27357e7	−	1.25982e8i	0.257494	−	0.445993i
$50$	6.99720e7	+	4.03983e7i	0.223910	+	0.129275i
$51$	−1.44057e8	−	3.40201e8i	−0.417527	−	0.986018i
$52$	−5.44226e7	−	9.42626e7i	−0.143140	−	0.247926i
$53$			7.02997e8i			1.68103i	0.541792	+	0.840513i	$0.317746\pi$
$53$			7.02997e8i			1.68103i	−0.541792	+	0.840513i	$0.682254\pi$
$54$	−4.99532e7	−	3.20813e8i	−0.108791	−	0.698688i
$55$	−5.54843e8			−1.10245
$56$	1.17436e8	−	6.78018e7i	0.213237	−	0.123112i
$57$	7.62975e7	−	3.23080e7i	0.126805	−	0.0536952i
$58$	−4.01985e8	+	6.96258e8i	−0.612448	+	1.06079i
$59$	−4.55962e7	−	2.63250e7i	−0.0637777	−	0.0368221i	0.467772	−	0.883849i	$-0.345057\pi$
$59$	−4.55962e7	−	2.63250e7i	−0.0637777	−	0.0368221i	−0.531550	+	0.847027i	$0.678390\pi$
$60$	2.73753e8	−	3.62626e8i	0.352049	−	0.466339i
$61$	−4.28509e8	−	7.42200e8i	−0.507354	−	0.878762i	−0.999964	−	0.00851229i	$-0.997290\pi$
$61$	−4.28509e8	−	7.42200e8i	−0.507354	−	0.878762i	0.492610	−	0.870250i	$-0.336043\pi$
$62$			1.10084e9i			1.20161i
$63$	6.70338e8	+	1.68374e8i	0.675447	+	0.169658i
$64$	−1.34218e8			−0.125000
$65$	6.72339e8	−	3.88175e8i	0.579457	−	0.334550i
$66$	−1.02531e8	+	8.29081e8i	−0.0818721	+	0.662030i
$67$	−2.39467e7	+	4.14769e7i	−0.0177367	+	0.0307208i	−0.874758	−	0.484561i	$-0.838979\pi$
$67$	−2.39467e7	+	4.14769e7i	−0.0177367	+	0.0307208i	0.857021	+	0.515282i	$0.172313\pi$
$68$	−6.74130e8	−	3.89209e8i	−0.463660	−	0.267694i
$69$	2.88421e8	+	3.56686e7i	0.184409	+	0.0228055i
$70$	4.83604e8	+	8.37627e8i	0.287740	+	0.498380i
$71$		−	2.22381e8i		−	0.123255i	−0.998099	−	0.0616276i	$-0.980371\pi$
$71$		−	2.22381e8i		−	0.123255i	0.998099	−	0.0616276i	$-0.0196291\pi$
$72$	−4.91270e8	−	4.76070e8i	−0.253897	−	0.246041i
$73$	−3.05274e9			−1.47257			−0.736284	−	0.676673i	$-0.763421\pi$
$73$	−3.05274e9			−1.47257			−0.736284	+	0.676673i	$0.763421\pi$
$74$	−2.32894e9	+	1.34461e9i	−1.04954	+	0.605953i
$75$	6.92513e8	+	5.22792e8i	0.291825	+	0.220304i
$76$	8.72886e7	−	1.51188e8i	0.0344262	−	0.0596280i
$77$	−1.54010e9	−	8.89177e8i	−0.568978	−	0.328499i
$78$	−4.55792e8	−	1.07638e9i	−0.157868	−	0.372815i
$79$	2.49610e9	+	4.32338e9i	0.811199	+	1.40504i	0.912026	+	0.410133i	$0.134518\pi$
$79$	2.49610e9	+	4.32338e9i	0.811199	+	1.40504i	−0.100827	+	0.994904i	$0.532149\pi$
$80$		−	9.57323e8i		−	0.292152i
$81$	−1.09551e8	−	3.48506e9i	−0.0314190	−	0.999506i
$82$	4.64215e9			1.25213
$83$	4.86087e9	−	2.80643e9i	1.23402	−	0.712464i	0.266158	−	0.963929i	$-0.414246\pi$
$83$	4.86087e9	−	2.80643e9i	1.23402	−	0.712464i	0.967866	+	0.251465i	$0.0809123\pi$
$84$	1.34100e9	−	5.67844e8i	0.320651	−	0.135779i
$85$	2.77608e9	−	4.80831e9i	0.625658	−	1.08367i
$86$	−1.73522e9	−	1.00183e9i	−0.368860	−	0.212962i
$87$	−5.20205e9	+	6.89087e9i	−1.04371	+	1.38254i
$88$	8.80089e8	+	1.52436e9i	0.166768	+	0.288851i
$89$		−	3.85676e9i		−	0.690673i	−0.938479	−	0.345336i	$-0.887765\pi$
$89$		−	3.85676e9i		−	0.690673i	0.938479	−	0.345336i	$-0.112235\pi$
$90$	3.39562e9	−	3.50404e9i	0.575051	−	0.593412i
$91$	2.48832e9			0.398748
$92$	5.30295e8	−	3.06166e8i	0.0804597	−	0.0464534i
$93$	−1.45097e9	+	1.17327e10i	−0.208565	+	1.68649i
$94$	2.64548e9	−	4.58211e9i	0.360467	−	0.624348i
$95$	1.07837e9	+	6.22596e8i	0.139363	+	0.0804615i
$96$	−1.43049e9	−	1.76907e8i	−0.175440	−	0.0216964i
$97$	−4.68129e9	−	8.10823e9i	−0.545138	−	0.944207i	−0.998598	−	0.0529305i	$-0.983144\pi$
$97$	−4.68129e9	−	8.10823e9i	−0.545138	−	0.944207i	0.453460	−	0.891277i	$-0.350190\pi$
$98$		−	3.29164e9i		−	0.364152i
$99$	−2.18555e9	+	8.70120e9i	−0.229819	+	0.914962i
$100$	1.82822e9			0.182822
$101$	6.27443e7	−	3.62254e7i	0.00596991	−	0.00344673i	−0.497012	−	0.867744i	$-0.665570\pi$
$101$	6.27443e7	−	3.62254e7i	0.00596991	−	0.00344673i	0.502982	+	0.864297i	$0.332236\pi$
$102$	−6.67187e9	−	5.03673e9i	−0.604292	−	0.456192i
$103$	4.76275e8	−	8.24932e8i	0.0410839	−	0.0711594i	−0.844752	−	0.535158i	$-0.820252\pi$
$103$	4.76275e8	−	8.24932e8i	0.0410839	−	0.0711594i	0.885836	+	0.463998i	$0.153586\pi$
$104$	−2.13292e9	−	1.23144e9i	−0.175310	−	0.101216i
$105$	4.05021e9	+	9.56484e9i	0.317345	+	0.749431i
$106$	7.95350e9	+	1.37759e10i	0.594332	+	1.02941i
$107$		−	8.93547e7i		−	0.00637087i	−0.999995	−	0.00318543i	$-0.998986\pi$
$107$		−	8.93547e7i		−	0.00637087i	0.999995	−	0.00318543i	$-0.00101396\pi$
$108$	−4.60846e9	−	5.72147e9i	−0.313644	−	0.389393i
$109$	−2.03023e9			−0.131951			−0.0659755	−	0.997821i	$-0.521016\pi$
$109$	−2.03023e9			−0.131951			−0.0659755	+	0.997821i	$0.521016\pi$
$110$	−1.08727e10	+	6.27734e9i	−0.675107	+	0.389773i
$111$	−2.65941e10	+	1.12612e10i	−1.57823	+	0.668298i
$112$	1.53418e9	−	2.65728e9i	0.0870535	−	0.150781i
$113$	−1.28328e10	−	7.40901e9i	−0.696512	−	0.402131i	0.109535	−	0.993983i	$-0.465064\pi$
$113$	−1.28328e10	−	7.40901e9i	−0.696512	−	0.402131i	−0.806047	+	0.591852i	$0.798397\pi$
$114$	1.12960e9	−	1.49631e9i	0.0586677	−	0.0777137i
$115$	2.18376e9	+	3.78239e9i	0.108572	+	0.188052i
$116$			1.81917e10i			0.866133i
$117$	−3.43909e9	−	1.20728e10i	−0.156861	−	0.550655i
$118$	−1.19133e9			−0.0520743
$119$	1.54113e10	−	8.89774e9i	0.645811	−	0.372859i
$120$	1.26181e9	−	1.02031e10i	0.0507092	−	0.410042i
$121$	−1.42692e9	+	2.47149e9i	−0.0550138	+	0.0952866i
$122$	−1.67941e10	−	9.69605e9i	−0.621379	−	0.358753i
$123$	4.94760e10	+	6.11861e9i	1.75739	+	0.217334i
$124$	1.24545e10	+	2.15719e10i	0.424834	+	0.735835i
$125$		−	2.26231e10i		−	0.741313i
$126$	1.50408e10	−	4.28456e9i	0.473608	−	0.134913i
$127$	−3.69110e10			−1.11722			−0.558609	−	0.829431i	$-0.688665\pi$
$127$	−3.69110e10			−1.11722			−0.558609	+	0.829431i	$0.688665\pi$
$128$	−2.63012e9	+	1.51850e9i	−0.0765466	+	0.0441942i
$129$	−1.71735e10	−	1.29646e10i	−0.480739	−	0.362920i
$130$	8.78340e9	−	1.52133e10i	0.236563	−	0.409738i
$131$	4.89461e10	+	2.82590e10i	1.26871	+	0.732489i	0.974743	−	0.223328i	$-0.0716921\pi$
$131$	4.89461e10	+	2.82590e10i	1.26871	+	0.732489i	0.293964	+	0.955816i	$0.405025\pi$
$132$	7.37079e9	+	1.74066e10i	0.183927	+	0.434355i
$133$	1.99551e9	+	3.45632e9i	0.0479508	+	0.0830532i
$134$			1.08371e9i			0.0250834i
$135$	4.08090e10	−	3.28704e10i	0.910096	−	0.733054i
$136$	−1.76136e10			−0.378576
$137$	2.53896e10	−	1.46587e10i	0.526081	−	0.303733i	−0.213338	−	0.976978i	$-0.568434\pi$
$137$	2.53896e10	−	1.46587e10i	0.526081	−	0.303733i	0.739419	+	0.673246i	$0.235100\pi$
$138$	6.05542e9	−	2.56415e9i	0.120990	−	0.0512329i
$139$	3.03788e10	−	5.26175e10i	0.585458	−	1.01404i	−0.409360	−	0.912373i	$-0.634248\pi$
$139$	3.03788e10	−	5.26175e10i	0.585458	−	1.01404i	0.994818	−	0.101670i	$-0.0324187\pi$
$140$	1.89533e10	+	1.09427e10i	0.352408	+	0.203463i
$141$	3.42350e10	−	4.53492e10i	0.614292	−	0.813719i
$142$	−2.51595e9	−	4.35776e9i	−0.0435773	−	0.0754781i
$143$			3.22991e10i			0.540145i
$144$	−1.50130e10	−	3.77094e9i	−0.242468	−	0.0609028i
$145$	−1.29755e11			−2.02434
$146$	−5.98212e10	+	3.45378e10i	−0.901760	+	0.520631i
$147$	4.33857e9	−	3.50823e10i	0.0632062	−	0.511095i
$148$	−3.04251e10	+	5.26979e10i	−0.428473	+	0.742138i
$149$	3.33005e10	+	1.92260e10i	0.453439	+	0.261793i	0.709282	−	0.704925i	$-0.249019\pi$
$149$	3.33005e10	+	1.92260e10i	0.453439	+	0.261793i	−0.255842	+	0.966719i	$0.582353\pi$
$150$	1.94852e10	+	2.40970e9i	0.256595	+	0.0317326i
$151$	3.59859e10	+	6.23294e10i	0.458403	+	0.793977i	0.998877	−	0.0473838i	$-0.0150884\pi$
$151$	3.59859e10	+	6.23294e10i	0.458403	+	0.793977i	−0.540474	+	0.841361i	$0.681755\pi$
$152$		−	3.95023e9i		−	0.0486860i
$153$	−6.44701e10	−	6.24753e10i	−0.768955	−	0.745163i
$154$	−4.02396e10			−0.464568
$155$	−1.53864e11	+	8.88335e10i	−1.71980	+	0.992929i
$156$	−2.11095e10	−	1.59360e10i	−0.228484	−	0.172487i
$157$	3.94461e10	−	6.83226e10i	0.413529	−	0.716253i	−0.581744	−	0.813372i	$-0.697630\pi$
$157$	3.94461e10	−	6.83226e10i	0.413529	−	0.716253i	0.995273	+	0.0971193i	$0.0309628\pi$
$158$	9.78269e10	+	5.64804e10i	0.993511	+	0.573604i
$159$	6.66110e10	+	1.57306e11i	0.655481	+	1.54796i
$160$	−1.08309e10	−	1.87596e10i	−0.103291	−	0.178906i
$161$			1.39986e10i			0.129406i
$162$	−4.15757e10	−	6.70536e10i	−0.372619	−	0.600962i
$163$	−6.72335e10			−0.584315			−0.292158	−	0.956370i	$-0.594373\pi$
$163$	−6.72335e10			−0.584315			−0.292158	+	0.956370i	$0.594373\pi$
$164$	9.09671e10	−	5.25199e10i	0.766770	−	0.442695i
$165$	−1.24155e11	+	5.25730e10i	−1.01518	+	0.429876i
$166$	6.35022e10	−	1.09989e11i	0.503788	−	0.872587i
$167$	5.54731e10	+	3.20274e10i	0.427071	+	0.246570i	0.698098	−	0.716002i	$-0.254030\pi$
$167$	5.54731e10	+	3.20274e10i	0.427071	+	0.246570i	−0.271027	+	0.962572i	$0.587363\pi$
$168$	1.98537e10	−	2.62991e10i	0.148353	−	0.196515i
$169$	4.63324e10	+	8.02501e10i	0.336087	+	0.582119i
$170$		−	1.25631e11i		−	0.884815i
$171$	1.40114e10	−	1.44588e10i	0.0958302	−	0.0988899i
$172$	−4.53376e10			−0.301173
$173$	6.49531e10	−	3.75007e10i	0.419150	−	0.241996i	−0.275563	−	0.961283i	$-0.588864\pi$
$173$	6.49531e10	−	3.75007e10i	0.419150	−	0.241996i	0.694714	+	0.719286i	$0.255531\pi$
$174$	−2.39777e10	+	1.93887e11i	−0.150336	+	1.21564i
$175$	−2.08975e10	+	3.61956e10i	−0.127322	+	0.220529i
$176$	3.44923e10	+	1.99141e10i	0.204249	+	0.117923i
$177$	−1.26972e10	−	1.57024e9i	−0.0730874	−	0.00903860i
$178$	−4.36342e10	−	7.55767e10i	−0.244190	−	0.422949i
$179$			1.52027e11i			0.827287i	0.910439	+	0.413643i	$0.135744\pi$
$179$			1.52027e11i			0.827287i	−0.910439	+	0.413643i	$0.864256\pi$
$180$	2.68967e10	−	1.07082e11i	0.142343	−	0.566701i
$181$	5.19877e10			0.267613			0.133807	−	0.991007i	$-0.457280\pi$
$181$	5.19877e10			0.267613			0.133807	+	0.991007i	$0.457280\pi$
$182$	4.87608e10	−	2.81521e10i	0.244182	−	0.140979i
$183$	−1.66211e11	−	1.25476e11i	−0.809849	−	0.611372i
$184$	6.92774e9	−	1.19992e10i	0.0328475	−	0.0568936i
$185$	−3.75874e11	−	2.17011e11i	−1.73454	−	1.00143i
$186$	1.04307e11	+	2.46329e11i	0.468544	+	1.10650i
$187$	1.15495e11	+	2.00044e11i	0.505076	+	0.874817i
$188$		−	1.19721e11i		−	0.509778i
$189$	1.65952e11	−	2.58401e10i	0.688136	−	0.107148i
$190$	2.81755e10			0.113790
$191$	1.04066e11	−	6.00827e10i	0.409396	−	0.236365i	−0.281134	−	0.959668i	$-0.590711\pi$
$191$	1.04066e11	−	6.00827e10i	0.409396	−	0.236365i	0.690530	+	0.723304i	$0.257377\pi$
$192$	−3.00333e10	+	1.27175e10i	−0.115106	+	0.0487412i
$193$	1.75779e11	−	3.04457e11i	0.656416	−	1.13695i	−0.325120	−	0.945673i	$-0.605405\pi$
$193$	1.75779e11	−	3.04457e11i	0.656416	−	1.13695i	0.981537	−	0.191274i	$-0.0612618\pi$
$194$	−1.83468e11	−	1.05925e11i	−0.667655	−	0.385471i
$195$	1.13665e11	−	1.50566e11i	0.403139	−	0.534016i
$196$	−3.72407e10	−	6.45027e10i	−0.128747	−	0.222996i
$197$		−	3.22893e10i		−	0.108825i	−0.998519	−	0.0544124i	$-0.982671\pi$
$197$		−	3.22893e10i		−	0.108825i	0.998519	−	0.0544124i	$-0.0173286\pi$
$198$	5.56149e10	+	1.95235e11i	0.182753	+	0.641551i
$199$	5.88252e11			1.88494			0.942471	−	0.334288i	$-0.108496\pi$
$199$	5.88252e11			1.88494			0.942471	+	0.334288i	$0.108496\pi$
$200$	3.58257e10	−	2.06839e10i	0.111955	−	0.0646373i
$201$	−1.42838e9	+	1.15501e10i	−0.00435376	+	0.0352052i
$202$	8.19688e8	−	1.41974e9i	0.00243720	−	0.00422136i
$203$	−3.60165e11	−	2.07941e11i	−1.04477	−	0.603199i
$204$	−1.87726e11	−	2.32157e10i	−0.531340	−	0.0657100i
$205$	3.74604e11	+	6.48833e11i	1.03467	+	1.79211i
$206$		−	2.15537e10i		−	0.0581014i
$207$	6.79183e10	−	1.93474e10i	0.178704	−	0.0509061i
$208$	−5.57287e10			−0.143140
$209$	−4.48642e10	+	2.59023e10i	−0.112504	+	0.0649543i
$210$	1.87581e11	+	1.41609e11i	0.459297	+	0.346732i
$211$	−7.82714e10	+	1.35570e11i	−0.187150	+	0.324154i	−0.944299	−	0.329089i	$-0.893259\pi$
$211$	−7.82714e10	+	1.35570e11i	−0.187150	+	0.324154i	0.757149	+	0.653243i	$0.226592\pi$
$212$	3.11712e11	+	1.79967e11i	0.727905	+	0.420256i
$213$	−2.10712e10	−	4.97611e10i	−0.0480609	−	0.113499i
$214$	−1.01093e9	−	1.75099e9i	−0.00225244	−	0.00390134i
$215$		−	3.23376e11i		−	0.703906i
$216$	−1.55038e11	−	5.99786e10i	−0.329738	−	0.127564i
$217$	−5.69449e11			−1.18347
$218$	−3.97842e10	+	2.29694e10i	−0.0808032	+	0.0466517i
$219$	−6.83097e11	+	2.89256e11i	−1.35601	+	0.574198i
$220$	−1.42040e11	+	2.46020e11i	−0.275611	+	0.477373i
$221$	−2.79906e11	−	1.61604e11i	−0.530947	−	0.306543i
$222$	−3.93730e11	+	5.21551e11i	−0.730185	+	0.967235i
$223$	−4.34379e11	−	7.52367e11i	−0.787671	−	1.36429i	−0.927390	−	0.374095i	$-0.877953\pi$
$223$	−4.34379e11	−	7.52367e11i	−0.787671	−	1.36429i	0.139719	−	0.990191i	$-0.455380\pi$
$224$		−	6.94291e10i		−	0.123112i
$225$	2.04497e11	+	5.13651e10i	0.354628	+	0.0890749i
$226$	−3.35293e11			−0.568699
$227$	8.19350e10	−	4.73052e10i	0.135938	−	0.0784837i	−0.430489	−	0.902596i	$-0.641659\pi$
$227$	8.19350e10	−	4.73052e10i	0.135938	−	0.0784837i	0.566427	+	0.824112i	$0.308325\pi$
$228$	5.20663e9	−	4.21015e10i	0.00845050	−	0.0683319i
$229$	1.89713e10	−	3.28592e10i	0.0301244	−	0.0521770i	−0.850570	−	0.525862i	$-0.823743\pi$
$229$	1.89713e10	−	3.28592e10i	0.0301244	−	0.0521770i	0.880695	+	0.473685i	$0.157076\pi$
$230$	8.55857e10	+	4.94129e10i	0.132973	+	0.0767717i
$231$	−4.28873e11	−	5.30380e10i	−0.652032	−	0.0806357i
$232$	2.05816e11	+	3.56484e11i	0.306224	+	0.530396i
$233$			1.02896e12i			1.49837i	0.662362	+	0.749184i	$0.269554\pi$
$233$			1.02896e12i			1.49837i	−0.662362	+	0.749184i	$0.730446\pi$
$234$	−2.03981e11	−	1.97669e11i	−0.290743	−	0.281748i
$235$	8.53923e11			1.19146
$236$	−2.33453e10	+	1.34784e10i	−0.0318888	+	0.0184110i
$237$	9.68194e11	+	7.30909e11i	1.29485	+	0.977511i
$238$	2.01333e11	−	3.48719e11i	0.263651	−	0.456657i
$239$	1.32651e11	+	7.65862e10i	0.170107	+	0.0982112i	0.582636	−	0.812733i	$-0.302021\pi$
$239$	1.32651e11	+	7.65862e10i	0.170107	+	0.0982112i	−0.412529	+	0.910944i	$0.635355\pi$
$240$	−9.07092e10	−	2.14216e11i	−0.113919	−	0.269027i
$241$	−2.12481e11	−	3.68028e11i	−0.261358	−	0.452685i	0.705245	−	0.708963i	$-0.250837\pi$
$241$	−2.12481e11	−	3.68028e11i	−0.261358	−	0.452685i	−0.966603	+	0.256279i	$0.917503\pi$
$242$			6.45748e10i			0.0778012i
$243$	−3.54734e11	−	7.69456e11i	−0.418669	−	0.908139i
$244$	−4.38793e11			−0.507354
$245$	4.60073e11	−	2.65623e11i	0.521191	−	0.300909i
$246$	1.03875e12	−	4.39857e11i	1.15302	−	0.488243i
$247$	3.62432e10	−	6.27750e10i	0.0394223	−	0.0682814i
$248$	4.88117e11	+	2.81814e11i	0.520314	+	0.300403i
$249$	8.21778e11	−	1.08856e12i	0.858534	−	1.13725i
$250$	−2.55951e11	−	4.43320e11i	−0.262094	−	0.453960i
$251$			6.85034e11i			0.687612i	0.939041	+	0.343806i	$0.111716\pi$
$251$			6.85034e11i			0.687612i	−0.939041	+	0.343806i	$0.888284\pi$
$252$	2.46265e11	−	2.54127e11i	0.242326	−	0.250063i
$253$	−1.81706e11			−0.175294
$254$	−7.23306e11	+	4.17601e11i	−0.684153	+	0.394996i
$255$	1.65589e11	−	1.33897e12i	0.153578	−	1.24186i
$256$	−3.43597e10	+	5.95128e10i	−0.0312500	+	0.0541266i
$257$	1.61709e12	+	9.33627e11i	1.44234	+	0.832737i	0.998006	−	0.0631235i	$-0.0201062\pi$
$257$	1.61709e12	+	9.33627e11i	1.44234	+	0.832737i	0.444336	+	0.895860i	$0.353440\pi$
$258$	−4.83208e11	−	5.97575e10i	−0.422703	−	0.0522750i
$259$	−6.95551e11	−	1.20473e12i	−0.596802	−	1.03369i
$260$		−	3.97491e11i		−	0.334550i
$261$	−5.11109e11	+	2.03485e12i	−0.421999	+	1.68008i
$262$	1.27886e12			1.03590
$263$	5.15828e11	−	2.97813e11i	0.409945	−	0.236682i	−0.280821	−	0.959760i	$-0.590607\pi$
$263$	5.15828e11	−	2.97813e11i	0.409945	−	0.236682i	0.690766	+	0.723078i	$0.257273\pi$
$264$	3.41371e11	+	2.57708e11i	0.266199	+	0.200959i
$265$	−1.28364e12	+	2.22332e12i	−0.982229	+	1.70127i
$266$	7.82077e10	+	4.51532e10i	0.0587275	+	0.0339063i
$267$	−3.65439e11	−	8.63008e11i	−0.269314	−	0.636002i
$268$	1.22607e10	+	2.12362e10i	0.00886834	+	0.0153604i
$269$		−	2.12934e11i		−	0.151176i	−0.997139	−	0.0755882i	$-0.975917\pi$
$269$		−	2.12934e11i		−	0.151176i	0.997139	−	0.0755882i	$-0.0240835\pi$
$270$	4.27804e11	−	1.10583e12i	0.298144	−	0.770670i
$271$	−1.78769e12			−1.22305			−0.611527	−	0.791224i	$-0.709444\pi$
$271$	−1.78769e12			−1.22305			−0.611527	+	0.791224i	$0.709444\pi$
$272$	−3.45155e11	+	1.99275e11i	−0.231830	+	0.133847i
$273$	5.56798e11	−	2.35775e11i	0.367185	−	0.155484i
$274$	3.31688e11	−	5.74500e11i	0.214772	−	0.371995i
$275$	−4.69830e11	−	2.71257e11i	−0.298729	−	0.172471i
$276$	8.96515e10	−	1.18756e11i	0.0559773	−	0.0741500i
$277$	−4.15440e11	−	7.19564e11i	−0.254747	−	0.441235i	0.710080	−	0.704121i	$-0.248659\pi$
$277$	−4.15440e11	−	7.19564e11i	−0.254747	−	0.441235i	−0.964827	+	0.262886i	$0.915326\pi$
$278$		−	1.37479e12i		−	0.827963i
$279$	7.87033e11	+	2.76286e12i	0.465556	+	1.63432i
$280$	4.95211e11			0.287740
$281$	7.78305e11	−	4.49355e11i	0.444241	−	0.256483i	−0.261154	−	0.965297i	$-0.584103\pi$
$281$	7.78305e11	−	4.49355e11i	0.444241	−	0.256483i	0.705395	+	0.708815i	$0.250770\pi$
$282$	1.57799e11	−	1.27598e12i	0.0884828	−	0.715484i
$283$	−9.41017e11	+	1.62989e12i	−0.518400	+	0.897896i	0.481371	+	0.876517i	$0.340139\pi$
$283$	−9.41017e11	+	1.62989e12i	−0.518400	+	0.897896i	−0.999771	+	0.0213787i	$0.993194\pi$
$284$	−9.86047e10	−	5.69295e10i	−0.0533711	−	0.0308138i
$285$	3.00294e11	+	3.71369e10i	0.159706	+	0.0197506i
$286$	3.65423e11	+	6.32931e11i	0.190970	+	0.330770i
$287$			2.40132e12i			1.23322i
$288$	−3.36857e11	+	9.59577e10i	−0.170013	+	0.0484303i
$289$	−2.95466e11			−0.146561
$290$	−2.54266e12	+	1.46801e12i	−1.23965	+	0.715712i
$291$	−1.81579e12	−	1.37077e12i	−0.870162	−	0.656903i
$292$	−7.81501e11	+	1.35360e12i	−0.368142	+	0.637640i
$293$	−2.76755e12	−	1.59785e12i	−1.28162	−	0.739941i	−0.304472	−	0.952521i	$-0.598480\pi$
$293$	−2.76755e12	−	1.59785e12i	−1.28162	−	0.739941i	−0.977144	+	0.212580i	$0.931813\pi$
$294$	−3.11893e11	−	7.36555e11i	−0.141993	−	0.335327i
$295$	−9.61362e10	−	1.66513e11i	−0.0430306	−	0.0745311i
$296$			1.37688e12i			0.605953i
$297$	3.35413e11	+	2.15411e12i	0.145144	+	0.932151i
$298$	8.70071e11			0.370232
$299$	2.20184e11	−	1.27123e11i	0.0921362	−	0.0531949i
$300$	4.09092e11	−	1.73229e11i	0.168351	−	0.0712877i
$301$	5.18233e11	−	8.97606e11i	0.209745	−	0.363290i
$302$	1.41035e12	+	8.14267e11i	0.561426	+	0.324140i
$303$	1.06075e10	−	1.40512e10i	0.00415337	−	0.00550174i
$304$	−4.46917e10	−	7.74084e10i	−0.0172131	−	0.0298140i
$305$		−	3.12974e12i		−	1.18580i
$306$	−1.97018e12	−	4.94866e11i	−0.734342	−	0.184451i
$307$	4.68391e12			1.71758			0.858790	−	0.512328i	$-0.171217\pi$
$307$	4.68391e12			1.71758			0.858790	+	0.512328i	$0.171217\pi$
$308$	−7.88531e11	+	4.55259e11i	−0.284489	+	0.164250i
$309$	2.84090e10	−	2.29720e11i	0.0100847	−	0.0815465i
$310$	−2.01007e12	+	3.48155e12i	−0.702107	+	1.21609i
$311$	−6.10835e11	−	3.52666e11i	−0.209953	−	0.121216i	0.391337	−	0.920248i	$-0.372013\pi$
$311$	−6.10835e11	−	3.52666e11i	−0.209953	−	0.121216i	−0.601290	+	0.799031i	$0.705346\pi$
$312$	−5.93956e11	−	7.34536e10i	−0.200901	−	0.0248451i
$313$	−7.37908e11	−	1.27809e12i	−0.245630	−	0.425443i	0.716679	−	0.697403i	$-0.245661\pi$
$313$	−7.37908e11	−	1.27809e12i	−0.245630	−	0.425443i	−0.962308	+	0.271960i	$0.912328\pi$
$314$		−	1.78513e12i		−	0.584818i
$315$	1.81259e12	+	1.75651e12i	0.584450	+	0.566367i
$316$	2.55601e12			0.811199
$317$	3.14283e12	−	1.81451e12i	0.981803	−	0.566844i	0.0789891	−	0.996875i	$-0.474831\pi$
$317$	3.14283e12	−	1.81451e12i	0.981803	−	0.566844i	0.902814	+	0.430031i	$0.141497\pi$
$318$	3.08502e12	+	2.32894e12i	0.948686	+	0.716182i
$319$	2.69914e12	−	4.67505e12i	0.817095	−	1.41525i
$320$	−4.24482e11	−	2.45075e11i	−0.126505	−	0.0730380i
$321$	−8.46662e9	−	1.99945e10i	−0.00248419	−	0.00586658i
$322$	1.58376e11	+	2.74315e11i	0.0457519	+	0.0792446i
$323$		−	5.18395e11i		−	0.147451i
$324$	−1.57334e12	−	8.43601e11i	−0.440654	−	0.236272i
$325$	7.59097e11			0.209354
$326$	−1.31750e12	+	7.60660e11i	−0.357819	+	0.206587i
$327$	−4.54295e11	+	1.92370e11i	−0.121506	+	0.0514516i
$328$	1.18839e12	−	2.05835e12i	0.313033	−	0.542188i
$329$	2.37027e12	+	1.36847e12i	0.614919	+	0.355023i
$330$	−1.83813e12	+	2.43487e12i	−0.469685	+	0.622165i
$331$	−2.20514e12	−	3.81942e12i	−0.555004	−	0.961296i	−0.997903	−	0.0647242i	$-0.979383\pi$
$331$	−2.20514e12	−	3.81942e12i	−0.555004	−	0.961296i	0.442899	−	0.896572i	$-0.353950\pi$
$332$		−	2.87378e12i		−	0.712464i
$333$	−4.88380e12	+	5.03973e12i	−1.19272	+	1.23080i
$334$	1.44940e12			0.348702
$335$	−1.51470e11	+	8.74510e10i	−0.0359006	+	0.0207272i
$336$	9.15114e10	−	7.39974e11i	0.0213687	−	0.172791i
$337$	−1.88574e12	+	3.26619e12i	−0.433842	+	0.751436i	−0.997200	−	0.0747767i	$-0.976176\pi$
$337$	−1.88574e12	+	3.26619e12i	−0.433842	+	0.751436i	0.563359	+	0.826212i	$0.309509\pi$
$338$	1.81585e12	+	1.04838e12i	0.411620	+	0.237649i
$339$	−3.57355e12	−	4.41936e11i	−0.798182	−	0.0987099i
$340$	−1.42135e12	−	2.46186e12i	−0.312829	−	0.541836i
$341$		−	7.39162e12i		−	1.60313i
$342$	1.10984e11	−	4.41855e11i	0.0237209	−	0.0944385i
$343$	5.00906e12			1.05508
$344$	−8.88432e11	+	5.12936e11i	−0.184430	+	0.106481i
$345$	8.47043e11	+	6.39449e11i	0.173304	+	0.130831i
$346$	8.48544e11	−	1.46972e12i	0.171117	−	0.296384i
$347$	2.11889e11	+	1.22334e11i	0.0421174	+	0.0243165i	0.520911	−	0.853611i	$-0.325592\pi$
$347$	2.11889e11	+	1.22334e11i	0.0421174	+	0.0243165i	−0.478793	+	0.877928i	$0.658926\pi$
$348$	1.72372e12	+	4.07068e12i	0.337731	+	0.797574i
$349$	3.20611e12	+	5.55314e12i	0.619228	+	1.07253i	0.989627	+	0.143662i	$0.0458878\pi$
$349$	3.20611e12	+	5.55314e12i	0.619228	+	1.07253i	−0.370399	+	0.928873i	$0.620779\pi$
$350$			9.45714e11i			0.180061i
$351$	−1.91349e12	−	2.37562e12i	−0.359161	−	0.445903i
$352$	9.01211e11			0.166768
$353$	2.14404e12	−	1.23786e12i	0.391165	−	0.225839i	−0.291500	−	0.956571i	$-0.594154\pi$
$353$	2.14404e12	−	1.23786e12i	0.391165	−	0.225839i	0.682665	+	0.730732i	$0.260821\pi$
$354$	−2.66579e11	+	1.12882e11i	−0.0479523	+	0.0203053i
$355$	4.06056e11	−	7.03310e11i	0.0720185	−	0.124740i
$356$	−1.71011e12	−	9.87330e11i	−0.299070	−	0.172668i
$357$	2.60543e12	−	3.45127e12i	0.449303	−	0.595166i
$358$	1.71999e12	+	2.97911e12i	0.292490	+	0.506607i
$359$			1.01918e13i			1.70914i	0.519333	+	0.854572i	$0.326180\pi$
$359$			1.01918e13i			1.70914i	−0.519333	+	0.854572i	$0.673820\pi$
$360$	−6.84429e11	−	2.40267e12i	−0.113192	−	0.397358i
$361$	−6.01481e12			−0.981037
$362$	1.01875e12	−	5.88174e11i	0.163879	−	0.0946156i
$363$	−8.51133e10	+	6.88238e11i	−0.0135041	+	0.109196i
$364$	6.37009e11	−	1.10333e12i	0.0996870	−	0.172663i
$365$	−9.65470e12	−	5.57414e12i	−1.49030	−	0.860427i
$366$	−4.67666e12	−	5.78354e11i	−0.712082	−	0.0880620i
$367$	3.92518e12	+	6.79862e12i	0.589562	+	1.02115i	0.994290	+	0.106714i	$0.0340330\pi$
$367$	3.92518e12	+	6.79862e12i	0.589562	+	1.02115i	−0.404728	+	0.914437i	$0.632634\pi$
$368$		−	3.13514e11i		−	0.0464534i
$369$	1.16508e13	−	3.31886e12i	1.70303	−	0.485128i
$370$	−9.82078e12			−1.41624
$371$	−7.12608e12	+	4.11424e12i	−1.01387	+	0.585356i
$372$	4.83090e12	+	3.64694e12i	0.678130	+	0.511934i
$373$	−2.63861e12	+	4.57020e12i	−0.365452	+	0.632982i	−0.988849	−	0.148924i	$-0.952419\pi$
$373$	−2.63861e12	+	4.57020e12i	−0.365452	+	0.632982i	0.623397	+	0.781906i	$0.285752\pi$
$374$	4.52648e12	+	2.61336e12i	0.618589	+	0.357143i
$375$	−2.14360e12	−	5.06226e12i	−0.289060	−	0.682634i
$376$	−1.35449e12	−	2.34604e12i	−0.180234	−	0.312174i
$377$			7.55341e12i			0.991828i
$378$	2.95964e12	−	2.38390e12i	0.383513	−	0.308908i
$379$	−2.20383e12			−0.281826			−0.140913	−	0.990022i	$-0.545004\pi$
$379$	−2.20383e12			−0.281826			−0.140913	+	0.990022i	$0.545004\pi$
$380$	5.52124e11	−	3.18769e11i	0.0696817	−	0.0402308i
$381$	−8.25941e12	+	3.49743e12i	−1.02878	+	0.435636i
$382$	1.35952e12	−	2.35475e12i	0.167135	−	0.289487i
$383$	1.79612e12	+	1.03699e12i	0.217942	+	0.125829i	0.604997	−	0.796228i	$-0.293174\pi$
$383$	1.79612e12	+	1.03699e12i	0.217942	+	0.125829i	−0.387055	+	0.922057i	$0.626508\pi$
$384$	−4.44647e11	+	5.88999e11i	−0.0532549	+	0.0705437i
$385$	−3.24718e12	−	5.62429e12i	−0.383887	−	0.664912i
$386$		−	7.95483e12i		−	0.928313i
$387$	−5.07126e12	−	1.27379e12i	−0.584199	−	0.146738i
$388$	−4.79364e12			−0.545138
$389$	−2.54334e12	+	1.46840e12i	−0.285533	+	0.164853i	−0.635926	−	0.771750i	$-0.719382\pi$
$389$	−2.54334e12	+	1.46840e12i	−0.285533	+	0.164853i	0.350392	+	0.936603i	$0.386048\pi$
$390$	5.23916e11	−	4.23646e12i	0.0580683	−	0.469548i
$391$	9.09138e11	−	1.57467e12i	0.0994824	−	0.172309i
$392$	−1.45953e12	−	8.42660e11i	−0.157682	−	0.0910379i
$393$	1.36301e13	+	1.68561e12i	1.45390	+	0.179802i
$394$	−3.65312e11	−	6.32739e11i	−0.0384754	−	0.0666413i
$395$			1.82310e13i			1.89595i
$396$	3.29865e12	+	3.19659e12i	0.338736	+	0.328255i
$397$	−1.21226e13			−1.22926			−0.614629	−	0.788816i	$-0.710694\pi$
$397$	−1.21226e13			−1.22926			−0.614629	+	0.788816i	$0.710694\pi$
$398$	1.15273e13	−	6.65531e12i	1.15429	−	0.666428i
$399$	7.74022e11	+	5.84325e11i	0.0765401	+	0.0577817i
$400$	4.68024e11	−	8.10642e11i	0.0457055	−	0.0791643i
$401$	−1.17147e13	−	6.76347e12i	−1.12982	−	0.652301i	−0.185929	−	0.982563i	$-0.559529\pi$
$401$	−1.17147e13	−	6.76347e12i	−1.12982	−	0.652301i	−0.943889	+	0.330263i	$0.892863\pi$
$402$	1.02684e11	+	2.42496e11i	0.00978078	+	0.0230980i
$403$	5.17127e12	+	8.95690e12i	0.486488	+	0.842621i
$404$		−	3.70949e10i		−	0.00344673i
$405$	6.01708e12	−	1.12220e13i	0.552218	−	1.02990i
$406$	−9.41035e12			−0.853052
$407$	1.56378e13	−	9.02847e12i	1.40024	−	0.808429i
$408$	−3.94131e12	+	1.66894e12i	−0.348610	+	0.147618i
$409$	−9.90430e11	+	1.71548e12i	−0.0865381	+	0.149888i	−0.906046	−	0.423180i	$-0.860914\pi$
$409$	−9.90430e11	+	1.71548e12i	−0.0865381	+	0.149888i	0.819508	+	0.573068i	$0.194247\pi$
$410$	1.46814e13	+	8.47632e12i	1.26721	+	0.731625i
$411$	4.29235e12	−	5.68583e12i	0.366004	−	0.484825i
$412$	−2.43853e11	−	4.22365e11i	−0.0205419	−	0.0355797i
$413$		−	6.16261e11i		−	0.0512878i
$414$	1.11203e12	−	1.14754e12i	0.0914357	−	0.0943551i
$415$	2.04976e13			1.66518
$416$	−1.09205e12	+	6.30498e11i	−0.0876552	+	0.0506078i
$417$	1.81205e12	−	1.46525e13i	0.143711	−	1.16206i
$418$	−5.86103e11	+	1.01516e12i	−0.0459296	+	0.0795524i
$419$	1.07020e13	+	6.17882e12i	0.828698	+	0.478449i	0.853407	−	0.521246i	$-0.174532\pi$
$419$	1.07020e13	+	6.17882e12i	0.828698	+	0.478449i	−0.0247086	+	0.999695i	$0.507866\pi$
$420$	5.27795e12	+	6.52716e11i	0.403849	+	0.0499434i
$421$	−6.40612e12	−	1.10957e13i	−0.484378	−	0.838968i	0.515460	−	0.856913i	$-0.327621\pi$
$421$	−6.40612e12	−	1.10957e13i	−0.484378	−	0.838968i	−0.999839	+	0.0179452i	$0.994288\pi$
$422$			3.54216e12i			0.264671i
$423$	3.36364e12	−	1.33914e13i	0.248375	−	0.988839i
$424$	8.14439e12			0.594332
$425$	4.70146e12	−	2.71439e12i	0.339069	−	0.195761i
$426$	−9.75892e11	−	7.36721e11i	−0.0695591	−	0.0525115i
$427$	5.01564e12	−	8.68735e12i	0.353335	−	0.611995i
$428$	−3.96203e10	−	2.28748e10i	−0.00275867	−	0.00159272i
$429$	3.06043e12	+	7.22742e12i	0.210619	+	0.497390i
$430$	−3.65858e12	−	6.33684e12i	−0.248869	−	0.431053i
$431$			6.16620e12i			0.414602i	0.978277	+	0.207301i	$0.0664679\pi$
$431$			6.16620e12i			0.414602i	−0.978277	+	0.207301i	$0.933532\pi$
$432$	−3.71669e12	+	5.78720e11i	−0.247023	+	0.0384636i
$433$	−9.49324e12			−0.623699			−0.311849	−	0.950132i	$-0.600948\pi$
$433$	−9.49324e12			−0.623699			−0.311849	+	0.950132i	$0.600948\pi$
$434$	−1.11589e13	+	6.44257e12i	−0.724722	+	0.418418i
$435$	−2.90346e13	+	1.22946e13i	−1.86410	+	0.789349i
$436$	−5.19739e11	+	9.00214e11i	−0.0329878	+	0.0571365i
$437$	3.53155e11	+	2.03894e11i	0.0221594	+	0.0127937i
$438$	−1.01133e13	+	1.33966e13i	−0.627371	+	0.831043i
$439$	1.17011e13	+	2.02669e13i	0.717635	+	1.24298i	0.961934	+	0.273281i	$0.0881089\pi$
$439$	1.17011e13	+	2.02669e13i	0.717635	+	1.24298i	−0.244299	+	0.969700i	$0.578558\pi$
$440$			6.42799e12i			0.389773i
$441$	−2.35333e12	−	8.26129e12i	−0.141088	−	0.495285i
$442$	−7.31336e12			−0.433517
$443$	−2.19110e13	+	1.26503e13i	−1.28423	+	0.741452i	−0.977619	−	0.210381i	$-0.932529\pi$
$443$	−2.19110e13	+	1.26503e13i	−1.28423	+	0.741452i	−0.306614	+	0.951834i	$0.599196\pi$
$444$	−1.81481e12	+	1.46748e13i	−0.105176	+	0.850468i
$445$	7.04224e12	−	1.21975e13i	0.403563	−	0.698991i
$446$	−1.70241e13	−	9.82889e12i	−0.964696	−	0.556968i
$447$	9.27322e12	+	1.14680e12i	0.519628	+	0.0642616i
$448$	−7.85500e11	−	1.36053e12i	−0.0435268	−	0.0753905i
$449$		−	2.10180e13i		−	1.15176i	−0.817536	−	0.575878i	$-0.804660\pi$
$449$		−	2.10180e13i		−	1.15176i	0.817536	−	0.575878i	$-0.195340\pi$
$450$	4.58843e12	−	1.30707e12i	0.248657	−	0.0708330i
$451$	−3.11699e13			−1.67052
$452$	−6.57038e12	+	3.79341e12i	−0.348256	+	0.201066i
$453$	1.39583e13	+	1.05374e13i	0.731713	+	0.552385i
$454$	1.07039e12	−	1.85398e12i	0.0554964	−	0.0961226i
$455$	7.86964e12	+	4.54354e12i	0.403550	+	0.232990i
$456$	−3.74296e11	−	8.83924e11i	−0.0189841	−	0.0448323i
$457$	1.56473e12	+	2.71019e12i	0.0784979	+	0.135962i	0.902602	−	0.430476i	$-0.141654\pi$
$457$	1.56473e12	+	2.71019e12i	0.0784979	+	0.135962i	−0.824104	+	0.566438i	$0.808321\pi$
$458$		−	8.58541e11i		−	0.0426024i
$459$	−2.03459e13	−	7.87108e12i	−0.998650	−	0.386341i
$460$	2.23617e12			0.108572
$461$	7.03756e12	−	4.06314e12i	0.338001	−	0.195145i	−0.321387	−	0.946948i	$-0.604149\pi$
$461$	7.03756e12	−	4.06314e12i	0.338001	−	0.195145i	0.659388	+	0.751803i	$0.270816\pi$
$462$	−9.00421e12	+	3.81281e12i	−0.427795	+	0.181149i
$463$	1.24398e13	−	2.15464e13i	0.584668	−	1.01267i	−0.410249	−	0.911974i	$-0.634558\pi$
$463$	1.24398e13	−	2.15464e13i	0.584668	−	1.01267i	0.994917	−	0.100701i	$-0.0321086\pi$
$464$	8.06631e12	+	4.65709e12i	0.375046	+	0.216533i
$465$	−2.60122e13	+	3.44569e13i	−1.19650	+	1.58494i
$466$	1.16413e13	+	2.01634e13i	0.529753	+	0.917559i
$467$		−	2.10330e13i		−	0.946929i	−0.880813	−	0.473464i	$-0.843003\pi$
$467$		−	2.10330e13i		−	0.946929i	0.880813	−	0.473464i	$-0.156997\pi$
$468$	−6.23356e12	−	1.56574e12i	−0.277656	−	0.0697412i
$469$	−5.60586e11			−0.0247046
$470$	1.67334e13	−	9.66104e12i	0.729617	−	0.421245i
$471$	2.35290e12	−	1.90259e13i	0.101508	−	0.820804i
$472$	−3.04981e11	+	5.28243e11i	−0.0130186	+	0.0225488i
$473$	1.16512e13	+	6.72683e12i	0.492113	+	0.284122i
$474$	2.72419e13	+	3.36897e12i	1.13853	+	0.140801i
$475$	6.08760e11	+	1.05440e12i	0.0251755	+	0.0436052i
$476$		−	9.11128e12i		−	0.372859i
$477$	2.98105e13	+	2.88881e13i	1.20719	+	1.16984i
$478$	3.46590e12			0.138892
$479$	−2.23029e13	+	1.28766e13i	−0.884473	+	0.510650i	−0.872130	−	0.489273i	$-0.837262\pi$
$479$	−2.23029e13	+	1.28766e13i	−0.884473	+	0.510650i	−0.0123421	+	0.999924i	$0.503929\pi$
$480$	−4.20110e12	−	3.17150e12i	−0.164876	−	0.124468i
$481$	−1.26329e13	+	2.18807e13i	−0.490655	+	0.849839i
$482$	−8.32752e12	−	4.80790e12i	−0.320096	−	0.184808i
$483$	1.32640e12	+	3.13239e12i	0.0504592	+	0.119163i
$484$	7.30581e11	+	1.26540e12i	0.0275069	+	0.0476433i
$485$		−	3.41912e13i		−	1.27411i
$486$	−1.56567e13	−	1.10648e13i	−0.577457	−	0.408097i
$487$	4.22848e13			1.54362			0.771809	−	0.635855i	$-0.219352\pi$
$487$	4.22848e13			1.54362			0.771809	+	0.635855i	$0.219352\pi$
$488$	−8.59856e12	+	4.96438e12i	−0.310689	+	0.179377i
$489$	−1.50445e13	+	6.37056e12i	−0.538064	+	0.227842i
$490$	6.01037e12	−	1.04103e13i	0.212775	−	0.368537i
$491$	−3.43809e13	−	1.98498e13i	−1.20479	−	0.695584i	−0.243171	−	0.969983i	$-0.578188\pi$
$491$	−3.43809e13	−	1.98498e13i	−1.20479	−	0.695584i	−0.961616	+	0.274399i	$0.911521\pi$
$492$	1.53789e13	−	2.03715e13i	0.533456	−	0.706640i
$493$	2.70096e13	+	4.67819e13i	0.927434	+	1.60636i
$494$		−	1.64018e12i		−	0.0557515i
$495$	−2.28001e13	+	2.35280e13i	−0.767203	+	0.791698i
$496$	1.27535e13			0.424834
$497$	2.25421e12	−	1.30147e12i	0.0743383	−	0.0429192i
$498$	3.78781e12	−	3.06287e13i	0.123663	−	0.999959i
$499$	2.38124e13	−	4.12444e13i	0.769664	−	1.33310i	−0.168081	−	0.985773i	$-0.553757\pi$
$499$	2.38124e13	−	4.12444e13i	0.769664	−	1.33310i	0.937745	−	0.347324i	$-0.112910\pi$
$500$	−1.00312e13	−	5.79151e12i	−0.320998	−	0.185328i
$501$	1.54477e13	+	1.91039e12i	0.489411	+	0.0605247i
$502$	7.75027e12	+	1.34239e13i	0.243108	+	0.421075i
$503$		−	1.97430e13i		−	0.613160i	−0.951845	−	0.306580i	$-0.900815\pi$
$503$		−	1.97430e13i		−	0.613160i	0.951845	−	0.306580i	$-0.0991846\pi$
$504$	1.95066e12	−	7.76603e12i	0.0599830	−	0.238806i
$505$	2.64583e11			0.00805574
$506$	−3.56069e12	+	2.05577e12i	−0.107345	+	0.0619756i
$507$	1.79715e13	+	1.35670e13i	0.536469	+	0.404991i
$508$	−9.44923e12	+	1.63665e13i	−0.279304	+	0.483769i
$509$	4.57444e12	+	2.64106e12i	0.133890	+	0.0773016i	0.565449	−	0.824783i	$-0.308703\pi$
$509$	4.57444e12	+	2.64106e12i	0.133890	+	0.0773016i	−0.431559	+	0.902085i	$0.642036\pi$
$510$	−1.19039e13	−	2.81119e13i	−0.345015	−	0.814777i
$511$	−1.78659e13	−	3.09447e13i	−0.512769	−	0.888141i
$512$			1.55494e12i			0.0441942i
$513$	1.76526e12	−	4.56300e12i	0.0496846	−	0.128429i
$514$	4.22511e13			1.17767
$515$	3.01257e12	−	1.73931e12i	0.0831574	−	0.0480109i
$516$	−1.01450e13	+	4.29587e12i	−0.277334	+	0.117436i
$517$	−1.77632e13	+	3.07668e13i	−0.480916	+	0.832971i
$518$	−2.72599e13	−	1.57385e13i	−0.730930	−	0.422002i
$519$	1.09810e13	−	1.45459e13i	0.291611	−	0.386280i
$520$	−4.49710e12	−	7.78921e12i	−0.118281	−	0.204869i
$521$			5.31437e12i			0.138441i	0.997601	+	0.0692203i	$0.0220511\pi$
$521$			5.31437e12i			0.138441i	−0.997601	+	0.0692203i	$0.977949\pi$
$522$	1.30060e13	+	4.56572e13i	0.335577	+	1.17803i
$523$	−6.24169e13			−1.59512			−0.797561	−	0.603239i	$-0.793877\pi$
$523$	−6.24169e13			−1.59512			−0.797561	+	0.603239i	$0.793877\pi$
$524$	2.50604e13	−	1.44686e13i	0.634354	−	0.366244i
$525$	−1.24651e12	+	1.00794e13i	−0.0312534	+	0.252720i
$526$	6.73875e12	−	1.16719e13i	0.167360	−	0.289875i
$527$	6.40563e13	+	3.69829e13i	1.57583	+	0.909805i
$528$	9.60510e12	+	1.18785e12i	0.234063	+	0.0289462i
$529$	−1.99981e13	−	3.46377e13i	−0.482737	−	0.836124i
$530$			5.80908e13i			1.38908i
$531$	−2.98998e12	+	8.51732e11i	−0.0708265	+	0.0201758i
$532$	2.04340e12			0.0479508
$533$	3.77706e13	−	2.18068e13i	0.878046	−	0.506940i
$534$	−1.69249e13	−	1.27770e13i	−0.389781	−	0.294253i
$535$	1.63157e11	−	2.82597e11i	0.00372252	−	0.00644760i
$536$	4.80520e11	+	2.77429e11i	0.0108614	+	0.00627086i
$537$	1.44050e13	+	3.40184e13i	0.322584	+	0.761802i
$538$	−2.40908e12	−	4.17264e12i	−0.0534489	−	0.0925763i
$539$			2.21019e13i			0.485831i
$540$	−4.12779e12	−	2.65097e13i	−0.0898976	−	0.577347i
$541$	−1.88018e13			−0.405709			−0.202854	−	0.979209i	$-0.565022\pi$
$541$	−1.88018e13			−0.405709			−0.202854	+	0.979209i	$0.565022\pi$
$542$	−3.50314e13	+	2.02254e13i	−0.748964	+	0.432415i
$543$	1.16330e13	−	4.92599e12i	0.246430	−	0.104350i
$544$	−4.50908e12	+	7.80996e12i	−0.0946441	+	0.163928i
$545$	−6.42088e12	−	3.70710e12i	−0.133540	−	0.0770995i
$546$	8.24349e12	−	1.09197e13i	0.169882	−	0.225033i
$547$	−1.43952e13	−	2.49333e13i	−0.293956	−	0.509146i	0.680786	−	0.732483i	$-0.261638\pi$
$547$	−1.43952e13	−	2.49333e13i	−0.293956	−	0.509146i	−0.974741	+	0.223336i	$0.928305\pi$
$548$		−	1.50105e13i		−	0.303733i
$549$	−4.90815e13	−	1.23282e13i	−0.984137	−	0.247194i
$550$	−1.22757e13			−0.243911
$551$	−1.04919e13	+	6.05748e12i	−0.206583	+	0.119271i
$552$	4.13229e11	−	3.34143e12i	0.00806298	−	0.0651984i
$553$	−2.92166e13	+	5.06046e13i	−0.564941	+	0.978507i
$554$	−1.62819e13	−	9.40034e12i	−0.312001	−	0.180134i
$555$	−1.04670e14	−	1.29444e13i	−1.98773	−	0.245819i
$556$	−1.55539e13	−	2.69402e13i	−0.292729	−	0.507022i
$557$			5.84339e13i			1.08991i	0.838467	+	0.544953i	$0.183452\pi$
$557$			5.84339e13i			1.08991i	−0.838467	+	0.544953i	$0.816548\pi$
$558$	4.66808e13	+	4.52365e13i	0.862913	+	0.836214i
$559$	−1.88247e13			−0.344880
$560$	9.70411e12	−	5.60267e12i	0.176204	−	0.101731i
$561$	4.47986e13	+	3.38194e13i	0.806214	+	0.608627i
$562$	1.01677e13	−	1.76110e13i	0.181361	−	0.314126i
$563$	4.14205e13	+	2.39141e13i	0.732273	+	0.422778i	0.819253	−	0.573432i	$-0.194388\pi$
$563$	4.14205e13	+	2.39141e13i	0.732273	+	0.422778i	−0.0869799	+	0.996210i	$0.527722\pi$
$564$	−1.13439e13	−	2.67894e13i	−0.198777	−	0.469426i
$565$	−2.70569e13	−	4.68640e13i	−0.469934	−	0.813949i
$566$			4.25856e13i			0.733129i
$567$	3.46859e13	−	2.15066e13i	0.591886	−	0.366992i
$568$	−2.57633e12			−0.0435773
$569$	−1.38211e13	+	7.97961e12i	−0.231729	+	0.133789i	−0.611370	−	0.791345i	$-0.709381\pi$
$569$	−1.38211e13	+	7.97961e12i	−0.231729	+	0.133789i	0.379640	+	0.925134i	$0.376048\pi$
$570$	6.30469e12	−	2.66971e12i	0.104783	−	0.0443700i
$571$	−1.68965e13	+	2.92656e13i	−0.278366	+	0.482144i	−0.970979	−	0.239166i	$-0.923126\pi$
$571$	−1.68965e13	+	2.92656e13i	−0.278366	+	0.482144i	0.692613	+	0.721309i	$0.256459\pi$
$572$	1.43216e13	+	8.26857e12i	0.233890	+	0.135036i
$573$	1.75934e13	−	2.33050e13i	0.284824	−	0.377291i
$574$	2.71678e13	+	4.70561e13i	0.436009	+	0.755190i
$575$			4.27047e12i			0.0679416i
$576$	−5.51538e12	+	5.69148e12i	−0.0869887	+	0.0897661i
$577$	1.06718e14			1.66862			0.834312	−	0.551293i	$-0.185865\pi$
$577$	1.06718e14			1.66862			0.834312	+	0.551293i	$0.185865\pi$
$578$	−5.78992e12	+	3.34281e12i	−0.0897498	+	0.0518170i
$579$	1.04849e13	−	8.47825e13i	0.161128	−	1.30291i
$580$	−3.32172e13	+	5.75339e13i	−0.506085	+	0.876564i
$581$	5.68959e13	+	3.28488e13i	0.859409	+	0.496180i
$582$	−5.10906e13	−	6.31829e12i	−0.765113	−	0.0946203i
$583$	−5.34042e13	−	9.24988e13i	−0.792926	−	1.37339i
$584$			3.53667e13i			0.520631i
$585$	1.11678e13	−	4.44616e13i	0.163000	−	0.648942i
$586$	−7.23103e13			−1.04644
$587$	−3.23922e13	+	1.87016e13i	−0.464782	+	0.268342i	−0.714053	−	0.700092i	$-0.753142\pi$
$587$	−3.23922e13	+	1.87016e13i	−0.464782	+	0.268342i	0.249271	+	0.968434i	$0.419809\pi$
$588$	−1.44450e13	−	1.09048e13i	−0.205509	−	0.155143i
$589$	−8.29422e12	+	1.43660e13i	−0.117004	+	0.202656i
$590$	−3.76775e12	−	2.17531e12i	−0.0527015	−	0.0304272i
$591$	−3.05951e12	−	7.22523e12i	−0.0424340	−	0.100211i
$592$	1.55777e13	+	2.69813e13i	0.214237	+	0.371069i
$593$		−	1.23401e14i		−	1.68285i	−0.540375	−	0.841424i	$-0.681718\pi$
$593$		−	1.23401e14i		−	1.68285i	0.540375	−	0.841424i	$-0.318282\pi$
$594$	3.09437e13	+	3.84171e13i	0.418447	+	0.519508i
$595$	6.49873e13			0.871452
$596$	1.70498e13	−	9.84374e12i	0.226720	−	0.130897i
$597$	1.31630e14	−	5.57386e13i	1.73574	−	0.734995i
$598$	2.87648e12	−	4.98220e12i	0.0376145	−	0.0651501i
$599$	−1.78778e13	−	1.03218e13i	−0.231836	−	0.133850i	0.379583	−	0.925158i	$-0.376067\pi$
$599$	−1.78778e13	−	1.03218e13i	−0.231836	−	0.133850i	−0.611419	+	0.791307i	$0.709401\pi$
$600$	6.05667e12	−	8.02293e12i	0.0778893	−	0.103176i
$601$	−2.94085e12	−	5.09370e12i	−0.0375060	−	0.0649623i	0.846663	−	0.532129i	$-0.178608\pi$
$601$	−2.94085e12	−	5.09370e12i	−0.0375060	−	0.0649623i	−0.884169	+	0.467167i	$0.845275\pi$
$602$		−	2.34525e13i		−	0.296625i
$603$	7.74784e11	+	2.71986e12i	0.00971839	+	0.0341161i
$604$	3.68495e13			0.458403
$605$	−9.02563e12	+	5.21095e12i	−0.111353	+	0.0642895i
$606$	4.88931e10	−	3.95357e11i	0.000598253	−	0.00483756i
$607$	−3.87427e13	+	6.71043e13i	−0.470161	+	0.814342i	−0.999418	−	0.0341194i	$-0.989137\pi$
$607$	−3.87427e13	+	6.71043e13i	−0.470161	+	0.814342i	0.529257	+	0.848461i	$0.322471\pi$
$608$	−1.75155e12	−	1.01126e12i	−0.0210817	−	0.0121715i
$609$	−1.00295e14	−	1.24034e13i	−1.19728	−	0.148065i
$610$	−3.54090e13	−	6.13302e13i	−0.419242	−	0.726148i
$611$		−	4.97095e13i		−	0.583758i
$612$	−4.42062e13	+	1.25927e13i	−0.514904	+	0.146677i
$613$	−5.62506e13			−0.649868			−0.324934	−	0.945737i	$-0.605342\pi$
$613$	−5.62506e13			−0.649868			−0.324934	+	0.945737i	$0.605342\pi$
$614$	9.17856e13	−	5.29924e13i	1.05180	−	0.607256i
$615$	1.45302e14	+	1.09692e14i	1.65157	+	1.24680i
$616$	−1.03013e13	+	1.78424e13i	−0.116142	+	0.201164i
$617$	−3.43547e13	−	1.98347e13i	−0.384202	−	0.221819i	0.295443	−	0.955360i	$-0.404533\pi$
$617$	−3.43547e13	−	1.98347e13i	−0.384202	−	0.221819i	−0.679645	+	0.733541i	$0.737866\pi$
$618$	−2.04228e12	−	4.82298e12i	−0.0226554	−	0.0535023i
$619$	4.19908e13	+	7.27303e13i	0.462063	+	0.800317i	0.999064	−	0.0432651i	$-0.0137760\pi$
$619$	4.19908e13	+	7.27303e13i	0.462063	+	0.800317i	−0.537001	+	0.843582i	$0.680443\pi$
$620$			9.09655e13i			0.992929i
$621$	1.33645e13	−	1.07647e13i	0.144709	−	0.116559i
$622$	−1.59598e13			−0.171426
$623$	3.90948e13	−	2.25714e13i	0.416562	−	0.240502i
$624$	−1.24701e13	+	5.28045e12i	−0.131810	+	0.0558147i
$625$	5.87439e13	−	1.01747e14i	0.615974	−	1.06690i
$626$	−2.89200e13	−	1.66970e13i	−0.300834	−	0.173686i
$627$	−7.58472e12	+	1.00471e13i	−0.0782712	+	0.103681i
$628$	−2.01964e13	−	3.49812e13i	−0.206764	−	0.358126i
$629$			1.80691e14i			1.83520i
$630$	5.53921e13	+	1.39133e13i	0.558142	+	0.140193i
$631$	1.76871e14			1.76811			0.884056	−	0.467381i	$-0.154802\pi$
$631$	1.76871e14			1.76811			0.884056	+	0.467381i	$0.154802\pi$
$632$	5.00874e13	−	2.89180e13i	0.496756	−	0.286802i
$633$	−4.66877e12	+	3.77523e13i	−0.0459392	+	0.371471i
$634$	4.10577e13	−	7.11141e13i	0.400819	−	0.694240i
$635$	−1.16736e14	−	6.73977e13i	−1.13067	−	0.652795i
$636$	8.68028e13	+	1.07348e13i	0.834158	+	0.103159i
$637$	−1.54627e13	−	2.67823e13i	−0.147431	−	0.255358i
$638$		−	1.22149e14i		−	1.15555i
$639$	−9.43001e12	−	9.13824e12i	−0.0885132	−	0.0857746i
$640$	−1.10908e13			−0.103291
$641$	−8.83702e13	+	5.10205e13i	−0.816612	+	0.471471i	−0.849247	−	0.527996i	$-0.822943\pi$
$641$	−8.83702e13	+	5.10205e13i	−0.816612	+	0.471471i	0.0326349	+	0.999467i	$0.489610\pi$
$642$	−3.92123e11	−	2.96021e11i	−0.00359540	−	0.00271424i
$643$	−7.34399e13	+	1.27202e14i	−0.668155	+	1.15728i	0.310265	+	0.950650i	$0.399582\pi$
$643$	−7.34399e13	+	1.27202e14i	−0.668155	+	1.15728i	−0.978420	+	0.206628i	$0.933751\pi$
$644$	6.20703e12	+	3.58363e12i	0.0560344	+	0.0323515i
$645$	−3.06408e13	−	7.23602e13i	−0.274474	−	0.648189i
$646$	−5.86497e12	−	1.01584e13i	−0.0521318	−	0.0902950i
$647$		−	7.59175e13i		−	0.669607i	−0.942288	−	0.334804i	$-0.891330\pi$
$647$		−	7.59175e13i		−	0.669607i	0.942288	−	0.334804i	$-0.108670\pi$
$648$	−4.03753e13	+	1.26918e12i	−0.353379	+	0.0111083i
$649$	7.99926e12			0.0694747
$650$	1.48752e13	−	8.58821e12i	0.128202	−	0.0740177i
$651$	−1.27423e14	+	5.39569e13i	−1.08979	+	0.461468i
$652$	−1.72118e13	+	2.98116e13i	−0.146079	+	0.253016i
$653$	−1.09403e14	−	6.31637e13i	−0.921430	−	0.531988i	−0.0373393	−	0.999303i	$-0.511888\pi$
$653$	−1.09403e14	−	6.31637e13i	−0.921430	−	0.531988i	−0.884091	+	0.467315i	$0.845222\pi$
$654$	−6.72591e12	+	8.90943e12i	−0.0562163	+	0.0744666i
$655$	1.03199e14	+	1.78746e14i	0.855992	+	1.48262i
$656$		−	5.37804e13i		−	0.442695i
$657$	−1.25445e14	+	1.29451e14i	−1.02477	+	1.05749i
$658$	6.19301e13			0.502079
$659$	−1.20644e14	+	6.96541e13i	−0.970689	+	0.560427i	−0.899446	−	0.437032i	$-0.856030\pi$
$659$	−1.20644e14	+	6.96541e13i	−0.970689	+	0.560427i	−0.0712426	+	0.997459i	$0.522696\pi$
$660$	−8.47246e12	+	6.85095e13i	−0.0676534	+	0.547055i
$661$	−1.75143e13	+	3.03357e13i	−0.138799	+	0.240407i	−0.927042	−	0.374957i	$-0.877658\pi$
$661$	−1.75143e13	+	3.03357e13i	−0.138799	+	0.240407i	0.788243	+	0.615364i	$0.210991\pi$
$662$	−8.64235e13	−	4.98966e13i	−0.679739	−	0.392447i
$663$	−7.79458e13	−	9.63943e12i	−0.608450	−	0.0752460i
$664$	−3.25131e13	−	5.63144e13i	−0.251894	−	0.436294i
$665$			1.45748e13i			0.112071i
$666$	−3.86845e13	+	1.54012e14i	−0.295234	+	1.17539i
$667$	−4.24934e13			−0.321878
$668$	2.84022e13	−	1.63980e13i	0.213536	−	0.123285i
$669$	−1.68488e14	−	1.27195e14i	−1.25730	−	0.949160i
$670$	−1.97879e12	+	3.42737e12i	−0.0146564	+	0.0253855i
$671$	1.12764e14	+	6.51046e13i	0.829010	+	0.478629i
$672$	−6.57860e12	−	1.55358e13i	−0.0480051	−	0.113367i
$673$	7.03073e13	+	1.21776e14i	0.509243	+	0.882035i	0.999943	+	0.0107063i	$0.00340797\pi$
$673$	7.03073e13	+	1.21776e14i	0.509243	+	0.882035i	−0.490699	+	0.871329i	$0.663259\pi$
$674$			8.53386e13i			0.613545i
$675$	5.06262e13	−	7.88292e12i	0.361290	−	0.0562559i
$676$	4.74444e13			0.336087
$677$	−7.18471e13	+	4.14810e13i	−0.505203	+	0.291679i	−0.730860	−	0.682528i	$-0.760881\pi$
$677$	−7.18471e13	+	4.14810e13i	−0.505203	+	0.291679i	0.225656	+	0.974207i	$0.427547\pi$
$678$	−7.50270e13	+	3.17700e13i	−0.523684	+	0.221753i
$679$	5.47938e13	−	9.49057e13i	0.379650	−	0.657572i
$680$	−5.57054e13	−	3.21615e13i	−0.383136	−	0.221204i
$681$	1.38519e13	−	1.83488e13i	0.0945745	−	0.125278i
$682$	−8.36267e13	−	1.44846e14i	−0.566791	−	0.981711i
$683$		−	1.09471e14i		−	0.736536i	−0.929720	−	0.368268i	$-0.879951\pi$
$683$		−	1.09471e14i		−	0.736536i	0.929720	−	0.368268i	$-0.120049\pi$
$684$	−2.82418e12	−	9.91420e12i	−0.0188630	−	0.0662182i
$685$	1.07064e14			0.709889
$686$	9.81571e13	−	5.66710e13i	0.646102	−	0.373027i
$687$	1.13161e12	−	9.15032e12i	0.00739454	−	0.0597933i
$688$	−1.16064e13	+	2.01029e13i	−0.0752933	+	0.130412i
$689$	1.29426e14	+	7.47244e13i	0.833541	+	0.481245i
$690$	2.38331e13	+	2.94740e12i	0.152383	+	0.0188449i
$691$	−3.92911e13	−	6.80542e13i	−0.249404	−	0.431981i	0.713956	−	0.700190i	$-0.246902\pi$
$691$	−3.92911e13	−	6.80542e13i	−0.249404	−	0.431981i	−0.963361	+	0.268209i	$0.913568\pi$
$692$		−	3.84007e13i		−	0.241996i
$693$	−1.00992e14	+	2.87689e13i	−0.631862	+	0.179993i
$694$	5.53623e12			0.0343888
$695$	1.92154e14	−	1.10940e14i	1.18502	−	0.684171i
$696$	7.98324e13	+	6.02670e13i	0.488802	+	0.369006i
$697$	1.55954e14	−	2.70121e14i	0.948054	−	1.64208i
$698$	1.25653e14	+	7.25459e13i	0.758397	+	0.437861i
$699$	9.74968e13	+	2.30245e14i	0.584258	+	1.37976i
$700$	1.06995e13	+	1.85321e13i	0.0636612	+	0.110264i
$701$		−	4.82226e13i		−	0.284879i	−0.989804	−	0.142439i	$-0.954505\pi$
$701$		−	4.82226e13i		−	0.284879i	0.989804	−	0.142439i	$-0.0454946\pi$
$702$	−6.43735e13	−	2.49038e13i	−0.377591	−	0.146076i
$703$	−4.05238e13			−0.236012
$704$	1.76601e13	−	1.01960e13i	0.102124	−	0.0589615i
$705$	1.91078e14	−	8.09117e13i	1.09715	−	0.464586i
$706$	2.80097e13	−	4.85142e13i	0.159693	−	0.276596i
$707$	7.34414e11	+	4.24014e11i	0.00415761	+	0.00240040i
$708$	−3.94674e12	+	5.22803e12i	−0.0221857	+	0.0293881i
$709$	−1.71184e13	−	2.96499e13i	−0.0955502	−	0.165498i	0.814288	−	0.580461i	$-0.197128\pi$
$709$	−1.71184e13	−	2.96499e13i	−0.0955502	−	0.165498i	−0.909838	+	0.414963i	$0.863794\pi$
$710$		−	1.83760e13i		−	0.101850i
$711$	2.85904e14	+	7.18128e13i	1.57352	+	0.395234i
$712$	−4.46815e13			−0.244190
$713$	−5.03890e13	+	2.90921e13i	−0.273456	+	0.157880i
$714$	1.20092e13	−	9.71080e13i	0.0647176	−	0.523316i
$715$	−5.89766e13	+	1.02150e14i	−0.315609	+	0.546651i
$716$	6.74096e13	+	3.89189e13i	0.358226	+	0.206822i
$717$	3.69395e13	+	4.56825e12i	0.194937	+	0.0241076i
$718$	1.15307e14	+	1.99718e14i	0.604274	+	1.04663i
$719$		−	9.44341e13i		−	0.491456i	−0.969339	−	0.245728i	$-0.920973\pi$
$719$		−	9.44341e13i		−	0.491456i	0.969339	−	0.245728i	$-0.0790270\pi$
$720$	−4.05951e13	−	3.93391e13i	−0.209803	−	0.203311i
$721$	1.11495e13			0.0572239
$722$	−1.17866e14	+	6.80498e13i	−0.600760	+	0.346849i
$723$	−8.24176e13	−	6.22187e13i	−0.417185	−	0.314941i
$724$	1.33089e13	−	2.30516e13i	0.0669034	−	0.115880i
$725$	−1.09874e14	−	6.34356e13i	−0.548534	−	0.316696i
$726$	6.11865e12	+	1.44496e13i	0.0303370	+	0.0716428i
$727$	−5.26458e13	−	9.11852e13i	−0.259234	−	0.449006i	0.706803	−	0.707410i	$-0.250137\pi$
$727$	−5.26458e13	−	9.11852e13i	−0.259234	−	0.449006i	−0.966037	+	0.258404i	$0.916803\pi$
$728$		−	2.88277e13i		−	0.140979i
$729$	−1.52285e14	−	1.38565e14i	−0.739639	−	0.673003i
$730$	−2.52257e14			−1.21683
$731$	−1.16590e14	+	6.73134e13i	−0.558567	+	0.322489i
$732$	−9.81867e13	+	4.15769e13i	−0.467194	+	0.197832i
$733$	1.24151e14	−	2.15036e14i	0.586721	−	1.01623i	−0.407938	−	0.913010i	$-0.633752\pi$
$733$	1.24151e14	−	2.15036e14i	0.586721	−	1.01623i	0.994659	−	0.103220i	$-0.0329147\pi$
$734$	1.53835e14	+	8.88167e13i	0.722063	+	0.416883i
$735$	7.77798e13	−	1.03031e14i	0.362602	−	0.480319i
$736$	−3.54700e12	−	6.14359e12i	−0.0164238	−	0.0284468i
$737$		−	7.27659e12i		−	0.0334650i
$738$	1.90759e14	−	1.96849e14i	0.871370	−	0.899191i
$739$	−2.17226e14			−0.985574			−0.492787	−	0.870150i	$-0.664022\pi$
$739$	−2.17226e14			−0.985574			−0.492787	+	0.870150i	$0.664022\pi$
$740$	−1.92447e14	+	1.11109e14i	−0.867268	+	0.500717i
$741$	2.16185e12	−	1.74810e13i	0.00967686	−	0.0782484i
$742$	−9.30947e13	+	1.61245e14i	−0.413910	+	0.716912i
$743$	7.81166e13	+	4.51006e13i	0.344984	+	0.199177i	0.662474	−	0.749085i	$-0.269507\pi$
$743$	7.81166e13	+	4.51006e13i	0.344984	+	0.199177i	−0.317490	+	0.948262i	$0.602840\pi$
$744$	1.35926e14	+	1.68098e13i	0.596264	+	0.0737390i
$745$	7.02116e13	+	1.21610e14i	0.305934	+	0.529893i
$746$			1.19410e14i			0.516827i
$747$	8.07408e13	−	3.21448e14i	0.347128	−	1.38200i
$748$	1.18267e14			0.505076
$749$	9.05763e11	−	5.22942e11i	0.00384243	−	0.00221843i
$750$	−9.92788e13	−	7.49475e13i	−0.418360	−	0.315828i
$751$	−1.60836e14	+	2.78576e14i	−0.673260	+	1.16612i	0.303714	+	0.952763i	$0.401773\pi$
$751$	−1.60836e14	+	2.78576e14i	−0.673260	+	1.16612i	−0.976974	+	0.213358i	$0.931560\pi$
$752$	−5.30849e13	−	3.06486e13i	−0.220740	−	0.127444i
$753$	6.49089e13	+	1.53287e14i	0.268120	+	0.633184i
$754$	8.54571e13	+	1.48016e14i	0.350664	+	0.607368i
$755$			2.62834e14i			1.07139i
$756$	3.10261e13	−	8.01992e13i	0.125637	−	0.324759i
$757$	−2.99206e14			−1.20362			−0.601812	−	0.798638i	$-0.705554\pi$
$757$	−2.99206e14			−1.20362			−0.601812	+	0.798638i	$0.705554\pi$
$758$	−4.31860e13	+	2.49334e13i	−0.172583	+	0.0996406i
$759$	−4.06594e13	+	1.72171e13i	−0.161418	+	0.0683521i
$760$	7.21292e12	−	1.24931e13i	0.0284474	−	0.0492724i
$761$	1.64389e14	+	9.49098e13i	0.644093	+	0.371867i	0.786189	−	0.617986i	$-0.212051\pi$
$761$	1.64389e14	+	9.49098e13i	0.644093	+	0.371867i	−0.142096	+	0.989853i	$0.545384\pi$
$762$	−1.22282e14	+	1.61980e14i	−0.475978	+	0.630502i
$763$	−1.18818e13	−	2.05799e13i	−0.0459472	−	0.0795829i
$764$		−	6.15247e13i		−	0.236365i
$765$	−8.98187e13	−	3.15306e14i	−0.342815	−	1.20344i
$766$	4.69287e13			0.177949
$767$	−9.69321e12	+	5.59638e12i	−0.0365167	+	0.0210829i
$768$	−2.04950e12	+	1.65726e13i	−0.00767084	+	0.0620275i
$769$	−8.68581e13	+	1.50443e14i	−0.322982	+	0.559421i	−0.981102	−	0.193492i	$-0.938019\pi$
$769$	−8.68581e13	+	1.50443e14i	−0.322982	+	0.559421i	0.658120	+	0.752913i	$0.271352\pi$
$770$	−1.27263e14	−	7.34754e13i	−0.470163	−	0.271449i
$771$	4.50312e14	+	5.56894e13i	1.65288	+	0.204409i
$772$	−8.99986e13	−	1.55882e14i	−0.328208	−	0.568473i
$773$			2.81170e13i			0.101876i	0.998702	+	0.0509380i	$0.0162211\pi$
$773$			2.81170e13i			0.101876i	−0.998702	+	0.0509380i	$0.983779\pi$
$774$	−1.13787e14	+	3.24137e13i	−0.409627	+	0.116687i
$775$	−1.73719e14			−0.621353
$776$	−9.39357e13	+	5.42338e13i	−0.333828	+	0.192735i
$777$	−2.69792e14	−	2.03671e14i	−0.952628	−	0.719158i
$778$	−3.32261e13	+	5.75493e13i	−0.116569	+	0.201903i
$779$	6.05804e13	+	3.49761e13i	0.211176	+	0.121923i
$780$	−3.76635e13	−	8.89448e13i	−0.130451	−	0.308069i
$781$	1.68935e13	+	2.92604e13i	0.0581385	+	0.100699i
$782$		−	4.11429e13i		−	0.140689i
$783$	7.84391e13	+	5.03757e14i	0.266516	+	1.71164i
$784$	−3.81344e13			−0.128747
$785$	2.49507e14	−	1.44053e14i	0.837018	−	0.483253i
$786$	2.86164e14	−	1.21175e14i	0.953899	−	0.403926i
$787$	1.20542e14	−	2.08785e14i	0.399268	−	0.691552i	−0.594368	−	0.804193i	$-0.702598\pi$
$787$	1.20542e14	−	2.08785e14i	0.399268	−	0.691552i	0.993636	+	0.112641i	$0.0359310\pi$
$788$	−1.43173e13	−	8.26607e12i	−0.0471225	−	0.0272062i
$789$	8.72057e13	−	1.15516e14i	0.285207	−	0.377797i
$790$	2.06261e14	+	3.57254e14i	0.670318	+	1.16102i
$791$		−	1.73443e14i		−	0.560111i
$792$	1.00805e14	+	2.53201e13i	0.323488	+	0.0812532i
$793$	−1.82192e14			−0.580982
$794$	−2.37554e14	+	1.37152e14i	−0.752764	+	0.434609i
$795$	−7.65670e13	+	6.19131e14i	−0.241105	+	1.94961i
$796$	1.50593e14	−	2.60834e14i	0.471236	−	0.816204i
$797$	1.07361e14	+	6.19847e13i	0.333852	+	0.192749i	0.657550	−	0.753411i	$-0.271593\pi$
$797$	1.07361e14	+	6.19847e13i	0.333852	+	0.192749i	−0.323698	+	0.946160i	$0.604926\pi$
$798$	2.17786e13	+	2.69332e12i	0.0672999	+	0.00832288i
$799$	−1.77751e14	−	3.07875e14i	−0.545858	−	0.945453i
$800$		−	2.11804e13i		−	0.0646373i
$801$	−1.63545e14	−	1.58485e14i	−0.495992	−	0.480646i
$802$	−3.06080e14			−0.922492
$803$	4.01672e14	−	2.31906e14i	1.20308	−	0.694598i
$804$	4.75572e12	+	3.59018e12i	0.0141558	+	0.0106865i
$805$	−2.55607e13	+	4.42724e13i	−0.0756123	+	0.130964i
$806$	2.02671e14	+	1.17012e14i	0.595823	+	0.343999i
$807$	−2.01761e13	−	4.76473e13i	−0.0589482	−	0.139210i
$808$	−4.19680e11	−	7.26908e11i	−0.00121860	−	0.00211068i
$809$			6.77823e14i			1.95602i	0.208556	+	0.978010i	$0.433124\pi$
$809$			6.77823e14i			1.95602i	−0.208556	+	0.978010i	$0.566876\pi$
$810$	−9.05255e12	−	2.87981e14i	−0.0259625	−	0.825922i
$811$	−4.41744e14			−1.25912			−0.629558	−	0.776953i	$-0.716764\pi$
$811$	−4.41744e14			−1.25912			−0.629558	+	0.776953i	$0.716764\pi$
$812$	−1.84404e14	+	1.06466e14i	−0.522386	+	0.301599i
$813$	−4.00023e14	+	1.69389e14i	−1.12624	+	0.476905i
$814$	2.04291e14	−	3.53842e14i	0.571646	−	0.990120i
$815$	−2.12635e14	−	1.22765e14i	−0.591353	−	0.341418i
$816$	−5.83517e13	+	7.72952e13i	−0.161288	+	0.213650i
$817$	−1.50965e13	−	2.61479e13i	−0.0414730	−	0.0718334i
$818$			4.48218e13i			0.122383i
$819$	1.02252e14	−	1.05517e14i	0.277493	−	0.286352i
$820$	3.83595e14			1.03467
$821$	2.03118e14	−	1.17270e14i	0.544543	−	0.314392i	−0.202375	−	0.979308i	$-0.564866\pi$
$821$	2.03118e14	−	1.17270e14i	0.544543	−	0.314392i	0.746918	+	0.664916i	$0.231533\pi$
$822$	1.97847e13	−	1.59982e14i	0.0527193	−	0.426296i
$823$	−9.58739e13	+	1.66058e14i	−0.253922	+	0.439807i	−0.964602	−	0.263709i	$-0.915054\pi$
$823$	−9.58739e13	+	1.66058e14i	−0.253922	+	0.439807i	0.710680	+	0.703516i	$0.248387\pi$
$824$	−9.55703e12	−	5.51776e12i	−0.0251586	−	0.0145253i
$825$	−1.30834e14	−	1.61800e13i	−0.342335	−	0.0423360i
$826$	−6.97220e12	−	1.20762e13i	−0.0181330	−	0.0314073i
$827$		−	1.83969e14i		−	0.475574i	−0.971317	−	0.237787i	$-0.923578\pi$
$827$		−	1.83969e14i		−	0.475574i	0.971317	−	0.237787i	$-0.0764220\pi$
$828$	8.80838e12	−	3.50683e13i	0.0226331	−	0.0901078i
$829$	4.36345e14			1.11444			0.557221	−	0.830365i	$-0.311868\pi$
$829$	4.36345e14			1.11444			0.557221	+	0.830365i	$0.311868\pi$
$830$	4.01669e14	−	2.31904e14i	1.01971	−	0.588731i
$831$	−1.61142e14	−	1.21649e14i	−0.406633	−	0.306976i
$832$	−1.42665e13	+	2.47104e13i	−0.0357851	+	0.0619816i
$833$	−1.91536e14	−	1.10584e14i	−0.477558	−	0.275718i
$834$	−1.30265e14	−	3.07629e14i	−0.322847	−	0.762425i
$835$	1.16961e14	+	2.02582e14i	0.288143	+	0.499079i
$836$			2.65240e13i			0.0649543i
$837$	4.37899e14	+	5.43658e14i	1.06597	+	1.32342i
$838$	2.79622e14			0.676629
$839$	−2.30963e14	+	1.33347e14i	−0.555562	+	0.320754i	−0.751362	−	0.659890i	$-0.770603\pi$
$839$	−2.30963e14	+	1.33347e14i	−0.555562	+	0.320754i	0.195800	+	0.980644i	$0.437270\pi$
$840$	1.10811e14	−	4.69227e13i	0.264964	−	0.112198i
$841$	4.20863e14	−	7.28957e14i	1.00037	−	1.73269i
$842$	−2.51068e14	−	1.44954e14i	−0.593240	−	0.342507i
$843$	1.31580e14	−	1.74297e14i	0.309067	−	0.409403i
$844$	4.00750e13	+	6.94119e13i	0.0935752	+	0.162077i
$845$			3.38402e14i			0.785507i
$846$	−8.55933e13	−	3.00473e14i	−0.197510	−	0.693352i
$847$	−3.34037e13			−0.0766262
$848$	1.59597e14	−	9.21432e13i	0.363953	−	0.210128i
$849$	−5.61302e13	+	4.53877e14i	−0.127250	+	1.02896i
$850$	6.14196e13	−	1.06382e14i	0.138424	−	0.239758i
$851$	−1.23095e14	−	7.10688e13i	−0.275799	−	0.159232i
$852$	−2.74585e13	−	3.39575e12i	−0.0611617	−	0.00756377i
$853$	3.10064e14	+	5.37047e14i	0.686604	+	1.18923i	0.972930	+	0.231101i	$0.0742329\pi$
$853$	3.10064e14	+	5.37047e14i	0.686604	+	1.18923i	−0.286325	+	0.958133i	$0.592434\pi$
$854$		−	2.26982e14i		−	0.499692i
$855$	7.07142e13	−	2.01438e13i	0.154766	−	0.0440870i
$856$	−1.03520e12			−0.00225244
$857$	4.01871e14	−	2.32021e14i	0.869326	−	0.501906i	0.00220211	−	0.999998i	$-0.499299\pi$
$857$	4.01871e14	−	2.32021e14i	0.869326	−	0.501906i	0.867124	+	0.498092i	$0.165966\pi$
$858$	1.41741e14	+	1.07003e14i	0.304831	+	0.230123i
$859$	2.94659e14	−	5.10364e14i	0.630019	−	1.09123i	−0.357528	−	0.933902i	$-0.616380\pi$
$859$	2.94659e14	−	5.10364e14i	0.630019	−	1.09123i	0.987547	−	0.157323i	$-0.0502864\pi$
$860$	−1.43386e14	−	8.27842e13i	−0.304800	−	0.175977i
$861$	2.27532e14	+	5.37332e14i	0.480869	+	1.13560i
$862$	6.97626e13	+	1.20832e14i	0.146584	+	0.253891i
$863$		−	6.65153e14i		−	1.38953i	−0.719238	−	0.694764i	$-0.755509\pi$
$863$		−	6.65153e14i		−	1.38953i	0.719238	−	0.694764i	$-0.244491\pi$
$864$	−6.62846e13	+	5.33901e13i	−0.137671	+	0.110890i
$865$	2.73898e14			0.565598
$866$	−1.86029e14	+	1.07404e14i	−0.381936	+	0.220511i
$867$	−6.61149e13	+	2.79962e13i	−0.134960	+	0.0571484i
$868$	−1.45779e14	+	2.52496e14i	−0.295867	+	0.512456i
$869$	−6.56863e14	−	3.79240e14i	−1.32549	−	0.765271i
$870$	−4.29862e14	+	5.69414e14i	−0.862447	+	1.14244i
$871$	5.09079e12	+	8.81751e12i	0.0101553	+	0.0175896i
$872$			2.35207e13i			0.0466517i
$873$	−5.36195e14	−	1.34681e14i	−1.05743	−	0.265603i
$874$	9.22718e12			0.0180931
$875$	2.29324e14	−	1.32400e14i	0.447104	−	0.258136i
$876$	−4.66153e13	+	3.76938e14i	−0.0903666	+	0.730717i
$877$	−6.38677e13	+	1.10622e14i	−0.123107	+	0.213228i	−0.920991	−	0.389583i	$-0.872619\pi$
$877$	−6.38677e13	+	1.10622e14i	−0.123107	+	0.213228i	0.797884	+	0.602811i	$0.205953\pi$
$878$	4.58587e14	+	2.64766e14i	0.878920	+	0.507445i
$879$	−7.70683e14	−	9.53091e13i	−1.46869	−	0.181631i
$880$	7.27244e13	+	1.25962e14i	0.137806	+	0.238686i
$881$			8.66184e14i			1.63204i	0.578024	+	0.816020i	$0.303824\pi$
$881$			8.66184e14i			1.63204i	−0.578024	+	0.816020i	$0.696176\pi$
$882$	−1.39581e14	−	1.35263e14i	−0.261508	−	0.253417i
$883$	−2.87960e14			−0.536448			−0.268224	−	0.963357i	$-0.586437\pi$
$883$	−2.87960e14			−0.536448			−0.268224	+	0.963357i	$0.586437\pi$
$884$	−1.43312e14	+	8.27412e13i	−0.265474	+	0.153271i
$885$	−3.72895e13	−	2.81506e13i	−0.0686863	−	0.0518527i
$886$	−2.86244e14	+	4.95790e14i	−0.524286	+	0.908090i
$887$	−3.02712e14	−	1.74771e14i	−0.551331	−	0.318311i	0.198328	−	0.980136i	$-0.436449\pi$
$887$	−3.02712e14	−	1.74771e14i	−0.551331	−	0.318311i	−0.749659	+	0.661825i	$0.769782\pi$
$888$	1.30464e14	+	3.08099e14i	0.236279	+	0.557988i
$889$	−2.16019e14	−	3.74157e14i	−0.389031	−	0.673821i
$890$		−	3.18696e14i		−	0.570724i
$891$	2.79162e14	+	4.50234e14i	0.497128	+	0.801771i
$892$	−4.44805e14			−0.787671
$893$	6.90475e13	−	3.98646e13i	0.121588	−	0.0701989i
$894$	1.94692e14	−	8.24418e13i	0.340926	−	0.144364i
$895$	−2.77594e14	+	4.80807e14i	−0.483387	+	0.837250i
$896$	−3.07852e13	−	1.77738e13i	−0.0533092	−	0.0307781i
$897$	3.72243e13	−	4.93089e13i	0.0641009	−	0.0849109i
$898$	−2.37792e14	−	4.11867e14i	−0.407207	−	0.705303i
$899$		−	1.72859e15i		−	2.94370i
$900$	7.51266e13	−	7.75253e13i	0.127228	−	0.131290i
$901$	1.06880e15			1.80000
$902$	−6.10803e14	+	3.52647e14i	−1.02298	+	0.590620i
$903$	3.09118e13	−	2.49957e14i	0.0514855	−	0.416319i
$904$	−8.58351e13	+	1.48671e14i	−0.142175	+	0.246254i
$905$	1.64418e14	+	9.49270e13i	0.270837	+	0.156368i
$906$	3.92742e14	+	4.85698e13i	0.643378	+	0.0795656i
$907$	2.54165e14	+	4.40226e14i	0.414075	+	0.717198i	0.995331	−	0.0965224i	$-0.0307720\pi$
$907$	2.54165e14	+	4.40226e14i	0.414075	+	0.717198i	−0.581256	+	0.813721i	$0.697439\pi$
$908$		−	4.84405e13i		−	0.0784837i
$909$	1.04220e12	−	4.14926e12i	0.00167932	−	0.00668577i
$910$	2.05617e14			0.329498
$911$	−6.03215e14	+	3.48266e14i	−0.961347	+	0.555034i	−0.896587	−	0.442867i	$-0.853961\pi$
$911$	−6.03215e14	+	3.48266e14i	−0.961347	+	0.555034i	−0.0647595	+	0.997901i	$0.520628\pi$
$912$	−1.73351e13	−	1.30866e13i	−0.0274760	−	0.0207421i
$913$	−4.26388e14	+	7.38526e14i	−0.672127	+	1.16416i
$914$	6.13246e13	+	3.54058e13i	0.0961400	+	0.0555064i
$915$	−2.96552e14	−	7.00328e14i	−0.462377	−	1.09193i
$916$	−9.71328e12	−	1.68239e13i	−0.0150622	−	0.0260885i
$917$			6.61536e14i			1.02025i
$918$	−4.87747e14	+	7.59463e13i	−0.748138	+	0.116491i
$919$	1.69107e14			0.257978			0.128989	−	0.991646i	$-0.458827\pi$
$919$	1.69107e14			0.257978			0.128989	+	0.991646i	$0.458827\pi$
$920$	4.38199e13	−	2.52994e13i	0.0664863	−	0.0383859i
$921$	1.04810e15	−	4.43814e14i	1.58162	−	0.669735i
$922$	9.19384e13	−	1.59242e14i	0.137988	−	0.239003i
$923$	−4.09418e13	−	2.36378e13i	−0.0611165	−	0.0352856i
$924$	−1.33309e14	+	1.76587e14i	−0.197924	+	0.262179i
$925$	−2.12188e14	−	3.67520e14i	−0.313337	−	0.542716i
$926$		−	5.62962e14i		−	0.826845i
$927$	−1.54096e13	−	5.40951e13i	−0.0225109	−	0.0790240i
$928$	2.10756e14			0.306224
$929$	−7.10341e14	+	4.10116e14i	−1.02657	+	0.592690i	−0.916000	−	0.401178i	$-0.868601\pi$
$929$	−7.10341e14	+	4.10116e14i	−1.02657	+	0.592690i	−0.110570	+	0.993868i	$0.535267\pi$
$930$	−1.19898e14	+	9.69510e14i	−0.172344	+	1.39360i
$931$	2.48008e13	−	4.29562e13i	0.0354582	−	0.0614154i
$932$	4.56246e14	+	2.63414e14i	0.648812	+	0.374592i
$933$	−1.70100e14	−	2.10360e13i	−0.240600	−	0.0297546i
$934$	−2.37961e14	−	4.12161e14i	−0.334790	−	0.579873i
$935$			8.43555e14i			1.18047i
$936$	−1.39867e14	+	3.98427e13i	−0.194686	+	0.0554587i
$937$	−1.44291e14			−0.199775			−0.0998873	−	0.994999i	$-0.531848\pi$
$937$	−1.44291e14			−0.199775			−0.0998873	+	0.994999i	$0.531848\pi$
$938$	−1.09852e13	+	6.34231e12i	−0.0151284	+	0.00873441i
$939$	−2.86221e14	−	2.16074e14i	−0.392080	−	0.295989i
$940$	2.18604e14	−	3.78634e14i	0.297865	−	0.515917i
$941$	−2.69158e14	−	1.55399e14i	−0.364804	−	0.210620i	0.306382	−	0.951909i	$-0.400882\pi$
$941$	−2.69158e14	−	1.55399e14i	−0.364804	−	0.210620i	−0.671186	+	0.741289i	$0.734215\pi$
$942$	−1.69146e14	−	3.99449e14i	−0.228038	−	0.538526i
$943$	1.22679e14	+	2.12486e14i	0.164518	+	0.284953i
$944$			1.38019e13i			0.0184110i
$945$	5.72030e14	+	2.21298e14i	0.759031	+	0.293642i
$946$	3.04421e14			0.401809
$947$	5.60207e14	−	3.23436e14i	0.735527	−	0.424657i	−0.0849139	−	0.996388i	$-0.527062\pi$
$947$	5.60207e14	−	3.23436e14i	0.735527	−	0.424657i	0.820441	+	0.571732i	$0.193728\pi$
$948$	5.71946e14	−	2.42189e14i	0.746988	−	0.316310i
$949$	−3.24488e14	+	5.62029e14i	−0.421568	+	0.730177i
$950$	2.38584e13	+	1.37747e13i	0.0308335	+	0.0178018i
$951$	5.31326e14	−	7.03817e14i	0.683059	−	0.904810i
$952$	−1.03082e14	−	1.78544e14i	−0.131826	−	0.228329i
$953$		−	2.79422e14i		−	0.355465i	−0.984079	−	0.177732i	$-0.943124\pi$
$953$		−	2.79422e14i		−	0.355465i	0.984079	−	0.177732i	$-0.0568761\pi$
$954$	9.10995e14	+	2.28822e14i	1.15285	+	0.289572i
$955$	4.38832e14			0.552435
$956$	6.79174e13	−	3.92121e13i	0.0850534	−	0.0491056i
$957$	1.61000e14	−	1.30187e15i	0.200570	−	1.62184i
$958$	−2.91364e14	+	5.04658e14i	−0.361084	+	0.625417i
$959$	2.97181e14	+	1.71578e14i	0.366377	+	0.211528i
$960$	−1.18206e14	−	1.46183e13i	−0.144972	−	0.0179284i
$961$	−7.73625e14	−	1.33996e15i	−0.943874	−	1.63484i
$962$			5.71698e14i			0.693891i
$963$	−3.78907e12	−	3.67183e12i	−0.00457511	−	0.00443355i
$964$	−2.17581e14			−0.261358
$965$	1.11185e15	−	6.41926e14i	1.32864	−	0.767093i
$966$	6.14310e13	+	4.63755e13i	0.0730302	+	0.0551319i
$967$	2.77987e14	−	4.81488e14i	0.328770	−	0.569447i	−0.653498	−	0.756928i	$-0.726699\pi$
$967$	2.77987e14	−	4.81488e14i	0.328770	−	0.569447i	0.982268	+	0.187482i	$0.0600325\pi$
$968$	2.86328e13	+	1.65312e13i	0.0336889	+	0.0194503i
$969$	−4.91194e13	−	1.15999e14i	−0.0574955	−	0.135780i
$970$	−3.86829e14	−	6.70008e14i	−0.450464	−	0.780227i
$971$			1.45357e15i			1.68400i	0.539480	+	0.841998i	$0.318621\pi$
$971$			1.45357e15i			1.68400i	−0.539480	+	0.841998i	$0.681379\pi$
$972$	−4.31992e14	−	3.96900e13i	−0.497903	−	0.0457457i
$973$	7.11158e14			0.815459
$974$	8.28610e14	−	4.78398e14i	0.945269	−	0.545751i
$975$	1.69860e14	−	7.19267e13i	0.192782	−	0.0816332i
$976$	−1.12331e14	+	1.94563e14i	−0.126838	+	0.219691i
$977$	1.28552e14	+	7.42193e13i	0.144413	+	0.0833766i	0.570465	−	0.821322i	$-0.306763\pi$
$977$	1.28552e14	+	7.42193e13i	0.144413	+	0.0833766i	−0.426053	+	0.904698i	$0.640096\pi$
$978$	−2.22736e14	+	2.95046e14i	−0.248941	+	0.329758i
$979$	2.92984e14	+	5.07463e14i	0.325785	+	0.564276i
$980$		−	2.71998e14i		−	0.300909i
$981$	−8.34278e13	+	8.60915e13i	−0.0918260	+	0.0947579i
$982$	−8.98301e14			−0.983704
$983$	−6.80507e14	+	3.92891e14i	−0.741421	+	0.428060i	−0.822586	−	0.568641i	$-0.807469\pi$
$983$	−6.80507e14	+	3.92891e14i	−0.741421	+	0.428060i	0.0811648	+	0.996701i	$0.474136\pi$
$984$	7.08856e13	−	5.73191e14i	0.0768391	−	0.621332i
$985$	5.89587e13	−	1.02119e14i	0.0635868	−	0.110136i
$986$	1.05855e15	+	6.11157e14i	1.13587	+	0.655795i
$987$	6.60050e14	+	8.16273e13i	0.704679	+	0.0871465i
$988$	−1.85565e13	−	3.21408e13i	−0.0197111	−	0.0341407i
$989$		−	1.05902e14i		−	0.111924i
$990$	−1.80599e14	+	7.19007e14i	−0.189906	+	0.756061i
$991$	−7.35983e14			−0.770015			−0.385008	−	0.922913i	$-0.625801\pi$
$991$	−7.35983e14			−0.770015			−0.385008	+	0.922913i	$0.625801\pi$
$992$	2.49916e14	−	1.44289e14i	0.260157	−	0.150202i
$993$	−8.55335e14	−	6.45709e14i	−0.885911	−	0.668792i
$994$	2.94489e13	−	5.10069e13i	0.0303485	−	0.0525651i
$995$	1.86043e15	+	1.07412e15i	1.90764	+	1.10138i
$996$	−2.72299e14	−	6.43052e14i	−0.277811	−	0.656069i
$997$	2.33176e14	+	4.03873e14i	0.236705	+	0.409986i	0.959767	−	0.280798i	$-0.0905991\pi$
$997$	2.33176e14	+	4.03873e14i	0.236705	+	0.409986i	−0.723062	+	0.690784i	$0.757266\pi$
$998$		−	1.07763e15i		−	1.08847i
$999$	−6.15296e14	+	1.59047e15i	−0.618381	+	1.59845i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.11.d.a.5.9	✓	20
3.2	odd	2		54.11.d.a.17.1		20
9.2	odd	6	inner	18.11.d.a.11.9	yes	20
9.4	even	3		162.11.b.c.161.12		20
9.5	odd	6		162.11.b.c.161.9		20
9.7	even	3		54.11.d.a.35.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.11.d.a.5.9	✓	20	1.1	even	1	trivial
18.11.d.a.11.9	yes	20	9.2	odd	6	inner
54.11.d.a.17.1		20	3.2	odd	2
54.11.d.a.35.1		20	9.7	even	3
162.11.b.c.161.9		20	9.5	odd	6
162.11.b.c.161.12		20	9.4	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 $\F_{q}$
Belyi maps

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} +(223.765 - 94.7529i) q^{3} +(256.000 - 443.405i) q^{4} +(3162.64 + 1825.95i) q^{5} +(3312.88 - 4388.38i) q^{6} +(5852.43 + 10136.7i) q^{7} -11585.2i q^{8} +(41092.8 - 42404.8i) q^{9} +82633.0 q^{10} +(-131578. + 75966.4i) q^{11} +(15270.0 - 123475. i) q^{12} +(106294. - 184107. i) q^{13} +(229368. + 132425. i) q^{14} +(880702. + 108915. i) q^{15} +(-131072. - 227023. i) q^{16} -1.52035e6i q^{17} +(325495. - 1.29587e6i) q^{18} +340971. q^{19} +(1.61927e6 - 934886. i) q^{20} +(2.27005e6 + 1.71371e6i) q^{21} +(-1.71892e6 + 2.97726e6i) q^{22} +(1.03573e6 + 597980. i) q^{23} +(-1.09773e6 - 2.59237e6i) q^{24} +(1.78537e6 + 3.09235e6i) q^{25} -4.81032e6i q^{26} +(5.17716e6 - 1.33824e7i) q^{27} +5.99289e6 q^{28} +(-3.07705e7 + 1.77654e7i) q^{29} +(1.84904e7 - 7.82972e6i) q^{30} +(-2.43253e7 + 4.21326e7i) q^{31} +(-5.13695e6 - 2.96582e6i) q^{32} +(-2.22445e7 + 2.94660e7i) q^{33} +(-1.72008e7 - 2.97926e7i) q^{34} +4.27450e7i q^{35} +(-8.28275e6 - 2.90764e7i) q^{36} -1.18848e8 q^{37} +(6.68164e6 - 3.85765e6i) q^{38} +(6.34027e6 - 5.12683e7i) q^{39} +(2.11541e7 - 3.66399e7i) q^{40} +(1.77670e8 + 1.02578e8i) q^{41} +(6.38722e7 + 7.89897e6i) q^{42} +(-4.42750e7 - 7.66865e7i) q^{43} +7.77896e7i q^{44} +(2.07391e8 - 5.90777e7i) q^{45} +2.70615e7 q^{46} +(2.02503e8 - 1.16915e8i) q^{47} +(-5.08405e7 - 3.83805e7i) q^{48} +(7.27357e7 - 1.25982e8i) q^{49} +(6.99720e7 + 4.03983e7i) q^{50} +(-1.44057e8 - 3.40201e8i) q^{51} +(-5.44226e7 - 9.42626e7i) q^{52} +7.02997e8i q^{53} +(-4.99532e7 - 3.20813e8i) q^{54} -5.54843e8 q^{55} +(1.17436e8 - 6.78018e7i) q^{56} +(7.62975e7 - 3.23080e7i) q^{57} +(-4.01985e8 + 6.96258e8i) q^{58} +(-4.55962e7 - 2.63250e7i) q^{59} +(2.73753e8 - 3.62626e8i) q^{60} +(-4.28509e8 - 7.42200e8i) q^{61} +1.10084e9i q^{62} +(6.70338e8 + 1.68374e8i) q^{63} -1.34218e8 q^{64} +(6.72339e8 - 3.88175e8i) q^{65} +(-1.02531e8 + 8.29081e8i) q^{66} +(-2.39467e7 + 4.14769e7i) q^{67} +(-6.74130e8 - 3.89209e8i) q^{68} +(2.88421e8 + 3.56686e7i) q^{69} +(4.83604e8 + 8.37627e8i) q^{70} -2.22381e8i q^{71} +(-4.91270e8 - 4.76070e8i) q^{72} -3.05274e9 q^{73} +(-2.32894e9 + 1.34461e9i) q^{74} +(6.92513e8 + 5.22792e8i) q^{75} +(8.72886e7 - 1.51188e8i) q^{76} +(-1.54010e9 - 8.89177e8i) q^{77} +(-4.55792e8 - 1.07638e9i) q^{78} +(2.49610e9 + 4.32338e9i) q^{79} -9.57323e8i q^{80} +(-1.09551e8 - 3.48506e9i) q^{81} +4.64215e9 q^{82} +(4.86087e9 - 2.80643e9i) q^{83} +(1.34100e9 - 5.67844e8i) q^{84} +(2.77608e9 - 4.80831e9i) q^{85} +(-1.73522e9 - 1.00183e9i) q^{86} +(-5.20205e9 + 6.89087e9i) q^{87} +(8.80089e8 + 1.52436e9i) q^{88} -3.85676e9i q^{89} +(3.39562e9 - 3.50404e9i) q^{90} +2.48832e9 q^{91} +(5.30295e8 - 3.06166e8i) q^{92} +(-1.45097e9 + 1.17327e10i) q^{93} +(2.64548e9 - 4.58211e9i) q^{94} +(1.07837e9 + 6.22596e8i) q^{95} +(-1.43049e9 - 1.76907e8i) q^{96} +(-4.68129e9 - 8.10823e9i) q^{97} -3.29164e9i q^{98} +(-2.18555e9 + 8.70120e9i) 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

Properties

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