LMFDB - Embedded newform 11.14.c.a.4.5

Error: no document with id 261356103 found in table mf_hecke_traces.

Error: table True does not exist

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [11,14,Mod(3,11)] 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("11.3"); S:= CuspForms(chi, 14); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(11, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 14, names="a")

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	11.c (of order $5$, degree $4$, 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:	$11.7954021847$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			4.5
Character	$\chi$	$=$	11.4
Dual form			11.14.c.a.3.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-38.1571 - 27.7228i) q^{2} +(-502.353 + 1546.08i) q^{3} +(-1844.05 - 5675.41i) q^{4} +(29618.8 - 21519.3i) q^{5} +(62030.1 - 45067.5i) q^{6} +(-28662.8 - 88215.0i) q^{7} +(-206371. + 635143. i) q^{8} +(-848181. - 616240. i) q^{9} -1.72674e6 q^{10} +(-4.12239e6 + 4.18671e6i) q^{11} +9.70102e6 q^{12} +(1.95148e7 + 1.41784e7i) q^{13} +(-1.35188e6 + 4.16064e6i) q^{14} +(1.83916e7 + 5.66034e7i) q^{15} +(-1.40668e7 + 1.02201e7i) q^{16} +(-4.30059e7 + 3.12456e7i) q^{17} +(1.52803e7 + 4.70279e7i) q^{18} +(-8.45952e7 + 2.60357e8i) q^{19} +(-1.76749e8 - 1.28416e8i) q^{20} +1.50787e8 q^{21} +(2.73366e8 - 4.54688e7i) q^{22} +8.98669e8 q^{23} +(-8.78314e8 - 6.38132e8i) q^{24} +(3.69736e7 - 1.13793e8i) q^{25} +(-3.51567e8 - 1.08201e9i) q^{26} +(-7.17973e8 + 5.21638e8i) q^{27} +(-4.47801e8 + 3.25346e8i) q^{28} +(9.11558e7 + 2.80549e8i) q^{29} +(8.67434e8 - 2.66969e9i) q^{30} +(-2.22932e9 - 1.61970e9i) q^{31} +6.29094e9 q^{32} +(-4.40211e9 - 8.47677e9i) q^{33} +2.50720e9 q^{34} +(-2.74728e9 - 1.99602e9i) q^{35} +(-1.93332e9 + 5.95015e9i) q^{36} +(4.64129e9 + 1.42844e10i) q^{37} +(1.04457e10 - 7.58928e9i) q^{38} +(-3.17242e10 + 2.30490e10i) q^{39} +(7.55540e9 + 2.32531e10i) q^{40} +(-2.46605e9 + 7.58973e9i) q^{41} +(-5.75358e9 - 4.18022e9i) q^{42} +6.16804e10 q^{43} +(3.13632e10 + 1.56758e10i) q^{44} -3.83831e10 q^{45} +(-3.42906e10 - 2.49136e10i) q^{46} +(-1.88772e10 + 5.80979e10i) q^{47} +(-8.73468e9 - 2.68826e10i) q^{48} +(7.14245e10 - 5.18930e10i) q^{49} +(-4.56547e9 + 3.31701e9i) q^{50} +(-2.67042e10 - 8.21870e10i) q^{51} +(4.44816e10 - 1.36900e11i) q^{52} +(-1.58251e11 - 1.14976e11i) q^{53} +4.18571e10 q^{54} +(-3.20051e10 + 2.12716e11i) q^{55} +6.19443e10 q^{56} +(-3.60038e11 - 2.61583e11i) q^{57} +(4.29935e9 - 1.32320e10i) q^{58} +(1.28108e11 + 3.94276e11i) q^{59} +(2.87332e11 - 2.08759e11i) q^{60} +(2.94943e11 - 2.14289e11i) q^{61} +(4.01620e10 + 1.23606e11i) q^{62} +(-3.00503e10 + 9.24854e10i) q^{63} +(-1.24809e11 - 9.06789e10i) q^{64} +8.83114e11 q^{65} +(-6.70277e10 + 4.45488e11i) q^{66} -1.25343e12 q^{67} +(2.56637e11 + 1.86458e11i) q^{68} +(-4.51449e11 + 1.38942e12i) q^{69} +(4.94933e10 + 1.52325e11i) q^{70} +(-1.21192e12 + 8.80509e11i) q^{71} +(5.66440e11 - 4.11543e11i) q^{72} +(-4.50948e11 - 1.38787e12i) q^{73} +(2.18905e11 - 6.73722e11i) q^{74} +(1.57360e11 + 1.14329e11i) q^{75} +1.63363e12 q^{76} +(4.87490e11 + 2.43654e11i) q^{77} +1.84949e12 q^{78} +(-6.68446e10 - 4.85654e10i) q^{79} +(-1.96712e11 + 6.05416e11i) q^{80} +(-9.62343e11 - 2.96179e12i) q^{81} +(3.04506e11 - 2.21237e11i) q^{82} +(-1.00556e12 + 7.30582e11i) q^{83} +(-2.78058e11 - 8.55776e11i) q^{84} +(-6.01398e11 + 1.85091e12i) q^{85} +(-2.35355e12 - 1.70995e12i) q^{86} -4.79544e11 q^{87} +(-1.80842e12 - 3.48233e12i) q^{88} -1.31315e12 q^{89} +(1.46459e12 + 1.06409e12i) q^{90} +(6.91394e11 - 2.12789e12i) q^{91} +(-1.65719e12 - 5.10032e12i) q^{92} +(3.62409e12 - 2.63306e12i) q^{93} +(2.33093e12 - 1.69352e12i) q^{94} +(3.09710e12 + 9.53190e12i) q^{95} +(-3.16027e12 + 9.72632e12i) q^{96} +(4.13535e12 + 3.00451e12i) q^{97} -4.16397e12 q^{98} +(6.07656e12 - 1.01071e12i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 59 q^{2} - 864 q^{3} - 44697 q^{4} - 52240 q^{5} - 130115 q^{6} + 390696 q^{7} + 876527 q^{8} - 3520244 q^{9} - 16293072 q^{10} - 82532 q^{11} + 62972038 q^{12} - 7063968 q^{13} + 2946296 q^{14}+ \cdots - 51636755872396 q^{99}+O(q^{100}) $ 48 * q + 59 * q^2 - 864 * q^3 - 44697 * q^4 - 52240 * q^5 - 130115 * q^6 + 390696 * q^7 + 876527 * q^8 - 3520244 * q^9 - 16293072 * q^10 - 82532 * q^11 + 62972038 * q^12 - 7063968 * q^13 + 2946296 * q^14 + 81100736 * q^15 + 60644511 * q^16 - 291410392 * q^17 + 126484674 * q^18 + 365166708 * q^19 - 788032074 * q^20 - 434553632 * q^21 - 733739679 * q^22 + 4188874272 * q^23 + 1308210897 * q^24 - 5079263484 * q^25 - 7197334352 * q^26 - 3672135540 * q^27 + 15293042118 * q^28 + 9462180848 * q^29 + 14934224730 * q^30 + 3808229976 * q^31 - 37924904892 * q^32 - 29220440404 * q^33 - 42631809486 * q^34 + 81447084648 * q^35 + 20776466352 * q^36 - 92150146992 * q^37 - 85759798456 * q^38 + 122431960136 * q^39 + 156222512604 * q^40 + 224837812784 * q^41 - 100995983242 * q^42 - 323982068136 * q^43 - 117395188832 * q^44 + 101655796640 * q^45 + 504337662372 * q^46 - 131674300816 * q^47 - 508856741764 * q^48 - 364186485732 * q^49 + 292932400779 * q^50 - 46205145276 * q^51 + 971895220146 * q^52 - 374673041144 * q^53 - 171438753484 * q^54 - 609291766368 * q^55 - 55316542488 * q^56 + 581441351340 * q^57 - 172510123284 * q^58 - 866818316348 * q^59 + 450475433796 * q^60 + 396717353376 * q^61 + 2190422590172 * q^62 - 814954660544 * q^63 + 687266758335 * q^64 - 1914281234704 * q^65 + 387191529606 * q^66 - 1385875174920 * q^67 - 1442260754434 * q^68 + 2415789828408 * q^69 + 6076465410072 * q^70 + 2500983206448 * q^71 - 6853058084009 * q^72 - 6144016960080 * q^73 - 9894533340936 * q^74 + 2088242191076 * q^75 + 7382638646262 * q^76 + 8181659595976 * q^77 + 485347989556 * q^78 - 9413148440424 * q^79 - 4271997351884 * q^80 + 19193312847832 * q^81 + 24451991571525 * q^82 - 4748400435188 * q^83 - 9210465158484 * q^84 - 9425037508176 * q^85 - 2302249550185 * q^86 - 22158779783712 * q^87 - 25622627417409 * q^88 - 12037611693640 * q^89 + 8065916202334 * q^90 + 23937874042464 * q^91 + 17043827782942 * q^92 + 18075650378312 * q^93 + 10662034186230 * q^94 + 17645734105464 * q^95 + 8702791487212 * q^96 - 18472776936684 * q^97 - 52286290693988 * q^98 - 51636755872396 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−38.1571	−	27.7228i	−0.421581	−	0.306296i	0.356693	−	0.934222i	$-0.383904\pi$
$2$	−38.1571	−	27.7228i	−0.421581	−	0.306296i	−0.778274	+	0.627925i	$0.783904\pi$
$3$	−502.353	+	1546.08i	−0.397851	+	1.22446i	0.528867	+	0.848705i	$0.322617\pi$
$3$	−502.353	+	1546.08i	−0.397851	+	1.22446i	−0.926719	+	0.375756i	$0.877383\pi$
$4$	−1844.05	−	5675.41i	−0.225104	−	0.692799i
$5$	29618.8	−	21519.3i	0.847739	−	0.615918i	−0.0767828	−	0.997048i	$-0.524465\pi$
$5$	29618.8	−	21519.3i	0.847739	−	0.615918i	0.924522	+	0.381130i	$0.124465\pi$
$6$	62030.1	−	45067.5i	0.542774	−	0.394349i
$7$	−28662.8	−	88215.0i	−0.0920834	−	0.283403i	0.894399	−	0.447269i	$-0.147604\pi$
$7$	−28662.8	−	88215.0i	−0.0920834	−	0.283403i	−0.986483	+	0.163866i	$0.947604\pi$
$8$	−206371.	+	635143.i	−0.278332	+	0.856617i
$9$	−848181.	−	616240.i	−0.532001	−	0.386521i
$10$	−1.72674e6			−0.546044
$11$	−4.12239e6	+	4.18671e6i	−0.701612	+	0.712559i
$11$	−4.12239e6	+	4.18671e6i	−0.701612	+	0.712559i
$12$	9.70102e6			0.937863
$13$	1.95148e7	+	1.41784e7i	1.12133	+	0.814693i	0.984410	−	0.175889i	$-0.0562801\pi$
$13$	1.95148e7	+	1.41784e7i	1.12133	+	0.814693i	0.136919	+	0.990582i	$0.456280\pi$
$14$	−1.35188e6	+	4.16064e6i	−0.0479849	+	0.147682i
$15$	1.83916e7	+	5.66034e7i	0.416894	+	1.28307i
$16$	−1.40668e7	+	1.02201e7i	−0.209612	+	0.152292i
$17$	−4.30059e7	+	3.12456e7i	−0.432126	+	0.313958i	−0.782498	−	0.622653i	$-0.786055\pi$
$17$	−4.30059e7	+	3.12456e7i	−0.432126	+	0.313958i	0.350373	+	0.936610i	$0.386055\pi$
$18$	1.52803e7	+	4.70279e7i	0.105891	+	0.325900i
$19$	−8.45952e7	+	2.60357e8i	−0.412522	+	1.26961i	0.501926	+	0.864911i	$0.332625\pi$
$19$	−8.45952e7	+	2.60357e8i	−0.412522	+	1.26961i	−0.914448	+	0.404703i	$0.867375\pi$
$20$	−1.76749e8	−	1.28416e8i	−0.617537	−	0.448667i
$21$	1.50787e8			0.383652
$22$	2.73366e8	−	4.54688e7i	0.514040	−	0.0855000i
$23$	8.98669e8			1.26581			0.632906	−	0.774229i	$-0.281862\pi$
$23$	8.98669e8			1.26581			0.632906	+	0.774229i	$0.281862\pi$
$24$	−8.78314e8	−	6.38132e8i	−0.938159	−	0.681613i
$25$	3.69736e7	−	1.13793e8i	0.0302888	−	0.0932193i
$26$	−3.51567e8	−	1.08201e9i	−0.223193	−	0.686918i
$27$	−7.17973e8	+	5.21638e8i	−0.356651	+	0.259122i
$28$	−4.47801e8	+	3.25346e8i	−0.175613	+	0.127591i
$29$	9.11558e7	+	2.80549e8i	0.0284575	+	0.0875833i	0.964277	−	0.264898i	$-0.0853382\pi$
$29$	9.11558e7	+	2.80549e8i	0.0284575	+	0.0875833i	−0.935819	+	0.352481i	$0.885338\pi$
$30$	8.67434e8	−	2.66969e9i	0.217244	−	0.668609i
$31$	−2.22932e9	−	1.61970e9i	−0.451151	−	0.327780i	0.338899	−	0.940823i	$-0.389945\pi$
$31$	−2.22932e9	−	1.61970e9i	−0.451151	−	0.327780i	−0.790050	+	0.613042i	$0.789945\pi$
$32$	6.29094e9			1.03572
$33$	−4.40211e9	−	8.47677e9i	−0.593363	−	1.14259i
$34$	2.50720e9			0.278340
$35$	−2.74728e9	−	1.99602e9i	−0.252616	−	0.183536i
$36$	−1.93332e9	+	5.95015e9i	−0.148026	+	0.455577i
$37$	4.64129e9	+	1.42844e10i	0.297391	+	0.915274i	0.982408	+	0.186747i	$0.0597946\pi$
$37$	4.64129e9	+	1.42844e10i	0.297391	+	0.915274i	−0.685017	+	0.728527i	$0.740205\pi$
$38$	1.04457e10	−	7.58928e9i	0.562790	−	0.408891i
$39$	−3.17242e10	+	2.30490e10i	−1.44368	+	1.04890i
$40$	7.55540e9	+	2.32531e10i	0.291654	+	0.897618i
$41$	−2.46605e9	+	7.58973e9i	−0.0810788	+	0.249535i	−0.983376	−	0.181579i	$-0.941879\pi$
$41$	−2.46605e9	+	7.58973e9i	−0.0810788	+	0.249535i	0.902298	+	0.431114i	$0.141879\pi$
$42$	−5.75358e9	−	4.18022e9i	−0.161740	−	0.117511i
$43$	6.16804e10			1.48800			0.743999	−	0.668181i	$-0.232927\pi$
$43$	6.16804e10			1.48800			0.743999	+	0.668181i	$0.232927\pi$
$44$	3.13632e10	+	1.56758e10i	0.651596	+	0.325676i
$45$	−3.83831e10			−0.689063
$46$	−3.42906e10	−	2.49136e10i	−0.533642	−	0.387713i
$47$	−1.88772e10	+	5.80979e10i	−0.255447	+	0.786184i	0.738294	+	0.674479i	$0.235631\pi$
$47$	−1.88772e10	+	5.80979e10i	−0.255447	+	0.786184i	−0.993741	+	0.111706i	$0.964369\pi$
$48$	−8.73468e9	−	2.68826e10i	−0.103081	−	0.317251i
$49$	7.14245e10	−	5.18930e10i	0.737179	−	0.535592i
$50$	−4.56547e9	+	3.31701e9i	−0.0413219	+	0.0300221i
$51$	−2.67042e10	−	8.21870e10i	−0.212507	−	0.654029i
$52$	4.44816e10	−	1.36900e11i	0.312003	−	0.960246i
$53$	−1.58251e11	−	1.14976e11i	−0.980737	−	0.712547i	−0.0228641	−	0.999739i	$-0.507278\pi$
$53$	−1.58251e11	−	1.14976e11i	−0.980737	−	0.712547i	−0.957873	+	0.287191i	$0.907278\pi$
$54$	4.18571e10			0.229726
$55$	−3.20051e10	+	2.12716e11i	−0.155906	+	1.03620i
$56$	6.19443e10			0.268398
$57$	−3.60038e11	−	2.61583e11i	−1.39047	−	1.01023i
$58$	4.29935e9	−	1.32320e10i	0.0148293	−	0.0456399i
$59$	1.28108e11	+	3.94276e11i	0.395401	+	1.21692i	0.928649	+	0.370960i	$0.120971\pi$
$59$	1.28108e11	+	3.94276e11i	0.395401	+	1.21692i	−0.533248	+	0.845959i	$0.679029\pi$
$60$	2.87332e11	−	2.08759e11i	0.795063	−	0.577647i
$61$	2.94943e11	−	2.14289e11i	0.732984	−	0.532544i	−0.157522	−	0.987515i	$-0.550351\pi$
$61$	2.94943e11	−	2.14289e11i	0.732984	−	0.532544i	0.890506	+	0.454972i	$0.150351\pi$
$62$	4.01620e10	+	1.23606e11i	0.0897987	+	0.276372i
$63$	−3.00503e10	+	9.24854e10i	−0.0605530	+	0.186363i
$64$	−1.24809e11	−	9.06789e10i	−0.227026	−	0.164944i
$65$	8.83114e11			1.45238
$66$	−6.70277e10	+	4.45488e11i	−0.0998203	+	0.663439i
$67$	−1.25343e12			−1.69283			−0.846416	−	0.532522i	$-0.821245\pi$
$67$	−1.25343e12			−1.69283			−0.846416	+	0.532522i	$0.821245\pi$
$68$	2.56637e11	+	1.86458e11i	0.314783	+	0.228703i
$69$	−4.51449e11	+	1.38942e12i	−0.503605	+	1.54994i
$70$	4.94933e10	+	1.52325e11i	0.0502816	+	0.154751i
$71$	−1.21192e12	+	8.80509e11i	−1.12278	+	0.815745i	−0.984628	−	0.174667i	$-0.944115\pi$
$71$	−1.21192e12	+	8.80509e11i	−1.12278	+	0.815745i	−0.138149	+	0.990411i	$0.544115\pi$
$72$	5.66440e11	−	4.11543e11i	0.479173	−	0.348140i
$73$	−4.50948e11	−	1.38787e12i	−0.348761	−	1.07338i	−0.959540	−	0.281574i	$-0.909143\pi$
$73$	−4.50948e11	−	1.38787e12i	−0.348761	−	1.07338i	0.610779	−	0.791801i	$-0.290857\pi$
$74$	2.18905e11	−	6.73722e11i	0.154971	−	0.476952i
$75$	1.57360e11	+	1.14329e11i	0.102093	+	0.0741748i
$76$	1.63363e12			0.972448
$77$	4.87490e11	+	2.43654e11i	0.266548	+	0.133224i
$78$	1.84949e12			0.929902
$79$	−6.68446e10	−	4.85654e10i	−0.0309379	−	0.0224777i	0.572209	−	0.820108i	$-0.306087\pi$
$79$	−6.68446e10	−	4.85654e10i	−0.0309379	−	0.0224777i	−0.603147	+	0.797630i	$0.706087\pi$
$80$	−1.96712e11	+	6.05416e11i	−0.0838968	+	0.258208i
$81$	−9.62343e11	−	2.96179e12i	−0.378597	−	1.16520i
$82$	3.04506e11	−	2.21237e11i	0.110613	−	0.0803650i
$83$	−1.00556e12	+	7.30582e11i	−0.337598	+	0.245280i	−0.743648	−	0.668571i	$-0.766906\pi$
$83$	−1.00556e12	+	7.30582e11i	−0.337598	+	0.245280i	0.406049	+	0.913851i	$0.366906\pi$
$84$	−2.78058e11	−	8.55776e11i	−0.0863616	−	0.265794i
$85$	−6.01398e11	+	1.85091e12i	−0.172957	+	0.532308i
$86$	−2.35355e12	−	1.70995e12i	−0.627311	−	0.455768i
$87$	−4.79544e11			−0.118564
$88$	−1.80842e12	−	3.48233e12i	−0.415110	−	0.799341i
$89$	−1.31315e12			−0.280078			−0.140039	−	0.990146i	$-0.544723\pi$
$89$	−1.31315e12			−0.280078			−0.140039	+	0.990146i	$0.544723\pi$
$90$	1.46459e12	+	1.06409e12i	0.290496	+	0.211058i
$91$	6.91394e11	−	2.12789e12i	0.127631	−	0.392808i
$92$	−1.65719e12	−	5.10032e12i	−0.284939	−	0.876953i
$93$	3.62409e12	−	2.63306e12i	0.580845	−	0.422009i
$94$	2.33093e12	−	1.69352e12i	0.348497	−	0.253198i
$95$	3.09710e12	+	9.53190e12i	0.432267	+	1.33038i
$96$	−3.16027e12	+	9.72632e12i	−0.412061	+	1.26819i
$97$	4.13535e12	+	3.00451e12i	0.504076	+	0.366233i	0.810572	−	0.585639i	$-0.199156\pi$
$97$	4.13535e12	+	3.00451e12i	0.504076	+	0.366233i	−0.306496	+	0.951872i	$0.599156\pi$
$98$	−4.16397e12			−0.474830
$99$	6.07656e12	−	1.01071e12i	0.648677	−	0.107894i
$100$	−7.14004e11			−0.0714004
$101$	4.48473e12	+	3.25835e12i	0.420385	+	0.305428i	0.777793	−	0.628521i	$-0.216339\pi$
$101$	4.48473e12	+	3.25835e12i	0.420385	+	0.305428i	−0.357408	+	0.933948i	$0.616339\pi$
$102$	−1.25950e12	+	3.87634e12i	−0.110738	+	0.340816i
$103$	−3.22445e12	−	9.92383e12i	−0.266081	−	0.818912i	−0.991442	−	0.130544i	$-0.958328\pi$
$103$	−3.22445e12	−	9.92383e12i	−0.266081	−	0.818912i	0.725362	−	0.688368i	$-0.241672\pi$
$104$	−1.30326e13	+	9.46872e12i	−1.00998	+	0.733795i
$105$	4.46611e12	−	3.24482e12i	0.325236	−	0.236298i
$106$	2.85094e12	+	8.77430e12i	0.195209	+	0.600793i
$107$	−6.36598e12	+	1.95925e13i	−0.410082	+	1.26210i	0.506494	+	0.862243i	$0.330941\pi$
$107$	−6.36598e12	+	1.95925e13i	−0.410082	+	1.26210i	−0.916576	+	0.399859i	$0.869059\pi$
$108$	4.28449e12	+	3.11286e12i	0.259803	+	0.188758i
$109$	5.47902e10			0.00312918			0.00156459	−	0.999999i	$-0.499502\pi$
$109$	5.47902e10			0.00312918			0.00156459	+	0.999999i	$0.499502\pi$
$110$	7.11831e12	−	7.22938e12i	0.383111	−	0.389089i
$111$	−2.44165e13			−1.23903
$112$	1.30476e12	+	9.47966e11i	0.0624618	+	0.0453812i
$113$	1.23214e13	−	3.79213e13i	0.556736	−	1.71346i	−0.134577	−	0.990903i	$-0.542968\pi$
$113$	1.23214e13	−	3.79213e13i	0.556736	−	1.71346i	0.691313	−	0.722555i	$-0.257032\pi$
$114$	6.48621e12	+	1.99625e13i	0.276764	+	0.851791i
$115$	2.66175e13	−	1.93387e13i	1.07308	−	0.779636i
$116$	1.42413e12	−	1.03469e12i	0.0542717	−	0.0394307i
$117$	−7.81484e12	−	2.40516e13i	−0.281652	−	0.866835i
$118$	6.04219e12	−	1.85959e13i	0.206045	−	0.634140i
$119$	3.98900e12	+	2.89818e12i	0.128768	+	0.0935556i
$120$	−3.97467e13			−1.21513
$121$	−5.34448e11	−	3.45186e13i	−0.0154811	−	0.999880i
$122$	−1.71949e13			−0.472128
$123$	−1.04955e13	−	7.62545e12i	−0.273288	−	0.198556i
$124$	−5.08146e12	+	1.56391e13i	−0.125530	+	0.386342i
$125$	1.24566e13	+	3.83376e13i	0.292069	+	0.898896i
$126$	3.71059e12	−	2.69590e12i	0.0826103	−	0.0600199i
$127$	2.91348e13	−	2.11676e13i	0.616151	−	0.447660i	−0.235424	−	0.971893i	$-0.575648\pi$
$127$	2.91348e13	−	2.11676e13i	0.616151	−	0.447660i	0.851575	+	0.524233i	$0.175648\pi$
$128$	−1.36768e13	−	4.20929e13i	−0.274866	−	0.845950i
$129$	−3.09853e13	+	9.53630e13i	−0.592002	+	1.82199i
$130$	−3.36971e13	−	2.44824e13i	−0.612295	−	0.444858i
$131$	8.23168e13			1.42307			0.711533	−	0.702653i	$-0.248001\pi$
$131$	8.23168e13			1.42307			0.711533	+	0.702653i	$0.248001\pi$
$132$	−3.99914e13	+	4.06154e13i	−0.658016	+	0.668283i
$133$	2.53922e13			0.397799
$134$	4.78273e13	+	3.47486e13i	0.713666	+	0.518509i
$135$	−1.00402e13	+	3.09006e13i	−0.142749	+	0.439336i
$136$	−1.09703e13	−	3.37631e13i	−0.148667	−	0.457551i
$137$	1.65512e13	−	1.20251e13i	0.213868	−	0.155384i	−0.475694	−	0.879611i	$-0.657803\pi$
$137$	1.65512e13	−	1.20251e13i	0.213868	−	0.155384i	0.689562	+	0.724227i	$0.257803\pi$
$138$	5.57445e13	−	4.05008e13i	0.687050	−	0.499171i
$139$	2.30039e13	+	7.07988e13i	0.270524	+	0.832587i	0.990369	+	0.138452i	$0.0442127\pi$
$139$	2.30039e13	+	7.07988e13i	0.270524	+	0.832587i	−0.719845	+	0.694135i	$0.755787\pi$
$140$	−6.26208e12	+	1.92727e13i	−0.0702889	+	0.216327i
$141$	−8.03412e13	−	5.83713e13i	−0.861022	−	0.625569i
$142$	7.06534e13			0.723201
$143$	−1.39809e14	+	2.32543e13i	−1.36725	+	0.227415i
$144$	1.82293e13			0.170378
$145$	8.73714e12	+	6.34790e12i	0.0780687	+	0.0567202i
$146$	−2.12689e13	+	6.54589e13i	−0.181740	+	0.559339i
$147$	4.43505e13	+	1.36497e14i	0.362523	+	1.11573i
$148$	7.25111e13	−	5.26824e13i	0.567157	−	0.412064i
$149$	−1.70774e14	+	1.24075e14i	−1.27853	+	0.928908i	−0.999508	−	0.0313766i	$-0.990011\pi$
$149$	−1.70774e14	+	1.24075e14i	−1.27853	+	0.928908i	−0.279024	+	0.960284i	$0.590011\pi$
$150$	−2.83489e12	−	8.72490e12i	−0.0203209	−	0.0625414i
$151$	5.86222e13	−	1.80420e14i	0.402450	−	1.23861i	−0.520556	−	0.853827i	$-0.674275\pi$
$151$	5.86222e13	−	1.80420e14i	0.402450	−	1.23861i	0.923006	−	0.384786i	$-0.125725\pi$
$152$	−1.47906e14	−	1.07460e14i	−0.972755	−	0.706748i
$153$	5.57316e13			0.351242
$154$	−1.18465e13	−	2.28117e13i	−0.0715656	−	0.137808i
$155$	−1.00885e14			−0.584344
$156$	1.89314e14	+	1.37545e14i	1.05165	+	0.764071i
$157$	1.71491e13	−	5.27794e13i	0.0913887	−	0.281266i	−0.894907	−	0.446253i	$-0.852758\pi$
$157$	1.71491e13	−	5.27794e13i	0.0913887	−	0.281266i	0.986296	+	0.164987i	$0.0527583\pi$
$158$	1.20423e12	+	3.70624e12i	0.00615798	+	0.0189523i
$159$	2.57260e14	−	1.86910e14i	1.26267	−	0.917386i
$160$	1.86330e14	−	1.35377e14i	0.878016	−	0.637916i
$161$	−2.57584e13	−	7.92761e13i	−0.116560	−	0.358735i
$162$	−4.53887e13	+	1.39692e14i	−0.197288	+	0.607190i
$163$	−3.44575e14	−	2.50349e14i	−1.43901	−	1.04550i	−0.988248	−	0.152862i	$-0.951151\pi$
$163$	−3.44575e14	−	2.50349e14i	−1.43901	−	1.04550i	−0.450766	−	0.892642i	$-0.648849\pi$
$164$	4.76224e13			0.191129
$165$	−3.12799e14	−	1.56341e14i	−1.20676	−	0.603154i
$166$	5.86231e13			0.217453
$167$	1.46927e14	+	1.06749e14i	0.524138	+	0.380808i	0.818160	−	0.574990i	$-0.194994\pi$
$167$	1.46927e14	+	1.06749e14i	0.524138	+	0.380808i	−0.294023	+	0.955798i	$0.594994\pi$
$168$	−3.11179e13	+	9.57711e13i	−0.106783	+	0.328643i
$169$	8.62093e13	+	2.65325e14i	0.284636	+	0.876021i
$170$	7.42601e13	−	5.39531e13i	0.235960	−	0.171435i
$171$	2.32195e14	−	1.68699e14i	0.710195	−	0.515987i
$172$	−1.13742e14	−	3.50061e14i	−0.334954	−	1.03088i
$173$	−1.70730e14	+	5.25452e14i	−0.484183	+	1.49016i	0.348979	+	0.937131i	$0.386528\pi$
$173$	−1.70730e14	+	5.25452e14i	−0.484183	+	1.49016i	−0.833161	+	0.553030i	$0.813472\pi$
$174$	1.82980e13	+	1.32943e13i	0.0499844	+	0.0363158i
$175$	−1.10980e13			−0.0292078
$176$	1.52002e13	−	1.01025e14i	0.0385492	−	0.256211i
$177$	−6.73938e14			−1.64738
$178$	5.01061e13	+	3.64042e13i	0.118076	+	0.0857870i
$179$	4.75606e13	−	1.46377e14i	0.108069	−	0.332604i	−0.882369	−	0.470558i	$-0.844053\pi$
$179$	4.75606e13	−	1.46377e14i	0.108069	−	0.332604i	0.990439	+	0.137954i	$0.0440527\pi$
$180$	7.07805e13	+	2.17840e14i	0.155111	+	0.477382i
$181$	1.87709e14	−	1.36379e14i	0.396803	−	0.288294i	−0.371435	−	0.928459i	$-0.621134\pi$
$181$	1.87709e14	−	1.36379e14i	0.396803	−	0.288294i	0.768237	+	0.640165i	$0.221134\pi$
$182$	−8.53727e13	+	6.20269e13i	−0.174123	+	0.126507i
$183$	1.83143e14	+	5.63655e14i	0.360460	+	1.10938i
$184$	−1.85459e14	+	5.70784e14i	−0.352316	+	1.08432i
$185$	4.44860e14	+	3.23210e14i	0.815844	+	0.592745i
$186$	−2.11281e14			−0.374133
$187$	4.64708e13	−	3.08860e14i	0.0794712	−	0.528192i
$188$	3.64540e14			0.602170
$189$	6.65954e13	+	4.83844e13i	0.106278	+	0.0772153i
$190$	1.46074e14	−	4.49570e14i	0.225255	−	0.693265i
$191$	2.23035e14	+	6.86430e14i	0.332396	+	1.02301i	0.967991	+	0.250986i	$0.0807549\pi$
$191$	2.23035e14	+	6.86430e14i	0.332396	+	1.02301i	−0.635595	+	0.772023i	$0.719245\pi$
$192$	2.02895e14	−	1.47412e14i	0.292290	−	0.212361i
$193$	7.82836e14	−	5.68764e14i	1.09031	−	0.792154i	0.110855	−	0.993837i	$-0.464641\pi$
$193$	7.82836e14	−	5.68764e14i	1.09031	−	0.792154i	0.979451	+	0.201683i	$0.0646410\pi$
$194$	−7.44998e13	−	2.29287e14i	−0.100333	−	0.308793i
$195$	−4.43635e14	+	1.36537e15i	−0.577831	+	1.77838i
$196$	−4.26224e14	−	3.09670e14i	−0.536999	−	0.390153i
$197$	−2.98597e14			−0.363961			−0.181981	−	0.983302i	$-0.558251\pi$
$197$	−2.98597e14			−0.363961			−0.181981	+	0.983302i	$0.558251\pi$
$198$	−2.59884e14	−	1.29893e14i	−0.306517	−	0.153201i
$199$	−8.17503e14			−0.933134			−0.466567	−	0.884486i	$-0.654509\pi$
$199$	−8.17503e14			−0.933134			−0.466567	+	0.884486i	$0.654509\pi$
$200$	6.46447e13	+	4.69671e13i	0.0714229	+	0.0518918i
$201$	6.29665e14	−	1.93791e15i	0.673496	−	2.07281i
$202$	−8.07940e13	−	2.48658e14i	−0.0836749	−	0.257525i
$203$	2.21358e13	−	1.60826e13i	0.0222009	−	0.0161299i
$204$	−4.17201e14	+	3.03114e14i	−0.405275	+	0.294449i
$205$	9.02842e13	+	2.77866e14i	0.0849594	+	0.261478i
$206$	−1.52080e14	+	4.68056e14i	−0.138655	+	0.426737i
$207$	−7.62234e14	−	5.53795e14i	−0.673412	−	0.489263i
$208$	−4.19416e14			−0.359115
$209$	−7.41307e14	−	1.42747e15i	−0.615244	−	1.18472i
$210$	−2.60370e14			−0.209491
$211$	1.55413e15	+	1.12914e15i	1.21242	+	0.880874i	0.995448	−	0.0953046i	$-0.0303825\pi$
$211$	1.55413e15	+	1.12914e15i	1.21242	+	0.880874i	0.216970	+	0.976178i	$0.430383\pi$
$212$	−3.60713e14	+	1.11016e15i	−0.272884	+	0.839851i
$213$	−7.52530e14	−	2.31605e15i	−0.552149	−	1.69934i
$214$	7.86065e14	−	5.71110e14i	0.559460	−	0.406472i
$215$	1.82690e15	−	1.32732e15i	1.26143	−	0.916485i
$216$	−1.83146e14	−	5.63667e14i	−0.122701	−	0.377636i
$217$	−7.89830e13	+	2.43085e14i	−0.0513506	+	0.158041i
$218$	−2.09064e12	−	1.51894e12i	−0.00131920	−	0.000958456i
$219$	2.37230e15			1.45306
$220$	1.26627e15	−	2.10618e14i	0.752973	−	0.125242i
$221$	−1.28226e15			−0.740334
$222$	9.31662e14	+	6.76892e14i	0.522353	+	0.379512i
$223$	−1.09823e15	+	3.38000e15i	−0.598013	+	1.84049i	−0.0588955	+	0.998264i	$0.518758\pi$
$223$	−1.09823e15	+	3.38000e15i	−0.598013	+	1.84049i	−0.539117	+	0.842231i	$0.681242\pi$
$224$	−1.80316e14	−	5.54955e14i	−0.0953722	−	0.293525i
$225$	−1.01484e14	+	7.37325e13i	−0.0521449	+	0.0378855i
$226$	−1.52143e15	+	1.10539e15i	−0.759535	+	0.551835i
$227$	4.52893e14	+	1.39386e15i	0.219699	+	0.676163i	0.998787	+	0.0492483i	$0.0156826\pi$
$227$	4.52893e14	+	1.39386e15i	0.219699	+	0.676163i	−0.779088	+	0.626915i	$0.784317\pi$
$228$	−8.20660e14	+	2.52573e15i	−0.386890	+	1.19072i
$229$	−1.23359e15	−	8.96252e14i	−0.565247	−	0.410676i	0.268128	−	0.963383i	$-0.413595\pi$
$229$	−1.23359e15	−	8.96252e14i	−0.565247	−	0.410676i	−0.833376	+	0.552707i	$0.813595\pi$
$230$	−1.55177e15			−0.691189
$231$	−6.21602e14	+	6.31300e14i	−0.269175	+	0.273375i
$232$	−1.97001e14			−0.0829460
$233$	−8.65620e13	−	6.28910e13i	−0.0354416	−	0.0257499i	0.569923	−	0.821698i	$-0.306973\pi$
$233$	−8.65620e13	−	6.28910e13i	−0.0354416	−	0.0257499i	−0.605365	+	0.795948i	$0.706973\pi$
$234$	−3.68586e14	+	1.13439e15i	−0.146769	+	0.451710i
$235$	6.91108e14	+	2.12701e15i	0.267673	+	0.823814i
$236$	2.00144e15	−	1.45413e15i	0.754074	−	0.547867i
$237$	1.08666e14	−	7.89503e13i	0.0398317	−	0.0289394i
$238$	−7.18633e13	−	2.21172e14i	−0.0256305	−	0.0788825i
$239$	9.01945e14	−	2.77590e15i	0.313035	−	0.963424i	−0.663520	−	0.748158i	$-0.730938\pi$
$239$	9.01945e14	−	2.77590e15i	0.313035	−	0.963424i	0.976556	−	0.215266i	$-0.0690617\pi$
$240$	−8.37205e14	−	6.08265e14i	−0.282787	−	0.205457i
$241$	4.59974e15			1.51225			0.756123	−	0.654430i	$-0.227091\pi$
$241$	4.59974e15			1.51225			0.756123	+	0.654430i	$0.227091\pi$
$242$	−9.36558e14	+	1.33195e15i	−0.299733	+	0.426272i
$243$	3.64770e15			1.13652
$244$	−1.76007e15	−	1.27876e15i	−0.533944	−	0.387933i
$245$	9.98807e14	−	3.07401e15i	0.295054	−	0.908084i
$246$	1.89081e14	+	5.81930e14i	0.0543962	+	0.167414i
$247$	−5.34230e15	+	3.88141e15i	−1.49692	+	1.08757i
$248$	1.48881e15	−	1.08168e15i	0.406352	−	0.295232i
$249$	−6.24395e14	−	1.92169e15i	−0.166021	−	0.510961i
$250$	5.87515e14	−	1.80818e15i	0.152198	−	0.468417i
$251$	1.25529e15	+	9.12023e14i	0.316859	+	0.230211i	0.734834	−	0.678247i	$-0.237260\pi$
$251$	1.25529e15	+	9.12023e14i	0.316859	+	0.230211i	−0.417975	+	0.908458i	$0.637260\pi$
$252$	5.80307e14			0.142743
$253$	−3.70467e15	+	3.76247e15i	−0.888108	+	0.901965i
$254$	−1.69853e15			−0.396874
$255$	−2.55955e15	−	1.85962e15i	−0.582979	−	0.423559i
$256$	−1.03560e15	+	3.18725e15i	−0.229949	+	0.707712i
$257$	−9.03384e14	−	2.78033e15i	−0.195572	−	0.601909i	−0.999969	−	0.00781761i	$-0.997512\pi$
$257$	−9.03384e14	−	2.78033e15i	−0.195572	−	0.601909i	0.804397	−	0.594092i	$-0.202488\pi$
$258$	3.82604e15	−	2.77978e15i	0.807647	−	0.586790i
$259$	1.12707e15	−	8.18862e14i	0.232007	−	0.168563i
$260$	−1.62851e15	−	5.01203e15i	−0.326936	−	1.00621i
$261$	9.55686e13	−	2.94130e14i	0.0187134	−	0.0575938i
$262$	−3.14097e15	−	2.28205e15i	−0.599937	−	0.435880i
$263$	3.46513e15			0.645665			0.322832	−	0.946456i	$-0.395365\pi$
$263$	3.46513e15			0.645665			0.322832	+	0.946456i	$0.395365\pi$
$264$	6.29243e15	−	1.04662e15i	1.14391	−	0.190266i
$265$	−7.16140e15			−1.27028
$266$	−9.68892e14	−	7.03941e14i	−0.167705	−	0.121844i
$267$	6.59665e14	−	2.03024e15i	0.111430	−	0.342945i
$268$	2.31139e15	+	7.11373e15i	0.381064	+	1.17279i
$269$	−7.20048e14	+	5.23145e14i	−0.115870	+	0.0841846i	−0.644211	−	0.764848i	$-0.722814\pi$
$269$	−7.20048e14	+	5.23145e14i	−0.115870	+	0.0841846i	0.528341	+	0.849032i	$0.322814\pi$
$270$	1.23975e15	−	9.00735e14i	0.194747	−	0.141492i
$271$	5.67635e14	+	1.74700e15i	0.0870500	+	0.267912i	0.985100	−	0.171980i	$-0.0550165\pi$
$271$	5.67635e14	+	1.74700e15i	0.0870500	+	0.267912i	−0.898050	+	0.439893i	$0.855017\pi$
$272$	2.85622e14	−	8.79053e14i	0.0427655	−	0.131619i
$273$	2.94257e15	+	2.13790e15i	0.430200	+	0.312558i
$274$	−9.64916e14			−0.137756
$275$	3.23999e14	+	6.23898e14i	0.0451733	+	0.0869863i
$276$	8.71801e15			1.18716
$277$	−5.86871e15	−	4.26387e15i	−0.780592	−	0.567134i	0.124564	−	0.992212i	$-0.460247\pi$
$277$	−5.86871e15	−	4.26387e15i	−0.780592	−	0.567134i	−0.905157	+	0.425078i	$0.860247\pi$
$278$	1.08498e15	−	3.33921e15i	0.140971	−	0.433863i
$279$	8.92747e14	+	2.74759e15i	0.113319	+	0.348759i
$280$	1.83471e15	−	1.33300e15i	0.227531	−	0.165311i
$281$	−9.48553e15	+	6.89164e15i	−1.14940	+	0.835087i	−0.988401	−	0.151868i	$-0.951471\pi$
$281$	−9.48553e15	+	6.89164e15i	−1.14940	+	0.835087i	−0.160998	+	0.986955i	$0.551471\pi$
$282$	1.44738e15	+	4.45457e15i	0.171381	+	0.527456i
$283$	3.10286e15	−	9.54962e15i	0.359046	−	1.10503i	−0.594580	−	0.804036i	$-0.702682\pi$
$283$	3.10286e15	−	9.54962e15i	0.359046	−	1.10503i	0.953626	−	0.300994i	$-0.0973183\pi$
$284$	7.23209e15	+	5.25442e15i	0.817889	+	0.594231i
$285$	−1.62929e16			−1.80098
$286$	5.97937e15	+	2.98857e15i	0.646065	+	0.322912i
$287$	7.40212e14			0.0781850
$288$	−5.33585e15	−	3.87672e15i	−0.551001	−	0.400326i
$289$	−2.18746e15	+	6.73232e15i	−0.220854	+	0.679718i
$290$	−1.57403e14	−	4.84435e14i	−0.0155391	−	0.0478243i
$291$	−6.72263e15	+	4.88427e15i	−0.648985	+	0.471515i
$292$	−7.04519e15	+	5.11863e15i	−0.665126	+	0.483242i
$293$	3.20871e15	+	9.87538e15i	0.296272	+	0.911831i	0.982791	+	0.184720i	$0.0591377\pi$
$293$	3.20871e15	+	9.87538e15i	0.296272	+	0.911831i	−0.686519	+	0.727111i	$0.740862\pi$
$294$	2.09178e15	−	6.43785e15i	0.188912	−	0.581411i
$295$	1.22789e16	+	8.92117e15i	1.08472	+	0.788095i
$296$	−1.00305e16			−0.866813
$297$	7.75819e14	−	5.15635e15i	0.0655908	−	0.435938i
$298$	9.95595e15			0.823525
$299$	1.75374e16	+	1.27416e16i	1.41939	+	1.03125i
$300$	3.58682e14	−	1.10391e15i	0.0284067	−	0.0874269i
$301$	−1.76793e15	−	5.44113e15i	−0.137020	−	0.421703i
$302$	−7.23861e15	+	5.25916e15i	−0.549048	+	0.398907i
$303$	−7.29059e15	+	5.29692e15i	−0.541235	+	0.393230i
$304$	−1.47090e15	−	4.52698e15i	−0.106882	−	0.328950i
$305$	4.12451e15	−	1.26939e16i	0.293375	−	0.902916i
$306$	−2.12656e15	−	1.54503e15i	−0.148077	−	0.107584i
$307$	−1.34755e15			−0.0918643			−0.0459321	−	0.998945i	$-0.514626\pi$
$307$	−1.34755e15			−0.0918643			−0.0459321	+	0.998945i	$0.514626\pi$
$308$	4.83879e14	−	3.21602e15i	0.0322966	−	0.214654i
$309$	1.69629e16			1.10859
$310$	3.84947e15	+	2.79680e15i	0.246348	+	0.178983i
$311$	8.19424e15	−	2.52193e16i	0.513531	−	1.58048i	−0.272409	−	0.962182i	$-0.587820\pi$
$311$	8.19424e15	−	2.52193e16i	0.513531	−	1.58048i	0.785940	−	0.618303i	$-0.212180\pi$
$312$	−8.09248e15	−	2.49061e16i	−0.496680	−	1.52862i
$313$	6.72770e14	−	4.88796e14i	0.0404416	−	0.0293825i	−0.567381	−	0.823456i	$-0.692043\pi$
$313$	6.72770e14	−	4.88796e14i	0.0404416	−	0.0293825i	0.607822	+	0.794073i	$0.292043\pi$
$314$	−2.11755e15	+	1.53849e15i	−0.124678	+	0.0905841i
$315$	1.10017e15	+	3.38597e15i	0.0634512	+	0.195283i
$316$	−1.52364e14	+	4.68928e14i	−0.00860827	+	0.0264935i
$317$	4.18487e15	+	3.04049e15i	0.231631	+	0.168290i	0.697547	−	0.716539i	$-0.254275\pi$
$317$	4.18487e15	+	3.04049e15i	0.231631	+	0.168290i	−0.465915	+	0.884829i	$0.654275\pi$
$318$	−1.49980e16			−0.813311
$319$	−1.55036e15	−	7.74889e14i	−0.0823744	−	0.0411718i
$320$	−5.64803e15			−0.294051
$321$	−2.70936e16	−	1.96847e16i	−1.38224	−	1.00426i
$322$	−1.21489e15	+	3.73904e15i	−0.0607398	+	0.186938i
$323$	−4.49693e15	−	1.38401e16i	−0.220343	−	0.678147i
$324$	−1.50347e16	+	1.09234e16i	−0.722027	+	0.524583i
$325$	2.33493e15	−	1.69643e15i	0.109909	−	0.0798534i
$326$	6.20765e15	+	1.91052e16i	0.286426	+	0.881529i
$327$	−2.75240e13	+	8.47101e13i	−0.00124495	+	0.00383155i
$328$	−4.31165e15	−	3.13259e15i	−0.191189	−	0.138907i
$329$	5.66618e15			0.246330
$330$	7.60132e15	+	1.46372e16i	0.324002	+	0.623904i
$331$	2.93684e16			1.22744			0.613718	−	0.789526i	$-0.289673\pi$
$331$	2.93684e16			1.22744			0.613718	+	0.789526i	$0.289673\pi$
$332$	6.00066e15	+	4.35973e15i	0.245924	+	0.178674i
$333$	4.86597e15	−	1.49759e16i	0.195561	−	0.601874i
$334$	−2.64695e15	−	8.14647e15i	−0.104326	−	0.321083i
$335$	−3.71251e16	+	2.69729e16i	−1.43508	+	1.04265i
$336$	−2.12109e15	+	1.54106e15i	−0.0804180	+	0.0584271i
$337$	−1.31560e16	−	4.04899e16i	−0.489247	−	1.50575i	−0.825734	−	0.564060i	$-0.809239\pi$
$337$	−1.31560e16	−	4.04899e16i	−0.489247	−	1.50575i	0.336486	−	0.941688i	$-0.390761\pi$
$338$	4.06605e15	−	1.25140e16i	0.148325	−	0.456497i
$339$	5.24398e16	+	3.80998e16i	1.87656	+	1.36340i
$340$	1.16137e16			0.407716
$341$	1.59714e16	−	2.65651e15i	0.550096	−	0.0914971i
$342$	−1.35367e16			−0.457449
$343$	−1.38955e16	−	1.00957e16i	−0.460748	−	0.334753i
$344$	−1.27290e16	+	3.91759e16i	−0.414157	+	1.27464i
$345$	1.65279e16	+	5.08677e16i	0.527709	+	1.62412i
$346$	2.10815e16	−	1.53166e16i	0.660553	−	0.479920i
$347$	3.07192e15	−	2.23188e15i	0.0944644	−	0.0686324i	−0.539550	−	0.841953i	$-0.681406\pi$
$347$	3.07192e15	−	2.23188e15i	0.0944644	−	0.0686324i	0.634015	+	0.773321i	$0.281406\pi$
$348$	8.84305e14	+	2.72161e15i	0.0266893	+	0.0821411i
$349$	8.70584e15	−	2.67938e16i	0.257896	−	0.793724i	−0.735349	−	0.677689i	$-0.762982\pi$
$349$	8.70584e15	−	2.67938e16i	0.257896	−	0.793724i	0.993245	−	0.116035i	$-0.0370184\pi$
$350$	4.23469e14	+	3.07668e14i	0.0123134	+	0.00894623i
$351$	−2.14071e16			−0.611028
$352$	−2.59337e16	+	2.63384e16i	−0.726671	+	0.738009i
$353$	4.64548e15			0.127789			0.0638947	−	0.997957i	$-0.479648\pi$
$353$	4.64548e15			0.127789			0.0638947	+	0.997957i	$0.479648\pi$
$354$	2.57156e16	+	1.86835e16i	0.694504	+	0.504587i
$355$	−1.69475e16	+	5.21592e16i	−0.449389	+	1.38308i
$356$	2.42152e15	+	7.45267e15i	0.0630468	+	0.194038i
$357$	−6.48471e15	+	4.71142e15i	−0.165786	+	0.120450i
$358$	−5.87274e15	+	4.26680e15i	−0.147435	+	0.107118i
$359$	−2.69023e15	−	8.27967e15i	−0.0663247	−	0.204126i	0.912402	−	0.409296i	$-0.134226\pi$
$359$	−2.69023e15	−	8.27967e15i	−0.0663247	−	0.204126i	−0.978727	+	0.205169i	$0.934226\pi$
$360$	7.92115e15	−	2.43788e16i	0.191788	−	0.590263i
$361$	−2.66080e16	−	1.93319e16i	−0.632726	−	0.459703i
$362$	−1.09432e16			−0.255588
$363$	5.36371e16	+	1.65142e16i	1.23047	+	0.378848i
$364$	−1.33516e16			−0.300867
$365$	−4.32226e16	−	3.14031e16i	−0.956770	−	0.695134i
$366$	8.63789e15	−	2.65847e16i	0.187837	−	0.578102i
$367$	−1.15368e16	−	3.55065e16i	−0.246464	−	0.758540i	−0.995392	−	0.0958878i	$-0.969431\pi$
$367$	−1.15368e16	−	3.55065e16i	−0.246464	−	0.758540i	0.748928	−	0.662652i	$-0.230569\pi$
$368$	−1.26414e16	+	9.18453e15i	−0.265329	+	0.192773i
$369$	6.76875e15	−	4.91778e15i	0.139584	−	0.101414i
$370$	−8.01431e15	−	2.46655e16i	−0.162388	−	0.499780i
$371$	−5.60669e15	+	1.72556e16i	−0.111629	+	0.343558i
$372$	−2.16267e16	−	1.57127e16i	−0.423118	−	0.307413i
$373$	9.40722e16			1.80865			0.904324	−	0.426848i	$-0.140376\pi$
$373$	9.40722e16			1.80865			0.904324	+	0.426848i	$0.140376\pi$
$374$	−1.03357e16	+	1.04969e16i	−0.195287	+	0.198334i
$375$	−6.55307e16			−1.21686
$376$	−3.30048e16	−	2.39794e16i	−0.602360	−	0.437640i
$377$	−2.19883e15	+	6.76730e15i	−0.0394432	+	0.121394i
$378$	−1.19974e15	−	3.69242e15i	−0.0211539	−	0.0651050i
$379$	6.38886e16	−	4.64178e16i	1.10731	−	0.804507i	0.125071	−	0.992148i	$-0.460084\pi$
$379$	6.38886e16	−	4.64178e16i	1.10731	−	0.804507i	0.982238	+	0.187641i	$0.0600842\pi$
$380$	4.83862e16	−	3.51546e16i	0.824382	−	0.598948i
$381$	1.80910e16	+	5.56784e16i	0.303006	+	0.932555i
$382$	1.05194e16	−	3.23754e16i	0.173212	−	0.533093i
$383$	−4.39766e16	−	3.19509e16i	−0.711917	−	0.517238i	0.171874	−	0.985119i	$-0.445018\pi$
$383$	−4.39766e16	−	3.19509e16i	−0.711917	−	0.517238i	−0.883792	+	0.467881i	$0.845018\pi$
$384$	7.19498e16			1.14519
$385$	1.96821e16	−	3.27372e15i	0.308019	−	0.0512326i
$386$	−4.56385e16			−0.702286
$387$	−5.23161e16	−	3.80099e16i	−0.791616	−	0.575142i
$388$	9.42601e15	−	2.90103e16i	0.140256	−	0.431664i
$389$	−8.87208e14	−	2.73054e15i	−0.0129823	−	0.0399555i	0.944355	−	0.328927i	$-0.106687\pi$
$389$	−8.87208e14	−	2.73054e15i	−0.0129823	−	0.0399555i	−0.957338	+	0.288971i	$0.906687\pi$
$390$	5.47796e16	−	3.97997e16i	0.788314	−	0.572743i
$391$	−3.86481e16	+	2.80795e16i	−0.546990	+	0.397411i
$392$	1.82195e16	+	5.60740e16i	0.253617	+	0.780552i
$393$	−4.13521e16	+	1.27269e17i	−0.566168	+	1.74249i
$394$	1.13936e16	+	8.27794e15i	0.153439	+	0.111480i
$395$	−3.02495e15			−0.0400716
$396$	−1.69417e16	−	3.26231e16i	−0.220769	−	0.425116i
$397$	4.87274e16			0.624648			0.312324	−	0.949976i	$-0.398893\pi$
$397$	4.87274e16			0.624648			0.312324	+	0.949976i	$0.398893\pi$
$398$	3.11936e16	+	2.26634e16i	0.393392	+	0.285816i
$399$	−1.27558e16	+	3.92584e16i	−0.158265	+	0.487089i
$400$	6.42880e14	+	1.97858e15i	0.00784766	+	0.0241526i
$401$	−2.01475e16	+	1.46380e16i	−0.241982	+	0.175810i	−0.702166	−	0.712013i	$-0.747783\pi$
$401$	−2.01475e16	+	1.46380e16i	−0.241982	+	0.175810i	0.460184	+	0.887824i	$0.347783\pi$
$402$	−7.77504e16	+	5.64890e16i	−0.918826	+	0.667566i
$403$	−2.05402e16	−	6.32163e16i	−0.238848	−	0.735099i
$404$	1.02224e16	−	3.14612e16i	0.116970	−	0.359995i
$405$	−9.22390e16	−	6.70156e16i	−1.03862	−	0.754602i
$406$	−1.29049e15			−0.0143000
$407$	−7.89380e16	−	3.94542e16i	−0.860840	−	0.430259i
$408$	5.77115e16			0.619400
$409$	1.33729e17	+	9.71595e16i	1.41261	+	1.02632i	0.992936	+	0.118648i	$0.0378559\pi$
$409$	1.33729e17	+	9.71595e16i	1.41261	+	1.02632i	0.419675	+	0.907674i	$0.362144\pi$
$410$	4.25824e15	−	1.31055e16i	0.0442726	−	0.136257i
$411$	1.02773e16	+	3.16304e16i	0.105174	+	0.323692i
$412$	−5.03758e16	+	3.66001e16i	−0.507446	+	0.368681i
$413$	3.11091e16	−	2.26021e16i	0.308469	−	0.224116i
$414$	1.37319e16	+	4.22625e16i	0.134038	+	0.412528i
$415$	−1.40618e16	+	4.32779e16i	−0.135123	+	0.415866i
$416$	1.22767e17	+	8.91951e16i	1.16138	+	0.843790i
$417$	−1.21017e17			−1.12710
$418$	−1.12873e16	+	7.50193e16i	−0.103501	+	0.687903i
$419$	6.37247e16			0.575330			0.287665	−	0.957731i	$-0.407121\pi$
$419$	6.37247e16			0.575330			0.287665	+	0.957731i	$0.407121\pi$
$420$	−2.66514e16	−	1.93634e16i	−0.236919	−	0.172132i
$421$	−1.13380e16	+	3.48947e16i	−0.0992435	+	0.305440i	−0.988336	−	0.152287i	$-0.951336\pi$
$421$	−1.13380e16	+	3.48947e16i	−0.0992435	+	0.305440i	0.889093	+	0.457727i	$0.151336\pi$
$422$	−2.79983e16	−	8.61699e16i	−0.241324	−	0.742719i
$423$	5.18135e16	−	3.76447e16i	0.439775	−	0.319515i
$424$	1.05685e17	−	7.67843e16i	0.883351	−	0.641792i
$425$	1.96545e15	+	6.04904e15i	0.0161784	+	0.0497918i
$426$	−3.54929e16	+	1.09236e17i	−0.287726	+	0.885531i
$427$	−2.73574e16	−	1.98763e16i	−0.218420	−	0.158692i
$428$	1.22935e17			0.966695
$429$	3.42802e16	−	2.27838e17i	0.265504	−	1.76463i
$430$	−1.06506e17			−0.812512
$431$	1.06497e17	+	7.73746e16i	0.800267	+	0.581428i	0.910993	−	0.412423i	$-0.135317\pi$
$431$	1.06497e17	+	7.73746e16i	0.800267	+	0.581428i	−0.110725	+	0.993851i	$0.535317\pi$
$432$	4.76838e15	−	1.46756e16i	0.0352961	−	0.108630i
$433$	2.45797e16	+	7.56486e16i	0.179228	+	0.551606i	0.999801	−	0.0199346i	$-0.00634580\pi$
$433$	2.45797e16	+	7.56486e16i	0.179228	+	0.551606i	−0.820573	+	0.571541i	$0.806346\pi$
$434$	9.75275e15	−	7.08579e15i	0.0700558	−	0.0508985i
$435$	−1.42035e16	+	1.03195e16i	−0.100511	+	0.0730258i
$436$	−1.01036e14	−	3.10957e14i	−0.000704391	−	0.00216789i
$437$	−7.60231e16	+	2.33975e17i	−0.522175	+	1.60709i
$438$	−9.05204e16	−	6.57669e16i	−0.612583	−	0.445067i
$439$	−1.92670e17			−1.28468			−0.642340	−	0.766420i	$-0.722036\pi$
$439$	−1.92670e17			−1.28468			−0.642340	+	0.766420i	$0.722036\pi$
$440$	−1.28501e17	−	6.42262e16i	−0.844233	−	0.421959i
$441$	−9.25594e16			−0.599197
$442$	4.89275e16	+	3.55479e16i	0.312111	+	0.226762i
$443$	5.91482e16	−	1.82039e17i	0.371807	−	1.14430i	−0.573801	−	0.818995i	$-0.694532\pi$
$443$	5.91482e16	−	1.82039e17i	0.371807	−	1.14430i	0.945608	−	0.325309i	$-0.105468\pi$
$444$	4.50252e16	+	1.38573e17i	0.278912	+	0.858402i
$445$	−3.88939e16	+	2.82581e16i	−0.237433	+	0.172505i
$446$	1.35608e17	−	9.85251e16i	0.815848	−	0.592748i
$447$	−1.06041e17	−	3.26360e17i	−0.628745	−	1.93508i
$448$	−4.42187e15	+	1.36091e16i	−0.0258404	+	0.0795285i
$449$	5.55697e16	+	4.03737e16i	0.320064	+	0.232540i	0.736203	−	0.676761i	$-0.236617\pi$
$449$	5.55697e16	+	4.03737e16i	0.320064	+	0.232540i	−0.416139	+	0.909301i	$0.636617\pi$
$450$	5.91641e15			0.0335875
$451$	−2.16100e16	−	4.16125e16i	−0.120922	−	0.232850i
$452$	−2.37940e17			−1.31241
$453$	2.49496e17	+	1.81269e17i	1.35652	+	0.985568i
$454$	2.13606e16	−	6.57412e16i	0.114486	−	0.352350i
$455$	−2.53125e16	−	7.79038e16i	−0.133740	−	0.411609i
$456$	2.40444e17	−	1.74693e17i	1.25240	−	0.909919i
$457$	2.09891e17	−	1.52495e17i	1.07780	−	0.783068i	0.100502	−	0.994937i	$-0.467955\pi$
$457$	2.09891e17	−	1.52495e17i	1.07780	−	0.783068i	0.977298	+	0.211869i	$0.0679550\pi$
$458$	2.22235e16	+	6.83968e16i	0.112509	+	0.346266i
$459$	1.45782e16	−	4.48670e16i	0.0727647	−	0.223947i
$460$	−1.58839e17	−	1.15403e17i	−0.781685	−	0.567928i
$461$	−6.44732e16			−0.312841			−0.156420	−	0.987691i	$-0.549995\pi$
$461$	−6.44732e16			−0.312841			−0.156420	+	0.987691i	$0.549995\pi$
$462$	4.12199e16	−	6.85609e15i	0.197213	−	0.0328022i
$463$	1.50759e17			0.711223			0.355612	−	0.934634i	$-0.384273\pi$
$463$	1.50759e17			0.711223			0.355612	+	0.934634i	$0.384273\pi$
$464$	−4.14952e15	−	3.01480e15i	−0.0193033	−	0.0140247i
$465$	5.06797e16	−	1.55976e17i	0.232482	−	0.715506i
$466$	1.55945e15	+	4.79948e15i	0.00705443	+	0.0217113i
$467$	−1.49448e17	+	1.08580e17i	−0.666698	+	0.484385i	−0.868918	−	0.494955i	$-0.835184\pi$
$467$	−1.49448e17	+	1.08580e17i	−0.666698	+	0.484385i	0.202220	+	0.979340i	$0.435184\pi$
$468$	−1.22092e17	+	8.87049e16i	−0.537141	+	0.390256i
$469$	3.59268e16	+	1.10571e17i	0.155882	+	0.479755i
$470$	3.25960e16	−	1.00320e17i	0.139485	−	0.429291i
$471$	7.29865e16	+	5.30278e16i	0.308039	+	0.223804i
$472$	−2.76859e17			−1.15249
$473$	−2.54271e17	+	2.58238e17i	−1.04400	+	1.06029i
$474$	−6.33510e15			−0.0256563
$475$	2.64991e16	+	1.92527e16i	0.105858	+	0.0769101i
$476$	9.09243e15	−	2.79836e16i	0.0358290	−	0.110270i
$477$	6.33726e16	+	1.95041e17i	0.246338	+	0.758151i
$478$	−1.11371e17	+	8.09160e16i	−0.427063	+	0.310279i
$479$	9.04646e16	−	6.57264e16i	0.342214	−	0.248633i	−0.403381	−	0.915032i	$-0.632165\pi$
$479$	9.04646e16	−	6.57264e16i	0.342214	−	0.248633i	0.745595	+	0.666399i	$0.232165\pi$
$480$	1.15700e17	+	3.56088e17i	0.431783	+	1.32889i
$481$	−1.11956e17	+	3.44564e17i	−0.412195	+	1.26861i
$482$	−1.75513e17	−	1.27518e17i	−0.637534	−	0.463195i
$483$	1.35507e17			0.485631
$484$	−1.94922e17	+	6.66873e16i	−0.689231	+	0.235802i
$485$	1.87139e17			0.652894
$486$	−1.39186e17	−	1.01124e17i	−0.479137	−	0.348113i
$487$	−7.69844e16	+	2.36934e17i	−0.261496	+	0.804801i	0.730985	+	0.682394i	$0.239061\pi$
$487$	−7.69844e16	+	2.36934e17i	−0.261496	+	0.804801i	−0.992480	+	0.122406i	$0.960939\pi$
$488$	7.52365e16	+	2.31554e17i	0.252174	+	0.776111i
$489$	5.60158e17	−	4.06979e17i	1.85269	−	1.34606i
$490$	−1.23332e17	+	8.96058e16i	−0.402532	+	0.292457i
$491$	−3.64276e16	−	1.12113e17i	−0.117328	−	0.361098i	0.875098	−	0.483947i	$-0.160797\pi$
$491$	−3.64276e16	−	1.12113e17i	−0.117328	−	0.361098i	−0.992425	+	0.122848i	$0.960797\pi$
$492$	−2.39232e16	+	7.36281e16i	−0.0760408	+	0.234030i
$493$	−1.26862e16	−	9.21703e15i	−0.0397947	−	0.0289125i
$494$	3.11450e17			0.964192
$495$	1.58230e17	−	1.60699e17i	0.483455	−	0.490998i
$496$	4.79130e16			0.144485
$497$	1.12411e17	+	8.16713e16i	0.334574	+	0.243082i
$498$	−2.94495e16	+	9.06362e16i	−0.0865141	+	0.266263i
$499$	1.86798e16	+	5.74905e16i	0.0541649	+	0.166703i	0.974479	−	0.224477i	$-0.0720673\pi$
$499$	1.86798e16	+	5.74905e16i	0.0541649	+	0.166703i	−0.920315	+	0.391179i	$0.872067\pi$
$500$	1.94611e17	−	1.41393e17i	0.557008	−	0.404690i
$501$	−2.38852e17	+	1.73536e17i	−0.674814	+	0.490281i
$502$	−2.26145e16	−	6.96004e16i	−0.0630686	−	0.194105i
$503$	1.06904e17	−	3.29017e17i	0.294308	−	0.905787i	−0.689145	−	0.724623i	$-0.742014\pi$
$503$	1.06904e17	−	3.29017e17i	0.294308	−	0.905787i	0.983453	−	0.181163i	$-0.0579862\pi$
$504$	−5.25400e16	−	3.81725e16i	−0.142788	−	0.103742i
$505$	2.02950e17			0.544495
$506$	2.45666e17	−	4.08614e16i	0.650678	−	0.108227i
$507$	−4.53522e17			−1.18590
$508$	−1.73861e17	−	1.26318e17i	−0.448837	−	0.326099i
$509$	−3.48445e16	+	1.07240e17i	−0.0888115	+	0.273334i	−0.985592	−	0.169143i	$-0.945900\pi$
$509$	−3.48445e16	+	1.07240e17i	−0.0888115	+	0.273334i	0.896780	+	0.442477i	$0.145900\pi$
$510$	4.61113e16	+	1.41916e17i	0.116038	+	0.357129i
$511$	−1.09506e17	+	7.95607e16i	−0.272083	+	0.197680i
$512$	−1.65451e17	+	1.20207e17i	−0.405896	+	0.294901i
$513$	−7.50752e16	−	2.31058e17i	−0.181859	−	0.559703i
$514$	−4.26080e16	+	1.31134e17i	−0.101913	+	0.313657i
$515$	−3.09058e17	−	2.24544e17i	−0.729950	−	0.530340i
$516$	5.98363e17			1.39554
$517$	−1.65420e17	−	3.18536e17i	−0.380978	−	0.733617i
$518$	−6.57068e16			−0.149440
$519$	−7.26625e17	−	5.27924e17i	−1.63201	−	1.18572i
$520$	−1.82249e17	+	5.60904e17i	−0.404243	+	1.24413i
$521$	−1.75560e17	−	5.40318e17i	−0.384575	−	1.18360i	−0.936788	−	0.349896i	$-0.886217\pi$
$521$	−1.75560e17	−	5.40318e17i	−0.384575	−	1.18360i	0.552214	−	0.833702i	$-0.313783\pi$
$522$	−1.18007e16	+	8.57373e15i	−0.0255300	+	0.0185486i
$523$	1.03007e17	−	7.48392e16i	0.220093	−	0.159907i	−0.472275	−	0.881451i	$-0.656567\pi$
$523$	1.03007e17	−	7.48392e16i	0.220093	−	0.159907i	0.692369	+	0.721544i	$0.256567\pi$
$524$	−1.51796e17	−	4.67181e17i	−0.320338	−	0.985898i
$525$	5.57512e15	−	1.71585e16i	0.0116203	−	0.0357637i
$526$	−1.32219e17	−	9.60631e16i	−0.272200	−	0.197765i
$527$	1.46483e17			0.297863
$528$	1.48558e17	+	7.42510e16i	0.298383	+	0.149136i
$529$	3.03570e17			0.602278
$530$	2.73258e17	+	1.98534e17i	0.535526	+	0.389082i
$531$	1.34310e17	−	4.13362e17i	0.260011	−	0.800233i
$532$	−4.68245e16	−	1.44111e17i	−0.0895462	−	0.275595i
$533$	−1.55734e17	+	1.13148e17i	−0.294210	+	0.213756i
$534$	−8.14549e16	+	5.91804e16i	−0.152019	+	0.110449i
$535$	2.33064e17	+	7.17296e17i	0.429710	+	1.32251i
$536$	2.58671e17	−	7.96108e17i	0.471169	−	1.45011i
$537$	2.02418e17	+	1.47065e17i	0.364264	+	0.264653i
$538$	4.19780e16			0.0746341
$539$	−7.71790e16	+	5.12957e17i	−0.135573	+	0.901061i
$540$	1.93888e17			0.336505
$541$	6.69309e17	+	4.86281e17i	1.14774	+	0.833884i	0.988179	−	0.153304i	$-0.0489914\pi$
$541$	6.69309e17	+	4.86281e17i	1.14774	+	0.833884i	0.159563	+	0.987188i	$0.448991\pi$
$542$	2.67724e16	−	8.23970e16i	0.0453620	−	0.139610i
$543$	1.16557e17	+	3.58724e17i	0.195136	+	0.600568i
$544$	−2.70547e17	+	1.96564e17i	−0.447559	+	0.325171i
$545$	1.62282e15	−	1.17905e15i	0.00265273	−	0.00192732i
$546$	−5.30115e16	−	1.63153e17i	−0.0856284	−	0.263537i
$547$	5.78601e16	−	1.78075e17i	0.0923552	−	0.284240i	−0.894200	−	0.447667i	$-0.852255\pi$
$547$	5.78601e16	−	1.78075e17i	0.0923552	−	0.284240i	0.986555	+	0.163427i	$0.0522549\pi$
$548$	−9.87688e16	−	7.17597e16i	−0.155792	−	0.113190i
$549$	−3.82218e17			−0.595787
$550$	4.93330e15	−	3.27883e16i	0.00759941	−	0.0505082i
$551$	−8.07543e16			−0.122936
$552$	−7.89314e17	−	5.73470e17i	−1.18753	−	0.862793i
$553$	−2.36825e15	+	7.28872e15i	−0.00352139	+	0.0108377i
$554$	1.05727e17	+	3.25394e17i	0.155372	+	0.478185i
$555$	−7.23186e17	+	5.25425e17i	−1.05038	+	0.763144i
$556$	3.59392e17	−	2.61113e17i	0.515919	−	0.374837i
$557$	1.26558e17	+	3.89506e17i	0.179569	+	0.552656i	0.999813	−	0.0193580i	$-0.00616224\pi$
$557$	1.26558e17	+	3.89506e17i	0.179569	+	0.552656i	−0.820244	+	0.572014i	$0.806162\pi$
$558$	4.21063e16	−	1.29590e17i	0.0590506	−	0.181739i
$559$	1.20368e18	+	8.74526e17i	1.66853	+	1.21226i
$560$	5.90451e16			0.0809024
$561$	4.54179e17	+	2.27005e17i	0.615132	+	0.307451i
$562$	5.52996e17			0.740349
$563$	−9.58964e16	−	6.96728e16i	−0.126911	−	0.0922059i	0.522519	−	0.852628i	$-0.324992\pi$
$563$	−9.58964e16	−	6.96728e16i	−0.126911	−	0.0922059i	−0.649430	+	0.760422i	$0.724992\pi$
$564$	−1.83128e17	+	5.63609e17i	−0.239574	+	0.737333i
$565$	−4.51096e17	−	1.38833e18i	−0.583383	−	1.79547i
$566$	−3.83138e17	+	2.78366e17i	−0.489834	+	0.355885i
$567$	−2.33691e17	+	1.69786e17i	−0.295360	+	0.214591i
$568$	−3.09145e17	−	9.51452e17i	−0.386277	−	1.18884i
$569$	−2.41104e17	+	7.42040e17i	−0.297834	+	0.916638i	0.684421	+	0.729087i	$0.260055\pi$
$569$	−2.41104e17	+	7.42040e17i	−0.297834	+	0.916638i	−0.982255	+	0.187551i	$0.939945\pi$
$570$	6.21692e17	+	4.51686e17i	0.759257	+	0.551633i
$571$	−1.56006e18			−1.88368			−0.941839	−	0.336064i	$-0.890904\pi$
$571$	−1.56006e18			−1.88368			−0.941839	+	0.336064i	$0.890904\pi$
$572$	3.89792e17	+	7.50589e17i	0.465327	+	0.896041i
$573$	−1.17332e18			−1.38488
$574$	−2.82444e16	−	2.05207e16i	−0.0329613	−	0.0239478i
$575$	3.32270e16	−	1.02262e17i	0.0383399	−	0.117998i
$576$	4.99805e16	+	1.53824e17i	0.0570236	+	0.175501i
$577$	−3.40785e17	+	2.47595e17i	−0.384448	+	0.279318i	−0.763177	−	0.646190i	$-0.776361\pi$
$577$	−3.40785e17	+	2.47595e17i	−0.384448	+	0.279318i	0.378728	+	0.925508i	$0.376361\pi$
$578$	2.70106e17	−	1.96244e17i	0.301303	−	0.218909i
$579$	4.86096e17	+	1.49605e18i	0.536181	+	1.65020i
$580$	1.99152e16	−	6.12927e16i	0.0217221	−	0.0668539i
$581$	9.32704e16	+	6.77649e16i	0.100600	+	0.0730904i
$582$	3.91922e17			0.418023
$583$	1.13374e18	−	1.88575e17i	1.19583	−	0.198902i
$584$	9.74562e17			1.01654
$585$	−7.49040e17	−	5.44210e17i	−0.772666	−	0.561375i
$586$	1.51338e17	−	4.65771e17i	0.154388	−	0.475157i
$587$	−4.07965e17	−	1.25559e18i	−0.411600	−	1.26677i	−0.915257	−	0.402870i	$-0.868013\pi$
$587$	−4.07965e17	−	1.25559e18i	−0.411600	−	1.26677i	0.503657	−	0.863903i	$-0.331987\pi$
$588$	6.92891e17	−	5.03415e17i	0.691373	−	0.502312i
$589$	6.10290e17	−	4.43402e17i	0.602264	−	0.437571i
$590$	−2.21209e17	−	6.80813e17i	−0.215906	−	0.664492i
$591$	1.50001e17	−	4.61656e17i	0.144802	−	0.445656i
$592$	−2.11277e17	−	1.53502e17i	−0.201726	−	0.146562i
$593$	−6.60882e17			−0.624120			−0.312060	−	0.950062i	$-0.601019\pi$
$593$	−6.60882e17			−0.624120			−0.312060	+	0.950062i	$0.601019\pi$
$594$	−1.72551e17	+	1.75244e17i	−0.161178	+	0.163693i
$595$	1.80516e17			0.166784
$596$	1.01909e18	+	7.40413e17i	0.931349	+	0.676665i
$597$	4.10675e17	−	1.26393e18i	0.371249	−	1.14259i
$598$	−3.15942e17	−	9.72370e17i	−0.282520	−	0.869508i
$599$	−7.06622e17	+	5.13391e17i	−0.625047	+	0.454123i	−0.854681	−	0.519154i	$-0.826247\pi$
$599$	−7.06622e17	+	5.13391e17i	−0.625047	+	0.454123i	0.229634	+	0.973277i	$0.426247\pi$
$600$	−1.05089e17	+	7.63520e16i	−0.0919552	+	0.0668093i
$601$	−7.82955e16	−	2.40969e17i	−0.0677724	−	0.208582i	0.911435	−	0.411444i	$-0.134976\pi$
$601$	−7.82955e16	−	2.40969e17i	−0.0677724	−	0.208582i	−0.979207	+	0.202862i	$0.934976\pi$
$602$	−8.33842e16	+	2.56630e17i	−0.0714013	+	0.219751i
$603$	1.06314e18	+	7.72413e17i	0.900588	+	0.654316i
$604$	−1.13206e18			−0.948703
$605$	−7.58645e17	−	1.01090e18i	−0.628968	−	0.838102i
$606$	4.25034e17			0.348619
$607$	5.15547e17	+	3.74566e17i	0.418352	+	0.303950i	0.776974	−	0.629532i	$-0.216754\pi$
$607$	5.15547e17	+	3.74566e17i	0.418352	+	0.303950i	−0.358623	+	0.933483i	$0.616754\pi$
$608$	−5.32183e17	+	1.63789e18i	−0.427256	+	1.31496i
$609$	1.37451e16	+	4.23030e16i	0.0109178	+	0.0336015i
$610$	−5.09291e17	+	3.70022e17i	−0.400241	+	0.290792i
$611$	−1.19212e18	+	8.66124e17i	−0.926939	+	0.673461i
$612$	−1.02772e17	−	3.16300e17i	−0.0790661	−	0.243340i
$613$	7.18221e17	−	2.21046e18i	0.546720	−	1.68263i	−0.170144	−	0.985419i	$-0.554423\pi$
$613$	7.18221e17	−	2.21046e18i	0.546720	−	1.68263i	0.716864	−	0.697213i	$-0.245577\pi$
$614$	5.14188e16	+	3.73579e16i	0.0387282	+	0.0281377i
$615$	−4.74959e17			−0.353971
$616$	−2.55359e17	+	2.59343e17i	−0.188311	+	0.191249i
$617$	5.47078e17			0.399205			0.199602	−	0.979877i	$-0.436035\pi$
$617$	5.47078e17			0.399205			0.199602	+	0.979877i	$0.436035\pi$
$618$	−6.47255e17	−	4.70258e17i	−0.467359	−	0.339556i
$619$	4.91758e17	−	1.51348e18i	0.351368	−	1.08140i	−0.606718	−	0.794917i	$-0.707514\pi$
$619$	4.91758e17	−	1.51348e18i	0.351368	−	1.08140i	0.958086	−	0.286482i	$-0.0924858\pi$
$620$	1.86036e17	+	5.72561e17i	0.131538	+	0.404833i
$621$	−6.45220e17	+	4.68780e17i	−0.451453	+	0.328000i
$622$	−1.01182e18	+	7.35129e17i	−0.700591	+	0.509009i
$623$	3.76386e16	+	1.15840e17i	0.0257906	+	0.0793752i
$624$	2.10695e17	−	6.48453e17i	0.142874	−	0.439722i
$625$	1.31211e18	+	9.53303e17i	0.880542	+	0.639751i
$626$	−3.92218e16			−0.0260492
$627$	2.57939e18	−	4.29028e17i	1.69542	−	0.281998i
$628$	−3.31168e17			−0.215433
$629$	−6.45928e17	−	4.69294e17i	−0.415868	−	0.302145i
$630$	5.18892e16	−	1.59699e17i	0.0330646	−	0.101762i
$631$	1.25266e17	+	3.85530e17i	0.0790029	+	0.243146i	0.982756	−	0.184909i	$-0.0591990\pi$
$631$	1.25266e17	+	3.85530e17i	0.0790029	+	0.243146i	−0.903753	+	0.428055i	$0.859199\pi$
$632$	4.46408e16	−	3.24334e16i	0.0278658	−	0.0202457i
$633$	−2.52648e18	+	1.83559e18i	−1.56096	+	1.13410i
$634$	−7.53920e16	−	2.32033e17i	−0.0461047	−	0.141896i
$635$	4.07423e17	−	1.25392e18i	0.246613	−	0.758998i
$636$	−1.53519e18	−	1.11538e18i	−0.919797	−	0.668272i
$637$	2.12959e18			1.26296
$638$	3.76751e16	+	7.25478e16i	0.0221167	+	0.0425882i
$639$	1.57053e18			0.912621
$640$	−1.31090e18	−	9.52426e17i	−0.754050	−	0.547850i
$641$	−1.32734e17	+	4.08514e17i	−0.0755798	+	0.232611i	−0.981708	−	0.190392i	$-0.939024\pi$
$641$	−1.32734e17	+	4.08514e17i	−0.0755798	+	0.232611i	0.906128	+	0.423003i	$0.139024\pi$
$642$	4.88101e17	+	1.50222e18i	0.275126	+	0.846752i
$643$	1.11875e17	−	8.12820e16i	0.0624255	−	0.0453548i	−0.556135	−	0.831092i	$-0.687716\pi$
$643$	1.11875e17	−	8.12820e16i	0.0624255	−	0.0453548i	0.618560	+	0.785737i	$0.287716\pi$
$644$	−4.02425e17	+	2.92379e17i	−0.222293	+	0.161506i
$645$	1.13440e18	+	3.49132e18i	0.620336	+	1.90920i
$646$	−2.12097e17	+	6.52768e17i	−0.114822	+	0.353384i
$647$	1.63671e18	+	1.18914e18i	0.877191	+	0.637316i	0.932507	−	0.361152i	$-0.117617\pi$
$647$	1.63671e18	+	1.18914e18i	0.877191	+	0.637316i	−0.0553160	+	0.998469i	$0.517617\pi$
$648$	2.07976e18			1.10351
$649$	−2.17883e18	−	1.08901e18i	−1.14455	−	0.572059i
$650$	−1.36124e17			−0.0707942
$651$	−3.36152e17	−	2.44229e17i	−0.173085	−	0.125754i
$652$	−7.85416e17	+	2.41726e18i	−0.400397	+	1.23229i
$653$	5.44048e17	+	1.67441e18i	0.274600	+	0.845133i	0.989325	+	0.145727i	$0.0465521\pi$
$653$	5.44048e17	+	1.67441e18i	0.274600	+	0.845133i	−0.714724	+	0.699406i	$0.753448\pi$
$654$	3.39864e15	−	2.46926e15i	0.00169844	−	0.00123399i
$655$	2.43812e18	−	1.77140e18i	1.20639	−	0.876492i
$656$	−4.28786e16	−	1.31967e17i	−0.0210071	−	0.0646531i
$657$	−4.72778e17	+	1.45506e18i	−0.229341	+	0.705840i
$658$	−2.16205e17	−	1.57082e17i	−0.103848	−	0.0754499i
$659$	−2.18830e18			−1.04076			−0.520382	−	0.853933i	$-0.674211\pi$
$659$	−2.18830e18			−1.04076			−0.520382	+	0.853933i	$0.674211\pi$
$660$	−3.10482e17	+	2.06357e18i	−0.146218	+	0.971814i
$661$	7.42068e16			0.0346046			0.0173023	−	0.999850i	$-0.494492\pi$
$661$	7.42068e16			0.0346046			0.0173023	+	0.999850i	$0.494492\pi$
$662$	−1.12061e18	−	8.14174e17i	−0.517463	−	0.375959i
$663$	6.44149e17	−	1.98249e18i	0.294543	−	0.906510i
$664$	−2.56506e17	−	7.89446e17i	−0.116146	−	0.357462i
$665$	7.52085e17	−	5.46421e17i	0.337230	−	0.245012i
$666$	−6.00845e17	+	4.36540e17i	−0.266797	+	0.193839i
$667$	8.19189e16	+	2.52120e17i	0.0360219	+	0.110864i
$668$	3.34902e17	−	1.03072e18i	0.145838	−	0.448844i
$669$	−4.67406e18	−	3.39590e18i	−2.01569	−	1.46449i
$670$	2.16435e18			0.924361
$671$	−3.18706e17	+	2.11823e18i	−0.134801	+	0.895934i
$672$	9.48589e17			0.397354
$673$	1.63141e18	+	1.18529e18i	0.676810	+	0.491731i	0.872298	−	0.488975i	$-0.162629\pi$
$673$	1.63141e18	+	1.18529e18i	0.676810	+	0.491731i	−0.195488	+	0.980706i	$0.562629\pi$
$674$	−6.20499e17	+	1.90970e18i	−0.254948	+	0.784650i
$675$	3.28127e16	+	1.00987e17i	0.0133527	+	0.0410953i
$676$	1.34685e18	−	9.78546e17i	0.542834	−	0.394392i
$677$	2.10820e18	−	1.53170e18i	0.841562	−	0.611431i	−0.0812443	−	0.996694i	$-0.525889\pi$
$677$	2.10820e18	−	1.53170e18i	0.841562	−	0.611431i	0.922807	+	0.385263i	$0.125889\pi$
$678$	−9.44722e17	−	2.90756e18i	−0.373518	−	1.14957i
$679$	1.46512e17	−	4.50918e17i	0.0573746	−	0.176581i
$680$	−1.05148e18	−	7.63949e17i	−0.407845	−	0.296317i
$681$	−2.38254e18			−0.915342
$682$	−6.83067e17	−	3.41406e17i	−0.259935	−	0.129919i
$683$	−8.63500e17			−0.325483			−0.162741	−	0.986669i	$-0.552034\pi$
$683$	−8.63500e17			−0.325483			−0.162741	+	0.986669i	$0.552034\pi$
$684$	−1.38562e18	−	1.00671e18i	−0.517343	−	0.375872i
$685$	2.31453e17	−	7.12339e17i	0.0856001	−	0.263450i
$686$	2.50333e17	+	7.70445e17i	0.0917088	+	0.282251i
$687$	2.00538e18	−	1.45699e18i	0.727741	−	0.528735i
$688$	−8.67647e17	+	6.30382e17i	−0.311902	+	0.226610i
$689$	−1.45807e18	−	4.48747e18i	−0.519222	−	1.59800i
$690$	7.79536e17	−	2.39917e18i	0.274990	−	0.846333i
$691$	1.69624e18	+	1.23239e18i	0.592760	+	0.430665i	0.843302	−	0.537440i	$-0.180609\pi$
$691$	1.69624e18	+	1.23239e18i	0.592760	+	0.430665i	−0.250542	+	0.968106i	$0.580609\pi$
$692$	3.29699e18			1.14137
$693$	−2.63331e17	−	5.07073e17i	−0.0903099	−	0.173902i
$694$	−1.79089e17			−0.0608462
$695$	2.20489e18	+	1.60194e18i	0.742139	+	0.539196i
$696$	9.89638e16	−	3.04579e17i	0.0330002	−	0.101564i
$697$	−1.31091e17	−	4.03456e17i	−0.0433072	−	0.133286i
$698$	−1.07499e18	+	7.81025e17i	−0.351839	+	0.255626i
$699$	1.40719e17	−	1.02239e17i	0.0456302	−	0.0331523i
$700$	2.04653e16	+	6.29858e16i	0.00657478	+	0.0202351i
$701$	−1.92030e17	+	5.91006e17i	−0.0611225	+	0.188116i	−0.976955	−	0.213444i	$-0.931532\pi$
$701$	−1.92030e17	+	5.91006e17i	−0.0611225	+	0.188116i	0.915833	+	0.401560i	$0.131532\pi$
$702$	8.16833e17	+	5.93464e17i	0.257598	+	0.187156i
$703$	−4.11168e18			−1.28472
$704$	8.94158e17	−	1.48725e17i	0.276816	−	0.0460427i
$705$	−3.63572e18			−1.11522
$706$	−1.77258e17	−	1.28786e17i	−0.0538735	−	0.0391414i
$707$	1.58890e17	−	4.89014e17i	0.0478488	−	0.147263i
$708$	1.24278e18	+	3.82488e18i	0.370832	+	1.14130i
$709$	1.78333e18	−	1.29567e18i	0.527269	−	0.383083i	−0.292066	−	0.956398i	$-0.594343\pi$
$709$	1.78333e18	−	1.29567e18i	0.527269	−	0.383083i	0.819335	+	0.573315i	$0.194343\pi$
$710$	2.09267e18	−	1.52041e18i	0.613085	−	0.445433i
$711$	2.67684e16	+	8.23846e16i	0.00777087	+	0.0239163i
$712$	2.70996e17	−	8.34039e17i	0.0779547	−	0.239920i
$713$	−2.00342e18	−	1.45557e18i	−0.571072	−	0.414908i
$714$	3.78052e17			0.106786
$715$	−3.64054e18	+	3.69734e18i	−1.01901	+	1.03491i
$716$	−9.18451e17			−0.254754
$717$	3.83868e18	+	2.78896e18i	1.05513	+	0.766599i
$718$	−1.26884e17	+	3.90509e17i	−0.0345620	+	0.106371i
$719$	−3.11313e15	−	9.58123e15i	−0.000840349	−	0.00258633i	0.950635	−	0.310310i	$-0.100433\pi$
$719$	−3.11313e15	−	9.58123e15i	−0.000840349	−	0.00258633i	−0.951476	+	0.307724i	$0.900433\pi$
$720$	5.39929e17	−	3.92281e17i	0.144436	−	0.104939i
$721$	−7.83009e17	+	5.68889e17i	−0.207581	+	0.150816i
$722$	4.79353e17	+	1.47530e18i	0.125940	+	0.387604i
$723$	−2.31069e18	+	7.11158e18i	−0.601649	+	1.85168i
$724$	−1.12015e18	−	8.13837e17i	−0.289052	−	0.210008i
$725$	3.52949e16			0.00902640
$726$	−1.58882e18	−	2.11710e18i	−0.402704	−	0.536604i
$727$	−1.78248e18			−0.447765			−0.223883	−	0.974616i	$-0.571873\pi$
$727$	−1.78248e18			−0.447765			−0.223883	+	0.974616i	$0.571873\pi$
$728$	1.20883e18	+	8.78268e17i	0.300962	+	0.218662i
$729$	−2.98148e17	+	9.17606e17i	−0.0735704	+	0.226426i
$730$	7.78671e17	+	2.39650e18i	0.190439	+	0.586110i
$731$	−2.65262e18	+	1.92724e18i	−0.643002	+	0.467168i
$732$	2.86125e18	−	2.07882e18i	0.687438	−	0.499453i
$733$	1.19666e18	+	3.68295e18i	0.284968	+	0.877042i	0.986408	+	0.164314i	$0.0525409\pi$
$733$	1.19666e18	+	3.68295e18i	0.284968	+	0.877042i	−0.701440	+	0.712729i	$0.747459\pi$
$734$	−5.44129e17	+	1.67466e18i	−0.128433	+	0.395277i
$735$	4.25093e18	+	3.08848e18i	0.994525	+	0.722565i
$736$	5.65347e18			1.31102
$737$	5.16713e18	−	5.24776e18i	1.18771	−	1.20624i
$738$	−3.94611e17			−0.0899089
$739$	2.00354e17	+	1.45565e17i	0.0452489	+	0.0328753i	0.610180	−	0.792263i	$-0.291097\pi$
$739$	2.00354e17	+	1.45565e17i	0.0452489	+	0.0328753i	−0.564931	+	0.825138i	$0.691097\pi$
$740$	1.01400e18	−	3.12078e18i	0.227004	−	0.698645i
$741$	−3.31726e18	−	1.02095e19i	−0.736141	−	2.26561i
$742$	6.92309e17	−	5.02992e17i	0.152291	−	0.110646i
$743$	1.95951e18	−	1.42367e18i	0.427287	−	0.310443i	−0.353276	−	0.935519i	$-0.614932\pi$
$743$	1.95951e18	−	1.42367e18i	0.427287	−	0.310443i	0.780563	+	0.625077i	$0.214932\pi$
$744$	9.24463e17	+	2.84521e18i	0.199832	+	0.615021i
$745$	−2.38812e18	+	7.34988e18i	−0.511730	+	1.57494i
$746$	−3.58953e18	−	2.60794e18i	−0.762491	−	0.553982i
$747$	1.30311e18			0.274408
$748$	−1.83860e18	+	3.05814e17i	−0.383820	+	0.0638405i
$749$	1.91082e18			0.395446
$750$	2.50046e18	+	1.81669e18i	0.513006	+	0.372721i
$751$	−2.20936e18	+	6.79972e18i	−0.449373	+	1.38303i	0.428242	+	0.903664i	$0.359133\pi$
$751$	−2.20936e18	+	6.79972e18i	−0.449373	+	1.38303i	−0.877615	+	0.479365i	$0.840867\pi$
$752$	−3.28227e17	−	1.01018e18i	−0.0661849	−	0.203696i
$753$	−2.04066e18	+	1.48263e18i	−0.407947	+	0.296391i
$754$	2.71509e17	−	1.97263e17i	0.0538110	−	0.0390960i
$755$	−2.14621e18	−	6.60534e18i	−0.421712	−	1.29790i
$756$	1.51796e17	−	4.67180e17i	0.0295711	−	0.0910106i
$757$	2.78088e17	+	2.02043e17i	0.0537105	+	0.0390230i	0.614317	−	0.789060i	$-0.289432\pi$
$757$	2.78088e17	+	2.02043e17i	0.0537105	+	0.0390230i	−0.560606	+	0.828083i	$0.689432\pi$
$758$	−3.72464e18			−0.713237
$759$	−3.95604e18	−	7.61781e18i	−0.751086	−	1.44630i
$760$	−6.69327e18			−1.25994
$761$	5.11735e18	+	3.71797e18i	0.955091	+	0.693914i	0.952006	−	0.306081i	$-0.0990178\pi$
$761$	5.11735e18	+	3.71797e18i	0.955091	+	0.693914i	0.00308569	+	0.999995i	$0.499018\pi$
$762$	8.53259e17	−	2.62606e18i	0.157897	−	0.485957i
$763$	−1.57044e15	−	4.83331e15i	−0.000288145	−	0.000886820i
$764$	3.48449e18	−	2.53163e18i	0.633916	−	0.460567i
$765$	1.65070e18	−	1.19930e18i	0.297762	−	0.216337i
$766$	7.92254e17	+	2.43831e18i	0.141702	+	0.436115i
$767$	−3.09018e18	+	9.51058e18i	−0.548041	+	1.68670i
$768$	−4.40752e18	−	3.20225e18i	−0.775079	−	0.563128i
$769$	−6.19461e18			−1.08017			−0.540085	−	0.841610i	$-0.681608\pi$
$769$	−6.19461e18			−1.08017			−0.540085	+	0.841610i	$0.681608\pi$
$770$	−8.41770e17	−	4.20728e17i	−0.145547	−	0.0727464i
$771$	4.75244e18			0.814823
$772$	−4.67156e18	−	3.39409e18i	−0.794236	−	0.577046i
$773$	2.77352e18	−	8.53602e18i	0.467590	−	1.43909i	−0.388106	−	0.921615i	$-0.626871\pi$
$773$	2.77352e18	−	8.53602e18i	0.467590	−	1.43909i	0.855696	−	0.517479i	$-0.173129\pi$
$774$	9.42494e17	+	2.90070e18i	0.157566	+	0.484938i
$775$	−2.66736e17	+	1.93795e17i	−0.0442203	+	0.0321279i
$776$	−2.76171e18	+	2.00650e18i	−0.454022	+	0.329866i
$777$	6.99844e17	+	2.15390e18i	0.114094	+	0.351147i
$778$	−4.18450e16	+	1.28786e17i	−0.00676513	+	0.0208209i
$779$	−1.76743e18	−	1.28411e18i	−0.283366	−	0.205877i
$780$	8.56711e18			1.36213
$781$	1.30956e18	−	8.70375e18i	0.206487	−	1.37238i
$782$	2.25314e18			0.352326
$783$	−2.11792e17	−	1.53876e17i	−0.0328442	−	0.0238627i
$784$	−4.74363e17	+	1.45994e18i	−0.0729552	+	0.224533i
$785$	−6.27841e17	−	1.93230e18i	−0.0957629	−	0.294728i
$786$	5.10612e18	−	3.70981e18i	0.772403	−	0.561184i
$787$	3.11444e18	−	2.26277e18i	0.467244	−	0.339473i	−0.329122	−	0.944287i	$-0.606753\pi$
$787$	3.11444e18	−	2.26277e18i	0.467244	−	0.339473i	0.796366	+	0.604815i	$0.206753\pi$
$788$	5.50629e17	+	1.69466e18i	0.0819291	+	0.252152i
$789$	−1.74072e18	+	5.35738e18i	−0.256879	+	0.790591i
$790$	1.15423e17	+	8.38600e16i	0.0168934	+	0.0122738i
$791$	−3.69839e18			−0.536866
$792$	−6.12077e17	+	4.06806e18i	−0.0881236	+	0.585699i
$793$	8.79403e18			1.25578
$794$	−1.85930e18	−	1.35086e18i	−0.263340	−	0.191327i
$795$	3.59755e18	−	1.10721e19i	0.505383	−	1.55541i
$796$	1.50752e18	+	4.63966e18i	0.210052	+	0.646475i
$797$	4.64196e18	−	3.37258e18i	0.641538	−	0.466104i	−0.218841	−	0.975761i	$-0.570227\pi$
$797$	4.64196e18	−	3.37258e18i	0.641538	−	0.466104i	0.860378	+	0.509656i	$0.170227\pi$
$798$	1.57508e18	−	1.14436e18i	0.215915	−	0.156872i
$799$	−1.00348e18	−	3.08838e18i	−0.136444	−	0.419930i
$800$	2.32599e17	−	7.15865e17i	0.0313706	−	0.0965487i
$801$	1.11379e18	+	8.09215e17i	0.149002	+	0.108256i
$802$	1.17458e18			0.155865
$803$	7.66962e18	+	3.83338e18i	1.00954	+	0.504580i
$804$	−1.21596e19			−1.58765
$805$	−2.46890e18	−	1.79376e18i	−0.319764	−	0.232322i
$806$	−9.68775e17	+	2.98158e18i	−0.124464	+	0.383062i
$807$	−4.47108e17	−	1.37606e18i	−0.0569816	−	0.175371i
$808$	−2.99503e18	+	2.17602e18i	−0.378641	+	0.275099i
$809$	−1.02126e19	+	7.41985e18i	−1.28076	+	0.930529i	−0.999576	−	0.0291236i	$-0.990728\pi$
$809$	−1.02126e19	+	7.41985e18i	−1.28076	+	0.930529i	−0.281188	+	0.959653i	$0.590728\pi$
$810$	1.66172e18	+	5.11424e18i	0.206731	+	0.636251i
$811$	1.02270e18	−	3.14754e18i	0.126215	−	0.388451i	−0.867905	−	0.496730i	$-0.834534\pi$
$811$	1.02270e18	−	3.14754e18i	0.126215	−	0.388451i	0.994121	+	0.108279i	$0.0345340\pi$
$812$	−1.32095e17	−	9.59727e16i	−0.0161723	−	0.0117499i
$813$	−2.98616e18			−0.362681
$814$	1.91827e18	+	3.69384e18i	0.231127	+	0.445061i
$815$	−1.55932e19			−1.86385
$816$	1.21561e18	+	8.83190e17i	0.144147	+	0.104729i
$817$	−5.21787e18	+	1.60589e19i	−0.613832	+	1.88918i
$818$	−2.40917e18	−	7.41466e18i	−0.281171	−	0.865356i
$819$	−1.89772e18	+	1.37877e18i	−0.219728	+	0.159642i
$820$	1.41052e18	−	1.02480e18i	0.162027	−	0.117720i
$821$	6.18023e17	+	1.90208e18i	0.0704327	+	0.216769i	0.980077	−	0.198619i	$-0.0636456\pi$
$821$	6.18023e17	+	1.90208e18i	0.0704327	+	0.216769i	−0.909644	+	0.415388i	$0.863646\pi$
$822$	4.84728e17	−	1.49184e18i	0.0548064	−	0.168677i
$823$	−2.22990e18	−	1.62012e18i	−0.250142	−	0.181739i	0.455648	−	0.890160i	$-0.349408\pi$
$823$	−2.22990e18	−	1.62012e18i	−0.250142	−	0.181739i	−0.705790	+	0.708421i	$0.749408\pi$
$824$	6.96849e18			0.775553
$825$	−1.12736e18	+	1.87513e17i	−0.124484	+	0.0207053i
$826$	−1.81363e18			−0.198691
$827$	5.49789e18	+	3.99445e18i	0.597600	+	0.434182i	0.845026	−	0.534725i	$-0.179585\pi$
$827$	5.49789e18	+	3.99445e18i	0.597600	+	0.434182i	−0.247426	+	0.968907i	$0.579585\pi$
$828$	−1.73742e18	+	5.34722e18i	−0.187373	+	0.576675i
$829$	3.44321e18	+	1.05971e19i	0.368434	+	1.13392i	0.947803	+	0.318857i	$0.103299\pi$
$829$	3.44321e18	+	1.05971e19i	0.368434	+	1.13392i	−0.579369	+	0.815065i	$0.696701\pi$
$830$	1.73634e18	−	1.26153e18i	0.184344	−	0.133933i
$831$	9.54046e18	−	6.93155e18i	1.00499	−	0.730170i
$832$	−1.14995e18	−	3.53917e18i	−0.120192	−	0.369913i
$833$	−1.45025e18	+	4.46341e18i	−0.150401	+	0.462886i
$834$	4.61766e18	+	3.35492e18i	0.475163	+	0.345226i
$835$	6.64897e18			0.678879
$836$	−6.73448e18	+	6.83956e18i	−0.682281	+	0.692926i
$837$	2.44549e18			0.245839
$838$	−2.43155e18	−	1.76663e18i	−0.242548	−	0.176221i
$839$	1.10736e18	−	3.40812e18i	0.109607	−	0.337335i	−0.881177	−	0.472786i	$-0.843248\pi$
$839$	1.10736e18	−	3.40812e18i	0.109607	−	0.337335i	0.990784	+	0.135451i	$0.0432483\pi$
$840$	1.13925e18	+	3.50626e18i	0.111893	+	0.344373i
$841$	8.23062e18	−	5.97990e18i	0.802156	−	0.582800i
$842$	1.40000e18	−	1.01716e18i	0.135394	−	0.0983697i
$843$	−5.88997e18	−	1.81275e19i	−0.565241	−	1.73963i
$844$	3.54245e18	−	1.09026e19i	0.337348	−	1.03825i
$845$	8.26302e18	+	6.00344e18i	0.780855	+	0.567324i
$846$	−3.02067e18			−0.283267
$847$	−3.02974e18	+	1.03654e18i	−0.281944	+	0.0964597i
$848$	3.40116e18			0.314090
$849$	1.32058e19	+	9.59456e18i	1.21022	+	0.879275i
$850$	9.27002e16	−	2.85302e17i	0.00843058	−	0.0259467i
$851$	4.17098e18	+	1.28370e19i	0.376440	+	1.15856i
$852$	−1.17568e19	+	8.54184e18i	−1.05301	+	0.765057i
$853$	3.38391e18	−	2.45856e18i	0.300781	−	0.218530i	−0.427150	−	0.904181i	$-0.640482\pi$
$853$	3.38391e18	−	2.45856e18i	0.300781	−	0.218530i	0.727931	+	0.685651i	$0.240482\pi$
$854$	4.92853e17	+	1.51684e18i	0.0434751	+	0.133803i
$855$	3.24703e18	−	9.99333e18i	0.284254	−	0.874844i
$856$	−1.11303e19	−	8.08662e18i	−0.967000	−	0.702567i
$857$	2.74026e18			0.236274			0.118137	−	0.992997i	$-0.462308\pi$
$857$	2.74026e18			0.236274			0.118137	+	0.992997i	$0.462308\pi$
$858$	−7.62432e18	+	7.74329e18i	−0.652430	+	0.662610i
$859$	2.02803e18			0.172234			0.0861169	−	0.996285i	$-0.472554\pi$
$859$	2.02803e18			0.172234			0.0861169	+	0.996285i	$0.472554\pi$
$860$	−1.09020e19	−	7.92075e18i	−0.918894	−	0.667615i
$861$	−3.71848e17	+	1.14443e18i	−0.0311060	+	0.0957345i
$862$	−1.91858e18	−	5.90479e18i	−0.159288	−	0.490238i
$863$	1.65617e18	−	1.20328e18i	0.136469	−	0.0991505i	−0.517456	−	0.855710i	$-0.673121\pi$
$863$	1.65617e18	−	1.20328e18i	0.136469	−	0.0991505i	0.653925	+	0.756559i	$0.273121\pi$
$864$	−4.51672e18	+	3.28159e18i	−0.369389	+	0.268377i
$865$	6.25055e18	+	1.92372e19i	0.507357	+	1.56148i
$866$	1.15930e18	−	3.56795e18i	0.0933961	−	0.287444i
$867$	−9.30985e18	−	6.76400e18i	−0.744421	−	0.540853i
$868$	1.52525e18			0.121050
$869$	4.78889e17	−	7.96534e16i	0.0377230	−	0.00627445i
$870$	8.28049e17			0.0647412
$871$	−2.44605e19	−	1.77716e19i	−1.89822	−	1.37914i
$872$	−1.13071e16	+	3.47996e16i	−0.000870950	+	0.00268051i
$873$	−1.65603e18	−	5.09673e18i	−0.126612	−	0.389672i
$874$	9.38727e18	−	6.82025e18i	0.712385	−	0.517578i
$875$	3.02491e18	−	2.19772e18i	0.227855	−	0.165547i
$876$	−4.37465e18	−	1.34638e19i	−0.327090	−	1.00668i
$877$	4.91409e18	−	1.51240e19i	0.364708	−	1.12246i	−0.585455	−	0.810705i	$-0.699084\pi$
$877$	4.91409e18	−	1.51240e19i	0.364708	−	1.12246i	0.950164	−	0.311752i	$-0.100916\pi$
$878$	7.35174e18	+	5.34136e18i	0.541597	+	0.393493i
$879$	−1.68801e19			−1.23437
$880$	−1.72378e18	−	3.31934e18i	−0.125125	−	0.240943i
$881$	2.34269e19			1.68800			0.843998	−	0.536347i	$-0.180196\pi$
$881$	2.34269e19			1.68800			0.843998	+	0.536347i	$0.180196\pi$
$882$	3.53180e18	+	2.56600e18i	0.252610	+	0.183532i
$883$	3.64441e18	−	1.12163e19i	0.258752	−	0.796355i	−0.734316	−	0.678808i	$-0.762497\pi$
$883$	3.64441e18	−	1.12163e19i	0.258752	−	0.796355i	0.993067	−	0.117547i	$-0.0375032\pi$
$884$	2.36456e18	+	7.27738e18i	0.166652	+	0.512903i
$885$	−1.99612e19	+	1.45027e19i	−1.39655	+	1.01465i
$886$	−7.30357e18	+	5.30635e18i	−0.507243	+	0.368533i
$887$	−1.92302e18	−	5.91845e18i	−0.132581	−	0.408042i	0.862625	−	0.505844i	$-0.168819\pi$
$887$	−1.92302e18	−	5.91845e18i	−0.132581	−	0.408042i	−0.995206	+	0.0978022i	$0.968819\pi$
$888$	5.03884e18	−	1.55080e19i	0.344863	−	1.06138i
$889$	−2.70239e18	−	1.96340e18i	−0.183606	−	0.133397i
$890$	2.26747e18			0.152935
$891$	1.63673e19	+	8.18060e18i	1.09590	+	0.547747i
$892$	2.12081e19			1.40971
$893$	−1.35293e19	−	9.82961e18i	−0.892773	−	0.648637i
$894$	−5.00140e18	+	1.53927e19i	−0.327641	+	1.00837i
$895$	−1.74123e18	−	5.35897e18i	−0.113242	−	0.348523i
$896$	−3.32121e18	+	2.41300e18i	−0.214434	+	0.155796i
$897$	−2.85096e19	+	2.07134e19i	−1.82743	+	1.32770i
$898$	−1.00111e18	−	3.08109e18i	−0.0637066	−	0.196069i
$899$	2.51188e17	−	7.73078e17i	0.0158694	−	0.0488411i
$900$	6.05604e17	+	4.39997e17i	0.0379850	+	0.0275978i
$901$	1.03982e19			0.647512
$902$	−3.29039e17	+	2.18690e18i	−0.0203425	+	0.135203i
$903$	9.30057e18			0.570873
$904$	2.15427e19	+	1.56517e19i	1.31282	+	0.953820i
$905$	2.62494e18	−	8.07874e18i	0.158820	−	0.488796i
$906$	−4.49476e18	−	1.38335e19i	−0.270006	−	0.830993i
$907$	−8.18553e18	+	5.94714e18i	−0.488202	+	0.354699i	−0.804492	−	0.593963i	$-0.797563\pi$
$907$	−8.18553e18	+	5.94714e18i	−0.488202	+	0.354699i	0.316291	+	0.948662i	$0.397563\pi$
$908$	7.07558e18	−	5.14071e18i	0.418990	−	0.304414i
$909$	−1.79594e18	−	5.52733e18i	−0.105591	−	0.324975i
$910$	−1.19386e18	+	3.67432e18i	−0.0696922	+	0.214490i
$911$	1.14835e19	+	8.34321e18i	0.665584	+	0.483575i	0.868544	−	0.495612i	$-0.165056\pi$
$911$	1.14835e19	+	8.34321e18i	0.665584	+	0.483575i	−0.202960	+	0.979187i	$0.565056\pi$
$912$	7.73800e18			0.445310
$913$	1.08658e18	−	7.22174e18i	0.0620869	−	0.412650i
$914$	−1.22364e19			−0.694231
$915$	1.75539e19	+	1.27537e19i	0.988866	+	0.718453i
$916$	−2.81180e18	+	8.65384e18i	−0.157277	+	0.484048i
$917$	−2.35943e18	−	7.26157e18i	−0.131041	−	0.403302i
$918$	−1.80010e18	+	1.30785e18i	−0.0992703	+	0.0721241i
$919$	1.95490e18	−	1.42032e18i	0.107047	−	0.0777741i	−0.532974	−	0.846132i	$-0.678926\pi$
$919$	1.95490e18	−	1.42032e18i	0.107047	−	0.0777741i	0.640021	+	0.768357i	$0.278926\pi$
$920$	6.78980e18	+	2.08969e19i	0.369178	+	1.13621i
$921$	6.76948e17	−	2.08343e18i	0.0365483	−	0.112484i
$922$	2.46011e18	+	1.78738e18i	0.131888	+	0.0958220i
$923$	−3.61345e19			−1.92358
$924$	4.72915e18	+	2.36369e18i	0.249986	+	0.124946i
$925$	1.79707e18			0.0943288
$926$	−5.75252e18	−	4.17945e18i	−0.299838	−	0.217845i
$927$	−3.38054e18	+	1.04042e19i	−0.174972	+	0.538508i
$928$	5.73455e17	+	1.76491e18i	0.0294739	+	0.0907114i
$929$	−1.76607e19	+	1.28313e19i	−0.901377	+	0.654888i	−0.938819	−	0.344410i	$-0.888079\pi$
$929$	−1.76607e19	+	1.28313e19i	−0.901377	+	0.654888i	0.0374426	+	0.999299i	$0.488079\pi$
$930$	−6.25788e18	+	4.54662e18i	−0.317167	+	0.230435i
$931$	7.46854e18	+	2.29858e19i	0.375892	+	1.15688i
$932$	−1.97307e17	+	6.07249e17i	−0.00986142	+	0.0303503i
$933$	3.48747e19	+	2.53380e19i	1.73093	+	1.25760i
$934$	8.71264e18			0.429433
$935$	−5.27005e18	−	1.01481e19i	−0.257952	−	0.496716i
$936$	1.68890e19			0.820938
$937$	−2.27191e19	−	1.65064e19i	−1.09669	−	0.796792i	−0.116173	−	0.993229i	$-0.537063\pi$
$937$	−2.27191e19	−	1.65064e19i	−1.09669	−	0.796792i	−0.980516	+	0.196437i	$0.937063\pi$
$938$	1.69448e18	−	5.21508e18i	0.0812304	−	0.250001i
$939$	4.17751e17	+	1.28571e18i	0.0198880	+	0.0612090i
$940$	1.07972e19	−	7.84465e18i	0.510483	−	0.370888i
$941$	−2.30918e19	+	1.67772e19i	−1.08424	+	0.787746i	−0.978417	−	0.206639i	$-0.933747\pi$
$941$	−2.30918e19	+	1.67772e19i	−1.08424	+	0.787746i	−0.105822	+	0.994385i	$0.533747\pi$
$942$	−1.31488e18	−	4.04678e18i	−0.0613132	−	0.188703i
$943$	−2.21617e18	+	6.82066e18i	−0.102630	+	0.315864i
$944$	−5.83162e18	−	4.23692e18i	−0.268208	−	0.194864i
$945$	3.01367e18			0.137654
$946$	1.68613e19	−	2.80453e18i	0.764891	−	0.127224i
$947$	−3.19378e19			−1.43890			−0.719449	−	0.694545i	$-0.755606\pi$
$947$	−3.19378e19			−1.43890			−0.719449	+	0.694545i	$0.755606\pi$
$948$	−6.48461e17	−	4.71135e17i	−0.0290155	−	0.0210810i
$949$	1.08776e19	−	3.34778e19i	0.483396	−	1.48774i
$950$	−4.77390e17	−	1.46926e18i	−0.0210703	−	0.0648476i
$951$	−6.80313e18	+	4.94277e18i	−0.298219	+	0.216669i
$952$	−2.66397e18	+	1.93549e18i	−0.115982	+	0.0842656i
$953$	6.36960e18	+	1.96036e19i	0.275428	+	0.847681i	0.989106	+	0.147206i	$0.0470282\pi$
$953$	6.36960e18	+	1.96036e19i	0.275428	+	0.847681i	−0.713678	+	0.700474i	$0.752972\pi$
$954$	2.98896e18	−	9.19906e18i	0.128368	−	0.395075i
$955$	2.13775e19	+	1.55317e19i	0.911875	+	0.662516i
$956$	−1.74176e19			−0.737925
$957$	1.97687e18	−	2.00771e18i	0.0831860	−	0.0844840i
$958$	−5.27399e18			−0.220426
$959$	−1.53520e18	−	1.11539e18i	−0.0637300	−	0.0463026i
$960$	2.83731e18	−	8.73233e18i	0.116988	−	0.360053i
$961$	−5.19898e18	−	1.60008e19i	−0.212920	−	0.655300i
$962$	1.38242e19	−	1.00438e19i	0.562343	−	0.408566i
$963$	1.74732e19	−	1.26950e19i	0.705993	−	0.512934i
$964$	−8.48216e18	−	2.61054e19i	−0.340413	−	1.04768i
$965$	1.09473e19	−	3.36922e19i	0.436393	−	1.34308i
$966$	−5.17057e18	−	3.75664e18i	−0.204733	−	0.148747i
$967$	−4.60593e19			−1.81153			−0.905764	−	0.423783i	$-0.860702\pi$
$967$	−4.60593e19			−1.81153			−0.905764	+	0.423783i	$0.860702\pi$
$968$	2.20345e19	+	6.78417e18i	0.860824	+	0.265037i
$969$	2.36571e19			0.918028
$970$	−7.14069e18	−	5.18801e18i	−0.275248	−	0.199979i
$971$	8.71891e18	−	2.68341e19i	0.333839	−	1.02745i	−0.633452	−	0.773782i	$-0.718363\pi$
$971$	8.71891e18	−	2.68341e19i	0.333839	−	1.02745i	0.967291	−	0.253669i	$-0.0816375\pi$
$972$	−6.72655e18	−	2.07022e19i	−0.255836	−	0.787383i
$973$	5.58616e18	−	4.05858e18i	0.211047	−	0.153335i
$974$	9.50596e18	−	6.90648e18i	0.356749	−	0.259193i
$975$	1.44986e18	+	4.46220e18i	0.0540500	+	0.166349i
$976$	−1.95885e18	+	6.02872e18i	−0.0725400	+	0.223255i
$977$	−2.80169e18	−	2.03554e18i	−0.103063	−	0.0748800i	0.535060	−	0.844814i	$-0.320289\pi$
$977$	−2.80169e18	−	2.03554e18i	−0.103063	−	0.0748800i	−0.638123	+	0.769934i	$0.720289\pi$
$978$	−3.26566e19			−1.19335
$979$	5.41332e18	−	5.49779e18i	0.196506	−	0.199572i
$980$	−1.92881e19			−0.695538
$981$	−4.64720e16	−	3.37639e16i	−0.00166472	−	0.00120949i
$982$	−1.71810e18	+	5.28778e18i	−0.0611399	+	0.188169i
$983$	1.52386e19	+	4.68997e19i	0.538702	+	1.65795i	0.735512	+	0.677512i	$0.236942\pi$
$983$	1.52386e19	+	4.68997e19i	0.538702	+	1.65795i	−0.196810	+	0.980442i	$0.563058\pi$
$984$	7.00922e18	−	5.09250e18i	0.246151	−	0.178839i
$985$	−8.84408e18	+	6.42560e18i	−0.308544	+	0.224170i
$986$	2.28546e17	+	7.03391e17i	0.00792087	+	0.0243779i
$987$	−2.84642e18	+	8.76038e18i	−0.0980026	+	0.301621i
$988$	3.18801e19	+	2.31622e19i	1.09043	+	0.792246i
$989$	5.54303e19			1.88352
$990$	−1.04926e19	+	1.74524e18i	−0.354206	+	0.0589149i
$991$	−2.03329e19			−0.681901			−0.340950	−	0.940081i	$-0.610749\pi$
$991$	−2.03329e19			−0.681901			−0.340950	+	0.940081i	$0.610749\pi$
$992$	−1.40245e19	−	1.01894e19i	−0.467264	−	0.339487i
$993$	−1.47533e19	+	4.54060e19i	−0.488337	+	1.50295i
$994$	−2.02512e18	−	6.23269e18i	−0.0665948	−	0.204958i
$995$	−2.42134e19	+	1.75921e19i	−0.791054	+	0.574734i
$996$	−9.75496e18	+	7.08739e18i	−0.316621	+	0.230039i
$997$	−3.15192e18	−	9.70062e18i	−0.101638	−	0.312810i	0.887288	−	0.461215i	$-0.152586\pi$
$997$	−3.15192e18	−	9.70062e18i	−0.101638	−	0.312810i	−0.988927	+	0.148404i	$0.952586\pi$
$998$	8.81029e17	−	2.71153e18i	0.0282255	−	0.0868691i
$999$	−1.07836e19	−	7.83475e18i	−0.343233	−	0.249373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.14.c.a.4.5	yes	48
11.3	even	5	inner	11.14.c.a.3.5	✓	48
11.5	even	5		121.14.a.h.1.15		24
11.6	odd	10		121.14.a.i.1.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.14.c.a.3.5	✓	48	11.3	even	5	inner
11.14.c.a.4.5	yes	48	1.1	even	1	trivial
121.14.a.h.1.15		24	11.5	even	5
121.14.a.i.1.10		24	11.6	odd	10

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:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	11.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-38.1571 - 27.7228i) q^{2} +(-502.353 + 1546.08i) q^{3} +(-1844.05 - 5675.41i) q^{4} +(29618.8 - 21519.3i) q^{5} +(62030.1 - 45067.5i) q^{6} +(-28662.8 - 88215.0i) q^{7} +(-206371. + 635143. i) q^{8} +(-848181. - 616240. i) q^{9} -1.72674e6 q^{10} +(-4.12239e6 + 4.18671e6i) q^{11} +9.70102e6 q^{12} +(1.95148e7 + 1.41784e7i) q^{13} +(-1.35188e6 + 4.16064e6i) q^{14} +(1.83916e7 + 5.66034e7i) q^{15} +(-1.40668e7 + 1.02201e7i) q^{16} +(-4.30059e7 + 3.12456e7i) q^{17} +(1.52803e7 + 4.70279e7i) q^{18} +(-8.45952e7 + 2.60357e8i) q^{19} +(-1.76749e8 - 1.28416e8i) q^{20} +1.50787e8 q^{21} +(2.73366e8 - 4.54688e7i) q^{22} +8.98669e8 q^{23} +(-8.78314e8 - 6.38132e8i) q^{24} +(3.69736e7 - 1.13793e8i) q^{25} +(-3.51567e8 - 1.08201e9i) q^{26} +(-7.17973e8 + 5.21638e8i) q^{27} +(-4.47801e8 + 3.25346e8i) q^{28} +(9.11558e7 + 2.80549e8i) q^{29} +(8.67434e8 - 2.66969e9i) q^{30} +(-2.22932e9 - 1.61970e9i) q^{31} +6.29094e9 q^{32} +(-4.40211e9 - 8.47677e9i) q^{33} +2.50720e9 q^{34} +(-2.74728e9 - 1.99602e9i) q^{35} +(-1.93332e9 + 5.95015e9i) q^{36} +(4.64129e9 + 1.42844e10i) q^{37} +(1.04457e10 - 7.58928e9i) q^{38} +(-3.17242e10 + 2.30490e10i) q^{39} +(7.55540e9 + 2.32531e10i) q^{40} +(-2.46605e9 + 7.58973e9i) q^{41} +(-5.75358e9 - 4.18022e9i) q^{42} +6.16804e10 q^{43} +(3.13632e10 + 1.56758e10i) q^{44} -3.83831e10 q^{45} +(-3.42906e10 - 2.49136e10i) q^{46} +(-1.88772e10 + 5.80979e10i) q^{47} +(-8.73468e9 - 2.68826e10i) q^{48} +(7.14245e10 - 5.18930e10i) q^{49} +(-4.56547e9 + 3.31701e9i) q^{50} +(-2.67042e10 - 8.21870e10i) q^{51} +(4.44816e10 - 1.36900e11i) q^{52} +(-1.58251e11 - 1.14976e11i) q^{53} +4.18571e10 q^{54} +(-3.20051e10 + 2.12716e11i) q^{55} +6.19443e10 q^{56} +(-3.60038e11 - 2.61583e11i) q^{57} +(4.29935e9 - 1.32320e10i) q^{58} +(1.28108e11 + 3.94276e11i) q^{59} +(2.87332e11 - 2.08759e11i) q^{60} +(2.94943e11 - 2.14289e11i) q^{61} +(4.01620e10 + 1.23606e11i) q^{62} +(-3.00503e10 + 9.24854e10i) q^{63} +(-1.24809e11 - 9.06789e10i) q^{64} +8.83114e11 q^{65} +(-6.70277e10 + 4.45488e11i) q^{66} -1.25343e12 q^{67} +(2.56637e11 + 1.86458e11i) q^{68} +(-4.51449e11 + 1.38942e12i) q^{69} +(4.94933e10 + 1.52325e11i) q^{70} +(-1.21192e12 + 8.80509e11i) q^{71} +(5.66440e11 - 4.11543e11i) q^{72} +(-4.50948e11 - 1.38787e12i) q^{73} +(2.18905e11 - 6.73722e11i) q^{74} +(1.57360e11 + 1.14329e11i) q^{75} +1.63363e12 q^{76} +(4.87490e11 + 2.43654e11i) q^{77} +1.84949e12 q^{78} +(-6.68446e10 - 4.85654e10i) q^{79} +(-1.96712e11 + 6.05416e11i) q^{80} +(-9.62343e11 - 2.96179e12i) q^{81} +(3.04506e11 - 2.21237e11i) q^{82} +(-1.00556e12 + 7.30582e11i) q^{83} +(-2.78058e11 - 8.55776e11i) q^{84} +(-6.01398e11 + 1.85091e12i) q^{85} +(-2.35355e12 - 1.70995e12i) q^{86} -4.79544e11 q^{87} +(-1.80842e12 - 3.48233e12i) q^{88} -1.31315e12 q^{89} +(1.46459e12 + 1.06409e12i) q^{90} +(6.91394e11 - 2.12789e12i) q^{91} +(-1.65719e12 - 5.10032e12i) q^{92} +(3.62409e12 - 2.63306e12i) q^{93} +(2.33093e12 - 1.69352e12i) q^{94} +(3.09710e12 + 9.53190e12i) q^{95} +(-3.16027e12 + 9.72632e12i) q^{96} +(4.13535e12 + 3.00451e12i) q^{97} -4.16397e12 q^{98} +(6.07656e12 - 1.01071e12i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 59 q^{2} - 864 q^{3} - 44697 q^{4} - 52240 q^{5} - 130115 q^{6} + 390696 q^{7} + 876527 q^{8} - 3520244 q^{9} - 16293072 q^{10} - 82532 q^{11} + 62972038 q^{12} - 7063968 q^{13} + 2946296 q^{14}+ \cdots - 51636755872396 q^{99}+O(q^{100}) \) 48 * q + 59 * q^2 - 864 * q^3 - 44697 * q^4 - 52240 * q^5 - 130115 * q^6 + 390696 * q^7 + 876527 * q^8 - 3520244 * q^9 - 16293072 * q^10 - 82532 * q^11 + 62972038 * q^12 - 7063968 * q^13 + 2946296 * q^14 + 81100736 * q^15 + 60644511 * q^16 - 291410392 * q^17 + 126484674 * q^18 + 365166708 * q^19 - 788032074 * q^20 - 434553632 * q^21 - 733739679 * q^22 + 4188874272 * q^23 + 1308210897 * q^24 - 5079263484 * q^25 - 7197334352 * q^26 - 3672135540 * q^27 + 15293042118 * q^28 + 9462180848 * q^29 + 14934224730 * q^30 + 3808229976 * q^31 - 37924904892 * q^32 - 29220440404 * q^33 - 42631809486 * q^34 + 81447084648 * q^35 + 20776466352 * q^36 - 92150146992 * q^37 - 85759798456 * q^38 + 122431960136 * q^39 + 156222512604 * q^40 + 224837812784 * q^41 - 100995983242 * q^42 - 323982068136 * q^43 - 117395188832 * q^44 + 101655796640 * q^45 + 504337662372 * q^46 - 131674300816 * q^47 - 508856741764 * q^48 - 364186485732 * q^49 + 292932400779 * q^50 - 46205145276 * q^51 + 971895220146 * q^52 - 374673041144 * q^53 - 171438753484 * q^54 - 609291766368 * q^55 - 55316542488 * q^56 + 581441351340 * q^57 - 172510123284 * q^58 - 866818316348 * q^59 + 450475433796 * q^60 + 396717353376 * q^61 + 2190422590172 * q^62 - 814954660544 * q^63 + 687266758335 * q^64 - 1914281234704 * q^65 + 387191529606 * q^66 - 1385875174920 * q^67 - 1442260754434 * q^68 + 2415789828408 * q^69 + 6076465410072 * q^70 + 2500983206448 * q^71 - 6853058084009 * q^72 - 6144016960080 * q^73 - 9894533340936 * q^74 + 2088242191076 * q^75 + 7382638646262 * q^76 + 8181659595976 * q^77 + 485347989556 * q^78 - 9413148440424 * q^79 - 4271997351884 * q^80 + 19193312847832 * q^81 + 24451991571525 * q^82 - 4748400435188 * q^83 - 9210465158484 * q^84 - 9425037508176 * q^85 - 2302249550185 * q^86 - 22158779783712 * q^87 - 25622627417409 * q^88 - 12037611693640 * q^89 + 8065916202334 * q^90 + 23937874042464 * q^91 + 17043827782942 * q^92 + 18075650378312 * q^93 + 10662034186230 * q^94 + 17645734105464 * q^95 + 8702791487212 * q^96 - 18472776936684 * q^97 - 52286290693988 * q^98 - 51636755872396 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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