LMFDB - Embedded newform 84.12.i.b.37.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,12,Mod(25,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("84.25");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	84.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$64.5408271670$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 581500324 x^{14} - 481772282104 x^{13} + \cdots + 79\!\cdots\!77 $ x^16 - 581500324x^14 - 481772282104x^13 + 132272376701859942x^12 + 189765040124256066208x^11 - 14668309022748191106194508x^10 - 25034330150368988089577197656x^9 + 804524023197576594568815873370179x^8 + 1124828921377792402289540847268007968x^7 - 19980431516277460534216470290766973558668x^6 + 592727132887361668148704829618109324342008x^5 + 215459975341822734071937522290785139860745873306x^4 - 372150170517680072482976606267991582419751904690704x^3 - 31534379943215460069637664338468383174583531082850128x^2 + 257934680050232001165280545701170549413209663811915341424x + 79978257504936591964642108900330900905737463001503418421877
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{42}\cdot 3^{15}\cdot 7^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.7
Root			$-10168.9 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	84.37
Dual form			84.12.i.b.25.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-121.500 - 210.444i) q^{3} +(4949.72 - 8573.16i) q^{5} +(29163.1 + 33568.4i) q^{7} +(-29524.5 + 51137.9i) q^{9} +O(q^{10})$	\(q+(-121.500 - 210.444i) q^{3} +(4949.72 - 8573.16i) q^{5} +(29163.1 + 33568.4i) q^{7} +(-29524.5 + 51137.9i) q^{9} +(25007.0 + 43313.5i) q^{11} +1.46252e6 q^{13} -2.40556e6 q^{15} +(3.16934e6 + 5.48946e6i) q^{17} +(-1.02494e7 + 1.77525e7i) q^{19} +(3.52097e6 - 1.02158e7i) q^{21} +(-2.36024e7 + 4.08806e7i) q^{23} +(-2.45854e7 - 4.25831e7i) q^{25} +1.43489e7 q^{27} -9.10208e7 q^{29} +(-4.83443e7 - 8.37349e7i) q^{31} +(6.07671e6 - 1.05252e7i) q^{33} +(4.32137e8 - 8.38657e7i) q^{35} +(-7.14098e7 + 1.23685e8i) q^{37} +(-1.77696e8 - 3.07778e8i) q^{39} +8.44357e8 q^{41} -1.55607e9 q^{43} +(2.92276e8 + 5.06237e8i) q^{45} +(-4.22680e8 + 7.32103e8i) q^{47} +(-2.76354e8 + 1.95792e9i) q^{49} +(7.70151e8 - 1.33394e9i) q^{51} +(1.26817e9 + 2.19654e9i) q^{53} +4.95111e8 q^{55} +4.98123e9 q^{57} +(2.80141e9 + 4.85219e9i) q^{59} +(-5.98273e8 + 1.03624e9i) q^{61} +(-2.57765e9 + 5.00249e8i) q^{63} +(7.23904e9 - 1.25384e10i) q^{65} +(-2.73114e9 - 4.73048e9i) q^{67} +1.14708e10 q^{69} +1.81232e10 q^{71} +(9.87533e9 + 1.71046e10i) q^{73} +(-5.97425e9 + 1.03477e10i) q^{75} +(-7.24683e8 + 2.10260e9i) q^{77} +(-2.14642e10 + 3.71770e10i) q^{79} +(-1.74339e9 - 3.01964e9i) q^{81} -5.21192e10 q^{83} +6.27494e10 q^{85} +(1.10590e10 + 1.91548e10i) q^{87} +(-1.39910e10 + 2.42332e10i) q^{89} +(4.26515e10 + 4.90944e10i) q^{91} +(-1.17477e10 + 2.03476e10i) q^{93} +(1.01464e11 + 1.75740e11i) q^{95} +5.42003e10 q^{97} -2.95328e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 1944 q^{3} - 2156 q^{5} + 50512 q^{7} - 472392 q^{9}+O(q^{10}) $ 16 * q - 1944 * q^3 - 2156 * q^5 + 50512 * q^7 - 472392 * q^9	$ 16 q - 1944 q^{3} - 2156 q^{5} + 50512 q^{7} - 472392 q^{9} - 222796 q^{11} + 2703176 q^{13} + 1047816 q^{15} + 5114600 q^{17} + 6910556 q^{19} - 18340668 q^{21} - 51387712 q^{23} - 191456372 q^{25} + 229582512 q^{27} + 118854616 q^{29} + 164659160 q^{31} - 54139428 q^{33} + 55239344 q^{35} + 75658364 q^{37} - 328435884 q^{39} - 1815568608 q^{41} + 10754408 q^{43} - 127309644 q^{45} - 1034359464 q^{47} + 4123496848 q^{49} + 1242847800 q^{51} - 665159988 q^{53} - 1264543896 q^{55} - 3358530216 q^{57} + 1040514580 q^{59} - 14391208024 q^{61} + 1474099236 q^{63} - 20938150200 q^{65} - 33307097284 q^{67} + 24974428032 q^{69} + 65848902896 q^{71} + 17709749204 q^{73} - 46523898396 q^{75} + 8594484604 q^{77} - 26626784032 q^{79} - 27894275208 q^{81} - 210306955048 q^{83} - 25867402032 q^{85} - 14440835844 q^{87} - 55951560072 q^{89} + 66078280292 q^{91} + 40012175880 q^{93} + 106810047392 q^{95} - 156216030712 q^{97} + 26311762008 q^{99}+O(q^{100}) $ 16 * q - 1944 * q^3 - 2156 * q^5 + 50512 * q^7 - 472392 * q^9 - 222796 * q^11 + 2703176 * q^13 + 1047816 * q^15 + 5114600 * q^17 + 6910556 * q^19 - 18340668 * q^21 - 51387712 * q^23 - 191456372 * q^25 + 229582512 * q^27 + 118854616 * q^29 + 164659160 * q^31 - 54139428 * q^33 + 55239344 * q^35 + 75658364 * q^37 - 328435884 * q^39 - 1815568608 * q^41 + 10754408 * q^43 - 127309644 * q^45 - 1034359464 * q^47 + 4123496848 * q^49 + 1242847800 * q^51 - 665159988 * q^53 - 1264543896 * q^55 - 3358530216 * q^57 + 1040514580 * q^59 - 14391208024 * q^61 + 1474099236 * q^63 - 20938150200 * q^65 - 33307097284 * q^67 + 24974428032 * q^69 + 65848902896 * q^71 + 17709749204 * q^73 - 46523898396 * q^75 + 8594484604 * q^77 - 26626784032 * q^79 - 27894275208 * q^81 - 210306955048 * q^83 - 25867402032 * q^85 - 14440835844 * q^87 - 55951560072 * q^89 + 66078280292 * q^91 + 40012175880 * q^93 + 106810047392 * q^95 - 156216030712 * q^97 + 26311762008 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−121.500	−	210.444i	−0.288675	−	0.500000i
$3$	−121.500	−	210.444i	−0.288675	−	0.500000i
$4$		0			0
$5$	4949.72	−	8573.16i	0.708346	−	1.22689i	−0.257124	−	0.966378i	$-0.582775\pi$
$5$	4949.72	−	8573.16i	0.708346	−	1.22689i	0.965470	−	0.260513i	$-0.0838917\pi$
$6$		0			0
$7$	29163.1	+	33568.4i	0.655835	+	0.754904i
$7$	29163.1	+	33568.4i	0.655835	+	0.754904i
$8$		0			0
$9$	−29524.5	+	51137.9i	−0.166667	+	0.288675i
$10$		0			0
$11$	25007.0	+	43313.5i	0.0468169	+	0.0810892i	0.888484	−	0.458907i	$-0.151759\pi$
$11$	25007.0	+	43313.5i	0.0468169	+	0.0810892i	−0.841667	+	0.539996i	$0.818426\pi$
$12$		0			0
$13$	1.46252e6			1.09248			0.546238	−	0.837630i	$-0.316059\pi$
$13$	1.46252e6			1.09248			0.546238	+	0.837630i	$0.316059\pi$
$14$		0			0
$15$	−2.40556e6			−0.817928
$16$		0			0
$17$	3.16934e6	+	5.48946e6i	0.541378	+	0.937693i	0.998825	+	0.0484569i	$0.0154304\pi$
$17$	3.16934e6	+	5.48946e6i	0.541378	+	0.937693i	−0.457448	+	0.889237i	$0.651236\pi$
$18$		0			0
$19$	−1.02494e7	+	1.77525e7i	−0.949632	+	1.64481i	−0.203431	+	0.979089i	$0.565209\pi$
$19$	−1.02494e7	+	1.77525e7i	−0.949632	+	1.64481i	−0.746201	+	0.665721i	$0.768124\pi$
$20$		0			0
$21$	3.52097e6	−	1.02158e7i	0.188129	−	0.545840i
$22$		0			0
$23$	−2.36024e7	+	4.08806e7i	−0.764634	+	1.32438i	0.175806	+	0.984425i	$0.443747\pi$
$23$	−2.36024e7	+	4.08806e7i	−0.764634	+	1.32438i	−0.940440	+	0.339960i	$0.889586\pi$
$24$		0			0
$25$	−2.45854e7	−	4.25831e7i	−0.503508	−	0.872102i
$26$		0			0
$27$	1.43489e7			0.192450
$28$		0			0
$29$	−9.10208e7			−0.824046			−0.412023	−	0.911173i	$-0.635178\pi$
$29$	−9.10208e7			−0.824046			−0.412023	+	0.911173i	$0.635178\pi$
$30$		0			0
$31$	−4.83443e7	−	8.37349e7i	−0.303289	−	0.525312i	0.673590	−	0.739105i	$-0.264751\pi$
$31$	−4.83443e7	−	8.37349e7i	−0.303289	−	0.525312i	−0.976879	+	0.213794i	$0.931418\pi$
$32$		0			0
$33$	6.07671e6	−	1.05252e7i	0.0270297	−	0.0468169i
$34$		0			0
$35$	4.32137e8	−	8.38657e7i	1.39074	−	0.269904i
$36$		0			0
$37$	−7.14098e7	+	1.23685e8i	−0.169297	+	0.293230i	−0.938173	−	0.346167i	$-0.887483\pi$
$37$	−7.14098e7	+	1.23685e8i	−0.169297	+	0.293230i	0.768876	+	0.639398i	$0.220816\pi$
$38$		0			0
$39$	−1.77696e8	−	3.07778e8i	−0.315371	−	0.546238i
$40$		0			0
$41$	8.44357e8			1.13819			0.569095	−	0.822272i	$-0.307294\pi$
$41$	8.44357e8			1.13819			0.569095	+	0.822272i	$0.307294\pi$
$42$		0			0
$43$	−1.55607e9			−1.61418			−0.807089	−	0.590430i	$-0.798958\pi$
$43$	−1.55607e9			−1.61418			−0.807089	+	0.590430i	$0.798958\pi$
$44$		0			0
$45$	2.92276e8	+	5.06237e8i	0.236115	+	0.408964i
$46$		0			0
$47$	−4.22680e8	+	7.32103e8i	−0.268827	+	0.465623i	−0.968559	−	0.248783i	$-0.919969\pi$
$47$	−4.22680e8	+	7.32103e8i	−0.268827	+	0.465623i	0.699732	+	0.714405i	$0.253303\pi$
$48$		0			0
$49$	−2.76354e8	+	1.95792e9i	−0.139762	+	0.990185i
$50$		0			0
$51$	7.70151e8	−	1.33394e9i	0.312564	−	0.541378i
$52$		0			0
$53$	1.26817e9	+	2.19654e9i	0.416544	+	0.721476i	0.995589	−	0.0938196i	$-0.0299077\pi$
$53$	1.26817e9	+	2.19654e9i	0.416544	+	0.721476i	−0.579045	+	0.815296i	$0.696574\pi$
$54$		0			0
$55$	4.95111e8			0.132650
$56$		0			0
$57$	4.98123e9			1.09654
$58$		0			0
$59$	2.80141e9	+	4.85219e9i	0.510142	+	0.883592i	0.999931	+	0.0117512i	$0.00374060\pi$
$59$	2.80141e9	+	4.85219e9i	0.510142	+	0.883592i	−0.489789	+	0.871841i	$0.662926\pi$
$60$		0			0
$61$	−5.98273e8	+	1.03624e9i	−0.0906955	+	0.157089i	−0.907804	−	0.419395i	$-0.862242\pi$
$61$	−5.98273e8	+	1.03624e9i	−0.0906955	+	0.157089i	0.817108	+	0.576484i	$0.195576\pi$
$62$		0			0
$63$	−2.57765e9	+	5.00249e8i	−0.327228	+	0.0635058i
$64$		0			0
$65$	7.23904e9	−	1.25384e10i	0.773851	−	1.34035i
$66$		0			0
$67$	−2.73114e9	−	4.73048e9i	−0.247134	−	0.428049i	0.715595	−	0.698515i	$-0.246156\pi$
$67$	−2.73114e9	−	4.73048e9i	−0.247134	−	0.428049i	−0.962730	+	0.270466i	$0.912822\pi$
$68$		0			0
$69$	1.14708e10			0.882923
$70$		0			0
$71$	1.81232e10			1.19210			0.596051	−	0.802947i	$-0.296736\pi$
$71$	1.81232e10			1.19210			0.596051	+	0.802947i	$0.296736\pi$
$72$		0			0
$73$	9.87533e9	+	1.71046e10i	0.557540	+	0.965687i	0.997701	+	0.0677684i	$0.0215879\pi$
$73$	9.87533e9	+	1.71046e10i	0.557540	+	0.965687i	−0.440161	+	0.897919i	$0.645079\pi$
$74$		0			0
$75$	−5.97425e9	+	1.03477e10i	−0.290701	+	0.503508i
$76$		0			0
$77$	−7.24683e8	+	2.10260e9i	−0.0305105	+	0.0885234i
$78$		0			0
$79$	−2.14642e10	+	3.71770e10i	−0.784811	+	1.35933i	0.144301	+	0.989534i	$0.453907\pi$
$79$	−2.14642e10	+	3.71770e10i	−0.784811	+	1.35933i	−0.929112	+	0.369799i	$0.879427\pi$
$80$		0			0
$81$	−1.74339e9	−	3.01964e9i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−5.21192e10			−1.45234			−0.726170	−	0.687515i	$-0.758701\pi$
$83$	−5.21192e10			−1.45234			−0.726170	+	0.687515i	$0.758701\pi$
$84$		0			0
$85$	6.27494e10			1.53393
$86$		0			0
$87$	1.10590e10	+	1.91548e10i	0.237882	+	0.412023i
$88$		0			0
$89$	−1.39910e10	+	2.42332e10i	−0.265586	+	0.460008i	−0.967717	−	0.252039i	$-0.918899\pi$
$89$	−1.39910e10	+	2.42332e10i	−0.265586	+	0.460008i	0.702131	+	0.712048i	$0.252232\pi$
$90$		0			0
$91$	4.26515e10	+	4.90944e10i	0.716484	+	0.824715i
$92$		0			0
$93$	−1.17477e10	+	2.03476e10i	−0.175104	+	0.303289i
$94$		0			0
$95$	1.01464e11	+	1.75740e11i	1.34534	+	2.33019i
$96$		0			0
$97$	5.42003e10			0.640851			0.320426	−	0.947274i	$-0.396174\pi$
$97$	5.42003e10			0.640851			0.320426	+	0.947274i	$0.396174\pi$
$98$		0			0
$99$	−2.95328e9			−0.0312112
$100$		0			0
$101$	6.07024e10	+	1.05140e11i	0.574696	+	0.995403i	0.996075	+	0.0885179i	$0.0282130\pi$
$101$	6.07024e10	+	1.05140e11i	0.574696	+	0.995403i	−0.421379	+	0.906885i	$0.638454\pi$
$102$		0			0
$103$	8.26479e10	−	1.43150e11i	0.702469	−	1.21671i	−0.265128	−	0.964213i	$-0.585414\pi$
$103$	8.26479e10	−	1.43150e11i	0.702469	−	1.21671i	0.967597	−	0.252499i	$-0.0812525\pi$
$104$		0			0
$105$	−7.01537e10	−	8.07510e10i	−0.536425	−	0.617457i
$106$		0			0
$107$	1.05098e11	−	1.82035e11i	0.724410	−	1.25472i	−0.234806	−	0.972042i	$-0.575446\pi$
$107$	1.05098e11	−	1.82035e11i	0.724410	−	1.25472i	0.959216	−	0.282673i	$-0.0912211\pi$
$108$		0			0
$109$	−4.57197e10	−	7.91888e10i	−0.284615	−	0.492967i	0.687901	−	0.725805i	$-0.258532\pi$
$109$	−4.57197e10	−	7.91888e10i	−0.284615	−	0.492967i	−0.972516	+	0.232837i	$0.925199\pi$
$110$		0			0
$111$	3.47052e10			0.195487
$112$		0			0
$113$	−3.60006e9			−0.0183814			−0.00919068	−	0.999958i	$-0.502926\pi$
$113$	−3.60006e9			−0.0183814			−0.00919068	+	0.999958i	$0.502926\pi$
$114$		0			0
$115$	2.33651e11	+	4.04695e11i	1.08325	+	1.87625i
$116$		0			0
$117$	−4.31800e10	+	7.47900e10i	−0.182079	+	0.315371i
$118$		0			0
$119$	−9.18449e10	+	2.66480e11i	−0.352815	+	1.02366i
$120$		0			0
$121$	1.41405e11	−	2.44921e11i	0.495616	−	0.858433i
$122$		0			0
$123$	−1.02589e11	−	1.77690e11i	−0.328567	−	0.569095i
$124$		0			0
$125$	−3.39174e9			−0.00994071
$126$		0			0
$127$	6.33083e11			1.70036			0.850179	−	0.526494i	$-0.176494\pi$
$127$	6.33083e11			1.70036			0.850179	+	0.526494i	$0.176494\pi$
$128$		0			0
$129$	1.89062e11	+	3.27465e11i	0.465973	+	0.807089i
$130$		0			0
$131$	−4.80539e10	+	8.32318e10i	−0.108827	+	0.188494i	−0.915295	−	0.402783i	$-0.868043\pi$
$131$	−4.80539e10	+	8.32318e10i	−0.108827	+	0.188494i	0.806468	+	0.591277i	$0.201376\pi$
$132$		0			0
$133$	−8.94831e11	+	1.73662e11i	−1.86448	+	0.361843i
$134$		0			0
$135$	7.10231e10	−	1.23016e11i	0.136321	−	0.236115i
$136$		0			0
$137$	−1.83227e10	−	3.17359e10i	−0.0324360	−	0.0561808i	0.849352	−	0.527827i	$-0.176993\pi$
$137$	−1.83227e10	−	3.17359e10i	−0.0324360	−	0.0561808i	−0.881788	+	0.471647i	$0.843660\pi$
$138$		0			0
$139$	−7.27117e11			−1.18856			−0.594282	−	0.804257i	$-0.702564\pi$
$139$	−7.27117e11			−1.18856			−0.594282	+	0.804257i	$0.702564\pi$
$140$		0			0
$141$	2.05422e11			0.310415
$142$		0			0
$143$	3.65732e10	+	6.33466e10i	0.0511463	+	0.0885880i
$144$		0			0
$145$	−4.50527e11	+	7.80336e11i	−0.583710	+	1.01102i
$146$		0			0
$147$	4.45610e11	−	1.79730e11i	0.535438	−	0.215961i
$148$		0			0
$149$	5.76995e11	−	9.99385e11i	0.643647	−	1.11483i	−0.340965	−	0.940076i	$-0.610754\pi$
$149$	5.76995e11	−	9.99385e11i	0.643647	−	1.11483i	0.984612	−	0.174754i	$-0.0559129\pi$
$150$		0			0
$151$	−3.74264e11	−	6.48245e11i	−0.387976	−	0.671995i	0.604201	−	0.796832i	$-0.293492\pi$
$151$	−3.74264e11	−	6.48245e11i	−0.387976	−	0.671995i	−0.992177	+	0.124837i	$0.960159\pi$
$152$		0			0
$153$	−3.74293e11			−0.360918
$154$		0			0
$155$	−9.57164e11			−0.859334
$156$		0			0
$157$	−1.07175e12	−	1.85633e12i	−0.896697	−	1.55312i	−0.831691	−	0.555239i	$-0.812627\pi$
$157$	−1.07175e12	−	1.85633e12i	−0.896697	−	1.55312i	−0.0650059	−	0.997885i	$-0.520707\pi$
$158$		0			0
$159$	3.08166e11	−	5.33759e11i	0.240492	−	0.416544i
$160$		0			0
$161$	−2.06062e12	+	3.99908e11i	−1.50126	+	0.291352i
$162$		0			0
$163$	1.02063e10	−	1.76779e10i	0.00694765	−	0.0120337i	−0.862531	−	0.506005i	$-0.831122\pi$
$163$	1.02063e10	−	1.76779e10i	0.00694765	−	0.0120337i	0.869478	+	0.493971i	$0.164455\pi$
$164$		0			0
$165$	−6.01560e10	−	1.04193e11i	−0.0382928	−	0.0663251i
$166$		0			0
$167$	−2.47826e11			−0.147641			−0.0738204	−	0.997272i	$-0.523519\pi$
$167$	−2.47826e11			−0.147641			−0.0738204	+	0.997272i	$0.523519\pi$
$168$		0			0
$169$	3.46792e11			0.193505
$170$		0			0
$171$	−6.05219e11	−	1.04827e12i	−0.316544	−	0.548270i
$172$		0			0
$173$	9.53660e11	−	1.65179e12i	0.467886	−	0.810402i	−0.531441	−	0.847096i	$-0.678349\pi$
$173$	9.53660e11	−	1.65179e12i	0.467886	−	0.810402i	0.999327	+	0.0366932i	$0.0116824\pi$
$174$		0			0
$175$	7.12463e11	−	2.06715e12i	0.328136	−	0.952056i
$176$		0			0
$177$	6.80744e11	−	1.17908e12i	0.294531	−	0.510142i
$178$		0			0
$179$	2.54501e11	+	4.40808e11i	0.103514	+	0.179291i	0.913130	−	0.407669i	$-0.133658\pi$
$179$	2.54501e11	+	4.40808e11i	0.103514	+	0.179291i	−0.809616	+	0.586959i	$0.800325\pi$
$180$		0			0
$181$	−1.05292e12			−0.402869			−0.201434	−	0.979502i	$-0.564560\pi$
$181$	−1.05292e12			−0.402869			−0.201434	+	0.979502i	$0.564560\pi$
$182$		0			0
$183$	2.90761e11			0.104726
$184$		0			0
$185$	7.06917e11	+	1.22442e12i	0.239841	+	0.415417i
$186$		0			0
$187$	−1.58512e11	+	2.74550e11i	−0.0506912	+	0.0877997i
$188$		0			0
$189$	4.18459e11	+	4.81671e11i	0.126215	+	0.145281i
$190$		0			0
$191$	−3.42442e12	+	5.93127e12i	−0.974773	+	1.68836i	−0.294092	+	0.955777i	$0.595017\pi$
$191$	−3.42442e12	+	5.93127e12i	−0.974773	+	1.68836i	−0.680681	+	0.732580i	$0.738316\pi$
$192$		0			0
$193$	−1.13876e12	−	1.97240e12i	−0.306104	−	0.530187i	0.671403	−	0.741093i	$-0.265692\pi$
$193$	−1.13876e12	−	1.97240e12i	−0.306104	−	0.530187i	−0.977506	+	0.210906i	$0.932359\pi$
$194$		0			0
$195$	−3.51817e12			−0.893567
$196$		0			0
$197$	2.51939e12			0.604966			0.302483	−	0.953155i	$-0.402184\pi$
$197$	2.51939e12			0.604966			0.302483	+	0.953155i	$0.402184\pi$
$198$		0			0
$199$	5.73459e11	+	9.93260e11i	0.130260	+	0.225617i	0.923777	−	0.382932i	$-0.125086\pi$
$199$	5.73459e11	+	9.93260e11i	0.130260	+	0.225617i	−0.793517	+	0.608548i	$0.791752\pi$
$200$		0			0
$201$	−6.63668e11	+	1.14951e12i	−0.142683	+	0.247134i
$202$		0			0
$203$	−2.65445e12	−	3.05543e12i	−0.540438	−	0.622076i
$204$		0			0
$205$	4.17933e12	−	7.23881e12i	0.806233	−	1.39644i
$206$		0			0
$207$	−1.39370e12	−	2.41396e12i	−0.254878	−	0.441462i
$208$		0			0
$209$	−1.02523e12			−0.177835
$210$		0			0
$211$	−1.08695e12			−0.178919			−0.0894593	−	0.995990i	$-0.528514\pi$
$211$	−1.08695e12			−0.178919			−0.0894593	+	0.995990i	$0.528514\pi$
$212$		0			0
$213$	−2.20197e12	−	3.81392e12i	−0.344130	−	0.596051i
$214$		0			0
$215$	−7.70209e12	+	1.33404e13i	−1.14340	+	1.98042i
$216$		0			0
$217$	1.40098e12	−	4.06481e12i	0.197653	−	0.573472i
$218$		0			0
$219$	2.39970e12	−	4.15641e12i	0.321896	−	0.557540i
$220$		0			0
$221$	4.63521e12	+	8.02843e12i	0.591442	+	1.02441i
$222$		0			0
$223$	1.60167e13			1.94489			0.972447	−	0.233124i	$-0.0748949\pi$
$223$	1.60167e13			1.94489			0.972447	+	0.233124i	$0.0748949\pi$
$224$		0			0
$225$	2.90348e12			0.335672
$226$		0			0
$227$	−5.82492e12	−	1.00891e13i	−0.641428	−	1.11099i	−0.985114	−	0.171901i	$-0.945009\pi$
$227$	−5.82492e12	−	1.00891e13i	−0.641428	−	1.11099i	0.343686	−	0.939085i	$-0.388324\pi$
$228$		0			0
$229$	4.67803e11	−	8.10258e11i	0.0490871	−	0.0850214i	−0.840438	−	0.541908i	$-0.817702\pi$
$229$	4.67803e11	−	8.10258e11i	0.0490871	−	0.0850214i	0.889525	+	0.456887i	$0.151035\pi$
$230$		0			0
$231$	5.30529e11	−	1.02961e11i	0.0530693	−	0.0102993i
$232$		0			0
$233$	−6.06338e12	+	1.05021e13i	−0.578438	+	1.00188i	0.417220	+	0.908805i	$0.363004\pi$
$233$	−6.06338e12	+	1.05021e13i	−0.578438	+	1.00188i	−0.995659	+	0.0930793i	$0.970329\pi$
$234$		0			0
$235$	4.18429e12	+	7.24741e12i	0.380846	+	0.659644i
$236$		0			0
$237$	1.04316e13			0.906222
$238$		0			0
$239$	2.98561e12			0.247654			0.123827	−	0.992304i	$-0.460483\pi$
$239$	2.98561e12			0.247654			0.123827	+	0.992304i	$0.460483\pi$
$240$		0			0
$241$	−4.35089e12	−	7.53596e12i	−0.344734	−	0.597097i	0.640571	−	0.767899i	$-0.278698\pi$
$241$	−4.35089e12	−	7.53596e12i	−0.344734	−	0.597097i	−0.985305	+	0.170802i	$0.945364\pi$
$242$		0			0
$243$	−4.23644e11	+	7.33773e11i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	1.54177e13	+	1.20604e13i	1.11585	+	0.872866i
$246$		0			0
$247$	−1.49900e13	+	2.59634e13i	−1.03745	+	1.79692i
$248$		0			0
$249$	6.33248e12	+	1.09682e13i	0.419254	+	0.726170i
$250$		0			0
$251$	1.10571e13			0.700544			0.350272	−	0.936648i	$-0.386089\pi$
$251$	1.10571e13			0.700544			0.350272	+	0.936648i	$0.386089\pi$
$252$		0			0
$253$	−2.36091e12			−0.143191
$254$		0			0
$255$	−7.62406e12	−	1.32053e13i	−0.442808	−	0.766965i
$256$		0			0
$257$	−1.27142e13	+	2.20217e13i	−0.707387	+	1.22523i	0.258436	+	0.966028i	$0.416793\pi$
$257$	−1.27142e13	+	2.20217e13i	−0.707387	+	1.22523i	−0.965823	+	0.259202i	$0.916540\pi$
$258$		0			0
$259$	−6.23446e12	+	1.20993e12i	−0.332392	+	0.0645079i
$260$		0			0
$261$	2.68734e12	−	4.65461e12i	0.137341	−	0.237882i
$262$		0			0
$263$	1.68147e13	+	2.91239e13i	0.824011	+	1.42723i	0.902673	+	0.430327i	$0.141602\pi$
$263$	1.68147e13	+	2.91239e13i	0.824011	+	1.42723i	−0.0786626	+	0.996901i	$0.525065\pi$
$264$		0			0
$265$	2.51084e13			1.18023
$266$		0			0
$267$	6.79965e12			0.306672
$268$		0			0
$269$	7.46102e12	+	1.29229e13i	0.322969	+	0.559398i	0.981099	−	0.193506i	$-0.0619858\pi$
$269$	7.46102e12	+	1.29229e13i	0.322969	+	0.559398i	−0.658130	+	0.752904i	$0.728652\pi$
$270$		0			0
$271$	1.07841e13	−	1.86786e13i	0.448179	−	0.776269i	−0.550089	−	0.835106i	$-0.685406\pi$
$271$	1.07841e13	−	1.86786e13i	0.448179	−	0.776269i	0.998268	+	0.0588375i	$0.0187394\pi$
$272$		0			0
$273$	5.14947e12	−	1.49407e13i	0.205527	−	0.596317i
$274$		0			0
$275$	1.22961e12	−	2.12975e12i	0.0471454	−	0.0816582i
$276$		0			0
$277$	−1.45333e13	−	2.51724e13i	−0.535457	−	0.927439i	−0.999141	−	0.0414380i	$-0.986806\pi$
$277$	−1.45333e13	−	2.51724e13i	−0.535457	−	0.927439i	0.463684	−	0.886001i	$-0.346527\pi$
$278$		0			0
$279$	5.70937e12			0.202193
$280$		0			0
$281$	2.02171e13			0.688390			0.344195	−	0.938898i	$-0.388152\pi$
$281$	2.02171e13			0.688390			0.344195	+	0.938898i	$0.388152\pi$
$282$		0			0
$283$	−2.44690e11	−	4.23815e11i	−0.00801291	−	0.0138788i	0.861991	−	0.506923i	$-0.169217\pi$
$283$	−2.44690e11	−	4.23815e11i	−0.00801291	−	0.0138788i	−0.870004	+	0.493045i	$0.835884\pi$
$284$		0			0
$285$	2.46557e13	−	4.27049e13i	0.776730	−	1.34534i
$286$		0			0
$287$	2.46241e13	+	2.83438e13i	0.746465	+	0.859225i
$288$		0			0
$289$	−2.95353e12	+	5.11566e12i	−0.0861794	+	0.149267i
$290$		0			0
$291$	−6.58534e12	−	1.14061e13i	−0.184998	−	0.320426i
$292$		0			0
$293$	−6.82921e13			−1.84756			−0.923780	−	0.382924i	$-0.874917\pi$
$293$	−6.82921e13			−1.84756			−0.923780	+	0.382924i	$0.874917\pi$
$294$		0			0
$295$	5.54649e13			1.44543
$296$		0			0
$297$	3.58824e11	+	6.21501e11i	0.00900991	+	0.0156056i
$298$		0			0
$299$	−3.45189e13	+	5.97885e13i	−0.835345	+	1.44686i
$300$		0			0
$301$	−4.53797e13	−	5.22347e13i	−1.05863	−	1.21855i
$302$		0			0
$303$	1.47507e13	−	2.55489e13i	0.331801	−	0.574696i
$304$		0			0
$305$	5.92257e12	+	1.02582e13i	0.128488	+	0.222547i
$306$		0			0
$307$	−2.82225e13			−0.590655			−0.295328	−	0.955396i	$-0.595429\pi$
$307$	−2.82225e13			−0.590655			−0.295328	+	0.955396i	$0.595429\pi$
$308$		0			0
$309$	−4.01669e13			−0.811142
$310$		0			0
$311$	3.53006e13	+	6.11425e13i	0.688019	+	1.19168i	0.972478	+	0.232996i	$0.0748528\pi$
$311$	3.53006e13	+	6.11425e13i	0.688019	+	1.19168i	−0.284459	+	0.958688i	$0.591814\pi$
$312$		0			0
$313$	1.75608e13	−	3.04162e13i	0.330408	−	0.572283i	−0.652184	−	0.758061i	$-0.726147\pi$
$313$	1.75608e13	−	3.04162e13i	0.330408	−	0.572283i	0.982592	+	0.185778i	$0.0594804\pi$
$314$		0			0
$315$	−8.46991e12	+	2.45747e13i	−0.153876	+	0.446457i
$316$		0			0
$317$	1.54610e13	−	2.67792e13i	0.271275	−	0.469863i	−0.697913	−	0.716182i	$-0.745888\pi$
$317$	1.54610e13	−	2.67792e13i	0.271275	−	0.469863i	0.969189	+	0.246319i	$0.0792212\pi$
$318$		0			0
$319$	−2.27616e12	−	3.94242e12i	−0.0385793	−	0.0668212i
$320$		0			0
$321$	−5.10777e13			−0.836477
$322$		0			0
$323$	−1.29936e14			−2.05644
$324$		0			0
$325$	−3.59565e13	−	6.22785e13i	−0.550071	−	0.952751i
$326$		0			0
$327$	−1.11099e13	+	1.92429e13i	−0.164322	+	0.284615i
$328$		0			0
$329$	−3.69022e13	+	7.16169e12i	−0.527807	+	0.102433i
$330$		0			0
$331$	−1.86187e13	+	3.22486e13i	−0.257571	+	0.446125i	−0.965591	−	0.260067i	$-0.916255\pi$
$331$	−1.86187e13	+	3.22486e13i	−0.257571	+	0.446125i	0.708020	+	0.706192i	$0.249589\pi$
$332$		0			0
$333$	−4.21668e12	−	7.30350e12i	−0.0564322	−	0.0977435i
$334$		0			0
$335$	−5.40736e13			−0.700227
$336$		0			0
$337$	9.01286e13			1.12953			0.564766	−	0.825251i	$-0.308967\pi$
$337$	9.01286e13			1.12953			0.564766	+	0.825251i	$0.308967\pi$
$338$		0			0
$339$	4.37407e11	+	7.57611e11i	0.00530624	+	0.00919068i
$340$		0			0
$341$	2.41790e12	−	4.18792e12i	0.0283981	−	0.0491869i
$342$		0			0
$343$	−7.37837e13	+	4.78222e13i	−0.839156	+	0.543891i
$344$		0			0
$345$	5.67771e13	−	9.83409e13i	0.625415	−	1.08325i
$346$		0			0
$347$	−4.20561e13	−	7.28433e13i	−0.448763	−	0.777280i	0.549543	−	0.835465i	$-0.314802\pi$
$347$	−4.20561e13	−	7.28433e13i	−0.448763	−	0.777280i	−0.998306	+	0.0581855i	$0.981469\pi$
$348$		0			0
$349$	1.62557e14			1.68061			0.840305	−	0.542114i	$-0.182376\pi$
$349$	1.62557e14			1.68061			0.840305	+	0.542114i	$0.182376\pi$
$350$		0			0
$351$	2.09855e13			0.210247
$352$		0			0
$353$	−7.77383e13	−	1.34647e14i	−0.754873	−	1.30748i	−0.945437	−	0.325804i	$-0.894365\pi$
$353$	−7.77383e13	−	1.34647e14i	−0.754873	−	1.30748i	0.190564	−	0.981675i	$-0.438968\pi$
$354$		0			0
$355$	8.97046e13	−	1.55373e14i	0.844421	−	1.46258i
$356$		0			0
$357$	6.72383e13	−	1.30491e13i	0.613679	−	0.119098i
$358$		0			0
$359$	−6.44669e13	+	1.11660e14i	−0.570581	+	0.988275i	0.425925	+	0.904758i	$0.359949\pi$
$359$	−6.44669e13	+	1.11660e14i	−0.570581	+	0.988275i	−0.996506	+	0.0835170i	$0.973385\pi$
$360$		0			0
$361$	−1.51857e14	−	2.63024e14i	−1.30360	−	2.25790i
$362$		0			0
$363$	−6.87229e13			−0.572288
$364$		0			0
$365$	1.95520e14			1.57972
$366$		0			0
$367$	8.09211e13	+	1.40159e14i	0.634452	+	1.09890i	0.986631	+	0.162970i	$0.0521074\pi$
$367$	8.09211e13	+	1.40159e14i	0.634452	+	1.09890i	−0.352179	+	0.935933i	$0.614559\pi$
$368$		0			0
$369$	−2.49292e13	+	4.31787e13i	−0.189698	+	0.328567i
$370$		0			0
$371$	−3.67506e13	+	1.06629e14i	−0.271461	+	0.787620i
$372$		0			0
$373$	7.49137e12	−	1.29754e13i	0.0537233	−	0.0930515i	−0.837913	−	0.545804i	$-0.816224\pi$
$373$	7.49137e12	−	1.29754e13i	0.0537233	−	0.0930515i	0.891636	+	0.452752i	$0.149558\pi$
$374$		0			0
$375$	4.12096e11	+	7.13772e11i	0.00286964	+	0.00497035i
$376$		0			0
$377$	−1.33119e14			−0.900251
$378$		0			0
$379$	−1.46414e14			−0.961758			−0.480879	−	0.876787i	$-0.659682\pi$
$379$	−1.46414e14			−0.961758			−0.480879	+	0.876787i	$0.659682\pi$
$380$		0			0
$381$	−7.69196e13	−	1.33229e14i	−0.490851	−	0.850179i
$382$		0			0
$383$	1.03039e14	−	1.78468e14i	0.638861	−	1.10654i	−0.346822	−	0.937931i	$-0.612739\pi$
$383$	1.03039e14	−	1.78468e14i	0.638861	−	1.10654i	0.985683	−	0.168609i	$-0.0539275\pi$
$384$		0			0
$385$	1.44390e13	+	1.66201e13i	0.0869966	+	0.100138i
$386$		0			0
$387$	4.59420e13	−	7.95740e13i	0.269030	−	0.465973i
$388$		0			0
$389$	4.28674e13	+	7.42485e13i	0.244008	+	0.422634i	0.961852	−	0.273569i	$-0.0882043\pi$
$389$	4.28674e13	+	7.42485e13i	0.244008	+	0.422634i	−0.717844	+	0.696204i	$0.754871\pi$
$390$		0			0
$391$	−2.99217e14			−1.65582
$392$		0			0
$393$	2.33542e13			0.125663
$394$		0			0
$395$	2.12483e14	+	3.68032e14i	1.11184	+	1.92576i
$396$		0			0
$397$	−5.18685e13	+	8.98388e13i	−0.263971	+	0.457210i	−0.967293	−	0.253660i	$-0.918366\pi$
$397$	−5.18685e13	+	8.98388e13i	−0.263971	+	0.457210i	0.703323	+	0.710871i	$0.251699\pi$
$398$		0			0
$399$	1.45268e14	+	1.67212e14i	0.719149	+	0.827783i
$400$		0			0
$401$	8.92898e13	−	1.54655e14i	0.430039	−	0.744850i	−0.566837	−	0.823830i	$-0.691833\pi$
$401$	8.92898e13	−	1.54655e14i	0.430039	−	0.744850i	0.996876	+	0.0789803i	$0.0251664\pi$
$402$		0			0
$403$	−7.07044e13	−	1.22464e14i	−0.331336	−	0.573891i
$404$		0			0
$405$	−3.45172e13			−0.157410
$406$		0			0
$407$	−7.14299e12			−0.0317038
$408$		0			0
$409$	1.39715e14	+	2.41994e14i	0.603622	+	1.04550i	0.992268	+	0.124117i	$0.0396099\pi$
$409$	1.39715e14	+	2.41994e14i	0.603622	+	1.04550i	−0.388645	+	0.921388i	$0.627057\pi$
$410$		0			0
$411$	−4.45243e12	+	7.71183e12i	−0.0187269	+	0.0324360i
$412$		0			0
$413$	−8.11826e13	+	2.35544e14i	−0.332459	+	0.964599i
$414$		0			0
$415$	−2.57975e14	+	4.46827e14i	−1.02876	+	1.78186i
$416$		0			0
$417$	8.83447e13	+	1.53017e14i	0.343109	+	0.594282i
$418$		0			0
$419$	1.47340e14			0.557370			0.278685	−	0.960383i	$-0.410102\pi$
$419$	1.47340e14			0.557370			0.278685	+	0.960383i	$0.410102\pi$
$420$		0			0
$421$	1.13118e14			0.416852			0.208426	−	0.978038i	$-0.433166\pi$
$421$	1.13118e14			0.416852			0.208426	+	0.978038i	$0.433166\pi$
$422$		0			0
$423$	−2.49588e13	−	4.32300e13i	−0.0896091	−	0.155208i
$424$		0			0
$425$	1.55839e14	−	2.69921e14i	0.545176	−	0.944273i
$426$		0			0
$427$	−5.22325e13	+	1.01369e13i	−0.178069	+	0.0345581i
$428$		0			0
$429$	8.88728e12	−	1.53932e13i	0.0295293	−	0.0511463i
$430$		0			0
$431$	2.21901e14	+	3.84344e14i	0.718678	+	1.24479i	0.961524	+	0.274722i	$0.0885859\pi$
$431$	2.21901e14	+	3.84344e14i	0.718678	+	1.24479i	−0.242845	+	0.970065i	$0.578081\pi$
$432$		0			0
$433$	3.99750e14			1.26213			0.631067	−	0.775729i	$-0.282617\pi$
$433$	3.99750e14			1.26213			0.631067	+	0.775729i	$0.282617\pi$
$434$		0			0
$435$	2.18956e14			0.674010
$436$		0			0
$437$	−4.83823e14	−	8.38006e14i	−1.45224	−	2.51536i
$438$		0			0
$439$	2.14931e14	−	3.72271e14i	0.629134	−	1.08969i	−0.358591	−	0.933495i	$-0.616743\pi$
$439$	2.14931e14	−	3.72271e14i	0.629134	−	1.08969i	0.987726	−	0.156198i	$-0.0499239\pi$
$440$		0			0
$441$	−9.19647e13	−	7.19388e13i	−0.262548	−	0.205377i
$442$		0			0
$443$	−6.77263e13	+	1.17305e14i	−0.188598	+	0.326661i	−0.944783	−	0.327697i	$-0.893728\pi$
$443$	−6.77263e13	+	1.17305e14i	−0.188598	+	0.326661i	0.756185	+	0.654358i	$0.227061\pi$
$444$		0			0
$445$	1.38503e14	+	2.39895e14i	0.376254	+	0.651690i
$446$		0			0
$447$	−2.80420e14			−0.743220
$448$		0			0
$449$	9.79795e13			0.253385			0.126692	−	0.991942i	$-0.459564\pi$
$449$	9.79795e13			0.253385			0.126692	+	0.991942i	$0.459564\pi$
$450$		0			0
$451$	2.11149e13	+	3.65720e13i	0.0532865	+	0.0922949i
$452$		0			0
$453$	−9.09462e13	+	1.57523e14i	−0.223998	+	0.387976i
$454$		0			0
$455$	6.32007e14	−	1.22655e14i	1.51935	−	0.294864i
$456$		0			0
$457$	−3.69842e14	+	6.40586e14i	−0.867916	+	1.50327i	−0.00379321	+	0.999993i	$0.501207\pi$
$457$	−3.69842e14	+	6.40586e14i	−0.867916	+	1.50327i	−0.864123	+	0.503281i	$0.832126\pi$
$458$		0			0
$459$	4.54766e13	+	7.87678e13i	0.104188	+	0.180459i
$460$		0			0
$461$	2.05197e14			0.459003			0.229501	−	0.973308i	$-0.426290\pi$
$461$	2.05197e14			0.459003			0.229501	+	0.973308i	$0.426290\pi$
$462$		0			0
$463$	3.01270e14			0.658052			0.329026	−	0.944321i	$-0.393280\pi$
$463$	3.01270e14			0.658052			0.329026	+	0.944321i	$0.393280\pi$
$464$		0			0
$465$	1.16295e14	+	2.01430e14i	0.248068	+	0.429667i
$466$		0			0
$467$	−1.92054e14	+	3.32648e14i	−0.400111	+	0.693013i	−0.993739	−	0.111727i	$-0.964362\pi$
$467$	−1.92054e14	+	3.32648e14i	−0.400111	+	0.693013i	0.593628	+	0.804740i	$0.297695\pi$
$468$		0			0
$469$	7.91463e13	−	2.29636e14i	0.161057	−	0.467293i
$470$		0			0
$471$	−2.60435e14	+	4.51087e14i	−0.517708	+	0.896697i
$472$		0			0
$473$	−3.89126e13	−	6.73986e13i	−0.0755707	−	0.130892i
$474$		0			0
$475$	1.00794e15			1.91259
$476$		0			0
$477$	−1.49769e14			−0.277696
$478$		0			0
$479$	−3.73993e14	−	6.47776e14i	−0.677671	−	1.17376i	−0.975681	−	0.219197i	$-0.929656\pi$
$479$	−3.73993e14	−	6.47776e14i	−0.677671	−	1.17376i	0.298010	−	0.954563i	$-0.403677\pi$
$480$		0			0
$481$	−1.04438e14	+	1.80892e14i	−0.184953	+	0.320347i
$482$		0			0
$483$	3.34523e14	+	3.85056e14i	0.579052	+	0.666523i
$484$		0			0
$485$	2.68276e14	−	4.64668e14i	0.453945	−	0.786255i
$486$		0			0
$487$	6.99482e13	+	1.21154e14i	0.115709	+	0.200414i	0.918063	−	0.396435i	$-0.129753\pi$
$487$	6.99482e13	+	1.21154e14i	0.115709	+	0.200414i	−0.802354	+	0.596848i	$0.796419\pi$
$488$		0			0
$489$	−4.96028e12			−0.00802245
$490$		0			0
$491$	2.86402e13			0.0452926			0.0226463	−	0.999744i	$-0.492791\pi$
$491$	2.86402e13			0.0452926			0.0226463	+	0.999744i	$0.492791\pi$
$492$		0			0
$493$	−2.88476e14	−	4.99655e14i	−0.446120	−	0.772703i
$494$		0			0
$495$	−1.46179e13	+	2.53190e13i	−0.0221084	+	0.0382928i
$496$		0			0
$497$	5.28528e14	+	6.08367e14i	0.781822	+	0.899923i
$498$		0			0
$499$	−5.75867e14	+	9.97430e14i	−0.833238	+	1.44321i	0.0622193	+	0.998063i	$0.480182\pi$
$499$	−5.75867e14	+	9.97430e14i	−0.833238	+	1.44321i	−0.895457	+	0.445148i	$0.853151\pi$
$500$		0			0
$501$	3.01109e13	+	5.21536e13i	0.0426202	+	0.0738204i
$502$		0			0
$503$	−9.85521e14			−1.36472			−0.682358	−	0.731019i	$-0.739045\pi$
$503$	−9.85521e14			−1.36472			−0.682358	+	0.731019i	$0.739045\pi$
$504$		0			0
$505$	1.20184e15			1.62833
$506$		0			0
$507$	−4.21352e13	−	7.29803e13i	−0.0558601	−	0.0967525i
$508$		0			0
$509$	3.82938e14	−	6.63268e14i	0.496799	−	0.860481i	−0.503194	−	0.864173i	$-0.667842\pi$
$509$	3.82938e14	−	6.63268e14i	0.496799	−	0.860481i	0.999993	+	0.00369203i	$0.00117521\pi$
$510$		0			0
$511$	−2.86179e14	+	8.30322e14i	−0.363348	+	1.05422i
$512$		0			0
$513$	−1.47068e14	+	2.54730e14i	−0.182757	+	0.316544i
$514$		0			0
$515$	−8.18168e14	−	1.41711e15i	−0.995183	−	1.72371i
$516$		0			0
$517$	−4.22799e13			−0.0503426
$518$		0			0
$519$	−4.63479e14			−0.540268
$520$		0			0
$521$	−3.90199e14	−	6.75845e14i	−0.445327	−	0.771329i	0.552748	−	0.833349i	$-0.313579\pi$
$521$	−3.90199e14	−	6.75845e14i	−0.445327	−	0.771329i	−0.998075	+	0.0620194i	$0.980246\pi$
$522$		0			0
$523$	−1.32813e14	+	2.30039e14i	−0.148416	+	0.257064i	−0.930642	−	0.365930i	$-0.880751\pi$
$523$	−1.32813e14	+	2.30039e14i	−0.148416	+	0.257064i	0.782226	+	0.622995i	$0.214084\pi$
$524$		0			0
$525$	−5.21584e14	+	1.01225e14i	−0.570752	+	0.110767i
$526$		0			0
$527$	3.06440e14	−	5.30769e14i	0.328388	−	0.568784i
$528$		0			0
$529$	−6.37744e14	−	1.10461e15i	−0.669330	−	1.15931i
$530$		0			0
$531$	−3.30841e14			−0.340095
$532$		0			0
$533$	1.23489e15			1.24345
$534$		0			0
$535$	−1.04041e15	−	1.80205e15i	−1.02627	−	1.77755i
$536$		0			0
$537$	6.18436e13	−	1.07116e14i	0.0597636	−	0.103514i
$538$		0			0
$539$	−9.17151e13	+	3.69919e13i	−0.0868365	+	0.0350242i
$540$		0			0
$541$	−2.32642e14	+	4.02947e14i	−0.215825	+	0.373820i	−0.953528	−	0.301306i	$-0.902577\pi$
$541$	−2.32642e14	+	4.02947e14i	−0.215825	+	0.373820i	0.737702	+	0.675126i	$0.235911\pi$
$542$		0			0
$543$	1.27930e14	+	2.21581e14i	0.116298	+	0.201434i
$544$		0			0
$545$	−9.05198e14			−0.806423
$546$		0			0
$547$	−4.31654e14			−0.376882			−0.188441	−	0.982084i	$-0.560343\pi$
$547$	−4.31654e14			−0.376882			−0.188441	+	0.982084i	$0.560343\pi$
$548$		0			0
$549$	−3.53274e13	−	6.11889e13i	−0.0302318	−	0.0523631i
$550$		0			0
$551$	9.32912e14	−	1.61585e15i	0.782540	−	1.35540i
$552$		0			0
$553$	−1.87394e15	+	3.63679e14i	−1.54087	+	0.299040i
$554$		0			0
$555$	1.71781e14	−	2.97533e14i	0.138472	−	0.239841i
$556$		0			0
$557$	1.93906e13	+	3.35855e13i	0.0153246	+	0.0265429i	0.873586	−	0.486670i	$-0.161789\pi$
$557$	1.93906e13	+	3.35855e13i	0.0153246	+	0.0265429i	−0.858261	+	0.513213i	$0.828455\pi$
$558$		0			0
$559$	−2.27577e15			−1.76345
$560$		0			0
$561$	7.70367e13			0.0585332
$562$		0			0
$563$	−2.67759e14	−	4.63772e14i	−0.199502	−	0.345548i	0.748865	−	0.662723i	$-0.230599\pi$
$563$	−2.67759e14	−	4.63772e14i	−0.199502	−	0.345548i	−0.948367	+	0.317175i	$0.897266\pi$
$564$		0			0
$565$	−1.78193e13	+	3.08639e13i	−0.0130204	+	0.0225519i
$566$		0			0
$567$	5.05220e13	−	1.46585e14i	0.0362055	−	0.105047i
$568$		0			0
$569$	−4.33929e14	+	7.51587e14i	−0.305001	+	0.528277i	−0.977262	−	0.212038i	$-0.931990\pi$
$569$	−4.33929e14	+	7.51587e14i	−0.305001	+	0.528277i	0.672261	+	0.740314i	$0.265323\pi$
$570$		0			0
$571$	5.01450e14	+	8.68538e14i	0.345724	+	0.598811i	0.985485	−	0.169762i	$-0.0543000\pi$
$571$	5.01450e14	+	8.68538e14i	0.345724	+	0.598811i	−0.639761	+	0.768574i	$0.720967\pi$
$572$		0			0
$573$	1.66427e15			1.12557
$574$		0			0
$575$	2.32110e15			1.54000
$576$		0			0
$577$	−1.70850e14	−	2.95920e14i	−0.111211	−	0.192623i	0.805048	−	0.593210i	$-0.202140\pi$
$577$	−1.70850e14	−	2.95920e14i	−0.111211	−	0.192623i	−0.916259	+	0.400587i	$0.868806\pi$
$578$		0			0
$579$	−2.76720e14	+	4.79292e14i	−0.176729	+	0.306104i
$580$		0			0
$581$	−1.51996e15	−	1.74956e15i	−0.952495	−	1.09638i
$582$		0			0
$583$	−6.34265e13	+	1.09858e14i	−0.0390026	+	0.0675545i
$584$		0			0
$585$	4.27458e14	+	7.40379e14i	0.257950	+	0.446783i
$586$		0			0
$587$	1.31315e15			0.777689			0.388845	−	0.921303i	$-0.372874\pi$
$587$	1.31315e15			0.777689			0.388845	+	0.921303i	$0.372874\pi$
$588$		0			0
$589$	1.98201e15			1.15205
$590$		0			0
$591$	−3.06106e14	−	5.30191e14i	−0.174639	−	0.302483i
$592$		0			0
$593$	−1.42951e15	+	2.47598e15i	−0.800543	+	1.38658i	0.118715	+	0.992928i	$0.462122\pi$
$593$	−1.42951e15	+	2.47598e15i	−0.800543	+	1.38658i	−0.919259	+	0.393654i	$0.871211\pi$
$594$		0			0
$595$	1.82997e15	+	2.10640e15i	1.00601	+	1.15797i
$596$		0			0
$597$	1.39351e14	−	2.41362e14i	0.0752055	−	0.130260i
$598$		0			0
$599$	−1.07552e15	−	1.86285e15i	−0.569862	−	0.987030i	−0.996579	−	0.0826451i	$-0.973663\pi$
$599$	−1.07552e15	−	1.86285e15i	−0.569862	−	0.987030i	0.426717	−	0.904385i	$-0.359670\pi$
$600$		0			0
$601$	−3.46561e15			−1.80289			−0.901447	−	0.432889i	$-0.857494\pi$
$601$	−3.46561e15			−1.80289			−0.901447	+	0.432889i	$0.857494\pi$
$602$		0			0
$603$	3.22543e14			0.164756
$604$		0			0
$605$	−1.39983e15	−	2.42458e15i	−0.702136	−	1.21613i
$606$		0			0
$607$	8.39119e14	−	1.45340e15i	0.413319	−	0.715890i	−0.581931	−	0.813238i	$-0.697703\pi$
$607$	8.39119e14	−	1.45340e15i	0.413319	−	0.715890i	0.995250	+	0.0973481i	$0.0310360\pi$
$608$		0			0
$609$	−3.20481e14	+	9.29847e14i	−0.155027	+	0.449797i
$610$		0			0
$611$	−6.18176e14	+	1.07071e15i	−0.293688	+	0.508682i
$612$		0			0
$613$	2.51033e14	+	4.34802e14i	0.117138	+	0.202889i	0.918632	−	0.395113i	$-0.129295\pi$
$613$	2.51033e14	+	4.34802e14i	0.117138	+	0.202889i	−0.801494	+	0.598002i	$0.795961\pi$
$614$		0			0
$615$	−2.03115e15			−0.930957
$616$		0			0
$617$	3.06387e15			1.37944			0.689719	−	0.724077i	$-0.257734\pi$
$617$	3.06387e15			1.37944			0.689719	+	0.724077i	$0.257734\pi$
$618$		0			0
$619$	6.07837e14	+	1.05280e15i	0.268837	+	0.465639i	0.968562	−	0.248773i	$-0.0800275\pi$
$619$	6.07837e14	+	1.05280e15i	0.268837	+	0.465639i	−0.699725	+	0.714412i	$0.746694\pi$
$620$		0			0
$621$	−3.38669e14	+	5.86592e14i	−0.147154	+	0.254878i
$622$		0			0
$623$	−1.22149e15	+	2.37058e14i	−0.521443	+	0.101197i
$624$		0			0
$625$	1.18367e15	−	2.05018e15i	0.496467	−	0.859906i
$626$		0			0
$627$	1.24566e14	+	2.15754e14i	0.0513366	+	0.0889176i
$628$		0			0
$629$	−9.05289e14			−0.366614
$630$		0			0
$631$	2.29369e15			0.912794			0.456397	−	0.889776i	$-0.349140\pi$
$631$	2.29369e15			0.912794			0.456397	+	0.889776i	$0.349140\pi$
$632$		0			0
$633$	1.32064e14	+	2.28742e14i	0.0516494	+	0.0894593i
$634$		0			0
$635$	3.13358e15	−	5.42753e15i	1.20444	−	2.08615i
$636$		0			0
$637$	−4.04173e14	+	2.86349e15i	−0.152686	+	1.08175i
$638$		0			0
$639$	−5.35078e14	+	9.26782e14i	−0.198684	+	0.344130i
$640$		0			0
$641$	9.49382e13	+	1.64438e14i	0.0346515	+	0.0600181i	0.882831	−	0.469691i	$-0.155635\pi$
$641$	9.49382e13	+	1.64438e14i	0.0346515	+	0.0600181i	−0.848180	+	0.529709i	$0.822301\pi$
$642$		0			0
$643$	1.75159e15			0.628452			0.314226	−	0.949348i	$-0.398255\pi$
$643$	1.75159e15			0.628452			0.314226	+	0.949348i	$0.398255\pi$
$644$		0			0
$645$	3.74321e15			1.32028
$646$		0			0
$647$	1.59994e15	+	2.77118e15i	0.554793	+	0.960930i	0.997920	+	0.0644710i	$0.0205360\pi$
$647$	1.59994e15	+	2.77118e15i	0.554793	+	0.960930i	−0.443126	+	0.896459i	$0.646131\pi$
$648$		0			0
$649$	−1.40110e14	+	2.42678e14i	−0.0477665	+	0.0827341i
$650$		0			0
$651$	−1.02563e15	+	1.99047e14i	−0.343793	+	0.0667206i
$652$		0			0
$653$	−1.12815e15	+	1.95401e15i	−0.371829	+	0.644026i	−0.989847	−	0.142138i	$-0.954602\pi$
$653$	−1.12815e15	+	1.95401e15i	−0.371829	+	0.644026i	0.618018	+	0.786164i	$0.287936\pi$
$654$		0			0
$655$	4.75706e14	+	8.23948e14i	0.154174	+	0.267038i
$656$		0			0
$657$	−1.16626e15			−0.371693
$658$		0			0
$659$	3.01218e15			0.944084			0.472042	−	0.881576i	$-0.343517\pi$
$659$	3.01218e15			0.944084			0.472042	+	0.881576i	$0.343517\pi$
$660$		0			0
$661$	−1.47975e15	−	2.56300e15i	−0.456121	−	0.790024i	0.542631	−	0.839971i	$-0.317428\pi$
$661$	−1.47975e15	−	2.56300e15i	−0.456121	−	0.790024i	−0.998752	+	0.0499469i	$0.984095\pi$
$662$		0			0
$663$	1.12636e15	−	1.95091e15i	0.341469	−	0.591442i
$664$		0			0
$665$	−2.94033e15	+	8.53111e15i	−0.876753	+	2.54382i
$666$		0			0
$667$	2.14831e15	−	3.72098e15i	0.630094	−	1.09135i
$668$		0			0
$669$	−1.94603e15	−	3.37062e15i	−0.561443	−	0.972447i
$670$		0			0
$671$	−5.98442e13			−0.0169843
$672$		0			0
$673$	4.01157e15			1.12004			0.560018	−	0.828481i	$-0.310794\pi$
$673$	4.01157e15			1.12004			0.560018	+	0.828481i	$0.310794\pi$
$674$		0			0
$675$	−3.52773e14	−	6.11021e14i	−0.0969002	−	0.167836i
$676$		0			0
$677$	−3.58231e15	+	6.20474e15i	−0.968111	+	1.67682i	−0.267096	+	0.963670i	$0.586064\pi$
$677$	−3.58231e15	+	6.20474e15i	−0.968111	+	1.67682i	−0.701015	+	0.713147i	$0.747269\pi$
$678$		0			0
$679$	1.58065e15	+	1.81942e15i	0.420293	+	0.483782i
$680$		0			0
$681$	−1.41546e15	+	2.45164e15i	−0.370329	+	0.641428i
$682$		0			0
$683$	7.37708e13	+	1.27775e14i	0.0189920	+	0.0328951i	0.875365	−	0.483462i	$-0.160621\pi$
$683$	7.37708e13	+	1.27775e14i	0.0189920	+	0.0328951i	−0.856373	+	0.516357i	$0.827288\pi$
$684$		0			0
$685$	−3.62770e14			−0.0919037
$686$		0			0
$687$	−2.27352e14			−0.0566809
$688$		0			0
$689$	1.85472e15	+	3.21248e15i	0.455065	+	0.788196i
$690$		0			0
$691$	1.43011e15	−	2.47703e15i	0.345335	−	0.598138i	−0.640079	−	0.768309i	$-0.721099\pi$
$691$	1.43011e15	−	2.47703e15i	0.345335	−	0.598138i	0.985415	+	0.170171i	$0.0544319\pi$
$692$		0			0
$693$	−8.61268e13	−	9.91370e13i	−0.0204694	−	0.0235615i
$694$		0			0
$695$	−3.59902e15	+	6.23369e15i	−0.841915	+	1.45824i
$696$		0			0
$697$	2.67606e15	+	4.63507e15i	0.616191	+	1.06727i
$698$		0			0
$699$	2.94680e15			0.667923
$700$		0			0
$701$	3.67571e14			0.0820147			0.0410073	−	0.999159i	$-0.486943\pi$
$701$	3.67571e14			0.0820147			0.0410073	+	0.999159i	$0.486943\pi$
$702$		0			0
$703$	−1.46382e15	−	2.53541e15i	−0.321539	−	0.556922i
$704$		0			0
$705$	1.01678e15	−	1.76112e15i	0.219881	−	0.380846i
$706$		0			0
$707$	−1.75910e15	+	5.10388e15i	−0.374528	+	1.08666i
$708$		0			0
$709$	−3.52656e15	+	6.10818e15i	−0.739259	+	1.28043i	0.213570	+	0.976928i	$0.431491\pi$
$709$	−3.52656e15	+	6.10818e15i	−0.739259	+	1.28043i	−0.952829	+	0.303507i	$0.901842\pi$
$710$		0			0
$711$	−1.26744e15	−	2.19527e15i	−0.261604	−	0.453111i
$712$		0			0
$713$	4.56418e15			0.927620
$714$		0			0
$715$	7.24108e14			0.144917
$716$		0			0
$717$	−3.62752e14	−	6.28304e14i	−0.0714914	−	0.123827i
$718$		0			0
$719$	3.63237e15	−	6.29146e15i	0.704988	−	1.22108i	−0.261708	−	0.965147i	$-0.584286\pi$
$719$	3.63237e15	−	6.29146e15i	0.704988	−	1.22108i	0.966696	−	0.255928i	$-0.0823810\pi$
$720$		0			0
$721$	7.21561e15	−	1.40035e15i	1.37921	−	0.267665i
$722$		0			0
$723$	−1.05727e15	+	1.83124e15i	−0.199032	+	0.344734i
$724$		0			0
$725$	2.23778e15	+	3.87595e15i	0.414914	+	0.718652i
$726$		0			0
$727$	−8.82541e15			−1.61174			−0.805871	−	0.592091i	$-0.798302\pi$
$727$	−8.82541e15			−1.61174			−0.805871	+	0.592091i	$0.798302\pi$
$728$		0			0
$729$	2.05891e14			0.0370370
$730$		0			0
$731$	−4.93171e15	−	8.54196e15i	−0.873880	−	1.51360i
$732$		0			0
$733$	−3.25078e15	+	5.63051e15i	−0.567434	+	0.982825i	0.429384	+	0.903122i	$0.358731\pi$
$733$	−3.25078e15	+	5.63051e15i	−0.567434	+	0.982825i	−0.996819	+	0.0797030i	$0.974603\pi$
$734$		0			0
$735$	6.64788e14	−	4.70990e15i	0.114315	−	0.809900i
$736$		0			0
$737$	1.36596e14	−	2.36591e14i	0.0231401	−	0.0400799i
$738$		0			0
$739$	−4.66487e15	−	8.07979e15i	−0.778565	−	1.34851i	−0.932769	−	0.360475i	$-0.882615\pi$
$739$	−4.66487e15	−	8.07979e15i	−0.778565	−	1.34851i	0.154204	−	0.988039i	$-0.450719\pi$
$740$		0			0
$741$	7.28512e15			1.19794
$742$		0			0
$743$	7.14846e15			1.15817			0.579087	−	0.815266i	$-0.303409\pi$
$743$	7.14846e15			1.15817			0.579087	+	0.815266i	$0.303409\pi$
$744$		0			0
$745$	−5.71193e15	−	9.89335e15i	−0.911850	−	1.57937i
$746$		0			0
$747$	1.53879e15	−	2.66527e15i	0.242057	−	0.419254i
$748$		0			0
$749$	9.17564e15	−	1.78073e15i	1.42228	−	0.276025i
$750$		0			0
$751$	2.33373e15	−	4.04213e15i	0.356476	−	0.617434i	−0.630893	−	0.775869i	$-0.717312\pi$
$751$	2.33373e15	−	4.04213e15i	0.356476	−	0.617434i	0.987369	+	0.158435i	$0.0506448\pi$
$752$		0			0
$753$	−1.34344e15	−	2.32690e15i	−0.202230	−	0.350272i
$754$		0			0
$755$	−7.41001e15			−1.09929
$756$		0			0
$757$	4.72097e15			0.690246			0.345123	−	0.938557i	$-0.387837\pi$
$757$	4.72097e15			0.690246			0.345123	+	0.938557i	$0.387837\pi$
$758$		0			0
$759$	2.86850e14	+	4.96839e14i	0.0413357	+	0.0715955i
$760$		0			0
$761$	6.09532e14	−	1.05574e15i	0.0865727	−	0.149948i	−0.819488	−	0.573097i	$-0.805742\pi$
$761$	6.09532e14	−	1.05574e15i	0.0865727	−	0.149948i	0.906060	+	0.423149i	$0.139075\pi$
$762$		0			0
$763$	1.32492e15	−	3.84413e15i	0.185483	−	0.538162i
$764$		0			0
$765$	−1.85265e15	+	3.20888e15i	−0.255655	+	0.442808i
$766$		0			0
$767$	4.09711e15	+	7.09641e15i	0.557318	+	0.965304i
$768$		0			0
$769$	4.52570e15			0.606864			0.303432	−	0.952853i	$-0.401867\pi$
$769$	4.52570e15			0.606864			0.303432	+	0.952853i	$0.401867\pi$
$770$		0			0
$771$	6.17911e15			0.816820
$772$		0			0
$773$	−2.34216e15	−	4.05675e15i	−0.305232	−	0.528677i	0.672081	−	0.740478i	$-0.265401\pi$
$773$	−2.34216e15	−	4.05675e15i	−0.305232	−	0.528677i	−0.977313	+	0.211800i	$0.932067\pi$
$774$		0			0
$775$	−2.37713e15	+	4.11731e15i	−0.305417	+	0.528998i
$776$		0			0
$777$	1.01211e15	+	1.16500e15i	0.128207	+	0.147574i
$778$		0			0
$779$	−8.65418e15	+	1.49895e16i	−1.08086	+	1.87211i
$780$		0			0
$781$	4.53207e14	+	7.84977e14i	0.0558105	+	0.0966666i
$782$		0			0
$783$	−1.30605e15			−0.158588
$784$		0			0
$785$	−2.12195e16			−2.54069
$786$		0			0
$787$	−6.54085e15	−	1.13291e16i	−0.772277	−	1.33762i	−0.936312	−	0.351169i	$-0.885784\pi$
$787$	−6.54085e15	−	1.13291e16i	−0.772277	−	1.33762i	0.164035	−	0.986455i	$-0.447549\pi$
$788$		0			0
$789$	4.08597e15	−	7.07712e15i	0.475743	−	0.824011i
$790$		0			0
$791$	−1.04989e14	−	1.20848e14i	−0.0120551	−	0.0138762i
$792$		0			0
$793$	−8.74984e14	+	1.51552e15i	−0.0990827	+	0.171616i
$794$		0			0
$795$	−3.05067e15	−	5.28392e15i	−0.340703	−	0.590115i
$796$		0			0
$797$	−1.03303e16			−1.13787			−0.568933	−	0.822384i	$-0.692644\pi$
$797$	−1.03303e16			−1.13787			−0.568933	+	0.822384i	$0.692644\pi$
$798$		0			0
$799$	−5.35847e15			−0.582148
$800$		0			0
$801$	−8.26157e14	−	1.43095e15i	−0.0885286	−	0.153336i
$802$		0			0
$803$	−4.93905e14	+	8.55469e14i	−0.0522045	+	0.0904209i
$804$		0			0
$805$	−6.77100e15	+	1.96455e16i	−0.705953	+	2.04826i
$806$		0			0
$807$	1.81303e15	−	3.14026e15i	0.186466	−	0.322969i
$808$		0			0
$809$	−5.46347e15	−	9.46301e15i	−0.554309	−	0.960091i	−0.997957	−	0.0638900i	$-0.979649\pi$
$809$	−5.46347e15	−	9.46301e15i	−0.554309	−	0.960091i	0.443648	−	0.896201i	$-0.353684\pi$
$810$		0			0
$811$	−1.55193e16			−1.55330			−0.776652	−	0.629930i	$-0.783084\pi$
$811$	−1.55193e16			−1.55330			−0.776652	+	0.629930i	$0.783084\pi$
$812$		0			0
$813$	−5.24106e15			−0.517513
$814$		0			0
$815$	−1.01037e14	−	1.75001e14i	−0.00984268	−	0.0170480i
$816$		0			0
$817$	1.59488e16	−	2.76241e16i	1.53287	−	2.65502i
$818$		0			0
$819$	−3.76985e15	+	7.31622e14i	−0.357489	+	0.0693786i
$820$		0			0
$821$	−7.25247e15	+	1.25617e16i	−0.678577	+	1.17533i	0.296833	+	0.954929i	$0.404069\pi$
$821$	−7.25247e15	+	1.25617e16i	−0.678577	+	1.17533i	−0.975410	+	0.220400i	$0.929264\pi$
$822$		0			0
$823$	1.41636e15	+	2.45320e15i	0.130760	+	0.226482i	0.923970	−	0.382466i	$-0.124925\pi$
$823$	1.41636e15	+	2.45320e15i	0.130760	+	0.226482i	−0.793210	+	0.608948i	$0.791592\pi$
$824$		0			0
$825$	−5.97593e14			−0.0544388
$826$		0			0
$827$	1.88975e16			1.69873			0.849363	−	0.527809i	$-0.176986\pi$
$827$	1.88975e16			1.69873			0.849363	+	0.527809i	$0.176986\pi$
$828$		0			0
$829$	1.55663e14	+	2.69617e14i	0.0138082	+	0.0239165i	0.872847	−	0.487994i	$-0.162271\pi$
$829$	1.55663e14	+	2.69617e14i	0.0138082	+	0.0239165i	−0.859039	+	0.511911i	$0.828938\pi$
$830$		0			0
$831$	−3.53158e15	+	6.11688e15i	−0.309146	+	0.535457i
$832$		0			0
$833$	−1.16238e16	+	4.68828e15i	−1.00415	+	0.405011i
$834$		0			0
$835$	−1.22667e15	+	2.12465e15i	−0.104581	+	0.181139i
$836$		0			0
$837$	−6.93689e14	−	1.20150e15i	−0.0583680	−	0.101096i
$838$		0			0
$839$	1.14467e16			0.950583			0.475292	−	0.879828i	$-0.342343\pi$
$839$	1.14467e16			0.950583			0.475292	+	0.879828i	$0.342343\pi$
$840$		0			0
$841$	−3.91573e15			−0.320948
$842$		0			0
$843$	−2.45638e15	−	4.25457e15i	−0.198721	−	0.344195i
$844$		0			0
$845$	1.71652e15	−	2.97310e15i	0.137068	−	0.237410i
$846$		0			0
$847$	1.23454e16	−	2.39590e15i	0.973077	−	0.188847i
$848$		0			0
$849$	−5.94596e13	+	1.02987e14i	−0.00462626	+	0.00801291i
$850$		0			0
$851$	−3.37089e15	−	5.83855e15i	−0.258900	−	0.448428i
$852$		0			0
$853$	7.10747e15			0.538884			0.269442	−	0.963017i	$-0.413161\pi$
$853$	7.10747e15			0.538884			0.269442	+	0.963017i	$0.413161\pi$
$854$		0			0
$855$	−1.19827e16			−0.896891
$856$		0			0
$857$	7.28558e15	+	1.26190e16i	0.538356	+	0.932460i	0.998993	+	0.0448714i	$0.0142878\pi$
$857$	7.28558e15	+	1.26190e16i	0.538356	+	0.932460i	−0.460637	+	0.887589i	$0.652379\pi$
$858$		0			0
$859$	6.82398e15	−	1.18195e16i	0.497824	−	0.862256i	−0.502173	−	0.864767i	$-0.667466\pi$
$859$	6.82398e15	−	1.18195e16i	0.497824	−	0.862256i	0.999997	+	0.00251138i	$0.000799397\pi$
$860$		0			0
$861$	2.97295e15	−	8.62576e15i	0.214127	−	0.621269i
$862$		0			0
$863$	9.49537e15	−	1.64465e16i	0.675231	−	1.16954i	−0.301170	−	0.953571i	$-0.597377\pi$
$863$	9.49537e15	−	1.64465e16i	0.675231	−	1.16954i	0.976401	−	0.215965i	$-0.0692896\pi$
$864$		0			0
$865$	−9.44070e15	−	1.63518e16i	−0.662851	−	1.14809i
$866$		0			0
$867$	1.43542e15			0.0995114
$868$		0			0
$869$	−2.14702e15			−0.146970
$870$		0			0
$871$	−3.99434e15	−	6.91840e15i	−0.269989	−	0.467634i
$872$		0			0
$873$	−1.60024e15	+	2.77169e15i	−0.106809	+	0.184998i
$874$		0			0
$875$	−9.89136e13	−	1.13855e14i	−0.00651946	−	0.00750429i
$876$		0			0
$877$	5.97907e15	−	1.03561e16i	0.389167	−	0.674057i	−0.603171	−	0.797612i	$-0.706096\pi$
$877$	5.97907e15	−	1.03561e16i	0.389167	−	0.674057i	0.992338	+	0.123555i	$0.0394296\pi$
$878$		0			0
$879$	8.29749e15	+	1.43717e16i	0.533345	+	0.923780i
$880$		0			0
$881$	−1.04006e16			−0.660221			−0.330111	−	0.943942i	$-0.607086\pi$
$881$	−1.04006e16			−0.660221			−0.330111	+	0.943942i	$0.607086\pi$
$882$		0			0
$883$	1.40425e16			0.880360			0.440180	−	0.897910i	$-0.354915\pi$
$883$	1.40425e16			0.880360			0.440180	+	0.897910i	$0.354915\pi$
$884$		0			0
$885$	−6.73898e15	−	1.16723e16i	−0.417259	−	0.722715i
$886$		0			0
$887$	−1.17716e16	+	2.03890e16i	−0.719873	+	1.24686i	0.241177	+	0.970481i	$0.422467\pi$
$887$	−1.17716e16	+	2.03890e16i	−0.719873	+	1.24686i	−0.961050	+	0.276375i	$0.910867\pi$
$888$		0			0
$889$	1.84627e16	+	2.12516e16i	1.11515	+	1.28361i
$890$		0			0
$891$	8.71941e13	−	1.51025e14i	0.00520187	−	0.00900991i
$892$		0			0
$893$	−8.66446e15	−	1.50073e16i	−0.510574	−	0.884340i
$894$		0			0
$895$	5.03882e15			0.293294
$896$		0			0
$897$	1.67762e16			0.964573
$898$		0			0
$899$	4.40034e15	+	7.62161e15i	0.249924	+	0.432881i
$900$		0			0
$901$	−8.03855e15	+	1.39232e16i	−0.451016	+	0.781182i
$902$		0			0
$903$	−5.47886e15	+	1.58964e16i	−0.303674	+	0.881082i
$904$		0			0
$905$	−5.21166e15	+	9.02686e15i	−0.285370	+	0.494276i
$906$		0			0
$907$	1.25037e16	+	2.16570e16i	0.676392	+	1.17154i	0.976060	+	0.217501i	$0.0697906\pi$
$907$	1.25037e16	+	2.16570e16i	0.676392	+	1.17154i	−0.299668	+	0.954043i	$0.596876\pi$
$908$		0			0
$909$	−7.16883e15			−0.383131
$910$		0			0
$911$	2.16094e16			1.14102			0.570508	−	0.821292i	$-0.306746\pi$
$911$	2.16094e16			1.14102			0.570508	+	0.821292i	$0.306746\pi$
$912$		0			0
$913$	−1.30335e15	−	2.25746e15i	−0.0679940	−	0.117769i
$914$		0			0
$915$	1.43918e15	−	2.49274e15i	0.0741823	−	0.128488i
$916$		0			0
$917$	−4.19536e15	+	8.14202e14i	−0.213667	+	0.0414668i
$918$		0			0
$919$	−1.18711e16	+	2.05614e16i	−0.597388	+	1.03471i	0.395817	+	0.918329i	$0.370461\pi$
$919$	−1.18711e16	+	2.05614e16i	−0.597388	+	1.03471i	−0.993205	+	0.116377i	$0.962872\pi$
$920$		0			0
$921$	3.42903e15	+	5.93925e15i	0.170507	+	0.295328i
$922$		0			0
$923$	2.65054e16			1.30234
$924$		0			0
$925$	7.02255e15			0.340969
$926$		0			0
$927$	4.88028e15	+	8.45289e15i	0.234156	+	0.405571i
$928$		0			0
$929$	7.80122e15	−	1.35121e16i	0.369893	−	0.640674i	−0.619655	−	0.784874i	$-0.712728\pi$
$929$	7.80122e15	−	1.35121e16i	0.369893	−	0.640674i	0.989549	+	0.144200i	$0.0460609\pi$
$930$		0			0
$931$	−3.19256e16	−	2.49736e16i	−1.49594	−	1.17019i
$932$		0			0
$933$	8.57806e15	−	1.48576e16i	0.397228	−	0.688019i
$934$		0			0
$935$	1.56918e15	+	2.71789e15i	0.0718138	+	0.124385i
$936$		0			0
$937$	8.89670e14			0.0402403			0.0201201	−	0.999798i	$-0.493595\pi$
$937$	8.89670e14			0.0402403			0.0201201	+	0.999798i	$0.493595\pi$
$938$		0			0
$939$	−8.53455e15			−0.381522
$940$		0			0
$941$	1.33102e16	+	2.30539e16i	0.588086	+	1.01860i	0.994483	+	0.104899i	$0.0334518\pi$
$941$	1.33102e16	+	2.30539e16i	0.588086	+	1.01860i	−0.406397	+	0.913697i	$0.633215\pi$
$942$		0			0
$943$	−1.99289e16	+	3.45178e16i	−0.870299	+	1.50740i
$944$		0			0
$945$	6.20069e15	−	1.20338e15i	0.267649	−	0.0519431i
$946$		0			0
$947$	1.01137e16	−	1.75174e16i	0.431503	−	0.747385i	−0.565500	−	0.824748i	$-0.691317\pi$
$947$	1.01137e16	−	1.75174e16i	0.431503	−	0.747385i	0.997003	+	0.0773632i	$0.0246501\pi$
$948$		0			0
$949$	1.44428e16	+	2.50157e16i	0.609099	+	1.05499i
$950$		0			0
$951$	−7.51403e15			−0.313242
$952$		0			0
$953$	1.14065e16			0.470046			0.235023	−	0.971990i	$-0.424484\pi$
$953$	1.14065e16			0.470046			0.235023	+	0.971990i	$0.424484\pi$
$954$		0			0
$955$	3.38998e16	+	5.87162e16i	1.38095	+	2.39188i
$956$		0			0
$957$	−5.53107e14	+	9.58009e14i	−0.0222737	+	0.0385793i
$958$		0			0
$959$	5.30978e14	−	1.54058e15i	0.0211385	−	0.0613314i
$960$		0			0
$961$	8.02989e15	−	1.39082e16i	0.316032	−	0.547383i
$962$		0			0
$963$	6.20594e15	+	1.07490e16i	0.241470	+	0.418238i
$964$		0			0
$965$	−2.25462e16			−0.867309
$966$		0			0
$967$	−1.90477e16			−0.724429			−0.362215	−	0.932095i	$-0.617979\pi$
$967$	−1.90477e16			−0.724429			−0.362215	+	0.932095i	$0.617979\pi$
$968$		0			0
$969$	1.57872e16	+	2.73443e16i	0.593642	+	1.02822i
$970$		0			0
$971$	1.73660e16	−	3.00788e16i	0.645646	−	1.11829i	−0.338506	−	0.940964i	$-0.609921\pi$
$971$	1.73660e16	−	3.00788e16i	0.645646	−	1.11829i	0.984152	−	0.177328i	$-0.0567453\pi$
$972$		0			0
$973$	−2.12050e16	−	2.44082e16i	−0.779502	−	0.897253i
$974$		0			0
$975$	−8.73743e15	+	1.51337e16i	−0.317584	+	0.550071i
$976$		0			0
$977$	−8.05853e15	−	1.39578e16i	−0.289625	−	0.501645i	0.684095	−	0.729393i	$-0.260197\pi$
$977$	−8.05853e15	−	1.39578e16i	−0.289625	−	0.501645i	−0.973720	+	0.227748i	$0.926864\pi$
$978$		0			0
$979$	−1.39950e15			−0.0497356
$980$		0			0
$981$	5.39940e15			0.189743
$982$		0			0
$983$	−7.46353e15	−	1.29272e16i	−0.259358	−	0.449222i	0.706712	−	0.707501i	$-0.250178\pi$
$983$	−7.46353e15	−	1.29272e16i	−0.259358	−	0.449222i	−0.966070	+	0.258280i	$0.916844\pi$
$984$		0			0
$985$	1.24703e16	−	2.15991e16i	0.428525	−	0.742227i
$986$		0			0
$987$	5.99075e15	+	6.89571e15i	0.203581	+	0.234334i
$988$		0			0
$989$	3.67269e16	−	6.36129e16i	1.23426	−	2.13779i
$990$		0			0
$991$	−1.12354e16	−	1.94603e16i	−0.373408	−	0.646762i	0.616679	−	0.787215i	$-0.288478\pi$
$991$	−1.12354e16	−	1.94603e16i	−0.373408	−	0.646762i	−0.990087	+	0.140452i	$0.955144\pi$
$992$		0			0
$993$	9.04871e15			0.297417
$994$		0			0
$995$	1.13538e16			0.369076
$996$		0			0
$997$	1.44345e16	+	2.50012e16i	0.464064	+	0.803782i	0.999159	−	0.0410101i	$-0.0130576\pi$
$997$	1.44345e16	+	2.50012e16i	0.464064	+	0.803782i	−0.535095	+	0.844792i	$0.679724\pi$
$998$		0			0
$999$	−1.02465e15	+	1.77475e15i	−0.0325812	+	0.0564322i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.12.i.b.37.7	yes	16
3.2	odd	2		252.12.k.d.37.2		16
7.4	even	3	inner	84.12.i.b.25.7	✓	16
21.11	odd	6		252.12.k.d.109.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.12.i.b.25.7	✓	16	7.4	even	3	inner
84.12.i.b.37.7	yes	16	1.1	even	1	trivial
252.12.k.d.37.2		16	3.2	odd	2
252.12.k.d.109.2		16	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	84.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-121.500 - 210.444i) q^{3} +(4949.72 - 8573.16i) q^{5} +(29163.1 + 33568.4i) q^{7} +(-29524.5 + 51137.9i) q^{9} +O(q^{10})\)	\(q+(-121.500 - 210.444i) q^{3} +(4949.72 - 8573.16i) q^{5} +(29163.1 + 33568.4i) q^{7} +(-29524.5 + 51137.9i) q^{9} +(25007.0 + 43313.5i) q^{11} +1.46252e6 q^{13} -2.40556e6 q^{15} +(3.16934e6 + 5.48946e6i) q^{17} +(-1.02494e7 + 1.77525e7i) q^{19} +(3.52097e6 - 1.02158e7i) q^{21} +(-2.36024e7 + 4.08806e7i) q^{23} +(-2.45854e7 - 4.25831e7i) q^{25} +1.43489e7 q^{27} -9.10208e7 q^{29} +(-4.83443e7 - 8.37349e7i) q^{31} +(6.07671e6 - 1.05252e7i) q^{33} +(4.32137e8 - 8.38657e7i) q^{35} +(-7.14098e7 + 1.23685e8i) q^{37} +(-1.77696e8 - 3.07778e8i) q^{39} +8.44357e8 q^{41} -1.55607e9 q^{43} +(2.92276e8 + 5.06237e8i) q^{45} +(-4.22680e8 + 7.32103e8i) q^{47} +(-2.76354e8 + 1.95792e9i) q^{49} +(7.70151e8 - 1.33394e9i) q^{51} +(1.26817e9 + 2.19654e9i) q^{53} +4.95111e8 q^{55} +4.98123e9 q^{57} +(2.80141e9 + 4.85219e9i) q^{59} +(-5.98273e8 + 1.03624e9i) q^{61} +(-2.57765e9 + 5.00249e8i) q^{63} +(7.23904e9 - 1.25384e10i) q^{65} +(-2.73114e9 - 4.73048e9i) q^{67} +1.14708e10 q^{69} +1.81232e10 q^{71} +(9.87533e9 + 1.71046e10i) q^{73} +(-5.97425e9 + 1.03477e10i) q^{75} +(-7.24683e8 + 2.10260e9i) q^{77} +(-2.14642e10 + 3.71770e10i) q^{79} +(-1.74339e9 - 3.01964e9i) q^{81} -5.21192e10 q^{83} +6.27494e10 q^{85} +(1.10590e10 + 1.91548e10i) q^{87} +(-1.39910e10 + 2.42332e10i) q^{89} +(4.26515e10 + 4.90944e10i) q^{91} +(-1.17477e10 + 2.03476e10i) q^{93} +(1.01464e11 + 1.75740e11i) q^{95} +5.42003e10 q^{97} -2.95328e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 1944 q^{3} - 2156 q^{5} + 50512 q^{7} - 472392 q^{9}+O(q^{10}) \) 16 * q - 1944 * q^3 - 2156 * q^5 + 50512 * q^7 - 472392 * q^9	\( 16 q - 1944 q^{3} - 2156 q^{5} + 50512 q^{7} - 472392 q^{9} - 222796 q^{11} + 2703176 q^{13} + 1047816 q^{15} + 5114600 q^{17} + 6910556 q^{19} - 18340668 q^{21} - 51387712 q^{23} - 191456372 q^{25} + 229582512 q^{27} + 118854616 q^{29} + 164659160 q^{31} - 54139428 q^{33} + 55239344 q^{35} + 75658364 q^{37} - 328435884 q^{39} - 1815568608 q^{41} + 10754408 q^{43} - 127309644 q^{45} - 1034359464 q^{47} + 4123496848 q^{49} + 1242847800 q^{51} - 665159988 q^{53} - 1264543896 q^{55} - 3358530216 q^{57} + 1040514580 q^{59} - 14391208024 q^{61} + 1474099236 q^{63} - 20938150200 q^{65} - 33307097284 q^{67} + 24974428032 q^{69} + 65848902896 q^{71} + 17709749204 q^{73} - 46523898396 q^{75} + 8594484604 q^{77} - 26626784032 q^{79} - 27894275208 q^{81} - 210306955048 q^{83} - 25867402032 q^{85} - 14440835844 q^{87} - 55951560072 q^{89} + 66078280292 q^{91} + 40012175880 q^{93} + 106810047392 q^{95} - 156216030712 q^{97} + 26311762008 q^{99}+O(q^{100}) \) 16 * q - 1944 * q^3 - 2156 * q^5 + 50512 * q^7 - 472392 * q^9 - 222796 * q^11 + 2703176 * q^13 + 1047816 * q^15 + 5114600 * q^17 + 6910556 * q^19 - 18340668 * q^21 - 51387712 * q^23 - 191456372 * q^25 + 229582512 * q^27 + 118854616 * q^29 + 164659160 * q^31 - 54139428 * q^33 + 55239344 * q^35 + 75658364 * q^37 - 328435884 * q^39 - 1815568608 * q^41 + 10754408 * q^43 - 127309644 * q^45 - 1034359464 * q^47 + 4123496848 * q^49 + 1242847800 * q^51 - 665159988 * q^53 - 1264543896 * q^55 - 3358530216 * q^57 + 1040514580 * q^59 - 14391208024 * q^61 + 1474099236 * q^63 - 20938150200 * q^65 - 33307097284 * q^67 + 24974428032 * q^69 + 65848902896 * q^71 + 17709749204 * q^73 - 46523898396 * q^75 + 8594484604 * q^77 - 26626784032 * q^79 - 27894275208 * q^81 - 210306955048 * q^83 - 25867402032 * q^85 - 14440835844 * q^87 - 55951560072 * q^89 + 66078280292 * q^91 + 40012175880 * q^93 + 106810047392 * q^95 - 156216030712 * q^97 + 26311762008 * q^99

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