LMFDB - Embedded newform 84.12.i.b.25.6

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			25.6
Root			$-6748.51 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	84.25
Dual form			84.12.i.b.37.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-121.500 + 210.444i) q^{3} +(3239.51 + 5610.99i) q^{5} +(-44011.6 - 6348.37i) q^{7} +(-29524.5 - 51137.9i) q^{9} +O(q^{10})$	\(q+(-121.500 + 210.444i) q^{3} +(3239.51 + 5610.99i) q^{5} +(-44011.6 - 6348.37i) q^{7} +(-29524.5 - 51137.9i) q^{9} +(153860. - 266493. i) q^{11} +584277. q^{13} -1.57440e6 q^{15} +(4.72018e6 - 8.17558e6i) q^{17} +(8.44479e6 + 1.46268e7i) q^{19} +(6.68339e6 - 8.49067e6i) q^{21} +(1.59358e7 + 2.76016e7i) q^{23} +(3.42527e6 - 5.93275e6i) q^{25} +1.43489e7 q^{27} -1.08011e8 q^{29} +(1.25482e8 - 2.17341e8i) q^{31} +(3.73879e7 + 6.47577e7i) q^{33} +(-1.06955e8 - 2.67514e8i) q^{35} +(8.03798e7 + 1.39222e8i) q^{37} +(-7.09896e7 + 1.22958e8i) q^{39} -5.43424e8 q^{41} +2.35306e8 q^{43} +(1.91290e8 - 3.31323e8i) q^{45} +(4.31156e8 + 7.46784e8i) q^{47} +(1.89672e9 + 5.58805e8i) q^{49} +(1.14700e9 + 1.98667e9i) q^{51} +(-1.83924e9 + 3.18566e9i) q^{53} +1.99372e9 q^{55} -4.10417e9 q^{57} +(-1.91162e9 + 3.31102e9i) q^{59} +(-2.30312e9 - 3.98912e9i) q^{61} +(9.74779e8 + 2.43810e9i) q^{63} +(1.89277e9 + 3.27837e9i) q^{65} +(9.21035e8 - 1.59528e9i) q^{67} -7.74479e9 q^{69} +1.51591e10 q^{71} +(-1.51263e10 + 2.61995e10i) q^{73} +(8.32342e8 + 1.44166e9i) q^{75} +(-8.46341e9 + 1.07520e10i) q^{77} +(1.74865e10 + 3.02876e10i) q^{79} +(-1.74339e9 + 3.01964e9i) q^{81} +2.03419e10 q^{83} +6.11641e10 q^{85} +(1.31233e10 - 2.27303e10i) q^{87} +(4.42219e10 + 7.65945e10i) q^{89} +(-2.57150e10 - 3.70921e9i) q^{91} +(3.04920e10 + 5.28138e10i) q^{93} +(-5.47139e10 + 9.47672e10i) q^{95} -9.58828e10 q^{97} -1.81705e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	3239.51	+	5610.99i	0.463600	+	0.802979i	0.999137	−	0.0415326i	$-0.0132241\pi$
$5$	3239.51	+	5610.99i	0.463600	+	0.802979i	−0.535537	+	0.844512i	$0.679891\pi$
$6$		0			0
$7$	−44011.6	−	6348.37i	−0.989757	−	0.142766i
$7$	−44011.6	−	6348.37i	−0.989757	−	0.142766i
$8$		0			0
$9$	−29524.5	−	51137.9i	−0.166667	−	0.288675i
$10$		0			0
$11$	153860.	−	266493.i	0.288048	−	0.498914i	−0.685296	−	0.728265i	$-0.740327\pi$
$11$	153860.	−	266493.i	0.288048	−	0.498914i	0.973344	+	0.229351i	$0.0736604\pi$
$12$		0			0
$13$	584277.			0.436446			0.218223	−	0.975899i	$-0.429974\pi$
$13$	584277.			0.436446			0.218223	+	0.975899i	$0.429974\pi$
$14$		0			0
$15$	−1.57440e6			−0.535319
$16$		0			0
$17$	4.72018e6	−	8.17558e6i	0.806286	−	1.39653i	−0.109134	−	0.994027i	$-0.534808\pi$
$17$	4.72018e6	−	8.17558e6i	0.806286	−	1.39653i	0.915419	−	0.402501i	$-0.131859\pi$
$18$		0			0
$19$	8.44479e6	+	1.46268e7i	0.782427	+	1.35520i	0.930524	+	0.366231i	$0.119352\pi$
$19$	8.44479e6	+	1.46268e7i	0.782427	+	1.35520i	−0.148097	+	0.988973i	$0.547315\pi$
$20$		0			0
$21$	6.68339e6	−	8.49067e6i	0.357101	−	0.453665i
$22$		0			0
$23$	1.59358e7	+	2.76016e7i	0.516262	+	0.894193i	0.999822	+	0.0188811i	$0.00601038\pi$
$23$	1.59358e7	+	2.76016e7i	0.516262	+	0.894193i	−0.483559	+	0.875312i	$0.660656\pi$
$24$		0			0
$25$	3.42527e6	−	5.93275e6i	0.0701496	−	0.121503i
$26$		0			0
$27$	1.43489e7			0.192450
$28$		0			0
$29$	−1.08011e8			−0.977864			−0.488932	−	0.872322i	$-0.662613\pi$
$29$	−1.08011e8			−0.977864			−0.488932	+	0.872322i	$0.662613\pi$
$30$		0			0
$31$	1.25482e8	−	2.17341e8i	0.787210	−	1.36349i	−0.140459	−	0.990086i	$-0.544858\pi$
$31$	1.25482e8	−	2.17341e8i	0.787210	−	1.36349i	0.927670	−	0.373402i	$-0.121809\pi$
$32$		0			0
$33$	3.73879e7	+	6.47577e7i	0.166305	+	0.288048i
$34$		0			0
$35$	−1.06955e8	−	2.67514e8i	−0.344214	−	0.860940i
$36$		0			0
$37$	8.03798e7	+	1.39222e8i	0.190563	+	0.330064i	0.945437	−	0.325805i	$-0.105635\pi$
$37$	8.03798e7	+	1.39222e8i	0.190563	+	0.330064i	−0.754874	+	0.655870i	$0.772302\pi$
$38$		0			0
$39$	−7.09896e7	+	1.22958e8i	−0.125991	+	0.218223i
$40$		0			0
$41$	−5.43424e8			−0.732534			−0.366267	−	0.930510i	$-0.619364\pi$
$41$	−5.43424e8			−0.732534			−0.366267	+	0.930510i	$0.619364\pi$
$42$		0			0
$43$	2.35306e8			0.244094			0.122047	−	0.992524i	$-0.461054\pi$
$43$	2.35306e8			0.244094			0.122047	+	0.992524i	$0.461054\pi$
$44$		0			0
$45$	1.91290e8	−	3.31323e8i	0.154533	−	0.267660i
$46$		0			0
$47$	4.31156e8	+	7.46784e8i	0.274218	+	0.474960i	0.969938	−	0.243354i	$-0.0782476\pi$
$47$	4.31156e8	+	7.46784e8i	0.274218	+	0.474960i	−0.695719	+	0.718314i	$0.744914\pi$
$48$		0			0
$49$	1.89672e9	+	5.58805e8i	0.959236	+	0.282606i
$50$		0			0
$51$	1.14700e9	+	1.98667e9i	0.465509	+	0.806286i
$52$		0			0
$53$	−1.83924e9	+	3.18566e9i	−0.604117	+	1.04636i	0.388073	+	0.921629i	$0.373141\pi$
$53$	−1.83924e9	+	3.18566e9i	−0.604117	+	1.04636i	−0.992190	+	0.124733i	$0.960192\pi$
$54$		0			0
$55$	1.99372e9			0.534156
$56$		0			0
$57$	−4.10417e9			−0.903469
$58$		0			0
$59$	−1.91162e9	+	3.31102e9i	−0.348109	+	0.602943i	−0.985914	−	0.167255i	$-0.946510\pi$
$59$	−1.91162e9	+	3.31102e9i	−0.348109	+	0.602943i	0.637804	+	0.770198i	$0.279843\pi$
$60$		0			0
$61$	−2.30312e9	−	3.98912e9i	−0.349142	−	0.604732i	0.636955	−	0.770901i	$-0.280194\pi$
$61$	−2.30312e9	−	3.98912e9i	−0.349142	−	0.604732i	−0.986097	+	0.166169i	$0.946860\pi$
$62$		0			0
$63$	9.74779e8	+	2.43810e9i	0.123747	+	0.309512i
$64$		0			0
$65$	1.89277e9	+	3.27837e9i	0.202336	+	0.350457i
$66$		0			0
$67$	9.21035e8	−	1.59528e9i	0.0833422	−	0.144353i	−0.821341	−	0.570437i	$-0.806774\pi$
$67$	9.21035e8	−	1.59528e9i	0.0833422	−	0.144353i	0.904684	+	0.426084i	$0.140107\pi$
$68$		0			0
$69$	−7.74479e9			−0.596128
$70$		0			0
$71$	1.51591e10			0.997131			0.498566	−	0.866852i	$-0.333860\pi$
$71$	1.51591e10			0.997131			0.498566	+	0.866852i	$0.333860\pi$
$72$		0			0
$73$	−1.51263e10	+	2.61995e10i	−0.853997	+	1.47917i	0.0235759	+	0.999722i	$0.492495\pi$
$73$	−1.51263e10	+	2.61995e10i	−0.853997	+	1.47917i	−0.877573	+	0.479444i	$0.840838\pi$
$74$		0			0
$75$	8.32342e8	+	1.44166e9i	0.0405009	+	0.0701496i
$76$		0			0
$77$	−8.46341e9	+	1.07520e10i	−0.356325	+	0.452680i
$78$		0			0
$79$	1.74865e10	+	3.02876e10i	0.639374	+	1.10743i	0.985570	+	0.169266i	$0.0541396\pi$
$79$	1.74865e10	+	3.02876e10i	0.639374	+	1.10743i	−0.346197	+	0.938162i	$0.612527\pi$
$80$		0			0
$81$	−1.74339e9	+	3.01964e9i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	2.03419e10			0.566842			0.283421	−	0.958996i	$-0.408531\pi$
$83$	2.03419e10			0.566842			0.283421	+	0.958996i	$0.408531\pi$
$84$		0			0
$85$	6.11641e10			1.49518
$86$		0			0
$87$	1.31233e10	−	2.27303e10i	0.282285	−	0.488932i
$88$		0			0
$89$	4.42219e10	+	7.65945e10i	0.839444	+	1.45396i	0.890360	+	0.455257i	$0.150453\pi$
$89$	4.42219e10	+	7.65945e10i	0.839444	+	1.45396i	−0.0509155	+	0.998703i	$0.516214\pi$
$90$		0			0
$91$	−2.57150e10	−	3.70921e9i	−0.431975	−	0.0623094i
$92$		0			0
$93$	3.04920e10	+	5.28138e10i	0.454496	+	0.787210i
$94$		0			0
$95$	−5.47139e10	+	9.47672e10i	−0.725467	+	1.25655i
$96$		0			0
$97$	−9.58828e10			−1.13370			−0.566848	−	0.823823i	$-0.691837\pi$
$97$	−9.58828e10			−1.13370			−0.566848	+	0.823823i	$0.691837\pi$
$98$		0			0
$99$	−1.81705e10			−0.192032
$100$		0			0
$101$	8.02124e10	−	1.38932e11i	0.759406	−	1.31533i	−0.183748	−	0.982973i	$-0.558823\pi$
$101$	8.02124e10	−	1.38932e11i	0.759406	−	1.31533i	0.943154	−	0.332357i	$-0.107844\pi$
$102$		0			0
$103$	6.76095e10	+	1.17103e11i	0.574650	+	0.995322i	0.996080	+	0.0884613i	$0.0281950\pi$
$103$	6.76095e10	+	1.17103e11i	0.574650	+	0.995322i	−0.421430	+	0.906861i	$0.638472\pi$
$104$		0			0
$105$	6.92919e10	+	9.99488e9i	0.529836	+	0.0764252i
$106$		0			0
$107$	4.11930e10	+	7.13484e10i	0.283931	+	0.491783i	0.972349	−	0.233531i	$-0.0750280\pi$
$107$	4.11930e10	+	7.13484e10i	0.283931	+	0.491783i	−0.688418	+	0.725314i	$0.741695\pi$
$108$		0			0
$109$	−1.13457e11	+	1.96514e11i	−0.706295	+	1.22334i	0.259927	+	0.965628i	$0.416301\pi$
$109$	−1.13457e11	+	1.96514e11i	−0.706295	+	1.22334i	−0.966222	+	0.257711i	$0.917032\pi$
$110$		0			0
$111$	−3.90646e10			−0.220043
$112$		0			0
$113$	−1.73656e11			−0.886661			−0.443331	−	0.896358i	$-0.646203\pi$
$113$	−1.73656e11			−0.886661			−0.443331	+	0.896358i	$0.646203\pi$
$114$		0			0
$115$	−1.03248e11	+	1.78831e11i	−0.478679	+	0.829096i
$116$		0			0
$117$	−1.72505e10	−	2.98787e10i	−0.0727409	−	0.125991i
$118$		0			0
$119$	−2.59644e11	+	3.29855e11i	−0.997403	+	1.26711i
$120$		0			0
$121$	9.53103e10	+	1.65082e11i	0.334057	+	0.578603i
$122$		0			0
$123$	6.60260e10	−	1.14360e11i	0.211464	−	0.366267i
$124$		0			0
$125$	3.60743e11			1.05729
$126$		0			0
$127$	5.34602e11			1.43585			0.717926	−	0.696119i	$-0.245091\pi$
$127$	5.34602e11			1.43585			0.717926	+	0.696119i	$0.245091\pi$
$128$		0			0
$129$	−2.85897e10	+	4.95188e10i	−0.0704639	+	0.122047i
$130$		0			0
$131$	2.15277e9	+	3.72871e9i	0.00487535	+	0.00844435i	0.868453	−	0.495772i	$-0.165115\pi$
$131$	2.15277e9	+	3.72871e9i	0.00487535	+	0.00844435i	−0.863577	+	0.504216i	$0.831781\pi$
$132$		0			0
$133$	−2.78813e11	−	6.97360e11i	−0.580936	−	1.45303i
$134$		0			0
$135$	4.64834e10	+	8.05115e10i	0.0892199	+	0.154533i
$136$		0			0
$137$	2.72967e11	−	4.72793e11i	0.483222	−	0.836966i	−0.516592	−	0.856232i	$-0.672800\pi$
$137$	2.72967e11	−	4.72793e11i	0.483222	−	0.836966i	0.999814	+	0.0192659i	$0.00613290\pi$
$138$		0			0
$139$	−1.98706e11			−0.324811			−0.162405	−	0.986724i	$-0.551925\pi$
$139$	−1.98706e11			−0.324811			−0.162405	+	0.986724i	$0.551925\pi$
$140$		0			0
$141$	−2.09542e11			−0.316640
$142$		0			0
$143$	8.98965e10	−	1.55705e11i	0.125717	−	0.217749i
$144$		0			0
$145$	−3.49902e11	−	6.06048e11i	−0.453338	−	0.785205i
$146$		0			0
$147$	−3.48049e11	+	3.31260e11i	−0.418211	+	0.398037i
$148$		0			0
$149$	4.06132e11	+	7.03441e11i	0.453047	+	0.784700i	0.998574	−	0.0533936i	$-0.0170038\pi$
$149$	4.06132e11	+	7.03441e11i	0.453047	+	0.784700i	−0.545527	+	0.838093i	$0.683670\pi$
$150$		0			0
$151$	7.00195e10	−	1.21277e11i	0.0725848	−	0.125721i	−0.827449	−	0.561541i	$-0.810209\pi$
$151$	7.00195e10	−	1.21277e11i	0.0725848	−	0.125721i	0.900033	+	0.435821i	$0.143542\pi$
$152$		0			0
$153$	−5.57443e11			−0.537524
$154$		0			0
$155$	1.62599e12			1.45980
$156$		0			0
$157$	8.58436e11	−	1.48686e12i	0.718224	−	1.24400i	−0.243479	−	0.969906i	$-0.578289\pi$
$157$	8.58436e11	−	1.48686e12i	0.718224	−	1.24400i	0.961703	−	0.274094i	$-0.0883780\pi$
$158$		0			0
$159$	−4.46935e11	−	7.74115e11i	−0.348787	−	0.604117i
$160$		0			0
$161$	−5.26135e11	−	1.31596e12i	−0.383314	−	0.958737i
$162$		0			0
$163$	−4.32301e11	−	7.48767e11i	−0.294276	−	0.509701i	0.680540	−	0.732711i	$-0.261745\pi$
$163$	−4.32301e11	−	7.48767e11i	−0.294276	−	0.509701i	−0.974816	+	0.223010i	$0.928412\pi$
$164$		0			0
$165$	−2.42236e11	+	4.19566e11i	−0.154198	+	0.267078i
$166$		0			0
$167$	−2.19947e12			−1.31032			−0.655160	−	0.755490i	$-0.727399\pi$
$167$	−2.19947e12			−1.31032			−0.655160	+	0.755490i	$0.727399\pi$
$168$		0			0
$169$	−1.45078e12			−0.809515
$170$		0			0
$171$	4.98656e11	−	8.63698e11i	0.260809	−	0.451735i
$172$		0			0
$173$	−4.03725e11	−	6.99272e11i	−0.198076	−	0.343078i	0.749828	−	0.661632i	$-0.230136\pi$
$173$	−4.03725e11	−	6.99272e11i	−0.198076	−	0.343078i	−0.947905	+	0.318554i	$0.896803\pi$
$174$		0			0
$175$	−1.88415e11	+	2.39365e11i	−0.0867774	+	0.110243i
$176$		0			0
$177$	−4.64524e11	−	8.04579e11i	−0.200981	−	0.348109i
$178$		0			0
$179$	1.33293e12	−	2.30870e12i	0.542145	−	0.939022i	−0.456636	−	0.889654i	$-0.650946\pi$
$179$	1.33293e12	−	2.30870e12i	0.542145	−	0.939022i	0.998781	−	0.0493684i	$-0.0157208\pi$
$180$		0			0
$181$	9.78597e11			0.374431			0.187216	−	0.982319i	$-0.440054\pi$
$181$	9.78597e11			0.374431			0.187216	+	0.982319i	$0.440054\pi$
$182$		0			0
$183$	1.11932e12			0.403155
$184$		0			0
$185$	−5.20782e11	+	9.02021e11i	−0.176690	+	0.306036i
$186$		0			0
$187$	−1.45249e12	−	2.51578e12i	−0.464498	−	0.804534i
$188$		0			0
$189$	−6.31519e11	−	9.10922e10i	−0.190479	−	0.0274752i
$190$		0			0
$191$	3.05977e10	+	5.29968e10i	0.00870975	+	0.0150857i	0.870347	−	0.492438i	$-0.163894\pi$
$191$	3.05977e10	+	5.29968e10i	0.00870975	+	0.0150857i	−0.861638	+	0.507524i	$0.830561\pi$
$192$		0			0
$193$	−4.45854e11	+	7.72242e11i	−0.119847	+	0.207581i	−0.919707	−	0.392605i	$-0.871574\pi$
$193$	−4.45854e11	+	7.72242e11i	−0.119847	+	0.207581i	0.799860	+	0.600187i	$0.204907\pi$
$194$		0			0
$195$	−9.19885e11			−0.233638
$196$		0			0
$197$	1.84992e12			0.444211			0.222105	−	0.975023i	$-0.428707\pi$
$197$	1.84992e12			0.444211			0.222105	+	0.975023i	$0.428707\pi$
$198$		0			0
$199$	−1.14607e12	+	1.98506e12i	−0.260328	+	0.450901i	−0.966329	−	0.257310i	$-0.917164\pi$
$199$	−1.14607e12	+	1.98506e12i	−0.260328	+	0.450901i	0.706001	+	0.708210i	$0.250497\pi$
$200$		0			0
$201$	2.23812e11	+	3.87653e11i	0.0481176	+	0.0833422i
$202$		0			0
$203$	4.75374e12	+	6.85693e11i	0.967847	+	0.139605i
$204$		0			0
$205$	−1.76043e12	−	3.04915e12i	−0.339603	−	0.588210i
$206$		0			0
$207$	9.40992e11	−	1.62985e12i	0.172087	−	0.298064i
$208$		0			0
$209$	5.19725e12			0.901506
$210$		0			0
$211$	−3.84826e12			−0.633449			−0.316724	−	0.948518i	$-0.602583\pi$
$211$	−3.84826e12			−0.633449			−0.316724	+	0.948518i	$0.602583\pi$
$212$		0			0
$213$	−1.84183e12	+	3.19014e12i	−0.287847	+	0.498566i
$214$		0			0
$215$	7.62276e11	+	1.32030e12i	0.113162	+	0.196002i
$216$		0			0
$217$	−6.90241e12	+	8.76891e12i	−0.973806	+	1.23714i
$218$		0			0
$219$	−3.67568e12	−	6.36647e12i	−0.493055	−	0.853997i
$220$		0			0
$221$	2.75789e12	−	4.77680e12i	0.351900	−	0.609509i
$222$		0			0
$223$	1.00191e13			1.21661			0.608303	−	0.793705i	$-0.291850\pi$
$223$	1.00191e13			1.21661			0.608303	+	0.793705i	$0.291850\pi$
$224$		0			0
$225$	−4.04518e11			−0.0467664
$226$		0			0
$227$	−3.22157e12	+	5.57992e12i	−0.354752	+	0.614449i	−0.987075	−	0.160256i	$-0.948768\pi$
$227$	−3.22157e12	+	5.57992e12i	−0.354752	+	0.614449i	0.632323	+	0.774704i	$0.282101\pi$
$228$		0			0
$229$	−8.43324e12	−	1.46068e13i	−0.884911	−	1.53271i	−0.845816	−	0.533475i	$-0.820886\pi$
$229$	−8.43324e12	−	1.46068e13i	−0.884911	−	1.53271i	−0.0390952	−	0.999235i	$-0.512448\pi$
$230$		0			0
$231$	−1.23440e12	−	3.08744e12i	−0.123478	−	0.308840i
$232$		0			0
$233$	7.37785e12	+	1.27788e13i	0.703837	+	1.21908i	0.967110	+	0.254360i	$0.0818647\pi$
$233$	7.37785e12	+	1.27788e13i	0.703837	+	1.21908i	−0.263273	+	0.964721i	$0.584802\pi$
$234$		0			0
$235$	−2.79346e12	+	4.83842e12i	−0.254255	+	0.440383i
$236$		0			0
$237$	−8.49846e12			−0.738285
$238$		0			0
$239$	2.22602e13			1.84646			0.923231	−	0.384247i	$-0.125539\pi$
$239$	2.22602e13			1.84646			0.923231	+	0.384247i	$0.125539\pi$
$240$		0			0
$241$	−5.59484e12	+	9.69055e12i	−0.443296	+	0.767812i	−0.997932	−	0.0642818i	$-0.979524\pi$
$241$	−5.59484e12	+	9.69055e12i	−0.443296	+	0.767812i	0.554636	+	0.832093i	$0.312858\pi$
$242$		0			0
$243$	−4.23644e11	−	7.33773e11i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	3.00900e12	+	1.24527e13i	0.217775	+	0.901263i
$246$		0			0
$247$	4.93409e12	+	8.54610e12i	0.341487	+	0.591473i
$248$		0			0
$249$	−2.47154e12	+	4.28084e12i	−0.163633	+	0.283421i
$250$		0			0
$251$	2.65870e13			1.68447			0.842237	−	0.539107i	$-0.181238\pi$
$251$	2.65870e13			1.68447			0.842237	+	0.539107i	$0.181238\pi$
$252$		0			0
$253$	9.80749e12			0.594833
$254$		0			0
$255$	−7.43144e12	+	1.28716e13i	−0.431621	+	0.747589i
$256$		0			0
$257$	8.80530e12	+	1.52512e13i	0.489905	+	0.848541i	0.999933	−	0.0116173i	$-0.00369798\pi$
$257$	8.80530e12	+	1.52512e13i	0.489905	+	0.848541i	−0.510027	+	0.860158i	$0.670365\pi$
$258$		0			0
$259$	−2.65382e12	−	6.63767e12i	−0.141489	−	0.353889i
$260$		0			0
$261$	3.18897e12	+	5.52345e12i	0.162977	+	0.282285i
$262$		0			0
$263$	−9.38995e12	+	1.62639e13i	−0.460158	+	0.797016i	−0.998968	−	0.0454104i	$-0.985540\pi$
$263$	−9.38995e12	+	1.62639e13i	−0.460158	+	0.797016i	0.538811	+	0.842427i	$0.318874\pi$
$264$		0			0
$265$	−2.38329e13			−1.12028
$266$		0			0
$267$	−2.14918e13			−0.969307
$268$		0			0
$269$	−1.02550e13	+	1.77621e13i	−0.443912	+	0.768878i	−0.997976	−	0.0635960i	$-0.979743\pi$
$269$	−1.02550e13	+	1.77621e13i	−0.443912	+	0.768878i	0.554064	+	0.832474i	$0.313076\pi$
$270$		0			0
$271$	1.99679e13	+	3.45854e13i	0.829853	+	1.43735i	0.898153	+	0.439683i	$0.144909\pi$
$271$	1.99679e13	+	3.45854e13i	0.829853	+	1.43735i	−0.0683002	+	0.997665i	$0.521758\pi$
$272$		0			0
$273$	3.90495e12	−	4.96090e12i	0.155855	−	0.198000i
$274$		0			0
$275$	−1.05402e12	−	1.82562e12i	−0.0404129	−	0.0699972i
$276$		0			0
$277$	8.57932e12	−	1.48598e13i	0.316092	−	0.547488i	−0.663577	−	0.748108i	$-0.730962\pi$
$277$	8.57932e12	−	1.48598e13i	0.316092	−	0.547488i	0.979669	+	0.200620i	$0.0642957\pi$
$278$		0			0
$279$	−1.48191e13			−0.524807
$280$		0			0
$281$	−2.74808e12			−0.0935718			−0.0467859	−	0.998905i	$-0.514898\pi$
$281$	−2.74808e12			−0.0935718			−0.0467859	+	0.998905i	$0.514898\pi$
$282$		0			0
$283$	−6.50503e12	+	1.12670e13i	−0.213022	+	0.368965i	−0.952659	−	0.304041i	$-0.901664\pi$
$283$	−6.50503e12	+	1.12670e13i	−0.213022	+	0.368965i	0.739637	+	0.673006i	$0.234997\pi$
$284$		0			0
$285$	−1.32955e13	−	2.30284e13i	−0.418849	−	0.725467i
$286$		0			0
$287$	2.39170e13	+	3.44986e12i	0.725030	+	0.104581i
$288$		0			0
$289$	−2.74242e13	−	4.75001e13i	−0.800194	−	1.38598i
$290$		0			0
$291$	1.16498e13	−	2.01780e13i	0.327270	−	0.566848i
$292$		0			0
$293$	1.21317e13			0.328208			0.164104	−	0.986443i	$-0.447527\pi$
$293$	1.21317e13			0.328208			0.164104	+	0.986443i	$0.447527\pi$
$294$		0			0
$295$	−2.47708e13			−0.645534
$296$		0			0
$297$	2.20772e12	−	3.82388e12i	0.0554348	−	0.0960160i
$298$		0			0
$299$	9.31091e12	+	1.61270e13i	0.225320	+	0.390266i
$300$		0			0
$301$	−1.03562e13	−	1.49381e12i	−0.241594	−	0.0348482i
$302$		0			0
$303$	1.94916e13	+	3.37605e13i	0.438443	+	0.759406i
$304$		0			0
$305$	1.49219e13	−	2.58455e13i	0.323725	−	0.560708i
$306$		0			0
$307$	2.49166e13			0.521467			0.260734	−	0.965411i	$-0.416036\pi$
$307$	2.49166e13			0.521467			0.260734	+	0.965411i	$0.416036\pi$
$308$		0			0
$309$	−3.28582e13			−0.663548
$310$		0			0
$311$	2.40293e13	−	4.16199e13i	0.468337	−	0.811184i	−0.531008	−	0.847367i	$-0.678187\pi$
$311$	2.40293e13	−	4.16199e13i	0.468337	−	0.811184i	0.999345	+	0.0361830i	$0.0115199\pi$
$312$		0			0
$313$	−2.23518e13	−	3.87144e13i	−0.420550	−	0.728415i	0.575443	−	0.817842i	$-0.304830\pi$
$313$	−2.23518e13	−	3.87144e13i	−0.420550	−	0.728415i	−0.995993	+	0.0894273i	$0.971496\pi$
$314$		0			0
$315$	−1.05223e13	+	1.33677e13i	−0.191163	+	0.242856i
$316$		0			0
$317$	2.52513e13	+	4.37365e13i	0.443055	+	0.767394i	0.997914	−	0.0645502i	$-0.0205613\pi$
$317$	2.52513e13	+	4.37365e13i	0.443055	+	0.767394i	−0.554859	+	0.831944i	$0.687228\pi$
$318$		0			0
$319$	−1.66185e13	+	2.87841e13i	−0.281672	+	0.487870i
$320$		0			0
$321$	−2.00198e13			−0.327855
$322$		0			0
$323$	1.59444e14			2.52344
$324$		0			0
$325$	2.00131e12	−	3.46637e12i	0.0306165	−	0.0530293i
$326$		0			0
$327$	−2.75701e13	−	4.77528e13i	−0.407780	−	0.706295i
$328$		0			0
$329$	−1.42350e13	−	3.56043e13i	−0.203601	−	0.509243i
$330$		0			0
$331$	−5.47976e13	−	9.49122e13i	−0.758067	−	1.31301i	−0.943835	−	0.330416i	$-0.892811\pi$
$331$	−5.47976e13	−	9.49122e13i	−0.758067	−	1.31301i	0.185769	−	0.982594i	$-0.440523\pi$
$332$		0			0
$333$	4.74635e12	−	8.22092e12i	0.0635209	−	0.110021i
$334$		0			0
$335$	1.19348e13			0.154550
$336$		0			0
$337$	6.51104e13			0.815992			0.407996	−	0.912984i	$-0.366228\pi$
$337$	6.51104e13			0.815992			0.407996	+	0.912984i	$0.366228\pi$
$338$		0			0
$339$	2.10992e13	−	3.65448e13i	0.255957	−	0.443331i
$340$		0			0
$341$	−3.86131e13	−	6.68799e13i	−0.453509	−	0.785500i
$342$		0			0
$343$	−7.99304e13	−	3.66350e13i	−0.909064	−	0.416657i
$344$		0			0
$345$	−2.50893e13	−	4.34559e13i	−0.276365	−	0.478679i
$346$		0			0
$347$	1.58107e13	−	2.73849e13i	0.168709	−	0.292212i	−0.769257	−	0.638939i	$-0.779374\pi$
$347$	1.58107e13	−	2.73849e13i	0.168709	−	0.292212i	0.937966	+	0.346727i	$0.112707\pi$
$348$		0			0
$349$	−1.82337e14			−1.88510			−0.942549	−	0.334068i	$-0.891578\pi$
$349$	−1.82337e14			−1.88510			−0.942549	+	0.334068i	$0.891578\pi$
$350$		0			0
$351$	8.38373e12			0.0839940
$352$		0			0
$353$	5.26328e13	−	9.11627e13i	0.511088	−	0.885230i	−0.488829	−	0.872379i	$-0.662576\pi$
$353$	5.26328e13	−	9.11627e13i	0.511088	−	0.885230i	0.999917	−	0.0128510i	$-0.00409072\pi$
$354$		0			0
$355$	4.91080e13	+	8.50575e13i	0.462270	+	0.800676i
$356$		0			0
$357$	−3.78694e13	−	9.47181e13i	−0.345631	−	0.864485i
$358$		0			0
$359$	6.42748e13	+	1.11327e14i	0.568881	+	0.985330i	0.996677	+	0.0814552i	$0.0259568\pi$
$359$	6.42748e13	+	1.11327e14i	0.568881	+	0.985330i	−0.427796	+	0.903875i	$0.640710\pi$
$360$		0			0
$361$	−8.43838e13	+	1.46157e14i	−0.724385	+	1.25467i
$362$		0			0
$363$	−4.63208e13			−0.385736
$364$		0			0
$365$	−1.96007e14			−1.58365
$366$		0			0
$367$	9.45396e13	−	1.63747e14i	0.741225	−	1.28384i	−0.210712	−	0.977548i	$-0.567578\pi$
$367$	9.45396e13	−	1.63747e14i	0.741225	−	1.28384i	0.951938	−	0.306292i	$-0.0990884\pi$
$368$		0			0
$369$	1.60443e13	+	2.77896e13i	0.122089	+	0.211464i
$370$		0			0
$371$	1.01172e14	−	1.28530e14i	0.747313	−	0.949396i
$372$		0			0
$373$	−1.09656e14	−	1.89929e14i	−0.786381	−	1.36205i	−0.928171	−	0.372155i	$-0.878619\pi$
$373$	−1.09656e14	−	1.89929e14i	−0.786381	−	1.36205i	0.141790	−	0.989897i	$-0.454714\pi$
$374$		0			0
$375$	−4.38302e13	+	7.59162e13i	−0.305212	+	0.528643i
$376$		0			0
$377$	−6.31082e13			−0.426784
$378$		0			0
$379$	4.98932e13			0.327737			0.163869	−	0.986482i	$-0.447603\pi$
$379$	4.98932e13			0.327737			0.163869	+	0.986482i	$0.447603\pi$
$380$		0			0
$381$	−6.49541e13	+	1.12504e14i	−0.414495	+	0.717926i
$382$		0			0
$383$	1.22245e14	+	2.11734e14i	0.757945	+	1.31280i	0.943897	+	0.330240i	$0.107130\pi$
$383$	1.22245e14	+	2.11734e14i	0.757945	+	1.31280i	−0.185952	+	0.982559i	$0.559537\pi$
$384$		0			0
$385$	−8.77467e13	−	1.26569e13i	−0.528685	−	0.0762591i
$386$		0			0
$387$	−6.94730e12	−	1.20331e13i	−0.0406823	−	0.0704639i
$388$		0			0
$389$	1.42290e13	−	2.46453e13i	0.0809937	−	0.140285i	−0.822683	−	0.568500i	$-0.807524\pi$
$389$	1.42290e13	−	2.46453e13i	0.0809937	−	0.140285i	0.903677	+	0.428215i	$0.140857\pi$
$390$		0			0
$391$	3.00879e14			1.66502
$392$		0			0
$393$	−1.04625e12			−0.00562957
$394$		0			0
$395$	−1.13295e14	+	1.96233e14i	−0.592828	+	1.02681i
$396$		0			0
$397$	5.53607e13	+	9.58875e13i	0.281743	+	0.487994i	0.971814	−	0.235748i	$-0.0757540\pi$
$397$	5.53607e13	+	9.58875e13i	0.281743	+	0.487994i	−0.690071	+	0.723742i	$0.742421\pi$
$398$		0			0
$399$	1.80631e14	+	2.60548e13i	0.894214	+	0.128984i
$400$		0			0
$401$	−2.25564e13	−	3.90688e13i	−0.108636	−	0.188164i	0.806582	−	0.591123i	$-0.201315\pi$
$401$	−2.25564e13	−	3.90688e13i	−0.108636	−	0.188164i	−0.915218	+	0.402959i	$0.867982\pi$
$402$		0			0
$403$	7.33160e13	−	1.26987e14i	0.343574	−	0.595088i
$404$		0			0
$405$	−2.25909e13			−0.103022
$406$		0			0
$407$	4.94688e13			0.219565
$408$		0			0
$409$	1.07447e13	−	1.86104e13i	0.0464213	−	0.0804041i	−0.841881	−	0.539663i	$-0.818552\pi$
$409$	1.07447e13	−	1.86104e13i	0.0464213	−	0.0804041i	0.888302	+	0.459259i	$0.151885\pi$
$410$		0			0
$411$	6.63310e13	+	1.14889e14i	0.278989	+	0.483222i
$412$		0			0
$413$	1.05153e14	−	1.33588e14i	0.430623	−	0.547069i
$414$		0			0
$415$	6.58977e13	+	1.14138e14i	0.262788	+	0.455163i
$416$		0			0
$417$	2.41428e13	−	4.18166e13i	0.0937648	−	0.162405i
$418$		0			0
$419$	−4.15127e14			−1.57038			−0.785189	−	0.619256i	$-0.787434\pi$
$419$	−4.15127e14			−1.57038			−0.785189	+	0.619256i	$0.787434\pi$
$420$		0			0
$421$	1.01947e14			0.375683			0.187842	−	0.982199i	$-0.439851\pi$
$421$	1.01947e14			0.375683			0.187842	+	0.982199i	$0.439851\pi$
$422$		0			0
$423$	2.54593e13	−	4.40969e13i	0.0914061	−	0.158320i
$424$		0			0
$425$	−3.23358e13	−	5.60072e13i	−0.113121	−	0.195932i
$426$		0			0
$427$	7.60396e13	+	1.90189e14i	0.259231	+	0.648383i
$428$		0			0
$429$	2.18449e13	+	3.78364e13i	0.0725829	+	0.125717i
$430$		0			0
$431$	−4.54120e13	+	7.86560e13i	−0.147077	+	0.254746i	−0.930146	−	0.367190i	$-0.880320\pi$
$431$	−4.54120e13	+	7.86560e13i	−0.147077	+	0.254746i	0.783069	+	0.621935i	$0.213653\pi$
$432$		0			0
$433$	2.65109e14			0.837029			0.418515	−	0.908210i	$-0.362551\pi$
$433$	2.65109e14			0.837029			0.418515	+	0.908210i	$0.362551\pi$
$434$		0			0
$435$	1.70052e14			0.523470
$436$		0			0
$437$	−2.69149e14	+	4.66179e14i	−0.807875	+	1.39928i
$438$		0			0
$439$	9.01623e13	+	1.56166e14i	0.263919	+	0.457121i	0.967280	−	0.253712i	$-0.0816516\pi$
$439$	9.01623e13	+	1.56166e14i	0.263919	+	0.457121i	−0.703361	+	0.710833i	$0.748318\pi$
$440$		0			0
$441$	−2.74237e13	−	1.13493e14i	−0.0782913	−	0.324009i
$442$		0			0
$443$	−1.03229e14	−	1.78798e14i	−0.287463	−	0.497901i	0.685740	−	0.727846i	$-0.259479\pi$
$443$	−1.03229e14	−	1.78798e14i	−0.287463	−	0.497901i	−0.973203	+	0.229946i	$0.926145\pi$
$444$		0			0
$445$	−2.86514e14	+	4.96257e14i	−0.778333	+	1.34811i
$446$		0			0
$447$	−1.97380e14			−0.523133
$448$		0			0
$449$	2.98661e14			0.772366			0.386183	−	0.922422i	$-0.373793\pi$
$449$	2.98661e14			0.772366			0.386183	+	0.922422i	$0.373793\pi$
$450$		0			0
$451$	−8.36110e13	+	1.44819e14i	−0.211005	+	0.365471i
$452$		0			0
$453$	1.70147e13	+	2.94704e13i	0.0419069	+	0.0725848i
$454$		0			0
$455$	−6.24915e13	−	1.56302e14i	−0.150231	−	0.375753i
$456$		0			0
$457$	3.32118e13	+	5.75245e13i	0.0779386	+	0.134994i	0.902360	−	0.430982i	$-0.141833\pi$
$457$	3.32118e13	+	5.75245e13i	0.0779386	+	0.134994i	−0.824422	+	0.565976i	$0.808500\pi$
$458$		0			0
$459$	6.77294e13	−	1.17311e14i	0.155170	−	0.268762i
$460$		0			0
$461$	−6.90622e13			−0.154485			−0.0772424	−	0.997012i	$-0.524612\pi$
$461$	−6.90622e13			−0.154485			−0.0772424	+	0.997012i	$0.524612\pi$
$462$		0			0
$463$	−2.06831e14			−0.451772			−0.225886	−	0.974154i	$-0.572528\pi$
$463$	−2.06831e14			−0.451772			−0.225886	+	0.974154i	$0.572528\pi$
$464$		0			0
$465$	−1.97558e14	+	3.42181e14i	−0.421409	+	0.729902i
$466$		0			0
$467$	3.93370e14	+	6.81337e14i	0.819518	+	1.41945i	0.906038	+	0.423196i	$0.139092\pi$
$467$	3.93370e14	+	6.81337e14i	0.819518	+	1.41945i	−0.0865201	+	0.996250i	$0.527575\pi$
$468$		0			0
$469$	−5.06637e13	+	6.43638e13i	−0.103097	+	0.130976i
$470$		0			0
$471$	2.08600e14	+	3.61306e14i	0.414667	+	0.718224i
$472$		0			0
$473$	3.62041e13	−	6.27074e13i	0.0703108	−	0.121782i
$474$		0			0
$475$	1.15703e14			0.219548
$476$		0			0
$477$	2.17211e14			0.402745
$478$		0			0
$479$	−6.50604e13	+	1.12688e14i	−0.117889	+	0.204189i	−0.918931	−	0.394419i	$-0.870946\pi$
$479$	−6.50604e13	+	1.12688e14i	−0.117889	+	0.204189i	0.801042	+	0.598608i	$0.204279\pi$
$480$		0			0
$481$	4.69641e13	+	8.13441e13i	0.0831702	+	0.144055i
$482$		0			0
$483$	3.40861e14	+	4.91668e13i	0.590022	+	0.0851066i
$484$		0			0
$485$	−3.10613e14	−	5.37997e14i	−0.525581	−	0.910334i
$486$		0			0
$487$	−3.32294e13	+	5.75550e13i	−0.0549684	+	0.0952081i	−0.892200	−	0.451640i	$-0.850839\pi$
$487$	−3.32294e13	+	5.75550e13i	−0.0549684	+	0.0952081i	0.837232	+	0.546848i	$0.184172\pi$
$488$		0			0
$489$	2.10098e14			0.339800
$490$		0			0
$491$	−2.37328e13			−0.0375320			−0.0187660	−	0.999824i	$-0.505974\pi$
$491$	−2.37328e13			−0.0375320			−0.0187660	+	0.999824i	$0.505974\pi$
$492$		0			0
$493$	−5.09830e14	+	8.83052e14i	−0.788438	+	1.36561i
$494$		0			0
$495$	−5.88635e13	−	1.01954e14i	−0.0890261	−	0.154198i
$496$		0			0
$497$	−6.67177e14	−	9.62356e13i	−0.986917	−	0.142356i
$498$		0			0
$499$	−4.56733e14	−	7.91084e14i	−0.660859	−	1.14464i	−0.980390	−	0.197066i	$-0.936859\pi$
$499$	−4.56733e14	−	7.91084e14i	−0.660859	−	1.14464i	0.319531	−	0.947576i	$-0.396475\pi$
$500$		0			0
$501$	2.67235e14	−	4.62865e14i	0.378257	−	0.655160i
$502$		0			0
$503$	−4.77391e12			−0.00661075			−0.00330537	−	0.999995i	$-0.501052\pi$
$503$	−4.77391e12			−0.00661075			−0.00330537	+	0.999995i	$0.501052\pi$
$504$		0			0
$505$	1.03939e15			1.40824
$506$		0			0
$507$	1.76270e14	−	3.05308e14i	0.233687	−	0.404758i
$508$		0			0
$509$	−6.48244e14	−	1.12279e15i	−0.840990	−	1.45664i	−0.889059	−	0.457793i	$-0.848640\pi$
$509$	−6.48244e14	−	1.12279e15i	−0.840990	−	1.45664i	0.0480692	−	0.998844i	$-0.484693\pi$
$510$		0			0
$511$	8.32056e14	−	1.05705e15i	1.05642	−	1.34209i
$512$		0			0
$513$	1.21173e14	+	2.09879e14i	0.150578	+	0.260809i
$514$		0			0
$515$	−4.38043e14	+	7.58712e14i	−0.532815	+	0.922863i
$516$		0			0
$517$	2.65350e14			0.315952
$518$		0			0
$519$	1.96210e14			0.228719
$520$		0			0
$521$	−2.33019e14	+	4.03600e14i	−0.265940	+	0.460621i	−0.967809	−	0.251684i	$-0.919016\pi$
$521$	−2.33019e14	+	4.03600e14i	−0.265940	+	0.460621i	0.701870	+	0.712305i	$0.252349\pi$
$522$		0			0
$523$	6.61957e14	+	1.14654e15i	0.739725	+	1.28124i	0.952619	+	0.304166i	$0.0983777\pi$
$523$	6.61957e14	+	1.14654e15i	0.739725	+	1.28124i	−0.212894	+	0.977075i	$0.568289\pi$
$524$		0			0
$525$	−2.74805e13	−	6.87338e13i	−0.0300711	−	0.0752132i
$526$		0			0
$527$	−1.18459e15	−	2.05177e15i	−1.26943	−	2.19872i
$528$		0			0
$529$	−3.14938e13	+	5.45489e13i	−0.0330536	+	0.0572505i
$530$		0			0
$531$	2.25759e14			0.232073
$532$		0			0
$533$	−3.17510e14			−0.319711
$534$		0			0
$535$	−2.66890e14	+	4.62267e14i	−0.263261	+	0.455982i
$536$		0			0
$537$	3.23902e14	+	5.61014e14i	0.313007	+	0.542145i
$538$		0			0
$539$	4.40746e14	−	4.19485e14i	0.417302	−	0.397172i
$540$		0			0
$541$	−8.67334e14	−	1.50227e15i	−0.804639	−	1.39368i	−0.916534	−	0.399956i	$-0.869025\pi$
$541$	−8.67334e14	−	1.50227e15i	−0.804639	−	1.39368i	0.111895	−	0.993720i	$-0.464308\pi$
$542$		0			0
$543$	−1.18900e14	+	2.05940e14i	−0.108089	+	0.187216i
$544$		0			0
$545$	−1.47018e15			−1.30975
$546$		0			0
$547$	1.77536e15			1.55009			0.775043	−	0.631908i	$-0.217728\pi$
$547$	1.77536e15			1.55009			0.775043	+	0.631908i	$0.217728\pi$
$548$		0			0
$549$	−1.35997e14	+	2.35554e14i	−0.116381	+	0.201577i
$550$		0			0
$551$	−9.12129e14	−	1.57985e15i	−0.765108	−	1.32521i
$552$		0			0
$553$	−5.77334e14	−	1.44402e15i	−0.474722	−	1.18736i
$554$		0			0
$555$	−1.26550e14	−	2.19191e14i	−0.102012	−	0.176690i
$556$		0			0
$557$	5.78568e14	−	1.00211e15i	0.457247	−	0.791975i	−0.541567	−	0.840657i	$-0.682169\pi$
$557$	5.78568e14	−	1.00211e15i	0.457247	−	0.791975i	0.998814	+	0.0486825i	$0.0155023\pi$
$558$		0			0
$559$	1.37484e14			0.106534
$560$		0			0
$561$	7.05909e14			0.536356
$562$		0			0
$563$	−3.74197e13	+	6.48129e13i	−0.0278808	+	0.0482909i	−0.879629	−	0.475660i	$-0.842209\pi$
$563$	−3.74197e13	+	6.48129e13i	−0.0278808	+	0.0482909i	0.851748	+	0.523951i	$0.175543\pi$
$564$		0			0
$565$	−5.62559e14	−	9.74380e14i	−0.411056	−	0.711971i
$566$		0			0
$567$	9.58994e13	−	1.21832e14i	0.0687241	−	0.0873080i
$568$		0			0
$569$	7.17284e14	+	1.24237e15i	0.504166	+	0.873242i	0.999988	+	0.00481770i	$0.00153353\pi$
$569$	7.17284e14	+	1.24237e15i	0.504166	+	0.873242i	−0.495822	+	0.868424i	$0.665133\pi$
$570$		0			0
$571$	5.10440e14	−	8.84108e14i	0.351922	−	0.609546i	−0.634665	−	0.772788i	$-0.718862\pi$
$571$	5.10440e14	−	8.84108e14i	0.351922	−	0.609546i	0.986586	+	0.163242i	$0.0521950\pi$
$572$		0			0
$573$	−1.48705e13			−0.0100571
$574$		0			0
$575$	2.18338e14			0.144862
$576$		0			0
$577$	3.42848e14	−	5.93830e14i	0.223169	−	0.386540i	−0.732599	−	0.680660i	$-0.761693\pi$
$577$	3.42848e14	−	5.93830e14i	0.223169	−	0.386540i	0.955769	+	0.294120i	$0.0950264\pi$
$578$		0			0
$579$	−1.08343e14	−	1.87655e14i	−0.0691938	−	0.119847i
$580$		0			0
$581$	−8.95281e14	−	1.29138e14i	−0.561036	−	0.0809255i
$582$		0			0
$583$	5.65970e14	+	9.80288e14i	0.348029	+	0.602805i
$584$		0			0
$585$	1.11766e14	−	1.93584e14i	0.0674454	−	0.116819i
$586$		0			0
$587$	−2.45428e15			−1.45350			−0.726749	−	0.686903i	$-0.758970\pi$
$587$	−2.45428e15			−1.45350			−0.726749	+	0.686903i	$0.758970\pi$
$588$		0			0
$589$	4.23866e15			2.46374
$590$		0			0
$591$	−2.24766e14	+	3.89305e14i	−0.128233	+	0.222105i
$592$		0			0
$593$	1.66959e14	+	2.89182e14i	0.0934995	+	0.161946i	0.908981	−	0.416837i	$-0.136861\pi$
$593$	1.66959e14	+	2.89182e14i	0.0934995	+	0.161946i	−0.815482	+	0.578783i	$0.803528\pi$
$594$		0			0
$595$	−2.69193e15	−	3.88293e14i	−1.47986	−	0.213460i
$596$		0			0
$597$	−2.78496e14	−	4.82369e14i	−0.150300	−	0.260328i
$598$		0			0
$599$	−1.76178e14	+	3.05148e14i	−0.0933476	+	0.161683i	−0.908918	−	0.416975i	$-0.863090\pi$
$599$	−1.76178e14	+	3.05148e14i	−0.0933476	+	0.161683i	0.815570	+	0.578658i	$0.196423\pi$
$600$		0			0
$601$	−1.86713e15			−0.971327			−0.485663	−	0.874146i	$-0.661422\pi$
$601$	−1.86713e15			−0.971327			−0.485663	+	0.874146i	$0.661422\pi$
$602$		0			0
$603$	−1.08772e14			−0.0555614
$604$		0			0
$605$	−6.17516e14	+	1.06957e15i	−0.309738	+	0.536481i
$606$		0			0
$607$	1.87189e14	+	3.24221e14i	0.0922025	+	0.159699i	0.908438	−	0.418020i	$-0.137276\pi$
$607$	1.87189e14	+	3.24221e14i	0.0922025	+	0.159699i	−0.816235	+	0.577720i	$0.803943\pi$
$608$		0			0
$609$	−7.21879e14	+	9.17084e14i	−0.349196	+	0.443623i
$610$		0			0
$611$	2.51914e14	+	4.36328e14i	0.119681	+	0.207294i
$612$		0			0
$613$	1.64601e14	−	2.85097e14i	0.0768067	−	0.133033i	−0.825064	−	0.565040i	$-0.808861\pi$
$613$	1.64601e14	−	2.85097e14i	0.0768067	−	0.133033i	0.901871	+	0.432006i	$0.142194\pi$
$614$		0			0
$615$	8.55567e14			0.392140
$616$		0			0
$617$	4.23369e15			1.90612			0.953061	−	0.302777i	$-0.0979139\pi$
$617$	4.23369e15			1.90612			0.953061	+	0.302777i	$0.0979139\pi$
$618$		0			0
$619$	−1.66928e15	+	2.89129e15i	−0.738298	+	1.27877i	0.214963	+	0.976622i	$0.431037\pi$
$619$	−1.66928e15	+	2.89129e15i	−0.738298	+	1.27877i	−0.953261	+	0.302148i	$0.902296\pi$
$620$		0			0
$621$	2.28661e14	+	3.96053e14i	0.0993547	+	0.172087i
$622$		0			0
$623$	−1.46003e15	−	3.65179e15i	−0.623270	−	1.55891i
$624$		0			0
$625$	1.00138e15	+	1.73444e15i	0.420008	+	0.727476i
$626$		0			0
$627$	−6.31465e14	+	1.09373e15i	−0.260242	+	0.450753i
$628$		0			0
$629$	1.51763e15			0.614592
$630$		0			0
$631$	−7.53088e14			−0.299698			−0.149849	−	0.988709i	$-0.547879\pi$
$631$	−7.53088e14			−0.299698			−0.149849	+	0.988709i	$0.547879\pi$
$632$		0			0
$633$	4.67564e14	−	8.09845e14i	0.182861	−	0.316724i
$634$		0			0
$635$	1.73185e15	+	2.99964e15i	0.665662	+	1.15296i
$636$		0			0
$637$	1.10821e15	+	3.26497e14i	0.418654	+	0.123342i
$638$		0			0
$639$	−4.47565e14	−	7.75205e14i	−0.166189	−	0.287847i
$640$		0			0
$641$	−7.70022e14	+	1.33372e15i	−0.281050	+	0.486793i	−0.971644	−	0.236450i	$-0.924016\pi$
$641$	−7.70022e14	+	1.33372e15i	−0.281050	+	0.486793i	0.690594	+	0.723243i	$0.257349\pi$
$642$		0			0
$643$	−4.35931e15			−1.56407			−0.782037	−	0.623232i	$-0.785819\pi$
$643$	−4.35931e15			−1.56407			−0.782037	+	0.623232i	$0.785819\pi$
$644$		0			0
$645$	−3.70466e14			−0.130668
$646$		0			0
$647$	−1.90014e15	+	3.29114e15i	−0.658890	+	1.14123i	0.322014	+	0.946735i	$0.395640\pi$
$647$	−1.90014e15	+	3.29114e15i	−0.658890	+	1.14123i	−0.980903	+	0.194496i	$0.937693\pi$
$648$		0			0
$649$	5.88242e14	+	1.01887e15i	0.200544	+	0.347353i
$650$		0			0
$651$	−1.00672e15	−	2.51800e15i	−0.337454	−	0.844033i
$652$		0			0
$653$	−1.23183e15	−	2.13359e15i	−0.406001	−	0.703215i	0.588436	−	0.808544i	$-0.299744\pi$
$653$	−1.23183e15	−	2.13359e15i	−0.406001	−	0.703215i	−0.994437	+	0.105329i	$0.966410\pi$
$654$		0			0
$655$	−1.39478e13	+	2.41583e13i	−0.00452043	+	0.00782961i
$656$		0			0
$657$	1.78638e15			0.569331
$658$		0			0
$659$	4.32943e15			1.35694			0.678471	−	0.734627i	$-0.262643\pi$
$659$	4.32943e15			1.35694			0.678471	+	0.734627i	$0.262643\pi$
$660$		0			0
$661$	−1.08449e15	+	1.87839e15i	−0.334284	+	0.578998i	−0.983347	−	0.181737i	$-0.941828\pi$
$661$	−1.08449e15	+	1.87839e15i	−0.334284	+	0.578998i	0.649063	+	0.760735i	$0.275161\pi$
$662$		0			0
$663$	6.70167e14	+	1.16076e15i	0.203170	+	0.351900i
$664$		0			0
$665$	3.00967e15	−	3.82352e15i	0.897427	−	1.14010i
$666$		0			0
$667$	−1.72124e15	−	2.98127e15i	−0.504834	−	0.874399i
$668$		0			0
$669$	−1.21732e15	+	2.10845e15i	−0.351204	+	0.608303i
$670$		0			0
$671$	−1.41743e15			−0.402279
$672$		0			0
$673$	8.47908e13			0.0236737			0.0118368	−	0.999930i	$-0.496232\pi$
$673$	8.47908e13			0.0236737			0.0118368	+	0.999930i	$0.496232\pi$
$674$		0			0
$675$	4.91489e13	−	8.51285e13i	0.0135003	−	0.0233832i
$676$		0			0
$677$	2.98941e15	+	5.17782e15i	0.807883	+	1.39929i	0.914328	+	0.404976i	$0.132720\pi$
$677$	2.98941e15	+	5.17782e15i	0.807883	+	1.39929i	−0.106445	+	0.994319i	$0.533947\pi$
$678$		0			0
$679$	4.21996e15	+	6.08700e14i	1.12208	+	0.161853i
$680$		0			0
$681$	−7.82841e14	−	1.35592e15i	−0.204816	−	0.354752i
$682$		0			0
$683$	−1.50741e15	+	2.61091e15i	−0.388077	+	0.672169i	−0.992191	−	0.124729i	$-0.960194\pi$
$683$	−1.50741e15	+	2.61091e15i	−0.388077	+	0.672169i	0.604114	+	0.796898i	$0.293527\pi$
$684$		0			0
$685$	3.53711e15			0.896088
$686$		0			0
$687$	4.09856e15			1.02181
$688$		0			0
$689$	−1.07463e15	+	1.86131e15i	−0.263664	+	0.456680i
$690$		0			0
$691$	1.26172e15	+	2.18537e15i	0.304673	+	0.527710i	0.977189	−	0.212374i	$-0.0681194\pi$
$691$	1.26172e15	+	2.18537e15i	0.304673	+	0.527710i	−0.672515	+	0.740083i	$0.734786\pi$
$692$		0			0
$693$	7.99714e14	+	1.15353e14i	0.190065	+	0.0274155i
$694$		0			0
$695$	−6.43710e14	−	1.11494e15i	−0.150582	−	0.260816i
$696$		0			0
$697$	−2.56506e15	+	4.44281e15i	−0.590632	+	1.02300i
$698$		0			0
$699$	−3.58563e15			−0.812721
$700$		0			0
$701$	6.09678e15			1.36035			0.680176	−	0.733049i	$-0.261903\pi$
$701$	6.09678e15			1.36035			0.680176	+	0.733049i	$0.261903\pi$
$702$		0			0
$703$	−1.35758e15	+	2.35140e15i	−0.298203	+	0.516502i
$704$		0			0
$705$	−6.78812e14	−	1.17574e15i	−0.146794	−	0.254255i
$706$		0			0
$707$	−4.41227e15	+	5.60541e15i	−0.939411	+	1.19344i
$708$		0			0
$709$	3.01210e15	+	5.21711e15i	0.631415	+	1.09364i	0.987263	+	0.159099i	$0.0508589\pi$
$709$	3.01210e15	+	5.21711e15i	0.631415	+	1.09364i	−0.355848	+	0.934544i	$0.615808\pi$
$710$		0			0
$711$	1.03256e15	−	1.78845e15i	0.213125	−	0.369143i
$712$		0			0
$713$	7.99860e15			1.62563
$714$		0			0
$715$	1.16488e15			0.233130
$716$		0			0
$717$	−2.70461e15	+	4.68452e15i	−0.533027	+	0.923231i
$718$		0			0
$719$	−7.19170e13	−	1.24564e14i	−0.0139580	−	0.0241759i	0.858962	−	0.512039i	$-0.171110\pi$
$719$	−7.19170e13	−	1.24564e14i	−0.0139580	−	0.0241759i	−0.872920	+	0.487863i	$0.837776\pi$
$720$		0			0
$721$	−2.23219e15	−	5.58311e15i	−0.426665	−	1.06717i
$722$		0			0
$723$	−1.35955e15	−	2.35480e15i	−0.255937	−	0.443296i
$724$		0			0
$725$	−3.69967e14	+	6.40801e14i	−0.0685968	+	0.118813i
$726$		0			0
$727$	−8.32629e15			−1.52059			−0.760295	−	0.649578i	$-0.774946\pi$
$727$	−8.32629e15			−1.52059			−0.760295	+	0.649578i	$0.774946\pi$
$728$		0			0
$729$	2.05891e14			0.0370370
$730$		0			0
$731$	1.11069e15	−	1.92377e15i	0.196810	−	0.340884i
$732$		0			0
$733$	−1.34131e15	−	2.32322e15i	−0.234131	−	0.405526i	0.724889	−	0.688866i	$-0.241891\pi$
$733$	−1.34131e15	−	2.32322e15i	−0.234131	−	0.405526i	−0.959020	+	0.283339i	$0.908558\pi$
$734$		0			0
$735$	−2.98620e15	−	8.79782e14i	−0.513498	−	0.151285i
$736$		0			0
$737$	−2.83420e14	−	4.90898e14i	−0.0480131	−	0.0831611i
$738$		0			0
$739$	4.12901e15	−	7.15166e15i	0.689131	−	1.19361i	−0.282989	−	0.959123i	$-0.591326\pi$
$739$	4.12901e15	−	7.15166e15i	0.689131	−	1.19361i	0.972119	−	0.234486i	$-0.0753408\pi$
$740$		0			0
$741$	−2.39797e15			−0.394315
$742$		0			0
$743$	2.41601e15			0.391435			0.195718	−	0.980660i	$-0.437296\pi$
$743$	2.41601e15			0.391435			0.195718	+	0.980660i	$0.437296\pi$
$744$		0			0
$745$	−2.63133e15	+	4.55760e15i	−0.420065	+	0.727574i
$746$		0			0
$747$	−6.00585e14	−	1.04024e15i	−0.0944737	−	0.163633i
$748$		0			0
$749$	−1.36003e15	−	3.40167e15i	−0.210813	−	0.527281i
$750$		0			0
$751$	−5.49081e15	−	9.51036e15i	−0.838719	−	1.45270i	−0.890966	−	0.454070i	$-0.849972\pi$
$751$	−5.49081e15	−	9.51036e15i	−0.838719	−	1.45270i	0.0522466	−	0.998634i	$-0.483362\pi$
$752$		0			0
$753$	−3.23033e15	+	5.59509e15i	−0.486266	+	0.842237i
$754$		0			0
$755$	9.07314e14			0.134601
$756$		0			0
$757$	−3.46816e15			−0.507075			−0.253537	−	0.967326i	$-0.581594\pi$
$757$	−3.46816e15			−0.507075			−0.253537	+	0.967326i	$0.581594\pi$
$758$		0			0
$759$	−1.19161e15	+	2.06393e15i	−0.171714	+	0.297417i
$760$		0			0
$761$	3.37973e15	+	5.85386e15i	0.480028	+	0.831432i	0.999738	−	0.0229104i	$-0.00729325\pi$
$761$	3.37973e15	+	5.85386e15i	0.480028	+	0.831432i	−0.519710	+	0.854343i	$0.673960\pi$
$762$		0			0
$763$	6.24098e15	−	7.92862e15i	0.873711	−	1.10997i
$764$		0			0
$765$	−1.80584e15	−	3.12781e15i	−0.249196	−	0.431621i
$766$		0			0
$767$	−1.11692e15	+	1.93455e15i	−0.151931	+	0.263152i
$768$		0			0
$769$	−8.71762e15			−1.16897			−0.584485	−	0.811405i	$-0.698703\pi$
$769$	−8.71762e15			−1.16897			−0.584485	+	0.811405i	$0.698703\pi$
$770$		0			0
$771$	−4.27938e15			−0.565694
$772$		0			0
$773$	−1.98343e15	+	3.43541e15i	−0.258482	+	0.447704i	−0.965835	−	0.259156i	$-0.916556\pi$
$773$	−1.98343e15	+	3.43541e15i	−0.258482	+	0.447704i	0.707354	+	0.706860i	$0.249889\pi$
$774$		0			0
$775$	−8.59618e14	−	1.48890e15i	−0.110445	−	0.191296i
$776$		0			0
$777$	1.71930e15	+	2.47997e14i	0.217789	+	0.0314145i
$778$		0			0
$779$	−4.58910e15	−	7.94856e15i	−0.573155	−	0.992733i
$780$		0			0
$781$	2.33237e15	−	4.03979e15i	0.287222	−	0.497482i
$782$		0			0
$783$	−1.54984e15			−0.188190
$784$		0			0
$785$	1.11236e16			1.33188
$786$		0			0
$787$	4.39520e14	−	7.61272e14i	0.0518941	−	0.0898832i	−0.838911	−	0.544268i	$-0.816808\pi$
$787$	4.39520e14	−	7.61272e14i	0.0518941	−	0.0898832i	0.890806	+	0.454385i	$0.150141\pi$
$788$		0			0
$789$	−2.28176e15	−	3.95212e15i	−0.265672	−	0.460158i
$790$		0			0
$791$	7.64288e15	+	1.10243e15i	0.877579	+	0.126585i
$792$		0			0
$793$	−1.34566e15	−	2.33075e15i	−0.152382	−	0.263933i
$794$		0			0
$795$	2.89570e15	−	5.01550e15i	0.323396	−	0.560138i
$796$		0			0
$797$	1.25139e16			1.37839			0.689193	−	0.724578i	$-0.257965\pi$
$797$	1.25139e16			1.37839			0.689193	+	0.724578i	$0.257965\pi$
$798$		0			0
$799$	8.14053e15			0.884393
$800$		0			0
$801$	2.61126e15	−	4.52283e15i	0.279815	−	0.484653i
$802$		0			0
$803$	4.65464e15	+	8.06208e15i	0.491984	+	0.852141i
$804$		0			0
$805$	5.67941e15	−	7.21519e15i	0.592142	−	0.752264i
$806$		0			0
$807$	−2.49196e15	−	4.31620e15i	−0.256293	−	0.443912i
$808$		0			0
$809$	5.81136e15	−	1.00656e16i	0.589605	−	1.02123i	−0.404679	−	0.914459i	$-0.632617\pi$
$809$	5.81136e15	−	1.00656e16i	0.589605	−	1.02123i	0.994284	−	0.106767i	$-0.0340500\pi$
$810$		0			0
$811$	−4.78327e15			−0.478752			−0.239376	−	0.970927i	$-0.576943\pi$
$811$	−4.78327e15			−0.478752			−0.239376	+	0.970927i	$0.576943\pi$
$812$		0			0
$813$	−9.70440e15			−0.958232
$814$		0			0
$815$	2.80088e15	−	4.85127e15i	0.272853	−	0.472595i
$816$		0			0
$817$	1.98711e15	+	3.44178e15i	0.190986	+	0.330797i
$818$		0			0
$819$	5.69541e14	+	1.42452e15i	0.0540086	+	0.135085i
$820$		0			0
$821$	−4.45650e15	−	7.71888e15i	−0.416971	−	0.722216i	0.578662	−	0.815568i	$-0.303575\pi$
$821$	−4.45650e15	−	7.71888e15i	−0.416971	−	0.722216i	−0.995633	+	0.0933519i	$0.970242\pi$
$822$		0			0
$823$	−5.97971e15	+	1.03572e16i	−0.552054	+	0.956185i	0.446073	+	0.894997i	$0.352822\pi$
$823$	−5.97971e15	+	1.03572e16i	−0.552054	+	0.956185i	−0.998126	+	0.0611881i	$0.980511\pi$
$824$		0			0
$825$	5.12255e14			0.0466648
$826$		0			0
$827$	−1.33380e16			−1.19897			−0.599486	−	0.800385i	$-0.704628\pi$
$827$	−1.33380e16			−1.19897			−0.599486	+	0.800385i	$0.704628\pi$
$828$		0			0
$829$	−9.19823e15	+	1.59318e16i	−0.815933	+	1.41324i	0.0927232	+	0.995692i	$0.470443\pi$
$829$	−9.19823e15	+	1.59318e16i	−0.815933	+	1.41324i	−0.908656	+	0.417545i	$0.862891\pi$
$830$		0			0
$831$	2.08477e15	+	3.61094e15i	0.182496	+	0.316092i
$832$		0			0
$833$	1.35214e16	−	1.28692e16i	1.16809	−	1.11174i
$834$		0			0
$835$	−7.12519e15	−	1.23412e16i	−0.607465	−	1.05216i
$836$		0			0
$837$	1.80052e15	−	3.11860e15i	0.151499	−	0.262403i
$838$		0			0
$839$	−9.68002e15			−0.803869			−0.401935	−	0.915668i	$-0.631662\pi$
$839$	−9.68002e15			−0.803869			−0.401935	+	0.915668i	$0.631662\pi$
$840$		0			0
$841$	−5.34159e14			−0.0437817
$842$		0			0
$843$	3.33892e14	−	5.78318e14i	0.0270118	−	0.0467859i
$844$		0			0
$845$	−4.69981e15	−	8.14032e15i	−0.375291	−	0.650024i
$846$		0			0
$847$	−3.14676e15	−	7.87061e15i	−0.248030	−	0.620368i
$848$		0			0
$849$	−1.58072e15	−	2.73789e15i	−0.122988	−	0.213022i
$850$		0			0
$851$	−2.56183e15	+	4.43722e15i	−0.196761	+	0.340799i
$852$		0			0
$853$	4.53181e15			0.343599			0.171800	−	0.985132i	$-0.445042\pi$
$853$	4.53181e15			0.343599			0.171800	+	0.985132i	$0.445042\pi$
$854$		0			0
$855$	6.46160e15			0.483645
$856$		0			0
$857$	4.76035e15	−	8.24516e15i	0.351758	−	0.609263i	−0.634800	−	0.772677i	$-0.718917\pi$
$857$	4.76035e15	−	8.24516e15i	0.351758	−	0.609263i	0.986558	+	0.163414i	$0.0522507\pi$
$858$		0			0
$859$	−7.08779e15	−	1.22764e16i	−0.517069	−	0.895589i	−0.999804	−	0.0198225i	$-0.993690\pi$
$859$	−7.08779e15	−	1.22764e16i	−0.517069	−	0.895589i	0.482735	−	0.875767i	$-0.339643\pi$
$860$		0			0
$861$	−3.63192e15	+	4.61403e15i	−0.261589	+	0.332325i
$862$		0			0
$863$	6.72665e15	+	1.16509e16i	0.478343	+	0.828515i	0.999692	−	0.0248291i	$-0.00790416\pi$
$863$	6.72665e15	+	1.16509e16i	0.478343	+	0.828515i	−0.521348	+	0.853344i	$0.674571\pi$
$864$		0			0
$865$	2.61574e15	−	4.53059e15i	0.183656	−	0.318102i
$866$		0			0
$867$	1.33281e16			0.923985
$868$		0			0
$869$	1.07619e16			0.736681
$870$		0			0
$871$	5.38139e14	−	9.32084e14i	0.0363743	−	0.0630022i
$872$		0			0
$873$	2.83089e15	+	4.90325e15i	0.188949	+	0.327270i
$874$		0			0
$875$	−1.58769e16	−	2.29013e15i	−1.04646	−	0.150944i
$876$		0			0
$877$	8.63403e14	+	1.49546e15i	0.0561973	+	0.0973366i	0.892755	−	0.450542i	$-0.148769\pi$
$877$	8.63403e14	+	1.49546e15i	0.0561973	+	0.0973366i	−0.836558	+	0.547878i	$0.815436\pi$
$878$		0			0
$879$	−1.47400e15	+	2.55304e15i	−0.0947454	+	0.164104i
$880$		0			0
$881$	−3.12123e16			−1.98134			−0.990670	−	0.136285i	$-0.956484\pi$
$881$	−3.12123e16			−1.98134			−0.990670	+	0.136285i	$0.956484\pi$
$882$		0			0
$883$	−5.18187e14			−0.0324865			−0.0162432	−	0.999868i	$-0.505171\pi$
$883$	−5.18187e14			−0.0324865			−0.0162432	+	0.999868i	$0.505171\pi$
$884$		0			0
$885$	3.00965e15	−	5.21287e15i	0.186350	−	0.322767i
$886$		0			0
$887$	9.54428e15	+	1.65312e16i	0.583664	+	1.01094i	0.995041	+	0.0994704i	$0.0317149\pi$
$887$	9.54428e15	+	1.65312e16i	0.583664	+	1.01094i	−0.411376	+	0.911466i	$0.634952\pi$
$888$		0			0
$889$	−2.35287e16	−	3.39385e15i	−1.42114	−	0.204990i
$890$		0			0
$891$	5.36475e14	+	9.29202e14i	0.0320053	+	0.0554348i
$892$		0			0
$893$	−7.28204e15	+	1.26129e16i	−0.429112	+	0.743243i
$894$		0			0
$895$	1.72721e16			1.00535
$896$		0			0
$897$	−4.52510e15			−0.260178
$898$		0			0
$899$	−1.35534e16	+	2.34751e16i	−0.769785	+	1.33331i
$900$		0			0
$901$	1.73631e16	+	3.00737e16i	0.974183	+	1.68733i
$902$		0			0
$903$	1.57264e15	−	1.99791e15i	0.0871662	−	0.110737i
$904$		0			0
$905$	3.17017e15	+	5.49090e15i	0.173586	+	0.300660i
$906$		0			0
$907$	−7.47127e15	+	1.29406e16i	−0.404161	+	0.700028i	−0.994223	−	0.107330i	$-0.965770\pi$
$907$	−7.47127e15	+	1.29406e16i	−0.404161	+	0.700028i	0.590062	+	0.807358i	$0.299103\pi$
$908$		0			0
$909$	−9.47293e15			−0.506271
$910$		0			0
$911$	2.17361e16			1.14770			0.573852	−	0.818959i	$-0.305448\pi$
$911$	2.17361e16			1.14770			0.573852	+	0.818959i	$0.305448\pi$
$912$		0			0
$913$	3.12980e15	−	5.42097e15i	0.163278	−	0.282805i
$914$		0			0
$915$	3.62603e15	+	6.28047e15i	0.186903	+	0.323725i
$916$		0			0
$917$	−7.10758e13	−	1.77773e14i	−0.00361985	−	0.00905388i
$918$		0			0
$919$	1.69066e16	+	2.92831e16i	0.850787	+	1.47361i	0.880500	+	0.474047i	$0.157207\pi$
$919$	1.69066e16	+	2.92831e16i	0.850787	+	1.47361i	−0.0297130	+	0.999558i	$0.509459\pi$
$920$		0			0
$921$	−3.02736e15	+	5.24354e15i	−0.150535	+	0.260734i
$922$		0			0
$923$	8.85710e15			0.435194
$924$		0			0
$925$	1.10129e15			0.0534716
$926$		0			0
$927$	3.99227e15	−	6.91482e15i	0.191550	−	0.331774i
$928$		0			0
$929$	−8.17628e15	−	1.41617e16i	−0.387676	−	0.671475i	0.604460	−	0.796635i	$-0.293389\pi$
$929$	−8.17628e15	−	1.41617e16i	−0.387676	−	0.671475i	−0.992137	+	0.125160i	$0.960056\pi$
$930$		0			0
$931$	7.84390e15	+	3.24620e16i	0.367543	+	1.52108i
$932$		0			0
$933$	5.83912e15	+	1.01136e16i	0.270395	+	0.468337i
$934$		0			0
$935$	9.41069e15	−	1.62998e16i	0.430683	−	0.745964i
$936$		0			0
$937$	4.22063e15			0.190902			0.0954508	−	0.995434i	$-0.469571\pi$
$937$	4.22063e15			0.190902			0.0954508	+	0.995434i	$0.469571\pi$
$938$		0			0
$939$	1.08630e16			0.485610
$940$		0			0
$941$	1.69807e16	−	2.94115e16i	0.750262	−	1.29949i	−0.197433	−	0.980316i	$-0.563261\pi$
$941$	1.69807e16	−	2.94115e16i	0.750262	−	1.29949i	0.947695	−	0.319176i	$-0.103406\pi$
$942$		0			0
$943$	−8.65989e15	−	1.49994e16i	−0.378180	−	0.655027i
$944$		0			0
$945$	−1.53469e15	−	3.83854e15i	−0.0662439	−	0.165688i
$946$		0			0
$947$	1.89987e16	+	3.29068e16i	0.810588	+	1.40398i	0.912453	+	0.409181i	$0.134186\pi$
$947$	1.89987e16	+	3.29068e16i	0.810588	+	1.40398i	−0.101865	+	0.994798i	$0.532481\pi$
$948$		0			0
$949$	−8.83793e15	+	1.53077e16i	−0.372723	+	0.645575i
$950$		0			0
$951$	−1.22721e16			−0.511596
$952$		0			0
$953$	−2.34699e16			−0.967163			−0.483582	−	0.875299i	$-0.660664\pi$
$953$	−2.34699e16			−0.967163			−0.483582	+	0.875299i	$0.660664\pi$
$954$		0			0
$955$	−1.98243e14	+	3.43367e14i	−0.00807568	+	0.0139875i
$956$		0			0
$957$	−4.03830e15	−	6.99454e15i	−0.162623	−	0.281672i
$958$		0			0
$959$	−1.50152e16	+	1.90755e16i	−0.597762	+	0.759405i
$960$		0			0
$961$	−1.87870e16	−	3.25401e16i	−0.739401	−	1.28068i
$962$		0			0
$963$	2.43241e15	−	4.21305e15i	0.0946437	−	0.163928i
$964$		0			0
$965$	−5.77739e15			−0.222245
$966$		0			0
$967$	3.48719e16			1.32627			0.663133	−	0.748502i	$-0.269227\pi$
$967$	3.48719e16			1.32627			0.663133	+	0.748502i	$0.269227\pi$
$968$		0			0
$969$	−1.93724e16	+	3.35540e16i	−0.728454	+	1.26172i
$970$		0			0
$971$	−1.10378e16	−	1.91180e16i	−0.410371	−	0.710783i	0.584559	−	0.811351i	$-0.301267\pi$
$971$	−1.10378e16	−	1.91180e16i	−0.410371	−	0.710783i	−0.994930	+	0.100568i	$0.967934\pi$
$972$		0			0
$973$	8.74540e15	+	1.26146e15i	0.321484	+	0.0463718i
$974$		0			0
$975$	4.86318e14	+	8.42327e14i	0.0176764	+	0.0306165i
$976$		0			0
$977$	−2.07614e16	+	3.59598e16i	−0.746168	+	1.29240i	0.203479	+	0.979079i	$0.434775\pi$
$977$	−2.07614e16	+	3.59598e16i	−0.746168	+	1.29240i	−0.949647	+	0.313322i	$0.898558\pi$
$978$		0			0
$979$	2.72158e16			0.967201
$980$		0			0
$981$	1.33991e16			0.470863
$982$		0			0
$983$	−9.25256e14	+	1.60259e15i	−0.0321527	+	0.0556902i	−0.881654	−	0.471896i	$-0.843570\pi$
$983$	−9.25256e14	+	1.60259e15i	−0.0321527	+	0.0556902i	0.849501	+	0.527587i	$0.176903\pi$
$984$		0			0
$985$	5.99283e15	+	1.03799e16i	0.205936	+	0.356692i
$986$		0			0
$987$	9.22228e15	+	1.33025e15i	0.313396	+	0.0452053i
$988$		0			0
$989$	3.74979e15	+	6.49483e15i	0.126017	+	0.218267i
$990$		0			0
$991$	2.85376e16	−	4.94286e16i	0.948447	−	1.64276i	0.199748	−	0.979847i	$-0.435988\pi$
$991$	2.85376e16	−	4.94286e16i	0.948447	−	1.64276i	0.748698	−	0.662911i	$-0.230679\pi$
$992$		0			0
$993$	2.66316e16			0.875340
$994$		0			0
$995$	−1.48508e16			−0.482752
$996$		0			0
$997$	1.99297e16	−	3.45192e16i	0.640733	−	1.10978i	−0.344536	−	0.938773i	$-0.611964\pi$
$997$	1.99297e16	−	3.45192e16i	0.640733	−	1.10978i	0.985269	−	0.171009i	$-0.0547028\pi$
$998$		0			0
$999$	1.15336e15	+	1.99768e15i	0.0366738	+	0.0635209i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.12.i.b.25.6	✓	16
3.2	odd	2		252.12.k.d.109.3		16
7.2	even	3	inner	84.12.i.b.37.6	yes	16
21.2	odd	6		252.12.k.d.37.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.12.i.b.25.6	✓	16	1.1	even	1	trivial
84.12.i.b.37.6	yes	16	7.2	even	3	inner
252.12.k.d.37.3		16	21.2	odd	6
252.12.k.d.109.3		16	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-121.500 + 210.444i) q^{3} +(3239.51 + 5610.99i) q^{5} +(-44011.6 - 6348.37i) q^{7} +(-29524.5 - 51137.9i) q^{9} +O(q^{10})\)	\(q+(-121.500 + 210.444i) q^{3} +(3239.51 + 5610.99i) q^{5} +(-44011.6 - 6348.37i) q^{7} +(-29524.5 - 51137.9i) q^{9} +(153860. - 266493. i) q^{11} +584277. q^{13} -1.57440e6 q^{15} +(4.72018e6 - 8.17558e6i) q^{17} +(8.44479e6 + 1.46268e7i) q^{19} +(6.68339e6 - 8.49067e6i) q^{21} +(1.59358e7 + 2.76016e7i) q^{23} +(3.42527e6 - 5.93275e6i) q^{25} +1.43489e7 q^{27} -1.08011e8 q^{29} +(1.25482e8 - 2.17341e8i) q^{31} +(3.73879e7 + 6.47577e7i) q^{33} +(-1.06955e8 - 2.67514e8i) q^{35} +(8.03798e7 + 1.39222e8i) q^{37} +(-7.09896e7 + 1.22958e8i) q^{39} -5.43424e8 q^{41} +2.35306e8 q^{43} +(1.91290e8 - 3.31323e8i) q^{45} +(4.31156e8 + 7.46784e8i) q^{47} +(1.89672e9 + 5.58805e8i) q^{49} +(1.14700e9 + 1.98667e9i) q^{51} +(-1.83924e9 + 3.18566e9i) q^{53} +1.99372e9 q^{55} -4.10417e9 q^{57} +(-1.91162e9 + 3.31102e9i) q^{59} +(-2.30312e9 - 3.98912e9i) q^{61} +(9.74779e8 + 2.43810e9i) q^{63} +(1.89277e9 + 3.27837e9i) q^{65} +(9.21035e8 - 1.59528e9i) q^{67} -7.74479e9 q^{69} +1.51591e10 q^{71} +(-1.51263e10 + 2.61995e10i) q^{73} +(8.32342e8 + 1.44166e9i) q^{75} +(-8.46341e9 + 1.07520e10i) q^{77} +(1.74865e10 + 3.02876e10i) q^{79} +(-1.74339e9 + 3.01964e9i) q^{81} +2.03419e10 q^{83} +6.11641e10 q^{85} +(1.31233e10 - 2.27303e10i) q^{87} +(4.42219e10 + 7.65945e10i) q^{89} +(-2.57150e10 - 3.70921e9i) q^{91} +(3.04920e10 + 5.28138e10i) q^{93} +(-5.47139e10 + 9.47672e10i) q^{95} -9.58828e10 q^{97} -1.81705e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 1944 q^{3} - 2156 q^{5} + 50512 q^{7} - 472392 q^{9}+O(q^{10}) \) 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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