LMFDB - Embedded newform 84.12.k.b.5.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,12,Mod(5,84)]

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, 3, 5]))

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

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

chi := DirichletCharacter("84.5");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	84.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$64.5408271670$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.6
Character	$\chi$	$=$	84.5
Dual form			84.12.k.b.17.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-310.222 - 284.445i) q^{3} +(-3956.77 + 6853.32i) q^{5} +(-29669.5 - 33121.7i) q^{7} +(15328.9 + 176483. i) q^{9} +O(q^{10})$	\(q+(-310.222 - 284.445i) q^{3} +(-3956.77 + 6853.32i) q^{5} +(-29669.5 - 33121.7i) q^{7} +(15328.9 + 176483. i) q^{9} +(363724. - 209996. i) q^{11} +1.44373e6i q^{13} +(3.17687e6 - 1.00057e6i) q^{15} +(-287593. - 498126. i) q^{17} +(6.18865e6 + 3.57302e6i) q^{19} +(-217162. + 1.87144e7i) q^{21} +(-870326. - 502483. i) q^{23} +(-6.89792e6 - 1.19475e7i) q^{25} +(4.54443e7 - 5.91091e7i) q^{27} +7.51861e7i q^{29} +(1.49459e8 - 8.62903e7i) q^{31} +(-1.72568e8 - 3.83140e7i) q^{33} +(3.44389e8 - 7.22798e7i) q^{35} +(2.71093e8 - 4.69547e8i) q^{37} +(4.10663e8 - 4.47879e8i) q^{39} -5.49836e8 q^{41} +5.27391e8 q^{43} +(-1.27014e9 - 5.93246e8i) q^{45} +(-1.34305e9 + 2.32623e9i) q^{47} +(-2.16767e8 + 1.96541e9i) q^{49} +(-5.24717e7 + 2.36334e8i) q^{51} +(-3.08162e9 + 1.77918e9i) q^{53} +3.32362e9i q^{55} +(-9.03529e8 - 2.86876e9i) q^{57} +(-2.78649e9 - 4.82635e9i) q^{59} +(-3.54241e9 - 2.04521e9i) q^{61} +(5.39060e9 - 5.74387e9i) q^{63} +(-9.89437e9 - 5.71252e9i) q^{65} +(-7.59665e9 - 1.31578e10i) q^{67} +(1.27066e8 + 4.03441e8i) q^{69} +1.95220e10i q^{71} +(-5.80661e9 + 3.35245e9i) q^{73} +(-1.25853e9 + 5.66848e9i) q^{75} +(-1.77469e10 - 5.81667e9i) q^{77} +(1.82341e10 - 3.15824e10i) q^{79} +(-3.09111e10 + 5.41055e9i) q^{81} -4.79805e10 q^{83} +4.55176e9 q^{85} +(2.13863e10 - 2.33244e10i) q^{87} +(1.32245e10 - 2.29055e10i) q^{89} +(4.78189e10 - 4.28349e10i) q^{91} +(-7.09104e10 - 1.57438e10i) q^{93} +(-4.89740e10 + 2.82752e10i) q^{95} +7.77493e10i q^{97} +(4.26361e10 + 6.09719e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 729 q^{3} - 27194 q^{7} - 172347 q^{9}+O(q^{10}) $ 56 * q - 729 * q^3 - 27194 * q^7 - 172347 * q^9	$ 56 q - 729 q^{3} - 27194 q^{7} - 172347 q^{9} - 4853058 q^{15} + 28700520 q^{19} - 11325429 q^{21} - 316601194 q^{25} - 1368416388 q^{31} + 40874949 q^{33} - 87435712 q^{37} + 1177474410 q^{39} - 3055078348 q^{43} + 4109921793 q^{45} - 742582522 q^{49} - 694793715 q^{51} + 14605100370 q^{57} + 72584834058 q^{61} - 7310837811 q^{63} + 6131679148 q^{67} - 74402605464 q^{73} - 161115157854 q^{75} + 52181713528 q^{79} + 44948282337 q^{81} + 4658488716 q^{85} + 243101263104 q^{87} - 85311757146 q^{91} - 256628211777 q^{93} + 157345775874 q^{99}+O(q^{100}) $ 56 * q - 729 * q^3 - 27194 * q^7 - 172347 * q^9 - 4853058 * q^15 + 28700520 * q^19 - 11325429 * q^21 - 316601194 * q^25 - 1368416388 * q^31 + 40874949 * q^33 - 87435712 * q^37 + 1177474410 * q^39 - 3055078348 * q^43 + 4109921793 * q^45 - 742582522 * q^49 - 694793715 * q^51 + 14605100370 * q^57 + 72584834058 * q^61 - 7310837811 * q^63 + 6131679148 * q^67 - 74402605464 * q^73 - 161115157854 * q^75 + 52181713528 * q^79 + 44948282337 * q^81 + 4658488716 * q^85 + 243101263104 * q^87 - 85311757146 * q^91 - 256628211777 * q^93 + 157345775874 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−310.222	−	284.445i	−0.737066	−	0.675821i
$3$	−310.222	−	284.445i	−0.737066	−	0.675821i
$4$		0			0
$5$	−3956.77	+	6853.32i	−0.566246	+	0.980767i	0.430686	+	0.902502i	$0.358272\pi$
$5$	−3956.77	+	6853.32i	−0.566246	+	0.980767i	−0.996933	+	0.0782655i	$0.975062\pi$
$6$		0			0
$7$	−29669.5	−	33121.7i	−0.667223	−	0.744858i
$7$	−29669.5	−	33121.7i	−0.667223	−	0.744858i
$8$		0			0
$9$	15328.9	+	176483.i	0.0865318	+	0.996249i
$10$		0			0
$11$	363724.	−	209996.i	0.680945	−	0.393144i	−0.119266	−	0.992862i	$-0.538054\pi$
$11$	363724.	−	209996.i	0.680945	−	0.393144i	0.800211	+	0.599719i	$0.204721\pi$
$12$		0			0
$13$			1.44373e6i			1.07845i	0.842163	+	0.539224i	$0.181282\pi$
$13$			1.44373e6i			1.07845i	−0.842163	+	0.539224i	$0.818718\pi$
$14$		0			0
$15$	3.17687e6	−	1.00057e6i	1.08018	−	0.340209i
$16$		0			0
$17$	−287593.	−	498126.i	−0.0491258	−	0.0850884i	0.840417	−	0.541940i	$-0.182310\pi$
$17$	−287593.	−	498126.i	−0.0491258	−	0.0850884i	−0.889543	+	0.456852i	$0.848977\pi$
$18$		0			0
$19$	6.18865e6	+	3.57302e6i	0.573391	+	0.331047i	0.758503	−	0.651670i	$-0.225931\pi$
$19$	6.18865e6	+	3.57302e6i	0.573391	+	0.331047i	−0.185112	+	0.982718i	$0.559265\pi$
$20$		0			0
$21$	−217162.	+	1.87144e7i	−0.0116032	+	0.999933i
$22$		0			0
$23$	−870326.	−	502483.i	−0.0281954	−	0.0162786i	0.485836	−	0.874050i	$-0.338515\pi$
$23$	−870326.	−	502483.i	−0.0281954	−	0.0162786i	−0.514031	+	0.857771i	$0.671849\pi$
$24$		0			0
$25$	−6.89792e6	−	1.19475e7i	−0.141269	−	0.244686i
$26$		0			0
$27$	4.54443e7	−	5.91091e7i	0.609506	−	0.792781i
$28$		0			0
$29$			7.51861e7i			0.680689i	0.940301	+	0.340344i	$0.110544\pi$
$29$			7.51861e7i			0.680689i	−0.940301	+	0.340344i	$0.889456\pi$
$30$		0			0
$31$	1.49459e8	−	8.62903e7i	0.937633	−	0.541343i	0.0484158	−	0.998827i	$-0.484583\pi$
$31$	1.49459e8	−	8.62903e7i	0.937633	−	0.541343i	0.889218	+	0.457484i	$0.151249\pi$
$32$		0			0
$33$	−1.72568e8	−	3.83140e7i	−0.767596	−	0.170424i
$34$		0			0
$35$	3.44389e8	−	7.22798e7i	1.10834	−	0.232618i
$36$		0			0
$37$	2.71093e8	−	4.69547e8i	0.642701	−	1.11319i	−0.342126	−	0.939654i	$-0.611147\pi$
$37$	2.71093e8	−	4.69547e8i	0.642701	−	1.11319i	0.984827	−	0.173537i	$-0.0555197\pi$
$38$		0			0
$39$	4.10663e8	−	4.47879e8i	0.728837	−	0.794886i
$40$		0			0
$41$	−5.49836e8			−0.741177			−0.370589	−	0.928797i	$-0.620844\pi$
$41$	−5.49836e8			−0.741177			−0.370589	+	0.928797i	$0.620844\pi$
$42$		0			0
$43$	5.27391e8			0.547087			0.273544	−	0.961860i	$-0.411804\pi$
$43$	5.27391e8			0.547087			0.273544	+	0.961860i	$0.411804\pi$
$44$		0			0
$45$	−1.27014e9	−	5.93246e8i	−1.02609	−	0.479255i
$46$		0			0
$47$	−1.34305e9	+	2.32623e9i	−0.854189	+	1.47950i	0.0232065	+	0.999731i	$0.492612\pi$
$47$	−1.34305e9	+	2.32623e9i	−0.854189	+	1.47950i	−0.877395	+	0.479768i	$0.840721\pi$
$48$		0			0
$49$	−2.16767e8	+	1.96541e9i	−0.109626	+	0.993973i
$50$		0			0
$51$	−5.24717e7	+	2.36334e8i	−0.0212956	+	0.0959160i
$52$		0			0
$53$	−3.08162e9	+	1.77918e9i	−1.01219	+	0.584388i	−0.911832	−	0.410563i	$-0.865332\pi$
$53$	−3.08162e9	+	1.77918e9i	−1.01219	+	0.584388i	−0.100358	+	0.994951i	$0.531999\pi$
$54$		0			0
$55$			3.32362e9i			0.890465i
$56$		0			0
$57$	−9.03529e8	−	2.86876e9i	−0.198898	−	0.631513i
$58$		0			0
$59$	−2.78649e9	−	4.82635e9i	−0.507425	−	0.878886i	−0.999963	−	0.00859497i	$-0.997264\pi$
$59$	−2.78649e9	−	4.82635e9i	−0.507425	−	0.878886i	0.492538	−	0.870291i	$-0.336069\pi$
$60$		0			0
$61$	−3.54241e9	−	2.04521e9i	−0.537012	−	0.310044i	0.206855	−	0.978372i	$-0.433677\pi$
$61$	−3.54241e9	−	2.04521e9i	−0.537012	−	0.310044i	−0.743867	+	0.668327i	$0.767011\pi$
$62$		0			0
$63$	5.39060e9	−	5.74387e9i	0.684328	−	0.729174i
$64$		0			0
$65$	−9.89437e9	−	5.71252e9i	−1.05771	−	0.610667i
$66$		0			0
$67$	−7.59665e9	−	1.31578e10i	−0.687402	−	1.19062i	−0.972675	−	0.232169i	$-0.925418\pi$
$67$	−7.59665e9	−	1.31578e10i	−0.687402	−	1.19062i	0.285273	−	0.958446i	$-0.407916\pi$
$68$		0			0
$69$	1.27066e8	+	4.03441e8i	0.00978044	+	0.0310535i
$70$		0			0
$71$			1.95220e10i			1.28412i	0.766656	+	0.642058i	$0.221919\pi$
$71$			1.95220e10i			1.28412i	−0.766656	+	0.642058i	$0.778081\pi$
$72$		0			0
$73$	−5.80661e9	+	3.35245e9i	−0.327829	+	0.189272i	−0.654877	−	0.755736i	$-0.727279\pi$
$73$	−5.80661e9	+	3.35245e9i	−0.327829	+	0.189272i	0.327048	+	0.945008i	$0.393946\pi$
$74$		0			0
$75$	−1.25853e9	+	5.66848e9i	−0.0612390	+	0.275822i
$76$		0			0
$77$	−1.77469e10	−	5.81667e9i	−0.747179	−	0.244893i
$78$		0			0
$79$	1.82341e10	−	3.15824e10i	0.666707	−	1.15477i	−0.312113	−	0.950045i	$-0.601037\pi$
$79$	1.82341e10	−	3.15824e10i	0.666707	−	1.15477i	0.978820	−	0.204725i	$-0.0656300\pi$
$80$		0			0
$81$	−3.09111e10	+	5.41055e9i	−0.985024	+	0.172415i
$82$		0			0
$83$	−4.79805e10			−1.33701			−0.668506	−	0.743707i	$-0.733066\pi$
$83$	−4.79805e10			−1.33701			−0.668506	+	0.743707i	$0.733066\pi$
$84$		0			0
$85$	4.55176e9			0.111269
$86$		0			0
$87$	2.13863e10	−	2.33244e10i	0.460024	−	0.501712i
$88$		0			0
$89$	1.32245e10	−	2.29055e10i	0.251035	−	0.434805i	−0.712776	−	0.701391i	$-0.752563\pi$
$89$	1.32245e10	−	2.29055e10i	0.251035	−	0.434805i	0.963811	+	0.266587i	$0.0858959\pi$
$90$		0			0
$91$	4.78189e10	−	4.28349e10i	0.803290	−	0.719565i
$92$		0			0
$93$	−7.09104e10	−	1.57438e10i	−1.05695	−	0.234667i
$94$		0			0
$95$	−4.89740e10	+	2.82752e10i	−0.649361	+	0.374909i
$96$		0			0
$97$			7.77493e10i			0.919288i	0.888103	+	0.459644i	$0.152023\pi$
$97$			7.77493e10i			0.919288i	−0.888103	+	0.459644i	$0.847977\pi$
$98$		0			0
$99$	4.26361e10	+	6.09719e10i	0.450593	+	0.644371i
$100$		0			0
$101$	−1.89580e10	−	3.28362e10i	−0.179484	−	0.310875i	0.762220	−	0.647318i	$-0.224109\pi$
$101$	−1.89580e10	−	3.28362e10i	−0.179484	−	0.310875i	−0.941704	+	0.336443i	$0.890776\pi$
$102$		0			0
$103$	−7.08160e10	−	4.08856e10i	−0.601903	−	0.347509i	0.167887	−	0.985806i	$-0.446306\pi$
$103$	−7.08160e10	−	4.08856e10i	−0.601903	−	0.347509i	−0.769790	+	0.638297i	$0.779639\pi$
$104$		0			0
$105$	−1.27397e11	−	7.55369e10i	−0.974131	−	0.577588i
$106$		0			0
$107$	−2.02018e11	−	1.16635e11i	−1.39245	−	0.803932i	−0.398866	−	0.917009i	$-0.630596\pi$
$107$	−2.02018e11	−	1.16635e11i	−1.39245	−	0.803932i	−0.993586	+	0.113077i	$0.963929\pi$
$108$		0			0
$109$	−6.27041e10	−	1.08607e11i	−0.390346	−	0.676099i	0.602149	−	0.798384i	$-0.294311\pi$
$109$	−6.27041e10	−	1.08607e11i	−0.390346	−	0.676099i	−0.992495	+	0.122284i	$0.960978\pi$
$110$		0			0
$111$	−2.17660e11	+	6.85529e10i	−1.22603	+	0.386144i
$112$		0			0
$113$		−	1.28230e11i		−	0.654726i	−0.944899	−	0.327363i	$-0.893840\pi$
$113$		−	1.28230e11i		−	0.654726i	0.944899	−	0.327363i	$-0.106160\pi$
$114$		0			0
$115$	6.88735e9	−	3.97641e9i	0.0319311	−	0.0184354i
$116$		0			0
$117$	−2.54794e11	+	2.21308e10i	−1.07440	+	0.0933200i
$118$		0			0
$119$	−7.96603e9	+	2.43047e10i	−0.0306009	+	0.0933647i
$120$		0			0
$121$	−5.44591e10	+	9.43260e10i	−0.190876	+	0.330607i
$122$		0			0
$123$	1.70571e11	+	1.56398e11i	0.546296	+	0.500903i
$124$		0			0
$125$	−2.77229e11			−0.812519
$126$		0			0
$127$	4.43714e11			1.19174			0.595871	−	0.803080i	$-0.296807\pi$
$127$	4.43714e11			1.19174			0.595871	+	0.803080i	$0.296807\pi$
$128$		0			0
$129$	−1.63609e11	−	1.50014e11i	−0.403239	−	0.369733i
$130$		0			0
$131$	−4.97204e10	+	8.61183e10i	−0.112601	+	0.195031i	−0.916818	−	0.399305i	$-0.869252\pi$
$131$	−4.97204e10	+	8.61183e10i	−0.112601	+	0.195031i	0.804217	+	0.594336i	$0.202585\pi$
$132$		0			0
$133$	−6.52697e10	−	3.10988e11i	−0.135997	−	0.647977i
$134$		0			0
$135$	2.25281e11	+	5.45325e11i	0.432403	+	1.04669i
$136$		0			0
$137$	3.04125e11	−	1.75587e11i	0.538380	−	0.310834i	−0.206042	−	0.978543i	$-0.566058\pi$
$137$	3.04125e11	−	1.75587e11i	0.538380	−	0.310834i	0.744422	+	0.667709i	$0.232725\pi$
$138$		0			0
$139$			7.65471e11i			1.25126i	0.780120	+	0.625630i	$0.215158\pi$
$139$			7.65471e11i			1.25126i	−0.780120	+	0.625630i	$0.784842\pi$
$140$		0			0
$141$	1.07833e12	−	3.39625e11i	1.62947	−	0.513209i
$142$		0			0
$143$	3.03179e11	+	5.25121e11i	0.423985	+	0.734363i
$144$		0			0
$145$	−5.15274e11	−	2.97494e11i	−0.667597	−	0.385437i
$146$		0			0
$147$	6.26297e11	−	5.48056e11i	0.752550	−	0.658536i
$148$		0			0
$149$	7.93584e11	+	4.58176e11i	0.885255	+	0.511102i	0.872388	−	0.488815i	$-0.162571\pi$
$149$	7.93584e11	+	4.58176e11i	0.885255	+	0.511102i	0.0128678	+	0.999917i	$0.495904\pi$
$150$		0			0
$151$	−8.53418e11	−	1.47816e12i	−0.884684	−	1.53232i	−0.846075	−	0.533064i	$-0.821041\pi$
$151$	−8.53418e11	−	1.47816e12i	−0.884684	−	1.53232i	−0.0386094	−	0.999254i	$-0.512293\pi$
$152$		0			0
$153$	8.35021e10	−	5.83909e10i	0.0805183	−	0.0563044i
$154$		0			0
$155$			1.36572e12i			1.22613i
$156$		0			0
$157$	3.01966e11	−	1.74340e11i	0.252644	−	0.145864i	−0.368330	−	0.929695i	$-0.620070\pi$
$157$	3.01966e11	−	1.74340e11i	0.252644	−	0.145864i	0.620974	+	0.783831i	$0.286737\pi$
$158$		0			0
$159$	1.46207e12	+	3.24613e11i	1.14099	+	0.253327i
$160$		0			0
$161$	9.17905e9	+	4.37351e10i	0.00668737	+	0.0318631i
$162$		0			0
$163$	7.02496e10	−	1.21676e11i	0.0478202	−	0.0828271i	−0.841125	−	0.540842i	$-0.818106\pi$
$163$	7.02496e10	−	1.21676e11i	0.0478202	−	0.0828271i	0.888945	+	0.458014i	$0.151439\pi$
$164$		0			0
$165$	9.45388e11	−	1.03106e12i	0.601795	−	0.656331i
$166$		0			0
$167$	6.81957e11			0.406272			0.203136	−	0.979151i	$-0.434887\pi$
$167$	6.81957e11			0.406272			0.203136	+	0.979151i	$0.434887\pi$
$168$		0			0
$169$	−2.92209e11			−0.163048
$170$		0			0
$171$	−5.35710e11	+	1.14696e12i	−0.280189	+	0.599886i
$172$		0			0
$173$	1.30594e12	−	2.26196e12i	0.640724	−	1.10977i	−0.344547	−	0.938769i	$-0.611967\pi$
$173$	1.30594e12	−	2.26196e12i	0.640724	−	1.10977i	0.985271	−	0.170998i	$-0.0546992\pi$
$174$		0			0
$175$	−1.91065e11	+	5.82949e11i	−0.0879979	+	0.268486i
$176$		0			0
$177$	−5.08399e11	+	2.28985e12i	−0.219964	+	0.990725i
$178$		0			0
$179$	2.89309e12	−	1.67033e12i	1.17671	−	0.679376i	0.221461	−	0.975169i	$-0.428917\pi$
$179$	2.89309e12	−	1.67033e12i	1.17671	−	0.679376i	0.955252	+	0.295794i	$0.0955841\pi$
$180$		0			0
$181$			4.27923e12i			1.63732i	0.574278	+	0.818660i	$0.305283\pi$
$181$			4.27923e12i			1.63732i	−0.574278	+	0.818660i	$0.694717\pi$
$182$		0			0
$183$	5.17184e11	+	1.64209e12i	0.186279	+	0.591447i
$184$		0			0
$185$	2.14530e12	+	3.71578e12i	0.727854	+	1.26068i
$186$		0			0
$187$	−2.09209e11	−	1.20787e11i	−0.0669039	−	0.0386270i
$188$		0			0
$189$	−3.30610e12	+	2.48546e11i	−0.997186	+	0.0749663i
$190$		0			0
$191$	−3.88256e12	−	2.24160e12i	−1.10519	−	0.638079i	−0.167607	−	0.985854i	$-0.553604\pi$
$191$	−3.88256e12	−	2.24160e12i	−1.10519	−	0.638079i	−0.937578	+	0.347775i	$0.886937\pi$
$192$		0			0
$193$	−5.94509e11	−	1.02972e12i	−0.159806	−	0.276792i	0.774993	−	0.631970i	$-0.217754\pi$
$193$	−5.94509e11	−	1.02972e12i	−0.159806	−	0.276792i	−0.934799	+	0.355178i	$0.884420\pi$
$194$		0			0
$195$	1.44456e12	+	4.58656e12i	0.366897	+	1.16492i
$196$		0			0
$197$		−	1.85082e12i		−	0.444426i	−0.974998	−	0.222213i	$-0.928672\pi$
$197$		−	1.85082e12i		−	0.444426i	0.974998	−	0.222213i	$-0.0713280\pi$
$198$		0			0
$199$	4.82368e12	−	2.78495e12i	1.09569	−	0.632595i	0.160602	−	0.987019i	$-0.448656\pi$
$199$	4.82368e12	−	2.78495e12i	1.09569	−	0.632595i	0.935085	+	0.354424i	$0.115323\pi$
$200$		0			0
$201$	−1.38602e12	+	6.24267e12i	−0.297982	+	1.34212i
$202$		0			0
$203$	2.49029e12	−	2.23073e12i	0.507016	−	0.454171i
$204$		0			0
$205$	2.17557e12	−	3.76820e12i	0.419689	−	0.726922i
$206$		0			0
$207$	7.53383e10	−	1.61300e11i	0.0137778	−	0.0294983i
$208$		0			0
$209$	3.00128e12			0.520597
$210$		0			0
$211$	−9.18196e12			−1.51141			−0.755704	−	0.654913i	$-0.772705\pi$
$211$	−9.18196e12			−1.51141			−0.755704	+	0.654913i	$0.772705\pi$
$212$		0			0
$213$	5.55295e12	−	6.05617e12i	0.867833	−	0.946478i
$214$		0			0
$215$	−2.08676e12	+	3.61438e12i	−0.309786	+	0.536565i
$216$		0			0
$217$	−7.29246e12	−	2.39015e12i	−1.02883	−	0.337207i
$218$		0			0
$219$	2.75493e12	+	6.11658e11i	0.369545	+	0.0820476i
$220$		0			0
$221$	7.19162e11	−	4.15208e11i	0.0917633	−	0.0529796i
$222$		0			0
$223$		−	1.29829e13i		−	1.57651i	−0.615350	−	0.788254i	$-0.710985\pi$
$223$		−	1.29829e13i		−	1.57651i	0.615350	−	0.788254i	$-0.289015\pi$
$224$		0			0
$225$	2.00280e12	−	1.40050e12i	0.231544	−	0.161913i
$226$		0			0
$227$	3.01090e12	+	5.21503e12i	0.331554	+	0.574268i	0.982817	−	0.184584i	$-0.0590938\pi$
$227$	3.01090e12	+	5.21503e12i	0.331554	+	0.574268i	−0.651263	+	0.758852i	$0.725760\pi$
$228$		0			0
$229$	2.84036e12	+	1.63988e12i	0.298043	+	0.172075i	0.641563	−	0.767070i	$-0.278286\pi$
$229$	2.84036e12	+	1.63988e12i	0.298043	+	0.172075i	−0.343521	+	0.939145i	$0.611620\pi$
$230$		0			0
$231$	3.85097e12	+	6.85249e12i	0.385216	+	0.685461i
$232$		0			0
$233$	−4.92836e12	−	2.84539e12i	−0.470159	−	0.271446i	0.246147	−	0.969232i	$-0.420835\pi$
$233$	−4.92836e12	−	2.84539e12i	−0.470159	−	0.271446i	−0.716306	+	0.697786i	$0.754169\pi$
$234$		0			0
$235$	−1.06283e13	−	1.84087e13i	−0.967362	−	1.67552i
$236$		0			0
$237$	−1.46401e13	+	4.61096e12i	−1.27182	+	0.400567i
$238$		0			0
$239$		−	2.66309e12i		−	0.220901i	−0.993882	−	0.110450i	$-0.964771\pi$
$239$		−	2.66309e12i		−	0.220901i	0.993882	−	0.110450i	$-0.0352293\pi$
$240$		0			0
$241$	1.73035e13	−	9.99020e12i	1.37101	−	0.791553i	0.379955	−	0.925005i	$-0.375939\pi$
$241$	1.73035e13	−	9.99020e12i	1.37101	−	0.791553i	0.991055	+	0.133451i	$0.0426060\pi$
$242$		0			0
$243$	1.11283e13	+	7.11404e12i	0.842549	+	0.538619i
$244$		0			0
$245$	−1.26119e13	−	9.26224e12i	−0.912780	−	0.670351i
$246$		0			0
$247$	−5.15849e12	+	8.93476e12i	−0.357017	+	0.618372i
$248$		0			0
$249$	1.48846e13	+	1.36478e13i	0.985466	+	0.903581i
$250$		0			0
$251$	−3.05056e13			−1.93274			−0.966372	−	0.257147i	$-0.917218\pi$
$251$	−3.05056e13			−1.93274			−0.966372	+	0.257147i	$0.917218\pi$
$252$		0			0
$253$	−4.22078e11			−0.0255994
$254$		0			0
$255$	−1.41206e12	−	1.29473e12i	−0.0820127	−	0.0751981i
$256$		0			0
$257$	−8.70202e12	+	1.50723e13i	−0.484159	+	0.838588i	−0.999834	−	0.0181959i	$-0.994208\pi$
$257$	−8.70202e12	+	1.50723e13i	−0.484159	+	0.838588i	0.515675	+	0.856784i	$0.327541\pi$
$258$		0			0
$259$	−2.35954e13	+	4.95217e12i	−1.25799	+	0.264026i
$260$		0			0
$261$	−1.32690e13	+	1.15252e12i	−0.678136	+	0.0589013i
$262$		0			0
$263$	−2.02789e13	+	1.17081e13i	−0.993777	+	0.573757i	−0.906401	−	0.422418i	$-0.861181\pi$
$263$	−2.02789e13	+	1.17081e13i	−0.993777	+	0.573757i	−0.0873756	+	0.996175i	$0.527848\pi$
$264$		0			0
$265$		−	2.81591e13i		−	1.32363i
$266$		0			0
$267$	−1.06179e13	+	3.34415e12i	−0.478879	+	0.150825i
$268$		0			0
$269$	−1.78031e12	−	3.08358e12i	−0.0770651	−	0.133481i	0.824917	−	0.565253i	$-0.191222\pi$
$269$	−1.78031e12	−	3.08358e12i	−0.0770651	−	0.133481i	−0.901982	+	0.431773i	$0.857888\pi$
$270$		0			0
$271$	2.05407e12	+	1.18592e12i	0.0853659	+	0.0492860i	0.542075	−	0.840330i	$-0.317639\pi$
$271$	2.05407e12	+	1.18592e12i	0.0853659	+	0.0492860i	−0.456709	+	0.889616i	$0.650972\pi$
$272$		0			0
$273$	−2.70187e13	−	3.13525e11i	−1.07837	−	0.0125135i
$274$		0			0
$275$	−5.01788e12	−	2.89707e12i	−0.192393	−	0.111078i
$276$		0			0
$277$	−1.64107e13	−	2.84241e13i	−0.604627	−	1.04725i	−0.992110	−	0.125369i	$-0.959989\pi$
$277$	−1.64107e13	−	2.84241e13i	−0.604627	−	1.04725i	0.387483	−	0.921877i	$-0.373345\pi$
$278$		0			0
$279$	1.75198e13	+	2.50542e13i	0.620448	+	0.887273i
$280$		0			0
$281$		−	2.66708e13i		−	0.908135i	−0.890967	−	0.454068i	$-0.849972\pi$
$281$		−	2.66708e13i		−	0.908135i	0.890967	−	0.454068i	$-0.150028\pi$
$282$		0			0
$283$	−2.46384e13	+	1.42250e13i	−0.806838	+	0.465828i	−0.845857	−	0.533410i	$-0.820910\pi$
$283$	−2.46384e13	+	1.42250e13i	−0.806838	+	0.465828i	0.0390186	+	0.999238i	$0.487577\pi$
$284$		0			0
$285$	2.32356e13	+	5.15884e12i	0.731993	+	0.162519i
$286$		0			0
$287$	1.63134e13	+	1.82115e13i	0.494531	+	0.552072i
$288$		0			0
$289$	1.69705e13	−	2.93938e13i	0.495173	−	0.857665i
$290$		0			0
$291$	2.21154e13	−	2.41196e13i	0.621274	−	0.677576i
$292$		0			0
$293$	−2.94747e12			−0.0797403			−0.0398701	−	0.999205i	$-0.512694\pi$
$293$	−2.94747e12			−0.0797403			−0.0398701	+	0.999205i	$0.512694\pi$
$294$		0			0
$295$	4.41020e13			1.14931
$296$		0			0
$297$	4.11649e12	−	3.10425e13i	0.103363	−	0.779464i
$298$		0			0
$299$	7.25452e11	−	1.25652e12i	0.0175556	−	0.0304073i
$300$		0			0
$301$	−1.56474e13	−	1.74681e13i	−0.365029	−	0.407502i
$302$		0			0
$303$	−3.45891e12	+	1.55790e13i	−0.0778045	+	0.350434i
$304$		0			0
$305$	2.80329e13	−	1.61848e13i	0.608162	−	0.351123i
$306$		0			0
$307$		−	3.64743e13i		−	0.763354i	−0.924296	−	0.381677i	$-0.875347\pi$
$307$		−	3.64743e13i		−	0.763354i	0.924296	−	0.381677i	$-0.124653\pi$
$308$		0			0
$309$	1.03390e13	+	3.28269e13i	0.208788	+	0.662915i
$310$		0			0
$311$	4.45806e13	+	7.72159e13i	0.868889	+	1.50496i	0.863134	+	0.504976i	$0.168499\pi$
$311$	4.45806e13	+	7.72159e13i	0.868889	+	1.50496i	0.00575498	+	0.999983i	$0.498168\pi$
$312$		0			0
$313$	−6.08237e13	−	3.51166e13i	−1.14440	−	0.660721i	−0.196885	−	0.980427i	$-0.563083\pi$
$313$	−6.08237e13	−	3.51166e13i	−1.14440	−	0.660721i	−0.947517	+	0.319706i	$0.896416\pi$
$314$		0			0
$315$	1.80352e13	+	5.96706e13i	0.327652	+	1.08406i
$316$		0			0
$317$	−3.47943e13	−	2.00885e13i	−0.610496	−	0.352470i	0.162664	−	0.986682i	$-0.447991\pi$
$317$	−3.47943e13	−	2.00885e13i	−0.610496	−	0.352470i	−0.773159	+	0.634212i	$0.781325\pi$
$318$		0			0
$319$	1.57888e13	+	2.73470e13i	0.267609	+	0.463512i
$320$		0			0
$321$	2.94943e13	+	9.36461e13i	0.483014	+	1.53360i
$322$		0			0
$323$		−	4.11030e12i		−	0.0650519i
$324$		0			0
$325$	1.72491e13	−	9.95877e12i	0.263881	−	0.152352i
$326$		0			0
$327$	−1.14404e13	+	5.15281e13i	−0.169211	+	0.762134i
$328$		0			0
$329$	1.16896e14	−	2.45340e13i	1.67195	−	0.350907i
$330$		0			0
$331$	1.33765e13	−	2.31688e13i	0.185050	−	0.320515i	−0.758544	−	0.651622i	$-0.774089\pi$
$331$	1.33765e13	−	2.31688e13i	0.185050	−	0.320515i	0.943593	+	0.331107i	$0.107422\pi$
$332$		0			0
$333$	8.70225e13	+	4.06456e13i	1.16463	+	0.543964i
$334$		0			0
$335$	1.20233e14			1.55696
$336$		0			0
$337$	−7.15665e13			−0.896902			−0.448451	−	0.893807i	$-0.648024\pi$
$337$	−7.15665e13			−0.896902			−0.448451	+	0.893807i	$0.648024\pi$
$338$		0			0
$339$	−3.64745e13	+	3.97799e13i	−0.442478	+	0.482576i
$340$		0			0
$341$	3.62412e13	−	6.27717e13i	0.425651	−	0.737250i
$342$		0			0
$343$	7.15291e13	−	5.11330e13i	0.813514	−	0.581546i
$344$		0			0
$345$	−3.26768e12	−	7.25501e11i	−0.0359944	−	0.00799159i
$346$		0			0
$347$	−2.89174e13	+	1.66955e13i	−0.308566	+	0.178151i	−0.646285	−	0.763097i	$-0.723678\pi$
$347$	−2.89174e13	+	1.66955e13i	−0.308566	+	0.178151i	0.337719	+	0.941247i	$0.390345\pi$
$348$		0			0
$349$			1.12717e14i			1.16533i	0.812712	+	0.582665i	$0.197990\pi$
$349$			1.12717e14i			1.16533i	−0.812712	+	0.582665i	$0.802010\pi$
$350$		0			0
$351$	8.53378e13	+	6.56094e13i	0.854973	+	0.657321i
$352$		0			0
$353$	−9.09345e13	−	1.57503e14i	−0.883014	−	1.52943i	−0.847973	−	0.530040i	$-0.822177\pi$
$353$	−9.09345e13	−	1.57503e14i	−0.883014	−	1.52943i	−0.0350413	−	0.999386i	$-0.511156\pi$
$354$		0			0
$355$	−1.33791e14	−	7.72441e13i	−1.25942	−	0.727126i
$356$		0			0
$357$	9.38461e12	−	5.27397e12i	0.0856527	−	0.0481352i
$358$		0			0
$359$	1.39713e14	+	8.06631e13i	1.23656	+	0.713930i	0.968390	−	0.249441i	$-0.0802470\pi$
$359$	1.39713e14	+	8.06631e13i	1.23656	+	0.713930i	0.268172	+	0.963371i	$0.413580\pi$
$360$		0			0
$361$	−3.27122e13	−	5.66592e13i	−0.280815	−	0.486386i
$362$		0			0
$363$	4.37250e13	−	1.37714e13i	0.364119	−	0.114681i
$364$		0			0
$365$		−	5.30594e13i		−	0.428698i
$366$		0			0
$367$	−1.08295e14	+	6.25240e13i	−0.849071	+	0.490212i	−0.860337	−	0.509725i	$-0.829747\pi$
$367$	−1.08295e14	+	6.25240e13i	−0.849071	+	0.490212i	0.0112660	+	0.999937i	$0.496414\pi$
$368$		0			0
$369$	−8.42836e12	−	9.70365e13i	−0.0641354	−	0.738397i
$370$		0			0
$371$	1.50360e14	+	4.92813e13i	1.11064	+	0.364020i
$372$		0			0
$373$	−4.05260e13	+	7.01932e13i	−0.290627	+	0.503380i	−0.973958	−	0.226728i	$-0.927197\pi$
$373$	−4.05260e13	+	7.01932e13i	−0.290627	+	0.503380i	0.683331	+	0.730108i	$0.260530\pi$
$374$		0			0
$375$	8.60027e13	+	7.88565e13i	0.598880	+	0.549118i
$376$		0			0
$377$	−1.08549e14			−0.734087
$378$		0			0
$379$	−5.43437e13			−0.356971			−0.178486	−	0.983942i	$-0.557120\pi$
$379$	−5.43437e13			−0.356971			−0.178486	+	0.983942i	$0.557120\pi$
$380$		0			0
$381$	−1.37650e14	−	1.26212e14i	−0.878392	−	0.805404i
$382$		0			0
$383$	−9.36135e13	+	1.62143e14i	−0.580424	+	1.00532i	0.415005	+	0.909819i	$0.363780\pi$
$383$	−9.36135e13	+	1.62143e14i	−0.580424	+	1.00532i	−0.995429	+	0.0955047i	$0.969553\pi$
$384$		0			0
$385$	1.10084e14	−	9.86102e13i	0.663270	−	0.594139i
$386$		0			0
$387$	8.08431e12	+	9.30754e13i	0.0473405	+	0.545035i
$388$		0			0
$389$	−1.51837e14	+	8.76630e13i	−0.864279	+	0.498992i	−0.865443	−	0.501008i	$-0.832963\pi$
$389$	−1.51837e14	+	8.76630e13i	−0.864279	+	0.498992i	0.00116383	+	0.999999i	$0.499630\pi$
$390$		0			0
$391$			5.78043e11i			0.00319880i
$392$		0			0
$393$	3.99203e13	−	1.25731e13i	0.214800	−	0.0676524i
$394$		0			0
$395$	1.44296e14	+	2.49928e14i	0.755040	+	1.30777i
$396$		0			0
$397$	1.24898e14	+	7.21100e13i	0.635635	+	0.366984i	0.782931	−	0.622108i	$-0.213724\pi$
$397$	1.24898e14	+	7.21100e13i	0.635635	+	0.366984i	−0.147296	+	0.989092i	$0.547057\pi$
$398$		0			0
$399$	−6.82110e13	+	1.15041e14i	−0.337678	+	0.569511i
$400$		0			0
$401$	−3.18153e14	−	1.83686e14i	−1.53229	−	0.884670i	−0.999256	−	0.0385794i	$-0.987717\pi$
$401$	−3.18153e14	−	1.83686e14i	−1.53229	−	0.884670i	−0.533038	−	0.846091i	$-0.678950\pi$
$402$		0			0
$403$	1.24580e14	+	2.15779e14i	0.583810	+	1.01119i
$404$		0			0
$405$	8.52278e13	−	2.33252e14i	0.388668	−	1.06371i
$406$		0			0
$407$		−	2.27714e14i		−	1.01070i
$408$		0			0
$409$	1.96559e13	−	1.13484e13i	0.0849211	−	0.0490292i	−0.456938	−	0.889498i	$-0.651054\pi$
$409$	1.96559e13	−	1.13484e13i	0.0849211	−	0.0490292i	0.541859	+	0.840469i	$0.317721\pi$
$410$		0			0
$411$	−1.44291e14	−	3.20360e13i	−0.606889	−	0.134744i
$412$		0			0
$413$	−7.71829e13	+	2.35489e14i	−0.316079	+	0.964373i
$414$		0			0
$415$	1.89848e14	−	3.28826e14i	0.757078	−	1.31130i
$416$		0			0
$417$	2.17735e14	−	2.37466e14i	0.845627	−	0.922260i
$418$		0			0
$419$	1.69917e14			0.642776			0.321388	−	0.946948i	$-0.395851\pi$
$419$	1.69917e14			0.642776			0.321388	+	0.946948i	$0.395851\pi$
$420$		0			0
$421$	3.36021e14			1.23827			0.619134	−	0.785286i	$-0.287484\pi$
$421$	3.36021e14			1.23827			0.619134	+	0.785286i	$0.287484\pi$
$422$		0			0
$423$	−4.31127e14	−	2.01366e14i	−1.54786	−	0.722961i
$424$		0			0
$425$	−3.96759e12	+	6.87207e12i	−0.0138799	+	0.0240408i
$426$		0			0
$427$	3.73606e13	+	1.78011e14i	0.127368	+	0.606866i
$428$		0			0
$429$	5.53153e13	−	2.49142e14i	0.183793	−	0.827812i
$430$		0			0
$431$	−1.97920e14	+	1.14269e14i	−0.641011	+	0.370088i	−0.785004	−	0.619491i	$-0.787339\pi$
$431$	−1.97920e14	+	1.14269e14i	−0.641011	+	0.370088i	0.143993	+	0.989579i	$0.454006\pi$
$432$		0			0
$433$		−	3.27684e14i		−	1.03460i	−0.855805	−	0.517299i	$-0.826938\pi$
$433$		−	3.27684e14i		−	1.03460i	0.855805	−	0.517299i	$-0.173062\pi$
$434$		0			0
$435$	7.52290e13	+	2.38857e14i	0.231576	+	0.735269i
$436$		0			0
$437$	−3.59076e12	−	6.21938e12i	−0.0107780	−	0.0186680i
$438$		0			0
$439$	−3.48291e14	−	2.01086e14i	−1.01950	−	0.588609i	−0.105542	−	0.994415i	$-0.533658\pi$
$439$	−3.48291e14	−	2.01086e14i	−1.01950	−	0.588609i	−0.913959	+	0.405806i	$0.866991\pi$
$440$		0			0
$441$	−3.50183e14	−	8.12815e12i	−0.999731	−	0.0232049i
$442$		0			0
$443$	−5.19138e14	−	2.99724e14i	−1.44565	−	0.834644i	−0.447428	−	0.894320i	$-0.647660\pi$
$443$	−5.19138e14	−	2.99724e14i	−1.44565	−	0.834644i	−0.998218	+	0.0596758i	$0.980993\pi$
$444$		0			0
$445$	1.04652e14	+	1.81263e14i	0.284295	+	0.492413i
$446$		0			0
$447$	−1.15862e14	−	3.67868e14i	−0.307078	−	0.974990i
$448$		0			0
$449$		−	5.03298e14i		−	1.30158i	−0.759258	−	0.650790i	$-0.774438\pi$
$449$		−	5.03298e14i		−	1.30158i	0.759258	−	0.650790i	$-0.225562\pi$
$450$		0			0
$451$	−1.99989e14	+	1.15463e14i	−0.504701	+	0.291389i
$452$		0			0
$453$	−1.55707e14	+	7.01310e14i	−0.383502	+	1.72731i
$454$		0			0
$455$	1.04353e14	+	4.97206e14i	0.250866	+	1.19529i
$456$		0			0
$457$	2.94369e13	−	5.09862e13i	0.0690801	−	0.119650i	−0.829417	−	0.558631i	$-0.811327\pi$
$457$	2.94369e13	−	5.09862e13i	0.0690801	−	0.119650i	0.898497	+	0.438980i	$0.144660\pi$
$458$		0			0
$459$	−4.25132e13	−	5.63761e12i	−0.0973990	−	0.0129159i
$460$		0			0
$461$	−3.78994e14			−0.847767			−0.423884	−	0.905717i	$-0.639333\pi$
$461$	−3.78994e14			−0.847767			−0.423884	+	0.905717i	$0.639333\pi$
$462$		0			0
$463$	−6.98091e14			−1.52481			−0.762406	−	0.647099i	$-0.775982\pi$
$463$	−6.98091e14			−1.52481			−0.762406	+	0.647099i	$0.775982\pi$
$464$		0			0
$465$	3.88473e14	−	4.23677e14i	0.828647	−	0.903741i
$466$		0			0
$467$	−6.08338e13	+	1.05367e14i	−0.126737	+	0.219514i	−0.922410	−	0.386211i	$-0.873784\pi$
$467$	−6.08338e13	+	1.05367e14i	−0.126737	+	0.219514i	0.795674	+	0.605725i	$0.207117\pi$
$468$		0			0
$469$	−2.10419e14	+	6.41999e14i	−0.428189	+	1.30642i
$470$		0			0
$471$	−1.43267e14	−	3.18085e13i	−0.284794	−	0.0632308i
$472$		0			0
$473$	1.91825e14	−	1.10750e14i	0.372536	−	0.215084i
$474$		0			0
$475$		−	9.85855e13i		−	0.187068i
$476$		0			0
$477$	−3.61231e14	−	5.16580e14i	−0.669783	−	0.957826i
$478$		0			0
$479$	−2.74582e14	−	4.75589e14i	−0.497538	−	0.861761i	0.502458	−	0.864601i	$-0.332429\pi$
$479$	−2.74582e14	−	4.75589e14i	−0.497538	−	0.861761i	−0.999996	+	0.00284086i	$0.999096\pi$
$480$		0			0
$481$	6.77902e14	+	3.91387e14i	1.20052	+	0.693120i
$482$		0			0
$483$	9.59269e12	−	1.61785e13i	0.0166047	−	0.0280046i
$484$		0			0
$485$	−5.32841e14	−	3.07636e14i	−0.901608	−	0.520544i
$486$		0			0
$487$	5.03806e14	+	8.72617e14i	0.833401	+	1.44349i	0.895326	+	0.445412i	$0.146943\pi$
$487$	5.03806e14	+	8.72617e14i	0.833401	+	1.44349i	−0.0619251	+	0.998081i	$0.519724\pi$
$488$		0			0
$489$	−5.64031e13	+	1.77644e13i	−0.0912230	+	0.0287311i
$490$		0			0
$491$			1.54729e14i			0.244694i	0.992487	+	0.122347i	$0.0390421\pi$
$491$			1.54729e14i			0.244694i	−0.992487	+	0.122347i	$0.960958\pi$
$492$		0			0
$493$	3.74522e13	−	2.16230e13i	0.0579187	−	0.0334394i
$494$		0			0
$495$	−5.86561e14	+	5.09473e13i	−0.887125	+	0.0770535i
$496$		0			0
$497$	6.46603e14	−	5.79209e14i	0.956484	−	0.856792i
$498$		0			0
$499$	−1.46837e14	+	2.54330e14i	−0.212463	+	0.367997i	−0.952485	−	0.304586i	$-0.901482\pi$
$499$	−1.46837e14	+	2.54330e14i	−0.212463	+	0.367997i	0.740022	+	0.672583i	$0.234815\pi$
$500$		0			0
$501$	−2.11558e14	−	1.93979e14i	−0.299449	−	0.274567i
$502$		0			0
$503$	9.55898e14			1.32369			0.661847	−	0.749639i	$-0.269773\pi$
$503$	9.55898e14			1.32369			0.661847	+	0.749639i	$0.269773\pi$
$504$		0			0
$505$	3.00049e14			0.406528
$506$		0			0
$507$	9.06497e13	+	8.31174e13i	0.120177	+	0.110191i
$508$		0			0
$509$	−4.79530e14	+	8.30570e14i	−0.622111	+	1.07753i	0.366981	+	0.930228i	$0.380391\pi$
$509$	−4.79530e14	+	8.30570e14i	−0.622111	+	1.07753i	−0.989092	+	0.147299i	$0.952942\pi$
$510$		0			0
$511$	2.83318e14	+	9.28593e13i	0.359716	+	0.117899i
$512$		0			0
$513$	4.92436e14	−	2.03432e14i	0.611934	−	0.252798i
$514$		0			0
$515$	5.60404e14	−	3.23550e14i	0.681650	−	0.393551i
$516$		0			0
$517$			1.12814e15i			1.34328i
$518$		0			0
$519$	−1.04854e15	+	3.30242e14i	−1.22226	+	0.384956i
$520$		0			0
$521$	6.89512e14	+	1.19427e15i	0.786927	+	1.36300i	0.927841	+	0.372976i	$0.121663\pi$
$521$	6.89512e14	+	1.19427e15i	0.786927	+	1.36300i	−0.140914	+	0.990022i	$0.545004\pi$
$522$		0			0
$523$	2.78174e14	+	1.60604e14i	0.310854	+	0.179472i	0.647309	−	0.762228i	$-0.275895\pi$
$523$	2.78174e14	+	1.60604e14i	0.310854	+	0.179472i	−0.336455	+	0.941700i	$0.609228\pi$
$524$		0			0
$525$	2.25090e14	−	1.26496e14i	0.246309	−	0.138421i
$526$		0			0
$527$	−8.59669e13	−	4.96330e13i	−0.0921240	−	0.0531878i
$528$		0			0
$529$	−4.75900e14	−	8.24283e14i	−0.499470	−	0.865107i
$530$		0			0
$531$	8.09052e14	−	5.65750e14i	0.831681	−	0.581573i
$532$		0			0
$533$		−	7.93817e14i		−	0.799321i
$534$		0			0
$535$	1.59868e15	−	9.22998e14i	1.57694	−	0.910447i
$536$		0			0
$537$	−1.37262e15	−	3.04753e14i	−1.32645	−	0.294503i
$538$		0			0
$539$	3.33885e14	+	7.60386e14i	0.316125	+	0.719940i
$540$		0			0
$541$	−1.48344e14	+	2.56939e14i	−0.137621	+	0.238367i	−0.926596	−	0.376059i	$-0.877279\pi$
$541$	−1.48344e14	+	2.56939e14i	−0.137621	+	0.238367i	0.788975	+	0.614426i	$0.210612\pi$
$542$		0			0
$543$	1.21721e15	−	1.32751e15i	1.10654	−	1.20681i
$544$		0			0
$545$	9.92421e14			0.884128
$546$		0			0
$547$	1.12665e15			0.983690			0.491845	−	0.870683i	$-0.336323\pi$
$547$	1.12665e15			0.983690			0.491845	+	0.870683i	$0.336323\pi$
$548$		0			0
$549$	3.06643e14	−	6.56523e14i	0.262413	−	0.561827i
$550$		0			0
$551$	−2.68641e14	+	4.65300e14i	−0.225340	+	0.390301i
$552$		0			0
$553$	−1.58706e15	+	3.33089e14i	−1.30498	+	0.273888i
$554$		0			0
$555$	3.91413e14	−	1.76294e15i	0.315518	−	1.42110i
$556$		0			0
$557$	1.62113e15	−	9.35958e14i	1.28119	−	0.739695i	0.304124	−	0.952633i	$-0.401636\pi$
$557$	1.62113e15	−	9.35958e14i	1.28119	−	0.739695i	0.977066	+	0.212937i	$0.0683031\pi$
$558$		0			0
$559$			7.61413e14i			0.590005i
$560$		0			0
$561$	3.05441e13	+	9.69793e13i	0.0232077	+	0.0736857i
$562$		0			0
$563$	2.82652e14	+	4.89568e14i	0.210599	+	0.364768i	0.951902	−	0.306402i	$-0.0991253\pi$
$563$	2.82652e14	+	4.89568e14i	0.210599	+	0.364768i	−0.741303	+	0.671170i	$0.765792\pi$
$564$		0			0
$565$	8.78804e14	+	5.07378e14i	0.642134	+	0.370736i
$566$		0			0
$567$	1.09632e15	+	8.63300e14i	0.785656	+	0.618664i
$568$		0			0
$569$	−1.01682e15	−	5.87063e14i	−0.714706	−	0.412636i	0.0980950	−	0.995177i	$-0.468725\pi$
$569$	−1.01682e15	−	5.87063e14i	−0.714706	−	0.412636i	−0.812801	+	0.582541i	$0.802058\pi$
$570$		0			0
$571$	1.05854e15	+	1.83345e15i	0.729809	+	1.26407i	0.956964	+	0.290208i	$0.0937246\pi$
$571$	1.05854e15	+	1.83345e15i	0.729809	+	1.26407i	−0.227154	+	0.973859i	$0.572942\pi$
$572$		0			0
$573$	5.66846e14	+	1.79977e15i	0.383367	+	1.21721i
$574$		0			0
$575$			1.38643e13i			0.00919869i
$576$		0			0
$577$	−1.45340e15	+	8.39121e14i	−0.946059	+	0.546208i	−0.891855	−	0.452322i	$-0.850596\pi$
$577$	−1.45340e15	+	8.39121e14i	−0.946059	+	0.546208i	−0.0542048	+	0.998530i	$0.517262\pi$
$578$		0			0
$579$	−1.08469e14	+	4.88547e14i	−0.0692744	+	0.312014i
$580$		0			0
$581$	1.42356e15	+	1.58920e15i	0.892086	+	0.995884i
$582$		0			0
$583$	−7.47240e14	+	1.29426e15i	−0.459497	+	0.795873i
$584$		0			0
$585$	8.56490e14	−	1.83375e15i	0.516851	−	1.10658i
$586$		0			0
$587$	−9.88936e14			−0.585677			−0.292839	−	0.956162i	$-0.594600\pi$
$587$	−9.88936e14			−0.585677			−0.292839	+	0.956162i	$0.594600\pi$
$588$		0			0
$589$	1.23327e15			0.716841
$590$		0			0
$591$	−5.26456e14	+	5.74165e14i	−0.300352	+	0.327571i
$592$		0			0
$593$	−1.29844e15	+	2.24897e15i	−0.727147	+	1.25946i	0.230937	+	0.972969i	$0.425821\pi$
$593$	−1.29844e15	+	2.24897e15i	−0.727147	+	1.25946i	−0.958084	+	0.286487i	$0.907512\pi$
$594$		0			0
$595$	−1.35048e14	−	1.50762e14i	−0.0742414	−	0.0828797i
$596$		0			0
$597$	−2.28858e15	−	5.08118e14i	−1.23511	−	0.274224i
$598$		0			0
$599$	2.58250e15	−	1.49101e15i	1.36834	−	0.790010i	0.377622	−	0.925960i	$-0.376742\pi$
$599$	2.58250e15	−	1.49101e15i	1.36834	−	0.790010i	0.990716	+	0.135950i	$0.0434087\pi$
$600$		0			0
$601$			2.60328e15i			1.35429i	0.735849	+	0.677145i	$0.236783\pi$
$601$			2.60328e15i			1.35429i	−0.735849	+	0.677145i	$0.763217\pi$
$602$		0			0
$603$	2.20567e15	−	1.54237e15i	1.12667	−	0.787850i
$604$		0			0
$605$	−4.30964e14	−	7.46452e14i	−0.216166	−	0.374410i
$606$		0			0
$607$	−2.24583e15	−	1.29663e15i	−1.10621	−	0.638673i	−0.168367	−	0.985724i	$-0.553849\pi$
$607$	−2.24583e15	−	1.29663e15i	−1.10621	−	0.638673i	−0.937846	+	0.347052i	$0.887183\pi$
$608$		0			0
$609$	−1.40707e15	−	1.63276e13i	−0.680643	−	0.00789818i
$610$		0			0
$611$	−3.35846e15	−	1.93901e15i	−1.59556	−	0.921198i
$612$		0			0
$613$	−8.43272e14	−	1.46059e15i	−0.393491	−	0.681546i	0.599416	−	0.800437i	$-0.295399\pi$
$613$	−8.43272e14	−	1.46059e15i	−0.393491	−	0.681546i	−0.992907	+	0.118891i	$0.962066\pi$
$614$		0			0
$615$	−1.74676e15	+	5.50150e14i	−0.800608	+	0.252155i
$616$		0			0
$617$			1.01872e15i			0.458655i	0.973349	+	0.229328i	$0.0736528\pi$
$617$			1.01872e15i			0.458655i	−0.973349	+	0.229328i	$0.926347\pi$
$618$		0			0
$619$	−8.90995e13	+	5.14416e13i	−0.0394073	+	0.0227518i	−0.519574	−	0.854425i	$-0.673909\pi$
$619$	−8.90995e13	+	5.14416e13i	−0.0394073	+	0.0227518i	0.480167	+	0.877177i	$0.340576\pi$
$620$		0			0
$621$	−6.92526e13	+	2.86092e13i	−0.0300907	+	0.0124309i
$622$		0			0
$623$	−1.15103e15	+	2.41577e14i	−0.491364	+	0.103127i
$624$		0			0
$625$	1.43374e15	−	2.48332e15i	0.601355	−	1.04158i
$626$		0			0
$627$	−9.31064e14	−	8.53699e14i	−0.383714	−	0.351830i
$628$		0			0
$629$	−3.11858e14			−0.126293
$630$		0			0
$631$	2.41852e15			0.962473			0.481237	−	0.876591i	$-0.340188\pi$
$631$	2.41852e15			0.962473			0.481237	+	0.876591i	$0.340188\pi$
$632$		0			0
$633$	2.84845e15	+	2.61176e15i	1.11401	+	1.02144i
$634$		0			0
$635$	−1.75567e15	+	3.04091e15i	−0.674819	+	1.16882i
$636$		0			0
$637$	−2.83753e15	−	3.12954e14i	−1.07195	−	0.118226i
$638$		0			0
$639$	−3.44530e15	+	2.99250e14i	−1.27930	+	0.111117i
$640$		0			0
$641$	3.53679e15	−	2.04197e15i	1.29089	−	0.745297i	0.312080	−	0.950056i	$-0.398974\pi$
$641$	3.53679e15	−	2.04197e15i	1.29089	−	0.745297i	0.978812	+	0.204759i	$0.0656411\pi$
$642$		0			0
$643$		−	2.12552e15i		−	0.762613i	−0.924449	−	0.381307i	$-0.875474\pi$
$643$		−	2.12552e15i		−	0.762613i	0.924449	−	0.381307i	$-0.124526\pi$
$644$		0			0
$645$	1.67545e15	−	5.27692e14i	0.590955	−	0.186124i
$646$		0			0
$647$	−2.14842e15	−	3.72118e15i	−0.744983	−	1.29035i	−0.950203	−	0.311632i	$-0.899124\pi$
$647$	−2.14842e15	−	3.72118e15i	−0.744983	−	1.29035i	0.205220	−	0.978716i	$-0.434209\pi$
$648$		0			0
$649$	−2.02703e15	−	1.17031e15i	−0.691057	−	0.398982i
$650$		0			0
$651$	1.58242e15	+	2.81578e15i	0.530427	+	0.943852i
$652$		0			0
$653$	1.34746e15	+	7.77954e14i	0.444111	+	0.256408i	0.705340	−	0.708869i	$-0.250794\pi$
$653$	1.34746e15	+	7.77954e14i	0.444111	+	0.256408i	−0.261229	+	0.965277i	$0.584128\pi$
$654$		0			0
$655$	−3.93464e14	−	6.81500e14i	−0.127520	−	0.220871i
$656$		0			0
$657$	−6.80657e14	−	9.73376e14i	−0.216930	−	0.310221i
$658$		0			0
$659$		−	5.17044e15i		−	1.62053i	−0.586062	−	0.810266i	$-0.699322\pi$
$659$		−	5.17044e15i		−	1.62053i	0.586062	−	0.810266i	$-0.300678\pi$
$660$		0			0
$661$	3.01184e15	−	1.73889e15i	0.928375	−	0.535998i	0.0420781	−	0.999114i	$-0.486602\pi$
$661$	3.01184e15	−	1.73889e15i	0.928375	−	0.535998i	0.886297	+	0.463116i	$0.153269\pi$
$662$		0			0
$663$	−3.41204e14	−	7.57552e13i	−0.103440	−	0.0229662i
$664$		0			0
$665$	2.38956e15	+	7.83193e14i	0.712522	+	0.233534i
$666$		0			0
$667$	3.77797e13	−	6.54364e13i	0.0110807	−	0.0191923i
$668$		0			0
$669$	−3.69293e15	+	4.02760e15i	−1.06544	+	1.16199i
$670$		0			0
$671$	−1.71794e15			−0.487568
$672$		0			0
$673$	−5.19492e14			−0.145043			−0.0725213	−	0.997367i	$-0.523105\pi$
$673$	−5.19492e14			−0.145043			−0.0725213	+	0.997367i	$0.523105\pi$
$674$		0			0
$675$	−1.01968e15	−	1.35218e14i	−0.280087	−	0.0371418i
$676$		0			0
$677$	−3.09956e15	+	5.36860e15i	−0.837651	+	1.45085i	0.0542031	+	0.998530i	$0.482738\pi$
$677$	−3.09956e15	+	5.36860e15i	−0.837651	+	1.45085i	−0.891854	+	0.452324i	$0.850595\pi$
$678$		0			0
$679$	2.57519e15	−	2.30678e15i	0.684739	−	0.613371i
$680$		0			0
$681$	5.49342e14	−	2.47426e15i	0.143725	−	0.647344i
$682$		0			0
$683$	6.86275e14	−	3.96221e14i	0.176679	−	0.102006i	−0.409053	−	0.912511i	$-0.634141\pi$
$683$	6.86275e14	−	3.96221e14i	0.176679	−	0.102006i	0.585731	+	0.810505i	$0.300807\pi$
$684$		0			0
$685$			2.77902e15i			0.704034i
$686$		0			0
$687$	−4.14687e14	−	1.31666e15i	−0.103385	−	0.328254i
$688$		0			0
$689$	−2.56866e15	−	4.44904e15i	−0.630232	−	1.09159i
$690$		0			0
$691$	−1.57810e15	−	9.11118e14i	−0.381071	−	0.220011i	0.297213	−	0.954811i	$-0.403943\pi$
$691$	−1.57810e15	−	9.11118e14i	−0.381071	−	0.220011i	−0.678284	+	0.734800i	$0.737276\pi$
$692$		0			0
$693$	7.54501e14	−	3.22119e15i	0.179319	−	0.765567i
$694$		0			0
$695$	−5.24602e15	−	3.02879e15i	−1.22719	−	0.708521i
$696$		0			0
$697$	1.58129e14	+	2.73888e14i	0.0364109	+	0.0630656i
$698$		0			0
$699$	7.19530e14	+	2.28455e15i	0.163089	+	0.517817i
$700$		0			0
$701$			5.75889e15i			1.28496i	0.766302	+	0.642481i	$0.222095\pi$
$701$			5.75889e15i			1.28496i	−0.766302	+	0.642481i	$0.777905\pi$
$702$		0			0
$703$	3.35540e15	−	1.93724e15i	0.737038	−	0.425529i
$704$		0			0
$705$	−1.93914e15	+	8.73395e15i	−0.419343	+	1.88873i
$706$		0			0
$707$	−5.25117e14	+	1.60216e15i	−0.111802	+	0.341113i
$708$		0			0
$709$	1.72464e15	−	2.98717e15i	0.361530	−	0.626189i	−0.626682	−	0.779275i	$-0.715588\pi$
$709$	1.72464e15	−	2.98717e15i	0.361530	−	0.626189i	0.988213	+	0.153086i	$0.0489210\pi$
$710$		0			0
$711$	5.85324e15	+	2.73388e15i	1.20813	+	0.564282i
$712$		0			0
$713$	−1.73437e14			−0.0352493
$714$		0			0
$715$	−4.79843e15			−0.960319
$716$		0			0
$717$	−7.57503e14	+	8.26150e14i	−0.149289	+	0.162818i
$718$		0			0
$719$	−1.63595e15	+	2.83355e15i	−0.317513	+	0.549949i	−0.979969	−	0.199153i	$-0.936181\pi$
$719$	−1.63595e15	+	2.83355e15i	−0.317513	+	0.549949i	0.662455	+	0.749101i	$0.269514\pi$
$720$		0			0
$721$	7.46874e14	+	3.55860e15i	0.142759	+	0.680198i
$722$		0			0
$723$	−8.20960e15	−	1.82272e15i	−1.54547	−	0.343131i
$724$		0			0
$725$	8.98290e14	−	5.18628e14i	0.166555	−	0.0961605i
$726$		0			0
$727$		−	6.23590e15i		−	1.13883i	−0.822049	−	0.569417i	$-0.807169\pi$
$727$		−	6.23590e15i		−	1.13883i	0.822049	−	0.569417i	$-0.192831\pi$
$728$		0			0
$729$	−1.42870e15	−	5.37233e15i	−0.257004	−	0.966410i
$730$		0			0
$731$	−1.51674e14	−	2.62707e14i	−0.0268761	−	0.0465508i
$732$		0			0
$733$	−2.42939e15	−	1.40261e15i	−0.424058	−	0.244830i	0.272754	−	0.962084i	$-0.412065\pi$
$733$	−2.42939e15	−	1.40261e15i	−0.424058	−	0.244830i	−0.696812	+	0.717254i	$0.745399\pi$
$734$		0			0
$735$	1.27789e15	+	6.46074e15i	0.219742	+	1.11097i
$736$		0			0
$737$	−5.52617e15	−	3.19053e15i	−0.936166	−	0.540496i
$738$		0			0
$739$	−2.43363e15	−	4.21517e15i	−0.406172	−	0.703511i	0.588285	−	0.808654i	$-0.299803\pi$
$739$	−2.43363e15	−	4.21517e15i	−0.406172	−	0.703511i	−0.994457	+	0.105143i	$0.966470\pi$
$740$		0			0
$741$	4.14173e15	−	1.30446e15i	0.681054	−	0.214501i
$742$		0			0
$743$		−	5.39615e15i		−	0.874270i	−0.899396	−	0.437135i	$-0.855993\pi$
$743$		−	5.39615e15i		−	0.874270i	0.899396	−	0.437135i	$-0.144007\pi$
$744$		0			0
$745$	−6.28005e15	+	3.62579e15i	−1.00254	+	0.578820i
$746$		0			0
$747$	−7.35486e14	−	8.46772e15i	−0.115694	−	1.33200i
$748$		0			0
$749$	2.13063e15	+	1.01517e16i	0.330261	+	1.57358i
$750$		0			0
$751$	5.36130e15	−	9.28604e15i	0.818936	−	1.41844i	−0.0875305	−	0.996162i	$-0.527898\pi$
$751$	5.36130e15	−	9.28604e15i	0.818936	−	1.41844i	0.906467	−	0.422277i	$-0.138769\pi$
$752$		0			0
$753$	9.46353e15	+	8.67718e15i	1.42456	+	1.30619i
$754$		0			0
$755$	1.35071e16			2.00380
$756$		0			0
$757$	−1.27253e16			−1.86055			−0.930277	−	0.366858i	$-0.880433\pi$
$757$	−1.27253e16			−1.86055			−0.930277	+	0.366858i	$0.880433\pi$
$758$		0			0
$759$	1.30938e14	+	1.20058e14i	0.0188684	+	0.0173006i
$760$		0			0
$761$	−3.35419e15	+	5.80963e15i	−0.476400	+	0.825150i	−0.999634	−	0.0270393i	$-0.991392\pi$
$761$	−3.35419e15	+	5.80963e15i	−0.476400	+	0.825150i	0.523234	+	0.852189i	$0.324725\pi$
$762$		0			0
$763$	−1.73684e15	+	5.29917e15i	−0.243150	+	0.741862i
$764$		0			0
$765$	6.97732e13	+	8.03306e14i	0.00962833	+	0.110852i
$766$		0			0
$767$	6.96796e15	−	4.02296e15i	0.947832	−	0.547231i
$768$		0			0
$769$		−	2.36172e15i		−	0.316689i	−0.987384	−	0.158344i	$-0.949384\pi$
$769$		−	2.36172e15i		−	0.316689i	0.987384	−	0.158344i	$-0.0506156\pi$
$770$		0			0
$771$	6.98682e15	−	2.20053e15i	0.923593	−	0.290890i
$772$		0			0
$773$	−1.77222e15	−	3.06958e15i	−0.230957	−	0.400029i	0.727133	−	0.686496i	$-0.240852\pi$
$773$	−1.77222e15	−	3.06958e15i	−0.230957	−	0.400029i	−0.958090	+	0.286468i	$0.907519\pi$
$774$		0			0
$775$	−2.06191e15	−	1.19045e15i	−0.264918	−	0.152950i
$776$		0			0
$777$	8.72844e15	+	5.17533e15i	1.10566	+	0.655575i
$778$		0			0
$779$	−3.40274e15	−	1.96457e15i	−0.424984	−	0.245365i
$780$		0			0
$781$	4.09955e15	+	7.10063e15i	0.504842	+	0.874412i
$782$		0			0
$783$	4.44418e15	+	3.41678e15i	0.539637	+	0.414884i
$784$		0			0
$785$			2.75929e15i			0.330380i
$786$		0			0
$787$	−1.88415e15	+	1.08781e15i	−0.222461	+	0.128438i	−0.607089	−	0.794634i	$-0.707663\pi$
$787$	−1.88415e15	+	1.08781e15i	−0.222461	+	0.128438i	0.384628	+	0.923072i	$0.374330\pi$
$788$		0			0
$789$	9.62128e15	+	2.13615e15i	1.12024	+	0.248718i
$790$		0			0
$791$	−4.24721e15	+	3.80453e15i	−0.487678	+	0.436848i
$792$		0			0
$793$	2.95274e15	−	5.11429e15i	0.334366	−	0.579139i
$794$		0			0
$795$	−8.00973e15	+	8.73559e15i	−0.894537	+	0.975603i
$796$		0			0
$797$	8.98808e15			0.990025			0.495013	−	0.868886i	$-0.335163\pi$
$797$	8.98808e15			0.990025			0.495013	+	0.868886i	$0.335163\pi$
$798$		0			0
$799$	1.54501e15			0.167851
$800$		0			0
$801$	4.24513e15	+	1.98277e15i	0.454896	+	0.212469i
$802$		0			0
$803$	−1.40800e15	+	2.43873e15i	−0.148822	+	0.257768i
$804$		0			0
$805$	−3.36050e14	−	1.10142e14i	−0.0350369	−	0.0114836i
$806$		0			0
$807$	−3.24819e14	+	1.46300e15i	−0.0334070	+	0.150466i
$808$		0			0
$809$	1.27846e16	−	7.38118e15i	1.29709	−	0.748874i	0.317188	−	0.948363i	$-0.397261\pi$
$809$	1.27846e16	−	7.38118e15i	1.29709	−	0.748874i	0.979900	+	0.199489i	$0.0639281\pi$
$810$		0			0
$811$		−	1.66586e16i		−	1.66734i	−0.552261	−	0.833671i	$-0.686235\pi$
$811$		−	1.66586e16i		−	1.66734i	0.552261	−	0.833671i	$-0.313765\pi$
$812$		0			0
$813$	−2.99890e14	−	9.52169e14i	−0.0296117	−	0.0940191i
$814$		0			0
$815$	5.55922e14	+	9.62885e14i	0.0541561	+	0.0938010i
$816$		0			0
$817$	3.26384e15	+	1.88438e15i	0.313695	+	0.181112i
$818$		0			0
$819$	8.29262e15	+	7.78260e15i	0.786376	+	0.738011i
$820$		0			0
$821$	1.41291e16	+	8.15745e15i	1.32199	+	0.763250i	0.984046	−	0.177916i	$-0.0569357\pi$
$821$	1.41291e16	+	8.15745e15i	1.32199	+	0.763250i	0.337943	+	0.941167i	$0.390269\pi$
$822$		0			0
$823$	6.67192e14	+	1.15561e15i	0.0615959	+	0.106687i	0.895179	−	0.445707i	$-0.147048\pi$
$823$	6.67192e14	+	1.15561e15i	0.0615959	+	0.106687i	−0.833583	+	0.552394i	$0.813714\pi$
$824$		0			0
$825$	7.32599e14	+	2.32605e15i	0.0667375	+	0.211896i
$826$		0			0
$827$		−	1.54809e15i		−	0.139160i	−0.997576	−	0.0695801i	$-0.977834\pi$
$827$		−	1.54809e15i		−	0.139160i	0.997576	−	0.0695801i	$-0.0221659\pi$
$828$		0			0
$829$	−1.13497e16	+	6.55276e15i	−1.00678	+	0.581265i	−0.910247	−	0.414065i	$-0.864109\pi$
$829$	−1.13497e16	+	6.55276e15i	−1.00678	+	0.581265i	−0.0965332	+	0.995330i	$0.530775\pi$
$830$		0			0
$831$	−2.99415e15	+	1.34857e16i	−0.262100	+	1.18051i
$832$		0			0
$833$	1.04136e15	−	4.57261e14i	0.0899610	−	0.0395018i
$834$		0			0
$835$	−2.69834e15	+	4.67367e15i	−0.230050	+	0.398458i
$836$		0			0
$837$	1.69152e15	−	1.27558e16i	0.142327	−	1.07329i
$838$		0			0
$839$	1.57899e16			1.31126			0.655631	−	0.755082i	$-0.272403\pi$
$839$	1.57899e16			1.31126			0.655631	+	0.755082i	$0.272403\pi$
$840$		0			0
$841$	6.54756e15			0.536663
$842$		0			0
$843$	−7.58637e15	+	8.27387e15i	−0.613737	+	0.669355i
$844$		0			0
$845$	1.15620e15	−	2.00260e15i	0.0923255	−	0.159912i
$846$		0			0
$847$	4.74001e15	−	9.94827e14i	0.373612	−	0.0784131i
$848$		0			0
$849$	1.16896e16	+	2.59536e15i	0.909509	+	0.201932i
$850$		0			0
$851$	−4.71879e14	+	2.72439e14i	−0.0362425	+	0.0209246i
$852$		0			0
$853$		−	1.86206e16i		−	1.41180i	−0.708309	−	0.705902i	$-0.750542\pi$
$853$		−	1.86206e16i		−	1.41180i	0.708309	−	0.705902i	$-0.249458\pi$
$854$		0			0
$855$	−5.74079e15	−	8.20964e15i	−0.429693	−	0.614484i
$856$		0			0
$857$	−5.37825e15	−	9.31540e15i	−0.397417	−	0.688346i	0.595989	−	0.802992i	$-0.296760\pi$
$857$	−5.37825e15	−	9.31540e15i	−0.397417	−	0.688346i	−0.993406	+	0.114646i	$0.963427\pi$
$858$		0			0
$859$	−1.21534e16	−	7.01678e15i	−0.886617	−	0.511888i	−0.0137823	−	0.999905i	$-0.504387\pi$
$859$	−1.21534e16	−	7.01678e15i	−0.886617	−	0.511888i	−0.872834	+	0.488017i	$0.837721\pi$
$860$		0			0
$861$	1.19404e14	−	1.02899e16i	0.00860004	−	0.741127i
$862$		0			0
$863$	−1.97250e15	−	1.13882e15i	−0.140267	−	0.0809834i	0.428224	−	0.903673i	$-0.359139\pi$
$863$	−1.97250e15	−	1.13882e15i	−0.140267	−	0.0809834i	−0.568491	+	0.822689i	$0.692473\pi$
$864$		0			0
$865$	1.03346e16	+	1.79001e16i	0.725615	+	1.25680i
$866$		0			0
$867$	−1.36256e16	+	4.29143e15i	−0.944604	+	0.297507i
$868$		0			0
$869$		−	1.53163e16i		−	1.04845i
$870$		0			0
$871$	1.89964e16	−	1.09676e16i	1.28402	−	0.741327i
$872$		0			0
$873$	−1.37214e16	+	1.19181e15i	−0.915840	+	0.0795477i
$874$		0			0
$875$	8.22525e15	+	9.18230e15i	0.542132	+	0.605211i
$876$		0			0
$877$	−4.45135e15	+	7.70996e15i	−0.289730	+	0.501827i	−0.973745	−	0.227640i	$-0.926899\pi$
$877$	−4.45135e15	+	7.70996e15i	−0.289730	+	0.501827i	0.684015	+	0.729468i	$0.260232\pi$
$878$		0			0
$879$	9.14372e14	+	8.38394e14i	0.0587738	+	0.0538902i
$880$		0			0
$881$	−2.28068e16			−1.44776			−0.723881	−	0.689925i	$-0.757644\pi$
$881$	−2.28068e16			−1.44776			−0.723881	+	0.689925i	$0.757644\pi$
$882$		0			0
$883$	1.40349e16			0.879883			0.439942	−	0.898026i	$-0.354999\pi$
$883$	1.40349e16			0.879883			0.439942	+	0.898026i	$0.354999\pi$
$884$		0			0
$885$	−1.36814e16	−	1.25446e16i	−0.847117	−	0.776728i
$886$		0			0
$887$	1.05437e16	−	1.82622e16i	0.644783	−	1.11680i	−0.339568	−	0.940581i	$-0.610281\pi$
$887$	1.05437e16	−	1.82622e16i	0.644783	−	1.11680i	0.984352	−	0.176216i	$-0.0563857\pi$
$888$		0			0
$889$	−1.31648e16	−	1.46965e16i	−0.795158	−	0.887679i
$890$		0			0
$891$	−1.01069e16	+	8.45916e15i	−0.602964	+	0.504661i
$892$		0			0
$893$	−1.66233e16	+	9.59748e15i	−0.979569	+	0.565554i
$894$		0			0
$895$			2.64364e16i			1.53878i
$896$		0			0
$897$	−5.82462e14	+	1.83449e14i	−0.0334895	+	0.0105477i
$898$		0			0
$899$	6.48783e15	+	1.12372e16i	0.368486	+	0.638237i
$900$		0			0
$901$	1.77251e15	+	1.02336e15i	0.0994493	+	0.0574171i
$902$		0			0
$903$	−1.14530e14	+	9.86983e15i	−0.00634797	+	0.547050i
$904$		0			0
$905$	−2.93269e16	−	1.69319e16i	−1.60583	−	0.927127i
$906$		0			0
$907$	−2.70935e15	−	4.69274e15i	−0.146563	−	0.253855i	0.783392	−	0.621528i	$-0.213488\pi$
$907$	−2.70935e15	−	4.69274e15i	−0.146563	−	0.253855i	−0.929955	+	0.367673i	$0.880155\pi$
$908$		0			0
$909$	5.50442e15	−	3.84910e15i	0.294178	−	0.205711i
$910$		0			0
$911$			2.06305e16i			1.08933i	0.838654	+	0.544664i	$0.183343\pi$
$911$			2.06305e16i			1.08933i	−0.838654	+	0.544664i	$0.816657\pi$
$912$		0			0
$913$	−1.74517e16	+	1.00757e16i	−0.910432	+	0.525638i
$914$		0			0
$915$	−1.33001e16	−	2.95294e15i	−0.685552	−	0.152208i
$916$		0			0
$917$	4.32757e15	−	9.08263e14i	0.220400	−	0.0462573i
$918$		0			0
$919$	−3.73749e15	+	6.47352e15i	−0.188081	+	0.325766i	−0.944610	−	0.328194i	$-0.893560\pi$
$919$	−3.73749e15	+	6.47352e15i	−0.188081	+	0.325766i	0.756530	+	0.653960i	$0.226893\pi$
$920$		0			0
$921$	−1.03749e16	+	1.13151e16i	−0.515890	+	0.562642i
$922$		0			0
$923$	−2.81846e16			−1.38485
$924$		0			0
$925$	−7.47992e15			−0.363176
$926$		0			0
$927$	6.13007e15	−	1.31245e16i	0.294122	−	0.629716i
$928$		0			0
$929$	−1.07530e16	+	1.86248e16i	−0.509852	+	0.883089i	0.490083	+	0.871676i	$0.336966\pi$
$929$	−1.07530e16	+	1.86248e16i	−0.509852	+	0.883089i	−0.999935	+	0.0114133i	$0.996367\pi$
$930$		0			0
$931$	−8.36394e15	+	1.13887e16i	−0.391911	+	0.533644i
$932$		0			0
$933$	8.13379e15	−	3.66349e16i	0.376655	−	1.69647i
$934$		0			0
$935$	1.65558e15	−	9.55851e14i	0.0757682	−	0.0437448i
$936$		0			0
$937$			2.14239e16i			0.969017i	0.874786	+	0.484509i	$0.161002\pi$
$937$			2.14239e16i			0.969017i	−0.874786	+	0.484509i	$0.838998\pi$
$938$		0			0
$939$	8.88012e15	+	2.81949e16i	0.396971	+	1.26041i
$940$		0			0
$941$	−6.58944e15	−	1.14132e16i	−0.291142	−	0.504273i	0.682938	−	0.730476i	$-0.260702\pi$
$941$	−6.58944e15	−	1.14132e16i	−0.291142	−	0.504273i	−0.974080	+	0.226203i	$0.927369\pi$
$942$		0			0
$943$	4.78536e14	+	2.76283e14i	0.0208978	+	0.0120654i
$944$		0			0
$945$	1.13781e16	−	2.36412e16i	0.491128	−	1.02046i
$946$		0			0
$947$	−8.23381e15	−	4.75379e15i	−0.351298	−	0.202822i	0.313959	−	0.949437i	$-0.398345\pi$
$947$	−8.23381e15	−	4.75379e15i	−0.351298	−	0.202822i	−0.665257	+	0.746614i	$0.731678\pi$
$948$		0			0
$949$	−4.84004e15	−	8.38320e15i	−0.204120	−	0.353546i
$950$		0			0
$951$	5.07990e15	+	1.61290e16i	0.211769	+	0.672379i
$952$		0			0
$953$		−	2.42402e16i		−	0.998909i	−0.866340	−	0.499454i	$-0.833534\pi$
$953$		−	2.42402e16i		−	0.998909i	0.866340	−	0.499454i	$-0.166466\pi$
$954$		0			0
$955$	3.07248e16	−	1.77390e16i	1.25161	−	0.722620i
$956$		0			0
$957$	2.88068e15	−	1.29747e16i	0.116006	−	0.522494i
$958$		0			0
$959$	−1.48390e16	−	4.86357e15i	−0.590747	−	0.193621i
$960$		0			0
$961$	2.18778e15	−	3.78935e15i	0.0861044	−	0.149137i
$962$		0			0
$963$	1.74874e16	−	3.74406e16i	0.680426	−	1.45679i
$964$		0			0
$965$	9.40933e15			0.361958
$966$		0			0
$967$	1.31942e16			0.501809			0.250904	−	0.968012i	$-0.419272\pi$
$967$	1.31942e16			0.501809			0.250904	+	0.968012i	$0.419272\pi$
$968$		0			0
$969$	−1.16916e15	+	1.27511e15i	−0.0439634	+	0.0479475i
$970$		0			0
$971$	−9.34749e15	+	1.61903e16i	−0.347528	+	0.601936i	−0.985810	−	0.167867i	$-0.946312\pi$
$971$	−9.34749e15	+	1.61903e16i	−0.347528	+	0.601936i	0.638282	+	0.769803i	$0.279645\pi$
$972$		0			0
$973$	2.53537e16	−	2.27111e16i	0.932010	−	0.834869i
$974$		0			0
$975$	−8.18378e15	−	1.81699e15i	−0.297460	−	0.0660430i
$976$		0			0
$977$	−7.06726e15	+	4.08028e15i	−0.253998	+	0.146646i	−0.621594	−	0.783340i	$-0.713514\pi$
$977$	−7.06726e15	+	4.08028e15i	−0.253998	+	0.146646i	0.367595	+	0.929986i	$0.380181\pi$
$978$		0			0
$979$		−	1.11084e16i		−	0.394771i
$980$		0			0
$981$	1.82060e16	−	1.27310e16i	0.639786	−	0.447386i
$982$		0			0
$983$	1.74611e16	+	3.02436e16i	0.606776	+	1.05097i	0.991768	+	0.128047i	$0.0408708\pi$
$983$	1.74611e16	+	3.02436e16i	0.606776	+	1.05097i	−0.384992	+	0.922920i	$0.625796\pi$
$984$		0			0
$985$	1.26842e16	+	7.32325e15i	0.435878	+	0.251654i
$986$		0			0
$987$	−4.32425e16	−	2.56396e16i	−1.46949	−	0.871298i
$988$		0			0
$989$	−4.59002e14	−	2.65005e14i	−0.0154254	−	0.00890583i
$990$		0			0
$991$	−1.67476e16	−	2.90077e16i	−0.556605	−	0.964068i	−0.997777	−	0.0666452i	$-0.978770\pi$
$991$	−1.67476e16	−	2.90077e16i	−0.556605	−	0.964068i	0.441172	−	0.897423i	$-0.354563\pi$
$992$		0			0
$993$	−1.07399e16	+	3.38259e15i	−0.353005	+	0.111180i
$994$		0			0
$995$			4.40776e16i			1.43282i
$996$		0			0
$997$	−1.49053e16	+	8.60555e15i	−0.479199	+	0.276666i	−0.720083	−	0.693888i	$-0.755896\pi$
$997$	−1.49053e16	+	8.60555e15i	−0.479199	+	0.276666i	0.240884	+	0.970554i	$0.422563\pi$
$998$		0			0
$999$	−1.54349e16	−	3.73623e16i	−0.490787	−	1.18802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.12.k.b.5.6	✓	56
3.2	odd	2	inner	84.12.k.b.5.17	yes	56
7.3	odd	6	inner	84.12.k.b.17.17	yes	56
21.17	even	6	inner	84.12.k.b.17.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.12.k.b.5.6	✓	56	1.1	even	1	trivial
84.12.k.b.5.17	yes	56	3.2	odd	2	inner
84.12.k.b.17.6	yes	56	21.17	even	6	inner
84.12.k.b.17.17	yes	56	7.3	odd	6	inner

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.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-310.222 - 284.445i) q^{3} +(-3956.77 + 6853.32i) q^{5} +(-29669.5 - 33121.7i) q^{7} +(15328.9 + 176483. i) q^{9} +O(q^{10})\)	\(q+(-310.222 - 284.445i) q^{3} +(-3956.77 + 6853.32i) q^{5} +(-29669.5 - 33121.7i) q^{7} +(15328.9 + 176483. i) q^{9} +(363724. - 209996. i) q^{11} +1.44373e6i q^{13} +(3.17687e6 - 1.00057e6i) q^{15} +(-287593. - 498126. i) q^{17} +(6.18865e6 + 3.57302e6i) q^{19} +(-217162. + 1.87144e7i) q^{21} +(-870326. - 502483. i) q^{23} +(-6.89792e6 - 1.19475e7i) q^{25} +(4.54443e7 - 5.91091e7i) q^{27} +7.51861e7i q^{29} +(1.49459e8 - 8.62903e7i) q^{31} +(-1.72568e8 - 3.83140e7i) q^{33} +(3.44389e8 - 7.22798e7i) q^{35} +(2.71093e8 - 4.69547e8i) q^{37} +(4.10663e8 - 4.47879e8i) q^{39} -5.49836e8 q^{41} +5.27391e8 q^{43} +(-1.27014e9 - 5.93246e8i) q^{45} +(-1.34305e9 + 2.32623e9i) q^{47} +(-2.16767e8 + 1.96541e9i) q^{49} +(-5.24717e7 + 2.36334e8i) q^{51} +(-3.08162e9 + 1.77918e9i) q^{53} +3.32362e9i q^{55} +(-9.03529e8 - 2.86876e9i) q^{57} +(-2.78649e9 - 4.82635e9i) q^{59} +(-3.54241e9 - 2.04521e9i) q^{61} +(5.39060e9 - 5.74387e9i) q^{63} +(-9.89437e9 - 5.71252e9i) q^{65} +(-7.59665e9 - 1.31578e10i) q^{67} +(1.27066e8 + 4.03441e8i) q^{69} +1.95220e10i q^{71} +(-5.80661e9 + 3.35245e9i) q^{73} +(-1.25853e9 + 5.66848e9i) q^{75} +(-1.77469e10 - 5.81667e9i) q^{77} +(1.82341e10 - 3.15824e10i) q^{79} +(-3.09111e10 + 5.41055e9i) q^{81} -4.79805e10 q^{83} +4.55176e9 q^{85} +(2.13863e10 - 2.33244e10i) q^{87} +(1.32245e10 - 2.29055e10i) q^{89} +(4.78189e10 - 4.28349e10i) q^{91} +(-7.09104e10 - 1.57438e10i) q^{93} +(-4.89740e10 + 2.82752e10i) q^{95} +7.77493e10i q^{97} +(4.26361e10 + 6.09719e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 729 q^{3} - 27194 q^{7} - 172347 q^{9}+O(q^{10}) \) 56 * q - 729 * q^3 - 27194 * q^7 - 172347 * q^9	\( 56 q - 729 q^{3} - 27194 q^{7} - 172347 q^{9} - 4853058 q^{15} + 28700520 q^{19} - 11325429 q^{21} - 316601194 q^{25} - 1368416388 q^{31} + 40874949 q^{33} - 87435712 q^{37} + 1177474410 q^{39} - 3055078348 q^{43} + 4109921793 q^{45} - 742582522 q^{49} - 694793715 q^{51} + 14605100370 q^{57} + 72584834058 q^{61} - 7310837811 q^{63} + 6131679148 q^{67} - 74402605464 q^{73} - 161115157854 q^{75} + 52181713528 q^{79} + 44948282337 q^{81} + 4658488716 q^{85} + 243101263104 q^{87} - 85311757146 q^{91} - 256628211777 q^{93} + 157345775874 q^{99}+O(q^{100}) \) 56 * q - 729 * q^3 - 27194 * q^7 - 172347 * q^9 - 4853058 * q^15 + 28700520 * q^19 - 11325429 * q^21 - 316601194 * q^25 - 1368416388 * q^31 + 40874949 * q^33 - 87435712 * q^37 + 1177474410 * q^39 - 3055078348 * q^43 + 4109921793 * q^45 - 742582522 * q^49 - 694793715 * q^51 + 14605100370 * q^57 + 72584834058 * q^61 - 7310837811 * q^63 + 6131679148 * q^67 - 74402605464 * q^73 - 161115157854 * q^75 + 52181713528 * q^79 + 44948282337 * q^81 + 4658488716 * q^85 + 243101263104 * q^87 - 85311757146 * q^91 - 256628211777 * q^93 + 157345775874 * q^99

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