LMFDB - Embedded newform 84.12.i.a.37.6

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:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} + 198245134 x^{12} + 414863096508 x^{11} + \cdots + 37\!\cdots\!56 $ x^14 - 6x^13 + 198245134x^12 + 414863096508x^11 + 26949056203541719x^10 + 65398284799267941978x^9 + 2028387875108119977261582x^8 + 6445062169106156227737324792x^7 + 111668469386916870576107083796769x^6 + 325583881393416391390922284227512022x^5 + 3320063138939962847561145196113433362264x^4 + 9575836750537552288866777850271834960214456x^3 + 68507643214686757134474644335292207644539438816x^2 + 142358467144947535218510754697116911147938126144352*x + 378103215519089647001740821506658140294236360807649856
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{30}\cdot 3^{12}\cdot 7^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.6
Root			$-3853.65 - 6674.72i$ of defining polynomial
Character	$\chi$	$=$	84.37
Dual form			84.12.i.a.25.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(121.500 + 210.444i) q^{3} +(4369.65 - 7568.45i) q^{5} +(-2593.70 + 44391.4i) q^{7} +(-29524.5 + 51137.9i) q^{9} +O(q^{10})$	\(q+(121.500 + 210.444i) q^{3} +(4369.65 - 7568.45i) q^{5} +(-2593.70 + 44391.4i) q^{7} +(-29524.5 + 51137.9i) q^{9} +(187116. + 324094. i) q^{11} -1.46722e6 q^{13} +2.12365e6 q^{15} +(-4.80119e6 - 8.31590e6i) q^{17} +(-1.40452e6 + 2.43270e6i) q^{19} +(-9.65705e6 + 4.84773e6i) q^{21} +(7.13014e6 - 1.23498e7i) q^{23} +(-1.37736e7 - 2.38566e7i) q^{25} -1.43489e7 q^{27} -9.71034e7 q^{29} +(1.41548e8 + 2.45168e8i) q^{31} +(-4.54691e7 + 7.87548e7i) q^{33} +(3.24641e8 + 2.13605e8i) q^{35} +(-2.34630e8 + 4.06392e8i) q^{37} +(-1.78267e8 - 3.08768e8i) q^{39} +5.02645e8 q^{41} -1.83098e9 q^{43} +(2.58023e8 + 4.46910e8i) q^{45} +(9.87927e8 - 1.71114e9i) q^{47} +(-1.96387e9 - 2.30276e8i) q^{49} +(1.16669e9 - 2.02076e9i) q^{51} +(-1.60585e9 - 2.78142e9i) q^{53} +3.27052e9 q^{55} -6.82597e8 q^{57} +(-2.85842e9 - 4.95094e9i) q^{59} +(-5.86773e9 + 1.01632e10i) q^{61} +(-2.19351e9 - 1.44327e9i) q^{63} +(-6.41124e9 + 1.11046e10i) q^{65} +(2.07880e9 + 3.60059e9i) q^{67} +3.46525e9 q^{69} +5.49068e9 q^{71} +(-8.63209e9 - 1.49512e10i) q^{73} +(3.34699e9 - 5.79715e9i) q^{75} +(-1.48723e10 + 7.46573e9i) q^{77} +(-6.75650e9 + 1.17026e10i) q^{79} +(-1.74339e9 - 3.01964e9i) q^{81} -7.12546e10 q^{83} -8.39181e10 q^{85} +(-1.17981e10 - 2.04349e10i) q^{87} +(-1.10945e10 + 1.92162e10i) q^{89} +(3.80553e9 - 6.51320e10i) q^{91} +(-3.43961e10 + 5.95758e10i) q^{93} +(1.22745e10 + 2.12601e10i) q^{95} -1.49556e9 q^{97} -2.20980e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 1701 q^{3} + 7218 q^{5} + 35001 q^{7} - 413343 q^{9}+O(q^{10}) $ 14 * q + 1701 * q^3 + 7218 * q^5 + 35001 * q^7 - 413343 * q^9	$ 14 q + 1701 q^{3} + 7218 q^{5} + 35001 q^{7} - 413343 q^{9} + 54450 q^{11} + 1534982 q^{13} + 3507948 q^{15} + 1478880 q^{17} - 22875935 q^{19} + 3394224 q^{21} + 62540568 q^{23} - 62136141 q^{25} - 200884698 q^{27} + 102097728 q^{29} + 188600405 q^{31} - 13231350 q^{33} - 253840734 q^{35} + 199685599 q^{37} + 186500313 q^{39} - 693868716 q^{41} - 620701754 q^{43} + 426215682 q^{45} + 2771987346 q^{47} - 5209147075 q^{49} - 359367840 q^{51} + 6487034184 q^{53} + 10046238656 q^{55} - 11117704410 q^{57} - 8183838888 q^{59} + 4069556330 q^{61} - 1241977617 q^{63} - 1520229906 q^{65} + 15766443531 q^{67} + 30394716048 q^{69} - 33183285444 q^{71} - 31685143839 q^{73} + 15099082263 q^{75} + 3261253500 q^{77} + 21999509987 q^{79} - 24407490807 q^{81} - 63053885988 q^{83} + 35204204624 q^{85} + 12404873952 q^{87} + 67041904680 q^{89} - 190876959523 q^{91} - 45829898415 q^{93} + 133488871470 q^{95} + 284083418100 q^{97} - 6430436100 q^{99}+O(q^{100}) $ 14 * q + 1701 * q^3 + 7218 * q^5 + 35001 * q^7 - 413343 * q^9 + 54450 * q^11 + 1534982 * q^13 + 3507948 * q^15 + 1478880 * q^17 - 22875935 * q^19 + 3394224 * q^21 + 62540568 * q^23 - 62136141 * q^25 - 200884698 * q^27 + 102097728 * q^29 + 188600405 * q^31 - 13231350 * q^33 - 253840734 * q^35 + 199685599 * q^37 + 186500313 * q^39 - 693868716 * q^41 - 620701754 * q^43 + 426215682 * q^45 + 2771987346 * q^47 - 5209147075 * q^49 - 359367840 * q^51 + 6487034184 * q^53 + 10046238656 * q^55 - 11117704410 * q^57 - 8183838888 * q^59 + 4069556330 * q^61 - 1241977617 * q^63 - 1520229906 * q^65 + 15766443531 * q^67 + 30394716048 * q^69 - 33183285444 * q^71 - 31685143839 * q^73 + 15099082263 * q^75 + 3261253500 * q^77 + 21999509987 * q^79 - 24407490807 * q^81 - 63053885988 * q^83 + 35204204624 * q^85 + 12404873952 * q^87 + 67041904680 * q^89 - 190876959523 * q^91 - 45829898415 * q^93 + 133488871470 * q^95 + 284083418100 * q^97 - 6430436100 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	121.500	+	210.444i	0.288675	+	0.500000i
$3$	121.500	+	210.444i	0.288675	+	0.500000i
$4$		0			0
$5$	4369.65	−	7568.45i	0.625333	−	1.08311i	−0.363143	−	0.931733i	$-0.618296\pi$
$5$	4369.65	−	7568.45i	0.625333	−	1.08311i	0.988476	−	0.151376i	$-0.0483703\pi$
$6$		0			0
$7$	−2593.70	+	44391.4i	−0.0583284	+	0.998297i
$7$	−2593.70	+	44391.4i	−0.0583284	+	0.998297i
$8$		0			0
$9$	−29524.5	+	51137.9i	−0.166667	+	0.288675i
$10$		0			0
$11$	187116.	+	324094.i	0.350308	+	0.606752i	0.986303	−	0.164941i	$-0.0527435\pi$
$11$	187116.	+	324094.i	0.350308	+	0.606752i	−0.635995	+	0.771693i	$0.719410\pi$
$12$		0			0
$13$	−1.46722e6			−1.09599			−0.547995	−	0.836481i	$-0.684609\pi$
$13$	−1.46722e6			−1.09599			−0.547995	+	0.836481i	$0.684609\pi$
$14$		0			0
$15$	2.12365e6			0.722073
$16$		0			0
$17$	−4.80119e6	−	8.31590e6i	−0.820124	−	1.42050i	−0.905589	−	0.424156i	$-0.860571\pi$
$17$	−4.80119e6	−	8.31590e6i	−0.820124	−	1.42050i	0.0854646	−	0.996341i	$-0.472763\pi$
$18$		0			0
$19$	−1.40452e6	+	2.43270e6i	−0.130132	+	0.225395i	−0.923727	−	0.383051i	$-0.874873\pi$
$19$	−1.40452e6	+	2.43270e6i	−0.130132	+	0.225395i	0.793595	+	0.608446i	$0.208207\pi$
$20$		0			0
$21$	−9.65705e6	+	4.84773e6i	−0.515987	+	0.259019i
$22$		0			0
$23$	7.13014e6	−	1.23498e7i	0.230991	−	0.400088i	−0.727109	−	0.686522i	$-0.759137\pi$
$23$	7.13014e6	−	1.23498e7i	0.230991	−	0.400088i	0.958100	+	0.286434i	$0.0924699\pi$
$24$		0			0
$25$	−1.37736e7	−	2.38566e7i	−0.282083	−	0.488583i
$26$		0			0
$27$	−1.43489e7			−0.192450
$28$		0			0
$29$	−9.71034e7			−0.879115			−0.439557	−	0.898215i	$-0.644865\pi$
$29$	−9.71034e7			−0.879115			−0.439557	+	0.898215i	$0.644865\pi$
$30$		0			0
$31$	1.41548e8	+	2.45168e8i	0.888002	+	1.53806i	0.842234	+	0.539113i	$0.181240\pi$
$31$	1.41548e8	+	2.45168e8i	0.888002	+	1.53806i	0.0457685	+	0.998952i	$0.485426\pi$
$32$		0			0
$33$	−4.54691e7	+	7.87548e7i	−0.202251	+	0.350308i
$34$		0			0
$35$	3.24641e8	+	2.13605e8i	1.04479	+	0.687445i
$36$		0			0
$37$	−2.34630e8	+	4.06392e8i	−0.556256	+	0.963464i	0.441548	+	0.897237i	$0.354429\pi$
$37$	−2.34630e8	+	4.06392e8i	−0.556256	+	0.963464i	−0.997805	+	0.0662267i	$0.978904\pi$
$38$		0			0
$39$	−1.78267e8	−	3.08768e8i	−0.316385	−	0.547995i
$40$		0			0
$41$	5.02645e8			0.677564			0.338782	−	0.940865i	$-0.389985\pi$
$41$	5.02645e8			0.677564			0.338782	+	0.940865i	$0.389985\pi$
$42$		0			0
$43$	−1.83098e9			−1.89936			−0.949682	−	0.313215i	$-0.898594\pi$
$43$	−1.83098e9			−1.89936			−0.949682	+	0.313215i	$0.898594\pi$
$44$		0			0
$45$	2.58023e8	+	4.46910e8i	0.208444	+	0.361036i
$46$		0			0
$47$	9.87927e8	−	1.71114e9i	0.628328	−	1.08830i	−0.359559	−	0.933122i	$-0.617073\pi$
$47$	9.87927e8	−	1.71114e9i	0.628328	−	1.08830i	0.987887	−	0.155174i	$-0.0495938\pi$
$48$		0			0
$49$	−1.96387e9	−	2.30276e8i	−0.993196	−	0.116458i
$50$		0			0
$51$	1.16669e9	−	2.02076e9i	0.473499	−	0.820124i
$52$		0			0
$53$	−1.60585e9	−	2.78142e9i	−0.527459	−	0.913585i	−0.999488	−	0.0320021i	$-0.989812\pi$
$53$	−1.60585e9	−	2.78142e9i	−0.527459	−	0.913585i	0.472029	−	0.881583i	$-0.343522\pi$
$54$		0			0
$55$	3.27052e9			0.876238
$56$		0			0
$57$	−6.82597e8			−0.150263
$58$		0			0
$59$	−2.85842e9	−	4.95094e9i	−0.520524	−	0.901574i	−0.999715	−	0.0238633i	$-0.992403\pi$
$59$	−2.85842e9	−	4.95094e9i	−0.520524	−	0.901574i	0.479191	−	0.877710i	$-0.340930\pi$
$60$		0			0
$61$	−5.86773e9	+	1.01632e10i	−0.889521	+	1.54070i	−0.0490780	+	0.998795i	$0.515628\pi$
$61$	−5.86773e9	+	1.01632e10i	−0.889521	+	1.54070i	−0.840443	+	0.541900i	$0.817705\pi$
$62$		0			0
$63$	−2.19351e9	−	1.44327e9i	−0.278462	−	0.183221i
$64$		0			0
$65$	−6.41124e9	+	1.11046e10i	−0.685360	+	1.18708i
$66$		0			0
$67$	2.07880e9	+	3.60059e9i	0.188106	+	0.325808i	0.944619	−	0.328170i	$-0.106432\pi$
$67$	2.07880e9	+	3.60059e9i	0.188106	+	0.325808i	−0.756513	+	0.653979i	$0.773099\pi$
$68$		0			0
$69$	3.46525e9			0.266725
$70$		0			0
$71$	5.49068e9			0.361165			0.180582	−	0.983560i	$-0.442202\pi$
$71$	5.49068e9			0.361165			0.180582	+	0.983560i	$0.442202\pi$
$72$		0			0
$73$	−8.63209e9	−	1.49512e10i	−0.487349	−	0.844113i	0.512545	−	0.858660i	$-0.328703\pi$
$73$	−8.63209e9	−	1.49512e10i	−0.487349	−	0.844113i	−0.999894	+	0.0145471i	$0.995369\pi$
$74$		0			0
$75$	3.34699e9	−	5.79715e9i	0.162861	−	0.282083i
$76$		0			0
$77$	−1.48723e10	+	7.46573e9i	−0.626152	+	0.314321i
$78$		0			0
$79$	−6.75650e9	+	1.17026e10i	−0.247043	+	0.427891i	−0.962704	−	0.270557i	$-0.912792\pi$
$79$	−6.75650e9	+	1.17026e10i	−0.247043	+	0.427891i	0.715661	+	0.698448i	$0.246126\pi$
$80$		0			0
$81$	−1.74339e9	−	3.01964e9i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−7.12546e10			−1.98556			−0.992781	−	0.119941i	$-0.961729\pi$
$83$	−7.12546e10			−1.98556			−0.992781	+	0.119941i	$0.961729\pi$
$84$		0			0
$85$	−8.39181e10			−2.05140
$86$		0			0
$87$	−1.17981e10	−	2.04349e10i	−0.253779	−	0.439557i
$88$		0			0
$89$	−1.10945e10	+	1.92162e10i	−0.210602	+	0.364773i	−0.951903	−	0.306399i	$-0.900876\pi$
$89$	−1.10945e10	+	1.92162e10i	−0.210602	+	0.364773i	0.741301	+	0.671173i	$0.234209\pi$
$90$		0			0
$91$	3.80553e9	−	6.51320e10i	0.0639274	−	1.09412i
$92$		0			0
$93$	−3.43961e10	+	5.95758e10i	−0.512688	+	0.888002i
$94$		0			0
$95$	1.22745e10	+	2.12601e10i	0.162751	+	0.281894i
$96$		0			0
$97$	−1.49556e9			−0.0176832			−0.00884158	−	0.999961i	$-0.502814\pi$
$97$	−1.49556e9			−0.0176832			−0.00884158	+	0.999961i	$0.502814\pi$
$98$		0			0
$99$	−2.20980e10			−0.233539
$100$		0			0
$101$	−6.14682e10	−	1.06466e11i	−0.581946	−	1.00796i	−0.995249	−	0.0973664i	$-0.968958\pi$
$101$	−6.14682e10	−	1.06466e11i	−0.581946	−	1.00796i	0.413303	−	0.910594i	$-0.364375\pi$
$102$		0			0
$103$	−1.69420e10	+	2.93445e10i	−0.143999	+	0.249414i	−0.928999	−	0.370082i	$-0.879330\pi$
$103$	−1.69420e10	+	2.93445e10i	−0.143999	+	0.249414i	0.785000	+	0.619496i	$0.212663\pi$
$104$		0			0
$105$	−5.50811e9	+	9.42718e10i	−0.0421174	+	0.720843i
$106$		0			0
$107$	−7.42585e10	+	1.28620e11i	−0.511842	+	0.886536i	0.488064	+	0.872808i	$0.337703\pi$
$107$	−7.42585e10	+	1.28620e11i	−0.511842	+	0.886536i	−0.999906	+	0.0137280i	$0.995630\pi$
$108$		0			0
$109$	−1.07653e10	−	1.86461e10i	−0.0670164	−	0.116076i	0.830570	−	0.556914i	$-0.188015\pi$
$109$	−1.07653e10	−	1.86461e10i	−0.0670164	−	0.116076i	−0.897587	+	0.440838i	$0.854681\pi$
$110$		0			0
$111$	−1.14030e11			−0.642309
$112$		0			0
$113$	−1.82750e11			−0.933094			−0.466547	−	0.884496i	$-0.654502\pi$
$113$	−1.82750e11			−0.933094			−0.466547	+	0.884496i	$0.654502\pi$
$114$		0			0
$115$	−6.23124e10	−	1.07928e11i	−0.288893	−	0.500377i
$116$		0			0
$117$	4.33190e10	−	7.50306e10i	0.182665	−	0.316385i
$118$		0			0
$119$	3.81608e11	−	1.91563e11i	1.46592	−	0.735873i
$120$		0			0
$121$	7.26313e10	−	1.25801e11i	0.254568	−	0.440925i
$122$		0			0
$123$	6.10714e10	+	1.05779e11i	0.195596	+	0.338782i
$124$		0			0
$125$	1.85980e11			0.545082
$126$		0			0
$127$	−4.96474e11			−1.33345			−0.666723	−	0.745305i	$-0.732304\pi$
$127$	−4.96474e11			−1.33345			−0.666723	+	0.745305i	$0.732304\pi$
$128$		0			0
$129$	−2.22465e11	−	3.85320e11i	−0.548299	−	0.949682i
$130$		0			0
$131$	−3.91437e11	+	6.77988e11i	−0.886481	+	1.53543i	−0.0424747	+	0.999098i	$0.513524\pi$
$131$	−3.91437e11	+	6.77988e11i	−0.886481	+	1.53543i	−0.844006	+	0.536333i	$0.819809\pi$
$132$		0			0
$133$	−1.04348e11	−	6.86584e10i	−0.217421	−	0.143057i
$134$		0			0
$135$	−6.26997e10	+	1.08599e11i	−0.120345	+	0.208444i
$136$		0			0
$137$	−1.32602e11	−	2.29674e11i	−0.234741	−	0.406583i	0.724457	−	0.689320i	$-0.242091\pi$
$137$	−1.32602e11	−	2.29674e11i	−0.234741	−	0.406583i	−0.959197	+	0.282738i	$0.908757\pi$
$138$		0			0
$139$	1.02770e12			1.67991			0.839957	−	0.542654i	$-0.182580\pi$
$139$	1.02770e12			1.67991			0.839957	+	0.542654i	$0.182580\pi$
$140$		0			0
$141$	4.80132e11			0.725531
$142$		0			0
$143$	−2.74540e11	−	4.75517e11i	−0.383935	−	0.664994i
$144$		0			0
$145$	−4.24308e11	+	7.34923e11i	−0.549740	+	0.952177i
$146$		0			0
$147$	−1.90150e11	−	4.41264e11i	−0.228482	−	0.530216i
$148$		0			0
$149$	−4.02235e11	+	6.96692e11i	−0.448700	+	0.777171i	−0.998302	−	0.0582560i	$-0.981446\pi$
$149$	−4.02235e11	+	6.96692e11i	−0.448700	+	0.777171i	0.549602	+	0.835427i	$0.314779\pi$
$150$		0			0
$151$	3.34640e11	+	5.79614e11i	0.346900	+	0.600849i	0.985697	−	0.168526i	$-0.0539008\pi$
$151$	3.34640e11	+	5.79614e11i	0.346900	+	0.600849i	−0.638797	+	0.769376i	$0.720568\pi$
$152$		0			0
$153$	5.67011e11			0.546750
$154$		0			0
$155$	2.47406e12			2.22119
$156$		0			0
$157$	−2.31087e11	−	4.00255e11i	−0.193343	−	0.334879i	0.753013	−	0.658005i	$-0.228600\pi$
$157$	−2.31087e11	−	4.00255e11i	−0.193343	−	0.334879i	−0.946356	+	0.323126i	$0.895266\pi$
$158$		0			0
$159$	3.90222e11	−	6.75885e11i	0.304528	−	0.527459i
$160$		0			0
$161$	5.29731e11	+	3.48549e11i	0.385934	+	0.253934i
$162$		0			0
$163$	−3.67279e11	+	6.36145e11i	−0.250014	+	0.433036i	−0.963529	−	0.267603i	$-0.913768\pi$
$163$	−3.67279e11	+	6.36145e11i	−0.250014	+	0.433036i	0.713516	+	0.700639i	$0.247102\pi$
$164$		0			0
$165$	3.97368e11	+	6.88262e11i	0.252948	+	0.438119i
$166$		0			0
$167$	9.03063e11			0.537994			0.268997	−	0.963141i	$-0.413308\pi$
$167$	9.03063e11			0.537994			0.268997	+	0.963141i	$0.413308\pi$
$168$		0			0
$169$	3.60576e11			0.201196
$170$		0			0
$171$	−8.29356e10	−	1.43649e11i	−0.0433773	−	0.0751316i
$172$		0			0
$173$	6.89805e11	−	1.19478e12i	0.338433	−	0.586183i	−0.645705	−	0.763587i	$-0.723437\pi$
$173$	6.89805e11	−	1.19478e12i	0.338433	−	0.586183i	0.984138	+	0.177404i	$0.0567698\pi$
$174$		0			0
$175$	1.09475e12	−	5.49553e11i	0.504204	−	0.253105i
$176$		0			0
$177$	6.94597e11	−	1.20308e12i	0.300525	−	0.520524i
$178$		0			0
$179$	1.12792e12	+	1.95361e12i	0.458761	+	0.794597i	0.998896	−	0.0469816i	$-0.0149602\pi$
$179$	1.12792e12	+	1.95361e12i	0.458761	+	0.794597i	−0.540135	+	0.841578i	$0.681627\pi$
$180$		0			0
$181$	2.59380e12			0.992442			0.496221	−	0.868196i	$-0.334721\pi$
$181$	2.59380e12			0.992442			0.496221	+	0.868196i	$0.334721\pi$
$182$		0			0
$183$	−2.85172e12			−1.02713
$184$		0			0
$185$	2.05051e12	+	3.55158e12i	0.695691	+	1.20497i
$186$		0			0
$187$	1.79676e12	−	3.11207e12i	0.574593	−	0.995224i
$188$		0			0
$189$	3.72167e10	−	6.36969e11i	0.0112253	−	0.192122i
$190$		0			0
$191$	6.95182e11	−	1.20409e12i	0.197886	−	0.342749i	−0.749957	−	0.661487i	$-0.769926\pi$
$191$	6.95182e11	−	1.20409e12i	0.197886	−	0.342749i	0.947843	+	0.318738i	$0.103259\pi$
$192$		0			0
$193$	−8.81673e11	−	1.52710e12i	−0.236997	−	0.410491i	0.722854	−	0.691000i	$-0.242830\pi$
$193$	−8.81673e11	−	1.52710e12i	−0.236997	−	0.410491i	−0.959851	+	0.280510i	$0.909496\pi$
$194$		0			0
$195$	−3.11586e12			−0.791385
$196$		0			0
$197$	3.76723e12			0.904603			0.452302	−	0.891865i	$-0.350603\pi$
$197$	3.76723e12			0.904603			0.452302	+	0.891865i	$0.350603\pi$
$198$		0			0
$199$	−2.33913e12	−	4.05148e12i	−0.531327	−	0.920285i	−0.999332	−	0.0365587i	$-0.988360\pi$
$199$	−2.33913e12	−	4.05148e12i	−0.531327	−	0.920285i	0.468005	−	0.883726i	$-0.344973\pi$
$200$		0			0
$201$	−5.05149e11	+	8.74943e11i	−0.108603	+	0.188106i
$202$		0			0
$203$	2.51857e11	−	4.31056e12i	0.0512774	−	0.877618i
$204$		0			0
$205$	2.19638e12	−	3.80425e12i	0.423703	−	0.733876i
$206$		0			0
$207$	4.21028e11	+	7.29242e11i	0.0769970	+	0.133363i
$208$		0			0
$209$	−1.05123e12			−0.182345
$210$		0			0
$211$	7.05695e12			1.16162			0.580809	−	0.814040i	$-0.302736\pi$
$211$	7.05695e12			1.16162			0.580809	+	0.814040i	$0.302736\pi$
$212$		0			0
$213$	6.67118e11	+	1.15548e12i	0.104259	+	0.180582i
$214$		0			0
$215$	−8.00076e12	+	1.38577e13i	−1.18774	+	2.05722i
$216$		0			0
$217$	−1.12505e13	+	5.64762e12i	−1.58724	+	0.796777i
$218$		0			0
$219$	2.09760e12	−	3.63314e12i	0.281371	−	0.487349i
$220$		0			0
$221$	7.04440e12	+	1.22013e13i	0.898849	+	1.55685i
$222$		0			0
$223$	−3.04173e12			−0.369355			−0.184678	−	0.982799i	$-0.559124\pi$
$223$	−3.04173e12			−0.369355			−0.184678	+	0.982799i	$0.559124\pi$
$224$		0			0
$225$	1.62664e12			0.188056
$226$		0			0
$227$	3.41166e12	+	5.90917e12i	0.375685	+	0.650705i	0.990429	−	0.138021i	$-0.0440742\pi$
$227$	3.41166e12	+	5.90917e12i	0.375685	+	0.650705i	−0.614744	+	0.788726i	$0.710741\pi$
$228$		0			0
$229$	−4.27487e12	+	7.40429e12i	−0.448568	+	0.776942i	−0.998293	−	0.0584035i	$-0.981399\pi$
$229$	−4.27487e12	+	7.40429e12i	−0.448568	+	0.776942i	0.549725	+	0.835345i	$0.314732\pi$
$230$		0			0
$231$	−3.37811e12	−	2.22271e12i	−0.337915	−	0.222339i
$232$		0			0
$233$	1.81026e12	−	3.13547e12i	0.172697	−	0.299120i	−0.766665	−	0.642047i	$-0.778085\pi$
$233$	1.81026e12	−	3.13547e12i	0.172697	−	0.299120i	0.939362	+	0.342928i	$0.111419\pi$
$234$		0			0
$235$	−8.63379e12	−	1.49542e13i	−0.785829	−	1.36110i
$236$		0			0
$237$	−3.28366e12			−0.285261
$238$		0			0
$239$	−1.39493e13			−1.15708			−0.578542	−	0.815653i	$-0.696378\pi$
$239$	−1.39493e13			−1.15708			−0.578542	+	0.815653i	$0.696378\pi$
$240$		0			0
$241$	−2.87382e12	−	4.97760e12i	−0.227701	−	0.394390i	0.729425	−	0.684061i	$-0.239788\pi$
$241$	−2.87382e12	−	4.97760e12i	−0.227701	−	0.394390i	−0.957126	+	0.289670i	$0.906454\pi$
$242$		0			0
$243$	4.23644e11	−	7.33773e11i	0.0320750	−	0.0555556i
$244$		0			0
$245$	−1.03243e13	+	1.38573e13i	−0.747215	+	1.00291i
$246$		0			0
$247$	2.06074e12	−	3.56931e12i	0.142623	−	0.247031i
$248$		0			0
$249$	−8.65744e12	−	1.49951e13i	−0.573182	−	0.992781i
$250$		0			0
$251$	−4.52239e12			−0.286525			−0.143262	−	0.989685i	$-0.545759\pi$
$251$	−4.52239e12			−0.286525			−0.143262	+	0.989685i	$0.545759\pi$
$252$		0			0
$253$	5.33665e12			0.323672
$254$		0			0
$255$	−1.01960e13	−	1.76601e13i	−0.592189	−	1.02570i
$256$		0			0
$257$	4.30977e12	−	7.46474e12i	0.239785	−	0.415320i	−0.720867	−	0.693073i	$-0.756256\pi$
$257$	4.30977e12	−	7.46474e12i	0.239785	−	0.415320i	0.960652	+	0.277753i	$0.0895897\pi$
$258$		0			0
$259$	−1.74318e13	−	1.14696e13i	−0.929378	−	0.611507i
$260$		0			0
$261$	2.86693e12	−	4.96567e12i	0.146519	−	0.253779i
$262$		0			0
$263$	5.22595e11	+	9.05161e11i	0.0256099	+	0.0443577i	0.878546	−	0.477657i	$-0.158514\pi$
$263$	5.22595e11	+	9.05161e11i	0.0256099	+	0.0443577i	−0.852936	+	0.522015i	$0.825181\pi$
$264$		0			0
$265$	−2.80680e13			−1.31935
$266$		0			0
$267$	−5.39192e12			−0.243182
$268$		0			0
$269$	1.59218e13	+	2.75774e13i	0.689217	+	1.19376i	0.972092	+	0.234601i	$0.0753785\pi$
$269$	1.59218e13	+	2.75774e13i	0.689217	+	1.19376i	−0.282875	+	0.959157i	$0.591288\pi$
$270$		0			0
$271$	−3.72516e12	+	6.45217e12i	−0.154815	+	0.268148i	−0.932992	−	0.359898i	$-0.882812\pi$
$271$	−3.72516e12	+	6.45217e12i	−0.154815	+	0.268148i	0.778176	+	0.628046i	$0.216145\pi$
$272$		0			0
$273$	1.41690e13	−	7.11269e12i	0.565517	−	0.283883i
$274$		0			0
$275$	5.15452e12	−	8.92788e12i	0.197632	−	0.342309i
$276$		0			0
$277$	−9.40906e12	−	1.62970e13i	−0.346663	−	0.600438i	0.638991	−	0.769214i	$-0.279352\pi$
$277$	−9.40906e12	−	1.62970e13i	−0.346663	−	0.600438i	−0.985654	+	0.168776i	$0.946019\pi$
$278$		0			0
$279$	−1.67165e13			−0.592001
$280$		0			0
$281$	3.63956e13			1.23926			0.619632	−	0.784893i	$-0.287282\pi$
$281$	3.63956e13			1.23926			0.619632	+	0.784893i	$0.287282\pi$
$282$		0			0
$283$	1.56832e13	+	2.71642e13i	0.513582	+	0.889551i	0.999876	+	0.0157553i	$0.00501529\pi$
$283$	1.56832e13	+	2.71642e13i	0.513582	+	0.889551i	−0.486293	+	0.873796i	$0.661651\pi$
$284$		0			0
$285$	−2.98271e12	+	5.16621e12i	−0.0939646	+	0.162751i
$286$		0			0
$287$	−1.30371e12	+	2.23131e13i	−0.0395212	+	0.676410i
$288$		0			0
$289$	−2.89669e13	+	5.01721e13i	−0.845208	+	1.46394i
$290$		0			0
$291$	−1.81711e11	−	3.14732e11i	−0.00510469	−	0.00884158i
$292$		0			0
$293$	2.57608e13			0.696926			0.348463	−	0.937323i	$-0.386704\pi$
$293$	2.57608e13			0.696926			0.348463	+	0.937323i	$0.386704\pi$
$294$		0			0
$295$	−4.99612e13			−1.30200
$296$		0			0
$297$	−2.68491e12	−	4.65039e12i	−0.0674169	−	0.116769i
$298$		0			0
$299$	−1.04615e13	+	1.81198e13i	−0.253164	+	0.438493i
$300$		0			0
$301$	4.74902e12	−	8.12800e13i	0.110787	−	1.89613i
$302$		0			0
$303$	1.49368e13	−	2.58712e13i	0.335987	−	0.581946i
$304$		0			0
$305$	5.12799e13	+	8.88193e13i	1.11249	+	1.92690i
$306$		0			0
$307$	6.16899e13			1.29108			0.645540	−	0.763726i	$-0.276632\pi$
$307$	6.16899e13			1.29108			0.645540	+	0.763726i	$0.276632\pi$
$308$		0			0
$309$	−8.23383e12			−0.166276
$310$		0			0
$311$	−3.04669e13	−	5.27702e13i	−0.593808	−	1.02851i	−0.993714	−	0.111950i	$-0.964290\pi$
$311$	−3.04669e13	−	5.27702e13i	−0.593808	−	1.02851i	0.399906	−	0.916556i	$-0.369043\pi$
$312$		0			0
$313$	3.06053e13	−	5.30100e13i	0.575842	−	0.997388i	−0.420108	−	0.907474i	$-0.638008\pi$
$313$	3.06053e13	−	5.30100e13i	0.575842	−	0.997388i	0.995950	−	0.0899133i	$-0.0286590\pi$
$314$		0			0
$315$	−2.05082e13	+	1.02949e13i	−0.372580	+	0.187031i
$316$		0			0
$317$	−2.14279e13	+	3.71143e13i	−0.375971	+	0.651201i	−0.990472	−	0.137715i	$-0.956024\pi$
$317$	−2.14279e13	+	3.71143e13i	−0.375971	+	0.651201i	0.614501	+	0.788916i	$0.289358\pi$
$318$		0			0
$319$	−1.81696e13	−	3.14706e13i	−0.307961	−	0.533404i
$320$		0			0
$321$	−3.60896e13			−0.591024
$322$		0			0
$323$	2.69735e13			0.426897
$324$		0			0
$325$	2.02089e13	+	3.50029e13i	0.309161	+	0.535482i
$326$		0			0
$327$	2.61597e12	−	4.53100e12i	0.0386919	−	0.0670164i
$328$		0			0
$329$	7.33976e13	+	4.82937e13i	1.04979	+	0.690737i
$330$		0			0
$331$	4.11133e13	−	7.12104e13i	0.568760	−	0.985120i	−0.427929	−	0.903812i	$-0.640757\pi$
$331$	4.11133e13	−	7.12104e13i	0.568760	−	0.985120i	0.996689	−	0.0813083i	$-0.0259098\pi$
$332$		0			0
$333$	−1.38547e13	−	2.39970e13i	−0.185419	−	0.321155i
$334$		0			0
$335$	3.63345e13			0.470515
$336$		0			0
$337$	−1.24643e13			−0.156208			−0.0781038	−	0.996945i	$-0.524887\pi$
$337$	−1.24643e13			−0.156208			−0.0781038	+	0.996945i	$0.524887\pi$
$338$		0			0
$339$	−2.22041e13	−	3.84586e13i	−0.269361	−	0.466547i
$340$		0			0
$341$	−5.29717e13	+	9.17496e13i	−0.622149	+	1.07759i
$342$		0			0
$343$	1.53160e13	−	8.65818e13i	0.174192	−	0.984712i
$344$		0			0
$345$	1.51419e13	−	2.62266e13i	0.166792	−	0.288893i
$346$		0			0
$347$	5.42614e13	+	9.39834e13i	0.579000	+	1.00286i	0.995594	+	0.0937650i	$0.0298902\pi$
$347$	5.42614e13	+	9.39834e13i	0.579000	+	1.00286i	−0.416594	+	0.909093i	$0.636776\pi$
$348$		0			0
$349$	1.85265e14			1.91538			0.957689	−	0.287805i	$-0.0929254\pi$
$349$	1.85265e14			1.91538			0.957689	+	0.287805i	$0.0929254\pi$
$350$		0			0
$351$	2.10530e13			0.210924
$352$		0			0
$353$	6.49842e13	+	1.12556e14i	0.631025	+	1.09297i	0.987343	+	0.158602i	$0.0506988\pi$
$353$	6.49842e13	+	1.12556e14i	0.631025	+	1.09297i	−0.356317	+	0.934365i	$0.615968\pi$
$354$		0			0
$355$	2.39924e13	−	4.15560e13i	0.225848	−	0.391181i
$356$		0			0
$357$	8.66786e13	+	5.70323e13i	0.791110	+	0.520530i
$358$		0			0
$359$	4.26902e13	−	7.39416e13i	0.377841	−	0.654439i	−0.612907	−	0.790155i	$-0.710000\pi$
$359$	4.26902e13	−	7.39416e13i	0.377841	−	0.654439i	0.990748	+	0.135716i	$0.0433334\pi$
$360$		0			0
$361$	5.42998e13	+	9.40500e13i	0.466131	+	0.807363i
$362$		0			0
$363$	3.52988e13			0.293950
$364$		0			0
$365$	−1.50877e14			−1.21902
$366$		0			0
$367$	−7.48295e13	−	1.29609e14i	−0.586691	−	1.01618i	−0.994662	−	0.103184i	$-0.967097\pi$
$367$	−7.48295e13	−	1.29609e14i	−0.586691	−	1.01618i	0.407971	−	0.912995i	$-0.366236\pi$
$368$		0			0
$369$	−1.48403e13	+	2.57042e13i	−0.112927	+	0.195596i
$370$		0			0
$371$	1.27636e14	−	6.40719e13i	0.942795	−	0.473273i
$372$		0			0
$373$	−1.00531e14	+	1.74124e14i	−0.720941	+	1.24871i	0.239682	+	0.970851i	$0.422957\pi$
$373$	−1.00531e14	+	1.74124e14i	−0.720941	+	1.24871i	−0.960623	+	0.277855i	$0.910377\pi$
$374$		0			0
$375$	2.25966e13	+	3.91385e13i	0.157352	+	0.272541i
$376$		0			0
$377$	1.42472e14			0.963502
$378$		0			0
$379$	4.13567e13			0.271663			0.135831	−	0.990732i	$-0.456629\pi$
$379$	4.13567e13			0.271663			0.135831	+	0.990732i	$0.456629\pi$
$380$		0			0
$381$	−6.03215e13	−	1.04480e14i	−0.384933	−	0.666723i
$382$		0			0
$383$	7.93848e13	−	1.37498e14i	0.492203	−	0.852520i	−0.507757	−	0.861500i	$-0.669525\pi$
$383$	7.93848e13	−	1.37498e14i	0.492203	−	0.852520i	0.999960	+	0.00898035i	$0.00285857\pi$
$384$		0			0
$385$	−8.48274e12	+	1.45183e14i	−0.0511096	+	0.874746i
$386$		0			0
$387$	5.40589e13	−	9.36328e13i	0.316561	−	0.548299i
$388$		0			0
$389$	−1.22332e14	−	2.11886e14i	−0.696336	−	1.20609i	−0.969728	−	0.244186i	$-0.921479\pi$
$389$	−1.22332e14	−	2.11886e14i	−0.696336	−	1.20609i	0.273393	−	0.961903i	$-0.411854\pi$
$390$		0			0
$391$	−1.36933e14			−0.757766
$392$		0			0
$393$	−1.90238e14			−1.02362
$394$		0			0
$395$	5.90471e13	+	1.02273e14i	0.308969	+	0.535149i
$396$		0			0
$397$	8.42369e13	−	1.45903e14i	0.428701	−	0.742532i	−0.568057	−	0.822989i	$-0.692305\pi$
$397$	8.42369e13	−	1.45903e14i	0.428701	−	0.742532i	0.996758	+	0.0804570i	$0.0256380\pi$
$398$		0			0
$399$	1.77045e12	−	3.03015e13i	0.00876462	−	0.150007i
$400$		0			0
$401$	7.93418e12	−	1.37424e13i	0.0382127	−	0.0661864i	−0.846287	−	0.532728i	$-0.821167\pi$
$401$	7.93418e12	−	1.37424e13i	0.0382127	−	0.0661864i	0.884499	+	0.466542i	$0.154500\pi$
$402$		0			0
$403$	−2.07682e14	−	3.59716e14i	−0.973242	−	1.68571i
$404$		0			0
$405$	−3.04720e13			−0.138963
$406$		0			0
$407$	−1.75612e14			−0.779445
$408$		0			0
$409$	2.14114e14	+	3.70857e14i	0.925054	+	1.60224i	0.791474	+	0.611202i	$0.209314\pi$
$409$	2.14114e14	+	3.70857e14i	0.925054	+	1.60224i	0.133580	+	0.991038i	$0.457353\pi$
$410$		0			0
$411$	3.22224e13	−	5.58108e13i	0.135528	−	0.234741i
$412$		0			0
$413$	2.27193e14	−	1.14048e14i	0.930400	−	0.467050i
$414$		0			0
$415$	−3.11358e14	+	5.39287e14i	−1.24164	+	2.15058i
$416$		0			0
$417$	1.24866e14	+	2.16274e14i	0.484949	+	0.839957i
$418$		0			0
$419$	−4.91139e14			−1.85792			−0.928961	−	0.370177i	$-0.879297\pi$
$419$	−4.91139e14			−1.85792			−0.928961	+	0.370177i	$0.879297\pi$
$420$		0			0
$421$	−3.45062e14			−1.27158			−0.635792	−	0.771860i	$-0.719326\pi$
$421$	−3.45062e14			−1.27158			−0.635792	+	0.771860i	$0.719326\pi$
$422$		0			0
$423$	5.83361e13	+	1.01041e14i	0.209443	+	0.362765i
$424$		0			0
$425$	−1.32259e14	+	2.29080e14i	−0.462687	+	0.801397i
$426$		0			0
$427$	−4.35940e14	−	2.86837e14i	−1.48619	−	0.977873i
$428$		0			0
$429$	6.67132e13	−	1.15551e14i	0.221665	−	0.383935i
$430$		0			0
$431$	6.66605e13	+	1.15459e14i	0.215896	+	0.373942i	0.953549	−	0.301237i	$-0.0973996\pi$
$431$	6.66605e13	+	1.15459e14i	0.215896	+	0.373942i	−0.737654	+	0.675179i	$0.764066\pi$
$432$		0			0
$433$	3.97238e14			1.25420			0.627101	−	0.778938i	$-0.284241\pi$
$433$	3.97238e14			1.25420			0.627101	+	0.778938i	$0.284241\pi$
$434$		0			0
$435$	−2.06214e14			−0.634785
$436$		0			0
$437$	2.00289e13	+	3.46910e13i	0.0601185	+	0.104128i
$438$		0			0
$439$	−1.73377e14	+	3.00297e14i	−0.507500	+	0.879016i	0.492462	+	0.870334i	$0.336097\pi$
$439$	−1.73377e14	+	3.00297e14i	−0.507500	+	0.879016i	−0.999962	+	0.00868222i	$0.997236\pi$
$440$		0			0
$441$	6.97582e13	−	9.36296e13i	0.199151	−	0.267301i
$442$		0			0
$443$	2.53509e14	−	4.39091e14i	0.705948	−	1.22274i	−0.260400	−	0.965501i	$-0.583854\pi$
$443$	2.53509e14	−	4.39091e14i	0.705948	−	1.22274i	0.966348	−	0.257238i	$-0.0828123\pi$
$444$		0			0
$445$	9.69581e13	+	1.67936e14i	0.263393	+	0.456210i
$446$		0			0
$447$	−1.95486e14			−0.518114
$448$		0			0
$449$	−2.75878e14			−0.713449			−0.356724	−	0.934210i	$-0.616106\pi$
$449$	−2.75878e14			−0.713449			−0.356724	+	0.934210i	$0.616106\pi$
$450$		0			0
$451$	9.40528e13	+	1.62904e14i	0.237356	+	0.411113i
$452$		0			0
$453$	−8.13176e13	+	1.40846e14i	−0.200283	+	0.346900i
$454$		0			0
$455$	−4.76320e14	−	3.13406e14i	−1.14508	−	0.753433i
$456$		0			0
$457$	3.28449e14	−	5.68890e14i	0.770776	−	1.33502i	−0.166362	−	0.986065i	$-0.553202\pi$
$457$	3.28449e14	−	5.68890e14i	0.770776	−	1.33502i	0.937138	−	0.348959i	$-0.113465\pi$
$458$		0			0
$459$	6.88918e13	+	1.19324e14i	0.157833	+	0.273375i
$460$		0			0
$461$	−5.34049e14			−1.19461			−0.597305	−	0.802014i	$-0.703762\pi$
$461$	−5.34049e14			−1.19461			−0.597305	+	0.802014i	$0.703762\pi$
$462$		0			0
$463$	2.79715e14			0.610972			0.305486	−	0.952197i	$-0.401181\pi$
$463$	2.79715e14			0.610972			0.305486	+	0.952197i	$0.401181\pi$
$464$		0			0
$465$	3.00598e14	+	5.20651e14i	0.641202	+	1.11059i
$466$		0			0
$467$	−1.78355e14	+	3.08920e14i	−0.371571	+	0.643581i	−0.989807	−	0.142412i	$-0.954514\pi$
$467$	−1.78355e14	+	3.08920e14i	−0.371571	+	0.643581i	0.618236	+	0.785992i	$0.287848\pi$
$468$		0			0
$469$	−1.65227e14	+	8.29421e13i	−0.336226	+	0.168781i
$470$		0			0
$471$	5.61542e13	−	9.72619e13i	0.111626	−	0.193343i
$472$		0			0
$473$	−3.42606e14	−	5.93411e14i	−0.665363	−	1.15244i
$474$		0			0
$475$	7.73813e13			0.146832
$476$		0			0
$477$	1.89648e14			0.351639
$478$		0			0
$479$	−2.96531e14	−	5.13606e14i	−0.537309	−	0.930647i	−0.999048	−	0.0436311i	$-0.986107\pi$
$479$	−2.96531e14	−	5.13606e14i	−0.537309	−	0.930647i	0.461738	−	0.887016i	$-0.347226\pi$
$480$		0			0
$481$	3.44255e14	−	5.96267e14i	0.609652	−	1.05595i
$482$		0			0
$483$	−8.98781e12	+	1.53827e14i	−0.0155577	+	0.266271i
$484$		0			0
$485$	−6.53508e12	+	1.13191e13i	−0.0110579	+	0.0191528i
$486$		0			0
$487$	−3.32548e14	−	5.75991e14i	−0.550105	−	0.952810i	−0.998266	−	0.0588573i	$-0.981254\pi$
$487$	−3.32548e14	−	5.75991e14i	−0.550105	−	0.952810i	0.448161	−	0.893953i	$-0.352079\pi$
$488$		0			0
$489$	−1.78497e14			−0.288691
$490$		0			0
$491$	−5.84281e14			−0.924004			−0.462002	−	0.886879i	$-0.652869\pi$
$491$	−5.84281e14			−0.924004			−0.462002	+	0.886879i	$0.652869\pi$
$492$		0			0
$493$	4.66212e14	+	8.07503e14i	0.720984	+	1.24878i
$494$		0			0
$495$	−9.65605e13	+	1.67248e14i	−0.146040	+	0.252948i
$496$		0			0
$497$	−1.42412e13	+	2.43739e14i	−0.0210662	+	0.360550i
$498$		0			0
$499$	1.10932e14	−	1.92140e14i	0.160511	−	0.278013i	−0.774541	−	0.632524i	$-0.782019\pi$
$499$	1.10932e14	−	1.92140e14i	0.160511	−	0.278013i	0.935052	+	0.354510i	$0.115352\pi$
$500$		0			0
$501$	1.09722e14	+	1.90044e14i	0.155305	+	0.268997i
$502$		0			0
$503$	3.43535e14			0.475716			0.237858	−	0.971300i	$-0.423555\pi$
$503$	3.43535e14			0.475716			0.237858	+	0.971300i	$0.423555\pi$
$504$		0			0
$505$	−1.07438e15			−1.45564
$506$		0			0
$507$	4.38100e13	+	7.58811e13i	0.0580803	+	0.100598i
$508$		0			0
$509$	4.73453e14	−	8.20045e14i	0.614228	−	1.06387i	−0.376292	−	0.926501i	$-0.622801\pi$
$509$	4.73453e14	−	8.20045e14i	0.614228	−	1.06387i	0.990519	−	0.137372i	$-0.0438656\pi$
$510$		0			0
$511$	6.86095e14	−	3.44412e14i	0.871102	−	0.437283i
$512$		0			0
$513$	2.01533e13	−	3.49066e13i	0.0250439	−	0.0433773i
$514$		0			0
$515$	1.48062e14	+	2.56450e14i	0.180095	+	0.311934i
$516$		0			0
$517$	7.39426e14			0.880434
$518$		0			0
$519$	3.35245e14			0.390789
$520$		0			0
$521$	7.35448e14	+	1.27383e15i	0.839352	+	1.45380i	0.890437	+	0.455107i	$0.150399\pi$
$521$	7.35448e14	+	1.27383e15i	0.839352	+	1.45380i	−0.0510845	+	0.998694i	$0.516268\pi$
$522$		0			0
$523$	−7.25890e14	+	1.25728e15i	−0.811169	+	1.40499i	0.100877	+	0.994899i	$0.467835\pi$
$523$	−7.25890e14	+	1.25728e15i	−0.811169	+	1.40499i	−0.912046	+	0.410088i	$0.865498\pi$
$524$		0			0
$525$	2.48663e14	+	1.63614e14i	0.272104	+	0.179037i
$526$		0			0
$527$	1.35920e15	−	2.35420e15i	1.45654	−	2.52281i
$528$		0			0
$529$	3.74727e14	+	6.49046e14i	0.393286	+	0.681192i
$530$		0			0
$531$	3.37574e14			0.347016
$532$		0			0
$533$	−7.37491e14			−0.742604
$534$		0			0
$535$	6.48968e14	+	1.12404e15i	0.640143	+	1.10876i
$536$		0			0
$537$	−2.74084e14	+	4.74728e14i	−0.264866	+	0.458761i
$538$		0			0
$539$	−2.92840e14	−	6.79567e14i	−0.277263	−	0.643419i
$540$		0			0
$541$	5.55684e13	−	9.62473e13i	0.0515517	−	0.0892901i	−0.839098	−	0.543980i	$-0.816917\pi$
$541$	5.55684e13	−	9.62473e13i	0.0515517	−	0.0892901i	0.890650	+	0.454690i	$0.150250\pi$
$542$		0			0
$543$	3.15147e14	+	5.45851e14i	0.286493	+	0.496221i
$544$		0			0
$545$	−1.88163e14			−0.167630
$546$		0			0
$547$	1.30110e14			0.113601			0.0568004	−	0.998386i	$-0.481910\pi$
$547$	1.30110e14			0.113601			0.0568004	+	0.998386i	$0.481910\pi$
$548$		0			0
$549$	−3.46484e14	−	6.00127e14i	−0.296507	−	0.513565i
$550$		0			0
$551$	1.36384e14	−	2.36224e14i	0.114401	−	0.198148i
$552$		0			0
$553$	−5.01971e14	−	3.30284e14i	−0.412753	−	0.271581i
$554$		0			0
$555$	−4.98273e14	+	8.63034e14i	−0.401657	+	0.695691i
$556$		0			0
$557$	3.73855e14	+	6.47536e14i	0.295461	+	0.511753i	0.975092	−	0.221801i	$-0.0711935\pi$
$557$	3.73855e14	+	6.47536e14i	0.295461	+	0.511753i	−0.679631	+	0.733554i	$0.737860\pi$
$558$		0			0
$559$	2.68646e15			2.08169
$560$		0			0
$561$	8.73223e14			0.663483
$562$		0			0
$563$	−6.57491e14	−	1.13881e15i	−0.489885	−	0.848505i	0.510047	−	0.860146i	$-0.329628\pi$
$563$	−6.57491e14	−	1.13881e15i	−0.489885	−	0.848505i	−0.999932	+	0.0116409i	$0.996294\pi$
$564$		0			0
$565$	−7.98553e14	+	1.38313e15i	−0.583495	+	1.01064i
$566$		0			0
$567$	1.38568e14	−	6.95596e13i	0.0993017	−	0.0498483i
$568$		0			0
$569$	3.17436e14	−	5.49816e14i	0.223120	−	0.386456i	−0.732633	−	0.680623i	$-0.761709\pi$
$569$	3.17436e14	−	5.49816e14i	0.223120	−	0.386456i	0.955754	+	0.294168i	$0.0950424\pi$
$570$		0			0
$571$	1.09098e15	+	1.88964e15i	0.752175	+	1.30281i	0.946767	+	0.321921i	$0.104328\pi$
$571$	1.09098e15	+	1.88964e15i	0.752175	+	1.30281i	−0.194592	+	0.980884i	$0.562338\pi$
$572$		0			0
$573$	3.37859e14			0.228499
$574$		0			0
$575$	−3.92831e14			−0.260635
$576$		0			0
$577$	6.92281e14	+	1.19907e15i	0.450625	+	0.780506i	0.998425	−	0.0561038i	$-0.0178678\pi$
$577$	6.92281e14	+	1.19907e15i	0.450625	+	0.780506i	−0.547800	+	0.836609i	$0.684534\pi$
$578$		0			0
$579$	2.14247e14	−	3.71086e14i	0.136830	−	0.236997i
$580$		0			0
$581$	1.84813e14	−	3.16309e15i	0.115815	−	1.98218i
$582$		0			0
$583$	6.00960e14	−	1.04089e15i	0.369546	−	0.640073i
$584$		0			0
$585$	−3.78577e14	−	6.55715e14i	−0.228453	−	0.395693i
$586$		0			0
$587$	1.75342e15			1.03843			0.519214	−	0.854644i	$-0.326225\pi$
$587$	1.75342e15			1.03843			0.519214	+	0.854644i	$0.326225\pi$
$588$		0			0
$589$	−7.95228e14			−0.462229
$590$		0			0
$591$	4.57719e14	+	7.92792e14i	0.261136	+	0.452302i
$592$		0			0
$593$	−6.44911e13	+	1.11702e14i	−0.0361160	+	0.0625547i	−0.883518	−	0.468396i	$-0.844832\pi$
$593$	−6.44911e13	+	1.11702e14i	−0.0361160	+	0.0625547i	0.847402	+	0.530951i	$0.178165\pi$
$594$		0			0
$595$	2.17658e14	−	3.72524e15i	0.119655	−	2.04791i
$596$		0			0
$597$	5.68407e14	−	9.84510e14i	0.306762	−	0.531327i
$598$		0			0
$599$	6.76065e14	+	1.17098e15i	0.358213	+	0.620443i	0.987662	−	0.156599i	$-0.0500529\pi$
$599$	6.76065e14	+	1.17098e15i	0.358213	+	0.620443i	−0.629449	+	0.777041i	$0.716720\pi$
$600$		0			0
$601$	−2.91836e15			−1.51820			−0.759102	−	0.650972i	$-0.774361\pi$
$601$	−2.91836e15			−1.51820			−0.759102	+	0.650972i	$0.774361\pi$
$602$		0			0
$603$	−2.45502e14			−0.125404
$604$		0			0
$605$	−6.34746e14	−	1.09941e15i	−0.318380	−	0.551450i
$606$		0			0
$607$	−1.15070e15	+	1.99307e15i	−0.566792	+	0.981712i	0.430089	+	0.902787i	$0.358482\pi$
$607$	−1.15070e15	+	1.99307e15i	−0.566792	+	0.981712i	−0.996881	+	0.0789255i	$0.974851\pi$
$608$		0			0
$609$	9.37733e14	−	4.70731e14i	0.453612	−	0.227708i
$610$		0			0
$611$	−1.44951e15	+	2.51062e15i	−0.688642	+	1.19276i
$612$		0			0
$613$	−7.45735e14	−	1.29165e15i	−0.347978	−	0.602716i	0.637912	−	0.770109i	$-0.279798\pi$
$613$	−7.45735e14	−	1.29165e15i	−0.347978	−	0.602716i	−0.985890	+	0.167393i	$0.946465\pi$
$614$		0			0
$615$	1.06744e15			0.489250
$616$		0			0
$617$	−2.52358e15			−1.13618			−0.568092	−	0.822965i	$-0.692318\pi$
$617$	−2.52358e15			−1.13618			−0.568092	+	0.822965i	$0.692318\pi$
$618$		0			0
$619$	1.92379e14	+	3.33211e14i	0.0850864	+	0.147374i	0.905428	−	0.424500i	$-0.139550\pi$
$619$	1.92379e14	+	3.33211e14i	0.0850864	+	0.147374i	−0.820342	+	0.571874i	$0.806217\pi$
$620$		0			0
$621$	−1.02310e14	+	1.77206e14i	−0.0444542	+	0.0769970i
$622$		0			0
$623$	−8.24260e14	−	5.42342e14i	−0.351868	−	0.231520i
$624$		0			0
$625$	1.48521e15	−	2.57246e15i	0.622941	−	1.07897i
$626$		0			0
$627$	−1.27725e14	−	2.21226e14i	−0.0526385	−	0.0911725i
$628$		0			0
$629$	4.50602e15			1.82480
$630$		0			0
$631$	−1.55149e15			−0.617430			−0.308715	−	0.951155i	$-0.599899\pi$
$631$	−1.55149e15			−0.617430			−0.308715	+	0.951155i	$0.599899\pi$
$632$		0			0
$633$	8.57420e14	+	1.48509e15i	0.335330	+	0.580809i
$634$		0			0
$635$	−2.16942e15	+	3.75754e15i	−0.833849	+	1.44427i
$636$		0			0
$637$	2.88143e15	+	3.37866e14i	1.08853	+	0.127637i
$638$		0			0
$639$	−1.62110e14	+	2.80782e14i	−0.0601941	+	0.104259i
$640$		0			0
$641$	−1.38803e15	−	2.40414e15i	−0.506617	−	0.877487i	−0.999971	−	0.00765798i	$-0.997562\pi$
$641$	−1.38803e15	−	2.40414e15i	−0.506617	−	0.877487i	0.493353	−	0.869829i	$-0.335771\pi$
$642$		0			0
$643$	1.84010e14			0.0660208			0.0330104	−	0.999455i	$-0.489491\pi$
$643$	1.84010e14			0.0660208			0.0330104	+	0.999455i	$0.489491\pi$
$644$		0			0
$645$	−3.88837e15			−1.37148
$646$		0			0
$647$	1.58133e15	+	2.73894e15i	0.548339	+	0.949751i	0.998389	+	0.0567471i	$0.0180729\pi$
$647$	1.58133e15	+	2.73894e15i	0.548339	+	0.949751i	−0.450050	+	0.893003i	$0.648594\pi$
$648$		0			0
$649$	1.06971e15	−	1.85280e15i	0.364688	−	0.631658i
$650$		0			0
$651$	−2.55544e15	−	1.68142e15i	−0.856586	−	0.563611i
$652$		0			0
$653$	−9.84937e14	+	1.70596e15i	−0.324628	+	0.562272i	−0.981437	−	0.191785i	$-0.938572\pi$
$653$	−9.84937e14	+	1.70596e15i	−0.324628	+	0.562272i	0.656809	+	0.754057i	$0.271906\pi$
$654$		0			0
$655$	3.42088e15	+	5.92514e15i	1.10869	+	1.92031i
$656$		0			0
$657$	1.01943e15			0.324899
$658$		0			0
$659$	−1.76846e15			−0.554275			−0.277138	−	0.960830i	$-0.589386\pi$
$659$	−1.76846e15			−0.554275			−0.277138	+	0.960830i	$0.589386\pi$
$660$		0			0
$661$	−3.05799e15	−	5.29659e15i	−0.942601	−	1.63263i	−0.760485	−	0.649355i	$-0.775039\pi$
$661$	−3.05799e15	−	5.29659e15i	−0.942601	−	1.63263i	−0.182116	−	0.983277i	$-0.558295\pi$
$662$		0			0
$663$	−1.71179e15	+	2.96491e15i	−0.518951	+	0.898849i
$664$		0			0
$665$	−9.75603e14	+	4.89742e14i	−0.290907	+	0.146032i
$666$		0			0
$667$	−6.92361e14	+	1.19920e15i	−0.203068	+	0.351723i
$668$		0			0
$669$	−3.69571e14	−	6.40115e14i	−0.106624	−	0.184678i
$670$		0			0
$671$	−4.39178e15			−1.24643
$672$		0			0
$673$	−6.23783e15			−1.74161			−0.870804	−	0.491630i	$-0.836401\pi$
$673$	−6.23783e15			−1.74161			−0.870804	+	0.491630i	$0.836401\pi$
$674$		0			0
$675$	1.97636e14	+	3.42316e14i	0.0542870	+	0.0940278i
$676$		0			0
$677$	−1.88137e15	+	3.25863e15i	−0.508437	+	0.880639i	0.491515	+	0.870869i	$0.336443\pi$
$677$	−1.88137e15	+	3.25863e15i	−0.508437	+	0.880639i	−0.999952	+	0.00976973i	$0.996890\pi$
$678$		0			0
$679$	3.87904e12	−	6.63902e13i	0.00103143	−	0.0176531i
$680$		0			0
$681$	−8.29034e14	+	1.43593e15i	−0.216902	+	0.375685i
$682$		0			0
$683$	−8.41737e14	−	1.45793e15i	−0.216702	−	0.375339i	0.737096	−	0.675788i	$-0.236197\pi$
$683$	−8.41737e14	−	1.45793e15i	−0.216702	−	0.375339i	−0.953798	+	0.300450i	$0.902863\pi$
$684$		0			0
$685$	−2.31770e15			−0.587164
$686$		0			0
$687$	−2.07759e15			−0.517961
$688$		0			0
$689$	2.35614e15	+	4.08095e15i	0.578090	+	1.00128i
$690$		0			0
$691$	−2.51320e14	+	4.35299e14i	−0.0606873	+	0.105114i	−0.894773	−	0.446522i	$-0.852663\pi$
$691$	−2.51320e14	+	4.35299e14i	−0.0606873	+	0.105114i	0.834085	+	0.551635i	$0.185996\pi$
$692$		0			0
$693$	5.73155e13	−	9.80961e14i	0.0136220	−	0.233141i
$694$		0			0
$695$	4.49071e15	−	7.77813e15i	1.05051	−	1.81953i
$696$		0			0
$697$	−2.41329e15	−	4.17995e15i	−0.555687	−	0.962478i
$698$		0			0
$699$	8.79788e14			0.199413
$700$		0			0
$701$	−6.33430e15			−1.41335			−0.706675	−	0.707539i	$-0.749806\pi$
$701$	−6.33430e15			−1.41335			−0.706675	+	0.707539i	$0.749806\pi$
$702$		0			0
$703$	−6.59087e14	−	1.14157e15i	−0.144773	−	0.250755i
$704$		0			0
$705$	2.09801e15	−	3.63386e15i	0.453699	−	0.785829i
$706$		0			0
$707$	4.88561e15	−	2.45252e15i	1.04019	−	0.522163i
$708$		0			0
$709$	3.17140e15	−	5.49302e15i	0.664808	−	1.15148i	−0.314529	−	0.949248i	$-0.601847\pi$
$709$	3.17140e15	−	5.49302e15i	0.664808	−	1.15148i	0.979337	−	0.202234i	$-0.0648201\pi$
$710$		0			0
$711$	−3.98965e14	−	6.91027e14i	−0.0823477	−	0.142630i
$712$		0			0
$713$	4.03703e15			0.820482
$714$		0			0
$715$	−4.79857e15			−0.960349
$716$		0			0
$717$	−1.69484e15	−	2.93555e15i	−0.334021	−	0.578542i
$718$		0			0
$719$	−3.08073e14	+	5.33598e14i	−0.0597922	+	0.103563i	−0.894372	−	0.447324i	$-0.852377\pi$
$719$	−3.08073e14	+	5.33598e14i	−0.0597922	+	0.103563i	0.834580	+	0.550887i	$0.185710\pi$
$720$		0			0
$721$	−1.25870e15	−	8.28192e14i	−0.240591	−	0.158302i
$722$		0			0
$723$	6.98338e14	−	1.20956e15i	0.131463	−	0.227701i
$724$		0			0
$725$	1.33746e15	+	2.31656e15i	0.247984	+	0.429520i
$726$		0			0
$727$	−6.43411e15			−1.17503			−0.587515	−	0.809213i	$-0.699894\pi$
$727$	−6.43411e15			−1.17503			−0.587515	+	0.809213i	$0.699894\pi$
$728$		0			0
$729$	2.05891e14			0.0370370
$730$		0			0
$731$	8.79091e15	+	1.52263e16i	1.55772	+	2.69804i
$732$		0			0
$733$	−3.31026e15	+	5.73354e15i	−0.577817	+	1.00081i	0.417912	+	0.908488i	$0.362762\pi$
$733$	−3.31026e15	+	5.73354e15i	−0.577817	+	1.00081i	−0.995729	+	0.0923215i	$0.970571\pi$
$734$		0			0
$735$	−4.17058e15	−	4.89026e14i	−0.717159	−	0.0840913i
$736$		0			0
$737$	−7.77953e14	+	1.34745e15i	−0.131790	+	0.228267i
$738$		0			0
$739$	2.04763e15	+	3.54660e15i	0.341749	+	0.591927i	0.984758	−	0.173932i	$-0.0556473\pi$
$739$	2.04763e15	+	3.54660e15i	0.341749	+	0.591927i	−0.643008	+	0.765859i	$0.722314\pi$
$740$		0			0
$741$	1.00152e15			0.164687
$742$		0			0
$743$	4.39356e15			0.711833			0.355916	−	0.934518i	$-0.384169\pi$
$743$	4.39356e15			0.711833			0.355916	+	0.934518i	$0.384169\pi$
$744$		0			0
$745$	3.51525e15	+	6.08860e15i	0.561174	+	0.971981i
$746$		0			0
$747$	2.10376e15	−	3.64381e15i	0.330927	−	0.573182i
$748$		0			0
$749$	−5.51700e15	−	3.63004e15i	−0.855171	−	0.562680i
$750$		0			0
$751$	3.06844e15	−	5.31470e15i	0.468704	−	0.811819i	−0.530656	−	0.847587i	$-0.678055\pi$
$751$	3.06844e15	−	5.31470e15i	0.468704	−	0.811819i	0.999360	+	0.0357685i	$0.0113879\pi$
$752$		0			0
$753$	−5.49470e14	−	9.51710e14i	−0.0827126	−	0.143262i
$754$		0			0
$755$	5.84904e15			0.867714
$756$		0			0
$757$	4.34233e15			0.634886			0.317443	−	0.948277i	$-0.397176\pi$
$757$	4.34233e15			0.634886			0.317443	+	0.948277i	$0.397176\pi$
$758$		0			0
$759$	6.48402e14	+	1.12307e15i	0.0934361	+	0.161836i
$760$		0			0
$761$	−1.35557e15	+	2.34792e15i	−0.192534	+	0.333478i	−0.946089	−	0.323906i	$-0.895004\pi$
$761$	−1.35557e15	+	2.34792e15i	−0.192534	+	0.333478i	0.753556	+	0.657384i	$0.228337\pi$
$762$		0			0
$763$	8.55648e14	−	4.29526e14i	0.119787	−	0.0601318i
$764$		0			0
$765$	2.47764e15	−	4.29140e15i	0.341901	−	0.592189i
$766$		0			0
$767$	4.19394e15	+	7.26412e15i	0.570489	+	0.988117i
$768$		0			0
$769$	2.57095e15			0.344746			0.172373	−	0.985032i	$-0.444857\pi$
$769$	2.57095e15			0.344746			0.172373	+	0.985032i	$0.444857\pi$
$770$		0			0
$771$	2.09455e15			0.276880
$772$		0			0
$773$	3.50482e15	+	6.07052e15i	0.456750	+	0.791114i	0.998787	−	0.0492406i	$-0.0156801\pi$
$773$	3.50482e15	+	6.07052e15i	0.456750	+	0.791114i	−0.542037	+	0.840355i	$0.682347\pi$
$774$		0			0
$775$	3.89925e15	−	6.75370e15i	0.500981	−	0.867725i
$776$		0			0
$777$	2.95761e14	−	5.06197e15i	0.0374649	−	0.641216i
$778$		0			0
$779$	−7.05976e14	+	1.22279e15i	−0.0881726	+	0.152719i
$780$		0			0
$781$	1.02739e15	+	1.77950e15i	0.126519	+	0.219137i
$782$		0			0
$783$	1.39333e15			0.169186
$784$		0			0
$785$	−4.03908e15			−0.483615
$786$		0			0
$787$	6.14541e15	+	1.06442e16i	0.725587	+	1.25675i	0.958732	+	0.284312i	$0.0917652\pi$
$787$	6.14541e15	+	1.06442e16i	0.725587	+	1.25675i	−0.233144	+	0.972442i	$0.574901\pi$
$788$		0			0
$789$	−1.26991e14	+	2.19954e14i	−0.0147859	+	0.0256099i
$790$		0			0
$791$	4.73998e14	−	8.11253e15i	0.0544259	−	0.931506i
$792$		0			0
$793$	8.60926e15	−	1.49117e16i	0.974907	−	1.68859i
$794$		0			0
$795$	−3.41027e15	−	5.90676e15i	−0.380863	−	0.659675i
$796$		0			0
$797$	2.76216e15			0.304249			0.152124	−	0.988361i	$-0.451389\pi$
$797$	2.76216e15			0.304249			0.152124	+	0.988361i	$0.451389\pi$
$798$		0			0
$799$	−1.89729e16			−2.06123
$800$		0			0
$801$	−6.55119e14	−	1.13470e15i	−0.0702007	−	0.121591i
$802$		0			0
$803$	3.23040e15	−	5.59521e15i	0.341445	−	0.591400i
$804$		0			0
$805$	4.95271e15	−	2.48621e15i	0.516376	−	0.259215i
$806$		0			0
$807$	−3.86901e15	+	6.70132e15i	−0.397919	+	0.689217i
$808$		0			0
$809$	−1.76416e15	−	3.05562e15i	−0.178987	−	0.310014i	0.762547	−	0.646933i	$-0.223949\pi$
$809$	−1.76416e15	−	3.05562e15i	−0.178987	−	0.310014i	−0.941534	+	0.336919i	$0.890615\pi$
$810$		0			0
$811$	−5.97305e15			−0.597835			−0.298918	−	0.954279i	$-0.596626\pi$
$811$	−5.97305e15			−0.597835			−0.298918	+	0.954279i	$0.596626\pi$
$812$		0			0
$813$	−1.81043e15			−0.178765
$814$		0			0
$815$	3.20976e15	+	5.55946e15i	0.312684	+	0.541584i
$816$		0			0
$817$	2.57166e15	−	4.45424e15i	0.247168	−	0.428107i
$818$		0			0
$819$	3.21836e15	+	2.11760e15i	0.305192	+	0.200808i
$820$		0			0
$821$	−2.98478e15	+	5.16980e15i	−0.279271	+	0.483711i	−0.971204	−	0.238251i	$-0.923426\pi$
$821$	−2.98478e15	+	5.16980e15i	−0.279271	+	0.483711i	0.691933	+	0.721962i	$0.256759\pi$
$822$		0			0
$823$	−1.70790e15	−	2.95817e15i	−0.157675	−	0.273101i	0.776355	−	0.630296i	$-0.217067\pi$
$823$	−1.70790e15	−	2.95817e15i	−0.157675	−	0.273101i	−0.934030	+	0.357195i	$0.883733\pi$
$824$		0			0
$825$	2.50509e15			0.228206
$826$		0			0
$827$	1.55894e16			1.40136			0.700680	−	0.713476i	$-0.252880\pi$
$827$	1.55894e16			1.40136			0.700680	+	0.713476i	$0.252880\pi$
$828$		0			0
$829$	4.00047e15	+	6.92902e15i	0.354863	+	0.614641i	0.987095	−	0.160138i	$-0.0511941\pi$
$829$	4.00047e15	+	6.92902e15i	0.354863	+	0.614641i	−0.632231	+	0.774780i	$0.717861\pi$
$830$		0			0
$831$	2.28640e15	−	3.96017e15i	0.200146	−	0.346663i
$832$		0			0
$833$	7.51397e15	+	1.74370e16i	0.649115	+	1.50634i
$834$		0			0
$835$	3.94607e15	−	6.83479e15i	0.336426	−	0.582706i
$836$		0			0
$837$	−2.03106e15	−	3.51789e15i	−0.170896	−	0.296001i
$838$		0			0
$839$	−2.17401e15			−0.180539			−0.0902694	−	0.995917i	$-0.528773\pi$
$839$	−2.17401e15			−0.180539			−0.0902694	+	0.995917i	$0.528773\pi$
$840$		0			0
$841$	−2.77143e15			−0.227157
$842$		0			0
$843$	4.42206e15	+	7.65924e15i	0.357745	+	0.619632i
$844$		0			0
$845$	1.57559e15	−	2.72900e15i	0.125815	−	0.217917i
$846$		0			0
$847$	5.39611e15	+	3.55050e15i	0.425326	+	0.279853i
$848$		0			0
$849$	−3.81103e15	+	6.60089e15i	−0.296517	+	0.513582i
$850$		0			0
$851$	3.34590e15	+	5.79526e15i	0.256980	+	0.445103i
$852$		0			0
$853$	2.07102e16			1.57024			0.785118	−	0.619347i	$-0.212602\pi$
$853$	2.07102e16			1.57024			0.785118	+	0.619347i	$0.212602\pi$
$854$		0			0
$855$	−1.44960e15			−0.108501
$856$		0			0
$857$	5.90563e15	+	1.02288e16i	0.436387	+	0.755844i	0.997408	−	0.0719576i	$-0.0229246\pi$
$857$	5.90563e15	+	1.02288e16i	0.436387	+	0.755844i	−0.561021	+	0.827802i	$0.689591\pi$
$858$		0			0
$859$	−5.97708e15	+	1.03526e16i	−0.436040	+	0.755244i	−0.997380	−	0.0723414i	$-0.976953\pi$
$859$	−5.97708e15	+	1.03526e16i	−0.436040	+	0.755244i	0.561339	+	0.827586i	$0.310286\pi$
$860$		0			0
$861$	−4.85407e15	+	2.43669e15i	−0.349614	+	0.175502i
$862$		0			0
$863$	−2.19037e15	+	3.79382e15i	−0.155760	+	0.269785i	−0.933336	−	0.359005i	$-0.883116\pi$
$863$	−2.19037e15	+	3.79382e15i	−0.155760	+	0.269785i	0.777575	+	0.628790i	$0.216449\pi$
$864$		0			0
$865$	−6.02841e15	−	1.04415e16i	−0.423267	−	0.733120i
$866$		0			0
$867$	−1.40779e16			−0.975962
$868$		0			0
$869$	−5.05699e15			−0.346165
$870$		0			0
$871$	−3.05006e15	−	5.28286e15i	−0.206162	−	0.357083i
$872$		0			0
$873$	4.41557e13	−	7.64800e13i	0.00294719	−	0.00510469i
$874$		0			0
$875$	−4.82377e14	+	8.25593e15i	−0.0317938	+	0.544154i
$876$		0			0
$877$	2.27454e15	−	3.93961e15i	0.148045	−	0.256422i	−0.782460	−	0.622701i	$-0.786035\pi$
$877$	2.27454e15	−	3.93961e15i	0.148045	−	0.256422i	0.930505	+	0.366279i	$0.119368\pi$
$878$		0			0
$879$	3.12993e15	+	5.42120e15i	0.201185	+	0.348463i
$880$		0			0
$881$	1.72331e15			0.109395			0.0546973	−	0.998503i	$-0.482581\pi$
$881$	1.72331e15			0.109395			0.0546973	+	0.998503i	$0.482581\pi$
$882$		0			0
$883$	−1.15205e16			−0.722252			−0.361126	−	0.932517i	$-0.617608\pi$
$883$	−1.15205e16			−0.722252			−0.361126	+	0.932517i	$0.617608\pi$
$884$		0			0
$885$	−6.07029e15	−	1.05141e16i	−0.375856	−	0.651002i
$886$		0			0
$887$	1.00305e16	−	1.73733e16i	0.613397	−	1.06244i	−0.377266	−	0.926105i	$-0.623136\pi$
$887$	1.00305e16	−	1.73733e16i	0.613397	−	1.06244i	0.990663	−	0.136331i	$-0.0435309\pi$
$888$		0			0
$889$	1.28770e15	−	2.20392e16i	0.0777778	−	1.33118i
$890$		0			0
$891$	6.52432e14	−	1.13005e15i	0.0389231	−	0.0674169i
$892$		0			0
$893$	2.77513e15	+	4.80666e15i	0.163531	+	0.283244i
$894$		0			0
$895$	1.97144e16			1.14751
$896$		0			0
$897$	−5.08429e15			−0.292329
$898$		0			0
$899$	−1.37448e16	−	2.38067e16i	−0.780656	−	1.35214i
$900$		0			0
$901$	−1.54200e16	+	2.67082e16i	−0.865163	+	1.49851i
$902$		0			0
$903$	1.76819e16	−	8.87612e15i	0.980047	−	0.491972i
$904$		0			0
$905$	1.13340e16	−	1.96311e16i	0.620607	−	1.07492i
$906$		0			0
$907$	−2.12443e15	−	3.67962e15i	−0.114922	−	0.199050i	0.802827	−	0.596212i	$-0.203328\pi$
$907$	−2.12443e15	−	3.67962e15i	−0.114922	−	0.199050i	−0.917748	+	0.397162i	$0.869995\pi$
$908$		0			0
$909$	7.25927e15			0.387964
$910$		0			0
$911$	−1.88898e16			−0.997417			−0.498708	−	0.866770i	$-0.666192\pi$
$911$	−1.88898e16			−0.997417			−0.498708	+	0.866770i	$0.666192\pi$
$912$		0			0
$913$	−1.33329e16	−	2.30932e16i	−0.695559	−	1.20474i
$914$		0			0
$915$	−1.24610e16	+	2.15831e16i	−0.642299	+	1.11249i
$916$		0			0
$917$	−2.90816e16	−	1.91349e16i	−1.48111	−	0.974531i
$918$		0			0
$919$	−1.29152e16	+	2.23698e16i	−0.649930	+	1.12571i	0.333209	+	0.942853i	$0.391869\pi$
$919$	−1.29152e16	+	2.23698e16i	−0.649930	+	1.12571i	−0.983139	+	0.182859i	$0.941465\pi$
$920$		0			0
$921$	7.49533e15	+	1.29823e16i	0.372703	+	0.645540i
$922$		0			0
$923$	−8.05604e15			−0.395833
$924$		0			0
$925$	1.29268e16			0.627643
$926$		0			0
$927$	−1.00041e15	−	1.73276e15i	−0.0479998	−	0.0831381i
$928$		0			0
$929$	−1.95524e16	+	3.38658e16i	−0.927073	+	1.60574i	−0.138880	+	0.990309i	$0.544350\pi$
$929$	−1.95524e16	+	3.38658e16i	−0.927073	+	1.60574i	−0.788193	+	0.615428i	$0.788983\pi$
$930$		0			0
$931$	3.31849e15	−	4.45409e15i	0.155495	−	0.208706i
$932$		0			0
$933$	7.40346e15	−	1.28232e16i	0.342835	−	0.593808i
$934$		0			0
$935$	−1.57024e16	−	2.71973e16i	−0.718624	−	1.24469i
$936$		0			0
$937$	−3.18034e16			−1.43849			−0.719244	−	0.694758i	$-0.755512\pi$
$937$	−3.18034e16			−1.43849			−0.719244	+	0.694758i	$0.755512\pi$
$938$		0			0
$939$	1.48742e16			0.664925
$940$		0			0
$941$	5.70365e14	+	9.87902e14i	0.0252006	+	0.0436486i	0.878351	−	0.478017i	$-0.158644\pi$
$941$	5.70365e14	+	9.87902e14i	0.0252006	+	0.0436486i	−0.853150	+	0.521666i	$0.825311\pi$
$942$		0			0
$943$	3.58393e15	−	6.20755e15i	0.156511	−	0.271085i
$944$		0			0
$945$	−4.65824e15	−	3.06500e15i	−0.201070	−	0.132299i
$946$		0			0
$947$	2.74228e15	−	4.74977e15i	0.117000	−	0.202650i	−0.801577	−	0.597891i	$-0.796006\pi$
$947$	2.74228e15	−	4.74977e15i	0.117000	−	0.202650i	0.918578	+	0.395241i	$0.129339\pi$
$948$		0			0
$949$	1.26652e16	+	2.19367e16i	0.534130	+	0.925140i
$950$		0			0
$951$	−1.04140e16			−0.434134
$952$		0			0
$953$	−3.36575e16			−1.38698			−0.693491	−	0.720465i	$-0.743928\pi$
$953$	−3.36575e16			−1.38698			−0.693491	+	0.720465i	$0.743928\pi$
$954$		0			0
$955$	−6.07540e15	−	1.05229e16i	−0.247489	−	0.428664i
$956$		0			0
$957$	4.41521e15	−	7.64736e15i	0.177801	−	0.307961i
$958$		0			0
$959$	1.05395e16	−	5.29070e15i	0.419582	−	0.210626i
$960$		0			0
$961$	−2.73674e16	+	4.74017e16i	−1.07710	+	1.86558i
$962$		0			0
$963$	−4.38489e15	−	7.59486e15i	−0.170614	−	0.295512i
$964$		0			0
$965$	−1.54104e16			−0.592808
$966$		0			0
$967$	−1.18992e15			−0.0452557			−0.0226278	−	0.999744i	$-0.507203\pi$
$967$	−1.18992e15			−0.0452557			−0.0226278	+	0.999744i	$0.507203\pi$
$968$		0			0
$969$	3.27728e15	+	5.67641e15i	0.123235	+	0.213449i
$970$		0			0
$971$	1.71577e16	−	2.97180e16i	0.637901	−	1.10488i	−0.347991	−	0.937498i	$-0.613136\pi$
$971$	1.71577e16	−	2.97180e16i	0.637901	−	1.10488i	0.985893	−	0.167379i	$-0.0535305\pi$
$972$		0			0
$973$	−2.66556e15	+	4.56213e16i	−0.0979867	+	1.67705i
$974$		0			0
$975$	−4.91077e15	+	8.50570e15i	−0.178494	+	0.309161i
$976$		0			0
$977$	2.49520e16	+	4.32182e16i	0.896779	+	1.55327i	0.831587	+	0.555395i	$0.187433\pi$
$977$	2.49520e16	+	4.32182e16i	0.896779	+	1.55327i	0.0651925	+	0.997873i	$0.479234\pi$
$978$		0			0
$979$	−8.30381e15			−0.295102
$980$		0			0
$981$	1.27136e15			0.0446776
$982$		0			0
$983$	−2.57997e16	−	4.46864e16i	−0.896542	−	1.55286i	−0.831885	−	0.554948i	$-0.812738\pi$
$983$	−2.57997e16	−	4.46864e16i	−0.896542	−	1.55286i	−0.0646570	−	0.997908i	$-0.520595\pi$
$984$		0			0
$985$	1.64615e16	−	2.85121e16i	0.565678	−	0.979784i
$986$		0			0
$987$	−1.24532e15	+	2.13138e16i	−0.0423191	+	0.724296i
$988$		0			0
$989$	−1.30552e16	+	2.26122e16i	−0.438736	+	0.759913i
$990$		0			0
$991$	7.64535e15	+	1.32421e16i	0.254093	+	0.440102i	0.964649	−	0.263539i	$-0.0848898\pi$
$991$	7.64535e15	+	1.32421e16i	0.254093	+	0.440102i	−0.710556	+	0.703641i	$0.751556\pi$
$992$		0			0
$993$	1.99811e16			0.656747
$994$		0			0
$995$	−4.08846e16			−1.32902
$996$		0			0
$997$	6.79957e15	+	1.17772e16i	0.218604	+	0.378633i	0.954381	−	0.298590i	$-0.0965163\pi$
$997$	6.79957e15	+	1.17772e16i	0.218604	+	0.378633i	−0.735777	+	0.677224i	$0.763183\pi$
$998$		0			0
$999$	3.36669e15	−	5.83128e15i	0.107052	−	0.185419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.12.i.a.37.6	yes	14
3.2	odd	2		252.12.k.b.37.2		14
7.4	even	3	inner	84.12.i.a.25.6	✓	14
21.11	odd	6		252.12.k.b.109.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.12.i.a.25.6	✓	14	7.4	even	3	inner
84.12.i.a.37.6	yes	14	1.1	even	1	trivial
252.12.k.b.37.2		14	3.2	odd	2
252.12.k.b.109.2		14	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(121.500 + 210.444i) q^{3} +(4369.65 - 7568.45i) q^{5} +(-2593.70 + 44391.4i) q^{7} +(-29524.5 + 51137.9i) q^{9} +O(q^{10})\)	\(q+(121.500 + 210.444i) q^{3} +(4369.65 - 7568.45i) q^{5} +(-2593.70 + 44391.4i) q^{7} +(-29524.5 + 51137.9i) q^{9} +(187116. + 324094. i) q^{11} -1.46722e6 q^{13} +2.12365e6 q^{15} +(-4.80119e6 - 8.31590e6i) q^{17} +(-1.40452e6 + 2.43270e6i) q^{19} +(-9.65705e6 + 4.84773e6i) q^{21} +(7.13014e6 - 1.23498e7i) q^{23} +(-1.37736e7 - 2.38566e7i) q^{25} -1.43489e7 q^{27} -9.71034e7 q^{29} +(1.41548e8 + 2.45168e8i) q^{31} +(-4.54691e7 + 7.87548e7i) q^{33} +(3.24641e8 + 2.13605e8i) q^{35} +(-2.34630e8 + 4.06392e8i) q^{37} +(-1.78267e8 - 3.08768e8i) q^{39} +5.02645e8 q^{41} -1.83098e9 q^{43} +(2.58023e8 + 4.46910e8i) q^{45} +(9.87927e8 - 1.71114e9i) q^{47} +(-1.96387e9 - 2.30276e8i) q^{49} +(1.16669e9 - 2.02076e9i) q^{51} +(-1.60585e9 - 2.78142e9i) q^{53} +3.27052e9 q^{55} -6.82597e8 q^{57} +(-2.85842e9 - 4.95094e9i) q^{59} +(-5.86773e9 + 1.01632e10i) q^{61} +(-2.19351e9 - 1.44327e9i) q^{63} +(-6.41124e9 + 1.11046e10i) q^{65} +(2.07880e9 + 3.60059e9i) q^{67} +3.46525e9 q^{69} +5.49068e9 q^{71} +(-8.63209e9 - 1.49512e10i) q^{73} +(3.34699e9 - 5.79715e9i) q^{75} +(-1.48723e10 + 7.46573e9i) q^{77} +(-6.75650e9 + 1.17026e10i) q^{79} +(-1.74339e9 - 3.01964e9i) q^{81} -7.12546e10 q^{83} -8.39181e10 q^{85} +(-1.17981e10 - 2.04349e10i) q^{87} +(-1.10945e10 + 1.92162e10i) q^{89} +(3.80553e9 - 6.51320e10i) q^{91} +(-3.43961e10 + 5.95758e10i) q^{93} +(1.22745e10 + 2.12601e10i) q^{95} -1.49556e9 q^{97} -2.20980e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 1701 q^{3} + 7218 q^{5} + 35001 q^{7} - 413343 q^{9}+O(q^{10}) \) 14 * q + 1701 * q^3 + 7218 * q^5 + 35001 * q^7 - 413343 * q^9	\( 14 q + 1701 q^{3} + 7218 q^{5} + 35001 q^{7} - 413343 q^{9} + 54450 q^{11} + 1534982 q^{13} + 3507948 q^{15} + 1478880 q^{17} - 22875935 q^{19} + 3394224 q^{21} + 62540568 q^{23} - 62136141 q^{25} - 200884698 q^{27} + 102097728 q^{29} + 188600405 q^{31} - 13231350 q^{33} - 253840734 q^{35} + 199685599 q^{37} + 186500313 q^{39} - 693868716 q^{41} - 620701754 q^{43} + 426215682 q^{45} + 2771987346 q^{47} - 5209147075 q^{49} - 359367840 q^{51} + 6487034184 q^{53} + 10046238656 q^{55} - 11117704410 q^{57} - 8183838888 q^{59} + 4069556330 q^{61} - 1241977617 q^{63} - 1520229906 q^{65} + 15766443531 q^{67} + 30394716048 q^{69} - 33183285444 q^{71} - 31685143839 q^{73} + 15099082263 q^{75} + 3261253500 q^{77} + 21999509987 q^{79} - 24407490807 q^{81} - 63053885988 q^{83} + 35204204624 q^{85} + 12404873952 q^{87} + 67041904680 q^{89} - 190876959523 q^{91} - 45829898415 q^{93} + 133488871470 q^{95} + 284083418100 q^{97} - 6430436100 q^{99}+O(q^{100}) \) 14 * q + 1701 * q^3 + 7218 * q^5 + 35001 * q^7 - 413343 * q^9 + 54450 * q^11 + 1534982 * q^13 + 3507948 * q^15 + 1478880 * q^17 - 22875935 * q^19 + 3394224 * q^21 + 62540568 * q^23 - 62136141 * q^25 - 200884698 * q^27 + 102097728 * q^29 + 188600405 * q^31 - 13231350 * q^33 - 253840734 * q^35 + 199685599 * q^37 + 186500313 * q^39 - 693868716 * q^41 - 620701754 * q^43 + 426215682 * q^45 + 2771987346 * q^47 - 5209147075 * q^49 - 359367840 * q^51 + 6487034184 * q^53 + 10046238656 * q^55 - 11117704410 * q^57 - 8183838888 * q^59 + 4069556330 * q^61 - 1241977617 * q^63 - 1520229906 * q^65 + 15766443531 * q^67 + 30394716048 * q^69 - 33183285444 * q^71 - 31685143839 * q^73 + 15099082263 * q^75 + 3261253500 * q^77 + 21999509987 * q^79 - 24407490807 * q^81 - 63053885988 * q^83 + 35204204624 * q^85 + 12404873952 * q^87 + 67041904680 * q^89 - 190876959523 * q^91 - 45829898415 * q^93 + 133488871470 * q^95 + 284083418100 * q^97 - 6430436100 * q^99

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