LMFDB - Embedded newform 252.12.k.d.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,12,Mod(37,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("252.37");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	252.k (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:	$193.622481501$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 581500324 x^{14} - 481772282104 x^{13} + \cdots + 79\!\cdots\!77 $ x^16 - 581500324x^14 - 481772282104x^13 + 132272376701859942x^12 + 189765040124256066208x^11 - 14668309022748191106194508x^10 - 25034330150368988089577197656x^9 + 804524023197576594568815873370179x^8 + 1124828921377792402289540847268007968x^7 - 19980431516277460534216470290766973558668x^6 + 592727132887361668148704829618109324342008x^5 + 215459975341822734071937522290785139860745873306x^4 - 372150170517680072482976606267991582419751904690704x^3 - 31534379943215460069637664338468383174583531082850128x^2 + 257934680050232001165280545701170549413209663811915341424x + 79978257504936591964642108900330900905737463001503418421877
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{42}\cdot 3^{15}\cdot 7^{9} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.1
Root			$-11427.1 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	252.109
Dual form			252.12.k.d.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5578.82 - 9662.79i) q^{5} +(24922.9 + 36826.3i) q^{7} +O(q^{10})$	$q+(-5578.82 - 9662.79i) q^{5} +(24922.9 + 36826.3i) q^{7} +(196201. - 339830. i) q^{11} -2.28291e6 q^{13} +(2.79207e6 - 4.83601e6i) q^{17} +(6.40868e6 + 1.11002e7i) q^{19} +(1.12939e7 + 1.95616e7i) q^{23} +(-3.78323e7 + 6.55275e7i) q^{25} -1.65025e8 q^{29} +(9.99385e7 - 1.73099e8i) q^{31} +(2.16805e8 - 4.46272e8i) q^{35} +(2.10302e8 + 3.64253e8i) q^{37} +7.64804e8 q^{41} -2.38223e8 q^{43} +(9.33471e7 + 1.61682e8i) q^{47} +(-7.35026e8 + 1.83564e9i) q^{49} +(-1.62451e9 + 2.81374e9i) q^{53} -4.37827e9 q^{55} +(-6.84439e7 + 1.18548e8i) q^{59} +(1.63005e9 + 2.82334e9i) q^{61} +(1.27359e10 + 2.20593e10i) q^{65} +(-7.66329e9 + 1.32732e10i) q^{67} -1.53915e10 q^{71} +(1.23489e10 - 2.13889e10i) q^{73} +(1.74046e10 - 1.24419e9i) q^{77} +(1.05790e10 + 1.83233e10i) q^{79} +5.62969e10 q^{83} -6.23059e10 q^{85} +(1.87036e10 + 3.23955e10i) q^{89} +(-5.68967e10 - 8.40711e10i) q^{91} +(7.15057e10 - 1.23851e11i) q^{95} -7.72068e10 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2156 q^{5} + 50512 q^{7}+O(q^{10}) $ 16 * q + 2156 * q^5 + 50512 * q^7	$ 16 q + 2156 q^{5} + 50512 q^{7} + 222796 q^{11} + 2703176 q^{13} - 5114600 q^{17} + 6910556 q^{19} + 51387712 q^{23} - 191456372 q^{25} - 118854616 q^{29} + 164659160 q^{31} - 55239344 q^{35} + 75658364 q^{37} + 1815568608 q^{41} + 10754408 q^{43} + 1034359464 q^{47} + 4123496848 q^{49} + 665159988 q^{53} - 1264543896 q^{55} - 1040514580 q^{59} - 14391208024 q^{61} + 20938150200 q^{65} - 33307097284 q^{67} - 65848902896 q^{71} + 17709749204 q^{73} - 8594484604 q^{77} - 26626784032 q^{79} + 210306955048 q^{83} - 25867402032 q^{85} + 55951560072 q^{89} + 66078280292 q^{91} - 106810047392 q^{95} - 156216030712 q^{97}+O(q^{100}) $ 16 * q + 2156 * q^5 + 50512 * q^7 + 222796 * q^11 + 2703176 * q^13 - 5114600 * q^17 + 6910556 * q^19 + 51387712 * q^23 - 191456372 * q^25 - 118854616 * q^29 + 164659160 * q^31 - 55239344 * q^35 + 75658364 * q^37 + 1815568608 * q^41 + 10754408 * q^43 + 1034359464 * q^47 + 4123496848 * q^49 + 665159988 * q^53 - 1264543896 * q^55 - 1040514580 * q^59 - 14391208024 * q^61 + 20938150200 * q^65 - 33307097284 * q^67 - 65848902896 * q^71 + 17709749204 * q^73 - 8594484604 * q^77 - 26626784032 * q^79 + 210306955048 * q^83 - 25867402032 * q^85 + 55951560072 * q^89 + 66078280292 * q^91 - 106810047392 * q^95 - 156216030712 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−5578.82	−	9662.79i	−0.798375	−	1.38283i	−0.920674	−	0.390333i	$-0.872360\pi$
$5$	−5578.82	−	9662.79i	−0.798375	−	1.38283i	0.122299	−	0.992493i	$-0.460973\pi$
$6$		0			0
$7$	24922.9	+	36826.3i	0.560479	+	0.828169i
$7$	24922.9	+	36826.3i	0.560479	+	0.828169i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	196201.	−	339830.i	0.367317	−	0.636211i	−0.621828	−	0.783154i	$-0.713610\pi$
$11$	196201.	−	339830.i	0.367317	−	0.636211i	0.989145	+	0.146942i	$0.0469432\pi$
$12$		0			0
$13$	−2.28291e6			−1.70530			−0.852649	−	0.522484i	$-0.825005\pi$
$13$	−2.28291e6			−1.70530			−0.852649	+	0.522484i	$0.825005\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.79207e6	−	4.83601e6i	0.476934	−	0.826073i	−0.522717	−	0.852506i	$-0.675082\pi$
$17$	2.79207e6	−	4.83601e6i	0.476934	−	0.826073i	0.999651	+	0.0264331i	$0.00841489\pi$
$18$		0			0
$19$	6.40868e6	+	1.11002e7i	0.593778	+	1.02845i	0.993718	+	0.111912i	$0.0356975\pi$
$19$	6.40868e6	+	1.11002e7i	0.593778	+	1.02845i	−0.399940	+	0.916541i	$0.630969\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.12939e7	+	1.95616e7i	0.365881	+	0.633725i	0.988917	−	0.148468i	$-0.0474342\pi$
$23$	1.12939e7	+	1.95616e7i	0.365881	+	0.633725i	−0.623036	+	0.782193i	$0.714101\pi$
$24$		0			0
$25$	−3.78323e7	+	6.55275e7i	−0.774806	+	1.34200i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.65025e8			−1.49403			−0.747016	−	0.664806i	$-0.768514\pi$
$29$	−1.65025e8			−1.49403			−0.747016	+	0.664806i	$0.768514\pi$
$30$		0			0
$31$	9.99385e7	−	1.73099e8i	0.626966	−	1.08594i	−0.361192	−	0.932492i	$-0.617630\pi$
$31$	9.99385e7	−	1.73099e8i	0.626966	−	1.08594i	0.988157	−	0.153445i	$-0.0490367\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.16805e8	−	4.46272e8i	0.697741	−	1.43623i
$36$		0			0
$37$	2.10302e8	+	3.64253e8i	0.498579	+	0.863563i	0.999999	−	0.00164058i	$-0.000522215\pi$
$37$	2.10302e8	+	3.64253e8i	0.498579	+	0.863563i	−0.501420	+	0.865204i	$0.667189\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	7.64804e8			1.03095			0.515476	−	0.856904i	$-0.327615\pi$
$41$	7.64804e8			1.03095			0.515476	+	0.856904i	$0.327615\pi$
$42$		0			0
$43$	−2.38223e8			−0.247120			−0.123560	−	0.992337i	$-0.539431\pi$
$43$	−2.38223e8			−0.247120			−0.123560	+	0.992337i	$0.539431\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	9.33471e7	+	1.61682e8i	0.0593694	+	0.102831i	0.894183	−	0.447703i	$-0.147758\pi$
$47$	9.33471e7	+	1.61682e8i	0.0593694	+	0.102831i	−0.834813	+	0.550533i	$0.814424\pi$
$48$		0			0
$49$	−7.35026e8	+	1.83564e9i	−0.371727	+	0.928342i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.62451e9	+	2.81374e9i	−0.533587	+	0.924200i	0.465643	+	0.884973i	$0.345823\pi$
$53$	−1.62451e9	+	2.81374e9i	−0.533587	+	0.924200i	−0.999230	+	0.0392276i	$0.987510\pi$
$54$		0			0
$55$	−4.37827e9			−1.17303
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.84439e7	+	1.18548e8i	−0.0124637	+	0.0215878i	−0.872190	−	0.489167i	$-0.837301\pi$
$59$	−6.84439e7	+	1.18548e8i	−0.0124637	+	0.0215878i	0.859726	+	0.510755i	$0.170634\pi$
$60$		0			0
$61$	1.63005e9	+	2.82334e9i	0.247109	+	0.428005i	0.962722	−	0.270492i	$-0.0871862\pi$
$61$	1.63005e9	+	2.82334e9i	0.247109	+	0.428005i	−0.715614	+	0.698496i	$0.753853\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.27359e10	+	2.20593e10i	1.36147	+	2.35813i
$66$		0			0
$67$	−7.66329e9	+	1.32732e10i	−0.693432	+	1.20106i	0.277275	+	0.960791i	$0.410569\pi$
$67$	−7.66329e9	+	1.32732e10i	−0.693432	+	1.20106i	−0.970707	+	0.240268i	$0.922765\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.53915e10			−1.01242			−0.506210	−	0.862410i	$-0.668954\pi$
$71$	−1.53915e10			−1.01242			−0.506210	+	0.862410i	$0.668954\pi$
$72$		0			0
$73$	1.23489e10	−	2.13889e10i	0.697192	−	1.20757i	−0.272244	−	0.962228i	$-0.587766\pi$
$73$	1.23489e10	−	2.13889e10i	0.697192	−	1.20757i	0.969436	−	0.245344i	$-0.0789008\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.74046e10	−	1.24419e9i	0.732764	−	0.0523826i
$78$		0			0
$79$	1.05790e10	+	1.83233e10i	0.386807	+	0.669970i	0.992018	−	0.126095i	$-0.0402445\pi$
$79$	1.05790e10	+	1.83233e10i	0.386807	+	0.669970i	−0.605211	+	0.796065i	$0.706911\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.62969e10			1.56875			0.784377	−	0.620284i	$-0.212983\pi$
$83$	5.62969e10			1.56875			0.784377	+	0.620284i	$0.212983\pi$
$84$		0			0
$85$	−6.23059e10			−1.52309
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.87036e10	+	3.23955e10i	0.355041	+	0.614950i	0.987125	−	0.159950i	$-0.0511334\pi$
$89$	1.87036e10	+	3.23955e10i	0.355041	+	0.614950i	−0.632084	+	0.774900i	$0.717800\pi$
$90$		0			0
$91$	−5.68967e10	−	8.40711e10i	−0.955783	−	1.41227i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7.15057e10	−	1.23851e11i	0.948115	−	1.64218i
$96$		0			0
$97$	−7.72068e10			−0.912874			−0.456437	−	0.889756i	$-0.650875\pi$
$97$	−7.72068e10			−0.912874			−0.456437	+	0.889756i	$0.650875\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.27863e10	+	1.08749e11i	−0.594426	+	1.02958i	0.399202	+	0.916863i	$0.369287\pi$
$101$	−6.27863e10	+	1.08749e11i	−0.594426	+	1.02958i	−0.993628	+	0.112712i	$0.964046\pi$
$102$		0			0
$103$	−9.56009e10	−	1.65586e11i	−0.812563	−	1.40740i	−0.911064	−	0.412264i	$-0.864738\pi$
$103$	−9.56009e10	−	1.65586e11i	−0.812563	−	1.40740i	0.0985011	−	0.995137i	$-0.468595\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.85938e10	−	4.95259e10i	−0.197088	−	0.341367i	0.750495	−	0.660876i	$-0.229815\pi$
$107$	−2.85938e10	−	4.95259e10i	−0.197088	−	0.341367i	−0.947583	+	0.319509i	$0.896482\pi$
$108$		0			0
$109$	1.21619e11	−	2.10650e11i	0.757102	−	1.31134i	−0.187220	−	0.982318i	$-0.559948\pi$
$109$	1.21619e11	−	2.10650e11i	0.757102	−	1.31134i	0.944322	−	0.329022i	$-0.106719\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.16630e10			−0.212726			−0.106363	−	0.994327i	$-0.533920\pi$
$113$	−4.16630e10			−0.212726			−0.106363	+	0.994327i	$0.533920\pi$
$114$		0			0
$115$	1.26013e11	−	2.18261e11i	0.584221	−	1.01190i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.47679e11	−	1.77057e10i	0.951439	−	0.0680149i
$120$		0			0
$121$	6.56664e10	+	1.13738e11i	0.230157	+	0.398643i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	2.99432e11			0.877592
$126$		0			0
$127$	−3.71377e10			−0.0997457			−0.0498728	−	0.998756i	$-0.515882\pi$
$127$	−3.71377e10			−0.0997457			−0.0498728	+	0.998756i	$0.515882\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.98899e11	+	3.44503e11i	0.450443	+	0.780191i	0.998414	−	0.0563070i	$-0.0179326\pi$
$131$	1.98899e11	+	3.44503e11i	0.450443	+	0.780191i	−0.547970	+	0.836498i	$0.684599\pi$
$132$		0			0
$133$	−2.49055e11	+	5.12656e11i	−0.518933	+	1.06817i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.18742e11	−	7.25282e11i	0.741282	−	1.28394i	−0.210630	−	0.977566i	$-0.567552\pi$
$137$	4.18742e11	−	7.25282e11i	0.741282	−	1.28394i	0.951912	−	0.306372i	$-0.0991150\pi$
$138$		0			0
$139$	−6.68822e11			−1.09327			−0.546637	−	0.837370i	$-0.684092\pi$
$139$	−6.68822e11			−1.09327			−0.546637	+	0.837370i	$0.684092\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.47908e11	+	7.75800e11i	−0.626384	+	1.08493i
$144$		0			0
$145$	9.20642e11	+	1.59460e12i	1.19280	+	2.06599i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.37890e11	−	5.85243e11i	−0.376922	−	0.652847i	0.613691	−	0.789546i	$-0.289684\pi$
$149$	−3.37890e11	−	5.85243e11i	−0.376922	−	0.652847i	−0.990613	+	0.136699i	$0.956351\pi$
$150$		0			0
$151$	2.19258e11	−	3.79765e11i	0.227291	−	0.393679i	−0.729714	−	0.683753i	$-0.760347\pi$
$151$	2.19258e11	−	3.79765e11i	0.227291	−	0.393679i	0.957004	+	0.290074i	$0.0936800\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.23015e12			−2.00221
$156$		0			0
$157$	1.47959e11	−	2.56272e11i	0.123792	−	0.214414i	−0.797468	−	0.603361i	$-0.793828\pi$
$157$	1.47959e11	−	2.56272e11i	0.123792	−	0.214414i	0.921260	+	0.388947i	$0.127161\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−4.38905e11	+	9.03443e11i	−0.319763	+	0.658201i
$162$		0			0
$163$	1.12083e12	+	1.94133e12i	0.762971	+	1.32150i	0.941313	+	0.337535i	$0.109593\pi$
$163$	1.12083e12	+	1.94133e12i	0.762971	+	1.32150i	−0.178342	+	0.983968i	$0.557073\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.62678e11			0.156489			0.0782445	−	0.996934i	$-0.475069\pi$
$167$	2.62678e11			0.156489			0.0782445	+	0.996934i	$0.475069\pi$
$168$		0			0
$169$	3.41951e12			1.90804
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.72304e11	+	1.68408e12i	0.477033	+	0.826245i	0.999654	−	0.0263201i	$-0.00837892\pi$
$173$	9.72304e11	+	1.68408e12i	0.477033	+	0.826245i	−0.522621	+	0.852565i	$0.675046\pi$
$174$		0			0
$175$	−3.35602e12	+	2.39910e11i	−1.54567	+	0.110494i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	2.23898e12	−	3.87802e12i	0.910663	−	1.57732i	0.0975338	−	0.995232i	$-0.468905\pi$
$179$	2.23898e12	−	3.87802e12i	0.910663	−	1.57732i	0.813129	−	0.582083i	$-0.197762\pi$
$180$		0			0
$181$	4.68844e12			1.79389			0.896945	−	0.442142i	$-0.145781\pi$
$181$	4.68844e12			1.79389			0.896945	+	0.442142i	$0.145781\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.34647e12	−	4.06421e12i	0.796105	−	1.37889i
$186$		0			0
$187$	−1.09561e12	−	1.89766e12i	−0.350371	−	0.606861i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.93575e12	−	3.35282e12i	−0.551019	−	0.954393i	−0.998201	−	0.0599500i	$-0.980906\pi$
$191$	−1.93575e12	−	3.35282e12i	−0.551019	−	0.954393i	0.447182	−	0.894443i	$-0.352427\pi$
$192$		0			0
$193$	1.46950e12	−	2.54524e12i	0.395005	−	0.684169i	−0.598097	−	0.801424i	$-0.704076\pi$
$193$	1.46950e12	−	2.54524e12i	0.395005	−	0.684169i	0.993102	+	0.117255i	$0.0374094\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3.10385e12			0.745309			0.372654	−	0.927970i	$-0.378448\pi$
$197$	3.10385e12			0.745309			0.372654	+	0.927970i	$0.378448\pi$
$198$		0			0
$199$	1.08230e12	−	1.87460e12i	0.245842	−	0.425810i	−0.716526	−	0.697560i	$-0.754269\pi$
$199$	1.08230e12	−	1.87460e12i	0.245842	−	0.425810i	0.962368	+	0.271750i	$0.0876023\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.11289e12	−	6.07725e12i	−0.837373	−	1.23731i
$204$		0			0
$205$	−4.26670e12	−	7.39014e12i	−0.823087	−	1.42563i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	5.02955e12			0.872418
$210$		0			0
$211$	2.54746e12			0.419328			0.209664	−	0.977773i	$-0.432763\pi$
$211$	2.54746e12			0.419328			0.209664	+	0.977773i	$0.432763\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.32900e12	+	2.30190e12i	0.197294	+	0.341724i
$216$		0			0
$217$	8.86534e12	−	6.33751e11i	1.25074	−	0.0894108i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−6.37405e12	+	1.10402e13i	−0.813314	+	1.40870i
$222$		0			0
$223$	−4.37566e12			−0.531333			−0.265667	−	0.964065i	$-0.585592\pi$
$223$	−4.37566e12			−0.531333			−0.265667	+	0.964065i	$0.585592\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.86393e12	−	1.18887e13i	0.755841	−	1.30915i	−0.189114	−	0.981955i	$-0.560562\pi$
$227$	6.86393e12	−	1.18887e13i	0.755841	−	1.30915i	0.944955	−	0.327200i	$-0.106105\pi$
$228$		0			0
$229$	5.79914e11	+	1.00444e12i	0.0608511	+	0.105397i	0.894846	−	0.446375i	$-0.147285\pi$
$229$	5.79914e11	+	1.00444e12i	0.0608511	+	0.105397i	−0.833995	+	0.551772i	$0.813952\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.23260e12	+	3.86698e12i	0.212987	+	0.368904i	0.952648	−	0.304075i	$-0.0983474\pi$
$233$	2.23260e12	+	3.86698e12i	0.212987	+	0.368904i	−0.739661	+	0.672980i	$0.765014\pi$
$234$		0			0
$235$	1.04153e12	−	1.80399e12i	0.0947981	−	0.164195i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.16228e13			1.79359			0.896795	−	0.442447i	$-0.145889\pi$
$239$	2.16228e13			1.79359			0.896795	+	0.442447i	$0.145889\pi$
$240$		0			0
$241$	−9.67406e12	+	1.67560e13i	−0.766505	+	1.32763i	0.172942	+	0.984932i	$0.444673\pi$
$241$	−9.67406e12	+	1.67560e13i	−0.766505	+	1.32763i	−0.939447	+	0.342694i	$0.888661\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.18379e13	−	3.13827e12i	1.58051	−	0.227131i
$246$		0			0
$247$	−1.46304e13	−	2.53407e13i	−1.01257	−	1.75382i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1.43958e13			0.912075			0.456037	−	0.889961i	$-0.349268\pi$
$251$	1.43958e13			0.912075			0.456037	+	0.889961i	$0.349268\pi$
$252$		0			0
$253$	8.86347e12			0.537577
$254$		0			0
$255$		0			0
$256$		0			0
$257$	8.96043e12	+	1.55199e13i	0.498536	+	0.863490i	0.999999	−	0.00168967i	$-0.000537838\pi$
$257$	8.96043e12	+	1.55199e13i	0.498536	+	0.863490i	−0.501463	+	0.865179i	$0.667205\pi$
$258$		0			0
$259$	−8.17278e12	+	1.68229e13i	−0.435734	+	0.896916i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	3.34897e12	−	5.80059e12i	0.164117	−	0.284260i	−0.772224	−	0.635350i	$-0.780856\pi$
$263$	3.34897e12	−	5.80059e12i	0.164117	−	0.284260i	0.936342	+	0.351091i	$0.114189\pi$
$264$		0			0
$265$	3.62514e13			1.70401
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.73220e13	−	3.00027e13i	0.749828	−	1.29874i	−0.198077	−	0.980187i	$-0.563469\pi$
$269$	1.73220e13	−	3.00027e13i	0.749828	−	1.29874i	0.947905	−	0.318554i	$-0.103197\pi$
$270$		0			0
$271$	−7.52159e12	−	1.30278e13i	−0.312593	−	0.541426i	0.666330	−	0.745657i	$-0.267864\pi$
$271$	−7.52159e12	−	1.30278e13i	−0.312593	−	0.541426i	−0.978923	+	0.204231i	$0.934531\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.48454e13	+	2.57131e13i	0.569198	+	0.985880i
$276$		0			0
$277$	−2.61416e12	+	4.52785e12i	−0.0963148	+	0.166822i	−0.910157	−	0.414264i	$-0.864039\pi$
$277$	−2.61416e12	+	4.52785e12i	−0.0963148	+	0.166822i	0.813842	+	0.581087i	$0.197372\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.40636e13			0.478863			0.239431	−	0.970913i	$-0.423039\pi$
$281$	1.40636e13			0.478863			0.239431	+	0.970913i	$0.423039\pi$
$282$		0			0
$283$	9.20998e12	−	1.59522e13i	0.301601	−	0.522389i	−0.674897	−	0.737911i	$-0.735812\pi$
$283$	9.20998e12	−	1.59522e13i	0.301601	−	0.522389i	0.976499	+	0.215523i	$0.0691455\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.90611e13	+	2.81649e13i	0.577827	+	0.853803i
$288$		0			0
$289$	1.54459e12	+	2.67531e12i	0.0450687	+	0.0780613i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−2.56171e13			−0.693040			−0.346520	−	0.938043i	$-0.612637\pi$
$293$	−2.56171e13			−0.693040			−0.346520	+	0.938043i	$0.612637\pi$
$294$		0			0
$295$	1.52734e12			0.0398030
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.57829e13	−	4.46573e13i	−0.623937	−	1.08069i
$300$		0			0
$301$	−5.93721e12	−	8.77288e12i	−0.138505	−	0.204657i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.81875e13	−	3.15018e13i	0.394571	−	0.683417i
$306$		0			0
$307$	4.44656e13			0.930600			0.465300	−	0.885153i	$-0.345946\pi$
$307$	4.44656e13			0.930600			0.465300	+	0.885153i	$0.345946\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.91286e13	−	8.50933e13i	0.957530	−	1.65849i	0.229061	−	0.973412i	$-0.426434\pi$
$311$	4.91286e13	−	8.50933e13i	0.957530	−	1.65849i	0.728469	−	0.685079i	$-0.240232\pi$
$312$		0			0
$313$	−1.19408e13	−	2.06821e13i	−0.224667	−	0.389135i	0.731552	−	0.681785i	$-0.238796\pi$
$313$	−1.19408e13	−	2.06821e13i	−0.224667	−	0.389135i	−0.956220	+	0.292650i	$0.905463\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.97132e13	−	8.61057e13i	−0.872259	−	1.51080i	−0.859654	−	0.510877i	$-0.829321\pi$
$317$	−4.97132e13	−	8.61057e13i	−0.872259	−	1.51080i	−0.0126053	−	0.999921i	$-0.504012\pi$
$318$		0			0
$319$	−3.23779e13	+	5.60802e13i	−0.548783	+	0.950520i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	7.15741e13			1.13277
$324$		0			0
$325$	8.63677e13	−	1.49593e14i	1.32127	−	2.28851i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−3.62767e12	+	7.46721e12i	−0.0518860	+	0.106802i
$330$		0			0
$331$	5.27130e12	+	9.13017e12i	0.0729229	+	0.126306i	0.900181	−	0.435516i	$-0.143434\pi$
$331$	5.27130e12	+	9.13017e12i	0.0729229	+	0.126306i	−0.827258	+	0.561822i	$0.810101\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.71008e14			2.21447
$336$		0			0
$337$	1.57113e14			1.96900			0.984502	−	0.175375i	$-0.0561139\pi$
$337$	1.57113e14			1.96900			0.984502	+	0.175375i	$0.0561139\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−3.92160e13	−	6.79241e13i	−0.460590	−	0.797765i
$342$		0			0
$343$	−8.59186e13	+	1.86810e13i	−0.977169	+	0.212463i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.53483e10	−	2.65840e10i	0.000163775	−	0.000283666i	−0.865944	−	0.500142i	$-0.833281\pi$
$347$	1.53483e10	−	2.65840e10i	0.000163775	−	0.000283666i	0.866107	+	0.499858i	$0.166615\pi$
$348$		0			0
$349$	1.00590e14			1.03995			0.519976	−	0.854181i	$-0.325941\pi$
$349$	1.00590e14			1.03995			0.519976	+	0.854181i	$0.325941\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−9.13814e13	+	1.58277e14i	−0.887354	+	1.53694i	−0.0443634	+	0.999015i	$0.514126\pi$
$353$	−9.13814e13	+	1.58277e14i	−0.887354	+	1.53694i	−0.842991	+	0.537928i	$0.819207\pi$
$354$		0			0
$355$	8.58665e13	+	1.48725e14i	0.808291	+	1.40000i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−3.57145e13	−	6.18593e13i	−0.316100	−	0.547502i	0.663570	−	0.748114i	$-0.269040\pi$
$359$	−3.57145e13	−	6.18593e13i	−0.316100	−	0.547502i	−0.979671	+	0.200612i	$0.935707\pi$
$360$		0			0
$361$	−2.38973e13	+	4.13913e13i	−0.205144	+	0.355319i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.75569e14			−2.22648
$366$		0			0
$367$	3.49074e13	−	6.04615e13i	0.273687	−	0.474040i	−0.696116	−	0.717930i	$-0.745090\pi$
$367$	3.49074e13	−	6.04615e13i	0.273687	−	0.474040i	0.969803	+	0.243889i	$0.0784233\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.44107e14	+	1.03017e13i	−1.06446	+	0.0760942i
$372$		0			0
$373$	−8.26603e13	−	1.43172e14i	−0.592787	−	1.02674i	−0.993855	−	0.110689i	$-0.964694\pi$
$373$	−8.26603e13	−	1.43172e14i	−0.592787	−	1.02674i	0.401068	−	0.916048i	$-0.368639\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.76736e14			2.54777
$378$		0			0
$379$	3.93971e13			0.258791			0.129395	−	0.991593i	$-0.458696\pi$
$379$	3.93971e13			0.258791			0.129395	+	0.991593i	$0.458696\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	3.88422e13	+	6.72766e13i	0.240830	+	0.417130i	0.960951	−	0.276719i	$-0.0892471\pi$
$383$	3.88422e13	+	6.72766e13i	0.240830	+	0.417130i	−0.720121	+	0.693848i	$0.755914\pi$
$384$		0			0
$385$	−1.09119e14	−	1.61235e14i	−0.657456	−	0.971464i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−5.89738e13	+	1.02146e14i	−0.335688	+	0.581429i	−0.983617	−	0.180272i	$-0.942302\pi$
$389$	−5.89738e13	+	1.02146e14i	−0.335688	+	0.581429i	0.647928	+	0.761701i	$0.275636\pi$
$390$		0			0
$391$	1.26133e14			0.698004
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.18036e14	−	2.04445e14i	0.617635	−	1.06977i
$396$		0			0
$397$	1.37279e14	+	2.37774e14i	0.698643	+	1.21009i	0.968937	+	0.247308i	$0.0795459\pi$
$397$	1.37279e14	+	2.37774e14i	0.698643	+	1.21009i	−0.270294	+	0.962778i	$0.587121\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.60090e13	−	1.66292e14i	−0.462400	−	0.800900i	0.536680	−	0.843786i	$-0.319678\pi$
$401$	−9.60090e13	−	1.66292e14i	−0.462400	−	0.800900i	−0.999080	+	0.0428855i	$0.986345\pi$
$402$		0			0
$403$	−2.28151e14	+	3.95168e14i	−1.06916	+	1.85184i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.65045e14			0.732545
$408$		0			0
$409$	−1.84891e14	+	3.20240e14i	−0.798798	+	1.38356i	0.121602	+	0.992579i	$0.461197\pi$
$409$	−1.84891e14	+	3.20240e14i	−0.798798	+	1.38356i	−0.920399	+	0.390979i	$0.872136\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−6.07151e12	+	4.34030e11i	−0.0248640	+	0.00177744i
$414$		0			0
$415$	−3.14070e14	−	5.43985e14i	−1.25245	−	2.16931i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−3.40515e13			−0.128813			−0.0644064	−	0.997924i	$-0.520515\pi$
$419$	−3.40515e13			−0.128813			−0.0644064	+	0.997924i	$0.520515\pi$
$420$		0			0
$421$	−2.32682e14			−0.857456			−0.428728	−	0.903434i	$-0.641038\pi$
$421$	−2.32682e14			−0.857456			−0.428728	+	0.903434i	$0.641038\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.11261e14	+	3.65915e14i	0.739062	+	1.28009i
$426$		0			0
$427$	−6.33474e13	+	1.30395e14i	−0.215961	+	0.444535i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	2.06089e14	−	3.56956e14i	0.667467	−	1.15609i	−0.311144	−	0.950363i	$-0.600712\pi$
$431$	2.06089e14	−	3.56956e14i	0.667467	−	1.15609i	0.978610	−	0.205723i	$-0.0659547\pi$
$432$		0			0
$433$	3.16336e14			0.998770			0.499385	−	0.866380i	$-0.333559\pi$
$433$	3.16336e14			0.998770			0.499385	+	0.866380i	$0.333559\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.44758e14	+	2.50728e14i	−0.434504	+	0.752584i
$438$		0			0
$439$	2.45107e14	+	4.24537e14i	0.717464	+	1.24268i	0.962002	+	0.273044i	$0.0880305\pi$
$439$	2.45107e14	+	4.24537e14i	0.717464	+	1.24268i	−0.244538	+	0.969640i	$0.578636\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.50000e14	+	4.33012e14i	0.696176	+	1.20581i	0.969783	+	0.243971i	$0.0784501\pi$
$443$	2.50000e14	+	4.33012e14i	0.696176	+	1.20581i	−0.273606	+	0.961842i	$0.588217\pi$
$444$		0			0
$445$	2.08687e14	−	3.61457e14i	0.566912	−	0.981921i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.51607e13			−0.0392071			−0.0196036	−	0.999808i	$-0.506240\pi$
$449$	−1.51607e13			−0.0392071			−0.0196036	+	0.999808i	$0.506240\pi$
$450$		0			0
$451$	1.50055e14	−	2.59903e14i	0.378686	−	0.655904i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−4.94945e14	+	1.01880e15i	−1.18986	+	2.44921i
$456$		0			0
$457$	−3.11245e14	−	5.39093e14i	−0.730405	−	1.26510i	−0.956710	−	0.291042i	$-0.905998\pi$
$457$	−3.11245e14	−	5.39093e14i	−0.730405	−	1.26510i	0.226306	−	0.974056i	$-0.427335\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−8.14992e14			−1.82305			−0.911524	−	0.411246i	$-0.865094\pi$
$461$	−8.14992e14			−1.82305			−0.911524	+	0.411246i	$0.865094\pi$
$462$		0			0
$463$	7.98210e13			0.174350			0.0871749	−	0.996193i	$-0.472216\pi$
$463$	7.98210e13			0.174350			0.0871749	+	0.996193i	$0.472216\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.26295e14	−	3.91955e14i	−0.471447	−	0.816570i	0.528020	−	0.849232i	$-0.322935\pi$
$467$	−2.26295e14	−	3.91955e14i	−0.471447	−	0.816570i	−0.999466	+	0.0326623i	$0.989601\pi$
$468$		0			0
$469$	−6.79794e14	+	4.85960e13i	−1.38333	+	0.0988895i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.67396e13	+	8.09553e13i	−0.0907713	+	0.157220i
$474$		0			0
$475$	−9.69821e14			−1.84025
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3.51335e14	−	6.08530e14i	0.636614	−	1.10265i	−0.349557	−	0.936915i	$-0.613668\pi$
$479$	3.51335e14	−	6.08530e14i	0.636614	−	1.10265i	0.986171	−	0.165732i	$-0.0529987\pi$
$480$		0			0
$481$	−4.80100e14	−	8.31558e14i	−0.850225	−	1.47263i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.30723e14	+	7.46033e14i	0.728816	+	1.26235i
$486$		0			0
$487$	−2.97188e14	+	5.14744e14i	−0.491611	+	0.851495i	−0.999953	−	0.00965994i	$-0.996925\pi$
$487$	−2.97188e14	+	5.14744e14i	−0.491611	+	0.851495i	0.508342	+	0.861155i	$0.330258\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−7.12724e14			−1.12713			−0.563564	−	0.826073i	$-0.690570\pi$
$491$	−7.12724e14			−1.12713			−0.563564	+	0.826073i	$0.690570\pi$
$492$		0			0
$493$	−4.60761e14	+	7.98062e14i	−0.712554	+	1.23418i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.83601e14	−	5.66813e14i	−0.567440	−	0.838455i
$498$		0			0
$499$	−4.67371e14	−	8.09510e14i	−0.676252	−	1.17130i	−0.976101	−	0.217316i	$-0.930270\pi$
$499$	−4.67371e14	−	8.09510e14i	−0.676252	−	1.17130i	0.299849	−	0.953987i	$-0.403064\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	7.21102e14			0.998556			0.499278	−	0.866442i	$-0.333599\pi$
$503$	7.21102e14			0.998556			0.499278	+	0.866442i	$0.333599\pi$
$504$		0			0
$505$	1.40109e15			1.89830
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.57952e13	+	7.93196e13i	0.0594117	+	0.102904i	0.894201	−	0.447665i	$-0.147744\pi$
$509$	4.57952e13	+	7.93196e13i	0.0594117	+	0.102904i	−0.834790	+	0.550569i	$0.814411\pi$
$510$		0			0
$511$	1.09544e15	−	7.83094e13i	1.39083	−	0.0994257i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.06668e15	+	1.84754e15i	−1.29746	+	2.24727i
$516$		0			0
$517$	7.32591e13			0.0872295
$518$		0			0
$519$		0			0
$520$		0			0
$521$	7.21411e14	−	1.24952e15i	0.823332	−	1.42605i	−0.0798550	−	0.996806i	$-0.525446\pi$
$521$	7.21411e14	−	1.24952e15i	0.823332	−	1.42605i	0.903187	−	0.429247i	$-0.141221\pi$
$522$		0			0
$523$	6.15443e14	+	1.06598e15i	0.687746	+	1.19121i	0.972565	+	0.232630i	$0.0747332\pi$
$523$	6.15443e14	+	1.06598e15i	0.687746	+	1.19121i	−0.284819	+	0.958581i	$0.591934\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.58072e14	−	9.66608e14i	−0.598042	−	1.03584i
$528$		0			0
$529$	2.21301e14	−	3.83305e14i	0.232262	−	0.402289i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.74598e15			−1.75808
$534$		0			0
$535$	−3.19039e14	+	5.52592e14i	−0.314701	+	0.545078i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	4.79591e14	+	6.09937e14i	0.454080	+	0.577493i
$540$		0			0
$541$	2.37856e14	+	4.11979e14i	0.220663	+	0.382200i	0.955010	−	0.296575i	$-0.0958445\pi$
$541$	2.37856e14	+	4.11979e14i	0.220663	+	0.382200i	−0.734346	+	0.678775i	$0.762511\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.71395e15			−2.41781
$546$		0			0
$547$	−2.16232e14			−0.188795			−0.0943975	−	0.995535i	$-0.530092\pi$
$547$	−2.16232e14			−0.188795			−0.0943975	+	0.995535i	$0.530092\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.05759e15	−	1.83180e15i	−0.887123	−	1.53654i
$552$		0			0
$553$	−4.11122e14	+	8.46255e14i	−0.338051	+	0.695846i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.41948e14	−	2.45861e14i	0.112183	−	0.194306i	−0.804467	−	0.593997i	$-0.797549\pi$
$557$	1.41948e14	−	2.45861e14i	0.112183	−	0.194306i	0.916650	+	0.399691i	$0.130882\pi$
$558$		0			0
$559$	5.43842e14			0.421413
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.12143e15	+	1.94238e15i	−0.835559	+	1.44723i	0.0580164	+	0.998316i	$0.481522\pi$
$563$	−1.12143e15	+	1.94238e15i	−0.835559	+	1.44723i	−0.893575	+	0.448914i	$0.851811\pi$
$564$		0			0
$565$	2.32430e14	+	4.02581e14i	0.169835	+	0.294162i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3.11079e14	+	5.38804e14i	0.218652	+	0.378716i	0.954396	−	0.298544i	$-0.0965008\pi$
$569$	3.11079e14	+	5.38804e14i	0.218652	+	0.378716i	−0.735744	+	0.677259i	$0.763167\pi$
$570$		0			0
$571$	−1.28739e15	+	2.22982e15i	−0.887585	+	1.53734i	−0.0448633	+	0.998993i	$0.514285\pi$
$571$	−1.28739e15	+	2.22982e15i	−0.887585	+	1.53734i	−0.842722	+	0.538349i	$0.819048\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.70909e15			−1.13395
$576$		0			0
$577$	−1.24489e15	+	2.15621e15i	−0.810332	+	1.40354i	0.102300	+	0.994754i	$0.467380\pi$
$577$	−1.24489e15	+	2.15621e15i	−0.810332	+	1.40354i	−0.912632	+	0.408783i	$0.865953\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.40308e15	+	2.07321e15i	0.879253	+	1.29919i
$582$		0			0
$583$	6.37460e14	+	1.10411e15i	0.391991	+	0.678948i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.39872e15			1.42059			0.710297	−	0.703902i	$-0.248560\pi$
$587$	2.39872e15			1.42059			0.710297	+	0.703902i	$0.248560\pi$
$588$		0			0
$589$	2.56190e15			1.48911
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−4.74884e13	−	8.22524e13i	−0.0265942	−	0.0460625i	0.852422	−	0.522854i	$-0.175133\pi$
$593$	−4.74884e13	−	8.22524e13i	−0.0265942	−	0.0460625i	−0.879016	+	0.476792i	$0.841800\pi$
$594$		0			0
$595$	−1.55284e15	−	2.29449e15i	−0.853658	−	1.26137i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−8.09261e14	+	1.40168e15i	−0.428787	+	0.742680i	−0.996766	−	0.0803629i	$-0.974392\pi$
$599$	−8.09261e14	+	1.40168e15i	−0.428787	+	0.742680i	0.567979	+	0.823043i	$0.307725\pi$
$600$		0			0
$601$	−6.48361e14			−0.337293			−0.168646	−	0.985677i	$-0.553940\pi$
$601$	−6.48361e14			−0.337293			−0.168646	+	0.985677i	$0.553940\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	7.32682e14	−	1.26904e15i	0.367503	−	0.636534i
$606$		0			0
$607$	−8.47944e14	−	1.46868e15i	−0.417666	−	0.723419i	0.578038	−	0.816010i	$-0.303819\pi$
$607$	−8.47944e14	−	1.46868e15i	−0.417666	−	0.723419i	−0.995704	+	0.0925906i	$0.970485\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.13103e14	−	3.69105e14i	−0.101243	−	0.175357i
$612$		0			0
$613$	−6.00792e14	+	1.04060e15i	−0.280344	+	0.485570i	−0.971469	−	0.237165i	$-0.923782\pi$
$613$	−6.00792e14	+	1.04060e15i	−0.280344	+	0.485570i	0.691125	+	0.722735i	$0.257115\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−2.76415e15			−1.24450			−0.622248	−	0.782820i	$-0.713781\pi$
$617$	−2.76415e15			−1.24450			−0.622248	+	0.782820i	$0.713781\pi$
$618$		0			0
$619$	1.21861e15	−	2.11070e15i	0.538972	−	0.933528i	−0.459987	−	0.887926i	$-0.652146\pi$
$619$	1.21861e15	−	2.11070e15i	0.538972	−	0.933528i	0.998960	−	0.0456021i	$-0.0145206\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−7.26860e14	+	1.49617e15i	−0.310289	+	0.638700i
$624$		0			0
$625$	1.76807e14	+	3.06239e14i	0.0741582	+	0.128446i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	2.34871e15			0.951155
$630$		0			0
$631$	1.10045e15			0.437935			0.218968	−	0.975732i	$-0.429731\pi$
$631$	1.10045e15			0.437935			0.218968	+	0.975732i	$0.429731\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	2.07184e14	+	3.58853e14i	0.0796345	+	0.137931i
$636$		0			0
$637$	1.67800e15	−	4.19059e15i	0.633906	−	1.58310i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.47446e15	−	2.55384e15i	0.538163	−	0.932126i	−0.460840	−	0.887483i	$-0.652452\pi$
$641$	1.47446e15	−	2.55384e15i	0.538163	−	0.932126i	0.999003	−	0.0446427i	$-0.0142149\pi$
$642$		0			0
$643$	−2.86149e15			−1.02667			−0.513337	−	0.858187i	$-0.671591\pi$
$643$	−2.86149e15			−1.02667			−0.513337	+	0.858187i	$0.671591\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.03509e14	−	8.72103e14i	0.174596	−	0.302409i	−0.765426	−	0.643524i	$-0.777471\pi$
$647$	5.03509e14	−	8.72103e14i	0.174596	−	0.302409i	0.940021	+	0.341116i	$0.110805\pi$
$648$		0			0
$649$	2.68575e13	+	4.65185e13i	0.00915628	+	0.0158591i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.08161e15	+	1.87340e15i	0.356489	+	0.617458i	0.987372	−	0.158421i	$-0.0506403\pi$
$653$	1.08161e15	+	1.87340e15i	0.356489	+	0.617458i	−0.630882	+	0.775878i	$0.717307\pi$
$654$		0			0
$655$	2.21924e15	−	3.84384e15i	0.719246	−	1.24577i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−2.09934e15			−0.657981			−0.328991	−	0.944333i	$-0.606708\pi$
$659$	−2.09934e15			−0.657981			−0.328991	+	0.944333i	$0.606708\pi$
$660$		0			0
$661$	−1.85165e15	+	3.20716e15i	−0.570758	+	0.988581i	0.425731	+	0.904850i	$0.360017\pi$
$661$	−1.85165e15	+	3.20716e15i	−0.570758	+	0.988581i	−0.996488	+	0.0837314i	$0.973316\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	6.34312e15	−	4.53447e14i	1.89140	−	0.135209i
$666$		0			0
$667$	−1.86377e15	−	3.22814e15i	−0.546638	−	0.946805i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1.27927e15			0.363069
$672$		0			0
$673$	1.46499e15			0.409027			0.204513	−	0.978864i	$-0.434439\pi$
$673$	1.46499e15			0.409027			0.204513	+	0.978864i	$0.434439\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−9.92626e14	−	1.71928e15i	−0.268255	−	0.464631i	0.700156	−	0.713990i	$-0.253114\pi$
$677$	−9.92626e14	−	1.71928e15i	−0.268255	−	0.464631i	−0.968411	+	0.249358i	$0.919780\pi$
$678$		0			0
$679$	−1.92422e15	−	2.84324e15i	−0.511647	−	0.756014i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	2.26798e15	−	3.92825e15i	0.583882	−	1.01131i	−0.411132	−	0.911576i	$-0.634866\pi$
$683$	2.26798e15	−	3.92825e15i	0.583882	−	1.01131i	0.995014	−	0.0997375i	$-0.0318003\pi$
$684$		0			0
$685$	−9.34433e15			−2.36728
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.70861e15	−	6.42350e15i	0.909925	−	1.57604i
$690$		0			0
$691$	1.08860e15	+	1.88552e15i	0.262869	+	0.455303i	0.967003	−	0.254764i	$-0.0819978\pi$
$691$	1.08860e15	+	1.88552e15i	0.262869	+	0.455303i	−0.704134	+	0.710067i	$0.748664\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	3.73123e15	+	6.46268e15i	0.872842	+	1.51181i
$696$		0			0
$697$	2.13539e15	−	3.69860e15i	0.491696	−	0.851642i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−1.04536e15			−0.233247			−0.116623	−	0.993176i	$-0.537207\pi$
$701$	−1.04536e15			−0.233247			−0.116623	+	0.993176i	$0.537207\pi$
$702$		0			0
$703$	−2.69551e15	+	4.66877e15i	−0.592090	+	1.02553i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−5.56964e15	+	3.98154e14i	−1.18583	+	0.0847703i
$708$		0			0
$709$	1.92041e15	+	3.32625e15i	0.402569	+	0.697270i	0.994035	−	0.109060i	$-0.0347841\pi$
$709$	1.92041e15	+	3.32625e15i	0.402569	+	0.697270i	−0.591466	+	0.806330i	$0.701451\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	4.51478e15			0.917580
$714$		0			0
$715$	9.99519e15			2.00036
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1.91066e15	+	3.30937e15i	0.370830	+	0.642297i	0.989694	−	0.143202i	$-0.0457398\pi$
$719$	1.91066e15	+	3.30937e15i	0.370830	+	0.642297i	−0.618863	+	0.785499i	$0.712406\pi$
$720$		0			0
$721$	3.71525e15	−	7.64750e15i	0.710141	−	1.46176i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	6.24326e15	−	1.08136e16i	1.15758	−	2.00499i
$726$		0			0
$727$	1.10567e14			0.0201923			0.0100962	−	0.999949i	$-0.496786\pi$
$727$	1.10567e14			0.0201923			0.0100962	+	0.999949i	$0.496786\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−6.65137e14	+	1.15205e15i	−0.117860	+	0.204139i
$732$		0			0
$733$	−2.31452e15	−	4.00887e15i	−0.404007	−	0.699761i	0.590198	−	0.807258i	$-0.299050\pi$
$733$	−2.31452e15	−	4.00887e15i	−0.404007	−	0.699761i	−0.994205	+	0.107497i	$0.965716\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.00708e15	+	5.20842e15i	0.509418	+	0.882338i
$738$		0			0
$739$	3.10450e15	−	5.37716e15i	0.518141	−	0.897446i	−0.481637	−	0.876371i	$-0.659958\pi$
$739$	3.10450e15	−	5.37716e15i	0.518141	−	0.897446i	0.999778	−	0.0210753i	$-0.00670898\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	3.31622e15			0.537286			0.268643	−	0.963240i	$-0.413425\pi$
$743$	3.31622e15			0.537286			0.268643	+	0.963240i	$0.413425\pi$
$744$		0			0
$745$	−3.77005e15	+	6.52992e15i	−0.601850	+	1.04243i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.11122e15	−	2.28733e15i	0.172246	−	0.354551i
$750$		0			0
$751$	3.72462e15	+	6.45123e15i	0.568934	+	0.985423i	0.996672	+	0.0815203i	$0.0259775\pi$
$751$	3.72462e15	+	6.45123e15i	0.568934	+	0.985423i	−0.427737	+	0.903903i	$0.640689\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−4.89279e15			−0.725852
$756$		0			0
$757$	−9.51588e15			−1.39130			−0.695651	−	0.718380i	$-0.744884\pi$
$757$	−9.51588e15			−1.39130			−0.695651	+	0.718380i	$0.744884\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−8.70949e14	−	1.50853e15i	−0.123702	−	0.214258i	0.797523	−	0.603289i	$-0.206143\pi$
$761$	−8.70949e14	−	1.50853e15i	−0.123702	−	0.214258i	−0.921225	+	0.389031i	$0.872810\pi$
$762$		0			0
$763$	1.07885e16	−	7.71233e14i	1.51035	−	0.107969i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.56251e14	−	2.70635e14i	0.0212544	−	0.0368137i
$768$		0			0
$769$	8.11684e15			1.08841			0.544205	−	0.838953i	$-0.316832\pi$
$769$	8.11684e15			1.08841			0.544205	+	0.838953i	$0.316832\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−3.78929e15	+	6.56324e15i	−0.493822	+	0.855325i	−0.999975	−	0.00711869i	$-0.997734\pi$
$773$	−3.78929e15	+	6.56324e15i	−0.493822	+	0.855325i	0.506152	+	0.862444i	$0.331067\pi$
$774$		0			0
$775$	7.56181e15	+	1.30974e16i	0.971553	+	1.68278i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4.90138e15	+	8.48944e15i	0.612157	+	1.06029i
$780$		0			0
$781$	−3.01983e15	+	5.23049e15i	−0.371879	+	0.644113i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.30174e15			−0.395330
$786$		0			0
$787$	−6.45454e15	+	1.11796e16i	−0.762086	+	1.31997i	0.179687	+	0.983724i	$0.442492\pi$
$787$	−6.45454e15	+	1.11796e16i	−0.762086	+	1.31997i	−0.941773	+	0.336248i	$0.890842\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.03836e15	−	1.53430e15i	−0.119228	−	0.176173i
$792$		0			0
$793$	−3.72127e15	−	6.44542e15i	−0.421394	−	0.729876i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.34695e14			0.0148365			0.00741823	−	0.999972i	$-0.497639\pi$
$797$	1.34695e14			0.0148365			0.00741823	+	0.999972i	$0.497639\pi$
$798$		0			0
$799$	1.04253e15			0.113261
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−4.84572e15	−	8.39304e15i	−0.512181	−	0.887123i
$804$		0			0
$805$	1.11784e16	−	7.99100e14i	1.16547	−	0.0833151i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	4.02674e15	−	6.97452e15i	0.408542	−	0.707616i	−0.586184	−	0.810178i	$-0.699371\pi$
$809$	4.02674e15	−	6.97452e15i	0.408542	−	0.707616i	0.994727	+	0.102562i	$0.0327039\pi$
$810$		0			0
$811$	1.14139e16			1.14240			0.571201	−	0.820810i	$-0.306478\pi$
$811$	1.14139e16			1.14240			0.571201	+	0.820810i	$0.306478\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.25058e16	−	2.16607e16i	1.21827	−	2.11011i
$816$		0			0
$817$	−1.52670e15	−	2.64432e15i	−0.146734	−	0.254151i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.00153e15	+	1.73471e15i	0.0937083	+	0.162308i	0.909069	−	0.416646i	$-0.136795\pi$
$821$	1.00153e15	+	1.73471e15i	0.0937083	+	0.162308i	−0.815360	+	0.578954i	$0.803461\pi$
$822$		0			0
$823$	2.61011e15	−	4.52084e15i	0.240968	−	0.417369i	−0.720022	−	0.693951i	$-0.755868\pi$
$823$	2.61011e15	−	4.52084e15i	0.240968	−	0.417369i	0.960990	+	0.276582i	$0.0892018\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.05282e16			−0.946395			−0.473198	−	0.880956i	$-0.656900\pi$
$827$	−1.05282e16			−0.946395			−0.473198	+	0.880956i	$0.656900\pi$
$828$		0			0
$829$	−4.64529e14	+	8.04589e14i	−0.0412063	+	0.0713714i	−0.885893	−	0.463890i	$-0.846453\pi$
$829$	−4.64529e14	+	8.04589e14i	−0.0412063	+	0.0713714i	0.844687	+	0.535261i	$0.179787\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	6.82491e15	+	8.67983e15i	0.589589	+	0.749831i
$834$		0			0
$835$	−1.46543e15	−	2.53821e15i	−0.124937	−	0.216397i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	5.65480e15			0.469598			0.234799	−	0.972044i	$-0.424557\pi$
$839$	5.65480e15			0.469598			0.234799	+	0.972044i	$0.424557\pi$
$840$		0			0
$841$	1.50326e16			1.23213
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.90768e16	−	3.30421e16i	−1.52333	−	2.63849i
$846$		0			0
$847$	−2.55194e15	+	5.25292e15i	−0.201146	+	0.414040i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−4.75025e15	+	8.22767e15i	−0.364841	+	0.631924i
$852$		0			0
$853$	−1.37095e16			−1.03945			−0.519725	−	0.854334i	$-0.673965\pi$
$853$	−1.37095e16			−1.03945			−0.519725	+	0.854334i	$0.673965\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.18745e16	−	2.05672e16i	0.877446	−	1.51978i	0.0233113	−	0.999728i	$-0.492579\pi$
$857$	1.18745e16	−	2.05672e16i	0.877446	−	1.51978i	0.854134	−	0.520052i	$-0.174088\pi$
$858$		0			0
$859$	−6.15402e15	−	1.06591e16i	−0.448948	−	0.777601i	0.549370	−	0.835579i	$-0.314868\pi$
$859$	−6.15402e15	−	1.06591e16i	−0.448948	−	0.777601i	−0.998318	+	0.0579783i	$0.981535\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.88641e14	+	1.71238e15i	0.0703039	+	0.121770i	0.899034	−	0.437878i	$-0.144270\pi$
$863$	9.88641e14	+	1.71238e15i	0.0703039	+	0.121770i	−0.828731	+	0.559648i	$0.810936\pi$
$864$		0			0
$865$	1.08486e16	−	1.87903e16i	0.761702	−	1.31931i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	8.30241e15			0.568323
$870$		0			0
$871$	1.74946e16	−	3.03015e16i	1.18251	−	2.04816i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	7.46270e15	+	1.10270e16i	0.491871	+	0.726794i
$876$		0			0
$877$	−8.28766e15	−	1.43546e16i	−0.539429	−	0.934318i	−0.998935	−	0.0461432i	$-0.985307\pi$
$877$	−8.28766e15	−	1.43546e16i	−0.539429	−	0.934318i	0.459506	−	0.888175i	$-0.348026\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−4.16808e15			−0.264587			−0.132293	−	0.991211i	$-0.542234\pi$
$881$	−4.16808e15			−0.264587			−0.132293	+	0.991211i	$0.542234\pi$
$882$		0			0
$883$	9.69534e15			0.607826			0.303913	−	0.952700i	$-0.401707\pi$
$883$	9.69534e15			0.607826			0.303913	+	0.952700i	$0.401707\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.04631e16	+	1.81226e16i	0.639852	+	1.10826i	0.985465	+	0.169879i	$0.0543377\pi$
$887$	1.04631e16	+	1.81226e16i	0.639852	+	1.10826i	−0.345613	+	0.938377i	$0.612329\pi$
$888$		0			0
$889$	−9.25578e14	−	1.36764e15i	−0.0559053	−	0.0826063i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.19646e15	+	2.07234e15i	−0.0705044	+	0.122117i
$894$		0			0
$895$	−4.99633e16			−2.90820
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−1.64923e16	+	2.85655e16i	−0.936706	+	1.62242i
$900$		0			0
$901$	9.07151e15	+	1.57123e16i	0.508971	+	0.881564i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.61559e16	−	4.53034e16i	−1.43220	−	2.48064i
$906$		0			0
$907$	−9.10092e15	+	1.57633e16i	−0.492317	+	0.852719i	−0.999961	−	0.00884840i	$-0.997183\pi$
$907$	−9.10092e15	+	1.57633e16i	−0.492317	+	0.852719i	0.507643	+	0.861567i	$0.330517\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	6.24694e15			0.329850			0.164925	−	0.986306i	$-0.447262\pi$
$911$	6.24694e15			0.329850			0.164925	+	0.986306i	$0.447262\pi$
$912$		0			0
$913$	1.10455e16	−	1.91313e16i	0.576230	−	0.998059i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−7.72964e15	+	1.59107e16i	−0.393666	+	0.810324i
$918$		0			0
$919$	9.67523e15	+	1.67580e16i	0.486884	+	0.843309i	0.999886	−	0.0150789i	$-0.00479996\pi$
$919$	9.67523e15	+	1.67580e16i	0.486884	+	0.843309i	−0.513002	+	0.858387i	$0.671467\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	3.51375e16			1.72648
$924$		0			0
$925$	−3.18248e16			−1.54521
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.36668e16	+	2.36716e16i	0.648009	+	1.12238i	0.983598	+	0.180375i	$0.0577313\pi$
$929$	1.36668e16	+	2.36716e16i	0.648009	+	1.12238i	−0.335589	+	0.942008i	$0.608935\pi$
$930$		0			0
$931$	−2.50864e16	+	3.60509e15i	−1.17548	+	0.168925i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.22245e16	+	2.11734e16i	−0.559456	+	0.969005i
$936$		0			0
$937$	2.80386e16			1.26820			0.634100	−	0.773251i	$-0.281371\pi$
$937$	2.80386e16			1.26820			0.634100	+	0.773251i	$0.281371\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.56608e16	+	2.71253e16i	−0.691944	+	1.19848i	0.279255	+	0.960217i	$0.409912\pi$
$941$	−1.56608e16	+	2.71253e16i	−0.691944	+	1.19848i	−0.971200	+	0.238266i	$0.923421\pi$
$942$		0			0
$943$	8.63761e15	+	1.49608e16i	0.377206	+	0.653341i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	4.36126e15	+	7.55392e15i	0.186075	+	0.322291i	0.943938	−	0.330123i	$-0.107090\pi$
$947$	4.36126e15	+	7.55392e15i	0.186075	+	0.322291i	−0.757864	+	0.652413i	$0.773757\pi$
$948$		0			0
$949$	−2.81914e16	+	4.88290e16i	−1.18892	+	2.05927i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	6.72272e15			0.277034			0.138517	−	0.990360i	$-0.455766\pi$
$953$	6.72272e15			0.277034			0.138517	+	0.990360i	$0.455766\pi$
$954$		0			0
$955$	−2.15984e16	+	3.74096e16i	−0.879840	+	1.52393i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	3.71457e16	−	2.65541e15i	1.47879	−	0.105713i
$960$		0			0
$961$	−7.27119e15	−	1.25941e16i	−0.286172	−	0.495664i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−3.27922e16			−1.26145
$966$		0			0
$967$	7.36720e15			0.280193			0.140096	−	0.990138i	$-0.455259\pi$
$967$	7.36720e15			0.280193			0.140096	+	0.990138i	$0.455259\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.65266e16	+	2.86249e16i	0.614436	+	1.06424i	0.990483	+	0.137634i	$0.0439499\pi$
$971$	1.65266e16	+	2.86249e16i	0.614436	+	1.06424i	−0.376047	+	0.926601i	$0.622717\pi$
$972$		0			0
$973$	−1.66690e16	−	2.46302e16i	−0.612757	−	0.905415i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−8.22861e14	+	1.42524e15i	−0.0295738	+	0.0512233i	−0.880433	−	0.474170i	$-0.842748\pi$
$977$	−8.22861e14	+	1.42524e15i	−0.0295738	+	0.0512233i	0.850860	+	0.525393i	$0.176082\pi$
$978$		0			0
$979$	1.46786e16			0.521651
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−4.50985e15	+	7.81128e15i	−0.156717	+	0.271443i	−0.933683	−	0.358100i	$-0.883425\pi$
$983$	−4.50985e15	+	7.81128e15i	−0.156717	+	0.271443i	0.776966	+	0.629543i	$0.216758\pi$
$984$		0			0
$985$	−1.73158e16	−	2.99918e16i	−0.595036	−	1.03063i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.69047e15	−	4.66003e15i	−0.0904166	−	0.156606i
$990$		0			0
$991$	−2.84665e15	+	4.93055e15i	−0.0946083	+	0.163866i	−0.909445	−	0.415824i	$-0.863493\pi$
$991$	−2.84665e15	+	4.93055e15i	−0.0946083	+	0.163866i	0.814837	+	0.579691i	$0.196827\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.41518e16			−0.785095
$996$		0			0
$997$	−3.63428e15	+	6.29476e15i	−0.116841	+	0.202375i	−0.918514	−	0.395388i	$-0.870610\pi$
$997$	−3.63428e15	+	6.29476e15i	−0.116841	+	0.202375i	0.801673	+	0.597763i	$0.203943\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.12.k.d.109.1		16
3.2	odd	2		84.12.i.b.25.8	✓	16
7.2	even	3	inner	252.12.k.d.37.1		16
21.2	odd	6		84.12.i.b.37.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.12.i.b.25.8	✓	16	3.2	odd	2
84.12.i.b.37.8	yes	16	21.2	odd	6
252.12.k.d.37.1		16	7.2	even	3	inner
252.12.k.d.109.1		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	252.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5578.82 - 9662.79i) q^{5} +(24922.9 + 36826.3i) q^{7} +O(q^{10})\)	\(q+(-5578.82 - 9662.79i) q^{5} +(24922.9 + 36826.3i) q^{7} +(196201. - 339830. i) q^{11} -2.28291e6 q^{13} +(2.79207e6 - 4.83601e6i) q^{17} +(6.40868e6 + 1.11002e7i) q^{19} +(1.12939e7 + 1.95616e7i) q^{23} +(-3.78323e7 + 6.55275e7i) q^{25} -1.65025e8 q^{29} +(9.99385e7 - 1.73099e8i) q^{31} +(2.16805e8 - 4.46272e8i) q^{35} +(2.10302e8 + 3.64253e8i) q^{37} +7.64804e8 q^{41} -2.38223e8 q^{43} +(9.33471e7 + 1.61682e8i) q^{47} +(-7.35026e8 + 1.83564e9i) q^{49} +(-1.62451e9 + 2.81374e9i) q^{53} -4.37827e9 q^{55} +(-6.84439e7 + 1.18548e8i) q^{59} +(1.63005e9 + 2.82334e9i) q^{61} +(1.27359e10 + 2.20593e10i) q^{65} +(-7.66329e9 + 1.32732e10i) q^{67} -1.53915e10 q^{71} +(1.23489e10 - 2.13889e10i) q^{73} +(1.74046e10 - 1.24419e9i) q^{77} +(1.05790e10 + 1.83233e10i) q^{79} +5.62969e10 q^{83} -6.23059e10 q^{85} +(1.87036e10 + 3.23955e10i) q^{89} +(-5.68967e10 - 8.40711e10i) q^{91} +(7.15057e10 - 1.23851e11i) q^{95} -7.72068e10 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2156 q^{5} + 50512 q^{7}+O(q^{10}) \) 16 * q + 2156 * q^5 + 50512 * q^7	\( 16 q + 2156 q^{5} + 50512 q^{7} + 222796 q^{11} + 2703176 q^{13} - 5114600 q^{17} + 6910556 q^{19} + 51387712 q^{23} - 191456372 q^{25} - 118854616 q^{29} + 164659160 q^{31} - 55239344 q^{35} + 75658364 q^{37} + 1815568608 q^{41} + 10754408 q^{43} + 1034359464 q^{47} + 4123496848 q^{49} + 665159988 q^{53} - 1264543896 q^{55} - 1040514580 q^{59} - 14391208024 q^{61} + 20938150200 q^{65} - 33307097284 q^{67} - 65848902896 q^{71} + 17709749204 q^{73} - 8594484604 q^{77} - 26626784032 q^{79} + 210306955048 q^{83} - 25867402032 q^{85} + 55951560072 q^{89} + 66078280292 q^{91} - 106810047392 q^{95} - 156216030712 q^{97}+O(q^{100}) \) 16 * q + 2156 * q^5 + 50512 * q^7 + 222796 * q^11 + 2703176 * q^13 - 5114600 * q^17 + 6910556 * q^19 + 51387712 * q^23 - 191456372 * q^25 - 118854616 * q^29 + 164659160 * q^31 - 55239344 * q^35 + 75658364 * q^37 + 1815568608 * q^41 + 10754408 * q^43 + 1034359464 * q^47 + 4123496848 * q^49 + 665159988 * q^53 - 1264543896 * q^55 - 1040514580 * q^59 - 14391208024 * q^61 + 20938150200 * q^65 - 33307097284 * q^67 - 65848902896 * q^71 + 17709749204 * q^73 - 8594484604 * q^77 - 26626784032 * q^79 + 210306955048 * q^83 - 25867402032 * q^85 + 55951560072 * q^89 + 66078280292 * q^91 - 106810047392 * q^95 - 156216030712 * q^97

Introduction

L-functions

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