LMFDB - Embedded newform 252.12.k.d.37.6

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			37.6
Root			$2410.13 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	252.37
Dual form			252.12.k.d.109.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1339.81 - 2320.63i) q^{5} +(-28039.7 + 34512.4i) q^{7} +O(q^{10})$	$q+(1339.81 - 2320.63i) q^{5} +(-28039.7 + 34512.4i) q^{7} +(239334. + 414539. i) q^{11} -1.17059e6 q^{13} +(2.40839e6 + 4.17145e6i) q^{17} +(-4.55281e6 + 7.88570e6i) q^{19} +(4.21644e6 - 7.30309e6i) q^{23} +(2.08239e7 + 3.60680e7i) q^{25} -3.65821e7 q^{29} +(-1.20947e7 - 2.09487e7i) q^{31} +(4.25223e7 + 1.11310e8i) q^{35} +(-1.66789e8 + 2.88888e8i) q^{37} -5.86887e7 q^{41} +8.57155e8 q^{43} +(-4.75883e8 + 8.24254e8i) q^{47} +(-4.04880e8 - 1.93543e9i) q^{49} +(9.09651e8 + 1.57556e9i) q^{53} +1.28265e9 q^{55} +(-8.43761e8 - 1.46144e9i) q^{59} +(3.82941e9 - 6.63273e9i) q^{61} +(-1.56837e9 + 2.71649e9i) q^{65} +(-2.92346e9 - 5.06358e9i) q^{67} -1.03360e10 q^{71} +(4.61314e9 + 7.99018e9i) q^{73} +(-2.10176e10 - 3.36355e9i) q^{77} +(9.94865e9 - 1.72316e10i) q^{79} -4.78020e10 q^{83} +1.29072e10 q^{85} +(9.70762e9 - 1.68141e10i) q^{89} +(3.28229e10 - 4.03997e10i) q^{91} +(1.21998e10 + 2.11307e10i) q^{95} +8.32856e10 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

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

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
$5$	1339.81	−	2320.63i	0.191739	−	0.332101i	−0.754088	−	0.656773i	$-0.771921\pi$
$5$	1339.81	−	2320.63i	0.191739	−	0.332101i	0.945826	+	0.324673i	$0.105254\pi$
$6$		0			0
$7$	−28039.7	+	34512.4i	−0.630571	+	0.776132i
$7$	−28039.7	+	34512.4i	−0.630571	+	0.776132i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	239334.	+	414539.i	0.448069	+	0.776079i	0.998260	−	0.0589601i	$-0.0187785\pi$
$11$	239334.	+	414539.i	0.448069	+	0.776079i	−0.550191	+	0.835039i	$0.685445\pi$
$12$		0			0
$13$	−1.17059e6			−0.874410			−0.437205	−	0.899362i	$-0.644032\pi$
$13$	−1.17059e6			−0.874410			−0.437205	+	0.899362i	$0.644032\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.40839e6	+	4.17145e6i	0.411394	+	0.712555i	0.995042	−	0.0994514i	$-0.0317088\pi$
$17$	2.40839e6	+	4.17145e6i	0.411394	+	0.712555i	−0.583649	+	0.812006i	$0.698375\pi$
$18$		0			0
$19$	−4.55281e6	+	7.88570e6i	−0.421827	+	0.730626i	−0.996118	−	0.0880250i	$-0.971944\pi$
$19$	−4.55281e6	+	7.88570e6i	−0.421827	+	0.730626i	0.574291	+	0.818651i	$0.305278\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.21644e6	−	7.30309e6i	0.136598	−	0.236594i	−0.789609	−	0.613610i	$-0.789717\pi$
$23$	4.21644e6	−	7.30309e6i	0.136598	−	0.236594i	0.926207	+	0.377016i	$0.123050\pi$
$24$		0			0
$25$	2.08239e7	+	3.60680e7i	0.426473	+	0.738672i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.65821e7			−0.331192			−0.165596	−	0.986194i	$-0.552955\pi$
$29$	−3.65821e7			−0.331192			−0.165596	+	0.986194i	$0.552955\pi$
$30$		0			0
$31$	−1.20947e7	−	2.09487e7i	−0.0758765	−	0.131422i	0.825591	−	0.564270i	$-0.190842\pi$
$31$	−1.20947e7	−	2.09487e7i	−0.0758765	−	0.131422i	−0.901467	+	0.432848i	$0.857509\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.25223e7	+	1.11310e8i	0.136849	+	0.358227i
$36$		0			0
$37$	−1.66789e8	+	2.88888e8i	−0.395420	+	0.684888i	−0.993155	−	0.116806i	$-0.962734\pi$
$37$	−1.66789e8	+	2.88888e8i	−0.395420	+	0.684888i	0.597734	+	0.801694i	$0.296068\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.86887e7			−0.0791122			−0.0395561	−	0.999217i	$-0.512594\pi$
$41$	−5.86887e7			−0.0791122			−0.0395561	+	0.999217i	$0.512594\pi$
$42$		0			0
$43$	8.57155e8			0.889166			0.444583	−	0.895738i	$-0.353352\pi$
$43$	8.57155e8			0.889166			0.444583	+	0.895738i	$0.353352\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.75883e8	+	8.24254e8i	−0.302665	+	0.524231i	−0.976739	−	0.214433i	$-0.931210\pi$
$47$	−4.75883e8	+	8.24254e8i	−0.302665	+	0.524231i	0.674074	+	0.738664i	$0.264543\pi$
$48$		0			0
$49$	−4.04880e8	−	1.93543e9i	−0.204761	−	0.978812i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	9.09651e8	+	1.57556e9i	0.298784	+	0.517509i	0.975858	−	0.218406i	$-0.0700857\pi$
$53$	9.09651e8	+	1.57556e9i	0.298784	+	0.517509i	−0.677074	+	0.735915i	$0.736752\pi$
$54$		0			0
$55$	1.28265e9			0.343649
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−8.43761e8	−	1.46144e9i	−0.153650	−	0.266130i	0.778916	−	0.627128i	$-0.215770\pi$
$59$	−8.43761e8	−	1.46144e9i	−0.153650	−	0.266130i	−0.932567	+	0.360998i	$0.882436\pi$
$60$		0			0
$61$	3.82941e9	−	6.63273e9i	0.580521	−	1.00549i	−0.414897	−	0.909868i	$-0.636182\pi$
$61$	3.82941e9	−	6.63273e9i	0.580521	−	1.00549i	0.995418	−	0.0956231i	$-0.0304843\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.56837e9	+	2.71649e9i	−0.167658	+	0.290392i
$66$		0			0
$67$	−2.92346e9	−	5.06358e9i	−0.264537	−	0.458191i	0.702906	−	0.711283i	$-0.251886\pi$
$67$	−2.92346e9	−	5.06358e9i	−0.264537	−	0.458191i	−0.967442	+	0.253093i	$0.918552\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.03360e10			−0.679877			−0.339939	−	0.940448i	$-0.610406\pi$
$71$	−1.03360e10			−0.679877			−0.339939	+	0.940448i	$0.610406\pi$
$72$		0			0
$73$	4.61314e9	+	7.99018e9i	0.260448	+	0.451109i	0.966361	−	0.257190i	$-0.0827965\pi$
$73$	4.61314e9	+	7.99018e9i	0.260448	+	0.451109i	−0.705913	+	0.708298i	$0.749463\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.10176e10	−	3.36355e9i	−0.884879	−	0.141612i
$78$		0			0
$79$	9.94865e9	−	1.72316e10i	0.363760	−	0.630051i	−0.624816	−	0.780772i	$-0.714826\pi$
$79$	9.94865e9	−	1.72316e10i	0.363760	−	0.630051i	0.988576	+	0.150721i	$0.0481594\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.78020e10			−1.33204			−0.666018	−	0.745935i	$-0.732003\pi$
$83$	−4.78020e10			−1.33204			−0.666018	+	0.745935i	$0.732003\pi$
$84$		0			0
$85$	1.29072e10			0.315520
$86$		0			0
$87$		0			0
$88$		0			0
$89$	9.70762e9	−	1.68141e10i	0.184276	−	0.319175i	−0.759057	−	0.651025i	$-0.774339\pi$
$89$	9.70762e9	−	1.68141e10i	0.184276	−	0.319175i	0.943332	+	0.331850i	$0.107673\pi$
$90$		0			0
$91$	3.28229e10	−	4.03997e10i	0.551377	−	0.678657i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.21998e10	+	2.11307e10i	0.161761	+	0.280178i
$96$		0			0
$97$	8.32856e10			0.984749			0.492374	−	0.870383i	$-0.336129\pi$
$97$	8.32856e10			0.984749			0.492374	+	0.870383i	$0.336129\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.46928e10	+	1.29372e11i	0.707149	+	1.22482i	0.965910	+	0.258877i	$0.0833523\pi$
$101$	7.46928e10	+	1.29372e11i	0.707149	+	1.22482i	−0.258761	+	0.965941i	$0.583314\pi$
$102$		0			0
$103$	3.62922e10	−	6.28600e10i	0.308467	−	0.534281i	−0.669560	−	0.742758i	$-0.733517\pi$
$103$	3.62922e10	−	6.28600e10i	0.308467	−	0.534281i	0.978027	+	0.208477i	$0.0668507\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.26123e11	+	2.18451e11i	−0.869326	+	1.50572i	−0.00663879	+	0.999978i	$0.502113\pi$
$107$	−1.26123e11	+	2.18451e11i	−0.869326	+	1.50572i	−0.862687	+	0.505738i	$0.831220\pi$
$108$		0			0
$109$	6.84739e10	+	1.18600e11i	0.426265	+	0.738312i	0.996538	−	0.0831430i	$-0.0264958\pi$
$109$	6.84739e10	+	1.18600e11i	0.426265	+	0.738312i	−0.570273	+	0.821455i	$0.693162\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.33958e11			−1.19456			−0.597279	−	0.802034i	$-0.703751\pi$
$113$	−2.33958e11			−1.19456			−0.597279	+	0.802034i	$0.703751\pi$
$114$		0			0
$115$	−1.12985e10	−	1.95696e10i	−0.0523821	−	0.0907284i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.11497e11	−	3.38470e10i	−0.812449	−	0.130020i
$120$		0			0
$121$	2.80940e10	−	4.86603e10i	0.0984679	−	0.170551i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	2.42442e11			0.710562
$126$		0			0
$127$	−2.05552e11			−0.552078			−0.276039	−	0.961146i	$-0.589022\pi$
$127$	−2.05552e11			−0.552078			−0.276039	+	0.961146i	$0.589022\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.71371e10	−	2.96824e10i	0.0388102	−	0.0672213i	−0.845968	−	0.533234i	$-0.820977\pi$
$131$	1.71371e10	−	2.96824e10i	0.0388102	−	0.0672213i	0.884778	+	0.466013i	$0.154310\pi$
$132$		0			0
$133$	−1.44495e11	−	3.78241e11i	−0.301070	−	0.788105i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.70171e10	−	1.33397e11i	−0.136340	−	0.236148i	0.789768	−	0.613405i	$-0.210201\pi$
$137$	−7.70171e10	−	1.33397e11i	−0.136340	−	0.236148i	−0.926109	+	0.377257i	$0.876867\pi$
$138$		0			0
$139$	−1.11480e11			−0.182228			−0.0911138	−	0.995840i	$-0.529043\pi$
$139$	−1.11480e11			−0.182228			−0.0911138	+	0.995840i	$0.529043\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.80161e11	−	4.85254e11i	−0.391796	−	0.678611i
$144$		0			0
$145$	−4.90132e10	+	8.48933e10i	−0.0635022	+	0.109989i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.33795e11	−	1.44418e12i	0.930112	−	1.61100i	0.146985	−	0.989139i	$-0.453043\pi$
$149$	8.33795e11	−	1.44418e12i	0.930112	−	1.61100i	0.783127	−	0.621862i	$-0.213623\pi$
$150$		0			0
$151$	3.71218e11	+	6.42968e11i	0.384818	+	0.666524i	0.991744	−	0.128234i	$-0.0409309\pi$
$151$	3.71218e11	+	6.42968e11i	0.384818	+	0.666524i	−0.606926	+	0.794758i	$0.707598\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.48188e10			−0.0581938
$156$		0			0
$157$	−4.37190e11	−	7.57235e11i	−0.365782	−	0.633552i	0.623120	−	0.782126i	$-0.285865\pi$
$157$	−4.37190e11	−	7.57235e11i	−0.365782	−	0.633552i	−0.988901	+	0.148574i	$0.952532\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1.33819e11	+	3.50296e11i	0.0974937	+	0.255207i
$162$		0			0
$163$	−5.70121e11	+	9.87478e11i	−0.388092	+	0.672196i	−0.992193	−	0.124712i	$-0.960199\pi$
$163$	−5.70121e11	+	9.87478e11i	−0.388092	+	0.672196i	0.604101	+	0.796908i	$0.293533\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.67533e12			−0.998068			−0.499034	−	0.866582i	$-0.666312\pi$
$167$	−1.67533e12			−0.998068			−0.499034	+	0.866582i	$0.666312\pi$
$168$		0			0
$169$	−4.21888e11			−0.235408
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.84651e12	−	3.19825e12i	0.905937	−	1.56913i	0.0862817	−	0.996271i	$-0.472502\pi$
$173$	1.84651e12	−	3.19825e12i	0.905937	−	1.56913i	0.819655	−	0.572858i	$-0.194165\pi$
$174$		0			0
$175$	−1.82869e12	−	2.92654e11i	−0.842228	−	0.134786i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	8.10662e11	+	1.40411e12i	0.329722	+	0.571096i	0.982457	−	0.186491i	$-0.0597115\pi$
$179$	8.10662e11	+	1.40411e12i	0.329722	+	0.571096i	−0.652734	+	0.757587i	$0.726378\pi$
$180$		0			0
$181$	−3.72161e12			−1.42396			−0.711982	−	0.702198i	$-0.752202\pi$
$181$	−3.72161e12			−1.42396			−0.711982	+	0.702198i	$0.752202\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.46934e11	+	7.74112e11i	0.151635	+	0.262639i
$186$		0			0
$187$	−1.15282e12	+	1.99674e12i	−0.368666	+	0.638548i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.15479e12	+	2.00015e12i	−0.328714	+	0.569349i	−0.982257	−	0.187540i	$-0.939948\pi$
$191$	−1.15479e12	+	2.00015e12i	−0.328714	+	0.569349i	0.653543	+	0.756889i	$0.273282\pi$
$192$		0			0
$193$	6.67031e11	+	1.15533e12i	0.179300	+	0.310557i	0.941641	−	0.336619i	$-0.109283\pi$
$193$	6.67031e11	+	1.15533e12i	0.179300	+	0.310557i	−0.762341	+	0.647176i	$0.775950\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.95053e12			−0.948618			−0.474309	−	0.880359i	$-0.657302\pi$
$197$	−3.95053e12			−0.948618			−0.474309	+	0.880359i	$0.657302\pi$
$198$		0			0
$199$	−5.18976e11	−	8.98893e11i	−0.117884	−	0.204181i	0.801045	−	0.598604i	$-0.204278\pi$
$199$	−5.18976e11	−	8.98893e11i	−0.117884	−	0.204181i	−0.918929	+	0.394423i	$0.870944\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.02575e12	−	1.26253e12i	0.208840	−	0.257048i
$204$		0			0
$205$	−7.86320e10	+	1.36195e11i	−0.0151689	+	0.0262732i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−4.35857e12			−0.756031
$210$		0			0
$211$	4.91335e12			0.808769			0.404385	−	0.914589i	$-0.367486\pi$
$211$	4.91335e12			0.808769			0.404385	+	0.914589i	$0.367486\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.14843e12	−	1.98914e12i	0.170487	−	0.295293i
$216$		0			0
$217$	1.06212e12	+	1.69977e11i	0.149846	+	0.0239807i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.81923e12	−	4.88305e12i	−0.359727	−	0.623065i
$222$		0			0
$223$	−8.25284e12			−1.00214			−0.501068	−	0.865408i	$-0.667059\pi$
$223$	−8.25284e12			−1.00214			−0.501068	+	0.865408i	$0.667059\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.55247e12	−	1.13492e13i	−0.721544	−	1.24975i	−0.960381	−	0.278691i	$-0.910099\pi$
$227$	−6.55247e12	−	1.13492e13i	−0.721544	−	1.24975i	0.238837	−	0.971060i	$-0.423234\pi$
$228$		0			0
$229$	3.18856e12	−	5.52274e12i	0.334579	−	0.579508i	−0.648825	−	0.760938i	$-0.724739\pi$
$229$	3.18856e12	−	5.52274e12i	0.334579	−	0.579508i	0.983404	+	0.181430i	$0.0580724\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.04721e12	+	5.27793e12i	−0.290700	+	0.503507i	−0.973975	−	0.226653i	$-0.927222\pi$
$233$	−3.04721e12	+	5.27793e12i	−0.290700	+	0.503507i	0.683275	+	0.730161i	$0.260555\pi$
$234$		0			0
$235$	1.27519e12	+	2.20869e12i	0.116065	+	0.201031i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.63982e13			−1.36022			−0.680108	−	0.733112i	$-0.738067\pi$
$239$	−1.63982e13			−1.36022			−0.680108	+	0.733112i	$0.738067\pi$
$240$		0			0
$241$	−7.93321e12	−	1.37407e13i	−0.628573	−	1.08872i	−0.987838	−	0.155484i	$-0.950306\pi$
$241$	−7.93321e12	−	1.37407e13i	−0.628573	−	1.08872i	0.359266	−	0.933235i	$-0.383027\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−5.03387e12	−	1.65354e12i	−0.364325	−	0.119675i
$246$		0			0
$247$	5.32946e12	−	9.23089e12i	0.368850	−	0.638867i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−2.61416e13			−1.65625			−0.828125	−	0.560544i	$-0.810592\pi$
$251$	−2.61416e13			−1.65625			−0.828125	+	0.560544i	$0.810592\pi$
$252$		0			0
$253$	4.03656e12			0.244821
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.97426e12	+	1.72759e13i	−0.554943	+	0.961190i	0.442965	+	0.896539i	$0.353927\pi$
$257$	−9.97426e12	+	1.72759e13i	−0.554943	+	0.961190i	−0.997908	+	0.0646509i	$0.979407\pi$
$258$		0			0
$259$	−5.29348e12	−	1.38566e13i	−0.282223	−	0.738769i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.90133e13	−	3.29321e13i	−0.931755	−	1.61385i	−0.780321	−	0.625379i	$-0.784944\pi$
$263$	−1.90133e13	−	3.29321e13i	−0.931755	−	1.61385i	−0.151434	−	0.988467i	$-0.548389\pi$
$264$		0			0
$265$	4.87505e12			0.229154
$266$		0			0
$267$		0			0
$268$		0			0
$269$	6.11726e12	+	1.05954e13i	0.264801	+	0.458649i	0.967511	−	0.252827i	$-0.0813604\pi$
$269$	6.11726e12	+	1.05954e13i	0.264801	+	0.458649i	−0.702710	+	0.711476i	$0.748027\pi$
$270$		0			0
$271$	−4.65635e12	+	8.06503e12i	−0.193515	+	0.335177i	−0.946413	−	0.322960i	$-0.895322\pi$
$271$	−4.65635e12	+	8.06503e12i	−0.193515	+	0.335177i	0.752898	+	0.658137i	$0.228655\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−9.96773e12	+	1.72646e13i	−0.382179	+	0.661953i
$276$		0			0
$277$	−1.90071e13	−	3.29212e13i	−0.700288	−	1.21293i	−0.968365	−	0.249537i	$-0.919722\pi$
$277$	−1.90071e13	−	3.29212e13i	−0.700288	−	1.21293i	0.268077	−	0.963397i	$-0.413612\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−3.06527e13			−1.04372			−0.521860	−	0.853031i	$-0.674762\pi$
$281$	−3.06527e13			−1.04372			−0.521860	+	0.853031i	$0.674762\pi$
$282$		0			0
$283$	3.55669e12	+	6.16037e12i	0.116472	+	0.201735i	0.918367	−	0.395729i	$-0.129508\pi$
$283$	3.55669e12	+	6.16037e12i	0.116472	+	0.201735i	−0.801895	+	0.597465i	$0.796175\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.64561e12	−	2.02549e12i	0.0498859	−	0.0614015i
$288$		0			0
$289$	5.53527e12	−	9.58736e12i	0.161510	−	0.279744i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.95279e12			−0.133992			−0.0669959	−	0.997753i	$-0.521341\pi$
$293$	−4.95279e12			−0.133992			−0.0669959	+	0.997753i	$0.521341\pi$
$294$		0			0
$295$	−4.52193e12			−0.117843
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−4.93571e12	+	8.54890e12i	−0.119442	+	0.206880i
$300$		0			0
$301$	−2.40343e13	+	2.95824e13i	−0.560682	+	0.690110i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.02614e13	−	1.77733e13i	−0.222616	−	0.385583i
$306$		0			0
$307$	2.23542e13			0.467842			0.233921	−	0.972256i	$-0.424844\pi$
$307$	2.23542e13			0.467842			0.233921	+	0.972256i	$0.424844\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−2.65812e13	−	4.60399e13i	−0.518074	−	0.897330i	−0.999780	−	0.0209972i	$-0.993316\pi$
$311$	−2.65812e13	−	4.60399e13i	−0.518074	−	0.897330i	0.481706	−	0.876333i	$-0.340017\pi$
$312$		0			0
$313$	−2.79998e13	+	4.84971e13i	−0.526819	+	0.912476i	0.472693	+	0.881227i	$0.343282\pi$
$313$	−2.79998e13	+	4.84971e13i	−0.526819	+	0.912476i	−0.999512	+	0.0312493i	$0.990051\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.41827e13	−	5.92062e13i	0.599764	−	1.03882i	−0.393092	−	0.919499i	$-0.628594\pi$
$317$	3.41827e13	−	5.92062e13i	0.599764	−	1.03882i	0.992856	−	0.119322i	$-0.0380722\pi$
$318$		0			0
$319$	−8.75535e12	−	1.51647e13i	−0.148397	−	0.257031i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−4.38598e13			−0.694148
$324$		0			0
$325$	−2.43761e13	−	4.22207e13i	−0.372912	−	0.645902i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.51033e13	−	3.95357e13i	−0.216021	−	0.565473i
$330$		0			0
$331$	−1.92107e13	+	3.32739e13i	−0.265759	+	0.460309i	−0.967762	−	0.251865i	$-0.918956\pi$
$331$	−1.92107e13	+	3.32739e13i	−0.265759	+	0.460309i	0.702003	+	0.712174i	$0.252289\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1.56676e13			−0.202887
$336$		0			0
$337$	−1.59403e14			−1.99771			−0.998855	−	0.0478440i	$-0.984765\pi$
$337$	−1.59403e14			−1.99771			−0.998855	+	0.0478440i	$0.984765\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	5.78938e12	−	1.00275e13i	0.0679959	−	0.117772i
$342$		0			0
$343$	7.81490e13	+	4.02955e13i	0.888803	+	0.458289i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.76248e13	−	6.51680e13i	−0.401478	−	0.695380i	0.592426	−	0.805625i	$-0.298170\pi$
$347$	−3.76248e13	−	6.51680e13i	−0.401478	−	0.695380i	−0.993905	+	0.110244i	$0.964837\pi$
$348$		0			0
$349$	−1.81299e14			−1.87437			−0.937187	−	0.348828i	$-0.886580\pi$
$349$	−1.81299e14			−1.87437			−0.937187	+	0.348828i	$0.886580\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	6.08571e12	+	1.05408e13i	0.0590949	+	0.102355i	0.894059	−	0.447948i	$-0.147845\pi$
$353$	6.08571e12	+	1.05408e13i	0.0590949	+	0.102355i	−0.834964	+	0.550304i	$0.814512\pi$
$354$		0			0
$355$	−1.38483e13	+	2.39859e13i	−0.130359	+	0.225788i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.61043e13	−	7.98551e13i	0.408058	−	0.706778i	−0.586614	−	0.809867i	$-0.699539\pi$
$359$	4.61043e13	−	7.98551e13i	0.408058	−	0.706778i	0.994672	+	0.103089i	$0.0328726\pi$
$360$		0			0
$361$	1.67890e13	+	2.90794e13i	0.144123	+	0.249629i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.47230e13			0.199751
$366$		0			0
$367$	−3.47460e13	−	6.01818e13i	−0.272421	−	0.471847i	0.697060	−	0.717013i	$-0.254491\pi$
$367$	−3.47460e13	−	6.01818e13i	−0.272421	−	0.471847i	−0.969481	+	0.245165i	$0.921158\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−7.98826e13	−	1.27840e13i	−0.590060	−	0.0944303i
$372$		0			0
$373$	2.75190e13	−	4.76643e13i	0.197349	−	0.341818i	−0.750319	−	0.661076i	$-0.770100\pi$
$373$	2.75190e13	−	4.76643e13i	0.197349	−	0.341818i	0.947668	+	0.319258i	$0.103434\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4.28225e13			0.289597
$378$		0			0
$379$	1.64609e14			1.08128			0.540640	−	0.841254i	$-0.318182\pi$
$379$	1.64609e14			1.08128			0.540640	+	0.841254i	$0.318182\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−2.37086e13	+	4.10645e13i	−0.146998	+	0.254609i	−0.930117	−	0.367264i	$-0.880295\pi$
$383$	−2.37086e13	+	4.10645e13i	−0.146998	+	0.254609i	0.783118	+	0.621873i	$0.213628\pi$
$384$		0			0
$385$	−3.59652e13	+	4.42674e13i	−0.216695	+	0.266717i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.47659e14	+	2.55752e14i	0.840496	+	1.45578i	0.889476	+	0.456982i	$0.151070\pi$
$389$	1.47659e14	+	2.55752e14i	0.840496	+	1.45578i	−0.0489795	+	0.998800i	$0.515597\pi$
$390$		0			0
$391$	4.06194e13			0.224782
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−2.66587e13	−	4.61742e13i	−0.139494	−	0.241610i
$396$		0			0
$397$	1.02252e14	−	1.77106e14i	0.520386	−	0.901335i	−0.479333	−	0.877633i	$-0.659121\pi$
$397$	1.02252e14	−	1.77106e14i	0.520386	−	0.901335i	0.999719	−	0.0237017i	$-0.00754518\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.18349e13	−	1.24422e14i	0.345972	−	0.599242i	−0.639558	−	0.768743i	$-0.720882\pi$
$401$	7.18349e13	−	1.24422e14i	0.345972	−	0.599242i	0.985530	+	0.169502i	$0.0542158\pi$
$402$		0			0
$403$	1.41579e13	+	2.45223e13i	0.0663472	+	0.114917i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.59674e14			−0.708703
$408$		0			0
$409$	−5.12511e13	−	8.87695e13i	−0.221424	−	0.383518i	0.733816	−	0.679348i	$-0.237737\pi$
$409$	−5.12511e13	−	8.87695e13i	−0.221424	−	0.383518i	−0.955241	+	0.295830i	$0.904404\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	7.40964e13	+	1.18580e13i	0.303439	+	0.0485610i
$414$		0			0
$415$	−6.40457e13	+	1.10930e14i	−0.255403	+	0.442371i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−2.06951e14			−0.782871			−0.391436	−	0.920206i	$-0.628021\pi$
$419$	−2.06951e14			−0.782871			−0.391436	+	0.920206i	$0.628021\pi$
$420$		0			0
$421$	−2.28895e13			−0.0843498			−0.0421749	−	0.999110i	$-0.513429\pi$
$421$	−2.28895e13			−0.0843498			−0.0421749	+	0.999110i	$0.513429\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.00304e14	+	1.73732e14i	−0.350896	+	0.607770i
$426$		0			0
$427$	1.21536e14	+	3.18142e14i	0.414335	+	1.08459i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	6.89096e13	+	1.19355e14i	0.223180	+	0.386559i	0.955772	−	0.294109i	$-0.0950230\pi$
$431$	6.89096e13	+	1.19355e14i	0.223180	+	0.386559i	−0.732592	+	0.680668i	$0.761690\pi$
$432$		0			0
$433$	1.37606e14			0.434463			0.217231	−	0.976120i	$-0.430297\pi$
$433$	1.37606e14			0.434463			0.217231	+	0.976120i	$0.430297\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3.83933e13	+	6.64992e13i	0.115241	+	0.199604i
$438$		0			0
$439$	2.24449e14	−	3.88757e14i	0.656996	−	1.13795i	−0.324393	−	0.945922i	$-0.605160\pi$
$439$	2.24449e14	−	3.88757e14i	0.656996	−	1.13795i	0.981389	−	0.192028i	$-0.0615066\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−9.09994e13	+	1.57616e14i	−0.253407	+	0.438913i	−0.964462	−	0.264223i	$-0.914884\pi$
$443$	−9.09994e13	+	1.57616e14i	−0.253407	+	0.438913i	0.711055	+	0.703137i	$0.248218\pi$
$444$		0			0
$445$	−2.60128e13	−	4.50555e13i	−0.0706654	−	0.122396i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−7.82493e13			−0.202360			−0.101180	−	0.994868i	$-0.532262\pi$
$449$	−7.82493e13			−0.202360			−0.101180	+	0.994868i	$0.532262\pi$
$450$		0			0
$451$	−1.40462e13	−	2.43288e13i	−0.0354478	−	0.0613973i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−4.97760e13	−	1.30298e14i	−0.119662	−	0.313238i
$456$		0			0
$457$	6.37712e12	−	1.10455e13i	0.0149653	−	0.0259206i	−0.858446	−	0.512904i	$-0.828570\pi$
$457$	6.37712e12	−	1.10455e13i	0.0149653	−	0.0259206i	0.873411	+	0.486984i	$0.161903\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	4.11130e14			0.919653			0.459826	−	0.888009i	$-0.347912\pi$
$461$	4.11130e14			0.919653			0.459826	+	0.888009i	$0.347912\pi$
$462$		0			0
$463$	8.91432e14			1.94712			0.973560	−	0.228430i	$-0.0733593\pi$
$463$	8.91432e14			1.94712			0.973560	+	0.228430i	$0.0733593\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.36710e13	+	1.62243e14i	−0.195147	+	0.338005i	−0.946949	−	0.321384i	$-0.895852\pi$
$467$	−9.36710e13	+	1.62243e14i	−0.195147	+	0.338005i	0.751802	+	0.659389i	$0.229185\pi$
$468$		0			0
$469$	2.56729e14	+	4.10857e13i	0.522425	+	0.0836064i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2.05147e14	+	3.55324e14i	0.398408	+	0.690063i
$474$		0			0
$475$	−3.79228e14			−0.719591
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3.54805e14	+	6.14540e14i	0.642901	+	1.11354i	0.984782	+	0.173794i	$0.0556028\pi$
$479$	3.54805e14	+	6.14540e14i	0.642901	+	1.11354i	−0.341881	+	0.939743i	$0.611064\pi$
$480$		0			0
$481$	1.95241e14	−	3.38168e14i	0.345759	−	0.598873i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.11587e14	−	1.93275e14i	0.188814	−	0.327036i
$486$		0			0
$487$	1.72334e14	+	2.98491e14i	0.285077	+	0.493768i	0.972628	−	0.232368i	$-0.0746475\pi$
$487$	1.72334e14	+	2.98491e14i	0.285077	+	0.493768i	−0.687551	+	0.726136i	$0.741314\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−2.50906e12			−0.00396791			−0.00198396	−	0.999998i	$-0.500632\pi$
$491$	−2.50906e12			−0.00396791			−0.00198396	+	0.999998i	$0.500632\pi$
$492$		0			0
$493$	−8.81039e13	−	1.52601e14i	−0.136250	−	0.235992i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.89817e14	−	3.56719e14i	0.428711	−	0.527674i
$498$		0			0
$499$	3.62370e12	−	6.27644e12i	0.00524324	−	0.00908155i	−0.863392	−	0.504534i	$-0.831664\pi$
$499$	3.62370e12	−	6.27644e12i	0.00524324	−	0.00908155i	0.868635	+	0.495452i	$0.164998\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.22748e15			1.69977			0.849887	−	0.526965i	$-0.176670\pi$
$503$	1.22748e15			1.69977			0.849887	+	0.526965i	$0.176670\pi$
$504$		0			0
$505$	4.00297e14			0.542351
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.64697e13	−	2.85263e13i	0.0213667	−	0.0370082i	−0.855144	−	0.518390i	$-0.826532\pi$
$509$	1.64697e13	−	2.85263e13i	0.0213667	−	0.0370082i	0.876511	+	0.481382i	$0.159865\pi$
$510$		0			0
$511$	−4.05111e14	−	6.48320e13i	−0.514350	−	0.0823142i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−9.72497e13	−	1.68441e14i	−0.118290	−	0.204884i
$516$		0			0
$517$	−4.55581e14			−0.542459
$518$		0			0
$519$		0			0
$520$		0			0
$521$	4.69615e14	+	8.13397e14i	0.535962	+	0.928314i	0.999116	+	0.0420361i	$0.0133844\pi$
$521$	4.69615e14	+	8.13397e14i	0.535962	+	0.928314i	−0.463154	+	0.886278i	$0.653282\pi$
$522$		0			0
$523$	−4.77717e14	+	8.27430e14i	−0.533840	+	0.924639i	0.465378	+	0.885112i	$0.345918\pi$
$523$	−4.77717e14	+	8.27430e14i	−0.533840	+	0.924639i	−0.999219	+	0.0395267i	$0.987415\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.82577e13	−	1.00905e14i	0.0624303	−	0.108132i
$528$		0			0
$529$	4.40848e14	+	7.63571e14i	0.462682	+	0.801389i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6.87002e13			0.0691765
$534$		0			0
$535$	3.37962e14	+	5.85367e14i	0.333366	+	0.577408i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	7.05410e14	−	6.31053e14i	0.667888	−	0.597486i
$540$		0			0
$541$	−5.37113e14	+	9.30307e14i	−0.498289	+	0.863061i	−0.999998	−	0.00197505i	$-0.999371\pi$
$541$	−5.37113e14	+	9.30307e14i	−0.498289	+	0.863061i	0.501709	+	0.865036i	$0.332705\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	3.66969e14			0.326926
$546$		0			0
$547$	1.38381e15			1.20822			0.604111	−	0.796900i	$-0.293528\pi$
$547$	1.38381e15			1.20822			0.604111	+	0.796900i	$0.293528\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1.66551e14	−	2.88475e14i	0.139706	−	0.241977i
$552$		0			0
$553$	3.15745e14	+	8.26519e14i	0.259626	+	0.679618i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	7.14824e14	+	1.23811e15i	0.564931	+	0.978490i	0.997056	+	0.0766761i	$0.0244307\pi$
$557$	7.14824e14	+	1.23811e15i	0.564931	+	0.978490i	−0.432125	+	0.901814i	$0.642236\pi$
$558$		0			0
$559$	−1.00337e15			−0.777495
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.27988e15	+	2.21682e15i	0.953615	+	1.65171i	0.737507	+	0.675340i	$0.236003\pi$
$563$	1.27988e15	+	2.21682e15i	0.953615	+	1.65171i	0.216108	+	0.976370i	$0.430664\pi$
$564$		0			0
$565$	−3.13461e14	+	5.42930e14i	−0.229043	+	0.396714i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.13256e15	−	1.96165e15i	0.796056	−	1.37881i	−0.126110	−	0.992016i	$-0.540249\pi$
$569$	1.13256e15	−	1.96165e15i	0.796056	−	1.37881i	0.922166	−	0.386794i	$-0.126417\pi$
$570$		0			0
$571$	−5.49376e14	−	9.51547e14i	−0.378766	−	0.656042i	0.612117	−	0.790767i	$-0.290318\pi$
$571$	−5.49376e14	−	9.51547e14i	−0.378766	−	0.656042i	−0.990883	+	0.134725i	$0.956985\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	3.51211e14			0.233021
$576$		0			0
$577$	−1.22669e15	−	2.12470e15i	−0.798490	−	1.38303i	−0.920599	−	0.390509i	$-0.872299\pi$
$577$	−1.22669e15	−	2.12470e15i	−0.798490	−	1.38303i	0.122109	−	0.992517i	$-0.461034\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.34035e15	−	1.64976e15i	0.839943	−	1.03384i
$582$		0			0
$583$	−4.35421e14	+	7.54172e14i	−0.267752	+	0.463760i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.57451e14			0.211693			0.105847	−	0.994382i	$-0.466245\pi$
$587$	3.57451e14			0.211693			0.105847	+	0.994382i	$0.466245\pi$
$588$		0			0
$589$	2.20260e14			0.128027
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−3.47719e14	+	6.02267e14i	−0.194728	+	0.337278i	−0.946811	−	0.321790i	$-0.895716\pi$
$593$	−3.47719e14	+	6.02267e14i	−0.194728	+	0.337278i	0.752084	+	0.659068i	$0.229049\pi$
$594$		0			0
$595$	−3.61913e14	+	4.45457e14i	−0.198958	+	0.244885i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.18753e14	−	2.05685e14i	−0.0629210	−	0.108982i	0.832849	−	0.553500i	$-0.186708\pi$
$599$	−1.18753e14	−	2.05685e14i	−0.0629210	−	0.108982i	−0.895770	+	0.444518i	$0.853375\pi$
$600$		0			0
$601$	2.93732e15			1.52806			0.764032	−	0.645178i	$-0.223217\pi$
$601$	2.93732e15			1.52806			0.764032	+	0.645178i	$0.223217\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−7.52816e13	−	1.30391e14i	−0.0377602	−	0.0654026i
$606$		0			0
$607$	8.62651e14	−	1.49416e15i	0.424910	−	0.735966i	−0.571502	−	0.820601i	$-0.693639\pi$
$607$	8.62651e14	−	1.49416e15i	0.424910	−	0.735966i	0.996412	+	0.0846345i	$0.0269723\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	5.57062e14	−	9.64860e14i	0.264653	−	0.458393i
$612$		0			0
$613$	−5.07686e14	−	8.79338e14i	−0.236899	−	0.410320i	0.722924	−	0.690927i	$-0.242798\pi$
$613$	−5.07686e14	−	8.79338e14i	−0.236899	−	0.410320i	−0.959823	+	0.280607i	$0.909464\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−4.29465e15			−1.93357			−0.966784	−	0.255595i	$-0.917729\pi$
$617$	−4.29465e15			−1.93357			−0.966784	+	0.255595i	$0.917729\pi$
$618$		0			0
$619$	−8.18875e14	−	1.41833e15i	−0.362175	−	0.627306i	0.626143	−	0.779708i	$-0.284633\pi$
$619$	−8.18875e14	−	1.41833e15i	−0.362175	−	0.627306i	−0.988319	+	0.152402i	$0.951299\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.08095e14	+	8.06495e14i	0.131523	+	0.344284i
$624$		0			0
$625$	−6.91964e14	+	1.19852e15i	−0.290231	+	0.502694i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−1.60678e15			−0.650694
$630$		0			0
$631$	2.24346e15			0.892804			0.446402	−	0.894832i	$-0.352705\pi$
$631$	2.24346e15			0.892804			0.446402	+	0.894832i	$0.352705\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.75401e14	+	4.77008e14i	−0.105855	+	0.183346i
$636$		0			0
$637$	4.73946e14	+	2.26559e15i	0.179045	+	0.855883i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9.60927e14	−	1.66437e15i	−0.350729	−	0.607480i	0.635649	−	0.771978i	$-0.280733\pi$
$641$	−9.60927e14	−	1.66437e15i	−0.350729	−	0.607480i	−0.986377	+	0.164499i	$0.947399\pi$
$642$		0			0
$643$	−8.48487e14			−0.304428			−0.152214	−	0.988348i	$-0.548640\pi$
$643$	−8.48487e14			−0.304428			−0.152214	+	0.988348i	$0.548640\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.54367e15	+	2.67372e15i	0.535280	+	0.927132i	0.999150	+	0.0412287i	$0.0131272\pi$
$647$	1.54367e15	+	2.67372e15i	0.535280	+	0.927132i	−0.463870	+	0.885903i	$0.653539\pi$
$648$		0			0
$649$	4.03882e14	−	6.99544e14i	0.137692	−	0.238489i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.33958e14	+	7.51637e14i	−0.143029	+	0.247734i	−0.928636	−	0.370992i	$-0.879018\pi$
$653$	−4.33958e14	+	7.51637e14i	−0.143029	+	0.247734i	0.785607	+	0.618726i	$0.212351\pi$
$654$		0			0
$655$	−4.59211e13	−	7.95378e13i	−0.0148828	−	0.0257778i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−3.99805e15			−1.25308			−0.626540	−	0.779389i	$-0.715529\pi$
$659$	−3.99805e15			−1.25308			−0.626540	+	0.779389i	$0.715529\pi$
$660$		0			0
$661$	−1.60004e15	−	2.77135e15i	−0.493200	−	0.854247i	0.506770	−	0.862081i	$-0.330839\pi$
$661$	−1.60004e15	−	2.77135e15i	−0.493200	−	0.854247i	−0.999969	+	0.00783472i	$0.997506\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1.07135e15	−	1.71454e14i	−0.319457	−	0.0511244i
$666$		0			0
$667$	−1.54246e14	+	2.67163e14i	−0.0452400	+	0.0783580i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	3.66604e15			1.04045
$672$		0			0
$673$	6.83323e15			1.90785			0.953923	−	0.300052i	$-0.0970041\pi$
$673$	6.83323e15			1.90785			0.953923	+	0.300052i	$0.0970041\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.59834e15	+	2.76841e15i	−0.431949	+	0.748158i	−0.997041	−	0.0768700i	$-0.975507\pi$
$677$	−1.59834e15	+	2.76841e15i	−0.431949	+	0.748158i	0.565092	+	0.825028i	$0.308841\pi$
$678$		0			0
$679$	−2.33530e15	+	2.87438e15i	−0.620954	+	0.764295i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.63286e14	+	2.82819e14i	0.0420372	+	0.0728106i	0.886278	−	0.463153i	$-0.153282\pi$
$683$	1.63286e14	+	2.82819e14i	0.0420372	+	0.0728106i	−0.844241	+	0.535963i	$0.819949\pi$
$684$		0			0
$685$	−4.12754e14			−0.104567
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.06482e15	−	1.84433e15i	−0.261260	−	0.452515i
$690$		0			0
$691$	−1.77293e12	+	3.07081e12i	−0.000428117	+	0.000741521i	−0.866239	−	0.499629i	$-0.833470\pi$
$691$	−1.77293e12	+	3.07081e12i	−0.000428117	+	0.000741521i	0.865811	+	0.500371i	$0.166803\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.49362e14	+	2.58703e14i	−0.0349401	+	0.0605180i
$696$		0			0
$697$	−1.41345e14	−	2.44817e14i	−0.0325463	−	0.0563718i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−6.37107e15			−1.42155			−0.710777	−	0.703418i	$-0.751656\pi$
$701$	−6.37107e15			−1.42155			−0.710777	+	0.703418i	$0.751656\pi$
$702$		0			0
$703$	−1.51872e15	−	2.63050e15i	−0.333598	−	0.577809i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−6.55928e15	−	1.04972e15i	−1.39653	−	0.223494i
$708$		0			0
$709$	3.87624e13	−	6.71385e13i	0.00812562	−	0.0140740i	−0.861934	−	0.507020i	$-0.830747\pi$
$709$	3.87624e13	−	6.71385e13i	0.00812562	−	0.0140740i	0.870060	+	0.492946i	$0.164080\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−2.03987e14			−0.0414582
$714$		0			0
$715$	−1.50146e15			−0.300490
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−2.30995e15	+	4.00095e15i	−0.448326	+	0.776523i	−0.998277	−	0.0586734i	$-0.981313\pi$
$719$	−2.30995e15	+	4.00095e15i	−0.448326	+	0.776523i	0.549951	+	0.835197i	$0.314646\pi$
$720$		0			0
$721$	1.15182e15	+	3.01511e15i	0.220162	+	0.576313i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−7.61781e14	−	1.31944e15i	−0.141244	−	0.244642i
$726$		0			0
$727$	−2.05407e14			−0.0375124			−0.0187562	−	0.999824i	$-0.505971\pi$
$727$	−2.05407e14			−0.0375124			−0.0187562	+	0.999824i	$0.505971\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.06436e15	+	3.57558e15i	0.365797	+	0.633579i
$732$		0			0
$733$	4.30318e15	−	7.45332e15i	0.751134	−	1.30100i	−0.196140	−	0.980576i	$-0.562841\pi$
$733$	4.30318e15	−	7.45332e15i	0.751134	−	1.30100i	0.947274	−	0.320426i	$-0.103826\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.39937e15	−	2.42378e15i	0.237061	−	0.410602i
$738$		0			0
$739$	−4.84230e15	−	8.38712e15i	−0.808179	−	1.39981i	−0.914124	−	0.405435i	$-0.867120\pi$
$739$	−4.84230e15	−	8.38712e15i	−0.808179	−	1.39981i	0.105945	−	0.994372i	$-0.466213\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−4.55474e15			−0.737947			−0.368974	−	0.929440i	$-0.620291\pi$
$743$	−4.55474e15			−0.737947			−0.368974	+	0.929440i	$0.620291\pi$
$744$		0			0
$745$	−2.23426e15	−	3.86985e15i	−0.356676	−	0.617782i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−4.00282e15	−	1.04781e16i	−0.620463	−	1.62417i
$750$		0			0
$751$	−4.98893e15	+	8.64108e15i	−0.762058	+	1.31992i	0.179731	+	0.983716i	$0.442477\pi$
$751$	−4.98893e15	+	8.64108e15i	−0.762058	+	1.31992i	−0.941788	+	0.336206i	$0.890856\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.98945e15			0.295138
$756$		0			0
$757$	2.16914e15			0.317146			0.158573	−	0.987347i	$-0.449311\pi$
$757$	2.16914e15			0.317146			0.158573	+	0.987347i	$0.449311\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	4.02973e15	−	6.97970e15i	0.572349	−	0.991337i	−0.423976	−	0.905674i	$-0.639366\pi$
$761$	4.02973e15	−	6.97970e15i	0.572349	−	0.991337i	0.996324	−	0.0856631i	$-0.0273009\pi$
$762$		0			0
$763$	−6.01316e15	−	9.62318e14i	−0.841818	−	0.134720i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	9.87695e14	+	1.71074e15i	0.134353	+	0.232707i
$768$		0			0
$769$	−2.54259e15			−0.340943			−0.170472	−	0.985363i	$-0.554529\pi$
$769$	−2.54259e15			−0.340943			−0.170472	+	0.985363i	$0.554529\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−6.44824e15	−	1.11687e16i	−0.840338	−	1.45551i	−0.889609	−	0.456723i	$-0.849023\pi$
$773$	−6.44824e15	−	1.11687e16i	−0.840338	−	1.45551i	0.0492707	−	0.998785i	$-0.484310\pi$
$774$		0			0
$775$	5.03719e14	−	8.72466e14i	0.0647185	−	0.112096i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.67199e14	−	4.62802e14i	0.0333717	−	0.0578015i
$780$		0			0
$781$	−2.47375e15	−	4.28467e15i	−0.304632	−	0.527638i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.34301e15			−0.280538
$786$		0			0
$787$	−2.43919e14	−	4.22480e14i	−0.0287995	−	0.0498821i	0.851266	−	0.524734i	$-0.175835\pi$
$787$	−2.43919e14	−	4.22480e14i	−0.0287995	−	0.0498821i	−0.880066	+	0.474852i	$0.842502\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	6.56012e15	−	8.07446e15i	0.753253	−	0.927134i
$792$		0			0
$793$	−4.48266e15	+	7.76419e15i	−0.507613	+	0.879212i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−5.38172e15			−0.592789			−0.296395	−	0.955066i	$-0.595784\pi$
$797$	−5.38172e15			−0.592789			−0.296395	+	0.955066i	$0.595784\pi$
$798$		0			0
$799$	−4.58445e15			−0.498058
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.20816e15	+	3.82465e15i	−0.233397	+	0.404256i
$804$		0			0
$805$	9.92198e14	+	1.58787e14i	0.103448	+	0.0165553i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−4.74273e14	−	8.21465e14i	−0.0481184	−	0.0833436i	0.840963	−	0.541093i	$-0.181989\pi$
$809$	−4.74273e14	−	8.21465e14i	−0.0481184	−	0.0833436i	−0.889081	+	0.457749i	$0.848656\pi$
$810$		0			0
$811$	−1.52399e16			−1.52534			−0.762671	−	0.646786i	$-0.776112\pi$
$811$	−1.52399e16			−1.52534			−0.762671	+	0.646786i	$0.776112\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.52771e15	+	2.64607e15i	0.148825	+	0.257772i
$816$		0			0
$817$	−3.90246e15	+	6.75926e15i	−0.375074	+	0.649648i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.90529e15	−	3.30005e15i	0.178268	−	0.308769i	−0.763020	−	0.646375i	$-0.776284\pi$
$821$	1.90529e15	−	3.30005e15i	0.178268	−	0.308769i	0.941287	+	0.337607i	$0.109617\pi$
$822$		0			0
$823$	8.29953e15	+	1.43752e16i	0.766221	+	1.32713i	0.939599	+	0.342279i	$0.111199\pi$
$823$	8.29953e15	+	1.43752e16i	0.766221	+	1.32713i	−0.173377	+	0.984855i	$0.555468\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.10710e16			−0.995187			−0.497594	−	0.867410i	$-0.665783\pi$
$827$	−1.10710e16			−0.995187			−0.497594	+	0.867410i	$0.665783\pi$
$828$		0			0
$829$	2.11428e15	+	3.66205e15i	0.187548	+	0.324843i	0.944432	−	0.328706i	$-0.106613\pi$
$829$	2.11428e15	+	3.66205e15i	0.187548	+	0.324843i	−0.756884	+	0.653549i	$0.773279\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	7.09845e15	−	6.35021e15i	0.613220	−	0.548581i
$834$		0			0
$835$	−2.24463e15	+	3.88782e15i	−0.191368	+	0.331459i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	3.99192e15			0.331506			0.165753	−	0.986167i	$-0.446995\pi$
$839$	3.99192e15			0.331506			0.165753	+	0.986167i	$0.446995\pi$
$840$		0			0
$841$	−1.08623e16			−0.890312
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−5.65251e14	+	9.79044e14i	−0.0451367	+	0.0781791i
$846$		0			0
$847$	8.91634e14	+	2.33401e15i	0.0702794	+	0.183969i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.40652e15	+	2.43616e15i	0.108027	+	0.187108i
$852$		0			0
$853$	−4.36392e15			−0.330869			−0.165435	−	0.986221i	$-0.552903\pi$
$853$	−4.36392e15			−0.330869			−0.165435	+	0.986221i	$0.552903\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	3.98415e15	+	6.90076e15i	0.294403	+	0.509920i	0.974846	−	0.222881i	$-0.0715460\pi$
$857$	3.98415e15	+	6.90076e15i	0.294403	+	0.509920i	−0.680443	+	0.732801i	$0.738213\pi$
$858$		0			0
$859$	1.00704e16	−	1.74424e16i	0.734653	−	1.27246i	−0.220223	−	0.975450i	$-0.570678\pi$
$859$	1.00704e16	−	1.74424e16i	0.734653	−	1.27246i	0.954875	−	0.297006i	$-0.0959883\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	4.55541e15	−	7.89021e15i	0.323943	−	0.561086i	−0.657355	−	0.753581i	$-0.728325\pi$
$863$	4.55541e15	−	7.89021e15i	0.323943	−	0.561086i	0.981298	+	0.192496i	$0.0616581\pi$
$864$		0			0
$865$	−4.94796e15	−	8.57011e15i	−0.347406	−	0.601725i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	9.52421e15			0.651959
$870$		0			0
$871$	3.42216e15	+	5.92736e15i	0.231313	+	0.400646i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−6.79798e15	+	8.36723e15i	−0.448060	+	0.551490i
$876$		0			0
$877$	1.47774e15	−	2.55952e15i	0.0961833	−	0.166594i	−0.813919	−	0.580979i	$-0.802670\pi$
$877$	1.47774e15	−	2.55952e15i	0.0961833	−	0.166594i	0.910102	+	0.414385i	$0.136003\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.08087e16			−0.686130			−0.343065	−	0.939312i	$-0.611465\pi$
$881$	−1.08087e16			−0.686130			−0.343065	+	0.939312i	$0.611465\pi$
$882$		0			0
$883$	2.74783e16			1.72269			0.861344	−	0.508023i	$-0.169623\pi$
$883$	2.74783e16			1.72269			0.861344	+	0.508023i	$0.169623\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1.20245e16	+	2.08271e16i	−0.735339	+	1.27364i	0.219235	+	0.975672i	$0.429644\pi$
$887$	−1.20245e16	+	2.08271e16i	−0.735339	+	1.27364i	−0.954574	+	0.297973i	$0.903689\pi$
$888$		0			0
$889$	5.76360e15	−	7.09407e15i	0.348124	−	0.428485i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−4.33321e15	−	7.50534e15i	−0.255345	−	0.442270i
$894$		0			0
$895$	4.34455e15			0.252882
$896$		0			0
$897$		0			0
$898$		0			0
$899$	4.42451e14	+	7.66348e14i	0.0251297	+	0.0435259i
$900$		0			0
$901$	−4.38159e15	+	7.58913e15i	−0.245836	+	0.425800i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−4.98627e15	+	8.63646e15i	−0.273029	+	0.472899i
$906$		0			0
$907$	4.85838e15	+	8.41496e15i	0.262816	+	0.455210i	0.966989	−	0.254818i	$-0.0820155\pi$
$907$	4.85838e15	+	8.41496e15i	0.262816	+	0.455210i	−0.704173	+	0.710028i	$0.748682\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	5.93775e15			0.313524			0.156762	−	0.987636i	$-0.449894\pi$
$911$	5.93775e15			0.313524			0.156762	+	0.987636i	$0.449894\pi$
$912$		0			0
$913$	−1.14406e16	−	1.98158e16i	−0.596845	−	1.03377i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	5.43890e14	+	1.42373e15i	0.0277000	+	0.0725096i
$918$		0			0
$919$	1.72099e15	−	2.98085e15i	0.0866052	−	0.150005i	−0.819469	−	0.573124i	$-0.805731\pi$
$919$	1.72099e15	−	2.98085e15i	0.0866052	−	0.150005i	0.906074	+	0.423119i	$0.139065\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.20991e16			0.594491
$924$		0			0
$925$	−1.38928e16			−0.674544
$926$		0			0
$927$		0			0
$928$		0			0
$929$	6.19181e13	−	1.07245e14i	0.00293583	−	0.00508501i	−0.864554	−	0.502540i	$-0.832399\pi$
$929$	6.19181e13	−	1.07245e14i	0.00293583	−	0.00508501i	0.867490	+	0.497455i	$0.165732\pi$
$930$		0			0
$931$	1.71056e16	+	5.61889e15i	0.801520	+	0.263286i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	3.08913e15	+	5.35053e15i	0.141375	+	0.244868i
$936$		0			0
$937$	1.36507e16			0.617431			0.308715	−	0.951155i	$-0.400101\pi$
$937$	1.36507e16			0.617431			0.308715	+	0.951155i	$0.400101\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	5.74968e15	+	9.95874e15i	0.254039	+	0.440009i	0.964634	−	0.263593i	$-0.0849075\pi$
$941$	5.74968e15	+	9.95874e15i	0.254039	+	0.440009i	−0.710595	+	0.703601i	$0.751574\pi$
$942$		0			0
$943$	−2.47458e14	+	4.28609e14i	−0.0108065	+	0.0187175i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.87367e15	+	1.36376e16i	−0.335933	+	0.581853i	−0.983664	−	0.180017i	$-0.942385\pi$
$947$	−7.87367e15	+	1.36376e16i	−0.335933	+	0.581853i	0.647731	+	0.761869i	$0.275718\pi$
$948$		0			0
$949$	−5.40007e15	−	9.35320e15i	−0.227738	−	0.394454i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.58973e15			−0.0655108			−0.0327554	−	0.999463i	$-0.510428\pi$
$953$	−1.58973e15			−0.0655108			−0.0327554	+	0.999463i	$0.510428\pi$
$954$		0			0
$955$	3.09439e15	+	5.35965e15i	0.126054	+	0.218332i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	6.76339e15	+	1.08238e15i	0.269254	+	0.0430901i
$960$		0			0
$961$	1.24117e16	−	2.14976e16i	0.488486	−	0.846082i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	3.57479e15			0.137515
$966$		0			0
$967$	1.96093e16			0.745791			0.372896	−	0.927873i	$-0.378365\pi$
$967$	1.96093e16			0.745791			0.372896	+	0.927873i	$0.378365\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.47881e14	+	2.56137e14i	−0.00549802	+	0.00952285i	−0.868761	−	0.495231i	$-0.835083\pi$
$971$	−1.47881e14	+	2.56137e14i	−0.00549802	+	0.00952285i	0.863263	+	0.504754i	$0.168417\pi$
$972$		0			0
$973$	3.12585e15	−	3.84743e15i	0.114907	−	0.141433i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−3.17338e15	−	5.49645e15i	−0.114052	−	0.197543i	0.803349	−	0.595509i	$-0.203050\pi$
$977$	−3.17338e15	−	5.49645e15i	−0.114052	−	0.197543i	−0.917400	+	0.397966i	$0.869716\pi$
$978$		0			0
$979$	9.29347e15			0.330273
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.25087e16	−	2.16656e16i	−0.434677	−	0.752882i	0.562592	−	0.826734i	$-0.309804\pi$
$983$	−1.25087e16	−	2.16656e16i	−0.434677	−	0.752882i	−0.997269	+	0.0738522i	$0.976471\pi$
$984$		0			0
$985$	−5.29298e15	+	9.16770e15i	−0.181887	+	0.315037i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.61415e15	−	6.25988e15i	0.121458	−	0.210371i
$990$		0			0
$991$	9.52802e15	+	1.65030e16i	0.316663	+	0.548477i	0.979790	−	0.200031i	$-0.0641042\pi$
$991$	9.52802e15	+	1.65030e16i	0.316663	+	0.548477i	−0.663126	+	0.748507i	$0.730771\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.78132e15			−0.0904117
$996$		0			0
$997$	−1.01547e16	−	1.75884e16i	−0.326470	−	0.565463i	0.655339	−	0.755335i	$-0.272526\pi$
$997$	−1.01547e16	−	1.75884e16i	−0.326470	−	0.565463i	−0.981809	+	0.189872i	$0.939193\pi$
$998$		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.37.6		16
3.2	odd	2		84.12.i.b.37.3	yes	16
7.4	even	3	inner	252.12.k.d.109.6		16
21.11	odd	6		84.12.i.b.25.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.12.i.b.25.3	✓	16	21.11	odd	6
84.12.i.b.37.3	yes	16	3.2	odd	2
252.12.k.d.37.6		16	1.1	even	1	trivial
252.12.k.d.109.6		16	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1339.81 - 2320.63i) q^{5} +(-28039.7 + 34512.4i) q^{7} +O(q^{10})\)	\(q+(1339.81 - 2320.63i) q^{5} +(-28039.7 + 34512.4i) q^{7} +(239334. + 414539. i) q^{11} -1.17059e6 q^{13} +(2.40839e6 + 4.17145e6i) q^{17} +(-4.55281e6 + 7.88570e6i) q^{19} +(4.21644e6 - 7.30309e6i) q^{23} +(2.08239e7 + 3.60680e7i) q^{25} -3.65821e7 q^{29} +(-1.20947e7 - 2.09487e7i) q^{31} +(4.25223e7 + 1.11310e8i) q^{35} +(-1.66789e8 + 2.88888e8i) q^{37} -5.86887e7 q^{41} +8.57155e8 q^{43} +(-4.75883e8 + 8.24254e8i) q^{47} +(-4.04880e8 - 1.93543e9i) q^{49} +(9.09651e8 + 1.57556e9i) q^{53} +1.28265e9 q^{55} +(-8.43761e8 - 1.46144e9i) q^{59} +(3.82941e9 - 6.63273e9i) q^{61} +(-1.56837e9 + 2.71649e9i) q^{65} +(-2.92346e9 - 5.06358e9i) q^{67} -1.03360e10 q^{71} +(4.61314e9 + 7.99018e9i) q^{73} +(-2.10176e10 - 3.36355e9i) q^{77} +(9.94865e9 - 1.72316e10i) q^{79} -4.78020e10 q^{83} +1.29072e10 q^{85} +(9.70762e9 - 1.68141e10i) q^{89} +(3.28229e10 - 4.03997e10i) q^{91} +(1.21998e10 + 2.11307e10i) q^{95} +8.32856e10 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2156 q^{5} + 50512 q^{7}+O(q^{10}) \) 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

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