LMFDB - Embedded newform 128.13.f.b.95.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,13,Mod(31,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("128.31");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	128.f (of order $4$, degree $2$, not 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:	$116.991208611$
Analytic rank:	$0$
Dimension:	$46$
Relative dimension:	$23$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			95.16
Character	$\chi$	$=$	128.95
Dual form			128.13.f.b.31.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(429.462 - 429.462i) q^{3} +(2473.08 - 2473.08i) q^{5} -198740. q^{7} +162567. i q^{9} +O(q^{10})$	\(q+(429.462 - 429.462i) q^{3} +(2473.08 - 2473.08i) q^{5} -198740. q^{7} +162567. i q^{9} +(1.13031e6 + 1.13031e6i) q^{11} +(-1.22142e6 - 1.22142e6i) q^{13} -2.12419e6i q^{15} -893652. q^{17} +(-2.55363e7 + 2.55363e7i) q^{19} +(-8.53512e7 + 8.53512e7i) q^{21} +2.41563e8 q^{23} +2.31908e8i q^{25} +(2.98050e8 + 2.98050e8i) q^{27} +(-1.87524e8 - 1.87524e8i) q^{29} -9.02639e8i q^{31} +9.70851e8 q^{33} +(-4.91501e8 + 4.91501e8i) q^{35} +(1.02150e9 - 1.02150e9i) q^{37} -1.04911e9 q^{39} -6.51861e9i q^{41} +(-6.20141e9 - 6.20141e9i) q^{43} +(4.02041e8 + 4.02041e8i) q^{45} -1.35555e10i q^{47} +2.56563e10 q^{49} +(-3.83789e8 + 3.83789e8i) q^{51} +(-9.75940e9 + 9.75940e9i) q^{53} +5.59071e9 q^{55} +2.19337e10i q^{57} +(2.24988e10 + 2.24988e10i) q^{59} +(-4.44929e9 - 4.44929e9i) q^{61} -3.23085e10i q^{63} -6.04137e9 q^{65} +(5.79808e10 - 5.79808e10i) q^{67} +(1.03742e11 - 1.03742e11i) q^{69} -2.01782e11 q^{71} +1.84468e11i q^{73} +(9.95957e10 + 9.95957e10i) q^{75} +(-2.24638e11 - 2.24638e11i) q^{77} -2.43967e11i q^{79} +1.69607e11 q^{81} +(6.52701e10 - 6.52701e10i) q^{83} +(-2.21008e9 + 2.21008e9i) q^{85} -1.61069e11 q^{87} -2.19569e11i q^{89} +(2.42746e11 + 2.42746e11i) q^{91} +(-3.87649e11 - 3.87649e11i) q^{93} +1.26307e11i q^{95} -4.30441e11 q^{97} +(-1.83751e11 + 1.83751e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 2 q^{3} + 2 q^{5} - 4 q^{7}+O(q^{10}) $ 46 * q + 2 * q^3 + 2 * q^5 - 4 * q^7	$ 46 q + 2 q^{3} + 2 q^{5} - 4 q^{7} - 2668318 q^{11} + 2 q^{13} - 4 q^{17} - 51868606 q^{19} + 1062884 q^{21} + 298270076 q^{23} - 970053760 q^{27} - 704570398 q^{29} - 4 q^{33} + 3815032900 q^{35} - 364298398 q^{37} + 15553507196 q^{39} - 363863518 q^{43} - 489344130 q^{45} + 67229109258 q^{49} - 33806024892 q^{51} + 11168756642 q^{53} - 74491808260 q^{55} - 104334793054 q^{59} + 106371743810 q^{61} - 75186419620 q^{65} + 43778233922 q^{67} + 214340079908 q^{69} - 188251854340 q^{71} - 308961520610 q^{75} + 341607754084 q^{77} - 941431788274 q^{81} + 1025936323202 q^{83} - 436332718748 q^{85} + 2368412421756 q^{87} + 2028231531652 q^{91} - 1534541270080 q^{93} - 4 q^{97} - 4950023059646 q^{99}+O(q^{100}) $ 46 * q + 2 * q^3 + 2 * q^5 - 4 * q^7 - 2668318 * q^11 + 2 * q^13 - 4 * q^17 - 51868606 * q^19 + 1062884 * q^21 + 298270076 * q^23 - 970053760 * q^27 - 704570398 * q^29 - 4 * q^33 + 3815032900 * q^35 - 364298398 * q^37 + 15553507196 * q^39 - 363863518 * q^43 - 489344130 * q^45 + 67229109258 * q^49 - 33806024892 * q^51 + 11168756642 * q^53 - 74491808260 * q^55 - 104334793054 * q^59 + 106371743810 * q^61 - 75186419620 * q^65 + 43778233922 * q^67 + 214340079908 * q^69 - 188251854340 * q^71 - 308961520610 * q^75 + 341607754084 * q^77 - 941431788274 * q^81 + 1025936323202 * q^83 - 436332718748 * q^85 + 2368412421756 * q^87 + 2028231531652 * q^91 - 1534541270080 * q^93 - 4 * q^97 - 4950023059646 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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
$3$	429.462	−	429.462i	0.589110	−	0.589110i	−0.348280	−	0.937391i	$-0.613234\pi$
$3$	429.462	−	429.462i	0.589110	−	0.589110i	0.937391	+	0.348280i	$0.113234\pi$
$4$		0			0
$5$	2473.08	−	2473.08i	0.158277	−	0.158277i	−0.623526	−	0.781803i	$-0.714300\pi$
$5$	2473.08	−	2473.08i	0.158277	−	0.158277i	0.781803	+	0.623526i	$0.214300\pi$
$6$		0			0
$7$	−198740.			−1.68926			−0.844631	−	0.535348i	$-0.820180\pi$
$7$	−198740.			−1.68926			−0.844631	+	0.535348i	$0.820180\pi$
$8$		0			0
$9$			162567.i			0.305898i
$10$		0			0
$11$	1.13031e6	+	1.13031e6i	0.638032	+	0.638032i	0.950070	−	0.312038i	$-0.101012\pi$
$11$	1.13031e6	+	1.13031e6i	0.638032	+	0.638032i	−0.312038	+	0.950070i	$0.601012\pi$
$12$		0			0
$13$	−1.22142e6	−	1.22142e6i	−0.253050	−	0.253050i	0.569170	−	0.822220i	$-0.307265\pi$
$13$	−1.22142e6	−	1.22142e6i	−0.253050	−	0.253050i	−0.822220	+	0.569170i	$0.807265\pi$
$14$		0			0
$15$		−	2.12419e6i		−	0.186486i
$16$		0			0
$17$	−893652.			−0.0370233			−0.0185116	−	0.999829i	$-0.505893\pi$
$17$	−893652.			−0.0370233			−0.0185116	+	0.999829i	$0.505893\pi$
$18$		0			0
$19$	−2.55363e7	+	2.55363e7i	−0.542795	+	0.542795i	−0.924347	−	0.381552i	$-0.875390\pi$
$19$	−2.55363e7	+	2.55363e7i	−0.542795	+	0.542795i	0.381552	+	0.924347i	$0.375390\pi$
$20$		0			0
$21$	−8.53512e7	+	8.53512e7i	−0.995162	+	0.995162i
$22$		0			0
$23$	2.41563e8			1.63179			0.815894	−	0.578201i	$-0.196245\pi$
$23$	2.41563e8			1.63179			0.815894	+	0.578201i	$0.196245\pi$
$24$		0			0
$25$			2.31908e8i			0.949897i
$26$		0			0
$27$	2.98050e8	+	2.98050e8i	0.769318	+	0.769318i
$28$		0			0
$29$	−1.87524e8	−	1.87524e8i	−0.315260	−	0.315260i	0.531683	−	0.846943i	$-0.321560\pi$
$29$	−1.87524e8	−	1.87524e8i	−0.315260	−	0.315260i	−0.846943	+	0.531683i	$0.821560\pi$
$30$		0			0
$31$		−	9.02639e8i		−	1.01705i	−0.861046	−	0.508527i	$-0.830190\pi$
$31$		−	9.02639e8i		−	1.01705i	0.861046	−	0.508527i	$-0.169810\pi$
$32$		0			0
$33$	9.70851e8			0.751742
$34$		0			0
$35$	−4.91501e8	+	4.91501e8i	−0.267372	+	0.267372i
$36$		0			0
$37$	1.02150e9	−	1.02150e9i	0.398132	−	0.398132i	−0.479442	−	0.877574i	$-0.659161\pi$
$37$	1.02150e9	−	1.02150e9i	0.398132	−	0.398132i	0.877574	+	0.479442i	$0.159161\pi$
$38$		0			0
$39$	−1.04911e9			−0.298149
$40$		0			0
$41$		−	6.51861e9i		−	1.37231i	−0.727456	−	0.686154i	$-0.759298\pi$
$41$		−	6.51861e9i		−	1.37231i	0.727456	−	0.686154i	$-0.240702\pi$
$42$		0			0
$43$	−6.20141e9	−	6.20141e9i	−0.981023	−	0.981023i	0.0187998	−	0.999823i	$-0.494015\pi$
$43$	−6.20141e9	−	6.20141e9i	−0.981023	−	0.981023i	−0.999823	+	0.0187998i	$0.994015\pi$
$44$		0			0
$45$	4.02041e8	+	4.02041e8i	0.0484167	+	0.0484167i
$46$		0			0
$47$		−	1.35555e10i		−	1.25756i	−0.777585	−	0.628778i	$-0.783556\pi$
$47$		−	1.35555e10i		−	1.25756i	0.777585	−	0.628778i	$-0.216444\pi$
$48$		0			0
$49$	2.56563e10			1.85361
$50$		0			0
$51$	−3.83789e8	+	3.83789e8i	−0.0218108	+	0.0218108i
$52$		0			0
$53$	−9.75940e9	+	9.75940e9i	−0.440319	+	0.440319i	−0.892119	−	0.451800i	$-0.850782\pi$
$53$	−9.75940e9	+	9.75940e9i	−0.440319	+	0.440319i	0.451800	+	0.892119i	$0.350782\pi$
$54$		0			0
$55$	5.59071e9			0.201972
$56$		0			0
$57$			2.19337e10i			0.639532i
$58$		0			0
$59$	2.24988e10	+	2.24988e10i	0.533393	+	0.533393i	0.921581	−	0.388187i	$-0.126899\pi$
$59$	2.24988e10	+	2.24988e10i	0.533393	+	0.533393i	−0.388187	+	0.921581i	$0.626899\pi$
$60$		0			0
$61$	−4.44929e9	−	4.44929e9i	−0.0863599	−	0.0863599i	0.662607	−	0.748967i	$-0.269450\pi$
$61$	−4.44929e9	−	4.44929e9i	−0.0863599	−	0.0863599i	−0.748967	+	0.662607i	$0.769450\pi$
$62$		0			0
$63$		−	3.23085e10i		−	0.516742i
$64$		0			0
$65$	−6.04137e9			−0.0801042
$66$		0			0
$67$	5.79808e10	−	5.79808e10i	0.640967	−	0.640967i	−0.309826	−	0.950793i	$-0.600271\pi$
$67$	5.79808e10	−	5.79808e10i	0.640967	−	0.640967i	0.950793	+	0.309826i	$0.100271\pi$
$68$		0			0
$69$	1.03742e11	−	1.03742e11i	0.961304	−	0.961304i
$70$		0			0
$71$	−2.01782e11			−1.57519			−0.787595	−	0.616194i	$-0.788674\pi$
$71$	−2.01782e11			−1.57519			−0.787595	+	0.616194i	$0.788674\pi$
$72$		0			0
$73$			1.84468e11i			1.21895i	0.792806	+	0.609474i	$0.208619\pi$
$73$			1.84468e11i			1.21895i	−0.792806	+	0.609474i	$0.791381\pi$
$74$		0			0
$75$	9.95957e10	+	9.95957e10i	0.559594	+	0.559594i
$76$		0			0
$77$	−2.24638e11	−	2.24638e11i	−1.07780	−	1.07780i
$78$		0			0
$79$		−	2.43967e11i		−	1.00362i	−0.864978	−	0.501809i	$-0.832668\pi$
$79$		−	2.43967e11i		−	1.00362i	0.864978	−	0.501809i	$-0.167332\pi$
$80$		0			0
$81$	1.69607e11			0.600529
$82$		0			0
$83$	6.52701e10	−	6.52701e10i	0.199639	−	0.199639i	−0.600206	−	0.799845i	$-0.704915\pi$
$83$	6.52701e10	−	6.52701e10i	0.199639	−	0.199639i	0.799845	+	0.600206i	$0.204915\pi$
$84$		0			0
$85$	−2.21008e9	+	2.21008e9i	−0.00585995	+	0.00585995i
$86$		0			0
$87$	−1.61069e11			−0.371446
$88$		0			0
$89$		−	2.19569e11i		−	0.441805i	−0.975296	−	0.220903i	$-0.929100\pi$
$89$		−	2.19569e11i		−	0.441805i	0.975296	−	0.220903i	$-0.0709003\pi$
$90$		0			0
$91$	2.42746e11	+	2.42746e11i	0.427468	+	0.427468i
$92$		0			0
$93$	−3.87649e11	−	3.87649e11i	−0.599157	−	0.599157i
$94$		0			0
$95$			1.26307e11i			0.171824i
$96$		0			0
$97$	−4.30441e11			−0.516753			−0.258377	−	0.966044i	$-0.583188\pi$
$97$	−4.30441e11			−0.516753			−0.258377	+	0.966044i	$0.583188\pi$
$98$		0			0
$99$	−1.83751e11	+	1.83751e11i	−0.195172	+	0.195172i
$100$		0			0
$101$	−1.40290e12	+	1.40290e12i	−1.32160	+	1.32160i	−0.409115	+	0.912483i	$0.634162\pi$
$101$	−1.40290e12	+	1.40290e12i	−1.32160	+	1.32160i	−0.912483	+	0.409115i	$0.865838\pi$
$102$		0			0
$103$	1.18637e12			0.993568			0.496784	−	0.867874i	$-0.334514\pi$
$103$	1.18637e12			0.993568			0.496784	+	0.867874i	$0.334514\pi$
$104$		0			0
$105$			4.22161e11i			0.315023i
$106$		0			0
$107$	1.23070e12	+	1.23070e12i	0.820069	+	0.820069i	0.986118	−	0.166048i	$-0.0531008\pi$
$107$	1.23070e12	+	1.23070e12i	0.820069	+	0.820069i	−0.166048	+	0.986118i	$0.553101\pi$
$108$		0			0
$109$	−1.47867e12	−	1.47867e12i	−0.881681	−	0.881681i	0.112025	−	0.993705i	$-0.464266\pi$
$109$	−1.47867e12	−	1.47867e12i	−0.881681	−	0.881681i	−0.993705	+	0.112025i	$0.964266\pi$
$110$		0			0
$111$		−	8.77388e11i		−	0.469087i
$112$		0			0
$113$	−2.85995e11			−0.137369			−0.0686844	−	0.997638i	$-0.521880\pi$
$113$	−2.85995e11			−0.137369			−0.0686844	+	0.997638i	$0.521880\pi$
$114$		0			0
$115$	5.97406e11	−	5.97406e11i	0.258275	−	0.258275i
$116$		0			0
$117$	1.98563e11	−	1.98563e11i	0.0774075	−	0.0774075i
$118$		0			0
$119$	1.77605e11			0.0625421
$120$		0			0
$121$		−	5.83217e11i		−	0.185831i
$122$		0			0
$123$	−2.79949e12	−	2.79949e12i	−0.808441	−	0.808441i
$124$		0			0
$125$	1.17731e12	+	1.17731e12i	0.308624	+	0.308624i
$126$		0			0
$127$		−	4.77949e12i		−	1.13909i	−0.821959	−	0.569546i	$-0.807119\pi$
$127$		−	4.77949e12i		−	1.13909i	0.821959	−	0.569546i	$-0.192881\pi$
$128$		0			0
$129$	−5.32653e12			−1.15586
$130$		0			0
$131$	3.11264e12	−	3.11264e12i	0.615886	−	0.615886i	−0.328587	−	0.944474i	$-0.606572\pi$
$131$	3.11264e12	−	3.11264e12i	0.615886	−	0.615886i	0.944474	+	0.328587i	$0.106572\pi$
$132$		0			0
$133$	5.07508e12	−	5.07508e12i	0.916923	−	0.916923i
$134$		0			0
$135$	1.47420e12			0.243531
$136$		0			0
$137$		−	1.18915e13i		−	1.79851i	−0.437426	−	0.899254i	$-0.644110\pi$
$137$		−	1.18915e13i		−	1.79851i	0.437426	−	0.899254i	$-0.355890\pi$
$138$		0			0
$139$	−7.43905e12	−	7.43905e12i	−1.03140	−	1.03140i	−0.999491	−	0.0319129i	$-0.989840\pi$
$139$	−7.43905e12	−	7.43905e12i	−1.03140	−	1.03140i	−0.0319129	−	0.999491i	$-0.510160\pi$
$140$		0			0
$141$	−5.82155e12	−	5.82155e12i	−0.740839	−	0.740839i
$142$		0			0
$143$		−	2.76118e12i		−	0.322908i
$144$		0			0
$145$	−9.27526e11			−0.0997972
$146$		0			0
$147$	1.10184e13	−	1.10184e13i	1.09198	−	1.09198i
$148$		0			0
$149$	−5.37585e12	+	5.37585e12i	−0.491281	+	0.491281i	−0.908710	−	0.417429i	$-0.862931\pi$
$149$	−5.37585e12	+	5.37585e12i	−0.491281	+	0.491281i	0.417429	+	0.908710i	$0.362931\pi$
$150$		0			0
$151$	1.58456e13			1.33674			0.668369	−	0.743830i	$-0.266993\pi$
$151$	1.58456e13			1.33674			0.668369	+	0.743830i	$0.266993\pi$
$152$		0			0
$153$		−	1.45278e11i		−	0.0113253i
$154$		0			0
$155$	−2.23230e12	−	2.23230e12i	−0.160976	−	0.160976i
$156$		0			0
$157$	1.32649e13	+	1.32649e13i	0.885736	+	0.885736i	0.994110	−	0.108374i	$-0.0345644\pi$
$157$	1.32649e13	+	1.32649e13i	0.885736	+	0.885736i	−0.108374	+	0.994110i	$0.534564\pi$
$158$		0			0
$159$			8.38257e12i			0.518794i
$160$		0			0
$161$	−4.80083e13			−2.75652
$162$		0			0
$163$	2.29709e13	−	2.29709e13i	1.22476	−	1.22476i	0.258843	−	0.965919i	$-0.416659\pi$
$163$	2.29709e13	−	2.29709e13i	1.22476	−	1.22476i	0.965919	−	0.258843i	$-0.0833413\pi$
$164$		0			0
$165$	2.40100e12	−	2.40100e12i	0.118984	−	0.118984i
$166$		0			0
$167$	1.56452e13			0.721244			0.360622	−	0.932712i	$-0.382564\pi$
$167$	1.56452e13			0.721244			0.360622	+	0.932712i	$0.382564\pi$
$168$		0			0
$169$		−	2.03143e13i		−	0.871931i
$170$		0			0
$171$	−4.15134e12	−	4.15134e12i	−0.166040	−	0.166040i
$172$		0			0
$173$	−3.25653e13	−	3.25653e13i	−1.21473	−	1.21473i	−0.969454	−	0.245274i	$-0.921122\pi$
$173$	−3.25653e13	−	3.25653e13i	−1.21473	−	1.21473i	−0.245274	−	0.969454i	$-0.578878\pi$
$174$		0			0
$175$		−	4.60895e13i		−	1.60463i
$176$		0			0
$177$	1.93248e13			0.628455
$178$		0			0
$179$	−2.58490e13	+	2.58490e13i	−0.785826	+	0.785826i	−0.980807	−	0.194981i	$-0.937535\pi$
$179$	−2.58490e13	+	2.58490e13i	−0.785826	+	0.785826i	0.194981	+	0.980807i	$0.437535\pi$
$180$		0			0
$181$	−2.89043e13	+	2.89043e13i	−0.822036	+	0.822036i	−0.986400	−	0.164364i	$-0.947443\pi$
$181$	−2.89043e13	+	2.89043e13i	−0.822036	+	0.822036i	0.164364	+	0.986400i	$0.447443\pi$
$182$		0			0
$183$	−3.82160e12			−0.101751
$184$		0			0
$185$		−	5.05250e12i		−	0.126031i
$186$		0			0
$187$	−1.01011e12	−	1.01011e12i	−0.0236220	−	0.0236220i
$188$		0			0
$189$	−5.92344e13	−	5.92344e13i	−1.29958	−	1.29958i
$190$		0			0
$191$		−	5.00275e13i		−	1.03041i	−0.857068	−	0.515203i	$-0.827716\pi$
$191$		−	5.00275e13i		−	1.03041i	0.857068	−	0.515203i	$-0.172284\pi$
$192$		0			0
$193$	−7.92766e12			−0.153392			−0.0766958	−	0.997055i	$-0.524437\pi$
$193$	−7.92766e12			−0.153392			−0.0766958	+	0.997055i	$0.524437\pi$
$194$		0			0
$195$	−2.59454e12	+	2.59454e12i	−0.0471902	+	0.0471902i
$196$		0			0
$197$	1.64387e13	−	1.64387e13i	0.281235	−	0.281235i	−0.552366	−	0.833602i	$-0.686275\pi$
$197$	1.64387e13	−	1.64387e13i	0.281235	−	0.281235i	0.833602	+	0.552366i	$0.186275\pi$
$198$		0			0
$199$	4.06190e13			0.654050			0.327025	−	0.945016i	$-0.393954\pi$
$199$	4.06190e13			0.654050			0.327025	+	0.945016i	$0.393954\pi$
$200$		0			0
$201$		−	4.98011e13i		−	0.755201i
$202$		0			0
$203$	3.72686e13	+	3.72686e13i	0.532558	+	0.532558i
$204$		0			0
$205$	−1.61211e13	−	1.61211e13i	−0.217205	−	0.217205i
$206$		0			0
$207$			3.92701e13i			0.499160i
$208$		0			0
$209$	−5.77279e13			−0.692641
$210$		0			0
$211$	1.05630e14	−	1.05630e14i	1.19699	−	1.19699i	0.221932	−	0.975062i	$-0.428764\pi$
$211$	1.05630e14	−	1.05630e14i	1.19699	−	1.19699i	0.975062	−	0.221932i	$-0.0712363\pi$
$212$		0			0
$213$	−8.66577e13	+	8.66577e13i	−0.927960	+	0.927960i
$214$		0			0
$215$	−3.06732e13			−0.310548
$216$		0			0
$217$			1.79390e14i			1.71807i
$218$		0			0
$219$	7.92221e13	+	7.92221e13i	0.718095	+	0.718095i
$220$		0			0
$221$	1.09153e12	+	1.09153e12i	0.00936875	+	0.00936875i
$222$		0			0
$223$		−	4.00292e13i		−	0.325498i	−0.986668	−	0.162749i	$-0.947964\pi$
$223$		−	4.00292e13i		−	0.325498i	0.986668	−	0.162749i	$-0.0520360\pi$
$224$		0			0
$225$	−3.77006e13			−0.290571
$226$		0			0
$227$	5.04842e13	−	5.04842e13i	0.368978	−	0.368978i	−0.498126	−	0.867104i	$-0.665978\pi$
$227$	5.04842e13	−	5.04842e13i	0.368978	−	0.368978i	0.867104	+	0.498126i	$0.165978\pi$
$228$		0			0
$229$	1.55290e14	−	1.55290e14i	1.07679	−	1.07679i	0.0799954	−	0.996795i	$-0.474509\pi$
$229$	1.55290e14	−	1.55290e14i	1.07679	−	1.07679i	0.996795	−	0.0799954i	$-0.0254906\pi$
$230$		0			0
$231$	−1.92947e14			−1.26989
$232$		0			0
$233$		−	5.00837e13i		−	0.313012i	−0.987677	−	0.156506i	$-0.949977\pi$
$233$		−	5.00837e13i		−	0.313012i	0.987677	−	0.156506i	$-0.0500230\pi$
$234$		0			0
$235$	−3.35238e13	−	3.35238e13i	−0.199043	−	0.199043i
$236$		0			0
$237$	−1.04774e14	−	1.04774e14i	−0.591242	−	0.591242i
$238$		0			0
$239$		−	7.01423e13i		−	0.376351i	−0.982135	−	0.188175i	$-0.939743\pi$
$239$		−	7.01423e13i		−	0.376351i	0.982135	−	0.188175i	$-0.0602573\pi$
$240$		0			0
$241$	2.51440e14			1.28331			0.641656	−	0.766992i	$-0.278248\pi$
$241$	2.51440e14			1.28331			0.641656	+	0.766992i	$0.278248\pi$
$242$		0			0
$243$	−8.55560e13	+	8.55560e13i	−0.415540	+	0.415540i
$244$		0			0
$245$	6.34503e13	−	6.34503e13i	0.293384	−	0.293384i
$246$		0			0
$247$	6.23813e13			0.274709
$248$		0			0
$249$		−	5.60620e13i		−	0.235219i
$250$		0			0
$251$	−1.63712e14	−	1.63712e14i	−0.654694	−	0.654694i	0.299425	−	0.954120i	$-0.403205\pi$
$251$	−1.63712e14	−	1.63712e14i	−0.654694	−	0.654694i	−0.954120	+	0.299425i	$0.903205\pi$
$252$		0			0
$253$	2.73042e14	+	2.73042e14i	1.04113	+	1.04113i
$254$		0			0
$255$			1.89829e12i			0.00690431i
$256$		0			0
$257$	2.08821e14			0.724729			0.362364	−	0.932036i	$-0.381970\pi$
$257$	2.08821e14			0.724729			0.362364	+	0.932036i	$0.381970\pi$
$258$		0			0
$259$	−2.03013e14	+	2.03013e14i	−0.672550	+	0.672550i
$260$		0			0
$261$	3.04852e13	−	3.04852e13i	0.0964375	−	0.0964375i
$262$		0			0
$263$	−1.87184e13			−0.0565631			−0.0282816	−	0.999600i	$-0.509004\pi$
$263$	−1.87184e13			−0.0565631			−0.0282816	+	0.999600i	$0.509004\pi$
$264$		0			0
$265$			4.82716e13i			0.139385i
$266$		0			0
$267$	−9.42964e13	−	9.42964e13i	−0.260272	−	0.260272i
$268$		0			0
$269$	2.74441e14	+	2.74441e14i	0.724328	+	0.724328i	0.969484	−	0.245155i	$-0.0788390\pi$
$269$	2.74441e14	+	2.74441e14i	0.724328	+	0.724328i	−0.245155	+	0.969484i	$0.578839\pi$
$270$		0			0
$271$		−	2.10685e12i		−	0.00531886i	−0.999996	−	0.00265943i	$-0.999153\pi$
$271$		−	2.10685e12i		−	0.00531886i	0.999996	−	0.00265943i	$-0.000846524\pi$
$272$		0			0
$273$	2.08500e14			0.503652
$274$		0			0
$275$	−2.62129e14	+	2.62129e14i	−0.606064	+	0.606064i
$276$		0			0
$277$	−1.30226e14	+	1.30226e14i	−0.288283	+	0.288283i	−0.836401	−	0.548118i	$-0.815344\pi$
$277$	−1.30226e14	+	1.30226e14i	−0.288283	+	0.288283i	0.548118	+	0.836401i	$0.315344\pi$
$278$		0			0
$279$	1.46739e14			0.311114
$280$		0			0
$281$		−	7.27818e13i		−	0.147838i	−0.997264	−	0.0739188i	$-0.976449\pi$
$281$		−	7.27818e13i		−	0.147838i	0.997264	−	0.0739188i	$-0.0235506\pi$
$282$		0			0
$283$	3.05864e14	+	3.05864e14i	0.595401	+	0.595401i	0.939085	−	0.343684i	$-0.111675\pi$
$283$	3.05864e14	+	3.05864e14i	0.595401	+	0.595401i	−0.343684	+	0.939085i	$0.611675\pi$
$284$		0			0
$285$	5.42438e13	+	5.42438e13i	0.101223	+	0.101223i
$286$		0			0
$287$			1.29551e15i			2.31819i
$288$		0			0
$289$	−5.81824e14			−0.998629
$290$		0			0
$291$	−1.84858e14	+	1.84858e14i	−0.304425	+	0.304425i
$292$		0			0
$293$	−5.05763e14	+	5.05763e14i	−0.799358	+	0.799358i	−0.982994	−	0.183636i	$-0.941213\pi$
$293$	−5.05763e14	+	5.05763e14i	−0.799358	+	0.799358i	0.183636	+	0.982994i	$0.441213\pi$
$294$		0			0
$295$	1.11283e14			0.168848
$296$		0			0
$297$			6.73778e14i			0.981699i
$298$		0			0
$299$	−2.95051e14	−	2.95051e14i	−0.412924	−	0.412924i
$300$		0			0
$301$	1.23247e15	+	1.23247e15i	1.65721	+	1.65721i
$302$		0			0
$303$			1.20499e15i			1.55713i
$304$		0			0
$305$	−2.20069e13			−0.0273376
$306$		0			0
$307$	−4.73053e14	+	4.73053e14i	−0.565041	+	0.565041i	−0.930735	−	0.365694i	$-0.880832\pi$
$307$	−4.73053e14	+	4.73053e14i	−0.565041	+	0.565041i	0.365694	+	0.930735i	$0.380832\pi$
$308$		0			0
$309$	5.09501e14	−	5.09501e14i	0.585321	−	0.585321i
$310$		0			0
$311$	2.03258e14			0.224639			0.112319	−	0.993672i	$-0.464172\pi$
$311$	2.03258e14			0.224639			0.112319	+	0.993672i	$0.464172\pi$
$312$		0			0
$313$		−	1.49068e15i		−	1.58532i	−0.609661	−	0.792662i	$-0.708694\pi$
$313$		−	1.49068e15i		−	1.58532i	0.609661	−	0.792662i	$-0.291306\pi$
$314$		0			0
$315$	−7.99016e13	−	7.99016e13i	−0.0817885	−	0.0817885i
$316$		0			0
$317$	−5.81092e14	−	5.81092e14i	−0.572650	−	0.572650i	0.360218	−	0.932868i	$-0.382702\pi$
$317$	−5.81092e14	−	5.81092e14i	−0.572650	−	0.572650i	−0.932868	+	0.360218i	$0.882702\pi$
$318$		0			0
$319$		−	4.23922e14i		−	0.402292i
$320$		0			0
$321$	1.05708e15			0.966223
$322$		0			0
$323$	2.28205e13	−	2.28205e13i	0.0200961	−	0.0200961i
$324$		0			0
$325$	2.83259e14	−	2.83259e14i	0.240371	−	0.240371i
$326$		0			0
$327$	−1.27006e15			−1.03881
$328$		0			0
$329$			2.69401e15i			2.12434i
$330$		0			0
$331$	9.37639e14	+	9.37639e14i	0.712964	+	0.712964i	0.967154	−	0.254190i	$-0.0818090\pi$
$331$	9.37639e14	+	9.37639e14i	0.712964	+	0.712964i	−0.254190	+	0.967154i	$0.581809\pi$
$332$		0			0
$333$	1.66061e14	+	1.66061e14i	0.121788	+	0.121788i
$334$		0			0
$335$		−	2.86783e14i		−	0.202901i
$336$		0			0
$337$	−2.46495e14			−0.168279			−0.0841393	−	0.996454i	$-0.526814\pi$
$337$	−2.46495e14			−0.168279			−0.0841393	+	0.996454i	$0.526814\pi$
$338$		0			0
$339$	−1.22824e14	+	1.22824e14i	−0.0809254	+	0.0809254i
$340$		0			0
$341$	1.02026e15	−	1.02026e15i	0.648912	−	0.648912i
$342$		0			0
$343$	−2.34812e15			−1.44197
$344$		0			0
$345$		−	5.13126e14i		−	0.304305i
$346$		0			0
$347$	−3.20660e14	−	3.20660e14i	−0.183682	−	0.183682i	0.609276	−	0.792958i	$-0.291460\pi$
$347$	−3.20660e14	−	3.20660e14i	−0.183682	−	0.183682i	−0.792958	+	0.609276i	$0.791460\pi$
$348$		0			0
$349$	−6.53380e14	−	6.53380e14i	−0.361587	−	0.361587i	0.502810	−	0.864397i	$-0.332300\pi$
$349$	−6.53380e14	−	6.53380e14i	−0.361587	−	0.361587i	−0.864397	+	0.502810i	$0.832300\pi$
$350$		0			0
$351$		−	7.28090e14i		−	0.389352i
$352$		0			0
$353$	1.43879e15			0.743615			0.371808	−	0.928310i	$-0.378738\pi$
$353$	1.43879e15			0.743615			0.371808	+	0.928310i	$0.378738\pi$
$354$		0			0
$355$	−4.99024e14	+	4.99024e14i	−0.249317	+	0.249317i
$356$		0			0
$357$	7.62743e13	−	7.62743e13i	0.0368442	−	0.0368442i
$358$		0			0
$359$	1.68200e15			0.785704			0.392852	−	0.919602i	$-0.371488\pi$
$359$	1.68200e15			0.785704			0.392852	+	0.919602i	$0.371488\pi$
$360$		0			0
$361$			9.09113e14i			0.410747i
$362$		0			0
$363$	−2.50469e14	−	2.50469e14i	−0.109475	−	0.109475i
$364$		0			0
$365$	4.56206e14	+	4.56206e14i	0.192932	+	0.192932i
$366$		0			0
$367$		−	1.13399e15i		−	0.464103i	−0.972703	−	0.232052i	$-0.925456\pi$
$367$		−	1.13399e15i		−	0.464103i	0.972703	−	0.232052i	$-0.0745439\pi$
$368$		0			0
$369$	1.05971e15			0.419786
$370$		0			0
$371$	1.93958e15	−	1.93958e15i	0.743815	−	0.743815i
$372$		0			0
$373$	−2.38287e15	+	2.38287e15i	−0.884804	+	0.884804i	−0.994018	−	0.109214i	$-0.965167\pi$
$373$	−2.38287e15	+	2.38287e15i	−0.884804	+	0.884804i	0.109214	+	0.994018i	$0.465167\pi$
$374$		0			0
$375$	1.01122e15			0.363628
$376$		0			0
$377$			4.58094e14i			0.159553i
$378$		0			0
$379$	2.42585e15	+	2.42585e15i	0.818520	+	0.818520i	0.985893	−	0.167374i	$-0.0535287\pi$
$379$	2.42585e15	+	2.42585e15i	0.818520	+	0.818520i	−0.167374	+	0.985893i	$0.553529\pi$
$380$		0			0
$381$	−2.05261e15	−	2.05261e15i	−0.671051	−	0.671051i
$382$		0			0
$383$		−	2.13559e15i		−	0.676589i	−0.941040	−	0.338294i	$-0.890150\pi$
$383$		−	2.13559e15i		−	0.676589i	0.941040	−	0.338294i	$-0.109850\pi$
$384$		0			0
$385$	−1.11110e15			−0.341184
$386$		0			0
$387$	1.00814e15	−	1.00814e15i	0.300093	−	0.300093i
$388$		0			0
$389$	−7.72519e14	+	7.72519e14i	−0.222952	+	0.222952i	−0.809740	−	0.586788i	$-0.800392\pi$
$389$	−7.72519e14	+	7.72519e14i	−0.222952	+	0.222952i	0.586788	+	0.809740i	$0.300392\pi$
$390$		0			0
$391$	−2.15874e14			−0.0604142
$392$		0			0
$393$		−	2.67352e15i		−	0.725650i
$394$		0			0
$395$	−6.03351e14	−	6.03351e14i	−0.158850	−	0.158850i
$396$		0			0
$397$	−7.26762e14	−	7.26762e14i	−0.185631	−	0.185631i	0.608174	−	0.793804i	$-0.291902\pi$
$397$	−7.26762e14	−	7.26762e14i	−0.185631	−	0.185631i	−0.793804	+	0.608174i	$0.791902\pi$
$398$		0			0
$399$		−	4.35910e15i		−	1.08034i
$400$		0			0
$401$	3.35792e15			0.807616			0.403808	−	0.914844i	$-0.367686\pi$
$401$	3.35792e15			0.807616			0.403808	+	0.914844i	$0.367686\pi$
$402$		0			0
$403$	−1.10251e15	+	1.10251e15i	−0.257366	+	0.257366i
$404$		0			0
$405$	4.19452e14	−	4.19452e14i	0.0950501	−	0.0950501i
$406$		0			0
$407$	2.30922e15			0.508042
$408$		0			0
$409$		−	6.03419e15i		−	1.28908i	−0.764572	−	0.644539i	$-0.777049\pi$
$409$		−	6.03419e15i		−	1.28908i	0.764572	−	0.644539i	$-0.222951\pi$
$410$		0			0
$411$	−5.10693e15	−	5.10693e15i	−1.05952	−	1.05952i
$412$		0			0
$413$	−4.47142e15	−	4.47142e15i	−0.901042	−	0.901042i
$414$		0			0
$415$		−	3.22837e14i		−	0.0631967i
$416$		0			0
$417$	−6.38957e15			−1.21522
$418$		0			0
$419$	3.28959e15	−	3.28959e15i	0.607936	−	0.607936i	−0.334470	−	0.942406i	$-0.608557\pi$
$419$	3.28959e15	−	3.28959e15i	0.607936	−	0.607936i	0.942406	+	0.334470i	$0.108557\pi$
$420$		0			0
$421$	3.95659e15	−	3.95659e15i	0.710605	−	0.710605i	−0.256057	−	0.966662i	$-0.582423\pi$
$421$	3.95659e15	−	3.95659e15i	0.710605	−	0.710605i	0.966662	+	0.256057i	$0.0824235\pi$
$422$		0			0
$423$	2.20367e15			0.384683
$424$		0			0
$425$		−	2.07245e14i		−	0.0351683i
$426$		0			0
$427$	8.84253e14	+	8.84253e14i	0.145884	+	0.145884i
$428$		0			0
$429$	−1.18582e15	−	1.18582e15i	−0.190229	−	0.190229i
$430$		0			0
$431$			1.34046e15i			0.209117i	0.994519	+	0.104559i	$0.0333430\pi$
$431$			1.34046e15i			0.209117i	−0.994519	+	0.104559i	$0.966657\pi$
$432$		0			0
$433$	−1.17609e16			−1.78448			−0.892239	−	0.451563i	$-0.850867\pi$
$433$	−1.17609e16			−1.78448			−0.892239	+	0.451563i	$0.850867\pi$
$434$		0			0
$435$	−3.98337e14	+	3.98337e14i	−0.0587916	+	0.0587916i
$436$		0			0
$437$	−6.16862e15	+	6.16862e15i	−0.885726	+	0.885726i
$438$		0			0
$439$	1.45425e14			0.0203166			0.0101583	−	0.999948i	$-0.496766\pi$
$439$	1.45425e14			0.0203166			0.0101583	+	0.999948i	$0.496766\pi$
$440$		0			0
$441$			4.17086e15i			0.567015i
$442$		0			0
$443$	3.82655e15	+	3.82655e15i	0.506273	+	0.506273i	0.913380	−	0.407107i	$-0.133463\pi$
$443$	3.82655e15	+	3.82655e15i	0.506273	+	0.506273i	−0.407107	+	0.913380i	$0.633463\pi$
$444$		0			0
$445$	−5.43012e14	−	5.43012e14i	−0.0699277	−	0.0699277i
$446$		0			0
$447$			4.61744e15i			0.578837i
$448$		0			0
$449$	−1.29311e16			−1.57818			−0.789089	−	0.614278i	$-0.789447\pi$
$449$	−1.29311e16			−1.57818			−0.789089	+	0.614278i	$0.789447\pi$
$450$		0			0
$451$	7.36806e15	−	7.36806e15i	0.875576	−	0.875576i
$452$		0			0
$453$	6.80507e15	−	6.80507e15i	0.787487	−	0.787487i
$454$		0			0
$455$	1.20066e15			0.135317
$456$		0			0
$457$			5.45708e15i			0.599050i	0.954088	+	0.299525i	$0.0968282\pi$
$457$			5.45708e15i			0.599050i	−0.954088	+	0.299525i	$0.903172\pi$
$458$		0			0
$459$	−2.66353e14	−	2.66353e14i	−0.0284827	−	0.0284827i
$460$		0			0
$461$	6.62004e15	+	6.62004e15i	0.689692	+	0.689692i	0.962164	−	0.272472i	$-0.0878412\pi$
$461$	6.62004e15	+	6.62004e15i	0.689692	+	0.689692i	−0.272472	+	0.962164i	$0.587841\pi$
$462$		0			0
$463$			1.80777e15i			0.183509i	0.995782	+	0.0917547i	$0.0292476\pi$
$463$			1.80777e15i			0.183509i	−0.995782	+	0.0917547i	$0.970752\pi$
$464$		0			0
$465$	−1.91737e15			−0.189666
$466$		0			0
$467$	1.20962e16	−	1.20962e16i	1.16613	−	1.16613i	0.183024	−	0.983108i	$-0.441411\pi$
$467$	1.20962e16	−	1.20962e16i	1.16613	−	1.16613i	0.983108	−	0.183024i	$-0.0585887\pi$
$468$		0			0
$469$	−1.15231e16	+	1.15231e16i	−1.08276	+	1.08276i
$470$		0			0
$471$	1.13935e16			1.04359
$472$		0			0
$473$		−	1.40190e16i		−	1.25185i
$474$		0			0
$475$	−5.92207e15	−	5.92207e15i	−0.515599	−	0.515599i
$476$		0			0
$477$	−1.58655e15	−	1.58655e15i	−0.134693	−	0.134693i
$478$		0			0
$479$			1.18773e15i			0.0983342i	0.998791	+	0.0491671i	$0.0156567\pi$
$479$			1.18773e15i			0.0983342i	−0.998791	+	0.0491671i	$0.984343\pi$
$480$		0			0
$481$	−2.49537e15			−0.201495
$482$		0			0
$483$	−2.06177e16	+	2.06177e16i	−1.62389	+	1.62389i
$484$		0			0
$485$	−1.06452e15	+	1.06452e15i	−0.0817903	+	0.0817903i
$486$		0			0
$487$	1.52824e16			1.14556			0.572780	−	0.819709i	$-0.305865\pi$
$487$	1.52824e16			1.14556			0.572780	+	0.819709i	$0.305865\pi$
$488$		0			0
$489$		−	1.97302e16i		−	1.44304i
$490$		0			0
$491$	−1.16766e16	−	1.16766e16i	−0.833349	−	0.833349i	0.154624	−	0.987973i	$-0.450583\pi$
$491$	−1.16766e16	−	1.16766e16i	−0.833349	−	0.833349i	−0.987973	+	0.154624i	$0.950583\pi$
$492$		0			0
$493$	1.67581e14	+	1.67581e14i	0.0116720	+	0.0116720i
$494$		0			0
$495$			9.08863e14i			0.0617828i
$496$		0			0
$497$	4.01022e16			2.66091
$498$		0			0
$499$	−2.85557e14	+	2.85557e14i	−0.0184965	+	0.0184965i	−0.716295	−	0.697798i	$-0.754163\pi$
$499$	−2.85557e14	+	2.85557e14i	−0.0184965	+	0.0184965i	0.697798	+	0.716295i	$0.254163\pi$
$500$		0			0
$501$	6.71901e15	−	6.71901e15i	0.424893	−	0.424893i
$502$		0			0
$503$	−1.98836e16			−1.22768			−0.613842	−	0.789429i	$-0.710377\pi$
$503$	−1.98836e16			−1.22768			−0.613842	+	0.789429i	$0.710377\pi$
$504$		0			0
$505$			6.93899e15i			0.418358i
$506$		0			0
$507$	−8.72422e15	−	8.72422e15i	−0.513664	−	0.513664i
$508$		0			0
$509$	5.02528e15	+	5.02528e15i	0.288971	+	0.288971i	0.836673	−	0.547702i	$-0.184497\pi$
$509$	5.02528e15	+	5.02528e15i	0.288971	+	0.288971i	−0.547702	+	0.836673i	$0.684497\pi$
$510$		0			0
$511$		−	3.66613e16i		−	2.05912i
$512$		0			0
$513$	−1.52221e16			−0.835164
$514$		0			0
$515$	2.93400e15	−	2.93400e15i	0.157259	−	0.157259i
$516$		0			0
$517$	1.53219e16	−	1.53219e16i	0.802360	−	0.802360i
$518$		0			0
$519$	−2.79711e16			−1.43122
$520$		0			0
$521$			9.03314e15i			0.451661i	0.974167	+	0.225830i	$0.0725095\pi$
$521$			9.03314e15i			0.451661i	−0.974167	+	0.225830i	$0.927490\pi$
$522$		0			0
$523$	1.82602e16	+	1.82602e16i	0.892268	+	0.892268i	0.994736	−	0.102468i	$-0.0326741\pi$
$523$	1.82602e16	+	1.82602e16i	0.892268	+	0.892268i	−0.102468	+	0.994736i	$0.532674\pi$
$524$		0			0
$525$	−1.97937e16	−	1.97937e16i	−0.945301	−	0.945301i
$526$		0			0
$527$			8.06645e14i			0.0376547i
$528$		0			0
$529$	3.64382e16			1.66273
$530$		0			0
$531$	−3.65756e15	+	3.65756e15i	−0.163164	+	0.163164i
$532$		0			0
$533$	−7.96199e15	+	7.96199e15i	−0.347263	+	0.347263i
$534$		0			0
$535$	6.08726e15			0.259597
$536$		0			0
$537$			2.22023e16i			0.925876i
$538$		0			0
$539$	2.89997e16	+	2.89997e16i	1.18266	+	1.18266i
$540$		0			0
$541$	2.80610e16	+	2.80610e16i	1.11923	+	1.11923i	0.991854	+	0.127378i	$0.0406561\pi$
$541$	2.80610e16	+	2.80610e16i	1.11923	+	1.11923i	0.127378	+	0.991854i	$0.459344\pi$
$542$		0			0
$543$			2.48265e16i			0.968540i
$544$		0			0
$545$	−7.31373e15			−0.279100
$546$		0			0
$547$	6.31941e14	−	6.31941e14i	0.0235913	−	0.0235913i	−0.695213	−	0.718804i	$-0.744690\pi$
$547$	6.31941e14	−	6.31941e14i	0.0235913	−	0.0235913i	0.718804	+	0.695213i	$0.244690\pi$
$548$		0			0
$549$	7.23306e14	−	7.23306e14i	0.0264173	−	0.0264173i
$550$		0			0
$551$	9.57734e15			0.342244
$552$		0			0
$553$			4.84860e16i			1.69537i
$554$		0			0
$555$	−2.16985e15	−	2.16985e15i	−0.0742459	−	0.0742459i
$556$		0			0
$557$	4.98142e15	+	4.98142e15i	0.166810	+	0.166810i	0.785576	−	0.618766i	$-0.212367\pi$
$557$	4.98142e15	+	4.98142e15i	0.166810	+	0.166810i	−0.618766	+	0.785576i	$0.712367\pi$
$558$		0			0
$559$			1.51491e16i			0.496496i
$560$		0			0
$561$	−8.67603e14			−0.0278320
$562$		0			0
$563$	−3.11380e16	+	3.11380e16i	−0.977779	+	0.977779i	−0.999758	−	0.0219790i	$-0.993003\pi$
$563$	−3.11380e16	+	3.11380e16i	−0.977779	+	0.977779i	0.0219790	+	0.999758i	$0.493003\pi$
$564$		0			0
$565$	−7.07290e14	+	7.07290e14i	−0.0217424	+	0.0217424i
$566$		0			0
$567$	−3.37077e16			−1.01445
$568$		0			0
$569$		−	5.94344e15i		−	0.175131i	−0.996159	−	0.0875657i	$-0.972091\pi$
$569$		−	5.94344e15i		−	0.175131i	0.996159	−	0.0875657i	$-0.0279088\pi$
$570$		0			0
$571$	5.13770e15	+	5.13770e15i	0.148235	+	0.148235i	0.777329	−	0.629094i	$-0.216574\pi$
$571$	5.13770e15	+	5.13770e15i	0.148235	+	0.148235i	−0.629094	+	0.777329i	$0.716574\pi$
$572$		0			0
$573$	−2.14849e16	−	2.14849e16i	−0.607023	−	0.607023i
$574$		0			0
$575$			5.60205e16i			1.55003i
$576$		0			0
$577$	4.29925e16			1.16503			0.582516	−	0.812819i	$-0.302068\pi$
$577$	4.29925e16			1.16503			0.582516	+	0.812819i	$0.302068\pi$
$578$		0			0
$579$	−3.40463e15	+	3.40463e15i	−0.0903646	+	0.0903646i
$580$		0			0
$581$	−1.29718e16	+	1.29718e16i	−0.337243	+	0.337243i
$582$		0			0
$583$	−2.20623e16			−0.561876
$584$		0			0
$585$		−	9.82125e14i		−	0.0245037i
$586$		0			0
$587$	2.22171e16	+	2.22171e16i	0.543073	+	0.543073i	0.924428	−	0.381356i	$-0.124543\pi$
$587$	2.22171e16	+	2.22171e16i	0.543073	+	0.543073i	−0.381356	+	0.924428i	$0.624543\pi$
$588$		0			0
$589$	2.30500e16	+	2.30500e16i	0.552051	+	0.552051i
$590$		0			0
$591$		−	1.41196e16i		−	0.331357i
$592$		0			0
$593$	−3.04709e16			−0.700739			−0.350370	−	0.936611i	$-0.613944\pi$
$593$	−3.04709e16			−0.700739			−0.350370	+	0.936611i	$0.613944\pi$
$594$		0			0
$595$	4.39231e14	−	4.39231e14i	0.00989899	−	0.00989899i
$596$		0			0
$597$	1.74443e16	−	1.74443e16i	0.385308	−	0.385308i
$598$		0			0
$599$	−3.50710e16			−0.759255			−0.379628	−	0.925139i	$-0.623948\pi$
$599$	−3.50710e16			−0.759255			−0.379628	+	0.925139i	$0.623948\pi$
$600$		0			0
$601$			1.43086e16i			0.303635i	0.988409	+	0.151817i	$0.0485125\pi$
$601$			1.43086e16i			0.303635i	−0.988409	+	0.151817i	$0.951487\pi$
$602$		0			0
$603$	9.42575e15	+	9.42575e15i	0.196070	+	0.196070i
$604$		0			0
$605$	−1.44234e15	−	1.44234e15i	−0.0294128	−	0.0294128i
$606$		0			0
$607$			2.01392e16i			0.402634i	0.979526	+	0.201317i	$0.0645222\pi$
$607$			2.01392e16i			0.402634i	−0.979526	+	0.201317i	$0.935478\pi$
$608$		0			0
$609$	3.20109e16			0.627471
$610$		0			0
$611$	−1.65570e16	+	1.65570e16i	−0.318225	+	0.318225i
$612$		0			0
$613$	4.64507e15	−	4.64507e15i	0.0875447	−	0.0875447i	−0.661978	−	0.749523i	$-0.730283\pi$
$613$	4.64507e15	−	4.64507e15i	0.0875447	−	0.0875447i	0.749523	+	0.661978i	$0.230283\pi$
$614$		0			0
$615$	−1.38467e16			−0.255916
$616$		0			0
$617$			9.37453e14i			0.0169918i	0.999964	+	0.00849589i	$0.00270436\pi$
$617$			9.37453e14i			0.0169918i	−0.999964	+	0.00849589i	$0.997296\pi$
$618$		0			0
$619$	−7.76378e16	−	7.76378e16i	−1.38016	−	1.38016i	−0.844318	−	0.535843i	$-0.819994\pi$
$619$	−7.76378e16	−	7.76378e16i	−1.38016	−	1.38016i	−0.535843	−	0.844318i	$-0.680006\pi$
$620$		0			0
$621$	7.19978e16	+	7.19978e16i	1.25536	+	1.25536i
$622$		0			0
$623$			4.36371e16i			0.746325i
$624$		0			0
$625$	−5.07951e16			−0.852200
$626$		0			0
$627$	−2.47919e16	+	2.47919e16i	−0.408042	+	0.408042i
$628$		0			0
$629$	−9.12864e14	+	9.12864e14i	−0.0147402	+	0.0147402i
$630$		0			0
$631$	9.31603e16			1.47589			0.737946	−	0.674860i	$-0.235796\pi$
$631$	9.31603e16			1.47589			0.737946	+	0.674860i	$0.235796\pi$
$632$		0			0
$633$		−	9.07279e16i		−	1.41032i
$634$		0			0
$635$	−1.18201e16	−	1.18201e16i	−0.180293	−	0.180293i
$636$		0			0
$637$	−3.13373e16	−	3.13373e16i	−0.469056	−	0.469056i
$638$		0			0
$639$		−	3.28030e16i		−	0.481847i
$640$		0			0
$641$	5.65996e16			0.815952			0.407976	−	0.912993i	$-0.366235\pi$
$641$	5.65996e16			0.815952			0.407976	+	0.912993i	$0.366235\pi$
$642$		0			0
$643$	−1.90580e16	+	1.90580e16i	−0.269656	+	0.269656i	−0.828962	−	0.559305i	$-0.811068\pi$
$643$	−1.90580e16	+	1.90580e16i	−0.269656	+	0.269656i	0.559305	+	0.828962i	$0.311068\pi$
$644$		0			0
$645$	−1.31730e16	+	1.31730e16i	−0.182947	+	0.182947i
$646$		0			0
$647$	5.08347e16			0.693003			0.346501	−	0.938050i	$-0.387370\pi$
$647$	5.08347e16			0.693003			0.346501	+	0.938050i	$0.387370\pi$
$648$		0			0
$649$			5.08614e16i			0.680644i
$650$		0			0
$651$	7.70413e16	+	7.70413e16i	1.01213	+	1.01213i
$652$		0			0
$653$	2.05384e16	+	2.05384e16i	0.264903	+	0.264903i	0.827042	−	0.562139i	$-0.190022\pi$
$653$	2.05384e16	+	2.05384e16i	0.264903	+	0.264903i	−0.562139	+	0.827042i	$0.690022\pi$
$654$		0			0
$655$		−	1.53956e16i		−	0.194962i
$656$		0			0
$657$	−2.99884e16			−0.372873
$658$		0			0
$659$	8.95193e16	−	8.95193e16i	1.09296	−	1.09296i	0.0977487	−	0.995211i	$-0.468836\pi$
$659$	8.95193e16	−	8.95193e16i	1.09296	−	1.09296i	0.995211	−	0.0977487i	$-0.0311642\pi$
$660$		0			0
$661$	3.03268e16	−	3.03268e16i	0.363595	−	0.363595i	−0.501539	−	0.865135i	$-0.667233\pi$
$661$	3.03268e16	−	3.03268e16i	0.363595	−	0.363595i	0.865135	+	0.501539i	$0.167233\pi$
$662$		0			0
$663$	9.37539e14			0.0110385
$664$		0			0
$665$		−	2.51022e16i		−	0.290256i
$666$		0			0
$667$	−4.52990e16	−	4.52990e16i	−0.514438	−	0.514438i
$668$		0			0
$669$	−1.71910e16	−	1.71910e16i	−0.191754	−	0.191754i
$670$		0			0
$671$		−	1.00582e16i		−	0.110201i
$672$		0			0
$673$	−4.39967e16			−0.473511			−0.236755	−	0.971569i	$-0.576084\pi$
$673$	−4.39967e16			−0.473511			−0.236755	+	0.971569i	$0.576084\pi$
$674$		0			0
$675$	−6.91202e16	+	6.91202e16i	−0.730773	+	0.730773i
$676$		0			0
$677$	−9.00086e16	+	9.00086e16i	−0.934871	+	0.934871i	−0.998005	−	0.0631338i	$-0.979891\pi$
$677$	−9.00086e16	+	9.00086e16i	−0.934871	+	0.934871i	0.0631338	+	0.998005i	$0.479891\pi$
$678$		0			0
$679$	8.55459e16			0.872932
$680$		0			0
$681$		−	4.33621e16i		−	0.434738i
$682$		0			0
$683$	−9.58839e16	−	9.58839e16i	−0.944542	−	0.944542i	0.0539988	−	0.998541i	$-0.482803\pi$
$683$	−9.58839e16	−	9.58839e16i	−0.944542	−	0.944542i	−0.998541	+	0.0539988i	$0.982803\pi$
$684$		0			0
$685$	−2.94086e16	−	2.94086e16i	−0.284663	−	0.284663i
$686$		0			0
$687$		−	1.33382e17i		−	1.26870i
$688$		0			0
$689$	2.38407e16			0.222846
$690$		0			0
$691$	−3.55457e16	+	3.55457e16i	−0.326526	+	0.326526i	−0.851264	−	0.524738i	$-0.824163\pi$
$691$	−3.55457e16	+	3.55457e16i	−0.326526	+	0.326526i	0.524738	+	0.851264i	$0.324163\pi$
$692$		0			0
$693$	3.65187e16	−	3.65187e16i	0.329698	−	0.329698i
$694$		0			0
$695$	−3.67948e16			−0.326496
$696$		0			0
$697$			5.82537e15i			0.0508074i
$698$		0			0
$699$	−2.15090e16	−	2.15090e16i	−0.184399	−	0.184399i
$700$		0			0
$701$	8.00190e16	+	8.00190e16i	0.674349	+	0.674349i	0.958716	−	0.284366i	$-0.0917832\pi$
$701$	8.00190e16	+	8.00190e16i	0.674349	+	0.674349i	−0.284366	+	0.958716i	$0.591783\pi$
$702$		0			0
$703$			5.21705e16i			0.432208i
$704$		0			0
$705$	−2.87944e16			−0.234516
$706$		0			0
$707$	2.78813e17	−	2.78813e17i	2.23253	−	2.23253i
$708$		0			0
$709$	5.57030e16	−	5.57030e16i	0.438532	−	0.438532i	−0.452986	−	0.891518i	$-0.649641\pi$
$709$	5.57030e16	−	5.57030e16i	0.438532	−	0.438532i	0.891518	+	0.452986i	$0.149641\pi$
$710$		0			0
$711$	3.96609e16			0.307005
$712$		0			0
$713$		−	2.18044e17i		−	1.65962i
$714$		0			0
$715$	−6.82864e15	−	6.82864e15i	−0.0511090	−	0.0511090i
$716$		0			0
$717$	−3.01234e16	−	3.01234e16i	−0.221712	−	0.221712i
$718$		0			0
$719$		−	4.86412e15i		−	0.0352072i	−0.999845	−	0.0176036i	$-0.994396\pi$
$719$		−	4.86412e15i		−	0.0352072i	0.999845	−	0.0176036i	$-0.00560368\pi$
$720$		0			0
$721$	−2.35780e17			−1.67840
$722$		0			0
$723$	1.07984e17	−	1.07984e17i	0.756013	−	0.756013i
$724$		0			0
$725$	4.34884e16	−	4.34884e16i	0.299465	−	0.299465i
$726$		0			0
$727$	−1.49349e17			−1.01157			−0.505784	−	0.862660i	$-0.668797\pi$
$727$	−1.49349e17			−1.01157			−0.505784	+	0.862660i	$0.668797\pi$
$728$		0			0
$729$			1.63622e17i			1.09013i
$730$		0			0
$731$	5.54190e15	+	5.54190e15i	0.0363207	+	0.0363207i
$732$		0			0
$733$	−1.66196e17	−	1.66196e17i	−1.07151	−	1.07151i	−0.997238	−	0.0742703i	$-0.976337\pi$
$733$	−1.66196e17	−	1.66196e17i	−1.07151	−	1.07151i	−0.0742703	−	0.997238i	$-0.523663\pi$
$734$		0			0
$735$		−	5.44989e16i		−	0.345672i
$736$		0			0
$737$	1.31073e17			0.817915
$738$		0			0
$739$	−1.51066e17	+	1.51066e17i	−0.927473	+	0.927473i	−0.997542	−	0.0700690i	$-0.977678\pi$
$739$	−1.51066e17	+	1.51066e17i	−0.927473	+	0.927473i	0.0700690	+	0.997542i	$0.477678\pi$
$740$		0			0
$741$	2.67904e16	−	2.67904e16i	0.161834	−	0.161834i
$742$		0			0
$743$	−2.11615e17			−1.25781			−0.628903	−	0.777484i	$-0.716496\pi$
$743$	−2.11615e17			−1.25781			−0.628903	+	0.777484i	$0.716496\pi$
$744$		0			0
$745$			2.65899e16i			0.155517i
$746$		0			0
$747$	1.06107e16	+	1.06107e16i	0.0610691	+	0.0610691i
$748$		0			0
$749$	−2.44590e17	−	2.44590e17i	−1.38531	−	1.38531i
$750$		0			0
$751$		−	1.32554e17i		−	0.738847i	−0.929261	−	0.369423i	$-0.879555\pi$
$751$		−	1.32554e17i		−	0.738847i	0.929261	−	0.369423i	$-0.120445\pi$
$752$		0			0
$753$	−1.40616e17			−0.771375
$754$		0			0
$755$	3.91874e16	−	3.91874e16i	0.211575	−	0.211575i
$756$		0			0
$757$	−4.52002e16	+	4.52002e16i	−0.240196	+	0.240196i	−0.816931	−	0.576735i	$-0.804326\pi$
$757$	−4.52002e16	+	4.52002e16i	−0.240196	+	0.240196i	0.576735	+	0.816931i	$0.304326\pi$
$758$		0			0
$759$	2.34522e17			1.22668
$760$		0			0
$761$			1.38931e15i			0.00715307i	0.999994	+	0.00357654i	$0.00113845\pi$
$761$			1.38931e15i			0.00715307i	−0.999994	+	0.00357654i	$0.998862\pi$
$762$		0			0
$763$	2.93870e17	+	2.93870e17i	1.48939	+	1.48939i
$764$		0			0
$765$	−3.59285e14	−	3.59285e14i	−0.00179254	−	0.00179254i
$766$		0			0
$767$		−	5.49612e16i		−	0.269951i
$768$		0			0
$769$	−1.18622e17			−0.573599			−0.286800	−	0.957991i	$-0.592591\pi$
$769$	−1.18622e17			−0.573599			−0.286800	+	0.957991i	$0.592591\pi$
$770$		0			0
$771$	8.96806e16	−	8.96806e16i	0.426945	−	0.426945i
$772$		0			0
$773$	−2.47609e17	+	2.47609e17i	−1.16062	+	1.16062i	−0.176280	+	0.984340i	$0.556406\pi$
$773$	−2.47609e17	+	2.47609e17i	−1.16062	+	1.16062i	−0.984340	+	0.176280i	$0.943594\pi$
$774$		0			0
$775$	2.09329e17			0.966095
$776$		0			0
$777$			1.74372e17i			0.792412i
$778$		0			0
$779$	1.66461e17	+	1.66461e17i	0.744882	+	0.744882i
$780$		0			0
$781$	−2.28077e17	−	2.28077e17i	−1.00502	−	1.00502i
$782$		0			0
$783$		−	1.11783e17i		−	0.485071i
$784$		0			0
$785$	6.56102e16			0.280384
$786$		0			0
$787$	−9.46687e15	+	9.46687e15i	−0.0398435	+	0.0398435i	−0.726748	−	0.686904i	$-0.758969\pi$
$787$	−9.46687e15	+	9.46687e15i	−0.0398435	+	0.0398435i	0.686904	+	0.726748i	$0.258969\pi$
$788$		0			0
$789$	−8.03882e15	+	8.03882e15i	−0.0333219	+	0.0333219i
$790$		0			0
$791$	5.68387e16			0.232052
$792$		0			0
$793$			1.08690e16i			0.0437068i
$794$		0			0
$795$	2.07308e16	+	2.07308e16i	0.0821133	+	0.0821133i
$796$		0			0
$797$	1.79399e17	+	1.79399e17i	0.699954	+	0.699954i	0.964400	−	0.264447i	$-0.0851893\pi$
$797$	1.79399e17	+	1.79399e17i	0.699954	+	0.699954i	−0.264447	+	0.964400i	$0.585189\pi$
$798$		0			0
$799$			1.21139e16i			0.0465588i
$800$		0			0
$801$	3.56946e16			0.135147
$802$		0			0
$803$	−2.08507e17	+	2.08507e17i	−0.777727	+	0.777727i
$804$		0			0
$805$	−1.18729e17	+	1.18729e17i	−0.436295	+	0.436295i
$806$		0			0
$807$	2.35724e17			0.853419
$808$		0			0
$809$		−	2.92721e17i		−	1.04415i	−0.852899	−	0.522075i	$-0.825158\pi$
$809$		−	2.92721e17i		−	1.04415i	0.852899	−	0.522075i	$-0.174842\pi$
$810$		0			0
$811$	−3.84598e17	−	3.84598e17i	−1.35170	−	1.35170i	−0.883756	−	0.467947i	$-0.844994\pi$
$811$	−3.84598e17	−	3.84598e17i	−1.35170	−	1.35170i	−0.467947	−	0.883756i	$-0.655006\pi$
$812$		0			0
$813$	−9.04813e14	−	9.04813e14i	−0.00313340	−	0.00313340i
$814$		0			0
$815$		−	1.13618e17i		−	0.387704i
$816$		0			0
$817$	3.16721e17			1.06499
$818$		0			0
$819$	−3.94624e16	+	3.94624e16i	−0.130762	+	0.130762i
$820$		0			0
$821$	−7.39546e15	+	7.39546e15i	−0.0241494	+	0.0241494i	−0.719078	−	0.694929i	$-0.755436\pi$
$821$	−7.39546e15	+	7.39546e15i	−0.0241494	+	0.0241494i	0.694929	+	0.719078i	$0.255436\pi$
$822$		0			0
$823$	−3.96070e17			−1.27460			−0.637298	−	0.770617i	$-0.719948\pi$
$823$	−3.96070e17			−1.27460			−0.637298	+	0.770617i	$0.719948\pi$
$824$		0			0
$825$			2.25149e17i			0.714078i
$826$		0			0
$827$	7.53385e16	+	7.53385e16i	0.235496	+	0.235496i	0.814982	−	0.579486i	$-0.196747\pi$
$827$	7.53385e16	+	7.53385e16i	0.235496	+	0.235496i	−0.579486	+	0.814982i	$0.696747\pi$
$828$		0			0
$829$	5.27616e16	+	5.27616e16i	0.162551	+	0.162551i	0.783696	−	0.621145i	$-0.213332\pi$
$829$	5.27616e16	+	5.27616e16i	0.162551	+	0.162551i	−0.621145	+	0.783696i	$0.713332\pi$
$830$		0			0
$831$			1.11854e17i			0.339661i
$832$		0			0
$833$	−2.29278e16			−0.0686267
$834$		0			0
$835$	3.86919e16	−	3.86919e16i	0.114157	−	0.114157i
$836$		0			0
$837$	2.69031e17	−	2.69031e17i	0.782437	−	0.782437i
$838$		0			0
$839$	−2.58496e17			−0.741109			−0.370555	−	0.928811i	$-0.620832\pi$
$839$	−2.58496e17			−0.741109			−0.370555	+	0.928811i	$0.620832\pi$
$840$		0			0
$841$		−	2.83484e17i		−	0.801222i
$842$		0			0
$843$	−3.12570e16	−	3.12570e16i	−0.0870926	−	0.0870926i
$844$		0			0
$845$	−5.02390e16	−	5.02390e16i	−0.138007	−	0.138007i
$846$		0			0
$847$			1.15909e17i			0.313917i
$848$		0			0
$849$	2.62713e17			0.701514
$850$		0			0
$851$	2.46756e17	−	2.46756e17i	0.649667	−	0.649667i
$852$		0			0
$853$	1.93060e17	−	1.93060e17i	0.501184	−	0.501184i	−0.410621	−	0.911806i	$-0.634688\pi$
$853$	1.93060e17	−	1.93060e17i	0.501184	−	0.501184i	0.911806	+	0.410621i	$0.134688\pi$
$854$		0			0
$855$	−2.05332e16			−0.0525607
$856$		0			0
$857$		−	2.79390e17i		−	0.705223i	−0.935770	−	0.352612i	$-0.885294\pi$
$857$		−	2.79390e17i		−	0.705223i	0.935770	−	0.352612i	$-0.114706\pi$
$858$		0			0
$859$	−4.20231e17	−	4.20231e17i	−1.04599	−	1.04599i	−0.998890	−	0.0471039i	$-0.985001\pi$
$859$	−4.20231e17	−	4.20231e17i	−1.04599	−	1.04599i	−0.0471039	−	0.998890i	$-0.514999\pi$
$860$		0			0
$861$	5.56371e17	+	5.56371e17i	1.36567	+	1.36567i
$862$		0			0
$863$			1.80725e17i			0.437476i	0.975784	+	0.218738i	$0.0701939\pi$
$863$			1.80725e17i			0.437476i	−0.975784	+	0.218738i	$0.929806\pi$
$864$		0			0
$865$	−1.61074e17			−0.384528
$866$		0			0
$867$	−2.49871e17	+	2.49871e17i	−0.588303	+	0.588303i
$868$		0			0
$869$	2.75759e17	−	2.75759e17i	0.640340	−	0.640340i
$870$		0			0
$871$	−1.41638e17			−0.324394
$872$		0			0
$873$		−	6.99753e16i		−	0.158074i
$874$		0			0
$875$	−2.33978e17	−	2.33978e17i	−0.521348	−	0.521348i
$876$		0			0
$877$	4.83076e17	+	4.83076e17i	1.06174	+	1.06174i	0.997964	+	0.0637754i	$0.0203141\pi$
$877$	4.83076e17	+	4.83076e17i	1.06174	+	1.06174i	0.0637754	+	0.997964i	$0.479686\pi$
$878$		0			0
$879$			4.34411e17i			0.941820i
$880$		0			0
$881$	−8.54286e16			−0.182704			−0.0913520	−	0.995819i	$-0.529119\pi$
$881$	−8.54286e16			−0.182704			−0.0913520	+	0.995819i	$0.529119\pi$
$882$		0			0
$883$	4.01918e14	−	4.01918e14i	0.000847956	−	0.000847956i	−0.706683	−	0.707531i	$-0.749809\pi$
$883$	4.01918e14	−	4.01918e14i	0.000847956	−	0.000847956i	0.707531	+	0.706683i	$0.249809\pi$
$884$		0			0
$885$	4.77917e16	−	4.77917e16i	0.0994702	−	0.0994702i
$886$		0			0
$887$	−2.56277e17			−0.526221			−0.263111	−	0.964766i	$-0.584748\pi$
$887$	−2.56277e17			−0.526221			−0.263111	+	0.964766i	$0.584748\pi$
$888$		0			0
$889$			9.49876e17i			1.92423i
$890$		0			0
$891$	1.91709e17	+	1.91709e17i	0.383156	+	0.383156i
$892$		0			0
$893$	3.46156e17	+	3.46156e17i	0.682595	+	0.682595i
$894$		0			0
$895$			1.27854e17i			0.248757i
$896$		0			0
$897$	−2.53426e17			−0.486516
$898$		0			0
$899$	−1.69267e17	+	1.69267e17i	−0.320637	+	0.320637i
$900$		0			0
$901$	8.72151e15	−	8.72151e15i	0.0163021	−	0.0163021i
$902$		0			0
$903$	1.05860e18			1.95256
$904$		0			0
$905$			1.42965e17i			0.260219i
$906$		0			0
$907$	5.99429e17	+	5.99429e17i	1.07670	+	1.07670i	0.996803	+	0.0798942i	$0.0254582\pi$
$907$	5.99429e17	+	5.99429e17i	1.07670	+	1.07670i	0.0798942	+	0.996803i	$0.474542\pi$
$908$		0			0
$909$	−2.28065e17	−	2.28065e17i	−0.404274	−	0.404274i
$910$		0			0
$911$			7.31773e17i			1.28017i	0.768306	+	0.640083i	$0.221100\pi$
$911$			7.31773e17i			1.28017i	−0.768306	+	0.640083i	$0.778900\pi$
$912$		0			0
$913$	1.47551e17			0.254752
$914$		0			0
$915$	−9.45113e15	+	9.45113e15i	−0.0161049	+	0.0161049i
$916$		0			0
$917$	−6.18606e17	+	6.18606e17i	−1.04039	+	1.04039i
$918$		0			0
$919$	−2.74353e17			−0.455425			−0.227713	−	0.973728i	$-0.573125\pi$
$919$	−2.74353e17			−0.455425			−0.227713	+	0.973728i	$0.573125\pi$
$920$		0			0
$921$			4.06316e17i			0.665743i
$922$		0			0
$923$	2.46462e17	+	2.46462e17i	0.398602	+	0.398602i
$924$		0			0
$925$	2.36894e17	+	2.36894e17i	0.378184	+	0.378184i
$926$		0			0
$927$			1.92864e17i			0.303930i
$928$		0			0
$929$	1.00371e18			1.56140			0.780699	−	0.624907i	$-0.214863\pi$
$929$	1.00371e18			1.56140			0.780699	+	0.624907i	$0.214863\pi$
$930$		0			0
$931$	−6.55167e17	+	6.55167e17i	−1.00613	+	1.00613i
$932$		0			0
$933$	8.72914e16	−	8.72914e16i	0.132337	−	0.132337i
$934$		0			0
$935$	−4.99615e15			−0.00747767
$936$		0			0
$937$		−	3.16458e17i		−	0.467604i	−0.972284	−	0.233802i	$-0.924883\pi$
$937$		−	3.16458e17i		−	0.467604i	0.972284	−	0.233802i	$-0.0751168\pi$
$938$		0			0
$939$	−6.40189e17	−	6.40189e17i	−0.933931	−	0.933931i
$940$		0			0
$941$	−3.90786e17	−	3.90786e17i	−0.562861	−	0.562861i	0.367258	−	0.930119i	$-0.380296\pi$
$941$	−3.90786e17	−	3.90786e17i	−0.562861	−	0.562861i	−0.930119	+	0.367258i	$0.880296\pi$
$942$		0			0
$943$		−	1.57466e18i		−	2.23932i
$944$		0			0
$945$	−2.92983e17			−0.411388
$946$		0			0
$947$	−2.66757e17	+	2.66757e17i	−0.369841	+	0.369841i	−0.867419	−	0.497578i	$-0.834223\pi$
$947$	−2.66757e17	+	2.66757e17i	−0.369841	+	0.369841i	0.497578	+	0.867419i	$0.334223\pi$
$948$		0			0
$949$	2.25314e17	−	2.25314e17i	0.308455	−	0.308455i
$950$		0			0
$951$	−4.99113e17			−0.674708
$952$		0			0
$953$		−	6.36650e17i		−	0.849852i	−0.905228	−	0.424926i	$-0.860300\pi$
$953$		−	6.36650e17i		−	0.849852i	0.905228	−	0.424926i	$-0.139700\pi$
$954$		0			0
$955$	−1.23722e17	−	1.23722e17i	−0.163090	−	0.163090i
$956$		0			0
$957$	−1.82058e17	−	1.82058e17i	−0.236995	−	0.236995i
$958$		0			0
$959$			2.36331e18i			3.03815i
$960$		0			0
$961$	−2.70935e16			−0.0343973
$962$		0			0
$963$	−2.00071e17	+	2.00071e17i	−0.250857	+	0.250857i
$964$		0			0
$965$	−1.96058e16	+	1.96058e16i	−0.0242784	+	0.0242784i
$966$		0			0
$967$	−5.84069e17			−0.714341			−0.357170	−	0.934039i	$-0.616258\pi$
$967$	−5.84069e17			−0.714341			−0.357170	+	0.934039i	$0.616258\pi$
$968$		0			0
$969$		−	1.96011e16i		−	0.0236776i
$970$		0			0
$971$	−4.70668e15	−	4.70668e15i	−0.00561564	−	0.00561564i	0.704293	−	0.709909i	$-0.251264\pi$
$971$	−4.70668e15	−	4.70668e15i	−0.00561564	−	0.00561564i	−0.709909	+	0.704293i	$0.751264\pi$
$972$		0			0
$973$	1.47844e18	+	1.47844e18i	1.74231	+	1.74231i
$974$		0			0
$975$		−	2.43297e17i		−	0.283211i
$976$		0			0
$977$	−4.16374e17			−0.478758			−0.239379	−	0.970926i	$-0.576944\pi$
$977$	−4.16374e17			−0.478758			−0.239379	+	0.970926i	$0.576944\pi$
$978$		0			0
$979$	2.48181e17	−	2.48181e17i	0.281886	−	0.281886i
$980$		0			0
$981$	2.40382e17	−	2.40382e17i	0.269704	−	0.269704i
$982$		0			0
$983$	−4.21754e17			−0.467453			−0.233726	−	0.972302i	$-0.575092\pi$
$983$	−4.21754e17			−0.467453			−0.233726	+	0.972302i	$0.575092\pi$
$984$		0			0
$985$		−	8.13085e16i		−	0.0890263i
$986$		0			0
$987$	1.15698e18	+	1.15698e18i	1.25147	+	1.25147i
$988$		0			0
$989$	−1.49803e18	−	1.49803e18i	−1.60082	−	1.60082i
$990$		0			0
$991$		−	6.95349e17i		−	0.734109i	−0.930199	−	0.367055i	$-0.880366\pi$
$991$		−	6.95349e17i		−	0.734109i	0.930199	−	0.367055i	$-0.119634\pi$
$992$		0			0
$993$	8.05359e17			0.840029
$994$		0			0
$995$	1.00454e17	−	1.00454e17i	0.103521	−	0.103521i
$996$		0			0
$997$	−8.24587e17	+	8.24587e17i	−0.839586	+	0.839586i	−0.988804	−	0.149218i	$-0.952324\pi$
$997$	−8.24587e17	+	8.24587e17i	−0.839586	+	0.839586i	0.149218	+	0.988804i	$0.452324\pi$
$998$		0			0
$999$	6.08914e17			0.612580

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.13.f.b.95.16		46
4.3	odd	2		128.13.f.a.95.8		46
8.3	odd	2		64.13.f.a.47.16		46
8.5	even	2		16.13.f.a.3.2	✓	46
16.3	odd	4		16.13.f.a.11.2	yes	46
16.5	even	4		128.13.f.a.31.8		46
16.11	odd	4	inner	128.13.f.b.31.16		46
16.13	even	4		64.13.f.a.15.16		46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.13.f.a.3.2	✓	46	8.5	even	2
16.13.f.a.11.2	yes	46	16.3	odd	4
64.13.f.a.15.16		46	16.13	even	4
64.13.f.a.47.16		46	8.3	odd	2
128.13.f.a.31.8		46	16.5	even	4
128.13.f.a.95.8		46	4.3	odd	2
128.13.f.b.31.16		46	16.11	odd	4	inner
128.13.f.b.95.16		46	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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	128.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(429.462 - 429.462i) q^{3} +(2473.08 - 2473.08i) q^{5} -198740. q^{7} +162567. i q^{9} +O(q^{10})\)	\(q+(429.462 - 429.462i) q^{3} +(2473.08 - 2473.08i) q^{5} -198740. q^{7} +162567. i q^{9} +(1.13031e6 + 1.13031e6i) q^{11} +(-1.22142e6 - 1.22142e6i) q^{13} -2.12419e6i q^{15} -893652. q^{17} +(-2.55363e7 + 2.55363e7i) q^{19} +(-8.53512e7 + 8.53512e7i) q^{21} +2.41563e8 q^{23} +2.31908e8i q^{25} +(2.98050e8 + 2.98050e8i) q^{27} +(-1.87524e8 - 1.87524e8i) q^{29} -9.02639e8i q^{31} +9.70851e8 q^{33} +(-4.91501e8 + 4.91501e8i) q^{35} +(1.02150e9 - 1.02150e9i) q^{37} -1.04911e9 q^{39} -6.51861e9i q^{41} +(-6.20141e9 - 6.20141e9i) q^{43} +(4.02041e8 + 4.02041e8i) q^{45} -1.35555e10i q^{47} +2.56563e10 q^{49} +(-3.83789e8 + 3.83789e8i) q^{51} +(-9.75940e9 + 9.75940e9i) q^{53} +5.59071e9 q^{55} +2.19337e10i q^{57} +(2.24988e10 + 2.24988e10i) q^{59} +(-4.44929e9 - 4.44929e9i) q^{61} -3.23085e10i q^{63} -6.04137e9 q^{65} +(5.79808e10 - 5.79808e10i) q^{67} +(1.03742e11 - 1.03742e11i) q^{69} -2.01782e11 q^{71} +1.84468e11i q^{73} +(9.95957e10 + 9.95957e10i) q^{75} +(-2.24638e11 - 2.24638e11i) q^{77} -2.43967e11i q^{79} +1.69607e11 q^{81} +(6.52701e10 - 6.52701e10i) q^{83} +(-2.21008e9 + 2.21008e9i) q^{85} -1.61069e11 q^{87} -2.19569e11i q^{89} +(2.42746e11 + 2.42746e11i) q^{91} +(-3.87649e11 - 3.87649e11i) q^{93} +1.26307e11i q^{95} -4.30441e11 q^{97} +(-1.83751e11 + 1.83751e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 2 q^{3} + 2 q^{5} - 4 q^{7}+O(q^{10}) \) 46 * q + 2 * q^3 + 2 * q^5 - 4 * q^7	\( 46 q + 2 q^{3} + 2 q^{5} - 4 q^{7} - 2668318 q^{11} + 2 q^{13} - 4 q^{17} - 51868606 q^{19} + 1062884 q^{21} + 298270076 q^{23} - 970053760 q^{27} - 704570398 q^{29} - 4 q^{33} + 3815032900 q^{35} - 364298398 q^{37} + 15553507196 q^{39} - 363863518 q^{43} - 489344130 q^{45} + 67229109258 q^{49} - 33806024892 q^{51} + 11168756642 q^{53} - 74491808260 q^{55} - 104334793054 q^{59} + 106371743810 q^{61} - 75186419620 q^{65} + 43778233922 q^{67} + 214340079908 q^{69} - 188251854340 q^{71} - 308961520610 q^{75} + 341607754084 q^{77} - 941431788274 q^{81} + 1025936323202 q^{83} - 436332718748 q^{85} + 2368412421756 q^{87} + 2028231531652 q^{91} - 1534541270080 q^{93} - 4 q^{97} - 4950023059646 q^{99}+O(q^{100}) \) 46 * q + 2 * q^3 + 2 * q^5 - 4 * q^7 - 2668318 * q^11 + 2 * q^13 - 4 * q^17 - 51868606 * q^19 + 1062884 * q^21 + 298270076 * q^23 - 970053760 * q^27 - 704570398 * q^29 - 4 * q^33 + 3815032900 * q^35 - 364298398 * q^37 + 15553507196 * q^39 - 363863518 * q^43 - 489344130 * q^45 + 67229109258 * q^49 - 33806024892 * q^51 + 11168756642 * q^53 - 74491808260 * q^55 - 104334793054 * q^59 + 106371743810 * q^61 - 75186419620 * q^65 + 43778233922 * q^67 + 214340079908 * q^69 - 188251854340 * q^71 - 308961520610 * q^75 + 341607754084 * q^77 - 941431788274 * q^81 + 1025936323202 * q^83 - 436332718748 * q^85 + 2368412421756 * q^87 + 2028231531652 * q^91 - 1534541270080 * q^93 - 4 * q^97 - 4950023059646 * q^99

Introduction

L-functions

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