LMFDB - Embedded newform 45.22.b.d.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,22,Mod(19,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("45.19");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	45.b (of order $2$, degree $1$, 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:	$125.764804929$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 31014725 x^{18} + 402351996349620 x^{16} + \cdots + 63\!\cdots\!24 $ x^20 + 31014725x^18 + 402351996349620x^16 + 2836808701650254846400x^14 + 11826517837807538556586613760x^12 + 29747895249547280861001474022195200x^10 + 44225957682534138504633463990733494026240x^8 + 36403720551913775493365925576655741076373504000x^6 + 14324509913517555111691817895610642729083973014650880x^4 + 1825107410106179411916840332357678356954903807034969292800*x^2 + 63759461742093950711107134018636375232221455481836521991962624
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	multiple of $ 2^{51}\cdot 3^{88}\cdot 5^{39}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.2
Root			$-2387.58i$ of defining polynomial
Character	$\chi$	$=$	45.19
Dual form			45.22.b.d.19.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2387.58i q^{2} -3.60339e6 q^{4} +(-9.00948e6 + 1.98914e7i) q^{5} +8.76258e8i q^{7} +3.59626e9i q^{8} +O(q^{10})$	\(q-2387.58i q^{2} -3.60339e6 q^{4} +(-9.00948e6 + 1.98914e7i) q^{5} +8.76258e8i q^{7} +3.59626e9i q^{8} +(4.74922e10 + 2.15109e10i) q^{10} +1.10419e11 q^{11} +6.22087e11i q^{13} +2.09214e12 q^{14} +1.02950e12 q^{16} +6.51559e12i q^{17} +4.44912e13 q^{19} +(3.24646e13 - 7.16763e13i) q^{20} -2.63633e14i q^{22} +2.65057e14i q^{23} +(-3.14496e14 - 3.58422e14i) q^{25} +1.48528e15 q^{26} -3.15750e15i q^{28} -1.28018e15 q^{29} -5.90644e15 q^{31} +5.08388e15i q^{32} +1.55565e16 q^{34} +(-1.74300e16 - 7.89463e15i) q^{35} -3.24650e16i q^{37} -1.06226e17i q^{38} +(-7.15345e16 - 3.24004e16i) q^{40} +4.85384e16 q^{41} -5.89988e16i q^{43} -3.97881e17 q^{44} +6.32845e17 q^{46} +3.80793e17i q^{47} -2.09282e17 q^{49} +(-8.55761e17 + 7.50884e17i) q^{50} -2.24162e18i q^{52} +7.98759e17i q^{53} +(-9.94813e17 + 2.19637e18i) q^{55} -3.15125e18 q^{56} +3.05653e18i q^{58} +3.84138e17 q^{59} +3.61141e18 q^{61} +1.41021e19i q^{62} +1.42972e19 q^{64} +(-1.23742e19 - 5.60468e18i) q^{65} +9.40156e18i q^{67} -2.34782e19i q^{68} +(-1.88491e19 + 4.16154e19i) q^{70} -8.73489e18 q^{71} -4.81680e19i q^{73} -7.75127e19 q^{74} -1.60319e20 q^{76} +9.67551e19i q^{77} -8.49792e19 q^{79} +(-9.27527e18 + 2.04782e19i) q^{80} -1.15889e20i q^{82} +1.25162e20i q^{83} +(-1.29604e20 - 5.87021e19i) q^{85} -1.40864e20 q^{86} +3.97093e20i q^{88} -1.17871e20 q^{89} -5.45109e20 q^{91} -9.55103e20i q^{92} +9.09175e20 q^{94} +(-4.00843e20 + 8.84991e20i) q^{95} +1.21305e21i q^{97} +4.99677e20i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20086410 q^{4} - 24944730 q^{5}+O(q^{10}) $ 20 * q - 20086410 * q^4 - 24944730 * q^5	$ 20 q - 20086410 q^{4} - 24944730 q^{5} - 1467444110 q^{10} - 11952443580 q^{11} + 3210119749140 q^{14} + 12123723095650 q^{16} + 152310844352560 q^{19} + 228448186221420 q^{20} + 141329092021400 q^{25} - 573110662319340 q^{26} - 51\!\cdots\!20 q^{29}+ \cdots - 23\!\cdots\!80 q^{95}+O(q^{100}) $ 20 * q - 20086410 * q^4 - 24944730 * q^5 - 1467444110 * q^10 - 11952443580 * q^11 + 3210119749140 * q^14 + 12123723095650 * q^16 + 152310844352560 * q^19 + 228448186221420 * q^20 + 141329092021400 * q^25 - 573110662319340 * q^26 - 5107306321462020 * q^29 - 11159342729449880 * q^31 - 72571936852862020 * q^34 - 71677038226172100 * q^35 - 324600549297895630 * q^40 + 314639459012042880 * q^41 + 98237641547534580 * q^44 - 476906572076519080 * q^46 - 907385772904909900 * q^49 - 1517876347798174200 * q^50 + 579473028579091680 * q^55 + 10293031248027060900 * q^56 + 9872270243072647260 * q^59 - 8886161742014816600 * q^61 + 29754567216376186910 * q^64 - 8919287112899553420 * q^65 + 115367644795510161000 * q^70 + 149325449942773260360 * q^71 - 260498047093221036060 * q^74 - 517472967324760441440 * q^76 + 98261416021599286600 * q^79 - 734236820229361105020 * q^80 + 1145807312247924282220 * q^85 + 2014542545589414764520 * q^86 - 1144207953427983163560 * q^89 - 3339621670514393150280 * q^91 + 3342639440249393189840 * q^94 - 2334023656701886699680 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	2387.58i		−	1.64871i	−0.566077	−	0.824353i	$-0.691539\pi$
$2$		−	2387.58i		−	1.64871i	0.566077	−	0.824353i	$-0.308461\pi$
$3$		0			0
$3$		0			0
$4$	−3.60339e6			−1.71823
$5$	−9.00948e6	+	1.98914e7i	−0.412586	+	0.910919i
$5$	−9.00948e6	+	1.98914e7i	−0.412586	+	0.910919i
$6$		0			0
$7$			8.76258e8i			1.17247i	0.810140	+	0.586236i	$0.199391\pi$
$7$			8.76258e8i			1.17247i	−0.810140	+	0.586236i	$0.800609\pi$
$8$			3.59626e9i			1.18415i
$9$		0			0
$10$	4.74922e10	+	2.15109e10i	1.50184	+	0.680233i
$11$	1.10419e11			1.28357			0.641784	−	0.766886i	$-0.278195\pi$
$11$	1.10419e11			1.28357			0.641784	+	0.766886i	$0.278195\pi$
$12$		0			0
$13$			6.22087e11i			1.25154i	0.780006	+	0.625772i	$0.215216\pi$
$13$			6.22087e11i			1.25154i	−0.780006	+	0.625772i	$0.784784\pi$
$14$	2.09214e12			1.93306
$15$		0			0
$16$	1.02950e12			0.234082
$17$			6.51559e12i			0.783863i	0.919994	+	0.391931i	$0.128193\pi$
$17$			6.51559e12i			0.783863i	−0.919994	+	0.391931i	$0.871807\pi$
$18$		0			0
$19$	4.44912e13			1.66480			0.832399	−	0.554177i	$-0.186967\pi$
$19$	4.44912e13			1.66480			0.832399	+	0.554177i	$0.186967\pi$
$20$	3.24646e13	−	7.16763e13i	0.708917	−	1.56517i
$21$		0			0
$22$		−	2.63633e14i		−	2.11622i
$23$			2.65057e14i			1.33413i	0.745001	+	0.667063i	$0.232449\pi$
$23$			2.65057e14i			1.33413i	−0.745001	+	0.667063i	$0.767551\pi$
$24$		0			0
$25$	−3.14496e14	−	3.58422e14i	−0.659545	−	0.751665i
$26$	1.48528e15			2.06343
$27$		0			0
$28$		−	3.15750e15i		−	2.01458i
$29$	−1.28018e15			−0.565056			−0.282528	−	0.959259i	$-0.591173\pi$
$29$	−1.28018e15			−0.565056			−0.282528	+	0.959259i	$0.591173\pi$
$30$		0			0
$31$	−5.90644e15			−1.29428			−0.647140	−	0.762371i	$-0.724035\pi$
$31$	−5.90644e15			−1.29428			−0.647140	+	0.762371i	$0.724035\pi$
$32$			5.08388e15i			0.798216i
$33$		0			0
$34$	1.55565e16			1.29236
$35$	−1.74300e16	−	7.89463e15i	−1.06803	−	0.483746i
$36$		0			0
$37$		−	3.24650e16i		−	1.10993i	−0.831872	−	0.554967i	$-0.812731\pi$
$37$		−	3.24650e16i		−	1.10993i	0.831872	−	0.554967i	$-0.187269\pi$
$38$		−	1.06226e17i		−	2.74476i
$39$		0			0
$40$	−7.15345e16	−	3.24004e16i	−1.07866	−	0.488563i
$41$	4.85384e16			0.564749			0.282374	−	0.959304i	$-0.408878\pi$
$41$	4.85384e16			0.564749			0.282374	+	0.959304i	$0.408878\pi$
$42$		0			0
$43$		−	5.89988e16i		−	0.416317i	−0.978095	−	0.208159i	$-0.933253\pi$
$43$		−	5.89988e16i		−	0.416317i	0.978095	−	0.208159i	$-0.0667470\pi$
$44$	−3.97881e17			−2.20546
$45$		0			0
$46$	6.32845e17			2.19958
$47$			3.80793e17i			1.05600i	0.849246	+	0.527998i	$0.177057\pi$
$47$			3.80793e17i			1.05600i	−0.849246	+	0.527998i	$0.822943\pi$
$48$		0			0
$49$	−2.09282e17			−0.374691
$50$	−8.55761e17	+	7.50884e17i	−1.23927	+	1.08740i
$51$		0			0
$52$		−	2.24162e18i		−	2.15044i
$53$			7.98759e17i			0.627363i	0.949528	+	0.313682i	$0.101562\pi$
$53$			7.98759e17i			0.627363i	−0.949528	+	0.313682i	$0.898438\pi$
$54$		0			0
$55$	−9.94813e17	+	2.19637e18i	−0.529582	+	1.16923i
$56$	−3.15125e18			−1.38838
$57$		0			0
$58$			3.05653e18i			0.931611i
$59$	3.84138e17			0.0978455			0.0489227	−	0.998803i	$-0.484421\pi$
$59$	3.84138e17			0.0978455			0.0489227	+	0.998803i	$0.484421\pi$
$60$		0			0
$61$	3.61141e18			0.648207			0.324104	−	0.946022i	$-0.394937\pi$
$61$	3.61141e18			0.648207			0.324104	+	0.946022i	$0.394937\pi$
$62$			1.41021e19i			2.13389i
$63$		0			0
$64$	1.42972e19			1.55010
$65$	−1.23742e19	−	5.60468e18i	−1.14005	−	0.516370i
$66$		0			0
$67$			9.40156e18i			0.630107i	0.949074	+	0.315054i	$0.102022\pi$
$67$			9.40156e18i			0.630107i	−0.949074	+	0.315054i	$0.897978\pi$
$68$		−	2.34782e19i		−	1.34686i
$69$		0			0
$70$	−1.88491e19	+	4.16154e19i	−0.797554	+	1.76086i
$71$	−8.73489e18			−0.318453			−0.159226	−	0.987242i	$-0.550900\pi$
$71$	−8.73489e18			−0.318453			−0.159226	+	0.987242i	$0.550900\pi$
$72$		0			0
$73$		−	4.81680e19i		−	1.31180i	−0.754847	−	0.655901i	$-0.772289\pi$
$73$		−	4.81680e19i		−	1.31180i	0.754847	−	0.655901i	$-0.227711\pi$
$74$	−7.75127e19			−1.82995
$75$		0			0
$76$	−1.60319e20			−2.86050
$77$			9.67551e19i			1.50495i
$78$		0			0
$79$	−8.49792e19			−1.00978			−0.504892	−	0.863183i	$-0.668468\pi$
$79$	−8.49792e19			−1.00978			−0.504892	+	0.863183i	$0.668468\pi$
$80$	−9.27527e18	+	2.04782e19i	−0.0965788	+	0.213229i
$81$		0			0
$82$		−	1.15889e20i		−	0.931104i
$83$			1.25162e20i			0.885428i	0.896663	+	0.442714i	$0.145984\pi$
$83$			1.25162e20i			0.885428i	−0.896663	+	0.442714i	$0.854016\pi$
$84$		0			0
$85$	−1.29604e20	−	5.87021e19i	−0.714035	−	0.323411i
$86$	−1.40864e20			−0.686384
$87$		0			0
$88$			3.97093e20i			1.51993i
$89$	−1.17871e20			−0.400694			−0.200347	−	0.979725i	$-0.564207\pi$
$89$	−1.17871e20			−0.400694			−0.200347	+	0.979725i	$0.564207\pi$
$90$		0			0
$91$	−5.45109e20			−1.46740
$92$		−	9.55103e20i		−	2.29233i
$93$		0			0
$94$	9.09175e20			1.74102
$95$	−4.00843e20	+	8.84991e20i	−0.686872	+	1.51649i
$96$		0			0
$97$			1.21305e21i			1.67023i	0.550078	+	0.835113i	$0.314598\pi$
$97$			1.21305e21i			1.67023i	−0.550078	+	0.835113i	$0.685402\pi$
$98$			4.99677e20i			0.617755i
$99$		0			0
$100$	1.13325e21	+	1.29153e21i	1.13325	+	1.29153i
$101$	5.76859e20			0.519632			0.259816	−	0.965658i	$-0.416338\pi$
$101$	5.76859e20			0.519632			0.259816	+	0.965658i	$0.416338\pi$
$102$		0			0
$103$		−	2.55658e21i		−	1.87443i	−0.348756	−	0.937214i	$-0.613396\pi$
$103$		−	2.55658e21i		−	1.87443i	0.348756	−	0.937214i	$-0.386604\pi$
$104$	−2.23719e21			−1.48201
$105$		0			0
$106$	1.90710e21			1.03434
$107$			7.39775e19i			0.0363555i	0.999835	+	0.0181777i	$0.00578647\pi$
$107$			7.39775e19i			0.0363555i	−0.999835	+	0.0181777i	$0.994214\pi$
$108$		0			0
$109$	6.54607e20			0.264851			0.132426	−	0.991193i	$-0.457723\pi$
$109$	6.54607e20			0.264851			0.132426	+	0.991193i	$0.457723\pi$
$110$	5.24402e21	+	2.37520e21i	1.92771	+	0.873125i
$111$		0			0
$112$			9.02109e20i			0.274454i
$113$			1.60631e21i			0.445148i	0.974916	+	0.222574i	$0.0714460\pi$
$113$			1.60631e21i			0.445148i	−0.974916	+	0.222574i	$0.928554\pi$
$114$		0			0
$115$	−5.27235e21	−	2.38803e21i	−1.21528	−	0.550442i
$116$	4.61298e21			0.970896
$117$		0			0
$118$		−	9.17159e20i		−	0.161318i
$119$	−5.70933e21			−0.919057
$120$		0			0
$121$	4.79200e21			0.647545
$122$		−	8.62254e21i		−	1.06870i
$123$		0			0
$124$	2.12832e22			2.22387
$125$	9.96294e21	−	3.02656e21i	0.956825	−	0.290666i
$126$		0			0
$127$		−	1.38046e22i		−	1.12224i	−0.827735	−	0.561120i	$-0.810371\pi$
$127$		−	1.38046e22i		−	1.12224i	0.827735	−	0.561120i	$-0.189629\pi$
$128$		−	2.34740e22i		−	1.75745i
$129$		0			0
$130$	−1.33816e22	+	2.95443e22i	−0.851342	+	1.87961i
$131$	2.97523e22			1.74652			0.873258	−	0.487259i	$-0.162003\pi$
$131$	2.97523e22			1.74652			0.873258	+	0.487259i	$0.162003\pi$
$132$		0			0
$133$			3.89858e22i			1.95193i
$134$	2.24470e22			1.03886
$135$		0			0
$136$	−2.34317e22			−0.928209
$137$			1.31132e22i			0.480998i	0.970649	+	0.240499i	$0.0773111\pi$
$137$			1.31132e22i			0.480998i	−0.970649	+	0.240499i	$0.922689\pi$
$138$		0			0
$139$	3.83710e22			1.20878			0.604391	−	0.796688i	$-0.293417\pi$
$139$	3.83710e22			1.20878			0.604391	+	0.796688i	$0.293417\pi$
$140$	6.28069e22	+	2.84474e22i	1.83511	+	0.831186i
$141$		0			0
$142$			2.08552e22i			0.525034i
$143$			6.86900e22i			1.60644i
$144$		0			0
$145$	1.15337e22	−	2.54645e22i	0.233134	−	0.514720i
$146$	−1.15005e23			−2.16278
$147$		0			0
$148$			1.16984e23i			1.90712i
$149$	−1.00244e23			−1.52265			−0.761326	−	0.648369i	$-0.775452\pi$
$149$	−1.00244e23			−1.52265			−0.761326	+	0.648369i	$0.775452\pi$
$150$		0			0
$151$	−1.25747e23			−1.66050			−0.830250	−	0.557391i	$-0.811803\pi$
$151$	−1.25747e23			−1.66050			−0.830250	+	0.557391i	$0.811803\pi$
$152$			1.60002e23i			1.97137i
$153$		0			0
$154$	2.31011e23			2.48121
$155$	5.32140e22	−	1.17487e23i	0.534002	−	1.17898i
$156$		0			0
$157$			2.01217e23i			1.76489i	0.470413	+	0.882446i	$0.344105\pi$
$157$			2.01217e23i			1.76489i	−0.470413	+	0.882446i	$0.655895\pi$
$158$			2.02895e23i			1.66483i
$159$		0			0
$160$	−1.01125e23	−	4.58031e22i	−0.727110	−	0.329333i
$161$	−2.32258e23			−1.56423
$162$		0			0
$163$			4.19267e22i			0.248039i	0.992280	+	0.124020i	$0.0395786\pi$
$163$			4.19267e22i			0.248039i	−0.992280	+	0.124020i	$0.960421\pi$
$164$	−1.74903e23			−0.970368
$165$		0			0
$166$	2.98835e23			1.45981
$167$		−	3.15517e23i		−	1.44710i	−0.690270	−	0.723552i	$-0.742508\pi$
$167$		−	3.15517e23i		−	1.44710i	0.690270	−	0.723552i	$-0.257492\pi$
$168$		0			0
$169$	−1.39928e23			−0.566363
$170$	−1.40156e23	+	3.09440e23i	−0.533209	+	1.17723i
$171$		0			0
$172$			2.12596e23i			0.715328i
$173$		−	1.49085e23i		−	0.472008i	−0.971752	−	0.236004i	$-0.924162\pi$
$173$		−	1.49085e23i		−	0.472008i	0.971752	−	0.236004i	$-0.0758379\pi$
$174$		0			0
$175$	3.14070e23	−	2.75579e23i	0.881306	−	0.773298i
$176$	1.13676e23			0.300459
$177$		0			0
$178$			2.81427e23i			0.660626i
$179$	5.40567e23			1.19644			0.598222	−	0.801330i	$-0.295874\pi$
$179$	5.40567e23			1.19644			0.598222	+	0.801330i	$0.295874\pi$
$180$		0			0
$181$	−6.19144e23			−1.21946			−0.609729	−	0.792610i	$-0.708722\pi$
$181$	−6.19144e23			−1.21946			−0.609729	+	0.792610i	$0.708722\pi$
$182$			1.30149e24i			2.41931i
$183$		0			0
$184$	−9.53213e23			−1.57980
$185$	6.45773e23	+	2.92493e23i	1.01106	+	0.457943i
$186$		0			0
$187$			7.19441e23i			1.00614i
$188$		−	1.37215e24i		−	1.81444i
$189$		0			0
$190$	2.11299e24	+	9.57044e23i	2.50025	+	1.13245i
$191$	−2.44367e23			−0.273648			−0.136824	−	0.990595i	$-0.543690\pi$
$191$	−2.44367e23			−0.273648			−0.136824	+	0.990595i	$0.543690\pi$
$192$		0			0
$193$			4.25935e23i			0.427555i	0.976882	+	0.213777i	$0.0685767\pi$
$193$			4.25935e23i			0.427555i	−0.976882	+	0.213777i	$0.931423\pi$
$194$	2.89625e24			2.75371
$195$		0			0
$196$	7.54124e23			0.643804
$197$			7.93527e23i			0.642194i	0.947046	+	0.321097i	$0.104052\pi$
$197$			7.93527e23i			0.642194i	−0.947046	+	0.321097i	$0.895948\pi$
$198$		0			0
$199$	9.08298e23			0.661106			0.330553	−	0.943787i	$-0.392765\pi$
$199$	9.08298e23			0.661106			0.330553	+	0.943787i	$0.392765\pi$
$200$	1.28898e24	−	1.13101e24i	0.890082	−	0.780999i
$201$		0			0
$202$		−	1.37730e24i		−	0.856719i
$203$		−	1.12177e24i		−	0.662513i
$204$		0			0
$205$	−4.37306e23	+	9.65496e23i	−0.233008	+	0.514440i
$206$	−6.10404e24			−3.09038
$207$		0			0
$208$			6.40440e23i			0.292963i
$209$	4.91265e24			2.13688
$210$		0			0
$211$	−3.95450e24			−1.55642			−0.778208	−	0.628006i	$-0.783871\pi$
$211$	−3.95450e24			−1.55642			−0.778208	+	0.628006i	$0.783871\pi$
$212$		−	2.87824e24i		−	1.07795i
$213$		0			0
$214$	1.76627e23			0.0599395
$215$	1.17357e24	+	5.31549e23i	0.379231	+	0.171767i
$216$		0			0
$217$		−	5.17557e24i		−	1.51751i
$218$		−	1.56293e24i		−	0.436662i
$219$		0			0
$220$	3.58470e24	−	7.91439e24i	0.909943	−	2.00900i
$221$	−4.05326e24			−0.981039
$222$		0			0
$223$		−	4.82026e24i		−	1.06138i	−0.847567	−	0.530688i	$-0.821933\pi$
$223$		−	4.82026e24i		−	1.06138i	0.847567	−	0.530688i	$-0.178067\pi$
$224$	−4.45479e24			−0.935886
$225$		0			0
$226$	3.83519e24			0.733918
$227$		−	4.54756e23i		−	0.0830820i	−0.999137	−	0.0415410i	$-0.986773\pi$
$227$		−	4.54756e23i		−	0.0830820i	0.999137	−	0.0415410i	$-0.0132267\pi$
$228$		0			0
$229$	−3.15414e24			−0.525543			−0.262772	−	0.964858i	$-0.584637\pi$
$229$	−3.15414e24			−0.525543			−0.262772	+	0.964858i	$0.584637\pi$
$230$	−5.70160e24	+	1.25881e25i	−0.907517	+	2.00364i
$231$		0			0
$232$		−	4.60385e24i		−	0.669110i
$233$			2.56872e24i			0.356845i	0.983954	+	0.178422i	$0.0570993\pi$
$233$			2.56872e24i			0.356845i	−0.983954	+	0.178422i	$0.942901\pi$
$234$		0			0
$235$	−7.57450e24	−	3.43075e24i	−0.961925	−	0.435689i
$236$	−1.38420e24			−0.168121
$237$		0			0
$238$			1.36315e25i			1.51525i
$239$	−2.06378e24			−0.219525			−0.109763	−	0.993958i	$-0.535009\pi$
$239$	−2.06378e24			−0.219525			−0.109763	+	0.993958i	$0.535009\pi$
$240$		0			0
$241$	−2.79054e24			−0.271963			−0.135982	−	0.990711i	$-0.543419\pi$
$241$	−2.79054e24			−0.271963			−0.135982	+	0.990711i	$0.543419\pi$
$242$		−	1.14413e25i		−	1.06761i
$243$		0			0
$244$	−1.30133e25			−1.11377
$245$	1.88552e24	−	4.16290e24i	0.154592	−	0.341313i
$246$		0			0
$247$			2.76774e25i			2.08357i
$248$		−	2.12411e25i		−	1.53262i
$249$		0			0
$250$	−7.22615e24	−	2.37873e25i	−0.479222	−	1.57752i
$251$	−2.77647e25			−1.76571			−0.882854	−	0.469648i	$-0.844381\pi$
$251$	−2.77647e25			−1.76571			−0.882854	+	0.469648i	$0.844381\pi$
$252$		0			0
$253$			2.92672e25i			1.71244i
$254$	−3.29596e25			−1.85024
$255$		0			0
$256$	−2.60627e25			−1.34741
$257$			3.62323e25i			1.79804i	0.437910	+	0.899019i	$0.355719\pi$
$257$			3.62323e25i			1.79804i	−0.437910	+	0.899019i	$0.644281\pi$
$258$		0			0
$259$	2.84477e25			1.30137
$260$	4.45889e25	+	2.01958e25i	1.95887	+	0.887241i
$261$		0			0
$262$		−	7.10361e25i		−	2.87949i
$263$		−	3.27196e25i		−	1.27430i	−0.770739	−	0.637151i	$-0.780113\pi$
$263$		−	3.27196e25i		−	1.27430i	0.770739	−	0.637151i	$-0.219887\pi$
$264$		0			0
$265$	−1.58884e25	−	7.19640e24i	−0.571477	−	0.258841i
$266$	9.30817e25			3.21815
$267$		0			0
$268$		−	3.38775e25i		−	1.08267i
$269$	−1.90716e25			−0.586121			−0.293061	−	0.956094i	$-0.594674\pi$
$269$	−1.90716e25			−0.586121			−0.293061	+	0.956094i	$0.594674\pi$
$270$		0			0
$271$	−5.72060e25			−1.62654			−0.813268	−	0.581889i	$-0.802314\pi$
$271$	−5.72060e25			−1.62654			−0.813268	+	0.581889i	$0.802314\pi$
$272$			6.70781e24i			0.183488i
$273$		0			0
$274$	3.13089e25			0.793024
$275$	−3.47261e25	−	3.95764e25i	−0.846571	−	0.964812i
$276$		0			0
$277$		−	1.19508e25i		−	0.269998i	−0.990846	−	0.134999i	$-0.956897\pi$
$277$		−	1.19508e25i		−	0.269998i	0.990846	−	0.134999i	$-0.0431030\pi$
$278$		−	9.16138e25i		−	1.99292i
$279$		0			0
$280$	2.83911e25	−	6.26826e25i	0.572826	−	1.26470i
$281$	2.63635e25			0.512374			0.256187	−	0.966627i	$-0.417534\pi$
$281$	2.63635e25			0.512374			0.256187	+	0.966627i	$0.417534\pi$
$282$		0			0
$283$		−	7.88642e24i		−	0.142273i	−0.997467	−	0.0711365i	$-0.977337\pi$
$283$		−	7.88642e24i		−	0.142273i	0.997467	−	0.0711365i	$-0.0226626\pi$
$284$	3.14752e25			0.547174
$285$		0			0
$286$	1.64003e26			2.64855
$287$			4.25322e25i			0.662152i
$288$		0			0
$289$	2.66391e25			0.385560
$290$	−6.07986e25	−	2.75378e25i	−0.848622	−	0.384370i
$291$		0			0
$292$			1.73568e26i			2.25398i
$293$			8.38525e25i			1.05052i	0.850941	+	0.525262i	$0.176033\pi$
$293$			8.38525e25i			1.05052i	−0.850941	+	0.525262i	$0.823967\pi$
$294$		0			0
$295$	−3.46088e24	+	7.64102e24i	−0.0403697	+	0.0891292i
$296$	1.16752e26			1.31433
$297$		0			0
$298$			2.39340e26i			2.51041i
$299$	−1.64889e26			−1.66972
$300$		0			0
$301$	5.16982e25			0.488120
$302$			3.00231e26i			2.73768i
$303$		0			0
$304$	4.58038e25			0.389698
$305$	−3.25370e25	+	7.18359e25i	−0.267441	+	0.590464i
$306$		0			0
$307$			1.09880e26i			0.843269i	0.906766	+	0.421634i	$0.138543\pi$
$307$			1.09880e26i			0.843269i	−0.906766	+	0.421634i	$0.861457\pi$
$308$		−	3.48646e26i		−	2.58584i
$309$		0			0
$310$	−2.80510e26	−	1.27053e26i	−1.94380	−	0.880412i
$311$	3.92080e25			0.262658			0.131329	−	0.991339i	$-0.458076\pi$
$311$	3.92080e25			0.262658			0.131329	+	0.991339i	$0.458076\pi$
$312$		0			0
$313$		−	2.47324e26i		−	1.54900i	−0.632577	−	0.774498i	$-0.718003\pi$
$313$		−	2.47324e26i		−	1.54900i	0.632577	−	0.774498i	$-0.281997\pi$
$314$	4.80422e26			2.90979
$315$		0			0
$316$	3.06213e26			1.73504
$317$		−	7.89343e25i		−	0.432657i	−0.976321	−	0.216328i	$-0.930592\pi$
$317$		−	7.89343e25i		−	0.432657i	0.976321	−	0.216328i	$-0.0694082\pi$
$318$		0			0
$319$	−1.41355e26			−0.725288
$320$	−1.28810e26	+	2.84391e26i	−0.639552	+	1.41202i
$321$		0			0
$322$			5.54535e26i			2.57895i
$323$			2.89886e26i			1.30497i
$324$		0			0
$325$	2.22970e26	−	1.95644e26i	0.940742	−	0.825450i
$326$	1.00103e26			0.408944
$327$		0			0
$328$			1.74557e26i			0.668746i
$329$	−3.33673e26			−1.23812
$330$		0			0
$331$	−2.32921e26			−0.810988			−0.405494	−	0.914098i	$-0.632900\pi$
$331$	−2.32921e26			−0.810988			−0.405494	+	0.914098i	$0.632900\pi$
$332$		−	4.51008e26i		−	1.52137i
$333$		0			0
$334$	−7.53322e26			−2.38585
$335$	−1.87010e26	−	8.47031e25i	−0.573976	−	0.259973i
$336$		0			0
$337$		−	1.21446e24i		−	0.00350161i	−0.999998	−	0.00175081i	$-0.999443\pi$
$337$		−	1.21446e24i		−	0.00350161i	0.999998	−	0.00175081i	$-0.000557299\pi$
$338$			3.34090e26i			0.933765i
$339$		0			0
$340$	4.67013e26	+	2.11526e26i	1.22688	+	0.555694i
$341$	−6.52181e26			−1.66130
$342$		0			0
$343$			3.06045e26i			0.733158i
$344$	2.12175e26			0.492981
$345$		0			0
$346$	−3.55952e26			−0.778203
$347$			7.09460e26i			1.50476i	0.658727	+	0.752382i	$0.271095\pi$
$347$			7.09460e26i			1.50476i	−0.658727	+	0.752382i	$0.728905\pi$
$348$		0			0
$349$	−5.40523e26			−1.07931			−0.539656	−	0.841886i	$-0.681446\pi$
$349$	−5.40523e26			−1.07931			−0.539656	+	0.841886i	$0.681446\pi$
$350$	−6.57968e26	−	7.49867e26i	−1.27494	−	1.45301i
$351$		0			0
$352$			5.61354e26i			1.02456i
$353$		−	4.72052e26i		−	0.836287i	−0.908381	−	0.418144i	$-0.862681\pi$
$353$		−	4.72052e26i		−	0.836287i	0.908381	−	0.418144i	$-0.137319\pi$
$354$		0			0
$355$	7.86968e25	−	1.73749e26i	0.131389	−	0.290084i
$356$	4.24736e26			0.688484
$357$		0			0
$358$		−	1.29065e27i		−	1.97258i
$359$	−3.20233e26			−0.475307			−0.237653	−	0.971350i	$-0.576378\pi$
$359$	−3.20233e26			−0.475307			−0.237653	+	0.971350i	$0.576378\pi$
$360$		0			0
$361$	1.26526e27			1.77155
$362$			1.47826e27i			2.01053i
$363$		0			0
$364$	1.96424e27			2.52133
$365$	9.58127e26	+	4.33968e26i	1.19495	+	0.541232i
$366$		0			0
$367$			5.97709e26i			0.703876i	0.936023	+	0.351938i	$0.114477\pi$
$367$			5.97709e26i			0.703876i	−0.936023	+	0.351938i	$0.885523\pi$
$368$			2.72877e26i			0.312294i
$369$		0			0
$370$	6.98349e26	−	1.54183e27i	0.755013	−	1.66694i
$371$	−6.99919e26			−0.735566
$372$		0			0
$373$			1.06103e27i			1.05386i	0.849908	+	0.526932i	$0.176658\pi$
$373$			1.06103e27i			1.05386i	−0.849908	+	0.526932i	$0.823342\pi$
$374$	1.71772e27			1.65883
$375$		0			0
$376$	−1.36943e27			−1.25045
$377$		−	7.96383e26i		−	0.707193i
$378$		0			0
$379$	2.28626e26			0.192050			0.0960248	−	0.995379i	$-0.469387\pi$
$379$	2.28626e26			0.192050			0.0960248	+	0.995379i	$0.469387\pi$
$380$	1.44439e27	−	3.18896e27i	1.18020	−	2.60569i
$381$		0			0
$382$			5.83446e26i			0.451165i
$383$			1.31136e27i			0.986587i	0.869863	+	0.493293i	$0.164207\pi$
$383$			1.31136e27i			0.986587i	−0.869863	+	0.493293i	$0.835793\pi$
$384$		0			0
$385$	−1.92459e27	−	8.71713e26i	−1.37088	−	0.620920i
$386$	1.01695e27			0.704911
$387$		0			0
$388$		−	4.37109e27i		−	2.86983i
$389$	−1.54163e27			−0.985164			−0.492582	−	0.870266i	$-0.663947\pi$
$389$	−1.54163e27			−0.985164			−0.492582	+	0.870266i	$0.663947\pi$
$390$		0			0
$391$	−1.72700e27			−1.04577
$392$		−	7.52632e26i		−	0.443689i
$393$		0			0
$394$	1.89461e27			1.05879
$395$	7.65618e26	−	1.69035e27i	0.416623	−	0.919830i
$396$		0			0
$397$			2.00697e27i			1.03572i	0.855467	+	0.517858i	$0.173270\pi$
$397$			2.00697e27i			1.03572i	−0.855467	+	0.517858i	$0.826730\pi$
$398$		−	2.16863e27i		−	1.08997i
$399$		0			0
$400$	−3.23774e26	−	3.68996e26i	−0.154387	−	0.175951i
$401$	−1.45786e27			−0.677174			−0.338587	−	0.940935i	$-0.609949\pi$
$401$	−1.45786e27			−0.677174			−0.338587	+	0.940935i	$0.609949\pi$
$402$		0			0
$403$		−	3.67432e27i		−	1.61985i
$404$	−2.07865e27			−0.892846
$405$		0			0
$406$	−2.67831e27			−1.09229
$407$		−	3.58473e27i		−	1.42467i
$408$		0			0
$409$	4.07184e26			0.153708			0.0768539	−	0.997042i	$-0.475513\pi$
$409$	4.07184e26			0.153708			0.0768539	+	0.997042i	$0.475513\pi$
$410$	2.30520e27	+	1.04410e27i	0.848160	+	0.384161i
$411$		0			0
$412$			9.21235e27i			3.22069i
$413$			3.36604e26i			0.114721i
$414$		0			0
$415$	−2.48965e27	−	1.12765e27i	−0.806552	−	0.365315i
$416$	−3.16262e27			−0.999003
$417$		0			0
$418$		−	1.17294e28i		−	3.52308i
$419$	6.24808e27			1.83020			0.915102	−	0.403222i	$-0.132110\pi$
$419$	6.24808e27			1.83020			0.915102	+	0.403222i	$0.132110\pi$
$420$		0			0
$421$	−2.35871e26			−0.0657222			−0.0328611	−	0.999460i	$-0.510462\pi$
$421$	−2.35871e26			−0.0657222			−0.0328611	+	0.999460i	$0.510462\pi$
$422$			9.44169e27i			2.56607i
$423$		0			0
$424$	−2.87254e27			−0.742891
$425$	2.33533e27	−	2.04912e27i	0.589202	−	0.516993i
$426$		0			0
$427$			3.16453e27i			0.760005i
$428$		−	2.66569e26i		−	0.0624670i
$429$		0			0
$430$	1.26911e27	−	2.80198e27i	0.283193	−	0.625240i
$431$	−4.15650e27			−0.905142			−0.452571	−	0.891728i	$-0.649493\pi$
$431$	−4.15650e27			−0.905142			−0.452571	+	0.891728i	$0.649493\pi$
$432$		0			0
$433$		−	5.57069e26i		−	0.115554i	−0.998330	−	0.0577771i	$-0.981599\pi$
$433$		−	5.57069e26i		−	0.115554i	0.998330	−	0.0577771i	$-0.0184013\pi$
$434$	−1.23571e28			−2.50192
$435$		0			0
$436$	−2.35880e27			−0.455075
$437$			1.17927e28i			2.22105i
$438$		0			0
$439$	2.53634e27			0.455333			0.227667	−	0.973739i	$-0.426890\pi$
$439$	2.53634e27			0.455333			0.227667	+	0.973739i	$0.426890\pi$
$440$	−7.89873e27	−	3.57760e27i	−1.38454	−	0.627103i
$441$		0			0
$442$			9.67749e27i			1.61744i
$443$			2.56725e27i			0.419014i	0.977807	+	0.209507i	$0.0671859\pi$
$443$			2.56725e27i			0.419014i	−0.977807	+	0.209507i	$0.932814\pi$
$444$		0			0
$445$	1.06196e27	−	2.34462e27i	0.165321	−	0.365000i
$446$	−1.15088e28			−1.74990
$447$		0			0
$448$			1.25280e28i			1.81745i
$449$	7.06573e27			1.00131			0.500657	−	0.865646i	$-0.333092\pi$
$449$	7.06573e27			1.00131			0.500657	+	0.865646i	$0.333092\pi$
$450$		0			0
$451$	5.35954e27			0.724893
$452$		−	5.78814e27i		−	0.764867i
$453$		0			0
$454$	−1.08577e27			−0.136978
$455$	4.91115e27	−	1.08430e28i	0.605429	−	1.33668i
$456$		0			0
$457$		−	6.21874e27i		−	0.732120i	−0.930591	−	0.366060i	$-0.880707\pi$
$457$		−	6.21874e27i		−	0.732120i	0.930591	−	0.366060i	$-0.119293\pi$
$458$			7.53076e27i			0.866466i
$459$		0			0
$460$	1.89983e28	+	8.60498e27i	2.08813	+	0.945786i
$461$	1.49683e28			1.60810			0.804051	−	0.594560i	$-0.202674\pi$
$461$	1.49683e28			1.60810			0.804051	+	0.594560i	$0.202674\pi$
$462$		0			0
$463$			3.94663e27i			0.405159i	0.979266	+	0.202580i	$0.0649325\pi$
$463$			3.94663e27i			0.405159i	−0.979266	+	0.202580i	$0.935067\pi$
$464$	−1.31795e27			−0.132269
$465$		0			0
$466$	6.13302e27			0.588331
$467$		−	8.85697e27i		−	0.830726i	−0.909656	−	0.415363i	$-0.863655\pi$
$467$		−	8.85697e27i		−	0.830726i	0.909656	−	0.415363i	$-0.136345\pi$
$468$		0			0
$469$	−8.23819e27			−0.738783
$470$	−8.19119e27	+	1.80847e28i	−0.718323	+	1.58593i
$471$		0			0
$472$			1.38146e27i			0.115863i
$473$		−	6.51456e27i		−	0.534371i
$474$		0			0
$475$	−1.39923e28	−	1.59466e28i	−1.09801	−	1.25137i
$476$	2.05729e28			1.57915
$477$		0			0
$478$			4.92743e27i			0.361933i
$479$	1.14619e28			0.823631			0.411816	−	0.911267i	$-0.364895\pi$
$479$	1.14619e28			0.823631			0.411816	+	0.911267i	$0.364895\pi$
$480$		0			0
$481$	2.01961e28			1.38913
$482$			6.66265e27i			0.448387i
$483$		0			0
$484$	−1.72674e28			−1.11263
$485$	−2.41292e28	−	1.09289e28i	−1.52144	−	0.689112i
$486$		0			0
$487$		−	1.56047e28i		−	0.942326i	−0.882046	−	0.471163i	$-0.843834\pi$
$487$		−	1.56047e28i		−	0.942326i	0.882046	−	0.471163i	$-0.156166\pi$
$488$			1.29876e28i			0.767573i
$489$		0			0
$490$	−9.93927e27	−	4.50183e27i	−0.562724	−	0.254877i
$491$	6.12854e27			0.339626			0.169813	−	0.985476i	$-0.445684\pi$
$491$	6.12854e27			0.339626			0.169813	+	0.985476i	$0.445684\pi$
$492$		0			0
$493$		−	8.34112e27i		−	0.442927i
$494$	6.60821e28			3.43519
$495$		0			0
$496$	−6.08069e27			−0.302967
$497$		−	7.65402e27i		−	0.373377i
$498$		0			0
$499$	−3.53336e27			−0.165247			−0.0826233	−	0.996581i	$-0.526330\pi$
$499$	−3.53336e27			−0.165247			−0.0826233	+	0.996581i	$0.526330\pi$
$500$	−3.59003e28	+	1.09059e28i	−1.64404	+	0.499430i
$501$		0			0
$502$			6.62904e28i			2.91113i
$503$		−	1.55458e28i		−	0.668575i	−0.942471	−	0.334287i	$-0.891504\pi$
$503$		−	1.55458e28i		−	0.668575i	0.942471	−	0.334287i	$-0.108496\pi$
$504$		0			0
$505$	−5.19720e27	+	1.14745e28i	−0.214393	+	0.473342i
$506$	6.98778e28			2.82331
$507$		0			0
$508$			4.97434e28i			1.92826i
$509$	−2.47938e27			−0.0941469			−0.0470735	−	0.998891i	$-0.514989\pi$
$509$	−2.47938e27			−0.0941469			−0.0470735	+	0.998891i	$0.514989\pi$
$510$		0			0
$511$	4.22076e28			1.53805
$512$			1.29983e28i			0.464035i
$513$		0			0
$514$	8.65076e28			2.96443
$515$	5.08539e28	+	2.30335e28i	1.70745	+	0.773363i
$516$		0			0
$517$			4.20466e28i			1.35544i
$518$		−	6.79211e28i		−	2.14557i
$519$		0			0
$520$	2.01559e28	−	4.45007e28i	0.611458	−	1.34999i
$521$	−5.55830e28			−1.65252			−0.826258	−	0.563292i	$-0.809535\pi$
$521$	−5.55830e28			−1.65252			−0.826258	+	0.563292i	$0.809535\pi$
$522$		0			0
$523$		−	1.46478e27i		−	0.0418315i	−0.999781	−	0.0209158i	$-0.993342\pi$
$523$		−	1.46478e27i		−	0.0418315i	0.999781	−	0.0209158i	$-0.00665818\pi$
$524$	−1.07209e29			−3.00091
$525$		0			0
$526$	−7.81207e28			−2.10095
$527$		−	3.84839e28i		−	1.01454i
$528$		0			0
$529$	−3.07836e28			−0.779893
$530$	−1.71820e28	+	3.79348e28i	−0.426753	+	0.942197i
$531$		0			0
$532$		−	1.40481e29i		−	3.35386i
$533$			3.01952e28i			0.706808i
$534$		0			0
$535$	−1.47151e27	−	6.66498e26i	−0.0331169	−	0.0149998i
$536$	−3.38104e28			−0.746140
$537$		0			0
$538$			4.55349e28i			0.966341i
$539$	−2.31086e28			−0.480941
$540$		0			0
$541$	6.62234e28			1.32569			0.662843	−	0.748759i	$-0.269350\pi$
$541$	6.62234e28			1.32569			0.662843	+	0.748759i	$0.269350\pi$
$542$			1.36584e29i			2.68168i
$543$		0			0
$544$	−3.31245e28			−0.625692
$545$	−5.89767e27	+	1.30210e28i	−0.109274	+	0.241258i
$546$		0			0
$547$		−	8.00185e28i		−	1.42667i	−0.700823	−	0.713335i	$-0.747184\pi$
$547$		−	8.00185e28i		−	1.42667i	0.700823	−	0.713335i	$-0.252816\pi$
$548$		−	4.72520e28i		−	0.826465i
$549$		0			0
$550$	−9.44918e28	+	8.29115e28i	−1.59069	+	1.39575i
$551$	−5.69567e28			−0.940704
$552$		0			0
$553$		−	7.44637e28i		−	1.18394i
$554$	−2.85335e28			−0.445146
$555$		0			0
$556$	−1.38266e29			−2.07696
$557$			5.93633e28i			0.875062i	0.899203	+	0.437531i	$0.144147\pi$
$557$			5.93633e28i			0.875062i	−0.899203	+	0.437531i	$0.855853\pi$
$558$		0			0
$559$	3.67024e28			0.521039
$560$	−1.79442e28	−	8.12753e27i	−0.250005	−	0.113236i
$561$		0			0
$562$		−	6.29450e28i		−	0.844753i
$563$		−	2.16875e28i		−	0.285674i	−0.989746	−	0.142837i	$-0.954377\pi$
$563$		−	2.16875e28i		−	0.285674i	0.989746	−	0.142837i	$-0.0456225\pi$
$564$		0			0
$565$	−3.19516e28	−	1.44720e28i	−0.405494	−	0.183662i
$566$	−1.88295e28			−0.234566
$567$		0			0
$568$		−	3.14129e28i		−	0.377095i
$569$	−1.70076e28			−0.200431			−0.100215	−	0.994966i	$-0.531953\pi$
$569$	−1.70076e28			−0.200431			−0.100215	+	0.994966i	$0.531953\pi$
$570$		0			0
$571$	−4.09152e28			−0.464736			−0.232368	−	0.972628i	$-0.574647\pi$
$571$	−4.09152e28			−0.464736			−0.232368	+	0.972628i	$0.574647\pi$
$572$		−	2.47516e29i		−	2.76023i
$573$		0			0
$574$	1.01549e29			1.09169
$575$	9.50022e28	−	8.33593e28i	1.00282	−	0.879917i
$576$		0			0
$577$		−	1.54135e29i		−	1.56876i	−0.620281	−	0.784380i	$-0.712981\pi$
$577$		−	1.54135e29i		−	1.56876i	0.620281	−	0.784380i	$-0.287019\pi$
$578$		−	6.36029e28i		−	0.635674i
$579$		0			0
$580$	−4.15606e28	+	9.17585e28i	−0.400578	+	0.884407i
$581$	−1.09674e29			−1.03814
$582$		0			0
$583$			8.81977e28i			0.805263i
$584$	1.73224e29			1.55337
$585$		0			0
$586$	2.00204e29			1.73200
$587$		−	4.81480e28i		−	0.409146i	−0.978851	−	0.204573i	$-0.934419\pi$
$587$		−	4.81480e28i		−	0.409146i	0.978851	−	0.204573i	$-0.0655806\pi$
$588$		0			0
$589$	−2.62785e29			−2.15471
$590$	1.82436e28	+	8.26313e27i	0.146948	+	0.0665577i
$591$		0			0
$592$		−	3.34227e28i		−	0.259815i
$593$			7.07719e28i			0.540489i	0.962792	+	0.270244i	$0.0871045\pi$
$593$			7.07719e28i			0.540489i	−0.962792	+	0.270244i	$0.912895\pi$
$594$		0			0
$595$	5.14381e28	−	1.13566e29i	0.379190	−	0.837186i
$596$	3.61217e29			2.61627
$597$		0			0
$598$			3.93685e29i			2.75287i
$599$	1.82931e29			1.25692			0.628458	−	0.777844i	$-0.283687\pi$
$599$	1.82931e29			1.25692			0.628458	+	0.777844i	$0.283687\pi$
$600$		0			0
$601$	−1.82502e29			−1.21084			−0.605419	−	0.795907i	$-0.706994\pi$
$601$	−1.82502e29			−1.21084			−0.605419	+	0.795907i	$0.706994\pi$
$602$		−	1.23434e29i		−	0.804767i
$603$		0			0
$604$	4.53114e29			2.85312
$605$	−4.31734e28	+	9.53193e28i	−0.267168	+	0.589861i
$606$		0			0
$607$		−	1.98079e29i		−	1.18401i	−0.805933	−	0.592007i	$-0.798336\pi$
$607$		−	1.98079e29i		−	1.18401i	0.805933	−	0.592007i	$-0.201664\pi$
$608$			2.26188e29i			1.32887i
$609$		0			0
$610$	1.71514e29	+	7.76846e28i	0.973501	+	0.440932i
$611$	−2.36887e29			−1.32162
$612$		0			0
$613$		−	1.05402e29i		−	0.568215i	−0.958792	−	0.284108i	$-0.908303\pi$
$613$		−	1.05402e29i		−	0.568215i	0.958792	−	0.284108i	$-0.0916973\pi$
$614$	2.62348e29			1.39030
$615$		0			0
$616$	−3.47956e29			−1.78208
$617$		−	2.71351e29i		−	1.36627i	−0.730291	−	0.683136i	$-0.760616\pi$
$617$		−	2.71351e29i		−	1.36627i	0.730291	−	0.683136i	$-0.239384\pi$
$618$		0			0
$619$	1.34723e29			0.655677			0.327839	−	0.944734i	$-0.393680\pi$
$619$	1.34723e29			0.655677			0.327839	+	0.944734i	$0.393680\pi$
$620$	−1.91751e29	+	4.23352e29i	−0.917538	+	2.02576i
$621$		0			0
$622$		−	9.36124e28i		−	0.433046i
$623$		−	1.03286e29i		−	0.469803i
$624$		0			0
$625$	−2.95586e28	+	2.25444e29i	−0.130000	+	0.991514i
$626$	−5.90505e29			−2.55384
$627$		0			0
$628$		−	7.25063e29i		−	3.03249i
$629$	2.11528e29			0.870035
$630$		0			0
$631$	−2.19411e29			−0.872870			−0.436435	−	0.899736i	$-0.643759\pi$
$631$	−2.19411e29			−0.872870			−0.436435	+	0.899736i	$0.643759\pi$
$632$		−	3.05607e29i		−	1.19573i
$633$		0			0
$634$	−1.88462e29			−0.713323
$635$	2.74593e29	+	1.24372e29i	1.02227	+	0.463020i
$636$		0			0
$637$		−	1.30192e29i		−	0.468942i
$638$			3.37498e29i			1.19579i
$639$		0			0
$640$	4.66930e29	+	2.11489e29i	1.60089	+	0.725099i
$641$	−4.79415e29			−1.61697			−0.808486	−	0.588516i	$-0.799713\pi$
$641$	−4.79415e29			−1.61697			−0.808486	+	0.588516i	$0.799713\pi$
$642$		0			0
$643$			3.40654e29i			1.11198i	0.831188	+	0.555991i	$0.187661\pi$
$643$			3.40654e29i			1.11198i	−0.831188	+	0.555991i	$0.812339\pi$
$644$	8.36916e29			2.68770
$645$		0			0
$646$	6.92127e29			2.15151
$647$		−	1.79416e29i		−	0.548740i	−0.961624	−	0.274370i	$-0.911531\pi$
$647$		−	1.79416e29i		−	0.548740i	0.961624	−	0.274370i	$-0.0884692\pi$
$648$		0			0
$649$	4.24159e28			0.125591
$650$	−4.67115e29	−	5.32358e29i	−1.36092	−	1.55101i
$651$		0			0
$652$		−	1.51078e29i		−	0.426188i
$653$			1.03635e29i			0.287686i	0.989601	+	0.143843i	$0.0459460\pi$
$653$			1.03635e29i			0.287686i	−0.989601	+	0.143843i	$0.954054\pi$
$654$		0			0
$655$	−2.68053e29	+	5.91814e29i	−0.720588	+	1.59093i
$656$	4.99704e28			0.132197
$657$		0			0
$658$			7.96671e29i			2.04130i
$659$	−4.66342e29			−1.17600			−0.588000	−	0.808861i	$-0.700085\pi$
$659$	−4.66342e29			−1.17600			−0.588000	+	0.808861i	$0.700085\pi$
$660$		0			0
$661$	3.43345e29			0.838717			0.419359	−	0.907821i	$-0.362255\pi$
$661$	3.43345e29			0.838717			0.419359	+	0.907821i	$0.362255\pi$
$662$			5.56117e29i			1.33708i
$663$		0			0
$664$	−4.50115e29			−1.04848
$665$	−7.75480e29	−	3.51242e29i	−1.77805	−	0.805339i
$666$		0			0
$667$		−	3.39320e29i		−	0.753857i
$668$			1.13693e30i			2.48646i
$669$		0			0
$670$	−2.02236e29	+	4.46501e29i	−0.428620	+	0.946318i
$671$	3.98767e29			0.832018
$672$		0			0
$673$		−	3.52314e29i		−	0.712478i	−0.934395	−	0.356239i	$-0.884059\pi$
$673$		−	3.52314e29i		−	0.712478i	0.934395	−	0.356239i	$-0.115941\pi$
$674$	−2.89961e27			−0.00577312
$675$		0			0
$676$	5.04215e29			0.973141
$677$			4.66819e29i			0.887090i	0.896252	+	0.443545i	$0.146279\pi$
$677$			4.66819e29i			0.887090i	−0.896252	+	0.443545i	$0.853721\pi$
$678$		0			0
$679$	−1.06294e30			−1.95829
$680$	2.11108e29	−	4.66089e29i	0.382966	−	0.845523i
$681$		0			0
$682$			1.55713e30i			2.73899i
$683$		−	6.85211e29i		−	1.18688i	−0.804878	−	0.593440i	$-0.797769\pi$
$683$		−	6.85211e29i		−	1.18688i	0.804878	−	0.593440i	$-0.202231\pi$
$684$		0			0
$685$	−2.60840e29	−	1.18143e29i	−0.438150	−	0.198453i
$686$	7.30708e29			1.20876
$687$		0			0
$688$		−	6.07394e28i		−	0.0974522i
$689$	−4.96898e29			−0.785173
$690$		0			0
$691$	−8.35817e29			−1.28113			−0.640563	−	0.767906i	$-0.721299\pi$
$691$	−8.35817e29			−1.28113			−0.640563	+	0.767906i	$0.721299\pi$
$692$			5.37211e29i			0.811019i
$693$		0			0
$694$	1.69389e30			2.48091
$695$	−3.45703e29	+	7.63252e29i	−0.498726	+	1.10110i
$696$		0			0
$697$			3.16256e29i			0.442685i
$698$			1.29054e30i			1.77947i
$699$		0			0
$700$	−1.13172e30	+	9.93019e29i	−1.51429	+	1.32870i
$701$	1.07923e30			1.42258			0.711288	−	0.702901i	$-0.248112\pi$
$701$	1.07923e30			1.42258			0.711288	+	0.702901i	$0.248112\pi$
$702$		0			0
$703$		−	1.44441e30i		−	1.84781i
$704$	1.57867e30			1.98966
$705$		0			0
$706$	−1.12706e30			−1.37879
$707$			5.05478e29i			0.609253i
$708$		0			0
$709$	1.13039e30			1.32264			0.661322	−	0.750102i	$-0.269996\pi$
$709$	1.13039e30			1.32264			0.661322	+	0.750102i	$0.269996\pi$
$710$	−4.14839e29	−	1.87895e29i	−0.478264	−	0.216622i
$711$		0			0
$712$		−	4.23895e29i		−	0.474481i
$713$		−	1.56554e30i		−	1.72673i
$714$		0			0
$715$	−1.36634e30	−	6.18861e29i	−1.46334	−	0.662795i
$716$	−1.94787e30			−2.05576
$717$		0			0
$718$			7.64581e29i			0.783640i
$719$	−8.61924e29			−0.870594			−0.435297	−	0.900287i	$-0.643357\pi$
$719$	−8.61924e29			−0.870594			−0.435297	+	0.900287i	$0.643357\pi$
$720$		0			0
$721$	2.24022e30			2.19771
$722$		−	3.02091e30i		−	2.92076i
$723$		0			0
$724$	2.23102e30			2.09531
$725$	4.02611e29	+	4.58844e29i	0.372680	+	0.424733i
$726$		0			0
$727$			1.05467e29i			0.0948434i	0.998875	+	0.0474217i	$0.0151005\pi$
$727$			1.05467e29i			0.0948434i	−0.998875	+	0.0474217i	$0.984900\pi$
$728$		−	1.96035e30i		−	1.73762i
$729$		0			0
$730$	1.03613e30	−	2.28760e30i	0.892331	−	1.97011i
$731$	3.84412e29			0.326336
$732$		0			0
$733$		−	8.43407e29i		−	0.695738i	−0.937543	−	0.347869i	$-0.886905\pi$
$733$		−	8.43407e29i		−	0.695738i	0.937543	−	0.347869i	$-0.113095\pi$
$734$	1.42708e30			1.16048
$735$		0			0
$736$	−1.34752e30			−1.06492
$737$			1.03811e30i			0.808785i
$738$		0			0
$739$	1.05159e30			0.796307			0.398154	−	0.917319i	$-0.369651\pi$
$739$	1.05159e30			0.796307			0.398154	+	0.917319i	$0.369651\pi$
$740$	−2.32697e30	−	1.05396e30i	−1.73723	−	0.786851i
$741$		0			0
$742$			1.67111e30i			1.21273i
$743$			1.23200e30i			0.881509i	0.897628	+	0.440755i	$0.145289\pi$
$743$			1.23200e30i			0.881509i	−0.897628	+	0.440755i	$0.854711\pi$
$744$		0			0
$745$	9.03143e29	−	1.99398e30i	0.628226	−	1.38701i
$746$	2.53329e30			1.73751
$747$		0			0
$748$		−	2.59243e30i		−	1.72878i
$749$	−6.48233e28			−0.0426258
$750$		0			0
$751$	−2.93994e30			−1.87983			−0.939915	−	0.341408i	$-0.889096\pi$
$751$	−2.93994e30			−1.87983			−0.939915	+	0.341408i	$0.889096\pi$
$752$			3.92027e29i			0.247189i
$753$		0			0
$754$	−1.90143e30			−1.16595
$755$	1.13291e30	−	2.50128e30i	0.685100	−	1.51258i
$756$		0			0
$757$		−	1.01914e30i		−	0.599414i	−0.954031	−	0.299707i	$-0.903111\pi$
$757$		−	1.01914e30i		−	0.599414i	0.954031	−	0.299707i	$-0.0968889\pi$
$758$		−	5.45862e29i		−	0.316633i
$759$		0			0
$760$	−3.18265e30	−	1.44153e30i	−1.79575	−	0.813358i
$761$	1.85986e30			1.03500			0.517500	−	0.855683i	$-0.326863\pi$
$761$	1.85986e30			1.03500			0.517500	+	0.855683i	$0.326863\pi$
$762$		0			0
$763$			5.73604e29i			0.310531i
$764$	8.80550e29			0.470190
$765$		0			0
$766$	3.13098e30			1.62659
$767$			2.38967e29i			0.122458i
$768$		0			0
$769$	2.17566e30			1.08484			0.542418	−	0.840109i	$-0.317509\pi$
$769$	2.17566e30			1.08484			0.542418	+	0.840109i	$0.317509\pi$
$770$	−2.08128e30	+	4.59511e30i	−1.02371	+	2.26018i
$771$		0			0
$772$		−	1.53481e30i		−	0.734636i
$773$			1.69040e30i			0.798189i	0.916910	+	0.399094i	$0.130675\pi$
$773$			1.69040e30i			0.798189i	−0.916910	+	0.399094i	$0.869325\pi$
$774$		0			0
$775$	1.85755e30	+	2.11700e30i	0.853636	+	0.972865i
$776$	−4.36244e30			−1.97779
$777$		0			0
$778$			3.68076e30i			1.62425i
$779$	2.15953e30			0.940192
$780$		0			0
$781$	−9.64493e29			−0.408755
$782$			4.12336e30i			1.72417i
$783$		0			0
$784$	−2.15456e29			−0.0877082
$785$	−4.00248e30	−	1.81286e30i	−1.60767	−	0.728170i
$786$		0			0
$787$			1.29849e30i			0.507813i	0.967229	+	0.253906i	$0.0817155\pi$
$787$			1.29849e30i			0.507813i	−0.967229	+	0.253906i	$0.918285\pi$
$788$		−	2.85939e30i		−	1.10344i
$789$		0			0
$790$	−4.03585e30	−	1.82797e30i	−1.51653	−	0.686888i
$791$	−1.40754e30			−0.521924
$792$		0			0
$793$			2.24661e30i			0.811260i
$794$	4.79180e30			1.70759
$795$		0			0
$796$	−3.27295e30			−1.13593
$797$		−	4.07673e30i		−	1.39637i	−0.715918	−	0.698184i	$-0.753992\pi$
$797$		−	4.07673e30i		−	1.39637i	0.715918	−	0.698184i	$-0.246008\pi$
$798$		0			0
$799$	−2.48109e30			−0.827755
$800$	1.82217e30	−	1.59886e30i	0.599991	−	0.526460i
$801$		0			0
$802$			3.48076e30i			1.11646i
$803$		−	5.31864e30i		−	1.68379i
$804$		0			0
$805$	2.09253e30	−	4.61993e30i	0.645378	−	1.42488i
$806$	−8.77274e30			−2.67065
$807$		0			0
$808$			2.07453e30i			0.615320i
$809$	−4.20285e29			−0.123051			−0.0615254	−	0.998106i	$-0.519597\pi$
$809$	−4.20285e29			−0.123051			−0.0615254	+	0.998106i	$0.519597\pi$
$810$		0			0
$811$	1.58234e30			0.451420			0.225710	−	0.974194i	$-0.427530\pi$
$811$	1.58234e30			0.451420			0.225710	+	0.974194i	$0.427530\pi$
$812$			4.04216e30i			1.13835i
$813$		0			0
$814$	−8.55884e30			−2.34887
$815$	−8.33979e29	−	3.77738e29i	−0.225944	−	0.102338i
$816$		0			0
$817$		−	2.62493e30i		−	0.693084i
$818$		−	9.72184e29i		−	0.253419i
$819$		0			0
$820$	1.57578e30	−	3.47906e30i	0.400360	−	0.883926i
$821$	−8.65746e29			−0.217164			−0.108582	−	0.994088i	$-0.534631\pi$
$821$	−8.65746e29			−0.217164			−0.108582	+	0.994088i	$0.534631\pi$
$822$		0			0
$823$		−	6.70681e29i		−	0.163990i	−0.996633	−	0.0819951i	$-0.973871\pi$
$823$		−	6.70681e29i		−	0.163990i	0.996633	−	0.0819951i	$-0.0261292\pi$
$824$	9.19412e30			2.21960
$825$		0			0
$826$	8.03668e29			0.189141
$827$			6.75355e30i			1.56937i	0.619897	+	0.784684i	$0.287175\pi$
$827$			6.75355e30i			1.56937i	−0.619897	+	0.784684i	$0.712825\pi$
$828$		0			0
$829$	2.45186e29			0.0555486			0.0277743	−	0.999614i	$-0.491158\pi$
$829$	2.45186e29			0.0555486			0.0277743	+	0.999614i	$0.491158\pi$
$830$	−2.69235e30	+	5.94423e30i	−0.602297	+	1.32977i
$831$		0			0
$832$			8.89410e30i			1.94002i
$833$		−	1.36359e30i		−	0.293706i
$834$		0			0
$835$	6.27607e30	+	2.84264e30i	1.31819	+	0.597055i
$836$	−1.77022e31			−3.67165
$837$		0			0
$838$		−	1.49178e31i		−	3.01747i
$839$	9.50527e30			1.89873			0.949366	−	0.314172i	$-0.101727\pi$
$839$	9.50527e30			1.89873			0.949366	+	0.314172i	$0.101727\pi$
$840$		0			0
$841$	−3.49398e30			−0.680711
$842$			5.63161e29i			0.108357i
$843$		0			0
$844$	1.42496e31			2.67428
$845$	1.26068e30	−	2.78336e30i	0.233673	−	0.515910i
$846$		0			0
$847$			4.19902e30i			0.759229i
$848$			8.22323e29i			0.146854i
$849$		0			0
$850$	−4.89245e30	−	5.57578e30i	−0.852369	−	0.971420i
$851$	8.60507e30			1.48079
$852$		0			0
$853$		−	7.37170e29i		−	0.123766i	−0.998083	−	0.0618832i	$-0.980289\pi$
$853$		−	7.37170e29i		−	0.123766i	0.998083	−	0.0618832i	$-0.0197106\pi$
$854$	7.55557e30			1.25302
$855$		0			0
$856$	−2.66042e29			−0.0430502
$857$			6.21542e30i			0.993510i	0.867891	+	0.496755i	$0.165475\pi$
$857$			6.21542e30i			0.993510i	−0.867891	+	0.496755i	$0.834525\pi$
$858$		0			0
$859$	−1.78321e30			−0.278147			−0.139073	−	0.990282i	$-0.544412\pi$
$859$	−1.78321e30			−0.278147			−0.139073	+	0.990282i	$0.544412\pi$
$860$	−4.22882e30	−	1.91538e30i	−0.651606	−	0.295135i
$861$		0			0
$862$			9.92398e30i			1.49231i
$863$		−	1.16050e30i		−	0.172399i	−0.996278	−	0.0861993i	$-0.972528\pi$
$863$		−	1.16050e30i		−	0.172399i	0.996278	−	0.0861993i	$-0.0274722\pi$
$864$		0			0
$865$	2.96550e30	+	1.34318e30i	0.429961	+	0.194744i
$866$	−1.33005e30			−0.190515
$867$		0			0
$868$			1.86496e31i			2.60742i
$869$	−9.38327e30			−1.29612
$870$		0			0
$871$	−5.84859e30			−0.788607
$872$			2.35413e30i			0.313623i
$873$		0			0
$874$	2.81560e31			3.66186
$875$	2.65204e30	+	8.73010e30i	0.340797	+	1.12185i
$876$		0			0
$877$			3.61643e29i			0.0453717i	0.999743	+	0.0226858i	$0.00722175\pi$
$877$			3.61643e29i			0.0453717i	−0.999743	+	0.0226858i	$0.992778\pi$
$878$		−	6.05571e30i		−	0.750711i
$879$		0			0
$880$	−1.02416e30	+	2.26117e30i	−0.123965	+	0.273694i
$881$	4.75866e30			0.569164			0.284582	−	0.958652i	$-0.408145\pi$
$881$	4.75866e30			0.569164			0.284582	+	0.958652i	$0.408145\pi$
$882$		0			0
$883$			3.94770e30i			0.461059i	0.973065	+	0.230530i	$0.0740459\pi$
$883$			3.94770e30i			0.461059i	−0.973065	+	0.230530i	$0.925954\pi$
$884$	1.46055e31			1.68565
$885$		0			0
$886$	6.12951e30			0.690831
$887$		−	1.28571e31i		−	1.43201i	−0.698095	−	0.716005i	$-0.745969\pi$
$887$		−	1.28571e31i		−	1.43201i	0.698095	−	0.716005i	$-0.254031\pi$
$888$		0			0
$889$	1.20964e31			1.31579
$890$	−5.59797e30	−	2.53551e30i	−0.601777	−	0.272565i
$891$		0			0
$892$			1.73693e31i			1.82369i
$893$			1.69420e31i			1.75802i
$894$		0			0
$895$	−4.87022e30	+	1.07526e31i	−0.493636	+	1.08986i
$896$	2.05693e31			2.06056
$897$		0			0
$898$		−	1.68700e31i		−	1.65087i
$899$	7.56131e30			0.731341
$900$		0			0
$901$	−5.20438e30			−0.491766
$902$		−	1.27963e31i		−	1.19514i
$903$		0			0
$904$	−5.77669e30			−0.527121
$905$	5.57817e30	−	1.23156e31i	0.503131	−	1.11083i
$906$		0			0
$907$		−	1.43790e31i		−	1.26722i	−0.773654	−	0.633609i	$-0.781573\pi$
$907$		−	1.43790e31i		−	1.26722i	0.773654	−	0.633609i	$-0.218427\pi$
$908$			1.63866e30i			0.142754i
$909$		0			0
$910$	−2.58884e31	−	1.17258e31i	−2.20380	−	0.998174i
$911$	−1.28284e30			−0.107952			−0.0539758	−	0.998542i	$-0.517189\pi$
$911$	−1.28284e30			−0.107952			−0.0539758	+	0.998542i	$0.517189\pi$
$912$		0			0
$913$			1.38202e31i			1.13651i
$914$	−1.48477e31			−1.20705
$915$		0			0
$916$	1.13656e31			0.903003
$917$			2.60707e31i			2.04774i
$918$		0			0
$919$	−1.98254e31			−1.52198			−0.760988	−	0.648765i	$-0.775286\pi$
$919$	−1.98254e31			−1.52198			−0.760988	+	0.648765i	$0.775286\pi$
$920$	8.58795e30	−	1.89607e31i	0.651805	−	1.43907i
$921$		0			0
$922$		−	3.57381e31i		−	2.65129i
$923$		−	5.43386e30i		−	0.398557i
$924$		0			0
$925$	−1.16362e31	+	1.02101e31i	−0.834298	+	0.732052i
$926$	9.42289e30			0.667988
$927$		0			0
$928$		−	6.50828e30i		−	0.451037i
$929$	−9.64247e30			−0.660729			−0.330364	−	0.943853i	$-0.607172\pi$
$929$	−9.64247e30			−0.660729			−0.330364	+	0.943853i	$0.607172\pi$
$930$		0			0
$931$	−9.31121e30			−0.623784
$932$		−	9.25608e30i		−	0.613141i
$933$		0			0
$934$	−2.11467e31			−1.36962
$935$	−1.43107e31	−	6.48179e30i	−0.916512	−	0.415120i
$936$		0			0
$937$		−	1.51040e31i		−	0.945861i	−0.881100	−	0.472930i	$-0.843196\pi$
$937$		−	1.51040e31i		−	0.945861i	0.881100	−	0.472930i	$-0.156804\pi$
$938$			1.96693e31i			1.21804i
$939$		0			0
$940$	2.72939e31	+	1.23623e31i	1.65281	+	0.748613i
$941$	−2.80176e31			−1.67780			−0.838899	−	0.544288i	$-0.816800\pi$
$941$	−2.80176e31			−1.67780			−0.838899	+	0.544288i	$0.816800\pi$
$942$		0			0
$943$			1.28655e31i			0.753446i
$944$	3.95470e29			0.0229038
$945$		0			0
$946$	−1.55540e31			−0.881021
$947$		−	7.64271e29i		−	0.0428127i	−0.999771	−	0.0214064i	$-0.993186\pi$
$947$		−	7.64271e29i		−	0.0428127i	0.999771	−	0.0214064i	$-0.00681438\pi$
$948$		0			0
$949$	2.99647e31			1.64178
$950$	−3.80738e31	+	3.34077e31i	−2.06314	+	1.81029i
$951$		0			0
$952$		−	2.05322e31i		−	1.08830i
$953$			2.10283e31i			1.10237i	0.834382	+	0.551187i	$0.185825\pi$
$953$			2.10283e31i			1.10237i	−0.834382	+	0.551187i	$0.814175\pi$
$954$		0			0
$955$	2.20162e30	−	4.86080e30i	0.112903	−	0.249271i
$956$	7.43659e30			0.377195
$957$		0			0
$958$		−	2.73661e31i		−	1.35792i
$959$	−1.14906e31			−0.563957
$960$		0			0
$961$	1.40606e31			0.675161
$962$		−	4.82197e31i		−	2.29027i
$963$		0			0
$964$	1.00554e31			0.467295
$965$	−8.47243e30	−	3.83745e30i	−0.389467	−	0.176403i
$966$		0			0
$967$			2.07417e31i			0.932967i	0.884530	+	0.466483i	$0.154479\pi$
$967$			2.07417e31i			0.932967i	−0.884530	+	0.466483i	$0.845521\pi$
$968$			1.72332e31i			0.766789i
$969$		0			0
$970$	−2.60937e31	+	5.76104e31i	−1.13614	+	2.50841i
$971$	2.53741e31			1.09292			0.546460	−	0.837485i	$-0.315975\pi$
$971$	2.53741e31			1.09292			0.546460	+	0.837485i	$0.315975\pi$
$972$		0			0
$973$			3.36229e31i			1.41726i
$974$	−3.72574e31			−1.55362
$975$		0			0
$976$	3.71795e30			0.151733
$977$		−	2.63670e31i		−	1.06455i	−0.846570	−	0.532277i	$-0.821337\pi$
$977$		−	2.63670e31i		−	1.06455i	0.846570	−	0.532277i	$-0.178663\pi$
$978$		0			0
$979$	−1.30152e31			−0.514318
$980$	−6.79426e30	+	1.50006e31i	−0.265625	+	0.586453i
$981$		0			0
$982$		−	1.46324e31i		−	0.559944i
$983$		−	9.74890e30i		−	0.369100i	−0.982823	−	0.184550i	$-0.940917\pi$
$983$		−	9.74890e30i		−	0.369100i	0.982823	−	0.184550i	$-0.0590827\pi$
$984$		0			0
$985$	−1.57843e31	−	7.14927e30i	−0.584987	−	0.264961i
$986$	−1.99151e31			−0.730255
$987$		0			0
$988$		−	9.97325e31i		−	3.58005i
$989$	1.56380e31			0.555420
$990$		0			0
$991$	3.38462e31			1.17689			0.588446	−	0.808537i	$-0.299740\pi$
$991$	3.38462e31			1.17689			0.588446	+	0.808537i	$0.299740\pi$
$992$		−	3.00276e31i		−	1.03312i
$993$		0			0
$994$	−1.82746e31			−0.615588
$995$	−8.18329e30	+	1.80673e31i	−0.272763	+	0.602214i
$996$		0			0
$997$			1.33109e31i			0.434417i	0.976125	+	0.217208i	$0.0696951\pi$
$997$			1.33109e31i			0.434417i	−0.976125	+	0.217208i	$0.930305\pi$
$998$			8.43619e30i			0.272443i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.22.b.d.19.2		20
3.2	odd	2		15.22.b.a.4.19	yes	20
5.4	even	2	inner	45.22.b.d.19.19		20
15.2	even	4		75.22.a.n.1.1		10
15.8	even	4		75.22.a.m.1.10		10
15.14	odd	2		15.22.b.a.4.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.22.b.a.4.2	✓	20	15.14	odd	2
15.22.b.a.4.19	yes	20	3.2	odd	2
45.22.b.d.19.2		20	1.1	even	1	trivial
45.22.b.d.19.19		20	5.4	even	2	inner
75.22.a.m.1.10		10	15.8	even	4
75.22.a.n.1.1		10	15.2	even	4

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	45.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2387.58i q^{2} -3.60339e6 q^{4} +(-9.00948e6 + 1.98914e7i) q^{5} +8.76258e8i q^{7} +3.59626e9i q^{8} +O(q^{10})\)	\(q-2387.58i q^{2} -3.60339e6 q^{4} +(-9.00948e6 + 1.98914e7i) q^{5} +8.76258e8i q^{7} +3.59626e9i q^{8} +(4.74922e10 + 2.15109e10i) q^{10} +1.10419e11 q^{11} +6.22087e11i q^{13} +2.09214e12 q^{14} +1.02950e12 q^{16} +6.51559e12i q^{17} +4.44912e13 q^{19} +(3.24646e13 - 7.16763e13i) q^{20} -2.63633e14i q^{22} +2.65057e14i q^{23} +(-3.14496e14 - 3.58422e14i) q^{25} +1.48528e15 q^{26} -3.15750e15i q^{28} -1.28018e15 q^{29} -5.90644e15 q^{31} +5.08388e15i q^{32} +1.55565e16 q^{34} +(-1.74300e16 - 7.89463e15i) q^{35} -3.24650e16i q^{37} -1.06226e17i q^{38} +(-7.15345e16 - 3.24004e16i) q^{40} +4.85384e16 q^{41} -5.89988e16i q^{43} -3.97881e17 q^{44} +6.32845e17 q^{46} +3.80793e17i q^{47} -2.09282e17 q^{49} +(-8.55761e17 + 7.50884e17i) q^{50} -2.24162e18i q^{52} +7.98759e17i q^{53} +(-9.94813e17 + 2.19637e18i) q^{55} -3.15125e18 q^{56} +3.05653e18i q^{58} +3.84138e17 q^{59} +3.61141e18 q^{61} +1.41021e19i q^{62} +1.42972e19 q^{64} +(-1.23742e19 - 5.60468e18i) q^{65} +9.40156e18i q^{67} -2.34782e19i q^{68} +(-1.88491e19 + 4.16154e19i) q^{70} -8.73489e18 q^{71} -4.81680e19i q^{73} -7.75127e19 q^{74} -1.60319e20 q^{76} +9.67551e19i q^{77} -8.49792e19 q^{79} +(-9.27527e18 + 2.04782e19i) q^{80} -1.15889e20i q^{82} +1.25162e20i q^{83} +(-1.29604e20 - 5.87021e19i) q^{85} -1.40864e20 q^{86} +3.97093e20i q^{88} -1.17871e20 q^{89} -5.45109e20 q^{91} -9.55103e20i q^{92} +9.09175e20 q^{94} +(-4.00843e20 + 8.84991e20i) q^{95} +1.21305e21i q^{97} +4.99677e20i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20086410 q^{4} - 24944730 q^{5}+O(q^{10}) \) 20 * q - 20086410 * q^4 - 24944730 * q^5	\( 20 q - 20086410 q^{4} - 24944730 q^{5} - 1467444110 q^{10} - 11952443580 q^{11} + 3210119749140 q^{14} + 12123723095650 q^{16} + 152310844352560 q^{19} + 228448186221420 q^{20} + 141329092021400 q^{25} - 573110662319340 q^{26} - 51\!\cdots\!20 q^{29}+ \cdots - 23\!\cdots\!80 q^{95}+O(q^{100}) \) 20 * q - 20086410 * q^4 - 24944730 * q^5 - 1467444110 * q^10 - 11952443580 * q^11 + 3210119749140 * q^14 + 12123723095650 * q^16 + 152310844352560 * q^19 + 228448186221420 * q^20 + 141329092021400 * q^25 - 573110662319340 * q^26 - 5107306321462020 * q^29 - 11159342729449880 * q^31 - 72571936852862020 * q^34 - 71677038226172100 * q^35 - 324600549297895630 * q^40 + 314639459012042880 * q^41 + 98237641547534580 * q^44 - 476906572076519080 * q^46 - 907385772904909900 * q^49 - 1517876347798174200 * q^50 + 579473028579091680 * q^55 + 10293031248027060900 * q^56 + 9872270243072647260 * q^59 - 8886161742014816600 * q^61 + 29754567216376186910 * q^64 - 8919287112899553420 * q^65 + 115367644795510161000 * q^70 + 149325449942773260360 * q^71 - 260498047093221036060 * q^74 - 517472967324760441440 * q^76 + 98261416021599286600 * q^79 - 734236820229361105020 * q^80 + 1145807312247924282220 * q^85 + 2014542545589414764520 * q^86 - 1144207953427983163560 * q^89 - 3339621670514393150280 * q^91 + 3342639440249393189840 * q^94 - 2334023656701886699680 * q^95

Introduction

L-functions

Modular forms

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