LMFDB - Embedded newform 1638.2.p.i.991.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(919,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1638.919");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.p (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.4
Root			$1.26359 + 0.635098i$ of defining polynomial
Character	$\chi$	$=$	1638.991
Dual form			1638.2.p.i.919.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.97513 + 3.42102i) q^{5} +(-1.48662 + 2.18860i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.97513 + 3.42102i) q^{5} +(-1.48662 + 2.18860i) q^{7} -1.00000 q^{8} +3.95025 q^{10} -4.91377 q^{11} +(-3.39335 - 1.21869i) q^{13} +(1.15207 + 2.38175i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.0702857 + 0.121738i) q^{17} -0.776963 q^{19} +(1.97513 - 3.42102i) q^{20} +(-2.45689 + 4.25545i) q^{22} +(4.76845 - 8.25920i) q^{23} +(-5.30226 + 9.18378i) q^{25} +(-2.75209 + 2.32938i) q^{26} +(2.63869 + 0.193156i) q^{28} +(0.629759 + 1.09077i) q^{29} +(-1.67992 + 2.90971i) q^{31} +(0.500000 + 0.866025i) q^{32} +0.140571 q^{34} +(-10.4235 - 0.763015i) q^{35} +(-5.56841 + 9.64476i) q^{37} +(-0.388481 + 0.672870i) q^{38} +(-1.97513 - 3.42102i) q^{40} +(-4.65505 - 8.06279i) q^{41} +(-0.541233 + 0.937443i) q^{43} +(2.45689 + 4.25545i) q^{44} +(-4.76845 - 8.25920i) q^{46} +(-3.33199 - 5.77118i) q^{47} +(-2.57990 - 6.50724i) q^{49} +(5.30226 + 9.18378i) q^{50} +(0.641255 + 3.54807i) q^{52} +(-5.53204 + 9.58177i) q^{53} +(-9.70533 - 16.8101i) q^{55} +(1.48662 - 2.18860i) q^{56} +1.25952 q^{58} +(0.215609 + 0.373446i) q^{59} -8.28114 q^{61} +(1.67992 + 2.90971i) q^{62} +1.00000 q^{64} +(-2.53312 - 14.0158i) q^{65} +8.19628 q^{67} +(0.0702857 - 0.121738i) q^{68} +(-5.87254 + 8.64551i) q^{70} +(-1.93865 + 3.35783i) q^{71} +(-0.0817820 + 0.141650i) q^{73} +(5.56841 + 9.64476i) q^{74} +(0.388481 + 0.672870i) q^{76} +(7.30493 - 10.7543i) q^{77} +(2.17517 + 3.76751i) q^{79} -3.95025 q^{80} -9.31010 q^{82} +10.5220 q^{83} +(-0.277647 + 0.480898i) q^{85} +(0.541233 + 0.937443i) q^{86} +4.91377 q^{88} +(-0.536369 + 0.929018i) q^{89} +(7.71185 - 5.61493i) q^{91} -9.53690 q^{92} -6.66398 q^{94} +(-1.53460 - 2.65801i) q^{95} +(-6.54097 + 11.3293i) q^{97} +(-6.92538 - 1.01936i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8	$ 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8} - 4 q^{10} - 12 q^{11} - 11 q^{13} + 3 q^{14} - 4 q^{16} - 4 q^{17} - 12 q^{19} - 2 q^{20} - 6 q^{22} + 10 q^{23} - 18 q^{25} - 10 q^{26} - 2 q^{29} + 6 q^{31} + 4 q^{32} - 8 q^{34} - 18 q^{35} - 28 q^{37} - 6 q^{38} + 2 q^{40} - 6 q^{43} + 6 q^{44} - 10 q^{46} - q^{47} - 7 q^{49} + 18 q^{50} + q^{52} - 7 q^{53} + q^{55} - 3 q^{56} - 4 q^{58} - 2 q^{59} - 48 q^{61} - 6 q^{62} + 8 q^{64} - 19 q^{65} + 30 q^{67} - 4 q^{68} - 18 q^{70} - 6 q^{71} + q^{73} + 28 q^{74} + 6 q^{76} + 22 q^{77} - 12 q^{79} + 4 q^{80} + 32 q^{83} - 13 q^{85} + 6 q^{86} + 12 q^{88} - 25 q^{89} + 34 q^{91} - 20 q^{92} - 2 q^{94} + 8 q^{95} - q^{97} - 2 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8 - 4 * q^10 - 12 * q^11 - 11 * q^13 + 3 * q^14 - 4 * q^16 - 4 * q^17 - 12 * q^19 - 2 * q^20 - 6 * q^22 + 10 * q^23 - 18 * q^25 - 10 * q^26 - 2 * q^29 + 6 * q^31 + 4 * q^32 - 8 * q^34 - 18 * q^35 - 28 * q^37 - 6 * q^38 + 2 * q^40 - 6 * q^43 + 6 * q^44 - 10 * q^46 - q^47 - 7 * q^49 + 18 * q^50 + q^52 - 7 * q^53 + q^55 - 3 * q^56 - 4 * q^58 - 2 * q^59 - 48 * q^61 - 6 * q^62 + 8 * q^64 - 19 * q^65 + 30 * q^67 - 4 * q^68 - 18 * q^70 - 6 * q^71 + q^73 + 28 * q^74 + 6 * q^76 + 22 * q^77 - 12 * q^79 + 4 * q^80 + 32 * q^83 - 13 * q^85 + 6 * q^86 + 12 * q^88 - 25 * q^89 + 34 * q^91 - 20 * q^92 - 2 * q^94 + 8 * q^95 - q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.97513	+	3.42102i	0.883304	+	1.52993i	0.847646	+	0.530563i	$0.178019\pi$
$5$	1.97513	+	3.42102i	0.883304	+	1.52993i	0.0356582	+	0.999364i	$0.488647\pi$
$6$		0			0
$7$	−1.48662	+	2.18860i	−0.561891	+	0.827211i
$7$	−1.48662	+	2.18860i	−0.561891	+	0.827211i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	3.95025			1.24918
$11$	−4.91377			−1.48156			−0.740779	−	0.671749i	$-0.765544\pi$
$11$	−4.91377			−1.48156			−0.740779	+	0.671749i	$0.765544\pi$
$12$		0			0
$13$	−3.39335	−	1.21869i	−0.941145	−	0.338004i
$13$	−3.39335	−	1.21869i	−0.941145	−	0.338004i
$14$	1.15207	+	2.38175i	0.307903	+	0.636550i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.0702857	+	0.121738i	0.0170468	+	0.0295259i	0.874423	−	0.485164i	$-0.161240\pi$
$17$	0.0702857	+	0.121738i	0.0170468	+	0.0295259i	−0.857376	+	0.514690i	$0.827907\pi$
$18$		0			0
$19$	−0.776963			−0.178248			−0.0891238	−	0.996021i	$-0.528407\pi$
$19$	−0.776963			−0.178248			−0.0891238	+	0.996021i	$0.528407\pi$
$20$	1.97513	−	3.42102i	0.441652	−	0.764963i
$21$		0			0
$22$	−2.45689	+	4.25545i	−0.523810	+	0.907266i
$23$	4.76845	−	8.25920i	0.994291	−	1.72216i	0.404735	−	0.914434i	$-0.367364\pi$
$23$	4.76845	−	8.25920i	0.994291	−	1.72216i	0.589556	−	0.807728i	$-0.299303\pi$
$24$		0			0
$25$	−5.30226	+	9.18378i	−1.06045	+	1.83676i
$26$	−2.75209	+	2.32938i	−0.539729	+	0.456829i
$27$		0			0
$28$	2.63869	+	0.193156i	0.498666	+	0.0365030i
$29$	0.629759	+	1.09077i	0.116943	+	0.202552i	0.918555	−	0.395293i	$-0.129357\pi$
$29$	0.629759	+	1.09077i	0.116943	+	0.202552i	−0.801612	+	0.597845i	$0.796024\pi$
$30$		0			0
$31$	−1.67992	+	2.90971i	−0.301723	+	0.522600i	−0.976526	−	0.215398i	$-0.930895\pi$
$31$	−1.67992	+	2.90971i	−0.301723	+	0.522600i	0.674803	+	0.737998i	$0.264229\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	0.140571			0.0241078
$35$	−10.4235	−	0.763015i	−1.76189	−	0.128973i
$36$		0			0
$37$	−5.56841	+	9.64476i	−0.915440	+	1.58559i	−0.109185	+	0.994021i	$0.534824\pi$
$37$	−5.56841	+	9.64476i	−0.915440	+	1.58559i	−0.806256	+	0.591567i	$0.798509\pi$
$38$	−0.388481	+	0.672870i	−0.0630200	+	0.109154i
$39$		0			0
$40$	−1.97513	−	3.42102i	−0.312295	−	0.540911i
$41$	−4.65505	−	8.06279i	−0.726997	−	1.25920i	−0.958147	−	0.286277i	$-0.907582\pi$
$41$	−4.65505	−	8.06279i	−0.726997	−	1.25920i	0.231150	−	0.972918i	$-0.425751\pi$
$42$		0			0
$43$	−0.541233	+	0.937443i	−0.0825372	+	0.142959i	−0.904339	−	0.426815i	$-0.859636\pi$
$43$	−0.541233	+	0.937443i	−0.0825372	+	0.142959i	0.821802	+	0.569773i	$0.192969\pi$
$44$	2.45689	+	4.25545i	0.370390	+	0.641534i
$45$		0			0
$46$	−4.76845	−	8.25920i	−0.703070	−	1.21775i
$47$	−3.33199	−	5.77118i	−0.486021	−	0.841813i	0.513850	−	0.857880i	$-0.328219\pi$
$47$	−3.33199	−	5.77118i	−0.486021	−	0.841813i	−0.999871	+	0.0160671i	$0.994885\pi$
$48$		0			0
$49$	−2.57990	−	6.50724i	−0.368557	−	0.929605i
$50$	5.30226	+	9.18378i	0.749852	+	1.29878i
$51$		0			0
$52$	0.641255	+	3.54807i	0.0889261	+	0.492029i
$53$	−5.53204	+	9.58177i	−0.759884	+	1.31616i	0.183026	+	0.983108i	$0.441411\pi$
$53$	−5.53204	+	9.58177i	−0.759884	+	1.31616i	−0.942910	+	0.333049i	$0.891923\pi$
$54$		0			0
$55$	−9.70533	−	16.8101i	−1.30867	−	2.26668i
$56$	1.48662	−	2.18860i	0.198658	−	0.292463i
$57$		0			0
$58$	1.25952			0.165383
$59$	0.215609	+	0.373446i	0.0280699	+	0.0486185i	0.879719	−	0.475494i	$-0.157731\pi$
$59$	0.215609	+	0.373446i	0.0280699	+	0.0486185i	−0.851649	+	0.524112i	$0.824397\pi$
$60$		0			0
$61$	−8.28114			−1.06029			−0.530146	−	0.847906i	$-0.677863\pi$
$61$	−8.28114			−1.06029			−0.530146	+	0.847906i	$0.677863\pi$
$62$	1.67992	+	2.90971i	0.213351	+	0.369534i
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.53312	−	14.0158i	−0.314195	−	1.73844i
$66$		0			0
$67$	8.19628			1.00134			0.500668	−	0.865640i	$-0.333088\pi$
$67$	8.19628			1.00134			0.500668	+	0.865640i	$0.333088\pi$
$68$	0.0702857	−	0.121738i	0.00852340	−	0.0147630i
$69$		0			0
$70$	−5.87254	+	8.64551i	−0.701903	+	1.03334i
$71$	−1.93865	+	3.35783i	−0.230075	+	0.398502i	−0.957830	−	0.287336i	$-0.907230\pi$
$71$	−1.93865	+	3.35783i	−0.230075	+	0.398502i	0.727755	+	0.685837i	$0.240564\pi$
$72$		0			0
$73$	−0.0817820	+	0.141650i	−0.00957185	+	0.0165789i	−0.870772	−	0.491688i	$-0.836380\pi$
$73$	−0.0817820	+	0.141650i	−0.00957185	+	0.0165789i	0.861200	+	0.508267i	$0.169714\pi$
$74$	5.56841	+	9.64476i	0.647314	+	1.12118i
$75$		0			0
$76$	0.388481	+	0.672870i	0.0445619	+	0.0771834i
$77$	7.30493	−	10.7543i	0.832474	−	1.22556i
$78$		0			0
$79$	2.17517	+	3.76751i	0.244726	+	0.423878i	0.962055	−	0.272857i	$-0.0879687\pi$
$79$	2.17517	+	3.76751i	0.244726	+	0.423878i	−0.717329	+	0.696735i	$0.754635\pi$
$80$	−3.95025			−0.441652
$81$		0			0
$82$	−9.31010			−1.02813
$83$	10.5220			1.15494			0.577472	−	0.816410i	$-0.304039\pi$
$83$	10.5220			1.15494			0.577472	+	0.816410i	$0.304039\pi$
$84$		0			0
$85$	−0.277647	+	0.480898i	−0.0301150	+	0.0521607i
$86$	0.541233	+	0.937443i	0.0583626	+	0.101087i
$87$		0			0
$88$	4.91377			0.523810
$89$	−0.536369	+	0.929018i	−0.0568550	+	0.0984757i	−0.893052	−	0.449953i	$-0.851441\pi$
$89$	−0.536369	+	0.929018i	−0.0568550	+	0.0984757i	0.836197	+	0.548429i	$0.184774\pi$
$90$		0			0
$91$	7.71185	−	5.61493i	0.808421	−	0.588604i
$92$	−9.53690			−0.994291
$93$		0			0
$94$	−6.66398			−0.687337
$95$	−1.53460	−	2.65801i	−0.157447	−	0.272706i
$96$		0			0
$97$	−6.54097	+	11.3293i	−0.664135	+	1.15032i	0.315384	+	0.948964i	$0.397867\pi$
$97$	−6.54097	+	11.3293i	−0.664135	+	1.15032i	−0.979519	+	0.201351i	$0.935467\pi$
$98$	−6.92538	−	1.01936i	−0.699569	−	0.102971i
$99$		0			0
$100$	10.6045			1.06045
$101$	−7.38523			−0.734858			−0.367429	−	0.930052i	$-0.619762\pi$
$101$	−7.38523			−0.734858			−0.367429	+	0.930052i	$0.619762\pi$
$102$		0			0
$103$	−1.99107	−	3.44863i	−0.196186	−	0.339804i	0.751103	−	0.660185i	$-0.229522\pi$
$103$	−1.99107	−	3.44863i	−0.196186	−	0.339804i	−0.947289	+	0.320382i	$0.896189\pi$
$104$	3.39335	+	1.21869i	0.332745	+	0.119502i
$105$		0			0
$106$	5.53204	+	9.58177i	0.537319	+	0.930664i
$107$	−3.53679	+	6.12590i	−0.341914	+	0.592213i	−0.984788	−	0.173759i	$-0.944409\pi$
$107$	−3.53679	+	6.12590i	−0.341914	+	0.592213i	0.642874	+	0.765972i	$0.277742\pi$
$108$		0			0
$109$	−7.42350	+	12.8579i	−0.711042	+	1.23156i	0.253424	+	0.967355i	$0.418443\pi$
$109$	−7.42350	+	12.8579i	−0.711042	+	1.23156i	−0.964466	+	0.264206i	$0.914890\pi$
$110$	−19.4107			−1.85073
$111$		0			0
$112$	−1.15207	−	2.38175i	−0.108860	−	0.225054i
$113$	0.785895	−	1.36121i	0.0739308	−	0.128052i	−0.826690	−	0.562658i	$-0.809779\pi$
$113$	0.785895	−	1.36121i	0.0739308	−	0.128052i	0.900621	+	0.434606i	$0.143112\pi$
$114$		0			0
$115$	37.6732			3.51304
$116$	0.629759	−	1.09077i	0.0584717	−	0.101276i
$117$		0			0
$118$	0.431218			0.0396969
$119$	−0.370925	−	0.0271522i	−0.0340026	−	0.00248904i
$120$		0			0
$121$	13.1452			1.19502
$122$	−4.14057	+	7.17168i	−0.374870	+	0.649293i
$123$		0			0
$124$	3.35985			0.301723
$125$	−22.1392			−1.98019
$126$		0			0
$127$	−5.42757	−	9.40083i	−0.481619	−	0.834188i	0.518159	−	0.855285i	$-0.326618\pi$
$127$	−5.42757	−	9.40083i	−0.481619	−	0.834188i	−0.999777	+	0.0210962i	$0.993284\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−13.4046	−	4.81414i	−1.17566	−	0.422228i
$131$	0.961751	+	1.66580i	0.0840285	+	0.145542i	0.904977	−	0.425461i	$-0.139888\pi$
$131$	0.961751	+	1.66580i	0.0840285	+	0.145542i	−0.820948	+	0.571003i	$0.806555\pi$
$132$		0			0
$133$	1.15505	−	1.70046i	0.100156	−	0.147448i
$134$	4.09814	−	7.09819i	0.354026	−	0.613190i
$135$		0			0
$136$	−0.0702857	−	0.121738i	−0.00602695	−	0.0104390i
$137$	7.94106	+	13.7543i	0.678450	+	1.17511i	0.975447	+	0.220232i	$0.0706815\pi$
$137$	7.94106	+	13.7543i	0.678450	+	1.17511i	−0.296997	+	0.954878i	$0.595985\pi$
$138$		0			0
$139$	2.94351	−	5.09831i	0.249665	−	0.432433i	−0.713768	−	0.700383i	$-0.753013\pi$
$139$	2.94351	−	5.09831i	0.249665	−	0.432433i	0.963433	+	0.267950i	$0.0863461\pi$
$140$	4.55096	+	9.40852i	0.384626	+	0.795165i
$141$		0			0
$142$	1.93865	+	3.35783i	0.162688	+	0.281783i
$143$	16.6741	+	5.98837i	1.39436	+	0.500773i
$144$		0			0
$145$	−2.48771	+	4.30884i	−0.206593	+	0.357829i
$146$	0.0817820	+	0.141650i	0.00676832	+	0.0117231i
$147$		0			0
$148$	11.1368			0.915440
$149$	13.2701			1.08713			0.543564	−	0.839368i	$-0.317075\pi$
$149$	13.2701			1.08713			0.543564	+	0.839368i	$0.317075\pi$
$150$		0			0
$151$	−8.06783	+	13.9739i	−0.656551	+	1.13718i	0.324952	+	0.945731i	$0.394652\pi$
$151$	−8.06783	+	13.9739i	−0.656551	+	1.13718i	−0.981503	+	0.191449i	$0.938681\pi$
$152$	0.776963			0.0630200
$153$		0			0
$154$	−5.66100	−	11.7034i	−0.456176	−	0.943086i
$155$	−13.2723			−1.06605
$156$		0			0
$157$	−8.85322	+	15.3342i	−0.706564	+	1.22380i	0.259561	+	0.965727i	$0.416422\pi$
$157$	−8.85322	+	15.3342i	−0.706564	+	1.22380i	−0.966124	+	0.258077i	$0.916911\pi$
$158$	4.35034			0.346095
$159$		0			0
$160$	−1.97513	+	3.42102i	−0.156148	+	0.270455i
$161$	10.9872	+	22.7145i	0.865909	+	1.79016i
$162$		0			0
$163$	3.27142			0.256237			0.128119	−	0.991759i	$-0.459106\pi$
$163$	3.27142			0.256237			0.128119	+	0.991759i	$0.459106\pi$
$164$	−4.65505	+	8.06279i	−0.363498	+	0.629598i
$165$		0			0
$166$	5.26102	−	9.11236i	0.408335	−	0.707256i
$167$	4.42914	+	7.67150i	0.342737	+	0.593638i	0.984940	−	0.172896i	$-0.0553126\pi$
$167$	4.42914	+	7.67150i	0.342737	+	0.593638i	−0.642203	+	0.766535i	$0.721979\pi$
$168$		0			0
$169$	10.0296	+	8.27088i	0.771506	+	0.636221i
$170$	0.277647	+	0.480898i	0.0212945	+	0.0368832i
$171$		0			0
$172$	1.08247			0.0825372
$173$	14.9497			1.13661			0.568303	−	0.822819i	$-0.307600\pi$
$173$	14.9497			1.13661			0.568303	+	0.822819i	$0.307600\pi$
$174$		0			0
$175$	−12.2171	−	25.2573i	−0.923527	−	1.90927i
$176$	2.45689	−	4.25545i	0.185195	−	0.320767i
$177$		0			0
$178$	0.536369	+	0.929018i	0.0402026	+	0.0696329i
$179$	23.2069			1.73456			0.867281	−	0.497819i	$-0.165866\pi$
$179$	23.2069			1.73456			0.867281	+	0.497819i	$0.165866\pi$
$180$		0			0
$181$	19.4618			1.44658			0.723291	−	0.690543i	$-0.242629\pi$
$181$	19.4618			1.44658			0.723291	+	0.690543i	$0.242629\pi$
$182$	−1.00674	−	9.48612i	−0.0746248	−	0.703158i
$183$		0			0
$184$	−4.76845	+	8.25920i	−0.351535	+	0.608876i
$185$	−43.9932			−3.23445
$186$		0			0
$187$	−0.345368	−	0.598195i	−0.0252558	−	0.0437444i
$188$	−3.33199	+	5.77118i	−0.243010	+	0.420906i
$189$		0			0
$190$	−3.06920			−0.222663
$191$	14.5964			1.05616			0.528078	−	0.849196i	$-0.322913\pi$
$191$	14.5964			1.05616			0.528078	+	0.849196i	$0.322913\pi$
$192$		0			0
$193$	−1.76860			−0.127307			−0.0636534	−	0.997972i	$-0.520275\pi$
$193$	−1.76860			−0.127307			−0.0636534	+	0.997972i	$0.520275\pi$
$194$	6.54097	+	11.3293i	0.469614	+	0.813396i
$195$		0			0
$196$	−4.34548	+	5.48788i	−0.310391	+	0.391991i
$197$	−2.92757	−	5.07070i	−0.208581	−	0.361272i	0.742687	−	0.669639i	$-0.233551\pi$
$197$	−2.92757	−	5.07070i	−0.208581	−	0.361272i	−0.951268	+	0.308366i	$0.900218\pi$
$198$		0			0
$199$	−6.96137	−	12.0575i	−0.493479	−	0.854730i	0.506493	−	0.862244i	$-0.330942\pi$
$199$	−6.96137	−	12.0575i	−0.493479	−	0.854730i	−0.999972	+	0.00751379i	$0.997608\pi$
$200$	5.30226	−	9.18378i	0.374926	−	0.649391i
$201$		0			0
$202$	−3.69262	+	6.39580i	−0.259812	+	0.450007i
$203$	−3.32348	−	0.243283i	−0.233262	−	0.0170751i
$204$		0			0
$205$	18.3886	−	31.8501i	1.28432	−	2.22450i
$206$	−3.98214			−0.277449
$207$		0			0
$208$	2.75209	−	2.32938i	0.190823	−	0.161513i
$209$	3.81782			0.264084
$210$		0			0
$211$	3.35399	+	5.80929i	0.230898	+	0.399928i	0.958073	−	0.286525i	$-0.0925002\pi$
$211$	3.35399	+	5.80929i	0.230898	+	0.399928i	−0.727174	+	0.686453i	$0.759167\pi$
$212$	11.0641			0.759884
$213$		0			0
$214$	3.53679	+	6.12590i	0.241770	+	0.418758i
$215$	−4.27601			−0.291622
$216$		0			0
$217$	−3.87077	−	8.00232i	−0.262765	−	0.543233i
$218$	7.42350	+	12.8579i	0.502783	+	0.870846i
$219$		0			0
$220$	−9.70533	+	16.8101i	−0.654333	+	1.13334i
$221$	−0.0901422	−	0.498757i	−0.00606362	−	0.0335500i
$222$		0			0
$223$	−1.02744	−	1.77957i	−0.0688023	−	0.119169i	0.829572	−	0.558400i	$-0.188584\pi$
$223$	−1.02744	−	1.77957i	−0.0688023	−	0.119169i	−0.898374	+	0.439231i	$0.855251\pi$
$224$	−2.63869	−	0.193156i	−0.176305	−	0.0129058i
$225$		0			0
$226$	−0.785895	−	1.36121i	−0.0522770	−	0.0905463i
$227$	−12.9149	−	22.3692i	−0.857190	−	1.48470i	−0.874598	−	0.484849i	$-0.838875\pi$
$227$	−12.9149	−	22.3692i	−0.857190	−	1.48470i	0.0174074	−	0.999848i	$-0.494459\pi$
$228$		0			0
$229$	5.39496	+	9.34435i	0.356509	+	0.617492i	0.987375	−	0.158400i	$-0.0506336\pi$
$229$	5.39496	+	9.34435i	0.356509	+	0.617492i	−0.630866	+	0.775892i	$0.717300\pi$
$230$	18.8366	−	32.6259i	1.24205	−	2.15129i
$231$		0			0
$232$	−0.629759	−	1.09077i	−0.0413457	−	0.0716129i
$233$	1.92109	+	3.32742i	0.125855	+	0.217987i	0.922067	−	0.387031i	$-0.126499\pi$
$233$	1.92109	+	3.32742i	0.125855	+	0.217987i	−0.796212	+	0.605018i	$0.793166\pi$
$234$		0			0
$235$	13.1622	−	22.7976i	0.858608	−	1.48715i
$236$	0.215609	−	0.373446i	0.0140350	−	0.0243093i
$237$		0			0
$238$	−0.208977	+	0.307654i	−0.0135460	+	0.0199423i
$239$	−10.2560			−0.663404			−0.331702	−	0.943384i	$-0.607623\pi$
$239$	−10.2560			−0.663404			−0.331702	+	0.943384i	$0.607623\pi$
$240$		0			0
$241$	0.316427	+	0.548068i	0.0203829	+	0.0353042i	0.876037	−	0.482244i	$-0.160178\pi$
$241$	0.316427	+	0.548068i	0.0203829	+	0.0353042i	−0.855654	+	0.517548i	$0.826845\pi$
$242$	6.57259	−	11.3841i	0.422502	−	0.731795i
$243$		0			0
$244$	4.14057	+	7.17168i	0.265073	+	0.459120i
$245$	17.1658	−	21.6785i	1.09668	−	1.38499i
$246$		0			0
$247$	2.63650	+	0.946878i	0.167757	+	0.0602484i
$248$	1.67992	−	2.90971i	0.106675	−	0.184767i
$249$		0			0
$250$	−11.0696	+	19.1731i	−0.700104	+	1.21262i
$251$	−7.53648	+	13.0536i	−0.475698	+	0.823934i	−0.999612	−	0.0278373i	$-0.991138\pi$
$251$	−7.53648	+	13.0536i	−0.475698	+	0.823934i	0.523914	+	0.851771i	$0.324471\pi$
$252$		0			0
$253$	−23.4311	+	40.5838i	−1.47310	+	2.55148i
$254$	−10.8551			−0.681112
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.56909	−	9.64595i	0.347390	−	0.601698i	−0.638395	−	0.769709i	$-0.720401\pi$
$257$	5.56909	−	9.64595i	0.347390	−	0.601698i	0.985785	+	0.168012i	$0.0537346\pi$
$258$		0			0
$259$	−12.8304	−	26.5251i	−0.797240	−	1.64819i
$260$	−10.8715	+	9.20163i	−0.674219	+	0.570661i
$261$		0			0
$262$	1.92350			0.118834
$263$	−17.1706			−1.05878			−0.529391	−	0.848378i	$-0.677580\pi$
$263$	−17.1706			−1.05878			−0.529391	+	0.848378i	$0.677580\pi$
$264$		0			0
$265$	−43.7059			−2.68483
$266$	−0.895114	−	1.85053i	−0.0548829	−	0.113463i
$267$		0			0
$268$	−4.09814	−	7.09819i	−0.250334	−	0.433591i
$269$	1.64355	+	2.84672i	0.100209	+	0.173568i	0.911771	−	0.410699i	$-0.134715\pi$
$269$	1.64355	+	2.84672i	0.100209	+	0.173568i	−0.811562	+	0.584267i	$0.801382\pi$
$270$		0			0
$271$	−7.36304	+	12.7532i	−0.447273	+	0.774699i	−0.998207	−	0.0598494i	$-0.980938\pi$
$271$	−7.36304	+	12.7532i	−0.447273	+	0.774699i	0.550935	+	0.834548i	$0.314271\pi$
$272$	−0.140571			−0.00852340
$273$		0			0
$274$	15.8821			0.959474
$275$	26.0541	−	45.1270i	1.57112	−	2.72126i
$276$		0			0
$277$	−9.25021	−	16.0218i	−0.555791	−	0.962659i	−0.997842	−	0.0656684i	$-0.979082\pi$
$277$	−9.25021	−	16.0218i	−0.555791	−	0.962659i	0.442050	−	0.896990i	$-0.354251\pi$
$278$	−2.94351	−	5.09831i	−0.176540	−	0.305776i
$279$		0			0
$280$	10.4235	+	0.763015i	0.622923	+	0.0455989i
$281$	31.3463			1.86996			0.934981	−	0.354698i	$-0.115416\pi$
$281$	31.3463			1.86996			0.934981	+	0.354698i	$0.115416\pi$
$282$		0			0
$283$	−14.7197			−0.874995			−0.437498	−	0.899220i	$-0.644135\pi$
$283$	−14.7197			−0.874995			−0.437498	+	0.899220i	$0.644135\pi$
$284$	3.87729			0.230075
$285$		0			0
$286$	13.5231	−	11.4460i	0.799640	−	0.676818i
$287$	24.5665	+	1.79830i	1.45011	+	0.106150i
$288$		0			0
$289$	8.49012	−	14.7053i	0.499419	−	0.865019i
$290$	2.48771	+	4.30884i	0.146083	+	0.253024i
$291$		0			0
$292$	0.163564			0.00957185
$293$	−8.39523	+	14.5410i	−0.490454	+	0.849492i	−0.999940	−	0.0109876i	$-0.996502\pi$
$293$	−8.39523	+	14.5410i	−0.490454	+	0.849492i	0.509485	+	0.860479i	$0.329836\pi$
$294$		0			0
$295$	−0.851711	+	1.47521i	−0.0495886	+	0.0858899i
$296$	5.56841	−	9.64476i	0.323657	−	0.560590i
$297$		0			0
$298$	6.63504	−	11.4922i	0.384358	−	0.665727i
$299$	−26.2464	+	22.2150i	−1.51787	+	1.28473i
$300$		0			0
$301$	−1.24707	−	2.57816i	−0.0718801	−	0.148603i
$302$	8.06783	+	13.9739i	0.464252	+	0.804107i
$303$		0			0
$304$	0.388481	−	0.672870i	0.0222809	−	0.0385917i
$305$	−16.3563	−	28.3300i	−0.936560	−	1.62217i
$306$		0			0
$307$	5.69511			0.325037			0.162519	−	0.986705i	$-0.448038\pi$
$307$	5.69511			0.325037			0.162519	+	0.986705i	$0.448038\pi$
$308$	−12.9659	−	0.949124i	−0.738802	−	0.0540814i
$309$		0			0
$310$	−6.63613	+	11.4941i	−0.376907	+	0.652822i
$311$	−0.183797	+	0.318345i	−0.0104221	+	0.0180517i	−0.871189	−	0.490947i	$-0.836651\pi$
$311$	−0.183797	+	0.318345i	−0.0104221	+	0.0180517i	0.860767	+	0.508999i	$0.169984\pi$
$312$		0			0
$313$	−2.95742	−	5.12240i	−0.167163	−	0.289535i	0.770258	−	0.637732i	$-0.220127\pi$
$313$	−2.95742	−	5.12240i	−0.167163	−	0.289535i	−0.937421	+	0.348197i	$0.886794\pi$
$314$	8.85322	+	15.3342i	0.499616	+	0.865360i
$315$		0			0
$316$	2.17517	−	3.76751i	0.122363	−	0.211939i
$317$	4.28899	+	7.42875i	0.240894	+	0.417240i	0.960969	−	0.276656i	$-0.0892262\pi$
$317$	4.28899	+	7.42875i	0.240894	+	0.417240i	−0.720075	+	0.693896i	$0.755893\pi$
$318$		0			0
$319$	−3.09449	−	5.35982i	−0.173258	−	0.300092i
$320$	1.97513	+	3.42102i	0.110413	+	0.191241i
$321$		0			0
$322$	25.1649	+	1.84211i	1.40239	+	0.102657i
$323$	−0.0546094	−	0.0945863i	−0.00303855	−	0.00526292i
$324$		0			0
$325$	29.1846	−	24.7019i	1.61887	−	1.37022i
$326$	1.63571	−	2.83313i	0.0905935	−	0.156912i
$327$		0			0
$328$	4.65505	+	8.06279i	0.257032	+	0.445193i
$329$	17.5842	+	1.28719i	0.969448	+	0.0709649i
$330$		0			0
$331$	−4.14977			−0.228092			−0.114046	−	0.993475i	$-0.536381\pi$
$331$	−4.14977			−0.228092			−0.114046	+	0.993475i	$0.536381\pi$
$332$	−5.26102	−	9.11236i	−0.288736	−	0.500106i
$333$		0			0
$334$	8.85828			0.484704
$335$	16.1887	+	28.0397i	0.884483	+	1.53197i
$336$		0			0
$337$	18.5391			1.00989			0.504945	−	0.863152i	$-0.331513\pi$
$337$	18.5391			1.00989			0.504945	+	0.863152i	$0.331513\pi$
$338$	12.1776	−	4.55044i	0.662373	−	0.247511i
$339$		0			0
$340$	0.555293			0.0301150
$341$	8.25477	−	14.2977i	0.447021	−	0.774262i
$342$		0			0
$343$	18.0770	+	4.02745i	0.976069	+	0.217462i
$344$	0.541233	−	0.937443i	0.0291813	−	0.0505435i
$345$		0			0
$346$	7.47486	−	12.9468i	0.401851	−	0.696027i
$347$	−11.4934	−	19.9072i	−0.616999	−	1.06867i	−0.990030	−	0.140854i	$-0.955015\pi$
$347$	−11.4934	−	19.9072i	−0.616999	−	1.06867i	0.373032	−	0.927819i	$-0.378318\pi$
$348$		0			0
$349$	7.29494	+	12.6352i	0.390489	+	0.676347i	0.992514	−	0.122130i	$-0.0389726\pi$
$349$	7.29494	+	12.6352i	0.390489	+	0.676347i	−0.602025	+	0.798477i	$0.705639\pi$
$350$	−27.9820	−	2.04832i	−1.49570	−	0.109487i
$351$		0			0
$352$	−2.45689	−	4.25545i	−0.130953	−	0.226816i
$353$	19.7304			1.05015			0.525073	−	0.851057i	$-0.324038\pi$
$353$	19.7304			1.05015			0.525073	+	0.851057i	$0.324038\pi$
$354$		0			0
$355$	−15.3163			−0.812904
$356$	1.07274			0.0568550
$357$		0			0
$358$	11.6034	−	20.0977i	0.613260	−	1.06220i
$359$	−18.8344	−	32.6222i	−0.994044	−	1.72173i	−0.591401	−	0.806378i	$-0.701425\pi$
$359$	−18.8344	−	32.6222i	−0.994044	−	1.72173i	−0.402644	−	0.915357i	$-0.631909\pi$
$360$		0			0
$361$	−18.3963			−0.968228
$362$	9.73088	−	16.8544i	0.511444	−	0.885847i
$363$		0			0
$364$	−8.71859	−	3.87119i	−0.456978	−	0.202906i
$365$	−0.646119			−0.0338194
$366$		0			0
$367$	2.50281			0.130646			0.0653229	−	0.997864i	$-0.479192\pi$
$367$	2.50281			0.130646			0.0653229	+	0.997864i	$0.479192\pi$
$368$	4.76845	+	8.25920i	0.248573	+	0.430540i
$369$		0			0
$370$	−21.9966	+	38.0993i	−1.14355	+	1.98069i
$371$	−12.7466	−	26.3519i	−0.661768	−	1.36812i
$372$		0			0
$373$	−13.1674			−0.681783			−0.340891	−	0.940103i	$-0.610729\pi$
$373$	−13.1674			−0.681783			−0.340891	+	0.940103i	$0.610729\pi$
$374$	−0.690736			−0.0357171
$375$		0			0
$376$	3.33199	+	5.77118i	0.171834	+	0.297626i
$377$	−0.807672	−	4.46886i	−0.0415972	−	0.230158i
$378$		0			0
$379$	−5.93228	−	10.2750i	−0.304721	−	0.527792i	0.672478	−	0.740117i	$-0.265230\pi$
$379$	−5.93228	−	10.2750i	−0.304721	−	0.527792i	−0.977199	+	0.212325i	$0.931896\pi$
$380$	−1.53460	+	2.65801i	−0.0787233	+	0.136353i
$381$		0			0
$382$	7.29819	−	12.6408i	0.373408	−	0.646761i
$383$	−16.4228			−0.839165			−0.419582	−	0.907717i	$-0.637823\pi$
$383$	−16.4228			−0.839165			−0.419582	+	0.907717i	$0.637823\pi$
$384$		0			0
$385$	51.2187	+	3.74928i	2.61035	+	0.191081i
$386$	−0.884301	+	1.53165i	−0.0450098	+	0.0779592i
$387$		0			0
$388$	13.0819			0.664135
$389$	−9.03721	+	15.6529i	−0.458205	+	0.793634i	−0.998866	−	0.0476065i	$-0.984841\pi$
$389$	−9.03721	+	15.6529i	−0.458205	+	0.793634i	0.540662	+	0.841240i	$0.318174\pi$
$390$		0			0
$391$	1.34062			0.0677979
$392$	2.57990	+	6.50724i	0.130305	+	0.328665i
$393$		0			0
$394$	−5.85514			−0.294978
$395$	−8.59248	+	14.8826i	−0.432335	+	0.748826i
$396$		0			0
$397$	−2.40982			−0.120945			−0.0604726	−	0.998170i	$-0.519261\pi$
$397$	−2.40982			−0.120945			−0.0604726	+	0.998170i	$0.519261\pi$
$398$	−13.9227			−0.697884
$399$		0			0
$400$	−5.30226	−	9.18378i	−0.265113	−	0.459189i
$401$	−12.4622	+	21.5851i	−0.622331	+	1.07791i	0.366719	+	0.930332i	$0.380481\pi$
$401$	−12.4622	+	21.5851i	−0.622331	+	1.07791i	−0.989051	+	0.147577i	$0.952852\pi$
$402$		0			0
$403$	9.24660	−	7.82635i	0.460606	−	0.389858i
$404$	3.69262	+	6.39580i	0.183715	+	0.318203i
$405$		0			0
$406$	−1.87243	+	2.75658i	−0.0929271	+	0.136807i
$407$	27.3619	−	47.3922i	1.35628	−	2.34914i
$408$		0			0
$409$	−13.7384	−	23.7957i	−0.679323	−	1.17662i	−0.975185	−	0.221391i	$-0.928940\pi$
$409$	−13.7384	−	23.7957i	−0.679323	−	1.17662i	0.295863	−	0.955231i	$-0.404393\pi$
$410$	−18.3886	−	31.8501i	−0.908150	−	1.57296i
$411$		0			0
$412$	−1.99107	+	3.44863i	−0.0980929	+	0.169902i
$413$	−1.13785	−	0.0832924i	−0.0559901	−	0.00409855i
$414$		0			0
$415$	20.7824	+	35.9961i	1.02017	+	1.76698i
$416$	−0.641255	−	3.54807i	−0.0314401	−	0.173958i
$417$		0			0
$418$	1.90891	−	3.30633i	0.0933678	−	0.161718i
$419$	5.16655	+	8.94872i	0.252402	+	0.437174i	0.964187	−	0.265224i	$-0.0854460\pi$
$419$	5.16655	+	8.94872i	0.252402	+	0.437174i	−0.711784	+	0.702398i	$0.752113\pi$
$420$		0			0
$421$	−16.8702			−0.822204			−0.411102	−	0.911589i	$-0.634856\pi$
$421$	−16.8702			−0.822204			−0.411102	+	0.911589i	$0.634856\pi$
$422$	6.70799			0.326540
$423$		0			0
$424$	5.53204	−	9.58177i	0.268659	−	0.465332i
$425$	−1.49069			−0.0723092
$426$		0			0
$427$	12.3109	−	18.1241i	0.595768	−	0.877085i
$428$	7.07358			0.341914
$429$		0			0
$430$	−2.13801	+	3.70314i	−0.103104	+	0.178581i
$431$	−24.3436			−1.17259			−0.586294	−	0.810098i	$-0.699414\pi$
$431$	−24.3436			−1.17259			−0.586294	+	0.810098i	$0.699414\pi$
$432$		0			0
$433$	0.984059	−	1.70444i	0.0472909	−	0.0819102i	−0.841411	−	0.540396i	$-0.818275\pi$
$433$	0.984059	−	1.70444i	0.0472909	−	0.0819102i	0.888702	+	0.458485i	$0.151608\pi$
$434$	−8.86560	−	0.648974i	−0.425562	−	0.0311518i
$435$		0			0
$436$	14.8470			0.711042
$437$	−3.70491	+	6.41709i	−0.177230	+	0.306971i
$438$		0			0
$439$	−10.1318	+	17.5488i	−0.483564	+	0.837558i	−0.999822	−	0.0188756i	$-0.993991\pi$
$439$	−10.1318	+	17.5488i	−0.483564	+	0.837558i	0.516258	+	0.856433i	$0.327325\pi$
$440$	9.70533	+	16.8101i	0.462683	+	0.801391i
$441$		0			0
$442$	−0.477008	−	0.171313i	−0.0226889	−	0.00814854i
$443$	14.2707	+	24.7177i	0.678024	+	1.17437i	0.975575	+	0.219666i	$0.0704967\pi$
$443$	14.2707	+	24.7177i	0.678024	+	1.17437i	−0.297551	+	0.954706i	$0.596170\pi$
$444$		0			0
$445$	−4.23759			−0.200881
$446$	−2.05487			−0.0973011
$447$		0			0
$448$	−1.48662	+	2.18860i	−0.0702364	+	0.103401i
$449$	−12.1517	+	21.0474i	−0.573475	+	0.993287i	0.422731	+	0.906255i	$0.361072\pi$
$449$	−12.1517	+	21.0474i	−0.573475	+	0.993287i	−0.996206	+	0.0870320i	$0.972262\pi$
$450$		0			0
$451$	22.8739	+	39.6187i	1.07709	+	1.86557i
$452$	−1.57179			−0.0739308
$453$		0			0
$454$	−25.8298			−1.21225
$455$	34.4407	+	15.2922i	1.61460	+	0.716909i
$456$		0			0
$457$	3.12651	−	5.41528i	0.146252	−	0.253316i	−0.783587	−	0.621282i	$-0.786612\pi$
$457$	3.12651	−	5.41528i	0.146252	−	0.253316i	0.929839	+	0.367966i	$0.119946\pi$
$458$	10.7899			0.504180
$459$		0			0
$460$	−18.8366	−	32.6259i	−0.878261	−	1.52119i
$461$	−9.65625	+	16.7251i	−0.449736	+	0.778966i	−0.998369	−	0.0570976i	$-0.981815\pi$
$461$	−9.65625	+	16.7251i	−0.449736	+	0.778966i	0.548632	+	0.836064i	$0.315149\pi$
$462$		0			0
$463$	21.4480			0.996772			0.498386	−	0.866955i	$-0.333926\pi$
$463$	21.4480			0.996772			0.498386	+	0.866955i	$0.333926\pi$
$464$	−1.25952			−0.0584717
$465$		0			0
$466$	3.84218			0.177986
$467$	−2.39255	−	4.14402i	−0.110714	−	0.191762i	0.805344	−	0.592807i	$-0.201980\pi$
$467$	−2.39255	−	4.14402i	−0.110714	−	0.191762i	−0.916058	+	0.401045i	$0.868647\pi$
$468$		0			0
$469$	−12.1848	+	17.9384i	−0.562641	+	0.828316i
$470$	−13.1622	−	22.7976i	−0.607128	−	1.05158i
$471$		0			0
$472$	−0.215609	−	0.373446i	−0.00992422	−	0.0171893i
$473$	2.65950	−	4.60638i	0.122284	−	0.211802i
$474$		0			0
$475$	4.11966	−	7.13545i	0.189023	−	0.327397i
$476$	0.161948	+	0.334806i	0.00742287	+	0.0153458i
$477$		0			0
$478$	−5.12799	+	8.88194i	−0.234549	+	0.406250i
$479$	11.7132			0.535190			0.267595	−	0.963532i	$-0.413771\pi$
$479$	11.7132			0.535190			0.267595	+	0.963532i	$0.413771\pi$
$480$		0			0
$481$	30.6495	−	25.9418i	1.39750	−	1.18285i
$482$	0.632854			0.0288257
$483$		0			0
$484$	−6.57259	−	11.3841i	−0.298754	−	0.517457i
$485$	−51.6770			−2.34653
$486$		0			0
$487$	12.8785	+	22.3062i	0.583581	+	1.01079i	0.995051	+	0.0993684i	$0.0316822\pi$
$487$	12.8785	+	22.3062i	0.583581	+	1.01079i	−0.411470	+	0.911423i	$0.634984\pi$
$488$	8.28114			0.374870
$489$		0			0
$490$	−10.1913	−	25.7052i	−0.460395	−	1.16124i
$491$	−2.35012	−	4.07053i	−0.106059	−	0.183700i	0.808111	−	0.589030i	$-0.200490\pi$
$491$	−2.35012	−	4.07053i	−0.106059	−	0.183700i	−0.914171	+	0.405330i	$0.867157\pi$
$492$		0			0
$493$	−0.0885262	+	0.153332i	−0.00398702	+	0.00690572i
$494$	2.13827	−	1.80984i	0.0962054	−	0.0814285i
$495$		0			0
$496$	−1.67992	−	2.90971i	−0.0754308	−	0.130650i
$497$	−4.46690	−	9.23475i	−0.200368	−	0.414235i
$498$		0			0
$499$	16.3247	+	28.2752i	0.730794	+	1.26577i	0.956544	+	0.291587i	$0.0941832\pi$
$499$	16.3247	+	28.2752i	0.730794	+	1.26577i	−0.225751	+	0.974185i	$0.572483\pi$
$500$	11.0696	+	19.1731i	0.495048	+	0.857449i
$501$		0			0
$502$	7.53648	+	13.0536i	0.336370	+	0.582609i
$503$	−7.49164	+	12.9759i	−0.334036	+	0.578567i	−0.983299	−	0.181997i	$-0.941744\pi$
$503$	−7.49164	+	12.9759i	−0.334036	+	0.578567i	0.649263	+	0.760564i	$0.275077\pi$
$504$		0			0
$505$	−14.5868	−	25.2650i	−0.649103	−	1.12428i
$506$	23.4311	+	40.5838i	1.04164	+	1.80417i
$507$		0			0
$508$	−5.42757	+	9.40083i	−0.240809	+	0.417094i
$509$	−0.210438	+	0.364489i	−0.00932749	+	0.0161557i	−0.870651	−	0.491900i	$-0.836302\pi$
$509$	−0.210438	+	0.364489i	−0.00932749	+	0.0161557i	0.861324	+	0.508056i	$0.169636\pi$
$510$		0			0
$511$	−0.188437	−	0.389569i	−0.00833595	−	0.0172335i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−5.56909	−	9.64595i	−0.245642	−	0.425464i
$515$	7.86522	−	13.6230i	0.346583	−	0.600300i
$516$		0			0
$517$	16.3727	+	28.3583i	0.720068	+	1.24720i
$518$	−29.3866	−	2.15114i	−1.29117	−	0.0945157i
$519$		0			0
$520$	2.53312	+	14.0158i	0.111085	+	0.614632i
$521$	15.5914	−	27.0050i	0.683070	−	1.18311i	−0.290969	−	0.956732i	$-0.593978\pi$
$521$	15.5914	−	27.0050i	0.683070	−	1.18311i	0.974039	−	0.226379i	$-0.0726888\pi$
$522$		0			0
$523$	−7.18192	+	12.4394i	−0.314043	+	0.543939i	−0.979234	−	0.202735i	$-0.935017\pi$
$523$	−7.18192	+	12.4394i	−0.314043	+	0.543939i	0.665190	+	0.746674i	$0.268350\pi$
$524$	0.961751	−	1.66580i	0.0420143	−	0.0727709i
$525$		0			0
$526$	−8.58528	+	14.8701i	−0.374336	+	0.648369i
$527$	−0.472299			−0.0205737
$528$		0			0
$529$	−33.9762	−	58.8486i	−1.47723	−	2.55863i
$530$	−21.8530	+	37.8504i	−0.949232	+	1.64412i
$531$		0			0
$532$	−2.05016	−	0.150075i	−0.0888859	−	0.00650657i
$533$	5.97015	+	33.0329i	0.258596	+	1.43081i
$534$		0			0
$535$	−27.9424			−1.20806
$536$	−8.19628			−0.354026
$537$		0			0
$538$	3.28711			0.141717
$539$	12.6771	+	31.9751i	0.546039	+	1.37726i
$540$		0			0
$541$	4.68698	+	8.11808i	0.201509	+	0.349024i	0.949015	−	0.315232i	$-0.102082\pi$
$541$	4.68698	+	8.11808i	0.201509	+	0.349024i	−0.747506	+	0.664255i	$0.768749\pi$
$542$	7.36304	+	12.7532i	0.316270	+	0.547795i
$543$		0			0
$544$	−0.0702857	+	0.121738i	−0.00301348	+	0.00521949i
$545$	−58.6494			−2.51227
$546$		0			0
$547$	17.7829			0.760343			0.380172	−	0.924916i	$-0.375865\pi$
$547$	17.7829			0.760343			0.380172	+	0.924916i	$0.375865\pi$
$548$	7.94106	−	13.7543i	0.339225	−	0.587555i
$549$		0			0
$550$	−26.0541	−	45.1270i	−1.11095	−	1.92422i
$551$	−0.489299	−	0.847491i	−0.0208449	−	0.0361043i
$552$		0			0
$553$	−11.4792	−	0.840294i	−0.488146	−	0.0357329i
$554$	−18.5004			−0.786008
$555$		0			0
$556$	−5.88702			−0.249665
$557$	−13.3641			−0.566257			−0.283128	−	0.959082i	$-0.591372\pi$
$557$	−13.3641			−0.566257			−0.283128	+	0.959082i	$0.591372\pi$
$558$		0			0
$559$	2.97904	−	2.52147i	0.126000	−	0.106647i
$560$	5.87254	−	8.64551i	0.248160	−	0.365339i
$561$		0			0
$562$	15.6731	−	27.1467i	0.661131	−	1.14511i
$563$	−13.6941	−	23.7189i	−0.577139	−	0.999634i	−0.995806	−	0.0914943i	$-0.970836\pi$
$563$	−13.6941	−	23.7189i	−0.577139	−	0.999634i	0.418666	−	0.908140i	$-0.362498\pi$
$564$		0			0
$565$	6.20897			0.261213
$566$	−7.35985	+	12.7476i	−0.309357	+	0.535823i
$567$		0			0
$568$	1.93865	−	3.35783i	0.0813438	−	0.140892i
$569$	−5.48808	+	9.50564i	−0.230072	+	0.398497i	−0.957829	−	0.287338i	$-0.907230\pi$
$569$	−5.48808	+	9.50564i	−0.230072	+	0.398497i	0.727757	+	0.685835i	$0.240563\pi$
$570$		0			0
$571$	−14.5552	+	25.2103i	−0.609115	+	1.05502i	0.382271	+	0.924050i	$0.375142\pi$
$571$	−14.5552	+	25.2103i	−0.609115	+	1.05502i	−0.991387	+	0.130969i	$0.958191\pi$
$572$	−3.15098	−	17.4344i	−0.131749	−	0.728969i
$573$		0			0
$574$	13.8406	−	20.3760i	0.577696	−	0.850480i
$575$	50.5671	+	87.5847i	2.10879	+	3.65254i
$576$		0			0
$577$	−10.0317	+	17.3753i	−0.417623	+	0.723345i	−0.995700	−	0.0926375i	$-0.970470\pi$
$577$	−10.0317	+	17.3753i	−0.417623	+	0.723345i	0.578076	+	0.815983i	$0.303804\pi$
$578$	−8.49012	−	14.7053i	−0.353142	−	0.611661i
$579$		0			0
$580$	4.97542			0.206593
$581$	−15.6423	+	23.0285i	−0.648953	+	0.955383i
$582$		0			0
$583$	27.1832	−	47.0826i	1.12581	−	1.94996i
$584$	0.0817820	−	0.141650i	0.00338416	−	0.00586154i
$585$		0			0
$586$	8.39523	+	14.5410i	0.346804	+	0.600681i
$587$	−16.0113	−	27.7323i	−0.660855	−	1.14463i	−0.980391	−	0.197060i	$-0.936860\pi$
$587$	−16.0113	−	27.7323i	−0.660855	−	1.14463i	0.319536	−	0.947574i	$-0.396473\pi$
$588$		0			0
$589$	1.30524	−	2.26074i	0.0537814	−	0.0931521i
$590$	0.851711	+	1.47521i	0.0350644	+	0.0607333i
$591$		0			0
$592$	−5.56841	−	9.64476i	−0.228860	−	0.396397i
$593$	−12.2192	−	21.1643i	−0.501784	−	0.869115i	−0.999998	−	0.00206106i	$-0.999344\pi$
$593$	−12.2192	−	21.1643i	−0.501784	−	0.869115i	0.498214	−	0.867054i	$-0.333989\pi$
$594$		0			0
$595$	−0.639735	−	1.32257i	−0.0262266	−	0.0542201i
$596$	−6.63504	−	11.4922i	−0.271782	−	0.470740i
$597$		0			0
$598$	6.11559	+	33.8376i	0.250085	+	1.38372i
$599$	7.93636	−	13.7462i	0.324271	−	0.561654i	−0.657093	−	0.753809i	$-0.728214\pi$
$599$	7.93636	−	13.7462i	0.324271	−	0.561654i	0.981365	+	0.192155i	$0.0615477\pi$
$600$		0			0
$601$	−0.0246085	−	0.0426231i	−0.00100380	−	0.00173863i	0.865523	−	0.500869i	$-0.166986\pi$
$601$	−0.0246085	−	0.0426231i	−0.00100380	−	0.00173863i	−0.866527	+	0.499130i	$0.833653\pi$
$602$	−2.85629	−	0.209085i	−0.116414	−	0.00852165i
$603$		0			0
$604$	16.1357			0.656551
$605$	25.9634	+	44.9699i	1.05556	+	1.82829i
$606$		0			0
$607$	13.2265			0.536847			0.268423	−	0.963301i	$-0.413497\pi$
$607$	13.2265			0.536847			0.268423	+	0.963301i	$0.413497\pi$
$608$	−0.388481	−	0.672870i	−0.0157550	−	0.0272885i
$609$		0			0
$610$	−32.7126			−1.32450
$611$	4.27331	+	23.6443i	0.172880	+	0.956545i
$612$		0			0
$613$	−2.35096			−0.0949543			−0.0474772	−	0.998872i	$-0.515118\pi$
$613$	−2.35096			−0.0949543			−0.0474772	+	0.998872i	$0.515118\pi$
$614$	2.84756	−	4.93211i	0.114918	−	0.199044i
$615$		0			0
$616$	−7.30493	+	10.7543i	−0.294324	+	0.433302i
$617$	16.1133	−	27.9090i	0.648697	−	1.12358i	−0.334738	−	0.942311i	$-0.608648\pi$
$617$	16.1133	−	27.9090i	0.648697	−	1.12358i	0.983434	−	0.181264i	$-0.0580189\pi$
$618$		0			0
$619$	9.49745	−	16.4501i	0.381735	−	0.661184i	−0.609575	−	0.792728i	$-0.708660\pi$
$619$	9.49745	−	16.4501i	0.381735	−	0.661184i	0.991310	+	0.131544i	$0.0419934\pi$
$620$	6.63613	+	11.4941i	0.266513	+	0.461615i
$621$		0			0
$622$	0.183797	+	0.318345i	0.00736957	+	0.0127645i
$623$	−1.23587	−	2.55500i	−0.0495140	−	0.102364i
$624$		0			0
$625$	−17.2165	−	29.8199i	−0.688662	−	1.19280i
$626$	−5.91484			−0.236404
$627$		0			0
$628$	17.7064			0.706564
$629$	−1.56552			−0.0624213
$630$		0			0
$631$	−11.7271	+	20.3119i	−0.466849	+	0.808606i	−0.999283	−	0.0378658i	$-0.987944\pi$
$631$	−11.7271	+	20.3119i	−0.466849	+	0.808606i	0.532434	+	0.846471i	$0.321277\pi$
$632$	−2.17517	−	3.76751i	−0.0865237	−	0.149863i
$633$		0			0
$634$	8.57798			0.340675
$635$	21.4403	−	37.1357i	0.850832	−	1.47368i
$636$		0			0
$637$	0.824188	+	25.2254i	0.0326555	+	0.999467i
$638$	−6.18899			−0.245024
$639$		0			0
$640$	3.95025			0.156148
$641$	2.80221	+	4.85357i	0.110681	+	0.191705i	0.916045	−	0.401076i	$-0.131364\pi$
$641$	2.80221	+	4.85357i	0.110681	+	0.191705i	−0.805364	+	0.592780i	$0.798030\pi$
$642$		0			0
$643$	11.5626	−	20.0270i	0.455983	−	0.789786i	−0.542761	−	0.839887i	$-0.682621\pi$
$643$	11.5626	−	20.0270i	0.455983	−	0.789786i	0.998744	+	0.0501012i	$0.0159544\pi$
$644$	14.1778	−	20.8724i	0.558683	−	0.822488i
$645$		0			0
$646$	−0.109219			−0.00429716
$647$	−17.7756			−0.698832			−0.349416	−	0.936968i	$-0.613620\pi$
$647$	−17.7756			−0.698832			−0.349416	+	0.936968i	$0.613620\pi$
$648$		0			0
$649$	−1.05945	−	1.83503i	−0.0415872	−	0.0720312i
$650$	−6.80020	−	37.6255i	−0.266726	−	1.47579i
$651$		0			0
$652$	−1.63571	−	2.83313i	−0.0640593	−	0.110954i
$653$	1.25251	−	2.16941i	0.0490145	−	0.0848956i	−0.840477	−	0.541847i	$-0.817725\pi$
$653$	1.25251	−	2.16941i	0.0490145	−	0.0848956i	0.889492	+	0.456951i	$0.151059\pi$
$654$		0			0
$655$	−3.79916	+	6.58034i	−0.148445	+	0.257115i
$656$	9.31010			0.363498
$657$		0			0
$658$	9.90683	−	14.5848i	0.386209	−	0.568573i
$659$	15.8598	−	27.4700i	0.617810	−	1.07008i	−0.372074	−	0.928203i	$-0.621353\pi$
$659$	15.8598	−	27.4700i	0.617810	−	1.07008i	0.989884	−	0.141876i	$-0.0453134\pi$
$660$		0			0
$661$	22.7146			0.883494			0.441747	−	0.897140i	$-0.354359\pi$
$661$	22.7146			0.883494			0.441747	+	0.897140i	$0.354359\pi$
$662$	−2.07489	+	3.59381i	−0.0806427	+	0.139677i
$663$		0			0
$664$	−10.5220			−0.408335
$665$	8.09867	+	0.592834i	0.314053	+	0.0229891i
$666$		0			0
$667$	12.0119			0.465103
$668$	4.42914	−	7.67150i	0.171369	−	0.296819i
$669$		0			0
$670$	32.3774			1.25085
$671$	40.6917			1.57088
$672$		0			0
$673$	−2.56027	−	4.43452i	−0.0986911	−	0.170938i	0.812452	−	0.583028i	$-0.198132\pi$
$673$	−2.56027	−	4.43452i	−0.0986911	−	0.170938i	−0.911143	+	0.412090i	$0.864799\pi$
$674$	9.26955	−	16.0553i	0.357050	−	0.618428i
$675$		0			0
$676$	2.14800	−	12.8213i	0.0826154	−	0.493127i
$677$	−1.02921	−	1.78264i	−0.0395556	−	0.0685123i	0.845570	−	0.533865i	$-0.179261\pi$
$677$	−1.02921	−	1.78264i	−0.0395556	−	0.0685123i	−0.885125	+	0.465353i	$0.845928\pi$
$678$		0			0
$679$	−15.0713	−	31.1579i	−0.578383	−	1.19573i
$680$	0.277647	−	0.480898i	0.0106473	−	0.0184416i
$681$		0			0
$682$	−8.25477	−	14.2977i	−0.316091	−	0.547486i
$683$	−13.4644	−	23.3211i	−0.515202	−	0.892356i	−0.999844	−	0.0176436i	$-0.994384\pi$
$683$	−13.4644	−	23.3211i	−0.515202	−	0.892356i	0.484642	−	0.874712i	$-0.338950\pi$
$684$		0			0
$685$	−31.3692	+	54.3330i	−1.19856	+	2.07596i
$686$	12.5264	−	13.6415i	0.478260	−	0.520833i
$687$		0			0
$688$	−0.541233	−	0.937443i	−0.0206343	−	0.0357397i
$689$	30.4493	−	25.7724i	1.16003	−	0.981850i
$690$		0			0
$691$	−25.6380	+	44.4064i	−0.975316	+	1.68930i	−0.296430	+	0.955055i	$0.595796\pi$
$691$	−25.6380	+	44.4064i	−0.975316	+	1.68930i	−0.678887	+	0.734243i	$0.737537\pi$
$692$	−7.47486	−	12.9468i	−0.284152	−	0.492165i
$693$		0			0
$694$	−22.9868			−0.872568
$695$	23.2552			0.882121
$696$		0			0
$697$	0.654367	−	1.13340i	0.0247859	−	0.0429305i
$698$	14.5899			0.552235
$699$		0			0
$700$	−15.7649	+	23.2090i	−0.595858	+	0.877217i
$701$	26.2809			0.992617			0.496308	−	0.868146i	$-0.334689\pi$
$701$	26.2809			0.992617			0.496308	+	0.868146i	$0.334689\pi$
$702$		0			0
$703$	4.32644	−	7.49362i	0.163175	−	0.282627i
$704$	−4.91377			−0.185195
$705$		0			0
$706$	9.86522	−	17.0871i	0.371283	−	0.643080i
$707$	10.9791	−	16.1633i	0.412910	−	0.607883i
$708$		0			0
$709$	8.75932			0.328963			0.164482	−	0.986380i	$-0.447405\pi$
$709$	8.75932			0.328963			0.164482	+	0.986380i	$0.447405\pi$
$710$	−7.65815	+	13.2643i	−0.287405	+	0.497800i
$711$		0			0
$712$	0.536369	−	0.929018i	0.0201013	−	0.0348164i
$713$	16.0213	+	27.7496i	0.600001	+	1.03923i
$714$		0			0
$715$	12.4472	+	68.8703i	0.465498	+	2.57560i
$716$	−11.6034	−	20.0977i	−0.433640	−	0.751087i
$717$		0			0
$718$	−37.6689			−1.40579
$719$	2.27601			0.0848810			0.0424405	−	0.999099i	$-0.486487\pi$
$719$	2.27601			0.0848810			0.0424405	+	0.999099i	$0.486487\pi$
$720$		0			0
$721$	10.5076	+	0.769173i	0.391324	+	0.0286455i
$722$	−9.19816	+	15.9317i	−0.342320	+	0.592916i
$723$		0			0
$724$	−9.73088	−	16.8544i	−0.361645	−	0.626388i
$725$	−13.3566			−0.496051
$726$		0			0
$727$	−39.8719			−1.47877			−0.739383	−	0.673285i	$-0.764883\pi$
$727$	−39.8719			−1.47877			−0.739383	+	0.673285i	$0.764883\pi$
$728$	−7.71185	+	5.61493i	−0.285820	+	0.208103i
$729$		0			0
$730$	−0.323060	+	0.559556i	−0.0119570	+	0.0207101i
$731$	−0.152164			−0.00562798
$732$		0			0
$733$	−12.8845	−	22.3167i	−0.475901	−	0.824284i	0.523718	−	0.851892i	$-0.324545\pi$
$733$	−12.8845	−	22.3167i	−0.475901	−	0.824284i	−0.999619	+	0.0276073i	$0.991211\pi$
$734$	1.25141	−	2.16750i	0.0461903	−	0.0800039i
$735$		0			0
$736$	9.53690			0.351535
$737$	−40.2747			−1.48354
$738$		0			0
$739$	12.8179			0.471512			0.235756	−	0.971812i	$-0.424243\pi$
$739$	12.8179			0.471512			0.235756	+	0.971812i	$0.424243\pi$
$740$	21.9966	+	38.0993i	0.808612	+	1.40056i
$741$		0			0
$742$	−29.1947	−	2.13709i	−1.07177	−	0.0784551i
$743$	10.1715	+	17.6176i	0.373156	+	0.646326i	0.990049	−	0.140721i	$-0.0449422\pi$
$743$	10.1715	+	17.6176i	0.373156	+	0.646326i	−0.616893	+	0.787047i	$0.711609\pi$
$744$		0			0
$745$	26.2101	+	45.3972i	0.960264	+	1.66323i
$746$	−6.58371	+	11.4033i	−0.241047	+	0.417505i
$747$		0			0
$748$	−0.345368	+	0.598195i	−0.0126279	+	0.0218722i
$749$	−8.14924	−	16.8475i	−0.297767	−	0.615594i
$750$		0			0
$751$	15.2371	−	26.3914i	0.556008	−	0.963034i	−0.441816	−	0.897106i	$-0.645666\pi$
$751$	15.2371	−	26.3914i	0.556008	−	0.963034i	0.997824	−	0.0659287i	$-0.0210010\pi$
$752$	6.66398			0.243010
$753$		0			0
$754$	−4.27398	−	1.53496i	−0.155649	−	0.0559001i
$755$	−63.7400			−2.31974
$756$		0			0
$757$	10.7264	+	18.5787i	0.389859	+	0.675256i	0.992430	−	0.122809i	$-0.0391904\pi$
$757$	10.7264	+	18.5787i	0.389859	+	0.675256i	−0.602571	+	0.798065i	$0.705857\pi$
$758$	−11.8646			−0.430940
$759$		0			0
$760$	1.53460	+	2.65801i	0.0556658	+	0.0964160i
$761$	50.0476			1.81422			0.907112	−	0.420890i	$-0.138282\pi$
$761$	50.0476			1.81422			0.907112	+	0.420890i	$0.138282\pi$
$762$		0			0
$763$	−17.1048	−	35.3619i	−0.619234	−	1.28019i
$764$	−7.29819	−	12.6408i	−0.264039	−	0.457329i
$765$		0			0
$766$	−8.21139	+	14.2225i	−0.296690	+	0.513881i
$767$	−0.276521	−	1.52999i	−0.00998460	−	0.0552448i
$768$		0			0
$769$	25.3820	+	43.9629i	0.915298	+	1.58534i	0.806465	+	0.591282i	$0.201378\pi$
$769$	25.3820	+	43.9629i	0.915298	+	1.58534i	0.108833	+	0.994060i	$0.465289\pi$
$770$	28.8563	−	42.4821i	1.03991	−	1.53095i
$771$		0			0
$772$	0.884301	+	1.53165i	0.0318267	+	0.0551255i
$773$	7.14225	+	12.3707i	0.256889	+	0.444944i	0.965407	−	0.260748i	$-0.0839693\pi$
$773$	7.14225	+	12.3707i	0.256889	+	0.444944i	−0.708518	+	0.705693i	$0.750636\pi$
$774$		0			0
$775$	−17.8148	−	30.8561i	−0.639925	−	1.10838i
$776$	6.54097	−	11.3293i	0.234807	−	0.406698i
$777$		0			0
$778$	9.03721	+	15.6529i	0.324000	+	0.561184i
$779$	3.61680	+	6.26448i	0.129585	+	0.224448i
$780$		0			0
$781$	9.52607	−	16.4996i	0.340870	−	0.590403i
$782$	0.670308	−	1.16101i	0.0239702	−	0.0415176i
$783$		0			0
$784$	6.92538	+	1.01936i	0.247335	+	0.0364056i
$785$	−69.9449			−2.49644
$786$		0			0
$787$	3.26997	+	5.66376i	0.116562	+	0.201891i	0.918403	−	0.395646i	$-0.129479\pi$
$787$	3.26997	+	5.66376i	0.116562	+	0.201891i	−0.801841	+	0.597537i	$0.796146\pi$
$788$	−2.92757	+	5.07070i	−0.104290	+	0.180636i
$789$		0			0
$790$	8.59248	+	14.8826i	0.305707	+	0.529500i
$791$	1.81081	+	3.74361i	0.0643849	+	0.133108i
$792$		0			0
$793$	28.1008	+	10.0922i	0.997888	+	0.358383i
$794$	−1.20491	+	2.08696i	−0.0427606	+	0.0740635i
$795$		0			0
$796$	−6.96137	+	12.0575i	−0.246739	+	0.427365i
$797$	24.2958	−	42.0815i	0.860601	−	1.49060i	−0.0107495	−	0.999942i	$-0.503422\pi$
$797$	24.2958	−	42.0815i	0.860601	−	1.49060i	0.871350	−	0.490662i	$-0.163245\pi$
$798$		0			0
$799$	0.468383	−	0.811263i	0.0165702	−	0.0287004i
$800$	−10.6045			−0.374926
$801$		0			0
$802$	12.4622	+	21.5851i	0.440055	+	0.762197i
$803$	0.401858	−	0.696038i	0.0141813	−	0.0245627i
$804$		0			0
$805$	−56.0058	+	82.4514i	−1.97395	+	2.90603i
$806$	−2.15452	−	11.9210i	−0.0758897	−	0.419898i
$807$		0			0
$808$	7.38523			0.259812
$809$	−41.7183			−1.46674			−0.733369	−	0.679831i	$-0.762053\pi$
$809$	−41.7183			−1.46674			−0.733369	+	0.679831i	$0.762053\pi$
$810$		0			0
$811$	2.40508			0.0844538			0.0422269	−	0.999108i	$-0.486555\pi$
$811$	2.40508			0.0844538			0.0422269	+	0.999108i	$0.486555\pi$
$812$	1.45105	+	2.99986i	0.0509219	+	0.105274i
$813$		0			0
$814$	−27.3619	−	47.3922i	−0.959034	−	1.66109i
$815$	6.46146	+	11.1916i	0.226335	+	0.392024i
$816$		0			0
$817$	0.420518	−	0.728358i	0.0147121	−	0.0254820i
$818$	−27.4769			−0.960707
$819$		0			0
$820$	−36.7773			−1.28432
$821$	−0.226645	+	0.392561i	−0.00790998	+	0.0137005i	−0.869953	−	0.493134i	$-0.835851\pi$
$821$	−0.226645	+	0.392561i	−0.00790998	+	0.0137005i	0.862043	+	0.506835i	$0.169185\pi$
$822$		0			0
$823$	2.09531	+	3.62919i	0.0730380	+	0.126506i	0.900231	−	0.435412i	$-0.143397\pi$
$823$	2.09531	+	3.62919i	0.0730380	+	0.126506i	−0.827193	+	0.561917i	$0.810064\pi$
$824$	1.99107	+	3.44863i	0.0693621	+	0.120139i
$825$		0			0
$826$	−0.641059	+	0.943763i	−0.0223053	+	0.0328377i
$827$	−1.35282			−0.0470421			−0.0235211	−	0.999723i	$-0.507488\pi$
$827$	−1.35282			−0.0470421			−0.0235211	+	0.999723i	$0.507488\pi$
$828$		0			0
$829$	−48.2162			−1.67462			−0.837309	−	0.546730i	$-0.815872\pi$
$829$	−48.2162			−1.67462			−0.837309	+	0.546730i	$0.815872\pi$
$830$	41.5648			1.44273
$831$		0			0
$832$	−3.39335	−	1.21869i	−0.117643	−	0.0422505i
$833$	0.610851	−	0.771439i	0.0211647	−	0.0267288i
$834$		0			0
$835$	−17.4962	+	30.3044i	−0.605482	+	1.04873i
$836$	−1.90891	−	3.30633i	−0.0660210	−	0.114352i
$837$		0			0
$838$	10.3331			0.356951
$839$	−14.1093	+	24.4380i	−0.487107	+	0.843694i	−0.999890	−	0.0148244i	$-0.995281\pi$
$839$	−14.1093	+	24.4380i	−0.487107	+	0.843694i	0.512783	+	0.858518i	$0.328614\pi$
$840$		0			0
$841$	13.7068	−	23.7409i	0.472649	−	0.818651i
$842$	−8.43511	+	14.6100i	−0.290693	+	0.503495i
$843$		0			0
$844$	3.35399	−	5.80929i	0.115449	−	0.199964i
$845$	−8.48514	+	50.6475i	−0.291898	+	1.74233i
$846$		0			0
$847$	−19.5419	+	28.7695i	−0.671468	+	0.988530i
$848$	−5.53204	−	9.58177i	−0.189971	−	0.329039i
$849$		0			0
$850$	−0.745346	+	1.29098i	−0.0255652	+	0.0442801i
$851$	53.1053	+	91.9811i	1.82043	+	3.15307i
$852$		0			0
$853$	−3.29308			−0.112753			−0.0563764	−	0.998410i	$-0.517955\pi$
$853$	−3.29308			−0.112753			−0.0563764	+	0.998410i	$0.517955\pi$
$854$	−9.54044	−	19.7236i	−0.326467	−	0.674929i
$855$		0			0
$856$	3.53679	−	6.12590i	0.120885	−	0.209379i
$857$	−16.7918	+	29.0842i	−0.573596	+	0.993497i	0.422597	+	0.906318i	$0.361119\pi$
$857$	−16.7918	+	29.0842i	−0.573596	+	0.993497i	−0.996193	+	0.0871794i	$0.972215\pi$
$858$		0			0
$859$	−13.6075	−	23.5688i	−0.464280	−	0.804157i	0.534888	−	0.844923i	$-0.320354\pi$
$859$	−13.6075	−	23.5688i	−0.464280	−	0.804157i	−0.999169	+	0.0407656i	$0.987020\pi$
$860$	2.13801	+	3.70314i	0.0729054	+	0.126276i
$861$		0			0
$862$	−12.1718	+	21.0822i	−0.414573	+	0.718061i
$863$	7.05959	+	12.2276i	0.240311	+	0.416231i	0.960803	−	0.277232i	$-0.0894172\pi$
$863$	7.05959	+	12.2276i	0.240311	+	0.416231i	−0.720492	+	0.693463i	$0.756084\pi$
$864$		0			0
$865$	29.5276	+	51.1433i	1.00397	+	1.73893i
$866$	−0.984059	−	1.70444i	−0.0334397	−	0.0579193i
$867$		0			0
$868$	−4.99483	+	7.35335i	−0.169536	+	0.249589i
$869$	−10.6883	−	18.5127i	−0.362576	−	0.628000i
$870$		0			0
$871$	−27.8128	−	9.98874i	−0.942402	−	0.338455i
$872$	7.42350	−	12.8579i	0.251391	−	0.435423i
$873$		0			0
$874$	3.70491	+	6.41709i	0.125320	+	0.217061i
$875$	32.9127	−	48.4538i	1.11265	−	1.63804i
$876$		0			0
$877$	−8.01911			−0.270786			−0.135393	−	0.990792i	$-0.543230\pi$
$877$	−8.01911			−0.270786			−0.135393	+	0.990792i	$0.543230\pi$
$878$	10.1318	+	17.5488i	0.341931	+	0.592243i
$879$		0			0
$880$	19.4107			0.654333
$881$	−13.1358	−	22.7519i	−0.442558	−	0.766532i	0.555321	−	0.831636i	$-0.312595\pi$
$881$	−13.1358	−	22.7519i	−0.442558	−	0.766532i	−0.997878	+	0.0651039i	$0.979262\pi$
$882$		0			0
$883$	−18.7341			−0.630452			−0.315226	−	0.949017i	$-0.602080\pi$
$883$	−18.7341			−0.630452			−0.315226	+	0.949017i	$0.602080\pi$
$884$	−0.386865	+	0.327444i	−0.0130117	+	0.0110131i
$885$		0			0
$886$	28.5415			0.958870
$887$	−6.11884	+	10.5981i	−0.205450	+	0.355851i	−0.950276	−	0.311408i	$-0.899199\pi$
$887$	−6.11884	+	10.5981i	−0.205450	+	0.355851i	0.744826	+	0.667259i	$0.232533\pi$
$888$		0			0
$889$	28.6434	+	2.09673i	0.960667	+	0.0703222i
$890$	−2.11879	+	3.66986i	−0.0710221	+	0.123014i
$891$		0			0
$892$	−1.02744	+	1.77957i	−0.0344011	+	0.0595845i
$893$	2.58883	+	4.48399i	0.0866320	+	0.150051i
$894$		0			0
$895$	45.8365	+	79.3911i	1.53214	+	2.65375i
$896$	1.15207	+	2.38175i	0.0384879	+	0.0795687i
$897$		0			0
$898$	12.1517	+	21.0474i	0.405508	+	0.702360i
$899$	−4.23179			−0.141138
$900$		0			0
$901$	−1.55529			−0.0518143
$902$	45.7477			1.52323
$903$		0			0
$904$	−0.785895	+	1.36121i	−0.0261385	+	0.0452732i
$905$	38.4395	+	66.5791i	1.27777	+	2.21316i
$906$		0			0
$907$	−22.8899			−0.760048			−0.380024	−	0.924977i	$-0.624084\pi$
$907$	−22.8899			−0.760048			−0.380024	+	0.924977i	$0.624084\pi$
$908$	−12.9149	+	22.3692i	−0.428595	+	0.742349i
$909$		0			0
$910$	30.4638	−	22.1804i	1.00986	−	0.735273i
$911$	−22.0074			−0.729139			−0.364570	−	0.931176i	$-0.618784\pi$
$911$	−22.0074			−0.729139			−0.364570	+	0.931176i	$0.618784\pi$
$912$		0			0
$913$	−51.7029			−1.71112
$914$	−3.12651	−	5.41528i	−0.103416	−	0.179121i
$915$		0			0
$916$	5.39496	−	9.34435i	0.178255	−	0.308746i
$917$	−5.07553	−	0.371536i	−0.167609	−	0.0122692i
$918$		0			0
$919$	49.9202			1.64672			0.823358	−	0.567522i	$-0.192098\pi$
$919$	49.9202			1.64672			0.823358	+	0.567522i	$0.192098\pi$
$920$	−37.6732			−1.24205
$921$		0			0
$922$	9.65625	+	16.7251i	0.318012	+	0.550812i
$923$	10.6707	−	9.03168i	0.351229	−	0.297281i
$924$		0			0
$925$	−59.0502	−	102.278i	−1.94156	−	3.36288i
$926$	10.7240	−	18.5745i	0.352412	−	0.610396i
$927$		0			0
$928$	−0.629759	+	1.09077i	−0.0206729	+	0.0358064i
$929$	−9.00296			−0.295377			−0.147689	−	0.989034i	$-0.547183\pi$
$929$	−9.00296			−0.295377			−0.147689	+	0.989034i	$0.547183\pi$
$930$		0			0
$931$	2.00449	+	5.05588i	0.0656944	+	0.165700i
$932$	1.92109	−	3.32742i	0.0629274	−	0.108993i
$933$		0			0
$934$	−4.78510			−0.156573
$935$	1.36429	−	2.36302i	0.0446171	−	0.0772791i
$936$		0			0
$937$	−42.4359			−1.38632			−0.693159	−	0.720784i	$-0.743782\pi$
$937$	−42.4359			−1.38632			−0.693159	+	0.720784i	$0.743782\pi$
$938$	9.44267	+	19.5215i	0.308314	+	0.637400i
$939$		0			0
$940$	−26.3244			−0.858608
$941$	4.68568	−	8.11583i	0.152749	−	0.264569i	−0.779488	−	0.626417i	$-0.784521\pi$
$941$	4.68568	−	8.11583i	0.152749	−	0.264569i	0.932237	+	0.361848i	$0.117854\pi$
$942$		0			0
$943$	−88.7895			−2.89138
$944$	−0.431218			−0.0140350
$945$		0			0
$946$	−2.65950	−	4.60638i	−0.0864677	−	0.149766i
$947$	−18.1411	+	31.4213i	−0.589507	+	1.02106i	0.404790	+	0.914409i	$0.367344\pi$
$947$	−18.1411	+	31.4213i	−0.589507	+	1.02106i	−0.994297	+	0.106646i	$0.965989\pi$
$948$		0			0
$949$	0.450143	−	0.381002i	0.0146122	−	0.0123679i
$950$	−4.11966	−	7.13545i	−0.133659	−	0.231505i
$951$		0			0
$952$	0.370925	+	0.0271522i	0.0120217	+	0.000880008i
$953$	−9.41368	+	16.3050i	−0.304939	+	0.528170i	−0.977248	−	0.212101i	$-0.931969\pi$
$953$	−9.41368	+	16.3050i	−0.304939	+	0.528170i	0.672309	+	0.740271i	$0.265303\pi$
$954$		0			0
$955$	28.8297	+	49.9345i	0.932907	+	1.61584i
$956$	5.12799	+	8.88194i	0.165851	+	0.287262i
$957$		0			0
$958$	5.85660	−	10.1439i	0.189218	−	0.327735i
$959$	−41.9080	−	3.06772i	−1.35328	−	0.0990620i
$960$		0			0
$961$	9.85571	+	17.0706i	0.317926	+	0.550664i
$962$	−7.14154	−	39.5142i	−0.230252	−	1.27399i
$963$		0			0
$964$	0.316427	−	0.548068i	0.0101914	−	0.0176521i
$965$	−3.49322	−	6.05043i	−0.112451	−	0.194770i
$966$		0			0
$967$	−9.63971			−0.309992			−0.154996	−	0.987915i	$-0.549536\pi$
$967$	−9.63971			−0.309992			−0.154996	+	0.987915i	$0.549536\pi$
$968$	−13.1452			−0.422502
$969$		0			0
$970$	−25.8385	+	44.7536i	−0.829624	+	1.43695i
$971$	−18.2733			−0.586419			−0.293209	−	0.956048i	$-0.594723\pi$
$971$	−18.2733			−0.586419			−0.293209	+	0.956048i	$0.594723\pi$
$972$		0			0
$973$	6.78225	+	14.0214i	0.217429	+	0.449506i
$974$	25.7570			0.825308
$975$		0			0
$976$	4.14057	−	7.17168i	0.132536	−	0.229560i
$977$	−32.0865			−1.02654			−0.513268	−	0.858228i	$-0.671565\pi$
$977$	−32.0865			−1.02654			−0.513268	+	0.858228i	$0.671565\pi$
$978$		0			0
$979$	2.63560	−	4.56499i	0.0842340	−	0.145898i
$980$	−27.3570	−	4.02672i	−0.873888	−	0.128629i
$981$		0			0
$982$	−4.70024			−0.149991
$983$	11.7559	−	20.3618i	0.374955	−	0.649442i	−0.615365	−	0.788242i	$-0.710991\pi$
$983$	11.7559	−	20.3618i	0.374955	−	0.649442i	0.990320	+	0.138801i	$0.0443247\pi$
$984$		0			0
$985$	11.5646	−	20.0306i	0.368480	−	0.638226i
$986$	0.0885262	+	0.153332i	0.00281925	+	0.00488308i
$987$		0			0
$988$	−0.498231	−	2.75672i	−0.0158509	−	0.0877029i
$989$	5.16168	+	8.94030i	0.164132	+	0.284285i
$990$		0			0
$991$	25.1859			0.800058			0.400029	−	0.916503i	$-0.369000\pi$
$991$	25.1859			0.800058			0.400029	+	0.916503i	$0.369000\pi$
$992$	−3.35985			−0.106675
$993$		0			0
$994$	−10.2310	−	0.748922i	−0.324507	−	0.0237544i
$995$	27.4992	−	47.6300i	0.871783	−	1.50997i
$996$		0			0
$997$	−7.49790	−	12.9867i	−0.237461	−	0.411294i	0.722524	−	0.691346i	$-0.242982\pi$
$997$	−7.49790	−	12.9867i	−0.237461	−	0.411294i	−0.959985	+	0.280052i	$0.909648\pi$
$998$	32.6494			1.03350
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.p.i.991.4		8
3.2	odd	2		546.2.k.b.445.1	yes	8
7.2	even	3		1638.2.m.g.289.4		8
13.9	even	3		1638.2.m.g.1621.4		8
21.2	odd	6		546.2.j.d.289.1	✓	8
39.35	odd	6		546.2.j.d.529.1	yes	8
91.9	even	3	inner	1638.2.p.i.919.4		8
273.191	odd	6		546.2.k.b.373.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.d.289.1	✓	8	21.2	odd	6
546.2.j.d.529.1	yes	8	39.35	odd	6
546.2.k.b.373.1	yes	8	273.191	odd	6
546.2.k.b.445.1	yes	8	3.2	odd	2
1638.2.m.g.289.4		8	7.2	even	3
1638.2.m.g.1621.4		8	13.9	even	3
1638.2.p.i.919.4		8	91.9	even	3	inner
1638.2.p.i.991.4		8	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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.p (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.97513 + 3.42102i) q^{5} +(-1.48662 + 2.18860i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.97513 + 3.42102i) q^{5} +(-1.48662 + 2.18860i) q^{7} -1.00000 q^{8} +3.95025 q^{10} -4.91377 q^{11} +(-3.39335 - 1.21869i) q^{13} +(1.15207 + 2.38175i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.0702857 + 0.121738i) q^{17} -0.776963 q^{19} +(1.97513 - 3.42102i) q^{20} +(-2.45689 + 4.25545i) q^{22} +(4.76845 - 8.25920i) q^{23} +(-5.30226 + 9.18378i) q^{25} +(-2.75209 + 2.32938i) q^{26} +(2.63869 + 0.193156i) q^{28} +(0.629759 + 1.09077i) q^{29} +(-1.67992 + 2.90971i) q^{31} +(0.500000 + 0.866025i) q^{32} +0.140571 q^{34} +(-10.4235 - 0.763015i) q^{35} +(-5.56841 + 9.64476i) q^{37} +(-0.388481 + 0.672870i) q^{38} +(-1.97513 - 3.42102i) q^{40} +(-4.65505 - 8.06279i) q^{41} +(-0.541233 + 0.937443i) q^{43} +(2.45689 + 4.25545i) q^{44} +(-4.76845 - 8.25920i) q^{46} +(-3.33199 - 5.77118i) q^{47} +(-2.57990 - 6.50724i) q^{49} +(5.30226 + 9.18378i) q^{50} +(0.641255 + 3.54807i) q^{52} +(-5.53204 + 9.58177i) q^{53} +(-9.70533 - 16.8101i) q^{55} +(1.48662 - 2.18860i) q^{56} +1.25952 q^{58} +(0.215609 + 0.373446i) q^{59} -8.28114 q^{61} +(1.67992 + 2.90971i) q^{62} +1.00000 q^{64} +(-2.53312 - 14.0158i) q^{65} +8.19628 q^{67} +(0.0702857 - 0.121738i) q^{68} +(-5.87254 + 8.64551i) q^{70} +(-1.93865 + 3.35783i) q^{71} +(-0.0817820 + 0.141650i) q^{73} +(5.56841 + 9.64476i) q^{74} +(0.388481 + 0.672870i) q^{76} +(7.30493 - 10.7543i) q^{77} +(2.17517 + 3.76751i) q^{79} -3.95025 q^{80} -9.31010 q^{82} +10.5220 q^{83} +(-0.277647 + 0.480898i) q^{85} +(0.541233 + 0.937443i) q^{86} +4.91377 q^{88} +(-0.536369 + 0.929018i) q^{89} +(7.71185 - 5.61493i) q^{91} -9.53690 q^{92} -6.66398 q^{94} +(-1.53460 - 2.65801i) q^{95} +(-6.54097 + 11.3293i) q^{97} +(-6.92538 - 1.01936i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8	\( 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8} - 4 q^{10} - 12 q^{11} - 11 q^{13} + 3 q^{14} - 4 q^{16} - 4 q^{17} - 12 q^{19} - 2 q^{20} - 6 q^{22} + 10 q^{23} - 18 q^{25} - 10 q^{26} - 2 q^{29} + 6 q^{31} + 4 q^{32} - 8 q^{34} - 18 q^{35} - 28 q^{37} - 6 q^{38} + 2 q^{40} - 6 q^{43} + 6 q^{44} - 10 q^{46} - q^{47} - 7 q^{49} + 18 q^{50} + q^{52} - 7 q^{53} + q^{55} - 3 q^{56} - 4 q^{58} - 2 q^{59} - 48 q^{61} - 6 q^{62} + 8 q^{64} - 19 q^{65} + 30 q^{67} - 4 q^{68} - 18 q^{70} - 6 q^{71} + q^{73} + 28 q^{74} + 6 q^{76} + 22 q^{77} - 12 q^{79} + 4 q^{80} + 32 q^{83} - 13 q^{85} + 6 q^{86} + 12 q^{88} - 25 q^{89} + 34 q^{91} - 20 q^{92} - 2 q^{94} + 8 q^{95} - q^{97} - 2 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8 - 4 * q^10 - 12 * q^11 - 11 * q^13 + 3 * q^14 - 4 * q^16 - 4 * q^17 - 12 * q^19 - 2 * q^20 - 6 * q^22 + 10 * q^23 - 18 * q^25 - 10 * q^26 - 2 * q^29 + 6 * q^31 + 4 * q^32 - 8 * q^34 - 18 * q^35 - 28 * q^37 - 6 * q^38 + 2 * q^40 - 6 * q^43 + 6 * q^44 - 10 * q^46 - q^47 - 7 * q^49 + 18 * q^50 + q^52 - 7 * q^53 + q^55 - 3 * q^56 - 4 * q^58 - 2 * q^59 - 48 * q^61 - 6 * q^62 + 8 * q^64 - 19 * q^65 + 30 * q^67 - 4 * q^68 - 18 * q^70 - 6 * q^71 + q^73 + 28 * q^74 + 6 * q^76 + 22 * q^77 - 12 * q^79 + 4 * q^80 + 32 * q^83 - 13 * q^85 + 6 * q^86 + 12 * q^88 - 25 * q^89 + 34 * q^91 - 20 * q^92 - 2 * q^94 + 8 * q^95 - q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more