LMFDB - Embedded newform 1323.2.f.d.883.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(442,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1323.442");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			883.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	1323.883
Dual form			1323.2.f.d.442.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.439693 + 0.761570i) q^{2} +(0.613341 + 1.06234i) q^{4} +(-0.673648 - 1.16679i) q^{5} -2.83750 q^{8} +O(q^{10})$	\(q+(-0.439693 + 0.761570i) q^{2} +(0.613341 + 1.06234i) q^{4} +(-0.673648 - 1.16679i) q^{5} -2.83750 q^{8} +1.18479 q^{10} +(0.826352 - 1.43128i) q^{11} +(-1.68479 - 2.91815i) q^{13} +(0.0209445 - 0.0362770i) q^{16} +0.467911 q^{17} +3.22668 q^{19} +(0.826352 - 1.43128i) q^{20} +(0.726682 + 1.25865i) q^{22} +(4.47178 + 7.74535i) q^{23} +(1.59240 - 2.75811i) q^{25} +2.96316 q^{26} +(3.13429 - 5.42874i) q^{29} +(4.61721 + 7.99724i) q^{31} +(-2.81908 - 4.88279i) q^{32} +(-0.205737 + 0.356347i) q^{34} +9.23442 q^{37} +(-1.41875 + 2.45734i) q^{38} +(1.91147 + 3.31077i) q^{40} +(-1.70574 - 2.95442i) q^{41} +(2.20574 - 3.82045i) q^{43} +2.02734 q^{44} -7.86484 q^{46} +(-4.67752 + 8.10170i) q^{47} +(1.40033 + 2.42544i) q^{50} +(2.06670 - 3.57964i) q^{52} +0.573978 q^{53} -2.22668 q^{55} +(2.75624 + 4.77396i) q^{58} +(5.19846 + 9.00400i) q^{59} +(3.81908 - 6.61484i) q^{61} -8.12061 q^{62} +5.04189 q^{64} +(-2.26991 + 3.93161i) q^{65} +(-0.298133 - 0.516382i) q^{67} +(0.286989 + 0.497079i) q^{68} +0.554378 q^{71} -2.04963 q^{73} +(-4.06031 + 7.03266i) q^{74} +(1.97906 + 3.42782i) q^{76} +(1.20187 - 2.08169i) q^{79} -0.0564370 q^{80} +3.00000 q^{82} +(7.52481 - 13.0334i) q^{83} +(-0.315207 - 0.545955i) q^{85} +(1.93969 + 3.35965i) q^{86} +(-2.34477 + 4.06126i) q^{88} +9.08647 q^{89} +(-5.48545 + 9.50108i) q^{92} +(-4.11334 - 7.12452i) q^{94} +(-2.17365 - 3.76487i) q^{95} +(-0.949493 + 1.64457i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 12 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 12 * q^8	$ 6 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 12 q^{8} + 6 q^{11} - 3 q^{13} - 3 q^{16} + 12 q^{17} + 6 q^{19} + 6 q^{20} - 9 q^{22} + 12 q^{23} + 6 q^{25} - 6 q^{26} + 9 q^{29} - 3 q^{31} + 9 q^{34} - 6 q^{37} - 6 q^{38} - 9 q^{40} + 3 q^{43} - 30 q^{44} - 3 q^{47} - 6 q^{50} - 21 q^{52} - 12 q^{53} + 9 q^{58} + 3 q^{59} + 6 q^{61} - 60 q^{62} + 24 q^{64} + 15 q^{65} + 12 q^{67} - 6 q^{68} - 18 q^{71} + 42 q^{73} - 30 q^{74} + 15 q^{76} + 21 q^{79} - 30 q^{80} + 18 q^{82} + 18 q^{83} - 9 q^{85} + 6 q^{86} - 27 q^{88} + 24 q^{89} + 3 q^{92} - 18 q^{94} - 12 q^{95} - 3 q^{97}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 12 * q^8 + 6 * q^11 - 3 * q^13 - 3 * q^16 + 12 * q^17 + 6 * q^19 + 6 * q^20 - 9 * q^22 + 12 * q^23 + 6 * q^25 - 6 * q^26 + 9 * q^29 - 3 * q^31 + 9 * q^34 - 6 * q^37 - 6 * q^38 - 9 * q^40 + 3 * q^43 - 30 * q^44 - 3 * q^47 - 6 * q^50 - 21 * q^52 - 12 * q^53 + 9 * q^58 + 3 * q^59 + 6 * q^61 - 60 * q^62 + 24 * q^64 + 15 * q^65 + 12 * q^67 - 6 * q^68 - 18 * q^71 + 42 * q^73 - 30 * q^74 + 15 * q^76 + 21 * q^79 - 30 * q^80 + 18 * q^82 + 18 * q^83 - 9 * q^85 + 6 * q^86 - 27 * q^88 + 24 * q^89 + 3 * q^92 - 18 * q^94 - 12 * q^95 - 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.439693	+	0.761570i	−0.310910	+	0.538511i	−0.978560	−	0.205964i	$-0.933967\pi$
$2$	−0.439693	+	0.761570i	−0.310910	+	0.538511i	0.667650	+	0.744475i	$0.267300\pi$
$3$		0			0
$3$		0			0
$4$	0.613341	+	1.06234i	0.306670	+	0.531169i
$5$	−0.673648	−	1.16679i	−0.301265	−	0.521806i	0.675158	−	0.737673i	$-0.264075\pi$
$5$	−0.673648	−	1.16679i	−0.301265	−	0.521806i	−0.976423	+	0.215867i	$0.930742\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−2.83750			−1.00321
$9$		0			0
$10$	1.18479			0.374664
$11$	0.826352	−	1.43128i	0.249154	−	0.431548i	−0.714137	−	0.700006i	$-0.753181\pi$
$11$	0.826352	−	1.43128i	0.249154	−	0.431548i	0.963291	+	0.268458i	$0.0865140\pi$
$12$		0			0
$13$	−1.68479	−	2.91815i	−0.467277	−	0.809348i	0.532024	−	0.846729i	$-0.321432\pi$
$13$	−1.68479	−	2.91815i	−0.467277	−	0.809348i	−0.999301	+	0.0373813i	$0.988098\pi$
$14$		0			0
$15$		0			0
$16$	0.0209445	−	0.0362770i	0.00523613	−	0.00906925i
$17$	0.467911			0.113485			0.0567426	−	0.998389i	$-0.481929\pi$
$17$	0.467911			0.113485			0.0567426	+	0.998389i	$0.481929\pi$
$18$		0			0
$19$	3.22668			0.740252			0.370126	−	0.928982i	$-0.379315\pi$
$19$	3.22668			0.740252			0.370126	+	0.928982i	$0.379315\pi$
$20$	0.826352	−	1.43128i	0.184778	−	0.320045i
$21$		0			0
$22$	0.726682	+	1.25865i	0.154929	+	0.268345i
$23$	4.47178	+	7.74535i	0.932431	+	1.61502i	0.779152	+	0.626835i	$0.215650\pi$
$23$	4.47178	+	7.74535i	0.932431	+	1.61502i	0.153279	+	0.988183i	$0.451017\pi$
$24$		0			0
$25$	1.59240	−	2.75811i	0.318479	−	0.551622i
$26$	2.96316			0.581124
$27$		0			0
$28$		0			0
$29$	3.13429	−	5.42874i	0.582022	−	1.00809i	−0.413217	−	0.910632i	$-0.635595\pi$
$29$	3.13429	−	5.42874i	0.582022	−	1.00809i	0.995239	−	0.0974595i	$-0.0310717\pi$
$30$		0			0
$31$	4.61721	+	7.99724i	0.829276	+	1.43635i	0.898607	+	0.438754i	$0.144580\pi$
$31$	4.61721	+	7.99724i	0.829276	+	1.43635i	−0.0693317	+	0.997594i	$0.522087\pi$
$32$	−2.81908	−	4.88279i	−0.498347	−	0.863163i
$33$		0			0
$34$	−0.205737	+	0.356347i	−0.0352836	+	0.0611130i
$35$		0			0
$36$		0			0
$37$	9.23442			1.51813			0.759065	−	0.651015i	$-0.225657\pi$
$37$	9.23442			1.51813			0.759065	+	0.651015i	$0.225657\pi$
$38$	−1.41875	+	2.45734i	−0.230151	+	0.398634i
$39$		0			0
$40$	1.91147	+	3.31077i	0.302231	+	0.523479i
$41$	−1.70574	−	2.95442i	−0.266391	−	0.461403i	0.701536	−	0.712634i	$-0.252498\pi$
$41$	−1.70574	−	2.95442i	−0.266391	−	0.461403i	−0.967927	+	0.251231i	$0.919165\pi$
$42$		0			0
$43$	2.20574	−	3.82045i	0.336372	−	0.582613i	−0.647376	−	0.762171i	$-0.724133\pi$
$43$	2.20574	−	3.82045i	0.336372	−	0.582613i	0.983747	+	0.179558i	$0.0574668\pi$
$44$	2.02734			0.305633
$45$		0			0
$46$	−7.86484			−1.15961
$47$	−4.67752	+	8.10170i	−0.682286	+	1.18175i	0.291995	+	0.956420i	$0.405681\pi$
$47$	−4.67752	+	8.10170i	−0.682286	+	1.18175i	−0.974281	+	0.225335i	$0.927652\pi$
$48$		0			0
$49$		0			0
$50$	1.40033	+	2.42544i	0.198037	+	0.343009i
$51$		0			0
$52$	2.06670	−	3.57964i	0.286600	−	0.496406i
$53$	0.573978			0.0788419			0.0394210	−	0.999223i	$-0.487449\pi$
$53$	0.573978			0.0788419			0.0394210	+	0.999223i	$0.487449\pi$
$54$		0			0
$55$	−2.22668			−0.300246
$56$		0			0
$57$		0			0
$58$	2.75624	+	4.77396i	0.361913	+	0.626851i
$59$	5.19846	+	9.00400i	0.676782	+	1.17222i	0.975945	+	0.218019i	$0.0699595\pi$
$59$	5.19846	+	9.00400i	0.676782	+	1.17222i	−0.299162	+	0.954202i	$0.596707\pi$
$60$		0			0
$61$	3.81908	−	6.61484i	0.488983	−	0.846943i	−0.510937	−	0.859618i	$-0.670701\pi$
$61$	3.81908	−	6.61484i	0.488983	−	0.846943i	0.999920	+	0.0126752i	$0.00403474\pi$
$62$	−8.12061			−1.03132
$63$		0			0
$64$	5.04189			0.630236
$65$	−2.26991	+	3.93161i	−0.281548	+	0.487656i
$66$		0			0
$67$	−0.298133	−	0.516382i	−0.0364228	−	0.0630861i	0.847239	−	0.531211i	$-0.178263\pi$
$67$	−0.298133	−	0.516382i	−0.0364228	−	0.0630861i	−0.883662	+	0.468125i	$0.844930\pi$
$68$	0.286989	+	0.497079i	0.0348025	+	0.0602797i
$69$		0			0
$70$		0			0
$71$	0.554378			0.0657925			0.0328963	−	0.999459i	$-0.489527\pi$
$71$	0.554378			0.0657925			0.0328963	+	0.999459i	$0.489527\pi$
$72$		0			0
$73$	−2.04963			−0.239891			−0.119946	−	0.992780i	$-0.538272\pi$
$73$	−2.04963			−0.239891			−0.119946	+	0.992780i	$0.538272\pi$
$74$	−4.06031	+	7.03266i	−0.472001	+	0.817530i
$75$		0			0
$76$	1.97906	+	3.42782i	0.227013	+	0.393198i
$77$		0			0
$78$		0			0
$79$	1.20187	−	2.08169i	0.135221	−	0.234209i	−0.790461	−	0.612512i	$-0.790159\pi$
$79$	1.20187	−	2.08169i	0.135221	−	0.234209i	0.925682	+	0.378303i	$0.123492\pi$
$80$	−0.0564370			−0.00630985
$81$		0			0
$82$	3.00000			0.331295
$83$	7.52481	−	13.0334i	0.825956	−	1.43060i	−0.0752309	−	0.997166i	$-0.523969\pi$
$83$	7.52481	−	13.0334i	0.825956	−	1.43060i	0.901187	−	0.433431i	$-0.142697\pi$
$84$		0			0
$85$	−0.315207	−	0.545955i	−0.0341891	−	0.0592172i
$86$	1.93969	+	3.35965i	0.209162	+	0.362280i
$87$		0			0
$88$	−2.34477	+	4.06126i	−0.249953	+	0.432932i
$89$	9.08647			0.963164			0.481582	−	0.876401i	$-0.340062\pi$
$89$	9.08647			0.963164			0.481582	+	0.876401i	$0.340062\pi$
$90$		0			0
$91$		0			0
$92$	−5.48545	+	9.50108i	−0.571898	+	0.990556i
$93$		0			0
$94$	−4.11334	−	7.12452i	−0.424259	−	0.734838i
$95$	−2.17365	−	3.76487i	−0.223012	−	0.386267i
$96$		0			0
$97$	−0.949493	+	1.64457i	−0.0964064	+	0.166981i	−0.910195	−	0.414181i	$-0.864068\pi$
$97$	−0.949493	+	1.64457i	−0.0964064	+	0.166981i	0.813788	+	0.581161i	$0.197402\pi$
$98$		0			0
$99$		0			0
$100$	3.90673			0.390673
$101$	0.854570	−	1.48016i	0.0850329	−	0.147281i	−0.820372	−	0.571830i	$-0.806234\pi$
$101$	0.854570	−	1.48016i	0.0850329	−	0.147281i	0.905405	+	0.424548i	$0.139567\pi$
$102$		0			0
$103$	−1.81908	−	3.15074i	−0.179239	−	0.310451i	0.762381	−	0.647128i	$-0.224030\pi$
$103$	−1.81908	−	3.15074i	−0.179239	−	0.310451i	−0.941620	+	0.336677i	$0.890697\pi$
$104$	4.78059	+	8.28023i	0.468776	+	0.811943i
$105$		0			0
$106$	−0.252374	+	0.437124i	−0.0245127	+	0.0424573i
$107$	−7.12836			−0.689124			−0.344562	−	0.938764i	$-0.611973\pi$
$107$	−7.12836			−0.689124			−0.344562	+	0.938764i	$0.611973\pi$
$108$		0			0
$109$	0.403733			0.0386706			0.0193353	−	0.999813i	$-0.493845\pi$
$109$	0.403733			0.0386706			0.0193353	+	0.999813i	$0.493845\pi$
$110$	0.979055	−	1.69577i	0.0933493	−	0.161686i
$111$		0			0
$112$		0			0
$113$	7.18479	+	12.4444i	0.675888	+	1.17067i	0.976208	+	0.216835i	$0.0695732\pi$
$113$	7.18479	+	12.4444i	0.675888	+	1.17067i	−0.300320	+	0.953839i	$0.597093\pi$
$114$		0			0
$115$	6.02481	−	10.4353i	0.561817	−	0.973095i
$116$	7.68954			0.713956
$117$		0			0
$118$	−9.14290			−0.841672
$119$		0			0
$120$		0			0
$121$	4.13429	+	7.16079i	0.375844	+	0.650981i
$122$	3.35844	+	5.81699i	0.304059	+	0.526646i
$123$		0			0
$124$	−5.66385	+	9.81007i	−0.508629	+	0.880971i
$125$	−11.0273			−0.986315
$126$		0			0
$127$	−20.7716			−1.84318			−0.921589	−	0.388167i	$-0.873108\pi$
$127$	−20.7716			−1.84318			−0.921589	+	0.388167i	$0.873108\pi$
$128$	3.42127	−	5.92582i	0.302401	−	0.523774i
$129$		0			0
$130$	−1.99613	−	3.45740i	−0.175072	−	0.303234i
$131$	3.58260	+	6.20524i	0.313013	+	0.542154i	0.979013	−	0.203797i	$-0.0653284\pi$
$131$	3.58260	+	6.20524i	0.313013	+	0.542154i	−0.666000	+	0.745952i	$0.731995\pi$
$132$		0			0
$133$		0			0
$134$	0.524348			0.0452968
$135$		0			0
$136$	−1.32770			−0.113849
$137$	1.28446	−	2.22475i	0.109739	−	0.190074i	−0.805925	−	0.592017i	$-0.798332\pi$
$137$	1.28446	−	2.22475i	0.109739	−	0.190074i	0.915665	+	0.401943i	$0.131665\pi$
$138$		0			0
$139$	−3.06670	−	5.31169i	−0.260114	−	0.450531i	0.706158	−	0.708055i	$-0.250427\pi$
$139$	−3.06670	−	5.31169i	−0.260114	−	0.450531i	−0.966272	+	0.257523i	$0.917094\pi$
$140$		0			0
$141$		0			0
$142$	−0.243756	+	0.422197i	−0.0204555	+	0.0354300i
$143$	−5.56893			−0.465697
$144$		0			0
$145$	−8.44562			−0.701371
$146$	0.901207	−	1.56094i	0.0745844	−	0.129184i
$147$		0			0
$148$	5.66385	+	9.81007i	0.465565	+	0.806383i
$149$	0.215537	+	0.373321i	0.0176575	+	0.0305837i	0.874719	−	0.484630i	$-0.161046\pi$
$149$	0.215537	+	0.373321i	0.0176575	+	0.0305837i	−0.857062	+	0.515214i	$0.827712\pi$
$150$		0			0
$151$	1.23530	−	2.13960i	0.100527	−	0.174118i	−0.811375	−	0.584526i	$-0.801280\pi$
$151$	1.23530	−	2.13960i	0.100527	−	0.174118i	0.911902	+	0.410408i	$0.134614\pi$
$152$	−9.15570			−0.742625
$153$		0			0
$154$		0			0
$155$	6.22075	−	10.7747i	0.499663	−	0.865441i
$156$		0			0
$157$	5.06670	+	8.77579i	0.404367	+	0.700384i	0.994248	−	0.107106i	$-0.0341585\pi$
$157$	5.06670	+	8.77579i	0.404367	+	0.700384i	−0.589881	+	0.807491i	$0.700825\pi$
$158$	1.05690	+	1.83061i	0.0840828	+	0.145636i
$159$		0			0
$160$	−3.79813	+	6.57856i	−0.300269	+	0.520081i
$161$		0			0
$162$		0			0
$163$	−2.59627			−0.203355			−0.101678	−	0.994817i	$-0.532421\pi$
$163$	−2.59627			−0.203355			−0.101678	+	0.994817i	$0.532421\pi$
$164$	2.09240	−	3.62414i	0.163389	−	0.282998i
$165$		0			0
$166$	6.61721	+	11.4613i	0.513595	+	0.889573i
$167$	11.5915	+	20.0771i	0.896979	+	1.55361i	0.831337	+	0.555769i	$0.187576\pi$
$167$	11.5915	+	20.0771i	0.896979	+	1.55361i	0.0656422	+	0.997843i	$0.479090\pi$
$168$		0			0
$169$	0.822948	−	1.42539i	0.0633037	−	0.109645i
$170$	0.554378			0.0425188
$171$		0			0
$172$	5.41147			0.412621
$173$	2.37598	−	4.11532i	0.180643	−	0.312882i	−0.761457	−	0.648215i	$-0.775516\pi$
$173$	2.37598	−	4.11532i	0.180643	−	0.312882i	0.942100	+	0.335333i	$0.108849\pi$
$174$		0			0
$175$		0			0
$176$	−0.0346151	−	0.0599551i	−0.00260921	−	0.00451929i
$177$		0			0
$178$	−3.99525	+	6.91998i	−0.299457	+	0.518674i
$179$	8.53209			0.637718			0.318859	−	0.947802i	$-0.396700\pi$
$179$	8.53209			0.637718			0.318859	+	0.947802i	$0.396700\pi$
$180$		0			0
$181$	17.2344			1.28102			0.640512	−	0.767948i	$-0.278722\pi$
$181$	17.2344			1.28102			0.640512	+	0.767948i	$0.278722\pi$
$182$		0			0
$183$		0			0
$184$	−12.6887	−	21.9774i	−0.935421	−	1.62020i
$185$	−6.22075	−	10.7747i	−0.457359	−	0.792169i
$186$		0			0
$187$	0.386659	−	0.669713i	0.0282753	−	0.0489743i
$188$	−11.4757			−0.836948
$189$		0			0
$190$	3.82295			0.277346
$191$	6.45471	−	11.1799i	0.467046	−	0.808948i	−0.532245	−	0.846590i	$-0.678651\pi$
$191$	6.45471	−	11.1799i	0.467046	−	0.808948i	0.999291	+	0.0376425i	$0.0119848\pi$
$192$		0			0
$193$	0.319078	+	0.552659i	0.0229677	+	0.0397813i	0.877281	−	0.479977i	$-0.159355\pi$
$193$	0.319078	+	0.552659i	0.0229677	+	0.0397813i	−0.854313	+	0.519759i	$0.826022\pi$
$194$	−0.834970	−	1.44621i	−0.0599473	−	0.103832i
$195$		0			0
$196$		0			0
$197$	−11.4456			−0.815467			−0.407733	−	0.913101i	$-0.633681\pi$
$197$	−11.4456			−0.815467			−0.407733	+	0.913101i	$0.633681\pi$
$198$		0			0
$199$	3.63816			0.257902			0.128951	−	0.991651i	$-0.458839\pi$
$199$	3.63816			0.257902			0.128951	+	0.991651i	$0.458839\pi$
$200$	−4.51842	+	7.82613i	−0.319500	+	0.553391i
$201$		0			0
$202$	0.751497	+	1.30163i	0.0528751	+	0.0915824i
$203$		0			0
$204$		0			0
$205$	−2.29813	+	3.98048i	−0.160509	+	0.278009i
$206$	3.19934			0.222909
$207$		0			0
$208$	−0.141149			−0.00978691
$209$	2.66637	−	4.61830i	0.184437	−	0.319454i
$210$		0			0
$211$	−2.91147	−	5.04282i	−0.200434	−	0.347162i	0.748234	−	0.663435i	$-0.230902\pi$
$211$	−2.91147	−	5.04282i	−0.200434	−	0.347162i	−0.948668	+	0.316273i	$0.897569\pi$
$212$	0.352044	+	0.609758i	0.0241785	+	0.0418784i
$213$		0			0
$214$	3.13429	−	5.42874i	0.214255	−	0.371101i
$215$	−5.94356			−0.405348
$216$		0			0
$217$		0			0
$218$	−0.177519	+	0.307471i	−0.0120231	+	0.0208246i
$219$		0			0
$220$	−1.36571	−	2.36549i	−0.0920765	−	0.159481i
$221$	−0.788333	−	1.36543i	−0.0530290	−	0.0918490i
$222$		0			0
$223$	3.54189	−	6.13473i	0.237182	−	0.410812i	−0.722722	−	0.691139i	$-0.757109\pi$
$223$	3.54189	−	6.13473i	0.237182	−	0.410812i	0.959905	+	0.280327i	$0.0904428\pi$
$224$		0			0
$225$		0			0
$226$	−12.6364			−0.840561
$227$	5.97178	−	10.3434i	0.396361	−	0.686517i	−0.596913	−	0.802306i	$-0.703606\pi$
$227$	5.97178	−	10.3434i	0.396361	−	0.686517i	0.993274	+	0.115789i	$0.0369395\pi$
$228$		0			0
$229$	−8.77631	−	15.2010i	−0.579955	−	1.00451i	−0.995484	−	0.0949315i	$-0.969737\pi$
$229$	−8.77631	−	15.2010i	−0.579955	−	1.00451i	0.415529	−	0.909580i	$-0.363597\pi$
$230$	5.29813	+	9.17664i	0.349349	+	0.605089i
$231$		0			0
$232$	−8.89352	+	15.4040i	−0.583888	+	1.01132i
$233$	−16.2540			−1.06484			−0.532418	−	0.846481i	$-0.678717\pi$
$233$	−16.2540			−1.06484			−0.532418	+	0.846481i	$0.678717\pi$
$234$		0			0
$235$	12.6040			0.822195
$236$	−6.37686	+	11.0450i	−0.415098	+	0.718971i
$237$		0			0
$238$		0			0
$239$	−7.54963	−	13.0763i	−0.488345	−	0.845838i	0.511565	−	0.859244i	$-0.329066\pi$
$239$	−7.54963	−	13.0763i	−0.488345	−	0.845838i	−0.999910	+	0.0134062i	$0.995733\pi$
$240$		0			0
$241$	−7.81908	+	13.5430i	−0.503671	+	0.872384i	0.496320	+	0.868140i	$0.334684\pi$
$241$	−7.81908	+	13.5430i	−0.503671	+	0.872384i	−0.999991	+	0.00424420i	$0.998649\pi$
$242$	−7.27126			−0.467414
$243$		0			0
$244$	9.36959			0.599826
$245$		0			0
$246$		0			0
$247$	−5.43629	−	9.41593i	−0.345903	−	0.599121i
$248$	−13.1013	−	22.6922i	−0.831935	−	1.44095i
$249$		0			0
$250$	4.84864	−	8.39809i	0.306655	−	0.531142i
$251$	19.0651			1.20338			0.601690	−	0.798730i	$-0.294494\pi$
$251$	19.0651			1.20338			0.601690	+	0.798730i	$0.294494\pi$
$252$		0			0
$253$	14.7811			0.929277
$254$	9.13310	−	15.8190i	0.573062	−	0.992572i
$255$		0			0
$256$	8.05051	+	13.9439i	0.503157	+	0.871493i
$257$	−13.2909	−	23.0204i	−0.829061	−	1.43598i	−0.898776	−	0.438409i	$-0.855542\pi$
$257$	−13.2909	−	23.0204i	−0.829061	−	1.43598i	0.0697146	−	0.997567i	$-0.477791\pi$
$258$		0			0
$259$		0			0
$260$	−5.56893			−0.345370
$261$		0			0
$262$	−6.30096			−0.389275
$263$	−0.367059	+	0.635765i	−0.0226338	+	0.0392029i	−0.877120	−	0.480270i	$-0.840539\pi$
$263$	−0.367059	+	0.635765i	−0.0226338	+	0.0392029i	0.854487	+	0.519473i	$0.173872\pi$
$264$		0			0
$265$	−0.386659	−	0.669713i	−0.0237523	−	0.0411402i
$266$		0			0
$267$		0			0
$268$	0.365715	−	0.633436i	0.0223396	−	0.0386933i
$269$	−20.8503			−1.27126			−0.635632	−	0.771992i	$-0.719261\pi$
$269$	−20.8503			−1.27126			−0.635632	+	0.771992i	$0.719261\pi$
$270$		0			0
$271$	−6.95811			−0.422675			−0.211338	−	0.977413i	$-0.567782\pi$
$271$	−6.95811			−0.422675			−0.211338	+	0.977413i	$0.567782\pi$
$272$	0.00980018	−	0.0169744i	0.000594223	−	0.00102922i
$273$		0			0
$274$	1.12954	+	1.95642i	0.0682379	+	0.118191i
$275$	−2.63176	−	4.55834i	−0.158701	−	0.274878i
$276$		0			0
$277$	−8.93629	+	15.4781i	−0.536930	+	0.929989i	0.462138	+	0.886808i	$0.347083\pi$
$277$	−8.93629	+	15.4781i	−0.536930	+	0.929989i	−0.999067	+	0.0431811i	$0.986251\pi$
$278$	5.39363			0.323488
$279$		0			0
$280$		0			0
$281$	11.1552	−	19.3214i	0.665465	−	1.15262i	−0.313694	−	0.949524i	$-0.601567\pi$
$281$	11.1552	−	19.3214i	0.665465	−	1.15262i	0.979159	−	0.203095i	$-0.0651001\pi$
$282$		0			0
$283$	−9.29726	−	16.1033i	−0.552665	−	0.957243i	−0.998081	−	0.0619196i	$-0.980278\pi$
$283$	−9.29726	−	16.1033i	−0.552665	−	0.957243i	0.445417	−	0.895323i	$-0.353056\pi$
$284$	0.340022	+	0.588936i	0.0201766	+	0.0349469i
$285$		0			0
$286$	2.44862	−	4.24113i	0.144790	−	0.250783i
$287$		0			0
$288$		0			0
$289$	−16.7811			−0.987121
$290$	3.71348	−	6.43193i	0.218063	−	0.377696i
$291$		0			0
$292$	−1.25712	−	2.17740i	−0.0735675	−	0.127423i
$293$	−6.54576	−	11.3376i	−0.382407	−	0.662349i	0.608998	−	0.793171i	$-0.291572\pi$
$293$	−6.54576	−	11.3376i	−0.382407	−	0.662349i	−0.991406	+	0.130822i	$0.958238\pi$
$294$		0			0
$295$	7.00387	−	12.1311i	0.407781	−	0.706298i
$296$	−26.2026			−1.52300
$297$		0			0
$298$	−0.379081			−0.0219595
$299$	15.0680	−	26.0986i	0.871408	−	1.50932i
$300$		0			0
$301$		0			0
$302$	1.08630	+	1.88153i	0.0625098	+	0.108270i
$303$		0			0
$304$	0.0675813	−	0.117054i	0.00387606	−	0.00671353i
$305$	−10.2909			−0.589253
$306$		0			0
$307$	−6.31046			−0.360157			−0.180078	−	0.983652i	$-0.557635\pi$
$307$	−6.31046			−0.360157			−0.180078	+	0.983652i	$0.557635\pi$
$308$		0			0
$309$		0			0
$310$	5.47044	+	9.47508i	0.310700	+	0.538148i
$311$	4.76217	+	8.24833i	0.270038	+	0.467720i	0.968871	−	0.247565i	$-0.0796304\pi$
$311$	4.76217	+	8.24833i	0.270038	+	0.467720i	−0.698833	+	0.715285i	$0.746297\pi$
$312$		0			0
$313$	−8.81433	+	15.2669i	−0.498215	+	0.862934i	−0.999998	−	0.00205946i	$-0.999344\pi$
$313$	−8.81433	+	15.2669i	−0.498215	+	0.862934i	0.501782	+	0.864994i	$0.332678\pi$
$314$	−8.91117			−0.502886
$315$		0			0
$316$	2.94862			0.165873
$317$	4.03849	−	6.99486i	0.226824	−	0.392871i	−0.730041	−	0.683403i	$-0.760499\pi$
$317$	4.03849	−	6.99486i	0.226824	−	0.392871i	0.956865	+	0.290533i	$0.0938325\pi$
$318$		0			0
$319$	−5.18004	−	8.97210i	−0.290027	−	0.502341i
$320$	−3.39646	−	5.88284i	−0.189868	−	0.328861i
$321$		0			0
$322$		0			0
$323$	1.50980			0.0840075
$324$		0			0
$325$	−10.7314			−0.595273
$326$	1.14156	−	1.97724i	0.0632251	−	0.109509i
$327$		0			0
$328$	4.84002	+	8.38316i	0.267246	+	0.462883i
$329$		0			0
$330$		0			0
$331$	−11.5248	+	19.9616i	−0.633461	+	1.09719i	0.353378	+	0.935481i	$0.385033\pi$
$331$	−11.5248	+	19.9616i	−0.633461	+	1.09719i	−0.986839	+	0.161706i	$0.948300\pi$
$332$	18.4611			1.01318
$333$		0			0
$334$	−20.3868			−1.11552
$335$	−0.401674	+	0.695720i	−0.0219458	+	0.0380112i
$336$		0			0
$337$	−14.5116	−	25.1348i	−0.790498	−	1.36918i	−0.925659	−	0.378359i	$-0.876489\pi$
$337$	−14.5116	−	25.1348i	−0.790498	−	1.36918i	0.135161	−	0.990824i	$-0.456845\pi$
$338$	0.723689	+	1.25347i	0.0393635	+	0.0681795i
$339$		0			0
$340$	0.386659	−	0.669713i	0.0209695	−	0.0363203i
$341$	15.2618			0.826471
$342$		0			0
$343$		0			0
$344$	−6.25877	+	10.8405i	−0.337450	+	0.584481i
$345$		0			0
$346$	2.08940	+	3.61895i	0.112327	+	0.194556i
$347$	6.47313	+	11.2118i	0.347496	+	0.601880i	0.985804	−	0.167901i	$-0.0536988\pi$
$347$	6.47313	+	11.2118i	0.347496	+	0.601880i	−0.638308	+	0.769781i	$0.720365\pi$
$348$		0			0
$349$	0.731429	−	1.26687i	0.0391525	−	0.0678141i	−0.845785	−	0.533524i	$-0.820868\pi$
$349$	0.731429	−	1.26687i	0.0391525	−	0.0678141i	0.884938	+	0.465710i	$0.154201\pi$
$350$		0			0
$351$		0			0
$352$	−9.31820			−0.496662
$353$	−7.16637	+	12.4125i	−0.381428	+	0.660652i	−0.991267	−	0.131873i	$-0.957901\pi$
$353$	−7.16637	+	12.4125i	−0.381428	+	0.660652i	0.609839	+	0.792525i	$0.291234\pi$
$354$		0			0
$355$	−0.373455	−	0.646844i	−0.0198210	−	0.0343309i
$356$	5.57310	+	9.65289i	0.295374	+	0.511602i
$357$		0			0
$358$	−3.75150	+	6.49778i	−0.198273	+	0.343418i
$359$	20.9368			1.10500			0.552500	−	0.833513i	$-0.313674\pi$
$359$	20.9368			1.10500			0.552500	+	0.833513i	$0.313674\pi$
$360$		0			0
$361$	−8.58853			−0.452028
$362$	−7.57785	+	13.1252i	−0.398283	+	0.689846i
$363$		0			0
$364$		0			0
$365$	1.38073	+	2.39149i	0.0722707	+	0.125176i
$366$		0			0
$367$	−6.02869	+	10.4420i	−0.314695	+	0.545067i	−0.979373	−	0.202063i	$-0.935236\pi$
$367$	−6.02869	+	10.4420i	−0.314695	+	0.545067i	0.664678	+	0.747130i	$0.268569\pi$
$368$	0.374638			0.0195293
$369$		0			0
$370$	10.9409			0.568789
$371$		0			0
$372$		0			0
$373$	0.390530	+	0.676417i	0.0202209	+	0.0350235i	0.875959	−	0.482386i	$-0.160230\pi$
$373$	0.390530	+	0.676417i	0.0202209	+	0.0350235i	−0.855738	+	0.517410i	$0.826896\pi$
$374$	0.340022	+	0.588936i	0.0175821	+	0.0304532i
$375$		0			0
$376$	13.2724	−	22.9885i	0.684474	−	1.18554i
$377$	−21.1225			−1.08786
$378$		0			0
$379$	−6.92396			−0.355660			−0.177830	−	0.984061i	$-0.556908\pi$
$379$	−6.92396			−0.355660			−0.177830	+	0.984061i	$0.556908\pi$
$380$	2.66637	−	4.61830i	0.136782	−	0.236914i
$381$		0			0
$382$	5.67617	+	9.83142i	0.290418	+	0.503019i
$383$	−3.86618	−	6.69642i	−0.197553	−	0.342171i	0.750182	−	0.661232i	$-0.229966\pi$
$383$	−3.86618	−	6.69642i	−0.197553	−	0.342171i	−0.947734	+	0.319061i	$0.896633\pi$
$384$		0			0
$385$		0			0
$386$	−0.561185			−0.0285636
$387$		0			0
$388$	−2.32945			−0.118260
$389$	2.69981	−	4.67620i	0.136886	−	0.237093i	−0.789431	−	0.613840i	$-0.789624\pi$
$389$	2.69981	−	4.67620i	0.136886	−	0.237093i	0.926316	+	0.376747i	$0.122957\pi$
$390$		0			0
$391$	2.09240	+	3.62414i	0.105817	+	0.183280i
$392$		0			0
$393$		0			0
$394$	5.03256	−	8.71664i	0.253536	−	0.439138i
$395$	−3.23854			−0.162949
$396$		0			0
$397$	29.2344			1.46723			0.733617	−	0.679563i	$-0.237831\pi$
$397$	29.2344			1.46723			0.733617	+	0.679563i	$0.237831\pi$
$398$	−1.59967	+	2.77071i	−0.0801842	+	0.138883i
$399$		0			0
$400$	−0.0667040	−	0.115535i	−0.00333520	−	0.00577674i
$401$	−13.6989	−	23.7272i	−0.684092	−	1.18488i	−0.973721	−	0.227743i	$-0.926865\pi$
$401$	−13.6989	−	23.7272i	−0.684092	−	1.18488i	0.289629	−	0.957139i	$-0.406468\pi$
$402$		0			0
$403$	15.5581	−	26.9474i	0.775003	−	1.34235i
$404$	2.09657			0.104308
$405$		0			0
$406$		0			0
$407$	7.63088	−	13.2171i	0.378249	−	0.655146i
$408$		0			0
$409$	−4.51249	−	7.81586i	−0.223128	−	0.386469i	0.732628	−	0.680629i	$-0.238294\pi$
$409$	−4.51249	−	7.81586i	−0.223128	−	0.386469i	−0.955756	+	0.294160i	$0.904960\pi$
$410$	−2.02094	−	3.50038i	−0.0998073	−	0.172871i
$411$		0			0
$412$	2.23143	−	3.86495i	0.109935	−	0.190412i
$413$		0			0
$414$		0			0
$415$	−20.2763			−0.995325
$416$	−9.49912	+	16.4530i	−0.465733	+	0.806673i
$417$		0			0
$418$	2.34477	+	4.06126i	0.114686	+	0.198643i
$419$	−0.0876485	−	0.151812i	−0.00428191	−	0.00741649i	0.863877	−	0.503704i	$-0.168030\pi$
$419$	−0.0876485	−	0.151812i	−0.00428191	−	0.00741649i	−0.868158	+	0.496287i	$0.834696\pi$
$420$		0			0
$421$	12.3525	−	21.3952i	0.602025	−	1.04274i	−0.390490	−	0.920607i	$-0.627694\pi$
$421$	12.3525	−	21.3952i	0.602025	−	1.04274i	0.992514	−	0.122130i	$-0.0389724\pi$
$422$	5.12061			0.249268
$423$		0			0
$424$	−1.62866			−0.0790947
$425$	0.745100	−	1.29055i	0.0361427	−	0.0626009i
$426$		0			0
$427$		0			0
$428$	−4.37211	−	7.57272i	−0.211334	−	0.366041i
$429$		0			0
$430$	2.61334	−	4.52644i	0.126026	−	0.218284i
$431$	29.3191			1.41225			0.706126	−	0.708086i	$-0.250441\pi$
$431$	29.3191			1.41225			0.706126	+	0.708086i	$0.250441\pi$
$432$		0			0
$433$	−19.6554			−0.944578			−0.472289	−	0.881444i	$-0.656572\pi$
$433$	−19.6554			−0.944578			−0.472289	+	0.881444i	$0.656572\pi$
$434$		0			0
$435$		0			0
$436$	0.247626	+	0.428901i	0.0118591	+	0.0205406i
$437$	14.4290	+	24.9918i	0.690233	+	1.19552i
$438$		0			0
$439$	−10.9650	+	18.9919i	−0.523330	+	0.906434i	0.476302	+	0.879282i	$0.341977\pi$
$439$	−10.9650	+	18.9919i	−0.523330	+	0.906434i	−0.999631	+	0.0271516i	$0.991356\pi$
$440$	6.31820			0.301208
$441$		0			0
$442$	1.38650			0.0659489
$443$	−9.35504	+	16.2034i	−0.444471	+	0.769847i	−0.998015	−	0.0629732i	$-0.979942\pi$
$443$	−9.35504	+	16.2034i	−0.444471	+	0.769847i	0.553544	+	0.832820i	$0.313275\pi$
$444$		0			0
$445$	−6.12108	−	10.6020i	−0.290167	−	0.502584i
$446$	3.11468	+	5.39479i	0.147485	+	0.255451i
$447$		0			0
$448$		0			0
$449$	−6.68004			−0.315251			−0.157625	−	0.987499i	$-0.550384\pi$
$449$	−6.68004			−0.315251			−0.157625	+	0.987499i	$0.550384\pi$
$450$		0			0
$451$	−5.63816			−0.265490
$452$	−8.81345	+	15.2653i	−0.414550	+	0.718022i
$453$		0			0
$454$	5.25150	+	9.09586i	0.246465	+	0.426890i
$455$		0			0
$456$		0			0
$457$	9.71436	−	16.8258i	0.454418	−	0.787076i	−0.544236	−	0.838932i	$-0.683180\pi$
$457$	9.71436	−	16.8258i	0.454418	−	0.787076i	0.998655	+	0.0518563i	$0.0165138\pi$
$458$	15.4355			0.721254
$459$		0			0
$460$	14.7811			0.689170
$461$	0.482926	−	0.836452i	0.0224921	−	0.0389575i	−0.854560	−	0.519352i	$-0.826173\pi$
$461$	0.482926	−	0.836452i	0.0224921	−	0.0389575i	0.877052	+	0.480395i	$0.159507\pi$
$462$		0			0
$463$	0.222811	+	0.385920i	0.0103549	+	0.0179352i	0.871156	−	0.491006i	$-0.163371\pi$
$463$	0.222811	+	0.385920i	0.0103549	+	0.0179352i	−0.860802	+	0.508941i	$0.830037\pi$
$464$	−0.131292	−	0.227405i	−0.00609509	−	0.0105570i
$465$		0			0
$466$	7.14677	−	12.3786i	0.331068	−	0.573426i
$467$	−34.2148			−1.58327			−0.791637	−	0.610992i	$-0.790771\pi$
$467$	−34.2148			−1.58327			−0.791637	+	0.610992i	$0.790771\pi$
$468$		0			0
$469$		0			0
$470$	−5.54189	+	9.59883i	−0.255628	+	0.442761i
$471$		0			0
$472$	−14.7506	−	25.5488i	−0.678952	−	1.17598i
$473$	−3.64543	−	6.31407i	−0.167617	−	0.290321i
$474$		0			0
$475$	5.13816	−	8.89955i	0.235755	−	0.408339i
$476$		0			0
$477$		0			0
$478$	13.2781			0.607325
$479$	10.8965	−	18.8732i	0.497872	−	0.862339i	−0.502125	−	0.864795i	$-0.667448\pi$
$479$	10.8965	−	18.8732i	0.497872	−	0.862339i	0.999997	+	0.00245553i	$0.000781622\pi$
$480$		0			0
$481$	−15.5581	−	26.9474i	−0.709388	−	1.22870i
$482$	−6.87598	−	11.9095i	−0.313192	−	0.542465i
$483$		0			0
$484$	−5.07145	+	8.78401i	−0.230521	+	0.399273i
$485$	2.55850			0.116175
$486$		0			0
$487$	19.3928			0.878772			0.439386	−	0.898298i	$-0.355196\pi$
$487$	19.3928			0.878772			0.439386	+	0.898298i	$0.355196\pi$
$488$	−10.8366	+	18.7696i	−0.490551	+	0.849659i
$489$		0			0
$490$		0			0
$491$	13.0783	+	22.6523i	0.590216	+	1.02228i	0.994203	+	0.107519i	$0.0342908\pi$
$491$	13.0783	+	22.6523i	0.590216	+	1.02228i	−0.403987	+	0.914765i	$0.632376\pi$
$492$		0			0
$493$	1.46657	−	2.54017i	0.0660509	−	0.114403i
$494$	9.56118			0.430178
$495$		0			0
$496$	0.386821			0.0173688
$497$		0			0
$498$		0			0
$499$	7.15064	+	12.3853i	0.320107	+	0.554441i	0.980510	−	0.196470i	$-0.0629479\pi$
$499$	7.15064	+	12.3853i	0.320107	+	0.554441i	−0.660403	+	0.750911i	$0.729615\pi$
$500$	−6.76352	−	11.7148i	−0.302474	−	0.523900i
$501$		0			0
$502$	−8.38279	+	14.5194i	−0.374142	+	0.648033i
$503$	18.7033			0.833937			0.416969	−	0.908921i	$-0.363092\pi$
$503$	18.7033			0.833937			0.416969	+	0.908921i	$0.363092\pi$
$504$		0			0
$505$	−2.30272			−0.102470
$506$	−6.49912	+	11.2568i	−0.288921	+	0.500426i
$507$		0			0
$508$	−12.7400	−	22.0664i	−0.565248	−	0.979039i
$509$	12.8045	+	22.1781i	0.567551	+	0.983027i	0.996807	+	0.0798442i	$0.0254423\pi$
$509$	12.8045	+	22.1781i	0.567551	+	0.983027i	−0.429257	+	0.903183i	$0.641224\pi$
$510$		0			0
$511$		0			0
$512$	−0.473897			−0.0209435
$513$		0			0
$514$	23.3756			1.03105
$515$	−2.45084	+	4.24497i	−0.107997	+	0.187056i
$516$		0			0
$517$	7.73055	+	13.3897i	0.339989	+	0.588879i
$518$		0			0
$519$		0			0
$520$	6.44087	−	11.1559i	0.282451	−	0.489220i
$521$	−21.2121			−0.929320			−0.464660	−	0.885489i	$-0.653824\pi$
$521$	−21.2121			−0.929320			−0.464660	+	0.885489i	$0.653824\pi$
$522$		0			0
$523$	−20.8057			−0.909770			−0.454885	−	0.890550i	$-0.650320\pi$
$523$	−20.8057			−0.909770			−0.454885	+	0.890550i	$0.650320\pi$
$524$	−4.39470	+	7.61185i	−0.191984	+	0.332525i
$525$		0			0
$526$	−0.322786	−	0.559082i	−0.0140741	−	0.0243771i
$527$	2.16044	+	3.74200i	0.0941104	+	0.163004i
$528$		0			0
$529$	−28.4937	+	49.3525i	−1.23885	+	2.14576i
$530$	0.680045			0.0295393
$531$		0			0
$532$		0			0
$533$	−5.74763	+	9.95518i	−0.248957	+	0.431207i
$534$		0			0
$535$	4.80200	+	8.31731i	0.207609	+	0.359589i
$536$	0.845952	+	1.46523i	0.0365396	+	0.0632884i
$537$		0			0
$538$	9.16772	−	15.8790i	0.395248	−	0.684590i
$539$		0			0
$540$		0			0
$541$	26.7297			1.14920			0.574599	−	0.818435i	$-0.305158\pi$
$541$	26.7297			1.14920			0.574599	+	0.818435i	$0.305158\pi$
$542$	3.05943	−	5.29909i	0.131414	−	0.227615i
$543$		0			0
$544$	−1.31908	−	2.28471i	−0.0565550	−	0.0979561i
$545$	−0.271974	−	0.471073i	−0.0116501	−	0.0201786i
$546$		0			0
$547$	−18.3812	+	31.8372i	−0.785923	+	1.36126i	0.142523	+	0.989792i	$0.454479\pi$
$547$	−18.3812	+	31.8372i	−0.785923	+	1.36126i	−0.928446	+	0.371467i	$0.878855\pi$
$548$	3.15125			0.134615
$549$		0			0
$550$	4.62866			0.197367
$551$	10.1133	−	17.5168i	0.430843	−	0.746242i
$552$		0			0
$553$		0			0
$554$	−7.85844	−	13.6112i	−0.333873	−	0.578285i
$555$		0			0
$556$	3.76187	−	6.51575i	0.159539	−	0.276329i
$557$	−32.3387			−1.37024			−0.685118	−	0.728432i	$-0.740249\pi$
$557$	−32.3387			−1.37024			−0.685118	+	0.728432i	$0.740249\pi$
$558$		0			0
$559$	−14.8648			−0.628716
$560$		0			0
$561$		0			0
$562$	9.80974	+	16.9910i	0.413799	+	0.716721i
$563$	8.87093	+	15.3649i	0.373865	+	0.647553i	0.990156	−	0.139965i	$-0.0446990\pi$
$563$	8.87093	+	15.3649i	0.373865	+	0.647553i	−0.616291	+	0.787518i	$0.711366\pi$
$564$		0			0
$565$	9.68004	−	16.7663i	0.407243	−	0.705365i
$566$	16.3517			0.687315
$567$		0			0
$568$	−1.57304			−0.0660035
$569$	−13.3007	+	23.0374i	−0.557593	+	0.965779i	0.440104	+	0.897947i	$0.354942\pi$
$569$	−13.3007	+	23.0374i	−0.557593	+	0.965779i	−0.997697	+	0.0678320i	$0.978392\pi$
$570$		0			0
$571$	5.00862	+	8.67518i	0.209604	+	0.363045i	0.951590	−	0.307371i	$-0.0994491\pi$
$571$	5.00862	+	8.67518i	0.209604	+	0.363045i	−0.741986	+	0.670416i	$0.766116\pi$
$572$	−3.41565	−	5.91608i	−0.142815	−	0.247364i
$573$		0			0
$574$		0			0
$575$	28.4834			1.18784
$576$		0			0
$577$	32.9145			1.37025			0.685124	−	0.728427i	$-0.259748\pi$
$577$	32.9145			1.37025			0.685124	+	0.728427i	$0.259748\pi$
$578$	7.37851	−	12.7800i	0.306905	−	0.531576i
$579$		0			0
$580$	−5.18004	−	8.97210i	−0.215090	−	0.372546i
$581$		0			0
$582$		0			0
$583$	0.474308	−	0.821525i	0.0196438	−	0.0340241i
$584$	5.81582			0.240660
$585$		0			0
$586$	11.5125			0.475577
$587$	7.53643	−	13.0535i	0.311062	−	0.538774i	−0.667531	−	0.744582i	$-0.732649\pi$
$587$	7.53643	−	13.0535i	0.311062	−	0.538774i	0.978592	+	0.205808i	$0.0659821\pi$
$588$		0			0
$589$	14.8983	+	25.8046i	0.613873	+	1.06326i
$590$	6.15910	+	10.6679i	0.253566	+	0.439189i
$591$		0			0
$592$	0.193411	−	0.334997i	0.00794913	−	0.0137683i
$593$	41.0009			1.68371			0.841853	−	0.539706i	$-0.181465\pi$
$593$	41.0009			1.68371			0.841853	+	0.539706i	$0.181465\pi$
$594$		0			0
$595$		0			0
$596$	−0.264396	+	0.457947i	−0.0108301	+	0.0187582i
$597$		0			0
$598$	13.2506	+	22.9507i	0.541858	+	0.938526i
$599$	3.03684	+	5.25996i	0.124082	+	0.214916i	0.921374	−	0.388678i	$-0.127068\pi$
$599$	3.03684	+	5.25996i	0.124082	+	0.214916i	−0.797292	+	0.603594i	$0.793735\pi$
$600$		0			0
$601$	−7.06758	+	12.2414i	−0.288293	+	0.499338i	−0.973402	−	0.229102i	$-0.926421\pi$
$601$	−7.06758	+	12.2414i	−0.288293	+	0.499338i	0.685110	+	0.728440i	$0.259754\pi$
$602$		0			0
$603$		0			0
$604$	3.03064			0.123315
$605$	5.57011	−	9.64771i	0.226457	−	0.392235i
$606$		0			0
$607$	23.0449	+	39.9149i	0.935363	+	1.62010i	0.773986	+	0.633203i	$0.218260\pi$
$607$	23.0449	+	39.9149i	0.935363	+	1.62010i	0.161377	+	0.986893i	$0.448406\pi$
$608$	−9.09627	−	15.7552i	−0.368902	−	0.638958i
$609$		0			0
$610$	4.52481	−	7.83721i	0.183204	−	0.317319i
$611$	31.5226			1.27527
$612$		0			0
$613$	−26.4938			−1.07008			−0.535038	−	0.844828i	$-0.679703\pi$
$613$	−26.4938			−1.07008			−0.535038	+	0.844828i	$0.679703\pi$
$614$	2.77466	−	4.80586i	0.111976	−	0.193949i
$615$		0			0
$616$		0			0
$617$	−1.12495	−	1.94847i	−0.0452889	−	0.0784426i	0.842492	−	0.538708i	$-0.181087\pi$
$617$	−1.12495	−	1.94847i	−0.0452889	−	0.0784426i	−0.887781	+	0.460266i	$0.847754\pi$
$618$		0			0
$619$	3.09539	−	5.36137i	0.124414	−	0.215492i	−0.797090	−	0.603861i	$-0.793628\pi$
$619$	3.09539	−	5.36137i	0.124414	−	0.215492i	0.921504	+	0.388369i	$0.126962\pi$
$620$	15.2618			0.612927
$621$		0			0
$622$	−8.37557			−0.335830
$623$		0			0
$624$		0			0
$625$	−0.533433	−	0.923933i	−0.0213373	−	0.0369573i
$626$	−7.75119	−	13.4255i	−0.309800	−	0.536589i
$627$		0			0
$628$	−6.21523	+	10.7651i	−0.248015	+	0.429574i
$629$	4.32089			0.172285
$630$		0			0
$631$	26.1661			1.04166			0.520829	−	0.853661i	$-0.325623\pi$
$631$	26.1661			1.04166			0.520829	+	0.853661i	$0.325623\pi$
$632$	−3.41029	+	5.90680i	−0.135654	+	0.234960i
$633$		0			0
$634$	3.55138	+	6.15118i	0.141043	+	0.244295i
$635$	13.9927	+	24.2361i	0.555284	+	0.961781i
$636$		0			0
$637$		0			0
$638$	9.11051			0.360689
$639$		0			0
$640$	−9.21894			−0.364411
$641$	2.44444	−	4.23389i	0.0965496	−	0.167229i	−0.813705	−	0.581278i	$-0.802553\pi$
$641$	2.44444	−	4.23389i	0.0965496	−	0.167229i	0.910254	+	0.414050i	$0.135886\pi$
$642$		0			0
$643$	−20.1839	−	34.9596i	−0.795976	−	1.37867i	−0.922218	−	0.386671i	$-0.873625\pi$
$643$	−20.1839	−	34.9596i	−0.795976	−	1.37867i	0.126242	−	0.992000i	$-0.459709\pi$
$644$		0			0
$645$		0			0
$646$	−0.663848	+	1.14982i	−0.0261188	+	0.0452390i
$647$	−2.28075			−0.0896657			−0.0448329	−	0.998995i	$-0.514276\pi$
$647$	−2.28075			−0.0896657			−0.0448329	+	0.998995i	$0.514276\pi$
$648$		0			0
$649$	17.1830			0.674493
$650$	4.71853	−	8.17273i	0.185076	−	0.320561i
$651$		0			0
$652$	−1.59240	−	2.75811i	−0.0623631	−	0.108016i
$653$	11.7396	+	20.3336i	0.459407	+	0.795717i	0.998930	−	0.0462542i	$-0.0147284\pi$
$653$	11.7396	+	20.3336i	0.459407	+	0.795717i	−0.539522	+	0.841971i	$0.681395\pi$
$654$		0			0
$655$	4.82682	−	8.36030i	0.188599	−	0.326664i
$656$	−0.142903			−0.00557944
$657$		0			0
$658$		0			0
$659$	−23.9812	+	41.5366i	−0.934174	+	1.61804i	−0.158073	+	0.987427i	$0.550528\pi$
$659$	−23.9812	+	41.5366i	−0.934174	+	1.61804i	−0.776101	+	0.630609i	$0.782805\pi$
$660$		0			0
$661$	14.6545	+	25.3824i	0.569995	+	0.987260i	0.996566	+	0.0828055i	$0.0263880\pi$
$661$	14.6545	+	25.3824i	0.569995	+	0.987260i	−0.426571	+	0.904454i	$0.640279\pi$
$662$	−10.1348	−	17.5539i	−0.393898	−	0.682252i
$663$		0			0
$664$	−21.3516	+	36.9821i	−0.828604	+	1.43518i
$665$		0			0
$666$		0			0
$667$	56.0634			2.17078
$668$	−14.2191	+	24.6282i	−0.550154	+	0.952894i
$669$		0			0
$670$	−0.353226	−	0.611806i	−0.0136463	−	0.0236361i
$671$	−6.31180	−	10.9324i	−0.243664	−	0.422039i
$672$		0			0
$673$	−13.1591	+	22.7922i	−0.507246	+	0.878576i	0.492719	+	0.870189i	$0.336003\pi$
$673$	−13.1591	+	22.7922i	−0.507246	+	0.878576i	−0.999965	+	0.00838731i	$0.997330\pi$
$674$	25.5226			0.983094
$675$		0			0
$676$	2.01899			0.0776535
$677$	−17.9454	+	31.0823i	−0.689697	+	1.19459i	0.282239	+	0.959344i	$0.408923\pi$
$677$	−17.9454	+	31.0823i	−0.689697	+	1.19459i	−0.971936	+	0.235246i	$0.924411\pi$
$678$		0			0
$679$		0			0
$680$	0.894400	+	1.54915i	0.0342987	+	0.0594070i
$681$		0			0
$682$	−6.71048	+	11.6229i	−0.256958	+	0.445064i
$683$	−35.0642			−1.34169			−0.670847	−	0.741596i	$-0.734069\pi$
$683$	−35.0642			−1.34169			−0.670847	+	0.741596i	$0.734069\pi$
$684$		0			0
$685$	−3.46110			−0.132242
$686$		0			0
$687$		0			0
$688$	−0.0923963	−	0.160035i	−0.00352257	−	0.00610128i
$689$	−0.967034	−	1.67495i	−0.0368411	−	0.0638106i
$690$		0			0
$691$	1.03343	−	1.78996i	0.0393136	−	0.0680932i	−0.845699	−	0.533660i	$-0.820816\pi$
$691$	1.03343	−	1.78996i	0.0393136	−	0.0680932i	0.885013	+	0.465567i	$0.154150\pi$
$692$	5.82915			0.221591
$693$		0			0
$694$	−11.3847			−0.432159
$695$	−4.13176	+	7.15642i	−0.156727	+	0.271458i
$696$		0			0
$697$	−0.798133	−	1.38241i	−0.0302315	−	0.0523624i
$698$	0.643208	+	1.11407i	0.0243458	+	0.0421681i
$699$		0			0
$700$		0			0
$701$	7.36009			0.277987			0.138993	−	0.990293i	$-0.455613\pi$
$701$	7.36009			0.277987			0.138993	+	0.990293i	$0.455613\pi$
$702$		0			0
$703$	29.7965			1.12380
$704$	4.16637	−	7.21637i	0.157026	−	0.271977i
$705$		0			0
$706$	−6.30200	−	10.9154i	−0.237179	−	0.410806i
$707$		0			0
$708$		0			0
$709$	−4.55438	+	7.88841i	−0.171043	+	0.296256i	−0.938785	−	0.344504i	$-0.888047\pi$
$709$	−4.55438	+	7.88841i	−0.171043	+	0.296256i	0.767742	+	0.640760i	$0.221380\pi$
$710$	0.656822			0.0246501
$711$		0			0
$712$	−25.7828			−0.966252
$713$	−41.2943	+	71.5239i	−1.54648	+	2.67859i
$714$		0			0
$715$	3.75150	+	6.49778i	0.140298	+	0.243003i
$716$	5.23308	+	9.06396i	0.195569	+	0.338736i
$717$		0			0
$718$	−9.20574	+	15.9448i	−0.343555	+	0.595055i
$719$	−25.9537			−0.967908			−0.483954	−	0.875093i	$-0.660800\pi$
$719$	−25.9537			−0.967908			−0.483954	+	0.875093i	$0.660800\pi$
$720$		0			0
$721$		0			0
$722$	3.77631	−	6.54076i	0.140540	−	0.243422i
$723$		0			0
$724$	10.5706	+	18.3088i	0.392852	+	0.680440i
$725$	−9.98205	−	17.2894i	−0.370724	−	0.642113i
$726$		0			0
$727$	−5.08007	+	8.79894i	−0.188409	+	0.326335i	−0.944720	−	0.327878i	$-0.893667\pi$
$727$	−5.08007	+	8.79894i	−0.188409	+	0.326335i	0.756311	+	0.654213i	$0.227000\pi$
$728$		0			0
$729$		0			0
$730$	−2.42839			−0.0898786
$731$	1.03209	−	1.78763i	0.0381732	−	0.0661179i
$732$		0			0
$733$	20.3307	+	35.2138i	0.750931	+	1.30065i	0.947372	+	0.320135i	$0.103728\pi$
$733$	20.3307	+	35.2138i	0.750931	+	1.30065i	−0.196441	+	0.980516i	$0.562938\pi$
$734$	−5.30154	−	9.18253i	−0.195683	−	0.338933i
$735$		0			0
$736$	25.2126	−	43.6695i	0.929349	−	1.60968i
$737$	−0.985452			−0.0362996
$738$		0			0
$739$	−25.3618			−0.932951			−0.466475	−	0.884534i	$-0.654476\pi$
$739$	−25.3618			−0.932951			−0.466475	+	0.884534i	$0.654476\pi$
$740$	7.63088	−	13.2171i	0.280517	−	0.485869i
$741$		0			0
$742$		0			0
$743$	−11.2221	−	19.4372i	−0.411699	−	0.713083i	0.583377	−	0.812202i	$-0.301731\pi$
$743$	−11.2221	−	19.4372i	−0.411699	−	0.713083i	−0.995076	+	0.0991184i	$0.968398\pi$
$744$		0			0
$745$	0.290393	−	0.502975i	0.0106392	−	0.0184276i
$746$	−0.686852			−0.0251474
$747$		0			0
$748$	0.948615			0.0346848
$749$		0			0
$750$		0			0
$751$	−12.1086	−	20.9727i	−0.441849	−	0.765305i	0.555978	−	0.831197i	$-0.312344\pi$
$751$	−12.1086	−	20.9727i	−0.441849	−	0.765305i	−0.997827	+	0.0658924i	$0.979011\pi$
$752$	0.195937	+	0.339373i	0.00714508	+	0.0123756i
$753$		0			0
$754$	9.28740	−	16.0862i	0.338227	−	0.585827i
$755$	−3.32863			−0.121141
$756$		0			0
$757$	9.11793			0.331397			0.165698	−	0.986176i	$-0.447012\pi$
$757$	9.11793			0.331397			0.165698	+	0.986176i	$0.447012\pi$
$758$	3.04442	−	5.27308i	0.110578	−	0.191527i
$759$		0			0
$760$	6.16772	+	10.6828i	0.223727	+	0.387506i
$761$	9.13610	+	15.8242i	0.331183	+	0.573626i	0.982744	−	0.184970i	$-0.0592188\pi$
$761$	9.13610	+	15.8242i	0.331183	+	0.573626i	−0.651561	+	0.758596i	$0.725886\pi$
$762$		0			0
$763$		0			0
$764$	15.8357			0.572917
$765$		0			0
$766$	6.79973			0.245684
$767$	17.5167	−	30.3398i	0.632490	−	1.09550i
$768$		0			0
$769$	9.26470	+	16.0469i	0.334094	+	0.578667i	0.983310	−	0.181936i	$-0.0582365\pi$
$769$	9.26470	+	16.0469i	0.334094	+	0.578667i	−0.649217	+	0.760604i	$0.724903\pi$
$770$		0			0
$771$		0			0
$772$	−0.391407	+	0.677937i	−0.0140870	+	0.0243995i
$773$	−2.96080			−0.106493			−0.0532463	−	0.998581i	$-0.516957\pi$
$773$	−2.96080			−0.106493			−0.0532463	+	0.998581i	$0.516957\pi$
$774$		0			0
$775$	29.4097			1.05643
$776$	2.69418	−	4.66646i	0.0967155	−	0.167516i
$777$		0			0
$778$	2.37417	+	4.11218i	0.0851181	+	0.147429i
$779$	−5.50387	−	9.53298i	−0.197197	−	0.341555i
$780$		0			0
$781$	0.458111	−	0.793471i	0.0163925	−	0.0283926i
$782$	−3.68004			−0.131598
$783$		0			0
$784$		0			0
$785$	6.82635	−	11.8236i	0.243643	−	0.422002i
$786$		0			0
$787$	−16.7010	−	28.9270i	−0.595326	−	1.03113i	−0.993501	−	0.113825i	$-0.963690\pi$
$787$	−16.7010	−	28.9270i	−0.595326	−	1.03113i	0.398175	−	0.917310i	$-0.369644\pi$
$788$	−7.02007	−	12.1591i	−0.250080	−	0.433150i
$789$		0			0
$790$	1.42396	−	2.46638i	0.0506623	−	0.0877497i
$791$		0			0
$792$		0			0
$793$	−25.7374			−0.913962
$794$	−12.8542	+	22.2641i	−0.456177	+	0.790122i
$795$		0			0
$796$	2.23143	+	3.86495i	0.0790909	+	0.136989i
$797$	−24.6755	−	42.7391i	−0.874050	−	1.51390i	−0.857772	−	0.514031i	$-0.828152\pi$
$797$	−24.6755	−	42.7391i	−0.874050	−	1.51390i	−0.0162779	−	0.999868i	$-0.505182\pi$
$798$		0			0
$799$	−2.18866	+	3.79088i	−0.0774293	+	0.134112i
$800$	−17.9564			−0.634853
$801$		0			0
$802$	24.0933			0.850763
$803$	−1.69372	+	2.93360i	−0.0597699	+	0.103525i
$804$		0			0
$805$		0			0
$806$	13.6816	+	23.6971i	0.481912	+	0.834696i
$807$		0			0
$808$	−2.42484	+	4.19995i	−0.0853056	+	0.147754i
$809$	−19.8280			−0.697115			−0.348558	−	0.937287i	$-0.613328\pi$
$809$	−19.8280			−0.697115			−0.348558	+	0.937287i	$0.613328\pi$
$810$		0			0
$811$	23.8557			0.837686			0.418843	−	0.908059i	$-0.362436\pi$
$811$	23.8557			0.837686			0.418843	+	0.908059i	$0.362436\pi$
$812$		0			0
$813$		0			0
$814$	6.71048	+	11.6229i	0.235202	+	0.407382i
$815$	1.74897	+	3.02931i	0.0612638	+	0.106112i
$816$		0			0
$817$	7.11721	−	12.3274i	0.249000	−	0.431280i
$818$	7.93643			0.277491
$819$		0			0
$820$	−5.63816			−0.196893
$821$	−25.4714	+	44.1177i	−0.888957	+	1.53972i	−0.0478469	+	0.998855i	$0.515236\pi$
$821$	−25.4714	+	44.1177i	−0.888957	+	1.53972i	−0.841110	+	0.540864i	$0.818097\pi$
$822$		0			0
$823$	−6.80747	−	11.7909i	−0.237293	−	0.411004i	0.722643	−	0.691221i	$-0.242927\pi$
$823$	−6.80747	−	11.7909i	−0.237293	−	0.411004i	−0.959937	+	0.280217i	$0.909594\pi$
$824$	5.16163	+	8.94020i	0.179814	+	0.311447i
$825$		0			0
$826$		0			0
$827$	−36.2158			−1.25935			−0.629673	−	0.776861i	$-0.716811\pi$
$827$	−36.2158			−1.25935			−0.629673	+	0.776861i	$0.716811\pi$
$828$		0			0
$829$	−25.3259			−0.879606			−0.439803	−	0.898094i	$-0.644952\pi$
$829$	−25.3259			−0.879606			−0.439803	+	0.898094i	$0.644952\pi$
$830$	8.91534	−	15.4418i	0.309456	−	0.535994i
$831$		0			0
$832$	−8.49454	−	14.7130i	−0.294495	−	0.510080i
$833$		0			0
$834$		0			0
$835$	15.6172	−	27.0498i	0.540456	−	0.936097i
$836$	6.54158			0.226245
$837$		0			0
$838$	0.154154			0.00532515
$839$	−4.35710	+	7.54671i	−0.150424	+	0.260541i	−0.931383	−	0.364040i	$-0.881397\pi$
$839$	−4.35710	+	7.54671i	−0.150424	+	0.260541i	0.780960	+	0.624582i	$0.214730\pi$
$840$		0			0
$841$	−5.14749	−	8.91571i	−0.177500	−	0.307438i
$842$	10.8626	+	18.8146i	0.374350	+	0.648394i
$843$		0			0
$844$	3.57145	−	6.18594i	0.122934	−	0.212929i
$845$	−2.21751			−0.0762847
$846$		0			0
$847$		0			0
$848$	0.0120217	−	0.0208222i	0.000412827	−	0.000715037i
$849$		0			0
$850$	0.655230	+	1.13489i	0.0224742	+	0.0389265i
$851$	41.2943	+	71.5239i	1.41555	+	2.45181i
$852$		0			0
$853$	−5.99067	+	10.3761i	−0.205117	+	0.355272i	−0.950170	−	0.311733i	$-0.899091\pi$
$853$	−5.99067	+	10.3761i	−0.205117	+	0.355272i	0.745053	+	0.667005i	$0.232424\pi$
$854$		0			0
$855$		0			0
$856$	20.2267			0.691334
$857$	−3.25015	+	5.62943i	−0.111023	+	0.192298i	−0.916183	−	0.400760i	$-0.868746\pi$
$857$	−3.25015	+	5.62943i	−0.111023	+	0.192298i	0.805160	+	0.593058i	$0.202079\pi$
$858$		0			0
$859$	−26.7763	−	46.3779i	−0.913596	−	1.58239i	−0.808944	−	0.587886i	$-0.799960\pi$
$859$	−26.7763	−	46.3779i	−0.913596	−	1.58239i	−0.104652	−	0.994509i	$-0.533373\pi$
$860$	−3.64543	−	6.31407i	−0.124308	−	0.215308i
$861$		0			0
$862$	−12.8914	+	22.3286i	−0.439083	+	0.760514i
$863$	−3.69965			−0.125937			−0.0629687	−	0.998016i	$-0.520057\pi$
$863$	−3.69965			−0.125937			−0.0629687	+	0.998016i	$0.520057\pi$
$864$		0			0
$865$	−6.40230			−0.217685
$866$	8.64233	−	14.9690i	0.293678	−	0.508666i
$867$		0			0
$868$		0			0
$869$	−1.98633	−	3.44042i	−0.0673816	−	0.116708i
$870$		0			0
$871$	−1.00459	+	1.73999i	−0.0340391	+	0.0589574i
$872$	−1.14559			−0.0387946
$873$		0			0
$874$	−25.3773			−0.858401
$875$		0			0
$876$		0			0
$877$	5.89440	+	10.2094i	0.199040	+	0.344747i	0.948217	−	0.317622i	$-0.102884\pi$
$877$	5.89440	+	10.2094i	0.199040	+	0.344747i	−0.749178	+	0.662369i	$0.769551\pi$
$878$	−9.64244	−	16.7012i	−0.325416	−	0.563638i
$879$		0			0
$880$	−0.0466368	+	0.0807773i	−0.00157213	+	0.00272300i
$881$	49.4858			1.66722			0.833609	−	0.552355i	$-0.186271\pi$
$881$	49.4858			1.66722			0.833609	+	0.552355i	$0.186271\pi$
$882$		0			0
$883$	−21.5357			−0.724734			−0.362367	−	0.932035i	$-0.618031\pi$
$883$	−21.5357			−0.724734			−0.362367	+	0.932035i	$0.618031\pi$
$884$	0.967034	−	1.67495i	0.0325249	−	0.0563347i
$885$		0			0
$886$	−8.22668	−	14.2490i	−0.276381	−	0.478706i
$887$	−5.94238	−	10.2925i	−0.199526	−	0.345589i	0.748849	−	0.662741i	$-0.230607\pi$
$887$	−5.94238	−	10.2925i	−0.199526	−	0.345589i	−0.948375	+	0.317152i	$0.897273\pi$
$888$		0			0
$889$		0			0
$890$	10.7656			0.360863
$891$		0			0
$892$	8.68954			0.290947
$893$	−15.0929	+	26.1416i	−0.505063	+	0.874795i
$894$		0			0
$895$	−5.74763	−	9.95518i	−0.192122	−	0.332765i
$896$		0			0
$897$		0			0
$898$	2.93717	−	5.08732i	0.0980145	−	0.169766i
$899$	57.8866			1.93063
$900$		0			0
$901$	0.268571			0.00894739
$902$	2.47906	−	4.29385i	0.0825435	−	0.142970i
$903$		0			0
$904$	−20.3868	−	35.3110i	−0.678056	−	1.17443i
$905$	−11.6099	−	20.1090i	−0.385927	−	0.668446i
$906$		0			0
$907$	13.0107	−	22.5353i	0.432014	−	0.748271i	−0.565032	−	0.825069i	$-0.691136\pi$
$907$	13.0107	−	22.5353i	0.432014	−	0.748271i	0.997047	+	0.0767980i	$0.0244697\pi$
$908$	14.6509			0.486209
$909$		0			0
$910$		0			0
$911$	−2.01636	+	3.49244i	−0.0668050	+	0.115710i	−0.897493	−	0.441028i	$-0.854614\pi$
$911$	−2.01636	+	3.49244i	−0.0668050	+	0.115710i	0.830688	+	0.556738i	$0.187947\pi$
$912$		0			0
$913$	−12.4363	−	21.5403i	−0.411581	−	0.712879i
$914$	8.54266	+	14.7963i	0.282566	+	0.489419i
$915$		0			0
$916$	10.7657	−	18.6468i	0.355710	−	0.616108i
$917$		0			0
$918$		0			0
$919$	27.4270			0.904732			0.452366	−	0.891832i	$-0.350580\pi$
$919$	27.4270			0.904732			0.452366	+	0.891832i	$0.350580\pi$
$920$	−17.0954	+	29.6101i	−0.563618	+	0.976216i
$921$		0			0
$922$	0.424678	+	0.735564i	0.0139860	+	0.0242245i
$923$	−0.934011	−	1.61775i	−0.0307434	−	0.0532491i
$924$		0			0
$925$	14.7049	−	25.4696i	0.483493	−	0.837434i
$926$	−0.391874			−0.0128778
$927$		0			0
$928$	−35.3432			−1.16020
$929$	−3.83837	+	6.64826i	−0.125933	+	0.218122i	−0.922097	−	0.386958i	$-0.873526\pi$
$929$	−3.83837	+	6.64826i	−0.125933	+	0.218122i	0.796164	+	0.605081i	$0.206859\pi$
$930$		0			0
$931$		0			0
$932$	−9.96926	−	17.2673i	−0.326554	−	0.565608i
$933$		0			0
$934$	15.0440	−	26.0570i	0.492255	−	0.852610i
$935$	−1.04189			−0.0340734
$936$		0			0
$937$	2.02465			0.0661425			0.0330713	−	0.999453i	$-0.489471\pi$
$937$	2.02465			0.0661425			0.0330713	+	0.999453i	$0.489471\pi$
$938$		0			0
$939$		0			0
$940$	7.73055	+	13.3897i	0.252143	+	0.436724i
$941$	3.06964	+	5.31677i	0.100067	+	0.173322i	0.911712	−	0.410829i	$-0.134761\pi$
$941$	3.06964	+	5.31677i	0.100067	+	0.173322i	−0.811645	+	0.584151i	$0.801427\pi$
$942$		0			0
$943$	15.2554	−	26.4231i	0.496783	−	0.860454i
$944$	0.435518			0.0141749
$945$		0			0
$946$	6.41147			0.208455
$947$	2.78224	−	4.81898i	0.0904107	−	0.156596i	−0.817273	−	0.576250i	$-0.804515\pi$
$947$	2.78224	−	4.81898i	0.0904107	−	0.156596i	0.907684	+	0.419654i	$0.137849\pi$
$948$		0			0
$949$	3.45320	+	5.98112i	0.112096	+	0.194155i
$950$	4.51842	+	7.82613i	0.146597	+	0.253913i
$951$		0			0
$952$		0			0
$953$	8.72018			0.282474			0.141237	−	0.989976i	$-0.454892\pi$
$953$	8.72018			0.282474			0.141237	+	0.989976i	$0.454892\pi$
$954$		0			0
$955$	−17.3928			−0.562818
$956$	9.26099	−	16.0405i	0.299522	−	0.518787i
$957$		0			0
$958$	9.58219	+	16.5968i	0.309586	+	0.536219i
$959$		0			0
$960$		0			0
$961$	−27.1373	+	47.0031i	−0.875396	+	1.51623i
$962$	27.3631			0.882222
$963$		0			0
$964$	−19.1830			−0.617844
$965$	0.429892	−	0.744596i	0.0138387	−	0.0239694i
$966$		0			0
$967$	28.8849	+	50.0301i	0.928876	+	1.60886i	0.785206	+	0.619235i	$0.212557\pi$
$967$	28.8849	+	50.0301i	0.928876	+	1.60886i	0.143670	+	0.989626i	$0.454110\pi$
$968$	−11.7310	−	20.3187i	−0.377049	−	0.653068i
$969$		0			0
$970$	−1.12495	+	1.94847i	−0.0361200	+	0.0625617i
$971$	−30.7192			−0.985828			−0.492914	−	0.870078i	$-0.664068\pi$
$971$	−30.7192			−0.985828			−0.492914	+	0.870078i	$0.664068\pi$
$972$		0			0
$973$		0			0
$974$	−8.52687	+	14.7690i	−0.273219	+	0.473229i
$975$		0			0
$976$	−0.159978	−	0.277089i	−0.00512076	−	0.00886941i
$977$	5.15002	+	8.92009i	0.164764	+	0.285379i	0.936571	−	0.350477i	$-0.113981\pi$
$977$	5.15002	+	8.92009i	0.164764	+	0.285379i	−0.771808	+	0.635856i	$0.780647\pi$
$978$		0			0
$979$	7.50862	−	13.0053i	0.239976	−	0.415651i
$980$		0			0
$981$		0			0
$982$	−23.0018			−0.734015
$983$	−6.84817	+	11.8614i	−0.218423	+	0.378319i	−0.954326	−	0.298767i	$-0.903425\pi$
$983$	−6.84817	+	11.8614i	−0.218423	+	0.378319i	0.735903	+	0.677087i	$0.236758\pi$
$984$		0			0
$985$	7.71032	+	13.3547i	0.245671	+	0.425515i
$986$	1.28968	+	2.23379i	0.0410717	+	0.0711383i
$987$		0			0
$988$	6.66860	−	11.5503i	0.212156	−	0.367465i
$989$	39.4543			1.25457
$990$		0			0
$991$	57.9813			1.84184			0.920919	−	0.389754i	$-0.127440\pi$
$991$	57.9813			1.84184			0.920919	+	0.389754i	$0.127440\pi$
$992$	26.0326	−	45.0897i	0.826534	−	1.43160i
$993$		0			0
$994$		0			0
$995$	−2.45084	−	4.24497i	−0.0776968	−	0.134575i
$996$		0			0
$997$	8.10876	−	14.0448i	0.256807	−	0.444803i	−0.708578	−	0.705633i	$-0.750663\pi$
$997$	8.10876	−	14.0448i	0.256807	−	0.444803i	0.965385	+	0.260830i	$0.0839962\pi$
$998$	−12.5763			−0.398097
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.f.d.883.1		6
3.2	odd	2		441.2.f.c.295.3		6
7.2	even	3		1323.2.h.b.802.3		6
7.3	odd	6		1323.2.g.d.667.1		6
7.4	even	3		1323.2.g.e.667.1		6
7.5	odd	6		1323.2.h.c.802.3		6
7.6	odd	2		189.2.f.b.127.1		6
9.2	odd	6		3969.2.a.q.1.1		3
9.4	even	3	inner	1323.2.f.d.442.1		6
9.5	odd	6		441.2.f.c.148.3		6
9.7	even	3		3969.2.a.l.1.3		3
21.2	odd	6		441.2.h.e.214.1		6
21.5	even	6		441.2.h.d.214.1		6
21.11	odd	6		441.2.g.b.79.3		6
21.17	even	6		441.2.g.c.79.3		6
21.20	even	2		63.2.f.a.43.3	yes	6
28.27	even	2		3024.2.r.k.2017.2		6
63.4	even	3		1323.2.h.b.226.3		6
63.5	even	6		441.2.g.c.67.3		6
63.13	odd	6		189.2.f.b.64.1		6
63.20	even	6		567.2.a.h.1.1		3
63.23	odd	6		441.2.g.b.67.3		6
63.31	odd	6		1323.2.h.c.226.3		6
63.32	odd	6		441.2.h.e.373.1		6
63.34	odd	6		567.2.a.c.1.3		3
63.40	odd	6		1323.2.g.d.361.1		6
63.41	even	6		63.2.f.a.22.3	✓	6
63.58	even	3		1323.2.g.e.361.1		6
63.59	even	6		441.2.h.d.373.1		6
84.83	odd	2		1008.2.r.h.673.2		6
252.83	odd	6		9072.2.a.ca.1.2		3
252.139	even	6		3024.2.r.k.1009.2		6
252.167	odd	6		1008.2.r.h.337.2		6
252.223	even	6		9072.2.a.bs.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.3	✓	6	63.41	even	6
63.2.f.a.43.3	yes	6	21.20	even	2
189.2.f.b.64.1		6	63.13	odd	6
189.2.f.b.127.1		6	7.6	odd	2
441.2.f.c.148.3		6	9.5	odd	6
441.2.f.c.295.3		6	3.2	odd	2
441.2.g.b.67.3		6	63.23	odd	6
441.2.g.b.79.3		6	21.11	odd	6
441.2.g.c.67.3		6	63.5	even	6
441.2.g.c.79.3		6	21.17	even	6
441.2.h.d.214.1		6	21.5	even	6
441.2.h.d.373.1		6	63.59	even	6
441.2.h.e.214.1		6	21.2	odd	6
441.2.h.e.373.1		6	63.32	odd	6
567.2.a.c.1.3		3	63.34	odd	6
567.2.a.h.1.1		3	63.20	even	6
1008.2.r.h.337.2		6	252.167	odd	6
1008.2.r.h.673.2		6	84.83	odd	2
1323.2.f.d.442.1		6	9.4	even	3	inner
1323.2.f.d.883.1		6	1.1	even	1	trivial
1323.2.g.d.361.1		6	63.40	odd	6
1323.2.g.d.667.1		6	7.3	odd	6
1323.2.g.e.361.1		6	63.58	even	3
1323.2.g.e.667.1		6	7.4	even	3
1323.2.h.b.226.3		6	63.4	even	3
1323.2.h.b.802.3		6	7.2	even	3
1323.2.h.c.226.3		6	63.31	odd	6
1323.2.h.c.802.3		6	7.5	odd	6
3024.2.r.k.1009.2		6	252.139	even	6
3024.2.r.k.2017.2		6	28.27	even	2
3969.2.a.l.1.3		3	9.7	even	3
3969.2.a.q.1.1		3	9.2	odd	6
9072.2.a.bs.1.2		3	252.223	even	6
9072.2.a.ca.1.2		3	252.83	odd	6

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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.439693 + 0.761570i) q^{2} +(0.613341 + 1.06234i) q^{4} +(-0.673648 - 1.16679i) q^{5} -2.83750 q^{8} +O(q^{10})\)	\(q+(-0.439693 + 0.761570i) q^{2} +(0.613341 + 1.06234i) q^{4} +(-0.673648 - 1.16679i) q^{5} -2.83750 q^{8} +1.18479 q^{10} +(0.826352 - 1.43128i) q^{11} +(-1.68479 - 2.91815i) q^{13} +(0.0209445 - 0.0362770i) q^{16} +0.467911 q^{17} +3.22668 q^{19} +(0.826352 - 1.43128i) q^{20} +(0.726682 + 1.25865i) q^{22} +(4.47178 + 7.74535i) q^{23} +(1.59240 - 2.75811i) q^{25} +2.96316 q^{26} +(3.13429 - 5.42874i) q^{29} +(4.61721 + 7.99724i) q^{31} +(-2.81908 - 4.88279i) q^{32} +(-0.205737 + 0.356347i) q^{34} +9.23442 q^{37} +(-1.41875 + 2.45734i) q^{38} +(1.91147 + 3.31077i) q^{40} +(-1.70574 - 2.95442i) q^{41} +(2.20574 - 3.82045i) q^{43} +2.02734 q^{44} -7.86484 q^{46} +(-4.67752 + 8.10170i) q^{47} +(1.40033 + 2.42544i) q^{50} +(2.06670 - 3.57964i) q^{52} +0.573978 q^{53} -2.22668 q^{55} +(2.75624 + 4.77396i) q^{58} +(5.19846 + 9.00400i) q^{59} +(3.81908 - 6.61484i) q^{61} -8.12061 q^{62} +5.04189 q^{64} +(-2.26991 + 3.93161i) q^{65} +(-0.298133 - 0.516382i) q^{67} +(0.286989 + 0.497079i) q^{68} +0.554378 q^{71} -2.04963 q^{73} +(-4.06031 + 7.03266i) q^{74} +(1.97906 + 3.42782i) q^{76} +(1.20187 - 2.08169i) q^{79} -0.0564370 q^{80} +3.00000 q^{82} +(7.52481 - 13.0334i) q^{83} +(-0.315207 - 0.545955i) q^{85} +(1.93969 + 3.35965i) q^{86} +(-2.34477 + 4.06126i) q^{88} +9.08647 q^{89} +(-5.48545 + 9.50108i) q^{92} +(-4.11334 - 7.12452i) q^{94} +(-2.17365 - 3.76487i) q^{95} +(-0.949493 + 1.64457i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 12 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 12 * q^8	\( 6 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 12 q^{8} + 6 q^{11} - 3 q^{13} - 3 q^{16} + 12 q^{17} + 6 q^{19} + 6 q^{20} - 9 q^{22} + 12 q^{23} + 6 q^{25} - 6 q^{26} + 9 q^{29} - 3 q^{31} + 9 q^{34} - 6 q^{37} - 6 q^{38} - 9 q^{40} + 3 q^{43} - 30 q^{44} - 3 q^{47} - 6 q^{50} - 21 q^{52} - 12 q^{53} + 9 q^{58} + 3 q^{59} + 6 q^{61} - 60 q^{62} + 24 q^{64} + 15 q^{65} + 12 q^{67} - 6 q^{68} - 18 q^{71} + 42 q^{73} - 30 q^{74} + 15 q^{76} + 21 q^{79} - 30 q^{80} + 18 q^{82} + 18 q^{83} - 9 q^{85} + 6 q^{86} - 27 q^{88} + 24 q^{89} + 3 q^{92} - 18 q^{94} - 12 q^{95} - 3 q^{97}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 12 * q^8 + 6 * q^11 - 3 * q^13 - 3 * q^16 + 12 * q^17 + 6 * q^19 + 6 * q^20 - 9 * q^22 + 12 * q^23 + 6 * q^25 - 6 * q^26 + 9 * q^29 - 3 * q^31 + 9 * q^34 - 6 * q^37 - 6 * q^38 - 9 * q^40 + 3 * q^43 - 30 * q^44 - 3 * q^47 - 6 * q^50 - 21 * q^52 - 12 * q^53 + 9 * q^58 + 3 * q^59 + 6 * q^61 - 60 * q^62 + 24 * q^64 + 15 * q^65 + 12 * q^67 - 6 * q^68 - 18 * q^71 + 42 * q^73 - 30 * q^74 + 15 * q^76 + 21 * q^79 - 30 * q^80 + 18 * q^82 + 18 * q^83 - 9 * q^85 + 6 * q^86 - 27 * q^88 + 24 * q^89 + 3 * q^92 - 18 * q^94 - 12 * q^95 - 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more