LMFDB - Embedded newform 1232.2.bn.b.241.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(241,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1, 3]))

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

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

chi := DirichletCharacter("1232.241");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.bn (of order $6$, 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:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			241.5
Root			$0.430324 + 1.60599i$ of defining polynomial
Character	$\chi$	$=$	1232.241
Dual form			1232.2.bn.b.593.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.889740 + 0.513691i) q^{3} +(1.09005 - 0.629341i) q^{5} +(-2.11465 - 1.59005i) q^{7} +(-0.972242 - 1.68397i) q^{9} +O(q^{10})$	\(q+(0.889740 + 0.513691i) q^{3} +(1.09005 - 0.629341i) q^{5} +(-2.11465 - 1.59005i) q^{7} +(-0.972242 - 1.68397i) q^{9} +(-1.45007 + 2.98283i) q^{11} -4.08338 q^{13} +1.29315 q^{15} +(-1.60096 + 2.77294i) q^{17} +(-3.81407 - 6.60616i) q^{19} +(-1.06469 - 2.50101i) q^{21} +(-4.12636 - 7.14707i) q^{23} +(-1.70786 + 2.95810i) q^{25} -5.07988i q^{27} -3.54386i q^{29} +(7.95304 + 4.59169i) q^{31} +(-2.82244 + 1.90905i) q^{33} +(-3.30576 - 0.402401i) q^{35} +(0.154122 + 0.266948i) q^{37} +(-3.63315 - 2.09760i) q^{39} -6.05276 q^{41} +7.57607i q^{43} +(-2.11959 - 1.22374i) q^{45} +(-4.07263 + 2.35133i) q^{47} +(1.94348 + 6.72480i) q^{49} +(-2.84887 + 1.64480i) q^{51} +(2.39830 - 4.15397i) q^{53} +(0.296567 + 4.16403i) q^{55} -7.83701i q^{57} +(-2.36710 - 1.36664i) q^{59} +(-0.755050 - 1.30779i) q^{61} +(-0.621652 + 5.10693i) q^{63} +(-4.45110 + 2.56984i) q^{65} +(1.69044 - 2.92792i) q^{67} -8.47871i q^{69} -3.50810 q^{71} +(0.483428 - 0.837321i) q^{73} +(-3.03910 + 1.75463i) q^{75} +(7.80925 - 4.00195i) q^{77} +(13.5212 - 7.80647i) q^{79} +(-0.307237 + 0.532150i) q^{81} +1.32998 q^{83} +4.03019i q^{85} +(1.82045 - 3.15311i) q^{87} +(9.22296 - 5.32488i) q^{89} +(8.63492 + 6.49279i) q^{91} +(4.71742 + 8.17082i) q^{93} +(-8.31505 - 4.80070i) q^{95} -10.6748i q^{97} +(6.43283 - 0.458154i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{5} + 16 q^{9}+O(q^{10}) $ 16 * q - 12 * q^5 + 16 * q^9	$ 16 q - 12 q^{5} + 16 q^{9} - 8 q^{11} + 8 q^{15} - 16 q^{23} + 12 q^{31} - 24 q^{33} - 16 q^{37} - 108 q^{45} - 24 q^{47} + 8 q^{49} - 28 q^{53} - 60 q^{59} - 12 q^{67} - 8 q^{71} - 60 q^{75} + 44 q^{77} - 8 q^{81} + 96 q^{89} + 36 q^{91} - 44 q^{93} - 56 q^{99}+O(q^{100}) $ 16 * q - 12 * q^5 + 16 * q^9 - 8 * q^11 + 8 * q^15 - 16 * q^23 + 12 * q^31 - 24 * q^33 - 16 * q^37 - 108 * q^45 - 24 * q^47 + 8 * q^49 - 28 * q^53 - 60 * q^59 - 12 * q^67 - 8 * q^71 - 60 * q^75 + 44 * q^77 - 8 * q^81 + 96 * q^89 + 36 * q^91 - 44 * q^93 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.889740	+	0.513691i	0.513691	+	0.296580i	0.734350	−	0.678771i	$-0.237487\pi$
$3$	0.889740	+	0.513691i	0.513691	+	0.296580i	−0.220658	+	0.975351i	$0.570821\pi$
$4$		0			0
$5$	1.09005	−	0.629341i	0.487486	−	0.281450i	−0.236045	−	0.971742i	$-0.575851\pi$
$5$	1.09005	−	0.629341i	0.487486	−	0.281450i	0.723531	+	0.690292i	$0.242518\pi$
$6$		0			0
$7$	−2.11465	−	1.59005i	−0.799262	−	0.600983i
$7$	−2.11465	−	1.59005i	−0.799262	−	0.600983i
$8$		0			0
$9$	−0.972242	−	1.68397i	−0.324081	−	0.561324i
$10$		0			0
$11$	−1.45007	+	2.98283i	−0.437213	+	0.899358i
$11$	−1.45007	+	2.98283i	−0.437213	+	0.899358i
$12$		0			0
$13$	−4.08338			−1.13253			−0.566263	−	0.824224i	$-0.691612\pi$
$13$	−4.08338			−1.13253			−0.566263	+	0.824224i	$0.691612\pi$
$14$		0			0
$15$	1.29315			0.333890
$16$		0			0
$17$	−1.60096	+	2.77294i	−0.388289	+	0.672537i	−0.992220	−	0.124501i	$-0.960267\pi$
$17$	−1.60096	+	2.77294i	−0.388289	+	0.672537i	0.603930	+	0.797037i	$0.293600\pi$
$18$		0			0
$19$	−3.81407	−	6.60616i	−0.875007	−	1.51556i	−0.856756	−	0.515723i	$-0.827524\pi$
$19$	−3.81407	−	6.60616i	−0.875007	−	1.51556i	−0.0182510	−	0.999833i	$-0.505810\pi$
$20$		0			0
$21$	−1.06469	−	2.50101i	−0.232335	−	0.545765i
$22$		0			0
$23$	−4.12636	−	7.14707i	−0.860407	−	1.49027i	−0.871537	−	0.490330i	$-0.836876\pi$
$23$	−4.12636	−	7.14707i	−0.860407	−	1.49027i	0.0111305	−	0.999938i	$-0.496457\pi$
$24$		0			0
$25$	−1.70786	+	2.95810i	−0.341572	+	0.591620i
$26$		0			0
$27$		−	5.07988i		−	0.977623i
$28$		0			0
$29$		−	3.54386i		−	0.658079i	−0.944316	−	0.329039i	$-0.893275\pi$
$29$		−	3.54386i		−	0.658079i	0.944316	−	0.329039i	$-0.106725\pi$
$30$		0			0
$31$	7.95304	+	4.59169i	1.42841	+	0.824692i	0.996995	−	0.0774626i	$-0.0246818\pi$
$31$	7.95304	+	4.59169i	1.42841	+	0.824692i	0.431413	+	0.902155i	$0.358015\pi$
$32$		0			0
$33$	−2.82244	+	1.90905i	−0.491324	+	0.332324i
$34$		0			0
$35$	−3.30576	−	0.402401i	−0.558775	−	0.0680182i
$36$		0			0
$37$	0.154122	+	0.266948i	0.0253376	+	0.0438860i	0.878416	−	0.477896i	$-0.158601\pi$
$37$	0.154122	+	0.266948i	0.0253376	+	0.0438860i	−0.853079	+	0.521782i	$0.825267\pi$
$38$		0			0
$39$	−3.63315	−	2.09760i	−0.581769	−	0.335885i
$40$		0			0
$41$	−6.05276			−0.945283			−0.472641	−	0.881255i	$-0.656699\pi$
$41$	−6.05276			−0.945283			−0.472641	+	0.881255i	$0.656699\pi$
$42$		0			0
$43$			7.57607i			1.15534i	0.816270	+	0.577670i	$0.196038\pi$
$43$			7.57607i			1.15534i	−0.816270	+	0.577670i	$0.803962\pi$
$44$		0			0
$45$	−2.11959	−	1.22374i	−0.315969	−	0.182425i
$46$		0			0
$47$	−4.07263	+	2.35133i	−0.594054	+	0.342977i	−0.766699	−	0.642007i	$-0.778102\pi$
$47$	−4.07263	+	2.35133i	−0.594054	+	0.342977i	0.172645	+	0.984984i	$0.444769\pi$
$48$		0			0
$49$	1.94348	+	6.72480i	0.277640	+	0.960685i
$50$		0			0
$51$	−2.84887	+	1.64480i	−0.398922	+	0.230317i
$52$		0			0
$53$	2.39830	−	4.15397i	0.329431	−	0.570592i	−0.652968	−	0.757386i	$-0.726476\pi$
$53$	2.39830	−	4.15397i	0.329431	−	0.570592i	0.982399	+	0.186794i	$0.0598097\pi$
$54$		0			0
$55$	0.296567	+	4.16403i	0.0399891	+	0.561478i
$56$		0			0
$57$		−	7.83701i		−	1.03804i
$58$		0			0
$59$	−2.36710	−	1.36664i	−0.308170	−	0.177922i	0.337938	−	0.941169i	$-0.390271\pi$
$59$	−2.36710	−	1.36664i	−0.308170	−	0.177922i	−0.646107	+	0.763247i	$0.723604\pi$
$60$		0			0
$61$	−0.755050	−	1.30779i	−0.0966743	−	0.167445i	0.813632	−	0.581380i	$-0.197487\pi$
$61$	−0.755050	−	1.30779i	−0.0966743	−	0.167445i	−0.910306	+	0.413936i	$0.864154\pi$
$62$		0			0
$63$	−0.621652	+	5.10693i	−0.0783208	+	0.643412i
$64$		0			0
$65$	−4.45110	+	2.56984i	−0.552090	+	0.318750i
$66$		0			0
$67$	1.69044	−	2.92792i	0.206520	−	0.357703i	−0.744096	−	0.668073i	$-0.767120\pi$
$67$	1.69044	−	2.92792i	0.206520	−	0.357703i	0.950616	+	0.310370i	$0.100453\pi$
$68$		0			0
$69$		−	8.47871i		−	1.02072i
$70$		0			0
$71$	−3.50810			−0.416334			−0.208167	−	0.978093i	$-0.566750\pi$
$71$	−3.50810			−0.416334			−0.208167	+	0.978093i	$0.566750\pi$
$72$		0			0
$73$	0.483428	−	0.837321i	0.0565809	−	0.0980011i	−0.836348	−	0.548200i	$-0.815313\pi$
$73$	0.483428	−	0.837321i	0.0565809	−	0.0980011i	0.892929	+	0.450198i	$0.148647\pi$
$74$		0			0
$75$	−3.03910	+	1.75463i	−0.350925	+	0.202607i
$76$		0			0
$77$	7.80925	−	4.00195i	0.889946	−	0.456065i
$78$		0			0
$79$	13.5212	−	7.80647i	1.52125	−	0.878296i	0.521568	−	0.853210i	$-0.325347\pi$
$79$	13.5212	−	7.80647i	1.52125	−	0.878296i	0.999685	−	0.0250865i	$-0.00798611\pi$
$80$		0			0
$81$	−0.307237	+	0.532150i	−0.0341374	+	0.0591278i
$82$		0			0
$83$	1.32998			0.145984			0.0729921	−	0.997333i	$-0.476745\pi$
$83$	1.32998			0.145984			0.0729921	+	0.997333i	$0.476745\pi$
$84$		0			0
$85$			4.03019i			0.437136i
$86$		0			0
$87$	1.82045	−	3.15311i	0.195173	−	0.338049i
$88$		0			0
$89$	9.22296	−	5.32488i	0.977631	−	0.564436i	0.0760772	−	0.997102i	$-0.475760\pi$
$89$	9.22296	−	5.32488i	0.977631	−	0.564436i	0.901554	+	0.432666i	$0.142427\pi$
$90$		0			0
$91$	8.63492	+	6.49279i	0.905186	+	0.680629i
$92$		0			0
$93$	4.71742	+	8.17082i	0.489174	+	0.847274i
$94$		0			0
$95$	−8.31505	−	4.80070i	−0.853106	−	0.492541i
$96$		0			0
$97$		−	10.6748i		−	1.08386i	−0.840424	−	0.541930i	$-0.817694\pi$
$97$		−	10.6748i		−	1.08386i	0.840424	−	0.541930i	$-0.182306\pi$
$98$		0			0
$99$	6.43283	−	0.458154i	0.646524	−	0.0460462i
$100$		0			0
$101$	5.03242	−	8.71642i	0.500745	−	0.867316i	−0.499255	−	0.866455i	$-0.666393\pi$
$101$	5.03242	−	8.71642i	0.500745	−	0.867316i	1.00000		0.000860457i	$-0.000273892\pi$
$102$		0			0
$103$	−2.49868	+	1.44261i	−0.246202	+	0.142145i	−0.618024	−	0.786159i	$-0.712067\pi$
$103$	−2.49868	+	1.44261i	−0.246202	+	0.142145i	0.371822	+	0.928304i	$0.378733\pi$
$104$		0			0
$105$	−2.73455	−	2.05617i	−0.266865	−	0.200662i
$106$		0			0
$107$	−14.1162	+	8.15002i	−1.36467	+	0.787892i	−0.990241	−	0.139364i	$-0.955494\pi$
$107$	−14.1162	+	8.15002i	−1.36467	+	0.787892i	−0.374428	+	0.927256i	$0.622161\pi$
$108$		0			0
$109$	−9.96227	−	5.75172i	−0.954213	−	0.550915i	−0.0598257	−	0.998209i	$-0.519054\pi$
$109$	−9.96227	−	5.75172i	−0.954213	−	0.550915i	−0.894387	+	0.447294i	$0.852388\pi$
$110$		0			0
$111$			0.316686i			0.0300585i
$112$		0			0
$113$	0.558958			0.0525824			0.0262912	−	0.999654i	$-0.491630\pi$
$113$	0.558958			0.0525824			0.0262912	+	0.999654i	$0.491630\pi$
$114$		0			0
$115$	−8.99589	−	5.19378i	−0.838872	−	0.484323i
$116$		0			0
$117$	3.97004	+	6.87631i	0.367030	+	0.635715i
$118$		0			0
$119$	7.79458	−	3.31819i	0.714528	−	0.304178i
$120$		0			0
$121$	−6.79458	−	8.65064i	−0.617689	−	0.786422i
$122$		0			0
$123$	−5.38538	−	3.10925i	−0.485584	−	0.280352i
$124$		0			0
$125$			10.5927i			0.947441i
$126$		0			0
$127$		−	11.2829i		−	1.00120i	−0.865679	−	0.500599i	$-0.833113\pi$
$127$		−	11.2829i		−	1.00120i	0.865679	−	0.500599i	$-0.166887\pi$
$128$		0			0
$129$	−3.89176	+	6.74073i	−0.342651	+	0.593488i
$130$		0			0
$131$	3.51694	+	6.09152i	0.307276	+	0.532218i	0.977766	−	0.209701i	$-0.0672490\pi$
$131$	3.51694	+	6.09152i	0.307276	+	0.532218i	−0.670489	+	0.741919i	$0.733916\pi$
$132$		0			0
$133$	−2.43871	+	20.0343i	−0.211463	+	1.73719i
$134$		0			0
$135$	−3.19698	−	5.53733i	−0.275152	−	0.476577i
$136$		0			0
$137$	−4.54487	+	7.87195i	−0.388294	+	0.672546i	−0.992220	−	0.124495i	$-0.960269\pi$
$137$	−4.54487	+	7.87195i	−0.388294	+	0.672546i	0.603926	+	0.797041i	$0.293602\pi$
$138$		0			0
$139$	−7.86546			−0.667140			−0.333570	−	0.942725i	$-0.608253\pi$
$139$	−7.86546			−0.667140			−0.333570	+	0.942725i	$0.608253\pi$
$140$		0			0
$141$	−4.83144			−0.406880
$142$		0			0
$143$	5.92120	−	12.1801i	0.495156	−	1.01855i
$144$		0			0
$145$	−2.23030	−	3.86299i	−0.185216	−	0.320804i
$146$		0			0
$147$	−1.72528	+	6.98167i	−0.142299	+	0.575838i
$148$		0			0
$149$	5.39617	−	3.11548i	0.442072	−	0.255230i	−0.262404	−	0.964958i	$-0.584515\pi$
$149$	5.39617	−	3.11548i	0.442072	−	0.255230i	0.704476	+	0.709728i	$0.251182\pi$
$150$		0			0
$151$	15.1642	+	8.75506i	1.23405	+	0.712476i	0.967871	−	0.251448i	$-0.0809069\pi$
$151$	15.1642	+	8.75506i	1.23405	+	0.712476i	0.266175	+	0.963925i	$0.414240\pi$
$152$		0			0
$153$	6.22607			0.503348
$154$		0			0
$155$	11.5590			0.928438
$156$		0			0
$157$	−6.73252	−	3.88702i	−0.537314	−	0.310218i	0.206676	−	0.978409i	$-0.433735\pi$
$157$	−6.73252	−	3.88702i	−0.537314	−	0.310218i	−0.743989	+	0.668191i	$0.767069\pi$
$158$		0			0
$159$	4.26772	−	2.46397i	0.338452	−	0.195405i
$160$		0			0
$161$	−2.63840	+	21.6747i	−0.207935	+	1.70820i
$162$		0			0
$163$	−9.10616	−	15.7723i	−0.713249	−	1.23538i	−0.963631	−	0.267237i	$-0.913889\pi$
$163$	−9.10616	−	15.7723i	−0.713249	−	1.23538i	0.250382	−	0.968147i	$-0.419444\pi$
$164$		0			0
$165$	−1.87516	+	3.85725i	−0.145981	+	0.300286i
$166$		0			0
$167$	14.3653			1.11162			0.555809	−	0.831310i	$-0.312409\pi$
$167$	14.3653			1.11162			0.555809	+	0.831310i	$0.312409\pi$
$168$		0			0
$169$	3.67402			0.282617
$170$		0			0
$171$	−7.41639	+	12.8456i	−0.567146	+	0.982325i
$172$		0			0
$173$	−2.38160	−	4.12505i	−0.181069	−	0.313621i	0.761176	−	0.648546i	$-0.224623\pi$
$173$	−2.38160	−	4.12505i	−0.181069	−	0.313621i	−0.942245	+	0.334924i	$0.891289\pi$
$174$		0			0
$175$	8.31505	−	3.53976i	0.628559	−	0.267580i
$176$		0			0
$177$	−1.40407	−	2.43191i	−0.105536	−	0.182794i
$178$		0			0
$179$	−1.94526	+	3.36928i	−0.145395	+	0.251832i	−0.929520	−	0.368771i	$-0.879779\pi$
$179$	−1.94526	+	3.36928i	−0.145395	+	0.251832i	0.784125	+	0.620603i	$0.213112\pi$
$180$		0			0
$181$		−	13.0698i		−	0.971474i	−0.874105	−	0.485737i	$-0.838551\pi$
$181$		−	13.0698i		−	0.971474i	0.874105	−	0.485737i	$-0.161449\pi$
$182$		0			0
$183$		−	1.55145i		−	0.114687i
$184$		0			0
$185$	0.336003	+	0.193991i	0.0247034	+	0.0142625i
$186$		0			0
$187$	−5.94971	−	8.79635i	−0.435086	−	0.643253i
$188$		0			0
$189$	−8.07727	+	10.7422i	−0.587535	+	0.781377i
$190$		0			0
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	0.953912	−	0.300088i	$-0.0970159\pi$
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	−0.736839	+	0.676068i	$0.763683\pi$
$192$		0			0
$193$	8.12582	+	4.69144i	0.584909	+	0.337698i	0.763082	−	0.646302i	$-0.223685\pi$
$193$	8.12582	+	4.69144i	0.584909	+	0.337698i	−0.178173	+	0.983999i	$0.557019\pi$
$194$		0			0
$195$	−5.28042			−0.378139
$196$		0			0
$197$			17.3471i			1.23593i	0.786205	+	0.617966i	$0.212043\pi$
$197$			17.3471i			1.23593i	−0.786205	+	0.617966i	$0.787957\pi$
$198$		0			0
$199$	−2.53353	−	1.46273i	−0.179597	−	0.103690i	0.407506	−	0.913202i	$-0.366398\pi$
$199$	−2.53353	−	1.46273i	−0.179597	−	0.103690i	−0.587103	+	0.809512i	$0.699732\pi$
$200$		0			0
$201$	3.00810	−	1.73673i	0.212175	−	0.122499i
$202$		0			0
$203$	−5.63492	+	7.49402i	−0.395494	+	0.525977i
$204$		0			0
$205$	−6.59782	+	3.80925i	−0.460812	+	0.266050i
$206$		0			0
$207$	−8.02365	+	13.8974i	−0.557682	+	0.965934i
$208$		0			0
$209$	25.2357	−	1.79732i	1.74559	−	0.124323i
$210$		0			0
$211$		−	0.252729i		−	0.0173986i	−0.999962	−	0.00869931i	$-0.997231\pi$
$211$		−	0.252729i		−	0.0173986i	0.999962	−	0.00869931i	$-0.00276911\pi$
$212$		0			0
$213$	−3.12129	−	1.80208i	−0.213867	−	0.123476i
$214$		0			0
$215$	4.76793	+	8.25830i	0.325170	+	0.563212i
$216$		0			0
$217$	−9.51686	−	22.3556i	−0.646047	−	1.51759i
$218$		0			0
$219$	0.860250	−	0.496665i	0.0581303	−	0.0335615i
$220$		0			0
$221$	6.53732	−	11.3230i	0.439748	−	0.761666i
$222$		0			0
$223$		−	19.0370i		−	1.27482i	−0.770527	−	0.637408i	$-0.780007\pi$
$223$		−	19.0370i		−	1.27482i	0.770527	−	0.637408i	$-0.219993\pi$
$224$		0			0
$225$	6.64181			0.442788
$226$		0			0
$227$	−9.20350	+	15.9409i	−0.610858	+	1.05804i	0.380238	+	0.924888i	$0.375842\pi$
$227$	−9.20350	+	15.9409i	−0.610858	+	1.05804i	−0.991096	+	0.133148i	$0.957491\pi$
$228$		0			0
$229$	−4.59674	+	2.65393i	−0.303761	+	0.175377i	−0.644131	−	0.764915i	$-0.722781\pi$
$229$	−4.59674	+	2.65393i	−0.303761	+	0.175377i	0.340370	+	0.940292i	$0.389448\pi$
$230$		0			0
$231$	9.00397	+	0.450846i	0.592418	+	0.0296635i
$232$		0			0
$233$	18.4629	−	10.6596i	1.20955	−	0.698332i	0.246887	−	0.969044i	$-0.420592\pi$
$233$	18.4629	−	10.6596i	1.20955	−	0.698332i	0.962660	+	0.270712i	$0.0872591\pi$
$234$		0			0
$235$	−2.95958	+	5.12614i	−0.193062	+	0.334393i
$236$		0			0
$237$	16.0405			1.04194
$238$		0			0
$239$		−	7.25163i		−	0.469069i	−0.972108	−	0.234535i	$-0.924643\pi$
$239$		−	7.25163i		−	0.469069i	0.972108	−	0.234535i	$-0.0753566\pi$
$240$		0			0
$241$	−1.77705	+	3.07794i	−0.114470	+	0.198267i	−0.917568	−	0.397580i	$-0.869850\pi$
$241$	−1.77705	+	3.07794i	−0.114470	+	0.198267i	0.803098	+	0.595847i	$0.203184\pi$
$242$		0			0
$243$	−13.7446	+	7.93547i	−0.881719	+	0.509060i
$244$		0			0
$245$	6.35068	+	6.10726i	0.405730	+	0.390179i
$246$		0			0
$247$	15.5743	+	26.9755i	0.990968	+	1.71641i
$248$		0			0
$249$	1.18334	+	0.683199i	0.0749908	+	0.0432960i
$250$		0			0
$251$		−	0.735728i		−	0.0464387i	−0.999730	−	0.0232194i	$-0.992608\pi$
$251$		−	0.735728i		−	0.0464387i	0.999730	−	0.0232194i	$-0.00739162\pi$
$252$		0			0
$253$	27.3021	−	1.94448i	1.71647	−	0.122249i
$254$		0			0
$255$	−2.07028	+	3.58582i	−0.129646	+	0.224553i
$256$		0			0
$257$	−14.0352	+	8.10325i	−0.875494	+	0.505467i	−0.869170	−	0.494513i	$-0.835346\pi$
$257$	−14.0352	+	8.10325i	−0.875494	+	0.505467i	−0.00632378	+	0.999980i	$0.502013\pi$
$258$		0			0
$259$	0.0985460	−	0.809564i	0.00612335	−	0.0503038i
$260$		0			0
$261$	−5.96777	+	3.44549i	−0.369396	+	0.213271i
$262$		0			0
$263$	21.0462	+	12.1510i	1.29776	+	0.749264i	0.980017	−	0.198911i	$-0.0637406\pi$
$263$	21.0462	+	12.1510i	1.29776	+	0.749264i	0.317746	+	0.948176i	$0.397074\pi$
$264$		0			0
$265$		−	6.03738i		−	0.370874i
$266$		0			0
$267$	10.9414			0.669601
$268$		0			0
$269$	−23.4246	−	13.5242i	−1.42822	−	0.824586i	−0.431244	−	0.902236i	$-0.641925\pi$
$269$	−23.4246	−	13.5242i	−1.42822	−	0.824586i	−0.996981	+	0.0776498i	$0.975258\pi$
$270$		0			0
$271$	5.22166	+	9.04417i	0.317193	+	0.549394i	0.979901	−	0.199483i	$-0.0639264\pi$
$271$	5.22166	+	9.04417i	0.317193	+	0.549394i	−0.662708	+	0.748878i	$0.730593\pi$
$272$		0			0
$273$	4.34754	+	10.2126i	0.263125	+	0.618093i
$274$		0			0
$275$	−6.34700	−	9.38372i	−0.382738	−	0.565859i
$276$		0			0
$277$	17.6675	+	10.2003i	1.06153	+	0.612877i	0.925856	−	0.377876i	$-0.123345\pi$
$277$	17.6675	+	10.2003i	1.06153	+	0.612877i	0.135678	+	0.990753i	$0.456679\pi$
$278$		0			0
$279$		−	17.8569i		−	1.06907i
$280$		0			0
$281$			9.99535i			0.596272i	0.954523	+	0.298136i	$0.0963650\pi$
$281$			9.99535i			0.596272i	−0.954523	+	0.298136i	$0.903635\pi$
$282$		0			0
$283$	1.74448	−	3.02153i	0.103699	−	0.179611i	−0.809507	−	0.587110i	$-0.800266\pi$
$283$	1.74448	−	3.02153i	0.103699	−	0.179611i	0.913206	+	0.407499i	$0.133599\pi$
$284$		0			0
$285$	−4.93215	−	8.54274i	−0.292156	−	0.506028i
$286$		0			0
$287$	12.7995	+	9.62420i	0.755529	+	0.568099i
$288$		0			0
$289$	3.37387	+	5.84372i	0.198463	+	0.343748i
$290$		0			0
$291$	5.48354	−	9.49778i	0.321451	−	0.556770i
$292$		0			0
$293$	−17.3549			−1.01388			−0.506942	−	0.861980i	$-0.669224\pi$
$293$	−17.3549			−1.01388			−0.506942	+	0.861980i	$0.669224\pi$
$294$		0			0
$295$	−3.44034			−0.200304
$296$		0			0
$297$	15.1524	+	7.36619i	0.879233	+	0.427430i
$298$		0			0
$299$	16.8495	+	29.1842i	0.974433	+	1.68777i
$300$		0			0
$301$	12.0463	−	16.0207i	0.694339	−	0.923419i
$302$		0			0
$303$	8.95510	−	5.17023i	0.514457	−	0.297022i
$304$		0			0
$305$	−1.64609	−	0.950368i	−0.0942546	−	0.0544179i
$306$		0			0
$307$	−22.6829			−1.29458			−0.647290	−	0.762244i	$-0.724098\pi$
$307$	−22.6829			−1.29458			−0.647290	+	0.762244i	$0.724098\pi$
$308$		0			0
$309$	−2.96423			−0.168629
$310$		0			0
$311$	−5.75141	−	3.32058i	−0.326133	−	0.188293i	0.327990	−	0.944681i	$-0.393629\pi$
$311$	−5.75141	−	3.32058i	−0.326133	−	0.188293i	−0.654123	+	0.756388i	$0.726962\pi$
$312$		0			0
$313$	−0.435583	+	0.251484i	−0.0246206	+	0.0142147i	−0.512260	−	0.858831i	$-0.671191\pi$
$313$	−0.435583	+	0.251484i	−0.0246206	+	0.0142147i	0.487639	+	0.873045i	$0.337858\pi$
$314$		0			0
$315$	2.53637	+	5.95804i	0.142908	+	0.335698i
$316$		0			0
$317$	5.27437	+	9.13547i	0.296238	+	0.513099i	0.975272	−	0.221008i	$-0.0709345\pi$
$317$	5.27437	+	9.13547i	0.296238	+	0.513099i	−0.679034	+	0.734107i	$0.737601\pi$
$318$		0			0
$319$	10.5707	+	5.13886i	0.591848	+	0.287721i
$320$		0			0
$321$	−16.7464			−0.934692
$322$		0			0
$323$	24.4246			1.35902
$324$		0			0
$325$	6.97385	−	12.0791i	0.386839	−	0.670025i
$326$		0			0
$327$	−5.90922	−	10.2351i	−0.326781	−	0.566001i
$328$		0			0
$329$	12.3509	+	1.50344i	0.680928	+	0.0828875i
$330$		0			0
$331$	−2.89029	−	5.00613i	−0.158865	−	0.275162i	0.775595	−	0.631231i	$-0.217450\pi$
$331$	−2.89029	−	5.00613i	−0.158865	−	0.275162i	−0.934460	+	0.356069i	$0.884117\pi$
$332$		0			0
$333$	0.299689	−	0.519076i	0.0164228	−	0.0284452i
$334$		0			0
$335$		−	4.25544i		−	0.232500i
$336$		0			0
$337$			11.1226i			0.605885i	0.953009	+	0.302943i	$0.0979690\pi$
$337$			11.1226i			0.605885i	−0.953009	+	0.302943i	$0.902031\pi$
$338$		0			0
$339$	0.497327	+	0.287132i	0.0270111	+	0.0155949i
$340$		0			0
$341$	−25.2287	+	17.0643i	−1.36621	+	0.924084i
$342$		0			0
$343$	6.58300	−	17.3108i	0.355449	−	0.934696i
$344$		0			0
$345$	−5.33600	−	9.24223i	−0.287281	−	0.497585i
$346$		0			0
$347$	12.7058	+	7.33569i	0.682083	+	0.393801i	0.800639	−	0.599147i	$-0.204493\pi$
$347$	12.7058	+	7.33569i	0.682083	+	0.393801i	−0.118557	+	0.992947i	$0.537827\pi$
$348$		0			0
$349$	24.6769			1.32093			0.660463	−	0.750859i	$-0.270360\pi$
$349$	24.6769			1.32093			0.660463	+	0.750859i	$0.270360\pi$
$350$		0			0
$351$			20.7431i			1.10718i
$352$		0			0
$353$	−16.6664	−	9.62237i	−0.887065	−	0.512147i	−0.0140834	−	0.999901i	$-0.504483\pi$
$353$	−16.6664	−	9.62237i	−0.887065	−	0.512147i	−0.872981	+	0.487754i	$0.837816\pi$
$354$		0			0
$355$	−3.82400	+	2.20779i	−0.202957	+	0.117177i
$356$		0			0
$357$	8.63967	+	1.05168i	0.457260	+	0.0556610i
$358$		0			0
$359$	−2.85275	+	1.64703i	−0.150562	+	0.0869271i	−0.573388	−	0.819284i	$-0.694371\pi$
$359$	−2.85275	+	1.64703i	−0.150562	+	0.0869271i	0.422826	+	0.906211i	$0.361038\pi$
$360$		0			0
$361$	−19.5942	+	33.9381i	−1.03127	+	1.78622i
$362$		0			0
$363$	−1.60165	−	11.1871i	−0.0840647	−	0.587173i
$364$		0			0
$365$		−	1.21696i		−	0.0636988i
$366$		0			0
$367$	−26.7957	−	15.4705i	−1.39873	−	0.807555i	−0.404467	−	0.914553i	$-0.632543\pi$
$367$	−26.7957	−	15.4705i	−1.39873	−	0.807555i	−0.994259	+	0.106998i	$0.965876\pi$
$368$		0			0
$369$	5.88475	+	10.1927i	0.306348	+	0.530610i
$370$		0			0
$371$	−11.6766	+	4.97077i	−0.606218	+	0.258070i
$372$		0			0
$373$	0.832767	−	0.480798i	0.0431191	−	0.0248948i	−0.478286	−	0.878204i	$-0.658742\pi$
$373$	0.832767	−	0.480798i	0.0431191	−	0.0248948i	0.521405	+	0.853310i	$0.325408\pi$
$374$		0			0
$375$	−5.44139	+	9.42476i	−0.280992	+	0.486692i
$376$		0			0
$377$			14.4709i			0.745292i
$378$		0			0
$379$	1.41216			0.0725379			0.0362689	−	0.999342i	$-0.488453\pi$
$379$	1.41216			0.0725379			0.0362689	+	0.999342i	$0.488453\pi$
$380$		0			0
$381$	5.79594	−	10.0389i	0.296935	−	0.514307i
$382$		0			0
$383$	−3.27426	+	1.89039i	−0.167307	+	0.0965946i	−0.581315	−	0.813678i	$-0.697462\pi$
$383$	−3.27426	+	1.89039i	−0.167307	+	0.0965946i	0.414009	+	0.910273i	$0.364128\pi$
$384$		0			0
$385$	5.99388	−	9.27702i	0.305477	−	0.472800i
$386$		0			0
$387$	12.7579	−	7.36578i	0.648520	−	0.374423i
$388$		0			0
$389$	1.68943	−	2.92618i	0.0856574	−	0.148363i	−0.820014	−	0.572344i	$-0.806034\pi$
$389$	1.68943	−	2.92618i	0.0856574	−	0.148363i	0.905671	+	0.423981i	$0.139368\pi$
$390$		0			0
$391$	26.4245			1.33635
$392$		0			0
$393$			7.22649i			0.364528i
$394$		0			0
$395$	9.82586	−	17.0189i	0.494393	−	0.856313i
$396$		0			0
$397$	−9.98525	+	5.76499i	−0.501145	+	0.289336i	−0.729186	−	0.684315i	$-0.760101\pi$
$397$	−9.98525	+	5.76499i	−0.501145	+	0.289336i	0.228041	+	0.973652i	$0.426768\pi$
$398$		0			0
$399$	−12.4612	+	16.5725i	−0.623843	+	0.829664i
$400$		0			0
$401$	−13.0261	−	22.5619i	−0.650494	−	1.12669i	−0.983003	−	0.183588i	$-0.941229\pi$
$401$	−13.0261	−	22.5619i	−0.650494	−	1.12669i	0.332509	−	0.943100i	$-0.392105\pi$
$402$		0			0
$403$	−32.4753	−	18.7496i	−1.61771	−	0.933986i
$404$		0			0
$405$			0.773427i			0.0384319i
$406$		0			0
$407$	−1.01975	+	0.0726278i	−0.0505471	+	0.00360003i
$408$		0			0
$409$	17.5109	−	30.3297i	0.865856	−	1.49971i	−0.000338063	−	1.00000i	$-0.500108\pi$
$409$	17.5109	−	30.3297i	0.865856	−	1.49971i	0.866194	−	0.499707i	$-0.166559\pi$
$410$		0			0
$411$	−8.08750	+	4.66932i	−0.398927	+	0.230321i
$412$		0			0
$413$	2.83254	+	6.65377i	0.139380	+	0.327411i
$414$		0			0
$415$	1.44974	−	0.837011i	0.0711652	−	0.0410872i
$416$		0			0
$417$	−6.99821	−	4.04042i	−0.342704	−	0.197860i
$418$		0			0
$419$			12.1242i			0.592307i	0.955140	+	0.296154i	$0.0957040\pi$
$419$			12.1242i			0.592307i	−0.955140	+	0.296154i	$0.904296\pi$
$420$		0			0
$421$	18.6940			0.911089			0.455545	−	0.890213i	$-0.349445\pi$
$421$	18.6940			0.911089			0.455545	+	0.890213i	$0.349445\pi$
$422$		0			0
$423$	7.91916	+	4.57213i	0.385043	+	0.222305i
$424$		0			0
$425$	−5.46842	−	9.47158i	−0.265257	−	0.459439i
$426$		0			0
$427$	−0.482779	+	3.96607i	−0.0233633	+	0.191932i
$428$		0			0
$429$	11.5251	−	7.79540i	0.556438	−	0.376366i
$430$		0			0
$431$	−29.3945	−	16.9709i	−1.41588	−	0.817461i	−0.419949	−	0.907548i	$-0.637952\pi$
$431$	−29.3945	−	16.9709i	−1.41588	−	0.817461i	−0.995934	+	0.0900869i	$0.971286\pi$
$432$		0			0
$433$		−	27.0949i		−	1.30210i	−0.759037	−	0.651048i	$-0.774330\pi$
$433$		−	27.0949i		−	1.30210i	0.759037	−	0.651048i	$-0.225670\pi$
$434$		0			0
$435$		−	4.58274i		−	0.219726i
$436$		0			0
$437$	−31.4765	+	54.5188i	−1.50572	+	2.60799i
$438$		0			0
$439$	−10.2269	−	17.7135i	−0.488104	−	0.845421i	0.511802	−	0.859103i	$-0.328978\pi$
$439$	−10.2269	−	17.7135i	−0.488104	−	0.845421i	−0.999906	+	0.0136821i	$0.995645\pi$
$440$		0			0
$441$	9.43485	−	9.81089i	0.449278	−	0.467185i
$442$		0			0
$443$	−1.79868	−	3.11541i	−0.0854579	−	0.148017i	0.820128	−	0.572180i	$-0.193902\pi$
$443$	−1.79868	−	3.11541i	−0.0854579	−	0.148017i	−0.905586	+	0.424162i	$0.860569\pi$
$444$		0			0
$445$	6.70233	−	11.6088i	0.317721	−	0.550309i
$446$		0			0
$447$	6.40159			0.302785
$448$		0			0
$449$	37.0664			1.74927			0.874637	−	0.484779i	$-0.161100\pi$
$449$	37.0664			1.74927			0.874637	+	0.484779i	$0.161100\pi$
$450$		0			0
$451$	8.77694	−	18.0544i	0.413290	−	0.850148i
$452$		0			0
$453$	8.99479	+	15.5794i	0.422612	+	0.731986i
$454$		0			0
$455$	13.4987	+	1.64316i	0.632828	+	0.0770324i
$456$		0			0
$457$	15.7194	−	9.07561i	0.735323	−	0.424539i	−0.0850431	−	0.996377i	$-0.527103\pi$
$457$	15.7194	−	9.07561i	0.735323	−	0.424539i	0.820366	+	0.571838i	$0.193769\pi$
$458$		0			0
$459$	14.0862	+	8.13267i	0.657487	+	0.379600i
$460$		0			0
$461$	−22.4278			−1.04457			−0.522284	−	0.852772i	$-0.674920\pi$
$461$	−22.4278			−1.04457			−0.522284	+	0.852772i	$0.674920\pi$
$462$		0			0
$463$	15.6274			0.726267			0.363134	−	0.931737i	$-0.381707\pi$
$463$	15.6274			0.726267			0.363134	+	0.931737i	$0.381707\pi$
$464$		0			0
$465$	10.2845	+	5.93774i	0.476931	+	0.275356i
$466$		0			0
$467$	5.27860	−	3.04760i	0.244264	−	0.141026i	−0.372871	−	0.927883i	$-0.621626\pi$
$467$	5.27860	−	3.04760i	0.244264	−	0.141026i	0.617135	+	0.786857i	$0.288293\pi$
$468$		0			0
$469$	−8.23022	+	3.50365i	−0.380036	+	0.161783i
$470$		0			0
$471$	−3.99346	−	6.91688i	−0.184009	−	0.318713i
$472$		0			0
$473$	−22.5982	−	10.9858i	−1.03906	−	0.505130i
$474$		0			0
$475$	26.0556			1.19551
$476$		0			0
$477$	−9.32690			−0.427049
$478$		0			0
$479$	15.3138	−	26.5242i	0.699704	−	1.21192i	−0.268865	−	0.963178i	$-0.586648\pi$
$479$	15.3138	−	26.5242i	0.699704	−	1.21192i	0.968569	−	0.248745i	$-0.0800182\pi$
$480$		0			0
$481$	−0.629341	−	1.09005i	−0.0286955	−	0.0497020i
$482$		0			0
$483$	−13.4816	+	17.9295i	−0.613433	+	0.815820i
$484$		0			0
$485$	−6.71808	−	11.6361i	−0.305052	−	0.528366i
$486$		0			0
$487$	−1.58726	+	2.74922i	−0.0719258	+	0.124579i	−0.899745	−	0.436415i	$-0.856248\pi$
$487$	−1.58726	+	2.74922i	−0.0719258	+	0.124579i	0.827819	+	0.560995i	$0.189581\pi$
$488$		0			0
$489$		−	18.7110i		−	0.846141i
$490$		0			0
$491$			32.6507i			1.47351i	0.676162	+	0.736753i	$0.263642\pi$
$491$			32.6507i			1.47351i	−0.676162	+	0.736753i	$0.736358\pi$
$492$		0			0
$493$	9.82691	+	5.67357i	0.442582	+	0.255525i
$494$		0			0
$495$	6.72378	−	4.54786i	0.302211	−	0.204411i
$496$		0			0
$497$	7.41839	+	5.57805i	0.332760	+	0.250210i
$498$		0			0
$499$	14.2274	+	24.6426i	0.636906	+	1.10315i	0.986108	+	0.166106i	$0.0531195\pi$
$499$	14.2274	+	24.6426i	0.636906	+	1.10315i	−0.349202	+	0.937048i	$0.613547\pi$
$500$		0			0
$501$	12.7814	+	7.37932i	0.571029	+	0.329684i
$502$		0			0
$503$	−22.5058			−1.00348			−0.501741	−	0.865018i	$-0.667307\pi$
$503$	−22.5058			−1.00348			−0.501741	+	0.865018i	$0.667307\pi$
$504$		0			0
$505$		−	12.6684i		−	0.563739i
$506$		0			0
$507$	3.26892	+	1.88731i	0.145178	+	0.0838185i
$508$		0			0
$509$	−11.6437	+	6.72249i	−0.516098	+	0.297969i	−0.735337	−	0.677702i	$-0.762976\pi$
$509$	−11.6437	+	6.72249i	−0.516098	+	0.297969i	0.219239	+	0.975671i	$0.429643\pi$
$510$		0			0
$511$	−2.35366	+	1.00197i	−0.104120	+	0.0443244i
$512$		0			0
$513$	−33.5585	+	19.3750i	−1.48164	+	0.855427i
$514$		0			0
$515$	−1.81579	+	3.14505i	−0.0800134	+	0.138587i
$516$		0			0
$517$	−1.10803	−	15.5576i	−0.0487310	−	0.684221i
$518$		0			0
$519$		−	4.89362i		−	0.214806i
$520$		0			0
$521$	34.2339	+	19.7649i	1.49981	+	0.865918i	1.00000		0.000215610i	$-6.86308e-5\pi$
$521$	34.2339	+	19.7649i	1.49981	+	0.865918i	0.499813	+	0.866133i	$0.333402\pi$
$522$		0			0
$523$	−14.8061	−	25.6449i	−0.647425	−	1.12137i	−0.983736	−	0.179622i	$-0.942512\pi$
$523$	−14.8061	−	25.6449i	−0.647425	−	1.12137i	0.336310	−	0.941751i	$-0.390821\pi$
$524$		0			0
$525$	9.21657	+	1.12191i	0.402244	+	0.0489641i
$526$		0			0
$527$	−25.4650	+	14.7022i	−1.10927	+	0.640438i
$528$		0			0
$529$	−22.5538	+	39.0643i	−0.980599	+	1.69845i
$530$		0			0
$531$			5.31483i			0.230644i
$532$		0			0
$533$	24.7158			1.07056
$534$		0			0
$535$	−10.2583	+	17.7679i	−0.443504	+	0.768172i
$536$		0			0
$537$	−3.46154	+	1.99852i	−0.149377	+	0.0862426i
$538$		0			0
$539$	−22.8771	−	3.95437i	−0.985388	−	0.170327i
$540$		0			0
$541$	−15.1111	+	8.72442i	−0.649679	+	0.375092i	−0.788333	−	0.615249i	$-0.789056\pi$
$541$	−15.1111	+	8.72442i	−0.649679	+	0.375092i	0.138654	+	0.990341i	$0.455722\pi$
$542$		0			0
$543$	6.71387	−	11.6288i	0.288120	−	0.499038i
$544$		0			0
$545$	−14.4792			−0.620220
$546$		0			0
$547$			1.16878i			0.0499734i	0.999688	+	0.0249867i	$0.00795434\pi$
$547$			1.16878i			0.0499734i	−0.999688	+	0.0249867i	$0.992046\pi$
$548$		0			0
$549$	−1.46818	+	2.54297i	−0.0626605	+	0.108531i
$550$		0			0
$551$	−23.4113	+	13.5165i	−0.997355	+	0.575823i
$552$		0			0
$553$	−41.0053	−	4.99146i	−1.74372	−	0.212258i
$554$		0			0
$555$	0.199303	+	0.345203i	0.00845995	+	0.0146531i
$556$		0			0
$557$	−4.20151	−	2.42574i	−0.178024	−	0.102782i	0.408340	−	0.912830i	$-0.366108\pi$
$557$	−4.20151	−	2.42574i	−0.178024	−	0.102782i	−0.586364	+	0.810048i	$0.699441\pi$
$558$		0			0
$559$		−	30.9360i		−	1.30845i
$560$		0			0
$561$	−0.775084	−	10.8828i	−0.0327241	−	0.459471i
$562$		0			0
$563$	−13.0572	+	22.6158i	−0.550297	+	0.953143i	0.447956	+	0.894056i	$0.352152\pi$
$563$	−13.0572	+	22.6158i	−0.550297	+	0.953143i	−0.998253	+	0.0590869i	$0.981181\pi$
$564$		0			0
$565$	0.609293	−	0.351776i	0.0256332	−	0.0147993i
$566$		0			0
$567$	1.49584	−	0.636788i	0.0628195	−	0.0267426i
$568$		0			0
$569$	6.47913	−	3.74073i	0.271619	−	0.156820i	−0.358004	−	0.933720i	$-0.616543\pi$
$569$	6.47913	−	3.74073i	0.271619	−	0.156820i	0.629623	+	0.776901i	$0.283209\pi$
$570$		0			0
$571$	−28.5249	−	16.4688i	−1.19373	−	0.689199i	−0.234578	−	0.972097i	$-0.575371\pi$
$571$	−28.5249	−	16.4688i	−1.19373	−	0.689199i	−0.959150	+	0.282898i	$0.908704\pi$
$572$		0			0
$573$			6.16430i			0.257517i
$574$		0			0
$575$	28.1890			1.17556
$576$		0			0
$577$	1.34703	+	0.777711i	0.0560778	+	0.0323765i	0.527777	−	0.849383i	$-0.323026\pi$
$577$	1.34703	+	0.777711i	0.0560778	+	0.0323765i	−0.471699	+	0.881760i	$0.656359\pi$
$578$		0			0
$579$	4.81991	+	8.34833i	0.200309	+	0.346945i
$580$		0			0
$581$	−2.81244	−	2.11473i	−0.116680	−	0.0877340i
$582$		0			0
$583$	8.91290	+	13.1773i	0.369134	+	0.545747i
$584$		0			0
$585$	8.65509	+	4.99702i	0.357844	+	0.206601i
$586$		0			0
$587$		−	42.8124i		−	1.76706i	−0.468376	−	0.883529i	$-0.655161\pi$
$587$		−	42.8124i		−	1.76706i	0.468376	−	0.883529i	$-0.344839\pi$
$588$		0			0
$589$		−	70.0520i		−	2.88644i
$590$		0			0
$591$	−8.91107	+	15.4344i	−0.366552	+	0.634887i
$592$		0			0
$593$	16.7711	+	29.0484i	0.688707	+	1.19288i	0.972256	+	0.233918i	$0.0751549\pi$
$593$	16.7711	+	29.0484i	0.688707	+	1.19288i	−0.283549	+	0.958958i	$0.591512\pi$
$594$		0			0
$595$	6.40821	−	8.52244i	0.262711	−	0.349386i
$596$		0			0
$597$	−1.50279	−	2.60290i	−0.0615050	−	0.106530i
$598$		0			0
$599$	7.00856	−	12.1392i	0.286362	−	0.495993i	−0.686577	−	0.727057i	$-0.740887\pi$
$599$	7.00856	−	12.1392i	0.286362	−	0.495993i	0.972939	+	0.231064i	$0.0742207\pi$
$600$		0			0
$601$	−36.1513			−1.47464			−0.737322	−	0.675542i	$-0.763910\pi$
$601$	−36.1513			−1.47464			−0.737322	+	0.675542i	$0.763910\pi$
$602$		0			0
$603$	−6.57405			−0.267716
$604$		0			0
$605$	−12.8506	−	5.15353i	−0.522453	−	0.209521i
$606$		0			0
$607$	−14.8196	−	25.6684i	−0.601511	−	1.04185i	−0.992593	−	0.121491i	$-0.961232\pi$
$607$	−14.8196	−	25.6684i	−0.601511	−	1.04185i	0.391082	−	0.920356i	$-0.372101\pi$
$608$		0			0
$609$	−8.86323	+	3.77312i	−0.359156	+	0.152894i
$610$		0			0
$611$	16.6301	−	9.60139i	0.672782	−	0.388431i
$612$		0			0
$613$	−28.9964	−	16.7411i	−1.17115	−	0.676166i	−0.217202	−	0.976127i	$-0.569693\pi$
$613$	−28.9964	−	16.7411i	−1.17115	−	0.676166i	−0.953951	+	0.299961i	$0.903026\pi$
$614$		0			0
$615$	−7.82712			−0.315620
$616$		0			0
$617$	8.79395			0.354031			0.177016	−	0.984208i	$-0.443356\pi$
$617$	8.79395			0.354031			0.177016	+	0.984208i	$0.443356\pi$
$618$		0			0
$619$	−24.2445	−	13.9976i	−0.974469	−	0.562610i	−0.0738736	−	0.997268i	$-0.523536\pi$
$619$	−24.2445	−	13.9976i	−0.974469	−	0.562610i	−0.900596	+	0.434657i	$0.856869\pi$
$620$		0			0
$621$	−36.3063	+	20.9614i	−1.45692	+	0.841153i
$622$		0			0
$623$	−27.9701	−	3.40473i	−1.12060	−	0.136408i
$624$		0			0
$625$	−1.87286	−	3.24390i	−0.0749146	−	0.129756i
$626$		0			0
$627$	23.3765	+	11.3642i	0.933567	+	0.453844i
$628$		0			0
$629$	−0.986974			−0.0393532
$630$		0			0
$631$	0.154087			0.00613412			0.00306706	−	0.999995i	$-0.499024\pi$
$631$	0.154087			0.00613412			0.00306706	+	0.999995i	$0.499024\pi$
$632$		0			0
$633$	0.129825	−	0.224863i	0.00516008	−	0.00893752i
$634$		0			0
$635$	−7.10081	−	12.2990i	−0.281787	−	0.488069i
$636$		0			0
$637$	−7.93596	−	27.4599i	−0.314434	−	1.08800i
$638$		0			0
$639$	3.41072	+	5.90754i	0.134926	+	0.233699i
$640$		0			0
$641$	9.92017	−	17.1822i	0.391823	−	0.678658i	−0.600867	−	0.799349i	$-0.705178\pi$
$641$	9.92017	−	17.1822i	0.391823	−	0.678658i	0.992690	+	0.120691i	$0.0385112\pi$
$642$		0			0
$643$			25.2948i			0.997529i	0.866737	+	0.498765i	$0.166213\pi$
$643$			25.2948i			0.997529i	−0.866737	+	0.498765i	$0.833787\pi$
$644$		0			0
$645$			9.79699i			0.385756i
$646$		0			0
$647$	−0.813596	−	0.469730i	−0.0319857	−	0.0184670i	0.483922	−	0.875111i	$-0.339212\pi$
$647$	−0.813596	−	0.469730i	−0.0319857	−	0.0184670i	−0.515908	+	0.856644i	$0.672545\pi$
$648$		0			0
$649$	7.50893	−	5.07892i	0.294751	−	0.199365i
$650$		0			0
$651$	3.01632	−	24.7794i	0.118219	−	0.971179i
$652$		0			0
$653$	5.50375	+	9.53278i	0.215379	+	0.373047i	0.953390	−	0.301742i	$-0.0975681\pi$
$653$	5.50375	+	9.53278i	0.215379	+	0.373047i	−0.738011	+	0.674789i	$0.764235\pi$
$654$		0			0
$655$	7.66729	+	4.42671i	0.299586	+	0.172966i
$656$		0			0
$657$	−1.88004			−0.0733472
$658$		0			0
$659$		−	29.9068i		−	1.16500i	−0.812830	−	0.582501i	$-0.802074\pi$
$659$		−	29.9068i		−	1.16500i	0.812830	−	0.582501i	$-0.197926\pi$
$660$		0			0
$661$	2.32896	+	1.34463i	0.0905861	+	0.0522999i	0.544609	−	0.838690i	$-0.316678\pi$
$661$	2.32896	+	1.34463i	0.0905861	+	0.0522999i	−0.454023	+	0.890990i	$0.650011\pi$
$662$		0			0
$663$	11.6330	−	6.71633i	0.451789	−	0.260841i
$664$		0			0
$665$	9.95006	+	23.3731i	0.385847	+	0.906371i
$666$		0			0
$667$	−25.3282	+	14.6233i	−0.980713	+	0.566215i
$668$		0			0
$669$	9.77917	−	16.9380i	0.378084	−	0.654862i
$670$		0			0
$671$	4.99578	−	0.355806i	0.192860	−	0.0137357i
$672$		0			0
$673$		−	3.56361i		−	0.137367i	−0.997638	−	0.0686836i	$-0.978120\pi$
$673$		−	3.56361i		−	0.137367i	0.997638	−	0.0686836i	$-0.0218799\pi$
$674$		0			0
$675$	15.0268	+	8.67572i	0.578381	+	0.333929i
$676$		0			0
$677$	−15.5901	−	27.0029i	−0.599178	−	1.03781i	−0.992943	−	0.118595i	$-0.962161\pi$
$677$	−15.5901	−	27.0029i	−0.599178	−	1.03781i	0.393765	−	0.919211i	$-0.371172\pi$
$678$		0			0
$679$	−16.9734	+	22.5734i	−0.651381	+	0.866288i
$680$		0			0
$681$	−16.3774	+	9.45552i	−0.627585	+	0.362336i
$682$		0			0
$683$	−7.79993	+	13.5099i	−0.298456	+	0.516941i	−0.975783	−	0.218741i	$-0.929805\pi$
$683$	−7.79993	+	13.5099i	−0.298456	+	0.516941i	0.677327	+	0.735682i	$0.263138\pi$
$684$		0			0
$685$			11.4411i			0.437142i
$686$		0			0
$687$	−5.45320			−0.208053
$688$		0			0
$689$	−9.79316	+	16.9623i	−0.373090	+	0.646210i
$690$		0			0
$691$	31.8902	−	18.4118i	1.21316	−	0.700419i	0.249714	−	0.968320i	$-0.419663\pi$
$691$	31.8902	−	18.4118i	1.21316	−	0.700419i	0.963447	+	0.267901i	$0.0863299\pi$
$692$		0			0
$693$	−14.3317	−	9.25969i	−0.544415	−	0.351747i
$694$		0			0
$695$	−8.57375	+	4.95006i	−0.325221	+	0.187766i
$696$		0			0
$697$	9.69021	−	16.7839i	0.367043	−	0.635737i
$698$		0			0
$699$	21.9029			0.828445
$700$		0			0
$701$		−	15.6940i		−	0.592754i	−0.955071	−	0.296377i	$-0.904222\pi$
$701$		−	15.6940i		−	0.592754i	0.955071	−	0.296377i	$-0.0957784\pi$
$702$		0			0
$703$	1.17567	−	2.03631i	0.0443411	−	0.0768010i
$704$		0			0
$705$	−5.26651	+	3.04062i	−0.198348	+	0.114516i
$706$		0			0
$707$	−24.5014	+	10.4303i	−0.921468	+	0.392273i
$708$		0			0
$709$	12.1733	+	21.0847i	0.457176	+	0.791852i	0.998810	−	0.0487621i	$-0.0155276\pi$
$709$	12.1733	+	21.0847i	0.457176	+	0.791852i	−0.541634	+	0.840614i	$0.682194\pi$
$710$		0			0
$711$	−26.2918	−	15.1796i	−0.986018	−	0.569278i
$712$		0			0
$713$		−	75.7880i		−	2.83828i
$714$		0			0
$715$	−1.21100	−	17.0033i	−0.0452887	−	0.635888i
$716$		0			0
$717$	3.72510	−	6.45207i	0.139116	−	0.240957i
$718$		0			0
$719$	−36.9070	+	21.3083i	−1.37640	+	0.794665i	−0.991724	−	0.128386i	$-0.959020\pi$
$719$	−36.9070	+	21.3083i	−1.37640	+	0.794665i	−0.384676	+	0.923051i	$0.625687\pi$
$720$		0			0
$721$	7.57766	+	0.922408i	0.282207	+	0.0343523i
$722$		0			0
$723$	−3.16222	+	1.82571i	−0.117604	+	0.0678988i
$724$		0			0
$725$	10.4831	+	6.05242i	0.389332	+	0.224781i
$726$		0			0
$727$		−	23.2698i		−	0.863031i	−0.902106	−	0.431515i	$-0.857979\pi$
$727$		−	23.2698i		−	0.863031i	0.902106	−	0.431515i	$-0.142021\pi$
$728$		0			0
$729$	−14.4621			−0.535633
$730$		0			0
$731$	−21.0080	−	12.1290i	−0.777008	−	0.448606i
$732$		0			0
$733$	−18.8378	−	32.6281i	−0.695791	−	1.20515i	−0.969913	−	0.243450i	$-0.921721\pi$
$733$	−18.8378	−	32.6281i	−0.695791	−	1.20515i	0.274122	−	0.961695i	$-0.411613\pi$
$734$		0			0
$735$	2.51320	+	8.69616i	0.0927009	+	0.320763i
$736$		0			0
$737$	6.28225	+	9.28799i	0.231410	+	0.342127i
$738$		0			0
$739$	−0.479784	−	0.277003i	−0.0176491	−	0.0101897i	0.491149	−	0.871075i	$-0.336577\pi$
$739$	−0.479784	−	0.277003i	−0.0176491	−	0.0101897i	−0.508799	+	0.860886i	$0.669910\pi$
$740$		0			0
$741$			32.0015i			1.17561i
$742$		0			0
$743$			20.1974i			0.740972i	0.928838	+	0.370486i	$0.120809\pi$
$743$			20.1974i			0.740972i	−0.928838	+	0.370486i	$0.879191\pi$
$744$		0			0
$745$	3.92140	−	6.79207i	0.143669	−	0.248842i
$746$		0			0
$747$	−1.29306	−	2.23965i	−0.0473107	−	0.0819445i
$748$		0			0
$749$	42.8098	+	5.21112i	1.56424	+	0.190410i
$750$		0			0
$751$	3.70031	+	6.40913i	0.135026	+	0.233872i	0.925607	−	0.378485i	$-0.123555\pi$
$751$	3.70031	+	6.40913i	0.135026	+	0.233872i	−0.790581	+	0.612357i	$0.790221\pi$
$752$		0			0
$753$	0.377937	−	0.654606i	0.0137728	−	0.0238552i
$754$		0			0
$755$	22.0397			0.802106
$756$		0			0
$757$	−29.1994			−1.06127			−0.530636	−	0.847600i	$-0.678047\pi$
$757$	−29.1994			−1.06127			−0.530636	+	0.847600i	$0.678047\pi$
$758$		0			0
$759$	25.2906	+	12.2947i	0.917990	+	0.446271i
$760$		0			0
$761$	−25.4831	−	44.1380i	−0.923761	−	1.60000i	−0.793541	−	0.608517i	$-0.791765\pi$
$761$	−25.4831	−	44.1380i	−0.923761	−	1.60000i	−0.130220	−	0.991485i	$-0.541568\pi$
$762$		0			0
$763$	11.9212	+	28.0034i	0.431576	+	1.01379i
$764$		0			0
$765$	6.78674	−	3.91832i	0.245375	−	0.141667i
$766$		0			0
$767$	9.66576	+	5.58053i	0.349010	+	0.201501i
$768$		0			0
$769$	32.9963			1.18988			0.594938	−	0.803771i	$-0.297176\pi$
$769$	32.9963			1.18988			0.594938	+	0.803771i	$0.297176\pi$
$770$		0			0
$771$	−16.6503			−0.599645
$772$		0			0
$773$	−28.1797	−	16.2696i	−1.01355	−	0.585175i	−0.101323	−	0.994854i	$-0.532308\pi$
$773$	−28.1797	−	16.2696i	−1.01355	−	0.585175i	−0.912230	+	0.409678i	$0.865641\pi$
$774$		0			0
$775$	−27.1654	+	15.6839i	−0.975808	+	0.563383i
$776$		0			0
$777$	0.503546	−	0.669679i	0.0180646	−	0.0240246i
$778$		0			0
$779$	23.0856	+	39.9855i	0.827129	+	1.43263i
$780$		0			0
$781$	5.08699	−	10.4641i	0.182027	−	0.374434i
$782$		0			0
$783$	−18.0024			−0.643353
$784$		0			0
$785$	−9.78505			−0.349243
$786$		0			0
$787$	10.0577	−	17.4205i	0.358519	−	0.620973i	−0.629195	−	0.777248i	$-0.716615\pi$
$787$	10.0577	−	17.4205i	0.358519	−	0.620973i	0.987714	+	0.156275i	$0.0499485\pi$
$788$		0			0
$789$	12.4838	+	21.6225i	0.444433	+	0.769781i
$790$		0			0
$791$	−1.18200	−	0.888772i	−0.0420271	−	0.0316011i
$792$		0			0
$793$	3.08316	+	5.34019i	0.109486	+	0.189636i
$794$		0			0
$795$	3.10135	−	5.37170i	0.109994	−	0.190515i
$796$		0			0
$797$			31.1568i			1.10363i	0.833966	+	0.551816i	$0.186065\pi$
$797$			31.1568i			1.10363i	−0.833966	+	0.551816i	$0.813935\pi$
$798$		0			0
$799$		−	15.0575i		−	0.532697i
$800$		0			0
$801$	−17.9339	−	10.3541i	−0.633663	−	0.365846i
$802$		0			0
$803$	1.79658	+	2.65616i	0.0634001	+	0.0937339i
$804$		0			0
$805$	10.7648	+	25.2870i	0.379409	+	0.891248i
$806$		0			0
$807$	−13.8945	−	24.0661i	−0.489111	−	0.847165i
$808$		0			0
$809$	12.6960	+	7.33001i	0.446366	+	0.257709i	0.706294	−	0.707918i	$-0.250366\pi$
$809$	12.6960	+	7.33001i	0.446366	+	0.257709i	−0.259928	+	0.965628i	$0.583699\pi$
$810$		0			0
$811$	−45.7501			−1.60650			−0.803251	−	0.595640i	$-0.796898\pi$
$811$	−45.7501			−1.60650			−0.803251	+	0.595640i	$0.796898\pi$
$812$		0			0
$813$			10.7293i			0.376292i
$814$		0			0
$815$	−19.8523	−	11.4618i	−0.695397	−	0.401488i
$816$		0			0
$817$	50.0487	−	28.8956i	1.75098	−	1.01093i
$818$		0			0
$819$	2.53844	−	20.8535i	0.0887004	−	0.728682i
$820$		0			0
$821$	−6.11121	+	3.52831i	−0.213283	+	0.123139i	−0.602836	−	0.797865i	$-0.705963\pi$
$821$	−6.11121	+	3.52831i	−0.213283	+	0.123139i	0.389553	+	0.921004i	$0.372629\pi$
$822$		0			0
$823$	−14.2038	+	24.6016i	−0.495112	+	0.857559i	−0.999984	−	0.00563530i	$-0.998206\pi$
$823$	−14.2038	+	24.6016i	−0.495112	+	0.857559i	0.504872	+	0.863194i	$0.331540\pi$
$824$		0			0
$825$	−0.826840	−	11.6095i	−0.0287869	−	0.404190i
$826$		0			0
$827$		−	0.161893i		−	0.00562957i	−0.999996	−	0.00281478i	$-0.999104\pi$
$827$		−	0.161893i		−	0.00562957i	0.999996	−	0.00281478i	$-0.000895975\pi$
$828$		0			0
$829$	−21.0966	−	12.1801i	−0.732715	−	0.423033i	0.0866997	−	0.996234i	$-0.472368\pi$
$829$	−21.0966	−	12.1801i	−0.732715	−	0.423033i	−0.819415	+	0.573201i	$0.805701\pi$
$830$		0			0
$831$	10.4796	+	18.1512i	0.363534	+	0.629660i
$832$		0			0
$833$	−21.7589	−	5.37697i	−0.753900	−	0.186301i
$834$		0			0
$835$	15.6589	−	9.04066i	0.541898	−	0.312865i
$836$		0			0
$837$	23.3252	−	40.4005i	0.806238	−	1.39644i
$838$		0			0
$839$		−	3.31341i		−	0.114392i	−0.998363	−	0.0571958i	$-0.981784\pi$
$839$		−	3.31341i		−	0.114392i	0.998363	−	0.0571958i	$-0.0182159\pi$
$840$		0			0
$841$	16.4410			0.566932
$842$		0			0
$843$	−5.13452	+	8.89326i	−0.176842	+	0.306300i
$844$		0			0
$845$	4.00487	−	2.31221i	0.137772	−	0.0795425i
$846$		0			0
$847$	0.613188	+	29.0968i	0.0210694	+	0.999778i
$848$		0			0
$849$	3.10427	−	1.79225i	0.106538	−	0.0615098i
$850$		0			0
$851$	1.27193	−	2.20305i	0.0436012	−	0.0755196i
$852$		0			0
$853$	17.0905			0.585169			0.292584	−	0.956240i	$-0.405485\pi$
$853$	17.0905			0.585169			0.292584	+	0.956240i	$0.405485\pi$
$854$		0			0
$855$			18.6698i			0.638492i
$856$		0			0
$857$	−11.2484	+	19.4827i	−0.384237	+	0.665517i	−0.991663	−	0.128859i	$-0.958869\pi$
$857$	−11.2484	+	19.4827i	−0.384237	+	0.665517i	0.607426	+	0.794376i	$0.292202\pi$
$858$		0			0
$859$	33.3698	−	19.2661i	1.13856	−	0.657350i	0.192489	−	0.981299i	$-0.438344\pi$
$859$	33.3698	−	19.2661i	1.13856	−	0.657350i	0.946074	+	0.323950i	$0.105011\pi$
$860$		0			0
$861$	6.44432	+	15.1380i	0.219622	+	0.515902i
$862$		0			0
$863$	−12.8730	−	22.2967i	−0.438202	−	0.758989i	0.559348	−	0.828933i	$-0.311051\pi$
$863$	−12.8730	−	22.2967i	−0.438202	−	0.758989i	−0.997551	+	0.0699437i	$0.977718\pi$
$864$		0			0
$865$	−5.19212	−	2.99767i	−0.176537	−	0.101924i
$866$		0			0
$867$			6.93252i			0.235441i
$868$		0			0
$869$	3.67867	+	51.6514i	0.124790	+	1.75215i
$870$		0			0
$871$	−6.90270	+	11.9558i	−0.233889	+	0.405108i
$872$		0			0
$873$	−17.9760	+	10.3785i	−0.608397	+	0.351258i
$874$		0			0
$875$	16.8430	−	22.3999i	0.569396	−	0.757254i
$876$		0			0
$877$	−14.7676	+	8.52609i	−0.498667	+	0.287906i	−0.728163	−	0.685404i	$-0.759626\pi$
$877$	−14.7676	+	8.52609i	−0.498667	+	0.287906i	0.229496	+	0.973310i	$0.426292\pi$
$878$		0			0
$879$	−15.4413	−	8.91506i	−0.520823	−	0.300697i
$880$		0			0
$881$			38.3968i			1.29362i	0.762651	+	0.646811i	$0.223898\pi$
$881$			38.3968i			1.29362i	−0.762651	+	0.646811i	$0.776102\pi$
$882$		0			0
$883$	35.3727			1.19038			0.595192	−	0.803583i	$-0.297076\pi$
$883$	35.3727			1.19038			0.595192	+	0.803583i	$0.297076\pi$
$884$		0			0
$885$	−3.06101	−	1.76727i	−0.102895	−	0.0594062i
$886$		0			0
$887$	−1.05289	−	1.82365i	−0.0353525	−	0.0612322i	0.847808	−	0.530304i	$-0.177922\pi$
$887$	−1.05289	−	1.82365i	−0.0353525	−	0.0612322i	−0.883160	+	0.469071i	$0.844589\pi$
$888$		0			0
$889$	−17.9404	+	23.8594i	−0.601702	+	0.800219i
$890$		0			0
$891$	−1.14180	−	1.68809i	−0.0382517	−	0.0565532i
$892$		0			0
$893$	31.0665	+	17.9363i	1.03960	+	0.600215i
$894$		0			0
$895$			4.89692i			0.163686i
$896$		0			0
$897$			34.6218i			1.15599i
$898$		0			0
$899$	16.2723	−	28.1845i	0.542712	−	0.940005i
$900$		0			0
$901$	7.67914	+	13.3007i	0.255829	+	0.443109i
$902$		0			0
$903$	18.9478	−	8.06618i	0.630544	−	0.268425i
$904$		0			0
$905$	−8.22539	−	14.2468i	−0.273421	−	0.473579i
$906$		0			0
$907$	25.2204	−	43.6831i	0.837431	−	1.45047i	−0.0546043	−	0.998508i	$-0.517390\pi$
$907$	25.2204	−	43.6831i	0.837431	−	1.45047i	0.892035	−	0.451965i	$-0.149277\pi$
$908$		0			0
$909$	−19.5709			−0.649127
$910$		0			0
$911$	1.24825			0.0413565			0.0206782	−	0.999786i	$-0.493417\pi$
$911$	1.24825			0.0413565			0.0206782	+	0.999786i	$0.493417\pi$
$912$		0			0
$913$	−1.92857	+	3.96711i	−0.0638262	+	0.131292i
$914$		0			0
$915$	−0.976392	−	1.69116i	−0.0322785	−	0.0559080i
$916$		0			0
$917$	2.24873	−	18.4735i	0.0742597	−	0.610050i
$918$		0			0
$919$	14.0660	−	8.12103i	0.463996	−	0.267888i	−0.249727	−	0.968316i	$-0.580341\pi$
$919$	14.0660	−	8.12103i	0.463996	−	0.267888i	0.713723	+	0.700428i	$0.247008\pi$
$920$		0			0
$921$	−20.1818	−	11.6520i	−0.665014	−	0.383946i
$922$		0			0
$923$	14.3249			0.471510
$924$		0			0
$925$	−1.05288			−0.0346184
$926$		0			0
$927$	4.85865	+	2.80514i	0.159579	+	0.0921329i
$928$		0			0
$929$	−20.7072	+	11.9553i	−0.679382	+	0.392242i	−0.799622	−	0.600503i	$-0.794967\pi$
$929$	−20.7072	+	11.9553i	−0.679382	+	0.392242i	0.120240	+	0.992745i	$0.461634\pi$
$930$		0			0
$931$	37.0125	−	38.4877i	1.21304	−	1.26138i
$932$		0			0
$933$	−3.41151	−	5.90890i	−0.111688	−	0.193449i
$934$		0			0
$935$	−12.0214	−	5.84407i	−0.393142	−	0.191122i
$936$		0			0
$937$	28.2482			0.922827			0.461414	−	0.887185i	$-0.347342\pi$
$937$	28.2482			0.922827			0.461414	+	0.887185i	$0.347342\pi$
$938$		0			0
$939$	−0.516740			−0.0168632
$940$		0			0
$941$	29.3512	−	50.8377i	0.956821	−	1.65726i	0.226677	−	0.973970i	$-0.427214\pi$
$941$	29.3512	−	50.8377i	0.956821	−	1.65726i	0.730144	−	0.683293i	$-0.239453\pi$
$942$		0			0
$943$	24.9759	+	43.2595i	0.813327	+	1.40872i
$944$		0			0
$945$	−2.04415	+	16.7929i	−0.0664961	+	0.546272i
$946$		0			0
$947$	−22.1672	−	38.3948i	−0.720338	−	1.24766i	−0.960864	−	0.277020i	$-0.910653\pi$
$947$	−22.1672	−	38.3948i	−0.720338	−	1.24766i	0.240526	−	0.970643i	$-0.422680\pi$
$948$		0			0
$949$	−1.97402	+	3.41910i	−0.0640794	+	0.110989i
$950$		0			0
$951$			10.8376i			0.351433i
$952$		0			0
$953$		−	13.9238i		−	0.451037i	−0.974239	−	0.225518i	$-0.927592\pi$
$953$		−	13.9238i		−	0.451037i	0.974239	−	0.225518i	$-0.0724075\pi$
$954$		0			0
$955$	6.54031	+	3.77605i	0.211639	+	0.122190i
$956$		0			0
$957$	6.76543	+	10.0023i	0.218695	+	0.323330i
$958$		0			0
$959$	22.1276	−	9.41982i	0.714537	−	0.304182i
$960$		0			0
$961$	26.6672	+	46.1890i	0.860233	+	1.48997i
$962$		0			0
$963$	27.4488	+	15.8476i	0.884526	+	0.510681i
$964$		0			0
$965$	11.8101			0.380180
$966$		0			0
$967$		−	29.3085i		−	0.942499i	−0.882000	−	0.471250i	$-0.843803\pi$
$967$		−	29.3085i		−	0.942499i	0.882000	−	0.471250i	$-0.156197\pi$
$968$		0			0
$969$	21.7316	+	12.5467i	0.698118	+	0.403059i
$970$		0			0
$971$	0.0286574	−	0.0165453i	0.000919659	−	0.000530965i	−0.499540	−	0.866291i	$-0.666498\pi$
$971$	0.0286574	−	0.0165453i	0.000919659	−	0.000530965i	0.500460	+	0.865760i	$0.333164\pi$
$972$		0			0
$973$	16.6327	+	12.5065i	0.533219	+	0.400939i
$974$		0			0
$975$	12.4098	−	7.16481i	0.397432	−	0.229458i
$976$		0			0
$977$	−21.0948	+	36.5373i	−0.674883	+	1.16893i	0.301620	+	0.953428i	$0.402473\pi$
$977$	−21.0948	+	36.5373i	−0.674883	+	1.16893i	−0.976503	+	0.215503i	$0.930861\pi$
$978$		0			0
$979$	2.50926	+	35.2320i	0.0801964	+	1.12602i
$980$		0			0
$981$			22.3683i			0.714164i
$982$		0			0
$983$	44.0056	+	25.4067i	1.40356	+	0.810347i	0.994756	−	0.102274i	$-0.0326120\pi$
$983$	44.0056	+	25.4067i	1.40356	+	0.810347i	0.408806	+	0.912621i	$0.365945\pi$
$984$		0			0
$985$	10.9173	+	18.9092i	0.347853	+	0.602499i
$986$		0			0
$987$	10.2168	+	7.68223i	0.325204	+	0.244528i
$988$		0			0
$989$	54.1467	−	31.2616i	1.72177	−	0.994062i
$990$		0			0
$991$	23.2614	−	40.2899i	0.738923	−	1.27985i	−0.214058	−	0.976821i	$-0.568668\pi$
$991$	23.2614	−	40.2899i	0.738923	−	1.27985i	0.952981	−	0.303030i	$-0.0979984\pi$
$992$		0			0
$993$		−	5.93886i		−	0.188464i
$994$		0			0
$995$	−3.68223			−0.116735
$996$		0			0
$997$	2.26888	−	3.92981i	0.0718560	−	0.124458i	−0.827859	−	0.560937i	$-0.810441\pi$
$997$	2.26888	−	3.92981i	0.0718560	−	0.124458i	0.899715	+	0.436478i	$0.143774\pi$
$998$		0			0
$999$	1.35606	−	0.782923i	0.0429039	−	0.0247706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.bn.b.241.5		16
4.3	odd	2		154.2.i.a.87.6	yes	16
7.5	odd	6	inner	1232.2.bn.b.593.6		16
11.10	odd	2	inner	1232.2.bn.b.241.6		16
12.11	even	2		1386.2.bk.c.703.1		16
28.3	even	6		1078.2.c.b.1077.12		16
28.11	odd	6		1078.2.c.b.1077.13		16
28.19	even	6		154.2.i.a.131.2	yes	16
28.23	odd	6		1078.2.i.c.901.3		16
28.27	even	2		1078.2.i.c.1011.7		16
44.43	even	2		154.2.i.a.87.2	✓	16
77.54	even	6	inner	1232.2.bn.b.593.5		16
84.47	odd	6		1386.2.bk.c.901.5		16
132.131	odd	2		1386.2.bk.c.703.5		16
308.87	odd	6		1078.2.c.b.1077.4		16
308.131	odd	6		154.2.i.a.131.6	yes	16
308.219	even	6		1078.2.i.c.901.7		16
308.263	even	6		1078.2.c.b.1077.5		16
308.307	odd	2		1078.2.i.c.1011.3		16
924.131	even	6		1386.2.bk.c.901.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.i.a.87.2	✓	16	44.43	even	2
154.2.i.a.87.6	yes	16	4.3	odd	2
154.2.i.a.131.2	yes	16	28.19	even	6
154.2.i.a.131.6	yes	16	308.131	odd	6
1078.2.c.b.1077.4		16	308.87	odd	6
1078.2.c.b.1077.5		16	308.263	even	6
1078.2.c.b.1077.12		16	28.3	even	6
1078.2.c.b.1077.13		16	28.11	odd	6
1078.2.i.c.901.3		16	28.23	odd	6
1078.2.i.c.901.7		16	308.219	even	6
1078.2.i.c.1011.3		16	308.307	odd	2
1078.2.i.c.1011.7		16	28.27	even	2
1232.2.bn.b.241.5		16	1.1	even	1	trivial
1232.2.bn.b.241.6		16	11.10	odd	2	inner
1232.2.bn.b.593.5		16	77.54	even	6	inner
1232.2.bn.b.593.6		16	7.5	odd	6	inner
1386.2.bk.c.703.1		16	12.11	even	2
1386.2.bk.c.703.5		16	132.131	odd	2
1386.2.bk.c.901.1		16	924.131	even	6
1386.2.bk.c.901.5		16	84.47	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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.bn (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.889740 + 0.513691i) q^{3} +(1.09005 - 0.629341i) q^{5} +(-2.11465 - 1.59005i) q^{7} +(-0.972242 - 1.68397i) q^{9} +O(q^{10})\)	\(q+(0.889740 + 0.513691i) q^{3} +(1.09005 - 0.629341i) q^{5} +(-2.11465 - 1.59005i) q^{7} +(-0.972242 - 1.68397i) q^{9} +(-1.45007 + 2.98283i) q^{11} -4.08338 q^{13} +1.29315 q^{15} +(-1.60096 + 2.77294i) q^{17} +(-3.81407 - 6.60616i) q^{19} +(-1.06469 - 2.50101i) q^{21} +(-4.12636 - 7.14707i) q^{23} +(-1.70786 + 2.95810i) q^{25} -5.07988i q^{27} -3.54386i q^{29} +(7.95304 + 4.59169i) q^{31} +(-2.82244 + 1.90905i) q^{33} +(-3.30576 - 0.402401i) q^{35} +(0.154122 + 0.266948i) q^{37} +(-3.63315 - 2.09760i) q^{39} -6.05276 q^{41} +7.57607i q^{43} +(-2.11959 - 1.22374i) q^{45} +(-4.07263 + 2.35133i) q^{47} +(1.94348 + 6.72480i) q^{49} +(-2.84887 + 1.64480i) q^{51} +(2.39830 - 4.15397i) q^{53} +(0.296567 + 4.16403i) q^{55} -7.83701i q^{57} +(-2.36710 - 1.36664i) q^{59} +(-0.755050 - 1.30779i) q^{61} +(-0.621652 + 5.10693i) q^{63} +(-4.45110 + 2.56984i) q^{65} +(1.69044 - 2.92792i) q^{67} -8.47871i q^{69} -3.50810 q^{71} +(0.483428 - 0.837321i) q^{73} +(-3.03910 + 1.75463i) q^{75} +(7.80925 - 4.00195i) q^{77} +(13.5212 - 7.80647i) q^{79} +(-0.307237 + 0.532150i) q^{81} +1.32998 q^{83} +4.03019i q^{85} +(1.82045 - 3.15311i) q^{87} +(9.22296 - 5.32488i) q^{89} +(8.63492 + 6.49279i) q^{91} +(4.71742 + 8.17082i) q^{93} +(-8.31505 - 4.80070i) q^{95} -10.6748i q^{97} +(6.43283 - 0.458154i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} + 16 q^{9}+O(q^{10}) \) 16 * q - 12 * q^5 + 16 * q^9	\( 16 q - 12 q^{5} + 16 q^{9} - 8 q^{11} + 8 q^{15} - 16 q^{23} + 12 q^{31} - 24 q^{33} - 16 q^{37} - 108 q^{45} - 24 q^{47} + 8 q^{49} - 28 q^{53} - 60 q^{59} - 12 q^{67} - 8 q^{71} - 60 q^{75} + 44 q^{77} - 8 q^{81} + 96 q^{89} + 36 q^{91} - 44 q^{93} - 56 q^{99}+O(q^{100}) \) 16 * q - 12 * q^5 + 16 * q^9 - 8 * q^11 + 8 * q^15 - 16 * q^23 + 12 * q^31 - 24 * q^33 - 16 * q^37 - 108 * q^45 - 24 * q^47 + 8 * q^49 - 28 * q^53 - 60 * q^59 - 12 * q^67 - 8 * q^71 - 60 * q^75 + 44 * q^77 - 8 * q^81 + 96 * q^89 + 36 * q^91 - 44 * q^93 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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