LMFDB - Embedded newform 960.3.i.b.929.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,3,Mod(929,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("960.929");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	960.i (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$26.1581053786$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			929.24
Character	$\chi$	$=$	960.929
Dual form			960.3.i.b.929.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31140 + 2.69819i) q^{3} +(1.53895 + 4.75727i) q^{5} +12.2496i q^{7} +(-5.56048 - 7.07680i) q^{9} +O(q^{10})$	\(q+(-1.31140 + 2.69819i) q^{3} +(1.53895 + 4.75727i) q^{5} +12.2496i q^{7} +(-5.56048 - 7.07680i) q^{9} +3.02475 q^{11} -13.7100 q^{13} +(-14.8542 - 2.08627i) q^{15} -25.8427 q^{17} -14.0811i q^{19} +(-33.0516 - 16.0640i) q^{21} -17.8268 q^{23} +(-20.2632 + 14.6424i) q^{25} +(26.3866 - 5.72273i) q^{27} +27.5927 q^{29} +33.8371 q^{31} +(-3.96664 + 8.16134i) q^{33} +(-58.2744 + 18.8515i) q^{35} +14.9061 q^{37} +(17.9792 - 36.9921i) q^{39} +69.4754i q^{41} +65.9219 q^{43} +(25.1089 - 37.3436i) q^{45} -11.8232 q^{47} -101.052 q^{49} +(33.8900 - 69.7285i) q^{51} -63.3827i q^{53} +(4.65495 + 14.3895i) q^{55} +(37.9935 + 18.4659i) q^{57} -28.6025 q^{59} -2.88594i q^{61} +(86.6876 - 68.1133i) q^{63} +(-21.0990 - 65.2220i) q^{65} -69.0261 q^{67} +(23.3780 - 48.1001i) q^{69} +69.9856i q^{71} -113.636i q^{73} +(-12.9350 - 73.8762i) q^{75} +37.0518i q^{77} +109.941 q^{79} +(-19.1622 + 78.7008i) q^{81} +16.4401i q^{83} +(-39.7707 - 122.941i) q^{85} +(-36.1849 + 74.4503i) q^{87} +66.4138i q^{89} -167.941i q^{91} +(-44.3739 + 91.2990i) q^{93} +(66.9876 - 21.6702i) q^{95} -62.9956i q^{97} +(-16.8190 - 21.4055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 32 q^{9}+O(q^{10}) $ 64 * q - 32 * q^9	$ 64 q - 32 q^{9} - 32 q^{25} - 320 q^{49} + 448 q^{81}+O(q^{100}) $ 64 * q - 32 * q^9 - 32 * q^25 - 320 * q^49 + 448 * q^81

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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
$3$	−1.31140	+	2.69819i	−0.437132	+	0.899397i
$3$	−1.31140	+	2.69819i	−0.437132	+	0.899397i
$4$		0			0
$5$	1.53895	+	4.75727i	0.307791	+	0.951454i
$5$	1.53895	+	4.75727i	0.307791	+	0.951454i
$6$		0			0
$7$			12.2496i			1.74994i	0.484181	+	0.874968i	$0.339118\pi$
$7$			12.2496i			1.74994i	−0.484181	+	0.874968i	$0.660882\pi$
$8$		0			0
$9$	−5.56048	−	7.07680i	−0.617831	−	0.786311i
$10$		0			0
$11$	3.02475			0.274977			0.137488	−	0.990503i	$-0.456097\pi$
$11$	3.02475			0.274977			0.137488	+	0.990503i	$0.456097\pi$
$12$		0			0
$13$	−13.7100			−1.05461			−0.527306	−	0.849675i	$-0.676798\pi$
$13$	−13.7100			−1.05461			−0.527306	+	0.849675i	$0.676798\pi$
$14$		0			0
$15$	−14.8542	−	2.08627i	−0.990280	−	0.139085i
$16$		0			0
$17$	−25.8427			−1.52016			−0.760079	−	0.649830i	$-0.774840\pi$
$17$	−25.8427			−1.52016			−0.760079	+	0.649830i	$0.774840\pi$
$18$		0			0
$19$		−	14.0811i		−	0.741111i	−0.928810	−	0.370556i	$-0.879167\pi$
$19$		−	14.0811i		−	0.741111i	0.928810	−	0.370556i	$-0.120833\pi$
$20$		0			0
$21$	−33.0516	−	16.0640i	−1.57389	−	0.764954i
$22$		0			0
$23$	−17.8268			−0.775078			−0.387539	−	0.921853i	$-0.626675\pi$
$23$	−17.8268			−0.775078			−0.387539	+	0.921853i	$0.626675\pi$
$24$		0			0
$25$	−20.2632	+	14.6424i	−0.810529	+	0.585698i
$26$		0			0
$27$	26.3866	−	5.72273i	0.977280	−	0.211953i
$28$		0			0
$29$	27.5927			0.951471			0.475736	−	0.879588i	$-0.342182\pi$
$29$	27.5927			0.951471			0.475736	+	0.879588i	$0.342182\pi$
$30$		0			0
$31$	33.8371			1.09152			0.545760	−	0.837942i	$-0.316241\pi$
$31$	33.8371			1.09152			0.545760	+	0.837942i	$0.316241\pi$
$32$		0			0
$33$	−3.96664	+	8.16134i	−0.120201	+	0.247313i
$34$		0			0
$35$	−58.2744	+	18.8515i	−1.66498	+	0.538615i
$36$		0			0
$37$	14.9061			0.402866			0.201433	−	0.979502i	$-0.435440\pi$
$37$	14.9061			0.402866			0.201433	+	0.979502i	$0.435440\pi$
$38$		0			0
$39$	17.9792	−	36.9921i	0.461005	−	0.948515i
$40$		0			0
$41$			69.4754i			1.69452i	0.531178	+	0.847260i	$0.321750\pi$
$41$			69.4754i			1.69452i	−0.531178	+	0.847260i	$0.678250\pi$
$42$		0			0
$43$	65.9219			1.53307			0.766534	−	0.642204i	$-0.221980\pi$
$43$	65.9219			1.53307			0.766534	+	0.642204i	$0.221980\pi$
$44$		0			0
$45$	25.1089	−	37.3436i	0.557976	−	0.829857i
$46$		0			0
$47$	−11.8232			−0.251557			−0.125779	−	0.992058i	$-0.540143\pi$
$47$	−11.8232			−0.251557			−0.125779	+	0.992058i	$0.540143\pi$
$48$		0			0
$49$	−101.052			−2.06228
$50$		0			0
$51$	33.8900	−	69.7285i	0.664510	−	1.36723i
$52$		0			0
$53$		−	63.3827i		−	1.19590i	−0.801534	−	0.597950i	$-0.795982\pi$
$53$		−	63.3827i		−	1.19590i	0.801534	−	0.597950i	$-0.204018\pi$
$54$		0			0
$55$	4.65495	+	14.3895i	0.0846354	+	0.261628i
$56$		0			0
$57$	37.9935	+	18.4659i	0.666553	+	0.323964i
$58$		0			0
$59$	−28.6025			−0.484788			−0.242394	−	0.970178i	$-0.577933\pi$
$59$	−28.6025			−0.484788			−0.242394	+	0.970178i	$0.577933\pi$
$60$		0			0
$61$		−	2.88594i		−	0.0473106i	−0.999720	−	0.0236553i	$-0.992470\pi$
$61$		−	2.88594i		−	0.0473106i	0.999720	−	0.0236553i	$-0.00753041\pi$
$62$		0			0
$63$	86.6876	−	68.1133i	1.37599	−	1.08116i
$64$		0			0
$65$	−21.0990	−	65.2220i	−0.324600	−	1.00342i
$66$		0			0
$67$	−69.0261			−1.03024			−0.515120	−	0.857118i	$-0.672253\pi$
$67$	−69.0261			−1.03024			−0.515120	+	0.857118i	$0.672253\pi$
$68$		0			0
$69$	23.3780	−	48.1001i	0.338811	−	0.697103i
$70$		0			0
$71$			69.9856i			0.985712i	0.870111	+	0.492856i	$0.164047\pi$
$71$			69.9856i			0.985712i	−0.870111	+	0.492856i	$0.835953\pi$
$72$		0			0
$73$		−	113.636i		−	1.55666i	−0.627857	−	0.778329i	$-0.716068\pi$
$73$		−	113.636i		−	1.55666i	0.627857	−	0.778329i	$-0.283932\pi$
$74$		0			0
$75$	−12.9350	−	73.8762i	−0.172466	−	0.985015i
$76$		0			0
$77$			37.0518i			0.481192i
$78$		0			0
$79$	109.941			1.39166			0.695829	−	0.718208i	$-0.255037\pi$
$79$	109.941			1.39166			0.695829	+	0.718208i	$0.255037\pi$
$80$		0			0
$81$	−19.1622	+	78.7008i	−0.236571	+	0.971614i
$82$		0			0
$83$			16.4401i			0.198073i	0.995084	+	0.0990365i	$0.0315761\pi$
$83$			16.4401i			0.198073i	−0.995084	+	0.0990365i	$0.968424\pi$
$84$		0			0
$85$	−39.7707	−	122.941i	−0.467891	−	1.44636i
$86$		0			0
$87$	−36.1849	+	74.4503i	−0.415919	+	0.855751i
$88$		0			0
$89$			66.4138i			0.746223i	0.927787	+	0.373111i	$0.121709\pi$
$89$			66.4138i			0.746223i	−0.927787	+	0.373111i	$0.878291\pi$
$90$		0			0
$91$		−	167.941i		−	1.84550i
$92$		0			0
$93$	−44.3739	+	91.2990i	−0.477138	+	0.981710i
$94$		0			0
$95$	66.9876	−	21.6702i	0.705133	−	0.228107i
$96$		0			0
$97$		−	62.9956i		−	0.649439i	−0.945810	−	0.324720i	$-0.894730\pi$
$97$		−	62.9956i		−	0.649439i	0.945810	−	0.324720i	$-0.105270\pi$
$98$		0			0
$99$	−16.8190	−	21.4055i	−0.169889	−	0.216217i
$100$		0			0
$101$	−128.697			−1.27422			−0.637112	−	0.770772i	$-0.719871\pi$
$101$	−128.697			−1.27422			−0.637112	+	0.770772i	$0.719871\pi$
$102$		0			0
$103$			84.1852i			0.817332i	0.912684	+	0.408666i	$0.134006\pi$
$103$			84.1852i			0.817332i	−0.912684	+	0.408666i	$0.865994\pi$
$104$		0			0
$105$	25.5559	−	181.957i	0.243390	−	1.73293i
$106$		0			0
$107$		−	15.3572i		−	0.143525i	−0.997422	−	0.0717626i	$-0.977138\pi$
$107$		−	15.3572i		−	0.143525i	0.997422	−	0.0717626i	$-0.0228624\pi$
$108$		0			0
$109$			79.9342i			0.733341i	0.930351	+	0.366670i	$0.119502\pi$
$109$			79.9342i			0.733341i	−0.930351	+	0.366670i	$0.880498\pi$
$110$		0			0
$111$	−19.5478	+	40.2194i	−0.176106	+	0.362337i
$112$		0			0
$113$	−16.9364			−0.149879			−0.0749396	−	0.997188i	$-0.523876\pi$
$113$	−16.9364			−0.149879			−0.0749396	+	0.997188i	$0.523876\pi$
$114$		0			0
$115$	−27.4346	−	84.8068i	−0.238562	−	0.737451i
$116$		0			0
$117$	76.2339	+	97.0227i	0.651572	+	0.829253i
$118$		0			0
$119$		−	316.561i		−	2.66018i
$120$		0			0
$121$	−111.851			−0.924388
$122$		0			0
$123$	−187.458	−	91.1098i	−1.52405	−	0.740730i
$124$		0			0
$125$	−100.842	−	73.8636i	−0.806738	−	0.590909i
$126$		0			0
$127$		−	59.1817i		−	0.465997i	−0.972477	−	0.232999i	$-0.925146\pi$
$127$		−	59.1817i		−	0.465997i	0.972477	−	0.232999i	$-0.0748538\pi$
$128$		0			0
$129$	−86.4498	+	177.870i	−0.670154	+	1.37884i
$130$		0			0
$131$	−62.0259			−0.473480			−0.236740	−	0.971573i	$-0.576079\pi$
$131$	−62.0259			−0.473480			−0.236740	+	0.971573i	$0.576079\pi$
$132$		0			0
$133$	172.487			1.29690
$134$		0			0
$135$	67.8323	+	116.721i	0.502462	+	0.864600i
$136$		0			0
$137$	−212.368			−1.55013			−0.775067	−	0.631880i	$-0.782284\pi$
$137$	−212.368			−1.55013			−0.775067	+	0.631880i	$0.782284\pi$
$138$		0			0
$139$		−	28.4083i		−	0.204377i	−0.994765	−	0.102188i	$-0.967416\pi$
$139$		−	28.4083i		−	0.204377i	0.994765	−	0.102188i	$-0.0325844\pi$
$140$		0			0
$141$	15.5049	−	31.9012i	0.109964	−	0.226250i
$142$		0			0
$143$	−41.4691			−0.289994
$144$		0			0
$145$	42.4639	+	131.266i	0.292854	+	0.905281i
$146$		0			0
$147$	132.519	−	272.656i	0.901488	−	1.85481i
$148$		0			0
$149$	83.2918			0.559006			0.279503	−	0.960145i	$-0.409830\pi$
$149$	83.2918			0.559006			0.279503	+	0.960145i	$0.409830\pi$
$150$		0			0
$151$	30.8984			0.204625			0.102313	−	0.994752i	$-0.467376\pi$
$151$	30.8984			0.204625			0.102313	+	0.994752i	$0.467376\pi$
$152$		0			0
$153$	143.698	+	182.884i	0.939200	+	1.19532i
$154$		0			0
$155$	52.0738	+	160.972i	0.335960	+	1.03853i
$156$		0			0
$157$	119.149			0.758912			0.379456	−	0.925210i	$-0.376111\pi$
$157$	119.149			0.758912			0.379456	+	0.925210i	$0.376111\pi$
$158$		0			0
$159$	171.019	+	83.1199i	1.07559	+	0.522766i
$160$		0			0
$161$		−	218.370i		−	1.35634i
$162$		0			0
$163$	217.566			1.33476			0.667380	−	0.744717i	$-0.267416\pi$
$163$	217.566			1.33476			0.667380	+	0.744717i	$0.267416\pi$
$164$		0			0
$165$	−44.9302	−	6.31045i	−0.272304	−	0.0382452i
$166$		0			0
$167$	−286.212			−1.71384			−0.856922	−	0.515446i	$-0.827626\pi$
$167$	−286.212			−1.71384			−0.856922	+	0.515446i	$0.827626\pi$
$168$		0			0
$169$	18.9630			0.112207
$170$		0			0
$171$	−99.6492	+	78.2977i	−0.582744	+	0.457881i
$172$		0			0
$173$		−	180.392i		−	1.04273i	−0.853333	−	0.521366i	$-0.825423\pi$
$173$		−	180.392i		−	1.04273i	0.853333	−	0.521366i	$-0.174577\pi$
$174$		0			0
$175$	−179.363	−	248.216i	−1.02493	−	1.41837i
$176$		0			0
$177$	37.5092	−	77.1750i	0.211917	−	0.436017i
$178$		0			0
$179$	67.6994			0.378209			0.189105	−	0.981957i	$-0.439441\pi$
$179$	67.6994			0.378209			0.189105	+	0.981957i	$0.439441\pi$
$180$		0			0
$181$		−	222.756i		−	1.23070i	−0.788255	−	0.615349i	$-0.789015\pi$
$181$		−	222.756i		−	1.23070i	0.788255	−	0.615349i	$-0.210985\pi$
$182$		0			0
$183$	7.78683	+	3.78462i	0.0425510	+	0.0206810i
$184$		0			0
$185$	22.9398	+	70.9121i	0.123999	+	0.383309i
$186$		0			0
$187$	−78.1676			−0.418008
$188$		0			0
$189$	70.1009	+	323.224i	0.370904	+	1.71018i
$190$		0			0
$191$		−	218.719i		−	1.14513i	−0.819860	−	0.572564i	$-0.805949\pi$
$191$		−	218.719i		−	1.14513i	0.819860	−	0.572564i	$-0.194051\pi$
$192$		0			0
$193$		−	108.928i		−	0.564393i	−0.959357	−	0.282196i	$-0.908937\pi$
$193$		−	108.928i		−	0.564393i	0.959357	−	0.282196i	$-0.0910630\pi$
$194$		0			0
$195$	203.651	+	28.6027i	1.04436	+	0.146681i
$196$		0			0
$197$			87.0371i			0.441813i	0.975295	+	0.220906i	$0.0709015\pi$
$197$			87.0371i			0.441813i	−0.975295	+	0.220906i	$0.929098\pi$
$198$		0			0
$199$	−76.1111			−0.382468			−0.191234	−	0.981544i	$-0.561249\pi$
$199$	−76.1111			−0.382468			−0.191234	+	0.981544i	$0.561249\pi$
$200$		0			0
$201$	90.5207	−	186.246i	0.450352	−	0.926596i
$202$		0			0
$203$			337.998i			1.66501i
$204$		0			0
$205$	−330.513	+	106.919i	−1.61226	+	0.521558i
$206$		0			0
$207$	99.1254	+	126.157i	0.478867	+	0.609452i
$208$		0			0
$209$		−	42.5918i		−	0.203788i
$210$		0			0
$211$			365.638i			1.73288i	0.499278	+	0.866442i	$0.333599\pi$
$211$			365.638i			1.73288i	−0.499278	+	0.866442i	$0.666401\pi$
$212$		0			0
$213$	−188.834	−	91.7789i	−0.886547	−	0.430887i
$214$		0			0
$215$	101.451	+	313.608i	0.471864	+	1.45864i
$216$		0			0
$217$			414.489i			1.91009i
$218$		0			0
$219$	306.612	+	149.022i	1.40005	+	0.680466i
$220$		0			0
$221$	354.302			1.60318
$222$		0			0
$223$			165.412i			0.741757i	0.928681	+	0.370879i	$0.120943\pi$
$223$			165.412i			0.741757i	−0.928681	+	0.370879i	$0.879057\pi$
$224$		0			0
$225$	216.295	+	61.9799i	0.961311	+	0.275466i
$226$		0			0
$227$			264.450i			1.16498i	0.812839	+	0.582489i	$0.197921\pi$
$227$			264.450i			1.16498i	−0.812839	+	0.582489i	$0.802079\pi$
$228$		0			0
$229$		−	147.492i		−	0.644068i	−0.946728	−	0.322034i	$-0.895634\pi$
$229$		−	147.492i		−	0.644068i	0.946728	−	0.322034i	$-0.104366\pi$
$230$		0			0
$231$	−99.9728	−	48.5896i	−0.432783	−	0.210345i
$232$		0			0
$233$	−374.411			−1.60691			−0.803457	−	0.595363i	$-0.797008\pi$
$233$	−374.411			−1.60691			−0.803457	+	0.595363i	$0.797008\pi$
$234$		0			0
$235$	−18.1954	−	56.2461i	−0.0774271	−	0.239345i
$236$		0			0
$237$	−144.176	+	296.642i	−0.608338	+	1.25165i
$238$		0			0
$239$			360.896i			1.51003i	0.655710	+	0.755013i	$0.272369\pi$
$239$			360.896i			1.51003i	−0.655710	+	0.755013i	$0.727631\pi$
$240$		0			0
$241$	102.174			0.423958			0.211979	−	0.977274i	$-0.432009\pi$
$241$	102.174			0.423958			0.211979	+	0.977274i	$0.432009\pi$
$242$		0			0
$243$	−187.220	−	154.911i	−0.770454	−	0.637495i
$244$		0			0
$245$	−155.514	−	480.729i	−0.634750	−	1.96216i
$246$		0			0
$247$			193.051i			0.781585i
$248$		0			0
$249$	−44.3584	−	21.5595i	−0.178146	−	0.0865841i
$250$		0			0
$251$	−479.581			−1.91068			−0.955340	−	0.295510i	$-0.904511\pi$
$251$	−479.581			−1.91068			−0.955340	+	0.295510i	$0.904511\pi$
$252$		0			0
$253$	−53.9215			−0.213128
$254$		0			0
$255$	383.873	+	53.9150i	1.50538	+	0.211431i
$256$		0			0
$257$	−295.439			−1.14957			−0.574785	−	0.818305i	$-0.694914\pi$
$257$	−295.439			−1.14957			−0.574785	+	0.818305i	$0.694914\pi$
$258$		0			0
$259$			182.593i			0.704991i
$260$		0			0
$261$	−153.428	−	195.268i	−0.587848	−	0.748153i
$262$		0			0
$263$	240.752			0.915407			0.457703	−	0.889105i	$-0.348672\pi$
$263$	240.752			0.915407			0.457703	+	0.889105i	$0.348672\pi$
$264$		0			0
$265$	301.529	−	97.5431i	1.13784	−	0.368087i
$266$		0			0
$267$	−179.197	−	87.0949i	−0.671151	−	0.326198i
$268$		0			0
$269$	309.312			1.14986			0.574930	−	0.818203i	$-0.305029\pi$
$269$	309.312			1.14986			0.574930	+	0.818203i	$0.305029\pi$
$270$		0			0
$271$	−297.780			−1.09882			−0.549410	−	0.835553i	$-0.685148\pi$
$271$	−297.780			−1.09882			−0.549410	+	0.835553i	$0.685148\pi$
$272$		0			0
$273$	453.137	+	220.237i	1.65984	+	0.806730i
$274$		0			0
$275$	−61.2911	+	44.2897i	−0.222877	+	0.161053i
$276$		0			0
$277$	−67.6010			−0.244047			−0.122023	−	0.992527i	$-0.538938\pi$
$277$	−67.6010			−0.244047			−0.122023	+	0.992527i	$0.538938\pi$
$278$		0			0
$279$	−188.150	−	239.458i	−0.674374	−	0.858274i
$280$		0			0
$281$		−	296.540i		−	1.05530i	−0.849461	−	0.527652i	$-0.823073\pi$
$281$		−	296.540i		−	1.05530i	0.849461	−	0.527652i	$-0.176927\pi$
$282$		0			0
$283$	188.471			0.665976			0.332988	−	0.942931i	$-0.391943\pi$
$283$	188.471			0.665976			0.332988	+	0.942931i	$0.391943\pi$
$284$		0			0
$285$	−29.3771	+	209.164i	−0.103077	+	0.733908i
$286$		0			0
$287$	−851.042			−2.96530
$288$		0			0
$289$	378.845			1.31088
$290$		0			0
$291$	169.974	+	82.6122i	0.584104	+	0.283891i
$292$		0			0
$293$			54.1870i			0.184938i	0.995716	+	0.0924692i	$0.0294760\pi$
$293$			54.1870i			0.184938i	−0.995716	+	0.0924692i	$0.970524\pi$
$294$		0			0
$295$	−44.0180	−	136.070i	−0.149213	−	0.461254i
$296$		0			0
$297$	79.8126	−	17.3098i	0.268729	−	0.0582822i
$298$		0			0
$299$	244.404			0.817406
$300$		0			0
$301$			807.514i			2.68277i
$302$		0			0
$303$	168.772	−	347.248i	0.557004	−	1.14603i
$304$		0			0
$305$	13.7292	−	4.44134i	0.0450138	−	0.0145618i
$306$		0			0
$307$	−285.099			−0.928662			−0.464331	−	0.885662i	$-0.653705\pi$
$307$	−285.099			−0.928662			−0.464331	+	0.885662i	$0.653705\pi$
$308$		0			0
$309$	−227.148	−	110.400i	−0.735106	−	0.357282i
$310$		0			0
$311$			276.078i			0.887709i	0.896099	+	0.443855i	$0.146389\pi$
$311$			276.078i			0.887709i	−0.896099	+	0.443855i	$0.853611\pi$
$312$		0			0
$313$		−	152.399i		−	0.486898i	−0.969914	−	0.243449i	$-0.921721\pi$
$313$		−	152.399i		−	0.486898i	0.969914	−	0.243449i	$-0.0782788\pi$
$314$		0			0
$315$	457.442	+	307.573i	1.45220	+	0.976423i
$316$		0			0
$317$			508.948i			1.60551i	0.596307	+	0.802757i	$0.296634\pi$
$317$			508.948i			1.60551i	−0.596307	+	0.802757i	$0.703366\pi$
$318$		0			0
$319$	83.4608			0.261633
$320$		0			0
$321$	41.4367	+	20.1394i	0.129086	+	0.0627395i
$322$		0			0
$323$			363.894i			1.12661i
$324$		0			0
$325$	277.808	−	200.747i	0.854794	−	0.617684i
$326$		0			0
$327$	−215.678	−	104.825i	−0.659565	−	0.320567i
$328$		0			0
$329$		−	144.829i		−	0.440209i
$330$		0			0
$331$			271.547i			0.820383i	0.911999	+	0.410191i	$0.134538\pi$
$331$			271.547i			0.820383i	−0.911999	+	0.410191i	$0.865462\pi$
$332$		0			0
$333$	−82.8848	−	105.487i	−0.248903	−	0.316778i
$334$		0			0
$335$	−106.228	−	328.376i	−0.317099	−	0.980227i
$336$		0			0
$337$			199.881i			0.593120i	0.955014	+	0.296560i	$0.0958395\pi$
$337$			199.881i			0.593120i	−0.955014	+	0.296560i	$0.904161\pi$
$338$		0			0
$339$	22.2103	−	45.6975i	0.0655171	−	0.134801i
$340$		0			0
$341$	102.349			0.300143
$342$		0			0
$343$		−	637.608i		−	1.85892i
$344$		0			0
$345$	264.803	+	37.1916i	0.767544	+	0.107802i
$346$		0			0
$347$		−	609.297i		−	1.75590i	−0.478753	−	0.877950i	$-0.658911\pi$
$347$		−	609.297i		−	1.75590i	0.478753	−	0.877950i	$-0.341089\pi$
$348$		0			0
$349$			444.680i			1.27415i	0.770800	+	0.637077i	$0.219857\pi$
$349$			444.680i			1.27415i	−0.770800	+	0.637077i	$0.780143\pi$
$350$		0			0
$351$	−361.759	+	78.4584i	−1.03065	+	0.223528i
$352$		0			0
$353$	221.451			0.627341			0.313671	−	0.949532i	$-0.398441\pi$
$353$	221.451			0.627341			0.313671	+	0.949532i	$0.398441\pi$
$354$		0			0
$355$	−332.940	+	107.705i	−0.937860	+	0.303393i
$356$		0			0
$357$	854.143	+	415.138i	2.39256	+	1.16285i
$358$		0			0
$359$		−	11.5997i		−	0.0323111i	−0.999869	−	0.0161556i	$-0.994857\pi$
$359$		−	11.5997i		−	0.0323111i	0.999869	−	0.0161556i	$-0.00514270\pi$
$360$		0			0
$361$	162.722			0.450754
$362$		0			0
$363$	146.681	−	301.795i	0.404080	−	0.831392i
$364$		0			0
$365$	540.597	−	174.881i	1.48109	−	0.479125i
$366$		0			0
$367$			433.927i			1.18236i	0.806538	+	0.591182i	$0.201338\pi$
$367$			433.927i			1.18236i	−0.806538	+	0.591182i	$0.798662\pi$
$368$		0			0
$369$	491.663	−	386.316i	1.33242	−	1.04693i
$370$		0			0
$371$	776.410			2.09275
$372$		0			0
$373$	−210.700			−0.564879			−0.282440	−	0.959285i	$-0.591144\pi$
$373$	−210.700			−0.564879			−0.282440	+	0.959285i	$0.591144\pi$
$374$		0			0
$375$	331.542	−	175.227i	0.884113	−	0.467273i
$376$		0			0
$377$	−378.294			−1.00343
$378$		0			0
$379$			290.509i			0.766514i	0.923642	+	0.383257i	$0.125198\pi$
$379$			290.509i			0.766514i	−0.923642	+	0.383257i	$0.874802\pi$
$380$		0			0
$381$	159.683	+	77.6106i	0.419117	+	0.203702i
$382$		0			0
$383$	−28.4785			−0.0743564			−0.0371782	−	0.999309i	$-0.511837\pi$
$383$	−28.4785			−0.0743564			−0.0371782	+	0.999309i	$0.511837\pi$
$384$		0			0
$385$	−176.265	+	57.0210i	−0.457832	+	0.148107i
$386$		0			0
$387$	−366.557	−	466.516i	−0.947176	−	1.20547i
$388$		0			0
$389$	−463.706			−1.19205			−0.596024	−	0.802967i	$-0.703254\pi$
$389$	−463.706			−1.19205			−0.596024	+	0.802967i	$0.703254\pi$
$390$		0			0
$391$	460.692			1.17824
$392$		0			0
$393$	81.3405	−	167.358i	0.206973	−	0.425847i
$394$		0			0
$395$	169.194	+	523.019i	0.428339	+	1.32410i
$396$		0			0
$397$	344.568			0.867930			0.433965	−	0.900930i	$-0.357114\pi$
$397$	344.568			0.867930			0.433965	+	0.900930i	$0.357114\pi$
$398$		0			0
$399$	−226.199	+	465.404i	−0.566916	+	1.16643i
$400$		0			0
$401$			300.230i			0.748704i	0.927287	+	0.374352i	$0.122135\pi$
$401$			300.230i			0.748704i	−0.927287	+	0.374352i	$0.877865\pi$
$402$		0			0
$403$	−463.905			−1.15113
$404$		0			0
$405$	−403.891	+	29.9570i	−0.997261	+	0.0739680i
$406$		0			0
$407$	45.0870			0.110779
$408$		0			0
$409$	113.232			0.276851			0.138425	−	0.990373i	$-0.455796\pi$
$409$	113.232			0.276851			0.138425	+	0.990373i	$0.455796\pi$
$410$		0			0
$411$	278.499	−	573.010i	0.677613	−	1.39419i
$412$		0			0
$413$		−	350.368i		−	0.848348i
$414$		0			0
$415$	−78.2098	+	25.3005i	−0.188457	+	0.0609651i
$416$		0			0
$417$	76.6512	+	37.2546i	0.183816	+	0.0893396i
$418$		0			0
$419$	−608.930			−1.45329			−0.726647	−	0.687011i	$-0.758922\pi$
$419$	−608.930			−1.45329			−0.726647	+	0.687011i	$0.758922\pi$
$420$		0			0
$421$			160.484i			0.381196i	0.981668	+	0.190598i	$0.0610428\pi$
$421$			160.484i			0.381196i	−0.981668	+	0.190598i	$0.938957\pi$
$422$		0			0
$423$	65.7426	+	83.6704i	0.155420	+	0.197802i
$424$		0			0
$425$	523.657	−	378.400i	1.23213	−	0.890354i
$426$		0			0
$427$	35.3515			0.0827905
$428$		0			0
$429$	54.3825	−	111.892i	0.126766	−	0.260820i
$430$		0			0
$431$		−	120.477i		−	0.279529i	−0.990185	−	0.139764i	$-0.955366\pi$
$431$		−	120.477i		−	0.279529i	0.990185	−	0.139764i	$-0.0446345\pi$
$432$		0			0
$433$		−	419.887i		−	0.969716i	−0.874593	−	0.484858i	$-0.838871\pi$
$433$		−	419.887i		−	0.969716i	0.874593	−	0.484858i	$-0.161129\pi$
$434$		0			0
$435$	−409.867	−	57.5659i	−0.942223	−	0.132335i
$436$		0			0
$437$			251.021i			0.574419i
$438$		0			0
$439$	−655.375			−1.49288			−0.746440	−	0.665452i	$-0.768239\pi$
$439$	−655.375			−1.49288			−0.746440	+	0.665452i	$0.768239\pi$
$440$		0			0
$441$	561.895	+	715.122i	1.27414	+	1.62159i
$442$		0			0
$443$			207.128i			0.467558i	0.972290	+	0.233779i	$0.0751092\pi$
$443$			207.128i			0.467558i	−0.972290	+	0.233779i	$0.924891\pi$
$444$		0			0
$445$	−315.948	+	102.208i	−0.709997	+	0.229681i
$446$		0			0
$447$	−109.229	+	224.737i	−0.244359	+	0.502768i
$448$		0			0
$449$		−	167.158i		−	0.372289i	−0.982522	−	0.186144i	$-0.940401\pi$
$449$		−	167.158i		−	0.372289i	0.982522	−	0.186144i	$-0.0595992\pi$
$450$		0			0
$451$			210.145i			0.465954i
$452$		0			0
$453$	−40.5201	+	83.3698i	−0.0894483	+	0.184039i
$454$		0			0
$455$	798.940	−	258.453i	1.75591	−	0.568029i
$456$		0			0
$457$		−	212.777i		−	0.465595i	−0.972525	−	0.232797i	$-0.925212\pi$
$457$		−	212.777i		−	0.465595i	0.972525	−	0.232797i	$-0.0747879\pi$
$458$		0			0
$459$	−681.900	+	147.891i	−1.48562	+	0.322202i
$460$		0			0
$461$	−657.831			−1.42696			−0.713482	−	0.700673i	$-0.752883\pi$
$461$	−657.831			−1.42696			−0.713482	+	0.700673i	$0.752883\pi$
$462$		0			0
$463$			185.882i			0.401472i	0.979645	+	0.200736i	$0.0643334\pi$
$463$			185.882i			0.401472i	−0.979645	+	0.200736i	$0.935667\pi$
$464$		0			0
$465$	−502.623	−	70.5935i	−1.08091	−	0.151814i
$466$		0			0
$467$			15.5127i			0.0332178i	0.999862	+	0.0166089i	$0.00528702\pi$
$467$			15.5127i			0.0332178i	−0.999862	+	0.0166089i	$0.994713\pi$
$468$		0			0
$469$		−	845.539i		−	1.80286i
$470$		0			0
$471$	−156.252	+	321.487i	−0.331745	+	0.682563i
$472$		0			0
$473$	199.397			0.421558
$474$		0			0
$475$	206.182	+	285.329i	0.434067	+	0.600692i
$476$		0			0
$477$	−448.547	+	352.438i	−0.940349	+	0.738863i
$478$		0			0
$479$		−	162.375i		−	0.338988i	−0.985531	−	0.169494i	$-0.945787\pi$
$479$		−	162.375i		−	0.338988i	0.985531	−	0.169494i	$-0.0542133\pi$
$480$		0			0
$481$	−204.361			−0.424868
$482$		0			0
$483$	589.204	+	286.370i	1.21988	+	0.592898i
$484$		0			0
$485$	299.687	−	96.9474i	0.617911	−	0.199892i
$486$		0			0
$487$			186.293i			0.382532i	0.981538	+	0.191266i	$0.0612593\pi$
$487$			186.293i			0.382532i	−0.981538	+	0.191266i	$0.938741\pi$
$488$		0			0
$489$	−285.315	+	587.034i	−0.583467	+	1.20048i
$490$		0			0
$491$	313.419			0.638328			0.319164	−	0.947699i	$-0.396598\pi$
$491$	313.419			0.638328			0.319164	+	0.947699i	$0.396598\pi$
$492$		0			0
$493$	−713.069			−1.44639
$494$		0			0
$495$	75.9481	−	112.955i	0.153431	−	0.228191i
$496$		0			0
$497$	−857.292			−1.72493
$498$		0			0
$499$		−	721.574i		−	1.44604i	−0.690827	−	0.723020i	$-0.742754\pi$
$499$		−	721.574i		−	1.44604i	0.690827	−	0.723020i	$-0.257246\pi$
$500$		0			0
$501$	375.338	−	772.255i	0.749177	−	1.54143i
$502$		0			0
$503$	371.171			0.737915			0.368957	−	0.929446i	$-0.379715\pi$
$503$	371.171			0.737915			0.368957	+	0.929446i	$0.379715\pi$
$504$		0			0
$505$	−198.058	−	612.244i	−0.392194	−	1.21236i
$506$		0			0
$507$	−24.8680	+	51.1658i	−0.0490493	+	0.100919i
$508$		0			0
$509$	−289.124			−0.568024			−0.284012	−	0.958821i	$-0.591666\pi$
$509$	−289.124			−0.568024			−0.284012	+	0.958821i	$0.591666\pi$
$510$		0			0
$511$	1391.99			2.72405
$512$		0			0
$513$	−80.5824	−	371.552i	−0.157081	−	0.724273i
$514$		0			0
$515$	−400.492	+	129.557i	−0.777654	+	0.251567i
$516$		0			0
$517$	−35.7622			−0.0691724
$518$		0			0
$519$	486.734	+	236.566i	0.937830	+	0.455812i
$520$		0			0
$521$			334.804i			0.642618i	0.946974	+	0.321309i	$0.104123\pi$
$521$			334.804i			0.642618i	−0.946974	+	0.321309i	$0.895877\pi$
$522$		0			0
$523$	−195.767			−0.374316			−0.187158	−	0.982330i	$-0.559928\pi$
$523$	−195.767			−0.374316			−0.187158	+	0.982330i	$0.559928\pi$
$524$		0			0
$525$	904.950	−	158.448i	1.72371	−	0.301805i
$526$		0			0
$527$	−874.442			−1.65928
$528$		0			0
$529$	−211.206			−0.399255
$530$		0			0
$531$	159.044	+	202.414i	0.299517	+	0.381194i
$532$		0			0
$533$		−	952.504i		−	1.78706i
$534$		0			0
$535$	73.0583	−	23.6340i	0.136558	−	0.0441758i
$536$		0			0
$537$	−88.7808	+	182.666i	−0.165327	+	0.340160i
$538$		0			0
$539$	−305.655			−0.567078
$540$		0			0
$541$			308.922i			0.571021i	0.958376	+	0.285510i	$0.0921631\pi$
$541$			308.922i			0.571021i	−0.958376	+	0.285510i	$0.907837\pi$
$542$		0			0
$543$	601.039	+	292.122i	1.10689	+	0.537978i
$544$		0			0
$545$	−380.268	+	123.015i	−0.697740	+	0.225716i
$546$		0			0
$547$	532.237			0.973011			0.486505	−	0.873678i	$-0.338271\pi$
$547$	532.237			0.973011			0.486505	+	0.873678i	$0.338271\pi$
$548$		0			0
$549$	−20.4233	+	16.0472i	−0.0372008	+	0.0292299i
$550$		0			0
$551$		−	388.535i		−	0.705146i
$552$		0			0
$553$			1346.73i			2.43531i
$554$		0			0
$555$	−221.418	−	31.0981i	−0.398951	−	0.0560327i
$556$		0			0
$557$			355.234i			0.637764i	0.947794	+	0.318882i	$0.103307\pi$
$557$			355.234i			0.637764i	−0.947794	+	0.318882i	$0.896693\pi$
$558$		0			0
$559$	−903.787			−1.61679
$560$		0			0
$561$	102.509	−	210.911i	0.182725	−	0.375956i
$562$		0			0
$563$		−	361.694i		−	0.642440i	−0.947005	−	0.321220i	$-0.895907\pi$
$563$		−	361.694i		−	0.642440i	0.947005	−	0.321220i	$-0.104093\pi$
$564$		0			0
$565$	−26.0643	−	80.5708i	−0.0461315	−	0.142603i
$566$		0			0
$567$	−964.049	−	234.729i	−1.70026	−	0.413984i
$568$		0			0
$569$		−	810.062i		−	1.42366i	−0.702352	−	0.711829i	$-0.747867\pi$
$569$		−	810.062i		−	1.42366i	0.702352	−	0.711829i	$-0.252133\pi$
$570$		0			0
$571$		−	781.618i		−	1.36886i	−0.729080	−	0.684429i	$-0.760052\pi$
$571$		−	781.618i		−	1.36886i	0.729080	−	0.684429i	$-0.239948\pi$
$572$		0			0
$573$	590.147	+	286.828i	1.02992	+	0.500572i
$574$		0			0
$575$	361.228	−	261.028i	0.628223	−	0.453961i
$576$		0			0
$577$			878.009i			1.52168i	0.648940	+	0.760839i	$0.275212\pi$
$577$			878.009i			1.52168i	−0.648940	+	0.760839i	$0.724788\pi$
$578$		0			0
$579$	293.908	+	142.848i	0.507613	+	0.246714i
$580$		0			0
$581$	−201.383			−0.346615
$582$		0			0
$583$		−	191.716i		−	0.328845i
$584$		0			0
$585$	−344.242	+	511.979i	−0.588449	+	0.875177i
$586$		0			0
$587$			138.105i			0.235272i	0.993057	+	0.117636i	$0.0375316\pi$
$587$			138.105i			0.235272i	−0.993057	+	0.117636i	$0.962468\pi$
$588$		0			0
$589$		−	476.464i		−	0.808937i
$590$		0			0
$591$	−234.843	−	114.140i	−0.397365	−	0.193131i
$592$		0			0
$593$	273.578			0.461345			0.230673	−	0.973031i	$-0.425907\pi$
$593$	273.578			0.461345			0.230673	+	0.973031i	$0.425907\pi$
$594$		0			0
$595$	1505.97	−	487.174i	2.53104	−	0.818779i
$596$		0			0
$597$	99.8119	−	205.362i	0.167189	−	0.343991i
$598$		0			0
$599$			821.780i			1.37192i	0.727639	+	0.685960i	$0.240618\pi$
$599$			821.780i			1.37192i	−0.727639	+	0.685960i	$0.759382\pi$
$600$		0			0
$601$	−933.331			−1.55296			−0.776482	−	0.630140i	$-0.782998\pi$
$601$	−933.331			−1.55296			−0.776482	+	0.630140i	$0.782998\pi$
$602$		0			0
$603$	383.818	+	488.484i	0.636514	+	0.810090i
$604$		0			0
$605$	−172.134	−	532.105i	−0.284518	−	0.879512i
$606$		0			0
$607$			268.120i			0.441714i	0.975306	+	0.220857i	$0.0708854\pi$
$607$			268.120i			0.441714i	−0.975306	+	0.220857i	$0.929115\pi$
$608$		0			0
$609$	−911.983	−	443.249i	−1.49751	−	0.727831i
$610$		0			0
$611$	162.096			0.265295
$612$		0			0
$613$	914.181			1.49132			0.745661	−	0.666325i	$-0.232134\pi$
$613$	914.181			1.49132			0.745661	+	0.666325i	$0.232134\pi$
$614$		0			0
$615$	144.945	−	1032.00i	0.235682	−	1.67805i
$616$		0			0
$617$	753.872			1.22183			0.610917	−	0.791695i	$-0.290801\pi$
$617$	753.872			1.22183			0.610917	+	0.791695i	$0.290801\pi$
$618$		0			0
$619$		−	525.804i		−	0.849440i	−0.905325	−	0.424720i	$-0.860372\pi$
$619$		−	525.804i		−	0.849440i	0.905325	−	0.424720i	$-0.139628\pi$
$620$		0			0
$621$	−470.387	+	102.018i	−0.757468	+	0.164280i
$622$		0			0
$623$	−813.540			−1.30584
$624$		0			0
$625$	196.197	−	593.407i	0.313916	−	0.949451i
$626$		0			0
$627$	114.921	+	55.8547i	0.183287	+	0.0890825i
$628$		0			0
$629$	−385.213			−0.612421
$630$		0			0
$631$	171.651			0.272030			0.136015	−	0.990707i	$-0.456570\pi$
$631$	171.651			0.272030			0.136015	+	0.990707i	$0.456570\pi$
$632$		0			0
$633$	−986.562	−	479.497i	−1.55855	−	0.757499i
$634$		0			0
$635$	281.543	−	91.0779i	0.443375	−	0.143430i
$636$		0			0
$637$	1385.41			2.17490
$638$		0			0
$639$	495.274	−	389.153i	0.775077	−	0.609003i
$640$		0			0
$641$			626.169i			0.976862i	0.872602	+	0.488431i	$0.162431\pi$
$641$			626.169i			0.976862i	−0.872602	+	0.488431i	$0.837569\pi$
$642$		0			0
$643$	265.568			0.413013			0.206507	−	0.978445i	$-0.433790\pi$
$643$	265.568			0.413013			0.206507	+	0.978445i	$0.433790\pi$
$644$		0			0
$645$	−979.218	−	137.531i	−1.51817	−	0.213227i
$646$		0			0
$647$	−25.6635			−0.0396654			−0.0198327	−	0.999803i	$-0.506313\pi$
$647$	−25.6635			−0.0396654			−0.0198327	+	0.999803i	$0.506313\pi$
$648$		0			0
$649$	−86.5153			−0.133306
$650$		0			0
$651$	−1118.37	−	543.560i	−1.71793	−	0.834962i
$652$		0			0
$653$			621.080i			0.951119i	0.879684	+	0.475559i	$0.157754\pi$
$653$			621.080i			0.951119i	−0.879684	+	0.475559i	$0.842246\pi$
$654$		0			0
$655$	−95.4550	−	295.074i	−0.145733	−	0.450494i
$656$		0			0
$657$	−804.180	+	631.870i	−1.22402	+	0.961751i
$658$		0			0
$659$	−460.999			−0.699543			−0.349771	−	0.936835i	$-0.613741\pi$
$659$	−460.999			−0.699543			−0.349771	+	0.936835i	$0.613741\pi$
$660$		0			0
$661$			9.42461i			0.0142581i	0.999975	+	0.00712905i	$0.00226927\pi$
$661$			9.42461i			0.0142581i	−0.999975	+	0.00712905i	$0.997731\pi$
$662$		0			0
$663$	−464.631	+	955.975i	−0.700801	+	1.44189i
$664$		0			0
$665$	265.450	+	820.569i	0.399173	+	1.23394i
$666$		0			0
$667$	−491.888			−0.737464
$668$		0			0
$669$	−446.313	−	216.921i	−0.667135	−	0.324246i
$670$		0			0
$671$		−	8.72925i		−	0.0130093i
$672$		0			0
$673$			254.588i			0.378288i	0.981949	+	0.189144i	$0.0605712\pi$
$673$			254.588i			0.378288i	−0.981949	+	0.189144i	$0.939429\pi$
$674$		0			0
$675$	−450.882	+	502.325i	−0.667974	+	0.744185i
$676$		0			0
$677$			1280.94i			1.89209i	0.324040	+	0.946043i	$0.394959\pi$
$677$			1280.94i			1.89209i	−0.324040	+	0.946043i	$0.605041\pi$
$678$		0			0
$679$	771.668			1.13648
$680$		0			0
$681$	−713.537	−	346.799i	−1.04778	−	0.509250i
$682$		0			0
$683$		−	484.089i		−	0.708768i	−0.935100	−	0.354384i	$-0.884691\pi$
$683$		−	484.089i		−	0.708768i	0.935100	−	0.354384i	$-0.115309\pi$
$684$		0			0
$685$	−326.825	−	1010.29i	−0.477117	−	1.47488i
$686$		0			0
$687$	397.960	+	193.420i	0.579273	+	0.281543i
$688$		0			0
$689$			868.974i			1.26121i
$690$		0			0
$691$			542.386i			0.784929i	0.919767	+	0.392464i	$0.128377\pi$
$691$			542.386i			0.784929i	−0.919767	+	0.392464i	$0.871623\pi$
$692$		0			0
$693$	262.208	−	206.026i	0.378367	−	0.297295i
$694$		0			0
$695$	135.146	−	43.7192i	0.194455	−	0.0629053i
$696$		0			0
$697$		−	1795.43i		−	2.57594i
$698$		0			0
$699$	491.001	−	1010.23i	0.702434	−	1.44525i
$700$		0			0
$701$	1233.95			1.76028			0.880138	−	0.474718i	$-0.157450\pi$
$701$	1233.95			1.76028			0.880138	+	0.474718i	$0.157450\pi$
$702$		0			0
$703$		−	209.894i		−	0.298569i
$704$		0			0
$705$	175.624	+	24.6664i	0.249112	+	0.0349878i
$706$		0			0
$707$		−	1576.48i		−	2.22981i
$708$		0			0
$709$		−	708.293i		−	0.999002i	−0.866313	−	0.499501i	$-0.833517\pi$
$709$		−	708.293i		−	0.999002i	0.866313	−	0.499501i	$-0.166483\pi$
$710$		0			0
$711$	−611.324	−	778.030i	−0.859808	−	1.09428i
$712$		0			0
$713$	−603.207			−0.846012
$714$		0			0
$715$	−63.8191	−	197.280i	−0.0892575	−	0.275916i
$716$		0			0
$717$	−973.767	−	473.278i	−1.35811	−	0.660081i
$718$		0			0
$719$		−	399.429i		−	0.555535i	−0.960648	−	0.277767i	$-0.910406\pi$
$719$		−	399.429i		−	0.555535i	0.960648	−	0.277767i	$-0.0895944\pi$
$720$		0			0
$721$	−1031.23			−1.43028
$722$		0			0
$723$	−133.991	+	275.685i	−0.185326	+	0.381307i
$724$		0			0
$725$	−559.117	+	404.024i	−0.771195	+	0.557275i
$726$		0			0
$727$			509.611i			0.700978i	0.936567	+	0.350489i	$0.113985\pi$
$727$			509.611i			0.700978i	−0.936567	+	0.350489i	$0.886015\pi$
$728$		0			0
$729$	663.501	−	302.006i	0.910152	−	0.414275i
$730$		0			0
$731$	−1703.60			−2.33051
$732$		0			0
$733$	−717.150			−0.978376			−0.489188	−	0.872178i	$-0.662707\pi$
$733$	−717.150			−0.978376			−0.489188	+	0.872178i	$0.662707\pi$
$734$		0			0
$735$	1501.04	+	210.821i	2.04223	+	0.286832i
$736$		0			0
$737$	−208.786			−0.283292
$738$		0			0
$739$		−	1361.02i		−	1.84171i	−0.389905	−	0.920855i	$-0.627492\pi$
$739$		−	1361.02i		−	1.84171i	0.389905	−	0.920855i	$-0.372508\pi$
$740$		0			0
$741$	−520.890	−	253.167i	−0.702955	−	0.341656i
$742$		0			0
$743$	1230.60			1.65625			0.828127	−	0.560540i	$-0.189406\pi$
$743$	1230.60			1.65625			0.828127	+	0.560540i	$0.189406\pi$
$744$		0			0
$745$	128.182	+	396.242i	0.172057	+	0.531868i
$746$		0			0
$747$	116.343	−	91.4146i	0.155747	−	0.122376i
$748$		0			0
$749$	188.119			0.251160
$750$		0			0
$751$	−477.996			−0.636479			−0.318239	−	0.948010i	$-0.603092\pi$
$751$	−477.996			−0.636479			−0.318239	+	0.948010i	$0.603092\pi$
$752$		0			0
$753$	628.921	−	1294.00i	0.835220	−	1.71846i
$754$		0			0
$755$	47.5513	+	146.992i	0.0629818	+	0.194692i
$756$		0			0
$757$	−710.649			−0.938770			−0.469385	−	0.882994i	$-0.655524\pi$
$757$	−710.649			−0.938770			−0.469385	+	0.882994i	$0.655524\pi$
$758$		0			0
$759$	70.7125	−	145.490i	0.0931653	−	0.191687i
$760$		0			0
$761$		−	134.002i		−	0.176087i	−0.996117	−	0.0880433i	$-0.971939\pi$
$761$		−	134.002i		−	0.176087i	0.996117	−	0.0880433i	$-0.0280614\pi$
$762$		0			0
$763$	−979.158			−1.28330
$764$		0			0
$765$	−648.882	+	965.058i	−0.848212	+	1.26151i
$766$		0			0
$767$	392.139			0.511264
$768$		0			0
$769$	−301.919			−0.392612			−0.196306	−	0.980543i	$-0.562895\pi$
$769$	−301.919			−0.392612			−0.196306	+	0.980543i	$0.562895\pi$
$770$		0			0
$771$	387.438	−	797.152i	0.502514	−	1.03392i
$772$		0			0
$773$			151.914i			0.196525i	0.995161	+	0.0982625i	$0.0313285\pi$
$773$			151.914i			0.196525i	−0.995161	+	0.0982625i	$0.968672\pi$
$774$		0			0
$775$	−685.649	+	495.458i	−0.884709	+	0.639301i
$776$		0			0
$777$	−492.670	−	239.451i	−0.634067	−	0.308174i
$778$		0			0
$779$	978.290			1.25583
$780$		0			0
$781$			211.689i			0.271048i
$782$		0			0
$783$	728.075	−	157.905i	0.929854	−	0.201667i
$784$		0			0
$785$	183.365	+	566.825i	0.233586	+	0.722070i
$786$		0			0
$787$	99.6831			0.126662			0.0633311	−	0.997993i	$-0.479828\pi$
$787$	99.6831			0.126662			0.0633311	+	0.997993i	$0.479828\pi$
$788$		0			0
$789$	−315.721	+	649.595i	−0.400154	+	0.823314i
$790$		0			0
$791$		−	207.463i		−	0.262279i
$792$		0			0
$793$			39.5662i			0.0498943i
$794$		0			0
$795$	−132.234	+	941.500i	−0.166332	+	1.18428i
$796$		0			0
$797$			72.9028i			0.0914715i	0.998954	+	0.0457358i	$0.0145632\pi$
$797$			72.9028i			0.0914715i	−0.998954	+	0.0457358i	$0.985437\pi$
$798$		0			0
$799$	305.543			0.382407
$800$		0			0
$801$	469.997	−	369.292i	0.586763	−	0.461039i
$802$		0			0
$803$		−	343.720i		−	0.428045i
$804$		0			0
$805$	1038.85	−	336.062i	1.29049	−	0.417468i
$806$		0			0
$807$	−405.631	+	834.584i	−0.502641	+	1.03418i
$808$		0			0
$809$			973.309i			1.20310i	0.798835	+	0.601551i	$0.205450\pi$
$809$			973.309i			1.20310i	−0.798835	+	0.601551i	$0.794550\pi$
$810$		0			0
$811$			215.941i			0.266266i	0.991098	+	0.133133i	$0.0425037\pi$
$811$			215.941i			0.266266i	−0.991098	+	0.133133i	$0.957496\pi$
$812$		0			0
$813$	390.508	−	803.468i	0.480330	−	0.988276i
$814$		0			0
$815$	334.824	+	1035.02i	0.410827	+	1.26996i
$816$		0			0
$817$		−	928.254i		−	1.13617i
$818$		0			0
$819$	−1188.48	+	933.831i	−1.45114	+	1.14021i
$820$		0			0
$821$	626.689			0.763324			0.381662	−	0.924302i	$-0.375352\pi$
$821$	626.689			0.763324			0.381662	+	0.924302i	$0.375352\pi$
$822$		0			0
$823$		−	153.375i		−	0.186361i	−0.995649	−	0.0931804i	$-0.970297\pi$
$823$		−	153.375i		−	0.186361i	0.995649	−	0.0931804i	$-0.0297033\pi$
$824$		0			0
$825$	−39.1250	−	223.457i	−0.0474243	−	0.270856i
$826$		0			0
$827$		−	44.0953i		−	0.0533196i	−0.999645	−	0.0266598i	$-0.991513\pi$
$827$		−	44.0953i		−	0.0533196i	0.999645	−	0.0266598i	$-0.00848709\pi$
$828$		0			0
$829$		−	333.433i		−	0.402211i	−0.979570	−	0.201105i	$-0.935547\pi$
$829$		−	333.433i		−	0.402211i	0.979570	−	0.201105i	$-0.0644533\pi$
$830$		0			0
$831$	88.6517	−	182.400i	0.106681	−	0.219495i
$832$		0			0
$833$	2611.44			3.13499
$834$		0			0
$835$	−440.467	−	1361.59i	−0.527506	−	1.63064i
$836$		0			0
$837$	892.845	−	193.641i	1.06672	−	0.231351i
$838$		0			0
$839$			1404.88i			1.67447i	0.546840	+	0.837237i	$0.315831\pi$
$839$			1404.88i			1.67447i	−0.546840	+	0.837237i	$0.684169\pi$
$840$		0			0
$841$	−79.6447			−0.0947024
$842$		0			0
$843$	800.122	+	388.882i	0.949137	+	0.461307i
$844$		0			0
$845$	29.1832	+	90.2120i	0.0345363	+	0.106760i
$846$		0			0
$847$		−	1370.12i		−	1.61762i
$848$		0			0
$849$	−247.161	+	508.532i	−0.291120	+	0.598977i
$850$		0			0
$851$	−265.727			−0.312253
$852$		0			0
$853$	−640.386			−0.750746			−0.375373	−	0.926874i	$-0.622485\pi$
$853$	−640.386			−0.750746			−0.375373	+	0.926874i	$0.622485\pi$
$854$		0			0
$855$	−525.839	−	353.562i	−0.615016	−	0.413522i
$856$		0			0
$857$	529.587			0.617955			0.308978	−	0.951069i	$-0.400013\pi$
$857$	529.587			0.617955			0.308978	+	0.951069i	$0.400013\pi$
$858$		0			0
$859$			1275.46i			1.48482i	0.669945	+	0.742410i	$0.266318\pi$
$859$			1275.46i			1.48482i	−0.669945	+	0.742410i	$0.733682\pi$
$860$		0			0
$861$	1116.05	−	2296.27i	1.29623	−	2.66699i
$862$		0			0
$863$	180.285			0.208905			0.104453	−	0.994530i	$-0.466691\pi$
$863$	180.285			0.208905			0.104453	+	0.994530i	$0.466691\pi$
$864$		0			0
$865$	858.176	−	277.616i	0.992111	−	0.320943i
$866$		0			0
$867$	−496.816	+	1022.20i	−0.573029	+	1.17900i
$868$		0			0
$869$	332.543			0.382674
$870$		0			0
$871$	946.346			1.08650
$872$		0			0
$873$	−445.807	+	350.285i	−0.510661	+	0.401243i
$874$		0			0
$875$	904.796	−	1235.27i	1.03405	−	1.41174i
$876$		0			0
$877$	1172.33			1.33675			0.668375	−	0.743825i	$-0.266990\pi$
$877$	1172.33			1.33675			0.668375	+	0.743825i	$0.266990\pi$
$878$		0			0
$879$	−146.207	−	71.0606i	−0.166333	−	0.0808426i
$880$		0			0
$881$		−	1361.82i		−	1.54576i	−0.634551	−	0.772881i	$-0.718815\pi$
$881$		−	1361.82i		−	1.54576i	0.634551	−	0.772881i	$-0.281185\pi$
$882$		0			0
$883$	−242.461			−0.274588			−0.137294	−	0.990530i	$-0.543841\pi$
$883$	−242.461			−0.274588			−0.137294	+	0.990530i	$0.543841\pi$
$884$		0			0
$885$	424.868	+	59.6727i	0.480076	+	0.0674268i
$886$		0			0
$887$	768.568			0.866481			0.433240	−	0.901278i	$-0.357370\pi$
$887$	768.568			0.866481			0.433240	+	0.901278i	$0.357370\pi$
$888$		0			0
$889$	724.949			0.815465
$890$		0			0
$891$	−57.9608	+	238.050i	−0.0650514	+	0.267171i
$892$		0			0
$893$			166.484i			0.186432i
$894$		0			0
$895$	104.186	+	322.065i	0.116409	+	0.359849i
$896$		0			0
$897$	−320.511	+	659.450i	−0.357315	+	0.735173i
$898$		0			0
$899$	933.656			1.03855
$900$		0			0
$901$			1637.98i			1.81796i
$902$		0			0
$903$	−2178.83	−	1058.97i	−2.41288	−	1.17273i
$904$		0			0
$905$	1059.71	−	342.812i	1.17095	−	0.378798i
$906$		0			0
$907$	390.266			0.430282			0.215141	−	0.976583i	$-0.430979\pi$
$907$	390.266			0.430282			0.215141	+	0.976583i	$0.430979\pi$
$908$		0			0
$909$	715.614	+	910.760i	0.787254	+	1.00194i
$910$		0			0
$911$			1007.79i			1.10624i	0.833101	+	0.553121i	$0.186563\pi$
$911$			1007.79i			1.10624i	−0.833101	+	0.553121i	$0.813437\pi$
$912$		0			0
$913$			49.7270i			0.0544655i
$914$		0			0
$915$	−6.02087	+	42.8684i	−0.00658019	+	0.0468507i
$916$		0			0
$917$		−	759.789i		−	0.828560i
$918$		0			0
$919$	86.2167			0.0938158			0.0469079	−	0.998899i	$-0.485063\pi$
$919$	86.2167			0.0938158			0.0469079	+	0.998899i	$0.485063\pi$
$920$		0			0
$921$	373.878	−	769.252i	0.405948	−	0.835236i
$922$		0			0
$923$		−	959.499i		−	1.03954i
$924$		0			0
$925$	−302.045	+	218.261i	−0.326535	+	0.235958i
$926$		0			0
$927$	595.762	−	468.110i	0.642677	−	0.504973i
$928$		0			0
$929$			950.507i			1.02315i	0.859238	+	0.511575i	$0.170938\pi$
$929$			950.507i			1.02315i	−0.859238	+	0.511575i	$0.829062\pi$
$930$		0			0
$931$			1422.92i			1.52838i
$932$		0			0
$933$	−744.910	−	362.047i	−0.798403	−	0.388046i
$934$		0			0
$935$	−120.296	−	371.864i	−0.128659	−	0.397716i
$936$		0			0
$937$			1522.58i			1.62495i	0.582993	+	0.812477i	$0.301882\pi$
$937$			1522.58i			1.62495i	−0.582993	+	0.812477i	$0.698118\pi$
$938$		0			0
$939$	411.202	+	199.856i	0.437915	+	0.212839i
$940$		0			0
$941$	−1788.60			−1.90075			−0.950374	−	0.311111i	$-0.899299\pi$
$941$	−1788.60			−1.90075			−0.950374	+	0.311111i	$0.899299\pi$
$942$		0			0
$943$		−	1238.52i		−	1.31339i
$944$		0			0
$945$	−1429.78	+	830.915i	−1.51299	+	0.879276i
$946$		0			0
$947$			195.826i			0.206786i	0.994641	+	0.103393i	$0.0329699\pi$
$947$			195.826i			0.206786i	−0.994641	+	0.103393i	$0.967030\pi$
$948$		0			0
$949$			1557.95i			1.64167i
$950$		0			0
$951$	−1373.24	−	667.432i	−1.44399	−	0.701822i
$952$		0			0
$953$	−1532.78			−1.60837			−0.804186	−	0.594378i	$-0.797398\pi$
$953$	−1532.78			−1.60837			−0.804186	+	0.594378i	$0.797398\pi$
$954$		0			0
$955$	1040.51	−	336.599i	1.08954	−	0.352460i
$956$		0			0
$957$	−109.450	+	225.193i	−0.114368	+	0.235312i
$958$		0			0
$959$		−	2601.42i		−	2.71263i
$960$		0			0
$961$	183.950			0.191415
$962$		0			0
$963$	−108.680	+	85.3933i	−0.112855	+	0.0886743i
$964$		0			0
$965$	518.199	−	167.635i	0.536994	−	0.173715i
$966$		0			0
$967$			232.608i			0.240546i	0.992741	+	0.120273i	$0.0383770\pi$
$967$			232.608i			0.240546i	−0.992741	+	0.120273i	$0.961623\pi$
$968$		0			0
$969$	−981.855	−	477.209i	−1.01327	−	0.492476i
$970$		0			0
$971$	500.031			0.514965			0.257482	−	0.966283i	$-0.417107\pi$
$971$	500.031			0.514965			0.257482	+	0.966283i	$0.417107\pi$
$972$		0			0
$973$	347.990			0.357646
$974$		0			0
$975$	177.338	+	1012.84i	0.181885	+	1.03881i
$976$		0			0
$977$	1764.27			1.80580			0.902900	−	0.429850i	$-0.141434\pi$
$977$	1764.27			1.80580			0.902900	+	0.429850i	$0.141434\pi$
$978$		0			0
$979$			200.885i			0.205194i
$980$		0			0
$981$	565.678	−	444.472i	0.576634	−	0.453080i
$982$		0			0
$983$	601.403			0.611804			0.305902	−	0.952063i	$-0.401042\pi$
$983$	601.403			0.611804			0.305902	+	0.952063i	$0.401042\pi$
$984$		0			0
$985$	−414.059	+	133.946i	−0.420365	+	0.135986i
$986$		0			0
$987$	390.776	+	189.928i	0.395923	+	0.192430i
$988$		0			0
$989$	−1175.18			−1.18825
$990$		0			0
$991$	1824.90			1.84148			0.920738	−	0.390181i	$-0.127588\pi$
$991$	1824.90			1.84148			0.920738	+	0.390181i	$0.127588\pi$
$992$		0			0
$993$	−732.685	−	356.106i	−0.737850	−	0.358616i
$994$		0			0
$995$	−117.132	−	362.081i	−0.117720	−	0.363901i
$996$		0			0
$997$	−1345.70			−1.34975			−0.674877	−	0.737930i	$-0.735803\pi$
$997$	−1345.70			−1.34975			−0.674877	+	0.737930i	$0.735803\pi$
$998$		0			0
$999$	393.320	−	85.3034i	0.393713	−	0.0853888i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.3.i.b.929.24	yes	64
3.2	odd	2	inner	960.3.i.b.929.17	✓	64
4.3	odd	2	inner	960.3.i.b.929.44	yes	64
5.4	even	2	inner	960.3.i.b.929.43	yes	64
8.3	odd	2	inner	960.3.i.b.929.21	yes	64
8.5	even	2	inner	960.3.i.b.929.41	yes	64
12.11	even	2	inner	960.3.i.b.929.45	yes	64
15.14	odd	2	inner	960.3.i.b.929.46	yes	64
20.19	odd	2	inner	960.3.i.b.929.23	yes	64
24.5	odd	2	inner	960.3.i.b.929.48	yes	64
24.11	even	2	inner	960.3.i.b.929.20	yes	64
40.19	odd	2	inner	960.3.i.b.929.42	yes	64
40.29	even	2	inner	960.3.i.b.929.22	yes	64
60.59	even	2	inner	960.3.i.b.929.18	yes	64
120.29	odd	2	inner	960.3.i.b.929.19	yes	64
120.59	even	2	inner	960.3.i.b.929.47	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.3.i.b.929.17	✓	64	3.2	odd	2	inner
960.3.i.b.929.18	yes	64	60.59	even	2	inner
960.3.i.b.929.19	yes	64	120.29	odd	2	inner
960.3.i.b.929.20	yes	64	24.11	even	2	inner
960.3.i.b.929.21	yes	64	8.3	odd	2	inner
960.3.i.b.929.22	yes	64	40.29	even	2	inner
960.3.i.b.929.23	yes	64	20.19	odd	2	inner
960.3.i.b.929.24	yes	64	1.1	even	1	trivial
960.3.i.b.929.41	yes	64	8.5	even	2	inner
960.3.i.b.929.42	yes	64	40.19	odd	2	inner
960.3.i.b.929.43	yes	64	5.4	even	2	inner
960.3.i.b.929.44	yes	64	4.3	odd	2	inner
960.3.i.b.929.45	yes	64	12.11	even	2	inner
960.3.i.b.929.46	yes	64	15.14	odd	2	inner
960.3.i.b.929.47	yes	64	120.59	even	2	inner
960.3.i.b.929.48	yes	64	24.5	odd	2	inner

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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	960.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31140 + 2.69819i) q^{3} +(1.53895 + 4.75727i) q^{5} +12.2496i q^{7} +(-5.56048 - 7.07680i) q^{9} +O(q^{10})\)	\(q+(-1.31140 + 2.69819i) q^{3} +(1.53895 + 4.75727i) q^{5} +12.2496i q^{7} +(-5.56048 - 7.07680i) q^{9} +3.02475 q^{11} -13.7100 q^{13} +(-14.8542 - 2.08627i) q^{15} -25.8427 q^{17} -14.0811i q^{19} +(-33.0516 - 16.0640i) q^{21} -17.8268 q^{23} +(-20.2632 + 14.6424i) q^{25} +(26.3866 - 5.72273i) q^{27} +27.5927 q^{29} +33.8371 q^{31} +(-3.96664 + 8.16134i) q^{33} +(-58.2744 + 18.8515i) q^{35} +14.9061 q^{37} +(17.9792 - 36.9921i) q^{39} +69.4754i q^{41} +65.9219 q^{43} +(25.1089 - 37.3436i) q^{45} -11.8232 q^{47} -101.052 q^{49} +(33.8900 - 69.7285i) q^{51} -63.3827i q^{53} +(4.65495 + 14.3895i) q^{55} +(37.9935 + 18.4659i) q^{57} -28.6025 q^{59} -2.88594i q^{61} +(86.6876 - 68.1133i) q^{63} +(-21.0990 - 65.2220i) q^{65} -69.0261 q^{67} +(23.3780 - 48.1001i) q^{69} +69.9856i q^{71} -113.636i q^{73} +(-12.9350 - 73.8762i) q^{75} +37.0518i q^{77} +109.941 q^{79} +(-19.1622 + 78.7008i) q^{81} +16.4401i q^{83} +(-39.7707 - 122.941i) q^{85} +(-36.1849 + 74.4503i) q^{87} +66.4138i q^{89} -167.941i q^{91} +(-44.3739 + 91.2990i) q^{93} +(66.9876 - 21.6702i) q^{95} -62.9956i q^{97} +(-16.8190 - 21.4055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 32 q^{9}+O(q^{10}) \) 64 * q - 32 * q^9	\( 64 q - 32 q^{9} - 32 q^{25} - 320 q^{49} + 448 q^{81}+O(q^{100}) \) 64 * q - 32 * q^9 - 32 * q^25 - 320 * q^49 + 448 * q^81

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