LMFDB - Embedded newform 960.3.i.b.929.23

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			929.23
Character	$\chi$	$=$	960.929
Dual form			960.3.i.b.929.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31140 + 2.69819i) q^{3} +(1.53895 - 4.75727i) q^{5} +12.2496i q^{7} +(-5.56048 - 7.07680i) q^{9} +O(q^{10})$	\(q+(-1.31140 + 2.69819i) q^{3} +(1.53895 - 4.75727i) q^{5} +12.2496i q^{7} +(-5.56048 - 7.07680i) q^{9} -3.02475 q^{11} +13.7100 q^{13} +(10.8178 + 10.3911i) q^{15} +25.8427 q^{17} +14.0811i q^{19} +(-33.0516 - 16.0640i) q^{21} -17.8268 q^{23} +(-20.2632 - 14.6424i) q^{25} +(26.3866 - 5.72273i) q^{27} +27.5927 q^{29} -33.8371 q^{31} +(3.96664 - 8.16134i) q^{33} +(58.2744 + 18.8515i) q^{35} -14.9061 q^{37} +(-17.9792 + 36.9921i) q^{39} +69.4754i q^{41} +65.9219 q^{43} +(-42.2236 + 15.5618i) q^{45} -11.8232 q^{47} -101.052 q^{49} +(-33.8900 + 69.7285i) q^{51} +63.3827i q^{53} +(-4.65495 + 14.3895i) q^{55} +(-37.9935 - 18.4659i) q^{57} +28.6025 q^{59} -2.88594i q^{61} +(86.6876 - 68.1133i) q^{63} +(21.0990 - 65.2220i) q^{65} -69.0261 q^{67} +(23.3780 - 48.1001i) q^{69} -69.9856i q^{71} +113.636i q^{73} +(66.0813 - 35.4720i) q^{75} -37.0518i q^{77} -109.941 q^{79} +(-19.1622 + 78.7008i) q^{81} +16.4401i q^{83} +(39.7707 - 122.941i) q^{85} +(-36.1849 + 74.4503i) q^{87} +66.4138i q^{89} +167.941i q^{91} +(44.3739 - 91.2990i) q^{93} +(66.9876 + 21.6702i) q^{95} +62.9956i q^{97} +(16.8190 + 21.4055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.543903\pi$
$11$	−3.02475			−0.274977			−0.137488	+	0.990503i	$0.543903\pi$
$12$		0			0
$13$	13.7100			1.05461			0.527306	−	0.849675i	$-0.323202\pi$
$13$	13.7100			1.05461			0.527306	+	0.849675i	$0.323202\pi$
$14$		0			0
$15$	10.8178	+	10.3911i	0.721190	+	0.692738i
$16$		0			0
$17$	25.8427			1.52016			0.760079	−	0.649830i	$-0.225160\pi$
$17$	25.8427			1.52016			0.760079	+	0.649830i	$0.225160\pi$
$18$		0			0
$19$			14.0811i			0.741111i	0.928810	+	0.370556i	$0.120833\pi$
$19$			14.0811i			0.741111i	−0.928810	+	0.370556i	$0.879167\pi$
$20$		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	$-0.683759\pi$
$31$	−33.8371			−1.09152			−0.545760	+	0.837942i	$0.683759\pi$
$32$		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	$-0.564560\pi$
$37$	−14.9061			−0.402866			−0.201433	+	0.979502i	$0.564560\pi$
$38$		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
$45$	−42.2236	+	15.5618i	−0.938302	+	0.345818i
$46$		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	$0.204018\pi$
$53$			63.3827i			1.19590i	−0.801534	+	0.597950i	$0.795982\pi$
$54$		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	$-0.422067\pi$
$59$	28.6025			0.484788			0.242394	+	0.970178i	$0.422067\pi$
$60$		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	$-0.835953\pi$
$71$		−	69.9856i		−	0.985712i	0.870111	−	0.492856i	$-0.164047\pi$
$72$		0			0
$73$			113.636i			1.55666i	0.627857	+	0.778329i	$0.283932\pi$
$73$			113.636i			1.55666i	−0.627857	+	0.778329i	$0.716068\pi$
$74$		0			0
$75$	66.0813	−	35.4720i	0.881084	−	0.472960i
$76$		0			0
$77$		−	37.0518i		−	0.481192i
$78$		0			0
$79$	−109.941			−1.39166			−0.695829	−	0.718208i	$-0.744963\pi$
$79$	−109.941			−1.39166			−0.695829	+	0.718208i	$0.744963\pi$
$80$		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	$0.105270\pi$
$97$			62.9956i			0.649439i	−0.945810	+	0.324720i	$0.894730\pi$
$98$		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
$105$	−127.286	+	132.514i	−1.21225	+	1.26204i
$106$		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	$-0.476124\pi$
$113$	16.9364			0.149879			0.0749396	+	0.997188i	$0.476124\pi$
$114$		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	$-0.423921\pi$
$131$	62.0259			0.473480			0.236740	+	0.971573i	$0.423921\pi$
$132$		0			0
$133$	−172.487			−1.29690
$134$		0			0
$135$	13.3831	−	134.335i	0.0991343	−	0.995074i
$136$		0			0
$137$	212.368			1.55013			0.775067	−	0.631880i	$-0.217716\pi$
$137$	212.368			1.55013			0.775067	+	0.631880i	$0.217716\pi$
$138$		0			0
$139$			28.4083i			0.204377i	0.994765	+	0.102188i	$0.0325844\pi$
$139$			28.4083i			0.204377i	−0.994765	+	0.102188i	$0.967416\pi$
$140$		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	$-0.532624\pi$
$151$	−30.8984			−0.204625			−0.102313	+	0.994752i	$0.532624\pi$
$152$		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	$-0.623889\pi$
$157$	−119.149			−0.758912			−0.379456	+	0.925210i	$0.623889\pi$
$158$		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
$165$	−32.7212	−	31.4303i	−0.198310	−	0.190487i
$166$		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	$0.174577\pi$
$173$			180.392i			1.04273i	−0.853333	+	0.521366i	$0.825423\pi$
$174$		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	$-0.560559\pi$
$179$	−67.6994			−0.378209			−0.189105	+	0.981957i	$0.560559\pi$
$180$		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	$0.194051\pi$
$191$			218.719i			1.14513i	−0.819860	+	0.572564i	$0.805949\pi$
$192$		0			0
$193$			108.928i			0.564393i	0.959357	+	0.282196i	$0.0910630\pi$
$193$			108.928i			0.564393i	−0.959357	+	0.282196i	$0.908937\pi$
$194$		0			0
$195$	148.312	+	142.461i	0.760575	+	0.730570i
$196$		0			0
$197$		−	87.0371i		−	0.441813i	−0.975295	−	0.220906i	$-0.929098\pi$
$197$		−	87.0371i		−	0.441813i	0.975295	−	0.220906i	$-0.0709015\pi$
$198$		0			0
$199$	76.1111			0.382468			0.191234	−	0.981544i	$-0.438751\pi$
$199$	76.1111			0.382468			0.191234	+	0.981544i	$0.438751\pi$
$200$		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	$-0.666401\pi$
$211$		−	365.638i		−	1.73288i	0.499278	−	0.866442i	$-0.333599\pi$
$212$		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
$225$	9.05155	+	224.818i	0.0402291	+	0.999190i
$226$		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	$-0.202992\pi$
$233$	374.411			1.60691			0.803457	+	0.595363i	$0.202992\pi$
$234$		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	$-0.727631\pi$
$239$		−	360.896i		−	1.51003i	0.655710	−	0.755013i	$-0.272369\pi$
$240$		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	$-0.0954894\pi$
$251$	479.581			1.91068			0.955340	+	0.295510i	$0.0954894\pi$
$252$		0			0
$253$	53.9215			0.213128
$254$		0			0
$255$	279.562	+	268.533i	1.09632	+	1.05307i
$256$		0			0
$257$	295.439			1.14957			0.574785	−	0.818305i	$-0.305086\pi$
$257$	295.439			1.14957			0.574785	+	0.818305i	$0.305086\pi$
$258$		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	$-0.314852\pi$
$271$	297.780			1.09882			0.549410	+	0.835553i	$0.314852\pi$
$272$		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	$-0.461062\pi$
$277$	67.6010			0.244047			0.122023	+	0.992527i	$0.461062\pi$
$278$		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
$285$	−146.318	+	152.327i	−0.513396	+	0.534482i
$286$		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	$-0.970524\pi$
$293$		−	54.1870i		−	0.184938i	0.995716	−	0.0924692i	$-0.0294760\pi$
$294$		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	$-0.853611\pi$
$311$		−	276.078i		−	0.887709i	0.896099	−	0.443855i	$-0.146389\pi$
$312$		0			0
$313$			152.399i			0.486898i	0.969914	+	0.243449i	$0.0782788\pi$
$313$			152.399i			0.486898i	−0.969914	+	0.243449i	$0.921721\pi$
$314$		0			0
$315$	−190.625	−	517.220i	−0.605159	−	1.64197i
$316$		0			0
$317$		−	508.948i		−	1.60551i	−0.596307	−	0.802757i	$-0.703366\pi$
$317$		−	508.948i		−	1.60551i	0.596307	−	0.802757i	$-0.296634\pi$
$318$		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	$-0.865462\pi$
$331$		−	271.547i		−	0.820383i	0.911999	−	0.410191i	$-0.134538\pi$
$332$		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	$-0.904161\pi$
$337$		−	199.881i		−	0.593120i	0.955014	−	0.296560i	$-0.0958395\pi$
$338$		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
$345$	−192.847	−	185.239i	−0.558978	−	0.536925i
$346$		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	$-0.601559\pi$
$353$	−221.451			−0.627341			−0.313671	+	0.949532i	$0.601559\pi$
$354$		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	$0.00514270\pi$
$359$			11.5997i			0.0323111i	−0.999869	+	0.0161556i	$0.994857\pi$
$360$		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	$-0.408856\pi$
$373$	210.700			0.564879			0.282440	+	0.959285i	$0.408856\pi$
$374$		0			0
$375$	−67.0539	−	368.956i	−0.178810	−	0.983884i
$376$		0			0
$377$	378.294			1.00343
$378$		0			0
$379$		−	290.509i		−	0.766514i	−0.923642	−	0.383257i	$-0.874802\pi$
$379$		−	290.509i		−	0.766514i	0.923642	−	0.383257i	$-0.125198\pi$
$380$		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	$-0.642886\pi$
$397$	−344.568			−0.867930			−0.433965	+	0.900930i	$0.642886\pi$
$398$		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
$405$	344.911	+	212.277i	0.851632	+	0.524140i
$406$		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	$-0.241078\pi$
$419$	608.930			1.45329			0.726647	+	0.687011i	$0.241078\pi$
$420$		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	$0.0446345\pi$
$431$			120.477i			0.279529i	−0.990185	+	0.139764i	$0.955366\pi$
$432$		0			0
$433$			419.887i			0.969716i	0.874593	+	0.484858i	$0.161129\pi$
$433$			419.887i			0.969716i	−0.874593	+	0.484858i	$0.838871\pi$
$434$		0			0
$435$	298.493	+	286.717i	0.686191	+	0.659120i
$436$		0			0
$437$		−	251.021i		−	0.574419i
$438$		0			0
$439$	655.375			1.49288			0.746440	−	0.665452i	$-0.231761\pi$
$439$	655.375			1.49288			0.746440	+	0.665452i	$0.231761\pi$
$440$		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	$0.0747879\pi$
$457$			212.777i			0.465595i	−0.972525	+	0.232797i	$0.925212\pi$
$458$		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
$465$	−366.045	−	351.604i	−0.787193	−	0.756137i
$466$		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	$0.0542133\pi$
$479$			162.375i			0.338988i	−0.985531	+	0.169494i	$0.945787\pi$
$480$		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	$-0.603402\pi$
$491$	−313.419			−0.638328			−0.319164	+	0.947699i	$0.603402\pi$
$492$		0			0
$493$	713.069			1.44639
$494$		0			0
$495$	127.716	−	47.0705i	0.258011	−	0.0950919i
$496$		0			0
$497$	857.292			1.72493
$498$		0			0
$499$			721.574i			1.44604i	0.690827	+	0.723020i	$0.257246\pi$
$499$			721.574i			1.44604i	−0.690827	+	0.723020i	$0.742754\pi$
$500$		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
$525$	434.517	+	809.466i	0.827651	+	1.54184i
$526$		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
$555$	−161.251	−	154.890i	−0.290543	−	0.279081i
$556$		0			0
$557$		−	355.234i		−	0.637764i	−0.947794	−	0.318882i	$-0.896693\pi$
$557$		−	355.234i		−	0.637764i	0.947794	−	0.318882i	$-0.103307\pi$
$558$		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	$0.239948\pi$
$571$			781.618i			1.36886i	−0.729080	+	0.684429i	$0.760052\pi$
$572$		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	$-0.724788\pi$
$577$		−	878.009i		−	1.52168i	0.648940	−	0.760839i	$-0.275212\pi$
$578$		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
$585$	−578.883	+	213.352i	−0.989544	+	0.364704i
$586$		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	$-0.574093\pi$
$593$	−273.578			−0.461345			−0.230673	+	0.973031i	$0.574093\pi$
$594$		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	$-0.759382\pi$
$599$		−	821.780i		−	1.37192i	0.727639	−	0.685960i	$-0.240618\pi$
$600$		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	$-0.767866\pi$
$613$	−914.181			−1.49132			−0.745661	+	0.666325i	$0.767866\pi$
$614$		0			0
$615$	−721.923	+	751.574i	−1.17386	+	1.22207i
$616$		0			0
$617$	−753.872			−1.22183			−0.610917	−	0.791695i	$-0.709199\pi$
$617$	−753.872			−1.22183			−0.610917	+	0.791695i	$0.709199\pi$
$618$		0			0
$619$			525.804i			0.849440i	0.905325	+	0.424720i	$0.139628\pi$
$619$			525.804i			0.849440i	−0.905325	+	0.424720i	$0.860372\pi$
$620$		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	$-0.543430\pi$
$631$	−171.651			−0.272030			−0.136015	+	0.990707i	$0.543430\pi$
$632$		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
$645$	713.133	+	684.999i	1.10563	+	1.06201i
$646$		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	$-0.842246\pi$
$653$		−	621.080i		−	0.951119i	0.879684	−	0.475559i	$-0.157754\pi$
$654$		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	$-0.386259\pi$
$659$	460.999			0.699543			0.349771	+	0.936835i	$0.386259\pi$
$660$		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	$-0.939429\pi$
$673$		−	254.588i		−	0.378288i	0.981949	−	0.189144i	$-0.0605712\pi$
$674$		0			0
$675$	−618.472	−	270.403i	−0.916255	−	0.400597i
$676$		0			0
$677$		−	1280.94i		−	1.89209i	−0.324040	−	0.946043i	$-0.605041\pi$
$677$		−	1280.94i		−	1.89209i	0.324040	−	0.946043i	$-0.394959\pi$
$678$		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	$-0.871623\pi$
$691$		−	542.386i		−	0.784929i	0.919767	−	0.392464i	$-0.128377\pi$
$692$		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
$705$	−127.901	−	122.856i	−0.181421	−	0.174263i
$706$		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	$0.0895944\pi$
$719$			399.429i			0.555535i	−0.960648	+	0.277767i	$0.910406\pi$
$720$		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	$-0.337293\pi$
$733$	717.150			0.978376			0.489188	+	0.872178i	$0.337293\pi$
$734$		0			0
$735$	−1093.16	−	1050.03i	−1.48729	−	1.42862i
$736$		0			0
$737$	208.786			0.283292
$738$		0			0
$739$			1361.02i			1.84171i	0.389905	+	0.920855i	$0.372508\pi$
$739$			1361.02i			1.84171i	−0.389905	+	0.920855i	$0.627492\pi$
$740$		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	$-0.396908\pi$
$751$	477.996			0.636479			0.318239	+	0.948010i	$0.396908\pi$
$752$		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	$-0.344476\pi$
$757$	710.649			0.938770			0.469385	+	0.882994i	$0.344476\pi$
$758$		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
$765$	−1091.17	+	402.159i	−1.42637	+	0.525698i
$766$		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	$-0.968672\pi$
$773$		−	151.914i		−	0.196525i	0.995161	−	0.0982625i	$-0.0313285\pi$
$774$		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
$795$	−658.614	+	685.664i	−0.828445	+	0.862471i
$796$		0			0
$797$		−	72.9028i		−	0.0914715i	−0.998954	−	0.0457358i	$-0.985437\pi$
$797$		−	72.9028i		−	0.0914715i	0.998954	−	0.0457358i	$-0.0145632\pi$
$798$		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	$-0.957496\pi$
$811$		−	215.941i		−	0.266266i	0.991098	−	0.133133i	$-0.0425037\pi$
$812$		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
$825$	−199.879	+	107.294i	−0.242278	+	0.130053i
$826$		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	$-0.684169\pi$
$839$		−	1404.88i		−	1.67447i	0.546840	−	0.837237i	$-0.315831\pi$
$840$		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	$-0.377515\pi$
$853$	640.386			0.750746			0.375373	+	0.926874i	$0.377515\pi$
$854$		0			0
$855$	−219.128	−	594.555i	−0.256290	−	0.695386i
$856$		0			0
$857$	−529.587			−0.617955			−0.308978	−	0.951069i	$-0.599987\pi$
$857$	−529.587			−0.617955			−0.308978	+	0.951069i	$0.599987\pi$
$858$		0			0
$859$		−	1275.46i		−	1.48482i	−0.669945	−	0.742410i	$-0.733682\pi$
$859$		−	1275.46i		−	1.48482i	0.669945	−	0.742410i	$-0.266318\pi$
$860$		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	$-0.733010\pi$
$877$	−1172.33			−1.33675			−0.668375	+	0.743825i	$0.733010\pi$
$878$		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
$885$	309.417	+	297.210i	0.349624	+	0.335831i
$886$		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	$-0.813437\pi$
$911$		−	1007.79i		−	1.10624i	0.833101	−	0.553121i	$-0.186563\pi$
$912$		0			0
$913$		−	49.7270i		−	0.0544655i
$914$		0			0
$915$	29.9880	−	31.2197i	0.0327738	−	0.0341199i
$916$		0			0
$917$			759.789i			0.828560i
$918$		0			0
$919$	−86.2167			−0.0938158			−0.0469079	−	0.998899i	$-0.514937\pi$
$919$	−86.2167			−0.0938158			−0.0469079	+	0.998899i	$0.514937\pi$
$920$		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	$-0.698118\pi$
$937$		−	1522.58i		−	1.62495i	0.582993	−	0.812477i	$-0.301882\pi$
$938$		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
$945$	1645.54	+	163.937i	1.74132	+	0.173479i
$946$		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	$-0.202602\pi$
$953$	1532.78			1.60837			0.804186	+	0.594378i	$0.202602\pi$
$954$		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	$-0.582893\pi$
$971$	−500.031			−0.514965			−0.257482	+	0.966283i	$0.582893\pi$
$972$		0			0
$973$	−347.990			−0.357646
$974$		0			0
$975$	905.972	−	486.320i	0.929202	−	0.498790i
$976$		0			0
$977$	−1764.27			−1.80580			−0.902900	−	0.429850i	$-0.858566\pi$
$977$	−1764.27			−1.80580			−0.902900	+	0.429850i	$0.858566\pi$
$978$		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	$-0.872412\pi$
$991$	−1824.90			−1.84148			−0.920738	+	0.390181i	$0.872412\pi$
$992$		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	$-0.264197\pi$
$997$	1345.70			1.34975			0.674877	+	0.737930i	$0.264197\pi$
$998$		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.929.23	yes	64
3.2	odd	2	inner	960.3.i.b.929.18	yes	64
4.3	odd	2	inner	960.3.i.b.929.43	yes	64
5.4	even	2	inner	960.3.i.b.929.44	yes	64
8.3	odd	2	inner	960.3.i.b.929.22	yes	64
8.5	even	2	inner	960.3.i.b.929.42	yes	64
12.11	even	2	inner	960.3.i.b.929.46	yes	64
15.14	odd	2	inner	960.3.i.b.929.45	yes	64
20.19	odd	2	inner	960.3.i.b.929.24	yes	64
24.5	odd	2	inner	960.3.i.b.929.47	yes	64
24.11	even	2	inner	960.3.i.b.929.19	yes	64
40.19	odd	2	inner	960.3.i.b.929.41	yes	64
40.29	even	2	inner	960.3.i.b.929.21	yes	64
60.59	even	2	inner	960.3.i.b.929.17	✓	64
120.29	odd	2	inner	960.3.i.b.929.20	yes	64
120.59	even	2	inner	960.3.i.b.929.48	yes	64

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

\(f(q)\)	\(=\)	\(q+(-1.31140 + 2.69819i) q^{3} +(1.53895 - 4.75727i) q^{5} +12.2496i q^{7} +(-5.56048 - 7.07680i) q^{9} +O(q^{10})\)	\(q+(-1.31140 + 2.69819i) q^{3} +(1.53895 - 4.75727i) q^{5} +12.2496i q^{7} +(-5.56048 - 7.07680i) q^{9} -3.02475 q^{11} +13.7100 q^{13} +(10.8178 + 10.3911i) q^{15} +25.8427 q^{17} +14.0811i q^{19} +(-33.0516 - 16.0640i) q^{21} -17.8268 q^{23} +(-20.2632 - 14.6424i) q^{25} +(26.3866 - 5.72273i) q^{27} +27.5927 q^{29} -33.8371 q^{31} +(3.96664 - 8.16134i) q^{33} +(58.2744 + 18.8515i) q^{35} -14.9061 q^{37} +(-17.9792 + 36.9921i) q^{39} +69.4754i q^{41} +65.9219 q^{43} +(-42.2236 + 15.5618i) q^{45} -11.8232 q^{47} -101.052 q^{49} +(-33.8900 + 69.7285i) q^{51} +63.3827i q^{53} +(-4.65495 + 14.3895i) q^{55} +(-37.9935 - 18.4659i) q^{57} +28.6025 q^{59} -2.88594i q^{61} +(86.6876 - 68.1133i) q^{63} +(21.0990 - 65.2220i) q^{65} -69.0261 q^{67} +(23.3780 - 48.1001i) q^{69} -69.9856i q^{71} +113.636i q^{73} +(66.0813 - 35.4720i) q^{75} -37.0518i q^{77} -109.941 q^{79} +(-19.1622 + 78.7008i) q^{81} +16.4401i q^{83} +(39.7707 - 122.941i) q^{85} +(-36.1849 + 74.4503i) q^{87} +66.4138i q^{89} +167.941i q^{91} +(44.3739 - 91.2990i) q^{93} +(66.9876 + 21.6702i) q^{95} +62.9956i q^{97} +(16.8190 + 21.4055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 32 q^{9}+O(q^{10}) \) 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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