LMFDB - Embedded newform 2880.2.u.a.719.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2880,2,Mod(719,2880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2880, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 2]))

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

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

chi := DirichletCharacter("2880.719");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2880 = 2^{6} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2880.u (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$22.9969157821$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 720)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			719.17
Character	$\chi$	$=$	2880.719
Dual form			2880.2.u.a.2159.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15480 - 1.91479i) q^{5} -3.02955i q^{7} +O(q^{10})$	$q+(-1.15480 - 1.91479i) q^{5} -3.02955i q^{7} +(1.30581 + 1.30581i) q^{11} +(1.56756 + 1.56756i) q^{13} +2.98571 q^{17} +(-1.25807 - 1.25807i) q^{19} +7.82148 q^{23} +(-2.33287 + 4.42241i) q^{25} +(7.12073 + 7.12073i) q^{29} -0.0502896i q^{31} +(-5.80096 + 3.49853i) q^{35} +(6.22957 - 6.22957i) q^{37} +4.05554 q^{41} +(-6.18655 - 6.18655i) q^{43} -5.87568i q^{47} -2.17818 q^{49} +(4.40639 + 4.40639i) q^{53} +(0.992408 - 4.00831i) q^{55} +(-8.20735 - 8.20735i) q^{59} +(-4.93899 + 4.93899i) q^{61} +(1.19133 - 4.81176i) q^{65} +(-1.29973 + 1.29973i) q^{67} -13.9687i q^{71} -3.85841 q^{73} +(3.95602 - 3.95602i) q^{77} +1.07096i q^{79} +(7.16503 + 7.16503i) q^{83} +(-3.44790 - 5.71702i) q^{85} -7.60356 q^{89} +(4.74899 - 4.74899i) q^{91} +(-0.956125 + 3.86176i) q^{95} -9.70129i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q + 16 q^{19} - 96 q^{49} - 64 q^{55} - 32 q^{61}+O(q^{100}) $ 96 * q + 16 * q^19 - 96 * q^49 - 64 * q^55 - 32 * q^61

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$2431$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.15480	−	1.91479i	−0.516443	−	0.856322i
$5$	−1.15480	−	1.91479i	−0.516443	−	0.856322i
$6$		0			0
$7$		−	3.02955i		−	1.14506i	−0.819883	−	0.572531i	$-0.805962\pi$
$7$		−	3.02955i		−	1.14506i	0.819883	−	0.572531i	$-0.194038\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.30581	+	1.30581i	0.393717	+	0.393717i	0.876010	−	0.482293i	$-0.160196\pi$
$11$	1.30581	+	1.30581i	0.393717	+	0.393717i	−0.482293	+	0.876010i	$0.660196\pi$
$12$		0			0
$13$	1.56756	+	1.56756i	0.434762	+	0.434762i	0.890245	−	0.455483i	$-0.150533\pi$
$13$	1.56756	+	1.56756i	0.434762	+	0.434762i	−0.455483	+	0.890245i	$0.650533\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.98571			0.724141			0.362071	−	0.932151i	$-0.382070\pi$
$17$	2.98571			0.724141			0.362071	+	0.932151i	$0.382070\pi$
$18$		0			0
$19$	−1.25807	−	1.25807i	−0.288621	−	0.288621i	0.547914	−	0.836535i	$-0.315422\pi$
$19$	−1.25807	−	1.25807i	−0.288621	−	0.288621i	−0.836535	+	0.547914i	$0.815422\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	7.82148			1.63089			0.815446	−	0.578834i	$-0.196492\pi$
$23$	7.82148			1.63089			0.815446	+	0.578834i	$0.196492\pi$
$24$		0			0
$25$	−2.33287	+	4.42241i	−0.466574	+	0.884482i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	7.12073	+	7.12073i	1.32229	+	1.32229i	0.911921	+	0.410365i	$0.134599\pi$
$29$	7.12073	+	7.12073i	1.32229	+	1.32229i	0.410365	+	0.911921i	$0.365401\pi$
$30$		0			0
$31$		−	0.0502896i		−	0.00903227i	−0.999990	−	0.00451614i	$-0.998562\pi$
$31$		−	0.0502896i		−	0.00903227i	0.999990	−	0.00451614i	$-0.00143754\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.80096	+	3.49853i	−0.980542	+	0.591359i
$36$		0			0
$37$	6.22957	−	6.22957i	1.02413	−	1.02413i	0.0244329	−	0.999701i	$-0.492222\pi$
$37$	6.22957	−	6.22957i	1.02413	−	1.02413i	0.999701	−	0.0244329i	$-0.00777799\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.05554			0.633368			0.316684	−	0.948531i	$-0.397430\pi$
$41$	4.05554			0.633368			0.316684	+	0.948531i	$0.397430\pi$
$42$		0			0
$43$	−6.18655	−	6.18655i	−0.943441	−	0.943441i	0.0550434	−	0.998484i	$-0.482470\pi$
$43$	−6.18655	−	6.18655i	−0.943441	−	0.943441i	−0.998484	+	0.0550434i	$0.982470\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	5.87568i		−	0.857057i	−0.903528	−	0.428528i	$-0.859032\pi$
$47$		−	5.87568i		−	0.857057i	0.903528	−	0.428528i	$-0.140968\pi$
$48$		0			0
$49$	−2.17818			−0.311168
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.40639	+	4.40639i	0.605264	+	0.605264i	0.941705	−	0.336440i	$-0.109223\pi$
$53$	4.40639	+	4.40639i	0.605264	+	0.605264i	−0.336440	+	0.941705i	$0.609223\pi$
$54$		0			0
$55$	0.992408	−	4.00831i	0.133816	−	0.540481i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−8.20735	−	8.20735i	−1.06851	−	1.06851i	−0.997474	−	0.0710318i	$-0.977371\pi$
$59$	−8.20735	−	8.20735i	−1.06851	−	1.06851i	−0.0710318	−	0.997474i	$-0.522629\pi$
$60$		0			0
$61$	−4.93899	+	4.93899i	−0.632373	+	0.632373i	−0.948663	−	0.316290i	$-0.897563\pi$
$61$	−4.93899	+	4.93899i	−0.632373	+	0.632373i	0.316290	+	0.948663i	$0.397563\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.19133	−	4.81176i	0.147767	−	0.596826i
$66$		0			0
$67$	−1.29973	+	1.29973i	−0.158787	+	0.158787i	−0.782029	−	0.623242i	$-0.785815\pi$
$67$	−1.29973	+	1.29973i	−0.158787	+	0.158787i	0.623242	+	0.782029i	$0.285815\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	13.9687i		−	1.65778i	−0.559414	−	0.828888i	$-0.688974\pi$
$71$		−	13.9687i		−	1.65778i	0.559414	−	0.828888i	$-0.311026\pi$
$72$		0			0
$73$	−3.85841			−0.451593			−0.225796	−	0.974175i	$-0.572498\pi$
$73$	−3.85841			−0.451593			−0.225796	+	0.974175i	$0.572498\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.95602	−	3.95602i	0.450830	−	0.450830i
$78$		0			0
$79$			1.07096i			0.120492i	0.998184	+	0.0602461i	$0.0191885\pi$
$79$			1.07096i			0.120492i	−0.998184	+	0.0602461i	$0.980811\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.16503	+	7.16503i	0.786464	+	0.786464i	0.980913	−	0.194448i	$-0.0622917\pi$
$83$	7.16503	+	7.16503i	0.786464	+	0.786464i	−0.194448	+	0.980913i	$0.562292\pi$
$84$		0			0
$85$	−3.44790	−	5.71702i	−0.373977	−	0.620098i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−7.60356			−0.805975			−0.402988	−	0.915205i	$-0.632028\pi$
$89$	−7.60356			−0.805975			−0.402988	+	0.915205i	$0.632028\pi$
$90$		0			0
$91$	4.74899	−	4.74899i	0.497830	−	0.497830i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.956125	+	3.86176i	−0.0980963	+	0.396209i
$96$		0			0
$97$		−	9.70129i		−	0.985017i	−0.870308	−	0.492508i	$-0.836080\pi$
$97$		−	9.70129i		−	0.985017i	0.870308	−	0.492508i	$-0.163920\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.49754	−	6.49754i	0.646530	−	0.646530i	−0.305623	−	0.952153i	$-0.598865\pi$
$101$	6.49754	−	6.49754i	0.646530	−	0.646530i	0.952153	+	0.305623i	$0.0988647\pi$
$102$		0			0
$103$		−	13.3352i		−	1.31396i	−0.753908	−	0.656980i	$-0.771833\pi$
$103$		−	13.3352i		−	1.31396i	0.753908	−	0.656980i	$-0.228167\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.06506	+	2.06506i	−0.199637	+	0.199637i	−0.799844	−	0.600208i	$-0.795085\pi$
$107$	−2.06506	+	2.06506i	−0.199637	+	0.199637i	0.600208	+	0.799844i	$0.295085\pi$
$108$		0			0
$109$	−9.84623	+	9.84623i	−0.943098	+	0.943098i	−0.998466	−	0.0553682i	$-0.982367\pi$
$109$	−9.84623	+	9.84623i	−0.943098	+	0.943098i	0.0553682	+	0.998466i	$0.482367\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.82213			0.265484			0.132742	−	0.991151i	$-0.457622\pi$
$113$	2.82213			0.265484			0.132742	+	0.991151i	$0.457622\pi$
$114$		0			0
$115$	−9.03225	−	14.9765i	−0.842262	−	1.39657i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		−	9.04536i		−	0.829187i
$120$		0			0
$121$		−	7.58971i		−	0.689974i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.1620	−	0.640034i	0.998360	−	0.0572464i
$126$		0			0
$127$	−4.95854			−0.439999			−0.219999	−	0.975500i	$-0.570606\pi$
$127$	−4.95854			−0.439999			−0.219999	+	0.975500i	$0.570606\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−9.28233	+	9.28233i	−0.811001	+	0.811001i	−0.984784	−	0.173783i	$-0.944401\pi$
$131$	−9.28233	+	9.28233i	−0.811001	+	0.811001i	0.173783	+	0.984784i	$0.444401\pi$
$132$		0			0
$133$	−3.81139	+	3.81139i	−0.330489	+	0.330489i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	6.60046i		−	0.563916i	−0.959427	−	0.281958i	$-0.909016\pi$
$137$		−	6.60046i		−	0.563916i	0.959427	−	0.281958i	$-0.0909838\pi$
$138$		0			0
$139$	0.376168	−	0.376168i	0.0319062	−	0.0319062i	−0.690974	−	0.722880i	$-0.742818\pi$
$139$	0.376168	−	0.376168i	0.0319062	−	0.0319062i	0.722880	+	0.690974i	$0.242818\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			4.09387i			0.342346i
$144$		0			0
$145$	5.41171	−	21.8578i	0.449418	−	1.81519i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−8.71533	+	8.71533i	−0.713988	+	0.713988i	−0.967367	−	0.253379i	$-0.918458\pi$
$149$	−8.71533	+	8.71533i	−0.713988	+	0.713988i	0.253379	+	0.967367i	$0.418458\pi$
$150$		0			0
$151$	−7.25811			−0.590657			−0.295328	−	0.955396i	$-0.595429\pi$
$151$	−7.25811			−0.590657			−0.295328	+	0.955396i	$0.595429\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.0962941	+	0.0580744i	−0.00773453	+	0.00466465i
$156$		0			0
$157$	−16.0087	−	16.0087i	−1.27764	−	1.27764i	−0.941988	−	0.335647i	$-0.891045\pi$
$157$	−16.0087	−	16.0087i	−1.27764	−	1.27764i	−0.335647	−	0.941988i	$-0.608955\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	23.6956i		−	1.86747i
$162$		0			0
$163$	3.07484	−	3.07484i	0.240840	−	0.240840i	−0.576357	−	0.817198i	$-0.695526\pi$
$163$	3.07484	−	3.07484i	0.240840	−	0.240840i	0.817198	+	0.576357i	$0.195526\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.32858			−0.489720			−0.244860	−	0.969558i	$-0.578742\pi$
$167$	−6.32858			−0.489720			−0.244860	+	0.969558i	$0.578742\pi$
$168$		0			0
$169$		−	8.08553i		−	0.621964i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.51897	−	3.51897i	0.267542	−	0.267542i	−0.560567	−	0.828109i	$-0.689417\pi$
$173$	3.51897	−	3.51897i	0.267542	−	0.267542i	0.828109	+	0.560567i	$0.189417\pi$
$174$		0			0
$175$	13.3979	+	7.06755i	1.01279	+	0.534257i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−6.22219	+	6.22219i	−0.465068	+	0.465068i	−0.900312	−	0.435244i	$-0.856662\pi$
$179$	−6.22219	+	6.22219i	−0.465068	+	0.465068i	0.435244	+	0.900312i	$0.356662\pi$
$180$		0			0
$181$	14.9790	+	14.9790i	1.11338	+	1.11338i	0.992690	+	0.120689i	$0.0385103\pi$
$181$	14.9790	+	14.9790i	1.11338	+	1.11338i	0.120689	+	0.992690i	$0.461490\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−19.1222	−	4.73443i	−1.40590	−	0.348082i
$186$		0			0
$187$	3.89877	+	3.89877i	0.285107	+	0.285107i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	20.4321			1.47842			0.739208	−	0.673477i	$-0.235200\pi$
$191$	20.4321			1.47842			0.739208	+	0.673477i	$0.235200\pi$
$192$		0			0
$193$		−	0.107996i		−	0.00777370i	−0.999992	−	0.00388685i	$-0.998763\pi$
$193$		−	0.107996i		−	0.00777370i	0.999992	−	0.00388685i	$-0.00123723\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	13.3111	+	13.3111i	0.948378	+	0.948378i	0.998731	−	0.0503537i	$-0.0160349\pi$
$197$	13.3111	+	13.3111i	0.948378	+	0.948378i	−0.0503537	+	0.998731i	$0.516035\pi$
$198$		0			0
$199$	27.0544			1.91784			0.958918	−	0.283684i	$-0.0915566\pi$
$199$	27.0544			1.91784			0.958918	+	0.283684i	$0.0915566\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	21.5726	−	21.5726i	1.51410	−	1.51410i
$204$		0			0
$205$	−4.68334	−	7.76552i	−0.327098	−	0.542367i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		−	3.28560i		−	0.227270i
$210$		0			0
$211$	5.20964	+	5.20964i	0.358646	+	0.358646i	0.863314	−	0.504667i	$-0.168385\pi$
$211$	5.20964	+	5.20964i	0.358646	+	0.358646i	−0.504667	+	0.863314i	$0.668385\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−4.70174	+	18.9902i	−0.320656	+	1.29512i
$216$		0			0
$217$	−0.152355			−0.0103425
$218$		0			0
$219$		0			0
$220$		0			0
$221$	4.68027	+	4.68027i	0.314829	+	0.314829i
$222$		0			0
$223$	−8.50474			−0.569519			−0.284760	−	0.958599i	$-0.591914\pi$
$223$	−8.50474			−0.569519			−0.284760	+	0.958599i	$0.591914\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	14.4132	+	14.4132i	0.956639	+	0.956639i	0.999098	−	0.0424594i	$-0.0135193\pi$
$227$	14.4132	+	14.4132i	0.956639	+	0.956639i	−0.0424594	+	0.999098i	$0.513519\pi$
$228$		0			0
$229$	−15.5816	−	15.5816i	−1.02966	−	1.02966i	−0.999546	−	0.0301163i	$-0.990412\pi$
$229$	−15.5816	−	15.5816i	−1.02966	−	1.02966i	−0.0301163	−	0.999546i	$-0.509588\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			17.5226i			1.14794i	0.818875	+	0.573972i	$0.194598\pi$
$233$			17.5226i			1.14794i	−0.818875	+	0.573972i	$0.805402\pi$
$234$		0			0
$235$	−11.2507	+	6.78524i	−0.733916	+	0.442620i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	23.9921			1.55192			0.775960	−	0.630782i	$-0.217266\pi$
$239$	23.9921			1.55192			0.775960	+	0.630782i	$0.217266\pi$
$240$		0			0
$241$	28.5345			1.83807			0.919033	−	0.394181i	$-0.128972\pi$
$241$	28.5345			1.83807			0.919033	+	0.394181i	$0.128972\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.51536	+	4.17076i	0.160700	+	0.266460i
$246$		0			0
$247$		−	3.94419i		−	0.250963i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−0.638332	−	0.638332i	−0.0402912	−	0.0402912i	0.686674	−	0.726965i	$-0.259070\pi$
$251$	−0.638332	−	0.638332i	−0.0402912	−	0.0402912i	−0.726965	+	0.686674i	$0.759070\pi$
$252$		0			0
$253$	10.2134	+	10.2134i	0.642110	+	0.642110i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.32219			−0.394367			−0.197184	−	0.980367i	$-0.563180\pi$
$257$	−6.32219			−0.394367			−0.197184	+	0.980367i	$0.563180\pi$
$258$		0			0
$259$	−18.8728	−	18.8728i	−1.17270	−	1.17270i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.335400			−0.0206817			−0.0103408	−	0.999947i	$-0.503292\pi$
$263$	−0.335400			−0.0206817			−0.0103408	+	0.999947i	$0.503292\pi$
$264$		0			0
$265$	3.34883	−	13.5258i	0.205717	−	0.830885i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	8.03777	+	8.03777i	0.490071	+	0.490071i	0.908329	−	0.418257i	$-0.137359\pi$
$269$	8.03777	+	8.03777i	0.490071	+	0.490071i	−0.418257	+	0.908329i	$0.637359\pi$
$270$		0			0
$271$			28.1406i			1.70942i	0.519105	+	0.854711i	$0.326265\pi$
$271$			28.1406i			1.70942i	−0.519105	+	0.854711i	$0.673735\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−8.82112	+	2.72854i	−0.531934	+	0.164537i
$276$		0			0
$277$	4.06316	−	4.06316i	0.244132	−	0.244132i	−0.574425	−	0.818557i	$-0.694774\pi$
$277$	4.06316	−	4.06316i	0.244132	−	0.244132i	0.818557	+	0.574425i	$0.194774\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.511034			0.0304858			0.0152429	−	0.999884i	$-0.495148\pi$
$281$	0.511034			0.0304858			0.0152429	+	0.999884i	$0.495148\pi$
$282$		0			0
$283$	−13.0685	−	13.0685i	−0.776839	−	0.776839i	0.202453	−	0.979292i	$-0.435109\pi$
$283$	−13.0685	−	13.0685i	−0.776839	−	0.776839i	−0.979292	+	0.202453i	$0.935109\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	12.2865i		−	0.725246i
$288$		0			0
$289$	−8.08553			−0.475620
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−19.3164	−	19.3164i	−1.12848	−	1.12848i	−0.990425	−	0.138054i	$-0.955915\pi$
$293$	−19.3164	−	19.3164i	−1.12848	−	1.12848i	−0.138054	−	0.990425i	$-0.544085\pi$
$294$		0			0
$295$	−6.23753	+	25.1932i	−0.363163	+	1.46681i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	12.2606	+	12.2606i	0.709050	+	0.709050i
$300$		0			0
$301$	−18.7425	+	18.7425i	−1.08030	+	1.08030i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	15.1607	+	3.75360i	0.868098	+	0.214930i
$306$		0			0
$307$	17.1442	−	17.1442i	0.978471	−	0.978471i	−0.0213024	−	0.999773i	$-0.506781\pi$
$307$	17.1442	−	17.1442i	0.978471	−	0.978471i	0.999773	+	0.0213024i	$0.00678126\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		−	21.2420i		−	1.20452i	−0.798299	−	0.602261i	$-0.794267\pi$
$311$		−	21.2420i		−	1.20452i	0.798299	−	0.602261i	$-0.205733\pi$
$312$		0			0
$313$	19.9351			1.12680			0.563400	−	0.826184i	$-0.309493\pi$
$313$	19.9351			1.12680			0.563400	+	0.826184i	$0.309493\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	14.9282	−	14.9282i	0.838450	−	0.838450i	−0.150205	−	0.988655i	$-0.547993\pi$
$317$	14.9282	−	14.9282i	0.838450	−	0.838450i	0.988655	+	0.150205i	$0.0479934\pi$
$318$		0			0
$319$			18.5967i			1.04121i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−3.75623	−	3.75623i	−0.209002	−	0.209002i
$324$		0			0
$325$	−10.5893	+	3.27547i	−0.587388	+	0.181690i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−17.8007			−0.981383
$330$		0			0
$331$	−5.72462	+	5.72462i	−0.314653	+	0.314653i	−0.846709	−	0.532056i	$-0.821420\pi$
$331$	−5.72462	+	5.72462i	−0.314653	+	0.314653i	0.532056	+	0.846709i	$0.321420\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	3.98964	+	0.987785i	0.217977	+	0.0539685i
$336$		0			0
$337$			28.0570i			1.52836i	0.645003	+	0.764180i	$0.276856\pi$
$337$			28.0570i			1.52836i	−0.645003	+	0.764180i	$0.723144\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.0656687	−	0.0656687i	0.00355616	−	0.00355616i
$342$		0			0
$343$		−	14.6080i		−	0.788756i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8.55200	+	8.55200i	−0.459095	+	0.459095i	−0.898358	−	0.439263i	$-0.855240\pi$
$347$	−8.55200	+	8.55200i	−0.459095	+	0.459095i	0.439263	+	0.898358i	$0.355240\pi$
$348$		0			0
$349$	5.51139	−	5.51139i	0.295018	−	0.295018i	−0.544041	−	0.839059i	$-0.683106\pi$
$349$	5.51139	−	5.51139i	0.295018	−	0.295018i	0.839059	+	0.544041i	$0.183106\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−22.2023			−1.18171			−0.590853	−	0.806779i	$-0.701209\pi$
$353$	−22.2023			−1.18171			−0.590853	+	0.806779i	$0.701209\pi$
$354$		0			0
$355$	−26.7471	+	16.1310i	−1.41959	+	0.856146i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	6.73781i		−	0.355608i	−0.984066	−	0.177804i	$-0.943101\pi$
$359$		−	6.73781i		−	0.355608i	0.984066	−	0.177804i	$-0.0568993\pi$
$360$		0			0
$361$		−	15.8345i		−	0.833396i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	4.45569	+	7.38806i	0.233222	+	0.386709i
$366$		0			0
$367$	−7.64267			−0.398944			−0.199472	−	0.979904i	$-0.563923\pi$
$367$	−7.64267			−0.398944			−0.199472	+	0.979904i	$0.563923\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	13.3494	−	13.3494i	0.693065	−	0.693065i
$372$		0			0
$373$	−5.20096	+	5.20096i	−0.269296	+	0.269296i	−0.828816	−	0.559521i	$-0.810985\pi$
$373$	−5.20096	+	5.20096i	−0.269296	+	0.269296i	0.559521	+	0.828816i	$0.310985\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			22.3243i			1.14976i
$378$		0			0
$379$	−7.64201	+	7.64201i	−0.392544	+	0.392544i	−0.875593	−	0.483049i	$-0.839529\pi$
$379$	−7.64201	+	7.64201i	−0.392544	+	0.392544i	0.483049	+	0.875593i	$0.339529\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		−	28.1288i		−	1.43732i	−0.695363	−	0.718658i	$-0.744757\pi$
$383$		−	28.1288i		−	1.43732i	0.695363	−	0.718658i	$-0.255243\pi$
$384$		0			0
$385$	−12.1434	−	3.00655i	−0.618884	−	0.153228i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.26812	+	8.26812i	−0.419210	+	0.419210i	−0.884931	−	0.465721i	$-0.845795\pi$
$389$	−8.26812	+	8.26812i	−0.419210	+	0.419210i	0.465721	+	0.884931i	$0.345795\pi$
$390$		0			0
$391$	23.3527			1.18100
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.05066	−	1.23674i	0.103180	−	0.0622273i
$396$		0			0
$397$	6.70437	+	6.70437i	0.336482	+	0.336482i	0.855042	−	0.518559i	$-0.173531\pi$
$397$	6.70437	+	6.70437i	0.336482	+	0.336482i	−0.518559	+	0.855042i	$0.673531\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	33.5732i		−	1.67657i	−0.545235	−	0.838283i	$-0.683560\pi$
$401$		−	33.5732i		−	1.67657i	0.545235	−	0.838283i	$-0.316440\pi$
$402$		0			0
$403$	0.0788317	−	0.0788317i	0.00392689	−	0.00392689i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	16.2693			0.806438
$408$		0			0
$409$			3.99913i			0.197744i	0.995100	+	0.0988720i	$0.0315234\pi$
$409$			3.99913i			0.197744i	−0.995100	+	0.0988720i	$0.968477\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−24.8646	+	24.8646i	−1.22351	+	1.22351i
$414$		0			0
$415$	5.44538	−	21.9937i	0.267303	−	1.07963i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−18.7540	+	18.7540i	−0.916195	+	0.916195i	−0.996750	−	0.0805555i	$-0.974331\pi$
$419$	−18.7540	+	18.7540i	−0.916195	+	0.916195i	0.0805555	+	0.996750i	$0.474331\pi$
$420$		0			0
$421$	1.12082	+	1.12082i	0.0546255	+	0.0546255i	0.733892	−	0.679266i	$-0.237702\pi$
$421$	1.12082	+	1.12082i	0.0546255	+	0.0546255i	−0.679266	+	0.733892i	$0.737702\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−6.96528	+	13.2040i	−0.337866	+	0.640490i
$426$		0			0
$427$	14.9629	+	14.9629i	0.724106	+	0.724106i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	37.3679			1.79995			0.899975	−	0.435941i	$-0.143584\pi$
$431$	37.3679			1.79995			0.899975	+	0.435941i	$0.143584\pi$
$432$		0			0
$433$			4.89665i			0.235318i	0.993054	+	0.117659i	$0.0375389\pi$
$433$			4.89665i			0.235318i	−0.993054	+	0.117659i	$0.962461\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−9.83997	−	9.83997i	−0.470710	−	0.470710i
$438$		0			0
$439$	−30.8742			−1.47354			−0.736772	−	0.676141i	$-0.763651\pi$
$439$	−30.8742			−1.47354			−0.736772	+	0.676141i	$0.763651\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−21.6532	+	21.6532i	−1.02878	+	1.02878i	−0.0292029	+	0.999574i	$0.509297\pi$
$443$	−21.6532	+	21.6532i	−1.02878	+	1.02878i	−0.999574	+	0.0292029i	$0.990703\pi$
$444$		0			0
$445$	8.78059	+	14.5592i	0.416240	+	0.690174i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			0.573598i			0.0270698i	0.999908	+	0.0135349i	$0.00430842\pi$
$449$			0.573598i			0.0270698i	−0.999908	+	0.0135349i	$0.995692\pi$
$450$		0			0
$451$	5.29577	+	5.29577i	0.249368	+	0.249368i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−14.5775	−	3.60920i	−0.683403	−	0.169202i
$456$		0			0
$457$	−30.6962			−1.43591			−0.717953	−	0.696092i	$-0.754921\pi$
$457$	−30.6962			−1.43591			−0.717953	+	0.696092i	$0.754921\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−3.93792	−	3.93792i	−0.183407	−	0.183407i	0.609431	−	0.792839i	$-0.291398\pi$
$461$	−3.93792	−	3.93792i	−0.183407	−	0.183407i	−0.792839	+	0.609431i	$0.791398\pi$
$462$		0			0
$463$	34.4600			1.60149			0.800746	−	0.599004i	$-0.204437\pi$
$463$	34.4600			1.60149			0.800746	+	0.599004i	$0.204437\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.24171	+	1.24171i	0.0574594	+	0.0574594i	0.735253	−	0.677793i	$-0.237064\pi$
$467$	1.24171	+	1.24171i	0.0574594	+	0.0574594i	−0.677793	+	0.735253i	$0.737064\pi$
$468$		0			0
$469$	3.93759	+	3.93759i	0.181821	+	0.181821i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		−	16.1569i		−	0.742897i
$474$		0			0
$475$	8.49862	−	2.62879i	0.389943	−	0.120617i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−29.6130			−1.35305			−0.676527	−	0.736418i	$-0.736516\pi$
$479$	−29.6130			−1.35305			−0.676527	+	0.736418i	$0.736516\pi$
$480$		0			0
$481$	19.5304			0.890509
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−18.5760	+	11.2031i	−0.843491	+	0.508705i
$486$		0			0
$487$			20.4343i			0.925966i	0.886367	+	0.462983i	$0.153221\pi$
$487$			20.4343i			0.925966i	−0.886367	+	0.462983i	$0.846779\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.49438	−	1.49438i	−0.0674405	−	0.0674405i	0.672582	−	0.740023i	$-0.265185\pi$
$491$	−1.49438	−	1.49438i	−0.0674405	−	0.0674405i	−0.740023	+	0.672582i	$0.765185\pi$
$492$		0			0
$493$	21.2604	+	21.2604i	0.957522	+	0.957522i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−42.3188			−1.89826
$498$		0			0
$499$	7.82960	+	7.82960i	0.350501	+	0.350501i	0.860296	−	0.509795i	$-0.170279\pi$
$499$	7.82960	+	7.82960i	0.350501	+	0.350501i	−0.509795	+	0.860296i	$0.670279\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	6.45561			0.287841			0.143921	−	0.989589i	$-0.454029\pi$
$503$	6.45561			0.287841			0.143921	+	0.989589i	$0.454029\pi$
$504$		0			0
$505$	−19.9448	−	4.93809i	−0.887533	−	0.219742i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	3.08846	+	3.08846i	0.136894	+	0.136894i	0.772233	−	0.635339i	$-0.219140\pi$
$509$	3.08846	+	3.08846i	0.136894	+	0.136894i	−0.635339	+	0.772233i	$0.719140\pi$
$510$		0			0
$511$			11.6892i			0.517102i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−25.5342	+	15.3995i	−1.12517	+	0.678585i
$516$		0			0
$517$	7.67253	−	7.67253i	0.337438	−	0.337438i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	6.66855			0.292155			0.146077	−	0.989273i	$-0.453335\pi$
$521$	6.66855			0.292155			0.146077	+	0.989273i	$0.453335\pi$
$522$		0			0
$523$	−13.2266	−	13.2266i	−0.578361	−	0.578361i	0.356091	−	0.934451i	$-0.384109\pi$
$523$	−13.2266	−	13.2266i	−0.578361	−	0.578361i	−0.934451	+	0.356091i	$0.884109\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	0.150150i		−	0.00654064i
$528$		0			0
$529$	38.1756			1.65981
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6.35728	+	6.35728i	0.275364	+	0.275364i
$534$		0			0
$535$	6.33889	+	1.56943i	0.274054	+	0.0678524i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−2.84429	−	2.84429i	−0.122512	−	0.122512i
$540$		0			0
$541$	21.3672	−	21.3672i	0.918646	−	0.918646i	−0.0782848	−	0.996931i	$-0.524944\pi$
$541$	21.3672	−	21.3672i	0.918646	−	0.918646i	0.996931	+	0.0782848i	$0.0249444\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	30.2239	+	7.48307i	1.29465	+	0.320539i
$546$		0			0
$547$	−14.3033	+	14.3033i	−0.611566	+	0.611566i	−0.943354	−	0.331788i	$-0.892348\pi$
$547$	−14.3033	+	14.3033i	−0.611566	+	0.611566i	0.331788	+	0.943354i	$0.392348\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	17.9168i		−	0.763279i
$552$		0			0
$553$	3.24452			0.137971
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−5.11093	+	5.11093i	−0.216557	+	0.216557i	−0.807046	−	0.590489i	$-0.798935\pi$
$557$	−5.11093	+	5.11093i	−0.216557	+	0.216557i	0.590489	+	0.807046i	$0.298935\pi$
$558$		0			0
$559$		−	19.3955i		−	0.820344i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−14.2208	−	14.2208i	−0.599336	−	0.599336i	0.340800	−	0.940136i	$-0.389302\pi$
$563$	−14.2208	−	14.2208i	−0.599336	−	0.599336i	−0.940136	+	0.340800i	$0.889302\pi$
$564$		0			0
$565$	−3.25900	−	5.40379i	−0.137107	−	0.227339i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.55464			−0.400551			−0.200276	−	0.979740i	$-0.564184\pi$
$569$	−9.55464			−0.400551			−0.200276	+	0.979740i	$0.564184\pi$
$570$		0			0
$571$	23.2036	−	23.2036i	0.971041	−	0.971041i	−0.0285510	−	0.999592i	$-0.509089\pi$
$571$	23.2036	−	23.2036i	0.971041	−	0.971041i	0.999592	+	0.0285510i	$0.00908932\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−18.2465	+	34.5898i	−0.760932	+	1.44249i
$576$		0			0
$577$			40.8559i			1.70085i	0.526095	+	0.850426i	$0.323656\pi$
$577$			40.8559i			1.70085i	−0.526095	+	0.850426i	$0.676344\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	21.7068	−	21.7068i	0.900551	−	0.900551i
$582$		0			0
$583$			11.5078i			0.476606i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−20.0208	+	20.0208i	−0.826345	+	0.826345i	−0.987009	−	0.160664i	$-0.948636\pi$
$587$	−20.0208	+	20.0208i	−0.826345	+	0.826345i	0.160664	+	0.987009i	$0.448636\pi$
$588$		0			0
$589$	−0.0632678	+	0.0632678i	−0.00260690	+	0.00260690i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.595901			0.0244707			0.0122354	−	0.999925i	$-0.496105\pi$
$593$	0.595901			0.0244707			0.0122354	+	0.999925i	$0.496105\pi$
$594$		0			0
$595$	−17.3200	+	10.4456i	−0.710051	+	0.428227i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			26.0628i			1.06490i	0.846462	+	0.532449i	$0.178728\pi$
$599$			26.0628i			1.06490i	−0.846462	+	0.532449i	$0.821272\pi$
$600$		0			0
$601$			38.7272i			1.57971i	0.613291	+	0.789857i	$0.289845\pi$
$601$			38.7272i			1.57971i	−0.613291	+	0.789857i	$0.710155\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−14.5327	+	8.76461i	−0.590840	+	0.356332i
$606$		0			0
$607$	−40.5499			−1.64587			−0.822934	−	0.568136i	$-0.807665\pi$
$607$	−40.5499			−1.64587			−0.822934	+	0.568136i	$0.807665\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	9.21047	−	9.21047i	0.372616	−	0.372616i
$612$		0			0
$613$	−5.91500	+	5.91500i	−0.238905	+	0.238905i	−0.816396	−	0.577492i	$-0.804032\pi$
$613$	−5.91500	+	5.91500i	−0.238905	+	0.238905i	0.577492	+	0.816396i	$0.304032\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	37.5004i		−	1.50971i	−0.655893	−	0.754854i	$-0.727708\pi$
$617$		−	37.5004i		−	1.50971i	0.655893	−	0.754854i	$-0.272292\pi$
$618$		0			0
$619$	19.2329	−	19.2329i	0.773034	−	0.773034i	−0.205602	−	0.978636i	$-0.565915\pi$
$619$	19.2329	−	19.2329i	0.773034	−	0.773034i	0.978636	+	0.205602i	$0.0659152\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$			23.0354i			0.922892i
$624$		0			0
$625$	−14.1154	−	20.6338i	−0.564617	−	0.825353i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	18.5997	−	18.5997i	0.741618	−	0.741618i
$630$		0			0
$631$	46.9373			1.86855			0.934273	−	0.356559i	$-0.116050\pi$
$631$	46.9373			1.86855			0.934273	+	0.356559i	$0.116050\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	5.72612	+	9.49457i	0.227234	+	0.376781i
$636$		0			0
$637$	−3.41441	−	3.41441i	−0.135284	−	0.135284i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			8.84689i			0.349431i	0.984619	+	0.174716i	$0.0559006\pi$
$641$			8.84689i			0.349431i	−0.984619	+	0.174716i	$0.944099\pi$
$642$		0			0
$643$	−18.7263	+	18.7263i	−0.738491	+	0.738491i	−0.972286	−	0.233795i	$-0.924886\pi$
$643$	−18.7263	+	18.7263i	−0.738491	+	0.738491i	0.233795	+	0.972286i	$0.424886\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−32.7789			−1.28867			−0.644335	−	0.764744i	$-0.722866\pi$
$647$	−32.7789			−1.28867			−0.644335	+	0.764744i	$0.722866\pi$
$648$		0			0
$649$		−	21.4345i		−	0.841378i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.54050	+	1.54050i	−0.0602843	+	0.0602843i	−0.736606	−	0.676322i	$-0.763573\pi$
$653$	−1.54050	+	1.54050i	−0.0602843	+	0.0602843i	0.676322	+	0.736606i	$0.263573\pi$
$654$		0			0
$655$	28.4930	+	7.05451i	1.11331	+	0.275643i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−6.00170	+	6.00170i	−0.233793	+	0.233793i	−0.814274	−	0.580481i	$-0.802865\pi$
$659$	−6.00170	+	6.00170i	−0.233793	+	0.233793i	0.580481	+	0.814274i	$0.302865\pi$
$660$		0			0
$661$	5.39733	+	5.39733i	0.209932	+	0.209932i	0.804239	−	0.594307i	$-0.202573\pi$
$661$	5.39733	+	5.39733i	0.209932	+	0.209932i	−0.594307	+	0.804239i	$0.702573\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	11.6994	+	2.89663i	0.453684	+	0.112326i
$666$		0			0
$667$	55.6947	+	55.6947i	2.15651	+	2.15651i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−12.8988			−0.497952
$672$		0			0
$673$		−	0.683677i		−	0.0263538i	−0.999913	−	0.0131769i	$-0.995806\pi$
$673$		−	0.683677i		−	0.0263538i	0.999913	−	0.0131769i	$-0.00419446\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	20.9613	+	20.9613i	0.805610	+	0.805610i	0.983966	−	0.178356i	$-0.0570779\pi$
$677$	20.9613	+	20.9613i	0.805610	+	0.805610i	−0.178356	+	0.983966i	$0.557078\pi$
$678$		0			0
$679$	−29.3905			−1.12791
$680$		0			0
$681$		0			0
$682$		0			0
$683$	9.01650	−	9.01650i	0.345007	−	0.345007i	−0.513239	−	0.858246i	$-0.671555\pi$
$683$	9.01650	−	9.01650i	0.345007	−	0.345007i	0.858246	+	0.513239i	$0.171555\pi$
$684$		0			0
$685$	−12.6385	+	7.62222i	−0.482893	+	0.291230i
$686$		0			0
$687$		0			0
$688$		0			0
$689$			13.8145i			0.526292i
$690$		0			0
$691$	11.0043	+	11.0043i	0.418623	+	0.418623i	0.884729	−	0.466106i	$-0.154343\pi$
$691$	11.0043	+	11.0043i	0.418623	+	0.418623i	−0.466106	+	0.884729i	$0.654343\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.15468	−	0.285886i	−0.0437997	−	0.0108443i
$696$		0			0
$697$	12.1087			0.458648
$698$		0			0
$699$		0			0
$700$		0			0
$701$	24.8888	+	24.8888i	0.940038	+	0.940038i	0.998301	−	0.0582634i	$-0.0185563\pi$
$701$	24.8888	+	24.8888i	0.940038	+	0.940038i	−0.0582634	+	0.998301i	$0.518556\pi$
$702$		0			0
$703$	−15.6745			−0.591173
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−19.6846	−	19.6846i	−0.740317	−	0.740317i
$708$		0			0
$709$	12.7063	+	12.7063i	0.477196	+	0.477196i	0.904234	−	0.427038i	$-0.140443\pi$
$709$	12.7063	+	12.7063i	0.477196	+	0.477196i	−0.427038	+	0.904234i	$0.640443\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	0.393339i		−	0.0147307i
$714$		0			0
$715$	7.83891	−	4.72760i	0.293159	−	0.176802i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.74421			−0.0650482			−0.0325241	−	0.999471i	$-0.510355\pi$
$719$	−1.74421			−0.0650482			−0.0325241	+	0.999471i	$0.510355\pi$
$720$		0			0
$721$	−40.3998			−1.50457
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−48.1025	+	14.8790i	−1.78648	+	0.552594i
$726$		0			0
$727$		−	2.82244i		−	0.104679i	−0.998629	−	0.0523393i	$-0.983332\pi$
$727$		−	2.82244i		−	0.104679i	0.998629	−	0.0523393i	$-0.0166677\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−18.4713	−	18.4713i	−0.683184	−	0.683184i
$732$		0			0
$733$	7.06892	+	7.06892i	0.261097	+	0.261097i	0.825500	−	0.564403i	$-0.190894\pi$
$733$	7.06892	+	7.06892i	0.261097	+	0.261097i	−0.564403	+	0.825500i	$0.690894\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.39440			−0.125034
$738$		0			0
$739$	−0.328385	−	0.328385i	−0.0120798	−	0.0120798i	0.701041	−	0.713121i	$-0.252719\pi$
$739$	−0.328385	−	0.328385i	−0.0120798	−	0.0120798i	−0.713121	+	0.701041i	$0.752719\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−35.2559			−1.29341			−0.646707	−	0.762739i	$-0.723854\pi$
$743$	−35.2559			−1.29341			−0.646707	+	0.762739i	$0.723854\pi$
$744$		0			0
$745$	26.7525	+	6.62359i	0.980137	+	0.242670i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	6.25619	+	6.25619i	0.228596	+	0.228596i
$750$		0			0
$751$		−	36.1388i		−	1.31872i	−0.751826	−	0.659362i	$-0.770827\pi$
$751$		−	36.1388i		−	1.31872i	0.751826	−	0.659362i	$-0.229173\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	8.38167	+	13.8978i	0.305040	+	0.505792i
$756$		0			0
$757$	15.0827	−	15.0827i	0.548188	−	0.548188i	−0.377728	−	0.925917i	$-0.623295\pi$
$757$	15.0827	−	15.0827i	0.548188	−	0.548188i	0.925917	+	0.377728i	$0.123295\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	27.3466			0.991312			0.495656	−	0.868519i	$-0.334928\pi$
$761$	27.3466			0.991312			0.495656	+	0.868519i	$0.334928\pi$
$762$		0			0
$763$	29.8296	+	29.8296i	1.07991	+	1.07991i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	25.7310i		−	0.929091i
$768$		0			0
$769$	−15.0021			−0.540989			−0.270494	−	0.962722i	$-0.587187\pi$
$769$	−15.0021			−0.540989			−0.270494	+	0.962722i	$0.587187\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−13.7968	−	13.7968i	−0.496236	−	0.496236i	0.414028	−	0.910264i	$-0.364121\pi$
$773$	−13.7968	−	13.7968i	−0.496236	−	0.496236i	−0.910264	+	0.414028i	$0.864121\pi$
$774$		0			0
$775$	0.222401	+	0.117319i	0.00798888	+	0.00421423i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−5.10215	−	5.10215i	−0.182803	−	0.182803i
$780$		0			0
$781$	18.2404	−	18.2404i	0.652695	−	0.652695i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−12.1665	+	49.1403i	−0.434242	+	1.75389i
$786$		0			0
$787$	29.8134	−	29.8134i	1.06273	−	1.06273i	0.0648379	−	0.997896i	$-0.479347\pi$
$787$	29.8134	−	29.8134i	1.06273	−	1.06273i	0.997896	−	0.0648379i	$-0.0206530\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	8.54978i		−	0.303995i
$792$		0			0
$793$	−15.4843			−0.549863
$794$		0			0
$795$		0			0
$796$		0			0
$797$	24.9525	−	24.9525i	0.883864	−	0.883864i	−0.110061	−	0.993925i	$-0.535105\pi$
$797$	24.9525	−	24.9525i	0.883864	−	0.883864i	0.993925	+	0.110061i	$0.0351047\pi$
$798$		0			0
$799$		−	17.5431i		−	0.620630i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.03836	−	5.03836i	−0.177800	−	0.177800i
$804$		0			0
$805$	−45.3721	+	27.3637i	−1.59916	+	0.964442i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	22.1769			0.779697			0.389848	−	0.920879i	$-0.372527\pi$
$809$	22.1769			0.779697			0.389848	+	0.920879i	$0.372527\pi$
$810$		0			0
$811$	−27.8631	+	27.8631i	−0.978404	+	0.978404i	−0.999772	−	0.0213673i	$-0.993198\pi$
$811$	−27.8631	+	27.8631i	−0.978404	+	0.978404i	0.0213673	+	0.999772i	$0.493198\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−9.43853	−	2.33686i	−0.330617	−	0.0818567i
$816$		0			0
$817$			15.5662i			0.544594i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	30.2046	−	30.2046i	1.05415	−	1.05415i	0.0557017	−	0.998447i	$-0.482260\pi$
$821$	30.2046	−	30.2046i	1.05415	−	1.05415i	0.998447	−	0.0557017i	$-0.0177396\pi$
$822$		0			0
$823$			12.8080i			0.446457i	0.974766	+	0.223229i	$0.0716596\pi$
$823$			12.8080i			0.446457i	−0.974766	+	0.223229i	$0.928340\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−21.4283	+	21.4283i	−0.745135	+	0.745135i	−0.973561	−	0.228426i	$-0.926642\pi$
$827$	−21.4283	+	21.4283i	−0.745135	+	0.745135i	0.228426	+	0.973561i	$0.426642\pi$
$828$		0			0
$829$	−17.4113	+	17.4113i	−0.604718	+	0.604718i	−0.941561	−	0.336843i	$-0.890641\pi$
$829$	−17.4113	+	17.4113i	−0.604718	+	0.604718i	0.336843	+	0.941561i	$0.390641\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−6.50340			−0.225329
$834$		0			0
$835$	7.30824	+	12.1179i	0.252912	+	0.419358i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			36.5655i			1.26238i	0.775628	+	0.631190i	$0.217433\pi$
$839$			36.5655i			1.26238i	−0.775628	+	0.631190i	$0.782567\pi$
$840$		0			0
$841$			72.4096i			2.49688i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−15.4821	+	9.33718i	−0.532601	+	0.321209i
$846$		0			0
$847$	−22.9934			−0.790063
$848$		0			0
$849$		0			0
$850$		0			0
$851$	48.7244	−	48.7244i	1.67025	−	1.67025i
$852$		0			0
$853$	−26.8053	+	26.8053i	−0.917795	+	0.917795i	−0.996869	−	0.0790740i	$-0.974804\pi$
$853$	−26.8053	+	26.8053i	−0.917795	+	0.917795i	0.0790740	+	0.996869i	$0.474804\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			9.52133i			0.325243i	0.986689	+	0.162621i	$0.0519949\pi$
$857$			9.52133i			0.325243i	−0.986689	+	0.162621i	$0.948005\pi$
$858$		0			0
$859$	6.51000	−	6.51000i	0.222118	−	0.222118i	−0.587272	−	0.809390i	$-0.699798\pi$
$859$	6.51000	−	6.51000i	0.222118	−	0.222118i	0.809390	+	0.587272i	$0.199798\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			42.9889i			1.46336i	0.681648	+	0.731680i	$0.261263\pi$
$863$			42.9889i			1.46336i	−0.681648	+	0.731680i	$0.738737\pi$
$864$		0			0
$865$	−10.8018	−	2.67439i	−0.367272	−	0.0909321i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.39847	+	1.39847i	−0.0474398	+	0.0474398i
$870$		0			0
$871$	−4.07480			−0.138069
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.93901	−	33.8159i	−0.0655507	−	1.14318i
$876$		0			0
$877$	−18.5212	−	18.5212i	−0.625417	−	0.625417i	0.321494	−	0.946911i	$-0.395815\pi$
$877$	−18.5212	−	18.5212i	−0.625417	−	0.625417i	−0.946911	+	0.321494i	$0.895815\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			12.3100i			0.414735i	0.978263	+	0.207368i	$0.0664896\pi$
$881$			12.3100i			0.414735i	−0.978263	+	0.207368i	$0.933510\pi$
$882$		0			0
$883$	−6.84210	+	6.84210i	−0.230255	+	0.230255i	−0.812799	−	0.582544i	$-0.802057\pi$
$883$	−6.84210	+	6.84210i	−0.230255	+	0.230255i	0.582544	+	0.812799i	$0.302057\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	26.1330			0.877461			0.438730	−	0.898619i	$-0.355428\pi$
$887$	26.1330			0.877461			0.438730	+	0.898619i	$0.355428\pi$
$888$		0			0
$889$			15.0221i			0.503826i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−7.39202	+	7.39202i	−0.247365	+	0.247365i
$894$		0			0
$895$	19.0996	+	4.72882i	0.638429	+	0.158067i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.358098	−	0.358098i	0.0119433	−	0.0119433i
$900$		0			0
$901$	13.1562	+	13.1562i	0.438297	+	0.438297i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	11.3839	−	45.9794i	0.378415	−	1.52841i
$906$		0			0
$907$	−19.0593	−	19.0593i	−0.632853	−	0.632853i	0.315930	−	0.948783i	$-0.397684\pi$
$907$	−19.0593	−	19.0593i	−0.632853	−	0.632853i	−0.948783	+	0.315930i	$0.897684\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−33.6231			−1.11398			−0.556992	−	0.830518i	$-0.688045\pi$
$911$	−33.6231			−1.11398			−0.556992	+	0.830518i	$0.688045\pi$
$912$		0			0
$913$			18.7124i			0.619289i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	28.1213	+	28.1213i	0.928647	+	0.928647i
$918$		0			0
$919$	0.574098			0.0189377			0.00946887	−	0.999955i	$-0.496986\pi$
$919$	0.574098			0.0189377			0.00946887	+	0.999955i	$0.496986\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	21.8967	−	21.8967i	0.720738	−	0.720738i
$924$		0			0
$925$	13.0169	+	42.0825i	0.427994	+	1.38366i
$926$		0			0
$927$		0			0
$928$		0			0
$929$		−	15.3771i		−	0.504506i	−0.967661	−	0.252253i	$-0.918829\pi$
$929$		−	15.3771i		−	0.504506i	0.967661	−	0.252253i	$-0.0811714\pi$
$930$		0			0
$931$	2.74030	+	2.74030i	0.0898096	+	0.0898096i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.96304	−	11.9677i	0.0969019	−	0.391384i
$936$		0			0
$937$	35.5511			1.16140			0.580702	−	0.814117i	$-0.302778\pi$
$937$	35.5511			1.16140			0.580702	+	0.814117i	$0.302778\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−11.8428	−	11.8428i	−0.386065	−	0.386065i	0.487216	−	0.873281i	$-0.338012\pi$
$941$	−11.8428	−	11.8428i	−0.386065	−	0.386065i	−0.873281	+	0.487216i	$0.838012\pi$
$942$		0			0
$943$	31.7203			1.03296
$944$		0			0
$945$		0			0
$946$		0			0
$947$	28.9882	+	28.9882i	0.941991	+	0.941991i	0.998407	−	0.0564161i	$-0.0179673\pi$
$947$	28.9882	+	28.9882i	0.941991	+	0.941991i	−0.0564161	+	0.998407i	$0.517967\pi$
$948$		0			0
$949$	−6.04828	−	6.04828i	−0.196335	−	0.196335i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	8.85819i		−	0.286945i	−0.989654	−	0.143472i	$-0.954173\pi$
$953$		−	8.85819i		−	0.286945i	0.989654	−	0.143472i	$-0.0458268\pi$
$954$		0			0
$955$	−23.5950	−	39.1233i	−0.763517	−	1.26600i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−19.9964			−0.645719
$960$		0			0
$961$	30.9975			0.999918
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.206789	+	0.124713i	−0.00665679	+	0.00401467i
$966$		0			0
$967$			16.3210i			0.524847i	0.964953	+	0.262424i	$0.0845218\pi$
$967$			16.3210i			0.524847i	−0.964953	+	0.262424i	$0.915478\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	5.74815	+	5.74815i	0.184467	+	0.184467i	0.793299	−	0.608832i	$-0.208362\pi$
$971$	5.74815	+	5.74815i	0.184467	+	0.184467i	−0.608832	+	0.793299i	$0.708362\pi$
$972$		0			0
$973$	−1.13962	−	1.13962i	−0.0365346	−	0.0365346i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−39.0104			−1.24805			−0.624027	−	0.781403i	$-0.714504\pi$
$977$	−39.0104			−1.24805			−0.624027	+	0.781403i	$0.714504\pi$
$978$		0			0
$979$	−9.92881	−	9.92881i	−0.317326	−	0.317326i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	0.0416029			0.00132693			0.000663463	−	1.00000i	$-0.499789\pi$
$983$	0.0416029			0.00132693			0.000663463		1.00000i	$0.499789\pi$
$984$		0			0
$985$	10.1164	−	40.8597i	0.322334	−	1.30190i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−48.3880	−	48.3880i	−1.53865	−	1.53865i
$990$		0			0
$991$			8.76665i			0.278482i	0.990259	+	0.139241i	$0.0444663\pi$
$991$			8.76665i			0.278482i	−0.990259	+	0.139241i	$0.955534\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−31.2424	−	51.8036i	−0.990452	−	1.64228i
$996$		0			0
$997$	29.7206	−	29.7206i	0.941260	−	0.941260i	−0.0571081	−	0.998368i	$-0.518188\pi$
$997$	29.7206	−	29.7206i	0.941260	−	0.941260i	0.998368	+	0.0571081i	$0.0181880\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2880.2.u.a.719.17		96
3.2	odd	2	inner	2880.2.u.a.719.32		96
4.3	odd	2		720.2.u.a.539.10	yes	96
5.4	even	2	inner	2880.2.u.a.719.41		96
12.11	even	2		720.2.u.a.539.39	yes	96
15.14	odd	2	inner	2880.2.u.a.719.8		96
16.3	odd	4	inner	2880.2.u.a.2159.8		96
16.13	even	4		720.2.u.a.179.9	✓	96
20.19	odd	2		720.2.u.a.539.40	yes	96
48.29	odd	4		720.2.u.a.179.40	yes	96
48.35	even	4	inner	2880.2.u.a.2159.41		96
60.59	even	2		720.2.u.a.539.9	yes	96
80.19	odd	4	inner	2880.2.u.a.2159.32		96
80.29	even	4		720.2.u.a.179.39	yes	96
240.29	odd	4		720.2.u.a.179.10	yes	96
240.179	even	4	inner	2880.2.u.a.2159.17		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.9	✓	96	16.13	even	4
720.2.u.a.179.10	yes	96	240.29	odd	4
720.2.u.a.179.39	yes	96	80.29	even	4
720.2.u.a.179.40	yes	96	48.29	odd	4
720.2.u.a.539.9	yes	96	60.59	even	2
720.2.u.a.539.10	yes	96	4.3	odd	2
720.2.u.a.539.39	yes	96	12.11	even	2
720.2.u.a.539.40	yes	96	20.19	odd	2
2880.2.u.a.719.8		96	15.14	odd	2	inner
2880.2.u.a.719.17		96	1.1	even	1	trivial
2880.2.u.a.719.32		96	3.2	odd	2	inner
2880.2.u.a.719.41		96	5.4	even	2	inner
2880.2.u.a.2159.8		96	16.3	odd	4	inner
2880.2.u.a.2159.17		96	240.179	even	4	inner
2880.2.u.a.2159.32		96	80.19	odd	4	inner
2880.2.u.a.2159.41		96	48.35	even	4	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:	\( N \)	\(=\)	\( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2880.u (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.15480 - 1.91479i) q^{5} -3.02955i q^{7} +O(q^{10})\)	\(q+(-1.15480 - 1.91479i) q^{5} -3.02955i q^{7} +(1.30581 + 1.30581i) q^{11} +(1.56756 + 1.56756i) q^{13} +2.98571 q^{17} +(-1.25807 - 1.25807i) q^{19} +7.82148 q^{23} +(-2.33287 + 4.42241i) q^{25} +(7.12073 + 7.12073i) q^{29} -0.0502896i q^{31} +(-5.80096 + 3.49853i) q^{35} +(6.22957 - 6.22957i) q^{37} +4.05554 q^{41} +(-6.18655 - 6.18655i) q^{43} -5.87568i q^{47} -2.17818 q^{49} +(4.40639 + 4.40639i) q^{53} +(0.992408 - 4.00831i) q^{55} +(-8.20735 - 8.20735i) q^{59} +(-4.93899 + 4.93899i) q^{61} +(1.19133 - 4.81176i) q^{65} +(-1.29973 + 1.29973i) q^{67} -13.9687i q^{71} -3.85841 q^{73} +(3.95602 - 3.95602i) q^{77} +1.07096i q^{79} +(7.16503 + 7.16503i) q^{83} +(-3.44790 - 5.71702i) q^{85} -7.60356 q^{89} +(4.74899 - 4.74899i) q^{91} +(-0.956125 + 3.86176i) q^{95} -9.70129i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q + 16 q^{19} - 96 q^{49} - 64 q^{55} - 32 q^{61}+O(q^{100}) \) 96 * q + 16 * q^19 - 96 * q^49 - 64 * q^55 - 32 * q^61

Introduction

L-functions

Modular forms

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