LMFDB - Embedded newform 2880.2.bc.a.593.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2880,2,Mod(593,2880)]

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([0, 3, 2, 3]))

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

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

chi := DirichletCharacter("2880.593");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2880 = 2^{6} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2880.bc (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			593.18
Character	$\chi$	$=$	2880.593
Dual form			2880.2.bc.a.1457.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08017 + 1.95786i) q^{5} +(-0.362166 - 0.362166i) q^{7} +O(q^{10})$	$q+(-1.08017 + 1.95786i) q^{5} +(-0.362166 - 0.362166i) q^{7} +(-1.85406 - 1.85406i) q^{11} -1.51440i q^{13} +(3.56625 + 3.56625i) q^{17} +(3.35279 - 3.35279i) q^{19} +(-2.64988 - 2.64988i) q^{23} +(-2.66645 - 4.22966i) q^{25} +(5.99791 + 5.99791i) q^{29} -8.31489 q^{31} +(1.10027 - 0.317869i) q^{35} +0.772321i q^{37} -7.12884 q^{41} +1.58286 q^{43} +(-4.58352 - 4.58352i) q^{47} -6.73767i q^{49} -2.42535i q^{53} +(5.63270 - 1.62729i) q^{55} +(3.01789 - 3.01789i) q^{59} +(0.217095 + 0.217095i) q^{61} +(2.96498 + 1.63581i) q^{65} +9.02347 q^{67} +13.2107 q^{71} +(7.27328 - 7.27328i) q^{73} +1.34296i q^{77} -17.0786i q^{79} +9.92456 q^{83} +(-10.8344 + 3.13006i) q^{85} +1.26424i q^{89} +(-0.548463 + 0.548463i) q^{91} +(2.94271 + 10.1859i) q^{95} +(4.89778 - 4.89778i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 16 q^{19} - 64 q^{43} + 32 q^{61}+O(q^{100}) $ 96 * q - 16 * q^19 - 64 * q^43 + 32 * q^61

Display 100 coefficients 10 coefficients

Character values

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

$n$	$577$	$641$	$901$	$2431$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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
$5$	−1.08017	+	1.95786i	−0.483068	+	0.875583i
$5$	−1.08017	+	1.95786i	−0.483068	+	0.875583i
$6$		0			0
$7$	−0.362166	−	0.362166i	−0.136886	−	0.136886i	0.635344	−	0.772230i	$-0.280858\pi$
$7$	−0.362166	−	0.362166i	−0.136886	−	0.136886i	−0.772230	+	0.635344i	$0.780858\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.85406	−	1.85406i	−0.559020	−	0.559020i	0.370008	−	0.929028i	$-0.379355\pi$
$11$	−1.85406	−	1.85406i	−0.559020	−	0.559020i	−0.929028	+	0.370008i	$0.879355\pi$
$12$		0			0
$13$		−	1.51440i		−	0.420018i	−0.977699	−	0.210009i	$-0.932651\pi$
$13$		−	1.51440i		−	0.420018i	0.977699	−	0.210009i	$-0.0673494\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.56625	+	3.56625i	0.864942	+	0.864942i	0.991907	−	0.126965i	$-0.0405237\pi$
$17$	3.56625	+	3.56625i	0.864942	+	0.864942i	−0.126965	+	0.991907i	$0.540524\pi$
$18$		0			0
$19$	3.35279	−	3.35279i	0.769184	−	0.769184i	−0.208779	−	0.977963i	$-0.566949\pi$
$19$	3.35279	−	3.35279i	0.769184	−	0.769184i	0.977963	+	0.208779i	$0.0669490\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.64988	−	2.64988i	−0.552538	−	0.552538i	0.374635	−	0.927172i	$-0.377768\pi$
$23$	−2.64988	−	2.64988i	−0.552538	−	0.552538i	−0.927172	+	0.374635i	$0.877768\pi$
$24$		0			0
$25$	−2.66645	−	4.22966i	−0.533290	−	0.845932i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	5.99791	+	5.99791i	1.11378	+	1.11378i	0.992634	+	0.121149i	$0.0386578\pi$
$29$	5.99791	+	5.99791i	1.11378	+	1.11378i	0.121149	+	0.992634i	$0.461342\pi$
$30$		0			0
$31$	−8.31489			−1.49340			−0.746699	−	0.665162i	$-0.768363\pi$
$31$	−8.31489			−1.49340			−0.746699	+	0.665162i	$0.768363\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.10027	−	0.317869i	0.185980	−	0.0537297i
$36$		0			0
$37$			0.772321i			0.126969i	0.997983	+	0.0634844i	$0.0202213\pi$
$37$			0.772321i			0.126969i	−0.997983	+	0.0634844i	$0.979779\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−7.12884			−1.11334			−0.556669	−	0.830735i	$-0.687921\pi$
$41$	−7.12884			−1.11334			−0.556669	+	0.830735i	$0.687921\pi$
$42$		0			0
$43$	1.58286			0.241384			0.120692	−	0.992690i	$-0.461489\pi$
$43$	1.58286			0.241384			0.120692	+	0.992690i	$0.461489\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.58352	−	4.58352i	−0.668575	−	0.668575i	0.288811	−	0.957386i	$-0.406740\pi$
$47$	−4.58352	−	4.58352i	−0.668575	−	0.668575i	−0.957386	+	0.288811i	$0.906740\pi$
$48$		0			0
$49$		−	6.73767i		−	0.962525i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	2.42535i		−	0.333147i	−0.986029	−	0.166574i	$-0.946730\pi$
$53$		−	2.42535i		−	0.333147i	0.986029	−	0.166574i	$-0.0532703\pi$
$54$		0			0
$55$	5.63270	−	1.62729i	0.759513	−	0.219424i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.01789	−	3.01789i	0.392896	−	0.392896i	−0.482822	−	0.875718i	$-0.660388\pi$
$59$	3.01789	−	3.01789i	0.392896	−	0.392896i	0.875718	+	0.482822i	$0.160388\pi$
$60$		0			0
$61$	0.217095	+	0.217095i	0.0277962	+	0.0277962i	0.720868	−	0.693072i	$-0.243743\pi$
$61$	0.217095	+	0.217095i	0.0277962	+	0.0277962i	−0.693072	+	0.720868i	$0.743743\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.96498	+	1.63581i	0.367761	+	0.202897i
$66$		0			0
$67$	9.02347			1.10239			0.551196	−	0.834376i	$-0.314172\pi$
$67$	9.02347			1.10239			0.551196	+	0.834376i	$0.314172\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	13.2107			1.56782			0.783911	−	0.620873i	$-0.213222\pi$
$71$	13.2107			1.56782			0.783911	+	0.620873i	$0.213222\pi$
$72$		0			0
$73$	7.27328	−	7.27328i	0.851274	−	0.851274i	−0.139016	−	0.990290i	$-0.544394\pi$
$73$	7.27328	−	7.27328i	0.851274	−	0.851274i	0.990290	+	0.139016i	$0.0443941\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			1.34296i			0.153044i
$78$		0			0
$79$		−	17.0786i		−	1.92150i	−0.277424	−	0.960748i	$-0.589481\pi$
$79$		−	17.0786i		−	1.92150i	0.277424	−	0.960748i	$-0.410519\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	9.92456			1.08936			0.544681	−	0.838643i	$-0.316651\pi$
$83$	9.92456			1.08936			0.544681	+	0.838643i	$0.316651\pi$
$84$		0			0
$85$	−10.8344	+	3.13006i	−1.17515	+	0.339502i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			1.26424i			0.134009i	0.997753	+	0.0670046i	$0.0213442\pi$
$89$			1.26424i			0.134009i	−0.997753	+	0.0670046i	$0.978656\pi$
$90$		0			0
$91$	−0.548463	+	0.548463i	−0.0574945	+	0.0574945i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.94271	+	10.1859i	0.301916	+	1.04505i
$96$		0			0
$97$	4.89778	−	4.89778i	0.497294	−	0.497294i	−0.413301	−	0.910595i	$-0.635624\pi$
$97$	4.89778	−	4.89778i	0.497294	−	0.497294i	0.910595	+	0.413301i	$0.135624\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.47728	+	5.47728i	0.545010	+	0.545010i	0.924993	−	0.379984i	$-0.124070\pi$
$101$	5.47728	+	5.47728i	0.545010	+	0.545010i	−0.379984	+	0.924993i	$0.624070\pi$
$102$		0			0
$103$	0.273667	−	0.273667i	0.0269652	−	0.0269652i	−0.693496	−	0.720461i	$-0.743930\pi$
$103$	0.273667	−	0.273667i	0.0269652	−	0.0269652i	0.720461	+	0.693496i	$0.243930\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.58441			−0.443192			−0.221596	−	0.975139i	$-0.571127\pi$
$107$	−4.58441			−0.443192			−0.221596	+	0.975139i	$0.571127\pi$
$108$		0			0
$109$	−2.20081	+	2.20081i	−0.210800	+	0.210800i	−0.804607	−	0.593808i	$-0.797624\pi$
$109$	−2.20081	+	2.20081i	−0.210800	+	0.210800i	0.593808	+	0.804607i	$0.297624\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	12.4079	−	12.4079i	1.16724	−	1.16724i	0.184383	−	0.982855i	$-0.440971\pi$
$113$	12.4079	−	12.4079i	1.16724	−	1.16724i	0.982855	−	0.184383i	$-0.0590286\pi$
$114$		0			0
$115$	8.05042	−	2.32577i	0.750706	−	0.216879i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		−	2.58315i		−	0.236797i
$120$		0			0
$121$		−	4.12492i		−	0.374993i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.1613	−	0.651781i	0.998299	−	0.0582971i
$126$		0			0
$127$	2.22776	−	2.22776i	0.197682	−	0.197682i	−0.601324	−	0.799005i	$-0.705360\pi$
$127$	2.22776	−	2.22776i	0.197682	−	0.197682i	0.799005	+	0.601324i	$0.205360\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	10.0412	−	10.0412i	0.877302	−	0.877302i	−0.115952	−	0.993255i	$-0.536992\pi$
$131$	10.0412	−	10.0412i	0.877302	−	0.877302i	0.993255	+	0.115952i	$0.0369920\pi$
$132$		0			0
$133$	−2.42854			−0.210581
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.73665	+	1.73665i	−0.148372	+	0.148372i	−0.777390	−	0.629018i	$-0.783457\pi$
$137$	−1.73665	+	1.73665i	−0.148372	+	0.148372i	0.629018	+	0.777390i	$0.283457\pi$
$138$		0			0
$139$	−1.54095	−	1.54095i	−0.130701	−	0.130701i	0.638730	−	0.769431i	$-0.279460\pi$
$139$	−1.54095	−	1.54095i	−0.130701	−	0.130701i	−0.769431	+	0.638730i	$0.779460\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.80778	+	2.80778i	−0.234799	+	0.234799i
$144$		0			0
$145$	−18.2219	+	5.26430i	−1.51324	+	0.437176i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−11.4570	+	11.4570i	−0.938594	+	0.938594i	−0.998221	−	0.0596263i	$-0.981009\pi$
$149$	−11.4570	+	11.4570i	−0.938594	+	0.938594i	0.0596263	+	0.998221i	$0.481009\pi$
$150$		0			0
$151$			1.38520i			0.112726i	0.998410	+	0.0563629i	$0.0179504\pi$
$151$			1.38520i			0.112726i	−0.998410	+	0.0563629i	$0.982050\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	8.98152	−	16.2794i	0.721413	−	1.30759i
$156$		0			0
$157$	12.3635			0.986715			0.493357	−	0.869827i	$-0.335769\pi$
$157$	12.3635			0.986715			0.493357	+	0.869827i	$0.335769\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			1.91939i			0.151269i
$162$		0			0
$163$			9.31225i			0.729392i	0.931127	+	0.364696i	$0.118827\pi$
$163$			9.31225i			0.729392i	−0.931127	+	0.364696i	$0.881173\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−10.4555	+	10.4555i	−0.809070	+	0.809070i	−0.984493	−	0.175423i	$-0.943871\pi$
$167$	−10.4555	+	10.4555i	−0.809070	+	0.809070i	0.175423	+	0.984493i	$0.443871\pi$
$168$		0			0
$169$	10.7066			0.823585
$170$		0			0
$171$		0			0
$172$		0			0
$173$	24.1540			1.83639			0.918197	−	0.396125i	$-0.129645\pi$
$173$	24.1540			1.83639			0.918197	+	0.396125i	$0.129645\pi$
$174$		0			0
$175$	−0.566141	+	2.49754i	−0.0427962	+	0.188796i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	12.8143	+	12.8143i	0.957786	+	0.957786i	0.999144	−	0.0413580i	$-0.0131684\pi$
$179$	12.8143	+	12.8143i	0.957786	+	0.957786i	−0.0413580	+	0.999144i	$0.513168\pi$
$180$		0			0
$181$	−4.89979	+	4.89979i	−0.364199	+	0.364199i	−0.865356	−	0.501158i	$-0.832908\pi$
$181$	−4.89979	+	4.89979i	−0.364199	+	0.364199i	0.501158	+	0.865356i	$0.332908\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.51210	−	0.834241i	−0.111172	−	0.0613346i
$186$		0			0
$187$		−	13.2241i		−	0.967040i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			24.1257i			1.74567i	0.488013	+	0.872836i	$0.337722\pi$
$191$			24.1257i			1.74567i	−0.488013	+	0.872836i	$0.662278\pi$
$192$		0			0
$193$	−10.3269	−	10.3269i	−0.743348	−	0.743348i	0.229873	−	0.973221i	$-0.426169\pi$
$193$	−10.3269	−	10.3269i	−0.743348	−	0.743348i	−0.973221	+	0.229873i	$0.926169\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	13.3091			0.948231			0.474115	−	0.880463i	$-0.342768\pi$
$197$	13.3091			0.948231			0.474115	+	0.880463i	$0.342768\pi$
$198$		0			0
$199$	11.4590			0.812309			0.406154	−	0.913804i	$-0.366870\pi$
$199$	11.4590			0.812309			0.406154	+	0.913804i	$0.366870\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		−	4.34447i		−	0.304922i
$204$		0			0
$205$	7.70038	−	13.9573i	0.537818	−	0.974819i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−12.4326			−0.859978
$210$		0			0
$211$	−6.69756	−	6.69756i	−0.461079	−	0.461079i	0.437930	−	0.899009i	$-0.355712\pi$
$211$	−6.69756	−	6.69756i	−0.461079	−	0.461079i	−0.899009	+	0.437930i	$0.855712\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.70976	+	3.09903i	−0.116605	+	0.211352i
$216$		0			0
$217$	3.01137	+	3.01137i	0.204425	+	0.204425i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	5.40071	−	5.40071i	0.363291	−	0.363291i
$222$		0			0
$223$	−18.2154	−	18.2154i	−1.21979	−	1.21979i	−0.967704	−	0.252088i	$-0.918883\pi$
$223$	−18.2154	−	18.2154i	−1.21979	−	1.21979i	−0.252088	−	0.967704i	$-0.581117\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	9.01336i		−	0.598238i	−0.954216	−	0.299119i	$-0.903307\pi$
$227$		−	9.01336i		−	0.598238i	0.954216	−	0.299119i	$-0.0966927\pi$
$228$		0			0
$229$	−7.34760	−	7.34760i	−0.485543	−	0.485543i	0.421353	−	0.906897i	$-0.361555\pi$
$229$	−7.34760	−	7.34760i	−0.485543	−	0.485543i	−0.906897	+	0.421353i	$0.861555\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−19.5639	−	19.5639i	−1.28167	−	1.28167i	−0.939715	−	0.341959i	$-0.888910\pi$
$233$	−19.5639	−	19.5639i	−1.28167	−	1.28167i	−0.341959	−	0.939715i	$-0.611090\pi$
$234$		0			0
$235$	13.9249	−	4.02291i	0.908360	−	0.262426i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	4.18763			0.270875			0.135438	−	0.990786i	$-0.456756\pi$
$239$	4.18763			0.270875			0.135438	+	0.990786i	$0.456756\pi$
$240$		0			0
$241$	17.0472			1.09811			0.549053	−	0.835787i	$-0.314988\pi$
$241$	17.0472			1.09811			0.549053	+	0.835787i	$0.314988\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	13.1914	+	7.27785i	0.842770	+	0.464965i
$246$		0			0
$247$	−5.07746	−	5.07746i	−0.323071	−	0.323071i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−9.06493	−	9.06493i	−0.572174	−	0.572174i	0.360562	−	0.932735i	$-0.382585\pi$
$251$	−9.06493	−	9.06493i	−0.572174	−	0.572174i	−0.932735	+	0.360562i	$0.882585\pi$
$252$		0			0
$253$			9.82606i			0.617759i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.71994	−	6.71994i	−0.419178	−	0.419178i	0.465742	−	0.884921i	$-0.345787\pi$
$257$	−6.71994	−	6.71994i	−0.419178	−	0.419178i	−0.884921	+	0.465742i	$0.845787\pi$
$258$		0			0
$259$	0.279709	−	0.279709i	0.0173802	−	0.0173802i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.56154	+	2.56154i	0.157951	+	0.157951i	0.781658	−	0.623707i	$-0.214374\pi$
$263$	2.56154	+	2.56154i	0.157951	+	0.157951i	−0.623707	+	0.781658i	$0.714374\pi$
$264$		0			0
$265$	4.74850	+	2.61980i	0.291698	+	0.160933i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−20.2120	−	20.2120i	−1.23235	−	1.23235i	−0.963059	−	0.269290i	$-0.913211\pi$
$269$	−20.2120	−	20.2120i	−1.23235	−	1.23235i	−0.269290	−	0.963059i	$-0.586789\pi$
$270$		0			0
$271$	−4.08473			−0.248129			−0.124065	−	0.992274i	$-0.539593\pi$
$271$	−4.08473			−0.248129			−0.124065	+	0.992274i	$0.539593\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.89828	+	12.7858i	−0.174773	+	0.771013i
$276$		0			0
$277$		−	13.8689i		−	0.833300i	−0.909067	−	0.416650i	$-0.863204\pi$
$277$		−	13.8689i		−	0.833300i	0.909067	−	0.416650i	$-0.136796\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−27.4121			−1.63527			−0.817635	−	0.575738i	$-0.804715\pi$
$281$	−27.4121			−1.63527			−0.817635	+	0.575738i	$0.804715\pi$
$282$		0			0
$283$	32.9362			1.95785			0.978927	−	0.204211i	$-0.0654630\pi$
$283$	32.9362			1.95785			0.978927	+	0.204211i	$0.0654630\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.58182	+	2.58182i	0.152400	+	0.152400i
$288$		0			0
$289$			8.43622i			0.496248i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	10.1833i		−	0.594915i	−0.954735	−	0.297458i	$-0.903861\pi$
$293$		−	10.1833i		−	0.594915i	0.954735	−	0.297458i	$-0.0961387\pi$
$294$		0			0
$295$	2.64877	+	9.16846i	0.154218	+	0.533809i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−4.01297	+	4.01297i	−0.232076	+	0.232076i
$300$		0			0
$301$	−0.573259	−	0.573259i	−0.0330421	−	0.0330421i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.659543	+	0.190542i	−0.0377653	+	0.0109104i
$306$		0			0
$307$	−28.5134			−1.62734			−0.813672	−	0.581324i	$-0.802535\pi$
$307$	−28.5134			−1.62734			−0.813672	+	0.581324i	$0.802535\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−19.1978			−1.08861			−0.544303	−	0.838889i	$-0.683206\pi$
$311$	−19.1978			−1.08861			−0.544303	+	0.838889i	$0.683206\pi$
$312$		0			0
$313$	19.7270	−	19.7270i	1.11503	−	1.11503i	0.122574	−	0.992459i	$-0.460885\pi$
$313$	19.7270	−	19.7270i	1.11503	−	1.11503i	0.992459	−	0.122574i	$-0.0391149\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	5.63768i		−	0.316644i	−0.987388	−	0.158322i	$-0.949392\pi$
$317$		−	5.63768i		−	0.316644i	0.987388	−	0.158322i	$-0.0506084\pi$
$318$		0			0
$319$		−	22.2410i		−	1.24525i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	23.9138			1.33060
$324$		0			0
$325$	−6.40539	+	4.03807i	−0.355307	+	0.223992i
$326$		0			0
$327$		0			0
$328$		0			0
$329$			3.31999i			0.183037i
$330$		0			0
$331$	−23.0111	+	23.0111i	−1.26480	+	1.26480i	−0.316064	+	0.948738i	$0.602361\pi$
$331$	−23.0111	+	23.0111i	−1.26480	+	1.26480i	−0.948738	+	0.316064i	$0.897639\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−9.74691	+	17.6667i	−0.532530	+	0.965235i
$336$		0			0
$337$	6.46596	−	6.46596i	0.352223	−	0.352223i	−0.508713	−	0.860936i	$-0.669879\pi$
$337$	6.46596	−	6.46596i	0.352223	−	0.352223i	0.860936	+	0.508713i	$0.169879\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	15.4163	+	15.4163i	0.834840	+	0.834840i
$342$		0			0
$343$	−4.97532	+	4.97532i	−0.268642	+	0.268642i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−30.1418			−1.61809			−0.809047	−	0.587744i	$-0.800016\pi$
$347$	−30.1418			−1.61809			−0.809047	+	0.587744i	$0.800016\pi$
$348$		0			0
$349$	−14.4081	+	14.4081i	−0.771248	+	0.771248i	−0.978325	−	0.207077i	$-0.933605\pi$
$349$	−14.4081	+	14.4081i	−0.771248	+	0.771248i	0.207077	+	0.978325i	$0.433605\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	4.52186	−	4.52186i	0.240674	−	0.240674i	−0.576455	−	0.817129i	$-0.695564\pi$
$353$	4.52186	−	4.52186i	0.240674	−	0.240674i	0.817129	+	0.576455i	$0.195564\pi$
$354$		0			0
$355$	−14.2698	+	25.8647i	−0.757365	+	1.37276i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			11.8239i			0.624043i	0.950075	+	0.312022i	$0.101006\pi$
$359$			11.8239i			0.624043i	−0.950075	+	0.312022i	$0.898994\pi$
$360$		0			0
$361$		−	3.48245i		−	0.183287i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	6.38369	+	22.0965i	0.334137	+	1.15658i
$366$		0			0
$367$	−20.5027	+	20.5027i	−1.07023	+	1.07023i	−0.0728913	+	0.997340i	$0.523223\pi$
$367$	−20.5027	+	20.5027i	−1.07023	+	1.07023i	−0.997340	+	0.0728913i	$0.976777\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.878378	+	0.878378i	−0.0456031	+	0.0456031i
$372$		0			0
$373$	4.84079			0.250647			0.125323	−	0.992116i	$-0.460003\pi$
$373$	4.84079			0.250647			0.125323	+	0.992116i	$0.460003\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	9.08321	−	9.08321i	0.467809	−	0.467809i
$378$		0			0
$379$	−8.79721	−	8.79721i	−0.451882	−	0.451882i	0.444097	−	0.895979i	$-0.353525\pi$
$379$	−8.79721	−	8.79721i	−0.451882	−	0.451882i	−0.895979	+	0.444097i	$0.853525\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.12453	−	7.12453i	0.364046	−	0.364046i	−0.501254	−	0.865300i	$-0.667128\pi$
$383$	7.12453	−	7.12453i	0.364046	−	0.364046i	0.865300	+	0.501254i	$0.167128\pi$
$384$		0			0
$385$	−2.62932	−	1.45062i	−0.134003	−	0.0739306i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.53897	+	8.53897i	−0.432943	+	0.432943i	−0.889628	−	0.456685i	$-0.849037\pi$
$389$	−8.53897	+	8.53897i	−0.432943	+	0.432943i	0.456685	+	0.889628i	$0.349037\pi$
$390$		0			0
$391$		−	18.9002i		−	0.955826i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	33.4376	+	18.4479i	1.68243	+	0.928213i
$396$		0			0
$397$	31.5285			1.58237			0.791186	−	0.611576i	$-0.209464\pi$
$397$	31.5285			1.58237			0.791186	+	0.611576i	$0.209464\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			20.4491i			1.02118i	0.859824	+	0.510590i	$0.170573\pi$
$401$			20.4491i			1.02118i	−0.859824	+	0.510590i	$0.829427\pi$
$402$		0			0
$403$			12.5920i			0.627255i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.43193	−	1.43193i	0.0709782	−	0.0709782i
$408$		0			0
$409$	4.36468			0.215819			0.107910	−	0.994161i	$-0.465584\pi$
$409$	4.36468			0.215819			0.107910	+	0.994161i	$0.465584\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.18596			−0.107564
$414$		0			0
$415$	−10.7202	+	19.4309i	−0.526236	+	0.953826i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−6.24171	−	6.24171i	−0.304928	−	0.304928i	0.538010	−	0.842938i	$-0.319176\pi$
$419$	−6.24171	−	6.24171i	−0.304928	−	0.304928i	−0.842938	+	0.538010i	$0.819176\pi$
$420$		0			0
$421$	5.64378	−	5.64378i	0.275061	−	0.275061i	−0.556073	−	0.831134i	$-0.687692\pi$
$421$	5.64378	−	5.64378i	0.275061	−	0.275061i	0.831134	+	0.556073i	$0.187692\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	5.57479	−	24.5932i	0.270417	−	1.19295i
$426$		0			0
$427$		−	0.157249i		−	0.00760981i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			16.9626i			0.817057i	0.912745	+	0.408529i	$0.133958\pi$
$431$			16.9626i			0.817057i	−0.912745	+	0.408529i	$0.866042\pi$
$432$		0			0
$433$	17.0788	+	17.0788i	0.820755	+	0.820755i	0.986216	−	0.165461i	$-0.0529112\pi$
$433$	17.0788	+	17.0788i	0.820755	+	0.820755i	−0.165461	+	0.986216i	$0.552911\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−17.7690			−0.850006
$438$		0			0
$439$	−38.4848			−1.83678			−0.918390	−	0.395677i	$-0.870510\pi$
$439$	−38.4848			−1.83678			−0.918390	+	0.395677i	$0.870510\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	37.2931i		−	1.77185i	−0.463831	−	0.885924i	$-0.653525\pi$
$443$		−	37.2931i		−	1.77185i	0.463831	−	0.885924i	$-0.346475\pi$
$444$		0			0
$445$	−2.47521	−	1.36560i	−0.117336	−	0.0647355i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−15.0829			−0.711808			−0.355904	−	0.934523i	$-0.615827\pi$
$449$	−15.0829			−0.711808			−0.355904	+	0.934523i	$0.615827\pi$
$450$		0			0
$451$	13.2173	+	13.2173i	0.622378	+	0.622378i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.481380	−	1.66625i	−0.0225675	−	0.0781150i
$456$		0			0
$457$	−13.9465	−	13.9465i	−0.652390	−	0.652390i	0.301178	−	0.953568i	$-0.402620\pi$
$457$	−13.9465	−	13.9465i	−0.652390	−	0.652390i	−0.953568	+	0.301178i	$0.902620\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	16.3095	−	16.3095i	0.759608	−	0.759608i	−0.216643	−	0.976251i	$-0.569511\pi$
$461$	16.3095	−	16.3095i	0.759608	−	0.759608i	0.976251	+	0.216643i	$0.0695106\pi$
$462$		0			0
$463$	26.2641	+	26.2641i	1.22059	+	1.22059i	0.967421	+	0.253174i	$0.0814744\pi$
$463$	26.2641	+	26.2641i	1.22059	+	1.22059i	0.253174	+	0.967421i	$0.418526\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	14.3650i		−	0.664732i	−0.943150	−	0.332366i	$-0.892153\pi$
$467$		−	14.3650i		−	0.664732i	0.943150	−	0.332366i	$-0.107847\pi$
$468$		0			0
$469$	−3.26799	−	3.26799i	−0.150902	−	0.150902i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.93472	−	2.93472i	−0.134939	−	0.134939i
$474$		0			0
$475$	−23.1212	−	5.24112i	−1.06088	−	0.240479i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−20.0609			−0.916607			−0.458304	−	0.888796i	$-0.651543\pi$
$479$	−20.0609			−0.916607			−0.458304	+	0.888796i	$0.651543\pi$
$480$		0			0
$481$	1.16960			0.0533292
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.29873	+	14.8796i	0.195195	+	0.675649i
$486$		0			0
$487$	16.1733	+	16.1733i	0.732883	+	0.732883i	0.971190	−	0.238307i	$-0.0765924\pi$
$487$	16.1733	+	16.1733i	0.732883	+	0.732883i	−0.238307	+	0.971190i	$0.576592\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−11.1262	−	11.1262i	−0.502119	−	0.502119i	0.409977	−	0.912096i	$-0.365537\pi$
$491$	−11.1262	−	11.1262i	−0.502119	−	0.502119i	−0.912096	+	0.409977i	$0.865537\pi$
$492$		0			0
$493$			42.7800i			1.92671i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.78447	−	4.78447i	−0.214613	−	0.214613i
$498$		0			0
$499$	23.7067	−	23.7067i	1.06126	−	1.06126i	0.0632583	−	0.997997i	$-0.479851\pi$
$499$	23.7067	−	23.7067i	1.06126	−	1.06126i	0.997997	−	0.0632583i	$-0.0201492\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−11.1346	−	11.1346i	−0.496467	−	0.496467i	0.413869	−	0.910336i	$-0.364177\pi$
$503$	−11.1346	−	11.1346i	−0.496467	−	0.496467i	−0.910336	+	0.413869i	$0.864177\pi$
$504$		0			0
$505$	−16.6402	+	4.80735i	−0.740478	+	0.213924i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−18.4704	−	18.4704i	−0.818685	−	0.818685i	0.167233	−	0.985917i	$-0.446517\pi$
$509$	−18.4704	−	18.4704i	−0.818685	−	0.818685i	−0.985917	+	0.167233i	$0.946517\pi$
$510$		0			0
$511$	−5.26827			−0.233055
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.240195	+	0.831411i	0.0105842	+	0.0366363i
$516$		0			0
$517$			16.9962i			0.747494i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	22.8882			1.00275			0.501376	−	0.865230i	$-0.332827\pi$
$521$	22.8882			1.00275			0.501376	+	0.865230i	$0.332827\pi$
$522$		0			0
$523$	40.4094			1.76698			0.883490	−	0.468449i	$-0.155187\pi$
$523$	40.4094			1.76698			0.883490	+	0.468449i	$0.155187\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−29.6530	−	29.6530i	−1.29170	−	1.29170i
$528$		0			0
$529$		−	8.95630i		−	0.389404i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			10.7959i			0.467622i
$534$		0			0
$535$	4.95196	−	8.97565i	0.214092	−	0.388051i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−12.4920	+	12.4920i	−0.538071	+	0.538071i
$540$		0			0
$541$	−12.6510	−	12.6510i	−0.543909	−	0.543909i	0.380763	−	0.924673i	$-0.375661\pi$
$541$	−12.6510	−	12.6510i	−0.543909	−	0.543909i	−0.924673	+	0.380763i	$0.875661\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.93163	−	6.68614i	−0.0827419	−	0.286403i
$546$		0			0
$547$	8.50044			0.363453			0.181726	−	0.983349i	$-0.441831\pi$
$547$	8.50044			0.363453			0.181726	+	0.983349i	$0.441831\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	40.2195			1.71341
$552$		0			0
$553$	−6.18530	+	6.18530i	−0.263026	+	0.263026i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			5.28315i			0.223854i	0.993716	+	0.111927i	$0.0357023\pi$
$557$			5.28315i			0.223854i	−0.993716	+	0.111927i	$0.964298\pi$
$558$		0			0
$559$		−	2.39708i		−	0.101386i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−19.8102			−0.834899			−0.417449	−	0.908700i	$-0.637076\pi$
$563$	−19.8102			−0.834899			−0.417449	+	0.908700i	$0.637076\pi$
$564$		0			0
$565$	10.8903	+	37.6957i	0.458158	+	1.58587i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	12.2122i		−	0.511961i	−0.966682	−	0.255980i	$-0.917602\pi$
$569$		−	12.2122i		−	0.511961i	0.966682	−	0.255980i	$-0.0823983\pi$
$570$		0			0
$571$	−11.0934	+	11.0934i	−0.464242	+	0.464242i	−0.900043	−	0.435801i	$-0.856465\pi$
$571$	−11.0934	+	11.0934i	−0.464242	+	0.464242i	0.435801	+	0.900043i	$0.356465\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−4.14231	+	18.2739i	−0.172746	+	0.762072i
$576$		0			0
$577$	−5.66081	+	5.66081i	−0.235663	+	0.235663i	−0.815051	−	0.579389i	$-0.803291\pi$
$577$	−5.66081	+	5.66081i	−0.235663	+	0.235663i	0.579389	+	0.815051i	$0.303291\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−3.59434	−	3.59434i	−0.149118	−	0.149118i
$582$		0			0
$583$	−4.49674	+	4.49674i	−0.186236	+	0.186236i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	16.3961			0.676740			0.338370	−	0.941013i	$-0.390124\pi$
$587$	16.3961			0.676740			0.338370	+	0.941013i	$0.390124\pi$
$588$		0			0
$589$	−27.8781	+	27.8781i	−1.14870	+	1.14870i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	16.9707	−	16.9707i	0.696903	−	0.696903i	−0.266838	−	0.963741i	$-0.585979\pi$
$593$	16.9707	−	16.9707i	0.696903	−	0.696903i	0.963741	+	0.266838i	$0.0859790\pi$
$594$		0			0
$595$	5.05745	+	2.79024i	0.207335	+	0.114389i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	24.4210i		−	0.997816i	−0.866655	−	0.498908i	$-0.833735\pi$
$599$		−	24.4210i		−	0.997816i	0.866655	−	0.498908i	$-0.166265\pi$
$600$		0			0
$601$			32.5990i			1.32974i	0.746958	+	0.664871i	$0.231514\pi$
$601$			32.5990i			1.32974i	−0.746958	+	0.664871i	$0.768486\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	8.07603	+	4.45563i	0.328337	+	0.181147i
$606$		0			0
$607$	6.26309	−	6.26309i	0.254211	−	0.254211i	−0.568484	−	0.822695i	$-0.692470\pi$
$607$	6.26309	−	6.26309i	0.254211	−	0.254211i	0.822695	+	0.568484i	$0.192470\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−6.94127	+	6.94127i	−0.280814	+	0.280814i
$612$		0			0
$613$	−13.9662			−0.564088			−0.282044	−	0.959402i	$-0.591012\pi$
$613$	−13.9662			−0.564088			−0.282044	+	0.959402i	$0.591012\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−27.8561	+	27.8561i	−1.12144	+	1.12144i	−0.129921	+	0.991524i	$0.541472\pi$
$617$	−27.8561	+	27.8561i	−1.12144	+	1.12144i	−0.991524	+	0.129921i	$0.958528\pi$
$618$		0			0
$619$	23.1419	+	23.1419i	0.930153	+	0.930153i	0.997715	−	0.0675623i	$-0.0215222\pi$
$619$	23.1419	+	23.1419i	0.930153	+	0.930153i	−0.0675623	+	0.997715i	$0.521522\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.457865	−	0.457865i	0.0183440	−	0.0183440i
$624$		0			0
$625$	−10.7801	+	22.5564i	−0.431203	+	0.902255i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.75429	+	2.75429i	−0.109821	+	0.109821i
$630$		0			0
$631$		−	14.8755i		−	0.592183i	−0.955160	−	0.296091i	$-0.904317\pi$
$631$		−	14.8755i		−	0.592183i	0.955160	−	0.296091i	$-0.0956833\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.95528	+	6.76801i	0.0775930	+	0.268580i
$636$		0			0
$637$	−10.2035			−0.404278
$638$		0			0
$639$		0			0
$640$		0			0
$641$			43.7307i			1.72726i	0.504128	+	0.863629i	$0.331814\pi$
$641$			43.7307i			1.72726i	−0.504128	+	0.863629i	$0.668186\pi$
$642$		0			0
$643$			34.6284i			1.36561i	0.730601	+	0.682805i	$0.239240\pi$
$643$			34.6284i			1.36561i	−0.730601	+	0.682805i	$0.760760\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	16.3206	−	16.3206i	0.641630	−	0.641630i	−0.309326	−	0.950956i	$-0.600103\pi$
$647$	16.3206	−	16.3206i	0.641630	−	0.641630i	0.950956	+	0.309326i	$0.100103\pi$
$648$		0			0
$649$	−11.1907			−0.439274
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−27.4520			−1.07428			−0.537140	−	0.843493i	$-0.680495\pi$
$653$	−27.4520			−1.07428			−0.537140	+	0.843493i	$0.680495\pi$
$654$		0			0
$655$	8.81304	+	30.5055i	0.344354	+	1.19195i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−5.99705	−	5.99705i	−0.233612	−	0.233612i	0.580587	−	0.814199i	$-0.302823\pi$
$659$	−5.99705	−	5.99705i	−0.233612	−	0.233612i	−0.814199	+	0.580587i	$0.802823\pi$
$660$		0			0
$661$	−15.4561	+	15.4561i	−0.601172	+	0.601172i	−0.940624	−	0.339451i	$-0.889759\pi$
$661$	−15.4561	+	15.4561i	−0.601172	+	0.601172i	0.339451	+	0.940624i	$0.389759\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.62324	−	4.75474i	0.101725	−	0.184381i
$666$		0			0
$667$		−	31.7874i		−	1.23081i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	0.805015i		−	0.0310773i
$672$		0			0
$673$	14.4033	+	14.4033i	0.555205	+	0.555205i	0.927938	−	0.372734i	$-0.121579\pi$
$673$	14.4033	+	14.4033i	0.555205	+	0.555205i	−0.372734	+	0.927938i	$0.621579\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−28.7267			−1.10406			−0.552028	−	0.833825i	$-0.686146\pi$
$677$	−28.7267			−1.10406			−0.552028	+	0.833825i	$0.686146\pi$
$678$		0			0
$679$	−3.54762			−0.136145
$680$		0			0
$681$		0			0
$682$		0			0
$683$			30.2996i			1.15938i	0.814837	+	0.579691i	$0.196827\pi$
$683$			30.2996i			1.15938i	−0.814837	+	0.579691i	$0.803173\pi$
$684$		0			0
$685$	−1.52424	−	5.27600i	−0.0582382	−	0.201586i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−3.67294			−0.139928
$690$		0			0
$691$	1.95585	+	1.95585i	0.0744042	+	0.0744042i	0.743330	−	0.668925i	$-0.233245\pi$
$691$	1.95585	+	1.95585i	0.0744042	+	0.0744042i	−0.668925	+	0.743330i	$0.733245\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.68145	−	1.35247i	0.177577	−	0.0513022i
$696$		0			0
$697$	−25.4232	−	25.4232i	−0.962972	−	0.962972i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	0.725238	−	0.725238i	0.0273919	−	0.0273919i	−0.693278	−	0.720670i	$-0.743834\pi$
$701$	0.725238	−	0.725238i	0.0273919	−	0.0273919i	0.720670	+	0.693278i	$0.243834\pi$
$702$		0			0
$703$	2.58943	+	2.58943i	0.0976624	+	0.0976624i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	3.96737i		−	0.149208i
$708$		0			0
$709$	22.8775	+	22.8775i	0.859184	+	0.859184i	0.991242	−	0.132058i	$-0.0421584\pi$
$709$	22.8775	+	22.8775i	0.859184	+	0.859184i	−0.132058	+	0.991242i	$0.542158\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	22.0334	+	22.0334i	0.825159	+	0.825159i
$714$		0			0
$715$	−2.46436	−	8.53015i	−0.0921619	−	0.319009i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−5.23101			−0.195084			−0.0975419	−	0.995231i	$-0.531098\pi$
$719$	−5.23101			−0.195084			−0.0975419	+	0.995231i	$0.531098\pi$
$720$		0			0
$721$	−0.198226			−0.00738232
$722$		0			0
$723$		0			0
$724$		0			0
$725$	9.37598	−	41.3622i	0.348215	−	1.53615i
$726$		0			0
$727$	−10.5393	−	10.5393i	−0.390880	−	0.390880i	0.484121	−	0.875001i	$-0.339139\pi$
$727$	−10.5393	−	10.5393i	−0.390880	−	0.390880i	−0.875001	+	0.484121i	$0.839139\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	5.64487	+	5.64487i	0.208783	+	0.208783i
$732$		0			0
$733$			13.1946i			0.487354i	0.969856	+	0.243677i	$0.0783537\pi$
$733$			13.1946i			0.487354i	−0.969856	+	0.243677i	$0.921646\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−16.7301	−	16.7301i	−0.616259	−	0.616259i
$738$		0			0
$739$	−32.6768	+	32.6768i	−1.20204	+	1.20204i	−0.228491	+	0.973546i	$0.573379\pi$
$739$	−32.6768	+	32.6768i	−1.20204	+	1.20204i	−0.973546	+	0.228491i	$0.926621\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−19.4098	−	19.4098i	−0.712077	−	0.712077i	0.254892	−	0.966969i	$-0.417960\pi$
$743$	−19.4098	−	19.4098i	−0.712077	−	0.712077i	−0.966969	+	0.254892i	$0.917960\pi$
$744$		0			0
$745$	−10.0557	−	34.8068i	−0.368412	−	1.27522i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.66032	+	1.66032i	0.0606667	+	0.0606667i
$750$		0			0
$751$	32.8768			1.19969			0.599845	−	0.800116i	$-0.295229\pi$
$751$	32.8768			1.19969			0.599845	+	0.800116i	$0.295229\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−2.71203	−	1.49625i	−0.0987007	−	0.0544542i
$756$		0			0
$757$		−	44.9820i		−	1.63490i	−0.576000	−	0.817449i	$-0.695387\pi$
$757$		−	44.9820i		−	1.63490i	0.576000	−	0.817449i	$-0.304613\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−26.7335			−0.969087			−0.484544	−	0.874767i	$-0.661014\pi$
$761$	−26.7335			−0.969087			−0.484544	+	0.874767i	$0.661014\pi$
$762$		0			0
$763$	1.59412			0.0577110
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.57029	−	4.57029i	−0.165023	−	0.165023i
$768$		0			0
$769$			10.5330i			0.379829i	0.981801	+	0.189914i	$0.0608210\pi$
$769$			10.5330i			0.379829i	−0.981801	+	0.189914i	$0.939179\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	28.7615i		−	1.03448i	−0.855840	−	0.517240i	$-0.826959\pi$
$773$		−	28.7615i		−	1.03448i	0.855840	−	0.517240i	$-0.173041\pi$
$774$		0			0
$775$	22.1713	+	35.1692i	0.796415	+	1.26331i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−23.9015	+	23.9015i	−0.856361	+	0.856361i
$780$		0			0
$781$	−24.4934	−	24.4934i	−0.876444	−	0.876444i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−13.3547	+	24.2060i	−0.476650	+	0.863951i
$786$		0			0
$787$	39.3480			1.40261			0.701303	−	0.712863i	$-0.252602\pi$
$787$	39.3480			1.40261			0.701303	+	0.712863i	$0.252602\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−8.98744			−0.319557
$792$		0			0
$793$	0.328768	−	0.328768i	0.0116749	−	0.0116749i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			24.3267i			0.861695i	0.902425	+	0.430847i	$0.141785\pi$
$797$			24.3267i			0.861695i	−0.902425	+	0.430847i	$0.858215\pi$
$798$		0			0
$799$		−	32.6919i		−	1.15656i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−26.9702			−0.951758
$804$		0			0
$805$	−3.75790	−	2.07327i	−0.132449	−	0.0730733i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			18.5597i			0.652524i	0.945279	+	0.326262i	$0.105789\pi$
$809$			18.5597i			0.652524i	−0.945279	+	0.326262i	$0.894211\pi$
$810$		0			0
$811$	−3.25704	+	3.25704i	−0.114370	+	0.114370i	−0.761976	−	0.647606i	$-0.775770\pi$
$811$	−3.25704	+	3.25704i	−0.114370	+	0.114370i	0.647606	+	0.761976i	$0.275770\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−18.2321	−	10.0588i	−0.638643	−	0.352346i
$816$		0			0
$817$	5.30701	−	5.30701i	0.185669	−	0.185669i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.189177	+	0.189177i	0.00660233	+	0.00660233i	0.710400	−	0.703798i	$-0.248514\pi$
$821$	0.189177	+	0.189177i	0.00660233	+	0.00660233i	−0.703798	+	0.710400i	$0.748514\pi$
$822$		0			0
$823$	−19.3237	+	19.3237i	−0.673583	+	0.673583i	−0.958540	−	0.284957i	$-0.908021\pi$
$823$	−19.3237	+	19.3237i	−0.673583	+	0.673583i	0.284957	+	0.958540i	$0.408021\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	44.5774			1.55011			0.775054	−	0.631895i	$-0.217723\pi$
$827$	44.5774			1.55011			0.775054	+	0.631895i	$0.217723\pi$
$828$		0			0
$829$	14.1544	−	14.1544i	0.491604	−	0.491604i	−0.417208	−	0.908811i	$-0.636991\pi$
$829$	14.1544	−	14.1544i	0.491604	−	0.491604i	0.908811	+	0.417208i	$0.136991\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	24.0282	−	24.0282i	0.832528	−	0.832528i
$834$		0			0
$835$	−9.17668	−	31.7642i	−0.317572	−	1.09924i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			11.9406i			0.412235i	0.978527	+	0.206118i	$0.0660830\pi$
$839$			11.9406i			0.412235i	−0.978527	+	0.206118i	$0.933917\pi$
$840$		0			0
$841$			42.9497i			1.48103i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−11.5650	+	20.9621i	−0.397848	+	0.721117i
$846$		0			0
$847$	−1.49391	+	1.49391i	−0.0513312	+	0.0513312i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	2.04656	−	2.04656i	0.0701551	−	0.0701551i
$852$		0			0
$853$	44.9230			1.53814			0.769068	−	0.639167i	$-0.220721\pi$
$853$	44.9230			1.53814			0.769068	+	0.639167i	$0.220721\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	10.7749	−	10.7749i	0.368063	−	0.368063i	−0.498708	−	0.866770i	$-0.666192\pi$
$857$	10.7749	−	10.7749i	0.368063	−	0.368063i	0.866770	+	0.498708i	$0.166192\pi$
$858$		0			0
$859$	3.96044	+	3.96044i	0.135128	+	0.135128i	0.771436	−	0.636307i	$-0.219539\pi$
$859$	3.96044	+	3.96044i	0.135128	+	0.135128i	−0.636307	+	0.771436i	$0.719539\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	36.9900	−	36.9900i	1.25915	−	1.25915i	0.307655	−	0.951498i	$-0.400456\pi$
$863$	36.9900	−	36.9900i	1.25915	−	1.25915i	0.951498	−	0.307655i	$-0.0995442\pi$
$864$		0			0
$865$	−26.0905	+	47.2902i	−0.887103	+	1.60791i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−31.6648	+	31.6648i	−1.07415	+	1.07415i
$870$		0			0
$871$		−	13.6651i		−	0.463025i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−4.27831	−	3.80620i	−0.144633	−	0.128673i
$876$		0			0
$877$	−37.0532			−1.25120			−0.625600	−	0.780144i	$-0.715146\pi$
$877$	−37.0532			−1.25120			−0.625600	+	0.780144i	$0.715146\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			27.1095i			0.913344i	0.889635	+	0.456672i	$0.150959\pi$
$881$			27.1095i			0.913344i	−0.889635	+	0.456672i	$0.849041\pi$
$882$		0			0
$883$		−	29.1226i		−	0.980053i	−0.871707	−	0.490027i	$-0.836987\pi$
$883$		−	29.1226i		−	0.980053i	0.871707	−	0.490027i	$-0.163013\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−13.4239	+	13.4239i	−0.450729	+	0.450729i	−0.895597	−	0.444867i	$-0.853251\pi$
$887$	−13.4239	+	13.4239i	−0.450729	+	0.450729i	0.444867	+	0.895597i	$0.353251\pi$
$888$		0			0
$889$	−1.61364			−0.0541197
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−30.7352			−1.02851
$894$		0			0
$895$	−38.9303	+	11.2470i	−1.30130	+	0.375945i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−49.8719	−	49.8719i	−1.66332	−	1.66332i
$900$		0			0
$901$	8.64939	−	8.64939i	0.288153	−	0.288153i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−4.30050	−	14.8857i	−0.142953	−	0.494819i
$906$		0			0
$907$			32.5221i			1.07988i	0.841704	+	0.539939i	$0.181553\pi$
$907$			32.5221i			1.07988i	−0.841704	+	0.539939i	$0.818447\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			3.98309i			0.131966i	0.997821	+	0.0659828i	$0.0210182\pi$
$911$			3.98309i			0.131966i	−0.997821	+	0.0659828i	$0.978982\pi$
$912$		0			0
$913$	−18.4007	−	18.4007i	−0.608975	−	0.608975i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−7.27315			−0.240181
$918$		0			0
$919$	−18.0099			−0.594092			−0.297046	−	0.954863i	$-0.596002\pi$
$919$	−18.0099			−0.594092			−0.297046	+	0.954863i	$0.596002\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	20.0063i		−	0.658514i
$924$		0			0
$925$	3.26666	−	2.05936i	0.107407	−	0.0677113i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	12.9904			0.426203			0.213101	−	0.977030i	$-0.431644\pi$
$929$	12.9904			0.426203			0.213101	+	0.977030i	$0.431644\pi$
$930$		0			0
$931$	−22.5900	−	22.5900i	−0.740358	−	0.740358i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	25.8909	+	14.2843i	0.846723	+	0.467146i
$936$		0			0
$937$	11.0673	+	11.0673i	0.361553	+	0.361553i	0.864384	−	0.502832i	$-0.167708\pi$
$937$	11.0673	+	11.0673i	0.361553	+	0.361553i	−0.502832	+	0.864384i	$0.667708\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−5.70322	+	5.70322i	−0.185920	+	0.185920i	−0.793929	−	0.608010i	$-0.791968\pi$
$941$	−5.70322	+	5.70322i	−0.185920	+	0.185920i	0.608010	+	0.793929i	$0.291968\pi$
$942$		0			0
$943$	18.8905	+	18.8905i	0.615161	+	0.615161i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			9.31138i			0.302579i	0.988489	+	0.151290i	$0.0483426\pi$
$947$			9.31138i			0.302579i	−0.988489	+	0.151290i	$0.951657\pi$
$948$		0			0
$949$	−11.0146	−	11.0146i	−0.357550	−	0.357550i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	31.7609	+	31.7609i	1.02884	+	1.02884i	0.999572	+	0.0292650i	$0.00931668\pi$
$953$	31.7609	+	31.7609i	1.02884	+	1.02884i	0.0292650	+	0.999572i	$0.490683\pi$
$954$		0			0
$955$	−47.2348	−	26.0599i	−1.52848	−	0.843279i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.25791			0.0406201
$960$		0			0
$961$	38.1375			1.23024
$962$		0			0
$963$		0			0
$964$		0			0
$965$	31.3736	−	9.06383i	1.00995	−	0.291775i
$966$		0			0
$967$	6.72087	+	6.72087i	0.216129	+	0.216129i	0.806865	−	0.590736i	$-0.201163\pi$
$967$	6.72087	+	6.72087i	0.216129	+	0.216129i	−0.590736	+	0.806865i	$0.701163\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−7.35810	−	7.35810i	−0.236133	−	0.236133i	0.579114	−	0.815247i	$-0.303399\pi$
$971$	−7.35810	−	7.35810i	−0.236133	−	0.236133i	−0.815247	+	0.579114i	$0.803399\pi$
$972$		0			0
$973$			1.11616i			0.0357823i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−29.7902	−	29.7902i	−0.953074	−	0.953074i	0.0458733	−	0.998947i	$-0.485393\pi$
$977$	−29.7902	−	29.7902i	−0.953074	−	0.953074i	−0.998947	+	0.0458733i	$0.985393\pi$
$978$		0			0
$979$	2.34398	−	2.34398i	0.0749138	−	0.0749138i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−17.6693	−	17.6693i	−0.563562	−	0.563562i	0.366755	−	0.930317i	$-0.380469\pi$
$983$	−17.6693	−	17.6693i	−0.563562	−	0.563562i	−0.930317	+	0.366755i	$0.880469\pi$
$984$		0			0
$985$	−14.3761	+	26.0573i	−0.458060	+	0.830255i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.19439	−	4.19439i	−0.133374	−	0.133374i
$990$		0			0
$991$	39.6611			1.25988			0.629938	−	0.776645i	$-0.283080\pi$
$991$	39.6611			1.25988			0.629938	+	0.776645i	$0.283080\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−12.3777	+	22.4352i	−0.392400	+	0.711244i
$996$		0			0
$997$		−	19.7882i		−	0.626699i	−0.949638	−	0.313350i	$-0.898549\pi$
$997$		−	19.7882i		−	0.626699i	0.949638	−	0.313350i	$-0.101451\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2880.2.bc.a.593.18		96
3.2	odd	2	inner	2880.2.bc.a.593.31		96
4.3	odd	2		720.2.bc.a.413.30	yes	96
5.2	odd	4		2880.2.bg.a.17.42		96
12.11	even	2		720.2.bc.a.413.19	yes	96
15.2	even	4		2880.2.bg.a.17.7		96
16.5	even	4		2880.2.bg.a.2033.7		96
16.11	odd	4		720.2.bg.a.53.6	yes	96
20.7	even	4		720.2.bg.a.557.43	yes	96
48.5	odd	4		2880.2.bg.a.2033.42		96
48.11	even	4		720.2.bg.a.53.43	yes	96
60.47	odd	4		720.2.bg.a.557.6	yes	96
80.27	even	4		720.2.bc.a.197.19	✓	96
80.37	odd	4	inner	2880.2.bc.a.1457.31		96
240.107	odd	4		720.2.bc.a.197.30	yes	96
240.197	even	4	inner	2880.2.bc.a.1457.18		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.bc.a.197.19	✓	96	80.27	even	4
720.2.bc.a.197.30	yes	96	240.107	odd	4
720.2.bc.a.413.19	yes	96	12.11	even	2
720.2.bc.a.413.30	yes	96	4.3	odd	2
720.2.bg.a.53.6	yes	96	16.11	odd	4
720.2.bg.a.53.43	yes	96	48.11	even	4
720.2.bg.a.557.6	yes	96	60.47	odd	4
720.2.bg.a.557.43	yes	96	20.7	even	4
2880.2.bc.a.593.18		96	1.1	even	1	trivial
2880.2.bc.a.593.31		96	3.2	odd	2	inner
2880.2.bc.a.1457.18		96	240.197	even	4	inner
2880.2.bc.a.1457.31		96	80.37	odd	4	inner
2880.2.bg.a.17.7		96	15.2	even	4
2880.2.bg.a.17.42		96	5.2	odd	4
2880.2.bg.a.2033.7		96	16.5	even	4
2880.2.bg.a.2033.42		96	48.5	odd	4

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.bc (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.08017 + 1.95786i) q^{5} +(-0.362166 - 0.362166i) q^{7} +O(q^{10})\)	\(q+(-1.08017 + 1.95786i) q^{5} +(-0.362166 - 0.362166i) q^{7} +(-1.85406 - 1.85406i) q^{11} -1.51440i q^{13} +(3.56625 + 3.56625i) q^{17} +(3.35279 - 3.35279i) q^{19} +(-2.64988 - 2.64988i) q^{23} +(-2.66645 - 4.22966i) q^{25} +(5.99791 + 5.99791i) q^{29} -8.31489 q^{31} +(1.10027 - 0.317869i) q^{35} +0.772321i q^{37} -7.12884 q^{41} +1.58286 q^{43} +(-4.58352 - 4.58352i) q^{47} -6.73767i q^{49} -2.42535i q^{53} +(5.63270 - 1.62729i) q^{55} +(3.01789 - 3.01789i) q^{59} +(0.217095 + 0.217095i) q^{61} +(2.96498 + 1.63581i) q^{65} +9.02347 q^{67} +13.2107 q^{71} +(7.27328 - 7.27328i) q^{73} +1.34296i q^{77} -17.0786i q^{79} +9.92456 q^{83} +(-10.8344 + 3.13006i) q^{85} +1.26424i q^{89} +(-0.548463 + 0.548463i) q^{91} +(2.94271 + 10.1859i) q^{95} +(4.89778 - 4.89778i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 16 q^{19} - 64 q^{43} + 32 q^{61}+O(q^{100}) \) 96 * q - 16 * q^19 - 64 * q^43 + 32 * q^61

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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