LMFDB - Embedded newform 3024.2.q.h.2305.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(2305,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 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("3024.2305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.q (of order $3$, 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:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2305.2
Root			$0.500000 - 1.41036i$ of defining polynomial
Character	$\chi$	$=$	3024.2305
Dual form			3024.2.q.h.2881.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.880438 + 1.52496i) q^{5} +(0.710533 + 2.54856i) q^{7} +O(q^{10})$	$q+(0.880438 + 1.52496i) q^{5} +(0.710533 + 2.54856i) q^{7} +(-3.06238 + 5.30420i) q^{11} +(-0.380438 + 0.658939i) q^{13} +(3.42107 + 5.92546i) q^{17} +(-0.971410 + 1.68253i) q^{19} +(0.210533 + 0.364654i) q^{23} +(0.949657 - 1.64485i) q^{25} +(-0.732287 - 1.26836i) q^{29} -7.70370 q^{31} +(-3.26088 + 3.32738i) q^{35} +(1.44282 - 2.49904i) q^{37} +(3.47141 - 6.01266i) q^{41} +(-4.33009 - 7.49994i) q^{43} +1.66019 q^{47} +(-5.99028 + 3.62167i) q^{49} +(0.112725 + 0.195246i) q^{53} -10.7850 q^{55} +1.98633 q^{59} -10.3502 q^{61} -1.33981 q^{65} -6.78495 q^{67} +10.7850 q^{71} +(0.153353 + 0.265616i) q^{73} +(-15.6940 - 4.03584i) q^{77} +13.4451 q^{79} +(-1.56238 - 2.70612i) q^{83} +(-6.02408 + 10.4340i) q^{85} +(-1.30150 + 2.25427i) q^{89} +(-1.94966 - 0.501371i) q^{91} -3.42107 q^{95} +(-1.81806 - 3.14897i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 5 q^{5} - 4 q^{7}+O(q^{10}) $ 6 * q + 5 * q^5 - 4 * q^7	$ 6 q + 5 q^{5} - 4 q^{7} - q^{11} - 2 q^{13} + 4 q^{17} + 3 q^{19} - 7 q^{23} - 2 q^{25} + 5 q^{29} - 28 q^{31} - 19 q^{35} - 9 q^{37} + 12 q^{41} - 18 q^{43} - 6 q^{47} - 12 q^{49} - 9 q^{53} - 14 q^{55} - 8 q^{59} - 8 q^{61} - 24 q^{65} + 10 q^{67} + 14 q^{71} - 25 q^{73} - 52 q^{77} + 14 q^{79} + 8 q^{83} + 14 q^{85} + 9 q^{89} - 4 q^{91} - 4 q^{95} - 28 q^{97}+O(q^{100}) $ 6 * q + 5 * q^5 - 4 * q^7 - q^11 - 2 * q^13 + 4 * q^17 + 3 * q^19 - 7 * q^23 - 2 * q^25 + 5 * q^29 - 28 * q^31 - 19 * q^35 - 9 * q^37 + 12 * q^41 - 18 * q^43 - 6 * q^47 - 12 * q^49 - 9 * q^53 - 14 * q^55 - 8 * q^59 - 8 * q^61 - 24 * q^65 + 10 * q^67 + 14 * q^71 - 25 * q^73 - 52 * q^77 + 14 * q^79 + 8 * q^83 + 14 * q^85 + 9 * q^89 - 4 * q^91 - 4 * q^95 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	0.880438	+	1.52496i	0.393744	+	0.681985i	0.992940	−	0.118618i	$-0.0378463\pi$
$5$	0.880438	+	1.52496i	0.393744	+	0.681985i	−0.599196	+	0.800602i	$0.704513\pi$
$6$		0			0
$7$	0.710533	+	2.54856i	0.268556	+	0.963264i
$7$	0.710533	+	2.54856i	0.268556	+	0.963264i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.06238	+	5.30420i	−0.923343	+	1.59928i	−0.129138	+	0.991627i	$0.541221\pi$
$11$	−3.06238	+	5.30420i	−0.923343	+	1.59928i	−0.794205	+	0.607650i	$0.792112\pi$
$12$		0			0
$13$	−0.380438	+	0.658939i	−0.105515	+	0.182757i	−0.913948	−	0.405831i	$-0.866982\pi$
$13$	−0.380438	+	0.658939i	−0.105515	+	0.182757i	0.808434	+	0.588587i	$0.200316\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.42107	+	5.92546i	0.829731	+	1.43714i	0.898250	+	0.439486i	$0.144839\pi$
$17$	3.42107	+	5.92546i	0.829731	+	1.43714i	−0.0685191	+	0.997650i	$0.521827\pi$
$18$		0			0
$19$	−0.971410	+	1.68253i	−0.222857	+	0.385999i	−0.955674	−	0.294426i	$-0.904872\pi$
$19$	−0.971410	+	1.68253i	−0.222857	+	0.385999i	0.732818	+	0.680425i	$0.238205\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.210533	+	0.364654i	0.0438992	+	0.0760357i	0.887140	−	0.461500i	$-0.152689\pi$
$23$	0.210533	+	0.364654i	0.0438992	+	0.0760357i	−0.843241	+	0.537536i	$0.819355\pi$
$24$		0			0
$25$	0.949657	−	1.64485i	0.189931	−	0.328971i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.732287	−	1.26836i	−0.135982	−	0.235528i	0.789990	−	0.613120i	$-0.210086\pi$
$29$	−0.732287	−	1.26836i	−0.135982	−	0.235528i	−0.925972	+	0.377592i	$0.876752\pi$
$30$		0			0
$31$	−7.70370			−1.38362			−0.691812	−	0.722077i	$-0.743187\pi$
$31$	−7.70370			−1.38362			−0.691812	+	0.722077i	$0.743187\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.26088	+	3.32738i	−0.551189	+	0.562431i
$36$		0			0
$37$	1.44282	−	2.49904i	0.237198	−	0.410839i	−0.722711	−	0.691150i	$-0.757104\pi$
$37$	1.44282	−	2.49904i	0.237198	−	0.410839i	0.959909	+	0.280311i	$0.0904376\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.47141	−	6.01266i	0.542143	−	0.939020i	−0.456638	−	0.889653i	$-0.650946\pi$
$41$	3.47141	−	6.01266i	0.542143	−	0.939020i	0.998781	−	0.0493667i	$-0.0157203\pi$
$42$		0			0
$43$	−4.33009	−	7.49994i	−0.660333	−	1.14373i	−0.980528	−	0.196379i	$-0.937082\pi$
$43$	−4.33009	−	7.49994i	−0.660333	−	1.14373i	0.320195	−	0.947352i	$-0.396252\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.66019			0.242164			0.121082	−	0.992643i	$-0.461364\pi$
$47$	1.66019			0.242164			0.121082	+	0.992643i	$0.461364\pi$
$48$		0			0
$49$	−5.99028	+	3.62167i	−0.855755	+	0.517381i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.112725	+	0.195246i	0.0154840	+	0.0268190i	0.873664	−	0.486531i	$-0.161738\pi$
$53$	0.112725	+	0.195246i	0.0154840	+	0.0268190i	−0.858180	+	0.513350i	$0.828404\pi$
$54$		0			0
$55$	−10.7850			−1.45424
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.98633			0.258598			0.129299	−	0.991606i	$-0.458727\pi$
$59$	1.98633			0.258598			0.129299	+	0.991606i	$0.458727\pi$
$60$		0			0
$61$	−10.3502			−1.32521			−0.662605	−	0.748969i	$-0.730549\pi$
$61$	−10.3502			−1.32521			−0.662605	+	0.748969i	$0.730549\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.33981			−0.166183
$66$		0			0
$67$	−6.78495			−0.828914			−0.414457	−	0.910069i	$-0.636028\pi$
$67$	−6.78495			−0.828914			−0.414457	+	0.910069i	$0.636028\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	10.7850			1.27994			0.639969	−	0.768401i	$-0.278947\pi$
$71$	10.7850			1.27994			0.639969	+	0.768401i	$0.278947\pi$
$72$		0			0
$73$	0.153353	+	0.265616i	0.0179487	+	0.0310880i	0.874860	−	0.484375i	$-0.160953\pi$
$73$	0.153353	+	0.265616i	0.0179487	+	0.0310880i	−0.856912	+	0.515463i	$0.827620\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−15.6940	−	4.03584i	−1.78850	−	0.459927i
$78$		0			0
$79$	13.4451			1.51270			0.756348	−	0.654169i	$-0.226982\pi$
$79$	13.4451			1.51270			0.756348	+	0.654169i	$0.226982\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.56238	−	2.70612i	−0.171494	−	0.297036i	0.767449	−	0.641110i	$-0.221526\pi$
$83$	−1.56238	−	2.70612i	−0.171494	−	0.297036i	−0.938942	+	0.344075i	$0.888193\pi$
$84$		0			0
$85$	−6.02408	+	10.4340i	−0.653403	+	1.13173i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.30150	+	2.25427i	−0.137959	+	0.238952i	−0.926724	−	0.375743i	$-0.877388\pi$
$89$	−1.30150	+	2.25427i	−0.137959	+	0.238952i	0.788765	+	0.614695i	$0.210721\pi$
$90$		0			0
$91$	−1.94966	−	0.501371i	−0.204380	−	0.0525580i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.42107			−0.350994
$96$		0			0
$97$	−1.81806	−	3.14897i	−0.184596	−	0.319729i	0.758845	−	0.651272i	$-0.225764\pi$
$97$	−1.81806	−	3.14897i	−0.184596	−	0.319729i	−0.943440	+	0.331543i	$0.892431\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.00520	+	6.93721i	−0.398532	+	0.690278i	−0.993545	−	0.113438i	$-0.963814\pi$
$101$	−4.00520	+	6.93721i	−0.398532	+	0.690278i	0.595013	+	0.803716i	$0.297147\pi$
$102$		0			0
$103$	−3.41423	−	5.91362i	−0.336414	−	0.582686i	0.647341	−	0.762200i	$-0.275881\pi$
$103$	−3.41423	−	5.91362i	−0.336414	−	0.582686i	−0.983755	+	0.179514i	$0.942548\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.77292	−	3.07078i	0.171394	−	0.296863i	−0.767513	−	0.641033i	$-0.778506\pi$
$107$	1.77292	−	3.07078i	0.171394	−	0.296863i	0.938908	+	0.344170i	$0.111840\pi$
$108$		0			0
$109$	0.351848	+	0.609419i	0.0337010	+	0.0583718i	0.882384	−	0.470530i	$-0.155937\pi$
$109$	0.351848	+	0.609419i	0.0337010	+	0.0583718i	−0.848683	+	0.528902i	$0.822604\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.25116	+	7.36323i	−0.399916	+	0.692674i	−0.993715	−	0.111939i	$-0.964294\pi$
$113$	−4.25116	+	7.36323i	−0.399916	+	0.692674i	0.593799	+	0.804613i	$0.297627\pi$
$114$		0			0
$115$	−0.370723	+	0.642111i	−0.0345701	+	0.0598772i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−12.6706	+	12.9290i	−1.16151	+	1.18520i
$120$		0			0
$121$	−13.2564	−	22.9607i	−1.20512	−	2.08734i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	12.1488			1.08663
$126$		0			0
$127$	18.9532			1.68183			0.840913	−	0.541170i	$-0.182018\pi$
$127$	18.9532			1.68183			0.840913	+	0.541170i	$0.182018\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.64652	+	6.31595i	0.318598	+	0.551827i	0.980196	−	0.198031i	$-0.0634548\pi$
$131$	3.64652	+	6.31595i	0.318598	+	0.551827i	−0.661598	+	0.749859i	$0.730121\pi$
$132$		0			0
$133$	−4.97825	−	1.28020i	−0.431669	−	0.111007i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.09097	+	7.08577i	−0.349515	+	0.605378i	−0.986163	−	0.165776i	$-0.946987\pi$
$137$	−4.09097	+	7.08577i	−0.349515	+	0.605378i	0.636648	+	0.771154i	$0.280320\pi$
$138$		0			0
$139$	6.23229	−	10.7946i	0.528616	−	0.915589i	−0.470828	−	0.882225i	$-0.656045\pi$
$139$	6.23229	−	10.7946i	0.528616	−	0.915589i	0.999443	−	0.0333640i	$-0.0106220\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.33009	−	4.03584i	−0.194852	−	0.337494i
$144$		0			0
$145$	1.28947	−	2.23342i	0.107084	−	0.185476i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.41423	+	7.64567i	0.361628	+	0.626358i	0.988229	−	0.152982i	$-0.0488878\pi$
$149$	4.41423	+	7.64567i	0.361628	+	0.626358i	−0.626601	+	0.779340i	$0.715554\pi$
$150$		0			0
$151$	−7.49316	+	12.9785i	−0.609785	+	1.05618i	0.381491	+	0.924373i	$0.375411\pi$
$151$	−7.49316	+	12.9785i	−0.609785	+	1.05618i	−0.991276	+	0.131806i	$0.957922\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.78263	−	11.7479i	−0.544794	−	0.943611i
$156$		0			0
$157$	18.9806			1.51481			0.757407	−	0.652943i	$-0.226466\pi$
$157$	18.9806			1.51481			0.757407	+	0.652943i	$0.226466\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.779752	+	0.795655i	−0.0614530	+	0.0627064i
$162$		0			0
$163$	7.51887	−	13.0231i	0.588924	−	1.02005i	−0.405450	−	0.914117i	$-0.632885\pi$
$163$	7.51887	−	13.0231i	0.588924	−	1.02005i	0.994374	−	0.105929i	$-0.0337815\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.572097	−	0.990901i	0.0442702	−	0.0766782i	−0.843041	−	0.537849i	$-0.819237\pi$
$167$	0.572097	−	0.990901i	0.0442702	−	0.0766782i	0.887311	+	0.461171i	$0.152570\pi$
$168$		0			0
$169$	6.21053	+	10.7570i	0.477733	+	0.827458i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.497677			−0.0378377			−0.0189188	−	0.999821i	$-0.506022\pi$
$173$	−0.497677			−0.0378377			−0.0189188	+	0.999821i	$0.506022\pi$
$174$		0			0
$175$	4.86677	+	1.25153i	0.367893	+	0.0946068i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.41423	+	7.64567i	0.329935	+	0.571464i	0.982499	−	0.186270i	$-0.0596398\pi$
$179$	4.41423	+	7.64567i	0.329935	+	0.571464i	−0.652564	+	0.757734i	$0.726306\pi$
$180$		0			0
$181$	1.32941			0.0988140			0.0494070	−	0.998779i	$-0.484267\pi$
$181$	1.32941			0.0988140			0.0494070	+	0.998779i	$0.484267\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	5.08126			0.373581
$186$		0			0
$187$	−41.9064			−3.06450
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−16.1683			−1.16989			−0.584947	−	0.811071i	$-0.698885\pi$
$191$	−16.1683			−1.16989			−0.584947	+	0.811071i	$0.698885\pi$
$192$		0			0
$193$	−14.1683			−1.01985			−0.509927	−	0.860218i	$-0.670328\pi$
$193$	−14.1683			−1.01985			−0.509927	+	0.860218i	$0.670328\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−15.8421			−1.12871			−0.564353	−	0.825534i	$-0.690874\pi$
$197$	−15.8421			−1.12871			−0.564353	+	0.825534i	$0.690874\pi$
$198$		0			0
$199$	4.47141	+	7.74471i	0.316970	+	0.549008i	0.979854	−	0.199714i	$-0.0640013\pi$
$199$	4.47141	+	7.74471i	0.316970	+	0.549008i	−0.662884	+	0.748722i	$0.730668\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.71217	−	2.76748i	0.190357	−	0.194239i
$204$		0			0
$205$	12.2255			0.853862
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−5.94966	−	10.3051i	−0.411546	−	0.712819i
$210$		0			0
$211$	−11.3856	+	19.7205i	−0.783820	+	1.35762i	0.145882	+	0.989302i	$0.453398\pi$
$211$	−11.3856	+	19.7205i	−0.783820	+	1.35762i	−0.929702	+	0.368314i	$0.879935\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	7.62476	−	13.2065i	0.520005	−	0.900674i
$216$		0			0
$217$	−5.47373	−	19.6333i	−0.371581	−	1.33280i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−5.20602			−0.350195
$222$		0			0
$223$	6.44282	+	11.1593i	0.431443	+	0.747281i	0.996998	−	0.0774293i	$-0.0246712\pi$
$223$	6.44282	+	11.1593i	0.431443	+	0.747281i	−0.565555	+	0.824711i	$0.691338\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.9984	+	19.0497i	−0.729987	+	1.26437i	0.226901	+	0.973918i	$0.427141\pi$
$227$	−10.9984	+	19.0497i	−0.729987	+	1.26437i	−0.956888	+	0.290457i	$0.906193\pi$
$228$		0			0
$229$	1.89931	+	3.28971i	0.125510	+	0.217390i	0.921932	−	0.387351i	$-0.126610\pi$
$229$	1.89931	+	3.28971i	0.125510	+	0.217390i	−0.796422	+	0.604741i	$0.793277\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.33530	−	5.77690i	0.218503	−	0.378458i	−0.735848	−	0.677147i	$-0.763216\pi$
$233$	3.33530	−	5.77690i	0.218503	−	0.378458i	0.954350	+	0.298689i	$0.0965495\pi$
$234$		0			0
$235$	1.46169	+	2.53173i	0.0953505	+	0.165152i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.82038	+	13.5453i	−0.505858	+	0.876172i	0.494119	+	0.869394i	$0.335491\pi$
$239$	−7.82038	+	13.5453i	−0.505858	+	0.876172i	−0.999977	+	0.00677786i	$0.997843\pi$
$240$		0			0
$241$	−10.7060	+	18.5434i	−0.689635	+	1.19448i	0.282320	+	0.959320i	$0.408896\pi$
$241$	−10.7060	+	18.5434i	−0.689635	+	1.19448i	−0.971956	+	0.235163i	$0.924437\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−10.7970	−	5.94631i	−0.689794	−	0.379896i
$246$		0			0
$247$	−0.739123	−	1.28020i	−0.0470293	−	0.0814571i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−23.6030			−1.48981			−0.744904	−	0.667171i	$-0.767505\pi$
$251$	−23.6030			−1.48981			−0.744904	+	0.667171i	$0.767505\pi$
$252$		0			0
$253$	−2.57893			−0.162136
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.1300	+	17.5456i	0.631890	+	1.09447i	0.987165	+	0.159704i	$0.0510538\pi$
$257$	10.1300	+	17.5456i	0.631890	+	1.09447i	−0.355275	+	0.934762i	$0.615613\pi$
$258$		0			0
$259$	7.39411	+	1.90146i	0.459448	+	0.118151i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	11.2443	−	19.4757i	0.693355	−	1.20093i	−0.277377	−	0.960761i	$-0.589465\pi$
$263$	11.2443	−	19.4757i	0.693355	−	1.20093i	0.970732	−	0.240165i	$-0.0772014\pi$
$264$		0			0
$265$	−0.198495	+	0.343803i	−0.0121935	+	0.0211197i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	12.6706	+	21.9461i	0.772540	+	1.33808i	0.936167	+	0.351556i	$0.114347\pi$
$269$	12.6706	+	21.9461i	0.772540	+	1.33808i	−0.163627	+	0.986522i	$0.552319\pi$
$270$		0			0
$271$	6.87880	−	11.9144i	0.417858	−	0.723751i	−0.577866	−	0.816132i	$-0.696114\pi$
$271$	6.87880	−	11.9144i	0.417858	−	0.723751i	0.995724	+	0.0923810i	$0.0294478\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5.81642	+	10.0743i	0.350743	+	0.607505i
$276$		0			0
$277$	1.64132	−	2.84284i	0.0986171	−	0.170810i	−0.812495	−	0.582968i	$-0.801891\pi$
$277$	1.64132	−	2.84284i	0.0986171	−	0.170810i	0.911112	+	0.412158i	$0.135225\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.634479	−	1.09895i	−0.0378498	−	0.0655578i	0.846480	−	0.532421i	$-0.178718\pi$
$281$	−0.634479	−	1.09895i	−0.0378498	−	0.0655578i	−0.884330	+	0.466863i	$0.845384\pi$
$282$		0			0
$283$	8.19235			0.486984			0.243492	−	0.969903i	$-0.421707\pi$
$283$	8.19235			0.486984			0.243492	+	0.969903i	$0.421707\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	17.7902	+	4.57489i	1.05012	+	0.270047i
$288$		0			0
$289$	−14.9074	+	25.8204i	−0.876906	+	1.51884i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−7.72545	+	13.3809i	−0.451326	+	0.781719i	−0.998469	−	0.0553202i	$-0.982382\pi$
$293$	−7.72545	+	13.3809i	−0.451326	+	0.781719i	0.547143	+	0.837039i	$0.315715\pi$
$294$		0			0
$295$	1.74884	+	3.02908i	0.101821	+	0.176360i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.320380			−0.0185280
$300$		0			0
$301$	16.0374	−	16.3645i	0.924378	−	0.943231i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−9.11273	−	15.7837i	−0.521793	−	0.903772i
$306$		0			0
$307$	−4.89931			−0.279619			−0.139809	−	0.990178i	$-0.544649\pi$
$307$	−4.89931			−0.279619			−0.139809	+	0.990178i	$0.544649\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−7.69002			−0.436061			−0.218031	−	0.975942i	$-0.569963\pi$
$311$	−7.69002			−0.436061			−0.218031	+	0.975942i	$0.569963\pi$
$312$		0			0
$313$	−1.72313			−0.0973969			−0.0486985	−	0.998814i	$-0.515507\pi$
$313$	−1.72313			−0.0973969			−0.0486985	+	0.998814i	$0.515507\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−33.2028			−1.86485			−0.932426	−	0.361361i	$-0.882312\pi$
$317$	−33.2028			−1.86485			−0.932426	+	0.361361i	$0.882312\pi$
$318$		0			0
$319$	8.97017			0.502233
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−13.2930			−0.739644
$324$		0			0
$325$	0.722572	+	1.25153i	0.0400811	+	0.0694224i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.17962	+	4.23109i	0.0650346	+	0.233267i
$330$		0			0
$331$	−2.88891			−0.158789			−0.0793944	−	0.996843i	$-0.525299\pi$
$331$	−2.88891			−0.158789			−0.0793944	+	0.996843i	$0.525299\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−5.97373	−	10.3468i	−0.326380	−	0.565307i
$336$		0			0
$337$	−4.36156	+	7.55445i	−0.237590	+	0.411517i	−0.960022	−	0.279924i	$-0.909691\pi$
$337$	−4.36156	+	7.55445i	−0.237590	+	0.411517i	0.722433	+	0.691441i	$0.243024\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	23.5917	−	40.8620i	1.27756	−	2.21280i
$342$		0			0
$343$	−13.4863	−	12.6933i	−0.728193	−	0.685372i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.69467			0.520437			0.260219	−	0.965550i	$-0.416205\pi$
$347$	9.69467			0.520437			0.260219	+	0.965550i	$0.416205\pi$
$348$		0			0
$349$	14.1992	+	24.5937i	0.760065	+	1.31647i	0.942817	+	0.333312i	$0.108166\pi$
$349$	14.1992	+	24.5937i	0.760065	+	1.31647i	−0.182752	+	0.983159i	$0.558500\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−2.19686	+	3.80507i	−0.116927	+	0.202524i	−0.918548	−	0.395308i	$-0.870638\pi$
$353$	−2.19686	+	3.80507i	−0.116927	+	0.202524i	0.801621	+	0.597832i	$0.203971\pi$
$354$		0			0
$355$	9.49549	+	16.4467i	0.503968	+	0.872898i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	16.0796	−	27.8507i	0.848650	−	1.46990i	−0.0337633	−	0.999430i	$-0.510749\pi$
$359$	16.0796	−	27.8507i	0.848650	−	1.46990i	0.882413	−	0.470475i	$-0.155917\pi$
$360$		0			0
$361$	7.61273	+	13.1856i	0.400670	+	0.693980i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.270036	+	0.467717i	−0.0141343	+	0.0244814i
$366$		0			0
$367$	17.3015	−	29.9671i	0.903131	−	1.56427i	0.0797249	−	0.996817i	$-0.474596\pi$
$367$	17.3015	−	29.9671i	0.903131	−	1.56427i	0.823406	−	0.567452i	$-0.192071\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.417500	+	0.426015i	−0.0216755	+	0.0221176i
$372$		0			0
$373$	−5.48796	−	9.50543i	−0.284156	−	0.492172i	0.688248	−	0.725475i	$-0.258380\pi$
$373$	−5.48796	−	9.50543i	−0.284156	−	0.492172i	−0.972404	+	0.233303i	$0.925047\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.11436			0.0573925
$378$		0			0
$379$	−33.9877			−1.74583			−0.872916	−	0.487871i	$-0.837774\pi$
$379$	−33.9877			−1.74583			−0.872916	+	0.487871i	$0.837774\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	10.5120	+	18.2074i	0.537140	+	0.930354i	0.999056	+	0.0434304i	$0.0138287\pi$
$383$	10.5120	+	18.2074i	0.537140	+	0.930354i	−0.461916	+	0.886923i	$0.652838\pi$
$384$		0			0
$385$	−7.66307	−	27.4861i	−0.390546	−	1.40082i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6.86909	−	11.8976i	0.348277	−	0.603233i	−0.637667	−	0.770312i	$-0.720100\pi$
$389$	6.86909	−	11.8976i	0.348277	−	0.603233i	0.985943	+	0.167080i	$0.0534337\pi$
$390$		0			0
$391$	−1.44050	+	2.49501i	−0.0728491	+	0.126178i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	11.8376	+	20.5034i	0.595615	+	1.03164i
$396$		0			0
$397$	−3.57893	+	6.19889i	−0.179622	+	0.311114i	−0.941751	−	0.336311i	$-0.890821\pi$
$397$	−3.57893	+	6.19889i	−0.179622	+	0.311114i	0.762129	+	0.647425i	$0.224154\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−4.63968	−	8.03616i	−0.231695	−	0.401307i	0.726612	−	0.687048i	$-0.241094\pi$
$401$	−4.63968	−	8.03616i	−0.231695	−	0.401307i	−0.958307	+	0.285741i	$0.907760\pi$
$402$		0			0
$403$	2.93078	−	5.07626i	0.145993	−	0.252867i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	8.83693	+	15.3060i	0.438030	+	0.758691i
$408$		0			0
$409$	15.1683			0.750023			0.375011	−	0.927020i	$-0.377639\pi$
$409$	15.1683			0.750023			0.375011	+	0.927020i	$0.377639\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.41135	+	5.06227i	0.0694481	+	0.249098i
$414$		0			0
$415$	2.75116	−	4.76515i	0.135049	−	0.233912i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−4.16827	+	7.21966i	−0.203633	+	0.352703i	−0.949696	−	0.313172i	$-0.898608\pi$
$419$	−4.16827	+	7.21966i	−0.203633	+	0.352703i	0.746063	+	0.665875i	$0.231942\pi$
$420$		0			0
$421$	−3.50232	−	6.06620i	−0.170693	−	0.295649i	0.767969	−	0.640486i	$-0.221267\pi$
$421$	−3.50232	−	6.06620i	−0.170693	−	0.295649i	−0.938662	+	0.344838i	$0.887934\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	12.9954			0.630367
$426$		0			0
$427$	−7.35417	−	26.3781i	−0.355893	−	1.27653i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.72545	−	2.98857i	−0.0831120	−	0.143954i	0.821473	−	0.570247i	$-0.193153\pi$
$431$	−1.72545	−	2.98857i	−0.0831120	−	0.143954i	−0.904585	+	0.426293i	$0.859819\pi$
$432$		0			0
$433$	28.2599			1.35809			0.679043	−	0.734099i	$-0.262395\pi$
$433$	28.2599			1.35809			0.679043	+	0.734099i	$0.262395\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.818057			−0.0391330
$438$		0			0
$439$	28.8960			1.37913			0.689566	−	0.724222i	$-0.257801\pi$
$439$	28.8960			1.37913			0.689566	+	0.724222i	$0.257801\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−13.7609			−0.653799			−0.326899	−	0.945059i	$-0.606004\pi$
$443$	−13.7609			−0.653799			−0.326899	+	0.945059i	$0.606004\pi$
$444$		0			0
$445$	−4.58358			−0.217283
$446$		0			0
$447$		0			0
$448$		0			0
$449$	20.2003			0.953309			0.476655	−	0.879091i	$-0.341849\pi$
$449$	20.2003			0.953309			0.476655	+	0.879091i	$0.341849\pi$
$450$		0			0
$451$	21.2616	+	36.8261i	1.00117	+	1.73407i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.951980	−	3.41458i	−0.0446295	−	0.160078i
$456$		0			0
$457$	20.0298			0.936956			0.468478	−	0.883475i	$-0.344803\pi$
$457$	20.0298			0.936956			0.468478	+	0.883475i	$0.344803\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−5.97661	−	10.3518i	−0.278359	−	0.482131i	0.692618	−	0.721304i	$-0.256457\pi$
$461$	−5.97661	−	10.3518i	−0.278359	−	0.482131i	−0.970977	+	0.239173i	$0.923124\pi$
$462$		0			0
$463$	−6.64527	+	11.5100i	−0.308832	+	0.534913i	−0.978107	−	0.208102i	$-0.933271\pi$
$463$	−6.64527	+	11.5100i	−0.308832	+	0.534913i	0.669275	+	0.743015i	$0.266605\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.61505	+	9.72555i	−0.259833	+	0.450045i	−0.966197	−	0.257804i	$-0.917001\pi$
$467$	−5.61505	+	9.72555i	−0.259833	+	0.450045i	0.706364	+	0.707849i	$0.250334\pi$
$468$		0			0
$469$	−4.82094	−	17.2918i	−0.222610	−	0.798463i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	53.0416			2.43886
$474$		0			0
$475$	1.84501	+	3.19565i	0.0846550	+	0.146627i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	16.3135	−	28.2559i	0.745385	−	1.29104i	−0.204630	−	0.978839i	$-0.565599\pi$
$479$	16.3135	−	28.2559i	0.745385	−	1.29104i	0.950015	−	0.312205i	$-0.101068\pi$
$480$		0			0
$481$	1.09781	+	1.90146i	0.0500557	+	0.0866991i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3.20137	−	5.54494i	0.145367	−	0.251783i
$486$		0			0
$487$	−1.84897	−	3.20251i	−0.0837848	−	0.145120i	0.821088	−	0.570802i	$-0.193368\pi$
$487$	−1.84897	−	3.20251i	−0.0837848	−	0.145120i	−0.904873	+	0.425682i	$0.860034\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−18.7804	+	32.5287i	−0.847549	+	1.46800i	0.0358393	+	0.999358i	$0.488590\pi$
$491$	−18.7804	+	32.5287i	−0.847549	+	1.46800i	−0.883389	+	0.468641i	$0.844744\pi$
$492$		0			0
$493$	5.01040	−	8.67827i	0.225657	−	0.390850i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	7.66307	+	27.4861i	0.343736	+	1.23292i
$498$		0			0
$499$	−15.8977	−	27.5356i	−0.711678	−	1.23266i	−0.964227	−	0.265078i	$-0.914602\pi$
$499$	−15.8977	−	27.5356i	−0.711678	−	1.23266i	0.252549	−	0.967584i	$-0.418731\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	30.8252			1.37443			0.687214	−	0.726455i	$-0.258834\pi$
$503$	30.8252			1.37443			0.687214	+	0.726455i	$0.258834\pi$
$504$		0			0
$505$	−14.1053			−0.627679
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.00808	+	6.94220i	0.177655	+	0.307708i	0.941077	−	0.338193i	$-0.109816\pi$
$509$	4.00808	+	6.94220i	0.177655	+	0.307708i	−0.763422	+	0.645900i	$0.776482\pi$
$510$		0			0
$511$	−0.567974	+	0.579559i	−0.0251257	+	0.0256382i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	6.01204	−	10.4132i	0.264922	−	0.458858i
$516$		0			0
$517$	−5.08414	+	8.80598i	−0.223600	+	0.387287i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−14.8646	−	25.7462i	−0.651229	−	1.12796i	−0.982825	−	0.184540i	$-0.940920\pi$
$521$	−14.8646	−	25.7462i	−0.651229	−	1.12796i	0.331596	−	0.943421i	$-0.392413\pi$
$522$		0			0
$523$	−13.4698	+	23.3303i	−0.588992	+	1.02016i	0.405373	+	0.914152i	$0.367142\pi$
$523$	−13.4698	+	23.3303i	−0.588992	+	1.02016i	−0.994365	+	0.106013i	$0.966192\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−26.3549	−	45.6480i	−1.14804	−	1.98846i
$528$		0			0
$529$	11.4114	−	19.7650i	0.496146	−	0.859350i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	2.64132	+	4.57489i	0.114408	+	0.198161i
$534$		0			0
$535$	6.24377			0.269942
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.865521	−	42.8646i	−0.0372806	−	1.84631i
$540$		0			0
$541$	7.15568	−	12.3940i	0.307647	−	0.532859i	−0.670201	−	0.742180i	$-0.733792\pi$
$541$	7.15568	−	12.3940i	0.307647	−	0.532859i	0.977847	+	0.209321i	$0.0671252\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.619562	+	1.07311i	−0.0265391	+	0.0459671i
$546$		0			0
$547$	−1.02463	−	1.77471i	−0.0438101	−	0.0758813i	0.843289	−	0.537461i	$-0.180616\pi$
$547$	−1.02463	−	1.77471i	−0.0438101	−	0.0758813i	−0.887099	+	0.461579i	$0.847283\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2.84540			0.121218
$552$		0			0
$553$	9.55322	+	34.2657i	0.406244	+	1.45713i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−8.84338	−	15.3172i	−0.374706	−	0.649010i	0.615577	−	0.788077i	$-0.288923\pi$
$557$	−8.84338	−	15.3172i	−0.374706	−	0.649010i	−0.990283	+	0.139067i	$0.955590\pi$
$558$		0			0
$559$	6.58934			0.278699
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.937063			0.0394925			0.0197462	−	0.999805i	$-0.493714\pi$
$563$	0.937063			0.0394925			0.0197462	+	0.999805i	$0.493714\pi$
$564$		0			0
$565$	−14.9715			−0.629858
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−23.5264			−0.986278			−0.493139	−	0.869951i	$-0.664151\pi$
$569$	−23.5264			−0.986278			−0.493139	+	0.869951i	$0.664151\pi$
$570$		0			0
$571$	0.484004			0.0202549			0.0101275	−	0.999949i	$-0.496776\pi$
$571$	0.484004			0.0202549			0.0101275	+	0.999949i	$0.496776\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.799737			0.0333514
$576$		0			0
$577$	−2.23065	−	3.86360i	−0.0928633	−	0.160844i	0.815852	−	0.578261i	$-0.196269\pi$
$577$	−2.23065	−	3.86360i	−0.0928633	−	0.160844i	−0.908715	+	0.417417i	$0.862935\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	5.78659	−	5.90461i	0.240068	−	0.244965i
$582$		0			0
$583$	−1.38083			−0.0571881
$584$		0			0
$585$		0			0
$586$		0			0
$587$	8.31518	+	14.4023i	0.343204	+	0.594447i	0.985026	−	0.172407i	$-0.0551544\pi$
$587$	8.31518	+	14.4023i	0.343204	+	0.594447i	−0.641822	+	0.766854i	$0.721821\pi$
$588$		0			0
$589$	7.48345	−	12.9617i	0.308350	−	0.534078i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−20.7632	+	35.9629i	−0.852642	+	1.47682i	0.0261726	+	0.999657i	$0.491668\pi$
$593$	−20.7632	+	35.9629i	−0.852642	+	1.47682i	−0.878815	+	0.477163i	$0.841665\pi$
$594$		0			0
$595$	−30.8720	−	7.93899i	−1.26563	−	0.325467i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	15.0766			0.616014			0.308007	−	0.951384i	$-0.400338\pi$
$599$	15.0766			0.616014			0.308007	+	0.951384i	$0.400338\pi$
$600$		0			0
$601$	−8.05555	−	13.9526i	−0.328593	−	0.569139i	0.653640	−	0.756805i	$-0.273241\pi$
$601$	−8.05555	−	13.9526i	−0.328593	−	0.569139i	−0.982233	+	0.187666i	$0.939908\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	23.3428	−	40.4310i	0.949021	−	1.64375i
$606$		0			0
$607$	9.78659	+	16.9509i	0.397225	+	0.688014i	0.993382	−	0.114853i	$-0.0366398\pi$
$607$	9.78659	+	16.9509i	0.397225	+	0.688014i	−0.596157	+	0.802868i	$0.703306\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.631600	+	1.09396i	−0.0255518	+	0.0442570i
$612$		0			0
$613$	−2.77579	−	4.80782i	−0.112113	−	0.194186i	0.804509	−	0.593941i	$-0.202429\pi$
$613$	−2.77579	−	4.80782i	−0.112113	−	0.194186i	−0.916622	+	0.399755i	$0.869095\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.634479	+	1.09895i	−0.0255431	+	0.0442420i	−0.878514	−	0.477716i	$-0.841465\pi$
$617$	−0.634479	+	1.09895i	−0.0255431	+	0.0442420i	0.852971	+	0.521958i	$0.174798\pi$
$618$		0			0
$619$	2.25116	−	3.89913i	0.0904818	−	0.156719i	−0.817232	−	0.576309i	$-0.804493\pi$
$619$	2.25116	−	3.89913i	0.0904818	−	0.156719i	0.907714	+	0.419589i	$0.137826\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−6.66991	−	1.71522i	−0.267224	−	0.0687190i
$624$		0			0
$625$	5.94802	+	10.3023i	0.237921	+	0.412091i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	19.7439			0.787242
$630$		0			0
$631$	1.69905			0.0676381			0.0338191	−	0.999428i	$-0.489233\pi$
$631$	1.69905			0.0676381			0.0338191	+	0.999428i	$0.489233\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	16.6871	+	28.9030i	0.662209	+	1.14698i
$636$		0			0
$637$	−0.107523	−	5.32505i	−0.00426023	−	0.210986i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.474289	+	0.821492i	−0.0187333	+	0.0324470i	−0.875240	−	0.483689i	$-0.839297\pi$
$641$	−0.474289	+	0.821492i	−0.0187333	+	0.0324470i	0.856507	+	0.516136i	$0.172630\pi$
$642$		0			0
$643$	9.84897	−	17.0589i	0.388405	−	0.672738i	−0.603830	−	0.797113i	$-0.706359\pi$
$643$	9.84897	−	17.0589i	0.388405	−	0.672738i	0.992235	+	0.124375i	$0.0396927\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	11.7271	+	20.3119i	0.461039	+	0.798543i	0.999013	−	0.0444181i	$-0.0141434\pi$
$647$	11.7271	+	20.3119i	0.461039	+	0.798543i	−0.537974	+	0.842962i	$0.680810\pi$
$648$		0			0
$649$	−6.08289	+	10.5359i	−0.238774	+	0.413569i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	11.3954	+	19.7373i	0.445935	+	0.772382i	0.998117	−	0.0613420i	$-0.0195380\pi$
$653$	11.3954	+	19.7373i	0.445935	+	0.772382i	−0.552182	+	0.833724i	$0.686205\pi$
$654$		0			0
$655$	−6.42107	+	11.1216i	−0.250892	+	0.434557i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−13.2398	−	22.9320i	−0.515750	−	0.893305i	−0.999833	−	0.0182828i	$-0.994180\pi$
$659$	−13.2398	−	22.9320i	−0.515750	−	0.893305i	0.484083	−	0.875022i	$-0.339153\pi$
$660$		0			0
$661$	−26.7382			−1.03999			−0.519997	−	0.854168i	$-0.674067\pi$
$661$	−26.7382			−1.03999			−0.519997	+	0.854168i	$0.674067\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−2.43078	−	8.71878i	−0.0942617	−	0.338100i
$666$		0			0
$667$	0.308342	−	0.534063i	0.0119390	−	0.0206790i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	31.6963	−	54.8996i	1.22362	−	2.11938i
$672$		0			0
$673$	−10.3856	−	17.9885i	−0.400337	−	0.693404i	0.593429	−	0.804886i	$-0.297774\pi$
$673$	−10.3856	−	17.9885i	−0.400337	−	0.693404i	−0.993766	+	0.111482i	$0.964440\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	20.6979			0.795486			0.397743	−	0.917497i	$-0.369793\pi$
$677$	20.6979			0.795486			0.397743	+	0.917497i	$0.369793\pi$
$678$		0			0
$679$	6.73353	−	6.87087i	0.258409	−	0.263680i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	14.2918	+	24.7541i	0.546860	+	0.947190i	0.998487	+	0.0549828i	$0.0175104\pi$
$683$	14.2918	+	24.7541i	0.546860	+	0.947190i	−0.451627	+	0.892207i	$0.649156\pi$
$684$		0			0
$685$	−14.4074			−0.550478
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.171540			−0.00653515
$690$		0			0
$691$	6.69794			0.254802			0.127401	−	0.991851i	$-0.459337\pi$
$691$	6.69794			0.254802			0.127401	+	0.991851i	$0.459337\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	21.9486			0.832557
$696$		0			0
$697$	47.5037			1.79933
$698$		0			0
$699$		0			0
$700$		0			0
$701$	25.1442			0.949683			0.474842	−	0.880071i	$-0.342505\pi$
$701$	25.1442			0.949683			0.474842	+	0.880071i	$0.342505\pi$
$702$		0			0
$703$	2.80314	+	4.85518i	0.105722	+	0.183117i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−20.5257	−	5.27836i	−0.771949	−	0.198513i
$708$		0			0
$709$	8.86621			0.332977			0.166489	−	0.986043i	$-0.446757\pi$
$709$	8.86621			0.332977			0.166489	+	0.986043i	$0.446757\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.62188	−	2.80919i	−0.0607401	−	0.105205i
$714$		0			0
$715$	4.10301	−	7.10662i	0.153444	−	0.265773i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	11.8015	−	20.4408i	0.440122	−	0.762313i	−0.557576	−	0.830126i	$-0.688269\pi$
$719$	11.8015	−	20.4408i	0.440122	−	0.762313i	0.997698	+	0.0678123i	$0.0216019\pi$
$720$		0			0
$721$	12.6453	−	12.9032i	0.470935	−	0.480540i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.78168			−0.103309
$726$		0			0
$727$	−3.25692	−	5.64115i	−0.120792	−	0.209219i	0.799288	−	0.600948i	$-0.205210\pi$
$727$	−3.25692	−	5.64115i	−0.120792	−	0.209219i	−0.920080	+	0.391730i	$0.871877\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	29.6271	−	51.3156i	1.09580	−	1.89798i
$732$		0			0
$733$	11.5991	+	20.0901i	0.428421	+	0.742047i	0.996733	−	0.0807664i	$-0.0257368\pi$
$733$	11.5991	+	20.0901i	0.428421	+	0.742047i	−0.568312	+	0.822813i	$0.692403\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	20.7781	−	35.9888i	0.765372	−	1.32566i
$738$		0			0
$739$	7.57838	+	13.1261i	0.278775	+	0.482853i	0.971081	−	0.238752i	$-0.0767383\pi$
$739$	7.57838	+	13.1261i	0.278775	+	0.482853i	−0.692305	+	0.721605i	$0.743405\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−5.21737	+	9.03675i	−0.191407	+	0.331526i	−0.945717	−	0.324992i	$-0.894638\pi$
$743$	−5.21737	+	9.03675i	−0.191407	+	0.331526i	0.754310	+	0.656518i	$0.227972\pi$
$744$		0			0
$745$	−7.77292	+	13.4631i	−0.284778	+	0.493249i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	9.08577	+	2.33648i	0.331987	+	0.0853733i
$750$		0			0
$751$	20.1059	+	34.8244i	0.733674	+	1.27076i	0.955303	+	0.295630i	$0.0955295\pi$
$751$	20.1059	+	34.8244i	0.733674	+	1.27076i	−0.221628	+	0.975131i	$0.571137\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−26.3891			−0.960397
$756$		0			0
$757$	−21.5206			−0.782181			−0.391091	−	0.920352i	$-0.627902\pi$
$757$	−21.5206			−0.782181			−0.391091	+	0.920352i	$0.627902\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−11.8313	−	20.4925i	−0.428886	−	0.742852i	0.567889	−	0.823105i	$-0.307760\pi$
$761$	−11.8313	−	20.4925i	−0.428886	−	0.742852i	−0.996774	+	0.0802535i	$0.974427\pi$
$762$		0			0
$763$	−1.30314	+	1.32972i	−0.0471768	+	0.0481390i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.755675	+	1.30887i	−0.0272858	+	0.0472605i
$768$		0			0
$769$	−5.62764	+	9.74736i	−0.202938	+	0.351499i	−0.949474	−	0.313846i	$-0.898382\pi$
$769$	−5.62764	+	9.74736i	−0.202938	+	0.351499i	0.746536	+	0.665345i	$0.231716\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−0.138992	−	0.240741i	−0.00499919	−	0.00865886i	0.863515	−	0.504323i	$-0.168258\pi$
$773$	−0.138992	−	0.240741i	−0.00499919	−	0.00865886i	−0.868514	+	0.495664i	$0.834925\pi$
$774$		0			0
$775$	−7.31587	+	12.6715i	−0.262794	+	0.455172i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.74433	+	11.6815i	0.241641	+	0.418534i
$780$		0			0
$781$	−33.0276	+	57.2056i	−1.18182	+	2.04698i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	16.7112	+	28.9447i	0.596449	+	1.03308i
$786$		0			0
$787$	29.3880			1.04757			0.523784	−	0.851851i	$-0.324520\pi$
$787$	29.3880			1.04757			0.523784	+	0.851851i	$0.324520\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−21.7862	−	5.60251i	−0.774628	−	0.199202i
$792$		0			0
$793$	3.93762	−	6.82015i	0.139829	−	0.242191i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−0.433105	+	0.750160i	−0.0153414	+	0.0265720i	−0.873594	−	0.486655i	$-0.838217\pi$
$797$	−0.433105	+	0.750160i	−0.0153414	+	0.0265720i	0.858253	+	0.513227i	$0.171550\pi$
$798$		0			0
$799$	5.67962	+	9.83739i	0.200931	+	0.348022i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.87851			−0.0662910
$804$		0			0
$805$	−1.89987	−	0.488568i	−0.0669616	−	0.0172197i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−9.66703	−	16.7438i	−0.339875	−	0.588680i	0.644534	−	0.764575i	$-0.277051\pi$
$809$	−9.66703	−	16.7438i	−0.339875	−	0.588680i	−0.984409	+	0.175895i	$0.943718\pi$
$810$		0			0
$811$	47.0391			1.65177			0.825884	−	0.563841i	$-0.190677\pi$
$811$	47.0391			1.65177			0.825884	+	0.563841i	$0.190677\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	26.4796			0.927541
$816$		0			0
$817$	16.8252			0.588639
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.41066			−0.0492325			−0.0246162	−	0.999697i	$-0.507836\pi$
$821$	−1.41066			−0.0492325			−0.0246162	+	0.999697i	$0.507836\pi$
$822$		0			0
$823$	35.0391			1.22139			0.610694	−	0.791867i	$-0.290891\pi$
$823$	35.0391			1.22139			0.610694	+	0.791867i	$0.290891\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−18.5997			−0.646776			−0.323388	−	0.946266i	$-0.604822\pi$
$827$	−18.5997			−0.646776			−0.323388	+	0.946266i	$0.604822\pi$
$828$		0			0
$829$	19.0848	+	33.0559i	0.662843	+	1.14808i	0.979865	+	0.199660i	$0.0639838\pi$
$829$	19.0848	+	33.0559i	0.662843	+	1.14808i	−0.317022	+	0.948418i	$0.602683\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−41.9532	−	23.1052i	−1.45359	−	0.800549i
$834$		0			0
$835$	2.01478			0.0697245
$836$		0			0
$837$		0			0
$838$		0			0
$839$	17.3691	+	30.0841i	0.599648	+	1.03862i	0.992873	+	0.119178i	$0.0380259\pi$
$839$	17.3691	+	30.0841i	0.599648	+	1.03862i	−0.393225	+	0.919442i	$0.628641\pi$
$840$		0			0
$841$	13.4275	−	23.2571i	0.463018	−	0.801970i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−10.9360	+	18.9417i	−0.376209	+	0.651614i
$846$		0			0
$847$	49.0976	−	50.0989i	1.68701	−	1.72142i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.21505			0.0416513
$852$		0			0
$853$	−21.1586	−	36.6477i	−0.724455	−	1.25479i	−0.959198	−	0.282736i	$-0.908758\pi$
$853$	−21.1586	−	36.6477i	−0.724455	−	1.25479i	0.234743	−	0.972058i	$-0.424575\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.46169	−	12.9240i	0.254887	−	0.441477i	−0.709978	−	0.704224i	$-0.751295\pi$
$857$	7.46169	−	12.9240i	0.254887	−	0.441477i	0.964865	+	0.262747i	$0.0846285\pi$
$858$		0			0
$859$	9.70658	+	16.8123i	0.331184	+	0.573628i	0.982744	−	0.184969i	$-0.0592186\pi$
$859$	9.70658	+	16.8123i	0.331184	+	0.573628i	−0.651560	+	0.758597i	$0.725885\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.542263	+	0.939227i	−0.0184588	+	0.0319717i	−0.875107	−	0.483929i	$-0.839209\pi$
$863$	−0.542263	+	0.939227i	−0.0184588	+	0.0319717i	0.856648	+	0.515901i	$0.172543\pi$
$864$		0			0
$865$	−0.438174	−	0.758939i	−0.0148984	−	0.0258047i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−41.1742	+	71.3157i	−1.39674	+	2.41922i
$870$		0			0
$871$	2.58126	−	4.47087i	0.0874625	−	0.151490i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	8.63216	+	30.9620i	0.291820	+	1.04671i
$876$		0			0
$877$	14.2850	+	24.7423i	0.482369	+	0.835487i	0.999795	−	0.0202407i	$-0.00644326\pi$
$877$	14.2850	+	24.7423i	0.482369	+	0.835487i	−0.517427	+	0.855728i	$0.673110\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−45.9967			−1.54967			−0.774835	−	0.632164i	$-0.782167\pi$
$881$	−45.9967			−1.54967			−0.774835	+	0.632164i	$0.782167\pi$
$882$		0			0
$883$	−32.9384			−1.10847			−0.554233	−	0.832361i	$-0.686988\pi$
$883$	−32.9384			−1.10847			−0.554233	+	0.832361i	$0.686988\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.1699	+	24.5430i	0.475779	+	0.824073i	0.999615	−	0.0277459i	$-0.00883293\pi$
$887$	14.1699	+	24.5430i	0.475779	+	0.824073i	−0.523836	+	0.851819i	$0.675500\pi$
$888$		0			0
$889$	13.4669	+	48.3034i	0.451665	+	1.62004i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.61273	+	2.79332i	−0.0539678	+	0.0934750i
$894$		0			0
$895$	−7.77292	+	13.4631i	−0.259820	+	0.450021i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	5.64132	+	9.77104i	0.188148	+	0.325883i
$900$		0			0
$901$	−0.771280	+	1.33590i	−0.0256951	+	0.0445052i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.17046	+	2.02730i	0.0389074	+	0.0673896i
$906$		0			0
$907$	3.97373	−	6.88271i	0.131946	−	0.228537i	−0.792481	−	0.609897i	$-0.791211\pi$
$907$	3.97373	−	6.88271i	0.131946	−	0.228537i	0.924427	+	0.381360i	$0.124544\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−4.00808	−	6.94220i	−0.132794	−	0.230005i	0.791959	−	0.610575i	$-0.209061\pi$
$911$	−4.00808	−	6.94220i	−0.132794	−	0.230005i	−0.924752	+	0.380569i	$0.875728\pi$
$912$		0			0
$913$	19.1384			0.633390
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−13.5056	+	13.7811i	−0.445994	+	0.455090i
$918$		0			0
$919$	12.0224	−	20.8235i	0.396584	−	0.686903i	−0.596718	−	0.802451i	$-0.703529\pi$
$919$	12.0224	−	20.8235i	0.396584	−	0.686903i	0.993302	+	0.115548i	$0.0368623\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−4.10301	+	7.10662i	−0.135052	+	0.233917i
$924$		0			0
$925$	−2.74037	−	4.74646i	−0.0901027	−	0.156062i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−27.8662			−0.914261			−0.457130	−	0.889400i	$-0.651123\pi$
$929$	−27.8662			−0.914261			−0.457130	+	0.889400i	$0.651123\pi$
$930$		0			0
$931$	−0.274550	−	13.5970i	−0.00899801	−	0.445623i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−36.8960	−	63.9058i	−1.20663	−	2.08994i
$936$		0			0
$937$	53.2211			1.73866			0.869328	−	0.494235i	$-0.164552\pi$
$937$	53.2211			1.73866			0.869328	+	0.494235i	$0.164552\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	30.0482			0.979542			0.489771	−	0.871851i	$-0.337080\pi$
$941$	30.0482			0.979542			0.489771	+	0.871851i	$0.337080\pi$
$942$		0			0
$943$	2.92339			0.0951987
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−39.6889			−1.28972			−0.644858	−	0.764302i	$-0.723084\pi$
$947$	−39.6889			−1.28972			−0.644858	+	0.764302i	$0.723084\pi$
$948$		0			0
$949$	−0.233366			−0.00757538
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−23.0643			−0.747126			−0.373563	−	0.927605i	$-0.621864\pi$
$953$	−23.0643			−0.747126			−0.373563	+	0.927605i	$0.621864\pi$
$954$		0			0
$955$	−14.2352	−	24.6560i	−0.460639	−	0.797850i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−20.9653	−	5.39140i	−0.677004	−	0.174097i
$960$		0			0
$961$	28.3469			0.914418
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−12.4743	−	21.6061i	−0.401562	−	0.695525i
$966$		0			0
$967$	−15.2902	+	26.4833i	−0.491698	+	0.851646i	−0.999954	−	0.00955967i	$-0.996957\pi$
$967$	−15.2902	+	26.4833i	−0.491698	+	0.851646i	0.508256	+	0.861206i	$0.330290\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	13.1030	−	22.6951i	0.420496	−	0.728320i	−0.575492	−	0.817807i	$-0.695190\pi$
$971$	13.1030	−	22.6951i	0.420496	−	0.728320i	0.995988	+	0.0894874i	$0.0285229\pi$
$972$		0			0
$973$	31.9390	+	8.21339i	1.02392	+	0.263309i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−21.0539			−0.673574			−0.336787	−	0.941581i	$-0.609340\pi$
$977$	−21.0539			−0.673574			−0.336787	+	0.941581i	$0.609340\pi$
$978$		0			0
$979$	−7.97141	−	13.8069i	−0.254767	−	0.441270i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	9.76483	−	16.9132i	0.311450	−	0.539447i	−0.667227	−	0.744855i	$-0.732519\pi$
$983$	9.76483	−	16.9132i	0.311450	−	0.539447i	0.978676	+	0.205408i	$0.0658521\pi$
$984$		0			0
$985$	−13.9480	−	24.1587i	−0.444421	−	0.769760i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.82326	−	3.15798i	0.0579762	−	0.100418i
$990$		0			0
$991$	7.49837	+	12.9875i	0.238193	+	0.412563i	0.960196	−	0.279327i	$-0.0901114\pi$
$991$	7.49837	+	12.9875i	0.238193	+	0.412563i	−0.722003	+	0.691890i	$0.756778\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−7.87360	+	13.6375i	−0.249610	+	0.432337i
$996$		0			0
$997$	29.2821	−	50.7180i	0.927373	−	1.60626i	0.139672	−	0.990198i	$-0.455395\pi$
$997$	29.2821	−	50.7180i	0.927373	−	1.60626i	0.787700	−	0.616059i	$-0.211272\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.q.h.2305.2		6
3.2	odd	2		1008.2.q.h.625.1		6
4.3	odd	2		378.2.e.c.37.2		6
7.4	even	3		3024.2.t.g.1873.2		6
9.2	odd	6		1008.2.t.g.961.2		6
9.7	even	3		3024.2.t.g.289.2		6
12.11	even	2		126.2.e.d.121.3	yes	6
21.11	odd	6		1008.2.t.g.193.2		6
28.3	even	6		2646.2.h.p.361.2		6
28.11	odd	6		378.2.h.d.361.2		6
28.19	even	6		2646.2.f.n.1765.2		6
28.23	odd	6		2646.2.f.o.1765.2		6
28.27	even	2		2646.2.e.o.1549.2		6
36.7	odd	6		378.2.h.d.289.2		6
36.11	even	6		126.2.h.c.79.2	yes	6
36.23	even	6		1134.2.g.k.163.2		6
36.31	odd	6		1134.2.g.n.163.2		6
63.11	odd	6		1008.2.q.h.529.1		6
63.25	even	3	inner	3024.2.q.h.2881.2		6
84.11	even	6		126.2.h.c.67.2	yes	6
84.23	even	6		882.2.f.l.589.1		6
84.47	odd	6		882.2.f.m.589.3		6
84.59	odd	6		882.2.h.o.67.2		6
84.83	odd	2		882.2.e.p.373.1		6
252.11	even	6		126.2.e.d.25.3	✓	6
252.23	even	6		7938.2.a.cb.1.2		3
252.47	odd	6		882.2.f.m.295.3		6
252.67	odd	6		1134.2.g.n.487.2		6
252.79	odd	6		2646.2.f.o.883.2		6
252.83	odd	6		882.2.h.o.79.2		6
252.95	even	6		1134.2.g.k.487.2		6
252.103	even	6		7938.2.a.bx.1.2		3
252.115	even	6		2646.2.e.o.2125.2		6
252.131	odd	6		7938.2.a.by.1.2		3
252.151	odd	6		378.2.e.c.235.2		6
252.187	even	6		2646.2.f.n.883.2		6
252.191	even	6		882.2.f.l.295.1		6
252.223	even	6		2646.2.h.p.667.2		6
252.227	odd	6		882.2.e.p.655.1		6
252.247	odd	6		7938.2.a.bu.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.3	✓	6	252.11	even	6
126.2.e.d.121.3	yes	6	12.11	even	2
126.2.h.c.67.2	yes	6	84.11	even	6
126.2.h.c.79.2	yes	6	36.11	even	6
378.2.e.c.37.2		6	4.3	odd	2
378.2.e.c.235.2		6	252.151	odd	6
378.2.h.d.289.2		6	36.7	odd	6
378.2.h.d.361.2		6	28.11	odd	6
882.2.e.p.373.1		6	84.83	odd	2
882.2.e.p.655.1		6	252.227	odd	6
882.2.f.l.295.1		6	252.191	even	6
882.2.f.l.589.1		6	84.23	even	6
882.2.f.m.295.3		6	252.47	odd	6
882.2.f.m.589.3		6	84.47	odd	6
882.2.h.o.67.2		6	84.59	odd	6
882.2.h.o.79.2		6	252.83	odd	6
1008.2.q.h.529.1		6	63.11	odd	6
1008.2.q.h.625.1		6	3.2	odd	2
1008.2.t.g.193.2		6	21.11	odd	6
1008.2.t.g.961.2		6	9.2	odd	6
1134.2.g.k.163.2		6	36.23	even	6
1134.2.g.k.487.2		6	252.95	even	6
1134.2.g.n.163.2		6	36.31	odd	6
1134.2.g.n.487.2		6	252.67	odd	6
2646.2.e.o.1549.2		6	28.27	even	2
2646.2.e.o.2125.2		6	252.115	even	6
2646.2.f.n.883.2		6	252.187	even	6
2646.2.f.n.1765.2		6	28.19	even	6
2646.2.f.o.883.2		6	252.79	odd	6
2646.2.f.o.1765.2		6	28.23	odd	6
2646.2.h.p.361.2		6	28.3	even	6
2646.2.h.p.667.2		6	252.223	even	6
3024.2.q.h.2305.2		6	1.1	even	1	trivial
3024.2.q.h.2881.2		6	63.25	even	3	inner
3024.2.t.g.289.2		6	9.7	even	3
3024.2.t.g.1873.2		6	7.4	even	3
7938.2.a.bu.1.2		3	252.247	odd	6
7938.2.a.bx.1.2		3	252.103	even	6
7938.2.a.by.1.2		3	252.131	odd	6
7938.2.a.cb.1.2		3	252.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.880438 + 1.52496i) q^{5} +(0.710533 + 2.54856i) q^{7} +O(q^{10})\)	\(q+(0.880438 + 1.52496i) q^{5} +(0.710533 + 2.54856i) q^{7} +(-3.06238 + 5.30420i) q^{11} +(-0.380438 + 0.658939i) q^{13} +(3.42107 + 5.92546i) q^{17} +(-0.971410 + 1.68253i) q^{19} +(0.210533 + 0.364654i) q^{23} +(0.949657 - 1.64485i) q^{25} +(-0.732287 - 1.26836i) q^{29} -7.70370 q^{31} +(-3.26088 + 3.32738i) q^{35} +(1.44282 - 2.49904i) q^{37} +(3.47141 - 6.01266i) q^{41} +(-4.33009 - 7.49994i) q^{43} +1.66019 q^{47} +(-5.99028 + 3.62167i) q^{49} +(0.112725 + 0.195246i) q^{53} -10.7850 q^{55} +1.98633 q^{59} -10.3502 q^{61} -1.33981 q^{65} -6.78495 q^{67} +10.7850 q^{71} +(0.153353 + 0.265616i) q^{73} +(-15.6940 - 4.03584i) q^{77} +13.4451 q^{79} +(-1.56238 - 2.70612i) q^{83} +(-6.02408 + 10.4340i) q^{85} +(-1.30150 + 2.25427i) q^{89} +(-1.94966 - 0.501371i) q^{91} -3.42107 q^{95} +(-1.81806 - 3.14897i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 5 q^{5} - 4 q^{7}+O(q^{10}) \) 6 * q + 5 * q^5 - 4 * q^7	\( 6 q + 5 q^{5} - 4 q^{7} - q^{11} - 2 q^{13} + 4 q^{17} + 3 q^{19} - 7 q^{23} - 2 q^{25} + 5 q^{29} - 28 q^{31} - 19 q^{35} - 9 q^{37} + 12 q^{41} - 18 q^{43} - 6 q^{47} - 12 q^{49} - 9 q^{53} - 14 q^{55} - 8 q^{59} - 8 q^{61} - 24 q^{65} + 10 q^{67} + 14 q^{71} - 25 q^{73} - 52 q^{77} + 14 q^{79} + 8 q^{83} + 14 q^{85} + 9 q^{89} - 4 q^{91} - 4 q^{95} - 28 q^{97}+O(q^{100}) \) 6 * q + 5 * q^5 - 4 * q^7 - q^11 - 2 * q^13 + 4 * q^17 + 3 * q^19 - 7 * q^23 - 2 * q^25 + 5 * q^29 - 28 * q^31 - 19 * q^35 - 9 * q^37 + 12 * q^41 - 18 * q^43 - 6 * q^47 - 12 * q^49 - 9 * q^53 - 14 * q^55 - 8 * q^59 - 8 * q^61 - 24 * q^65 + 10 * q^67 + 14 * q^71 - 25 * q^73 - 52 * q^77 + 14 * q^79 + 8 * q^83 + 14 * q^85 + 9 * q^89 - 4 * q^91 - 4 * q^95 - 28 * q^97

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