LMFDB - Embedded newform 2548.2.l.k.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2548,2,Mod(373,2548)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2548, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("2548.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.l (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:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.2
Root			$-0.651388 - 1.12824i$ of defining polynomial
Character	$\chi$	$=$	2548.373
Dual form			2548.2.l.k.1537.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.30278 q^{3} +(0.151388 - 0.262211i) q^{5} +2.30278 q^{9} +6.30278 q^{11} +(-1.80278 - 3.12250i) q^{13} +(0.348612 - 0.603814i) q^{15} +(0.802776 - 1.39045i) q^{17} +3.69722 q^{19} +(-1.00000 - 1.73205i) q^{23} +(2.45416 + 4.25074i) q^{25} -1.60555 q^{27} +(0.151388 - 0.262211i) q^{29} +(0.197224 + 0.341603i) q^{31} +14.5139 q^{33} +(-4.60555 - 7.97705i) q^{37} +(-4.15139 - 7.19041i) q^{39} +(0.697224 - 1.20763i) q^{41} +(2.95416 + 5.11676i) q^{43} +(0.348612 - 0.603814i) q^{45} +(-5.80278 + 10.0507i) q^{47} +(1.84861 - 3.20189i) q^{51} +(-5.40833 - 9.36750i) q^{53} +(0.954163 - 1.65266i) q^{55} +8.51388 q^{57} +(2.80278 - 4.85455i) q^{59} +7.21110 q^{61} -1.09167 q^{65} +13.0000 q^{67} +(-2.30278 - 3.98852i) q^{69} +(4.90833 + 8.50147i) q^{71} +(-5.60555 - 9.70910i) q^{73} +(5.65139 + 9.78849i) q^{75} +(-4.00000 + 6.92820i) q^{79} -10.6056 q^{81} -4.39445 q^{83} +(-0.243061 - 0.420994i) q^{85} +(0.348612 - 0.603814i) q^{87} +(-2.54584 - 4.40952i) q^{89} +(0.454163 + 0.786634i) q^{93} +(0.559715 - 0.969454i) q^{95} +(3.04584 + 5.27554i) q^{97} +14.5139 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 3 q^{5} + 2 q^{9} + 18 q^{11} + 5 q^{15} - 4 q^{17} + 22 q^{19} - 4 q^{23} - q^{25} + 8 q^{27} - 3 q^{29} + 8 q^{31} + 22 q^{33} - 4 q^{37} - 13 q^{39} + 10 q^{41} + q^{43} + 5 q^{45}+ \cdots + 22 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 3 * q^5 + 2 * q^9 + 18 * q^11 + 5 * q^15 - 4 * q^17 + 22 * q^19 - 4 * q^23 - q^25 + 8 * q^27 - 3 * q^29 + 8 * q^31 + 22 * q^33 - 4 * q^37 - 13 * q^39 + 10 * q^41 + q^43 + 5 * q^45 - 16 * q^47 + 11 * q^51 - 7 * q^55 - 2 * q^57 + 4 * q^59 - 26 * q^65 + 52 * q^67 - 2 * q^69 - 2 * q^71 - 8 * q^73 + 19 * q^75 - 16 * q^79 - 28 * q^81 - 32 * q^83 - 19 * q^85 + 5 * q^87 - 21 * q^89 - 9 * q^93 - 23 * q^95 + 23 * q^97 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	2.30278			1.32951			0.664754	−	0.747062i	$-0.268536\pi$
$3$	2.30278			1.32951			0.664754	+	0.747062i	$0.268536\pi$
$4$		0			0
$5$	0.151388	−	0.262211i	0.0677027	−	0.117265i	−0.830187	−	0.557485i	$-0.811766\pi$
$5$	0.151388	−	0.262211i	0.0677027	−	0.117265i	0.897890	+	0.440221i	$0.145100\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	2.30278			0.767592
$10$		0			0
$11$	6.30278			1.90036			0.950179	−	0.311704i	$-0.100900\pi$
$11$	6.30278			1.90036			0.950179	+	0.311704i	$0.100900\pi$
$12$		0			0
$13$	−1.80278	−	3.12250i	−0.500000	−	0.866025i
$13$	−1.80278	−	3.12250i	−0.500000	−	0.866025i
$14$		0			0
$15$	0.348612	−	0.603814i	0.0900113	−	0.155904i
$16$		0			0
$17$	0.802776	−	1.39045i	0.194702	−	0.337233i	−0.752101	−	0.659048i	$-0.770959\pi$
$17$	0.802776	−	1.39045i	0.194702	−	0.337233i	0.946803	+	0.321815i	$0.104293\pi$
$18$		0			0
$19$	3.69722			0.848201			0.424101	−	0.905615i	$-0.360590\pi$
$19$	3.69722			0.848201			0.424101	+	0.905615i	$0.360590\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.00000	−	1.73205i	−0.208514	−	0.361158i	0.742732	−	0.669588i	$-0.233529\pi$
$23$	−1.00000	−	1.73205i	−0.208514	−	0.361158i	−0.951247	+	0.308431i	$0.900196\pi$
$24$		0			0
$25$	2.45416	+	4.25074i	0.490833	+	0.850147i
$26$		0			0
$27$	−1.60555			−0.308988
$28$		0			0
$29$	0.151388	−	0.262211i	0.0281120	−	0.0486914i	−0.851627	−	0.524148i	$-0.824384\pi$
$29$	0.151388	−	0.262211i	0.0281120	−	0.0486914i	0.879739	+	0.475457i	$0.157717\pi$
$30$		0			0
$31$	0.197224	+	0.341603i	0.0354225	+	0.0613536i	0.883193	−	0.469009i	$-0.155389\pi$
$31$	0.197224	+	0.341603i	0.0354225	+	0.0613536i	−0.847771	+	0.530363i	$0.822056\pi$
$32$		0			0
$33$	14.5139			2.52654
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.60555	−	7.97705i	−0.757148	−	1.31142i	−0.944299	−	0.329088i	$-0.893259\pi$
$37$	−4.60555	−	7.97705i	−0.757148	−	1.31142i	0.187151	−	0.982331i	$-0.440074\pi$
$38$		0			0
$39$	−4.15139	−	7.19041i	−0.664754	−	1.15139i
$40$		0			0
$41$	0.697224	−	1.20763i	0.108888	−	0.188600i	−0.806432	−	0.591327i	$-0.798604\pi$
$41$	0.697224	−	1.20763i	0.108888	−	0.188600i	0.915320	+	0.402727i	$0.131938\pi$
$42$		0			0
$43$	2.95416	+	5.11676i	0.450506	+	0.780299i	0.998417	−	0.0562374i	$-0.0179104\pi$
$43$	2.95416	+	5.11676i	0.450506	+	0.780299i	−0.547912	+	0.836536i	$0.684577\pi$
$44$		0			0
$45$	0.348612	−	0.603814i	0.0519680	−	0.0900113i
$46$		0			0
$47$	−5.80278	+	10.0507i	−0.846422	+	1.46605i	0.0379589	+	0.999279i	$0.487914\pi$
$47$	−5.80278	+	10.0507i	−0.846422	+	1.46605i	−0.884381	+	0.466766i	$0.845419\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	1.84861	−	3.20189i	0.258857	−	0.448354i
$52$		0			0
$53$	−5.40833	−	9.36750i	−0.742891	−	1.28672i	−0.951174	−	0.308656i	$-0.900121\pi$
$53$	−5.40833	−	9.36750i	−0.742891	−	1.28672i	0.208283	−	0.978069i	$-0.433213\pi$
$54$		0			0
$55$	0.954163	−	1.65266i	0.128659	−	0.222845i
$56$		0			0
$57$	8.51388			1.12769
$58$		0			0
$59$	2.80278	−	4.85455i	0.364890	−	0.632009i	−0.623868	−	0.781530i	$-0.714440\pi$
$59$	2.80278	−	4.85455i	0.364890	−	0.632009i	0.988759	+	0.149521i	$0.0477732\pi$
$60$		0			0
$61$	7.21110			0.923287			0.461644	−	0.887066i	$-0.347260\pi$
$61$	7.21110			0.923287			0.461644	+	0.887066i	$0.347260\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.09167			−0.135405
$66$		0			0
$67$	13.0000			1.58820			0.794101	−	0.607785i	$-0.207942\pi$
$67$	13.0000			1.58820			0.794101	+	0.607785i	$0.207942\pi$
$68$		0			0
$69$	−2.30278	−	3.98852i	−0.277222	−	0.480162i
$70$		0			0
$71$	4.90833	+	8.50147i	0.582511	+	1.00894i	0.995181	+	0.0980582i	$0.0312631\pi$
$71$	4.90833	+	8.50147i	0.582511	+	1.00894i	−0.412669	+	0.910881i	$0.635404\pi$
$72$		0			0
$73$	−5.60555	−	9.70910i	−0.656080	−	1.13636i	−0.981622	−	0.190836i	$-0.938880\pi$
$73$	−5.60555	−	9.70910i	−0.656080	−	1.13636i	0.325542	−	0.945528i	$-0.394453\pi$
$74$		0			0
$75$	5.65139	+	9.78849i	0.652566	+	1.13028i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$		0			0
$81$	−10.6056			−1.17839
$82$		0			0
$83$	−4.39445			−0.482353			−0.241177	−	0.970481i	$-0.577533\pi$
$83$	−4.39445			−0.482353			−0.241177	+	0.970481i	$0.577533\pi$
$84$		0			0
$85$	−0.243061	−	0.420994i	−0.0263637	−	0.0456632i
$86$		0			0
$87$	0.348612	−	0.603814i	0.0373751	−	0.0647357i
$88$		0			0
$89$	−2.54584	−	4.40952i	−0.269858	−	0.467408i	0.698967	−	0.715154i	$-0.253643\pi$
$89$	−2.54584	−	4.40952i	−0.269858	−	0.467408i	−0.968825	+	0.247746i	$0.920310\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	0.454163	+	0.786634i	0.0470946	+	0.0815702i
$94$		0			0
$95$	0.559715	−	0.969454i	0.0574255	−	0.0994639i
$96$		0			0
$97$	3.04584	+	5.27554i	0.309258	+	0.535650i	0.978200	−	0.207664i	$-0.0665861\pi$
$97$	3.04584	+	5.27554i	0.309258	+	0.535650i	−0.668942	+	0.743314i	$0.733253\pi$
$98$		0			0
$99$	14.5139			1.45870
$100$		0			0
$101$	9.51388			0.946666			0.473333	−	0.880884i	$-0.343051\pi$
$101$	9.51388			0.946666			0.473333	+	0.880884i	$0.343051\pi$
$102$		0			0
$103$	3.40833	−	5.90340i	0.335832	−	0.581679i	−0.647812	−	0.761800i	$-0.724316\pi$
$103$	3.40833	−	5.90340i	0.335832	−	0.581679i	0.983644	+	0.180121i	$0.0576491\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.75694	+	13.4354i	0.749892	+	1.29885i	0.947874	+	0.318645i	$0.103228\pi$
$107$	7.75694	+	13.4354i	0.749892	+	1.29885i	−0.197983	+	0.980206i	$0.563439\pi$
$108$		0			0
$109$	1.80278	+	3.12250i	0.172675	+	0.299081i	0.939354	−	0.342949i	$-0.111426\pi$
$109$	1.80278	+	3.12250i	0.172675	+	0.299081i	−0.766679	+	0.642030i	$0.778092\pi$
$110$		0			0
$111$	−10.6056	−	18.3694i	−1.00663	−	1.74354i
$112$		0			0
$113$	5.10555	+	8.84307i	0.480290	+	0.831886i	0.999744	−	0.0226117i	$-0.00719814\pi$
$113$	5.10555	+	8.84307i	0.480290	+	0.831886i	−0.519454	+	0.854498i	$0.673865\pi$
$114$		0			0
$115$	−0.605551			−0.0564679
$116$		0			0
$117$	−4.15139	−	7.19041i	−0.383796	−	0.664754i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	28.7250			2.61136
$122$		0			0
$123$	1.60555	−	2.78090i	0.144768	−	0.250745i
$124$		0			0
$125$	3.00000			0.268328
$126$		0			0
$127$	5.95416	−	10.3129i	0.528347	−	0.915123i	−0.471107	−	0.882076i	$-0.656146\pi$
$127$	5.95416	−	10.3129i	0.528347	−	0.915123i	0.999454	−	0.0330472i	$-0.0105212\pi$
$128$		0			0
$129$	6.80278	+	11.7828i	0.598951	+	1.03741i
$130$		0			0
$131$	6.25694	−	10.8373i	0.546671	−	0.946862i	−0.451828	−	0.892105i	$-0.649228\pi$
$131$	6.25694	−	10.8373i	0.546671	−	0.946862i	0.998500	−	0.0547576i	$-0.0174386\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.243061	+	0.420994i	−0.0209194	+	0.0362334i
$136$		0			0
$137$	−1.15139	+	1.99426i	−0.0983697	+	0.170381i	−0.911010	−	0.412384i	$-0.864696\pi$
$137$	−1.15139	+	1.99426i	−0.0983697	+	0.170381i	0.812640	+	0.582766i	$0.198029\pi$
$138$		0			0
$139$	−3.95416	−	6.84881i	−0.335388	−	0.580909i	0.648171	−	0.761494i	$-0.275534\pi$
$139$	−3.95416	−	6.84881i	−0.335388	−	0.580909i	−0.983559	+	0.180586i	$0.942201\pi$
$140$		0			0
$141$	−13.3625	+	23.1445i	−1.12532	+	1.94912i
$142$		0			0
$143$	−11.3625	−	19.6804i	−0.950179	−	1.64576i
$144$		0			0
$145$	−0.0458365	−	0.0793912i	−0.00380652	−	0.00659308i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.908327			−0.0744130			−0.0372065	−	0.999308i	$-0.511846\pi$
$149$	−0.908327			−0.0744130			−0.0372065	+	0.999308i	$0.511846\pi$
$150$		0			0
$151$	6.10555	+	10.5751i	0.496863	+	0.860591i	0.999993	−	0.00361884i	$-0.00115192\pi$
$151$	6.10555	+	10.5751i	0.496863	+	0.860591i	−0.503131	+	0.864210i	$0.667819\pi$
$152$		0			0
$153$	1.84861	−	3.20189i	0.149451	−	0.258857i
$154$		0			0
$155$	0.119429			0.00959281
$156$		0			0
$157$	−10.3486	−	17.9243i	−0.825909	−	1.43052i	−0.901222	−	0.433357i	$-0.857329\pi$
$157$	−10.3486	−	17.9243i	−0.825909	−	1.43052i	0.0753133	−	0.997160i	$-0.476004\pi$
$158$		0			0
$159$	−12.4542	−	21.5712i	−0.987679	−	1.71071i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−8.60555			−0.674039			−0.337019	−	0.941498i	$-0.609419\pi$
$163$	−8.60555			−0.674039			−0.337019	+	0.941498i	$0.609419\pi$
$164$		0			0
$165$	2.19722	−	3.80570i	0.171054	−	0.296274i
$166$		0			0
$167$	−11.4083	+	19.7598i	−0.882803	+	1.52906i	−0.0345914	+	0.999402i	$0.511013\pi$
$167$	−11.4083	+	19.7598i	−0.882803	+	1.52906i	−0.848211	+	0.529658i	$0.822320\pi$
$168$		0			0
$169$	−6.50000	+	11.2583i	−0.500000	+	0.866025i
$170$		0			0
$171$	8.51388			0.651073
$172$		0			0
$173$	−20.8167			−1.58266			−0.791330	−	0.611389i	$-0.790611\pi$
$173$	−20.8167			−1.58266			−0.791330	+	0.611389i	$0.790611\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	6.45416	−	11.1789i	0.485125	−	0.840261i
$178$		0			0
$179$	−1.18335			−0.0884474			−0.0442237	−	0.999022i	$-0.514081\pi$
$179$	−1.18335			−0.0884474			−0.0442237	+	0.999022i	$0.514081\pi$
$180$		0			0
$181$	1.39445			0.103649			0.0518243	−	0.998656i	$-0.483496\pi$
$181$	1.39445			0.103649			0.0518243	+	0.998656i	$0.483496\pi$
$182$		0			0
$183$	16.6056			1.22752
$184$		0			0
$185$	−2.78890			−0.205044
$186$		0			0
$187$	5.05971	−	8.76368i	0.370003	−	0.640864i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.51388			0.688400			0.344200	−	0.938896i	$-0.388150\pi$
$191$	9.51388			0.688400			0.344200	+	0.938896i	$0.388150\pi$
$192$		0			0
$193$	−25.6333			−1.84513			−0.922563	−	0.385847i	$-0.873909\pi$
$193$	−25.6333			−1.84513			−0.922563	+	0.385847i	$0.873909\pi$
$194$		0			0
$195$	−2.51388			−0.180023
$196$		0			0
$197$	−3.45416	+	5.98279i	−0.246099	+	0.426256i	−0.962440	−	0.271494i	$-0.912482\pi$
$197$	−3.45416	+	5.98279i	−0.246099	+	0.426256i	0.716341	+	0.697750i	$0.245815\pi$
$198$		0			0
$199$	−8.71110	+	15.0881i	−0.617514	+	1.06957i	0.372424	+	0.928063i	$0.378527\pi$
$199$	−8.71110	+	15.0881i	−0.617514	+	1.06957i	−0.989938	+	0.141502i	$0.954807\pi$
$200$		0			0
$201$	29.9361			2.11153
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−0.211103	−	0.365640i	−0.0147440	−	0.0255374i
$206$		0			0
$207$	−2.30278	−	3.98852i	−0.160054	−	0.277222i
$208$		0			0
$209$	23.3028			1.61189
$210$		0			0
$211$	−8.71110	+	15.0881i	−0.599697	+	1.03871i	0.393169	+	0.919466i	$0.371379\pi$
$211$	−8.71110	+	15.0881i	−0.599697	+	1.03871i	−0.992866	+	0.119239i	$0.961954\pi$
$212$		0			0
$213$	11.3028	+	19.5770i	0.774453	+	1.34139i
$214$		0			0
$215$	1.78890			0.122002
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−12.9083	−	22.3579i	−0.872264	−	1.51081i
$220$		0			0
$221$	−5.78890			−0.389403
$222$		0			0
$223$	−7.04584	+	12.2037i	−0.471824	+	0.817223i	−0.999480	−	0.0322347i	$-0.989738\pi$
$223$	−7.04584	+	12.2037i	−0.471824	+	0.817223i	0.527656	+	0.849458i	$0.323071\pi$
$224$		0			0
$225$	5.65139	+	9.78849i	0.376759	+	0.652566i
$226$		0			0
$227$	−6.10555	+	10.5751i	−0.405240	+	0.701896i	−0.994349	−	0.106157i	$-0.966145\pi$
$227$	−6.10555	+	10.5751i	−0.405240	+	0.701896i	0.589110	+	0.808053i	$0.299479\pi$
$228$		0			0
$229$	−0.697224	+	1.20763i	−0.0460739	+	0.0798023i	−0.888143	−	0.459568i	$-0.848004\pi$
$229$	−0.697224	+	1.20763i	−0.0460739	+	0.0798023i	0.842069	+	0.539370i	$0.181338\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.05971	+	7.03163i	−0.265961	+	0.460658i	−0.967815	−	0.251663i	$-0.919022\pi$
$233$	−4.05971	+	7.03163i	−0.265961	+	0.460658i	0.701854	+	0.712321i	$0.252356\pi$
$234$		0			0
$235$	1.75694	+	3.04311i	0.114610	+	0.198510i
$236$		0			0
$237$	−9.21110	+	15.9541i	−0.598325	+	1.03633i
$238$		0			0
$239$	9.00000			0.582162			0.291081	−	0.956698i	$-0.405985\pi$
$239$	9.00000			0.582162			0.291081	+	0.956698i	$0.405985\pi$
$240$		0			0
$241$	−2.44029	+	4.22670i	−0.157193	+	0.272266i	−0.933855	−	0.357651i	$-0.883578\pi$
$241$	−2.44029	+	4.22670i	−0.157193	+	0.272266i	0.776663	+	0.629917i	$0.216911\pi$
$242$		0			0
$243$	−19.6056			−1.25770
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−6.66527	−	11.5446i	−0.424101	−	0.734564i
$248$		0			0
$249$	−10.1194			−0.641293
$250$		0			0
$251$	−13.1194	−	22.7235i	−0.828091	−	1.43430i	−0.899534	−	0.436851i	$-0.856094\pi$
$251$	−13.1194	−	22.7235i	−0.828091	−	1.43430i	0.0714428	−	0.997445i	$-0.477240\pi$
$252$		0			0
$253$	−6.30278	−	10.9167i	−0.396252	−	0.686329i
$254$		0			0
$255$	−0.559715	−	0.969454i	−0.0350507	−	0.0607096i
$256$		0			0
$257$	1.04584	+	1.81144i	0.0652375	+	0.112995i	0.896799	−	0.442438i	$-0.145886\pi$
$257$	1.04584	+	1.81144i	0.0652375	+	0.112995i	−0.831562	+	0.555432i	$0.812553\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	0.348612	−	0.603814i	0.0215786	−	0.0373751i
$262$		0			0
$263$	10.3944			0.640949			0.320475	−	0.947257i	$-0.396158\pi$
$263$	10.3944			0.640949			0.320475	+	0.947257i	$0.396158\pi$
$264$		0			0
$265$	−3.27502			−0.201183
$266$		0			0
$267$	−5.86249	−	10.1541i	−0.358779	−	0.621423i
$268$		0			0
$269$	12.7708	−	22.1197i	0.778650	−	1.34866i	−0.154069	−	0.988060i	$-0.549238\pi$
$269$	12.7708	−	22.1197i	0.778650	−	1.34866i	0.932720	−	0.360602i	$-0.117429\pi$
$270$		0			0
$271$	1.10555	+	1.91487i	0.0671575	+	0.116320i	0.897649	−	0.440711i	$-0.145274\pi$
$271$	1.10555	+	1.91487i	0.0671575	+	0.116320i	−0.830492	+	0.557031i	$0.811940\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	15.4680	+	26.7914i	0.932758	+	1.61558i
$276$		0			0
$277$	1.71110	−	2.96372i	0.102810	−	0.178072i	−0.810031	−	0.586387i	$-0.800550\pi$
$277$	1.71110	−	2.96372i	0.102810	−	0.178072i	0.912841	+	0.408314i	$0.133883\pi$
$278$		0			0
$279$	0.454163	+	0.786634i	0.0271901	+	0.0470946i
$280$		0			0
$281$	−15.8167			−0.943542			−0.471771	−	0.881721i	$-0.656385\pi$
$281$	−15.8167			−0.943542			−0.471771	+	0.881721i	$0.656385\pi$
$282$		0			0
$283$	−20.4222			−1.21397			−0.606987	−	0.794712i	$-0.707622\pi$
$283$	−20.4222			−1.21397			−0.606987	+	0.794712i	$0.707622\pi$
$284$		0			0
$285$	1.28890	−	2.23244i	0.0763477	−	0.132238i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	7.21110	+	12.4900i	0.424183	+	0.734706i
$290$		0			0
$291$	7.01388	+	12.1484i	0.411161	+	0.712151i
$292$		0			0
$293$	−11.6972	−	20.2602i	−0.683359	−	1.18361i	−0.973949	−	0.226765i	$-0.927185\pi$
$293$	−11.6972	−	20.2602i	−0.683359	−	1.18361i	0.290590	−	0.956848i	$-0.406148\pi$
$294$		0			0
$295$	−0.848612	−	1.46984i	−0.0494081	−	0.0855774i
$296$		0			0
$297$	−10.1194			−0.587189
$298$		0			0
$299$	−3.60555	+	6.24500i	−0.208514	+	0.361158i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	21.9083			1.25860
$304$		0			0
$305$	1.09167	−	1.89083i	0.0625090	−	0.108269i
$306$		0			0
$307$	−12.5139			−0.714205			−0.357102	−	0.934065i	$-0.616235\pi$
$307$	−12.5139			−0.714205			−0.357102	+	0.934065i	$0.616235\pi$
$308$		0			0
$309$	7.84861	−	13.5942i	0.446492	−	0.773347i
$310$		0			0
$311$	−1.04584	−	1.81144i	−0.0593039	−	0.102717i	0.834849	−	0.550479i	$-0.185555\pi$
$311$	−1.04584	−	1.81144i	−0.0593039	−	0.102717i	−0.894153	+	0.447761i	$0.852221\pi$
$312$		0			0
$313$	−12.5139	+	21.6747i	−0.707326	+	1.22512i	0.258519	+	0.966006i	$0.416765\pi$
$313$	−12.5139	+	21.6747i	−0.707326	+	1.22512i	−0.965845	+	0.259119i	$0.916568\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−14.6194	+	25.3216i	−0.821109	+	1.42220i	0.0837481	+	0.996487i	$0.473311\pi$
$317$	−14.6194	+	25.3216i	−0.821109	+	1.42220i	−0.904857	+	0.425715i	$0.860022\pi$
$318$		0			0
$319$	0.954163	−	1.65266i	0.0534229	−	0.0925312i
$320$		0			0
$321$	17.8625	+	30.9387i	0.996987	+	1.72683i
$322$		0			0
$323$	2.96804	−	5.14080i	0.165146	−	0.286042i
$324$		0			0
$325$	8.84861	−	15.3262i	0.490833	−	0.850147i
$326$		0			0
$327$	4.15139	+	7.19041i	0.229572	+	0.397631i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−29.3305			−1.61215			−0.806076	−	0.591812i	$-0.798413\pi$
$331$	−29.3305			−1.61215			−0.806076	+	0.591812i	$0.798413\pi$
$332$		0			0
$333$	−10.6056	−	18.3694i	−0.581181	−	1.00663i
$334$		0			0
$335$	1.96804	−	3.40875i	0.107526	−	0.186240i
$336$		0			0
$337$	10.3028			0.561228			0.280614	−	0.959821i	$-0.409462\pi$
$337$	10.3028			0.561228			0.280614	+	0.959821i	$0.409462\pi$
$338$		0			0
$339$	11.7569	+	20.3636i	0.638549	+	1.10600i
$340$		0			0
$341$	1.24306	+	2.15304i	0.0673155	+	0.116594i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−1.39445			−0.0750746
$346$		0			0
$347$	8.30278	−	14.3808i	0.445716	−	0.772003i	−0.552385	−	0.833589i	$-0.686282\pi$
$347$	8.30278	−	14.3808i	0.445716	−	0.772003i	0.998102	+	0.0615854i	$0.0196157\pi$
$348$		0			0
$349$	3.89445	−	6.74538i	0.208465	−	0.361072i	−0.742766	−	0.669551i	$-0.766487\pi$
$349$	3.89445	−	6.74538i	0.208465	−	0.361072i	0.951231	+	0.308479i	$0.0998199\pi$
$350$		0			0
$351$	2.89445	+	5.01333i	0.154494	+	0.267592i
$352$		0			0
$353$	10.9083			0.580592			0.290296	−	0.956937i	$-0.406246\pi$
$353$	10.9083			0.580592			0.290296	+	0.956937i	$0.406246\pi$
$354$		0			0
$355$	2.97224			0.157750
$356$		0			0
$357$		0			0
$358$		0			0
$359$	2.86249	−	4.95798i	0.151076	−	0.261672i	−0.780547	−	0.625097i	$-0.785059\pi$
$359$	2.86249	−	4.95798i	0.151076	−	0.261672i	0.931623	+	0.363425i	$0.118393\pi$
$360$		0			0
$361$	−5.33053			−0.280554
$362$		0			0
$363$	66.1472			3.47183
$364$		0			0
$365$	−3.39445			−0.177674
$366$		0			0
$367$	11.2111			0.585215			0.292607	−	0.956233i	$-0.405477\pi$
$367$	11.2111			0.585215			0.292607	+	0.956233i	$0.405477\pi$
$368$		0			0
$369$	1.60555	−	2.78090i	0.0835817	−	0.144768i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.48612			−0.0769485			−0.0384742	−	0.999260i	$-0.512250\pi$
$373$	−1.48612			−0.0769485			−0.0384742	+	0.999260i	$0.512250\pi$
$374$		0			0
$375$	6.90833			0.356744
$376$		0			0
$377$	−1.09167			−0.0562240
$378$		0			0
$379$	7.45416	−	12.9110i	0.382895	−	0.663193i	−0.608580	−	0.793493i	$-0.708261\pi$
$379$	7.45416	−	12.9110i	0.382895	−	0.663193i	0.991475	+	0.130300i	$0.0415939\pi$
$380$		0			0
$381$	13.7111	−	23.7483i	0.702441	−	1.21666i
$382$		0			0
$383$	−9.90833			−0.506292			−0.253146	−	0.967428i	$-0.581465\pi$
$383$	−9.90833			−0.506292			−0.253146	+	0.967428i	$0.581465\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.80278	+	11.7828i	0.345805	+	0.598951i
$388$		0			0
$389$	13.6056	+	23.5655i	0.689829	+	1.19482i	0.971893	+	0.235423i	$0.0756476\pi$
$389$	13.6056	+	23.5655i	0.689829	+	1.19482i	−0.282064	+	0.959396i	$0.591019\pi$
$390$		0			0
$391$	−3.21110			−0.162392
$392$		0			0
$393$	14.4083	−	24.9560i	0.726804	−	1.25886i
$394$		0			0
$395$	1.21110	+	2.09769i	0.0609372	+	0.105546i
$396$		0			0
$397$	−10.0000			−0.501886			−0.250943	−	0.968002i	$-0.580741\pi$
$397$	−10.0000			−0.501886			−0.250943	+	0.968002i	$0.580741\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−7.84861	−	13.5942i	−0.391941	−	0.678862i	0.600765	−	0.799426i	$-0.294863\pi$
$401$	−7.84861	−	13.5942i	−0.391941	−	0.678862i	−0.992706	+	0.120564i	$0.961530\pi$
$402$		0			0
$403$	0.711103	−	1.23167i	0.0354225	−	0.0613536i
$404$		0			0
$405$	−1.60555	+	2.78090i	−0.0797805	+	0.138184i
$406$		0			0
$407$	−29.0278	−	50.2775i	−1.43885	−	2.49217i
$408$		0			0
$409$	−10.9680	+	18.9972i	−0.542335	+	0.939351i	0.456435	+	0.889757i	$0.349126\pi$
$409$	−10.9680	+	18.9972i	−0.542335	+	0.939351i	−0.998769	+	0.0495944i	$0.984207\pi$
$410$		0			0
$411$	−2.65139	+	4.59234i	−0.130783	+	0.226523i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−0.665266	+	1.15227i	−0.0326566	+	0.0565629i
$416$		0			0
$417$	−9.10555	−	15.7713i	−0.445901	−	0.772323i
$418$		0			0
$419$	18.1056	−	31.3597i	0.884514	−	1.53202i	0.0382445	−	0.999268i	$-0.487823\pi$
$419$	18.1056	−	31.3597i	0.884514	−	1.53202i	0.846270	−	0.532755i	$-0.178843\pi$
$420$		0			0
$421$	−14.0000			−0.682318			−0.341159	−	0.940006i	$-0.610819\pi$
$421$	−14.0000			−0.682318			−0.341159	+	0.940006i	$0.610819\pi$
$422$		0			0
$423$	−13.3625	+	23.1445i	−0.649707	+	1.12532i
$424$		0			0
$425$	7.88057			0.382264
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−26.1653	−	45.3196i	−1.26327	−	2.18805i
$430$		0			0
$431$	40.3305			1.94265			0.971327	−	0.237749i	$-0.0764095\pi$
$431$	40.3305			1.94265			0.971327	+	0.237749i	$0.0764095\pi$
$432$		0			0
$433$	−5.80278	−	10.0507i	−0.278864	−	0.483006i	0.692239	−	0.721668i	$-0.256624\pi$
$433$	−5.80278	−	10.0507i	−0.278864	−	0.483006i	−0.971103	+	0.238662i	$0.923291\pi$
$434$		0			0
$435$	−0.105551	−	0.182820i	−0.00506080	−	0.00876556i
$436$		0			0
$437$	−3.69722	−	6.40378i	−0.176862	−	0.306334i
$438$		0			0
$439$	14.5597	+	25.2182i	0.694897	+	1.20360i	0.970215	+	0.242244i	$0.0778835\pi$
$439$	14.5597	+	25.2182i	0.694897	+	1.20360i	−0.275318	+	0.961353i	$0.588783\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−0.908327	+	1.57327i	−0.0431559	+	0.0747482i	−0.886797	−	0.462160i	$-0.847075\pi$
$443$	−0.908327	+	1.57327i	−0.0431559	+	0.0747482i	0.843641	+	0.536908i	$0.180408\pi$
$444$		0			0
$445$	−1.54163			−0.0730805
$446$		0			0
$447$	−2.09167			−0.0989327
$448$		0			0
$449$	11.6056	+	20.1014i	0.547700	+	0.948644i	0.998432	+	0.0559845i	$0.0178297\pi$
$449$	11.6056	+	20.1014i	0.547700	+	0.948644i	−0.450732	+	0.892659i	$0.648837\pi$
$450$		0			0
$451$	4.39445	−	7.61141i	0.206927	−	0.358407i
$452$		0			0
$453$	14.0597	+	24.3521i	0.660583	+	1.14416i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.788897	+	1.36641i	0.0369031	+	0.0639180i	0.883887	−	0.467700i	$-0.154917\pi$
$457$	0.788897	+	1.36641i	0.0369031	+	0.0639180i	−0.846984	+	0.531618i	$0.821584\pi$
$458$		0			0
$459$	−1.28890	+	2.23244i	−0.0601606	+	0.104201i
$460$		0			0
$461$	16.5736	+	28.7063i	0.771909	+	1.33699i	0.936515	+	0.350627i	$0.114031\pi$
$461$	16.5736	+	28.7063i	0.771909	+	1.33699i	−0.164606	+	0.986359i	$0.552635\pi$
$462$		0			0
$463$	−35.8444			−1.66583			−0.832916	−	0.553400i	$-0.813330\pi$
$463$	−35.8444			−1.66583			−0.832916	+	0.553400i	$0.813330\pi$
$464$		0			0
$465$	0.275019			0.0127537
$466$		0			0
$467$	18.0139	−	31.2010i	0.833583	−	1.44381i	−0.0615962	−	0.998101i	$-0.519619\pi$
$467$	18.0139	−	31.2010i	0.833583	−	1.44381i	0.895179	−	0.445707i	$-0.147048\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−23.8305	−	41.2757i	−1.09805	−	1.90188i
$472$		0			0
$473$	18.6194	+	32.2498i	0.856122	+	1.48285i
$474$		0			0
$475$	9.07359	+	15.7159i	0.416325	+	0.721096i
$476$		0			0
$477$	−12.4542	−	21.5712i	−0.570237	−	0.987679i
$478$		0			0
$479$	−26.7250			−1.22110			−0.610548	−	0.791979i	$-0.709051\pi$
$479$	−26.7250			−1.22110			−0.610548	+	0.791979i	$0.709051\pi$
$480$		0			0
$481$	−16.6056	+	28.7617i	−0.757148	+	1.31142i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.84441			0.0837504
$486$		0			0
$487$	−2.04584	+	3.54349i	−0.0927057	+	0.160571i	−0.908649	−	0.417561i	$-0.862885\pi$
$487$	−2.04584	+	3.54349i	−0.0927057	+	0.160571i	0.815943	+	0.578132i	$0.196218\pi$
$488$		0			0
$489$	−19.8167			−0.896140
$490$		0			0
$491$	5.04584	−	8.73965i	0.227715	−	0.394415i	−0.729415	−	0.684071i	$-0.760208\pi$
$491$	5.04584	−	8.73965i	0.227715	−	0.394415i	0.957131	+	0.289657i	$0.0935411\pi$
$492$		0			0
$493$	−0.243061	−	0.420994i	−0.0109469	−	0.0189606i
$494$		0			0
$495$	2.19722	−	3.80570i	0.0987579	−	0.171054i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−14.7708	+	25.5838i	−0.661233	+	1.14529i	0.319059	+	0.947735i	$0.396633\pi$
$499$	−14.7708	+	25.5838i	−0.661233	+	1.14529i	−0.980292	+	0.197554i	$0.936700\pi$
$500$		0			0
$501$	−26.2708	+	45.5024i	−1.17369	+	2.03290i
$502$		0			0
$503$	−10.0597	−	17.4239i	−0.448541	−	0.776895i	0.549751	−	0.835329i	$-0.314723\pi$
$503$	−10.0597	−	17.4239i	−0.448541	−	0.776895i	−0.998291	+	0.0584338i	$0.981389\pi$
$504$		0			0
$505$	1.44029	−	2.49465i	0.0640919	−	0.111010i
$506$		0			0
$507$	−14.9680	+	25.9254i	−0.664754	+	1.15139i
$508$		0			0
$509$	−3.71110	−	6.42782i	−0.164492	−	0.284908i	0.771983	−	0.635643i	$-0.219265\pi$
$509$	−3.71110	−	6.42782i	−0.164492	−	0.284908i	−0.936475	+	0.350735i	$0.885932\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−5.93608			−0.262084
$514$		0			0
$515$	−1.03196	−	1.78740i	−0.0454735	−	0.0787624i
$516$		0			0
$517$	−36.5736	+	63.3473i	−1.60850	+	2.78601i
$518$		0			0
$519$	−47.9361			−2.10416
$520$		0			0
$521$	11.7250	+	20.3083i	0.513681	+	0.889721i	0.999874	+	0.0158699i	$0.00505174\pi$
$521$	11.7250	+	20.3083i	0.513681	+	0.889721i	−0.486193	+	0.873851i	$0.661615\pi$
$522$		0			0
$523$	17.7250	+	30.7006i	0.775059	+	1.34244i	0.934761	+	0.355277i	$0.115613\pi$
$523$	17.7250	+	30.7006i	0.775059	+	1.34244i	−0.159702	+	0.987165i	$0.551053\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.633308			0.0275873
$528$		0			0
$529$	9.50000	−	16.4545i	0.413043	−	0.715412i
$530$		0			0
$531$	6.45416	−	11.1789i	0.280087	−	0.485125i
$532$		0			0
$533$	−5.02776			−0.217776
$534$		0			0
$535$	4.69722			0.203079
$536$		0			0
$537$	−2.72498			−0.117592
$538$		0			0
$539$		0			0
$540$		0			0
$541$	4.05971	−	7.03163i	0.174541	−	0.302313i	−0.765461	−	0.643482i	$-0.777489\pi$
$541$	4.05971	−	7.03163i	0.174541	−	0.302313i	0.940002	+	0.341168i	$0.110823\pi$
$542$		0			0
$543$	3.21110			0.137802
$544$		0			0
$545$	1.09167			0.0467621
$546$		0			0
$547$	−37.2389			−1.59222			−0.796109	−	0.605153i	$-0.793112\pi$
$547$	−37.2389			−1.59222			−0.796109	+	0.605153i	$0.793112\pi$
$548$		0			0
$549$	16.6056			0.708708
$550$		0			0
$551$	0.559715	−	0.969454i	0.0238446	−	0.0413001i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−6.42221			−0.272607
$556$		0			0
$557$	5.30278			0.224686			0.112343	−	0.993669i	$-0.464164\pi$
$557$	5.30278			0.224686			0.112343	+	0.993669i	$0.464164\pi$
$558$		0			0
$559$	10.6514	−	18.4487i	0.450506	−	0.780299i
$560$		0			0
$561$	11.6514	−	20.1808i	0.491922	−	0.852034i
$562$		0			0
$563$	18.8167	−	32.5914i	0.793027	−	1.37356i	−0.131057	−	0.991375i	$-0.541837\pi$
$563$	18.8167	−	32.5914i	0.793027	−	1.37356i	0.924084	−	0.382189i	$-0.124830\pi$
$564$		0			0
$565$	3.09167			0.130068
$566$		0			0
$567$		0			0
$568$		0			0
$569$	2.39445	+	4.14731i	0.100381	+	0.173864i	0.911841	−	0.410542i	$-0.134661\pi$
$569$	2.39445	+	4.14731i	0.100381	+	0.173864i	−0.811461	+	0.584407i	$0.801327\pi$
$570$		0			0
$571$	−9.94029	−	17.2171i	−0.415988	−	0.720512i	0.579544	−	0.814941i	$-0.303231\pi$
$571$	−9.94029	−	17.2171i	−0.415988	−	0.720512i	−0.995532	+	0.0944289i	$0.969898\pi$
$572$		0			0
$573$	21.9083			0.915233
$574$		0			0
$575$	4.90833	−	8.50147i	0.204691	−	0.354536i
$576$		0			0
$577$	14.4083	+	24.9560i	0.599826	+	1.03893i	0.992846	+	0.119400i	$0.0380971\pi$
$577$	14.4083	+	24.9560i	0.599826	+	1.03893i	−0.393020	+	0.919530i	$0.628570\pi$
$578$		0			0
$579$	−59.0278			−2.45311
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−34.0875	−	59.0412i	−1.41176	−	2.44524i
$584$		0			0
$585$	−2.51388			−0.103936
$586$		0			0
$587$	−11.7431	+	20.3396i	−0.484688	+	0.839504i	−0.999845	−	0.0175914i	$-0.994400\pi$
$587$	−11.7431	+	20.3396i	−0.484688	+	0.839504i	0.515157	+	0.857096i	$0.327734\pi$
$588$		0			0
$589$	0.729183	+	1.26298i	0.0300455	+	0.0520402i
$590$		0			0
$591$	−7.95416	+	13.7770i	−0.327191	+	0.566711i
$592$		0			0
$593$	9.04584	−	15.6678i	0.371468	−	0.643401i	−0.618324	−	0.785924i	$-0.712188\pi$
$593$	9.04584	−	15.6678i	0.371468	−	0.643401i	0.989792	+	0.142522i	$0.0455212\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−20.0597	+	34.7444i	−0.820989	+	1.42200i
$598$		0			0
$599$	−8.07359	−	13.9839i	−0.329878	−	0.571366i	0.652609	−	0.757695i	$-0.273674\pi$
$599$	−8.07359	−	13.9839i	−0.329878	−	0.571366i	−0.982487	+	0.186329i	$0.940341\pi$
$600$		0			0
$601$	−10.0597	+	17.4239i	−0.410344	+	0.710737i	−0.994927	−	0.100597i	$-0.967925\pi$
$601$	−10.0597	+	17.4239i	−0.410344	+	0.710737i	0.584583	+	0.811334i	$0.301258\pi$
$602$		0			0
$603$	29.9361			1.21909
$604$		0			0
$605$	4.34861	−	7.53202i	0.176796	−	0.306220i
$606$		0			0
$607$	−39.8444			−1.61723			−0.808617	−	0.588335i	$-0.799784\pi$
$607$	−39.8444			−1.61723			−0.808617	+	0.588335i	$0.799784\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	41.8444			1.69284
$612$		0			0
$613$	−33.7250			−1.36214			−0.681070	−	0.732219i	$-0.738485\pi$
$613$	−33.7250			−1.36214			−0.681070	+	0.732219i	$0.738485\pi$
$614$		0			0
$615$	−0.486122	−	0.841988i	−0.0196023	−	0.0339522i
$616$		0			0
$617$	−14.3167	−	24.7972i	−0.576367	−	0.998297i	−0.995892	−	0.0905527i	$-0.971137\pi$
$617$	−14.3167	−	24.7972i	−0.576367	−	0.998297i	0.419525	−	0.907744i	$-0.362197\pi$
$618$		0			0
$619$	4.21110	+	7.29384i	0.169259	+	0.293164i	0.938159	−	0.346204i	$-0.112529\pi$
$619$	4.21110	+	7.29384i	0.169259	+	0.293164i	−0.768901	+	0.639368i	$0.779196\pi$
$620$		0			0
$621$	1.60555	+	2.78090i	0.0644286	+	0.111594i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−11.8167	+	20.4670i	−0.472666	+	0.818682i
$626$		0			0
$627$	53.6611			2.14302
$628$		0			0
$629$	−14.7889			−0.589672
$630$		0			0
$631$	15.5458	+	26.9262i	0.618870	+	1.07191i	0.989692	+	0.143210i	$0.0457426\pi$
$631$	15.5458	+	26.9262i	0.618870	+	1.07191i	−0.370822	+	0.928704i	$0.620924\pi$
$632$		0			0
$633$	−20.0597	+	34.7444i	−0.797302	+	1.38097i
$634$		0			0
$635$	−1.80278	−	3.12250i	−0.0715410	−	0.123913i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	11.3028	+	19.5770i	0.447131	+	0.774453i
$640$		0			0
$641$	4.34861	−	7.53202i	0.171760	−	0.297497i	−0.767275	−	0.641318i	$-0.778388\pi$
$641$	4.34861	−	7.53202i	0.171760	−	0.297497i	0.939035	+	0.343821i	$0.111721\pi$
$642$		0			0
$643$	9.50000	+	16.4545i	0.374643	+	0.648901i	0.990274	−	0.139134i	$-0.0444318\pi$
$643$	9.50000	+	16.4545i	0.374643	+	0.648901i	−0.615630	+	0.788035i	$0.711098\pi$
$644$		0			0
$645$	4.11943			0.162202
$646$		0			0
$647$	14.6056			0.574203			0.287102	−	0.957900i	$-0.407308\pi$
$647$	14.6056			0.574203			0.287102	+	0.957900i	$0.407308\pi$
$648$		0			0
$649$	17.6653	−	30.5971i	0.693422	−	1.20104i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	19.6791	+	34.0853i	0.770104	+	1.33386i	0.937505	+	0.347971i	$0.113129\pi$
$653$	19.6791	+	34.0853i	0.770104	+	1.33386i	−0.167401	+	0.985889i	$0.553537\pi$
$654$		0			0
$655$	−1.89445	−	3.28128i	−0.0740222	−	0.128210i
$656$		0			0
$657$	−12.9083	−	22.3579i	−0.503602	−	0.872264i
$658$		0			0
$659$	−24.6333	−	42.6661i	−0.959577	−	1.66204i	−0.723527	−	0.690296i	$-0.757480\pi$
$659$	−24.6333	−	42.6661i	−0.959577	−	1.66204i	−0.236050	−	0.971741i	$-0.575853\pi$
$660$		0			0
$661$	−5.39445			−0.209820			−0.104910	−	0.994482i	$-0.533455\pi$
$661$	−5.39445			−0.209820			−0.104910	+	0.994482i	$0.533455\pi$
$662$		0			0
$663$	−13.3305			−0.517715
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.605551			−0.0234470
$668$		0			0
$669$	−16.2250	+	28.1025i	−0.627294	+	1.08651i
$670$		0			0
$671$	45.4500			1.75458
$672$		0			0
$673$	−16.8944	+	29.2620i	−0.651233	+	1.12797i	0.331591	+	0.943423i	$0.392415\pi$
$673$	−16.8944	+	29.2620i	−0.651233	+	1.12797i	−0.982824	+	0.184546i	$0.940919\pi$
$674$		0			0
$675$	−3.94029	−	6.82477i	−0.151662	−	0.262686i
$676$		0			0
$677$	−7.15139	+	12.3866i	−0.274850	+	0.476054i	−0.970097	−	0.242716i	$-0.921962\pi$
$677$	−7.15139	+	12.3866i	−0.274850	+	0.476054i	0.695247	+	0.718771i	$0.255295\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−14.0597	+	24.3521i	−0.538769	+	0.933176i
$682$		0			0
$683$	−5.59167	+	9.68506i	−0.213959	+	0.370589i	−0.952950	−	0.303127i	$-0.901969\pi$
$683$	−5.59167	+	9.68506i	−0.213959	+	0.370589i	0.738991	+	0.673716i	$0.235303\pi$
$684$		0			0
$685$	0.348612	+	0.603814i	0.0133198	+	0.0230705i
$686$		0			0
$687$	−1.60555	+	2.78090i	−0.0612556	+	0.106098i
$688$		0			0
$689$	−19.5000	+	33.7750i	−0.742891	+	1.28672i
$690$		0			0
$691$	−22.2708	−	38.5742i	−0.847222	−	1.46743i	−0.883678	−	0.468096i	$-0.844940\pi$
$691$	−22.2708	−	38.5742i	−0.847222	−	1.46743i	0.0364558	−	0.999335i	$-0.488393\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.39445			−0.0908266
$696$		0			0
$697$	−1.11943	−	1.93891i	−0.0424014	−	0.0734414i
$698$		0			0
$699$	−9.34861	+	16.1923i	−0.353597	+	0.612448i
$700$		0			0
$701$	−19.8167			−0.748465			−0.374232	−	0.927335i	$-0.622094\pi$
$701$	−19.8167			−0.748465			−0.374232	+	0.927335i	$0.622094\pi$
$702$		0			0
$703$	−17.0278	−	29.4929i	−0.642214	−	1.11235i
$704$		0			0
$705$	4.04584	+	7.00759i	0.152375	+	0.263921i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−3.51388			−0.131966			−0.0659832	−	0.997821i	$-0.521018\pi$
$709$	−3.51388			−0.131966			−0.0659832	+	0.997821i	$0.521018\pi$
$710$		0			0
$711$	−9.21110	+	15.9541i	−0.345443	+	0.598325i
$712$		0			0
$713$	0.394449	−	0.683205i	0.0147722	−	0.0255862i
$714$		0			0
$715$	−6.88057			−0.257319
$716$		0			0
$717$	20.7250			0.773989
$718$		0			0
$719$	−20.8167			−0.776330			−0.388165	−	0.921590i	$-0.626891\pi$
$719$	−20.8167			−0.776330			−0.388165	+	0.921590i	$0.626891\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−5.61943	+	9.73314i	−0.208989	+	0.361979i
$724$		0			0
$725$	1.48612			0.0551932
$726$		0			0
$727$	41.6056			1.54306			0.771532	−	0.636190i	$-0.219491\pi$
$727$	41.6056			1.54306			0.771532	+	0.636190i	$0.219491\pi$
$728$		0			0
$729$	−13.3305			−0.493723
$730$		0			0
$731$	9.48612			0.350857
$732$		0			0
$733$	−8.46804	+	14.6671i	−0.312774	+	0.541741i	−0.978962	−	0.204043i	$-0.934592\pi$
$733$	−8.46804	+	14.6671i	−0.312774	+	0.541741i	0.666188	+	0.745784i	$0.267925\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	81.9361			3.01815
$738$		0			0
$739$	−34.6056			−1.27299			−0.636493	−	0.771283i	$-0.719616\pi$
$739$	−34.6056			−1.27299			−0.636493	+	0.771283i	$0.719616\pi$
$740$		0			0
$741$	−15.3486	−	26.5846i	−0.563845	−	0.976609i
$742$		0			0
$743$	−2.13751	+	3.70228i	−0.0784176	+	0.135823i	−0.902567	−	0.430549i	$-0.858320\pi$
$743$	−2.13751	+	3.70228i	−0.0784176	+	0.135823i	0.824150	+	0.566372i	$0.191653\pi$
$744$		0			0
$745$	−0.137510	+	0.238174i	−0.00503796	+	0.00872601i
$746$		0			0
$747$	−10.1194			−0.370251
$748$		0			0
$749$		0			0
$750$		0			0
$751$	8.89445	+	15.4056i	0.324563	+	0.562160i	0.981424	−	0.191852i	$-0.0614494\pi$
$751$	8.89445	+	15.4056i	0.324563	+	0.562160i	−0.656861	+	0.754012i	$0.728116\pi$
$752$		0			0
$753$	−30.2111	−	52.3272i	−1.10095	−	1.90691i
$754$		0			0
$755$	3.69722			0.134556
$756$		0			0
$757$	21.2111	−	36.7387i	0.770931	−	1.33529i	−0.166123	−	0.986105i	$-0.553125\pi$
$757$	21.2111	−	36.7387i	0.770931	−	1.33529i	0.937053	−	0.349186i	$-0.113542\pi$
$758$		0			0
$759$	−14.5139	−	25.1388i	−0.526820	−	0.912480i
$760$		0			0
$761$	−42.6972			−1.54777			−0.773887	−	0.633324i	$-0.781690\pi$
$761$	−42.6972			−1.54777			−0.773887	+	0.633324i	$0.781690\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.559715	−	0.969454i	−0.0202365	−	0.0350507i
$766$		0			0
$767$	−20.2111			−0.729781
$768$		0			0
$769$	12.8028	−	22.1751i	0.461680	−	0.799653i	−0.537365	−	0.843350i	$-0.680580\pi$
$769$	12.8028	−	22.1751i	0.461680	−	0.799653i	0.999045	+	0.0436968i	$0.0139135\pi$
$770$		0			0
$771$	2.40833	+	4.17134i	0.0867338	+	0.150227i
$772$		0			0
$773$	13.4083	−	23.2239i	0.482264	−	0.835306i	−0.517529	−	0.855666i	$-0.673148\pi$
$773$	13.4083	−	23.2239i	0.482264	−	0.835306i	0.999793	+	0.0203601i	$0.00648127\pi$
$774$		0			0
$775$	−0.968042	+	1.67670i	−0.0347731	+	0.0602287i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.57779	−	4.46487i	0.0923591	−	0.159971i
$780$		0			0
$781$	30.9361	+	53.5829i	1.10698	+	1.91735i
$782$		0			0
$783$	−0.243061	+	0.420994i	−0.00868629	+	0.0150451i
$784$		0			0
$785$	−6.26662			−0.223665
$786$		0			0
$787$	−19.0000	+	32.9090i	−0.677277	+	1.17308i	0.298521	+	0.954403i	$0.403507\pi$
$787$	−19.0000	+	32.9090i	−0.677277	+	1.17308i	−0.975798	+	0.218675i	$0.929827\pi$
$788$		0			0
$789$	23.9361			0.852147
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−13.0000	−	22.5167i	−0.461644	−	0.799590i
$794$		0			0
$795$	−7.54163			−0.267474
$796$		0			0
$797$	−5.72498	−	9.91596i	−0.202789	−	0.351241i	0.746637	−	0.665232i	$-0.231667\pi$
$797$	−5.72498	−	9.91596i	−0.202789	−	0.351241i	−0.949426	+	0.313991i	$0.898334\pi$
$798$		0			0
$799$	9.31665	+	16.1369i	0.329600	+	0.570883i
$800$		0			0
$801$	−5.86249	−	10.1541i	−0.207141	−	0.358779i
$802$		0			0
$803$	−35.3305	−	61.1943i	−1.24679	−	2.15950i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	29.4083	−	50.9367i	1.03522	−	1.79306i
$808$		0			0
$809$	−5.36669			−0.188683			−0.0943414	−	0.995540i	$-0.530075\pi$
$809$	−5.36669			−0.188683			−0.0943414	+	0.995540i	$0.530075\pi$
$810$		0			0
$811$	16.7250			0.587294			0.293647	−	0.955914i	$-0.405131\pi$
$811$	16.7250			0.587294			0.293647	+	0.955914i	$0.405131\pi$
$812$		0			0
$813$	2.54584	+	4.40952i	0.0892864	+	0.154649i
$814$		0			0
$815$	−1.30278	+	2.25647i	−0.0456342	+	0.0790408i
$816$		0			0
$817$	10.9222	+	18.9178i	0.382120	+	0.661851i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	21.9222	+	37.9704i	0.765090	+	1.32518i	0.940199	+	0.340626i	$0.110639\pi$
$821$	21.9222	+	37.9704i	0.765090	+	1.32518i	−0.175109	+	0.984549i	$0.556028\pi$
$822$		0			0
$823$	18.8028	−	32.5674i	0.655424	−	1.13523i	−0.326364	−	0.945244i	$-0.605823\pi$
$823$	18.8028	−	32.5674i	0.655424	−	1.13523i	0.981787	−	0.189983i	$-0.0608432\pi$
$824$		0			0
$825$	35.6194	+	61.6947i	1.24011	+	2.14793i
$826$		0			0
$827$	38.9361			1.35394			0.676970	−	0.736010i	$-0.263293\pi$
$827$	38.9361			1.35394			0.676970	+	0.736010i	$0.263293\pi$
$828$		0			0
$829$	−43.9361			−1.52596			−0.762982	−	0.646420i	$-0.776265\pi$
$829$	−43.9361			−1.52596			−0.762982	+	0.646420i	$0.776265\pi$
$830$		0			0
$831$	3.94029	−	6.82477i	0.136687	−	0.236749i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	3.45416	+	5.98279i	0.119536	+	0.207043i
$836$		0			0
$837$	−0.316654	−	0.548461i	−0.0109452	−	0.0189576i
$838$		0			0
$839$	−18.9680	−	32.8536i	−0.654850	−	1.13423i	−0.981932	−	0.189237i	$-0.939399\pi$
$839$	−18.9680	−	32.8536i	−0.654850	−	1.13423i	0.327082	−	0.944996i	$-0.393935\pi$
$840$		0			0
$841$	14.4542	+	25.0353i	0.498419	+	0.863288i
$842$		0			0
$843$	−36.4222			−1.25445
$844$		0			0
$845$	1.96804	+	3.40875i	0.0677027	+	0.117265i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−47.0278			−1.61399
$850$		0			0
$851$	−9.21110	+	15.9541i	−0.315753	+	0.546899i
$852$		0			0
$853$	−11.0000			−0.376633			−0.188316	−	0.982108i	$-0.560303\pi$
$853$	−11.0000			−0.376633			−0.188316	+	0.982108i	$0.560303\pi$
$854$		0			0
$855$	1.28890	−	2.23244i	0.0440794	−	0.0763477i
$856$		0			0
$857$	23.4680	+	40.6478i	0.801653	+	1.38850i	0.918528	+	0.395357i	$0.129379\pi$
$857$	23.4680	+	40.6478i	0.801653	+	1.38850i	−0.116874	+	0.993147i	$0.537288\pi$
$858$		0			0
$859$	21.6056	−	37.4219i	0.737172	−	1.27682i	−0.216592	−	0.976262i	$-0.569494\pi$
$859$	21.6056	−	37.4219i	0.737172	−	1.27682i	0.953764	−	0.300557i	$-0.0971725\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−18.3944	+	31.8601i	−0.626154	+	1.08453i	0.362162	+	0.932115i	$0.382039\pi$
$863$	−18.3944	+	31.8601i	−0.626154	+	1.08453i	−0.988316	+	0.152416i	$0.951295\pi$
$864$		0			0
$865$	−3.15139	+	5.45836i	−0.107150	+	0.185590i
$866$		0			0
$867$	16.6056	+	28.7617i	0.563954	+	0.976797i
$868$		0			0
$869$	−25.2111	+	43.6669i	−0.855228	+	1.48130i
$870$		0			0
$871$	−23.4361	−	40.5925i	−0.794101	−	1.37542i
$872$		0			0
$873$	7.01388	+	12.1484i	0.237384	+	0.411161i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−2.02776			−0.0684725			−0.0342362	−	0.999414i	$-0.510900\pi$
$877$	−2.02776			−0.0684725			−0.0342362	+	0.999414i	$0.510900\pi$
$878$		0			0
$879$	−26.9361	−	46.6547i	−0.908532	−	1.57362i
$880$		0			0
$881$	−24.1056	+	41.7520i	−0.812137	+	1.40666i	0.0992291	+	0.995065i	$0.468362\pi$
$881$	−24.1056	+	41.7520i	−0.812137	+	1.40666i	−0.911366	+	0.411597i	$0.864971\pi$
$882$		0			0
$883$	−5.97224			−0.200982			−0.100491	−	0.994938i	$-0.532041\pi$
$883$	−5.97224			−0.200982			−0.100491	+	0.994938i	$0.532041\pi$
$884$		0			0
$885$	−1.95416	−	3.38471i	−0.0656885	−	0.113776i
$886$		0			0
$887$	21.3028	+	36.8975i	0.715277	+	1.23890i	0.962853	+	0.270028i	$0.0870329\pi$
$887$	21.3028	+	36.8975i	0.715277	+	1.23890i	−0.247575	+	0.968869i	$0.579634\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−66.8444			−2.23937
$892$		0			0
$893$	−21.4542	+	37.1597i	−0.717936	+	1.24350i
$894$		0			0
$895$	−0.179144	+	0.310287i	−0.00598813	+	0.0103717i
$896$		0			0
$897$	−8.30278	+	14.3808i	−0.277222	+	0.480162i
$898$		0			0
$899$	0.119429			0.00398320
$900$		0			0
$901$	−17.3667			−0.578568
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.211103	−	0.365640i	0.00701729	−	0.0121543i
$906$		0			0
$907$	51.6333			1.71446			0.857228	−	0.514937i	$-0.172185\pi$
$907$	51.6333			1.71446			0.857228	+	0.514937i	$0.172185\pi$
$908$		0			0
$909$	21.9083			0.726653
$910$		0			0
$911$	4.54163			0.150471			0.0752355	−	0.997166i	$-0.476029\pi$
$911$	4.54163			0.150471			0.0752355	+	0.997166i	$0.476029\pi$
$912$		0			0
$913$	−27.6972			−0.916644
$914$		0			0
$915$	2.51388	−	4.35416i	0.0831062	−	0.143944i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−27.2111			−0.897611			−0.448806	−	0.893629i	$-0.648150\pi$
$919$	−27.2111			−0.897611			−0.448806	+	0.893629i	$0.648150\pi$
$920$		0			0
$921$	−28.8167			−0.949541
$922$		0			0
$923$	17.6972	−	30.6525i	0.582511	−	1.00894i
$924$		0			0
$925$	22.6056	−	39.1540i	0.743266	−	1.28737i
$926$		0			0
$927$	7.84861	−	13.5942i	0.257782	−	0.446492i
$928$		0			0
$929$	−42.6333			−1.39875			−0.699377	−	0.714753i	$-0.746539\pi$
$929$	−42.6333			−1.39875			−0.699377	+	0.714753i	$0.746539\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−2.40833	−	4.17134i	−0.0788451	−	0.136564i
$934$		0			0
$935$	−1.53196	−	2.65343i	−0.0501004	−	0.0867764i
$936$		0			0
$937$	−5.36669			−0.175322			−0.0876611	−	0.996150i	$-0.527939\pi$
$937$	−5.36669			−0.175322			−0.0876611	+	0.996150i	$0.527939\pi$
$938$		0			0
$939$	−28.8167	+	49.9119i	−0.940396	+	1.62881i
$940$		0			0
$941$	3.89445	+	6.74538i	0.126955	+	0.219893i	0.922496	−	0.386008i	$-0.126146\pi$
$941$	3.89445	+	6.74538i	0.126955	+	0.219893i	−0.795540	+	0.605901i	$0.792813\pi$
$942$		0			0
$943$	−2.78890			−0.0908190
$944$		0			0
$945$		0			0
$946$		0			0
$947$	13.8486	+	23.9865i	0.450019	+	0.779457i	0.998387	−	0.0567811i	$-0.0180837\pi$
$947$	13.8486	+	23.9865i	0.450019	+	0.779457i	−0.548367	+	0.836238i	$0.684750\pi$
$948$		0			0
$949$	−20.2111	+	35.0067i	−0.656080	+	1.13636i
$950$		0			0
$951$	−33.6653	+	58.3100i	−1.09167	+	1.89083i
$952$		0			0
$953$	8.31665	+	14.4049i	0.269403	+	0.466619i	0.968708	−	0.248204i	$-0.0798404\pi$
$953$	8.31665	+	14.4049i	0.269403	+	0.466619i	−0.699305	+	0.714823i	$0.746507\pi$
$954$		0			0
$955$	1.44029	−	2.49465i	0.0466065	−	0.0807249i
$956$		0			0
$957$	2.19722	−	3.80570i	0.0710262	−	0.123021i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	15.4222	−	26.7120i	0.497490	−	0.861679i
$962$		0			0
$963$	17.8625	+	30.9387i	0.575611	+	0.996987i
$964$		0			0
$965$	−3.88057	+	6.72135i	−0.124920	+	0.216368i
$966$		0			0
$967$	30.3944			0.977420			0.488710	−	0.872446i	$-0.337468\pi$
$967$	30.3944			0.977420			0.488710	+	0.872446i	$0.337468\pi$
$968$		0			0
$969$	6.83473	−	11.8381i	0.219563	−	0.380295i
$970$		0			0
$971$	39.0000			1.25157			0.625785	−	0.779996i	$-0.284779\pi$
$971$	39.0000			1.25157			0.625785	+	0.779996i	$0.284779\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	20.3764	−	35.2929i	0.652566	−	1.13028i
$976$		0			0
$977$	30.6333			0.980046			0.490023	−	0.871709i	$-0.336988\pi$
$977$	30.6333			0.980046			0.490023	+	0.871709i	$0.336988\pi$
$978$		0			0
$979$	−16.0458	−	27.7922i	−0.512827	−	0.888243i
$980$		0			0
$981$	4.15139	+	7.19041i	0.132544	+	0.229572i
$982$		0			0
$983$	2.77082	+	4.79920i	0.0883753	+	0.153071i	0.906825	−	0.421508i	$-0.138499\pi$
$983$	2.77082	+	4.79920i	0.0883753	+	0.153071i	−0.818449	+	0.574579i	$0.805166\pi$
$984$		0			0
$985$	1.04584	+	1.81144i	0.0333231	+	0.0577173i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	5.90833	−	10.2335i	0.187874	−	0.325407i
$990$		0			0
$991$	−24.9083			−0.791239			−0.395620	−	0.918414i	$-0.629470\pi$
$991$	−24.9083			−0.791239			−0.395620	+	0.918414i	$0.629470\pi$
$992$		0			0
$993$	−67.5416			−2.14337
$994$		0			0
$995$	2.63751	+	4.56830i	0.0836147	+	0.144825i
$996$		0			0
$997$	16.1972	−	28.0544i	0.512971	−	0.888492i	−0.486916	−	0.873449i	$-0.661878\pi$
$997$	16.1972	−	28.0544i	0.512971	−	0.888492i	0.999887	−	0.0150432i	$-0.00478859\pi$
$998$		0			0
$999$	7.39445	+	12.8076i	0.233950	+	0.405213i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.l.k.373.2		4
7.2	even	3		364.2.k.c.113.1	yes	4
7.3	odd	6		2548.2.i.l.165.2		4
7.4	even	3		2548.2.i.j.165.1		4
7.5	odd	6		2548.2.k.f.1569.2		4
7.6	odd	2		2548.2.l.i.373.1		4
13.3	even	3		2548.2.i.j.1745.1		4
21.2	odd	6		3276.2.z.d.3025.2		4
28.23	odd	6		1456.2.s.m.113.2		4
91.3	odd	6		2548.2.l.i.1537.1		4
91.9	even	3		4732.2.a.k.1.2		2
91.16	even	3		364.2.k.c.29.1	✓	4
91.30	even	6		4732.2.a.j.1.2		2
91.55	odd	6		2548.2.i.l.1745.2		4
91.58	odd	12		4732.2.g.g.337.4		4
91.68	odd	6		2548.2.k.f.393.2		4
91.72	odd	12		4732.2.g.g.337.3		4
91.81	even	3	inner	2548.2.l.k.1537.2		4
273.107	odd	6		3276.2.z.d.757.2		4
364.107	odd	6		1456.2.s.m.1121.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.k.c.29.1	✓	4	91.16	even	3
364.2.k.c.113.1	yes	4	7.2	even	3
1456.2.s.m.113.2		4	28.23	odd	6
1456.2.s.m.1121.2		4	364.107	odd	6
2548.2.i.j.165.1		4	7.4	even	3
2548.2.i.j.1745.1		4	13.3	even	3
2548.2.i.l.165.2		4	7.3	odd	6
2548.2.i.l.1745.2		4	91.55	odd	6
2548.2.k.f.393.2		4	91.68	odd	6
2548.2.k.f.1569.2		4	7.5	odd	6
2548.2.l.i.373.1		4	7.6	odd	2
2548.2.l.i.1537.1		4	91.3	odd	6
2548.2.l.k.373.2		4	1.1	even	1	trivial
2548.2.l.k.1537.2		4	91.81	even	3	inner
3276.2.z.d.757.2		4	273.107	odd	6
3276.2.z.d.3025.2		4	21.2	odd	6
4732.2.a.j.1.2		2	91.30	even	6
4732.2.a.k.1.2		2	91.9	even	3
4732.2.g.g.337.3		4	91.72	odd	12
4732.2.g.g.337.4		4	91.58	odd	12

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:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.30278 q^{3} +(0.151388 - 0.262211i) q^{5} +2.30278 q^{9} +6.30278 q^{11} +(-1.80278 - 3.12250i) q^{13} +(0.348612 - 0.603814i) q^{15} +(0.802776 - 1.39045i) q^{17} +3.69722 q^{19} +(-1.00000 - 1.73205i) q^{23} +(2.45416 + 4.25074i) q^{25} -1.60555 q^{27} +(0.151388 - 0.262211i) q^{29} +(0.197224 + 0.341603i) q^{31} +14.5139 q^{33} +(-4.60555 - 7.97705i) q^{37} +(-4.15139 - 7.19041i) q^{39} +(0.697224 - 1.20763i) q^{41} +(2.95416 + 5.11676i) q^{43} +(0.348612 - 0.603814i) q^{45} +(-5.80278 + 10.0507i) q^{47} +(1.84861 - 3.20189i) q^{51} +(-5.40833 - 9.36750i) q^{53} +(0.954163 - 1.65266i) q^{55} +8.51388 q^{57} +(2.80278 - 4.85455i) q^{59} +7.21110 q^{61} -1.09167 q^{65} +13.0000 q^{67} +(-2.30278 - 3.98852i) q^{69} +(4.90833 + 8.50147i) q^{71} +(-5.60555 - 9.70910i) q^{73} +(5.65139 + 9.78849i) q^{75} +(-4.00000 + 6.92820i) q^{79} -10.6056 q^{81} -4.39445 q^{83} +(-0.243061 - 0.420994i) q^{85} +(0.348612 - 0.603814i) q^{87} +(-2.54584 - 4.40952i) q^{89} +(0.454163 + 0.786634i) q^{93} +(0.559715 - 0.969454i) q^{95} +(3.04584 + 5.27554i) q^{97} +14.5139 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 3 q^{5} + 2 q^{9} + 18 q^{11} + 5 q^{15} - 4 q^{17} + 22 q^{19} - 4 q^{23} - q^{25} + 8 q^{27} - 3 q^{29} + 8 q^{31} + 22 q^{33} - 4 q^{37} - 13 q^{39} + 10 q^{41} + q^{43} + 5 q^{45}+ \cdots + 22 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 3 * q^5 + 2 * q^9 + 18 * q^11 + 5 * q^15 - 4 * q^17 + 22 * q^19 - 4 * q^23 - q^25 + 8 * q^27 - 3 * q^29 + 8 * q^31 + 22 * q^33 - 4 * q^37 - 13 * q^39 + 10 * q^41 + q^43 + 5 * q^45 - 16 * q^47 + 11 * q^51 - 7 * q^55 - 2 * q^57 + 4 * q^59 - 26 * q^65 + 52 * q^67 - 2 * q^69 - 2 * q^71 - 8 * q^73 + 19 * q^75 - 16 * q^79 - 28 * q^81 - 32 * q^83 - 19 * q^85 + 5 * q^87 - 21 * q^89 - 9 * q^93 - 23 * q^95 + 23 * q^97 + 22 * q^99

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