LMFDB - Embedded newform 2156.2.i.e.1145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2156,2,Mod(177,2156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2156, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2156.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2156 = 2^{2} \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2156.i (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:	$17.2157466758$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 308)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1145.2
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2156.1145
Dual form			2156.2.i.e.177.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 2.12132i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.22474 - 2.12132i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(-1.50000 - 2.59808i) q^{9} +(0.500000 - 0.866025i) q^{11} +4.44949 q^{13} -4.89898 q^{15} +(-2.22474 + 3.85337i) q^{17} +(-2.44949 - 4.24264i) q^{19} +(-4.44949 - 7.70674i) q^{23} +(0.500000 - 0.866025i) q^{25} -6.89898 q^{29} +(-0.775255 + 1.34278i) q^{31} +(-1.22474 - 2.12132i) q^{33} +(-2.00000 - 3.46410i) q^{37} +(5.44949 - 9.43879i) q^{39} +5.34847 q^{41} -6.89898 q^{43} +(-3.00000 + 5.19615i) q^{45} +(0.775255 + 1.34278i) q^{47} +(5.44949 + 9.43879i) q^{51} +(4.89898 - 8.48528i) q^{53} -2.00000 q^{55} -12.0000 q^{57} +(3.67423 - 6.36396i) q^{59} +(4.67423 + 8.09601i) q^{61} +(-4.44949 - 7.70674i) q^{65} +(-7.34847 + 12.7279i) q^{67} -21.7980 q^{69} -3.10102 q^{71} +(-3.77526 + 6.53893i) q^{73} +(-1.22474 - 2.12132i) q^{75} +(0.550510 + 0.953512i) q^{79} +(4.50000 - 7.79423i) q^{81} -7.10102 q^{83} +8.89898 q^{85} +(-8.44949 + 14.6349i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(1.89898 + 3.28913i) q^{93} +(-4.89898 + 8.48528i) q^{95} +14.8990 q^{97} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{5} - 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^5 - 6 * q^9	$ 4 q - 4 q^{5} - 6 q^{9} + 2 q^{11} + 8 q^{13} - 4 q^{17} - 8 q^{23} + 2 q^{25} - 8 q^{29} - 8 q^{31} - 8 q^{37} + 12 q^{39} - 8 q^{41} - 8 q^{43} - 12 q^{45} + 8 q^{47} + 12 q^{51} - 8 q^{55} - 48 q^{57} + 4 q^{61} - 8 q^{65} - 48 q^{69} - 32 q^{71} - 20 q^{73} + 12 q^{79} + 18 q^{81} - 48 q^{83} + 16 q^{85} - 24 q^{87} - 12 q^{89} - 12 q^{93} + 40 q^{97} - 12 q^{99}+O(q^{100}) $ 4 * q - 4 * q^5 - 6 * q^9 + 2 * q^11 + 8 * q^13 - 4 * q^17 - 8 * q^23 + 2 * q^25 - 8 * q^29 - 8 * q^31 - 8 * q^37 + 12 * q^39 - 8 * q^41 - 8 * q^43 - 12 * q^45 + 8 * q^47 + 12 * q^51 - 8 * q^55 - 48 * q^57 + 4 * q^61 - 8 * q^65 - 48 * q^69 - 32 * q^71 - 20 * q^73 + 12 * q^79 + 18 * q^81 - 48 * q^83 + 16 * q^85 - 24 * q^87 - 12 * q^89 - 12 * q^93 + 40 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2156\mathbb{Z}\right)^\times$.

$n$	$981$	$1079$	$1277$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	1.22474	−	2.12132i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$3$	1.22474	−	2.12132i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$4$		0			0
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	0.550990	−	0.834512i	$-0.314250\pi$
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	−0.998203	+	0.0599153i	$0.980917\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$		0			0
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	4.44949			1.23407			0.617033	−	0.786937i	$-0.288334\pi$
$13$	4.44949			1.23407			0.617033	+	0.786937i	$0.288334\pi$
$14$		0			0
$15$	−4.89898			−1.26491
$16$		0			0
$17$	−2.22474	+	3.85337i	−0.539580	+	0.934580i	0.459347	+	0.888257i	$0.348084\pi$
$17$	−2.22474	+	3.85337i	−0.539580	+	0.934580i	−0.998927	+	0.0463227i	$0.985250\pi$
$18$		0			0
$19$	−2.44949	−	4.24264i	−0.561951	−	0.973329i	−0.997326	−	0.0730792i	$-0.976717\pi$
$19$	−2.44949	−	4.24264i	−0.561951	−	0.973329i	0.435375	−	0.900249i	$-0.356616\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.44949	−	7.70674i	−0.927783	−	1.60697i	−0.787024	−	0.616923i	$-0.788379\pi$
$23$	−4.44949	−	7.70674i	−0.927783	−	1.60697i	−0.140759	−	0.990044i	$-0.544954\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−6.89898			−1.28111			−0.640554	−	0.767913i	$-0.721295\pi$
$29$	−6.89898			−1.28111			−0.640554	+	0.767913i	$0.721295\pi$
$30$		0			0
$31$	−0.775255	+	1.34278i	−0.139240	+	0.241171i	−0.927209	−	0.374544i	$-0.877799\pi$
$31$	−0.775255	+	1.34278i	−0.139240	+	0.241171i	0.787969	+	0.615715i	$0.211133\pi$
$32$		0			0
$33$	−1.22474	−	2.12132i	−0.213201	−	0.369274i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	0.653476	−	0.756948i	$-0.273310\pi$
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	−0.982274	+	0.187453i	$0.939977\pi$
$38$		0			0
$39$	5.44949	−	9.43879i	0.872617	−	1.51142i
$40$		0			0
$41$	5.34847			0.835291			0.417645	−	0.908610i	$-0.362855\pi$
$41$	5.34847			0.835291			0.417645	+	0.908610i	$0.362855\pi$
$42$		0			0
$43$	−6.89898			−1.05208			−0.526042	−	0.850458i	$-0.676325\pi$
$43$	−6.89898			−1.05208			−0.526042	+	0.850458i	$0.676325\pi$
$44$		0			0
$45$	−3.00000	+	5.19615i	−0.447214	+	0.774597i
$46$		0			0
$47$	0.775255	+	1.34278i	0.113083	+	0.195865i	0.917012	−	0.398860i	$-0.130594\pi$
$47$	0.775255	+	1.34278i	0.113083	+	0.195865i	−0.803929	+	0.594725i	$0.797261\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	5.44949	+	9.43879i	0.763081	+	1.32170i
$52$		0			0
$53$	4.89898	−	8.48528i	0.672927	−	1.16554i	−0.304144	−	0.952626i	$-0.598370\pi$
$53$	4.89898	−	8.48528i	0.672927	−	1.16554i	0.977070	−	0.212917i	$-0.0682964\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$		0			0
$57$	−12.0000			−1.58944
$58$		0			0
$59$	3.67423	−	6.36396i	0.478345	−	0.828517i	−0.521347	−	0.853345i	$-0.674570\pi$
$59$	3.67423	−	6.36396i	0.478345	−	0.828517i	0.999692	+	0.0248275i	$0.00790366\pi$
$60$		0			0
$61$	4.67423	+	8.09601i	0.598474	+	1.03659i	0.993046	+	0.117723i	$0.0375595\pi$
$61$	4.67423	+	8.09601i	0.598474	+	1.03659i	−0.394572	+	0.918865i	$0.629107\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.44949	−	7.70674i	−0.551891	−	0.955904i
$66$		0			0
$67$	−7.34847	+	12.7279i	−0.897758	+	1.55496i	−0.0674052	+	0.997726i	$0.521472\pi$
$67$	−7.34847	+	12.7279i	−0.897758	+	1.55496i	−0.830353	+	0.557237i	$0.811861\pi$
$68$		0			0
$69$	−21.7980			−2.62417
$70$		0			0
$71$	−3.10102			−0.368023			−0.184012	−	0.982924i	$-0.558908\pi$
$71$	−3.10102			−0.368023			−0.184012	+	0.982924i	$0.558908\pi$
$72$		0			0
$73$	−3.77526	+	6.53893i	−0.441860	+	0.765324i	−0.997828	−	0.0658798i	$-0.979015\pi$
$73$	−3.77526	+	6.53893i	−0.441860	+	0.765324i	0.555967	+	0.831204i	$0.312348\pi$
$74$		0			0
$75$	−1.22474	−	2.12132i	−0.141421	−	0.244949i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.550510	+	0.953512i	0.0619372	+	0.107278i	0.895331	−	0.445401i	$-0.146939\pi$
$79$	0.550510	+	0.953512i	0.0619372	+	0.107278i	−0.833394	+	0.552679i	$0.813605\pi$
$80$		0			0
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$		0			0
$83$	−7.10102			−0.779438			−0.389719	−	0.920934i	$-0.627428\pi$
$83$	−7.10102			−0.779438			−0.389719	+	0.920934i	$0.627428\pi$
$84$		0			0
$85$	8.89898			0.965230
$86$		0			0
$87$	−8.44949	+	14.6349i	−0.905880	+	1.56903i
$88$		0			0
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.89898	+	3.28913i	0.196915	+	0.341067i
$94$		0			0
$95$	−4.89898	+	8.48528i	−0.502625	+	0.870572i
$96$		0			0
$97$	14.8990			1.51276			0.756381	−	0.654131i	$-0.226966\pi$
$97$	14.8990			1.51276			0.756381	+	0.654131i	$0.226966\pi$
$98$		0			0
$99$	−3.00000			−0.301511
$100$		0			0
$101$	1.77526	−	3.07483i	0.176644	−	0.305957i	−0.764085	−	0.645116i	$-0.776809\pi$
$101$	1.77526	−	3.07483i	0.176644	−	0.305957i	0.940729	+	0.339159i	$0.110142\pi$
$102$		0			0
$103$	−4.77526	−	8.27098i	−0.470520	−	0.814964i	0.528912	−	0.848677i	$-0.322600\pi$
$103$	−4.77526	−	8.27098i	−0.470520	−	0.814964i	−0.999432	+	0.0337125i	$0.989267\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	0.946357	−	0.323122i	$-0.104732\pi$
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	−0.753010	+	0.658009i	$0.771399\pi$
$108$		0			0
$109$	−2.55051	+	4.41761i	−0.244295	+	0.423131i	−0.961933	−	0.273285i	$-0.911890\pi$
$109$	−2.55051	+	4.41761i	−0.244295	+	0.423131i	0.717638	+	0.696416i	$0.245223\pi$
$110$		0			0
$111$	−9.79796			−0.929981
$112$		0			0
$113$	−10.0000			−0.940721			−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000			−0.940721			−0.470360	+	0.882474i	$0.655876\pi$
$114$		0			0
$115$	−8.89898	+	15.4135i	−0.829834	+	1.43731i
$116$		0			0
$117$	−6.67423	−	11.5601i	−0.617033	−	1.06873i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	6.55051	−	11.3458i	0.590640	−	1.02302i
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$	17.7980			1.57931			0.789657	−	0.613549i	$-0.210259\pi$
$127$	17.7980			1.57931			0.789657	+	0.613549i	$0.210259\pi$
$128$		0			0
$129$	−8.44949	+	14.6349i	−0.743936	+	1.28854i
$130$		0			0
$131$	4.89898	+	8.48528i	0.428026	+	0.741362i	0.996698	−	0.0812020i	$-0.0258759\pi$
$131$	4.89898	+	8.48528i	0.428026	+	0.741362i	−0.568672	+	0.822564i	$0.692543\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.89898	−	8.48528i	0.418548	−	0.724947i	−0.577246	−	0.816571i	$-0.695872\pi$
$137$	4.89898	−	8.48528i	0.418548	−	0.724947i	0.995794	+	0.0916241i	$0.0292058\pi$
$138$		0			0
$139$	−6.69694			−0.568027			−0.284013	−	0.958820i	$-0.591666\pi$
$139$	−6.69694			−0.568027			−0.284013	+	0.958820i	$0.591666\pi$
$140$		0			0
$141$	3.79796			0.319846
$142$		0			0
$143$	2.22474	−	3.85337i	0.186043	−	0.322235i
$144$		0			0
$145$	6.89898	+	11.9494i	0.572929	+	0.992342i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.89898	+	6.75323i	0.319417	+	0.553246i	0.980366	−	0.197184i	$-0.0631797\pi$
$149$	3.89898	+	6.75323i	0.319417	+	0.553246i	−0.660950	+	0.750430i	$0.729846\pi$
$150$		0			0
$151$	10.3485	−	17.9241i	0.842146	−	1.45864i	−0.0459299	−	0.998945i	$-0.514625\pi$
$151$	10.3485	−	17.9241i	0.842146	−	1.45864i	0.888076	−	0.459696i	$-0.152042\pi$
$152$		0			0
$153$	13.3485			1.07916
$154$		0			0
$155$	3.10102			0.249080
$156$		0			0
$157$	−5.00000	+	8.66025i	−0.399043	+	0.691164i	−0.993608	−	0.112884i	$-0.963991\pi$
$157$	−5.00000	+	8.66025i	−0.399043	+	0.691164i	0.594565	+	0.804048i	$0.297324\pi$
$158$		0			0
$159$	−12.0000	−	20.7846i	−0.951662	−	1.64833i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	0.449490	+	0.778539i	0.0352068	+	0.0609799i	0.883092	−	0.469200i	$-0.155458\pi$
$163$	0.449490	+	0.778539i	0.0352068	+	0.0609799i	−0.847885	+	0.530180i	$0.822124\pi$
$164$		0			0
$165$	−2.44949	+	4.24264i	−0.190693	+	0.330289i
$166$		0			0
$167$	−5.79796			−0.448660			−0.224330	−	0.974513i	$-0.572019\pi$
$167$	−5.79796			−0.448660			−0.224330	+	0.974513i	$0.572019\pi$
$168$		0			0
$169$	6.79796			0.522920
$170$		0			0
$171$	−7.34847	+	12.7279i	−0.561951	+	0.973329i
$172$		0			0
$173$	7.12372	+	12.3387i	0.541607	+	0.938090i	0.998812	+	0.0487292i	$0.0155171\pi$
$173$	7.12372	+	12.3387i	0.541607	+	0.938090i	−0.457205	+	0.889361i	$0.651150\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−9.00000	−	15.5885i	−0.676481	−	1.17170i
$178$		0			0
$179$	−11.7980	+	20.4347i	−0.881821	+	1.52736i	−0.0325062	+	0.999472i	$0.510349\pi$
$179$	−11.7980	+	20.4347i	−0.881821	+	1.52736i	−0.849315	+	0.527887i	$0.822984\pi$
$180$		0			0
$181$	18.8990			1.40475			0.702375	−	0.711807i	$-0.252123\pi$
$181$	18.8990			1.40475			0.702375	+	0.711807i	$0.252123\pi$
$182$		0			0
$183$	22.8990			1.69274
$184$		0			0
$185$	−4.00000	+	6.92820i	−0.294086	+	0.509372i
$186$		0			0
$187$	2.22474	+	3.85337i	0.162689	+	0.281786i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.89898	−	15.4135i	−0.643908	−	1.11528i	−0.984553	−	0.175089i	$-0.943979\pi$
$191$	−8.89898	−	15.4135i	−0.643908	−	1.11528i	0.340645	−	0.940192i	$-0.389355\pi$
$192$		0			0
$193$	8.79796	−	15.2385i	0.633291	−	1.09689i	−0.353584	−	0.935403i	$-0.615037\pi$
$193$	8.79796	−	15.2385i	0.633291	−	1.09689i	0.986874	−	0.161489i	$-0.0516297\pi$
$194$		0			0
$195$	−21.7980			−1.56098
$196$		0			0
$197$	13.5959			0.968669			0.484335	−	0.874883i	$-0.339062\pi$
$197$	13.5959			0.968669			0.484335	+	0.874883i	$0.339062\pi$
$198$		0			0
$199$	9.02270	−	15.6278i	0.639603	−	1.10782i	−0.345917	−	0.938265i	$-0.612432\pi$
$199$	9.02270	−	15.6278i	0.639603	−	1.10782i	0.985520	−	0.169559i	$-0.0542344\pi$
$200$		0			0
$201$	18.0000	+	31.1769i	1.26962	+	2.19905i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−5.34847	−	9.26382i	−0.373553	−	0.647013i
$206$		0			0
$207$	−13.3485	+	23.1202i	−0.927783	+	1.60697i
$208$		0			0
$209$	−4.89898			−0.338869
$210$		0			0
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$		0			0
$213$	−3.79796	+	6.57826i	−0.260232	+	0.450735i
$214$		0			0
$215$	6.89898	+	11.9494i	0.470506	+	0.814941i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	9.24745	+	16.0171i	0.624885	+	1.08233i
$220$		0			0
$221$	−9.89898	+	17.1455i	−0.665877	+	1.15333i
$222$		0			0
$223$	21.1464			1.41607			0.708035	−	0.706178i	$-0.249582\pi$
$223$	21.1464			1.41607			0.708035	+	0.706178i	$0.249582\pi$
$224$		0			0
$225$	−3.00000			−0.200000
$226$		0			0
$227$	8.89898	−	15.4135i	0.590646	−	1.02303i	−0.403500	−	0.914980i	$-0.632206\pi$
$227$	8.89898	−	15.4135i	0.590646	−	1.02303i	0.994146	−	0.108049i	$-0.0344604\pi$
$228$		0			0
$229$	7.44949	+	12.9029i	0.492276	+	0.852647i	0.999960	−	0.00889590i	$-0.00283169\pi$
$229$	7.44949	+	12.9029i	0.492276	+	0.852647i	−0.507684	+	0.861543i	$0.669498\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.44949	+	9.43879i	0.357008	+	0.618356i	0.987459	−	0.157873i	$-0.0504636\pi$
$233$	5.44949	+	9.43879i	0.357008	+	0.618356i	−0.630452	+	0.776229i	$0.717130\pi$
$234$		0			0
$235$	1.55051	−	2.68556i	0.101144	−	0.175187i
$236$		0			0
$237$	2.69694			0.175185
$238$		0			0
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$		0			0
$241$	−6.67423	+	11.5601i	−0.429925	+	0.744652i	−0.996866	−	0.0791061i	$-0.974793\pi$
$241$	−6.67423	+	11.5601i	−0.429925	+	0.744652i	0.566941	+	0.823758i	$0.308127\pi$
$242$		0			0
$243$	−11.0227	−	19.0919i	−0.707107	−	1.22474i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−10.8990	−	18.8776i	−0.693485	−	1.20115i
$248$		0			0
$249$	−8.69694	+	15.0635i	−0.551146	+	0.954613i
$250$		0			0
$251$	−2.44949			−0.154610			−0.0773052	−	0.997007i	$-0.524632\pi$
$251$	−2.44949			−0.154610			−0.0773052	+	0.997007i	$0.524632\pi$
$252$		0			0
$253$	−8.89898			−0.559474
$254$		0			0
$255$	10.8990	−	18.8776i	0.682521	−	1.18216i
$256$		0			0
$257$	−7.89898	−	13.6814i	−0.492725	−	0.853424i	0.507240	−	0.861805i	$-0.330666\pi$
$257$	−7.89898	−	13.6814i	−0.492725	−	0.853424i	−0.999965	+	0.00838040i	$0.997332\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	10.3485	+	17.9241i	0.640554	+	1.10947i
$262$		0			0
$263$	9.79796	−	16.9706i	0.604168	−	1.04645i	−0.388014	−	0.921653i	$-0.626839\pi$
$263$	9.79796	−	16.9706i	0.604168	−	1.04645i	0.992182	−	0.124796i	$-0.0398278\pi$
$264$		0			0
$265$	−19.5959			−1.20377
$266$		0			0
$267$	−14.6969			−0.899438
$268$		0			0
$269$	11.4495	−	19.8311i	0.698088	−	1.20912i	−0.271041	−	0.962568i	$-0.587368\pi$
$269$	11.4495	−	19.8311i	0.698088	−	1.20912i	0.969129	−	0.246556i	$-0.0792988\pi$
$270$		0			0
$271$	−15.3485	−	26.5843i	−0.932353	−	1.61488i	−0.779287	−	0.626667i	$-0.784419\pi$
$271$	−15.3485	−	26.5843i	−0.932353	−	1.61488i	−0.153066	−	0.988216i	$-0.548915\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.500000	−	0.866025i	−0.0301511	−	0.0522233i
$276$		0			0
$277$	1.89898	−	3.28913i	0.114099	−	0.197625i	−0.803320	−	0.595547i	$-0.796935\pi$
$277$	1.89898	−	3.28913i	0.114099	−	0.197625i	0.917419	+	0.397922i	$0.130269\pi$
$278$		0			0
$279$	4.65153			0.278480
$280$		0			0
$281$	−14.8990			−0.888799			−0.444399	−	0.895829i	$-0.646583\pi$
$281$	−14.8990			−0.888799			−0.444399	+	0.895829i	$0.646583\pi$
$282$		0			0
$283$	12.0000	−	20.7846i	0.713326	−	1.23552i	−0.250276	−	0.968175i	$-0.580521\pi$
$283$	12.0000	−	20.7846i	0.713326	−	1.23552i	0.963602	−	0.267342i	$-0.0861454\pi$
$284$		0			0
$285$	12.0000	+	20.7846i	0.710819	+	1.23117i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−1.39898	−	2.42310i	−0.0822929	−	0.142536i
$290$		0			0
$291$	18.2474	−	31.6055i	1.06968	−	1.85275i
$292$		0			0
$293$	−25.3485			−1.48087			−0.740437	−	0.672126i	$-0.765381\pi$
$293$	−25.3485			−1.48087			−0.740437	+	0.672126i	$0.765381\pi$
$294$		0			0
$295$	−14.6969			−0.855689
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−19.7980	−	34.2911i	−1.14495	−	1.98310i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−4.34847	−	7.53177i	−0.249813	−	0.432689i
$304$		0			0
$305$	9.34847	−	16.1920i	0.535292	−	0.927153i
$306$		0			0
$307$	17.7980			1.01578			0.507892	−	0.861421i	$-0.330425\pi$
$307$	17.7980			1.01578			0.507892	+	0.861421i	$0.330425\pi$
$308$		0			0
$309$	−23.3939			−1.33083
$310$		0			0
$311$	3.22474	−	5.58542i	0.182859	−	0.316720i	−0.759994	−	0.649930i	$-0.774798\pi$
$311$	3.22474	−	5.58542i	0.182859	−	0.316720i	0.942853	+	0.333210i	$0.108132\pi$
$312$		0			0
$313$	16.7980	+	29.0949i	0.949477	+	1.64454i	0.746529	+	0.665352i	$0.231719\pi$
$313$	16.7980	+	29.0949i	0.949477	+	1.64454i	0.202947	+	0.979190i	$0.434948\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−12.7980	−	22.1667i	−0.718805	−	1.24501i	−0.961474	−	0.274898i	$-0.911356\pi$
$317$	−12.7980	−	22.1667i	−0.718805	−	1.24501i	0.242669	−	0.970109i	$-0.421977\pi$
$318$		0			0
$319$	−3.44949	+	5.97469i	−0.193134	+	0.334519i
$320$		0			0
$321$	9.79796			0.546869
$322$		0			0
$323$	21.7980			1.21287
$324$		0			0
$325$	2.22474	−	3.85337i	0.123407	−	0.213747i
$326$		0			0
$327$	6.24745	+	10.8209i	0.345485	+	0.598397i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	16.0000	+	27.7128i	0.879440	+	1.52323i	0.851957	+	0.523612i	$0.175416\pi$
$331$	16.0000	+	27.7128i	0.879440	+	1.52323i	0.0274825	+	0.999622i	$0.491251\pi$
$332$		0			0
$333$	−6.00000	+	10.3923i	−0.328798	+	0.569495i
$334$		0			0
$335$	29.3939			1.60596
$336$		0			0
$337$	−8.69694			−0.473752			−0.236876	−	0.971540i	$-0.576124\pi$
$337$	−8.69694			−0.473752			−0.236876	+	0.971540i	$0.576124\pi$
$338$		0			0
$339$	−12.2474	+	21.2132i	−0.665190	+	1.15214i
$340$		0			0
$341$	0.775255	+	1.34278i	0.0419824	+	0.0727157i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	21.7980	+	37.7552i	1.17356	+	2.03267i
$346$		0			0
$347$	11.2474	−	19.4812i	0.603795	−	1.04580i	−0.388446	−	0.921471i	$-0.626988\pi$
$347$	11.2474	−	19.4812i	0.603795	−	1.04580i	0.992241	−	0.124332i	$-0.0396787\pi$
$348$		0			0
$349$	26.2474			1.40499			0.702497	−	0.711687i	$-0.252068\pi$
$349$	26.2474			1.40499			0.702497	+	0.711687i	$0.252068\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	6.79796	−	11.7744i	0.361819	−	0.626689i	−0.626441	−	0.779469i	$-0.715489\pi$
$353$	6.79796	−	11.7744i	0.361819	−	0.626689i	0.988260	+	0.152780i	$0.0488226\pi$
$354$		0			0
$355$	3.10102	+	5.37113i	0.164585	+	0.285070i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.34847	−	4.06767i	−0.123947	−	0.214683i	0.797374	−	0.603486i	$-0.206222\pi$
$359$	−2.34847	−	4.06767i	−0.123947	−	0.214683i	−0.921321	+	0.388803i	$0.872889\pi$
$360$		0			0
$361$	−2.50000	+	4.33013i	−0.131579	+	0.227901i
$362$		0			0
$363$	−2.44949			−0.128565
$364$		0			0
$365$	15.1010			0.790424
$366$		0			0
$367$	6.57321	−	11.3851i	0.343119	−	0.594300i	−0.641891	−	0.766796i	$-0.721850\pi$
$367$	6.57321	−	11.3851i	0.343119	−	0.594300i	0.985010	+	0.172496i	$0.0551833\pi$
$368$		0			0
$369$	−8.02270	−	13.8957i	−0.417645	−	0.723383i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−11.8990	−	20.6096i	−0.616106	−	1.06713i	−0.990189	−	0.139732i	$-0.955376\pi$
$373$	−11.8990	−	20.6096i	−0.616106	−	1.06713i	0.374084	−	0.927395i	$-0.377957\pi$
$374$		0			0
$375$	−14.6969	+	25.4558i	−0.758947	+	1.31453i
$376$		0			0
$377$	−30.6969			−1.58097
$378$		0			0
$379$	−12.8990			−0.662576			−0.331288	−	0.943530i	$-0.607483\pi$
$379$	−12.8990			−0.662576			−0.331288	+	0.943530i	$0.607483\pi$
$380$		0			0
$381$	21.7980	−	37.7552i	1.11674	−	1.93426i
$382$		0			0
$383$	−6.32577	−	10.9565i	−0.323232	−	0.559853i	0.657921	−	0.753087i	$-0.271436\pi$
$383$	−6.32577	−	10.9565i	−0.323232	−	0.559853i	−0.981153	+	0.193233i	$0.938103\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	10.3485	+	17.9241i	0.526042	+	0.911132i
$388$		0			0
$389$	−12.7980	+	22.1667i	−0.648882	+	1.12390i	0.334508	+	0.942393i	$0.391430\pi$
$389$	−12.7980	+	22.1667i	−0.648882	+	1.12390i	−0.983390	+	0.181504i	$0.941903\pi$
$390$		0			0
$391$	39.5959			2.00245
$392$		0			0
$393$	24.0000			1.21064
$394$		0			0
$395$	1.10102	−	1.90702i	0.0553984	−	0.0959528i
$396$		0			0
$397$	−6.79796	−	11.7744i	−0.341180	−	0.590941i	0.643472	−	0.765469i	$-0.277493\pi$
$397$	−6.79796	−	11.7744i	−0.341180	−	0.590941i	−0.984652	+	0.174529i	$0.944160\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4.10102	+	7.10318i	0.204795	+	0.354716i	0.950067	−	0.312045i	$-0.101014\pi$
$401$	4.10102	+	7.10318i	0.204795	+	0.354716i	−0.745272	+	0.666760i	$0.767680\pi$
$402$		0			0
$403$	−3.44949	+	5.97469i	−0.171831	+	0.297621i
$404$		0			0
$405$	−18.0000			−0.894427
$406$		0			0
$407$	−4.00000			−0.198273
$408$		0			0
$409$	8.22474	−	14.2457i	0.406687	−	0.704403i	−0.587829	−	0.808985i	$-0.700017\pi$
$409$	8.22474	−	14.2457i	0.406687	−	0.704403i	0.994516	+	0.104582i	$0.0333505\pi$
$410$		0			0
$411$	−12.0000	−	20.7846i	−0.591916	−	1.02523i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	7.10102	+	12.2993i	0.348575	+	0.603750i
$416$		0			0
$417$	−8.20204	+	14.2064i	−0.401656	+	0.695688i
$418$		0			0
$419$	13.5505			0.661986			0.330993	−	0.943633i	$-0.392616\pi$
$419$	13.5505			0.661986			0.330993	+	0.943633i	$0.392616\pi$
$420$		0			0
$421$	13.7980			0.672471			0.336236	−	0.941778i	$-0.390846\pi$
$421$	13.7980			0.672471			0.336236	+	0.941778i	$0.390846\pi$
$422$		0			0
$423$	2.32577	−	4.02834i	0.113083	−	0.195865i
$424$		0			0
$425$	2.22474	+	3.85337i	0.107916	+	0.186916i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−5.44949	−	9.43879i	−0.263104	−	0.455709i
$430$		0			0
$431$	9.44949	−	16.3670i	0.455166	−	0.788370i	−0.543532	−	0.839389i	$-0.682913\pi$
$431$	9.44949	−	16.3670i	0.455166	−	0.788370i	0.998698	+	0.0510181i	$0.0162466\pi$
$432$		0			0
$433$	30.8990			1.48491			0.742455	−	0.669896i	$-0.233661\pi$
$433$	30.8990			1.48491			0.742455	+	0.669896i	$0.233661\pi$
$434$		0			0
$435$	33.7980			1.62049
$436$		0			0
$437$	−21.7980	+	37.7552i	−1.04274	+	1.80607i
$438$		0			0
$439$	7.55051	+	13.0779i	0.360366	+	0.624173i	0.988021	−	0.154319i	$-0.0493184\pi$
$439$	7.55051	+	13.0779i	0.360366	+	0.624173i	−0.627655	+	0.778492i	$0.715985\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	−0.996551	−	0.0829786i	$-0.973557\pi$
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	0.426414	−	0.904528i	$-0.359777\pi$
$444$		0			0
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$		0			0
$447$	19.1010			0.903447
$448$		0			0
$449$	−19.5959			−0.924789			−0.462394	−	0.886674i	$-0.653010\pi$
$449$	−19.5959			−0.924789			−0.462394	+	0.886674i	$0.653010\pi$
$450$		0			0
$451$	2.67423	−	4.63191i	0.125925	−	0.218108i
$452$		0			0
$453$	−25.3485	−	43.9048i	−1.19097	−	2.06283i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	19.6969	+	34.1161i	0.921384	+	1.59588i	0.797276	+	0.603615i	$0.206274\pi$
$457$	19.6969	+	34.1161i	0.921384	+	1.59588i	0.124108	+	0.992269i	$0.460393\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−22.6515			−1.05499			−0.527493	−	0.849559i	$-0.676868\pi$
$461$	−22.6515			−1.05499			−0.527493	+	0.849559i	$0.676868\pi$
$462$		0			0
$463$	−15.1010			−0.701804			−0.350902	−	0.936412i	$-0.614125\pi$
$463$	−15.1010			−0.701804			−0.350902	+	0.936412i	$0.614125\pi$
$464$		0			0
$465$	3.79796	−	6.57826i	0.176126	−	0.305059i
$466$		0			0
$467$	3.67423	+	6.36396i	0.170023	+	0.294489i	0.938428	−	0.345476i	$-0.112282\pi$
$467$	3.67423	+	6.36396i	0.170023	+	0.294489i	−0.768404	+	0.639965i	$0.778949\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	12.2474	+	21.2132i	0.564333	+	0.977453i
$472$		0			0
$473$	−3.44949	+	5.97469i	−0.158608	+	0.274717i
$474$		0			0
$475$	−4.89898			−0.224781
$476$		0			0
$477$	−29.3939			−1.34585
$478$		0			0
$479$	4.44949	−	7.70674i	0.203302	−	0.352130i	−0.746288	−	0.665623i	$-0.768166\pi$
$479$	4.44949	−	7.70674i	0.203302	−	0.352130i	0.949591	+	0.313493i	$0.101499\pi$
$480$		0			0
$481$	−8.89898	−	15.4135i	−0.405759	−	0.702794i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−14.8990	−	25.8058i	−0.676528	−	1.17178i
$486$		0			0
$487$	−13.5505	+	23.4702i	−0.614032	+	1.06354i	0.376521	+	0.926408i	$0.377120\pi$
$487$	−13.5505	+	23.4702i	−0.614032	+	1.06354i	−0.990553	+	0.137127i	$0.956213\pi$
$488$		0			0
$489$	2.20204			0.0995797
$490$		0			0
$491$	3.30306			0.149065			0.0745325	−	0.997219i	$-0.476254\pi$
$491$	3.30306			0.149065			0.0745325	+	0.997219i	$0.476254\pi$
$492$		0			0
$493$	15.3485	−	26.5843i	0.691260	−	1.19730i
$494$		0			0
$495$	3.00000	+	5.19615i	0.134840	+	0.233550i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	6.65153	+	11.5208i	0.297763	+	0.515741i	0.975624	−	0.219449i	$-0.0704260\pi$
$499$	6.65153	+	11.5208i	0.297763	+	0.515741i	−0.677861	+	0.735191i	$0.737093\pi$
$500$		0			0
$501$	−7.10102	+	12.2993i	−0.317250	+	0.549493i
$502$		0			0
$503$	24.4949			1.09217			0.546087	−	0.837729i	$-0.316117\pi$
$503$	24.4949			1.09217			0.546087	+	0.837729i	$0.316117\pi$
$504$		0			0
$505$	−7.10102			−0.315991
$506$		0			0
$507$	8.32577	−	14.4206i	0.369760	−	0.640443i
$508$		0			0
$509$	−2.34847	−	4.06767i	−0.104094	−	0.180296i	0.809274	−	0.587432i	$-0.199861\pi$
$509$	−2.34847	−	4.06767i	−0.104094	−	0.180296i	−0.913368	+	0.407136i	$0.866528\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−9.55051	+	16.5420i	−0.420846	+	0.728926i
$516$		0			0
$517$	1.55051			0.0681914
$518$		0			0
$519$	34.8990			1.53190
$520$		0			0
$521$	9.44949	−	16.3670i	0.413990	−	0.717051i	−0.581332	−	0.813666i	$-0.697468\pi$
$521$	9.44949	−	16.3670i	0.413990	−	0.717051i	0.995322	+	0.0966152i	$0.0308016\pi$
$522$		0			0
$523$	16.6969	+	28.9199i	0.730106	+	1.26458i	0.956837	+	0.290624i	$0.0938627\pi$
$523$	16.6969	+	28.9199i	0.730106	+	1.26458i	−0.226731	+	0.973957i	$0.572804\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.44949	−	5.97469i	−0.150262	−	0.260262i
$528$		0			0
$529$	−28.0959	+	48.6636i	−1.22156	+	2.11581i
$530$		0			0
$531$	−22.0454			−0.956689
$532$		0			0
$533$	23.7980			1.03080
$534$		0			0
$535$	4.00000	−	6.92820i	0.172935	−	0.299532i
$536$		0			0
$537$	28.8990	+	50.0545i	1.24708	+	2.16001i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−10.7980	−	18.7026i	−0.464241	−	0.804088i	0.534926	−	0.844899i	$-0.320339\pi$
$541$	−10.7980	−	18.7026i	−0.464241	−	0.804088i	−0.999167	+	0.0408105i	$0.987006\pi$
$542$		0			0
$543$	23.1464	−	40.0908i	0.993308	−	1.72046i
$544$		0			0
$545$	10.2020			0.437007
$546$		0			0
$547$	−12.0000			−0.513083			−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000			−0.513083			−0.256541	+	0.966533i	$0.582583\pi$
$548$		0			0
$549$	14.0227	−	24.2880i	0.598474	−	1.03659i
$550$		0			0
$551$	16.8990	+	29.2699i	0.719921	+	1.24694i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	9.79796	+	16.9706i	0.415900	+	0.720360i
$556$		0			0
$557$	12.1010	−	20.9596i	0.512737	−	0.888086i	−0.487154	−	0.873316i	$-0.661965\pi$
$557$	12.1010	−	20.9596i	0.512737	−	0.888086i	0.999891	−	0.0147700i	$-0.00470162\pi$
$558$		0			0
$559$	−30.6969			−1.29834
$560$		0			0
$561$	10.8990			0.460155
$562$		0			0
$563$	−21.1464	+	36.6267i	−0.891216	+	1.54363i	−0.0527963	+	0.998605i	$0.516813\pi$
$563$	−21.1464	+	36.6267i	−0.891216	+	1.54363i	−0.838419	+	0.545026i	$0.816520\pi$
$564$		0			0
$565$	10.0000	+	17.3205i	0.420703	+	0.728679i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−10.3485	−	17.9241i	−0.433830	−	0.751416i	0.563369	−	0.826205i	$-0.309505\pi$
$569$	−10.3485	−	17.9241i	−0.433830	−	0.751416i	−0.997199	+	0.0747891i	$0.976172\pi$
$570$		0			0
$571$	14.8990	−	25.8058i	0.623503	−	1.07994i	−0.365325	−	0.930880i	$-0.619042\pi$
$571$	14.8990	−	25.8058i	0.623503	−	1.07994i	0.988828	−	0.149059i	$-0.0476244\pi$
$572$		0			0
$573$	−43.5959			−1.82125
$574$		0			0
$575$	−8.89898			−0.371113
$576$		0			0
$577$	−13.2474	+	22.9453i	−0.551499	+	0.955223i	0.446668	+	0.894700i	$0.352610\pi$
$577$	−13.2474	+	22.9453i	−0.551499	+	0.955223i	−0.998167	+	0.0605238i	$0.980723\pi$
$578$		0			0
$579$	−21.5505	−	37.3266i	−0.895609	−	1.55124i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−4.89898	−	8.48528i	−0.202895	−	0.351424i
$584$		0			0
$585$	−13.3485	+	23.1202i	−0.551891	+	0.955904i
$586$		0			0
$587$	26.4495			1.09169			0.545844	−	0.837887i	$-0.316209\pi$
$587$	26.4495			1.09169			0.545844	+	0.837887i	$0.316209\pi$
$588$		0			0
$589$	7.59592			0.312984
$590$		0			0
$591$	16.6515	−	28.8413i	0.684952	−	1.18637i
$592$		0			0
$593$	17.5732	+	30.4377i	0.721645	+	1.24993i	0.960340	+	0.278832i	$0.0899472\pi$
$593$	17.5732	+	30.4377i	0.721645	+	1.24993i	−0.238695	+	0.971095i	$0.576719\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−22.1010	−	38.2801i	−0.904535	−	1.56670i
$598$		0			0
$599$	8.44949	−	14.6349i	0.345237	−	0.597968i	−0.640160	−	0.768242i	$-0.721132\pi$
$599$	8.44949	−	14.6349i	0.345237	−	0.597968i	0.985397	+	0.170274i	$0.0544653\pi$
$600$		0			0
$601$	21.3485			0.870822			0.435411	−	0.900232i	$-0.356603\pi$
$601$	21.3485			0.870822			0.435411	+	0.900232i	$0.356603\pi$
$602$		0			0
$603$	44.0908			1.79552
$604$		0			0
$605$	−1.00000	+	1.73205i	−0.0406558	+	0.0704179i
$606$		0			0
$607$	11.7980	+	20.4347i	0.478864	+	0.829417i	0.999706	−	0.0242357i	$-0.00771523\pi$
$607$	11.7980	+	20.4347i	0.478864	+	0.829417i	−0.520842	+	0.853653i	$0.674382\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	3.44949	+	5.97469i	0.139551	+	0.241710i
$612$		0			0
$613$	−6.34847	+	10.9959i	−0.256412	+	0.444119i	−0.965278	−	0.261224i	$-0.915874\pi$
$613$	−6.34847	+	10.9959i	−0.256412	+	0.444119i	0.708866	+	0.705343i	$0.249207\pi$
$614$		0			0
$615$	−26.2020			−1.05657
$616$		0			0
$617$	29.3939			1.18335			0.591676	−	0.806176i	$-0.298466\pi$
$617$	29.3939			1.18335			0.591676	+	0.806176i	$0.298466\pi$
$618$		0			0
$619$	−5.22474	+	9.04952i	−0.210000	+	0.363731i	−0.951714	−	0.306985i	$-0.900680\pi$
$619$	−5.22474	+	9.04952i	−0.210000	+	0.363731i	0.741714	+	0.670716i	$0.234013\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$		0			0
$627$	−6.00000	+	10.3923i	−0.239617	+	0.415029i
$628$		0			0
$629$	17.7980			0.709651
$630$		0			0
$631$	−21.7980			−0.867763			−0.433882	−	0.900970i	$-0.642856\pi$
$631$	−21.7980			−0.867763			−0.433882	+	0.900970i	$0.642856\pi$
$632$		0			0
$633$	−24.4949	+	42.4264i	−0.973585	+	1.68630i
$634$		0			0
$635$	−17.7980	−	30.8270i	−0.706290	−	1.22333i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	4.65153	+	8.05669i	0.184012	+	0.318718i
$640$		0			0
$641$	−15.7980	+	27.3629i	−0.623982	+	1.08077i	0.364755	+	0.931104i	$0.381153\pi$
$641$	−15.7980	+	27.3629i	−0.623982	+	1.08077i	−0.988737	+	0.149665i	$0.952181\pi$
$642$		0			0
$643$	−20.2474			−0.798481			−0.399241	−	0.916846i	$-0.630726\pi$
$643$	−20.2474			−0.798481			−0.399241	+	0.916846i	$0.630726\pi$
$644$		0			0
$645$	33.7980			1.33079
$646$		0			0
$647$	12.1237	−	20.9989i	0.476633	−	0.825552i	−0.523009	−	0.852327i	$-0.675190\pi$
$647$	12.1237	−	20.9989i	0.476633	−	0.825552i	0.999641	+	0.0267751i	$0.00852381\pi$
$648$		0			0
$649$	−3.67423	−	6.36396i	−0.144226	−	0.249807i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	21.6969	+	37.5802i	0.849067	+	1.47063i	0.882042	+	0.471171i	$0.156168\pi$
$653$	21.6969	+	37.5802i	0.849067	+	1.47063i	−0.0329752	+	0.999456i	$0.510498\pi$
$654$		0			0
$655$	9.79796	−	16.9706i	0.382838	−	0.663095i
$656$		0			0
$657$	22.6515			0.883720
$658$		0			0
$659$	14.8990			0.580382			0.290191	−	0.956969i	$-0.406281\pi$
$659$	14.8990			0.580382			0.290191	+	0.956969i	$0.406281\pi$
$660$		0			0
$661$	−4.79796	+	8.31031i	−0.186619	+	0.323234i	−0.944121	−	0.329599i	$-0.893086\pi$
$661$	−4.79796	+	8.31031i	−0.186619	+	0.323234i	0.757502	+	0.652833i	$0.226420\pi$
$662$		0			0
$663$	24.2474	+	41.9978i	0.941693	+	1.63106i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	30.6969	+	53.1687i	1.18859	+	2.05870i
$668$		0			0
$669$	25.8990	−	44.8583i	1.00131	−	1.73432i
$670$		0			0
$671$	9.34847			0.360894
$672$		0			0
$673$	36.6969			1.41456			0.707282	−	0.706932i	$-0.249921\pi$
$673$	36.6969			1.41456			0.707282	+	0.706932i	$0.249921\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	12.4722	+	21.6025i	0.479345	+	0.830250i	0.999719	−	0.0236879i	$-0.00754081\pi$
$677$	12.4722	+	21.6025i	0.479345	+	0.830250i	−0.520374	+	0.853938i	$0.674207\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−21.7980	−	37.7552i	−0.835300	−	1.44678i
$682$		0			0
$683$	22.8990	−	39.6622i	0.876205	−	1.51763i	0.0207316	−	0.999785i	$-0.493400\pi$
$683$	22.8990	−	39.6622i	0.876205	−	1.51763i	0.855473	−	0.517847i	$-0.173266\pi$
$684$		0			0
$685$	−19.5959			−0.748722
$686$		0			0
$687$	36.4949			1.39237
$688$		0			0
$689$	21.7980	−	37.7552i	0.830436	−	1.43836i
$690$		0			0
$691$	3.42679	+	5.93537i	0.130361	+	0.225792i	0.923816	−	0.382837i	$-0.125053\pi$
$691$	3.42679	+	5.93537i	0.130361	+	0.225792i	−0.793455	+	0.608629i	$0.791720\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.69694	+	11.5994i	0.254029	+	0.439992i
$696$		0			0
$697$	−11.8990	+	20.6096i	−0.450706	+	0.780646i
$698$		0			0
$699$	26.6969			1.00977
$700$		0			0
$701$	8.69694			0.328479			0.164239	−	0.986421i	$-0.447483\pi$
$701$	8.69694			0.328479			0.164239	+	0.986421i	$0.447483\pi$
$702$		0			0
$703$	−9.79796	+	16.9706i	−0.369537	+	0.640057i
$704$		0			0
$705$	−3.79796	−	6.57826i	−0.143039	−	0.247752i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	7.89898	+	13.6814i	0.296652	+	0.513817i	0.975368	−	0.220584i	$-0.0707964\pi$
$709$	7.89898	+	13.6814i	0.296652	+	0.513817i	−0.678716	+	0.734401i	$0.737463\pi$
$710$		0			0
$711$	1.65153	−	2.86054i	0.0619372	−	0.107278i
$712$		0			0
$713$	13.7980			0.516738
$714$		0			0
$715$	−8.89898			−0.332803
$716$		0			0
$717$	19.5959	−	33.9411i	0.731823	−	1.26755i
$718$		0			0
$719$	−5.42679	−	9.39947i	−0.202385	−	0.350541i	0.746911	−	0.664924i	$-0.231536\pi$
$719$	−5.42679	−	9.39947i	−0.202385	−	0.350541i	−0.949296	+	0.314383i	$0.898203\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	16.3485	+	28.3164i	0.608006	+	1.05310i
$724$		0			0
$725$	−3.44949	+	5.97469i	−0.128111	+	0.221894i
$726$		0			0
$727$	−6.44949			−0.239198			−0.119599	−	0.992822i	$-0.538161\pi$
$727$	−6.44949			−0.239198			−0.119599	+	0.992822i	$0.538161\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	15.3485	−	26.5843i	0.567684	−	0.983257i
$732$		0			0
$733$	−15.3258	−	26.5450i	−0.566070	−	0.980462i	−0.996949	−	0.0780525i	$-0.975130\pi$
$733$	−15.3258	−	26.5450i	−0.566070	−	0.980462i	0.430879	−	0.902410i	$-0.358204\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.34847	+	12.7279i	0.270684	+	0.468839i
$738$		0			0
$739$	−8.69694	+	15.0635i	−0.319922	+	0.554121i	−0.980471	−	0.196661i	$-0.936990\pi$
$739$	−8.69694	+	15.0635i	−0.319922	+	0.554121i	0.660549	+	0.750783i	$0.270323\pi$
$740$		0			0
$741$	−53.3939			−1.96147
$742$		0			0
$743$	19.5959			0.718905			0.359452	−	0.933163i	$-0.382964\pi$
$743$	19.5959			0.718905			0.359452	+	0.933163i	$0.382964\pi$
$744$		0			0
$745$	7.79796	−	13.5065i	0.285695	−	0.494838i
$746$		0			0
$747$	10.6515	+	18.4490i	0.389719	+	0.675013i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	1.55051	+	2.68556i	0.0565789	+	0.0979976i	0.892928	−	0.450200i	$-0.148647\pi$
$751$	1.55051	+	2.68556i	0.0565789	+	0.0979976i	−0.836349	+	0.548198i	$0.815314\pi$
$752$		0			0
$753$	−3.00000	+	5.19615i	−0.109326	+	0.189358i
$754$		0			0
$755$	−41.3939			−1.50648
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$		0			0
$759$	−10.8990	+	18.8776i	−0.395608	+	0.685213i
$760$		0			0
$761$	6.92168	+	11.9887i	0.250911	+	0.434590i	0.963777	−	0.266710i	$-0.0859366\pi$
$761$	6.92168	+	11.9887i	0.250911	+	0.434590i	−0.712866	+	0.701300i	$0.752603\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−13.3485	−	23.1202i	−0.482615	−	0.835914i
$766$		0			0
$767$	16.3485	−	28.3164i	0.590309	−	1.02245i
$768$		0			0
$769$	4.85357			0.175024			0.0875121	−	0.996163i	$-0.472108\pi$
$769$	4.85357			0.175024			0.0875121	+	0.996163i	$0.472108\pi$
$770$		0			0
$771$	−38.6969			−1.39364
$772$		0			0
$773$	−16.3485	+	28.3164i	−0.588014	+	1.01847i	0.406479	+	0.913660i	$0.366757\pi$
$773$	−16.3485	+	28.3164i	−0.588014	+	1.01847i	−0.994492	+	0.104809i	$0.966577\pi$
$774$		0			0
$775$	0.775255	+	1.34278i	0.0278480	+	0.0482341i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−13.1010	−	22.6916i	−0.469393	−	0.813012i
$780$		0			0
$781$	−1.55051	+	2.68556i	−0.0554816	+	0.0960970i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	20.0000			0.713831
$786$		0			0
$787$	9.34847	−	16.1920i	0.333237	−	0.577183i	−0.649908	−	0.760013i	$-0.725192\pi$
$787$	9.34847	−	16.1920i	0.333237	−	0.577183i	0.983145	+	0.182830i	$0.0585258\pi$
$788$		0			0
$789$	−24.0000	−	41.5692i	−0.854423	−	1.47990i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	20.7980	+	36.0231i	0.738557	+	1.27922i
$794$		0			0
$795$	−24.0000	+	41.5692i	−0.851192	+	1.47431i
$796$		0			0
$797$	−12.2020			−0.432218			−0.216109	−	0.976369i	$-0.569337\pi$
$797$	−12.2020			−0.432218			−0.216109	+	0.976369i	$0.569337\pi$
$798$		0			0
$799$	−6.89898			−0.244068
$800$		0			0
$801$	−9.00000	+	15.5885i	−0.317999	+	0.550791i
$802$		0			0
$803$	3.77526	+	6.53893i	0.133226	+	0.230754i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−28.0454	−	48.5761i	−0.987245	−	1.70996i
$808$		0			0
$809$	−6.79796	+	11.7744i	−0.239004	+	0.413966i	−0.960429	−	0.278526i	$-0.910154\pi$
$809$	−6.79796	+	11.7744i	−0.239004	+	0.413966i	0.721425	+	0.692492i	$0.243487\pi$
$810$		0			0
$811$	15.5959			0.547647			0.273823	−	0.961780i	$-0.411712\pi$
$811$	15.5959			0.547647			0.273823	+	0.961780i	$0.411712\pi$
$812$		0			0
$813$	−75.1918			−2.63709
$814$		0			0
$815$	0.898979	−	1.55708i	0.0314899	−	0.0545421i
$816$		0			0
$817$	16.8990	+	29.2699i	0.591220	+	1.02402i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.89898	−	3.28913i	−0.0662748	−	0.114791i	0.830984	−	0.556296i	$-0.187778\pi$
$821$	−1.89898	−	3.28913i	−0.0662748	−	0.114791i	−0.897259	+	0.441505i	$0.854445\pi$
$822$		0			0
$823$	21.5959	−	37.4052i	0.752786	−	1.30386i	−0.193681	−	0.981065i	$-0.562043\pi$
$823$	21.5959	−	37.4052i	0.752786	−	1.30386i	0.946467	−	0.322800i	$-0.104624\pi$
$824$		0			0
$825$	−2.44949			−0.0852803
$826$		0			0
$827$	23.3031			0.810327			0.405163	−	0.914244i	$-0.367215\pi$
$827$	23.3031			0.810327			0.405163	+	0.914244i	$0.367215\pi$
$828$		0			0
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	−0.718481	−	0.695546i	$-0.755162\pi$
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	0.961601	+	0.274450i	$0.0884958\pi$
$830$		0			0
$831$	−4.65153	−	8.05669i	−0.161360	−	0.279483i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	5.79796	+	10.0424i	0.200647	+	0.347530i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	14.4495			0.498852			0.249426	−	0.968394i	$-0.419758\pi$
$839$	14.4495			0.498852			0.249426	+	0.968394i	$0.419758\pi$
$840$		0			0
$841$	18.5959			0.641239
$842$		0			0
$843$	−18.2474	+	31.6055i	−0.628476	+	1.08855i
$844$		0			0
$845$	−6.79796	−	11.7744i	−0.233857	−	0.405052i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−29.3939	−	50.9117i	−1.00880	−	1.74728i
$850$		0			0
$851$	−17.7980	+	30.8270i	−0.610106	+	1.05673i
$852$		0			0
$853$	8.85357			0.303141			0.151570	−	0.988446i	$-0.451567\pi$
$853$	8.85357			0.303141			0.151570	+	0.988446i	$0.451567\pi$
$854$		0			0
$855$	29.3939			1.00525
$856$		0			0
$857$	−21.5732	+	37.3659i	−0.736927	+	1.27639i	0.216946	+	0.976184i	$0.430391\pi$
$857$	−21.5732	+	37.3659i	−0.736927	+	1.27639i	−0.953873	+	0.300211i	$0.902943\pi$
$858$		0			0
$859$	19.9217	+	34.5054i	0.679719	+	1.17731i	0.975065	+	0.221918i	$0.0712316\pi$
$859$	19.9217	+	34.5054i	0.679719	+	1.17731i	−0.295346	+	0.955390i	$0.595435\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	16.0000	+	27.7128i	0.544646	+	0.943355i	0.998629	+	0.0523446i	$0.0166694\pi$
$863$	16.0000	+	27.7128i	0.544646	+	0.943355i	−0.453983	+	0.891010i	$0.649997\pi$
$864$		0			0
$865$	14.2474	−	24.6773i	0.484428	−	0.839054i
$866$		0			0
$867$	−6.85357			−0.232760
$868$		0			0
$869$	1.10102			0.0373496
$870$		0			0
$871$	−32.6969	+	56.6328i	−1.10789	+	1.91893i
$872$		0			0
$873$	−22.3485	−	38.7087i	−0.756381	−	1.31009i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−3.65153	−	6.32464i	−0.123303	−	0.213568i	0.797765	−	0.602968i	$-0.206016\pi$
$877$	−3.65153	−	6.32464i	−0.123303	−	0.213568i	−0.921068	+	0.389401i	$0.872682\pi$
$878$		0			0
$879$	−31.0454	+	53.7722i	−1.04714	+	1.81369i
$880$		0			0
$881$	8.69694			0.293007			0.146504	−	0.989210i	$-0.453198\pi$
$881$	8.69694			0.293007			0.146504	+	0.989210i	$0.453198\pi$
$882$		0			0
$883$	−10.2020			−0.343326			−0.171663	−	0.985156i	$-0.554914\pi$
$883$	−10.2020			−0.343326			−0.171663	+	0.985156i	$0.554914\pi$
$884$		0			0
$885$	−18.0000	+	31.1769i	−0.605063	+	1.04800i
$886$		0			0
$887$	−19.1464	−	33.1626i	−0.642874	−	1.11349i	−0.984788	−	0.173759i	$-0.944408\pi$
$887$	−19.1464	−	33.1626i	−0.642874	−	1.11349i	0.341914	−	0.939731i	$-0.388925\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−4.50000	−	7.79423i	−0.150756	−	0.261116i
$892$		0			0
$893$	3.79796	−	6.57826i	0.127094	−	0.220133i
$894$		0			0
$895$	47.1918			1.57745
$896$		0			0
$897$	−96.9898			−3.23839
$898$		0			0
$899$	5.34847	−	9.26382i	0.178381	−	0.308966i
$900$		0			0
$901$	21.7980	+	37.7552i	0.726195	+	1.25781i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−18.8990	−	32.7340i	−0.628223	−	1.08811i
$906$		0			0
$907$	−6.44949	+	11.1708i	−0.214152	+	0.370922i	−0.953010	−	0.302939i	$-0.902032\pi$
$907$	−6.44949	+	11.1708i	−0.214152	+	0.370922i	0.738858	+	0.673861i	$0.235365\pi$
$908$		0			0
$909$	−10.6515			−0.353289
$910$		0			0
$911$	−12.4949			−0.413974			−0.206987	−	0.978344i	$-0.566366\pi$
$911$	−12.4949			−0.413974			−0.206987	+	0.978344i	$0.566366\pi$
$912$		0			0
$913$	−3.55051	+	6.14966i	−0.117505	+	0.203524i
$914$		0			0
$915$	−22.8990	−	39.6622i	−0.757017	−	1.31119i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−21.7980	−	37.7552i	−0.719048	−	1.24543i	−0.961377	−	0.275234i	$-0.911245\pi$
$919$	−21.7980	−	37.7552i	−0.719048	−	1.24543i	0.242329	−	0.970194i	$-0.422089\pi$
$920$		0			0
$921$	21.7980	−	37.7552i	0.718267	−	1.24408i
$922$		0			0
$923$	−13.7980			−0.454165
$924$		0			0
$925$	−4.00000			−0.131519
$926$		0			0
$927$	−14.3258	+	24.8130i	−0.470520	+	0.814964i
$928$		0			0
$929$	−8.14643	−	14.1100i	−0.267276	−	0.462935i	0.700882	−	0.713278i	$-0.252790\pi$
$929$	−8.14643	−	14.1100i	−0.267276	−	0.462935i	−0.968157	+	0.250343i	$0.919457\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−7.89898	−	13.6814i	−0.258601	−	0.447910i
$934$		0			0
$935$	4.44949	−	7.70674i	0.145514	−	0.252037i
$936$		0			0
$937$	−20.9444			−0.684223			−0.342112	−	0.939659i	$-0.611142\pi$
$937$	−20.9444			−0.684223			−0.342112	+	0.939659i	$0.611142\pi$
$938$		0			0
$939$	82.2929			2.68553
$940$		0			0
$941$	−24.2247	+	41.9585i	−0.789704	+	1.36781i	0.136444	+	0.990648i	$0.456433\pi$
$941$	−24.2247	+	41.9585i	−0.789704	+	1.36781i	−0.926148	+	0.377160i	$0.876901\pi$
$942$		0			0
$943$	−23.7980	−	41.2193i	−0.774968	−	1.34228i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−19.7980	−	34.2911i	−0.643347	−	1.11431i	−0.984681	−	0.174368i	$-0.944212\pi$
$947$	−19.7980	−	34.2911i	−0.643347	−	1.11431i	0.341333	−	0.939942i	$-0.389121\pi$
$948$		0			0
$949$	−16.7980	+	29.0949i	−0.545285	+	0.944461i
$950$		0			0
$951$	−62.6969			−2.03309
$952$		0			0
$953$	−24.2020			−0.783981			−0.391991	−	0.919969i	$-0.628213\pi$
$953$	−24.2020			−0.783981			−0.391991	+	0.919969i	$0.628213\pi$
$954$		0			0
$955$	−17.7980	+	30.8270i	−0.575928	+	0.997537i
$956$		0			0
$957$	8.44949	+	14.6349i	0.273133	+	0.473081i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	14.2980	+	24.7648i	0.461224	+	0.798864i
$962$		0			0
$963$	6.00000	−	10.3923i	0.193347	−	0.334887i
$964$		0			0
$965$	−35.1918			−1.13287
$966$		0			0
$967$	−29.1010			−0.935826			−0.467913	−	0.883775i	$-0.654994\pi$
$967$	−29.1010			−0.935826			−0.467913	+	0.883775i	$0.654994\pi$
$968$		0			0
$969$	26.6969	−	46.2405i	0.857629	−	1.48546i
$970$		0			0
$971$	−3.02270	−	5.23548i	−0.0970032	−	0.168014i	0.813440	−	0.581649i	$-0.197592\pi$
$971$	−3.02270	−	5.23548i	−0.0970032	−	0.168014i	−0.910443	+	0.413635i	$0.864259\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−5.44949	−	9.43879i	−0.174523	−	0.302283i
$976$		0			0
$977$	−11.8990	+	20.6096i	−0.380682	+	0.659361i	−0.991160	−	0.132673i	$-0.957644\pi$
$977$	−11.8990	+	20.6096i	−0.380682	+	0.659361i	0.610478	+	0.792033i	$0.290977\pi$
$978$		0			0
$979$	−6.00000			−0.191761
$980$		0			0
$981$	15.3031			0.488589
$982$		0			0
$983$	−2.32577	+	4.02834i	−0.0741804	+	0.128484i	−0.900730	−	0.434380i	$-0.856967\pi$
$983$	−2.32577	+	4.02834i	−0.0741804	+	0.128484i	0.826549	+	0.562865i	$0.190301\pi$
$984$		0			0
$985$	−13.5959	−	23.5488i	−0.433202	−	0.750328i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	30.6969	+	53.1687i	0.976106	+	1.69066i
$990$		0			0
$991$	14.0454	−	24.3274i	0.446167	−	0.772784i	−0.551966	−	0.833867i	$-0.686122\pi$
$991$	14.0454	−	24.3274i	0.446167	−	0.772784i	0.998133	+	0.0610828i	$0.0194554\pi$
$992$		0			0
$993$	78.3837			2.48743
$994$		0			0
$995$	−36.0908			−1.14416
$996$		0			0
$997$	−16.4722	+	28.5307i	−0.521680	+	0.903576i	0.478002	+	0.878359i	$0.341361\pi$
$997$	−16.4722	+	28.5307i	−0.521680	+	0.903576i	−0.999682	+	0.0252170i	$0.991972\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2156.2.i.e.1145.2		4
7.2	even	3	inner	2156.2.i.e.177.2		4
7.3	odd	6		2156.2.a.c.1.2		2
7.4	even	3		308.2.a.b.1.1	✓	2
7.5	odd	6		2156.2.i.i.177.1		4
7.6	odd	2		2156.2.i.i.1145.1		4
21.11	odd	6		2772.2.a.n.1.2		2
28.3	even	6		8624.2.a.bj.1.1		2
28.11	odd	6		1232.2.a.n.1.2		2
35.4	even	6		7700.2.a.s.1.2		2
35.18	odd	12		7700.2.e.j.1849.2		4
35.32	odd	12		7700.2.e.j.1849.3		4
56.11	odd	6		4928.2.a.bq.1.1		2
56.53	even	6		4928.2.a.bp.1.2		2
77.32	odd	6		3388.2.a.h.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.a.b.1.1	✓	2	7.4	even	3
1232.2.a.n.1.2		2	28.11	odd	6
2156.2.a.c.1.2		2	7.3	odd	6
2156.2.i.e.177.2		4	7.2	even	3	inner
2156.2.i.e.1145.2		4	1.1	even	1	trivial
2156.2.i.i.177.1		4	7.5	odd	6
2156.2.i.i.1145.1		4	7.6	odd	2
2772.2.a.n.1.2		2	21.11	odd	6
3388.2.a.h.1.1		2	77.32	odd	6
4928.2.a.bp.1.2		2	56.53	even	6
4928.2.a.bq.1.1		2	56.11	odd	6
7700.2.a.s.1.2		2	35.4	even	6
7700.2.e.j.1849.2		4	35.18	odd	12
7700.2.e.j.1849.3		4	35.32	odd	12
8624.2.a.bj.1.1		2	28.3	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:	\( N \)	\(=\)	\( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2156.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 2.12132i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.22474 - 2.12132i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(-1.50000 - 2.59808i) q^{9} +(0.500000 - 0.866025i) q^{11} +4.44949 q^{13} -4.89898 q^{15} +(-2.22474 + 3.85337i) q^{17} +(-2.44949 - 4.24264i) q^{19} +(-4.44949 - 7.70674i) q^{23} +(0.500000 - 0.866025i) q^{25} -6.89898 q^{29} +(-0.775255 + 1.34278i) q^{31} +(-1.22474 - 2.12132i) q^{33} +(-2.00000 - 3.46410i) q^{37} +(5.44949 - 9.43879i) q^{39} +5.34847 q^{41} -6.89898 q^{43} +(-3.00000 + 5.19615i) q^{45} +(0.775255 + 1.34278i) q^{47} +(5.44949 + 9.43879i) q^{51} +(4.89898 - 8.48528i) q^{53} -2.00000 q^{55} -12.0000 q^{57} +(3.67423 - 6.36396i) q^{59} +(4.67423 + 8.09601i) q^{61} +(-4.44949 - 7.70674i) q^{65} +(-7.34847 + 12.7279i) q^{67} -21.7980 q^{69} -3.10102 q^{71} +(-3.77526 + 6.53893i) q^{73} +(-1.22474 - 2.12132i) q^{75} +(0.550510 + 0.953512i) q^{79} +(4.50000 - 7.79423i) q^{81} -7.10102 q^{83} +8.89898 q^{85} +(-8.44949 + 14.6349i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(1.89898 + 3.28913i) q^{93} +(-4.89898 + 8.48528i) q^{95} +14.8990 q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5} - 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^5 - 6 * q^9	\( 4 q - 4 q^{5} - 6 q^{9} + 2 q^{11} + 8 q^{13} - 4 q^{17} - 8 q^{23} + 2 q^{25} - 8 q^{29} - 8 q^{31} - 8 q^{37} + 12 q^{39} - 8 q^{41} - 8 q^{43} - 12 q^{45} + 8 q^{47} + 12 q^{51} - 8 q^{55} - 48 q^{57} + 4 q^{61} - 8 q^{65} - 48 q^{69} - 32 q^{71} - 20 q^{73} + 12 q^{79} + 18 q^{81} - 48 q^{83} + 16 q^{85} - 24 q^{87} - 12 q^{89} - 12 q^{93} + 40 q^{97} - 12 q^{99}+O(q^{100}) \) 4 * q - 4 * q^5 - 6 * q^9 + 2 * q^11 + 8 * q^13 - 4 * q^17 - 8 * q^23 + 2 * q^25 - 8 * q^29 - 8 * q^31 - 8 * q^37 + 12 * q^39 - 8 * q^41 - 8 * q^43 - 12 * q^45 + 8 * q^47 + 12 * q^51 - 8 * q^55 - 48 * q^57 + 4 * q^61 - 8 * q^65 - 48 * q^69 - 32 * q^71 - 20 * q^73 + 12 * q^79 + 18 * q^81 - 48 * q^83 + 16 * q^85 - 24 * q^87 - 12 * q^89 - 12 * q^93 + 40 * q^97 - 12 * q^99

Introduction

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