LMFDB - Embedded newform 588.4.i.l.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,4,Mod(361,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("588.361");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	588.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:	$34.6931230834$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 27x^{6} + 10x^{5} + 446x^{4} + 62x^{3} + 3061x^{2} + 2142x + 14161 $ x^8 - 2x^7 + 27x^6 + 10x^5 + 446x^4 + 62x^3 + 3061x^2 + 2142*x + 14161
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$1.44795 - 2.50793i$ of defining polynomial
Character	$\chi$	$=$	588.361
Dual form			588.4.i.l.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 2.59808i) q^{3} +(-8.32734 - 14.4234i) q^{5} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 - 2.59808i) q^{3} +(-8.32734 - 14.4234i) q^{5} +(-4.50000 - 7.79423i) q^{9} +(35.8800 - 62.1460i) q^{11} +65.3878 q^{13} -49.9641 q^{15} +(45.2158 - 78.3160i) q^{17} +(81.9092 + 141.871i) q^{19} +(-39.6144 - 68.6142i) q^{23} +(-76.1893 + 131.964i) q^{25} -27.0000 q^{27} -43.2995 q^{29} +(67.8179 - 117.464i) q^{31} +(-107.640 - 186.438i) q^{33} +(-135.370 - 234.468i) q^{37} +(98.0817 - 169.882i) q^{39} -152.241 q^{41} -177.641 q^{43} +(-74.9461 + 129.810i) q^{45} +(-22.8166 - 39.5194i) q^{47} +(-135.647 - 234.948i) q^{51} +(79.2188 - 137.211i) q^{53} -1195.14 q^{55} +491.455 q^{57} +(-195.884 + 339.282i) q^{59} +(275.647 + 477.435i) q^{61} +(-544.506 - 943.113i) q^{65} +(-229.315 + 397.185i) q^{67} -237.687 q^{69} -486.786 q^{71} +(287.446 - 497.871i) q^{73} +(228.568 + 395.891i) q^{75} +(334.160 + 578.782i) q^{79} +(-40.5000 + 70.1481i) q^{81} -76.2450 q^{83} -1506.11 q^{85} +(-64.9493 + 112.495i) q^{87} +(683.401 + 1183.69i) q^{89} +(-203.454 - 352.392i) q^{93} +(1364.17 - 2362.82i) q^{95} -242.655 q^{97} -645.840 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{3} - 36 q^{9}+O(q^{10}) $ 8 * q + 12 * q^3 - 36 * q^9	$ 8 q + 12 q^{3} - 36 q^{9} + 48 q^{17} + 192 q^{19} - 192 q^{23} - 324 q^{25} - 216 q^{27} + 192 q^{29} + 48 q^{31} - 256 q^{37} - 2016 q^{41} - 224 q^{43} + 864 q^{47} - 144 q^{51} + 648 q^{53} - 4704 q^{55} + 1152 q^{57} + 336 q^{59} + 960 q^{61} + 360 q^{65} - 720 q^{67} - 1152 q^{69} - 2688 q^{71} + 672 q^{73} + 972 q^{75} + 1984 q^{79} - 324 q^{81} - 6240 q^{83} + 1360 q^{85} + 288 q^{87} + 2160 q^{89} - 144 q^{93} + 3744 q^{95} - 4032 q^{97}+O(q^{100}) $ 8 * q + 12 * q^3 - 36 * q^9 + 48 * q^17 + 192 * q^19 - 192 * q^23 - 324 * q^25 - 216 * q^27 + 192 * q^29 + 48 * q^31 - 256 * q^37 - 2016 * q^41 - 224 * q^43 + 864 * q^47 - 144 * q^51 + 648 * q^53 - 4704 * q^55 + 1152 * q^57 + 336 * q^59 + 960 * q^61 + 360 * q^65 - 720 * q^67 - 1152 * q^69 - 2688 * q^71 + 672 * q^73 + 972 * q^75 + 1984 * q^79 - 324 * q^81 - 6240 * q^83 + 1360 * q^85 + 288 * q^87 + 2160 * q^89 - 144 * q^93 + 3744 * q^95 - 4032 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$4$		0			0
$5$	−8.32734	−	14.4234i	−0.744820	−	1.29007i	−0.950279	−	0.311401i	$-0.899202\pi$
$5$	−8.32734	−	14.4234i	−0.744820	−	1.29007i	0.205459	−	0.978666i	$-0.434131\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$		0			0
$11$	35.8800	−	62.1460i	0.983475	−	1.70343i	0.334949	−	0.942236i	$-0.391281\pi$
$11$	35.8800	−	62.1460i	0.983475	−	1.70343i	0.648526	−	0.761192i	$-0.275386\pi$
$12$		0			0
$13$	65.3878			1.39502			0.697512	−	0.716573i	$-0.254291\pi$
$13$	65.3878			1.39502			0.697512	+	0.716573i	$0.254291\pi$
$14$		0			0
$15$	−49.9641			−0.860044
$16$		0			0
$17$	45.2158	−	78.3160i	0.645085	−	1.11732i	−0.339197	−	0.940715i	$-0.610155\pi$
$17$	45.2158	−	78.3160i	0.645085	−	1.11732i	0.984282	−	0.176604i	$-0.0565112\pi$
$18$		0			0
$19$	81.9092	+	141.871i	0.989014	+	1.71302i	0.622526	+	0.782599i	$0.286107\pi$
$19$	81.9092	+	141.871i	0.989014	+	1.71302i	0.366488	+	0.930423i	$0.380560\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−39.6144	−	68.6142i	−0.359138	−	0.622045i	0.628679	−	0.777665i	$-0.283596\pi$
$23$	−39.6144	−	68.6142i	−0.359138	−	0.622045i	−0.987817	+	0.155619i	$0.950263\pi$
$24$		0			0
$25$	−76.1893	+	131.964i	−0.609514	+	1.05571i
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	−43.2995			−0.277259			−0.138630	−	0.990344i	$-0.544270\pi$
$29$	−43.2995			−0.277259			−0.138630	+	0.990344i	$0.544270\pi$
$30$		0			0
$31$	67.8179	−	117.464i	0.392918	−	0.680554i	−0.599915	−	0.800064i	$-0.704799\pi$
$31$	67.8179	−	117.464i	0.392918	−	0.680554i	0.992833	+	0.119510i	$0.0381323\pi$
$32$		0			0
$33$	−107.640	−	186.438i	−0.567810	−	0.983475i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−135.370	−	234.468i	−0.601479	−	1.04179i	−0.992597	−	0.121452i	$-0.961245\pi$
$37$	−135.370	−	234.468i	−0.601479	−	1.04179i	0.391118	−	0.920340i	$-0.372088\pi$
$38$		0			0
$39$	98.0817	−	169.882i	0.402709	−	0.697512i
$40$		0			0
$41$	−152.241			−0.579902			−0.289951	−	0.957041i	$-0.593639\pi$
$41$	−152.241			−0.579902			−0.289951	+	0.957041i	$0.593639\pi$
$42$		0			0
$43$	−177.641			−0.630001			−0.315001	−	0.949091i	$-0.602005\pi$
$43$	−177.641			−0.630001			−0.315001	+	0.949091i	$0.602005\pi$
$44$		0			0
$45$	−74.9461	+	129.810i	−0.248273	+	0.430022i
$46$		0			0
$47$	−22.8166	−	39.5194i	−0.0708114	−	0.122649i	0.828446	−	0.560069i	$-0.189226\pi$
$47$	−22.8166	−	39.5194i	−0.0708114	−	0.122649i	−0.899257	+	0.437420i	$0.855892\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−135.647	−	234.948i	−0.372440	−	0.645085i
$52$		0			0
$53$	79.2188	−	137.211i	0.205312	−	0.355611i	−0.744920	−	0.667154i	$-0.767512\pi$
$53$	79.2188	−	137.211i	0.205312	−	0.355611i	0.950232	+	0.311543i	$0.100846\pi$
$54$		0			0
$55$	−1195.14			−2.93005
$56$		0			0
$57$	491.455			1.14201
$58$		0			0
$59$	−195.884	+	339.282i	−0.432237	+	0.748656i	−0.997066	−	0.0765519i	$-0.975609\pi$
$59$	−195.884	+	339.282i	−0.432237	+	0.748656i	0.564829	+	0.825208i	$0.308942\pi$
$60$		0			0
$61$	275.647	+	477.435i	0.578574	+	1.00212i	0.995643	+	0.0932450i	$0.0297240\pi$
$61$	275.647	+	477.435i	0.578574	+	1.00212i	−0.417069	+	0.908875i	$0.636943\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−544.506	−	943.113i	−1.03904	−	1.79967i
$66$		0			0
$67$	−229.315	+	397.185i	−0.418139	+	0.724237i	−0.995752	−	0.0920729i	$-0.970651\pi$
$67$	−229.315	+	397.185i	−0.418139	+	0.724237i	0.577614	+	0.816310i	$0.303984\pi$
$68$		0			0
$69$	−237.687			−0.414697
$70$		0			0
$71$	−486.786			−0.813674			−0.406837	−	0.913501i	$-0.633368\pi$
$71$	−486.786			−0.813674			−0.406837	+	0.913501i	$0.633368\pi$
$72$		0			0
$73$	287.446	−	497.871i	0.460863	−	0.798238i	−0.538141	−	0.842855i	$-0.680873\pi$
$73$	287.446	−	497.871i	0.460863	−	0.798238i	0.999004	+	0.0446164i	$0.0142066\pi$
$74$		0			0
$75$	228.568	+	395.891i	0.351903	+	0.609514i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	334.160	+	578.782i	0.475897	+	0.824279i	0.999619	−	0.0276111i	$-0.00878999\pi$
$79$	334.160	+	578.782i	0.475897	+	0.824279i	−0.523721	+	0.851890i	$0.675457\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−76.2450			−0.100831			−0.0504155	−	0.998728i	$-0.516055\pi$
$83$	−76.2450			−0.100831			−0.0504155	+	0.998728i	$0.516055\pi$
$84$		0			0
$85$	−1506.11			−1.92189
$86$		0			0
$87$	−64.9493	+	112.495i	−0.0800379	+	0.138630i
$88$		0			0
$89$	683.401	+	1183.69i	0.813937	+	1.40978i	0.910089	+	0.414413i	$0.136013\pi$
$89$	683.401	+	1183.69i	0.813937	+	1.40978i	−0.0961518	+	0.995367i	$0.530653\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−203.454	−	352.392i	−0.226851	−	0.392918i
$94$		0			0
$95$	1364.17	−	2362.82i	1.47327	−	2.55179i
$96$		0			0
$97$	−242.655			−0.253999			−0.127000	−	0.991903i	$-0.540535\pi$
$97$	−242.655			−0.253999			−0.127000	+	0.991903i	$0.540535\pi$
$98$		0			0
$99$	−645.840			−0.655650
$100$		0			0
$101$	347.371	−	601.665i	0.342225	−	0.592751i	−0.642620	−	0.766185i	$-0.722153\pi$
$101$	347.371	−	601.665i	0.342225	−	0.592751i	0.984846	+	0.173433i	$0.0554861\pi$
$102$		0			0
$103$	−87.1089	−	150.877i	−0.0833310	−	0.144334i	0.821348	−	0.570428i	$-0.193223\pi$
$103$	−87.1089	−	150.877i	−0.0833310	−	0.144334i	−0.904679	+	0.426094i	$0.859889\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−23.8025	−	41.2272i	−0.0215054	−	0.0372485i	0.855072	−	0.518509i	$-0.173513\pi$
$107$	−23.8025	−	41.2272i	−0.0215054	−	0.0372485i	−0.876578	+	0.481260i	$0.840179\pi$
$108$		0			0
$109$	816.549	−	1414.30i	0.717534	−	1.24281i	−0.244440	−	0.969664i	$-0.578604\pi$
$109$	816.549	−	1414.30i	0.717534	−	1.24281i	0.961974	−	0.273141i	$-0.0880626\pi$
$110$		0			0
$111$	−812.221			−0.694528
$112$		0			0
$113$	−1127.29			−0.938464			−0.469232	−	0.883075i	$-0.655469\pi$
$113$	−1127.29			−0.938464			−0.469232	+	0.883075i	$0.655469\pi$
$114$		0			0
$115$	−659.766	+	1142.75i	−0.534987	+	0.926624i
$116$		0			0
$117$	−294.245	−	509.647i	−0.232504	−	0.402709i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−1909.25	−	3306.91i	−1.43445	−	2.48453i
$122$		0			0
$123$	−228.361	+	395.533i	−0.167403	+	0.289951i
$124$		0			0
$125$	455.982			0.326274
$126$		0			0
$127$	2398.66			1.67596			0.837979	−	0.545702i	$-0.183737\pi$
$127$	2398.66			1.67596			0.837979	+	0.545702i	$0.183737\pi$
$128$		0			0
$129$	−266.462	+	461.526i	−0.181866	+	0.315001i
$130$		0			0
$131$	774.482	+	1341.44i	0.516541	+	0.894675i	0.999816	+	0.0192062i	$0.00611389\pi$
$131$	774.482	+	1341.44i	0.516541	+	0.894675i	−0.483275	+	0.875469i	$0.660553\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	224.838	+	389.431i	0.143341	+	0.248273i
$136$		0			0
$137$	−761.634	+	1319.19i	−0.474969	+	0.822671i	−0.999589	−	0.0286657i	$-0.990874\pi$
$137$	−761.634	+	1319.19i	−0.474969	+	0.822671i	0.524620	+	0.851337i	$0.324207\pi$
$138$		0			0
$139$	−551.445			−0.336496			−0.168248	−	0.985745i	$-0.553811\pi$
$139$	−551.445			−0.336496			−0.168248	+	0.985745i	$0.553811\pi$
$140$		0			0
$141$	−136.899			−0.0817660
$142$		0			0
$143$	2346.11	−	4063.59i	1.37197	−	2.37632i
$144$		0			0
$145$	360.570	+	624.526i	0.206508	+	0.357683i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1200.12	+	2078.67i	0.659851	+	1.14290i	0.980654	+	0.195749i	$0.0627139\pi$
$149$	1200.12	+	2078.67i	0.659851	+	1.14290i	−0.320803	+	0.947146i	$0.603953\pi$
$150$		0			0
$151$	−310.780	+	538.287i	−0.167490	+	0.290100i	−0.937537	−	0.347887i	$-0.886899\pi$
$151$	−310.780	+	538.287i	−0.167490	+	0.290100i	0.770047	+	0.637987i	$0.220233\pi$
$152$		0			0
$153$	−813.884			−0.430056
$154$		0			0
$155$	−2258.97			−1.17061
$156$		0			0
$157$	−1345.79	+	2330.97i	−0.684112	+	1.18492i	0.289603	+	0.957147i	$0.406477\pi$
$157$	−1345.79	+	2330.97i	−0.684112	+	1.18492i	−0.973715	+	0.227770i	$0.926857\pi$
$158$		0			0
$159$	−237.657	−	411.633i	−0.118537	−	0.205312i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−528.653	−	915.654i	−0.254032	−	0.439997i	0.710600	−	0.703596i	$-0.248424\pi$
$163$	−528.653	−	915.654i	−0.254032	−	0.439997i	−0.964632	+	0.263599i	$0.915090\pi$
$164$		0			0
$165$	−1792.71	+	3105.06i	−0.845832	+	1.46502i
$166$		0			0
$167$	243.840			0.112987			0.0564937	−	0.998403i	$-0.482008\pi$
$167$	243.840			0.112987			0.0564937	+	0.998403i	$0.482008\pi$
$168$		0			0
$169$	2078.56			0.946090
$170$		0			0
$171$	737.183	−	1276.84i	0.329671	−	0.571007i
$172$		0			0
$173$	−843.632	−	1461.21i	−0.370753	−	0.642162i	0.618929	−	0.785447i	$-0.287567\pi$
$173$	−843.632	−	1461.21i	−0.370753	−	0.642162i	−0.989682	+	0.143285i	$0.954234\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	587.653	+	1017.85i	0.249552	+	0.432237i
$178$		0			0
$179$	179.570	−	311.024i	0.0749814	−	0.129872i	−0.826097	−	0.563528i	$-0.809444\pi$
$179$	179.570	−	311.024i	0.0749814	−	0.129872i	0.901078	+	0.433657i	$0.142777\pi$
$180$		0			0
$181$	−2982.58			−1.22483			−0.612413	−	0.790538i	$-0.709801\pi$
$181$	−2982.58			−1.22483			−0.612413	+	0.790538i	$0.709801\pi$
$182$		0			0
$183$	1653.88			0.668080
$184$		0			0
$185$	−2254.55	+	3904.99i	−0.895988	+	1.55190i
$186$		0			0
$187$	−3244.68	−	5619.96i	−1.26885	−	2.19771i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1745.39	−	3023.10i	−0.661213	−	1.14525i	−0.980297	−	0.197528i	$-0.936709\pi$
$191$	−1745.39	−	3023.10i	−0.661213	−	1.14525i	0.319084	−	0.947726i	$-0.396625\pi$
$192$		0			0
$193$	−802.114	+	1389.30i	−0.299158	+	0.518156i	−0.975943	−	0.218024i	$-0.930039\pi$
$193$	−802.114	+	1389.30i	−0.299158	+	0.518156i	0.676786	+	0.736180i	$0.263372\pi$
$194$		0			0
$195$	−3267.04			−1.19978
$196$		0			0
$197$	−455.935			−0.164893			−0.0824467	−	0.996595i	$-0.526273\pi$
$197$	−455.935			−0.164893			−0.0824467	+	0.996595i	$0.526273\pi$
$198$		0			0
$199$	1042.08	−	1804.94i	0.371212	−	0.642958i	−0.618541	−	0.785753i	$-0.712276\pi$
$199$	1042.08	−	1804.94i	0.371212	−	0.642958i	0.989752	+	0.142795i	$0.0456091\pi$
$200$		0			0
$201$	687.945	+	1191.56i	0.241412	+	0.418139i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	1267.76	+	2195.83i	0.431923	+	0.748113i
$206$		0			0
$207$	−356.530	+	617.528i	−0.119713	+	0.207348i
$208$		0			0
$209$	11755.6			3.89068
$210$		0			0
$211$	2568.06			0.837880			0.418940	−	0.908014i	$-0.362402\pi$
$211$	2568.06			0.837880			0.418940	+	0.908014i	$0.362402\pi$
$212$		0			0
$213$	−730.178	+	1264.71i	−0.234887	+	0.406837i
$214$		0			0
$215$	1479.28	+	2562.19i	0.469238	+	0.812743i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−862.338	−	1493.61i	−0.266079	−	0.460863i
$220$		0			0
$221$	2956.56	−	5120.91i	0.899908	−	1.55869i
$222$		0			0
$223$	4659.55			1.39922			0.699612	−	0.714523i	$-0.253356\pi$
$223$	4659.55			1.39922			0.699612	+	0.714523i	$0.253356\pi$
$224$		0			0
$225$	1371.41			0.406343
$226$		0			0
$227$	2414.39	−	4181.84i	0.705940	−	1.22272i	−0.260411	−	0.965498i	$-0.583858\pi$
$227$	2414.39	−	4181.84i	0.705940	−	1.22272i	0.966351	−	0.257227i	$-0.0828087\pi$
$228$		0			0
$229$	−1611.29	−	2790.84i	−0.464966	−	0.805345i	0.534234	−	0.845337i	$-0.320600\pi$
$229$	−1611.29	−	2790.84i	−0.464966	−	0.805345i	−0.999200	+	0.0399917i	$0.987267\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2851.21	+	4938.44i	0.801670	+	1.38853i	0.918517	+	0.395383i	$0.129388\pi$
$233$	2851.21	+	4938.44i	0.801670	+	1.38853i	−0.116847	+	0.993150i	$0.537279\pi$
$234$		0			0
$235$	−380.003	+	658.184i	−0.105484	+	0.182703i
$236$		0			0
$237$	2004.96			0.549519
$238$		0			0
$239$	1994.47			0.539796			0.269898	−	0.962889i	$-0.413010\pi$
$239$	1994.47			0.539796			0.269898	+	0.962889i	$0.413010\pi$
$240$		0			0
$241$	−710.443	+	1230.52i	−0.189891	+	0.328900i	−0.945214	−	0.326452i	$-0.894147\pi$
$241$	−710.443	+	1230.52i	−0.189891	+	0.328900i	0.755323	+	0.655353i	$0.227480\pi$
$242$		0			0
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	5355.86	+	9276.62i	1.37970	+	2.38971i
$248$		0			0
$249$	−114.367	+	198.090i	−0.0291074	+	0.0504155i
$250$		0			0
$251$	3855.44			0.969534			0.484767	−	0.874643i	$-0.338904\pi$
$251$	3855.44			0.969534			0.484767	+	0.874643i	$0.338904\pi$
$252$		0			0
$253$	−5685.46			−1.41281
$254$		0			0
$255$	−2259.16	+	3912.99i	−0.554801	+	0.960944i
$256$		0			0
$257$	2026.64	+	3510.24i	0.491900	+	0.851996i	0.999956	−	0.00932793i	$-0.00296922\pi$
$257$	2026.64	+	3510.24i	0.491900	+	0.851996i	−0.508056	+	0.861324i	$0.669636\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	194.848	+	337.486i	0.0462099	+	0.0800379i
$262$		0			0
$263$	250.393	−	433.694i	0.0587069	−	0.101683i	−0.835178	−	0.549979i	$-0.814636\pi$
$263$	250.393	−	433.694i	0.0587069	−	0.101683i	0.893885	+	0.448296i	$0.147969\pi$
$264$		0			0
$265$	−2638.73			−0.611683
$266$		0			0
$267$	4100.41			0.939853
$268$		0			0
$269$	1640.87	−	2842.07i	0.371917	−	0.644179i	−0.617943	−	0.786223i	$-0.712034\pi$
$269$	1640.87	−	2842.07i	0.371917	−	0.644179i	0.989860	+	0.142043i	$0.0453672\pi$
$270$		0			0
$271$	1662.18	+	2878.98i	0.372584	+	0.645334i	0.989962	−	0.141332i	$-0.0451386\pi$
$271$	1662.18	+	2878.98i	0.372584	+	0.645334i	−0.617378	+	0.786666i	$0.711805\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5467.34	+	9469.71i	1.19888	+	2.07653i
$276$		0			0
$277$	−4309.87	+	7464.92i	−0.934856	+	1.61922i	−0.159966	+	0.987122i	$0.551139\pi$
$277$	−4309.87	+	7464.92i	−0.934856	+	1.61922i	−0.774890	+	0.632096i	$0.782195\pi$
$278$		0			0
$279$	−1220.72			−0.261945
$280$		0			0
$281$	−7710.80			−1.63697			−0.818484	−	0.574529i	$-0.805185\pi$
$281$	−7710.80			−1.63697			−0.818484	+	0.574529i	$0.805185\pi$
$282$		0			0
$283$	−69.6354	+	120.612i	−0.0146268	+	0.0253344i	−0.873246	−	0.487279i	$-0.837989\pi$
$283$	−69.6354	+	120.612i	−0.0146268	+	0.0253344i	0.858619	+	0.512614i	$0.171323\pi$
$284$		0			0
$285$	−4092.52	−	7088.45i	−0.850596	−	1.47327i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−1632.43	−	2827.46i	−0.332268	−	0.575506i
$290$		0			0
$291$	−363.983	+	630.437i	−0.0733232	+	0.127000i
$292$		0			0
$293$	4437.09			0.884702			0.442351	−	0.896842i	$-0.354145\pi$
$293$	4437.09			0.884702			0.442351	+	0.896842i	$0.354145\pi$
$294$		0			0
$295$	6524.79			1.28776
$296$		0			0
$297$	−968.760	+	1677.94i	−0.189270	+	0.327825i
$298$		0			0
$299$	−2590.30	−	4486.53i	−0.501006	−	0.867768i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−1042.11	−	1804.99i	−0.197584	−	0.342225i
$304$		0			0
$305$	4590.82	−	7951.53i	0.861867	−	1.49280i
$306$		0			0
$307$	299.480			0.0556749			0.0278375	−	0.999612i	$-0.491138\pi$
$307$	299.480			0.0556749			0.0278375	+	0.999612i	$0.491138\pi$
$308$		0			0
$309$	−522.654			−0.0962224
$310$		0			0
$311$	456.972	−	791.498i	0.0833199	−	0.144314i	−0.821354	−	0.570419i	$-0.806781\pi$
$311$	456.972	−	791.498i	0.0833199	−	0.144314i	0.904674	+	0.426104i	$0.140114\pi$
$312$		0			0
$313$	1943.69	+	3366.57i	0.351002	+	0.607954i	0.986425	−	0.164210i	$-0.0525075\pi$
$313$	1943.69	+	3366.57i	0.351002	+	0.607954i	−0.635423	+	0.772164i	$0.719174\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1439.65	−	2493.55i	−0.255075	−	0.441803i	0.709841	−	0.704362i	$-0.248767\pi$
$317$	−1439.65	−	2493.55i	−0.255075	−	0.441803i	−0.964916	+	0.262559i	$0.915434\pi$
$318$		0			0
$319$	−1553.59	+	2690.89i	−0.272678	+	0.472291i
$320$		0			0
$321$	−142.815			−0.0248323
$322$		0			0
$323$	14814.4			2.55199
$324$		0			0
$325$	−4981.85	+	8628.81i	−0.850287	+	1.47274i
$326$		0			0
$327$	−2449.65	−	4242.91i	−0.414269	−	0.717534i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1405.39	+	2434.21i	0.233376	+	0.404219i	0.958799	−	0.284084i	$-0.0916894\pi$
$331$	1405.39	+	2434.21i	0.233376	+	0.404219i	−0.725424	+	0.688303i	$0.758356\pi$
$332$		0			0
$333$	−1218.33	+	2110.21i	−0.200493	+	0.347264i
$334$		0			0
$335$	7638.34			1.24575
$336$		0			0
$337$	2960.90			0.478607			0.239303	−	0.970945i	$-0.423081\pi$
$337$	2960.90			0.478607			0.239303	+	0.970945i	$0.423081\pi$
$338$		0			0
$339$	−1690.93	+	2928.78i	−0.270911	+	0.469232i
$340$		0			0
$341$	−4866.61	−	8429.22i	−0.772850	−	1.33862i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	1979.30	+	3428.24i	0.308875	+	0.534987i
$346$		0			0
$347$	2142.26	−	3710.50i	0.331419	−	0.574034i	−0.651371	−	0.758759i	$-0.725806\pi$
$347$	2142.26	−	3710.50i	0.331419	−	0.574034i	0.982790	+	0.184725i	$0.0591393\pi$
$348$		0			0
$349$	−3295.36			−0.505434			−0.252717	−	0.967540i	$-0.581324\pi$
$349$	−3295.36			−0.505434			−0.252717	+	0.967540i	$0.581324\pi$
$350$		0			0
$351$	−1765.47			−0.268472
$352$		0			0
$353$	−5314.83	+	9205.56i	−0.801360	+	1.38800i	0.117362	+	0.993089i	$0.462556\pi$
$353$	−5314.83	+	9205.56i	−0.801360	+	1.38800i	−0.918721	+	0.394906i	$0.870777\pi$
$354$		0			0
$355$	4053.63	+	7021.09i	0.606040	+	1.04969i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1592.51	−	2758.30i	−0.234121	−	0.405509i	0.724896	−	0.688858i	$-0.241888\pi$
$359$	−1592.51	−	2758.30i	−0.234121	−	0.405509i	−0.959017	+	0.283349i	$0.908554\pi$
$360$		0			0
$361$	−9988.74	+	17301.0i	−1.45630	+	2.52238i
$362$		0			0
$363$	−11455.5			−1.65636
$364$		0			0
$365$	−9574.65			−1.37304
$366$		0			0
$367$	3801.52	−	6584.42i	0.540702	−	0.936523i	−0.458162	−	0.888869i	$-0.651492\pi$
$367$	3801.52	−	6584.42i	0.540702	−	0.936523i	0.998864	−	0.0476544i	$-0.0151746\pi$
$368$		0			0
$369$	685.083	+	1186.60i	0.0966504	+	0.167403i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−755.978	−	1309.39i	−0.104941	−	0.181763i	0.808773	−	0.588121i	$-0.200132\pi$
$373$	−755.978	−	1309.39i	−0.104941	−	0.181763i	−0.913714	+	0.406358i	$0.866799\pi$
$374$		0			0
$375$	683.972	−	1184.67i	0.0941871	−	0.163137i
$376$		0			0
$377$	−2831.26			−0.386783
$378$		0			0
$379$	8848.36			1.19923			0.599617	−	0.800287i	$-0.295320\pi$
$379$	8848.36			1.19923			0.599617	+	0.800287i	$0.295320\pi$
$380$		0			0
$381$	3597.99	−	6231.90i	0.483807	−	0.837979i
$382$		0			0
$383$	2067.05	+	3580.24i	0.275774	+	0.477654i	0.970330	−	0.241784i	$-0.0777326\pi$
$383$	2067.05	+	3580.24i	0.275774	+	0.477654i	−0.694556	+	0.719438i	$0.744399\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	799.386	+	1384.58i	0.105000	+	0.181866i
$388$		0			0
$389$	−3815.30	+	6608.30i	−0.497284	+	0.861322i	−0.999995	−	0.00313295i	$-0.999003\pi$
$389$	−3815.30	+	6608.30i	−0.497284	+	0.861322i	0.502711	+	0.864455i	$0.332336\pi$
$390$		0			0
$391$	−7164.79			−0.926698
$392$		0			0
$393$	4646.89			0.596450
$394$		0			0
$395$	5565.32	−	9639.43i	0.708916	−	1.22788i
$396$		0			0
$397$	−5809.25	−	10061.9i	−0.734403	−	1.27202i	−0.954985	−	0.296654i	$-0.904129\pi$
$397$	−5809.25	−	10061.9i	−0.734403	−	1.27202i	0.220582	−	0.975368i	$-0.429204\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1523.51	−	2638.79i	−0.189726	−	0.328616i	0.755433	−	0.655226i	$-0.227427\pi$
$401$	−1523.51	−	2638.79i	−0.189726	−	0.328616i	−0.945159	+	0.326611i	$0.894093\pi$
$402$		0			0
$403$	4434.46	−	7680.71i	0.548130	−	0.949388i
$404$		0			0
$405$	1349.03			0.165516
$406$		0			0
$407$	−19428.3			−2.36616
$408$		0			0
$409$	5791.42	−	10031.0i	0.700164	−	1.21272i	−0.268244	−	0.963351i	$-0.586443\pi$
$409$	5791.42	−	10031.0i	0.700164	−	1.21272i	0.968408	−	0.249369i	$-0.0802233\pi$
$410$		0			0
$411$	2284.90	+	3957.57i	0.274224	+	0.474969i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	634.918	+	1099.71i	0.0751010	+	0.130079i
$416$		0			0
$417$	−827.167	+	1432.70i	−0.0971380	+	0.168248i
$418$		0			0
$419$	1318.83			0.153768			0.0768841	−	0.997040i	$-0.475503\pi$
$419$	1318.83			0.153768			0.0768841	+	0.997040i	$0.475503\pi$
$420$		0			0
$421$	−9733.56			−1.12680			−0.563402	−	0.826183i	$-0.690508\pi$
$421$	−9733.56			−1.12680			−0.563402	+	0.826183i	$0.690508\pi$
$422$		0			0
$423$	−205.349	+	355.675i	−0.0236038	+	0.0408830i
$424$		0			0
$425$	6889.92	+	11933.7i	0.786377	+	1.36204i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−7038.34	−	12190.8i	−0.792108	−	1.37197i
$430$		0			0
$431$	7214.47	−	12495.8i	0.806284	−	1.39653i	−0.109136	−	0.994027i	$-0.534808\pi$
$431$	7214.47	−	12495.8i	0.806284	−	1.39653i	0.915421	−	0.402499i	$-0.131858\pi$
$432$		0			0
$433$	16620.3			1.84463			0.922313	−	0.386444i	$-0.126297\pi$
$433$	16620.3			1.84463			0.922313	+	0.386444i	$0.126297\pi$
$434$		0			0
$435$	2163.42			0.238455
$436$		0			0
$437$	6489.57	−	11240.3i	0.710385	−	1.23042i
$438$		0			0
$439$	−257.783	−	446.493i	−0.0280257	−	0.0485420i	0.851672	−	0.524075i	$-0.175589\pi$
$439$	−257.783	−	446.493i	−0.0280257	−	0.0485420i	−0.879698	+	0.475533i	$0.842255\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4488.05	−	7773.52i	−0.481340	−	0.833705i	0.518431	−	0.855120i	$-0.326516\pi$
$443$	−4488.05	−	7773.52i	−0.481340	−	0.833705i	−0.999771	+	0.0214146i	$0.993183\pi$
$444$		0			0
$445$	11381.8	−	19713.9i	1.21247	−	2.10007i
$446$		0			0
$447$	7200.73			0.761930
$448$		0			0
$449$	2106.83			0.221442			0.110721	−	0.993852i	$-0.464684\pi$
$449$	2106.83			0.221442			0.110721	+	0.993852i	$0.464684\pi$
$450$		0			0
$451$	−5462.39	+	9461.14i	−0.570319	+	0.987822i
$452$		0			0
$453$	932.340	+	1614.86i	0.0967001	+	0.167490i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−7863.08	−	13619.3i	−0.804857	−	1.39405i	−0.916388	−	0.400292i	$-0.868909\pi$
$457$	−7863.08	−	13619.3i	−0.804857	−	1.39405i	0.111531	−	0.993761i	$-0.464425\pi$
$458$		0			0
$459$	−1220.83	+	2114.53i	−0.124147	+	0.215028i
$460$		0			0
$461$	7921.16			0.800272			0.400136	−	0.916456i	$-0.368963\pi$
$461$	7921.16			0.800272			0.400136	+	0.916456i	$0.368963\pi$
$462$		0			0
$463$	−5821.20			−0.584306			−0.292153	−	0.956372i	$-0.594372\pi$
$463$	−5821.20			−0.584306			−0.292153	+	0.956372i	$0.594372\pi$
$464$		0			0
$465$	−3388.46	+	5868.98i	−0.337927	+	0.585306i
$466$		0			0
$467$	5893.94	+	10208.6i	0.584024	+	1.01156i	0.994996	+	0.0999112i	$0.0318559\pi$
$467$	5893.94	+	10208.6i	0.584024	+	1.01156i	−0.410973	+	0.911648i	$0.634811\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	4037.36	+	6992.92i	0.394972	+	0.684112i
$472$		0			0
$473$	−6373.77	+	11039.7i	−0.619590	+	1.07316i
$474$		0			0
$475$	−24962.4			−2.41127
$476$		0			0
$477$	−1425.94			−0.136875
$478$		0			0
$479$	−2657.21	+	4602.43i	−0.253468	+	0.439020i	−0.964478	−	0.264162i	$-0.914905\pi$
$479$	−2657.21	+	4602.43i	−0.253468	+	0.439020i	0.711010	+	0.703182i	$0.248238\pi$
$480$		0			0
$481$	−8851.56	−	15331.3i	−0.839078	−	1.45332i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2020.67	+	3499.91i	0.189184	+	0.327676i
$486$		0			0
$487$	9331.34	−	16162.4i	0.868261	−	1.50387i	0.00448933	−	0.999990i	$-0.498571\pi$
$487$	9331.34	−	16162.4i	0.868261	−	1.50387i	0.863772	−	0.503883i	$-0.168096\pi$
$488$		0			0
$489$	−3171.92			−0.293331
$490$		0			0
$491$	13519.1			1.24259			0.621293	−	0.783578i	$-0.286608\pi$
$491$	13519.1			1.24259			0.621293	+	0.783578i	$0.286608\pi$
$492$		0			0
$493$	−1957.82	+	3391.05i	−0.178856	+	0.309787i
$494$		0			0
$495$	5378.13	+	9315.19i	0.488341	+	0.845832i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−6916.17	−	11979.2i	−0.620462	−	1.07467i	−0.989400	−	0.145217i	$-0.953612\pi$
$499$	−6916.17	−	11979.2i	−0.620462	−	1.07467i	0.368938	−	0.929454i	$-0.379721\pi$
$500$		0			0
$501$	365.760	−	633.515i	0.0326167	−	0.0564937i
$502$		0			0
$503$	−13469.0			−1.19394			−0.596970	−	0.802264i	$-0.703629\pi$
$503$	−13469.0			−1.19394			−0.596970	+	0.802264i	$0.703629\pi$
$504$		0			0
$505$	−11570.7			−1.01958
$506$		0			0
$507$	3117.84	−	5400.26i	0.273113	−	0.473045i
$508$		0			0
$509$	4387.62	+	7599.59i	0.382079	+	0.661779i	0.991359	−	0.131175i	$-0.0418750\pi$
$509$	4387.62	+	7599.59i	0.382079	+	0.661779i	−0.609281	+	0.792955i	$0.708542\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−2211.55	−	3830.51i	−0.190336	−	0.329671i
$514$		0			0
$515$	−1450.77	+	2512.81i	−0.124133	+	0.215005i
$516$		0			0
$517$	−3274.63			−0.278565
$518$		0			0
$519$	−5061.79			−0.428108
$520$		0			0
$521$	−830.382	+	1438.26i	−0.0698267	+	0.120943i	−0.898825	−	0.438308i	$-0.855578\pi$
$521$	−830.382	+	1438.26i	−0.0698267	+	0.120943i	0.828998	+	0.559251i	$0.188911\pi$
$522$		0			0
$523$	3162.41	+	5477.45i	0.264402	+	0.457958i	0.967407	−	0.253227i	$-0.0814920\pi$
$523$	3162.41	+	5477.45i	0.264402	+	0.457958i	−0.703005	+	0.711185i	$0.748159\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6132.88	−	10622.5i	−0.506931	−	0.878030i
$528$		0			0
$529$	2944.90	−	5100.71i	0.242040	−	0.419225i
$530$		0			0
$531$	3525.92			0.288158
$532$		0			0
$533$	−9954.68			−0.808977
$534$		0			0
$535$	−396.424	+	686.626i	−0.0320353	+	0.0554868i
$536$		0			0
$537$	−538.709	−	933.071i	−0.0432905	−	0.0749814i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−2233.94	−	3869.30i	−0.177532	−	0.307494i	0.763503	−	0.645804i	$-0.223478\pi$
$541$	−2233.94	−	3869.30i	−0.177532	−	0.307494i	−0.941034	+	0.338311i	$0.890145\pi$
$542$		0			0
$543$	−4473.87	+	7748.97i	−0.353577	+	0.612413i
$544$		0			0
$545$	−27198.7			−2.13774
$546$		0			0
$547$	−10939.0			−0.855063			−0.427531	−	0.904000i	$-0.640617\pi$
$547$	−10939.0			−0.855063			−0.427531	+	0.904000i	$0.640617\pi$
$548$		0			0
$549$	2480.83	−	4296.92i	0.192858	−	0.334040i
$550$		0			0
$551$	−3546.63	−	6142.94i	−0.274213	−	0.474951i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	6763.65	+	11715.0i	0.517299	+	0.895988i
$556$		0			0
$557$	7162.57	−	12405.9i	0.544862	−	0.943728i	−0.453754	−	0.891127i	$-0.649915\pi$
$557$	7162.57	−	12405.9i	0.544862	−	0.943728i	0.998616	−	0.0526011i	$-0.0167512\pi$
$558$		0			0
$559$	−11615.6			−0.878867
$560$		0			0
$561$	−19468.1			−1.46514
$562$		0			0
$563$	10201.4	−	17669.4i	0.763656	−	1.32269i	−0.177299	−	0.984157i	$-0.556736\pi$
$563$	10201.4	−	17669.4i	0.763656	−	1.32269i	0.940954	−	0.338533i	$-0.109931\pi$
$564$		0			0
$565$	9387.32	+	16259.3i	0.698987	+	1.21068i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3625.21	+	6279.05i	0.267095	+	0.462622i	0.968110	−	0.250524i	$-0.0806030\pi$
$569$	3625.21	+	6279.05i	0.267095	+	0.462622i	−0.701016	+	0.713146i	$0.747270\pi$
$570$		0			0
$571$	−12447.4	+	21559.5i	−0.912272	+	1.58010i	−0.101424	+	0.994843i	$0.532340\pi$
$571$	−12447.4	+	21559.5i	−0.912272	+	1.58010i	−0.810847	+	0.585258i	$0.800993\pi$
$572$		0			0
$573$	−10472.3			−0.763503
$574$		0			0
$575$	12072.8			0.875599
$576$		0			0
$577$	681.723	−	1180.78i	0.0491863	−	0.0851932i	−0.840384	−	0.541991i	$-0.817671\pi$
$577$	681.723	−	1180.78i	0.0491863	−	0.0851932i	0.889570	+	0.456798i	$0.151004\pi$
$578$		0			0
$579$	2406.34	+	4167.90i	0.172719	+	0.299158i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−5684.74	−	9846.26i	−0.403839	−	0.699469i
$584$		0			0
$585$	−4900.56	+	8488.01i	−0.346347	+	0.599891i
$586$		0			0
$587$	−23854.8			−1.67733			−0.838666	−	0.544647i	$-0.816664\pi$
$587$	−23854.8			−1.67733			−0.838666	+	0.544647i	$0.816664\pi$
$588$		0			0
$589$	22219.6			1.55440
$590$		0			0
$591$	−683.902	+	1184.55i	−0.0476006	+	0.0824467i
$592$		0			0
$593$	1718.60	+	2976.71i	0.119013	+	0.206136i	0.919377	−	0.393378i	$-0.128694\pi$
$593$	1718.60	+	2976.71i	0.119013	+	0.206136i	−0.800364	+	0.599514i	$0.795360\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−3126.24	−	5414.81i	−0.214319	−	0.371212i
$598$		0			0
$599$	−8255.87	+	14299.6i	−0.563148	+	0.975401i	0.434071	+	0.900879i	$0.357077\pi$
$599$	−8255.87	+	14299.6i	−0.563148	+	0.975401i	−0.997219	+	0.0745226i	$0.976257\pi$
$600$		0			0
$601$	11148.3			0.756656			0.378328	−	0.925672i	$-0.376499\pi$
$601$	11148.3			0.756656			0.378328	+	0.925672i	$0.376499\pi$
$602$		0			0
$603$	4127.67			0.278759
$604$		0			0
$605$	−31797.9	+	55075.6i	−2.13681	+	3.70106i
$606$		0			0
$607$	−195.791	−	339.121i	−0.0130921	−	0.0226763i	0.859405	−	0.511295i	$-0.170834\pi$
$607$	−195.791	−	339.121i	−0.0130921	−	0.0226763i	−0.872497	+	0.488619i	$0.837501\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1491.92	−	2584.09i	−0.0987836	−	0.171098i
$612$		0			0
$613$	5870.25	−	10167.6i	0.386782	−	0.669925i	−0.605233	−	0.796048i	$-0.706920\pi$
$613$	5870.25	−	10167.6i	0.386782	−	0.669925i	0.992015	+	0.126123i	$0.0402534\pi$
$614$		0			0
$615$	7606.56			0.498742
$616$		0			0
$617$	−8818.95			−0.575426			−0.287713	−	0.957717i	$-0.592895\pi$
$617$	−8818.95			−0.575426			−0.287713	+	0.957717i	$0.592895\pi$
$618$		0			0
$619$	−7962.35	+	13791.2i	−0.517018	+	0.895501i	0.482787	+	0.875738i	$0.339625\pi$
$619$	−7962.35	+	13791.2i	−0.517018	+	0.895501i	−0.999805	+	0.0197631i	$0.993709\pi$
$620$		0			0
$621$	1069.59	+	1852.58i	0.0691162	+	0.119713i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	5726.55	+	9918.67i	0.366499	+	0.634795i
$626$		0			0
$627$	17633.4	−	30542.0i	1.12314	−	1.94534i
$628$		0			0
$629$	−24483.5			−1.55202
$630$		0			0
$631$	29206.4			1.84261			0.921307	−	0.388836i	$-0.127123\pi$
$631$	29206.4			1.84261			0.921307	+	0.388836i	$0.127123\pi$
$632$		0			0
$633$	3852.09	−	6672.02i	0.241875	−	0.418940i
$634$		0			0
$635$	−19974.5	−	34596.8i	−1.24829	−	2.16210i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	2190.54	+	3794.12i	0.135612	+	0.234887i
$640$		0			0
$641$	−2806.51	+	4861.01i	−0.172933	+	0.299530i	−0.939444	−	0.342702i	$-0.888658\pi$
$641$	−2806.51	+	4861.01i	−0.172933	+	0.299530i	0.766511	+	0.642232i	$0.221991\pi$
$642$		0			0
$643$	18995.0			1.16499			0.582496	−	0.812834i	$-0.302076\pi$
$643$	18995.0			1.16499			0.582496	+	0.812834i	$0.302076\pi$
$644$		0			0
$645$	8875.68			0.541829
$646$		0			0
$647$	11332.5	−	19628.5i	0.688604	−	1.19270i	−0.283686	−	0.958917i	$-0.591557\pi$
$647$	11332.5	−	19628.5i	0.688604	−	1.19270i	0.972290	−	0.233779i	$-0.0751093\pi$
$648$		0			0
$649$	14056.7	+	24346.9i	0.850188	+	1.47257i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−13263.9	−	22973.7i	−0.794879	−	1.37677i	−0.922916	−	0.385001i	$-0.874201\pi$
$653$	−13263.9	−	22973.7i	−0.794879	−	1.37677i	0.128037	−	0.991769i	$-0.459132\pi$
$654$		0			0
$655$	12898.8	−	22341.3i	0.769460	−	1.33274i
$656$		0			0
$657$	−5174.03			−0.307242
$658$		0			0
$659$	−17114.8			−1.01168			−0.505839	−	0.862628i	$-0.668817\pi$
$659$	−17114.8			−1.01168			−0.505839	+	0.862628i	$0.668817\pi$
$660$		0			0
$661$	−595.908	+	1032.14i	−0.0350653	+	0.0607348i	−0.883025	−	0.469325i	$-0.844497\pi$
$661$	−595.908	+	1032.14i	−0.0350653	+	0.0607348i	0.847960	+	0.530060i	$0.177831\pi$
$662$		0			0
$663$	−8869.68	−	15362.7i	−0.519562	−	0.899908i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	1715.29	+	2970.96i	0.0995744	+	0.172468i
$668$		0			0
$669$	6989.33	−	12105.9i	0.403921	−	0.699612i
$670$		0			0
$671$	39560.9			2.27605
$672$		0			0
$673$	−9415.20			−0.539271			−0.269636	−	0.962962i	$-0.586903\pi$
$673$	−9415.20			−0.539271			−0.269636	+	0.962962i	$0.586903\pi$
$674$		0			0
$675$	2057.11	−	3563.02i	0.117301	−	0.203171i
$676$		0			0
$677$	3958.56	+	6856.43i	0.224727	+	0.389238i	0.956237	−	0.292592i	$-0.0945177\pi$
$677$	3958.56	+	6856.43i	0.224727	+	0.389238i	−0.731511	+	0.681830i	$0.761184\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−7243.16	−	12545.5i	−0.407575	−	0.705940i
$682$		0			0
$683$	−14617.2	+	25317.7i	−0.818904	+	1.41838i	0.0875859	+	0.996157i	$0.472085\pi$
$683$	−14617.2	+	25317.7i	−0.818904	+	1.41838i	−0.906490	+	0.422227i	$0.861249\pi$
$684$		0			0
$685$	25369.6			1.41507
$686$		0			0
$687$	−9667.76			−0.536897
$688$		0			0
$689$	5179.94	−	8971.93i	0.286415	−	0.496086i
$690$		0			0
$691$	−611.228	−	1058.68i	−0.0336501	−	0.0582836i	0.848710	−	0.528859i	$-0.177380\pi$
$691$	−611.228	−	1058.68i	−0.0336501	−	0.0582836i	−0.882360	+	0.470575i	$0.844047\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4592.07	+	7953.70i	0.250629	+	0.434102i
$696$		0			0
$697$	−6883.68	+	11922.9i	−0.374086	+	0.647936i
$698$		0			0
$699$	17107.3			0.925688
$700$		0			0
$701$	13054.6			0.703372			0.351686	−	0.936118i	$-0.385608\pi$
$701$	13054.6			0.703372			0.351686	+	0.936118i	$0.385608\pi$
$702$		0			0
$703$	22176.1	−	38410.2i	1.18974	−	2.06069i
$704$		0			0
$705$	1140.01	+	1974.55i	0.0609010	+	0.105484i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	9987.87	+	17299.5i	0.529058	+	0.916356i	0.999426	+	0.0338854i	$0.0107881\pi$
$709$	9987.87	+	17299.5i	0.529058	+	0.916356i	−0.470367	+	0.882471i	$0.655879\pi$
$710$		0			0
$711$	3007.44	−	5209.03i	0.158632	−	0.274760i
$712$		0			0
$713$	−10746.3			−0.564447
$714$		0			0
$715$	−78147.5			−4.08749
$716$		0			0
$717$	2991.70	−	5181.77i	0.155826	−	0.269898i
$718$		0			0
$719$	3256.13	+	5639.78i	0.168892	+	0.292529i	0.938030	−	0.346553i	$-0.112648\pi$
$719$	3256.13	+	5639.78i	0.168892	+	0.292529i	−0.769139	+	0.639082i	$0.779315\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	2131.33	+	3691.57i	0.109633	+	0.189891i
$724$		0			0
$725$	3298.96	−	5713.97i	0.168994	−	0.292705i
$726$		0			0
$727$	−11437.1			−0.583467			−0.291733	−	0.956500i	$-0.594232\pi$
$727$	−11437.1			−0.583467			−0.291733	+	0.956500i	$0.594232\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−8032.19	+	13912.2i	−0.406404	+	0.703913i
$732$		0			0
$733$	−6138.02	−	10631.4i	−0.309295	−	0.535714i	0.668914	−	0.743340i	$-0.266760\pi$
$733$	−6138.02	−	10631.4i	−0.309295	−	0.535714i	−0.978208	+	0.207626i	$0.933426\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	16455.6	+	28502.0i	0.822458	+	1.42454i
$738$		0			0
$739$	−6046.91	+	10473.5i	−0.301000	+	0.521347i	−0.976363	−	0.216138i	$-0.930654\pi$
$739$	−6046.91	+	10473.5i	−0.301000	+	0.521347i	0.675363	+	0.737486i	$0.263987\pi$
$740$		0			0
$741$	32135.2			1.59314
$742$		0			0
$743$	34331.6			1.69516			0.847580	−	0.530668i	$-0.178059\pi$
$743$	34331.6			1.69516			0.847580	+	0.530668i	$0.178059\pi$
$744$		0			0
$745$	19987.6	−	34619.6i	0.982940	−	1.70250i
$746$		0			0
$747$	343.102	+	594.271i	0.0168052	+	0.0291074i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	7278.96	+	12607.5i	0.353679	+	0.612590i	0.986891	−	0.161388i	$-0.0515971\pi$
$751$	7278.96	+	12607.5i	0.353679	+	0.612590i	−0.633212	+	0.773979i	$0.718264\pi$
$752$		0			0
$753$	5783.16	−	10016.7i	0.279880	−	0.484767i
$754$		0			0
$755$	10351.9			0.498998
$756$		0			0
$757$	27115.5			1.30189			0.650944	−	0.759126i	$-0.274373\pi$
$757$	27115.5			1.30189			0.650944	+	0.759126i	$0.274373\pi$
$758$		0			0
$759$	−8528.19	+	14771.3i	−0.407844	+	0.706407i
$760$		0			0
$761$	−5481.98	−	9495.06i	−0.261132	−	0.452294i	0.705411	−	0.708799i	$-0.250762\pi$
$761$	−5481.98	−	9495.06i	−0.261132	−	0.452294i	−0.966543	+	0.256504i	$0.917429\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	6777.49	+	11739.0i	0.320315	+	0.554801i
$766$		0			0
$767$	−12808.4	+	22184.9i	−0.602981	+	1.04439i
$768$		0			0
$769$	7835.53			0.367434			0.183717	−	0.982979i	$-0.441187\pi$
$769$	7835.53			0.367434			0.183717	+	0.982979i	$0.441187\pi$
$770$		0			0
$771$	12159.8			0.567997
$772$		0			0
$773$	−14383.9	+	24913.6i	−0.669278	+	1.15922i	0.308828	+	0.951118i	$0.400063\pi$
$773$	−14383.9	+	24913.6i	−0.669278	+	1.15922i	−0.978106	+	0.208106i	$0.933270\pi$
$774$		0			0
$775$	10334.0	+	17899.0i	0.478978	+	0.829614i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−12469.9	−	21598.5i	−0.573531	−	0.993386i
$780$		0			0
$781$	−17465.9	+	30251.8i	−0.800228	+	1.38603i
$782$		0			0
$783$	1169.09			0.0533586
$784$		0			0
$785$	44827.3			2.03816
$786$		0			0
$787$	−1347.91	+	2334.65i	−0.0610520	+	0.105745i	−0.894936	−	0.446195i	$-0.852779\pi$
$787$	−1347.91	+	2334.65i	−0.0610520	+	0.105745i	0.833884	+	0.551940i	$0.186112\pi$
$788$		0			0
$789$	−751.180	−	1301.08i	−0.0338944	−	0.0587069i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	18024.0	+	31218.4i	0.807125	+	1.39798i
$794$		0			0
$795$	−3958.09	+	6855.62i	−0.176578	+	0.305841i
$796$		0			0
$797$	−12592.1			−0.559643			−0.279822	−	0.960052i	$-0.590275\pi$
$797$	−12592.1			−0.559643			−0.279822	+	0.960052i	$0.590275\pi$
$798$		0			0
$799$	−4126.67			−0.182717
$800$		0			0
$801$	6150.61	−	10653.2i	0.271312	−	0.469927i
$802$		0			0
$803$	−20627.1	−	35727.2i	−0.906495	−	1.57009i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−4922.62	−	8526.22i	−0.214726	−	0.371917i
$808$		0			0
$809$	3899.74	−	6754.56i	0.169478	−	0.293545i	−0.768758	−	0.639539i	$-0.779125\pi$
$809$	3899.74	−	6754.56i	0.169478	−	0.293545i	0.938236	+	0.345995i	$0.112458\pi$
$810$		0			0
$811$	19323.5			0.836669			0.418335	−	0.908293i	$-0.362614\pi$
$811$	19323.5			0.836669			0.418335	+	0.908293i	$0.362614\pi$
$812$		0			0
$813$	9973.08			0.430223
$814$		0			0
$815$	−8804.55	+	15249.9i	−0.378417	+	0.655438i
$816$		0			0
$817$	−14550.5	−	25202.1i	−0.623080	−	1.07921i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−542.649	−	939.896i	−0.0230677	−	0.0399545i	0.854261	−	0.519844i	$-0.174010\pi$
$821$	−542.649	−	939.896i	−0.0230677	−	0.0399545i	−0.877329	+	0.479890i	$0.840677\pi$
$822$		0			0
$823$	12175.4	−	21088.4i	0.515683	−	0.893190i	−0.484151	−	0.874985i	$-0.660871\pi$
$823$	12175.4	−	21088.4i	0.515683	−	0.893190i	0.999834	−	0.0182053i	$-0.00579524\pi$
$824$		0			0
$825$	32804.1			1.38435
$826$		0			0
$827$	31664.9			1.33143			0.665716	−	0.746205i	$-0.268126\pi$
$827$	31664.9			1.33143			0.665716	+	0.746205i	$0.268126\pi$
$828$		0			0
$829$	−1709.01	+	2960.09i	−0.0716000	+	0.124015i	−0.899603	−	0.436709i	$-0.856144\pi$
$829$	−1709.01	+	2960.09i	−0.0716000	+	0.124015i	0.828003	+	0.560724i	$0.189477\pi$
$830$		0			0
$831$	12929.6	+	22394.8i	0.539740	+	0.934856i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−2030.54	−	3517.00i	−0.0841554	−	0.145761i
$836$		0			0
$837$	−1831.08	+	3171.53i	−0.0756171	+	0.130973i
$838$		0			0
$839$	−9114.25			−0.375040			−0.187520	−	0.982261i	$-0.560045\pi$
$839$	−9114.25			−0.375040			−0.187520	+	0.982261i	$0.560045\pi$
$840$		0			0
$841$	−22514.2			−0.923127
$842$		0			0
$843$	−11566.2	+	20033.3i	−0.472552	+	0.818484i
$844$		0			0
$845$	−17308.9	−	29979.9i	−0.704667	−	1.22052i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	208.906	+	361.836i	0.00844481	+	0.0146268i
$850$		0			0
$851$	−10725.2	+	18576.6i	−0.432028	+	0.748295i
$852$		0			0
$853$	36229.5			1.45425			0.727124	−	0.686506i	$-0.240857\pi$
$853$	36229.5			1.45425			0.727124	+	0.686506i	$0.240857\pi$
$854$		0			0
$855$	−24555.1			−0.982183
$856$		0			0
$857$	4322.59	−	7486.95i	0.172295	−	0.298424i	−0.766927	−	0.641735i	$-0.778215\pi$
$857$	4322.59	−	7486.95i	0.172295	−	0.298424i	0.939222	+	0.343311i	$0.111548\pi$
$858$		0			0
$859$	−4106.29	−	7112.31i	−0.163102	−	0.282501i	0.772877	−	0.634555i	$-0.218817\pi$
$859$	−4106.29	−	7112.31i	−0.163102	−	0.282501i	−0.935980	+	0.352054i	$0.885483\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1305.80	+	2261.72i	0.0515065	+	0.0892119i	0.890629	−	0.454730i	$-0.150264\pi$
$863$	1305.80	+	2261.72i	0.0515065	+	0.0892119i	−0.839123	+	0.543942i	$0.816931\pi$
$864$		0			0
$865$	−14050.4	+	24336.1i	−0.552288	+	0.956591i
$866$		0			0
$867$	−9794.61			−0.383670
$868$		0			0
$869$	47958.6			1.87213
$870$		0			0
$871$	−14994.4	+	25971.1i	−0.583313	+	1.01033i
$872$		0			0
$873$	1091.95	+	1891.31i	0.0423332	+	0.0733232i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	3223.29	+	5582.90i	0.124108	+	0.214961i	0.921384	−	0.388654i	$-0.127060\pi$
$877$	3223.29	+	5582.90i	0.124108	+	0.214961i	−0.797276	+	0.603615i	$0.793726\pi$
$878$		0			0
$879$	6655.64	−	11527.9i	0.255392	−	0.442351i
$880$		0			0
$881$	−37166.3			−1.42130			−0.710649	−	0.703547i	$-0.751599\pi$
$881$	−37166.3			−1.42130			−0.710649	+	0.703547i	$0.751599\pi$
$882$		0			0
$883$	24377.3			0.929060			0.464530	−	0.885557i	$-0.346223\pi$
$883$	24377.3			0.929060			0.464530	+	0.885557i	$0.346223\pi$
$884$		0			0
$885$	9787.18	−	16951.9i	0.371743	−	0.643878i
$886$		0			0
$887$	−18172.2	−	31475.2i	−0.687896	−	1.19147i	−0.972517	−	0.232831i	$-0.925201\pi$
$887$	−18172.2	−	31475.2i	−0.687896	−	1.19147i	0.284621	−	0.958640i	$-0.408132\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	2906.28	+	5033.82i	0.109275	+	0.189270i
$892$		0			0
$893$	3737.77	−	6474.01i	0.140067	−	0.242603i
$894$		0			0
$895$	−5981.35			−0.223391
$896$		0			0
$897$	−15541.8			−0.578512
$898$		0			0
$899$	−2936.48	+	5086.14i	−0.108940	+	0.188690i
$900$		0			0
$901$	−7163.88	−	12408.2i	−0.264887	−	0.458798i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	24837.0	+	43018.9i	0.912275	+	1.58011i
$906$		0			0
$907$	−163.437	+	283.082i	−0.00598329	+	0.0103634i	−0.869002	−	0.494809i	$-0.835238\pi$
$907$	−163.437	+	283.082i	−0.00598329	+	0.0103634i	0.863018	+	0.505173i	$0.168571\pi$
$908$		0			0
$909$	−6252.68			−0.228150
$910$		0			0
$911$	−38230.7			−1.39038			−0.695191	−	0.718825i	$-0.744680\pi$
$911$	−38230.7			−1.39038			−0.695191	+	0.718825i	$0.744680\pi$
$912$		0			0
$913$	−2735.67	+	4738.32i	−0.0991648	+	0.171758i
$914$		0			0
$915$	−13772.5	−	23854.6i	−0.497599	−	0.861867i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	10024.7	+	17363.2i	0.359829	+	0.623243i	0.987932	−	0.154888i	$-0.0495016\pi$
$919$	10024.7	+	17363.2i	0.359829	+	0.623243i	−0.628103	+	0.778130i	$0.716168\pi$
$920$		0			0
$921$	449.219	−	778.071i	0.0160720	−	0.0278375i
$922$		0			0
$923$	−31829.8			−1.13509
$924$		0			0
$925$	41255.0			1.46644
$926$		0			0
$927$	−783.980	+	1357.89i	−0.0277770	+	0.0481112i
$928$		0			0
$929$	21670.7	+	37534.8i	0.765332	+	1.32559i	0.940071	+	0.340980i	$0.110759\pi$
$929$	21670.7	+	37534.8i	0.765332	+	1.32559i	−0.174738	+	0.984615i	$0.555908\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−1370.92	−	2374.49i	−0.0481048	−	0.0833199i
$934$		0			0
$935$	−54039.2	+	93598.6i	−1.89013	+	3.27380i
$936$		0			0
$937$	−17530.0			−0.611185			−0.305592	−	0.952162i	$-0.598854\pi$
$937$	−17530.0			−0.611185			−0.305592	+	0.952162i	$0.598854\pi$
$938$		0			0
$939$	11662.1			0.405303
$940$		0			0
$941$	−16312.5	+	28254.1i	−0.565115	+	0.978807i	0.431924	+	0.901910i	$0.357835\pi$
$941$	−16312.5	+	28254.1i	−0.565115	+	0.978807i	−0.997039	+	0.0768974i	$0.975499\pi$
$942$		0			0
$943$	6030.93	+	10445.9i	0.208265	+	0.360726i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9697.09	+	16795.8i	0.332749	+	0.576338i	0.983050	−	0.183339i	$-0.0586906\pi$
$947$	9697.09	+	16795.8i	0.332749	+	0.576338i	−0.650301	+	0.759677i	$0.725357\pi$
$948$		0			0
$949$	18795.5	−	32554.7i	0.642915	−	1.11356i
$950$		0			0
$951$	−8637.91			−0.294536
$952$		0			0
$953$	−49618.5			−1.68657			−0.843285	−	0.537467i	$-0.819381\pi$
$953$	−49618.5			−1.68657			−0.843285	+	0.537467i	$0.819381\pi$
$954$		0			0
$955$	−29068.9	+	50348.7i	−0.984970	+	1.70602i
$956$		0			0
$957$	4660.76	+	8072.67i	0.157430	+	0.272678i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	5696.96	+	9867.43i	0.191231	+	0.331222i
$962$		0			0
$963$	−214.223	+	371.045i	−0.00716847	+	0.0124162i
$964$		0			0
$965$	26717.9			0.891274
$966$		0			0
$967$	28432.8			0.945538			0.472769	−	0.881186i	$-0.343254\pi$
$967$	28432.8			0.945538			0.472769	+	0.881186i	$0.343254\pi$
$968$		0			0
$969$	22221.5	−	38488.8i	0.736696	−	1.27600i
$970$		0			0
$971$	21345.1	+	36970.8i	0.705455	+	1.22188i	0.966527	+	0.256565i	$0.0825907\pi$
$971$	21345.1	+	36970.8i	0.705455	+	1.22188i	−0.261072	+	0.965319i	$0.584076\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	14945.5	+	25886.4i	0.490913	+	0.850287i
$976$		0			0
$977$	−11367.5	+	19689.1i	−0.372241	+	0.644740i	−0.989910	−	0.141698i	$-0.954744\pi$
$977$	−11367.5	+	19689.1i	−0.372241	+	0.644740i	0.617669	+	0.786438i	$0.288077\pi$
$978$		0			0
$979$	98081.7			3.20195
$980$		0			0
$981$	−14697.9			−0.478356
$982$		0			0
$983$	2821.91	−	4887.70i	0.0915616	−	0.158589i	−0.816607	−	0.577194i	$-0.804147\pi$
$983$	2821.91	−	4887.70i	0.0915616	−	0.158589i	0.908168	+	0.418605i	$0.137481\pi$
$984$		0			0
$985$	3796.73	+	6576.12i	0.122816	+	0.212724i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	7037.16	+	12188.7i	0.226257	+	0.391889i
$990$		0			0
$991$	27422.3	−	47496.8i	0.879009	−	1.52249i	0.0265782	−	0.999647i	$-0.491539\pi$
$991$	27422.3	−	47496.8i	0.879009	−	1.52249i	0.852430	−	0.522841i	$-0.175128\pi$
$992$		0			0
$993$	8432.36			0.269479
$994$		0			0
$995$	−34711.0			−1.10594
$996$		0			0
$997$	22440.6	−	38868.2i	0.712838	−	1.23467i	−0.250949	−	0.968000i	$-0.580743\pi$
$997$	22440.6	−	38868.2i	0.712838	−	1.23467i	0.963787	−	0.266672i	$-0.0859240\pi$
$998$		0			0
$999$	3655.00	+	6330.64i	0.115755	+	0.200493i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.4.i.l.361.1		8
3.2	odd	2		1764.4.k.bb.361.4		8
7.2	even	3	inner	588.4.i.l.373.1		8
7.3	odd	6		588.4.a.k.1.1	yes	4
7.4	even	3		588.4.a.j.1.4	✓	4
7.5	odd	6		588.4.i.k.373.4		8
7.6	odd	2		588.4.i.k.361.4		8
21.2	odd	6		1764.4.k.bb.1549.4		8
21.5	even	6		1764.4.k.bd.1549.1		8
21.11	odd	6		1764.4.a.bc.1.1		4
21.17	even	6		1764.4.a.ba.1.4		4
21.20	even	2		1764.4.k.bd.361.1		8
28.3	even	6		2352.4.a.cl.1.1		4
28.11	odd	6		2352.4.a.cq.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.4.a.j.1.4	✓	4	7.4	even	3
588.4.a.k.1.1	yes	4	7.3	odd	6
588.4.i.k.361.4		8	7.6	odd	2
588.4.i.k.373.4		8	7.5	odd	6
588.4.i.l.361.1		8	1.1	even	1	trivial
588.4.i.l.373.1		8	7.2	even	3	inner
1764.4.a.ba.1.4		4	21.17	even	6
1764.4.a.bc.1.1		4	21.11	odd	6
1764.4.k.bb.361.4		8	3.2	odd	2
1764.4.k.bb.1549.4		8	21.2	odd	6
1764.4.k.bd.361.1		8	21.20	even	2
1764.4.k.bd.1549.1		8	21.5	even	6
2352.4.a.cl.1.1		4	28.3	even	6
2352.4.a.cq.1.4		4	28.11	odd	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	588.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{3} +(-8.32734 - 14.4234i) q^{5} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 2.59808i) q^{3} +(-8.32734 - 14.4234i) q^{5} +(-4.50000 - 7.79423i) q^{9} +(35.8800 - 62.1460i) q^{11} +65.3878 q^{13} -49.9641 q^{15} +(45.2158 - 78.3160i) q^{17} +(81.9092 + 141.871i) q^{19} +(-39.6144 - 68.6142i) q^{23} +(-76.1893 + 131.964i) q^{25} -27.0000 q^{27} -43.2995 q^{29} +(67.8179 - 117.464i) q^{31} +(-107.640 - 186.438i) q^{33} +(-135.370 - 234.468i) q^{37} +(98.0817 - 169.882i) q^{39} -152.241 q^{41} -177.641 q^{43} +(-74.9461 + 129.810i) q^{45} +(-22.8166 - 39.5194i) q^{47} +(-135.647 - 234.948i) q^{51} +(79.2188 - 137.211i) q^{53} -1195.14 q^{55} +491.455 q^{57} +(-195.884 + 339.282i) q^{59} +(275.647 + 477.435i) q^{61} +(-544.506 - 943.113i) q^{65} +(-229.315 + 397.185i) q^{67} -237.687 q^{69} -486.786 q^{71} +(287.446 - 497.871i) q^{73} +(228.568 + 395.891i) q^{75} +(334.160 + 578.782i) q^{79} +(-40.5000 + 70.1481i) q^{81} -76.2450 q^{83} -1506.11 q^{85} +(-64.9493 + 112.495i) q^{87} +(683.401 + 1183.69i) q^{89} +(-203.454 - 352.392i) q^{93} +(1364.17 - 2362.82i) q^{95} -242.655 q^{97} -645.840 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{3} - 36 q^{9}+O(q^{10}) \) 8 * q + 12 * q^3 - 36 * q^9	\( 8 q + 12 q^{3} - 36 q^{9} + 48 q^{17} + 192 q^{19} - 192 q^{23} - 324 q^{25} - 216 q^{27} + 192 q^{29} + 48 q^{31} - 256 q^{37} - 2016 q^{41} - 224 q^{43} + 864 q^{47} - 144 q^{51} + 648 q^{53} - 4704 q^{55} + 1152 q^{57} + 336 q^{59} + 960 q^{61} + 360 q^{65} - 720 q^{67} - 1152 q^{69} - 2688 q^{71} + 672 q^{73} + 972 q^{75} + 1984 q^{79} - 324 q^{81} - 6240 q^{83} + 1360 q^{85} + 288 q^{87} + 2160 q^{89} - 144 q^{93} + 3744 q^{95} - 4032 q^{97}+O(q^{100}) \) 8 * q + 12 * q^3 - 36 * q^9 + 48 * q^17 + 192 * q^19 - 192 * q^23 - 324 * q^25 - 216 * q^27 + 192 * q^29 + 48 * q^31 - 256 * q^37 - 2016 * q^41 - 224 * q^43 + 864 * q^47 - 144 * q^51 + 648 * q^53 - 4704 * q^55 + 1152 * q^57 + 336 * q^59 + 960 * q^61 + 360 * q^65 - 720 * q^67 - 1152 * q^69 - 2688 * q^71 + 672 * q^73 + 972 * q^75 + 1984 * q^79 - 324 * q^81 - 6240 * q^83 + 1360 * q^85 + 288 * q^87 + 2160 * q^89 - 144 * q^93 + 3744 * q^95 - 4032 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more