LMFDB - Embedded newform 588.4.i.f.373.1

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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	588.373
Dual form			588.4.i.f.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 2.59808i) q^{3} +(-3.00000 + 5.19615i) q^{5} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 + 2.59808i) q^{3} +(-3.00000 + 5.19615i) q^{5} +(-4.50000 + 7.79423i) q^{9} +(-18.0000 - 31.1769i) q^{11} +62.0000 q^{13} -18.0000 q^{15} +(-57.0000 - 98.7269i) q^{17} +(38.0000 - 65.8179i) q^{19} +(12.0000 - 20.7846i) q^{23} +(44.5000 + 77.0763i) q^{25} -27.0000 q^{27} +54.0000 q^{29} +(56.0000 + 96.9948i) q^{31} +(54.0000 - 93.5307i) q^{33} +(89.0000 - 154.153i) q^{37} +(93.0000 + 161.081i) q^{39} +378.000 q^{41} -172.000 q^{43} +(-27.0000 - 46.7654i) q^{45} +(96.0000 - 166.277i) q^{47} +(171.000 - 296.181i) q^{51} +(201.000 + 348.142i) q^{53} +216.000 q^{55} +228.000 q^{57} +(-198.000 - 342.946i) q^{59} +(-127.000 + 219.970i) q^{61} +(-186.000 + 322.161i) q^{65} +(506.000 + 876.418i) q^{67} +72.0000 q^{69} +840.000 q^{71} +(-445.000 - 770.763i) q^{73} +(-133.500 + 231.229i) q^{75} +(-40.0000 + 69.2820i) q^{79} +(-40.5000 - 70.1481i) q^{81} -108.000 q^{83} +684.000 q^{85} +(81.0000 + 140.296i) q^{87} +(819.000 - 1418.55i) q^{89} +(-168.000 + 290.985i) q^{93} +(228.000 + 394.908i) q^{95} +1010.00 q^{97} +324.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} - 6 q^{5} - 9 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 - 6 * q^5 - 9 * q^9	$ 2 q + 3 q^{3} - 6 q^{5} - 9 q^{9} - 36 q^{11} + 124 q^{13} - 36 q^{15} - 114 q^{17} + 76 q^{19} + 24 q^{23} + 89 q^{25} - 54 q^{27} + 108 q^{29} + 112 q^{31} + 108 q^{33} + 178 q^{37} + 186 q^{39} + 756 q^{41} - 344 q^{43} - 54 q^{45} + 192 q^{47} + 342 q^{51} + 402 q^{53} + 432 q^{55} + 456 q^{57} - 396 q^{59} - 254 q^{61} - 372 q^{65} + 1012 q^{67} + 144 q^{69} + 1680 q^{71} - 890 q^{73} - 267 q^{75} - 80 q^{79} - 81 q^{81} - 216 q^{83} + 1368 q^{85} + 162 q^{87} + 1638 q^{89} - 336 q^{93} + 456 q^{95} + 2020 q^{97} + 648 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 - 6 * q^5 - 9 * q^9 - 36 * q^11 + 124 * q^13 - 36 * q^15 - 114 * q^17 + 76 * q^19 + 24 * q^23 + 89 * q^25 - 54 * q^27 + 108 * q^29 + 112 * q^31 + 108 * q^33 + 178 * q^37 + 186 * q^39 + 756 * q^41 - 344 * q^43 - 54 * q^45 + 192 * q^47 + 342 * q^51 + 402 * q^53 + 432 * q^55 + 456 * q^57 - 396 * q^59 - 254 * q^61 - 372 * q^65 + 1012 * q^67 + 144 * q^69 + 1680 * q^71 - 890 * q^73 - 267 * q^75 - 80 * q^79 - 81 * q^81 - 216 * q^83 + 1368 * q^85 + 162 * q^87 + 1638 * q^89 - 336 * q^93 + 456 * q^95 + 2020 * q^97 + 648 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$		0			0
$5$	−3.00000	+	5.19615i	−0.268328	+	0.464758i	−0.968430	−	0.249285i	$-0.919804\pi$
$5$	−3.00000	+	5.19615i	−0.268328	+	0.464758i	0.700102	+	0.714043i	$0.253138\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	−18.0000	−	31.1769i	−0.493382	−	0.854563i	0.506589	−	0.862188i	$-0.330906\pi$
$11$	−18.0000	−	31.1769i	−0.493382	−	0.854563i	−0.999971	+	0.00762479i	$0.997573\pi$
$12$		0			0
$13$	62.0000			1.32275			0.661373	−	0.750057i	$-0.269974\pi$
$13$	62.0000			1.32275			0.661373	+	0.750057i	$0.269974\pi$
$14$		0			0
$15$	−18.0000			−0.309839
$16$		0			0
$17$	−57.0000	−	98.7269i	−0.813208	−	1.40852i	−0.910608	−	0.413272i	$-0.864386\pi$
$17$	−57.0000	−	98.7269i	−0.813208	−	1.40852i	0.0974001	−	0.995245i	$-0.468947\pi$
$18$		0			0
$19$	38.0000	−	65.8179i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	38.0000	−	65.8179i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	12.0000	−	20.7846i	0.108790	−	0.188430i	−0.806490	−	0.591247i	$-0.798636\pi$
$23$	12.0000	−	20.7846i	0.108790	−	0.188430i	0.915280	+	0.402817i	$0.131969\pi$
$24$		0			0
$25$	44.5000	+	77.0763i	0.356000	+	0.616610i
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	54.0000			0.345778			0.172889	−	0.984941i	$-0.444690\pi$
$29$	54.0000			0.345778			0.172889	+	0.984941i	$0.444690\pi$
$30$		0			0
$31$	56.0000	+	96.9948i	0.324448	+	0.561961i	0.981401	−	0.191971i	$-0.0614880\pi$
$31$	56.0000	+	96.9948i	0.324448	+	0.561961i	−0.656952	+	0.753932i	$0.728155\pi$
$32$		0			0
$33$	54.0000	−	93.5307i	0.284854	−	0.493382i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	89.0000	−	154.153i	0.395446	−	0.684933i	−0.597712	−	0.801711i	$-0.703923\pi$
$37$	89.0000	−	154.153i	0.395446	−	0.684933i	0.993158	+	0.116778i	$0.0372566\pi$
$38$		0			0
$39$	93.0000	+	161.081i	0.381844	+	0.661373i
$40$		0			0
$41$	378.000			1.43985			0.719923	−	0.694054i	$-0.244177\pi$
$41$	378.000			1.43985			0.719923	+	0.694054i	$0.244177\pi$
$42$		0			0
$43$	−172.000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−172.000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	−27.0000	−	46.7654i	−0.0894427	−	0.154919i
$46$		0			0
$47$	96.0000	−	166.277i	0.297937	−	0.516042i	−0.677727	−	0.735314i	$-0.737035\pi$
$47$	96.0000	−	166.277i	0.297937	−	0.516042i	0.975664	+	0.219272i	$0.0703681\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	171.000	−	296.181i	0.469506	−	0.813208i
$52$		0			0
$53$	201.000	+	348.142i	0.520933	+	0.902283i	0.999704	+	0.0243430i	$0.00774937\pi$
$53$	201.000	+	348.142i	0.520933	+	0.902283i	−0.478770	+	0.877940i	$0.658917\pi$
$54$		0			0
$55$	216.000			0.529553
$56$		0			0
$57$	228.000			0.529813
$58$		0			0
$59$	−198.000	−	342.946i	−0.436905	−	0.756742i	0.560544	−	0.828125i	$-0.310592\pi$
$59$	−198.000	−	342.946i	−0.436905	−	0.756742i	−0.997449	+	0.0713828i	$0.977259\pi$
$60$		0			0
$61$	−127.000	+	219.970i	−0.266569	+	0.461710i	−0.967973	−	0.251053i	$-0.919223\pi$
$61$	−127.000	+	219.970i	−0.266569	+	0.461710i	0.701405	+	0.712763i	$0.252557\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−186.000	+	322.161i	−0.354930	+	0.614757i
$66$		0			0
$67$	506.000	+	876.418i	0.922653	+	1.59808i	0.795293	+	0.606225i	$0.207317\pi$
$67$	506.000	+	876.418i	0.922653	+	1.59808i	0.127360	+	0.991857i	$0.459350\pi$
$68$		0			0
$69$	72.0000			0.125620
$70$		0			0
$71$	840.000			1.40408			0.702040	−	0.712138i	$-0.252273\pi$
$71$	840.000			1.40408			0.702040	+	0.712138i	$0.252273\pi$
$72$		0			0
$73$	−445.000	−	770.763i	−0.713470	−	1.23577i	−0.963547	−	0.267540i	$-0.913789\pi$
$73$	−445.000	−	770.763i	−0.713470	−	1.23577i	0.250077	−	0.968226i	$-0.419544\pi$
$74$		0			0
$75$	−133.500	+	231.229i	−0.205537	+	0.356000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−40.0000	+	69.2820i	−0.0569665	+	0.0986688i	−0.893102	−	0.449854i	$-0.851476\pi$
$79$	−40.0000	+	69.2820i	−0.0569665	+	0.0986688i	0.836136	+	0.548522i	$0.184809\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−108.000			−0.142826			−0.0714129	−	0.997447i	$-0.522751\pi$
$83$	−108.000			−0.142826			−0.0714129	+	0.997447i	$0.522751\pi$
$84$		0			0
$85$	684.000			0.872826
$86$		0			0
$87$	81.0000	+	140.296i	0.0998174	+	0.172889i
$88$		0			0
$89$	819.000	−	1418.55i	0.975436	−	1.68951i	0.296948	−	0.954894i	$-0.404031\pi$
$89$	819.000	−	1418.55i	0.975436	−	1.68951i	0.678488	−	0.734612i	$-0.262636\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−168.000	+	290.985i	−0.187320	+	0.324448i
$94$		0			0
$95$	228.000	+	394.908i	0.246235	+	0.426491i
$96$		0			0
$97$	1010.00			1.05722			0.528608	−	0.848866i	$-0.322714\pi$
$97$	1010.00			1.05722			0.528608	+	0.848866i	$0.322714\pi$
$98$		0			0
$99$	324.000			0.328921
$100$		0			0
$101$	−3.00000	−	5.19615i	−0.00295556	−	0.00511917i	0.864544	−	0.502557i	$-0.167607\pi$
$101$	−3.00000	−	5.19615i	−0.00295556	−	0.00511917i	−0.867499	+	0.497438i	$0.834274\pi$
$102$		0			0
$103$	236.000	−	408.764i	0.225765	−	0.391036i	−0.730784	−	0.682609i	$-0.760845\pi$
$103$	236.000	−	408.764i	0.225765	−	0.391036i	0.956549	+	0.291573i	$0.0941786\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	486.000	−	841.777i	0.439097	−	0.760539i	−0.558523	−	0.829489i	$-0.688632\pi$
$107$	486.000	−	841.777i	0.439097	−	0.760539i	0.997620	+	0.0689505i	$0.0219651\pi$
$108$		0			0
$109$	893.000	+	1546.72i	0.784715	+	1.35917i	0.929169	+	0.369654i	$0.120524\pi$
$109$	893.000	+	1546.72i	0.784715	+	1.35917i	−0.144455	+	0.989511i	$0.546143\pi$
$110$		0			0
$111$	534.000			0.456622
$112$		0			0
$113$	−2286.00			−1.90309			−0.951543	−	0.307515i	$-0.900503\pi$
$113$	−2286.00			−1.90309			−0.951543	+	0.307515i	$0.900503\pi$
$114$		0			0
$115$	72.0000	+	124.708i	0.0583829	+	0.101122i
$116$		0			0
$117$	−279.000	+	483.242i	−0.220458	+	0.381844i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	17.5000	−	30.3109i	0.0131480	−	0.0227730i
$122$		0			0
$123$	567.000	+	982.073i	0.415648	+	0.719923i
$124$		0			0
$125$	−1284.00			−0.918756
$126$		0			0
$127$	1328.00			0.927881			0.463941	−	0.885866i	$-0.346435\pi$
$127$	1328.00			0.927881			0.463941	+	0.885866i	$0.346435\pi$
$128$		0			0
$129$	−258.000	−	446.869i	−0.176090	−	0.304997i
$130$		0			0
$131$	606.000	−	1049.62i	0.404171	−	0.700046i	−0.590053	−	0.807364i	$-0.700893\pi$
$131$	606.000	−	1049.62i	0.404171	−	0.700046i	0.994225	+	0.107319i	$0.0342266\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	81.0000	−	140.296i	0.0516398	−	0.0894427i
$136$		0			0
$137$	627.000	+	1086.00i	0.391009	+	0.677247i	0.992583	−	0.121570i	$-0.0387928\pi$
$137$	627.000	+	1086.00i	0.391009	+	0.677247i	−0.601574	+	0.798817i	$0.705459\pi$
$138$		0			0
$139$	−340.000			−0.207471			−0.103735	−	0.994605i	$-0.533079\pi$
$139$	−340.000			−0.207471			−0.103735	+	0.994605i	$0.533079\pi$
$140$		0			0
$141$	576.000			0.344028
$142$		0			0
$143$	−1116.00	−	1932.97i	−0.652620	−	1.13037i
$144$		0			0
$145$	−162.000	+	280.592i	−0.0927818	+	0.160703i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−519.000	+	898.934i	−0.285357	+	0.494252i	−0.972696	−	0.232085i	$-0.925445\pi$
$149$	−519.000	+	898.934i	−0.285357	+	0.494252i	0.687339	+	0.726337i	$0.258779\pi$
$150$		0			0
$151$	−1468.00	−	2542.65i	−0.791153	−	1.37032i	−0.925253	−	0.379350i	$-0.876148\pi$
$151$	−1468.00	−	2542.65i	−0.791153	−	1.37032i	0.134100	−	0.990968i	$-0.457186\pi$
$152$		0			0
$153$	1026.00			0.542138
$154$		0			0
$155$	−672.000			−0.348234
$156$		0			0
$157$	665.000	+	1151.81i	0.338043	+	0.585508i	0.984065	−	0.177811i	$-0.0569017\pi$
$157$	665.000	+	1151.81i	0.338043	+	0.585508i	−0.646021	+	0.763319i	$0.723568\pi$
$158$		0			0
$159$	−603.000	+	1044.43i	−0.300761	+	0.520933i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1682.00	−	2913.31i	0.808248	−	1.39993i	−0.105828	−	0.994384i	$-0.533749\pi$
$163$	1682.00	−	2913.31i	0.808248	−	1.39993i	0.914076	−	0.405542i	$-0.132917\pi$
$164$		0			0
$165$	324.000	+	561.184i	0.152869	+	0.264777i
$166$		0			0
$167$	3048.00			1.41234			0.706172	−	0.708041i	$-0.250421\pi$
$167$	3048.00			1.41234			0.706172	+	0.708041i	$0.250421\pi$
$168$		0			0
$169$	1647.00			0.749659
$170$		0			0
$171$	342.000	+	592.361i	0.152944	+	0.264906i
$172$		0			0
$173$	1353.00	−	2343.46i	0.594605	−	1.02989i	−0.398997	−	0.916952i	$-0.630642\pi$
$173$	1353.00	−	2343.46i	0.594605	−	1.02989i	0.993602	−	0.112934i	$-0.0360249\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	594.000	−	1028.84i	0.252247	−	0.436905i
$178$		0			0
$179$	−2358.00	−	4084.18i	−0.984610	−	1.70539i	−0.643657	−	0.765314i	$-0.722584\pi$
$179$	−2358.00	−	4084.18i	−0.984610	−	1.70539i	−0.340953	−	0.940080i	$-0.610750\pi$
$180$		0			0
$181$	1910.00			0.784360			0.392180	−	0.919888i	$-0.371721\pi$
$181$	1910.00			0.784360			0.392180	+	0.919888i	$0.371721\pi$
$182$		0			0
$183$	−762.000			−0.307807
$184$		0			0
$185$	534.000	+	924.915i	0.212219	+	0.367574i
$186$		0			0
$187$	−2052.00	+	3554.17i	−0.802444	+	1.38987i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2040.00	+	3533.38i	−0.772823	+	1.33857i	0.163187	+	0.986595i	$0.447823\pi$
$191$	−2040.00	+	3533.38i	−0.772823	+	1.33857i	−0.936010	+	0.351974i	$0.885511\pi$
$192$		0			0
$193$	1343.00	+	2326.14i	0.500887	+	0.867562i	0.999999	+	0.00102491i	$0.000326238\pi$
$193$	1343.00	+	2326.14i	0.500887	+	0.867562i	−0.499112	+	0.866537i	$0.666340\pi$
$194$		0			0
$195$	−1116.00			−0.409838
$196$		0			0
$197$	510.000			0.184447			0.0922233	−	0.995738i	$-0.470603\pi$
$197$	510.000			0.184447			0.0922233	+	0.995738i	$0.470603\pi$
$198$		0			0
$199$	−676.000	−	1170.87i	−0.240806	−	0.417088i	0.720138	−	0.693831i	$-0.244078\pi$
$199$	−676.000	−	1170.87i	−0.240806	−	0.417088i	−0.960944	+	0.276743i	$0.910745\pi$
$200$		0			0
$201$	−1518.00	+	2629.25i	−0.532694	+	0.922653i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−1134.00	+	1964.15i	−0.386351	+	0.669180i
$206$		0			0
$207$	108.000	+	187.061i	0.0362634	+	0.0628100i
$208$		0			0
$209$	−2736.00			−0.905517
$210$		0			0
$211$	−3364.00			−1.09757			−0.548785	−	0.835963i	$-0.684909\pi$
$211$	−3364.00			−1.09757			−0.548785	+	0.835963i	$0.684909\pi$
$212$		0			0
$213$	1260.00	+	2182.38i	0.405323	+	0.702040i
$214$		0			0
$215$	516.000	−	893.738i	0.163679	−	0.283500i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	1335.00	−	2312.29i	0.411922	−	0.713470i
$220$		0			0
$221$	−3534.00	−	6121.07i	−1.07567	−	1.86311i
$222$		0			0
$223$	−4768.00			−1.43179			−0.715894	−	0.698209i	$-0.753981\pi$
$223$	−4768.00			−1.43179			−0.715894	+	0.698209i	$0.753981\pi$
$224$		0			0
$225$	−801.000			−0.237333
$226$		0			0
$227$	−210.000	−	363.731i	−0.0614017	−	0.106351i	0.833690	−	0.552232i	$-0.186224\pi$
$227$	−210.000	−	363.731i	−0.0614017	−	0.106351i	−0.895092	+	0.445881i	$0.852890\pi$
$228$		0			0
$229$	941.000	−	1629.86i	0.271542	−	0.470324i	−0.697715	−	0.716375i	$-0.745800\pi$
$229$	941.000	−	1629.86i	0.271542	−	0.470324i	0.969257	+	0.246051i	$0.0791332\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2541.00	+	4401.14i	−0.714448	+	1.23746i	0.248724	+	0.968574i	$0.419989\pi$
$233$	−2541.00	+	4401.14i	−0.714448	+	1.23746i	−0.963172	+	0.268886i	$0.913344\pi$
$234$		0			0
$235$	576.000	+	997.661i	0.159890	+	0.276937i
$236$		0			0
$237$	−240.000			−0.0657792
$238$		0			0
$239$	−5424.00			−1.46799			−0.733995	−	0.679155i	$-0.762346\pi$
$239$	−5424.00			−1.46799			−0.733995	+	0.679155i	$0.762346\pi$
$240$		0			0
$241$	1295.00	+	2243.01i	0.346134	+	0.599522i	0.985559	−	0.169332i	$-0.0541609\pi$
$241$	1295.00	+	2243.01i	0.346134	+	0.599522i	−0.639425	+	0.768853i	$0.720828\pi$
$242$		0			0
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2356.00	−	4080.71i	0.606918	−	1.05121i
$248$		0			0
$249$	−162.000	−	280.592i	−0.0412303	−	0.0714129i
$250$		0			0
$251$	−4932.00			−1.24026			−0.620130	−	0.784499i	$-0.712920\pi$
$251$	−4932.00			−1.24026			−0.620130	+	0.784499i	$0.712920\pi$
$252$		0			0
$253$	−864.000			−0.214700
$254$		0			0
$255$	1026.00	+	1777.08i	0.251963	+	0.436413i
$256$		0			0
$257$	1719.00	−	2977.40i	0.417231	−	0.722665i	−0.578429	−	0.815733i	$-0.696334\pi$
$257$	1719.00	−	2977.40i	0.417231	−	0.722665i	0.995660	+	0.0930680i	$0.0296674\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−243.000	+	420.888i	−0.0576296	+	0.0998174i
$262$		0			0
$263$	−3060.00	−	5300.08i	−0.717444	−	1.24265i	−0.962009	−	0.273016i	$-0.911979\pi$
$263$	−3060.00	−	5300.08i	−0.717444	−	1.24265i	0.244566	−	0.969633i	$-0.421355\pi$
$264$		0			0
$265$	−2412.00			−0.559124
$266$		0			0
$267$	4914.00			1.12634
$268$		0			0
$269$	9.00000	+	15.5885i	0.00203992	+	0.00353325i	0.867044	−	0.498232i	$-0.166017\pi$
$269$	9.00000	+	15.5885i	0.00203992	+	0.00353325i	−0.865004	+	0.501766i	$0.832684\pi$
$270$		0			0
$271$	−3448.00	+	5972.11i	−0.772882	+	1.33867i	0.163095	+	0.986610i	$0.447852\pi$
$271$	−3448.00	+	5972.11i	−0.772882	+	1.33867i	−0.935977	+	0.352061i	$0.885481\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1602.00	−	2774.75i	0.351288	−	0.608449i
$276$		0			0
$277$	−3127.00	−	5416.12i	−0.678279	−	1.17481i	−0.975499	−	0.220004i	$-0.929393\pi$
$277$	−3127.00	−	5416.12i	−0.678279	−	1.17481i	0.297220	−	0.954809i	$-0.403940\pi$
$278$		0			0
$279$	−1008.00			−0.216299
$280$		0			0
$281$	1194.00			0.253481			0.126740	−	0.991936i	$-0.459549\pi$
$281$	1194.00			0.253481			0.126740	+	0.991936i	$0.459549\pi$
$282$		0			0
$283$	3578.00	+	6197.28i	0.751555	+	1.30173i	0.947069	+	0.321030i	$0.104029\pi$
$283$	3578.00	+	6197.28i	0.751555	+	1.30173i	−0.195514	+	0.980701i	$0.562638\pi$
$284$		0			0
$285$	−684.000	+	1184.72i	−0.142164	+	0.246235i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−4041.50	+	7000.08i	−0.822613	+	1.42481i
$290$		0			0
$291$	1515.00	+	2624.06i	0.305192	+	0.528608i
$292$		0			0
$293$	−3738.00			−0.745312			−0.372656	−	0.927970i	$-0.621553\pi$
$293$	−3738.00			−0.745312			−0.372656	+	0.927970i	$0.621553\pi$
$294$		0			0
$295$	2376.00			0.468936
$296$		0			0
$297$	486.000	+	841.777i	0.0949514	+	0.164461i
$298$		0			0
$299$	744.000	−	1288.65i	0.143902	−	0.249245i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	9.00000	−	15.5885i	0.00170639	−	0.00295556i
$304$		0			0
$305$	−762.000	−	1319.82i	−0.143056	−	0.247780i
$306$		0			0
$307$	−844.000			−0.156904			−0.0784522	−	0.996918i	$-0.524998\pi$
$307$	−844.000			−0.156904			−0.0784522	+	0.996918i	$0.524998\pi$
$308$		0			0
$309$	1416.00			0.260691
$310$		0			0
$311$	−3156.00	−	5466.35i	−0.575435	−	0.996683i	−0.995994	−	0.0894178i	$-0.971499\pi$
$311$	−3156.00	−	5466.35i	−0.575435	−	0.996683i	0.420559	−	0.907265i	$-0.361834\pi$
$312$		0			0
$313$	−4141.00	+	7172.42i	−0.747806	+	1.29524i	0.201067	+	0.979578i	$0.435559\pi$
$313$	−4141.00	+	7172.42i	−0.747806	+	1.29524i	−0.948872	+	0.315660i	$0.897774\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4659.00	+	8069.62i	−0.825475	+	1.42976i	0.0760811	+	0.997102i	$0.475759\pi$
$317$	−4659.00	+	8069.62i	−0.825475	+	1.42976i	−0.901556	+	0.432663i	$0.857574\pi$
$318$		0			0
$319$	−972.000	−	1683.55i	−0.170600	−	0.295489i
$320$		0			0
$321$	2916.00			0.507026
$322$		0			0
$323$	−8664.00			−1.49250
$324$		0			0
$325$	2759.00	+	4778.73i	0.470898	+	0.815619i
$326$		0			0
$327$	−2679.00	+	4640.16i	−0.453055	+	0.784715i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−826.000	+	1430.67i	−0.137163	+	0.237574i	−0.926422	−	0.376487i	$-0.877132\pi$
$331$	−826.000	+	1430.67i	−0.137163	+	0.237574i	0.789258	+	0.614061i	$0.210465\pi$
$332$		0			0
$333$	801.000	+	1387.37i	0.131815	+	0.228311i
$334$		0			0
$335$	−6072.00			−0.990295
$336$		0			0
$337$	−1294.00			−0.209165			−0.104583	−	0.994516i	$-0.533351\pi$
$337$	−1294.00			−0.209165			−0.104583	+	0.994516i	$0.533351\pi$
$338$		0			0
$339$	−3429.00	−	5939.20i	−0.549374	−	0.951543i
$340$		0			0
$341$	2016.00	−	3491.81i	0.320154	−	0.554523i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−216.000	+	374.123i	−0.0337074	+	0.0583829i
$346$		0			0
$347$	−1818.00	−	3148.87i	−0.281255	−	0.487147i	0.690439	−	0.723390i	$-0.257417\pi$
$347$	−1818.00	−	3148.87i	−0.281255	−	0.487147i	−0.971694	+	0.236243i	$0.924084\pi$
$348$		0			0
$349$	10478.0			1.60709			0.803545	−	0.595244i	$-0.202945\pi$
$349$	10478.0			1.60709			0.803545	+	0.595244i	$0.202945\pi$
$350$		0			0
$351$	−1674.00			−0.254563
$352$		0			0
$353$	3783.00	+	6552.35i	0.570393	+	0.987950i	0.996525	+	0.0832890i	$0.0265425\pi$
$353$	3783.00	+	6552.35i	0.570393	+	0.987950i	−0.426132	+	0.904661i	$0.640124\pi$
$354$		0			0
$355$	−2520.00	+	4364.77i	−0.376754	+	0.652557i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4020.00	−	6962.84i	0.590996	−	1.02363i	−0.403103	−	0.915155i	$-0.632068\pi$
$359$	4020.00	−	6962.84i	0.590996	−	1.02363i	0.994099	−	0.108480i	$-0.0345984\pi$
$360$		0			0
$361$	541.500	+	937.906i	0.0789474	+	0.136741i
$362$		0			0
$363$	105.000			0.0151820
$364$		0			0
$365$	5340.00			0.765776
$366$		0			0
$367$	−3784.00	−	6554.08i	−0.538210	−	0.932208i	−0.999001	−	0.0446985i	$-0.985767\pi$
$367$	−3784.00	−	6554.08i	−0.538210	−	0.932208i	0.460790	−	0.887509i	$-0.347566\pi$
$368$		0			0
$369$	−1701.00	+	2946.22i	−0.239974	+	0.415648i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	6761.00	−	11710.4i	0.938529	−	1.62558i	0.170312	−	0.985390i	$-0.445522\pi$
$373$	6761.00	−	11710.4i	0.938529	−	1.62558i	0.768217	−	0.640190i	$-0.221144\pi$
$374$		0			0
$375$	−1926.00	−	3335.93i	−0.265222	−	0.459378i
$376$		0			0
$377$	3348.00			0.457376
$378$		0			0
$379$	2468.00			0.334492			0.167246	−	0.985915i	$-0.446513\pi$
$379$	2468.00			0.334492			0.167246	+	0.985915i	$0.446513\pi$
$380$		0			0
$381$	1992.00	+	3450.25i	0.267856	+	0.463941i
$382$		0			0
$383$	6168.00	−	10683.3i	0.822898	−	1.42530i	−0.0806166	−	0.996745i	$-0.525689\pi$
$383$	6168.00	−	10683.3i	0.822898	−	1.42530i	0.903515	−	0.428557i	$-0.140978\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	774.000	−	1340.61i	0.101666	−	0.176090i
$388$		0			0
$389$	1881.00	+	3257.99i	0.245168	+	0.424644i	0.962179	−	0.272418i	$-0.0878234\pi$
$389$	1881.00	+	3257.99i	0.245168	+	0.424644i	−0.717011	+	0.697062i	$0.754490\pi$
$390$		0			0
$391$	−2736.00			−0.353876
$392$		0			0
$393$	3636.00			0.466697
$394$		0			0
$395$	−240.000	−	415.692i	−0.0305714	−	0.0529513i
$396$		0			0
$397$	4385.00	−	7595.04i	0.554350	−	0.960162i	−0.443604	−	0.896223i	$-0.646300\pi$
$397$	4385.00	−	7595.04i	0.554350	−	0.960162i	0.997954	−	0.0639390i	$-0.0203663\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3321.00	+	5752.14i	−0.413573	+	0.716330i	−0.995277	−	0.0970706i	$-0.969053\pi$
$401$	−3321.00	+	5752.14i	−0.413573	+	0.716330i	0.581704	+	0.813400i	$0.302386\pi$
$402$		0			0
$403$	3472.00	+	6013.68i	0.429163	+	0.743332i
$404$		0			0
$405$	486.000			0.0596285
$406$		0			0
$407$	−6408.00			−0.780424
$408$		0			0
$409$	755.000	+	1307.70i	0.0912771	+	0.158097i	0.908049	−	0.418864i	$-0.137572\pi$
$409$	755.000	+	1307.70i	0.0912771	+	0.158097i	−0.816772	+	0.576961i	$0.804238\pi$
$410$		0			0
$411$	−1881.00	+	3257.99i	−0.225749	+	0.391009i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	324.000	−	561.184i	0.0383242	−	0.0663794i
$416$		0			0
$417$	−510.000	−	883.346i	−0.0598916	−	0.103735i
$418$		0			0
$419$	−1260.00			−0.146909			−0.0734547	−	0.997299i	$-0.523402\pi$
$419$	−1260.00			−0.146909			−0.0734547	+	0.997299i	$0.523402\pi$
$420$		0			0
$421$	3998.00			0.462828			0.231414	−	0.972855i	$-0.425665\pi$
$421$	3998.00			0.462828			0.231414	+	0.972855i	$0.425665\pi$
$422$		0			0
$423$	864.000	+	1496.49i	0.0993123	+	0.172014i
$424$		0			0
$425$	5073.00	−	8786.69i	0.579004	−	1.00286i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	3348.00	−	5798.91i	0.376790	−	0.652620i
$430$		0			0
$431$	1368.00	+	2369.45i	0.152887	+	0.264808i	0.932288	−	0.361718i	$-0.117810\pi$
$431$	1368.00	+	2369.45i	0.152887	+	0.264808i	−0.779401	+	0.626526i	$0.784476\pi$
$432$		0			0
$433$	2690.00			0.298552			0.149276	−	0.988796i	$-0.452306\pi$
$433$	2690.00			0.298552			0.149276	+	0.988796i	$0.452306\pi$
$434$		0			0
$435$	−972.000			−0.107135
$436$		0			0
$437$	−912.000	−	1579.63i	−0.0998327	−	0.172915i
$438$		0			0
$439$	620.000	−	1073.87i	0.0674054	−	0.116750i	−0.830353	−	0.557238i	$-0.811861\pi$
$439$	620.000	−	1073.87i	0.0674054	−	0.116750i	0.897758	+	0.440488i	$0.145195\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1950.00	−	3377.50i	0.209136	−	0.362234i	−0.742307	−	0.670060i	$-0.766268\pi$
$443$	1950.00	−	3377.50i	0.209136	−	0.362234i	0.951443	+	0.307826i	$0.0996015\pi$
$444$		0			0
$445$	4914.00	+	8511.30i	0.523474	+	0.906684i
$446$		0			0
$447$	−3114.00			−0.329501
$448$		0			0
$449$	−10878.0			−1.14335			−0.571675	−	0.820480i	$-0.693706\pi$
$449$	−10878.0			−1.14335			−0.571675	+	0.820480i	$0.693706\pi$
$450$		0			0
$451$	−6804.00	−	11784.9i	−0.710394	−	1.23044i
$452$		0			0
$453$	4404.00	−	7627.95i	0.456773	−	0.791153i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1165.00	+	2017.84i	−0.119248	+	0.206544i	−0.919470	−	0.393160i	$-0.871382\pi$
$457$	−1165.00	+	2017.84i	−0.119248	+	0.206544i	0.800222	+	0.599704i	$0.204715\pi$
$458$		0			0
$459$	1539.00	+	2665.63i	0.156502	+	0.271069i
$460$		0			0
$461$	15150.0			1.53060			0.765299	−	0.643675i	$-0.222591\pi$
$461$	15150.0			1.53060			0.765299	+	0.643675i	$0.222591\pi$
$462$		0			0
$463$	−2992.00			−0.300324			−0.150162	−	0.988661i	$-0.547980\pi$
$463$	−2992.00			−0.300324			−0.150162	+	0.988661i	$0.547980\pi$
$464$		0			0
$465$	−1008.00	−	1745.91i	−0.100527	−	0.174117i
$466$		0			0
$467$	−4362.00	+	7555.21i	−0.432225	+	0.748636i	−0.997065	−	0.0765646i	$-0.975605\pi$
$467$	−4362.00	+	7555.21i	−0.432225	+	0.748636i	0.564839	+	0.825201i	$0.308938\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−1995.00	+	3455.44i	−0.195169	+	0.338043i
$472$		0			0
$473$	3096.00	+	5362.43i	0.300960	+	0.521279i
$474$		0			0
$475$	6764.00			0.653376
$476$		0			0
$477$	−3618.00			−0.347289
$478$		0			0
$479$	−4872.00	−	8438.55i	−0.464734	−	0.804942i	0.534456	−	0.845196i	$-0.320517\pi$
$479$	−4872.00	−	8438.55i	−0.464734	−	0.804942i	−0.999189	+	0.0402542i	$0.987183\pi$
$480$		0			0
$481$	5518.00	−	9557.46i	0.523075	−	0.905993i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3030.00	+	5248.11i	−0.283681	+	0.491350i
$486$		0			0
$487$	−2068.00	−	3581.88i	−0.192423	−	0.333286i	0.753630	−	0.657299i	$-0.228301\pi$
$487$	−2068.00	−	3581.88i	−0.192423	−	0.333286i	−0.946053	+	0.324013i	$0.894968\pi$
$488$		0			0
$489$	10092.0			0.933284
$490$		0			0
$491$	16212.0			1.49010			0.745048	−	0.667011i	$-0.232426\pi$
$491$	16212.0			1.49010			0.745048	+	0.667011i	$0.232426\pi$
$492$		0			0
$493$	−3078.00	−	5331.25i	−0.281189	−	0.487034i
$494$		0			0
$495$	−972.000	+	1683.55i	−0.0882589	+	0.152869i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−1198.00	+	2075.00i	−0.107475	+	0.186152i	−0.914747	−	0.404028i	$-0.867610\pi$
$499$	−1198.00	+	2075.00i	−0.107475	+	0.186152i	0.807272	+	0.590180i	$0.200943\pi$
$500$		0			0
$501$	4572.00	+	7918.94i	0.407708	+	0.706172i
$502$		0			0
$503$	13128.0			1.16371			0.581857	−	0.813291i	$-0.302326\pi$
$503$	13128.0			1.16371			0.581857	+	0.813291i	$0.302326\pi$
$504$		0			0
$505$	36.0000			0.00317224
$506$		0			0
$507$	2470.50	+	4279.03i	0.216408	+	0.374829i
$508$		0			0
$509$	−6399.00	+	11083.4i	−0.557231	+	0.965153i	0.440495	+	0.897755i	$0.354803\pi$
$509$	−6399.00	+	11083.4i	−0.557231	+	0.965153i	−0.997726	+	0.0673977i	$0.978530\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−1026.00	+	1777.08i	−0.0883022	+	0.152944i
$514$		0			0
$515$	1416.00	+	2452.58i	0.121158	+	0.209852i
$516$		0			0
$517$	−6912.00			−0.587987
$518$		0			0
$519$	8118.00			0.686591
$520$		0			0
$521$	−3693.00	−	6396.46i	−0.310544	−	0.537877i	0.667936	−	0.744218i	$-0.267178\pi$
$521$	−3693.00	−	6396.46i	−0.310544	−	0.537877i	−0.978480	+	0.206341i	$0.933844\pi$
$522$		0			0
$523$	−2590.00	+	4486.01i	−0.216545	+	0.375066i	−0.953749	−	0.300603i	$-0.902812\pi$
$523$	−2590.00	+	4486.01i	−0.216545	+	0.375066i	0.737205	+	0.675669i	$0.236145\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6384.00	−	11057.4i	0.527688	−	0.913982i
$528$		0			0
$529$	5795.50	+	10038.1i	0.476329	+	0.825027i
$530$		0			0
$531$	3564.00			0.291270
$532$		0			0
$533$	23436.0			1.90455
$534$		0			0
$535$	2916.00	+	5050.66i	0.235644	+	0.408148i
$536$		0			0
$537$	7074.00	−	12252.5i	0.568465	−	0.984610i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−2035.00	+	3524.72i	−0.161722	+	0.280110i	−0.935486	−	0.353363i	$-0.885038\pi$
$541$	−2035.00	+	3524.72i	−0.161722	+	0.280110i	0.773764	+	0.633473i	$0.218371\pi$
$542$		0			0
$543$	2865.00	+	4962.33i	0.226425	+	0.392180i
$544$		0			0
$545$	−10716.0			−0.842244
$546$		0			0
$547$	14780.0			1.15530			0.577648	−	0.816286i	$-0.303971\pi$
$547$	14780.0			1.15530			0.577648	+	0.816286i	$0.303971\pi$
$548$		0			0
$549$	−1143.00	−	1979.73i	−0.0888562	−	0.153903i
$550$		0			0
$551$	2052.00	−	3554.17i	0.158654	−	0.274796i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−1602.00	+	2774.75i	−0.122525	+	0.212219i
$556$		0			0
$557$	3429.00	+	5939.20i	0.260846	+	0.451799i	0.966467	−	0.256791i	$-0.0826651\pi$
$557$	3429.00	+	5939.20i	0.260846	+	0.451799i	−0.705621	+	0.708590i	$0.749332\pi$
$558$		0			0
$559$	−10664.0			−0.806868
$560$		0			0
$561$	−12312.0			−0.926583
$562$		0			0
$563$	−3330.00	−	5767.73i	−0.249277	−	0.431760i	0.714049	−	0.700096i	$-0.246860\pi$
$563$	−3330.00	−	5767.73i	−0.249277	−	0.431760i	−0.963325	+	0.268336i	$0.913526\pi$
$564$		0			0
$565$	6858.00	−	11878.4i	0.510652	−	0.884475i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	75.0000	−	129.904i	0.00552577	−	0.00957092i	−0.863249	−	0.504778i	$-0.831574\pi$
$569$	75.0000	−	129.904i	0.00552577	−	0.00957092i	0.868775	+	0.495207i	$0.164908\pi$
$570$		0			0
$571$	4094.00	+	7091.02i	0.300050	+	0.519702i	0.976147	−	0.217111i	$-0.0696633\pi$
$571$	4094.00	+	7091.02i	0.300050	+	0.519702i	−0.676097	+	0.736813i	$0.736330\pi$
$572$		0			0
$573$	−12240.0			−0.892379
$574$		0			0
$575$	2136.00			0.154917
$576$		0			0
$577$	2927.00	+	5069.71i	0.211183	+	0.365780i	0.952085	−	0.305833i	$-0.0989351\pi$
$577$	2927.00	+	5069.71i	0.211183	+	0.365780i	−0.740902	+	0.671613i	$0.765602\pi$
$578$		0			0
$579$	−4029.00	+	6978.43i	−0.289187	+	0.500887i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	7236.00	−	12533.1i	0.514039	−	0.890341i
$584$		0			0
$585$	−1674.00	−	2899.45i	−0.118310	−	0.204919i
$586$		0			0
$587$	17580.0			1.23612			0.618062	−	0.786130i	$-0.287918\pi$
$587$	17580.0			1.23612			0.618062	+	0.786130i	$0.287918\pi$
$588$		0			0
$589$	8512.00			0.595468
$590$		0			0
$591$	765.000	+	1325.02i	0.0532452	+	0.0922233i
$592$		0			0
$593$	−8577.00	+	14855.8i	−0.593955	+	1.02876i	0.399739	+	0.916629i	$0.369101\pi$
$593$	−8577.00	+	14855.8i	−0.593955	+	1.02876i	−0.993693	+	0.112131i	$0.964232\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2028.00	−	3512.60i	0.139029	−	0.240806i
$598$		0			0
$599$	9060.00	+	15692.4i	0.617999	+	1.07041i	0.989850	+	0.142114i	$0.0453899\pi$
$599$	9060.00	+	15692.4i	0.617999	+	1.07041i	−0.371851	+	0.928292i	$0.621277\pi$
$600$		0			0
$601$	17546.0			1.19088			0.595438	−	0.803401i	$-0.296979\pi$
$601$	17546.0			1.19088			0.595438	+	0.803401i	$0.296979\pi$
$602$		0			0
$603$	−9108.00			−0.615102
$604$		0			0
$605$	105.000	+	181.865i	0.00705596	+	0.0122213i
$606$		0			0
$607$	7280.00	−	12609.3i	0.486798	−	0.843158i	−0.513087	−	0.858336i	$-0.671498\pi$
$607$	7280.00	−	12609.3i	0.486798	−	0.843158i	0.999885	+	0.0151784i	$0.00483163\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	5952.00	−	10309.2i	0.394095	−	0.682593i
$612$		0			0
$613$	2249.00	+	3895.38i	0.148183	+	0.256661i	0.930556	−	0.366150i	$-0.119324\pi$
$613$	2249.00	+	3895.38i	0.148183	+	0.256661i	−0.782373	+	0.622810i	$0.785991\pi$
$614$		0			0
$615$	−6804.00			−0.446120
$616$		0			0
$617$	−5478.00			−0.357433			−0.178716	−	0.983901i	$-0.557194\pi$
$617$	−5478.00			−0.357433			−0.178716	+	0.983901i	$0.557194\pi$
$618$		0			0
$619$	−3022.00	−	5234.26i	−0.196227	−	0.339875i	0.751075	−	0.660217i	$-0.229536\pi$
$619$	−3022.00	−	5234.26i	−0.196227	−	0.339875i	−0.947302	+	0.320342i	$0.896202\pi$
$620$		0			0
$621$	−324.000	+	561.184i	−0.0209367	+	0.0362634i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−1710.50	+	2962.67i	−0.109472	+	0.189611i
$626$		0			0
$627$	−4104.00	−	7108.34i	−0.261400	−	0.452759i
$628$		0			0
$629$	−20292.0			−1.28632
$630$		0			0
$631$	−15352.0			−0.968547			−0.484274	−	0.874917i	$-0.660916\pi$
$631$	−15352.0			−0.968547			−0.484274	+	0.874917i	$0.660916\pi$
$632$		0			0
$633$	−5046.00	−	8739.93i	−0.316841	−	0.548785i
$634$		0			0
$635$	−3984.00	+	6900.49i	−0.248977	+	0.431240i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−3780.00	+	6547.15i	−0.234013	+	0.405323i
$640$		0			0
$641$	11199.0	+	19397.2i	0.690068	+	1.19523i	0.971815	+	0.235745i	$0.0757530\pi$
$641$	11199.0	+	19397.2i	0.690068	+	1.19523i	−0.281746	+	0.959489i	$0.590914\pi$
$642$		0			0
$643$	3764.00			0.230852			0.115426	−	0.993316i	$-0.463177\pi$
$643$	3764.00			0.230852			0.115426	+	0.993316i	$0.463177\pi$
$644$		0			0
$645$	3096.00			0.189000
$646$		0			0
$647$	8844.00	+	15318.3i	0.537393	+	0.930793i	0.999043	+	0.0437305i	$0.0139243\pi$
$647$	8844.00	+	15318.3i	0.537393	+	0.930793i	−0.461650	+	0.887062i	$0.652742\pi$
$648$		0			0
$649$	−7128.00	+	12346.1i	−0.431122	+	0.746726i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−9939.00	+	17214.9i	−0.595625	+	1.03165i	0.397833	+	0.917458i	$0.369762\pi$
$653$	−9939.00	+	17214.9i	−0.595625	+	1.03165i	−0.993458	+	0.114195i	$0.963571\pi$
$654$		0			0
$655$	3636.00	+	6297.74i	0.216901	+	0.375684i
$656$		0			0
$657$	8010.00			0.475647
$658$		0			0
$659$	−20004.0			−1.18247			−0.591233	−	0.806501i	$-0.701359\pi$
$659$	−20004.0			−1.18247			−0.591233	+	0.806501i	$0.701359\pi$
$660$		0			0
$661$	653.000	+	1131.03i	0.0384247	+	0.0665536i	0.884598	−	0.466354i	$-0.154433\pi$
$661$	653.000	+	1131.03i	0.0384247	+	0.0665536i	−0.846173	+	0.532908i	$0.821099\pi$
$662$		0			0
$663$	10602.0	−	18363.2i	0.621037	−	1.07567i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	648.000	−	1122.37i	0.0376172	−	0.0651549i
$668$		0			0
$669$	−7152.00	−	12387.6i	−0.413322	−	0.715894i
$670$		0			0
$671$	9144.00			0.526081
$672$		0			0
$673$	−13054.0			−0.747689			−0.373845	−	0.927491i	$-0.621961\pi$
$673$	−13054.0			−0.747689			−0.373845	+	0.927491i	$0.621961\pi$
$674$		0			0
$675$	−1201.50	−	2081.06i	−0.0685122	−	0.118667i
$676$		0			0
$677$	−2523.00	+	4369.96i	−0.143230	+	0.248082i	−0.928711	−	0.370804i	$-0.879082\pi$
$677$	−2523.00	+	4369.96i	−0.143230	+	0.248082i	0.785481	+	0.618886i	$0.212416\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	630.000	−	1091.19i	0.0354503	−	0.0614017i
$682$		0			0
$683$	−6234.00	−	10797.6i	−0.349249	−	0.604918i	0.636867	−	0.770974i	$-0.280230\pi$
$683$	−6234.00	−	10797.6i	−0.349249	−	0.604918i	−0.986116	+	0.166056i	$0.946897\pi$
$684$		0			0
$685$	−7524.00			−0.419675
$686$		0			0
$687$	5646.00			0.313549
$688$		0			0
$689$	12462.0	+	21584.8i	0.689063	+	1.19349i
$690$		0			0
$691$	11606.0	−	20102.2i	0.638948	−	1.10669i	−0.346716	−	0.937970i	$-0.612703\pi$
$691$	11606.0	−	20102.2i	0.638948	−	1.10669i	0.985664	−	0.168720i	$-0.0539634\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1020.00	−	1766.69i	0.0556702	−	0.0964237i
$696$		0			0
$697$	−21546.0	−	37318.8i	−1.17089	−	2.02805i
$698$		0			0
$699$	−15246.0			−0.824974
$700$		0			0
$701$	35958.0			1.93740			0.968698	−	0.248241i	$-0.0798526\pi$
$701$	35958.0			1.93740			0.968698	+	0.248241i	$0.0798526\pi$
$702$		0			0
$703$	−6764.00	−	11715.6i	−0.362886	−	0.628538i
$704$		0			0
$705$	−1728.00	+	2992.98i	−0.0923124	+	0.159890i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−3223.00	+	5582.40i	−0.170723	+	0.295700i	−0.938673	−	0.344809i	$-0.887944\pi$
$709$	−3223.00	+	5582.40i	−0.170723	+	0.295700i	0.767950	+	0.640510i	$0.221277\pi$
$710$		0			0
$711$	−360.000	−	623.538i	−0.0189888	−	0.0328896i
$712$		0			0
$713$	2688.00			0.141187
$714$		0			0
$715$	13392.0			0.700465
$716$		0			0
$717$	−8136.00	−	14092.0i	−0.423772	−	0.733995i
$718$		0			0
$719$	2352.00	−	4073.78i	0.121996	−	0.211302i	−0.798559	−	0.601917i	$-0.794404\pi$
$719$	2352.00	−	4073.78i	0.121996	−	0.211302i	0.920555	+	0.390614i	$0.127737\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−3885.00	+	6729.02i	−0.199841	+	0.346134i
$724$		0			0
$725$	2403.00	+	4162.12i	0.123097	+	0.213210i
$726$		0			0
$727$	−10600.0			−0.540760			−0.270380	−	0.962754i	$-0.587149\pi$
$727$	−10600.0			−0.540760			−0.270380	+	0.962754i	$0.587149\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	9804.00	+	16981.0i	0.496052	+	0.859187i
$732$		0			0
$733$	−6271.00	+	10861.7i	−0.315995	+	0.547320i	−0.979649	−	0.200720i	$-0.935672\pi$
$733$	−6271.00	+	10861.7i	−0.315995	+	0.547320i	0.663653	+	0.748040i	$0.269005\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	18216.0	−	31551.0i	0.910441	−	1.57693i
$738$		0			0
$739$	−11662.0	−	20199.2i	−0.580506	−	1.00547i	−0.995419	−	0.0956044i	$-0.969522\pi$
$739$	−11662.0	−	20199.2i	−0.580506	−	1.00547i	0.414914	−	0.909861i	$-0.363812\pi$
$740$		0			0
$741$	14136.0			0.700808
$742$		0			0
$743$	−6312.00			−0.311662			−0.155831	−	0.987784i	$-0.549806\pi$
$743$	−6312.00			−0.311662			−0.155831	+	0.987784i	$0.549806\pi$
$744$		0			0
$745$	−3114.00	−	5393.61i	−0.153138	−	0.265244i
$746$		0			0
$747$	486.000	−	841.777i	0.0238043	−	0.0412303i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−17920.0	+	31038.4i	−0.870719	+	1.50813i	−0.00946509	+	0.999955i	$0.503013\pi$
$751$	−17920.0	+	31038.4i	−0.870719	+	1.50813i	−0.861254	+	0.508175i	$0.830320\pi$
$752$		0			0
$753$	−7398.00	−	12813.7i	−0.358032	−	0.620130i
$754$		0			0
$755$	17616.0			0.849155
$756$		0			0
$757$	−34594.0			−1.66095			−0.830476	−	0.557055i	$-0.811931\pi$
$757$	−34594.0			−1.66095			−0.830476	+	0.557055i	$0.811931\pi$
$758$		0			0
$759$	−1296.00	−	2244.74i	−0.0619787	−	0.107350i
$760$		0			0
$761$	−11973.0	+	20737.8i	−0.570330	+	0.987840i	0.426202	+	0.904628i	$0.359851\pi$
$761$	−11973.0	+	20737.8i	−0.570330	+	0.987840i	−0.996532	+	0.0832121i	$0.973482\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−3078.00	+	5331.25i	−0.145471	+	0.251963i
$766$		0			0
$767$	−12276.0	−	21262.7i	−0.577915	−	1.00098i
$768$		0			0
$769$	18770.0			0.880187			0.440093	−	0.897952i	$-0.354945\pi$
$769$	18770.0			0.880187			0.440093	+	0.897952i	$0.354945\pi$
$770$		0			0
$771$	10314.0			0.481776
$772$		0			0
$773$	−15171.0	−	26276.9i	−0.705903	−	1.22266i	−0.966365	−	0.257176i	$-0.917208\pi$
$773$	−15171.0	−	26276.9i	−0.705903	−	1.22266i	0.260462	−	0.965484i	$-0.416125\pi$
$774$		0			0
$775$	−4984.00	+	8632.54i	−0.231007	+	0.400116i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	14364.0	−	24879.2i	0.660647	−	1.14427i
$780$		0			0
$781$	−15120.0	−	26188.6i	−0.692748	−	1.19987i
$782$		0			0
$783$	−1458.00			−0.0665449
$784$		0			0
$785$	−7980.00			−0.362826
$786$		0			0
$787$	13094.0	+	22679.5i	0.593076	+	1.02724i	0.993815	+	0.111045i	$0.0354199\pi$
$787$	13094.0	+	22679.5i	0.593076	+	1.02724i	−0.400739	+	0.916192i	$0.631247\pi$
$788$		0			0
$789$	9180.00	−	15900.2i	0.414216	−	0.717444i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−7874.00	+	13638.2i	−0.352603	+	0.610726i
$794$		0			0
$795$	−3618.00	−	6266.56i	−0.161405	−	0.279562i
$796$		0			0
$797$	−34818.0			−1.54745			−0.773724	−	0.633522i	$-0.781609\pi$
$797$	−34818.0			−1.54745			−0.773724	+	0.633522i	$0.781609\pi$
$798$		0			0
$799$	−21888.0			−0.969139
$800$		0			0
$801$	7371.00	+	12766.9i	0.325145	+	0.563168i
$802$		0			0
$803$	−16020.0	+	27747.5i	−0.704027	+	1.21941i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−27.0000	+	46.7654i	−0.00117775	+	0.00203992i
$808$		0			0
$809$	10851.0	+	18794.5i	0.471571	+	0.816785i	0.999471	−	0.0325217i	$-0.0103538\pi$
$809$	10851.0	+	18794.5i	0.471571	+	0.816785i	−0.527900	+	0.849306i	$0.677020\pi$
$810$		0			0
$811$	−20356.0			−0.881376			−0.440688	−	0.897660i	$-0.645265\pi$
$811$	−20356.0			−0.881376			−0.440688	+	0.897660i	$0.645265\pi$
$812$		0			0
$813$	−20688.0			−0.892448
$814$		0			0
$815$	10092.0	+	17479.9i	0.433751	+	0.751279i
$816$		0			0
$817$	−6536.00	+	11320.7i	−0.279885	+	0.484774i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	9945.00	−	17225.2i	0.422756	−	0.732235i	−0.573452	−	0.819239i	$-0.694396\pi$
$821$	9945.00	−	17225.2i	0.422756	−	0.732235i	0.996208	+	0.0870040i	$0.0277293\pi$
$822$		0			0
$823$	−2116.00	−	3665.02i	−0.0896223	−	0.155230i	0.817729	−	0.575603i	$-0.195233\pi$
$823$	−2116.00	−	3665.02i	−0.0896223	−	0.155230i	−0.907352	+	0.420373i	$0.861899\pi$
$824$		0			0
$825$	9612.00			0.405633
$826$		0			0
$827$	9636.00			0.405171			0.202586	−	0.979265i	$-0.435066\pi$
$827$	9636.00			0.405171			0.202586	+	0.979265i	$0.435066\pi$
$828$		0			0
$829$	−17647.0	−	30565.5i	−0.739331	−	1.28056i	−0.952797	−	0.303609i	$-0.901808\pi$
$829$	−17647.0	−	30565.5i	−0.739331	−	1.28056i	0.213465	−	0.976951i	$-0.431525\pi$
$830$		0			0
$831$	9381.00	−	16248.4i	0.391604	−	0.678279i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−9144.00	+	15837.9i	−0.378971	+	0.656398i
$836$		0			0
$837$	−1512.00	−	2618.86i	−0.0624401	−	0.108149i
$838$		0			0
$839$	−3768.00			−0.155049			−0.0775243	−	0.996990i	$-0.524702\pi$
$839$	−3768.00			−0.155049			−0.0775243	+	0.996990i	$0.524702\pi$
$840$		0			0
$841$	−21473.0			−0.880438
$842$		0			0
$843$	1791.00	+	3102.10i	0.0731736	+	0.126740i
$844$		0			0
$845$	−4941.00	+	8558.06i	−0.201155	+	0.348410i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−10734.0	+	18591.8i	−0.433910	+	0.751555i
$850$		0			0
$851$	−2136.00	−	3699.66i	−0.0860413	−	0.149028i
$852$		0			0
$853$	−39466.0			−1.58416			−0.792081	−	0.610416i	$-0.791002\pi$
$853$	−39466.0			−1.58416			−0.792081	+	0.610416i	$0.791002\pi$
$854$		0			0
$855$	−4104.00			−0.164157
$856$		0			0
$857$	17019.0	+	29477.8i	0.678364	+	1.17496i	0.975473	+	0.220117i	$0.0706441\pi$
$857$	17019.0	+	29477.8i	0.678364	+	1.17496i	−0.297109	+	0.954843i	$0.596023\pi$
$858$		0			0
$859$	1682.00	−	2913.31i	0.0668092	−	0.115717i	−0.830686	−	0.556741i	$-0.812051\pi$
$859$	1682.00	−	2913.31i	0.0668092	−	0.115717i	0.897495	+	0.441024i	$0.145385\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−6552.00	+	11348.4i	−0.258439	+	0.447629i	−0.965824	−	0.259199i	$-0.916541\pi$
$863$	−6552.00	+	11348.4i	−0.258439	+	0.447629i	0.707385	+	0.706828i	$0.249875\pi$
$864$		0			0
$865$	8118.00	+	14060.8i	0.319099	+	0.552695i
$866$		0			0
$867$	−24249.0			−0.949872
$868$		0			0
$869$	2880.00			0.112425
$870$		0			0
$871$	31372.0	+	54337.9i	1.22044	+	2.11386i
$872$		0			0
$873$	−4545.00	+	7872.17i	−0.176203	+	0.305192i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	20429.0	−	35384.1i	0.786589	−	1.36241i	−0.141457	−	0.989944i	$-0.545179\pi$
$877$	20429.0	−	35384.1i	0.786589	−	1.36241i	0.928045	−	0.372467i	$-0.121488\pi$
$878$		0			0
$879$	−5607.00	−	9711.61i	−0.215153	−	0.372656i
$880$		0			0
$881$	−37374.0			−1.42924			−0.714621	−	0.699512i	$-0.753401\pi$
$881$	−37374.0			−1.42924			−0.714621	+	0.699512i	$0.753401\pi$
$882$		0			0
$883$	9788.00			0.373038			0.186519	−	0.982451i	$-0.440279\pi$
$883$	9788.00			0.373038			0.186519	+	0.982451i	$0.440279\pi$
$884$		0			0
$885$	3564.00	+	6173.03i	0.135370	+	0.234468i
$886$		0			0
$887$	−25212.0	+	43668.5i	−0.954381	+	1.65304i	−0.218603	+	0.975814i	$0.570150\pi$
$887$	−25212.0	+	43668.5i	−0.954381	+	1.65304i	−0.735778	+	0.677223i	$0.763183\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1458.00	+	2525.33i	−0.0548202	+	0.0949514i
$892$		0			0
$893$	−7296.00	−	12637.0i	−0.273406	−	0.473553i
$894$		0			0
$895$	28296.0			1.05679
$896$		0			0
$897$	4464.00			0.166163
$898$		0			0
$899$	3024.00	+	5237.72i	0.112187	+	0.194313i
$900$		0			0
$901$	22914.0	−	39688.2i	0.847254	−	1.46749i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−5730.00	+	9924.65i	−0.210466	+	0.364538i
$906$		0			0
$907$	6206.00	+	10749.1i	0.227196	+	0.393515i	0.956976	−	0.290167i	$-0.0937108\pi$
$907$	6206.00	+	10749.1i	0.227196	+	0.393515i	−0.729780	+	0.683682i	$0.760378\pi$
$908$		0			0
$909$	54.0000			0.00197037
$910$		0			0
$911$	6576.00			0.239158			0.119579	−	0.992825i	$-0.461846\pi$
$911$	6576.00			0.239158			0.119579	+	0.992825i	$0.461846\pi$
$912$		0			0
$913$	1944.00	+	3367.11i	0.0704677	+	0.122054i
$914$		0			0
$915$	2286.00	−	3959.47i	0.0825933	−	0.143056i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−4132.00	+	7156.83i	−0.148316	+	0.256890i	−0.930605	−	0.366025i	$-0.880718\pi$
$919$	−4132.00	+	7156.83i	−0.148316	+	0.256890i	0.782289	+	0.622915i	$0.214052\pi$
$920$		0			0
$921$	−1266.00	−	2192.78i	−0.0452944	−	0.0784522i
$922$		0			0
$923$	52080.0			1.85724
$924$		0			0
$925$	15842.0			0.563115
$926$		0			0
$927$	2124.00	+	3678.88i	0.0752549	+	0.130345i
$928$		0			0
$929$	−19713.0	+	34143.9i	−0.696192	+	1.20584i	0.273585	+	0.961848i	$0.411791\pi$
$929$	−19713.0	+	34143.9i	−0.696192	+	1.20584i	−0.969777	+	0.243992i	$0.921543\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	9468.00	−	16399.1i	0.332228	−	0.575435i
$934$		0			0
$935$	−12312.0	−	21325.0i	−0.430637	−	0.745885i
$936$		0			0
$937$	−4678.00			−0.163099			−0.0815494	−	0.996669i	$-0.525987\pi$
$937$	−4678.00			−0.163099			−0.0815494	+	0.996669i	$0.525987\pi$
$938$		0			0
$939$	−24846.0			−0.863492
$940$		0			0
$941$	8673.00	+	15022.1i	0.300459	+	0.520410i	0.976240	−	0.216692i	$-0.0695269\pi$
$941$	8673.00	+	15022.1i	0.300459	+	0.520410i	−0.675781	+	0.737102i	$0.736194\pi$
$942$		0			0
$943$	4536.00	−	7856.58i	0.156641	−	0.271310i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9726.00	+	16845.9i	−0.333741	+	0.578056i	−0.983242	−	0.182304i	$-0.941644\pi$
$947$	−9726.00	+	16845.9i	−0.333741	+	0.578056i	0.649501	+	0.760360i	$0.274978\pi$
$948$		0			0
$949$	−27590.0	−	47787.3i	−0.943740	−	1.63461i
$950$		0			0
$951$	−27954.0			−0.953176
$952$		0			0
$953$	4458.00			0.151531			0.0757654	−	0.997126i	$-0.475860\pi$
$953$	4458.00			0.151531			0.0757654	+	0.997126i	$0.475860\pi$
$954$		0			0
$955$	−12240.0	−	21200.3i	−0.414740	−	0.718351i
$956$		0			0
$957$	2916.00	−	5050.66i	0.0984962	−	0.170600i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	8623.50	−	14936.3i	0.289467	−	0.501371i
$962$		0			0
$963$	4374.00	+	7575.99i	0.146366	+	0.253513i
$964$		0			0
$965$	−16116.0			−0.537609
$966$		0			0
$967$	52520.0			1.74657			0.873283	−	0.487213i	$-0.161987\pi$
$967$	52520.0			1.74657			0.873283	+	0.487213i	$0.161987\pi$
$968$		0			0
$969$	−12996.0	−	22509.7i	−0.430848	−	0.746251i
$970$		0			0
$971$	5202.00	−	9010.13i	0.171926	−	0.297785i	−0.767167	−	0.641447i	$-0.778334\pi$
$971$	5202.00	−	9010.13i	0.171926	−	0.297785i	0.939093	+	0.343663i	$0.111668\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−8277.00	+	14336.2i	−0.271873	+	0.470898i
$976$		0			0
$977$	3783.00	+	6552.35i	0.123878	+	0.214563i	0.921294	−	0.388867i	$-0.127133\pi$
$977$	3783.00	+	6552.35i	0.123878	+	0.214563i	−0.797416	+	0.603430i	$0.793800\pi$
$978$		0			0
$979$	−58968.0			−1.92505
$980$		0			0
$981$	−16074.0			−0.523143
$982$		0			0
$983$	−22188.0	−	38430.7i	−0.719926	−	1.24695i	−0.961029	−	0.276449i	$-0.910842\pi$
$983$	−22188.0	−	38430.7i	−0.719926	−	1.24695i	0.241103	−	0.970500i	$-0.422491\pi$
$984$		0			0
$985$	−1530.00	+	2650.04i	−0.0494922	+	0.0857231i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2064.00	+	3574.95i	−0.0663614	+	0.114941i
$990$		0			0
$991$	13664.0	+	23666.7i	0.437993	+	0.758626i	0.997535	−	0.0701759i	$-0.0223561\pi$
$991$	13664.0	+	23666.7i	0.437993	+	0.758626i	−0.559541	+	0.828802i	$0.689023\pi$
$992$		0			0
$993$	−4956.00			−0.158383
$994$		0			0
$995$	8112.00			0.258460
$996$		0			0
$997$	−1387.00	−	2402.35i	−0.0440589	−	0.0763123i	0.843155	−	0.537671i	$-0.180696\pi$
$997$	−1387.00	−	2402.35i	−0.0440589	−	0.0763123i	−0.887214	+	0.461358i	$0.847362\pi$
$998$		0			0
$999$	−2403.00	+	4162.12i	−0.0761037	+	0.131815i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.4.i.f.373.1		2
3.2	odd	2		1764.4.k.l.1549.1		2
7.2	even	3		84.4.a.a.1.1	✓	1
7.3	odd	6		588.4.i.c.361.1		2
7.4	even	3	inner	588.4.i.f.361.1		2
7.5	odd	6		588.4.a.d.1.1		1
7.6	odd	2		588.4.i.c.373.1		2
21.2	odd	6		252.4.a.b.1.1		1
21.5	even	6		1764.4.a.j.1.1		1
21.11	odd	6		1764.4.k.l.361.1		2
21.17	even	6		1764.4.k.f.361.1		2
21.20	even	2		1764.4.k.f.1549.1		2
28.19	even	6		2352.4.a.d.1.1		1
28.23	odd	6		336.4.a.k.1.1		1
35.2	odd	12		2100.4.k.j.1849.2		2
35.9	even	6		2100.4.a.l.1.1		1
35.23	odd	12		2100.4.k.j.1849.1		2
56.37	even	6		1344.4.a.q.1.1		1
56.51	odd	6		1344.4.a.d.1.1		1
84.23	even	6		1008.4.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.a.a.1.1	✓	1	7.2	even	3
252.4.a.b.1.1		1	21.2	odd	6
336.4.a.k.1.1		1	28.23	odd	6
588.4.a.d.1.1		1	7.5	odd	6
588.4.i.c.361.1		2	7.3	odd	6
588.4.i.c.373.1		2	7.6	odd	2
588.4.i.f.361.1		2	7.4	even	3	inner
588.4.i.f.373.1		2	1.1	even	1	trivial
1008.4.a.h.1.1		1	84.23	even	6
1344.4.a.d.1.1		1	56.51	odd	6
1344.4.a.q.1.1		1	56.37	even	6
1764.4.a.j.1.1		1	21.5	even	6
1764.4.k.f.361.1		2	21.17	even	6
1764.4.k.f.1549.1		2	21.20	even	2
1764.4.k.l.361.1		2	21.11	odd	6
1764.4.k.l.1549.1		2	3.2	odd	2
2100.4.a.l.1.1		1	35.9	even	6
2100.4.k.j.1849.1		2	35.23	odd	12
2100.4.k.j.1849.2		2	35.2	odd	12
2352.4.a.d.1.1		1	28.19	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	588.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{3} +(-3.00000 + 5.19615i) q^{5} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 2.59808i) q^{3} +(-3.00000 + 5.19615i) q^{5} +(-4.50000 + 7.79423i) q^{9} +(-18.0000 - 31.1769i) q^{11} +62.0000 q^{13} -18.0000 q^{15} +(-57.0000 - 98.7269i) q^{17} +(38.0000 - 65.8179i) q^{19} +(12.0000 - 20.7846i) q^{23} +(44.5000 + 77.0763i) q^{25} -27.0000 q^{27} +54.0000 q^{29} +(56.0000 + 96.9948i) q^{31} +(54.0000 - 93.5307i) q^{33} +(89.0000 - 154.153i) q^{37} +(93.0000 + 161.081i) q^{39} +378.000 q^{41} -172.000 q^{43} +(-27.0000 - 46.7654i) q^{45} +(96.0000 - 166.277i) q^{47} +(171.000 - 296.181i) q^{51} +(201.000 + 348.142i) q^{53} +216.000 q^{55} +228.000 q^{57} +(-198.000 - 342.946i) q^{59} +(-127.000 + 219.970i) q^{61} +(-186.000 + 322.161i) q^{65} +(506.000 + 876.418i) q^{67} +72.0000 q^{69} +840.000 q^{71} +(-445.000 - 770.763i) q^{73} +(-133.500 + 231.229i) q^{75} +(-40.0000 + 69.2820i) q^{79} +(-40.5000 - 70.1481i) q^{81} -108.000 q^{83} +684.000 q^{85} +(81.0000 + 140.296i) q^{87} +(819.000 - 1418.55i) q^{89} +(-168.000 + 290.985i) q^{93} +(228.000 + 394.908i) q^{95} +1010.00 q^{97} +324.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} - 6 q^{5} - 9 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 - 6 * q^5 - 9 * q^9	\( 2 q + 3 q^{3} - 6 q^{5} - 9 q^{9} - 36 q^{11} + 124 q^{13} - 36 q^{15} - 114 q^{17} + 76 q^{19} + 24 q^{23} + 89 q^{25} - 54 q^{27} + 108 q^{29} + 112 q^{31} + 108 q^{33} + 178 q^{37} + 186 q^{39} + 756 q^{41} - 344 q^{43} - 54 q^{45} + 192 q^{47} + 342 q^{51} + 402 q^{53} + 432 q^{55} + 456 q^{57} - 396 q^{59} - 254 q^{61} - 372 q^{65} + 1012 q^{67} + 144 q^{69} + 1680 q^{71} - 890 q^{73} - 267 q^{75} - 80 q^{79} - 81 q^{81} - 216 q^{83} + 1368 q^{85} + 162 q^{87} + 1638 q^{89} - 336 q^{93} + 456 q^{95} + 2020 q^{97} + 648 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 - 6 * q^5 - 9 * q^9 - 36 * q^11 + 124 * q^13 - 36 * q^15 - 114 * q^17 + 76 * q^19 + 24 * q^23 + 89 * q^25 - 54 * q^27 + 108 * q^29 + 112 * q^31 + 108 * q^33 + 178 * q^37 + 186 * q^39 + 756 * q^41 - 344 * q^43 - 54 * q^45 + 192 * q^47 + 342 * q^51 + 402 * q^53 + 432 * q^55 + 456 * q^57 - 396 * q^59 - 254 * q^61 - 372 * q^65 + 1012 * q^67 + 144 * q^69 + 1680 * q^71 - 890 * q^73 - 267 * q^75 - 80 * q^79 - 81 * q^81 - 216 * q^83 + 1368 * q^85 + 162 * q^87 + 1638 * q^89 - 336 * q^93 + 456 * q^95 + 2020 * q^97 + 648 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more