LMFDB - Embedded newform 588.4.i.h.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:	$\Z[a_1, \ldots, a_{5}]$
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.h.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 2.59808i) q^{3} +(7.00000 - 12.1244i) q^{5} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 + 2.59808i) q^{3} +(7.00000 - 12.1244i) q^{5} +(-4.50000 + 7.79423i) q^{9} +(-2.00000 - 3.46410i) q^{11} -54.0000 q^{13} +42.0000 q^{15} +(-7.00000 - 12.1244i) q^{17} +(46.0000 - 79.6743i) q^{19} +(76.0000 - 131.636i) q^{23} +(-35.5000 - 61.4878i) q^{25} -27.0000 q^{27} -106.000 q^{29} +(-72.0000 - 124.708i) q^{31} +(6.00000 - 10.3923i) q^{33} +(-79.0000 + 136.832i) q^{37} +(-81.0000 - 140.296i) q^{39} +390.000 q^{41} -508.000 q^{43} +(63.0000 + 109.119i) q^{45} +(-264.000 + 457.261i) q^{47} +(21.0000 - 36.3731i) q^{51} +(-303.000 - 524.811i) q^{53} -56.0000 q^{55} +276.000 q^{57} +(-182.000 - 315.233i) q^{59} +(339.000 - 587.165i) q^{61} +(-378.000 + 654.715i) q^{65} +(-422.000 - 730.925i) q^{67} +456.000 q^{69} -8.00000 q^{71} +(-211.000 - 365.463i) q^{73} +(106.500 - 184.463i) q^{75} +(-192.000 + 332.554i) q^{79} +(-40.5000 - 70.1481i) q^{81} +548.000 q^{83} -196.000 q^{85} +(-159.000 - 275.396i) q^{87} +(597.000 - 1034.03i) q^{89} +(216.000 - 374.123i) q^{93} +(-644.000 - 1115.44i) q^{95} +1502.00 q^{97} +36.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} + 14 q^{5} - 9 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 + 14 * q^5 - 9 * q^9	$ 2 q + 3 q^{3} + 14 q^{5} - 9 q^{9} - 4 q^{11} - 108 q^{13} + 84 q^{15} - 14 q^{17} + 92 q^{19} + 152 q^{23} - 71 q^{25} - 54 q^{27} - 212 q^{29} - 144 q^{31} + 12 q^{33} - 158 q^{37} - 162 q^{39} + 780 q^{41} - 1016 q^{43} + 126 q^{45} - 528 q^{47} + 42 q^{51} - 606 q^{53} - 112 q^{55} + 552 q^{57} - 364 q^{59} + 678 q^{61} - 756 q^{65} - 844 q^{67} + 912 q^{69} - 16 q^{71} - 422 q^{73} + 213 q^{75} - 384 q^{79} - 81 q^{81} + 1096 q^{83} - 392 q^{85} - 318 q^{87} + 1194 q^{89} + 432 q^{93} - 1288 q^{95} + 3004 q^{97} + 72 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 + 14 * q^5 - 9 * q^9 - 4 * q^11 - 108 * q^13 + 84 * q^15 - 14 * q^17 + 92 * q^19 + 152 * q^23 - 71 * q^25 - 54 * q^27 - 212 * q^29 - 144 * q^31 + 12 * q^33 - 158 * q^37 - 162 * q^39 + 780 * q^41 - 1016 * q^43 + 126 * q^45 - 528 * q^47 + 42 * q^51 - 606 * q^53 - 112 * q^55 + 552 * q^57 - 364 * q^59 + 678 * q^61 - 756 * q^65 - 844 * q^67 + 912 * q^69 - 16 * q^71 - 422 * q^73 + 213 * q^75 - 384 * q^79 - 81 * q^81 + 1096 * q^83 - 392 * q^85 - 318 * q^87 + 1194 * q^89 + 432 * q^93 - 1288 * q^95 + 3004 * q^97 + 72 * 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
$5$	7.00000	−	12.1244i	0.626099	−	1.08444i	−0.362228	−	0.932089i	$-0.617984\pi$
$5$	7.00000	−	12.1244i	0.626099	−	1.08444i	0.988327	−	0.152346i	$-0.0486828\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	−2.00000	−	3.46410i	−0.0548202	−	0.0949514i	0.837313	−	0.546724i	$-0.184125\pi$
$11$	−2.00000	−	3.46410i	−0.0548202	−	0.0949514i	−0.892133	+	0.451772i	$0.850792\pi$
$12$		0			0
$13$	−54.0000			−1.15207			−0.576035	−	0.817425i	$-0.695401\pi$
$13$	−54.0000			−1.15207			−0.576035	+	0.817425i	$0.695401\pi$
$14$		0			0
$15$	42.0000			0.722957
$16$		0			0
$17$	−7.00000	−	12.1244i	−0.0998676	−	0.172976i	0.811762	−	0.583988i	$-0.198509\pi$
$17$	−7.00000	−	12.1244i	−0.0998676	−	0.172976i	−0.911630	+	0.411012i	$0.865175\pi$
$18$		0			0
$19$	46.0000	−	79.6743i	0.555428	−	0.962029i	−0.442443	−	0.896797i	$-0.645888\pi$
$19$	46.0000	−	79.6743i	0.555428	−	0.962029i	0.997870	−	0.0652319i	$-0.0207787\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	76.0000	−	131.636i	0.689004	−	1.19339i	−0.283156	−	0.959074i	$-0.591381\pi$
$23$	76.0000	−	131.636i	0.689004	−	1.19339i	0.972160	−	0.234316i	$-0.0752852\pi$
$24$		0			0
$25$	−35.5000	−	61.4878i	−0.284000	−	0.491902i
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	−106.000			−0.678748			−0.339374	−	0.940651i	$-0.610215\pi$
$29$	−106.000			−0.678748			−0.339374	+	0.940651i	$0.610215\pi$
$30$		0			0
$31$	−72.0000	−	124.708i	−0.417148	−	0.722521i	0.578503	−	0.815680i	$-0.303637\pi$
$31$	−72.0000	−	124.708i	−0.417148	−	0.722521i	−0.995651	+	0.0931587i	$0.970304\pi$
$32$		0			0
$33$	6.00000	−	10.3923i	0.0316505	−	0.0548202i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−79.0000	+	136.832i	−0.351014	+	0.607974i	−0.986427	−	0.164198i	$-0.947496\pi$
$37$	−79.0000	+	136.832i	−0.351014	+	0.607974i	0.635413	+	0.772172i	$0.280830\pi$
$38$		0			0
$39$	−81.0000	−	140.296i	−0.332574	−	0.576035i
$40$		0			0
$41$	390.000			1.48556			0.742778	−	0.669538i	$-0.233508\pi$
$41$	390.000			1.48556			0.742778	+	0.669538i	$0.233508\pi$
$42$		0			0
$43$	−508.000			−1.80161			−0.900806	−	0.434223i	$-0.857023\pi$
$43$	−508.000			−1.80161			−0.900806	+	0.434223i	$0.857023\pi$
$44$		0			0
$45$	63.0000	+	109.119i	0.208700	+	0.361478i
$46$		0			0
$47$	−264.000	+	457.261i	−0.819327	+	1.41912i	0.0868522	+	0.996221i	$0.472319\pi$
$47$	−264.000	+	457.261i	−0.819327	+	1.41912i	−0.906179	+	0.422894i	$0.861014\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	21.0000	−	36.3731i	0.0576586	−	0.0998676i
$52$		0			0
$53$	−303.000	−	524.811i	−0.785288	−	1.36016i	−0.928827	−	0.370514i	$-0.879182\pi$
$53$	−303.000	−	524.811i	−0.785288	−	1.36016i	0.143539	−	0.989645i	$-0.454152\pi$
$54$		0			0
$55$	−56.0000			−0.137292
$56$		0			0
$57$	276.000			0.641353
$58$		0			0
$59$	−182.000	−	315.233i	−0.401600	−	0.695591i	0.592319	−	0.805703i	$-0.298212\pi$
$59$	−182.000	−	315.233i	−0.401600	−	0.695591i	−0.993919	+	0.110112i	$0.964879\pi$
$60$		0			0
$61$	339.000	−	587.165i	0.711549	−	1.23244i	−0.252726	−	0.967538i	$-0.581327\pi$
$61$	339.000	−	587.165i	0.711549	−	1.23244i	0.964275	−	0.264902i	$-0.0853395\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−378.000	+	654.715i	−0.721310	+	1.24935i
$66$		0			0
$67$	−422.000	−	730.925i	−0.769485	−	1.33279i	−0.937842	−	0.347061i	$-0.887180\pi$
$67$	−422.000	−	730.925i	−0.769485	−	1.33279i	0.168357	−	0.985726i	$-0.446154\pi$
$68$		0			0
$69$	456.000			0.795593
$70$		0			0
$71$	−8.00000			−0.0133722			−0.00668609	−	0.999978i	$-0.502128\pi$
$71$	−8.00000			−0.0133722			−0.00668609	+	0.999978i	$0.502128\pi$
$72$		0			0
$73$	−211.000	−	365.463i	−0.338297	−	0.585948i	0.645816	−	0.763494i	$-0.276518\pi$
$73$	−211.000	−	365.463i	−0.338297	−	0.585948i	−0.984113	+	0.177546i	$0.943184\pi$
$74$		0			0
$75$	106.500	−	184.463i	0.163967	−	0.284000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−192.000	+	332.554i	−0.273439	+	0.473610i	−0.969740	−	0.244139i	$-0.921495\pi$
$79$	−192.000	+	332.554i	−0.273439	+	0.473610i	0.696301	+	0.717750i	$0.254828\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	548.000			0.724709			0.362354	−	0.932040i	$-0.381973\pi$
$83$	548.000			0.724709			0.362354	+	0.932040i	$0.381973\pi$
$84$		0			0
$85$	−196.000			−0.250108
$86$		0			0
$87$	−159.000	−	275.396i	−0.195938	−	0.339374i
$88$		0			0
$89$	597.000	−	1034.03i	0.711032	−	1.23154i	−0.253438	−	0.967352i	$-0.581561\pi$
$89$	597.000	−	1034.03i	0.711032	−	1.23154i	0.964470	−	0.264192i	$-0.0851054\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	216.000	−	374.123i	0.240840	−	0.417148i
$94$		0			0
$95$	−644.000	−	1115.44i	−0.695505	−	1.20465i
$96$		0			0
$97$	1502.00			1.57222			0.786108	−	0.618089i	$-0.212093\pi$
$97$	1502.00			1.57222			0.786108	+	0.618089i	$0.212093\pi$
$98$		0			0
$99$	36.0000			0.0365468
$100$		0			0
$101$	199.000	+	344.678i	0.196052	+	0.339572i	0.947245	−	0.320511i	$-0.103855\pi$
$101$	199.000	+	344.678i	0.196052	+	0.339572i	−0.751193	+	0.660083i	$0.770521\pi$
$102$		0			0
$103$	580.000	−	1004.59i	0.554846	−	0.961021i	−0.443070	−	0.896487i	$-0.646111\pi$
$103$	580.000	−	1004.59i	0.554846	−	0.961021i	0.997916	−	0.0645337i	$-0.0205560\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−162.000	+	280.592i	−0.146366	+	0.253513i	−0.929882	−	0.367859i	$-0.880091\pi$
$107$	−162.000	+	280.592i	−0.146366	+	0.253513i	0.783516	+	0.621372i	$0.213424\pi$
$108$		0			0
$109$	469.000	+	812.332i	0.412129	+	0.713828i	0.995122	−	0.0986487i	$-0.0314520\pi$
$109$	469.000	+	812.332i	0.412129	+	0.713828i	−0.582993	+	0.812477i	$0.698119\pi$
$110$		0			0
$111$	−474.000			−0.405316
$112$		0			0
$113$	−622.000			−0.517813			−0.258906	−	0.965902i	$-0.583362\pi$
$113$	−622.000			−0.517813			−0.258906	+	0.965902i	$0.583362\pi$
$114$		0			0
$115$	−1064.00	−	1842.90i	−0.862770	−	1.49436i
$116$		0			0
$117$	243.000	−	420.888i	0.192012	−	0.332574i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	657.500	−	1138.82i	0.493989	−	0.855615i
$122$		0			0
$123$	585.000	+	1013.25i	0.428843	+	0.742778i
$124$		0			0
$125$	756.000			0.540950
$126$		0			0
$127$	1200.00			0.838447			0.419224	−	0.907883i	$-0.362302\pi$
$127$	1200.00			0.838447			0.419224	+	0.907883i	$0.362302\pi$
$128$		0			0
$129$	−762.000	−	1319.82i	−0.520080	−	0.900806i
$130$		0			0
$131$	−698.000	+	1208.97i	−0.465531	+	0.806323i	−0.999225	−	0.0393543i	$-0.987470\pi$
$131$	−698.000	+	1208.97i	−0.465531	+	0.806323i	0.533694	+	0.845677i	$0.320803\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−189.000	+	327.358i	−0.120493	+	0.208700i
$136$		0			0
$137$	−1405.00	−	2433.53i	−0.876184	−	1.51760i	−0.855496	−	0.517810i	$-0.826747\pi$
$137$	−1405.00	−	2433.53i	−0.876184	−	1.51760i	−0.0206885	−	0.999786i	$-0.506586\pi$
$138$		0			0
$139$	−4.00000			−0.00244083			−0.00122042	−	0.999999i	$-0.500388\pi$
$139$	−4.00000			−0.00244083			−0.00122042	+	0.999999i	$0.500388\pi$
$140$		0			0
$141$	−1584.00			−0.946077
$142$		0			0
$143$	108.000	+	187.061i	0.0631567	+	0.109391i
$144$		0			0
$145$	−742.000	+	1285.18i	−0.424964	+	0.736059i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−687.000	+	1189.92i	−0.377726	+	0.654241i	−0.990731	−	0.135838i	$-0.956627\pi$
$149$	−687.000	+	1189.92i	−0.377726	+	0.654241i	0.613005	+	0.790079i	$0.289961\pi$
$150$		0			0
$151$	−1052.00	−	1822.12i	−0.566957	−	0.981999i	−0.996865	−	0.0791258i	$-0.974787\pi$
$151$	−1052.00	−	1822.12i	−0.566957	−	0.981999i	0.429907	−	0.902873i	$-0.358546\pi$
$152$		0			0
$153$	126.000			0.0665784
$154$		0			0
$155$	−2016.00			−1.04470
$156$		0			0
$157$	1603.00	+	2776.48i	0.814862	+	1.41138i	0.909427	+	0.415864i	$0.136521\pi$
$157$	1603.00	+	2776.48i	0.814862	+	1.41138i	−0.0945650	+	0.995519i	$0.530146\pi$
$158$		0			0
$159$	909.000	−	1574.43i	0.453386	−	0.785288i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−166.000	+	287.520i	−0.0797676	+	0.138162i	−0.903150	−	0.429326i	$-0.858751\pi$
$163$	−166.000	+	287.520i	−0.0797676	+	0.138162i	0.823382	+	0.567488i	$0.192084\pi$
$164$		0			0
$165$	−84.0000	−	145.492i	−0.0396327	−	0.0686458i
$166$		0			0
$167$	−1496.00			−0.693197			−0.346599	−	0.938014i	$-0.612663\pi$
$167$	−1496.00			−0.693197			−0.346599	+	0.938014i	$0.612663\pi$
$168$		0			0
$169$	719.000			0.327264
$170$		0			0
$171$	414.000	+	717.069i	0.185143	+	0.320676i
$172$		0			0
$173$	−1661.00	+	2876.94i	−0.729962	+	1.26433i	0.226936	+	0.973910i	$0.427129\pi$
$173$	−1661.00	+	2876.94i	−0.729962	+	1.26433i	−0.956899	+	0.290422i	$0.906204\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	546.000	−	945.700i	0.231864	−	0.401600i
$178$		0			0
$179$	450.000	+	779.423i	0.187903	+	0.325457i	0.944551	−	0.328365i	$-0.106498\pi$
$179$	450.000	+	779.423i	0.187903	+	0.325457i	−0.756648	+	0.653822i	$0.773164\pi$
$180$		0			0
$181$	−1902.00			−0.781075			−0.390537	−	0.920587i	$-0.627711\pi$
$181$	−1902.00			−0.781075			−0.390537	+	0.920587i	$0.627711\pi$
$182$		0			0
$183$	2034.00			0.821626
$184$		0			0
$185$	1106.00	+	1915.65i	0.439539	+	0.761304i
$186$		0			0
$187$	−28.0000	+	48.4974i	−0.0109495	+	0.0189651i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2064.00	+	3574.95i	−0.781915	+	1.35432i	0.148910	+	0.988851i	$0.452424\pi$
$191$	−2064.00	+	3574.95i	−0.781915	+	1.35432i	−0.930825	+	0.365466i	$0.880910\pi$
$192$		0			0
$193$	671.000	+	1162.21i	0.250257	+	0.433458i	0.963597	−	0.267361i	$-0.0861515\pi$
$193$	671.000	+	1162.21i	0.250257	+	0.433458i	−0.713339	+	0.700819i	$0.752818\pi$
$194$		0			0
$195$	−2268.00			−0.832897
$196$		0			0
$197$	−3506.00			−1.26798			−0.633990	−	0.773341i	$-0.718584\pi$
$197$	−3506.00			−1.26798			−0.633990	+	0.773341i	$0.718584\pi$
$198$		0			0
$199$	340.000	+	588.897i	0.121115	+	0.209778i	0.920208	−	0.391430i	$-0.128020\pi$
$199$	340.000	+	588.897i	0.121115	+	0.209778i	−0.799092	+	0.601208i	$0.794686\pi$
$200$		0			0
$201$	1266.00	−	2192.78i	0.444262	−	0.769485i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	2730.00	−	4728.50i	0.930105	−	1.61099i
$206$		0			0
$207$	684.000	+	1184.72i	0.229668	+	0.397797i
$208$		0			0
$209$	−368.000			−0.121795
$210$		0			0
$211$	5372.00			1.75272			0.876360	−	0.481657i	$-0.159965\pi$
$211$	5372.00			1.75272			0.876360	+	0.481657i	$0.159965\pi$
$212$		0			0
$213$	−12.0000	−	20.7846i	−0.00386022	−	0.00668609i
$214$		0			0
$215$	−3556.00	+	6159.17i	−1.12799	+	1.95373i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	633.000	−	1096.39i	0.195316	−	0.338297i
$220$		0			0
$221$	378.000	+	654.715i	0.115054	+	0.199280i
$222$		0			0
$223$	1072.00			0.321912			0.160956	−	0.986962i	$-0.448542\pi$
$223$	1072.00			0.321912			0.160956	+	0.986962i	$0.448542\pi$
$224$		0			0
$225$	639.000			0.189333
$226$		0			0
$227$	−1434.00	−	2483.76i	−0.419286	−	0.726225i	0.576582	−	0.817039i	$-0.304386\pi$
$227$	−1434.00	−	2483.76i	−0.419286	−	0.726225i	−0.995868	+	0.0908148i	$0.971053\pi$
$228$		0			0
$229$	2399.00	−	4155.19i	0.692272	−	1.19905i	−0.278819	−	0.960344i	$-0.589943\pi$
$229$	2399.00	−	4155.19i	0.692272	−	1.19905i	0.971092	−	0.238707i	$-0.0767237\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2563.00	−	4439.25i	0.720634	−	1.24817i	−0.240112	−	0.970745i	$-0.577184\pi$
$233$	2563.00	−	4439.25i	0.720634	−	1.24817i	0.960746	−	0.277429i	$-0.0894825\pi$
$234$		0			0
$235$	3696.00	+	6401.66i	1.02596	+	1.77701i
$236$		0			0
$237$	−1152.00			−0.315740
$238$		0			0
$239$	−528.000			−0.142902			−0.0714508	−	0.997444i	$-0.522763\pi$
$239$	−528.000			−0.142902			−0.0714508	+	0.997444i	$0.522763\pi$
$240$		0			0
$241$	−407.000	−	704.945i	−0.108785	−	0.188421i	0.806493	−	0.591243i	$-0.201363\pi$
$241$	−407.000	−	704.945i	−0.108785	−	0.188421i	−0.915278	+	0.402822i	$0.868029\pi$
$242$		0			0
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−2484.00	+	4302.41i	−0.639891	+	1.10832i
$248$		0			0
$249$	822.000	+	1423.75i	0.209205	+	0.362354i
$250$		0			0
$251$	1932.00			0.485844			0.242922	−	0.970046i	$-0.421894\pi$
$251$	1932.00			0.485844			0.242922	+	0.970046i	$0.421894\pi$
$252$		0			0
$253$	−608.000			−0.151086
$254$		0			0
$255$	−294.000	−	509.223i	−0.0722000	−	0.125054i
$256$		0			0
$257$	−1647.00	+	2852.69i	−0.399755	+	0.692396i	−0.993695	−	0.112113i	$-0.964238\pi$
$257$	−1647.00	+	2852.69i	−0.399755	+	0.692396i	0.593940	+	0.804509i	$0.297571\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	477.000	−	826.188i	0.113125	−	0.195938i
$262$		0			0
$263$	3540.00	+	6131.46i	0.829984	+	1.43757i	0.898050	+	0.439893i	$0.144984\pi$
$263$	3540.00	+	6131.46i	0.829984	+	1.43757i	−0.0680662	+	0.997681i	$0.521683\pi$
$264$		0			0
$265$	−8484.00			−1.96667
$266$		0			0
$267$	3582.00			0.821029
$268$		0			0
$269$	3907.00	+	6767.12i	0.885554	+	1.53382i	0.845078	+	0.534644i	$0.179554\pi$
$269$	3907.00	+	6767.12i	0.885554	+	1.53382i	0.0404764	+	0.999180i	$0.487112\pi$
$270$		0			0
$271$	1584.00	−	2743.57i	0.355060	−	0.614981i	−0.632069	−	0.774912i	$-0.717794\pi$
$271$	1584.00	−	2743.57i	0.355060	−	0.614981i	0.987128	+	0.159931i	$0.0511272\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−142.000	+	245.951i	−0.0311379	+	0.0539324i
$276$		0			0
$277$	3929.00	+	6805.23i	0.852241	+	1.47612i	0.879181	+	0.476488i	$0.158090\pi$
$277$	3929.00	+	6805.23i	0.852241	+	1.47612i	−0.0269403	+	0.999637i	$0.508576\pi$
$278$		0			0
$279$	1296.00			0.278099
$280$		0			0
$281$	6730.00			1.42875			0.714374	−	0.699764i	$-0.246712\pi$
$281$	6730.00			1.42875			0.714374	+	0.699764i	$0.246712\pi$
$282$		0			0
$283$	−1510.00	−	2615.40i	−0.317174	−	0.549361i	0.662723	−	0.748864i	$-0.269401\pi$
$283$	−1510.00	−	2615.40i	−0.317174	−	0.549361i	−0.979897	+	0.199503i	$0.936067\pi$
$284$		0			0
$285$	1932.00	−	3346.32i	0.401550	−	0.695505i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	2358.50	−	4085.04i	0.480053	−	0.831476i
$290$		0			0
$291$	2253.00	+	3902.31i	0.453860	+	0.786108i
$292$		0			0
$293$	6834.00			1.36262			0.681308	−	0.731997i	$-0.261411\pi$
$293$	6834.00			1.36262			0.681308	+	0.731997i	$0.261411\pi$
$294$		0			0
$295$	−5096.00			−1.00576
$296$		0			0
$297$	54.0000	+	93.5307i	0.0105502	+	0.0182734i
$298$		0			0
$299$	−4104.00	+	7108.34i	−0.793781	+	1.37487i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−597.000	+	1034.03i	−0.113191	+	0.196052i
$304$		0			0
$305$	−4746.00	−	8220.31i	−0.891001	−	1.54326i
$306$		0			0
$307$	−2332.00			−0.433532			−0.216766	−	0.976224i	$-0.569551\pi$
$307$	−2332.00			−0.433532			−0.216766	+	0.976224i	$0.569551\pi$
$308$		0			0
$309$	3480.00			0.640681
$310$		0			0
$311$	4420.00	+	7655.66i	0.805901	+	1.39586i	0.915681	+	0.401906i	$0.131652\pi$
$311$	4420.00	+	7655.66i	0.805901	+	1.39586i	−0.109780	+	0.993956i	$0.535015\pi$
$312$		0			0
$313$	−523.000	+	905.863i	−0.0944464	+	0.163586i	−0.909377	−	0.415972i	$-0.863441\pi$
$313$	−523.000	+	905.863i	−0.0944464	+	0.163586i	0.814931	+	0.579558i	$0.196775\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3771.00	+	6531.56i	−0.668140	+	1.15725i	0.310283	+	0.950644i	$0.399576\pi$
$317$	−3771.00	+	6531.56i	−0.668140	+	1.15725i	−0.978424	+	0.206609i	$0.933757\pi$
$318$		0			0
$319$	212.000	+	367.195i	0.0372092	+	0.0644482i
$320$		0			0
$321$	−972.000			−0.169009
$322$		0			0
$323$	−1288.00			−0.221877
$324$		0			0
$325$	1917.00	+	3320.34i	0.327188	+	0.566706i
$326$		0			0
$327$	−1407.00	+	2437.00i	−0.237943	+	0.412129i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1378.00	+	2386.77i	−0.228827	+	0.396340i	−0.957461	−	0.288564i	$-0.906822\pi$
$331$	−1378.00	+	2386.77i	−0.228827	+	0.396340i	0.728634	+	0.684904i	$0.240156\pi$
$332$		0			0
$333$	−711.000	−	1231.49i	−0.117005	−	0.202658i
$334$		0			0
$335$	−11816.0			−1.92710
$336$		0			0
$337$	3954.00			0.639134			0.319567	−	0.947564i	$-0.396463\pi$
$337$	3954.00			0.639134			0.319567	+	0.947564i	$0.396463\pi$
$338$		0			0
$339$	−933.000	−	1616.00i	−0.149480	−	0.258906i
$340$		0			0
$341$	−288.000	+	498.831i	−0.0457363	+	0.0792176i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	3192.00	−	5528.71i	0.498120	−	0.862770i
$346$		0			0
$347$	−3450.00	−	5975.58i	−0.533734	−	0.924454i	−0.999223	−	0.0394010i	$-0.987455\pi$
$347$	−3450.00	−	5975.58i	−0.533734	−	0.924454i	0.465489	−	0.885053i	$-0.345878\pi$
$348$		0			0
$349$	2426.00			0.372094			0.186047	−	0.982541i	$-0.440432\pi$
$349$	2426.00			0.372094			0.186047	+	0.982541i	$0.440432\pi$
$350$		0			0
$351$	1458.00			0.221716
$352$		0			0
$353$	−735.000	−	1273.06i	−0.110822	−	0.191949i	0.805280	−	0.592895i	$-0.202015\pi$
$353$	−735.000	−	1273.06i	−0.110822	−	0.191949i	−0.916102	+	0.400946i	$0.868682\pi$
$354$		0			0
$355$	−56.0000	+	96.9948i	−0.00837231	+	0.0145013i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−3436.00	+	5951.33i	−0.505140	+	0.874928i	0.494843	+	0.868983i	$0.335226\pi$
$359$	−3436.00	+	5951.33i	−0.505140	+	0.874928i	−0.999982	+	0.00594499i	$0.998108\pi$
$360$		0			0
$361$	−802.500	−	1389.97i	−0.117000	−	0.202649i
$362$		0			0
$363$	3945.00			0.570410
$364$		0			0
$365$	−5908.00			−0.847230
$366$		0			0
$367$	−3536.00	−	6124.53i	−0.502937	−	0.871112i	−0.999994	−	0.00339411i	$-0.998920\pi$
$367$	−3536.00	−	6124.53i	−0.502937	−	0.871112i	0.497058	−	0.867717i	$-0.334414\pi$
$368$		0			0
$369$	−1755.00	+	3039.75i	−0.247593	+	0.428843i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	409.000	−	708.409i	0.0567754	−	0.0983378i	−0.836241	−	0.548362i	$-0.815251\pi$
$373$	409.000	−	708.409i	0.0567754	−	0.0983378i	0.893016	+	0.450025i	$0.148585\pi$
$374$		0			0
$375$	1134.00	+	1964.15i	0.156159	+	0.270475i
$376$		0			0
$377$	5724.00			0.781966
$378$		0			0
$379$	−5132.00			−0.695549			−0.347775	−	0.937578i	$-0.613063\pi$
$379$	−5132.00			−0.695549			−0.347775	+	0.937578i	$0.613063\pi$
$380$		0			0
$381$	1800.00	+	3117.69i	0.242039	+	0.419224i
$382$		0			0
$383$	−4288.00	+	7427.03i	−0.572080	+	0.990871i	0.424272	+	0.905535i	$0.360530\pi$
$383$	−4288.00	+	7427.03i	−0.572080	+	0.990871i	−0.996352	+	0.0853367i	$0.972803\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2286.00	−	3959.47i	0.300269	−	0.520080i
$388$		0			0
$389$	1865.00	+	3230.27i	0.243083	+	0.421032i	0.961591	−	0.274487i	$-0.0885080\pi$
$389$	1865.00	+	3230.27i	0.243083	+	0.421032i	−0.718508	+	0.695519i	$0.755175\pi$
$390$		0			0
$391$	−2128.00			−0.275237
$392$		0			0
$393$	−4188.00			−0.537549
$394$		0			0
$395$	2688.00	+	4655.75i	0.342400	+	0.593054i
$396$		0			0
$397$	3339.00	−	5783.32i	0.422115	−	0.731124i	−0.574031	−	0.818833i	$-0.694621\pi$
$397$	3339.00	−	5783.32i	0.422115	−	0.731124i	0.996146	+	0.0877090i	$0.0279546\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1527.00	−	2644.84i	0.190161	−	0.329369i	−0.755142	−	0.655561i	$-0.772432\pi$
$401$	1527.00	−	2644.84i	0.190161	−	0.329369i	0.945304	+	0.326192i	$0.105766\pi$
$402$		0			0
$403$	3888.00	+	6734.21i	0.480583	+	0.832395i
$404$		0			0
$405$	−1134.00			−0.139133
$406$		0			0
$407$	632.000			0.0769707
$408$		0			0
$409$	133.000	+	230.363i	0.0160793	+	0.0278501i	0.873953	−	0.486010i	$-0.161548\pi$
$409$	133.000	+	230.363i	0.0160793	+	0.0278501i	−0.857874	+	0.513860i	$0.828215\pi$
$410$		0			0
$411$	4215.00	−	7300.59i	0.505865	−	0.876184i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	3836.00	−	6644.15i	0.453739	−	0.785900i
$416$		0			0
$417$	−6.00000	−	10.3923i	−0.000704607	−	0.00122042i
$418$		0			0
$419$	−8844.00			−1.03116			−0.515582	−	0.856840i	$-0.672424\pi$
$419$	−8844.00			−1.03116			−0.515582	+	0.856840i	$0.672424\pi$
$420$		0			0
$421$	−4482.00			−0.518858			−0.259429	−	0.965762i	$-0.583534\pi$
$421$	−4482.00			−0.518858			−0.259429	+	0.965762i	$0.583534\pi$
$422$		0			0
$423$	−2376.00	−	4115.35i	−0.273109	−	0.473039i
$424$		0			0
$425$	−497.000	+	860.829i	−0.0567248	+	0.0982502i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−324.000	+	561.184i	−0.0364636	+	0.0631567i
$430$		0			0
$431$	−4968.00	−	8604.83i	−0.555221	−	0.961671i	−0.997886	−	0.0649838i	$-0.979300\pi$
$431$	−4968.00	−	8604.83i	−0.555221	−	0.961671i	0.442666	−	0.896687i	$-0.354033\pi$
$432$		0			0
$433$	11758.0			1.30497			0.652487	−	0.757800i	$-0.273726\pi$
$433$	11758.0			1.30497			0.652487	+	0.757800i	$0.273726\pi$
$434$		0			0
$435$	−4452.00			−0.490706
$436$		0			0
$437$	−6992.00	−	12110.5i	−0.765384	−	1.32568i
$438$		0			0
$439$	−2052.00	+	3554.17i	−0.223090	+	0.386404i	−0.955745	−	0.294197i	$-0.904948\pi$
$439$	−2052.00	+	3554.17i	−0.223090	+	0.386404i	0.732655	+	0.680601i	$0.238281\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4874.00	+	8442.02i	−0.522733	+	0.905400i	0.476917	+	0.878948i	$0.341754\pi$
$443$	−4874.00	+	8442.02i	−0.522733	+	0.905400i	−0.999650	+	0.0264519i	$0.991579\pi$
$444$		0			0
$445$	−8358.00	−	14476.5i	−0.890353	−	1.54214i
$446$		0			0
$447$	−4122.00			−0.436161
$448$		0			0
$449$	−478.000			−0.0502410			−0.0251205	−	0.999684i	$-0.507997\pi$
$449$	−478.000			−0.0502410			−0.0251205	+	0.999684i	$0.507997\pi$
$450$		0			0
$451$	−780.000	−	1351.00i	−0.0814385	−	0.141056i
$452$		0			0
$453$	3156.00	−	5466.35i	0.327333	−	0.566957i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	5587.00	−	9676.97i	0.571879	−	0.990524i	−0.424494	−	0.905431i	$-0.639548\pi$
$457$	5587.00	−	9676.97i	0.571879	−	0.990524i	0.996373	−	0.0850931i	$-0.0271188\pi$
$458$		0			0
$459$	189.000	+	327.358i	0.0192195	+	0.0332892i
$460$		0			0
$461$	11674.0			1.17942			0.589710	−	0.807615i	$-0.299242\pi$
$461$	11674.0			1.17942			0.589710	+	0.807615i	$0.299242\pi$
$462$		0			0
$463$	10528.0			1.05676			0.528378	−	0.849009i	$-0.322801\pi$
$463$	10528.0			1.05676			0.528378	+	0.849009i	$0.322801\pi$
$464$		0			0
$465$	−3024.00	−	5237.72i	−0.301580	−	0.522352i
$466$		0			0
$467$	8302.00	−	14379.5i	0.822635	−	1.42485i	−0.0810777	−	0.996708i	$-0.525836\pi$
$467$	8302.00	−	14379.5i	0.822635	−	1.42485i	0.903713	−	0.428139i	$-0.140830\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−4809.00	+	8329.43i	−0.470461	+	0.814862i
$472$		0			0
$473$	1016.00	+	1759.76i	0.0987648	+	0.171066i
$474$		0			0
$475$	−6532.00			−0.630966
$476$		0			0
$477$	5454.00			0.523525
$478$		0			0
$479$	−4288.00	−	7427.03i	−0.409027	−	0.708455i	0.585754	−	0.810489i	$-0.300798\pi$
$479$	−4288.00	−	7427.03i	−0.409027	−	0.708455i	−0.994781	+	0.102034i	$0.967465\pi$
$480$		0			0
$481$	4266.00	−	7388.93i	0.404393	−	0.700429i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	10514.0	−	18210.8i	0.984363	−	1.70497i
$486$		0			0
$487$	−4852.00	−	8403.91i	−0.451468	−	0.781966i	0.547009	−	0.837127i	$-0.315766\pi$
$487$	−4852.00	−	8403.91i	−0.451468	−	0.781966i	−0.998478	+	0.0551605i	$0.982433\pi$
$488$		0			0
$489$	−996.000			−0.0921077
$490$		0			0
$491$	−4092.00			−0.376109			−0.188054	−	0.982159i	$-0.560218\pi$
$491$	−4092.00			−0.376109			−0.188054	+	0.982159i	$0.560218\pi$
$492$		0			0
$493$	742.000	+	1285.18i	0.0677850	+	0.117407i
$494$		0			0
$495$	252.000	−	436.477i	0.0228819	−	0.0396327i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−8942.00	+	15488.0i	−0.802202	+	1.38945i	0.115961	+	0.993254i	$0.463005\pi$
$499$	−8942.00	+	15488.0i	−0.802202	+	1.38945i	−0.918164	+	0.396201i	$0.870328\pi$
$500$		0			0
$501$	−2244.00	−	3886.72i	−0.200109	−	0.346599i
$502$		0			0
$503$	7704.00			0.682911			0.341456	−	0.939898i	$-0.389080\pi$
$503$	7704.00			0.682911			0.341456	+	0.939898i	$0.389080\pi$
$504$		0			0
$505$	5572.00			0.490992
$506$		0			0
$507$	1078.50	+	1868.02i	0.0944731	+	0.163632i
$508$		0			0
$509$	7179.00	−	12434.4i	0.625154	−	1.08280i	−0.363357	−	0.931650i	$-0.618369\pi$
$509$	7179.00	−	12434.4i	0.625154	−	1.08280i	0.988511	−	0.151149i	$-0.0482973\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−1242.00	+	2151.21i	−0.106892	+	0.185143i
$514$		0			0
$515$	−8120.00	−	14064.3i	−0.694777	−	1.20339i
$516$		0			0
$517$	2112.00			0.179663
$518$		0			0
$519$	−9966.00			−0.842888
$520$		0			0
$521$	2541.00	+	4401.14i	0.213672	+	0.370091i	0.952861	−	0.303407i	$-0.0981242\pi$
$521$	2541.00	+	4401.14i	0.213672	+	0.370091i	−0.739189	+	0.673498i	$0.764791\pi$
$522$		0			0
$523$	−878.000	+	1520.74i	−0.0734078	+	0.127146i	−0.900393	−	0.435078i	$-0.856721\pi$
$523$	−878.000	+	1520.74i	−0.0734078	+	0.127146i	0.826985	+	0.562224i	$0.190054\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1008.00	+	1745.91i	−0.0833191	+	0.144313i
$528$		0			0
$529$	−5468.50	−	9471.72i	−0.449453	−	0.778476i
$530$		0			0
$531$	3276.00			0.267733
$532$		0			0
$533$	−21060.0			−1.71146
$534$		0			0
$535$	2268.00	+	3928.29i	0.183279	+	0.317448i
$536$		0			0
$537$	−1350.00	+	2338.27i	−0.108486	+	0.187903i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−8115.00	+	14055.6i	−0.644900	+	1.11700i	0.339424	+	0.940633i	$0.389768\pi$
$541$	−8115.00	+	14055.6i	−0.644900	+	1.11700i	−0.984325	+	0.176367i	$0.943566\pi$
$542$		0			0
$543$	−2853.00	−	4941.54i	−0.225477	−	0.390537i
$544$		0			0
$545$	13132.0			1.03213
$546$		0			0
$547$	17676.0			1.38167			0.690833	−	0.723014i	$-0.257244\pi$
$547$	17676.0			1.38167			0.690833	+	0.723014i	$0.257244\pi$
$548$		0			0
$549$	3051.00	+	5284.49i	0.237183	+	0.410813i
$550$		0			0
$551$	−4876.00	+	8445.48i	−0.376996	+	0.652976i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−3318.00	+	5746.94i	−0.253768	+	0.439539i
$556$		0			0
$557$	6125.00	+	10608.8i	0.465933	+	0.807019i	0.999243	−	0.0389004i	$-0.0123855\pi$
$557$	6125.00	+	10608.8i	0.465933	+	0.807019i	−0.533310	+	0.845920i	$0.679052\pi$
$558$		0			0
$559$	27432.0			2.07558
$560$		0			0
$561$	−168.000			−0.0126434
$562$		0			0
$563$	−5026.00	−	8705.29i	−0.376236	−	0.651659i	0.614276	−	0.789092i	$-0.289448\pi$
$563$	−5026.00	−	8705.29i	−0.376236	−	0.651659i	−0.990511	+	0.137432i	$0.956115\pi$
$564$		0			0
$565$	−4354.00	+	7541.35i	−0.324202	+	0.561534i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−12837.0	+	22234.3i	−0.945791	+	1.63816i	−0.191631	+	0.981467i	$0.561378\pi$
$569$	−12837.0	+	22234.3i	−0.945791	+	1.63816i	−0.754160	+	0.656691i	$0.771956\pi$
$570$		0			0
$571$	−1866.00	−	3232.01i	−0.136759	−	0.236874i	0.789509	−	0.613739i	$-0.210335\pi$
$571$	−1866.00	−	3232.01i	−0.136759	−	0.236874i	−0.926268	+	0.376865i	$0.877002\pi$
$572$		0			0
$573$	−12384.0			−0.902878
$574$		0			0
$575$	−10792.0			−0.782709
$576$		0			0
$577$	−607.000	−	1051.35i	−0.0437950	−	0.0758552i	0.843297	−	0.537448i	$-0.180612\pi$
$577$	−607.000	−	1051.35i	−0.0437950	−	0.0758552i	−0.887092	+	0.461593i	$0.847278\pi$
$578$		0			0
$579$	−2013.00	+	3486.62i	−0.144486	+	0.250257i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1212.00	+	2099.25i	−0.0860993	+	0.149128i
$584$		0			0
$585$	−3402.00	−	5892.44i	−0.240437	−	0.416448i
$586$		0			0
$587$	−7108.00			−0.499793			−0.249897	−	0.968273i	$-0.580397\pi$
$587$	−7108.00			−0.499793			−0.249897	+	0.968273i	$0.580397\pi$
$588$		0			0
$589$	−13248.0			−0.926782
$590$		0			0
$591$	−5259.00	−	9108.86i	−0.366034	−	0.633990i
$592$		0			0
$593$	3081.00	−	5336.45i	0.213358	−	0.369548i	−0.739405	−	0.673261i	$-0.764893\pi$
$593$	3081.00	−	5336.45i	0.213358	−	0.369548i	0.952763	+	0.303713i	$0.0982265\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1020.00	+	1766.69i	−0.0699260	+	0.121115i
$598$		0			0
$599$	−1236.00	−	2140.81i	−0.0843098	−	0.146029i	0.820787	−	0.571234i	$-0.193535\pi$
$599$	−1236.00	−	2140.81i	−0.0843098	−	0.146029i	−0.905097	+	0.425205i	$0.860202\pi$
$600$		0			0
$601$	13750.0			0.933235			0.466617	−	0.884459i	$-0.345472\pi$
$601$	13750.0			0.933235			0.466617	+	0.884459i	$0.345472\pi$
$602$		0			0
$603$	7596.00			0.512990
$604$		0			0
$605$	−9205.00	−	15943.5i	−0.618573	−	1.07140i
$606$		0			0
$607$	−5688.00	+	9851.90i	−0.380344	+	0.658775i	−0.991111	−	0.133035i	$-0.957528\pi$
$607$	−5688.00	+	9851.90i	−0.380344	+	0.658775i	0.610767	+	0.791810i	$0.290861\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	14256.0	−	24692.1i	0.943921	−	1.63492i
$612$		0			0
$613$	−10191.0	−	17651.3i	−0.671469	−	1.16302i	−0.977488	−	0.210993i	$-0.932330\pi$
$613$	−10191.0	−	17651.3i	−0.671469	−	1.16302i	0.306018	−	0.952026i	$-0.401003\pi$
$614$		0			0
$615$	16380.0			1.07399
$616$		0			0
$617$	21178.0			1.38184			0.690919	−	0.722932i	$-0.257206\pi$
$617$	21178.0			1.38184			0.690919	+	0.722932i	$0.257206\pi$
$618$		0			0
$619$	−2350.00	−	4070.32i	−0.152592	−	0.264297i	0.779588	−	0.626293i	$-0.215429\pi$
$619$	−2350.00	−	4070.32i	−0.152592	−	0.264297i	−0.932180	+	0.361996i	$0.882095\pi$
$620$		0			0
$621$	−2052.00	+	3554.17i	−0.132599	+	0.229668i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	9729.50	−	16852.0i	0.622688	−	1.07853i
$626$		0			0
$627$	−552.000	−	956.092i	−0.0351591	−	0.0608973i
$628$		0			0
$629$	2212.00			0.140220
$630$		0			0
$631$	−21736.0			−1.37131			−0.685655	−	0.727927i	$-0.740484\pi$
$631$	−21736.0			−1.37131			−0.685655	+	0.727927i	$0.740484\pi$
$632$		0			0
$633$	8058.00	+	13956.9i	0.505966	+	0.876360i
$634$		0			0
$635$	8400.00	−	14549.2i	0.524951	−	0.909242i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	36.0000	−	62.3538i	0.00222870	−	0.00386022i
$640$		0			0
$641$	6511.00	+	11277.4i	0.401200	+	0.694898i	0.993871	−	0.110546i	$-0.0352600\pi$
$641$	6511.00	+	11277.4i	0.401200	+	0.694898i	−0.592671	+	0.805444i	$0.701927\pi$
$642$		0			0
$643$	−3308.00			−0.202885			−0.101442	−	0.994841i	$-0.532346\pi$
$643$	−3308.00			−0.202885			−0.101442	+	0.994841i	$0.532346\pi$
$644$		0			0
$645$	−21336.0			−1.30249
$646$		0			0
$647$	−6900.00	−	11951.2i	−0.419269	−	0.726195i	0.576597	−	0.817029i	$-0.304380\pi$
$647$	−6900.00	−	11951.2i	−0.419269	−	0.726195i	−0.995866	+	0.0908335i	$0.971047\pi$
$648$		0			0
$649$	−728.000	+	1260.93i	−0.0440316	+	0.0762649i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1341.00	−	2322.68i	0.0803635	−	0.139194i	−0.823043	−	0.567980i	$-0.807725\pi$
$653$	1341.00	−	2322.68i	0.0803635	−	0.139194i	0.903406	+	0.428786i	$0.141059\pi$
$654$		0			0
$655$	9772.00	+	16925.6i	0.582937	+	1.00968i
$656$		0			0
$657$	3798.00			0.225531
$658$		0			0
$659$	23836.0			1.40898			0.704491	−	0.709713i	$-0.251175\pi$
$659$	23836.0			1.40898			0.704491	+	0.709713i	$0.251175\pi$
$660$		0			0
$661$	−5641.00	−	9770.50i	−0.331936	−	0.574929i	0.650956	−	0.759116i	$-0.274368\pi$
$661$	−5641.00	−	9770.50i	−0.331936	−	0.574929i	−0.982891	+	0.184186i	$0.941035\pi$
$662$		0			0
$663$	−1134.00	+	1964.15i	−0.0664267	+	0.115054i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−8056.00	+	13953.4i	−0.467661	+	0.810012i
$668$		0			0
$669$	1608.00	+	2785.14i	0.0929281	+	0.160956i
$670$		0			0
$671$	−2712.00			−0.156029
$672$		0			0
$673$	−13726.0			−0.786179			−0.393089	−	0.919500i	$-0.628594\pi$
$673$	−13726.0			−0.786179			−0.393089	+	0.919500i	$0.628594\pi$
$674$		0			0
$675$	958.500	+	1660.17i	0.0546558	+	0.0946667i
$676$		0			0
$677$	2487.00	−	4307.61i	0.141186	−	0.244542i	−0.786757	−	0.617263i	$-0.788242\pi$
$677$	2487.00	−	4307.61i	0.141186	−	0.244542i	0.927944	+	0.372721i	$0.121575\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	4302.00	−	7451.28i	0.242075	−	0.419286i
$682$		0			0
$683$	4494.00	+	7783.84i	0.251769	+	0.436076i	0.964013	−	0.265855i	$-0.0856544\pi$
$683$	4494.00	+	7783.84i	0.251769	+	0.436076i	−0.712244	+	0.701932i	$0.752321\pi$
$684$		0			0
$685$	−39340.0			−2.19431
$686$		0			0
$687$	14394.0			0.799367
$688$		0			0
$689$	16362.0	+	28339.8i	0.904706	+	1.56700i
$690$		0			0
$691$	5086.00	−	8809.21i	0.280001	−	0.484976i	−0.691384	−	0.722488i	$-0.742999\pi$
$691$	5086.00	−	8809.21i	0.280001	−	0.484976i	0.971385	+	0.237512i	$0.0763319\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−28.0000	+	48.4974i	−0.00152820	+	0.00264692i
$696$		0			0
$697$	−2730.00	−	4728.50i	−0.148359	−	0.256965i
$698$		0			0
$699$	15378.0			0.832116
$700$		0			0
$701$	27446.0			1.47877			0.739387	−	0.673280i	$-0.235115\pi$
$701$	27446.0			1.47877			0.739387	+	0.673280i	$0.235115\pi$
$702$		0			0
$703$	7268.00	+	12588.5i	0.389926	+	0.675371i
$704$		0			0
$705$	−11088.0	+	19205.0i	−0.592338	+	1.02596i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1999.00	+	3462.37i	−0.105887	+	0.183402i	−0.914100	−	0.405488i	$-0.867102\pi$
$709$	−1999.00	+	3462.37i	−0.105887	+	0.183402i	0.808213	+	0.588890i	$0.200435\pi$
$710$		0			0
$711$	−1728.00	−	2992.98i	−0.0911464	−	0.157870i
$712$		0			0
$713$	−21888.0			−1.14967
$714$		0			0
$715$	3024.00			0.158169
$716$		0			0
$717$	−792.000	−	1371.78i	−0.0412521	−	0.0714508i
$718$		0			0
$719$	12936.0	−	22405.8i	0.670976	−	1.16216i	−0.306652	−	0.951822i	$-0.599209\pi$
$719$	12936.0	−	22405.8i	0.670976	−	1.16216i	0.977628	−	0.210342i	$-0.0674578\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	1221.00	−	2114.83i	0.0628070	−	0.108785i
$724$		0			0
$725$	3763.00	+	6517.71i	0.192765	+	0.333878i
$726$		0			0
$727$	−12088.0			−0.616670			−0.308335	−	0.951278i	$-0.599772\pi$
$727$	−12088.0			−0.616670			−0.308335	+	0.951278i	$0.599772\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	3556.00	+	6159.17i	0.179923	+	0.311635i
$732$		0			0
$733$	3987.00	−	6905.69i	0.200905	−	0.347977i	−0.747915	−	0.663794i	$-0.768945\pi$
$733$	3987.00	−	6905.69i	0.200905	−	0.347977i	0.948820	+	0.315817i	$0.102278\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1688.00	+	2923.70i	−0.0843667	+	0.146127i
$738$		0			0
$739$	15882.0	+	27508.4i	0.790567	+	1.36930i	0.925616	+	0.378463i	$0.123547\pi$
$739$	15882.0	+	27508.4i	0.790567	+	1.36930i	−0.135050	+	0.990839i	$0.543119\pi$
$740$		0			0
$741$	−14904.0			−0.738883
$742$		0			0
$743$	888.000			0.0438460			0.0219230	−	0.999760i	$-0.493021\pi$
$743$	888.000			0.0438460			0.0219230	+	0.999760i	$0.493021\pi$
$744$		0			0
$745$	9618.00	+	16658.9i	0.472988	+	0.819240i
$746$		0			0
$747$	−2466.00	+	4271.24i	−0.120785	+	0.209205i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	17328.0	−	30013.0i	0.841954	−	1.45831i	−0.0462858	−	0.998928i	$-0.514738\pi$
$751$	17328.0	−	30013.0i	0.841954	−	1.45831i	0.888240	−	0.459379i	$-0.151928\pi$
$752$		0			0
$753$	2898.00	+	5019.48i	0.140251	+	0.242922i
$754$		0			0
$755$	−29456.0			−1.41989
$756$		0			0
$757$	−22866.0			−1.09786			−0.548929	−	0.835869i	$-0.684964\pi$
$757$	−22866.0			−1.09786			−0.548929	+	0.835869i	$0.684964\pi$
$758$		0			0
$759$	−912.000	−	1579.63i	−0.0436146	−	0.0755428i
$760$		0			0
$761$	11285.0	−	19546.2i	0.537557	−	0.931076i	−0.461478	−	0.887152i	$-0.652681\pi$
$761$	11285.0	−	19546.2i	0.537557	−	0.931076i	0.999035	−	0.0439244i	$-0.0139861\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	882.000	−	1527.67i	0.0416847	−	0.0722000i
$766$		0			0
$767$	9828.00	+	17022.6i	0.462671	+	0.801369i
$768$		0			0
$769$	1790.00			0.0839389			0.0419695	−	0.999119i	$-0.486637\pi$
$769$	1790.00			0.0839389			0.0419695	+	0.999119i	$0.486637\pi$
$770$		0			0
$771$	−9882.00			−0.461597
$772$		0			0
$773$	1495.00	+	2589.42i	0.0695620	+	0.120485i	0.898709	−	0.438546i	$-0.144507\pi$
$773$	1495.00	+	2589.42i	0.0695620	+	0.120485i	−0.829147	+	0.559031i	$0.811173\pi$
$774$		0			0
$775$	−5112.00	+	8854.24i	−0.236940	+	0.410392i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	17940.0	−	31073.0i	0.825118	−	1.42915i
$780$		0			0
$781$	16.0000	+	27.7128i	0.000733067	+	0.00126971i
$782$		0			0
$783$	2862.00			0.130625
$784$		0			0
$785$	44884.0			2.04074
$786$		0			0
$787$	−15378.0	−	26635.5i	−0.696527	−	1.20642i	−0.969663	−	0.244444i	$-0.921394\pi$
$787$	−15378.0	−	26635.5i	−0.696527	−	1.20642i	0.273137	−	0.961975i	$-0.411939\pi$
$788$		0			0
$789$	−10620.0	+	18394.4i	−0.479191	+	0.829984i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−18306.0	+	31706.9i	−0.819754	+	1.41986i
$794$		0			0
$795$	−12726.0	−	22042.1i	−0.567729	−	0.983336i
$796$		0			0
$797$	−15126.0			−0.672259			−0.336129	−	0.941816i	$-0.609118\pi$
$797$	−15126.0			−0.672259			−0.336129	+	0.941816i	$0.609118\pi$
$798$		0			0
$799$	7392.00			0.327297
$800$		0			0
$801$	5373.00	+	9306.31i	0.237011	+	0.410515i
$802$		0			0
$803$	−844.000	+	1461.85i	−0.0370911	+	0.0642436i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−11721.0	+	20301.4i	−0.511275	+	0.885554i
$808$		0			0
$809$	3251.00	+	5630.90i	0.141284	+	0.244712i	0.927981	−	0.372629i	$-0.121543\pi$
$809$	3251.00	+	5630.90i	0.141284	+	0.244712i	−0.786696	+	0.617340i	$0.788210\pi$
$810$		0			0
$811$	8252.00			0.357296			0.178648	−	0.983913i	$-0.442828\pi$
$811$	8252.00			0.357296			0.178648	+	0.983913i	$0.442828\pi$
$812$		0			0
$813$	9504.00			0.409987
$814$		0			0
$815$	2324.00	+	4025.29i	0.0998849	+	0.173006i
$816$		0			0
$817$	−23368.0	+	40474.6i	−1.00066	+	1.73320i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	10993.0	−	19040.4i	0.467306	−	0.809398i	−0.531996	−	0.846747i	$-0.678558\pi$
$821$	10993.0	−	19040.4i	0.467306	−	0.809398i	0.999302	+	0.0373488i	$0.0118913\pi$
$822$		0			0
$823$	−1868.00	−	3235.47i	−0.0791183	−	0.137037i	0.823751	−	0.566951i	$-0.191877\pi$
$823$	−1868.00	−	3235.47i	−0.0791183	−	0.137037i	−0.902870	+	0.429914i	$0.858544\pi$
$824$		0			0
$825$	−852.000			−0.0359549
$826$		0			0
$827$	−23820.0			−1.00158			−0.500788	−	0.865570i	$-0.666956\pi$
$827$	−23820.0			−1.00158			−0.500788	+	0.865570i	$0.666956\pi$
$828$		0			0
$829$	3971.00	+	6877.97i	0.166367	+	0.288157i	0.937140	−	0.348954i	$-0.113463\pi$
$829$	3971.00	+	6877.97i	0.166367	+	0.288157i	−0.770773	+	0.637110i	$0.780130\pi$
$830$		0			0
$831$	−11787.0	+	20415.7i	−0.492042	+	0.852241i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−10472.0	+	18138.0i	−0.434010	+	0.751728i
$836$		0			0
$837$	1944.00	+	3367.11i	0.0802801	+	0.139049i
$838$		0			0
$839$	−21016.0			−0.864783			−0.432391	−	0.901686i	$-0.642330\pi$
$839$	−21016.0			−0.864783			−0.432391	+	0.901686i	$0.642330\pi$
$840$		0			0
$841$	−13153.0			−0.539301
$842$		0			0
$843$	10095.0	+	17485.1i	0.412444	+	0.714374i
$844$		0			0
$845$	5033.00	−	8717.41i	0.204900	−	0.354897i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	4530.00	−	7846.19i	0.183120	−	0.317174i
$850$		0			0
$851$	12008.0	+	20798.5i	0.483700	+	0.837793i
$852$		0			0
$853$	−24878.0			−0.998601			−0.499300	−	0.866429i	$-0.666410\pi$
$853$	−24878.0			−0.998601			−0.499300	+	0.866429i	$0.666410\pi$
$854$		0			0
$855$	11592.0			0.463670
$856$		0			0
$857$	−3195.00	−	5533.90i	−0.127350	−	0.220577i	0.795299	−	0.606217i	$-0.207314\pi$
$857$	−3195.00	−	5533.90i	−0.127350	−	0.220577i	−0.922649	+	0.385640i	$0.873981\pi$
$858$		0			0
$859$	−23222.0	+	40221.7i	−0.922380	+	1.59761i	−0.126658	+	0.991946i	$0.540425\pi$
$859$	−23222.0	+	40221.7i	−0.922380	+	1.59761i	−0.795722	+	0.605663i	$0.792908\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	12704.0	−	22004.0i	0.501100	−	0.867930i	−0.498899	−	0.866660i	$-0.666262\pi$
$863$	12704.0	−	22004.0i	0.501100	−	0.867930i	0.999999	−	0.00127049i	$-0.000404409\pi$
$864$		0			0
$865$	23254.0	+	40277.1i	0.914057	+	1.58319i
$866$		0			0
$867$	14151.0			0.554317
$868$		0			0
$869$	1536.00			0.0599600
$870$		0			0
$871$	22788.0	+	39470.0i	0.886500	+	1.53546i
$872$		0			0
$873$	−6759.00	+	11706.9i	−0.262036	+	0.453860i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−539.000	+	933.575i	−0.0207534	+	0.0359460i	−0.876216	−	0.481919i	$-0.839940\pi$
$877$	−539.000	+	933.575i	−0.0207534	+	0.0359460i	0.855462	+	0.517865i	$0.173273\pi$
$878$		0			0
$879$	10251.0	+	17755.3i	0.393353	+	0.681308i
$880$		0			0
$881$	45006.0			1.72110			0.860551	−	0.509364i	$-0.170119\pi$
$881$	45006.0			1.72110			0.860551	+	0.509364i	$0.170119\pi$
$882$		0			0
$883$	4028.00			0.153514			0.0767571	−	0.997050i	$-0.475543\pi$
$883$	4028.00			0.153514			0.0767571	+	0.997050i	$0.475543\pi$
$884$		0			0
$885$	−7644.00	−	13239.8i	−0.290339	−	0.502882i
$886$		0			0
$887$	−14652.0	+	25378.0i	−0.554640	+	0.960665i	0.443291	+	0.896378i	$0.353811\pi$
$887$	−14652.0	+	25378.0i	−0.554640	+	0.960665i	−0.997931	+	0.0642876i	$0.979523\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−162.000	+	280.592i	−0.00609114	+	0.0105502i
$892$		0			0
$893$	24288.0	+	42068.1i	0.910153	+	1.57643i
$894$		0			0
$895$	12600.0			0.470583
$896$		0			0
$897$	−24624.0			−0.916579
$898$		0			0
$899$	7632.00	+	13219.0i	0.283138	+	0.490410i
$900$		0			0
$901$	−4242.00	+	7347.36i	−0.156850	+	0.271672i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−13314.0	+	23060.5i	−0.489030	+	0.847025i
$906$		0			0
$907$	−25458.0	−	44094.5i	−0.931995	−	1.61426i	−0.779908	−	0.625895i	$-0.784734\pi$
$907$	−25458.0	−	44094.5i	−0.931995	−	1.61426i	−0.152087	−	0.988367i	$-0.548599\pi$
$908$		0			0
$909$	−3582.00			−0.130701
$910$		0			0
$911$	−24432.0			−0.888549			−0.444275	−	0.895891i	$-0.646539\pi$
$911$	−24432.0			−0.888549			−0.444275	+	0.895891i	$0.646539\pi$
$912$		0			0
$913$	−1096.00	−	1898.33i	−0.0397287	−	0.0688121i
$914$		0			0
$915$	14238.0	−	24660.9i	0.514419	−	0.891001i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	10180.0	−	17632.3i	0.365405	−	0.632900i	−0.623436	−	0.781874i	$-0.714264\pi$
$919$	10180.0	−	17632.3i	0.365405	−	0.632900i	0.988841	+	0.148974i	$0.0475972\pi$
$920$		0			0
$921$	−3498.00	−	6058.71i	−0.125150	−	0.216766i
$922$		0			0
$923$	432.000			0.0154057
$924$		0			0
$925$	11218.0			0.398752
$926$		0			0
$927$	5220.00	+	9041.31i	0.184949	+	0.320340i
$928$		0			0
$929$	11601.0	−	20093.5i	0.409706	−	0.709631i	−0.585151	−	0.810924i	$-0.698965\pi$
$929$	11601.0	−	20093.5i	0.409706	−	0.709631i	0.994857	+	0.101293i	$0.0322981\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−13260.0	+	22967.0i	−0.465287	+	0.805901i
$934$		0			0
$935$	392.000	+	678.964i	0.0137110	+	0.0237481i
$936$		0			0
$937$	1990.00			0.0693815			0.0346908	−	0.999398i	$-0.488955\pi$
$937$	1990.00			0.0693815			0.0346908	+	0.999398i	$0.488955\pi$
$938$		0			0
$939$	−3138.00			−0.109057
$940$		0			0
$941$	−25565.0	−	44279.9i	−0.885648	−	1.53399i	−0.844969	−	0.534816i	$-0.820381\pi$
$941$	−25565.0	−	44279.9i	−0.885648	−	1.53399i	−0.0406798	−	0.999172i	$-0.512952\pi$
$942$		0			0
$943$	29640.0	−	51338.0i	1.02355	−	1.77285i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	23522.0	−	40741.3i	0.807141	−	1.39801i	−0.107696	−	0.994184i	$-0.534347\pi$
$947$	23522.0	−	40741.3i	0.807141	−	1.39801i	0.914836	−	0.403825i	$-0.132319\pi$
$948$		0			0
$949$	11394.0	+	19735.0i	0.389742	+	0.675052i
$950$		0			0
$951$	−22626.0			−0.771502
$952$		0			0
$953$	46858.0			1.59274			0.796369	−	0.604811i	$-0.206751\pi$
$953$	46858.0			1.59274			0.796369	+	0.604811i	$0.206751\pi$
$954$		0			0
$955$	28896.0	+	50049.3i	0.979113	+	1.69587i
$956$		0			0
$957$	−636.000	+	1101.58i	−0.0214827	+	0.0372092i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	4527.50	−	7841.86i	0.151975	−	0.263229i
$962$		0			0
$963$	−1458.00	−	2525.33i	−0.0487886	−	0.0845043i
$964$		0			0
$965$	18788.0			0.626743
$966$		0			0
$967$	30632.0			1.01867			0.509337	−	0.860567i	$-0.329890\pi$
$967$	30632.0			1.01867			0.509337	+	0.860567i	$0.329890\pi$
$968$		0			0
$969$	−1932.00	−	3346.32i	−0.0640503	−	0.110938i
$970$		0			0
$971$	−1902.00	+	3294.36i	−0.0628611	+	0.108879i	−0.895743	−	0.444572i	$-0.853356\pi$
$971$	−1902.00	+	3294.36i	−0.0628611	+	0.108879i	0.832882	+	0.553450i	$0.186689\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−5751.00	+	9961.02i	−0.188902	+	0.327188i
$976$		0			0
$977$	24663.0	+	42717.6i	0.807614	+	1.39883i	0.914512	+	0.404559i	$0.132575\pi$
$977$	24663.0	+	42717.6i	0.807614	+	1.39883i	−0.106897	+	0.994270i	$0.534092\pi$
$978$		0			0
$979$	−4776.00			−0.155916
$980$		0			0
$981$	−8442.00			−0.274753
$982$		0			0
$983$	5556.00	+	9623.27i	0.180274	+	0.312243i	0.941974	−	0.335687i	$-0.108968\pi$
$983$	5556.00	+	9623.27i	0.180274	+	0.312243i	−0.761700	+	0.647930i	$0.775635\pi$
$984$		0			0
$985$	−24542.0	+	42508.0i	−0.793881	+	1.37504i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−38608.0	+	66871.0i	−1.24132	+	2.15002i
$990$		0			0
$991$	−6808.00	−	11791.8i	−0.218227	−	0.377981i	0.736039	−	0.676939i	$-0.236694\pi$
$991$	−6808.00	−	11791.8i	−0.218227	−	0.377981i	−0.954266	+	0.298959i	$0.903361\pi$
$992$		0			0
$993$	−8268.00			−0.264227
$994$		0			0
$995$	9520.00			0.303321
$996$		0			0
$997$	−28337.0	−	49081.1i	−0.900142	−	1.55909i	−0.827308	−	0.561748i	$-0.810129\pi$
$997$	−28337.0	−	49081.1i	−0.900142	−	1.55909i	−0.0728338	−	0.997344i	$-0.523204\pi$
$998$		0			0
$999$	2133.00	−	3694.46i	0.0675527	−	0.117005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.4.i.h.373.1		2
3.2	odd	2		1764.4.k.c.1549.1		2
7.2	even	3		588.4.a.a.1.1		1
7.3	odd	6		588.4.i.a.361.1		2
7.4	even	3	inner	588.4.i.h.361.1		2
7.5	odd	6		84.4.a.b.1.1	✓	1
7.6	odd	2		588.4.i.a.373.1		2
21.2	odd	6		1764.4.a.l.1.1		1
21.5	even	6		252.4.a.a.1.1		1
21.11	odd	6		1764.4.k.c.361.1		2
21.17	even	6		1764.4.k.n.361.1		2
21.20	even	2		1764.4.k.n.1549.1		2
28.19	even	6		336.4.a.e.1.1		1
28.23	odd	6		2352.4.a.v.1.1		1
35.12	even	12		2100.4.k.g.1849.1		2
35.19	odd	6		2100.4.a.g.1.1		1
35.33	even	12		2100.4.k.g.1849.2		2
56.5	odd	6		1344.4.a.b.1.1		1
56.19	even	6		1344.4.a.p.1.1		1
84.47	odd	6		1008.4.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.a.b.1.1	✓	1	7.5	odd	6
252.4.a.a.1.1		1	21.5	even	6
336.4.a.e.1.1		1	28.19	even	6
588.4.a.a.1.1		1	7.2	even	3
588.4.i.a.361.1		2	7.3	odd	6
588.4.i.a.373.1		2	7.6	odd	2
588.4.i.h.361.1		2	7.4	even	3	inner
588.4.i.h.373.1		2	1.1	even	1	trivial
1008.4.a.d.1.1		1	84.47	odd	6
1344.4.a.b.1.1		1	56.5	odd	6
1344.4.a.p.1.1		1	56.19	even	6
1764.4.a.l.1.1		1	21.2	odd	6
1764.4.k.c.361.1		2	21.11	odd	6
1764.4.k.c.1549.1		2	3.2	odd	2
1764.4.k.n.361.1		2	21.17	even	6
1764.4.k.n.1549.1		2	21.20	even	2
2100.4.a.g.1.1		1	35.19	odd	6
2100.4.k.g.1849.1		2	35.12	even	12
2100.4.k.g.1849.2		2	35.33	even	12
2352.4.a.v.1.1		1	28.23	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)

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{3} +(7.00000 - 12.1244i) q^{5} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 2.59808i) q^{3} +(7.00000 - 12.1244i) q^{5} +(-4.50000 + 7.79423i) q^{9} +(-2.00000 - 3.46410i) q^{11} -54.0000 q^{13} +42.0000 q^{15} +(-7.00000 - 12.1244i) q^{17} +(46.0000 - 79.6743i) q^{19} +(76.0000 - 131.636i) q^{23} +(-35.5000 - 61.4878i) q^{25} -27.0000 q^{27} -106.000 q^{29} +(-72.0000 - 124.708i) q^{31} +(6.00000 - 10.3923i) q^{33} +(-79.0000 + 136.832i) q^{37} +(-81.0000 - 140.296i) q^{39} +390.000 q^{41} -508.000 q^{43} +(63.0000 + 109.119i) q^{45} +(-264.000 + 457.261i) q^{47} +(21.0000 - 36.3731i) q^{51} +(-303.000 - 524.811i) q^{53} -56.0000 q^{55} +276.000 q^{57} +(-182.000 - 315.233i) q^{59} +(339.000 - 587.165i) q^{61} +(-378.000 + 654.715i) q^{65} +(-422.000 - 730.925i) q^{67} +456.000 q^{69} -8.00000 q^{71} +(-211.000 - 365.463i) q^{73} +(106.500 - 184.463i) q^{75} +(-192.000 + 332.554i) q^{79} +(-40.5000 - 70.1481i) q^{81} +548.000 q^{83} -196.000 q^{85} +(-159.000 - 275.396i) q^{87} +(597.000 - 1034.03i) q^{89} +(216.000 - 374.123i) q^{93} +(-644.000 - 1115.44i) q^{95} +1502.00 q^{97} +36.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} + 14 q^{5} - 9 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 + 14 * q^5 - 9 * q^9	\( 2 q + 3 q^{3} + 14 q^{5} - 9 q^{9} - 4 q^{11} - 108 q^{13} + 84 q^{15} - 14 q^{17} + 92 q^{19} + 152 q^{23} - 71 q^{25} - 54 q^{27} - 212 q^{29} - 144 q^{31} + 12 q^{33} - 158 q^{37} - 162 q^{39} + 780 q^{41} - 1016 q^{43} + 126 q^{45} - 528 q^{47} + 42 q^{51} - 606 q^{53} - 112 q^{55} + 552 q^{57} - 364 q^{59} + 678 q^{61} - 756 q^{65} - 844 q^{67} + 912 q^{69} - 16 q^{71} - 422 q^{73} + 213 q^{75} - 384 q^{79} - 81 q^{81} + 1096 q^{83} - 392 q^{85} - 318 q^{87} + 1194 q^{89} + 432 q^{93} - 1288 q^{95} + 3004 q^{97} + 72 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 + 14 * q^5 - 9 * q^9 - 4 * q^11 - 108 * q^13 + 84 * q^15 - 14 * q^17 + 92 * q^19 + 152 * q^23 - 71 * q^25 - 54 * q^27 - 212 * q^29 - 144 * q^31 + 12 * q^33 - 158 * q^37 - 162 * q^39 + 780 * q^41 - 1016 * q^43 + 126 * q^45 - 528 * q^47 + 42 * q^51 - 606 * q^53 - 112 * q^55 + 552 * q^57 - 364 * q^59 + 678 * q^61 - 756 * q^65 - 844 * q^67 + 912 * q^69 - 16 * q^71 - 422 * q^73 + 213 * q^75 - 384 * q^79 - 81 * q^81 + 1096 * q^83 - 392 * q^85 - 318 * q^87 + 1194 * q^89 + 432 * q^93 - 1288 * q^95 + 3004 * q^97 + 72 * q^99

Introduction

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