LMFDB - Embedded newform 27.4.c.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,4,Mod(10,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("27.10");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	27.c (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:	$1.59305157015$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			19.2
Root			$1.68614 - 0.396143i$ of defining polynomial
Character	$\chi$	$=$	27.19
Dual form			27.4.c.a.10.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.18614 - 3.78651i) q^{2} +(-5.55842 - 9.62747i) q^{4} +(2.31386 + 4.00772i) q^{5} +(-6.05842 + 10.4935i) q^{7} -13.6277 q^{8} +O(q^{10})$	\(q+(2.18614 - 3.78651i) q^{2} +(-5.55842 - 9.62747i) q^{4} +(2.31386 + 4.00772i) q^{5} +(-6.05842 + 10.4935i) q^{7} -13.6277 q^{8} +20.2337 q^{10} +(5.01087 - 8.67909i) q^{11} +(24.2921 + 42.0752i) q^{13} +(26.4891 + 45.8805i) q^{14} +(14.6753 - 25.4183i) q^{16} -75.3505 q^{17} -116.052 q^{19} +(25.7228 - 44.5532i) q^{20} +(-21.9090 - 37.9474i) q^{22} +(-19.0367 - 32.9725i) q^{23} +(51.7921 - 89.7066i) q^{25} +212.424 q^{26} +134.701 q^{28} +(-11.3139 + 19.5962i) q^{29} +(-15.0584 - 26.0820i) q^{31} +(-118.675 - 205.552i) q^{32} +(-164.727 + 285.315i) q^{34} -56.0733 q^{35} +130.103 q^{37} +(-253.705 + 439.430i) q^{38} +(-31.5326 - 54.6161i) q^{40} +(173.742 + 300.930i) q^{41} +(-13.3832 + 23.1803i) q^{43} -111.410 q^{44} -166.467 q^{46} +(230.439 - 399.132i) q^{47} +(98.0910 + 169.899i) q^{49} +(-226.450 - 392.222i) q^{50} +(270.052 - 467.743i) q^{52} +438.310 q^{53} +46.3778 q^{55} +(82.5625 - 143.002i) q^{56} +(49.4674 + 85.6800i) q^{58} +(4.18487 + 7.24841i) q^{59} +(41.0448 - 71.0916i) q^{61} -131.679 q^{62} -802.959 q^{64} +(-112.417 + 194.712i) q^{65} +(-341.785 - 591.989i) q^{67} +(418.830 + 725.435i) q^{68} +(-122.584 + 212.322i) q^{70} -1097.61 q^{71} +470.464 q^{73} +(284.424 - 492.637i) q^{74} +(645.064 + 1117.28i) q^{76} +(60.7160 + 105.163i) q^{77} +(-243.017 + 420.919i) q^{79} +135.826 q^{80} +1519.30 q^{82} +(49.5829 - 85.8802i) q^{83} +(-174.351 - 301.984i) q^{85} +(58.5149 + 101.351i) q^{86} +(-68.2868 + 118.276i) q^{88} -8.80426 q^{89} -588.687 q^{91} +(-211.628 + 366.550i) q^{92} +(-1007.54 - 1745.12i) q^{94} +(-268.527 - 465.103i) q^{95} +(-330.486 + 572.419i) q^{97} +857.763 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 5 q^{4} + 15 q^{5} - 7 q^{7} - 66 q^{8}+O(q^{10}) $ 4 * q + 3 * q^2 - 5 * q^4 + 15 * q^5 - 7 * q^7 - 66 * q^8	$ 4 q + 3 q^{2} - 5 q^{4} + 15 q^{5} - 7 q^{7} - 66 q^{8} + 12 q^{10} + 66 q^{11} + 11 q^{13} + 60 q^{14} + 7 q^{16} - 198 q^{17} - 154 q^{19} - 12 q^{20} + 33 q^{22} + 33 q^{23} + 121 q^{25} + 528 q^{26} + 332 q^{28} - 51 q^{29} - 43 q^{31} - 423 q^{32} - 297 q^{34} - 6 q^{35} - 100 q^{37} - 561 q^{38} - 264 q^{40} + 132 q^{41} - 88 q^{43} + 462 q^{44} - 528 q^{46} + 399 q^{47} + 513 q^{49} - 429 q^{50} + 770 q^{52} - 108 q^{53} + 1254 q^{55} + 66 q^{56} + 60 q^{58} + 798 q^{59} - 439 q^{61} - 228 q^{62} - 1454 q^{64} + 165 q^{65} - 988 q^{67} + 693 q^{68} - 318 q^{70} - 2736 q^{71} - 910 q^{73} + 816 q^{74} + 1529 q^{76} - 165 q^{77} + 803 q^{79} - 192 q^{80} + 3630 q^{82} + 813 q^{83} - 594 q^{85} + 33 q^{86} - 1221 q^{88} + 792 q^{89} - 1562 q^{91} - 858 q^{92} - 2100 q^{94} - 132 q^{95} - 736 q^{97} + 846 q^{98}+O(q^{100}) $ 4 * q + 3 * q^2 - 5 * q^4 + 15 * q^5 - 7 * q^7 - 66 * q^8 + 12 * q^10 + 66 * q^11 + 11 * q^13 + 60 * q^14 + 7 * q^16 - 198 * q^17 - 154 * q^19 - 12 * q^20 + 33 * q^22 + 33 * q^23 + 121 * q^25 + 528 * q^26 + 332 * q^28 - 51 * q^29 - 43 * q^31 - 423 * q^32 - 297 * q^34 - 6 * q^35 - 100 * q^37 - 561 * q^38 - 264 * q^40 + 132 * q^41 - 88 * q^43 + 462 * q^44 - 528 * q^46 + 399 * q^47 + 513 * q^49 - 429 * q^50 + 770 * q^52 - 108 * q^53 + 1254 * q^55 + 66 * q^56 + 60 * q^58 + 798 * q^59 - 439 * q^61 - 228 * q^62 - 1454 * q^64 + 165 * q^65 - 988 * q^67 + 693 * q^68 - 318 * q^70 - 2736 * q^71 - 910 * q^73 + 816 * q^74 + 1529 * q^76 - 165 * q^77 + 803 * q^79 - 192 * q^80 + 3630 * q^82 + 813 * q^83 - 594 * q^85 + 33 * q^86 - 1221 * q^88 + 792 * q^89 - 1562 * q^91 - 858 * q^92 - 2100 * q^94 - 132 * q^95 - 736 * q^97 + 846 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	2.18614	−	3.78651i	0.772917	−	1.33873i	−0.163040	−	0.986619i	$-0.552130\pi$
$2$	2.18614	−	3.78651i	0.772917	−	1.33873i	0.935958	−	0.352113i	$-0.114537\pi$
$3$		0			0
$3$		0			0
$4$	−5.55842	−	9.62747i	−0.694803	−	1.20343i
$5$	2.31386	+	4.00772i	0.206958	+	0.358462i	0.950755	−	0.309944i	$-0.100310\pi$
$5$	2.31386	+	4.00772i	0.206958	+	0.358462i	−0.743797	+	0.668406i	$0.766977\pi$
$6$		0			0
$7$	−6.05842	+	10.4935i	−0.327124	+	0.566595i	−0.981940	−	0.189193i	$-0.939413\pi$
$7$	−6.05842	+	10.4935i	−0.327124	+	0.566595i	0.654816	+	0.755788i	$0.272746\pi$
$8$	−13.6277			−0.602266
$9$		0			0
$10$	20.2337			0.639845
$11$	5.01087	−	8.67909i	0.137349	−	0.237895i	−0.789144	−	0.614209i	$-0.789475\pi$
$11$	5.01087	−	8.67909i	0.137349	−	0.237895i	0.926492	+	0.376314i	$0.122809\pi$
$12$		0			0
$13$	24.2921	+	42.0752i	0.518263	+	0.897658i	0.999775	+	0.0212183i	$0.00675450\pi$
$13$	24.2921	+	42.0752i	0.518263	+	0.897658i	−0.481512	+	0.876440i	$0.659912\pi$
$14$	26.4891	+	45.8805i	0.505680	+	0.875863i
$15$		0			0
$16$	14.6753	−	25.4183i	0.229301	−	0.397161i
$17$	−75.3505			−1.07501			−0.537506	−	0.843260i	$-0.680633\pi$
$17$	−75.3505			−1.07501			−0.537506	+	0.843260i	$0.680633\pi$
$18$		0			0
$19$	−116.052			−1.40127			−0.700633	−	0.713522i	$-0.747099\pi$
$19$	−116.052			−1.40127			−0.700633	+	0.713522i	$0.747099\pi$
$20$	25.7228	−	44.5532i	0.287590	−	0.498120i
$21$		0			0
$22$	−21.9090	−	37.9474i	−0.212318	−	0.367746i
$23$	−19.0367	−	32.9725i	−0.172584	−	0.298923i	0.766739	−	0.641959i	$-0.221878\pi$
$23$	−19.0367	−	32.9725i	−0.172584	−	0.298923i	−0.939322	+	0.343036i	$0.888545\pi$
$24$		0			0
$25$	51.7921	−	89.7066i	0.414337	−	0.717653i
$26$	212.424			1.60230
$27$		0			0
$28$	134.701			0.909147
$29$	−11.3139	+	19.5962i	−0.0724459	+	0.125480i	−0.899973	−	0.435946i	$-0.856414\pi$
$29$	−11.3139	+	19.5962i	−0.0724459	+	0.125480i	0.827527	+	0.561426i	$0.189747\pi$
$30$		0			0
$31$	−15.0584	−	26.0820i	−0.0872443	−	0.151112i	0.819101	−	0.573649i	$-0.194473\pi$
$31$	−15.0584	−	26.0820i	−0.0872443	−	0.151112i	−0.906345	+	0.422538i	$0.861139\pi$
$32$	−118.675	−	205.552i	−0.655594	−	1.13552i
$33$		0			0
$34$	−164.727	+	285.315i	−0.830895	+	1.43915i
$35$	−56.0733			−0.270804
$36$		0			0
$37$	130.103			0.578077			0.289038	−	0.957318i	$-0.406665\pi$
$37$	130.103			0.578077			0.289038	+	0.957318i	$0.406665\pi$
$38$	−253.705	+	439.430i	−1.08306	+	1.87592i
$39$		0			0
$40$	−31.5326	−	54.6161i	−0.124644	−	0.215889i
$41$	173.742	+	300.930i	0.661803	+	1.14628i	0.980142	+	0.198299i	$0.0635417\pi$
$41$	173.742	+	300.930i	0.661803	+	1.14628i	−0.318339	+	0.947977i	$0.603125\pi$
$42$		0			0
$43$	−13.3832	+	23.1803i	−0.0474631	+	0.0822085i	−0.888781	−	0.458332i	$-0.848447\pi$
$43$	−13.3832	+	23.1803i	−0.0474631	+	0.0822085i	0.841318	+	0.540541i	$0.181780\pi$
$44$	−111.410			−0.381721
$45$		0			0
$46$	−166.467			−0.533571
$47$	230.439	−	399.132i	0.715169	−	1.23871i	−0.247725	−	0.968830i	$-0.579683\pi$
$47$	230.439	−	399.132i	0.715169	−	1.23871i	0.962894	−	0.269879i	$-0.0869837\pi$
$48$		0			0
$49$	98.0910	+	169.899i	0.285980	+	0.495331i
$50$	−226.450	−	392.222i	−0.640496	−	1.10937i
$51$		0			0
$52$	270.052	−	467.743i	0.720181	−	1.24739i
$53$	438.310			1.13597			0.567985	−	0.823039i	$-0.307723\pi$
$53$	438.310			1.13597			0.567985	+	0.823039i	$0.307723\pi$
$54$		0			0
$55$	46.3778			0.113702
$56$	82.5625	−	143.002i	0.197016	−	0.341241i
$57$		0			0
$58$	49.4674	+	85.6800i	0.111989	+	0.193971i
$59$	4.18487	+	7.24841i	0.00923430	+	0.0159943i	0.870606	−	0.491982i	$-0.163727\pi$
$59$	4.18487	+	7.24841i	0.00923430	+	0.0159943i	−0.861371	+	0.507976i	$0.830394\pi$
$60$		0			0
$61$	41.0448	−	71.0916i	0.0861515	−	0.149219i	−0.819730	−	0.572750i	$-0.805876\pi$
$61$	41.0448	−	71.0916i	0.0861515	−	0.149219i	0.905881	+	0.423532i	$0.139210\pi$
$62$	−131.679			−0.269730
$63$		0			0
$64$	−802.959			−1.56828
$65$	−112.417	+	194.712i	−0.214517	+	0.371555i
$66$		0			0
$67$	−341.785	−	591.989i	−0.623220	−	1.07945i	−0.988882	−	0.148701i	$-0.952491\pi$
$67$	−341.785	−	591.989i	−0.623220	−	1.07945i	0.365663	−	0.930747i	$-0.380842\pi$
$68$	418.830	+	725.435i	0.746921	+	1.29370i
$69$		0			0
$70$	−122.584	+	212.322i	−0.209309	+	0.362533i
$71$	−1097.61			−1.83468			−0.917339	−	0.398107i	$-0.869667\pi$
$71$	−1097.61			−1.83468			−0.917339	+	0.398107i	$0.869667\pi$
$72$		0			0
$73$	470.464			0.754297			0.377149	−	0.926153i	$-0.376905\pi$
$73$	470.464			0.754297			0.377149	+	0.926153i	$0.376905\pi$
$74$	284.424	−	492.637i	0.446805	−	0.773890i
$75$		0			0
$76$	645.064	+	1117.28i	0.973604	+	1.68633i
$77$	60.7160	+	105.163i	0.0898601	+	0.155642i
$78$		0			0
$79$	−243.017	+	420.919i	−0.346096	+	0.599456i	−0.985552	−	0.169371i	$-0.945826\pi$
$79$	−243.017	+	420.919i	−0.346096	+	0.599456i	0.639456	+	0.768828i	$0.279160\pi$
$80$	135.826			0.189823
$81$		0			0
$82$	1519.30			2.04608
$83$	49.5829	−	85.8802i	0.0655715	−	0.113573i	−0.831376	−	0.555711i	$-0.812446\pi$
$83$	49.5829	−	85.8802i	0.0655715	−	0.113573i	0.896947	+	0.442137i	$0.145780\pi$
$84$		0			0
$85$	−174.351	−	301.984i	−0.222482	−	0.385350i
$86$	58.5149	+	101.351i	0.0733701	+	0.127081i
$87$		0			0
$88$	−68.2868	+	118.276i	−0.0827204	+	0.143276i
$89$	−8.80426			−0.0104859			−0.00524297	−	0.999986i	$-0.501669\pi$
$89$	−8.80426			−0.0104859			−0.00524297	+	0.999986i	$0.501669\pi$
$90$		0			0
$91$	−588.687			−0.678145
$92$	−211.628	+	366.550i	−0.239823	+	0.415386i
$93$		0			0
$94$	−1007.54	−	1745.12i	−1.10553	−	1.91484i
$95$	−268.527	−	465.103i	−0.290003	−	0.502300i
$96$		0			0
$97$	−330.486	+	572.419i	−0.345936	+	0.599179i	−0.985523	−	0.169540i	$-0.945772\pi$
$97$	−330.486	+	572.419i	−0.345936	+	0.599179i	0.639587	+	0.768719i	$0.279105\pi$
$98$	857.763			0.884155
$99$		0			0
$100$	−1151.53			−1.15153
$101$	−282.561	+	489.410i	−0.278375	+	0.482160i	−0.970981	−	0.239156i	$-0.923129\pi$
$101$	−282.561	+	489.410i	−0.278375	+	0.482160i	0.692606	+	0.721316i	$0.256463\pi$
$102$		0			0
$103$	485.591	+	841.068i	0.464531	+	0.804592i	0.999180	−	0.0404826i	$-0.0128895\pi$
$103$	485.591	+	841.068i	0.464531	+	0.804592i	−0.534649	+	0.845074i	$0.679556\pi$
$104$	−331.046	−	573.389i	−0.312132	−	0.540629i
$105$		0			0
$106$	958.206	−	1659.66i	0.878012	−	1.52076i
$107$	563.845			0.509430			0.254715	−	0.967016i	$-0.418018\pi$
$107$	563.845			0.509430			0.254715	+	0.967016i	$0.418018\pi$
$108$		0			0
$109$	225.484			0.198142			0.0990709	−	0.995080i	$-0.468413\pi$
$109$	225.484			0.198142			0.0990709	+	0.995080i	$0.468413\pi$
$110$	101.388	−	175.610i	0.0878819	−	0.152216i
$111$		0			0
$112$	177.818	+	307.990i	0.150020	+	0.259842i
$113$	−345.531	−	598.478i	−0.287654	−	0.498231i	0.685596	−	0.727983i	$-0.259542\pi$
$113$	−345.531	−	598.478i	−0.287654	−	0.498231i	−0.973249	+	0.229752i	$0.926209\pi$
$114$		0			0
$115$	88.0964	−	152.587i	0.0714350	−	0.123729i
$116$	251.549			0.201342
$117$		0			0
$118$	36.5949			0.0285494
$119$	456.505	−	790.690i	0.351662	−	0.609096i
$120$		0			0
$121$	615.282	+	1065.70i	0.462271	+	0.800676i
$122$	−179.459	−	310.833i	−0.133176	−	0.230668i
$123$		0			0
$124$	−167.402	+	289.949i	−0.121235	+	0.209985i
$125$	1057.82			0.756917
$126$		0			0
$127$	−895.897			−0.625968			−0.312984	−	0.949758i	$-0.601329\pi$
$127$	−895.897			−0.625968			−0.312984	+	0.949758i	$0.601329\pi$
$128$	−805.979	+	1396.00i	−0.556556	+	0.963983i
$129$		0			0
$130$	491.519	+	851.336i	0.331608	+	0.574362i
$131$	827.428	+	1433.15i	0.551853	+	0.955837i	0.998141	+	0.0609476i	$0.0194122\pi$
$131$	827.428	+	1433.15i	0.551853	+	0.955837i	−0.446288	+	0.894889i	$0.647254\pi$
$132$		0			0
$133$	703.090	−	1217.79i	0.458388	−	0.793951i
$134$	−2988.76			−1.92679
$135$		0			0
$136$	1026.86			0.647442
$137$	−1325.55	+	2295.91i	−0.826635	+	1.43177i	0.0740277	+	0.997256i	$0.476415\pi$
$137$	−1325.55	+	2295.91i	−0.826635	+	1.43177i	−0.900663	+	0.434518i	$0.856919\pi$
$138$		0			0
$139$	−317.084	−	549.206i	−0.193487	−	0.335130i	0.752916	−	0.658116i	$-0.228646\pi$
$139$	−317.084	−	549.206i	−0.193487	−	0.335130i	−0.946404	+	0.322986i	$0.895313\pi$
$140$	311.679	+	539.844i	0.188155	+	0.325894i
$141$		0			0
$142$	−2399.53	+	4156.10i	−1.41805	+	2.45614i
$143$	486.899			0.284731
$144$		0			0
$145$	−104.715			−0.0599730
$146$	1028.50	−	1781.42i	0.583009	−	1.00980i
$147$		0			0
$148$	−723.168	−	1252.56i	−0.401649	−	0.695677i
$149$	−1703.16	−	2949.96i	−0.936432	−	1.62195i	−0.772060	−	0.635550i	$-0.780773\pi$
$149$	−1703.16	−	2949.96i	−0.936432	−	1.62195i	−0.164372	−	0.986398i	$-0.552560\pi$
$150$		0			0
$151$	875.159	−	1515.82i	0.471652	−	0.816925i	−0.527822	−	0.849355i	$-0.676991\pi$
$151$	875.159	−	1515.82i	0.471652	−	0.816925i	0.999474	+	0.0324302i	$0.0103247\pi$
$152$	1581.52			0.843935
$153$		0			0
$154$	530.935			0.277818
$155$	69.6861	−	120.700i	0.0361118	−	0.0625474i
$156$		0			0
$157$	−1089.29	−	1886.70i	−0.553723	−	0.959076i	−0.998002	−	0.0631876i	$-0.979873\pi$
$157$	−1089.29	−	1886.70i	−0.553723	−	0.959076i	0.444279	−	0.895889i	$-0.353460\pi$
$158$	1062.54	+	1840.37i	0.535008	+	0.926660i
$159$		0			0
$160$	549.196	−	951.235i	0.271361	−	0.470011i
$161$	461.329			0.225825
$162$		0			0
$163$	2188.41			1.05159			0.525797	−	0.850610i	$-0.323767\pi$
$163$	2188.41			1.05159			0.525797	+	0.850610i	$0.323767\pi$
$164$	1931.46	−	3345.39i	0.919645	−	1.59287i
$165$		0			0
$166$	−216.791	−	375.492i	−0.101363	−	0.175565i
$167$	960.520	+	1663.67i	0.445074	+	0.770890i	0.998057	−	0.0623020i	$-0.0198442\pi$
$167$	960.520	+	1663.67i	0.445074	+	0.770890i	−0.552984	+	0.833192i	$0.686511\pi$
$168$		0			0
$169$	−81.7132	+	141.531i	−0.0371931	+	0.0644203i
$170$	−1524.62			−0.687841
$171$		0			0
$172$	297.557			0.131910
$173$	1584.91	−	2745.15i	0.696525	−	1.20642i	−0.273139	−	0.961974i	$-0.588062\pi$
$173$	1584.91	−	2745.15i	0.696525	−	1.20642i	0.969664	−	0.244442i	$-0.0786047\pi$
$174$		0			0
$175$	627.557	+	1086.96i	0.271079	+	0.469523i
$176$	−147.072	−	254.736i	−0.0629884	−	0.109099i
$177$		0			0
$178$	−19.2473	+	33.3374i	−0.00810477	+	0.0140379i
$179$	−1368.78			−0.571551			−0.285776	−	0.958297i	$-0.592251\pi$
$179$	−1368.78			−0.571551			−0.285776	+	0.958297i	$0.592251\pi$
$180$		0			0
$181$	−3951.44			−1.62270			−0.811350	−	0.584561i	$-0.801267\pi$
$181$	−3951.44			−1.62270			−0.811350	+	0.584561i	$0.801267\pi$
$182$	−1286.95	+	2229.07i	−0.524150	+	0.907855i
$183$		0			0
$184$	259.426	+	449.340i	0.103941	+	0.180031i
$185$	301.040	+	521.417i	0.119637	+	0.207218i
$186$		0			0
$187$	−377.572	+	653.974i	−0.147651	+	0.255740i
$188$	−5123.50			−1.98761
$189$		0			0
$190$	−2348.15			−0.896594
$191$	−1201.29	+	2080.70i	−0.455092	+	0.788243i	−0.998693	−	0.0511008i	$-0.983727\pi$
$191$	−1201.29	+	2080.70i	−0.455092	+	0.788243i	0.543601	+	0.839344i	$0.317060\pi$
$192$		0			0
$193$	667.535	+	1156.20i	0.248965	+	0.431220i	0.963239	−	0.268646i	$-0.0865763\pi$
$193$	667.535	+	1156.20i	0.248965	+	0.431220i	−0.714274	+	0.699866i	$0.753243\pi$
$194$	1444.98	+	2502.78i	0.534760	+	0.926232i
$195$		0			0
$196$	1090.46	−	1888.74i	0.397399	−	0.688315i
$197$	2630.89			0.951487			0.475743	−	0.879584i	$-0.342179\pi$
$197$	2630.89			0.951487			0.475743	+	0.879584i	$0.342179\pi$
$198$		0			0
$199$	2477.34			0.882483			0.441241	−	0.897388i	$-0.354538\pi$
$199$	2477.34			0.882483			0.441241	+	0.897388i	$0.354538\pi$
$200$	−705.808	+	1222.50i	−0.249541	+	0.432218i
$201$		0			0
$202$	1235.44	+	2139.84i	0.430322	+	0.745340i
$203$	−137.088	−	237.444i	−0.0473976	−	0.0820950i
$204$		0			0
$205$	−804.028	+	1392.62i	−0.273931	+	0.474462i
$206$	4246.28			1.43618
$207$		0			0
$208$	1425.97			0.475353
$209$	−581.520	+	1007.22i	−0.192462	+	0.333354i
$210$		0			0
$211$	1392.36	+	2411.65i	0.454286	+	0.786847i	0.998647	−	0.0520047i	$-0.0165611\pi$
$211$	1392.36	+	2411.65i	0.454286	+	0.786847i	−0.544361	+	0.838851i	$0.683228\pi$
$212$	−2436.31	−	4219.81i	−0.789276	−	1.36707i
$213$		0			0
$214$	1232.64	−	2135.00i	0.393747	−	0.681990i
$215$	−123.867			−0.0392914
$216$		0			0
$217$	364.921			0.114159
$218$	492.940	−	853.797i	0.153147	−	0.265259i
$219$		0			0
$220$	−257.788	−	446.501i	−0.0790002	−	0.136832i
$221$	−1830.42	−	3170.39i	−0.557138	−	0.964992i
$222$		0			0
$223$	21.5288	−	37.2890i	0.00646491	−	0.0111976i	−0.862775	−	0.505588i	$-0.831275\pi$
$223$	21.5288	−	37.2890i	0.00646491	−	0.0111976i	0.869240	+	0.494391i	$0.164609\pi$
$224$	2875.94			0.857843
$225$		0			0
$226$	−3021.52			−0.889330
$227$	341.630	−	591.721i	0.0998889	−	0.173013i	−0.811750	−	0.584006i	$-0.801485\pi$
$227$	341.630	−	591.721i	0.0998889	−	0.173013i	0.911639	+	0.410993i	$0.134818\pi$
$228$		0			0
$229$	−2147.15	−	3718.98i	−0.619598	−	1.07317i	−0.989559	−	0.144127i	$-0.953962\pi$
$229$	−2147.15	−	3718.98i	−0.619598	−	1.07317i	0.369962	−	0.929047i	$-0.379371\pi$
$230$	−385.182	−	667.155i	−0.110427	−	0.191265i
$231$		0			0
$232$	154.182	−	267.051i	0.0436317	−	0.0755723i
$233$	−3466.34			−0.974625			−0.487313	−	0.873228i	$-0.662023\pi$
$233$	−3466.34			−0.974625			−0.487313	+	0.873228i	$0.662023\pi$
$234$		0			0
$235$	2132.81			0.592040
$236$	46.5225	−	80.5794i	0.0128320	−	0.0222257i
$237$		0			0
$238$	−1995.97	−	3457.12i	−0.543611	−	0.941562i
$239$	2821.69	+	4887.30i	0.763681	+	1.32273i	0.940941	+	0.338570i	$0.109943\pi$
$239$	2821.69	+	4887.30i	0.763681	+	1.32273i	−0.177261	+	0.984164i	$0.556724\pi$
$240$		0			0
$241$	−3294.71	+	5706.61i	−0.880627	+	1.52529i	−0.0299825	+	0.999550i	$0.509545\pi$
$241$	−3294.71	+	5706.61i	−0.880627	+	1.52529i	−0.850645	+	0.525741i	$0.823788\pi$
$242$	5380.37			1.42919
$243$		0			0
$244$	−912.577			−0.239433
$245$	−453.938	+	786.243i	−0.118372	+	0.205025i
$246$		0			0
$247$	−2819.14	−	4882.89i	−0.726225	−	1.25786i
$248$	205.212	+	355.438i	0.0525442	+	0.0910093i
$249$		0			0
$250$	2312.55	−	4005.46i	0.585034	−	1.01331i
$251$	−4135.47			−1.03996			−0.519978	−	0.854180i	$-0.674060\pi$
$251$	−4135.47			−1.03996			−0.519978	+	0.854180i	$0.674060\pi$
$252$		0			0
$253$	−381.562			−0.0948165
$254$	−1958.56	+	3392.32i	−0.483822	+	0.838004i
$255$		0			0
$256$	312.132	+	540.628i	0.0762041	+	0.131989i
$257$	−1672.31	−	2896.53i	−0.405898	−	0.703036i	0.588527	−	0.808477i	$-0.299708\pi$
$257$	−1672.31	−	2896.53i	−0.405898	−	0.703036i	−0.994426	+	0.105441i	$0.966375\pi$
$258$		0			0
$259$	−788.220	+	1365.24i	−0.189103	+	0.327536i
$260$	2499.45			0.596189
$261$		0			0
$262$	7235.49			1.70615
$263$	3260.75	−	5647.78i	0.764511	−	1.32417i	−0.175994	−	0.984391i	$-0.556314\pi$
$263$	3260.75	−	5647.78i	0.764511	−	1.32417i	0.940505	−	0.339780i	$-0.110353\pi$
$264$		0			0
$265$	1014.19	+	1756.62i	0.235098	+	0.407202i
$266$	−3074.11	−	5324.51i	−0.708592	−	1.22732i
$267$		0			0
$268$	−3799.57	+	6581.05i	−0.866029	+	1.50001i
$269$	2904.99			0.658441			0.329220	−	0.944253i	$-0.393214\pi$
$269$	2904.99			0.658441			0.329220	+	0.944253i	$0.393214\pi$
$270$		0			0
$271$	−1335.38			−0.299331			−0.149665	−	0.988737i	$-0.547820\pi$
$271$	−1335.38			−0.299331			−0.149665	+	0.988737i	$0.547820\pi$
$272$	−1105.79	+	1915.28i	−0.246501	+	0.426953i
$273$		0			0
$274$	5795.66	+	10038.4i	1.27784	+	2.21329i
$275$	−519.048	−	899.017i	−0.113817	−	0.197137i
$276$		0			0
$277$	4187.82	−	7253.51i	0.908381	−	1.57336i	0.0920685	−	0.995753i	$-0.470652\pi$
$277$	4187.82	−	7253.51i	0.908381	−	1.57336i	0.816313	−	0.577610i	$-0.196015\pi$
$278$	−2772.76			−0.598199
$279$		0			0
$280$	764.152			0.163096
$281$	−2589.67	+	4485.43i	−0.549774	+	0.952237i	0.448516	+	0.893775i	$0.351953\pi$
$281$	−2589.67	+	4485.43i	−0.549774	+	0.952237i	−0.998290	+	0.0584616i	$0.981380\pi$
$282$		0			0
$283$	1540.03	+	2667.42i	0.323482	+	0.560288i	0.981204	−	0.192973i	$-0.0618130\pi$
$283$	1540.03	+	2667.42i	0.323482	+	0.560288i	−0.657722	+	0.753261i	$0.728480\pi$
$284$	6100.97	+	10567.2i	1.27474	+	2.20791i
$285$		0			0
$286$	1064.43	−	1843.65i	0.220074	−	0.381179i
$287$	−4210.40			−0.865966
$288$		0			0
$289$	764.703			0.155649
$290$	−228.921	+	396.503i	−0.0463542	+	0.0802878i
$291$		0			0
$292$	−2615.04	−	4529.38i	−0.524088	−	0.907747i
$293$	1824.45	+	3160.04i	0.363773	+	0.630073i	0.988578	−	0.150708i	$-0.0481552\pi$
$293$	1824.45	+	3160.04i	0.363773	+	0.630073i	−0.624806	+	0.780780i	$0.714822\pi$
$294$		0			0
$295$	−19.3664	+	33.5436i	−0.00382222	+	0.00662028i
$296$	−1773.01			−0.348156
$297$		0			0
$298$	−14893.4			−2.89514
$299$	924.882	−	1601.94i	0.178887	−	0.309842i
$300$		0			0
$301$	−162.162	−	280.872i	−0.0310526	−	0.0537847i
$302$	−3826.44	−	6627.59i	−0.729096	−	1.26283i
$303$		0			0
$304$	−1703.09	+	2949.84i	−0.321312	+	0.556528i
$305$	379.887			0.0713190
$306$		0			0
$307$	−3439.25			−0.639376			−0.319688	−	0.947523i	$-0.603578\pi$
$307$	−3439.25			−0.639376			−0.319688	+	0.947523i	$0.603578\pi$
$308$	674.970	−	1169.08i	0.124870	−	0.216281i
$309$		0			0
$310$	−304.687	−	527.734i	−0.0558228	−	0.0966880i
$311$	3587.66	+	6214.02i	0.654141	+	1.13301i	0.982108	+	0.188316i	$0.0603030\pi$
$311$	3587.66	+	6214.02i	0.654141	+	1.13301i	−0.327968	+	0.944689i	$0.606364\pi$
$312$		0			0
$313$	2428.65	−	4206.54i	0.438579	−	0.759642i	−0.559001	−	0.829167i	$-0.688815\pi$
$313$	2428.65	−	4206.54i	0.438579	−	0.759642i	0.997580	+	0.0695253i	$0.0221485\pi$
$314$	−9525.33			−1.71193
$315$		0			0
$316$	5403.17			0.961874
$317$	3773.97	−	6536.70i	0.668666	−	1.15816i	−0.309611	−	0.950863i	$-0.600199\pi$
$317$	3773.97	−	6536.70i	0.668666	−	1.15816i	0.978277	−	0.207300i	$-0.0664677\pi$
$318$		0			0
$319$	113.385	+	196.388i	0.0199007	+	0.0344690i
$320$	−1857.93	−	3218.04i	−0.324568	−	0.562168i
$321$		0			0
$322$	1008.53	−	1746.82i	0.174544	−	0.302319i
$323$	8744.55			1.50638
$324$		0			0
$325$	5032.56			0.858942
$326$	4784.18	−	8286.44i	0.812795	−	1.40780i
$327$		0			0
$328$	−2367.70	−	4100.98i	−0.398581	−	0.690363i
$329$	2792.19	+	4836.22i	0.467898	+	0.810423i
$330$		0			0
$331$	1564.86	−	2710.41i	0.259856	−	0.450084i	−0.706347	−	0.707866i	$-0.749658\pi$
$331$	1564.86	−	2710.41i	0.259856	−	0.450084i	0.966203	+	0.257782i	$0.0829915\pi$
$332$	−1102.41			−0.182237
$333$		0			0
$334$	8399.33			1.37602
$335$	1581.69	−	2739.56i	0.257960	−	0.446801i
$336$		0			0
$337$	4614.99	+	7993.39i	0.745978	+	1.29207i	0.949737	+	0.313050i	$0.101351\pi$
$337$	4614.99	+	7993.39i	0.745978	+	1.29207i	−0.203759	+	0.979021i	$0.565316\pi$
$338$	357.273	+	618.815i	0.0574944	+	0.0995832i
$339$		0			0
$340$	−1938.23	+	3357.11i	−0.309162	+	0.535485i
$341$	−301.823			−0.0479315
$342$		0			0
$343$	−6533.19			−1.02845
$344$	182.382	−	315.895i	0.0285854	−	0.0495113i
$345$		0			0
$346$	−6929.69	−	12002.6i	−1.07671	−	1.86492i
$347$	−4052.20	−	7018.61i	−0.626897	−	1.08582i	−0.988171	−	0.153358i	$-0.950991\pi$
$347$	−4052.20	−	7018.61i	−0.626897	−	1.08582i	0.361273	−	0.932460i	$-0.382342\pi$
$348$		0			0
$349$	−1538.21	+	2664.26i	−0.235927	+	0.408638i	−0.959542	−	0.281566i	$-0.909146\pi$
$349$	−1538.21	+	2664.26i	−0.235927	+	0.408638i	0.723615	+	0.690204i	$0.242479\pi$
$350$	5487.71			0.838087
$351$		0			0
$352$	−2378.67			−0.360180
$353$	−3075.04	+	5326.13i	−0.463649	+	0.803063i	−0.999139	−	0.0414780i	$-0.986793\pi$
$353$	−3075.04	+	5326.13i	−0.463649	+	0.803063i	0.535491	+	0.844541i	$0.320127\pi$
$354$		0			0
$355$	−2539.71	−	4398.91i	−0.379701	−	0.657662i
$356$	48.9378	+	84.7627i	0.00728566	+	0.0126191i
$357$		0			0
$358$	−2992.35	+	5182.91i	−0.441762	+	0.765154i
$359$	−3307.94			−0.486313			−0.243156	−	0.969987i	$-0.578183\pi$
$359$	−3307.94			−0.486313			−0.243156	+	0.969987i	$0.578183\pi$
$360$		0			0
$361$	6608.97			0.963548
$362$	−8638.41	+	14962.2i	−1.25421	+	2.17236i
$363$		0			0
$364$	3272.17	+	5667.57i	0.471177	+	0.816103i
$365$	1088.59	+	1885.49i	0.156108	+	0.270387i
$366$		0			0
$367$	−1474.65	+	2554.16i	−0.209744	+	0.363287i	−0.951634	−	0.307235i	$-0.900596\pi$
$367$	−1474.65	+	2554.16i	−0.209744	+	0.363287i	0.741890	+	0.670522i	$0.233930\pi$
$368$	−1117.47			−0.158294
$369$		0			0
$370$	2632.47			0.369880
$371$	−2655.46	+	4599.40i	−0.371603	+	0.643636i
$372$		0			0
$373$	−581.790	−	1007.69i	−0.0807612	−	0.139883i	0.822816	−	0.568308i	$-0.192402\pi$
$373$	−581.790	−	1007.69i	−0.0807612	−	0.139883i	−0.903577	+	0.428425i	$0.859068\pi$
$374$	1650.85	+	2859.36i	0.228245	+	0.395331i
$375$		0			0
$376$	−3140.36	+	5439.25i	−0.430722	+	0.746032i
$377$	−1099.35			−0.150184
$378$		0			0
$379$	−4016.67			−0.544387			−0.272193	−	0.962243i	$-0.587749\pi$
$379$	−4016.67			−0.544387			−0.272193	+	0.962243i	$0.587749\pi$
$380$	−2985.17	+	5170.47i	−0.402990	+	0.697999i
$381$		0			0
$382$	5252.40	+	9097.42i	0.703497	+	1.21849i
$383$	−5401.65	−	9355.93i	−0.720656	−	1.24821i	−0.960737	−	0.277460i	$-0.910507\pi$
$383$	−5401.65	−	9355.93i	−0.720656	−	1.24821i	0.240081	−	0.970753i	$-0.422826\pi$
$384$		0			0
$385$	−280.977	+	486.666i	−0.0371945	+	0.0644228i
$386$	5837.30			0.769717
$387$		0			0
$388$	7347.93			0.961429
$389$	1032.29	−	1787.99i	0.134549	−	0.233045i	−0.790876	−	0.611976i	$-0.790375\pi$
$389$	1032.29	−	1787.99i	0.134549	−	0.233045i	0.925425	+	0.378931i	$0.123708\pi$
$390$		0			0
$391$	1434.42	+	2484.49i	0.185529	+	0.321346i
$392$	−1336.76	−	2315.33i	−0.172236	−	0.298321i
$393$		0			0
$394$	5751.49	−	9961.87i	0.735421	−	1.27379i
$395$	−2249.23			−0.286509
$396$		0			0
$397$	−7937.61			−1.00347			−0.501735	−	0.865022i	$-0.667305\pi$
$397$	−7937.61			−1.00347			−0.501735	+	0.865022i	$0.667305\pi$
$398$	5415.82	−	9380.47i	0.682086	−	1.18141i
$399$		0			0
$400$	−1520.13	−	2632.94i	−0.190016	−	0.329117i
$401$	1289.10	+	2232.79i	0.160536	+	0.278056i	0.935061	−	0.354487i	$-0.115344\pi$
$401$	1289.10	+	2232.79i	0.160536	+	0.278056i	−0.774525	+	0.632543i	$0.782011\pi$
$402$		0			0
$403$	731.602	−	1267.17i	0.0904310	−	0.156631i
$404$	6282.38			0.773663
$405$		0			0
$406$	−1198.78			−0.146538
$407$	651.931	−	1129.18i	0.0793981	−	0.137521i
$408$		0			0
$409$	−2922.88	−	5062.57i	−0.353367	−	0.612049i	0.633470	−	0.773767i	$-0.281630\pi$
$409$	−2922.88	−	5062.57i	−0.353367	−	0.612049i	−0.986837	+	0.161718i	$0.948297\pi$
$410$	3515.44	+	6088.92i	0.423451	+	0.733439i
$411$		0			0
$412$	5398.24	−	9350.03i	0.645515	−	1.11806i
$413$	−101.415			−0.0120830
$414$		0			0
$415$	458.912			0.0542822
$416$	5765.75	−	9986.56i	0.679541	−	1.17700i
$417$		0			0
$418$	2542.57	+	4403.86i	0.297515	+	0.515310i
$419$	−4370.66	−	7570.20i	−0.509596	−	0.882646i	−0.999938	−	0.0111158i	$-0.996462\pi$
$419$	−4370.66	−	7570.20i	−0.509596	−	0.882646i	0.490343	−	0.871530i	$-0.336872\pi$
$420$		0			0
$421$	−528.254	+	914.963i	−0.0611533	+	0.105921i	−0.894981	−	0.446104i	$-0.852811\pi$
$421$	−528.254	+	914.963i	−0.0611533	+	0.105921i	0.833828	+	0.552024i	$0.186145\pi$
$422$	12175.6			1.40450
$423$		0			0
$424$	−5973.16			−0.684156
$425$	−3902.56	+	6759.44i	−0.445417	+	0.771484i
$426$		0			0
$427$	497.333	+	861.406i	0.0563645	+	0.0976261i
$428$	−3134.09	−	5428.40i	−0.353953	−	0.613065i
$429$		0			0
$430$	−270.791	+	469.023i	−0.0303690	+	0.0526007i
$431$	−9868.64			−1.10291			−0.551457	−	0.834203i	$-0.685928\pi$
$431$	−9868.64			−1.10291			−0.551457	+	0.834203i	$0.685928\pi$
$432$		0			0
$433$	477.948			0.0530456			0.0265228	−	0.999648i	$-0.491557\pi$
$433$	477.948			0.0530456			0.0265228	+	0.999648i	$0.491557\pi$
$434$	797.769	−	1381.78i	0.0882353	−	0.152828i
$435$		0			0
$436$	−1253.34	−	2170.84i	−0.137669	−	0.238450i
$437$	2209.24	+	3826.51i	0.241835	+	0.418871i
$438$		0			0
$439$	526.239	−	911.473i	0.0572119	−	0.0990939i	−0.836001	−	0.548728i	$-0.815112\pi$
$439$	526.239	−	911.473i	0.0572119	−	0.0990939i	0.893213	+	0.449634i	$0.148446\pi$
$440$	−632.024			−0.0684786
$441$		0			0
$442$	−16006.3			−1.72249
$443$	−5249.35	+	9092.14i	−0.562989	+	0.975126i	0.434245	+	0.900795i	$0.357015\pi$
$443$	−5249.35	+	9092.14i	−0.562989	+	0.975126i	−0.997234	+	0.0743307i	$0.976318\pi$
$444$		0			0
$445$	−20.3718	−	35.2850i	−0.00217015	−	0.00375881i
$446$	−94.1300	−	163.038i	−0.00999369	−	0.0173096i
$447$		0			0
$448$	4864.66	−	8425.85i	0.513022	−	0.888580i
$449$	7329.40			0.770369			0.385184	−	0.922840i	$-0.374138\pi$
$449$	7329.40			0.770369			0.385184	+	0.922840i	$0.374138\pi$
$450$		0			0
$451$	3482.39			0.363591
$452$	−3841.22	+	6653.18i	−0.399725	+	0.692344i
$453$		0			0
$454$	−1493.70	−	2587.17i	−0.154412	−	0.267449i
$455$	−1362.14	−	2359.30i	−0.140347	−	0.243089i
$456$		0			0
$457$	−3572.20	+	6187.23i	−0.365646	+	0.633318i	−0.988880	−	0.148718i	$-0.952485\pi$
$457$	−3572.20	+	6187.23i	−0.365646	+	0.633318i	0.623233	+	0.782036i	$0.285819\pi$
$458$	−18775.9			−1.91559
$459$		0			0
$460$	−1958.71			−0.198533
$461$	2859.34	−	4952.53i	0.288878	−	0.500352i	−0.684664	−	0.728859i	$-0.740051\pi$
$461$	2859.34	−	4952.53i	0.288878	−	0.500352i	0.973542	+	0.228507i	$0.0733843\pi$
$462$		0			0
$463$	−394.233	−	682.831i	−0.0395714	−	0.0685397i	0.845561	−	0.533878i	$-0.179266\pi$
$463$	−394.233	−	682.831i	−0.0395714	−	0.0685397i	−0.885133	+	0.465339i	$0.845933\pi$
$464$	332.068	+	575.158i	0.0332238	+	0.0575454i
$465$		0			0
$466$	−7577.91	+	13125.3i	−0.753305	+	1.30476i
$467$	17068.0			1.69125			0.845626	−	0.533776i	$-0.179228\pi$
$467$	17068.0			1.69125			0.845626	+	0.533776i	$0.179228\pi$
$468$		0			0
$469$	8282.72			0.815481
$470$	4662.63	−	8075.91i	0.457598	−	0.792583i
$471$		0			0
$472$	−57.0302	−	98.7793i	−0.00556150	−	0.00963280i
$473$	134.123	+	232.307i	0.0130380	+	0.0225824i
$474$		0			0
$475$	−6010.56	+	10410.6i	−0.580596	+	1.00562i
$476$	−10149.8			−0.977343
$477$		0			0
$478$	24674.4			2.36105
$479$	758.994	−	1314.62i	0.0723994	−	0.125399i	−0.827553	−	0.561388i	$-0.810268\pi$
$479$	758.994	−	1314.62i	0.0723994	−	0.125399i	0.899952	+	0.435988i	$0.143601\pi$
$480$		0			0
$481$	3160.48	+	5474.11i	0.299596	+	0.518915i
$482$	14405.4	+	24950.9i	1.36130	+	2.35785i
$483$		0			0
$484$	6840.00	−	11847.2i	0.642374	−	1.11262i
$485$	−3058.80			−0.286377
$486$		0			0
$487$	12737.3			1.18518			0.592591	−	0.805503i	$-0.298105\pi$
$487$	12737.3			1.18518			0.592591	+	0.805503i	$0.298105\pi$
$488$	−559.347	+	968.817i	−0.0518861	+	0.0898694i
$489$		0			0
$490$	1984.74	+	3437.68i	0.182983	+	0.316936i
$491$	2823.85	+	4891.05i	0.259549	+	0.449552i	0.966121	−	0.258089i	$-0.0830928\pi$
$491$	2823.85	+	4891.05i	0.259549	+	0.449552i	−0.706572	+	0.707641i	$0.749759\pi$
$492$		0			0
$493$	852.505	−	1476.58i	0.0778801	−	0.134892i
$494$	−24652.1			−2.24525
$495$		0			0
$496$	−883.945			−0.0800208
$497$	6649.78	−	11517.7i	0.600167	−	1.03952i
$498$		0			0
$499$	−5423.14	−	9393.15i	−0.486519	−	0.842676i	0.513361	−	0.858173i	$-0.328400\pi$
$499$	−5423.14	−	9393.15i	−0.486519	−	0.842676i	−0.999880	+	0.0154970i	$0.995067\pi$
$500$	−5879.83	−	10184.2i	−0.525908	−	0.910899i
$501$		0			0
$502$	−9040.73	+	15659.0i	−0.803800	+	1.39222i
$503$	12345.7			1.09437			0.547186	−	0.837011i	$-0.315699\pi$
$503$	12345.7			1.09437			0.547186	+	0.837011i	$0.315699\pi$
$504$		0			0
$505$	−2615.23			−0.230448
$506$	−834.147	+	1444.79i	−0.0732853	+	0.126934i
$507$		0			0
$508$	4979.77	+	8625.22i	0.434925	+	0.753311i
$509$	−2947.87	−	5105.87i	−0.256704	−	0.444624i	0.708653	−	0.705557i	$-0.249303\pi$
$509$	−2947.87	−	5105.87i	−0.256704	−	0.444624i	−0.965357	+	0.260933i	$0.915970\pi$
$510$		0			0
$511$	−2850.27	+	4936.82i	−0.246749	+	0.427381i
$512$	−10166.2			−0.877514
$513$		0			0
$514$	−14623.6			−1.25490
$515$	−2247.18	+	3892.23i	−0.192277	+	0.333033i
$516$		0			0
$517$	−2309.40	−	4000.00i	−0.196455	−	0.340270i
$518$	3446.32	+	5969.20i	0.292322	+	0.506316i
$519$		0			0
$520$	1531.99	−	2653.48i	0.129196	−	0.223775i
$521$	−5211.51			−0.438235			−0.219118	−	0.975698i	$-0.570318\pi$
$521$	−5211.51			−0.438235			−0.219118	+	0.975698i	$0.570318\pi$
$522$		0			0
$523$	−9809.86			−0.820182			−0.410091	−	0.912045i	$-0.634503\pi$
$523$	−9809.86			−0.820182			−0.410091	+	0.912045i	$0.634503\pi$
$524$	9198.38	−	15932.1i	0.766857	−	1.32824i
$525$		0			0
$526$	−14256.9	−	24693.7i	−1.18181	−	2.04695i
$527$	1134.66	+	1965.29i	0.0937886	+	0.162447i
$528$		0			0
$529$	5358.71	−	9281.56i	0.440430	−	0.762847i
$530$	8868.62			0.726846
$531$		0			0
$532$	−15632.3			−1.27396
$533$	−8441.11	+	14620.4i	−0.685976	+	1.18814i
$534$		0			0
$535$	1304.66	+	2259.73i	0.105430	+	0.182611i
$536$	4657.75	+	8067.47i	0.375344	+	0.650115i
$537$		0			0
$538$	6350.72	−	10999.8i	0.508920	−	0.881476i
$539$	1966.09			0.157116
$540$		0			0
$541$	8084.25			0.642456			0.321228	−	0.947002i	$-0.395904\pi$
$541$	8084.25			0.642456			0.321228	+	0.947002i	$0.395904\pi$
$542$	−2919.33	+	5056.43i	−0.231358	+	0.400724i
$543$		0			0
$544$	8942.24	+	15488.4i	0.704771	+	1.22070i
$545$	521.738	+	903.677i	0.0410070	+	0.0710262i
$546$		0			0
$547$	12033.6	−	20842.7i	0.940617	−	1.62920i	0.176319	−	0.984333i	$-0.443581\pi$
$547$	12033.6	−	20842.7i	0.940617	−	1.62920i	0.764298	−	0.644863i	$-0.223086\pi$
$548$	29471.8			2.29739
$549$		0			0
$550$	−4538.84			−0.351885
$551$	1312.99	−	2274.17i	0.101516	−	0.175831i
$552$		0			0
$553$	−2944.60	−	5100.20i	−0.226433	−	0.392193i
$554$	−18310.3	−	31714.4i	−1.40421	−	2.43216i
$555$		0			0
$556$	−3524.98	+	6105.44i	−0.268871	+	0.465698i
$557$	−4582.37			−0.348584			−0.174292	−	0.984694i	$-0.555764\pi$
$557$	−4582.37			−0.348584			−0.174292	+	0.984694i	$0.555764\pi$
$558$		0			0
$559$	−1300.42			−0.0983934
$560$	−822.891	+	1425.29i	−0.0620955	+	0.107553i
$561$		0			0
$562$	11322.7	+	19611.6i	0.849860	+	1.47200i
$563$	−1547.66	−	2680.62i	−0.115854	−	0.200666i	0.802267	−	0.596966i	$-0.203627\pi$
$563$	−1547.66	−	2680.62i	−0.115854	−	0.200666i	−0.918121	+	0.396300i	$0.870294\pi$
$564$		0			0
$565$	1599.02	−	2769.59i	0.119064	−	0.206226i
$566$	13466.9			1.00010
$567$		0			0
$568$	14957.9			1.10496
$569$	10282.5	−	17809.9i	0.757586	−	1.31218i	−0.186492	−	0.982456i	$-0.559712\pi$
$569$	10282.5	−	17809.9i	0.757586	−	1.31218i	0.944078	−	0.329721i	$-0.106955\pi$
$570$		0			0
$571$	584.992	+	1013.24i	0.0428742	+	0.0742602i	0.886666	−	0.462410i	$-0.153015\pi$
$571$	584.992	+	1013.24i	0.0428742	+	0.0742602i	−0.843792	+	0.536670i	$0.819682\pi$
$572$	−2706.39	−	4687.60i	−0.197832	−	0.342655i
$573$		0			0
$574$	−9204.54	+	15942.7i	−0.669320	+	1.15930i
$575$	−3943.80			−0.286031
$576$		0			0
$577$	−13073.0			−0.943214			−0.471607	−	0.881809i	$-0.656326\pi$
$577$	−13073.0			−0.943214			−0.471607	+	0.881809i	$0.656326\pi$
$578$	1671.75	−	2895.55i	0.120304	−	0.208372i
$579$		0			0
$580$	582.049	+	1008.14i	0.0416694	+	0.0721735i
$581$	600.789	+	1040.60i	0.0429000	+	0.0743050i
$582$		0			0
$583$	2196.31	−	3804.13i	0.156024	−	0.270242i
$584$	−6411.36			−0.454287
$585$		0			0
$586$	15954.0			1.12466
$587$	−7273.91	+	12598.8i	−0.511459	+	0.885873i	0.488453	+	0.872590i	$0.337561\pi$
$587$	−7273.91	+	12598.8i	−0.511459	+	0.885873i	−0.999912	+	0.0132825i	$0.995772\pi$
$588$		0			0
$589$	1747.55	+	3026.85i	0.122252	+	0.211747i
$590$	84.6754	+	146.662i	0.00590852	+	0.0102339i
$591$		0			0
$592$	1909.30	−	3307.00i	0.132554	−	0.229589i
$593$	−19018.0			−1.31699			−0.658494	−	0.752586i	$-0.728806\pi$
$593$	−19018.0			−1.31699			−0.658494	+	0.752586i	$0.728806\pi$
$594$		0			0
$595$	4225.16			0.291117
$596$	−18933.8	+	32794.3i	−1.30127	+	2.25387i
$597$		0			0
$598$	−4043.84	−	7004.14i	−0.276530	−	0.478964i
$599$	5587.20	+	9677.32i	0.381113	+	0.660108i	0.991222	−	0.132210i	$-0.0422074\pi$
$599$	5587.20	+	9677.32i	0.381113	+	0.660108i	−0.610108	+	0.792318i	$0.708874\pi$
$600$		0			0
$601$	−2294.27	+	3973.79i	−0.155716	+	0.269708i	−0.933319	−	0.359047i	$-0.883102\pi$
$601$	−2294.27	+	3973.79i	−0.155716	+	0.269708i	0.777604	+	0.628755i	$0.216435\pi$
$602$	−1418.03			−0.0960045
$603$		0			0
$604$	−19458.0			−1.31082
$605$	−2847.35	+	4931.76i	−0.191341	+	0.331413i
$606$		0			0
$607$	5744.99	+	9950.61i	0.384155	+	0.665375i	0.991652	−	0.128947i	$-0.0411596\pi$
$607$	5744.99	+	9950.61i	0.384155	+	0.665375i	−0.607497	+	0.794322i	$0.707826\pi$
$608$	13772.5	+	23854.6i	0.918662	+	1.59117i
$609$		0			0
$610$	830.487	−	1438.45i	0.0551237	−	0.0954770i
$611$	22391.4			1.48258
$612$		0			0
$613$	−22966.9			−1.51326			−0.756628	−	0.653846i	$-0.773154\pi$
$613$	−22966.9			−1.51326			−0.756628	+	0.653846i	$0.773154\pi$
$614$	−7518.69	+	13022.7i	−0.494185	+	0.855953i
$615$		0			0
$616$	−827.420	−	1433.13i	−0.0541197	−	0.0937380i
$617$	−4248.31	−	7358.29i	−0.277197	−	0.480120i	0.693490	−	0.720466i	$-0.256072\pi$
$617$	−4248.31	−	7358.29i	−0.277197	−	0.480120i	−0.970687	+	0.240347i	$0.922739\pi$
$618$		0			0
$619$	−7169.94	+	12418.7i	−0.465564	+	0.806381i	−0.999227	−	0.0393163i	$-0.987482\pi$
$619$	−7169.94	+	12418.7i	−0.465564	+	0.806381i	0.533662	+	0.845698i	$0.320815\pi$
$620$	−1549.38			−0.100362
$621$		0			0
$622$	31372.6			2.02239
$623$	53.3399	−	92.3874i	0.00343021	−	0.00594129i
$624$		0			0
$625$	−4026.36	−	6973.86i	−0.257687	−	0.446327i
$626$	−10618.7	−	18392.2i	−0.677971	−	1.17428i
$627$		0			0
$628$	−12109.4	+	20974.1i	−0.769456	+	1.33274i
$629$	−9803.34			−0.621439
$630$		0			0
$631$	17834.3			1.12516			0.562578	−	0.826744i	$-0.309810\pi$
$631$	17834.3			1.12516			0.562578	+	0.826744i	$0.309810\pi$
$632$	3311.77	−	5736.16i	0.208442	−	0.361032i
$633$		0			0
$634$	−16500.8	−	28580.3i	−1.03365	−	1.79033i
$635$	−2072.98	−	3590.51i	−0.129549	−	0.224386i
$636$		0			0
$637$	−4765.68	+	8254.39i	−0.296425	+	0.513424i
$638$	991.499			0.0615264
$639$		0			0
$640$	−7459.69			−0.460735
$641$	13173.0	−	22816.3i	0.811705	−	1.40591i	−0.0999654	−	0.994991i	$-0.531873\pi$
$641$	13173.0	−	22816.3i	0.811705	−	1.40591i	0.911670	−	0.410923i	$-0.134793\pi$
$642$		0			0
$643$	10782.5	+	18675.9i	0.661309	+	1.14542i	0.980272	+	0.197653i	$0.0633321\pi$
$643$	10782.5	+	18675.9i	0.661309	+	1.14542i	−0.318963	+	0.947767i	$0.603335\pi$
$644$	−2564.26	−	4441.43i	−0.156904	−	0.271765i
$645$		0			0
$646$	19116.8	−	33111.3i	1.16431	−	2.01664i
$647$	−4186.32			−0.254376			−0.127188	−	0.991879i	$-0.540595\pi$
$647$	−4186.32			−0.254376			−0.127188	+	0.991879i	$0.540595\pi$
$648$		0			0
$649$	83.8794			0.00507328
$650$	11001.9	−	19055.8i	0.663891	−	1.14989i
$651$		0			0
$652$	−12164.1	−	21068.9i	−0.730650	−	1.26552i
$653$	1402.57	+	2429.33i	0.0840534	+	0.145585i	0.904987	−	0.425438i	$-0.139880\pi$
$653$	1402.57	+	2429.33i	0.0840534	+	0.145585i	−0.820934	+	0.571023i	$0.806547\pi$
$654$		0			0
$655$	−3829.10	+	6632.20i	−0.228420	+	0.395636i
$656$	10198.8			0.607008
$657$		0			0
$658$	24416.5			1.44659
$659$	−9536.15	+	16517.1i	−0.563696	+	0.976350i	0.433474	+	0.901166i	$0.357288\pi$
$659$	−9536.15	+	16517.1i	−0.563696	+	0.976350i	−0.997170	+	0.0751839i	$0.976046\pi$
$660$		0			0
$661$	12256.5	+	21228.9i	0.721216	+	1.24918i	0.960513	+	0.278237i	$0.0897500\pi$
$661$	12256.5	+	21228.9i	0.721216	+	1.24918i	−0.239296	+	0.970947i	$0.576917\pi$
$662$	−6842.00	−	11850.7i	−0.401695	−	0.695756i
$663$		0			0
$664$	−675.702	+	1170.35i	−0.0394915	+	0.0684012i
$665$	6507.40			0.379468
$666$		0			0
$667$	861.513			0.0500119
$668$	10678.0	−	18494.8i	0.618477	−	1.07123i
$669$		0			0
$670$	−6915.58	−	11978.1i	−0.398764	−	0.690680i
$671$	−411.340	−	712.462i	−0.0236656	−	0.0409900i
$672$		0			0
$673$	1773.32	−	3071.49i	0.101570	−	0.175924i	−0.810762	−	0.585376i	$-0.800947\pi$
$673$	1773.32	−	3071.49i	0.101570	−	0.175924i	0.912332	+	0.409452i	$0.134280\pi$
$674$	40356.1			2.30632
$675$		0			0
$676$	1816.79			0.103367
$677$	8937.50	−	15480.2i	0.507380	−	0.878807i	−0.492584	−	0.870265i	$-0.663948\pi$
$677$	8937.50	−	15480.2i	0.507380	−	0.878807i	0.999964	−	0.00854232i	$-0.00271914\pi$
$678$		0			0
$679$	−4004.45	−	6935.91i	−0.226328	−	0.392012i
$680$	2376.00	+	4115.35i	0.133993	+	0.232083i
$681$		0			0
$682$	−659.829	+	1142.86i	−0.0370471	+	0.0641675i
$683$	−2857.23			−0.160072			−0.0800358	−	0.996792i	$-0.525503\pi$
$683$	−2857.23			−0.160072			−0.0800358	+	0.996792i	$0.525503\pi$
$684$		0			0
$685$	−12268.5			−0.684315
$686$	−14282.5	+	24737.9i	−0.794908	+	1.37682i
$687$		0			0
$688$	392.803	+	680.354i	0.0217667	+	0.0377010i
$689$	10647.5	+	18441.9i	0.588732	+	1.01971i
$690$		0			0
$691$	7813.79	−	13533.9i	0.430175	−	0.745084i	−0.566714	−	0.823915i	$-0.691785\pi$
$691$	7813.79	−	13533.9i	0.430175	−	0.745084i	0.996888	+	0.0788308i	$0.0251187\pi$
$692$	−35238.5			−1.93579
$693$		0			0
$694$	−35434.7			−1.93816
$695$	1467.38	−	2541.57i	0.0800874	−	0.138716i
$696$		0			0
$697$	−13091.5	−	22675.2i	−0.711445	−	1.23226i
$698$	6725.49	+	11648.9i	0.364704	+	0.631687i
$699$		0			0
$700$	6976.45	−	12083.6i	0.376693	−	0.652451i
$701$	−17562.6			−0.946264			−0.473132	−	0.880992i	$-0.656877\pi$
$701$	−17562.6			−0.946264			−0.473132	+	0.880992i	$0.656877\pi$
$702$		0			0
$703$	−15098.7			−0.810039
$704$	−4023.53	+	6968.95i	−0.215401	+	0.373086i
$705$		0			0
$706$	13445.0	+	23287.3i	0.716724	+	1.24140i
$707$	−3423.75	−	5930.11i	−0.182126	−	0.315452i
$708$		0			0
$709$	−10001.8	+	17323.6i	−0.529795	+	0.917632i	0.469601	+	0.882879i	$0.344398\pi$
$709$	−10001.8	+	17323.6i	−0.529795	+	0.917632i	−0.999396	+	0.0347532i	$0.988935\pi$
$710$	−22208.7			−1.17391
$711$		0			0
$712$	119.982			0.00631533
$713$	−573.324	+	993.027i	−0.0301138	+	0.0521587i
$714$		0			0
$715$	1126.62	+	1951.36i	0.0589273	+	0.102065i
$716$	7608.27	+	13177.9i	0.397115	+	0.687824i
$717$		0			0
$718$	−7231.62	+	12525.5i	−0.375880	+	0.651043i
$719$	−25504.1			−1.32287			−0.661435	−	0.750002i	$-0.730052\pi$
$719$	−25504.1			−1.32287			−0.661435	+	0.750002i	$0.730052\pi$
$720$		0			0
$721$	−11767.7			−0.607837
$722$	14448.1	−	25024.9i	0.744743	−	1.28993i
$723$		0			0
$724$	21963.8	+	38042.4i	1.12746	+	1.95281i
$725$	1171.94	+	2029.85i	0.0600340	+	0.103982i
$726$		0			0
$727$	11954.9	−	20706.5i	0.609879	−	1.05634i	−0.381380	−	0.924418i	$-0.624551\pi$
$727$	11954.9	−	20706.5i	0.609879	−	1.05634i	0.991260	−	0.131924i	$-0.0421155\pi$
$728$	8022.47			0.408424
$729$		0			0
$730$	9519.23			0.482634
$731$	1008.43	−	1746.65i	0.0510233	−	0.0883750i
$732$		0			0
$733$	4252.77	+	7366.02i	0.214297	+	0.371173i	0.953055	−	0.302798i	$-0.0979206\pi$
$733$	4252.77	+	7366.02i	0.214297	+	0.371173i	−0.738758	+	0.673971i	$0.764587\pi$
$734$	6447.57	+	11167.5i	0.324229	+	0.561581i
$735$		0			0
$736$	−4518.36	+	7826.04i	−0.226290	+	0.391945i
$737$	−6850.57			−0.342394
$738$		0			0
$739$	25802.5			1.28438			0.642192	−	0.766544i	$-0.278025\pi$
$739$	25802.5			1.28438			0.642192	+	0.766544i	$0.278025\pi$
$740$	3346.62	−	5796.52i	0.166249	−	0.287952i
$741$		0			0
$742$	11610.4	+	20109.9i	0.574437	+	0.994955i
$743$	13668.8	+	23675.0i	0.674911	+	1.16898i	0.976495	+	0.215541i	$0.0691514\pi$
$743$	13668.8	+	23675.0i	0.674911	+	1.16898i	−0.301584	+	0.953440i	$0.597515\pi$
$744$		0			0
$745$	7881.75	−	13651.6i	0.387604	−	0.671350i
$746$	−5087.50			−0.249687
$747$		0			0
$748$	8394.82			0.410354
$749$	−3416.01	+	5916.71i	−0.166647	+	0.288641i
$750$		0			0
$751$	−1668.32	−	2889.61i	−0.0810623	−	0.140404i	0.822644	−	0.568557i	$-0.192498\pi$
$751$	−1668.32	−	2889.61i	−0.0810623	−	0.140404i	−0.903706	+	0.428153i	$0.859165\pi$
$752$	−6763.50	−	11714.7i	−0.327978	−	0.568075i
$753$		0			0
$754$	−2403.33	+	4162.70i	−0.116080	+	0.201056i
$755$	8099.98			0.390448
$756$		0			0
$757$	33149.5			1.59160			0.795798	−	0.605562i	$-0.207052\pi$
$757$	33149.5			1.59160			0.795798	+	0.605562i	$0.207052\pi$
$758$	−8781.01	+	15209.2i	−0.420766	+	0.728788i
$759$		0			0
$760$	3659.41	+	6338.29i	0.174659	+	0.302518i
$761$	−5498.42	−	9523.54i	−0.261915	−	0.453651i	0.704836	−	0.709371i	$-0.251021\pi$
$761$	−5498.42	−	9523.54i	−0.261915	−	0.453651i	−0.966751	+	0.255720i	$0.917687\pi$
$762$		0			0
$763$	−1366.08	+	2366.12i	−0.0648169	+	0.112266i
$764$	26709.2			1.26480
$765$		0			0
$766$	−47235.0			−2.22803
$767$	−203.319	+	352.158i	−0.00957159	+	0.0165785i
$768$		0			0
$769$	−16642.5	−	28825.6i	−0.780420	−	1.35173i	−0.931697	−	0.363236i	$-0.881672\pi$
$769$	−16642.5	−	28825.6i	−0.780420	−	1.35173i	0.151277	−	0.988491i	$-0.451661\pi$
$770$	1228.51	+	2127.84i	0.0574966	+	0.0995870i
$771$		0			0
$772$	7420.88	−	12853.3i	0.345963	−	0.599225i
$773$	7242.46			0.336990			0.168495	−	0.985703i	$-0.446109\pi$
$773$	7242.46			0.336990			0.168495	+	0.985703i	$0.446109\pi$
$774$		0			0
$775$	−3119.63			−0.144594
$776$	4503.77	−	7800.77i	0.208345	−	0.360865i
$777$		0			0
$778$	−4513.48	−	7817.58i	−0.207990	−	0.360249i
$779$	−20163.0	−	34923.4i	−0.927362	−	1.60624i
$780$		0			0
$781$	−5499.98	+	9526.24i	−0.251991	+	0.436461i
$782$	12543.4			0.573595
$783$		0			0
$784$	5758.05			0.262302
$785$	5040.91	−	8731.11i	0.229195	−	0.396977i
$786$		0			0
$787$	−8707.15	−	15081.2i	−0.394379	−	0.683084i	0.598643	−	0.801016i	$-0.295707\pi$
$787$	−8707.15	−	15081.2i	−0.394379	−	0.683084i	−0.993022	+	0.117932i	$0.962374\pi$
$788$	−14623.6	−	25328.8i	−0.661096	−	1.14505i
$789$		0			0
$790$	−4917.14	+	8516.74i	−0.221448	+	0.383559i
$791$	8373.50			0.376394
$792$		0			0
$793$	3988.26			0.178597
$794$	−17352.7	+	30055.8i	−0.775599	+	1.34338i
$795$		0			0
$796$	−13770.1	−	23850.5i	−0.613151	−	1.06201i
$797$	14566.5	+	25229.9i	0.647391	+	1.12131i	0.983744	+	0.179578i	$0.0574732\pi$
$797$	14566.5	+	25229.9i	0.647391	+	1.12131i	−0.336353	+	0.941736i	$0.609193\pi$
$798$		0			0
$799$	−17363.7	+	30074.8i	−0.768815	+	1.33163i
$800$	−24585.8			−1.08655
$801$		0			0
$802$	11272.7			0.496323
$803$	2357.44	−	4083.20i	0.103602	−	0.179443i
$804$		0			0
$805$	1067.45	+	1848.88i	0.0467362	+	0.0809495i
$806$	−3198.77	−	5540.43i	−0.139791	−	0.242126i
$807$		0			0
$808$	3850.66	−	6669.55i	0.167656	−	0.290388i
$809$	36440.1			1.58364			0.791820	−	0.610754i	$-0.209134\pi$
$809$	36440.1			1.58364			0.791820	+	0.610754i	$0.209134\pi$
$810$		0			0
$811$	−18922.0			−0.819286			−0.409643	−	0.912246i	$-0.634347\pi$
$811$	−18922.0			−0.819286			−0.409643	+	0.912246i	$0.634347\pi$
$812$	−1523.99	+	2639.63i	−0.0658639	+	0.114080i
$813$		0			0
$814$	−2850.42	−	4937.08i	−0.122736	−	0.212585i
$815$	5063.68	+	8770.55i	0.217636	+	0.376956i
$816$		0			0
$817$	1553.14	−	2690.11i	0.0665084	−	0.115196i
$818$	−25559.3			−1.09249
$819$		0			0
$820$	17876.5			0.761311
$821$	−8955.36	+	15511.1i	−0.380687	+	0.659369i	−0.991161	−	0.132667i	$-0.957646\pi$
$821$	−8955.36	+	15511.1i	−0.380687	+	0.659369i	0.610474	+	0.792037i	$0.290979\pi$
$822$		0			0
$823$	−8762.22	−	15176.6i	−0.371120	−	0.642799i	0.618618	−	0.785692i	$-0.287693\pi$
$823$	−8762.22	−	15176.6i	−0.371120	−	0.642799i	−0.989738	+	0.142893i	$0.954360\pi$
$824$	−6617.50	−	11461.8i	−0.279771	−	0.484578i
$825$		0			0
$826$	−221.707	+	384.008i	−0.00933920	+	0.0161760i
$827$	17643.9			0.741885			0.370943	−	0.928656i	$-0.379035\pi$
$827$	17643.9			0.741885			0.370943	+	0.928656i	$0.379035\pi$
$828$		0			0
$829$	45178.6			1.89278			0.946391	−	0.323023i	$-0.104699\pi$
$829$	45178.6			1.89278			0.946391	+	0.323023i	$0.104699\pi$
$830$	1003.25	−	1737.67i	0.0419556	−	0.0726693i
$831$		0			0
$832$	−19505.6	−	33784.6i	−0.812781	−	1.40778i
$833$	−7391.21	−	12802.0i	−0.307431	−	0.532487i
$834$		0			0
$835$	−4445.02	+	7699.00i	−0.184223	+	0.319084i
$836$	12929.3			0.534893
$837$		0			0
$838$	−38219.5			−1.57550
$839$	13388.0	−	23188.7i	0.550901	−	0.954188i	−0.447309	−	0.894379i	$-0.647618\pi$
$839$	13388.0	−	23188.7i	0.550901	−	0.954188i	0.998210	−	0.0598087i	$-0.0190491\pi$
$840$		0			0
$841$	11938.5	+	20678.1i	0.489503	+	0.847844i
$842$	2309.68	+	4000.48i	0.0945329	+	0.163736i
$843$		0			0
$844$	15478.7	−	26809.9i	0.631278	−	1.09341i
$845$	−756.291			−0.0307896
$846$		0			0
$847$	−14910.6			−0.604879
$848$	6432.31	−	11141.1i	0.260479	−	0.451163i
$849$		0			0
$850$	17063.1	+	29554.2i	0.688541	+	1.19259i
$851$	−2476.73	−	4289.83i	−0.0997665	−	0.172801i
$852$		0			0
$853$	3955.88	−	6851.78i	0.158789	−	0.275030i	−0.775644	−	0.631171i	$-0.782575\pi$
$853$	3955.88	−	6851.78i	0.158789	−	0.275030i	0.934432	+	0.356141i	$0.115908\pi$
$854$	4348.96			0.174260
$855$		0			0
$856$	−7683.92			−0.306812
$857$	924.149	−	1600.67i	0.0368359	−	0.0638016i	−0.847020	−	0.531561i	$-0.821605\pi$
$857$	924.149	−	1600.67i	0.0368359	−	0.0638016i	0.883856	+	0.467760i	$0.154939\pi$
$858$		0			0
$859$	9427.10	+	16328.2i	0.374445	+	0.648558i	0.990244	−	0.139345i	$-0.0444998\pi$
$859$	9427.10	+	16328.2i	0.374445	+	0.648558i	−0.615799	+	0.787904i	$0.711167\pi$
$860$	688.505	+	1192.53i	0.0272998	+	0.0472846i
$861$		0			0
$862$	−21574.2	+	37367.7i	−0.852461	+	1.47651i
$863$	−2086.03			−0.0822821			−0.0411410	−	0.999153i	$-0.513099\pi$
$863$	−2086.03			−0.0822821			−0.0411410	+	0.999153i	$0.513099\pi$
$864$		0			0
$865$	14669.1			0.576605
$866$	1044.86	−	1809.75i	0.0409999	−	0.0710138i
$867$		0			0
$868$	−2028.39	−	3513.27i	−0.0793178	−	0.137383i
$869$	2435.46	+	4218.34i	0.0950717	+	0.164669i
$870$		0			0
$871$	16605.4	−	28761.3i	0.645983	−	1.11888i
$872$	−3072.83			−0.119334
$873$		0			0
$874$	19318.8			0.747675
$875$	−6408.74	+	11100.3i	−0.247606	+	0.428866i
$876$		0			0
$877$	12388.6	+	21457.7i	0.477005	+	0.826197i	0.999653	−	0.0263520i	$-0.00838907\pi$
$877$	12388.6	+	21457.7i	0.477005	+	0.826197i	−0.522648	+	0.852549i	$0.675056\pi$
$878$	−2300.86	−	3985.21i	−0.0884401	−	0.153183i
$879$		0			0
$880$	680.607	−	1178.85i	0.0260719	−	0.0451578i
$881$	−3741.26			−0.143072			−0.0715359	−	0.997438i	$-0.522790\pi$
$881$	−3741.26			−0.143072			−0.0715359	+	0.997438i	$0.522790\pi$
$882$		0			0
$883$	14131.6			0.538580			0.269290	−	0.963059i	$-0.413211\pi$
$883$	14131.6			0.538580			0.269290	+	0.963059i	$0.413211\pi$
$884$	−20348.5	+	35244.7i	−0.774203	+	1.34096i
$885$		0			0
$886$	22951.6	+	39753.4i	0.870288	+	1.50738i
$887$	13311.3	+	23055.8i	0.503888	+	0.872759i	0.999990	+	0.00449496i	$0.00143080\pi$
$887$	13311.3	+	23055.8i	0.503888	+	0.872759i	−0.496102	+	0.868264i	$0.665236\pi$
$888$		0			0
$889$	5427.72	−	9401.09i	0.204769	−	0.354671i
$890$	−178.143			−0.00670938
$891$		0			0
$892$	−478.665			−0.0179674
$893$	−26742.8	+	46319.9i	−1.00214	+	1.73576i
$894$		0			0
$895$	−3167.17	−	5485.70i	−0.118287	−	0.204879i
$896$	−9765.93	−	16915.1i	−0.364126	−	0.630684i
$897$		0			0
$898$	16023.1	−	27752.8i	0.595431	−	1.03132i
$899$	681.475			0.0252820
$900$		0			0
$901$	−33026.9			−1.22118
$902$	7613.00	−	13186.1i	0.281026	−	0.486751i
$903$		0			0
$904$	4708.80	+	8155.89i	0.173244	+	0.300067i
$905$	−9143.09	−	15836.3i	−0.335830	−	0.581675i
$906$		0			0
$907$	−26309.7	+	45569.7i	−0.963174	+	1.66827i	−0.248731	+	0.968572i	$0.580014\pi$
$907$	−26309.7	+	45569.7i	−0.963174	+	1.66827i	−0.714443	+	0.699694i	$0.753320\pi$
$908$	−7595.70			−0.277612
$909$		0			0
$910$	−11911.3			−0.433908
$911$	5090.22	−	8816.52i	0.185122	−	0.320641i	−0.758495	−	0.651678i	$-0.774065\pi$
$911$	5090.22	−	8816.52i	0.185122	−	0.320641i	0.943618	+	0.331037i	$0.107399\pi$
$912$		0			0
$913$	−496.908	−	860.670i	−0.0180123	−	0.0311983i
$914$	15618.7	+	27052.3i	0.565229	+	0.979005i
$915$		0			0
$916$	−23869.6	+	41343.3i	−0.860996	+	1.49129i
$917$	−20051.6			−0.722097
$918$		0			0
$919$	−45618.2			−1.63744			−0.818718	−	0.574195i	$-0.805315\pi$
$919$	−45618.2			−1.63744			−0.818718	+	0.574195i	$0.805315\pi$
$920$	−1200.55	+	2079.42i	−0.0430229	+	0.0745178i
$921$		0			0
$922$	−12501.9	−	21653.9i	−0.446558	−	0.773462i
$923$	−26663.2	−	46182.1i	−0.950846	−	1.64691i
$924$		0			0
$925$	6738.32	−	11671.1i	0.239518	−	0.414858i
$926$	−3447.39			−0.122342
$927$		0			0
$928$	5370.70			0.189980
$929$	−6600.20	+	11431.9i	−0.233095	+	0.403733i	−0.958717	−	0.284361i	$-0.908219\pi$
$929$	−6600.20	+	11431.9i	−0.233095	+	0.403733i	0.725622	+	0.688093i	$0.241552\pi$
$930$		0			0
$931$	−11383.6	−	19717.0i	−0.400734	−	0.694091i
$932$	19267.4	+	33372.1i	0.677172	+	1.17290i
$933$		0			0
$934$	37313.1	−	64628.2i	1.30720	−	2.26413i
$935$	−3494.59			−0.122230
$936$		0			0
$937$	−13468.1			−0.469565			−0.234783	−	0.972048i	$-0.575438\pi$
$937$	−13468.1			−0.469565			−0.234783	+	0.972048i	$0.575438\pi$
$938$	18107.2	−	31362.6i	0.630299	−	1.09171i
$939$		0			0
$940$	−11855.1	−	20533.6i	−0.411351	−	0.712480i
$941$	6942.05	+	12024.0i	0.240493	+	0.416547i	0.960855	−	0.277052i	$-0.0893574\pi$
$941$	6942.05	+	12024.0i	0.240493	+	0.416547i	−0.720362	+	0.693599i	$0.756024\pi$
$942$		0			0
$943$	6614.93	−	11457.4i	0.228432	−	0.395657i
$944$	245.656			0.00846974
$945$		0			0
$946$	1172.84			0.0403091
$947$	2638.32	−	4569.70i	0.0905320	−	0.156806i	−0.817203	−	0.576350i	$-0.804477\pi$
$947$	2638.32	−	4569.70i	0.0905320	−	0.156806i	0.907735	+	0.419544i	$0.137810\pi$
$948$		0			0
$949$	11428.6	+	19794.9i	0.390924	+	0.677101i
$950$	26279.8	+	45518.0i	0.897506	+	1.55453i
$951$		0			0
$952$	−6221.13	+	10775.3i	−0.211794	+	0.366838i
$953$	26131.4			0.888225			0.444112	−	0.895971i	$-0.353519\pi$
$953$	26131.4			0.888225			0.444112	+	0.895971i	$0.353519\pi$
$954$		0			0
$955$	−11118.5			−0.376740
$956$	31368.2	−	54331.4i	1.06121	−	1.83808i
$957$		0			0
$958$	−3318.54	−	5747.87i	−0.111918	−	0.193847i
$959$	−16061.4	−	27819.2i	−0.540825	−	0.936736i
$960$		0			0
$961$	14442.0	−	25014.3i	0.484777	−	0.839658i
$962$	27637.0			0.926251
$963$		0			0
$964$	73253.6			2.44745
$965$	−3089.16	+	5350.59i	−0.103050	+	0.178489i
$966$		0			0
$967$	1998.77	+	3461.96i	0.0664695	+	0.115128i	0.897345	−	0.441330i	$-0.145493\pi$
$967$	1998.77	+	3461.96i	0.0664695	+	0.115128i	−0.830875	+	0.556458i	$0.812160\pi$
$968$	−8384.89	−	14523.1i	−0.278410	−	0.482220i
$969$		0			0
$970$	−6686.96	+	11582.2i	−0.221346	+	0.383382i
$971$	−41785.1			−1.38100			−0.690499	−	0.723334i	$-0.742609\pi$
$971$	−41785.1			−1.38100			−0.690499	+	0.723334i	$0.742609\pi$
$972$		0			0
$973$	7684.12			0.253177
$974$	27845.6	−	48230.0i	0.916048	−	1.58664i
$975$		0			0
$976$	−1204.69	−	2086.58i	−0.0395093	−	0.0684321i
$977$	6122.55	+	10604.6i	0.200489	+	0.347257i	0.948686	−	0.316220i	$-0.102414\pi$
$977$	6122.55	+	10604.6i	0.200489	+	0.347257i	−0.748197	+	0.663476i	$0.769080\pi$
$978$		0			0
$979$	−44.1170	+	76.4129i	−0.00144023	+	0.00249455i
$980$	10092.7			0.328979
$981$		0			0
$982$	24693.3			0.802439
$983$	21891.5	−	37917.3i	0.710307	−	1.23029i	−0.254435	−	0.967090i	$-0.581889\pi$
$983$	21891.5	−	37917.3i	0.710307	−	1.23029i	0.964742	−	0.263198i	$-0.0847773\pi$
$984$		0			0
$985$	6087.50	+	10543.9i	0.196918	+	0.341071i
$986$	−3727.39	−	6456.03i	−0.120390	−	0.208521i
$987$		0			0
$988$	−31339.9	+	54282.3i	−1.00917	+	1.74793i
$989$	1019.08			0.0327654
$990$		0			0
$991$	5178.38			0.165991			0.0829953	−	0.996550i	$-0.473551\pi$
$991$	5178.38			0.165991			0.0829953	+	0.996550i	$0.473551\pi$
$992$	−3574.12	+	6190.57i	−0.114394	+	0.198136i
$993$		0			0
$994$	−29074.7	−	50358.8i	−0.927760	−	1.60693i
$995$	5732.22	+	9928.50i	0.182637	+	0.316336i
$996$		0			0
$997$	−12860.5	+	22275.0i	−0.408520	+	0.707578i	−0.994724	−	0.102586i	$-0.967288\pi$
$997$	−12860.5	+	22275.0i	−0.408520	+	0.707578i	0.586204	+	0.810164i	$0.300622\pi$
$998$	−47423.0			−1.50416
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.4.c.a.19.2		4
3.2	odd	2		9.4.c.a.7.1	yes	4
4.3	odd	2		432.4.i.c.289.1		4
9.2	odd	6		81.4.a.d.1.2		2
9.4	even	3	inner	27.4.c.a.10.2		4
9.5	odd	6		9.4.c.a.4.1	✓	4
9.7	even	3		81.4.a.a.1.1		2
12.11	even	2		144.4.i.c.97.1		4
15.2	even	4		225.4.k.b.124.1		8
15.8	even	4		225.4.k.b.124.4		8
15.14	odd	2		225.4.e.b.151.2		4
36.7	odd	6		1296.4.a.i.1.2		2
36.11	even	6		1296.4.a.u.1.1		2
36.23	even	6		144.4.i.c.49.1		4
36.31	odd	6		432.4.i.c.145.1		4
45.14	odd	6		225.4.e.b.76.2		4
45.23	even	12		225.4.k.b.49.1		8
45.29	odd	6		2025.4.a.g.1.1		2
45.32	even	12		225.4.k.b.49.4		8
45.34	even	6		2025.4.a.n.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.4.c.a.4.1	✓	4	9.5	odd	6
9.4.c.a.7.1	yes	4	3.2	odd	2
27.4.c.a.10.2		4	9.4	even	3	inner
27.4.c.a.19.2		4	1.1	even	1	trivial
81.4.a.a.1.1		2	9.7	even	3
81.4.a.d.1.2		2	9.2	odd	6
144.4.i.c.49.1		4	36.23	even	6
144.4.i.c.97.1		4	12.11	even	2
225.4.e.b.76.2		4	45.14	odd	6
225.4.e.b.151.2		4	15.14	odd	2
225.4.k.b.49.1		8	45.23	even	12
225.4.k.b.49.4		8	45.32	even	12
225.4.k.b.124.1		8	15.2	even	4
225.4.k.b.124.4		8	15.8	even	4
432.4.i.c.145.1		4	36.31	odd	6
432.4.i.c.289.1		4	4.3	odd	2
1296.4.a.i.1.2		2	36.7	odd	6
1296.4.a.u.1.1		2	36.11	even	6
2025.4.a.g.1.1		2	45.29	odd	6
2025.4.a.n.1.2		2	45.34	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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	27.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.18614 - 3.78651i) q^{2} +(-5.55842 - 9.62747i) q^{4} +(2.31386 + 4.00772i) q^{5} +(-6.05842 + 10.4935i) q^{7} -13.6277 q^{8} +O(q^{10})\)	\(q+(2.18614 - 3.78651i) q^{2} +(-5.55842 - 9.62747i) q^{4} +(2.31386 + 4.00772i) q^{5} +(-6.05842 + 10.4935i) q^{7} -13.6277 q^{8} +20.2337 q^{10} +(5.01087 - 8.67909i) q^{11} +(24.2921 + 42.0752i) q^{13} +(26.4891 + 45.8805i) q^{14} +(14.6753 - 25.4183i) q^{16} -75.3505 q^{17} -116.052 q^{19} +(25.7228 - 44.5532i) q^{20} +(-21.9090 - 37.9474i) q^{22} +(-19.0367 - 32.9725i) q^{23} +(51.7921 - 89.7066i) q^{25} +212.424 q^{26} +134.701 q^{28} +(-11.3139 + 19.5962i) q^{29} +(-15.0584 - 26.0820i) q^{31} +(-118.675 - 205.552i) q^{32} +(-164.727 + 285.315i) q^{34} -56.0733 q^{35} +130.103 q^{37} +(-253.705 + 439.430i) q^{38} +(-31.5326 - 54.6161i) q^{40} +(173.742 + 300.930i) q^{41} +(-13.3832 + 23.1803i) q^{43} -111.410 q^{44} -166.467 q^{46} +(230.439 - 399.132i) q^{47} +(98.0910 + 169.899i) q^{49} +(-226.450 - 392.222i) q^{50} +(270.052 - 467.743i) q^{52} +438.310 q^{53} +46.3778 q^{55} +(82.5625 - 143.002i) q^{56} +(49.4674 + 85.6800i) q^{58} +(4.18487 + 7.24841i) q^{59} +(41.0448 - 71.0916i) q^{61} -131.679 q^{62} -802.959 q^{64} +(-112.417 + 194.712i) q^{65} +(-341.785 - 591.989i) q^{67} +(418.830 + 725.435i) q^{68} +(-122.584 + 212.322i) q^{70} -1097.61 q^{71} +470.464 q^{73} +(284.424 - 492.637i) q^{74} +(645.064 + 1117.28i) q^{76} +(60.7160 + 105.163i) q^{77} +(-243.017 + 420.919i) q^{79} +135.826 q^{80} +1519.30 q^{82} +(49.5829 - 85.8802i) q^{83} +(-174.351 - 301.984i) q^{85} +(58.5149 + 101.351i) q^{86} +(-68.2868 + 118.276i) q^{88} -8.80426 q^{89} -588.687 q^{91} +(-211.628 + 366.550i) q^{92} +(-1007.54 - 1745.12i) q^{94} +(-268.527 - 465.103i) q^{95} +(-330.486 + 572.419i) q^{97} +857.763 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 5 q^{4} + 15 q^{5} - 7 q^{7} - 66 q^{8}+O(q^{10}) \) 4 * q + 3 * q^2 - 5 * q^4 + 15 * q^5 - 7 * q^7 - 66 * q^8	\( 4 q + 3 q^{2} - 5 q^{4} + 15 q^{5} - 7 q^{7} - 66 q^{8} + 12 q^{10} + 66 q^{11} + 11 q^{13} + 60 q^{14} + 7 q^{16} - 198 q^{17} - 154 q^{19} - 12 q^{20} + 33 q^{22} + 33 q^{23} + 121 q^{25} + 528 q^{26} + 332 q^{28} - 51 q^{29} - 43 q^{31} - 423 q^{32} - 297 q^{34} - 6 q^{35} - 100 q^{37} - 561 q^{38} - 264 q^{40} + 132 q^{41} - 88 q^{43} + 462 q^{44} - 528 q^{46} + 399 q^{47} + 513 q^{49} - 429 q^{50} + 770 q^{52} - 108 q^{53} + 1254 q^{55} + 66 q^{56} + 60 q^{58} + 798 q^{59} - 439 q^{61} - 228 q^{62} - 1454 q^{64} + 165 q^{65} - 988 q^{67} + 693 q^{68} - 318 q^{70} - 2736 q^{71} - 910 q^{73} + 816 q^{74} + 1529 q^{76} - 165 q^{77} + 803 q^{79} - 192 q^{80} + 3630 q^{82} + 813 q^{83} - 594 q^{85} + 33 q^{86} - 1221 q^{88} + 792 q^{89} - 1562 q^{91} - 858 q^{92} - 2100 q^{94} - 132 q^{95} - 736 q^{97} + 846 q^{98}+O(q^{100}) \) 4 * q + 3 * q^2 - 5 * q^4 + 15 * q^5 - 7 * q^7 - 66 * q^8 + 12 * q^10 + 66 * q^11 + 11 * q^13 + 60 * q^14 + 7 * q^16 - 198 * q^17 - 154 * q^19 - 12 * q^20 + 33 * q^22 + 33 * q^23 + 121 * q^25 + 528 * q^26 + 332 * q^28 - 51 * q^29 - 43 * q^31 - 423 * q^32 - 297 * q^34 - 6 * q^35 - 100 * q^37 - 561 * q^38 - 264 * q^40 + 132 * q^41 - 88 * q^43 + 462 * q^44 - 528 * q^46 + 399 * q^47 + 513 * q^49 - 429 * q^50 + 770 * q^52 - 108 * q^53 + 1254 * q^55 + 66 * q^56 + 60 * q^58 + 798 * q^59 - 439 * q^61 - 228 * q^62 - 1454 * q^64 + 165 * q^65 - 988 * q^67 + 693 * q^68 - 318 * q^70 - 2736 * q^71 - 910 * q^73 + 816 * q^74 + 1529 * q^76 - 165 * q^77 + 803 * q^79 - 192 * q^80 + 3630 * q^82 + 813 * q^83 - 594 * q^85 + 33 * q^86 - 1221 * q^88 + 792 * q^89 - 1562 * q^91 - 858 * q^92 - 2100 * q^94 - 132 * q^95 - 736 * q^97 + 846 * q^98

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