LMFDB - Embedded newform 144.4.i.c.97.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [144,4,Mod(49,144)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("144.49"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(144, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	144.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.49627504083$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			97.1
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	144.97
Dual form			144.4.i.c.49.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.55842 + 3.78651i) q^{3} +(-2.31386 - 4.00772i) q^{5} +(6.05842 - 10.4935i) q^{7} +(-1.67527 - 26.9480i) q^{9} +(5.01087 - 8.67909i) q^{11} +(24.2921 + 42.0752i) q^{13} +(23.4090 + 5.49972i) q^{15} +75.3505 q^{17} +116.052 q^{19} +(18.1753 + 60.2805i) q^{21} +(-19.0367 - 32.9725i) q^{23} +(51.7921 - 89.7066i) q^{25} +(108.000 + 89.5489i) q^{27} +(11.3139 - 19.5962i) q^{29} +(15.0584 + 26.0820i) q^{31} +(15.0326 + 49.8576i) q^{33} -56.0733 q^{35} +130.103 q^{37} +(-245.759 - 57.7390i) q^{39} +(-173.742 - 300.930i) q^{41} +(13.3832 - 23.1803i) q^{43} +(-104.124 + 69.0678i) q^{45} +(230.439 - 399.132i) q^{47} +(98.0910 + 169.899i) q^{49} +(-268.129 + 285.315i) q^{51} -438.310 q^{53} -46.3778 q^{55} +(-412.961 + 439.430i) q^{57} +(4.18487 + 7.24841i) q^{59} +(41.0448 - 71.0916i) q^{61} +(-292.928 - 145.683i) q^{63} +(112.417 - 194.712i) q^{65} +(341.785 + 591.989i) q^{67} +(192.591 + 45.2475i) q^{69} -1097.61 q^{71} +470.464 q^{73} +(155.376 + 515.325i) q^{75} +(-60.7160 - 105.163i) q^{77} +(243.017 - 420.919i) q^{79} +(-723.387 + 90.2901i) q^{81} +(49.5829 - 85.8802i) q^{83} +(-174.351 - 301.984i) q^{85} +(33.9416 + 112.571i) q^{87} +8.80426 q^{89} +588.687 q^{91} +(-152.344 - 35.7918i) q^{93} +(-268.527 - 465.103i) q^{95} +(-330.486 + 572.419i) q^{97} +(-242.278 - 120.493i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{3} - 15 q^{5} + 7 q^{7} + 45 q^{9} + 66 q^{11} + 11 q^{13} - 27 q^{15} + 198 q^{17} + 154 q^{19} + 21 q^{21} + 33 q^{23} + 121 q^{25} + 432 q^{27} + 51 q^{29} + 43 q^{31} + 198 q^{33} - 6 q^{35}+ \cdots - 297 q^{99}+O(q^{100}) $ 4 * q + 3 * q^3 - 15 * q^5 + 7 * q^7 + 45 * q^9 + 66 * q^11 + 11 * q^13 - 27 * q^15 + 198 * q^17 + 154 * q^19 + 21 * q^21 + 33 * q^23 + 121 * q^25 + 432 * q^27 + 51 * q^29 + 43 * q^31 + 198 * q^33 - 6 * q^35 - 100 * q^37 - 759 * q^39 - 132 * q^41 + 88 * q^43 - 675 * q^45 + 399 * q^47 + 513 * q^49 - 297 * q^51 + 108 * q^53 - 1254 * q^55 - 1221 * q^57 + 798 * q^59 - 439 * q^61 - 603 * q^63 - 165 * q^65 + 988 * q^67 + 891 * q^69 - 2736 * q^71 - 910 * q^73 + 363 * q^75 + 165 * q^77 - 803 * q^79 - 567 * q^81 + 813 * q^83 - 594 * q^85 + 153 * q^87 - 792 * q^89 + 1562 * q^91 - 213 * q^93 - 132 * q^95 - 736 * q^97 - 297 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−3.55842	+	3.78651i	−0.684819	+	0.728714i
$3$	−3.55842	+	3.78651i	−0.684819	+	0.728714i
$4$		0			0
$5$	−2.31386	−	4.00772i	−0.206958	−	0.358462i	0.743797	−	0.668406i	$-0.233023\pi$
$5$	−2.31386	−	4.00772i	−0.206958	−	0.358462i	−0.950755	+	0.309944i	$0.899690\pi$
$6$		0			0
$7$	6.05842	−	10.4935i	0.327124	−	0.566595i	−0.654816	−	0.755788i	$-0.727254\pi$
$7$	6.05842	−	10.4935i	0.327124	−	0.566595i	0.981940	+	0.189193i	$0.0605872\pi$
$8$		0			0
$9$	−1.67527	−	26.9480i	−0.0620469	−	0.998073i
$10$		0			0
$11$	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	$0.659912\pi$
$14$		0			0
$15$	23.4090	+	5.49972i	0.402944	+	0.0946681i
$16$		0			0
$17$	75.3505			1.07501			0.537506	−	0.843260i	$-0.319367\pi$
$17$	75.3505			1.07501			0.537506	+	0.843260i	$0.319367\pi$
$18$		0			0
$19$	116.052			1.40127			0.700633	−	0.713522i	$-0.252901\pi$
$19$	116.052			1.40127			0.700633	+	0.713522i	$0.252901\pi$
$20$		0			0
$21$	18.1753	+	60.2805i	0.188865	+	0.626395i
$22$		0			0
$23$	−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
$26$		0			0
$27$	108.000	+	89.5489i	0.769800	+	0.638285i
$28$		0			0
$29$	11.3139	−	19.5962i	0.0724459	−	0.125480i	−0.827527	−	0.561426i	$-0.810253\pi$
$29$	11.3139	−	19.5962i	0.0724459	−	0.125480i	0.899973	+	0.435946i	$0.143586\pi$
$30$		0			0
$31$	15.0584	+	26.0820i	0.0872443	+	0.151112i	0.906345	−	0.422538i	$-0.138861\pi$
$31$	15.0584	+	26.0820i	0.0872443	+	0.151112i	−0.819101	+	0.573649i	$0.805527\pi$
$32$		0			0
$33$	15.0326	+	49.8576i	0.0792983	+	0.263003i
$34$		0			0
$35$	−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	$0.406665\pi$
$38$		0			0
$39$	−245.759	−	57.7390i	−1.00905	−	0.237068i
$40$		0			0
$41$	−173.742	−	300.930i	−0.661803	−	1.14628i	−0.980142	−	0.198299i	$-0.936458\pi$
$41$	−173.742	−	300.930i	−0.661803	−	1.14628i	0.318339	−	0.947977i	$-0.396875\pi$
$42$		0			0
$43$	13.3832	−	23.1803i	0.0474631	−	0.0822085i	−0.841318	−	0.540541i	$-0.818220\pi$
$43$	13.3832	−	23.1803i	0.0474631	−	0.0822085i	0.888781	+	0.458332i	$0.151553\pi$
$44$		0			0
$45$	−104.124	+	69.0678i	−0.344930	+	0.228801i
$46$		0			0
$47$	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
$50$		0			0
$51$	−268.129	+	285.315i	−0.736188	+	0.783375i
$52$		0			0
$53$	−438.310			−1.13597			−0.567985	−	0.823039i	$-0.692277\pi$
$53$	−438.310			−1.13597			−0.567985	+	0.823039i	$0.692277\pi$
$54$		0			0
$55$	−46.3778			−0.113702
$56$		0			0
$57$	−412.961	+	439.430i	−0.959613	+	1.02112i
$58$		0			0
$59$	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	$0.139210\pi$
$62$		0			0
$63$	−292.928	−	145.683i	−0.585801	−	0.291338i
$64$		0			0
$65$	112.417	−	194.712i	0.214517	−	0.371555i
$66$		0			0
$67$	341.785	+	591.989i	0.623220	+	1.07945i	0.988882	+	0.148701i	$0.0475091\pi$
$67$	341.785	+	591.989i	0.623220	+	1.07945i	−0.365663	+	0.930747i	$0.619158\pi$
$68$		0			0
$69$	192.591	+	45.2475i	0.336018	+	0.0789444i
$70$		0			0
$71$	−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	$0.376905\pi$
$74$		0			0
$75$	155.376	+	515.325i	0.239218	+	0.793395i
$76$		0			0
$77$	−60.7160	−	105.163i	−0.0898601	−	0.155642i
$78$		0			0
$79$	243.017	−	420.919i	0.346096	−	0.599456i	−0.639456	−	0.768828i	$-0.720840\pi$
$79$	243.017	−	420.919i	0.346096	−	0.599456i	0.985552	+	0.169371i	$0.0541737\pi$
$80$		0			0
$81$	−723.387	+	90.2901i	−0.992300	+	0.123855i
$82$		0			0
$83$	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
$86$		0			0
$87$	33.9416	+	112.571i	0.0418267	+	0.138723i
$88$		0			0
$89$	8.80426			0.0104859			0.00524297	−	0.999986i	$-0.498331\pi$
$89$	8.80426			0.0104859			0.00524297	+	0.999986i	$0.498331\pi$
$90$		0			0
$91$	588.687			0.678145
$92$		0			0
$93$	−152.344	−	35.7918i	−0.169864	−	0.0399079i
$94$		0			0
$95$	−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	$0.279105\pi$
$98$		0			0
$99$	−242.278	−	120.493i	−0.245959	−	0.122323i
$100$		0			0
$101$	282.561	−	489.410i	0.278375	−	0.482160i	−0.692606	−	0.721316i	$-0.743537\pi$
$101$	282.561	−	489.410i	0.278375	−	0.482160i	0.970981	+	0.239156i	$0.0768708\pi$
$102$		0			0
$103$	−485.591	−	841.068i	−0.464531	−	0.804592i	0.534649	−	0.845074i	$-0.320444\pi$
$103$	−485.591	−	841.068i	−0.464531	−	0.804592i	−0.999180	+	0.0404826i	$0.987110\pi$
$104$		0			0
$105$	199.533	−	212.322i	0.185451	−	0.197338i
$106$		0			0
$107$	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	$0.468413\pi$
$110$		0			0
$111$	−462.962	+	492.637i	−0.395878	+	0.421252i
$112$		0			0
$113$	345.531	+	598.478i	0.287654	+	0.498231i	0.973249	−	0.229752i	$-0.0737915\pi$
$113$	345.531	+	598.478i	0.287654	+	0.498231i	−0.685596	+	0.727983i	$0.740458\pi$
$114$		0			0
$115$	−88.0964	+	152.587i	−0.0714350	+	0.123729i
$116$		0			0
$117$	1093.14	−	725.110i	0.863772	−	0.572961i
$118$		0			0
$119$	456.505	−	790.690i	0.351662	−	0.609096i
$120$		0			0
$121$	615.282	+	1065.70i	0.462271	+	0.800676i
$122$		0			0
$123$	1757.72	+	412.960i	1.28852	+	0.302726i
$124$		0			0
$125$	−1057.82			−0.756917
$126$		0			0
$127$	895.897			0.625968			0.312984	−	0.949758i	$-0.398671\pi$
$127$	895.897			0.625968			0.312984	+	0.949758i	$0.398671\pi$
$128$		0			0
$129$	40.1495	+	133.161i	0.0274028	+	0.0908849i
$130$		0			0
$131$	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
$134$		0			0
$135$	108.990	−	640.037i	0.0694843	−	0.408042i
$136$		0			0
$137$	1325.55	−	2295.91i	0.826635	−	1.43177i	−0.0740277	−	0.997256i	$-0.523585\pi$
$137$	1325.55	−	2295.91i	0.826635	−	1.43177i	0.900663	−	0.434518i	$-0.143081\pi$
$138$		0			0
$139$	317.084	+	549.206i	0.193487	+	0.335130i	0.946404	−	0.322986i	$-0.104687\pi$
$139$	317.084	+	549.206i	0.193487	+	0.335130i	−0.752916	+	0.658116i	$0.771354\pi$
$140$		0			0
$141$	691.316	+	2292.84i	0.412903	+	1.36944i
$142$		0			0
$143$	486.899			0.284731
$144$		0			0
$145$	−104.715			−0.0599730
$146$		0			0
$147$	−992.372	−	233.149i	−0.556799	−	0.130815i
$148$		0			0
$149$	1703.16	+	2949.96i	0.936432	+	1.62195i	0.772060	+	0.635550i	$0.219227\pi$
$149$	1703.16	+	2949.96i	0.936432	+	1.62195i	0.164372	+	0.986398i	$0.447440\pi$
$150$		0			0
$151$	−875.159	+	1515.82i	−0.471652	+	0.816925i	−0.999474	−	0.0324302i	$-0.989675\pi$
$151$	−875.159	+	1515.82i	−0.471652	+	0.816925i	0.527822	+	0.849355i	$0.323009\pi$
$152$		0			0
$153$	−126.232	−	2030.54i	−0.0667011	−	1.07294i
$154$		0			0
$155$	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	$-0.353460\pi$
$158$		0			0
$159$	1559.69	−	1659.66i	0.777934	−	0.827797i
$160$		0			0
$161$	−461.329			−0.225825
$162$		0			0
$163$	−2188.41			−1.05159			−0.525797	−	0.850610i	$-0.676233\pi$
$163$	−2188.41			−1.05159			−0.525797	+	0.850610i	$0.676233\pi$
$164$		0			0
$165$	165.032	−	175.610i	0.0778650	−	0.0828559i
$166$		0			0
$167$	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
$170$		0			0
$171$	−194.417	−	3127.36i	−0.0869442	−	1.39857i
$172$		0			0
$173$	−1584.91	+	2745.15i	−0.696525	+	1.20642i	0.273139	+	0.961974i	$0.411938\pi$
$173$	−1584.91	+	2745.15i	−0.696525	+	1.20642i	−0.969664	+	0.244442i	$0.921395\pi$
$174$		0			0
$175$	−627.557	−	1086.96i	−0.271079	−	0.469523i
$176$		0			0
$177$	−42.3377	−	9.94685i	−0.0179791	−	0.00422402i
$178$		0			0
$179$	−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	$0.801267\pi$
$182$		0			0
$183$	123.134	+	408.390i	0.0497396	+	0.164968i
$184$		0			0
$185$	−301.040	−	521.417i	−0.119637	−	0.207218i
$186$		0			0
$187$	377.572	−	653.974i	0.147651	−	0.255740i
$188$		0			0
$189$	1593.99	−	590.773i	0.613469	−	0.227367i
$190$		0			0
$191$	−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	$0.753243\pi$
$194$		0			0
$195$	337.251	+	1118.54i	0.123852	+	0.410769i
$196$		0			0
$197$	−2630.89			−0.951487			−0.475743	−	0.879584i	$-0.657821\pi$
$197$	−2630.89			−0.951487			−0.475743	+	0.879584i	$0.657821\pi$
$198$		0			0
$199$	−2477.34			−0.882483			−0.441241	−	0.897388i	$-0.645462\pi$
$199$	−2477.34			−0.882483			−0.441241	+	0.897388i	$0.645462\pi$
$200$		0			0
$201$	−3457.79	−	812.376i	−1.21340	−	0.285078i
$202$		0			0
$203$	−137.088	−	237.444i	−0.0473976	−	0.0820950i
$204$		0			0
$205$	−804.028	+	1392.62i	−0.273931	+	0.474462i
$206$		0			0
$207$	−856.650	+	568.238i	−0.287639	+	0.190798i
$208$		0			0
$209$	581.520	−	1007.22i	0.192462	−	0.333354i
$210$		0			0
$211$	−1392.36	−	2411.65i	−0.454286	−	0.786847i	0.544361	−	0.838851i	$-0.316772\pi$
$211$	−1392.36	−	2411.65i	−0.454286	−	0.786847i	−0.998647	+	0.0520047i	$0.983439\pi$
$212$		0			0
$213$	3905.75	−	4156.10i	1.25642	−	1.33696i
$214$		0			0
$215$	−123.867			−0.0392914
$216$		0			0
$217$	364.921			0.114159
$218$		0			0
$219$	−1674.11	+	1781.42i	−0.516557	+	0.549667i
$220$		0			0
$221$	1830.42	+	3170.39i	0.557138	+	0.964992i
$222$		0			0
$223$	−21.5288	+	37.2890i	−0.00646491	+	0.0111976i	−0.869240	−	0.494391i	$-0.835391\pi$
$223$	−21.5288	+	37.2890i	−0.00646491	+	0.0111976i	0.862775	+	0.505588i	$0.168725\pi$
$224$		0			0
$225$	−2504.18	−	1245.41i	−0.741978	−	0.369010i
$226$		0			0
$227$	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	$-0.379371\pi$
$230$		0			0
$231$	614.254	+	144.313i	0.174957	+	0.0411045i
$232$		0			0
$233$	3466.34			0.974625			0.487313	−	0.873228i	$-0.337977\pi$
$233$	3466.34			0.974625			0.487313	+	0.873228i	$0.337977\pi$
$234$		0			0
$235$	−2132.81			−0.592040
$236$		0			0
$237$	729.052	+	2417.99i	0.199819	+	0.662724i
$238$		0			0
$239$	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	$0.823788\pi$
$242$		0			0
$243$	2232.23	−	3060.40i	0.589291	−	0.807921i
$244$		0			0
$245$	453.938	−	786.243i	0.118372	−	0.205025i
$246$		0			0
$247$	2819.14	+	4882.89i	0.726225	+	1.25786i
$248$		0			0
$249$	148.749	+	493.344i	0.0378577	+	0.125560i
$250$		0			0
$251$	−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
$254$		0			0
$255$	1763.88	+	414.407i	0.433170	+	0.101769i
$256$		0			0
$257$	1672.31	+	2896.53i	0.405898	+	0.703036i	0.994426	−	0.105441i	$-0.0336254\pi$
$257$	1672.31	+	2896.53i	0.405898	+	0.703036i	−0.588527	+	0.808477i	$0.700292\pi$
$258$		0			0
$259$	788.220	−	1365.24i	0.189103	−	0.327536i
$260$		0			0
$261$	−547.031	−	272.057i	−0.129733	−	0.0645207i
$262$		0			0
$263$	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
$266$		0			0
$267$	−31.3293	+	33.3374i	−0.00718097	+	0.00764125i
$268$		0			0
$269$	−2904.99			−0.658441			−0.329220	−	0.944253i	$-0.606786\pi$
$269$	−2904.99			−0.658441			−0.329220	+	0.944253i	$0.606786\pi$
$270$		0			0
$271$	1335.38			0.299331			0.149665	−	0.988737i	$-0.452180\pi$
$271$	1335.38			0.299331			0.149665	+	0.988737i	$0.452180\pi$
$272$		0			0
$273$	−2094.80	+	2229.07i	−0.464406	+	0.494174i
$274$		0			0
$275$	−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	$-0.196015\pi$
$278$		0			0
$279$	677.629	−	449.488i	0.145407	−	0.0964522i
$280$		0			0
$281$	2589.67	−	4485.43i	0.549774	−	0.952237i	−0.448516	−	0.893775i	$-0.648047\pi$
$281$	2589.67	−	4485.43i	0.549774	−	0.952237i	0.998290	−	0.0584616i	$-0.0186195\pi$
$282$		0			0
$283$	−1540.03	−	2667.42i	−0.323482	−	0.560288i	0.657722	−	0.753261i	$-0.271520\pi$
$283$	−1540.03	−	2667.42i	−0.323482	−	0.560288i	−0.981204	+	0.192973i	$0.938187\pi$
$284$		0			0
$285$	2716.65	+	638.252i	0.564632	+	0.132655i
$286$		0			0
$287$	−4210.40			−0.865966
$288$		0			0
$289$	764.703			0.155649
$290$		0			0
$291$	−991.459	−	3288.30i	−0.199726	−	0.662417i
$292$		0			0
$293$	−1824.45	−	3160.04i	−0.363773	−	0.630073i	0.624806	−	0.780780i	$-0.285178\pi$
$293$	−1824.45	−	3160.04i	−0.363773	−	0.630073i	−0.988578	+	0.150708i	$0.951845\pi$
$294$		0			0
$295$	19.3664	−	33.5436i	0.00382222	−	0.00662028i
$296$		0			0
$297$	1318.38	−	488.624i	0.257576	−	0.0954640i
$298$		0			0
$299$	924.882	−	1601.94i	0.178887	−	0.309842i
$300$		0			0
$301$	−162.162	−	280.872i	−0.0310526	−	0.0537847i
$302$		0			0
$303$	847.684	+	2811.45i	0.160720	+	0.533048i
$304$		0			0
$305$	−379.887			−0.0713190
$306$		0			0
$307$	3439.25			0.639376			0.319688	−	0.947523i	$-0.396422\pi$
$307$	3439.25			0.639376			0.319688	+	0.947523i	$0.396422\pi$
$308$		0			0
$309$	4912.65	+	1154.18i	0.904436	+	0.212489i
$310$		0			0
$311$	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	$0.0221485\pi$
$314$		0			0
$315$	93.9378	+	1511.06i	0.0168025	+	0.270282i
$316$		0			0
$317$	−3773.97	+	6536.70i	−0.668666	+	1.15816i	0.309611	+	0.950863i	$0.399801\pi$
$317$	−3773.97	+	6536.70i	−0.668666	+	1.15816i	−0.978277	+	0.207300i	$0.933532\pi$
$318$		0			0
$319$	−113.385	−	196.388i	−0.0199007	−	0.0344690i
$320$		0			0
$321$	−2006.40	+	2135.00i	−0.348867	+	0.371228i
$322$		0			0
$323$	8744.55			1.50638
$324$		0			0
$325$	5032.56			0.858942
$326$		0			0
$327$	−802.367	+	853.797i	−0.135691	+	0.144389i
$328$		0			0
$329$	−2792.19	−	4836.22i	−0.467898	−	0.810423i
$330$		0			0
$331$	−1564.86	+	2710.41i	−0.259856	+	0.450084i	−0.966203	−	0.257782i	$-0.917008\pi$
$331$	−1564.86	+	2710.41i	−0.259856	+	0.450084i	0.706347	+	0.707866i	$0.250342\pi$
$332$		0			0
$333$	−217.957	−	3506.02i	−0.0358679	−	0.576963i
$334$		0			0
$335$	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	$0.565316\pi$
$338$		0			0
$339$	−3495.69	−	821.280i	−0.560058	−	0.131581i
$340$		0			0
$341$	301.823			0.0479315
$342$		0			0
$343$	6533.19			1.02845
$344$		0			0
$345$	−264.289	−	876.548i	−0.0412430	−	0.136788i
$346$		0			0
$347$	−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	$0.242479\pi$
$350$		0			0
$351$	−1144.24	+	6719.45i	−0.174002	+	1.02182i
$352$		0			0
$353$	3075.04	−	5326.13i	0.463649	−	0.803063i	−0.535491	−	0.844541i	$-0.679873\pi$
$353$	3075.04	−	5326.13i	0.463649	−	0.803063i	0.999139	+	0.0414780i	$0.0132067\pi$
$354$		0			0
$355$	2539.71	+	4398.91i	0.379701	+	0.657662i
$356$		0			0
$357$	1369.52	+	4542.17i	0.203032	+	0.673381i
$358$		0			0
$359$	−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
$362$		0			0
$363$	−6224.71	−	1462.44i	−0.900035	−	0.211455i
$364$		0			0
$365$	−1088.59	−	1885.49i	−0.156108	−	0.270387i
$366$		0			0
$367$	1474.65	−	2554.16i	0.209744	−	0.363287i	−0.741890	−	0.670522i	$-0.766070\pi$
$367$	1474.65	−	2554.16i	0.209744	−	0.363287i	0.951634	+	0.307235i	$0.0994037\pi$
$368$		0			0
$369$	−7818.38	+	5186.13i	−1.10300	+	0.731650i
$370$		0			0
$371$	−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	$0.859068\pi$
$374$		0			0
$375$	3764.18	−	4005.46i	0.518351	−	0.551576i
$376$		0			0
$377$	1099.35			0.150184
$378$		0			0
$379$	4016.67			0.544387			0.272193	−	0.962243i	$-0.412251\pi$
$379$	4016.67			0.544387			0.272193	+	0.962243i	$0.412251\pi$
$380$		0			0
$381$	−3187.98	+	3392.32i	−0.428675	+	0.456152i
$382$		0			0
$383$	−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
$386$		0			0
$387$	−647.083	−	321.816i	−0.0849950	−	0.0422708i
$388$		0			0
$389$	−1032.29	+	1787.99i	−0.134549	+	0.233045i	−0.925425	−	0.378931i	$-0.876292\pi$
$389$	−1032.29	+	1787.99i	−0.134549	+	0.233045i	0.790876	+	0.611976i	$0.209625\pi$
$390$		0			0
$391$	−1434.42	−	2484.49i	−0.185529	−	0.321346i
$392$		0			0
$393$	−8370.96	−	1966.68i	−1.07445	−	0.252432i
$394$		0			0
$395$	−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	$0.667305\pi$
$398$		0			0
$399$	2109.27	+	6995.65i	0.264650	+	0.877746i
$400$		0			0
$401$	−1289.10	−	2232.79i	−0.160536	−	0.278056i	0.774525	−	0.632543i	$-0.217989\pi$
$401$	−1289.10	−	2232.79i	−0.160536	−	0.278056i	−0.935061	+	0.354487i	$0.884656\pi$
$402$		0			0
$403$	−731.602	+	1267.17i	−0.0904310	+	0.156631i
$404$		0			0
$405$	2035.67	+	2690.22i	0.249762	+	0.330069i
$406$		0			0
$407$	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	$0.948297\pi$
$410$		0			0
$411$	3976.64	+	13189.0i	0.477258	+	1.58289i
$412$		0			0
$413$	101.415			0.0120830
$414$		0			0
$415$	−458.912			−0.0542822
$416$		0			0
$417$	−3207.89	−	753.665i	−0.376717	−	0.0885063i
$418$		0			0
$419$	−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	$0.186145\pi$
$422$		0			0
$423$	−11141.8	−	5541.21i	−1.28070	−	0.636933i
$424$		0			0
$425$	3902.56	−	6759.44i	0.445417	−	0.771484i
$426$		0			0
$427$	−497.333	−	861.406i	−0.0563645	−	0.0976261i
$428$		0			0
$429$	−1732.59	+	1843.65i	−0.194989	+	0.207487i
$430$		0			0
$431$	−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	$0.491557\pi$
$434$		0			0
$435$	372.619	−	396.503i	0.0410706	−	0.0437031i
$436$		0			0
$437$	−2209.24	−	3826.51i	−0.241835	−	0.418871i
$438$		0			0
$439$	−526.239	+	911.473i	−0.0572119	+	0.0990939i	−0.893213	−	0.449634i	$-0.851554\pi$
$439$	−526.239	+	911.473i	−0.0572119	+	0.0990939i	0.836001	+	0.548728i	$0.184888\pi$
$440$		0			0
$441$	4414.10	−	2927.98i	0.476633	−	0.316162i
$442$		0			0
$443$	−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
$446$		0			0
$447$	−17230.6	−	4048.18i	−1.82322	−	0.428349i
$448$		0			0
$449$	−7329.40			−0.770369			−0.385184	−	0.922840i	$-0.625862\pi$
$449$	−7329.40			−0.770369			−0.385184	+	0.922840i	$0.625862\pi$
$450$		0			0
$451$	−3482.39			−0.363591
$452$		0			0
$453$	−2625.48	−	8707.72i	−0.272308	−	0.903144i
$454$		0			0
$455$	−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	$0.285819\pi$
$458$		0			0
$459$	8137.86	+	6747.55i	0.827544	+	0.686163i
$460$		0			0
$461$	−2859.34	+	4952.53i	−0.288878	+	0.500352i	−0.973542	−	0.228507i	$-0.926616\pi$
$461$	−2859.34	+	4952.53i	−0.288878	+	0.500352i	0.684664	+	0.728859i	$0.259949\pi$
$462$		0			0
$463$	394.233	+	682.831i	0.0395714	+	0.0685397i	0.885133	−	0.465339i	$-0.154067\pi$
$463$	394.233	+	682.831i	0.0395714	+	0.0685397i	−0.845561	+	0.533878i	$0.820734\pi$
$464$		0			0
$465$	209.058	+	693.368i	0.0208491	+	0.0691488i
$466$		0			0
$467$	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
$470$		0			0
$471$	11020.1	+	2589.08i	1.07809	+	0.253288i
$472$		0			0
$473$	−134.123	−	232.307i	−0.0130380	−	0.0225824i
$474$		0			0
$475$	6010.56	−	10410.6i	0.580596	−	1.00562i
$476$		0			0
$477$	734.285	+	11811.6i	0.0704834	+	1.13378i
$478$		0			0
$479$	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
$482$		0			0
$483$	1641.60	−	1746.82i	0.154649	−	0.164562i
$484$		0			0
$485$	3058.80			0.286377
$486$		0			0
$487$	−12737.3			−1.18518			−0.592591	−	0.805503i	$-0.701895\pi$
$487$	−12737.3			−1.18518			−0.592591	+	0.805503i	$0.701895\pi$
$488$		0			0
$489$	7787.30	−	8286.44i	0.720151	−	0.766310i
$490$		0			0
$491$	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
$494$		0			0
$495$	77.6952	+	1249.79i	0.00705483	+	0.113482i
$496$		0			0
$497$	−6649.78	+	11517.7i	−0.600167	+	1.03952i
$498$		0			0
$499$	5423.14	+	9393.15i	0.486519	+	0.842676i	0.999880	−	0.0154970i	$-0.00493306\pi$
$499$	5423.14	+	9393.15i	0.486519	+	0.842676i	−0.513361	+	0.858173i	$0.671600\pi$
$500$		0			0
$501$	−9717.43	−	2283.02i	−0.866553	−	0.203589i
$502$		0			0
$503$	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
$506$		0			0
$507$	−245.140	−	813.036i	−0.0214734	−	0.0712193i
$508$		0			0
$509$	2947.87	+	5105.87i	0.256704	+	0.444624i	0.965357	−	0.260933i	$-0.0840302\pi$
$509$	2947.87	+	5105.87i	0.256704	+	0.444624i	−0.708653	+	0.705557i	$0.750697\pi$
$510$		0			0
$511$	2850.27	−	4936.82i	0.246749	−	0.427381i
$512$		0			0
$513$	12533.6	+	10392.3i	1.07870	+	0.894407i
$514$		0			0
$515$	−2247.18	+	3892.23i	−0.192277	+	0.333033i
$516$		0			0
$517$	−2309.40	−	4000.00i	−0.196455	−	0.340270i
$518$		0			0
$519$	−4754.74	−	15769.7i	−0.402139	−	1.33374i
$520$		0			0
$521$	5211.51			0.438235			0.219118	−	0.975698i	$-0.429682\pi$
$521$	5211.51			0.438235			0.219118	+	0.975698i	$0.429682\pi$
$522$		0			0
$523$	9809.86			0.820182			0.410091	−	0.912045i	$-0.365497\pi$
$523$	9809.86			0.820182			0.410091	+	0.912045i	$0.365497\pi$
$524$		0			0
$525$	6348.90	+	1491.62i	0.527788	+	0.123999i
$526$		0			0
$527$	1134.66	+	1965.29i	0.0937886	+	0.162447i
$528$		0			0
$529$	5358.71	−	9281.56i	0.440430	−	0.762847i
$530$		0			0
$531$	188.319	−	124.917i	0.0153905	−	0.0102089i
$532$		0			0
$533$	8441.11	−	14620.4i	0.685976	−	1.18814i
$534$		0			0
$535$	−1304.66	−	2259.73i	−0.105430	−	0.182611i
$536$		0			0
$537$	4870.71	−	5182.91i	0.391409	−	0.416497i
$538$		0			0
$539$	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	$0.395904\pi$
$542$		0			0
$543$	14060.9	−	14962.2i	1.11125	−	1.18248i
$544$		0			0
$545$	−521.738	−	903.677i	−0.0410070	−	0.0710262i
$546$		0			0
$547$	−12033.6	+	20842.7i	−0.940617	+	1.62920i	−0.176319	+	0.984333i	$0.556419\pi$
$547$	−12033.6	+	20842.7i	−0.940617	+	1.62920i	−0.764298	+	0.644863i	$0.776914\pi$
$548$		0			0
$549$	−1984.54	−	986.976i	−0.154277	−	0.0767270i
$550$		0			0
$551$	1312.99	−	2274.17i	0.101516	−	0.175831i
$552$		0			0
$553$	−2944.60	−	5100.20i	−0.226433	−	0.392193i
$554$		0			0
$555$	3045.58	+	715.531i	0.232933	+	0.0547254i
$556$		0			0
$557$	4582.37			0.348584			0.174292	−	0.984694i	$-0.444236\pi$
$557$	4582.37			0.348584			0.174292	+	0.984694i	$0.444236\pi$
$558$		0			0
$559$	1300.42			0.0983934
$560$		0			0
$561$	1132.72	+	3756.79i	0.0852466	+	0.282731i
$562$		0			0
$563$	−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
$566$		0			0
$567$	−3435.13	+	8137.87i	−0.254430	+	0.602749i
$568$		0			0
$569$	−10282.5	+	17809.9i	−0.757586	+	1.31218i	0.186492	+	0.982456i	$0.440288\pi$
$569$	−10282.5	+	17809.9i	−0.757586	+	1.31218i	−0.944078	+	0.329721i	$0.893045\pi$
$570$		0			0
$571$	−584.992	−	1013.24i	−0.0428742	−	0.0742602i	0.843792	−	0.536670i	$-0.180318\pi$
$571$	−584.992	−	1013.24i	−0.0428742	−	0.0742602i	−0.886666	+	0.462410i	$0.846985\pi$
$572$		0			0
$573$	−3603.88	−	11952.7i	−0.262748	−	0.871435i
$574$		0			0
$575$	−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	$0.656326\pi$
$578$		0			0
$579$	−6753.35	−	1586.64i	−0.484731	−	0.113883i
$580$		0			0
$581$	−600.789	−	1040.60i	−0.0429000	−	0.0743050i
$582$		0			0
$583$	−2196.31	+	3804.13i	−0.156024	+	0.270242i
$584$		0			0
$585$	−5435.42	−	2703.22i	−0.384149	−	0.191050i
$586$		0			0
$587$	−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
$590$		0			0
$591$	9361.80	−	9961.87i	0.651596	−	0.693361i
$592$		0			0
$593$	19018.0			1.31699			0.658494	−	0.752586i	$-0.271194\pi$
$593$	19018.0			1.31699			0.658494	+	0.752586i	$0.271194\pi$
$594$		0			0
$595$	−4225.16			−0.291117
$596$		0			0
$597$	8815.43	−	9380.47i	0.604341	−	0.643077i
$598$		0			0
$599$	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	$0.216435\pi$
$602$		0			0
$603$	15380.3	−	10202.2i	1.03870	−	0.688995i
$604$		0			0
$605$	2847.35	−	4931.76i	0.191341	−	0.331413i
$606$		0			0
$607$	−5744.99	−	9950.61i	−0.384155	−	0.665375i	0.607497	−	0.794322i	$-0.292174\pi$
$607$	−5744.99	−	9950.61i	−0.384155	−	0.665375i	−0.991652	+	0.128947i	$0.958840\pi$
$608$		0			0
$609$	1386.90	+	325.840i	0.0922825	+	0.0216809i
$610$		0			0
$611$	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	$0.773154\pi$
$614$		0			0
$615$	−2412.08	−	7999.98i	−0.158154	−	0.524537i
$616$		0			0
$617$	4248.31	+	7358.29i	0.277197	+	0.480120i	0.970687	−	0.240347i	$-0.0772612\pi$
$617$	4248.31	+	7358.29i	0.277197	+	0.480120i	−0.693490	+	0.720466i	$0.743928\pi$
$618$		0			0
$619$	7169.94	−	12418.7i	0.465564	−	0.806381i	−0.533662	−	0.845698i	$-0.679185\pi$
$619$	7169.94	−	12418.7i	0.465564	−	0.806381i	0.999227	+	0.0393163i	$0.0125180\pi$
$620$		0			0
$621$	896.688	−	5265.74i	0.0579434	−	0.340269i
$622$		0			0
$623$	53.3399	−	92.3874i	0.00343021	−	0.00594129i
$624$		0			0
$625$	−4026.36	−	6973.86i	−0.257687	−	0.446327i
$626$		0			0
$627$	1744.56	+	5786.05i	0.111118	+	0.368537i
$628$		0			0
$629$	9803.34			0.621439
$630$		0			0
$631$	−17834.3			−1.12516			−0.562578	−	0.826744i	$-0.690190\pi$
$631$	−17834.3			−1.12516			−0.562578	+	0.826744i	$0.690190\pi$
$632$		0			0
$633$	14086.3	+	3309.46i	0.884489	+	0.207803i
$634$		0			0
$635$	−2072.98	−	3590.51i	−0.129549	−	0.224386i
$636$		0			0
$637$	−4765.68	+	8254.39i	−0.296425	+	0.513424i
$638$		0			0
$639$	1838.79	+	29578.3i	0.113836	+	1.83114i
$640$		0			0
$641$	−13173.0	+	22816.3i	−0.811705	+	1.40591i	0.0999654	+	0.994991i	$0.468127\pi$
$641$	−13173.0	+	22816.3i	−0.811705	+	1.40591i	−0.911670	+	0.410923i	$0.865207\pi$
$642$		0			0
$643$	−10782.5	−	18675.9i	−0.661309	−	1.14542i	−0.980272	−	0.197653i	$-0.936668\pi$
$643$	−10782.5	−	18675.9i	−0.661309	−	1.14542i	0.318963	−	0.947767i	$-0.396665\pi$
$644$		0			0
$645$	440.771	−	469.023i	0.0269075	−	0.0286322i
$646$		0			0
$647$	−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
$650$		0			0
$651$	−1298.54	+	1381.78i	−0.0781781	+	0.0831891i
$652$		0			0
$653$	−1402.57	−	2429.33i	−0.0840534	−	0.145585i	0.820934	−	0.571023i	$-0.193453\pi$
$653$	−1402.57	−	2429.33i	−0.0840534	−	0.145585i	−0.904987	+	0.425438i	$0.860120\pi$
$654$		0			0
$655$	3829.10	−	6632.20i	0.228420	−	0.395636i
$656$		0			0
$657$	−788.153	−	12678.1i	−0.0468018	−	0.752844i
$658$		0			0
$659$	−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	$0.576917\pi$
$662$		0			0
$663$	−18518.1	−	4350.66i	−1.08474	−	0.254850i
$664$		0			0
$665$	−6507.40			−0.379468
$666$		0			0
$667$	−861.513			−0.0500119
$668$		0			0
$669$	−64.5864	−	214.209i	−0.00373252	−	0.0123794i
$670$		0			0
$671$	−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	$0.134280\pi$
$674$		0			0
$675$	13626.7	−	5050.38i	0.777023	−	0.287984i
$676$		0			0
$677$	−8937.50	+	15480.2i	−0.507380	+	0.878807i	0.492584	+	0.870265i	$0.336052\pi$
$677$	−8937.50	+	15480.2i	−0.507380	+	0.878807i	−0.999964	+	0.00854232i	$0.997281\pi$
$678$		0			0
$679$	4004.45	+	6935.91i	0.226328	+	0.392012i
$680$		0			0
$681$	1024.89	+	3399.18i	0.0576709	+	0.191273i
$682$		0			0
$683$	−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
$686$		0			0
$687$	21722.4	+	5103.48i	1.20635	+	0.283421i
$688$		0			0
$689$	−10647.5	−	18441.9i	−0.588732	−	1.01971i
$690$		0			0
$691$	−7813.79	+	13533.9i	−0.430175	+	0.745084i	−0.996888	−	0.0788308i	$-0.974881\pi$
$691$	−7813.79	+	13533.9i	−0.430175	+	0.745084i	0.566714	+	0.823915i	$0.308215\pi$
$692$		0			0
$693$	−2732.22	+	1812.35i	−0.149767	+	0.0993441i
$694$		0			0
$695$	1467.38	−	2541.57i	0.0800874	−	0.138716i
$696$		0			0
$697$	−13091.5	−	22675.2i	−0.711445	−	1.23226i
$698$		0			0
$699$	−12334.7	+	13125.3i	−0.667442	+	0.710223i
$700$		0			0
$701$	17562.6			0.946264			0.473132	−	0.880992i	$-0.343123\pi$
$701$	17562.6			0.946264			0.473132	+	0.880992i	$0.343123\pi$
$702$		0			0
$703$	15098.7			0.810039
$704$		0			0
$705$	7589.44	−	8075.91i	0.405440	−	0.431427i
$706$		0			0
$707$	−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	$0.988935\pi$
$710$		0			0
$711$	−11750.0	−	5843.68i	−0.619775	−	0.308235i
$712$		0			0
$713$	573.324	−	993.027i	0.0301138	−	0.0521587i
$714$		0			0
$715$	−1126.62	−	1951.36i	−0.0589273	−	0.102065i
$716$		0			0
$717$	−28546.6	−	6706.75i	−1.48688	−	0.349328i
$718$		0			0
$719$	−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
$722$		0			0
$723$	−9884.14	−	32782.0i	−0.508430	−	1.68627i
$724$		0			0
$725$	−1171.94	−	2029.85i	−0.0600340	−	0.103982i
$726$		0			0
$727$	−11954.9	+	20706.5i	−0.609879	+	1.05634i	0.381380	+	0.924418i	$0.375449\pi$
$727$	−11954.9	+	20706.5i	−0.609879	+	1.05634i	−0.991260	+	0.131924i	$0.957885\pi$
$728$		0			0
$729$	3645.00	+	19342.6i	0.185185	+	0.982704i
$730$		0			0
$731$	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	$0.764587\pi$
$734$		0			0
$735$	1361.81	+	4516.62i	0.0683418	+	0.226664i
$736$		0			0
$737$	6850.57			0.342394
$738$		0			0
$739$	−25802.5			−1.28438			−0.642192	−	0.766544i	$-0.721975\pi$
$739$	−25802.5			−1.28438			−0.642192	+	0.766544i	$0.721975\pi$
$740$		0			0
$741$	−28520.8	−	6700.70i	−1.41395	−	0.332195i
$742$		0			0
$743$	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
$746$		0			0
$747$	−2397.36	−	1192.29i	−0.117423	−	0.0583983i
$748$		0			0
$749$	3416.01	−	5916.71i	0.166647	−	0.288641i
$750$		0			0
$751$	1668.32	+	2889.61i	0.0810623	+	0.140404i	0.903706	−	0.428153i	$-0.140835\pi$
$751$	1668.32	+	2889.61i	0.0810623	+	0.140404i	−0.822644	+	0.568557i	$0.807502\pi$
$752$		0			0
$753$	14715.8	−	15659.0i	0.712181	−	0.757830i
$754$		0			0
$755$	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	$0.207052\pi$
$758$		0			0
$759$	1357.76	−	1444.79i	0.0649321	−	0.0690940i
$760$		0			0
$761$	5498.42	+	9523.54i	0.261915	+	0.453651i	0.966751	−	0.255720i	$-0.0823125\pi$
$761$	5498.42	+	9523.54i	0.261915	+	0.453651i	−0.704836	+	0.709371i	$0.748979\pi$
$762$		0			0
$763$	1366.08	−	2366.12i	0.0648169	−	0.112266i
$764$		0			0
$765$	−7845.77	+	5204.30i	−0.370803	+	0.245963i
$766$		0			0
$767$	−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	$-0.451661\pi$
$770$		0			0
$771$	−16918.5	−	3974.85i	−0.790279	−	0.185669i
$772$		0			0
$773$	−7242.46			−0.336990			−0.168495	−	0.985703i	$-0.553891\pi$
$773$	−7242.46			−0.336990			−0.168495	+	0.985703i	$0.553891\pi$
$774$		0			0
$775$	3119.63			0.144594
$776$		0			0
$777$	2364.66	+	7842.69i	0.109179	+	0.362104i
$778$		0			0
$779$	−20163.0	−	34923.4i	−0.927362	−	1.60624i
$780$		0			0
$781$	−5499.98	+	9526.24i	−0.251991	+	0.436461i
$782$		0			0
$783$	2976.71	−	1103.24i	0.135861	−	0.0503534i
$784$		0			0
$785$	−5040.91	+	8731.11i	−0.229195	+	0.396977i
$786$		0			0
$787$	8707.15	+	15081.2i	0.394379	+	0.683084i	0.993022	−	0.117932i	$-0.0376264\pi$
$787$	8707.15	+	15081.2i	0.394379	+	0.683084i	−0.598643	+	0.801016i	$0.704293\pi$
$788$		0			0
$789$	9782.25	+	32444.0i	0.441391	+	1.46393i
$790$		0			0
$791$	8373.50			0.376394
$792$		0			0
$793$	3988.26			0.178597
$794$		0			0
$795$	−10260.4	−	2410.58i	−0.457733	−	0.107540i
$796$		0			0
$797$	−14566.5	−	25229.9i	−0.647391	−	1.12131i	−0.983744	−	0.179578i	$-0.942527\pi$
$797$	−14566.5	−	25229.9i	−0.647391	−	1.12131i	0.336353	−	0.941736i	$-0.390807\pi$
$798$		0			0
$799$	17363.7	−	30074.8i	0.768815	−	1.33163i
$800$		0			0
$801$	−14.7495	−	237.257i	−0.000650620	−	0.0104657i
$802$		0			0
$803$	2357.44	−	4083.20i	0.103602	−	0.179443i
$804$		0			0
$805$	1067.45	+	1848.88i	0.0467362	+	0.0809495i
$806$		0			0
$807$	10337.2	−	10999.8i	0.450912	−	0.479815i
$808$		0			0
$809$	−36440.1			−1.58364			−0.791820	−	0.610754i	$-0.790866\pi$
$809$	−36440.1			−1.58364			−0.791820	+	0.610754i	$0.790866\pi$
$810$		0			0
$811$	18922.0			0.819286			0.409643	−	0.912246i	$-0.365653\pi$
$811$	18922.0			0.819286			0.409643	+	0.912246i	$0.365653\pi$
$812$		0			0
$813$	−4751.85	+	5056.43i	−0.204987	+	0.218126i
$814$		0			0
$815$	5063.68	+	8770.55i	0.217636	+	0.376956i
$816$		0			0
$817$	1553.14	−	2690.11i	0.0665084	−	0.115196i
$818$		0			0
$819$	−986.208	−	15863.9i	−0.0420768	−	0.676839i
$820$		0			0
$821$	8955.36	−	15511.1i	0.380687	−	0.659369i	−0.610474	−	0.792037i	$-0.709021\pi$
$821$	8955.36	−	15511.1i	0.380687	−	0.659369i	0.991161	+	0.132667i	$0.0423542\pi$
$822$		0			0
$823$	8762.22	+	15176.6i	0.371120	+	0.642799i	0.989738	−	0.142893i	$-0.0456405\pi$
$823$	8762.22	+	15176.6i	0.371120	+	0.642799i	−0.618618	+	0.785692i	$0.712307\pi$
$824$		0			0
$825$	5251.12	+	1233.70i	0.221601	+	0.0520631i
$826$		0			0
$827$	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	$0.104699\pi$
$830$		0			0
$831$	12563.5	+	41668.3i	0.524454	+	1.73942i
$832$		0			0
$833$	7391.21	+	12802.0i	0.307431	+	0.532487i
$834$		0			0
$835$	4445.02	−	7699.00i	0.184223	−	0.319084i
$836$		0			0
$837$	−709.300	+	4165.32i	−0.0292915	+	0.172012i
$838$		0			0
$839$	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
$842$		0			0
$843$	7769.00	+	25766.9i	0.317412	+	1.05274i
$844$		0			0
$845$	756.291			0.0307896
$846$		0			0
$847$	14910.6			0.604879
$848$		0			0
$849$	15580.3	+	3660.45i	0.629816	+	0.147970i
$850$		0			0
$851$	−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	$0.115908\pi$
$854$		0			0
$855$	−12083.7	+	8015.43i	−0.483339	+	0.320611i
$856$		0			0
$857$	−924.149	+	1600.67i	−0.0368359	+	0.0638016i	−0.883856	−	0.467760i	$-0.845061\pi$
$857$	−924.149	+	1600.67i	−0.0368359	+	0.0638016i	0.847020	+	0.531561i	$0.178395\pi$
$858$		0			0
$859$	−9427.10	−	16328.2i	−0.374445	−	0.648558i	0.615799	−	0.787904i	$-0.288833\pi$
$859$	−9427.10	−	16328.2i	−0.374445	−	0.648558i	−0.990244	+	0.139345i	$0.955500\pi$
$860$		0			0
$861$	14982.4	−	15942.7i	0.593030	−	0.631041i
$862$		0			0
$863$	−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
$866$		0			0
$867$	−2721.13	+	2895.55i	−0.106591	+	0.113423i
$868$		0			0
$869$	−2435.46	−	4218.34i	−0.0950717	−	0.164669i
$870$		0			0
$871$	−16605.4	+	28761.3i	−0.645983	+	1.11888i
$872$		0			0
$873$	15979.2	+	7946.98i	0.619489	+	0.308092i
$874$		0			0
$875$	−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	$0.675056\pi$
$878$		0			0
$879$	18457.6	+	4336.46i	0.708261	+	0.166399i
$880$		0			0
$881$	3741.26			0.143072			0.0715359	−	0.997438i	$-0.477210\pi$
$881$	3741.26			0.143072			0.0715359	+	0.997438i	$0.477210\pi$
$882$		0			0
$883$	−14131.6			−0.538580			−0.269290	−	0.963059i	$-0.586789\pi$
$883$	−14131.6			−0.538580			−0.269290	+	0.963059i	$0.586789\pi$
$884$		0			0
$885$	58.0992	+	192.693i	0.00220676	+	0.00731900i
$886$		0			0
$887$	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
$890$		0			0
$891$	−2841.17	+	6730.77i	−0.106827	+	0.253074i
$892$		0			0
$893$	26742.8	−	46319.9i	1.00214	−	1.73576i
$894$		0			0
$895$	3167.17	+	5485.70i	0.118287	+	0.204879i
$896$		0			0
$897$	2774.65	+	9202.46i	0.103281	+	0.342543i
$898$		0			0
$899$	681.475			0.0252820
$900$		0			0
$901$	−33026.9			−1.22118
$902$		0			0
$903$	1640.56	+	385.436i	0.0604591	+	0.0142043i
$904$		0			0
$905$	9143.09	+	15836.3i	0.335830	+	0.581675i
$906$		0			0
$907$	26309.7	−	45569.7i	0.963174	−	1.66827i	0.248731	−	0.968572i	$-0.419986\pi$
$907$	26309.7	−	45569.7i	0.963174	−	1.66827i	0.714443	−	0.699694i	$-0.246680\pi$
$908$		0			0
$909$	−13662.0	−	6794.56i	−0.498503	−	0.247922i
$910$		0			0
$911$	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
$914$		0			0
$915$	1351.80	−	1438.45i	0.0488406	−	0.0519711i
$916$		0			0
$917$	20051.6			0.722097
$918$		0			0
$919$	45618.2			1.63744			0.818718	−	0.574195i	$-0.194685\pi$
$919$	45618.2			1.63744			0.818718	+	0.574195i	$0.194685\pi$
$920$		0			0
$921$	−12238.3	+	13022.7i	−0.437857	+	0.465922i
$922$		0			0
$923$	−26663.2	−	46182.1i	−0.950846	−	1.64691i
$924$		0			0
$925$	6738.32	−	11671.1i	0.239518	−	0.414858i
$926$		0			0
$927$	−21851.6	+	14494.7i	−0.774219	+	0.513558i
$928$		0			0
$929$	6600.20	−	11431.9i	0.233095	−	0.403733i	−0.725622	−	0.688093i	$-0.758448\pi$
$929$	6600.20	−	11431.9i	0.233095	−	0.403733i	0.958717	+	0.284361i	$0.0917813\pi$
$930$		0			0
$931$	11383.6	+	19717.0i	0.400734	+	0.694091i
$932$		0			0
$933$	−36295.8	−	8527.38i	−1.27360	−	0.299222i
$934$		0			0
$935$	−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	$0.575438\pi$
$938$		0			0
$939$	7285.95	+	24164.8i	0.253214	+	0.839816i
$940$		0			0
$941$	−6942.05	−	12024.0i	−0.240493	−	0.416547i	0.720362	−	0.693599i	$-0.243976\pi$
$941$	−6942.05	−	12024.0i	−0.240493	−	0.416547i	−0.960855	+	0.277052i	$0.910643\pi$
$942$		0			0
$943$	−6614.93	+	11457.4i	−0.228432	+	0.395657i
$944$		0			0
$945$	−6055.92	−	5021.30i	−0.208465	−	0.172850i
$946$		0			0
$947$	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
$950$		0			0
$951$	−11321.9	−	37550.5i	−0.386054	−	1.28040i
$952$		0			0
$953$	−26131.4			−0.888225			−0.444112	−	0.895971i	$-0.646481\pi$
$953$	−26131.4			−0.888225			−0.444112	+	0.895971i	$0.646481\pi$
$954$		0			0
$955$	11118.5			0.376740
$956$		0			0
$957$	1147.09	+	269.500i	0.0387464	+	0.00910312i
$958$		0			0
$959$	−16061.4	−	27819.2i	−0.540825	−	0.936736i
$960$		0			0
$961$	14442.0	−	25014.3i	0.484777	−	0.839658i
$962$		0			0
$963$	−944.591	−	15194.5i	−0.0316085	−	0.508448i
$964$		0			0
$965$	3089.16	−	5350.59i	0.103050	−	0.178489i
$966$		0			0
$967$	−1998.77	−	3461.96i	−0.0664695	−	0.115128i	0.830875	−	0.556458i	$-0.187840\pi$
$967$	−1998.77	−	3461.96i	−0.0664695	−	0.115128i	−0.897345	+	0.441330i	$0.854507\pi$
$968$		0			0
$969$	−31116.8	+	33111.3i	−1.03159	+	1.09772i
$970$		0			0
$971$	−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
$974$		0			0
$975$	−17908.0	+	19055.8i	−0.588219	+	0.625923i
$976$		0			0
$977$	−6122.55	−	10604.6i	−0.200489	−	0.347257i	0.748197	−	0.663476i	$-0.230920\pi$
$977$	−6122.55	−	10604.6i	−0.200489	−	0.347257i	−0.948686	+	0.316220i	$0.897586\pi$
$978$		0			0
$979$	44.1170	−	76.4129i	0.00144023	−	0.00249455i
$980$		0			0
$981$	−377.746	−	6076.34i	−0.0122941	−	0.197760i
$982$		0			0
$983$	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
$986$		0			0
$987$	28248.2	+	6636.65i	0.910992	+	0.214029i
$988$		0			0
$989$	−1019.08			−0.0327654
$990$		0			0
$991$	−5178.38			−0.165991			−0.0829953	−	0.996550i	$-0.526449\pi$
$991$	−5178.38			−0.165991			−0.0829953	+	0.996550i	$0.526449\pi$
$992$		0			0
$993$	−4694.57	−	15570.1i	−0.150028	−	0.497587i
$994$		0			0
$995$	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	$0.300622\pi$
$998$		0			0
$999$	14051.1	+	11650.6i	0.445004	+	0.368977i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.4.c.a.4.1	✓	4	36.31	odd	6
9.4.c.a.7.1	yes	4	4.3	odd	2
27.4.c.a.10.2		4	36.23	even	6
27.4.c.a.19.2		4	12.11	even	2
81.4.a.a.1.1		2	36.11	even	6
81.4.a.d.1.2		2	36.7	odd	6
144.4.i.c.49.1		4	9.4	even	3	inner
144.4.i.c.97.1		4	1.1	even	1	trivial
225.4.e.b.76.2		4	180.139	odd	6
225.4.e.b.151.2		4	20.19	odd	2
225.4.k.b.49.1		8	180.103	even	12
225.4.k.b.49.4		8	180.67	even	12
225.4.k.b.124.1		8	20.7	even	4
225.4.k.b.124.4		8	20.3	even	4
432.4.i.c.145.1		4	9.5	odd	6
432.4.i.c.289.1		4	3.2	odd	2
1296.4.a.i.1.2		2	9.2	odd	6
1296.4.a.u.1.1		2	9.7	even	3
2025.4.a.g.1.1		2	180.79	odd	6
2025.4.a.n.1.2		2	180.119	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	144.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.55842 + 3.78651i) q^{3} +(-2.31386 - 4.00772i) q^{5} +(6.05842 - 10.4935i) q^{7} +(-1.67527 - 26.9480i) q^{9} +(5.01087 - 8.67909i) q^{11} +(24.2921 + 42.0752i) q^{13} +(23.4090 + 5.49972i) q^{15} +75.3505 q^{17} +116.052 q^{19} +(18.1753 + 60.2805i) q^{21} +(-19.0367 - 32.9725i) q^{23} +(51.7921 - 89.7066i) q^{25} +(108.000 + 89.5489i) q^{27} +(11.3139 - 19.5962i) q^{29} +(15.0584 + 26.0820i) q^{31} +(15.0326 + 49.8576i) q^{33} -56.0733 q^{35} +130.103 q^{37} +(-245.759 - 57.7390i) q^{39} +(-173.742 - 300.930i) q^{41} +(13.3832 - 23.1803i) q^{43} +(-104.124 + 69.0678i) q^{45} +(230.439 - 399.132i) q^{47} +(98.0910 + 169.899i) q^{49} +(-268.129 + 285.315i) q^{51} -438.310 q^{53} -46.3778 q^{55} +(-412.961 + 439.430i) q^{57} +(4.18487 + 7.24841i) q^{59} +(41.0448 - 71.0916i) q^{61} +(-292.928 - 145.683i) q^{63} +(112.417 - 194.712i) q^{65} +(341.785 + 591.989i) q^{67} +(192.591 + 45.2475i) q^{69} -1097.61 q^{71} +470.464 q^{73} +(155.376 + 515.325i) q^{75} +(-60.7160 - 105.163i) q^{77} +(243.017 - 420.919i) q^{79} +(-723.387 + 90.2901i) q^{81} +(49.5829 - 85.8802i) q^{83} +(-174.351 - 301.984i) q^{85} +(33.9416 + 112.571i) q^{87} +8.80426 q^{89} +588.687 q^{91} +(-152.344 - 35.7918i) q^{93} +(-268.527 - 465.103i) q^{95} +(-330.486 + 572.419i) q^{97} +(-242.278 - 120.493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{3} - 15 q^{5} + 7 q^{7} + 45 q^{9} + 66 q^{11} + 11 q^{13} - 27 q^{15} + 198 q^{17} + 154 q^{19} + 21 q^{21} + 33 q^{23} + 121 q^{25} + 432 q^{27} + 51 q^{29} + 43 q^{31} + 198 q^{33} - 6 q^{35}+ \cdots - 297 q^{99}+O(q^{100}) \) 4 * q + 3 * q^3 - 15 * q^5 + 7 * q^7 + 45 * q^9 + 66 * q^11 + 11 * q^13 - 27 * q^15 + 198 * q^17 + 154 * q^19 + 21 * q^21 + 33 * q^23 + 121 * q^25 + 432 * q^27 + 51 * q^29 + 43 * q^31 + 198 * q^33 - 6 * q^35 - 100 * q^37 - 759 * q^39 - 132 * q^41 + 88 * q^43 - 675 * q^45 + 399 * q^47 + 513 * q^49 - 297 * q^51 + 108 * q^53 - 1254 * q^55 - 1221 * q^57 + 798 * q^59 - 439 * q^61 - 603 * q^63 - 165 * q^65 + 988 * q^67 + 891 * q^69 - 2736 * q^71 - 910 * q^73 + 363 * q^75 + 165 * q^77 - 803 * q^79 - 567 * q^81 + 813 * q^83 - 594 * q^85 + 153 * q^87 - 792 * q^89 + 1562 * q^91 - 213 * q^93 - 132 * q^95 - 736 * q^97 - 297 * q^99

Introduction

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