LMFDB - Embedded newform 144.4.i.c.97.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,4,Mod(49,144)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			97.2
Root			$1.68614 - 0.396143i$ of defining polynomial
Character	$\chi$	$=$	144.97
Dual form			144.4.i.c.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.05842 - 1.18843i) q^{3} +(-5.18614 - 8.98266i) q^{5} +(-2.55842 + 4.43132i) q^{7} +(24.1753 - 12.0232i) q^{9} +O(q^{10})$	\(q+(5.05842 - 1.18843i) q^{3} +(-5.18614 - 8.98266i) q^{5} +(-2.55842 + 4.43132i) q^{7} +(24.1753 - 12.0232i) q^{9} +(27.9891 - 48.4786i) q^{11} +(-18.7921 - 32.5489i) q^{13} +(-36.9090 - 39.2747i) q^{15} +23.6495 q^{17} -39.0516 q^{19} +(-7.67527 + 25.4560i) q^{21} +(35.5367 + 61.5513i) q^{23} +(8.70789 - 15.0825i) q^{25} +(108.000 - 89.5489i) q^{27} +(14.1861 - 24.5711i) q^{29} +(6.44158 + 11.1571i) q^{31} +(83.9674 - 278.488i) q^{33} +53.0733 q^{35} -180.103 q^{37} +(-133.741 - 142.313i) q^{39} +(107.742 + 186.614i) q^{41} +(30.6168 - 53.0299i) q^{43} +(-233.376 - 154.804i) q^{45} +(-30.9388 + 53.5876i) q^{47} +(158.409 + 274.372i) q^{49} +(119.629 - 28.1057i) q^{51} +492.310 q^{53} -580.622 q^{55} +(-197.539 + 46.4101i) q^{57} +(394.815 + 683.840i) q^{59} +(-260.545 + 451.277i) q^{61} +(-8.57207 + 137.889i) q^{63} +(-194.917 + 337.606i) q^{65} +(152.215 + 263.644i) q^{67} +(252.909 + 269.120i) q^{69} -270.391 q^{71} -925.464 q^{73} +(26.1237 - 86.6424i) q^{75} +(143.216 + 248.057i) q^{77} +(-644.517 + 1116.34i) q^{79} +(439.887 - 581.326i) q^{81} +(356.917 - 618.198i) q^{83} +(-122.649 - 212.435i) q^{85} +(42.5584 - 141.150i) q^{87} -404.804 q^{89} +192.313 q^{91} +(45.8437 + 48.7822i) q^{93} +(202.527 + 350.787i) q^{95} +(-37.5137 + 64.9756i) q^{97} +(93.7785 - 1508.50i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{3} - 15 q^{5} + 7 q^{7} + 45 q^{9}+O(q^{10}) $ 4 * q + 3 * q^3 - 15 * q^5 + 7 * q^7 + 45 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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
$3$	5.05842	−	1.18843i	0.973494	−	0.228714i
$3$	5.05842	−	1.18843i	0.973494	−	0.228714i
$4$		0			0
$5$	−5.18614	−	8.98266i	−0.463863	−	0.803433i	0.535287	−	0.844670i	$-0.320204\pi$
$5$	−5.18614	−	8.98266i	−0.463863	−	0.803433i	−0.999149	+	0.0412369i	$0.986870\pi$
$6$		0			0
$7$	−2.55842	+	4.43132i	−0.138142	+	0.239269i	−0.926793	−	0.375572i	$-0.877446\pi$
$7$	−2.55842	+	4.43132i	−0.138142	+	0.239269i	0.788651	+	0.614841i	$0.210780\pi$
$8$		0			0
$9$	24.1753	−	12.0232i	0.895380	−	0.445302i
$10$		0			0
$11$	27.9891	−	48.4786i	0.767185	−	1.32880i	−0.171898	−	0.985115i	$-0.554990\pi$
$11$	27.9891	−	48.4786i	0.767185	−	1.32880i	0.939083	−	0.343689i	$-0.111677\pi$
$12$		0			0
$13$	−18.7921	−	32.5489i	−0.400923	−	0.694418i	0.592915	−	0.805265i	$-0.297977\pi$
$13$	−18.7921	−	32.5489i	−0.400923	−	0.694418i	−0.993838	+	0.110847i	$0.964644\pi$
$14$		0			0
$15$	−36.9090	−	39.2747i	−0.635323	−	0.676046i
$16$		0			0
$17$	23.6495			0.337402			0.168701	−	0.985667i	$-0.446043\pi$
$17$	23.6495			0.337402			0.168701	+	0.985667i	$0.446043\pi$
$18$		0			0
$19$	−39.0516			−0.471529			−0.235764	−	0.971810i	$-0.575759\pi$
$19$	−39.0516			−0.471529			−0.235764	+	0.971810i	$0.575759\pi$
$20$		0			0
$21$	−7.67527	+	25.4560i	−0.0797562	+	0.264521i
$22$		0			0
$23$	35.5367	+	61.5513i	0.322170	+	0.558015i	0.980936	−	0.194334i	$-0.0622544\pi$
$23$	35.5367	+	61.5513i	0.322170	+	0.558015i	−0.658766	+	0.752348i	$0.728921\pi$
$24$		0			0
$25$	8.70789	−	15.0825i	0.0696631	−	0.120660i
$26$		0			0
$27$	108.000	−	89.5489i	0.769800	−	0.638285i
$28$		0			0
$29$	14.1861	−	24.5711i	0.0908379	−	0.157336i	−0.817026	−	0.576601i	$-0.804379\pi$
$29$	14.1861	−	24.5711i	0.0908379	−	0.157336i	0.907864	+	0.419265i	$0.137712\pi$
$30$		0			0
$31$	6.44158	+	11.1571i	0.0373207	+	0.0646413i	0.884082	−	0.467331i	$-0.154784\pi$
$31$	6.44158	+	11.1571i	0.0373207	+	0.0646413i	−0.846762	+	0.531972i	$0.821451\pi$
$32$		0			0
$33$	83.9674	−	278.488i	0.442935	−	1.46905i
$34$		0			0
$35$	53.0733			0.256315
$36$		0			0
$37$	−180.103			−0.800237			−0.400119	−	0.916463i	$-0.631031\pi$
$37$	−180.103			−0.800237			−0.400119	+	0.916463i	$0.631031\pi$
$38$		0			0
$39$	−133.741	−	142.313i	−0.549119	−	0.584315i
$40$		0			0
$41$	107.742	+	186.614i	0.410401	+	0.710835i	0.994934	−	0.100535i	$-0.0320554\pi$
$41$	107.742	+	186.614i	0.410401	+	0.710835i	−0.584533	+	0.811370i	$0.698722\pi$
$42$		0			0
$43$	30.6168	−	53.0299i	0.108582	−	0.188069i	−0.806614	−	0.591078i	$-0.798702\pi$
$43$	30.6168	−	53.0299i	0.108582	−	0.188069i	0.915196	+	0.403009i	$0.132036\pi$
$44$		0			0
$45$	−233.376	−	154.804i	−0.773104	−	0.512819i
$46$		0			0
$47$	−30.9388	+	53.5876i	−0.0960189	+	0.166310i	−0.910033	−	0.414535i	$-0.863944\pi$
$47$	−30.9388	+	53.5876i	−0.0960189	+	0.166310i	0.814014	+	0.580845i	$0.197278\pi$
$48$		0			0
$49$	158.409	+	274.372i	0.461834	+	0.799919i
$50$		0			0
$51$	119.629	−	28.1057i	0.328459	−	0.0771685i
$52$		0			0
$53$	492.310			1.27592			0.637962	−	0.770068i	$-0.279778\pi$
$53$	492.310			1.27592			0.637962	+	0.770068i	$0.279778\pi$
$54$		0			0
$55$	−580.622			−1.42347
$56$		0			0
$57$	−197.539	+	46.4101i	−0.459031	+	0.107845i
$58$		0			0
$59$	394.815	+	683.840i	0.871196	+	1.50896i	0.860761	+	0.509010i	$0.169988\pi$
$59$	394.815	+	683.840i	0.871196	+	1.50896i	0.0104351	+	0.999946i	$0.496678\pi$
$60$		0			0
$61$	−260.545	+	451.277i	−0.546874	+	0.947214i	0.451612	+	0.892214i	$0.350849\pi$
$61$	−260.545	+	451.277i	−0.546874	+	0.947214i	−0.998486	+	0.0549998i	$0.982484\pi$
$62$		0			0
$63$	−8.57207	+	137.889i	−0.0171425	+	0.275751i
$64$		0			0
$65$	−194.917	+	337.606i	−0.371946	+	0.644229i
$66$		0			0
$67$	152.215	+	263.644i	0.277552	+	0.480734i	0.970776	−	0.239988i	$-0.0771436\pi$
$67$	152.215	+	263.644i	0.277552	+	0.480734i	−0.693224	+	0.720722i	$0.743810\pi$
$68$		0			0
$69$	252.909	+	269.120i	0.441256	+	0.469539i
$70$		0			0
$71$	−270.391			−0.451966			−0.225983	−	0.974131i	$-0.572559\pi$
$71$	−270.391			−0.451966			−0.225983	+	0.974131i	$0.572559\pi$
$72$		0			0
$73$	−925.464			−1.48380			−0.741900	−	0.670510i	$-0.766075\pi$
$73$	−925.464			−1.48380			−0.741900	+	0.670510i	$0.766075\pi$
$74$		0			0
$75$	26.1237	−	86.6424i	0.0402200	−	0.133395i
$76$		0			0
$77$	143.216	+	248.057i	0.211961	+	0.367127i
$78$		0			0
$79$	−644.517	+	1116.34i	−0.917897	+	1.58984i	−0.115294	+	0.993331i	$0.536781\pi$
$79$	−644.517	+	1116.34i	−0.917897	+	1.58984i	−0.802603	+	0.596513i	$0.796552\pi$
$80$		0			0
$81$	439.887	−	581.326i	0.603411	−	0.797430i
$82$		0			0
$83$	356.917	−	618.198i	0.472009	−	0.817543i	−0.527478	−	0.849569i	$-0.676862\pi$
$83$	356.917	−	618.198i	0.472009	−	0.817543i	0.999487	+	0.0320252i	$0.0101957\pi$
$84$		0			0
$85$	−122.649	−	212.435i	−0.156508	−	0.271080i
$86$		0			0
$87$	42.5584	−	141.150i	0.0524453	−	0.173941i
$88$		0			0
$89$	−404.804			−0.482125			−0.241063	−	0.970510i	$-0.577496\pi$
$89$	−404.804			−0.482125			−0.241063	+	0.970510i	$0.577496\pi$
$90$		0			0
$91$	192.313			0.221537
$92$		0			0
$93$	45.8437	+	48.7822i	0.0511158	+	0.0543922i
$94$		0			0
$95$	202.527	+	350.787i	0.218725	+	0.378842i
$96$		0			0
$97$	−37.5137	+	64.9756i	−0.0392674	+	0.0680131i	−0.884991	−	0.465608i	$-0.845836\pi$
$97$	−37.5137	+	64.9756i	−0.0392674	+	0.0680131i	0.845724	+	0.533621i	$0.179169\pi$
$98$		0			0
$99$	93.7785	−	1508.50i	0.0952029	−	1.53141i
$100$		0			0
$101$	543.939	−	942.130i	0.535881	−	0.928172i	−0.463240	−	0.886233i	$-0.653313\pi$
$101$	543.939	−	942.130i	0.535881	−	0.928172i	0.999120	−	0.0419392i	$-0.0133536\pi$
$102$		0			0
$103$	−545.909	−	945.542i	−0.522233	−	0.904534i	−0.999665	−	0.0258657i	$-0.991766\pi$
$103$	−545.909	−	945.542i	−0.522233	−	0.904534i	0.477432	−	0.878669i	$-0.341568\pi$
$104$		0			0
$105$	268.467	−	63.0740i	0.249521	−	0.0586228i
$106$		0			0
$107$	1029.15			0.929833			0.464917	−	0.885354i	$-0.346084\pi$
$107$	1029.15			0.929833			0.464917	+	0.885354i	$0.346084\pi$
$108$		0			0
$109$	1776.52			1.56110			0.780548	−	0.625096i	$-0.214940\pi$
$109$	1776.52			1.56110			0.780548	+	0.625096i	$0.214940\pi$
$110$		0			0
$111$	−911.038	+	214.040i	−0.779026	+	0.183025i
$112$		0			0
$113$	807.969	+	1399.44i	0.672631	+	1.16503i	0.977155	+	0.212526i	$0.0681692\pi$
$113$	807.969	+	1399.44i	0.672631	+	1.16503i	−0.304524	+	0.952505i	$0.598498\pi$
$114$		0			0
$115$	368.596	−	638.428i	0.298885	−	0.517684i
$116$		0			0
$117$	−845.645	−	560.937i	−0.668204	−	0.443237i
$118$		0			0
$119$	−60.5053	+	104.798i	−0.0466094	+	0.0807298i
$120$		0			0
$121$	−901.282	−	1561.07i	−0.677147	−	1.17285i
$122$		0			0
$123$	766.781	+	815.930i	0.562100	+	0.598130i
$124$		0			0
$125$	−1477.18			−1.05698
$126$		0			0
$127$	1206.10			0.842711			0.421356	−	0.906895i	$-0.361554\pi$
$127$	1206.10			0.842711			0.421356	+	0.906895i	$0.361554\pi$
$128$		0			0
$129$	91.8505	−	304.634i	0.0626898	−	0.207919i
$130$		0			0
$131$	−513.928	−	890.149i	−0.342764	−	0.593684i	0.642181	−	0.766553i	$-0.278030\pi$
$131$	−513.928	−	890.149i	−0.342764	−	0.593684i	−0.984945	+	0.172869i	$0.944696\pi$
$132$		0			0
$133$	99.9105	−	173.050i	0.0651379	−	0.112822i
$134$		0			0
$135$	−1364.49	−	505.714i	−0.869901	−	0.322407i
$136$		0			0
$137$	630.454	−	1091.98i	0.393163	−	0.680978i	−0.599702	−	0.800223i	$-0.704714\pi$
$137$	630.454	−	1091.98i	0.393163	−	0.680978i	0.992865	+	0.119245i	$0.0380475\pi$
$138$		0			0
$139$	230.916	+	399.958i	0.140907	+	0.244057i	0.927838	−	0.372983i	$-0.121665\pi$
$139$	230.916	+	399.958i	0.140907	+	0.244057i	−0.786932	+	0.617040i	$0.788332\pi$
$140$		0			0
$141$	−92.8164	+	307.837i	−0.0554365	+	0.183862i
$142$		0			0
$143$	−2103.90			−1.23033
$144$		0			0
$145$	−294.285			−0.168545
$146$		0			0
$147$	1127.37	+	1199.63i	0.632545	+	0.673089i
$148$		0			0
$149$	−729.661	−	1263.81i	−0.401182	−	0.694868i	0.592687	−	0.805433i	$-0.298067\pi$
$149$	−729.661	−	1263.81i	−0.401182	−	0.694868i	−0.993869	+	0.110565i	$0.964734\pi$
$150$		0			0
$151$	770.659	−	1334.82i	0.415333	−	0.719378i	−0.580130	−	0.814524i	$-0.696998\pi$
$151$	770.659	−	1334.82i	0.415333	−	0.719378i	0.995463	+	0.0951456i	$0.0303317\pi$
$152$		0			0
$153$	571.732	−	284.341i	0.302103	−	0.150246i
$154$		0			0
$155$	66.8139	−	115.725i	0.0346233	−	0.0599694i
$156$		0			0
$157$	1607.79	+	2784.77i	0.817295	+	1.41560i	0.907668	+	0.419688i	$0.137861\pi$
$157$	1607.79	+	2784.77i	0.817295	+	1.41560i	−0.0903734	+	0.995908i	$0.528806\pi$
$158$		0			0
$159$	2490.31	−	585.076i	1.24210	−	0.291821i
$160$		0			0
$161$	−363.671			−0.178021
$162$		0			0
$163$	−947.587			−0.455342			−0.227671	−	0.973738i	$-0.573111\pi$
$163$	−947.587			−0.455342			−0.227671	+	0.973738i	$0.573111\pi$
$164$		0			0
$165$	−2937.03	+	690.029i	−1.38574	+	0.325568i
$166$		0			0
$167$	342.980	+	594.058i	0.158926	+	0.275267i	0.934481	−	0.356012i	$-0.115864\pi$
$167$	342.980	+	594.058i	0.158926	+	0.275267i	−0.775556	+	0.631279i	$0.782530\pi$
$168$		0			0
$169$	392.213	−	679.333i	0.178522	−	0.309209i
$170$		0			0
$171$	−944.083	+	469.524i	−0.422198	+	0.209973i
$172$		0			0
$173$	1106.41	−	1916.36i	0.486237	−	0.842188i	−0.513637	−	0.858007i	$-0.671702\pi$
$173$	1106.41	−	1916.36i	0.486237	−	0.842188i	0.999875	+	0.0158193i	$0.00503566\pi$
$174$		0			0
$175$	44.5569	+	77.1748i	0.0192468	+	0.0333364i
$176$		0			0
$177$	2809.84	+	2989.94i	1.19322	+	1.26970i
$178$		0			0
$179$	−3023.22			−1.26238			−0.631190	−	0.775629i	$-0.717433\pi$
$179$	−3023.22			−1.26238			−0.631190	+	0.775629i	$0.717433\pi$
$180$		0			0
$181$	391.445			0.160751			0.0803753	−	0.996765i	$-0.474388\pi$
$181$	391.445			0.160751			0.0803753	+	0.996765i	$0.474388\pi$
$182$		0			0
$183$	−781.634	+	2592.39i	−0.315738	+	1.04718i
$184$		0			0
$185$	934.040	+	1617.81i	0.371200	+	0.642937i
$186$		0			0
$187$	661.928	−	1146.49i	0.258850	−	0.448341i
$188$		0			0
$189$	120.510	+	707.686i	0.0463799	+	0.272363i
$190$		0			0
$191$	1742.79	−	3018.61i	0.660231	−	1.14355i	−0.320324	−	0.947308i	$-0.603792\pi$
$191$	1742.79	−	3018.61i	0.660231	−	1.14355i	0.980555	−	0.196246i	$-0.0628750\pi$
$192$		0			0
$193$	−1107.53	−	1918.31i	−0.413068	−	0.715455i	0.582156	−	0.813077i	$-0.302209\pi$
$193$	−1107.53	−	1918.31i	−0.413068	−	0.715455i	−0.995223	+	0.0976228i	$0.968876\pi$
$194$		0			0
$195$	−584.751	+	1939.40i	−0.214743	+	0.712222i
$196$		0			0
$197$	−3975.11			−1.43764			−0.718820	−	0.695196i	$-0.755318\pi$
$197$	−3975.11			−1.43764			−0.718820	+	0.695196i	$0.755318\pi$
$198$		0			0
$199$	1555.34			0.554046			0.277023	−	0.960863i	$-0.410652\pi$
$199$	1555.34			0.554046			0.277023	+	0.960863i	$0.410652\pi$
$200$		0			0
$201$	1083.29	+	1152.72i	0.380146	+	0.404512i
$202$		0			0
$203$	72.5883	+	125.727i	0.0250970	+	0.0434693i
$204$		0			0
$205$	1117.53	−	1935.62i	0.380739	−	0.659460i
$206$		0			0
$207$	1599.15	+	1060.76i	0.536950	+	0.356172i
$208$		0			0
$209$	−1093.02	+	1893.17i	−0.361750	+	0.626570i
$210$		0			0
$211$	873.865	+	1513.58i	0.285115	+	0.493834i	0.972637	−	0.232329i	$-0.0746347\pi$
$211$	873.865	+	1513.58i	0.285115	+	0.493834i	−0.687522	+	0.726164i	$0.741301\pi$
$212$		0			0
$213$	−1367.75	+	321.341i	−0.439986	+	0.103371i
$214$		0			0
$215$	−635.133			−0.201468
$216$		0			0
$217$	−65.9211			−0.0206222
$218$		0			0
$219$	−4681.39	+	1099.85i	−1.44447	+	0.339365i
$220$		0			0
$221$	−444.423	−	769.764i	−0.135272	−	0.234298i
$222$		0			0
$223$	−1270.97	+	2201.39i	−0.381662	+	0.661057i	−0.991300	−	0.131622i	$-0.957981\pi$
$223$	−1270.97	+	2201.39i	−0.381662	+	0.661057i	0.609638	+	0.792680i	$0.291315\pi$
$224$		0			0
$225$	29.1761	−	469.320i	0.00864476	−	0.139058i
$226$		0			0
$227$	−1496.63	+	2592.24i	−0.437598	+	0.757943i	−0.997504	−	0.0706140i	$-0.977504\pi$
$227$	−1496.63	+	2592.24i	−0.437598	+	0.757943i	0.559905	+	0.828557i	$0.310837\pi$
$228$		0			0
$229$	2152.65	+	3728.50i	0.621185	+	1.07592i	0.989265	+	0.146130i	$0.0466816\pi$
$229$	2152.65	+	3728.50i	0.621185	+	1.07592i	−0.368081	+	0.929794i	$0.619985\pi$
$230$		0			0
$231$	1019.25	+	1084.58i	0.290309	+	0.308917i
$232$		0			0
$233$	−5581.34			−1.56930			−0.784648	−	0.619942i	$-0.787156\pi$
$233$	−5581.34			−1.56930			−0.784648	+	0.619942i	$0.787156\pi$
$234$		0			0
$235$	641.812			0.178158
$236$		0			0
$237$	−1933.55	+	6412.87i	−0.529948	+	1.75764i
$238$		0			0
$239$	704.814	+	1220.77i	0.190756	+	0.330399i	0.945501	−	0.325619i	$-0.105573\pi$
$239$	704.814	+	1220.77i	0.190756	+	0.330399i	−0.754745	+	0.656018i	$0.772239\pi$
$240$		0			0
$241$	−313.286	+	542.627i	−0.0837366	+	0.145036i	−0.904852	−	0.425726i	$-0.860019\pi$
$241$	−313.286	+	542.627i	−0.0837366	+	0.145036i	0.821116	+	0.570762i	$0.193352\pi$
$242$		0			0
$243$	1534.27	−	3463.37i	0.405034	−	0.914302i
$244$		0			0
$245$	1643.06	−	2845.87i	0.428455	−	0.742105i
$246$		0			0
$247$	733.862	+	1271.09i	0.189047	+	0.327438i
$248$		0			0
$249$	1070.75	−	3551.28i	0.272514	−	0.903828i
$250$		0			0
$251$	−1705.53			−0.428892			−0.214446	−	0.976736i	$-0.568795\pi$
$251$	−1705.53			−0.428892			−0.214446	+	0.976736i	$0.568795\pi$
$252$		0			0
$253$	3978.56			0.988656
$254$		0			0
$255$	−872.877	−	928.826i	−0.214360	−	0.228099i
$256$		0			0
$257$	1798.69	+	3115.42i	0.436573	+	0.756166i	0.997423	−	0.0717513i	$-0.0228588\pi$
$257$	1798.69	+	3115.42i	0.436573	+	0.756166i	−0.560850	+	0.827918i	$0.689525\pi$
$258$		0			0
$259$	460.780	−	798.094i	0.110546	−	0.191472i
$260$		0			0
$261$	47.5311	−	764.576i	0.0112724	−	0.181326i
$262$		0			0
$263$	2068.75	−	3583.18i	0.485037	−	0.840108i	−0.514815	−	0.857301i	$-0.672140\pi$
$263$	2068.75	−	3583.18i	0.485037	−	0.840108i	0.999852	+	0.0171926i	$0.00547285\pi$
$264$		0			0
$265$	−2553.19	−	4422.25i	−0.591853	−	1.02512i
$266$		0			0
$267$	−2047.67	+	481.082i	−0.469346	+	0.110269i
$268$		0			0
$269$	6090.99			1.38057			0.690287	−	0.723536i	$-0.257484\pi$
$269$	6090.99			1.38057			0.690287	+	0.723536i	$0.257484\pi$
$270$		0			0
$271$	3196.62			0.716534			0.358267	−	0.933619i	$-0.383368\pi$
$271$	3196.62			0.716534			0.358267	+	0.933619i	$0.383368\pi$
$272$		0			0
$273$	972.798	−	228.550i	0.215665	−	0.0506684i
$274$		0			0
$275$	−487.452	−	844.292i	−0.106889	−	0.185137i
$276$		0			0
$277$	1559.68	−	2701.45i	0.338311	−	0.585972i	−0.645804	−	0.763503i	$-0.723478\pi$
$277$	1559.68	−	2701.45i	0.338311	−	0.585972i	0.984115	+	0.177531i	$0.0568111\pi$
$278$		0			0
$279$	289.871	+	192.279i	0.0622012	+	0.0412596i
$280$		0			0
$281$	−2474.17	+	4285.38i	−0.525254	+	0.909767i	0.474313	+	0.880356i	$0.342696\pi$
$281$	−2474.17	+	4285.38i	−0.525254	+	0.909767i	−0.999567	+	0.0294105i	$0.990637\pi$
$282$		0			0
$283$	−2272.47	−	3936.03i	−0.477329	−	0.826758i	0.522333	−	0.852741i	$-0.325062\pi$
$283$	−2272.47	−	3936.03i	−0.477329	−	0.826758i	−0.999662	+	0.0259834i	$0.991728\pi$
$284$		0			0
$285$	1441.35	+	1533.74i	0.299573	+	0.318775i
$286$		0			0
$287$	−1102.60			−0.226774
$288$		0			0
$289$	−4353.70			−0.886160
$290$		0			0
$291$	−112.541	+	373.256i	−0.0226710	+	0.0751913i
$292$		0			0
$293$	−3430.05	−	5941.03i	−0.683911	−	1.18457i	−0.973778	−	0.227501i	$-0.926944\pi$
$293$	−3430.05	−	5941.03i	−0.683911	−	1.18457i	0.289867	−	0.957067i	$-0.406389\pi$
$294$		0			0
$295$	4095.13	−	7092.98i	0.808230	−	1.39990i
$296$		0			0
$297$	−1318.38	−	7742.08i	−0.257576	−	1.51260i
$298$		0			0
$299$	1335.62	−	2313.36i	0.258330	−	0.447441i
$300$		0			0
$301$	156.662	+	271.346i	0.0299994	+	0.0519605i
$302$		0			0
$303$	1631.82	−	5412.12i	0.309391	−	1.02613i
$304$		0			0
$305$	5404.89			1.01470
$306$		0			0
$307$	−6332.25			−1.17720			−0.588600	−	0.808424i	$-0.700321\pi$
$307$	−6332.25			−1.17720			−0.588600	+	0.808424i	$0.700321\pi$
$308$		0			0
$309$	−3885.15	−	4134.18i	−0.715270	−	0.761117i
$310$		0			0
$311$	3538.84	+	6129.44i	0.645238	+	1.11758i	0.984247	+	0.176801i	$0.0565750\pi$
$311$	3538.84	+	6129.44i	0.645238	+	1.11758i	−0.339009	+	0.940783i	$0.610092\pi$
$312$		0			0
$313$	−690.649	+	1196.24i	−0.124721	+	0.216024i	−0.921624	−	0.388084i	$-0.873137\pi$
$313$	−690.649	+	1196.24i	−0.124721	+	0.216024i	0.796903	+	0.604108i	$0.206470\pi$
$314$		0			0
$315$	1283.06	−	638.110i	0.229500	−	0.114138i
$316$		0			0
$317$	4087.47	−	7079.70i	0.724211	−	1.25437i	−0.235086	−	0.971974i	$-0.575537\pi$
$317$	4087.47	−	7079.70i	0.724211	−	1.25437i	0.959298	−	0.282396i	$-0.0911294\pi$
$318$		0			0
$319$	−794.115	−	1375.45i	−0.139379	−	0.241412i
$320$		0			0
$321$	5205.90	−	1223.08i	0.905187	−	0.212665i
$322$		0			0
$323$	−923.549			−0.159095
$324$		0			0
$325$	−654.559			−0.111718
$326$		0			0
$327$	8986.37	−	2111.27i	1.51972	−	0.357044i
$328$		0			0
$329$	−158.309	−	274.199i	−0.0265284	−	0.0459486i
$330$		0			0
$331$	−4830.64	+	8366.92i	−0.802163	+	1.38939i	0.116026	+	0.993246i	$0.462984\pi$
$331$	−4830.64	+	8366.92i	−0.802163	+	1.38939i	−0.918189	+	0.396142i	$0.870349\pi$
$332$		0			0
$333$	−4354.04	+	2165.41i	−0.716517	+	0.356348i
$334$		0			0
$335$	1578.81	−	2734.59i	0.257492	−	0.445989i
$336$		0			0
$337$	2478.01	+	4292.04i	0.400552	+	0.693776i	0.993793	−	0.111249i	$-0.0354852\pi$
$337$	2478.01	+	4292.04i	0.400552	+	0.693776i	−0.593241	+	0.805025i	$0.702152\pi$
$338$		0			0
$339$	5750.19	+	6118.76i	0.921260	+	0.980311i
$340$		0			0
$341$	721.177			0.114528
$342$		0			0
$343$	−3376.19			−0.531478
$344$		0			0
$345$	1105.79	−	3667.49i	0.172561	−	0.572321i
$346$		0			0
$347$	−507.802	−	879.540i	−0.0785598	−	0.136070i	0.824069	−	0.566490i	$-0.191699\pi$
$347$	−507.802	−	879.540i	−0.0785598	−	0.136070i	−0.902629	+	0.430420i	$0.858365\pi$
$348$		0			0
$349$	−6079.29	+	10529.6i	−0.932426	+	1.61501i	−0.153267	+	0.988185i	$0.548979\pi$
$349$	−6079.29	+	10529.6i	−0.932426	+	1.61501i	−0.779160	+	0.626825i	$0.784354\pi$
$350$		0			0
$351$	−4944.26	−	1832.47i	−0.751867	−	0.278661i
$352$		0			0
$353$	−2118.04	+	3668.56i	−0.319354	+	0.553138i	−0.980353	−	0.197249i	$-0.936799\pi$
$353$	−2118.04	+	3668.56i	−0.319354	+	0.553138i	0.660999	+	0.750387i	$0.270133\pi$
$354$		0			0
$355$	1402.29	+	2428.83i	0.209650	+	0.363124i
$356$		0			0
$357$	−181.516	+	602.020i	−0.0269099	+	0.0892501i
$358$		0			0
$359$	517.939			0.0761443			0.0380721	−	0.999275i	$-0.487878\pi$
$359$	517.939			0.0761443			0.0380721	+	0.999275i	$0.487878\pi$
$360$		0			0
$361$	−5333.97			−0.777660
$362$		0			0
$363$	−6414.29	−	6825.42i	−0.927445	−	0.986892i
$364$		0			0
$365$	4799.59	+	8313.13i	0.688279	+	1.19213i
$366$		0			0
$367$	−2308.15	+	3997.83i	−0.328295	+	0.568624i	−0.982174	−	0.187976i	$-0.939807\pi$
$367$	−2308.15	+	3997.83i	−0.328295	+	0.568624i	0.653879	+	0.756600i	$0.273141\pi$
$368$		0			0
$369$	4848.38	+	3216.05i	0.684002	+	0.453715i
$370$		0			0
$371$	−1259.54	+	2181.58i	−0.176258	+	0.305288i
$372$		0			0
$373$	−2382.71	−	4126.98i	−0.330756	−	0.572887i	0.651904	−	0.758301i	$-0.273970\pi$
$373$	−2382.71	−	4126.98i	−0.330756	−	0.572887i	−0.982660	+	0.185415i	$0.940637\pi$
$374$		0			0
$375$	−7472.18	+	1755.52i	−1.02896	+	0.241746i
$376$		0			0
$377$	−1066.35			−0.145676
$378$		0			0
$379$	2000.33			0.271108			0.135554	−	0.990770i	$-0.456719\pi$
$379$	2000.33			0.271108			0.135554	+	0.990770i	$0.456719\pi$
$380$		0			0
$381$	6100.98	−	1433.37i	0.820374	−	0.192740i
$382$		0			0
$383$	495.147	+	857.619i	0.0660596	+	0.114419i	0.897164	−	0.441699i	$-0.145624\pi$
$383$	495.147	+	857.619i	0.0660596	+	0.114419i	−0.831104	+	0.556117i	$0.812291\pi$
$384$		0			0
$385$	1485.48	−	2572.92i	0.196641	−	0.340593i
$386$		0			0
$387$	102.583	−	1650.12i	0.0134743	−	0.216746i
$388$		0			0
$389$	−202.205	+	350.230i	−0.0263553	+	0.0456487i	−0.878902	−	0.477002i	$-0.841723\pi$
$389$	−202.205	+	350.230i	−0.0263553	+	0.0456487i	0.852547	+	0.522651i	$0.175057\pi$
$390$		0			0
$391$	840.423	+	1455.66i	0.108701	+	0.188275i
$392$		0			0
$393$	−3657.54	−	3891.98i	−0.469462	−	0.499553i
$394$		0			0
$395$	13370.2			1.70311
$396$		0			0
$397$	2919.61			0.369096			0.184548	−	0.982824i	$-0.440918\pi$
$397$	2919.61			0.369096			0.184548	+	0.982824i	$0.440918\pi$
$398$		0			0
$399$	299.731	−	994.097i	0.0376074	−	0.124730i
$400$		0			0
$401$	5093.10	+	8821.52i	0.634258	+	1.09857i	0.986672	+	0.162723i	$0.0520277\pi$
$401$	5093.10	+	8821.52i	0.634258	+	1.09857i	−0.352414	+	0.935844i	$0.614639\pi$
$402$		0			0
$403$	242.102	−	419.332i	0.0299254	−	0.0518323i
$404$		0			0
$405$	−7503.17	−	936.514i	−0.920582	−	0.114903i
$406$		0			0
$407$	−5040.93	+	8731.15i	−0.613930	+	1.06336i
$408$		0			0
$409$	−3457.12	−	5987.91i	−0.417955	−	0.723920i	0.577778	−	0.816194i	$-0.303920\pi$
$409$	−3457.12	−	5987.91i	−0.417955	−	0.723920i	−0.995734	+	0.0922740i	$0.970586\pi$
$410$		0			0
$411$	1891.36	−	6272.94i	0.226993	−	0.752850i
$412$		0			0
$413$	−4040.41			−0.481394
$414$		0			0
$415$	−7404.09			−0.875789
$416$		0			0
$417$	1643.39	+	1748.73i	0.192991	+	0.205361i
$418$		0			0
$419$	2560.16	+	4434.32i	0.298501	+	0.517019i	0.975793	−	0.218695i	$-0.0701801\pi$
$419$	2560.16	+	4434.32i	0.298501	+	0.517019i	−0.677292	+	0.735714i	$0.736847\pi$
$420$		0			0
$421$	−933.246	+	1616.43i	−0.108037	+	0.187126i	−0.914975	−	0.403511i	$-0.867790\pi$
$421$	−933.246	+	1616.43i	−0.108037	+	0.187126i	0.806938	+	0.590636i	$0.201123\pi$
$422$		0			0
$423$	−103.661	+	1667.48i	−0.0119153	+	0.191668i
$424$		0			0
$425$	205.937	−	356.693i	0.0235045	−	0.0407110i
$426$		0			0
$427$	−1333.17	−	2309.11i	−0.151092	−	0.261700i
$428$		0			0
$429$	−10642.4	+	2500.34i	−1.19772	+	0.281393i
$430$		0			0
$431$	4090.64			0.457168			0.228584	−	0.973524i	$-0.426590\pi$
$431$	4090.64			0.457168			0.228584	+	0.973524i	$0.426590\pi$
$432$		0			0
$433$	633.052			0.0702599			0.0351299	−	0.999383i	$-0.488815\pi$
$433$	633.052			0.0702599			0.0351299	+	0.999383i	$0.488815\pi$
$434$		0			0
$435$	−1488.62	+	349.738i	−0.164078	+	0.0385486i
$436$		0			0
$437$	−1387.76	−	2403.68i	−0.151912	−	0.263120i
$438$		0			0
$439$	−5653.26	+	9791.74i	−0.614614	+	1.06454i	0.375838	+	0.926685i	$0.377355\pi$
$439$	−5653.26	+	9791.74i	−0.614614	+	1.06454i	−0.990452	+	0.137857i	$0.955979\pi$
$440$		0			0
$441$	7128.40	+	4728.45i	0.769723	+	0.510576i
$442$		0			0
$443$	−4140.65	+	7171.82i	−0.444082	+	0.769172i	−0.997988	−	0.0634071i	$-0.979803\pi$
$443$	−4140.65	+	7171.82i	−0.444082	+	0.769172i	0.553906	+	0.832579i	$0.313137\pi$
$444$		0			0
$445$	2099.37	+	3636.22i	0.223640	+	0.387356i
$446$		0			0
$447$	−5192.88	−	5525.73i	−0.549474	−	0.584694i
$448$		0			0
$449$	6888.40			0.724017			0.362008	−	0.932175i	$-0.382091\pi$
$449$	6888.40			0.724017			0.362008	+	0.932175i	$0.382091\pi$
$450$		0			0
$451$	12062.4			1.25941
$452$		0			0
$453$	2311.98	−	7667.96i	0.239793	−	0.795302i
$454$		0			0
$455$	−997.360	−	1727.48i	−0.102763	−	0.177990i
$456$		0			0
$457$	−2141.80	+	3709.71i	−0.219233	+	0.379722i	−0.954574	−	0.297975i	$-0.903689\pi$
$457$	−2141.80	+	3709.71i	−0.219233	+	0.379722i	0.735341	+	0.677697i	$0.237022\pi$
$458$		0			0
$459$	2554.14	−	2117.78i	0.259732	−	0.215359i
$460$		0			0
$461$	−6889.16	+	11932.4i	−0.696009	+	1.20552i	0.273831	+	0.961778i	$0.411709\pi$
$461$	−6889.16	+	11932.4i	−0.696009	+	1.20552i	−0.969840	+	0.243744i	$0.921624\pi$
$462$		0			0
$463$	2867.27	+	4966.25i	0.287804	+	0.498491i	0.973285	−	0.229599i	$-0.0737415\pi$
$463$	2867.27	+	4966.25i	0.287804	+	0.498491i	−0.685481	+	0.728090i	$0.740408\pi$
$464$		0			0
$465$	200.442	−	664.790i	0.0199898	−	0.0662987i
$466$		0			0
$467$	8950.97			0.886941			0.443470	−	0.896289i	$-0.353747\pi$
$467$	8950.97			0.886941			0.443470	+	0.896289i	$0.353747\pi$
$468$		0			0
$469$	−1557.72			−0.153366
$470$		0			0
$471$	11442.4	+	12175.8i	1.11940	+	1.19115i
$472$		0			0
$473$	−1713.88	−	2968.52i	−0.166605	−	0.288568i
$474$		0			0
$475$	−340.057	+	588.996i	−0.0328482	+	0.0568947i
$476$		0			0
$477$	11901.7	−	5919.12i	1.14244	−	0.568172i
$478$		0			0
$479$	4840.51	−	8384.00i	0.461729	−	0.799739i	−0.537318	−	0.843380i	$-0.680562\pi$
$479$	4840.51	−	8384.00i	0.461729	−	0.799739i	0.999047	+	0.0436411i	$0.0138958\pi$
$480$		0			0
$481$	3384.52	+	5862.16i	0.320833	+	0.555699i
$482$		0			0
$483$	−1839.60	+	432.198i	−0.173302	+	0.0407157i
$484$		0			0
$485$	778.204			0.0728586
$486$		0			0
$487$	−8704.66			−0.809950			−0.404975	−	0.914328i	$-0.632720\pi$
$487$	−8704.66			−0.809950			−0.404975	+	0.914328i	$0.632720\pi$
$488$		0			0
$489$	−4793.30	+	1126.14i	−0.443273	+	0.104143i
$490$		0			0
$491$	−7797.85	−	13506.3i	−0.716725	−	1.24140i	−0.962290	−	0.272024i	$-0.912307\pi$
$491$	−7797.85	−	13506.3i	−0.716725	−	1.24140i	0.245565	−	0.969380i	$-0.421026\pi$
$492$		0			0
$493$	335.495	−	581.094i	0.0306489	−	0.0530855i
$494$		0			0
$495$	−14036.7	+	6980.92i	−1.27455	+	0.633876i
$496$		0			0
$497$	691.776	−	1198.19i	0.0624354	−	0.108141i
$498$		0			0
$499$	−4848.14	−	8397.22i	−0.434935	−	0.753329i	0.562355	−	0.826896i	$-0.309895\pi$
$499$	−4848.14	−	8397.22i	−0.434935	−	0.753329i	−0.997290	+	0.0735663i	$0.976562\pi$
$500$		0			0
$501$	2440.93	+	2597.39i	0.217670	+	0.231622i
$502$		0			0
$503$	−20949.7			−1.85706			−0.928532	−	0.371253i	$-0.878928\pi$
$503$	−20949.7			−1.85706			−0.928532	+	0.371253i	$0.878928\pi$
$504$		0			0
$505$	−11283.8			−0.994300
$506$		0			0
$507$	1176.64	−	3902.47i	0.103070	−	0.341844i
$508$		0			0
$509$	−5637.37	−	9764.22i	−0.490908	−	0.850278i	0.509037	−	0.860745i	$-0.330002\pi$
$509$	−5637.37	−	9764.22i	−0.490908	−	0.850278i	−0.999945	+	0.0104668i	$0.996668\pi$
$510$		0			0
$511$	2367.73	−	4101.03i	0.204975	−	0.355027i
$512$		0			0
$513$	−4217.57	+	3497.03i	−0.362983	+	0.300970i
$514$		0			0
$515$	−5662.32	+	9807.43i	−0.484489	+	0.839159i
$516$		0			0
$517$	1731.90	+	2999.74i	0.147329	+	0.255181i
$518$		0			0
$519$	3319.24	−	11008.7i	0.280729	−	0.931074i
$520$		0			0
$521$	8675.49			0.729520			0.364760	−	0.931102i	$-0.381151\pi$
$521$	8675.49			0.729520			0.364760	+	0.931102i	$0.381151\pi$
$522$		0			0
$523$	4226.14			0.353339			0.176670	−	0.984270i	$-0.443468\pi$
$523$	4226.14			0.353339			0.176670	+	0.984270i	$0.443468\pi$
$524$		0			0
$525$	317.105	+	337.430i	0.0263611	+	0.0280508i
$526$		0			0
$527$	152.340	+	263.860i	0.0125921	+	0.0218101i
$528$		0			0
$529$	3557.79	−	6162.27i	0.292413	−	0.506474i
$530$		0			0
$531$	17766.7	+	11785.1i	1.45199	+	0.963143i
$532$		0			0
$533$	4049.39	−	7013.75i	0.329078	−	0.569980i
$534$		0			0
$535$	−5337.34	−	9244.55i	−0.431315	−	0.747059i
$536$		0			0
$537$	−15292.7	+	3592.88i	−1.22892	+	0.288723i
$538$		0			0
$539$	17734.9			1.41725
$540$		0			0
$541$	13357.8			1.06154			0.530771	−	0.847515i	$-0.321902\pi$
$541$	13357.8			1.06154			0.530771	+	0.847515i	$0.321902\pi$
$542$		0			0
$543$	1980.09	−	465.205i	0.156490	−	0.0367658i
$544$		0			0
$545$	−9213.26	−	15957.8i	−0.724134	−	1.25424i
$546$		0			0
$547$	10835.6	−	18767.7i	0.846974	−	1.46700i	−0.0369219	−	0.999318i	$-0.511755\pi$
$547$	10835.6	−	18767.7i	0.846974	−	1.46700i	0.883896	−	0.467684i	$-0.154911\pi$
$548$		0			0
$549$	−872.964	+	14042.3i	−0.0678637	+	1.09164i
$550$		0			0
$551$	−553.991	+	959.541i	−0.0428327	+	0.0741884i
$552$		0			0
$553$	−3297.90	−	5712.12i	−0.253600	−	0.439248i
$554$		0			0
$555$	6647.42	+	7073.50i	0.508410	+	0.540997i
$556$		0			0
$557$	7477.63			0.568828			0.284414	−	0.958702i	$-0.408201\pi$
$557$	7477.63			0.568828			0.284414	+	0.958702i	$0.408201\pi$
$558$		0			0
$559$	−2301.42			−0.174132
$560$		0			0
$561$	1985.78	−	6586.10i	0.149447	−	0.495660i
$562$		0			0
$563$	−11652.3	−	20182.4i	−0.872269	−	1.51082i	−0.859643	−	0.510895i	$-0.829314\pi$
$563$	−11652.3	−	20182.4i	−0.872269	−	1.51082i	−0.0126262	−	0.999920i	$-0.504019\pi$
$564$		0			0
$565$	8380.48	−	14515.4i	0.624017	−	1.08083i
$566$		0			0
$567$	1450.63	+	3436.56i	0.107444	+	0.254536i
$568$		0			0
$569$	7324.54	−	12686.5i	0.539650	−	0.934701i	−0.459273	−	0.888295i	$-0.651890\pi$
$569$	7324.54	−	12686.5i	0.539650	−	0.934701i	0.998923	−	0.0464057i	$-0.0147767\pi$
$570$		0			0
$571$	11582.0	+	20060.6i	0.848846	+	1.47025i	0.882239	+	0.470803i	$0.156036\pi$
$571$	11582.0	+	20060.6i	0.848846	+	1.47025i	−0.0333922	+	0.999442i	$0.510631\pi$
$572$		0			0
$573$	5228.38	−	17340.6i	0.381185	−	1.26425i
$574$		0			0
$575$	1237.80			0.0897735
$576$		0			0
$577$	7865.97			0.567529			0.283765	−	0.958894i	$-0.408417\pi$
$577$	7865.97			0.567529			0.283765	+	0.958894i	$0.408417\pi$
$578$		0			0
$579$	−7882.15	−	8387.38i	−0.565753	−	0.602016i
$580$		0			0
$581$	1826.29	+	3163.23i	0.130408	+	0.225874i
$582$		0			0
$583$	13779.3	−	23866.5i	0.978869	−	1.69545i
$584$		0			0
$585$	−653.076	+	10505.2i	−0.0461562	+	0.742459i
$586$		0			0
$587$	−478.091	+	828.078i	−0.0336166	+	0.0582256i	−0.882344	−	0.470605i	$-0.844036\pi$
$587$	−478.091	+	828.078i	−0.0336166	+	0.0582256i	0.848728	+	0.528830i	$0.177369\pi$
$588$		0			0
$589$	−251.554	−	435.704i	−0.0175978	−	0.0304803i
$590$		0			0
$591$	−20107.8	+	4724.15i	−1.39953	+	0.328808i
$592$		0			0
$593$	−16966.0			−1.17489			−0.587444	−	0.809265i	$-0.699866\pi$
$593$	−16966.0			−1.17489			−0.587444	+	0.809265i	$0.699866\pi$
$594$		0			0
$595$	1255.16			0.0864813
$596$		0			0
$597$	7867.57	−	1848.42i	0.539361	−	0.126718i
$598$		0			0
$599$	−3095.70	−	5361.92i	−0.211164	−	0.365746i	0.740915	−	0.671598i	$-0.234392\pi$
$599$	−3095.70	−	5361.92i	−0.211164	−	0.365746i	−0.952079	+	0.305852i	$0.901059\pi$
$600$		0			0
$601$	1359.27	−	2354.33i	0.0922559	−	0.159792i	−0.816204	−	0.577764i	$-0.803926\pi$
$601$	1359.27	−	2354.33i	0.0922559	−	0.159792i	0.908460	+	0.417972i	$0.137259\pi$
$602$		0			0
$603$	6849.66	+	4543.55i	0.462587	+	0.306845i
$604$		0			0
$605$	−9348.35	+	16191.8i	−0.628206	+	1.08808i
$606$		0			0
$607$	8412.49	+	14570.9i	0.562524	+	0.974321i	0.997275	+	0.0737701i	$0.0235031\pi$
$607$	8412.49	+	14570.9i	0.562524	+	0.974321i	−0.434751	+	0.900551i	$0.643164\pi$
$608$		0			0
$609$	516.599	+	549.712i	0.0343738	+	0.0365771i
$610$		0			0
$611$	2325.62			0.153985
$612$		0			0
$613$	−20175.1			−1.32930			−0.664652	−	0.747153i	$-0.731420\pi$
$613$	−20175.1			−1.32930			−0.664652	+	0.747153i	$0.731420\pi$
$614$		0			0
$615$	3352.58	−	11119.3i	0.219820	−	0.729060i
$616$		0			0
$617$	−5655.31	−	9795.29i	−0.369002	−	0.639130i	0.620408	−	0.784280i	$-0.286967\pi$
$617$	−5655.31	−	9795.29i	−0.369002	−	0.639130i	−0.989410	+	0.145149i	$0.953634\pi$
$618$		0			0
$619$	−8529.94	+	14774.3i	−0.553873	+	0.959336i	0.444117	+	0.895969i	$0.353517\pi$
$619$	−8529.94	+	14774.3i	−0.553873	+	0.959336i	−0.997990	+	0.0633676i	$0.979816\pi$
$620$		0			0
$621$	9349.81	+	3465.27i	0.604179	+	0.223924i
$622$		0			0
$623$	1035.66	−	1793.82i	0.0666017	−	0.115357i
$624$		0			0
$625$	6572.36	+	11383.7i	0.420631	+	0.728554i
$626$		0			0
$627$	−3279.06	+	10875.4i	−0.208857	+	0.692699i
$628$		0			0
$629$	−4259.34			−0.270002
$630$		0			0
$631$	13186.3			0.831916			0.415958	−	0.909384i	$-0.363446\pi$
$631$	13186.3			0.831916			0.415958	+	0.909384i	$0.363446\pi$
$632$		0			0
$633$	6219.16	+	6617.79i	0.390505	+	0.415535i
$634$		0			0
$635$	−6255.02	−	10834.0i	−0.390902	−	0.677063i
$636$		0			0
$637$	5953.68	−	10312.1i	0.370319	−	0.641412i
$638$		0			0
$639$	−6536.79	+	3250.96i	−0.404681	+	0.201261i
$640$		0			0
$641$	−8180.99	+	14169.9i	−0.504102	+	0.873131i	0.495886	+	0.868387i	$0.334843\pi$
$641$	−8180.99	+	14169.9i	−0.504102	+	0.873131i	−0.999989	+	0.00474343i	$0.998490\pi$
$642$		0			0
$643$	−14022.5	−	24287.6i	−0.860019	−	1.48960i	−0.871910	−	0.489667i	$-0.837118\pi$
$643$	−14022.5	−	24287.6i	−0.860019	−	1.48960i	0.0118907	−	0.999929i	$-0.496215\pi$
$644$		0			0
$645$	−3212.77	+	754.811i	−0.196128	+	0.0460786i
$646$		0			0
$647$	−21247.7			−1.29109			−0.645543	−	0.763724i	$-0.723369\pi$
$647$	−21247.7			−1.29109			−0.645543	+	0.763724i	$0.723369\pi$
$648$		0			0
$649$	44202.1			2.67347
$650$		0			0
$651$	−333.457	+	78.3426i	−0.0200756	+	0.00471657i
$652$		0			0
$653$	−629.928	−	1091.07i	−0.0377504	−	0.0653856i	0.846533	−	0.532336i	$-0.178686\pi$
$653$	−629.928	−	1091.07i	−0.0377504	−	0.0653856i	−0.884283	+	0.466951i	$0.845353\pi$
$654$		0			0
$655$	−5330.60	+	9232.87i	−0.317991	+	0.550776i
$656$		0			0
$657$	−22373.3	+	11127.0i	−1.32857	+	0.660740i
$658$		0			0
$659$	−6023.35	+	10432.7i	−0.356049	+	0.616695i	−0.987297	−	0.158886i	$-0.949210\pi$
$659$	−6023.35	+	10432.7i	−0.356049	+	0.616695i	0.631248	+	0.775581i	$0.282543\pi$
$660$		0			0
$661$	−6554.04	−	11351.9i	−0.385662	−	0.667986i	0.606199	−	0.795313i	$-0.292693\pi$
$661$	−6554.04	−	11351.9i	−0.385662	−	0.667986i	−0.991861	+	0.127327i	$0.959360\pi$
$662$		0			0
$663$	−3162.89	−	3365.62i	−0.185274	−	0.197149i
$664$		0			0
$665$	−2072.60			−0.120860
$666$		0			0
$667$	2016.51			0.117061
$668$		0			0
$669$	−3812.91	+	12646.0i	−0.220352	+	0.730826i
$670$		0			0
$671$	14584.8	+	25261.7i	0.839108	+	1.45338i
$672$		0			0
$673$	−1371.82	+	2376.07i	−0.0785734	+	0.136093i	−0.902635	−	0.430408i	$-0.858370\pi$
$673$	−1371.82	+	2376.07i	−0.0785734	+	0.136093i	0.824061	+	0.566501i	$0.191703\pi$
$674$		0			0
$675$	−410.169	−	2408.69i	−0.0233888	−	0.137349i
$676$		0			0
$677$	−12502.0	+	21654.1i	−0.709735	+	1.22930i	0.255220	+	0.966883i	$0.417852\pi$
$677$	−12502.0	+	21654.1i	−0.709735	+	1.22930i	−0.964955	+	0.262415i	$0.915481\pi$
$678$		0			0
$679$	−191.952	−	332.470i	−0.0108489	−	0.0187909i
$680$		0			0
$681$	−4489.89	+	14891.3i	−0.252648	+	0.837937i
$682$		0			0
$683$	4846.23			0.271502			0.135751	−	0.990743i	$-0.456655\pi$
$683$	4846.23			0.271502			0.135751	+	0.990743i	$0.456655\pi$
$684$		0			0
$685$	−13078.5			−0.729494
$686$		0			0
$687$	15320.1	+	16302.1i	0.850798	+	0.905331i
$688$		0			0
$689$	−9251.54	−	16024.1i	−0.511546	−	0.886024i
$690$		0			0
$691$	1742.29	−	3017.73i	0.0959187	−	0.166136i	−0.814073	−	0.580763i	$-0.802754\pi$
$691$	1742.29	−	3017.73i	0.0959187	−	0.166136i	0.909992	+	0.414627i	$0.136088\pi$
$692$		0			0
$693$	6444.72	+	4274.94i	0.353268	+	0.234331i
$694$		0			0
$695$	2395.12	−	4148.48i	0.130723	−	0.226418i
$696$		0			0
$697$	2548.04	+	4413.33i	0.138470	+	0.239837i
$698$		0			0
$699$	−28232.8	+	6633.04i	−1.52770	+	0.358919i
$700$		0			0
$701$	15701.4			0.845981			0.422991	−	0.906134i	$-0.360980\pi$
$701$	15701.4			0.845981			0.422991	+	0.906134i	$0.360980\pi$
$702$		0			0
$703$	7033.32			0.377335
$704$		0			0
$705$	3246.56	−	762.749i	0.173436	−	0.0407472i
$706$		0			0
$707$	2783.25	+	4820.73i	0.148055	+	0.256439i
$708$		0			0
$709$	−7821.72	+	13547.6i	−0.414317	+	0.717618i	−0.995356	−	0.0962572i	$-0.969313\pi$
$709$	−7821.72	+	13547.6i	−0.414317	+	0.717618i	0.581039	+	0.813875i	$0.302646\pi$
$710$		0			0
$711$	−2159.48	+	34736.9i	−0.113905	+	1.83226i
$712$		0			0
$713$	−457.824	+	792.975i	−0.0240472	+	0.0416510i
$714$		0			0
$715$	10911.1	+	18898.6i	0.570703	+	0.988486i
$716$		0			0
$717$	5016.05	+	5337.57i	0.261266	+	0.278013i
$718$		0			0
$719$	6964.13			0.361222			0.180611	−	0.983555i	$-0.442193\pi$
$719$	6964.13			0.361222			0.180611	+	0.983555i	$0.442193\pi$
$720$		0			0
$721$	5586.66			0.288569
$722$		0			0
$723$	−939.858	+	3117.16i	−0.0483454	+	0.160343i
$724$		0			0
$725$	−247.063	−	427.925i	−0.0126561	−	0.0219210i
$726$		0			0
$727$	−7103.61	+	12303.8i	−0.362391	+	0.627680i	−0.988354	−	0.152173i	$-0.951373\pi$
$727$	−7103.61	+	12303.8i	−0.362391	+	0.627680i	0.625963	+	0.779853i	$0.284706\pi$
$728$		0			0
$729$	3645.00	−	19342.6i	0.185185	−	0.982704i
$730$		0			0
$731$	724.072	−	1254.13i	0.0366358	−	0.0634551i
$732$		0			0
$733$	−13265.3	−	22976.1i	−0.668437	−	1.15777i	−0.978341	−	0.206998i	$-0.933630\pi$
$733$	−13265.3	−	22976.1i	−0.668437	−	1.15777i	0.309905	−	0.950768i	$-0.399703\pi$
$734$		0			0
$735$	4929.19	−	16348.3i	0.247368	−	0.820428i
$736$		0			0
$737$	17041.4			0.851735
$738$		0			0
$739$	5683.47			0.282909			0.141455	−	0.989945i	$-0.454822\pi$
$739$	5683.47			0.282909			0.141455	+	0.989945i	$0.454822\pi$
$740$		0			0
$741$	5222.78	+	5557.55i	0.258925	+	0.275522i
$742$		0			0
$743$	−7784.28	−	13482.8i	−0.384358	−	0.665727i	0.607322	−	0.794456i	$-0.292244\pi$
$743$	−7784.28	−	13482.8i	−0.384358	−	0.665727i	−0.991680	+	0.128729i	$0.958910\pi$
$744$		0			0
$745$	−7568.25	+	13108.6i	−0.372187	+	0.644647i
$746$		0			0
$747$	1195.86	−	19236.4i	0.0585734	−	0.942199i
$748$		0			0
$749$	−2633.01	+	4560.51i	−0.128449	+	0.222480i
$750$		0			0
$751$	−4130.82	−	7154.79i	−0.200713	−	0.347646i	0.748045	−	0.663648i	$-0.230993\pi$
$751$	−4130.82	−	7154.79i	−0.200713	−	0.347646i	−0.948758	+	0.316002i	$0.897659\pi$
$752$		0			0
$753$	−8627.27	+	2026.90i	−0.417523	+	0.0980933i
$754$		0			0
$755$	−15987.0			−0.770630
$756$		0			0
$757$	−13381.5			−0.642481			−0.321240	−	0.946998i	$-0.604100\pi$
$757$	−13381.5			−0.642481			−0.321240	+	0.946998i	$0.604100\pi$
$758$		0			0
$759$	20125.2	−	4728.24i	0.962451	−	0.226119i
$760$		0			0
$761$	−2724.92	−	4719.70i	−0.129801	−	0.224821i	0.793799	−	0.608181i	$-0.208100\pi$
$761$	−2724.92	−	4719.70i	−0.129801	−	0.224821i	−0.923599	+	0.383359i	$0.874767\pi$
$762$		0			0
$763$	−4545.08	+	7872.31i	−0.215652	+	0.373521i
$764$		0			0
$765$	−5519.23	−	3661.04i	−0.260847	−	0.173026i
$766$		0			0
$767$	14838.8	−	25701.6i	0.698564	−	1.20995i
$768$		0			0
$769$	9681.98	+	16769.7i	0.454020	+	0.786385i	0.998631	−	0.0523033i	$-0.0166563\pi$
$769$	9681.98	+	16769.7i	0.454020	+	0.786385i	−0.544612	+	0.838688i	$0.683323\pi$
$770$		0			0
$771$	12801.0	+	13621.5i	0.597946	+	0.636273i
$772$		0			0
$773$	−1865.54			−0.0868033			−0.0434017	−	0.999058i	$-0.513820\pi$
$773$	−1865.54			−0.0868033			−0.0434017	+	0.999058i	$0.513820\pi$
$774$		0			0
$775$	224.370			0.0103995
$776$		0			0
$777$	1382.34	−	4584.70i	0.0638239	−	0.211680i
$778$		0			0
$779$	−4207.49	−	7287.58i	−0.193516	−	0.335179i
$780$		0			0
$781$	−7568.02	+	13108.2i	−0.346741	+	0.600574i
$782$		0			0
$783$	−668.212	−	3924.03i	−0.0304980	−	0.179098i
$784$		0			0
$785$	16676.4	−	28884.4i	0.758225	−	1.31328i
$786$		0			0
$787$	−9603.65	−	16634.0i	−0.434985	−	0.753416i	0.562310	−	0.826927i	$-0.309913\pi$
$787$	−9603.65	−	16634.0i	−0.434985	−	0.753416i	−0.997294	+	0.0735110i	$0.976580\pi$
$788$		0			0
$789$	6206.25	−	20583.8i	0.280036	−	0.928775i
$790$		0			0
$791$	−8268.50			−0.371674
$792$		0			0
$793$	19584.7			0.877017
$794$		0			0
$795$	−18170.6	−	19335.3i	−0.810624	−	0.862582i
$796$		0			0
$797$	−93.0372	−	161.145i	−0.00413494	−	0.00716193i	0.863951	−	0.503577i	$-0.167983\pi$
$797$	−93.0372	−	161.145i	−0.00413494	−	0.00716193i	−0.868085	+	0.496415i	$0.834650\pi$
$798$		0			0
$799$	−731.686	+	1267.32i	−0.0323970	+	0.0561132i
$800$		0			0
$801$	−9786.25	+	4867.03i	−0.431686	+	0.214692i
$802$		0			0
$803$	−25902.9	+	44865.2i	−1.13835	+	1.97168i
$804$		0			0
$805$	1886.05	+	3266.73i	0.0825771	+	0.143028i
$806$		0			0
$807$	30810.8	−	7238.72i	1.34398	−	0.315756i
$808$		0			0
$809$	5903.09			0.256541			0.128270	−	0.991739i	$-0.459057\pi$
$809$	5903.09			0.256541			0.128270	+	0.991739i	$0.459057\pi$
$810$		0			0
$811$	−23111.0			−1.00066			−0.500331	−	0.865834i	$-0.666788\pi$
$811$	−23111.0			−1.00066			−0.500331	+	0.865834i	$0.666788\pi$
$812$		0			0
$813$	16169.8	−	3798.96i	0.697542	−	0.163881i
$814$		0			0
$815$	4914.32	+	8511.85i	0.211216	+	0.365837i
$816$		0			0
$817$	−1195.64	+	2070.90i	−0.0511995	+	0.0886802i
$818$		0			0
$819$	4649.21	−	2312.21i	0.198360	−	0.0986508i
$820$		0			0
$821$	4822.14	−	8352.20i	0.204987	−	0.355047i	−0.745142	−	0.666906i	$-0.767618\pi$
$821$	4822.14	−	8352.20i	0.204987	−	0.355047i	0.950128	+	0.311859i	$0.100952\pi$
$822$		0			0
$823$	−16786.7	−	29075.5i	−0.710994	−	1.23148i	−0.964484	−	0.264140i	$-0.914912\pi$
$823$	−16786.7	−	29075.5i	−0.710994	−	1.23148i	0.253490	−	0.967338i	$-0.418422\pi$
$824$		0			0
$825$	−3469.12	−	3691.48i	−0.146399	−	0.155783i
$826$		0			0
$827$	25916.1			1.08971			0.544855	−	0.838530i	$-0.316585\pi$
$827$	25916.1			1.08971			0.544855	+	0.838530i	$0.316585\pi$
$828$		0			0
$829$	−28650.6			−1.20033			−0.600166	−	0.799876i	$-0.704899\pi$
$829$	−28650.6			−1.20033			−0.600166	+	0.799876i	$0.704899\pi$
$830$		0			0
$831$	4679.04	−	15518.6i	0.195324	−	0.647816i
$832$		0			0
$833$	3746.29	+	6488.76i	0.155824	+	0.269895i
$834$		0			0
$835$	3557.48	−	6161.74i	0.147439	−	0.255372i
$836$		0			0
$837$	1694.80	+	628.135i	0.0699891	+	0.0259397i
$838$		0			0
$839$	356.480	−	617.441i	0.0146687	−	0.0254070i	−0.858598	−	0.512650i	$-0.828664\pi$
$839$	356.480	−	617.441i	0.0146687	−	0.0254070i	0.873267	+	0.487243i	$0.161997\pi$
$840$		0			0
$841$	11792.0	+	20424.4i	0.483497	+	0.837441i
$842$		0			0
$843$	−7422.50	+	24617.6i	−0.303256	+	1.00578i
$844$		0			0
$845$	−8136.29			−0.331239
$846$		0			0
$847$	9223.44			0.374169
$848$		0			0
$849$	−16172.8	−	17209.4i	−0.653767	−	0.695672i
$850$		0			0
$851$	−6400.27	−	11085.6i	−0.257812	−	0.446544i
$852$		0			0
$853$	15183.6	−	26298.8i	0.609469	−	1.05563i	−0.381859	−	0.924221i	$-0.624716\pi$
$853$	15183.6	−	26298.8i	0.609469	−	1.05563i	0.991328	−	0.131411i	$-0.0419508\pi$
$854$		0			0
$855$	9113.72	+	6045.36i	0.364541	+	0.241809i
$856$		0			0
$857$	−4540.35	+	7864.12i	−0.180975	+	0.313458i	−0.942213	−	0.335015i	$-0.891259\pi$
$857$	−4540.35	+	7864.12i	−0.180975	+	0.313458i	0.761238	+	0.648473i	$0.224592\pi$
$858$		0			0
$859$	13080.1	+	22655.4i	0.519543	+	0.899874i	0.999742	+	0.0227150i	$0.00723102\pi$
$859$	13080.1	+	22655.4i	0.519543	+	0.899874i	−0.480199	+	0.877159i	$0.659436\pi$
$860$		0			0
$861$	−5577.39	+	1310.36i	−0.220763	+	0.0518663i
$862$		0			0
$863$	40102.0			1.58180			0.790898	−	0.611949i	$-0.209614\pi$
$863$	40102.0			1.58180			0.790898	+	0.611949i	$0.209614\pi$
$864$		0			0
$865$	−22952.1			−0.902189
$866$		0			0
$867$	−22022.9	+	5174.07i	−0.862671	+	0.202677i
$868$		0			0
$869$	36079.0	+	62490.6i	1.40839	+	2.43941i
$870$		0			0
$871$	5720.87	−	9908.84i	0.222554	−	0.385474i
$872$		0			0
$873$	−125.691	+	2021.83i	−0.00487284	+	0.0783834i
$874$		0			0
$875$	3779.24	−	6545.84i	0.146013	−	0.252903i
$876$		0			0
$877$	−12626.1	−	21869.0i	−0.486149	−	0.842036i	0.513724	−	0.857956i	$-0.328266\pi$
$877$	−12626.1	−	21869.0i	−0.486149	−	0.842036i	−0.999873	+	0.0159201i	$0.994932\pi$
$878$		0			0
$879$	−24411.1	−	25975.8i	−0.936709	−	0.996750i
$880$		0			0
$881$	−2049.26			−0.0783670			−0.0391835	−	0.999232i	$-0.512476\pi$
$881$	−2049.26			−0.0783670			−0.0391835	+	0.999232i	$0.512476\pi$
$882$		0			0
$883$	−39413.4			−1.50211			−0.751057	−	0.660237i	$-0.770456\pi$
$883$	−39413.4			−1.50211			−0.751057	+	0.660237i	$0.770456\pi$
$884$		0			0
$885$	12285.4	−	40746.1i	0.466632	−	1.54764i
$886$		0			0
$887$	18484.2	+	32015.6i	0.699707	+	1.21193i	0.968568	+	0.248749i	$0.0800194\pi$
$887$	18484.2	+	32015.6i	0.699707	+	1.21193i	−0.268861	+	0.963179i	$0.586647\pi$
$888$		0			0
$889$	−3085.72	+	5344.63i	−0.116414	+	0.201634i
$890$		0			0
$891$	−15869.8	−	37595.9i	−0.596700	−	1.41359i
$892$		0			0
$893$	1208.21	−	2092.68i	0.0452757	−	0.0784198i
$894$		0			0
$895$	15678.8	+	27156.5i	0.585570	+	1.01424i
$896$		0			0
$897$	4006.85	−	13289.2i	0.149147	−	0.494665i
$898$		0			0
$899$	365.525			0.0135605
$900$		0			0
$901$	11642.9			0.430499
$902$		0			0
$903$	1114.94	+	1186.40i	0.0410883	+	0.0437220i
$904$		0			0
$905$	−2030.09	−	3516.21i	−0.0745662	−	0.129152i
$906$		0			0
$907$	1355.31	−	2347.47i	0.0496167	−	0.0859386i	−0.840150	−	0.542353i	$-0.817533\pi$
$907$	1355.31	−	2347.47i	0.0496167	−	0.0859386i	0.889767	+	0.456415i	$0.150867\pi$
$908$		0			0
$909$	1822.48	−	29316.1i	0.0664994	−	1.06970i
$910$		0			0
$911$	11498.3	−	19915.6i	0.418172	−	0.724296i	−0.577583	−	0.816332i	$-0.696004\pi$
$911$	11498.3	−	19915.6i	0.418172	−	0.724296i	0.995756	+	0.0920360i	$0.0293375\pi$
$912$		0			0
$913$	−19979.6	−	34605.7i	−0.724237	−	1.25441i
$914$		0			0
$915$	27340.2	−	6423.33i	0.987802	−	0.232075i
$916$		0			0
$917$	5259.38			0.189400
$918$		0			0
$919$	39103.8			1.40361			0.701804	−	0.712370i	$-0.252378\pi$
$919$	39103.8			1.40361			0.701804	+	0.712370i	$0.252378\pi$
$920$		0			0
$921$	−32031.2	+	7525.44i	−1.14600	+	0.269242i
$922$		0			0
$923$	5081.23	+	8800.94i	0.181203	+	0.313853i
$924$		0			0
$925$	−1568.32	+	2716.41i	−0.0557470	+	0.0965567i
$926$		0			0
$927$	−24565.9	−	16295.2i	−0.870388	−	0.577350i
$928$		0			0
$929$	17977.3	−	31137.6i	0.634894	−	1.09967i	−0.351644	−	0.936134i	$-0.614377\pi$
$929$	17977.3	−	31137.6i	0.634894	−	1.09967i	0.986538	−	0.163534i	$-0.0522894\pi$
$930$		0			0
$931$	−6186.12	−	10714.7i	−0.217768	−	0.377185i
$932$		0			0
$933$	25185.3	+	26799.6i	0.883742	+	0.940387i
$934$		0			0
$935$	−13731.4			−0.480283
$936$		0			0
$937$	−7263.94			−0.253258			−0.126629	−	0.991950i	$-0.540416\pi$
$937$	−7263.94			−0.253258			−0.126629	+	0.991950i	$0.540416\pi$
$938$		0			0
$939$	−2071.95	+	6871.87i	−0.0720079	+	0.238823i
$940$		0			0
$941$	−3739.45	−	6476.92i	−0.129546	−	0.224380i	0.793955	−	0.607977i	$-0.208019\pi$
$941$	−3739.45	−	6476.92i	−0.129546	−	0.224380i	−0.923501	+	0.383597i	$0.874685\pi$
$942$		0			0
$943$	−7657.57	+	13263.3i	−0.264438	+	0.458020i
$944$		0			0
$945$	5731.92	−	4752.66i	0.197312	−	0.163602i
$946$		0			0
$947$	6745.68	−	11683.9i	0.231473	−	0.400923i	−0.726769	−	0.686882i	$-0.758979\pi$
$947$	6745.68	−	11683.9i	0.231473	−	0.400923i	0.958242	+	0.285959i	$0.0923121\pi$
$948$		0			0
$949$	17391.4	+	30122.8i	0.594889	+	1.03038i
$950$		0			0
$951$	12262.4	−	40669.8i	0.418124	−	1.38676i
$952$		0			0
$953$	−13981.6			−0.475246			−0.237623	−	0.971357i	$-0.576368\pi$
$953$	−13981.6			−0.475246			−0.237623	+	0.971357i	$0.576368\pi$
$954$		0			0
$955$	−36153.5			−1.22503
$956$		0			0
$957$	−5651.59	−	6013.85i	−0.190899	−	0.203135i
$958$		0			0
$959$	3225.93	+	5587.48i	0.108624	+	0.188143i
$960$		0			0
$961$	14812.5	−	25656.0i	0.497214	−	0.861200i
$962$		0			0
$963$	24880.1	−	12373.7i	0.832554	−	0.414057i
$964$		0			0
$965$	−11487.7	+	19897.2i	−0.383213	+	0.663745i
$966$		0			0
$967$	−4540.73	−	7864.78i	−0.151003	−	0.261545i	0.780593	−	0.625039i	$-0.214917\pi$
$967$	−4540.73	−	7864.78i	−0.151003	−	0.261545i	−0.931597	+	0.363494i	$0.881584\pi$
$968$		0			0
$969$	−4671.70	+	1097.57i	−0.154878	+	0.0363872i
$970$		0			0
$971$	9709.13			0.320887			0.160443	−	0.987045i	$-0.448708\pi$
$971$	9709.13			0.320887			0.160443	+	0.987045i	$0.448708\pi$
$972$		0			0
$973$	−2363.12			−0.0778604
$974$		0			0
$975$	−3311.03	+	777.897i	−0.108757	+	0.0255514i
$976$		0			0
$977$	−5427.45	−	9400.63i	−0.177727	−	0.307833i	0.763374	−	0.645956i	$-0.223541\pi$
$977$	−5427.45	−	9400.63i	−0.177727	−	0.307833i	−0.941102	+	0.338123i	$0.890208\pi$
$978$		0			0
$979$	−11330.1	+	19624.3i	−0.369880	+	0.640650i
$980$		0			0
$981$	42947.7	−	21359.3i	1.39777	−	0.695159i
$982$		0			0
$983$	−3755.05	+	6503.94i	−0.121839	+	0.211031i	−0.920493	−	0.390759i	$-0.872212\pi$
$983$	−3755.05	+	6503.94i	−0.121839	+	0.211031i	0.798654	+	0.601790i	$0.205546\pi$
$984$		0			0
$985$	20615.5	+	35707.1i	0.666867	+	1.15505i
$986$		0			0
$987$	−1126.66	−	1198.88i	−0.0363343	−	0.0386633i
$988$		0			0
$989$	4352.08			0.139927
$990$		0			0
$991$	−46125.6			−1.47854			−0.739268	−	0.673412i	$-0.764828\pi$
$991$	−46125.6			−1.47854			−0.739268	+	0.673412i	$0.764828\pi$
$992$		0			0
$993$	−14491.9	+	48064.3i	−0.463129	+	1.53603i
$994$		0			0
$995$	−8066.22	−	13971.1i	−0.257001	−	0.445139i
$996$		0			0
$997$	−22675.0	+	39274.3i	−0.720287	+	1.24757i	0.240598	+	0.970625i	$0.422656\pi$
$997$	−22675.0	+	39274.3i	−0.720287	+	1.24757i	−0.960885	+	0.276948i	$0.910677\pi$
$998$		0			0
$999$	−19451.1	+	16128.0i	−0.616023	+	0.510779i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.4.i.c.97.2		4
3.2	odd	2		432.4.i.c.289.2		4
4.3	odd	2		9.4.c.a.7.2	yes	4
9.2	odd	6		1296.4.a.i.1.1		2
9.4	even	3	inner	144.4.i.c.49.2		4
9.5	odd	6		432.4.i.c.145.2		4
9.7	even	3		1296.4.a.u.1.2		2
12.11	even	2		27.4.c.a.19.1		4
20.3	even	4		225.4.k.b.124.2		8
20.7	even	4		225.4.k.b.124.3		8
20.19	odd	2		225.4.e.b.151.1		4
36.7	odd	6		81.4.a.d.1.1		2
36.11	even	6		81.4.a.a.1.2		2
36.23	even	6		27.4.c.a.10.1		4
36.31	odd	6		9.4.c.a.4.2	✓	4
180.67	even	12		225.4.k.b.49.2		8
180.79	odd	6		2025.4.a.g.1.2		2
180.103	even	12		225.4.k.b.49.3		8
180.119	even	6		2025.4.a.n.1.1		2
180.139	odd	6		225.4.e.b.76.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.4.c.a.4.2	✓	4	36.31	odd	6
9.4.c.a.7.2	yes	4	4.3	odd	2
27.4.c.a.10.1		4	36.23	even	6
27.4.c.a.19.1		4	12.11	even	2
81.4.a.a.1.2		2	36.11	even	6
81.4.a.d.1.1		2	36.7	odd	6
144.4.i.c.49.2		4	9.4	even	3	inner
144.4.i.c.97.2		4	1.1	even	1	trivial
225.4.e.b.76.1		4	180.139	odd	6
225.4.e.b.151.1		4	20.19	odd	2
225.4.k.b.49.2		8	180.67	even	12
225.4.k.b.49.3		8	180.103	even	12
225.4.k.b.124.2		8	20.3	even	4
225.4.k.b.124.3		8	20.7	even	4
432.4.i.c.145.2		4	9.5	odd	6
432.4.i.c.289.2		4	3.2	odd	2
1296.4.a.i.1.1		2	9.2	odd	6
1296.4.a.u.1.2		2	9.7	even	3
2025.4.a.g.1.2		2	180.79	odd	6
2025.4.a.n.1.1		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(5.05842 - 1.18843i) q^{3} +(-5.18614 - 8.98266i) q^{5} +(-2.55842 + 4.43132i) q^{7} +(24.1753 - 12.0232i) q^{9} +O(q^{10})\)	\(q+(5.05842 - 1.18843i) q^{3} +(-5.18614 - 8.98266i) q^{5} +(-2.55842 + 4.43132i) q^{7} +(24.1753 - 12.0232i) q^{9} +(27.9891 - 48.4786i) q^{11} +(-18.7921 - 32.5489i) q^{13} +(-36.9090 - 39.2747i) q^{15} +23.6495 q^{17} -39.0516 q^{19} +(-7.67527 + 25.4560i) q^{21} +(35.5367 + 61.5513i) q^{23} +(8.70789 - 15.0825i) q^{25} +(108.000 - 89.5489i) q^{27} +(14.1861 - 24.5711i) q^{29} +(6.44158 + 11.1571i) q^{31} +(83.9674 - 278.488i) q^{33} +53.0733 q^{35} -180.103 q^{37} +(-133.741 - 142.313i) q^{39} +(107.742 + 186.614i) q^{41} +(30.6168 - 53.0299i) q^{43} +(-233.376 - 154.804i) q^{45} +(-30.9388 + 53.5876i) q^{47} +(158.409 + 274.372i) q^{49} +(119.629 - 28.1057i) q^{51} +492.310 q^{53} -580.622 q^{55} +(-197.539 + 46.4101i) q^{57} +(394.815 + 683.840i) q^{59} +(-260.545 + 451.277i) q^{61} +(-8.57207 + 137.889i) q^{63} +(-194.917 + 337.606i) q^{65} +(152.215 + 263.644i) q^{67} +(252.909 + 269.120i) q^{69} -270.391 q^{71} -925.464 q^{73} +(26.1237 - 86.6424i) q^{75} +(143.216 + 248.057i) q^{77} +(-644.517 + 1116.34i) q^{79} +(439.887 - 581.326i) q^{81} +(356.917 - 618.198i) q^{83} +(-122.649 - 212.435i) q^{85} +(42.5584 - 141.150i) q^{87} -404.804 q^{89} +192.313 q^{91} +(45.8437 + 48.7822i) q^{93} +(202.527 + 350.787i) q^{95} +(-37.5137 + 64.9756i) q^{97} +(93.7785 - 1508.50i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{3} - 15 q^{5} + 7 q^{7} + 45 q^{9}+O(q^{10}) \) 4 * q + 3 * q^3 - 15 * q^5 + 7 * q^7 + 45 * q^9	\( 4 q + 3 q^{3} - 15 q^{5} + 7 q^{7} + 45 q^{9} + 66 q^{11} + 11 q^{13} - 27 q^{15} + 198 q^{17} + 154 q^{19} + 21 q^{21} + 33 q^{23} + 121 q^{25} + 432 q^{27} + 51 q^{29} + 43 q^{31} + 198 q^{33} - 6 q^{35} - 100 q^{37} - 759 q^{39} - 132 q^{41} + 88 q^{43} - 675 q^{45} + 399 q^{47} + 513 q^{49} - 297 q^{51} + 108 q^{53} - 1254 q^{55} - 1221 q^{57} + 798 q^{59} - 439 q^{61} - 603 q^{63} - 165 q^{65} + 988 q^{67} + 891 q^{69} - 2736 q^{71} - 910 q^{73} + 363 q^{75} + 165 q^{77} - 803 q^{79} - 567 q^{81} + 813 q^{83} - 594 q^{85} + 153 q^{87} - 792 q^{89} + 1562 q^{91} - 213 q^{93} - 132 q^{95} - 736 q^{97} - 297 q^{99}+O(q^{100}) \) 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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