LMFDB - Embedded newform 27.4.c.a.10.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,4,Mod(10,27)] 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("27.10"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	27.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			10.1
Root			$-1.18614 - 1.26217i$ of defining polynomial
Character	$\chi$	$=$	27.10
Dual form			27.4.c.a.19.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.686141 - 1.18843i) q^{2} +(3.05842 - 5.29734i) q^{4} +(5.18614 - 8.98266i) q^{5} +(2.55842 + 4.43132i) q^{7} -19.3723 q^{8} -14.2337 q^{10} +(27.9891 + 48.4786i) q^{11} +(-18.7921 + 32.5489i) q^{13} +(3.51087 - 6.08101i) q^{14} +(-11.1753 - 19.3561i) q^{16} -23.6495 q^{17} +39.0516 q^{19} +(-31.7228 - 54.9455i) q^{20} +(38.4090 - 66.5263i) q^{22} +(35.5367 - 61.5513i) q^{23} +(8.70789 + 15.0825i) q^{25} +51.5761 q^{26} +31.2989 q^{28} +(-14.1861 - 24.5711i) q^{29} +(-6.44158 + 11.1571i) q^{31} +(-92.8247 + 160.777i) q^{32} +(16.2269 + 28.1057i) q^{34} +53.0733 q^{35} -180.103 q^{37} +(-26.7949 - 46.4101i) q^{38} +(-100.467 + 174.015i) q^{40} +(-107.742 + 186.614i) q^{41} +(-30.6168 - 53.0299i) q^{43} +342.410 q^{44} -97.5326 q^{46} +(-30.9388 - 53.5876i) q^{47} +(158.409 - 274.372i) q^{49} +(11.9497 - 20.6974i) q^{50} +(114.948 + 199.096i) q^{52} -492.310 q^{53} +580.622 q^{55} +(-49.5625 - 85.8447i) q^{56} +(-19.4674 + 33.7185i) q^{58} +(394.815 - 683.840i) q^{59} +(-260.545 - 451.277i) q^{61} +17.6793 q^{62} +75.9590 q^{64} +(194.917 + 337.606i) q^{65} +(-152.215 + 263.644i) q^{67} +(-72.3301 + 125.279i) q^{68} +(-36.4158 - 63.0740i) q^{70} -270.391 q^{71} -925.464 q^{73} +(123.576 + 214.040i) q^{74} +(119.436 - 206.870i) q^{76} +(-143.216 + 248.057i) q^{77} +(644.517 + 1116.34i) q^{79} -231.826 q^{80} +295.704 q^{82} +(356.917 + 618.198i) q^{83} +(-122.649 + 212.435i) q^{85} +(-42.0149 + 72.7720i) q^{86} +(-542.213 - 939.141i) q^{88} +404.804 q^{89} -192.313 q^{91} +(-217.372 - 376.500i) q^{92} +(-42.4567 + 73.5372i) q^{94} +(202.527 - 350.787i) q^{95} +(-37.5137 - 64.9756i) q^{97} -434.763 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 5 q^{4} + 15 q^{5} - 7 q^{7} - 66 q^{8} + 12 q^{10} + 66 q^{11} + 11 q^{13} + 60 q^{14} + 7 q^{16} - 198 q^{17} - 154 q^{19} - 12 q^{20} + 33 q^{22} + 33 q^{23} + 121 q^{25} + 528 q^{26}+ \cdots + 846 q^{98}+O(q^{100}) $ 4 * q + 3 * q^2 - 5 * q^4 + 15 * q^5 - 7 * q^7 - 66 * q^8 + 12 * q^10 + 66 * q^11 + 11 * q^13 + 60 * q^14 + 7 * q^16 - 198 * q^17 - 154 * q^19 - 12 * q^20 + 33 * q^22 + 33 * q^23 + 121 * q^25 + 528 * q^26 + 332 * q^28 - 51 * q^29 - 43 * q^31 - 423 * q^32 - 297 * q^34 - 6 * q^35 - 100 * q^37 - 561 * q^38 - 264 * q^40 + 132 * q^41 - 88 * q^43 + 462 * q^44 - 528 * q^46 + 399 * q^47 + 513 * q^49 - 429 * q^50 + 770 * q^52 - 108 * q^53 + 1254 * q^55 + 66 * q^56 + 60 * q^58 + 798 * q^59 - 439 * q^61 - 228 * q^62 - 1454 * q^64 + 165 * q^65 - 988 * q^67 + 693 * q^68 - 318 * q^70 - 2736 * q^71 - 910 * q^73 + 816 * q^74 + 1529 * q^76 - 165 * q^77 + 803 * q^79 - 192 * q^80 + 3630 * q^82 + 813 * q^83 - 594 * q^85 + 33 * q^86 - 1221 * q^88 + 792 * q^89 - 1562 * q^91 - 858 * q^92 - 2100 * q^94 - 132 * q^95 - 736 * q^97 + 846 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	−0.686141	−	1.18843i	−0.242587	−	0.420174i	0.718863	−	0.695152i	$-0.244663\pi$
$2$	−0.686141	−	1.18843i	−0.242587	−	0.420174i	−0.961451	+	0.274978i	$0.911329\pi$
$3$		0			0
$3$		0			0
$4$	3.05842	−	5.29734i	0.382303	−	0.662168i
$5$	5.18614	−	8.98266i	0.463863	−	0.803433i	−0.535287	−	0.844670i	$-0.679796\pi$
$5$	5.18614	−	8.98266i	0.463863	−	0.803433i	0.999149	+	0.0412369i	$0.0131298\pi$
$6$		0			0
$7$	2.55842	+	4.43132i	0.138142	+	0.239269i	0.926793	−	0.375572i	$-0.122554\pi$
$7$	2.55842	+	4.43132i	0.138142	+	0.239269i	−0.788651	+	0.614841i	$0.789220\pi$
$8$	−19.3723			−0.856142
$9$		0			0
$10$	−14.2337			−0.450109
$11$	27.9891	+	48.4786i	0.767185	+	1.32880i	0.939083	+	0.343689i	$0.111677\pi$
$11$	27.9891	+	48.4786i	0.767185	+	1.32880i	−0.171898	+	0.985115i	$0.554990\pi$
$12$		0			0
$13$	−18.7921	+	32.5489i	−0.400923	+	0.694418i	−0.993838	−	0.110847i	$-0.964644\pi$
$13$	−18.7921	+	32.5489i	−0.400923	+	0.694418i	0.592915	+	0.805265i	$0.297977\pi$
$14$	3.51087	−	6.08101i	0.0670229	−	0.116087i
$15$		0			0
$16$	−11.1753	−	19.3561i	−0.174614	−	0.302440i
$17$	−23.6495			−0.337402			−0.168701	−	0.985667i	$-0.553957\pi$
$17$	−23.6495			−0.337402			−0.168701	+	0.985667i	$0.553957\pi$
$18$		0			0
$19$	39.0516			0.471529			0.235764	−	0.971810i	$-0.424241\pi$
$19$	39.0516			0.471529			0.235764	+	0.971810i	$0.424241\pi$
$20$	−31.7228	−	54.9455i	−0.354672	−	0.614310i
$21$		0			0
$22$	38.4090	−	66.5263i	0.372219	−	0.644702i
$23$	35.5367	−	61.5513i	0.322170	−	0.558015i	−0.658766	−	0.752348i	$-0.728921\pi$
$23$	35.5367	−	61.5513i	0.322170	−	0.558015i	0.980936	+	0.194334i	$0.0622544\pi$
$24$		0			0
$25$	8.70789	+	15.0825i	0.0696631	+	0.120660i
$26$	51.5761			0.389035
$27$		0			0
$28$	31.2989			0.211248
$29$	−14.1861	−	24.5711i	−0.0908379	−	0.157336i	0.817026	−	0.576601i	$-0.195621\pi$
$29$	−14.1861	−	24.5711i	−0.0908379	−	0.157336i	−0.907864	+	0.419265i	$0.862288\pi$
$30$		0			0
$31$	−6.44158	+	11.1571i	−0.0373207	+	0.0646413i	−0.884082	−	0.467331i	$-0.845216\pi$
$31$	−6.44158	+	11.1571i	−0.0373207	+	0.0646413i	0.846762	+	0.531972i	$0.178549\pi$
$32$	−92.8247	+	160.777i	−0.512789	+	0.888177i
$33$		0			0
$34$	16.2269	+	28.1057i	0.0818495	+	0.141768i
$35$	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	$0.631031\pi$
$38$	−26.7949	−	46.4101i	−0.114387	−	0.198124i
$39$		0			0
$40$	−100.467	+	174.015i	−0.397132	+	0.687853i
$41$	−107.742	+	186.614i	−0.410401	+	0.710835i	−0.994934	−	0.100535i	$-0.967945\pi$
$41$	−107.742	+	186.614i	−0.410401	+	0.710835i	0.584533	+	0.811370i	$0.301278\pi$
$42$		0			0
$43$	−30.6168	−	53.0299i	−0.108582	−	0.188069i	0.806614	−	0.591078i	$-0.201298\pi$
$43$	−30.6168	−	53.0299i	−0.108582	−	0.188069i	−0.915196	+	0.403009i	$0.867964\pi$
$44$	342.410			1.17319
$45$		0			0
$46$	−97.5326			−0.312617
$47$	−30.9388	−	53.5876i	−0.0960189	−	0.166310i	0.814014	−	0.580845i	$-0.197278\pi$
$47$	−30.9388	−	53.5876i	−0.0960189	−	0.166310i	−0.910033	+	0.414535i	$0.863944\pi$
$48$		0			0
$49$	158.409	−	274.372i	0.461834	−	0.799919i
$50$	11.9497	−	20.6974i	0.0337988	−	0.0585412i
$51$		0			0
$52$	114.948	+	199.096i	0.306548	+	0.530956i
$53$	−492.310			−1.27592			−0.637962	−	0.770068i	$-0.720222\pi$
$53$	−492.310			−1.27592			−0.637962	+	0.770068i	$0.720222\pi$
$54$		0			0
$55$	580.622			1.42347
$56$	−49.5625	−	85.8447i	−0.118269	−	0.204848i
$57$		0			0
$58$	−19.4674	+	33.7185i	−0.0440723	+	0.0763354i
$59$	394.815	−	683.840i	0.871196	−	1.50896i	0.0104351	−	0.999946i	$-0.496678\pi$
$59$	394.815	−	683.840i	0.871196	−	1.50896i	0.860761	−	0.509010i	$-0.169988\pi$
$60$		0			0
$61$	−260.545	−	451.277i	−0.546874	−	0.947214i	−0.998486	−	0.0549998i	$-0.982484\pi$
$61$	−260.545	−	451.277i	−0.546874	−	0.947214i	0.451612	−	0.892214i	$-0.350849\pi$
$62$	17.6793			0.0362141
$63$		0			0
$64$	75.9590			0.148358
$65$	194.917	+	337.606i	0.371946	+	0.644229i
$66$		0			0
$67$	−152.215	+	263.644i	−0.277552	+	0.480734i	−0.970776	−	0.239988i	$-0.922856\pi$
$67$	−152.215	+	263.644i	−0.277552	+	0.480734i	0.693224	+	0.720722i	$0.256190\pi$
$68$	−72.3301	+	125.279i	−0.128990	+	0.223417i
$69$		0			0
$70$	−36.4158	−	63.0740i	−0.0621788	−	0.107697i
$71$	−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	$0.766075\pi$
$74$	123.576	+	214.040i	0.194127	+	0.336239i
$75$		0			0
$76$	119.436	−	206.870i	0.180267	−	0.312231i
$77$	−143.216	+	248.057i	−0.211961	+	0.367127i
$78$		0			0
$79$	644.517	+	1116.34i	0.917897	+	1.58984i	0.802603	+	0.596513i	$0.203448\pi$
$79$	644.517	+	1116.34i	0.917897	+	1.58984i	0.115294	+	0.993331i	$0.463219\pi$
$80$	−231.826			−0.323987
$81$		0			0
$82$	295.704			0.398232
$83$	356.917	+	618.198i	0.472009	+	0.817543i	0.999487	−	0.0320252i	$-0.0101957\pi$
$83$	356.917	+	618.198i	0.472009	+	0.817543i	−0.527478	+	0.849569i	$0.676862\pi$
$84$		0			0
$85$	−122.649	+	212.435i	−0.156508	+	0.271080i
$86$	−42.0149	+	72.7720i	−0.0526812	+	0.0912466i
$87$		0			0
$88$	−542.213	−	939.141i	−0.656820	−	1.13764i
$89$	404.804			0.482125			0.241063	−	0.970510i	$-0.422504\pi$
$89$	404.804			0.482125			0.241063	+	0.970510i	$0.422504\pi$
$90$		0			0
$91$	−192.313			−0.221537
$92$	−217.372	−	376.500i	−0.246333	−	0.426661i
$93$		0			0
$94$	−42.4567	+	73.5372i	−0.0465859	+	0.0806892i
$95$	202.527	−	350.787i	0.218725	−	0.378842i
$96$		0			0
$97$	−37.5137	−	64.9756i	−0.0392674	−	0.0680131i	0.845724	−	0.533621i	$-0.179169\pi$
$97$	−37.5137	−	64.9756i	−0.0392674	−	0.0680131i	−0.884991	+	0.465608i	$0.845836\pi$
$98$	−434.763			−0.448140
$99$		0			0
$100$	106.530			0.106530
$101$	−543.939	−	942.130i	−0.535881	−	0.928172i	−0.999120	−	0.0419392i	$-0.986646\pi$
$101$	−543.939	−	942.130i	−0.535881	−	0.928172i	0.463240	−	0.886233i	$-0.346687\pi$
$102$		0			0
$103$	545.909	−	945.542i	0.522233	−	0.904534i	−0.477432	−	0.878669i	$-0.658432\pi$
$103$	545.909	−	945.542i	0.522233	−	0.904534i	0.999665	−	0.0258657i	$-0.00823423\pi$
$104$	364.046	−	630.546i	0.343247	−	0.594521i
$105$		0			0
$106$	337.794	+	585.076i	0.309523	+	0.536109i
$107$	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	$0.214940\pi$
$110$	−398.388	−	690.029i	−0.345317	−	0.598106i
$111$		0			0
$112$	57.1821	−	99.0423i	0.0482429	−	0.0835591i
$113$	−807.969	+	1399.44i	−0.672631	+	1.16503i	0.304524	+	0.952505i	$0.401502\pi$
$113$	−807.969	+	1399.44i	−0.672631	+	1.16503i	−0.977155	+	0.212526i	$0.931831\pi$
$114$		0			0
$115$	−368.596	−	638.428i	−0.298885	−	0.517684i
$116$	−173.549			−0.138910
$117$		0			0
$118$	−1083.59			−0.845364
$119$	−60.5053	−	104.798i	−0.0466094	−	0.0807298i
$120$		0			0
$121$	−901.282	+	1561.07i	−0.677147	+	1.17285i
$122$	−357.541	+	619.279i	−0.265330	+	0.459564i
$123$		0			0
$124$	39.4021	+	68.2465i	0.0285356	+	0.0494251i
$125$	1477.18			1.05698
$126$		0			0
$127$	−1206.10			−0.842711			−0.421356	−	0.906895i	$-0.638446\pi$
$127$	−1206.10			−0.842711			−0.421356	+	0.906895i	$0.638446\pi$
$128$	690.479	+	1195.95i	0.476799	+	0.825841i
$129$		0			0
$130$	267.481	−	463.291i	0.180459	−	0.312564i
$131$	−513.928	+	890.149i	−0.342764	+	0.593684i	−0.984945	−	0.172869i	$-0.944696\pi$
$131$	−513.928	+	890.149i	−0.342764	+	0.593684i	0.642181	+	0.766553i	$0.278030\pi$
$132$		0			0
$133$	99.9105	+	173.050i	0.0651379	+	0.112822i
$134$	417.763			0.269322
$135$		0			0
$136$	458.144			0.288864
$137$	−630.454	−	1091.98i	−0.393163	−	0.680978i	0.599702	−	0.800223i	$-0.295286\pi$
$137$	−630.454	−	1091.98i	−0.393163	−	0.680978i	−0.992865	+	0.119245i	$0.961952\pi$
$138$		0			0
$139$	−230.916	+	399.958i	−0.140907	+	0.244057i	−0.927838	−	0.372983i	$-0.878335\pi$
$139$	−230.916	+	399.958i	−0.140907	+	0.244057i	0.786932	+	0.617040i	$0.211668\pi$
$140$	162.321	−	281.148i	0.0979900	−	0.169724i
$141$		0			0
$142$	185.527	+	321.341i	0.109641	+	0.189904i
$143$	−2103.90			−1.23033
$144$		0			0
$145$	−294.285			−0.168545
$146$	634.999	+	1099.85i	0.359951	+	0.623454i
$147$		0			0
$148$	−550.832	+	954.068i	−0.305933	+	0.529891i
$149$	729.661	−	1263.81i	0.401182	−	0.694868i	−0.592687	−	0.805433i	$-0.701933\pi$
$149$	729.661	−	1263.81i	0.401182	−	0.694868i	0.993869	+	0.110565i	$0.0352660\pi$
$150$		0			0
$151$	−770.659	−	1334.82i	−0.415333	−	0.719378i	0.580130	−	0.814524i	$-0.303002\pi$
$151$	−770.659	−	1334.82i	−0.415333	−	0.719378i	−0.995463	+	0.0951456i	$0.969668\pi$
$152$	−756.518			−0.403696
$153$		0			0
$154$	393.065			0.205676
$155$	66.8139	+	115.725i	0.0346233	+	0.0599694i
$156$		0			0
$157$	1607.79	−	2784.77i	0.817295	−	1.41560i	−0.0903734	−	0.995908i	$-0.528806\pi$
$157$	1607.79	−	2784.77i	0.817295	−	1.41560i	0.907668	−	0.419688i	$-0.137861\pi$
$158$	884.459	−	1531.93i	0.445341	−	0.771352i
$159$		0			0
$160$	962.804	+	1667.63i	0.475727	+	0.823984i
$161$	363.671			0.178021
$162$		0			0
$163$	947.587			0.455342			0.227671	−	0.973738i	$-0.426889\pi$
$163$	947.587			0.455342			0.227671	+	0.973738i	$0.426889\pi$
$164$	659.040	+	1141.49i	0.313795	+	0.543509i
$165$		0			0
$166$	489.791	−	848.342i	0.229007	−	0.396651i
$167$	342.980	−	594.058i	0.158926	−	0.275267i	−0.775556	−	0.631279i	$-0.782530\pi$
$167$	342.980	−	594.058i	0.158926	−	0.275267i	0.934481	+	0.356012i	$0.115864\pi$
$168$		0			0
$169$	392.213	+	679.333i	0.178522	+	0.309209i
$170$	336.619			0.151868
$171$		0			0
$172$	−374.557			−0.166045
$173$	−1106.41	−	1916.36i	−0.486237	−	0.842188i	0.513637	−	0.858007i	$-0.328298\pi$
$173$	−1106.41	−	1916.36i	−0.486237	−	0.842188i	−0.999875	+	0.0158193i	$0.994964\pi$
$174$		0			0
$175$	−44.5569	+	77.1748i	−0.0192468	+	0.0333364i
$176$	625.572	−	1083.52i	0.267922	−	0.464054i
$177$		0			0
$178$	−277.753	−	481.082i	−0.116958	−	0.202576i
$179$	−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	$0.474388\pi$
$182$	131.953	+	228.550i	0.0537420	+	0.0930839i
$183$		0			0
$184$	−688.426	+	1192.39i	−0.275823	+	0.477740i
$185$	−934.040	+	1617.81i	−0.371200	+	0.642937i
$186$		0			0
$187$	−661.928	−	1146.49i	−0.258850	−	0.448341i
$188$	−378.496			−0.146833
$189$		0			0
$190$	−555.848			−0.212239
$191$	1742.79	+	3018.61i	0.660231	+	1.14355i	0.980555	+	0.196246i	$0.0628750\pi$
$191$	1742.79	+	3018.61i	0.660231	+	1.14355i	−0.320324	+	0.947308i	$0.603792\pi$
$192$		0			0
$193$	−1107.53	+	1918.31i	−0.413068	+	0.715455i	−0.995223	−	0.0976228i	$-0.968876\pi$
$193$	−1107.53	+	1918.31i	−0.413068	+	0.715455i	0.582156	+	0.813077i	$0.302209\pi$
$194$	−51.4793	+	89.1647i	−0.0190515	+	0.0329982i
$195$		0			0
$196$	−968.963	−	1678.29i	−0.353121	−	0.611623i
$197$	3975.11			1.43764			0.718820	−	0.695196i	$-0.244682\pi$
$197$	3975.11			1.43764			0.718820	+	0.695196i	$0.244682\pi$
$198$		0			0
$199$	−1555.34			−0.554046			−0.277023	−	0.960863i	$-0.589348\pi$
$199$	−1555.34			−0.554046			−0.277023	+	0.960863i	$0.589348\pi$
$200$	−168.692	−	292.183i	−0.0596415	−	0.103302i
$201$		0			0
$202$	−746.437	+	1292.87i	−0.259996	+	0.450326i
$203$	72.5883	−	125.727i	0.0250970	−	0.0434693i
$204$		0			0
$205$	1117.53	+	1935.62i	0.380739	+	0.659460i
$206$	−1498.28			−0.506749
$207$		0			0
$208$	840.027			0.280026
$209$	1093.02	+	1893.17i	0.361750	+	0.626570i
$210$		0			0
$211$	−873.865	+	1513.58i	−0.285115	+	0.493834i	−0.972637	−	0.232329i	$-0.925365\pi$
$211$	−873.865	+	1513.58i	−0.285115	+	0.493834i	0.687522	+	0.726164i	$0.258699\pi$
$212$	−1505.69	+	2607.93i	−0.487789	+	0.844875i
$213$		0			0
$214$	−706.145	−	1223.08i	−0.225566	−	0.390691i
$215$	−635.133			−0.201468
$216$		0			0
$217$	−65.9211			−0.0206222
$218$	−1218.94	−	2111.27i	−0.378702	−	0.655931i
$219$		0			0
$220$	1775.79	−	3075.75i	0.544198	−	0.942579i
$221$	444.423	−	769.764i	0.135272	−	0.234298i
$222$		0			0
$223$	1270.97	+	2201.39i	0.381662	+	0.661057i	0.991300	−	0.131622i	$-0.0420187\pi$
$223$	1270.97	+	2201.39i	0.381662	+	0.661057i	−0.609638	+	0.792680i	$0.708685\pi$
$224$	−949.939			−0.283350
$225$		0			0
$226$	2217.52			0.652687
$227$	−1496.63	−	2592.24i	−0.437598	−	0.757943i	0.559905	−	0.828557i	$-0.310837\pi$
$227$	−1496.63	−	2592.24i	−0.437598	−	0.757943i	−0.997504	+	0.0706140i	$0.977504\pi$
$228$		0			0
$229$	2152.65	−	3728.50i	0.621185	−	1.07592i	−0.368081	−	0.929794i	$-0.619985\pi$
$229$	2152.65	−	3728.50i	0.621185	−	1.07592i	0.989265	−	0.146130i	$-0.0466816\pi$
$230$	−505.818	+	876.102i	−0.145012	+	0.251167i
$231$		0			0
$232$	274.818	+	475.999i	0.0777702	+	0.134702i
$233$	5581.34			1.56930			0.784648	−	0.619942i	$-0.212844\pi$
$233$	5581.34			1.56930			0.784648	+	0.619942i	$0.212844\pi$
$234$		0			0
$235$	−641.812			−0.178158
$236$	−2415.02	−	4182.94i	−0.666121	−	1.15376i
$237$		0			0
$238$	−83.0303	+	143.813i	−0.0226137	+	0.0391680i
$239$	704.814	−	1220.77i	0.190756	−	0.330399i	−0.754745	−	0.656018i	$-0.772239\pi$
$239$	704.814	−	1220.77i	0.190756	−	0.330399i	0.945501	+	0.325619i	$0.105573\pi$
$240$		0			0
$241$	−313.286	−	542.627i	−0.0837366	−	0.145036i	0.821116	−	0.570762i	$-0.193352\pi$
$241$	−313.286	−	542.627i	−0.0837366	−	0.145036i	−0.904852	+	0.425726i	$0.860019\pi$
$242$	2473.63			0.657069
$243$		0			0
$244$	−3187.42			−0.836286
$245$	−1643.06	−	2845.87i	−0.428455	−	0.742105i
$246$		0			0
$247$	−733.862	+	1271.09i	−0.189047	+	0.327438i
$248$	124.788	−	216.139i	0.0319518	−	0.0553422i
$249$		0			0
$250$	−1013.55	−	1755.52i	−0.256410	−	0.444116i
$251$	−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
$254$	827.556	+	1433.37i	0.204431	+	0.354085i
$255$		0			0
$256$	1251.37	−	2167.43i	0.305510	−	0.529158i
$257$	−1798.69	+	3115.42i	−0.436573	+	0.756166i	−0.997423	−	0.0717513i	$-0.977141\pi$
$257$	−1798.69	+	3115.42i	−0.436573	+	0.756166i	0.560850	+	0.827918i	$0.310475\pi$
$258$		0			0
$259$	−460.780	−	798.094i	−0.110546	−	0.191472i
$260$	2384.55			0.568784
$261$		0			0
$262$	1410.51			0.332601
$263$	2068.75	+	3583.18i	0.485037	+	0.840108i	0.999852	−	0.0171926i	$-0.00547285\pi$
$263$	2068.75	+	3583.18i	0.485037	+	0.840108i	−0.514815	+	0.857301i	$0.672140\pi$
$264$		0			0
$265$	−2553.19	+	4422.25i	−0.591853	+	1.02512i
$266$	137.105	−	237.473i	0.0316032	−	0.0547384i
$267$		0			0
$268$	931.074	+	1612.67i	0.212218	+	0.367572i
$269$	−6090.99			−1.38057			−0.690287	−	0.723536i	$-0.742516\pi$
$269$	−6090.99			−1.38057			−0.690287	+	0.723536i	$0.742516\pi$
$270$		0			0
$271$	−3196.62			−0.716534			−0.358267	−	0.933619i	$-0.616632\pi$
$271$	−3196.62			−0.716534			−0.358267	+	0.933619i	$0.616632\pi$
$272$	264.289	+	457.762i	0.0589150	+	0.102044i
$273$		0			0
$274$	−865.160	+	1498.50i	−0.190753	+	0.330393i
$275$	−487.452	+	844.292i	−0.106889	+	0.185137i
$276$		0			0
$277$	1559.68	+	2701.45i	0.338311	+	0.585972i	0.984115	−	0.177531i	$-0.0568111\pi$
$277$	1559.68	+	2701.45i	0.338311	+	0.585972i	−0.645804	+	0.763503i	$0.723478\pi$
$278$	633.763			0.136729
$279$		0			0
$280$	−1028.15			−0.219442
$281$	2474.17	+	4285.38i	0.525254	+	0.909767i	0.999567	+	0.0294105i	$0.00936301\pi$
$281$	2474.17	+	4285.38i	0.525254	+	0.909767i	−0.474313	+	0.880356i	$0.657304\pi$
$282$		0			0
$283$	2272.47	−	3936.03i	0.477329	−	0.826758i	−0.522333	−	0.852741i	$-0.674938\pi$
$283$	2272.47	−	3936.03i	0.477329	−	0.826758i	0.999662	+	0.0259834i	$0.00827171\pi$
$284$	−826.971	+	1432.36i	−0.172788	+	0.299277i
$285$		0			0
$286$	1443.57	+	2500.34i	0.298462	+	0.516951i
$287$	−1102.60			−0.226774
$288$		0			0
$289$	−4353.70			−0.886160
$290$	201.921	+	349.738i	0.0408869	+	0.0708183i
$291$		0			0
$292$	−2830.46	+	4902.50i	−0.567261	+	0.982525i
$293$	3430.05	−	5941.03i	0.683911	−	1.18457i	−0.289867	−	0.957067i	$-0.593611\pi$
$293$	3430.05	−	5941.03i	0.683911	−	1.18457i	0.973778	−	0.227501i	$-0.0730555\pi$
$294$		0			0
$295$	−4095.13	−	7092.98i	−0.808230	−	1.39990i
$296$	3489.01			0.685117
$297$		0			0
$298$	−2002.60			−0.389287
$299$	1335.62	+	2313.36i	0.258330	+	0.447441i
$300$		0			0
$301$	156.662	−	271.346i	0.0299994	−	0.0519605i
$302$	−1057.56	+	1831.75i	−0.201509	+	0.349024i
$303$		0			0
$304$	−436.412	−	755.888i	−0.0823353	−	0.142609i
$305$	−5404.89			−1.01470
$306$		0			0
$307$	6332.25			1.17720			0.588600	−	0.808424i	$-0.299679\pi$
$307$	6332.25			1.17720			0.588600	+	0.808424i	$0.299679\pi$
$308$	876.030	+	1517.33i	0.162066	+	0.280707i
$309$		0			0
$310$	91.6874	−	158.807i	0.0167984	−	0.0290956i
$311$	3538.84	−	6129.44i	0.645238	−	1.11758i	−0.339009	−	0.940783i	$-0.610092\pi$
$311$	3538.84	−	6129.44i	0.645238	−	1.11758i	0.984247	−	0.176801i	$-0.0565750\pi$
$312$		0			0
$313$	−690.649	−	1196.24i	−0.124721	−	0.216024i	0.796903	−	0.604108i	$-0.206470\pi$
$313$	−690.649	−	1196.24i	−0.124721	−	0.216024i	−0.921624	+	0.388084i	$0.873137\pi$
$314$	−4412.67			−0.793062
$315$		0			0
$316$	7884.83			1.40366
$317$	−4087.47	−	7079.70i	−0.724211	−	1.25437i	−0.959298	−	0.282396i	$-0.908871\pi$
$317$	−4087.47	−	7079.70i	−0.724211	−	1.25437i	0.235086	−	0.971974i	$-0.424463\pi$
$318$		0			0
$319$	794.115	−	1375.45i	0.139379	−	0.241412i
$320$	393.934	−	682.314i	0.0688175	−	0.119195i
$321$		0			0
$322$	−249.530	−	432.198i	−0.0431855	−	0.0747995i
$323$	−923.549			−0.159095
$324$		0			0
$325$	−654.559			−0.111718
$326$	−650.178	−	1126.14i	−0.110460	−	0.191323i
$327$		0			0
$328$	2087.20	−	3615.14i	0.351361	−	0.608576i
$329$	158.309	−	274.199i	0.0265284	−	0.0459486i
$330$		0			0
$331$	4830.64	+	8366.92i	0.802163	+	1.38939i	0.918189	+	0.396142i	$0.129651\pi$
$331$	4830.64	+	8366.92i	0.802163	+	1.38939i	−0.116026	+	0.993246i	$0.537016\pi$
$332$	4366.41			0.721801
$333$		0			0
$334$	−941.329			−0.154213
$335$	1578.81	+	2734.59i	0.257492	+	0.445989i
$336$		0			0
$337$	2478.01	−	4292.04i	0.400552	−	0.693776i	−0.593241	−	0.805025i	$-0.702152\pi$
$337$	2478.01	−	4292.04i	0.400552	−	0.693776i	0.993793	+	0.111249i	$0.0354852\pi$
$338$	538.227	−	932.236i	0.0866144	−	0.150021i
$339$		0			0
$340$	750.228	+	1299.43i	0.119667	+	0.207269i
$341$	−721.177			−0.114528
$342$		0			0
$343$	3376.19			0.531478
$344$	593.118	+	1027.31i	0.0929616	+	0.161014i
$345$		0			0
$346$	−1518.31	+	2629.79i	−0.235910	+	0.408608i
$347$	−507.802	+	879.540i	−0.0785598	+	0.136070i	−0.902629	−	0.430420i	$-0.858365\pi$
$347$	−507.802	+	879.540i	−0.0785598	+	0.136070i	0.824069	+	0.566490i	$0.191699\pi$
$348$		0			0
$349$	−6079.29	−	10529.6i	−0.932426	−	1.61501i	−0.779160	−	0.626825i	$-0.784354\pi$
$349$	−6079.29	−	10529.6i	−0.932426	−	1.61501i	−0.153267	−	0.988185i	$-0.548979\pi$
$350$	122.289			0.0186761
$351$		0			0
$352$	−10392.3			−1.57362
$353$	2118.04	+	3668.56i	0.319354	+	0.553138i	0.980353	−	0.197249i	$-0.0632007\pi$
$353$	2118.04	+	3668.56i	0.319354	+	0.553138i	−0.660999	+	0.750387i	$0.729867\pi$
$354$		0			0
$355$	−1402.29	+	2428.83i	−0.209650	+	0.363124i
$356$	1238.06	−	2144.39i	0.184318	−	0.319248i
$357$		0			0
$358$	2074.35	+	3592.88i	0.306237	+	0.530418i
$359$	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
$362$	−268.586	−	465.205i	−0.0389961	−	0.0675432i
$363$		0			0
$364$	−588.173	+	1018.75i	−0.0846941	+	0.146694i
$365$	−4799.59	+	8313.13i	−0.688279	+	1.19213i
$366$		0			0
$367$	2308.15	+	3997.83i	0.328295	+	0.568624i	0.982174	−	0.187976i	$-0.0601926\pi$
$367$	2308.15	+	3997.83i	0.328295	+	0.568624i	−0.653879	+	0.756600i	$0.726859\pi$
$368$	−1588.53			−0.225021
$369$		0			0
$370$	2563.53			0.360194
$371$	−1259.54	−	2181.58i	−0.176258	−	0.305288i
$372$		0			0
$373$	−2382.71	+	4126.98i	−0.330756	+	0.572887i	−0.982660	−	0.185415i	$-0.940637\pi$
$373$	−2382.71	+	4126.98i	−0.330756	+	0.572887i	0.651904	+	0.758301i	$0.273970\pi$
$374$	−908.351	+	1573.31i	−0.125588	+	0.217524i
$375$		0			0
$376$	599.355	+	1038.11i	0.0822058	+	0.142385i
$377$	1066.35			0.145676
$378$		0			0
$379$	−2000.33			−0.271108			−0.135554	−	0.990770i	$-0.543281\pi$
$379$	−2000.33			−0.271108			−0.135554	+	0.990770i	$0.543281\pi$
$380$	−1238.83	−	2145.71i	−0.167238	−	0.289665i
$381$		0			0
$382$	2391.60	−	4142.38i	0.320327	−	0.554823i
$383$	495.147	−	857.619i	0.0660596	−	0.114419i	−0.831104	−	0.556117i	$-0.812291\pi$
$383$	495.147	−	857.619i	0.0660596	−	0.114419i	0.897164	+	0.441699i	$0.145624\pi$
$384$		0			0
$385$	1485.48	+	2572.92i	0.196641	+	0.340593i
$386$	3039.70			0.400820
$387$		0			0
$388$	−458.930			−0.0600481
$389$	202.205	+	350.230i	0.0263553	+	0.0456487i	0.878902	−	0.477002i	$-0.158277\pi$
$389$	202.205	+	350.230i	0.0263553	+	0.0456487i	−0.852547	+	0.522651i	$0.824943\pi$
$390$		0			0
$391$	−840.423	+	1455.66i	−0.108701	+	0.188275i
$392$	−3068.74	+	5315.22i	−0.395395	+	0.684845i
$393$		0			0
$394$	−2727.49	−	4724.15i	−0.348753	−	0.604059i
$395$	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	$0.440918\pi$
$398$	1067.18	+	1848.42i	0.134405	+	0.232796i
$399$		0			0
$400$	194.626	−	337.102i	0.0243282	−	0.0421378i
$401$	−5093.10	+	8821.52i	−0.634258	+	1.09857i	0.352414	+	0.935844i	$0.385361\pi$
$401$	−5093.10	+	8821.52i	−0.634258	+	1.09857i	−0.986672	+	0.162723i	$0.947972\pi$
$402$		0			0
$403$	−242.102	−	419.332i	−0.0299254	−	0.0518323i
$404$	−6654.38			−0.819474
$405$		0			0
$406$	−199.223			−0.0243529
$407$	−5040.93	−	8731.15i	−0.613930	−	1.06336i
$408$		0			0
$409$	−3457.12	+	5987.91i	−0.417955	+	0.723920i	−0.995734	−	0.0922740i	$-0.970586\pi$
$409$	−3457.12	+	5987.91i	−0.417955	+	0.723920i	0.577778	+	0.816194i	$0.303920\pi$
$410$	1533.56	−	2656.21i	0.184725	−	0.319953i
$411$		0			0
$412$	−3339.24	−	5783.73i	−0.399302	−	0.691612i
$413$	4040.41			0.481394
$414$		0			0
$415$	7404.09			0.875789
$416$	−3488.75	−	6042.68i	−0.411177	−	0.712180i
$417$		0			0
$418$	1499.93	−	2597.96i	0.175512	−	0.303996i
$419$	2560.16	−	4434.32i	0.298501	−	0.517019i	−0.677292	−	0.735714i	$-0.736847\pi$
$419$	2560.16	−	4434.32i	0.298501	−	0.517019i	0.975793	+	0.218695i	$0.0701801\pi$
$420$		0			0
$421$	−933.246	−	1616.43i	−0.108037	−	0.187126i	0.806938	−	0.590636i	$-0.201123\pi$
$421$	−933.246	−	1616.43i	−0.108037	−	0.187126i	−0.914975	+	0.403511i	$0.867790\pi$
$422$	2398.38			0.276662
$423$		0			0
$424$	9537.16			1.09237
$425$	−205.937	−	356.693i	−0.0235045	−	0.0407110i
$426$		0			0
$427$	1333.17	−	2309.11i	0.151092	−	0.261700i
$428$	3147.59	−	5451.79i	0.355478	−	0.615706i
$429$		0			0
$430$	435.791	+	754.811i	0.0488737	+	0.0846517i
$431$	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	$0.488815\pi$
$434$	45.2311	+	78.3426i	0.00500268	+	0.00866490i
$435$		0			0
$436$	5433.34	−	9410.81i	0.596811	−	1.03371i
$437$	1387.76	−	2403.68i	0.151912	−	0.263120i
$438$		0			0
$439$	5653.26	+	9791.74i	0.614614	+	1.06454i	0.990452	+	0.137857i	$0.0440214\pi$
$439$	5653.26	+	9791.74i	0.614614	+	1.06454i	−0.375838	+	0.926685i	$0.622645\pi$
$440$	−11248.0			−1.21870
$441$		0			0
$442$	−1219.75			−0.131261
$443$	−4140.65	−	7171.82i	−0.444082	−	0.769172i	0.553906	−	0.832579i	$-0.313137\pi$
$443$	−4140.65	−	7171.82i	−0.444082	−	0.769172i	−0.997988	+	0.0634071i	$0.979803\pi$
$444$		0			0
$445$	2099.37	−	3636.22i	0.223640	−	0.387356i
$446$	1744.13	−	3020.92i	0.185173	−	0.320728i
$447$		0			0
$448$	194.335	+	336.599i	0.0204944	+	0.0354973i
$449$	−6888.40			−0.724017			−0.362008	−	0.932175i	$-0.617909\pi$
$449$	−6888.40			−0.724017			−0.362008	+	0.932175i	$0.617909\pi$
$450$		0			0
$451$	−12062.4			−1.25941
$452$	4942.22	+	8560.17i	0.514297	+	0.890789i
$453$		0			0
$454$	−2053.80	+	3557.28i	−0.212312	+	0.367735i
$455$	−997.360	+	1727.48i	−0.102763	+	0.177990i
$456$		0			0
$457$	−2141.80	−	3709.71i	−0.219233	−	0.379722i	0.735341	−	0.677697i	$-0.237022\pi$
$457$	−2141.80	−	3709.71i	−0.219233	−	0.379722i	−0.954574	+	0.297975i	$0.903689\pi$
$458$	−5908.09			−0.602766
$459$		0			0
$460$	−4509.29			−0.457058
$461$	6889.16	+	11932.4i	0.696009	+	1.20552i	0.969840	+	0.243744i	$0.0783758\pi$
$461$	6889.16	+	11932.4i	0.696009	+	1.20552i	−0.273831	+	0.961778i	$0.588291\pi$
$462$		0			0
$463$	−2867.27	+	4966.25i	−0.287804	+	0.498491i	−0.973285	−	0.229599i	$-0.926258\pi$
$463$	−2867.27	+	4966.25i	−0.287804	+	0.498491i	0.685481	+	0.728090i	$0.259592\pi$
$464$	−317.068	+	549.178i	−0.0317231	+	0.0549460i
$465$		0			0
$466$	−3829.59	−	6633.04i	−0.380691	−	0.659377i
$467$	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
$470$	440.373	+	762.749i	0.0432189	+	0.0748574i
$471$		0			0
$472$	−7648.47	+	13247.5i	−0.745867	+	1.29188i
$473$	1713.88	−	2968.52i	0.166605	−	0.288568i
$474$		0			0
$475$	340.057	+	588.996i	0.0328482	+	0.0568947i
$476$	−740.203			−0.0712755
$477$		0			0
$478$	−1934.41			−0.185100
$479$	4840.51	+	8384.00i	0.461729	+	0.799739i	0.999047	−	0.0436411i	$-0.0138958\pi$
$479$	4840.51	+	8384.00i	0.461729	+	0.799739i	−0.537318	+	0.843380i	$0.680562\pi$
$480$		0			0
$481$	3384.52	−	5862.16i	0.320833	−	0.555699i
$482$	−429.917	+	744.637i	−0.0406269	+	0.0703678i
$483$		0			0
$484$	5513.00	+	9548.80i	0.517750	+	0.896769i
$485$	−778.204			−0.0728586
$486$		0			0
$487$	8704.66			0.809950			0.404975	−	0.914328i	$-0.367280\pi$
$487$	8704.66			0.809950			0.404975	+	0.914328i	$0.367280\pi$
$488$	5047.35	+	8742.26i	0.468202	+	0.810950i
$489$		0			0
$490$	−2254.74	+	3905.33i	−0.207875	+	0.360051i
$491$	−7797.85	+	13506.3i	−0.716725	+	1.24140i	0.245565	+	0.969380i	$0.421026\pi$
$491$	−7797.85	+	13506.3i	−0.716725	+	1.24140i	−0.962290	+	0.272024i	$0.912307\pi$
$492$		0			0
$493$	335.495	+	581.094i	0.0306489	+	0.0530855i
$494$	2014.13			0.183441
$495$		0			0
$496$	287.945			0.0260668
$497$	−691.776	−	1198.19i	−0.0624354	−	0.108141i
$498$		0			0
$499$	4848.14	−	8397.22i	0.434935	−	0.753329i	−0.562355	−	0.826896i	$-0.690105\pi$
$499$	4848.14	−	8397.22i	0.434935	−	0.753329i	0.997290	+	0.0735663i	$0.0234381\pi$
$500$	4517.83	−	7825.11i	0.404087	−	0.699899i
$501$		0			0
$502$	1170.23	+	2026.90i	0.104044	+	0.180209i
$503$	−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
$506$	−2729.85	−	4728.24i	−0.239835	−	0.415407i
$507$		0			0
$508$	−3688.77	+	6389.14i	−0.322171	+	0.558016i
$509$	5637.37	−	9764.22i	0.490908	−	0.850278i	−0.509037	−	0.860745i	$-0.669998\pi$
$509$	5637.37	−	9764.22i	0.490908	−	0.850278i	0.999945	+	0.0104668i	$0.00333174\pi$
$510$		0			0
$511$	−2367.73	−	4101.03i	−0.204975	−	0.355027i
$512$	7613.21			0.657148
$513$		0			0
$514$	4936.62			0.423628
$515$	−5662.32	−	9807.43i	−0.484489	−	0.839159i
$516$		0			0
$517$	1731.90	−	2999.74i	0.147329	−	0.255181i
$518$	−632.320	+	1095.21i	−0.0536342	+	0.0928972i
$519$		0			0
$520$	−3775.99	−	6540.20i	−0.318439	−	0.551552i
$521$	−8675.49			−0.729520			−0.364760	−	0.931102i	$-0.618849\pi$
$521$	−8675.49			−0.729520			−0.364760	+	0.931102i	$0.618849\pi$
$522$		0			0
$523$	−4226.14			−0.353339			−0.176670	−	0.984270i	$-0.556532\pi$
$523$	−4226.14			−0.353339			−0.176670	+	0.984270i	$0.556532\pi$
$524$	3143.62	+	5444.90i	0.262079	+	0.453934i
$525$		0			0
$526$	2838.91	−	4917.14i	0.235328	−	0.407599i
$527$	152.340	−	263.860i	0.0125921	−	0.0218101i
$528$		0			0
$529$	3557.79	+	6162.27i	0.292413	+	0.506474i
$530$	7007.38			0.574304
$531$		0			0
$532$	1222.27			0.0996095
$533$	−4049.39	−	7013.75i	−0.329078	−	0.569980i
$534$		0			0
$535$	5337.34	−	9244.55i	0.431315	−	0.747059i
$536$	2948.75	−	5107.38i	0.237624	−	0.411577i
$537$		0			0
$538$	4179.28	+	7238.72i	0.334910	+	0.580081i
$539$	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	$0.321902\pi$
$542$	2193.33	+	3798.96i	0.173822	+	0.301069i
$543$		0			0
$544$	2195.26	−	3802.29i	0.173016	−	0.299673i
$545$	9213.26	−	15957.8i	0.724134	−	1.25424i
$546$		0			0
$547$	−10835.6	−	18767.7i	−0.846974	−	1.46700i	−0.883896	−	0.467684i	$-0.845089\pi$
$547$	−10835.6	−	18767.7i	−0.846974	−	1.46700i	0.0369219	−	0.999318i	$-0.488245\pi$
$548$	−7712.78			−0.601229
$549$		0			0
$550$	1337.84			0.103720
$551$	−553.991	−	959.541i	−0.0428327	−	0.0741884i
$552$		0			0
$553$	−3297.90	+	5712.12i	−0.253600	+	0.439248i
$554$	2140.32	−	3707.15i	0.164140	−	0.284299i
$555$		0			0
$556$	1412.48	+	2446.48i	0.107738	+	0.186608i
$557$	−7477.63			−0.568828			−0.284414	−	0.958702i	$-0.591799\pi$
$557$	−7477.63			−0.568828			−0.284414	+	0.958702i	$0.591799\pi$
$558$		0			0
$559$	2301.42			0.174132
$560$	−593.109	−	1027.29i	−0.0447561	−	0.0775198i
$561$		0			0
$562$	3395.25	−	5880.75i	0.254840	−	0.441396i
$563$	−11652.3	+	20182.4i	−0.872269	+	1.51082i	−0.0126262	+	0.999920i	$0.504019\pi$
$563$	−11652.3	+	20182.4i	−0.872269	+	1.51082i	−0.859643	+	0.510895i	$0.829314\pi$
$564$		0			0
$565$	8380.48	+	14515.4i	0.624017	+	1.08083i
$566$	−6236.92			−0.463176
$567$		0			0
$568$	5238.10			0.386947
$569$	−7324.54	−	12686.5i	−0.539650	−	0.934701i	−0.998923	−	0.0464057i	$-0.985223\pi$
$569$	−7324.54	−	12686.5i	−0.539650	−	0.934701i	0.459273	−	0.888295i	$-0.348110\pi$
$570$		0			0
$571$	−11582.0	+	20060.6i	−0.848846	+	1.47025i	0.0333922	+	0.999442i	$0.489369\pi$
$571$	−11582.0	+	20060.6i	−0.848846	+	1.47025i	−0.882239	+	0.470803i	$0.843964\pi$
$572$	−6434.61	+	11145.1i	−0.470358	+	0.814683i
$573$		0			0
$574$	756.536	+	1310.36i	0.0550125	+	0.0952845i
$575$	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	$0.408417\pi$
$578$	2987.25	+	5174.07i	0.214971	+	0.372341i
$579$		0			0
$580$	−900.049	+	1558.93i	−0.0644353	+	0.111605i
$581$	−1826.29	+	3163.23i	−0.130408	+	0.225874i
$582$		0			0
$583$	−13779.3	−	23866.5i	−0.978869	−	1.69545i
$584$	17928.4			1.27034
$585$		0			0
$586$	−9413.99			−0.663632
$587$	−478.091	−	828.078i	−0.0336166	−	0.0582256i	0.848728	−	0.528830i	$-0.177369\pi$
$587$	−478.091	−	828.078i	−0.0336166	−	0.0582256i	−0.882344	+	0.470605i	$0.844036\pi$
$588$		0			0
$589$	−251.554	+	435.704i	−0.0175978	+	0.0304803i
$590$	−5619.68	+	9733.56i	−0.392133	+	0.679194i
$591$		0			0
$592$	2012.70	+	3486.10i	0.139732	+	0.242023i
$593$	16966.0			1.17489			0.587444	−	0.809265i	$-0.300134\pi$
$593$	16966.0			1.17489			0.587444	+	0.809265i	$0.300134\pi$
$594$		0			0
$595$	−1255.16			−0.0864813
$596$	−4463.22	−	7730.53i	−0.306746	−	0.531300i
$597$		0			0
$598$	1832.84	−	3174.58i	0.125335	−	0.217087i
$599$	−3095.70	+	5361.92i	−0.211164	+	0.365746i	−0.952079	−	0.305852i	$-0.901059\pi$
$599$	−3095.70	+	5361.92i	−0.211164	+	0.365746i	0.740915	+	0.671598i	$0.234392\pi$
$600$		0			0
$601$	1359.27	+	2354.33i	0.0922559	+	0.159792i	0.908460	−	0.417972i	$-0.137259\pi$
$601$	1359.27	+	2354.33i	0.0922559	+	0.159792i	−0.816204	+	0.577764i	$0.803926\pi$
$602$	−429.968			−0.0291099
$603$		0			0
$604$	−9428.00			−0.635132
$605$	9348.35	+	16191.8i	0.628206	+	1.08808i
$606$		0			0
$607$	−8412.49	+	14570.9i	−0.562524	+	0.974321i	0.434751	+	0.900551i	$0.356836\pi$
$607$	−8412.49	+	14570.9i	−0.562524	+	0.974321i	−0.997275	+	0.0737701i	$0.976497\pi$
$608$	−3624.95	+	6278.60i	−0.241795	+	0.418801i
$609$		0			0
$610$	3708.51	+	6423.33i	0.246153	+	0.426349i
$611$	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	$0.731420\pi$
$614$	−4344.81	−	7525.44i	−0.285574	−	0.494629i
$615$		0			0
$616$	2774.42	−	4805.44i	0.181468	−	0.314313i
$617$	5655.31	−	9795.29i	0.369002	−	0.639130i	−0.620408	−	0.784280i	$-0.713033\pi$
$617$	5655.31	−	9795.29i	0.369002	−	0.639130i	0.989410	+	0.145149i	$0.0463662\pi$
$618$		0			0
$619$	8529.94	+	14774.3i	0.553873	+	0.959336i	0.997990	+	0.0633676i	$0.0201841\pi$
$619$	8529.94	+	14774.3i	0.553873	+	0.959336i	−0.444117	+	0.895969i	$0.646483\pi$
$620$	817.380			0.0529464
$621$		0			0
$622$	−9712.56			−0.626106
$623$	1035.66	+	1793.82i	0.0666017	+	0.115357i
$624$		0			0
$625$	6572.36	−	11383.7i	0.420631	−	0.728554i
$626$	−947.764	+	1641.58i	−0.0605116	+	0.104809i
$627$		0			0
$628$	−9834.58	−	17034.0i	−0.624908	−	1.08237i
$629$	4259.34			0.270002
$630$		0			0
$631$	−13186.3			−0.831916			−0.415958	−	0.909384i	$-0.636554\pi$
$631$	−13186.3			−0.831916			−0.415958	+	0.909384i	$0.636554\pi$
$632$	−12485.8	−	21626.0i	−0.785850	−	1.36113i
$633$		0			0
$634$	−5609.15	+	9715.34i	−0.351369	+	0.608589i
$635$	−6255.02	+	10834.0i	−0.390902	+	0.677063i
$636$		0			0
$637$	5953.68	+	10312.1i	0.370319	+	0.641412i
$638$	−2179.50			−0.135246
$639$		0			0
$640$	14323.7			0.884677
$641$	8180.99	+	14169.9i	0.504102	+	0.873131i	0.999989	+	0.00474343i	$0.00150989\pi$
$641$	8180.99	+	14169.9i	0.504102	+	0.873131i	−0.495886	+	0.868387i	$0.665157\pi$
$642$		0			0
$643$	14022.5	−	24287.6i	0.860019	−	1.48960i	−0.0118907	−	0.999929i	$-0.503785\pi$
$643$	14022.5	−	24287.6i	0.860019	−	1.48960i	0.871910	−	0.489667i	$-0.162882\pi$
$644$	1112.26	−	1926.49i	0.0680577	−	0.117879i
$645$		0			0
$646$	633.685	+	1097.57i	0.0385944	+	0.0668475i
$647$	−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
$650$	449.119	+	777.897i	0.0271014	+	0.0469410i
$651$		0			0
$652$	2898.12	−	5019.69i	0.174079	−	0.301513i
$653$	629.928	−	1091.07i	0.0377504	−	0.0653856i	−0.846533	−	0.532336i	$-0.821314\pi$
$653$	629.928	−	1091.07i	0.0377504	−	0.0653856i	0.884283	+	0.466951i	$0.154647\pi$
$654$		0			0
$655$	5330.60	+	9232.87i	0.317991	+	0.550776i
$656$	4816.17			0.286646
$657$		0			0
$658$	−434.489			−0.0257419
$659$	−6023.35	−	10432.7i	−0.356049	−	0.616695i	0.631248	−	0.775581i	$-0.282543\pi$
$659$	−6023.35	−	10432.7i	−0.356049	−	0.616695i	−0.987297	+	0.158886i	$0.949210\pi$
$660$		0			0
$661$	−6554.04	+	11351.9i	−0.385662	+	0.667986i	−0.991861	−	0.127327i	$-0.959360\pi$
$661$	−6554.04	+	11351.9i	−0.385662	+	0.667986i	0.606199	+	0.795313i	$0.292693\pi$
$662$	6629.00	−	11481.8i	0.389189	−	0.674096i
$663$		0			0
$664$	−6914.30	−	11975.9i	−0.404107	−	0.699933i
$665$	2072.60			0.120860
$666$		0			0
$667$	−2016.51			−0.117061
$668$	−2097.95	−	3633.76i	−0.121515	−	0.210471i
$669$		0			0
$670$	2166.58	−	3752.62i	0.124929	−	0.216383i
$671$	14584.8	−	25261.7i	0.839108	−	1.45338i
$672$		0			0
$673$	−1371.82	−	2376.07i	−0.0785734	−	0.136093i	0.824061	−	0.566501i	$-0.191703\pi$
$673$	−1371.82	−	2376.07i	−0.0785734	−	0.136093i	−0.902635	+	0.430408i	$0.858370\pi$
$674$	−6801.06			−0.388675
$675$		0			0
$676$	4798.21			0.272998
$677$	12502.0	+	21654.1i	0.709735	+	1.22930i	0.964955	+	0.262415i	$0.0845189\pi$
$677$	12502.0	+	21654.1i	0.709735	+	1.22930i	−0.255220	+	0.966883i	$0.582148\pi$
$678$		0			0
$679$	191.952	−	332.470i	0.0108489	−	0.0187909i
$680$	2376.00	−	4115.35i	0.133993	−	0.232083i
$681$		0			0
$682$	494.829	+	857.068i	0.0277829	+	0.0481215i
$683$	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
$686$	−2316.54	−	4012.36i	−0.128930	−	0.223313i
$687$		0			0
$688$	−684.303	+	1185.25i	−0.0379198	+	0.0656790i
$689$	9251.54	−	16024.1i	0.511546	−	0.886024i
$690$		0			0
$691$	−1742.29	−	3017.73i	−0.0959187	−	0.166136i	0.814073	−	0.580763i	$-0.197246\pi$
$691$	−1742.29	−	3017.73i	−0.0959187	−	0.166136i	−0.909992	+	0.414627i	$0.863912\pi$
$692$	−13535.5			−0.743560
$693$		0			0
$694$	1393.70			0.0762305
$695$	2395.12	+	4148.48i	0.130723	+	0.226418i
$696$		0			0
$697$	2548.04	−	4413.33i	0.138470	−	0.239837i
$698$	−8342.49	+	14449.6i	−0.452390	+	0.783562i
$699$		0			0
$700$	272.548	+	472.066i	0.0147162	+	0.0254892i
$701$	−15701.4			−0.845981			−0.422991	−	0.906134i	$-0.639020\pi$
$701$	−15701.4			−0.845981			−0.422991	+	0.906134i	$0.639020\pi$
$702$		0			0
$703$	−7033.32			−0.377335
$704$	2126.03	+	3682.39i	0.113818	+	0.197138i
$705$		0			0
$706$	2906.55	−	5034.29i	0.154943	−	0.268368i
$707$	2783.25	−	4820.73i	0.148055	−	0.256439i
$708$		0			0
$709$	−7821.72	−	13547.6i	−0.414317	−	0.717618i	0.581039	−	0.813875i	$-0.302646\pi$
$709$	−7821.72	−	13547.6i	−0.414317	−	0.717618i	−0.995356	+	0.0962572i	$0.969313\pi$
$710$	3848.67			0.203434
$711$		0			0
$712$	−7841.98			−0.412768
$713$	457.824	+	792.975i	0.0240472	+	0.0416510i
$714$		0			0
$715$	−10911.1	+	18898.6i	−0.570703	+	0.988486i
$716$	−9246.27	+	16015.0i	−0.482611	+	0.835907i
$717$		0			0
$718$	−355.379	−	615.535i	−0.0184716	−	0.0319938i
$719$	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
$722$	3659.86	+	6339.06i	0.188651	+	0.326752i
$723$		0			0
$724$	1197.20	−	2073.62i	0.0614554	−	0.106444i
$725$	247.063	−	427.925i	0.0126561	−	0.0219210i
$726$		0			0
$727$	7103.61	+	12303.8i	0.362391	+	0.627680i	0.988354	−	0.152173i	$-0.0486272\pi$
$727$	7103.61	+	12303.8i	0.362391	+	0.627680i	−0.625963	+	0.779853i	$0.715294\pi$
$728$	3725.53			0.189667
$729$		0			0
$730$	13172.8			0.667871
$731$	724.072	+	1254.13i	0.0366358	+	0.0634551i
$732$		0			0
$733$	−13265.3	+	22976.1i	−0.668437	+	1.15777i	0.309905	+	0.950768i	$0.399703\pi$
$733$	−13265.3	+	22976.1i	−0.668437	+	1.15777i	−0.978341	+	0.206998i	$0.933630\pi$
$734$	3167.43	−	5486.15i	0.159280	−	0.275882i
$735$		0			0
$736$	6597.36	+	11427.0i	0.330410	+	0.572288i
$737$	−17041.4			−0.851735
$738$		0			0
$739$	−5683.47			−0.282909			−0.141455	−	0.989945i	$-0.545178\pi$
$739$	−5683.47			−0.282909			−0.141455	+	0.989945i	$0.545178\pi$
$740$	5713.38	+	9895.86i	0.283822	+	0.491594i
$741$		0			0
$742$	−1728.44	+	2993.74i	−0.0855161	+	0.148118i
$743$	−7784.28	+	13482.8i	−0.384358	+	0.665727i	−0.991680	−	0.128729i	$-0.958910\pi$
$743$	−7784.28	+	13482.8i	−0.384358	+	0.665727i	0.607322	+	0.794456i	$0.292244\pi$
$744$		0			0
$745$	−7568.25	−	13108.6i	−0.372187	−	0.644647i
$746$	6539.50			0.320949
$747$		0			0
$748$	−8097.82			−0.395836
$749$	2633.01	+	4560.51i	0.128449	+	0.222480i
$750$		0			0
$751$	4130.82	−	7154.79i	0.200713	−	0.347646i	−0.748045	−	0.663648i	$-0.769007\pi$
$751$	4130.82	−	7154.79i	0.200713	−	0.347646i	0.948758	+	0.316002i	$0.102341\pi$
$752$	−691.499	+	1197.71i	−0.0335324	+	0.0580798i
$753$		0			0
$754$	−731.666	−	1267.28i	−0.0353391	−	0.0612092i
$755$	−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	$0.604100\pi$
$758$	1372.51	+	2377.25i	0.0657674	+	0.113913i
$759$		0			0
$760$	−3923.41	+	6795.55i	−0.187259	+	0.324343i
$761$	2724.92	−	4719.70i	0.129801	−	0.224821i	−0.793799	−	0.608181i	$-0.791900\pi$
$761$	2724.92	−	4719.70i	0.129801	−	0.224821i	0.923599	+	0.383359i	$0.125233\pi$
$762$		0			0
$763$	4545.08	+	7872.31i	0.215652	+	0.373521i
$764$	21320.8			1.00963
$765$		0			0
$766$	−1358.96			−0.0641009
$767$	14838.8	+	25701.6i	0.698564	+	1.20995i
$768$		0			0
$769$	9681.98	−	16769.7i	0.454020	−	0.786385i	−0.544612	−	0.838688i	$-0.683323\pi$
$769$	9681.98	−	16769.7i	0.454020	−	0.786385i	0.998631	+	0.0523033i	$0.0166563\pi$
$770$	2038.49	−	3530.77i	0.0954054	−	0.165247i
$771$		0			0
$772$	6774.62	+	11734.0i	0.315834	+	0.547041i
$773$	1865.54			0.0868033			0.0434017	−	0.999058i	$-0.486180\pi$
$773$	1865.54			0.0868033			0.0434017	+	0.999058i	$0.486180\pi$
$774$		0			0
$775$	−224.370			−0.0103995
$776$	726.725	+	1258.72i	0.0336184	+	0.0582288i
$777$		0			0
$778$	277.483	−	480.614i	0.0127869	−	0.0221476i
$779$	−4207.49	+	7287.58i	−0.193516	+	0.335179i
$780$		0			0
$781$	−7568.02	−	13108.2i	−0.346741	−	0.600574i
$782$	2306.59			0.105478
$783$		0			0
$784$	−7081.05			−0.322570
$785$	−16676.4	−	28884.4i	−0.758225	−	1.31328i
$786$		0			0
$787$	9603.65	−	16634.0i	0.434985	−	0.753416i	−0.562310	−	0.826927i	$-0.690087\pi$
$787$	9603.65	−	16634.0i	0.434985	−	0.753416i	0.997294	+	0.0735110i	$0.0234204\pi$
$788$	12157.6	−	21057.5i	0.549614	−	0.951959i
$789$		0			0
$790$	−9173.86	−	15889.6i	−0.413154	−	0.715603i
$791$	−8268.50			−0.371674
$792$		0			0
$793$	19584.7			0.877017
$794$	−2003.26	−	3469.76i	−0.0895380	−	0.155084i
$795$		0			0
$796$	−4756.89	+	8239.18i	−0.211813	+	0.366872i
$797$	93.0372	−	161.145i	0.00413494	−	0.00716193i	−0.863951	−	0.503577i	$-0.832017\pi$
$797$	93.0372	−	161.145i	0.00413494	−	0.00716193i	0.868085	+	0.496415i	$0.165350\pi$
$798$		0			0
$799$	731.686	+	1267.32i	0.0323970	+	0.0561132i
$800$	−3233.23			−0.142890
$801$		0			0
$802$	13978.3			0.615452
$803$	−25902.9	−	44865.2i	−1.13835	−	1.97168i
$804$		0			0
$805$	1886.05	−	3266.73i	0.0825771	−	0.143028i
$806$	−332.232	+	575.442i	−0.0145191	+	0.0251477i
$807$		0			0
$808$	10537.3	+	18251.2i	0.458790	+	0.794647i
$809$	−5903.09			−0.256541			−0.128270	−	0.991739i	$-0.540943\pi$
$809$	−5903.09			−0.256541			−0.128270	+	0.991739i	$0.540943\pi$
$810$		0			0
$811$	23111.0			1.00066			0.500331	−	0.865834i	$-0.333212\pi$
$811$	23111.0			1.00066			0.500331	+	0.865834i	$0.333212\pi$
$812$	−444.011	−	769.050i	−0.0191893	−	0.0332369i
$813$		0			0
$814$	−6917.58	+	11981.6i	−0.297863	+	0.515915i
$815$	4914.32	−	8511.85i	0.211216	−	0.365837i
$816$		0			0
$817$	−1195.64	−	2070.90i	−0.0511995	−	0.0886802i
$818$	9488.29			0.405563
$819$		0			0
$820$	13671.5			0.582231
$821$	−4822.14	−	8352.20i	−0.204987	−	0.355047i	0.745142	−	0.666906i	$-0.232382\pi$
$821$	−4822.14	−	8352.20i	−0.204987	−	0.355047i	−0.950128	+	0.311859i	$0.899048\pi$
$822$		0			0
$823$	16786.7	−	29075.5i	0.710994	−	1.23148i	−0.253490	−	0.967338i	$-0.581578\pi$
$823$	16786.7	−	29075.5i	0.710994	−	1.23148i	0.964484	−	0.264140i	$-0.0850882\pi$
$824$	−10575.5	+	18317.3i	−0.447106	+	0.774410i
$825$		0			0
$826$	−2772.29	−	4801.75i	−0.116780	−	0.202269i
$827$	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	$0.704899\pi$
$830$	−5080.25	−	8799.24i	−0.212455	−	0.367983i
$831$		0			0
$832$	−1427.43	+	2472.38i	−0.0594799	+	0.103022i
$833$	−3746.29	+	6488.76i	−0.155824	+	0.269895i
$834$		0			0
$835$	−3557.48	−	6161.74i	−0.147439	−	0.255372i
$836$	13371.7			0.553192
$837$		0			0
$838$	−7026.51			−0.289650
$839$	356.480	+	617.441i	0.0146687	+	0.0254070i	0.873267	−	0.487243i	$-0.161997\pi$
$839$	356.480	+	617.441i	0.0146687	+	0.0254070i	−0.858598	+	0.512650i	$0.828664\pi$
$840$		0			0
$841$	11792.0	−	20424.4i	0.483497	−	0.837441i
$842$	−1280.68	+	2218.20i	−0.0524169	+	0.0907887i
$843$		0			0
$844$	5345.30	+	9258.32i	0.218001	+	0.377588i
$845$	8136.29			0.331239
$846$		0			0
$847$	−9223.44			−0.374169
$848$	5501.69	+	9529.21i	0.222793	+	0.385890i
$849$		0			0
$850$	−282.603	+	489.484i	−0.0114038	+	0.0197519i
$851$	−6400.27	+	11085.6i	−0.257812	+	0.446544i
$852$		0			0
$853$	15183.6	+	26298.8i	0.609469	+	1.05563i	0.991328	+	0.131411i	$0.0419508\pi$
$853$	15183.6	+	26298.8i	0.609469	+	1.05563i	−0.381859	+	0.924221i	$0.624716\pi$
$854$	−3658.96			−0.146612
$855$		0			0
$856$	−19937.1			−0.796069
$857$	4540.35	+	7864.12i	0.180975	+	0.313458i	0.942213	−	0.335015i	$-0.108741\pi$
$857$	4540.35	+	7864.12i	0.180975	+	0.313458i	−0.761238	+	0.648473i	$0.775408\pi$
$858$		0			0
$859$	−13080.1	+	22655.4i	−0.519543	+	0.899874i	0.480199	+	0.877159i	$0.340564\pi$
$859$	−13080.1	+	22655.4i	−0.519543	+	0.899874i	−0.999742	+	0.0227150i	$0.992769\pi$
$860$	−1942.50	+	3364.52i	−0.0770219	+	0.133406i
$861$		0			0
$862$	−2806.76	−	4861.45i	−0.110903	−	0.192090i
$863$	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
$866$	−434.362	−	752.338i	−0.0170442	−	0.0295213i
$867$		0			0
$868$	−201.615	+	349.207i	−0.00788392	+	0.0136554i
$869$	−36079.0	+	62490.6i	−1.40839	+	2.43941i
$870$		0			0
$871$	−5720.87	−	9908.84i	−0.222554	−	0.385474i
$872$	−34415.2			−1.33652
$873$		0			0
$874$	−3808.80			−0.147408
$875$	3779.24	+	6545.84i	0.146013	+	0.252903i
$876$		0			0
$877$	−12626.1	+	21869.0i	−0.486149	+	0.842036i	−0.999873	−	0.0159201i	$-0.994932\pi$
$877$	−12626.1	+	21869.0i	−0.486149	+	0.842036i	0.513724	+	0.857956i	$0.328266\pi$
$878$	7757.86	−	13437.0i	0.298195	−	0.516489i
$879$		0			0
$880$	−6488.61	−	11238.6i	−0.248558	−	0.430515i
$881$	2049.26			0.0783670			0.0391835	−	0.999232i	$-0.487524\pi$
$881$	2049.26			0.0783670			0.0391835	+	0.999232i	$0.487524\pi$
$882$		0			0
$883$	39413.4			1.50211			0.751057	−	0.660237i	$-0.229544\pi$
$883$	39413.4			1.50211			0.751057	+	0.660237i	$0.229544\pi$
$884$	−2718.47	−	4708.53i	−0.103430	−	0.179146i
$885$		0			0
$886$	−5682.14	+	9841.75i	−0.215457	+	0.373183i
$887$	18484.2	−	32015.6i	0.699707	−	1.21193i	−0.268861	−	0.963179i	$-0.586647\pi$
$887$	18484.2	−	32015.6i	0.699707	−	1.21193i	0.968568	−	0.248749i	$-0.0800194\pi$
$888$		0			0
$889$	−3085.72	−	5344.63i	−0.116414	−	0.201634i
$890$	−5761.86			−0.217009
$891$		0			0
$892$	15548.7			0.583641
$893$	−1208.21	−	2092.68i	−0.0452757	−	0.0784198i
$894$		0			0
$895$	−15678.8	+	27156.5i	−0.585570	+	1.01424i
$896$	−3533.07	+	6119.46i	−0.131732	+	0.228166i
$897$		0			0
$898$	4726.41	+	8186.38i	0.175637	+	0.304213i
$899$	365.525			0.0135605
$900$		0			0
$901$	11642.9			0.430499
$902$	8276.50	+	14335.3i	0.305518	+	0.529173i
$903$		0			0
$904$	15652.2	−	27110.4i	0.575868	−	0.997432i
$905$	2030.09	−	3516.21i	0.0745662	−	0.129152i
$906$		0			0
$907$	−1355.31	−	2347.47i	−0.0496167	−	0.0859386i	0.840150	−	0.542353i	$-0.182467\pi$
$907$	−1355.31	−	2347.47i	−0.0496167	−	0.0859386i	−0.889767	+	0.456415i	$0.849133\pi$
$908$	−18309.3			−0.669180
$909$		0			0
$910$	2737.32			0.0997156
$911$	11498.3	+	19915.6i	0.418172	+	0.724296i	0.995756	−	0.0920360i	$-0.0293375\pi$
$911$	11498.3	+	19915.6i	0.418172	+	0.724296i	−0.577583	+	0.816332i	$0.696004\pi$
$912$		0			0
$913$	−19979.6	+	34605.7i	−0.724237	+	1.25441i
$914$	−2939.15	+	5090.77i	−0.106366	+	0.184231i
$915$		0			0
$916$	−13167.4	−	22806.7i	−0.474961	−	0.822657i
$917$	−5259.38			−0.189400
$918$		0			0
$919$	−39103.8			−1.40361			−0.701804	−	0.712370i	$-0.747622\pi$
$919$	−39103.8			−1.40361			−0.701804	+	0.712370i	$0.747622\pi$
$920$	7140.55	+	12367.8i	0.255888	+	0.443211i
$921$		0			0
$922$	9453.86	−	16374.6i	0.337686	−	0.584889i
$923$	5081.23	−	8800.94i	0.181203	−	0.313853i
$924$		0			0
$925$	−1568.32	−	2716.41i	−0.0557470	−	0.0965567i
$926$	7869.39			0.279270
$927$		0			0
$928$	5267.30			0.186323
$929$	−17977.3	−	31137.6i	−0.634894	−	1.09967i	−0.986538	−	0.163534i	$-0.947711\pi$
$929$	−17977.3	−	31137.6i	−0.634894	−	1.09967i	0.351644	−	0.936134i	$-0.385623\pi$
$930$		0			0
$931$	6186.12	−	10714.7i	0.217768	−	0.377185i
$932$	17070.1	−	29566.3i	0.599946	−	1.03914i
$933$		0			0
$934$	−6141.62	−	10637.6i	−0.215161	−	0.372669i
$935$	−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	$0.540416\pi$
$938$	1068.81	+	1851.24i	0.0372047	+	0.0644404i
$939$		0			0
$940$	−1962.93	+	3399.90i	−0.0681104	+	0.117971i
$941$	3739.45	−	6476.92i	0.129546	−	0.224380i	−0.793955	−	0.607977i	$-0.791981\pi$
$941$	3739.45	−	6476.92i	0.129546	−	0.224380i	0.923501	+	0.383597i	$0.125315\pi$
$942$		0			0
$943$	7657.57	+	13263.3i	0.264438	+	0.458020i
$944$	−17648.7			−0.608490
$945$		0			0
$946$	−4703.84			−0.161665
$947$	6745.68	+	11683.9i	0.231473	+	0.400923i	0.958242	−	0.285959i	$-0.0923121\pi$
$947$	6745.68	+	11683.9i	0.231473	+	0.400923i	−0.726769	+	0.686882i	$0.758979\pi$
$948$		0			0
$949$	17391.4	−	30122.8i	0.594889	−	1.03038i
$950$	466.654	−	808.268i	0.0159371	−	0.0276039i
$951$		0			0
$952$	1172.13	+	2030.18i	0.0399042	+	0.0691161i
$953$	13981.6			0.475246			0.237623	−	0.971357i	$-0.423632\pi$
$953$	13981.6			0.475246			0.237623	+	0.971357i	$0.423632\pi$
$954$		0			0
$955$	36153.5			1.22503
$956$	−4311.24	−	7467.29i	−0.145853	−	0.252625i
$957$		0			0
$958$	6642.54	−	11505.2i	0.224019	−	0.388013i
$959$	3225.93	−	5587.48i	0.108624	−	0.188143i
$960$		0			0
$961$	14812.5	+	25656.0i	0.497214	+	0.861200i
$962$	−9289.02			−0.311320
$963$		0			0
$964$	−3832.64			−0.128051
$965$	11487.7	+	19897.2i	0.383213	+	0.663745i
$966$		0			0
$967$	4540.73	−	7864.78i	0.151003	−	0.261545i	−0.780593	−	0.625039i	$-0.785083\pi$
$967$	4540.73	−	7864.78i	0.151003	−	0.261545i	0.931597	+	0.363494i	$0.118416\pi$
$968$	17459.9	−	30241.4i	0.579734	−	1.00413i
$969$		0			0
$970$	533.958	+	924.842i	0.0176746	+	0.0306133i
$971$	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
$974$	−5972.62	−	10344.9i	−0.196484	−	0.340320i
$975$		0			0
$976$	−5823.31	+	10086.3i	−0.190983	+	0.330793i
$977$	5427.45	−	9400.63i	0.177727	−	0.307833i	−0.763374	−	0.645956i	$-0.776459\pi$
$977$	5427.45	−	9400.63i	0.177727	−	0.307833i	0.941102	+	0.338123i	$0.109792\pi$
$978$		0			0
$979$	11330.1	+	19624.3i	0.369880	+	0.640650i
$980$	−20100.7			−0.655198
$981$		0			0
$982$	21401.7			0.695474
$983$	−3755.05	−	6503.94i	−0.121839	−	0.211031i	0.798654	−	0.601790i	$-0.205546\pi$
$983$	−3755.05	−	6503.94i	−0.121839	−	0.211031i	−0.920493	+	0.390759i	$0.872212\pi$
$984$		0			0
$985$	20615.5	−	35707.1i	0.666867	−	1.15505i
$986$	460.393	−	797.424i	0.0148701	−	0.0257557i
$987$		0			0
$988$	4488.92	+	7775.04i	0.144546	+	0.250361i
$989$	−4352.08			−0.139927
$990$		0			0
$991$	46125.6			1.47854			0.739268	−	0.673412i	$-0.235172\pi$
$991$	46125.6			1.47854			0.739268	+	0.673412i	$0.235172\pi$
$992$	−1195.88	−	2071.32i	−0.0382753	−	0.0662947i
$993$		0			0
$994$	−949.311	+	1644.25i	−0.0302921	+	0.0524674i
$995$	−8066.22	+	13971.1i	−0.257001	+	0.445139i
$996$		0			0
$997$	−22675.0	−	39274.3i	−0.720287	−	1.24757i	−0.960885	−	0.276948i	$-0.910677\pi$
$997$	−22675.0	−	39274.3i	−0.720287	−	1.24757i	0.240598	−	0.970625i	$-0.422656\pi$
$998$	−13306.0			−0.422039
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.4.c.a.4.2	✓	4	3.2	odd	2
9.4.c.a.7.2	yes	4	9.2	odd	6
27.4.c.a.10.1		4	1.1	even	1	trivial
27.4.c.a.19.1		4	9.7	even	3	inner
81.4.a.a.1.2		2	9.4	even	3
81.4.a.d.1.1		2	9.5	odd	6
144.4.i.c.49.2		4	12.11	even	2
144.4.i.c.97.2		4	36.11	even	6
225.4.e.b.76.1		4	15.14	odd	2
225.4.e.b.151.1		4	45.29	odd	6
225.4.k.b.49.2		8	15.2	even	4
225.4.k.b.49.3		8	15.8	even	4
225.4.k.b.124.2		8	45.38	even	12
225.4.k.b.124.3		8	45.2	even	12
432.4.i.c.145.2		4	4.3	odd	2
432.4.i.c.289.2		4	36.7	odd	6
1296.4.a.i.1.1		2	36.31	odd	6
1296.4.a.u.1.2		2	36.23	even	6
2025.4.a.g.1.2		2	45.14	odd	6
2025.4.a.n.1.1		2	45.4	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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	27.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.686141 - 1.18843i) q^{2} +(3.05842 - 5.29734i) q^{4} +(5.18614 - 8.98266i) q^{5} +(2.55842 + 4.43132i) q^{7} -19.3723 q^{8} -14.2337 q^{10} +(27.9891 + 48.4786i) q^{11} +(-18.7921 + 32.5489i) q^{13} +(3.51087 - 6.08101i) q^{14} +(-11.1753 - 19.3561i) q^{16} -23.6495 q^{17} +39.0516 q^{19} +(-31.7228 - 54.9455i) q^{20} +(38.4090 - 66.5263i) q^{22} +(35.5367 - 61.5513i) q^{23} +(8.70789 + 15.0825i) q^{25} +51.5761 q^{26} +31.2989 q^{28} +(-14.1861 - 24.5711i) q^{29} +(-6.44158 + 11.1571i) q^{31} +(-92.8247 + 160.777i) q^{32} +(16.2269 + 28.1057i) q^{34} +53.0733 q^{35} -180.103 q^{37} +(-26.7949 - 46.4101i) q^{38} +(-100.467 + 174.015i) q^{40} +(-107.742 + 186.614i) q^{41} +(-30.6168 - 53.0299i) q^{43} +342.410 q^{44} -97.5326 q^{46} +(-30.9388 - 53.5876i) q^{47} +(158.409 - 274.372i) q^{49} +(11.9497 - 20.6974i) q^{50} +(114.948 + 199.096i) q^{52} -492.310 q^{53} +580.622 q^{55} +(-49.5625 - 85.8447i) q^{56} +(-19.4674 + 33.7185i) q^{58} +(394.815 - 683.840i) q^{59} +(-260.545 - 451.277i) q^{61} +17.6793 q^{62} +75.9590 q^{64} +(194.917 + 337.606i) q^{65} +(-152.215 + 263.644i) q^{67} +(-72.3301 + 125.279i) q^{68} +(-36.4158 - 63.0740i) q^{70} -270.391 q^{71} -925.464 q^{73} +(123.576 + 214.040i) q^{74} +(119.436 - 206.870i) q^{76} +(-143.216 + 248.057i) q^{77} +(644.517 + 1116.34i) q^{79} -231.826 q^{80} +295.704 q^{82} +(356.917 + 618.198i) q^{83} +(-122.649 + 212.435i) q^{85} +(-42.0149 + 72.7720i) q^{86} +(-542.213 - 939.141i) q^{88} +404.804 q^{89} -192.313 q^{91} +(-217.372 - 376.500i) q^{92} +(-42.4567 + 73.5372i) q^{94} +(202.527 - 350.787i) q^{95} +(-37.5137 - 64.9756i) q^{97} -434.763 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 5 q^{4} + 15 q^{5} - 7 q^{7} - 66 q^{8} + 12 q^{10} + 66 q^{11} + 11 q^{13} + 60 q^{14} + 7 q^{16} - 198 q^{17} - 154 q^{19} - 12 q^{20} + 33 q^{22} + 33 q^{23} + 121 q^{25} + 528 q^{26}+ \cdots + 846 q^{98}+O(q^{100}) \) 4 * q + 3 * q^2 - 5 * q^4 + 15 * q^5 - 7 * q^7 - 66 * q^8 + 12 * q^10 + 66 * q^11 + 11 * q^13 + 60 * q^14 + 7 * q^16 - 198 * q^17 - 154 * q^19 - 12 * q^20 + 33 * q^22 + 33 * q^23 + 121 * q^25 + 528 * q^26 + 332 * q^28 - 51 * q^29 - 43 * q^31 - 423 * q^32 - 297 * q^34 - 6 * q^35 - 100 * q^37 - 561 * q^38 - 264 * q^40 + 132 * q^41 - 88 * q^43 + 462 * q^44 - 528 * q^46 + 399 * q^47 + 513 * q^49 - 429 * q^50 + 770 * q^52 - 108 * q^53 + 1254 * q^55 + 66 * q^56 + 60 * q^58 + 798 * q^59 - 439 * q^61 - 228 * q^62 - 1454 * q^64 + 165 * q^65 - 988 * q^67 + 693 * q^68 - 318 * q^70 - 2736 * q^71 - 910 * q^73 + 816 * q^74 + 1529 * q^76 - 165 * q^77 + 803 * q^79 - 192 * q^80 + 3630 * q^82 + 813 * q^83 - 594 * q^85 + 33 * q^86 - 1221 * q^88 + 792 * q^89 - 1562 * q^91 - 858 * q^92 - 2100 * q^94 - 132 * q^95 - 736 * q^97 + 846 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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