LMFDB - Embedded newform 9.4.c.a.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,4,Mod(4,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("9.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	9.c (of order $3$, degree $2$, 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:	$0.531017190052$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.2
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	9.7
Dual form			9.4.c.a.4.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.686141 - 1.18843i) q^{2} +(-5.05842 + 1.18843i) q^{3} +(3.05842 + 5.29734i) q^{4} +(-5.18614 - 8.98266i) q^{5} +(-2.05842 + 6.82701i) q^{6} +(2.55842 - 4.43132i) q^{7} +19.3723 q^{8} +(24.1753 - 12.0232i) q^{9} +O(q^{10})$	\(q+(0.686141 - 1.18843i) q^{2} +(-5.05842 + 1.18843i) q^{3} +(3.05842 + 5.29734i) q^{4} +(-5.18614 - 8.98266i) q^{5} +(-2.05842 + 6.82701i) q^{6} +(2.55842 - 4.43132i) q^{7} +19.3723 q^{8} +(24.1753 - 12.0232i) q^{9} -14.2337 q^{10} +(-27.9891 + 48.4786i) q^{11} +(-21.7663 - 23.1615i) q^{12} +(-18.7921 - 32.5489i) q^{13} +(-3.51087 - 6.08101i) q^{14} +(36.9090 + 39.2747i) q^{15} +(-11.1753 + 19.3561i) q^{16} +23.6495 q^{17} +(2.29894 - 36.9802i) q^{18} +39.0516 q^{19} +(31.7228 - 54.9455i) q^{20} +(-7.67527 + 25.4560i) q^{21} +(38.4090 + 66.5263i) q^{22} +(-35.5367 - 61.5513i) q^{23} +(-97.9932 + 23.0226i) q^{24} +(8.70789 - 15.0825i) q^{25} -51.5761 q^{26} +(-108.000 + 89.5489i) q^{27} +31.2989 q^{28} +(14.1861 - 24.5711i) q^{29} +(72.0000 - 16.9157i) q^{30} +(-6.44158 - 11.1571i) q^{31} +(92.8247 + 160.777i) q^{32} +(83.9674 - 278.488i) q^{33} +(16.2269 - 28.1057i) q^{34} -53.0733 q^{35} +(137.629 + 91.2927i) q^{36} -180.103 q^{37} +(26.7949 - 46.4101i) q^{38} +(133.741 + 142.313i) q^{39} +(-100.467 - 174.015i) q^{40} +(107.742 + 186.614i) q^{41} +(24.9863 + 26.5879i) q^{42} +(-30.6168 + 53.0299i) q^{43} -342.410 q^{44} +(-233.376 - 154.804i) q^{45} -97.5326 q^{46} +(30.9388 - 53.5876i) q^{47} +(33.5258 - 111.192i) q^{48} +(158.409 + 274.372i) q^{49} +(-11.9497 - 20.6974i) q^{50} +(-119.629 + 28.1057i) q^{51} +(114.948 - 199.096i) q^{52} +492.310 q^{53} +(32.3194 + 189.794i) q^{54} +580.622 q^{55} +(49.5625 - 85.8447i) q^{56} +(-197.539 + 46.4101i) q^{57} +(-19.4674 - 33.7185i) q^{58} +(-394.815 - 683.840i) q^{59} +(-95.1684 + 315.638i) q^{60} +(-260.545 + 451.277i) q^{61} -17.6793 q^{62} +(8.57207 - 137.889i) q^{63} +75.9590 q^{64} +(-194.917 + 337.606i) q^{65} +(-273.351 - 290.872i) q^{66} +(-152.215 - 263.644i) q^{67} +(72.3301 + 125.279i) q^{68} +(252.909 + 269.120i) q^{69} +(-36.4158 + 63.0740i) q^{70} +270.391 q^{71} +(468.330 - 232.916i) q^{72} -925.464 q^{73} +(-123.576 + 214.040i) q^{74} +(-26.1237 + 86.6424i) q^{75} +(119.436 + 206.870i) q^{76} +(143.216 + 248.057i) q^{77} +(260.894 - 61.2946i) q^{78} +(644.517 - 1116.34i) q^{79} +231.826 q^{80} +(439.887 - 581.326i) q^{81} +295.704 q^{82} +(-356.917 + 618.198i) q^{83} +(-158.323 + 37.1966i) q^{84} +(-122.649 - 212.435i) q^{85} +(42.0149 + 72.7720i) q^{86} +(-42.5584 + 141.150i) q^{87} +(-542.213 + 939.141i) q^{88} -404.804 q^{89} +(-344.103 + 171.134i) q^{90} -192.313 q^{91} +(217.372 - 376.500i) q^{92} +(45.8437 + 48.7822i) q^{93} +(-42.4567 - 73.5372i) q^{94} +(-202.527 - 350.787i) q^{95} +(-660.619 - 702.963i) q^{96} +(-37.5137 + 64.9756i) q^{97} +434.763 q^{98} +(-93.7785 + 1508.50i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - 3 q^{3} - 5 q^{4} - 15 q^{5} + 9 q^{6} - 7 q^{7} + 66 q^{8} + 45 q^{9}+O(q^{10}) $ 4 * q - 3 * q^2 - 3 * q^3 - 5 * q^4 - 15 * q^5 + 9 * q^6 - 7 * q^7 + 66 * q^8 + 45 * q^9	\( 4 q - 3 q^{2} - 3 q^{3} - 5 q^{4} - 15 q^{5} + 9 q^{6} - 7 q^{7} + 66 q^{8} + 45 q^{9} + 12 q^{10} - 66 q^{11} - 156 q^{12} + 11 q^{13} - 60 q^{14} + 27 q^{15} + 7 q^{16} + 198 q^{17} + 216 q^{18} - 154 q^{19} + 12 q^{20} + 21 q^{21} + 33 q^{22} - 33 q^{23} - 99 q^{24} + 121 q^{25} - 528 q^{26} - 432 q^{27} + 332 q^{28} + 51 q^{29} + 288 q^{30} - 43 q^{31} + 423 q^{32} + 198 q^{33} - 297 q^{34} + 6 q^{35} - 225 q^{36} - 100 q^{37} + 561 q^{38} + 759 q^{39} - 264 q^{40} - 132 q^{41} - 486 q^{42} - 88 q^{43} - 462 q^{44} - 675 q^{45} - 528 q^{46} - 399 q^{47} - 21 q^{48} + 513 q^{49} + 429 q^{50} + 297 q^{51} + 770 q^{52} + 108 q^{53} + 1215 q^{54} + 1254 q^{55} - 66 q^{56} - 1221 q^{57} + 60 q^{58} - 798 q^{59} - 36 q^{60} - 439 q^{61} + 228 q^{62} + 603 q^{63} - 1454 q^{64} - 165 q^{65} - 990 q^{66} - 988 q^{67} - 693 q^{68} + 891 q^{69} - 318 q^{70} + 2736 q^{71} + 891 q^{72} - 910 q^{73} - 816 q^{74} - 363 q^{75} + 1529 q^{76} + 165 q^{77} - 990 q^{78} + 803 q^{79} + 192 q^{80} - 567 q^{81} + 3630 q^{82} - 813 q^{83} + 642 q^{84} - 594 q^{85} - 33 q^{86} - 153 q^{87} - 1221 q^{88} - 792 q^{89} - 756 q^{90} - 1562 q^{91} + 858 q^{92} - 213 q^{93} - 2100 q^{94} + 132 q^{95} + 1080 q^{96} - 736 q^{97} - 846 q^{98} + 297 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 - 3 * q^3 - 5 * q^4 - 15 * q^5 + 9 * q^6 - 7 * q^7 + 66 * q^8 + 45 * q^9 + 12 * q^10 - 66 * q^11 - 156 * q^12 + 11 * q^13 - 60 * q^14 + 27 * q^15 + 7 * q^16 + 198 * q^17 + 216 * q^18 - 154 * q^19 + 12 * q^20 + 21 * q^21 + 33 * q^22 - 33 * q^23 - 99 * q^24 + 121 * q^25 - 528 * q^26 - 432 * q^27 + 332 * q^28 + 51 * q^29 + 288 * q^30 - 43 * q^31 + 423 * q^32 + 198 * q^33 - 297 * q^34 + 6 * q^35 - 225 * q^36 - 100 * q^37 + 561 * q^38 + 759 * q^39 - 264 * q^40 - 132 * q^41 - 486 * q^42 - 88 * q^43 - 462 * q^44 - 675 * q^45 - 528 * q^46 - 399 * q^47 - 21 * q^48 + 513 * q^49 + 429 * q^50 + 297 * q^51 + 770 * q^52 + 108 * q^53 + 1215 * q^54 + 1254 * q^55 - 66 * q^56 - 1221 * q^57 + 60 * q^58 - 798 * q^59 - 36 * q^60 - 439 * q^61 + 228 * q^62 + 603 * q^63 - 1454 * q^64 - 165 * q^65 - 990 * q^66 - 988 * q^67 - 693 * q^68 + 891 * q^69 - 318 * q^70 + 2736 * q^71 + 891 * q^72 - 910 * q^73 - 816 * q^74 - 363 * q^75 + 1529 * q^76 + 165 * q^77 - 990 * q^78 + 803 * q^79 + 192 * q^80 - 567 * q^81 + 3630 * q^82 - 813 * q^83 + 642 * q^84 - 594 * q^85 - 33 * q^86 - 153 * q^87 - 1221 * q^88 - 792 * q^89 - 756 * q^90 - 1562 * q^91 + 858 * q^92 - 213 * q^93 - 2100 * q^94 + 132 * q^95 + 1080 * q^96 - 736 * q^97 - 846 * q^98 + 297 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.686141	−	1.18843i	0.242587	−	0.420174i	−0.718863	−	0.695152i	$-0.755337\pi$
$2$	0.686141	−	1.18843i	0.242587	−	0.420174i	0.961451	+	0.274978i	$0.0886706\pi$
$3$	−5.05842	+	1.18843i	−0.973494	+	0.228714i
$3$	−5.05842	+	1.18843i	−0.973494	+	0.228714i
$4$	3.05842	+	5.29734i	0.382303	+	0.662168i
$5$	−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	$0.986870\pi$
$6$	−2.05842	+	6.82701i	−0.140058	+	0.464519i
$7$	2.55842	−	4.43132i	0.138142	−	0.239269i	−0.788651	−	0.614841i	$-0.789220\pi$
$7$	2.55842	−	4.43132i	0.138142	−	0.239269i	0.926793	+	0.375572i	$0.122554\pi$
$8$	19.3723			0.856142
$9$	24.1753	−	12.0232i	0.895380	−	0.445302i
$10$	−14.2337			−0.450109
$11$	−27.9891	+	48.4786i	−0.767185	+	1.32880i	0.171898	+	0.985115i	$0.445010\pi$
$11$	−27.9891	+	48.4786i	−0.767185	+	1.32880i	−0.939083	+	0.343689i	$0.888323\pi$
$12$	−21.7663	−	23.1615i	−0.523616	−	0.557178i
$13$	−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	$0.964644\pi$
$14$	−3.51087	−	6.08101i	−0.0670229	−	0.116087i
$15$	36.9090	+	39.2747i	0.635323	+	0.676046i
$16$	−11.1753	+	19.3561i	−0.174614	+	0.302440i
$17$	23.6495			0.337402			0.168701	−	0.985667i	$-0.446043\pi$
$17$	23.6495			0.337402			0.168701	+	0.985667i	$0.446043\pi$
$18$	2.29894	−	36.9802i	0.0301036	−	0.484240i
$19$	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
$21$	−7.67527	+	25.4560i	−0.0797562	+	0.264521i
$22$	38.4090	+	66.5263i	0.372219	+	0.644702i
$23$	−35.5367	−	61.5513i	−0.322170	−	0.558015i	0.658766	−	0.752348i	$-0.271079\pi$
$23$	−35.5367	−	61.5513i	−0.322170	−	0.558015i	−0.980936	+	0.194334i	$0.937746\pi$
$24$	−97.9932	+	23.0226i	−0.833449	+	0.195811i
$25$	8.70789	−	15.0825i	0.0696631	−	0.120660i
$26$	−51.5761			−0.389035
$27$	−108.000	+	89.5489i	−0.769800	+	0.638285i
$28$	31.2989			0.211248
$29$	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	$0.137712\pi$
$30$	72.0000	−	16.9157i	0.438178	−	0.102946i
$31$	−6.44158	−	11.1571i	−0.0373207	−	0.0646413i	0.846762	−	0.531972i	$-0.178549\pi$
$31$	−6.44158	−	11.1571i	−0.0373207	−	0.0646413i	−0.884082	+	0.467331i	$0.845216\pi$
$32$	92.8247	+	160.777i	0.512789	+	0.888177i
$33$	83.9674	−	278.488i	0.442935	−	1.46905i
$34$	16.2269	−	28.1057i	0.0818495	−	0.141768i
$35$	−53.0733			−0.256315
$36$	137.629	+	91.2927i	0.637171	+	0.422652i
$37$	−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
$39$	133.741	+	142.313i	0.549119	+	0.584315i
$40$	−100.467	−	174.015i	−0.397132	−	0.687853i
$41$	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	$0.698722\pi$
$42$	24.9863	+	26.5879i	0.0917971	+	0.0976810i
$43$	−30.6168	+	53.0299i	−0.108582	+	0.188069i	−0.915196	−	0.403009i	$-0.867964\pi$
$43$	−30.6168	+	53.0299i	−0.108582	+	0.188069i	0.806614	+	0.591078i	$0.201298\pi$
$44$	−342.410			−1.17319
$45$	−233.376	−	154.804i	−0.773104	−	0.512819i
$46$	−97.5326			−0.312617
$47$	30.9388	−	53.5876i	0.0960189	−	0.166310i	−0.814014	−	0.580845i	$-0.802722\pi$
$47$	30.9388	−	53.5876i	0.0960189	−	0.166310i	0.910033	+	0.414535i	$0.136056\pi$
$48$	33.5258	−	111.192i	0.100813	−	0.334359i
$49$	158.409	+	274.372i	0.461834	+	0.799919i
$50$	−11.9497	−	20.6974i	−0.0337988	−	0.0585412i
$51$	−119.629	+	28.1057i	−0.328459	+	0.0771685i
$52$	114.948	−	199.096i	0.306548	−	0.530956i
$53$	492.310			1.27592			0.637962	−	0.770068i	$-0.279778\pi$
$53$	492.310			1.27592			0.637962	+	0.770068i	$0.279778\pi$
$54$	32.3194	+	189.794i	0.0814466	+	0.478290i
$55$	580.622			1.42347
$56$	49.5625	−	85.8447i	0.118269	−	0.204848i
$57$	−197.539	+	46.4101i	−0.459031	+	0.107845i
$58$	−19.4674	−	33.7185i	−0.0440723	−	0.0763354i
$59$	−394.815	−	683.840i	−0.871196	−	1.50896i	−0.860761	−	0.509010i	$-0.830012\pi$
$59$	−394.815	−	683.840i	−0.871196	−	1.50896i	−0.0104351	−	0.999946i	$-0.503322\pi$
$60$	−95.1684	+	315.638i	−0.204770	+	0.679145i
$61$	−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	$0.982484\pi$
$62$	−17.6793			−0.0362141
$63$	8.57207	−	137.889i	0.0171425	−	0.275751i
$64$	75.9590			0.148358
$65$	−194.917	+	337.606i	−0.371946	+	0.644229i
$66$	−273.351	−	290.872i	−0.509805	−	0.542482i
$67$	−152.215	−	263.644i	−0.277552	−	0.480734i	0.693224	−	0.720722i	$-0.256190\pi$
$67$	−152.215	−	263.644i	−0.277552	−	0.480734i	−0.970776	+	0.239988i	$0.922856\pi$
$68$	72.3301	+	125.279i	0.128990	+	0.223417i
$69$	252.909	+	269.120i	0.441256	+	0.469539i
$70$	−36.4158	+	63.0740i	−0.0621788	+	0.107697i
$71$	270.391			0.451966			0.225983	−	0.974131i	$-0.427441\pi$
$71$	270.391			0.451966			0.225983	+	0.974131i	$0.427441\pi$
$72$	468.330	−	232.916i	0.766573	−	0.381242i
$73$	−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
$75$	−26.1237	+	86.6424i	−0.0402200	+	0.133395i
$76$	119.436	+	206.870i	0.180267	+	0.312231i
$77$	143.216	+	248.057i	0.211961	+	0.367127i
$78$	260.894	−	61.2946i	0.378723	−	0.0889776i
$79$	644.517	−	1116.34i	0.917897	−	1.58984i	0.115294	−	0.993331i	$-0.463219\pi$
$79$	644.517	−	1116.34i	0.917897	−	1.58984i	0.802603	−	0.596513i	$-0.203448\pi$
$80$	231.826			0.323987
$81$	439.887	−	581.326i	0.603411	−	0.797430i
$82$	295.704			0.398232
$83$	−356.917	+	618.198i	−0.472009	+	0.817543i	−0.999487	−	0.0320252i	$-0.989804\pi$
$83$	−356.917	+	618.198i	−0.472009	+	0.817543i	0.527478	+	0.849569i	$0.323138\pi$
$84$	−158.323	+	37.1966i	−0.205649	+	0.0483153i
$85$	−122.649	−	212.435i	−0.156508	−	0.271080i
$86$	42.0149	+	72.7720i	0.0526812	+	0.0912466i
$87$	−42.5584	+	141.150i	−0.0524453	+	0.173941i
$88$	−542.213	+	939.141i	−0.656820	+	1.13764i
$89$	−404.804			−0.482125			−0.241063	−	0.970510i	$-0.577496\pi$
$89$	−404.804			−0.482125			−0.241063	+	0.970510i	$0.577496\pi$
$90$	−344.103	+	171.134i	−0.403018	+	0.200435i
$91$	−192.313			−0.221537
$92$	217.372	−	376.500i	0.246333	−	0.426661i
$93$	45.8437	+	48.7822i	0.0511158	+	0.0543922i
$94$	−42.4567	−	73.5372i	−0.0465859	−	0.0806892i
$95$	−202.527	−	350.787i	−0.218725	−	0.378842i
$96$	−660.619	−	702.963i	−0.702335	−	0.747353i
$97$	−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	$0.179169\pi$
$98$	434.763			0.448140
$99$	−93.7785	+	1508.50i	−0.0952029	+	1.53141i
$100$	106.530			0.106530
$101$	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	$-0.0133536\pi$
$102$	−48.6806	+	161.455i	−0.0472558	+	0.156730i
$103$	545.909	+	945.542i	0.522233	+	0.904534i	0.999665	+	0.0258657i	$0.00823423\pi$
$103$	545.909	+	945.542i	0.522233	+	0.904534i	−0.477432	+	0.878669i	$0.658432\pi$
$104$	−364.046	−	630.546i	−0.343247	−	0.594521i
$105$	268.467	−	63.0740i	0.249521	−	0.0586228i
$106$	337.794	−	585.076i	0.309523	−	0.536109i
$107$	−1029.15			−0.929833			−0.464917	−	0.885354i	$-0.653916\pi$
$107$	−1029.15			−0.929833			−0.464917	+	0.885354i	$0.653916\pi$
$108$	−804.681	−	298.235i	−0.716948	−	0.265719i
$109$	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
$111$	911.038	−	214.040i	0.779026	−	0.183025i
$112$	57.1821	+	99.0423i	0.0482429	+	0.0835591i
$113$	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	$0.598498\pi$
$114$	−80.3847	+	266.606i	−0.0660413	+	0.219034i
$115$	−368.596	+	638.428i	−0.298885	+	0.517684i
$116$	173.549			0.138910
$117$	−845.645	−	560.937i	−0.668204	−	0.443237i
$118$	−1083.59			−0.845364
$119$	60.5053	−	104.798i	0.0466094	−	0.0807298i
$120$	715.011	+	760.841i	0.543927	+	0.578791i
$121$	−901.282	−	1561.07i	−0.677147	−	1.17285i
$122$	357.541	+	619.279i	0.265330	+	0.459564i
$123$	−766.781	−	815.930i	−0.562100	−	0.598130i
$124$	39.4021	−	68.2465i	0.0285356	−	0.0494251i
$125$	−1477.18			−1.05698
$126$	−157.989	−	104.798i	−0.111705	−	0.0740966i
$127$	−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
$129$	91.8505	−	304.634i	0.0626898	−	0.207919i
$130$	267.481	+	463.291i	0.180459	+	0.312564i
$131$	513.928	+	890.149i	0.342764	+	0.593684i	0.984945	−	0.172869i	$-0.0553036\pi$
$131$	513.928	+	890.149i	0.342764	+	0.593684i	−0.642181	+	0.766553i	$0.721970\pi$
$132$	1732.06	−	406.931i	1.14209	−	0.268324i
$133$	99.9105	−	173.050i	0.0651379	−	0.112822i
$134$	−417.763			−0.269322
$135$	1364.49	+	505.714i	0.869901	+	0.322407i
$136$	458.144			0.288864
$137$	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	$0.0380475\pi$
$138$	493.361	−	115.911i	0.304331	−	0.0714998i
$139$	−230.916	−	399.958i	−0.140907	−	0.244057i	0.786932	−	0.617040i	$-0.211668\pi$
$139$	−230.916	−	399.958i	−0.140907	−	0.244057i	−0.927838	+	0.372983i	$0.878335\pi$
$140$	−162.321	−	281.148i	−0.0979900	−	0.169724i
$141$	−92.8164	+	307.837i	−0.0554365	+	0.183862i
$142$	185.527	−	321.341i	0.109641	−	0.189904i
$143$	2103.90			1.23033
$144$	−37.4431	+	602.302i	−0.0216685	+	0.348554i
$145$	−294.285			−0.168545
$146$	−634.999	+	1099.85i	−0.359951	+	0.623454i
$147$	−1127.37	−	1199.63i	−0.632545	−	0.673089i
$148$	−550.832	−	954.068i	−0.305933	−	0.529891i
$149$	−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	$0.964734\pi$
$150$	85.0440	+	90.4950i	0.0462921	+	0.0492593i
$151$	−770.659	+	1334.82i	−0.415333	+	0.719378i	−0.995463	−	0.0951456i	$-0.969668\pi$
$151$	−770.659	+	1334.82i	−0.415333	+	0.719378i	0.580130	+	0.814524i	$0.303002\pi$
$152$	756.518			0.403696
$153$	571.732	−	284.341i	0.302103	−	0.150246i
$154$	393.065			0.205676
$155$	−66.8139	+	115.725i	−0.0346233	+	0.0599694i
$156$	−344.845	+	1143.72i	−0.176985	+	0.586994i
$157$	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	$0.528806\pi$
$158$	−884.459	−	1531.93i	−0.445341	−	0.771352i
$159$	−2490.31	+	585.076i	−1.24210	+	0.291821i
$160$	962.804	−	1667.63i	0.475727	−	0.823984i
$161$	−363.671			−0.178021
$162$	−389.042	−	921.647i	−0.188679	−	0.446984i
$163$	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
$165$	−2937.03	+	690.029i	−1.38574	+	0.325568i
$166$	489.791	+	848.342i	0.229007	+	0.396651i
$167$	−342.980	−	594.058i	−0.158926	−	0.275267i	0.775556	−	0.631279i	$-0.217470\pi$
$167$	−342.980	−	594.058i	−0.158926	−	0.275267i	−0.934481	+	0.356012i	$0.884136\pi$
$168$	−148.687	+	493.140i	−0.0682826	+	0.226468i
$169$	392.213	−	679.333i	0.178522	−	0.309209i
$170$	−336.619			−0.151868
$171$	944.083	−	469.524i	0.422198	−	0.209973i
$172$	−374.557			−0.166045
$173$	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	$0.00503566\pi$
$174$	138.546	+	147.427i	0.0603630	+	0.0642321i
$175$	−44.5569	−	77.1748i	−0.0192468	−	0.0333364i
$176$	−625.572	−	1083.52i	−0.267922	−	0.464054i
$177$	2809.84	+	2989.94i	1.19322	+	1.26970i
$178$	−277.753	+	481.082i	−0.116958	+	0.202576i
$179$	3023.22			1.26238			0.631190	−	0.775629i	$-0.282567\pi$
$179$	3023.22			1.26238			0.631190	+	0.775629i	$0.282567\pi$
$180$	106.288	−	1709.73i	0.0440126	−	0.707977i
$181$	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
$183$	781.634	−	2592.39i	0.315738	−	1.04718i
$184$	−688.426	−	1192.39i	−0.275823	−	0.477740i
$185$	934.040	+	1617.81i	0.371200	+	0.642937i
$186$	89.4294	−	21.0106i	0.0352542	−	0.00828266i
$187$	−661.928	+	1146.49i	−0.258850	+	0.448341i
$188$	378.496			0.146833
$189$	120.510	+	707.686i	0.0463799	+	0.272363i
$190$	−555.848			−0.212239
$191$	−1742.79	+	3018.61i	−0.660231	+	1.14355i	0.320324	+	0.947308i	$0.396208\pi$
$191$	−1742.79	+	3018.61i	−0.660231	+	1.14355i	−0.980555	+	0.196246i	$0.937125\pi$
$192$	−384.233	+	90.2720i	−0.144425	+	0.0339314i
$193$	−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	$0.968876\pi$
$194$	51.4793	+	89.1647i	0.0190515	+	0.0329982i
$195$	584.751	−	1939.40i	0.214743	−	0.712222i
$196$	−968.963	+	1678.29i	−0.353121	+	0.611623i
$197$	−3975.11			−1.43764			−0.718820	−	0.695196i	$-0.755318\pi$
$197$	−3975.11			−1.43764			−0.718820	+	0.695196i	$0.755318\pi$
$198$	1728.40	+	1146.49i	0.620365	+	0.411504i
$199$	−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
$201$	1083.29	+	1152.72i	0.380146	+	0.404512i
$202$	−746.437	−	1292.87i	−0.259996	−	0.450326i
$203$	−72.5883	−	125.727i	−0.0250970	−	0.0434693i
$204$	−514.762	−	547.756i	−0.176669	−	0.187993i
$205$	1117.53	−	1935.62i	0.380739	−	0.659460i
$206$	1498.28			0.506749
$207$	−1599.15	−	1060.76i	−0.536950	−	0.356172i
$208$	840.027			0.280026
$209$	−1093.02	+	1893.17i	−0.361750	+	0.626570i
$210$	109.247	−	362.332i	0.0358990	−	0.119063i
$211$	−873.865	−	1513.58i	−0.285115	−	0.493834i	0.687522	−	0.726164i	$-0.258699\pi$
$211$	−873.865	−	1513.58i	−0.285115	−	0.493834i	−0.972637	+	0.232329i	$0.925365\pi$
$212$	1505.69	+	2607.93i	0.487789	+	0.844875i
$213$	−1367.75	+	321.341i	−0.439986	+	0.103371i
$214$	−706.145	+	1223.08i	−0.225566	+	0.390691i
$215$	635.133			0.201468
$216$	−2092.21	+	1734.77i	−0.659058	+	0.546462i
$217$	−65.9211			−0.0206222
$218$	1218.94	−	2111.27i	0.378702	−	0.655931i
$219$	4681.39	−	1099.85i	1.44447	−	0.339365i
$220$	1775.79	+	3075.75i	0.544198	+	0.942579i
$221$	−444.423	−	769.764i	−0.135272	−	0.234298i
$222$	370.728	−	1229.57i	0.112080	−	0.371726i
$223$	1270.97	−	2201.39i	0.381662	−	0.661057i	−0.609638	−	0.792680i	$-0.708685\pi$
$223$	1270.97	−	2201.39i	0.381662	−	0.661057i	0.991300	+	0.131622i	$0.0420187\pi$
$224$	949.939			0.283350
$225$	29.1761	−	469.320i	0.00864476	−	0.139058i
$226$	2217.52			0.652687
$227$	1496.63	−	2592.24i	0.437598	−	0.757943i	−0.559905	−	0.828557i	$-0.689163\pi$
$227$	1496.63	−	2592.24i	0.437598	−	0.757943i	0.997504	+	0.0706140i	$0.0224959\pi$
$228$	−850.009	−	904.492i	−0.246900	−	0.262726i
$229$	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	$0.619985\pi$
$230$	505.818	+	876.102i	0.145012	+	0.251167i
$231$	−1019.25	−	1084.58i	−0.290309	−	0.308917i
$232$	274.818	−	475.999i	0.0777702	−	0.134702i
$233$	−5581.34			−1.56930			−0.784648	−	0.619942i	$-0.787156\pi$
$233$	−5581.34			−1.56930			−0.784648	+	0.619942i	$0.787156\pi$
$234$	−1246.87	+	620.108i	−0.348334	+	0.173238i
$235$	−641.812			−0.178158
$236$	2415.02	−	4182.94i	0.666121	−	1.15376i
$237$	−1933.55	+	6412.87i	−0.529948	+	1.75764i
$238$	−83.0303	−	143.813i	−0.0226137	−	0.0391680i
$239$	−704.814	−	1220.77i	−0.190756	−	0.330399i	0.754745	−	0.656018i	$-0.227761\pi$
$239$	−704.814	−	1220.77i	−0.190756	−	0.330399i	−0.945501	+	0.325619i	$0.894427\pi$
$240$	−1172.67	+	275.509i	−0.315399	+	0.0741001i
$241$	−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	$0.193352\pi$
$242$	−2473.63			−0.657069
$243$	−1534.27	+	3463.37i	−0.405034	+	0.914302i
$244$	−3187.42			−0.836286
$245$	1643.06	−	2845.87i	0.428455	−	0.742105i
$246$	−1495.80	+	351.424i	−0.387677	+	0.0910811i
$247$	−733.862	−	1271.09i	−0.189047	−	0.327438i
$248$	−124.788	−	216.139i	−0.0319518	−	0.0553422i
$249$	1070.75	−	3551.28i	0.272514	−	0.903828i
$250$	−1013.55	+	1755.52i	−0.256410	+	0.444116i
$251$	1705.53			0.428892			0.214446	−	0.976736i	$-0.431205\pi$
$251$	1705.53			0.428892			0.214446	+	0.976736i	$0.431205\pi$
$252$	756.660	−	376.312i	0.189147	−	0.0940692i
$253$	3978.56			0.988656
$254$	−827.556	+	1433.37i	−0.204431	+	0.354085i
$255$	872.877	+	928.826i	0.214360	+	0.228099i
$256$	1251.37	+	2167.43i	0.305510	+	0.529158i
$257$	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	$0.689525\pi$
$258$	−299.014	−	318.180i	−0.0721542	−	0.0767791i
$259$	−460.780	+	798.094i	−0.110546	+	0.191472i
$260$	−2384.55			−0.568784
$261$	47.5311	−	764.576i	0.0112724	−	0.181326i
$262$	1410.51			0.332601
$263$	−2068.75	+	3583.18i	−0.485037	+	0.840108i	−0.999852	−	0.0171926i	$-0.994527\pi$
$263$	−2068.75	+	3583.18i	−0.485037	+	0.840108i	0.514815	+	0.857301i	$0.327860\pi$
$264$	1626.64	−	5394.95i	0.379215	−	1.25771i
$265$	−2553.19	−	4422.25i	−0.591853	−	1.02512i
$266$	−137.105	−	237.473i	−0.0316032	−	0.0547384i
$267$	2047.67	−	481.082i	0.469346	−	0.110269i
$268$	931.074	−	1612.67i	0.212218	−	0.367572i
$269$	6090.99			1.38057			0.690287	−	0.723536i	$-0.257484\pi$
$269$	6090.99			1.38057			0.690287	+	0.723536i	$0.257484\pi$
$270$	1537.24	−	1274.61i	0.346494	−	0.287298i
$271$	−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
$273$	972.798	−	228.550i	0.215665	−	0.0506684i
$274$	−865.160	−	1498.50i	−0.190753	−	0.330393i
$275$	487.452	+	844.292i	0.106889	+	0.185137i
$276$	−652.117	+	2162.83i	−0.142220	+	0.471692i
$277$	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	$0.0568111\pi$
$278$	−633.763			−0.136729
$279$	−289.871	−	192.279i	−0.0622012	−	0.0412596i
$280$	−1028.15			−0.219442
$281$	−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	$0.990637\pi$
$282$	302.158	+	321.525i	0.0638058	+	0.0678956i
$283$	2272.47	+	3936.03i	0.477329	+	0.826758i	0.999662	−	0.0259834i	$-0.00827171\pi$
$283$	2272.47	+	3936.03i	0.477329	+	0.826758i	−0.522333	+	0.852741i	$0.674938\pi$
$284$	826.971	+	1432.36i	0.172788	+	0.299277i
$285$	1441.35	+	1533.74i	0.299573	+	0.318775i
$286$	1443.57	−	2500.34i	0.298462	−	0.516951i
$287$	1102.60			0.226774
$288$	4177.11	+	2770.78i	0.854648	+	0.566910i
$289$	−4353.70			−0.886160
$290$	−201.921	+	349.738i	−0.0408869	+	0.0708183i
$291$	112.541	−	373.256i	0.0226710	−	0.0751913i
$292$	−2830.46	−	4902.50i	−0.567261	−	0.982525i
$293$	−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	$-0.406389\pi$
$294$	−2199.22	+	516.686i	−0.436262	+	0.102496i
$295$	−4095.13	+	7092.98i	−0.808230	+	1.39990i
$296$	−3489.01			−0.685117
$297$	−1318.38	−	7742.08i	−0.257576	−	1.51260i
$298$	−2002.60			−0.389287
$299$	−1335.62	+	2313.36i	−0.258330	+	0.447441i
$300$	−538.872	+	126.603i	−0.103706	+	0.0243648i
$301$	156.662	+	271.346i	0.0299994	+	0.0519605i
$302$	1057.56	+	1831.75i	0.201509	+	0.349024i
$303$	−1631.82	+	5412.12i	−0.309391	+	1.02613i
$304$	−436.412	+	755.888i	−0.0823353	+	0.142609i
$305$	5404.89			1.01470
$306$	54.3686	−	874.562i	0.0101570	−	0.163384i
$307$	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
$309$	−3885.15	−	4134.18i	−0.715270	−	0.761117i
$310$	91.6874	+	158.807i	0.0167984	+	0.0290956i
$311$	−3538.84	−	6129.44i	−0.645238	−	1.11758i	−0.984247	−	0.176801i	$-0.943425\pi$
$311$	−3538.84	−	6129.44i	−0.645238	−	1.11758i	0.339009	−	0.940783i	$-0.389908\pi$
$312$	2590.86	+	2756.93i	0.470123	+	0.500257i
$313$	−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	$0.206470\pi$
$314$	4412.67			0.793062
$315$	−1283.06	+	638.110i	−0.229500	+	0.114138i
$316$	7884.83			1.40366
$317$	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	$-0.0911294\pi$
$318$	−1013.38	+	3361.00i	−0.178703	+	0.592691i
$319$	794.115	+	1375.45i	0.139379	+	0.241412i
$320$	−393.934	−	682.314i	−0.0688175	−	0.119195i
$321$	5205.90	−	1223.08i	0.905187	−	0.212665i
$322$	−249.530	+	432.198i	−0.0431855	+	0.0747995i
$323$	923.549			0.159095
$324$	4424.85	+	552.290i	0.758718	+	0.0947000i
$325$	−654.559			−0.111718
$326$	650.178	−	1126.14i	0.110460	−	0.191323i
$327$	−8986.37	+	2111.27i	−1.51972	+	0.357044i
$328$	2087.20	+	3615.14i	0.351361	+	0.608576i
$329$	−158.309	−	274.199i	−0.0265284	−	0.0459486i
$330$	−1195.17	+	3963.92i	−0.199369	+	0.661231i
$331$	4830.64	−	8366.92i	0.802163	−	1.38939i	−0.116026	−	0.993246i	$-0.537016\pi$
$331$	4830.64	−	8366.92i	0.802163	−	1.38939i	0.918189	−	0.396142i	$-0.129651\pi$
$332$	−4366.41			−0.721801
$333$	−4354.04	+	2165.41i	−0.716517	+	0.356348i
$334$	−941.329			−0.154213
$335$	−1578.81	+	2734.59i	−0.257492	+	0.445989i
$336$	−406.956	−	433.041i	−0.0660752	−	0.0703104i
$337$	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	$0.702152\pi$
$338$	−538.227	−	932.236i	−0.0866144	−	0.150021i
$339$	−5750.19	−	6118.76i	−0.921260	−	0.980311i
$340$	750.228	−	1299.43i	0.119667	−	0.207269i
$341$	721.177			0.114528
$342$	89.7771	−	1444.14i	0.0141947	−	0.228333i
$343$	3376.19			0.531478
$344$	−593.118	+	1027.31i	−0.0929616	+	0.161014i
$345$	1105.79	−	3667.49i	0.172561	−	0.572321i
$346$	−1518.31	−	2629.79i	−0.235910	−	0.408608i
$347$	507.802	+	879.540i	0.0785598	+	0.136070i	0.902629	−	0.430420i	$-0.141635\pi$
$347$	507.802	+	879.540i	0.0785598	+	0.136070i	−0.824069	+	0.566490i	$0.808301\pi$
$348$	−877.883	+	206.251i	−0.135228	+	0.0317707i
$349$	−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	$0.784354\pi$
$350$	−122.289			−0.0186761
$351$	4944.26	+	1832.47i	0.751867	+	0.278661i
$352$	−10392.3			−1.57362
$353$	−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	$0.270133\pi$
$354$	5481.28	−	1287.78i	0.822957	−	0.193346i
$355$	−1402.29	−	2428.83i	−0.209650	−	0.363124i
$356$	−1238.06	−	2144.39i	−0.184318	−	0.319248i
$357$	−181.516	+	602.020i	−0.0269099	+	0.0892501i
$358$	2074.35	−	3592.88i	0.306237	−	0.530418i
$359$	−517.939			−0.0761443			−0.0380721	−	0.999275i	$-0.512122\pi$
$359$	−517.939			−0.0761443			−0.0380721	+	0.999275i	$0.512122\pi$
$360$	−4521.03	−	2998.91i	−0.661887	−	0.439046i
$361$	−5333.97			−0.777660
$362$	268.586	−	465.205i	0.0389961	−	0.0675432i
$363$	6414.29	+	6825.42i	0.927445	+	0.986892i
$364$	−588.173	−	1018.75i	−0.0846941	−	0.146694i
$365$	4799.59	+	8313.13i	0.688279	+	1.19213i
$366$	−2544.56	−	2707.66i	−0.363405	−	0.386699i
$367$	2308.15	−	3997.83i	0.328295	−	0.568624i	−0.653879	−	0.756600i	$-0.726859\pi$
$367$	2308.15	−	3997.83i	0.328295	−	0.568624i	0.982174	+	0.187976i	$0.0601926\pi$
$368$	1588.53			0.225021
$369$	4848.38	+	3216.05i	0.684002	+	0.453715i
$370$	2563.53			0.360194
$371$	1259.54	−	2181.58i	0.176258	−	0.305288i
$372$	−118.206	+	392.046i	−0.0164750	+	0.0546415i
$373$	−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	$0.940637\pi$
$374$	908.351	+	1573.31i	0.125588	+	0.217524i
$375$	7472.18	−	1755.52i	1.02896	−	0.241746i
$376$	599.355	−	1038.11i	0.0822058	−	0.142385i
$377$	−1066.35			−0.145676
$378$	923.722	+	342.355i	0.125691	+	0.0465842i
$379$	−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
$381$	6100.98	−	1433.37i	0.820374	−	0.192740i
$382$	2391.60	+	4142.38i	0.320327	+	0.554823i
$383$	−495.147	−	857.619i	−0.0660596	−	0.114419i	0.831104	−	0.556117i	$-0.187709\pi$
$383$	−495.147	−	857.619i	−0.0660596	−	0.114419i	−0.897164	+	0.441699i	$0.854376\pi$
$384$	2071.44	−	6870.18i	0.275280	−	0.913001i
$385$	1485.48	−	2572.92i	0.196641	−	0.340593i
$386$	−3039.70			−0.400820
$387$	−102.583	+	1650.12i	−0.0134743	+	0.216746i
$388$	−458.930			−0.0600481
$389$	−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	$0.175057\pi$
$390$	−1903.62	−	2025.64i	−0.247163	−	0.263005i
$391$	−840.423	−	1455.66i	−0.108701	−	0.188275i
$392$	3068.74	+	5315.22i	0.395395	+	0.684845i
$393$	−3657.54	−	3891.98i	−0.469462	−	0.499553i
$394$	−2727.49	+	4724.15i	−0.348753	+	0.604059i
$395$	−13370.2			−1.70311
$396$	−8277.86	+	4116.85i	−1.05045	+	0.522424i
$397$	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
$399$	−299.731	+	994.097i	−0.0376074	+	0.124730i
$400$	194.626	+	337.102i	0.0243282	+	0.0421378i
$401$	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	$0.614639\pi$
$402$	2113.22	−	496.482i	0.262184	−	0.0615977i
$403$	−242.102	+	419.332i	−0.0299254	+	0.0518323i
$404$	6654.38			0.819474
$405$	−7503.17	−	936.514i	−0.920582	−	0.114903i
$406$	−199.223			−0.0243529
$407$	5040.93	−	8731.15i	0.613930	−	1.06336i
$408$	−2317.49	+	544.472i	−0.281208	+	0.0660672i
$409$	−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	$0.970586\pi$
$410$	−1533.56	−	2656.21i	−0.184725	−	0.319953i
$411$	−1891.36	+	6272.94i	−0.226993	+	0.752850i
$412$	−3339.24	+	5783.73i	−0.399302	+	0.691612i
$413$	−4040.41			−0.481394
$414$	−2357.88	+	1172.65i	−0.279911	+	0.139209i
$415$	7404.09			0.875789
$416$	3488.75	−	6042.68i	0.411177	−	0.712180i
$417$	1643.39	+	1748.73i	0.192991	+	0.205361i
$418$	1499.93	+	2597.96i	0.175512	+	0.303996i
$419$	−2560.16	−	4434.32i	−0.298501	−	0.517019i	0.677292	−	0.735714i	$-0.263153\pi$
$419$	−2560.16	−	4434.32i	−0.298501	−	0.517019i	−0.975793	+	0.218695i	$0.929820\pi$
$420$	1155.21	+	1229.26i	0.134211	+	0.142813i
$421$	−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	$0.201123\pi$
$422$	−2398.38			−0.276662
$423$	103.661	−	1667.48i	0.0119153	−	0.191668i
$424$	9537.16			1.09237
$425$	205.937	−	356.693i	0.0235045	−	0.0407110i
$426$	−556.580	+	1845.97i	−0.0633014	+	0.209947i
$427$	1333.17	+	2309.11i	0.151092	+	0.261700i
$428$	−3147.59	−	5451.79i	−0.355478	−	0.615706i
$429$	−10642.4	+	2500.34i	−1.19772	+	0.281393i
$430$	435.791	−	754.811i	0.0488737	−	0.0846517i
$431$	−4090.64			−0.457168			−0.228584	−	0.973524i	$-0.573410\pi$
$431$	−4090.64			−0.457168			−0.228584	+	0.973524i	$0.573410\pi$
$432$	−526.391	−	3091.19i	−0.0586250	−	0.344271i
$433$	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
$435$	1488.62	−	349.738i	0.164078	−	0.0385486i
$436$	5433.34	+	9410.81i	0.596811	+	1.03371i
$437$	−1387.76	−	2403.68i	−0.151912	−	0.263120i
$438$	1905.00	−	6318.16i	0.207818	−	0.689254i
$439$	5653.26	−	9791.74i	0.614614	−	1.06454i	−0.375838	−	0.926685i	$-0.622645\pi$
$439$	5653.26	−	9791.74i	0.614614	−	1.06454i	0.990452	−	0.137857i	$-0.0440214\pi$
$440$	11248.0			1.21870
$441$	7128.40	+	4728.45i	0.769723	+	0.510576i
$442$	−1219.75			−0.131261
$443$	4140.65	−	7171.82i	0.444082	−	0.769172i	−0.553906	−	0.832579i	$-0.686863\pi$
$443$	4140.65	−	7171.82i	0.444082	−	0.769172i	0.997988	+	0.0634071i	$0.0201967\pi$
$444$	3920.18	+	4171.45i	0.419017	+	0.445875i
$445$	2099.37	+	3636.22i	0.223640	+	0.387356i
$446$	−1744.13	−	3020.92i	−0.185173	−	0.320728i
$447$	5192.88	+	5525.73i	0.549474	+	0.584694i
$448$	194.335	−	336.599i	0.0204944	−	0.0354973i
$449$	6888.40			0.724017			0.362008	−	0.932175i	$-0.382091\pi$
$449$	6888.40			0.724017			0.362008	+	0.932175i	$0.382091\pi$
$450$	−537.735	−	356.693i	−0.0563313	−	0.0373660i
$451$	−12062.4			−1.25941
$452$	−4942.22	+	8560.17i	−0.514297	+	0.890789i
$453$	2311.98	−	7667.96i	0.239793	−	0.795302i
$454$	−2053.80	−	3557.28i	−0.212312	−	0.367735i
$455$	997.360	+	1727.48i	0.102763	+	0.177990i
$456$	−3826.79	+	899.070i	−0.392995	+	0.0923307i
$457$	−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	$0.237022\pi$
$458$	5908.09			0.602766
$459$	−2554.14	+	2117.78i	−0.259732	+	0.215359i
$460$	−4509.29			−0.457058
$461$	−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	$0.921624\pi$
$462$	−1988.29	+	467.131i	−0.200224	+	0.0470409i
$463$	−2867.27	−	4966.25i	−0.287804	−	0.498491i	0.685481	−	0.728090i	$-0.259592\pi$
$463$	−2867.27	−	4966.25i	−0.287804	−	0.498491i	−0.973285	+	0.229599i	$0.926258\pi$
$464$	317.068	+	549.178i	0.0317231	+	0.0549460i
$465$	200.442	−	664.790i	0.0199898	−	0.0662987i
$466$	−3829.59	+	6633.04i	−0.380691	+	0.659377i
$467$	−8950.97			−0.886941			−0.443470	−	0.896289i	$-0.646253\pi$
$467$	−8950.97			−0.886941			−0.443470	+	0.896289i	$0.646253\pi$
$468$	385.138	−	6195.25i	0.0380406	−	0.611914i
$469$	−1557.72			−0.153366
$470$	−440.373	+	762.749i	−0.0432189	+	0.0748574i
$471$	−11442.4	−	12175.8i	−1.11940	−	1.19115i
$472$	−7648.47	−	13247.5i	−0.745867	−	1.29188i
$473$	−1713.88	−	2968.52i	−0.166605	−	0.288568i
$474$	6294.56	+	6698.02i	0.609955	+	0.649051i
$475$	340.057	−	588.996i	0.0328482	−	0.0568947i
$476$	740.203			0.0712755
$477$	11901.7	−	5919.12i	1.14244	−	0.568172i
$478$	−1934.41			−0.185100
$479$	−4840.51	+	8384.00i	−0.461729	+	0.799739i	−0.999047	−	0.0436411i	$-0.986104\pi$
$479$	−4840.51	+	8384.00i	−0.461729	+	0.799739i	0.537318	+	0.843380i	$0.319438\pi$
$480$	−2888.41	+	9579.78i	−0.274661	+	0.910948i
$481$	3384.52	+	5862.16i	0.320833	+	0.555699i
$482$	429.917	+	744.637i	0.0406269	+	0.0703678i
$483$	1839.60	−	432.198i	0.173302	−	0.0407157i
$484$	5513.00	−	9548.80i	0.517750	−	0.896769i
$485$	778.204			0.0728586
$486$	3063.25	+	4199.73i	0.285909	+	0.391983i
$487$	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
$489$	−4793.30	+	1126.14i	−0.443273	+	0.104143i
$490$	−2254.74	−	3905.33i	−0.207875	−	0.360051i
$491$	7797.85	+	13506.3i	0.716725	+	1.24140i	0.962290	+	0.272024i	$0.0876930\pi$
$491$	7797.85	+	13506.3i	0.716725	+	1.24140i	−0.245565	+	0.969380i	$0.578974\pi$
$492$	1977.12	−	6557.36i	0.181170	−	0.600871i
$493$	335.495	−	581.094i	0.0306489	−	0.0530855i
$494$	−2014.13			−0.183441
$495$	14036.7	−	6980.92i	1.27455	−	0.633876i
$496$	287.945			0.0260668
$497$	691.776	−	1198.19i	0.0624354	−	0.108141i
$498$	−3485.76	−	3709.19i	−0.313656	−	0.333761i
$499$	4848.14	+	8397.22i	0.434935	+	0.753329i	0.997290	−	0.0735663i	$-0.0234381\pi$
$499$	4848.14	+	8397.22i	0.434935	+	0.753329i	−0.562355	+	0.826896i	$0.690105\pi$
$500$	−4517.83	−	7825.11i	−0.404087	−	0.699899i
$501$	2440.93	+	2597.39i	0.217670	+	0.231622i
$502$	1170.23	−	2026.90i	0.104044	−	0.180209i
$503$	20949.7			1.85706			0.928532	−	0.371253i	$-0.121072\pi$
$503$	20949.7			1.85706			0.928532	+	0.371253i	$0.121072\pi$
$504$	166.061	−	2671.22i	0.0146764	−	0.236082i
$505$	−11283.8			−0.994300
$506$	2729.85	−	4728.24i	0.239835	−	0.415407i
$507$	−1176.64	+	3902.47i	−0.103070	+	0.341844i
$508$	−3688.77	−	6389.14i	−0.322171	−	0.558016i
$509$	−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	$0.996668\pi$
$510$	1702.76	−	400.048i	0.147842	−	0.0347342i
$511$	−2367.73	+	4101.03i	−0.204975	+	0.355027i
$512$	−7613.21			−0.657148
$513$	−4217.57	+	3497.03i	−0.362983	+	0.300970i
$514$	4936.62			0.423628
$515$	5662.32	−	9807.43i	0.484489	−	0.839159i
$516$	1894.67	−	445.135i	0.161644	−	0.0379767i
$517$	1731.90	+	2999.74i	0.147329	+	0.255181i
$518$	632.320	+	1095.21i	0.0536342	+	0.0928972i
$519$	−3319.24	+	11008.7i	−0.280729	+	0.931074i
$520$	−3775.99	+	6540.20i	−0.318439	+	0.551552i
$521$	8675.49			0.729520			0.364760	−	0.931102i	$-0.381151\pi$
$521$	8675.49			0.729520			0.364760	+	0.931102i	$0.381151\pi$
$522$	−876.032	−	581.094i	−0.0734538	−	0.0487237i
$523$	−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
$525$	317.105	+	337.430i	0.0263611	+	0.0280508i
$526$	2838.91	+	4917.14i	0.235328	+	0.407599i
$527$	−152.340	−	263.860i	−0.0125921	−	0.0218101i
$528$	4452.10	+	4737.46i	0.366956	+	0.390477i
$529$	3557.79	−	6162.27i	0.292413	−	0.506474i
$530$	−7007.38			−0.574304
$531$	−17766.7	−	11785.1i	−1.45199	−	0.963143i
$532$	1222.27			0.0996095
$533$	4049.39	−	7013.75i	0.329078	−	0.569980i
$534$	833.258	−	2763.60i	0.0675255	−	0.223957i
$535$	5337.34	+	9244.55i	0.431315	+	0.747059i
$536$	−2948.75	−	5107.38i	−0.237624	−	0.411577i
$537$	−15292.7	+	3592.88i	−1.22892	+	0.288723i
$538$	4179.28	−	7238.72i	0.334910	−	0.580081i
$539$	−17734.9			−1.41725
$540$	1494.25	+	8774.86i	0.119078	+	0.699277i
$541$	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
$543$	−1980.09	+	465.205i	−0.156490	+	0.0367658i
$544$	2195.26	+	3802.29i	0.173016	+	0.299673i
$545$	−9213.26	−	15957.8i	−0.724134	−	1.25424i
$546$	395.860	−	1312.92i	0.0310280	−	0.102908i
$547$	−10835.6	+	18767.7i	−0.846974	+	1.46700i	0.0369219	+	0.999318i	$0.488245\pi$
$547$	−10835.6	+	18767.7i	−0.846974	+	1.46700i	−0.883896	+	0.467684i	$0.845089\pi$
$548$	7712.78			0.601229
$549$	−872.964	+	14042.3i	−0.0678637	+	1.09164i
$550$	1337.84			0.103720
$551$	553.991	−	959.541i	0.0428327	−	0.0741884i
$552$	4899.42	+	5213.46i	0.377778	+	0.401992i
$553$	−3297.90	−	5712.12i	−0.253600	−	0.439248i
$554$	−2140.32	−	3707.15i	−0.164140	−	0.284299i
$555$	−6647.42	−	7073.50i	−0.508410	−	0.540997i
$556$	1412.48	−	2446.48i	0.107738	−	0.186608i
$557$	7477.63			0.568828			0.284414	−	0.958702i	$-0.408201\pi$
$557$	7477.63			0.568828			0.284414	+	0.958702i	$0.408201\pi$
$558$	−427.402	+	212.561i	−0.0324254	+	0.0161262i
$559$	2301.42			0.174132
$560$	593.109	−	1027.29i	0.0447561	−	0.0775198i
$561$	1985.78	−	6586.10i	0.149447	−	0.495660i
$562$	3395.25	+	5880.75i	0.254840	+	0.441396i
$563$	11652.3	+	20182.4i	0.872269	+	1.51082i	0.859643	+	0.510895i	$0.170686\pi$
$563$	11652.3	+	20182.4i	0.872269	+	1.51082i	0.0126262	+	0.999920i	$0.495981\pi$
$564$	−1914.59	+	449.816i	−0.142941	+	0.0335827i
$565$	8380.48	−	14515.4i	0.624017	−	1.08083i
$566$	6236.92			0.463176
$567$	−1450.63	−	3436.56i	−0.107444	−	0.254536i
$568$	5238.10			0.386947
$569$	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	$-0.0147767\pi$
$570$	2811.71	−	660.587i	0.206614	−	0.0485420i
$571$	−11582.0	−	20060.6i	−0.848846	−	1.47025i	−0.882239	−	0.470803i	$-0.843964\pi$
$571$	−11582.0	−	20060.6i	−0.848846	−	1.47025i	0.0333922	−	0.999442i	$-0.489369\pi$
$572$	6434.61	+	11145.1i	0.470358	+	0.814683i
$573$	5228.38	−	17340.6i	0.381185	−	1.26425i
$574$	756.536	−	1310.36i	0.0550125	−	0.0952845i
$575$	−1237.80			−0.0897735
$576$	1836.33	−	913.268i	0.132836	−	0.0660640i
$577$	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
$579$	7882.15	+	8387.38i	0.565753	+	0.602016i
$580$	−900.049	−	1558.93i	−0.0644353	−	0.111605i
$581$	1826.29	+	3163.23i	0.130408	+	0.225874i
$582$	−366.370	−	389.853i	−0.0260937	−	0.0277662i
$583$	−13779.3	+	23866.5i	−0.978869	+	1.69545i
$584$	−17928.4			−1.27034
$585$	−653.076	+	10505.2i	−0.0461562	+	0.742459i
$586$	−9413.99			−0.663632
$587$	478.091	−	828.078i	0.0336166	−	0.0582256i	−0.848728	−	0.528830i	$-0.822631\pi$
$587$	478.091	−	828.078i	0.0336166	−	0.0582256i	0.882344	+	0.470605i	$0.155964\pi$
$588$	2906.89	−	9641.06i	0.203874	−	0.676174i
$589$	−251.554	−	435.704i	−0.0175978	−	0.0304803i
$590$	5619.68	+	9733.56i	0.392133	+	0.679194i
$591$	20107.8	−	4724.15i	1.39953	−	0.328808i
$592$	2012.70	−	3486.10i	0.139732	−	0.242023i
$593$	−16966.0			−1.17489			−0.587444	−	0.809265i	$-0.699866\pi$
$593$	−16966.0			−1.17489			−0.587444	+	0.809265i	$0.699866\pi$
$594$	−10105.5	−	3745.36i	−0.698038	−	0.258710i
$595$	−1255.16			−0.0864813
$596$	4463.22	−	7730.53i	0.306746	−	0.531300i
$597$	7867.57	−	1848.42i	0.539361	−	0.126718i
$598$	1832.84	+	3174.58i	0.125335	+	0.217087i
$599$	3095.70	+	5361.92i	0.211164	+	0.365746i	0.952079	−	0.305852i	$-0.0989414\pi$
$599$	3095.70	+	5361.92i	0.211164	+	0.365746i	−0.740915	+	0.671598i	$0.765608\pi$
$600$	−506.075	+	1678.46i	−0.0344340	+	0.114205i
$601$	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	$0.137259\pi$
$602$	429.968			0.0291099
$603$	−6849.66	−	4543.55i	−0.462587	−	0.306845i
$604$	−9428.00			−0.635132
$605$	−9348.35	+	16191.8i	−0.628206	+	1.08808i
$606$	5312.28	+	5652.78i	0.356100	+	0.378925i
$607$	−8412.49	−	14570.9i	−0.562524	−	0.974321i	−0.997275	−	0.0737701i	$-0.976497\pi$
$607$	−8412.49	−	14570.9i	−0.562524	−	0.974321i	0.434751	−	0.900551i	$-0.356836\pi$
$608$	3624.95	+	6278.60i	0.241795	+	0.418801i
$609$	516.599	+	549.712i	0.0343738	+	0.0365771i
$610$	3708.51	−	6423.33i	0.246153	−	0.426349i
$611$	−2325.62			−0.153985
$612$	3254.85	+	2159.02i	0.214983	+	0.142604i
$613$	−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
$615$	−3352.58	+	11119.3i	−0.219820	+	0.729060i
$616$	2774.42	+	4805.44i	0.181468	+	0.314313i
$617$	−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	$0.953634\pi$
$618$	−7578.94	+	1780.60i	−0.493317	+	0.115900i
$619$	8529.94	−	14774.3i	0.553873	−	0.959336i	−0.444117	−	0.895969i	$-0.646483\pi$
$619$	8529.94	−	14774.3i	0.553873	−	0.959336i	0.997990	−	0.0633676i	$-0.0201841\pi$
$620$	−817.380			−0.0529464
$621$	9349.81	+	3465.27i	0.604179	+	0.223924i
$622$	−9712.56			−0.626106
$623$	−1035.66	+	1793.82i	−0.0666017	+	0.115357i
$624$	−4249.21	+	998.314i	−0.272604	+	0.0640457i
$625$	6572.36	+	11383.7i	0.420631	+	0.728554i
$626$	947.764	+	1641.58i	0.0605116	+	0.104809i
$627$	3279.06	−	10875.4i	0.208857	−	0.692699i
$628$	−9834.58	+	17034.0i	−0.624908	+	1.08237i
$629$	−4259.34			−0.270002
$630$	−122.012	+	1962.66i	−0.00771601	+	0.124118i
$631$	−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
$633$	6219.16	+	6617.79i	0.390505	+	0.415535i
$634$	−5609.15	−	9715.34i	−0.351369	−	0.608589i
$635$	6255.02	+	10834.0i	0.390902	+	0.677063i
$636$	−10715.8	−	11402.6i	−0.668094	−	0.710917i
$637$	5953.68	−	10312.1i	0.370319	−	0.641412i
$638$	2179.50			0.135246
$639$	6536.79	−	3250.96i	0.404681	−	0.201261i
$640$	14323.7			0.884677
$641$	−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	$0.998490\pi$
$642$	2118.43	−	7026.05i	0.130230	−	0.431926i
$643$	14022.5	+	24287.6i	0.860019	+	1.48960i	0.871910	+	0.489667i	$0.162882\pi$
$643$	14022.5	+	24287.6i	0.860019	+	1.48960i	−0.0118907	+	0.999929i	$0.503785\pi$
$644$	−1112.26	−	1926.49i	−0.0680577	−	0.117879i
$645$	−3212.77	+	754.811i	−0.196128	+	0.0460786i
$646$	633.685	−	1097.57i	0.0385944	−	0.0668475i
$647$	21247.7			1.29109			0.645543	−	0.763724i	$-0.276631\pi$
$647$	21247.7			1.29109			0.645543	+	0.763724i	$0.276631\pi$
$648$	8521.61	−	11261.6i	0.516606	−	0.682713i
$649$	44202.1			2.67347
$650$	−449.119	+	777.897i	−0.0271014	+	0.0469410i
$651$	333.457	−	78.3426i	0.0200756	−	0.00471657i
$652$	2898.12	+	5019.69i	0.174079	+	0.301513i
$653$	−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	$0.845353\pi$
$654$	−3656.82	+	12128.3i	−0.218644	+	0.725159i
$655$	5330.60	−	9232.87i	0.317991	−	0.550776i
$656$	−4816.17			−0.286646
$657$	−22373.3	+	11127.0i	−1.32857	+	0.660740i
$658$	−434.489			−0.0257419
$659$	6023.35	−	10432.7i	0.356049	−	0.616695i	−0.631248	−	0.775581i	$-0.717457\pi$
$659$	6023.35	−	10432.7i	0.356049	−	0.616695i	0.987297	+	0.158886i	$0.0507902\pi$
$660$	−12638.0	−	13448.1i	−0.745354	−	0.793129i
$661$	−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	$0.959360\pi$
$662$	−6629.00	−	11481.8i	−0.389189	−	0.674096i
$663$	3162.89	+	3365.62i	0.185274	+	0.197149i
$664$	−6914.30	+	11975.9i	−0.404107	+	0.699933i
$665$	−2072.60			−0.120860
$666$	−414.046	+	6660.25i	−0.0240900	+	0.387507i
$667$	−2016.51			−0.117061
$668$	2097.95	−	3633.76i	0.121515	−	0.210471i
$669$	−3812.91	+	12646.0i	−0.220352	+	0.730826i
$670$	2166.58	+	3752.62i	0.124929	+	0.216383i
$671$	−14584.8	−	25261.7i	−0.839108	−	1.45338i
$672$	−4805.19	+	1128.94i	−0.275840	+	0.0648061i
$673$	−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	$0.191703\pi$
$674$	6801.06			0.388675
$675$	410.169	+	2408.69i	0.0233888	+	0.137349i
$676$	4798.21			0.272998
$677$	−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	$0.915481\pi$
$678$	−11217.2	+	2635.37i	−0.635387	+	0.149278i
$679$	191.952	+	332.470i	0.0108489	+	0.0187909i
$680$	−2376.00	−	4115.35i	−0.133993	−	0.232083i
$681$	−4489.89	+	14891.3i	−0.252648	+	0.837937i
$682$	494.829	−	857.068i	0.0277829	−	0.0481215i
$683$	−4846.23			−0.271502			−0.135751	−	0.990743i	$-0.543345\pi$
$683$	−4846.23			−0.271502			−0.135751	+	0.990743i	$0.543345\pi$
$684$	5374.63	+	3565.13i	0.300445	+	0.199292i
$685$	−13078.5			−0.729494
$686$	2316.54	−	4012.36i	0.128930	−	0.223313i
$687$	−15320.1	−	16302.1i	−0.850798	−	0.905331i
$688$	−684.303	−	1185.25i	−0.0379198	−	0.0656790i
$689$	−9251.54	−	16024.1i	−0.511546	−	0.886024i
$690$	−3599.83	−	3830.57i	−0.198613	−	0.211344i
$691$	−1742.29	+	3017.73i	−0.0959187	+	0.166136i	−0.909992	−	0.414627i	$-0.863912\pi$
$691$	−1742.29	+	3017.73i	−0.0959187	+	0.166136i	0.814073	+	0.580763i	$0.197246\pi$
$692$	13535.5			0.743560
$693$	6444.72	+	4274.94i	0.353268	+	0.234331i
$694$	1393.70			0.0762305
$695$	−2395.12	+	4148.48i	−0.130723	+	0.226418i
$696$	−824.454	+	2734.40i	−0.0449006	+	0.148919i
$697$	2548.04	+	4413.33i	0.138470	+	0.239837i
$698$	8342.49	+	14449.6i	0.452390	+	0.783562i
$699$	28232.8	−	6633.04i	1.52770	−	0.358919i
$700$	272.548	−	472.066i	0.0147162	−	0.0254892i
$701$	15701.4			0.845981			0.422991	−	0.906134i	$-0.360980\pi$
$701$	15701.4			0.845981			0.422991	+	0.906134i	$0.360980\pi$
$702$	5570.22	−	4618.58i	0.299479	−	0.248315i
$703$	−7033.32			−0.377335
$704$	−2126.03	+	3682.39i	−0.113818	+	0.197138i
$705$	3246.56	−	762.749i	0.173436	−	0.0407472i
$706$	2906.55	+	5034.29i	0.154943	+	0.268368i
$707$	−2783.25	−	4820.73i	−0.148055	−	0.256439i
$708$	−7245.07	+	24029.2i	−0.384585	+	1.27552i
$709$	−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	$0.302646\pi$
$710$	−3848.67			−0.203434
$711$	2159.48	−	34736.9i	0.113905	−	1.83226i
$712$	−7841.98			−0.412768
$713$	−457.824	+	792.975i	−0.0240472	+	0.0416510i
$714$	590.914	+	628.790i	0.0309725	+	0.0329578i
$715$	−10911.1	−	18898.6i	−0.570703	−	0.988486i
$716$	9246.27	+	16015.0i	0.482611	+	0.835907i
$717$	5016.05	+	5337.57i	0.261266	+	0.278013i
$718$	−355.379	+	615.535i	−0.0184716	+	0.0319938i
$719$	−6964.13			−0.361222			−0.180611	−	0.983555i	$-0.557807\pi$
$719$	−6964.13			−0.361222			−0.180611	+	0.983555i	$0.557807\pi$
$720$	5604.46	−	2787.28i	0.290091	−	0.144272i
$721$	5586.66			0.288569
$722$	−3659.86	+	6339.06i	−0.188651	+	0.326752i
$723$	939.858	−	3117.16i	0.0483454	−	0.160343i
$724$	1197.20	+	2073.62i	0.0614554	+	0.106444i
$725$	−247.063	−	427.925i	−0.0126561	−	0.0219210i
$726$	12512.6	−	2939.73i	0.639652	−	0.150281i
$727$	7103.61	−	12303.8i	0.362391	−	0.627680i	−0.625963	−	0.779853i	$-0.715294\pi$
$727$	7103.61	−	12303.8i	0.362391	−	0.627680i	0.988354	+	0.152173i	$0.0486272\pi$
$728$	−3725.53			−0.189667
$729$	3645.00	−	19342.6i	0.185185	−	0.982704i
$730$	13172.8			0.667871
$731$	−724.072	+	1254.13i	−0.0366358	+	0.0634551i
$732$	16123.3	−	3788.03i	0.814120	−	0.191270i
$733$	−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	$-0.399703\pi$
$734$	−3167.43	−	5486.15i	−0.159280	−	0.275882i
$735$	−4929.19	+	16348.3i	−0.247368	+	0.820428i
$736$	6597.36	−	11427.0i	0.330410	−	0.572288i
$737$	17041.4			0.851735
$738$	7148.72	−	3555.30i	0.356569	−	0.177334i
$739$	−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
$741$	5222.78	+	5557.55i	0.258925	+	0.275522i
$742$	−1728.44	−	2993.74i	−0.0855161	−	0.148118i
$743$	7784.28	+	13482.8i	0.384358	+	0.665727i	0.991680	−	0.128729i	$-0.0410896\pi$
$743$	7784.28	+	13482.8i	0.384358	+	0.665727i	−0.607322	+	0.794456i	$0.707756\pi$
$744$	888.097	+	945.022i	0.0437624	+	0.0465674i
$745$	−7568.25	+	13108.6i	−0.372187	+	0.644647i
$746$	−6539.50			−0.320949
$747$	−1195.86	+	19236.4i	−0.0585734	+	0.942199i
$748$	−8097.82			−0.395836
$749$	−2633.01	+	4560.51i	−0.128449	+	0.222480i
$750$	3040.65	−	10084.7i	0.148039	−	0.490988i
$751$	4130.82	+	7154.79i	0.200713	+	0.347646i	0.948758	−	0.316002i	$-0.102341\pi$
$751$	4130.82	+	7154.79i	0.200713	+	0.347646i	−0.748045	+	0.663648i	$0.769007\pi$
$752$	691.499	+	1197.71i	0.0335324	+	0.0580798i
$753$	−8627.27	+	2026.90i	−0.417523	+	0.0980933i
$754$	−731.666	+	1267.28i	−0.0353391	+	0.0612092i
$755$	15987.0			0.770630
$756$	−3380.29	+	2802.78i	−0.162619	+	0.134836i
$757$	−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
$759$	−20125.2	+	4728.24i	−0.962451	+	0.226119i
$760$	−3923.41	−	6795.55i	−0.187259	−	0.324343i
$761$	−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	$0.874767\pi$
$762$	2482.67	−	8234.08i	0.118028	−	0.391456i
$763$	4545.08	−	7872.31i	0.215652	−	0.373521i
$764$	−21320.8			−1.00963
$765$	−5519.23	−	3661.04i	−0.260847	−	0.173026i

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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	9.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.686141 - 1.18843i) q^{2} +(-5.05842 + 1.18843i) q^{3} +(3.05842 + 5.29734i) q^{4} +(-5.18614 - 8.98266i) q^{5} +(-2.05842 + 6.82701i) q^{6} +(2.55842 - 4.43132i) q^{7} +19.3723 q^{8} +(24.1753 - 12.0232i) q^{9} +O(q^{10})\)	\(q+(0.686141 - 1.18843i) q^{2} +(-5.05842 + 1.18843i) q^{3} +(3.05842 + 5.29734i) q^{4} +(-5.18614 - 8.98266i) q^{5} +(-2.05842 + 6.82701i) q^{6} +(2.55842 - 4.43132i) q^{7} +19.3723 q^{8} +(24.1753 - 12.0232i) q^{9} -14.2337 q^{10} +(-27.9891 + 48.4786i) q^{11} +(-21.7663 - 23.1615i) q^{12} +(-18.7921 - 32.5489i) q^{13} +(-3.51087 - 6.08101i) q^{14} +(36.9090 + 39.2747i) q^{15} +(-11.1753 + 19.3561i) q^{16} +23.6495 q^{17} +(2.29894 - 36.9802i) q^{18} +39.0516 q^{19} +(31.7228 - 54.9455i) q^{20} +(-7.67527 + 25.4560i) q^{21} +(38.4090 + 66.5263i) q^{22} +(-35.5367 - 61.5513i) q^{23} +(-97.9932 + 23.0226i) q^{24} +(8.70789 - 15.0825i) q^{25} -51.5761 q^{26} +(-108.000 + 89.5489i) q^{27} +31.2989 q^{28} +(14.1861 - 24.5711i) q^{29} +(72.0000 - 16.9157i) q^{30} +(-6.44158 - 11.1571i) q^{31} +(92.8247 + 160.777i) q^{32} +(83.9674 - 278.488i) q^{33} +(16.2269 - 28.1057i) q^{34} -53.0733 q^{35} +(137.629 + 91.2927i) q^{36} -180.103 q^{37} +(26.7949 - 46.4101i) q^{38} +(133.741 + 142.313i) q^{39} +(-100.467 - 174.015i) q^{40} +(107.742 + 186.614i) q^{41} +(24.9863 + 26.5879i) q^{42} +(-30.6168 + 53.0299i) q^{43} -342.410 q^{44} +(-233.376 - 154.804i) q^{45} -97.5326 q^{46} +(30.9388 - 53.5876i) q^{47} +(33.5258 - 111.192i) q^{48} +(158.409 + 274.372i) q^{49} +(-11.9497 - 20.6974i) q^{50} +(-119.629 + 28.1057i) q^{51} +(114.948 - 199.096i) q^{52} +492.310 q^{53} +(32.3194 + 189.794i) q^{54} +580.622 q^{55} +(49.5625 - 85.8447i) q^{56} +(-197.539 + 46.4101i) q^{57} +(-19.4674 - 33.7185i) q^{58} +(-394.815 - 683.840i) q^{59} +(-95.1684 + 315.638i) q^{60} +(-260.545 + 451.277i) q^{61} -17.6793 q^{62} +(8.57207 - 137.889i) q^{63} +75.9590 q^{64} +(-194.917 + 337.606i) q^{65} +(-273.351 - 290.872i) q^{66} +(-152.215 - 263.644i) q^{67} +(72.3301 + 125.279i) q^{68} +(252.909 + 269.120i) q^{69} +(-36.4158 + 63.0740i) q^{70} +270.391 q^{71} +(468.330 - 232.916i) q^{72} -925.464 q^{73} +(-123.576 + 214.040i) q^{74} +(-26.1237 + 86.6424i) q^{75} +(119.436 + 206.870i) q^{76} +(143.216 + 248.057i) q^{77} +(260.894 - 61.2946i) q^{78} +(644.517 - 1116.34i) q^{79} +231.826 q^{80} +(439.887 - 581.326i) q^{81} +295.704 q^{82} +(-356.917 + 618.198i) q^{83} +(-158.323 + 37.1966i) q^{84} +(-122.649 - 212.435i) q^{85} +(42.0149 + 72.7720i) q^{86} +(-42.5584 + 141.150i) q^{87} +(-542.213 + 939.141i) q^{88} -404.804 q^{89} +(-344.103 + 171.134i) q^{90} -192.313 q^{91} +(217.372 - 376.500i) q^{92} +(45.8437 + 48.7822i) q^{93} +(-42.4567 - 73.5372i) q^{94} +(-202.527 - 350.787i) q^{95} +(-660.619 - 702.963i) q^{96} +(-37.5137 + 64.9756i) q^{97} +434.763 q^{98} +(-93.7785 + 1508.50i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 3 q^{3} - 5 q^{4} - 15 q^{5} + 9 q^{6} - 7 q^{7} + 66 q^{8} + 45 q^{9}+O(q^{10}) \) 4 * q - 3 * q^2 - 3 * q^3 - 5 * q^4 - 15 * q^5 + 9 * q^6 - 7 * q^7 + 66 * q^8 + 45 * q^9	\( 4 q - 3 q^{2} - 3 q^{3} - 5 q^{4} - 15 q^{5} + 9 q^{6} - 7 q^{7} + 66 q^{8} + 45 q^{9} + 12 q^{10} - 66 q^{11} - 156 q^{12} + 11 q^{13} - 60 q^{14} + 27 q^{15} + 7 q^{16} + 198 q^{17} + 216 q^{18} - 154 q^{19} + 12 q^{20} + 21 q^{21} + 33 q^{22} - 33 q^{23} - 99 q^{24} + 121 q^{25} - 528 q^{26} - 432 q^{27} + 332 q^{28} + 51 q^{29} + 288 q^{30} - 43 q^{31} + 423 q^{32} + 198 q^{33} - 297 q^{34} + 6 q^{35} - 225 q^{36} - 100 q^{37} + 561 q^{38} + 759 q^{39} - 264 q^{40} - 132 q^{41} - 486 q^{42} - 88 q^{43} - 462 q^{44} - 675 q^{45} - 528 q^{46} - 399 q^{47} - 21 q^{48} + 513 q^{49} + 429 q^{50} + 297 q^{51} + 770 q^{52} + 108 q^{53} + 1215 q^{54} + 1254 q^{55} - 66 q^{56} - 1221 q^{57} + 60 q^{58} - 798 q^{59} - 36 q^{60} - 439 q^{61} + 228 q^{62} + 603 q^{63} - 1454 q^{64} - 165 q^{65} - 990 q^{66} - 988 q^{67} - 693 q^{68} + 891 q^{69} - 318 q^{70} + 2736 q^{71} + 891 q^{72} - 910 q^{73} - 816 q^{74} - 363 q^{75} + 1529 q^{76} + 165 q^{77} - 990 q^{78} + 803 q^{79} + 192 q^{80} - 567 q^{81} + 3630 q^{82} - 813 q^{83} + 642 q^{84} - 594 q^{85} - 33 q^{86} - 153 q^{87} - 1221 q^{88} - 792 q^{89} - 756 q^{90} - 1562 q^{91} + 858 q^{92} - 213 q^{93} - 2100 q^{94} + 132 q^{95} + 1080 q^{96} - 736 q^{97} - 846 q^{98} + 297 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 - 3 * q^3 - 5 * q^4 - 15 * q^5 + 9 * q^6 - 7 * q^7 + 66 * q^8 + 45 * q^9 + 12 * q^10 - 66 * q^11 - 156 * q^12 + 11 * q^13 - 60 * q^14 + 27 * q^15 + 7 * q^16 + 198 * q^17 + 216 * q^18 - 154 * q^19 + 12 * q^20 + 21 * q^21 + 33 * q^22 - 33 * q^23 - 99 * q^24 + 121 * q^25 - 528 * q^26 - 432 * q^27 + 332 * q^28 + 51 * q^29 + 288 * q^30 - 43 * q^31 + 423 * q^32 + 198 * q^33 - 297 * q^34 + 6 * q^35 - 225 * q^36 - 100 * q^37 + 561 * q^38 + 759 * q^39 - 264 * q^40 - 132 * q^41 - 486 * q^42 - 88 * q^43 - 462 * q^44 - 675 * q^45 - 528 * q^46 - 399 * q^47 - 21 * q^48 + 513 * q^49 + 429 * q^50 + 297 * q^51 + 770 * q^52 + 108 * q^53 + 1215 * q^54 + 1254 * q^55 - 66 * q^56 - 1221 * q^57 + 60 * q^58 - 798 * q^59 - 36 * q^60 - 439 * q^61 + 228 * q^62 + 603 * q^63 - 1454 * q^64 - 165 * q^65 - 990 * q^66 - 988 * q^67 - 693 * q^68 + 891 * q^69 - 318 * q^70 + 2736 * q^71 + 891 * q^72 - 910 * q^73 - 816 * q^74 - 363 * q^75 + 1529 * q^76 + 165 * q^77 - 990 * q^78 + 803 * q^79 + 192 * q^80 - 567 * q^81 + 3630 * q^82 - 813 * q^83 + 642 * q^84 - 594 * q^85 - 33 * q^86 - 153 * q^87 - 1221 * q^88 - 792 * q^89 - 756 * q^90 - 1562 * q^91 + 858 * q^92 - 213 * q^93 - 2100 * q^94 + 132 * q^95 + 1080 * q^96 - 736 * q^97 - 846 * q^98 + 297 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more