LMFDB - Embedded newform 9.4.c.a.4.1

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			4.1
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	9.4
Dual form			9.4.c.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.18614 - 3.78651i) q^{2} +(3.55842 + 3.78651i) q^{3} +(-5.55842 + 9.62747i) q^{4} +(-2.31386 + 4.00772i) q^{5} +(6.55842 - 21.7518i) q^{6} +(-6.05842 - 10.4935i) q^{7} +13.6277 q^{8} +(-1.67527 + 26.9480i) q^{9} +O(q^{10})$	\(q+(-2.18614 - 3.78651i) q^{2} +(3.55842 + 3.78651i) q^{3} +(-5.55842 + 9.62747i) q^{4} +(-2.31386 + 4.00772i) q^{5} +(6.55842 - 21.7518i) q^{6} +(-6.05842 - 10.4935i) q^{7} +13.6277 q^{8} +(-1.67527 + 26.9480i) q^{9} +20.2337 q^{10} +(-5.01087 - 8.67909i) q^{11} +(-56.2337 + 13.2116i) q^{12} +(24.2921 - 42.0752i) q^{13} +(-26.4891 + 45.8805i) q^{14} +(-23.4090 + 5.49972i) q^{15} +(14.6753 + 25.4183i) q^{16} +75.3505 q^{17} +(105.701 - 52.5687i) q^{18} -116.052 q^{19} +(-25.7228 - 44.5532i) q^{20} +(18.1753 - 60.2805i) q^{21} +(-21.9090 + 37.9474i) q^{22} +(19.0367 - 32.9725i) q^{23} +(48.4932 + 51.6014i) q^{24} +(51.7921 + 89.7066i) q^{25} -212.424 q^{26} +(-108.000 + 89.5489i) q^{27} +134.701 q^{28} +(11.3139 + 19.5962i) q^{29} +(72.0000 + 76.6150i) q^{30} +(-15.0584 + 26.0820i) q^{31} +(118.675 - 205.552i) q^{32} +(15.0326 - 49.8576i) q^{33} +(-164.727 - 285.315i) q^{34} +56.0733 q^{35} +(-250.129 - 165.917i) q^{36} +130.103 q^{37} +(253.705 + 439.430i) q^{38} +(245.759 - 57.7390i) q^{39} +(-31.5326 + 54.6161i) q^{40} +(-173.742 + 300.930i) q^{41} +(-267.986 + 62.9610i) q^{42} +(-13.3832 - 23.1803i) q^{43} +111.410 q^{44} +(-104.124 - 69.0678i) q^{45} -166.467 q^{46} +(-230.439 - 399.132i) q^{47} +(-44.0258 + 146.017i) q^{48} +(98.0910 - 169.899i) q^{49} +(226.450 - 392.222i) q^{50} +(268.129 + 285.315i) q^{51} +(270.052 + 467.743i) q^{52} -438.310 q^{53} +(575.181 + 213.176i) q^{54} +46.3778 q^{55} +(-82.5625 - 143.002i) q^{56} +(-412.961 - 439.430i) q^{57} +(49.4674 - 85.6800i) q^{58} +(-4.18487 + 7.24841i) q^{59} +(77.1684 - 255.939i) q^{60} +(41.0448 + 71.0916i) q^{61} +131.679 q^{62} +(292.928 - 145.683i) q^{63} -802.959 q^{64} +(112.417 + 194.712i) q^{65} +(-221.649 + 52.0745i) q^{66} +(-341.785 + 591.989i) q^{67} +(-418.830 + 725.435i) q^{68} +(192.591 - 45.2475i) q^{69} +(-122.584 - 212.322i) q^{70} +1097.61 q^{71} +(-22.8301 + 367.239i) q^{72} +470.464 q^{73} +(-284.424 - 492.637i) q^{74} +(-155.376 + 515.325i) q^{75} +(645.064 - 1117.28i) q^{76} +(-60.7160 + 105.163i) q^{77} +(-755.894 - 804.344i) q^{78} +(-243.017 - 420.919i) q^{79} -135.826 q^{80} +(-723.387 - 90.2901i) q^{81} +1519.30 q^{82} +(-49.5829 - 85.8802i) q^{83} +(479.323 + 510.046i) q^{84} +(-174.351 + 301.984i) q^{85} +(-58.5149 + 101.351i) q^{86} +(-33.9416 + 112.571i) q^{87} +(-68.2868 - 118.276i) q^{88} +8.80426 q^{89} +(-33.8968 + 545.257i) q^{90} -588.687 q^{91} +(211.628 + 366.550i) q^{92} +(-152.344 + 35.7918i) q^{93} +(-1007.54 + 1745.12i) q^{94} +(268.527 - 465.103i) q^{95} +(1200.62 - 282.075i) q^{96} +(-330.486 - 572.419i) q^{97} -857.763 q^{98} +(242.278 - 120.493i) 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 $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.18614	−	3.78651i	−0.772917	−	1.33873i	−0.935958	−	0.352113i	$-0.885463\pi$
$2$	−2.18614	−	3.78651i	−0.772917	−	1.33873i	0.163040	−	0.986619i	$-0.447870\pi$
$3$	3.55842	+	3.78651i	0.684819	+	0.728714i
$3$	3.55842	+	3.78651i	0.684819	+	0.728714i
$4$	−5.55842	+	9.62747i	−0.694803	+	1.20343i
$5$	−2.31386	+	4.00772i	−0.206958	+	0.358462i	−0.950755	−	0.309944i	$-0.899690\pi$
$5$	−2.31386	+	4.00772i	−0.206958	+	0.358462i	0.743797	+	0.668406i	$0.233023\pi$
$6$	6.55842	−	21.7518i	0.446244	−	1.48002i
$7$	−6.05842	−	10.4935i	−0.327124	−	0.566595i	0.654816	−	0.755788i	$-0.272746\pi$
$7$	−6.05842	−	10.4935i	−0.327124	−	0.566595i	−0.981940	+	0.189193i	$0.939413\pi$
$8$	13.6277			0.602266
$9$	−1.67527	+	26.9480i	−0.0620469	+	0.998073i
$10$	20.2337			0.639845
$11$	−5.01087	−	8.67909i	−0.137349	−	0.237895i	0.789144	−	0.614209i	$-0.210525\pi$
$11$	−5.01087	−	8.67909i	−0.137349	−	0.237895i	−0.926492	+	0.376314i	$0.877191\pi$
$12$	−56.2337	+	13.2116i	−1.35277	+	0.317822i
$13$	24.2921	−	42.0752i	0.518263	−	0.897658i	−0.481512	−	0.876440i	$-0.659912\pi$
$13$	24.2921	−	42.0752i	0.518263	−	0.897658i	0.999775	−	0.0212183i	$-0.00675450\pi$
$14$	−26.4891	+	45.8805i	−0.505680	+	0.875863i
$15$	−23.4090	+	5.49972i	−0.402944	+	0.0946681i
$16$	14.6753	+	25.4183i	0.229301	+	0.397161i
$17$	75.3505			1.07501			0.537506	−	0.843260i	$-0.319367\pi$
$17$	75.3505			1.07501			0.537506	+	0.843260i	$0.319367\pi$
$18$	105.701	−	52.5687i	1.38411	−	0.688364i
$19$	−116.052			−1.40127			−0.700633	−	0.713522i	$-0.747099\pi$
$19$	−116.052			−1.40127			−0.700633	+	0.713522i	$0.747099\pi$
$20$	−25.7228	−	44.5532i	−0.287590	−	0.498120i
$21$	18.1753	−	60.2805i	0.188865	−	0.626395i
$22$	−21.9090	+	37.9474i	−0.212318	+	0.367746i
$23$	19.0367	−	32.9725i	0.172584	−	0.298923i	−0.766739	−	0.641959i	$-0.778122\pi$
$23$	19.0367	−	32.9725i	0.172584	−	0.298923i	0.939322	+	0.343036i	$0.111455\pi$
$24$	48.4932	+	51.6014i	0.412443	+	0.438879i
$25$	51.7921	+	89.7066i	0.414337	+	0.717653i
$26$	−212.424			−1.60230
$27$	−108.000	+	89.5489i	−0.769800	+	0.638285i
$28$	134.701			0.909147
$29$	11.3139	+	19.5962i	0.0724459	+	0.125480i	0.899973	−	0.435946i	$-0.143586\pi$
$29$	11.3139	+	19.5962i	0.0724459	+	0.125480i	−0.827527	+	0.561426i	$0.810253\pi$
$30$	72.0000	+	76.6150i	0.438178	+	0.466264i
$31$	−15.0584	+	26.0820i	−0.0872443	+	0.151112i	−0.906345	−	0.422538i	$-0.861139\pi$
$31$	−15.0584	+	26.0820i	−0.0872443	+	0.151112i	0.819101	+	0.573649i	$0.194473\pi$
$32$	118.675	−	205.552i	0.655594	−	1.13552i
$33$	15.0326	−	49.8576i	0.0792983	−	0.263003i
$34$	−164.727	−	285.315i	−0.830895	−	1.43915i
$35$	56.0733			0.270804
$36$	−250.129	−	165.917i	−1.15800	−	0.768133i
$37$	130.103			0.578077			0.289038	−	0.957318i	$-0.406665\pi$
$37$	130.103			0.578077			0.289038	+	0.957318i	$0.406665\pi$
$38$	253.705	+	439.430i	1.08306	+	1.87592i
$39$	245.759	−	57.7390i	1.00905	−	0.237068i
$40$	−31.5326	+	54.6161i	−0.124644	+	0.215889i
$41$	−173.742	+	300.930i	−0.661803	+	1.14628i	0.318339	+	0.947977i	$0.396875\pi$
$41$	−173.742	+	300.930i	−0.661803	+	1.14628i	−0.980142	+	0.198299i	$0.936458\pi$
$42$	−267.986	+	62.9610i	−0.984552	+	0.231312i
$43$	−13.3832	−	23.1803i	−0.0474631	−	0.0822085i	0.841318	−	0.540541i	$-0.181780\pi$
$43$	−13.3832	−	23.1803i	−0.0474631	−	0.0822085i	−0.888781	+	0.458332i	$0.848447\pi$
$44$	111.410			0.381721
$45$	−104.124	−	69.0678i	−0.344930	−	0.228801i
$46$	−166.467			−0.533571
$47$	−230.439	−	399.132i	−0.715169	−	1.23871i	−0.962894	−	0.269879i	$-0.913016\pi$
$47$	−230.439	−	399.132i	−0.715169	−	1.23871i	0.247725	−	0.968830i	$-0.420317\pi$
$48$	−44.0258	+	146.017i	−0.132387	+	0.439078i
$49$	98.0910	−	169.899i	0.285980	−	0.495331i
$50$	226.450	−	392.222i	0.640496	−	1.10937i
$51$	268.129	+	285.315i	0.736188	+	0.783375i
$52$	270.052	+	467.743i	0.720181	+	1.24739i
$53$	−438.310			−1.13597			−0.567985	−	0.823039i	$-0.692277\pi$
$53$	−438.310			−1.13597			−0.567985	+	0.823039i	$0.692277\pi$
$54$	575.181	+	213.176i	1.44948	+	0.537215i
$55$	46.3778			0.113702
$56$	−82.5625	−	143.002i	−0.197016	−	0.341241i
$57$	−412.961	−	439.430i	−0.959613	−	1.02112i
$58$	49.4674	−	85.6800i	0.111989	−	0.193971i
$59$	−4.18487	+	7.24841i	−0.00923430	+	0.0159943i	−0.870606	−	0.491982i	$-0.836273\pi$
$59$	−4.18487	+	7.24841i	−0.00923430	+	0.0159943i	0.861371	+	0.507976i	$0.169606\pi$
$60$	77.1684	−	255.939i	0.166040	−	0.550693i
$61$	41.0448	+	71.0916i	0.0861515	+	0.149219i	0.905881	−	0.423532i	$-0.139210\pi$
$61$	41.0448	+	71.0916i	0.0861515	+	0.149219i	−0.819730	+	0.572750i	$0.805876\pi$
$62$	131.679			0.269730
$63$	292.928	−	145.683i	0.585801	−	0.291338i
$64$	−802.959			−1.56828
$65$	112.417	+	194.712i	0.214517	+	0.371555i
$66$	−221.649	+	52.0745i	−0.413381	+	0.0971202i
$67$	−341.785	+	591.989i	−0.623220	+	1.07945i	0.365663	+	0.930747i	$0.380842\pi$
$67$	−341.785	+	591.989i	−0.623220	+	1.07945i	−0.988882	+	0.148701i	$0.952491\pi$
$68$	−418.830	+	725.435i	−0.746921	+	1.29370i
$69$	192.591	−	45.2475i	0.336018	−	0.0789444i
$70$	−122.584	−	212.322i	−0.209309	−	0.362533i
$71$	1097.61			1.83468			0.917339	−	0.398107i	$-0.130333\pi$
$71$	1097.61			1.83468			0.917339	+	0.398107i	$0.130333\pi$
$72$	−22.8301	+	367.239i	−0.0373687	+	0.601105i
$73$	470.464			0.754297			0.377149	−	0.926153i	$-0.376905\pi$
$73$	470.464			0.754297			0.377149	+	0.926153i	$0.376905\pi$
$74$	−284.424	−	492.637i	−0.446805	−	0.773890i
$75$	−155.376	+	515.325i	−0.239218	+	0.793395i
$76$	645.064	−	1117.28i	0.973604	−	1.68633i
$77$	−60.7160	+	105.163i	−0.0898601	+	0.155642i
$78$	−755.894	−	804.344i	−1.09728	−	1.16762i
$79$	−243.017	−	420.919i	−0.346096	−	0.599456i	0.639456	−	0.768828i	$-0.279160\pi$
$79$	−243.017	−	420.919i	−0.346096	−	0.599456i	−0.985552	+	0.169371i	$0.945826\pi$
$80$	−135.826			−0.189823
$81$	−723.387	−	90.2901i	−0.992300	−	0.123855i
$82$	1519.30			2.04608
$83$	−49.5829	−	85.8802i	−0.0655715	−	0.113573i	0.831376	−	0.555711i	$-0.187554\pi$
$83$	−49.5829	−	85.8802i	−0.0655715	−	0.113573i	−0.896947	+	0.442137i	$0.854220\pi$
$84$	479.323	+	510.046i	0.622601	+	0.662508i
$85$	−174.351	+	301.984i	−0.222482	+	0.385350i
$86$	−58.5149	+	101.351i	−0.0733701	+	0.127081i
$87$	−33.9416	+	112.571i	−0.0418267	+	0.138723i
$88$	−68.2868	−	118.276i	−0.0827204	−	0.143276i
$89$	8.80426			0.0104859			0.00524297	−	0.999986i	$-0.498331\pi$
$89$	8.80426			0.0104859			0.00524297	+	0.999986i	$0.498331\pi$
$90$	−33.8968	+	545.257i	−0.0397004	+	0.638613i
$91$	−588.687			−0.678145
$92$	211.628	+	366.550i	0.239823	+	0.415386i
$93$	−152.344	+	35.7918i	−0.169864	+	0.0399079i
$94$	−1007.54	+	1745.12i	−1.10553	+	1.91484i
$95$	268.527	−	465.103i	0.290003	−	0.502300i
$96$	1200.62	−	282.075i	1.27643	−	0.299887i
$97$	−330.486	−	572.419i	−0.345936	−	0.599179i	0.639587	−	0.768719i	$-0.279105\pi$
$97$	−330.486	−	572.419i	−0.345936	−	0.599179i	−0.985523	+	0.169540i	$0.945772\pi$
$98$	−857.763			−0.884155
$99$	242.278	−	120.493i	0.245959	−	0.122323i
$100$	−1151.53			−1.15153
$101$	282.561	+	489.410i	0.278375	+	0.482160i	0.970981	−	0.239156i	$-0.0768708\pi$
$101$	282.561	+	489.410i	0.278375	+	0.482160i	−0.692606	+	0.721316i	$0.743537\pi$
$102$	494.181	−	1639.01i	0.479717	−	1.59104i
$103$	485.591	−	841.068i	0.464531	−	0.804592i	−0.534649	−	0.845074i	$-0.679556\pi$
$103$	485.591	−	841.068i	0.464531	−	0.804592i	0.999180	+	0.0404826i	$0.0128895\pi$
$104$	331.046	−	573.389i	0.312132	−	0.540629i
$105$	199.533	+	212.322i	0.185451	+	0.197338i
$106$	958.206	+	1659.66i	0.878012	+	1.52076i
$107$	−563.845			−0.509430			−0.254715	−	0.967016i	$-0.581982\pi$
$107$	−563.845			−0.509430			−0.254715	+	0.967016i	$0.581982\pi$
$108$	−261.819	−	1537.52i	−0.233274	−	1.36989i
$109$	225.484			0.198142			0.0990709	−	0.995080i	$-0.468413\pi$
$109$	225.484			0.198142			0.0990709	+	0.995080i	$0.468413\pi$
$110$	−101.388	−	175.610i	−0.0878819	−	0.152216i
$111$	462.962	+	492.637i	0.395878	+	0.421252i
$112$	177.818	−	307.990i	0.150020	−	0.259842i
$113$	345.531	−	598.478i	0.287654	−	0.498231i	−0.685596	−	0.727983i	$-0.740458\pi$
$113$	345.531	−	598.478i	0.287654	−	0.498231i	0.973249	+	0.229752i	$0.0737915\pi$
$114$	−761.115	+	2524.33i	−0.625307	+	2.07391i
$115$	88.0964	+	152.587i	0.0714350	+	0.123729i
$116$	−251.549			−0.201342
$117$	1093.14	+	725.110i	0.863772	+	0.572961i
$118$	36.5949			0.0285494
$119$	−456.505	−	790.690i	−0.351662	−	0.609096i
$120$	−319.011	+	74.9487i	−0.242680	+	0.0570154i
$121$	615.282	−	1065.70i	0.462271	−	0.800676i
$122$	179.459	−	310.833i	0.133176	−	0.230668i
$123$	−1757.72	+	412.960i	−1.28852	+	0.302726i
$124$	−167.402	−	289.949i	−0.121235	−	0.209985i
$125$	−1057.82			−0.756917
$126$	−1192.01	−	790.690i	−0.842800	−	0.559050i
$127$	−895.897			−0.625968			−0.312984	−	0.949758i	$-0.601329\pi$
$127$	−895.897			−0.625968			−0.312984	+	0.949758i	$0.601329\pi$
$128$	805.979	+	1396.00i	0.556556	+	0.963983i
$129$	40.1495	−	133.161i	0.0274028	−	0.0908849i
$130$	491.519	−	851.336i	0.331608	−	0.574362i
$131$	−827.428	+	1433.15i	−0.551853	+	0.955837i	0.446288	+	0.894889i	$0.352746\pi$
$131$	−827.428	+	1433.15i	−0.551853	+	0.955837i	−0.998141	+	0.0609476i	$0.980588\pi$
$132$	396.445	+	421.856i	0.261410	+	0.278165i
$133$	703.090	+	1217.79i	0.458388	+	0.793951i
$134$	2988.76			1.92679
$135$	−108.990	−	640.037i	−0.0694843	−	0.408042i
$136$	1026.86			0.647442
$137$	1325.55	+	2295.91i	0.826635	+	1.43177i	0.900663	+	0.434518i	$0.143081\pi$
$137$	1325.55	+	2295.91i	0.826635	+	1.43177i	−0.0740277	+	0.997256i	$0.523585\pi$
$138$	−592.361	−	630.330i	−0.365400	−	0.388821i
$139$	−317.084	+	549.206i	−0.193487	+	0.335130i	−0.946404	−	0.322986i	$-0.895313\pi$
$139$	−317.084	+	549.206i	−0.193487	+	0.335130i	0.752916	+	0.658116i	$0.228646\pi$
$140$	−311.679	+	539.844i	−0.188155	+	0.325894i
$141$	691.316	−	2292.84i	0.412903	−	1.36944i
$142$	−2399.53	−	4156.10i	−1.41805	−	2.45614i
$143$	−486.899			−0.284731
$144$	−709.557	+	352.886i	−0.410623	+	0.204217i
$145$	−104.715			−0.0599730
$146$	−1028.50	−	1781.42i	−0.583009	−	1.00980i
$147$	992.372	−	233.149i	0.556799	−	0.130815i
$148$	−723.168	+	1252.56i	−0.401649	+	0.695677i
$149$	1703.16	−	2949.96i	0.936432	−	1.62195i	0.164372	−	0.986398i	$-0.447440\pi$
$149$	1703.16	−	2949.96i	0.936432	−	1.62195i	0.772060	−	0.635550i	$-0.219227\pi$
$150$	2290.96	−	538.239i	1.24704	−	0.292980i
$151$	875.159	+	1515.82i	0.471652	+	0.816925i	0.999474	−	0.0324302i	$-0.0103247\pi$
$151$	875.159	+	1515.82i	0.471652	+	0.816925i	−0.527822	+	0.849355i	$0.676991\pi$
$152$	−1581.52			−0.843935
$153$	−126.232	+	2030.54i	−0.0667011	+	1.07294i
$154$	530.935			0.277818
$155$	−69.6861	−	120.700i	−0.0361118	−	0.0625474i
$156$	−810.155	+	2686.98i	−0.415797	+	1.37904i
$157$	−1089.29	+	1886.70i	−0.553723	+	0.959076i	0.444279	+	0.895889i	$0.353460\pi$
$157$	−1089.29	+	1886.70i	−0.553723	+	0.959076i	−0.998002	+	0.0631876i	$0.979873\pi$
$158$	−1062.54	+	1840.37i	−0.535008	+	0.926660i
$159$	−1559.69	−	1659.66i	−0.777934	−	0.827797i
$160$	549.196	+	951.235i	0.271361	+	0.470011i
$161$	−461.329			−0.225825
$162$	1239.54	+	2936.50i	0.601158	+	1.42415i
$163$	2188.41			1.05159			0.525797	−	0.850610i	$-0.323767\pi$
$163$	2188.41			1.05159			0.525797	+	0.850610i	$0.323767\pi$
$164$	−1931.46	−	3345.39i	−0.919645	−	1.59287i
$165$	165.032	+	175.610i	0.0778650	+	0.0828559i
$166$	−216.791	+	375.492i	−0.101363	+	0.175565i
$167$	−960.520	+	1663.67i	−0.445074	+	0.770890i	−0.998057	−	0.0623020i	$-0.980156\pi$
$167$	−960.520	+	1663.67i	−0.445074	+	0.770890i	0.552984	+	0.833192i	$0.313489\pi$
$168$	247.687	−	821.486i	0.113747	−	0.377256i
$169$	−81.7132	−	141.531i	−0.0371931	−	0.0644203i
$170$	1524.62			0.687841
$171$	194.417	−	3127.36i	0.0869442	−	1.39857i
$172$	297.557			0.131910
$173$	−1584.91	−	2745.15i	−0.696525	−	1.20642i	−0.969664	−	0.244442i	$-0.921395\pi$
$173$	−1584.91	−	2745.15i	−0.696525	−	1.20642i	0.273139	−	0.961974i	$-0.411938\pi$
$174$	500.454	−	117.577i	0.218042	−	0.0512270i
$175$	627.557	−	1086.96i	0.271079	−	0.469523i
$176$	147.072	−	254.736i	0.0629884	−	0.109099i
$177$	−42.3377	+	9.94685i	−0.0179791	+	0.00422402i
$178$	−19.2473	−	33.3374i	−0.00810477	−	0.0140379i
$179$	1368.78			0.571551			0.285776	−	0.958297i	$-0.407749\pi$
$179$	1368.78			0.571551			0.285776	+	0.958297i	$0.407749\pi$
$180$	1243.71	−	618.539i	0.515004	−	0.256129i
$181$	−3951.44			−1.62270			−0.811350	−	0.584561i	$-0.801267\pi$
$181$	−3951.44			−1.62270			−0.811350	+	0.584561i	$0.801267\pi$
$182$	1286.95	+	2229.07i	0.524150	+	0.907855i
$183$	−123.134	+	408.390i	−0.0497396	+	0.164968i
$184$	259.426	−	449.340i	0.103941	−	0.180031i
$185$	−301.040	+	521.417i	−0.119637	+	0.207218i
$186$	468.571	+	498.605i	0.184716	+	0.196556i
$187$	−377.572	−	653.974i	−0.147651	−	0.255740i
$188$	5123.50			1.98761
$189$	1593.99	+	590.773i	0.613469	+	0.227367i
$190$	−2348.15			−0.896594
$191$	1201.29	+	2080.70i	0.455092	+	0.788243i	0.998693	−	0.0511008i	$-0.0162730\pi$
$191$	1201.29	+	2080.70i	0.455092	+	0.788243i	−0.543601	+	0.839344i	$0.682940\pi$
$192$	−2857.27	−	3040.41i	−1.07399	−	1.14283i
$193$	667.535	−	1156.20i	0.248965	−	0.431220i	−0.714274	−	0.699866i	$-0.753243\pi$
$193$	667.535	−	1156.20i	0.248965	−	0.431220i	0.963239	+	0.268646i	$0.0865763\pi$
$194$	−1444.98	+	2502.78i	−0.534760	+	0.926232i
$195$	−337.251	+	1118.54i	−0.123852	+	0.410769i
$196$	1090.46	+	1888.74i	0.397399	+	0.688315i
$197$	−2630.89			−0.951487			−0.475743	−	0.879584i	$-0.657821\pi$
$197$	−2630.89			−0.951487			−0.475743	+	0.879584i	$0.657821\pi$
$198$	−985.903	−	653.974i	−0.353864	−	0.234727i
$199$	2477.34			0.882483			0.441241	−	0.897388i	$-0.354538\pi$
$199$	2477.34			0.882483			0.441241	+	0.897388i	$0.354538\pi$
$200$	705.808	+	1222.50i	0.249541	+	0.432218i
$201$	−3457.79	+	812.376i	−1.21340	+	0.285078i
$202$	1235.44	−	2139.84i	0.430322	−	0.745340i
$203$	137.088	−	237.444i	0.0473976	−	0.0820950i
$204$	−4237.24	+	995.501i	−1.45425	+	0.341662i
$205$	−804.028	−	1392.62i	−0.273931	−	0.474462i
$206$	−4246.28			−1.43618
$207$	856.650	+	568.238i	0.287639	+	0.190798i
$208$	1425.97			0.475353
$209$	581.520	+	1007.22i	0.192462	+	0.333354i
$210$	367.753	−	1219.70i	0.120844	−	0.400796i
$211$	1392.36	−	2411.65i	0.454286	−	0.786847i	−0.544361	−	0.838851i	$-0.683228\pi$
$211$	1392.36	−	2411.65i	0.454286	−	0.786847i	0.998647	+	0.0520047i	$0.0165611\pi$
$212$	2436.31	−	4219.81i	0.789276	−	1.36707i
$213$	3905.75	+	4156.10i	1.25642	+	1.33696i
$214$	1232.64	+	2135.00i	0.393747	+	0.681990i
$215$	123.867			0.0392914
$216$	−1471.79	+	1220.35i	−0.463624	+	0.384417i
$217$	364.921			0.114159
$218$	−492.940	−	853.797i	−0.153147	−	0.265259i
$219$	1674.11	+	1781.42i	0.516557	+	0.549667i
$220$	−257.788	+	446.501i	−0.0790002	+	0.136832i
$221$	1830.42	−	3170.39i	0.557138	−	0.964992i
$222$	853.272	−	2829.98i	0.257963	−	0.855567i
$223$	21.5288	+	37.2890i	0.00646491	+	0.0111976i	0.869240	−	0.494391i	$-0.164609\pi$
$223$	21.5288	+	37.2890i	0.00646491	+	0.0111976i	−0.862775	+	0.505588i	$0.831275\pi$
$224$	−2875.94			−0.857843
$225$	−2504.18	+	1245.41i	−0.741978	+	0.369010i
$226$	−3021.52			−0.889330
$227$	−341.630	−	591.721i	−0.0998889	−	0.173013i	0.811750	−	0.584006i	$-0.198515\pi$
$227$	−341.630	−	591.721i	−0.0998889	−	0.173013i	−0.911639	+	0.410993i	$0.865182\pi$
$228$	6526.01	−	1533.23i	1.89559	−	0.445353i
$229$	−2147.15	+	3718.98i	−0.619598	+	1.07317i	0.369962	+	0.929047i	$0.379371\pi$
$229$	−2147.15	+	3718.98i	−0.619598	+	1.07317i	−0.989559	+	0.144127i	$0.953962\pi$
$230$	385.182	−	667.155i	0.110427	−	0.191265i
$231$	−614.254	+	144.313i	−0.174957	+	0.0411045i
$232$	154.182	+	267.051i	0.0436317	+	0.0755723i
$233$	3466.34			0.974625			0.487313	−	0.873228i	$-0.337977\pi$
$233$	3466.34			0.974625			0.487313	+	0.873228i	$0.337977\pi$
$234$	355.866	−	5724.39i	0.0994176	−	1.59921i
$235$	2132.81			0.592040
$236$	−46.5225	−	80.5794i	−0.0128320	−	0.0222257i
$237$	729.052	−	2417.99i	0.199819	−	0.662724i
$238$	−1995.97	+	3457.12i	−0.543611	+	0.941562i
$239$	−2821.69	+	4887.30i	−0.763681	+	1.32273i	0.177261	+	0.984164i	$0.443276\pi$
$239$	−2821.69	+	4887.30i	−0.763681	+	1.32273i	−0.940941	+	0.338570i	$0.890057\pi$
$240$	−483.326	−	514.306i	−0.129994	−	0.138326i
$241$	−3294.71	−	5706.61i	−0.880627	−	1.52529i	−0.850645	−	0.525741i	$-0.823788\pi$
$241$	−3294.71	−	5706.61i	−0.880627	−	1.52529i	−0.0299825	−	0.999550i	$-0.509545\pi$
$242$	−5380.37			−1.42919
$243$	−2232.23	−	3060.40i	−0.589291	−	0.807921i
$244$	−912.577			−0.239433
$245$	453.938	+	786.243i	0.118372	+	0.205025i
$246$	5406.30	+	5752.82i	1.40119	+	1.49100i
$247$	−2819.14	+	4882.89i	−0.726225	+	1.25786i
$248$	−205.212	+	355.438i	−0.0525442	+	0.0910093i
$249$	148.749	−	493.344i	0.0378577	−	0.125560i
$250$	2312.55	+	4005.46i	0.585034	+	1.01331i
$251$	4135.47			1.03996			0.519978	−	0.854180i	$-0.325940\pi$
$251$	4135.47			1.03996			0.519978	+	0.854180i	$0.325940\pi$
$252$	−225.660	+	3629.92i	−0.0564097	+	0.907395i
$253$	−381.562			−0.0948165
$254$	1958.56	+	3392.32i	0.483822	+	0.838004i
$255$	−1763.88	+	414.407i	−0.433170	+	0.101769i
$256$	312.132	−	540.628i	0.0762041	−	0.131989i
$257$	1672.31	−	2896.53i	0.405898	−	0.703036i	−0.588527	−	0.808477i	$-0.700292\pi$
$257$	1672.31	−	2896.53i	0.405898	−	0.703036i	0.994426	+	0.105441i	$0.0336254\pi$
$258$	−591.986	+	139.082i	−0.142851	+	0.0335615i
$259$	−788.220	−	1365.24i	−0.189103	−	0.327536i
$260$	−2499.45			−0.596189
$261$	−547.031	+	272.057i	−0.129733	+	0.0645207i
$262$	7235.49			1.70615
$263$	−3260.75	−	5647.78i	−0.764511	−	1.32417i	−0.940505	−	0.339780i	$-0.889647\pi$
$263$	−3260.75	−	5647.78i	−0.764511	−	1.32417i	0.175994	−	0.984391i	$-0.443686\pi$
$264$	204.860	−	679.445i	0.0477587	−	0.158398i
$265$	1014.19	−	1756.62i	0.235098	−	0.407202i
$266$	3074.11	−	5324.51i	0.708592	−	1.22732i
$267$	31.3293	+	33.3374i	0.00718097	+	0.00764125i
$268$	−3799.57	−	6581.05i	−0.866029	−	1.50001i
$269$	−2904.99			−0.658441			−0.329220	−	0.944253i	$-0.606786\pi$
$269$	−2904.99			−0.658441			−0.329220	+	0.944253i	$0.606786\pi$
$270$	−2185.24	+	1811.90i	−0.492553	+	0.408404i
$271$	−1335.38			−0.299331			−0.149665	−	0.988737i	$-0.547820\pi$
$271$	−1335.38			−0.299331			−0.149665	+	0.988737i	$0.547820\pi$
$272$	1105.79	+	1915.28i	0.246501	+	0.426953i
$273$	−2094.80	−	2229.07i	−0.464406	−	0.494174i
$274$	5795.66	−	10038.4i	1.27784	−	2.21329i
$275$	519.048	−	899.017i	0.113817	−	0.197137i
$276$	−634.883	+	2105.67i	−0.138462	+	0.459226i
$277$	4187.82	+	7253.51i	0.908381	+	1.57336i	0.816313	+	0.577610i	$0.196015\pi$
$277$	4187.82	+	7253.51i	0.908381	+	1.57336i	0.0920685	+	0.995753i	$0.470652\pi$
$278$	2772.76			0.598199
$279$	−677.629	−	449.488i	−0.145407	−	0.0964522i
$280$	764.152			0.163096
$281$	2589.67	+	4485.43i	0.549774	+	0.952237i	0.998290	+	0.0584616i	$0.0186195\pi$
$281$	2589.67	+	4485.43i	0.549774	+	0.952237i	−0.448516	+	0.893775i	$0.648047\pi$
$282$	−10193.2	+	2394.79i	−2.15246	+	0.505701i
$283$	1540.03	−	2667.42i	0.323482	−	0.560288i	−0.657722	−	0.753261i	$-0.728480\pi$
$283$	1540.03	−	2667.42i	0.323482	−	0.560288i	0.981204	+	0.192973i	$0.0618130\pi$
$284$	−6100.97	+	10567.2i	−1.27474	+	2.20791i
$285$	2716.65	−	638.252i	0.564632	−	0.132655i
$286$	1064.43	+	1843.65i	0.220074	+	0.381179i
$287$	4210.40			0.865966
$288$	5340.39	+	3542.41i	1.09266	+	0.724787i
$289$	764.703			0.155649
$290$	228.921	+	396.503i	0.0463542	+	0.0802878i
$291$	991.459	−	3288.30i	0.199726	−	0.662417i
$292$	−2615.04	+	4529.38i	−0.524088	+	0.907747i
$293$	−1824.45	+	3160.04i	−0.363773	+	0.630073i	−0.988578	−	0.150708i	$-0.951845\pi$
$293$	−1824.45	+	3160.04i	−0.363773	+	0.630073i	0.624806	+	0.780780i	$0.285178\pi$
$294$	−3052.28	−	3247.93i	−0.605486	−	0.644296i
$295$	−19.3664	−	33.5436i	−0.00382222	−	0.00662028i
$296$	1773.01			0.348156
$297$	1318.38	+	488.624i	0.257576	+	0.0954640i
$298$	−14893.4			−2.89514
$299$	−924.882	−	1601.94i	−0.178887	−	0.309842i
$300$	−4097.63	−	4360.27i	−0.788589	−	0.839135i
$301$	−162.162	+	280.872i	−0.0310526	+	0.0537847i
$302$	3826.44	−	6627.59i	0.729096	−	1.26283i
$303$	−847.684	+	2811.45i	−0.160720	+	0.533048i
$304$	−1703.09	−	2949.84i	−0.321312	−	0.556528i
$305$	−379.887			−0.0713190
$306$	7964.63	−	3961.08i	1.48793	−	0.739999i
$307$	−3439.25			−0.639376			−0.319688	−	0.947523i	$-0.603578\pi$
$307$	−3439.25			−0.639376			−0.319688	+	0.947523i	$0.603578\pi$
$308$	−674.970	−	1169.08i	−0.124870	−	0.216281i
$309$	4912.65	−	1154.18i	0.904436	−	0.212489i
$310$	−304.687	+	527.734i	−0.0558228	+	0.0966880i
$311$	−3587.66	+	6214.02i	−0.654141	+	1.13301i	0.327968	+	0.944689i	$0.393636\pi$
$311$	−3587.66	+	6214.02i	−0.654141	+	1.13301i	−0.982108	+	0.188316i	$0.939697\pi$
$312$	3349.14	−	786.850i	0.607717	−	0.142778i
$313$	2428.65	+	4206.54i	0.438579	+	0.759642i	0.997580	−	0.0695253i	$-0.0221485\pi$
$313$	2428.65	+	4206.54i	0.438579	+	0.759642i	−0.559001	+	0.829167i	$0.688815\pi$
$314$	9525.33			1.71193
$315$	−93.9378	+	1511.06i	−0.0168025	+	0.270282i
$316$	5403.17			0.961874
$317$	−3773.97	−	6536.70i	−0.668666	−	1.15816i	−0.978277	−	0.207300i	$-0.933532\pi$
$317$	−3773.97	−	6536.70i	−0.668666	−	1.15816i	0.309611	−	0.950863i	$-0.399801\pi$
$318$	−2874.62	+	9534.03i	−0.506920	+	1.68126i
$319$	113.385	−	196.388i	0.0199007	−	0.0344690i
$320$	1857.93	−	3218.04i	0.324568	−	0.562168i
$321$	−2006.40	−	2135.00i	−0.348867	−	0.371228i
$322$	1008.53	+	1746.82i	0.174544	+	0.302319i
$323$	−8744.55			−1.50638
$324$	4890.15	−	6462.52i	0.838504	−	1.10811i
$325$	5032.56			0.858942
$326$	−4784.18	−	8286.44i	−0.812795	−	1.40780i
$327$	802.367	+	853.797i	0.135691	+	0.144389i
$328$	−2367.70	+	4100.98i	−0.398581	+	0.690363i
$329$	−2792.19	+	4836.22i	−0.467898	+	0.810423i
$330$	304.165	−	1008.80i	0.0507387	−	0.168281i
$331$	1564.86	+	2710.41i	0.259856	+	0.450084i	0.966203	−	0.257782i	$-0.0829915\pi$
$331$	1564.86	+	2710.41i	0.259856	+	0.450084i	−0.706347	+	0.707866i	$0.749658\pi$
$332$	1102.41			0.182237
$333$	−217.957	+	3506.02i	−0.0358679	+	0.576963i
$334$	8399.33			1.37602
$335$	−1581.69	−	2739.56i	−0.257960	−	0.446801i
$336$	1798.96	−	422.648i	0.292087	−	0.0686231i
$337$	4614.99	−	7993.39i	0.745978	−	1.29207i	−0.203759	−	0.979021i	$-0.565316\pi$
$337$	4614.99	−	7993.39i	0.745978	−	1.29207i	0.949737	−	0.313050i	$-0.101351\pi$
$338$	−357.273	+	618.815i	−0.0574944	+	0.0995832i
$339$	3495.69	−	821.280i	0.560058	−	0.131581i
$340$	−1938.23	−	3357.11i	−0.309162	−	0.535485i
$341$	301.823			0.0479315
$342$	−12266.8	+	6100.68i	−1.93951	+	0.964581i
$343$	−6533.19			−1.02845
$344$	−182.382	−	315.895i	−0.0285854	−	0.0495113i
$345$	−264.289	+	876.548i	−0.0412430	+	0.136788i
$346$	−6929.69	+	12002.6i	−1.07671	+	1.86492i
$347$	4052.20	−	7018.61i	0.626897	−	1.08582i	−0.361273	−	0.932460i	$-0.617658\pi$
$347$	4052.20	−	7018.61i	0.626897	−	1.08582i	0.988171	−	0.153358i	$-0.0490088\pi$
$348$	−895.117	−	952.491i	−0.137883	−	0.146721i
$349$	−1538.21	−	2664.26i	−0.235927	−	0.408638i	0.723615	−	0.690204i	$-0.242479\pi$
$349$	−1538.21	−	2664.26i	−0.235927	−	0.408638i	−0.959542	+	0.281566i	$0.909146\pi$
$350$	−5487.71			−0.838087
$351$	1144.24	+	6719.45i	0.174002	+	1.02182i
$352$	−2378.67			−0.360180
$353$	3075.04	+	5326.13i	0.463649	+	0.803063i	0.999139	−	0.0414780i	$-0.0132067\pi$
$353$	3075.04	+	5326.13i	0.463649	+	0.803063i	−0.535491	+	0.844541i	$0.679873\pi$
$354$	130.220	+	138.567i	0.0195512	+	0.0208043i
$355$	−2539.71	+	4398.91i	−0.379701	+	0.657662i
$356$	−48.9378	+	84.7627i	−0.00728566	+	0.0126191i
$357$	1369.52	−	4542.17i	0.203032	−	0.673381i
$358$	−2992.35	−	5182.91i	−0.441762	−	0.765154i
$359$	3307.94			0.486313			0.243156	−	0.969987i	$-0.421817\pi$
$359$	3307.94			0.486313			0.243156	+	0.969987i	$0.421817\pi$
$360$	−1418.97	−	941.237i	−0.207739	−	0.137799i
$361$	6608.97			0.963548
$362$	8638.41	+	14962.2i	1.25421	+	2.17236i
$363$	6224.71	−	1462.44i	0.900035	−	0.211455i
$364$	3272.17	−	5667.57i	0.471177	−	0.816103i
$365$	−1088.59	+	1885.49i	−0.156108	+	0.270387i
$366$	1815.56	−	426.550i	0.259292	−	0.0609183i
$367$	−1474.65	−	2554.16i	−0.209744	−	0.363287i	0.741890	−	0.670522i	$-0.233930\pi$
$367$	−1474.65	−	2554.16i	−0.209744	−	0.363287i	−0.951634	+	0.307235i	$0.900596\pi$
$368$	1117.47			0.158294
$369$	−7818.38	−	5186.13i	−1.10300	−	0.731650i
$370$	2632.47			0.369880
$371$	2655.46	+	4599.40i	0.371603	+	0.643636i
$372$	502.206	−	1665.63i	0.0699951	−	0.232148i
$373$	−581.790	+	1007.69i	−0.0807612	+	0.139883i	−0.903577	−	0.428425i	$-0.859068\pi$
$373$	−581.790	+	1007.69i	−0.0807612	+	0.139883i	0.822816	+	0.568308i	$0.192402\pi$
$374$	−1650.85	+	2859.36i	−0.228245	+	0.395331i
$375$	−3764.18	−	4005.46i	−0.518351	−	0.551576i
$376$	−3140.36	−	5439.25i	−0.430722	−	0.746032i
$377$	1099.35			0.150184
$378$	−1247.72	−	7327.17i	−0.169778	−	0.997007i
$379$	−4016.67			−0.544387			−0.272193	−	0.962243i	$-0.587749\pi$
$379$	−4016.67			−0.544387			−0.272193	+	0.962243i	$0.587749\pi$
$380$	2985.17	+	5170.47i	0.402990	+	0.697999i
$381$	−3187.98	−	3392.32i	−0.428675	−	0.456152i
$382$	5252.40	−	9097.42i	0.703497	−	1.21849i
$383$	5401.65	−	9355.93i	0.720656	−	1.24821i	−0.240081	−	0.970753i	$-0.577174\pi$
$383$	5401.65	−	9355.93i	0.720656	−	1.24821i	0.960737	−	0.277460i	$-0.0894926\pi$
$384$	−2417.94	+	8019.39i	−0.321328	+	1.06572i
$385$	−280.977	−	486.666i	−0.0371945	−	0.0644228i
$386$	−5837.30			−0.769717
$387$	647.083	−	321.816i	0.0849950	−	0.0422708i
$388$	7347.93			0.961429
$389$	−1032.29	−	1787.99i	−0.134549	−	0.233045i	0.790876	−	0.611976i	$-0.209625\pi$
$389$	−1032.29	−	1787.99i	−0.134549	−	0.233045i	−0.925425	+	0.378931i	$0.876292\pi$
$390$	4972.62	−	1168.27i	0.645637	−	0.151687i
$391$	1434.42	−	2484.49i	0.185529	−	0.321346i
$392$	1336.76	−	2315.33i	0.172236	−	0.298321i
$393$	−8370.96	+	1966.68i	−1.07445	+	0.252432i
$394$	5751.49	+	9961.87i	0.735421	+	1.27379i
$395$	2249.23			0.286509
$396$	−186.642	+	3002.28i	−0.0236846	+	0.380985i
$397$	−7937.61			−1.00347			−0.501735	−	0.865022i	$-0.667305\pi$
$397$	−7937.61			−1.00347			−0.501735	+	0.865022i	$0.667305\pi$
$398$	−5415.82	−	9380.47i	−0.682086	−	1.18141i
$399$	−2109.27	+	6995.65i	−0.264650	+	0.877746i
$400$	−1520.13	+	2632.94i	−0.190016	+	0.329117i
$401$	−1289.10	+	2232.79i	−0.160536	+	0.278056i	−0.935061	−	0.354487i	$-0.884656\pi$
$401$	−1289.10	+	2232.79i	−0.160536	+	0.278056i	0.774525	+	0.632543i	$0.217989\pi$
$402$	10635.3	+	11317.0i	1.31950	+	1.40408i
$403$	731.602	+	1267.17i	0.0904310	+	0.156631i
$404$	−6282.38			−0.773663
$405$	2035.67	−	2690.22i	0.249762	−	0.330069i
$406$	−1198.78			−0.146538
$407$	−651.931	−	1129.18i	−0.0793981	−	0.137521i
$408$	3653.99	+	3888.20i	0.443381	+	0.471800i
$409$	−2922.88	+	5062.57i	−0.353367	+	0.612049i	−0.986837	−	0.161718i	$-0.948297\pi$
$409$	−2922.88	+	5062.57i	−0.353367	+	0.612049i	0.633470	+	0.773767i	$0.281630\pi$
$410$	−3515.44	+	6088.92i	−0.423451	+	0.733439i
$411$	−3976.64	+	13189.0i	−0.477258	+	1.58289i
$412$	5398.24	+	9350.03i	0.645515	+	1.11806i
$413$	101.415			0.0120830
$414$	278.877	−	4485.96i	0.0331064	−	0.532543i
$415$	458.912			0.0542822
$416$	−5765.75	−	9986.56i	−0.679541	−	1.17700i
$417$	−3207.89	+	753.665i	−0.376717	+	0.0885063i
$418$	2542.57	−	4403.86i	0.297515	−	0.515310i
$419$	4370.66	−	7570.20i	0.509596	−	0.882646i	−0.490343	−	0.871530i	$-0.663128\pi$
$419$	4370.66	−	7570.20i	0.509596	−	0.882646i	0.999938	−	0.0111158i	$-0.00353834\pi$
$420$	−3153.21	+	740.818i	−0.366336	+	0.0860672i
$421$	−528.254	−	914.963i	−0.0611533	−	0.105921i	0.833828	−	0.552024i	$-0.186145\pi$
$421$	−528.254	−	914.963i	−0.0611533	−	0.105921i	−0.894981	+	0.446104i	$0.852811\pi$
$422$	−12175.6			−1.40450
$423$	11141.8	−	5541.21i	1.28070	−	0.636933i
$424$	−5973.16			−0.684156
$425$	3902.56	+	6759.44i	0.445417	+	0.771484i
$426$	7198.58	−	23875.0i	0.818714	−	2.71537i
$427$	497.333	−	861.406i	0.0563645	−	0.0976261i
$428$	3134.09	−	5428.40i	0.353953	−	0.613065i
$429$	−1732.59	−	1843.65i	−0.194989	−	0.207487i
$430$	−270.791	−	469.023i	−0.0303690	−	0.0526007i
$431$	9868.64			1.10291			0.551457	−	0.834203i	$-0.314072\pi$
$431$	9868.64			1.10291			0.551457	+	0.834203i	$0.314072\pi$
$432$	−3861.11	−	1431.02i	−0.430018	−	0.159375i
$433$	477.948			0.0530456			0.0265228	−	0.999648i	$-0.491557\pi$
$433$	477.948			0.0530456			0.0265228	+	0.999648i	$0.491557\pi$
$434$	−797.769	−	1381.78i	−0.0882353	−	0.152828i
$435$	−372.619	−	396.503i	−0.0410706	−	0.0437031i
$436$	−1253.34	+	2170.84i	−0.137669	+	0.238450i
$437$	−2209.24	+	3826.51i	−0.241835	+	0.418871i
$438$	3085.50	−	10233.5i	0.336601	−	1.11638i
$439$	526.239	+	911.473i	0.0572119	+	0.0990939i	0.893213	−	0.449634i	$-0.148446\pi$
$439$	526.239	+	911.473i	0.0572119	+	0.0990939i	−0.836001	+	0.548728i	$0.815112\pi$
$440$	632.024			0.0684786
$441$	4414.10	+	2927.98i	0.476633	+	0.316162i
$442$	−16006.3			−1.72249
$443$	5249.35	+	9092.14i	0.562989	+	0.975126i	0.997234	+	0.0743307i	$0.0236820\pi$
$443$	5249.35	+	9092.14i	0.562989	+	0.975126i	−0.434245	+	0.900795i	$0.642985\pi$
$444$	−7316.18	+	1718.87i	−0.782006	+	0.183725i
$445$	−20.3718	+	35.2850i	−0.00217015	+	0.00375881i
$446$	94.1300	−	163.038i	0.00999369	−	0.0173096i
$447$	17230.6	−	4048.18i	1.82322	−	0.428349i
$448$	4864.66	+	8425.85i	0.513022	+	0.888580i
$449$	−7329.40			−0.770369			−0.385184	−	0.922840i	$-0.625862\pi$
$449$	−7329.40			−0.770369			−0.385184	+	0.922840i	$0.625862\pi$
$450$	10190.2	+	6759.44i	1.06749	+	0.708095i
$451$	3482.39			0.363591
$452$	3841.22	+	6653.18i	0.399725	+	0.692344i
$453$	−2625.48	+	8707.72i	−0.272308	+	0.903144i
$454$	−1493.70	+	2587.17i	−0.154412	+	0.267449i
$455$	1362.14	−	2359.30i	0.140347	−	0.243089i
$456$	−5627.71	−	5988.43i	−0.577942	−	0.614987i
$457$	−3572.20	−	6187.23i	−0.365646	−	0.633318i	0.623233	−	0.782036i	$-0.285819\pi$
$457$	−3572.20	−	6187.23i	−0.365646	−	0.633318i	−0.988880	+	0.148718i	$0.952485\pi$
$458$	18775.9			1.91559
$459$	−8137.86	+	6747.55i	−0.827544	+	0.686163i
$460$	−1958.71			−0.198533
$461$	−2859.34	−	4952.53i	−0.288878	−	0.500352i	0.684664	−	0.728859i	$-0.259949\pi$
$461$	−2859.34	−	4952.53i	−0.288878	−	0.500352i	−0.973542	+	0.228507i	$0.926616\pi$
$462$	1889.29	+	2010.39i	0.190255	+	0.202450i
$463$	−394.233	+	682.831i	−0.0395714	+	0.0685397i	−0.885133	−	0.465339i	$-0.845933\pi$
$463$	−394.233	+	682.831i	−0.0395714	+	0.0685397i	0.845561	+	0.533878i	$0.179266\pi$
$464$	−332.068	+	575.158i	−0.0332238	+	0.0575454i
$465$	209.058	−	693.368i	0.0208491	−	0.0691488i
$466$	−7577.91	−	13125.3i	−0.753305	−	1.30476i
$467$	−17068.0			−1.69125			−0.845626	−	0.533776i	$-0.820772\pi$
$467$	−17068.0			−1.69125			−0.845626	+	0.533776i	$0.820772\pi$
$468$	−13057.1	+	6493.75i	−1.28967	+	0.641397i
$469$	8282.72			0.815481
$470$	−4662.63	−	8075.91i	−0.457598	−	0.792583i
$471$	−11020.1	+	2589.08i	−1.07809	+	0.253288i
$472$	−57.0302	+	98.7793i	−0.00556150	+	0.00963280i
$473$	−134.123	+	232.307i	−0.0130380	+	0.0225824i
$474$	−10749.6	+	2525.51i	−1.04165	+	0.244727i
$475$	−6010.56	−	10410.6i	−0.580596	−	1.00562i
$476$	10149.8			0.977343
$477$	734.285	−	11811.6i	0.0704834	−	1.13378i
$478$	24674.4			2.36105
$479$	−758.994	−	1314.62i	−0.0723994	−	0.125399i	0.827553	−	0.561388i	$-0.189732\pi$
$479$	−758.994	−	1314.62i	−0.0723994	−	0.125399i	−0.899952	+	0.435988i	$0.856399\pi$
$480$	−1647.59	+	5464.43i	−0.156670	+	0.519616i
$481$	3160.48	−	5474.11i	0.299596	−	0.518915i
$482$	−14405.4	+	24950.9i	−1.36130	+	2.35785i
$483$	−1641.60	−	1746.82i	−0.154649	−	0.164562i
$484$	6840.00	+	11847.2i	0.642374	+	1.11262i
$485$	3058.80			0.286377
$486$	−6708.25	+	15142.8i	−0.626116	+	1.41336i
$487$	12737.3			1.18518			0.592591	−	0.805503i	$-0.298105\pi$
$487$	12737.3			1.18518			0.592591	+	0.805503i	$0.298105\pi$
$488$	559.347	+	968.817i	0.0518861	+	0.0898694i
$489$	7787.30	+	8286.44i	0.720151	+	0.766310i
$490$	1984.74	−	3437.68i	0.182983	−	0.316936i
$491$	−2823.85	+	4891.05i	−0.259549	+	0.449552i	−0.966121	−	0.258089i	$-0.916907\pi$
$491$	−2823.85	+	4891.05i	−0.259549	+	0.449552i	0.706572	+	0.707641i	$0.250241\pi$
$492$	5794.38	−	19217.8i	0.530957	−	1.76099i
$493$	852.505	+	1476.58i	0.0778801	+	0.134892i
$494$	24652.1			2.24525
$495$	−77.6952	+	1249.79i	−0.00705483	+	0.113482i
$496$	−883.945			−0.0800208
$497$	−6649.78	−	11517.7i	−0.600167	−	1.03952i
$498$	−2193.24	+	515.281i	−0.197352	+	0.0463661i
$499$	−5423.14	+	9393.15i	−0.486519	+	0.842676i	−0.999880	−	0.0154970i	$-0.995067\pi$
$499$	−5423.14	+	9393.15i	−0.486519	+	0.842676i	0.513361	+	0.858173i	$0.328400\pi$
$500$	5879.83	−	10184.2i	0.525908	−	0.910899i
$501$	−9717.43	+	2283.02i	−0.866553	+	0.203589i
$502$	−9040.73	−	15659.0i	−0.803800	−	1.39222i
$503$	−12345.7			−1.09437			−0.547186	−	0.837011i	$-0.684301\pi$
$503$	−12345.7			−1.09437			−0.547186	+	0.837011i	$0.684301\pi$
$504$	3991.94	−	1985.32i	0.352808	−	0.175463i
$505$	−2615.23			−0.230448
$506$	834.147	+	1444.79i	0.0732853	+	0.126934i
$507$	245.140	−	813.036i	0.0214734	−	0.0712193i
$508$	4979.77	−	8625.22i	0.434925	−	0.753311i
$509$	2947.87	−	5105.87i	0.256704	−	0.444624i	−0.708653	−	0.705557i	$-0.750697\pi$
$509$	2947.87	−	5105.87i	0.256704	−	0.444624i	0.965357	+	0.260933i	$0.0840302\pi$
$510$	5425.24	+	5772.98i	0.471046	+	0.501239i
$511$	−2850.27	−	4936.82i	−0.246749	−	0.427381i
$512$	10166.2			0.877514
$513$	12533.6	−	10392.3i	1.07870	−	0.894407i
$514$	−14623.6			−1.25490
$515$	2247.18	+	3892.23i	0.192277	+	0.333033i
$516$	1058.83	+	1126.70i	0.0903344	+	0.0961245i
$517$	−2309.40	+	4000.00i	−0.196455	+	0.340270i
$518$	−3446.32	+	5969.20i	−0.292322	+	0.506316i
$519$	4754.74	−	15769.7i	0.402139	−	1.33374i
$520$	1531.99	+	2653.48i	0.129196	+	0.223775i
$521$	5211.51			0.438235			0.219118	−	0.975698i	$-0.429682\pi$
$521$	5211.51			0.438235			0.219118	+	0.975698i	$0.429682\pi$
$522$	2226.03	+	1476.58i	0.186649	+	0.123809i
$523$	−9809.86			−0.820182			−0.410091	−	0.912045i	$-0.634503\pi$
$523$	−9809.86			−0.820182			−0.410091	+	0.912045i	$0.634503\pi$
$524$	−9198.38	−	15932.1i	−0.766857	−	1.32824i
$525$	6348.90	−	1491.62i	0.527788	−	0.123999i
$526$	−14256.9	+	24693.7i	−1.18181	+	2.04695i
$527$	−1134.66	+	1965.29i	−0.0937886	+	0.162447i
$528$	1487.90	−	349.569i	0.122638	−	0.0288126i
$529$	5358.71	+	9281.56i	0.440430	+	0.762847i
$530$	−8868.62			−0.726846
$531$	−188.319	−	124.917i	−0.0153905	−	0.0102089i
$532$	−15632.3			−1.27396
$533$	8441.11	+	14620.4i	0.685976	+	1.18814i
$534$	57.7420	−	191.509i	0.00467929	−	0.0155195i
$535$	1304.66	−	2259.73i	0.105430	−	0.182611i
$536$	−4657.75	+	8067.47i	−0.375344	+	0.650115i
$537$	4870.71	+	5182.91i	0.391409	+	0.416497i
$538$	6350.72	+	10999.8i	0.508920	+	0.881476i
$539$	−1966.09			−0.157116
$540$	6767.75	+	2508.30i	0.539329	+	0.199889i
$541$	8084.25			0.642456			0.321228	−	0.947002i	$-0.395904\pi$
$541$	8084.25			0.642456			0.321228	+	0.947002i	$0.395904\pi$
$542$	2919.33	+	5056.43i	0.231358	+	0.400724i
$543$	−14060.9	−	14962.2i	−1.11125	−	1.18248i
$544$	8942.24	−	15488.4i	0.704771	−	1.22070i
$545$	−521.738	+	903.677i	−0.0410070	+	0.0710262i
$546$	−3860.86	+	12805.0i	−0.302618	+	1.00367i
$547$	12033.6	+	20842.7i	0.940617	+	1.62920i	0.764298	+	0.644863i	$0.223086\pi$
$547$	12033.6	+	20842.7i	0.940617	+	1.62920i	0.176319	+	0.984333i	$0.443581\pi$
$548$	−29471.8			−2.29739
$549$	−1984.54	+	986.976i	−0.154277	+	0.0767270i
$550$	−4538.84			−0.351885
$551$	−1312.99	−	2274.17i	−0.101516	−	0.175831i
$552$	2624.58	−	616.621i	0.202372	−	0.0475455i
$553$	−2944.60	+	5100.20i	−0.226433	+	0.392193i
$554$	18310.3	−	31714.4i	1.40421	−	2.43216i
$555$	−3045.58	+	715.531i	−0.232933	+	0.0547254i
$556$	−3524.98	−	6105.44i	−0.268871	−	0.465698i
$557$	4582.37			0.348584			0.174292	−	0.984694i	$-0.444236\pi$
$557$	4582.37			0.348584			0.174292	+	0.984694i	$0.444236\pi$
$558$	−220.598	+	3548.49i	−0.0167359	+	0.269211i
$559$	−1300.42			−0.0983934
$560$	822.891	+	1425.29i	0.0620955	+	0.107553i
$561$	1132.72	−	3756.79i	0.0852466	−	0.282731i
$562$	11322.7	−	19611.6i	0.849860	−	1.47200i
$563$	1547.66	−	2680.62i	0.115854	−	0.200666i	−0.802267	−	0.596966i	$-0.796373\pi$
$563$	1547.66	−	2680.62i	0.115854	−	0.200666i	0.918121	+	0.396300i	$0.129706\pi$
$564$	18231.6	+	19400.2i	1.36115	+	1.44840i
$565$	1599.02	+	2769.59i	0.119064	+	0.206226i
$566$	−13466.9			−1.00010
$567$	3435.13	+	8137.87i	0.254430	+	0.602749i
$568$	14957.9			1.10496
$569$	−10282.5	−	17809.9i	−0.757586	−	1.31218i	−0.944078	−	0.329721i	$-0.893045\pi$
$569$	−10282.5	−	17809.9i	−0.757586	−	1.31218i	0.186492	−	0.982456i	$-0.440288\pi$
$570$	−8355.71	−	8891.29i	−0.614004	−	0.653360i
$571$	584.992	−	1013.24i	0.0428742	−	0.0742602i	−0.843792	−	0.536670i	$-0.819682\pi$
$571$	584.992	−	1013.24i	0.0428742	−	0.0742602i	0.886666	+	0.462410i	$0.153015\pi$
$572$	2706.39	−	4687.60i	0.197832	−	0.342655i
$573$	−3603.88	+	11952.7i	−0.262748	+	0.871435i
$574$	−9204.54	−	15942.7i	−0.669320	−	1.15930i
$575$	3943.80			0.286031
$576$	1345.17	−	21638.1i	0.0973069	−	1.56526i
$577$	−13073.0			−0.943214			−0.471607	−	0.881809i	$-0.656326\pi$
$577$	−13073.0			−0.943214			−0.471607	+	0.881809i	$0.656326\pi$
$578$	−1671.75	−	2895.55i	−0.120304	−	0.208372i
$579$	6753.35	−	1586.64i	0.484731	−	0.113883i
$580$	582.049	−	1008.14i	0.0416694	−	0.0721735i
$581$	−600.789	+	1040.60i	−0.0429000	+	0.0743050i
$582$	−14618.6	+	3434.51i	−1.04117	+	0.244614i
$583$	2196.31	+	3804.13i	0.156024	+	0.270242i
$584$	6411.36			0.454287
$585$	−5435.42	+	2703.22i	−0.384149	+	0.191050i
$586$	15954.0			1.12466
$587$	7273.91	+	12598.8i	0.511459	+	0.885873i	0.999912	+	0.0132825i	$0.00422807\pi$
$587$	7273.91	+	12598.8i	0.511459	+	0.885873i	−0.488453	+	0.872590i	$0.662439\pi$
$588$	−3271.39	+	10850.0i	−0.229438	+	0.760961i
$589$	1747.55	−	3026.85i	0.122252	−	0.211747i
$590$	−84.6754	+	146.662i	−0.00590852	+	0.0102339i
$591$	−9361.80	−	9961.87i	−0.651596	−	0.693361i
$592$	1909.30	+	3307.00i	0.132554	+	0.229589i
$593$	19018.0			1.31699			0.658494	−	0.752586i	$-0.271194\pi$
$593$	19018.0			1.31699			0.658494	+	0.752586i	$0.271194\pi$
$594$	−1031.98	−	6060.24i	−0.0712840	−	0.418611i
$595$	4225.16			0.291117
$596$	18933.8	+	32794.3i	1.30127	+	2.25387i
$597$	8815.43	+	9380.47i	0.604341	+	0.643077i
$598$	−4043.84	+	7004.14i	−0.276530	+	0.478964i
$599$	−5587.20	+	9677.32i	−0.381113	+	0.660108i	−0.991222	−	0.132210i	$-0.957793\pi$
$599$	−5587.20	+	9677.32i	−0.381113	+	0.660108i	0.610108	+	0.792318i	$0.291126\pi$
$600$	−2117.42	+	7022.70i	−0.144073	+	0.477834i
$601$	−2294.27	−	3973.79i	−0.155716	−	0.269708i	0.777604	−	0.628755i	$-0.216435\pi$
$601$	−2294.27	−	3973.79i	−0.155716	−	0.269708i	−0.933319	+	0.359047i	$0.883102\pi$
$602$	1418.03			0.0960045
$603$	−15380.3	−	10202.2i	−1.03870	−	0.688995i
$604$	−19458.0			−1.31082
$605$	2847.35	+	4931.76i	0.191341	+	0.331413i
$606$	12498.7	−	2936.46i	0.837832	−	0.196841i
$607$	5744.99	−	9950.61i	0.384155	−	0.665375i	−0.607497	−	0.794322i	$-0.707826\pi$
$607$	5744.99	−	9950.61i	0.384155	−	0.665375i	0.991652	+	0.128947i	$0.0411596\pi$
$608$	−13772.5	+	23854.6i	−0.918662	+	1.59117i
$609$	1386.90	−	325.840i	0.0922825	−	0.0216809i
$610$	830.487	+	1438.45i	0.0551237	+	0.0954770i
$611$	−22391.4			−1.48258
$612$	−18847.4	−	12501.9i	−1.24487	−	0.825752i
$613$	−22966.9			−1.51326			−0.756628	−	0.653846i	$-0.773154\pi$
$613$	−22966.9			−1.51326			−0.756628	+	0.653846i	$0.773154\pi$
$614$	7518.69	+	13022.7i	0.494185	+	0.855953i
$615$	2412.08	−	7999.98i	0.158154	−	0.524537i
$616$	−827.420	+	1433.13i	−0.0541197	+	0.0937380i
$617$	4248.31	−	7358.29i	0.277197	−	0.480120i	−0.693490	−	0.720466i	$-0.743928\pi$
$617$	4248.31	−	7358.29i	0.277197	−	0.480120i	0.970687	+	0.240347i	$0.0772612\pi$
$618$	−15110.1	−	16078.6i	−0.983521	−	1.04656i
$619$	−7169.94	−	12418.7i	−0.465564	−	0.806381i	0.533662	−	0.845698i	$-0.320815\pi$
$619$	−7169.94	−	12418.7i	−0.465564	−	0.806381i	−0.999227	+	0.0393163i	$0.987482\pi$
$620$	1549.38			0.100362
$621$	896.688	+	5265.74i	0.0579434	+	0.340269i
$622$	31372.6			2.02239
$623$	−53.3399	−	92.3874i	−0.00343021	−	0.00594129i
$624$	5074.21	+	5399.46i	0.325531	+	0.346396i
$625$	−4026.36	+	6973.86i	−0.257687	+	0.446327i
$626$	10618.7	−	18392.2i	0.677971	−	1.17428i
$627$	−1744.56	+	5786.05i	−0.111118	+	0.368537i
$628$	−12109.4	−	20974.1i	−0.769456	−	1.33274i
$629$	9803.34			0.621439
$630$	5927.01	−	2947.70i	0.374822	−	0.186411i
$631$	17834.3			1.12516			0.562578	−	0.826744i	$-0.309810\pi$
$631$	17834.3			1.12516			0.562578	+	0.826744i	$0.309810\pi$
$632$	−3311.77	−	5736.16i	−0.208442	−	0.361032i
$633$	14086.3	−	3309.46i	0.884489	−	0.207803i
$634$	−16500.8	+	28580.3i	−1.03365	+	1.79033i
$635$	2072.98	−	3590.51i	0.129549	−	0.224386i
$636$	24647.8	−	5790.77i	1.53671	−	0.361036i
$637$	−4765.68	−	8254.39i	−0.296425	−	0.513424i
$638$	−991.499			−0.0615264
$639$	−1838.79	+	29578.3i	−0.113836	+	1.83114i
$640$	−7459.69			−0.460735
$641$	−13173.0	−	22816.3i	−0.811705	−	1.40591i	−0.911670	−	0.410923i	$-0.865207\pi$
$641$	−13173.0	−	22816.3i	−0.811705	−	1.40591i	0.0999654	−	0.994991i	$-0.468127\pi$
$642$	−3697.93	+	12264.7i	−0.227330	+	0.753968i
$643$	10782.5	−	18675.9i	0.661309	−	1.14542i	−0.318963	−	0.947767i	$-0.603335\pi$
$643$	10782.5	−	18675.9i	0.661309	−	1.14542i	0.980272	−	0.197653i	$-0.0633321\pi$
$644$	2564.26	−	4441.43i	0.156904	−	0.271765i
$645$	440.771	+	469.023i	0.0269075	+	0.0286322i
$646$	19116.8	+	33111.3i	1.16431	+	2.01664i
$647$	4186.32			0.254376			0.127188	−	0.991879i	$-0.459405\pi$
$647$	4186.32			0.254376			0.127188	+	0.991879i	$0.459405\pi$
$648$	−9858.11	−	1230.45i	−0.597629	−	0.0745934i
$649$	83.8794			0.00507328
$650$	−11001.9	−	19055.8i	−0.663891	−	1.14989i
$651$	1298.54	+	1381.78i	0.0781781	+	0.0831891i
$652$	−12164.1	+	21068.9i	−0.730650	+	1.26552i
$653$	−1402.57	+	2429.33i	−0.0840534	+	0.145585i	−0.904987	−	0.425438i	$-0.860120\pi$
$653$	−1402.57	+	2429.33i	−0.0840534	+	0.145585i	0.820934	+	0.571023i	$0.193453\pi$
$654$	1478.82	−	4904.69i	0.0884196	−	0.293255i
$655$	−3829.10	−	6632.20i	−0.228420	−	0.395636i
$656$	−10198.8			−0.607008
$657$	−788.153	+	12678.1i	−0.0468018	+	0.752844i
$658$	24416.5			1.44659
$659$	9536.15	+	16517.1i	0.563696	+	0.976350i	0.997170	+	0.0751839i	$0.0239544\pi$
$659$	9536.15	+	16517.1i	0.563696	+	0.976350i	−0.433474	+	0.901166i	$0.642712\pi$
$660$	−2608.00	+	612.725i	−0.153812	+	0.0361368i
$661$	12256.5	−	21228.9i	0.721216	−	1.24918i	−0.239296	−	0.970947i	$-0.576917\pi$
$661$	12256.5	−	21228.9i	0.721216	−	1.24918i	0.960513	−	0.278237i	$-0.0897500\pi$
$662$	6842.00	−	11850.7i	0.401695	−	0.695756i
$663$	18518.1	−	4350.66i	1.08474	−	0.254850i
$664$	−675.702	−	1170.35i	−0.0394915	−	0.0684012i
$665$	−6507.40			−0.379468
$666$	13752.0	−	6839.35i	0.800122	−	0.397927i
$667$	861.513			0.0500119
$668$	−10678.0	−	18494.8i	−0.618477	−	1.07123i
$669$	−64.5864	+	214.209i	−0.00373252	+	0.0123794i
$670$	−6915.58	+	11978.1i	−0.398764	+	0.690680i
$671$	411.340	−	712.462i	0.0236656	−	0.0409900i
$672$	−10233.8	−	10889.8i	−0.587467	−	0.625122i
$673$	1773.32	+	3071.49i	0.101570	+	0.175924i	0.912332	−	0.409452i	$-0.134280\pi$
$673$	1773.32	+	3071.49i	0.101570	+	0.175924i	−0.810762	+	0.585376i	$0.800947\pi$
$674$	−40356.1			−2.30632
$675$	−13626.7	−	5050.38i	−0.777023	−	0.287984i
$676$	1816.79			0.103367
$677$	−8937.50	−	15480.2i	−0.507380	−	0.878807i	−0.999964	−	0.00854232i	$-0.997281\pi$
$677$	−8937.50	−	15480.2i	−0.507380	−	0.878807i	0.492584	−	0.870265i	$-0.336052\pi$
$678$	−10751.8	−	11441.0i	−0.609030	−	0.648067i
$679$	−4004.45	+	6935.91i	−0.226328	+	0.392012i
$680$	−2376.00	+	4115.35i	−0.133993	+	0.232083i
$681$	1024.89	−	3399.18i	0.0576709	−	0.191273i
$682$	−659.829	−	1142.86i	−0.0370471	−	0.0641675i
$683$	2857.23			0.160072			0.0800358	−	0.996792i	$-0.474497\pi$
$683$	2857.23			0.160072			0.0800358	+	0.996792i	$0.474497\pi$
$684$	29027.9	+	19254.9i	1.62267	+	1.07636i
$685$	−12268.5			−0.684315
$686$	14282.5	+	24737.9i	0.794908	+	1.37682i
$687$	−21722.4	+	5103.48i	−1.20635	+	0.283421i
$688$	392.803	−	680.354i	0.0217667	−	0.0377010i
$689$	−10647.5	+	18441.9i	−0.588732	+	1.01971i
$690$	3896.83	−	915.524i	0.215000	−	0.0505122i
$691$	7813.79	+	13533.9i	0.430175	+	0.745084i	0.996888	−	0.0788308i	$-0.0251187\pi$
$691$	7813.79	+	13533.9i	0.430175	+	0.745084i	−0.566714	+	0.823915i	$0.691785\pi$
$692$	35238.5			1.93579
$693$	−2732.22	−	1812.35i	−0.149767	−	0.0993441i
$694$	−35434.7			−1.93816
$695$	−1467.38	−	2541.57i	−0.0800874	−	0.138716i
$696$	−462.546	+	1534.09i	−0.0251908	+	0.0835483i
$697$	−13091.5	+	22675.2i	−0.711445	+	1.23226i
$698$	−6725.49	+	11648.9i	−0.364704	+	0.631687i
$699$	12334.7	+	13125.3i	0.667442	+	0.710223i
$700$	6976.45	+	12083.6i	0.376693	+	0.652451i
$701$	17562.6			0.946264			0.473132	−	0.880992i	$-0.343123\pi$
$701$	17562.6			0.946264			0.473132	+	0.880992i	$0.343123\pi$
$702$	22941.8	−	19022.3i	1.23345	−	1.02272i
$703$	−15098.7			−0.810039
$704$	4023.53	+	6968.95i	0.215401	+	0.373086i
$705$	7589.44	+	8075.91i	0.405440	+	0.431427i
$706$	13445.0	−	23287.3i	0.716724	−	1.24140i
$707$	3423.75	−	5930.11i	0.182126	−	0.315452i
$708$	139.568	−	462.893i	0.00740858	−	0.0245715i
$709$	−10001.8	−	17323.6i	−0.529795	−	0.917632i	−0.999396	−	0.0347532i	$-0.988935\pi$
$709$	−10001.8	−	17323.6i	−0.529795	−	0.917632i	0.469601	−	0.882879i	$-0.344398\pi$
$710$	22208.7			1.17391
$711$	11750.0	−	5843.68i	0.619775	−	0.308235i
$712$	119.982			0.00631533
$713$	573.324	+	993.027i	0.0301138	+	0.0521587i
$714$	−20192.9	+	4744.14i	−1.05840	+	0.248663i
$715$	1126.62	−	1951.36i	0.0589273	−	0.102065i
$716$	−7608.27	+	13177.9i	−0.397115	+	0.687824i
$717$	−28546.6	+	6706.75i	−1.48688	+	0.349328i
$718$	−7231.62	−	12525.5i	−0.375880	−	0.651043i
$719$	25504.1			1.32287			0.661435	−	0.750002i	$-0.269948\pi$
$719$	25504.1			1.32287			0.661435	+	0.750002i	$0.269948\pi$
$720$	227.545	−	3660.24i	0.0117779	−	0.189457i
$721$	−11767.7			−0.607837
$722$	−14448.1	−	25024.9i	−0.744743	−	1.28993i
$723$	9884.14	−	32782.0i	0.508430	−	1.68627i
$724$	21963.8	−	38042.4i	1.12746	−	1.95281i
$725$	−1171.94	+	2029.85i	−0.0600340	+	0.103982i
$726$	−19145.6	−	20372.8i	−0.978735	−	1.04147i
$727$	11954.9	+	20706.5i	0.609879	+	1.05634i	0.991260	+	0.131924i	$0.0421155\pi$
$727$	11954.9	+	20706.5i	0.609879	+	1.05634i	−0.381380	+	0.924418i	$0.624551\pi$
$728$	−8022.47			−0.408424
$729$	3645.00	−	19342.6i	0.185185	−	0.982704i
$730$	9519.23			0.482634
$731$	−1008.43	−	1746.65i	−0.0510233	−	0.0883750i
$732$	−3247.33	−	3455.48i	−0.163968	−	0.174478i
$733$	4252.77	−	7366.02i	0.214297	−	0.371173i	−0.738758	−	0.673971i	$-0.764587\pi$
$733$	4252.77	−	7366.02i	0.214297	−	0.371173i	0.953055	+	0.302798i	$0.0979206\pi$
$734$	−6447.57	+	11167.5i	−0.324229	+	0.561581i
$735$	−1361.81	+	4516.62i	−0.0683418	+	0.226664i
$736$	−4518.36	−	7826.04i	−0.226290	−	0.391945i
$737$	6850.57			0.342394
$738$	−2545.22	+	40942.0i	−0.126953	+	2.04213i
$739$	25802.5			1.28438			0.642192	−	0.766544i	$-0.278025\pi$
$739$	25802.5			1.28438			0.642192	+	0.766544i	$0.278025\pi$
$740$	−3346.62	−	5796.52i	−0.166249	−	0.287952i
$741$	−28520.8	+	6700.70i	−1.41395	+	0.332195i
$742$	11610.4	−	20109.9i	0.574437	−	0.994955i
$743$	−13668.8	+	23675.0i	−0.674911	+	1.16898i	0.301584	+	0.953440i	$0.402485\pi$
$743$	−13668.8	+	23675.0i	−0.674911	+	1.16898i	−0.976495	+	0.215541i	$0.930849\pi$
$744$	−2076.10	+	487.760i	−0.102303	+	0.0240352i
$745$	7881.75	+	13651.6i	0.387604	+	0.671350i
$746$	5087.50			0.249687
$747$	2397.36	−	1192.29i	0.117423	−	0.0583983i
$748$	8394.82			0.410354
$749$	3416.01	+	5916.71i	0.166647	+	0.288641i
$750$	−6937.65	+	23009.6i	−0.337770	+	1.12026i
$751$	−1668.32	+	2889.61i	−0.0810623	+	0.140404i	−0.903706	−	0.428153i	$-0.859165\pi$
$751$	−1668.32	+	2889.61i	−0.0810623	+	0.140404i	0.822644	+	0.568557i	$0.192498\pi$
$752$	6763.50	−	11714.7i	0.327978	−	0.568075i
$753$	14715.8	+	15659.0i	0.712181	+	0.757830i
$754$	−2403.33	−	4162.70i	−0.116080	−	0.201056i
$755$	−8099.98			−0.390448
$756$	−14547.7	+	12062.3i	−0.699861	+	0.580294i
$757$	33149.5			1.59160			0.795798	−	0.605562i	$-0.207052\pi$
$757$	33149.5			1.59160			0.795798	+	0.605562i	$0.207052\pi$
$758$	8781.01	+	15209.2i	0.420766	+	0.728788i
$759$	−1357.76	−	1444.79i	−0.0649321	−	0.0690940i
$760$	3659.41	−	6338.29i	0.174659	−	0.302518i
$761$	5498.42	−	9523.54i	0.261915	−	0.453651i	−0.704836	−	0.709371i	$-0.748979\pi$
$761$	5498.42	−	9523.54i	0.261915	−	0.453651i	0.966751	+	0.255720i	$0.0823125\pi$
$762$	−5875.67	+	19487.4i	−0.279335	+	0.926448i
$763$	−1366.08	−	2366.12i	−0.0648169	−	0.112266i
$764$	−26709.2			−1.26480
$765$	−7845.77	−	5204.30i	−0.370803	−	0.245963i
$766$	−47235.0			−2.22803
$767$	203.319	+	352.158i	0.00957159	+	0.0165785i
$768$	3157.79	−	741.894i	0.148368	−	0.0348578i
$769$	−16642.5	+	28825.6i	−0.780420	+	1.35173i	0.151277	+	0.988491i	$0.451661\pi$
$769$	−16642.5	+	28825.6i	−0.780420	+	1.35173i	−0.931697	+	0.363236i	$0.881672\pi$
$770$	−1228.51	+	2127.84i	−0.0574966	+	0.0995870i
$771$	16918.5	−	3974.85i	0.790279	−	0.185669i
$772$	7420.88	+	12853.3i	0.345963	+	0.599225i
$773$	−7242.46			−0.336990			−0.168495	−	0.985703i	$-0.553891\pi$
$773$	−7242.46			−0.336990			−0.168495	+	0.985703i	$0.553891\pi$
$774$	−2633.17	−	1746.65i	−0.122283	−	0.0811137i
$775$	−3119.63			−0.144594
$776$	−4503.77	−	7800.77i	−0.208345	−	0.360865i
$777$	2364.66	−	7842.69i	0.109179	−	0.362104i
$778$	−4513.48	+	7817.58i	−0.207990	+	0.360249i
$779$	20163.0	−	34923.4i	0.927362	−	1.60624i
$780$	−8894.08	−	9464.17i	−0.408281	−	0.434451i
$781$	−5499.98	−	9526.24i	−0.251991	−	0.436461i
$782$	−12543.4			−0.573595
$783$	−2976.71	−	1103.24i	−0.135861	−	0.0503534i
$784$	5758.05			0.262302
$785$	−5040.91	−	8731.11i	−0.229195	−	0.396977i
$786$	25746.9	+	27397.2i	1.16840	+	1.24329i
$787$	−8707.15	+	15081.2i	−0.394379	+	0.683084i	−0.993022	−	0.117932i	$-0.962374\pi$
$787$	−8707.15	+	15081.2i	−0.394379	+	0.683084i	0.598643	+	0.801016i	$0.295707\pi$
$788$	14623.6	−	25328.8i	0.661096	−	1.14505i
$789$	9782.25	−	32444.0i	0.441391	−	1.46393i
$790$	−4917.14	−	8516.74i	−0.221448	−	0.383559i
$791$	−8373.50			−0.376394
$792$	3301.70	−	1642.05i	0.148132	−	0.0736712i
$793$	3988.26			0.178597
$794$	17352.7	+	30055.8i	0.775599	+	1.34338i
$795$	10260.4	−	2410.58i	0.457733	−	0.107540i
$796$	−13770.1	+	23850.5i	−0.613151	+	1.06201i
$797$	−14566.5	+	25229.9i	−0.647391	+	1.12131i	0.336353	+	0.941736i	$0.390807\pi$
$797$	−14566.5	+	25229.9i	−0.647391	+	1.12131i	−0.983744	+	0.179578i	$0.942527\pi$
$798$	31100.2	−	7306.72i	1.37962	−	0.324129i
$799$	−17363.7	−	30074.8i	−0.768815	−	1.33163i
$800$	24585.8			1.08655
$801$	−14.7495	+	237.257i	−0.000650620	+	0.0104657i
$802$	11272.7			0.496323
$803$	−2357.44	−	4083.20i	−0.103602	−	0.179443i
$804$	11398.7	−	37805.3i	0.500002	−	1.65832i
$805$	1067.45	−	1848.88i	0.0467362	−	0.0809495i
$806$	3198.77	−	5540.43i	0.139791	−	0.242126i
$807$	−10337.2	−	10999.8i	−0.450912	−	0.479815i
$808$	3850.66	+	6669.55i	0.167656	+	0.290388i
$809$	−36440.1			−1.58364			−0.791820	−	0.610754i	$-0.790866\pi$
$809$	−36440.1			−1.58364			−0.791820	+	0.610754i	$0.790866\pi$
$810$	−14636.8	−	1826.90i	−0.634919	−	0.0792478i
$811$	−18922.0			−0.819286			−0.409643	−	0.912246i	$-0.634347\pi$
$811$	−18922.0			−0.819286			−0.409643	+	0.912246i	$0.634347\pi$
$812$	1523.99	+	2639.63i	0.0658639	+	0.114080i
$813$	−4751.85	−	5056.43i	−0.204987	−	0.218126i
$814$	−2850.42	+	4937.08i	−0.122736	+	0.212585i
$815$	−5063.68	+	8770.55i	−0.217636	+	0.376956i
$816$	−3317.37	+	11002.5i	−0.142318	+	0.472014i
$817$	1553.14	+	2690.11i	0.0665084	+	0.115196i
$818$	25559.3			1.09249
$819$	986.208	−	15863.9i	0.0420768	−	0.676839i
$820$	17876.5			0.761311
$821$	8955.36	+	15511.1i	0.380687	+	0.659369i	0.991161	−	0.132667i	$-0.0423542\pi$
$821$	8955.36	+	15511.1i	0.380687	+	0.659369i	−0.610474	+	0.792037i	$0.709021\pi$
$822$	58633.8	−	13775.5i	2.48794	−	0.584519i
$823$	−8762.22	+	15176.6i	−0.371120	+	0.642799i	−0.989738	−	0.142893i	$-0.954360\pi$
$823$	−8762.22	+	15176.6i	−0.371120	+	0.642799i	0.618618	+	0.785692i	$0.287693\pi$
$824$	6617.50	−	11461.8i	0.279771	−	0.484578i
$825$	5251.12	−	1233.70i	0.221601	−	0.0520631i
$826$	−221.707	−	384.008i	−0.00933920	−	0.0161760i
$827$	−17643.9			−0.741885			−0.370943	−	0.928656i	$-0.620965\pi$
$827$	−17643.9			−0.741885			−0.370943	+	0.928656i	$0.620965\pi$
$828$	−10232.3	+	5088.87i	−0.429466	+	0.213588i
$829$	45178.6			1.89278			0.946391	−	0.323023i	$-0.104699\pi$
$829$	45178.6			1.89278			0.946391	+	0.323023i	$0.104699\pi$
$830$	−1003.25	−	1737.67i	−0.0419556	−	0.0726693i
$831$	−12563.5	+	41668.3i	−0.524454	+	1.73942i
$832$	−19505.6	+	33784.6i	−0.812781	+	1.40778i
$833$	7391.21	−	12802.0i	0.307431	−	0.532487i
$834$	9866.66	+	10499.1i	0.409658	+	0.435916i
$835$	−4445.02	−	7699.00i	−0.184223	−	0.319084i
$836$	−12929.3			−0.534893
$837$	−709.300	−	4165.32i	−0.0292915	−	0.172012i
$838$	−38219.5			−1.57550
$839$	−13388.0	−	23188.7i	−0.550901	−	0.954188i	−0.998210	−	0.0598087i	$-0.980951\pi$
$839$	−13388.0	−	23188.7i	−0.550901	−	0.954188i	0.447309	−	0.894379i	$-0.352382\pi$
$840$	2719.17	+	2893.47i	0.111691	+	0.118850i
$841$	11938.5	−	20678.1i	0.489503	−	0.847844i
$842$	−2309.68	+	4000.48i	−0.0945329	+	0.163736i
$843$	−7769.00	+	25766.9i	−0.317412	+	1.05274i
$844$	15478.7	+	26809.9i	0.631278	+	1.09341i
$845$	756.291			0.0307896
$846$	−45339.4	−	30074.8i	−1.84256	−	1.22221i
$847$	−14910.6			−0.604879
$848$	−6432.31	−	11141.1i	−0.260479	−	0.451163i
$849$	15580.3	−	3660.45i	0.629816	−	0.147970i
$850$	17063.1	−	29554.2i	0.688541	−	1.19259i
$851$	2476.73	−	4289.83i	0.0997665	−	0.172801i
$852$	−61722.6	+	14501.2i	−2.48190	+	0.583100i
$853$	3955.88	+	6851.78i	0.158789	+	0.275030i	0.934432	−	0.356141i	$-0.115908\pi$
$853$	3955.88	+	6851.78i	0.158789	+	0.275030i	−0.775644	+	0.631171i	$0.782575\pi$
$854$	−4348.96			−0.174260
$855$	12083.7	+	8015.43i	0.483339	+	0.320611i
$856$	−7683.92			−0.306812
$857$	−924.149	−	1600.67i	−0.0368359	−	0.0638016i	0.847020	−	0.531561i	$-0.178395\pi$
$857$	−924.149	−	1600.67i	−0.0368359	−	0.0638016i	−0.883856	+	0.467760i	$0.845061\pi$
$858$	−3193.29	+	10590.9i	−0.127060	+	0.421409i
$859$	9427.10	−	16328.2i	0.374445	−	0.648558i	−0.615799	−	0.787904i	$-0.711167\pi$
$859$	9427.10	−	16328.2i	0.374445	−	0.648558i	0.990244	+	0.139345i	$0.0444998\pi$
$860$	−688.505	+	1192.53i	−0.0272998	+	0.0472846i
$861$	14982.4	+	15942.7i	0.593030	+	0.631041i
$862$	−21574.2	−	37367.7i	−0.852461	−	1.47651i
$863$	2086.03			0.0822821			0.0411410	−	0.999153i	$-0.486901\pi$
$863$	2086.03			0.0822821			0.0411410	+	0.999153i	$0.486901\pi$
$864$	5589.98	+	32826.8i	0.220110	+	1.29258i
$865$	14669.1			0.576605
$866$	−1044.86	−	1809.75i	−0.0409999	−	0.0710138i
$867$	2721.13	+	2895.55i	0.106591	+	0.113423i
$868$	−2028.39	+	3513.27i	−0.0793178	+	0.137383i
$869$	−2435.46	+	4218.34i	−0.0950717	+	0.164669i
$870$	−686.763	+	2277.74i	−0.0267626	+	0.0887615i
$871$	16605.4	+	28761.3i	0.645983	+	1.11888i
$872$	3072.83			0.119334
$873$	15979.2	−	7946.98i	0.619489	−	0.308092i
$874$	19318.8			0.747675
$875$	6408.74	+	11100.3i	0.247606	+	0.428866i
$876$	−26455.9	+	6215.59i	−1.02039	+	0.239732i
$877$	12388.6	−	21457.7i	0.477005	−	0.826197i	−0.522648	−	0.852549i	$-0.675056\pi$
$877$	12388.6	−	21457.7i	0.477005	−	0.826197i	0.999653	+	0.0263520i	$0.00838907\pi$
$878$	2300.86	−	3985.21i	0.0884401	−	0.153183i
$879$	−18457.6	+	4336.46i	−0.708261	+	0.166399i
$880$	680.607	+	1178.85i	0.0260719	+	0.0451578i
$881$	3741.26			0.143072			0.0715359	−	0.997438i	$-0.477210\pi$
$881$	3741.26			0.143072			0.0715359	+	0.997438i	$0.477210\pi$
$882$	1436.98	−	23115.0i	0.0548591	−	0.882451i
$883$	14131.6			0.538580			0.269290	−	0.963059i	$-0.413211\pi$
$883$	14131.6			0.538580			0.269290	+	0.963059i	$0.413211\pi$
$884$	20348.5	+	35244.7i	0.774203	+	1.34096i
$885$	58.0992	−	192.693i	0.00220676	−	0.00731900i
$886$	22951.6	−	39753.4i	0.870288	−	1.50738i
$887$	−13311.3	+	23055.8i	−0.503888	+	0.872759i	0.496102	+	0.868264i	$0.334764\pi$
$887$	−13311.3	+	23055.8i	−0.503888	+	0.872759i	−0.999990	+	0.00449496i	$0.998569\pi$
$888$	6309.12	+	6713.51i	0.238424	+	0.253706i
$889$	5427.72	+	9401.09i	0.204769	+	0.354671i
$890$	178.143			0.00670938
$891$	2841.17	+	6730.77i	0.106827	+	0.253074i
$892$	−478.665			−0.0179674
$893$	26742.8	+	46319.9i	1.00214	+	1.73576i
$894$	−52997.0	−	56394.0i	−1.98265	−	2.10973i
$895$	−3167.17	+	5485.70i	−0.118287	+	0.204879i
$896$	9765.93	−	16915.1i	0.364126	−	0.630684i
$897$	2774.65	−	9202.46i	0.103281	−	0.342543i
$898$	16023.1	+	27752.8i	0.595431	+	1.03132i
$899$	−681.475			−0.0252820
$900$	1929.12	−	31031.4i	0.0714488	−	1.14931i
$901$	−33026.9			−1.22118
$902$	−7613.00	−	13186.1i	−0.281026	−	0.486751i
$903$	−1640.56	+	385.436i	−0.0604591	+	0.0142043i
$904$	4708.80	−	8155.89i	0.173244	−	0.300067i
$905$	9143.09	−	15836.3i	0.335830	−	0.581675i
$906$	38711.5	−	9094.91i	1.41954	−	0.333508i
$907$	−26309.7	−	45569.7i	−0.963174	−	1.66827i	−0.714443	−	0.699694i	$-0.753320\pi$
$907$	−26309.7	−	45569.7i	−0.963174	−	1.66827i	−0.248731	−	0.968572i	$-0.580014\pi$
$908$	7595.70			0.277612
$909$	−13662.0	+	6794.56i	−0.498503	+	0.247922i
$910$	−11911.3			−0.433908
$911$	−5090.22	−	8816.52i	−0.185122	−	0.320641i	0.758495	−	0.651678i	$-0.225935\pi$
$911$	−5090.22	−	8816.52i	−0.185122	−	0.320641i	−0.943618	+	0.331037i	$0.892601\pi$
$912$	5109.26	−	16945.5i	0.185509	−	0.615265i
$913$	−496.908	+	860.670i	−0.0180123	+	0.0311983i
$914$	−15618.7	+	27052.3i	−0.565229	+	0.979005i
$915$	−1351.80	−	1438.45i	−0.0488406	−	0.0519711i
$916$	−23869.6	−	41343.3i	−0.860996	−	1.49129i
$917$	20051.6			0.722097
$918$	43340.2	+	16062.9i	1.55821	+	0.577512i
$919$	−45618.2			−1.63744			−0.818718	−	0.574195i	$-0.805315\pi$
$919$	−45618.2			−1.63744			−0.818718	+	0.574195i	$0.805315\pi$
$920$	1200.55	+	2079.42i	0.0430229	+	0.0745178i
$921$	−12238.3	−	13022.7i	−0.437857	−	0.465922i
$922$	−12501.9	+	21653.9i	−0.446558	+	0.773462i
$923$	26663.2	−	46182.1i	0.950846	−	1.64691i
$924$	2024.91	−	6715.87i	0.0720938	−	0.239108i
$925$	6738.32	+	11671.1i	0.239518	+	0.414858i
$926$	3447.39			0.122342
$927$	21851.6	+	14494.7i	0.774219	+	0.513558i
$928$	5370.70			0.189980
$929$	6600.20	+	11431.9i	0.233095	+	0.403733i	0.958717	−	0.284361i	$-0.0917813\pi$
$929$	6600.20	+	11431.9i	0.233095	+	0.403733i	−0.725622	+	0.688093i	$0.758448\pi$
$930$	−3082.47	+	724.200i	−0.108686	+	0.0255349i
$931$	−11383.6	+	19717.0i	−0.400734	+	0.694091i
$932$	−19267.4	+	33372.1i	−0.677172	+	1.17290i
$933$	−36295.8	+	8527.38i	−1.27360	+	0.299222i
$934$	37313.1	+	64628.2i	1.30720	+	2.26413i
$935$	3494.59			0.122230
$936$	14897.1	+	9881.60i	0.520220	+	0.345075i
$937$	−13468.1			−0.469565			−0.234783	−	0.972048i	$-0.575438\pi$
$937$	−13468.1			−0.469565			−0.234783	+	0.972048i	$0.575438\pi$
$938$	−18107.2	−	31362.6i	−0.630299	−	1.09171i
$939$	−7285.95	+	24164.8i	−0.253214	+	0.839816i
$940$	−11855.1	+	20533.6i	−0.411351	+	0.712480i
$941$	−6942.05	+	12024.0i	−0.240493	+	0.416547i	−0.960855	−	0.277052i	$-0.910643\pi$
$941$	−6942.05	+	12024.0i	−0.240493	+	0.416547i	0.720362	+	0.693599i	$0.243976\pi$
$942$	33895.1	+	36067.7i	1.17236	+	1.24751i
$943$	6614.93	+	11457.4i	0.228432	+	0.395657i
$944$	−245.656			−0.00846974
$945$	−6055.92	+	5021.30i	−0.208465	+	0.172850i
$946$	1172.84			0.0403091
$947$	−2638.32	−	4569.70i	−0.0905320	−	0.156806i	0.817203	−	0.576350i	$-0.195523\pi$
$947$	−2638.32	−	4569.70i	−0.0905320	−	0.156806i	−0.907735	+	0.419544i	$0.862190\pi$
$948$	19226.8	+	20459.2i	0.658710	+	0.700931i
$949$	11428.6	−	19794.9i	0.390924	−	0.677101i
$950$	−26279.8	+	45518.0i	−0.897506	+	1.55453i
$951$	11321.9	−	37550.5i	0.386054	−	1.28040i
$952$	−6221.13	−	10775.3i	−0.211794	−	0.366838i
$953$	−26131.4			−0.888225			−0.444112	−	0.895971i	$-0.646481\pi$
$953$	−26131.4			−0.888225			−0.444112	+	0.895971i	$0.646481\pi$
$954$	−46329.8	+	23041.3i	−1.57231	+	0.781961i
$955$	−11118.5			−0.376740
$956$	−31368.2	−	54331.4i	−1.06121	−	1.83808i
$957$	1147.09	−	269.500i	0.0387464	−	0.00910312i
$958$	−3318.54	+	5747.87i	−0.111918	+	0.193847i
$959$	16061.4	−	27819.2i	0.540825	−	0.936736i
$960$	18796.4	−	4416.05i	0.631929	−	0.148466i
$961$	14442.0	+	25014.3i	0.484777	+	0.839658i
$962$	−27637.0			−0.926251
$963$	944.591	−	15194.5i	0.0316085	−	0.508448i
$964$	73253.6			2.44745
$965$	3089.16	+	5350.59i	0.103050	+	0.178489i
$966$	−3025.59	+	10034.7i	−0.100773	+	0.334226i
$967$	1998.77	−	3461.96i	0.0664695	−	0.115128i	−0.830875	−	0.556458i	$-0.812160\pi$
$967$	1998.77	−	3461.96i	0.0664695	−	0.115128i	0.897345	+	0.441330i	$0.145493\pi$
$968$	8384.89	−	14523.1i	0.278410	−	0.482220i
$969$	−31116.8	−	33111.3i	−1.03159	−	1.09772i
$970$	−6686.96	−	11582.2i	−0.221346	−	0.383382i
$971$	41785.1			1.38100			0.690499	−	0.723334i	$-0.257391\pi$
$971$	41785.1			1.38100			0.690499	+	0.723334i	$0.257391\pi$
$972$	41871.6	−	4479.75i	1.38172	−	0.147827i
$973$	7684.12			0.253177
$974$	−27845.6	−	48230.0i	−0.916048	−	1.58664i
$975$	17908.0	+	19055.8i	0.588219	+	0.625923i
$976$	−1204.69	+	2086.58i	−0.0395093	+	0.0684321i
$977$	−6122.55	+	10604.6i	−0.200489	+	0.347257i	−0.948686	−	0.316220i	$-0.897586\pi$
$977$	−6122.55	+	10604.6i	−0.200489	+	0.347257i	0.748197	+	0.663476i	$0.230920\pi$
$978$	14352.5	−	47602.0i	0.469267	−	1.55638i
$979$	−44.1170	−	76.4129i	−0.00144023	−	0.00249455i
$980$	−10092.7			−0.328979
$981$	−377.746	+	6076.34i	−0.0122941	+	0.197760i
$982$	24693.3			0.802439
$983$	−21891.5	−	37917.3i	−0.710307	−	1.23029i	−0.964742	−	0.263198i	$-0.915223\pi$
$983$	−21891.5	−	37917.3i	−0.710307	−	1.23029i	0.254435	−	0.967090i	$-0.418111\pi$
$984$	−23953.7	+	5627.70i	−0.776032	+	0.182322i
$985$	6087.50	−	10543.9i	0.196918	−	0.341071i
$986$	3727.39	−	6456.03i	0.120390	−	0.208521i
$987$	−28248.2	+	6636.65i	−0.910992	+	0.214029i
$988$	−31339.9	−	54282.3i	−1.00917	−	1.74793i
$989$	−1019.08			−0.0327654
$990$	4902.19	−	2438.02i	0.157375	−	0.0782681i
$991$	5178.38			0.165991			0.0829953	−	0.996550i	$-0.473551\pi$
$991$	5178.38			0.165991			0.0829953	+	0.996550i	$0.473551\pi$
$992$	3574.12	+	6190.57i	0.114394	+	0.198136i
$993$	−4694.57	+	15570.1i	−0.150028	+	0.497587i
$994$	−29074.7	+	50358.8i	−0.927760	+	1.60693i
$995$	−5732.22	+	9928.50i	−0.182637	+	0.316336i
$996$	3922.85	+	4174.29i	0.124799	+	0.132799i
$997$	−12860.5	−	22275.0i	−0.408520	−	0.707578i	0.586204	−	0.810164i	$-0.300622\pi$
$997$	−12860.5	−	22275.0i	−0.408520	−	0.707578i	−0.994724	+	0.102586i	$0.967288\pi$
$998$	47423.0			1.50416
$999$	−14051.1	+	11650.6i	−0.445004	+	0.368977i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.4.c.a.4.1	✓	4	1.1	even	1	trivial
9.4.c.a.7.1	yes	4	9.7	even	3	inner
27.4.c.a.10.2		4	3.2	odd	2
27.4.c.a.19.2		4	9.2	odd	6
81.4.a.a.1.1		2	9.5	odd	6
81.4.a.d.1.2		2	9.4	even	3
144.4.i.c.49.1		4	4.3	odd	2
144.4.i.c.97.1		4	36.7	odd	6
225.4.e.b.76.2		4	5.4	even	2
225.4.e.b.151.2		4	45.34	even	6
225.4.k.b.49.1		8	5.3	odd	4
225.4.k.b.49.4		8	5.2	odd	4
225.4.k.b.124.1		8	45.7	odd	12
225.4.k.b.124.4		8	45.43	odd	12
432.4.i.c.145.1		4	12.11	even	2
432.4.i.c.289.1		4	36.11	even	6
1296.4.a.i.1.2		2	36.23	even	6
1296.4.a.u.1.1		2	36.31	odd	6
2025.4.a.g.1.1		2	45.4	even	6
2025.4.a.n.1.2		2	45.14	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.18614 - 3.78651i) q^{2} +(3.55842 + 3.78651i) q^{3} +(-5.55842 + 9.62747i) q^{4} +(-2.31386 + 4.00772i) q^{5} +(6.55842 - 21.7518i) q^{6} +(-6.05842 - 10.4935i) q^{7} +13.6277 q^{8} +(-1.67527 + 26.9480i) q^{9} +O(q^{10})\)	\(q+(-2.18614 - 3.78651i) q^{2} +(3.55842 + 3.78651i) q^{3} +(-5.55842 + 9.62747i) q^{4} +(-2.31386 + 4.00772i) q^{5} +(6.55842 - 21.7518i) q^{6} +(-6.05842 - 10.4935i) q^{7} +13.6277 q^{8} +(-1.67527 + 26.9480i) q^{9} +20.2337 q^{10} +(-5.01087 - 8.67909i) q^{11} +(-56.2337 + 13.2116i) q^{12} +(24.2921 - 42.0752i) q^{13} +(-26.4891 + 45.8805i) q^{14} +(-23.4090 + 5.49972i) q^{15} +(14.6753 + 25.4183i) q^{16} +75.3505 q^{17} +(105.701 - 52.5687i) q^{18} -116.052 q^{19} +(-25.7228 - 44.5532i) q^{20} +(18.1753 - 60.2805i) q^{21} +(-21.9090 + 37.9474i) q^{22} +(19.0367 - 32.9725i) q^{23} +(48.4932 + 51.6014i) q^{24} +(51.7921 + 89.7066i) q^{25} -212.424 q^{26} +(-108.000 + 89.5489i) q^{27} +134.701 q^{28} +(11.3139 + 19.5962i) q^{29} +(72.0000 + 76.6150i) q^{30} +(-15.0584 + 26.0820i) q^{31} +(118.675 - 205.552i) q^{32} +(15.0326 - 49.8576i) q^{33} +(-164.727 - 285.315i) q^{34} +56.0733 q^{35} +(-250.129 - 165.917i) q^{36} +130.103 q^{37} +(253.705 + 439.430i) q^{38} +(245.759 - 57.7390i) q^{39} +(-31.5326 + 54.6161i) q^{40} +(-173.742 + 300.930i) q^{41} +(-267.986 + 62.9610i) q^{42} +(-13.3832 - 23.1803i) q^{43} +111.410 q^{44} +(-104.124 - 69.0678i) q^{45} -166.467 q^{46} +(-230.439 - 399.132i) q^{47} +(-44.0258 + 146.017i) q^{48} +(98.0910 - 169.899i) q^{49} +(226.450 - 392.222i) q^{50} +(268.129 + 285.315i) q^{51} +(270.052 + 467.743i) q^{52} -438.310 q^{53} +(575.181 + 213.176i) q^{54} +46.3778 q^{55} +(-82.5625 - 143.002i) q^{56} +(-412.961 - 439.430i) q^{57} +(49.4674 - 85.6800i) q^{58} +(-4.18487 + 7.24841i) q^{59} +(77.1684 - 255.939i) q^{60} +(41.0448 + 71.0916i) q^{61} +131.679 q^{62} +(292.928 - 145.683i) q^{63} -802.959 q^{64} +(112.417 + 194.712i) q^{65} +(-221.649 + 52.0745i) q^{66} +(-341.785 + 591.989i) q^{67} +(-418.830 + 725.435i) q^{68} +(192.591 - 45.2475i) q^{69} +(-122.584 - 212.322i) q^{70} +1097.61 q^{71} +(-22.8301 + 367.239i) q^{72} +470.464 q^{73} +(-284.424 - 492.637i) q^{74} +(-155.376 + 515.325i) q^{75} +(645.064 - 1117.28i) q^{76} +(-60.7160 + 105.163i) q^{77} +(-755.894 - 804.344i) q^{78} +(-243.017 - 420.919i) q^{79} -135.826 q^{80} +(-723.387 - 90.2901i) q^{81} +1519.30 q^{82} +(-49.5829 - 85.8802i) q^{83} +(479.323 + 510.046i) q^{84} +(-174.351 + 301.984i) q^{85} +(-58.5149 + 101.351i) q^{86} +(-33.9416 + 112.571i) q^{87} +(-68.2868 - 118.276i) q^{88} +8.80426 q^{89} +(-33.8968 + 545.257i) q^{90} -588.687 q^{91} +(211.628 + 366.550i) q^{92} +(-152.344 + 35.7918i) q^{93} +(-1007.54 + 1745.12i) q^{94} +(268.527 - 465.103i) q^{95} +(1200.62 - 282.075i) q^{96} +(-330.486 - 572.419i) q^{97} -857.763 q^{98} +(242.278 - 120.493i) 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

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