LMFDB - Embedded newform 9.4.c.a.7.1

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			7.1
Root			$1.68614 - 0.396143i$ of defining polynomial
Character	$\chi$	$=$	9.7
Dual form			9.4.c.a.4.1

$q$-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 $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.18614	+	3.78651i	−0.772917	+	1.33873i	0.163040	+	0.986619i	$0.447870\pi$
$2$	−2.18614	+	3.78651i	−0.772917	+	1.33873i	−0.935958	+	0.352113i	$0.885463\pi$
$3$	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	0.743797	−	0.668406i	$-0.233023\pi$
$5$	−2.31386	−	4.00772i	−0.206958	−	0.358462i	−0.950755	+	0.309944i	$0.899690\pi$
$6$	6.55842	+	21.7518i	0.446244	+	1.48002i
$7$	−6.05842	+	10.4935i	−0.327124	+	0.566595i	−0.981940	−	0.189193i	$-0.939413\pi$
$7$	−6.05842	+	10.4935i	−0.327124	+	0.566595i	0.654816	+	0.755788i	$0.272746\pi$
$8$	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	−0.926492	−	0.376314i	$-0.877191\pi$
$11$	−5.01087	+	8.67909i	−0.137349	+	0.237895i	0.789144	+	0.614209i	$0.210525\pi$
$12$	−56.2337	−	13.2116i	−1.35277	−	0.317822i
$13$	24.2921	+	42.0752i	0.518263	+	0.897658i	0.999775	+	0.0212183i	$0.00675450\pi$
$13$	24.2921	+	42.0752i	0.518263	+	0.897658i	−0.481512	+	0.876440i	$0.659912\pi$
$14$	−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	0.939322	−	0.343036i	$-0.111455\pi$
$23$	19.0367	+	32.9725i	0.172584	+	0.298923i	−0.766739	+	0.641959i	$0.778122\pi$
$24$	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	−0.827527	−	0.561426i	$-0.810253\pi$
$29$	11.3139	−	19.5962i	0.0724459	−	0.125480i	0.899973	+	0.435946i	$0.143586\pi$
$30$	72.0000	−	76.6150i	0.438178	−	0.466264i
$31$	−15.0584	−	26.0820i	−0.0872443	−	0.151112i	0.819101	−	0.573649i	$-0.194473\pi$
$31$	−15.0584	−	26.0820i	−0.0872443	−	0.151112i	−0.906345	+	0.422538i	$0.861139\pi$
$32$	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	−0.980142	−	0.198299i	$-0.936458\pi$
$41$	−173.742	−	300.930i	−0.661803	−	1.14628i	0.318339	−	0.947977i	$-0.396875\pi$
$42$	−267.986	−	62.9610i	−0.984552	−	0.231312i
$43$	−13.3832	+	23.1803i	−0.0474631	+	0.0822085i	−0.888781	−	0.458332i	$-0.848447\pi$
$43$	−13.3832	+	23.1803i	−0.0474631	+	0.0822085i	0.841318	+	0.540541i	$0.181780\pi$
$44$	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	0.247725	+	0.968830i	$0.420317\pi$
$47$	−230.439	+	399.132i	−0.715169	+	1.23871i	−0.962894	+	0.269879i	$0.913016\pi$
$48$	−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	0.861371	−	0.507976i	$-0.169606\pi$
$59$	−4.18487	−	7.24841i	−0.00923430	−	0.0159943i	−0.870606	+	0.491982i	$0.836273\pi$
$60$	77.1684	+	255.939i	0.166040	+	0.550693i
$61$	41.0448	−	71.0916i	0.0861515	−	0.149219i	−0.819730	−	0.572750i	$-0.805876\pi$
$61$	41.0448	−	71.0916i	0.0861515	−	0.149219i	0.905881	+	0.423532i	$0.139210\pi$
$62$	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	−0.988882	−	0.148701i	$-0.952491\pi$
$67$	−341.785	−	591.989i	−0.623220	−	1.07945i	0.365663	−	0.930747i	$-0.380842\pi$
$68$	−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	−0.985552	−	0.169371i	$-0.945826\pi$
$79$	−243.017	+	420.919i	−0.346096	+	0.599456i	0.639456	+	0.768828i	$0.279160\pi$
$80$	−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	−0.896947	−	0.442137i	$-0.854220\pi$
$83$	−49.5829	+	85.8802i	−0.0655715	+	0.113573i	0.831376	+	0.555711i	$0.187554\pi$
$84$	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	−0.985523	−	0.169540i	$-0.945772\pi$
$97$	−330.486	+	572.419i	−0.345936	+	0.599179i	0.639587	+	0.768719i	$0.279105\pi$
$98$	−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	−0.692606	−	0.721316i	$-0.743537\pi$
$101$	282.561	−	489.410i	0.278375	−	0.482160i	0.970981	+	0.239156i	$0.0768708\pi$
$102$	494.181	+	1639.01i	0.479717	+	1.59104i
$103$	485.591	+	841.068i	0.464531	+	0.804592i	0.999180	−	0.0404826i	$-0.0128895\pi$
$103$	485.591	+	841.068i	0.464531	+	0.804592i	−0.534649	+	0.845074i	$0.679556\pi$
$104$	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	0.973249	−	0.229752i	$-0.0737915\pi$
$113$	345.531	+	598.478i	0.287654	+	0.498231i	−0.685596	+	0.727983i	$0.740458\pi$
$114$	−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	−0.998141	−	0.0609476i	$-0.980588\pi$
$131$	−827.428	−	1433.15i	−0.551853	−	0.955837i	0.446288	−	0.894889i	$-0.352746\pi$
$132$	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	−0.0740277	−	0.997256i	$-0.523585\pi$
$137$	1325.55	−	2295.91i	0.826635	−	1.43177i	0.900663	−	0.434518i	$-0.143081\pi$
$138$	−592.361	+	630.330i	−0.365400	+	0.388821i
$139$	−317.084	−	549.206i	−0.193487	−	0.335130i	0.752916	−	0.658116i	$-0.228646\pi$
$139$	−317.084	−	549.206i	−0.193487	−	0.335130i	−0.946404	+	0.322986i	$0.895313\pi$
$140$	−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	0.772060	+	0.635550i	$0.219227\pi$
$149$	1703.16	+	2949.96i	0.936432	+	1.62195i	0.164372	+	0.986398i	$0.447440\pi$
$150$	2290.96	+	538.239i	1.24704	+	0.292980i
$151$	875.159	−	1515.82i	0.471652	−	0.816925i	−0.527822	−	0.849355i	$-0.676991\pi$
$151$	875.159	−	1515.82i	0.471652	−	0.816925i	0.999474	+	0.0324302i	$0.0103247\pi$
$152$	−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	−0.998002	−	0.0631876i	$-0.979873\pi$
$157$	−1089.29	−	1886.70i	−0.553723	−	0.959076i	0.444279	−	0.895889i	$-0.353460\pi$
$158$	−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	0.552984	−	0.833192i	$-0.313489\pi$
$167$	−960.520	−	1663.67i	−0.445074	−	0.770890i	−0.998057	+	0.0623020i	$0.980156\pi$
$168$	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	0.273139	+	0.961974i	$0.411938\pi$
$173$	−1584.91	+	2745.15i	−0.696525	+	1.20642i	−0.969664	+	0.244442i	$0.921395\pi$
$174$	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	−0.543601	−	0.839344i	$-0.682940\pi$
$191$	1201.29	−	2080.70i	0.455092	−	0.788243i	0.998693	+	0.0511008i	$0.0162730\pi$
$192$	−2857.27	+	3040.41i	−1.07399	+	1.14283i
$193$	667.535	+	1156.20i	0.248965	+	0.431220i	0.963239	−	0.268646i	$-0.0865763\pi$
$193$	667.535	+	1156.20i	0.248965	+	0.431220i	−0.714274	+	0.699866i	$0.753243\pi$
$194$	−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	0.998647	−	0.0520047i	$-0.0165611\pi$
$211$	1392.36	+	2411.65i	0.454286	+	0.786847i	−0.544361	+	0.838851i	$0.683228\pi$
$212$	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	−0.862775	−	0.505588i	$-0.831275\pi$
$223$	21.5288	−	37.2890i	0.00646491	−	0.0111976i	0.869240	+	0.494391i	$0.164609\pi$
$224$	−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	−0.911639	−	0.410993i	$-0.865182\pi$
$227$	−341.630	+	591.721i	−0.0998889	+	0.173013i	0.811750	+	0.584006i	$0.198515\pi$
$228$	6526.01	+	1533.23i	1.89559	+	0.445353i
$229$	−2147.15	−	3718.98i	−0.619598	−	1.07317i	−0.989559	−	0.144127i	$-0.953962\pi$
$229$	−2147.15	−	3718.98i	−0.619598	−	1.07317i	0.369962	−	0.929047i	$-0.379371\pi$
$230$	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	−0.940941	−	0.338570i	$-0.890057\pi$
$239$	−2821.69	−	4887.30i	−0.763681	−	1.32273i	0.177261	−	0.984164i	$-0.443276\pi$
$240$	−483.326	+	514.306i	−0.129994	+	0.138326i
$241$	−3294.71	+	5706.61i	−0.880627	+	1.52529i	−0.0299825	+	0.999550i	$0.509545\pi$
$241$	−3294.71	+	5706.61i	−0.880627	+	1.52529i	−0.850645	+	0.525741i	$0.823788\pi$
$242$	−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	0.994426	−	0.105441i	$-0.0336254\pi$
$257$	1672.31	+	2896.53i	0.405898	+	0.703036i	−0.588527	+	0.808477i	$0.700292\pi$
$258$	−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	0.175994	+	0.984391i	$0.443686\pi$
$263$	−3260.75	+	5647.78i	−0.764511	+	1.32417i	−0.940505	+	0.339780i	$0.889647\pi$
$264$	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	0.0920685	−	0.995753i	$-0.470652\pi$
$277$	4187.82	−	7253.51i	0.908381	−	1.57336i	0.816313	−	0.577610i	$-0.196015\pi$
$278$	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	−0.448516	−	0.893775i	$-0.648047\pi$
$281$	2589.67	−	4485.43i	0.549774	−	0.952237i	0.998290	−	0.0584616i	$-0.0186195\pi$
$282$	−10193.2	−	2394.79i	−2.15246	−	0.505701i
$283$	1540.03	+	2667.42i	0.323482	+	0.560288i	0.981204	−	0.192973i	$-0.0618130\pi$
$283$	1540.03	+	2667.42i	0.323482	+	0.560288i	−0.657722	+	0.753261i	$0.728480\pi$
$284$	−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	0.624806	−	0.780780i	$-0.285178\pi$
$293$	−1824.45	−	3160.04i	−0.363773	−	0.630073i	−0.988578	+	0.150708i	$0.951845\pi$
$294$	−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	−0.982108	−	0.188316i	$-0.939697\pi$
$311$	−3587.66	−	6214.02i	−0.654141	−	1.13301i	0.327968	−	0.944689i	$-0.393636\pi$
$312$	3349.14	+	786.850i	0.607717	+	0.142778i
$313$	2428.65	−	4206.54i	0.438579	−	0.759642i	−0.559001	−	0.829167i	$-0.688815\pi$
$313$	2428.65	−	4206.54i	0.438579	−	0.759642i	0.997580	+	0.0695253i	$0.0221485\pi$
$314$	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	0.309611	+	0.950863i	$0.399801\pi$
$317$	−3773.97	+	6536.70i	−0.668666	+	1.15816i	−0.978277	+	0.207300i	$0.933532\pi$
$318$	−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	−0.706347	−	0.707866i	$-0.749658\pi$
$331$	1564.86	−	2710.41i	0.259856	−	0.450084i	0.966203	+	0.257782i	$0.0829915\pi$
$332$	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	0.949737	+	0.313050i	$0.101351\pi$
$337$	4614.99	+	7993.39i	0.745978	+	1.29207i	−0.203759	+	0.979021i	$0.565316\pi$
$338$	−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	0.988171	+	0.153358i	$0.0490088\pi$
$347$	4052.20	+	7018.61i	0.626897	+	1.08582i	−0.361273	+	0.932460i	$0.617658\pi$
$348$	−895.117	+	952.491i	−0.137883	+	0.146721i
$349$	−1538.21	+	2664.26i	−0.235927	+	0.408638i	−0.959542	−	0.281566i	$-0.909146\pi$
$349$	−1538.21	+	2664.26i	−0.235927	+	0.408638i	0.723615	+	0.690204i	$0.242479\pi$
$350$	−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	−0.535491	−	0.844541i	$-0.679873\pi$
$353$	3075.04	−	5326.13i	0.463649	−	0.803063i	0.999139	+	0.0414780i	$0.0132067\pi$
$354$	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	−0.951634	−	0.307235i	$-0.900596\pi$
$367$	−1474.65	+	2554.16i	−0.209744	+	0.363287i	0.741890	+	0.670522i	$0.233930\pi$
$368$	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	0.822816	−	0.568308i	$-0.192402\pi$
$373$	−581.790	−	1007.69i	−0.0807612	−	0.139883i	−0.903577	+	0.428425i	$0.859068\pi$
$374$	−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	0.960737	+	0.277460i	$0.0894926\pi$
$383$	5401.65	+	9355.93i	0.720656	+	1.24821i	−0.240081	+	0.970753i	$0.577174\pi$
$384$	−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	−0.925425	−	0.378931i	$-0.876292\pi$
$389$	−1032.29	+	1787.99i	−0.134549	+	0.233045i	0.790876	+	0.611976i	$0.209625\pi$
$390$	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	0.774525	−	0.632543i	$-0.217989\pi$
$401$	−1289.10	−	2232.79i	−0.160536	−	0.278056i	−0.935061	+	0.354487i	$0.884656\pi$
$402$	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	0.633470	−	0.773767i	$-0.281630\pi$
$409$	−2922.88	−	5062.57i	−0.353367	−	0.612049i	−0.986837	+	0.161718i	$0.948297\pi$
$410$	−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	0.999938	+	0.0111158i	$0.00353834\pi$
$419$	4370.66	+	7570.20i	0.509596	+	0.882646i	−0.490343	+	0.871530i	$0.663128\pi$
$420$	−3153.21	−	740.818i	−0.366336	−	0.0860672i
$421$	−528.254	+	914.963i	−0.0611533	+	0.105921i	−0.894981	−	0.446104i	$-0.852811\pi$
$421$	−528.254	+	914.963i	−0.0611533	+	0.105921i	0.833828	+	0.552024i	$0.186145\pi$
$422$	−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	−0.836001	−	0.548728i	$-0.815112\pi$
$439$	526.239	−	911.473i	0.0572119	−	0.0990939i	0.893213	+	0.449634i	$0.148446\pi$
$440$	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	−0.434245	−	0.900795i	$-0.642985\pi$
$443$	5249.35	−	9092.14i	0.562989	−	0.975126i	0.997234	−	0.0743307i	$-0.0236820\pi$
$444$	−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	−0.988880	−	0.148718i	$-0.952485\pi$
$457$	−3572.20	+	6187.23i	−0.365646	+	0.633318i	0.623233	+	0.782036i	$0.285819\pi$
$458$	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	−0.973542	−	0.228507i	$-0.926616\pi$
$461$	−2859.34	+	4952.53i	−0.288878	+	0.500352i	0.684664	+	0.728859i	$0.259949\pi$
$462$	1889.29	−	2010.39i	0.190255	−	0.202450i
$463$	−394.233	−	682.831i	−0.0395714	−	0.0685397i	0.845561	−	0.533878i	$-0.179266\pi$
$463$	−394.233	−	682.831i	−0.0395714	−	0.0685397i	−0.885133	+	0.465339i	$0.845933\pi$
$464$	−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	−0.899952	−	0.435988i	$-0.856399\pi$
$479$	−758.994	+	1314.62i	−0.0723994	+	0.125399i	0.827553	+	0.561388i	$0.189732\pi$
$480$	−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	0.706572	−	0.707641i	$-0.250241\pi$
$491$	−2823.85	−	4891.05i	−0.259549	−	0.449552i	−0.966121	+	0.258089i	$0.916907\pi$
$492$	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	0.513361	−	0.858173i	$-0.328400\pi$
$499$	−5423.14	−	9393.15i	−0.486519	−	0.842676i	−0.999880	+	0.0154970i	$0.995067\pi$
$500$	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	0.965357	−	0.260933i	$-0.0840302\pi$
$509$	2947.87	+	5105.87i	0.256704	+	0.444624i	−0.708653	+	0.705557i	$0.750697\pi$
$510$	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	0.176319	−	0.984333i	$-0.443581\pi$
$547$	12033.6	−	20842.7i	0.940617	−	1.62920i	0.764298	−	0.644863i	$-0.223086\pi$
$548$	−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	0.918121	−	0.396300i	$-0.129706\pi$
$563$	1547.66	+	2680.62i	0.115854	+	0.200666i	−0.802267	+	0.596966i	$0.796373\pi$
$564$	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	0.186492	+	0.982456i	$0.440288\pi$
$569$	−10282.5	+	17809.9i	−0.757586	+	1.31218i	−0.944078	+	0.329721i	$0.893045\pi$
$570$	−8355.71	+	8891.29i	−0.614004	+	0.653360i
$571$	584.992	+	1013.24i	0.0428742	+	0.0742602i	0.886666	−	0.462410i	$-0.153015\pi$
$571$	584.992	+	1013.24i	0.0428742	+	0.0742602i	−0.843792	+	0.536670i	$0.819682\pi$
$572$	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	−0.488453	−	0.872590i	$-0.662439\pi$
$587$	7273.91	−	12598.8i	0.511459	−	0.885873i	0.999912	−	0.0132825i	$-0.00422807\pi$
$588$	−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	0.610108	−	0.792318i	$-0.291126\pi$
$599$	−5587.20	−	9677.32i	−0.381113	−	0.660108i	−0.991222	+	0.132210i	$0.957793\pi$
$600$	−2117.42	−	7022.70i	−0.144073	−	0.477834i
$601$	−2294.27	+	3973.79i	−0.155716	+	0.269708i	−0.933319	−	0.359047i	$-0.883102\pi$
$601$	−2294.27	+	3973.79i	−0.155716	+	0.269708i	0.777604	+	0.628755i	$0.216435\pi$
$602$	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	0.991652	−	0.128947i	$-0.0411596\pi$
$607$	5744.99	+	9950.61i	0.384155	+	0.665375i	−0.607497	+	0.794322i	$0.707826\pi$
$608$	−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	0.970687	−	0.240347i	$-0.0772612\pi$
$617$	4248.31	+	7358.29i	0.277197	+	0.480120i	−0.693490	+	0.720466i	$0.743928\pi$
$618$	−15110.1	+	16078.6i	−0.983521	+	1.04656i
$619$	−7169.94	+	12418.7i	−0.465564	+	0.806381i	−0.999227	−	0.0393163i	$-0.987482\pi$
$619$	−7169.94	+	12418.7i	−0.465564	+	0.806381i	0.533662	+	0.845698i	$0.320815\pi$
$620$	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	0.0999654	+	0.994991i	$0.468127\pi$
$641$	−13173.0	+	22816.3i	−0.811705	+	1.40591i	−0.911670	+	0.410923i	$0.865207\pi$
$642$	−3697.93	−	12264.7i	−0.227330	−	0.753968i
$643$	10782.5	+	18675.9i	0.661309	+	1.14542i	0.980272	+	0.197653i	$0.0633321\pi$
$643$	10782.5	+	18675.9i	0.661309	+	1.14542i	−0.318963	+	0.947767i	$0.603335\pi$
$644$	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	0.820934	−	0.571023i	$-0.193453\pi$
$653$	−1402.57	−	2429.33i	−0.0840534	−	0.145585i	−0.904987	+	0.425438i	$0.860120\pi$
$654$	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	−0.433474	−	0.901166i	$-0.642712\pi$
$659$	9536.15	−	16517.1i	0.563696	−	0.976350i	0.997170	−	0.0751839i	$-0.0239544\pi$
$660$	−2608.00	−	612.725i	−0.153812	−	0.0361368i
$661$	12256.5	+	21228.9i	0.721216	+	1.24918i	0.960513	+	0.278237i	$0.0897500\pi$
$661$	12256.5	+	21228.9i	0.721216	+	1.24918i	−0.239296	+	0.970947i	$0.576917\pi$
$662$	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	−0.810762	−	0.585376i	$-0.800947\pi$
$673$	1773.32	−	3071.49i	0.101570	−	0.175924i	0.912332	+	0.409452i	$0.134280\pi$
$674$	−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	0.492584	+	0.870265i	$0.336052\pi$
$677$	−8937.50	+	15480.2i	−0.507380	+	0.878807i	−0.999964	+	0.00854232i	$0.997281\pi$
$678$	−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	−0.566714	−	0.823915i	$-0.691785\pi$
$691$	7813.79	−	13533.9i	0.430175	−	0.745084i	0.996888	+	0.0788308i	$0.0251187\pi$
$692$	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	0.469601	+	0.882879i	$0.344398\pi$
$709$	−10001.8	+	17323.6i	−0.529795	+	0.917632i	−0.999396	+	0.0347532i	$0.988935\pi$
$710$	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	−0.381380	−	0.924418i	$-0.624551\pi$
$727$	11954.9	−	20706.5i	0.609879	−	1.05634i	0.991260	−	0.131924i	$-0.0421155\pi$
$728$	−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	0.953055	−	0.302798i	$-0.0979206\pi$
$733$	4252.77	+	7366.02i	0.214297	+	0.371173i	−0.738758	+	0.673971i	$0.764587\pi$
$734$	−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	−0.976495	−	0.215541i	$-0.930849\pi$
$743$	−13668.8	−	23675.0i	−0.674911	−	1.16898i	0.301584	−	0.953440i	$-0.402485\pi$
$744$	−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	0.822644	−	0.568557i	$-0.192498\pi$
$751$	−1668.32	−	2889.61i	−0.0810623	−	0.140404i	−0.903706	+	0.428153i	$0.859165\pi$
$752$	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	0.966751	−	0.255720i	$-0.0823125\pi$
$761$	5498.42	+	9523.54i	0.261915	+	0.453651i	−0.704836	+	0.709371i	$0.748979\pi$
$762$	−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
$766$

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

L-functions

Modular forms

Varieties

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