LMFDB - Embedded newform 287.2.e.d.247.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(165,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("287.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.e (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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			247.2
Character	$\chi$	$=$	287.247
Dual form			287.2.e.d.165.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28712 + 2.22936i) q^{2} +(-0.234126 - 0.405518i) q^{3} +(-2.31337 - 4.00687i) q^{4} +(-1.12112 + 1.94184i) q^{5} +1.20539 q^{6} +(1.72083 - 2.00966i) q^{7} +6.76185 q^{8} +(1.39037 - 2.40819i) q^{9} +O(q^{10})$	\(q+(-1.28712 + 2.22936i) q^{2} +(-0.234126 - 0.405518i) q^{3} +(-2.31337 - 4.00687i) q^{4} +(-1.12112 + 1.94184i) q^{5} +1.20539 q^{6} +(1.72083 - 2.00966i) q^{7} +6.76185 q^{8} +(1.39037 - 2.40819i) q^{9} +(-2.88604 - 4.99876i) q^{10} +(-2.88384 - 4.99496i) q^{11} +(-1.08324 + 1.87622i) q^{12} -0.0725380 q^{13} +(2.26535 + 6.42303i) q^{14} +1.04993 q^{15} +(-4.07659 + 7.06087i) q^{16} +(2.50501 + 4.33880i) q^{17} +(3.57915 + 6.19927i) q^{18} +(2.53270 - 4.38676i) q^{19} +10.3742 q^{20} +(-1.21785 - 0.227312i) q^{21} +14.8474 q^{22} +(-0.954630 + 1.65347i) q^{23} +(-1.58312 - 2.74205i) q^{24} +(-0.0138182 - 0.0239338i) q^{25} +(0.0933653 - 0.161713i) q^{26} -2.70684 q^{27} +(-12.0334 - 2.24604i) q^{28} +6.90161 q^{29} +(-1.35139 + 2.34068i) q^{30} +(-2.28779 - 3.96257i) q^{31} +(-3.73229 - 6.46452i) q^{32} +(-1.35036 + 2.33890i) q^{33} -12.8970 q^{34} +(1.97319 + 5.59464i) q^{35} -12.8657 q^{36} +(2.49730 - 4.32545i) q^{37} +(6.51979 + 11.2926i) q^{38} +(0.0169830 + 0.0294155i) q^{39} +(-7.58084 + 13.1304i) q^{40} +1.00000 q^{41} +(2.07428 - 2.42244i) q^{42} -6.83836 q^{43} +(-13.3428 + 23.1103i) q^{44} +(3.11754 + 5.39974i) q^{45} +(-2.45745 - 4.25643i) q^{46} +(4.82657 - 8.35986i) q^{47} +3.81774 q^{48} +(-1.07750 - 6.91657i) q^{49} +0.0711428 q^{50} +(1.17297 - 2.03165i) q^{51} +(0.167807 + 0.290650i) q^{52} +(-6.13569 - 10.6273i) q^{53} +(3.48404 - 6.03453i) q^{54} +12.9325 q^{55} +(11.6360 - 13.5890i) q^{56} -2.37188 q^{57} +(-8.88321 + 15.3862i) q^{58} +(1.11166 + 1.92544i) q^{59} +(-2.42888 - 4.20694i) q^{60} +(1.29562 - 2.24408i) q^{61} +11.7787 q^{62} +(-2.44707 - 6.93826i) q^{63} +2.90930 q^{64} +(0.0813238 - 0.140857i) q^{65} +(-3.47617 - 6.02090i) q^{66} +(0.505908 + 0.876259i) q^{67} +(11.5900 - 20.0745i) q^{68} +0.894015 q^{69} +(-15.0122 - 2.80204i) q^{70} -3.95904 q^{71} +(9.40147 - 16.2838i) q^{72} +(7.66585 + 13.2776i) q^{73} +(6.42866 + 11.1348i) q^{74} +(-0.00647039 + 0.0112071i) q^{75} -23.4362 q^{76} +(-15.0008 - 2.79991i) q^{77} -0.0874370 q^{78} +(2.74168 - 4.74873i) q^{79} +(-9.14070 - 15.8321i) q^{80} +(-3.53737 - 6.12690i) q^{81} +(-1.28712 + 2.22936i) q^{82} +4.84224 q^{83} +(1.90651 + 5.40560i) q^{84} -11.2337 q^{85} +(8.80180 - 15.2452i) q^{86} +(-1.61585 - 2.79873i) q^{87} +(-19.5001 - 33.7752i) q^{88} +(-6.29000 + 10.8946i) q^{89} -16.0506 q^{90} +(-0.124825 + 0.145777i) q^{91} +8.83364 q^{92} +(-1.07126 + 1.85548i) q^{93} +(12.4248 + 21.5203i) q^{94} +(5.67892 + 9.83617i) q^{95} +(-1.74765 + 3.02703i) q^{96} +18.1362 q^{97} +(16.8064 + 6.50033i) q^{98} -16.0384 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9}+O(q^{10}) $ 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9} + 2 q^{10} - 15 q^{11} - 4 q^{12} - 10 q^{13} + 21 q^{14} + 48 q^{15} - 33 q^{16} - 4 q^{17} - 10 q^{18} - 5 q^{19} - 52 q^{20} + 12 q^{21} + 32 q^{22} - 12 q^{23} - 16 q^{24} - 24 q^{25} - 31 q^{26} - 22 q^{27} + 60 q^{28} + 28 q^{29} + 33 q^{30} + 3 q^{31} - 16 q^{32} - 4 q^{33} - 48 q^{34} + 45 q^{35} + 114 q^{36} - 24 q^{37} - 45 q^{39} - 36 q^{40} + 34 q^{41} + 65 q^{42} + 28 q^{43} + 9 q^{44} + 21 q^{45} - 44 q^{46} - 19 q^{47} - 120 q^{48} - 10 q^{49} - 8 q^{50} - 2 q^{51} + 25 q^{52} - 4 q^{53} - 68 q^{54} + 18 q^{55} + 25 q^{56} - 24 q^{57} + q^{58} + 27 q^{59} - 66 q^{60} + q^{61} - 46 q^{62} + 37 q^{63} + 150 q^{64} - 22 q^{65} + 16 q^{66} - 49 q^{67} - 45 q^{68} + 24 q^{69} + 73 q^{70} + 80 q^{71} + 23 q^{72} + 14 q^{73} - 33 q^{74} - 27 q^{75} - 18 q^{76} - 20 q^{77} - 24 q^{78} - 61 q^{79} + 82 q^{80} - 53 q^{81} - 3 q^{82} - 36 q^{83} + 188 q^{84} - 26 q^{85} + 4 q^{86} + 17 q^{87} - 74 q^{88} - 18 q^{89} - 40 q^{90} + 7 q^{91} + 56 q^{92} + 36 q^{93} + 5 q^{94} - 20 q^{95} - 148 q^{96} + 52 q^{97} + 142 q^{98} + 76 q^{99}+O(q^{100}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9 + 2 * q^10 - 15 * q^11 - 4 * q^12 - 10 * q^13 + 21 * q^14 + 48 * q^15 - 33 * q^16 - 4 * q^17 - 10 * q^18 - 5 * q^19 - 52 * q^20 + 12 * q^21 + 32 * q^22 - 12 * q^23 - 16 * q^24 - 24 * q^25 - 31 * q^26 - 22 * q^27 + 60 * q^28 + 28 * q^29 + 33 * q^30 + 3 * q^31 - 16 * q^32 - 4 * q^33 - 48 * q^34 + 45 * q^35 + 114 * q^36 - 24 * q^37 - 45 * q^39 - 36 * q^40 + 34 * q^41 + 65 * q^42 + 28 * q^43 + 9 * q^44 + 21 * q^45 - 44 * q^46 - 19 * q^47 - 120 * q^48 - 10 * q^49 - 8 * q^50 - 2 * q^51 + 25 * q^52 - 4 * q^53 - 68 * q^54 + 18 * q^55 + 25 * q^56 - 24 * q^57 + q^58 + 27 * q^59 - 66 * q^60 + q^61 - 46 * q^62 + 37 * q^63 + 150 * q^64 - 22 * q^65 + 16 * q^66 - 49 * q^67 - 45 * q^68 + 24 * q^69 + 73 * q^70 + 80 * q^71 + 23 * q^72 + 14 * q^73 - 33 * q^74 - 27 * q^75 - 18 * q^76 - 20 * q^77 - 24 * q^78 - 61 * q^79 + 82 * q^80 - 53 * q^81 - 3 * q^82 - 36 * q^83 + 188 * q^84 - 26 * q^85 + 4 * q^86 + 17 * q^87 - 74 * q^88 - 18 * q^89 - 40 * q^90 + 7 * q^91 + 56 * q^92 + 36 * q^93 + 5 * q^94 - 20 * q^95 - 148 * q^96 + 52 * q^97 + 142 * q^98 + 76 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.28712	+	2.22936i	−0.910133	+	1.57640i	−0.0962574	+	0.995356i	$0.530687\pi$
$2$	−1.28712	+	2.22936i	−0.910133	+	1.57640i	−0.813875	+	0.581040i	$0.802646\pi$
$3$	−0.234126	−	0.405518i	−0.135173	−	0.234126i	0.790491	−	0.612474i	$-0.209826\pi$
$3$	−0.234126	−	0.405518i	−0.135173	−	0.234126i	−0.925663	+	0.378348i	$0.876492\pi$
$4$	−2.31337	−	4.00687i	−1.15668	−	2.00343i
$5$	−1.12112	+	1.94184i	−0.501380	+	0.868415i	0.498619	+	0.866821i	$0.333841\pi$
$5$	−1.12112	+	1.94184i	−0.501380	+	0.868415i	−0.999999	+	0.00159412i	$0.999493\pi$
$6$	1.20539			0.492100
$7$	1.72083	−	2.00966i	0.650412	−	0.759582i
$7$	1.72083	−	2.00966i	0.650412	−	0.759582i
$8$	6.76185			2.39067
$9$	1.39037	−	2.40819i	0.463457	−	0.802731i
$10$	−2.88604	−	4.99876i	−0.912644	−	1.58075i
$11$	−2.88384	−	4.99496i	−0.869511	−	1.50604i	−0.862497	−	0.506061i	$-0.831101\pi$
$11$	−2.88384	−	4.99496i	−0.869511	−	1.50604i	−0.00701324	−	0.999975i	$-0.502232\pi$
$12$	−1.08324	+	1.87622i	−0.312704	+	0.541619i
$13$	−0.0725380			−0.0201184			−0.0100592	−	0.999949i	$-0.503202\pi$
$13$	−0.0725380			−0.0201184			−0.0100592	+	0.999949i	$0.503202\pi$
$14$	2.26535	+	6.42303i	0.605441	+	1.71663i
$15$	1.04993			0.271091
$16$	−4.07659	+	7.06087i	−1.01915	+	1.76522i
$17$	2.50501	+	4.33880i	0.607554	+	1.05231i	0.991642	+	0.129018i	$0.0411824\pi$
$17$	2.50501	+	4.33880i	0.607554	+	1.05231i	−0.384089	+	0.923296i	$0.625484\pi$
$18$	3.57915	+	6.19927i	0.843614	+	1.46118i
$19$	2.53270	−	4.38676i	0.581041	−	1.00639i	−0.414315	−	0.910133i	$-0.635979\pi$
$19$	2.53270	−	4.38676i	0.581041	−	1.00639i	0.995356	−	0.0962591i	$-0.0306877\pi$
$20$	10.3742			2.31975
$21$	−1.21785	−	0.227312i	−0.265756	−	0.0496035i
$22$	14.8474			3.16548
$23$	−0.954630	+	1.65347i	−0.199054	+	0.344772i	−0.948222	−	0.317608i	$-0.897120\pi$
$23$	−0.954630	+	1.65347i	−0.199054	+	0.344772i	0.749168	+	0.662380i	$0.230454\pi$
$24$	−1.58312	−	2.74205i	−0.323154	−	0.559719i
$25$	−0.0138182	−	0.0239338i	−0.00276364	−	0.00478676i
$26$	0.0933653	−	0.161713i	0.0183104	−	0.0317146i
$27$	−2.70684			−0.520932
$28$	−12.0334	−	2.24604i	−2.27409	−	0.424461i
$29$	6.90161			1.28160			0.640798	−	0.767709i	$-0.278603\pi$
$29$	6.90161			1.28160			0.640798	+	0.767709i	$0.278603\pi$
$30$	−1.35139	+	2.34068i	−0.246729	+	0.427347i
$31$	−2.28779	−	3.96257i	−0.410899	−	0.711699i	0.584089	−	0.811690i	$-0.301452\pi$
$31$	−2.28779	−	3.96257i	−0.410899	−	0.711699i	−0.994988	+	0.0999910i	$0.968119\pi$
$32$	−3.73229	−	6.46452i	−0.659783	−	1.14278i
$33$	−1.35036	+	2.33890i	−0.235068	+	0.407150i
$34$	−12.8970			−2.21182
$35$	1.97319	+	5.59464i	0.333529	+	0.945667i
$36$	−12.8657			−2.14429
$37$	2.49730	−	4.32545i	0.410554	−	0.711100i	−0.584397	−	0.811468i	$-0.698669\pi$
$37$	2.49730	−	4.32545i	0.410554	−	0.711100i	0.994950	+	0.100368i	$0.0320021\pi$
$38$	6.51979	+	11.2926i	1.05765	+	1.83190i
$39$	0.0169830	+	0.0294155i	0.00271946	+	0.00471025i
$40$	−7.58084	+	13.1304i	−1.19864	+	2.07610i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	2.07428	−	2.42244i	0.320068	−	0.373790i
$43$	−6.83836			−1.04284			−0.521420	−	0.853300i	$-0.674597\pi$
$43$	−6.83836			−1.04284			−0.521420	+	0.853300i	$0.674597\pi$
$44$	−13.3428	+	23.1103i	−2.01150	+	3.48401i
$45$	3.11754	+	5.39974i	0.464736	+	0.804946i
$46$	−2.45745	−	4.25643i	−0.362331	−	0.627576i
$47$	4.82657	−	8.35986i	0.704027	−	1.21941i	−0.263015	−	0.964792i	$-0.584717\pi$
$47$	4.82657	−	8.35986i	0.704027	−	1.21941i	0.967042	−	0.254619i	$-0.0819499\pi$
$48$	3.81774			0.551044
$49$	−1.07750	−	6.91657i	−0.153929	−	0.988082i
$50$	0.0711428			0.0100611
$51$	1.17297	−	2.03165i	0.164249	−	0.284488i
$52$	0.167807	+	0.290650i	0.0232707	+	0.0403060i
$53$	−6.13569	−	10.6273i	−0.842802	−	1.45978i	−0.887517	−	0.460775i	$-0.847571\pi$
$53$	−6.13569	−	10.6273i	−0.842802	−	1.45978i	0.0447152	−	0.999000i	$-0.485762\pi$
$54$	3.48404	−	6.03453i	0.474117	−	0.821195i
$55$	12.9325			1.74382
$56$	11.6360	−	13.5890i	1.55492	−	1.81591i
$57$	−2.37188			−0.314163
$58$	−8.88321	+	15.3862i	−1.16642	+	2.02030i
$59$	1.11166	+	1.92544i	0.144725	+	0.250672i	0.929270	−	0.369400i	$-0.120437\pi$
$59$	1.11166	+	1.92544i	0.144725	+	0.250672i	−0.784545	+	0.620072i	$0.787103\pi$
$60$	−2.42888	−	4.20694i	−0.313567	−	0.543114i
$61$	1.29562	−	2.24408i	0.165887	−	0.287325i	−0.771083	−	0.636735i	$-0.780285\pi$
$61$	1.29562	−	2.24408i	0.165887	−	0.287325i	0.936970	+	0.349410i	$0.113618\pi$
$62$	11.7787			1.49589
$63$	−2.44707	−	6.93826i	−0.308302	−	0.874139i
$64$	2.90930			0.363663
$65$	0.0813238	−	0.140857i	0.0100870	−	0.0174712i
$66$	−3.47617	−	6.02090i	−0.427886	−	0.741121i
$67$	0.505908	+	0.876259i	0.0618065	+	0.107052i	0.895273	−	0.445518i	$-0.146980\pi$
$67$	0.505908	+	0.876259i	0.0618065	+	0.107052i	−0.833466	+	0.552570i	$0.813647\pi$
$68$	11.5900	−	20.0745i	1.40549	−	2.43439i
$69$	0.894015			0.107627
$70$	−15.0122	−	2.80204i	−1.79430	−	0.334908i
$71$	−3.95904			−0.469851			−0.234926	−	0.972013i	$-0.575485\pi$
$71$	−3.95904			−0.469851			−0.234926	+	0.972013i	$0.575485\pi$
$72$	9.40147	−	16.2838i	1.10797	−	1.91907i
$73$	7.66585	+	13.2776i	0.897220	+	1.55403i	0.831033	+	0.556223i	$0.187750\pi$
$73$	7.66585	+	13.2776i	0.897220	+	1.55403i	0.0661868	+	0.997807i	$0.478917\pi$
$74$	6.42866	+	11.1348i	0.747317	+	1.29439i
$75$	−0.00647039	+	0.0112071i	−0.000747137	+	0.00129408i
$76$	−23.4362			−2.68832
$77$	−15.0008	−	2.79991i	−1.70950	−	0.319079i
$78$	−0.0874370			−0.00990029
$79$	2.74168	−	4.74873i	0.308463	−	0.534274i	−0.669563	−	0.742755i	$-0.733519\pi$
$79$	2.74168	−	4.74873i	0.308463	−	0.534274i	0.978026	+	0.208481i	$0.0668520\pi$
$80$	−9.14070	−	15.8321i	−1.02196	−	1.77009i
$81$	−3.53737	−	6.12690i	−0.393041	−	0.680767i
$82$	−1.28712	+	2.22936i	−0.142139	+	0.246192i
$83$	4.84224			0.531505			0.265752	−	0.964041i	$-0.414380\pi$
$83$	4.84224			0.531505			0.265752	+	0.964041i	$0.414380\pi$
$84$	1.90651	+	5.40560i	0.208018	+	0.589799i
$85$	−11.2337			−1.21846
$86$	8.80180	−	15.2452i	0.949122	−	1.64393i
$87$	−1.61585	−	2.79873i	−0.173237	−	0.300055i
$88$	−19.5001	−	33.7752i	−2.07872	−	3.60044i
$89$	−6.29000	+	10.8946i	−0.666739	+	1.15483i	0.312072	+	0.950058i	$0.398977\pi$
$89$	−6.29000	+	10.8946i	−0.666739	+	1.15483i	−0.978811	+	0.204767i	$0.934356\pi$
$90$	−16.0506			−1.69188
$91$	−0.124825	+	0.145777i	−0.0130853	+	0.0152816i
$92$	8.83364			0.920970
$93$	−1.07126	+	1.85548i	−0.111085	+	0.192404i
$94$	12.4248	+	21.5203i	1.28152	+	2.21965i
$95$	5.67892	+	9.83617i	0.582645	+	1.00917i
$96$	−1.74765	+	3.02703i	−0.178369	+	0.308944i
$97$	18.1362			1.84145			0.920724	−	0.390216i	$-0.127600\pi$
$97$	18.1362			1.84145			0.920724	+	0.390216i	$0.127600\pi$
$98$	16.8064	+	6.50033i	1.69770	+	0.656632i
$99$	−16.0384			−1.61192
$100$	−0.0639331	+	0.110735i	−0.00639331	+	0.0110735i
$101$	−5.08820	−	8.81302i	−0.506295	−	0.876928i	−0.999973	−	0.00728377i	$-0.997681\pi$
$101$	−5.08820	−	8.81302i	−0.506295	−	0.876928i	0.493679	−	0.869644i	$-0.335652\pi$
$102$	3.01952	+	5.22997i	0.298977	+	0.517844i
$103$	0.271597	−	0.470420i	0.0267613	−	0.0463519i	−0.852335	−	0.522997i	$-0.824814\pi$
$103$	0.271597	−	0.470420i	0.0267613	−	0.0463519i	0.879096	+	0.476645i	$0.158147\pi$
$104$	−0.490491			−0.0480966
$105$	1.80675	−	2.11001i	0.176321	−	0.205916i
$106$	31.5895			3.06825
$107$	0.198392	−	0.343625i	0.0191793	−	0.0332195i	−0.856276	−	0.516518i	$-0.827228\pi$
$107$	0.198392	−	0.343625i	0.0191793	−	0.0332195i	0.875456	+	0.483298i	$0.160561\pi$
$108$	6.26192	+	10.8460i	0.602553	+	1.04365i
$109$	3.16557	+	5.48293i	0.303206	+	0.525169i	0.976860	−	0.213878i	$-0.0686095\pi$
$109$	3.16557	+	5.48293i	0.303206	+	0.525169i	−0.673654	+	0.739047i	$0.735276\pi$
$110$	−16.6457	+	28.8313i	−1.58711	+	2.74895i
$111$	−2.33873			−0.221983
$112$	7.17486	+	20.3431i	0.677960	+	1.92224i
$113$	−4.39846			−0.413773			−0.206886	−	0.978365i	$-0.566333\pi$
$113$	−4.39846			−0.413773			−0.206886	+	0.978365i	$0.566333\pi$
$114$	3.05290	−	5.28778i	0.285930	−	0.495246i
$115$	−2.14051	−	3.70747i	−0.199604	−	0.345723i
$116$	−15.9659	−	27.6538i	−1.48240	−	2.56759i
$117$	−0.100855	+	0.174686i	−0.00932402	+	0.0161497i
$118$	−5.72335			−0.526877
$119$	13.0302	+	2.43210i	1.19448	+	0.222951i
$120$	7.09949			0.648091
$121$	−11.1331	+	19.2831i	−1.01210	+	1.75300i
$122$	3.33524	+	5.77681i	0.301959	+	0.523008i
$123$	−0.234126	−	0.405518i	−0.0211104	−	0.0365643i
$124$	−10.5850	+	18.3338i	−0.950561	+	1.64642i
$125$	−11.1492			−0.997217
$126$	18.6176	+	3.47498i	1.65858	+	0.309576i
$127$	−11.7138			−1.03943			−0.519715	−	0.854340i	$-0.673962\pi$
$127$	−11.7138			−1.03943			−0.519715	+	0.854340i	$0.673962\pi$
$128$	3.71996	−	6.44316i	0.328801	−	0.569500i
$129$	1.60104	+	2.77308i	0.140963	+	0.244156i
$130$	0.209347	+	0.362600i	0.0183610	+	0.0318021i
$131$	−11.1068	+	19.2375i	−0.970404	+	1.68079i	−0.276069	+	0.961138i	$0.589032\pi$
$131$	−11.1068	+	19.2375i	−0.970404	+	1.68079i	−0.694335	+	0.719652i	$0.744301\pi$
$132$	12.4955			1.08760
$133$	−4.45759	−	12.6387i	−0.386522	−	1.09592i
$134$	−2.60466			−0.225009
$135$	3.03469	−	5.25624i	0.261185	−	0.452385i
$136$	16.9385	+	29.3383i	1.45246	+	2.51574i
$137$	2.97602	+	5.15462i	0.254259	+	0.440389i	0.964694	−	0.263374i	$-0.0848353\pi$
$137$	2.97602	+	5.15462i	0.254259	+	0.440389i	−0.710435	+	0.703762i	$0.751502\pi$
$138$	−1.15071	+	1.99308i	−0.0979546	+	0.169662i
$139$	8.89834			0.754747			0.377374	−	0.926061i	$-0.376827\pi$
$139$	8.89834			0.754747			0.377374	+	0.926061i	$0.376827\pi$
$140$	17.8523	−	20.8487i	1.50879	−	1.76204i
$141$	−4.52010			−0.380661
$142$	5.09576	−	8.82612i	0.427627	−	0.740671i
$143$	0.209188	+	0.362325i	0.0174932	+	0.0302991i
$144$	11.3359	+	19.6344i	0.944662	+	1.63620i
$145$	−7.73753	+	13.4018i	−0.642567	+	1.11296i
$146$	−39.4675			−3.26636
$147$	−2.55252	+	2.05630i	−0.210529	+	0.169600i
$148$	−23.1087			−1.89952
$149$	−4.07689	+	7.06138i	−0.333992	+	0.578491i	−0.983291	−	0.182043i	$-0.941729\pi$
$149$	−4.07689	+	7.06138i	−0.333992	+	0.578491i	0.649299	+	0.760533i	$0.275062\pi$
$150$	−0.0166564	−	0.0288497i	−0.00135999	−	0.00235557i
$151$	4.09730	+	7.09673i	0.333433	+	0.577524i	0.983183	−	0.182625i	$-0.0584594\pi$
$151$	4.09730	+	7.09673i	0.333433	+	0.577524i	−0.649749	+	0.760149i	$0.725126\pi$
$152$	17.1257	−	29.6626i	1.38908	−	2.40596i
$153$	13.9316			1.12630
$154$	25.5498	−	29.8383i	2.05887	−	2.40444i
$155$	10.2596			0.824067
$156$	0.0785760	−	0.136098i	0.00629111	−	0.0108965i
$157$	3.82420	+	6.62372i	0.305205	+	0.528630i	0.977307	−	0.211828i	$-0.0679418\pi$
$157$	3.82420	+	6.62372i	0.305205	+	0.528630i	−0.672102	+	0.740458i	$0.734608\pi$
$158$	7.05776	+	12.2244i	0.561485	+	0.972521i
$159$	−2.87305	+	4.97626i	−0.227847	+	0.394643i
$160$	16.7374			1.32321
$161$	1.68016	+	4.76382i	0.132415	+	0.375442i
$162$	18.2121			1.43088
$163$	0.410790	−	0.711508i	0.0321755	−	0.0557296i	−0.849489	−	0.527606i	$-0.823090\pi$
$163$	0.410790	−	0.711508i	0.0321755	−	0.0557296i	0.881665	+	0.471876i	$0.156423\pi$
$164$	−2.31337	−	4.00687i	−0.180644	−	0.312884i
$165$	−3.02784	−	5.24437i	−0.235717	−	0.408274i
$166$	−6.23255	+	10.7951i	−0.483740	+	0.837862i
$167$	7.82917			0.605840			0.302920	−	0.953016i	$-0.402039\pi$
$167$	7.82917			0.605840			0.302920	+	0.953016i	$0.402039\pi$
$168$	−8.23489	−	1.53705i	−0.635335	−	0.118586i
$169$	−12.9947			−0.999595
$170$	14.4591	−	25.0439i	1.10896	−	1.92078i
$171$	−7.04278	−	12.1984i	−0.538575	−	0.932839i
$172$	15.8196	+	27.4004i	1.20623	+	2.08926i
$173$	6.68141	−	11.5725i	0.507978	−	0.879845i	−0.491979	−	0.870607i	$-0.663726\pi$
$173$	6.68141	−	11.5725i	0.507978	−	0.879845i	0.999957	−	0.00923737i	$-0.00294039\pi$
$174$	8.31916			0.630674
$175$	−0.0718777	−	0.0134160i	−0.00543344	−	0.00101416i
$176$	47.0250			3.54464
$177$	0.520535	−	0.901593i	0.0391258	−	0.0677679i
$178$	−16.1920	−	28.0454i	−1.21364	−	2.10209i
$179$	−4.10969	−	7.11819i	−0.307172	−	0.532038i	0.670570	−	0.741846i	$-0.266050\pi$
$179$	−4.10969	−	7.11819i	−0.307172	−	0.532038i	−0.977743	+	0.209808i	$0.932716\pi$
$180$	14.4240	−	24.9832i	1.07510	−	1.86213i
$181$	−13.3667			−0.993542			−0.496771	−	0.867882i	$-0.665481\pi$
$181$	−13.3667			−0.993542			−0.496771	+	0.867882i	$0.665481\pi$
$182$	−0.164324	−	0.465914i	−0.0121805	−	0.0345358i
$183$	−1.21335			−0.0896937
$184$	−6.45506	+	11.1805i	−0.475874	+	0.824237i
$185$	5.59955	+	9.69870i	0.411687	+	0.713062i
$186$	−2.75769	−	4.77646i	−0.202204	−	0.350227i
$187$	14.4481	−	25.0248i	1.05655	−	1.83000i
$188$	−44.6625			−3.25734
$189$	−4.65801	+	5.43985i	−0.338820	+	0.395691i
$190$	−29.2378			−2.12114
$191$	1.17397	−	2.03338i	0.0849457	−	0.147130i	−0.820422	−	0.571758i	$-0.806262\pi$
$191$	1.17397	−	2.03338i	0.0849457	−	0.147130i	0.905368	+	0.424628i	$0.139595\pi$
$192$	−0.681143	−	1.17978i	−0.0491573	−	0.0851429i
$193$	2.35527	+	4.07945i	0.169536	+	0.293645i	0.938257	−	0.345939i	$-0.112440\pi$
$193$	2.35527	+	4.07945i	0.169536	+	0.293645i	−0.768721	+	0.639585i	$0.779106\pi$
$194$	−23.3434	+	40.4320i	−1.67596	+	2.90285i
$195$	−0.0761601			−0.00545394
$196$	−25.2211	+	20.3180i	−1.80151	+	1.45128i
$197$	−6.92302			−0.493245			−0.246622	−	0.969112i	$-0.579321\pi$
$197$	−6.92302			−0.493245			−0.246622	+	0.969112i	$0.579321\pi$
$198$	20.6434	−	35.7554i	1.46706	−	2.54103i
$199$	11.8544	+	20.5325i	0.840338	+	1.45551i	0.889609	+	0.456722i	$0.150977\pi$
$199$	11.8544	+	20.5325i	0.840338	+	1.45551i	−0.0492718	+	0.998785i	$0.515690\pi$
$200$	−0.0934365	−	0.161837i	−0.00660696	−	0.0114436i
$201$	0.236892	−	0.410310i	0.0167091	−	0.0289410i
$202$	26.1965			1.84318
$203$	11.8765	−	13.8699i	0.833565	−	0.973478i
$204$	−10.8541			−0.759938
$205$	−1.12112	+	1.94184i	−0.0783024	+	0.135624i
$206$	0.699157	+	1.21098i	0.0487126	+	0.0843727i
$207$	2.65458	+	4.59786i	0.184506	+	0.319574i
$208$	0.295708	−	0.512181i	0.0205037	−	0.0355134i
$209$	−29.2156			−2.02089
$210$	2.37847	+	6.74375i	0.164130	+	0.465363i
$211$	7.20963			0.496331			0.248166	−	0.968718i	$-0.420172\pi$
$211$	7.20963			0.496331			0.248166	+	0.968718i	$0.420172\pi$
$212$	−28.3882	+	49.1698i	−1.94971	+	3.37699i
$213$	0.926913	+	1.60546i	0.0635110	+	0.110004i
$214$	0.510709	+	0.884574i	0.0349114	+	0.0604682i
$215$	7.66662	−	13.2790i	0.522859	−	0.905618i
$216$	−18.3033			−1.24538
$217$	−11.9003	−	2.22121i	−0.807847	−	0.150785i
$218$	−16.2979			−1.10383
$219$	3.58955	−	6.21728i	0.242559	−	0.420125i
$220$	−29.9177	−	51.8189i	−2.01705	−	3.49363i
$221$	−0.181708	−	0.314728i	−0.0122230	−	0.0211709i
$222$	3.01023	−	5.21388i	0.202034	−	0.349932i
$223$	1.24287			0.0832285			0.0416142	−	0.999134i	$-0.486750\pi$
$223$	1.24287			0.0832285			0.0416142	+	0.999134i	$0.486750\pi$
$224$	−19.4142	−	3.62367i	−1.29716	−	0.242117i
$225$	−0.0768496			−0.00512331
$226$	5.66136	−	9.80576i	0.376588	−	0.652269i
$227$	−7.75252	−	13.4278i	−0.514553	−	0.891231i	−0.999857	−	0.0168863i	$-0.994625\pi$
$227$	−7.75252	−	13.4278i	−0.514553	−	0.891231i	0.485305	−	0.874345i	$-0.338709\pi$
$228$	5.48703	+	9.50382i	0.363388	+	0.629406i
$229$	1.62264	−	2.81049i	0.107227	−	0.185722i	−0.807419	−	0.589978i	$-0.799136\pi$
$229$	1.62264	−	2.81049i	0.107227	−	0.185722i	0.914646	+	0.404256i	$0.132470\pi$
$230$	11.0204			0.726663
$231$	2.37666	+	6.73862i	0.156373	+	0.443369i
$232$	46.6676			3.06388
$233$	0.0743321	−	0.128747i	0.00486966	−	0.00843450i	−0.863580	−	0.504211i	$-0.831783\pi$
$233$	0.0743321	−	0.128747i	0.00486966	−	0.00843450i	0.868450	+	0.495777i	$0.165117\pi$
$234$	−0.259625	−	0.449683i	−0.0169722	−	0.0293967i
$235$	10.8223	+	18.7448i	0.705970	+	1.22278i
$236$	5.14333	−	8.90852i	0.334803	−	0.579895i
$237$	−2.56759			−0.166783
$238$	−22.1935	+	25.9187i	−1.43859	+	1.68006i
$239$	15.7243			1.01712			0.508561	−	0.861026i	$-0.330178\pi$
$239$	15.7243			1.01712			0.508561	+	0.861026i	$0.330178\pi$
$240$	−4.28015	+	7.41343i	−0.276282	+	0.478535i
$241$	−7.25193	−	12.5607i	−0.467138	−	0.809106i	0.532158	−	0.846645i	$-0.321381\pi$
$241$	−7.25193	−	12.5607i	−0.467138	−	0.809106i	−0.999295	+	0.0375393i	$0.988048\pi$
$242$	−28.6593	−	49.6393i	−1.84229	−	3.19093i
$243$	−5.71664	+	9.90152i	−0.366723	+	0.635183i
$244$	−11.9890			−0.767516
$245$	14.6389	+	5.66197i	0.935243	+	0.361730i
$246$	1.20539			0.0768531
$247$	−0.183717	+	0.318207i	−0.0116896	+	0.0202470i
$248$	−15.4697	−	26.7943i	−0.982327	−	1.70144i
$249$	−1.13369	−	1.96362i	−0.0718449	−	0.124439i
$250$	14.3504	−	24.8557i	0.907600	−	1.57201i
$251$	17.6114			1.11162			0.555812	−	0.831308i	$-0.312407\pi$
$251$	17.6114			1.11162			0.555812	+	0.831308i	$0.312407\pi$
$252$	−22.1397	+	25.8558i	−1.39467	+	1.62876i
$253$	11.0120			0.692319
$254$	15.0771	−	26.1142i	0.946019	−	1.63855i
$255$	2.63009	+	4.55545i	0.164703	+	0.285273i
$256$	12.4854	+	21.6253i	0.780337	+	1.35158i
$257$	−14.9619	+	25.9148i	−0.933298	+	1.61652i	−0.155656	+	0.987811i	$0.549749\pi$
$257$	−14.9619	+	25.9148i	−0.933298	+	1.61652i	−0.777641	+	0.628708i	$0.783584\pi$
$258$	−8.24292			−0.513182
$259$	−4.39528	−	12.4621i	−0.273110	−	0.774357i
$260$	−0.752527			−0.0466698
$261$	9.59579	−	16.6204i	0.593965	−	1.02878i
$262$	−28.5916	−	49.5221i	−1.76639	−	3.05948i
$263$	15.0015	+	25.9833i	0.925030	+	1.60220i	0.791513	+	0.611152i	$0.209294\pi$
$263$	15.0015	+	25.9833i	0.925030	+	1.60220i	0.133517	+	0.991047i	$0.457373\pi$
$264$	−9.13096	+	15.8153i	−0.561971	+	0.973363i
$265$	27.5154			1.69026
$266$	33.9138	+	6.33003i	2.07939	+	0.388119i
$267$	5.89061			0.360499
$268$	2.34070	−	4.05421i	0.142981	−	0.247651i
$269$	−2.33703	−	4.04785i	−0.142491	−	0.246802i	0.785943	−	0.618299i	$-0.212178\pi$
$269$	−2.33703	−	4.04785i	−0.142491	−	0.246802i	−0.928434	+	0.371497i	$0.878845\pi$
$270$	7.81204	+	13.5309i	0.475426	+	0.823462i
$271$	4.35338	−	7.54027i	0.264449	−	0.458039i	−0.702970	−	0.711219i	$-0.748143\pi$
$271$	4.35338	−	7.54027i	0.264449	−	0.458039i	0.967419	+	0.253180i	$0.0814766\pi$
$272$	−40.8476			−2.47675
$273$	0.0883401	+	0.0164888i	0.00534659	+	0.000997946i
$274$	−15.3220			−0.925636
$275$	−0.0796989	+	0.138043i	−0.00480603	+	0.00832428i
$276$	−2.06818	−	3.58220i	−0.124490	−	0.215623i
$277$	−3.26589	−	5.65669i	−0.196228	−	0.339877i	0.751074	−	0.660218i	$-0.229536\pi$
$277$	−3.26589	−	5.65669i	−0.196228	−	0.339877i	−0.947302	+	0.320340i	$0.896203\pi$
$278$	−11.4532	+	19.8376i	−0.686920	+	1.18978i
$279$	−12.7235			−0.761736
$280$	13.3424	+	37.8301i	0.797360	+	2.26078i
$281$	22.9384			1.36839			0.684195	−	0.729299i	$-0.260154\pi$
$281$	22.9384			1.36839			0.684195	+	0.729299i	$0.260154\pi$
$282$	5.81792	−	10.0769i	0.346452	−	0.600072i
$283$	8.95582	+	15.5119i	0.532369	+	0.922089i	0.999286	+	0.0377883i	$0.0120313\pi$
$283$	8.95582	+	15.5119i	0.532369	+	0.922089i	−0.466917	+	0.884301i	$0.654635\pi$
$284$	9.15870	+	15.8633i	0.543469	+	0.941315i
$285$	2.65916	−	4.60581i	0.157515	−	0.272824i
$286$	−1.07700			−0.0636845
$287$	1.72083	−	2.00966i	0.101577	−	0.118627i
$288$	−20.7571			−1.22312
$289$	−4.05013	+	7.01504i	−0.238243	+	0.412649i
$290$	−19.9183	−	34.4995i	−1.16964	−	2.02588i
$291$	−4.24614	−	7.35454i	−0.248913	−	0.431130i
$292$	35.4678	−	61.4321i	2.07560	−	3.59504i
$293$	0.775720			0.0453181			0.0226590	−	0.999743i	$-0.492787\pi$
$293$	0.775720			0.0453181			0.0226590	+	0.999743i	$0.492787\pi$
$294$	−1.29882	−	8.33720i	−0.0757486	−	0.486235i
$295$	−4.98520			−0.290249
$296$	16.8864	−	29.2481i	0.981500	−	1.70001i
$297$	7.80610	+	13.5206i	0.452956	+	0.784543i
$298$	−10.4949	−	18.1777i	−0.607954	−	1.05301i
$299$	0.0692470	−	0.119939i	0.00400466	−	0.00693627i
$300$	0.0598736			0.00345680
$301$	−11.7676	+	13.7428i	−0.678275	+	0.792122i
$302$	−21.0949			−1.21387
$303$	−2.38256	+	4.12671i	−0.136874	+	0.237073i
$304$	20.6496	+	35.7661i	1.18433	+	2.05133i
$305$	2.90509	+	5.03177i	0.166345	+	0.288118i
$306$	−17.9316	+	31.0585i	−1.02508	+	1.77549i
$307$	−2.48064			−0.141577			−0.0707887	−	0.997491i	$-0.522552\pi$
$307$	−2.48064			−0.141577			−0.0707887	+	0.997491i	$0.522552\pi$
$308$	23.4834	+	66.5834i	1.33809	+	3.79394i
$309$	−0.254352			−0.0144696
$310$	−13.2053	+	22.8722i	−0.750010	+	1.29906i
$311$	−0.746946	−	1.29375i	−0.0423554	−	0.0733617i	0.844071	−	0.536232i	$-0.180153\pi$
$311$	−0.746946	−	1.29375i	−0.0423554	−	0.0733617i	−0.886426	+	0.462870i	$0.846820\pi$
$312$	0.114837	+	0.198903i	0.00650135	+	0.0112607i
$313$	7.39703	−	12.8120i	0.418105	−	0.724179i	−0.577644	−	0.816289i	$-0.696028\pi$
$313$	7.39703	−	12.8120i	0.418105	−	0.724179i	0.995749	+	0.0921098i	$0.0293611\pi$
$314$	−19.6889			−1.11111
$315$	16.2164	+	3.02681i	0.913692	+	0.170541i
$316$	−25.3701			−1.42718
$317$	−7.61961	+	13.1975i	−0.427960	+	0.741248i	−0.996692	−	0.0812749i	$-0.974101\pi$
$317$	−7.61961	+	13.1975i	−0.427960	+	0.741248i	0.568732	+	0.822523i	$0.307434\pi$
$318$	−7.39592	−	12.8101i	−0.414743	−	0.718356i
$319$	−19.9031	−	34.4733i	−1.11436	−	1.93013i
$320$	−3.26168	+	5.64939i	−0.182333	+	0.315811i
$321$	−0.185795			−0.0103700
$322$	−12.7828	−	2.38593i	−0.712360	−	0.132963i
$323$	25.3777			1.41205
$324$	−16.3665	+	28.3475i	−0.909248	+	1.57486i
$325$	0.00100234	+	0.00173611i	5.56001e−5	+	9.63022e-5i
$326$	1.05747	+	1.83160i	0.0585680	+	0.101443i
$327$	1.48228	−	2.56739i	0.0819705	−	0.141977i
$328$	6.76185			0.373361
$329$	−8.49482	−	24.0857i	−0.468335	−	1.32788i
$330$	15.5888			0.858135
$331$	−10.6424	+	18.4331i	−0.584957	+	1.01318i	0.409924	+	0.912120i	$0.365555\pi$
$331$	−10.6424	+	18.4331i	−0.584957	+	1.01318i	−0.994881	+	0.101056i	$0.967778\pi$
$332$	−11.2019	−	19.4022i	−0.614783	−	1.06483i
$333$	−6.94434	−	12.0280i	−0.380548	−	0.659128i
$334$	−10.0771	+	17.4540i	−0.551394	+	0.955043i
$335$	−2.26873			−0.123954
$336$	6.56968	−	7.67239i	0.358405	−	0.418563i
$337$	−19.3612			−1.05467			−0.527336	−	0.849657i	$-0.676809\pi$
$337$	−19.3612			−1.05467			−0.527336	+	0.849657i	$0.676809\pi$
$338$	16.7258	−	28.9700i	0.909764	−	1.57576i
$339$	1.02979	+	1.78366i	0.0559307	+	0.0968749i
$340$	25.9876	+	45.0118i	1.40937	+	2.44111i
$341$	−13.1953	+	22.8548i	−0.714563	+	1.23766i
$342$	36.2597			1.96070
$343$	−15.7542	−	9.73681i	−0.850646	−	0.525738i
$344$	−46.2399			−2.49309
$345$	−1.00230	+	1.73603i	−0.0539619	+	0.0934647i
$346$	17.1996	+	29.7906i	0.924656	+	1.60155i
$347$	−4.60038	−	7.96808i	−0.246961	−	0.427749i	0.715720	−	0.698387i	$-0.246099\pi$
$347$	−4.60038	−	7.96808i	−0.246961	−	0.427749i	−0.962681	+	0.270638i	$0.912765\pi$
$348$	−7.47608	+	12.9490i	−0.400760	+	0.694137i
$349$	5.22287			0.279574			0.139787	−	0.990182i	$-0.455358\pi$
$349$	5.22287			0.279574			0.139787	+	0.990182i	$0.455358\pi$
$350$	0.122424	−	0.142973i	0.00654386	−	0.00764224i
$351$	0.196349			0.0104803
$352$	−21.5267	+	37.2853i	−1.14738	+	1.98731i
$353$	16.4924	+	28.5657i	0.877803	+	1.52040i	0.853746	+	0.520689i	$0.174325\pi$
$353$	16.4924	+	28.5657i	0.877803	+	1.52040i	0.0240568	+	0.999711i	$0.492342\pi$
$354$	1.33998	+	2.32092i	0.0712193	+	0.123356i
$355$	4.43855	−	7.68780i	0.235574	−	0.408026i
$356$	58.2043			3.08482
$357$	−2.06445	−	5.85341i	−0.109262	−	0.309795i
$358$	21.1587			1.11827
$359$	−5.30829	+	9.19423i	−0.280161	+	0.485253i	−0.971424	−	0.237350i	$-0.923721\pi$
$359$	−5.30829	+	9.19423i	−0.280161	+	0.485253i	0.691263	+	0.722603i	$0.257054\pi$
$360$	21.0804	+	36.5122i	1.11103	+	1.92436i
$361$	−3.32913	−	5.76622i	−0.175217	−	0.303485i
$362$	17.2046	−	29.7993i	0.904255	−	1.56622i
$363$	10.4262			0.547232
$364$	0.872877	+	0.162923i	0.0457512	+	0.00853950i
$365$	−34.3773			−1.79939
$366$	1.56173	−	2.70500i	0.0816331	−	0.141393i
$367$	0.744179	+	1.28896i	0.0388458	+	0.0672829i	0.884795	−	0.465981i	$-0.154299\pi$
$367$	0.744179	+	1.28896i	0.0388458	+	0.0672829i	−0.845949	+	0.533264i	$0.820965\pi$
$368$	−7.78328	−	13.4810i	−0.405731	−	0.702747i
$369$	1.39037	−	2.40819i	0.0723798	−	0.125365i
$370$	−28.8292			−1.49876
$371$	−31.9158	−	5.95712i	−1.65699	−	0.309278i
$372$	9.91289			0.513959
$373$	1.65195	−	2.86126i	0.0855348	−	0.148151i	−0.820084	−	0.572243i	$-0.806073\pi$
$373$	1.65195	−	2.86126i	0.0855348	−	0.148151i	0.905619	+	0.424092i	$0.139407\pi$
$374$	37.1929	+	64.4200i	1.92320	+	3.33108i
$375$	2.61032	+	4.52121i	0.134797	+	0.233474i
$376$	32.6365	−	56.5281i	1.68310	−	2.91521i
$377$	−0.500629			−0.0257837
$378$	−6.13195	−	17.3861i	−0.315394	−	0.894246i
$379$	18.2983			0.939922			0.469961	−	0.882687i	$-0.344268\pi$
$379$	18.2983			0.939922			0.469961	+	0.882687i	$0.344268\pi$
$380$	26.2748	−	45.5093i	1.34787	−	2.33458i
$381$	2.74250	+	4.75015i	0.140502	+	0.243357i
$382$	3.02209	+	5.23442i	0.154624	+	0.267816i
$383$	−18.6315	+	32.2708i	−0.952027	+	1.64896i	−0.210997	+	0.977487i	$0.567671\pi$
$383$	−18.6315	+	32.2708i	−0.952027	+	1.64896i	−0.741030	+	0.671472i	$0.765662\pi$
$384$	−3.48376			−0.177780
$385$	22.2546	−	25.9900i	1.13420	−	1.32457i
$386$	−12.1261			−0.617201
$387$	−9.50785	+	16.4681i	−0.483311	+	0.837119i
$388$	−41.9556	−	72.6692i	−2.12997	−	3.68922i
$389$	1.86176	+	3.22467i	0.0943952	+	0.163497i	0.909356	−	0.416019i	$-0.136575\pi$
$389$	1.86176	+	3.22467i	0.0943952	+	0.163497i	−0.814961	+	0.579516i	$0.803242\pi$
$390$	0.0980273	−	0.169788i	0.00496380	−	0.00859756i
$391$	−9.56543			−0.483744
$392$	−7.28592	−	46.7688i	−0.367995	−	2.36218i
$393$	10.4015			0.524689
$394$	8.91077	−	15.4339i	0.448918	−	0.777549i
$395$	6.14751	+	10.6478i	0.309315	+	0.535749i
$396$	37.1027	+	64.2638i	1.86448	+	3.22938i
$397$	5.08753	−	8.81186i	0.255336	−	0.442255i	−0.709651	−	0.704553i	$-0.751147\pi$
$397$	5.08753	−	8.81186i	0.255336	−	0.442255i	0.964987	+	0.262299i	$0.0844807\pi$
$398$	−61.0323			−3.05928
$399$	−4.08160	+	4.76669i	−0.204336	+	0.238633i
$400$	0.225325			0.0112662
$401$	17.5282	−	30.3598i	0.875319	−	1.51610i	0.0188959	−	0.999821i	$-0.493985\pi$
$401$	17.5282	−	30.3598i	0.875319	−	1.51610i	0.856423	−	0.516275i	$-0.172682\pi$
$402$	0.609819	+	1.05624i	0.0304150	+	0.0526803i
$403$	0.165952	+	0.287437i	0.00826665	+	0.0143183i
$404$	−23.5417	+	40.7755i	−1.17124	+	2.02866i
$405$	15.8633			0.788251
$406$	15.6346	+	44.3292i	0.775931	+	2.20002i
$407$	−28.8073			−1.42792
$408$	7.93148	−	13.7377i	0.392667	−	0.680119i
$409$	8.28742	+	14.3542i	0.409787	+	0.709771i	0.994866	−	0.101205i	$-0.0322698\pi$
$409$	8.28742	+	14.3542i	0.409787	+	0.709771i	−0.585079	+	0.810976i	$0.698936\pi$
$410$	−2.88604	−	4.99876i	−0.142531	−	0.246871i
$411$	1.39353	−	2.41366i	0.0687376	−	0.119057i
$412$	−2.51321			−0.123817
$413$	5.78247	+	1.07930i	0.284537	+	0.0531090i
$414$	−13.6671			−0.671700
$415$	−5.42873	+	9.40284i	−0.266486	+	0.461567i
$416$	0.270733	+	0.468924i	0.0132738	+	0.0229909i
$417$	−2.08333	−	3.60844i	−0.102021	−	0.176706i
$418$	37.6040	−	65.1321i	1.83927	−	3.18572i
$419$	8.81409			0.430597			0.215298	−	0.976548i	$-0.430928\pi$
$419$	8.81409			0.430597			0.215298	+	0.976548i	$0.430928\pi$
$420$	−12.6342	−	2.35819i	−0.616487	−	0.115068i
$421$	31.9405			1.55668			0.778342	−	0.627841i	$-0.216061\pi$
$421$	31.9405			1.55668			0.778342	+	0.627841i	$0.216061\pi$
$422$	−9.27967	+	16.0729i	−0.451727	+	0.782415i
$423$	−13.4214	−	23.2466i	−0.652572	−	1.13029i
$424$	−41.4886	−	71.8604i	−2.01486	−	3.48985i
$425$	0.0692294	−	0.119909i	0.00335812	−	0.00581643i
$426$	−4.77220			−0.231214
$427$	−2.28031	−	6.46544i	−0.110352	−	0.312885i
$428$	−1.83581			−0.0887373
$429$	0.0979528	−	0.169659i	0.00472920	−	0.00819122i
$430$	19.7357	+	34.1833i	0.951742	+	1.64847i
$431$	−15.2381	−	26.3932i	−0.733994	−	1.27131i	−0.955164	−	0.296079i	$-0.904321\pi$
$431$	−15.2381	−	26.3932i	−0.733994	−	1.27131i	0.221170	−	0.975235i	$-0.429012\pi$
$432$	11.0347	−	19.1126i	0.530907	−	0.919558i
$433$	26.5128			1.27412			0.637062	−	0.770813i	$-0.280150\pi$
$433$	26.5128			1.27412			0.637062	+	0.770813i	$0.280150\pi$
$434$	20.2691	−	23.6712i	0.972946	−	1.13625i
$435$	7.24622			0.347430
$436$	14.6462	−	25.3680i	0.701428	−	1.21491i
$437$	4.83558	+	8.37547i	0.231317	+	0.400653i
$438$	9.24037	+	16.0048i	0.441522	+	0.764739i
$439$	8.34610	−	14.4559i	0.398338	−	0.689941i	−0.595183	−	0.803590i	$-0.702921\pi$
$439$	8.34610	−	14.4559i	0.398338	−	0.689941i	0.993521	+	0.113649i	$0.0362539\pi$
$440$	87.4478			4.16891
$441$	−18.1546	−	7.02176i	−0.864503	−	0.334369i
$442$	0.935524			0.0444983
$443$	−1.53949	+	2.66648i	−0.0731434	+	0.126688i	−0.900277	−	0.435317i	$-0.856636\pi$
$443$	−1.53949	+	2.66648i	−0.0731434	+	0.126688i	0.827134	+	0.562005i	$0.189970\pi$
$444$	5.41034	+	9.37099i	0.256763	+	0.444727i
$445$	−14.1037	−	24.4283i	−0.668579	−	1.15801i
$446$	−1.59972	+	2.77080i	−0.0757490	+	0.131201i
$447$	3.81802			0.180586
$448$	5.00641	−	5.84673i	0.236531	−	0.276232i
$449$	−22.4476			−1.05937			−0.529683	−	0.848196i	$-0.677689\pi$
$449$	−22.4476			−1.05937			−0.529683	+	0.848196i	$0.677689\pi$
$450$	0.0989148	−	0.171325i	0.00466289	−	0.00807636i
$451$	−2.88384	−	4.99496i	−0.135795	−	0.235203i
$452$	10.1753	+	17.6241i	0.478604	+	0.828966i
$453$	1.91857	−	3.32306i	0.0901422	−	0.156131i
$454$	39.9137			1.87324
$455$	−0.143131	−	0.405824i	−0.00671009	−	0.0190253i
$456$	−16.0383			−0.751063
$457$	19.3182	−	33.4600i	0.903666	−	1.56519i	0.0809669	−	0.996717i	$-0.474199\pi$
$457$	19.3182	−	33.4600i	0.903666	−	1.56519i	0.822699	−	0.568478i	$-0.192467\pi$
$458$	4.17706	+	7.23488i	0.195181	+	0.338064i
$459$	−6.78066	−	11.7445i	−0.316494	−	0.548184i
$460$	−9.90356	+	17.1535i	−0.461756	+	0.799785i
$461$	−12.2417			−0.570155			−0.285077	−	0.958504i	$-0.592019\pi$
$461$	−12.2417			−0.570155			−0.285077	+	0.958504i	$0.592019\pi$
$462$	−18.0819	−	3.37500i	−0.841244	−	0.157019i
$463$	32.9753			1.53249			0.766246	−	0.642547i	$-0.222122\pi$
$463$	32.9753			1.53249			0.766246	+	0.642547i	$0.222122\pi$
$464$	−28.1350	+	48.7313i	−1.30614	+	2.26230i
$465$	−2.40203	−	4.16043i	−0.111391	−	0.192935i
$466$	0.191349	+	0.331426i	0.00886407	+	0.0153530i
$467$	−3.00957	+	5.21273i	−0.139266	+	0.241216i	−0.927219	−	0.374519i	$-0.877808\pi$
$467$	−3.00957	+	5.21273i	−0.139266	+	0.241216i	0.787953	+	0.615736i	$0.211141\pi$
$468$	0.933256			0.0431398
$469$	2.63157	+	0.491184i	0.121514	+	0.0226808i
$470$	−55.7186			−2.57011
$471$	1.79069	−	3.10157i	0.0825107	−	0.142913i
$472$	7.51685	+	13.0196i	0.345991	+	0.599274i
$473$	19.7207	+	34.1573i	0.906760	+	1.57055i
$474$	3.30481	−	5.72410i	0.151795	−	0.262916i
$475$	−0.139989			−0.00642315
$476$	−20.3986	−	57.8367i	−0.934967	−	2.65094i
$477$	−34.1235			−1.56241
$478$	−20.2391	+	35.0552i	−0.925716	+	1.60339i
$479$	−10.2918	−	17.8259i	−0.470245	−	0.814487i	0.529176	−	0.848512i	$-0.322501\pi$
$479$	−10.2918	−	17.8259i	−0.470245	−	0.814487i	−0.999421	+	0.0340244i	$0.989168\pi$
$480$	−3.91866	−	6.78731i	−0.178861	−	0.309797i
$481$	−0.181149	+	0.313760i	−0.00825970	+	0.0143062i
$482$	37.3365			1.70063
$483$	1.53845	−	1.79667i	0.0700017	−	0.0817513i
$484$	103.020			4.68271
$485$	−20.3328	+	35.2174i	−0.923265	+	1.59914i
$486$	−14.7160	−	25.4889i	−0.667533	−	1.15620i
$487$	1.73187	+	2.99969i	0.0784785	+	0.135929i	0.902594	−	0.430494i	$-0.141660\pi$
$487$	1.73187	+	2.99969i	0.0784785	+	0.135929i	−0.824115	+	0.566422i	$0.808327\pi$
$488$	8.76079	−	15.1741i	0.396582	−	0.686901i
$489$	−0.384706			−0.0173970
$490$	−31.4646	+	25.3477i	−1.42142	+	1.14509i
$491$	−8.93553			−0.403255			−0.201627	−	0.979462i	$-0.564623\pi$
$491$	−8.93553			−0.403255			−0.201627	+	0.979462i	$0.564623\pi$
$492$	−1.08324	+	1.87622i	−0.0488361	+	0.0845867i
$493$	17.2886	+	29.9447i	0.778639	+	1.34864i
$494$	−0.472933	−	0.819143i	−0.0212782	−	0.0368550i
$495$	17.9810	−	31.1440i	0.808185	−	1.39982i
$496$	37.3056			1.67507
$497$	−6.81282	+	7.95633i	−0.305597	+	0.356890i
$498$	5.83681			0.261554
$499$	−3.29472	+	5.70662i	−0.147492	+	0.255463i	−0.930300	−	0.366800i	$-0.880453\pi$
$499$	−3.29472	+	5.70662i	−0.147492	+	0.255463i	0.782808	+	0.622263i	$0.213787\pi$
$500$	25.7922	+	44.6735i	1.15346	+	1.99786i
$501$	−1.83301	−	3.17487i	−0.0818929	−	0.141843i
$502$	−22.6681	+	39.2623i	−1.01173	+	1.75236i
$503$	−21.0935			−0.940511			−0.470255	−	0.882530i	$-0.655838\pi$
$503$	−21.0935			−0.940511			−0.470255	+	0.882530i	$0.655838\pi$
$504$	−16.5467	−	46.9155i	−0.737050	−	2.08978i
$505$	22.8179			1.01538
$506$	−14.1738	+	24.5497i	−0.630102	+	1.09137i
$507$	3.04241	+	5.26960i	0.135118	+	0.234031i
$508$	27.0983	+	46.9356i	1.20229	+	2.08243i
$509$	0.106788	−	0.184963i	0.00473332	−	0.00819834i	−0.863649	−	0.504094i	$-0.831827\pi$
$509$	0.106788	−	0.184963i	0.00473332	−	0.00819834i	0.868382	+	0.495895i	$0.165160\pi$
$510$	−13.5410			−0.599605
$511$	39.8752	+	7.44274i	1.76398	+	0.329248i
$512$	−49.4010			−2.18324
$513$	−6.85562	+	11.8743i	−0.302683	+	0.524262i
$514$	−38.5156	−	66.7110i	−1.69885	−	2.94249i
$515$	0.608986	+	1.05479i	0.0268351	+	0.0464798i
$516$	7.40757	−	12.8303i	0.326100	−	0.564822i
$517$	−55.6762			−2.44864
$518$	33.4398	+	6.24156i	1.46926	+	0.274238i
$519$	−6.25717			−0.274659
$520$	0.549899	−	0.952454i	0.0241147	−	0.0417679i
$521$	7.06576	+	12.2382i	0.309556	+	0.536167i	0.978265	−	0.207357i	$-0.0664861\pi$
$521$	7.06576	+	12.2382i	0.309556	+	0.536167i	−0.668709	+	0.743524i	$0.733153\pi$
$522$	24.7019	+	42.7850i	1.08117	+	1.87265i
$523$	−19.2443	+	33.3321i	−0.841495	+	1.45751i	0.0471356	+	0.998888i	$0.484991\pi$
$523$	−19.2443	+	33.3321i	−0.841495	+	1.45751i	−0.888631	+	0.458624i	$0.848343\pi$
$524$	102.776			4.48980
$525$	0.0113880	+	0.0322887i	0.000497012	+	0.00140920i
$526$	−77.2349			−3.36760
$527$	11.4619	−	19.8525i	0.499287	−	0.864790i
$528$	−11.0098	−	19.0695i	−0.479139	−	0.829892i
$529$	9.67736	+	16.7617i	0.420755	+	0.728769i
$530$	−35.4156	+	61.3417i	−1.53836	+	2.66451i
$531$	6.18245			0.268296
$532$	−40.3297	+	47.0990i	−1.74852	+	2.04200i
$533$	−0.0725380			−0.00314197
$534$	−7.58193	+	13.1323i	−0.328102	+	0.568290i
$535$	0.444842	+	0.770489i	0.0192322	+	0.0333111i
$536$	3.42087	+	5.92513i	0.147759	+	0.255927i
$537$	−1.92437	+	3.33310i	−0.0830426	+	0.143834i
$538$	12.0321			0.518743
$539$	−31.4406	+	25.3284i	−1.35424	+	1.09097i
$540$	−28.0814			−1.20843
$541$	4.88655	−	8.46376i	0.210089	−	0.363885i	−0.741653	−	0.670784i	$-0.765958\pi$
$541$	4.88655	−	8.46376i	0.210089	−	0.363885i	0.951742	+	0.306898i	$0.0992912\pi$
$542$	11.2067	+	19.4105i	0.481367	+	0.833753i
$543$	3.12950	+	5.42045i	0.134300	+	0.232614i
$544$	18.6989	−	32.3874i	0.801707	−	1.38860i
$545$	−14.1959			−0.608087
$546$	−0.150464	+	0.175719i	−0.00643926	+	0.00752008i
$547$	−32.3733			−1.38418			−0.692092	−	0.721810i	$-0.743311\pi$
$547$	−32.3733			−1.38418			−0.692092	+	0.721810i	$0.743311\pi$
$548$	13.7692	−	23.8490i	0.588193	−	1.01878i
$549$	−3.60278	−	6.24021i	−0.153763	−	0.266325i
$550$	−0.205164	−	0.355355i	−0.00874824	−	0.0151524i
$551$	17.4797	−	30.2757i	0.744660	−	1.28979i
$552$	6.04519			0.257300
$553$	−4.82540	−	13.6816i	−0.205197	−	0.581801i
$554$	16.8144			0.714375
$555$	2.62200	−	4.54143i	0.111298	−	0.192773i
$556$	−20.5851	−	35.6545i	−0.873003	−	1.51209i
$557$	15.9513	+	27.6285i	0.675879	+	1.17066i	0.976211	+	0.216822i	$0.0695692\pi$
$557$	15.9513	+	27.6285i	0.675879	+	1.17066i	−0.300332	+	0.953835i	$0.597097\pi$
$558$	16.3767	−	28.3653i	0.693281	−	1.20080i
$559$	0.496041			0.0209803
$560$	−47.5469	−	8.87467i	−2.00922	−	0.375023i
$561$	−13.5307			−0.571266
$562$	−29.5245	+	51.1380i	−1.24542	+	2.15713i
$563$	−16.2536	−	28.1521i	−0.685009	−	1.18647i	−0.973434	−	0.228968i	$-0.926465\pi$
$563$	−16.2536	−	28.1521i	−0.685009	−	1.18647i	0.288425	−	0.957502i	$-0.406868\pi$
$564$	10.4566	+	18.1114i	0.440304	+	0.762629i
$565$	4.93120	−	8.54109i	0.207457	−	0.359326i
$566$	−46.1090			−1.93810
$567$	−18.4002	−	3.43442i	−0.772737	−	0.144232i
$568$	−26.7704			−1.12326
$569$	17.7780	−	30.7924i	0.745293	−	1.29089i	−0.204764	−	0.978811i	$-0.565643\pi$
$569$	17.7780	−	30.7924i	0.745293	−	1.29089i	0.950058	−	0.312075i	$-0.101024\pi$
$570$	6.84534	+	11.8565i	0.286720	+	0.496613i
$571$	−2.56954	−	4.45057i	−0.107532	−	0.186250i	0.807238	−	0.590226i	$-0.200961\pi$
$571$	−2.56954	−	4.45057i	−0.107532	−	0.186250i	−0.914770	+	0.403976i	$0.867628\pi$
$572$	0.967858	−	1.67638i	0.0404682	−	0.0700929i
$573$	−1.09943			−0.0459293
$574$	2.26535	+	6.42303i	0.0945540	+	0.268092i
$575$	0.0527651			0.00220045
$576$	4.04501	−	7.00616i	0.168542	−	0.291923i
$577$	11.7011	+	20.2670i	0.487125	+	0.843725i	0.999890	−	0.0148037i	$-0.00471233\pi$
$577$	11.7011	+	20.2670i	0.487125	+	0.843725i	−0.512766	+	0.858529i	$0.671379\pi$
$578$	−10.4260	−	18.0584i	−0.433666	−	0.751131i
$579$	1.10286	−	1.91021i	0.0458333	−	0.0793856i
$580$	71.5989			2.97298
$581$	8.33266	−	9.73128i	0.345697	−	0.403722i
$582$	21.8612			0.906177
$583$	−35.3887	+	61.2950i	−1.46565	+	2.53858i
$584$	51.8353	+	89.7814i	2.14496	+	3.71518i
$585$	−0.226140	−	0.391687i	−0.00934976	−	0.0161943i
$586$	−0.998447	+	1.72936i	−0.0412455	+	0.0714392i
$587$	21.6605			0.894023			0.447011	−	0.894528i	$-0.352488\pi$
$587$	21.6605			0.894023			0.447011	+	0.894528i	$0.352488\pi$
$588$	14.1442	+	5.47066i	0.583298	+	0.225606i
$589$	−23.1771			−0.954998
$590$	6.41656	−	11.1138i	0.264165	−	0.457548i
$591$	1.62086	+	2.80741i	0.0666732	+	0.115481i
$592$	20.3610	+	35.2662i	0.836830	+	1.44943i
$593$	−0.487742	+	0.844794i	−0.0200292	+	0.0346915i	−0.875866	−	0.482554i	$-0.839709\pi$
$593$	−0.487742	+	0.844794i	−0.0200292	+	0.0346915i	0.855837	+	0.517245i	$0.173043\pi$
$594$	−40.1896			−1.64900
$595$	−19.3312	+	22.5759i	−0.792501	+	0.925521i
$596$	37.7253			1.54529
$597$	5.55085	−	9.61436i	0.227181	−	0.393490i
$598$	0.178259	+	0.308753i	0.00728954	+	0.0126259i
$599$	−2.42058	−	4.19256i	−0.0989021	−	0.171303i	0.812328	−	0.583200i	$-0.198200\pi$
$599$	−2.42058	−	4.19256i	−0.0989021	−	0.171303i	−0.911230	+	0.411897i	$0.864866\pi$
$600$	−0.0437518	+	0.0757804i	−0.00178616	+	0.00309372i
$601$	−19.3928			−0.791048			−0.395524	−	0.918456i	$-0.629437\pi$
$601$	−19.3928			−0.791048			−0.395524	+	0.918456i	$0.629437\pi$
$602$	−15.4913	−	43.9230i	−0.631378	−	1.79017i
$603$	2.81360			0.114579
$604$	18.9571	−	32.8347i	0.771353	−	1.33602i
$605$	−24.9630	−	43.2372i	−1.01489	−	1.75784i
$606$	−6.13329	−	10.6232i	−0.249148	−	0.431537i
$607$	2.57666	−	4.46291i	0.104583	−	0.181144i	−0.808984	−	0.587830i	$-0.799982\pi$
$607$	2.57666	−	4.46291i	0.104583	−	0.181144i	0.913568	+	0.406686i	$0.133316\pi$
$608$	−37.8111			−1.53344
$609$	−8.40509	−	1.56882i	−0.340592	−	0.0635717i
$610$	−14.9568			−0.605584
$611$	−0.350110	+	0.606408i	−0.0141639	+	0.0245326i
$612$	−32.2288	−	55.8219i	−1.30277	−	2.25647i
$613$	−10.5649	−	18.2990i	−0.426713	−	0.739088i	0.569866	−	0.821738i	$-0.306995\pi$
$613$	−10.5649	−	18.2990i	−0.426713	−	0.739088i	−0.996579	+	0.0826494i	$0.973662\pi$
$614$	3.19288	−	5.53023i	0.128854	−	0.223182i
$615$	1.04993			0.0423374
$616$	−101.433	−	18.9326i	−4.08685	−	0.762815i
$617$	10.2828			0.413969			0.206985	−	0.978344i	$-0.433635\pi$
$617$	10.2828			0.413969			0.206985	+	0.978344i	$0.433635\pi$
$618$	0.327382	−	0.567042i	0.0131692	−	0.0228098i
$619$	15.3550	+	26.5956i	0.617170	+	1.06897i	0.990000	+	0.141069i	$0.0450541\pi$
$619$	15.3550	+	26.5956i	0.617170	+	1.06897i	−0.372830	+	0.927900i	$0.621613\pi$
$620$	−23.7341	−	41.1087i	−0.953184	−	1.65096i
$621$	2.58403	−	4.47568i	0.103694	−	0.179603i
$622$	3.84564			0.154196
$623$	11.0705	+	31.3885i	0.443530	+	1.25755i
$624$	−0.276932			−0.0110861
$625$	12.5687	−	21.7696i	0.502748	−	0.870786i
$626$	19.0418	+	32.9813i	0.761062	+	1.31820i
$627$	6.84013	+	11.8475i	0.273168	+	0.473142i
$628$	17.6936	−	30.6462i	0.706050	−	1.22291i
$629$	25.0230			0.997734
$630$	−27.6204	+	32.2564i	−1.10042	+	1.28513i
$631$	33.2191			1.32243			0.661216	−	0.750195i	$-0.270041\pi$
$631$	33.2191			1.32243			0.661216	+	0.750195i	$0.270041\pi$
$632$	18.5388	−	32.1102i	0.737435	−	1.27728i
$633$	−1.68796	−	2.92363i	−0.0670904	−	0.116204i
$634$	−19.6147	−	33.9737i	−0.779000	−	1.34927i
$635$	13.1325	−	22.7462i	0.521149	−	0.902657i
$636$	26.5856			1.05419
$637$	0.0781601	+	0.501715i	0.00309682	+	0.0198787i
$638$	102.471			4.05687
$639$	−5.50452	+	9.53412i	−0.217756	+	0.377164i
$640$	8.34104	+	14.4471i	0.329709	+	0.571072i
$641$	−1.18968	−	2.06059i	−0.0469897	−	0.0813885i	0.841574	−	0.540142i	$-0.181629\pi$
$641$	−1.18968	−	2.06059i	−0.0469897	−	0.0813885i	−0.888564	+	0.458753i	$0.848296\pi$
$642$	0.239140	−	0.414203i	0.00943812	−	0.0163473i
$643$	21.1865			0.835515			0.417757	−	0.908559i	$-0.362816\pi$
$643$	21.1865			0.835515			0.417757	+	0.908559i	$0.362816\pi$
$644$	15.2012	−	17.7526i	0.599010	−	0.699552i
$645$	−7.17981			−0.282705
$646$	−32.6642	+	56.5761i	−1.28516	+	2.22596i
$647$	1.64556	+	2.85019i	0.0646935	+	0.112052i	0.896558	−	0.442926i	$-0.146060\pi$
$647$	1.64556	+	2.85019i	0.0646935	+	0.112052i	−0.831865	+	0.554979i	$0.812726\pi$
$648$	−23.9192	−	41.4292i	−0.939633	−	1.62749i
$649$	6.41168	−	11.1054i	0.251680	−	0.435923i
$650$	−0.00516056			−0.000202414
$651$	1.88544	+	5.34584i	0.0738961	+	0.209520i
$652$	−3.80123			−0.148868
$653$	−16.5632	+	28.6883i	−0.648168	+	1.12266i	0.335392	+	0.942079i	$0.391131\pi$
$653$	−16.5632	+	28.6883i	−0.648168	+	1.12266i	−0.983560	+	0.180581i	$0.942202\pi$
$654$	3.81576	+	6.60909i	0.149208	+	0.258436i
$655$	−24.9041	−	43.1351i	−0.973083	−	1.68543i
$656$	−4.07659	+	7.06087i	−0.159164	+	0.275680i
$657$	42.6335			1.66329
$658$	64.6295	+	12.0631i	2.51952	+	0.470271i
$659$	15.3837			0.599266			0.299633	−	0.954055i	$-0.403136\pi$
$659$	15.3837			0.599266			0.299633	+	0.954055i	$0.403136\pi$
$660$	−14.0090	+	24.2643i	−0.545299	+	0.944486i
$661$	−24.4819	−	42.4039i	−0.952236	−	1.64932i	−0.740571	−	0.671978i	$-0.765445\pi$
$661$	−24.4819	−	42.4039i	−0.952236	−	1.64932i	−0.211665	−	0.977342i	$-0.567889\pi$
$662$	−27.3960	−	47.4513i	−1.06478	−	1.84425i
$663$	−0.0850853	+	0.147372i	−0.00330444	+	0.00572346i
$664$	32.7425			1.27066
$665$	29.5398	+	5.51364i	1.14551	+	0.213810i
$666$	35.7529			1.38540
$667$	−6.58848	+	11.4116i	−0.255107	+	0.441858i
$668$	−18.1117	−	31.3705i	−0.700764	−	1.21376i
$669$	−0.290987	−	0.504005i	−0.0112502	−	0.0194859i
$670$	2.92014	−	5.05783i	0.112815	−	0.195401i
$671$	−14.9455			−0.576963
$672$	3.07589	+	8.72119i	0.118655	+	0.336427i
$673$	18.9400			0.730082			0.365041	−	0.930992i	$-0.381055\pi$
$673$	18.9400			0.730082			0.365041	+	0.930992i	$0.381055\pi$
$674$	24.9202	−	43.1631i	0.959892	−	1.66258i
$675$	0.0374037	+	0.0647851i	0.00143967	+	0.00249358i
$676$	30.0616	+	52.0682i	1.15621	+	2.00262i
$677$	−13.4222	+	23.2480i	−0.515859	+	0.893494i	0.483972	+	0.875084i	$0.339194\pi$
$677$	−13.4222	+	23.2480i	−0.515859	+	0.893494i	−0.999831	+	0.0184100i	$0.994140\pi$
$678$	−5.30188			−0.203618
$679$	31.2092	−	36.4476i	1.19770	−	1.39873i
$680$	−75.9603			−2.91294
$681$	−3.63013	+	6.28757i	−0.139107	+	0.240940i
$682$	−33.9678	−	58.8339i	−1.30069	−	2.25287i
$683$	−22.5684	−	39.0896i	−0.863556	−	1.49572i	−0.868474	−	0.495736i	$-0.834899\pi$
$683$	−22.5684	−	39.0896i	−0.863556	−	1.49572i	0.00491721	−	0.999988i	$-0.498435\pi$
$684$	−32.5850	+	56.4390i	−1.24592	+	2.15800i
$685$	−13.3459			−0.509920
$686$	41.9844	−	22.5893i	1.60297	−	0.862464i
$687$	−1.51960			−0.0579765
$688$	27.8772	−	48.2847i	1.06281	−	1.84084i
$689$	0.445071	+	0.770885i	0.0169558	+	0.0293684i
$690$	−2.58016	−	4.46896i	−0.0982249	−	0.170131i
$691$	−13.5673	+	23.4992i	−0.516123	+	0.893951i	0.483702	+	0.875233i	$0.339292\pi$
$691$	−13.5673	+	23.4992i	−0.516123	+	0.893951i	−0.999825	+	0.0187182i	$0.994041\pi$
$692$	−61.8262			−2.35028
$693$	−27.5994	+	32.2319i	−1.04841	+	1.22439i
$694$	23.6850			0.899070
$695$	−9.97610	+	17.2791i	−0.378415	+	0.655434i
$696$	−10.9261	−	18.9246i	−0.414153	−	0.717334i
$697$	2.50501	+	4.33880i	0.0948840	+	0.164344i
$698$	−6.72247	+	11.6437i	−0.254449	+	0.440719i
$699$	−0.0696123			−0.00263298
$700$	0.112523	+	0.319040i	0.00425297	+	0.0120586i
$701$	48.7878			1.84269			0.921344	−	0.388748i	$-0.127092\pi$
$701$	48.7878			1.84269			0.921344	+	0.388748i	$0.127092\pi$
$702$	−0.252725	+	0.437733i	−0.00953850	+	0.0165212i
$703$	−12.6498	−	21.9101i	−0.477097	−	0.826356i
$704$	−8.38997	−	14.5319i	−0.316209	−	0.547690i
$705$	5.06757	−	8.77729i	0.190856	−	0.330572i
$706$	−84.9110			−3.19567
$707$	−26.4671	−	4.94011i	−0.995399	−	0.185792i
$708$	−4.81675			−0.181025
$709$	−6.09726	+	10.5608i	−0.228987	+	0.396618i	−0.957508	−	0.288406i	$-0.906875\pi$
$709$	−6.09726	+	10.5608i	−0.228987	+	0.396618i	0.728521	+	0.685024i	$0.240208\pi$
$710$	11.4259	+	19.7903i	0.428807	+	0.742715i
$711$	−7.62390	−	13.2050i	−0.285919	−	0.495226i
$712$	−42.5320	+	73.6677i	−1.59396	+	2.76081i
$713$	8.73598			0.327165
$714$	15.7066	+	2.93164i	0.587803	+	0.109714i
$715$	−0.938100			−0.0350829
$716$	−19.0144	+	32.9339i	−0.710602	+	1.23080i
$717$	−3.68147	−	6.37650i	−0.137487	−	0.238135i
$718$	−13.6648	−	23.6682i	−0.509967	−	0.883289i
$719$	−5.18678	+	8.98377i	−0.193434	+	0.335038i	−0.946386	−	0.323038i	$-0.895296\pi$
$719$	−5.18678	+	8.98377i	−0.193434	+	0.335038i	0.752952	+	0.658076i	$0.228629\pi$
$720$	−50.8358			−1.89454
$721$	−0.478015	−	1.35533i	−0.0178022	−	0.0504752i
$722$	17.1400			0.637884
$723$	−3.39573	+	5.88157i	−0.126288	+	0.218738i
$724$	30.9222	+	53.5587i	1.14921	+	1.99049i
$725$	−0.0953678	−	0.165182i	−0.00354187	−	0.00613470i
$726$	−13.4197	+	23.2437i	−0.498054	+	0.862654i
$727$	−34.5870			−1.28276			−0.641380	−	0.767224i	$-0.721638\pi$
$727$	−34.5870			−1.28276			−0.641380	+	0.767224i	$0.721638\pi$
$728$	−0.844051	+	0.985723i	−0.0312826	+	0.0365333i
$729$	−15.8706			−0.587798
$730$	44.2478	−	76.6395i	1.63769	−	2.83655i
$731$	−17.1301	−	29.6703i	−0.633581	−	1.09739i
$732$	2.80693	+	4.86175i	0.103747	+	0.179695i
$733$	−13.6580	+	23.6564i	−0.504470	+	0.873768i	0.495516	+	0.868599i	$0.334979\pi$
$733$	−13.6580	+	23.6564i	−0.504470	+	0.873768i	−0.999987	+	0.00516970i	$0.998354\pi$
$734$	−3.83140			−0.141419
$735$	−1.13131	−	7.26194i	−0.0417289	−	0.267861i
$736$	14.2518			0.525330
$737$	2.91792	−	5.05398i	0.107483	−	0.186166i
$738$	3.57915	+	6.19927i	0.131750	+	0.228198i
$739$	16.4927	+	28.5662i	0.606695	+	1.05083i	0.991781	+	0.127946i	$0.0408383\pi$
$739$	16.4927	+	28.5662i	0.606695	+	1.05083i	−0.385086	+	0.922881i	$0.625828\pi$
$740$	25.9076	−	44.8733i	0.952382	−	1.64957i
$741$	0.172052			0.00632048
$742$	54.3601	−	63.4843i	1.99562	−	2.33058i
$743$	33.5846			1.23210			0.616049	−	0.787708i	$-0.288732\pi$
$743$	33.5846			1.23210			0.616049	+	0.787708i	$0.288732\pi$
$744$	−7.24372	+	12.5465i	−0.265567	+	0.459976i
$745$	−9.14136	−	15.8333i	−0.334913	−	0.580087i
$746$	4.25253	+	7.36559i	0.155696	+	0.269673i
$747$	6.73251	−	11.6610i	0.246330	−	0.426655i
$748$	−133.695			−4.88837
$749$	−0.349172	−	0.990020i	−0.0127585	−	0.0361745i
$750$	−13.4392			−0.490731
$751$	−3.11327	+	5.39234i	−0.113605	+	0.196769i	−0.917221	−	0.398378i	$-0.869573\pi$
$751$	−3.11327	+	5.39234i	−0.113605	+	0.196769i	0.803616	+	0.595148i	$0.202906\pi$
$752$	39.3519	+	68.1595i	1.43502	+	2.48552i
$753$	−4.12330	−	7.14176i	−0.150261	−	0.260260i
$754$	0.644371	−	1.11608i	0.0234666	−	0.0406454i
$755$	−18.3742			−0.668707
$756$	32.5724	+	6.07967i	1.18465	+	0.221115i
$757$	−5.40058			−0.196288			−0.0981438	−	0.995172i	$-0.531291\pi$
$757$	−5.40058			−0.196288			−0.0981438	+	0.995172i	$0.531291\pi$
$758$	−23.5522	+	40.7936i	−0.855454	+	1.48169i
$759$	−2.57820	−	4.46557i	−0.0935826	−	0.162090i
$760$	38.4000	+	66.5107i	1.39291	+	2.41260i
$761$	7.81531	−	13.5365i	0.283305	−	0.490698i	−0.688892	−	0.724864i	$-0.741903\pi$
$761$	7.81531	−	13.5365i	0.283305	−	0.490698i	0.972197	+	0.234166i	$0.0752359\pi$
$762$	−14.1197			−0.511504
$763$	16.4662	+	3.07344i	0.596118	+	0.111266i
$764$	−10.8633			−0.393021
$765$	−15.6189	+	27.0528i	−0.564704	+	0.978096i
$766$	−47.9621	−	83.0728i	−1.73294	−	3.00154i
$767$	−0.0806374	−	0.139668i	−0.00291165	−	0.00504312i
$768$	5.84631	−	10.1261i	0.210960	−	0.365394i
$769$	−3.23902			−0.116802			−0.0584009	−	0.998293i	$-0.518600\pi$
$769$	−3.23902			−0.116802			−0.0584009	+	0.998293i	$0.518600\pi$
$770$	29.2967	+	83.0660i	1.05578	+	2.99349i
$771$	14.0119			0.504625
$772$	10.8972	−	18.8745i	0.392199	−	0.679309i
$773$	−4.21109	−	7.29383i	−0.151462	−	0.262341i	0.780303	−	0.625402i	$-0.215065\pi$
$773$	−4.21109	−	7.29383i	−0.151462	−	0.262341i	−0.931765	+	0.363061i	$0.881732\pi$
$774$	−24.4755	−	42.3928i	−0.879754	−	1.52378i
$775$	−0.0632263	+	0.109511i	−0.00227115	+	0.00393376i
$776$	122.634			4.40230
$777$	−4.02455	+	4.70007i	−0.144380	+	0.168614i
$778$	−9.58527			−0.343649
$779$	2.53270	−	4.38676i	0.0907434	−	0.157172i
$780$	0.176186	+	0.305163i	0.00630847	+	0.0109266i
$781$	11.4172	+	19.7752i	0.408541	+	0.707613i
$782$	12.3119	−	21.3248i	0.440272	−	0.762573i
$783$	−18.6816			−0.667625
$784$	53.2295	+	20.5879i	1.90105	+	0.735283i
$785$	−17.1496			−0.612094
$786$	−13.3881	+	23.1888i	−0.477536	+	0.827117i
$787$	9.57934	+	16.5919i	0.341467	+	0.591437i	0.984705	−	0.174228i	$-0.0557430\pi$
$787$	9.57934	+	16.5919i	0.341467	+	0.591437i	−0.643239	+	0.765666i	$0.722410\pi$
$788$	16.0155	+	27.7396i	0.570528	+	0.988183i
$789$	7.02446	−	12.1667i	0.250078	−	0.433147i
$790$	−31.6504			−1.12607
$791$	−7.56900	+	8.83943i	−0.269123	+	0.314294i
$792$	−108.449			−3.85358
$793$	−0.0939818	+	0.162781i	−0.00333739	+	0.00578053i
$794$	13.0965	+	22.6839i	0.464779	+	0.805021i
$795$	−6.44206	−	11.1580i	−0.228476	−	0.395733i
$796$	54.8472	−	94.9982i	1.94401	−	3.36712i
$797$	49.1450			1.74080			0.870402	−	0.492342i	$-0.163859\pi$
$797$	49.1450			1.74080			0.870402	+	0.492342i	$0.163859\pi$
$798$	−5.37315	−	15.2347i	−0.190207	−	0.539301i
$799$	48.3624			1.71094
$800$	−0.103147	+	0.178656i	−0.00364680	+	0.00631645i
$801$	17.4909	+	30.2951i	0.618009	+	1.07042i
$802$	45.1220	+	78.1536i	1.59331	+	2.75970i
$803$	44.2142	−	76.5812i	1.56028	−	2.70249i
$804$	−2.19208			−0.0773086
$805$	−11.1342	−	2.07821i	−0.392430	−	0.0732473i
$806$	−0.854401			−0.0300950
$807$	−1.09432	+	1.89541i	−0.0385218	+	0.0667217i
$808$	−34.4056	−	59.5923i	−1.21039	−	2.09645i
$809$	−21.9530	−	38.0237i	−0.771826	−	1.33684i	−0.936561	−	0.350503i	$-0.886011\pi$
$809$	−21.9530	−	38.0237i	−0.771826	−	1.33684i	0.164736	−	0.986338i	$-0.447323\pi$
$810$	−20.4179	+	35.3649i	−0.717413	+	1.24260i
$811$	21.3942			0.751252			0.375626	−	0.926771i	$-0.377428\pi$
$811$	21.3942			0.751252			0.375626	+	0.926771i	$0.377428\pi$
$812$	−83.0496	−	15.5013i	−2.91447	−	0.543988i
$813$	−4.07696			−0.142985
$814$	37.0785	−	64.2218i	1.29960	−	2.25097i
$815$	0.921088	+	1.59537i	0.0322643	+	0.0558834i
$816$	9.56348	+	16.5644i	0.334789	+	0.579871i
$817$	−17.3195	+	29.9983i	−0.605933	+	1.04951i
$818$	−42.6677			−1.49184
$819$	0.177506	+	0.503288i	0.00620255	+	0.0175863i
$820$	10.3742			0.362284
$821$	25.7975	−	44.6826i	0.900340	−	1.55943i	0.0732872	−	0.997311i	$-0.476651\pi$
$821$	25.7975	−	44.6826i	0.900340	−	1.55943i	0.827053	−	0.562124i	$-0.190016\pi$
$822$	3.58728	+	6.21335i	0.125121	+	0.216715i
$823$	−16.2342	−	28.1185i	−0.565889	−	0.980148i	−0.996966	−	0.0778332i	$-0.975200\pi$
$823$	−16.2342	−	28.1185i	−0.565889	−	0.980148i	0.431078	−	0.902315i	$-0.358134\pi$
$824$	1.83650	−	3.18091i	0.0639775	−	0.110812i
$825$	0.0746383			0.00259857
$826$	−9.84889	+	11.5020i	−0.342687	+	0.400206i
$827$	19.7906			0.688187			0.344094	−	0.938935i	$-0.388186\pi$
$827$	19.7906			0.688187			0.344094	+	0.938935i	$0.388186\pi$
$828$	12.2820	−	21.2731i	0.426830	−	0.739291i
$829$	−1.59334	−	2.75974i	−0.0553389	−	0.0958498i	0.837029	−	0.547159i	$-0.184291\pi$
$829$	−1.59334	−	2.75974i	−0.0553389	−	0.0958498i	−0.892368	+	0.451309i	$0.850957\pi$
$830$	−13.9749	−	24.2052i	−0.485075	−	0.840175i
$831$	−1.52926	+	2.64875i	−0.0530494	+	0.0918843i
$832$	−0.211035			−0.00731633
$833$	27.3105	−	22.0012i	0.946252	−	0.762295i
$834$	10.7260			0.371411
$835$	−8.77744	+	15.2030i	−0.303756	+	0.526120i
$836$	67.5864	+	117.063i	2.33752	+	4.04871i
$837$	6.19269	+	10.7261i	0.214051	+	0.370747i
$838$	−11.3448	+	19.6498i	−0.391900	+	0.678791i
$839$	−0.366627			−0.0126574			−0.00632868	−	0.999980i	$-0.502014\pi$
$839$	−0.366627			−0.0126574			−0.00632868	+	0.999980i	$0.502014\pi$
$840$	12.2170	−	14.2676i	0.421526	−	0.492278i
$841$	18.6322			0.642490
$842$	−41.1113	+	71.2068i	−1.41679	+	2.45395i
$843$	−5.37048	−	9.30194i	−0.184969	−	0.320376i
$844$	−16.6785	−	28.8880i	−0.574098	−	0.994367i
$845$	14.5687	−	25.2337i	0.501177	−	0.868064i
$846$	69.1000			2.37571
$847$	19.5944	+	55.5566i	0.673270	+	1.90895i
$848$	100.051			3.43576
$849$	4.19358	−	7.26350i	0.143923	−	0.249283i
$850$	0.178213	+	0.308674i	0.00611267	+	0.0105874i
$851$	4.76800	+	8.25841i	0.163445	+	0.283095i
$852$	4.28858	−	7.42803i	0.146924	−	0.254480i
$853$	26.5967			0.910654			0.455327	−	0.890324i	$-0.349522\pi$
$853$	26.5967			0.910654			0.455327	+	0.890324i	$0.349522\pi$
$854$	17.3488	+	3.23818i	0.593665	+	0.110808i
$855$	31.5832			1.08012
$856$	1.34150	−	2.32354i	0.0458514	−	0.0794169i
$857$	−12.9762	−	22.4754i	−0.443257	−	0.767744i	0.554672	−	0.832069i	$-0.312844\pi$
$857$	−12.9762	−	22.4754i	−0.443257	−	0.767744i	−0.997929	+	0.0643255i	$0.979510\pi$
$858$	0.252154	+	0.436744i	0.00860841	+	0.0149102i
$859$	−28.5466	+	49.4442i	−0.973998	+	1.68701i	−0.290796	+	0.956785i	$0.593920\pi$
$859$	−28.5466	+	49.4442i	−0.973998	+	1.68701i	−0.683202	+	0.730230i	$0.739413\pi$
$860$	−70.9428			−2.41913
$861$	−1.21785	−	0.227312i	−0.0415041	−	0.00774677i
$862$	78.4532			2.67213
$863$	15.4515	−	26.7627i	0.525974	−	0.911014i	−0.473568	−	0.880757i	$-0.657034\pi$
$863$	15.4515	−	26.7627i	0.525974	−	0.911014i	0.999542	−	0.0302564i	$-0.00963239\pi$
$864$	10.1027	+	17.4984i	0.343702	+	0.595309i
$865$	14.9813	+	25.9484i	0.509380	+	0.882273i
$866$	−34.1252	+	59.1066i	−1.15962	+	2.00852i
$867$	3.79297			0.128816
$868$	18.6297	+	52.8215i	0.632335	+	1.79288i
$869$	−31.6263			−1.07285
$870$	−9.32677	+	16.1544i	−0.316207	+	0.547687i
$871$	−0.0366976	−	0.0635621i	−0.00124345	−	0.00215372i
$872$	21.4051	+	37.0747i	0.724868	+	1.25551i
$873$	25.2160	−	43.6753i	0.853431	−	1.47819i
$874$	−24.8959			−0.842118
$875$	−19.1859	+	22.4062i	−0.648602	+	0.757468i
$876$	−33.2158			−1.12226
$877$	4.98205	−	8.62916i	0.168232	−	0.291386i	−0.769566	−	0.638567i	$-0.779528\pi$
$877$	4.98205	−	8.62916i	0.168232	−	0.291386i	0.937798	+	0.347181i	$0.112861\pi$
$878$	21.4849	+	37.2129i	0.725080	+	1.25588i
$879$	−0.181616	−	0.314569i	−0.00612576	−	0.0106101i
$880$	−52.7206	+	91.3148i	−1.77721	+	3.07822i
$881$	−2.35418			−0.0793143			−0.0396572	−	0.999213i	$-0.512627\pi$
$881$	−2.35418			−0.0793143			−0.0396572	+	0.999213i	$0.512627\pi$
$882$	39.0212	−	31.4352i	1.31391	−	1.05848i
$883$	27.5946			0.928631			0.464315	−	0.885670i	$-0.346300\pi$
$883$	27.5946			0.928631			0.464315	+	0.885670i	$0.346300\pi$
$884$	−0.840716	+	1.45616i	−0.0282763	+	0.0489761i
$885$	1.16716	+	2.02159i	0.0392338	+	0.0679549i
$886$	−3.96303	−	6.86416i	−0.133140	−	0.230606i
$887$	9.89136	−	17.1323i	0.332119	−	0.575248i	−0.650808	−	0.759242i	$-0.725570\pi$
$887$	9.89136	−	17.1323i	0.332119	−	0.575248i	0.982927	+	0.183995i	$0.0589030\pi$
$888$	−15.8141			−0.530688
$889$	−20.1574	+	23.5408i	−0.676057	+	0.789532i
$890$	72.6127			2.43398
$891$	−20.4024	+	35.3380i	−0.683507	+	1.18387i
$892$	−2.87521	−	4.98000i	−0.0962690	−	0.166743i
$893$	−24.4485	−	42.3460i	−0.818137	−	1.41705i
$894$	−4.91426	+	8.51175i	−0.164357	+	0.284675i
$895$	18.4298			0.616040
$896$	−6.54718	−	18.5634i	−0.218726	−	0.620161i
$897$	−0.0648501			−0.00216528
$898$	28.8928	−	50.0437i	0.964164	−	1.66998i
$899$	−15.7894	−	27.3481i	−0.526607	−	0.912111i
$900$	0.177781	+	0.307926i	0.00592604	+	0.0102642i
$901$	30.7399	−	53.2431i	1.02409	−	1.77378i
$902$	14.8474			0.494365
$903$	8.32806	+	1.55444i	0.277141	+	0.0517285i
$904$	−29.7417			−0.989196
$905$	14.9857	−	25.9560i	0.498142	−	0.862807i
$906$	4.93886	+	8.55436i	0.164083	+	0.284199i
$907$	1.26200	+	2.18585i	0.0419041	+	0.0725800i	0.886217	−	0.463271i	$-0.153324\pi$
$907$	1.26200	+	2.18585i	0.0419041	+	0.0725800i	−0.844313	+	0.535851i	$0.819991\pi$
$908$	−35.8688	+	62.1266i	−1.19035	+	2.06174i
$909$	−28.2979			−0.938583
$910$	1.08896	+	0.203255i	0.0360985	+	0.00673782i
$911$	−44.3294			−1.46870			−0.734350	−	0.678771i	$-0.762513\pi$
$911$	−44.3294			−1.46870			−0.734350	+	0.678771i	$0.762513\pi$
$912$	9.66920	−	16.7475i	0.320179	−	0.554566i
$913$	−13.9643	−	24.1868i	−0.462149	−	0.800466i
$914$	49.7297	+	86.1343i	1.64491	+	2.84907i
$915$	1.36031	−	2.35613i	0.0449706	−	0.0778914i
$916$	−15.0150			−0.496110
$917$	19.5481	+	55.4254i	0.645535	+	1.83031i
$918$	34.9102			1.15221
$919$	−24.5944	+	42.5987i	−0.811294	+	1.40520i	0.100665	+	0.994920i	$0.467903\pi$
$919$	−24.5944	+	42.5987i	−0.811294	+	1.40520i	−0.911959	+	0.410282i	$0.865430\pi$
$920$	−14.4738	−	25.0694i	−0.477187	−	0.826512i
$921$	0.580781	+	1.00594i	0.0191374	+	0.0331469i
$922$	15.7566	−	27.2913i	0.518917	−	0.898790i
$923$	0.287181			0.00945267
$924$	21.5027	−	25.1119i	0.707386	−	0.826119i
$925$	−0.138033			−0.00453849
$926$	−42.4432	+	73.5139i	−1.39477	+	2.41582i
$927$	−0.755241	−	1.30812i	−0.0248054	−	0.0429642i
$928$	−25.7588	−	44.6156i	−0.845575	−	1.46458i
$929$	−3.78923	+	6.56313i	−0.124321	+	0.215329i	−0.921467	−	0.388456i	$-0.873008\pi$
$929$	−3.78923	+	6.56313i	−0.124321	+	0.215329i	0.797147	+	0.603786i	$0.206342\pi$
$930$	12.3668			0.405524
$931$	−33.0704	−	12.7908i	−1.08384	−	0.419203i
$932$	−0.687830			−0.0225306
$933$	−0.349759	+	0.605800i	−0.0114506	+	0.0198330i
$934$	−7.74737	−	13.4188i	−0.253502	−	0.439078i
$935$	32.3961	+	56.1116i	1.05946	+	1.83505i
$936$	−0.681964	+	1.18120i	−0.0222907	+	0.0386086i
$937$	−15.1160			−0.493817			−0.246909	−	0.969039i	$-0.579415\pi$
$937$	−15.1160			−0.493817			−0.246909	+	0.969039i	$0.579415\pi$
$938$	−4.48217	+	5.23450i	−0.146348	+	0.170912i
$939$	−6.92735			−0.226065
$940$	50.0719	−	86.7272i	1.63317	−	2.82873i
$941$	−14.4030	−	24.9468i	−0.469525	−	0.813241i	0.529868	−	0.848080i	$-0.322242\pi$
$941$	−14.4030	−	24.9468i	−0.469525	−	0.813241i	−0.999393	+	0.0348389i	$0.988908\pi$
$942$	4.60968	+	7.98419i	0.150191	+	0.260139i
$943$	−0.954630	+	1.65347i	−0.0310870	+	0.0538443i
$944$	−18.1271			−0.589986
$945$	−5.34110	−	15.1438i	−0.173746	−	0.492628i
$946$	−101.532			−3.30109
$947$	−20.3172	+	35.1905i	−0.660221	+	1.14354i	0.320337	+	0.947304i	$0.396204\pi$
$947$	−20.3172	+	35.1905i	−0.660221	+	1.14354i	−0.980557	+	0.196232i	$0.937129\pi$
$948$	5.93979	+	10.2880i	0.192915	+	0.334139i
$949$	−0.556066	−	0.963134i	−0.0180507	−	0.0312647i
$950$	0.180183	−	0.312087i	0.00584592	−	0.0101254i
$951$	7.13579			0.231394
$952$	88.1084	+	16.4455i	2.85561	+	0.533002i
$953$	37.5104			1.21508			0.607541	−	0.794289i	$-0.292156\pi$
$953$	37.5104			1.21508			0.607541	+	0.794289i	$0.292156\pi$
$954$	43.9211	−	76.0736i	1.42200	−	2.46297i
$955$	2.63233	+	4.55932i	0.0851801	+	0.147536i
$956$	−36.3761	−	63.0053i	−1.17649	−	2.03774i
$957$	−9.31968	+	16.1422i	−0.301263	+	0.521802i
$958$	52.9872			1.71194
$959$	15.4803	+	2.88941i	0.499884	+	0.0933038i
$960$	3.05457			0.0985859
$961$	5.03202	−	8.71572i	0.162323	−	0.281152i
$962$	−0.466323	−	0.807694i	−0.0150348	−	0.0260411i
$963$	−0.551676	−	0.955531i	−0.0177775	−	0.0307916i
$964$	−33.5527	+	58.1150i	−1.08066	+	1.87176i
$965$	−10.5622			−0.340008
$966$	2.02526	+	5.74228i	0.0651616	+	0.184755i
$967$	−35.6540			−1.14655			−0.573277	−	0.819361i	$-0.694328\pi$
$967$	−35.6540			−1.14655			−0.573277	+	0.819361i	$0.694328\pi$
$968$	−75.2802	+	130.389i	−2.41960	+	4.19086i
$969$	−5.94158	−	10.2911i	−0.190871	−	0.330599i
$970$	−52.3416	−	90.6583i	−1.68059	−	2.91086i
$971$	−8.77259	+	15.1946i	−0.281526	+	0.487617i	−0.971761	−	0.235968i	$-0.924174\pi$
$971$	−8.77259	+	15.1946i	−0.281526	+	0.487617i	0.690235	+	0.723585i	$0.257507\pi$
$972$	52.8987			1.69673
$973$	15.3125	−	17.8827i	0.490896	−	0.573292i
$974$	−8.91651			−0.285703
$975$	0.000469350	0	0.000812938i	1.50312e−5	0	2.60348e-5i
$976$	10.5634	+	18.2964i	0.338127	+	0.585654i
$977$	24.9926	+	43.2884i	0.799583	+	1.38492i	0.919888	+	0.392182i	$0.128280\pi$
$977$	24.9926	+	43.2884i	0.799583	+	1.38492i	−0.120305	+	0.992737i	$0.538387\pi$
$978$	0.495163	−	0.857648i	0.0158336	−	0.0274246i
$979$	72.5575			2.31895
$980$	−11.1783	−	71.7542i	−0.357077	−	2.29210i
$981$	17.6052			0.562092
$982$	11.5011	−	19.9205i	0.367015	−	0.635689i
$983$	26.7804	+	46.3850i	0.854163	+	1.47945i	0.877420	+	0.479723i	$0.159263\pi$
$983$	26.7804	+	46.3850i	0.854163	+	1.47945i	−0.0232572	+	0.999730i	$0.507404\pi$
$984$	−1.58312	−	2.74205i	−0.0504682	−	0.0874134i
$985$	7.76153	−	13.4434i	0.247303	−	0.428341i
$986$	−89.0101			−2.83466
$987$	−7.77831	+	9.08388i	−0.247586	+	0.289143i
$988$	1.70002			0.0540848
$989$	6.52810	−	11.3070i	0.207582	−	0.359542i
$990$	46.2875	+	80.1722i	1.47111	+	2.54804i
$991$	−4.96572	−	8.60088i	−0.157741	−	0.273216i	0.776312	−	0.630348i	$-0.217088\pi$
$991$	−4.96572	−	8.60088i	−0.157741	−	0.273216i	−0.934054	+	0.357132i	$0.883755\pi$
$992$	−17.0774	+	29.5790i	−0.542209	+	0.939133i
$993$	9.96661			0.316281
$994$	−8.96861	−	25.4290i	−0.284467	−	0.806559i
$995$	−53.1609			−1.68531
$996$	−5.24530	+	9.08512i	−0.166204	+	0.287873i
$997$	8.63827	+	14.9619i	0.273577	+	0.473849i	0.969775	−	0.244001i	$-0.0784599\pi$
$997$	8.63827	+	14.9619i	0.273577	+	0.473849i	−0.696198	+	0.717849i	$0.745127\pi$
$998$	−8.48140	−	14.6902i	−0.268474	−	0.465011i
$999$	−6.75980	+	11.7083i	−0.213871	+	0.370435i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.e.d.247.2	yes	34
7.2	even	3		2009.2.a.s.1.16		17
7.4	even	3	inner	287.2.e.d.165.2	✓	34
7.5	odd	6		2009.2.a.r.1.16		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.2	✓	34	7.4	even	3	inner
287.2.e.d.247.2	yes	34	1.1	even	1	trivial
2009.2.a.r.1.16		17	7.5	odd	6
2009.2.a.s.1.16		17	7.2	even	3

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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28712 + 2.22936i) q^{2} +(-0.234126 - 0.405518i) q^{3} +(-2.31337 - 4.00687i) q^{4} +(-1.12112 + 1.94184i) q^{5} +1.20539 q^{6} +(1.72083 - 2.00966i) q^{7} +6.76185 q^{8} +(1.39037 - 2.40819i) q^{9} +O(q^{10})\)	\(q+(-1.28712 + 2.22936i) q^{2} +(-0.234126 - 0.405518i) q^{3} +(-2.31337 - 4.00687i) q^{4} +(-1.12112 + 1.94184i) q^{5} +1.20539 q^{6} +(1.72083 - 2.00966i) q^{7} +6.76185 q^{8} +(1.39037 - 2.40819i) q^{9} +(-2.88604 - 4.99876i) q^{10} +(-2.88384 - 4.99496i) q^{11} +(-1.08324 + 1.87622i) q^{12} -0.0725380 q^{13} +(2.26535 + 6.42303i) q^{14} +1.04993 q^{15} +(-4.07659 + 7.06087i) q^{16} +(2.50501 + 4.33880i) q^{17} +(3.57915 + 6.19927i) q^{18} +(2.53270 - 4.38676i) q^{19} +10.3742 q^{20} +(-1.21785 - 0.227312i) q^{21} +14.8474 q^{22} +(-0.954630 + 1.65347i) q^{23} +(-1.58312 - 2.74205i) q^{24} +(-0.0138182 - 0.0239338i) q^{25} +(0.0933653 - 0.161713i) q^{26} -2.70684 q^{27} +(-12.0334 - 2.24604i) q^{28} +6.90161 q^{29} +(-1.35139 + 2.34068i) q^{30} +(-2.28779 - 3.96257i) q^{31} +(-3.73229 - 6.46452i) q^{32} +(-1.35036 + 2.33890i) q^{33} -12.8970 q^{34} +(1.97319 + 5.59464i) q^{35} -12.8657 q^{36} +(2.49730 - 4.32545i) q^{37} +(6.51979 + 11.2926i) q^{38} +(0.0169830 + 0.0294155i) q^{39} +(-7.58084 + 13.1304i) q^{40} +1.00000 q^{41} +(2.07428 - 2.42244i) q^{42} -6.83836 q^{43} +(-13.3428 + 23.1103i) q^{44} +(3.11754 + 5.39974i) q^{45} +(-2.45745 - 4.25643i) q^{46} +(4.82657 - 8.35986i) q^{47} +3.81774 q^{48} +(-1.07750 - 6.91657i) q^{49} +0.0711428 q^{50} +(1.17297 - 2.03165i) q^{51} +(0.167807 + 0.290650i) q^{52} +(-6.13569 - 10.6273i) q^{53} +(3.48404 - 6.03453i) q^{54} +12.9325 q^{55} +(11.6360 - 13.5890i) q^{56} -2.37188 q^{57} +(-8.88321 + 15.3862i) q^{58} +(1.11166 + 1.92544i) q^{59} +(-2.42888 - 4.20694i) q^{60} +(1.29562 - 2.24408i) q^{61} +11.7787 q^{62} +(-2.44707 - 6.93826i) q^{63} +2.90930 q^{64} +(0.0813238 - 0.140857i) q^{65} +(-3.47617 - 6.02090i) q^{66} +(0.505908 + 0.876259i) q^{67} +(11.5900 - 20.0745i) q^{68} +0.894015 q^{69} +(-15.0122 - 2.80204i) q^{70} -3.95904 q^{71} +(9.40147 - 16.2838i) q^{72} +(7.66585 + 13.2776i) q^{73} +(6.42866 + 11.1348i) q^{74} +(-0.00647039 + 0.0112071i) q^{75} -23.4362 q^{76} +(-15.0008 - 2.79991i) q^{77} -0.0874370 q^{78} +(2.74168 - 4.74873i) q^{79} +(-9.14070 - 15.8321i) q^{80} +(-3.53737 - 6.12690i) q^{81} +(-1.28712 + 2.22936i) q^{82} +4.84224 q^{83} +(1.90651 + 5.40560i) q^{84} -11.2337 q^{85} +(8.80180 - 15.2452i) q^{86} +(-1.61585 - 2.79873i) q^{87} +(-19.5001 - 33.7752i) q^{88} +(-6.29000 + 10.8946i) q^{89} -16.0506 q^{90} +(-0.124825 + 0.145777i) q^{91} +8.83364 q^{92} +(-1.07126 + 1.85548i) q^{93} +(12.4248 + 21.5203i) q^{94} +(5.67892 + 9.83617i) q^{95} +(-1.74765 + 3.02703i) q^{96} +18.1362 q^{97} +(16.8064 + 6.50033i) q^{98} -16.0384 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9}+O(q^{10}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9} + 2 q^{10} - 15 q^{11} - 4 q^{12} - 10 q^{13} + 21 q^{14} + 48 q^{15} - 33 q^{16} - 4 q^{17} - 10 q^{18} - 5 q^{19} - 52 q^{20} + 12 q^{21} + 32 q^{22} - 12 q^{23} - 16 q^{24} - 24 q^{25} - 31 q^{26} - 22 q^{27} + 60 q^{28} + 28 q^{29} + 33 q^{30} + 3 q^{31} - 16 q^{32} - 4 q^{33} - 48 q^{34} + 45 q^{35} + 114 q^{36} - 24 q^{37} - 45 q^{39} - 36 q^{40} + 34 q^{41} + 65 q^{42} + 28 q^{43} + 9 q^{44} + 21 q^{45} - 44 q^{46} - 19 q^{47} - 120 q^{48} - 10 q^{49} - 8 q^{50} - 2 q^{51} + 25 q^{52} - 4 q^{53} - 68 q^{54} + 18 q^{55} + 25 q^{56} - 24 q^{57} + q^{58} + 27 q^{59} - 66 q^{60} + q^{61} - 46 q^{62} + 37 q^{63} + 150 q^{64} - 22 q^{65} + 16 q^{66} - 49 q^{67} - 45 q^{68} + 24 q^{69} + 73 q^{70} + 80 q^{71} + 23 q^{72} + 14 q^{73} - 33 q^{74} - 27 q^{75} - 18 q^{76} - 20 q^{77} - 24 q^{78} - 61 q^{79} + 82 q^{80} - 53 q^{81} - 3 q^{82} - 36 q^{83} + 188 q^{84} - 26 q^{85} + 4 q^{86} + 17 q^{87} - 74 q^{88} - 18 q^{89} - 40 q^{90} + 7 q^{91} + 56 q^{92} + 36 q^{93} + 5 q^{94} - 20 q^{95} - 148 q^{96} + 52 q^{97} + 142 q^{98} + 76 q^{99}+O(q^{100}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9 + 2 * q^10 - 15 * q^11 - 4 * q^12 - 10 * q^13 + 21 * q^14 + 48 * q^15 - 33 * q^16 - 4 * q^17 - 10 * q^18 - 5 * q^19 - 52 * q^20 + 12 * q^21 + 32 * q^22 - 12 * q^23 - 16 * q^24 - 24 * q^25 - 31 * q^26 - 22 * q^27 + 60 * q^28 + 28 * q^29 + 33 * q^30 + 3 * q^31 - 16 * q^32 - 4 * q^33 - 48 * q^34 + 45 * q^35 + 114 * q^36 - 24 * q^37 - 45 * q^39 - 36 * q^40 + 34 * q^41 + 65 * q^42 + 28 * q^43 + 9 * q^44 + 21 * q^45 - 44 * q^46 - 19 * q^47 - 120 * q^48 - 10 * q^49 - 8 * q^50 - 2 * q^51 + 25 * q^52 - 4 * q^53 - 68 * q^54 + 18 * q^55 + 25 * q^56 - 24 * q^57 + q^58 + 27 * q^59 - 66 * q^60 + q^61 - 46 * q^62 + 37 * q^63 + 150 * q^64 - 22 * q^65 + 16 * q^66 - 49 * q^67 - 45 * q^68 + 24 * q^69 + 73 * q^70 + 80 * q^71 + 23 * q^72 + 14 * q^73 - 33 * q^74 - 27 * q^75 - 18 * q^76 - 20 * q^77 - 24 * q^78 - 61 * q^79 + 82 * q^80 - 53 * q^81 - 3 * q^82 - 36 * q^83 + 188 * q^84 - 26 * q^85 + 4 * q^86 + 17 * q^87 - 74 * q^88 - 18 * q^89 - 40 * q^90 + 7 * q^91 + 56 * q^92 + 36 * q^93 + 5 * q^94 - 20 * q^95 - 148 * q^96 + 52 * q^97 + 142 * q^98 + 76 * q^99

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