LMFDB - Embedded newform 201.2.e.c.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,2,Mod(37,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("201.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	201.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:	$1.60499308063$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.3665654523963.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 8x^{8} + 21x^{6} - 5x^{5} + 26x^{4} + 4x^{3} + 13x^{2} - 3x + 1 $ x^10 - 2x^9 + 8x^8 + 21x^6 - 5x^5 + 26x^4 + 4x^3 + 13x^2 - 3x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.2
Root			$-0.725148 - 1.25599i$ of defining polynomial
Character	$\chi$	$=$	201.163
Dual form			201.2.e.c.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453162 + 0.784899i) q^{2} +1.00000 q^{3} +(0.589289 + 1.02068i) q^{4} +3.35662 q^{5} +(-0.453162 + 0.784899i) q^{6} +(-0.380391 - 0.658856i) q^{7} -2.88082 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.453162 + 0.784899i) q^{2} +1.00000 q^{3} +(0.589289 + 1.02068i) q^{4} +3.35662 q^{5} +(-0.453162 + 0.784899i) q^{6} +(-0.380391 - 0.658856i) q^{7} -2.88082 q^{8} +1.00000 q^{9} +(-1.52109 + 2.63461i) q^{10} +(-2.61236 - 4.52473i) q^{11} +(0.589289 + 1.02068i) q^{12} +(-0.140700 + 0.243700i) q^{13} +0.689514 q^{14} +3.35662 q^{15} +(0.126899 - 0.219795i) q^{16} +(1.03230 - 1.78799i) q^{17} +(-0.453162 + 0.784899i) q^{18} +(-3.87950 + 6.71949i) q^{19} +(1.97802 + 3.42603i) q^{20} +(-0.380391 - 0.658856i) q^{21} +4.73528 q^{22} +(-2.16711 + 3.75354i) q^{23} -2.88082 q^{24} +6.26689 q^{25} +(-0.127520 - 0.220871i) q^{26} +1.00000 q^{27} +(0.448320 - 0.776514i) q^{28} +(-5.25353 - 9.09938i) q^{29} +(-1.52109 + 2.63461i) q^{30} +(2.39555 + 4.14921i) q^{31} +(-2.76581 - 4.79052i) q^{32} +(-2.61236 - 4.52473i) q^{33} +(0.935594 + 1.62050i) q^{34} +(-1.27683 - 2.21153i) q^{35} +(0.589289 + 1.02068i) q^{36} +(2.00879 - 3.47933i) q^{37} +(-3.51608 - 6.09003i) q^{38} +(-0.140700 + 0.243700i) q^{39} -9.66981 q^{40} +(5.04129 + 8.73177i) q^{41} +0.689514 q^{42} -5.47666 q^{43} +(3.07887 - 5.33275i) q^{44} +3.35662 q^{45} +(-1.96410 - 3.40192i) q^{46} +(-3.83021 - 6.63413i) q^{47} +(0.126899 - 0.219795i) q^{48} +(3.21061 - 5.56093i) q^{49} +(-2.83992 + 4.91888i) q^{50} +(1.03230 - 1.78799i) q^{51} -0.331652 q^{52} -0.763418 q^{53} +(-0.453162 + 0.784899i) q^{54} +(-8.76868 - 15.1878i) q^{55} +(1.09584 + 1.89805i) q^{56} +(-3.87950 + 6.71949i) q^{57} +9.52279 q^{58} +8.13803 q^{59} +(1.97802 + 3.42603i) q^{60} +(-4.98018 + 8.62592i) q^{61} -4.34228 q^{62} +(-0.380391 - 0.658856i) q^{63} +5.52103 q^{64} +(-0.472277 + 0.818008i) q^{65} +4.73528 q^{66} +(0.0778994 - 8.18498i) q^{67} +2.43328 q^{68} +(-2.16711 + 3.75354i) q^{69} +2.31444 q^{70} +(1.04970 + 1.81814i) q^{71} -2.88082 q^{72} +(4.10751 - 7.11442i) q^{73} +(1.82062 + 3.15340i) q^{74} +6.26689 q^{75} -9.14459 q^{76} +(-1.98743 + 3.44234i) q^{77} +(-0.127520 - 0.220871i) q^{78} +(2.06029 + 3.56852i) q^{79} +(0.425950 - 0.737768i) q^{80} +1.00000 q^{81} -9.13808 q^{82} +(-3.21087 + 5.56140i) q^{83} +(0.448320 - 0.776514i) q^{84} +(3.46502 - 6.00160i) q^{85} +(2.48181 - 4.29862i) q^{86} +(-5.25353 - 9.09938i) q^{87} +(7.52573 + 13.0349i) q^{88} -3.76761 q^{89} +(-1.52109 + 2.63461i) q^{90} +0.214084 q^{91} -5.10821 q^{92} +(2.39555 + 4.14921i) q^{93} +6.94282 q^{94} +(-13.0220 + 22.5548i) q^{95} +(-2.76581 - 4.79052i) q^{96} +(2.28671 - 3.96071i) q^{97} +(2.90985 + 5.04000i) q^{98} +(-2.61236 - 4.52473i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} + 10 q^{9}+O(q^{10}) $ 10 * q + 10 * q^3 - 6 * q^4 + 6 * q^5 - q^7 + 10 * q^9	\( 10 q + 10 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} + 10 q^{9} - 12 q^{10} + 6 q^{11} - 6 q^{12} - q^{13} - 6 q^{14} + 6 q^{15} - 24 q^{16} + 8 q^{17} - 5 q^{19} - 8 q^{20} - q^{21} + 22 q^{22} - 7 q^{23} - 8 q^{25} - 17 q^{26} + 10 q^{27} + 3 q^{28} - 12 q^{29} - 12 q^{30} - 12 q^{31} - 5 q^{32} + 6 q^{33} - 5 q^{35} - 6 q^{36} - 17 q^{37} + 30 q^{38} - q^{39} + 34 q^{40} + 13 q^{41} - 6 q^{42} - 4 q^{43} + 43 q^{44} + 6 q^{45} - 26 q^{46} - 25 q^{47} - 24 q^{48} + 16 q^{49} - 25 q^{50} + 8 q^{51} + 64 q^{52} - 12 q^{53} - 14 q^{55} - 11 q^{56} - 5 q^{57} + 4 q^{58} - 12 q^{59} - 8 q^{60} + 9 q^{61} + 46 q^{62} - q^{63} + 64 q^{64} - 14 q^{65} + 22 q^{66} + 2 q^{67} - 98 q^{68} - 7 q^{69} + 2 q^{70} + 29 q^{71} + 12 q^{73} + 15 q^{74} - 8 q^{75} - 6 q^{76} + 4 q^{77} - 17 q^{78} - q^{79} - 13 q^{80} + 10 q^{81} - 2 q^{82} - 6 q^{83} + 3 q^{84} + 9 q^{85} - 21 q^{86} - 12 q^{87} + 18 q^{88} - 4 q^{89} - 12 q^{90} - 40 q^{91} - 12 q^{93} + 30 q^{94} - 14 q^{95} - 5 q^{96} + 11 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + 10 * q^3 - 6 * q^4 + 6 * q^5 - q^7 + 10 * q^9 - 12 * q^10 + 6 * q^11 - 6 * q^12 - q^13 - 6 * q^14 + 6 * q^15 - 24 * q^16 + 8 * q^17 - 5 * q^19 - 8 * q^20 - q^21 + 22 * q^22 - 7 * q^23 - 8 * q^25 - 17 * q^26 + 10 * q^27 + 3 * q^28 - 12 * q^29 - 12 * q^30 - 12 * q^31 - 5 * q^32 + 6 * q^33 - 5 * q^35 - 6 * q^36 - 17 * q^37 + 30 * q^38 - q^39 + 34 * q^40 + 13 * q^41 - 6 * q^42 - 4 * q^43 + 43 * q^44 + 6 * q^45 - 26 * q^46 - 25 * q^47 - 24 * q^48 + 16 * q^49 - 25 * q^50 + 8 * q^51 + 64 * q^52 - 12 * q^53 - 14 * q^55 - 11 * q^56 - 5 * q^57 + 4 * q^58 - 12 * q^59 - 8 * q^60 + 9 * q^61 + 46 * q^62 - q^63 + 64 * q^64 - 14 * q^65 + 22 * q^66 + 2 * q^67 - 98 * q^68 - 7 * q^69 + 2 * q^70 + 29 * q^71 + 12 * q^73 + 15 * q^74 - 8 * q^75 - 6 * q^76 + 4 * q^77 - 17 * q^78 - q^79 - 13 * q^80 + 10 * q^81 - 2 * q^82 - 6 * q^83 + 3 * q^84 + 9 * q^85 - 21 * q^86 - 12 * q^87 + 18 * q^88 - 4 * q^89 - 12 * q^90 - 40 * q^91 - 12 * q^93 + 30 * q^94 - 14 * q^95 - 5 * q^96 + 11 * q^97 + 12 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.453162	+	0.784899i	−0.320434	+	0.555007i	−0.980578	−	0.196132i	$-0.937162\pi$
$2$	−0.453162	+	0.784899i	−0.320434	+	0.555007i	0.660144	+	0.751139i	$0.270495\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.589289	+	1.02068i	0.294645	+	0.510339i
$5$	3.35662			1.50113			0.750563	−	0.660799i	$-0.229782\pi$
$5$	3.35662			1.50113			0.750563	+	0.660799i	$0.229782\pi$
$6$	−0.453162	+	0.784899i	−0.185002	+	0.320434i
$7$	−0.380391	−	0.658856i	−0.143774	−	0.249024i	0.785141	−	0.619317i	$-0.212591\pi$
$7$	−0.380391	−	0.658856i	−0.143774	−	0.249024i	−0.928915	+	0.370293i	$0.879257\pi$
$8$	−2.88082			−1.01852
$9$	1.00000			0.333333
$10$	−1.52109	+	2.63461i	−0.481011	+	0.833136i
$11$	−2.61236	−	4.52473i	−0.787655	−	1.36426i	−0.927400	−	0.374071i	$-0.877962\pi$
$11$	−2.61236	−	4.52473i	−0.787655	−	1.36426i	0.139745	−	0.990188i	$-0.455372\pi$
$12$	0.589289	+	1.02068i	0.170113	+	0.294645i
$13$	−0.140700	+	0.243700i	−0.0390232	+	0.0675902i	−0.884877	−	0.465824i	$-0.845758\pi$
$13$	−0.140700	+	0.243700i	−0.0390232	+	0.0675902i	0.845854	+	0.533414i	$0.179091\pi$
$14$	0.689514			0.184280
$15$	3.35662			0.866675
$16$	0.126899	−	0.219795i	0.0317247	−	0.0549487i
$17$	1.03230	−	1.78799i	0.250368	−	0.433651i	−0.713259	−	0.700901i	$-0.752782\pi$
$17$	1.03230	−	1.78799i	0.250368	−	0.433651i	0.963627	+	0.267250i	$0.0861149\pi$
$18$	−0.453162	+	0.784899i	−0.106811	+	0.185002i
$19$	−3.87950	+	6.71949i	−0.890019	+	1.54156i	−0.0501674	+	0.998741i	$0.515975\pi$
$19$	−3.87950	+	6.71949i	−0.890019	+	1.54156i	−0.839851	+	0.542817i	$0.817358\pi$
$20$	1.97802	+	3.42603i	0.442299	+	0.766084i
$21$	−0.380391	−	0.658856i	−0.0830081	−	0.143774i
$22$	4.73528			1.00956
$23$	−2.16711	+	3.75354i	−0.451873	+	0.782666i	−0.998502	−	0.0547080i	$-0.982577\pi$
$23$	−2.16711	+	3.75354i	−0.451873	+	0.782666i	0.546630	+	0.837374i	$0.315911\pi$
$24$	−2.88082			−0.588045
$25$	6.26689			1.25338
$26$	−0.127520	−	0.220871i	−0.0250087	−	0.0433163i
$27$	1.00000			0.192450
$28$	0.448320	−	0.776514i	0.0847246	−	0.146747i
$29$	−5.25353	−	9.09938i	−0.975556	−	1.68971i	−0.678089	−	0.734980i	$-0.737191\pi$
$29$	−5.25353	−	9.09938i	−0.975556	−	1.68971i	−0.297467	−	0.954732i	$-0.596142\pi$
$30$	−1.52109	+	2.63461i	−0.277712	+	0.481011i
$31$	2.39555	+	4.14921i	0.430253	+	0.745220i	0.996895	−	0.0787442i	$-0.0250910\pi$
$31$	2.39555	+	4.14921i	0.430253	+	0.745220i	−0.566642	+	0.823964i	$0.691758\pi$
$32$	−2.76581	−	4.79052i	−0.488930	−	0.846852i
$33$	−2.61236	−	4.52473i	−0.454753	−	0.787655i
$34$	0.935594	+	1.62050i	0.160453	+	0.277913i
$35$	−1.27683	−	2.21153i	−0.215823	−	0.373817i
$36$	0.589289	+	1.02068i	0.0982148	+	0.170113i
$37$	2.00879	−	3.47933i	0.330243	−	0.571998i	−0.652316	−	0.757947i	$-0.726202\pi$
$37$	2.00879	−	3.47933i	0.330243	−	0.571998i	0.982559	+	0.185949i	$0.0595358\pi$
$38$	−3.51608	−	6.09003i	−0.570384	−	0.987934i
$39$	−0.140700	+	0.243700i	−0.0225301	+	0.0390232i
$40$	−9.66981			−1.52893
$41$	5.04129	+	8.73177i	0.787318	+	1.36367i	0.927605	+	0.373563i	$0.121864\pi$
$41$	5.04129	+	8.73177i	0.787318	+	1.36367i	−0.140287	+	0.990111i	$0.544803\pi$
$42$	0.689514			0.106394
$43$	−5.47666			−0.835182			−0.417591	−	0.908635i	$-0.637126\pi$
$43$	−5.47666			−0.835182			−0.417591	+	0.908635i	$0.637126\pi$
$44$	3.07887	−	5.33275i	0.464156	−	0.803943i
$45$	3.35662			0.500375
$46$	−1.96410	−	3.40192i	−0.289590	−	0.501585i
$47$	−3.83021	−	6.63413i	−0.558694	−	0.967687i	−0.997606	−	0.0691565i	$-0.977969\pi$
$47$	−3.83021	−	6.63413i	−0.558694	−	0.967687i	0.438912	−	0.898530i	$-0.355364\pi$
$48$	0.126899	−	0.219795i	0.0183162	−	0.0317247i
$49$	3.21061	−	5.56093i	0.458658	−	0.794419i
$50$	−2.83992	+	4.91888i	−0.401625	+	0.695635i
$51$	1.03230	−	1.78799i	0.144550	−	0.250368i
$52$	−0.331652			−0.0459919
$53$	−0.763418			−0.104864			−0.0524318	−	0.998625i	$-0.516697\pi$
$53$	−0.763418			−0.104864			−0.0524318	+	0.998625i	$0.516697\pi$
$54$	−0.453162	+	0.784899i	−0.0616675	+	0.106811i
$55$	−8.76868	−	15.1878i	−1.18237	−	2.04792i
$56$	1.09584	+	1.89805i	0.146437	+	0.253637i
$57$	−3.87950	+	6.71949i	−0.513852	+	0.890019i
$58$	9.52279			1.25040
$59$	8.13803			1.05948			0.529741	−	0.848160i	$-0.322289\pi$
$59$	8.13803			1.05948			0.529741	+	0.848160i	$0.322289\pi$
$60$	1.97802	+	3.42603i	0.255361	+	0.442299i
$61$	−4.98018	+	8.62592i	−0.637647	+	1.10444i	0.348301	+	0.937383i	$0.386759\pi$
$61$	−4.98018	+	8.62592i	−0.637647	+	1.10444i	−0.985948	+	0.167054i	$0.946575\pi$
$62$	−4.34228			−0.551470
$63$	−0.380391	−	0.658856i	−0.0479248	−	0.0830081i
$64$	5.52103			0.690128
$65$	−0.472277	+	0.818008i	−0.0585788	+	0.101461i
$66$	4.73528			0.582872
$67$	0.0778994	−	8.18498i	0.00951693	−	0.999955i
$67$	0.0778994	−	8.18498i	0.00951693	−	0.999955i
$68$	2.43328			0.295079
$69$	−2.16711	+	3.75354i	−0.260889	+	0.451873i
$70$	2.31444			0.276628
$71$	1.04970	+	1.81814i	0.124577	+	0.215774i	0.921567	−	0.388218i	$-0.126909\pi$
$71$	1.04970	+	1.81814i	0.124577	+	0.215774i	−0.796991	+	0.603992i	$0.793576\pi$
$72$	−2.88082			−0.339508
$73$	4.10751	−	7.11442i	0.480748	−	0.832680i	−0.519008	−	0.854770i	$-0.673698\pi$
$73$	4.10751	−	7.11442i	0.480748	−	0.832680i	0.999756	+	0.0220891i	$0.00703176\pi$
$74$	1.82062	+	3.15340i	0.211642	+	0.366575i
$75$	6.26689			0.723639
$76$	−9.14459			−1.04896
$77$	−1.98743	+	3.44234i	−0.226489	+	0.392290i
$78$	−0.127520	−	0.220871i	−0.0144388	−	0.0250087i
$79$	2.06029	+	3.56852i	0.231800	+	0.401490i	0.958338	−	0.285637i	$-0.0922050\pi$
$79$	2.06029	+	3.56852i	0.231800	+	0.401490i	−0.726538	+	0.687127i	$0.758872\pi$
$80$	0.425950	−	0.737768i	0.0476227	−	0.0824849i
$81$	1.00000			0.111111
$82$	−9.13808			−1.00913
$83$	−3.21087	+	5.56140i	−0.352439	+	0.610443i	−0.986676	−	0.162696i	$-0.947981\pi$
$83$	−3.21087	+	5.56140i	−0.352439	+	0.610443i	0.634237	+	0.773139i	$0.281314\pi$
$84$	0.448320	−	0.776514i	0.0489158	−	0.0847246i
$85$	3.46502	−	6.00160i	0.375835	−	0.650965i
$86$	2.48181	−	4.29862i	0.267621	−	0.463532i
$87$	−5.25353	−	9.09938i	−0.563237	−	0.975556i
$88$	7.52573	+	13.0349i	0.802245	+	1.38953i
$89$	−3.76761			−0.399366			−0.199683	−	0.979861i	$-0.563991\pi$
$89$	−3.76761			−0.399366			−0.199683	+	0.979861i	$0.563991\pi$
$90$	−1.52109	+	2.63461i	−0.160337	+	0.277712i
$91$	0.214084			0.0224421
$92$	−5.10821			−0.532567
$93$	2.39555	+	4.14921i	0.248407	+	0.430253i
$94$	6.94282			0.716098
$95$	−13.0220	+	22.5548i	−1.33603	+	2.31407i
$96$	−2.76581	−	4.79052i	−0.282284	−	0.488930i
$97$	2.28671	−	3.96071i	0.232181	−	0.402149i	−0.726269	−	0.687411i	$-0.758747\pi$
$97$	2.28671	−	3.96071i	0.232181	−	0.402149i	0.958450	+	0.285262i	$0.0920806\pi$
$98$	2.90985	+	5.04000i	0.293939	+	0.509117i
$99$	−2.61236	−	4.52473i	−0.262552	−	0.454753i
$100$	3.69301	+	6.39648i	0.369301	+	0.639648i
$101$	7.20210	+	12.4744i	0.716636	+	1.24125i	0.962325	+	0.271901i	$0.0876522\pi$
$101$	7.20210	+	12.4744i	0.716636	+	1.24125i	−0.245690	+	0.969349i	$0.579014\pi$
$102$	0.935594	+	1.62050i	0.0926376	+	0.160453i
$103$	2.06381	+	3.57462i	0.203353	+	0.352218i	0.949607	−	0.313444i	$-0.101483\pi$
$103$	2.06381	+	3.57462i	0.203353	+	0.352218i	−0.746254	+	0.665662i	$0.768149\pi$
$104$	0.405332	−	0.702055i	0.0397461	−	0.0688422i
$105$	−1.27683	−	2.21153i	−0.124606	−	0.215823i
$106$	0.345952	−	0.599206i	0.0336018	−	0.0582000i
$107$	13.1384			1.27014			0.635070	−	0.772454i	$-0.280971\pi$
$107$	13.1384			1.27014			0.635070	+	0.772454i	$0.280971\pi$
$108$	0.589289	+	1.02068i	0.0567044	+	0.0982148i
$109$	8.41375			0.805891			0.402946	−	0.915224i	$-0.367986\pi$
$109$	8.41375			0.805891			0.402946	+	0.915224i	$0.367986\pi$
$110$	15.8945			1.51548
$111$	2.00879	−	3.47933i	0.190666	−	0.330243i
$112$	−0.193084			−0.0182448
$113$	2.50616	+	4.34080i	0.235760	+	0.408348i	0.959493	−	0.281732i	$-0.0909089\pi$
$113$	2.50616	+	4.34080i	0.235760	+	0.408348i	−0.723734	+	0.690080i	$0.757576\pi$
$114$	−3.51608	−	6.09003i	−0.329311	−	0.570384i
$115$	−7.27415	+	12.5992i	−0.678318	+	1.17488i
$116$	6.19169	−	10.7243i	0.574884	−	0.995729i
$117$	−0.140700	+	0.243700i	−0.0130077	+	0.0225301i
$118$	−3.68784	+	6.38753i	−0.339494	+	0.588020i
$119$	−1.57070			−0.143986
$120$	−9.66981			−0.882729
$121$	−8.14881	+	14.1141i	−0.740801	+	1.28310i
$122$	−4.51365	−	7.81788i	−0.408647	−	0.707797i
$123$	5.04129	+	8.73177i	0.454558	+	0.787318i
$124$	−2.82334	+	4.89017i	−0.253543	+	0.439150i
$125$	4.25248			0.380354
$126$	0.689514			0.0614268
$127$	0.509618	+	0.882684i	0.0452213	+	0.0783256i	0.887750	−	0.460326i	$-0.152267\pi$
$127$	0.509618	+	0.882684i	0.0452213	+	0.0783256i	−0.842529	+	0.538651i	$0.818934\pi$
$128$	3.02970	−	5.24759i	0.267790	−	0.463826i
$129$	−5.47666			−0.482193
$130$	−0.428036	−	0.741379i	−0.0375412	−	0.0650233i
$131$	−6.41911			−0.560840			−0.280420	−	0.959877i	$-0.590474\pi$
$131$	−6.41911			−0.560840			−0.280420	+	0.959877i	$0.590474\pi$
$132$	3.07887	−	5.33275i	0.267981	−	0.464156i
$133$	5.90291			0.511847
$134$	6.38908	+	3.77026i	0.551933	+	0.325701i
$135$	3.35662			0.288892
$136$	−2.97386	+	5.15087i	−0.255006	+	0.441684i
$137$	−3.31012			−0.282802			−0.141401	−	0.989952i	$-0.545161\pi$
$137$	−3.31012			−0.282802			−0.141401	+	0.989952i	$0.545161\pi$
$138$	−1.96410	−	3.40192i	−0.167195	−	0.289590i
$139$	−3.70587			−0.314328			−0.157164	−	0.987573i	$-0.550235\pi$
$139$	−3.70587			−0.314328			−0.157164	+	0.987573i	$0.550235\pi$
$140$	1.50484	−	2.60646i	0.127182	−	0.220286i
$141$	−3.83021	−	6.63413i	−0.322562	−	0.558694i
$142$	−1.90274			−0.159675
$143$	1.47024			0.122947
$144$	0.126899	−	0.219795i	0.0105749	−	0.0183162i
$145$	−17.6341	−	30.5432i	−1.46443	−	2.53647i
$146$	3.72274	+	6.44797i	0.308096	+	0.533638i
$147$	3.21061	−	5.56093i	0.264806	−	0.458658i
$148$	4.73504			0.389218
$149$	−0.182938			−0.0149869			−0.00749344	−	0.999972i	$-0.502385\pi$
$149$	−0.182938			−0.0149869			−0.00749344	+	0.999972i	$0.502385\pi$
$150$	−2.83992	+	4.91888i	−0.231878	+	0.401625i
$151$	9.86336	−	17.0838i	0.802669	−	1.39026i	−0.115184	−	0.993344i	$-0.536746\pi$
$151$	9.86336	−	17.0838i	0.802669	−	1.39026i	0.917853	−	0.396920i	$-0.129921\pi$
$152$	11.1761	−	19.3576i	0.906505	−	1.57011i
$153$	1.03230	−	1.78799i	0.0834562	−	0.144550i
$154$	−1.80126	−	3.11987i	−0.145149	−	0.251406i
$155$	8.04094	+	13.9273i	0.645864	+	1.11867i
$156$	−0.331652			−0.0265534
$157$	−0.421051	+	0.729282i	−0.0336035	+	0.0582030i	−0.882338	−	0.470616i	$-0.844032\pi$
$157$	−0.421051	+	0.729282i	−0.0336035	+	0.0582030i	0.848735	+	0.528819i	$0.177365\pi$
$158$	−3.73457			−0.297107
$159$	−0.763418			−0.0605430
$160$	−9.28377	−	16.0800i	−0.733946	−	1.27123i
$161$	3.29739			0.259871
$162$	−0.453162	+	0.784899i	−0.0356037	+	0.0616675i
$163$	−0.708240	−	1.22671i	−0.0554737	−	0.0960832i	0.836955	−	0.547272i	$-0.184334\pi$
$163$	−0.708240	−	1.22671i	−0.0554737	−	0.0960832i	−0.892429	+	0.451188i	$0.851000\pi$
$164$	−5.94156	+	10.2911i	−0.463958	+	0.803598i
$165$	−8.76868	−	15.1878i	−0.682641	−	1.18237i
$166$	−2.91009	−	5.04042i	−0.225867	−	0.391213i
$167$	−4.31765	−	7.47839i	−0.334110	−	0.578695i	0.649204	−	0.760615i	$-0.275102\pi$
$167$	−4.31765	−	7.47839i	−0.334110	−	0.578695i	−0.983313	+	0.181920i	$0.941769\pi$
$168$	1.09584	+	1.89805i	0.0845457	+	0.146437i
$169$	6.46041	+	11.1898i	0.496954	+	0.860750i
$170$	3.14043	+	5.43939i	0.240860	+	0.417182i
$171$	−3.87950	+	6.71949i	−0.296673	+	0.513852i
$172$	−3.22733	−	5.58991i	−0.246082	−	0.426226i
$173$	−2.12177	+	3.67501i	−0.161315	+	0.279406i	−0.935341	−	0.353748i	$-0.884907\pi$
$173$	−2.12177	+	3.67501i	−0.161315	+	0.279406i	0.774025	+	0.633155i	$0.218240\pi$
$174$	9.52279			0.721921
$175$	−2.38387	−	4.12898i	−0.180204	−	0.312122i
$176$	−1.32602			−0.0999523
$177$	8.13803			0.611692
$178$	1.70734	−	2.95719i	0.127970	−	0.221651i
$179$	−18.2217			−1.36195			−0.680976	−	0.732306i	$-0.738444\pi$
$179$	−18.2217			−1.36195			−0.680976	+	0.732306i	$0.738444\pi$
$180$	1.97802	+	3.42603i	0.147433	+	0.255361i
$181$	9.20193	+	15.9382i	0.683974	+	1.18468i	0.973758	+	0.227585i	$0.0730831\pi$
$181$	9.20193	+	15.9382i	0.683974	+	1.18468i	−0.289784	+	0.957092i	$0.593584\pi$
$182$	−0.0970148	+	0.168035i	−0.00719122	+	0.0124556i
$183$	−4.98018	+	8.62592i	−0.368146	+	0.637647i
$184$	6.24304	−	10.8133i	0.460243	−	0.797164i
$185$	6.74275	−	11.6788i	0.495737	−	0.858642i
$186$	−4.34228			−0.318391
$187$	−10.7869			−0.788816
$188$	4.51421	−	7.81884i	0.329232	−	0.570247i
$189$	−0.380391	−	0.658856i	−0.0276694	−	0.0479248i
$190$	−11.8022	−	20.4419i	−0.856218	−	1.48301i
$191$	−4.58443	+	7.94046i	−0.331718	+	0.574552i	−0.982849	−	0.184413i	$-0.940961\pi$
$191$	−4.58443	+	7.94046i	−0.331718	+	0.574552i	0.651131	+	0.758965i	$0.274295\pi$
$192$	5.52103			0.398446
$193$	−26.3218			−1.89469			−0.947344	−	0.320219i	$-0.896244\pi$
$193$	−26.3218			−1.89469			−0.947344	+	0.320219i	$0.896244\pi$
$194$	2.07250	+	3.58968i	0.148797	+	0.257724i
$195$	−0.472277	+	0.818008i	−0.0338205	+	0.0585788i
$196$	7.56790			0.540564
$197$	−1.58406	−	2.74367i	−0.112860	−	0.195478i	0.804063	−	0.594545i	$-0.202668\pi$
$197$	−1.58406	−	2.74367i	−0.112860	−	0.195478i	−0.916922	+	0.399066i	$0.869334\pi$
$198$	4.73528			0.336522
$199$	−4.83354	+	8.37195i	−0.342641	+	0.593471i	−0.984922	−	0.172997i	$-0.944655\pi$
$199$	−4.83354	+	8.37195i	−0.342641	+	0.593471i	0.642281	+	0.766469i	$0.277988\pi$
$200$	−18.0538			−1.27660
$201$	0.0778994	−	8.18498i	0.00549460	−	0.577324i
$202$	−13.0549			−0.918537
$203$	−3.99679	+	6.92264i	−0.280520	+	0.485874i
$204$	2.43328			0.170364
$205$	16.9217	+	29.3092i	1.18186	+	2.04705i
$206$	−3.74096			−0.260645
$207$	−2.16711	+	3.75354i	−0.150624	+	0.260889i
$208$	0.0357093	+	0.0618504i	0.00247600	+	0.00428855i
$209$	40.5386			2.80411
$210$	2.31444			0.159711
$211$	−6.35073	+	10.9998i	−0.437202	+	0.757256i	−0.997473	−	0.0710534i	$-0.977364\pi$
$211$	−6.35073	+	10.9998i	−0.437202	+	0.757256i	0.560270	+	0.828310i	$0.310697\pi$
$212$	−0.449874	−	0.779204i	−0.0308975	−	0.0535160i
$213$	1.04970	+	1.81814i	0.0719245	+	0.124577i
$214$	−5.95384	+	10.3123i	−0.406996	+	0.704938i
$215$	−18.3831			−1.25371
$216$	−2.88082			−0.196015
$217$	1.82249	−	3.15664i	0.123719	−	0.214287i
$218$	−3.81279	+	6.60394i	−0.258235	+	0.447276i
$219$	4.10751	−	7.11442i	0.277560	−	0.480748i
$220$	10.3346	−	17.9000i	0.696757	−	1.20682i
$221$	0.290488	+	0.503141i	0.0195404	+	0.0338449i
$222$	1.82062	+	3.15340i	0.122192	+	0.211642i
$223$	26.5085			1.77514			0.887569	−	0.460676i	$-0.152393\pi$
$223$	26.5085			1.77514			0.887569	+	0.460676i	$0.152393\pi$
$224$	−2.10418	+	3.64454i	−0.140591	+	0.243511i
$225$	6.26689			0.417793
$226$	−4.54278			−0.302181
$227$	−10.6148	−	18.3853i	−0.704528	−	1.22028i	−0.966862	−	0.255301i	$-0.917825\pi$
$227$	−10.6148	−	18.3853i	−0.704528	−	1.22028i	0.262334	−	0.964977i	$-0.415508\pi$
$228$	−9.14459			−0.605615
$229$	0.543083	−	0.940648i	0.0358880	−	0.0621598i	−0.847524	−	0.530758i	$-0.821907\pi$
$229$	0.543083	−	0.940648i	0.0358880	−	0.0621598i	0.883412	+	0.468598i	$0.155241\pi$
$230$	−6.59273	−	11.4189i	−0.434712	−	0.752943i
$231$	−1.98743	+	3.44234i	−0.130763	+	0.226489i
$232$	15.1345	+	26.2137i	0.993626	+	1.72101i
$233$	0.573224	+	0.992853i	0.0375532	+	0.0650440i	0.884191	−	0.467125i	$-0.154710\pi$
$233$	0.573224	+	0.992853i	0.0375532	+	0.0650440i	−0.846638	+	0.532169i	$0.821377\pi$
$234$	−0.127520	−	0.220871i	−0.00833623	−	0.0144388i
$235$	−12.8566	−	22.2682i	−0.838670	−	1.45262i
$236$	4.79565	+	8.30631i	0.312170	+	0.540695i
$237$	2.06029	+	3.56852i	0.133830	+	0.231800i
$238$	0.711783	−	1.23284i	0.0461380	−	0.0799134i
$239$	5.57475	+	9.65574i	0.360600	+	0.624578i	0.988060	−	0.154071i	$-0.0492385\pi$
$239$	5.57475	+	9.65574i	0.360600	+	0.624578i	−0.627459	+	0.778649i	$0.715905\pi$
$240$	0.425950	−	0.737768i	0.0274950	−	0.0476227i
$241$	−1.83905			−0.118463			−0.0592317	−	0.998244i	$-0.518865\pi$
$241$	−1.83905			−0.118463			−0.0592317	+	0.998244i	$0.518865\pi$
$242$	−7.38545	−	12.7920i	−0.474755	−	0.822300i
$243$	1.00000			0.0641500
$244$	−11.7391			−0.751516
$245$	10.7768	−	18.6659i	0.688503	−	1.19252i
$246$	−9.13808			−0.582623
$247$	−1.09169	−	1.89087i	−0.0694628	−	0.120313i
$248$	−6.90114	−	11.9531i	−0.438223	−	0.759024i
$249$	−3.21087	+	5.56140i	−0.203481	+	0.352439i
$250$	−1.92706	+	3.33777i	−0.121878	+	0.211099i
$251$	−9.69268	+	16.7882i	−0.611797	+	1.05966i	0.379141	+	0.925339i	$0.376220\pi$
$251$	−9.69268	+	16.7882i	−0.611797	+	1.05966i	−0.990937	+	0.134324i	$0.957114\pi$
$252$	0.448320	−	0.776514i	0.0282415	−	0.0489158i
$253$	22.6450			1.42368
$254$	−0.923758			−0.0579617
$255$	3.46502	−	6.00160i	0.216988	−	0.375835i
$256$	8.26691	+	14.3187i	0.516682	+	0.894920i
$257$	−2.30266	−	3.98832i	−0.143636	−	0.248785i	0.785227	−	0.619208i	$-0.212546\pi$
$257$	−2.30266	−	3.98832i	−0.143636	−	0.248785i	−0.928863	+	0.370423i	$0.879213\pi$
$258$	2.48181	−	4.29862i	0.154511	−	0.267621i
$259$	−3.05651			−0.189922
$260$	−1.11323			−0.0690396
$261$	−5.25353	−	9.09938i	−0.325185	−	0.563237i
$262$	2.90890	−	5.03835i	0.179712	−	0.311271i
$263$	−16.9451			−1.04488			−0.522441	−	0.852676i	$-0.674978\pi$
$263$	−16.9451			−1.04488			−0.522441	+	0.852676i	$0.674978\pi$
$264$	7.52573	+	13.0349i	0.463176	+	0.802245i
$265$	−2.56250			−0.157413
$266$	−2.67497	+	4.63319i	−0.164013	+	0.284079i
$267$	−3.76761			−0.230574
$268$	8.40014	−	4.74381i	0.513120	−	0.289774i
$269$	−6.36617			−0.388152			−0.194076	−	0.980986i	$-0.562171\pi$
$269$	−6.36617			−0.388152			−0.194076	+	0.980986i	$0.562171\pi$
$270$	−1.52109	+	2.63461i	−0.0925707	+	0.160337i
$271$	9.52019			0.578311			0.289155	−	0.957282i	$-0.406626\pi$
$271$	9.52019			0.578311			0.289155	+	0.957282i	$0.406626\pi$
$272$	−0.261994	−	0.453787i	−0.0158857	−	0.0275149i
$273$	0.214084			0.0129570
$274$	1.50002	−	2.59811i	0.0906194	−	0.156957i
$275$	−16.3714	−	28.3560i	−0.987230	−	1.70993i
$276$	−5.10821			−0.307478
$277$	−8.01791			−0.481749			−0.240875	−	0.970556i	$-0.577434\pi$
$277$	−8.01791			−0.481749			−0.240875	+	0.970556i	$0.577434\pi$
$278$	1.67936	−	2.90874i	0.100721	−	0.174454i
$279$	2.39555	+	4.14921i	0.143418	+	0.248407i
$280$	3.67831	+	6.37102i	0.219821	+	0.380741i
$281$	3.28109	−	5.68302i	0.195734	−	0.339020i	−0.751407	−	0.659839i	$-0.770625\pi$
$281$	3.28109	−	5.68302i	0.195734	−	0.339020i	0.947141	+	0.320818i	$0.103958\pi$
$282$	6.94282			0.413439
$283$	27.3905			1.62820			0.814098	−	0.580727i	$-0.197232\pi$
$283$	27.3905			1.62820			0.814098	+	0.580727i	$0.197232\pi$
$284$	−1.23716	+	2.14282i	−0.0734118	+	0.127153i
$285$	−13.0220	+	22.5548i	−0.771357	+	1.33603i
$286$	−0.666255	+	1.15399i	−0.0393965	+	0.0682367i
$287$	3.83532	−	6.64298i	0.226392	−	0.392122i
$288$	−2.76581	−	4.79052i	−0.162977	−	0.282284i
$289$	6.36873	+	11.0310i	0.374631	+	0.648880i
$290$	31.9644			1.87701
$291$	2.28671	−	3.96071i	0.134050	−	0.232181i
$292$	9.68205			0.566599
$293$	31.1715			1.82106			0.910530	−	0.413444i	$-0.135674\pi$
$293$	31.1715			1.82106			0.910530	+	0.413444i	$0.135674\pi$
$294$	2.90985	+	5.04000i	0.169706	+	0.293939i
$295$	27.3163			1.59041
$296$	−5.78697	+	10.0233i	−0.336361	+	0.582594i
$297$	−2.61236	−	4.52473i	−0.151584	−	0.262552i
$298$	0.0829005	−	0.143588i	0.00480230	−	0.00831782i
$299$	−0.609824	−	1.05625i	−0.0352670	−	0.0610843i
$300$	3.69301	+	6.39648i	0.213216	+	0.369301i
$301$	2.08327	+	3.60833i	0.120078	+	0.207981i
$302$	8.93940	+	15.4835i	0.514404	+	0.890975i
$303$	7.20210	+	12.4744i	0.413750	+	0.716636i
$304$	0.984607	+	1.70539i	0.0564711	+	0.0978108i
$305$	−16.7166	+	28.9539i	−0.957188	+	1.65790i
$306$	0.935594	+	1.62050i	0.0534843	+	0.0926376i
$307$	5.57475	−	9.65574i	0.318168	−	0.551082i	−0.661938	−	0.749558i	$-0.730266\pi$
$307$	5.57475	−	9.65574i	0.318168	−	0.551082i	0.980106	+	0.198476i	$0.0635992\pi$
$308$	−4.68469			−0.266935
$309$	2.06381	+	3.57462i	0.117406	+	0.203353i
$310$	−14.5754			−0.827826
$311$	−9.37680			−0.531710			−0.265855	−	0.964013i	$-0.585654\pi$
$311$	−9.37680			−0.531710			−0.265855	+	0.964013i	$0.585654\pi$
$312$	0.405332	−	0.702055i	0.0229474	−	0.0397461i
$313$	−26.3734			−1.49071			−0.745357	−	0.666666i	$-0.767721\pi$
$313$	−26.3734			−1.49071			−0.745357	+	0.666666i	$0.767721\pi$
$314$	−0.381608	−	0.660965i	−0.0215354	−	0.0373004i
$315$	−1.27683	−	2.21153i	−0.0719411	−	0.124606i
$316$	−2.42821	+	4.20578i	−0.136597	+	0.236594i
$317$	−12.6014	+	21.8262i	−0.707763	+	1.22588i	0.257922	+	0.966166i	$0.416962\pi$
$317$	−12.6014	+	21.8262i	−0.707763	+	1.22588i	−0.965685	+	0.259716i	$0.916371\pi$
$318$	0.345952	−	0.599206i	0.0194000	−	0.0336018i
$319$	−27.4482	+	47.5416i	−1.53680	+	2.66182i
$320$	18.5320			1.03597
$321$	13.1384			0.733316
$322$	−1.49425	+	2.58812i	−0.0832713	+	0.144230i
$323$	8.00959	+	13.8730i	0.445665	+	0.771915i
$324$	0.589289	+	1.02068i	0.0327383	+	0.0567044i
$325$	−0.881753	+	1.52724i	−0.0489109	+	0.0847161i
$326$	1.28379			0.0711025
$327$	8.41375			0.465281
$328$	−14.5231	−	25.1547i	−0.801901	−	1.38893i
$329$	−2.91396	+	5.04712i	−0.160652	+	0.278257i
$330$	15.8945			0.874965
$331$	−13.0908	−	22.6739i	−0.719535	−	1.24627i	−0.961184	−	0.275908i	$-0.911021\pi$
$331$	−13.0908	−	22.6739i	−0.719535	−	1.24627i	0.241649	−	0.970364i	$-0.422312\pi$
$332$	−7.56853			−0.415377
$333$	2.00879	−	3.47933i	0.110081	−	0.190666i
$334$	7.82637			0.428240
$335$	0.261479	−	27.4739i	0.0142861	−	1.50106i
$336$	−0.193084			−0.0105336
$337$	13.0815	−	22.6578i	0.712594	−	1.23425i	−0.251286	−	0.967913i	$-0.580853\pi$
$337$	13.0815	−	22.6578i	0.712594	−	1.23425i	0.963880	−	0.266336i	$-0.0858132\pi$
$338$	−11.7104			−0.636964
$339$	2.50616	+	4.34080i	0.136116	+	0.235760i
$340$	8.16760			0.442950
$341$	12.5160	−	21.6784i	0.677782	−	1.17395i
$342$	−3.51608	−	6.09003i	−0.190128	−	0.329311i
$343$	−10.2106			−0.551321
$344$	15.7773			0.850653
$345$	−7.27415	+	12.5992i	−0.391627	+	0.678318i
$346$	−1.92301	−	3.33075i	−0.103382	−	0.179062i
$347$	−16.9336	−	29.3299i	−0.909043	−	1.57451i	−0.815396	−	0.578904i	$-0.803481\pi$
$347$	−16.9336	−	29.3299i	−0.909043	−	1.57451i	−0.0936477	−	0.995605i	$-0.529853\pi$
$348$	6.19169	−	10.7243i	0.331910	−	0.574884i
$349$	30.7320			1.64505			0.822523	−	0.568731i	$-0.192566\pi$
$349$	30.7320			1.64505			0.822523	+	0.568731i	$0.192566\pi$
$350$	4.32111			0.230973
$351$	−0.140700	+	0.243700i	−0.00751002	+	0.0130077i
$352$	−14.4506	+	25.0291i	−0.770217	+	1.33405i
$353$	−10.0190	+	17.3534i	−0.533257	+	0.923629i	0.465988	+	0.884791i	$0.345699\pi$
$353$	−10.0190	+	17.3534i	−0.533257	+	0.923629i	−0.999246	+	0.0388379i	$0.987634\pi$
$354$	−3.68784	+	6.38753i	−0.196007	+	0.339494i
$355$	3.52346	+	6.10281i	0.187006	+	0.323903i
$356$	−2.22021	−	3.84552i	−0.117671	−	0.203812i
$357$	−1.57070			−0.0831305
$358$	8.25736	−	14.3022i	0.436415	−	0.755893i
$359$	17.2285			0.909287			0.454644	−	0.890673i	$-0.349767\pi$
$359$	17.2285			0.909287			0.454644	+	0.890673i	$0.349767\pi$
$360$	−9.66981			−0.509644
$361$	−20.6011	−	35.6821i	−1.08427	−	1.87800i
$362$	−16.6798			−0.876673
$363$	−8.14881	+	14.1141i	−0.427701	+	0.740801i
$364$	0.126158	+	0.218511i	0.00661245	+	0.0114531i
$365$	13.7874	−	23.8804i	0.721664	−	1.24996i
$366$	−4.51365	−	7.81788i	−0.235932	−	0.408647i
$367$	13.9652	+	24.1884i	0.728978	+	1.26263i	0.957316	+	0.289044i	$0.0933375\pi$
$367$	13.9652	+	24.1884i	0.728978	+	1.26263i	−0.228338	+	0.973582i	$0.573329\pi$
$368$	0.550005	+	0.952637i	0.0286710	+	0.0496596i
$369$	5.04129	+	8.73177i	0.262439	+	0.454558i
$370$	6.11111	+	10.5848i	0.317702	+	0.550275i
$371$	0.290397	+	0.502983i	0.0150767	+	0.0261136i
$372$	−2.82334	+	4.89017i	−0.146383	+	0.253543i
$373$	−3.18920	−	5.52385i	−0.165130	−	0.286014i	0.771571	−	0.636143i	$-0.219471\pi$
$373$	−3.18920	−	5.52385i	−0.165130	−	0.286014i	−0.936702	+	0.350129i	$0.886138\pi$
$374$	4.88821	−	8.46662i	0.252763	−	0.437799i
$375$	4.25248			0.219597
$376$	11.0342	+	19.1117i	0.569043	+	0.985612i
$377$	2.95669			0.152277
$378$	0.689514			0.0354648
$379$	−0.477585	+	0.827201i	−0.0245319	+	0.0424905i	−0.878031	−	0.478604i	$-0.841143\pi$
$379$	−0.477585	+	0.827201i	−0.0245319	+	0.0424905i	0.853499	+	0.521095i	$0.174476\pi$
$380$	−30.6949			−1.57462
$381$	0.509618	+	0.882684i	0.0261085	+	0.0452213i
$382$	−4.15497	−	7.19663i	−0.212587	−	0.368211i
$383$	−4.53609	+	7.85673i	−0.231783	+	0.401460i	−0.958333	−	0.285654i	$-0.907789\pi$
$383$	−4.53609	+	7.85673i	−0.231783	+	0.401460i	0.726550	+	0.687114i	$0.241123\pi$
$384$	3.02970	−	5.24759i	0.154609	−	0.267790i
$385$	−6.67106	+	11.5546i	−0.339989	+	0.588877i
$386$	11.9280	−	20.6600i	0.607122	−	1.05157i
$387$	−5.47666			−0.278394
$388$	5.39014			0.273643
$389$	5.71035	−	9.89062i	0.289526	−	0.501475i	−0.684170	−	0.729322i	$-0.739836\pi$
$389$	5.71035	−	9.89062i	0.289526	−	0.501475i	0.973697	+	0.227848i	$0.0731688\pi$
$390$	−0.428036	−	0.741379i	−0.0216744	−	0.0375412i
$391$	4.47419	+	7.74952i	0.226269	+	0.391910i
$392$	−9.24917	+	16.0200i	−0.467154	+	0.809134i
$393$	−6.41911			−0.323801
$394$	2.87134			0.144656
$395$	6.91560	+	11.9782i	0.347962	+	0.602687i
$396$	3.07887	−	5.33275i	0.154719	−	0.267981i
$397$	−26.6254			−1.33629			−0.668145	−	0.744031i	$-0.732912\pi$
$397$	−26.6254			−1.33629			−0.668145	+	0.744031i	$0.732912\pi$
$398$	−4.38075	−	7.58769i	−0.219587	−	0.380336i
$399$	5.90291			0.295515
$400$	0.795260	−	1.37743i	0.0397630	−	0.0688716i
$401$	29.4202			1.46918			0.734589	−	0.678513i	$-0.237375\pi$
$401$	29.4202			1.46918			0.734589	+	0.678513i	$0.237375\pi$
$402$	6.38908	+	3.77026i	0.318658	+	0.188044i
$403$	−1.34822			−0.0671594
$404$	−8.48824	+	14.7021i	−0.422306	+	0.731455i
$405$	3.35662			0.166792
$406$	−3.62238	−	6.27415i	−0.179776	−	0.311381i
$407$	−20.9907			−1.04047
$408$	−2.97386	+	5.15087i	−0.147228	+	0.255006i
$409$	−7.23071	−	12.5240i	−0.357536	−	0.619270i	0.630013	−	0.776585i	$-0.283050\pi$
$409$	−7.23071	−	12.5240i	−0.357536	−	0.619270i	−0.987549	+	0.157315i	$0.949716\pi$
$410$	−30.6731			−1.51483
$411$	−3.31012			−0.163276
$412$	−2.43236	+	4.21297i	−0.119834	+	0.207558i
$413$	−3.09563	−	5.36179i	−0.152326	−	0.263837i
$414$	−1.96410	−	3.40192i	−0.0965301	−	0.167195i
$415$	−10.7777	+	18.6675i	−0.529056	+	0.916351i
$416$	1.55660			0.0763185
$417$	−3.70587			−0.181477
$418$	−18.3705	+	31.8187i	−0.898531	+	1.55630i
$419$	−4.60705	+	7.97965i	−0.225069	+	0.389831i	−0.956340	−	0.292256i	$-0.905594\pi$
$419$	−4.60705	+	7.97965i	−0.225069	+	0.389831i	0.731271	+	0.682087i	$0.238928\pi$
$420$	1.50484	−	2.60646i	0.0734287	−	0.127182i
$421$	8.99291	−	15.5762i	0.438287	−	0.759136i	−0.559270	−	0.828986i	$-0.688919\pi$
$421$	8.99291	−	15.5762i	0.438287	−	0.759136i	0.997558	+	0.0698494i	$0.0222519\pi$
$422$	−5.75581	−	9.96936i	−0.280189	−	0.485301i
$423$	−3.83021	−	6.63413i	−0.186231	−	0.322562i
$424$	2.19927			0.106806
$425$	6.46929	−	11.2051i	0.313807	−	0.543529i
$426$	−1.90274			−0.0921881
$427$	7.57766			0.366709
$428$	7.74234	+	13.4101i	0.374240	+	0.648203i
$429$	1.47024			0.0709837
$430$	8.33049	−	14.4288i	0.401732	−	0.695820i
$431$	6.18877	+	10.7193i	0.298103	+	0.516329i	0.975702	−	0.219102i	$-0.0703129\pi$
$431$	6.18877	+	10.7193i	0.298103	+	0.516329i	−0.677599	+	0.735431i	$0.736980\pi$
$432$	0.126899	−	0.219795i	0.00610541	−	0.0105749i
$433$	−2.84653	−	4.93033i	−0.136795	−	0.236937i	0.789486	−	0.613768i	$-0.210347\pi$
$433$	−2.84653	−	4.93033i	−0.136795	−	0.236937i	−0.926282	+	0.376831i	$0.877014\pi$
$434$	1.65176	+	2.86094i	0.0792872	+	0.137329i
$435$	−17.6341	−	30.5432i	−0.845490	−	1.46443i
$436$	4.95813	+	8.58774i	0.237451	+	0.411278i
$437$	−16.8146	−	29.1237i	−0.804350	−	1.39318i
$438$	3.72274	+	6.44797i	0.177879	+	0.308096i
$439$	4.58901	−	7.94840i	0.219022	−	0.379356i	−0.735488	−	0.677538i	$-0.763047\pi$
$439$	4.58901	−	7.94840i	0.219022	−	0.379356i	0.954509	+	0.298182i	$0.0963802\pi$
$440$	25.2610	+	43.7533i	1.20427	+	2.08586i
$441$	3.21061	−	5.56093i	0.152886	−	0.264806i
$442$	−0.526553			−0.0250456
$443$	−17.2322	−	29.8470i	−0.818726	−	1.41808i	−0.906621	−	0.421946i	$-0.861347\pi$
$443$	−17.2322	−	29.8470i	−0.818726	−	1.41808i	0.0878945	−	0.996130i	$-0.471986\pi$
$444$	4.73504			0.224715
$445$	−12.6464			−0.599499
$446$	−12.0126	+	20.8065i	−0.568814	+	0.985214i
$447$	−0.182938			−0.00865267
$448$	−2.10015	−	3.63756i	−0.0992227	−	0.171859i
$449$	−16.3753	−	28.3629i	−0.772799	−	1.33853i	−0.936023	−	0.351938i	$-0.885523\pi$
$449$	−16.3753	−	28.3629i	−0.772799	−	1.33853i	0.163225	−	0.986589i	$-0.447810\pi$
$450$	−2.83992	+	4.91888i	−0.133875	+	0.231878i
$451$	26.3393	−	45.6210i	1.24027	−	2.14821i
$452$	−2.95370	+	5.11597i	−0.138931	+	0.240635i
$453$	9.86336	−	17.0838i	0.463421	−	0.802669i
$454$	19.2409			0.903018
$455$	0.718600			0.0336885
$456$	11.1761	−	19.3576i	0.523371	−	0.906505i
$457$	−0.121120	−	0.209786i	−0.00566575	−	0.00981337i	0.863179	−	0.504899i	$-0.168470\pi$
$457$	−0.121120	−	0.209786i	−0.00566575	−	0.00981337i	−0.868844	+	0.495085i	$0.835137\pi$
$458$	0.492209	+	0.852531i	0.0229994	+	0.0398362i
$459$	1.03230	−	1.78799i	0.0481834	−	0.0834562i
$460$	−17.1463			−0.799450
$461$	−27.3404			−1.27337			−0.636686	−	0.771123i	$-0.719695\pi$
$461$	−27.3404			−1.27337			−0.636686	+	0.771123i	$0.719695\pi$
$462$	−1.80126	−	3.11987i	−0.0838021	−	0.145149i
$463$	11.3668	−	19.6879i	0.528259	−	0.914972i	−0.471198	−	0.882028i	$-0.656178\pi$
$463$	11.3668	−	19.6879i	0.528259	−	0.914972i	0.999457	−	0.0329445i	$-0.0104884\pi$
$464$	−2.66666			−0.123797
$465$	8.04094	+	13.9273i	0.372890	+	0.645864i
$466$	−1.03905			−0.0481332
$467$	14.3961	−	24.9348i	0.666174	−	1.15385i	−0.312792	−	0.949822i	$-0.601264\pi$
$467$	14.3961	−	24.9348i	0.666174	−	1.15385i	0.978966	−	0.204025i	$-0.0654025\pi$
$468$	−0.331652			−0.0153306
$469$	−5.42236	+	3.06217i	−0.250381	+	0.141398i
$470$	23.3044			1.07495
$471$	−0.421051	+	0.729282i	−0.0194010	+	0.0336035i
$472$	−23.4442			−1.07911
$473$	14.3070	+	24.7804i	0.657836	+	1.13940i
$474$	−3.73457			−0.171535
$475$	−24.3124	+	42.1104i	−1.11553	+	1.93216i
$476$	−0.925599	−	1.60318i	−0.0424247	−	0.0734818i
$477$	−0.763418			−0.0349545
$478$	−10.1050			−0.462194
$479$	8.30071	−	14.3773i	0.379269	−	0.656914i	−0.611687	−	0.791100i	$-0.709509\pi$
$479$	8.30071	−	14.3773i	0.379269	−	0.656914i	0.990956	+	0.134186i	$0.0428421\pi$
$480$	−9.28377	−	16.0800i	−0.423744	−	0.733946i
$481$	0.565275	+	0.979085i	0.0257743	+	0.0446424i
$482$	0.833385	−	1.44346i	0.0379596	−	0.0657480i
$483$	3.29739			0.150036
$484$	−19.2080			−0.873091
$485$	7.67563	−	13.2946i	0.348532	−	0.603676i
$486$	−0.453162	+	0.784899i	−0.0205558	+	0.0356037i
$487$	5.71230	−	9.89399i	0.258849	−	0.448340i	−0.707085	−	0.707129i	$-0.749990\pi$
$487$	5.71230	−	9.89399i	0.258849	−	0.448340i	0.965934	+	0.258789i	$0.0833234\pi$
$488$	14.3470	−	24.8497i	0.649458	−	1.12489i
$489$	−0.708240	−	1.22671i	−0.0320277	−	0.0554737i
$490$	9.76725	+	16.9174i	0.441239	+	0.764249i
$491$	−17.5306			−0.791147			−0.395573	−	0.918434i	$-0.629454\pi$
$491$	−17.5306			−0.791147			−0.395573	+	0.918434i	$0.629454\pi$
$492$	−5.94156	+	10.2911i	−0.267866	+	0.463958i
$493$	−21.6928			−0.976994
$494$	1.97885			0.0890328
$495$	−8.76868	−	15.1878i	−0.394123	−	0.682641i
$496$	1.21597			0.0545985
$497$	0.798596	−	1.38321i	0.0358219	−	0.0620454i
$498$	−2.91009	−	5.04042i	−0.130404	−	0.225867i
$499$	18.5604	−	32.1476i	0.830878	−	1.43912i	−0.0664657	−	0.997789i	$-0.521172\pi$
$499$	18.5604	−	32.1476i	0.830878	−	1.43912i	0.897343	−	0.441333i	$-0.145494\pi$
$500$	2.50594	+	4.34042i	0.112069	+	0.194109i
$501$	−4.31765	−	7.47839i	−0.192898	−	0.334110i
$502$	−8.78471	−	15.2156i	−0.392081	−	0.679104i
$503$	14.6480	+	25.3710i	0.653121	+	1.13124i	0.982361	+	0.186992i	$0.0598739\pi$
$503$	14.6480	+	25.3710i	0.653121	+	1.13124i	−0.329241	+	0.944246i	$0.606793\pi$
$504$	1.09584	+	1.89805i	0.0488125	+	0.0845457i
$505$	24.1747	+	41.8718i	1.07576	+	1.86327i
$506$	−10.2618	+	17.7740i	−0.456195	+	0.790152i
$507$	6.46041	+	11.1898i	0.286917	+	0.496954i
$508$	−0.600625	+	1.04031i	−0.0266484	+	0.0461564i
$509$	0.591311			0.0262094			0.0131047	−	0.999914i	$-0.495829\pi$
$509$	0.591311			0.0262094			0.0131047	+	0.999914i	$0.495829\pi$
$510$	3.14043	+	5.43939i	0.139061	+	0.240860i
$511$	−6.24985			−0.276477
$512$	−2.86620			−0.126669
$513$	−3.87950	+	6.71949i	−0.171284	+	0.296673i
$514$	4.17391			0.184103
$515$	6.92743	+	11.9987i	0.305259	+	0.528724i
$516$	−3.22733	−	5.58991i	−0.142075	−	0.246082i
$517$	−20.0118	+	34.6614i	−0.880117	+	1.52441i
$518$	1.38509	−	2.39905i	0.0608574	−	0.105408i
$519$	−2.12177	+	3.67501i	−0.0931354	+	0.161315i
$520$	1.36054	−	2.35653i	0.0596638	−	0.103341i
$521$	16.9321			0.741809			0.370905	−	0.928671i	$-0.379048\pi$
$521$	16.9321			0.741809			0.370905	+	0.928671i	$0.379048\pi$
$522$	9.52279			0.416801
$523$	16.3292	−	28.2831i	0.714027	−	1.23673i	−0.249306	−	0.968425i	$-0.580203\pi$
$523$	16.3292	−	28.2831i	0.714027	−	1.23673i	0.963333	−	0.268307i	$-0.0864642\pi$
$524$	−3.78271	−	6.55185i	−0.165249	−	0.286219i
$525$	−2.38387	−	4.12898i	−0.104041	−	0.180204i
$526$	7.67888	−	13.3002i	0.334815	−	0.579917i
$527$	9.89165			0.430887
$528$	−1.32602			−0.0577075
$529$	2.10731	+	3.64997i	0.0916222	+	0.158694i
$530$	1.16123	−	2.01131i	0.0504405	−	0.0873656i
$531$	8.13803			0.353160
$532$	3.47852	+	6.02497i	0.150813	+	0.261216i
$533$	−2.83724			−0.122895
$534$	1.70734	−	2.95719i	0.0738837	−	0.127970i
$535$	44.1007			1.90664
$536$	−0.224414	+	23.5795i	−0.00969321	+	1.01848i
$537$	−18.2217			−0.786323
$538$	2.88491	−	4.99680i	0.124377	−	0.215427i
$539$	−33.5490			−1.44506
$540$	1.97802	+	3.42603i	0.0851204	+	0.147433i
$541$	−43.9236			−1.88842			−0.944211	−	0.329340i	$-0.893174\pi$
$541$	−43.9236			−1.88842			−0.944211	+	0.329340i	$0.893174\pi$
$542$	−4.31419	+	7.47239i	−0.185310	+	0.320967i
$543$	9.20193	+	15.9382i	0.394892	+	0.683974i
$544$	−11.4205			−0.489651
$545$	28.2418			1.20974
$546$	−0.0970148	+	0.168035i	−0.00415185	+	0.00719122i
$547$	17.9145	+	31.0289i	0.765971	+	1.32670i	0.939732	+	0.341912i	$0.111075\pi$
$547$	17.9145	+	31.0289i	0.765971	+	1.32670i	−0.173761	+	0.984788i	$0.555592\pi$
$548$	−1.95061	−	3.37856i	−0.0833261	−	0.144325i
$549$	−4.98018	+	8.62592i	−0.212549	+	0.368146i
$550$	29.6755			1.26537
$551$	81.5243			3.47305
$552$	6.24304	−	10.8133i	0.265721	−	0.460243i
$553$	1.56743	−	2.71487i	0.0666539	−	0.115448i
$554$	3.63341	−	6.29325i	0.154369	−	0.267374i
$555$	6.74275	−	11.6788i	0.286214	−	0.495737i
$556$	−2.18383	−	3.78251i	−0.0926150	−	0.160414i
$557$	0.0422292	+	0.0731430i	0.00178931	+	0.00309917i	0.866919	−	0.498450i	$-0.166097\pi$
$557$	0.0422292	+	0.0731430i	0.00178931	+	0.00309917i	−0.865129	+	0.501549i	$0.832764\pi$
$558$	−4.34228			−0.183823
$559$	0.770567	−	1.33466i	0.0325915	−	0.0564501i
$560$	−0.648111			−0.0273877
$561$	−10.7869			−0.455423
$562$	2.97373	+	5.15065i	0.125439	+	0.217267i
$563$	22.5348			0.949729			0.474865	−	0.880059i	$-0.342497\pi$
$563$	22.5348			0.949729			0.474865	+	0.880059i	$0.342497\pi$
$564$	4.51421	−	7.81884i	0.190082	−	0.329232i
$565$	8.41222	+	14.5704i	0.353905	+	0.612981i
$566$	−12.4123	+	21.4988i	−0.521729	+	0.903661i
$567$	−0.380391	−	0.658856i	−0.0159749	−	0.0276694i
$568$	−3.02401	−	5.23773i	−0.126885	−	0.219770i
$569$	4.86550	+	8.42730i	0.203973	+	0.353291i	0.949805	−	0.312843i	$-0.101281\pi$
$569$	4.86550	+	8.42730i	0.203973	+	0.353291i	−0.745832	+	0.666134i	$0.767948\pi$
$570$	−11.8022	−	20.4419i	−0.494338	−	0.856218i
$571$	−14.9718	−	25.9319i	−0.626549	−	1.08521i	−0.988239	−	0.152916i	$-0.951133\pi$
$571$	−14.9718	−	25.9319i	−0.626549	−	1.08521i	0.361690	−	0.932298i	$-0.382200\pi$
$572$	0.866394	+	1.50064i	0.0362258	+	0.0627448i
$573$	−4.58443	+	7.94046i	−0.191517	+	0.331718i
$574$	3.47604	+	6.02068i	0.145087	+	0.251298i
$575$	−13.5810	+	23.5230i	−0.566368	+	0.980978i
$576$	5.52103			0.230043
$577$	−16.7339	−	28.9839i	−0.696640	−	1.20662i	−0.969625	−	0.244597i	$-0.921344\pi$
$577$	−16.7339	−	28.9839i	−0.696640	−	1.20662i	0.272985	−	0.962018i	$-0.411989\pi$
$578$	−11.5443			−0.480178
$579$	−26.3218			−1.09390
$580$	20.7832	−	35.9975i	0.862974	−	1.49471i
$581$	4.88555			0.202687
$582$	2.07250	+	3.58968i	0.0859080	+	0.148797i
$583$	1.99432	+	3.45426i	0.0825963	+	0.143061i
$584$	−11.8330	+	20.4954i	−0.489653	+	0.848104i
$585$	−0.472277	+	0.818008i	−0.0195263	+	0.0338205i
$586$	−14.1257	+	24.4665i	−0.583529	+	1.01070i
$587$	−3.57595	+	6.19373i	−0.147595	+	0.255643i	−0.930338	−	0.366703i	$-0.880487\pi$
$587$	−3.57595	+	6.19373i	−0.147595	+	0.255643i	0.782743	+	0.622345i	$0.213820\pi$
$588$	7.56790			0.312095
$589$	−37.1741			−1.53173
$590$	−12.3787	+	21.4405i	−0.509622	+	0.882692i
$591$	−1.58406	−	2.74367i	−0.0651595	−	0.112860i
$592$	−0.509826	−	0.883045i	−0.0209537	−	0.0362929i
$593$	−4.54991	+	7.88068i	−0.186843	+	0.323621i	−0.944196	−	0.329385i	$-0.893159\pi$
$593$	−4.54991	+	7.88068i	−0.186843	+	0.323621i	0.757353	+	0.653005i	$0.226492\pi$
$594$	4.73528			0.194291
$595$	−5.27225			−0.216141
$596$	−0.107803	−	0.186721i	−0.00441580	−	0.00764839i
$597$	−4.83354	+	8.37195i	−0.197824	+	0.342641i
$598$	1.10540			0.0452030
$599$	8.98649	+	15.5651i	0.367178	+	0.635971i	0.989123	−	0.147090i	$-0.0469906\pi$
$599$	8.98649	+	15.5651i	0.367178	+	0.635971i	−0.621945	+	0.783061i	$0.713657\pi$
$600$	−18.0538			−0.737043
$601$	−3.36513	+	5.82857i	−0.137266	+	0.237752i	−0.926461	−	0.376391i	$-0.877165\pi$
$601$	−3.36513	+	5.82857i	−0.137266	+	0.237752i	0.789195	+	0.614143i	$0.210498\pi$
$602$	−3.77623			−0.153908
$603$	0.0778994	−	8.18498i	0.00317231	−	0.333318i
$604$	23.2495			0.946008
$605$	−27.3524	+	47.3758i	−1.11204	+	1.92610i
$606$	−13.0549			−0.530317
$607$	19.2274	+	33.3027i	0.780414	+	1.35172i	0.931701	+	0.363227i	$0.118325\pi$
$607$	19.2274	+	33.3027i	0.780414	+	1.35172i	−0.151287	+	0.988490i	$0.548342\pi$
$608$	42.9198			1.74063
$609$	−3.99679	+	6.92264i	−0.161958	+	0.280520i
$610$	−15.1506	−	26.2416i	−0.613430	−	1.06249i
$611$	2.15565			0.0872082
$612$	2.43328			0.0983596
$613$	0.374123	−	0.648000i	0.0151107	−	0.0261725i	−0.858371	−	0.513029i	$-0.828523\pi$
$613$	0.374123	−	0.648000i	0.0151107	−	0.0261725i	0.873482	+	0.486857i	$0.161857\pi$
$614$	5.05252	+	8.75123i	0.203903	+	0.353171i
$615$	16.9217	+	29.3092i	0.682349	+	1.18186i
$616$	5.72544	−	9.91675i	0.230684	−	0.399557i
$617$	35.6174			1.43390			0.716950	−	0.697124i	$-0.245537\pi$
$617$	35.6174			1.43390			0.716950	+	0.697124i	$0.245537\pi$
$618$	−3.74096			−0.150483
$619$	0.134275	−	0.232571i	0.00539697	−	0.00934783i	−0.863314	−	0.504667i	$-0.831615\pi$
$619$	0.134275	−	0.232571i	0.00539697	−	0.00934783i	0.868711	+	0.495319i	$0.164949\pi$
$620$	−9.47688	+	16.4144i	−0.380600	+	0.659219i
$621$	−2.16711	+	3.75354i	−0.0869629	+	0.150624i
$622$	4.24921	−	7.35984i	0.170378	−	0.295103i
$623$	1.43317	+	2.48231i	0.0574186	+	0.0994518i
$624$	0.0357093	+	0.0618504i	0.00142952	+	0.00247600i
$625$	−17.0605			−0.682420
$626$	11.9514	−	20.7005i	0.477675	−	0.827357i
$627$	40.5386			1.61895
$628$	−0.992483			−0.0396044
$629$	−4.14734	−	7.18340i	−0.165365	−	0.286421i
$630$	2.31444			0.0922094
$631$	−10.1226	+	17.5329i	−0.402975	+	0.697972i	−0.994083	−	0.108619i	$-0.965357\pi$
$631$	−10.1226	+	17.5329i	−0.402975	+	0.697972i	0.591109	+	0.806592i	$0.298690\pi$
$632$	−5.93531	−	10.2803i	−0.236094	−	0.408927i
$633$	−6.35073	+	10.9998i	−0.252419	+	0.437202i
$634$	−11.4209	−	19.7816i	−0.453582	−	0.785628i
$635$	1.71059	+	2.96284i	0.0678829	+	0.117577i
$636$	−0.449874	−	0.779204i	−0.0178387	−	0.0308975i
$637$	0.903466	+	1.56485i	0.0357966	+	0.0620016i
$638$	−24.8769	−	43.0881i	−0.984887	−	1.70587i
$639$	1.04970	+	1.81814i	0.0415256	+	0.0719245i
$640$	10.1695	−	17.6142i	0.401987	−	0.696261i
$641$	5.14645	+	8.91391i	0.203273	+	0.352078i	0.949581	−	0.313522i	$-0.101509\pi$
$641$	5.14645	+	8.91391i	0.203273	+	0.352078i	−0.746308	+	0.665600i	$0.768176\pi$
$642$	−5.95384	+	10.3123i	−0.234979	+	0.406996i
$643$	−10.3290			−0.407338			−0.203669	−	0.979040i	$-0.565287\pi$
$643$	−10.3290			−0.407338			−0.203669	+	0.979040i	$0.565287\pi$
$644$	1.94312	+	3.36557i	0.0765695	+	0.132622i
$645$	−18.3831			−0.723832
$646$	−14.5185			−0.571225
$647$	−2.41633	+	4.18520i	−0.0949956	+	0.164537i	−0.909607	−	0.415470i	$-0.863617\pi$
$647$	−2.41633	+	4.18520i	−0.0949956	+	0.164537i	0.814611	+	0.580007i	$0.196950\pi$
$648$	−2.88082			−0.113169
$649$	−21.2594	−	36.8224i	−0.834506	−	1.44541i
$650$	−0.799153	−	1.38417i	−0.0313454	−	0.0542918i
$651$	1.82249	−	3.15664i	0.0714290	−	0.123719i
$652$	0.834717	−	1.44577i	0.0326900	−	0.0566208i
$653$	−19.0879	+	33.0613i	−0.746968	+	1.29379i	0.202301	+	0.979323i	$0.435158\pi$
$653$	−19.0879	+	33.0613i	−0.746968	+	1.29379i	−0.949270	+	0.314463i	$0.898175\pi$
$654$	−3.81279	+	6.60394i	−0.149092	+	0.258235i
$655$	−21.5465			−0.841892
$656$	2.55893			0.0999095
$657$	4.10751	−	7.11442i	0.160249	−	0.277560i
$658$	−2.64099	−	4.57432i	−0.102956	−	0.178326i
$659$	−16.0525	−	27.8037i	−0.625317	−	1.08308i	−0.988480	−	0.151354i	$-0.951637\pi$
$659$	−16.0525	−	27.8037i	−0.625317	−	1.08308i	0.363163	−	0.931726i	$-0.381697\pi$
$660$	10.3346	−	17.9000i	0.402273	−	0.696757i
$661$	−11.5036			−0.447438			−0.223719	−	0.974654i	$-0.571820\pi$
$661$	−11.5036			−0.447438			−0.223719	+	0.974654i	$0.571820\pi$
$662$	23.7290			0.922254
$663$	0.290488	+	0.503141i	0.0112816	+	0.0195404i
$664$	9.24995	−	16.0214i	0.358968	−	0.621750i
$665$	19.8138			0.768347
$666$	1.82062	+	3.15340i	0.0705474	+	0.122192i
$667$	45.5398			1.76331
$668$	5.08869	−	8.81386i	0.196887	−	0.341019i
$669$	26.5085			1.02488
$670$	21.4457	+	12.6553i	0.828520	+	0.488918i
$671$	52.0400			2.00898
$672$	−2.10418	+	3.64454i	−0.0811704	+	0.140591i
$673$	−30.6520			−1.18155			−0.590774	−	0.806837i	$-0.701178\pi$
$673$	−30.6520			−1.18155			−0.590774	+	0.806837i	$0.701178\pi$
$674$	11.8561	+	20.5353i	0.456678	+	0.790990i
$675$	6.26689			0.241213
$676$	−7.61409	+	13.1880i	−0.292850	+	0.507231i
$677$	10.2992	+	17.8387i	0.395829	+	0.685595i	0.993207	−	0.116365i	$-0.0371241\pi$
$677$	10.2992	+	17.8387i	0.395829	+	0.685595i	−0.597378	+	0.801960i	$0.703791\pi$
$678$	−4.54278			−0.174464
$679$	−3.47938			−0.133526
$680$	−9.98211	+	17.2895i	−0.382796	+	0.663023i
$681$	−10.6148	−	18.3853i	−0.406759	−	0.704528i
$682$	11.3436	+	19.6477i	0.434368	+	0.752348i
$683$	−11.6194	+	20.1254i	−0.444604	+	0.770077i	−0.998025	−	0.0628252i	$-0.979989\pi$
$683$	−11.6194	+	20.1254i	−0.444604	+	0.770077i	0.553420	+	0.832902i	$0.313322\pi$
$684$	−9.14459			−0.349652
$685$	−11.1108			−0.424522
$686$	4.62706	−	8.01430i	0.176662	−	0.305987i
$687$	0.543083	−	0.940648i	0.0207199	−	0.0358880i
$688$	−0.694980	+	1.20374i	−0.0264959	+	0.0458922i
$689$	0.107413	−	0.186045i	0.00409211	−	0.00708775i
$690$	−6.59273	−	11.4189i	−0.250981	−	0.434712i
$691$	−14.6112	−	25.3073i	−0.555836	−	0.962737i	−0.997838	−	0.0657226i	$-0.979065\pi$
$691$	−14.6112	−	25.3073i	−0.555836	−	0.962737i	0.442002	−	0.897014i	$-0.354269\pi$
$692$	−5.00134			−0.190123
$693$	−1.98743	+	3.44234i	−0.0754963	+	0.130763i
$694$	30.6946			1.16515
$695$	−12.4392			−0.471846
$696$	15.1345	+	26.2137i	0.573670	+	0.993626i
$697$	20.8164			0.788478
$698$	−13.9266	+	24.1215i	−0.527128	+	0.913013i
$699$	0.573224	+	0.992853i	0.0216813	+	0.0375532i
$700$	2.80958	−	4.86633i	0.106192	−	0.183930i
$701$	1.15088	+	1.99337i	0.0434680	+	0.0752887i	0.886941	−	0.461883i	$-0.152826\pi$
$701$	1.15088	+	1.99337i	0.0434680	+	0.0752887i	−0.843473	+	0.537172i	$0.819493\pi$
$702$	−0.127520	−	0.220871i	−0.00481293	−	0.00833623i
$703$	15.5862	+	26.9961i	0.587846	+	1.01818i
$704$	−14.4229	−	24.9812i	−0.543583	−	0.941513i
$705$	−12.8566	−	22.2682i	−0.484207	−	0.838670i
$706$	−9.08045	−	15.7278i	−0.341747	−	0.591924i
$707$	5.47923	−	9.49030i	0.206068	−	0.356919i
$708$	4.79565	+	8.30631i	0.180232	+	0.312170i
$709$	−2.57895	+	4.46687i	−0.0968545	+	0.167757i	−0.910381	−	0.413771i	$-0.864211\pi$
$709$	−2.57895	+	4.46687i	−0.0968545	+	0.167757i	0.813527	+	0.581528i	$0.197545\pi$
$710$	−6.38678			−0.239692
$711$	2.06029	+	3.56852i	0.0772668	+	0.133830i
$712$	10.8538			0.406764
$713$	−20.7656			−0.777678
$714$	0.711783	−	1.23284i	0.0266378	−	0.0461380i
$715$	4.93502			0.184559
$716$	−10.7378	−	18.5985i	−0.401292	−	0.695057i
$717$	5.57475	+	9.65574i	0.208193	+	0.360600i
$718$	−7.80731	+	13.5227i	−0.291366	+	0.504661i
$719$	−4.82385	+	8.35515i	−0.179899	+	0.311595i	−0.941846	−	0.336045i	$-0.890910\pi$
$719$	−4.82385	+	8.35515i	−0.179899	+	0.311595i	0.761947	+	0.647640i	$0.224244\pi$
$720$	0.425950	−	0.737768i	0.0158742	−	0.0274950i
$721$	1.57011	−	2.71951i	0.0584739	−	0.101280i
$722$	37.3424			1.38974
$723$	−1.83905			−0.0683948
$724$	−10.8452	+	18.7844i	−0.403058	+	0.698117i
$725$	−32.9233	−	57.0248i	−1.22274	−	2.11785i
$726$	−7.38545	−	12.7920i	−0.274100	−	0.474755i
$727$	15.4591	−	26.7760i	0.573348	−	0.993068i	−0.422871	−	0.906190i	$-0.638978\pi$
$727$	15.4591	−	26.7760i	0.573348	−	0.993068i	0.996219	−	0.0868778i	$-0.0276890\pi$
$728$	−0.616738			−0.0228578
$729$	1.00000			0.0370370
$730$	12.4958	+	21.6434i	0.462491	+	0.801057i
$731$	−5.65353	+	9.79220i	−0.209103	+	0.362178i
$732$	−11.7391			−0.433888
$733$	19.7567	+	34.2196i	0.729731	+	1.26393i	0.956997	+	0.290098i	$0.0936879\pi$
$733$	19.7567	+	34.2196i	0.729731	+	1.26393i	−0.227266	+	0.973833i	$0.572979\pi$
$734$	−25.3140			−0.934356
$735$	10.7768	−	18.6659i	0.397508	−	0.688503i
$736$	23.9752			0.883737
$737$	−37.2384	+	21.0296i	−1.37169	+	0.774636i
$738$	−9.13808			−0.336377
$739$	−11.8264	+	20.4839i	−0.435040	+	0.753512i	−0.997299	−	0.0734494i	$-0.976599\pi$
$739$	−11.8264	+	20.4839i	−0.435040	+	0.753512i	0.562259	+	0.826962i	$0.309933\pi$
$740$	15.8937			0.584265
$741$	−1.09169	−	1.89087i	−0.0401044	−	0.0694628i
$742$	−0.526388			−0.0193243
$743$	18.5197	−	32.0771i	0.679422	−	1.17679i	−0.295733	−	0.955271i	$-0.595564\pi$
$743$	18.5197	−	32.0771i	0.679422	−	1.17679i	0.975155	−	0.221523i	$-0.0711029\pi$
$744$	−6.90114	−	11.9531i	−0.253008	−	0.438223i
$745$	−0.614054			−0.0224972
$746$	5.78089			0.211653
$747$	−3.21087	+	5.56140i	−0.117480	+	0.203481i
$748$	−6.35660	−	11.0100i	−0.232420	−	0.402564i
$749$	−4.99774	−	8.65635i	−0.182614	−	0.316296i
$750$	−1.92706	+	3.33777i	−0.0703663	+	0.121878i
$751$	22.1684			0.808937			0.404468	−	0.914552i	$-0.367457\pi$
$751$	22.1684			0.808937			0.404468	+	0.914552i	$0.367457\pi$
$752$	−1.94420			−0.0708975
$753$	−9.69268	+	16.7882i	−0.353221	+	0.611797i
$754$	−1.33986	+	2.32070i	−0.0487948	+	0.0845150i
$755$	33.1076	−	57.3440i	1.20491	−	2.08696i
$756$	0.448320	−	0.776514i	0.0163053	−	0.0282415i
$757$	14.8994	+	25.8065i	0.541528	+	0.937954i	0.998817	+	0.0486359i	$0.0154874\pi$
$757$	14.8994	+	25.8065i	0.541528	+	0.937954i	−0.457288	+	0.889318i	$0.651179\pi$
$758$	−0.432846	−	0.749712i	−0.0157217	−	0.0272308i
$759$	22.6450			0.821961
$760$	37.5141	−	64.9763i	1.36078	−	2.35694i
$761$	27.9709			1.01394			0.506972	−	0.861962i	$-0.330765\pi$
$761$	27.9709			1.01394			0.506972	+	0.861962i	$0.330765\pi$
$762$	−0.923758			−0.0334642
$763$	−3.20051	−	5.54345i	−0.115866	−	0.200687i
$764$	−10.8062			−0.390955
$765$	3.46502	−	6.00160i	0.125278	−	0.216988i
$766$	−4.11116	−	7.12074i	−0.148542	−	0.257283i
$767$	−1.14502	+	1.98324i	−0.0413444	+	0.0716105i
$768$	8.26691	+	14.3187i	0.298307	+	0.516682i
$769$	2.73493	+	4.73704i	0.0986241	+	0.170822i	0.911115	−	0.412151i	$-0.135223\pi$
$769$	2.73493	+	4.73704i	0.0986241	+	0.170822i	−0.812491	+	0.582973i	$0.801889\pi$
$770$	−6.04613	−	10.4722i	−0.217888	−	0.377392i
$771$	−2.30266	−	3.98832i	−0.0829282	−	0.143636i
$772$	−15.5112	−	26.8661i	−0.558259	−	0.966933i
$773$	−16.5540	−	28.6724i	−0.595408	−	1.03128i	−0.993489	−	0.113926i	$-0.963657\pi$
$773$	−16.5540	−	28.6724i	−0.595408	−	1.03128i	0.398082	−	0.917350i	$-0.369676\pi$
$774$	2.48181	−	4.29862i	0.0892068	−	0.154511i
$775$	15.0126	+	26.0027i	0.539270	+	0.934043i
$776$	−6.58761	+	11.4101i	−0.236481	+	0.409598i
$777$	−3.05651			−0.109652
$778$	5.17543	+	8.96410i	0.185548	+	0.321379i
$779$	−78.2308			−2.80291
$780$	−1.11323			−0.0398601
$781$	5.48440	−	9.49926i	0.196247	−	0.339910i
$782$	−8.11012			−0.290017
$783$	−5.25353	−	9.09938i	−0.187746	−	0.325185i
$784$	−0.814843	−	1.41135i	−0.0291015	−	0.0504053i
$785$	−1.41331	+	2.44792i	−0.0504431	+	0.0873701i
$786$	2.90890	−	5.03835i	0.103757	−	0.179712i
$787$	−7.46282	+	12.9260i	−0.266021	+	0.460761i	−0.967831	−	0.251603i	$-0.919042\pi$
$787$	−7.46282	+	12.9260i	−0.266021	+	0.460761i	0.701810	+	0.712364i	$0.252376\pi$
$788$	1.86694	−	3.23363i	0.0665069	−	0.115193i
$789$	−16.9451			−0.603262
$790$	−12.5355			−0.445994
$791$	1.90664	−	3.30240i	0.0677923	−	0.117420i
$792$	7.52573	+	13.0349i	0.267415	+	0.463176i
$793$	−1.40142	−	2.42734i	−0.0497660	−	0.0861973i
$794$	12.0656	−	20.8983i	0.428193	−	0.741651i
$795$	−2.56250			−0.0908826
$796$	−11.3934			−0.403829
$797$	−27.4135	−	47.4815i	−0.971035	−	1.68188i	−0.692444	−	0.721472i	$-0.743466\pi$
$797$	−27.4135	−	47.4815i	−0.971035	−	1.68188i	−0.278591	−	0.960410i	$-0.589867\pi$
$798$	−2.67497	+	4.63319i	−0.0946930	+	0.164013i
$799$	−15.8157			−0.559518
$800$	−17.3330	−	30.0217i	−0.612815	−	1.06143i
$801$	−3.76761			−0.133122
$802$	−13.3321	+	23.0919i	−0.470774	+	0.815404i
$803$	−42.9212			−1.51465
$804$	8.40014	−	4.74381i	0.296250	−	0.167301i
$805$	11.0681			0.390099
$806$	0.610960	−	1.05821i	0.0215201	−	0.0372740i
$807$	−6.36617			−0.224100
$808$	−20.7479	−	35.9365i	−0.729910	−	1.26424i
$809$	−44.0493			−1.54869			−0.774345	−	0.632763i	$-0.781921\pi$
$809$	−44.0493			−1.54869			−0.774345	+	0.632763i	$0.781921\pi$
$810$	−1.52109	+	2.63461i	−0.0534457	+	0.0925707i
$811$	−20.6819	−	35.8221i	−0.726240	−	1.25788i	−0.958462	−	0.285222i	$-0.907933\pi$
$811$	−20.6819	−	35.8221i	−0.726240	−	1.25788i	0.232222	−	0.972663i	$-0.425401\pi$
$812$	−9.42106			−0.330614
$813$	9.52019			0.333888
$814$	9.51219	−	16.4756i	0.333402	−	0.577469i
$815$	−2.37729	−	4.11759i	−0.0832730	−	0.144233i
$816$	−0.261994	−	0.453787i	−0.00917162	−	0.0158857i
$817$	21.2467	−	36.8004i	0.743328	−	1.28748i
$818$	13.1067			0.458266
$819$	0.214084			0.00748071
$820$	−19.9435	+	34.5432i	−0.696459	+	1.20630i
$821$	19.1458	−	33.1616i	0.668194	−	1.15735i	−0.310215	−	0.950667i	$-0.600401\pi$
$821$	19.1458	−	33.1616i	0.668194	−	1.15735i	0.978409	−	0.206680i	$-0.0662658\pi$
$822$	1.50002	−	2.59811i	0.0523191	−	0.0906194i
$823$	−11.3018	+	19.5752i	−0.393955	+	0.682349i	−0.992967	−	0.118390i	$-0.962227\pi$
$823$	−11.3018	+	19.5752i	−0.393955	+	0.682349i	0.599012	+	0.800740i	$0.295560\pi$
$824$	−5.94546	−	10.2978i	−0.207120	−	0.358742i
$825$	−16.3714	−	28.3560i	−0.569978	−	0.987230i
$826$	5.61129			0.195242
$827$	−1.15827	+	2.00617i	−0.0402768	+	0.0697615i	−0.885461	−	0.464714i	$-0.846157\pi$
$827$	−1.15827	+	2.00617i	−0.0402768	+	0.0697615i	0.845184	+	0.534475i	$0.179491\pi$
$828$	−5.10821			−0.177522
$829$	−3.05210			−0.106004			−0.0530018	−	0.998594i	$-0.516879\pi$
$829$	−3.05210			−0.106004			−0.0530018	+	0.998594i	$0.516879\pi$
$830$	−9.76806	−	16.9188i	−0.339054	−	0.587260i
$831$	−8.01791			−0.278138
$832$	−0.776810	+	1.34547i	−0.0269310	+	0.0466459i
$833$	−6.62859	−	11.4811i	−0.229667	−	0.397795i
$834$	1.67936	−	2.90874i	0.0581515	−	0.100721i
$835$	−14.4927	−	25.1021i	−0.501541	−	0.868694i
$836$	23.8889	+	41.3768i	0.826216	+	1.43105i
$837$	2.39555	+	4.14921i	0.0828022	+	0.143418i
$838$	−4.17548	−	7.23214i	−0.144240	−	0.249830i
$839$	20.9738	+	36.3277i	0.724097	+	1.25417i	0.959345	+	0.282237i	$0.0910764\pi$
$839$	20.9738	+	36.3277i	0.724097	+	1.25417i	−0.235248	+	0.971935i	$0.575590\pi$
$840$	3.67831	+	6.37102i	0.126914	+	0.219821i
$841$	−40.6991	+	70.4930i	−1.40342	+	2.43079i
$842$	8.15048	+	14.1170i	0.280884	+	0.486506i
$843$	3.28109	−	5.68302i	0.113007	−	0.195734i
$844$	−14.9697			−0.515277
$845$	21.6851	+	37.5597i	0.745991	+	1.29209i
$846$	6.94282			0.238699
$847$	12.3989			0.426032
$848$	−0.0968767	+	0.167795i	−0.00332676	+	0.00576212i
$849$	27.3905			0.940040
$850$	5.86327	+	10.1555i	0.201108	+	0.348330i
$851$	8.70653	+	15.0802i	0.298456	+	0.516941i
$852$	−1.23716	+	2.14282i	−0.0423843	+	0.0734118i
$853$	9.80425	−	16.9815i	0.335691	−	0.581434i	−0.647926	−	0.761703i	$-0.724363\pi$
$853$	9.80425	−	16.9815i	0.335691	−	0.581434i	0.983617	+	0.180269i	$0.0576968\pi$
$854$	−3.43391	+	5.94770i	−0.117506	+	0.203526i
$855$	−13.0220	+	22.5548i	−0.445343	+	0.771357i
$856$	−37.8495			−1.29367
$857$	−5.00228			−0.170875			−0.0854373	−	0.996344i	$-0.527229\pi$
$857$	−5.00228			−0.170875			−0.0854373	+	0.996344i	$0.527229\pi$
$858$	−0.666255	+	1.15399i	−0.0227456	+	0.0393965i
$859$	−2.81401	−	4.87401i	−0.0960127	−	0.166299i	0.814018	−	0.580840i	$-0.197276\pi$
$859$	−2.81401	−	4.87401i	−0.0960127	−	0.166299i	−0.910031	+	0.414541i	$0.863942\pi$
$860$	−10.8329	−	18.7632i	−0.369400	−	0.639819i
$861$	3.83532	−	6.64298i	0.130707	−	0.226392i
$862$	−11.2181			−0.382088
$863$	13.4220			0.456890			0.228445	−	0.973557i	$-0.426636\pi$
$863$	13.4220			0.456890			0.228445	+	0.973557i	$0.426636\pi$
$864$	−2.76581	−	4.79052i	−0.0940947	−	0.162977i
$865$	−7.12197	+	12.3356i	−0.242154	+	0.419424i
$866$	5.15975			0.175335
$867$	6.36873	+	11.0310i	0.216293	+	0.374631i
$868$	4.29589			0.145812
$869$	10.7644	−	18.6445i	0.365157	−	0.632471i
$870$	31.9644			1.08369
$871$	1.98372	+	1.17061i	0.0672157	+	0.0396647i
$872$	−24.2385			−0.820819
$873$	2.28671	−	3.96071i	0.0773935	−	0.134050i
$874$	30.4789			1.03096
$875$	−1.61761	−	2.80178i	−0.0546850	−	0.0947173i
$876$	9.68205			0.327126
$877$	−21.4278	+	37.1140i	−0.723565	+	1.25325i	0.235996	+	0.971754i	$0.424165\pi$
$877$	−21.4278	+	37.1140i	−0.723565	+	1.25325i	−0.959562	+	0.281498i	$0.909169\pi$
$878$	4.15913	+	7.20382i	0.140364	+	0.243117i
$879$	31.1715			1.05139
$880$	−4.45094			−0.150041
$881$	0.805006	−	1.39431i	0.0271213	−	0.0469755i	−0.852146	−	0.523304i	$-0.824699\pi$
$881$	0.805006	−	1.39431i	0.0271213	−	0.0469755i	0.879268	+	0.476328i	$0.158033\pi$
$882$	2.90985	+	5.04000i	0.0979796	+	0.169706i
$883$	5.56486	+	9.63862i	0.187273	+	0.324366i	0.944340	−	0.328971i	$-0.106702\pi$
$883$	5.56486	+	9.63862i	0.187273	+	0.324366i	−0.757067	+	0.653337i	$0.773369\pi$
$884$	−0.342363	+	0.592991i	−0.0115149	+	0.0199444i
$885$	27.3163			0.918227
$886$	31.2359			1.04939
$887$	−12.8975	+	22.3391i	−0.433056	+	0.750075i	−0.997135	−	0.0756462i	$-0.975898\pi$
$887$	−12.8975	+	22.3391i	−0.433056	+	0.750075i	0.564079	+	0.825721i	$0.309231\pi$
$888$	−5.78697	+	10.0233i	−0.194198	+	0.336361i
$889$	0.387708	−	0.671530i	0.0130033	−	0.0225224i
$890$	5.73088	−	9.92618i	0.192100	−	0.332726i
$891$	−2.61236	−	4.52473i	−0.0875172	−	0.151584i
$892$	15.6211	+	27.0566i	0.523034	+	0.905922i
$893$	59.4373			1.98899
$894$	0.0829005	−	0.143588i	0.00277261	−	0.00480230i
$895$	−61.1632			−2.04446
$896$	−4.60988			−0.154005
$897$	−0.609824	−	1.05625i	−0.0203614	−	0.0352670i
$898$	29.6826			0.990523
$899$	25.1702	−	43.5960i	0.839472	−	1.45401i
$900$	3.69301	+	6.39648i	0.123100	+	0.213216i
$901$	−0.788073	+	1.36498i	−0.0262545	+	0.0454742i
$902$	23.8719	+	41.3474i	0.794848	+	1.37672i
$903$	2.08327	+	3.60833i	0.0693269	+	0.120078i
$904$	−7.21979	−	12.5050i	−0.240127	−	0.415912i
$905$	30.8874	+	53.4985i	1.02673	+	1.77835i
$906$	8.93940	+	15.4835i	0.296992	+	0.514404i
$907$	−2.77734	−	4.81050i	−0.0922202	−	0.159730i	0.816225	−	0.577734i	$-0.196063\pi$
$907$	−2.77734	−	4.81050i	−0.0922202	−	0.159730i	−0.908445	+	0.418004i	$0.862730\pi$
$908$	12.5104	−	21.6686i	0.415171	−	0.719097i
$909$	7.20210	+	12.4744i	0.238879	+	0.413750i
$910$	−0.325642	+	0.564028i	−0.0107949	+	0.0186973i
$911$	−32.7793			−1.08603			−0.543014	−	0.839724i	$-0.682717\pi$
$911$	−32.7793			−1.08603			−0.543014	+	0.839724i	$0.682717\pi$
$912$	0.984607	+	1.70539i	0.0326036	+	0.0564711i
$913$	33.5518			1.11040
$914$	0.219548			0.00726199
$915$	−16.7166	+	28.9539i	−0.552633	+	0.957188i
$916$	1.28013			0.0422968
$917$	2.44177	+	4.22927i	0.0806344	+	0.139663i
$918$	0.935594	+	1.62050i	0.0308792	+	0.0534843i
$919$	6.38111	−	11.0524i	0.210493	−	0.364585i	−0.741376	−	0.671090i	$-0.765826\pi$
$919$	6.38111	−	11.0524i	0.210493	−	0.364585i	0.951869	+	0.306505i	$0.0991597\pi$
$920$	20.9555	−	36.2960i	0.690883	−	1.19664i
$921$	5.57475	−	9.65574i	0.183694	−	0.318168i
$922$	12.3896	−	21.4595i	0.408031	−	0.706731i
$923$	−0.590774			−0.0194456
$924$	−4.68469			−0.154115
$925$	12.5889	−	21.8046i	0.413920	−	0.716931i
$926$	10.3020	+	17.8436i	0.338544	+	0.586376i
$927$	2.06381	+	3.57462i	0.0677844	+	0.117406i
$928$	−29.0605	+	50.3343i	−0.953958	+	1.65230i
$929$	12.1365			0.398187			0.199093	−	0.979981i	$-0.436200\pi$
$929$	12.1365			0.398187			0.199093	+	0.979981i	$0.436200\pi$
$930$	−14.5754			−0.477946
$931$	24.9111	+	43.1473i	0.816428	+	1.41410i
$932$	−0.675590	+	1.17016i	−0.0221297	+	0.0383297i
$933$	−9.37680			−0.306983
$934$	13.0476	+	22.5990i	0.426929	+	0.739463i
$935$	−36.2075			−1.18411
$936$	0.405332	−	0.702055i	0.0132487	−	0.0229474i
$937$	19.1801			0.626587			0.313294	−	0.949656i	$-0.398568\pi$
$937$	19.1801			0.626587			0.313294	+	0.949656i	$0.398568\pi$
$938$	0.0537128	−	5.64366i	0.00175378	−	0.184272i
$939$	−26.3734			−0.860664
$940$	15.1525	−	26.2449i	0.494219	−	0.856013i
$941$	−21.1715			−0.690171			−0.345085	−	0.938571i	$-0.612150\pi$
$941$	−21.1715			−0.690171			−0.345085	+	0.938571i	$0.612150\pi$
$942$	−0.381608	−	0.660965i	−0.0124335	−	0.0215354i
$943$	−43.7000			−1.42307
$944$	1.03270	−	1.78870i	0.0336117	−	0.0582171i
$945$	−1.27683	−	2.21153i	−0.0415352	−	0.0719411i
$946$	−25.9335			−0.843171
$947$	21.0128			0.682824			0.341412	−	0.939914i	$-0.389095\pi$
$947$	21.0128			0.682824			0.341412	+	0.939914i	$0.389095\pi$
$948$	−2.42821	+	4.20578i	−0.0788646	+	0.136597i
$949$	1.15586	+	2.00200i	0.0375207	+	0.0649877i
$950$	−22.0349	−	38.1656i	−0.714907	−	1.23826i
$951$	−12.6014	+	21.8262i	−0.408627	+	0.707763i
$952$	4.52491			0.146653
$953$	8.36629			0.271011			0.135505	−	0.990777i	$-0.456734\pi$
$953$	8.36629			0.271011			0.135505	+	0.990777i	$0.456734\pi$
$954$	0.345952	−	0.599206i	0.0112006	−	0.0194000i
$955$	−15.3882	+	26.6531i	−0.497950	+	0.862475i
$956$	−6.57027	+	11.3800i	−0.212498	+	0.368057i
$957$	−27.4482	+	47.5416i	−0.887273	+	1.53680i
$958$	7.52313	+	13.0304i	0.243061	+	0.420994i
$959$	1.25914	+	2.18089i	0.0406597	+	0.0704246i
$960$	18.5320			0.598117
$961$	4.02271	−	6.96754i	0.129765	−	0.224759i
$962$	−1.02464			−0.0330358
$963$	13.1384			0.423380
$964$	−1.08373	−	1.87707i	−0.0349046	−	0.0604565i
$965$	−88.3524			−2.84416
$966$	−1.49425	+	2.58812i	−0.0480767	+	0.0832713i
$967$	−11.1256	−	19.2701i	−0.357775	−	0.619684i	0.629814	−	0.776746i	$-0.283131\pi$
$967$	−11.1256	−	19.2701i	−0.357775	−	0.619684i	−0.987589	+	0.157062i	$0.949798\pi$
$968$	23.4752	−	40.6603i	0.754523	−	1.30687i
$969$	8.00959	+	13.8730i	0.257305	+	0.445665i
$970$	6.95660	+	12.0492i	0.223363	+	0.386876i
$971$	2.90960	+	5.03957i	0.0933734	+	0.161728i	0.908929	−	0.416952i	$-0.136902\pi$
$971$	2.90960	+	5.03957i	0.0933734	+	0.161728i	−0.815555	+	0.578679i	$0.803568\pi$
$972$	0.589289	+	1.02068i	0.0189015	+	0.0327383i
$973$	1.40968	+	2.44164i	0.0451923	+	0.0782753i
$974$	5.17719	+	8.96716i	0.165888	+	0.287326i
$975$	−0.881753	+	1.52724i	−0.0282387	+	0.0489109i
$976$	1.26396	+	2.18924i	0.0404582	+	0.0700757i
$977$	6.56724	−	11.3748i	0.210105	−	0.363912i	−0.741643	−	0.670795i	$-0.765953\pi$
$977$	6.56724	−	11.3748i	0.210105	−	0.363912i	0.951747	+	0.306884i	$0.0992862\pi$
$978$	1.28379			0.0410511
$979$	9.84234	+	17.0474i	0.314563	+	0.544838i
$980$	25.4026			0.811455
$981$	8.41375			0.268630
$982$	7.94421	−	13.7598i	0.253510	−	0.439092i
$983$	−24.0218			−0.766177			−0.383089	−	0.923712i	$-0.625140\pi$
$983$	−24.0218			−0.766177			−0.383089	+	0.923712i	$0.625140\pi$
$984$	−14.5231	−	25.1547i	−0.462978	−	0.801901i
$985$	−5.31708	−	9.20946i	−0.169416	−	0.293438i
$986$	9.83034	−	17.0266i	0.313062	−	0.542239i
$987$	−2.91396	+	5.04712i	−0.0927523	+	0.160652i
$988$	1.28665	−	2.22854i	0.0409337	−	0.0708992i
$989$	11.8685	−	20.5568i	0.377396	−	0.653669i
$990$	15.8945			0.505161
$991$	38.3105			1.21697			0.608486	−	0.793564i	$-0.291777\pi$
$991$	38.3105			1.21697			0.608486	+	0.793564i	$0.291777\pi$
$992$	13.2512	−	22.9518i	0.420728	−	0.728721i
$993$	−13.0908	−	22.6739i	−0.415424	−	0.719535i
$994$	0.723786	+	1.25363i	0.0229571	+	0.0397628i
$995$	−16.2244	+	28.1014i	−0.514347	+	0.890875i
$996$	−7.56853			−0.239818
$997$	−12.5186			−0.396469			−0.198235	−	0.980155i	$-0.563521\pi$
$997$	−12.5186			−0.396469			−0.198235	+	0.980155i	$0.563521\pi$
$998$	16.8217	+	29.1361i	0.532482	+	0.922286i
$999$	2.00879	−	3.47933i	0.0635554	−	0.110081i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.e.c.163.2	yes	10
3.2	odd	2		603.2.g.f.163.4		10
67.37	even	3	inner	201.2.e.c.37.2	✓	10
201.104	odd	6		603.2.g.f.37.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.e.c.37.2	✓	10	67.37	even	3	inner
201.2.e.c.163.2	yes	10	1.1	even	1	trivial
603.2.g.f.37.4		10	201.104	odd	6
603.2.g.f.163.4		10	3.2	odd	2

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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	201.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453162 + 0.784899i) q^{2} +1.00000 q^{3} +(0.589289 + 1.02068i) q^{4} +3.35662 q^{5} +(-0.453162 + 0.784899i) q^{6} +(-0.380391 - 0.658856i) q^{7} -2.88082 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.453162 + 0.784899i) q^{2} +1.00000 q^{3} +(0.589289 + 1.02068i) q^{4} +3.35662 q^{5} +(-0.453162 + 0.784899i) q^{6} +(-0.380391 - 0.658856i) q^{7} -2.88082 q^{8} +1.00000 q^{9} +(-1.52109 + 2.63461i) q^{10} +(-2.61236 - 4.52473i) q^{11} +(0.589289 + 1.02068i) q^{12} +(-0.140700 + 0.243700i) q^{13} +0.689514 q^{14} +3.35662 q^{15} +(0.126899 - 0.219795i) q^{16} +(1.03230 - 1.78799i) q^{17} +(-0.453162 + 0.784899i) q^{18} +(-3.87950 + 6.71949i) q^{19} +(1.97802 + 3.42603i) q^{20} +(-0.380391 - 0.658856i) q^{21} +4.73528 q^{22} +(-2.16711 + 3.75354i) q^{23} -2.88082 q^{24} +6.26689 q^{25} +(-0.127520 - 0.220871i) q^{26} +1.00000 q^{27} +(0.448320 - 0.776514i) q^{28} +(-5.25353 - 9.09938i) q^{29} +(-1.52109 + 2.63461i) q^{30} +(2.39555 + 4.14921i) q^{31} +(-2.76581 - 4.79052i) q^{32} +(-2.61236 - 4.52473i) q^{33} +(0.935594 + 1.62050i) q^{34} +(-1.27683 - 2.21153i) q^{35} +(0.589289 + 1.02068i) q^{36} +(2.00879 - 3.47933i) q^{37} +(-3.51608 - 6.09003i) q^{38} +(-0.140700 + 0.243700i) q^{39} -9.66981 q^{40} +(5.04129 + 8.73177i) q^{41} +0.689514 q^{42} -5.47666 q^{43} +(3.07887 - 5.33275i) q^{44} +3.35662 q^{45} +(-1.96410 - 3.40192i) q^{46} +(-3.83021 - 6.63413i) q^{47} +(0.126899 - 0.219795i) q^{48} +(3.21061 - 5.56093i) q^{49} +(-2.83992 + 4.91888i) q^{50} +(1.03230 - 1.78799i) q^{51} -0.331652 q^{52} -0.763418 q^{53} +(-0.453162 + 0.784899i) q^{54} +(-8.76868 - 15.1878i) q^{55} +(1.09584 + 1.89805i) q^{56} +(-3.87950 + 6.71949i) q^{57} +9.52279 q^{58} +8.13803 q^{59} +(1.97802 + 3.42603i) q^{60} +(-4.98018 + 8.62592i) q^{61} -4.34228 q^{62} +(-0.380391 - 0.658856i) q^{63} +5.52103 q^{64} +(-0.472277 + 0.818008i) q^{65} +4.73528 q^{66} +(0.0778994 - 8.18498i) q^{67} +2.43328 q^{68} +(-2.16711 + 3.75354i) q^{69} +2.31444 q^{70} +(1.04970 + 1.81814i) q^{71} -2.88082 q^{72} +(4.10751 - 7.11442i) q^{73} +(1.82062 + 3.15340i) q^{74} +6.26689 q^{75} -9.14459 q^{76} +(-1.98743 + 3.44234i) q^{77} +(-0.127520 - 0.220871i) q^{78} +(2.06029 + 3.56852i) q^{79} +(0.425950 - 0.737768i) q^{80} +1.00000 q^{81} -9.13808 q^{82} +(-3.21087 + 5.56140i) q^{83} +(0.448320 - 0.776514i) q^{84} +(3.46502 - 6.00160i) q^{85} +(2.48181 - 4.29862i) q^{86} +(-5.25353 - 9.09938i) q^{87} +(7.52573 + 13.0349i) q^{88} -3.76761 q^{89} +(-1.52109 + 2.63461i) q^{90} +0.214084 q^{91} -5.10821 q^{92} +(2.39555 + 4.14921i) q^{93} +6.94282 q^{94} +(-13.0220 + 22.5548i) q^{95} +(-2.76581 - 4.79052i) q^{96} +(2.28671 - 3.96071i) q^{97} +(2.90985 + 5.04000i) q^{98} +(-2.61236 - 4.52473i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} + 10 q^{9}+O(q^{10}) \) 10 * q + 10 * q^3 - 6 * q^4 + 6 * q^5 - q^7 + 10 * q^9	\( 10 q + 10 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} + 10 q^{9} - 12 q^{10} + 6 q^{11} - 6 q^{12} - q^{13} - 6 q^{14} + 6 q^{15} - 24 q^{16} + 8 q^{17} - 5 q^{19} - 8 q^{20} - q^{21} + 22 q^{22} - 7 q^{23} - 8 q^{25} - 17 q^{26} + 10 q^{27} + 3 q^{28} - 12 q^{29} - 12 q^{30} - 12 q^{31} - 5 q^{32} + 6 q^{33} - 5 q^{35} - 6 q^{36} - 17 q^{37} + 30 q^{38} - q^{39} + 34 q^{40} + 13 q^{41} - 6 q^{42} - 4 q^{43} + 43 q^{44} + 6 q^{45} - 26 q^{46} - 25 q^{47} - 24 q^{48} + 16 q^{49} - 25 q^{50} + 8 q^{51} + 64 q^{52} - 12 q^{53} - 14 q^{55} - 11 q^{56} - 5 q^{57} + 4 q^{58} - 12 q^{59} - 8 q^{60} + 9 q^{61} + 46 q^{62} - q^{63} + 64 q^{64} - 14 q^{65} + 22 q^{66} + 2 q^{67} - 98 q^{68} - 7 q^{69} + 2 q^{70} + 29 q^{71} + 12 q^{73} + 15 q^{74} - 8 q^{75} - 6 q^{76} + 4 q^{77} - 17 q^{78} - q^{79} - 13 q^{80} + 10 q^{81} - 2 q^{82} - 6 q^{83} + 3 q^{84} + 9 q^{85} - 21 q^{86} - 12 q^{87} + 18 q^{88} - 4 q^{89} - 12 q^{90} - 40 q^{91} - 12 q^{93} + 30 q^{94} - 14 q^{95} - 5 q^{96} + 11 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + 10 * q^3 - 6 * q^4 + 6 * q^5 - q^7 + 10 * q^9 - 12 * q^10 + 6 * q^11 - 6 * q^12 - q^13 - 6 * q^14 + 6 * q^15 - 24 * q^16 + 8 * q^17 - 5 * q^19 - 8 * q^20 - q^21 + 22 * q^22 - 7 * q^23 - 8 * q^25 - 17 * q^26 + 10 * q^27 + 3 * q^28 - 12 * q^29 - 12 * q^30 - 12 * q^31 - 5 * q^32 + 6 * q^33 - 5 * q^35 - 6 * q^36 - 17 * q^37 + 30 * q^38 - q^39 + 34 * q^40 + 13 * q^41 - 6 * q^42 - 4 * q^43 + 43 * q^44 + 6 * q^45 - 26 * q^46 - 25 * q^47 - 24 * q^48 + 16 * q^49 - 25 * q^50 + 8 * q^51 + 64 * q^52 - 12 * q^53 - 14 * q^55 - 11 * q^56 - 5 * q^57 + 4 * q^58 - 12 * q^59 - 8 * q^60 + 9 * q^61 + 46 * q^62 - q^63 + 64 * q^64 - 14 * q^65 + 22 * q^66 + 2 * q^67 - 98 * q^68 - 7 * q^69 + 2 * q^70 + 29 * q^71 + 12 * q^73 + 15 * q^74 - 8 * q^75 - 6 * q^76 + 4 * q^77 - 17 * q^78 - q^79 - 13 * q^80 + 10 * q^81 - 2 * q^82 - 6 * q^83 + 3 * q^84 + 9 * q^85 - 21 * q^86 - 12 * q^87 + 18 * q^88 - 4 * q^89 - 12 * q^90 - 40 * q^91 - 12 * q^93 + 30 * q^94 - 14 * q^95 - 5 * q^96 + 11 * q^97 + 12 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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