LMFDB - Embedded newform 45.2.e.b.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,2,Mod(16,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, 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("45.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	45.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:	$0.359326809096$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.2
Root			$-1.62241 + 0.606458i$ of defining polynomial
Character	$\chi$	$=$	45.16
Dual form			45.2.e.b.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.285997 + 0.495361i) q^{2} +(0.285997 - 1.70828i) q^{3} +(0.836412 + 1.44871i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.764419 + 0.630233i) q^{6} +(-0.714003 + 1.23669i) q^{7} -2.10083 q^{8} +(-2.83641 - 0.977122i) q^{9} +O(q^{10})$	\(q+(-0.285997 + 0.495361i) q^{2} +(0.285997 - 1.70828i) q^{3} +(0.836412 + 1.44871i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.764419 + 0.630233i) q^{6} +(-0.714003 + 1.23669i) q^{7} -2.10083 q^{8} +(-2.83641 - 0.977122i) q^{9} +0.571993 q^{10} +(-1.33641 + 2.31473i) q^{11} +(2.71400 - 1.01450i) q^{12} +(-2.33641 - 4.04678i) q^{13} +(-0.408405 - 0.707378i) q^{14} +(-1.62241 + 0.606458i) q^{15} +(-1.07199 + 1.85675i) q^{16} +2.67282 q^{17} +(1.29523 - 1.12559i) q^{18} +4.67282 q^{19} +(0.836412 - 1.44871i) q^{20} +(1.90841 + 1.57340i) q^{21} +(-0.764419 - 1.32401i) q^{22} +(2.95882 + 5.12483i) q^{23} +(-0.600830 + 3.58880i) q^{24} +(-0.500000 + 0.866025i) q^{25} +2.67282 q^{26} +(-2.48040 + 4.56592i) q^{27} -2.38880 q^{28} +(4.74482 - 8.21826i) q^{29} +(0.163588 - 0.977122i) q^{30} +(-3.48040 - 6.02823i) q^{31} +(-2.71400 - 4.70079i) q^{32} +(3.57199 + 2.94497i) q^{33} +(-0.764419 + 1.32401i) q^{34} +1.42801 q^{35} +(-0.956844 - 4.92641i) q^{36} -1.81681 q^{37} +(-1.33641 + 2.31473i) q^{38} +(-7.58123 + 2.83387i) q^{39} +(1.05042 + 1.81937i) q^{40} +(0.735581 + 1.27406i) q^{41} +(-1.32520 + 0.495361i) q^{42} +(-0.235581 + 0.408039i) q^{43} -4.47116 q^{44} +(0.571993 + 2.94497i) q^{45} -3.38485 q^{46} +(-3.47842 + 6.02480i) q^{47} +(2.86525 + 2.36228i) q^{48} +(2.48040 + 4.29618i) q^{49} +(-0.285997 - 0.495361i) q^{50} +(0.764419 - 4.56592i) q^{51} +(3.90841 - 6.76956i) q^{52} -1.14399 q^{53} +(-1.55239 - 2.53453i) q^{54} +2.67282 q^{55} +(1.50000 - 2.59808i) q^{56} +(1.33641 - 7.98247i) q^{57} +(2.71400 + 4.70079i) q^{58} +(0.571993 + 0.990721i) q^{59} +(-2.23558 - 1.84315i) q^{60} +(1.26442 - 2.19004i) q^{61} +3.98153 q^{62} +(3.23360 - 2.81009i) q^{63} -1.18319 q^{64} +(-2.33641 + 4.04678i) q^{65} +(-2.48040 + 0.927175i) q^{66} +(3.29523 + 5.70751i) q^{67} +(2.23558 + 3.87214i) q^{68} +(9.60083 - 3.58880i) q^{69} +(-0.408405 + 0.707378i) q^{70} -12.8745 q^{71} +(5.95882 + 2.05277i) q^{72} -1.71203 q^{73} +(0.519602 - 0.899976i) q^{74} +(1.33641 + 1.10182i) q^{75} +(3.90841 + 6.76956i) q^{76} +(-1.90841 - 3.30545i) q^{77} +(0.764419 - 4.56592i) q^{78} +(0.143987 - 0.249392i) q^{79} +2.14399 q^{80} +(7.09046 + 5.54304i) q^{81} -0.841495 q^{82} +(2.14201 - 3.71007i) q^{83} +(-0.683190 + 4.08074i) q^{84} +(-1.33641 - 2.31473i) q^{85} +(-0.134751 - 0.233396i) q^{86} +(-12.6821 - 10.4559i) q^{87} +(2.80757 - 4.86286i) q^{88} -3.00000 q^{89} +(-1.62241 - 0.558907i) q^{90} +6.67282 q^{91} +(-4.94958 + 8.57293i) q^{92} +(-11.2933 + 4.22143i) q^{93} +(-1.98963 - 3.44615i) q^{94} +(-2.33641 - 4.04678i) q^{95} +(-8.80644 + 3.29186i) q^{96} +(-3.91764 + 6.78555i) q^{97} -2.83754 q^{98} +(6.05239 - 5.25970i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} + q^{3} - 5 q^{4} - 3 q^{5} - 4 q^{6} - 5 q^{7} + 6 q^{8} - 7 q^{9}+O(q^{10}) $ 6 * q - q^2 + q^3 - 5 * q^4 - 3 * q^5 - 4 * q^6 - 5 * q^7 + 6 * q^8 - 7 * q^9	\( 6 q - q^{2} + q^{3} - 5 q^{4} - 3 q^{5} - 4 q^{6} - 5 q^{7} + 6 q^{8} - 7 q^{9} + 2 q^{10} + 2 q^{11} + 17 q^{12} - 4 q^{13} + 9 q^{14} + q^{15} - 5 q^{16} - 4 q^{17} - 23 q^{18} + 8 q^{19} - 5 q^{20} + 4 q^{22} - 3 q^{23} + 15 q^{24} - 3 q^{25} - 4 q^{26} - 2 q^{27} + 10 q^{28} + 7 q^{29} + 11 q^{30} - 8 q^{31} - 17 q^{32} + 20 q^{33} + 4 q^{34} + 10 q^{35} + 10 q^{36} + 12 q^{37} + 2 q^{38} - 14 q^{39} - 3 q^{40} + 13 q^{41} - 33 q^{42} - 10 q^{43} - 44 q^{44} + 2 q^{45} - 6 q^{46} - 13 q^{47} - 10 q^{48} + 2 q^{49} - q^{50} - 4 q^{51} + 12 q^{52} - 4 q^{53} + 5 q^{54} - 4 q^{55} + 9 q^{56} - 2 q^{57} + 17 q^{58} + 2 q^{59} - 22 q^{60} - q^{61} + 84 q^{62} + 33 q^{63} - 30 q^{64} - 4 q^{65} - 2 q^{66} - 11 q^{67} + 22 q^{68} + 39 q^{69} + 9 q^{70} - 20 q^{71} + 15 q^{72} - 16 q^{73} + 16 q^{74} - 2 q^{75} + 12 q^{76} - 4 q^{78} - 2 q^{79} + 10 q^{80} - 19 q^{81} - 58 q^{82} + 15 q^{83} - 27 q^{84} + 2 q^{85} - 28 q^{86} - 26 q^{87} + 24 q^{88} - 18 q^{89} + q^{90} + 20 q^{91} - 39 q^{92} - 42 q^{93} + 31 q^{94} - 4 q^{95} + 13 q^{96} + 18 q^{97} - 80 q^{98} + 22 q^{99}+O(q^{100}) \) 6 * q - q^2 + q^3 - 5 * q^4 - 3 * q^5 - 4 * q^6 - 5 * q^7 + 6 * q^8 - 7 * q^9 + 2 * q^10 + 2 * q^11 + 17 * q^12 - 4 * q^13 + 9 * q^14 + q^15 - 5 * q^16 - 4 * q^17 - 23 * q^18 + 8 * q^19 - 5 * q^20 + 4 * q^22 - 3 * q^23 + 15 * q^24 - 3 * q^25 - 4 * q^26 - 2 * q^27 + 10 * q^28 + 7 * q^29 + 11 * q^30 - 8 * q^31 - 17 * q^32 + 20 * q^33 + 4 * q^34 + 10 * q^35 + 10 * q^36 + 12 * q^37 + 2 * q^38 - 14 * q^39 - 3 * q^40 + 13 * q^41 - 33 * q^42 - 10 * q^43 - 44 * q^44 + 2 * q^45 - 6 * q^46 - 13 * q^47 - 10 * q^48 + 2 * q^49 - q^50 - 4 * q^51 + 12 * q^52 - 4 * q^53 + 5 * q^54 - 4 * q^55 + 9 * q^56 - 2 * q^57 + 17 * q^58 + 2 * q^59 - 22 * q^60 - q^61 + 84 * q^62 + 33 * q^63 - 30 * q^64 - 4 * q^65 - 2 * q^66 - 11 * q^67 + 22 * q^68 + 39 * q^69 + 9 * q^70 - 20 * q^71 + 15 * q^72 - 16 * q^73 + 16 * q^74 - 2 * q^75 + 12 * q^76 - 4 * q^78 - 2 * q^79 + 10 * q^80 - 19 * q^81 - 58 * q^82 + 15 * q^83 - 27 * q^84 + 2 * q^85 - 28 * q^86 - 26 * q^87 + 24 * q^88 - 18 * q^89 + q^90 + 20 * q^91 - 39 * q^92 - 42 * q^93 + 31 * q^94 - 4 * q^95 + 13 * q^96 + 18 * q^97 - 80 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.285997	+	0.495361i	−0.202230	+	0.350273i	−0.949247	−	0.314533i	$-0.898152\pi$
$2$	−0.285997	+	0.495361i	−0.202230	+	0.350273i	0.747017	+	0.664805i	$0.231486\pi$
$3$	0.285997	−	1.70828i	0.165120	−	0.986273i
$3$	0.285997	−	1.70828i	0.165120	−	0.986273i
$4$	0.836412	+	1.44871i	0.418206	+	0.724354i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.764419	+	0.630233i	0.312073	+	0.257291i
$7$	−0.714003	+	1.23669i	−0.269868	+	0.467425i	−0.968828	−	0.247736i	$-0.920313\pi$
$7$	−0.714003	+	1.23669i	−0.269868	+	0.467425i	0.698960	+	0.715161i	$0.253647\pi$
$8$	−2.10083			−0.742756
$9$	−2.83641	−	0.977122i	−0.945471	−	0.325707i
$10$	0.571993			0.180880
$11$	−1.33641	+	2.31473i	−0.402943	+	0.697918i	−0.994080	−	0.108653i	$-0.965346\pi$
$11$	−1.33641	+	2.31473i	−0.402943	+	0.697918i	0.591136	+	0.806572i	$0.298679\pi$
$12$	2.71400	−	1.01450i	0.783465	−	0.292860i
$13$	−2.33641	−	4.04678i	−0.648004	−	1.12238i	−0.983599	−	0.180370i	$-0.942271\pi$
$13$	−2.33641	−	4.04678i	−0.648004	−	1.12238i	0.335595	−	0.942006i	$-0.391063\pi$
$14$	−0.408405	−	0.707378i	−0.109151	−	0.189055i
$15$	−1.62241	+	0.606458i	−0.418904	+	0.156587i
$16$	−1.07199	+	1.85675i	−0.267998	+	0.464187i
$17$	2.67282			0.648255			0.324127	−	0.946013i	$-0.394929\pi$
$17$	2.67282			0.648255			0.324127	+	0.946013i	$0.394929\pi$
$18$	1.29523	−	1.12559i	0.305289	−	0.265305i
$19$	4.67282			1.07202			0.536010	−	0.844212i	$-0.319931\pi$
$19$	4.67282			1.07202			0.536010	+	0.844212i	$0.319931\pi$
$20$	0.836412	−	1.44871i	0.187027	−	0.323941i
$21$	1.90841	+	1.57340i	0.416448	+	0.343345i
$22$	−0.764419	−	1.32401i	−0.162975	−	0.282280i
$23$	2.95882	+	5.12483i	0.616957	+	1.06860i	0.990038	+	0.140802i	$0.0449680\pi$
$23$	2.95882	+	5.12483i	0.616957	+	1.06860i	−0.373081	+	0.927799i	$0.621699\pi$
$24$	−0.600830	+	3.58880i	−0.122644	+	0.732560i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.67282			0.524184
$27$	−2.48040	+	4.56592i	−0.477353	+	0.878712i
$28$	−2.38880			−0.451441
$29$	4.74482	−	8.21826i	0.881090	−	1.52609i	0.0309603	−	0.999521i	$-0.490143\pi$
$29$	4.74482	−	8.21826i	0.881090	−	1.52609i	0.850130	−	0.526573i	$-0.176523\pi$
$30$	0.163588	−	0.977122i	0.0298670	−	0.178397i
$31$	−3.48040	−	6.02823i	−0.625098	−	1.08270i	−0.988522	−	0.151078i	$-0.951726\pi$
$31$	−3.48040	−	6.02823i	−0.625098	−	1.08270i	0.363424	−	0.931624i	$-0.381608\pi$
$32$	−2.71400	−	4.70079i	−0.479773	−	0.830990i
$33$	3.57199	+	2.94497i	0.621804	+	0.512653i
$34$	−0.764419	+	1.32401i	−0.131097	+	0.227066i
$35$	1.42801			0.241377
$36$	−0.956844	−	4.92641i	−0.159474	−	0.821068i
$37$	−1.81681			−0.298682			−0.149341	−	0.988786i	$-0.547715\pi$
$37$	−1.81681			−0.298682			−0.149341	+	0.988786i	$0.547715\pi$
$38$	−1.33641	+	2.31473i	−0.216795	+	0.375499i
$39$	−7.58123	+	2.83387i	−1.21397	+	0.453782i
$40$	1.05042	+	1.81937i	0.166085	+	0.287668i
$41$	0.735581	+	1.27406i	0.114879	+	0.198975i	0.917731	−	0.397202i	$-0.130019\pi$
$41$	0.735581	+	1.27406i	0.114879	+	0.198975i	−0.802853	+	0.596177i	$0.796685\pi$
$42$	−1.32520	+	0.495361i	−0.204483	+	0.0764358i
$43$	−0.235581	+	0.408039i	−0.0359258	+	0.0622254i	−0.883429	−	0.468565i	$-0.844771\pi$
$43$	−0.235581	+	0.408039i	−0.0359258	+	0.0622254i	0.847503	+	0.530790i	$0.178105\pi$
$44$	−4.47116			−0.674053
$45$	0.571993	+	2.94497i	0.0852677	+	0.439010i
$46$	−3.38485			−0.499069
$47$	−3.47842	+	6.02480i	−0.507380	+	0.878808i	0.492584	+	0.870265i	$0.336053\pi$
$47$	−3.47842	+	6.02480i	−0.507380	+	0.878808i	−0.999964	+	0.00854274i	$0.997281\pi$
$48$	2.86525	+	2.36228i	0.413563	+	0.340966i
$49$	2.48040	+	4.29618i	0.354343	+	0.613739i
$50$	−0.285997	−	0.495361i	−0.0404460	−	0.0700546i
$51$	0.764419	−	4.56592i	0.107040	−	0.639357i
$52$	3.90841	−	6.76956i	0.541998	−	0.938769i
$53$	−1.14399			−0.157139			−0.0785693	−	0.996909i	$-0.525035\pi$
$53$	−1.14399			−0.157139			−0.0785693	+	0.996909i	$0.525035\pi$
$54$	−1.55239	−	2.53453i	−0.211254	−	0.344906i
$55$	2.67282			0.360403
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$	1.33641	−	7.98247i	0.177012	−	1.05730i
$58$	2.71400	+	4.70079i	0.356366	+	0.617244i
$59$	0.571993	+	0.990721i	0.0744672	+	0.128981i	0.900854	−	0.434121i	$-0.142941\pi$
$59$	0.571993	+	0.990721i	0.0744672	+	0.128981i	−0.826387	+	0.563102i	$0.809608\pi$
$60$	−2.23558	−	1.84315i	−0.288612	−	0.237949i
$61$	1.26442	−	2.19004i	0.161892	−	0.280406i	−0.773655	−	0.633607i	$-0.781574\pi$
$61$	1.26442	−	2.19004i	0.161892	−	0.280406i	0.935547	+	0.353201i	$0.114907\pi$
$62$	3.98153			0.505655
$63$	3.23360	−	2.81009i	0.407396	−	0.354039i
$64$	−1.18319			−0.147899
$65$	−2.33641	+	4.04678i	−0.289796	+	0.501942i
$66$	−2.48040	+	0.927175i	−0.305316	+	0.114127i
$67$	3.29523	+	5.70751i	0.402577	+	0.697283i	0.994036	−	0.109051i	$-0.0347813\pi$
$67$	3.29523	+	5.70751i	0.402577	+	0.697283i	−0.591459	+	0.806335i	$0.701448\pi$
$68$	2.23558	+	3.87214i	0.271104	+	0.469566i
$69$	9.60083	−	3.58880i	1.15580	−	0.432040i
$70$	−0.408405	+	0.707378i	−0.0488137	+	0.0845479i
$71$	−12.8745			−1.52792			−0.763960	−	0.645263i	$-0.776748\pi$
$71$	−12.8745			−1.52792			−0.763960	+	0.645263i	$0.776748\pi$
$72$	5.95882	+	2.05277i	0.702254	+	0.241921i
$73$	−1.71203			−0.200378			−0.100189	−	0.994968i	$-0.531945\pi$
$73$	−1.71203			−0.200378			−0.100189	+	0.994968i	$0.531945\pi$
$74$	0.519602	−	0.899976i	0.0604025	−	0.104620i
$75$	1.33641	+	1.10182i	0.154316	+	0.127227i
$76$	3.90841	+	6.76956i	0.448325	+	0.776521i
$77$	−1.90841	−	3.30545i	−0.217483	−	0.376692i
$78$	0.764419	−	4.56592i	0.0865534	−	0.516989i
$79$	0.143987	−	0.249392i	0.0161998	−	0.0280588i	−0.857812	−	0.513964i	$-0.828177\pi$
$79$	0.143987	−	0.249392i	0.0161998	−	0.0280588i	0.874012	+	0.485905i	$0.161510\pi$
$80$	2.14399			0.239705
$81$	7.09046	+	5.54304i	0.787829	+	0.615894i
$82$	−0.841495			−0.0929276
$83$	2.14201	−	3.71007i	0.235116	−	0.407233i	−0.724190	−	0.689600i	$-0.757786\pi$
$83$	2.14201	−	3.71007i	0.235116	−	0.407233i	0.959306	+	0.282367i	$0.0911196\pi$
$84$	−0.683190	+	4.08074i	−0.0745421	+	0.445245i
$85$	−1.33641	−	2.31473i	−0.144954	−	0.251068i
$86$	−0.134751	−	0.233396i	−0.0145306	−	0.0251677i
$87$	−12.6821	−	10.4559i	−1.35966	−	1.12098i
$88$	2.80757	−	4.86286i	0.299288	−	0.518383i
$89$	−3.00000			−0.317999			−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000			−0.317999			−0.159000	+	0.987279i	$0.550827\pi$
$90$	−1.62241	−	0.558907i	−0.171017	−	0.0589140i
$91$	6.67282			0.699502
$92$	−4.94958	+	8.57293i	−0.516030	+	0.893790i
$93$	−11.2933	+	4.22143i	−1.17106	+	0.437742i
$94$	−1.98963	−	3.44615i	−0.205215	−	0.355443i
$95$	−2.33641	−	4.04678i	−0.239711	−	0.415191i
$96$	−8.80644	+	3.29186i	−0.898804	+	0.335974i
$97$	−3.91764	+	6.78555i	−0.397776	+	0.688968i	−0.993451	−	0.114257i	$-0.963551\pi$
$97$	−3.91764	+	6.78555i	−0.397776	+	0.688968i	0.595675	+	0.803225i	$0.296885\pi$
$98$	−2.83754			−0.286635
$99$	6.05239	−	5.25970i	0.608288	−	0.528620i
$100$	−1.67282			−0.167282
$101$	2.10083	−	3.63875i	0.209040	−	0.362069i	−0.742372	−	0.669988i	$-0.766299\pi$
$101$	2.10083	−	3.63875i	0.209040	−	0.362069i	0.951413	+	0.307919i	$0.0996326\pi$
$102$	2.04316	+	1.68450i	0.202303	+	0.166790i
$103$	0.908405	+	1.57340i	0.0895078	+	0.155032i	0.907303	−	0.420477i	$-0.138137\pi$
$103$	0.908405	+	1.57340i	0.0895078	+	0.155032i	−0.817795	+	0.575509i	$0.804804\pi$
$104$	4.90841	+	8.50161i	0.481309	+	0.833651i
$105$	0.408405	−	2.43943i	0.0398563	−	0.238064i
$106$	0.327176	−	0.566686i	0.0317782	−	0.0550414i
$107$	11.9176			1.15212			0.576061	−	0.817407i	$-0.304589\pi$
$107$	11.9176			1.15212			0.576061	+	0.817407i	$0.304589\pi$
$108$	−8.68932	+	0.225617i	−0.836130	+	0.0217100i
$109$	−16.6521			−1.59498			−0.797491	−	0.603331i	$-0.793840\pi$
$109$	−16.6521			−1.59498			−0.797491	+	0.603331i	$0.793840\pi$
$110$	−0.764419	+	1.32401i	−0.0728845	+	0.126240i
$111$	−0.519602	+	3.10361i	−0.0493184	+	0.294582i
$112$	−1.53081	−	2.65145i	−0.144648	−	0.250538i
$113$	−10.0616	−	17.4272i	−0.946518	−	1.63942i	−0.752682	−	0.658384i	$-0.771240\pi$
$113$	−10.0616	−	17.4272i	−0.946518	−	1.63942i	−0.193836	−	0.981034i	$-0.562093\pi$
$114$	3.57199	+	2.94497i	0.334548	+	0.275821i
$115$	2.95882	−	5.12483i	0.275911	−	0.477893i
$116$	15.8745			1.47391
$117$	2.67282	+	13.7613i	0.247103	+	1.27223i
$118$	−0.654353			−0.0602380
$119$	−1.90841	+	3.30545i	−0.174943	+	0.303011i
$120$	3.40841	−	1.27406i	0.311143	−	0.116306i
$121$	1.92801	+	3.33941i	0.175273	+	0.303582i
$122$	0.723239	+	1.25269i	0.0654790	+	0.113413i
$123$	2.38683	−	0.892198i	0.215213	−	0.0804468i
$124$	5.82209	−	10.0842i	0.522839	−	0.905584i
$125$	1.00000			0.0894427
$126$	0.467210	+	2.40548i	0.0416224	+	0.214297i
$127$	2.18714			0.194078			0.0970388	−	0.995281i	$-0.469063\pi$
$127$	2.18714			0.194078			0.0970388	+	0.995281i	$0.469063\pi$
$128$	5.76640	−	9.98769i	0.509682	−	0.882795i
$129$	0.629668	+	0.519136i	0.0554391	+	0.0457074i
$130$	−1.33641	−	2.31473i	−0.117211	−	0.203016i
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	0.966803	−	0.255524i	$-0.0822479\pi$
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	−0.704692	+	0.709514i	$0.748915\pi$
$132$	−1.27874	+	7.63798i	−0.111300	+	0.664801i
$133$	−3.33641	+	5.77883i	−0.289304	+	0.501089i
$134$	−3.76970			−0.325653
$135$	5.19440	−	0.134872i	0.447063	−	0.0116079i
$136$	−5.61515			−0.481495
$137$	5.10083	−	8.83490i	0.435793	−	0.754816i	−0.561567	−	0.827431i	$-0.689801\pi$
$137$	5.10083	−	8.83490i	0.435793	−	0.754816i	0.997360	+	0.0726153i	$0.0231345\pi$
$138$	−0.968056	+	5.78226i	−0.0824064	+	0.492218i
$139$	−4.00000	−	6.92820i	−0.339276	−	0.587643i	0.645021	−	0.764165i	$-0.276849\pi$
$139$	−4.00000	−	6.92820i	−0.339276	−	0.587643i	−0.984297	+	0.176522i	$0.943515\pi$
$140$	1.19440	+	2.06876i	0.100945	+	0.174843i
$141$	9.29721	+	7.66518i	0.782966	+	0.645524i
$142$	3.68206	−	6.37751i	0.308992	−	0.535189i
$143$	12.4896			1.04444
$144$	4.85488	−	4.21903i	0.404574	−	0.351586i
$145$	−9.48963			−0.788071
$146$	0.489634	−	0.848071i	0.0405224	−	0.0701868i
$147$	8.04844	−	3.00851i	0.663824	−	0.248138i
$148$	−1.51960	−	2.63203i	−0.124910	−	0.216351i
$149$	10.0381	+	17.3865i	0.822351	+	1.42435i	0.903927	+	0.427687i	$0.140671\pi$
$149$	10.0381	+	17.3865i	0.822351	+	1.42435i	−0.0815762	+	0.996667i	$0.525995\pi$
$150$	−0.928007	+	0.346890i	−0.0757714	+	0.0283234i
$151$	−1.51960	+	2.63203i	−0.123663	+	0.214191i	−0.921210	−	0.389066i	$-0.872798\pi$
$151$	−1.51960	+	2.63203i	−0.123663	+	0.214191i	0.797546	+	0.603258i	$0.206131\pi$
$152$	−9.81681			−0.796248
$153$	−7.58123	−	2.61168i	−0.612906	−	0.211141i
$154$	2.18319			0.175926
$155$	−3.48040	+	6.02823i	−0.279552	+	0.484199i
$156$	−10.4465	−	8.61270i	−0.836388	−	0.689568i
$157$	−0.100830	−	0.174643i	−0.00804714	−	0.0139381i	0.861974	−	0.506953i	$-0.169228\pi$
$157$	−0.100830	−	0.174643i	−0.00804714	−	0.0139381i	−0.870021	+	0.493015i	$0.835895\pi$
$158$	0.0823593	+	0.142651i	0.00655216	+	0.0113487i
$159$	−0.327176	+	1.95424i	−0.0259468	+	0.154982i
$160$	−2.71400	+	4.70079i	−0.214561	+	0.371630i
$161$	−8.45043			−0.665987
$162$	−4.77365	+	1.92705i	−0.375054	+	0.151403i
$163$	17.8168			1.39552			0.697760	−	0.716331i	$-0.254180\pi$
$163$	17.8168			1.39552			0.697760	+	0.716331i	$0.254180\pi$
$164$	−1.23050	+	2.13129i	−0.0960858	+	0.166425i
$165$	0.764419	−	4.56592i	0.0595099	−	0.355456i
$166$	1.22522	+	2.12214i	0.0950952	+	0.164710i
$167$	−7.05042	−	12.2117i	−0.545578	−	0.944968i	−0.998570	−	0.0534538i	$-0.982977\pi$
$167$	−7.05042	−	12.2117i	−0.545578	−	0.944968i	0.452993	−	0.891514i	$-0.350356\pi$
$168$	−4.00924	−	3.30545i	−0.309319	−	0.255021i
$169$	−4.41764	+	7.65158i	−0.339819	+	0.588583i
$170$	1.52884			0.117256
$171$	−13.2541	−	4.56592i	−1.01356	−	0.349165i
$172$	−0.788172			−0.0600976
$173$	−2.18319	+	3.78140i	−0.165985	+	0.287494i	−0.937005	−	0.349317i	$-0.886414\pi$
$173$	−2.18319	+	3.78140i	−0.165985	+	0.287494i	0.771020	+	0.636811i	$0.219747\pi$
$174$	8.80644	−	3.29186i	0.667615	−	0.249555i
$175$	−0.714003	−	1.23669i	−0.0539736	−	0.0934850i
$176$	−2.86525	−	4.96276i	−0.215976	−	0.374082i
$177$	1.85601	−	0.693779i	0.139507	−	0.0521476i
$178$	0.857990	−	1.48608i	0.0643091	−	0.111387i
$179$	−15.1625			−1.13330			−0.566648	−	0.823960i	$-0.691760\pi$
$179$	−15.1625			−1.13330			−0.566648	+	0.823960i	$0.691760\pi$
$180$	−3.78797	+	3.29186i	−0.282339	+	0.245360i
$181$	3.20166			0.237978			0.118989	−	0.992896i	$-0.462035\pi$
$181$	3.20166			0.237978			0.118989	+	0.992896i	$0.462035\pi$
$182$	−1.90841	+	3.30545i	−0.141460	+	0.245017i
$183$	−3.37957	−	2.78632i	−0.249825	−	0.205971i
$184$	−6.21598	−	10.7664i	−0.458248	−	0.793709i
$185$	0.908405	+	1.57340i	0.0667873	+	0.115679i
$186$	1.13870	−	6.80155i	0.0834938	−	0.498714i
$187$	−3.57199	+	6.18687i	−0.261210	+	0.452429i
$188$	−11.6376			−0.848757
$189$	−3.87562	−	6.32757i	−0.281910	−	0.460263i
$190$	2.67282			0.193907
$191$	1.41877	−	2.45738i	0.102659	−	0.177810i	−0.810121	−	0.586263i	$-0.800598\pi$
$191$	1.41877	−	2.45738i	0.102659	−	0.177810i	0.912779	+	0.408453i	$0.133932\pi$
$192$	−0.338388	+	2.02121i	−0.0244211	+	0.145869i
$193$	9.39409	+	16.2710i	0.676201	+	1.17121i	0.976116	+	0.217249i	$0.0697083\pi$
$193$	9.39409	+	16.2710i	0.676201	+	1.17121i	−0.299915	+	0.953966i	$0.596958\pi$
$194$	−2.24086	−	3.88129i	−0.160885	−	0.278660i
$195$	6.24482	+	5.14860i	0.447201	+	0.368699i
$196$	−4.14927	+	7.18675i	−0.296376	+	0.513339i
$197$	5.83528			0.415747			0.207873	−	0.978156i	$-0.433346\pi$
$197$	5.83528			0.415747			0.207873	+	0.978156i	$0.433346\pi$
$198$	0.874485	+	4.50237i	0.0621469	+	0.319970i
$199$	13.0761			0.926943			0.463472	−	0.886112i	$-0.346604\pi$
$199$	13.0761			0.926943			0.463472	+	0.886112i	$0.346604\pi$
$200$	1.05042	−	1.81937i	0.0742756	−	0.128649i
$201$	10.6924	−	3.99684i	0.754186	−	0.281915i
$202$	1.20166	+	2.08134i	0.0845486	+	0.146442i
$203$	6.77563	+	11.7357i	0.475556	+	0.823687i
$204$	7.25405	−	2.71157i	0.507885	−	0.189848i
$205$	0.735581	−	1.27406i	0.0513752	−	0.0889845i
$206$	−1.03920			−0.0724047
$207$	−3.38485	−	17.4272i	−0.235263	−	1.21128i
$208$	10.0185			0.694656
$209$	−6.24482	+	10.8163i	−0.431963	+	0.748182i
$210$	1.09159	+	0.899976i	0.0753272	+	0.0621043i
$211$	−4.19243	−	7.26149i	−0.288618	−	0.499902i	0.684862	−	0.728673i	$-0.259863\pi$
$211$	−4.19243	−	7.26149i	−0.288618	−	0.499902i	−0.973480	+	0.228771i	$0.926529\pi$
$212$	−0.956844	−	1.65730i	−0.0657163	−	0.113824i
$213$	−3.68206	+	21.9932i	−0.252291	+	1.50695i
$214$	−3.40841	+	5.90353i	−0.232994	+	0.403557i
$215$	0.471163			0.0321330
$216$	5.21090	−	9.59222i	0.354557	−	0.652668i
$217$	9.94006			0.674776
$218$	4.76244	−	8.24879i	0.322553	−	0.558679i
$219$	−0.489634	+	2.92461i	−0.0330864	+	0.197627i
$220$	2.23558	+	3.87214i	0.150723	+	0.261060i
$221$	−6.24482	−	10.8163i	−0.420072	−	0.727586i
$222$	−1.38880	−	1.14501i	−0.0932104	−	0.0768482i
$223$	−4.58321	+	7.93834i	−0.306914	+	0.531591i	−0.977686	−	0.210073i	$-0.932630\pi$
$223$	−4.58321	+	7.93834i	−0.306914	+	0.531591i	0.670772	+	0.741664i	$0.265963\pi$
$224$	7.75123			0.517901
$225$	2.26442	−	1.96784i	0.150961	−	0.131190i
$226$	11.5104			0.765658
$227$	1.33641	−	2.31473i	0.0887008	−	0.153634i	−0.818261	−	0.574846i	$-0.805062\pi$
$227$	1.33641	−	2.31473i	0.0887008	−	0.153634i	0.906962	+	0.421212i	$0.138395\pi$
$228$	12.6821	−	4.74056i	0.839890	−	0.313951i
$229$	−1.27365	−	2.20603i	−0.0841654	−	0.145779i	0.820870	−	0.571115i	$-0.193489\pi$
$229$	−1.27365	−	2.20603i	−0.0841654	−	0.145779i	−0.905035	+	0.425336i	$0.860156\pi$
$230$	1.69243	+	2.93137i	0.111595	+	0.193289i
$231$	−6.19243	+	2.31473i	−0.407432	+	0.152298i
$232$	−9.96806	+	17.2652i	−0.654435	+	1.13351i
$233$	−6.22013			−0.407494			−0.203747	−	0.979024i	$-0.565312\pi$
$233$	−6.22013			−0.407494			−0.203747	+	0.979024i	$0.565312\pi$
$234$	−7.58123	−	2.61168i	−0.495600	−	0.170731i
$235$	6.95684			0.453814
$236$	−0.956844	+	1.65730i	−0.0622852	+	0.107881i
$237$	−0.384851	−	0.317294i	−0.0249987	−	0.0206105i
$238$	−1.09159	−	1.89070i	−0.0707576	−	0.122556i
$239$	−4.06163	−	7.03494i	−0.262725	−	0.455053i	0.704240	−	0.709962i	$-0.251288\pi$
$239$	−4.06163	−	7.03494i	−0.262725	−	0.455053i	−0.966965	+	0.254909i	$0.917954\pi$
$240$	0.613173	−	3.66252i	0.0395801	−	0.236415i
$241$	13.1821	−	22.8320i	0.849131	−	1.47074i	−0.0328536	−	0.999460i	$-0.510460\pi$
$241$	13.1821	−	22.8320i	0.849131	−	1.47074i	0.881985	−	0.471278i	$-0.156207\pi$
$242$	−2.20561			−0.141782
$243$	11.4969	−	10.5272i	0.737526	−	0.675319i
$244$	4.23030			0.270817
$245$	2.48040	−	4.29618i	0.158467	−	0.274473i
$246$	−0.240665	+	1.43751i	−0.0153442	+	0.0916520i
$247$	−10.9176	−	18.9099i	−0.694673	−	1.20321i
$248$	7.31173	+	12.6643i	0.464295	+	0.804183i
$249$	−5.72522	−	4.72021i	−0.362821	−	0.299131i
$250$	−0.285997	+	0.495361i	−0.0180880	+	0.0313294i
$251$	−0.549569			−0.0346885			−0.0173443	−	0.999850i	$-0.505521\pi$
$251$	−0.549569			−0.0346885			−0.0173443	+	0.999850i	$0.505521\pi$
$252$	6.77563	+	2.33415i	0.426825	+	0.147038i
$253$	−15.8168			−0.994394
$254$	−0.625515	+	1.08342i	−0.0392483	+	0.0679801i
$255$	−4.33641	+	1.62095i	−0.271557	+	0.101508i
$256$	2.11515	+	3.66355i	0.132197	+	0.228972i
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	0.997374	+	0.0724199i	$0.0230722\pi$
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	−0.435970	+	0.899961i	$0.643595\pi$
$258$	−0.437242	+	0.163441i	−0.0272215	+	0.0101754i
$259$	1.29721	−	2.24683i	0.0806046	−	0.139611i
$260$	−7.81681			−0.484778
$261$	−21.4885	+	18.6741i	−1.33010	+	1.15590i
$262$	−3.43196			−0.212027
$263$	−5.94761	+	10.3016i	−0.366745	+	0.635221i	−0.989055	−	0.147550i	$-0.952861\pi$
$263$	−5.94761	+	10.3016i	−0.366745	+	0.635221i	0.622309	+	0.782771i	$0.286195\pi$
$264$	−7.50415	−	6.18687i	−0.461849	−	0.380776i
$265$	0.571993	+	0.990721i	0.0351373	+	0.0608595i
$266$	−1.90841	−	3.30545i	−0.117012	−	0.202670i
$267$	−0.857990	+	5.12483i	−0.0525081	+	0.313634i
$268$	−5.51234	+	9.54766i	−0.336720	+	0.583216i
$269$	28.5737			1.74217			0.871084	−	0.491134i	$-0.163417\pi$
$269$	28.5737			1.74217			0.871084	+	0.491134i	$0.163417\pi$
$270$	−1.41877	+	2.61168i	−0.0863437	+	0.158942i
$271$	−23.3641			−1.41927			−0.709635	−	0.704570i	$-0.751140\pi$
$271$	−23.3641			−1.41927			−0.709635	+	0.704570i	$0.751140\pi$
$272$	−2.86525	+	4.96276i	−0.173731	+	0.300911i
$273$	1.90841	−	11.3990i	0.115502	−	0.689900i
$274$	2.91764	+	5.05350i	0.176261	+	0.305293i
$275$	−1.33641	−	2.31473i	−0.0805887	−	0.139584i
$276$	13.2294	+	10.9071i	0.796314	+	0.656529i
$277$	7.53807	−	13.0563i	0.452919	−	0.784479i	−0.545647	−	0.838015i	$-0.683716\pi$
$277$	7.53807	−	13.0563i	0.452919	−	0.784479i	0.998566	+	0.0535366i	$0.0170494\pi$
$278$	4.57595			0.274447
$279$	3.98153	+	20.4993i	0.238368	+	1.22726i
$280$	−3.00000			−0.179284
$281$	−3.32605	+	5.76088i	−0.198415	+	0.343665i	−0.948015	−	0.318226i	$-0.896913\pi$
$281$	−3.32605	+	5.76088i	−0.198415	+	0.343665i	0.749599	+	0.661892i	$0.230246\pi$
$282$	−6.45600	+	2.41326i	−0.384449	+	0.143707i
$283$	−13.4485	−	23.2934i	−0.799428	−	1.38465i	−0.919989	−	0.391943i	$-0.871803\pi$
$283$	−13.4485	−	23.2934i	−0.799428	−	1.38465i	0.120562	−	0.992706i	$-0.461530\pi$
$284$	−10.7684	−	18.6514i	−0.638985	−	1.10675i
$285$	−7.58123	+	2.83387i	−0.449073	+	0.167864i
$286$	−3.57199	+	6.18687i	−0.211216	+	0.365838i
$287$	−2.10083			−0.124008
$288$	3.10478	+	15.9853i	0.182951	+	0.941943i
$289$	−9.85601			−0.579765
$290$	2.71400	−	4.70079i	0.159372	−	0.276040i
$291$	10.4712	+	8.63306i	0.613830	+	0.506079i
$292$	−1.43196	−	2.48023i	−0.0837991	−	0.145144i
$293$	−6.19243	−	10.7256i	−0.361765	−	0.626596i	0.626486	−	0.779433i	$-0.284493\pi$
$293$	−6.19243	−	10.7256i	−0.361765	−	0.626596i	−0.988251	+	0.152837i	$0.951159\pi$
$294$	−0.811528	+	4.84730i	−0.0473292	+	0.282701i
$295$	0.571993	−	0.990721i	0.0333027	−	0.0576820i
$296$	3.81681			0.221848
$297$	−7.25405	−	11.8434i	−0.420923	−	0.687224i
$298$	−11.4834			−0.665217
$299$	13.8260	−	23.9474i	0.799581	−	1.38491i
$300$	−0.478422	+	2.85764i	−0.0276217	+	0.164986i
$301$	−0.336412	−	0.582682i	−0.0193905	−	0.0335853i
$302$	−0.869202	−	1.50550i	−0.0500169	−	0.0866319i
$303$	−5.61515	−	4.62947i	−0.322582	−	0.265956i
$304$	−5.00924	+	8.67625i	−0.287299	+	0.497617i
$305$	−2.52884			−0.144801
$306$	3.46193	−	3.00851i	0.197905	−	0.171985i
$307$	−2.49359			−0.142317			−0.0711583	−	0.997465i	$-0.522670\pi$
$307$	−2.49359			−0.142317			−0.0711583	+	0.997465i	$0.522670\pi$
$308$	3.19243	−	5.52944i	0.181905	−	0.315069i
$309$	2.94761	−	1.10182i	0.167684	−	0.0626802i
$310$	−1.99076	−	3.44811i	−0.113068	−	0.195839i
$311$	12.1101	+	20.9752i	0.686699	+	1.18940i	0.972900	+	0.231228i	$0.0742742\pi$
$311$	12.1101	+	20.9752i	0.686699	+	1.18940i	−0.286201	+	0.958170i	$0.592392\pi$
$312$	15.9269	−	5.95348i	0.901682	−	0.337049i
$313$	17.5420	−	30.3837i	0.991534	−	1.71739i	0.383315	−	0.923618i	$-0.374782\pi$
$313$	17.5420	−	30.3837i	0.991534	−	1.71739i	0.608219	−	0.793770i	$-0.291884\pi$
$314$	0.115349			0.00650950
$315$	−4.05042	−	1.39534i	−0.228215	−	0.0786183i
$316$	0.481728			0.0270993
$317$	5.23558	−	9.06829i	0.294060	−	0.509326i	−0.680706	−	0.732557i	$-0.738327\pi$
$317$	5.23558	−	9.06829i	0.294060	−	0.509326i	0.974766	+	0.223231i	$0.0716603\pi$
$318$	−0.874485	−	0.720978i	−0.0490387	−	0.0404304i
$319$	12.6821	+	21.9660i	0.710059	+	1.22986i
$320$	0.591595	+	1.02467i	0.0330712	+	0.0572809i
$321$	3.40841	−	20.3586i	0.190239	−	1.13631i
$322$	2.41679	−	4.18601i	0.134683	−	0.233277i
$323$	12.4896			0.694942
$324$	−2.09970	+	14.9083i	−0.116650	+	0.828238i
$325$	4.67282			0.259202
$326$	−5.09555	+	8.82575i	−0.282216	+	0.488813i
$327$	−4.76244	+	28.4464i	−0.263364	+	1.57309i
$328$	−1.54533	−	2.67659i	−0.0853267	−	0.147790i
$329$	−4.96721	−	8.60346i	−0.273851	−	0.474324i
$330$	2.04316	+	1.68450i	0.112472	+	0.0927287i
$331$	−8.38880	+	14.5298i	−0.461090	+	0.798632i	−0.999016	−	0.0443606i	$-0.985875\pi$
$331$	−8.38880	+	14.5298i	−0.461090	+	0.798632i	0.537925	+	0.842993i	$0.319208\pi$
$332$	7.16641			0.393308
$333$	5.15322	+	1.77525i	0.282395	+	0.0972829i
$334$	8.06558			0.441329
$335$	3.29523	−	5.70751i	0.180038	−	0.311835i
$336$	−4.96721	+	1.85675i	−0.270984	+	0.101294i
$337$	13.5905	+	23.5394i	0.740320	+	1.28227i	0.952350	+	0.305008i	$0.0986592\pi$
$337$	13.5905	+	23.5394i	0.740320	+	1.28227i	−0.212030	+	0.977263i	$0.568007\pi$
$338$	−2.52686	−	4.37665i	−0.137443	−	0.238058i
$339$	−32.6481	+	12.2039i	−1.77320	+	0.662825i
$340$	2.23558	−	3.87214i	0.121241	−	0.209996i
$341$	18.6050			1.00752
$342$	6.05239	−	5.25970i	0.327276	−	0.284412i
$343$	−17.0801			−0.922239
$344$	0.494917	−	0.857221i	0.0266841	−	0.0462182i
$345$	−7.90841	−	6.52016i	−0.425774	−	0.351034i
$346$	−1.24877	−	2.16293i	−0.0671343	−	0.116280i
$347$	11.7829	+	20.4086i	0.632539	+	1.09559i	0.987031	+	0.160530i	$0.0513204\pi$
$347$	11.7829	+	20.4086i	0.632539	+	1.09559i	−0.354492	+	0.935059i	$0.615346\pi$
$348$	4.54005	−	27.1180i	0.243372	−	1.45368i
$349$	5.35601	−	9.27689i	0.286701	−	0.496580i	−0.686319	−	0.727300i	$-0.740775\pi$
$349$	5.35601	−	9.27689i	0.286701	−	0.496580i	0.973020	+	0.230720i	$0.0741081\pi$
$350$	0.816810			0.0436603
$351$	24.2725	−	0.630233i	1.29557	−	0.0336393i
$352$	14.5081			0.773285
$353$	−13.6336	+	23.6141i	−0.725644	+	1.25685i	0.233064	+	0.972461i	$0.425125\pi$
$353$	−13.6336	+	23.6141i	−0.725644	+	1.25685i	−0.958708	+	0.284392i	$0.908208\pi$
$354$	−0.187143	+	1.11781i	−0.00994652	+	0.0594112i
$355$	6.43724	+	11.1496i	0.341653	+	0.591761i
$356$	−2.50924	−	4.34612i	−0.132989	−	0.230344i
$357$	5.10083	+	4.20543i	0.269965	+	0.222575i
$358$	4.33641	−	7.51089i	0.229186	−	0.396963i
$359$	−10.6807			−0.563707			−0.281854	−	0.959457i	$-0.590949\pi$
$359$	−10.6807			−0.563707			−0.281854	+	0.959457i	$0.590949\pi$
$360$	−1.20166	−	6.18687i	−0.0633331	−	0.326077i
$361$	2.83528			0.149225
$362$	−0.915664	+	1.58598i	−0.0481262	+	0.0833571i
$363$	6.25603	−	2.33851i	0.328356	−	0.122740i
$364$	5.58123	+	9.66697i	0.292536	+	0.506687i
$365$	0.856013	+	1.48266i	0.0448058	+	0.0776059i
$366$	2.34678	−	0.877227i	0.122668	−	0.0458534i
$367$	4.23558	−	7.33624i	0.221096	−	0.382949i	−0.734045	−	0.679100i	$-0.762370\pi$
$367$	4.23558	−	7.33624i	0.221096	−	0.382949i	0.955141	+	0.296152i	$0.0957034\pi$
$368$	−12.6873			−0.661373
$369$	−0.841495	−	4.33252i	−0.0438065	−	0.225542i
$370$	−1.03920			−0.0540256
$371$	0.816810	−	1.41476i	0.0424067	−	0.0734505i
$372$	−15.5614	−	12.8298i	−0.806822	−	0.665193i
$373$	−5.06163	−	8.76700i	−0.262081	−	0.453938i	0.704714	−	0.709492i	$-0.251075\pi$
$373$	−5.06163	−	8.76700i	−0.262081	−	0.453938i	−0.966795	+	0.255554i	$0.917742\pi$
$374$	−2.04316	−	3.53885i	−0.105649	−	0.182990i
$375$	0.285997	−	1.70828i	0.0147688	−	0.0882150i
$376$	7.30757	−	12.6571i	0.376859	−	0.652740i
$377$	−44.3434			−2.28380
$378$	4.24284	−	0.110165i	0.218228	−	0.00566626i
$379$	11.9216			0.612371			0.306186	−	0.951972i	$-0.400947\pi$
$379$	11.9216			0.612371			0.306186	+	0.951972i	$0.400947\pi$
$380$	3.90841	−	6.76956i	0.200497	−	0.347271i
$381$	0.625515	−	3.73624i	0.0320461	−	0.191414i
$382$	0.811528	+	1.40561i	0.0415214	+	0.0719171i
$383$	−4.90841	−	8.50161i	−0.250808	−	0.434412i	0.712941	−	0.701224i	$-0.247363\pi$
$383$	−4.90841	−	8.50161i	−0.250808	−	0.434412i	−0.963748	+	0.266813i	$0.914030\pi$
$384$	−15.4126	−	12.7070i	−0.786519	−	0.648453i
$385$	−1.90841	+	3.30545i	−0.0972613	+	0.168462i
$386$	−10.7467			−0.546993
$387$	1.06691	−	0.927175i	0.0542341	−	0.0471309i
$388$	−13.1070			−0.665409
$389$	−4.61007	+	7.98487i	−0.233740	+	0.404849i	−0.958906	−	0.283725i	$-0.908430\pi$
$389$	−4.61007	+	7.98487i	−0.233740	+	0.404849i	0.725166	+	0.688574i	$0.241763\pi$
$390$	−4.33641	+	1.62095i	−0.219583	+	0.0820802i
$391$	7.90841	+	13.6978i	0.399945	+	0.692725i
$392$	−5.21090	−	9.02554i	−0.263190	−	0.455858i
$393$	9.73445	−	3.63875i	0.491038	−	0.183550i
$394$	−1.66887	+	2.89057i	−0.0840765	+	0.145625i
$395$	−0.287973			−0.0144895
$396$	12.6821	+	4.36887i	0.637297	+	0.219544i
$397$	−22.9793			−1.15330			−0.576648	−	0.816993i	$-0.695640\pi$
$397$	−22.9793			−1.15330			−0.576648	+	0.816993i	$0.695640\pi$
$398$	−3.73973	+	6.47741i	−0.187456	+	0.324683i
$399$	8.91764	+	7.35224i	0.446440	+	0.368072i
$400$	−1.07199	−	1.85675i	−0.0535997	−	0.0928373i
$401$	5.53279	+	9.58307i	0.276294	+	0.478556i	0.970461	−	0.241259i	$-0.0775602\pi$
$401$	5.53279	+	9.58307i	0.276294	+	0.478556i	−0.694167	+	0.719814i	$0.744227\pi$
$402$	−1.07812	+	6.43969i	−0.0537718	+	0.321183i
$403$	−16.2633	+	28.1688i	−0.810132	+	1.40319i
$404$	7.02864			0.349688
$405$	1.25518	−	8.91204i	0.0623705	−	0.442843i
$406$	−7.75123			−0.384687
$407$	2.42801	−	4.20543i	0.120352	−	0.208455i
$408$	−1.60591	+	9.59222i	−0.0795046	+	0.474886i
$409$	8.81681	+	15.2712i	0.435963	+	0.755110i	0.997374	−	0.0724270i	$-0.0230744\pi$
$409$	8.81681	+	15.2712i	0.435963	+	0.755110i	−0.561411	+	0.827537i	$0.689741\pi$
$410$	0.420748	+	0.728756i	0.0207792	+	0.0359907i
$411$	−13.6336	−	11.2404i	−0.672497	−	0.554447i
$412$	−1.51960	+	2.63203i	−0.0748654	+	0.129671i
$413$	−1.63362			−0.0803852
$414$	9.60083	+	3.30741i	0.471855	+	0.162550i
$415$	−4.28402			−0.210294
$416$	−12.6821	+	21.9660i	−0.621789	+	1.07697i
$417$	−12.9793	+	4.85166i	−0.635597	+	0.237587i
$418$	−3.57199	−	6.18687i	−0.174712	−	0.302610i
$419$	−18.5173	−	32.0730i	−0.904631	−	1.56687i	−0.821411	−	0.570336i	$-0.806813\pi$
$419$	−18.5173	−	32.0730i	−0.904631	−	1.56687i	−0.0832199	−	0.996531i	$-0.526520\pi$
$420$	3.87562	−	1.44871i	0.189111	−	0.0706897i
$421$	−2.52884	+	4.38007i	−0.123248	+	0.213472i	−0.921047	−	0.389452i	$-0.872664\pi$
$421$	−2.52884	+	4.38007i	−0.123248	+	0.213472i	0.797799	+	0.602924i	$0.205998\pi$
$422$	4.79608			0.233469
$423$	15.7532	−	13.6900i	0.765947	−	0.665630i
$424$	2.40332			0.116716
$425$	−1.33641	+	2.31473i	−0.0648255	+	0.112281i
$426$	−9.84150	−	8.11392i	−0.476822	−	0.393121i
$427$	1.80560	+	3.12739i	0.0873790	+	0.151345i
$428$	9.96806	+	17.2652i	0.481824	+	0.834544i
$429$	3.57199	−	21.3357i	0.172457	−	1.03010i
$430$	−0.134751	+	0.233396i	−0.00649827	+	0.0112553i
$431$	−5.23030			−0.251935			−0.125967	−	0.992034i	$-0.540203\pi$
$431$	−5.23030			−0.251935			−0.125967	+	0.992034i	$0.540203\pi$
$432$	−5.81879	−	9.50011i	−0.279957	−	0.457074i
$433$	34.3434			1.65044			0.825219	−	0.564813i	$-0.191052\pi$
$433$	34.3434			1.65044			0.825219	+	0.564813i	$0.191052\pi$
$434$	−2.84283	+	4.92392i	−0.136460	+	0.236356i
$435$	−2.71400	+	16.2109i	−0.130127	+	0.777254i
$436$	−13.9280	−	24.1240i	−0.667031	−	1.15533i
$437$	13.8260	+	23.9474i	0.661389	+	1.14556i
$438$	−1.30871	−	1.07898i	−0.0625324	−	0.0515554i
$439$	9.77365	−	16.9285i	0.466471	−	0.807952i	−0.532796	−	0.846244i	$-0.678859\pi$
$439$	9.77365	−	16.9285i	0.466471	−	0.807952i	0.999267	+	0.0382924i	$0.0121918\pi$
$440$	−5.61515			−0.267692
$441$	−2.83754	−	14.6094i	−0.135121	−	0.695685i
$442$	7.14399			0.339805
$443$	−5.25208	+	9.09686i	−0.249534	+	0.432205i	−0.963396	−	0.268081i	$-0.913611\pi$
$443$	−5.25208	+	9.09686i	−0.249534	+	0.432205i	0.713863	+	0.700286i	$0.246944\pi$
$444$	−4.93083	+	1.84315i	−0.234007	+	0.0874719i
$445$	1.50000	+	2.59808i	0.0711068	+	0.123161i
$446$	−2.62156	−	4.54068i	−0.124135	−	0.215007i
$447$	32.5717	−	12.1753i	1.54059	−	0.575873i
$448$	0.844801	−	1.46324i	0.0399131	−	0.0691315i
$449$	22.8560			1.07864			0.539321	−	0.842100i	$-0.318681\pi$
$449$	22.8560			1.07864			0.539321	+	0.842100i	$0.318681\pi$
$450$	0.327176	+	1.68450i	0.0154232	+	0.0794081i
$451$	−3.93216			−0.185158
$452$	16.8313	−	29.1527i	0.791679	−	1.37123i
$453$	4.06163	+	3.34865i	0.190832	+	0.157333i
$454$	0.764419	+	1.32401i	0.0358759	+	0.0621390i
$455$	−3.33641	−	5.77883i	−0.156413	−	0.270916i
$456$	−2.80757	+	16.7698i	−0.131477	+	0.785319i
$457$	7.01319	−	12.1472i	0.328063	−	0.568222i	−0.654064	−	0.756439i	$-0.726937\pi$
$457$	7.01319	−	12.1472i	0.328063	−	0.568222i	0.982127	+	0.188217i	$0.0602708\pi$
$458$	1.45704			0.0680832
$459$	−6.62967	+	12.2039i	−0.309446	+	0.569629i
$460$	9.89917			0.461551
$461$	12.0513	−	20.8734i	0.561283	−	0.972171i	−0.436102	−	0.899897i	$-0.643641\pi$
$461$	12.0513	−	20.8734i	0.561283	−	0.972171i	0.997385	−	0.0722736i	$-0.0230255\pi$
$462$	0.624385	−	3.72949i	0.0290490	−	0.173512i
$463$	16.9700	+	29.3930i	0.788664	+	1.36601i	0.926785	+	0.375591i	$0.122560\pi$
$463$	16.9700	+	29.3930i	0.788664	+	1.36601i	−0.138121	+	0.990415i	$0.544106\pi$
$464$	10.1728	+	17.6198i	0.472261	+	0.817981i
$465$	9.30249	+	7.66953i	0.431393	+	0.355666i
$466$	1.77894	−	3.08121i	0.0824077	−	0.142734i
$467$	−27.3720			−1.26663			−0.633313	−	0.773896i	$-0.718305\pi$
$467$	−27.3720			−1.26663			−0.633313	+	0.773896i	$0.718305\pi$
$468$	−17.7005	+	15.3823i	−0.818207	+	0.711045i
$469$	−9.41123			−0.434570
$470$	−1.98963	+	3.44615i	−0.0917750	+	0.158959i
$471$	−0.327176	+	0.122299i	−0.0150755	+	0.00563523i
$472$	−1.20166	−	2.08134i	−0.0553109	−	0.0958013i
$473$	−0.629668	−	1.09062i	−0.0289521	−	0.0501466i
$474$	0.267241	−	0.0998949i	0.0122748	−	0.00458832i
$475$	−2.33641	+	4.04678i	−0.107202	+	0.185679i
$476$	−6.38485			−0.292649
$477$	3.24482	+	1.11781i	0.148570	+	0.0511812i
$478$	4.64645			0.212524
$479$	−2.61515	+	4.52957i	−0.119489	+	0.206961i	−0.919565	−	0.392937i	$-0.871459\pi$
$479$	−2.61515	+	4.52957i	−0.119489	+	0.206961i	0.800076	+	0.599898i	$0.204792\pi$
$480$	7.25405	+	5.98068i	0.331101	+	0.272979i
$481$	4.24482	+	7.35224i	0.193547	+	0.335233i
$482$	7.54005	+	13.0597i	0.343440	+	0.594855i
$483$	−2.41679	+	14.4357i	−0.109968	+	0.656846i
$484$	−3.22522	+	5.58624i	−0.146601	+	0.253920i
$485$	7.83528			0.355782
$486$	1.92668	+	8.70585i	0.0873958	+	0.394905i
$487$	−24.0185			−1.08838			−0.544190	−	0.838962i	$-0.683163\pi$
$487$	−24.0185			−1.08838			−0.544190	+	0.838962i	$0.683163\pi$
$488$	−2.65633	+	4.60090i	−0.120246	+	0.208273i
$489$	5.09555	−	30.4360i	0.230429	−	1.37636i
$490$	1.41877	+	2.45738i	0.0640935	+	0.111013i
$491$	−7.38880	−	12.7978i	−0.333452	−	0.577556i	0.649734	−	0.760161i	$-0.274880\pi$
$491$	−7.38880	−	12.7978i	−0.333452	−	0.577556i	−0.983186	+	0.182606i	$0.941547\pi$
$492$	3.28890	+	2.71157i	0.148275	+	0.122247i
$493$	12.6821	−	21.9660i	0.571171	−	0.989298i
$494$	12.4896			0.561935
$495$	−7.58123	−	2.61168i	−0.340751	−	0.117386i
$496$	14.9239			0.670101
$497$	9.19243	−	15.9217i	0.412337	−	0.714188i
$498$	3.97560	−	1.48608i	0.178151	−	0.0665929i
$499$	−12.4280	−	21.5259i	−0.556354	−	0.963633i	−0.997797	−	0.0663440i	$-0.978867\pi$
$499$	−12.4280	−	21.5259i	−0.556354	−	0.963633i	0.441443	−	0.897289i	$-0.354467\pi$
$500$	0.836412	+	1.44871i	0.0374055	+	0.0647882i
$501$	−22.8773	+	8.55155i	−1.02208	+	0.382055i
$502$	0.157175	−	0.272235i	0.00701506	−	0.0121504i
$503$	38.9154			1.73515			0.867576	−	0.497305i	$-0.165677\pi$
$503$	38.9154			1.73515			0.867576	+	0.497305i	$0.165677\pi$
$504$	−6.79326	+	5.90353i	−0.302596	+	0.262964i
$505$	−4.20166			−0.186971
$506$	4.52355	−	7.83503i	0.201097	−	0.348309i
$507$	11.8076	+	9.73487i	0.524393	+	0.432341i
$508$	1.82935	+	3.16853i	0.0811644	+	0.140581i
$509$	−1.01037	−	1.75001i	−0.0447837	−	0.0775676i	0.842765	−	0.538282i	$-0.180927\pi$
$509$	−1.01037	−	1.75001i	−0.0447837	−	0.0775676i	−0.887548	+	0.460715i	$0.847593\pi$
$510$	0.437242	−	2.61168i	0.0193614	−	0.115647i
$511$	1.22239	−	2.11725i	0.0540755	−	0.0936615i
$512$	20.6459			0.912428
$513$	−11.5905	+	21.3357i	−0.511732	+	0.941996i
$514$	−10.2959			−0.454132
$515$	0.908405	−	1.57340i	0.0400291	−	0.0693325i
$516$	−0.225415	+	1.34642i	−0.00992333	+	0.0592726i
$517$	−9.29721	−	16.1032i	−0.408891	−	0.708220i
$518$	0.741995	+	1.28517i	0.0326014	+	0.0564672i
$519$	5.83528	+	4.81096i	0.256140	+	0.211178i
$520$	4.90841	−	8.50161i	0.215248	−	0.372820i
$521$	−23.0290			−1.00892			−0.504460	−	0.863435i	$-0.668308\pi$
$521$	−23.0290			−1.00892			−0.504460	+	0.863435i	$0.668308\pi$
$522$	−3.10478	−	15.9853i	−0.135893	−	0.699657i
$523$	−41.1170			−1.79792			−0.898961	−	0.438028i	$-0.855677\pi$
$523$	−41.1170			−1.79792			−0.898961	+	0.438028i	$0.855677\pi$
$524$	−5.01847	+	8.69225i	−0.219233	+	0.379723i
$525$	−2.31681	+	0.866025i	−0.101114	+	0.0377964i
$526$	−3.40199	−	5.89242i	−0.148334	−	0.256922i
$527$	−9.30249	−	16.1124i	−0.405223	−	0.701867i
$528$	−9.29721	+	3.47530i	−0.404609	+	0.151243i
$529$	−6.00924	+	10.4083i	−0.261271	+	0.452535i
$530$	−0.654353			−0.0284233
$531$	−0.654353	−	3.36900i	−0.0283965	−	0.146202i
$532$	−11.1625			−0.483954
$533$	3.43724	−	5.95348i	0.148883	−	0.257874i
$534$	−2.29326	−	1.89070i	−0.0992389	−	0.0818185i
$535$	−5.95882	−	10.3210i	−0.257622	−	0.446215i
$536$	−6.92272	−	11.9905i	−0.299016	−	0.517911i
$537$	−4.33641	+	25.9017i	−0.187130	+	1.11774i
$538$	−8.17198	+	14.1543i	−0.352319	+	0.610234i
$539$	−13.2593			−0.571120
$540$	4.54005	+	7.41236i	0.195373	+	0.318977i
$541$	5.20957			0.223977			0.111988	−	0.993710i	$-0.464278\pi$
$541$	5.20957			0.223977			0.111988	+	0.993710i	$0.464278\pi$
$542$	6.68206	−	11.5737i	0.287019	−	0.497132i
$543$	0.915664	−	5.46932i	0.0392949	−	0.234711i
$544$	−7.25405	−	12.5644i	−0.311015	−	0.538694i
$545$	8.32605	+	14.4211i	0.356649	+	0.617734i
$546$	5.10083	+	4.20543i	0.218295	+	0.179976i
$547$	−20.0204	+	34.6764i	−0.856013	+	1.48266i	0.0196900	+	0.999806i	$0.493732\pi$
$547$	−20.0204	+	34.6764i	−0.856013	+	1.48266i	−0.875702	+	0.482851i	$0.839601\pi$
$548$	17.0656			0.729005
$549$	−5.72635	+	4.97636i	−0.244394	+	0.212386i
$550$	1.52884			0.0651898
$551$	22.1717	−	38.4025i	0.944546	−	1.63600i
$552$	−20.1697	+	7.53946i	−0.858480	+	0.320901i
$553$	0.205614	+	0.356133i	0.00874359	+	0.0151443i
$554$	4.31173	+	7.46813i	0.183188	+	0.317290i
$555$	2.94761	−	1.10182i	0.125119	−	0.0467696i
$556$	6.69129	−	11.5897i	0.283774	−	0.491511i
$557$	−14.4033			−0.610288			−0.305144	−	0.952306i	$-0.598705\pi$
$557$	−14.4033			−0.610288			−0.305144	+	0.952306i	$0.598705\pi$
$558$	−11.2933	−	3.89044i	−0.478082	−	0.164695i
$559$	2.20166			0.0931203
$560$	−1.53081	+	2.65145i	−0.0646887	+	0.112044i
$561$	9.54731	+	7.87137i	0.403088	+	0.332330i
$562$	−1.90248	−	3.29518i	−0.0802511	−	0.138999i
$563$	−14.6840	−	25.4335i	−0.618858	−	1.07189i	−0.989694	−	0.143196i	$-0.954262\pi$
$563$	−14.6840	−	25.4335i	−0.618858	−	1.07189i	0.370836	−	0.928698i	$-0.379071\pi$
$564$	−3.32831	+	19.8802i	−0.140147	+	0.837107i
$565$	−10.0616	+	17.4272i	−0.423296	+	0.733170i
$566$	15.3849			0.646674
$567$	−11.9176	+	4.81096i	−0.500494	+	0.202041i
$568$	27.0471			1.13487
$569$	−23.4033	+	40.5357i	−0.981118	+	1.69935i	−0.323062	+	0.946378i	$0.604712\pi$
$569$	−23.4033	+	40.5357i	−0.981118	+	1.69935i	−0.658056	+	0.752969i	$0.728621\pi$
$570$	0.764419	−	4.56592i	0.0320180	−	0.191245i
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	10.4465	+	18.0938i	0.436789	+	0.756541i
$573$	−3.79213	−	3.12646i	−0.158418	−	0.130610i
$574$	0.600830	−	1.04067i	0.0250782	−	0.0434367i
$575$	−5.91764			−0.246783
$576$	3.35601	+	1.15612i	0.139834	+	0.0481717i
$577$	28.2386			1.17559			0.587794	−	0.809010i	$-0.299996\pi$
$577$	28.2386			1.17559			0.587794	+	0.809010i	$0.299996\pi$
$578$	2.81879	−	4.88228i	0.117246	−	0.203076i
$579$	30.4821	−	11.3942i	1.26679	−	0.473528i
$580$	−7.93724	−	13.7477i	−0.329576	−	0.570842i
$581$	3.05880	+	5.29801i	0.126901	+	0.219798i
$582$	−7.27119	+	2.71798i	−0.301401	+	0.112664i
$583$	1.52884	−	2.64802i	0.0633180	−	0.109670i
$584$	3.59668			0.148832
$585$	10.5812	−	9.19539i	0.437480	−	0.380182i
$586$	7.08405			0.292639
$587$	−9.04118	+	15.6598i	−0.373169	+	0.646348i	−0.990051	−	0.140707i	$-0.955062\pi$
$587$	−9.04118	+	15.6598i	−0.373169	+	0.646348i	0.616882	+	0.787056i	$0.288396\pi$
$588$	11.0903	+	9.14348i	0.457355	+	0.377071i
$589$	−16.2633	−	28.1688i	−0.670117	−	1.16068i
$590$	0.327176	+	0.566686i	0.0134696	+	0.0233301i
$591$	1.66887	−	9.96827i	0.0686482	−	0.410040i
$592$	1.94761	−	3.37336i	0.0800462	−	0.138644i
$593$	−7.73840			−0.317778			−0.158889	−	0.987296i	$-0.550791\pi$
$593$	−7.73840			−0.317778			−0.158889	+	0.987296i	$0.550791\pi$
$594$	7.94139	−	0.206197i	0.325839	−	0.00846037i
$595$	3.81681			0.156474
$596$	−16.7919	+	29.0845i	−0.687824	+	1.19135i
$597$	3.73973	−	22.3377i	0.153057	−	0.914220i
$598$	7.90841	+	13.6978i	0.323399	+	0.560143i
$599$	13.9608	+	24.1808i	0.570423	+	0.988001i	0.996522	+	0.0833249i	$0.0265539\pi$
$599$	13.9608	+	24.1808i	0.570423	+	0.988001i	−0.426100	+	0.904676i	$0.640113\pi$
$600$	−2.80757	−	2.31473i	−0.114619	−	0.0944986i
$601$	−19.2201	+	33.2902i	−0.784006	+	1.35794i	0.145586	+	0.989346i	$0.453493\pi$
$601$	−19.2201	+	33.2902i	−0.784006	+	1.35794i	−0.929591	+	0.368592i	$0.879840\pi$
$602$	0.384851			0.0156853
$603$	−3.76970	−	19.4087i	−0.153514	−	0.790383i
$604$	−5.08405			−0.206867
$605$	1.92801	−	3.33941i	0.0783846	−	0.135766i
$606$	3.89917	−	1.45751i	0.158393	−	0.0592074i
$607$	0.319917	+	0.554113i	0.0129850	+	0.0224907i	0.872445	−	0.488712i	$-0.162533\pi$
$607$	0.319917	+	0.554113i	0.0129850	+	0.0224907i	−0.859460	+	0.511203i	$0.829200\pi$
$608$	−12.6821	−	21.9660i	−0.514325	−	0.890838i
$609$	21.9857	−	8.21826i	0.890905	−	0.333021i
$610$	0.723239	−	1.25269i	0.0292831	−	0.0507198i
$611$	32.5081			1.31514
$612$	−2.55748	−	13.1674i	−0.103380	−	0.532261i
$613$	42.7467			1.72652			0.863262	−	0.504757i	$-0.168418\pi$
$613$	42.7467			1.72652			0.863262	+	0.504757i	$0.168418\pi$
$614$	0.713157	−	1.23522i	0.0287807	−	0.0498496i
$615$	−1.96608	−	1.62095i	−0.0792800	−	0.0653632i
$616$	4.00924	+	6.94420i	0.161537	+	0.279790i
$617$	−10.5513	−	18.2753i	−0.424778	−	0.735737i	0.571622	−	0.820517i	$-0.306314\pi$
$617$	−10.5513	−	18.2753i	−0.424778	−	0.735737i	−0.996400	+	0.0847805i	$0.972981\pi$
$618$	−0.297209	+	1.77525i	−0.0119555	+	0.0714109i
$619$	6.82605	−	11.8231i	0.274362	−	0.475209i	−0.695612	−	0.718418i	$-0.744867\pi$
$619$	6.82605	−	11.8231i	0.274362	−	0.475209i	0.969974	+	0.243209i	$0.0782000\pi$
$620$	−11.6442			−0.467642
$621$	−30.7386	+	0.798123i	−1.23350	+	0.0320276i
$622$	−13.8538			−0.555485
$623$	2.14201	−	3.71007i	0.0858178	−	0.148641i
$624$	2.86525	−	17.1143i	0.114702	−	0.685121i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	10.0339	+	17.3793i	0.401036	+	0.694615i
$627$	16.6913	+	13.7613i	0.666586	+	0.549574i
$628$	0.168672	−	0.292148i	0.00673073	−	0.0116580i
$629$	−4.85601			−0.193622
$630$	1.84960	−	1.60735i	0.0736898	−	0.0640385i
$631$	33.2593			1.32403			0.662017	−	0.749489i	$-0.269701\pi$
$631$	33.2593			1.32403			0.662017	+	0.749489i	$0.269701\pi$
$632$	−0.302491	+	0.523930i	−0.0120325	+	0.0208408i
$633$	−13.6037	+	5.08506i	−0.540697	+	0.202113i
$634$	2.99472	+	5.18700i	0.118935	+	0.206002i
$635$	−1.09357	−	1.89412i	−0.0433971	−	0.0751659i
$636$	−3.10478	+	1.16057i	−0.123113	+	0.0460196i
$637$	11.5905	−	20.0753i	0.459231	−	0.795411i
$638$	−14.5081			−0.574381
$639$	36.5173	+	12.5799i	1.44460	+	0.497655i
$640$	−11.5328			−0.455874
$641$	−13.1429	+	22.7641i	−0.519112	+	0.899128i	0.480642	+	0.876917i	$0.340404\pi$
$641$	−13.1429	+	22.7641i	−0.519112	+	0.899128i	−0.999753	+	0.0222106i	$0.992930\pi$
$642$	9.11007	+	7.51089i	0.359546	+	0.296431i
$643$	−10.2913	−	17.8250i	−0.405848	−	0.702950i	0.588571	−	0.808445i	$-0.299691\pi$
$643$	−10.2913	−	17.8250i	−0.405848	−	0.702950i	−0.994420	+	0.105495i	$0.966357\pi$
$644$	−7.06804	−	12.2422i	−0.278520	−	0.482410i
$645$	0.134751	−	0.804876i	0.00530581	−	0.0316920i
$646$	−3.57199	+	6.18687i	−0.140538	+	0.243419i
$647$	23.2527			0.914159			0.457079	−	0.889426i	$-0.348896\pi$
$647$	23.2527			0.914159			0.457079	+	0.889426i	$0.348896\pi$
$648$	−14.8959	−	11.6450i	−0.585165	−	0.457458i
$649$	−3.05767			−0.120024
$650$	−1.33641	+	2.31473i	−0.0524184	+	0.0907913i
$651$	2.84283	−	16.9804i	0.111419	−	0.665513i
$652$	14.9022	+	25.8114i	0.583615	+	1.01085i
$653$	−9.37957	−	16.2459i	−0.367051	−	0.635751i	0.622052	−	0.782976i	$-0.286299\pi$
$653$	−9.37957	−	16.2459i	−0.367051	−	0.635751i	−0.989103	+	0.147225i	$0.952966\pi$
$654$	−12.7292	−	10.4947i	−0.497750	−	0.410375i
$655$	3.00000	−	5.19615i	0.117220	−	0.203030i
$656$	−3.15415			−0.123149
$657$	4.85601	+	1.67286i	0.189451	+	0.0652645i
$658$	5.68242			0.221524
$659$	0.140034	−	0.242545i	0.00545494	−	0.00944823i	−0.863285	−	0.504717i	$-0.831597\pi$
$659$	0.140034	−	0.242545i	0.00545494	−	0.00944823i	0.868740	+	0.495268i	$0.164930\pi$
$660$	7.25405	−	2.71157i	0.282364	−	0.105548i
$661$	19.8930	+	34.4556i	0.773746	+	1.34017i	0.935496	+	0.353336i	$0.114953\pi$
$661$	19.8930	+	34.4556i	0.773746	+	1.34017i	−0.161750	+	0.986832i	$0.551714\pi$
$662$	−4.79834	−	8.31097i	−0.186493	−	0.323015i
$663$	−20.2633	+	7.57443i	−0.786961	+	0.294167i
$664$	−4.50000	+	7.79423i	−0.174634	+	0.302475i
$665$	6.67282			0.258761
$666$	−2.35319	+	2.04499i	−0.0911843	+	0.0792417i
$667$	56.1562			2.17438
$668$	11.7941	−	20.4280i	0.456327	−	0.790382i
$669$	12.2501	+	10.0997i	0.473616	+	0.390478i
$670$	1.88485	+	3.26466i	0.0728181	+	0.126125i
$671$	3.37957	+	5.85358i	0.130467	+	0.225975i
$672$	2.21683	−	13.2412i	0.0855159	−	0.510792i
$673$	−16.7644	+	29.0368i	−0.646221	+	1.11929i	0.337797	+	0.941219i	$0.390318\pi$
$673$	−16.7644	+	29.0368i	−0.646221	+	1.11929i	−0.984018	+	0.178068i	$0.943015\pi$
$674$	−15.5473			−0.598860
$675$	−2.71400	−	4.43105i	−0.104462	−	0.170551i
$676$	−14.7799			−0.568456
$677$	−13.7437	+	23.8048i	−0.528213	+	0.914891i	0.471246	+	0.882002i	$0.343804\pi$
$677$	−13.7437	+	23.8048i	−0.528213	+	0.914891i	−0.999459	+	0.0328897i	$0.989529\pi$
$678$	3.29193	−	19.6629i	0.126426	−	0.755148i
$679$	−5.59442	−	9.68981i	−0.214694	−	0.371861i
$680$	2.80757	+	4.86286i	0.107666	+	0.186482i
$681$	−3.57199	−	2.94497i	−0.136879	−	0.112851i
$682$	−5.32096	+	9.21618i	−0.203750	+	0.352906i
$683$	−34.5865			−1.32342			−0.661708	−	0.749762i	$-0.730168\pi$
$683$	−34.5865			−1.32342			−0.661708	+	0.749762i	$0.730168\pi$
$684$	−4.47116	−	23.0202i	−0.170959	−	0.880201i
$685$	−10.2017			−0.389785
$686$	4.88485	−	8.46081i	0.186504	−	0.323035i
$687$	−4.13277	+	1.54483i	−0.157675	+	0.0589391i
$688$	−0.505083	−	0.874830i	−0.0192561	−	0.0333526i
$689$	2.67282	+	4.62947i	0.101826	+	0.176369i
$690$	5.49161	−	2.05277i	0.209062	−	0.0781475i
$691$	−20.3641	+	35.2717i	−0.774688	+	1.34180i	0.160282	+	0.987071i	$0.448760\pi$
$691$	−20.3641	+	35.2717i	−0.774688	+	1.34180i	−0.934970	+	0.354727i	$0.884574\pi$
$692$	−7.30418			−0.277663
$693$	2.18319	+	11.2404i	0.0829325	+	0.426987i
$694$	−13.4795			−0.511674
$695$	−4.00000	+	6.92820i	−0.151729	+	0.262802i
$696$	26.6429	+	21.9660i	1.00989	+	0.832618i
$697$	1.96608	+	3.40535i	0.0744706	+	0.128987i
$698$	3.06360	+	5.30632i	0.115959	+	0.200847i
$699$	−1.77894	+	10.6257i	−0.0672856	+	0.401901i
$700$	1.19440	−	2.06876i	0.0451441	−	0.0781919i
$701$	−19.4712			−0.735416			−0.367708	−	0.929941i	$-0.619857\pi$
$701$	−19.4712			−0.735416			−0.367708	+	0.929941i	$0.619857\pi$
$702$	−6.62967	+	12.2039i	−0.250221	+	0.460606i
$703$	−8.48963			−0.320193
$704$	1.58123	−	2.73877i	0.0595948	−	0.103221i
$705$	1.98963	−	11.8842i	0.0749339	−	0.447585i
$706$	−7.79834	−	13.5071i	−0.293494	−	0.508347i
$707$	3.00000	+	5.19615i	0.112827	+	0.195421i
$708$	2.55748	+	2.10854i	0.0961158	+	0.0792436i
$709$	−7.54316	+	13.0651i	−0.283289	+	0.490671i	−0.972193	−	0.234182i	$-0.924759\pi$
$709$	−7.54316	+	13.0651i	−0.283289	+	0.490671i	0.688904	+	0.724853i	$0.258092\pi$
$710$	−7.36412			−0.276370
$711$	−0.652092	+	0.566686i	−0.0244553	+	0.0212524i
$712$	6.30249			0.236196
$713$	20.5957	−	35.6729i	0.771317	−	1.33596i
$714$	−3.54203	+	1.32401i	−0.132557	+	0.0495499i
$715$	−6.24482	−	10.8163i	−0.233543	−	0.404508i
$716$	−12.6821	−	21.9660i	−0.473951	−	0.820907i
$717$	−13.1792	+	4.92641i	−0.492188	+	0.183980i
$718$	3.05465	−	5.29081i	0.113999	−	0.197451i
$719$	−3.43196			−0.127990			−0.0639952	−	0.997950i	$-0.520384\pi$
$719$	−3.43196			−0.127990			−0.0639952	+	0.997950i	$0.520384\pi$
$720$	−6.08123	−	2.09494i	−0.226634	−	0.0780737i
$721$	−2.59442			−0.0966211
$722$	−0.810881	+	1.40449i	−0.0301779	+	0.0522696i
$723$	−35.2333	−	29.0485i	−1.31034	−	1.08032i
$724$	2.67791	+	4.63827i	0.0995236	+	0.172380i
$725$	4.74482	+	8.21826i	0.176218	+	0.305219i
$726$	−0.630798	+	3.76780i	−0.0234111	+	0.139836i
$727$	17.8857	−	30.9789i	0.663344	−	1.14895i	−0.316388	−	0.948630i	$-0.602470\pi$
$727$	17.8857	−	30.9789i	0.663344	−	1.14895i	0.979732	−	0.200315i	$-0.0641966\pi$
$728$	−14.0185			−0.519559
$729$	−14.6952	−	22.6506i	−0.544268	−	0.838911i
$730$	−0.979268			−0.0362443
$731$	−0.629668	+	1.09062i	−0.0232891	+	0.0403379i
$732$	1.20985	−	7.22652i	0.0447174	−	0.267100i
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	0.994471	−	0.105010i	$-0.0334875\pi$
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	−0.588177	+	0.808732i	$0.700154\pi$
$734$	2.42272	+	4.19628i	0.0894244	+	0.154888i
$735$	−6.62967	−	5.46590i	−0.244539	−	0.201613i
$736$	16.0605	−	27.8176i	0.591998	−	1.02537i
$737$	−17.6151			−0.648862
$738$	2.38683	+	0.822244i	0.0878603	+	0.0302672i
$739$	6.08631			0.223889			0.111944	−	0.993714i	$-0.464292\pi$
$739$	6.08631			0.223889			0.111944	+	0.993714i	$0.464292\pi$
$740$	−1.51960	+	2.63203i	−0.0558617	+	0.0967552i
$741$	−35.4257	+	13.2422i	−1.30140	+	0.486463i
$742$	0.467210	+	0.809231i	0.0171518	+	0.0297078i
$743$	12.7509	+	22.0853i	0.467787	+	0.810231i	0.999322	−	0.0368054i	$-0.0117182\pi$
$743$	12.7509	+	22.0853i	0.467787	+	0.810231i	−0.531536	+	0.847036i	$0.678385\pi$
$744$	23.7252	−	8.86850i	0.869809	−	0.325135i
$745$	10.0381	−	17.3865i	0.367767	−	0.636990i
$746$	5.79043			0.212003
$747$	−9.70081	+	8.43028i	−0.354934	+	0.308448i
$748$	−11.9506			−0.436958
$749$	−8.50924	+	14.7384i	−0.310921	+	0.538530i
$750$	0.764419	+	0.630233i	0.0279126	+	0.0230128i
$751$	9.19638	+	15.9286i	0.335581	+	0.581243i	0.983596	−	0.180384i	$-0.0577342\pi$
$751$	9.19638	+	15.9286i	0.335581	+	0.581243i	−0.648016	+	0.761627i	$0.724401\pi$
$752$	−7.45769	−	12.9171i	−0.271954	−	0.471038i
$753$	−0.157175	+	0.938816i	−0.00572777	+	0.0342124i
$754$	12.6821	−	21.9660i	0.461853	−	0.799953i
$755$	3.03920			0.110608
$756$	5.92518	−	10.9071i	0.215497	−	0.396687i
$757$	−41.8986			−1.52283			−0.761415	−	0.648264i	$-0.775495\pi$
$757$	−41.8986			−1.52283			−0.761415	+	0.648264i	$0.775495\pi$
$758$	−3.40954	+	5.90549i	−0.123840	+	0.214497i
$759$	−4.52355	+	27.0195i	−0.164195	+	0.980745i
$760$	4.90841	+	8.50161i	0.178047	+	0.308386i
$761$	3.98568	+	6.90340i	0.144481	+	0.250248i	0.929179	−	0.369630i	$-0.120515\pi$
$761$	3.98568	+	6.90340i	0.144481	+	0.250248i	−0.784698	+	0.619878i	$0.787182\pi$
$762$	1.67189	+	1.37841i	0.0605663	+	0.0499345i
$763$	11.8896	−	20.5935i	0.430434	−	0.745534i
$764$	4.74671			0.171730
$765$	1.52884	+	7.87137i	0.0552752	+	0.284590i
$766$	5.61515			0.202884
$767$	2.67282	−	4.62947i	0.0965101	−	0.167160i
$768$	6.86327	−	2.56550i	0.247657	−	0.0925744i
$769$	−3.01432	−	5.22095i	−0.108699	−	0.188272i	0.806544	−	0.591174i	$-0.201335\pi$
$769$	−3.01432	−	5.22095i	−0.108699	−	0.188272i	−0.915244	+	0.402901i	$0.868002\pi$
$770$	−1.09159	−	1.89070i	−0.0393383	−	0.0681360i
$771$	29.2034	−	10.9162i	1.05173	−	0.393139i
$772$	−15.7147	+	27.2186i	−0.565583	+	0.979618i
$773$	44.4033			1.59708			0.798538	−	0.601944i	$-0.205607\pi$
$773$	44.4033			1.59708			0.798538	+	0.601944i	$0.205607\pi$
$774$	0.154153	+	0.793674i	0.00554093	+	0.0285280i
$775$	6.96080			0.250039
$776$	8.23030	−	14.2553i	0.295451	−	0.511735i
$777$	−3.46721	−	2.85858i	−0.124385	−	0.102551i
$778$	−2.63693	−	4.56729i	−0.0945384	−	0.163745i
$779$	3.43724	+	5.95348i	0.123152	+	0.213305i
$780$	−2.23558	+	13.3533i	−0.0800467	+	0.478124i
$781$	17.2056	−	29.8010i	0.615665	−	1.06636i
$782$	−9.04711			−0.323524
$783$	25.7549	+	42.0490i	0.920405	+	1.50271i
$784$	−10.6359			−0.379853
$785$	−0.100830	+	0.174643i	−0.00359879	+	0.00623329i
$786$	−0.981529	+	5.86273i	−0.0350100	+	0.209117i
$787$	−8.41877	−	14.5817i	−0.300097	−	0.519783i	0.676061	−	0.736846i	$-0.263686\pi$
$787$	−8.41877	−	14.5817i	−0.300097	−	0.519783i	−0.976158	+	0.217063i	$0.930352\pi$
$788$	4.88070	+	8.45362i	0.173868	+	0.301148i
$789$	15.8969	+	13.1064i	0.565945	+	0.466599i
$790$	0.0823593	−	0.142651i	0.00293021	−	0.00507528i
$791$	28.7361			1.02174
$792$	−12.7150	+	11.0497i	−0.451810	+	0.392635i
$793$	−11.8168			−0.419627
$794$	6.57199	−	11.3830i	0.233231	−	0.403968i
$795$	1.85601	−	0.693779i	0.0658260	−	0.0246058i
$796$	10.9370	+	18.9435i	0.387653	+	0.671435i
$797$	16.6860	+	28.9010i	0.591049	+	1.02373i	0.994091	+	0.108545i	$0.0346193\pi$
$797$	16.6860	+	28.9010i	0.591049	+	1.02373i	−0.403043	+	0.915181i	$0.632047\pi$
$798$	−6.19243	+	2.31473i	−0.219209	+	0.0819407i
$799$	−9.29721	+	16.1032i	−0.328912	+	0.569692i
$800$	5.42801			0.191909
$801$	8.50924	+	2.93137i	0.300659	+	0.103575i
$802$	−6.32944			−0.223500
$803$	2.28797	−	3.96289i	0.0807408	−	0.139847i
$804$	14.7335	+	12.1472i	0.519611	+	0.428399i
$805$	4.22522	+	7.31829i	0.148919	+	0.257936i
$806$	−9.30249	−	16.1124i	−0.327666	−	0.567535i
$807$	8.17198	−	48.8117i	0.287667	−	1.71825i
$808$	−4.41349	+	7.64439i	−0.155266	+	0.268929i
$809$	29.1809			1.02595			0.512973	−	0.858404i	$-0.328544\pi$
$809$	29.1809			1.02595			0.512973	+	0.858404i	$0.328544\pi$
$810$	4.05570	+	3.17058i	0.142503	+	0.111403i
$811$	−15.5552			−0.546217			−0.273109	−	0.961983i	$-0.588052\pi$
$811$	−15.5552			−0.546217			−0.273109	+	0.961983i	$0.588052\pi$
$812$	−11.3344	+	19.6318i	−0.397761	+	0.688942i
$813$	−6.68206	+	39.9124i	−0.234350	+	1.39979i
$814$	1.38880	+	2.40548i	0.0486775	+	0.0843120i
$815$	−8.90841	−	15.4298i	−0.312048	−	0.540483i
$816$	7.65831	+	6.31397i	0.268094	+	0.221033i
$817$	−1.10083	+	1.90669i	−0.0385132	+	0.0667068i
$818$	−10.0863			−0.352660
$819$	−18.9269	−	6.52016i	−0.661359	−	0.227833i
$820$	2.46100			0.0859417
$821$	11.8588	−	20.5401i	0.413876	−	0.716855i	−0.581434	−	0.813594i	$-0.697508\pi$
$821$	11.8588	−	20.5401i	0.413876	−	0.716855i	0.995310	+	0.0967393i	$0.0308413\pi$
$822$	9.46721	−	3.53885i	0.330207	−	0.123432i
$823$	−9.68404	−	16.7732i	−0.337564	−	0.584678i	0.646410	−	0.762990i	$-0.276270\pi$
$823$	−9.68404	−	16.7732i	−0.337564	−	0.584678i	−0.983974	+	0.178312i	$0.942936\pi$
$824$	−1.90841	−	3.30545i	−0.0664824	−	0.115151i
$825$	−4.33641	+	1.62095i	−0.150974	+	0.0564344i
$826$	0.467210	−	0.809231i	0.0162563	−	0.0281568i
$827$	52.2241			1.81601			0.908005	−	0.418960i	$-0.137605\pi$
$827$	52.2241			1.81601			0.908005	+	0.418960i	$0.137605\pi$
$828$	22.4159	−	19.4800i	0.779005	−	0.676977i
$829$	−26.6442			−0.925391			−0.462695	−	0.886517i	$-0.653118\pi$
$829$	−26.6442			−0.925391			−0.462695	+	0.886517i	$0.653118\pi$
$830$	1.22522	−	2.12214i	0.0425278	−	0.0736604i
$831$	−20.1479	−	16.6112i	−0.698924	−	0.576235i
$832$	2.76442	+	4.78811i	0.0958390	+	0.165998i
$833$	6.62967	+	11.4829i	0.229704	+	0.397860i
$834$	1.30871	−	7.81698i	0.0453168	−	0.270680i
$835$	−7.05042	+	12.2117i	−0.243990	+	0.422603i
$836$	−20.8930			−0.722598
$837$	36.1572	−	0.938816i	1.24977	−	0.0324502i
$838$	21.1836			0.731775
$839$	12.5196	−	21.6846i	0.432225	−	0.748635i	−0.564840	−	0.825201i	$-0.691062\pi$
$839$	12.5196	−	21.6846i	0.432225	−	0.748635i	0.997065	+	0.0765655i	$0.0243954\pi$
$840$	−0.857990	+	5.12483i	−0.0296035	+	0.176823i
$841$	−30.5266	−	52.8736i	−1.05264	−	1.82323i
$842$	−1.44648	−	2.50537i	−0.0498489	−	0.0863409i
$843$	8.88993	+	7.32940i	0.306186	+	0.252438i
$844$	7.01319	−	12.1472i	0.241404	−	0.418124i
$845$	8.83528			0.303943
$846$	2.27611	+	11.7188i	0.0782544	+	0.402901i
$847$	−5.50641			−0.189203
$848$	1.22635	−	2.12409i	0.0421129	−	0.0729417i
$849$	−43.6378	+	16.3118i	−1.49764	+	0.559821i
$850$	−0.764419	−	1.32401i	−0.0262193	−	0.0454132i
$851$	−5.37562	−	9.31084i	−0.184274	−	0.319171i
$852$	−34.9414	+	13.0611i	−1.19707	+	0.447467i
$853$	5.43724	−	9.41758i	0.186168	−	0.322452i	−0.757802	−	0.652485i	$-0.773727\pi$
$853$	5.43724	−	9.41758i	0.186168	−	0.322452i	0.943969	+	0.330033i	$0.107060\pi$
$854$	−2.06558			−0.0706827
$855$	2.67282	+	13.7613i	0.0914086	+	0.470627i
$856$	−25.0369			−0.855745
$857$	9.29721	−	16.1032i	0.317587	−	0.550076i	−0.662397	−	0.749153i	$-0.730461\pi$
$857$	9.29721	−	16.1032i	0.317587	−	0.550076i	0.979984	+	0.199077i	$0.0637942\pi$
$858$	9.54731	+	7.87137i	0.325940	+	0.268724i
$859$	2.33246	+	4.03994i	0.0795825	+	0.137841i	0.903070	−	0.429494i	$-0.141308\pi$
$859$	2.33246	+	4.03994i	0.0795825	+	0.137841i	−0.823487	+	0.567335i	$0.807975\pi$
$860$	0.394086	+	0.682577i	0.0134382	+	0.0232757i
$861$	−0.600830	+	3.58880i	−0.0204762	+	0.122306i
$862$	1.49585	−	2.59088i	0.0509488	−	0.0882459i
$863$	−28.0594			−0.955152			−0.477576	−	0.878590i	$-0.658484\pi$
$863$	−28.0594			−0.955152			−0.477576	+	0.878590i	$0.658484\pi$
$864$	28.1952	−	0.732086i	0.959222	−	0.0249061i
$865$	4.36638			0.148461
$866$	−9.82209	+	17.0124i	−0.333768	+	0.578104i
$867$	−2.81879	+	16.8368i	−0.0957310	+	0.571807i
$868$	8.31399	+	14.4002i	0.282195	+	0.488776i
$869$	0.384851	+	0.666581i	0.0130552	+	0.0226122i
$870$	−7.25405	−	5.98068i	−0.245935	−	0.202764i
$871$	15.3980	−	26.6702i	0.521743	−	0.903685i
$872$	34.9832			1.18468
$873$	17.7424	−	15.4186i	0.600488	−	0.521841i
$874$	−15.8168			−0.535012
$875$	−0.714003	+	1.23669i	−0.0241377	+	0.0418078i
$876$	−4.64645	+	1.73685i	−0.156989	+	0.0586826i
$877$	−17.3342	−	30.0236i	−0.585333	−	1.01383i	−0.994834	−	0.101516i	$-0.967631\pi$
$877$	−17.3342	−	30.0236i	−0.585333	−	1.01383i	0.409501	−	0.912310i	$-0.365703\pi$
$878$	5.59046	+	9.68297i	0.188669	+	0.326784i
$879$	−20.0933	+	7.51089i	−0.677730	+	0.253336i
$880$	−2.86525	+	4.96276i	−0.0965875	+	0.167294i
$881$	−5.29854			−0.178512			−0.0892561	−	0.996009i	$-0.528449\pi$
$881$	−5.29854			−0.178512			−0.0892561	+	0.996009i	$0.528449\pi$
$882$	8.04844	+	2.77263i	0.271005	+	0.0933592i
$883$	−10.3025			−0.346706			−0.173353	−	0.984860i	$-0.555460\pi$
$883$	−10.3025			−0.346706			−0.173353	+	0.984860i	$0.555460\pi$
$884$	10.4465	−	18.0938i	0.351353	−	0.608561i
$885$	−1.52884	−	1.26047i	−0.0513913	−	0.0423701i
$886$	−3.00415	−	5.20334i	−0.100926	−	0.174810i
$887$	−20.7252	−	35.8971i	−0.695885	−	1.20531i	−0.969882	−	0.243577i	$-0.921679\pi$
$887$	−20.7252	−	35.8971i	−0.695885	−	1.20531i	0.273997	−	0.961731i	$-0.411654\pi$
$888$	1.09159	−	6.52016i	0.0366315	−	0.218802i
$889$	−1.56163	+	2.70482i	−0.0523753	+	0.0907167i
$890$	−1.71598			−0.0575198
$891$	−22.3064	+	9.00475i	−0.747294	+	0.301670i
$892$	−15.3338			−0.513413
$893$	−16.2541	+	28.1528i	−0.543921	+	0.942099i
$894$	−3.28422	+	19.6168i	−0.109841	+	0.656086i
$895$	7.58123	+	13.1311i	0.253413	+	0.438923i
$896$	8.23445	+	14.2625i	0.275094	+	0.476476i
$897$	−36.9546	−	30.4676i	−1.23388	−	1.01728i
$898$	−6.53674	+	11.3220i	−0.218134	+	0.377819i
$899$	−66.0554			−2.20307
$900$	4.74482	+	1.63455i	0.158161	+	0.0544851i
$901$	−3.05767			−0.101866
$902$	1.12458	−	1.94784i	0.0374446	−	0.0648559i
$903$	−1.09159	+	0.408039i	−0.0363260	+	0.0135787i
$904$	21.1378	+	36.6117i	0.703032	+	1.21769i
$905$	−1.60083	−	2.77272i	−0.0532134	−	0.0921683i
$906$	−2.82040	+	1.05427i	−0.0937015	+	0.0350257i
$907$	8.39606	−	14.5424i	0.278787	−	0.482873i	−0.692297	−	0.721613i	$-0.743401\pi$
$907$	8.39606	−	14.5424i	0.278787	−	0.482873i	0.971083	+	0.238740i	$0.0767344\pi$
$908$	4.47116			0.148381
$909$	−9.51432	+	8.26821i	−0.315570	+	0.274239i
$910$	3.81681			0.126526
$911$	−18.6768	+	32.3491i	−0.618789	+	1.07177i	0.370918	+	0.928666i	$0.379043\pi$
$911$	−18.6768	+	32.3491i	−0.618789	+	1.07177i	−0.989707	+	0.143109i	$0.954290\pi$
$912$	13.3888	+	11.0385i	0.443348	+	0.365522i
$913$	5.72522	+	9.91636i	0.189477	+	0.328184i
$914$	4.01150	+	6.94812i	0.132689	+	0.229823i
$915$	−0.723239	+	4.31995i	−0.0239095	+	0.142813i
$916$	2.13060	−	3.69031i	0.0703970	−	0.121931i
$917$	−8.56804			−0.282942
$918$	−4.14927	−	6.77435i	−0.136946	−	0.223587i
$919$	37.1316			1.22486			0.612429	−	0.790526i	$-0.290193\pi$
$919$	37.1316			1.22486			0.612429	+	0.790526i	$0.290193\pi$
$920$	−6.21598	+	10.7664i	−0.204935	+	0.354957i
$921$	−0.713157	+	4.25973i	−0.0234993	+	0.140363i
$922$	6.89324	+	11.9394i	0.227017	+	0.393205i
$923$	30.0801	+	52.1003i	0.990098	+	1.71490i
$924$	−8.53279	−	7.03494i	−0.280708	−	0.231433i
$925$	0.908405	−	1.57340i	0.0298682	−	0.0517332i
$926$	−19.4135			−0.637967
$927$	−1.03920	−	5.35044i	−0.0341319	−	0.175732i
$928$	−51.5098			−1.69089
$929$	23.9977	−	41.5653i	0.787340	−	1.36371i	−0.140251	−	0.990116i	$-0.544791\pi$
$929$	23.9977	−	41.5653i	0.787340	−	1.36371i	0.927591	−	0.373597i	$-0.121876\pi$
$930$	−6.45967	+	2.41463i	−0.211821	+	0.0791788i
$931$	11.5905	+	20.0753i	0.379862	+	0.657941i
$932$	−5.20259	−	9.01115i	−0.170417	−	0.295170i
$933$	39.2949	−	14.6885i	1.28646	−	0.480879i
$934$	7.82831	−	13.5590i	0.256150	−	0.443665i
$935$	7.14399			0.233633
$936$	−5.61515	−	28.9102i	−0.183537	−	0.944958i
$937$	22.0079			0.718967			0.359483	−	0.933151i	$-0.382953\pi$
$937$	22.0079			0.718967			0.359483	+	0.933151i	$0.382953\pi$
$938$	2.69158	−	4.66195i	0.0878832	−	0.152218i
$939$	−46.8867	−	38.6562i	−1.53009	−	1.26150i
$940$	5.81879	+	10.0784i	0.189788	+	0.328722i
$941$	−20.2921	−	35.1470i	−0.661504	−	1.14576i	−0.980220	−	0.197909i	$-0.936585\pi$
$941$	−20.2921	−	35.1470i	−0.661504	−	1.14576i	0.318716	−	0.947850i	$-0.396748\pi$
$942$	0.0329893	−	0.197047i	0.00107485	−	0.00642015i
$943$	−4.35291	+	7.53946i	−0.141750	+	0.245518i
$944$	−2.45269			−0.0798283
$945$	−3.54203	+	6.52016i	−0.115222	+	0.212101i
$946$	0.720331			0.0234200
$947$	−15.1160	+	26.1817i	−0.491204	+	0.850790i	−0.999949	−	0.0101273i	$-0.996776\pi$
$947$	−15.1160	+	26.1817i	−0.491204	+	0.850790i	0.508745	+	0.860917i	$0.330110\pi$
$948$	0.137773	−	0.822925i	0.00447465	−	0.0267273i
$949$	4.00000	+	6.92820i	0.129845	+	0.224899i
$950$	−1.33641	−	2.31473i	−0.0433589	−	0.0750999i
$951$	−13.9938	−	11.5373i	−0.453780	−	0.374123i
$952$	4.00924	−	6.94420i	0.129940	−	0.225063i
$953$	2.50811			0.0812455			0.0406227	−	0.999175i	$-0.487066\pi$
$953$	2.50811			0.0812455			0.0406227	+	0.999175i	$0.487066\pi$
$954$	−1.48173	+	1.28766i	−0.0479727	+	0.0416896i
$955$	−2.83754			−0.0918207
$956$	6.79439	−	11.7682i	0.219746	−	0.380612i
$957$	41.1510	−	15.3823i	1.33022	−	0.497238i
$958$	−1.49585	−	2.59088i	−0.0483286	−	0.0837077i
$959$	7.28402	+	12.6163i	0.235213	+	0.407401i
$960$	1.91962	−	0.717554i	0.0619554	−	0.0231590i
$961$	−8.72635	+	15.1145i	−0.281495	+	0.487564i
$962$	−4.85601			−0.156564
$963$	−33.8033	−	11.6450i	−1.08930	−	0.375255i
$964$	44.1025			1.42045
$965$	9.39409	−	16.2710i	0.302406	−	0.523783i
$966$	−6.45967	−	5.32574i	−0.207836	−	0.171353i
$967$	10.8765	+	18.8386i	0.349763	+	0.605808i	0.986207	−	0.165515i	$-0.0529286\pi$
$967$	10.8765	+	18.8386i	0.349763	+	0.605808i	−0.636444	+	0.771323i	$0.719595\pi$
$968$	−4.05042	−	7.01552i	−0.130185	−	0.225488i
$969$	3.57199	−	21.3357i	0.114749	−	0.685403i
$970$	−2.24086	+	3.88129i	−0.0719498	+	0.124621i
$971$	22.7512			0.730122			0.365061	−	0.930984i	$-0.381048\pi$
$971$	22.7512			0.730122			0.365061	+	0.930984i	$0.381048\pi$
$972$	24.8669	+	7.85058i	0.797608	+	0.251808i
$973$	11.4241			0.366238
$974$	6.86920	−	11.8978i	0.220103	−	0.381230i
$975$	1.33641	−	7.98247i	0.0427994	−	0.255644i
$976$	2.71090	+	4.69541i	0.0867737	+	0.150296i
$977$	−19.6389	−	34.0156i	−0.628304	−	1.08825i	−0.987892	−	0.155143i	$-0.950416\pi$
$977$	−19.6389	−	34.0156i	−0.628304	−	1.08825i	0.359588	−	0.933111i	$-0.382917\pi$
$978$	13.6195	+	11.2287i	0.435504	+	0.359055i
$979$	4.00924	−	6.94420i	0.128136	−	0.221938i
$980$	8.29854			0.265087
$981$	47.2322	+	16.2711i	1.50801	+	0.519497i
$982$	8.45269			0.269736
$983$	−16.8949	+	29.2629i	−0.538865	+	0.933341i	0.460101	+	0.887867i	$0.347813\pi$
$983$	−16.8949	+	29.2629i	−0.538865	+	0.933341i	−0.998966	+	0.0454743i	$0.985520\pi$
$984$	−5.01432	+	1.87436i	−0.159851	+	0.0597523i
$985$	−2.91764	−	5.05350i	−0.0929638	−	0.161018i
$986$	7.25405	+	12.5644i	0.231016	+	0.400132i
$987$	−16.1177	+	6.02480i	−0.513032	+	0.191772i
$988$	18.2633	−	31.6329i	0.581033	−	1.00638i
$989$	−2.78817			−0.0886587
$990$	3.46193	−	3.00851i	0.110027	−	0.0956168i
$991$	−23.7983			−0.755979			−0.377990	−	0.925810i	$-0.623384\pi$
$991$	−23.7983			−0.755979			−0.377990	+	0.925810i	$0.623384\pi$
$992$	−18.8916	+	32.7213i	−0.599810	+	1.03890i
$993$	22.4218	+	18.4859i	0.711534	+	0.586631i
$994$	5.25801	+	9.10713i	0.166774	+	0.288861i
$995$	−6.53807	−	11.3243i	−0.207271	−	0.359004i
$996$	2.04957	−	12.2422i	0.0649431	−	0.387909i
$997$	−25.8392	+	44.7549i	−0.818337	+	1.41740i	0.0885702	+	0.996070i	$0.471770\pi$
$997$	−25.8392	+	44.7549i	−0.818337	+	1.41740i	−0.906907	+	0.421331i	$0.861563\pi$
$998$	14.2175			0.450046
$999$	4.50641	−	8.29541i	0.142577	−	0.262455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.2.e.b.16.2	✓	6
3.2	odd	2		135.2.e.b.46.2		6
4.3	odd	2		720.2.q.i.241.2		6
5.2	odd	4		225.2.k.b.124.3		12
5.3	odd	4		225.2.k.b.124.4		12
5.4	even	2		225.2.e.b.151.2		6
9.2	odd	6		405.2.a.i.1.2		3
9.4	even	3	inner	45.2.e.b.31.2	yes	6
9.5	odd	6		135.2.e.b.91.2		6
9.7	even	3		405.2.a.j.1.2		3
12.11	even	2		2160.2.q.k.721.2		6
15.2	even	4		675.2.k.b.424.4		12
15.8	even	4		675.2.k.b.424.3		12
15.14	odd	2		675.2.e.b.451.2		6
36.7	odd	6		6480.2.a.bv.1.2		3
36.11	even	6		6480.2.a.bs.1.2		3
36.23	even	6		2160.2.q.k.1441.2		6
36.31	odd	6		720.2.q.i.481.2		6
45.2	even	12		2025.2.b.m.649.3		6
45.4	even	6		225.2.e.b.76.2		6
45.7	odd	12		2025.2.b.l.649.4		6
45.13	odd	12		225.2.k.b.49.3		12
45.14	odd	6		675.2.e.b.226.2		6
45.22	odd	12		225.2.k.b.49.4		12
45.23	even	12		675.2.k.b.199.4		12
45.29	odd	6		2025.2.a.o.1.2		3
45.32	even	12		675.2.k.b.199.3		12
45.34	even	6		2025.2.a.n.1.2		3
45.38	even	12		2025.2.b.m.649.4		6
45.43	odd	12		2025.2.b.l.649.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.e.b.16.2	✓	6	1.1	even	1	trivial
45.2.e.b.31.2	yes	6	9.4	even	3	inner
135.2.e.b.46.2		6	3.2	odd	2
135.2.e.b.91.2		6	9.5	odd	6
225.2.e.b.76.2		6	45.4	even	6
225.2.e.b.151.2		6	5.4	even	2
225.2.k.b.49.3		12	45.13	odd	12
225.2.k.b.49.4		12	45.22	odd	12
225.2.k.b.124.3		12	5.2	odd	4
225.2.k.b.124.4		12	5.3	odd	4
405.2.a.i.1.2		3	9.2	odd	6
405.2.a.j.1.2		3	9.7	even	3
675.2.e.b.226.2		6	45.14	odd	6
675.2.e.b.451.2		6	15.14	odd	2
675.2.k.b.199.3		12	45.32	even	12
675.2.k.b.199.4		12	45.23	even	12
675.2.k.b.424.3		12	15.8	even	4
675.2.k.b.424.4		12	15.2	even	4
720.2.q.i.241.2		6	4.3	odd	2
720.2.q.i.481.2		6	36.31	odd	6
2025.2.a.n.1.2		3	45.34	even	6
2025.2.a.o.1.2		3	45.29	odd	6
2025.2.b.l.649.3		6	45.43	odd	12
2025.2.b.l.649.4		6	45.7	odd	12
2025.2.b.m.649.3		6	45.2	even	12
2025.2.b.m.649.4		6	45.38	even	12
2160.2.q.k.721.2		6	12.11	even	2
2160.2.q.k.1441.2		6	36.23	even	6
6480.2.a.bs.1.2		3	36.11	even	6
6480.2.a.bv.1.2		3	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	45.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.285997 + 0.495361i) q^{2} +(0.285997 - 1.70828i) q^{3} +(0.836412 + 1.44871i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.764419 + 0.630233i) q^{6} +(-0.714003 + 1.23669i) q^{7} -2.10083 q^{8} +(-2.83641 - 0.977122i) q^{9} +O(q^{10})\)	\(q+(-0.285997 + 0.495361i) q^{2} +(0.285997 - 1.70828i) q^{3} +(0.836412 + 1.44871i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.764419 + 0.630233i) q^{6} +(-0.714003 + 1.23669i) q^{7} -2.10083 q^{8} +(-2.83641 - 0.977122i) q^{9} +0.571993 q^{10} +(-1.33641 + 2.31473i) q^{11} +(2.71400 - 1.01450i) q^{12} +(-2.33641 - 4.04678i) q^{13} +(-0.408405 - 0.707378i) q^{14} +(-1.62241 + 0.606458i) q^{15} +(-1.07199 + 1.85675i) q^{16} +2.67282 q^{17} +(1.29523 - 1.12559i) q^{18} +4.67282 q^{19} +(0.836412 - 1.44871i) q^{20} +(1.90841 + 1.57340i) q^{21} +(-0.764419 - 1.32401i) q^{22} +(2.95882 + 5.12483i) q^{23} +(-0.600830 + 3.58880i) q^{24} +(-0.500000 + 0.866025i) q^{25} +2.67282 q^{26} +(-2.48040 + 4.56592i) q^{27} -2.38880 q^{28} +(4.74482 - 8.21826i) q^{29} +(0.163588 - 0.977122i) q^{30} +(-3.48040 - 6.02823i) q^{31} +(-2.71400 - 4.70079i) q^{32} +(3.57199 + 2.94497i) q^{33} +(-0.764419 + 1.32401i) q^{34} +1.42801 q^{35} +(-0.956844 - 4.92641i) q^{36} -1.81681 q^{37} +(-1.33641 + 2.31473i) q^{38} +(-7.58123 + 2.83387i) q^{39} +(1.05042 + 1.81937i) q^{40} +(0.735581 + 1.27406i) q^{41} +(-1.32520 + 0.495361i) q^{42} +(-0.235581 + 0.408039i) q^{43} -4.47116 q^{44} +(0.571993 + 2.94497i) q^{45} -3.38485 q^{46} +(-3.47842 + 6.02480i) q^{47} +(2.86525 + 2.36228i) q^{48} +(2.48040 + 4.29618i) q^{49} +(-0.285997 - 0.495361i) q^{50} +(0.764419 - 4.56592i) q^{51} +(3.90841 - 6.76956i) q^{52} -1.14399 q^{53} +(-1.55239 - 2.53453i) q^{54} +2.67282 q^{55} +(1.50000 - 2.59808i) q^{56} +(1.33641 - 7.98247i) q^{57} +(2.71400 + 4.70079i) q^{58} +(0.571993 + 0.990721i) q^{59} +(-2.23558 - 1.84315i) q^{60} +(1.26442 - 2.19004i) q^{61} +3.98153 q^{62} +(3.23360 - 2.81009i) q^{63} -1.18319 q^{64} +(-2.33641 + 4.04678i) q^{65} +(-2.48040 + 0.927175i) q^{66} +(3.29523 + 5.70751i) q^{67} +(2.23558 + 3.87214i) q^{68} +(9.60083 - 3.58880i) q^{69} +(-0.408405 + 0.707378i) q^{70} -12.8745 q^{71} +(5.95882 + 2.05277i) q^{72} -1.71203 q^{73} +(0.519602 - 0.899976i) q^{74} +(1.33641 + 1.10182i) q^{75} +(3.90841 + 6.76956i) q^{76} +(-1.90841 - 3.30545i) q^{77} +(0.764419 - 4.56592i) q^{78} +(0.143987 - 0.249392i) q^{79} +2.14399 q^{80} +(7.09046 + 5.54304i) q^{81} -0.841495 q^{82} +(2.14201 - 3.71007i) q^{83} +(-0.683190 + 4.08074i) q^{84} +(-1.33641 - 2.31473i) q^{85} +(-0.134751 - 0.233396i) q^{86} +(-12.6821 - 10.4559i) q^{87} +(2.80757 - 4.86286i) q^{88} -3.00000 q^{89} +(-1.62241 - 0.558907i) q^{90} +6.67282 q^{91} +(-4.94958 + 8.57293i) q^{92} +(-11.2933 + 4.22143i) q^{93} +(-1.98963 - 3.44615i) q^{94} +(-2.33641 - 4.04678i) q^{95} +(-8.80644 + 3.29186i) q^{96} +(-3.91764 + 6.78555i) q^{97} -2.83754 q^{98} +(6.05239 - 5.25970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + q^{3} - 5 q^{4} - 3 q^{5} - 4 q^{6} - 5 q^{7} + 6 q^{8} - 7 q^{9}+O(q^{10}) \) 6 * q - q^2 + q^3 - 5 * q^4 - 3 * q^5 - 4 * q^6 - 5 * q^7 + 6 * q^8 - 7 * q^9	\( 6 q - q^{2} + q^{3} - 5 q^{4} - 3 q^{5} - 4 q^{6} - 5 q^{7} + 6 q^{8} - 7 q^{9} + 2 q^{10} + 2 q^{11} + 17 q^{12} - 4 q^{13} + 9 q^{14} + q^{15} - 5 q^{16} - 4 q^{17} - 23 q^{18} + 8 q^{19} - 5 q^{20} + 4 q^{22} - 3 q^{23} + 15 q^{24} - 3 q^{25} - 4 q^{26} - 2 q^{27} + 10 q^{28} + 7 q^{29} + 11 q^{30} - 8 q^{31} - 17 q^{32} + 20 q^{33} + 4 q^{34} + 10 q^{35} + 10 q^{36} + 12 q^{37} + 2 q^{38} - 14 q^{39} - 3 q^{40} + 13 q^{41} - 33 q^{42} - 10 q^{43} - 44 q^{44} + 2 q^{45} - 6 q^{46} - 13 q^{47} - 10 q^{48} + 2 q^{49} - q^{50} - 4 q^{51} + 12 q^{52} - 4 q^{53} + 5 q^{54} - 4 q^{55} + 9 q^{56} - 2 q^{57} + 17 q^{58} + 2 q^{59} - 22 q^{60} - q^{61} + 84 q^{62} + 33 q^{63} - 30 q^{64} - 4 q^{65} - 2 q^{66} - 11 q^{67} + 22 q^{68} + 39 q^{69} + 9 q^{70} - 20 q^{71} + 15 q^{72} - 16 q^{73} + 16 q^{74} - 2 q^{75} + 12 q^{76} - 4 q^{78} - 2 q^{79} + 10 q^{80} - 19 q^{81} - 58 q^{82} + 15 q^{83} - 27 q^{84} + 2 q^{85} - 28 q^{86} - 26 q^{87} + 24 q^{88} - 18 q^{89} + q^{90} + 20 q^{91} - 39 q^{92} - 42 q^{93} + 31 q^{94} - 4 q^{95} + 13 q^{96} + 18 q^{97} - 80 q^{98} + 22 q^{99}+O(q^{100}) \) 6 * q - q^2 + q^3 - 5 * q^4 - 3 * q^5 - 4 * q^6 - 5 * q^7 + 6 * q^8 - 7 * q^9 + 2 * q^10 + 2 * q^11 + 17 * q^12 - 4 * q^13 + 9 * q^14 + q^15 - 5 * q^16 - 4 * q^17 - 23 * q^18 + 8 * q^19 - 5 * q^20 + 4 * q^22 - 3 * q^23 + 15 * q^24 - 3 * q^25 - 4 * q^26 - 2 * q^27 + 10 * q^28 + 7 * q^29 + 11 * q^30 - 8 * q^31 - 17 * q^32 + 20 * q^33 + 4 * q^34 + 10 * q^35 + 10 * q^36 + 12 * q^37 + 2 * q^38 - 14 * q^39 - 3 * q^40 + 13 * q^41 - 33 * q^42 - 10 * q^43 - 44 * q^44 + 2 * q^45 - 6 * q^46 - 13 * q^47 - 10 * q^48 + 2 * q^49 - q^50 - 4 * q^51 + 12 * q^52 - 4 * q^53 + 5 * q^54 - 4 * q^55 + 9 * q^56 - 2 * q^57 + 17 * q^58 + 2 * q^59 - 22 * q^60 - q^61 + 84 * q^62 + 33 * q^63 - 30 * q^64 - 4 * q^65 - 2 * q^66 - 11 * q^67 + 22 * q^68 + 39 * q^69 + 9 * q^70 - 20 * q^71 + 15 * q^72 - 16 * q^73 + 16 * q^74 - 2 * q^75 + 12 * q^76 - 4 * q^78 - 2 * q^79 + 10 * q^80 - 19 * q^81 - 58 * q^82 + 15 * q^83 - 27 * q^84 + 2 * q^85 - 28 * q^86 - 26 * q^87 + 24 * q^88 - 18 * q^89 + q^90 + 20 * q^91 - 39 * q^92 - 42 * q^93 + 31 * q^94 - 4 * q^95 + 13 * q^96 + 18 * q^97 - 80 * q^98 + 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more