LMFDB - Embedded newform 45.2.e.b.31.2

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			31.2
Root			$-1.62241 - 0.606458i$ of defining polynomial
Character	$\chi$	$=$	45.31
Dual form			45.2.e.b.16.2

$q$-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 $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.285997	−	0.495361i	−0.202230	−	0.350273i	0.747017	−	0.664805i	$-0.231486\pi$
$2$	−0.285997	−	0.495361i	−0.202230	−	0.350273i	−0.949247	+	0.314533i	$0.898152\pi$
$3$	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	0.698960	−	0.715161i	$-0.253647\pi$
$7$	−0.714003	−	1.23669i	−0.269868	−	0.467425i	−0.968828	+	0.247736i	$0.920313\pi$
$8$	−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	0.591136	−	0.806572i	$-0.298679\pi$
$11$	−1.33641	−	2.31473i	−0.402943	−	0.697918i	−0.994080	+	0.108653i	$0.965346\pi$
$12$	2.71400	+	1.01450i	0.783465	+	0.292860i
$13$	−2.33641	+	4.04678i	−0.648004	+	1.12238i	0.335595	+	0.942006i	$0.391063\pi$
$13$	−2.33641	+	4.04678i	−0.648004	+	1.12238i	−0.983599	+	0.180370i	$0.942271\pi$
$14$	−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	−0.373081	−	0.927799i	$-0.621699\pi$
$23$	2.95882	−	5.12483i	0.616957	−	1.06860i	0.990038	−	0.140802i	$-0.0449680\pi$
$24$	−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	0.850130	+	0.526573i	$0.176523\pi$
$29$	4.74482	+	8.21826i	0.881090	+	1.52609i	0.0309603	+	0.999521i	$0.490143\pi$
$30$	0.163588	+	0.977122i	0.0298670	+	0.178397i
$31$	−3.48040	+	6.02823i	−0.625098	+	1.08270i	0.363424	+	0.931624i	$0.381608\pi$
$31$	−3.48040	+	6.02823i	−0.625098	+	1.08270i	−0.988522	+	0.151078i	$0.951726\pi$
$32$	−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	−0.802853	−	0.596177i	$-0.796685\pi$
$41$	0.735581	−	1.27406i	0.114879	−	0.198975i	0.917731	+	0.397202i	$0.130019\pi$
$42$	−1.32520	−	0.495361i	−0.204483	−	0.0764358i
$43$	−0.235581	−	0.408039i	−0.0359258	−	0.0622254i	0.847503	−	0.530790i	$-0.178105\pi$
$43$	−0.235581	−	0.408039i	−0.0359258	−	0.0622254i	−0.883429	+	0.468565i	$0.844771\pi$
$44$	−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	−0.999964	−	0.00854274i	$-0.997281\pi$
$47$	−3.47842	−	6.02480i	−0.507380	−	0.878808i	0.492584	−	0.870265i	$-0.336053\pi$
$48$	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	−0.826387	−	0.563102i	$-0.809608\pi$
$59$	0.571993	−	0.990721i	0.0744672	−	0.128981i	0.900854	+	0.434121i	$0.142941\pi$
$60$	−2.23558	+	1.84315i	−0.288612	+	0.237949i
$61$	1.26442	+	2.19004i	0.161892	+	0.280406i	0.935547	−	0.353201i	$-0.114907\pi$
$61$	1.26442	+	2.19004i	0.161892	+	0.280406i	−0.773655	+	0.633607i	$0.781574\pi$
$62$	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	−0.591459	−	0.806335i	$-0.701448\pi$
$67$	3.29523	−	5.70751i	0.402577	−	0.697283i	0.994036	+	0.109051i	$0.0347813\pi$
$68$	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	0.874012	−	0.485905i	$-0.161510\pi$
$79$	0.143987	+	0.249392i	0.0161998	+	0.0280588i	−0.857812	+	0.513964i	$0.828177\pi$
$80$	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	0.959306	−	0.282367i	$-0.0911196\pi$
$83$	2.14201	+	3.71007i	0.235116	+	0.407233i	−0.724190	+	0.689600i	$0.757786\pi$
$84$	−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	0.595675	−	0.803225i	$-0.296885\pi$
$97$	−3.91764	−	6.78555i	−0.397776	−	0.688968i	−0.993451	+	0.114257i	$0.963551\pi$
$98$	−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	0.951413	−	0.307919i	$-0.0996326\pi$
$101$	2.10083	+	3.63875i	0.209040	+	0.362069i	−0.742372	+	0.669988i	$0.766299\pi$
$102$	2.04316	−	1.68450i	0.202303	−	0.166790i
$103$	0.908405	−	1.57340i	0.0895078	−	0.155032i	−0.817795	−	0.575509i	$-0.804804\pi$
$103$	0.908405	−	1.57340i	0.0895078	−	0.155032i	0.907303	+	0.420477i	$0.138137\pi$
$104$	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	−0.193836	+	0.981034i	$0.562093\pi$
$113$	−10.0616	+	17.4272i	−0.946518	+	1.63942i	−0.752682	+	0.658384i	$0.771240\pi$
$114$	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	−0.704692	−	0.709514i	$-0.748915\pi$
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	0.966803	+	0.255524i	$0.0822479\pi$
$132$	−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	0.997360	−	0.0726153i	$-0.0231345\pi$
$137$	5.10083	+	8.83490i	0.435793	+	0.754816i	−0.561567	+	0.827431i	$0.689801\pi$
$138$	−0.968056	−	5.78226i	−0.0824064	−	0.492218i
$139$	−4.00000	+	6.92820i	−0.339276	+	0.587643i	−0.984297	−	0.176522i	$-0.943515\pi$
$139$	−4.00000	+	6.92820i	−0.339276	+	0.587643i	0.645021	+	0.764165i	$0.276849\pi$
$140$	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	−0.0815762	−	0.996667i	$-0.525995\pi$
$149$	10.0381	−	17.3865i	0.822351	−	1.42435i	0.903927	−	0.427687i	$-0.140671\pi$
$150$	−0.928007	−	0.346890i	−0.0757714	−	0.0283234i
$151$	−1.51960	−	2.63203i	−0.123663	−	0.214191i	0.797546	−	0.603258i	$-0.206131\pi$
$151$	−1.51960	−	2.63203i	−0.123663	−	0.214191i	−0.921210	+	0.389066i	$0.872798\pi$
$152$	−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	−0.870021	−	0.493015i	$-0.835895\pi$
$157$	−0.100830	+	0.174643i	−0.00804714	+	0.0139381i	0.861974	+	0.506953i	$0.169228\pi$
$158$	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	0.452993	+	0.891514i	$0.350356\pi$
$167$	−7.05042	+	12.2117i	−0.545578	+	0.944968i	−0.998570	+	0.0534538i	$0.982977\pi$
$168$	−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	0.771020	−	0.636811i	$-0.219747\pi$
$173$	−2.18319	−	3.78140i	−0.165985	−	0.287494i	−0.937005	+	0.349317i	$0.886414\pi$
$174$	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	0.912779	−	0.408453i	$-0.133932\pi$
$191$	1.41877	+	2.45738i	0.102659	+	0.177810i	−0.810121	+	0.586263i	$0.800598\pi$
$192$	−0.338388	−	2.02121i	−0.0244211	−	0.145869i
$193$	9.39409	−	16.2710i	0.676201	−	1.17121i	−0.299915	−	0.953966i	$-0.596958\pi$
$193$	9.39409	−	16.2710i	0.676201	−	1.17121i	0.976116	−	0.217249i	$-0.0697083\pi$
$194$	−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	−0.973480	−	0.228771i	$-0.926529\pi$
$211$	−4.19243	+	7.26149i	−0.288618	+	0.499902i	0.684862	+	0.728673i	$0.259863\pi$
$212$	−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	0.670772	−	0.741664i	$-0.265963\pi$
$223$	−4.58321	−	7.93834i	−0.306914	−	0.531591i	−0.977686	+	0.210073i	$0.932630\pi$
$224$	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	0.906962	−	0.421212i	$-0.138395\pi$
$227$	1.33641	+	2.31473i	0.0887008	+	0.153634i	−0.818261	+	0.574846i	$0.805062\pi$
$228$	12.6821	+	4.74056i	0.839890	+	0.313951i
$229$	−1.27365	+	2.20603i	−0.0841654	+	0.145779i	−0.905035	−	0.425336i	$-0.860156\pi$
$229$	−1.27365	+	2.20603i	−0.0841654	+	0.145779i	0.820870	+	0.571115i	$0.193489\pi$
$230$	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	−0.966965	−	0.254909i	$-0.917954\pi$
$239$	−4.06163	+	7.03494i	−0.262725	+	0.455053i	0.704240	+	0.709962i	$0.251288\pi$
$240$	0.613173	+	3.66252i	0.0395801	+	0.236415i
$241$	13.1821	+	22.8320i	0.849131	+	1.47074i	0.881985	+	0.471278i	$0.156207\pi$
$241$	13.1821	+	22.8320i	0.849131	+	1.47074i	−0.0328536	+	0.999460i	$0.510460\pi$
$242$	−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	−0.435970	−	0.899961i	$-0.643595\pi$
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	0.997374	−	0.0724199i	$-0.0230722\pi$
$258$	−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	0.622309	−	0.782771i	$-0.286195\pi$
$263$	−5.94761	−	10.3016i	−0.366745	−	0.635221i	−0.989055	+	0.147550i	$0.952861\pi$
$264$	−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	0.998566	−	0.0535366i	$-0.0170494\pi$
$277$	7.53807	+	13.0563i	0.452919	+	0.784479i	−0.545647	+	0.838015i	$0.683716\pi$
$278$	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	0.749599	−	0.661892i	$-0.230246\pi$
$281$	−3.32605	−	5.76088i	−0.198415	−	0.343665i	−0.948015	+	0.318226i	$0.896913\pi$
$282$	−6.45600	−	2.41326i	−0.384449	−	0.143707i
$283$	−13.4485	+	23.2934i	−0.799428	+	1.38465i	0.120562	+	0.992706i	$0.461530\pi$
$283$	−13.4485	+	23.2934i	−0.799428	+	1.38465i	−0.919989	+	0.391943i	$0.871803\pi$
$284$	−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	−0.988251	−	0.152837i	$-0.951159\pi$
$293$	−6.19243	+	10.7256i	−0.361765	+	0.626596i	0.626486	+	0.779433i	$0.284493\pi$
$294$	−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	−0.286201	−	0.958170i	$-0.592392\pi$
$311$	12.1101	−	20.9752i	0.686699	−	1.18940i	0.972900	−	0.231228i	$-0.0742742\pi$
$312$	15.9269	+	5.95348i	0.901682	+	0.337049i
$313$	17.5420	+	30.3837i	0.991534	+	1.71739i	0.608219	+	0.793770i	$0.291884\pi$
$313$	17.5420	+	30.3837i	0.991534	+	1.71739i	0.383315	+	0.923618i	$0.374782\pi$
$314$	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	0.974766	−	0.223231i	$-0.0716603\pi$
$317$	5.23558	+	9.06829i	0.294060	+	0.509326i	−0.680706	+	0.732557i	$0.738327\pi$
$318$	−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	0.537925	−	0.842993i	$-0.319208\pi$
$331$	−8.38880	−	14.5298i	−0.461090	−	0.798632i	−0.999016	+	0.0443606i	$0.985875\pi$
$332$	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	−0.212030	−	0.977263i	$-0.568007\pi$
$337$	13.5905	−	23.5394i	0.740320	−	1.28227i	0.952350	−	0.305008i	$-0.0986592\pi$
$338$	−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	−0.354492	−	0.935059i	$-0.615346\pi$
$347$	11.7829	−	20.4086i	0.632539	−	1.09559i	0.987031	−	0.160530i	$-0.0513204\pi$
$348$	4.54005	+	27.1180i	0.243372	+	1.45368i
$349$	5.35601	+	9.27689i	0.286701	+	0.496580i	0.973020	−	0.230720i	$-0.0741081\pi$
$349$	5.35601	+	9.27689i	0.286701	+	0.496580i	−0.686319	+	0.727300i	$0.740775\pi$
$350$	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	−0.958708	−	0.284392i	$-0.908208\pi$
$353$	−13.6336	−	23.6141i	−0.725644	−	1.25685i	0.233064	−	0.972461i	$-0.425125\pi$
$354$	−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	0.955141	−	0.296152i	$-0.0957034\pi$
$367$	4.23558	+	7.33624i	0.221096	+	0.382949i	−0.734045	+	0.679100i	$0.762370\pi$
$368$	−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	−0.966795	−	0.255554i	$-0.917742\pi$
$373$	−5.06163	+	8.76700i	−0.262081	+	0.453938i	0.704714	+	0.709492i	$0.251075\pi$
$374$	−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	−0.963748	−	0.266813i	$-0.914030\pi$
$383$	−4.90841	+	8.50161i	−0.250808	+	0.434412i	0.712941	+	0.701224i	$0.247363\pi$
$384$	−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	0.725166	−	0.688574i	$-0.241763\pi$
$389$	−4.61007	−	7.98487i	−0.233740	−	0.404849i	−0.958906	+	0.283725i	$0.908430\pi$
$390$	−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	−0.694167	−	0.719814i	$-0.744227\pi$
$401$	5.53279	−	9.58307i	0.276294	−	0.478556i	0.970461	+	0.241259i	$0.0775602\pi$
$402$	−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	−0.561411	−	0.827537i	$-0.689741\pi$
$409$	8.81681	−	15.2712i	0.435963	−	0.755110i	0.997374	+	0.0724270i	$0.0230744\pi$
$410$	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	−0.0832199	+	0.996531i	$0.526520\pi$
$419$	−18.5173	+	32.0730i	−0.904631	+	1.56687i	−0.821411	+	0.570336i	$0.806813\pi$
$420$	3.87562	+	1.44871i	0.189111	+	0.0706897i
$421$	−2.52884	−	4.38007i	−0.123248	−	0.213472i	0.797799	−	0.602924i	$-0.205998\pi$
$421$	−2.52884	−	4.38007i	−0.123248	−	0.213472i	−0.921047	+	0.389452i	$0.872664\pi$
$422$	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	0.999267	−	0.0382924i	$-0.0121918\pi$
$439$	9.77365	+	16.9285i	0.466471	+	0.807952i	−0.532796	+	0.846244i	$0.678859\pi$
$440$	−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	0.713863	−	0.700286i	$-0.246944\pi$
$443$	−5.25208	−	9.09686i	−0.249534	−	0.432205i	−0.963396	+	0.268081i	$0.913611\pi$
$444$	−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	0.982127	−	0.188217i	$-0.0602708\pi$
$457$	7.01319	+	12.1472i	0.328063	+	0.568222i	−0.654064	+	0.756439i	$0.726937\pi$
$458$	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	0.997385	+	0.0722736i	$0.0230255\pi$
$461$	12.0513	+	20.8734i	0.561283	+	0.972171i	−0.436102	+	0.899897i	$0.643641\pi$
$462$	0.624385	+	3.72949i	0.0290490	+	0.173512i
$463$	16.9700	−	29.3930i	0.788664	−	1.36601i	−0.138121	−	0.990415i	$-0.544106\pi$
$463$	16.9700	−	29.3930i	0.788664	−	1.36601i	0.926785	−	0.375591i	$-0.122560\pi$
$464$	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	0.800076	−	0.599898i	$-0.204792\pi$
$479$	−2.61515	−	4.52957i	−0.119489	−	0.206961i	−0.919565	+	0.392937i	$0.871459\pi$
$480$	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	−0.983186	−	0.182606i	$-0.941547\pi$
$491$	−7.38880	+	12.7978i	−0.333452	+	0.577556i	0.649734	+	0.760161i	$0.274880\pi$
$492$	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	0.441443	+	0.897289i	$0.354467\pi$
$499$	−12.4280	+	21.5259i	−0.556354	+	0.963633i	−0.997797	+	0.0663440i	$0.978867\pi$
$500$	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	−0.887548	−	0.460715i	$-0.847593\pi$
$509$	−1.01037	+	1.75001i	−0.0447837	+	0.0775676i	0.842765	+	0.538282i	$0.180927\pi$
$510$	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	−0.875702	−	0.482851i	$-0.839601\pi$
$547$	−20.0204	−	34.6764i	−0.856013	−	1.48266i	0.0196900	−	0.999806i	$-0.493732\pi$
$548$	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	0.370836	+	0.928698i	$0.379071\pi$
$563$	−14.6840	+	25.4335i	−0.618858	+	1.07189i	−0.989694	+	0.143196i	$0.954262\pi$
$564$	−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	−0.658056	−	0.752969i	$-0.728621\pi$
$569$	−23.4033	−	40.5357i	−0.981118	−	1.69935i	−0.323062	−	0.946378i	$-0.604712\pi$
$570$	0.764419	+	4.56592i	0.0320180	+	0.191245i
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$	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	0.616882	−	0.787056i	$-0.288396\pi$
$587$	−9.04118	−	15.6598i	−0.373169	−	0.646348i	−0.990051	+	0.140707i	$0.955062\pi$
$588$	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	−0.426100	−	0.904676i	$-0.640113\pi$
$599$	13.9608	−	24.1808i	0.570423	−	0.988001i	0.996522	−	0.0833249i	$-0.0265539\pi$
$600$	−2.80757	+	2.31473i	−0.114619	+	0.0944986i
$601$	−19.2201	−	33.2902i	−0.784006	−	1.35794i	−0.929591	−	0.368592i	$-0.879840\pi$
$601$	−19.2201	−	33.2902i	−0.784006	−	1.35794i	0.145586	−	0.989346i	$-0.453493\pi$
$602$	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	−0.859460	−	0.511203i	$-0.829200\pi$
$607$	0.319917	−	0.554113i	0.0129850	−	0.0224907i	0.872445	+	0.488712i	$0.162533\pi$
$608$	−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	−0.996400	−	0.0847805i	$-0.972981\pi$
$617$	−10.5513	+	18.2753i	−0.424778	+	0.735737i	0.571622	+	0.820517i	$0.306314\pi$
$618$	−0.297209	−	1.77525i	−0.0119555	−	0.0714109i
$619$	6.82605	+	11.8231i	0.274362	+	0.475209i	0.969974	−	0.243209i	$-0.0782000\pi$
$619$	6.82605	+	11.8231i	0.274362	+	0.475209i	−0.695612	+	0.718418i	$0.744867\pi$
$620$	−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	−0.999753	−	0.0222106i	$-0.992930\pi$
$641$	−13.1429	−	22.7641i	−0.519112	−	0.899128i	0.480642	−	0.876917i	$-0.340404\pi$
$642$	9.11007	−	7.51089i	0.359546	−	0.296431i
$643$	−10.2913	+	17.8250i	−0.405848	+	0.702950i	−0.994420	−	0.105495i	$-0.966357\pi$
$643$	−10.2913	+	17.8250i	−0.405848	+	0.702950i	0.588571	+	0.808445i	$0.299691\pi$
$644$	−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	−0.989103	−	0.147225i	$-0.952966\pi$
$653$	−9.37957	+	16.2459i	−0.367051	+	0.635751i	0.622052	+	0.782976i	$0.286299\pi$
$654$	−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	0.868740	−	0.495268i	$-0.164930\pi$
$659$	0.140034	+	0.242545i	0.00545494	+	0.00944823i	−0.863285	+	0.504717i	$0.831597\pi$
$660$	7.25405	+	2.71157i	0.282364	+	0.105548i
$661$	19.8930	−	34.4556i	0.773746	−	1.34017i	−0.161750	−	0.986832i	$-0.551714\pi$
$661$	19.8930	−	34.4556i	0.773746	−	1.34017i	0.935496	−	0.353336i	$-0.114953\pi$
$662$	−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	−0.984018	−	0.178068i	$-0.943015\pi$
$673$	−16.7644	−	29.0368i	−0.646221	−	1.11929i	0.337797	−	0.941219i	$-0.390318\pi$
$674$	−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	−0.999459	−	0.0328897i	$-0.989529\pi$
$677$	−13.7437	−	23.8048i	−0.528213	−	0.914891i	0.471246	−	0.882002i	$-0.343804\pi$
$678$	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	−0.934970	−	0.354727i	$-0.884574\pi$
$691$	−20.3641	−	35.2717i	−0.774688	−	1.34180i	0.160282	−	0.987071i	$-0.448760\pi$
$692$	−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	0.688904	−	0.724853i	$-0.258092\pi$
$709$	−7.54316	−	13.0651i	−0.283289	−	0.490671i	−0.972193	+	0.234182i	$0.924759\pi$
$710$	−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	0.979732	+	0.200315i	$0.0641966\pi$
$727$	17.8857	+	30.9789i	0.663344	+	1.14895i	−0.316388	+	0.948630i	$0.602470\pi$
$728$	−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	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$	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	−0.531536	−	0.847036i	$-0.678385\pi$
$743$	12.7509	−	22.0853i	0.467787	−	0.810231i	0.999322	+	0.0368054i	$0.0117182\pi$
$744$	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	−0.648016	−	0.761627i	$-0.724401\pi$
$751$	9.19638	−	15.9286i	0.335581	−	0.581243i	0.983596	+	0.180384i	$0.0577342\pi$
$752$	−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	−0.784698	−	0.619878i	$-0.787182\pi$
$761$	3.98568	−	6.90340i	0.144481	−	0.250248i	0.929179	+	0.369630i	$0.120515\pi$
$762$	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	−0.915244	−	0.402901i	$-0.868002\pi$
$769$	−3.01432	+	5.22095i	−0.108699	+	0.188272i	0.806544	+	0.591174i	$0.201335\pi$
$770$	−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	−0.976158	−	0.217063i	$-0.930352\pi$
$787$	−8.41877	+	14.5817i	−0.300097	+	0.519783i	0.676061	+	0.736846i	$0.263686\pi$
$788$	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	−0.403043	−	0.915181i	$-0.632047\pi$
$797$	16.6860	−	28.9010i	0.591049	−	1.02373i	0.994091	−	0.108545i	$-0.0346193\pi$
$798$	−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	0.995310	−	0.0967393i	$-0.0308413\pi$
$821$	11.8588	+	20.5401i	0.413876	+	0.716855i	−0.581434	+	0.813594i	$0.697508\pi$
$822$	9.46721	+	3.53885i	0.330207	+	0.123432i
$823$	−9.68404	+	16.7732i	−0.337564	+	0.584678i	−0.983974	−	0.178312i	$-0.942936\pi$
$823$	−9.68404	+	16.7732i	−0.337564	+	0.584678i	0.646410	+	0.762990i	$0.276270\pi$
$824$	−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	0.997065	−	0.0765655i	$-0.0243954\pi$
$839$	12.5196	+	21.6846i	0.432225	+	0.748635i	−0.564840	+	0.825201i	$0.691062\pi$
$840$	−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	0.943969	−	0.330033i	$-0.107060\pi$
$853$	5.43724	+	9.41758i	0.186168	+	0.322452i	−0.757802	+	0.652485i	$0.773727\pi$
$854$	−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	0.979984	−	0.199077i	$-0.0637942\pi$
$857$	9.29721	+	16.1032i	0.317587	+	0.550076i	−0.662397	+	0.749153i	$0.730461\pi$
$858$	9.54731	−	7.87137i	0.325940	−	0.268724i
$859$	2.33246	−	4.03994i	0.0795825	−	0.137841i	−0.823487	−	0.567335i	$-0.807975\pi$
$859$	2.33246	−	4.03994i	0.0795825	−	0.137841i	0.903070	+	0.429494i	$0.141308\pi$
$860$	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	0.409501	+	0.912310i	$0.365703\pi$
$877$	−17.3342	+	30.0236i	−0.585333	+	1.01383i	−0.994834	+	0.101516i	$0.967631\pi$
$878$	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	0.273997	+	0.961731i	$0.411654\pi$
$887$	−20.7252	+	35.8971i	−0.695885	+	1.20531i	−0.969882	+	0.243577i	$0.921679\pi$
$888$	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	0.971083	−	0.238740i	$-0.0767344\pi$
$907$	8.39606	+	14.5424i	0.278787	+	0.482873i	−0.692297	+	0.721613i	$0.743401\pi$
$908$	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	−0.989707	−	0.143109i	$-0.954290\pi$
$911$	−18.6768	−	32.3491i	−0.618789	−	1.07177i	0.370918	−	0.928666i	$-0.379043\pi$
$912$	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	0.927591	+	0.373597i	$0.121876\pi$
$929$	23.9977	+	41.5653i	0.787340	+	1.36371i	−0.140251	+	0.990116i	$0.544791\pi$
$930$	−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	0.318716	+	0.947850i	$0.396748\pi$
$941$	−20.2921	+	35.1470i	−0.661504	+	1.14576i	−0.980220	+	0.197909i	$0.936585\pi$
$942$	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	0.508745	−	0.860917i	$-0.330110\pi$
$947$	−15.1160	−	26.1817i	−0.491204	−	0.850790i	−0.999949	+	0.0101273i	$0.996776\pi$
$948$	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	−0.636444	−	0.771323i	$-0.719595\pi$
$967$	10.8765	−	18.8386i	0.349763	−	0.605808i	0.986207	+	0.165515i	$0.0529286\pi$
$968$	−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	0.359588	+	0.933111i	$0.382917\pi$
$977$	−19.6389	+	34.0156i	−0.628304	+	1.08825i	−0.987892	+	0.155143i	$0.950416\pi$
$978$	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	−0.998966	−	0.0454743i	$-0.985520\pi$
$983$	−16.8949	−	29.2629i	−0.538865	−	0.933341i	0.460101	−	0.887867i	$-0.347813\pi$
$984$	−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	−0.906907	−	0.421331i	$-0.861563\pi$
$997$	−25.8392	−	44.7549i	−0.818337	−	1.41740i	0.0885702	−	0.996070i	$-0.471770\pi$
$998$	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.31.2	yes	6
3.2	odd	2		135.2.e.b.91.2		6
4.3	odd	2		720.2.q.i.481.2		6
5.2	odd	4		225.2.k.b.49.4		12
5.3	odd	4		225.2.k.b.49.3		12
5.4	even	2		225.2.e.b.76.2		6
9.2	odd	6		135.2.e.b.46.2		6
9.4	even	3		405.2.a.j.1.2		3
9.5	odd	6		405.2.a.i.1.2		3
9.7	even	3	inner	45.2.e.b.16.2	✓	6
12.11	even	2		2160.2.q.k.1441.2		6
15.2	even	4		675.2.k.b.199.3		12
15.8	even	4		675.2.k.b.199.4		12
15.14	odd	2		675.2.e.b.226.2		6
36.7	odd	6		720.2.q.i.241.2		6
36.11	even	6		2160.2.q.k.721.2		6
36.23	even	6		6480.2.a.bs.1.2		3
36.31	odd	6		6480.2.a.bv.1.2		3
45.2	even	12		675.2.k.b.424.4		12
45.4	even	6		2025.2.a.n.1.2		3
45.7	odd	12		225.2.k.b.124.3		12
45.13	odd	12		2025.2.b.l.649.3		6
45.14	odd	6		2025.2.a.o.1.2		3
45.22	odd	12		2025.2.b.l.649.4		6
45.23	even	12		2025.2.b.m.649.4		6
45.29	odd	6		675.2.e.b.451.2		6
45.32	even	12		2025.2.b.m.649.3		6
45.34	even	6		225.2.e.b.151.2		6
45.38	even	12		675.2.k.b.424.3		12
45.43	odd	12		225.2.k.b.124.4		12

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

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