LMFDB - Embedded newform 570.2.s.a.221.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(221,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("570.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.s (of order $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			221.9
Character	$\chi$	$=$	570.221
Dual form			570.2.s.a.521.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.37489 + 1.05342i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.224845 - 1.71739i) q^{6} -1.74360 q^{7} +1.00000 q^{8} +(0.780619 + 2.89666i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.37489 + 1.05342i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.224845 - 1.71739i) q^{6} -1.74360 q^{7} +1.00000 q^{8} +(0.780619 + 2.89666i) q^{9} +(-0.866025 - 0.500000i) q^{10} -4.48400i q^{11} +(-1.59973 + 0.663976i) q^{12} +(3.14527 + 1.81592i) q^{13} +(0.871800 + 1.51000i) q^{14} +(1.71739 + 0.224845i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(5.72021 - 3.30257i) q^{17} +(2.11827 - 2.12437i) q^{18} +(3.74911 + 2.22354i) q^{19} +1.00000i q^{20} +(-2.39725 - 1.83674i) q^{21} +(-3.88325 + 2.24200i) q^{22} +(1.69230 + 0.977053i) q^{23} +(1.37489 + 1.05342i) q^{24} +(0.500000 - 0.866025i) q^{25} -3.63184i q^{26} +(-1.97813 + 4.80489i) q^{27} +(0.871800 - 1.51000i) q^{28} +(-0.271323 + 0.469946i) q^{29} +(-0.663976 - 1.59973i) q^{30} +8.66957i q^{31} +(-0.500000 + 0.866025i) q^{32} +(4.72353 - 6.16498i) q^{33} +(-5.72021 - 3.30257i) q^{34} +(-1.51000 + 0.871800i) q^{35} +(-2.89889 - 0.772294i) q^{36} -0.251265i q^{37} +(0.0510884 - 4.35860i) q^{38} +(2.41146 + 5.80997i) q^{39} +(0.866025 - 0.500000i) q^{40} +(2.28336 + 3.95489i) q^{41} +(-0.392039 + 2.99445i) q^{42} +(-2.13741 - 3.70210i) q^{43} +(3.88325 + 2.24200i) q^{44} +(2.12437 + 2.11827i) q^{45} -1.95411i q^{46} +(1.28818 + 0.743732i) q^{47} +(0.224845 - 1.71739i) q^{48} -3.95986 q^{49} -1.00000 q^{50} +(11.3436 + 1.48513i) q^{51} +(-3.14527 + 1.81592i) q^{52} +(-0.0649443 + 0.112487i) q^{53} +(5.15023 - 0.689332i) q^{54} +(-2.24200 - 3.88325i) q^{55} -1.74360 q^{56} +(2.81228 + 7.00650i) q^{57} +0.542647 q^{58} +(-3.22878 - 5.59241i) q^{59} +(-1.05342 + 1.37489i) q^{60} +(1.04215 - 1.80505i) q^{61} +(7.50806 - 4.33478i) q^{62} +(-1.36109 - 5.05062i) q^{63} +1.00000 q^{64} +3.63184 q^{65} +(-7.70079 - 1.00820i) q^{66} +(-7.40682 - 4.27633i) q^{67} +6.60513i q^{68} +(1.29748 + 3.12604i) q^{69} +(1.51000 + 0.871800i) q^{70} +(-4.78907 - 8.29492i) q^{71} +(0.780619 + 2.89666i) q^{72} +(-3.51522 - 6.08853i) q^{73} +(-0.217602 + 0.125633i) q^{74} +(1.59973 - 0.663976i) q^{75} +(-3.80020 + 2.13506i) q^{76} +7.81830i q^{77} +(3.82585 - 4.99337i) q^{78} +(-5.04814 + 2.91454i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(-7.78127 + 4.52237i) q^{81} +(2.28336 - 3.95489i) q^{82} -10.2566i q^{83} +(2.78929 - 1.15771i) q^{84} +(3.30257 - 5.72021i) q^{85} +(-2.13741 + 3.70210i) q^{86} +(-0.868088 + 0.360305i) q^{87} -4.48400i q^{88} +(-2.10618 + 3.64801i) q^{89} +(0.772294 - 2.89889i) q^{90} +(-5.48409 - 3.16624i) q^{91} +(-1.69230 + 0.977053i) q^{92} +(-9.13268 + 11.9197i) q^{93} -1.48746i q^{94} +(4.35860 + 0.0510884i) q^{95} +(-1.59973 + 0.663976i) q^{96} +(9.01717 - 5.20607i) q^{97} +(1.97993 + 3.42934i) q^{98} +(12.9886 - 3.50029i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9}+O(q^{10}) $ 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * q^9	$ 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9} - 2 q^{12} + 18 q^{13} + 6 q^{14} - 12 q^{16} + 12 q^{17} + 2 q^{18} + 6 q^{19} - 6 q^{21} + 18 q^{22} + 4 q^{24} + 12 q^{25} + 28 q^{27} + 6 q^{28} - 12 q^{32} - 22 q^{33} - 12 q^{34} + 2 q^{36} + 6 q^{38} + 40 q^{39} + 6 q^{41} - 6 q^{42} - 22 q^{43} - 18 q^{44} + 8 q^{45} + 12 q^{47} - 2 q^{48} + 12 q^{49} - 24 q^{50} - 20 q^{51} - 18 q^{52} + 8 q^{53} + 4 q^{54} - 12 q^{56} + 26 q^{59} + 22 q^{61} - 18 q^{62} + 6 q^{63} + 24 q^{64} + 8 q^{65} + 8 q^{66} - 48 q^{67} - 64 q^{69} + 24 q^{71} - 4 q^{72} - 8 q^{73} + 30 q^{74} + 2 q^{75} - 12 q^{76} - 38 q^{78} + 18 q^{79} - 12 q^{81} + 6 q^{82} + 12 q^{84} - 22 q^{86} - 24 q^{87} + 28 q^{89} + 8 q^{90} + 18 q^{91} + 2 q^{93} - 2 q^{96} + 6 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) $ 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * q^9 - 2 * q^12 + 18 * q^13 + 6 * q^14 - 12 * q^16 + 12 * q^17 + 2 * q^18 + 6 * q^19 - 6 * q^21 + 18 * q^22 + 4 * q^24 + 12 * q^25 + 28 * q^27 + 6 * q^28 - 12 * q^32 - 22 * q^33 - 12 * q^34 + 2 * q^36 + 6 * q^38 + 40 * q^39 + 6 * q^41 - 6 * q^42 - 22 * q^43 - 18 * q^44 + 8 * q^45 + 12 * q^47 - 2 * q^48 + 12 * q^49 - 24 * q^50 - 20 * q^51 - 18 * q^52 + 8 * q^53 + 4 * q^54 - 12 * q^56 + 26 * q^59 + 22 * q^61 - 18 * q^62 + 6 * q^63 + 24 * q^64 + 8 * q^65 + 8 * q^66 - 48 * q^67 - 64 * q^69 + 24 * q^71 - 4 * q^72 - 8 * q^73 + 30 * q^74 + 2 * q^75 - 12 * q^76 - 38 * q^78 + 18 * q^79 - 12 * q^81 + 6 * q^82 + 12 * q^84 - 22 * q^86 - 24 * q^87 + 28 * q^89 + 8 * q^90 + 18 * q^91 + 2 * q^93 - 2 * q^96 + 6 * q^97 - 6 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.37489	+	1.05342i	0.793790	+	0.608192i
$3$	1.37489	+	1.05342i	0.793790	+	0.608192i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	0.224845	−	1.71739i	0.0917925	−	0.701123i
$7$	−1.74360			−0.659019			−0.329510	−	0.944152i	$-0.606883\pi$
$7$	−1.74360			−0.659019			−0.329510	+	0.944152i	$0.606883\pi$
$8$	1.00000			0.353553
$9$	0.780619	+	2.89666i	0.260206	+	0.965553i
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$		−	4.48400i		−	1.35198i	−0.736913	−	0.675988i	$-0.763717\pi$
$11$		−	4.48400i		−	1.35198i	0.736913	−	0.675988i	$-0.236283\pi$
$12$	−1.59973	+	0.663976i	−0.461802	+	0.191673i
$13$	3.14527	+	1.81592i	0.872341	+	0.503646i	0.868125	−	0.496345i	$-0.165325\pi$
$13$	3.14527	+	1.81592i	0.872341	+	0.503646i	0.00421545	+	0.999991i	$0.498658\pi$
$14$	0.871800	+	1.51000i	0.232998	+	0.403565i
$15$	1.71739	+	0.224845i	0.443429	+	0.0580546i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	5.72021	−	3.30257i	1.38736	−	0.800990i	0.394339	−	0.918965i	$-0.370974\pi$
$17$	5.72021	−	3.30257i	1.38736	−	0.800990i	0.993017	+	0.117975i	$0.0376402\pi$
$18$	2.11827	−	2.12437i	0.499281	−	0.500718i
$19$	3.74911	+	2.22354i	0.860106	+	0.510116i
$19$	3.74911	+	2.22354i	0.860106	+	0.510116i
$20$			1.00000i			0.223607i
$21$	−2.39725	−	1.83674i	−0.523123	−	0.400810i
$22$	−3.88325	+	2.24200i	−0.827913	+	0.477996i
$23$	1.69230	+	0.977053i	0.352870	+	0.203730i	0.665949	−	0.745998i	$-0.268027\pi$
$23$	1.69230	+	0.977053i	0.352870	+	0.203730i	−0.313079	+	0.949727i	$0.601360\pi$
$24$	1.37489	+	1.05342i	0.280647	+	0.215028i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		−	3.63184i		−	0.712263i
$27$	−1.97813	+	4.80489i	−0.380692	+	0.924702i
$28$	0.871800	−	1.51000i	0.164755	−	0.285364i
$29$	−0.271323	+	0.469946i	−0.0503835	+	0.0872668i	−0.890117	−	0.455732i	$-0.849378\pi$
$29$	−0.271323	+	0.469946i	−0.0503835	+	0.0872668i	0.839734	+	0.542998i	$0.182711\pi$
$30$	−0.663976	−	1.59973i	−0.121225	−	0.292069i
$31$			8.66957i			1.55710i	0.627583	+	0.778550i	$0.284044\pi$
$31$			8.66957i			1.55710i	−0.627583	+	0.778550i	$0.715956\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	4.72353	−	6.16498i	0.822260	−	1.07319i
$34$	−5.72021	−	3.30257i	−0.981009	−	0.566386i
$35$	−1.51000	+	0.871800i	−0.255237	+	0.147361i
$36$	−2.89889	−	0.772294i	−0.483148	−	0.128716i
$37$		−	0.251265i		−	0.0413078i	−0.999787	−	0.0206539i	$-0.993425\pi$
$37$		−	0.251265i		−	0.0413078i	0.999787	−	0.0206539i	$-0.00657480\pi$
$38$	0.0510884	−	4.35860i	0.00828764	−	0.707058i
$39$	2.41146	+	5.80997i	0.386142	+	0.930340i
$40$	0.866025	−	0.500000i	0.136931	−	0.0790569i
$41$	2.28336	+	3.95489i	0.356600	+	0.617650i	0.987390	−	0.158304i	$-0.0506025\pi$
$41$	2.28336	+	3.95489i	0.356600	+	0.617650i	−0.630790	+	0.775953i	$0.717269\pi$
$42$	−0.392039	+	2.99445i	−0.0604930	+	0.462054i
$43$	−2.13741	−	3.70210i	−0.325952	−	0.564566i	0.655752	−	0.754976i	$-0.272351\pi$
$43$	−2.13741	−	3.70210i	−0.325952	−	0.564566i	−0.981705	+	0.190410i	$0.939018\pi$
$44$	3.88325	+	2.24200i	0.585423	+	0.337994i
$45$	2.12437	+	2.11827i	0.316682	+	0.315773i
$46$		−	1.95411i		−	0.288117i
$47$	1.28818	+	0.743732i	0.187901	+	0.108484i	0.590999	−	0.806672i	$-0.298734\pi$
$47$	1.28818	+	0.743732i	0.187901	+	0.108484i	−0.403099	+	0.915156i	$0.632067\pi$
$48$	0.224845	−	1.71739i	0.0324535	−	0.247885i
$49$	−3.95986			−0.565694
$50$	−1.00000			−0.141421
$51$	11.3436	+	1.48513i	1.58842	+	0.207960i
$52$	−3.14527	+	1.81592i	−0.436170	+	0.251823i
$53$	−0.0649443	+	0.112487i	−0.00892079	+	0.0154513i	−0.870451	−	0.492254i	$-0.836173\pi$
$53$	−0.0649443	+	0.112487i	−0.00892079	+	0.0154513i	0.861531	+	0.507706i	$0.169506\pi$
$54$	5.15023	−	0.689332i	0.700857	−	0.0938062i
$55$	−2.24200	−	3.88325i	−0.302311	−	0.523618i
$56$	−1.74360			−0.232998
$57$	2.81228	+	7.00650i	0.372495	+	0.928034i
$58$	0.542647			0.0712530
$59$	−3.22878	−	5.59241i	−0.420351	−	0.728069i	0.575623	−	0.817715i	$-0.304760\pi$
$59$	−3.22878	−	5.59241i	−0.420351	−	0.728069i	−0.995974	+	0.0896460i	$0.971426\pi$
$60$	−1.05342	+	1.37489i	−0.135996	+	0.177497i
$61$	1.04215	−	1.80505i	0.133433	−	0.231114i	−0.791564	−	0.611086i	$-0.790733\pi$
$61$	1.04215	−	1.80505i	0.133433	−	0.231114i	0.924998	+	0.379972i	$0.124066\pi$
$62$	7.50806	−	4.33478i	0.953525	−	0.550518i
$63$	−1.36109	−	5.05062i	−0.171481	−	0.636318i
$64$	1.00000			0.125000
$65$	3.63184			0.450475
$66$	−7.70079	−	1.00820i	−0.947902	−	0.124101i
$67$	−7.40682	−	4.27633i	−0.904888	−	0.522437i	−0.0261048	−	0.999659i	$-0.508310\pi$
$67$	−7.40682	−	4.27633i	−0.904888	−	0.522437i	−0.878783	+	0.477222i	$0.841644\pi$
$68$			6.60513i			0.800990i
$69$	1.29748	+	3.12604i	0.156198	+	0.376331i
$70$	1.51000	+	0.871800i	0.180480	+	0.104200i
$71$	−4.78907	−	8.29492i	−0.568358	−	0.984426i	−0.996729	−	0.0808224i	$-0.974245\pi$
$71$	−4.78907	−	8.29492i	−0.568358	−	0.984426i	0.428370	−	0.903603i	$-0.359088\pi$
$72$	0.780619	+	2.89666i	0.0919968	+	0.341375i
$73$	−3.51522	−	6.08853i	−0.411425	−	0.712609i	0.583621	−	0.812026i	$-0.301635\pi$
$73$	−3.51522	−	6.08853i	−0.411425	−	0.712609i	−0.995046	+	0.0994174i	$0.968302\pi$
$74$	−0.217602	+	0.125633i	−0.0252957	+	0.0146045i
$75$	1.59973	−	0.663976i	0.184721	−	0.0766694i
$76$	−3.80020	+	2.13506i	−0.435913	+	0.244908i
$77$			7.81830i			0.890978i
$78$	3.82585	−	4.99337i	0.433193	−	0.565388i
$79$	−5.04814	+	2.91454i	−0.567960	+	0.327912i	−0.756334	−	0.654186i	$-0.773012\pi$
$79$	−5.04814	+	2.91454i	−0.567960	+	0.327912i	0.188374	+	0.982097i	$0.439678\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	−7.78127	+	4.52237i	−0.864586	+	0.502486i
$82$	2.28336	−	3.95489i	0.252154	−	0.436744i
$83$		−	10.2566i		−	1.12581i	−0.826523	−	0.562903i	$-0.809685\pi$
$83$		−	10.2566i		−	1.12581i	0.826523	−	0.562903i	$-0.190315\pi$
$84$	2.78929	−	1.15771i	0.304336	−	0.126316i
$85$	3.30257	−	5.72021i	0.358214	−	0.620444i
$86$	−2.13741	+	3.70210i	−0.230483	+	0.399208i
$87$	−0.868088	+	0.360305i	−0.0930688	+	0.0386287i
$88$		−	4.48400i		−	0.477996i
$89$	−2.10618	+	3.64801i	−0.223255	+	0.386689i	−0.955794	−	0.294036i	$-0.905002\pi$
$89$	−2.10618	+	3.64801i	−0.223255	+	0.386689i	0.732540	+	0.680724i	$0.238335\pi$
$90$	0.772294	−	2.89889i	0.0814070	−	0.305570i
$91$	−5.48409	−	3.16624i	−0.574889	−	0.331912i
$92$	−1.69230	+	0.977053i	−0.176435	+	0.101865i
$93$	−9.13268	+	11.9197i	−0.947015	+	1.23601i
$94$		−	1.48746i		−	0.153420i
$95$	4.35860	+	0.0510884i	0.447183	+	0.00524156i
$96$	−1.59973	+	0.663976i	−0.163272	+	0.0677668i
$97$	9.01717	−	5.20607i	0.915555	−	0.528596i	0.0333409	−	0.999444i	$-0.489385\pi$
$97$	9.01717	−	5.20607i	0.915555	−	0.528596i	0.882214	+	0.470848i	$0.156052\pi$
$98$	1.97993	+	3.42934i	0.200003	+	0.346415i
$99$	12.9886	−	3.50029i	1.30540	−	0.351792i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	9.94712	+	5.74297i	0.989776	+	0.571447i	0.905207	−	0.424970i	$-0.139715\pi$
$101$	9.94712	+	5.74297i	0.989776	+	0.571447i	0.0845686	+	0.996418i	$0.473049\pi$
$102$	−4.38565	−	10.5664i	−0.434244	−	1.04623i
$103$		−	17.6607i		−	1.74016i	−0.492909	−	0.870081i	$-0.664066\pi$
$103$		−	17.6607i		−	1.74016i	0.492909	−	0.870081i	$-0.335934\pi$
$104$	3.14527	+	1.81592i	0.308419	+	0.178066i
$105$	−2.99445	−	0.392039i	−0.292228	−	0.0382591i
$106$	0.129889			0.0126159
$107$	−20.1581			−1.94875			−0.974377	−	0.224920i	$-0.927788\pi$
$107$	−20.1581			−1.94875			−0.974377	+	0.224920i	$0.927788\pi$
$108$	−3.17209	−	4.11556i	−0.305235	−	0.396020i
$109$	−5.41805	+	3.12812i	−0.518955	+	0.299619i	−0.736507	−	0.676430i	$-0.763526\pi$
$109$	−5.41805	+	3.12812i	−0.518955	+	0.299619i	0.217552	+	0.976049i	$0.430193\pi$
$110$	−2.24200	+	3.88325i	−0.213766	+	0.370254i
$111$	0.264688	−	0.345461i	0.0251230	−	0.0327897i
$112$	0.871800	+	1.51000i	0.0823774	+	0.142682i
$113$	6.35512			0.597840			0.298920	−	0.954278i	$-0.403374\pi$
$113$	6.35512			0.597840			0.298920	+	0.954278i	$0.403374\pi$
$114$	4.66167	−	5.93876i	0.436605	−	0.556215i
$115$	1.95411			0.182221
$116$	−0.271323	−	0.469946i	−0.0251917	−	0.0436334i
$117$	−2.80485	+	10.5283i	−0.259309	+	0.973343i
$118$	−3.22878	+	5.59241i	−0.297233	+	0.514823i
$119$	−9.97377	+	5.75836i	−0.914294	+	0.527868i
$120$	1.71739	+	0.224845i	0.156776	+	0.0205254i
$121$	−9.10622			−0.827839
$122$	−2.08430			−0.188703
$123$	−1.02680	+	7.84285i	−0.0925835	+	0.707166i
$124$	−7.50806	−	4.33478i	−0.674244	−	0.389275i
$125$		−	1.00000i		−	0.0894427i
$126$	−3.69342	+	3.70404i	−0.329036	+	0.329982i
$127$	10.3685	+	5.98626i	0.920056	+	0.531195i	0.883653	−	0.468142i	$-0.155077\pi$
$127$	10.3685	+	5.98626i	0.920056	+	0.531195i	0.0364032	+	0.999337i	$0.488410\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	0.961171	−	7.34156i	0.0846264	−	0.646388i
$130$	−1.81592	−	3.14527i	−0.159267	−	0.275858i
$131$	−7.92681	+	4.57655i	−0.692569	+	0.399855i	−0.804574	−	0.593853i	$-0.797606\pi$
$131$	−7.92681	+	4.57655i	−0.692569	+	0.399855i	0.112005	+	0.993708i	$0.464273\pi$
$132$	2.97727	+	7.17318i	0.259138	+	0.624345i
$133$	−6.53696	−	3.87697i	−0.566826	−	0.336176i
$134$			8.55266i			0.738838i
$135$	0.689332	+	5.15023i	0.0593282	+	0.443261i
$136$	5.72021	−	3.30257i	0.490504	−	0.283193i
$137$	−13.2938	−	7.67520i	−1.13577	−	0.655737i	−0.190390	−	0.981709i	$-0.560975\pi$
$137$	−13.2938	−	7.67520i	−1.13577	−	0.655737i	−0.945380	+	0.325972i	$0.894309\pi$
$138$	2.05849	−	2.68667i	0.175230	−	0.228705i
$139$	−7.91901	+	13.7161i	−0.671682	+	1.16339i	0.305745	+	0.952113i	$0.401094\pi$
$139$	−7.91901	+	13.7161i	−0.671682	+	1.16339i	−0.977427	+	0.211273i	$0.932239\pi$
$140$		−	1.74360i		−	0.147361i
$141$	0.987641	+	2.37954i	0.0831743	+	0.200393i
$142$	−4.78907	+	8.29492i	−0.401890	+	0.696094i
$143$	8.14259	−	14.1034i	0.680918	−	1.17938i
$144$	2.11827	−	2.12437i	0.176523	−	0.177030i
$145$			0.542647i			0.0450644i
$146$	−3.51522	+	6.08853i	−0.290921	+	0.503891i
$147$	−5.44435	−	4.17139i	−0.449042	−	0.344050i
$148$	0.217602	+	0.125633i	0.0178868	+	0.0103269i
$149$	−17.1301	+	9.89007i	−1.40335	+	0.810226i	−0.994735	−	0.102480i	$-0.967322\pi$
$149$	−17.1301	+	9.89007i	−1.40335	+	0.810226i	−0.408618	+	0.912706i	$0.633989\pi$
$150$	−1.37489	−	1.05342i	−0.112259	−	0.0860113i
$151$			21.5191i			1.75120i	0.483038	+	0.875599i	$0.339533\pi$
$151$			21.5191i			1.75120i	−0.483038	+	0.875599i	$0.660467\pi$
$152$	3.74911	+	2.22354i	0.304093	+	0.180353i
$153$	14.0317	+	13.9915i	1.13440	+	1.13114i
$154$	6.77084	−	3.90915i	0.545610	−	0.315008i
$155$	4.33478	+	7.50806i	0.348178	+	0.603062i
$156$	−6.23731	−	0.816601i	−0.499385	−	0.0653804i
$157$	6.77384	+	11.7326i	0.540611	+	0.936366i	0.998869	+	0.0475464i	$0.0151402\pi$
$157$	6.77384	+	11.7326i	0.540611	+	0.936366i	−0.458258	+	0.888819i	$0.651526\pi$
$158$	5.04814	+	2.91454i	0.401608	+	0.231869i
$159$	−0.207787	+	0.0862430i	−0.0164786	+	0.00683951i
$160$			1.00000i			0.0790569i
$161$	−2.95070	−	1.70359i	−0.232548	−	0.134262i
$162$	7.80712	+	4.47759i	0.613386	+	0.351793i
$163$	7.90301			0.619011			0.309506	−	0.950898i	$-0.399836\pi$
$163$	7.90301			0.619011			0.309506	+	0.950898i	$0.399836\pi$
$164$	−4.56671			−0.356600
$165$	1.00820	−	7.70079i	0.0784885	−	0.599506i
$166$	−8.88246	+	5.12829i	−0.689412	+	0.398032i
$167$	−4.08621	+	7.07753i	−0.316201	+	0.547676i	−0.979692	−	0.200508i	$-0.935741\pi$
$167$	−4.08621	+	7.07753i	−0.316201	+	0.547676i	0.663491	+	0.748184i	$0.269074\pi$
$168$	−2.39725	−	1.83674i	−0.184952	−	0.141708i
$169$	0.0951480	+	0.164801i	0.00731908	+	0.0126770i
$170$	−6.60513			−0.506591
$171$	−3.51422	+	12.5956i	−0.268739	+	0.963213i
$172$	4.27482			0.325952
$173$	8.82834	+	15.2911i	0.671206	+	1.16256i	0.977562	+	0.210647i	$0.0675569\pi$
$173$	8.82834	+	15.2911i	0.671206	+	1.16256i	−0.306356	+	0.951917i	$0.599110\pi$
$174$	0.746077	+	0.571634i	0.0565600	+	0.0433355i
$175$	−0.871800	+	1.51000i	−0.0659019	+	0.114145i
$176$	−3.88325	+	2.24200i	−0.292711	+	0.168997i
$177$	1.45195	−	11.0902i	0.109135	−	0.833588i
$178$	4.21236			0.315730
$179$	−19.9723			−1.49280			−0.746402	−	0.665496i	$-0.768220\pi$
$179$	−19.9723			−1.49280			−0.746402	+	0.665496i	$0.768220\pi$
$180$	−2.89666	+	0.780619i	−0.215904	+	0.0581839i
$181$	2.87130	+	1.65774i	0.213422	+	0.123219i	0.602901	−	0.797816i	$-0.294012\pi$
$181$	2.87130	+	1.65774i	0.213422	+	0.123219i	−0.389479	+	0.921035i	$0.627345\pi$
$182$			6.33249i			0.469395i
$183$	3.33431	−	1.38392i	0.246480	−	0.102303i
$184$	1.69230	+	0.977053i	0.124758	+	0.0720293i
$185$	−0.125633	−	0.217602i	−0.00923670	−	0.0159984i
$186$	14.8891	+	1.94931i	1.09172	+	0.142930i
$187$	−14.8087	−	25.6494i	−1.08292	−	1.87567i
$188$	−1.28818	+	0.743732i	−0.0939503	+	0.0542422i
$189$	3.44908	−	8.37781i	0.250883	−	0.609396i
$190$	−2.13506	−	3.80020i	−0.154893	−	0.275696i
$191$		−	9.19637i		−	0.665426i	−0.943028	−	0.332713i	$-0.892036\pi$
$191$		−	9.19637i		−	0.665426i	0.943028	−	0.332713i	$-0.107964\pi$
$192$	1.37489	+	1.05342i	0.0992238	+	0.0760239i
$193$	11.3952	−	6.57904i	0.820247	−	0.473570i	−0.0302545	−	0.999542i	$-0.509632\pi$
$193$	11.3952	−	6.57904i	0.820247	−	0.473570i	0.850502	+	0.525972i	$0.176298\pi$
$194$	−9.01717	−	5.20607i	−0.647395	−	0.373774i
$195$	4.99337	+	3.82585i	0.357583	+	0.273975i
$196$	1.97993	−	3.42934i	0.141423	−	0.244953i
$197$		−	27.4692i		−	1.95710i	−0.206016	−	0.978549i	$-0.566050\pi$
$197$		−	27.4692i		−	1.95710i	0.206016	−	0.978549i	$-0.433950\pi$
$198$	−9.52565	−	9.49832i	−0.676958	−	0.675016i
$199$	−4.51192	+	7.81487i	−0.319841	+	0.553981i	−0.980455	−	0.196745i	$-0.936963\pi$
$199$	−4.51192	+	7.81487i	−0.319841	+	0.553981i	0.660613	+	0.750726i	$0.270296\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−5.67876	−	13.6820i	−0.400549	−	0.965050i
$202$		−	11.4859i		−	0.808149i
$203$	0.473080	−	0.819398i	0.0332037	−	0.0575105i
$204$	−6.95797	+	9.08130i	−0.487155	+	0.635818i
$205$	3.95489	+	2.28336i	0.276221	+	0.159476i
$206$	−15.2946	+	8.83036i	−1.06563	+	0.615240i
$207$	−1.50914	+	5.66474i	−0.104893	+	0.393726i
$208$		−	3.63184i		−	0.251823i
$209$	9.97036	−	16.8110i	0.689664	−	1.16284i
$210$	1.15771	+	2.78929i	0.0798895	+	0.192479i
$211$	−18.1457	+	10.4764i	−1.24920	+	0.721226i	−0.970950	−	0.239282i	$-0.923088\pi$
$211$	−18.1457	+	10.4764i	−1.24920	+	0.721226i	−0.278251	+	0.960508i	$0.589755\pi$
$212$	−0.0649443	−	0.112487i	−0.00446040	−	0.00772563i
$213$	2.15360	−	16.4495i	0.147562	−	1.12710i
$214$	10.0790	+	17.4574i	0.688989	+	1.19336i
$215$	−3.70210	−	2.13741i	−0.252481	−	0.145770i
$216$	−1.97813	+	4.80489i	−0.134595	+	0.326931i
$217$		−	15.1163i		−	1.02616i
$218$	5.41805	+	3.12812i	0.366957	+	0.211863i
$219$	1.58076	−	12.0740i	0.106818	−	0.815887i
$220$	4.48400			0.302311
$221$	23.9888			1.61366
$222$	−0.431522	−	0.0564957i	−0.0289618	−	0.00379174i
$223$	−11.2359	+	6.48704i	−0.752410	+	0.434404i	−0.826564	−	0.562843i	$-0.809708\pi$
$223$	−11.2359	+	6.48704i	−0.752410	+	0.434404i	0.0741541	+	0.997247i	$0.476374\pi$
$224$	0.871800	−	1.51000i	0.0582496	−	0.100891i
$225$	2.89889	+	0.772294i	0.193259	+	0.0514863i
$226$	−3.17756	−	5.50370i	−0.211368	−	0.366100i
$227$	21.2257			1.40880			0.704401	−	0.709803i	$-0.251216\pi$
$227$	21.2257			1.40880			0.704401	+	0.709803i	$0.251216\pi$
$228$	−7.47395	−	1.06775i	−0.494974	−	0.0707133i
$229$	9.69163			0.640441			0.320220	−	0.947343i	$-0.396243\pi$
$229$	9.69163			0.640441			0.320220	+	0.947343i	$0.396243\pi$
$230$	−0.977053	−	1.69230i	−0.0644249	−	0.111587i
$231$	−8.23594	+	10.7493i	−0.541885	+	0.707250i
$232$	−0.271323	+	0.469946i	−0.0178133	+	0.0308535i
$233$	−14.0033	+	8.08481i	−0.917387	+	0.529654i	−0.882801	−	0.469748i	$-0.844345\pi$
$233$	−14.0033	+	8.08481i	−0.917387	+	0.529654i	−0.0345867	+	0.999402i	$0.511011\pi$
$234$	10.5202	−	2.83509i	0.687728	−	0.185335i
$235$	1.48746			0.0970314
$236$	6.45756			0.420351
$237$	−10.0108	−	1.31064i	−0.650274	−	0.0851352i
$238$	9.97377	+	5.75836i	0.646503	+	0.373259i
$239$		−	21.3293i		−	1.37968i	−0.723964	−	0.689838i	$-0.757682\pi$
$239$		−	21.3293i		−	1.37968i	0.723964	−	0.689838i	$-0.242318\pi$
$240$	−0.663976	−	1.59973i	−0.0428595	−	0.103262i
$241$	3.63151	+	2.09666i	0.233926	+	0.135057i	0.612382	−	0.790562i	$-0.290211\pi$
$241$	3.63151	+	2.09666i	0.233926	+	0.135057i	−0.378456	+	0.925619i	$0.623545\pi$
$242$	4.55311	+	7.88622i	0.292685	+	0.506946i
$243$	−15.4623	−	1.97919i	−0.991907	−	0.126965i
$244$	1.04215	+	1.80505i	0.0667167	+	0.115557i
$245$	−3.42934	+	1.97993i	−0.219092	+	0.126493i
$246$	7.30551	−	3.03219i	0.465782	−	0.193325i
$247$	7.75419	+	13.8017i	0.493387	+	0.878184i
$248$			8.66957i			0.550518i
$249$	10.8045	−	14.1016i	0.684705	−	0.893654i
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$	20.8600	+	12.0435i	1.31667	+	0.760179i	0.983191	−	0.182579i	$-0.0584444\pi$
$251$	20.8600	+	12.0435i	1.31667	+	0.760179i	0.333478	+	0.942758i	$0.391778\pi$
$252$	5.05451	+	1.34657i	0.318404	+	0.0848261i
$253$	4.38110	−	7.58829i	0.275437	−	0.477072i
$254$		−	11.9725i		−	0.751223i
$255$	10.5664	−	4.38565i	0.661696	−	0.274640i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.58082	+	9.66626i	−0.348122	+	0.602965i	−0.985916	−	0.167242i	$-0.946514\pi$
$257$	−5.58082	+	9.66626i	−0.348122	+	0.602965i	0.637794	+	0.770207i	$0.279847\pi$
$258$	−6.83856	+	2.83838i	−0.425750	+	0.176710i
$259$			0.438106i			0.0272226i
$260$	−1.81592	+	3.14527i	−0.112619	+	0.195061i
$261$	−1.57307	−	0.419083i	−0.0973708	−	0.0259406i
$262$	7.92681	+	4.57655i	0.489720	+	0.282740i
$263$	12.8454	−	7.41629i	0.792081	−	0.457308i	−0.0486138	−	0.998818i	$-0.515480\pi$
$263$	12.8454	−	7.41629i	0.792081	−	0.457308i	0.840695	+	0.541510i	$0.182147\pi$
$264$	4.72353	−	6.16498i	0.290713	−	0.379428i
$265$			0.129889i			0.00797900i
$266$	−0.0890778	+	7.59966i	−0.00546171	+	0.465965i
$267$	−6.73865	+	2.79691i	−0.412398	+	0.171168i
$268$	7.40682	−	4.27633i	0.452444	−	0.261219i
$269$	−3.20285	−	5.54749i	−0.195281	−	0.338237i	0.751712	−	0.659492i	$-0.229229\pi$
$269$	−3.20285	−	5.54749i	−0.195281	−	0.338237i	−0.946993	+	0.321255i	$0.895895\pi$
$270$	4.11556	−	3.17209i	0.250465	−	0.193047i
$271$	8.80426	+	15.2494i	0.534820	+	0.926336i	0.999172	+	0.0406852i	$0.0129541\pi$
$271$	8.80426	+	15.2494i	0.534820	+	0.926336i	−0.464352	+	0.885651i	$0.653713\pi$
$272$	−5.72021	−	3.30257i	−0.346839	−	0.200248i
$273$	−4.20462	−	10.1303i	−0.254475	−	0.613112i
$274$			15.3504i			0.927352i
$275$	−3.88325	−	2.24200i	−0.234169	−	0.135198i
$276$	−3.35597	−	0.439370i	−0.202006	−	0.0264470i
$277$	−27.5243			−1.65377			−0.826887	−	0.562369i	$-0.809890\pi$
$277$	−27.5243			−1.65377			−0.826887	+	0.562369i	$0.809890\pi$
$278$	15.8380			0.949901
$279$	−25.1128	+	6.76762i	−1.50346	+	0.405167i
$280$	−1.51000	+	0.871800i	−0.0902399	+	0.0521000i
$281$	2.25447	−	3.90486i	0.134490	−	0.232944i	−0.790912	−	0.611930i	$-0.790394\pi$
$281$	2.25447	−	3.90486i	0.134490	−	0.232944i	0.925403	+	0.378985i	$0.123727\pi$
$282$	1.56692	−	2.04509i	0.0933089	−	0.121783i
$283$	−14.2001	−	24.5953i	−0.844109	−	1.46204i	−0.886393	−	0.462934i	$-0.846797\pi$
$283$	−14.2001	−	24.5953i	−0.844109	−	1.46204i	0.0422840	−	0.999106i	$-0.486537\pi$
$284$	9.57815			0.568358
$285$	5.93876	+	4.66167i	0.351782	+	0.276134i
$286$	−16.2852			−0.962963
$287$	−3.98126	−	6.89574i	−0.235006	−	0.407043i
$288$	−2.89889	−	0.772294i	−0.170819	−	0.0455079i
$289$	13.3139	−	23.0603i	0.783170	−	1.35649i
$290$	0.469946	−	0.271323i	0.0275962	−	0.0159327i
$291$	17.8817	+	2.34111i	1.04825	+	0.137238i
$292$	7.03043			0.411425
$293$	14.9955			0.876047			0.438024	−	0.898963i	$-0.355679\pi$
$293$	14.9955			0.876047			0.438024	+	0.898963i	$0.355679\pi$
$294$	−0.890353	+	6.80064i	−0.0519264	+	0.396621i
$295$	−5.59241	−	3.22878i	−0.325603	−	0.187987i
$296$		−	0.251265i		−	0.0146045i
$297$	21.5451	+	8.86995i	1.25017	+	0.514686i
$298$	17.1301	+	9.89007i	0.992320	+	0.572916i
$299$	3.54850	+	6.14619i	0.205215	+	0.355443i
$300$	−0.224845	+	1.71739i	−0.0129814	+	0.0991538i
$301$	3.72679	+	6.45499i	0.214809	+	0.372060i
$302$	18.6361	−	10.7595i	1.07239	−	0.619142i
$303$	7.62640	+	18.3744i	0.438125	+	1.05558i
$304$	0.0510884	−	4.35860i	0.00293012	−	0.249983i
$305$		−	2.08430i		−	0.119347i
$306$	5.10111	−	19.1476i	0.291611	−	1.09459i
$307$	17.6339	−	10.1810i	1.00642	−	0.581058i	0.0962802	−	0.995354i	$-0.469306\pi$
$307$	17.6339	−	10.1810i	1.00642	−	0.581058i	0.910142	+	0.414296i	$0.135972\pi$
$308$	−6.77084	−	3.90915i	−0.385805	−	0.222744i
$309$	18.6041	−	24.2815i	1.05835	−	1.38132i
$310$	4.33478	−	7.50806i	0.246199	−	0.426429i
$311$		−	12.1717i		−	0.690194i	−0.938567	−	0.345097i	$-0.887846\pi$
$311$		−	12.1717i		−	0.690194i	0.938567	−	0.345097i	$-0.112154\pi$
$312$	2.41146	+	5.80997i	0.136522	+	0.328925i
$313$	−6.57209	+	11.3832i	−0.371476	+	0.643416i	−0.989793	−	0.142513i	$-0.954482\pi$
$313$	−6.57209	+	11.3832i	−0.371476	+	0.643416i	0.618317	+	0.785929i	$0.287815\pi$
$314$	6.77384	−	11.7326i	0.382270	−	0.662110i
$315$	−3.70404	−	3.69342i	−0.208699	−	0.208101i
$316$		−	5.82909i		−	0.327912i
$317$	3.43470	−	5.94907i	0.192912	−	0.334133i	−0.753302	−	0.657675i	$-0.771540\pi$
$317$	3.43470	−	5.94907i	0.192912	−	0.334133i	0.946214	+	0.323542i	$0.104874\pi$
$318$	0.178582	+	0.136827i	0.0100144	+	0.00767288i
$319$	2.10724	+	1.21661i	0.117983	+	0.0681173i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	−27.7150	−	21.2349i	−1.54690	−	1.18522i
$322$			3.40718i			0.189875i
$323$	28.7891	+	0.337446i	1.60187	+	0.0187760i
$324$	−0.0258539	−	8.99996i	−0.00143633	−	0.499998i
$325$	3.14527	−	1.81592i	0.174468	−	0.100729i
$326$	−3.95150	−	6.84420i	−0.218854	−	0.379065i
$327$	−10.7444	−	1.40668i	−0.594168	−	0.0777896i
$328$	2.28336	+	3.95489i	0.126077	+	0.218372i
$329$	−2.24607	−	1.29677i	−0.123830	−	0.0714933i
$330$	−7.17318	+	2.97727i	−0.394871	+	0.163893i
$331$		−	7.78853i		−	0.428096i	−0.976823	−	0.214048i	$-0.931335\pi$
$331$		−	7.78853i		−	0.428096i	0.976823	−	0.214048i	$-0.0686649\pi$
$332$	8.88246	+	5.12829i	0.487488	+	0.281451i
$333$	0.727830	−	0.196142i	0.0398848	−	0.0107485i
$334$	8.17243			0.447175
$335$	−8.55266			−0.467282
$336$	−0.392039	+	2.99445i	−0.0213875	+	0.163361i
$337$	23.2844	−	13.4433i	1.26838	−	0.732301i	0.293700	−	0.955898i	$-0.405113\pi$
$337$	23.2844	−	13.4433i	1.26838	−	0.732301i	0.974682	+	0.223597i	$0.0717799\pi$
$338$	0.0951480	−	0.164801i	0.00517537	−	0.00896401i
$339$	8.73756	+	6.69460i	0.474559	+	0.363601i
$340$	3.30257	+	5.72021i	0.179107	+	0.310222i
$341$	38.8743			2.10516
$342$	12.6653	−	3.25442i	0.684859	−	0.175979i
$343$	19.1096			1.03182
$344$	−2.13741	−	3.70210i	−0.115241	−	0.199604i
$345$	2.68667	+	2.05849i	0.144645	+	0.110825i
$346$	8.82834	−	15.2911i	0.474615	−	0.822057i
$347$	−24.5180	+	14.1555i	−1.31620	+	0.759906i	−0.983114	−	0.182992i	$-0.941422\pi$
$347$	−24.5180	+	14.1555i	−1.31620	+	0.759906i	−0.333081	+	0.942898i	$0.608088\pi$
$348$	0.122011	−	0.931939i	0.00654049	−	0.0499572i
$349$	4.70839			0.252034			0.126017	−	0.992028i	$-0.459781\pi$
$349$	4.70839			0.252034			0.126017	+	0.992028i	$0.459781\pi$
$350$	1.74360			0.0931994
$351$	−14.9471	+	11.5205i	−0.797816	+	0.614921i
$352$	3.88325	+	2.24200i	0.206978	+	0.119499i
$353$			16.8453i			0.896587i	0.893886	+	0.448293i	$0.147968\pi$
$353$			16.8453i			0.896587i	−0.893886	+	0.448293i	$0.852032\pi$
$354$	−10.3303	+	4.28766i	−0.549052	+	0.227887i
$355$	−8.29492	−	4.78907i	−0.440249	−	0.254178i
$356$	−2.10618	−	3.64801i	−0.111627	−	0.193344i
$357$	−19.7787	−	2.58947i	−1.04680	−	0.137049i
$358$	9.98617	+	17.2966i	0.527786	+	0.914152i
$359$	−27.5785	+	15.9225i	−1.45554	+	0.840356i	−0.998787	−	0.0492381i	$-0.984321\pi$
$359$	−27.5785	+	15.9225i	−1.45554	+	0.840356i	−0.456752	+	0.889594i	$0.650987\pi$
$360$	2.12437	+	2.11827i	0.111964	+	0.111643i
$361$	9.11171	+	16.6726i	0.479564	+	0.877507i
$362$		−	3.31549i		−	0.174258i
$363$	−12.5200	−	9.59267i	−0.657130	−	0.503484i
$364$	5.48409	−	3.16624i	0.287445	−	0.165956i
$365$	−6.08853	−	3.51522i	−0.318688	−	0.183995i
$366$	−2.86567	−	2.19564i	−0.149791	−	0.114768i
$367$	−15.1447	+	26.2313i	−0.790545	+	1.36926i	0.135085	+	0.990834i	$0.456869\pi$
$367$	−15.1447	+	26.2313i	−0.790545	+	1.36926i	−0.925630	+	0.378430i	$0.876464\pi$
$368$		−	1.95411i		−	0.101865i
$369$	−9.67353	+	9.70136i	−0.503584	+	0.505033i
$370$	−0.125633	+	0.217602i	−0.00653133	+	0.0113126i
$371$	0.113237	−	0.196132i	0.00587897	−	0.0101827i
$372$	−5.75639	−	13.8690i	−0.298455	−	0.719072i
$373$			37.2564i			1.92906i	0.263966	+	0.964532i	$0.414969\pi$
$373$			37.2564i			1.92906i	−0.263966	+	0.964532i	$0.585031\pi$
$374$	−14.8087	+	25.6494i	−0.765740	+	1.32630i
$375$	1.05342	−	1.37489i	0.0543983	−	0.0709988i
$376$	1.28818	+	0.743732i	0.0664329	+	0.0383550i
$377$	−1.70677	+	0.985405i	−0.0879032	+	0.0507509i
$378$	−8.97994	+	1.20192i	−0.461878	+	0.0618200i
$379$		−	33.6356i		−	1.72775i	−0.503709	−	0.863873i	$-0.668032\pi$
$379$		−	33.6356i		−	1.72775i	0.503709	−	0.863873i	$-0.331968\pi$
$380$	−2.22354	+	3.74911i	−0.114065	+	0.192325i
$381$	7.94947	+	19.1528i	0.407264	+	0.981228i
$382$	−7.96429	+	4.59818i	−0.407488	+	0.235264i
$383$	−4.65017	−	8.05432i	−0.237612	−	0.411557i	0.722416	−	0.691458i	$-0.243031\pi$
$383$	−4.65017	−	8.05432i	−0.237612	−	0.411557i	−0.960029	+	0.279902i	$0.909698\pi$
$384$	0.224845	−	1.71739i	0.0114741	−	0.0876404i
$385$	3.90915	+	6.77084i	0.199229	+	0.345074i
$386$	−11.3952	−	6.57904i	−0.580002	−	0.334865i
$387$	9.05523	−	9.08128i	0.460303	−	0.461628i
$388$			10.4121i			0.528596i
$389$	7.08705	+	4.09171i	0.359328	+	0.207458i	0.668786	−	0.743455i	$-0.266814\pi$
$389$	7.08705	+	4.09171i	0.359328	+	0.207458i	−0.309458	+	0.950913i	$0.600148\pi$
$390$	0.816601	−	6.23731i	0.0413502	−	0.315839i
$391$	12.9071			0.652741
$392$	−3.95986			−0.200003
$393$	−15.7195	−	2.05802i	−0.792943	−	0.103814i
$394$	−23.7890	+	13.7346i	−1.19847	+	0.691938i
$395$	−2.91454	+	5.04814i	−0.146647	+	0.253999i
$396$	−3.46296	+	12.9986i	−0.174021	+	0.653205i
$397$	2.72560	+	4.72088i	0.136794	+	0.236934i	0.926281	−	0.376833i	$-0.122987\pi$
$397$	2.72560	+	4.72088i	0.136794	+	0.236934i	−0.789487	+	0.613767i	$0.789653\pi$
$398$	9.02384			0.452324
$399$	−4.90349	−	12.2165i	−0.245482	−	0.611592i
$400$	−1.00000			−0.0500000
$401$	−14.4054	−	24.9508i	−0.719369	−	1.24598i	−0.961250	−	0.275678i	$-0.911098\pi$
$401$	−14.4054	−	24.9508i	−0.719369	−	1.24598i	0.241881	−	0.970306i	$-0.422236\pi$
$402$	−9.00953	+	11.7589i	−0.449355	+	0.586482i
$403$	−15.7433	+	27.2681i	−0.784228	+	1.35832i
$404$	−9.94712	+	5.74297i	−0.494888	+	0.285724i
$405$	−4.47759	+	7.80712i	−0.222493	+	0.387939i
$406$	−0.946159			−0.0469571
$407$	−1.12667			−0.0558471
$408$	11.3436	+	1.48513i	0.561593	+	0.0735249i
$409$	25.3296	+	14.6240i	1.25247	+	0.723113i	0.971599	−	0.236633i	$-0.0760440\pi$
$409$	25.3296	+	14.6240i	1.25247	+	0.723113i	0.280869	+	0.959746i	$0.409377\pi$
$410$		−	4.56671i		−	0.225534i
$411$	−10.1923	−	24.5565i	−0.502749	−	1.21128i
$412$	15.2946	+	8.83036i	0.753512	+	0.435040i
$413$	5.62970	+	9.75092i	0.277019	+	0.479812i
$414$	5.66038	−	1.52541i	0.278192	−	0.0749698i
$415$	−5.12829	−	8.88246i	−0.251738	−	0.436023i
$416$	−3.14527	+	1.81592i	−0.154210	+	0.0890329i
$417$	−25.3365	+	10.5161i	−1.24074	+	0.514974i
$418$	−19.5439	−	0.229080i	−0.955926	−	0.0112047i
$419$		−	1.11183i		−	0.0543167i	−0.999631	−	0.0271583i	$-0.991354\pi$
$419$		−	1.11183i		−	0.0543167i	0.999631	−	0.0271583i	$-0.00864583\pi$
$420$	1.83674	−	2.39725i	0.0896238	−	0.116974i
$421$	17.1508	−	9.90200i	0.835877	−	0.482594i	−0.0199835	−	0.999800i	$-0.506361\pi$
$421$	17.1508	−	9.90200i	0.835877	−	0.482594i	0.855861	+	0.517206i	$0.173028\pi$
$422$	18.1457	+	10.4764i	0.883318	+	0.509984i
$423$	−1.14876	+	4.31199i	−0.0558546	+	0.209656i
$424$	−0.0649443	+	0.112487i	−0.00315398	+	0.00546285i
$425$		−	6.60513i		−	0.320396i
$426$	−15.3224	+	6.35966i	−0.742375	+	0.308127i
$427$	−1.81709	+	3.14729i	−0.0879352	+	0.152308i
$428$	10.0790	−	17.4574i	0.487189	−	0.843835i
$429$	26.0519	−	10.8130i	1.25780	−	0.522055i
$430$			4.27482i			0.206150i
$431$	−3.16146	+	5.47581i	−0.152282	+	0.263760i	−0.932066	−	0.362288i	$-0.881996\pi$
$431$	−3.16146	+	5.47581i	−0.152282	+	0.263760i	0.779784	+	0.626049i	$0.215329\pi$
$432$	5.15023	−	0.689332i	0.247790	−	0.0331655i
$433$	−24.2858	−	14.0214i	−1.16710	−	0.673827i	−0.214107	−	0.976810i	$-0.568684\pi$
$433$	−24.2858	−	14.0214i	−1.16710	−	0.673827i	−0.952996	+	0.302983i	$0.902017\pi$
$434$	−13.0911	+	7.55813i	−0.628391	+	0.362802i
$435$	−0.571634	+	0.746077i	−0.0274078	+	0.0357717i
$436$		−	6.25623i		−	0.299619i
$437$	4.17212	+	7.42600i	0.199580	+	0.355234i
$438$	−11.2468	+	4.66804i	−0.537393	+	0.223048i
$439$	−8.39710	+	4.84807i	−0.400772	+	0.231386i	−0.686817	−	0.726830i	$-0.740993\pi$
$439$	−8.39710	+	4.84807i	−0.400772	+	0.231386i	0.286045	+	0.958216i	$0.407659\pi$
$440$	−2.24200	−	3.88325i	−0.106883	−	0.185127i
$441$	−3.09114	−	11.4704i	−0.147197	−	0.546208i
$442$	−11.9944	−	20.7749i	−0.570516	−	0.988163i
$443$	−8.85438	−	5.11208i	−0.420684	−	0.242882i	0.274686	−	0.961534i	$-0.411426\pi$
$443$	−8.85438	−	5.11208i	−0.420684	−	0.242882i	−0.695370	+	0.718652i	$0.744760\pi$
$444$	0.166834	+	0.401957i	0.00791760	+	0.0190760i
$445$			4.21236i			0.199685i
$446$	11.2359	+	6.48704i	0.532034	+	0.307170i
$447$	−33.9703	−	4.44746i	−1.60674	−	0.210358i
$448$	−1.74360			−0.0823774
$449$	6.66710			0.314640			0.157320	−	0.987548i	$-0.449715\pi$
$449$	6.66710			0.314640			0.157320	+	0.987548i	$0.449715\pi$
$450$	−0.780619	−	2.89666i	−0.0367987	−	0.136550i
$451$	17.7337	−	10.2386i	0.835048	−	0.482115i
$452$	−3.17756	+	5.50370i	−0.149460	+	0.258872i
$453$	−22.6686	+	29.5863i	−1.06506	+	1.39008i
$454$	−10.6129	−	18.3820i	−0.498086	−	0.862711i
$455$	−6.33249			−0.296872
$456$	2.81228	+	7.00650i	0.131697	+	0.328110i
$457$	−12.8650			−0.601800			−0.300900	−	0.953656i	$-0.597287\pi$
$457$	−12.8650			−0.601800			−0.300900	+	0.953656i	$0.597287\pi$
$458$	−4.84581	−	8.39319i	−0.226430	−	0.392188i
$459$	4.55313	+	34.0179i	0.212522	+	1.58782i
$460$	−0.977053	+	1.69230i	−0.0455553	+	0.0789041i
$461$	4.75855	−	2.74735i	0.221628	−	0.127957i	−0.385076	−	0.922885i	$-0.625825\pi$
$461$	4.75855	−	2.74735i	0.221628	−	0.127957i	0.606704	+	0.794928i	$0.292491\pi$
$462$	13.4271	+	1.75790i	0.624685	+	0.0817850i
$463$	9.12169			0.423921			0.211960	−	0.977278i	$-0.432015\pi$
$463$	9.12169			0.423921			0.211960	+	0.977278i	$0.432015\pi$
$464$	0.542647			0.0251917
$465$	−1.94931	+	14.8891i	−0.0903969	+	0.690464i
$466$	14.0033	+	8.08481i	0.648691	+	0.374522i
$467$		−	31.0365i		−	1.43620i	−0.695940	−	0.718100i	$-0.745012\pi$
$467$		−	31.0365i		−	1.43620i	0.695940	−	0.718100i	$-0.254988\pi$
$468$	−7.71536	−	7.69323i	−0.356643	−	0.355620i
$469$	12.9145	+	7.45621i	0.596338	+	0.344296i
$470$	−0.743732	−	1.28818i	−0.0343058	−	0.0594194i
$471$	−3.04612	+	23.2667i	−0.140358	+	1.07207i
$472$	−3.22878	−	5.59241i	−0.148617	−	0.257411i
$473$	−16.6002	+	9.58414i	−0.763279	+	0.440679i
$474$	3.87037	+	9.32496i	0.177772	+	0.428310i
$475$	3.80020	−	2.13506i	0.174365	−	0.0979631i
$476$		−	11.5167i		−	0.527868i
$477$	−0.376533	−	0.100312i	−0.0172403	−	0.00459298i
$478$	−18.4717	+	10.6646i	−0.844876	+	0.487789i
$479$	−5.77360	−	3.33339i	−0.263802	−	0.152306i	0.362265	−	0.932075i	$-0.382003\pi$
$479$	−5.77360	−	3.33339i	−0.263802	−	0.152306i	−0.626068	+	0.779769i	$0.715337\pi$
$480$	−1.05342	+	1.37489i	−0.0480818	+	0.0627546i
$481$	0.456278	−	0.790297i	0.0208045	−	0.0360345i
$482$		−	4.19331i		−	0.191000i
$483$	−2.26229	−	5.45057i	−0.102938	−	0.248009i
$484$	4.55311	−	7.88622i	0.206960	−	0.358465i
$485$	5.20607	−	9.01717i	0.236395	−	0.409449i
$486$	6.01712	+	14.3803i	0.272942	+	0.652306i
$487$			21.6443i			0.980797i	0.871498	+	0.490399i	$0.163149\pi$
$487$			21.6443i			0.980797i	−0.871498	+	0.490399i	$0.836851\pi$
$488$	1.04215	−	1.80505i	0.0471759	−	0.0817110i
$489$	10.8657	+	8.32517i	0.491365	+	0.376477i
$490$	3.42934	+	1.97993i	0.154922	+	0.0894441i
$491$	2.23804	−	1.29214i	0.101002	−	0.0583132i	−0.448648	−	0.893708i	$-0.648094\pi$
$491$	2.23804	−	1.29214i	0.101002	−	0.0583132i	0.549650	+	0.835395i	$0.314761\pi$
$492$	−6.27870	−	4.81066i	−0.283066	−	0.216881i
$493$			3.58426i			0.161427i
$494$	8.07557	−	13.6162i	0.363337	−	0.612622i
$495$	9.49832	−	9.52565i	0.426918	−	0.428146i
$496$	7.50806	−	4.33478i	0.337122	−	0.194638i
$497$	8.35023	+	14.4630i	0.374559	+	0.648755i
$498$	−17.6146	−	2.30614i	−0.789329	−	0.103340i
$499$	−9.18058	−	15.9012i	−0.410979	−	0.711837i	0.584018	−	0.811741i	$-0.301480\pi$
$499$	−9.18058	−	15.9012i	−0.410979	−	0.711837i	−0.994997	+	0.0999040i	$0.968146\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	−13.0737	+	5.42630i	−0.584089	+	0.242429i
$502$		−	24.0870i		−	1.07506i
$503$	−26.6006	−	15.3579i	−1.18606	−	0.684774i	−0.228654	−	0.973508i	$-0.573432\pi$
$503$	−26.6006	−	15.3579i	−1.18606	−	0.684774i	−0.957409	+	0.288734i	$0.906766\pi$
$504$	−1.36109	−	5.05062i	−0.0606276	−	0.224972i
$505$	11.4859			0.511118
$506$	−8.76220			−0.389527
$507$	−0.0427871	+	0.326814i	−0.00190024	+	0.0145143i
$508$	−10.3685	+	5.98626i	−0.460028	+	0.265597i
$509$	1.76397	−	3.05529i	0.0781868	−	0.135424i	−0.824281	−	0.566181i	$-0.808420\pi$
$509$	1.76397	−	3.05529i	0.0781868	−	0.135424i	0.902468	+	0.430758i	$0.141754\pi$
$510$	−9.08130	−	6.95797i	−0.402127	−	0.308104i
$511$	6.12913	+	10.6160i	0.271137	+	0.469623i
$512$	1.00000			0.0441942
$513$	−18.1001	+	13.6156i	−0.799141	+	0.601144i
$514$	11.1616			0.492319
$515$	−8.83036	−	15.2946i	−0.389112	−	0.673962i
$516$	5.87739	+	4.50318i	0.258738	+	0.198241i
$517$	3.33489	−	5.77620i	0.146668	−	0.254037i
$518$	0.379411	−	0.219053i	0.0166704	−	0.00962465i
$519$	−3.97001	+	30.3235i	−0.174264	+	1.33105i
$520$	3.63184			0.159267
$521$	10.7293			0.470059			0.235030	−	0.971988i	$-0.424481\pi$
$521$	10.7293			0.470059			0.235030	+	0.971988i	$0.424481\pi$
$522$	0.423600	+	1.57186i	0.0185405	+	0.0687986i
$523$	16.2359	+	9.37381i	0.709947	+	0.409888i	0.811042	−	0.584989i	$-0.198901\pi$
$523$	16.2359	+	9.37381i	0.709947	+	0.409888i	−0.101094	+	0.994877i	$0.532234\pi$
$524$		−	9.15309i		−	0.399855i
$525$	−2.78929	+	1.15771i	−0.121735	+	0.0505266i
$526$	−12.8454	−	7.41629i	−0.560086	−	0.323366i
$527$	28.6318	+	49.5918i	1.24722	+	2.16025i
$528$	−7.70079	−	1.00820i	−0.335134	−	0.0438764i
$529$	−9.59074	−	16.6116i	−0.416989	−	0.722245i
$530$	0.112487	−	0.0649443i	0.00488612	−	0.00282100i
$531$	13.6789	−	13.7182i	0.593612	−	0.595319i
$532$	6.62603	−	3.72268i	0.287275	−	0.161399i
$533$			16.5856i			0.718402i
$534$	5.79152	+	4.43738i	0.250623	+	0.192024i
$535$	−17.4574	+	10.0790i	−0.754749	+	0.435755i
$536$	−7.40682	−	4.27633i	−0.319926	−	0.184709i
$537$	−27.4597	−	21.0392i	−1.18497	−	0.907910i
$538$	−3.20285	+	5.54749i	−0.138084	+	0.239169i
$539$			17.7560i			0.764805i
$540$	−4.80489	−	1.97813i	−0.206770	−	0.0851253i
$541$	18.9536	−	32.8286i	0.814878	−	1.41141i	−0.0945373	−	0.995521i	$-0.530137\pi$
$541$	18.9536	−	32.8286i	0.814878	−	1.41141i	0.909415	−	0.415889i	$-0.136529\pi$
$542$	8.80426	−	15.2494i	0.378175	−	0.655019i
$543$	2.20141	+	5.30389i	0.0944714	+	0.227612i
$544$			6.60513i			0.283193i
$545$	−3.12812	+	5.41805i	−0.133994	+	0.232084i
$546$	−6.67076	+	8.70644i	−0.285482	+	0.372601i
$547$	14.2392	+	8.22099i	0.608823	+	0.351504i	0.772505	−	0.635009i	$-0.219004\pi$
$547$	14.2392	+	8.22099i	0.608823	+	0.351504i	−0.163682	+	0.986513i	$0.552337\pi$
$548$	13.2938	−	7.67520i	0.567885	−	0.327868i
$549$	6.04215	+	1.60969i	0.257873	+	0.0686999i
$550$			4.48400i			0.191198i
$551$	−2.06217	+	1.15858i	−0.0878513	+	0.0493572i
$552$	1.29748	+	3.12604i	0.0552244	+	0.133053i
$553$	8.80193	−	5.08180i	0.374296	−	0.216100i
$554$	13.7621	+	23.8367i	0.584697	+	1.01273i
$555$	0.0564957	−	0.431522i	0.00239811	−	0.0183171i
$556$	−7.91901	−	13.7161i	−0.335841	−	0.581693i
$557$	−10.7408	−	6.20119i	−0.455101	−	0.262753i	0.254881	−	0.966972i	$-0.417964\pi$
$557$	−10.7408	−	6.20119i	−0.455101	−	0.262753i	−0.709982	+	0.704220i	$0.751297\pi$
$558$	18.4173	+	18.3645i	0.779667	+	0.777431i
$559$		−	15.5255i		−	0.656658i
$560$	1.51000	+	0.871800i	0.0638092	+	0.0368403i
$561$	6.65931	−	50.8648i	0.281156	−	2.14751i
$562$	−4.50894			−0.190198
$563$	10.1274			0.426819			0.213410	−	0.976963i	$-0.431543\pi$
$563$	10.1274			0.426819			0.213410	+	0.976963i	$0.431543\pi$
$564$	−2.55456	−	0.334448i	−0.107566	−	0.0140828i
$565$	5.50370	−	3.17756i	0.231542	−	0.133681i
$566$	−14.2001	+	24.5953i	−0.596875	+	1.03382i
$567$	13.5674	−	7.88521i	0.569778	−	0.331148i
$568$	−4.78907	−	8.29492i	−0.200945	−	0.348047i
$569$	−19.0157			−0.797180			−0.398590	−	0.917129i	$-0.630500\pi$
$569$	−19.0157			−0.797180			−0.398590	+	0.917129i	$0.630500\pi$
$570$	1.06775	−	7.47395i	0.0447230	−	0.313049i
$571$	0.0688168			0.00287989			0.00143995	−	0.999999i	$-0.499542\pi$
$571$	0.0688168			0.00287989			0.00143995	+	0.999999i	$0.499542\pi$
$572$	8.14259	+	14.1034i	0.340459	+	0.589692i
$573$	9.68763	−	12.6440i	0.404706	−	0.528209i
$574$	−3.98126	+	6.89574i	−0.166175	+	0.287823i
$575$	1.69230	−	0.977053i	0.0705740	−	0.0407459i
$576$	0.780619	+	2.89666i	0.0325258	+	0.120694i
$577$	20.4867			0.852872			0.426436	−	0.904518i	$-0.359769\pi$
$577$	20.4867			0.852872			0.426436	+	0.904518i	$0.359769\pi$
$578$	−26.6278			−1.10757
$579$	22.5976	+	2.95853i	0.939126	+	0.122952i
$580$	−0.469946	−	0.271323i	−0.0195134	−	0.0112661i
$581$			17.8834i			0.741927i
$582$	−6.91341	−	16.6566i	−0.286570	−	0.690438i
$583$	0.504391	+	0.291210i	0.0208897	+	0.0120607i
$584$	−3.51522	−	6.08853i	−0.145461	−	0.251945i
$585$	2.83509	+	10.5202i	0.117216	+	0.434957i
$586$	−7.49776	−	12.9865i	−0.309730	−	0.536467i
$587$	−18.2857	+	10.5573i	−0.754733	+	0.435745i	−0.827401	−	0.561611i	$-0.810182\pi$
$587$	−18.2857	+	10.5573i	−0.754733	+	0.435745i	0.0726687	+	0.997356i	$0.476848\pi$
$588$	6.33470	−	2.62925i	0.261239	−	0.108428i
$589$	−19.2772	+	32.5032i	−0.794302	+	1.33927i
$590$			6.45756i			0.265853i
$591$	28.9365	−	37.7670i	1.19029	−	1.55352i
$592$	−0.217602	+	0.125633i	−0.00894340	+	0.00516347i
$593$	5.51015	+	3.18129i	0.226275	+	0.130640i	0.608852	−	0.793284i	$-0.291630\pi$
$593$	5.51015	+	3.18129i	0.226275	+	0.130640i	−0.382578	+	0.923923i	$0.624964\pi$
$594$	−3.09096	−	23.0936i	−0.126824	−	0.947542i
$595$	−5.75836	+	9.97377i	−0.236070	+	0.408885i
$596$		−	19.7801i		−	0.810226i
$597$	−14.4357	+	5.99161i	−0.590814	+	0.245220i
$598$	3.54850	−	6.14619i	0.145109	−	0.251336i
$599$	−21.4869	+	37.2163i	−0.877929	+	1.52062i	−0.0243194	+	0.999704i	$0.507742\pi$
$599$	−21.4869	+	37.2163i	−0.877929	+	1.52062i	−0.853610	+	0.520913i	$0.825591\pi$
$600$	1.59973	−	0.663976i	0.0653087	−	0.0271067i
$601$		−	15.3531i		−	0.626264i	−0.949710	−	0.313132i	$-0.898622\pi$
$601$		−	15.3531i		−	0.626264i	0.949710	−	0.313132i	$-0.101378\pi$
$602$	3.72679	−	6.45499i	0.151893	−	0.263086i
$603$	6.60517	−	24.7932i	0.268983	−	1.00966i
$604$	−18.6361	−	10.7595i	−0.758291	−	0.437800i
$605$	−7.88622	+	4.55311i	−0.320621	+	0.185110i
$606$	12.0995	−	15.7919i	0.491509	−	0.641501i
$607$			8.61899i			0.349834i	0.984583	+	0.174917i	$0.0559657\pi$
$607$			8.61899i			0.349834i	−0.984583	+	0.174917i	$0.944034\pi$
$608$	−3.80020	+	2.13506i	−0.154119	+	0.0865879i
$609$	1.51360	−	0.628227i	0.0613341	−	0.0254571i
$610$	−1.80505	+	1.04215i	−0.0730845	+	0.0421954i
$611$	2.70112	+	4.67848i	0.109276	+	0.189271i
$612$	−19.1328	+	5.15609i	−0.773399	+	0.208423i
$613$	−15.0671	−	26.0970i	−0.608555	−	1.05405i	−0.991479	−	0.130268i	$-0.958416\pi$
$613$	−15.0671	−	26.0970i	−0.608555	−	1.05405i	0.382924	−	0.923780i	$-0.374917\pi$
$614$	−17.6339	−	10.1810i	−0.711648	−	0.410870i
$615$	3.03219	+	7.30551i	0.122270	+	0.294586i
$616$			7.81830i			0.315008i
$617$	23.8215	+	13.7533i	0.959017	+	0.553688i	0.895870	−	0.444316i	$-0.146553\pi$
$617$	23.8215	+	13.7533i	0.959017	+	0.553688i	0.0631463	+	0.998004i	$0.479887\pi$
$618$	−30.3304	−	3.97092i	−1.22007	−	0.159734i
$619$	16.8953			0.679078			0.339539	−	0.940592i	$-0.389729\pi$
$619$	16.8953			0.679078			0.339539	+	0.940592i	$0.389729\pi$
$620$	−8.66957			−0.348178
$621$	−8.04224	+	6.19860i	−0.322724	+	0.248741i
$622$	−10.5410	+	6.08585i	−0.422656	+	0.244020i
$623$	3.67234	−	6.36068i	0.147129	−	0.254835i
$624$	3.82585	−	4.99337i	0.153157	−	0.199895i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	13.1442			0.525347
$627$	31.4171	−	12.6102i	1.25468	−	0.503605i
$628$	−13.5477			−0.540611
$629$	−0.829821	−	1.43729i	−0.0330871	−	0.0573086i
$630$	−1.34657	+	5.05451i	−0.0536487	+	0.201376i
$631$	19.8257	−	34.3391i	0.789247	−	1.36702i	−0.137182	−	0.990546i	$-0.543804\pi$
$631$	19.8257	−	34.3391i	0.789247	−	1.36702i	0.926429	−	0.376470i	$-0.122862\pi$
$632$	−5.04814	+	2.91454i	−0.200804	+	0.115934i
$633$	−35.9843	−	4.71113i	−1.43025	−	0.187251i
$634$	−6.86939			−0.272818
$635$	11.9725			0.475115
$636$	0.0292048	−	0.223070i	0.00115804	−	0.00884531i
$637$	−12.4548	−	7.19079i	−0.493478	−	0.284910i
$638$		−	2.43323i		−	0.0963324i
$639$	20.2891	−	20.3475i	0.802625	−	0.804934i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$	14.2303	+	24.6475i	0.562062	+	0.973520i	0.997316	+	0.0732121i	$0.0233250\pi$
$641$	14.2303	+	24.6475i	0.562062	+	0.973520i	−0.435255	+	0.900307i	$0.643342\pi$
$642$	−4.53244	+	34.6194i	−0.178881	+	1.36632i
$643$	−1.54529	−	2.67653i	−0.0609405	−	0.105552i	0.833946	−	0.551847i	$-0.186077\pi$
$643$	−1.54529	−	2.67653i	−0.0609405	−	0.105552i	−0.894886	+	0.446295i	$0.852743\pi$
$644$	2.95070	−	1.70359i	0.116274	−	0.0671308i
$645$	−2.83838	−	6.83856i	−0.111761	−	0.269268i
$646$	−14.1023	−	25.1008i	−0.554849	−	0.987580i
$647$		−	7.89351i		−	0.310326i	−0.987889	−	0.155163i	$-0.950410\pi$
$647$		−	7.89351i		−	0.310326i	0.987889	−	0.155163i	$-0.0495903\pi$
$648$	−7.78127	+	4.52237i	−0.305677	+	0.177656i
$649$	−25.0763	+	14.4778i	−0.984332	+	0.568305i
$650$	−3.14527	−	1.81592i	−0.123368	−	0.0712263i
$651$	15.9237	−	20.7831i	0.624101	−	0.814555i
$652$	−3.95150	+	6.84420i	−0.154753	+	0.268040i
$653$		−	18.1037i		−	0.708453i	−0.935160	−	0.354227i	$-0.884744\pi$
$653$		−	18.1037i		−	0.708453i	0.935160	−	0.354227i	$-0.115256\pi$
$654$	4.15399	+	10.0083i	0.162434	+	0.391355i
$655$	−4.57655	+	7.92681i	−0.178820	+	0.309726i
$656$	2.28336	−	3.95489i	0.0891501	−	0.154412i
$657$	14.8924	−	14.9352i	0.581006	−	0.582678i
$658$			2.59354i			0.101107i
$659$	8.56885	−	14.8417i	0.333795	−	0.578150i	−0.649457	−	0.760398i	$-0.725004\pi$
$659$	8.56885	−	14.8417i	0.333795	−	0.578150i	0.983253	+	0.182248i	$0.0583373\pi$
$660$	6.16498	+	4.72353i	0.239972	+	0.183863i
$661$	−31.8623	−	18.3957i	−1.23930	−	0.715510i	−0.270348	−	0.962763i	$-0.587139\pi$
$661$	−31.8623	−	18.3957i	−1.23930	−	0.715510i	−0.968951	+	0.247253i	$0.920472\pi$
$662$	−6.74506	+	3.89426i	−0.262154	+	0.151355i
$663$	32.9819	+	25.2703i	1.28091	+	0.981416i
$664$		−	10.2566i		−	0.398032i
$665$	−7.59966	−	0.0890778i	−0.294702	−	0.00345429i
$666$	−0.533779	−	0.532248i	−0.0206835	−	0.0206242i
$667$	−0.918324	+	0.530195i	−0.0355576	+	0.0205292i
$668$	−4.08621	−	7.07753i	−0.158100	−	0.273838i
$669$	−22.2816	−	2.91715i	−0.861457	−	0.112784i
$670$	4.27633	+	7.40682i	0.165209	+	0.286151i
$671$	−8.09386	−	4.67299i	−0.312460	−	0.180399i
$672$	2.78929	−	1.15771i	0.107599	−	0.0446596i
$673$			19.1641i			0.738723i	0.929286	+	0.369361i	$0.120424\pi$
$673$			19.1641i			0.738723i	−0.929286	+	0.369361i	$0.879576\pi$
$674$	−23.2844	−	13.4433i	−0.896881	−	0.517815i
$675$	3.17209	+	4.11556i	0.122094	+	0.158408i
$676$	−0.190296			−0.00731908
$677$	45.3076			1.74131			0.870656	−	0.491892i	$-0.163694\pi$
$677$	45.3076			1.74131			0.870656	+	0.491892i	$0.163694\pi$
$678$	1.42892	−	10.9143i	0.0548772	−	0.419159i
$679$	−15.7223	+	9.07730i	−0.603368	+	0.348355i
$680$	3.30257	−	5.72021i	0.126648	−	0.219360i
$681$	29.1829	+	22.3596i	1.11829	+	0.856821i
$682$	−19.4372	−	33.6661i	−0.744287	−	1.28914i
$683$	38.3931			1.46907			0.734535	−	0.678571i	$-0.237400\pi$
$683$	38.3931			1.46907			0.734535	+	0.678571i	$0.237400\pi$
$684$	−9.15104	−	9.34123i	−0.349899	−	0.357171i
$685$	−15.3504			−0.586509
$686$	−9.55481	−	16.5494i	−0.364804	−	0.631859i
$687$	13.3249	+	10.2093i	0.508376	+	0.389511i
$688$	−2.13741	+	3.70210i	−0.0814880	+	0.141141i
$689$	−0.408535	+	0.235868i	−0.0155639	+	0.00898585i
$690$	0.439370	−	3.35597i	0.0167265	−	0.127760i
$691$	25.7083			0.977988			0.488994	−	0.872287i	$-0.337364\pi$
$691$	25.7083			0.977988			0.488994	+	0.872287i	$0.337364\pi$
$692$	−17.6567			−0.671206
$693$	−22.6469	+	6.10311i	−0.860286	+	0.231838i
$694$	24.5180	+	14.1555i	0.930691	+	0.537335i
$695$			15.8380i			0.600770i
$696$	−0.868088	+	0.360305i	−0.0329048	+	0.0136573i
$697$	26.1226	+	15.0819i	0.989463	+	0.571267i
$698$	−2.35419	−	4.07758i	−0.0891075	−	0.154339i
$699$	−27.7696	−	3.63566i	−1.05034	−	0.137513i
$700$	−0.871800	−	1.51000i	−0.0329510	−	0.0570727i
$701$	−35.5687	+	20.5356i	−1.34341	+	0.775619i	−0.987307	−	0.158826i	$-0.949229\pi$
$701$	−35.5687	+	20.5356i	−1.34341	+	0.775619i	−0.356106	+	0.934446i	$0.615896\pi$
$702$	17.4506	+	7.18428i	0.658631	+	0.271153i
$703$	0.558700	−	0.942022i	0.0210718	−	0.0355290i
$704$		−	4.48400i		−	0.168997i
$705$	2.04509	+	1.56692i	0.0770226	+	0.0590137i
$706$	14.5885	−	8.42267i	0.549045	−	0.316991i
$707$	−17.3438	−	10.0135i	−0.652281	−	0.376595i
$708$	8.87840	+	6.80251i	0.333671	+	0.255654i
$709$	−4.57770	+	7.92881i	−0.171919	+	0.297773i	−0.939091	−	0.343669i	$-0.888330\pi$
$709$	−4.57770	+	7.92881i	−0.171919	+	0.297773i	0.767172	+	0.641442i	$0.221663\pi$
$710$			9.57815i			0.359461i
$711$	−12.3831	−	12.3476i	−0.464403	−	0.463071i
$712$	−2.10618	+	3.64801i	−0.0789325	+	0.136715i
$713$	−8.47062	+	14.6715i	−0.317227	+	0.549454i
$714$	7.64682	+	18.4236i	0.286175	+	0.689487i
$715$		−	16.2852i		−	0.609031i
$716$	9.98617	−	17.2966i	0.373201	−	0.646403i
$717$	22.4687	−	29.3253i	0.839107	−	1.09517i
$718$	27.5785	+	15.9225i	1.02922	+	0.594221i
$719$	−40.8433	+	23.5809i	−1.52320	+	0.879420i	−0.523576	+	0.851979i	$0.675402\pi$
$719$	−40.8433	+	23.5809i	−1.52320	+	0.879420i	−0.999623	+	0.0274407i	$0.991264\pi$
$720$	0.772294	−	2.89889i	0.0287817	−	0.108035i
$721$			30.7932i			1.14680i
$722$	9.88307	−	16.2273i	0.367810	−	0.603917i
$723$	2.78426	+	6.70817i	0.103548	+	0.249479i
$724$	−2.87130	+	1.65774i	−0.106711	+	0.0616096i
$725$	0.271323	+	0.469946i	0.0100767	+	0.0174534i
$726$	−2.04749	+	15.6390i	−0.0759893	+	0.580417i
$727$	0.839710	+	1.45442i	0.0311431	+	0.0539414i	0.881177	−	0.472787i	$-0.156752\pi$
$727$	0.839710	+	1.45442i	0.0311431	+	0.0539414i	−0.850034	+	0.526728i	$0.823419\pi$
$728$	−5.48409	−	3.16624i	−0.203254	−	0.117349i
$729$	−19.1740	−	19.0094i	−0.710147	−	0.704053i
$730$			7.03043i			0.260208i
$731$	−24.4529	−	14.1179i	−0.904423	−	0.522169i
$732$	−0.468643	+	3.57956i	−0.0173216	+	0.132304i
$733$	−50.5483			−1.86704			−0.933522	−	0.358519i	$-0.883282\pi$
$733$	−50.5483			−1.86704			−0.933522	+	0.358519i	$0.883282\pi$
$734$	30.2893			1.11800
$735$	−6.80064	−	0.890353i	−0.250845	−	0.0328412i
$736$	−1.69230	+	0.977053i	−0.0623792	+	0.0360146i
$737$	−19.1751	+	33.2122i	−0.706322	+	1.22339i
$738$	13.2384	+	3.52684i	0.487312	+	0.129825i
$739$	23.1698	+	40.1313i	0.852316	+	1.47626i	0.879113	+	0.476614i	$0.158136\pi$
$739$	23.1698	+	40.1313i	0.852316	+	1.47626i	−0.0267963	+	0.999641i	$0.508531\pi$
$740$	0.251265			0.00923670
$741$	−3.87789	+	27.1442i	−0.142458	+	0.997168i
$742$	−0.226474			−0.00831412
$743$	−8.82641	−	15.2878i	−0.323810	−	0.560855i	0.657461	−	0.753488i	$-0.271630\pi$
$743$	−8.82641	−	15.2878i	−0.323810	−	0.560855i	−0.981271	+	0.192634i	$0.938297\pi$
$744$	−9.13268	+	11.9197i	−0.334820	+	0.436996i
$745$	−9.89007	+	17.1301i	−0.362344	+	0.627598i
$746$	32.2650	−	18.6282i	1.18131	−	0.682027i
$747$	29.7098	−	8.00647i	1.08703	−	0.292942i
$748$	29.6174			1.08292
$749$	35.1476			1.28427
$750$	−1.71739	−	0.224845i	−0.0627104	−	0.00821017i
$751$	21.4154	+	12.3642i	0.781459	+	0.451176i	0.836947	−	0.547284i	$-0.184338\pi$
$751$	21.4154	+	12.3642i	0.781459	+	0.451176i	−0.0554880	+	0.998459i	$0.517671\pi$
$752$		−	1.48746i		−	0.0542422i
$753$	15.9932	+	38.5327i	0.582825	+	1.40421i
$754$	1.70677	+	0.985405i	0.0621569	+	0.0358863i
$755$	10.7595	+	18.6361i	0.391580	+	0.678236i
$756$	5.53086	+	7.17589i	0.201155	+	0.260985i
$757$	−11.0903	−	19.2089i	−0.403084	−	0.698161i	0.591013	−	0.806662i	$-0.298728\pi$
$757$	−11.0903	−	19.2089i	−0.403084	−	0.698161i	−0.994096	+	0.108501i	$0.965395\pi$
$758$	−29.1293	+	16.8178i	−1.05802	+	0.610851i
$759$	14.0172	−	5.81789i	0.508790	−	0.211176i
$760$	4.35860	+	0.0510884i	0.158103	+	0.00185317i
$761$		−	1.21908i		−	0.0441915i	−0.999756	−	0.0220957i	$-0.992966\pi$
$761$		−	1.21908i		−	0.0441915i	0.999756	−	0.0220957i	$-0.00703386\pi$
$762$	12.6121	−	16.4608i	0.456887	−	0.596313i
$763$	9.44692	−	5.45418i	0.342002	−	0.197455i
$764$	7.96429	+	4.59818i	0.288138	+	0.166356i
$765$	19.1476	+	5.10111i	0.692281	+	0.184431i
$766$	−4.65017	+	8.05432i	−0.168017	+	0.291015i
$767$		−	23.4528i		−	0.846833i
$768$	−1.59973	+	0.663976i	−0.0577253	+	0.0239592i
$769$	−3.96820	+	6.87313i	−0.143097	+	0.247851i	−0.928661	−	0.370929i	$-0.879039\pi$
$769$	−3.96820	+	6.87313i	−0.143097	+	0.247851i	0.785564	+	0.618780i	$0.212373\pi$
$770$	3.90915	−	6.77084i	0.140876	−	0.244004i
$771$	−17.8556	+	7.41106i	−0.643054	+	0.266903i
$772$			13.1581i			0.473570i
$773$	24.0038	−	41.5758i	0.863357	−	1.49538i	−0.00531153	−	0.999986i	$-0.501691\pi$
$773$	24.0038	−	41.5758i	0.863357	−	1.49538i	0.868669	−	0.495393i	$-0.164976\pi$
$774$	−12.3922	−	3.30142i	−0.445430	−	0.118667i
$775$	7.50806	+	4.33478i	0.269698	+	0.155710i
$776$	9.01717	−	5.20607i	0.323698	−	0.186887i
$777$	−0.461509	+	0.602346i	−0.0165566	+	0.0216090i
$778$		−	8.18343i		−	0.293390i
$779$	−0.233306	+	19.9045i	−0.00835906	+	0.713152i
$780$	−5.80997	+	2.41146i	−0.208030	+	0.0863441i
$781$	−37.1944	+	21.4742i	−1.33092	+	0.768407i
$782$	−6.45356	−	11.1779i	−0.230779	−	0.399721i
$783$	−1.72133	−	2.23330i	−0.0615152	−	0.0798115i
$784$	1.97993	+	3.42934i	0.0707117	+	0.122476i
$785$	11.7326	+	6.77384i	0.418755	+	0.241769i
$786$	6.07744	+	14.6425i	0.216775	+	0.522280i
$787$		−	17.2022i		−	0.613193i	−0.951840	−	0.306597i	$-0.900810\pi$
$787$		−	17.2022i		−	0.613193i	0.951840	−	0.306597i	$-0.0991902\pi$
$788$	23.7890	+	13.7346i	0.847448	+	0.489274i
$789$	25.4734	+	3.33503i	0.906877	+	0.118730i
$790$	5.82909			0.207390
$791$	−11.0808			−0.393988
$792$	12.9886	−	3.50029i	0.461530	−	0.124377i
$793$	6.55568	−	3.78492i	0.232799	−	0.134407i
$794$	2.72560	−	4.72088i	0.0967281	−	0.167538i
$795$	−0.136827	+	0.178582i	−0.00485276	+	0.00633365i
$796$	−4.51192	−	7.81487i	−0.159921	−	0.276991i
$797$	−13.6397			−0.483142			−0.241571	−	0.970383i	$-0.577663\pi$
$797$	−13.6397			−0.483142			−0.241571	+	0.970383i	$0.577663\pi$
$798$	−8.12809	+	10.3548i	−0.287731	+	0.366557i
$799$	9.82490			0.347580
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−12.2112	−	3.25318i	−0.431461	−	0.114946i
$802$	−14.4054	+	24.9508i	−0.508671	+	0.881044i
$803$	−27.3010	+	15.7622i	−0.963430	+	0.556237i
$804$	14.6883	+	1.92302i	0.518016	+	0.0678197i
$805$	−3.40718			−0.120087
$806$	31.4865			1.10907
$807$	1.44029	−	11.0011i	0.0507005	−	0.387257i
$808$	9.94712	+	5.74297i	0.349939	+	0.202037i
$809$		−	48.0047i		−	1.68776i	−0.536535	−	0.843878i	$-0.680267\pi$
$809$		−	48.0047i		−	1.68776i	0.536535	−	0.843878i	$-0.319733\pi$
$810$	8.99996	−	0.0258539i	0.316226	−	0.000908415i
$811$	−16.9494	−	9.78575i	−0.595175	−	0.343624i	0.171966	−	0.985103i	$-0.444988\pi$
$811$	−16.9494	−	9.78575i	−0.595175	−	0.343624i	−0.767141	+	0.641479i	$0.778321\pi$
$812$	0.473080	+	0.819398i	0.0166018	+	0.0287552i
$813$	−3.95918	+	30.2408i	−0.138855	+	1.06059i
$814$	0.563337	+	0.975727i	0.0197449	+	0.0341992i
$815$	6.84420	−	3.95150i	0.239742	−	0.138415i
$816$	−4.38565	−	10.5664i	−0.153529	−	0.369899i
$817$	0.218394	−	18.6322i	0.00764064	−	0.651859i
$818$		−	29.2481i		−	1.02264i
$819$	4.89054	−	18.3572i	0.170889	−	0.641452i
$820$	−3.95489	+	2.28336i	−0.138111	+	0.0797382i
$821$	−19.8535	−	11.4624i	−0.692892	−	0.400041i	0.111803	−	0.993730i	$-0.464338\pi$
$821$	−19.8535	−	11.4624i	−0.692892	−	0.400041i	−0.804694	+	0.593689i	$0.797671\pi$
$822$	−16.1704	+	21.1050i	−0.564008	+	0.736123i
$823$	−16.1127	+	27.9080i	−0.561653	+	0.972811i	0.435700	+	0.900092i	$0.356501\pi$
$823$	−16.1127	+	27.9080i	−0.561653	+	0.972811i	−0.997352	+	0.0727192i	$0.976832\pi$
$824$		−	17.6607i		−	0.615240i
$825$	−2.97727	−	7.17318i	−0.103655	−	0.249738i
$826$	5.62970	−	9.75092i	0.195882	−	0.339278i
$827$	20.0676	−	34.7581i	0.697819	−	1.20866i	−0.271402	−	0.962466i	$-0.587487\pi$
$827$	20.0676	−	34.7581i	0.697819	−	1.20866i	0.969221	−	0.246192i	$-0.0791795\pi$
$828$	−4.15123	−	4.13932i	−0.144265	−	0.143851i
$829$		−	43.1212i		−	1.49766i	−0.662762	−	0.748830i	$-0.730616\pi$
$829$		−	43.1212i		−	1.49766i	0.662762	−	0.748830i	$-0.269384\pi$
$830$	−5.12829	+	8.88246i	−0.178005	+	0.308315i
$831$	−37.8427	−	28.9946i	−1.31275	−	1.00581i
$832$	3.14527	+	1.81592i	0.109043	+	0.0629558i
$833$	−22.6512	+	13.0777i	−0.784819	+	0.453115i
$834$	21.7755	+	16.6841i	0.754022	+	0.577722i
$835$			8.17243i			0.282819i
$836$	9.57358	+	17.0401i	0.331109	+	0.589344i
$837$	−41.6563	−	17.1496i	−1.43985	−	0.592776i
$838$	−0.962877	+	0.555917i	−0.0332620	+	0.0192038i
$839$	16.9630	+	29.3808i	0.585628	+	1.01434i	0.994797	+	0.101879i	$0.0324854\pi$
$839$	16.9630	+	29.3808i	0.585628	+	1.01434i	−0.409169	+	0.912459i	$0.634181\pi$
$840$	−2.99445	−	0.392039i	−0.103318	−	0.0135266i
$841$	14.3528	+	24.8597i	0.494923	+	0.857232i
$842$	−17.1508	−	9.90200i	−0.591054	−	0.341245i
$843$	7.21309	−	2.99383i	0.248432	−	0.103113i
$844$		−	20.9528i		−	0.721226i
$845$	0.164801	+	0.0951480i	0.00566934	+	0.00327319i
$846$	4.30868	−	1.16114i	0.148135	−	0.0399209i
$847$	15.8776			0.545561
$848$	0.129889			0.00446040
$849$	6.38564	−	48.7744i	0.219155	−	1.67393i
$850$	−5.72021	+	3.30257i	−0.196202	+	0.113277i
$851$	0.245499	−	0.425218i	0.00841561	−	0.0145763i
$852$	13.1689	+	10.0898i	0.451157	+	0.345671i
$853$	3.13675	+	5.43302i	0.107400	+	0.186023i	0.914716	−	0.404096i	$-0.132414\pi$
$853$	3.13675	+	5.43302i	0.107400	+	0.186023i	−0.807316	+	0.590119i	$0.799081\pi$
$854$	3.63418			0.124359
$855$	3.25442	+	12.6653i	0.111299	+	0.433143i
$856$	−20.1581			−0.688989
$857$	5.57983	+	9.66455i	0.190603	+	0.330135i	0.945450	−	0.325766i	$-0.105622\pi$
$857$	5.57983	+	9.66455i	0.190603	+	0.330135i	−0.754847	+	0.655901i	$0.772289\pi$
$858$	−22.3903	−	17.1551i	−0.764391	−	0.585666i
$859$	26.7797	−	46.3839i	0.913713	−	1.58260i	0.104937	−	0.994479i	$-0.466536\pi$
$859$	26.7797	−	46.3839i	0.913713	−	1.58260i	0.808775	−	0.588118i	$-0.200131\pi$
$860$	3.70210	−	2.13741i	0.126241	−	0.0728851i
$861$	1.79033	−	13.6748i	0.0610143	−	0.466036i
$862$	6.32292			0.215359
$863$	−12.4085			−0.422390			−0.211195	−	0.977444i	$-0.567736\pi$
$863$	−12.4085			−0.422390			−0.211195	+	0.977444i	$0.567736\pi$
$864$	−3.17209	−	4.11556i	−0.107917	−	0.140014i
$865$	15.2911	+	8.82834i	0.519914	+	0.300173i
$866$			28.0429i			0.952935i
$867$	42.5973	−	17.6802i	1.44668	−	0.600452i
$868$	13.0911	+	7.55813i	0.444340	+	0.256540i
$869$	13.0688	+	22.6358i	0.443329	+	0.767868i
$870$	0.931939	+	0.122011i	0.0315957	+	0.00413657i
$871$	−15.5310	−	26.9004i	−0.526247	−	0.911486i
$872$	−5.41805	+	3.12812i	−0.183478	+	0.105931i
$873$	22.1192	+	22.0557i	0.748621	+	0.746473i
$874$	4.34504	−	7.32616i	0.146973	−	0.247811i
$875$			1.74360i			0.0589445i
$876$	9.66604	+	7.40599i	0.326585	+	0.250225i
$877$	−21.0398	+	12.1473i	−0.710463	+	0.410186i	−0.811232	−	0.584724i	$-0.801203\pi$
$877$	−21.0398	+	12.1473i	−0.710463	+	0.410186i	0.100770	+	0.994910i	$0.467869\pi$
$878$	8.39710	+	4.84807i	0.283388	+	0.163614i
$879$	20.6171	+	15.7966i	0.695398	+	0.532805i
$880$	−2.24200	+	3.88325i	−0.0755777	+	0.130904i
$881$			45.6855i			1.53918i	0.638536	+	0.769592i	$0.279540\pi$
$881$			45.6855i			1.53918i	−0.638536	+	0.769592i	$0.720460\pi$
$882$	−8.38805	+	8.41218i	−0.282440	+	0.283253i
$883$	15.2288	−	26.3771i	0.512491	−	0.887660i	−0.487404	−	0.873176i	$-0.662056\pi$
$883$	15.2288	−	26.3771i	0.512491	−	0.887660i	0.999895	−	0.0144835i	$-0.00461041\pi$
$884$	−11.9944	+	20.7749i	−0.403416	+	0.698736i
$885$	−4.28766	−	10.3303i	−0.144128	−	0.347251i
$886$			10.2242i			0.343487i
$887$	−7.35088	+	12.7321i	−0.246818	+	0.427502i	−0.962641	−	0.270780i	$-0.912718\pi$
$887$	−7.35088	+	12.7321i	−0.246818	+	0.427502i	0.715823	+	0.698282i	$0.246052\pi$
$888$	0.264688	−	0.345461i	0.00888233	−	0.0115929i
$889$	−18.0785	−	10.4376i	−0.606335	−	0.350067i
$890$	3.64801	−	2.10618i	0.122282	−	0.0705994i
$891$	20.2783	+	34.8912i	0.679349	+	1.16890i
$892$		−	12.9741i		−	0.434404i
$893$	3.17582	+	5.65266i	0.106275	+	0.189159i
$894$	13.1335	+	31.6429i	0.439251	+	1.05830i
$895$	−17.2966	+	9.98617i	−0.578160	+	0.333801i
$896$	0.871800	+	1.51000i	0.0291248	+	0.0504456i
$897$	−1.59572	+	12.1884i	−0.0532797	+	0.406958i
$898$	−3.33355	−	5.77387i	−0.111242	−	0.192677i
$899$	−4.07423	−	2.35226i	−0.135883	−	0.0784521i
$900$	−2.11827	+	2.12437i	−0.0706090	+	0.0708122i
$901$			0.857932i			0.0285819i
$902$	−17.7337	−	10.2386i	−0.590468	−	0.340907i
$903$	−1.67590	+	12.8007i	−0.0557704	+	0.425982i
$904$	6.35512			0.211368
$905$	3.31549			0.110211
$906$	36.9568	+	4.83845i	1.22781	+	0.160747i
$907$	5.41439	−	3.12600i	0.179782	−	0.103797i	−0.407408	−	0.913246i	$-0.633567\pi$
$907$	5.41439	−	3.12600i	0.179782	−	0.103797i	0.587190	+	0.809449i	$0.300234\pi$
$908$	−10.6129	+	18.3820i	−0.352200	+	0.610029i
$909$	−8.87053	+	33.2965i	−0.294217	+	1.10438i
$910$	3.16624	+	5.48409i	0.104960	+	0.181796i
$911$	49.4685			1.63896			0.819481	−	0.573106i	$-0.194262\pi$
$911$	49.4685			1.63896			0.819481	+	0.573106i	$0.194262\pi$
$912$	4.66167	−	5.93876i	0.154363	−	0.196652i
$913$	−45.9905			−1.52206
$914$	6.43251	+	11.1414i	0.212768	+	0.368526i
$915$	2.19564	−	2.86567i	0.0725855	−	0.0947361i
$916$	−4.84581	+	8.39319i	−0.160110	+	0.277319i
$917$	13.8212	−	7.97967i	0.456416	−	0.263512i
$918$	27.1838	−	20.9521i	0.897200	−	0.691522i
$919$	27.8719			0.919409			0.459705	−	0.888072i	$-0.347955\pi$
$919$	27.8719			0.919409			0.459705	+	0.888072i	$0.347955\pi$
$920$	1.95411			0.0644249
$921$	34.9695	+	4.57827i	1.15228	+	0.150859i
$922$	−4.75855	−	2.74735i	−0.156715	−	0.0904792i
$923$		−	34.7863i		−	1.14501i
$924$	−5.19116	−	12.5072i	−0.170777	−	0.411456i
$925$	−0.217602	−	0.125633i	−0.00715472	−	0.00413078i
$926$	−4.56084	−	7.89961i	−0.149879	−	0.259597i
$927$	51.1571	−	13.7863i	1.68022	−	0.452801i
$928$	−0.271323	−	0.469946i	−0.00890663	−	0.0154267i
$929$	38.9043	−	22.4614i	1.27641	−	0.736934i	0.300222	−	0.953869i	$-0.402939\pi$
$929$	38.9043	−	22.4614i	1.27641	−	0.736934i	0.976186	+	0.216935i	$0.0696060\pi$
$930$	13.8690	−	5.75639i	0.454781	−	0.188759i
$931$	−14.8460	−	8.80492i	−0.486557	−	0.288569i
$932$		−	16.1696i		−	0.529654i
$933$	12.8219	−	16.7347i	0.419770	−	0.547869i
$934$	−26.8784	+	15.5183i	−0.879489	+	0.507773i
$935$	−25.6494	−	14.8087i	−0.838826	−	0.484296i
$936$	−2.80485	+	10.5283i	−0.0916795	+	0.344129i
$937$	5.70404	−	9.87968i	0.186343	−	0.322755i	−0.757685	−	0.652620i	$-0.773670\pi$
$937$	5.70404	−	9.87968i	0.186343	−	0.322755i	0.944028	+	0.329865i	$0.107003\pi$
$938$		−	14.9124i		−	0.486908i
$939$	−21.0271	+	8.72742i	−0.686195	+	0.284809i
$940$	−0.743732	+	1.28818i	−0.0242579	+	0.0420158i
$941$	9.04539	−	15.6671i	0.294871	−	0.510732i	−0.680084	−	0.733134i	$-0.738057\pi$
$941$	9.04539	−	15.6671i	0.294871	−	0.510732i	0.974955	+	0.222403i	$0.0713899\pi$
$942$	21.6726	−	8.99533i	0.706132	−	0.293084i
$943$			8.92384i			0.290600i
$944$	−3.22878	+	5.59241i	−0.105088	+	0.182017i
$945$	−1.20192	−	8.97994i	−0.0390984	−	0.292117i
$946$	16.6002	+	9.58414i	0.539720	+	0.311607i
$947$	18.9963	−	10.9675i	0.617296	−	0.356396i	−0.158520	−	0.987356i	$-0.550672\pi$
$947$	18.9963	−	10.9675i	0.617296	−	0.356396i	0.775815	+	0.630960i	$0.217339\pi$
$948$	6.14047	−	8.01432i	0.199433	−	0.260293i
$949$		−	25.5334i		−	0.828850i
$950$	−3.74911	−	2.22354i	−0.121637	−	0.0721413i
$951$	10.9892	−	4.56111i	0.356348	−	0.147904i
$952$	−9.97377	+	5.75836i	−0.323252	+	0.186629i
$953$	17.8637	+	30.9409i	0.578663	+	1.00227i	0.995633	+	0.0933541i	$0.0297589\pi$
$953$	17.8637	+	30.9409i	0.578663	+	1.00227i	−0.416969	+	0.908920i	$0.636908\pi$
$954$	0.101393	+	0.376243i	0.00328274	+	0.0121813i
$955$	−4.59818	−	7.96429i	−0.148794	−	0.257718i
$956$	18.4717	+	10.6646i	0.597417	+	0.344919i
$957$	1.61560	+	3.89251i	0.0522251	+	0.125827i
$958$			6.66678i			0.215394i
$959$	23.1792	+	13.3825i	0.748494	+	0.432143i
$960$	1.71739	+	0.224845i	0.0554287	+	0.00725683i
$961$	−44.1614			−1.42456
$962$	−0.912557			−0.0294220
$963$	−15.7358	−	58.3911i	−0.507078	−	1.88163i
$964$	−3.63151	+	2.09666i	−0.116963	+	0.0675287i
$965$	6.57904	−	11.3952i	0.211787	−	0.366826i
$966$	−3.58919	+	4.68448i	−0.115480	+	0.150721i
$967$	−3.90937	−	6.77123i	−0.125717	−	0.217748i	0.796296	−	0.604907i	$-0.206790\pi$
$967$	−3.90937	−	6.77123i	−0.125717	−	0.217748i	−0.922013	+	0.387159i	$0.873456\pi$
$968$	−9.10622			−0.292685
$969$	39.2263	+	30.7910i	1.26013	+	0.989148i
$970$	−10.4121			−0.334314
$971$	3.20611	+	5.55314i	0.102889	+	0.178209i	0.912874	−	0.408242i	$-0.133858\pi$
$971$	3.20611	+	5.55314i	0.102889	+	0.178209i	−0.809985	+	0.586451i	$0.800525\pi$
$972$	9.44518	−	12.4012i	0.302954	−	0.397767i
$973$	13.8076	−	23.9154i	0.442651	−	0.766694i
$974$	18.7445	−	10.8222i	0.600613	−	0.346764i
$975$	6.23731	+	0.816601i	0.199754	+	0.0261522i
$976$	−2.08430			−0.0667167
$977$	−10.1495			−0.324713			−0.162356	−	0.986732i	$-0.551909\pi$
$977$	−10.1495			−0.324713			−0.162356	+	0.986732i	$0.551909\pi$
$978$	1.77695	−	13.5726i	0.0568206	−	0.434003i
$979$	16.3577	+	9.44411i	0.522794	+	0.301835i
$980$		−	3.95986i		−	0.126493i
$981$	−13.2905	−	13.2524i	−0.424334	−	0.423116i
$982$	−2.23804	−	1.29214i	−0.0714188	−	0.0412337i
$983$	−9.71885	−	16.8335i	−0.309983	−	0.536907i	0.668375	−	0.743824i	$-0.266990\pi$
$983$	−9.71885	−	16.8335i	−0.309983	−	0.536907i	−0.978358	+	0.206918i	$0.933657\pi$
$984$	−1.02680	+	7.84285i	−0.0327332	+	0.250021i
$985$	−13.7346	−	23.7890i	−0.437620	−	0.757981i
$986$	3.10406	−	1.79213i	0.0988533	−	0.0570730i
$987$	−1.72205	−	4.14897i	−0.0548135	−	0.132063i
$988$	−15.8298	−	0.185545i	−0.503612	−	0.00590298i
$989$		−	8.35345i		−	0.265624i
$990$	−12.9986	−	3.46296i	−0.413123	−	0.110060i
$991$	−10.1730	+	5.87340i	−0.323157	+	0.186575i	−0.652799	−	0.757531i	$-0.726405\pi$
$991$	−10.1730	+	5.87340i	−0.323157	+	0.186575i	0.329642	+	0.944106i	$0.393072\pi$
$992$	−7.50806	−	4.33478i	−0.238381	−	0.137630i
$993$	8.20458	−	10.7083i	0.260364	−	0.339819i
$994$	8.35023	−	14.4630i	0.264853	−	0.458739i
$995$			9.02384i			0.286075i
$996$	6.81012	+	16.4078i	0.215787	+	0.519900i
$997$	−26.3056	+	45.5626i	−0.833105	+	1.44298i	0.0624587	+	0.998048i	$0.480106\pi$
$997$	−26.3056	+	45.5626i	−0.833105	+	1.44298i	−0.895564	+	0.444933i	$0.853228\pi$
$998$	−9.18058	+	15.9012i	−0.290606	+	0.503345i
$999$	1.20730	+	0.497037i	0.0381974	+	0.0157255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.s.a.221.9	✓	24
3.2	odd	2		570.2.s.b.221.5	yes	24
19.8	odd	6		570.2.s.b.521.5	yes	24
57.8	even	6	inner	570.2.s.a.521.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.s.a.221.9	✓	24	1.1	even	1	trivial
570.2.s.a.521.9	yes	24	57.8	even	6	inner
570.2.s.b.221.5	yes	24	3.2	odd	2
570.2.s.b.521.5	yes	24	19.8	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.37489 + 1.05342i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.224845 - 1.71739i) q^{6} -1.74360 q^{7} +1.00000 q^{8} +(0.780619 + 2.89666i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.37489 + 1.05342i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.224845 - 1.71739i) q^{6} -1.74360 q^{7} +1.00000 q^{8} +(0.780619 + 2.89666i) q^{9} +(-0.866025 - 0.500000i) q^{10} -4.48400i q^{11} +(-1.59973 + 0.663976i) q^{12} +(3.14527 + 1.81592i) q^{13} +(0.871800 + 1.51000i) q^{14} +(1.71739 + 0.224845i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(5.72021 - 3.30257i) q^{17} +(2.11827 - 2.12437i) q^{18} +(3.74911 + 2.22354i) q^{19} +1.00000i q^{20} +(-2.39725 - 1.83674i) q^{21} +(-3.88325 + 2.24200i) q^{22} +(1.69230 + 0.977053i) q^{23} +(1.37489 + 1.05342i) q^{24} +(0.500000 - 0.866025i) q^{25} -3.63184i q^{26} +(-1.97813 + 4.80489i) q^{27} +(0.871800 - 1.51000i) q^{28} +(-0.271323 + 0.469946i) q^{29} +(-0.663976 - 1.59973i) q^{30} +8.66957i q^{31} +(-0.500000 + 0.866025i) q^{32} +(4.72353 - 6.16498i) q^{33} +(-5.72021 - 3.30257i) q^{34} +(-1.51000 + 0.871800i) q^{35} +(-2.89889 - 0.772294i) q^{36} -0.251265i q^{37} +(0.0510884 - 4.35860i) q^{38} +(2.41146 + 5.80997i) q^{39} +(0.866025 - 0.500000i) q^{40} +(2.28336 + 3.95489i) q^{41} +(-0.392039 + 2.99445i) q^{42} +(-2.13741 - 3.70210i) q^{43} +(3.88325 + 2.24200i) q^{44} +(2.12437 + 2.11827i) q^{45} -1.95411i q^{46} +(1.28818 + 0.743732i) q^{47} +(0.224845 - 1.71739i) q^{48} -3.95986 q^{49} -1.00000 q^{50} +(11.3436 + 1.48513i) q^{51} +(-3.14527 + 1.81592i) q^{52} +(-0.0649443 + 0.112487i) q^{53} +(5.15023 - 0.689332i) q^{54} +(-2.24200 - 3.88325i) q^{55} -1.74360 q^{56} +(2.81228 + 7.00650i) q^{57} +0.542647 q^{58} +(-3.22878 - 5.59241i) q^{59} +(-1.05342 + 1.37489i) q^{60} +(1.04215 - 1.80505i) q^{61} +(7.50806 - 4.33478i) q^{62} +(-1.36109 - 5.05062i) q^{63} +1.00000 q^{64} +3.63184 q^{65} +(-7.70079 - 1.00820i) q^{66} +(-7.40682 - 4.27633i) q^{67} +6.60513i q^{68} +(1.29748 + 3.12604i) q^{69} +(1.51000 + 0.871800i) q^{70} +(-4.78907 - 8.29492i) q^{71} +(0.780619 + 2.89666i) q^{72} +(-3.51522 - 6.08853i) q^{73} +(-0.217602 + 0.125633i) q^{74} +(1.59973 - 0.663976i) q^{75} +(-3.80020 + 2.13506i) q^{76} +7.81830i q^{77} +(3.82585 - 4.99337i) q^{78} +(-5.04814 + 2.91454i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(-7.78127 + 4.52237i) q^{81} +(2.28336 - 3.95489i) q^{82} -10.2566i q^{83} +(2.78929 - 1.15771i) q^{84} +(3.30257 - 5.72021i) q^{85} +(-2.13741 + 3.70210i) q^{86} +(-0.868088 + 0.360305i) q^{87} -4.48400i q^{88} +(-2.10618 + 3.64801i) q^{89} +(0.772294 - 2.89889i) q^{90} +(-5.48409 - 3.16624i) q^{91} +(-1.69230 + 0.977053i) q^{92} +(-9.13268 + 11.9197i) q^{93} -1.48746i q^{94} +(4.35860 + 0.0510884i) q^{95} +(-1.59973 + 0.663976i) q^{96} +(9.01717 - 5.20607i) q^{97} +(1.97993 + 3.42934i) q^{98} +(12.9886 - 3.50029i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9}+O(q^{10}) \) 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * q^9	\( 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9} - 2 q^{12} + 18 q^{13} + 6 q^{14} - 12 q^{16} + 12 q^{17} + 2 q^{18} + 6 q^{19} - 6 q^{21} + 18 q^{22} + 4 q^{24} + 12 q^{25} + 28 q^{27} + 6 q^{28} - 12 q^{32} - 22 q^{33} - 12 q^{34} + 2 q^{36} + 6 q^{38} + 40 q^{39} + 6 q^{41} - 6 q^{42} - 22 q^{43} - 18 q^{44} + 8 q^{45} + 12 q^{47} - 2 q^{48} + 12 q^{49} - 24 q^{50} - 20 q^{51} - 18 q^{52} + 8 q^{53} + 4 q^{54} - 12 q^{56} + 26 q^{59} + 22 q^{61} - 18 q^{62} + 6 q^{63} + 24 q^{64} + 8 q^{65} + 8 q^{66} - 48 q^{67} - 64 q^{69} + 24 q^{71} - 4 q^{72} - 8 q^{73} + 30 q^{74} + 2 q^{75} - 12 q^{76} - 38 q^{78} + 18 q^{79} - 12 q^{81} + 6 q^{82} + 12 q^{84} - 22 q^{86} - 24 q^{87} + 28 q^{89} + 8 q^{90} + 18 q^{91} + 2 q^{93} - 2 q^{96} + 6 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * q^9 - 2 * q^12 + 18 * q^13 + 6 * q^14 - 12 * q^16 + 12 * q^17 + 2 * q^18 + 6 * q^19 - 6 * q^21 + 18 * q^22 + 4 * q^24 + 12 * q^25 + 28 * q^27 + 6 * q^28 - 12 * q^32 - 22 * q^33 - 12 * q^34 + 2 * q^36 + 6 * q^38 + 40 * q^39 + 6 * q^41 - 6 * q^42 - 22 * q^43 - 18 * q^44 + 8 * q^45 + 12 * q^47 - 2 * q^48 + 12 * q^49 - 24 * q^50 - 20 * q^51 - 18 * q^52 + 8 * q^53 + 4 * q^54 - 12 * q^56 + 26 * q^59 + 22 * q^61 - 18 * q^62 + 6 * q^63 + 24 * q^64 + 8 * q^65 + 8 * q^66 - 48 * q^67 - 64 * q^69 + 24 * q^71 - 4 * q^72 - 8 * q^73 + 30 * q^74 + 2 * q^75 - 12 * q^76 - 38 * q^78 + 18 * q^79 - 12 * q^81 + 6 * q^82 + 12 * q^84 - 22 * q^86 - 24 * q^87 + 28 * q^89 + 8 * q^90 + 18 * q^91 + 2 * q^93 - 2 * q^96 + 6 * q^97 - 6 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more