LMFDB - Embedded newform 570.2.s.b.221.5

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			221.5
Character	$\chi$	$=$	570.221
Dual form			570.2.s.b.521.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.224845 - 1.71739i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.37489 - 1.05342i) q^{6} -1.74360 q^{7} -1.00000 q^{8} +(-2.89889 + 0.772294i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.224845 - 1.71739i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.37489 - 1.05342i) q^{6} -1.74360 q^{7} -1.00000 q^{8} +(-2.89889 + 0.772294i) 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} +(1.05342 + 1.37489i) 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} +(0.392039 + 2.99445i) q^{21} +(-3.88325 + 2.24200i) q^{22} +(-1.69230 - 0.977053i) q^{23} +(0.224845 + 1.71739i) 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} +(7.70079 - 1.00820i) q^{33} +(-5.72021 - 3.30257i) q^{34} +(1.51000 - 0.871800i) q^{35} +(0.780619 - 2.89666i) 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} +(-2.39725 + 1.83674i) 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} +(-1.37489 + 1.05342i) q^{48} -3.95986 q^{49} +1.00000 q^{50} +(6.95797 + 9.08130i) q^{51} +(-3.14527 + 1.81592i) q^{52} +(0.0649443 - 0.112487i) q^{53} +(-3.17209 + 4.11556i) q^{54} +(-2.24200 - 3.88325i) q^{55} +1.74360 q^{56} +(2.97573 - 6.93866i) q^{57} +0.542647 q^{58} +(3.22878 + 5.59241i) q^{59} +(-1.71739 + 0.224845i) q^{60} +(1.04215 - 1.80505i) q^{61} +(-7.50806 + 4.33478i) q^{62} +(5.05451 - 1.34657i) q^{63} +1.00000 q^{64} -3.63184 q^{65} +(4.72353 + 6.16498i) 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} +(2.89889 - 0.772294i) 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} +(6.23731 - 0.816601i) q^{78} +(-5.04814 + 2.91454i) q^{79} +(0.866025 + 0.500000i) q^{80} +(7.80712 - 4.47759i) 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} +(2.89666 + 0.780619i) q^{90} +(-5.48409 - 3.16624i) q^{91} +(1.69230 - 0.977053i) q^{92} +(14.8891 - 1.94931i) 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} +(-3.46296 - 12.9986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9	$ 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 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} - 2 q^{24} + 12 q^{25} - 28 q^{27} + 6 q^{28} + 12 q^{32} - 8 q^{33} - 12 q^{34} - 4 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} - 4 q^{48} + 12 q^{49} + 24 q^{50} - 4 q^{51} - 18 q^{52} - 8 q^{53} - 32 q^{54} + 12 q^{56} - 20 q^{57} - 26 q^{59} + 22 q^{61} + 18 q^{62} + 30 q^{63} + 24 q^{64} - 8 q^{65} - 22 q^{66} - 48 q^{67} + 64 q^{69} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 30 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 18 q^{79} - 6 q^{81} + 6 q^{82} - 12 q^{84} + 22 q^{86} - 24 q^{87} - 28 q^{89} + 16 q^{90} + 18 q^{91} + 14 q^{93} - 2 q^{96} + 6 q^{97} + 6 q^{98} - 52 q^{99}+O(q^{100}) $ 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * 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 - 2 * q^24 + 12 * q^25 - 28 * q^27 + 6 * q^28 + 12 * q^32 - 8 * q^33 - 12 * q^34 - 4 * 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 - 4 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 - 18 * q^52 - 8 * q^53 - 32 * q^54 + 12 * q^56 - 20 * q^57 - 26 * q^59 + 22 * q^61 + 18 * q^62 + 30 * q^63 + 24 * q^64 - 8 * q^65 - 22 * q^66 - 48 * q^67 + 64 * q^69 - 24 * q^71 - 2 * q^72 - 8 * q^73 - 30 * q^74 - 2 * q^75 - 12 * q^76 + 2 * q^78 + 18 * q^79 - 6 * q^81 + 6 * q^82 - 12 * q^84 + 22 * q^86 - 24 * q^87 - 28 * q^89 + 16 * q^90 + 18 * q^91 + 14 * q^93 - 2 * q^96 + 6 * q^97 + 6 * q^98 - 52 * 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
$3$	−0.224845	−	1.71739i	−0.129814	−	0.991538i
$3$	−0.224845	−	1.71739i	−0.129814	−	0.991538i
$4$	−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
$6$	1.37489	−	1.05342i	0.561295	−	0.430056i
$7$	−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
$9$	−2.89889	+	0.772294i	−0.966297	+	0.257431i
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$			4.48400i			1.35198i	0.736913	+	0.675988i	$0.236283\pi$
$11$			4.48400i			1.35198i	−0.736913	+	0.675988i	$0.763717\pi$
$12$	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
$15$	1.05342	+	1.37489i	0.271992	+	0.354994i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.72021	+	3.30257i	−1.38736	+	0.800990i	−0.993017	−	0.117975i	$-0.962360\pi$
$17$	−5.72021	+	3.30257i	−1.38736	+	0.800990i	−0.394339	+	0.918965i	$0.629026\pi$
$18$	−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
$21$	0.392039	+	2.99445i	0.0855500	+	0.653443i
$22$	−3.88325	+	2.24200i	−0.827913	+	0.477996i
$23$	−1.69230	−	0.977053i	−0.352870	−	0.203730i	0.313079	−	0.949727i	$-0.398640\pi$
$23$	−1.69230	−	0.977053i	−0.352870	−	0.203730i	−0.665949	+	0.745998i	$0.731973\pi$
$24$	0.224845	+	1.71739i	0.0458962	+	0.350562i
$25$	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	−0.839734	−	0.542998i	$-0.817289\pi$
$29$	0.271323	−	0.469946i	0.0503835	−	0.0872668i	0.890117	+	0.455732i	$0.150622\pi$
$30$	−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
$33$	7.70079	−	1.00820i	1.34054	−	0.175506i
$34$	−5.72021	−	3.30257i	−0.981009	−	0.566386i
$35$	1.51000	−	0.871800i	0.255237	−	0.147361i
$36$	0.780619	−	2.89666i	0.130103	−	0.482777i
$37$		−	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	0.630790	−	0.775953i	$-0.282731\pi$
$41$	−2.28336	−	3.95489i	−0.356600	−	0.617650i	−0.987390	+	0.158304i	$0.949398\pi$
$42$	−2.39725	+	1.83674i	−0.369904	+	0.283415i
$43$	−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	0.403099	−	0.915156i	$-0.367933\pi$
$47$	−1.28818	−	0.743732i	−0.187901	−	0.108484i	−0.590999	+	0.806672i	$0.701266\pi$
$48$	−1.37489	+	1.05342i	−0.198448	+	0.152048i
$49$	−3.95986			−0.565694
$50$	1.00000			0.141421
$51$	6.95797	+	9.08130i	0.974311	+	1.27164i
$52$	−3.14527	+	1.81592i	−0.436170	+	0.251823i
$53$	0.0649443	−	0.112487i	0.00892079	−	0.0154513i	−0.861531	−	0.507706i	$-0.830494\pi$
$53$	0.0649443	−	0.112487i	0.00892079	−	0.0154513i	0.870451	+	0.492254i	$0.163827\pi$
$54$	−3.17209	+	4.11556i	−0.431667	+	0.560057i
$55$	−2.24200	−	3.88325i	−0.302311	−	0.523618i
$56$	1.74360			0.232998
$57$	2.97573	−	6.93866i	0.394146	−	0.919048i
$58$	0.542647			0.0712530
$59$	3.22878	+	5.59241i	0.420351	+	0.728069i	0.995974	−	0.0896460i	$-0.0285736\pi$
$59$	3.22878	+	5.59241i	0.420351	+	0.728069i	−0.575623	+	0.817715i	$0.695240\pi$
$60$	−1.71739	+	0.224845i	−0.221715	+	0.0290273i
$61$	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
$63$	5.05451	−	1.34657i	0.636808	−	0.169652i
$64$	1.00000			0.125000
$65$	−3.63184			−0.450475
$66$	4.72353	+	6.16498i	0.581426	+	0.758857i
$67$	−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	$0.0257546\pi$
$71$	4.78907	+	8.29492i	0.568358	+	0.984426i	−0.428370	+	0.903603i	$0.640912\pi$
$72$	2.89889	−	0.772294i	0.341637	−	0.0910157i
$73$	−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
$78$	6.23731	−	0.816601i	0.706236	−	0.0924619i
$79$	−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
$81$	7.80712	−	4.47759i	0.867458	−	0.497510i
$82$	2.28336	−	3.95489i	0.252154	−	0.436744i
$83$			10.2566i			1.12581i	0.826523	+	0.562903i	$0.190315\pi$
$83$			10.2566i			1.12581i	−0.826523	+	0.562903i	$0.809685\pi$
$84$	−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	−0.732540	−	0.680724i	$-0.761665\pi$
$89$	2.10618	−	3.64801i	0.223255	−	0.386689i	0.955794	+	0.294036i	$0.0949984\pi$
$90$	2.89666	+	0.780619i	0.305335	+	0.0822844i
$91$	−5.48409	−	3.16624i	−0.574889	−	0.331912i
$92$	1.69230	−	0.977053i	0.176435	−	0.101865i
$93$	14.8891	−	1.94931i	1.54392	−	0.202134i
$94$		−	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
$99$	−3.46296	−	12.9986i	−0.348041	−	1.30641i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−9.94712	−	5.74297i	−0.989776	−	0.571447i	−0.0845686	−	0.996418i	$-0.526951\pi$
$101$	−9.94712	−	5.74297i	−0.989776	−	0.571447i	−0.905207	+	0.424970i	$0.860285\pi$
$102$	−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
$105$	−1.83674	−	2.39725i	−0.179248	−	0.233948i
$106$	0.129889			0.0126159
$107$	20.1581			1.94875			0.974377	−	0.224920i	$-0.0722120\pi$
$107$	20.1581			1.94875			0.974377	+	0.224920i	$0.0722120\pi$
$108$	−5.15023	−	0.689332i	−0.495581	−	0.0663310i
$109$	−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
$111$	−0.431522	+	0.0564957i	−0.0409582	+	0.00536233i
$112$	0.871800	+	1.51000i	0.0823774	+	0.142682i
$113$	−6.35512			−0.597840			−0.298920	−	0.954278i	$-0.596626\pi$
$113$	−6.35512			−0.597840			−0.298920	+	0.954278i	$0.596626\pi$
$114$	7.49692	−	0.892269i	0.702151	−	0.0835686i
$115$	1.95411			0.182221
$116$	0.271323	+	0.469946i	0.0251917	+	0.0436334i
$117$	−10.5202	−	2.83509i	−0.972594	−	0.262104i
$118$	−3.22878	+	5.59241i	−0.297233	+	0.514823i
$119$	9.97377	−	5.75836i	0.914294	−	0.527868i
$120$	−1.05342	−	1.37489i	−0.0961635	−	0.125509i
$121$	−9.10622			−0.827839
$122$	2.08430			0.188703
$123$	−6.27870	+	4.81066i	−0.566132	+	0.433763i
$124$	−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
$129$	−5.87739	+	4.50318i	−0.517475	+	0.396483i
$130$	−1.81592	−	3.14527i	−0.159267	−	0.275858i
$131$	7.92681	−	4.57655i	0.692569	−	0.399855i	−0.112005	−	0.993708i	$-0.535727\pi$
$131$	7.92681	−	4.57655i	0.692569	−	0.399855i	0.804574	+	0.593853i	$0.202394\pi$
$132$	−2.97727	+	7.17318i	−0.259138	+	0.624345i
$133$	−6.53696	−	3.87697i	−0.566826	−	0.336176i
$134$		−	8.55266i		−	0.738838i
$135$	−4.11556	−	3.17209i	−0.354211	−	0.273010i
$136$	5.72021	−	3.30257i	0.490504	−	0.283193i
$137$	13.2938	+	7.67520i	1.13577	+	0.655737i	0.945380	−	0.325972i	$-0.105691\pi$
$137$	13.2938	+	7.67520i	1.13577	+	0.655737i	0.190390	+	0.981709i	$0.439025\pi$
$138$	−3.35597	+	0.439370i	−0.285679	+	0.0374017i
$139$	−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
$147$	0.890353	+	6.80064i	0.0734351	+	0.560907i
$148$	0.217602	+	0.125633i	0.0178868	+	0.0103269i
$149$	17.1301	−	9.89007i	1.40335	−	0.810226i	0.408618	−	0.912706i	$-0.366011\pi$
$149$	17.1301	−	9.89007i	1.40335	−	0.810226i	0.994735	+	0.102480i	$0.0326776\pi$
$150$	−0.224845	−	1.71739i	−0.0183585	−	0.140225i
$151$			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
$156$	3.82585	+	4.99337i	0.306313	+	0.399790i
$157$	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
$162$	7.78127	+	4.52237i	0.611354	+	0.355311i
$163$	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
$165$	−6.16498	+	4.72353i	−0.479943	+	0.367726i
$166$	−8.88246	+	5.12829i	−0.689412	+	0.398032i
$167$	4.08621	−	7.07753i	0.316201	−	0.547676i	−0.663491	−	0.748184i	$-0.730926\pi$
$167$	4.08621	−	7.07753i	0.316201	−	0.547676i	0.979692	+	0.200508i	$0.0642594\pi$
$168$	−0.392039	−	2.99445i	−0.0302465	−	0.231027i
$169$	0.0951480	+	0.164801i	0.00731908	+	0.0126770i
$170$	6.60513			0.506591
$171$	−12.5855	−	3.55039i	−0.962437	−	0.271505i
$172$	4.27482			0.325952
$173$	−8.82834	−	15.2911i	−0.671206	−	1.16256i	−0.977562	−	0.210647i	$-0.932443\pi$
$173$	−8.82834	−	15.2911i	−0.671206	−	1.16256i	0.306356	−	0.951917i	$-0.400890\pi$
$174$	−0.122011	−	0.931939i	−0.00924965	−	0.0706501i
$175$	−0.871800	+	1.51000i	−0.0659019	+	0.114145i
$176$	3.88325	−	2.24200i	0.292711	−	0.168997i
$177$	8.87840	−	6.80251i	0.667341	−	0.511308i
$178$	4.21236			0.315730
$179$	19.9723			1.49280			0.746402	−	0.665496i	$-0.231780\pi$
$179$	19.9723			1.49280			0.746402	+	0.665496i	$0.231780\pi$
$180$	0.772294	+	2.89889i	0.0575634	+	0.216070i
$181$	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
$186$	9.13268	+	11.9197i	0.669641	+	0.873992i
$187$	−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	$0.107964\pi$
$191$			9.19637i			0.665426i	−0.943028	+	0.332713i	$0.892036\pi$
$192$	−0.224845	−	1.71739i	−0.0162268	−	0.123942i
$193$	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
$195$	0.816601	+	6.23731i	0.0584780	+	0.446663i
$196$	1.97993	−	3.42934i	0.141423	−	0.244953i
$197$			27.4692i			1.95710i	0.206016	+	0.978549i	$0.433950\pi$
$197$			27.4692i			1.95710i	−0.206016	+	0.978549i	$0.566050\pi$
$198$	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
$204$	−11.3436	+	1.48513i	−0.794212	+	0.103980i
$205$	3.95489	+	2.28336i	0.276221	+	0.159476i
$206$	15.2946	−	8.83036i	1.06563	−	0.615240i
$207$	5.66038	+	1.52541i	0.393423	+	0.106023i
$208$		−	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
$213$	13.1689	−	10.0898i	0.902315	−	0.691342i
$214$	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
$219$	−9.66604	+	7.40599i	−0.653170	+	0.500450i
$220$	4.48400			0.302311
$221$	−23.9888			−1.61366
$222$	−0.264688	−	0.345461i	−0.0177647	−	0.0231858i
$223$	−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
$225$	−0.780619	+	2.89666i	−0.0520412	+	0.193111i
$226$	−3.17756	−	5.50370i	−0.211368	−	0.366100i
$227$	−21.2257			−1.40880			−0.704401	−	0.709803i	$-0.748784\pi$
$227$	−21.2257			−1.40880			−0.704401	+	0.709803i	$0.748784\pi$
$228$	4.52119	+	6.04639i	0.299423	+	0.400432i
$229$	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
$231$	−13.4271	+	1.75790i	−0.883439	+	0.115662i
$232$	−0.271323	+	0.469946i	−0.0178133	+	0.0308535i
$233$	14.0033	−	8.08481i	0.917387	−	0.529654i	0.0345867	−	0.999402i	$-0.488989\pi$
$233$	14.0033	−	8.08481i	0.917387	−	0.529654i	0.882801	+	0.469748i	$0.155655\pi$
$234$	−2.80485	−	10.5283i	−0.183359	−	0.688258i
$235$	1.48746			0.0970314
$236$	−6.45756			−0.420351
$237$	6.14047	+	8.01432i	0.398866	+	0.520586i
$238$	9.97377	+	5.75836i	0.646503	+	0.373259i
$239$			21.3293i			1.37968i	0.723964	+	0.689838i	$0.242318\pi$
$239$			21.3293i			1.37968i	−0.723964	+	0.689838i	$0.757682\pi$
$240$	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
$243$	−9.44518	−	12.4012i	−0.605909	−	0.795534i
$244$	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
$249$	17.6146	−	2.30614i	1.11628	−	0.146145i
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$	−20.8600	−	12.0435i	−1.31667	−	0.760179i	−0.333478	−	0.942758i	$-0.608222\pi$
$251$	−20.8600	−	12.0435i	−1.31667	−	0.760179i	−0.983191	+	0.182579i	$0.941556\pi$
$252$	−1.36109	+	5.05062i	−0.0857404	+	0.318159i
$253$	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	−0.637794	−	0.770207i	$-0.720153\pi$
$257$	5.58082	−	9.66626i	0.348122	−	0.602965i	0.985916	+	0.167242i	$0.0534862\pi$
$258$	−6.83856	−	2.83838i	−0.425750	−	0.176710i
$259$			0.438106i			0.0272226i
$260$	1.81592	−	3.14527i	0.112619	−	0.195061i
$261$	−0.423600	+	1.57186i	−0.0262202	+	0.0972959i
$262$	7.92681	+	4.57655i	0.489720	+	0.282740i
$263$	−12.8454	+	7.41629i	−0.792081	+	0.457308i	−0.840695	−	0.541510i	$-0.817853\pi$
$263$	−12.8454	+	7.41629i	−0.792081	+	0.457308i	0.0486138	+	0.998818i	$0.484520\pi$
$264$	−7.70079	+	1.00820i	−0.473951	+	0.0620506i
$265$			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	0.946993	−	0.321255i	$-0.104105\pi$
$269$	3.20285	+	5.54749i	0.195281	+	0.338237i	−0.751712	+	0.659492i	$0.770771\pi$
$270$	0.689332	−	5.15023i	0.0419514	−	0.313433i
$271$	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
$276$	−2.05849	−	2.68667i	−0.123907	−	0.161719i
$277$	−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
$279$	−6.69546	−	25.1321i	−0.400846	−	1.50462i
$280$	−1.51000	+	0.871800i	−0.0902399	+	0.0521000i
$281$	−2.25447	+	3.90486i	−0.134490	+	0.232944i	−0.925403	−	0.378985i	$-0.876273\pi$
$281$	−2.25447	+	3.90486i	−0.134490	+	0.232944i	0.790912	+	0.611930i	$0.209606\pi$
$282$	−2.55456	+	0.334448i	−0.152122	+	0.0199161i
$283$	−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
$285$	0.892269	+	7.49692i	0.0528534	+	0.444079i
$286$	−16.2852			−0.962963
$287$	3.98126	+	6.89574i	0.235006	+	0.407043i
$288$	−0.780619	+	2.89666i	−0.0459984	+	0.170687i
$289$	13.3139	−	23.0603i	0.783170	−	1.35649i
$290$	−0.469946	+	0.271323i	−0.0275962	+	0.0159327i
$291$	−10.9683	−	14.3155i	−0.642975	−	0.839189i
$292$	7.03043			0.411425
$293$	−14.9955			−0.876047			−0.438024	−	0.898963i	$-0.644321\pi$
$293$	−14.9955			−0.876047			−0.438024	+	0.898963i	$0.644321\pi$
$294$	−5.44435	+	4.17139i	−0.317521	+	0.243280i
$295$	−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
$300$	1.37489	−	1.05342i	0.0793790	−	0.0608192i
$301$	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
$306$	19.1328	+	5.15609i	1.09375	+	0.294754i
$307$	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
$309$	−30.3304	+	3.97092i	−1.72544	+	0.225898i
$310$	4.33478	−	7.50806i	0.246199	−	0.426429i
$311$			12.1717i			0.690194i	0.938567	+	0.345097i	$0.112154\pi$
$311$			12.1717i			0.690194i	−0.938567	+	0.345097i	$0.887846\pi$
$312$	−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	−0.946214	−	0.323542i	$-0.895126\pi$
$317$	−3.43470	+	5.94907i	−0.192912	+	0.334133i	0.753302	+	0.657675i	$0.228460\pi$
$318$	−0.0292048	−	0.223070i	−0.00163772	−	0.0125092i
$319$	2.10724	+	1.21661i	0.117983	+	0.0681173i
$320$	−0.866025	+	0.500000i	−0.0484123	+	0.0279508i
$321$	−4.53244	−	34.6194i	−0.252976	−	1.93226i
$322$			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
$327$	6.59043	+	8.60160i	0.364452	+	0.475669i
$328$	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
$333$	0.194051	+	0.728391i	0.0106339	+	0.0399156i
$334$	8.17243			0.447175
$335$	8.55266			0.467282
$336$	2.39725	−	1.83674i	0.130781	−	0.100202i
$337$	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
$339$	1.42892	+	10.9143i	0.0776080	+	0.592781i
$340$	3.30257	+	5.72021i	0.179107	+	0.310222i
$341$	−38.8743			−2.10516
$342$	−3.21802	−	12.6746i	−0.174011	−	0.685361i
$343$	19.1096			1.03182
$344$	2.13741	+	3.70210i	0.115241	+	0.199604i
$345$	−0.439370	−	3.35597i	−0.0236549	−	0.180679i
$346$	8.82834	−	15.2911i	0.474615	−	0.822057i
$347$	24.5180	−	14.1555i	1.31620	−	0.759906i	0.333081	−	0.942898i	$-0.391912\pi$
$347$	24.5180	−	14.1555i	1.31620	−	0.759906i	0.983114	+	0.182992i	$0.0585783\pi$
$348$	0.746077	−	0.571634i	0.0399939	−	0.0306428i
$349$	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
$351$	−2.50355	+	18.7048i	−0.133629	+	0.998389i
$352$	3.88325	+	2.24200i	0.206978	+	0.119499i
$353$		−	16.8453i		−	0.896587i	−0.893886	−	0.448293i	$-0.852032\pi$
$353$		−	16.8453i		−	0.896587i	0.893886	−	0.448293i	$-0.147968\pi$
$354$	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
$357$	−12.1319	−	15.8342i	−0.642089	−	0.838033i
$358$	9.98617	+	17.2966i	0.527786	+	0.914152i
$359$	27.5785	−	15.9225i	1.45554	−	0.840356i	0.456752	−	0.889594i	$-0.349013\pi$
$359$	27.5785	−	15.9225i	1.45554	−	0.840356i	0.998787	+	0.0492381i	$0.0156793\pi$
$360$	−2.12437	+	2.11827i	−0.111964	+	0.111643i
$361$	9.11171	+	16.6726i	0.479564	+	0.877507i
$362$			3.31549i			0.174258i
$363$	2.04749	+	15.6390i	0.107465	+	0.820834i
$364$	5.48409	−	3.16624i	0.287445	−	0.165956i
$365$	6.08853	+	3.51522i	0.318688	+	0.183995i
$366$	−0.468643	−	3.57956i	−0.0244964	−	0.187107i
$367$	−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
$375$	1.71739	−	0.224845i	0.0886859	−	0.0116109i
$376$	1.28818	+	0.743732i	0.0664329	+	0.0383550i
$377$	1.70677	−	0.985405i	0.0879032	−	0.0507509i
$378$	5.53086	−	7.17589i	0.284477	−	0.369088i
$379$		−	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	0.960029	−	0.279902i	$-0.0903019\pi$
$383$	4.65017	+	8.05432i	0.237612	+	0.411557i	−0.722416	+	0.691458i	$0.756969\pi$
$384$	1.37489	−	1.05342i	0.0701618	−	0.0537570i
$385$	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	0.309458	−	0.950913i	$-0.399852\pi$
$389$	−7.08705	−	4.09171i	−0.359328	−	0.207458i	−0.668786	+	0.743455i	$0.733186\pi$
$390$	−4.99337	+	3.82585i	−0.252849	+	0.193730i
$391$	12.9071			0.652741
$392$	3.95986			0.200003
$393$	−9.64204	−	12.5845i	−0.486377	−	0.634802i
$394$	−23.7890	+	13.7346i	−1.19847	+	0.691938i
$395$	2.91454	−	5.04814i	0.146647	−	0.253999i
$396$	12.9886	+	3.50029i	0.652702	+	0.175896i
$397$	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
$399$	−5.18849	+	12.0983i	−0.259749	+	0.605670i
$400$	−1.00000			−0.0500000
$401$	14.4054	+	24.9508i	0.719369	+	1.24598i	0.961250	+	0.275678i	$0.0889024\pi$
$401$	14.4054	+	24.9508i	0.719369	+	1.24598i	−0.241881	+	0.970306i	$0.577764\pi$
$402$	−14.6883	+	1.92302i	−0.732586	+	0.0959116i
$403$	−15.7433	+	27.2681i	−0.784228	+	1.35832i
$404$	9.94712	−	5.74297i	0.494888	−	0.285724i
$405$	−4.52237	+	7.78127i	−0.224718	+	0.386654i
$406$	−0.946159			−0.0469571
$407$	1.12667			0.0558471
$408$	−6.95797	−	9.08130i	−0.344471	−	0.449591i
$409$	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
$414$	1.50914	+	5.66474i	0.0741704	+	0.278407i
$415$	−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	$0.00864583\pi$
$419$			1.11183i			0.0543167i	−0.999631	+	0.0271583i	$0.991354\pi$
$420$	2.99445	−	0.392039i	0.146114	−	0.0191296i
$421$	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
$423$	4.30868	+	1.16114i	0.209495	+	0.0564566i
$424$	−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	−0.779784	−	0.626049i	$-0.784671\pi$
$431$	3.16146	−	5.47581i	0.152282	−	0.263760i	0.932066	+	0.362288i	$0.118004\pi$
$432$	3.17209	−	4.11556i	0.152617	−	0.198010i
$433$	−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
$435$	0.931939	−	0.122011i	0.0446830	−	0.00584999i
$436$		−	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
$441$	11.4792	−	3.05817i	0.546628	−	0.145627i
$442$	−11.9944	−	20.7749i	−0.570516	−	0.988163i
$443$	8.85438	+	5.11208i	0.420684	+	0.242882i	0.695370	−	0.718652i	$-0.255240\pi$
$443$	8.85438	+	5.11208i	0.420684	+	0.242882i	−0.274686	+	0.961534i	$0.588574\pi$
$444$	0.166834	−	0.401957i	0.00791760	−	0.0190760i
$445$			4.21236i			0.199685i
$446$	−11.2359	−	6.48704i	−0.532034	−	0.307170i
$447$	−20.8368	−	27.1954i	−0.985545	−	1.28630i
$448$	−1.74360			−0.0823774
$449$	−6.66710			−0.314640			−0.157320	−	0.987548i	$-0.550285\pi$
$449$	−6.66710			−0.314640			−0.157320	+	0.987548i	$0.550285\pi$
$450$	−2.89889	+	0.772294i	−0.136655	+	0.0364063i
$451$	17.7337	−	10.2386i	0.835048	−	0.482115i
$452$	3.17756	−	5.50370i	0.149460	−	0.258872i
$453$	36.9568	−	4.83845i	1.73638	−	0.227330i
$454$	−10.6129	−	18.3820i	−0.498086	−	0.862711i
$455$	6.33249			0.296872
$456$	−2.97573	+	6.93866i	−0.139352	+	0.324933i
$457$	−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
$459$	−27.1838	−	20.9521i	−1.26883	−	0.977960i
$460$	−0.977053	+	1.69230i	−0.0455553	+	0.0789041i
$461$	−4.75855	+	2.74735i	−0.221628	+	0.127957i	−0.606704	−	0.794928i	$-0.707509\pi$
$461$	−4.75855	+	2.74735i	−0.221628	+	0.127957i	0.385076	+	0.922885i	$0.374175\pi$
$462$	−8.23594	−	10.7493i	−0.383171	−	0.500101i
$463$	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
$465$	−11.9197	+	9.13268i	−0.552761	+	0.423518i
$466$	14.0033	+	8.08481i	0.648691	+	0.374522i
$467$			31.0365i			1.43620i	0.695940	+	0.718100i	$0.254988\pi$
$467$			31.0365i			1.43620i	−0.695940	+	0.718100i	$0.745012\pi$
$468$	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
$471$	18.6265	−	14.2714i	0.858263	−	0.657590i
$472$	−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
$477$	−0.101393	+	0.376243i	−0.00464249	+	0.0172270i
$478$	−18.4717	+	10.6646i	−0.844876	+	0.487789i
$479$	5.77360	+	3.33339i	0.263802	+	0.152306i	0.626068	−	0.779769i	$-0.284663\pi$
$479$	5.77360	+	3.33339i	0.263802	+	0.152306i	−0.362265	+	0.932075i	$0.617997\pi$
$480$	1.71739	−	0.224845i	0.0783880	−	0.0102627i
$481$	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
$489$	−1.77695	−	13.5726i	−0.0803564	−	0.613773i
$490$	3.42934	+	1.97993i	0.154922	+	0.0894441i
$491$	−2.23804	+	1.29214i	−0.101002	+	0.0583132i	−0.549650	−	0.835395i	$-0.685239\pi$
$491$	−2.23804	+	1.29214i	−0.101002	+	0.0583132i	0.448648	+	0.893708i	$0.351906\pi$
$492$	−1.02680	−	7.84285i	−0.0462918	−	0.353583i
$493$			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
$498$	10.8045	+	14.1016i	0.484160	+	0.631908i
$499$	−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	0.957409	−	0.288734i	$-0.0932343\pi$
$503$	26.6006	+	15.3579i	1.18606	+	0.684774i	0.228654	+	0.973508i	$0.426568\pi$
$504$	−5.05451	+	1.34657i	−0.225146	+	0.0599811i
$505$	11.4859			0.511118
$506$	8.76220			0.389527
$507$	0.261635	−	0.200461i	0.0116196	−	0.00890281i
$508$	−10.3685	+	5.98626i	−0.460028	+	0.265597i
$509$	−1.76397	+	3.05529i	−0.0781868	+	0.135424i	−0.902468	−	0.430758i	$-0.858246\pi$
$509$	−1.76397	+	3.05529i	−0.0781868	+	0.135424i	0.824281	+	0.566181i	$0.191580\pi$
$510$	−1.48513	−	11.3436i	−0.0657626	−	0.502304i
$511$	6.12913	+	10.6160i	0.271137	+	0.469623i
$512$	−1.00000			−0.0441942
$513$	−3.26764	+	22.4126i	−0.144270	+	0.989538i
$514$	11.1616			0.492319
$515$	8.83036	+	15.2946i	0.389112	+	0.673962i
$516$	−0.961171	−	7.34156i	−0.0423132	−	0.323194i
$517$	3.33489	−	5.77620i	0.146668	−	0.254037i
$518$	−0.379411	+	0.219053i	−0.0166704	+	0.00962465i
$519$	−24.2759	+	18.5999i	−1.06559	+	0.816444i
$520$	3.63184			0.159267
$521$	−10.7293			−0.470059			−0.235030	−	0.971988i	$-0.575519\pi$
$521$	−10.7293			−0.470059			−0.235030	+	0.971988i	$0.575519\pi$
$522$	−1.57307	+	0.419083i	−0.0688516	+	0.0183428i
$523$	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
$528$	−4.72353	−	6.16498i	−0.205565	−	0.268296i
$529$	−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
$534$	−0.947128	−	7.23429i	−0.0409862	−	0.313058i
$535$	−17.4574	+	10.0790i	−0.754749	+	0.435755i
$536$	7.40682	+	4.27633i	0.319926	+	0.184709i
$537$	−4.49068	−	34.3004i	−0.193787	−	1.48017i
$538$	−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
$546$	−10.8754	+	1.42383i	−0.465423	+	0.0609341i
$547$	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
$549$	−1.62704	+	6.03750i	−0.0694404	+	0.257674i
$550$			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
$555$	0.345461	−	0.264688i	0.0146640	−	0.0112354i
$556$	−7.91901	−	13.7161i	−0.335841	−	0.581693i
$557$	10.7408	+	6.20119i	0.455101	+	0.262753i	0.709982	−	0.704220i	$-0.248703\pi$
$557$	10.7408	+	6.20119i	0.455101	+	0.262753i	−0.254881	+	0.966972i	$0.582036\pi$
$558$	18.4173	−	18.3645i	0.779667	−	0.777431i
$559$		−	15.5255i		−	0.656658i
$560$	−1.51000	−	0.871800i	−0.0638092	−	0.0368403i
$561$	−40.7205	+	31.1995i	−1.71922	+	1.31724i
$562$	−4.50894			−0.190198
$563$	−10.1274			−0.426819			−0.213410	−	0.976963i	$-0.568457\pi$
$563$	−10.1274			−0.426819			−0.213410	+	0.976963i	$0.568457\pi$
$564$	−1.56692	−	2.04509i	−0.0659793	−	0.0861139i
$565$	5.50370	−	3.17756i	0.231542	−	0.133681i
$566$	14.2001	−	24.5953i	0.596875	−	1.03382i
$567$	−13.6125	+	7.80713i	−0.571671	+	0.327869i
$568$	−4.78907	−	8.29492i	−0.200945	−	0.348047i
$569$	19.0157			0.797180			0.398590	−	0.917129i	$-0.369500\pi$
$569$	19.0157			0.797180			0.398590	+	0.917129i	$0.369500\pi$
$570$	−6.04639	+	4.52119i	−0.253255	+	0.189372i
$571$	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
$573$	15.7938	−	2.06775i	0.659795	−	0.0863817i
$574$	−3.98126	+	6.89574i	−0.166175	+	0.287823i
$575$	−1.69230	+	0.977053i	−0.0705740	+	0.0407459i
$576$	−2.89889	+	0.772294i	−0.120787	+	0.0321789i
$577$	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
$579$	−13.8610	−	18.0909i	−0.576042	−	0.751831i
$580$	−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
$585$	10.5283	−	2.80485i	0.435292	−	0.115966i
$586$	−7.49776	−	12.9865i	−0.309730	−	0.536467i
$587$	18.2857	−	10.5573i	0.754733	−	0.435745i	−0.0726687	−	0.997356i	$-0.523152\pi$
$587$	18.2857	−	10.5573i	0.754733	−	0.435745i	0.827401	+	0.561611i	$0.189818\pi$
$588$	−6.33470	−	2.62925i	−0.261239	−	0.108428i
$589$	−19.2772	+	32.5032i	−0.794302	+	1.33927i
$590$		−	6.45756i		−	0.265853i
$591$	47.1754	−	6.17630i	1.94054	−	0.254059i
$592$	−0.217602	+	0.125633i	−0.00894340	+	0.00516347i
$593$	−5.51015	−	3.18129i	−0.226275	−	0.130640i	0.382578	−	0.923923i	$-0.375036\pi$
$593$	−5.51015	−	3.18129i	−0.226275	−	0.130640i	−0.608852	+	0.793284i	$0.708370\pi$
$594$	−18.4542	−	14.2236i	−0.757183	−	0.583603i
$595$	−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	$-0.492258\pi$
$599$	21.4869	−	37.2163i	0.877929	−	1.52062i	0.853610	−	0.520913i	$-0.174409\pi$
$600$	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
$603$	24.7742	+	6.67637i	1.00888	+	0.271883i
$604$	−18.6361	−	10.7595i	−0.758291	−	0.437800i
$605$	7.88622	−	4.55311i	0.320621	−	0.185110i
$606$	−19.7259	+	2.58255i	−0.801310	+	0.104909i
$607$			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
$612$	5.10111	+	19.1476i	0.206200	+	0.773994i
$613$	−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	−0.0631463	−	0.998004i	$-0.520113\pi$
$617$	−23.8215	−	13.7533i	−0.959017	−	0.553688i	−0.895870	+	0.444316i	$0.853447\pi$
$618$	−18.6041	−	24.2815i	−0.748368	−	0.976743i
$619$	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
$621$	1.34703	−	10.0641i	0.0540543	−	0.403858i
$622$	−10.5410	+	6.08585i	−0.422656	+	0.244020i
$623$	−3.67234	+	6.36068i	−0.147129	+	0.254835i
$624$	−6.23731	+	0.816601i	−0.249692	+	0.0326902i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−13.1442			−0.525347
$627$	31.1129	+	13.3432i	1.24253	+	0.532875i
$628$	−13.5477			−0.540611
$629$	0.829821	+	1.43729i	0.0330871	+	0.0573086i
$630$	−5.05062	−	1.36109i	−0.201221	−	0.0542270i
$631$	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
$633$	22.0721	+	28.8077i	0.877288	+	1.14501i
$634$	−6.86939			−0.272818
$635$	−11.9725			−0.475115
$636$	0.178582	−	0.136827i	0.00708124	−	0.00542555i
$637$	−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	$-0.976675\pi$
$641$	−14.2303	−	24.6475i	−0.562062	−	0.973520i	0.435255	−	0.900307i	$-0.356658\pi$
$642$	27.7150	−	21.2349i	1.09383	−	0.838074i
$643$	−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	$0.0495903\pi$
$647$			7.89351i			0.310326i	−0.987889	+	0.155163i	$0.950410\pi$
$648$	−7.80712	+	4.47759i	−0.306693	+	0.175896i
$649$	−25.0763	+	14.4778i	−0.984332	+	0.568305i
$650$	3.14527	+	1.81592i	0.123368	+	0.0712263i
$651$	−25.9606	+	3.39881i	−1.01748	+	0.133210i
$652$	−3.95150	+	6.84420i	−0.154753	+	0.268040i
$653$			18.1037i			0.708453i	0.935160	+	0.354227i	$0.115256\pi$
$653$			18.1037i			0.708453i	−0.935160	+	0.354227i	$0.884744\pi$
$654$	−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	−0.983253	−	0.182248i	$-0.941663\pi$
$659$	−8.56885	+	14.8417i	−0.333795	+	0.578150i	0.649457	+	0.760398i	$0.274996\pi$
$660$	−1.00820	−	7.70079i	−0.0392442	−	0.299753i
$661$	−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
$663$	5.39376	+	41.1983i	0.209476	+	1.60001i
$664$		−	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
$669$	13.6671	+	17.8379i	0.528402	+	0.689652i
$670$	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
$675$	5.15023	+	0.689332i	0.198232	+	0.0265324i
$676$	−0.190296			−0.00731908
$677$	−45.3076			−1.74131			−0.870656	−	0.491892i	$-0.836306\pi$
$677$	−45.3076			−1.74131			−0.870656	+	0.491892i	$0.836306\pi$
$678$	−8.73756	+	6.69460i	−0.335564	+	0.257105i
$679$	−15.7223	+	9.07730i	−0.603368	+	0.348355i
$680$	−3.30257	+	5.72021i	−0.126648	+	0.219360i
$681$	4.77249	+	36.4530i	0.182882	+	1.39688i
$682$	−19.4372	−	33.6661i	−0.744287	−	1.28914i
$683$	−38.3931			−1.46907			−0.734535	−	0.678571i	$-0.762600\pi$
$683$	−38.3931			−1.46907			−0.734535	+	0.678571i	$0.762600\pi$
$684$	9.36748	−	9.12417i	0.358174	−	0.348871i
$685$	−15.3504			−0.586509
$686$	9.55481	+	16.5494i	0.364804	+	0.631859i
$687$	−2.17911	−	16.6443i	−0.0831382	−	0.635021i
$688$	−2.13741	+	3.70210i	−0.0814880	+	0.141141i
$689$	0.408535	−	0.235868i	0.0155639	−	0.00898585i
$690$	2.68667	−	2.05849i	0.102280	−	0.0783654i
$691$	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
$693$	6.03803	+	22.6644i	0.229366	+	0.860949i
$694$	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
$699$	−17.0334	−	22.2314i	−0.644262	−	0.840868i
$700$	−0.871800	−	1.51000i	−0.0329510	−	0.0570727i
$701$	35.5687	−	20.5356i	1.34341	−	0.775619i	0.356106	−	0.934446i	$-0.384104\pi$
$701$	35.5687	−	20.5356i	1.34341	−	0.775619i	0.987307	+	0.158826i	$0.0507710\pi$
$702$	−17.4506	+	7.18428i	−0.658631	+	0.271153i
$703$	0.558700	−	0.942022i	0.0210718	−	0.0355290i
$704$			4.48400i			0.168997i
$705$	−0.334448	−	2.55456i	−0.0125961	−	0.0962104i
$706$	14.5885	−	8.42267i	0.549045	−	0.316991i
$707$	17.3438	+	10.0135i	0.652281	+	0.376595i
$708$	1.45195	+	11.0902i	0.0545675	+	0.416794i
$709$	−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
$717$	36.6308	−	4.79577i	1.36800	−	0.179101i
$718$	27.5785	+	15.9225i	1.02922	+	0.594221i
$719$	40.8433	−	23.5809i	1.52320	−	0.879420i	0.523576	−	0.851979i	$-0.324598\pi$
$719$	40.8433	−	23.5809i	1.52320	−	0.879420i	0.999623	−	0.0274407i	$-0.00873575\pi$
$720$	−2.89666	−	0.780619i	−0.107952	−	0.0290919i
$721$			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
$726$	−12.5200	+	9.59267i	−0.464661	+	0.356017i
$727$	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
$732$	2.86567	−	2.19564i	0.105918	−	0.0811531i
$733$	−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
$735$	−4.17139	−	5.44435i	−0.153864	−	0.200818i
$736$	−1.69230	+	0.977053i	−0.0623792	+	0.0360146i
$737$	19.1751	−	33.2122i	0.706322	−	1.22339i
$738$	−3.56486	+	13.2282i	−0.131224	+	0.486937i
$739$	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
$741$	21.9596	−	16.4203i	0.806704	−	0.603213i
$742$	−0.226474			−0.00831412
$743$	8.82641	+	15.2878i	0.323810	+	0.560855i	0.981271	−	0.192634i	$-0.0617030\pi$
$743$	8.82641	+	15.2878i	0.323810	+	0.560855i	−0.657461	+	0.753488i	$0.728370\pi$
$744$	−14.8891	+	1.94931i	−0.545860	+	0.0714650i
$745$	−9.89007	+	17.1301i	−0.362344	+	0.627598i
$746$	−32.2650	+	18.6282i	−1.18131	+	0.682027i
$747$	−7.92109	−	29.7327i	−0.289818	−	1.08786i
$748$	29.6174			1.08292
$749$	−35.1476			−1.28427
$750$	1.05342	+	1.37489i	0.0384654	+	0.0502037i
$751$	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
$756$	8.97994	+	1.20192i	0.326597	+	0.0437134i
$757$	−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	$0.00703386\pi$
$761$			1.21908i			0.0441915i	−0.999756	+	0.0220957i	$0.992966\pi$
$762$	20.5615	−	2.69196i	0.744866	−	0.0975193i
$763$	9.44692	−	5.45418i	0.342002	−	0.197455i
$764$	−7.96429	−	4.59818i	−0.288138	−	0.166356i
$765$	−5.15609	+	19.1328i	−0.186419	+	0.691749i
$766$	−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	$0.498309\pi$
$773$	−24.0038	+	41.5758i	−0.863357	+	1.49538i	−0.868669	+	0.495393i	$0.835024\pi$
$774$	−3.33701	+	12.3827i	−0.119946	+	0.445087i
$775$	7.50806	+	4.33478i	0.269698	+	0.155710i
$776$	−9.01717	+	5.20607i	−0.323698	+	0.186887i
$777$	0.752402	−	0.0985059i	0.0269923	−	0.00353388i
$778$		−	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
$783$	2.79475	+	0.374064i	0.0998763	+	0.0133679i
$784$	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
$789$	15.6249	+	20.3931i	0.556262	+	0.726013i
$790$	5.82909			0.207390
$791$	11.0808			0.393988
$792$	3.46296	+	12.9986i	0.123051	+	0.461886i
$793$	6.55568	−	3.78492i	0.232799	−	0.134407i
$794$	−2.72560	+	4.72088i	−0.0967281	+	0.167538i
$795$	0.223070	−	0.0292048i	0.00791148	−	0.00103579i
$796$	−4.51192	−	7.81487i	−0.159921	−	0.276991i
$797$	13.6397			0.483142			0.241571	−	0.970383i	$-0.422337\pi$
$797$	13.6397			0.483142			0.241571	+	0.970383i	$0.422337\pi$
$798$	−13.0716	+	1.55576i	−0.462731	+	0.0550733i
$799$	9.82490			0.347580
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−3.28825	+	12.2018i	−0.116185	+	0.431129i
$802$	−14.4054	+	24.9508i	−0.508671	+	0.881044i
$803$	27.3010	−	15.7622i	0.963430	−	0.556237i
$804$	−9.00953	−	11.7589i	−0.317742	−	0.414705i
$805$	−3.40718			−0.120087
$806$	−31.4865			−1.10907
$807$	8.80709	−	6.74787i	0.310024	−	0.237536i
$808$	9.94712	+	5.74297i	0.349939	+	0.202037i
$809$			48.0047i			1.68776i	0.536535	+	0.843878i	$0.319733\pi$
$809$			48.0047i			1.68776i	−0.536535	+	0.843878i	$0.680267\pi$
$810$	−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
$813$	24.2097	−	18.5491i	0.849071	−	0.650547i
$814$	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
$819$	18.3431	+	4.94326i	0.640958	+	0.172731i
$820$	−3.95489	+	2.28336i	−0.138111	+	0.0797382i
$821$	19.8535	+	11.4624i	0.692892	+	0.400041i	0.804694	−	0.593689i	$-0.202329\pi$
$821$	19.8535	+	11.4624i	0.692892	+	0.400041i	−0.111803	+	0.993730i	$0.535662\pi$
$822$	26.3627	−	3.45146i	0.919505	−	0.120383i
$823$	−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	$0.412513\pi$
$827$	−20.0676	+	34.7581i	−0.697819	+	1.20866i	−0.969221	+	0.246192i	$0.920821\pi$
$828$	−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
$831$	6.18869	+	47.2700i	0.214683	+	1.63978i
$832$	3.14527	+	1.81592i	0.109043	+	0.0629558i
$833$	22.6512	−	13.0777i	0.784819	−	0.453115i
$834$	3.56109	+	27.2001i	0.123311	+	0.941863i
$835$			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	$-0.967515\pi$
$839$	−16.9630	−	29.3808i	−0.585628	−	1.01434i	0.409169	−	0.912459i	$-0.365819\pi$
$840$	1.83674	+	2.39725i	0.0633736	+	0.0827130i
$841$	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
$846$	1.14876	+	4.31199i	0.0394952	+	0.148249i
$847$	15.8776			0.545561
$848$	−0.129889			−0.00446040
$849$	−39.0470	+	29.9173i	−1.34009	+	1.02676i
$850$	−5.72021	+	3.30257i	−0.196202	+	0.113277i
$851$	−0.245499	+	0.425218i	−0.00841561	+	0.0145763i
$852$	2.15360	+	16.4495i	0.0737810	+	0.563549i
$853$	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
$855$	12.6746	−	3.21802i	0.433461	−	0.110054i
$856$	−20.1581			−0.688989
$857$	−5.57983	−	9.66455i	−0.190603	−	0.330135i	0.754847	−	0.655901i	$-0.227711\pi$
$857$	−5.57983	−	9.66455i	−0.190603	−	0.330135i	−0.945450	+	0.325766i	$0.894378\pi$
$858$	3.66164	+	27.9681i	0.125006	+	0.954815i
$859$	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
$861$	10.9476	−	8.38787i	0.373092	−	0.285858i
$862$	6.32292			0.215359
$863$	12.4085			0.422390			0.211195	−	0.977444i	$-0.432264\pi$
$863$	12.4085			0.422390			0.211195	+	0.977444i	$0.432264\pi$
$864$	5.15023	+	0.689332i	0.175214	+	0.0234515i
$865$	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
$870$	0.571634	+	0.746077i	0.0193802	+	0.0252944i
$871$	−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
$876$	−1.58076	−	12.0740i	−0.0534088	−	0.407944i
$877$	−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
$879$	3.37166	+	25.7532i	0.113723	+	0.868635i
$880$	−2.24200	+	3.88325i	−0.0755777	+	0.130904i
$881$		−	45.6855i		−	1.53918i	−0.638536	−	0.769592i	$-0.720460\pi$
$881$		−	45.6855i		−	1.53918i	0.638536	−	0.769592i	$-0.279540\pi$
$882$	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	−0.715823	−	0.698282i	$-0.753948\pi$
$887$	7.35088	−	12.7321i	0.246818	−	0.427502i	0.962641	+	0.270780i	$0.0872816\pi$
$888$	0.431522	−	0.0564957i	0.0144809	−	0.00189587i
$889$	−18.0785	−	10.4376i	−0.606335	−	0.350067i
$890$	−3.64801	+	2.10618i	−0.122282	+	0.0705994i
$891$	20.0775	+	35.0071i	0.672622	+	1.17278i
$892$		−	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
$897$	−9.75757	+	7.47612i	−0.325796	+	0.249620i
$898$	−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
$903$	10.2478	−	7.85174i	0.341026	−	0.261290i
$904$	6.35512			0.211368
$905$	−3.31549			−0.110211
$906$	22.6686	+	29.5863i	0.753114	+	0.982938i
$907$	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
$909$	33.2709	+	8.96614i	1.10353	+	0.297388i
$910$	3.16624	+	5.48409i	0.104960	+	0.181796i
$911$	−49.4685			−1.63896			−0.819481	−	0.573106i	$-0.805738\pi$
$911$	−49.4685			−1.63896			−0.819481	+	0.573106i	$0.805738\pi$
$912$	−7.49692	+	0.892269i	−0.248248	+	0.0295460i
$913$	−45.9905			−1.52206
$914$	−6.43251	−	11.1414i	−0.212768	−	0.368526i
$915$	3.57956	−	0.468643i	0.118337	−	0.0154929i
$916$	−4.84581	+	8.39319i	−0.160110	+	0.277319i
$917$	−13.8212	+	7.97967i	−0.456416	+	0.263512i
$918$	4.55313	−	34.0179i	0.150276	−	1.12276i
$919$	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
$921$	−21.4496	−	27.9953i	−0.706789	−	0.922477i
$922$	−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
$927$	13.6393	+	51.1965i	0.447972	+	1.68151i
$928$	−0.271323	−	0.469946i	−0.00890663	−	0.0154267i
$929$	−38.9043	+	22.4614i	−1.27641	+	0.736934i	−0.976186	−	0.216935i	$-0.930394\pi$
$929$	−38.9043	+	22.4614i	−1.27641	+	0.736934i	−0.300222	+	0.953869i	$0.597061\pi$
$930$	−13.8690	−	5.75639i	−0.454781	−	0.188759i
$931$	−14.8460	−	8.80492i	−0.486557	−	0.288569i
$932$			16.1696i			0.529654i
$933$	20.9036	−	2.73674i	0.684353	−	0.0895969i
$934$	−26.8784	+	15.5183i	−0.879489	+	0.507773i
$935$	25.6494	+	14.8087i	0.838826	+	0.484296i
$936$	10.5202	+	2.83509i	0.343864	+	0.0926677i
$937$	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	−0.974955	−	0.222403i	$-0.928610\pi$
$941$	−9.04539	+	15.6671i	−0.294871	+	0.510732i	0.680084	+	0.733134i	$0.261943\pi$
$942$	21.6726	+	8.99533i	0.706132	+	0.293084i
$943$			8.92384i			0.290600i
$944$	3.22878	−	5.59241i	0.105088	−	0.182017i
$945$	7.17589	+	5.53086i	0.233432	+	0.179919i
$946$	16.6002	+	9.58414i	0.539720	+	0.311607i
$947$	−18.9963	+	10.9675i	−0.617296	+	0.356396i	−0.775815	−	0.630960i	$-0.782661\pi$
$947$	−18.9963	+	10.9675i	−0.617296	+	0.356396i	0.158520	+	0.987356i	$0.449328\pi$
$948$	−10.0108	+	1.31064i	−0.325137	+	0.0425676i
$949$		−	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	$-0.970241\pi$
$953$	−17.8637	−	30.9409i	−0.578663	−	1.00227i	0.416969	−	0.908920i	$-0.363092\pi$
$954$	−0.376533	+	0.100312i	−0.0121907	+	0.00324773i
$955$	−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
$960$	1.05342	+	1.37489i	0.0339989	+	0.0443742i
$961$	−44.1614			−1.42456
$962$	0.912557			0.0294220
$963$	−58.4360	+	15.5680i	−1.88307	+	0.501671i
$964$	−3.63151	+	2.09666i	−0.116963	+	0.0675287i
$965$	−6.57904	+	11.3952i	−0.211787	+	0.366826i
$966$	5.85147	−	0.766086i	0.188268	−	0.0246484i
$967$	−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
$969$	5.89356	+	49.5182i	0.189328	+	1.59075i
$970$	−10.4121			−0.334314
$971$	−3.20611	−	5.55314i	−0.102889	−	0.178209i	0.809985	−	0.586451i	$-0.199475\pi$
$971$	−3.20611	−	5.55314i	−0.102889	−	0.178209i	−0.912874	+	0.408242i	$0.866142\pi$
$972$	15.4623	−	1.97919i	0.495954	−	0.0634826i
$973$	13.8076	−	23.9154i	0.442651	−	0.766694i
$974$	−18.7445	+	10.8222i	−0.600613	+	0.346764i
$975$	−3.82585	−	4.99337i	−0.122525	−	0.159916i
$976$	−2.08430			−0.0667167
$977$	10.1495			0.324713			0.162356	−	0.986732i	$-0.448091\pi$
$977$	10.1495			0.324713			0.162356	+	0.986732i	$0.448091\pi$
$978$	10.8657	−	8.32517i	0.347448	−	0.266210i
$979$	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	0.978358	−	0.206918i	$-0.0663433\pi$
$983$	9.71885	+	16.8335i	0.309983	+	0.536907i	−0.668375	+	0.743824i	$0.733010\pi$
$984$	6.27870	−	4.81066i	0.200158	−	0.153358i
$985$	−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
$990$	−3.50029	+	12.9886i	−0.111247	+	0.412805i
$991$	−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
$993$	−13.3760	+	1.75121i	−0.424474	+	0.0555729i
$994$	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.b.221.5	yes	24
3.2	odd	2		570.2.s.a.221.9	✓	24
19.8	odd	6		570.2.s.a.521.9	yes	24
57.8	even	6	inner	570.2.s.b.521.5	yes	24

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

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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.224845 - 1.71739i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.37489 - 1.05342i) q^{6} -1.74360 q^{7} -1.00000 q^{8} +(-2.89889 + 0.772294i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.224845 - 1.71739i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.37489 - 1.05342i) q^{6} -1.74360 q^{7} -1.00000 q^{8} +(-2.89889 + 0.772294i) 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} +(1.05342 + 1.37489i) 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} +(0.392039 + 2.99445i) q^{21} +(-3.88325 + 2.24200i) q^{22} +(-1.69230 - 0.977053i) q^{23} +(0.224845 + 1.71739i) 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} +(7.70079 - 1.00820i) q^{33} +(-5.72021 - 3.30257i) q^{34} +(1.51000 - 0.871800i) q^{35} +(0.780619 - 2.89666i) 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} +(-2.39725 + 1.83674i) 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} +(-1.37489 + 1.05342i) q^{48} -3.95986 q^{49} +1.00000 q^{50} +(6.95797 + 9.08130i) q^{51} +(-3.14527 + 1.81592i) q^{52} +(0.0649443 - 0.112487i) q^{53} +(-3.17209 + 4.11556i) q^{54} +(-2.24200 - 3.88325i) q^{55} +1.74360 q^{56} +(2.97573 - 6.93866i) q^{57} +0.542647 q^{58} +(3.22878 + 5.59241i) q^{59} +(-1.71739 + 0.224845i) q^{60} +(1.04215 - 1.80505i) q^{61} +(-7.50806 + 4.33478i) q^{62} +(5.05451 - 1.34657i) q^{63} +1.00000 q^{64} -3.63184 q^{65} +(4.72353 + 6.16498i) 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} +(2.89889 - 0.772294i) 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} +(6.23731 - 0.816601i) q^{78} +(-5.04814 + 2.91454i) q^{79} +(0.866025 + 0.500000i) q^{80} +(7.80712 - 4.47759i) 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} +(2.89666 + 0.780619i) q^{90} +(-5.48409 - 3.16624i) q^{91} +(1.69230 - 0.977053i) q^{92} +(14.8891 - 1.94931i) 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} +(-3.46296 - 12.9986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9	\( 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9} + 2 q^{12} + 18 q^{13} - 6 q^{14} - 12 q^{16} - 12 q^{17} - 2 q^{18} + 6 q^{19} + 6 q^{21} + 18 q^{22} - 2 q^{24} + 12 q^{25} - 28 q^{27} + 6 q^{28} + 12 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 6 q^{38} + 40 q^{39} - 6 q^{41} - 6 q^{42} - 22 q^{43} + 18 q^{44} + 8 q^{45} - 12 q^{47} - 4 q^{48} + 12 q^{49} + 24 q^{50} - 4 q^{51} - 18 q^{52} - 8 q^{53} - 32 q^{54} + 12 q^{56} - 20 q^{57} - 26 q^{59} + 22 q^{61} + 18 q^{62} + 30 q^{63} + 24 q^{64} - 8 q^{65} - 22 q^{66} - 48 q^{67} + 64 q^{69} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 30 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 18 q^{79} - 6 q^{81} + 6 q^{82} - 12 q^{84} + 22 q^{86} - 24 q^{87} - 28 q^{89} + 16 q^{90} + 18 q^{91} + 14 q^{93} - 2 q^{96} + 6 q^{97} + 6 q^{98} - 52 q^{99}+O(q^{100}) \) 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * 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 - 2 * q^24 + 12 * q^25 - 28 * q^27 + 6 * q^28 + 12 * q^32 - 8 * q^33 - 12 * q^34 - 4 * 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 - 4 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 - 18 * q^52 - 8 * q^53 - 32 * q^54 + 12 * q^56 - 20 * q^57 - 26 * q^59 + 22 * q^61 + 18 * q^62 + 30 * q^63 + 24 * q^64 - 8 * q^65 - 22 * q^66 - 48 * q^67 + 64 * q^69 - 24 * q^71 - 2 * q^72 - 8 * q^73 - 30 * q^74 - 2 * q^75 - 12 * q^76 + 2 * q^78 + 18 * q^79 - 6 * q^81 + 6 * q^82 - 12 * q^84 + 22 * q^86 - 24 * q^87 - 28 * q^89 + 16 * q^90 + 18 * q^91 + 14 * q^93 - 2 * q^96 + 6 * q^97 + 6 * q^98 - 52 * q^99

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