LMFDB - Embedded newform 544.2.bd.b.69.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [544,2,Mod(69,544)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("544.69"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(544, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 544 = 2^{5} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	544.bd (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [128,0,0,0,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.34386186996$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			69.10
Character	$\chi$	$=$	544.69
Dual form			544.2.bd.b.205.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.818572 - 1.15323i) q^{2} +(-0.0536177 - 0.129444i) q^{3} +(-0.659879 + 1.88800i) q^{4} +(-3.50023 - 1.44984i) q^{5} +(-0.105389 + 0.167793i) q^{6} +(-2.01400 - 2.01400i) q^{7} +(2.71746 - 0.784477i) q^{8} +(2.10744 - 2.10744i) q^{9} +(1.19319 + 5.22337i) q^{10} +(-1.77133 + 4.27636i) q^{11} +(0.279773 - 0.0158127i) q^{12} +(-0.920081 + 0.381110i) q^{13} +(-0.674001 + 3.97121i) q^{14} +0.530822i q^{15} +(-3.12912 - 2.49171i) q^{16} +1.00000i q^{17} +(-4.15545 - 0.705270i) q^{18} +(3.38440 - 1.40186i) q^{19} +(5.04703 - 5.65173i) q^{20} +(-0.152715 + 0.368688i) q^{21} +(6.38159 - 1.45776i) q^{22} +(-3.91278 + 3.91278i) q^{23} +(-0.247250 - 0.309699i) q^{24} +(6.61402 + 6.61402i) q^{25} +(1.19266 + 0.749099i) q^{26} +(-0.774126 - 0.320653i) q^{27} +(5.13144 - 2.47345i) q^{28} +(3.79829 + 9.16989i) q^{29} +(0.612160 - 0.434517i) q^{30} +4.54645 q^{31} +(-0.312099 + 5.64824i) q^{32} +0.648526 q^{33} +(1.15323 - 0.818572i) q^{34} +(4.12948 + 9.96946i) q^{35} +(2.58820 + 5.36951i) q^{36} +(-9.31891 - 3.86002i) q^{37} +(-4.38705 - 2.75546i) q^{38} +(0.0986652 + 0.0986652i) q^{39} +(-10.6491 - 1.19404i) q^{40} +(2.94592 - 2.94592i) q^{41} +(0.550190 - 0.125682i) q^{42} +(-2.43976 + 5.89010i) q^{43} +(-6.90493 - 6.16615i) q^{44} +(-10.4320 + 4.32106i) q^{45} +(7.71524 + 1.30944i) q^{46} +8.88060i q^{47} +(-0.154762 + 0.538647i) q^{48} +1.11241i q^{49} +(2.21343 - 13.0415i) q^{50} +(0.129444 - 0.0536177i) q^{51} +(-0.112396 - 1.98860i) q^{52} +(-2.33269 + 5.63162i) q^{53} +(0.263891 + 1.15522i) q^{54} +(12.4001 - 12.4001i) q^{55} +(-7.05291 - 3.89304i) q^{56} +(-0.362927 - 0.362927i) q^{57} +(7.46581 - 11.8865i) q^{58} +(6.46363 + 2.67732i) q^{59} +(-1.00220 - 0.350278i) q^{60} +(-2.41447 - 5.82904i) q^{61} +(-3.72160 - 5.24310i) q^{62} -8.48878 q^{63} +(6.76919 - 4.26357i) q^{64} +3.77304 q^{65} +(-0.530865 - 0.747899i) q^{66} +(1.55759 + 3.76035i) q^{67} +(-1.88800 - 0.659879i) q^{68} +(0.716283 + 0.296694i) q^{69} +(8.11679 - 12.9230i) q^{70} +(-5.26831 - 5.26831i) q^{71} +(4.07365 - 7.38012i) q^{72} +(2.18456 - 2.18456i) q^{73} +(3.17671 + 13.9066i) q^{74} +(0.501520 - 1.21078i) q^{75} +(0.413433 + 7.31482i) q^{76} +(12.1801 - 5.04515i) q^{77} +(0.0330191 - 0.194548i) q^{78} +5.51206i q^{79} +(7.34006 + 13.2583i) q^{80} -8.82371i q^{81} +(-5.80877 - 0.985874i) q^{82} +(-9.94525 + 4.11946i) q^{83} +(-0.595310 - 0.531616i) q^{84} +(1.44984 - 3.50023i) q^{85} +(8.78976 - 2.00787i) q^{86} +(0.983336 - 0.983336i) q^{87} +(-1.45881 + 13.0104i) q^{88} +(-2.92406 - 2.92406i) q^{89} +(13.5225 + 8.49336i) q^{90} +(2.62060 + 1.08549i) q^{91} +(-4.80539 - 9.96932i) q^{92} +(-0.243770 - 0.588513i) q^{93} +(10.2414 - 7.26942i) q^{94} -13.8786 q^{95} +(0.747867 - 0.262446i) q^{96} -15.9224 q^{97} +(1.28287 - 0.910590i) q^{98} +(5.27921 + 12.7451i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 20 q^{6} - 24 q^{8} - 16 q^{12} - 20 q^{16} - 20 q^{18} - 48 q^{22} - 8 q^{23} + 68 q^{24} + 20 q^{26} - 24 q^{27} + 20 q^{30} + 48 q^{31} - 24 q^{35} + 8 q^{36} + 68 q^{38} - 24 q^{39} - 36 q^{40}+ \cdots - 136 q^{99}+O(q^{100}) $ 128 * q + 20 * q^6 - 24 * q^8 - 16 * q^12 - 20 * q^16 - 20 * q^18 - 48 * q^22 - 8 * q^23 + 68 * q^24 + 20 * q^26 - 24 * q^27 + 20 * q^30 + 48 * q^31 - 24 * q^35 + 8 * q^36 + 68 * q^38 - 24 * q^39 - 36 * q^40 - 16 * q^42 - 8 * q^43 - 40 * q^44 - 80 * q^45 + 12 * q^50 + 56 * q^52 - 16 * q^53 - 136 * q^54 + 32 * q^55 + 128 * q^56 - 32 * q^58 + 20 * q^60 - 12 * q^62 - 80 * q^63 + 12 * q^64 - 8 * q^66 + 40 * q^67 - 4 * q^68 + 100 * q^70 - 44 * q^72 + 84 * q^74 + 32 * q^75 - 32 * q^76 - 16 * q^77 - 64 * q^78 + 44 * q^80 + 40 * q^82 + 84 * q^84 - 120 * q^86 - 56 * q^87 + 128 * q^88 - 68 * q^90 - 56 * q^91 - 40 * q^92 + 32 * q^95 - 72 * q^96 - 12 * q^98 - 136 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/544\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$	$1$

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 $

$2$	−0.818572	−	1.15323i	−0.578818	−	0.815457i
$2$	−0.818572	−	1.15323i	−0.578818	−	0.815457i
$3$	−0.0536177	−	0.129444i	−0.0309562	−	0.0747348i	0.907645	−	0.419738i	$-0.137878\pi$
$3$	−0.0536177	−	0.129444i	−0.0309562	−	0.0747348i	−0.938602	+	0.345003i	$0.887878\pi$
$4$	−0.659879	+	1.88800i	−0.329939	+	0.944002i
$5$	−3.50023	−	1.44984i	−1.56535	−	0.648389i	−0.579341	−	0.815085i	$-0.696690\pi$
$5$	−3.50023	−	1.44984i	−1.56535	−	0.648389i	−0.986008	+	0.166696i	$0.946690\pi$
$6$	−0.105389	+	0.167793i	−0.0430250	+	0.0685013i
$7$	−2.01400	−	2.01400i	−0.761221	−	0.761221i	0.215322	−	0.976543i	$-0.430920\pi$
$7$	−2.01400	−	2.01400i	−0.761221	−	0.761221i	−0.976543	+	0.215322i	$0.930920\pi$
$8$	2.71746	−	0.784477i	0.960768	−	0.277354i
$9$	2.10744	−	2.10744i	0.702480	−	0.702480i
$10$	1.19319	+	5.22337i	0.377320	+	1.65177i
$11$	−1.77133	+	4.27636i	−0.534075	+	1.28937i	0.394728	+	0.918798i	$0.370839\pi$
$11$	−1.77133	+	4.27636i	−0.534075	+	1.28937i	−0.928803	+	0.370574i	$0.879161\pi$
$12$	0.279773	−	0.0158127i	0.0807635	−	0.00456475i
$13$	−0.920081	+	0.381110i	−0.255185	+	0.105701i	−0.506609	−	0.862176i	$-0.669101\pi$
$13$	−0.920081	+	0.381110i	−0.255185	+	0.105701i	0.251424	+	0.967877i	$0.419101\pi$
$14$	−0.674001	+	3.97121i	−0.180134	+	1.06135i
$15$			0.530822i			0.137058i
$16$	−3.12912	−	2.49171i	−0.782280	−	0.622927i
$17$			1.00000i			0.242536i
$17$			1.00000i			0.242536i
$18$	−4.15545	−	0.705270i	−0.979450	−	0.166234i
$19$	3.38440	−	1.40186i	0.776434	−	0.321610i	0.0409586	−	0.999161i	$-0.486959\pi$
$19$	3.38440	−	1.40186i	0.776434	−	0.321610i	0.735475	+	0.677551i	$0.236959\pi$
$20$	5.04703	−	5.65173i	1.12855	−	1.26376i
$21$	−0.152715	+	0.368688i	−0.0333252	+	0.0804542i
$22$	6.38159	−	1.45776i	1.36056	−	0.310796i
$23$	−3.91278	+	3.91278i	−0.815872	+	0.815872i	−0.985507	−	0.169635i	$-0.945741\pi$
$23$	−3.91278	+	3.91278i	−0.815872	+	0.815872i	0.169635	+	0.985507i	$0.445741\pi$
$24$	−0.247250	−	0.309699i	−0.0504697	−	0.0632170i
$25$	6.61402	+	6.61402i	1.32280	+	1.32280i
$26$	1.19266	+	0.749099i	0.233900	+	0.146910i
$27$	−0.774126	−	0.320653i	−0.148981	−	0.0617098i
$28$	5.13144	−	2.47345i	0.969752	−	0.467438i
$29$	3.79829	+	9.16989i	0.705325	+	1.70281i	0.711364	+	0.702824i	$0.248078\pi$
$29$	3.79829	+	9.16989i	0.705325	+	1.70281i	−0.00603911	+	0.999982i	$0.501922\pi$
$30$	0.612160	−	0.434517i	0.111765	−	0.0793315i
$31$	4.54645			0.816567			0.408283	−	0.912855i	$-0.366128\pi$
$31$	4.54645			0.816567			0.408283	+	0.912855i	$0.366128\pi$
$32$	−0.312099	+	5.64824i	−0.0551719	+	0.998477i
$33$	0.648526			0.112894
$34$	1.15323	−	0.818572i	0.197777	−	0.140384i
$35$	4.12948	+	9.96946i	0.698010	+	1.68515i
$36$	2.58820	+	5.36951i	0.431367	+	0.894918i
$37$	−9.31891	−	3.86002i	−1.53202	−	0.634583i	−0.552065	−	0.833801i	$-0.686160\pi$
$37$	−9.31891	−	3.86002i	−1.53202	−	0.634583i	−0.979955	+	0.199218i	$0.936160\pi$
$38$	−4.38705	−	2.75546i	−0.711673	−	0.446995i
$39$	0.0986652	+	0.0986652i	0.0157991	+	0.0157991i
$40$	−10.6491	−	1.19404i	−1.68377	−	0.188795i
$41$	2.94592	−	2.94592i	0.460075	−	0.460075i	−0.438605	−	0.898680i	$-0.644527\pi$
$41$	2.94592	−	2.94592i	0.460075	−	0.460075i	0.898680	+	0.438605i	$0.144527\pi$
$42$	0.550190	−	0.125682i	0.0848962	−	0.0193931i
$43$	−2.43976	+	5.89010i	−0.372060	+	0.898232i	0.621341	+	0.783540i	$0.286588\pi$
$43$	−2.43976	+	5.89010i	−0.372060	+	0.898232i	−0.993401	+	0.114692i	$0.963412\pi$
$44$	−6.90493	−	6.16615i	−1.04096	−	0.929582i
$45$	−10.4320	+	4.32106i	−1.55511	+	0.644146i
$46$	7.71524	+	1.30944i	1.13755	+	0.193067i
$47$			8.88060i			1.29537i	0.761909	+	0.647685i	$0.224263\pi$
$47$			8.88060i			1.29537i	−0.761909	+	0.647685i	$0.775737\pi$
$48$	−0.154762	+	0.538647i	−0.0223379	+	0.0777470i
$49$			1.11241i			0.158916i
$50$	2.21343	−	13.0415i	0.313027	−	1.84435i
$51$	0.129444	−	0.0536177i	0.0181259	−	0.00750797i
$52$	−0.112396	−	1.98860i	−0.0155865	−	0.275770i
$53$	−2.33269	+	5.63162i	−0.320420	+	0.773562i	0.678810	+	0.734314i	$0.262496\pi$
$53$	−2.33269	+	5.63162i	−0.320420	+	0.773562i	−0.999230	+	0.0392477i	$0.987504\pi$
$54$	0.263891	+	1.15522i	0.0359110	+	0.157206i
$55$	12.4001	−	12.4001i	1.67203	−	1.67203i
$56$	−7.05291	−	3.89304i	−0.942485	−	0.520229i
$57$	−0.362927	−	0.362927i	−0.0480709	−	0.0480709i
$58$	7.46581	−	11.8865i	0.980309	−	1.56078i
$59$	6.46363	+	2.67732i	0.841493	+	0.348558i	0.761442	−	0.648233i	$-0.224492\pi$
$59$	6.46363	+	2.67732i	0.841493	+	0.348558i	0.0800508	+	0.996791i	$0.474492\pi$
$60$	−1.00220	−	0.350278i	−0.129383	−	0.0452207i
$61$	−2.41447	−	5.82904i	−0.309141	−	0.746332i	−0.999733	−	0.0230878i	$-0.992650\pi$
$61$	−2.41447	−	5.82904i	−0.309141	−	0.746332i	0.690593	−	0.723244i	$-0.257350\pi$
$62$	−3.72160	−	5.24310i	−0.472644	−	0.665875i
$63$	−8.48878			−1.06949
$64$	6.76919	−	4.26357i	0.846149	−	0.532946i
$65$	3.77304			0.467989
$66$	−0.530865	−	0.747899i	−0.0653450	−	0.0920601i
$67$	1.55759	+	3.76035i	0.190290	+	0.459400i	0.990014	−	0.140967i	$-0.0450211\pi$
$67$	1.55759	+	3.76035i	0.190290	+	0.459400i	−0.799725	+	0.600367i	$0.795021\pi$
$68$	−1.88800	−	0.659879i	−0.228954	−	0.0800220i
$69$	0.716283	+	0.296694i	0.0862303	+	0.0357178i
$70$	8.11679	−	12.9230i	0.970142	−	1.54459i
$71$	−5.26831	−	5.26831i	−0.625234	−	0.625234i	0.321631	−	0.946865i	$-0.395769\pi$
$71$	−5.26831	−	5.26831i	−0.625234	−	0.625234i	−0.946865	+	0.321631i	$0.895769\pi$
$72$	4.07365	−	7.38012i	0.480084	−	0.869756i
$73$	2.18456	−	2.18456i	0.255684	−	0.255684i	−0.567612	−	0.823296i	$-0.692133\pi$
$73$	2.18456	−	2.18456i	0.255684	−	0.255684i	0.823296	+	0.567612i	$0.192133\pi$
$74$	3.17671	+	13.9066i	0.369286	+	1.61660i
$75$	0.501520	−	1.21078i	0.0579106	−	0.139809i
$76$	0.413433	+	7.31482i	0.0474240	+	0.839067i
$77$	12.1801	−	5.04515i	1.38805	−	0.574948i
$78$	0.0330191	−	0.194548i	0.00373867	−	0.0220283i
$79$			5.51206i			0.620156i	0.950711	+	0.310078i	$0.100355\pi$
$79$			5.51206i			0.620156i	−0.950711	+	0.310078i	$0.899645\pi$
$80$	7.34006	+	13.2583i	0.820643	+	1.48232i
$81$		−	8.82371i		−	0.980412i
$82$	−5.80877	−	0.985874i	−0.641471	−	0.108872i
$83$	−9.94525	+	4.11946i	−1.09163	+	0.452169i	−0.854576	−	0.519327i	$-0.826183\pi$
$83$	−9.94525	+	4.11946i	−1.09163	+	0.452169i	−0.237057	+	0.971496i	$0.576183\pi$
$84$	−0.595310	−	0.531616i	−0.0649537	−	0.0580041i
$85$	1.44984	−	3.50023i	0.157257	−	0.379653i
$86$	8.78976	−	2.00787i	0.947825	−	0.216514i
$87$	0.983336	−	0.983336i	0.105425	−	0.105425i
$88$	−1.45881	+	13.0104i	−0.155509	+	1.38691i
$89$	−2.92406	−	2.92406i	−0.309949	−	0.309949i	0.534940	−	0.844890i	$-0.320334\pi$
$89$	−2.92406	−	2.92406i	−0.309949	−	0.309949i	−0.844890	+	0.534940i	$0.820334\pi$
$90$	13.5225	+	8.49336i	1.42540	+	0.895279i
$91$	2.62060	+	1.08549i	0.274714	+	0.113790i
$92$	−4.80539	−	9.96932i	−0.500997	−	1.03937i
$93$	−0.243770	−	0.588513i	−0.0252778	−	0.0610260i
$94$	10.2414	−	7.26942i	1.05632	−	0.749783i
$95$	−13.8786			−1.42392
$96$	0.747867	−	0.262446i	0.0763289	−	0.0267858i
$97$	−15.9224			−1.61668			−0.808338	−	0.588719i	$-0.799632\pi$
$97$	−15.9224			−1.61668			−0.808338	+	0.588719i	$0.799632\pi$
$98$	1.28287	−	0.910590i	0.129589	−	0.0919835i
$99$	5.27921	+	12.7451i	0.530580	+	1.28093i
$100$	−16.8518	+	8.12285i	−1.68518	+	0.812285i
$101$	−11.2449	−	4.65778i	−1.11891	−	0.463466i	−0.254910	−	0.966965i	$-0.582046\pi$
$101$	−11.2449	−	4.65778i	−1.11891	−	0.463466i	−0.863996	+	0.503498i	$0.832046\pi$
$102$	−0.167793	−	0.105389i	−0.0166140	−	0.0104351i
$103$	−1.18539	−	1.18539i	−0.116800	−	0.116800i	0.646291	−	0.763091i	$-0.276319\pi$
$103$	−1.18539	−	1.18539i	−0.116800	−	0.116800i	−0.763091	+	0.646291i	$0.776319\pi$
$104$	−2.20131	+	1.75743i	−0.215857	+	0.172331i
$105$	1.06908	−	1.06908i	0.104331	−	0.104331i
$106$	8.40403	−	1.91976i	0.816271	−	0.186463i
$107$	−4.41604	+	10.6613i	−0.426914	+	1.03066i	0.553346	+	0.832952i	$0.313351\pi$
$107$	−4.41604	+	10.6613i	−0.426914	+	1.03066i	−0.980260	+	0.197711i	$0.936649\pi$
$108$	1.11622	−	1.24996i	0.107409	−	0.120278i
$109$	12.5127	−	5.18294i	1.19850	−	0.496436i	0.307987	−	0.951390i	$-0.400345\pi$
$109$	12.5127	−	5.18294i	1.19850	−	0.496436i	0.890515	+	0.454955i	$0.150345\pi$
$110$	−24.4505	−	4.14979i	−2.33127	−	0.395667i
$111$			1.41325i			0.134139i
$112$	1.28375	+	11.3204i	0.121303	+	1.06967i
$113$		−	10.0740i		−	0.947687i	−0.880609	−	0.473843i	$-0.842866\pi$
$113$		−	10.0740i		−	0.947687i	0.880609	−	0.473843i	$-0.157134\pi$
$114$	−0.121456	+	0.715620i	−0.0113754	+	0.0670240i
$115$	19.3686	−	8.02272i	1.80613	−	0.748122i
$116$	−19.8192	+	1.12018i	−1.84017	+	0.104006i
$117$	−1.13585	+	2.74218i	−0.105009	+	0.253515i
$118$	−2.20338	−	9.64563i	−0.202837	−	0.887952i
$119$	2.01400	−	2.01400i	0.184623	−	0.184623i
$120$	0.416418	+	1.44249i	0.0380136	+	0.131681i
$121$	−7.37150	−	7.37150i	−0.670136	−	0.670136i
$122$	−4.74580	+	7.55592i	−0.429665	+	0.684081i
$123$	−0.539286	−	0.223380i	−0.0486258	−	0.0201415i
$124$	−3.00011	+	8.58372i	−0.269417	+	0.770841i
$125$	−6.31209	−	15.2387i	−0.564571	−	1.36299i
$126$	6.94868	+	9.78951i	0.619037	+	0.872119i
$127$	10.0605			0.892727			0.446363	−	0.894852i	$-0.352719\pi$
$127$	10.0605			0.892727			0.446363	+	0.894852i	$0.352719\pi$
$128$	−10.4580	−	4.31640i	−0.924361	−	0.381519i
$129$	0.893256			0.0786468
$130$	−3.08851	−	4.35119i	−0.270880	−	0.381624i
$131$	0.391057	+	0.944095i	0.0341668	+	0.0824860i	0.940042	−	0.341059i	$-0.110786\pi$
$131$	0.391057	+	0.944095i	0.0341668	+	0.0824860i	−0.905875	+	0.423545i	$0.860786\pi$
$132$	−0.427948	+	1.22442i	−0.0372481	+	0.106572i
$133$	−9.63954	−	3.99283i	−0.835854	−	0.346222i
$134$	3.06155	−	4.87438i	0.264478	−	0.421082i
$135$	2.24472	+	2.24472i	0.193195	+	0.193195i
$136$	0.784477	+	2.71746i	0.0672683	+	0.233020i
$137$	−11.9637	+	11.9637i	−1.02213	+	1.02213i	−0.0223798	+	0.999750i	$0.507124\pi$
$137$	−11.9637	+	11.9637i	−1.02213	+	1.02213i	−0.999750	+	0.0223798i	$0.992876\pi$
$138$	−0.244173	−	1.06890i	−0.0207854	−	0.0909912i
$139$	−8.72040	+	21.0529i	−0.739655	+	1.78568i	−0.132370	+	0.991200i	$0.542259\pi$
$139$	−8.72040	+	21.0529i	−0.739655	+	1.78568i	−0.607284	+	0.794484i	$0.707741\pi$
$140$	−21.5473	+	1.21785i	−1.82108	+	0.102927i
$141$	1.14955	−	0.476157i	0.0968092	−	0.0400997i
$142$	−1.76308	+	10.3881i	−0.147954	+	0.871747i
$143$		−	4.60967i		−	0.385480i
$144$	−11.8456	+	1.34331i	−0.987129	+	0.111943i
$145$		−	37.6036i		−	3.12281i
$146$	−4.30753	−	0.731081i	−0.356493	−	0.0605047i
$147$	0.143996	−	0.0596450i	0.0118766	−	0.00491943i
$148$	13.4371	−	15.0470i	1.10452	−	1.23686i
$149$	3.73372	−	9.01401i	0.305879	−	0.738456i	−0.693952	−	0.720022i	$-0.744132\pi$
$149$	3.73372	−	9.01401i	0.305879	−	0.738456i	0.999830	−	0.0184344i	$-0.00586819\pi$
$150$	−1.80684	+	0.412741i	−0.147528	+	0.0337001i
$151$	−1.76431	+	1.76431i	−0.143577	+	0.143577i	−0.775242	−	0.631665i	$-0.782372\pi$
$151$	−1.76431	+	1.76431i	−0.143577	+	0.143577i	0.631665	+	0.775242i	$0.282372\pi$
$152$	8.09724	−	6.46449i	0.656773	−	0.524339i
$153$	2.10744	+	2.10744i	0.170376	+	0.170376i
$154$	−15.7885	−	9.91659i	−1.27227	−	0.799102i
$155$	−15.9136	−	6.59164i	−1.27821	−	0.529453i
$156$	−0.251387	+	0.121173i	−0.0201271	+	0.00970163i
$157$	2.13213	+	5.14742i	0.170162	+	0.410808i	0.985838	−	0.167701i	$-0.0536344\pi$
$157$	2.13213	+	5.14742i	0.170162	+	0.410808i	−0.815675	+	0.578510i	$0.803634\pi$
$158$	6.35668	−	4.51202i	0.505710	−	0.358957i
$159$	0.854055			0.0677310
$160$	9.28147	−	19.3176i	0.733765	−	1.52719i
$161$	15.7607			1.24212
$162$	−10.1758	+	7.22284i	−0.799484	+	0.567480i
$163$	−2.45074	−	5.91660i	−0.191956	−	0.463424i	0.798372	−	0.602164i	$-0.205695\pi$
$163$	−2.45074	−	5.91660i	−0.191956	−	0.463424i	−0.990329	+	0.138740i	$0.955695\pi$
$164$	3.61796	+	7.50586i	0.282515	+	0.586109i
$165$	−2.26999	−	0.940260i	−0.176718	−	0.0731992i
$166$	12.8916	+	8.09709i	1.00058	+	0.628456i
$167$	12.4607	+	12.4607i	0.964236	+	0.964236i	0.999382	−	0.0351462i	$-0.0111897\pi$
$167$	12.4607	+	12.4607i	0.964236	+	0.964236i	−0.0351462	+	0.999382i	$0.511190\pi$
$168$	−0.125771	+	1.12170i	−0.00970348	+	0.0865407i
$169$	−8.49108	+	8.49108i	−0.653160	+	0.653160i
$170$	−5.22337	+	1.19319i	−0.400614	+	0.0915134i
$171$	4.17807	−	10.0868i	0.319505	−	0.771353i
$172$	−9.51059	−	8.49303i	−0.725176	−	0.647587i
$173$	2.19220	−	0.908040i	0.166670	−	0.0690370i	−0.297788	−	0.954632i	$-0.596249\pi$
$173$	2.19220	−	0.908040i	0.166670	−	0.0690370i	0.464459	+	0.885595i	$0.346249\pi$
$174$	−1.93894	−	0.329081i	−0.146991	−	0.0249475i
$175$		−	26.6413i		−	2.01389i
$176$	16.1981	−	8.96762i	1.22098	−	0.675960i
$177$		−	0.980233i		−	0.0736788i
$178$	−0.978558	+	5.76566i	−0.0733460	+	0.432155i
$179$	−4.66337	+	1.93163i	−0.348557	+	0.144377i	−0.550091	−	0.835105i	$-0.685407\pi$
$179$	−4.66337	+	1.93163i	−0.348557	+	0.144377i	0.201535	+	0.979481i	$0.435407\pi$
$180$	−1.27435	−	22.5470i	−0.0949848	−	1.68055i
$181$	−9.30908	+	22.4741i	−0.691938	+	1.67049i	0.0488997	+	0.998804i	$0.484429\pi$
$181$	−9.30908	+	22.4741i	−0.691938	+	1.67049i	−0.740838	+	0.671684i	$0.765571\pi$
$182$	−0.893334	−	3.91071i	−0.0662184	−	0.289881i
$183$	−0.625079	+	0.625079i	−0.0462071	+	0.0462071i
$184$	−7.56335	+	13.7023i	−0.557578	+	1.01015i
$185$	27.0219	+	27.0219i	1.98669	+	1.98669i
$186$	−0.479147	+	0.762863i	−0.0351328	+	0.0559359i
$187$	−4.27636	−	1.77133i	−0.312719	−	0.129532i
$188$	−16.7666	−	5.86012i	−1.22283	−	0.427393i
$189$	0.913295	+	2.20489i	0.0664324	+	0.160382i
$190$	11.3607	+	16.0053i	0.824190	+	1.16114i
$191$	−17.4799			−1.26480			−0.632400	−	0.774642i	$-0.717930\pi$
$191$	−17.4799			−1.26480			−0.632400	+	0.774642i	$0.717930\pi$
$192$	−0.914844	−	0.647632i	−0.0660232	−	0.0467388i
$193$	−11.5393			−0.830618			−0.415309	−	0.909680i	$-0.636327\pi$
$193$	−11.5393			−0.830618			−0.415309	+	0.909680i	$0.636327\pi$
$194$	13.0336	+	18.3622i	0.935761	+	1.31833i
$195$	−0.202302	−	0.488400i	−0.0144871	−	0.0349750i
$196$	−2.10024	−	0.734057i	−0.150017	−	0.0524327i
$197$	−5.42327	−	2.24639i	−0.386392	−	0.160049i	0.181027	−	0.983478i	$-0.442058\pi$
$197$	−5.42327	−	2.24639i	−0.386392	−	0.160049i	−0.567419	+	0.823429i	$0.692058\pi$
$198$	10.3767	−	16.5210i	0.737437	−	1.17409i
$199$	11.6555	+	11.6555i	0.826237	+	0.826237i	0.986994	−	0.160757i	$-0.0513936\pi$
$199$	11.6555	+	11.6555i	0.826237	+	0.826237i	−0.160757	+	0.986994i	$0.551394\pi$
$200$	23.1619	+	12.7848i	1.63779	+	0.904022i
$201$	0.403243	−	0.403243i	0.0284425	−	0.0284425i
$202$	3.83325	+	16.7807i	0.269707	+	1.18068i
$203$	10.8184	−	26.1179i	0.759303	−	1.83312i
$204$	0.0158127	+	0.279773i	0.00110711	+	0.0195880i
$205$	−14.5825	+	6.04027i	−1.01849	+	0.421871i
$206$	−0.396698	+	2.33735i	−0.0276393	+	0.162851i
$207$			16.4919i			1.14627i
$208$	3.82866	+	1.10003i	0.265470	+	0.0762736i
$209$			16.9561i			1.17288i
$210$	−2.10801	−	0.357775i	−0.145467	−	0.0246888i
$211$	−19.8911	+	8.23915i	−1.36936	+	0.567206i	−0.941614	−	0.336694i	$-0.890691\pi$
$211$	−19.8911	+	8.23915i	−1.36936	+	0.567206i	−0.427743	+	0.903900i	$0.640691\pi$
$212$	−9.09322	−	8.12032i	−0.624525	−	0.557706i
$213$	−0.399479	+	0.964429i	−0.0273719	+	0.0660816i
$214$	15.9097	−	3.63430i	1.08757	−	0.248436i
$215$	17.0794	−	17.0794i	1.16481	−	1.16481i
$216$	−2.35520	−	0.264080i	−0.160251	−	0.0179683i
$217$	−9.15656	−	9.15656i	−0.621588	−	0.621588i
$218$	−16.2197	−	10.1874i	−1.09854	−	0.689980i
$219$	−0.399911	−	0.165648i	−0.0270235	−	0.0111935i
$220$	15.2289	+	31.5940i	1.02673	+	2.13007i
$221$	−0.381110	−	0.920081i	−0.0256362	−	0.0618914i
$222$	1.62980	−	1.15685i	0.109385	−	0.0776424i
$223$	22.0108			1.47395			0.736976	−	0.675918i	$-0.236253\pi$
$223$	22.0108			1.47395			0.736976	+	0.675918i	$0.236253\pi$
$224$	12.0041	−	10.7470i	0.802060	−	0.718064i
$225$	27.8773			1.85849
$226$	−11.6177	+	8.24634i	−0.772797	+	0.548538i
$227$	0.0801173	+	0.193420i	0.00531757	+	0.0128377i	0.926516	−	0.376255i	$-0.122788\pi$
$227$	0.0801173	+	0.193420i	0.00531757	+	0.0128377i	−0.921198	+	0.389093i	$0.872788\pi$
$228$	0.924695	−	0.445720i	0.0612394	−	0.0295185i
$229$	4.93805	+	2.04541i	0.326316	+	0.135164i	0.539826	−	0.841776i	$-0.318490\pi$
$229$	4.93805	+	2.04541i	0.326316	+	0.135164i	−0.213511	+	0.976941i	$0.568490\pi$
$230$	−25.1066	−	15.7692i	−1.65548	−	1.03979i
$231$	−1.30613	−	1.30613i	−0.0859372	−	0.0859372i
$232$	17.5153	+	21.9391i	1.14993	+	1.44038i
$233$	6.97878	−	6.97878i	0.457195	−	0.457195i	−0.440539	−	0.897734i	$-0.645213\pi$
$233$	6.97878	−	6.97878i	0.457195	−	0.457195i	0.897734	+	0.440539i	$0.145213\pi$
$234$	4.09214	−	0.934779i	0.267512	−	0.0611084i
$235$	12.8755	−	31.0841i	0.839903	−	2.02771i
$236$	−9.32001	+	10.4367i	−0.606681	+	0.679368i
$237$	0.713506	−	0.295544i	0.0463472	−	0.0191976i
$238$	−3.97121	−	0.674001i	−0.257416	−	0.0436890i
$239$		−	16.4041i		−	1.06109i	−0.847656	−	0.530547i	$-0.821987\pi$
$239$		−	16.4041i		−	1.06109i	0.847656	−	0.530547i	$-0.178013\pi$
$240$	1.32265	−	1.66101i	0.0853769	−	0.107218i
$241$		−	0.466567i		−	0.0300542i	−0.999887	−	0.0150271i	$-0.995217\pi$
$241$		−	0.466567i		−	0.0300542i	0.999887	−	0.0150271i	$-0.00478346\pi$
$242$	−2.46693	+	14.5351i	−0.158580	+	0.934354i
$243$	−3.46456	+	1.43507i	−0.222251	+	0.0920596i
$244$	12.5985	−	0.712066i	0.806536	−	0.0455854i
$245$	1.61282	−	3.89370i	0.103039	−	0.248759i
$246$	0.183837	+	0.804774i	0.0117210	+	0.0513105i
$247$	−2.57966	+	2.57966i	−0.164140	+	0.164140i
$248$	12.3548	−	3.56658i	0.784531	−	0.226478i
$249$	1.06648	+	1.06648i	0.0675856	+	0.0675856i
$250$	−12.4069	+	19.7533i	−0.784679	+	1.24931i
$251$	3.99002	+	1.65272i	0.251848	+	0.104319i	0.505036	−	0.863098i	$-0.331479\pi$
$251$	3.99002	+	1.65272i	0.251848	+	0.104319i	−0.253188	+	0.967417i	$0.581479\pi$
$252$	5.60156	−	16.0268i	0.352865	−	1.00960i
$253$	−9.80166	−	23.6633i	−0.616225	−	1.48770i
$254$	−8.23526	−	11.6021i	−0.516726	−	0.727980i
$255$	−0.530822			−0.0332414
$256$	3.58279	+	15.5937i	0.223925	+	0.974606i
$257$	−6.39167			−0.398701			−0.199351	−	0.979928i	$-0.563883\pi$
$257$	−6.39167			−0.398701			−0.199351	+	0.979928i	$0.563883\pi$
$258$	−0.731194	−	1.03013i	−0.0455222	−	0.0641330i
$259$	10.9942	+	26.5424i	0.683148	+	1.64926i
$260$	−2.48975	+	7.12352i	−0.154408	+	0.441782i
$261$	27.3297	+	11.3203i	1.69166	+	0.700710i
$262$	0.768650	−	1.22379i	0.0474874	−	0.0756059i
$263$	3.73009	+	3.73009i	0.230007	+	0.230007i	0.812696	−	0.582689i	$-0.197999\pi$
$263$	3.73009	+	3.73009i	0.230007	+	0.230007i	−0.582689	+	0.812696i	$0.697999\pi$
$264$	1.76234	−	0.508753i	0.108465	−	0.0313116i
$265$	16.3299	−	16.3299i	1.00314	−	1.00314i
$266$	3.28601	+	14.3850i	0.201478	+	0.882003i
$267$	−0.221722	+	0.535284i	−0.0135692	+	0.0327589i
$268$	−8.12738	+	0.459359i	−0.496459	+	0.0280598i
$269$	18.8211	−	7.79594i	1.14754	−	0.475327i	0.273833	−	0.961777i	$-0.411708\pi$
$269$	18.8211	−	7.79594i	1.14754	−	0.475327i	0.873708	+	0.486450i	$0.161708\pi$
$270$	0.751213	−	4.42615i	0.0457173	−	0.269367i
$271$		−	17.2805i		−	1.04972i	−0.851190	−	0.524858i	$-0.824118\pi$
$271$		−	17.2805i		−	1.04972i	0.851190	−	0.524858i	$-0.175882\pi$
$272$	2.49171	−	3.12912i	0.151082	−	0.189731i
$273$		−	0.397424i		−	0.0240532i
$274$	23.5901	+	4.00375i	1.42513	+	0.241875i
$275$	−39.9996	+	16.5684i	−2.41206	+	0.999110i
$276$	−1.03282	+	1.15656i	−0.0621684	+	0.0696169i
$277$	−5.80430	+	14.0128i	−0.348746	+	0.841948i	0.648022	+	0.761621i	$0.275596\pi$
$277$	−5.80430	+	14.0128i	−0.348746	+	0.841948i	−0.996769	+	0.0803267i	$0.974404\pi$
$278$	31.4171	−	7.17670i	1.88427	−	0.430430i
$279$	9.58137	−	9.58137i	0.573622	−	0.573622i
$280$	19.0425	+	23.8521i	1.13801	+	1.42544i
$281$	19.2064	+	19.2064i	1.14576	+	1.14576i	0.987378	+	0.158380i	$0.0506269\pi$
$281$	19.2064	+	19.2064i	1.14576	+	1.14576i	0.158380	+	0.987378i	$0.449373\pi$
$282$	−1.49010	−	0.935921i	−0.0887344	−	0.0557333i
$283$	4.98467	+	2.06472i	0.296308	+	0.122735i	0.525885	−	0.850556i	$-0.323734\pi$
$283$	4.98467	+	2.06472i	0.296308	+	0.122735i	−0.229577	+	0.973290i	$0.573734\pi$
$284$	13.4230	−	6.47015i	0.796511	−	0.383933i
$285$	0.744141	+	1.79651i	0.0440791	+	0.106416i
$286$	−5.31601	+	3.77335i	−0.314342	+	0.223123i
$287$	−11.8662			−0.700438
$288$	11.2456	+	12.5610i	0.662653	+	0.740167i
$289$	−1.00000			−0.0588235
$290$	−43.3656	+	30.7813i	−2.54652	+	1.80754i
$291$	0.853722	+	2.06107i	0.0500461	+	0.120822i
$292$	2.68292	+	5.56601i	0.157006	+	0.325726i
$293$	−1.47458	−	0.610791i	−0.0861458	−	0.0356828i	0.339194	−	0.940716i	$-0.389846\pi$
$293$	−1.47458	−	0.610791i	−0.0861458	−	0.0356828i	−0.425340	+	0.905034i	$0.639846\pi$
$294$	−0.186655	−	0.117236i	−0.0108860	−	0.00683737i
$295$	−18.7425	−	18.7425i	−1.09123	−	1.09123i
$296$	−28.3519	−	3.17899i	−1.64792	−	0.184775i
$297$	2.74246	−	2.74246i	0.159134	−	0.159134i
$298$	−13.4515	+	3.07277i	−0.779227	+	0.178001i
$299$	2.10888	−	5.09128i	0.121960	−	0.294436i
$300$	1.95501	+	1.74584i	0.112873	+	0.100796i
$301$	16.7764	−	6.94900i	0.966974	−	0.400534i
$302$	3.47886	+	0.590438i	0.200186	+	0.0339759i
$303$			1.70533i			0.0979684i
$304$	−14.0832	−	4.04633i	−0.807728	−	0.232073i
$305$			23.9036i			1.36871i
$306$	0.705270	−	4.15545i	0.0403176	−	0.237551i
$307$	20.0984	−	8.32504i	1.14708	−	0.475135i	0.273525	−	0.961865i	$-0.411810\pi$
$307$	20.0984	−	8.32504i	1.14708	−	0.475135i	0.873553	+	0.486730i	$0.161810\pi$
$308$	1.48790	+	26.3252i	0.0847809	+	1.50002i
$309$	−0.0898841	+	0.216999i	−0.00511333	+	0.0123447i
$310$	5.42478	+	23.7478i	0.308107	+	1.34878i
$311$	−5.33466	+	5.33466i	−0.302501	+	0.302501i	−0.841992	−	0.539491i	$-0.818617\pi$
$311$	−5.33466	+	5.33466i	−0.302501	+	0.302501i	0.539491	+	0.841992i	$0.318617\pi$
$312$	0.345519	+	0.190718i	0.0195612	+	0.0107973i
$313$	20.9294	+	20.9294i	1.18300	+	1.18300i	0.978963	+	0.204039i	$0.0654070\pi$
$313$	20.9294	+	20.9294i	1.18300	+	1.18300i	0.204039	+	0.978963i	$0.434593\pi$
$314$	4.19085	−	6.67237i	0.236503	−	0.376543i
$315$	29.7127	+	12.3074i	1.67412	+	0.693443i
$316$	−10.4068	−	3.63729i	−0.585428	−	0.204614i
$317$	−7.41022	−	17.8899i	−0.416200	−	1.00479i	−0.983439	−	0.181241i	$-0.941988\pi$
$317$	−7.41022	−	17.8899i	−0.416200	−	1.00479i	0.567239	−	0.823553i	$-0.308012\pi$
$318$	−0.699106	−	0.984922i	−0.0392039	−	0.0552317i
$319$	−45.9418			−2.57225
$320$	−29.8752	+	5.10921i	−1.67008	+	0.285613i
$321$	1.61682			0.0902420
$322$	−12.9013	−	18.1757i	−0.718961	−	1.01289i
$323$	1.40186	+	3.38440i	0.0780018	+	0.188313i
$324$	16.6592	+	5.82258i	0.925511	+	0.323476i
$325$	−8.60611	−	3.56477i	−0.477381	−	0.197738i
$326$	−4.81709	+	7.66943i	−0.266794	+	0.424770i
$327$	−1.34181	−	1.34181i	−0.0742021	−	0.0742021i
$328$	5.69442	−	10.3164i	0.314422	−	0.569629i
$329$	17.8856	−	17.8856i	0.986063	−	0.986063i
$330$	0.773814	+	3.38749i	0.0425971	+	0.186475i
$331$	9.07582	−	21.9110i	0.498852	−	1.20434i	−0.451250	−	0.892397i	$-0.649022\pi$
$331$	9.07582	−	21.9110i	0.498852	−	1.20434i	0.950102	−	0.311938i	$-0.100978\pi$
$332$	−1.21490	−	21.4950i	−0.0666761	−	1.17969i
$333$	−27.7738	+	11.5043i	−1.52199	+	0.630431i
$334$	4.17006	−	24.5700i	0.228175	−	1.34441i
$335$		−	15.4203i		−	0.842504i
$336$	1.39653	−	0.773146i	0.0761868	−	0.0421786i
$337$		−	1.99377i		−	0.108608i	−0.998524	−	0.0543039i	$-0.982706\pi$
$337$		−	1.99377i		−	0.108608i	0.998524	−	0.0543039i	$-0.0172940\pi$
$338$	16.7427	+	2.84161i	0.910685	+	0.154563i
$339$	−1.30403	+	0.540147i	−0.0708252	+	0.0293367i
$340$	5.65173	+	5.04703i	0.306508	+	0.273714i
$341$	−8.05325	+	19.4423i	−0.436108	+	1.05286i
$342$	−15.0524	+	3.43846i	−0.813941	+	0.185931i
$343$	−11.8576	+	11.8576i	−0.640251	+	0.640251i
$344$	−2.00931	+	17.9201i	−0.108335	+	0.966185i
$345$	−2.07699	−	2.07699i	−0.111822	−	0.111822i
$346$	−2.84166	−	1.78482i	−0.152768	−	0.0959524i
$347$	−24.3255	−	10.0760i	−1.30586	−	0.540906i	−0.382188	−	0.924085i	$-0.624829\pi$
$347$	−24.3255	−	10.0760i	−1.30586	−	0.540906i	−0.923674	+	0.383179i	$0.874829\pi$
$348$	1.20766	+	2.50542i	0.0647374	+	0.134305i
$349$	−1.61155	−	3.89063i	−0.0862644	−	0.208261i	0.874860	−	0.484375i	$-0.160953\pi$
$349$	−1.61155	−	3.89063i	−0.0862644	−	0.208261i	−0.961125	+	0.276115i	$0.910953\pi$
$350$	−30.7236	+	21.8079i	−1.64224	+	1.16568i
$351$	0.834463			0.0445403
$352$	−23.6011	−	11.3395i	−1.25794	−	0.604399i
$353$	8.27359			0.440359			0.220179	−	0.975459i	$-0.429336\pi$
$353$	8.27359			0.440359			0.220179	+	0.975459i	$0.429336\pi$
$354$	−1.13043	+	0.802392i	−0.0600819	+	0.0426466i
$355$	10.8021	+	26.0785i	0.573315	+	1.38410i
$356$	7.45016	−	3.59111i	0.394857	−	0.190328i
$357$	−0.368688	−	0.152715i	−0.0195130	−	0.00808256i
$358$	6.04492	+	3.79676i	0.319484	+	0.200665i
$359$	7.91041	+	7.91041i	0.417495	+	0.417495i	0.884340	−	0.466844i	$-0.154609\pi$
$359$	7.91041	+	7.91041i	0.417495	+	0.417495i	−0.466844	+	0.884340i	$0.654609\pi$
$360$	−24.9587	+	19.9260i	−1.31544	+	1.05019i
$361$	−3.94610	+	3.94610i	−0.207690	+	0.207690i
$362$	33.5380	−	7.66117i	1.76272	−	0.402662i
$363$	−0.558957	+	1.34944i	−0.0293376	+	0.0708273i
$364$	−3.77869	+	4.23142i	−0.198057	+	0.221787i
$365$	−10.8137	+	4.47920i	−0.566017	+	0.234452i
$366$	1.23253	+	0.209187i	0.0644254	+	0.0109344i
$367$			0.897677i			0.0468584i	0.999725	+	0.0234292i	$0.00745843\pi$
$367$			0.897677i			0.0468584i	−0.999725	+	0.0234292i	$0.992542\pi$
$368$	21.9931	−	2.49406i	1.14647	−	0.130012i
$369$		−	12.4167i		−	0.646387i
$370$	9.04308	−	53.2819i	0.470128	−	2.76999i
$371$	16.0401	−	6.64404i	0.832762	−	0.344942i
$372$	1.27197	−	0.0718919i	0.0659488	−	0.00372742i
$373$	5.58697	−	13.4881i	0.289282	−	0.698389i	−0.710705	−	0.703491i	$-0.751624\pi$
$373$	5.58697	−	13.4881i	0.289282	−	0.698389i	0.999987	+	0.00510112i	$0.00162374\pi$
$374$	1.45776	+	6.38159i	0.0753792	+	0.329984i
$375$	−1.63413	+	1.63413i	−0.0843862	+	0.0843862i
$376$	6.96662	+	24.1327i	0.359276	+	1.24455i
$377$	−6.98947	−	6.98947i	−0.359976	−	0.359976i
$378$	1.79515	−	2.85810i	0.0923323	−	0.147005i
$379$	−9.32896	−	3.86418i	−0.479196	−	0.198490i	0.129992	−	0.991515i	$-0.458505\pi$
$379$	−9.32896	−	3.86418i	−0.479196	−	0.198490i	−0.609189	+	0.793025i	$0.708505\pi$
$380$	9.15822	−	26.2029i	0.469807	−	1.34418i
$381$	−0.539421	−	1.30228i	−0.0276354	−	0.0667177i
$382$	14.3086	+	20.1583i	0.732089	+	1.03139i
$383$	−14.9299			−0.762882			−0.381441	−	0.924393i	$-0.624572\pi$
$383$	−14.9299			−0.762882			−0.381441	+	0.924393i	$0.624572\pi$
$384$	0.00199724	+	1.58516i	0.000101921	+	0.0808923i
$385$	−49.9477			−2.54557
$386$	9.44576	+	13.3075i	0.480777	+	0.677333i
$387$	7.27139	+	17.5547i	0.369625	+	0.892355i
$388$	10.5069	−	30.0616i	0.533405	−	1.52614i
$389$	−11.4726	−	4.75212i	−0.581686	−	0.240942i	0.0723835	−	0.997377i	$-0.476939\pi$
$389$	−11.4726	−	4.75212i	−0.581686	−	0.240942i	−0.654069	+	0.756435i	$0.726939\pi$
$390$	−0.397639	+	0.633091i	−0.0201352	+	0.0320578i
$391$	−3.91278	−	3.91278i	−0.197878	−	0.197878i
$392$	0.872662	+	3.02294i	0.0440761	+	0.152681i
$393$	0.101240	−	0.101240i	0.00510690	−	0.00510690i
$394$	1.84873	+	8.09312i	0.0931379	+	0.407725i
$395$	7.99162	−	19.2935i	0.402102	−	0.970760i
$396$	−27.5465	+	1.55693i	−1.38426	+	0.0782385i
$397$	17.7546	−	7.35420i	0.891078	−	0.369097i	0.110295	−	0.993899i	$-0.464820\pi$
$397$	17.7546	−	7.35420i	0.891078	−	0.369097i	0.780783	+	0.624802i	$0.214820\pi$
$398$	3.90060	−	22.9824i	0.195520	−	1.15200i
$399$			1.46187i			0.0731851i
$400$	−4.21587	−	37.1763i	−0.210793	−	1.85881i
$401$			6.37530i			0.318367i	0.987249	+	0.159184i	$0.0508862\pi$
$401$			6.37530i			0.318367i	−0.987249	+	0.159184i	$0.949114\pi$
$402$	−0.795115	−	0.134948i	−0.0396567	−	0.00673060i
$403$	−4.18310	+	1.73270i	−0.208375	+	0.0863119i
$404$	16.2142	−	18.1568i	0.806684	−	0.903335i
$405$	−12.7930	+	30.8850i	−0.635689	+	1.53469i
$406$	−38.9756	+	8.90332i	−1.93433	+	0.441864i
$407$	33.0137	−	33.0137i	1.63643	−	1.63643i
$408$	0.309699	−	0.247250i	0.0153324	−	0.0122407i
$409$	−2.31405	−	2.31405i	−0.114422	−	0.114422i	0.647577	−	0.762000i	$-0.275782\pi$
$409$	−2.31405	−	2.31405i	−0.114422	−	0.114422i	−0.762000	+	0.647577i	$0.775782\pi$
$410$	18.9027	+	11.8726i	0.933536	+	0.586345i
$411$	2.19010	+	0.907171i	0.108030	+	0.0447474i
$412$	3.02023	−	1.45580i	0.148796	−	0.0717223i
$413$	−7.62563	−	18.4099i	−0.375233	−	0.905892i
$414$	19.0190	−	13.4998i	0.934731	−	0.663480i
$415$	40.7832			2.00197
$416$	−1.86544	−	5.31578i	−0.0914609	−	0.260628i
$417$	3.19275			0.156350
$418$	19.5542	−	13.8798i	0.956429	−	0.678882i
$419$	−12.1850	−	29.4173i	−0.595278	−	1.43713i	−0.878345	−	0.478027i	$-0.841352\pi$
$419$	−12.1850	−	29.4173i	−0.595278	−	1.43713i	0.283068	−	0.959100i	$-0.408648\pi$
$420$	1.31296	+	2.72388i	0.0640660	+	0.132912i
$421$	−7.74792	−	3.20929i	−0.377611	−	0.156411i	0.185802	−	0.982587i	$-0.440512\pi$
$421$	−7.74792	−	3.20929i	−0.377611	−	0.156411i	−0.563412	+	0.826176i	$0.690512\pi$
$422$	25.7839	+	16.1946i	1.25514	+	0.788342i
$423$	18.7153	+	18.7153i	0.909971	+	0.909971i
$424$	−1.92113	+	17.1336i	−0.0932983	+	0.832083i
$425$	−6.61402	+	6.61402i	−0.320827	+	0.320827i
$426$	1.43921	−	0.328763i	0.0697300	−	0.0159286i
$427$	−6.87695	+	16.6024i	−0.332799	+	0.803448i
$428$	−17.2145	−	15.3726i	−0.832092	−	0.743064i
$429$	−0.596696	+	0.247160i	−0.0288088	+	0.0119330i
$430$	−33.6773	−	5.71576i	−1.62406	−	0.275639i
$431$		−	1.65034i		−	0.0794942i	−0.999210	−	0.0397471i	$-0.987345\pi$
$431$		−	1.65034i		−	0.0794942i	0.999210	−	0.0397471i	$-0.0126552\pi$
$432$	1.62336	+	2.93226i	0.0781039	+	0.141078i
$433$		−	11.8133i		−	0.567710i	−0.958867	−	0.283855i	$-0.908386\pi$
$433$		−	11.8133i		−	0.567710i	0.958867	−	0.283855i	$-0.0916135\pi$
$434$	−3.06431	+	18.0549i	−0.147092	+	0.866664i
$435$	−4.86758	+	2.01622i	−0.233383	+	0.0966703i
$436$	1.52854	+	27.0442i	0.0732036	+	1.29518i
$437$	−7.75723	+	18.7276i	−0.371079	+	0.895863i
$438$	0.136325	+	0.596784i	0.00651387	+	0.0285155i
$439$	−23.3081	+	23.3081i	−1.11243	+	1.11243i	−0.119612	+	0.992821i	$0.538165\pi$
$439$	−23.3081	+	23.3081i	−1.11243	+	1.11243i	−0.992821	+	0.119612i	$0.961835\pi$
$440$	23.9692	−	43.4244i	1.14269	−	2.07018i
$441$	2.34434	+	2.34434i	0.111635	+	0.111635i
$442$	−0.749099	+	1.19266i	−0.0356310	+	0.0567291i
$443$	18.1692	+	7.52593i	0.863245	+	0.357568i	0.769976	−	0.638073i	$-0.220268\pi$
$443$	18.1692	+	7.52593i	0.863245	+	0.357568i	0.0932694	+	0.995641i	$0.470268\pi$
$444$	−2.66822	−	0.932571i	−0.126628	−	0.0442579i
$445$	5.99545	+	14.4743i	0.284211	+	0.686147i
$446$	−18.0174	−	25.3835i	−0.853151	−	1.20194i
$447$	−1.36701			−0.0646572
$448$	−22.2200	−	5.04633i	−1.04980	−	0.238417i
$449$	−2.99249			−0.141224			−0.0706121	−	0.997504i	$-0.522495\pi$
$449$	−2.99249			−0.141224			−0.0706121	+	0.997504i	$0.522495\pi$
$450$	−22.8196	−	32.1489i	−1.07573	−	1.51552i
$451$	7.37963	+	17.8160i	0.347493	+	0.838923i
$452$	19.0198	+	6.64765i	0.894618	+	0.312679i
$453$	0.322977	+	0.133782i	0.0151748	+	0.00628561i
$454$	0.157476	−	0.250722i	0.00739072	−	0.0117670i
$455$	−7.59892	−	7.59892i	−0.356243	−	0.356243i
$456$	−1.27095	−	0.701532i	−0.0595176	−	0.0328523i
$457$	−1.92271	+	1.92271i	−0.0899404	+	0.0899404i	−0.750646	−	0.660705i	$-0.770257\pi$
$457$	−1.92271	+	1.92271i	−0.0899404	+	0.0899404i	0.660705	+	0.750646i	$0.270257\pi$
$458$	−1.68333	−	7.36902i	−0.0786567	−	0.344332i
$459$	0.320653	−	0.774126i	0.0149668	−	0.0361331i
$460$	2.36603	+	41.8619i	0.110317	+	1.95182i
$461$	−20.2037	+	8.36865i	−0.940981	+	0.389767i	−0.799834	−	0.600222i	$-0.795079\pi$
$461$	−20.2037	+	8.36865i	−0.940981	+	0.389767i	−0.141147	+	0.989989i	$0.545079\pi$
$462$	−0.437107	+	2.57544i	−0.0203361	+	0.119820i
$463$			17.6134i			0.818564i	0.912408	+	0.409282i	$0.134221\pi$
$463$			17.6134i			0.818564i	−0.912408	+	0.409282i	$0.865779\pi$
$464$	10.9634	−	38.1579i	0.508961	−	1.77144i
$465$			2.41336i			0.111917i
$466$	−13.7608	−	2.33550i	−0.637455	−	0.108190i
$467$	−35.1869	+	14.5749i	−1.62825	+	0.674445i	−0.995035	−	0.0995278i	$-0.968267\pi$
$467$	−35.1869	+	14.5749i	−1.62825	+	0.674445i	−0.633219	+	0.773973i	$0.718267\pi$
$468$	−4.42773	−	3.95399i	−0.204672	−	0.182773i
$469$	4.43637	−	10.7103i	0.204853	−	0.494558i
$470$	−46.3867	+	10.5962i	−2.13966	+	0.488768i
$471$	0.551985	−	0.551985i	0.0254341	−	0.0254341i
$472$	19.6650	+	2.20496i	0.905153	+	0.101491i
$473$	−20.8666	−	20.8666i	−0.959447	−	0.959447i
$474$	−0.924886	−	0.580913i	−0.0424814	−	0.0266822i
$475$	31.6564	+	13.1125i	1.45250	+	0.601644i
$476$	2.47345	+	5.13144i	0.113370	+	0.235199i
$477$	6.95228	+	16.7843i	0.318323	+	0.768500i
$478$	−18.9177	+	13.4279i	−0.865276	+	0.614180i
$479$	−27.9433			−1.27676			−0.638381	−	0.769721i	$-0.720396\pi$
$479$	−27.9433			−1.27676			−0.638381	+	0.769721i	$0.720396\pi$
$480$	−2.99821	−	0.165669i	−0.136849	−	0.00756173i
$481$	10.0452			0.458024
$482$	−0.538059	+	0.381919i	−0.0245079	+	0.0173959i
$483$	−0.845053	−	2.04014i	−0.0384512	−	0.0928295i
$484$	18.7817	−	9.05313i	0.853714	−	0.411506i
$485$	55.7321	+	23.0850i	2.53066	+	1.04823i
$486$	4.49095	+	2.82073i	0.203714	+	0.127951i
$487$	−17.3607	−	17.3607i	−0.786690	−	0.786690i	0.194260	−	0.980950i	$-0.437769\pi$
$487$	−17.3607	−	17.3607i	−0.786690	−	0.786690i	−0.980950	+	0.194260i	$0.937769\pi$
$488$	−11.1340	−	13.9461i	−0.504011	−	0.631310i
$489$	−0.634468	+	0.634468i	−0.0286917	+	0.0286917i
$490$	−5.81054	+	1.32732i	−0.262494	+	0.0599622i
$491$	−8.59305	+	20.7454i	−0.387799	+	0.936229i	0.602607	+	0.798038i	$0.294129\pi$
$491$	−8.59305	+	20.7454i	−0.387799	+	0.936229i	−0.990406	+	0.138191i	$0.955871\pi$
$492$	0.777605	−	0.870772i	0.0350572	−	0.0392574i
$493$	−9.16989	+	3.79829i	−0.412991	+	0.171066i
$494$	5.08657	+	0.863301i	0.228856	+	0.0388418i
$495$		−	52.2649i		−	2.34913i
$496$	−14.2264	−	11.3284i	−0.638784	−	0.508661i
$497$			21.2208i			0.951882i
$498$	0.356906	−	2.10289i	0.0159934	−	0.0942328i
$499$	−8.39760	+	3.47840i	−0.375928	+	0.155715i	−0.562644	−	0.826699i	$-0.690216\pi$
$499$	−8.39760	+	3.47840i	−0.375928	+	0.155715i	0.186716	+	0.982414i	$0.440216\pi$
$500$	32.9360	−	1.86154i	1.47294	−	0.0832507i
$501$	0.944853	−	2.28108i	0.0422129	−	0.101911i
$502$	−1.36015	−	5.95428i	−0.0607066	−	0.265753i
$503$	1.62779	−	1.62779i	0.0725796	−	0.0725796i	−0.669885	−	0.742465i	$-0.733657\pi$
$503$	1.62779	−	1.62779i	0.0725796	−	0.0725796i	0.742465	+	0.669885i	$0.233657\pi$
$504$	−23.0679	+	6.65925i	−1.02753	+	0.296626i
$505$	32.6066	+	32.6066i	1.45097	+	1.45097i
$506$	−19.2659	+	30.6737i	−0.856472	+	1.36361i
$507$	1.55440	+	0.643852i	0.0690331	+	0.0285945i
$508$	−6.63872	+	18.9943i	−0.294546	+	0.842736i
$509$	0.364173	+	0.879191i	0.0161417	+	0.0389694i	0.931745	−	0.363114i	$-0.118286\pi$
$509$	0.364173	+	0.879191i	0.0161417	+	0.0389694i	−0.915603	+	0.402083i	$0.868286\pi$
$510$	0.434517	+	0.612160i	0.0192407	+	0.0271069i
$511$	−8.79943			−0.389264
$512$	15.0504	−	16.8964i	0.665138	−	0.746721i
$513$	−3.06946			−0.135520
$514$	5.23204	+	7.37106i	0.230776	+	0.325124i
$515$	2.43050	+	5.86775i	0.107101	+	0.258564i
$516$	−0.589440	+	1.68647i	−0.0259487	+	0.0742427i
$517$	−37.9767	−	15.7305i	−1.67021	−	0.691825i
$518$	21.6099	−	34.4057i	0.949486	−	1.51170i
$519$	−0.235082	−	0.235082i	−0.0103189	−	0.0103189i
$520$	10.2531	−	2.95986i	0.449628	−	0.129799i
$521$	16.7648	−	16.7648i	0.734477	−	0.734477i	−0.237026	−	0.971503i	$-0.576173\pi$
$521$	16.7648	−	16.7648i	0.734477	−	0.734477i	0.971503	+	0.237026i	$0.0761726\pi$
$522$	−9.31637	−	40.7839i	−0.407767	−	1.78506i
$523$	12.1054	−	29.2251i	0.529333	−	1.27792i	−0.402627	−	0.915364i	$-0.631903\pi$
$523$	12.1054	−	29.2251i	0.529333	−	1.27792i	0.931961	−	0.362560i	$-0.118097\pi$
$524$	−2.04051	+	0.115329i	−0.0891399	+	0.00503818i
$525$	−3.44857	+	1.42845i	−0.150508	+	0.0623425i
$526$	1.24830	−	7.35499i	0.0544285	−	0.320693i
$527$			4.54645i			0.198046i
$528$	−2.02932	−	1.61594i	−0.0883146	−	0.0703246i
$529$		−	7.61976i		−	0.331294i
$530$	−32.1994	−	5.46493i	−1.39865	−	0.237381i
$531$	19.2640	−	7.97941i	0.835986	−	0.346277i
$532$	13.8994	−	15.5647i	0.602616	−	0.674816i
$533$	−1.58777	+	3.83321i	−0.0687738	+	0.166035i
$534$	0.798801	−	0.182472i	0.0345675	−	0.00789636i
$535$	30.9143	−	30.9143i	1.33654	−	1.33654i
$536$	7.18259	+	8.99672i	0.310241	+	0.388599i
$537$	0.500078	+	0.500078i	0.0215800	+	0.0215800i
$538$	−24.3969	−	15.3235i	−1.05183	−	0.660642i
$539$	−4.75708	−	1.97045i	−0.204902	−	0.0848732i
$540$	−5.71928	+	2.75680i	−0.246119	+	0.118634i
$541$	14.7922	+	35.7115i	0.635966	+	1.53536i	0.832009	+	0.554762i	$0.187191\pi$
$541$	14.7922	+	35.7115i	0.635966	+	1.53536i	−0.196043	+	0.980595i	$0.562809\pi$
$542$	−19.9284	+	14.1453i	−0.855998	+	0.607595i
$543$	3.40828			0.146263
$544$	−5.64824	−	0.312099i	−0.242166	−	0.0133811i
$545$	−51.3118			−2.19796
$546$	−0.458321	+	0.325320i	−0.0196143	+	0.0139224i
$547$	−12.9117	−	31.1717i	−0.552066	−	1.33280i	−0.915925	−	0.401350i	$-0.868541\pi$
$547$	−12.9117	−	31.1717i	−0.552066	−	1.33280i	0.363859	−	0.931454i	$-0.381459\pi$
$548$	−14.6930	−	30.4822i	−0.627652	−	1.30213i
$549$	−17.3727	−	7.19600i	−0.741448	−	0.307118i
$550$	51.8497	+	32.5663i	2.21088	+	1.38863i
$551$	25.7099	+	25.7099i	1.09528	+	1.09528i
$552$	2.17922	+	0.244348i	0.0927538	+	0.0104001i
$553$	11.1013	−	11.1013i	0.472076	−	0.472076i
$554$	20.9112	−	4.77681i	0.888433	−	0.202947i
$555$	2.04899	−	4.94669i	0.0869746	−	0.209975i
$556$	−33.9936	−	30.3565i	−1.44165	−	1.28740i
$557$	−34.8898	+	14.4518i	−1.47833	+	0.612344i	−0.968741	−	0.248075i	$-0.920202\pi$
$557$	−34.8898	+	14.4518i	−1.47833	+	0.612344i	−0.509588	+	0.860419i	$0.670202\pi$
$558$	−18.8926	−	3.20648i	−0.799786	−	0.135741i
$559$		−	6.34919i		−	0.268542i
$560$	11.9193	−	41.4851i	0.503683	−	1.75307i
$561$			0.648526i			0.0273808i
$562$	6.42757	−	37.8712i	0.271131	−	1.59750i
$563$	1.10048	−	0.455835i	0.0463798	−	0.0192111i	−0.359373	−	0.933194i	$-0.617009\pi$
$563$	1.10048	−	0.455835i	0.0463798	−	0.0192111i	0.405753	+	0.913983i	$0.367009\pi$
$564$	0.140427	+	2.48455i	0.00591303	+	0.104619i
$565$	−14.6058	+	35.2615i	−0.614470	+	1.48346i
$566$	−1.69922	−	7.43859i	−0.0714235	−	0.312667i
$567$	−17.7710	+	17.7710i	−0.746311	+	0.746311i
$568$	−18.4493	−	10.1836i	−0.774116	−	0.427293i
$569$	−0.753794	−	0.753794i	−0.0316007	−	0.0316007i	0.691130	−	0.722731i	$-0.257113\pi$
$569$	−0.753794	−	0.753794i	−0.0316007	−	0.0316007i	−0.722731	+	0.691130i	$0.757113\pi$
$570$	1.46266	−	2.32874i	0.0612641	−	0.0975403i
$571$	−34.2739	−	14.1967i	−1.43432	−	0.594114i	−0.475905	−	0.879497i	$-0.657879\pi$
$571$	−34.2739	−	14.1967i	−1.43432	−	0.594114i	−0.958414	+	0.285383i	$0.907879\pi$
$572$	8.70308	+	3.04182i	0.363894	+	0.127185i
$573$	0.937231	+	2.26268i	0.0391534	+	0.0945246i
$574$	9.71333	+	13.6844i	0.405426	+	0.571177i
$575$	−51.7585			−2.15848
$576$	5.28045	−	23.2509i	0.220019	−	0.968787i
$577$	10.8775			0.452838			0.226419	−	0.974030i	$-0.427298\pi$
$577$	10.8775			0.452838			0.226419	+	0.974030i	$0.427298\pi$
$578$	0.818572	+	1.15323i	0.0340481	+	0.0479680i
$579$	0.618711	+	1.49370i	0.0257128	+	0.0620761i
$580$	70.9958	+	24.8138i	2.94794	+	1.03034i
$581$	28.3264	+	11.7332i	1.17518	+	0.486774i
$582$	1.67805	−	2.67167i	0.0695575	−	0.110744i
$583$	−19.9509	−	19.9509i	−0.826281	−	0.826281i
$584$	4.22273	−	7.65021i	0.174738	−	0.316568i
$585$	7.95146	−	7.95146i	0.328752	−	0.328752i
$586$	0.502668	+	2.20051i	0.0207650	+	0.0909020i
$587$	−0.894800	+	2.16024i	−0.0369324	+	0.0891626i	−0.941269	−	0.337656i	$-0.890366\pi$
$587$	−0.894800	+	2.16024i	−0.0369324	+	0.0891626i	0.904337	+	0.426819i	$0.140366\pi$
$588$	0.0175903	+	0.311223i	0.000725412	+	0.0128346i
$589$	15.3870	−	6.37350i	0.634010	−	0.262616i
$590$	−6.27231	+	36.9565i	−0.258227	+	1.52147i
$591$			0.822459i			0.0338314i
$592$	19.5420	+	35.2985i	0.803170	+	1.45076i
$593$			22.2471i			0.913577i	0.889575	+	0.456789i	$0.151000\pi$
$593$			22.2471i			0.913577i	−0.889575	+	0.456789i	$0.849000\pi$
$594$	−5.40759	−	0.917785i	−0.221876	−	0.0376572i
$595$	−9.96946	+	4.12948i	−0.408708	+	0.169292i
$596$	14.5547	+	12.9974i	0.596183	+	0.532396i
$597$	0.883800	−	2.13368i	0.0361715	−	0.0873258i
$598$	−7.59769	+	1.73556i	−0.310692	+	0.0709724i
$599$	−12.8974	+	12.8974i	−0.526974	+	0.526974i	−0.919669	−	0.392695i	$-0.871543\pi$
$599$	−12.8974	+	12.8974i	−0.526974	+	0.526974i	0.392695	+	0.919669i	$0.371543\pi$
$600$	0.413036	−	3.68367i	0.0168621	−	0.150385i
$601$	−6.02308	−	6.02308i	−0.245687	−	0.245687i	0.573511	−	0.819198i	$-0.305581\pi$
$601$	−6.02308	−	6.02308i	−0.245687	−	0.245687i	−0.819198	+	0.573511i	$0.805581\pi$
$602$	−21.7465	−	13.6587i	−0.886320	−	0.556689i
$603$	11.2072	+	4.64219i	0.456394	+	0.189045i
$604$	−2.16679	−	4.49524i	−0.0881654	−	0.182909i
$605$	15.1144	+	36.4894i	0.614488	+	1.48351i
$606$	1.96663	−	1.39593i	0.0798890	−	0.0567059i
$607$	38.8697			1.57767			0.788836	−	0.614604i	$-0.210684\pi$
$607$	38.8697			1.57767			0.788836	+	0.614604i	$0.210684\pi$
$608$	6.86179	+	19.5534i	0.278282	+	0.792995i
$609$	−3.96088			−0.160503
$610$	27.5663	−	19.5668i	1.11613	−	0.792236i
$611$	−3.38449	−	8.17088i	−0.136922	−	0.330558i
$612$	−5.36951	+	2.58820i	−0.217050	+	0.104622i
$613$	−11.4495	−	4.74256i	−0.462443	−	0.191550i	0.139283	−	0.990253i	$-0.455520\pi$
$613$	−11.4495	−	4.74256i	−0.462443	−	0.191550i	−0.601726	+	0.798703i	$0.705520\pi$
$614$	−26.0527	−	16.3635i	−1.05140	−	0.660375i
$615$	1.56376	+	1.56376i	0.0630569	+	0.0630569i
$616$	29.1410	−	23.2650i	1.17413	−	0.937372i
$617$	−1.75161	+	1.75161i	−0.0705172	+	0.0705172i	−0.741486	−	0.670969i	$-0.765879\pi$
$617$	−1.75161	+	1.75161i	−0.0705172	+	0.0705172i	0.670969	+	0.741486i	$0.265879\pi$
$618$	0.323827	−	0.0739727i	0.0130262	−	0.00297562i
$619$	−9.56760	+	23.0982i	−0.384554	+	0.928396i	0.606518	+	0.795070i	$0.292566\pi$
$619$	−9.56760	+	23.0982i	−0.384554	+	0.928396i	−0.991072	+	0.133326i	$0.957434\pi$
$620$	22.9461	−	25.6953i	0.921537	−	1.03195i
$621$	4.28363	−	1.77434i	0.171896	−	0.0712018i
$622$	10.5189	+	1.78528i	0.421769	+	0.0715834i
$623$			11.7781i			0.471880i
$624$	−0.0628906	−	0.554580i	−0.00251764	−	0.0222010i
$625$			15.7224i			0.628897i
$626$	7.00420	−	41.2687i	0.279944	−	1.64943i
$627$	2.19487	−	0.909145i	0.0876546	−	0.0363077i
$628$	−11.1253	+	0.628801i	−0.443947	+	0.0250919i
$629$	3.86002	−	9.31891i	0.153909	−	0.371569i
$630$	−10.1287	−	44.3400i	−0.403538	−	1.76655i
$631$	−25.4991	+	25.4991i	−1.01510	+	1.01510i	−0.0152200	+	0.999884i	$0.504845\pi$
$631$	−25.4991	+	25.4991i	−1.01510	+	1.01510i	−0.999884	+	0.0152200i	$0.995155\pi$
$632$	4.32408	+	14.9788i	0.172003	+	0.595825i
$633$	2.13302	+	2.13302i	0.0847801	+	0.0847801i
$634$	−14.5653	+	23.1898i	−0.578463	+	0.920986i
$635$	−35.2141	−	14.5862i	−1.39743	−	0.578834i
$636$	−0.563573	+	1.61246i	−0.0223471	+	0.0639382i
$637$	−0.423952	−	1.02351i	−0.0167976	−	0.0405529i
$638$	37.6067	+	52.9814i	1.48886	+	2.09755i
$639$	−22.2053			−0.878428
$640$	30.3471	+	30.2707i	1.19958	+	1.19656i
$641$	27.1158			1.07101			0.535504	−	0.844532i	$-0.320122\pi$
$641$	27.1158			1.07101			0.535504	+	0.844532i	$0.320122\pi$
$642$	−1.32348	−	1.86456i	−0.0522337	−	0.0735885i
$643$	−5.57006	−	13.4473i	−0.219662	−	0.530310i	0.775181	−	0.631739i	$-0.217659\pi$
$643$	−5.57006	−	13.4473i	−0.219662	−	0.530310i	−0.994843	+	0.101429i	$0.967659\pi$
$644$	−10.4002	+	29.7563i	−0.409824	+	1.17256i
$645$	−3.12660	−	1.29508i	−0.123110	−	0.0509937i
$646$	2.75546	−	4.38705i	0.108412	−	0.172606i
$647$	−2.53044	−	2.53044i	−0.0994819	−	0.0994819i	0.655614	−	0.755096i	$-0.272410\pi$
$647$	−2.53044	−	2.53044i	−0.0994819	−	0.0994819i	−0.755096	+	0.655614i	$0.772410\pi$
$648$	−6.92199	−	23.9781i	−0.271922	−	0.941948i
$649$	−22.8984	+	22.8984i	−0.898841	+	0.898841i
$650$	2.93373	+	12.8428i	0.115070	+	0.503738i
$651$	−0.694313	+	1.67622i	−0.0272123	+	0.0656962i
$652$	12.7878	−	0.722763i	0.500807	−	0.0283056i
$653$	35.4115	−	14.6679i	1.38576	−	0.574000i	0.439743	−	0.898123i	$-0.355069\pi$
$653$	35.4115	−	14.6679i	1.38576	−	0.574000i	0.946015	+	0.324124i	$0.105069\pi$
$654$	−0.449046	+	2.64578i	−0.0175591	+	0.103458i
$655$		−	3.87152i		−	0.151273i
$656$	−16.5585	+	1.87777i	−0.646501	+	0.0733146i
$657$		−	9.20767i		−	0.359225i
$658$	−35.2668	−	5.98554i	−1.37484	−	0.233341i
$659$	11.6513	−	4.82614i	0.453871	−	0.188000i	−0.144023	−	0.989574i	$-0.546004\pi$
$659$	11.6513	−	4.82614i	0.453871	−	0.188000i	0.597895	+	0.801575i	$0.296004\pi$
$660$	3.27313	−	3.66529i	0.127406	−	0.142671i
$661$	15.5350	−	37.5048i	0.604242	−	1.45877i	−0.264935	−	0.964266i	$-0.585350\pi$
$661$	15.5350	−	37.5048i	0.604242	−	1.45877i	0.869177	−	0.494502i	$-0.164650\pi$
$662$	−32.6976	+	7.46921i	−1.27083	+	0.290299i
$663$	−0.0986652	+	0.0986652i	−0.00383184	+	0.00383184i
$664$	−23.7942	+	18.9963i	−0.923395	+	0.737199i
$665$	27.9516	+	27.9516i	1.08392	+	1.08392i
$666$	36.0020	+	22.6125i	1.39505	+	0.876216i
$667$	−50.7417	−	21.0179i	−1.96473	−	0.813816i
$668$	−31.7483	+	15.3033i	−1.22838	+	0.592102i
$669$	−1.18017	−	2.84918i	−0.0456279	−	0.110156i
$670$	−17.7832	+	12.6227i	−0.687025	+	0.487656i
$671$	29.2039			1.12740
$672$	−2.03477	−	0.977640i	−0.0784931	−	0.0377133i
$673$	15.5570			0.599677			0.299839	−	0.953990i	$-0.403067\pi$
$673$	15.5570			0.599677			0.299839	+	0.953990i	$0.403067\pi$
$674$	−2.29928	+	1.63205i	−0.0885650	+	0.0628642i
$675$	−2.99928	−	7.24090i	−0.115442	−	0.278702i
$676$	−10.4281	−	21.6343i	−0.401082	−	0.832088i
$677$	34.8053	+	14.4168i	1.33768	+	0.554083i	0.932835	−	0.360304i	$-0.117327\pi$
$677$	34.8053	+	14.4168i	1.33768	+	0.554083i	0.404841	+	0.914387i	$0.367327\pi$
$678$	1.69036	+	1.06170i	0.0649177	+	0.0407742i
$679$	32.0678	+	32.0678i	1.23065	+	1.23065i
$680$	1.19404	−	10.6491i	0.0457895	−	0.408374i
$681$	0.0207415	−	0.0207415i	0.000794815	−	0.000794815i
$682$	29.0136	−	6.62765i	1.11099	−	0.253786i
$683$	18.0920	−	43.6778i	0.692269	−	1.67129i	−0.0478885	−	0.998853i	$-0.515249\pi$
$683$	18.0920	−	43.6778i	0.692269	−	1.67129i	0.740158	−	0.672433i	$-0.234751\pi$
$684$	16.2868	+	14.5442i	0.622742	+	0.556113i
$685$	59.2212	−	24.5302i	2.26273	−	0.937252i
$686$	23.3809	+	3.96824i	0.892686	+	0.151508i
$687$		−	0.748873i		−	0.0285713i
$688$	22.3107	−	12.3517i	0.850588	−	0.470903i
$689$		−	6.07056i		−	0.231270i
$690$	−0.695082	+	4.09542i	−0.0264613	+	0.155910i
$691$	16.7332	−	6.93112i	0.636561	−	0.263672i	−0.0409770	−	0.999160i	$-0.513047\pi$
$691$	16.7332	−	6.93112i	0.636561	−	0.263672i	0.677538	+	0.735488i	$0.263047\pi$
$692$	0.267796	+	4.73809i	0.0101801	+	0.180115i
$693$	15.0364	−	36.3011i	0.571186	−	1.37896i
$694$	8.29230	+	36.3008i	0.314771	+	1.37796i
$695$	61.0468	−	61.0468i	2.31564	−	2.31564i
$696$	1.90077	−	3.44358i	0.0720486	−	0.130529i
$697$	2.94592	+	2.94592i	0.111585	+	0.111585i
$698$	−3.16762	+	5.04325i	−0.119896	+	0.190890i
$699$	−1.27755	−	0.529179i	−0.0483214	−	0.0200154i
$700$	50.2989	+	17.5800i	1.90112	+	0.664463i
$701$	−13.6079	−	32.8523i	−0.513963	−	1.24082i	−0.941560	−	0.336846i	$-0.890640\pi$
$701$	−13.6079	−	32.8523i	−0.513963	−	1.24082i	0.427597	−	0.903970i	$-0.359360\pi$
$702$	−0.683068	−	0.962328i	−0.0257808	−	0.0363207i
$703$	−36.9501			−1.39360
$704$	6.24211	+	36.4997i	0.235258	+	1.37563i
$705$	−4.71402			−0.177540
$706$	−6.77253	−	9.54135i	−0.254888	−	0.359094i
$707$	13.2664	+	32.0280i	0.498935	+	1.20454i
$708$	1.85068	+	0.646835i	0.0695530	+	0.0243095i
$709$	45.2333	+	18.7362i	1.69877	+	0.703654i	0.999932	−	0.0116250i	$-0.00370045\pi$
$709$	45.2333	+	18.7362i	1.69877	+	0.703654i	0.698839	+	0.715279i	$0.253700\pi$
$710$	21.2322	−	33.8044i	0.796832	−	1.26866i
$711$	11.6163	+	11.6163i	0.435647	+	0.435647i
$712$	−10.2399	−	5.65216i	−0.383755	−	0.211824i
$713$	−17.7893	+	17.7893i	−0.666214	+	0.666214i
$714$	0.125682	+	0.550190i	0.00470351	+	0.0205904i
$715$	−6.68330	+	16.1349i	−0.249941	+	0.603411i
$716$	−0.569670	−	10.0791i	−0.0212896	−	0.376674i
$717$	−2.12342	+	0.879550i	−0.0793006	+	0.0328474i
$718$	2.64728	−	15.5978i	0.0987955	−	0.582103i
$719$			32.5717i			1.21472i	0.794427	+	0.607359i	$0.207771\pi$
$719$			32.5717i			1.21472i	−0.794427	+	0.607359i	$0.792229\pi$
$720$	43.4097	+	12.4723i	1.61779	+	0.464815i
$721$			4.77474i			0.177821i
$722$	7.78093	+	1.32059i	0.289576	+	0.0491474i
$723$	−0.0603945	+	0.0250162i	−0.00224610	+	0.000930363i
$724$	−36.2883	−	32.4058i	−1.34865	−	1.20435i
$725$	−35.5279	+	85.7718i	−1.31947	+	3.18549i
$726$	2.01376	−	0.460010i	0.0747378	−	0.0170726i
$727$	22.8883	−	22.8883i	0.848882	−	0.848882i	−0.141112	−	0.989994i	$-0.545068\pi$
$727$	22.8883	−	22.8883i	0.848882	−	0.848882i	0.989994	+	0.141112i	$0.0450677\pi$
$728$	7.97293	+	0.893974i	0.295496	+	0.0331329i
$729$	−18.3464	−	18.3464i	−0.679496	−	0.679496i
$730$	14.0174	+	8.80418i	0.518806	+	0.325857i
$731$	−5.89010	−	2.43976i	−0.217853	−	0.0902378i
$732$	−0.767675	−	1.59263i	−0.0283741	−	0.0588652i
$733$	−7.36385	−	17.7779i	−0.271990	−	0.656642i	0.727578	−	0.686025i	$-0.240646\pi$
$733$	−7.36385	−	17.7779i	−0.271990	−	0.656642i	−0.999568	+	0.0293825i	$0.990646\pi$
$734$	1.03523	−	0.734814i	0.0382110	−	0.0271225i
$735$	−0.590494			−0.0217807
$736$	−20.8792	−	23.3215i	−0.769616	−	0.859642i
$737$	−18.8396			−0.693966
$738$	−14.3193	+	10.1640i	−0.527101	+	0.374141i
$739$	−13.2594	−	32.0110i	−0.487754	−	1.17754i	−0.955847	−	0.293864i	$-0.905059\pi$
$739$	−13.2594	−	32.0110i	−0.487754	−	1.17754i	0.468093	−	0.883679i	$-0.344941\pi$
$740$	−68.8486	+	33.1863i	−2.53093	+	1.21995i
$741$	0.472237	+	0.195607i	0.0173481	+	0.00718581i
$742$	−20.7921	−	13.0593i	−0.763303	−	0.479423i
$743$	−6.56863	−	6.56863i	−0.240980	−	0.240980i	0.576276	−	0.817255i	$-0.304505\pi$
$743$	−6.56863	−	6.56863i	−0.240980	−	0.240980i	−0.817255	+	0.576276i	$0.804505\pi$
$744$	−1.12411	−	1.40803i	−0.0412119	−	0.0516209i
$745$	−26.1378	+	26.1378i	−0.957614	+	0.957614i
$746$	−20.1283	+	4.59796i	−0.736948	+	0.168343i
$747$	−12.2775	+	29.6405i	−0.449210	+	1.08449i
$748$	6.16615	−	6.90493i	0.225457	−	0.252469i
$749$	30.3657	−	12.5779i	1.10954	−	0.459586i
$750$	3.22218	+	0.546874i	0.117658	+	0.0199690i
$751$			47.2596i			1.72453i	0.506461	+	0.862263i	$0.330954\pi$
$751$			47.2596i			1.72453i	−0.506461	+	0.862263i	$0.669046\pi$
$752$	22.1279	−	27.7885i	0.806920	−	1.01334i
$753$		−	0.605101i		−	0.0220511i
$754$	−2.33908	+	13.7819i	−0.0851843	+	0.501906i
$755$	8.73343	−	3.61751i	0.317842	−	0.131655i
$756$	−4.76550	+	0.269346i	−0.173320	+	0.00979601i
$757$	3.35240	−	8.09340i	0.121845	−	0.294160i	−0.851175	−	0.524883i	$-0.824109\pi$
$757$	3.35240	−	8.09340i	0.121845	−	0.294160i	0.973019	+	0.230723i	$0.0741092\pi$
$758$	3.18014	+	13.9215i	0.115508	+	0.505653i
$759$	−2.53754	+	2.53754i	−0.0921069	+	0.0921069i
$760$	−37.7147	+	10.8875i	−1.36806	+	0.394930i
$761$	−14.2680	−	14.2680i	−0.517213	−	0.517213i	0.399514	−	0.916727i	$-0.369179\pi$
$761$	−14.2680	−	14.2680i	−0.517213	−	0.517213i	−0.916727	+	0.399514i	$0.869179\pi$
$762$	−1.06027	+	1.68809i	−0.0384096	+	0.0611529i
$763$	−35.6391	−	14.7622i	−1.29022	−	0.534428i
$764$	11.5346	−	33.0021i	0.417307	−	1.19397i
$765$	−4.32106	−	10.4320i	−0.156228	−	0.377169i
$766$	12.2212	+	17.2176i	0.441570	+	0.622097i
$767$	−6.96742			−0.251579
$768$	1.82642	−	1.29987i	0.0659052	−	0.0469050i
$769$	−6.26029			−0.225752			−0.112876	−	0.993609i	$-0.536006\pi$
$769$	−6.26029			−0.225752			−0.112876	+	0.993609i	$0.536006\pi$
$770$	40.8858	+	57.6011i	1.47342	+	2.07580i
$771$	0.342706	+	0.827366i	0.0123423	+	0.0297969i
$772$	7.61455	−	21.7863i	0.274053	−	0.784105i
$773$	−34.4716	−	14.2786i	−1.23986	−	0.513565i	−0.336187	−	0.941795i	$-0.609137\pi$
$773$	−34.4716	−	14.2786i	−1.23986	−	0.513565i	−0.903670	+	0.428230i	$0.859137\pi$
$774$	14.2924	−	22.7554i	0.513731	−	0.817924i
$775$	30.0703	+	30.0703i	1.08016	+	1.08016i
$776$	−43.2685	+	12.4908i	−1.55325	+	0.448392i
$777$	2.84628	−	2.84628i	0.102110	−	0.102110i
$778$	3.91089	+	17.1205i	0.140212	+	0.613801i
$779$	5.84039	−	14.0999i	0.209254	−	0.505183i
$780$	1.05560	−	0.0596622i	0.0377964	−	0.00213625i
$781$	31.8611	−	13.1973i	1.14008	−	0.472237i
$782$	−1.30944	+	7.71524i	−0.0468256	+	0.275896i
$783$		−	8.31658i		−	0.297210i
$784$	2.77181	−	3.48087i	0.0989931	−	0.124317i
$785$		−	21.1084i		−	0.753390i
$786$	−0.199626	−	0.0338808i	−0.00712042	−	0.00120849i
$787$	−16.9126	+	7.00542i	−0.602868	+	0.249716i	−0.663176	−	0.748464i	$-0.730792\pi$
$787$	−16.9126	+	7.00542i	−0.602868	+	0.249716i	0.0603077	+	0.998180i	$0.480792\pi$
$788$	7.81990	−	8.75682i	0.278572	−	0.311949i
$789$	0.282841	−	0.682838i	0.0100694	−	0.0243097i
$790$	−28.7915	+	6.57693i	−1.02436	+	0.233997i
$791$	−20.2892	+	20.2892i	−0.721399	+	0.721399i
$792$	24.3443	+	30.4930i	0.865037	+	1.08352i
$793$	4.44301	+	4.44301i	0.157776	+	0.157776i
$794$	−23.0145	−	14.4552i	−0.816754	−	0.512996i
$795$	−2.98939	−	1.23825i	−0.106023	−	0.0439160i
$796$	−29.6969	+	14.3144i	−1.05258	+	0.507361i
$797$	11.4607	+	27.6686i	0.405960	+	0.980073i	0.986190	+	0.165621i	$0.0529627\pi$
$797$	11.4607	+	27.6686i	0.405960	+	0.980073i	−0.580230	+	0.814453i	$0.697037\pi$
$798$	1.68587	−	1.19665i	0.0596793	−	0.0423609i
$799$	−8.88060			−0.314173
$800$	−39.4218	+	35.2934i	−1.39377	+	1.24781i
$801$	−12.3245			−0.435466
$802$	7.35219	−	5.21864i	0.259615	−	0.184277i
$803$	5.47241	+	13.2116i	0.193117	+	0.466226i
$804$	0.495233	+	1.02741i	0.0174655	+	0.0362341i
$805$	−55.1661	−	22.8505i	−1.94435	−	0.805376i
$806$	5.42237	+	3.40574i	0.190995	+	0.119962i
$807$	−2.01828	−	2.01828i	−0.0710470	−	0.0710470i
$808$	−34.2114	−	3.83600i	−1.20355	−	0.134950i
$809$	−25.5887	+	25.5887i	−0.899651	+	0.899651i	−0.995405	−	0.0957544i	$-0.969474\pi$
$809$	−25.5887	+	25.5887i	−0.899651	+	0.899651i	0.0957544	+	0.995405i	$0.469474\pi$
$810$	46.0895	−	10.5284i	1.61942	−	0.369929i
$811$	1.76206	−	4.25399i	0.0618743	−	0.149378i	−0.889918	−	0.456120i	$-0.849239\pi$
$811$	1.76206	−	4.25399i	0.0618743	−	0.149378i	0.951793	+	0.306742i	$0.0992389\pi$
$812$	42.1720	+	37.6599i	1.47995	+	1.32160i
$813$	−2.23687	+	0.926541i	−0.0784503	+	0.0324952i
$814$	−65.0965	−	11.0483i	−2.28163	−	0.387242i
$815$			24.2626i			0.849883i
$816$	−0.538647	−	0.154762i	−0.0188564	−	0.00541774i
$817$			23.3547i			0.817076i
$818$	−0.774413	+	4.56284i	−0.0270767	+	0.159536i
$819$	7.81036	−	3.23516i	0.272916	−	0.113046i
$820$	−1.78138	−	31.5177i	−0.0622084	−	1.10065i
$821$	−0.977668	+	2.36030i	−0.0341208	+	0.0823750i	−0.940021	−	0.341115i	$-0.889195\pi$
$821$	−0.977668	+	2.36030i	−0.0341208	+	0.0823750i	0.905901	+	0.423490i	$0.139195\pi$
$822$	−0.746582	−	3.26828i	−0.0260400	−	0.113994i
$823$	22.7572	−	22.7572i	0.793266	−	0.793266i	−0.188757	−	0.982024i	$-0.560446\pi$
$823$	22.7572	−	22.7572i	0.793266	−	0.793266i	0.982024	+	0.188757i	$0.0604460\pi$
$824$	−4.15115	−	2.29133i	−0.144612	−	0.0798224i
$825$	4.28937	+	4.28937i	0.149337	+	0.149337i
$826$	−14.9887	+	23.8639i	−0.521524	+	0.830333i
$827$	16.8407	+	6.97563i	0.585607	+	0.242567i	0.655760	−	0.754970i	$-0.272348\pi$
$827$	16.8407	+	6.97563i	0.585607	+	0.242567i	−0.0701522	+	0.997536i	$0.522348\pi$
$828$	−31.1368	−	10.8827i	−1.08208	−	0.378198i
$829$	15.0210	+	36.2640i	0.521702	+	1.25950i	0.936845	+	0.349744i	$0.113731\pi$
$829$	15.0210	+	36.2640i	0.521702	+	1.25950i	−0.415144	+	0.909756i	$0.636269\pi$
$830$	−33.3840	−	47.0324i	−1.15878	−	1.63252i
$831$	2.12509			0.0737187
$832$	−4.60332	+	6.50264i	−0.159591	+	0.225438i
$833$	−1.11241			−0.0385428
$834$	−2.61350	−	3.68198i	−0.0904980	−	0.127496i
$835$	−25.5492	−	61.6812i	−0.884166	−	2.13457i
$836$	−32.0131	−	11.1889i	−1.10720	−	0.386978i
$837$	−3.51952	−	1.45783i	−0.121653	−	0.0503901i
$838$	−23.9505	+	38.1323i	−0.827358	+	1.31726i
$839$	2.87565	+	2.87565i	0.0992783	+	0.0992783i	0.755001	−	0.655723i	$-0.227636\pi$
$839$	2.87565	+	2.87565i	0.0992783	+	0.0992783i	−0.655723	+	0.755001i	$0.727636\pi$
$840$	2.06651	−	3.74384i	0.0713014	−	0.129175i
$841$	−49.1537	+	49.1537i	−1.69496	+	1.69496i
$842$	2.64118	+	11.5622i	0.0910211	+	0.398459i
$843$	1.45636	−	3.51597i	0.0501597	−	0.121096i
$844$	−2.42986	−	42.9912i	−0.0836393	−	1.47982i
$845$	42.0315	−	17.4100i	1.44593	−	0.598922i
$846$	6.26323	−	36.9029i	0.215334	−	1.26875i
$847$			29.6924i			1.02024i
$848$	21.3316	−	11.8096i	0.732531	−	0.405544i
$849$		−	0.755943i		−	0.0259439i
$850$	13.0415	+	2.21343i	0.447321	+	0.0759201i
$851$	51.5663	−	21.3595i	1.76767	−	0.732193i
$852$	−1.55724	−	1.39062i	−0.0533501	−	0.0476420i
$853$	6.93596	−	16.7449i	0.237483	−	0.573334i	−0.759538	−	0.650462i	$-0.774575\pi$
$853$	6.93596	−	16.7449i	0.237483	−	0.573334i	0.997021	+	0.0771284i	$0.0245751\pi$
$854$	24.7757	−	5.65959i	0.847807	−	0.193667i
$855$	−29.2484	+	29.2484i	−1.00027	+	1.00027i
$856$	−3.63690	+	32.4358i	−0.124307	+	1.10863i
$857$	8.07275	+	8.07275i	0.275760	+	0.275760i	0.831414	−	0.555654i	$-0.187532\pi$
$857$	8.07275	+	8.07275i	0.275760	+	0.275760i	−0.555654	+	0.831414i	$0.687532\pi$
$858$	0.773471	+	0.485810i	0.0264059	+	0.0165853i
$859$	−0.652447	−	0.270252i	−0.0222612	−	0.00922089i	0.371525	−	0.928423i	$-0.378835\pi$
$859$	−0.652447	−	0.270252i	−0.0222612	−	0.00922089i	−0.393786	+	0.919202i	$0.628835\pi$
$860$	20.9757	+	43.5164i	0.715265	+	1.48390i
$861$	0.636237	+	1.53601i	0.0216829	+	0.0523471i
$862$	−1.90323	+	1.35093i	−0.0648241	+	0.0460127i
$863$	−15.2396			−0.518761			−0.259381	−	0.965775i	$-0.583518\pi$
$863$	−15.2396			−0.518761			−0.259381	+	0.965775i	$0.583518\pi$
$864$	2.05273	−	4.27237i	0.0698353	−	0.145349i
$865$	−8.98973			−0.305660
$866$	−13.6234	+	9.67003i	−0.462943	+	0.328601i
$867$	0.0536177	+	0.129444i	0.00182095	+	0.00439617i
$868$	23.3299	−	11.2454i	0.791867	−	0.381694i
$869$	−23.5716	−	9.76367i	−0.799611	−	0.331210i
$870$	6.30963	+	3.96302i	0.213917	+	0.134359i
$871$	−2.86622	−	2.86622i	−0.0971180	−	0.0971180i
$872$	29.9370	−	23.9004i	1.01379	−	0.809369i
$873$	−33.5555	+	33.5555i	−1.13568	+	1.13568i
$874$	27.9471	−	6.38403i	0.945324	−	0.215943i
$875$	−17.9783	+	43.4034i	−0.607777	+	1.46730i
$876$	0.576638	−	0.645726i	0.0194828	−	0.0218170i
$877$	−6.56412	+	2.71895i	−0.221655	+	0.0918123i	−0.490747	−	0.871302i	$-0.663276\pi$
$877$	−6.56412	+	2.71895i	−0.221655	+	0.0918123i	0.269093	+	0.963114i	$0.413276\pi$
$878$	45.9589	+	7.80022i	1.55104	+	0.263245i
$879$			0.223625i			0.00754270i
$880$	−69.6988	+	7.90399i	−2.34955	+	0.266444i
$881$		−	31.0636i		−	1.04656i	−0.852161	−	0.523280i	$-0.824708\pi$
$881$		−	31.0636i		−	1.04656i	0.852161	−	0.523280i	$-0.175292\pi$
$882$	0.784552	−	4.62258i	0.0264172	−	0.155650i
$883$	−0.451526	+	0.187028i	−0.0151951	+	0.00629400i	−0.390268	−	0.920701i	$-0.627618\pi$
$883$	−0.451526	+	0.187028i	−0.0151951	+	0.00629400i	0.375073	+	0.926995i	$0.377618\pi$
$884$	1.98860	−	0.112396i	0.0668840	−	0.00378028i
$885$	−1.42118	+	3.43104i	−0.0477725	+	0.115333i
$886$	−6.19368	−	27.1138i	−0.208081	−	0.910906i
$887$	10.8780	−	10.8780i	0.365248	−	0.365248i	−0.500493	−	0.865741i	$-0.666848\pi$
$887$	10.8780	−	10.8780i	0.365248	−	0.365248i	0.865741	+	0.500493i	$0.166848\pi$
$888$	1.10866	+	3.84044i	0.0372042	+	0.128877i
$889$	−20.2619	−	20.2619i	−0.679563	−	0.679563i
$890$	11.7845	−	18.7624i	0.395017	−	0.628917i
$891$	37.7334	+	15.6297i	1.26412	+	0.523614i
$892$	−14.5245	+	41.5565i	−0.486315	+	1.39141i
$893$	12.4494	+	30.0555i	0.416603	+	1.00577i
$894$	1.11899	+	1.57647i	0.0374248	+	0.0527252i
$895$	19.1234			0.639225
$896$	12.3691	+	29.7556i	0.413223	+	0.994064i
$897$	−0.772111			−0.0257800
$898$	2.44957	+	3.45102i	0.0817431	+	0.115162i
$899$	17.2687	+	41.6904i	0.575945	+	1.39045i
$900$	−18.3956	+	52.6325i	−0.613188	+	1.75442i
$901$	−5.63162	−	2.33269i	−0.187616	−	0.0777132i
$902$	14.5052	−	23.0941i	0.482970	−	0.768949i
$903$	−1.79902	−	1.79902i	−0.0598676	−	0.0598676i
$904$	−7.90285	−	27.3758i	−0.262845	−	0.910507i
$905$	65.1678	−	65.1678i	2.16625	−	2.16625i
$906$	−0.110099	−	0.481977i	−0.00365781	−	0.0160126i
$907$	8.06448	−	19.4694i	0.267777	−	0.646470i	−0.731601	−	0.681733i	$-0.761227\pi$
$907$	8.06448	−	19.4694i	0.267777	−	0.646470i	0.999378	+	0.0352627i	$0.0112268\pi$
$908$	−0.418046	+	0.0236279i	−0.0138733	+	0.000784120i
$909$	−33.5139	+	13.8819i	−1.11159	+	0.460434i
$910$	−2.54304	+	14.9836i	−0.0843008	+	0.496700i
$911$			24.2557i			0.803626i	0.915722	+	0.401813i	$0.131620\pi$
$911$			24.2557i			0.803626i	−0.915722	+	0.401813i	$0.868380\pi$
$912$	0.231335	+	2.03995i	0.00766026	+	0.0675495i
$913$		−	49.8264i		−	1.64901i
$914$	3.79120	+	0.643448i	0.125402	+	0.0212834i
$915$	3.09418	−	1.28165i	0.102291	−	0.0423701i
$916$	−7.12025	+	7.97334i	−0.235260	+	0.263447i
$917$	1.11382	−	2.68900i	0.0367816	−	0.0887986i
$918$	−1.15522	+	0.263891i	−0.0381280	+	0.00870970i
$919$	−35.7803	+	35.7803i	−1.18028	+	1.18028i	−0.200611	+	0.979671i	$0.564293\pi$
$919$	−35.7803	+	35.7803i	−1.18028	+	1.18028i	−0.979671	+	0.200611i	$0.935707\pi$
$920$	46.3397	−	36.9956i	1.52777	−	1.21971i
$921$	−2.15526	−	2.15526i	−0.0710183	−	0.0710183i
$922$	26.1892	+	16.4492i	0.862495	+	0.541725i
$923$	6.85508	+	2.83947i	0.225638	+	0.0934622i
$924$	3.32787	−	1.60410i	0.109479	−	0.0527709i
$925$	−36.1052	−	87.1658i	−1.18713	−	2.86599i
$926$	20.3123	−	14.4178i	0.667504	−	0.473800i
$927$	−4.99626			−0.164099
$928$	−52.9792	+	18.5917i	−1.73913	+	0.610304i
$929$	−55.5661			−1.82306			−0.911532	−	0.411229i	$-0.865100\pi$
$929$	−55.5661			−1.82306			−0.911532	+	0.411229i	$0.865100\pi$
$930$	2.78316	−	1.97551i	0.0912633	−	0.0647795i
$931$	1.55945	+	3.76485i	0.0511089	+	0.123388i
$932$	8.57082	+	17.7811i	0.280746	+	0.582440i
$933$	0.976574	+	0.404510i	0.0319716	+	0.0132431i
$934$	45.6112	+	28.6480i	1.49244	+	0.937390i
$935$	12.4001	+	12.4001i	0.405527	+	0.405527i
$936$	−0.935448	+	8.34282i	−0.0305761	+	0.272694i
$937$	−1.77380	+	1.77380i	−0.0579475	+	0.0579475i	−0.735487	−	0.677539i	$-0.763046\pi$
$937$	−1.77380	+	1.77380i	−0.0579475	+	0.0579475i	0.677539	+	0.735487i	$0.263046\pi$
$938$	−15.9830	+	3.65104i	−0.521863	+	0.119211i
$939$	1.58701	−	3.83139i	0.0517902	−	0.125033i
$940$	50.1907	+	44.8207i	1.63704	+	1.46189i
$941$	20.2165	−	8.37397i	0.659041	−	0.272984i	−0.0279942	−	0.999608i	$-0.508912\pi$
$941$	20.2165	−	8.37397i	0.659041	−	0.272984i	0.687035	+	0.726625i	$0.258912\pi$
$942$	−1.08840	−	0.184726i	−0.0354621	−	0.00601869i
$943$			23.0535i			0.750725i
$944$	−13.5544	−	24.4831i	−0.441157	−	0.796858i
$945$		−	9.04175i		−	0.294128i
$946$	−6.98316	+	41.1448i	−0.227042	+	1.33773i
$947$	33.6839	−	13.9523i	1.09458	−	0.453389i	0.238978	−	0.971025i	$-0.423188\pi$
$947$	33.6839	−	13.9523i	1.09458	−	0.453389i	0.855601	+	0.517636i	$0.173188\pi$
$948$	0.0871608	+	1.54213i	0.00283085	+	0.0500859i
$949$	−1.17742	+	2.84253i	−0.0382206	+	0.0922726i
$950$	−10.7913	−	47.2407i	−0.350117	−	1.53269i
$951$	−1.91842	+	1.91842i	−0.0622092	+	0.0622092i
$952$	3.89304	−	7.05291i	0.126174	−	0.228586i
$953$	−5.87142	−	5.87142i	−0.190194	−	0.190194i	0.605586	−	0.795780i	$-0.292939\pi$
$953$	−5.87142	−	5.87142i	−0.190194	−	0.190194i	−0.795780	+	0.605586i	$0.792939\pi$
$954$	13.6652	−	21.7567i	0.442427	−	0.704401i
$955$	61.1836	+	25.3431i	1.97986	+	0.820083i
$956$	30.9710	+	10.8247i	1.00167	+	0.350096i
$957$	2.46329	+	5.94691i	0.0796269	+	0.192236i
$958$	22.8736	+	32.2250i	0.739013	+	1.04114i
$959$	48.1899			1.55613
$960$	2.26320	+	3.59324i	0.0730444	+	0.115971i
$961$	−10.3298			−0.333219
$962$	−8.22276	−	11.5845i	−0.265113	−	0.373499i
$963$	13.1614	+	31.7745i	0.424121	+	1.02392i
$964$	0.880880	+	0.307877i	0.0283712	+	0.00991607i
$965$	40.3902	+	16.7302i	1.30021	+	0.538564i
$966$	−1.66101	+	2.64454i	−0.0534422	+	0.0850867i
$967$	10.9472	+	10.9472i	0.352037	+	0.352037i	0.860867	−	0.508830i	$-0.169922\pi$
$967$	10.9472	+	10.9472i	0.352037	+	0.352037i	−0.508830	+	0.860867i	$0.669922\pi$
$968$	−25.8145	−	14.2490i	−0.829710	−	0.457980i
$969$	0.362927	−	0.362927i	0.0116589	−	0.0116589i
$970$	−18.9984	−	83.1686i	−0.610003	−	2.67038i
$971$	−5.59003	+	13.4955i	−0.179393	+	0.433092i	−0.987840	−	0.155477i	$-0.950309\pi$
$971$	−5.59003	+	13.4955i	−0.179393	+	0.433092i	0.808447	+	0.588569i	$0.200309\pi$
$972$	−0.423225	−	7.48807i	−0.0135750	−	0.240180i
$973$	59.9635	−	24.8377i	1.92234	−	0.796260i
$974$	−5.80990	+	34.2319i	−0.186161	+	1.09686i
$975$			1.30515i			0.0417982i
$976$	−6.96910	+	24.2559i	−0.223075	+	0.776412i
$977$			33.4266i			1.06941i	0.845039	+	0.534705i	$0.179577\pi$
$977$			33.4266i			1.06941i	−0.845039	+	0.534705i	$0.820423\pi$
$978$	1.25105	+	0.212330i	0.0400040	+	0.00678955i
$979$	17.6838	−	7.32487i	0.565176	−	0.234104i
$980$	6.28705	+	5.61439i	0.200833	+	0.179345i
$981$	15.4471	−	37.2925i	0.493187	−	1.19066i
$982$	30.9583	−	7.07189i	0.987919	−	0.225673i
$983$	20.8793	−	20.8793i	0.665947	−	0.665947i	−0.290828	−	0.956775i	$-0.593931\pi$
$983$	20.8793	−	20.8793i	0.665947	−	0.665947i	0.956775	+	0.290828i	$0.0939309\pi$
$984$	−1.64073	−	0.183968i	−0.0523044	−	0.00586469i
$985$	15.7258	+	15.7258i	0.501065	+	0.501065i
$986$	11.8865	+	7.46581i	0.378544	+	0.237760i
$987$	−3.27417	−	1.35621i	−0.104218	−	0.0431685i
$988$	−3.16814	−	6.57266i	−0.100792	−	0.209104i
$989$	−13.5004	−	32.5930i	−0.429289	−	1.03640i
$990$	−60.2735	+	42.7826i	−1.91562	+	1.35972i
$991$	32.1135			1.02012			0.510059	−	0.860139i	$-0.329623\pi$
$991$	32.1135			1.02012			0.510059	+	0.860139i	$0.329623\pi$
$992$	−1.41894	+	25.6794i	−0.0450515	+	0.815323i
$993$	−3.32288			−0.105448
$994$	24.4724	−	17.3708i	0.776219	−	0.550967i
$995$	−23.8983	−	57.6956i	−0.757627	−	1.82907i
$996$	−2.71727	+	1.30977i	−0.0861000	+	0.0415018i
$997$	9.00842	+	3.73141i	0.285299	+	0.118175i	0.520744	−	0.853713i	$-0.325655\pi$
$997$	9.00842	+	3.73141i	0.285299	+	0.118175i	−0.235445	+	0.971888i	$0.575655\pi$
$998$	10.8854	+	6.83704i	0.344572	+	0.216423i
$999$	5.97628	+	5.97628i	0.189081	+	0.189081i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	544.2.bd.b.69.10	✓	128
32.13	even	8	inner	544.2.bd.b.205.10	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.2.bd.b.69.10	✓	128	1.1	even	1	trivial
544.2.bd.b.205.10	yes	128	32.13	even	8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	544.bd (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.818572 - 1.15323i) q^{2} +(-0.0536177 - 0.129444i) q^{3} +(-0.659879 + 1.88800i) q^{4} +(-3.50023 - 1.44984i) q^{5} +(-0.105389 + 0.167793i) q^{6} +(-2.01400 - 2.01400i) q^{7} +(2.71746 - 0.784477i) q^{8} +(2.10744 - 2.10744i) q^{9} +(1.19319 + 5.22337i) q^{10} +(-1.77133 + 4.27636i) q^{11} +(0.279773 - 0.0158127i) q^{12} +(-0.920081 + 0.381110i) q^{13} +(-0.674001 + 3.97121i) q^{14} +0.530822i q^{15} +(-3.12912 - 2.49171i) q^{16} +1.00000i q^{17} +(-4.15545 - 0.705270i) q^{18} +(3.38440 - 1.40186i) q^{19} +(5.04703 - 5.65173i) q^{20} +(-0.152715 + 0.368688i) q^{21} +(6.38159 - 1.45776i) q^{22} +(-3.91278 + 3.91278i) q^{23} +(-0.247250 - 0.309699i) q^{24} +(6.61402 + 6.61402i) q^{25} +(1.19266 + 0.749099i) q^{26} +(-0.774126 - 0.320653i) q^{27} +(5.13144 - 2.47345i) q^{28} +(3.79829 + 9.16989i) q^{29} +(0.612160 - 0.434517i) q^{30} +4.54645 q^{31} +(-0.312099 + 5.64824i) q^{32} +0.648526 q^{33} +(1.15323 - 0.818572i) q^{34} +(4.12948 + 9.96946i) q^{35} +(2.58820 + 5.36951i) q^{36} +(-9.31891 - 3.86002i) q^{37} +(-4.38705 - 2.75546i) q^{38} +(0.0986652 + 0.0986652i) q^{39} +(-10.6491 - 1.19404i) q^{40} +(2.94592 - 2.94592i) q^{41} +(0.550190 - 0.125682i) q^{42} +(-2.43976 + 5.89010i) q^{43} +(-6.90493 - 6.16615i) q^{44} +(-10.4320 + 4.32106i) q^{45} +(7.71524 + 1.30944i) q^{46} +8.88060i q^{47} +(-0.154762 + 0.538647i) q^{48} +1.11241i q^{49} +(2.21343 - 13.0415i) q^{50} +(0.129444 - 0.0536177i) q^{51} +(-0.112396 - 1.98860i) q^{52} +(-2.33269 + 5.63162i) q^{53} +(0.263891 + 1.15522i) q^{54} +(12.4001 - 12.4001i) q^{55} +(-7.05291 - 3.89304i) q^{56} +(-0.362927 - 0.362927i) q^{57} +(7.46581 - 11.8865i) q^{58} +(6.46363 + 2.67732i) q^{59} +(-1.00220 - 0.350278i) q^{60} +(-2.41447 - 5.82904i) q^{61} +(-3.72160 - 5.24310i) q^{62} -8.48878 q^{63} +(6.76919 - 4.26357i) q^{64} +3.77304 q^{65} +(-0.530865 - 0.747899i) q^{66} +(1.55759 + 3.76035i) q^{67} +(-1.88800 - 0.659879i) q^{68} +(0.716283 + 0.296694i) q^{69} +(8.11679 - 12.9230i) q^{70} +(-5.26831 - 5.26831i) q^{71} +(4.07365 - 7.38012i) q^{72} +(2.18456 - 2.18456i) q^{73} +(3.17671 + 13.9066i) q^{74} +(0.501520 - 1.21078i) q^{75} +(0.413433 + 7.31482i) q^{76} +(12.1801 - 5.04515i) q^{77} +(0.0330191 - 0.194548i) q^{78} +5.51206i q^{79} +(7.34006 + 13.2583i) q^{80} -8.82371i q^{81} +(-5.80877 - 0.985874i) q^{82} +(-9.94525 + 4.11946i) q^{83} +(-0.595310 - 0.531616i) q^{84} +(1.44984 - 3.50023i) q^{85} +(8.78976 - 2.00787i) q^{86} +(0.983336 - 0.983336i) q^{87} +(-1.45881 + 13.0104i) q^{88} +(-2.92406 - 2.92406i) q^{89} +(13.5225 + 8.49336i) q^{90} +(2.62060 + 1.08549i) q^{91} +(-4.80539 - 9.96932i) q^{92} +(-0.243770 - 0.588513i) q^{93} +(10.2414 - 7.26942i) q^{94} -13.8786 q^{95} +(0.747867 - 0.262446i) q^{96} -15.9224 q^{97} +(1.28287 - 0.910590i) q^{98} +(5.27921 + 12.7451i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 20 q^{6} - 24 q^{8} - 16 q^{12} - 20 q^{16} - 20 q^{18} - 48 q^{22} - 8 q^{23} + 68 q^{24} + 20 q^{26} - 24 q^{27} + 20 q^{30} + 48 q^{31} - 24 q^{35} + 8 q^{36} + 68 q^{38} - 24 q^{39} - 36 q^{40}+ \cdots - 136 q^{99}+O(q^{100}) \) 128 * q + 20 * q^6 - 24 * q^8 - 16 * q^12 - 20 * q^16 - 20 * q^18 - 48 * q^22 - 8 * q^23 + 68 * q^24 + 20 * q^26 - 24 * q^27 + 20 * q^30 + 48 * q^31 - 24 * q^35 + 8 * q^36 + 68 * q^38 - 24 * q^39 - 36 * q^40 - 16 * q^42 - 8 * q^43 - 40 * q^44 - 80 * q^45 + 12 * q^50 + 56 * q^52 - 16 * q^53 - 136 * q^54 + 32 * q^55 + 128 * q^56 - 32 * q^58 + 20 * q^60 - 12 * q^62 - 80 * q^63 + 12 * q^64 - 8 * q^66 + 40 * q^67 - 4 * q^68 + 100 * q^70 - 44 * q^72 + 84 * q^74 + 32 * q^75 - 32 * q^76 - 16 * q^77 - 64 * q^78 + 44 * q^80 + 40 * q^82 + 84 * q^84 - 120 * q^86 - 56 * q^87 + 128 * q^88 - 68 * q^90 - 56 * q^91 - 40 * q^92 + 32 * q^95 - 72 * q^96 - 12 * q^98 - 136 * q^99

Introduction

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