LMFDB - Embedded newform 425.2.r.a.154.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(69,425)] 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("425.69"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([9, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.r (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			154.6
Character	$\chi$	$=$	425.154
Dual form			425.2.r.a.69.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.14124 - 0.695730i) q^{2} +(1.08145 - 1.48849i) q^{3} +(2.48282 + 1.80387i) q^{4} +(-0.133284 - 2.23209i) q^{5} +(-3.35124 + 2.43482i) q^{6} +4.38149i q^{7} +(-1.41458 - 1.94701i) q^{8} +(-0.119019 - 0.366304i) q^{9} +(-1.26754 + 4.87217i) q^{10} +(1.54742 - 4.76246i) q^{11} +(5.37011 - 1.74485i) q^{12} +(5.16707 - 1.67888i) q^{13} +(3.04833 - 9.38180i) q^{14} +(-3.46659 - 2.21551i) q^{15} +(-0.222341 - 0.684295i) q^{16} +(0.587785 + 0.809017i) q^{17} +0.867149i q^{18} +(2.84744 - 2.06879i) q^{19} +(3.69549 - 5.78231i) q^{20} +(6.52181 + 4.73838i) q^{21} +(-6.62677 + 9.12097i) q^{22} +(-3.72988 - 1.21191i) q^{23} -4.42791 q^{24} +(-4.96447 + 0.595005i) q^{25} -12.2320 q^{26} +(4.57553 + 1.48668i) q^{27} +(-7.90365 + 10.8784i) q^{28} +(-1.35616 - 0.985311i) q^{29} +(5.88140 + 7.15575i) q^{30} +(4.45495 - 3.23671i) q^{31} +6.43319i q^{32} +(-5.41543 - 7.45370i) q^{33} +(-0.695730 - 2.14124i) q^{34} +(9.77988 - 0.583982i) q^{35} +(0.365263 - 1.12416i) q^{36} +(-5.69639 + 1.85087i) q^{37} +(-7.53636 + 2.44871i) q^{38} +(3.08894 - 9.50678i) q^{39} +(-4.15735 + 3.41698i) q^{40} +(-1.38219 - 4.25393i) q^{41} +(-10.6681 - 14.6834i) q^{42} +2.73959i q^{43} +(12.4328 - 9.03298i) q^{44} +(-0.801761 + 0.314485i) q^{45} +(7.14340 + 5.18998i) q^{46} +(-2.75987 + 3.79863i) q^{47} +(-1.25902 - 0.409080i) q^{48} -12.1974 q^{49} +(11.0441 + 2.17989i) q^{50} +1.83988 q^{51} +(15.8574 + 5.15238i) q^{52} +(4.49551 - 6.18754i) q^{53} +(-8.76297 - 6.36667i) q^{54} +(-10.8365 - 2.81922i) q^{55} +(8.53078 - 6.19797i) q^{56} -6.47569i q^{57} +(2.21836 + 3.05331i) q^{58} +(-1.96156 - 6.03707i) q^{59} +(-4.61043 - 11.7540i) q^{60} +(-0.481029 + 1.48046i) q^{61} +(-11.7910 + 3.83112i) q^{62} +(1.60496 - 0.521482i) q^{63} +(4.03108 - 12.4064i) q^{64} +(-4.43611 - 11.3096i) q^{65} +(6.40995 + 19.7278i) q^{66} +(-6.97108 - 9.59486i) q^{67} +3.06893i q^{68} +(-5.83762 + 4.24128i) q^{69} +(-21.3473 - 5.55371i) q^{70} +(12.2357 + 8.88975i) q^{71} +(-0.544833 + 0.749898i) q^{72} +(1.39360 + 0.452808i) q^{73} +13.4850 q^{74} +(-4.48319 + 8.03305i) q^{75} +10.8015 q^{76} +(20.8666 + 6.77999i) q^{77} +(-13.2283 + 18.2072i) q^{78} +(-3.22393 - 2.34232i) q^{79} +(-1.49777 + 0.587491i) q^{80} +(8.09593 - 5.88204i) q^{81} +10.0703i q^{82} +(6.78571 + 9.33973i) q^{83} +(7.64506 + 23.5291i) q^{84} +(1.72746 - 1.41982i) q^{85} +(1.90601 - 5.86610i) q^{86} +(-2.93326 + 0.953074i) q^{87} +(-11.4615 + 3.72406i) q^{88} +(-4.22214 + 12.9944i) q^{89} +(1.93556 - 0.115577i) q^{90} +(7.35600 + 22.6394i) q^{91} +(-7.07449 - 9.73720i) q^{92} -10.1315i q^{93} +(8.55235 - 6.21364i) q^{94} +(-4.99724 - 6.08001i) q^{95} +(9.57576 + 6.95719i) q^{96} +(6.46389 - 8.89679i) q^{97} +(26.1176 + 8.48612i) q^{98} -1.92868 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) $ 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$

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 $

$2$	−2.14124	−	0.695730i	−1.51408	−	0.491955i	−0.569995	−	0.821648i	$-0.693055\pi$
$2$	−2.14124	−	0.695730i	−1.51408	−	0.491955i	−0.944088	+	0.329693i	$0.893055\pi$
$3$	1.08145	−	1.48849i	0.624378	−	0.859382i	−0.373285	−	0.927717i	$-0.621769\pi$
$3$	1.08145	−	1.48849i	0.624378	−	0.859382i	0.997662	+	0.0683347i	$0.0217686\pi$
$4$	2.48282	+	1.80387i	1.24141	+	0.901937i
$5$	−0.133284	−	2.23209i	−0.0596064	−	0.998222i
$5$	−0.133284	−	2.23209i	−0.0596064	−	0.998222i
$6$	−3.35124	+	2.43482i	−1.36814	+	0.994010i
$7$			4.38149i			1.65605i	0.560694	+	0.828023i	$0.310535\pi$
$7$			4.38149i			1.65605i	−0.560694	+	0.828023i	$0.689465\pi$
$8$	−1.41458	−	1.94701i	−0.500130	−	0.688370i
$9$	−0.119019	−	0.366304i	−0.0396731	−	0.122101i
$10$	−1.26754	+	4.87217i	−0.400832	+	1.54071i
$11$	1.54742	−	4.76246i	0.466564	−	1.43594i	−0.390442	−	0.920628i	$-0.627678\pi$
$11$	1.54742	−	4.76246i	0.466564	−	1.43594i	0.857005	−	0.515307i	$-0.172322\pi$
$12$	5.37011	−	1.74485i	1.55022	−	0.503696i
$13$	5.16707	−	1.67888i	1.43309	−	0.465638i	0.513352	−	0.858178i	$-0.328404\pi$
$13$	5.16707	−	1.67888i	1.43309	−	0.465638i	0.919735	+	0.392540i	$0.128404\pi$
$14$	3.04833	−	9.38180i	0.814701	−	2.50739i
$15$	−3.46659	−	2.21551i	−0.895071	−	0.572043i
$16$	−0.222341	−	0.684295i	−0.0555852	−	0.171074i
$17$	0.587785	+	0.809017i	0.142559	+	0.196215i
$17$	0.587785	+	0.809017i	0.142559	+	0.196215i
$18$			0.867149i			0.204389i
$19$	2.84744	−	2.06879i	0.653248	−	0.474612i	−0.211128	−	0.977458i	$-0.567714\pi$
$19$	2.84744	−	2.06879i	0.653248	−	0.474612i	0.864376	+	0.502846i	$0.167714\pi$
$20$	3.69549	−	5.78231i	0.826338	−	1.29296i
$21$	6.52181	+	4.73838i	1.42318	+	1.03400i
$22$	−6.62677	+	9.12097i	−1.41283	+	1.94460i
$23$	−3.72988	−	1.21191i	−0.777734	−	0.252701i	−0.106862	−	0.994274i	$-0.534080\pi$
$23$	−3.72988	−	1.21191i	−0.777734	−	0.252701i	−0.670872	+	0.741573i	$0.734080\pi$
$24$	−4.42791			−0.903843
$25$	−4.96447	+	0.595005i	−0.992894	+	0.119001i
$26$	−12.2320			−2.39889
$27$	4.57553	+	1.48668i	0.880562	+	0.286112i
$28$	−7.90365	+	10.8784i	−1.49365	+	2.05583i
$29$	−1.35616	−	0.985311i	−0.251833	−	0.182968i	0.454706	−	0.890642i	$-0.349745\pi$
$29$	−1.35616	−	0.985311i	−0.251833	−	0.182968i	−0.706539	+	0.707674i	$0.749745\pi$
$30$	5.88140	+	7.15575i	1.07379	+	1.30646i
$31$	4.45495	−	3.23671i	0.800133	−	0.581331i	−0.110820	−	0.993840i	$-0.535348\pi$
$31$	4.45495	−	3.23671i	0.800133	−	0.581331i	0.910953	+	0.412510i	$0.135348\pi$
$32$			6.43319i			1.13724i
$33$	−5.41543	−	7.45370i	−0.942705	−	1.29752i
$34$	−0.695730	−	2.14124i	−0.119317	−	0.367219i
$35$	9.77988	−	0.583982i	1.65310	−	0.0987110i
$36$	0.365263	−	1.12416i	0.0608771	−	0.187360i
$37$	−5.69639	+	1.85087i	−0.936481	+	0.304281i	−0.737210	−	0.675663i	$-0.763857\pi$
$37$	−5.69639	+	1.85087i	−0.936481	+	0.304281i	−0.199271	+	0.979944i	$0.563857\pi$
$38$	−7.53636	+	2.44871i	−1.22256	+	0.397234i
$39$	3.08894	−	9.50678i	0.494626	−	1.52230i
$40$	−4.15735	+	3.41698i	−0.657335	+	0.540272i
$41$	−1.38219	−	4.25393i	−0.215861	−	0.664352i	−0.999091	−	0.0426203i	$-0.986429\pi$
$41$	−1.38219	−	4.25393i	−0.215861	−	0.664352i	0.783230	−	0.621732i	$-0.213571\pi$
$42$	−10.6681	−	14.6834i	−1.64613	−	2.26570i
$43$			2.73959i			0.417783i	0.977939	+	0.208892i	$0.0669856\pi$
$43$			2.73959i			0.417783i	−0.977939	+	0.208892i	$0.933014\pi$
$44$	12.4328	−	9.03298i	1.87432	−	1.36177i
$45$	−0.801761	+	0.314485i	−0.119519	+	0.0468806i
$46$	7.14340	+	5.18998i	1.05324	+	0.765221i
$47$	−2.75987	+	3.79863i	−0.402568	+	0.554087i	−0.961386	−	0.275203i	$-0.911255\pi$
$47$	−2.75987	+	3.79863i	−0.402568	+	0.554087i	0.558818	+	0.829290i	$0.311255\pi$
$48$	−1.25902	−	0.409080i	−0.181724	−	0.0590457i
$49$	−12.1974			−1.74249
$50$	11.0441	+	2.17989i	1.56187	+	0.308282i
$51$	1.83988			0.257635
$52$	15.8574	+	5.15238i	2.19902	+	0.714507i
$53$	4.49551	−	6.18754i	0.617506	−	0.849925i	−0.379662	−	0.925125i	$-0.623960\pi$
$53$	4.49551	−	6.18754i	0.617506	−	0.849925i	0.997168	+	0.0752006i	$0.0239597\pi$
$54$	−8.76297	−	6.36667i	−1.19249	−	0.866394i
$55$	−10.8365	−	2.81922i	−1.46119	−	0.380143i
$56$	8.53078	−	6.19797i	1.13997	−	0.828239i
$57$		−	6.47569i		−	0.857727i
$58$	2.21836	+	3.05331i	0.291285	+	0.400919i
$59$	−1.96156	−	6.03707i	−0.255374	−	0.785959i	−0.993756	−	0.111577i	$-0.964410\pi$
$59$	−1.96156	−	6.03707i	−0.255374	−	0.785959i	0.738382	−	0.674382i	$-0.235590\pi$
$60$	−4.61043	−	11.7540i	−0.595203	−	1.51744i
$61$	−0.481029	+	1.48046i	−0.0615895	+	0.189553i	−0.977117	−	0.212702i	$-0.931774\pi$
$61$	−0.481029	+	1.48046i	−0.0615895	+	0.189553i	0.915528	+	0.402255i	$0.131774\pi$
$62$	−11.7910	+	3.83112i	−1.49746	+	0.486553i
$63$	1.60496	−	0.521482i	0.202205	−	0.0657005i
$64$	4.03108	−	12.4064i	0.503885	−	1.55080i
$65$	−4.43611	−	11.3096i	−0.550231	−	1.40278i
$66$	6.40995	+	19.7278i	0.789011	+	2.42832i
$67$	−6.97108	−	9.59486i	−0.851653	−	1.17220i	−0.983496	−	0.180929i	$-0.942090\pi$
$67$	−6.97108	−	9.59486i	−0.851653	−	1.17220i	0.131844	−	0.991271i	$-0.457910\pi$
$68$			3.06893i			0.372163i
$69$	−5.83762	+	4.24128i	−0.702767	+	0.510590i
$70$	−21.3473	−	5.55371i	−2.55150	−	0.663796i
$71$	12.2357	+	8.88975i	1.45211	+	1.05502i	0.985333	+	0.170645i	$0.0545851\pi$
$71$	12.2357	+	8.88975i	1.45211	+	1.05502i	0.466777	+	0.884375i	$0.345415\pi$
$72$	−0.544833	+	0.749898i	−0.0642092	+	0.0883764i
$73$	1.39360	+	0.452808i	0.163108	+	0.0529972i	0.389433	−	0.921055i	$-0.372671\pi$
$73$	1.39360	+	0.452808i	0.163108	+	0.0529972i	−0.226325	+	0.974052i	$0.572671\pi$
$74$	13.4850			1.56760
$75$	−4.48319	+	8.03305i	−0.517674	+	0.927577i
$76$	10.8015			1.23902
$77$	20.8666	+	6.77999i	2.37798	+	0.772651i
$78$	−13.2283	+	18.2072i	−1.49781	+	2.06156i
$79$	−3.22393	−	2.34232i	−0.362721	−	0.263532i	0.391465	−	0.920193i	$-0.371968\pi$
$79$	−3.22393	−	2.34232i	−0.362721	−	0.263532i	−0.754186	+	0.656661i	$0.771968\pi$
$80$	−1.49777	+	0.587491i	−0.167456	+	0.0656835i
$81$	8.09593	−	5.88204i	0.899548	−	0.653560i
$82$			10.0703i			1.11208i
$83$	6.78571	+	9.33973i	0.744829	+	1.02517i	0.998326	+	0.0578327i	$0.0184190\pi$
$83$	6.78571	+	9.33973i	0.744829	+	1.02517i	−0.253498	+	0.967336i	$0.581581\pi$
$84$	7.64506	+	23.5291i	0.834144	+	2.56723i
$85$	1.72746	−	1.41982i	0.187369	−	0.154001i
$86$	1.90601	−	5.86610i	0.205531	−	0.632558i
$87$	−2.93326	+	0.953074i	−0.314478	+	0.102180i
$88$	−11.4615	+	3.72406i	−1.22180	+	0.396986i
$89$	−4.22214	+	12.9944i	−0.447546	+	1.37740i	0.432121	+	0.901815i	$0.357765\pi$
$89$	−4.22214	+	12.9944i	−0.447546	+	1.37740i	−0.879667	+	0.475589i	$0.842235\pi$
$90$	1.93556	−	0.115577i	0.204026	−	0.0121829i
$91$	7.35600	+	22.6394i	0.771118	+	2.37326i
$92$	−7.07449	−	9.73720i	−0.737566	−	1.01517i
$93$		−	10.1315i		−	1.05059i
$94$	8.55235	−	6.21364i	0.882107	−	0.640888i
$95$	−4.99724	−	6.08001i	−0.512706	−	0.623796i
$96$	9.57576	+	6.95719i	0.977322	+	0.710066i
$97$	6.46389	−	8.89679i	0.656309	−	0.903332i	−0.343043	−	0.939320i	$-0.611458\pi$
$97$	6.46389	−	8.89679i	0.656309	−	0.903332i	0.999352	+	0.0359878i	$0.0114577\pi$
$98$	26.1176	+	8.48612i	2.63827	+	0.857227i
$99$	−1.92868			−0.193840
$100$	−13.3992	−	7.47799i	−1.33992	−	0.747799i
$101$	−3.12700			−0.311148			−0.155574	−	0.987824i	$-0.549723\pi$
$101$	−3.12700			−0.311148			−0.155574	+	0.987824i	$0.549723\pi$
$102$	−3.93962	−	1.28006i	−0.390080	−	0.126745i
$103$	−3.18436	+	4.38290i	−0.313765	+	0.431860i	−0.936551	−	0.350532i	$-0.886001\pi$
$103$	−3.18436	+	4.38290i	−0.313765	+	0.431860i	0.622786	+	0.782392i	$0.286001\pi$
$104$	−10.5780	−	7.68539i	−1.03726	−	0.753615i
$105$	9.70724	−	15.1888i	0.947329	−	1.48228i
$106$	−13.9308	+	10.1213i	−1.35308	+	0.983071i
$107$		−	11.3245i		−	1.09478i	−0.836879	−	0.547389i	$-0.815622\pi$
$107$		−	11.3245i		−	1.09478i	0.836879	−	0.547389i	$-0.184378\pi$
$108$	8.67844	+	11.9448i	0.835083	+	1.14939i
$109$	2.07387	+	6.38271i	0.198640	+	0.611353i	0.999915	+	0.0130554i	$0.00415577\pi$
$109$	2.07387	+	6.38271i	0.198640	+	0.611353i	−0.801274	+	0.598297i	$0.795844\pi$
$110$	21.2421	+	13.5759i	2.02535	+	1.29441i
$111$	−3.40538	+	10.4807i	−0.323224	+	0.994782i
$112$	2.99823	−	0.974184i	0.283306	−	0.0920517i
$113$	−2.19227	+	0.712311i	−0.206231	+	0.0670086i	−0.410311	−	0.911946i	$-0.634580\pi$
$113$	−2.19227	+	0.712311i	−0.206231	+	0.0670086i	0.204080	+	0.978954i	$0.434580\pi$
$114$	−4.50533	+	13.8660i	−0.421963	+	1.29867i
$115$	−2.20797	+	8.48697i	−0.205894	+	0.791414i
$116$	−1.58974	−	4.89270i	−0.147603	−	0.454276i
$117$	−1.22996	−	1.69290i	−0.113710	−	0.156508i
$118$			14.2915i			1.31564i
$119$	−3.54470	+	2.57537i	−0.324942	+	0.236084i
$120$	0.590170	+	9.88350i	0.0538749	+	0.902236i
$121$	−11.3873	−	8.27337i	−1.03521	−	0.752125i
$122$	2.06000	−	2.83534i	0.186503	−	0.256700i
$123$	−7.82671	−	2.54305i	−0.705711	−	0.229299i
$124$	16.8995			1.51762
$125$	1.98979	+	11.0019i	0.177972	+	0.984036i
$126$	−3.79940			−0.338478
$127$	12.8916	+	4.18872i	1.14394	+	0.371689i	0.818858	−	0.573997i	$-0.194608\pi$
$127$	12.8916	+	4.18872i	1.14394	+	0.371689i	0.325083	+	0.945685i	$0.394608\pi$
$128$	−9.70032	+	13.3514i	−0.857396	+	1.18010i
$129$	4.07786	+	2.96274i	0.359035	+	0.260854i
$130$	1.63033	+	27.3029i	0.142989	+	2.39462i
$131$	−5.02960	+	3.65422i	−0.439438	+	0.319270i	−0.785412	−	0.618974i	$-0.787549\pi$
$131$	−5.02960	+	3.65422i	−0.439438	+	0.319270i	0.345974	+	0.938244i	$0.387549\pi$
$132$		−	28.2749i		−	2.46102i
$133$	9.06436	+	12.4760i	0.785980	+	1.08181i
$134$	8.25129	+	25.3949i	0.712803	+	2.19378i
$135$	2.70856	−	10.4112i	0.233116	−	0.896050i
$136$	0.743690	−	2.28884i	0.0637709	−	0.196267i
$137$	−12.3527	+	4.01364i	−1.05536	+	0.342908i	−0.784771	−	0.619786i	$-0.787219\pi$
$137$	−12.3527	+	4.01364i	−1.05536	+	0.342908i	−0.270592	+	0.962694i	$0.587219\pi$
$138$	15.4505	−	5.02017i	1.31523	−	0.427346i
$139$	4.28927	−	13.2010i	0.363811	−	1.11969i	−0.586912	−	0.809651i	$-0.699656\pi$
$139$	4.28927	−	13.2010i	0.363811	−	1.11969i	0.950722	−	0.310044i	$-0.100344\pi$
$140$	25.3351	+	16.1918i	2.14121	+	1.36845i
$141$	2.66957	+	8.21608i	0.224818	+	0.691919i
$142$	−20.0147	−	27.5478i	−1.67959	−	2.31176i
$143$		−	27.2059i		−	2.27507i
$144$	−0.224197	+	0.162889i	−0.0186831	+	0.0135741i
$145$	−2.01855	+	3.15841i	−0.167632	+	0.262292i
$146$	−2.66899	−	1.93914i	−0.220888	−	0.160484i
$147$	−13.1910	+	18.1558i	−1.08797	+	1.49746i
$148$	−17.4819	−	5.68020i	−1.43700	−	0.466910i
$149$	3.72754			0.305372			0.152686	−	0.988275i	$-0.451208\pi$
$149$	3.72754			0.305372			0.152686	+	0.988275i	$0.451208\pi$
$150$	15.1884	−	14.0816i	1.24013	−	1.14976i
$151$	3.58849			0.292027			0.146013	−	0.989283i	$-0.453356\pi$
$151$	3.58849			0.292027			0.146013	+	0.989283i	$0.453356\pi$
$152$	−8.05588	−	2.61751i	−0.653418	−	0.212308i
$153$	0.226388	−	0.311597i	0.0183024	−	0.0251911i
$154$	−39.9634	−	29.0351i	−3.22034	−	2.33972i
$155$	−7.81841	−	9.51246i	−0.627990	−	0.764059i
$156$	24.8183	−	18.0316i	1.98706	−	1.44368i
$157$			22.1837i			1.77046i	0.465157	+	0.885228i	$0.345998\pi$
$157$			22.1837i			1.77046i	−0.465157	+	0.885228i	$0.654002\pi$
$158$	5.27358	+	7.25846i	0.419543	+	0.577452i
$159$	−4.34843	−	13.3831i	−0.344853	−	1.06135i
$160$	14.3595	−	0.857441i	1.13522	−	0.0677867i
$161$	5.30998	−	16.3424i	0.418485	−	1.28796i
$162$	−21.4276	+	6.96225i	−1.68351	+	0.547006i
$163$	2.93896	−	0.954927i	0.230197	−	0.0747957i	−0.191647	−	0.981464i	$-0.561383\pi$
$163$	2.93896	−	0.954927i	0.230197	−	0.0747957i	0.421844	+	0.906668i	$0.361383\pi$
$164$	4.24184	−	13.0550i	0.331232	−	1.01943i
$165$	−15.9155	+	13.0812i	−1.23902	+	1.01837i
$166$	−8.03188	−	24.7196i	−0.623395	−	1.91861i
$167$	5.84400	+	8.04357i	0.452222	+	0.622430i	0.972873	−	0.231339i	$-0.0743107\pi$
$167$	5.84400	+	8.04357i	0.452222	+	0.622430i	−0.520651	+	0.853770i	$0.674311\pi$
$168$		−	19.4008i		−	1.49681i
$169$	13.3627	−	9.70859i	1.02790	−	0.746815i
$170$	−4.68671	+	1.83833i	−0.359454	+	0.140993i
$171$	−1.09671	−	0.796803i	−0.0838671	−	0.0609330i
$172$	−4.94187	+	6.80190i	−0.376814	+	0.518640i
$173$	−15.6643	−	5.08964i	−1.19093	−	0.386958i	−0.354516	−	0.935050i	$-0.615354\pi$
$173$	−15.6643	−	5.08964i	−1.19093	−	0.386958i	−0.836418	+	0.548092i	$0.815354\pi$
$174$	6.94388			0.526414
$175$	−2.60700	−	21.7518i	−0.197071	−	1.64428i
$176$	−3.60298			−0.271585
$177$	−11.1075	−	3.60904i	−0.834889	−	0.271272i
$178$	18.0812	−	24.8866i	1.35524	−	1.86533i
$179$	18.4521	+	13.4062i	1.37917	+	1.00203i	0.996957	+	0.0779556i	$0.0248392\pi$
$179$	18.4521	+	13.4062i	1.37917	+	1.00203i	0.382217	+	0.924073i	$0.375161\pi$
$180$	−2.55792	−	0.665467i	−0.190656	−	0.0496010i
$181$	−17.5195	+	12.7287i	−1.30222	+	0.946116i	−0.999975	−	0.00711506i	$-0.997735\pi$
$181$	−17.5195	+	12.7287i	−1.30222	+	0.946116i	−0.302242	+	0.953231i	$0.597735\pi$
$182$		−	53.5942i		−	3.97267i
$183$	1.68344	+	2.31705i	0.124443	+	0.171282i
$184$	2.91662	+	8.97645i	0.215016	+	0.661752i
$185$	4.89055	+	12.4682i	0.359561	+	0.916679i
$186$	−7.04880	+	21.6940i	−0.516843	+	1.59068i
$187$	4.76246	−	1.54742i	0.348265	−	0.113158i
$188$	−13.7045	+	4.45286i	−0.999504	+	0.324758i
$189$	−6.51387	+	20.0476i	−0.473814	+	1.45825i
$190$	6.47023	+	16.4955i	0.469400	+	1.19671i
$191$	−3.24665	−	9.99216i	−0.234919	−	0.723008i	−0.997132	−	0.0756810i	$-0.975887\pi$
$191$	−3.24665	−	9.99216i	−0.234919	−	0.723008i	0.762213	−	0.647327i	$-0.224113\pi$
$192$	−14.1074	−	19.4172i	−1.01811	−	1.40131i
$193$			14.4285i			1.03859i	0.854596	+	0.519293i	$0.173805\pi$
$193$			14.4285i			1.03859i	−0.854596	+	0.519293i	$0.826195\pi$
$194$	−20.0305	+	14.5530i	−1.43811	+	1.04484i
$195$	−21.6317	−	5.62770i	−1.54908	−	0.403008i
$196$	−30.2840	−	22.0026i	−2.16314	−	1.57162i
$197$	−1.87241	+	2.57716i	−0.133404	+	0.183615i	−0.870493	−	0.492181i	$-0.836200\pi$
$197$	−1.87241	+	2.57716i	−0.133404	+	0.183615i	0.737089	+	0.675796i	$0.236200\pi$
$198$	4.12976	+	1.34184i	0.293489	+	0.0953604i
$199$	−0.482209			−0.0341829			−0.0170914	−	0.999854i	$-0.505441\pi$
$199$	−0.482209			−0.0341829			−0.0170914	+	0.999854i	$0.505441\pi$
$200$	8.18113	+	8.82417i	0.578493	+	0.623963i
$201$	−21.8208			−1.53912
$202$	6.69564	+	2.17554i	0.471103	+	0.153071i
$203$	4.31713	−	5.94202i	0.303003	−	0.417048i
$204$	4.56809	+	3.31891i	0.319830	+	0.232370i
$205$	−9.31094	+	3.65215i	−0.650304	+	0.255077i
$206$	9.86779	−	7.16937i	0.687522	−	0.499514i
$207$			1.51051i			0.104988i
$208$	−2.29770	−	3.16251i	−0.159317	−	0.219281i
$209$	−5.44633	−	16.7621i	−0.376731	−	1.15946i
$210$	−31.3528	+	25.7693i	−2.16355	+	1.77825i
$211$	4.36987	−	13.4491i	0.300834	−	0.925873i	−0.680364	−	0.732874i	$-0.738178\pi$
$211$	4.36987	−	13.4491i	0.300834	−	0.925873i	0.981199	−	0.192999i	$-0.0618215\pi$
$212$	22.3231	−	7.25322i	1.53316	−	0.498153i
$213$	26.4647	−	8.59890i	1.81333	−	0.589187i
$214$	−7.87877	+	24.2484i	−0.538582	+	1.65758i
$215$	6.11501	−	0.365143i	0.417040	−	0.0249026i
$216$	−3.57789	−	11.0116i	−0.243445	−	0.749245i
$217$	14.1816	+	19.5193i	0.962710	+	1.32506i
$218$		−	15.1097i		−	1.02336i
$219$	2.18111	−	1.58467i	0.147386	−	0.107082i
$220$	−21.8195	−	26.5473i	−1.47107	−	1.78982i
$221$	4.39537	+	3.19342i	0.295665	+	0.214813i
$222$	14.5834	−	20.0724i	0.978776	−	1.34717i
$223$	23.2997	+	7.57052i	1.56026	+	0.506960i	0.956878	−	0.290491i	$-0.0938186\pi$
$223$	23.2997	+	7.57052i	1.56026	+	0.506960i	0.603384	+	0.797451i	$0.293819\pi$
$224$	−28.1869			−1.88332
$225$	0.808821	+	1.74769i	0.0539214	+	0.116513i
$226$	5.18974			0.345216
$227$	8.00915	+	2.60233i	0.531586	+	0.172723i	0.562497	−	0.826799i	$-0.309841\pi$
$227$	8.00915	+	2.60233i	0.531586	+	0.172723i	−0.0309110	+	0.999522i	$0.509841\pi$
$228$	11.6813	−	16.0780i	0.773615	−	1.06479i
$229$	23.7765	+	17.2747i	1.57120	+	1.14154i	0.925998	+	0.377529i	$0.123226\pi$
$229$	23.7765	+	17.2747i	1.57120	+	1.14154i	0.645200	+	0.764013i	$0.276774\pi$
$230$	10.6324	−	16.6365i	0.701081	−	1.09698i
$231$	32.6583	−	23.7276i	2.14876	−	1.56116i
$232$			4.03426i			0.264862i
$233$	−9.96020	−	13.7090i	−0.652515	−	0.898109i	0.346690	−	0.937980i	$-0.387306\pi$
$233$	−9.96020	−	13.7090i	−0.652515	−	0.898109i	−0.999205	+	0.0398703i	$0.987306\pi$
$234$	1.45584	+	4.48062i	0.0951713	+	0.292907i
$235$	8.84674	+	5.65398i	0.577098	+	0.368825i
$236$	6.01990	−	18.5274i	0.391862	−	1.20603i
$237$	−6.97307	+	2.26569i	−0.452950	+	0.147172i
$238$	9.38180	−	3.04833i	0.608132	−	0.197594i
$239$	−2.61216	+	8.03941i	−0.168967	+	0.520026i	−0.999307	−	0.0372311i	$-0.988146\pi$
$239$	−2.61216	+	8.03941i	−0.168967	+	0.520026i	0.830340	+	0.557257i	$0.188146\pi$
$240$	−0.745298	+	2.86477i	−0.0481088	+	0.184920i
$241$	2.74337	+	8.44321i	0.176716	+	0.543875i	0.999708	−	0.0241779i	$-0.00769681\pi$
$241$	2.74337	+	8.44321i	0.176716	+	0.543875i	−0.822992	+	0.568053i	$0.807697\pi$
$242$	18.6269	+	25.6377i	1.19738	+	1.64806i
$243$		−	3.97889i		−	0.255246i
$244$	−3.86487	+	2.80799i	−0.247423	+	0.179763i
$245$	1.62572	+	27.2258i	0.103864	+	1.73939i
$246$	14.9896	+	10.8906i	0.955700	+	0.694357i
$247$	11.2397	−	15.4701i	0.715163	−	0.984338i
$248$	−12.6038	−	4.09522i	−0.800341	−	0.260047i
$249$	21.2406			1.34607
$250$	3.39371	−	24.9419i	0.214637	−	1.57747i
$251$	−25.3643			−1.60098			−0.800489	−	0.599347i	$-0.795427\pi$
$251$	−25.3643			−1.60098			−0.800489	+	0.599347i	$0.795427\pi$
$252$	4.92550	+	1.60039i	0.310278	+	0.100815i
$253$	−11.5434	+	15.8881i	−0.725725	+	0.998875i
$254$	−24.6897	−	17.9381i	−1.54917	−	1.12554i
$255$	−0.245227	−	4.10678i	−0.0153567	−	0.257177i
$256$	8.95262	−	6.50446i	0.559539	−	0.406529i
$257$			9.60204i			0.598958i	0.954103	+	0.299479i	$0.0968129\pi$
$257$			9.60204i			0.598958i	−0.954103	+	0.299479i	$0.903187\pi$
$258$	−6.67039	−	9.18101i	−0.415280	−	0.571585i
$259$	−8.10957	−	24.9587i	−0.503904	−	1.55086i
$260$	9.38705	−	36.0819i	0.582160	−	2.23770i
$261$	−0.199514	+	0.614040i	−0.0123496	+	0.0380081i
$262$	13.3119	−	4.32530i	0.822412	−	0.267218i
$263$	−27.2554	+	8.85582i	−1.68064	+	0.546073i	−0.985036	−	0.172351i	$-0.944864\pi$
$263$	−27.2554	+	8.85582i	−1.68064	+	0.546073i	−0.695605	+	0.718425i	$0.744864\pi$
$264$	−6.85182	+	21.0877i	−0.421700	+	1.29786i
$265$	−14.4104	−	9.20970i	−0.885221	−	0.565747i
$266$	−10.7290	−	33.0205i	−0.657837	−	2.02461i
$267$	14.7760	+	20.3375i	0.904279	+	1.24463i
$268$		−	36.3973i		−	2.22332i
$269$	1.19700	−	0.869674i	0.0729826	−	0.0530250i	−0.550696	−	0.834706i	$-0.685638\pi$
$269$	1.19700	−	0.869674i	0.0729826	−	0.0530250i	0.623678	+	0.781681i	$0.285638\pi$
$270$	−13.0430	+	20.4083i	−0.793773	+	1.24201i
$271$	17.0860	+	12.4137i	1.03790	+	0.754079i	0.969875	−	0.243604i	$-0.0783298\pi$
$271$	17.0860	+	12.4137i	1.03790	+	0.754079i	0.0680265	+	0.997684i	$0.478330\pi$
$272$	0.422917	−	0.582096i	0.0256431	−	0.0352947i
$273$	41.6538	+	13.5342i	2.52101	+	0.819124i
$274$	29.2425			1.76660
$275$	−4.84842	+	24.5638i	−0.292371	+	1.48125i
$276$	−22.1445			−1.33294
$277$	−0.322393	−	0.104752i	−0.0193707	−	0.00629393i	0.299316	−	0.954154i	$-0.403242\pi$
$277$	−0.322393	−	0.104752i	−0.0193707	−	0.00629393i	−0.318686	+	0.947860i	$0.603242\pi$
$278$	−18.3687	+	25.2823i	−1.10168	+	1.51633i
$279$	−1.71585	−	1.24663i	−0.102725	−	0.0746341i
$280$	−14.9715	−	18.2154i	−0.894716	−	1.08858i
$281$	1.02639	−	0.745717i	0.0612294	−	0.0444858i	−0.556750	−	0.830680i	$-0.687952\pi$
$281$	1.02639	−	0.745717i	0.0612294	−	0.0444858i	0.617979	+	0.786195i	$0.287952\pi$
$282$		−	19.4499i		−	1.15822i
$283$	1.19086	+	1.63908i	0.0707893	+	0.0974331i	0.842944	−	0.538002i	$-0.180821\pi$
$283$	1.19086	+	1.63908i	0.0707893	+	0.0974331i	−0.772154	+	0.635435i	$0.780821\pi$
$284$	14.3430	+	44.1433i	0.851102	+	2.61942i
$285$	−14.4543	+	0.863107i	−0.856201	+	0.0511260i
$286$	−18.9279	+	58.2542i	−1.11923	+	3.44464i
$287$	18.6385	−	6.05603i	1.10020	−	0.357476i
$288$	2.35650	−	0.765674i	0.138858	−	0.0451178i
$289$	−0.309017	+	0.951057i	−0.0181775	+	0.0559445i
$290$	6.51960	−	5.35854i	0.382844	−	0.314664i
$291$	−6.25241	−	19.2429i	−0.366523	−	1.12804i
$292$	2.64325	+	3.63812i	0.154684	+	0.212905i
$293$		−	1.82547i		−	0.106645i	−0.998577	−	0.0533227i	$-0.983019\pi$
$293$		−	1.82547i		−	0.106645i	0.998577	−	0.0533227i	$-0.0169812\pi$
$294$	40.8765	−	29.6985i	2.38397	−	1.73205i
$295$	−13.2138	+	5.18303i	−0.769340	+	0.301768i
$296$	11.6617	+	8.47270i	0.677821	+	0.492466i
$297$	14.1605	−	19.4903i	0.821676	−	1.13094i
$298$	−7.98155	−	2.59336i	−0.462359	−	0.150229i
$299$	−21.3072			−1.23223
$300$	−25.6216	+	11.8575i	−1.47926	+	0.684594i
$301$	−12.0035			−0.691868
$302$	−7.68380	−	2.49662i	−0.442153	−	0.143664i
$303$	−3.38170	+	4.65451i	−0.194274	+	0.267395i
$304$	−2.04876	−	1.48851i	−0.117505	−	0.0853721i
$305$	3.36863	+	0.876381i	0.192887	+	0.0501814i
$306$	−0.701538	+	0.509697i	−0.0401043	+	0.0291375i
$307$		−	19.7199i		−	1.12548i	−0.826635	−	0.562738i	$-0.809748\pi$
$307$		−	19.7199i		−	1.12548i	0.826635	−	0.562738i	$-0.190252\pi$
$308$	39.5779	+	54.4743i	2.25516	+	3.10396i
$309$	3.08018	+	9.47981i	0.175225	+	0.539287i
$310$	10.1230	+	25.8079i	0.574946	+	1.46579i
$311$	−2.78338	+	8.56636i	−0.157831	+	0.485754i	−0.998437	−	0.0558937i	$-0.982199\pi$
$311$	−2.78338	+	8.56636i	−0.157831	+	0.485754i	0.840606	+	0.541647i	$0.182199\pi$
$312$	−22.8793	+	7.43394i	−1.29529	+	0.420864i
$313$	−13.7844	+	4.47883i	−0.779141	+	0.253158i	−0.671473	−	0.741029i	$-0.734338\pi$
$313$	−13.7844	+	4.47883i	−0.779141	+	0.253158i	−0.107668	+	0.994187i	$0.534338\pi$
$314$	15.4339	−	47.5007i	0.870985	−	2.68062i
$315$	−1.37791	−	3.51290i	−0.0776365	−	0.197930i
$316$	−3.77919	−	11.6311i	−0.212596	−	0.654303i
$317$	−2.05597	−	2.82980i	−0.115475	−	0.158937i	0.747367	−	0.664411i	$-0.231318\pi$
$317$	−2.05597	−	2.82980i	−0.115475	−	0.158937i	−0.862842	+	0.505474i	$0.831318\pi$
$318$			31.6817i			1.77662i
$319$	−6.79106	+	4.93399i	−0.380226	+	0.276250i
$320$	−28.2295	−	7.34417i	−1.57808	−	0.410551i
$321$	−16.8564	−	12.2469i	−0.940832	−	0.683554i
$322$	−22.7398	+	31.2987i	−1.26724	+	1.74421i
$323$	3.34737	+	1.08763i	0.186252	+	0.0605171i
$324$	30.7112			1.70618
$325$	−24.6528	+	11.4092i	−1.36749	+	0.632868i
$326$	−6.95739			−0.385334
$327$	11.7434	+	3.81567i	0.649412	+	0.211007i
$328$	−6.32721	+	8.70865i	−0.349362	+	0.480855i
$329$	−16.6436	−	12.0923i	−0.917594	−	0.666671i
$330$	43.1799	−	16.9370i	2.37698	−	0.932351i
$331$	−23.9396	+	17.3931i	−1.31584	+	0.956014i	−0.315866	+	0.948804i	$0.602295\pi$
$331$	−23.9396	+	17.3931i	−1.31584	+	0.956014i	−0.999974	+	0.00720969i	$0.997705\pi$
$332$			35.4294i			1.94444i
$333$	1.35596	+	1.86632i	0.0743063	+	0.102274i
$334$	−6.91723	−	21.2890i	−0.378494	−	1.16488i
$335$	−20.4875	+	16.8389i	−1.11935	+	0.920009i
$336$	1.79238	−	5.51638i	0.0977823	−	0.300943i
$337$	−21.7116	+	7.05453i	−1.18271	+	0.384285i	−0.833372	−	0.552713i	$-0.813593\pi$
$337$	−21.7116	+	7.05453i	−1.18271	+	0.384285i	−0.349335	+	0.936998i	$0.613593\pi$
$338$	−35.3673	+	11.4915i	−1.92373	+	0.625057i
$339$	−1.31057	+	4.03351i	−0.0711802	+	0.219070i
$340$	6.85014	−	0.409040i	0.371501	−	0.0221833i
$341$	−8.52104	−	26.2251i	−0.461440	−	1.42017i
$342$	1.79395	+	2.46915i	0.0970055	+	0.133517i
$343$		−	22.7725i		−	1.22960i
$344$	5.33399	−	3.87537i	0.287589	−	0.208946i
$345$	10.2450	+	12.4648i	0.551571	+	0.671083i
$346$	29.9999	+	21.7962i	1.61281	+	1.17177i
$347$	−13.9980	+	19.2666i	−0.751453	+	1.03429i	0.246424	+	0.969162i	$0.420745\pi$
$347$	−13.9980	+	19.2666i	−0.751453	+	1.03429i	−0.997877	+	0.0651248i	$0.979255\pi$
$348$	−9.00198	−	2.92492i	−0.482557	−	0.156792i
$349$	−3.74351			−0.200385			−0.100193	−	0.994968i	$-0.531946\pi$
$349$	−3.74351			−0.200385			−0.100193	+	0.994968i	$0.531946\pi$
$350$	−9.55114	+	48.3894i	−0.510530	+	2.58652i
$351$	26.1380			1.39515
$352$	30.6378	+	9.95482i	1.63300	+	0.530594i
$353$	−16.0607	+	22.1057i	−0.854826	+	1.17657i	0.127952	+	0.991780i	$0.459160\pi$
$353$	−16.0607	+	22.1057i	−0.854826	+	1.17657i	−0.982779	+	0.184787i	$0.940840\pi$
$354$	21.2728	+	15.4556i	1.13064	+	0.821456i
$355$	18.2119	−	28.4961i	0.966589	−	1.51241i
$356$	−33.9231	+	24.6466i	−1.79792	+	1.30627i
$357$			8.06141i			0.426655i
$358$	−30.1832	−	41.5436i	−1.59523	−	2.19565i
$359$	−2.56176	−	7.88427i	−0.135204	−	0.416116i	0.860417	−	0.509590i	$-0.170203\pi$
$359$	−2.56176	−	7.88427i	−0.135204	−	0.416116i	−0.995622	+	0.0934739i	$0.970203\pi$
$360$	1.74646	+	1.11617i	0.0920465	+	0.0588272i
$361$	−2.04328	+	6.28858i	−0.107541	+	0.330978i
$362$	46.3692	−	15.0663i	2.43711	−	0.791866i
$363$	−24.6297	+	8.00268i	−1.29273	+	0.420032i
$364$	−22.5751	+	69.4790i	−1.18326	+	3.64169i
$365$	0.824964	−	3.17099i	0.0431806	−	0.165977i
$366$	−1.99260	−	6.13258i	−0.104155	−	0.320555i
$367$	−17.7309	−	24.4044i	−0.925543	−	1.27390i	−0.961573	−	0.274551i	$-0.911471\pi$
$367$	−17.7309	−	24.4044i	−0.925543	−	1.27390i	0.0360292	−	0.999351i	$-0.488529\pi$
$368$			2.82180i			0.147096i
$369$	−1.39372	+	1.01260i	−0.0725544	+	0.0527138i
$370$	−1.79734	−	30.0998i	−0.0934392	−	1.56482i
$371$	27.1106	+	19.6970i	1.40751	+	1.02262i
$372$	18.2760	−	25.1547i	0.947566	−	1.30421i
$373$	20.8676	+	6.78030i	1.08048	+	0.351070i	0.794562	−	0.607183i	$-0.207700\pi$
$373$	20.8676	+	6.78030i	1.08048	+	0.351070i	0.285921	+	0.958253i	$0.407700\pi$
$374$	−11.2741			−0.582972
$375$	18.5280	+	8.93620i	0.956784	+	0.461464i
$376$	11.3000			0.582753
$377$	−8.66162	−	2.81433i	−0.446096	−	0.144945i
$378$	27.8955	−	38.3948i	1.43479	−	1.97482i
$379$	−0.981148	−	0.712845i	−0.0503982	−	0.0366164i	0.562301	−	0.826933i	$-0.309916\pi$
$379$	−0.981148	−	0.712845i	−0.0503982	−	0.0366164i	−0.612699	+	0.790316i	$0.709916\pi$
$380$	−1.43967	−	24.1100i	−0.0738535	−	1.23682i
$381$	20.1765	−	14.6591i	1.03367	−	0.751008i
$382$			23.6544i			1.21026i
$383$	−2.30108	−	3.16717i	−0.117580	−	0.161835i	0.746170	−	0.665755i	$-0.231890\pi$
$383$	−2.30108	−	3.16717i	−0.117580	−	0.161835i	−0.863750	+	0.503920i	$0.831890\pi$
$384$	9.38295	+	28.8777i	0.478821	+	1.47366i
$385$	12.3524	−	47.4799i	0.629535	−	2.41980i
$386$	10.0383	−	30.8949i	0.510938	−	1.57251i
$387$	1.00352	−	0.326064i	0.0510119	−	0.0165748i
$388$	32.0974	−	10.4291i	1.62950	−	0.529456i
$389$	−2.16043	+	6.64913i	−0.109538	+	0.337124i	−0.990769	−	0.135563i	$-0.956716\pi$
$389$	−2.16043	+	6.64913i	−0.109538	+	0.337124i	0.881230	+	0.472687i	$0.156716\pi$
$390$	42.4033	+	27.1001i	2.14717	+	1.37227i
$391$	−1.21191	−	3.72988i	−0.0612890	−	0.188628i
$392$	17.2543	+	23.7485i	0.871472	+	1.19948i
$393$			11.4384i			0.576990i
$394$	5.80229	−	4.21561i	0.292315	−	0.212379i
$395$	−4.79859	+	7.50831i	−0.241443	+	0.377784i
$396$	−4.78856	−	3.47910i	−0.240634	−	0.174831i
$397$	−4.79924	+	6.60559i	−0.240867	+	0.331525i	−0.912287	−	0.409552i	$-0.865685\pi$
$397$	−4.79924	+	6.60559i	−0.240867	+	0.331525i	0.671420	+	0.741077i	$0.265685\pi$
$398$	1.03252	+	0.335487i	0.0517557	+	0.0168165i
$399$	28.3732			1.42044
$400$	1.51096	+	3.26487i	0.0755482	+	0.163243i
$401$	−2.43570			−0.121633			−0.0608165	−	0.998149i	$-0.519370\pi$
$401$	−2.43570			−0.121633			−0.0608165	+	0.998149i	$0.519370\pi$
$402$	46.7235	+	15.1814i	2.33035	+	0.757178i
$403$	17.5850	−	24.2036i	0.875970	−	1.20567i
$404$	−7.76377	−	5.64071i	−0.386262	−	0.280636i
$405$	−14.2083	−	17.2869i	−0.706017	−	0.858992i
$406$	−13.3780	+	9.71971i	−0.663941	+	0.482381i
$407$			29.9929i			1.48669i
$408$	−2.60266	−	3.58225i	−0.128851	−	0.177348i
$409$	10.2770	+	31.6295i	0.508167	+	1.56398i	0.795380	+	0.606111i	$0.207271\pi$
$409$	10.2770	+	31.6295i	0.508167	+	1.56398i	−0.287213	+	0.957867i	$0.592729\pi$
$410$	22.4778	−	1.34221i	1.11010	−	0.0662870i
$411$	−7.38460	+	22.7275i	−0.364256	+	1.12106i
$412$	−15.8124	+	5.13776i	−0.779021	+	0.253119i
$413$	26.4513	−	8.59456i	1.30158	−	0.422911i
$414$	1.05091	−	3.23436i	0.0516493	−	0.158960i
$415$	19.9427	−	16.3912i	0.978949	−	0.804611i
$416$	10.8006	+	33.2407i	0.529541	+	1.62976i
$417$	−15.0110	−	20.6608i	−0.735090	−	1.01176i
$418$			39.6808i			1.94085i
$419$	14.3456	−	10.4227i	0.700826	−	0.509180i	−0.179375	−	0.983781i	$-0.557408\pi$
$419$	14.3456	−	10.4227i	0.700826	−	0.509180i	0.880201	+	0.474601i	$0.157408\pi$
$420$	51.5001	−	20.2005i	2.51295	−	0.985685i
$421$	−9.06728	−	6.58776i	−0.441912	−	0.321068i	0.344482	−	0.938793i	$-0.388054\pi$
$421$	−9.06728	−	6.58776i	−0.441912	−	0.321068i	−0.786394	+	0.617725i	$0.788054\pi$
$422$	−18.7139	+	25.7574i	−0.910977	+	1.25385i
$423$	1.71993	+	0.558839i	0.0836259	+	0.0271717i
$424$	−18.4065			−0.893896
$425$	−3.39941	−	3.66661i	−0.164896	−	0.177857i
$426$	−62.6496			−3.03539
$427$	−6.48660	−	2.10762i	−0.313909	−	0.101995i
$428$	20.4279	−	28.1166i	0.987420	−	1.35907i
$429$	−40.4958	−	29.4219i	−1.95515	−	1.42050i
$430$	−13.3477	−	3.47254i	−0.643684	−	0.167461i
$431$	23.0408	−	16.7401i	1.10983	−	0.806342i	0.127197	−	0.991877i	$-0.459402\pi$
$431$	23.0408	−	16.7401i	1.10983	−	0.806342i	0.982638	+	0.185535i	$0.0594019\pi$
$432$		−	3.46156i		−	0.166544i
$433$	−12.6541	−	17.4169i	−0.608118	−	0.837002i	0.388303	−	0.921532i	$-0.373061\pi$
$433$	−12.6541	−	17.4169i	−0.608118	−	0.837002i	−0.996421	+	0.0845295i	$0.973061\pi$
$434$	−16.7860	−	51.6620i	−0.805754	−	2.47986i
$435$	2.51830	+	6.42027i	0.120743	+	0.307829i
$436$	−6.36456	+	19.5881i	−0.304807	+	0.938100i
$437$	−13.1278	+	4.26548i	−0.627988	+	0.204046i
$438$	−5.77279	+	1.87569i	−0.275834	+	0.0896240i
$439$	−3.09157	+	9.51486i	−0.147552	+	0.454120i	−0.997330	−	0.0730212i	$-0.976736\pi$
$439$	−3.09157	+	9.51486i	−0.147552	+	0.454120i	0.849778	+	0.527141i	$0.176736\pi$
$440$	9.84008	+	25.0867i	0.469107	+	1.19596i
$441$	1.45173	+	4.46797i	0.0691300	+	0.212760i
$442$	−7.18977	−	9.89587i	−0.341982	−	0.470698i
$443$		−	12.6152i		−	0.599368i	−0.954039	−	0.299684i	$-0.903119\pi$
$443$		−	12.6152i		−	0.599368i	0.954039	−	0.299684i	$-0.0968812\pi$
$444$	−27.3608	+	19.8788i	−1.29848	+	0.943404i
$445$	29.5675	+	7.69226i	1.40163	+	0.364648i
$446$	−44.6231	−	32.4206i	−2.11296	−	1.53516i
$447$	4.03116	−	5.54842i	0.190668	−	0.262431i
$448$	54.3584	+	17.6621i	2.56819	+	0.834457i
$449$	−7.92591			−0.374047			−0.187024	−	0.982355i	$-0.559884\pi$
$449$	−7.92591			−0.374047			−0.187024	+	0.982355i	$0.559884\pi$
$450$	−0.515957	−	4.30493i	−0.0243225	−	0.202937i
$451$	−22.3980			−1.05468
$452$	−6.72792	−	2.18604i	−0.316455	−	0.102822i
$453$	3.88078	−	5.34144i	0.182335	−	0.250963i
$454$	−15.3390	−	11.1444i	−0.719893	−	0.523033i
$455$	49.5529	−	19.4368i	2.32308	−	0.911209i
$456$	−12.6082	+	9.16040i	−0.590433	+	0.428975i
$457$			2.90103i			0.135704i	0.997695	+	0.0678522i	$0.0216146\pi$
$457$			2.90103i			0.135704i	−0.997695	+	0.0678522i	$0.978385\pi$
$458$	−38.8927	−	53.5312i	−1.81734	−	2.50135i
$459$	1.48668	+	4.57553i	0.0693923	+	0.213568i
$460$	−20.7914	+	17.0887i	−0.969404	+	0.796766i
$461$	0.185099	−	0.569675i	0.00862091	−	0.0265324i	−0.946654	−	0.322253i	$-0.895560\pi$
$461$	0.185099	−	0.569675i	0.00862091	−	0.0265324i	0.955274	+	0.295721i	$0.0955598\pi$
$462$	−86.4371	+	28.0851i	−4.02142	+	1.30664i
$463$	19.3206	−	6.27765i	0.897906	−	0.291747i	0.176533	−	0.984295i	$-0.443512\pi$
$463$	19.3206	−	6.27765i	0.897906	−	0.291747i	0.721372	+	0.692547i	$0.243512\pi$
$464$	−0.372713	+	1.14709i	−0.0173027	+	0.0532524i
$465$	−22.6145	+	1.35037i	−1.04872	+	0.0626219i
$466$	11.7894	+	36.2839i	0.546132	+	1.68082i
$467$	−2.12490	−	2.92467i	−0.0983285	−	0.135338i	0.757018	−	0.653394i	$-0.226656\pi$
$467$	−2.12490	−	2.92467i	−0.0983285	−	0.135338i	−0.855346	+	0.518057i	$0.826656\pi$
$468$		−	6.42186i		−	0.296851i
$469$	42.0398	−	30.5437i	1.94122	−	1.41038i
$470$	−15.0093	−	18.2614i	−0.692328	−	0.842338i
$471$	33.0204	+	23.9907i	1.52150	+	1.10543i
$472$	−8.97941	+	12.3591i	−0.413311	+	0.568873i
$473$	13.0472	+	4.23928i	0.599909	+	0.194922i
$474$	16.5073			0.758205
$475$	−12.9051	+	11.9647i	−0.592126	+	0.548977i
$476$	−13.4465			−0.616319
$477$	−2.80158	−	0.910287i	−0.128275	−	0.0416792i
$478$	11.1865	−	15.3969i	0.511659	−	0.704238i
$479$	11.6698	+	8.47864i	0.533209	+	0.387399i	0.821557	−	0.570127i	$-0.193106\pi$
$479$	11.6698	+	8.47864i	0.533209	+	0.387399i	−0.288348	+	0.957526i	$0.593106\pi$
$480$	14.2528	−	22.3013i	0.650549	−	1.01791i
$481$	−26.3263	+	19.1272i	−1.20037	+	0.872123i
$482$		−	19.9876i		−	0.910408i
$483$	−18.5831	−	25.5774i	−0.845560	−	1.16381i
$484$	−13.3485	−	41.0826i	−0.606752	−	1.86739i
$485$	−20.7200	−	13.2422i	−0.940846	−	0.601298i
$486$	−2.76824	+	8.51975i	−0.125570	+	0.386464i
$487$	−20.1418	+	6.54447i	−0.912713	+	0.296558i	−0.727474	−	0.686135i	$-0.759306\pi$
$487$	−20.1418	+	6.54447i	−0.912713	+	0.296558i	−0.185239	+	0.982694i	$0.559306\pi$
$488$	3.56291	−	1.15766i	0.161285	−	0.0524048i
$489$	1.75695	−	5.40734i	0.0794521	−	0.244528i
$490$	15.4607	−	59.4279i	0.698445	−	2.68468i
$491$	−2.91084	−	8.95863i	−0.131364	−	0.404297i	0.863643	−	0.504105i	$-0.168177\pi$
$491$	−2.91084	−	8.95863i	−0.131364	−	0.404297i	−0.995007	+	0.0998073i	$0.968177\pi$
$492$	−14.8450	−	20.4324i	−0.669263	−	0.921162i
$493$		−	1.67631i		−	0.0754973i
$494$	−34.8298	+	25.3053i	−1.56707	+	1.13854i
$495$	0.257062	+	4.30499i	0.0115541	+	0.193495i
$496$	−3.20538	−	2.32885i	−0.143926	−	0.104568i
$497$	−38.9503	+	53.6105i	−1.74716	+	2.40476i
$498$	−45.4811	−	14.7777i	−2.03806	−	0.662204i
$499$	0.395435			0.0177021			0.00885106	−	0.999961i	$-0.497183\pi$
$499$	0.395435			0.0177021			0.00885106	+	0.999961i	$0.497183\pi$
$500$	−14.9057	+	30.9049i	−0.666602	+	1.38211i
$501$	18.2928			0.817263
$502$	54.3109	+	17.6467i	2.42401	+	0.787610i
$503$	16.2835	−	22.4123i	0.726044	−	0.999314i	−0.273258	−	0.961941i	$-0.588101\pi$
$503$	16.2835	−	22.4123i	0.726044	−	0.999314i	0.999301	−	0.0373726i	$-0.0118988\pi$
$504$	−3.28567	−	2.38718i	−0.146355	−	0.106333i
$505$	0.416779	+	6.97974i	0.0185464	+	0.310594i
$506$	35.7709	−	25.9891i	1.59021	−	1.15535i
$507$		−	30.3897i		−	1.34966i
$508$	24.4515	+	33.6546i	1.08486	+	1.49318i
$509$	1.90483	+	5.86246i	0.0844301	+	0.259849i	0.984355	−	0.176195i	$-0.0563790\pi$
$509$	1.90483	+	5.86246i	0.0844301	+	0.259849i	−0.899925	+	0.436044i	$0.856379\pi$
$510$	−2.33212	+	8.96420i	−0.103268	+	0.396941i
$511$	−1.98397	+	6.10604i	−0.0877658	+	0.270115i
$512$	7.69589	−	2.50054i	0.340113	−	0.110510i
$513$	16.1042	−	5.23256i	0.711017	−	0.231023i
$514$	6.68042	−	20.5602i	0.294661	−	0.906873i
$515$	10.2075	+	6.52362i	0.449794	+	0.287465i
$516$	4.78018	+	14.7119i	0.210436	+	0.647655i
$517$	13.8202	+	19.0218i	0.607810	+	0.836578i
$518$			59.0845i			2.59602i
$519$	−24.5161	+	17.8120i	−1.07614	+	0.781859i
$520$	−15.7446	+	24.6355i	−0.690447	+	1.08034i
$521$	25.9163	+	18.8293i	1.13542	+	0.824928i	0.986474	−	0.163918i	$-0.0524133\pi$
$521$	25.9163	+	18.8293i	1.13542	+	0.824928i	0.148942	+	0.988846i	$0.452413\pi$
$522$	0.854412	−	1.17600i	0.0373966	−	0.0514720i
$523$	−35.2793	−	11.4629i	−1.54266	−	0.501239i	−0.590548	−	0.807002i	$-0.701088\pi$
$523$	−35.2793	−	11.4629i	−1.54266	−	0.501239i	−0.952108	+	0.305763i	$0.901088\pi$
$524$	−19.0793			−0.833485
$525$	−35.1967	−	19.6430i	−1.53611	−	0.857292i
$526$	64.5215			2.81327
$527$	5.23711	+	1.70164i	0.228132	+	0.0741246i
$528$	−3.89646	+	5.36301i	−0.169571	+	0.233395i
$529$	−6.16410	−	4.47848i	−0.268005	−	0.194717i
$530$	24.4485	+	29.7459i	1.06198	+	1.29208i
$531$	−1.97794	+	1.43706i	−0.0858352	+	0.0623629i
$532$			47.3267i			2.05187i
$533$	−14.2837	−	19.6598i	−0.618695	−	0.851561i
$534$	−17.4896	−	53.8275i	−0.756850	−	2.32934i
$535$	−25.2772	+	1.50937i	−1.09283	+	0.0652558i
$536$	−8.82009	+	27.1454i	−0.380970	+	1.17250i
$537$	39.9102	−	12.9676i	1.72225	−	0.559593i
$538$	−3.16813	+	1.02939i	−0.136588	+	0.0443800i
$539$	−18.8745	+	58.0898i	−0.812982	+	2.50210i
$540$	25.5053	−	20.9631i	1.09757	−	0.902109i
$541$	−7.54380	−	23.2174i	−0.324333	−	0.998196i	−0.971741	−	0.236051i	$-0.924147\pi$
$541$	−7.54380	−	23.2174i	−0.324333	−	0.998196i	0.647407	−	0.762144i	$-0.275853\pi$
$542$	−27.9486	−	38.4679i	−1.20050	−	1.65234i
$543$			39.8432i			1.70984i
$544$	−5.20456	+	3.78133i	−0.223144	+	0.162123i
$545$	13.9704	−	5.47978i	0.598425	−	0.234728i
$546$	−79.7746	−	57.9596i	−3.41404	−	2.48044i
$547$	8.00837	−	11.0226i	0.342413	−	0.471291i	−0.602731	−	0.797944i	$-0.705921\pi$
$547$	8.00837	−	11.0226i	0.342413	−	0.471291i	0.945144	+	0.326653i	$0.105921\pi$
$548$	−37.9096	−	12.3176i	−1.61942	−	0.526181i
$549$	0.599549			0.0255881
$550$	27.4714	−	49.2237i	1.17138	−	2.09891i
$551$	−5.90000			−0.251348
$552$	16.5156	+	5.36624i	0.702950	+	0.228402i
$553$	10.2629	−	14.1256i	0.436421	−	0.600683i
$554$	0.617441	+	0.448597i	0.0262326	+	0.0190591i
$555$	23.8477	+	6.20421i	1.01228	+	0.263354i
$556$	34.4624	−	25.0384i	1.46153	−	1.06187i
$557$		−	9.29003i		−	0.393631i	−0.980441	−	0.196816i	$-0.936940\pi$
$557$		−	9.29003i		−	0.393631i	0.980441	−	0.196816i	$-0.0630600\pi$
$558$	2.80671	+	3.86311i	0.118818	+	0.163538i
$559$	4.59944	+	14.1556i	0.194536	+	0.598719i
$560$	−2.57408	−	6.56248i	−0.108775	−	0.277315i
$561$	2.84706	−	8.76235i	0.120203	−	0.369947i
$562$	−2.71657	+	0.882666i	−0.114591	+	0.0372330i
$563$	1.91463	−	0.622102i	0.0806922	−	0.0262185i	−0.268393	−	0.963310i	$-0.586492\pi$
$563$	1.91463	−	0.622102i	0.0806922	−	0.0262185i	0.349085	+	0.937091i	$0.386492\pi$
$564$	−8.19273	+	25.2146i	−0.344976	+	1.06173i
$565$	1.88214	+	4.79840i	0.0791821	+	0.201870i
$566$	−1.40956	−	4.33817i	−0.0592481	−	0.182347i
$567$	25.7721	+	35.4722i	1.08233	+	1.48969i
$568$		−	36.3982i		−	1.52724i
$569$	−33.6342	+	24.4366i	−1.41002	+	1.02444i	−0.416697	+	0.909045i	$0.636813\pi$
$569$	−33.6342	+	24.4366i	−1.41002	+	1.02444i	−0.993320	+	0.115392i	$0.963187\pi$
$570$	31.5507	+	8.20820i	1.32151	+	0.343804i
$571$	20.1781	+	14.6603i	0.844428	+	0.613513i	0.923604	−	0.383348i	$-0.125229\pi$
$571$	20.1781	+	14.6603i	0.844428	+	0.613513i	−0.0791764	+	0.996861i	$0.525229\pi$
$572$	49.0760	−	67.5473i	2.05197	−	2.82429i
$573$	−18.3844	−	5.97345i	−0.768018	−	0.249544i
$574$	−44.1229			−1.84165
$575$	19.2380	+	3.79721i	0.802279	+	0.158354i
$576$	−5.02428			−0.209345
$577$	−30.8847	−	10.0350i	−1.28575	−	0.417764i	−0.415145	−	0.909755i	$-0.636269\pi$
$577$	−30.8847	−	10.0350i	−1.28575	−	0.417764i	−0.870600	+	0.491991i	$0.836269\pi$
$578$	1.32336	−	1.82144i	0.0550444	−	0.0757621i
$579$	21.4767	+	15.6038i	0.892543	+	0.648470i
$580$	−10.7091	+	4.20055i	−0.444670	+	0.174419i
$581$	−40.9219	+	29.7315i	−1.69773	+	1.23347i
$582$			45.5536i			1.88826i
$583$	−22.5115	−	30.9844i	−0.932331	−	1.28324i
$584$	−1.08974	−	3.35388i	−0.0450938	−	0.138785i
$585$	−3.61477	+	2.97103i	−0.149452	+	0.122837i
$586$	−1.27004	+	3.90877i	−0.0524647	+	0.161470i
$587$	39.4884	−	12.8306i	1.62986	−	0.529574i	0.655621	−	0.755090i	$-0.272407\pi$
$587$	39.4884	−	12.8306i	1.62986	−	0.529574i	0.974239	+	0.225517i	$0.0724071\pi$
$588$	−65.5016	+	21.2827i	−2.70124	+	0.877686i
$589$	5.98914	−	18.4327i	0.246778	−	0.759506i
$590$	31.9000	−	1.90483i	1.31330	−	0.0784206i
$591$	1.81115	+	5.57415i	0.0745008	+	0.229290i
$592$	2.53308	+	3.48649i	0.104109	+	0.143294i
$593$			23.1063i			0.948862i	0.880293	+	0.474431i	$0.157346\pi$
$593$			23.1063i			0.948862i	−0.880293	+	0.474431i	$0.842654\pi$
$594$	−43.8810	+	31.8814i	−1.80046	+	1.30811i
$595$	6.22092	+	7.56884i	0.255033	+	0.310292i
$596$	9.25482	+	6.72402i	0.379092	+	0.275427i
$597$	−0.521487	+	0.717765i	−0.0213430	+	0.0293762i
$598$	45.6238	+	14.8241i	1.86570	+	0.606201i
$599$	−17.1616			−0.701204			−0.350602	−	0.936525i	$-0.614023\pi$
$599$	−17.1616			−0.701204			−0.350602	+	0.936525i	$0.614023\pi$
$600$	21.9822	−	2.63463i	0.897421	−	0.107558i
$601$	14.5591			0.593876			0.296938	−	0.954897i	$-0.404034\pi$
$601$	14.5591			0.593876			0.296938	+	0.954897i	$0.404034\pi$
$602$	25.7023	+	8.35117i	1.04755	+	0.340368i
$603$	−2.68494	+	3.69551i	−0.109339	+	0.150493i
$604$	8.90956	+	6.47318i	0.362525	+	0.263390i
$605$	−16.9492	+	26.5203i	−0.689082	+	1.07820i
$606$	10.4793	−	7.61366i	0.425693	−	0.309284i
$607$		−	15.0544i		−	0.611039i	−0.952186	−	0.305520i	$-0.901170\pi$
$607$		−	15.0544i		−	0.611039i	0.952186	−	0.305520i	$-0.0988302\pi$
$608$	13.3089	+	18.3181i	0.539747	+	0.742898i
$609$	−4.17588	−	12.8520i	−0.169215	−	0.520791i
$610$	−6.60331	−	4.22019i	−0.267360	−	0.170871i
$611$	−7.88296	+	24.2613i	−0.318911	+	0.981506i
$612$	1.12416	−	0.365263i	0.0454416	−	0.0147649i
$613$	26.4289	−	8.58727i	1.06745	−	0.346837i	0.277958	−	0.960593i	$-0.410342\pi$
$613$	26.4289	−	8.58727i	1.06745	−	0.346837i	0.789495	+	0.613757i	$0.210342\pi$
$614$	−13.7197	+	42.2250i	−0.553684	+	1.70406i
$615$	−4.63315	+	17.8089i	−0.186827	+	0.718124i
$616$	−16.3169	−	50.2183i	−0.657427	−	2.02335i
$617$	−1.26046	−	1.73488i	−0.0507444	−	0.0698437i	0.782891	−	0.622159i	$-0.213744\pi$
$617$	−1.26046	−	1.73488i	−0.0507444	−	0.0698437i	−0.833635	+	0.552316i	$0.813744\pi$
$618$		−	22.4415i		−	0.902729i
$619$	26.1997	−	19.0352i	1.05306	−	0.765090i	0.0802645	−	0.996774i	$-0.474424\pi$
$619$	26.1997	−	19.0352i	1.05306	−	0.765090i	0.972791	+	0.231684i	$0.0744235\pi$
$620$	−2.25243	−	37.7212i	−0.0904597	−	1.51492i
$621$	−15.2645	−	11.0903i	−0.612542	−	0.445038i
$622$	11.9197	−	16.4061i	0.477938	−	0.657826i
$623$	−56.9349	−	18.4993i	−2.28105	−	0.741157i
$624$	−7.19224			−0.287920
$625$	24.2919	−	5.90776i	0.971678	−	0.236311i
$626$	32.6318			1.30423
$627$	−30.8402	−	10.0206i	−1.23164	−	0.400184i
$628$	−40.0167	+	55.0783i	−1.59684	+	2.19786i
$629$	−4.84564	−	3.52057i	−0.193208	−	0.140374i
$630$	0.506400	+	8.48061i	0.0201754	+	0.337876i
$631$	−21.8137	+	15.8486i	−0.868391	+	0.630923i	−0.930155	−	0.367168i	$-0.880327\pi$
$631$	−21.8137	+	15.8486i	−0.868391	+	0.630923i	0.0617637	+	0.998091i	$0.480327\pi$
$632$			9.59043i			0.381487i
$633$	−15.2931	−	21.0491i	−0.607845	−	0.836626i
$634$	2.43354	+	7.48966i	0.0966482	+	0.297453i
$635$	7.63137	−	29.3334i	0.302842	−	1.16406i
$636$	13.3450	−	41.0718i	0.529165	−	1.62860i
$637$	−63.0250	+	20.4781i	−2.49714	+	0.811370i
$638$	17.9740	−	5.84010i	0.711597	−	0.231212i
$639$	1.80007	−	5.54004i	0.0712095	−	0.219160i
$640$	31.0943	+	19.8725i	1.22911	+	0.785529i
$641$	−7.57249	−	23.3057i	−0.299095	−	0.920521i	−0.981815	−	0.189841i	$-0.939203\pi$
$641$	−7.57249	−	23.3057i	−0.299095	−	0.920521i	0.682719	−	0.730681i	$-0.260797\pi$
$642$	27.5730	+	37.9510i	1.08822	+	1.49781i
$643$		−	23.3381i		−	0.920366i	−0.887824	−	0.460183i	$-0.847784\pi$
$643$		−	23.3381i		−	0.920366i	0.887824	−	0.460183i	$-0.152216\pi$
$644$	42.6634	−	30.9968i	1.68117	−	1.22144i
$645$	6.06959	−	9.49704i	0.238990	−	0.373946i
$646$	−6.41081	−	4.65773i	−0.252230	−	0.183256i
$647$	−1.58787	+	2.18551i	−0.0624254	+	0.0859212i	−0.839088	−	0.543995i	$-0.816911\pi$
$647$	−1.58787	+	2.18551i	−0.0624254	+	0.0859212i	0.776663	+	0.629917i	$0.216911\pi$
$648$	−22.9047	−	7.44219i	−0.899782	−	0.292357i
$649$	−31.7866			−1.24773
$650$	60.7252	−	7.27807i	2.38184	−	0.285470i
$651$	44.3911			1.73983
$652$	9.01949	+	2.93061i	0.353230	+	0.114772i
$653$	−14.3742	+	19.7844i	−0.562507	+	0.774225i	−0.991643	−	0.129015i	$-0.958818\pi$
$653$	−14.3742	+	19.7844i	−0.562507	+	0.774225i	0.429135	+	0.903240i	$0.358818\pi$
$654$	−22.4907	−	16.3405i	−0.879458	−	0.638963i
$655$	8.82691	+	10.7395i	0.344896	+	0.419626i
$656$	−2.60363	+	1.89164i	−0.101654	+	0.0738563i
$657$		−	0.564374i		−	0.0220183i
$658$	27.2250	+	37.4720i	1.06134	+	1.46081i
$659$	11.7408	+	36.1345i	0.457358	+	1.40760i	0.868345	+	0.495961i	$0.165184\pi$
$659$	11.7408	+	36.1345i	0.457358	+	1.40760i	−0.410987	+	0.911641i	$0.634816\pi$
$660$	−63.1123	+	3.76860i	−2.45664	+	0.146692i
$661$	−7.80826	+	24.0314i	−0.303706	+	0.934712i	0.676451	+	0.736488i	$0.263517\pi$
$661$	−7.80826	+	24.0314i	−0.303706	+	0.934712i	−0.980157	+	0.198224i	$0.936483\pi$
$662$	63.3613	−	20.5873i	2.46261	−	0.800149i
$663$	9.50678	−	3.08894i	0.369213	−	0.119965i
$664$	8.58556	−	26.4236i	0.333184	−	1.02544i
$665$	26.6395	−	21.8953i	1.03304	−	0.849065i
$666$	−1.60498	−	4.93962i	−0.0621917	−	0.191406i
$667$	3.86422	+	5.31865i	0.149623	+	0.205939i
$668$			30.5126i			1.18057i
$669$	36.4662	−	26.4942i	1.40986	−	1.02433i
$670$	55.5839	−	21.8024i	2.14739	−	0.842299i
$671$	6.30626	+	4.58176i	0.243450	+	0.176877i
$672$	−30.4829	+	41.9561i	−1.17590	+	1.61849i
$673$	−37.3431	−	12.1335i	−1.43947	−	0.467713i	−0.517740	−	0.855538i	$-0.673226\pi$
$673$	−37.3431	−	12.1335i	−1.43947	−	0.467713i	−0.921733	+	0.387825i	$0.873226\pi$
$674$	51.3977			1.97977
$675$	−23.5997	−	4.65812i	−0.908352	−	0.179291i
$676$	50.6903			1.94963
$677$	−6.88202	−	2.23610i	−0.264498	−	0.0859405i	0.173766	−	0.984787i	$-0.444406\pi$
$677$	−6.88202	−	2.23610i	−0.264498	−	0.0859405i	−0.438264	+	0.898846i	$0.644406\pi$
$678$	5.61246	−	7.72489i	0.215545	−	0.296673i
$679$	38.9812	+	28.3215i	1.49596	+	1.08688i
$680$	−5.20803	−	1.35492i	−0.199719	−	0.0519587i
$681$	12.5351	−	9.10726i	0.480345	−	0.348991i
$682$			62.0824i			2.37726i
$683$	5.92945	+	8.16118i	0.226884	+	0.312279i	0.907249	−	0.420595i	$-0.138179\pi$
$683$	5.92945	+	8.16118i	0.226884	+	0.312279i	−0.680365	+	0.732874i	$0.738179\pi$
$684$	−1.28559	−	3.95664i	−0.0491557	−	0.151286i
$685$	10.6052	+	27.0374i	0.405205	+	1.03305i
$686$	−15.8435	+	48.7613i	−0.604908	+	1.86171i
$687$	51.4265	−	16.7095i	1.96204	−	0.637506i
$688$	1.87468	−	0.609122i	0.0714717	−	0.0232226i
$689$	12.8405	−	39.5189i	0.489183	−	1.50555i
$690$	−13.2648	−	33.8178i	−0.504982	−	1.28742i
$691$	3.15240	+	9.70209i	0.119923	+	0.369085i	0.992942	−	0.118601i	$-0.0378411\pi$
$691$	3.15240	+	9.70209i	0.119923	+	0.369085i	−0.873019	+	0.487686i	$0.837841\pi$
$692$	−29.7106	−	40.8931i	−1.12943	−	1.55452i
$693$		−	8.45049i		−	0.321007i
$694$	43.3775	−	31.5156i	1.64659	−	1.19631i
$695$	−30.0376	−	7.81455i	−1.13939	−	0.296423i
$696$	6.00497	+	4.36287i	0.227618	+	0.165374i
$697$	2.62907	−	3.61861i	0.0995832	−	0.137065i
$698$	8.01573	+	2.60447i	0.303400	+	0.0985806i
$699$	−31.1773			−1.17923
$700$	32.7647	−	58.7084i	1.23839	−	2.21897i
$701$	20.7358			0.783181			0.391591	−	0.920140i	$-0.371925\pi$
$701$	20.7358			0.783181			0.391591	+	0.920140i	$0.371925\pi$
$702$	−55.9677	−	18.1850i	−2.11237	−	0.686349i
$703$	−12.3911	+	17.0549i	−0.467339	+	0.643236i
$704$	−52.8471	−	38.3957i	−1.99175	−	1.44709i
$705$	17.9832	−	7.05379i	0.677288	−	0.265661i
$706$	49.7694	−	36.1596i	1.87310	−	1.36088i
$707$		−	13.7009i		−	0.515275i
$708$	−21.0676	−	28.9971i	−0.791769	−	1.08978i
$709$	−4.87602	−	15.0069i	−0.183123	−	0.563594i	0.816788	−	0.576938i	$-0.195753\pi$
$709$	−4.87602	−	15.0069i	−0.183123	−	0.563594i	−0.999911	+	0.0133435i	$0.995753\pi$
$710$	−58.8216	+	48.3462i	−2.20754	+	1.81440i
$711$	−0.474292	+	1.45972i	−0.0177873	+	0.0547438i
$712$	31.2728	−	10.1611i	1.17200	−	0.380805i
$713$	−20.5390	+	6.67354i	−0.769193	+	0.249926i
$714$	5.60856	−	17.2614i	0.209895	−	0.645991i
$715$	−60.7260	+	3.62611i	−2.27102	+	0.135609i
$716$	21.6301	+	66.5705i	0.808353	+	2.48786i
$717$	9.14167	+	12.5824i	0.341402	+	0.469900i
$718$			18.6644i			0.696549i
$719$	38.4531	−	27.9378i	1.43406	−	1.04190i	0.444814	−	0.895623i	$-0.353270\pi$
$719$	38.4531	−	27.9378i	1.43406	−	1.04190i	0.989243	−	0.146281i	$-0.0467304\pi$
$720$	0.393464	+	0.478718i	0.0146636	+	0.0178408i
$721$	−19.2036	−	13.9522i	−0.715180	−	0.519609i
$722$	8.75031	−	12.0438i	0.325653	−	0.448223i
$723$	15.5345	+	5.04746i	0.577734	+	0.187717i
$724$	−66.4588			−2.46992
$725$	7.31891	+	4.08463i	0.271817	+	0.151699i
$726$	58.3058			2.16393
$727$	−17.0668	−	5.54534i	−0.632973	−	0.205665i	−0.0250815	−	0.999685i	$-0.507985\pi$
$727$	−17.0668	−	5.54534i	−0.632973	−	0.205665i	−0.607892	+	0.794020i	$0.707985\pi$
$728$	33.6734	−	46.3475i	1.24802	−	1.71775i
$729$	18.3652	+	13.3431i	0.680194	+	0.494190i
$730$	−3.97260	+	6.21590i	−0.147033	+	0.230061i
$731$	−2.21637	+	1.61029i	−0.0819755	+	0.0595587i
$732$			8.78954i			0.324871i
$733$	9.44638	+	13.0018i	0.348910	+	0.480233i	0.947017	−	0.321183i	$-0.104080\pi$
$733$	9.44638	+	13.0018i	0.348910	+	0.480233i	−0.598107	+	0.801416i	$0.704080\pi$
$734$	20.9871	+	64.5916i	0.774647	+	2.38412i
$735$	42.2836	+	27.0236i	1.55965	+	0.996779i
$736$	7.79646	−	23.9950i	0.287381	−	0.884468i
$737$	−56.4823	+	18.3522i	−2.08055	+	0.676012i
$738$	3.68879	−	1.19856i	0.135786	−	0.0441196i
$739$	−2.52011	+	7.75611i	−0.0927038	+	0.285313i	−0.986648	−	0.162864i	$-0.947927\pi$
$739$	−2.52011	+	7.75611i	−0.0927038	+	0.285313i	0.893945	+	0.448177i	$0.147927\pi$
$740$	−10.3487	+	39.7782i	−0.380425	+	1.46228i
$741$	−10.8719	−	33.4603i	−0.399390	−	1.22920i
$742$	−44.3465	−	61.0377i	−1.62801	−	2.24076i
$743$			4.63794i			0.170149i	0.996375	+	0.0850747i	$0.0271129\pi$
$743$			4.63794i			0.170149i	−0.996375	+	0.0850747i	$0.972887\pi$
$744$	−19.7261	+	14.3319i	−0.723195	+	0.525432i
$745$	−0.496822	−	8.32022i	−0.0182021	−	0.304829i
$746$	−39.9652	−	29.0364i	−1.46323	−	1.06310i
$747$	2.61355	−	3.59724i	0.0956248	−	0.131616i
$748$	14.6157	+	4.74892i	0.534402	+	0.173638i
$749$	49.6180			1.81300
$750$	−33.4558	−	32.0250i	−1.22163	−	1.16939i
$751$	25.2490			0.921347			0.460674	−	0.887570i	$-0.347608\pi$
$751$	25.2490			0.921347			0.460674	+	0.887570i	$0.347608\pi$
$752$	3.21301	+	1.04397i	0.117167	+	0.0380697i
$753$	−27.4303	+	37.7546i	−0.999615	+	1.37585i
$754$	16.5886	+	12.0523i	0.604120	+	0.438919i
$755$	−0.478288	−	8.00983i	−0.0174067	−	0.291508i
$756$	−52.3362	+	38.0245i	−1.90345	+	1.38294i
$757$			38.2681i			1.39088i	0.718586	+	0.695438i	$0.244790\pi$
$757$			38.2681i			1.39088i	−0.718586	+	0.695438i	$0.755210\pi$
$758$	1.60492	+	2.20898i	0.0582934	+	0.0802339i
$759$	11.1657	+	34.3644i	0.405289	+	1.24735i
$760$	−4.76881	+	18.3303i	−0.172983	+	0.664911i
$761$	3.29603	−	10.1441i	0.119481	−	0.367725i	−0.873374	−	0.487050i	$-0.838073\pi$
$761$	3.29603	−	10.1441i	0.119481	−	0.367725i	0.992855	+	0.119325i	$0.0380730\pi$
$762$	−53.4014	+	17.3512i	−1.93453	+	0.628567i
$763$	−27.9658	+	9.08662i	−1.01243	+	0.328958i
$764$	9.96376	−	30.6653i	0.360476	−	1.10943i
$765$	−0.725687	−	0.463789i	−0.0262373	−	0.0167683i
$766$	2.72367	+	8.38259i	0.0984102	+	0.302875i
$767$	−20.2710	−	27.9007i	−0.731945	−	1.00744i
$768$		−	20.3602i		−	0.734685i
$769$	−14.9540	+	10.8647i	−0.539253	+	0.391791i	−0.823808	−	0.566869i	$-0.808154\pi$
$769$	−14.9540	+	10.8647i	−0.539253	+	0.391791i	0.284554	+	0.958660i	$0.408154\pi$
$770$	−59.4825	+	93.0719i	−2.14360	+	3.35408i
$771$	14.2926	+	10.3842i	0.514734	+	0.373976i
$772$	−26.0272	+	35.8234i	−0.936740	+	1.28931i
$773$	−10.8312	−	3.51926i	−0.389570	−	0.126579i	0.107681	−	0.994185i	$-0.465657\pi$
$773$	−10.8312	−	3.51926i	−0.389570	−	0.126579i	−0.497252	+	0.867606i	$0.665657\pi$
$774$	−2.37563			−0.0853902
$775$	−20.1906	+	18.7193i	−0.725268	+	0.672416i
$776$	−26.4658			−0.950067
$777$	−45.9209	−	14.9206i	−1.64740	−	0.535274i
$778$	9.25200	−	12.7343i	0.331700	−	0.456546i
$779$	−12.7362	−	9.25336i	−0.456320	−	0.331536i
$780$	−43.5560	−	52.9935i	−1.55956	−	1.89747i
$781$	61.2708	−	44.5158i	2.19244	−	1.59290i
$782$			8.82972i			0.315750i
$783$	−4.74033	−	6.52451i	−0.169406	−	0.233167i
$784$	2.71199	+	8.34664i	0.0968567	+	0.298094i
$785$	49.5162	−	2.95674i	1.76731	−	0.105531i
$786$	7.95803	−	24.4923i	0.283854	−	0.873611i
$787$	5.33786	−	1.73438i	0.190274	−	0.0618238i	−0.212330	−	0.977198i	$-0.568105\pi$
$787$	5.33786	−	1.73438i	0.190274	−	0.0618238i	0.402604	+	0.915374i	$0.368105\pi$
$788$	−9.29774	+	3.02102i	−0.331218	+	0.107619i
$789$	−16.2936	+	50.1466i	−0.580069	+	1.78527i
$790$	15.4987	−	12.7386i	0.551418	−	0.453217i
$791$	−3.12098	−	9.60539i	−0.110969	−	0.341528i
$792$	2.72828	+	3.75515i	0.0969450	+	0.133433i
$793$			8.45721i			0.300324i
$794$	14.8720	−	10.8052i	0.527788	−	0.383460i
$795$	−29.2927	+	11.4898i	−1.03891	+	0.407503i
$796$	−1.19724	−	0.869844i	−0.0424350	−	0.0308308i
$797$	25.7206	−	35.4013i	0.911070	−	1.25398i	−0.0557301	−	0.998446i	$-0.517749\pi$
$797$	25.7206	−	35.4013i	0.911070	−	1.25398i	0.966800	−	0.255534i	$-0.0822514\pi$
$798$	−60.7537	−	19.7401i	−2.15066	−	0.698791i
$799$	−4.69536			−0.166110
$800$	−3.82778	−	31.9374i	−0.135332	−	1.12916i
$801$	5.26242			0.185938
$802$	5.21541	+	1.69459i	0.184163	+	0.0598380i
$803$	4.31296	−	5.93628i	0.152201	−	0.209487i
$804$	−54.1771	−	39.3620i	−1.91068	−	1.38819i
$805$	−37.1855	−	9.67417i	−1.31062	−	0.340970i
$806$	−54.4928	+	39.5913i	−1.91943	+	1.39455i
$807$		−	2.72224i		−	0.0958275i
$808$	4.42339	+	6.08828i	0.155614	+	0.214185i
$809$	1.86004	+	5.72460i	0.0653954	+	0.201266i	0.978415	−	0.206649i	$-0.0662558\pi$
$809$	1.86004	+	5.72460i	0.0653954	+	0.201266i	−0.913020	+	0.407915i	$0.866256\pi$
$810$	18.3963	+	46.9004i	0.646382	+	1.64791i
$811$	8.67579	−	26.7014i	0.304648	−	0.937611i	−0.675160	−	0.737671i	$-0.735925\pi$
$811$	8.67579	−	26.7014i	0.304648	−	0.937611i	0.979808	−	0.199940i	$-0.0640747\pi$
$812$	21.4373	−	6.96540i	0.752302	−	0.244438i
$813$	36.9555	−	12.0076i	1.29608	−	0.421123i
$814$	20.8670	−	64.2219i	0.731387	−	2.25098i
$815$	−2.52320	−	6.43276i	−0.0883840	−	0.225330i
$816$	−0.409080	−	1.25902i	−0.0143207	−	0.0440745i
$817$	5.66762	+	7.80081i	0.198285	+	0.272916i
$818$		−	74.8763i		−	2.61799i
$819$	7.41741	−	5.38906i	0.259185	−	0.188309i
$820$	−29.7054	−	7.72814i	−1.03736	−	0.269878i
$821$	14.2516	+	10.3544i	0.497386	+	0.361372i	0.808018	−	0.589158i	$-0.200541\pi$
$821$	14.2516	+	10.3544i	0.497386	+	0.361372i	−0.310632	+	0.950530i	$0.600541\pi$
$822$	31.6244	−	43.5272i	1.10303	−	1.51819i
$823$	25.0573	+	8.14160i	0.873442	+	0.283798i	0.711232	−	0.702958i	$-0.248138\pi$
$823$	25.0573	+	8.14160i	0.873442	+	0.283798i	0.162210	+	0.986756i	$0.448138\pi$
$824$	13.0381			0.454203
$825$	31.3197	+	33.7815i	1.09041	+	1.17612i
$826$	−62.6180			−2.17876
$827$	5.42667	+	1.76323i	0.188704	+	0.0613136i	0.401844	−	0.915708i	$-0.368369\pi$
$827$	5.42667	+	1.76323i	0.188704	+	0.0613136i	−0.213141	+	0.977022i	$0.568369\pi$
$828$	−2.72477	+	3.75033i	−0.0946924	+	0.130333i
$829$	0.129207	+	0.0938745i	0.00448755	+	0.00326039i	0.590027	−	0.807384i	$-0.299117\pi$
$829$	0.129207	+	0.0938745i	0.00448755	+	0.00326039i	−0.585539	+	0.810644i	$0.699117\pi$
$830$	−54.1059	+	21.2226i	−1.87804	+	0.736648i
$831$	−0.504576	+	0.366596i	−0.0175035	+	0.0127171i
$832$		−	70.8724i		−	2.45706i
$833$	−7.16947	−	9.86793i	−0.248407	−	0.341903i
$834$	17.7677	+	54.6833i	0.615244	+	1.89353i
$835$	17.1751	−	14.1164i	0.594368	−	0.488519i
$836$	16.7144	−	51.4418i	0.578081	−	1.77915i
$837$	25.1957	−	8.18659i	0.870892	−	0.282970i
$838$	−37.9686	+	12.3367i	−1.31160	+	0.426166i
$839$	12.1186	−	37.2971i	0.418380	−	1.28764i	−0.490813	−	0.871265i	$-0.663300\pi$
$839$	12.1186	−	37.2971i	0.418380	−	1.28764i	0.909193	−	0.416375i	$-0.136700\pi$
$840$	−43.3044	+	2.58582i	−1.49414	+	0.0892193i
$841$	−8.09315	−	24.9081i	−0.279074	−	0.858902i
$842$	14.8319	+	20.4143i	0.511140	+	0.703524i
$843$		−	2.33424i		−	0.0803954i
$844$	35.1101	−	25.5090i	1.20854	−	0.878055i
$845$	−23.4515	−	28.5328i	−0.806756	−	0.981560i
$846$	−3.29398	−	2.39321i	−0.113249	−	0.0822804i
$847$	36.2497	−	49.8934i	1.24555	−	1.71436i
$848$	−5.23364	−	1.70051i	−0.179724	−	0.0583959i
$849$	3.72762			0.127931
$850$	4.72798	+	10.2161i	0.162168	+	0.350411i
$851$	23.4900			0.805226
$852$	81.2184	+	26.3894i	2.78250	+	0.904088i
$853$	22.4492	−	30.8987i	0.768646	−	1.05795i	−0.227799	−	0.973708i	$-0.573153\pi$
$853$	22.4492	−	30.8987i	0.768646	−	1.05795i	0.996445	−	0.0842428i	$-0.0268471\pi$
$854$	12.4230	+	9.02584i	0.425107	+	0.308858i
$855$	−1.63236	+	2.55415i	−0.0558257	+	0.0873500i
$856$	−22.0488	+	16.0194i	−0.753612	+	0.547531i
$857$			44.3370i			1.51452i	0.653113	+	0.757261i	$0.273463\pi$
$857$			44.3370i			1.51452i	−0.653113	+	0.757261i	$0.726537\pi$
$858$	66.2413	+	91.1734i	2.26144	+	3.11261i
$859$	2.61390	+	8.04475i	0.0891850	+	0.274483i	0.985695	−	0.168541i	$-0.0539056\pi$
$859$	2.61390	+	8.04475i	0.0891850	+	0.274483i	−0.896510	+	0.443024i	$0.853906\pi$
$860$	15.8411	+	10.1241i	0.540179	+	0.345230i
$861$	11.1424	−	34.2927i	0.379731	−	1.16869i
$862$	−60.9823	+	19.8144i	−2.07707	+	0.674880i
$863$	17.5595	−	5.70542i	0.597731	−	0.194215i	0.00550295	−	0.999985i	$-0.498248\pi$
$863$	17.5595	−	5.70542i	0.597731	−	0.194215i	0.592228	+	0.805770i	$0.298248\pi$
$864$	−9.56409	+	29.4353i	−0.325377	+	1.00141i
$865$	−9.27274	+	35.6425i	−0.315283	+	1.21188i
$866$	14.9780	+	46.0975i	0.508973	+	1.56646i
$867$	1.08145	+	1.48849i	0.0367281	+	0.0505519i
$868$			74.0448i			2.51324i
$869$	−16.1440	+	11.7293i	−0.547647	+	0.397889i
$870$	−0.925509	−	15.4994i	−0.0313777	−	0.525478i
$871$	−52.1287	−	37.8737i	−1.76631	−	1.28330i
$872$	9.49351	−	13.0667i	0.321491	−	0.442494i
$873$	−4.02826	−	1.30886i	−0.136336	−	0.0442982i
$874$	31.0774			1.05121
$875$	−48.2045	+	8.71824i	−1.62961	+	0.294730i
$876$	8.27387			0.279548
$877$	5.26821	+	1.71175i	0.177895	+	0.0578015i	0.396610	−	0.917987i	$-0.370187\pi$
$877$	5.26821	+	1.71175i	0.177895	+	0.0578015i	−0.218715	+	0.975789i	$0.570187\pi$
$878$	13.2395	−	18.2227i	0.446813	−	0.614986i
$879$	−2.71721	−	1.97417i	−0.0916491	−	0.0665869i
$880$	0.480220	+	8.04218i	0.0161882	+	0.271102i
$881$	3.76268	−	2.73375i	0.126768	−	0.0921023i	−0.522595	−	0.852581i	$-0.675036\pi$
$881$	3.76268	−	2.73375i	0.126768	−	0.0921023i	0.649362	+	0.760479i	$0.275036\pi$
$882$		−	10.5770i		−	0.356146i
$883$	−27.5947	−	37.9809i	−0.928637	−	1.27816i	−0.960389	−	0.278663i	$-0.910109\pi$
$883$	−27.5947	−	37.9809i	−0.928637	−	1.27816i	0.0317523	−	0.999496i	$-0.489891\pi$
$884$	5.15238	+	15.8574i	0.173293	+	0.533342i
$885$	−6.57525	+	25.2739i	−0.221025	+	0.849574i
$886$	−8.77679	+	27.0122i	−0.294862	+	0.907492i
$887$	−35.3376	+	11.4819i	−1.18652	+	0.385524i	−0.834786	−	0.550575i	$-0.814408\pi$
$887$	−35.3376	+	11.4819i	−1.18652	+	0.385524i	−0.351736	+	0.936099i	$0.614408\pi$
$888$	25.2231	−	8.19549i	0.846432	−	0.275023i
$889$	−18.3528	+	56.4842i	−0.615534	+	1.89442i
$890$	−57.9592	−	37.0419i	−1.94280	−	1.24165i
$891$	−15.4852	−	47.6585i	−0.518773	−	1.59662i
$892$	44.1926	+	60.8259i	1.47968	+	2.03660i
$893$			16.5259i			0.553020i
$894$	−12.4919	+	9.07588i	−0.417791	+	0.303543i
$895$	27.4646	−	42.9736i	0.918039	−	1.43645i
$896$	−58.4988	−	42.5018i	−1.95431	−	1.41989i
$897$	−23.0428	+	31.7156i	−0.769375	+	1.05895i
$898$	16.9713	+	5.51430i	0.566338	+	0.184014i
$899$	−9.23082			−0.307865
$900$	−1.14445	+	5.79821i	−0.0381485	+	0.193274i
$901$	7.64823			0.254799
$902$	47.9594	+	15.5829i	1.59687	+	0.518855i
$903$	−12.9812	+	17.8671i	−0.431987	+	0.594579i
$904$	4.48801	+	3.26073i	0.149269	+	0.108450i
$905$	30.7467	+	37.4087i	1.02205	+	1.24351i
$906$	−12.0259	+	8.73730i	−0.399533	+	0.290277i
$907$		−	35.9038i		−	1.19217i	−0.802922	−	0.596084i	$-0.796723\pi$
$907$		−	35.9038i		−	1.19217i	0.802922	−	0.596084i	$-0.203277\pi$
$908$	15.1910	+	20.9086i	0.504131	+	0.693877i
$909$	0.372173	+	1.14543i	0.0123442	+	0.0379915i
$910$	−119.627	+	7.14325i	−3.96560	+	0.236796i
$911$	−14.4151	+	44.3652i	−0.477595	+	1.46989i	0.364831	+	0.931074i	$0.381127\pi$
$911$	−14.4151	+	44.3652i	−0.477595	+	1.46989i	−0.842426	+	0.538812i	$0.818873\pi$
$912$	−4.43128	+	1.43981i	−0.146734	+	0.0476769i
$913$	54.9804	−	17.8642i	1.81959	−	0.591219i
$914$	2.01833	−	6.21179i	0.0667605	−	0.205468i
$915$	4.94750	−	4.06642i	0.163559	−	0.134432i
$916$	27.8715	+	85.7798i	0.920902	+	2.83424i
$917$	−16.0109	−	22.0371i	−0.528727	−	0.727730i
$918$		−	10.8316i		−	0.357497i
$919$	33.5425	−	24.3701i	1.10647	−	0.803894i	0.124362	−	0.992237i	$-0.460312\pi$
$919$	33.5425	−	24.3701i	1.10647	−	0.803894i	0.982103	+	0.188343i	$0.0603116\pi$
$920$	19.6475	−	7.70659i	0.647759	−	0.254079i
$921$	−29.3530	−	21.3262i	−0.967213	−	0.702722i
$922$	−0.792680	+	1.09103i	−0.0261055	+	0.0359312i
$923$	78.1475	+	25.3917i	2.57226	+	0.835777i
$924$	123.886			4.07556
$925$	27.1783	−	12.5780i	0.893617	−	0.413561i
$926$	−45.7376			−1.50303
$927$	1.98447	+	0.644795i	0.0651787	+	0.0211778i
$928$	6.33869	−	8.72446i	0.208078	−	0.286394i
$929$	−21.9578	−	15.9532i	−0.720411	−	0.523409i	0.166105	−	0.986108i	$-0.446881\pi$
$929$	−21.9578	−	15.9532i	−0.720411	−	0.523409i	−0.886515	+	0.462699i	$0.846881\pi$
$930$	49.3625	+	12.8421i	1.61866	+	0.421109i
$931$	−34.7315	+	25.2339i	−1.13828	+	0.827007i
$932$		−	52.0041i		−	1.70345i
$933$	9.74088	+	13.4072i	0.318902	+	0.438931i
$934$	2.51513	+	7.74076i	0.0822975	+	0.253286i
$935$	−4.08874	−	10.4240i	−0.133716	−	0.340901i
$936$	−1.55620	+	4.78949i	−0.0508659	+	0.156549i
$937$	20.1037	−	6.53210i	0.656761	−	0.213394i	0.0383679	−	0.999264i	$-0.487784\pi$
$937$	20.1037	−	6.53210i	0.656761	−	0.213394i	0.618393	+	0.785869i	$0.287784\pi$
$938$	−111.267	+	36.1529i	−3.63300	+	1.18043i
$939$	−8.24050	+	25.3617i	−0.268919	+	0.827646i
$940$	11.7658	+	29.9962i	0.383758	+	0.978369i
$941$	5.58426	+	17.1866i	0.182042	+	0.560266i	0.999885	−	0.0151746i	$-0.00483041\pi$
$941$	5.58426	+	17.1866i	0.182042	+	0.560266i	−0.817843	+	0.575441i	$0.804830\pi$
$942$	−54.0134	−	74.3430i	−1.75985	−	2.42223i
$943$			17.5417i			0.571238i
$944$	−3.69500	+	2.68457i	−0.120262	+	0.0873754i
$945$	45.6164	+	11.8675i	1.48390	+	0.386051i
$946$	−24.9877	−	18.1546i	−0.812419	−	0.590257i
$947$	25.8302	−	35.5522i	0.839368	−	1.15529i	−0.146739	−	0.989175i	$-0.546878\pi$
$947$	25.8302	−	35.5522i	0.839368	−	1.15529i	0.986106	−	0.166115i	$-0.0531223\pi$
$948$	−21.3999	−	6.95325i	−0.695036	−	0.225831i
$949$	7.96104			0.258426
$950$	35.9570	−	16.6407i	1.16660	−	0.539896i
$951$	−6.43557			−0.208688
$952$	10.0285	+	3.25847i	0.325027	+	0.105608i
$953$	−15.2901	+	21.0451i	−0.495296	+	0.681717i	−0.981354	−	0.192210i	$-0.938435\pi$
$953$	−15.2901	+	21.0451i	−0.495296	+	0.681717i	0.486058	+	0.873927i	$0.338435\pi$
$954$	5.36552	+	3.89828i	0.173715	+	0.126211i
$955$	−21.8707	+	8.57862i	−0.707719	+	0.277598i
$956$	−20.9876	+	15.2484i	−0.678788	+	0.493168i
$957$			15.4443i			0.499244i
$958$	−19.0891	−	26.2738i	−0.616739	−	0.848869i
$959$	−17.5857	−	54.1232i	−0.567872	−	1.74773i
$960$	−41.4606	+	34.0770i	−1.33814	+	1.09983i
$961$	−0.209238	+	0.643970i	−0.00674963	+	0.0207732i
$962$	69.6781	−	22.6398i	2.24651	−	0.729936i
$963$	−4.14820	+	1.34783i	−0.133674	+	0.0434332i
$964$	−8.41921	+	25.9117i	−0.271165	+	0.834559i
$965$	32.2058	−	1.92309i	1.03674	−	0.0619065i
$966$	21.9958	+	67.6962i	0.707704	+	2.17809i
$967$	25.6494	+	35.3034i	0.824829	+	1.13528i	0.988864	+	0.148825i	$0.0475491\pi$
$967$	25.6494	+	35.3034i	0.824829	+	1.13528i	−0.164035	+	0.986455i	$0.552451\pi$
$968$			33.8745i			1.08877i
$969$	5.23895	−	3.80632i	0.168299	−	0.122277i
$970$	35.1534	+	42.7702i	1.12871	+	1.37327i
$971$	6.94970	+	5.04925i	0.223027	+	0.162038i	0.693688	−	0.720276i	$-0.255985\pi$
$971$	6.94970	+	5.04925i	0.223027	+	0.162038i	−0.470661	+	0.882314i	$0.655985\pi$
$972$	7.17742	−	9.87888i	0.230216	−	0.316865i
$973$	57.8400	+	18.7934i	1.85427	+	0.602488i
$974$	47.6816			1.52782
$975$	−9.67838	+	49.0341i	−0.309956	+	1.57035i
$976$	1.12002			0.0358510
$977$	−33.3202	−	10.8264i	−1.06601	−	0.346367i	−0.277077	−	0.960848i	$-0.589366\pi$
$977$	−33.3202	−	10.8264i	−1.06601	−	0.346367i	−0.788932	+	0.614481i	$0.789366\pi$
$978$	−7.52410	+	10.3560i	−0.240594	+	0.331149i
$979$	55.3519	+	40.2155i	1.76906	+	1.28529i
$980$	−45.0755	+	70.5293i	−1.43989	+	2.25298i
$981$	2.09118	−	1.51933i	0.0667663	−	0.0485085i
$982$			21.2077i			0.676765i
$983$	10.0674	+	13.8566i	0.321101	+	0.441958i	0.938803	−	0.344455i	$-0.111936\pi$
$983$	10.0674	+	13.8566i	0.321101	+	0.441958i	−0.617702	+	0.786412i	$0.711936\pi$
$984$	6.12019	+	18.8360i	0.195105	+	0.600470i
$985$	6.00202	+	3.83591i	0.191240	+	0.122222i
$986$	−1.16626	+	3.58938i	−0.0371413	+	0.114309i
$987$	−35.9987	+	11.6967i	−1.14585	+	0.372309i
$988$	55.8122	−	18.1345i	1.77562	−	0.576934i
$989$	3.32014	−	10.2183i	0.105574	−	0.324924i
$990$	2.44468	−	9.39685i	0.0776970	−	0.298651i
$991$	−6.87433	−	21.1570i	−0.218370	−	0.672075i	−0.998897	−	0.0469526i	$-0.985049\pi$
$991$	−6.87433	−	21.1570i	−0.218370	−	0.672075i	0.780527	−	0.625122i	$-0.214951\pi$
$992$	20.8224	+	28.6595i	0.661111	+	0.909941i
$993$			54.4438i			1.72772i
$994$	120.700	−	87.6939i	3.82838	−	2.78148i
$995$	0.0642707	+	1.07633i	0.00203752	+	0.0341221i
$996$	52.7365	+	38.3153i	1.67102	+	1.21407i
$997$	22.1463	−	30.4818i	0.701380	−	0.965367i	−0.298560	−	0.954391i	$-0.596506\pi$
$997$	22.1463	−	30.4818i	0.701380	−	0.965367i	0.999940	−	0.0109758i	$-0.00349378\pi$
$998$	−0.846721	−	0.275116i	−0.0268025	−	0.00870865i
$999$	−28.8157			−0.911688

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.r.a.154.6	yes	160
25.19	even	10	inner	425.2.r.a.69.6	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.r.a.69.6	✓	160	25.19	even	10	inner
425.2.r.a.154.6	yes	160	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.14124 - 0.695730i) q^{2} +(1.08145 - 1.48849i) q^{3} +(2.48282 + 1.80387i) q^{4} +(-0.133284 - 2.23209i) q^{5} +(-3.35124 + 2.43482i) q^{6} +4.38149i q^{7} +(-1.41458 - 1.94701i) q^{8} +(-0.119019 - 0.366304i) q^{9} +(-1.26754 + 4.87217i) q^{10} +(1.54742 - 4.76246i) q^{11} +(5.37011 - 1.74485i) q^{12} +(5.16707 - 1.67888i) q^{13} +(3.04833 - 9.38180i) q^{14} +(-3.46659 - 2.21551i) q^{15} +(-0.222341 - 0.684295i) q^{16} +(0.587785 + 0.809017i) q^{17} +0.867149i q^{18} +(2.84744 - 2.06879i) q^{19} +(3.69549 - 5.78231i) q^{20} +(6.52181 + 4.73838i) q^{21} +(-6.62677 + 9.12097i) q^{22} +(-3.72988 - 1.21191i) q^{23} -4.42791 q^{24} +(-4.96447 + 0.595005i) q^{25} -12.2320 q^{26} +(4.57553 + 1.48668i) q^{27} +(-7.90365 + 10.8784i) q^{28} +(-1.35616 - 0.985311i) q^{29} +(5.88140 + 7.15575i) q^{30} +(4.45495 - 3.23671i) q^{31} +6.43319i q^{32} +(-5.41543 - 7.45370i) q^{33} +(-0.695730 - 2.14124i) q^{34} +(9.77988 - 0.583982i) q^{35} +(0.365263 - 1.12416i) q^{36} +(-5.69639 + 1.85087i) q^{37} +(-7.53636 + 2.44871i) q^{38} +(3.08894 - 9.50678i) q^{39} +(-4.15735 + 3.41698i) q^{40} +(-1.38219 - 4.25393i) q^{41} +(-10.6681 - 14.6834i) q^{42} +2.73959i q^{43} +(12.4328 - 9.03298i) q^{44} +(-0.801761 + 0.314485i) q^{45} +(7.14340 + 5.18998i) q^{46} +(-2.75987 + 3.79863i) q^{47} +(-1.25902 - 0.409080i) q^{48} -12.1974 q^{49} +(11.0441 + 2.17989i) q^{50} +1.83988 q^{51} +(15.8574 + 5.15238i) q^{52} +(4.49551 - 6.18754i) q^{53} +(-8.76297 - 6.36667i) q^{54} +(-10.8365 - 2.81922i) q^{55} +(8.53078 - 6.19797i) q^{56} -6.47569i q^{57} +(2.21836 + 3.05331i) q^{58} +(-1.96156 - 6.03707i) q^{59} +(-4.61043 - 11.7540i) q^{60} +(-0.481029 + 1.48046i) q^{61} +(-11.7910 + 3.83112i) q^{62} +(1.60496 - 0.521482i) q^{63} +(4.03108 - 12.4064i) q^{64} +(-4.43611 - 11.3096i) q^{65} +(6.40995 + 19.7278i) q^{66} +(-6.97108 - 9.59486i) q^{67} +3.06893i q^{68} +(-5.83762 + 4.24128i) q^{69} +(-21.3473 - 5.55371i) q^{70} +(12.2357 + 8.88975i) q^{71} +(-0.544833 + 0.749898i) q^{72} +(1.39360 + 0.452808i) q^{73} +13.4850 q^{74} +(-4.48319 + 8.03305i) q^{75} +10.8015 q^{76} +(20.8666 + 6.77999i) q^{77} +(-13.2283 + 18.2072i) q^{78} +(-3.22393 - 2.34232i) q^{79} +(-1.49777 + 0.587491i) q^{80} +(8.09593 - 5.88204i) q^{81} +10.0703i q^{82} +(6.78571 + 9.33973i) q^{83} +(7.64506 + 23.5291i) q^{84} +(1.72746 - 1.41982i) q^{85} +(1.90601 - 5.86610i) q^{86} +(-2.93326 + 0.953074i) q^{87} +(-11.4615 + 3.72406i) q^{88} +(-4.22214 + 12.9944i) q^{89} +(1.93556 - 0.115577i) q^{90} +(7.35600 + 22.6394i) q^{91} +(-7.07449 - 9.73720i) q^{92} -10.1315i q^{93} +(8.55235 - 6.21364i) q^{94} +(-4.99724 - 6.08001i) q^{95} +(9.57576 + 6.95719i) q^{96} +(6.46389 - 8.89679i) q^{97} +(26.1176 + 8.48612i) q^{98} -1.92868 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) \) 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Introduction

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