LMFDB - Embedded newform 425.2.k.c.86.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(86,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("425.86");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.1
Character	$\chi$	$=$	425.86
Dual form			425.2.k.c.341.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.14699 + 1.55988i) q^{2} +(-0.173809 + 0.534928i) q^{3} +(1.55831 - 4.79598i) q^{4} +(0.731696 - 2.11297i) q^{5} +(-0.461258 - 1.41961i) q^{6} -2.73519 q^{7} +(2.49532 + 7.67982i) q^{8} +(2.17111 + 1.57741i) q^{9} +(1.72503 + 5.67787i) q^{10} +(-1.98728 + 1.44384i) q^{11} +(2.29466 + 1.66717i) q^{12} +(-0.605542 - 0.439952i) q^{13} +(5.87243 - 4.26657i) q^{14} +(1.00311 + 0.758656i) q^{15} +(-9.17762 - 6.66793i) q^{16} +(-0.309017 - 0.951057i) q^{17} -7.12192 q^{18} +(-2.03360 - 6.25878i) q^{19} +(-8.99353 - 6.80185i) q^{20} +(0.475400 - 1.46313i) q^{21} +(2.01445 - 6.19983i) q^{22} +(-0.549666 + 0.399356i) q^{23} -4.54186 q^{24} +(-3.92924 - 3.09209i) q^{25} +1.98637 q^{26} +(-2.58627 + 1.87903i) q^{27} +(-4.26227 + 13.1179i) q^{28} +(0.782209 - 2.40739i) q^{29} +(-3.33708 - 0.0640975i) q^{30} +(-3.05027 - 9.38776i) q^{31} +13.9554 q^{32} +(-0.426946 - 1.31400i) q^{33} +(2.14699 + 1.55988i) q^{34} +(-2.00133 + 5.77937i) q^{35} +(10.9485 - 7.95453i) q^{36} +(3.80421 + 2.76392i) q^{37} +(14.1291 + 10.2654i) q^{38} +(0.340591 - 0.247454i) q^{39} +(18.0530 + 0.346756i) q^{40} +(0.121810 + 0.0884998i) q^{41} +(1.26163 + 3.88290i) q^{42} -11.5902 q^{43} +(3.82785 + 11.7809i) q^{44} +(4.92160 - 3.43330i) q^{45} +(0.557180 - 1.71482i) q^{46} +(2.48474 - 7.64725i) q^{47} +(5.16202 - 3.75042i) q^{48} +0.481275 q^{49} +(13.2593 + 0.509550i) q^{50} +0.562457 q^{51} +(-3.05362 + 2.21859i) q^{52} +(3.00720 - 9.25521i) q^{53} +(2.62163 - 8.06853i) q^{54} +(1.59671 + 5.25551i) q^{55} +(-6.82519 - 21.0058i) q^{56} +3.70146 q^{57} +(2.07585 + 6.38880i) q^{58} +(4.52500 + 3.28760i) q^{59} +(5.20165 - 3.62867i) q^{60} +(-5.68375 + 4.12948i) q^{61} +(21.1927 + 15.3974i) q^{62} +(-5.93841 - 4.31451i) q^{63} +(-11.6068 + 8.43282i) q^{64} +(-1.37268 + 0.957579i) q^{65} +(2.96634 + 2.15517i) q^{66} +(-4.48680 - 13.8089i) q^{67} -5.04279 q^{68} +(-0.118090 - 0.363443i) q^{69} +(-4.71828 - 15.5301i) q^{70} +(-3.84951 + 11.8476i) q^{71} +(-6.69656 + 20.6099i) q^{72} +(-0.966538 + 0.702231i) q^{73} -12.4790 q^{74} +(2.33698 - 1.56443i) q^{75} -33.1860 q^{76} +(5.43559 - 3.94919i) q^{77} +(-0.345248 + 1.06256i) q^{78} +(0.502069 - 1.54521i) q^{79} +(-20.8043 + 14.5131i) q^{80} +(1.93224 + 5.94683i) q^{81} -0.399573 q^{82} +(-1.16664 - 3.59056i) q^{83} +(-6.27633 - 4.56002i) q^{84} +(-2.23566 - 0.0429417i) q^{85} +(24.8841 - 18.0793i) q^{86} +(1.15183 + 0.836851i) q^{87} +(-16.0474 - 11.6591i) q^{88} +(4.25505 - 3.09148i) q^{89} +(-5.21108 + 15.0484i) q^{90} +(1.65627 + 1.20335i) q^{91} +(1.05875 + 3.25851i) q^{92} +5.55194 q^{93} +(6.59407 + 20.2945i) q^{94} +(-14.7126 - 0.282594i) q^{95} +(-2.42556 + 7.46511i) q^{96} +(1.74846 - 5.38120i) q^{97} +(-1.03329 + 0.750732i) q^{98} -6.59213 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) $ 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

Character values

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

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−2.14699	+	1.55988i	−1.51815	+	1.10300i	−0.555757	+	0.831345i	$0.687572\pi$
$2$	−2.14699	+	1.55988i	−1.51815	+	1.10300i	−0.962394	+	0.271657i	$0.912428\pi$
$3$	−0.173809	+	0.534928i	−0.100348	+	0.308841i	−0.988611	−	0.150496i	$-0.951913\pi$
$3$	−0.173809	+	0.534928i	−0.100348	+	0.308841i	0.888262	+	0.459337i	$0.151913\pi$
$4$	1.55831	−	4.79598i	0.779154	−	2.39799i
$5$	0.731696	−	2.11297i	0.327224	−	0.944947i
$5$	0.731696	−	2.11297i	0.327224	−	0.944947i
$6$	−0.461258	−	1.41961i	−0.188308	−	0.579552i
$7$	−2.73519			−1.03381			−0.516903	−	0.856044i	$-0.672915\pi$
$7$	−2.73519			−1.03381			−0.516903	+	0.856044i	$0.672915\pi$
$8$	2.49532	+	7.67982i	0.882230	+	2.71523i
$9$	2.17111	+	1.57741i	0.723704	+	0.525802i
$10$	1.72503	+	5.67787i	0.545502	+	1.79550i
$11$	−1.98728	+	1.44384i	−0.599187	+	0.435335i	−0.845590	−	0.533832i	$-0.820751\pi$
$11$	−1.98728	+	1.44384i	−0.599187	+	0.435335i	0.246403	+	0.969167i	$0.420751\pi$
$12$	2.29466	+	1.66717i	0.662410	+	0.481269i
$13$	−0.605542	−	0.439952i	−0.167947	−	0.122021i	0.500637	−	0.865657i	$-0.333099\pi$
$13$	−0.605542	−	0.439952i	−0.167947	−	0.122021i	−0.668584	+	0.743637i	$0.733099\pi$
$14$	5.87243	−	4.26657i	1.56947	−	1.14029i
$15$	1.00311	+	0.758656i	0.259002	+	0.195884i
$16$	−9.17762	−	6.66793i	−2.29441	−	1.66698i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$18$	−7.12192			−1.67865
$19$	−2.03360	−	6.25878i	−0.466540	−	1.43586i	−0.857035	−	0.515258i	$-0.827696\pi$
$19$	−2.03360	−	6.25878i	−0.466540	−	1.43586i	0.390495	−	0.920605i	$-0.372304\pi$
$20$	−8.99353	−	6.80185i	−2.01101	−	1.52094i
$21$	0.475400	−	1.46313i	0.103741	−	0.319281i
$22$	2.01445	−	6.19983i	0.429482	−	1.32181i
$23$	−0.549666	+	0.399356i	−0.114613	+	0.0832714i	−0.643615	−	0.765349i	$-0.722566\pi$
$23$	−0.549666	+	0.399356i	−0.114613	+	0.0832714i	0.529002	+	0.848620i	$0.322566\pi$
$24$	−4.54186			−0.927103
$25$	−3.92924	−	3.09209i	−0.785849	−	0.618419i
$26$	1.98637			0.389559
$27$	−2.58627	+	1.87903i	−0.497727	+	0.361620i
$28$	−4.26227	+	13.1179i	−0.805494	+	2.47905i
$29$	0.782209	−	2.40739i	0.145252	−	0.447041i	−0.851791	−	0.523882i	$-0.824483\pi$
$29$	0.782209	−	2.40739i	0.145252	−	0.447041i	0.997043	+	0.0768407i	$0.0244833\pi$
$30$	−3.33708	−	0.0640975i	−0.609264	−	0.0117025i
$31$	−3.05027	−	9.38776i	−0.547844	−	1.68609i	−0.714130	−	0.700014i	$-0.753177\pi$
$31$	−3.05027	−	9.38776i	−0.547844	−	1.68609i	0.166285	−	0.986078i	$-0.446823\pi$
$32$	13.9554			2.46698
$33$	−0.426946	−	1.31400i	−0.0743217	−	0.228739i
$34$	2.14699	+	1.55988i	0.368206	+	0.267517i
$35$	−2.00133	+	5.77937i	−0.338286	+	0.976891i
$36$	10.9485	−	7.95453i	1.82474	−	1.32575i
$37$	3.80421	+	2.76392i	0.625409	+	0.454386i	0.854807	−	0.518947i	$-0.173676\pi$
$37$	3.80421	+	2.76392i	0.625409	+	0.454386i	−0.229398	+	0.973333i	$0.573676\pi$
$38$	14.1291	+	10.2654i	2.29204	+	1.66526i
$39$	0.340591	−	0.247454i	0.0545383	−	0.0396244i
$40$	18.0530	+	0.346756i	2.85443	+	0.0548269i
$41$	0.121810	+	0.0884998i	0.0190235	+	0.0138214i	0.597256	−	0.802050i	$-0.296257\pi$
$41$	0.121810	+	0.0884998i	0.0190235	+	0.0138214i	−0.578233	+	0.815872i	$0.696257\pi$
$42$	1.26163	+	3.88290i	0.194674	+	0.599144i
$43$	−11.5902			−1.76749			−0.883746	−	0.467967i	$-0.844986\pi$
$43$	−11.5902			−1.76749			−0.883746	+	0.467967i	$0.844986\pi$
$44$	3.82785	+	11.7809i	0.577070	+	1.77604i
$45$	4.92160	−	3.43330i	0.733668	−	0.511807i
$46$	0.557180	−	1.71482i	0.0821518	−	0.252837i
$47$	2.48474	−	7.64725i	0.362437	−	1.11547i	−0.589134	−	0.808035i	$-0.700531\pi$
$47$	2.48474	−	7.64725i	0.362437	−	1.11547i	0.951571	−	0.307430i	$-0.0994691\pi$
$48$	5.16202	−	3.75042i	0.745073	−	0.541327i
$49$	0.481275			0.0687536
$50$	13.2593	+	0.509550i	1.87515	+	0.0720612i
$51$	0.562457			0.0787597
$52$	−3.05362	+	2.21859i	−0.423462	+	0.307663i
$53$	3.00720	−	9.25521i	0.413071	−	1.27130i	−0.500894	−	0.865509i	$-0.666995\pi$
$53$	3.00720	−	9.25521i	0.413071	−	1.27130i	0.913965	−	0.405793i	$-0.133005\pi$
$54$	2.62163	−	8.06853i	0.356758	−	1.09799i
$55$	1.59671	+	5.25551i	0.215300	+	0.708652i
$56$	−6.82519	−	21.0058i	−0.912055	−	2.80702i
$57$	3.70146			0.490270
$58$	2.07585	+	6.38880i	0.272572	+	0.838890i
$59$	4.52500	+	3.28760i	0.589104	+	0.428009i	0.841995	−	0.539485i	$-0.181381\pi$
$59$	4.52500	+	3.28760i	0.589104	+	0.428009i	−0.252890	+	0.967495i	$0.581381\pi$
$60$	5.20165	−	3.62867i	0.671531	−	0.468460i
$61$	−5.68375	+	4.12948i	−0.727729	+	0.528726i	−0.888844	−	0.458209i	$-0.848491\pi$
$61$	−5.68375	+	4.12948i	−0.727729	+	0.528726i	0.161115	+	0.986936i	$0.448491\pi$
$62$	21.1927	+	15.3974i	2.69147	+	1.95547i
$63$	−5.93841	−	4.31451i	−0.748169	−	0.543577i
$64$	−11.6068	+	8.43282i	−1.45085	+	1.05410i
$65$	−1.37268	+	0.957579i	−0.170260	+	0.118773i
$66$	2.96634	+	2.15517i	0.365131	+	0.265283i
$67$	−4.48680	−	13.8089i	−0.548149	−	1.68703i	−0.713382	−	0.700775i	$-0.752838\pi$
$67$	−4.48680	−	13.8089i	−0.548149	−	1.68703i	0.165233	−	0.986255i	$-0.447162\pi$
$68$	−5.04279			−0.611528
$69$	−0.118090	−	0.363443i	−0.0142163	−	0.0437534i
$70$	−4.71828	−	15.5301i	−0.563943	−	1.85620i
$71$	−3.84951	+	11.8476i	−0.456853	+	1.40605i	0.412092	+	0.911142i	$0.364798\pi$
$71$	−3.84951	+	11.8476i	−0.456853	+	1.40605i	−0.868946	+	0.494908i	$0.835202\pi$
$72$	−6.69656	+	20.6099i	−0.789197	+	2.42890i
$73$	−0.966538	+	0.702231i	−0.113125	+	0.0821899i	−0.642909	−	0.765942i	$-0.722273\pi$
$73$	−0.966538	+	0.702231i	−0.113125	+	0.0821899i	0.529785	+	0.848132i	$0.322273\pi$
$74$	−12.4790			−1.45065
$75$	2.33698	−	1.56443i	0.269852	−	0.180645i
$76$	−33.1860			−3.80669
$77$	5.43559	−	3.94919i	0.619443	−	0.450052i
$78$	−0.345248	+	1.06256i	−0.0390916	+	0.120312i
$79$	0.502069	−	1.54521i	0.0564872	−	0.173850i	−0.918832	−	0.394648i	$-0.870866\pi$
$79$	0.502069	−	1.54521i	0.0564872	−	0.173850i	0.975319	+	0.220799i	$0.0708664\pi$
$80$	−20.8043	+	14.5131i	−2.32600	+	1.62261i
$81$	1.93224	+	5.94683i	0.214693	+	0.660759i
$82$	−0.399573			−0.0441255
$83$	−1.16664	−	3.59056i	−0.128056	−	0.394115i	0.866390	−	0.499369i	$-0.166435\pi$
$83$	−1.16664	−	3.59056i	−0.128056	−	0.394115i	−0.994445	+	0.105253i	$0.966435\pi$
$84$	−6.27633	−	4.56002i	−0.684803	−	0.497539i
$85$	−2.23566	−	0.0429417i	−0.242491	−	0.00465768i
$86$	24.8841	−	18.0793i	2.68332	−	1.94955i
$87$	1.15183	+	0.836851i	0.123489	+	0.0897198i
$88$	−16.0474	−	11.6591i	−1.71065	−	1.24286i
$89$	4.25505	−	3.09148i	0.451035	−	0.327696i	−0.338969	−	0.940797i	$-0.610078\pi$
$89$	4.25505	−	3.09148i	0.451035	−	0.327696i	0.790004	+	0.613101i	$0.210078\pi$
$90$	−5.21108	+	15.0484i	−0.549296	+	1.58624i
$91$	1.65627	+	1.20335i	0.173625	+	0.126146i
$92$	1.05875	+	3.25851i	0.110383	+	0.339723i
$93$	5.55194			0.575709
$94$	6.59407	+	20.2945i	0.680126	+	2.09321i
$95$	−14.7126	−	0.282594i	−1.50948	−	0.0289935i
$96$	−2.42556	+	7.46511i	−0.247558	+	0.761905i
$97$	1.74846	−	5.38120i	0.177529	−	0.546378i	−0.822211	−	0.569183i	$-0.807260\pi$
$97$	1.74846	−	5.38120i	0.177529	−	0.546378i	0.999740	+	0.0228050i	$0.00725970\pi$
$98$	−1.03329	+	0.750732i	−0.104378	+	0.0758353i
$99$	−6.59213			−0.662534
$100$	−20.9526	+	14.0261i	−2.09526	+	1.40261i
$101$	11.8111			1.17525			0.587623	−	0.809135i	$-0.300064\pi$
$101$	11.8111			1.17525			0.587623	+	0.809135i	$0.300064\pi$
$102$	−1.20759	+	0.877365i	−0.119569	+	0.0868721i
$103$	−1.86423	+	5.73751i	−0.183688	+	0.565334i	−0.999923	−	0.0123859i	$-0.996057\pi$
$103$	−1.86423	+	5.73751i	−0.183688	+	0.565334i	0.816235	+	0.577720i	$0.196057\pi$
$104$	1.86773	−	5.74828i	0.183146	−	0.563665i
$105$	−2.74370	−	2.07507i	−0.267757	−	0.202506i
$106$	7.98059	+	24.5617i	0.775143	+	2.38565i
$107$	−13.7732			−1.33151			−0.665755	−	0.746170i	$-0.731890\pi$
$107$	−13.7732			−1.33151			−0.665755	+	0.746170i	$0.731890\pi$
$108$	4.98160	+	15.3318i	0.479355	+	1.47530i
$109$	−9.77327	−	7.10069i	−0.936109	−	0.680123i	0.0113717	−	0.999935i	$-0.496380\pi$
$109$	−9.77327	−	7.10069i	−0.936109	−	0.680123i	−0.947481	+	0.319812i	$0.896380\pi$
$110$	−11.6261	−	8.79285i	−1.10850	−	0.838365i
$111$	−2.13970	+	1.55459i	−0.203092	+	0.147555i
$112$	25.1026	+	18.2381i	2.37197	+	1.72334i
$113$	8.22714	+	5.97737i	0.773944	+	0.562303i	0.903155	−	0.429314i	$-0.141245\pi$
$113$	8.22714	+	5.97737i	0.773944	+	0.562303i	−0.129211	+	0.991617i	$0.541245\pi$
$114$	−7.94699	+	5.77383i	−0.744304	+	0.540768i
$115$	0.441636	+	1.45363i	0.0411828	+	0.135552i
$116$	−10.3269	−	7.50291i	−0.958826	−	0.696628i
$117$	−0.620717	−	1.91037i	−0.0573854	−	0.176614i
$118$	−14.8434			−1.36644
$119$	0.845221	+	2.60132i	0.0774813	+	0.238463i
$120$	−3.32326	+	9.59679i	−0.303371	+	0.876063i
$121$	−1.53459	+	4.72298i	−0.139508	+	0.429362i
$122$	5.76145	−	17.7319i	0.521617	−	1.60537i
$123$	−0.0685126	+	0.0497773i	−0.00617757	+	0.00448827i
$124$	−49.7768			−4.47008
$125$	−9.40850	+	6.03988i	−0.841522	+	0.540223i
$126$	19.4798			1.73540
$127$	16.3067	−	11.8475i	1.44699	−	1.05130i	0.460466	−	0.887677i	$-0.347682\pi$
$127$	16.3067	−	11.8475i	1.44699	−	1.05130i	0.986523	−	0.163622i	$-0.0523177\pi$
$128$	3.14057	−	9.66568i	0.277590	−	0.854333i
$129$	2.01448	−	6.19993i	0.177365	−	0.545874i
$130$	1.45342	−	4.19712i	0.127473	−	0.368112i
$131$	1.21113	+	3.72747i	0.105817	+	0.325670i	0.989921	−	0.141619i	$-0.0452307\pi$
$131$	1.21113	+	3.72747i	0.105817	+	0.325670i	−0.884105	+	0.467289i	$0.845231\pi$
$132$	−6.96725			−0.606421
$133$	5.56229	+	17.1190i	0.482312	+	1.48440i
$134$	31.1734	+	22.6488i	2.69297	+	1.95656i
$135$	2.07797	+	6.83957i	0.178843	+	0.588657i
$136$	6.53284	−	4.74639i	0.560187	−	0.407000i
$137$	−4.93524	−	3.58566i	−0.421646	−	0.306344i	0.356654	−	0.934237i	$-0.383918\pi$
$137$	−4.93524	−	3.58566i	−0.421646	−	0.306344i	−0.778300	+	0.627893i	$0.783918\pi$
$138$	0.820465	+	0.596103i	0.0698426	+	0.0507437i
$139$	8.11941	−	5.89910i	0.688679	−	0.500355i	−0.187546	−	0.982256i	$-0.560053\pi$
$139$	8.11941	−	5.89910i	0.688679	−	0.500355i	0.876226	+	0.481901i	$0.160053\pi$
$140$	24.5990	+	18.6044i	2.07900	+	1.57236i
$141$	3.65886	+	2.65832i	0.308131	+	0.223871i
$142$	−10.2159	−	31.4414i	−0.857303	−	2.63851i
$143$	1.83860			0.153752
$144$	−9.40762	−	28.9537i	−0.783968	−	2.41281i
$145$	−4.51439	−	3.41426i	−0.374900	−	0.283539i
$146$	0.979752	−	3.01537i	0.0810848	−	0.249553i
$147$	−0.0836498	+	0.257448i	−0.00689932	+	0.0212339i
$148$	19.1839	−	13.9379i	1.57690	−	1.14569i
$149$	−19.4809			−1.59594			−0.797968	−	0.602700i	$-0.794092\pi$
$149$	−19.4809			−1.59594			−0.797968	+	0.602700i	$0.794092\pi$
$150$	−2.57716	+	7.00423i	−0.210424	+	0.571893i
$151$	7.81881			0.636286			0.318143	−	0.948043i	$-0.396941\pi$
$151$	7.81881			0.636286			0.318143	+	0.948043i	$0.396941\pi$
$152$	42.9918	−	31.2354i	3.48710	−	2.53352i
$153$	0.829291	−	2.55230i	0.0670442	−	0.206341i
$154$	−5.50990	+	16.9577i	−0.444001	+	1.36649i
$155$	−22.0679	−	0.423872i	−1.77253	−	0.0340462i
$156$	−0.656039	−	2.01908i	−0.0525251	−	0.161656i
$157$	6.83118			0.545187			0.272594	−	0.962129i	$-0.412119\pi$
$157$	6.83118			0.545187			0.272594	+	0.962129i	$0.412119\pi$
$158$	1.33240	+	4.10072i	0.106000	+	0.326235i
$159$	4.42820	+	3.21727i	0.351179	+	0.255146i
$160$	10.2111	−	29.4872i	0.807256	−	2.33117i
$161$	1.50344	−	1.09231i	0.118488	−	0.0860864i
$162$	−13.4248	−	9.75372i	−1.05475	−	0.766324i
$163$	1.13350	+	0.823537i	0.0887827	+	0.0645044i	0.631291	−	0.775546i	$-0.282525\pi$
$163$	1.13350	+	0.823537i	0.0887827	+	0.0645044i	−0.542508	+	0.840050i	$0.682525\pi$
$164$	0.614260	−	0.446286i	0.0479657	−	0.0348491i
$165$	−3.08884	−	0.0593294i	−0.240466	−	0.00461879i
$166$	8.10562	+	5.88908i	0.629118	+	0.457081i
$167$	1.31487	+	4.04675i	0.101748	+	0.313147i	0.988953	−	0.148227i	$-0.0473566\pi$
$167$	1.31487	+	4.04675i	0.101748	+	0.313147i	−0.887206	+	0.461374i	$0.847357\pi$
$168$	12.4229			0.958444
$169$	−3.84410	−	11.8309i	−0.295700	−	0.910070i
$170$	4.86691	−	3.39516i	0.373275	−	0.260397i
$171$	5.45746	−	16.7963i	0.417342	−	1.28445i
$172$	−18.0611	+	55.5864i	−1.37715	+	4.23843i
$173$	−10.0476	+	7.29998i	−0.763902	+	0.555007i	−0.900105	−	0.435674i	$-0.856510\pi$
$173$	−10.0476	+	7.29998i	−0.763902	+	0.555007i	0.136203	+	0.990681i	$0.456510\pi$
$174$	−3.77835			−0.286436
$175$	10.7472	+	8.45747i	0.812415	+	0.639325i
$176$	27.8659			2.10047
$177$	−2.54512	+	1.84913i	−0.191303	+	0.138989i
$178$	−4.31323	+	13.2747i	−0.323290	+	0.994984i
$179$	−2.85923	+	8.79981i	−0.213709	+	0.657729i	0.785534	+	0.618819i	$0.212389\pi$
$179$	−2.85923	+	8.79981i	−0.213709	+	0.657729i	−0.999243	+	0.0389099i	$0.987611\pi$
$180$	−8.79669	−	28.9540i	−0.655667	−	2.15811i
$181$	7.82993	+	24.0981i	0.581994	+	1.79119i	0.611019	+	0.791616i	$0.290760\pi$
$181$	7.82993	+	24.0981i	0.581994	+	1.79119i	−0.0290248	+	0.999579i	$0.509240\pi$
$182$	−5.43309			−0.402728
$183$	−1.22109	−	3.75814i	−0.0902658	−	0.277809i
$184$	−4.43857	−	3.22481i	−0.327216	−	0.237736i
$185$	8.62360	−	6.01582i	0.634019	−	0.442292i
$186$	−11.9200	+	8.66036i	−0.874014	+	0.635008i
$187$	1.98728	+	1.44384i	0.145324	+	0.105584i
$188$	−32.8041	−	23.8335i	−2.39248	−	1.73824i
$189$	7.07394	−	5.13952i	0.514553	−	0.373845i
$190$	32.0285	−	22.3431i	2.32359	−	1.62094i
$191$	3.16322	+	2.29822i	0.228883	+	0.166293i	0.696316	−	0.717735i	$-0.254821\pi$
$191$	3.16322	+	2.29822i	0.228883	+	0.166293i	−0.467433	+	0.884028i	$0.654821\pi$
$192$	−2.49359	−	7.67449i	−0.179960	−	0.553858i
$193$	12.0930			0.870476			0.435238	−	0.900315i	$-0.356664\pi$
$193$	12.0930			0.870476			0.435238	+	0.900315i	$0.356664\pi$
$194$	4.64010	+	14.2808i	0.333140	+	1.02530i
$195$	−0.273653	−	0.900719i	−0.0195967	−	0.0645018i
$196$	0.749975	−	2.30819i	0.0535697	−	0.164870i
$197$	−5.98911	+	18.4326i	−0.426706	+	1.31327i	0.474644	+	0.880178i	$0.342577\pi$
$197$	−5.98911	+	18.4326i	−0.426706	+	1.31327i	−0.901351	+	0.433090i	$0.857423\pi$
$198$	14.1532	−	10.2829i	1.00583	−	0.730776i
$199$	21.4547			1.52089			0.760443	−	0.649405i	$-0.224982\pi$
$199$	21.4547			1.52089			0.760443	+	0.649405i	$0.224982\pi$
$200$	13.9420	−	37.8917i	0.985847	−	2.67934i
$201$	8.16663			0.576030
$202$	−25.3583	+	18.4239i	−1.78420	+	1.29630i
$203$	−2.13949	+	6.58468i	−0.150163	+	0.462154i
$204$	0.876481	−	2.69753i	0.0613659	−	0.188865i
$205$	0.276125	−	0.192624i	0.0192854	−	0.0134535i
$206$	−4.94734	−	15.2264i	−0.344698	−	1.06087i
$207$	−1.82333			−0.126730
$208$	2.62387	+	8.07543i	0.181932	+	0.559931i
$209$	13.0780	+	9.50175i	0.904626	+	0.657250i
$210$	9.12755	+	0.175319i	0.629861	+	0.0120982i
$211$	−18.8850	+	13.7207i	−1.30010	+	0.944575i	−0.999957	−	0.00932095i	$-0.997033\pi$
$211$	−18.8850	+	13.7207i	−1.30010	+	0.944575i	−0.300139	+	0.953896i	$0.597033\pi$
$212$	−39.7017	−	28.8450i	−2.72672	−	1.98108i
$213$	−5.66853	−	4.11843i	−0.388401	−	0.282190i
$214$	29.5710	−	21.4846i	2.02143	−	1.46866i
$215$	−8.48051	+	24.4897i	−0.578366	+	1.67019i
$216$	−20.8842	−	15.1733i	−1.42099	−	1.03241i
$217$	8.34307	+	25.6773i	0.566364	+	1.74309i
$218$	32.0593			2.17133
$219$	−0.207650	−	0.639082i	−0.0140317	−	0.0431852i
$220$	27.6935	+	0.531927i	1.86709	+	0.0358625i
$221$	−0.231297	+	0.711858i	−0.0155587	+	0.0478847i
$222$	2.16896	−	6.67536i	0.145571	−	0.448021i
$223$	0.919159	−	0.667808i	0.0615514	−	0.0447197i	−0.556584	−	0.830791i	$-0.687888\pi$
$223$	0.919159	−	0.667808i	0.0615514	−	0.0447197i	0.618136	+	0.786072i	$0.287888\pi$
$224$	−38.1706			−2.55038
$225$	−3.65334	−	12.9113i	−0.243556	−	0.860753i
$226$	−26.9876			−1.79519
$227$	15.4365	−	11.2152i	1.02455	−	0.744381i	0.0573420	−	0.998355i	$-0.481737\pi$
$227$	15.4365	−	11.2152i	1.02455	−	0.744381i	0.967211	+	0.253973i	$0.0817375\pi$
$228$	5.76801	−	17.7521i	0.381996	−	1.17566i
$229$	4.79900	−	14.7698i	0.317127	−	0.976016i	−0.657743	−	0.753242i	$-0.728489\pi$
$229$	4.79900	−	14.7698i	0.317127	−	0.976016i	0.974870	−	0.222774i	$-0.0715111\pi$
$230$	−3.21568	−	2.43203i	−0.212036	−	0.160363i
$231$	1.16778	+	3.59405i	0.0768342	+	0.236471i
$232$	20.4402			1.34196
$233$	−3.39821	−	10.4586i	−0.222624	−	0.685167i	−0.998524	−	0.0543111i	$-0.982704\pi$
$233$	−3.39821	−	10.4586i	−0.222624	−	0.685167i	0.775900	−	0.630856i	$-0.217296\pi$
$234$	4.31262	+	3.13331i	0.281925	+	0.204831i
$235$	−14.3403	−	10.8456i	−0.935458	−	0.707491i
$236$	22.8186	−	16.5787i	1.48537	−	1.07918i
$237$	0.739312	+	0.537142i	0.0480235	+	0.0348911i
$238$	−5.87243	−	4.26657i	−0.380653	−	0.276561i
$239$	−8.91262	+	6.47540i	−0.576509	+	0.418859i	−0.837464	−	0.546492i	$-0.815963\pi$
$239$	−8.91262	+	6.47540i	−0.576509	+	0.418859i	0.260955	+	0.965351i	$0.415963\pi$
$240$	−4.14749	−	13.6513i	−0.267719	−	0.881189i
$241$	−6.29409	−	4.57292i	−0.405438	−	0.294568i	0.366314	−	0.930491i	$-0.380619\pi$
$241$	−6.29409	−	4.57292i	−0.405438	−	0.294568i	−0.771752	+	0.635923i	$0.780619\pi$
$242$	−4.07253	−	12.5340i	−0.261792	−	0.805714i
$243$	−13.1074			−0.840838
$244$	10.9479	+	33.6941i	0.700867	+	2.15705i
$245$	0.352147	−	1.01692i	0.0224978	−	0.0649685i
$246$	0.0694493	−	0.213743i	0.00442792	−	0.0136277i
$247$	−1.52213	+	4.68465i	−0.0968510	+	0.298077i
$248$	64.4849	−	46.8510i	4.09479	−	2.97504i
$249$	2.12347			0.134569
$250$	10.7785	−	27.6437i	0.681690	−	1.74834i
$251$	18.5313			1.16968			0.584842	−	0.811147i	$-0.301156\pi$
$251$	18.5313			1.16968			0.584842	+	0.811147i	$0.301156\pi$
$252$	−29.9462	+	21.7572i	−1.88643	+	1.37057i
$253$	0.515733	−	1.58726i	0.0324238	−	0.0997903i
$254$	−16.5297	+	50.8731i	−1.03716	+	3.19206i
$255$	0.411547	−	1.18845i	0.0257721	−	0.0744237i
$256$	−0.532264	−	1.63814i	−0.0332665	−	0.102384i
$257$	−24.1779			−1.50818			−0.754088	−	0.656773i	$-0.771921\pi$
$257$	−24.1779			−1.50818			−0.754088	+	0.656773i	$0.771921\pi$
$258$	5.34608	+	16.4535i	0.332832	+	1.02435i
$259$	−10.4053	−	7.55986i	−0.646551	−	0.469747i
$260$	2.45348	+	8.07553i	0.152158	+	0.500823i
$261$	5.49569	−	3.99286i	0.340175	−	0.247152i
$262$	−8.41468	−	6.11362i	−0.519860	−	0.377701i
$263$	12.7157	+	9.23849i	0.784083	+	0.569669i	0.906202	−	0.422846i	$-0.138969\pi$
$263$	12.7157	+	9.23849i	0.784083	+	0.569669i	−0.122119	+	0.992515i	$0.538969\pi$
$264$	9.02595	−	6.55773i	0.555509	−	0.403601i
$265$	−17.3556	−	13.1261i	−1.06615	−	0.806331i
$266$	−38.6457	−	28.0778i	−2.36952	−	1.72156i
$267$	0.914153	+	2.81347i	0.0559453	+	0.172182i
$268$	−73.2192			−4.47257
$269$	1.31173	+	4.03710i	0.0799778	+	0.246147i	0.983049	−	0.183345i	$-0.0586927\pi$
$269$	1.31173	+	4.03710i	0.0799778	+	0.246147i	−0.903071	+	0.429492i	$0.858693\pi$
$270$	−15.1303	−	11.4431i	−0.920801	−	0.696406i
$271$	−4.90959	+	15.1102i	−0.298236	+	0.917877i	0.683879	+	0.729596i	$0.260292\pi$
$271$	−4.90959	+	15.1102i	−0.298236	+	0.917877i	−0.982115	+	0.188281i	$0.939708\pi$
$272$	−3.50554	+	10.7889i	−0.212555	+	0.654176i
$273$	−0.931583	+	0.676835i	−0.0563820	+	0.0409639i
$274$	16.1891			0.978020
$275$	12.2730	+	0.471645i	0.740090	+	0.0284413i
$276$	−1.92709			−0.115997
$277$	20.1314	−	14.6263i	1.20958	−	0.878811i	0.214387	−	0.976749i	$-0.431225\pi$
$277$	20.1314	−	14.6263i	1.20958	−	0.878811i	0.995193	+	0.0979382i	$0.0312247\pi$
$278$	−8.23041	+	25.3306i	−0.493627	+	1.51923i
$279$	8.18583	−	25.1934i	0.490073	−	1.50829i
$280$	−49.3784	−	0.948444i	−2.95093	−	0.0566804i
$281$	−0.0404478	−	0.124486i	−0.00241292	−	0.00742619i	0.949843	−	0.312728i	$-0.101243\pi$
$281$	−0.0404478	−	0.124486i	−0.00241292	−	0.00742619i	−0.952256	+	0.305302i	$0.901243\pi$
$282$	−12.0022			−0.714720
$283$	5.05096	+	15.5452i	0.300248	+	0.924069i	0.981408	+	0.191934i	$0.0614760\pi$
$283$	5.05096	+	15.5452i	0.300248	+	0.924069i	−0.681160	+	0.732135i	$0.738524\pi$
$284$	50.8221	+	36.9244i	3.01573	+	2.19106i
$285$	2.70834	−	7.82105i	0.160428	−	0.463279i
$286$	−3.94747	+	2.86800i	−0.233419	+	0.169588i
$287$	−0.333173	−	0.242064i	−0.0196666	−	0.0142886i
$288$	30.2987	+	22.0133i	1.78537	+	1.29714i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	15.0182	+	0.288464i	0.881898	+	0.0169392i
$291$	2.57466	+	1.87060i	0.150929	+	0.109656i
$292$	1.86172	+	5.72979i	0.108949	+	0.335311i
$293$	−9.46138			−0.552739			−0.276370	−	0.961051i	$-0.589131\pi$
$293$	−9.46138			−0.552739			−0.276370	+	0.961051i	$0.589131\pi$
$294$	−0.221992	−	0.683221i	−0.0129468	−	0.0398463i
$295$	10.2575	−	7.15564i	0.597215	−	0.416617i
$296$	−11.7337	+	36.1125i	−0.682006	+	2.09900i
$297$	2.42661	−	7.46833i	0.140806	−	0.433356i
$298$	41.8253	−	30.3878i	2.42287	−	1.76032i
$299$	0.508543			0.0294098
$300$	−3.86123	−	13.6460i	−0.222928	−	0.787852i
$301$	31.7015			1.82724
$302$	−16.7869	+	12.1964i	−0.965978	+	0.701824i
$303$	−2.05287	+	6.31808i	−0.117934	+	0.362964i
$304$	−23.0695	+	71.0007i	−1.32313	+	4.07217i
$305$	4.56668	+	15.0311i	0.261488	+	0.860677i
$306$	2.20079	+	6.77335i	0.125811	+	0.387207i
$307$	−18.6528			−1.06457			−0.532287	−	0.846564i	$-0.678667\pi$
$307$	−18.6528			−1.06457			−0.532287	+	0.846564i	$0.678667\pi$
$308$	−10.4699	−	32.2230i	−0.596578	−	1.83608i
$309$	−2.74514	−	1.99446i	−0.156165	−	0.113461i
$310$	48.0407	−	33.5132i	2.72853	−	1.90342i
$311$	−10.8275	+	7.86665i	−0.613972	+	0.446077i	−0.850811	−	0.525472i	$-0.823889\pi$
$311$	−10.8275	+	7.86665i	−0.613972	+	0.446077i	0.236839	+	0.971549i	$0.423889\pi$
$312$	2.75029	+	1.99820i	0.155704	+	0.113126i
$313$	3.26363	+	2.37117i	0.184471	+	0.134026i	0.676188	−	0.736729i	$-0.263631\pi$
$313$	3.26363	+	2.37117i	0.184471	+	0.134026i	−0.491717	+	0.870755i	$0.663631\pi$
$314$	−14.6665	+	10.6558i	−0.827677	+	0.601342i
$315$	−13.4615	+	9.39075i	−0.758470	+	0.529109i
$316$	−6.62841	−	4.81582i	−0.372877	−	0.270911i
$317$	−7.03348	−	21.6468i	−0.395040	−	1.21581i	−0.928931	−	0.370254i	$-0.879271\pi$
$317$	−7.03348	−	21.6468i	−0.395040	−	1.21581i	0.533891	−	0.845553i	$-0.320729\pi$
$318$	−14.5259			−0.814569
$319$	1.92143	+	5.91354i	0.107579	+	0.331095i
$320$	9.32562	+	30.6950i	0.521318	+	1.71590i
$321$	2.39391	−	7.36770i	0.133615	−	0.411225i
$322$	−1.52400	+	4.69038i	−0.0849289	+	0.261384i
$323$	−5.32404	+	3.86814i	−0.296237	+	0.215229i
$324$	31.5319			1.75177
$325$	1.01895	+	3.60107i	0.0565211	+	0.199752i
$326$	−3.71823			−0.205934
$327$	5.49704	−	3.99383i	0.303987	−	0.220859i
$328$	−0.375708	+	1.15631i	−0.0207450	+	0.0638466i
$329$	−6.79624	+	20.9167i	−0.374689	+	1.15317i
$330$	6.72425	−	4.69084i	0.370158	−	0.258222i
$331$	−0.190243	−	0.585508i	−0.0104567	−	0.0321824i	0.945692	−	0.325064i	$-0.105386\pi$
$331$	−0.190243	−	0.585508i	−0.0104567	−	0.0321824i	−0.956149	+	0.292882i	$0.905386\pi$
$332$	−19.0383			−1.04486
$333$	3.89955	+	12.0016i	0.213694	+	0.657682i
$334$	−9.13546	−	6.63730i	−0.499870	−	0.363177i
$335$	−32.4608	−	0.623495i	−1.77352	−	0.0340652i
$336$	−14.1191	+	10.2581i	−0.770260	+	0.559627i
$337$	10.3230	+	7.50013i	0.562332	+	0.408558i	0.832312	−	0.554308i	$-0.187017\pi$
$337$	10.3230	+	7.50013i	0.562332	+	0.408558i	−0.269980	+	0.962866i	$0.587017\pi$
$338$	26.7080	+	19.4045i	1.45273	+	1.05547i
$339$	−4.62741	+	3.36201i	−0.251326	+	0.182599i
$340$	−3.68979	+	10.6552i	−0.200107	+	0.577862i
$341$	19.6162	+	14.2520i	1.06228	+	0.771789i
$342$	14.4831	+	44.5745i	0.783159	+	2.41032i
$343$	17.8300			0.962728
$344$	−28.9214	−	89.0108i	−1.55933	−	4.79914i
$345$	−0.854348	−	0.0164100i	−0.0459966	−	0.000883487i
$346$	10.1849	−	31.3460i	0.547545	−	1.68517i
$347$	−1.90419	+	5.86048i	−0.102222	+	0.314607i	−0.989068	−	0.147457i	$-0.952891\pi$
$347$	−1.90419	+	5.86048i	−0.102222	+	0.314607i	0.886846	+	0.462064i	$0.152891\pi$
$348$	5.80842	−	4.22006i	0.311364	−	0.226219i
$349$	6.50347			0.348123			0.174061	−	0.984735i	$-0.444311\pi$
$349$	6.50347			0.348123			0.174061	+	0.984735i	$0.444311\pi$
$350$	−36.2668	−	1.39372i	−1.93854	−	0.0744973i
$351$	2.39278			0.127717
$352$	−27.7332	+	20.1493i	−1.47818	+	1.07396i
$353$	2.51726	−	7.74733i	0.133980	−	0.412349i	−0.861450	−	0.507843i	$-0.830443\pi$
$353$	2.51726	−	7.74733i	0.133980	−	0.412349i	0.995430	+	0.0954941i	$0.0304431\pi$
$354$	2.57991	−	7.94015i	0.137121	−	0.422014i
$355$	22.2169	+	16.8027i	1.17915	+	0.891795i
$356$	−8.19598	−	25.2246i	−0.434386	−	1.33690i
$357$	−1.53843			−0.0814222
$358$	−7.58790	−	23.3532i	−0.401033	−	1.23425i
$359$	11.6821	+	8.48751i	0.616555	+	0.447954i	0.851717	−	0.524003i	$-0.175562\pi$
$359$	11.6821	+	8.48751i	0.616555	+	0.447954i	−0.235161	+	0.971956i	$0.575562\pi$
$360$	38.6481	+	29.2298i	2.03694	+	1.54054i
$361$	−19.6655	+	14.2878i	−1.03503	+	0.751990i
$362$	−54.4009	−	39.5245i	−2.85925	−	2.07736i
$363$	−2.25973	−	1.64179i	−0.118605	−	0.0861717i
$364$	8.35225	−	6.06826i	0.437777	−	0.318063i
$365$	0.776578	+	2.55608i	0.0406479	+	0.133791i
$366$	8.48391	+	6.16392i	0.443461	+	0.322193i
$367$	4.57623	+	14.0842i	0.238877	+	0.735188i	0.996583	+	0.0825923i	$0.0263199\pi$
$367$	4.57623	+	14.0842i	0.238877	+	0.735188i	−0.757706	+	0.652596i	$0.773680\pi$
$368$	7.70750			0.401781
$369$	0.124862	+	0.384286i	0.00650006	+	0.0200051i
$370$	−9.13082	+	26.3677i	−0.474689	+	1.37079i
$371$	−8.22527	+	25.3148i	−0.427035	+	1.31428i
$372$	8.65163	−	26.6270i	0.448566	−	1.38054i
$373$	2.76811	−	2.01115i	0.143327	−	0.104133i	−0.513811	−	0.857903i	$-0.671767\pi$
$373$	2.76811	−	2.01115i	0.143327	−	0.104133i	0.657138	+	0.753770i	$0.271767\pi$
$374$	−6.51889			−0.337084
$375$	−1.59562	−	6.08265i	−0.0823977	−	0.314107i
$376$	64.9297			3.34849
$377$	−1.53280	+	1.11364i	−0.0789431	+	0.0573555i
$378$	−7.17065	+	22.0690i	−0.368818	+	1.13511i
$379$	6.62643	−	20.3940i	0.340377	−	1.04757i	−0.623636	−	0.781715i	$-0.714345\pi$
$379$	6.62643	−	20.3940i	0.340377	−	1.04757i	0.964013	−	0.265857i	$-0.0856548\pi$
$380$	−24.2820	+	70.1208i	−1.24564	+	3.59712i
$381$	3.50333	+	10.7821i	0.179481	+	0.552386i
$382$	−10.3764			−0.530900
$383$	2.91777	+	8.97998i	0.149091	+	0.458855i	0.997514	−	0.0704630i	$-0.0224477\pi$
$383$	2.91777	+	8.97998i	0.149091	+	0.458855i	−0.848423	+	0.529318i	$0.822448\pi$
$384$	4.62458	+	3.35996i	0.235997	+	0.171462i
$385$	−4.36730	−	14.3748i	−0.222578	−	0.732609i
$386$	−25.9636	+	18.8637i	−1.32151	+	0.960136i
$387$	−25.1637	−	18.2825i	−1.27914	−	0.929350i
$388$	−23.0835	−	16.7711i	−1.17189	−	0.851425i
$389$	25.9382	−	18.8452i	1.31512	−	0.955490i	0.315140	−	0.949045i	$-0.397949\pi$
$389$	25.9382	−	18.8452i	1.31512	−	0.955490i	0.999979	−	0.00644463i	$-0.00205141\pi$
$390$	1.99254	+	1.50697i	0.100896	+	0.0763084i
$391$	0.549666	+	0.399356i	0.0277978	+	0.0201963i
$392$	1.20094	+	3.69611i	0.0606565	+	0.186682i
$393$	−2.20443			−0.111199
$394$	−15.8941	−	48.9169i	−0.800731	−	2.46440i
$395$	−2.89761	−	2.19148i	−0.145795	−	0.110265i
$396$	−10.2726	+	31.6157i	−0.516216	+	1.58875i
$397$	2.36298	−	7.27251i	0.118595	−	0.364997i	−0.874085	−	0.485773i	$-0.838538\pi$
$397$	2.36298	−	7.27251i	0.118595	−	0.364997i	0.992680	+	0.120776i	$0.0385383\pi$
$398$	−46.0631	+	33.4668i	−2.30893	+	1.67754i
$399$	−10.1242			−0.506844
$400$	15.4432	+	54.5780i	0.772162	+	2.72890i
$401$	−32.2753			−1.61175			−0.805876	−	0.592085i	$-0.798305\pi$
$401$	−32.2753			−1.61175			−0.805876	+	0.592085i	$0.798305\pi$
$402$	−17.5337	+	12.7390i	−0.874500	+	0.635362i
$403$	−2.28310	+	7.02666i	−0.113729	+	0.350023i
$404$	18.4053	−	56.6457i	0.915698	−	2.81823i
$405$	13.9793	+	0.268509i	0.694635	+	0.0133423i
$406$	−5.67784	−	17.4746i	−0.281786	−	0.867249i
$407$	−11.5507			−0.572547
$408$	1.40351	+	4.31957i	0.0694842	+	0.213850i
$409$	−7.54164	−	5.47933i	−0.372910	−	0.270935i	0.385506	−	0.922705i	$-0.374027\pi$
$409$	−7.54164	−	5.47933i	−0.372910	−	0.270935i	−0.758417	+	0.651770i	$0.774027\pi$
$410$	−0.292366	+	0.844284i	−0.0144389	+	0.0416962i
$411$	2.77586	−	2.01678i	0.136923	−	0.0994804i
$412$	24.6119	+	17.8816i	1.21254	+	0.880965i
$413$	−12.3767	−	8.99223i	−0.609019	−	0.442478i
$414$	3.91468	−	2.84418i	0.192396	−	0.139784i
$415$	−8.44036	−	0.162120i	−0.414321	−	0.00795814i
$416$	−8.45056	−	6.13969i	−0.414323	−	0.301023i
$417$	1.74437	+	5.36862i	0.0854221	+	0.262902i
$418$	−42.9000			−2.09831
$419$	−10.9290	−	33.6361i	−0.533918	−	1.64323i	−0.745976	−	0.665973i	$-0.768017\pi$
$419$	−10.9290	−	33.6361i	−0.533918	−	1.64323i	0.212058	−	0.977257i	$-0.431983\pi$
$420$	−14.2275	+	9.92512i	−0.694232	+	0.484296i
$421$	10.8865	−	33.5053i	0.530577	−	1.63295i	−0.222441	−	0.974946i	$-0.571402\pi$
$421$	10.8865	−	33.5053i	0.530577	−	1.63295i	0.753017	−	0.658001i	$-0.228598\pi$
$422$	19.1432	−	58.9166i	0.931874	−	2.86801i
$423$	17.4575	−	12.6836i	0.848811	−	0.616697i
$424$	78.5823			3.81629
$425$	−1.72655	+	4.69244i	−0.0837502	+	0.227617i
$426$	18.5945			0.900908
$427$	15.5461	−	11.2949i	0.752330	−	0.546600i
$428$	−21.4630	+	66.0562i	−1.03745	+	3.19295i
$429$	−0.319565	+	0.983521i	−0.0154288	+	0.0474848i
$430$	−19.9935	−	65.8078i	−0.964170	−	3.17353i
$431$	4.13309	+	12.7203i	0.199084	+	0.612717i	0.999905	+	0.0138132i	$0.00439701\pi$
$431$	4.13309	+	12.7203i	0.199084	+	0.612717i	−0.800821	+	0.598904i	$0.795603\pi$
$432$	36.2651			1.74480
$433$	−6.04915	−	18.6174i	−0.290703	−	0.894693i	−0.984631	−	0.174648i	$-0.944121\pi$
$433$	−6.04915	−	18.6174i	−0.290703	−	0.894693i	0.693927	−	0.720045i	$-0.255879\pi$
$434$	−57.9660	−	42.1148i	−2.78246	−	2.02157i
$435$	2.61102	−	1.82145i	0.125189	−	0.0873318i
$436$	−49.2846	+	35.8073i	−2.36030	+	1.71486i
$437$	3.61728	+	2.62811i	0.173038	+	0.125719i
$438$	1.44271	+	1.04819i	0.0689356	+	0.0500846i
$439$	−16.3880	+	11.9066i	−0.782156	+	0.568269i	−0.905625	−	0.424079i	$-0.860598\pi$
$439$	−16.3880	+	11.9066i	−0.782156	+	0.568269i	0.123470	+	0.992348i	$0.460598\pi$
$440$	−36.3770	+	25.3766i	−1.73421	+	1.20978i
$441$	1.04490	+	0.759166i	0.0497573	+	0.0361508i
$442$	−0.613821	−	1.88915i	−0.0291965	−	0.0898576i
$443$	7.06622			0.335726			0.167863	−	0.985810i	$-0.446313\pi$
$443$	7.06622			0.335726			0.167863	+	0.985810i	$0.446313\pi$
$444$	4.12145	+	12.6845i	0.195595	+	0.601980i
$445$	−3.41878	−	11.2528i	−0.162066	−	0.533434i
$446$	−0.931725	+	2.86755i	−0.0441184	+	0.135783i
$447$	3.38595	−	10.4209i	0.160150	−	0.492890i
$448$	31.7468	−	23.0654i	1.49989	−	1.08974i
$449$	7.09855			0.335001			0.167501	−	0.985872i	$-0.446430\pi$
$449$	7.09855			0.335001			0.167501	+	0.985872i	$0.446430\pi$
$450$	27.9838	+	22.0216i	1.31917	+	1.03811i
$451$	−0.369850			−0.0174155
$452$	41.4878	−	30.1426i	1.95142	−	1.41779i
$453$	−1.35898	+	4.18250i	−0.0638503	+	0.196511i
$454$	−15.6475	+	48.1580i	−0.734373	+	2.26017i
$455$	3.75453	−	2.61916i	0.176015	−	0.122788i
$456$	9.23633	+	28.4265i	0.432531	+	1.33119i
$457$	15.2133			0.711649			0.355824	−	0.934553i	$-0.384200\pi$
$457$	15.2133			0.711649			0.355824	+	0.934553i	$0.384200\pi$
$458$	12.7357	+	39.1965i	0.595101	+	1.83153i
$459$	2.58627	+	1.87903i	0.120717	+	0.0877058i
$460$	7.65979	+	0.147127i	0.357140	+	0.00685982i
$461$	33.8244	−	24.5748i	1.57536	−	1.14456i	0.653571	−	0.756865i	$-0.273270\pi$
$461$	33.8244	−	24.5748i	1.57536	−	1.14456i	0.921786	−	0.387699i	$-0.126730\pi$
$462$	−8.11350	−	5.89480i	−0.377474	−	0.274251i
$463$	−18.6840	−	13.5747i	−0.868317	−	0.630869i	0.0618178	−	0.998087i	$-0.480310\pi$
$463$	−18.6840	−	13.5747i	−0.868317	−	0.630869i	−0.930135	+	0.367218i	$0.880310\pi$
$464$	−23.2311	+	16.8784i	−1.07848	+	0.783560i
$465$	4.06233	−	11.7311i	0.188386	−	0.544015i
$466$	23.6101	+	17.1538i	1.09372	+	0.794633i
$467$	8.75238	+	26.9370i	0.405012	+	1.24650i	0.920885	+	0.389833i	$0.127467\pi$
$467$	8.75238	+	26.9370i	0.405012	+	1.24650i	−0.515874	+	0.856665i	$0.672533\pi$
$468$	−10.1294			−0.468231
$469$	12.2722	+	37.7701i	0.566680	+	1.74406i
$470$	47.7063	+	0.916327i	2.20053	+	0.0422670i
$471$	−1.18732	+	3.65419i	−0.0547087	+	0.168376i
$472$	−13.9569	+	42.9548i	−0.642417	+	1.97715i
$473$	23.0330	−	16.7345i	1.05906	−	0.769451i
$474$	−2.42517			−0.111392
$475$	−11.3622	+	30.8804i	−0.521335	+	1.41689i
$476$	13.7930			0.632201
$477$	21.1282	−	15.3505i	0.967394	−	0.702853i
$478$	9.03447	−	27.8052i	0.413227	−	1.27178i
$479$	0.631623	−	1.94394i	0.0288596	−	0.0888207i	−0.935589	−	0.353090i	$-0.885131\pi$
$479$	0.631623	−	1.94394i	0.0288596	−	0.0888207i	0.964449	+	0.264270i	$0.0851309\pi$
$480$	13.9988	+	10.5873i	0.638953	+	0.483243i
$481$	−1.08762	−	3.34734i	−0.0495911	−	0.152626i
$482$	20.6466			0.940425
$483$	0.322998	+	0.994087i	0.0146969	+	0.0452325i
$484$	20.2600	+	14.7197i	0.920907	+	0.669078i
$485$	−10.0909	−	7.63183i	−0.458206	−	0.346543i
$486$	28.1414	−	20.4459i	1.27652	−	0.927446i
$487$	−8.75116	−	6.35809i	−0.396553	−	0.288113i	0.371583	−	0.928400i	$-0.378815\pi$
$487$	−8.75116	−	6.35809i	−0.396553	−	0.288113i	−0.768135	+	0.640287i	$0.778815\pi$
$488$	−45.8965	−	33.3457i	−2.07764	−	1.50949i
$489$	−0.637545	+	0.463204i	−0.0288308	+	0.0209468i
$490$	0.830213	+	2.73262i	0.0375052	+	0.123447i
$491$	−20.9049	−	15.1883i	−0.943423	−	0.685437i	0.00581926	−	0.999983i	$-0.498148\pi$
$491$	−20.9049	−	15.1883i	−0.943423	−	0.685437i	−0.949242	+	0.314546i	$0.898148\pi$
$492$	0.131967	+	0.406154i	0.00594954	+	0.0183108i
$493$	−2.53128			−0.114003
$494$	−4.03948	−	12.4322i	−0.181745	−	0.559353i
$495$	−4.82343	+	13.9289i	−0.216797	+	0.626060i
$496$	−34.6027	+	106.496i	−1.55371	+	4.78182i
$497$	10.5292	−	32.4054i	0.472297	−	1.45358i
$498$	−4.55906	+	3.31235i	−0.204296	+	0.148430i
$499$	11.2964			0.505695			0.252847	−	0.967506i	$-0.418633\pi$
$499$	11.2964			0.505695			0.252847	+	0.967506i	$0.418633\pi$
$500$	14.3058	+	54.5350i	0.639775	+	2.43888i
$501$	−2.39326			−0.106923
$502$	−39.7865	+	28.9066i	−1.77576	+	1.29016i
$503$	10.6324	−	32.7232i	0.474076	−	1.45906i	−0.373123	−	0.927782i	$-0.621713\pi$
$503$	10.6324	−	32.7232i	0.474076	−	1.45906i	0.847199	−	0.531275i	$-0.178287\pi$
$504$	18.3164	−	56.3720i	0.815876	−	2.51101i
$505$	8.64212	−	24.9564i	0.384569	−	1.11055i
$506$	1.36866	+	4.21232i	0.0608446	+	0.187260i
$507$	6.99683			0.310740
$508$	−31.4096	−	96.6689i	−1.39358	−	4.28899i
$509$	−31.8478	−	23.1388i	−1.41163	−	1.02561i	−0.993083	−	0.117413i	$-0.962540\pi$
$509$	−31.8478	−	23.1388i	−1.41163	−	1.02561i	−0.418546	−	0.908196i	$-0.637460\pi$
$510$	0.970254	+	3.19356i	0.0429636	+	0.141413i
$511$	2.64367	−	1.92074i	0.116949	−	0.0849684i
$512$	20.1423	+	14.6342i	0.890172	+	0.646748i
$513$	17.0199	+	12.3657i	0.751447	+	0.545958i
$514$	51.9097	−	37.7146i	2.28964	−	1.66352i
$515$	10.7591	+	8.13717i	0.474103	+	0.358566i
$516$	−26.5956	−	19.3228i	−1.17080	−	0.850639i
$517$	6.10355	+	18.7848i	0.268434	+	0.826154i
$518$	34.1324			1.49969
$519$	−2.15861	−	6.64352i	−0.0947525	−	0.291618i
$520$	−10.7793	−	8.15244i	−0.472704	−	0.357508i
$521$	11.8071	−	36.3386i	0.517280	−	1.59202i	−0.261815	−	0.965118i	$-0.584321\pi$
$521$	11.8071	−	36.3386i	0.517280	−	1.59202i	0.779095	−	0.626906i	$-0.215679\pi$
$522$	−5.57083	+	17.1452i	−0.243828	+	0.750427i
$523$	24.1241	−	17.5272i	1.05487	−	0.766411i	0.0817406	−	0.996654i	$-0.473952\pi$
$523$	24.1241	−	17.5272i	1.05487	−	0.766411i	0.973133	+	0.230243i	$0.0739521\pi$
$524$	19.7642			0.863401
$525$	−6.39210	+	4.27902i	−0.278974	+	0.186752i
$526$	−41.7114			−1.81870
$527$	−7.98570	+	5.80195i	−0.347863	+	0.252737i
$528$	−4.84334	+	14.9063i	−0.210779	+	0.648713i
$529$	−6.96474	+	21.4353i	−0.302815	+	0.931969i
$530$	57.7374	+	1.10900i	2.50795	+	0.0481719i
$531$	4.63839	+	14.2755i	0.201289	+	0.619504i
$532$	90.7700			3.93538
$533$	−0.0348252	−	0.107181i	−0.00150845	−	0.00464252i
$534$	−6.35136	−	4.61453i	−0.274850	−	0.199690i
$535$	−10.0778	+	29.1024i	−0.435702	+	1.25821i
$536$	94.8541	−	68.9155i	4.09707	−	2.97670i
$537$	−4.21031	−	3.05897i	−0.181688	−	0.132004i
$538$	−9.11368	−	6.62147i	−0.392918	−	0.285472i
$539$	−0.956428	+	0.694886i	−0.0411963	+	0.0299309i
$540$	36.0406	+	0.692255i	1.55094	+	0.0297899i
$541$	−21.9252	−	15.9296i	−0.942640	−	0.684868i	0.00641495	−	0.999979i	$-0.497958\pi$
$541$	−21.9252	−	15.9296i	−0.942640	−	0.684868i	−0.949055	+	0.315112i	$0.897958\pi$
$542$	−13.0292	−	40.0997i	−0.559652	−	1.72243i
$543$	−14.2516			−0.611596
$544$	−4.31244	−	13.2723i	−0.184894	−	0.569047i
$545$	−22.1546	+	15.4550i	−0.948998	+	0.662021i
$546$	0.944319	−	2.90631i	0.0404131	−	0.124379i
$547$	−1.74656	+	5.37537i	−0.0746777	+	0.229834i	−0.981427	−	0.191836i	$-0.938556\pi$
$547$	−1.74656	+	5.37537i	−0.0746777	+	0.229834i	0.906749	+	0.421670i	$0.138556\pi$
$548$	−24.8874	+	18.0817i	−1.06314	+	0.772414i
$549$	−18.8539			−0.804666
$550$	−27.0857	+	18.1318i	−1.15494	+	0.773142i
$551$	−16.6580			−0.709656
$552$	2.49650	−	1.81382i	0.106258	−	0.0772012i
$553$	−1.37325	+	4.22644i	−0.0583967	+	0.179727i
$554$	−20.4066	+	62.8052i	−0.866995	+	2.66834i
$555$	1.71917	+	5.65861i	0.0729749	+	0.240194i
$556$	−15.6394	−	48.1331i	−0.663259	−	2.04130i
$557$	19.4818			0.825470			0.412735	−	0.910851i	$-0.364574\pi$
$557$	19.4818			0.825470			0.412735	+	0.910851i	$0.364574\pi$
$558$	21.7238	+	66.8589i	0.919640	+	2.83036i
$559$	7.01837	+	5.09914i	0.296845	+	0.215671i
$560$	56.9039	−	39.6961i	2.40463	−	1.67747i
$561$	−1.11776	+	0.812099i	−0.0471918	+	0.0342869i
$562$	0.281024	+	0.204176i	0.0118543	+	0.00861263i
$563$	−29.5589	−	21.4758i	−1.24576	−	0.905097i	−0.247792	−	0.968813i	$-0.579705\pi$
$563$	−29.5589	−	21.4758i	−1.24576	−	0.905097i	−0.997968	+	0.0637160i	$0.979705\pi$
$564$	18.4509	−	13.4053i	0.776921	−	0.564466i
$565$	18.6497	−	13.0100i	0.784600	−	0.547337i
$566$	−35.0931	−	25.4966i	−1.47507	−	1.07170i
$567$	−5.28505	−	16.2657i	−0.221951	−	0.683096i
$568$	−100.593			−4.22079
$569$	−5.12170	−	15.7630i	−0.214713	−	0.660818i	−0.999174	−	0.0406398i	$-0.987060\pi$
$569$	−5.12170	−	15.7630i	−0.214713	−	0.660818i	0.784461	−	0.620178i	$-0.212940\pi$
$570$	6.38512	+	21.0164i	0.267443	+	0.880280i
$571$	1.60834	−	4.94997i	0.0673070	−	0.207150i	−0.911746	−	0.410754i	$-0.865266\pi$
$571$	1.60834	−	4.94997i	0.0673070	−	0.207150i	0.979053	+	0.203604i	$0.0652656\pi$
$572$	2.86511	−	8.81791i	0.119796	−	0.368695i
$573$	−1.77918	+	1.29265i	−0.0743262	+	0.0540011i
$574$	1.09291			0.0456171
$575$	3.39462	+	0.130453i	0.141565	+	0.00544028i
$576$	−38.5016			−1.60423
$577$	24.7180	−	17.9587i	1.02902	−	0.747630i	0.0609117	−	0.998143i	$-0.480599\pi$
$577$	24.7180	−	17.9587i	1.02902	−	0.747630i	0.968113	+	0.250513i	$0.0805992\pi$
$578$	0.820077	−	2.52394i	0.0341107	−	0.104982i
$579$	−2.10187	+	6.46890i	−0.0873509	+	0.268839i
$580$	−23.4095	+	16.3305i	−0.972028	+	0.678086i
$581$	3.19100	+	9.82087i	0.132385	+	0.407439i
$582$	−8.44567			−0.350084
$583$	7.38693	+	22.7346i	0.305935	+	0.941572i
$584$	−7.80483	−	5.67054i	−0.322966	−	0.234649i
$585$	−4.49073	−	0.0862563i	−0.185669	−	0.00356626i
$586$	20.3135	−	14.7586i	0.839142	−	0.609672i
$587$	25.8747	+	18.7991i	1.06796	+	0.775921i	0.975545	−	0.219799i	$-0.0705402\pi$
$587$	25.8747	+	18.7991i	1.06796	+	0.775921i	0.0924187	+	0.995720i	$0.470540\pi$
$588$	1.10436	+	0.802366i	0.0455431	+	0.0330890i
$589$	−52.5529	+	38.1819i	−2.16540	+	1.57326i
$590$	−10.8608	+	31.3636i	−0.447134	+	1.29122i
$591$	−8.81915	−	6.40749i	−0.362771	−	0.263569i
$592$	−16.4840	−	50.7325i	−0.677487	−	2.08509i
$593$	29.0991			1.19496			0.597478	−	0.801886i	$-0.296170\pi$
$593$	29.0991			1.19496			0.597478	+	0.801886i	$0.296170\pi$
$594$	6.43979	+	19.8196i	0.264228	+	0.813210i
$595$	6.11495	+	0.117454i	0.250688	+	0.00481514i
$596$	−30.3572	+	93.4299i	−1.24348	+	3.82704i
$597$	−3.72902	+	11.4767i	−0.152619	+	0.469711i
$598$	−1.09184	+	0.793267i	−0.0446486	+	0.0324391i
$599$	−0.536507			−0.0219211			−0.0109605	−	0.999940i	$-0.503489\pi$
$599$	−0.536507			−0.0219211			−0.0109605	+	0.999940i	$0.503489\pi$
$600$	17.8461	+	14.0439i	0.728563	+	0.573338i
$601$	−28.2731			−1.15328			−0.576642	−	0.816997i	$-0.695637\pi$
$601$	−28.2731			−1.15328			−0.576642	+	0.816997i	$0.695637\pi$
$602$	−68.0627	+	49.4505i	−2.77403	+	2.01545i
$603$	12.0410	−	37.0582i	0.490346	−	1.50913i
$604$	12.1841	−	37.4989i	0.495765	−	1.52581i
$605$	8.85664	+	6.69832i	0.360074	+	0.272325i
$606$	−5.44796	−	16.7671i	−0.221308	−	0.681116i
$607$	45.7397			1.85652			0.928258	−	0.371937i	$-0.121306\pi$
$607$	45.7397			1.85652			0.928258	+	0.371937i	$0.121306\pi$
$608$	−28.3796	−	87.3435i	−1.15095	−	3.54225i
$609$	−3.15047	−	2.28895i	−0.127663	−	0.0927528i
$610$	−33.2513	−	25.1481i	−1.34631	−	1.01822i
$611$	−4.86904	+	3.53757i	−0.196980	+	0.143115i
$612$	−10.9485	−	7.95453i	−0.442566	−	0.321543i
$613$	−1.95802	−	1.42259i	−0.0790838	−	0.0574577i	0.547541	−	0.836779i	$-0.315564\pi$
$613$	−1.95802	−	1.42259i	−0.0790838	−	0.0574577i	−0.626625	+	0.779321i	$0.715564\pi$
$614$	40.0475	−	29.0962i	1.61618	−	1.17423i
$615$	0.0550474	+	0.181187i	0.00221972	+	0.00730615i
$616$	43.8926	+	31.8898i	1.76848	+	1.28488i
$617$	9.05048	+	27.8545i	0.364359	+	1.12138i	0.950382	+	0.311086i	$0.100693\pi$
$617$	9.05048	+	27.8545i	0.364359	+	1.12138i	−0.586023	+	0.810294i	$0.699307\pi$
$618$	9.00490			0.362230
$619$	−7.61984	−	23.4515i	−0.306267	−	0.942594i	−0.979201	−	0.202891i	$-0.934966\pi$
$619$	−7.61984	−	23.4515i	−0.306267	−	0.942594i	0.672934	−	0.739703i	$-0.265034\pi$
$620$	−36.4214	+	105.177i	−1.46272	+	4.22399i
$621$	0.671180	−	2.06568i	0.0269335	−	0.0828929i
$622$	10.9755	−	33.7793i	0.440079	−	1.35442i
$623$	−11.6384	+	8.45578i	−0.466282	+	0.338774i
$624$	−4.77583			−0.191186
$625$	5.87790	+	24.2992i	0.235116	+	0.971967i
$626$	−10.7057			−0.427887
$627$	−7.35583	+	5.34432i	−0.293763	+	0.213432i
$628$	10.6451	−	32.7622i	0.424785	−	1.30735i
$629$	1.45308	−	4.47212i	0.0579381	−	0.178315i
$630$	14.2533	−	41.1602i	0.567865	−	1.63986i
$631$	6.91570	+	21.2843i	0.275310	+	0.847316i	0.989137	+	0.146994i	$0.0469599\pi$
$631$	6.91570	+	21.2843i	0.275310	+	0.847316i	−0.713828	+	0.700321i	$0.753040\pi$
$632$	13.1198			0.521876
$633$	−4.05724	−	12.4869i	−0.161261	−	0.496309i
$634$	48.8673	+	35.5042i	1.94077	+	1.41005i
$635$	−13.1019	−	43.1244i	−0.519932	−	1.71134i
$636$	22.3305	−	16.2240i	0.885461	−	0.643325i
$637$	−0.291433	−	0.211738i	−0.0115470	−	0.00838937i
$638$	−13.3497	−	9.69913i	−0.528520	−	0.383992i
$639$	−27.0462	+	19.6502i	−1.06993	+	0.777350i
$640$	−18.1253	−	13.7082i	−0.716465	−	0.541866i
$641$	14.9092	+	10.8322i	0.588879	+	0.427846i	0.841914	−	0.539611i	$-0.181429\pi$
$641$	14.9092	+	10.8322i	0.588879	+	0.427846i	−0.253035	+	0.967457i	$0.581429\pi$
$642$	6.35302	+	19.5526i	0.250734	+	0.771679i
$643$	−35.6257			−1.40494			−0.702469	−	0.711714i	$-0.747919\pi$
$643$	−35.6257			−1.40494			−0.702469	+	0.711714i	$0.747919\pi$
$644$	−2.89589	−	8.91264i	−0.114114	−	0.351207i
$645$	−11.6263	−	8.79299i	−0.457783	−	0.346224i
$646$	5.39682	−	16.6097i	0.212335	−	0.653501i
$647$	−8.46383	+	26.0490i	−0.332747	+	1.02409i	0.635074	+	0.772452i	$0.280970\pi$
$647$	−8.46383	+	26.0490i	−0.332747	+	1.02409i	−0.967821	+	0.251640i	$0.919030\pi$
$648$	−40.8490	+	29.6785i	−1.60470	+	1.16588i
$649$	−13.7392			−0.539311
$650$	−7.80492	−	6.14203i	−0.306134	−	0.240910i
$651$	−15.1856			−0.595171
$652$	5.71601	−	4.15292i	0.223856	−	0.162641i
$653$	−2.41512	+	7.43298i	−0.0945110	+	0.290875i	−0.987126	−	0.159945i	$-0.948868\pi$
$653$	−2.41512	+	7.43298i	−0.0945110	+	0.290875i	0.892615	+	0.450820i	$0.148868\pi$
$654$	−5.57219	+	17.1494i	−0.217890	+	0.670596i
$655$	8.76218	+	0.168301i	0.342367	+	0.00657606i
$656$	−0.527811	−	1.62444i	−0.0206076	−	0.0634236i
$657$	−3.20617			−0.125084
$658$	−18.0360	−	55.5093i	−0.703118	−	2.16398i
$659$	9.10866	+	6.61783i	0.354823	+	0.257794i	0.750890	−	0.660428i	$-0.229625\pi$
$659$	9.10866	+	6.61783i	0.354823	+	0.257794i	−0.396067	+	0.918222i	$0.629625\pi$
$660$	−5.09791	+	14.7216i	−0.198436	+	0.573036i
$661$	−21.2740	+	15.4565i	−0.827463	+	0.601187i	−0.918841	−	0.394629i	$-0.870873\pi$
$661$	−21.2740	+	15.4565i	−0.827463	+	0.601187i	0.0913771	+	0.995816i	$0.470873\pi$
$662$	1.32177	+	0.960323i	0.0513721	+	0.0373240i
$663$	−0.340591	−	0.247454i	−0.0132275	−	0.00961032i
$664$	24.6637	−	17.9192i	0.957137	−	0.695401i
$665$	40.2417	+	0.772949i	1.56051	+	0.0299737i
$666$	−27.0933	−	19.6844i	−1.04984	−	0.762756i
$667$	0.531452	+	1.63564i	0.0205779	+	0.0633322i
$668$	21.4571			0.830201
$669$	0.197471	+	0.607755i	0.00763469	+	0.0234972i
$670$	70.6655	−	49.2963i	2.73005	−	1.90448i
$671$	5.33287	−	16.4129i	0.205873	−	0.633612i
$672$	6.63438	−	20.4185i	0.255927	−	0.787662i
$673$	−28.0725	+	20.3959i	−1.08212	+	0.786203i	−0.978051	−	0.208367i	$-0.933185\pi$
$673$	−28.0725	+	20.3959i	−1.08212	+	0.786203i	−0.104066	+	0.994570i	$0.533185\pi$
$674$	−33.8628			−1.30434
$675$	15.9722	+	0.613805i	0.614771	+	0.0236253i
$676$	−62.7311			−2.41274
$677$	−22.4105	+	16.2822i	−0.861307	+	0.625776i	−0.928240	−	0.371981i	$-0.878679\pi$
$677$	−22.4105	+	16.2822i	−0.861307	+	0.625776i	0.0669334	+	0.997757i	$0.478679\pi$
$678$	4.69067	−	14.4364i	0.180144	−	0.554427i
$679$	−4.78236	+	14.7186i	−0.183530	+	0.564848i
$680$	−5.24890	−	17.2766i	−0.201286	−	0.662527i
$681$	3.31636	+	10.2067i	0.127083	+	0.391121i
$682$	−64.3472			−2.46398
$683$	−0.181323	−	0.558054i	−0.00693813	−	0.0213534i	0.947528	−	0.319674i	$-0.103573\pi$
$683$	−0.181323	−	0.558054i	−0.00693813	−	0.0213534i	−0.954466	+	0.298321i	$0.903573\pi$
$684$	−72.0505	−	52.3477i	−2.75492	−	2.00157i
$685$	−11.1875	+	7.80438i	−0.427451	+	0.298190i
$686$	−38.2808	+	27.8126i	−1.46157	+	1.06189i
$687$	7.06667	+	5.13424i	0.269610	+	0.195883i
$688$	106.371	+	77.2828i	4.05534	+	2.94638i
$689$	−5.89284	+	4.28140i	−0.224499	+	0.163108i
$690$	1.85988	−	1.29745i	0.0708043	−	0.0493930i
$691$	−0.877224	−	0.637341i	−0.0333712	−	0.0242456i	0.570975	−	0.820968i	$-0.306565\pi$
$691$	−0.877224	−	0.637341i	−0.0333712	−	0.0242456i	−0.604346	+	0.796722i	$0.706565\pi$
$692$	19.3534	+	59.5635i	0.735704	+	2.26426i
$693$	18.0307			0.684932
$694$	−5.05338	−	15.5527i	−0.191824	−	0.590372i
$695$	−6.52365	−	21.4724i	−0.247456	−	0.814494i
$696$	−3.55268	+	10.9340i	−0.134664	+	0.414453i
$697$	0.0465271	−	0.143196i	0.00176234	−	0.00542393i
$698$	−13.9629	+	10.1446i	−0.528503	+	0.383980i
$699$	6.18525			0.233948
$700$	57.3094	−	38.3642i	2.16609	−	1.45003i
$701$	23.3009			0.880063			0.440032	−	0.897982i	$-0.354967\pi$
$701$	23.3009			0.880063			0.440032	+	0.897982i	$0.354967\pi$
$702$	−5.13728	+	3.73245i	−0.193894	+	0.140872i
$703$	9.56253	−	29.4305i	0.360658	−	1.10999i
$704$	10.8902	−	33.5167i	0.410442	−	1.26321i
$705$	8.29410	−	5.78596i	0.312374	−	0.217912i
$706$	6.68037	+	20.5601i	0.251419	+	0.773788i
$707$	−32.3056			−1.21498
$708$	4.90234	+	15.0878i	0.184241	+	0.567036i
$709$	6.75876	+	4.91052i	0.253830	+	0.184419i	0.707423	−	0.706791i	$-0.249858\pi$
$709$	6.75876	+	4.91052i	0.253830	+	0.184419i	−0.453592	+	0.891209i	$0.649858\pi$
$710$	−73.9096	−	1.41963i	−2.77378	−	0.0532778i
$711$	3.52747	−	2.56286i	0.132290	−	0.0961146i
$712$	34.3597	+	24.9638i	1.28769	+	0.935558i
$713$	5.42568	+	3.94199i	0.203193	+	0.147629i
$714$	3.30299	−	2.39976i	0.123611	−	0.0898088i
$715$	1.34530	−	3.88491i	0.0503113	−	0.145287i
$716$	37.7482	+	27.4256i	1.41071	+	1.02494i
$717$	−1.91478	−	5.89309i	−0.0715088	−	0.220081i
$718$	−38.3208			−1.43012
$719$	6.33401	+	19.4941i	0.236219	+	0.727007i	0.996957	+	0.0779482i	$0.0248369\pi$
$719$	6.33401	+	19.4941i	0.236219	+	0.727007i	−0.760739	+	0.649058i	$0.775163\pi$
$720$	−68.0616	−	1.30730i	−2.53651	−	0.0487203i
$721$	5.09903	−	15.6932i	0.189898	−	0.584445i
$722$	19.9343	−	61.3516i	0.741879	−	2.28327i
$723$	3.54015	−	2.57207i	0.131660	−	0.0956564i
$724$	127.775			4.74873
$725$	−10.5174	+	7.04056i	−0.390605	+	0.261480i
$726$	7.41262			0.275108
$727$	−19.0908	+	13.8703i	−0.708039	+	0.514420i	−0.882540	−	0.470237i	$-0.844169\pi$
$727$	−19.0908	+	13.8703i	−0.708039	+	0.514420i	0.174502	+	0.984657i	$0.444169\pi$
$728$	−5.10860	+	15.7227i	−0.189337	+	0.582720i
$729$	−3.51855	+	10.8290i	−0.130317	+	0.401073i
$730$	−5.65448	−	4.27651i	−0.209282	−	0.158281i
$731$	3.58157	+	11.0230i	0.132469	+	0.407699i
$732$	−19.9268			−0.736515
$733$	−4.77475	−	14.6952i	−0.176359	−	0.542778i	0.823334	−	0.567558i	$-0.192112\pi$
$733$	−4.77475	−	14.6952i	−0.176359	−	0.542778i	−0.999693	+	0.0247796i	$0.992112\pi$
$734$	−31.7947	−	23.1002i	−1.17356	−	0.852645i
$735$	0.482772	+	0.365122i	0.0178073	+	0.0134677i
$736$	−7.67078	+	5.57315i	−0.282749	+	0.205429i
$737$	28.8545	+	20.9640i	1.06287	+	0.772218i
$738$	−0.867518	−	0.630289i	−0.0319338	−	0.0232012i
$739$	13.2520	−	9.62817i	0.487484	−	0.354178i	−0.316732	−	0.948515i	$-0.602586\pi$
$739$	13.2520	−	9.62817i	0.487484	−	0.354178i	0.804216	+	0.594337i	$0.202586\pi$
$740$	−15.4135	−	50.7331i	−0.566612	−	1.86499i
$741$	−2.24139	−	1.62846i	−0.0823395	−	0.0598231i
$742$	−21.8284	−	67.1810i	−0.801347	−	2.46629i
$743$	27.0293			0.991608			0.495804	−	0.868435i	$-0.334873\pi$
$743$	27.0293			0.991608			0.495804	+	0.868435i	$0.334873\pi$
$744$	13.8539	+	42.6379i	0.507908	+	1.56318i
$745$	−14.2541	+	41.1624i	−0.522229	+	1.50807i
$746$	−2.80596	+	8.63585i	−0.102733	+	0.316181i
$747$	3.13086	−	9.63578i	0.114552	−	0.352555i
$748$	10.0214	−	7.28100i	0.366420	−	0.266220i
$749$	37.6725			1.37652
$750$	12.9140	+	10.5704i	0.471553	+	0.385977i
$751$	−20.1945			−0.736907			−0.368454	−	0.929646i	$-0.620113\pi$
$751$	−20.1945			−0.736907			−0.368454	+	0.929646i	$0.620113\pi$
$752$	−73.7953	+	53.6155i	−2.69104	+	1.95515i
$753$	−3.22090	+	9.91291i	−0.117376	+	0.361246i
$754$	1.55375	−	4.78196i	0.0565843	−	0.174149i
$755$	5.72099	−	16.5209i	0.208208	−	0.601256i
$756$	−13.6256	−	41.9354i	−0.495560	−	1.52518i
$757$	−27.8115			−1.01083			−0.505413	−	0.862878i	$-0.668660\pi$
$757$	−27.8115			−1.01083			−0.505413	+	0.862878i	$0.668660\pi$
$758$	17.5854	+	54.1222i	0.638730	+	1.96581i
$759$	0.759432	+	0.551760i	0.0275656	+	0.0200276i
$760$	−34.5424	−	113.695i	−1.25298	−	4.12415i
$761$	16.2510	−	11.8071i	0.589100	−	0.428006i	−0.252893	−	0.967494i	$-0.581382\pi$
$761$	16.2510	−	11.8071i	0.589100	−	0.428006i	0.841993	+	0.539488i	$0.181382\pi$
$762$	−24.3405	−	17.6844i	−0.881762	−	0.640637i
$763$	26.7318	+	19.4218i	0.967755	+	0.703115i
$764$	15.9515	−	11.5894i	0.577104	−	0.419291i
$765$	−4.78612	−	3.61977i	−0.173043	−	0.130873i
$766$	−20.2721	−	14.7286i	−0.732461	−	0.532164i
$767$	−1.29369	−	3.98157i	−0.0467124	−	0.143766i
$768$	0.968800			0.0349586
$769$	−1.31999	−	4.06250i	−0.0475999	−	0.146498i	0.924432	−	0.381348i	$-0.124540\pi$
$769$	−1.31999	−	4.06250i	−0.0475999	−	0.146498i	−0.972032	+	0.234850i	$0.924540\pi$
$770$	31.7995	+	24.0501i	1.14598	+	0.866707i
$771$	4.20233	−	12.9334i	0.151343	−	0.465787i
$772$	18.8447	−	57.9980i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.14699 + 1.55988i) q^{2} +(-0.173809 + 0.534928i) q^{3} +(1.55831 - 4.79598i) q^{4} +(0.731696 - 2.11297i) q^{5} +(-0.461258 - 1.41961i) q^{6} -2.73519 q^{7} +(2.49532 + 7.67982i) q^{8} +(2.17111 + 1.57741i) q^{9} +(1.72503 + 5.67787i) q^{10} +(-1.98728 + 1.44384i) q^{11} +(2.29466 + 1.66717i) q^{12} +(-0.605542 - 0.439952i) q^{13} +(5.87243 - 4.26657i) q^{14} +(1.00311 + 0.758656i) q^{15} +(-9.17762 - 6.66793i) q^{16} +(-0.309017 - 0.951057i) q^{17} -7.12192 q^{18} +(-2.03360 - 6.25878i) q^{19} +(-8.99353 - 6.80185i) q^{20} +(0.475400 - 1.46313i) q^{21} +(2.01445 - 6.19983i) q^{22} +(-0.549666 + 0.399356i) q^{23} -4.54186 q^{24} +(-3.92924 - 3.09209i) q^{25} +1.98637 q^{26} +(-2.58627 + 1.87903i) q^{27} +(-4.26227 + 13.1179i) q^{28} +(0.782209 - 2.40739i) q^{29} +(-3.33708 - 0.0640975i) q^{30} +(-3.05027 - 9.38776i) q^{31} +13.9554 q^{32} +(-0.426946 - 1.31400i) q^{33} +(2.14699 + 1.55988i) q^{34} +(-2.00133 + 5.77937i) q^{35} +(10.9485 - 7.95453i) q^{36} +(3.80421 + 2.76392i) q^{37} +(14.1291 + 10.2654i) q^{38} +(0.340591 - 0.247454i) q^{39} +(18.0530 + 0.346756i) q^{40} +(0.121810 + 0.0884998i) q^{41} +(1.26163 + 3.88290i) q^{42} -11.5902 q^{43} +(3.82785 + 11.7809i) q^{44} +(4.92160 - 3.43330i) q^{45} +(0.557180 - 1.71482i) q^{46} +(2.48474 - 7.64725i) q^{47} +(5.16202 - 3.75042i) q^{48} +0.481275 q^{49} +(13.2593 + 0.509550i) q^{50} +0.562457 q^{51} +(-3.05362 + 2.21859i) q^{52} +(3.00720 - 9.25521i) q^{53} +(2.62163 - 8.06853i) q^{54} +(1.59671 + 5.25551i) q^{55} +(-6.82519 - 21.0058i) q^{56} +3.70146 q^{57} +(2.07585 + 6.38880i) q^{58} +(4.52500 + 3.28760i) q^{59} +(5.20165 - 3.62867i) q^{60} +(-5.68375 + 4.12948i) q^{61} +(21.1927 + 15.3974i) q^{62} +(-5.93841 - 4.31451i) q^{63} +(-11.6068 + 8.43282i) q^{64} +(-1.37268 + 0.957579i) q^{65} +(2.96634 + 2.15517i) q^{66} +(-4.48680 - 13.8089i) q^{67} -5.04279 q^{68} +(-0.118090 - 0.363443i) q^{69} +(-4.71828 - 15.5301i) q^{70} +(-3.84951 + 11.8476i) q^{71} +(-6.69656 + 20.6099i) q^{72} +(-0.966538 + 0.702231i) q^{73} -12.4790 q^{74} +(2.33698 - 1.56443i) q^{75} -33.1860 q^{76} +(5.43559 - 3.94919i) q^{77} +(-0.345248 + 1.06256i) q^{78} +(0.502069 - 1.54521i) q^{79} +(-20.8043 + 14.5131i) q^{80} +(1.93224 + 5.94683i) q^{81} -0.399573 q^{82} +(-1.16664 - 3.59056i) q^{83} +(-6.27633 - 4.56002i) q^{84} +(-2.23566 - 0.0429417i) q^{85} +(24.8841 - 18.0793i) q^{86} +(1.15183 + 0.836851i) q^{87} +(-16.0474 - 11.6591i) q^{88} +(4.25505 - 3.09148i) q^{89} +(-5.21108 + 15.0484i) q^{90} +(1.65627 + 1.20335i) q^{91} +(1.05875 + 3.25851i) q^{92} +5.55194 q^{93} +(6.59407 + 20.2945i) q^{94} +(-14.7126 - 0.282594i) q^{95} +(-2.42556 + 7.46511i) q^{96} +(1.74846 - 5.38120i) q^{97} +(-1.03329 + 0.750732i) q^{98} -6.59213 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) \) 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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