LMFDB - Embedded newform 435.2.f.e.289.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,2,Mod(289,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("435.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	435.f (of order $2$, degree $1$, 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:	$3.47349248793$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 11 x^{9} + 55 x^{8} - 66 x^{7} + 328 x^{6} - 214 x^{5} + 207 x^{4} + 383 x^{3} + \cdots + 209 $ x^12 - x^11 - 11x^9 + 55x^8 - 66x^7 + 328x^6 - 214x^5 + 207x^4 + 383x^3 + 16x^2 - 107*x + 209
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			289.4
Root			$2.44773 - 1.33046i$ of defining polynomial
Character	$\chi$	$=$	435.289
Dual form			435.2.f.e.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.97264 q^{2} -1.00000 q^{3} +1.89129 q^{4} +(1.38075 + 1.75885i) q^{5} +1.97264 q^{6} -0.520254i q^{7} +0.214447 q^{8} +1.00000 q^{9} +(-2.72371 - 3.46956i) q^{10} +2.16411i q^{11} -1.89129 q^{12} -1.53375i q^{13} +1.02627i q^{14} +(-1.38075 - 1.75885i) q^{15} -4.20560 q^{16} +2.47957 q^{17} -1.97264 q^{18} -4.70989i q^{19} +(2.61139 + 3.32649i) q^{20} +0.520254i q^{21} -4.26900i q^{22} +1.46369i q^{23} -0.214447 q^{24} +(-1.18708 + 4.85704i) q^{25} +3.02552i q^{26} -1.00000 q^{27} -0.983951i q^{28} +(2.29579 + 4.87128i) q^{29} +(2.72371 + 3.46956i) q^{30} +4.64210i q^{31} +7.86723 q^{32} -2.16411i q^{33} -4.89129 q^{34} +(0.915047 - 0.718339i) q^{35} +1.89129 q^{36} +1.77536 q^{37} +9.29090i q^{38} +1.53375i q^{39} +(0.296097 + 0.377179i) q^{40} +9.71408i q^{41} -1.02627i q^{42} +5.39269 q^{43} +4.09296i q^{44} +(1.38075 + 1.75885i) q^{45} -2.88733i q^{46} +3.68312 q^{47} +4.20560 q^{48} +6.72934 q^{49} +(2.34168 - 9.58117i) q^{50} -2.47957 q^{51} -2.90076i q^{52} +7.74965i q^{53} +1.97264 q^{54} +(-3.80634 + 2.98808i) q^{55} -0.111567i q^{56} +4.70989i q^{57} +(-4.52876 - 9.60925i) q^{58} -1.91288 q^{59} +(-2.61139 - 3.32649i) q^{60} +7.66501i q^{61} -9.15717i q^{62} -0.520254i q^{63} -7.10796 q^{64} +(2.69763 - 2.11771i) q^{65} +4.26900i q^{66} +7.88749i q^{67} +4.68959 q^{68} -1.46369i q^{69} +(-1.80505 + 1.41702i) q^{70} -9.78001 q^{71} +0.214447 q^{72} -4.70676 q^{73} -3.50215 q^{74} +(1.18708 - 4.85704i) q^{75} -8.90777i q^{76} +1.12589 q^{77} -3.02552i q^{78} -12.3714i q^{79} +(-5.80687 - 7.39701i) q^{80} +1.00000 q^{81} -19.1623i q^{82} +7.32647i q^{83} +0.983951i q^{84} +(3.42366 + 4.36119i) q^{85} -10.6378 q^{86} +(-2.29579 - 4.87128i) q^{87} +0.464086i q^{88} -7.66235i q^{89} +(-2.72371 - 3.46956i) q^{90} -0.797938 q^{91} +2.76827i q^{92} -4.64210i q^{93} -7.26545 q^{94} +(8.28397 - 6.50316i) q^{95} -7.86723 q^{96} -1.64507 q^{97} -13.2745 q^{98} +2.16411i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{3} + 16 q^{4} - 6 q^{5} + 12 q^{9} - 2 q^{10} - 16 q^{12} + 6 q^{15} + 32 q^{16} + 8 q^{17} - 20 q^{20} + 12 q^{25} - 12 q^{27} + 8 q^{29} + 2 q^{30} + 40 q^{32} - 52 q^{34} + 14 q^{35} + 16 q^{36}+ \cdots + 112 q^{98}+O(q^{100}) $ 12 * q - 12 * q^3 + 16 * q^4 - 6 * q^5 + 12 * q^9 - 2 * q^10 - 16 * q^12 + 6 * q^15 + 32 * q^16 + 8 * q^17 - 20 * q^20 + 12 * q^25 - 12 * q^27 + 8 * q^29 + 2 * q^30 + 40 * q^32 - 52 * q^34 + 14 * q^35 + 16 * q^36 - 20 * q^37 + 22 * q^40 - 44 * q^43 - 6 * q^45 + 32 * q^47 - 32 * q^48 - 4 * q^49 - 24 * q^50 - 8 * q^51 - 42 * q^55 + 24 * q^58 - 28 * q^59 + 20 * q^60 - 4 * q^64 + 22 * q^65 - 16 * q^68 + 26 * q^70 - 16 * q^71 + 36 * q^73 - 28 * q^74 - 12 * q^75 - 22 * q^80 + 12 * q^81 - 30 * q^85 - 16 * q^86 - 8 * q^87 - 2 * q^90 + 24 * q^91 - 28 * q^94 - 16 * q^95 - 40 * q^96 + 40 * q^97 + 112 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/435\mathbb{Z}\right)^\times$.

$n$	$31$	$146$	$262$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.97264			−1.39486			−0.697432	−	0.716651i	$-0.745674\pi$
$2$	−1.97264			−1.39486			−0.697432	+	0.716651i	$0.745674\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.89129			0.945645
$5$	1.38075	+	1.75885i	0.617488	+	0.786580i
$5$	1.38075	+	1.75885i	0.617488	+	0.786580i
$6$	1.97264			0.805325
$7$		−	0.520254i		−	0.196638i	−0.995155	−	0.0983188i	$-0.968654\pi$
$7$		−	0.520254i		−	0.196638i	0.995155	−	0.0983188i	$-0.0313465\pi$
$8$	0.214447			0.0758184
$9$	1.00000			0.333333
$10$	−2.72371	−	3.46956i	−0.861312	−	1.09717i
$11$			2.16411i			0.652504i	0.945283	+	0.326252i	$0.105786\pi$
$11$			2.16411i			0.652504i	−0.945283	+	0.326252i	$0.894214\pi$
$12$	−1.89129			−0.545968
$13$		−	1.53375i		−	0.425385i	−0.977119	−	0.212692i	$-0.931777\pi$
$13$		−	1.53375i		−	0.425385i	0.977119	−	0.212692i	$-0.0682232\pi$
$14$			1.02627i			0.274283i
$15$	−1.38075	−	1.75885i	−0.356507	−	0.454132i
$16$	−4.20560			−1.05140
$17$	2.47957			0.601384			0.300692	−	0.953721i	$-0.402782\pi$
$17$	2.47957			0.601384			0.300692	+	0.953721i	$0.402782\pi$
$18$	−1.97264			−0.464955
$19$		−	4.70989i		−	1.08052i	−0.841497	−	0.540262i	$-0.818325\pi$
$19$		−	4.70989i		−	1.08052i	0.841497	−	0.540262i	$-0.181675\pi$
$20$	2.61139	+	3.32649i	0.583924	+	0.743825i
$21$			0.520254i			0.113529i
$22$		−	4.26900i		−	0.910153i
$23$			1.46369i			0.305201i	0.988288	+	0.152600i	$0.0487648\pi$
$23$			1.46369i			0.305201i	−0.988288	+	0.152600i	$0.951235\pi$
$24$	−0.214447			−0.0437738
$25$	−1.18708	+	4.85704i	−0.237416	+	0.971408i
$26$			3.02552i			0.593354i
$27$	−1.00000			−0.192450
$28$		−	0.983951i		−	0.185949i
$29$	2.29579	+	4.87128i	0.426318	+	0.904573i
$29$	2.29579	+	4.87128i	0.426318	+	0.904573i
$30$	2.72371	+	3.46956i	0.497279	+	0.633453i
$31$			4.64210i			0.833746i	0.908965	+	0.416873i	$0.136874\pi$
$31$			4.64210i			0.833746i	−0.908965	+	0.416873i	$0.863126\pi$
$32$	7.86723			1.39074
$33$		−	2.16411i		−	0.376723i
$34$	−4.89129			−0.838849
$35$	0.915047	−	0.718339i	0.154671	−	0.121421i
$36$	1.89129			0.315215
$37$	1.77536			0.291868			0.145934	−	0.989294i	$-0.453381\pi$
$37$	1.77536			0.291868			0.145934	+	0.989294i	$0.453381\pi$
$38$			9.29090i			1.50718i
$39$			1.53375i			0.245596i
$40$	0.296097	+	0.377179i	0.0468170	+	0.0596372i
$41$			9.71408i			1.51708i	0.651624	+	0.758542i	$0.274088\pi$
$41$			9.71408i			1.51708i	−0.651624	+	0.758542i	$0.725912\pi$
$42$		−	1.02627i		−	0.158357i
$43$	5.39269			0.822377			0.411188	−	0.911550i	$-0.365114\pi$
$43$	5.39269			0.822377			0.411188	+	0.911550i	$0.365114\pi$
$44$			4.09296i			0.617036i
$45$	1.38075	+	1.75885i	0.205829	+	0.262193i
$46$		−	2.88733i		−	0.425714i
$47$	3.68312			0.537238			0.268619	−	0.963246i	$-0.413433\pi$
$47$	3.68312			0.537238			0.268619	+	0.963246i	$0.413433\pi$
$48$	4.20560			0.607027
$49$	6.72934			0.961334
$50$	2.34168	−	9.58117i	0.331163	−	1.35498i
$51$	−2.47957			−0.347209
$52$		−	2.90076i		−	0.402263i
$53$			7.74965i			1.06450i	0.846588	+	0.532248i	$0.178653\pi$
$53$			7.74965i			1.06450i	−0.846588	+	0.532248i	$0.821347\pi$
$54$	1.97264			0.268442
$55$	−3.80634	+	2.98808i	−0.513246	+	0.402913i
$56$		−	0.111567i		−	0.0149087i
$57$			4.70989i			0.623840i
$58$	−4.52876	−	9.60925i	−0.594655	−	1.26176i
$59$	−1.91288			−0.249035			−0.124518	−	0.992217i	$-0.539738\pi$
$59$	−1.91288			−0.249035			−0.124518	+	0.992217i	$0.539738\pi$
$60$	−2.61139	−	3.32649i	−0.337129	−	0.429448i
$61$			7.66501i			0.981404i	0.871328	+	0.490702i	$0.163260\pi$
$61$			7.66501i			0.981404i	−0.871328	+	0.490702i	$0.836740\pi$
$62$		−	9.15717i		−	1.16296i
$63$		−	0.520254i		−	0.0655458i
$64$	−7.10796			−0.888495
$65$	2.69763	−	2.11771i	0.334599	−	0.262670i
$66$			4.26900i			0.525477i
$67$			7.88749i			0.963611i	0.876278	+	0.481805i	$0.160019\pi$
$67$			7.88749i			0.963611i	−0.876278	+	0.481805i	$0.839981\pi$
$68$	4.68959			0.568696
$69$		−	1.46369i		−	0.176208i
$70$	−1.80505	+	1.41702i	−0.215745	+	0.169366i
$71$	−9.78001			−1.16067			−0.580337	−	0.814376i	$-0.697079\pi$
$71$	−9.78001			−1.16067			−0.580337	+	0.814376i	$0.697079\pi$
$72$	0.214447			0.0252728
$73$	−4.70676			−0.550885			−0.275442	−	0.961318i	$-0.588824\pi$
$73$	−4.70676			−0.550885			−0.275442	+	0.961318i	$0.588824\pi$
$74$	−3.50215			−0.407116
$75$	1.18708	−	4.85704i	0.137072	−	0.560843i
$76$		−	8.90777i		−	1.02179i
$77$	1.12589			0.128307
$78$		−	3.02552i		−	0.342573i
$79$		−	12.3714i		−	1.39189i	−0.718093	−	0.695947i	$-0.754985\pi$
$79$		−	12.3714i		−	1.39189i	0.718093	−	0.695947i	$-0.245015\pi$
$80$	−5.80687	−	7.39701i	−0.649228	−	0.827011i
$81$	1.00000			0.111111
$82$		−	19.1623i		−	2.11613i
$83$			7.32647i			0.804184i	0.915599	+	0.402092i	$0.131717\pi$
$83$			7.32647i			0.804184i	−0.915599	+	0.402092i	$0.868283\pi$
$84$			0.983951i			0.107358i
$85$	3.42366	+	4.36119i	0.371348	+	0.473037i
$86$	−10.6378			−1.14710
$87$	−2.29579	−	4.87128i	−0.246135	−	0.522256i
$88$			0.464086i			0.0494718i
$89$		−	7.66235i		−	0.812207i	−0.913827	−	0.406104i	$-0.866887\pi$
$89$		−	7.66235i		−	0.812207i	0.913827	−	0.406104i	$-0.133113\pi$
$90$	−2.72371	−	3.46956i	−0.287104	−	0.365724i
$91$	−0.797938			−0.0836466
$92$			2.76827i			0.288612i
$93$		−	4.64210i		−	0.481364i
$94$	−7.26545			−0.749374
$95$	8.28397	−	6.50316i	0.849918	−	0.667210i
$96$	−7.86723			−0.802946
$97$	−1.64507			−0.167031			−0.0835156	−	0.996506i	$-0.526615\pi$
$97$	−1.64507			−0.167031			−0.0835156	+	0.996506i	$0.526615\pi$
$98$	−13.2745			−1.34093
$99$			2.16411i			0.217501i
$100$	−2.24512	+	9.18607i	−0.224512	+	0.918607i
$101$		−	3.20388i		−	0.318798i	−0.987214	−	0.159399i	$-0.949044\pi$
$101$		−	3.20388i		−	0.318798i	0.987214	−	0.159399i	$-0.0509556\pi$
$102$	4.89129			0.484310
$103$			7.80019i			0.768575i	0.923213	+	0.384288i	$0.125553\pi$
$103$			7.80019i			0.768575i	−0.923213	+	0.384288i	$0.874447\pi$
$104$		−	0.328907i		−	0.0322520i
$105$	−0.915047	+	0.718339i	−0.0892994	+	0.0701027i
$106$		−	15.2872i		−	1.48483i
$107$		−	18.4094i		−	1.77971i	−0.456246	−	0.889854i	$-0.650806\pi$
$107$		−	18.4094i		−	1.77971i	0.456246	−	0.889854i	$-0.349194\pi$
$108$	−1.89129			−0.181989
$109$	17.4302			1.66951			0.834755	−	0.550621i	$-0.185609\pi$
$109$	17.4302			1.66951			0.834755	+	0.550621i	$0.185609\pi$
$110$	7.50851	−	5.89440i	0.715909	−	0.562009i
$111$	−1.77536			−0.168510
$112$			2.18798i			0.206745i
$113$	−6.78282			−0.638074			−0.319037	−	0.947742i	$-0.603359\pi$
$113$	−6.78282			−0.638074			−0.319037	+	0.947742i	$0.603359\pi$
$114$		−	9.29090i		−	0.870172i
$115$	−2.57441	+	2.02099i	−0.240065	+	0.188458i
$116$	4.34201	+	9.21299i	0.403145	+	0.855405i
$117$		−	1.53375i		−	0.141795i
$118$	3.77341			0.347370
$119$		−	1.29001i		−	0.118255i
$120$	−0.296097	−	0.377179i	−0.0270298	−	0.0344316i
$121$	6.31663			0.574239
$122$		−	15.1203i		−	1.36892i
$123$		−	9.71408i		−	0.875889i
$124$			8.77956i			0.788428i
$125$	−10.1818	+	4.61844i	−0.910692	+	0.413086i
$126$			1.02627i			0.0914275i
$127$	−14.0473			−1.24649			−0.623247	−	0.782025i	$-0.714187\pi$
$127$	−14.0473			−1.24649			−0.623247	+	0.782025i	$0.714187\pi$
$128$	−1.71304			−0.151413
$129$	−5.39269			−0.474799
$130$	−5.32143	+	4.17748i	−0.466720	+	0.366389i
$131$			9.19950i			0.803764i	0.915692	+	0.401882i	$0.131644\pi$
$131$			9.19950i			0.803764i	−0.915692	+	0.401882i	$0.868356\pi$
$132$		−	4.09296i		−	0.356246i
$133$	−2.45034			−0.212471
$134$		−	15.5591i		−	1.34411i
$135$	−1.38075	−	1.75885i	−0.118836	−	0.151377i
$136$	0.531736			0.0455960
$137$	16.6227			1.42017			0.710086	−	0.704115i	$-0.248656\pi$
$137$	16.6227			1.42017			0.710086	+	0.704115i	$0.248656\pi$
$138$			2.88733i			0.245786i
$139$	1.13775			0.0965027			0.0482514	−	0.998835i	$-0.484635\pi$
$139$	1.13775			0.0965027			0.0482514	+	0.998835i	$0.484635\pi$
$140$	1.73062	−	1.35859i	0.146264	−	0.114821i
$141$	−3.68312			−0.310175
$142$	19.2924			1.61898
$143$	3.31920			0.277565
$144$	−4.20560			−0.350467
$145$	−5.39792	+	10.7639i	−0.448273	+	0.893897i
$146$	9.28472			0.768409
$147$	−6.72934			−0.555026
$148$	3.35773			0.276003
$149$	0.981478			0.0804058			0.0402029	−	0.999192i	$-0.487200\pi$
$149$	0.981478			0.0804058			0.0402029	+	0.999192i	$0.487200\pi$
$150$	−2.34168	+	9.58117i	−0.191197	+	0.782299i
$151$	11.4798			0.934214			0.467107	−	0.884201i	$-0.345296\pi$
$151$	11.4798			0.934214			0.467107	+	0.884201i	$0.345296\pi$
$152$		−	1.01002i		−	0.0819235i
$153$	2.47957			0.200461
$154$	−2.22096			−0.178970
$155$	−8.16475	+	6.40956i	−0.655808	+	0.514829i
$156$			2.90076i			0.232247i
$157$	−8.00465			−0.638841			−0.319420	−	0.947613i	$-0.603488\pi$
$157$	−8.00465			−0.638841			−0.319420	+	0.947613i	$0.603488\pi$
$158$			24.4043i			1.94150i
$159$		−	7.74965i		−	0.614587i
$160$	10.8626	+	13.8372i	0.858767	+	1.09393i
$161$	0.761492			0.0600140
$162$	−1.97264			−0.154985
$163$	−2.46129			−0.192783			−0.0963915	−	0.995344i	$-0.530730\pi$
$163$	−2.46129			−0.192783			−0.0963915	+	0.995344i	$0.530730\pi$
$164$			18.3721i			1.43462i
$165$	3.80634	−	2.98808i	0.296323	−	0.232622i
$166$		−	14.4524i		−	1.12173i
$167$		−	4.98139i		−	0.385471i	−0.981251	−	0.192736i	$-0.938264\pi$
$167$		−	4.98139i		−	0.385471i	0.981251	−	0.192736i	$-0.0617360\pi$
$168$			0.111567i			0.00860757i
$169$	10.6476			0.819048
$170$	−6.75363	−	8.60303i	−0.517980	−	0.659822i
$171$		−	4.70989i		−	0.360174i
$172$	10.1991			0.777676
$173$			15.0543i			1.14456i	0.820058	+	0.572280i	$0.193941\pi$
$173$			15.0543i			1.14456i	−0.820058	+	0.572280i	$0.806059\pi$
$174$	4.52876	+	9.60925i	0.343325	+	0.728475i
$175$	2.52689	+	0.617584i	0.191015	+	0.0466850i
$176$		−	9.10139i		−	0.686043i
$177$	1.91288			0.143781
$178$			15.1150i			1.13292i
$179$	−25.1991			−1.88347			−0.941736	−	0.336352i	$-0.890807\pi$
$179$	−25.1991			−1.88347			−0.941736	+	0.336352i	$0.890807\pi$
$180$	2.61139	+	3.32649i	0.194641	+	0.247942i
$181$	5.27495			0.392084			0.196042	−	0.980595i	$-0.437191\pi$
$181$	5.27495			0.392084			0.196042	+	0.980595i	$0.437191\pi$
$182$	1.57404			0.116676
$183$		−	7.66501i		−	0.566614i
$184$			0.313884i			0.0231398i
$185$	2.45133	+	3.12259i	0.180225	+	0.229578i
$186$			9.15717i			0.671437i
$187$			5.36606i			0.392405i
$188$	6.96585			0.508037
$189$			0.520254i			0.0378429i
$190$	−16.3413	+	12.8284i	−1.18552	+	0.930667i
$191$		−	3.31544i		−	0.239897i	−0.992780	−	0.119949i	$-0.961727\pi$
$191$		−	3.31544i		−	0.239897i	0.992780	−	0.119949i	$-0.0382730\pi$
$192$	7.10796			0.512973
$193$	5.69128			0.409667			0.204834	−	0.978797i	$-0.434335\pi$
$193$	5.69128			0.409667			0.204834	+	0.978797i	$0.434335\pi$
$194$	3.24512			0.232986
$195$	−2.69763	+	2.11771i	−0.193181	+	0.151653i
$196$	12.7271			0.909080
$197$		−	0.314623i		−	0.0224160i	−0.999937	−	0.0112080i	$-0.996432\pi$
$197$		−	0.314623i		−	0.0224160i	0.999937	−	0.0112080i	$-0.00356769\pi$
$198$		−	4.26900i		−	0.303384i
$199$	2.94247			0.208586			0.104293	−	0.994547i	$-0.466742\pi$
$199$	2.94247			0.208586			0.104293	+	0.994547i	$0.466742\pi$
$200$	−0.254566	+	1.04158i	−0.0180005	+	0.0736506i
$201$		−	7.88749i		−	0.556341i
$202$			6.32008i			0.444679i
$203$	2.53430	−	1.19440i	0.177873	−	0.0838301i
$204$	−4.68959			−0.328337
$205$	−17.0856	+	13.4127i	−1.19331	+	0.936782i
$206$		−	15.3869i		−	1.07206i
$207$			1.46369i			0.101734i
$208$			6.45033i			0.447250i
$209$	10.1927			0.705045
$210$	1.80505	−	1.41702i	0.124561	−	0.0977837i
$211$		−	6.92301i		−	0.476600i	−0.971192	−	0.238300i	$-0.923410\pi$
$211$		−	6.92301i		−	0.476600i	0.971192	−	0.238300i	$-0.0765901\pi$
$212$			14.6568i			1.00664i
$213$	9.78001			0.670115
$214$			36.3151i			2.48245i
$215$	7.44593	+	9.48491i	0.507808	+	0.646865i
$216$	−0.214447			−0.0145913
$217$	2.41507			0.163946
$218$	−34.3834			−2.32874
$219$	4.70676			0.318053
$220$	−7.19888	+	5.65133i	−0.485349	+	0.381013i
$221$		−	3.80303i		−	0.255820i
$222$	3.50215			0.235049
$223$		−	28.4693i		−	1.90644i	−0.302272	−	0.953222i	$-0.597745\pi$
$223$		−	28.4693i		−	1.90644i	0.302272	−	0.953222i	$-0.402255\pi$
$224$		−	4.09296i		−	0.273472i
$225$	−1.18708	+	4.85704i	−0.0791388	+	0.323803i
$226$	13.3800			0.890026
$227$			7.15024i			0.474578i	0.971439	+	0.237289i	$0.0762589\pi$
$227$			7.15024i			0.474578i	−0.971439	+	0.237289i	$0.923741\pi$
$228$			8.90777i			0.589931i
$229$		−	9.94406i		−	0.657122i	−0.944483	−	0.328561i	$-0.893436\pi$
$229$		−	9.94406i		−	0.657122i	0.944483	−	0.328561i	$-0.106564\pi$
$230$	5.07837	−	3.98667i	0.334858	−	0.262873i
$231$	−1.12589			−0.0740779
$232$	0.492325	+	1.04463i	0.0323227	+	0.0685833i
$233$		−	13.5734i		−	0.889222i	−0.895724	−	0.444611i	$-0.853342\pi$
$233$		−	13.5734i		−	0.889222i	0.895724	−	0.444611i	$-0.146658\pi$
$234$			3.02552i			0.197785i
$235$	5.08545	+	6.47804i	0.331738	+	0.422581i
$236$	−3.61780			−0.235499
$237$			12.3714i			0.803611i
$238$			2.54471i			0.164949i
$239$	15.5469			1.00564			0.502821	−	0.864390i	$-0.332295\pi$
$239$	15.5469			1.00564			0.502821	+	0.864390i	$0.332295\pi$
$240$	5.80687	+	7.39701i	0.374832	+	0.477475i
$241$	−18.2171			−1.17346			−0.586732	−	0.809781i	$-0.699586\pi$
$241$	−18.2171			−1.17346			−0.586732	+	0.809781i	$0.699586\pi$
$242$	−12.4604			−0.800985
$243$	−1.00000			−0.0641500
$244$			14.4967i			0.928059i
$245$	9.29150	+	11.8359i	0.593612	+	0.756166i
$246$			19.1623i			1.22175i
$247$	−7.22378			−0.459638
$248$			0.995484i			0.0632133i
$249$		−	7.32647i		−	0.464296i
$250$	20.0851	−	9.11050i	1.27029	−	0.576199i
$251$			5.16558i			0.326048i	0.986622	+	0.163024i	$0.0521248\pi$
$251$			5.16558i			0.326048i	−0.986622	+	0.163024i	$0.947875\pi$
$252$		−	0.983951i		−	0.0619831i
$253$	−3.16759			−0.199145
$254$	27.7102			1.73869
$255$	−3.42366	−	4.36119i	−0.214398	−	0.273108i
$256$	17.5951			1.09970
$257$		−	19.6922i		−	1.22837i	−0.789163	−	0.614184i	$-0.789485\pi$
$257$		−	19.6922i		−	1.22837i	0.789163	−	0.614184i	$-0.210515\pi$
$258$	10.6378			0.662281
$259$		−	0.923640i		−	0.0573922i
$260$	5.10199	−	4.00521i	0.316412	−	0.248393i
$261$	2.29579	+	4.87128i	0.142106	+	0.301524i
$262$		−	18.1472i		−	1.12114i
$263$	11.9634			0.737697			0.368848	−	0.929490i	$-0.379752\pi$
$263$	11.9634			0.737697			0.368848	+	0.929490i	$0.379752\pi$
$264$		−	0.464086i		−	0.0285625i
$265$	−13.6304	+	10.7003i	−0.837312	+	0.657314i
$266$	4.83363			0.296369
$267$			7.66235i			0.468928i
$268$			14.9175i			0.911233i
$269$		−	16.5561i		−	1.00945i	−0.863282	−	0.504723i	$-0.831595\pi$
$269$		−	16.5561i		−	1.00945i	0.863282	−	0.504723i	$-0.168405\pi$
$270$	2.72371	+	3.46956i	0.165760	+	0.211151i
$271$		−	25.4539i		−	1.54621i	−0.634277	−	0.773106i	$-0.718702\pi$
$271$		−	25.4539i		−	1.54621i	0.634277	−	0.773106i	$-0.281298\pi$
$272$	−10.4281			−0.632296
$273$	0.797938			0.0482934
$274$	−32.7905			−1.98095
$275$	−10.5112	−	2.56897i	−0.633847	−	0.154915i
$276$		−	2.76827i		−	0.166630i
$277$			30.7150i			1.84549i	0.385415	+	0.922743i	$0.374058\pi$
$277$			30.7150i			1.84549i	−0.385415	+	0.922743i	$0.625942\pi$
$278$	−2.24437			−0.134608
$279$			4.64210i			0.277915i
$280$	0.196229	−	0.154045i	0.0117269	−	0.00920597i
$281$	22.7775			1.35879			0.679395	−	0.733773i	$-0.262242\pi$
$281$	22.7775			1.35879			0.679395	+	0.733773i	$0.262242\pi$
$282$	7.26545			0.432651
$283$		−	30.6646i		−	1.82282i	−0.411499	−	0.911410i	$-0.634995\pi$
$283$		−	30.6646i		−	1.82282i	0.411499	−	0.911410i	$-0.365005\pi$
$284$	−18.4968			−1.09759
$285$	−8.28397	+	6.50316i	−0.490700	+	0.385214i
$286$	−6.54756			−0.387165
$287$	5.05379			0.298316
$288$	7.86723			0.463581
$289$	−10.8517			−0.638337
$290$	10.6481	−	21.2333i	0.625280	−	1.24686i
$291$	1.64507			0.0964355
$292$	−8.90185			−0.520941
$293$	−0.956588			−0.0558845			−0.0279422	−	0.999610i	$-0.508895\pi$
$293$	−0.956588			−0.0558845			−0.0279422	+	0.999610i	$0.508895\pi$
$294$	13.2745			0.774186
$295$	−2.64120	−	3.36446i	−0.153776	−	0.195886i
$296$	0.380721			0.0221290
$297$		−	2.16411i		−	0.125574i
$298$	−1.93610			−0.112155
$299$	2.24493			0.129828
$300$	2.24512	−	9.18607i	0.129622	−	0.530358i
$301$		−	2.80557i		−	0.161710i
$302$	−22.6455			−1.30310
$303$			3.20388i			0.184058i
$304$			19.8079i			1.13606i
$305$	−13.4816	+	10.5834i	−0.771953	+	0.606005i
$306$	−4.89129			−0.279616
$307$	31.8260			1.81641			0.908203	−	0.418530i	$-0.137455\pi$
$307$	31.8260			1.81641			0.908203	+	0.418530i	$0.137455\pi$
$308$	2.12938			0.121333
$309$		−	7.80019i		−	0.443737i
$310$	16.1061	−	12.6437i	0.914763	−	0.718116i
$311$		−	1.83226i		−	0.103898i	−0.998650	−	0.0519489i	$-0.983457\pi$
$311$		−	1.83226i		−	0.103898i	0.998650	−	0.0519489i	$-0.0165433\pi$
$312$			0.328907i			0.0186207i
$313$		−	16.8539i		−	0.952639i	−0.879272	−	0.476320i	$-0.841971\pi$
$313$		−	16.8539i		−	0.952639i	0.879272	−	0.476320i	$-0.158029\pi$
$314$	15.7903			0.891095
$315$	0.915047	−	0.718339i	0.0515571	−	0.0404738i
$316$		−	23.3979i		−	1.31624i
$317$	−29.0897			−1.63384			−0.816920	−	0.576751i	$-0.804320\pi$
$317$	−29.0897			−1.63384			−0.816920	+	0.576751i	$0.804320\pi$
$318$			15.2872i			0.857265i
$319$	−10.5420	+	4.96835i	−0.590237	+	0.278174i
$320$	−9.81429	−	12.5018i	−0.548635	−	0.698873i
$321$			18.4094i			1.02751i
$322$	−1.50215			−0.0837113
$323$		−	11.6785i		−	0.649810i
$324$	1.89129			0.105072
$325$	7.44947	+	1.82068i	0.413222	+	0.100993i
$326$	4.85522			0.268906
$327$	−17.4302			−0.963892
$328$			2.08315i			0.115023i
$329$		−	1.91616i		−	0.105641i
$330$	−7.50851	+	5.89440i	−0.413330	+	0.324476i
$331$		−	15.3405i		−	0.843191i	−0.906784	−	0.421596i	$-0.861470\pi$
$331$		−	15.3405i		−	0.843191i	0.906784	−	0.421596i	$-0.138530\pi$
$332$			13.8565i			0.760472i
$333$	1.77536			0.0972893
$334$			9.82646i			0.537680i
$335$	−13.8729	+	10.8906i	−0.757957	+	0.595018i
$336$		−	2.18798i		−	0.119364i
$337$	−21.0799			−1.14830			−0.574148	−	0.818751i	$-0.694667\pi$
$337$	−21.0799			−1.14830			−0.574148	+	0.818751i	$0.694667\pi$
$338$	−21.0039			−1.14246
$339$	6.78282			0.368392
$340$	6.47513	+	8.24826i	0.351163	+	0.447325i
$341$	−10.0460			−0.544022
$342$			9.29090i			0.502394i
$343$		−	7.14274i		−	0.385672i
$344$	1.15644			0.0623513
$345$	2.57441	−	2.02099i	0.138602	−	0.108806i
$346$		−	29.6967i		−	1.59650i
$347$			24.5985i			1.32051i	0.751040	+	0.660257i	$0.229553\pi$
$347$			24.5985i			1.32051i	−0.751040	+	0.660257i	$0.770447\pi$
$348$	−4.34201	−	9.21299i	−0.232756	−	0.493868i
$349$	−22.7037			−1.21530			−0.607649	−	0.794205i	$-0.707887\pi$
$349$	−22.7037			−1.21530			−0.607649	+	0.794205i	$0.707887\pi$
$350$	−4.98464	−	1.21827i	−0.266440	−	0.0651192i
$351$			1.53375i			0.0818653i
$352$			17.0255i			0.907464i
$353$			1.38426i			0.0736769i	0.999321	+	0.0368385i	$0.0117287\pi$
$353$			1.38426i			0.0736769i	−0.999321	+	0.0368385i	$0.988271\pi$
$354$	−3.77341			−0.200554
$355$	−13.5037	−	17.2015i	−0.716703	−	0.912963i
$356$		−	14.4917i		−	0.768059i
$357$			1.29001i			0.0682744i
$358$	49.7087			2.62719
$359$		−	21.6876i		−	1.14463i	−0.820035	−	0.572313i	$-0.806046\pi$
$359$		−	21.6876i		−	1.14463i	0.820035	−	0.572313i	$-0.193954\pi$
$360$	0.296097	+	0.377179i	0.0156057	+	0.0198791i
$361$	−3.18307			−0.167530
$362$	−10.4056			−0.546904
$363$	−6.31663			−0.331537
$364$	−1.50913			−0.0791000
$365$	−6.49884	−	8.27847i	−0.340165	−	0.433315i
$366$			15.1203i			0.790349i
$367$	0.210815			0.0110044			0.00550222	−	0.999985i	$-0.498249\pi$
$367$	0.210815			0.0110044			0.00550222	+	0.999985i	$0.498249\pi$
$368$		−	6.15571i		−	0.320889i
$369$			9.71408i			0.505695i
$370$	−4.83557	−	6.15974i	−0.251389	−	0.320229i
$371$	4.03179			0.209320
$372$		−	8.77956i		−	0.455199i
$373$		−	5.66464i		−	0.293304i	−0.989188	−	0.146652i	$-0.953150\pi$
$373$		−	5.66464i		−	0.293304i	0.989188	−	0.146652i	$-0.0468498\pi$
$374$		−	10.5853i		−	0.547352i
$375$	10.1818	−	4.61844i	0.525788	−	0.238495i
$376$	0.789833			0.0407325
$377$	7.47131	−	3.52116i	0.384792	−	0.181349i
$378$		−	1.02627i		−	0.0527857i
$379$			12.5695i			0.645650i	0.946459	+	0.322825i	$0.104633\pi$
$379$			12.5695i			0.645650i	−0.946459	+	0.322825i	$0.895367\pi$
$380$	15.6674	−	12.2994i	0.803720	−	0.630944i
$381$	14.0473			0.719664
$382$			6.54016i			0.334624i
$383$		−	23.0968i		−	1.18019i	−0.807333	−	0.590096i	$-0.799090\pi$
$383$		−	23.0968i		−	1.18019i	0.807333	−	0.590096i	$-0.200910\pi$
$384$	1.71304			0.0874182
$385$	1.55456	+	1.98026i	0.0792279	+	0.100923i
$386$	−11.2268			−0.571430
$387$	5.39269			0.274126
$388$	−3.11130			−0.157952
$389$			20.5826i			1.04358i	0.853074	+	0.521789i	$0.174735\pi$
$389$			20.5826i			1.04358i	−0.853074	+	0.521789i	$0.825265\pi$
$390$	5.32143	−	4.17748i	0.269461	−	0.211535i
$391$			3.62933i			0.183543i
$392$	1.44308			0.0728868
$393$		−	9.19950i		−	0.464053i
$394$			0.620637i			0.0312672i
$395$	21.7594	−	17.0818i	1.09484	−	0.859479i
$396$			4.09296i			0.205679i
$397$		−	26.2539i		−	1.31764i	−0.752298	−	0.658822i	$-0.771055\pi$
$397$		−	26.2539i		−	1.31764i	0.752298	−	0.658822i	$-0.228945\pi$
$398$	−5.80441			−0.290949
$399$	2.45034			0.122670
$400$	4.99240	−	20.4268i	0.249620	−	1.02134i
$401$	−17.1621			−0.857034			−0.428517	−	0.903534i	$-0.640964\pi$
$401$	−17.1621			−0.857034			−0.428517	+	0.903534i	$0.640964\pi$
$402$			15.5591i			0.776020i
$403$	7.11981			0.354663
$404$		−	6.05946i		−	0.301469i
$405$	1.38075	+	1.75885i	0.0686098	+	0.0873978i
$406$	−4.99925	+	2.35611i	−0.248109	+	0.116932i
$407$			3.84208i			0.190445i
$408$	−0.531736			−0.0263249
$409$		−	14.9034i		−	0.736925i	−0.929643	−	0.368462i	$-0.879884\pi$
$409$		−	14.9034i		−	0.736925i	0.929643	−	0.368462i	$-0.120116\pi$
$410$	33.7036	−	26.4583i	1.66450	−	1.30668i
$411$	−16.6227			−0.819936
$412$			14.7524i			0.726799i
$413$			0.995181i			0.0489697i
$414$		−	2.88733i		−	0.141905i
$415$	−12.8861	+	10.1160i	−0.632555	+	0.496574i
$416$		−	12.0663i		−	0.591601i
$417$	−1.13775			−0.0557159
$418$	−20.1065			−0.983442
$419$	−19.5741			−0.956259			−0.478129	−	0.878289i	$-0.658685\pi$
$419$	−19.5741			−0.956259			−0.478129	+	0.878289i	$0.658685\pi$
$420$	−1.73062	+	1.35859i	−0.0844455	+	0.0662922i
$421$		−	8.71742i		−	0.424861i	−0.977176	−	0.212431i	$-0.931862\pi$
$421$		−	8.71742i		−	0.424861i	0.977176	−	0.212431i	$-0.0681379\pi$
$422$			13.6566i			0.664792i
$423$	3.68312			0.179079
$424$			1.66189i			0.0807084i
$425$	−2.94345	+	12.0434i	−0.142778	+	0.584190i
$426$	−19.2924			−0.934720
$427$	3.98775			0.192981
$428$		−	34.8176i		−	1.68297i
$429$	−3.31920			−0.160252
$430$	−14.6881	−	18.7103i	−0.708323	−	0.902289i
$431$	−26.7125			−1.28669			−0.643347	−	0.765574i	$-0.722455\pi$
$431$	−26.7125			−1.28669			−0.643347	+	0.765574i	$0.722455\pi$
$432$	4.20560			0.202342
$433$	34.3298			1.64978			0.824892	−	0.565290i	$-0.191236\pi$
$433$	34.3298			1.64978			0.824892	+	0.565290i	$0.191236\pi$
$434$	−4.76406			−0.228682
$435$	5.39792	−	10.7639i	0.258811	−	0.516092i
$436$	32.9655			1.57876
$437$	6.89383			0.329777
$438$	−9.28472			−0.443641
$439$	−30.4762			−1.45455			−0.727274	−	0.686347i	$-0.759213\pi$
$439$	−30.4762			−1.45455			−0.727274	+	0.686347i	$0.759213\pi$
$440$	−0.816257	+	0.640785i	−0.0389135	+	0.0305482i
$441$	6.72934			0.320445
$442$			7.50200i			0.356834i
$443$	17.3948			0.826451			0.413225	−	0.910629i	$-0.364402\pi$
$443$	17.3948			0.826451			0.413225	+	0.910629i	$0.364402\pi$
$444$	−3.35773			−0.159351
$445$	13.4769	−	10.5798i	0.638866	−	0.501528i
$446$			56.1595i			2.65923i
$447$	−0.981478			−0.0464223
$448$			3.69795i			0.174712i
$449$		−	1.06526i		−	0.0502726i	−0.999684	−	0.0251363i	$-0.991998\pi$
$449$		−	1.06526i		−	0.0502726i	0.999684	−	0.0251363i	$-0.00800197\pi$
$450$	2.34168	−	9.58117i	0.110388	−	0.451661i
$451$	−21.0223			−0.989903
$452$	−12.8283			−0.603391
$453$	−11.4798			−0.539368
$454$		−	14.1048i		−	0.661972i
$455$	−1.10175	−	1.40345i	−0.0516508	−	0.0657948i
$456$			1.01002i			0.0472986i
$457$		−	1.01761i		−	0.0476020i	−0.999717	−	0.0238010i	$-0.992423\pi$
$457$		−	1.01761i		−	0.0476020i	0.999717	−	0.0238010i	$-0.00757681\pi$
$458$			19.6160i			0.916596i
$459$	−2.47957			−0.115736
$460$	−4.86895	+	3.82227i	−0.227016	+	0.178214i
$461$			3.17621i			0.147931i	0.997261	+	0.0739655i	$0.0235655\pi$
$461$			3.17621i			0.147931i	−0.997261	+	0.0739655i	$0.976435\pi$
$462$	2.22096			0.103329
$463$			1.75704i			0.0816565i	0.999166	+	0.0408283i	$0.0129997\pi$
$463$			1.75704i			0.0816565i	−0.999166	+	0.0408283i	$0.987000\pi$
$464$	−9.65519	−	20.4867i	−0.448231	−	0.951069i
$465$	8.16475	−	6.40956i	0.378631	−	0.297236i
$466$			26.7753i			1.24034i
$467$	35.9537			1.66374			0.831870	−	0.554970i	$-0.187270\pi$
$467$	35.9537			1.66374			0.831870	+	0.554970i	$0.187270\pi$
$468$		−	2.90076i		−	0.134088i
$469$	4.10350			0.189482
$470$	−10.0317	−	12.7788i	−0.462730	−	0.589443i
$471$	8.00465			0.368835
$472$	−0.410210			−0.0188815
$473$			11.6704i			0.536604i
$474$		−	24.4043i		−	1.12093i
$475$	22.8761	+	5.59103i	1.04963	+	0.256534i
$476$		−	2.43978i		−	0.111827i
$477$			7.74965i			0.354832i
$478$	−30.6683			−1.40273
$479$			41.1172i			1.87869i	0.342969	+	0.939347i	$0.388567\pi$
$479$			41.1172i			1.87869i	−0.342969	+	0.939347i	$0.611433\pi$
$480$	−10.8626	−	13.8372i	−0.495809	−	0.631581i
$481$		−	2.72296i		−	0.124156i
$482$	35.9356			1.63682
$483$	−0.761492			−0.0346491
$484$	11.9466			0.543026
$485$	−2.27142	−	2.89342i	−0.103140	−	0.131383i
$486$	1.97264			0.0894805
$487$		−	9.80926i		−	0.444500i	−0.974990	−	0.222250i	$-0.928660\pi$
$487$		−	9.80926i		−	0.444500i	0.974990	−	0.222250i	$-0.0713401\pi$
$488$			1.64374i			0.0744085i
$489$	2.46129			0.111303
$490$	−18.3287	−	23.3478i	−0.828008	−	1.05475i
$491$			41.7524i			1.88426i	0.335245	+	0.942131i	$0.391181\pi$
$491$			41.7524i			1.88426i	−0.335245	+	0.942131i	$0.608819\pi$
$492$		−	18.3721i		−	0.828280i
$493$	5.69258	+	12.0787i	0.256381	+	0.543996i
$494$	14.2499			0.641132
$495$	−3.80634	+	2.98808i	−0.171082	+	0.134304i
$496$		−	19.5228i		−	0.876602i
$497$			5.08809i			0.228232i
$498$			14.4524i			0.647629i
$499$	2.50030			0.111929			0.0559644	−	0.998433i	$-0.482177\pi$
$499$	2.50030			0.111929			0.0559644	+	0.998433i	$0.482177\pi$
$500$	−19.2568	+	8.73481i	−0.861191	+	0.390633i
$501$			4.98139i			0.222552i
$502$		−	10.1898i		−	0.454793i
$503$	23.3850			1.04268			0.521342	−	0.853348i	$-0.325431\pi$
$503$	23.3850			1.04268			0.521342	+	0.853348i	$0.325431\pi$
$504$		−	0.111567i		−	0.00496958i
$505$	5.63513	−	4.42374i	0.250760	−	0.196854i
$506$	6.24850			0.277780
$507$	−10.6476			−0.472877
$508$	−26.5675			−1.17874
$509$	19.8085			0.877997			0.438999	−	0.898488i	$-0.355333\pi$
$509$	19.8085			0.877997			0.438999	+	0.898488i	$0.355333\pi$
$510$	6.75363	+	8.60303i	0.299056	+	0.380948i
$511$			2.44871i			0.108325i
$512$	−31.2827			−1.38251
$513$			4.70989i			0.207947i
$514$			38.8456i			1.71340i
$515$	−13.7193	+	10.7701i	−0.604546	+	0.474586i
$516$	−10.1991			−0.448992
$517$			7.97068i			0.350550i
$518$			1.82200i			0.0800543i
$519$		−	15.0543i		−	0.660812i
$520$	0.578497	−	0.454137i	0.0253688	−	0.0199152i
$521$	−26.0978			−1.14337			−0.571684	−	0.820474i	$-0.693709\pi$
$521$	−26.0978			−1.14337			−0.571684	+	0.820474i	$0.693709\pi$
$522$	−4.52876	−	9.60925i	−0.198218	−	0.420585i
$523$			20.8084i			0.909888i	0.890520	+	0.454944i	$0.150341\pi$
$523$			20.8084i			0.909888i	−0.890520	+	0.454944i	$0.849659\pi$
$524$			17.3989i			0.760075i
$525$	−2.52689	−	0.617584i	−0.110283	−	0.0269536i
$526$	−23.5995			−1.02899
$527$			11.5104i			0.501402i
$528$			9.10139i			0.396087i
$529$	20.8576			0.906852
$530$	26.8879	−	21.1078i	1.16794	−	0.916863i
$531$	−1.91288			−0.0830118
$532$	−4.63430			−0.200922
$533$	14.8989			0.645345
$534$		−	15.1150i		−	0.654091i
$535$	32.3794	−	25.4188i	1.39988	−	1.09895i
$536$			1.69145i			0.0730594i
$537$	25.1991			1.08742
$538$			32.6592i			1.40804i
$539$			14.5630i			0.627274i
$540$	−2.61139	−	3.32649i	−0.112376	−	0.143149i
$541$			46.2267i			1.98744i	0.111881	+	0.993722i	$0.464312\pi$
$541$			46.2267i			1.98744i	−0.111881	+	0.993722i	$0.535688\pi$
$542$			50.2112i			2.15676i
$543$	−5.27495			−0.226370
$544$	19.5074			0.836371
$545$	24.0667	+	30.6570i	1.03090	+	1.31320i
$546$	−1.57404			−0.0673627
$547$			24.3321i			1.04037i	0.854055	+	0.520183i	$0.174136\pi$
$547$			24.3321i			1.04037i	−0.854055	+	0.520183i	$0.825864\pi$
$548$	31.4383			1.34298
$549$			7.66501i			0.327135i
$550$	20.7347	+	5.06765i	0.884130	+	0.216085i
$551$	22.9432	−	10.8129i	0.977412	−	0.460646i
$552$		−	0.313884i		−	0.0133598i
$553$	−6.43628			−0.273699
$554$		−	60.5895i		−	2.57420i
$555$	−2.45133	−	3.12259i	−0.104053	−	0.132547i
$556$	2.15181			0.0912573
$557$		−	32.6439i		−	1.38316i	−0.722298	−	0.691582i	$-0.756914\pi$
$557$		−	32.6439i		−	1.38316i	0.722298	−	0.691582i	$-0.243086\pi$
$558$		−	9.15717i		−	0.387654i
$559$		−	8.27101i		−	0.349827i
$560$	−3.84832	+	3.02105i	−0.162621	+	0.127663i
$561$		−	5.36606i		−	0.226555i
$562$	−44.9316			−1.89533
$563$	−5.69605			−0.240060			−0.120030	−	0.992770i	$-0.538299\pi$
$563$	−5.69605			−0.240060			−0.120030	+	0.992770i	$0.538299\pi$
$564$	−6.96585			−0.293315
$565$	−9.36535	−	11.9299i	−0.394003	−	0.501896i
$566$			60.4900i			2.54259i
$567$		−	0.520254i		−	0.0218486i
$568$	−2.09729			−0.0880004
$569$		−	23.0314i		−	0.965526i	−0.875751	−	0.482763i	$-0.839633\pi$
$569$		−	23.0314i		−	0.965526i	0.875751	−	0.482763i	$-0.160367\pi$
$570$	16.3413	−	12.8284i	0.684460	−	0.537321i
$571$	12.1948			0.510336			0.255168	−	0.966897i	$-0.417869\pi$
$571$	12.1948			0.510336			0.255168	+	0.966897i	$0.417869\pi$
$572$	6.27756			0.262478
$573$			3.31544i			0.138505i
$574$	−9.96928			−0.416110
$575$	−7.10921	−	1.73752i	−0.296475	−	0.0724597i
$576$	−7.10796			−0.296165
$577$	23.1192			0.962466			0.481233	−	0.876593i	$-0.340189\pi$
$577$	23.1192			0.962466			0.481233	+	0.876593i	$0.340189\pi$
$578$	21.4065			0.890393
$579$	−5.69128			−0.236522
$580$	−10.2090	+	20.3577i	−0.423907	+	0.845309i
$581$	3.81162			0.158133
$582$	−3.24512			−0.134514
$583$	−16.7711			−0.694588
$584$	−1.00935			−0.0417672
$585$	2.69763	−	2.11771i	0.111533	−	0.0875567i
$586$	1.88700			0.0779512
$587$		−	16.0091i		−	0.660767i	−0.943847	−	0.330384i	$-0.892822\pi$
$587$		−	16.0091i		−	0.660767i	0.943847	−	0.330384i	$-0.107178\pi$
$588$	−12.7271			−0.524858
$589$	21.8638			0.900882
$590$	5.21012	+	6.63684i	0.214497	+	0.273235i
$591$			0.314623i			0.0129419i
$592$	−7.46648			−0.306870
$593$		−	20.9155i		−	0.858896i	−0.903092	−	0.429448i	$-0.858708\pi$
$593$		−	20.9155i		−	0.858896i	0.903092	−	0.429448i	$-0.141292\pi$
$594$			4.26900i			0.175159i
$595$	2.26892	−	1.78117i	0.0930168	−	0.0730209i
$596$	1.85626			0.0760353
$597$	−2.94247			−0.120427
$598$	−4.42843			−0.181092
$599$			39.3957i			1.60967i	0.593502	+	0.804833i	$0.297745\pi$
$599$			39.3957i			1.60967i	−0.593502	+	0.804833i	$0.702255\pi$
$600$	0.254566	−	1.04158i	0.0103926	−	0.0425222i
$601$			18.3996i			0.750533i	0.926917	+	0.375267i	$0.122449\pi$
$601$			18.3996i			0.750533i	−0.926917	+	0.375267i	$0.877551\pi$
$602$			5.53436i			0.225564i
$603$			7.88749i			0.321204i
$604$	21.7116			0.883434
$605$	8.72166	+	11.1100i	0.354586	+	0.451685i
$606$		−	6.32008i		−	0.256736i
$607$	−34.8854			−1.41596			−0.707978	−	0.706235i	$-0.750392\pi$
$607$	−34.8854			−1.41596			−0.707978	+	0.706235i	$0.750392\pi$
$608$		−	37.0538i		−	1.50273i
$609$	−2.53430	+	1.19440i	−0.102695	+	0.0483993i
$610$	26.5942	−	20.8772i	1.07677	−	0.845295i
$611$		−	5.64897i		−	0.228533i
$612$	4.68959			0.189565
$613$			34.3711i			1.38824i	0.719861	+	0.694118i	$0.244205\pi$
$613$			34.3711i			1.38824i	−0.719861	+	0.694118i	$0.755795\pi$
$614$	−62.7811			−2.53364
$615$	17.0856	−	13.4127i	0.688957	−	0.540851i
$616$	0.241443			0.00972801
$617$	−32.4140			−1.30494			−0.652469	−	0.757815i	$-0.726267\pi$
$617$	−32.4140			−1.30494			−0.652469	+	0.757815i	$0.726267\pi$
$618$			15.3869i			0.618953i
$619$		−	37.2406i		−	1.49683i	−0.663232	−	0.748414i	$-0.730816\pi$
$619$		−	37.2406i		−	1.49683i	0.663232	−	0.748414i	$-0.269184\pi$
$620$	−15.4419	+	12.1223i	−0.620161	+	0.486845i
$621$		−	1.46369i		−	0.0587359i
$622$			3.61437i			0.144923i
$623$	−3.98637			−0.159710
$624$		−	6.45033i		−	0.258220i
$625$	−22.1817	−	11.5314i	−0.887267	−	0.461256i
$626$			33.2466i			1.32880i
$627$	−10.1927			−0.407058
$628$	−15.1391			−0.604116
$629$	4.40214			0.175525
$630$	−1.80505	+	1.41702i	−0.0719151	+	0.0564554i
$631$	−20.0296			−0.797366			−0.398683	−	0.917089i	$-0.630533\pi$
$631$	−20.0296			−0.797366			−0.398683	+	0.917089i	$0.630533\pi$
$632$		−	2.65301i		−	0.105531i
$633$			6.92301i			0.275165i
$634$	57.3834			2.27898
$635$	−19.3957	−	24.7070i	−0.769696	−	0.980468i
$636$		−	14.6568i		−	0.581181i
$637$		−	10.3211i		−	0.408937i
$638$	20.7955	−	9.80073i	0.823301	−	0.388015i
$639$	−9.78001			−0.386891
$640$	−2.36527	−	3.01297i	−0.0934956	−	0.119098i
$641$		−	30.4877i		−	1.20419i	−0.798424	−	0.602096i	$-0.794332\pi$
$641$		−	30.4877i		−	1.20419i	0.798424	−	0.602096i	$-0.205668\pi$
$642$		−	36.3151i		−	1.43324i
$643$		−	9.71287i		−	0.383038i	−0.981489	−	0.191519i	$-0.938659\pi$
$643$		−	9.71287i		−	0.383038i	0.981489	−	0.191519i	$-0.0613414\pi$
$644$	1.44020			0.0567519
$645$	−7.44593	−	9.48491i	−0.293183	−	0.373468i
$646$			23.0374i			0.906396i
$647$			26.7628i			1.05215i	0.850437	+	0.526077i	$0.176337\pi$
$647$			26.7628i			1.05215i	−0.850437	+	0.526077i	$0.823663\pi$
$648$	0.214447			0.00842427
$649$		−	4.13967i		−	0.162496i
$650$	−14.6951	−	3.59154i	−0.576389	−	0.140872i
$651$	−2.41507			−0.0946542
$652$	−4.65501			−0.182304
$653$	−47.1066			−1.84342			−0.921712	−	0.387875i	$-0.873209\pi$
$653$	−47.1066			−1.84342			−0.921712	+	0.387875i	$0.873209\pi$
$654$	34.3834			1.34450
$655$	−16.1805	+	12.7022i	−0.632224	+	0.496315i
$656$		−	40.8536i		−	1.59506i
$657$	−4.70676			−0.183628
$658$			3.77988i			0.147355i
$659$		−	18.2896i		−	0.712460i	−0.934398	−	0.356230i	$-0.884062\pi$
$659$		−	18.2896i		−	0.712460i	0.934398	−	0.356230i	$-0.115938\pi$
$660$	7.19888	−	5.65133i	0.280216	−	0.219978i
$661$	27.5526			1.07167			0.535836	−	0.844322i	$-0.319997\pi$
$661$	27.5526			1.07167			0.535836	+	0.844322i	$0.319997\pi$
$662$			30.2613i			1.17614i
$663$			3.80303i			0.147698i
$664$			1.57114i			0.0609719i
$665$	−3.38330	−	4.30977i	−0.131199	−	0.167126i
$666$	−3.50215			−0.135705
$667$	−7.13005	+	3.36033i	−0.276077	+	0.130113i
$668$		−	9.42124i		−	0.364519i
$669$			28.4693i			1.10069i
$670$	27.3661	−	21.4832i	1.05725	−	0.829969i
$671$	−16.5879			−0.640369
$672$			4.09296i			0.157889i
$673$		−	23.9569i		−	0.923472i	−0.887017	−	0.461736i	$-0.847227\pi$
$673$		−	23.9569i		−	0.923472i	0.887017	−	0.461736i	$-0.152773\pi$
$674$	41.5830			1.60172
$675$	1.18708	−	4.85704i	0.0456908	−	0.186948i
$676$	20.1377			0.774528
$677$	22.9391			0.881620			0.440810	−	0.897600i	$-0.354691\pi$
$677$	22.9391			0.881620			0.440810	+	0.897600i	$0.354691\pi$
$678$	−13.3800			−0.513857
$679$			0.855852i			0.0328446i
$680$	0.734192	+	0.935242i	0.0281550	+	0.0358649i
$681$		−	7.15024i		−	0.273998i
$682$	19.8171			0.758837
$683$		−	34.1942i		−	1.30840i	−0.756320	−	0.654202i	$-0.773005\pi$
$683$		−	34.1942i		−	1.30840i	0.756320	−	0.654202i	$-0.226995\pi$
$684$		−	8.90777i		−	0.340597i
$685$	22.9517	+	29.2367i	0.876939	+	1.11708i
$686$			14.0900i			0.537960i
$687$			9.94406i			0.379390i
$688$	−22.6795			−0.864648
$689$	11.8860			0.452821
$690$	−5.07837	+	3.98667i	−0.193330	+	0.151770i
$691$	3.83582			0.145922			0.0729608	−	0.997335i	$-0.476755\pi$
$691$	3.83582			0.145922			0.0729608	+	0.997335i	$0.476755\pi$
$692$			28.4721i			1.08235i
$693$	1.12589			0.0427689
$694$		−	48.5238i		−	1.84194i
$695$	1.57094	+	2.00113i	0.0595893	+	0.0759071i
$696$	−0.492325	−	1.04463i	−0.0186615	−	0.0395966i
$697$			24.0868i			0.912351i
$698$	44.7860			1.69518
$699$			13.5734i			0.513393i
$700$	4.77909	+	1.16803i	0.180633	+	0.0441474i
$701$	49.0619			1.85304			0.926522	−	0.376241i	$-0.122783\pi$
$701$	49.0619			1.85304			0.926522	+	0.376241i	$0.122783\pi$
$702$		−	3.02552i		−	0.114191i
$703$		−	8.36177i		−	0.315370i
$704$		−	15.3824i		−	0.579746i
$705$	−5.08545	−	6.47804i	−0.191529	−	0.243977i
$706$		−	2.73065i		−	0.102769i
$707$	−1.66683			−0.0626876
$708$	3.61780			0.135965
$709$	−9.68605			−0.363767			−0.181884	−	0.983320i	$-0.558219\pi$
$709$	−9.68605			−0.363767			−0.181884	+	0.983320i	$0.558219\pi$
$710$	26.6379	+	33.9324i	0.999702	+	1.27346i
$711$		−	12.3714i		−	0.463965i
$712$		−	1.64317i		−	0.0615802i
$713$	−6.79461			−0.254460
$714$		−	2.54471i		−	0.0952335i
$715$	4.58297	+	5.83796i	0.171393	+	0.218327i
$716$	−47.6589			−1.78110
$717$	−15.5469			−0.580608
$718$			42.7817i			1.59660i
$719$	−34.8915			−1.30123			−0.650617	−	0.759406i	$-0.725490\pi$
$719$	−34.8915			−1.30123			−0.650617	+	0.759406i	$0.725490\pi$
$720$	−5.80687	−	7.39701i	−0.216409	−	0.275670i
$721$	4.05808			0.151131
$722$	6.27904			0.233682
$723$	18.2171			0.677500
$724$	9.97646			0.370772
$725$	−26.3853	+	5.36815i	−0.979925	+	0.199368i
$726$	12.4604			0.462449
$727$	−26.3086			−0.975731			−0.487866	−	0.872919i	$-0.662224\pi$
$727$	−26.3086			−0.975731			−0.487866	+	0.872919i	$0.662224\pi$
$728$	−0.171115			−0.00634195
$729$	1.00000			0.0370370
$730$	12.8198	+	16.3304i	0.474484	+	0.604415i
$731$	13.3715			0.494565
$732$		−	14.4967i		−	0.535815i
$733$	−30.8872			−1.14084			−0.570422	−	0.821352i	$-0.693220\pi$
$733$	−30.8872			−1.14084			−0.570422	+	0.821352i	$0.693220\pi$
$734$	−0.415861			−0.0153497
$735$	−9.29150	−	11.8359i	−0.342722	−	0.436573i
$736$			11.5152i			0.424456i
$737$	−17.0694			−0.628759
$738$		−	19.1623i		−	0.705375i
$739$			7.59328i			0.279323i	0.990199	+	0.139662i	$0.0446015\pi$
$739$			7.59328i			0.279323i	−0.990199	+	0.139662i	$0.955398\pi$
$740$	4.63617	+	5.90573i	0.170429	+	0.217099i
$741$	7.22378			0.265372
$742$	−7.95324			−0.291973
$743$	33.4121			1.22577			0.612886	−	0.790172i	$-0.290009\pi$
$743$	33.4121			1.22577			0.612886	+	0.790172i	$0.290009\pi$
$744$		−	0.995484i		−	0.0364962i
$745$	1.35517	+	1.72627i	0.0496497	+	0.0632456i
$746$			11.1743i			0.409119i
$747$			7.32647i			0.268061i
$748$			10.1488i			0.371076i
$749$	−9.57758			−0.349957
$750$	−20.0851	+	9.11050i	−0.733403	+	0.332669i
$751$		−	24.7607i		−	0.903532i	−0.892137	−	0.451766i	$-0.850794\pi$
$751$		−	24.7607i		−	0.903532i	0.892137	−	0.451766i	$-0.149206\pi$
$752$	−15.4897			−0.564853
$753$		−	5.16558i		−	0.188244i
$754$	−14.7382	+	6.94597i	−0.536732	+	0.252957i
$755$	15.8507	+	20.1912i	0.576866	+	0.734834i
$756$			0.983951i			0.0357859i
$757$	29.8424			1.08464			0.542321	−	0.840172i	$-0.317546\pi$
$757$	29.8424			1.08464			0.542321	+	0.840172i	$0.317546\pi$
$758$		−	24.7950i		−	0.900594i
$759$	3.16759			0.114976
$760$	1.77647	−	1.39458i	0.0644394	−	0.0505868i
$761$	−19.7600			−0.716300			−0.358150	−	0.933664i	$-0.616592\pi$
$761$	−19.7600			−0.716300			−0.358150	+	0.933664i	$0.616592\pi$
$762$	−27.7102			−1.00383
$763$		−	9.06813i		−	0.328288i
$764$		−	6.27046i		−	0.226857i
$765$	3.42366	+	4.36119i	0.123783	+	0.157679i
$766$			45.5616i			1.64621i
$767$			2.93387i			0.105936i
$768$	−17.5951			−0.634909
$769$		−	32.7782i		−	1.18201i	−0.806667	−	0.591007i	$-0.798731\pi$
$769$		−	32.7782i		−	1.18201i	0.806667	−	0.591007i	$-0.201269\pi$
$770$	−3.06659	−	3.90633i	−0.110512	−	0.140774i
$771$			19.6922i			0.709198i
$772$	10.7639			0.387400
$773$	−26.1210			−0.939507			−0.469753	−	0.882798i	$-0.655657\pi$
$773$	−26.1210			−0.939507			−0.469753	+	0.882798i	$0.655657\pi$
$774$	−10.6378			−0.382368
$775$	−22.5469	−	5.51056i	−0.809908	−	0.197945i
$776$	−0.352779			−0.0126640
$777$			0.923640i			0.0331354i
$778$		−	40.6019i		−	1.45565i
$779$	45.7523			1.63924
$780$	−5.10199	+	4.00521i	−0.182681	+	0.143410i
$781$		−	21.1650i		−	0.757344i
$782$		−	7.15934i		−	0.256018i
$783$	−2.29579	−	4.87128i	−0.0820449	−	0.174085i
$784$	−28.3009			−1.01075
$785$	−11.0524	−	14.0789i	−0.394477	−	0.502499i
$786$			18.1472i			0.647291i
$787$			37.7291i			1.34490i	0.740143	+	0.672449i	$0.234758\pi$
$787$			37.7291i			1.34490i	−0.740143	+	0.672449i	$0.765242\pi$
$788$		−	0.595044i		−	0.0211976i
$789$	−11.9634			−0.425909
$790$	−42.9234	+	33.6962i	−1.52715	+	1.19886i
$791$			3.52879i			0.125469i
$792$			0.464086i			0.0164906i
$793$	11.7562			0.417474
$794$			51.7893i			1.83793i
$795$	13.6304	−	10.7003i	0.483422	−	0.379500i
$796$	5.56506			0.197248
$797$	13.7227			0.486084			0.243042	−	0.970016i	$-0.421855\pi$
$797$	13.7227			0.486084			0.243042	+	0.970016i	$0.421855\pi$
$798$	−4.83363			−0.171108
$799$	9.13256			0.323087
$800$	−9.33904	+	38.2114i	−0.330185	+	1.35098i
$801$		−	7.66235i		−	0.270736i
$802$	33.8546			1.19545
$803$		−	10.1859i		−	0.359454i
$804$		−	14.9175i		−	0.526101i
$805$	1.05143	+	1.33935i	0.0370579	+	0.0472058i
$806$	−14.0448			−0.494707
$807$			16.5561i			0.582804i
$808$		−	0.687061i		−	0.0241707i
$809$			20.1211i			0.707422i	0.935355	+	0.353711i	$0.115080\pi$
$809$			20.1211i			0.707422i	−0.935355	+	0.353711i	$0.884920\pi$
$810$	−2.72371	−	3.46956i	−0.0957013	−	0.121908i
$811$	−18.6829			−0.656044			−0.328022	−	0.944670i	$-0.606382\pi$
$811$	−18.6829			−0.656044			−0.328022	+	0.944670i	$0.606382\pi$
$812$	4.79310	−	2.25895i	0.168205	−	0.0792735i
$813$			25.4539i			0.892706i
$814$		−	7.57903i		−	0.265645i
$815$	−3.39841	−	4.32903i	−0.119041	−	0.151639i
$816$	10.4281			0.365056
$817$		−	25.3990i		−	0.888597i
$818$			29.3989i			1.02791i
$819$	−0.797938			−0.0278822
$820$	−32.3138	+	25.3672i	−1.12845	+	0.885863i
$821$	23.2361			0.810944			0.405472	−	0.914107i	$-0.367107\pi$
$821$	23.2361			0.810944			0.405472	+	0.914107i	$0.367107\pi$
$822$	32.7905			1.14370
$823$	23.2939			0.811976			0.405988	−	0.913878i	$-0.366928\pi$
$823$	23.2939			0.811976			0.405988	+	0.913878i	$0.366928\pi$
$824$			1.67273i			0.0582722i
$825$	10.5112	+	2.56897i	0.365952	+	0.0894402i
$826$		−	1.96313i		−	0.0683060i
$827$	−7.45967			−0.259398			−0.129699	−	0.991553i	$-0.541401\pi$
$827$	−7.45967			−0.259398			−0.129699	+	0.991553i	$0.541401\pi$
$828$			2.76827i			0.0962039i
$829$		−	13.0042i		−	0.451654i	−0.974167	−	0.225827i	$-0.927492\pi$
$829$		−	13.0042i		−	0.451654i	0.974167	−	0.225827i	$-0.0725084\pi$
$830$	25.4196	−	19.9552i	0.882328	−	0.692653i
$831$		−	30.7150i		−	1.06549i
$832$			10.9018i			0.377952i
$833$	16.6859			0.578131
$834$	2.24437			0.0777160
$835$	8.76149	−	6.87803i	0.303204	−	0.238024i
$836$	19.2774			0.666722
$837$		−	4.64210i		−	0.160455i
$838$	38.6126			1.33385
$839$			42.3972i			1.46371i	0.681459	+	0.731857i	$0.261346\pi$
$839$			42.3972i			1.46371i	−0.681459	+	0.731857i	$0.738654\pi$
$840$	−0.196229	+	0.154045i	−0.00677054	+	0.00531507i
$841$	−18.4587	+	22.3669i	−0.636506	+	0.771272i
$842$			17.1963i			0.592623i
$843$	−22.7775			−0.784498
$844$		−	13.0934i		−	0.450694i
$845$	14.7017	+	18.7275i	0.505752	+	0.644247i
$846$	−7.26545			−0.249791
$847$		−	3.28625i		−	0.112917i
$848$		−	32.5920i		−	1.11921i
$849$			30.6646i			1.05241i
$850$	5.80636	−	23.7572i	0.199157	−	0.814865i
$851$			2.59859i			0.0890784i
$852$	18.4968			0.633691
$853$	33.8135			1.15775			0.578876	−	0.815416i	$-0.303492\pi$
$853$	33.8135			1.15775			0.578876	+	0.815416i	$0.303492\pi$
$854$	−7.86638			−0.269182
$855$	8.28397	−	6.50316i	0.283306	−	0.222403i
$856$		−	3.94784i		−	0.134935i
$857$		−	39.2819i		−	1.34184i	−0.741528	−	0.670922i	$-0.765898\pi$
$857$		−	39.2819i		−	1.34184i	0.741528	−	0.670922i	$-0.234102\pi$
$858$	6.54756			0.223530
$859$			11.9843i			0.408900i	0.978877	+	0.204450i	$0.0655406\pi$
$859$			11.9843i			0.408900i	−0.978877	+	0.204450i	$0.934459\pi$
$860$	14.0824	+	17.9387i	0.480206	+	0.611705i
$861$	−5.05379			−0.172233
$862$	52.6940			1.79476
$863$			36.8424i			1.25413i	0.778967	+	0.627065i	$0.215744\pi$
$863$			36.8424i			1.25413i	−0.778967	+	0.627065i	$0.784256\pi$
$864$	−7.86723			−0.267649
$865$	−26.4783	+	20.7862i	−0.900288	+	0.706752i
$866$	−67.7202			−2.30122
$867$	10.8517			0.368544
$868$	4.56760			0.155034
$869$	26.7731			0.908216
$870$	−10.6481	+	21.2333i	−0.361005	+	0.719877i
$871$	12.0974			0.409905
$872$	3.73785			0.126580
$873$	−1.64507			−0.0556771
$874$	−13.5990			−0.459993
$875$	2.40276	+	5.29715i	0.0812282	+	0.179076i
$876$	8.90185			0.300766
$877$			2.27276i			0.0767456i	0.999263	+	0.0383728i	$0.0122174\pi$
$877$			2.27276i			0.0767456i	−0.999263	+	0.0383728i	$0.987783\pi$
$878$	60.1184			2.02890
$879$	0.956588			0.0322649
$880$	16.0079	−	12.5667i	0.539628	−	0.423623i
$881$		−	55.3714i		−	1.86551i	−0.360512	−	0.932755i	$-0.617398\pi$
$881$		−	55.3714i		−	1.86551i	0.360512	−	0.932755i	$-0.382602\pi$
$882$	−13.2745			−0.446976
$883$			7.65846i			0.257728i	0.991662	+	0.128864i	$0.0411330\pi$
$883$			7.65846i			0.257728i	−0.991662	+	0.128864i	$0.958867\pi$
$884$		−	7.19264i		−	0.241915i
$885$	2.64120	+	3.36446i	0.0887828	+	0.113095i
$886$	−34.3136			−1.15279
$887$	3.86090			0.129636			0.0648181	−	0.997897i	$-0.479353\pi$
$887$	3.86090			0.129636			0.0648181	+	0.997897i	$0.479353\pi$
$888$	−0.380721			−0.0127762
$889$			7.30815i			0.245108i
$890$	−26.5850	+	20.8700i	−0.891131	+	0.699564i
$891$			2.16411i			0.0725004i
$892$		−	53.8436i		−	1.80282i
$893$		−	17.3471i		−	0.580498i
$894$	1.93610			0.0647528
$895$	−34.7936	−	44.3214i	−1.16302	−	1.48150i
$896$			0.891216i			0.0297734i
$897$	−2.24493			−0.0749561
$898$			2.10136i			0.0701234i
$899$	−22.6130	+	10.6573i	−0.754185	+	0.355441i
$900$	−2.24512	+	9.18607i	−0.0748372	+	0.306202i
$901$			19.2158i			0.640171i
$902$	41.4694			1.38078
$903$			2.80557i			0.0933634i
$904$	−1.45455			−0.0483777
$905$	7.28337	+	9.27784i	0.242107	+	0.308406i
$906$	22.6455			0.752346
$907$	−4.71465			−0.156547			−0.0782737	−	0.996932i	$-0.524941\pi$
$907$	−4.71465			−0.156547			−0.0782737	+	0.996932i	$0.524941\pi$
$908$			13.5232i			0.448782i
$909$		−	3.20388i		−	0.106266i
$910$	2.17335	+	2.76850i	0.0720458	+	0.0917747i
$911$		−	6.38523i		−	0.211552i	−0.994390	−	0.105776i	$-0.966267\pi$
$911$		−	6.38523i		−	0.211552i	0.994390	−	0.105776i	$-0.0337326\pi$
$912$		−	19.8079i		−	0.655906i
$913$	−15.8553			−0.524733
$914$			2.00738i			0.0663983i
$915$	13.4816	−	10.5834i	0.445687	−	0.349877i
$916$		−	18.8071i		−	0.621404i
$917$	4.78607			0.158050
$918$	4.89129			0.161437
$919$	40.2376			1.32732			0.663658	−	0.748036i	$-0.269003\pi$
$919$	40.2376			1.32732			0.663658	+	0.748036i	$0.269003\pi$
$920$	−0.552074	+	0.433394i	−0.0182013	+	0.0142886i
$921$	−31.8260			−1.04870
$922$		−	6.26551i		−	0.206344i
$923$			15.0001i			0.493733i
$924$	−2.12938			−0.0700514
$925$	−2.10750	+	8.62301i	−0.0692943	+	0.283523i
$926$		−	3.46600i		−	0.113900i
$927$			7.80019i			0.256192i
$928$	18.0615	+	38.3234i	0.592899	+	1.25803i
$929$	−56.7497			−1.86190			−0.930949	−	0.365149i	$-0.881018\pi$
$929$	−56.7497			−1.86190			−0.930949	+	0.365149i	$0.881018\pi$
$930$	−16.1061	+	12.6437i	−0.528139	+	0.414604i
$931$		−	31.6944i		−	1.03874i
$932$		−	25.6712i		−	0.840888i
$933$			1.83226i			0.0599854i
$934$	−70.9236			−2.32069
$935$	−9.43808	+	7.40917i	−0.308658	+	0.242306i
$936$		−	0.328907i		−	0.0107507i
$937$		−	42.7198i		−	1.39559i	−0.716296	−	0.697797i	$-0.754164\pi$
$937$		−	42.7198i		−	1.39559i	0.716296	−	0.697797i	$-0.245836\pi$
$938$	−8.09471			−0.264302
$939$			16.8539i			0.550006i
$940$	9.61806	+	12.2519i	0.313707	+	0.399611i
$941$	32.3400			1.05425			0.527127	−	0.849787i	$-0.323269\pi$
$941$	32.3400			1.05425			0.527127	+	0.849787i	$0.323269\pi$
$942$	−15.7903			−0.514474
$943$	−14.2184			−0.463016
$944$	8.04480			0.261836
$945$	−0.915047	+	0.718339i	−0.0297665	+	0.0233676i
$946$		−	23.0214i		−	0.748489i
$947$	−44.3486			−1.44114			−0.720568	−	0.693384i	$-0.756119\pi$
$947$	−44.3486			−1.44114			−0.720568	+	0.693384i	$0.756119\pi$
$948$			23.3979i			0.759930i
$949$			7.21898i			0.234338i
$950$	−45.1263	−	11.0291i	−1.46409	−	0.357830i
$951$	29.0897			0.943298
$952$		−	0.276638i		−	0.00896588i
$953$		−	26.0460i		−	0.843712i	−0.906663	−	0.421856i	$-0.861379\pi$
$953$		−	26.0460i		−	0.843712i	0.906663	−	0.421856i	$-0.138621\pi$
$954$		−	15.2872i		−	0.494942i
$955$	5.83136	−	4.57779i	0.188698	−	0.148134i
$956$	29.4036			0.950981
$957$	10.5420	−	4.96835i	0.340774	−	0.160604i
$958$		−	81.1093i		−	2.62052i
$959$		−	8.64802i		−	0.279259i
$960$	9.81429	+	12.5018i	0.316755	+	0.403494i
$961$	9.45088			0.304867
$962$			5.37140i			0.173181i
$963$		−	18.4094i		−	0.593236i
$964$	−34.4537			−1.10968
$965$	7.85821	+	10.0101i	0.252965	+	0.322236i
$966$	1.50215			0.0483307
$967$	−15.3861			−0.494785			−0.247392	−	0.968915i	$-0.579574\pi$
$967$	−15.3861			−0.494785			−0.247392	+	0.968915i	$0.579574\pi$
$968$	1.35458			0.0435379
$969$			11.6785i			0.375168i
$970$	4.48068	+	5.70766i	0.143866	+	0.183262i
$971$		−	9.79636i		−	0.314380i	−0.987568	−	0.157190i	$-0.949756\pi$
$971$		−	9.79636i		−	0.314380i	0.987568	−	0.157190i	$-0.0502436\pi$
$972$	−1.89129			−0.0606631
$973$		−	0.591919i		−	0.0189761i
$974$			19.3501i			0.620017i
$975$	−7.44947	−	1.82068i	−0.238574	−	0.0583085i
$976$		−	32.2360i		−	1.03185i
$977$		−	26.1850i		−	0.837734i	−0.908048	−	0.418867i	$-0.862427\pi$
$977$		−	26.1850i		−	0.837734i	0.908048	−	0.418867i	$-0.137573\pi$
$978$	−4.85522			−0.155253
$979$	16.5822			0.529968
$980$	17.5729	+	22.3851i	0.561346	+	0.715064i
$981$	17.4302			0.556503
$982$		−	82.3623i		−	2.62829i
$983$	−0.127997			−0.00408247			−0.00204123	−	0.999998i	$-0.500650\pi$
$983$	−0.127997			−0.00408247			−0.00204123	+	0.999998i	$0.500650\pi$
$984$		−	2.08315i		−	0.0664085i
$985$	0.553374	−	0.434415i	0.0176320	−	0.0138416i
$986$	−11.2294	−	23.8268i	−0.357617	−	0.758801i
$987$			1.91616i			0.0609920i
$988$	−13.6623			−0.434654
$989$			7.89323i			0.250990i
$990$	7.50851	−	5.89440i	0.238636	−	0.187336i
$991$	18.1627			0.576957			0.288478	−	0.957486i	$-0.406851\pi$
$991$	18.1627			0.576957			0.288478	+	0.957486i	$0.406851\pi$
$992$			36.5205i			1.15953i
$993$			15.3405i			0.486817i
$994$		−	10.0369i		−	0.318353i
$995$	4.06280	+	5.17535i	0.128799	+	0.164070i
$996$		−	13.8565i		−	0.439059i
$997$	−51.0941			−1.61817			−0.809083	−	0.587694i	$-0.800036\pi$
$997$	−51.0941			−1.61817			−0.809083	+	0.587694i	$0.800036\pi$
$998$	−4.93218			−0.156125
$999$	−1.77536			−0.0561700

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.2.f.e.289.4	yes	12
3.2	odd	2		1305.2.f.k.289.9		12
5.2	odd	4		2175.2.d.j.376.17		24
5.3	odd	4		2175.2.d.j.376.8		24
5.4	even	2		435.2.f.f.289.9	yes	12
15.14	odd	2		1305.2.f.l.289.4		12
29.28	even	2		435.2.f.f.289.10	yes	12
87.86	odd	2		1305.2.f.l.289.3		12
145.28	odd	4		2175.2.d.j.376.7		24
145.57	odd	4		2175.2.d.j.376.18		24
145.144	even	2	inner	435.2.f.e.289.3	✓	12
435.434	odd	2		1305.2.f.k.289.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.f.e.289.3	✓	12	145.144	even	2	inner
435.2.f.e.289.4	yes	12	1.1	even	1	trivial
435.2.f.f.289.9	yes	12	5.4	even	2
435.2.f.f.289.10	yes	12	29.28	even	2
1305.2.f.k.289.9		12	3.2	odd	2
1305.2.f.k.289.10		12	435.434	odd	2
1305.2.f.l.289.3		12	87.86	odd	2
1305.2.f.l.289.4		12	15.14	odd	2
2175.2.d.j.376.7		24	145.28	odd	4
2175.2.d.j.376.8		24	5.3	odd	4
2175.2.d.j.376.17		24	5.2	odd	4
2175.2.d.j.376.18		24	145.57	odd	4

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:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.97264 q^{2} -1.00000 q^{3} +1.89129 q^{4} +(1.38075 + 1.75885i) q^{5} +1.97264 q^{6} -0.520254i q^{7} +0.214447 q^{8} +1.00000 q^{9} +(-2.72371 - 3.46956i) q^{10} +2.16411i q^{11} -1.89129 q^{12} -1.53375i q^{13} +1.02627i q^{14} +(-1.38075 - 1.75885i) q^{15} -4.20560 q^{16} +2.47957 q^{17} -1.97264 q^{18} -4.70989i q^{19} +(2.61139 + 3.32649i) q^{20} +0.520254i q^{21} -4.26900i q^{22} +1.46369i q^{23} -0.214447 q^{24} +(-1.18708 + 4.85704i) q^{25} +3.02552i q^{26} -1.00000 q^{27} -0.983951i q^{28} +(2.29579 + 4.87128i) q^{29} +(2.72371 + 3.46956i) q^{30} +4.64210i q^{31} +7.86723 q^{32} -2.16411i q^{33} -4.89129 q^{34} +(0.915047 - 0.718339i) q^{35} +1.89129 q^{36} +1.77536 q^{37} +9.29090i q^{38} +1.53375i q^{39} +(0.296097 + 0.377179i) q^{40} +9.71408i q^{41} -1.02627i q^{42} +5.39269 q^{43} +4.09296i q^{44} +(1.38075 + 1.75885i) q^{45} -2.88733i q^{46} +3.68312 q^{47} +4.20560 q^{48} +6.72934 q^{49} +(2.34168 - 9.58117i) q^{50} -2.47957 q^{51} -2.90076i q^{52} +7.74965i q^{53} +1.97264 q^{54} +(-3.80634 + 2.98808i) q^{55} -0.111567i q^{56} +4.70989i q^{57} +(-4.52876 - 9.60925i) q^{58} -1.91288 q^{59} +(-2.61139 - 3.32649i) q^{60} +7.66501i q^{61} -9.15717i q^{62} -0.520254i q^{63} -7.10796 q^{64} +(2.69763 - 2.11771i) q^{65} +4.26900i q^{66} +7.88749i q^{67} +4.68959 q^{68} -1.46369i q^{69} +(-1.80505 + 1.41702i) q^{70} -9.78001 q^{71} +0.214447 q^{72} -4.70676 q^{73} -3.50215 q^{74} +(1.18708 - 4.85704i) q^{75} -8.90777i q^{76} +1.12589 q^{77} -3.02552i q^{78} -12.3714i q^{79} +(-5.80687 - 7.39701i) q^{80} +1.00000 q^{81} -19.1623i q^{82} +7.32647i q^{83} +0.983951i q^{84} +(3.42366 + 4.36119i) q^{85} -10.6378 q^{86} +(-2.29579 - 4.87128i) q^{87} +0.464086i q^{88} -7.66235i q^{89} +(-2.72371 - 3.46956i) q^{90} -0.797938 q^{91} +2.76827i q^{92} -4.64210i q^{93} -7.26545 q^{94} +(8.28397 - 6.50316i) q^{95} -7.86723 q^{96} -1.64507 q^{97} -13.2745 q^{98} +2.16411i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{3} + 16 q^{4} - 6 q^{5} + 12 q^{9} - 2 q^{10} - 16 q^{12} + 6 q^{15} + 32 q^{16} + 8 q^{17} - 20 q^{20} + 12 q^{25} - 12 q^{27} + 8 q^{29} + 2 q^{30} + 40 q^{32} - 52 q^{34} + 14 q^{35} + 16 q^{36}+ \cdots + 112 q^{98}+O(q^{100}) \) 12 * q - 12 * q^3 + 16 * q^4 - 6 * q^5 + 12 * q^9 - 2 * q^10 - 16 * q^12 + 6 * q^15 + 32 * q^16 + 8 * q^17 - 20 * q^20 + 12 * q^25 - 12 * q^27 + 8 * q^29 + 2 * q^30 + 40 * q^32 - 52 * q^34 + 14 * q^35 + 16 * q^36 - 20 * q^37 + 22 * q^40 - 44 * q^43 - 6 * q^45 + 32 * q^47 - 32 * q^48 - 4 * q^49 - 24 * q^50 - 8 * q^51 - 42 * q^55 + 24 * q^58 - 28 * q^59 + 20 * q^60 - 4 * q^64 + 22 * q^65 - 16 * q^68 + 26 * q^70 - 16 * q^71 + 36 * q^73 - 28 * q^74 - 12 * q^75 - 22 * q^80 + 12 * q^81 - 30 * q^85 - 16 * q^86 - 8 * q^87 - 2 * q^90 + 24 * q^91 - 28 * q^94 - 16 * q^95 - 40 * q^96 + 40 * q^97 + 112 * q^98

Introduction

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