LMFDB - Embedded newform 1805.2.b.j.1084.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1084,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1805.1084");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.b (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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22x^{14} + 190x^{12} + 820x^{10} + 1862x^{8} + 2154x^{6} + 1163x^{4} + 256x^{2} + 16 $ x^16 + 22x^14 + 190x^12 + 820x^10 + 1862x^8 + 2154x^6 + 1163x^4 + 256*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1084.13
Root			$1.85244i$ of defining polynomial
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.j.1084.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.85244i q^{2} +1.45440i q^{3} -1.43152 q^{4} +(-0.323421 + 2.21255i) q^{5} -2.69418 q^{6} +0.477604i q^{7} +1.05306i q^{8} +0.884731 q^{9} +O(q^{10})$	\(q+1.85244i q^{2} +1.45440i q^{3} -1.43152 q^{4} +(-0.323421 + 2.21255i) q^{5} -2.69418 q^{6} +0.477604i q^{7} +1.05306i q^{8} +0.884731 q^{9} +(-4.09862 - 0.599118i) q^{10} +1.95728 q^{11} -2.08200i q^{12} -3.06043i q^{13} -0.884731 q^{14} +(-3.21793 - 0.470383i) q^{15} -4.81379 q^{16} +0.973502i q^{17} +1.63891i q^{18} +(0.462986 - 3.16733i) q^{20} -0.694625 q^{21} +3.62574i q^{22} +5.59328i q^{23} -1.53157 q^{24} +(-4.79080 - 1.43117i) q^{25} +5.66926 q^{26} +5.64994i q^{27} -0.683702i q^{28} -10.1756 q^{29} +(0.871355 - 5.96102i) q^{30} -5.60367 q^{31} -6.81111i q^{32} +2.84666i q^{33} -1.80335 q^{34} +(-1.05672 - 0.154467i) q^{35} -1.26651 q^{36} -5.65754i q^{37} +4.45108 q^{39} +(-2.32996 - 0.340584i) q^{40} -10.4679 q^{41} -1.28675i q^{42} -6.20983i q^{43} -2.80189 q^{44} +(-0.286141 + 1.95752i) q^{45} -10.3612 q^{46} +2.47845i q^{47} -7.00115i q^{48} +6.77189 q^{49} +(2.65116 - 8.87465i) q^{50} -1.41586 q^{51} +4.38109i q^{52} +10.7711i q^{53} -10.4662 q^{54} +(-0.633026 + 4.33059i) q^{55} -0.502948 q^{56} -18.8496i q^{58} +7.32031 q^{59} +(4.60655 + 0.673365i) q^{60} +8.76766 q^{61} -10.3805i q^{62} +0.422551i q^{63} +2.98958 q^{64} +(6.77138 + 0.989809i) q^{65} -5.27326 q^{66} +8.82042i q^{67} -1.39359i q^{68} -8.13485 q^{69} +(0.286141 - 1.95752i) q^{70} +13.1846 q^{71} +0.931679i q^{72} -4.97121i q^{73} +10.4802 q^{74} +(2.08150 - 6.96772i) q^{75} +0.934804i q^{77} +8.24535i q^{78} -0.707984 q^{79} +(1.55688 - 10.6508i) q^{80} -5.56306 q^{81} -19.3911i q^{82} +11.8783i q^{83} +0.994373 q^{84} +(-2.15393 - 0.314851i) q^{85} +11.5033 q^{86} -14.7993i q^{87} +2.06114i q^{88} +2.14855 q^{89} +(-3.62618 - 0.530058i) q^{90} +1.46167 q^{91} -8.00692i q^{92} -8.14996i q^{93} -4.59117 q^{94} +9.90605 q^{96} +5.89541i q^{97} +12.5445i q^{98} +1.73167 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9}+O(q^{10}) $ 16 * q - 12 * q^4 + 4 * q^5 - 10 * q^6 - 6 * q^9	$ 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9} + 16 q^{10} - 22 q^{11} + 6 q^{14} - 10 q^{15} + 8 q^{16} - 14 q^{20} + 20 q^{21} + 14 q^{24} + 4 q^{25} - 16 q^{26} + 2 q^{29} - 12 q^{30} - 16 q^{31} - 8 q^{34} - 10 q^{35} + 18 q^{36} + 36 q^{39} - 38 q^{40} - 26 q^{41} + 64 q^{44} - 2 q^{45} - 2 q^{46} + 20 q^{49} + 48 q^{50} + 38 q^{51} + 12 q^{54} - 10 q^{55} - 6 q^{56} + 10 q^{59} + 10 q^{60} - 30 q^{61} + 16 q^{64} + 36 q^{65} + 4 q^{66} + 68 q^{69} + 2 q^{70} + 20 q^{71} + 40 q^{74} + 32 q^{75} + 12 q^{79} + 40 q^{80} - 48 q^{81} - 2 q^{84} - 2 q^{85} + 20 q^{86} - 30 q^{90} + 86 q^{91} - 38 q^{94} + 22 q^{96} + 32 q^{99}+O(q^{100}) $ 16 * q - 12 * q^4 + 4 * q^5 - 10 * q^6 - 6 * q^9 + 16 * q^10 - 22 * q^11 + 6 * q^14 - 10 * q^15 + 8 * q^16 - 14 * q^20 + 20 * q^21 + 14 * q^24 + 4 * q^25 - 16 * q^26 + 2 * q^29 - 12 * q^30 - 16 * q^31 - 8 * q^34 - 10 * q^35 + 18 * q^36 + 36 * q^39 - 38 * q^40 - 26 * q^41 + 64 * q^44 - 2 * q^45 - 2 * q^46 + 20 * q^49 + 48 * q^50 + 38 * q^51 + 12 * q^54 - 10 * q^55 - 6 * q^56 + 10 * q^59 + 10 * q^60 - 30 * q^61 + 16 * q^64 + 36 * q^65 + 4 * q^66 + 68 * q^69 + 2 * q^70 + 20 * q^71 + 40 * q^74 + 32 * q^75 + 12 * q^79 + 40 * q^80 - 48 * q^81 - 2 * q^84 - 2 * q^85 + 20 * q^86 - 30 * q^90 + 86 * q^91 - 38 * q^94 + 22 * q^96 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times$.

$n$	$362$	$1446$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.85244i			1.30987i	0.755685	+	0.654936i	$0.227304\pi$
$2$			1.85244i			1.30987i	−0.755685	+	0.654936i	$0.772696\pi$
$3$			1.45440i			0.839696i	0.907594	+	0.419848i	$0.137917\pi$
$3$			1.45440i			0.839696i	−0.907594	+	0.419848i	$0.862083\pi$
$4$	−1.43152			−0.715762
$5$	−0.323421	+	2.21255i	−0.144638	+	0.989485i
$5$	−0.323421	+	2.21255i	−0.144638	+	0.989485i
$6$	−2.69418			−1.09989
$7$			0.477604i			0.180517i	0.995918	+	0.0902586i	$0.0287694\pi$
$7$			0.477604i			0.180517i	−0.995918	+	0.0902586i	$0.971231\pi$
$8$			1.05306i			0.372315i
$9$	0.884731			0.294910
$10$	−4.09862	−	0.599118i	−1.29610	−	0.189458i
$11$	1.95728			0.590142			0.295071	−	0.955475i	$-0.404657\pi$
$11$	1.95728			0.590142			0.295071	+	0.955475i	$0.404657\pi$
$12$		−	2.08200i		−	0.601023i
$13$		−	3.06043i		−	0.848812i	−0.905472	−	0.424406i	$-0.860483\pi$
$13$		−	3.06043i		−	0.848812i	0.905472	−	0.424406i	$-0.139517\pi$
$14$	−0.884731			−0.236454
$15$	−3.21793	−	0.470383i	−0.830866	−	0.121452i
$16$	−4.81379			−1.20345
$17$			0.973502i			0.236109i	0.993007	+	0.118054i	$0.0376657\pi$
$17$			0.973502i			0.236109i	−0.993007	+	0.118054i	$0.962334\pi$
$18$			1.63891i			0.386295i
$19$		0			0
$19$		0			0
$20$	0.462986	−	3.16733i	0.103527	−	0.708236i
$21$	−0.694625			−0.151580
$22$			3.62574i			0.773010i
$23$			5.59328i			1.16628i	0.812372	+	0.583140i	$0.198176\pi$
$23$			5.59328i			1.16628i	−0.812372	+	0.583140i	$0.801824\pi$
$24$	−1.53157			−0.312631
$25$	−4.79080	−	1.43117i	−0.958159	−	0.286235i
$26$	5.66926			1.11183
$27$			5.64994i			1.08733i
$28$		−	0.683702i		−	0.129207i
$29$	−10.1756			−1.88955			−0.944777	−	0.327714i	$-0.893722\pi$
$29$	−10.1756			−1.88955			−0.944777	+	0.327714i	$0.893722\pi$
$30$	0.871355	−	5.96102i	0.159087	−	1.08833i
$31$	−5.60367			−1.00645			−0.503225	−	0.864156i	$-0.667853\pi$
$31$	−5.60367			−1.00645			−0.503225	+	0.864156i	$0.667853\pi$
$32$		−	6.81111i		−	1.20405i
$33$			2.84666i			0.495540i
$34$	−1.80335			−0.309272
$35$	−1.05672	−	0.154467i	−0.178619	−	0.0261097i
$36$	−1.26651			−0.211086
$37$		−	5.65754i		−	0.930094i	−0.885286	−	0.465047i	$-0.846037\pi$
$37$		−	5.65754i		−	0.930094i	0.885286	−	0.465047i	$-0.153963\pi$
$38$		0			0
$39$	4.45108			0.712744
$40$	−2.32996	−	0.340584i	−0.368400	−	0.0538510i
$41$	−10.4679			−1.63481			−0.817404	−	0.576065i	$-0.804587\pi$
$41$	−10.4679			−1.63481			−0.817404	+	0.576065i	$0.804587\pi$
$42$		−	1.28675i		−	0.198550i
$43$		−	6.20983i		−	0.946990i	−0.880796	−	0.473495i	$-0.842992\pi$
$43$		−	6.20983i		−	0.946990i	0.880796	−	0.473495i	$-0.157008\pi$
$44$	−2.80189			−0.422401
$45$	−0.286141	+	1.95752i	−0.0426554	+	0.291809i
$46$	−10.3612			−1.52768
$47$			2.47845i			0.361519i	0.983527	+	0.180759i	$0.0578555\pi$
$47$			2.47845i			0.361519i	−0.983527	+	0.180759i	$0.942144\pi$
$48$		−	7.00115i		−	1.01053i
$49$	6.77189			0.967414
$50$	2.65116	−	8.87465i	0.374931	−	1.25507i
$51$	−1.41586			−0.198260
$52$			4.38109i			0.607547i
$53$			10.7711i			1.47953i	0.672866	+	0.739764i	$0.265063\pi$
$53$			10.7711i			1.47953i	−0.672866	+	0.739764i	$0.734937\pi$
$54$	−10.4662			−1.42426
$55$	−0.633026	+	4.33059i	−0.0853572	+	0.583936i
$56$	−0.502948			−0.0672092
$57$		0			0
$58$		−	18.8496i		−	2.47507i
$59$	7.32031			0.953024			0.476512	−	0.879168i	$-0.341901\pi$
$59$	7.32031			0.953024			0.476512	+	0.879168i	$0.341901\pi$
$60$	4.60655	+	0.673365i	0.594703	+	0.0869310i
$61$	8.76766			1.12258			0.561292	−	0.827618i	$-0.310305\pi$
$61$	8.76766			1.12258			0.561292	+	0.827618i	$0.310305\pi$
$62$		−	10.3805i		−	1.31832i
$63$			0.422551i			0.0532364i
$64$	2.98958			0.373698
$65$	6.77138	+	0.989809i	0.839886	+	0.122771i
$66$	−5.27326			−0.649093
$67$			8.82042i			1.07759i	0.842438	+	0.538793i	$0.181120\pi$
$67$			8.82042i			1.07759i	−0.842438	+	0.538793i	$0.818880\pi$
$68$		−	1.39359i		−	0.168998i
$69$	−8.13485			−0.979321
$70$	0.286141	−	1.95752i	0.0342004	−	0.233968i
$71$	13.1846			1.56472			0.782362	−	0.622825i	$-0.214015\pi$
$71$	13.1846			1.56472			0.782362	+	0.622825i	$0.214015\pi$
$72$			0.931679i			0.109799i
$73$		−	4.97121i		−	0.581836i	−0.956748	−	0.290918i	$-0.906039\pi$
$73$		−	4.97121i		−	0.581836i	0.956748	−	0.290918i	$-0.0939606\pi$
$74$	10.4802			1.21830
$75$	2.08150	−	6.96772i	0.240350	−	0.804563i
$76$		0			0
$77$			0.934804i			0.106531i
$78$			8.24535i			0.933603i
$79$	−0.707984			−0.0796544			−0.0398272	−	0.999207i	$-0.512681\pi$
$79$	−0.707984			−0.0796544			−0.0398272	+	0.999207i	$0.512681\pi$
$80$	1.55688	−	10.6508i	0.174065	−	1.19079i
$81$	−5.56306			−0.618118
$82$		−	19.3911i		−	2.14139i
$83$			11.8783i			1.30382i	0.758297	+	0.651909i	$0.226032\pi$
$83$			11.8783i			1.30382i	−0.758297	+	0.651909i	$0.773968\pi$
$84$	0.994373			0.108495
$85$	−2.15393	−	0.314851i	−0.233626	−	0.0341504i
$86$	11.5033			1.24043
$87$		−	14.7993i		−	1.58665i
$88$			2.06114i			0.219718i
$89$	2.14855			0.227746			0.113873	−	0.993495i	$-0.463674\pi$
$89$	2.14855			0.227746			0.113873	+	0.993495i	$0.463674\pi$
$90$	−3.62618	−	0.530058i	−0.382232	−	0.0558730i
$91$	1.46167			0.153225
$92$		−	8.00692i		−	0.834779i
$93$		−	8.14996i		−	0.845112i
$94$	−4.59117			−0.473543
$95$		0			0
$96$	9.90605			1.01103
$97$			5.89541i			0.598588i	0.954161	+	0.299294i	$0.0967512\pi$
$97$			5.89541i			0.598588i	−0.954161	+	0.299294i	$0.903249\pi$
$98$			12.5445i			1.26719i
$99$	1.73167			0.174039
$100$	6.85815	+	2.04876i	0.685815	+	0.204876i
$101$	0.258211			0.0256930			0.0128465	−	0.999917i	$-0.495911\pi$
$101$	0.258211			0.0256930			0.0128465	+	0.999917i	$0.495911\pi$
$102$		−	2.62279i		−	0.259695i
$103$		−	14.3714i		−	1.41605i	−0.706186	−	0.708026i	$-0.749586\pi$
$103$		−	14.3714i		−	1.41605i	0.706186	−	0.708026i	$-0.250414\pi$
$104$	3.22283			0.316025
$105$	0.224657	−	1.53690i	0.0219242	−	0.149986i
$106$	−19.9529			−1.93799
$107$		−	5.73115i		−	0.554051i	−0.960863	−	0.277026i	$-0.910651\pi$
$107$		−	5.73115i		−	0.554051i	0.960863	−	0.277026i	$-0.0893487\pi$
$108$		−	8.08803i		−	0.778271i
$109$	−5.77812			−0.553444			−0.276722	−	0.960950i	$-0.589248\pi$
$109$	−5.77812			−0.553444			−0.276722	+	0.960950i	$0.589248\pi$
$110$	−8.02214	−	1.17264i	−0.764881	−	0.111807i
$111$	8.22830			0.780996
$112$		−	2.29908i		−	0.217243i
$113$			13.9762i			1.31477i	0.753554	+	0.657386i	$0.228338\pi$
$113$			13.9762i			1.31477i	−0.753554	+	0.657386i	$0.771662\pi$
$114$		0			0
$115$	−12.3754	−	1.80899i	−1.15402	−	0.168689i
$116$	14.5666			1.35247
$117$		−	2.70766i		−	0.250323i
$118$			13.5604i			1.24834i
$119$	−0.464948			−0.0426217
$120$	0.495344	−	3.38869i	0.0452185	−	0.309344i
$121$	−7.16906			−0.651733
$122$			16.2415i			1.47044i
$123$		−	15.2244i		−	1.37274i
$124$	8.02180			0.720379
$125$	4.71600	−	10.1370i	0.421812	−	0.906683i
$126$	−0.782749			−0.0697328
$127$		−	9.23319i		−	0.819313i	−0.912240	−	0.409657i	$-0.865649\pi$
$127$		−	9.23319i		−	0.819313i	0.912240	−	0.409657i	$-0.134351\pi$
$128$		−	8.08421i		−	0.714550i
$129$	9.03155			0.795184
$130$	−1.83356	+	12.5436i	−0.160814	+	1.10014i
$131$	−13.9316			−1.21721			−0.608603	−	0.793475i	$-0.708270\pi$
$131$	−13.9316			−1.21721			−0.608603	+	0.793475i	$0.708270\pi$
$132$		−	4.07506i		−	0.354689i
$133$		0			0
$134$	−16.3393			−1.41150
$135$	−12.5008	−	1.82731i	−1.07590	−	0.157270i
$136$	−1.02516			−0.0879068
$137$			3.84336i			0.328360i	0.986430	+	0.164180i	$0.0524978\pi$
$137$			3.84336i			0.328360i	−0.986430	+	0.164180i	$0.947502\pi$
$138$		−	15.0693i		−	1.28278i
$139$	18.8730			1.60079			0.800395	−	0.599473i	$-0.204623\pi$
$139$	18.8730			1.60079			0.800395	+	0.599473i	$0.204623\pi$
$140$	1.51273	+	0.221124i	0.127849	+	0.0186884i
$141$	−3.60464			−0.303566
$142$			24.4236i			2.04959i
$143$		−	5.99012i		−	0.500919i
$144$	−4.25891			−0.354909
$145$	3.29099	−	22.5140i	0.273302	−	1.86968i
$146$	9.20885			0.762130
$147$			9.84902i			0.812333i
$148$			8.09891i			0.665726i
$149$	23.9268			1.96016			0.980082	−	0.198594i	$-0.0636375\pi$
$149$	23.9268			1.96016			0.980082	+	0.198594i	$0.0636375\pi$
$150$	12.9073	+	3.85584i	1.05387	+	0.314828i
$151$	5.90301			0.480380			0.240190	−	0.970726i	$-0.422790\pi$
$151$	5.90301			0.480380			0.240190	+	0.970726i	$0.422790\pi$
$152$		0			0
$153$			0.861288i			0.0696310i
$154$	−1.73167			−0.139542
$155$	1.81235	−	12.3984i	0.145571	−	0.995866i
$156$	−6.37184			−0.510155
$157$			10.5707i			0.843631i	0.906682	+	0.421815i	$0.138607\pi$
$157$			10.5707i			0.843631i	−0.906682	+	0.421815i	$0.861393\pi$
$158$		−	1.31150i		−	0.104337i
$159$	−15.6655			−1.24235
$160$	15.0700	+	2.20286i	1.19138	+	0.174151i
$161$	−2.67137			−0.210534
$162$		−	10.3052i		−	0.809654i
$163$			18.6090i			1.45757i	0.684743	+	0.728785i	$0.259915\pi$
$163$			18.6090i			1.45757i	−0.684743	+	0.728785i	$0.740085\pi$
$164$	14.9850			1.17013
$165$	−6.29839	−	0.920670i	−0.490329	−	0.0716741i
$166$	−22.0039			−1.70783
$167$			2.77731i			0.214914i	0.994210	+	0.107457i	$0.0342708\pi$
$167$			2.77731i			0.214914i	−0.994210	+	0.107457i	$0.965729\pi$
$168$		−	0.731485i		−	0.0564353i
$169$	3.63375			0.279519
$170$	0.583242	−	3.99001i	0.0447327	−	0.306020i
$171$		0			0
$172$			8.88952i			0.677820i
$173$			8.92075i			0.678232i	0.940745	+	0.339116i	$0.110128\pi$
$173$			8.92075i			0.678232i	−0.940745	+	0.339116i	$0.889872\pi$
$174$	27.4148			2.07831
$175$	0.683534	−	2.28810i	0.0516703	−	0.172964i
$176$	−9.42192			−0.710204
$177$			10.6466i			0.800250i
$178$			3.98006i			0.298318i
$179$	15.2646			1.14093			0.570467	−	0.821321i	$-0.306762\pi$
$179$	15.2646			1.14093			0.570467	+	0.821321i	$0.306762\pi$
$180$	0.409618	−	2.80223i	0.0305311	−	0.208866i
$181$	8.54101			0.634848			0.317424	−	0.948284i	$-0.397182\pi$
$181$	8.54101			0.634848			0.317424	+	0.948284i	$0.397182\pi$
$182$			2.70766i			0.200705i
$183$			12.7516i			0.942629i
$184$	−5.89009			−0.434223
$185$	12.5176	+	1.82977i	0.920313	+	0.134527i
$186$	15.0973			1.10699
$187$			1.90542i			0.139338i
$188$		−	3.54796i		−	0.258761i
$189$	−2.69843			−0.196282
$190$		0			0
$191$	−16.2967			−1.17919			−0.589594	−	0.807700i	$-0.700712\pi$
$191$	−16.2967			−1.17919			−0.589594	+	0.807700i	$0.700712\pi$
$192$			4.34804i			0.313792i
$193$			16.4692i			1.18548i	0.805394	+	0.592739i	$0.201954\pi$
$193$			16.4692i			1.18548i	−0.805394	+	0.592739i	$0.798046\pi$
$194$	−10.9209			−0.784074
$195$	−1.43958	+	9.84827i	−0.103090	+	0.705249i
$196$	−9.69414			−0.692438
$197$		−	10.0229i		−	0.714102i	−0.934085	−	0.357051i	$-0.883782\pi$
$197$		−	10.0229i		−	0.714102i	0.934085	−	0.357051i	$-0.116218\pi$
$198$			3.20780i			0.227969i
$199$	12.6643			0.897748			0.448874	−	0.893595i	$-0.351825\pi$
$199$	12.6643			0.897748			0.448874	+	0.893595i	$0.351825\pi$
$200$	1.50712	−	5.04502i	0.106569	−	0.356737i
$201$	−12.8284			−0.904845
$202$			0.478321i			0.0336545i
$203$		−	4.85988i		−	0.341097i
$204$	2.02684			0.141907
$205$	3.38553	−	23.1607i	0.236456	−	1.61762i
$206$	26.6221			1.85485
$207$			4.94855i			0.343948i
$208$			14.7323i			1.02150i
$209$		0			0
$210$	2.84700	+	0.416162i	0.196462	+	0.0287179i
$211$	−5.73609			−0.394888			−0.197444	−	0.980314i	$-0.563264\pi$
$211$	−5.73609			−0.394888			−0.197444	+	0.980314i	$0.563264\pi$
$212$		−	15.4191i		−	1.05899i
$213$			19.1756i			1.31389i
$214$	10.6166			0.725736
$215$	13.7396	+	2.00839i	0.937032	+	0.136971i
$216$	−5.94975			−0.404829
$217$		−	2.67634i		−	0.181682i
$218$		−	10.7036i		−	0.724940i
$219$	7.23010			0.488565
$220$	0.906192	−	6.19934i	0.0610955	−	0.417960i
$221$	2.97934			0.200412
$222$			15.2424i			1.02300i
$223$			12.8478i			0.860353i	0.902745	+	0.430176i	$0.141549\pi$
$223$			12.8478i			0.860353i	−0.902745	+	0.430176i	$0.858451\pi$
$224$	3.25301			0.217351
$225$	−4.23857	−	1.26620i	−0.282571	−	0.0844136i
$226$	−25.8901			−1.72218
$227$		−	15.5808i		−	1.03413i	−0.855945	−	0.517067i	$-0.827024\pi$
$227$		−	15.5808i		−	1.03413i	0.855945	−	0.517067i	$-0.172976\pi$
$228$		0			0
$229$	3.77930			0.249743			0.124871	−	0.992173i	$-0.460148\pi$
$229$	3.77930			0.249743			0.124871	+	0.992173i	$0.460148\pi$
$230$	3.35103	−	22.9247i	0.220961	−	1.51161i
$231$	−1.35958			−0.0894535
$232$		−	10.7155i		−	0.703508i
$233$			11.0745i			0.725512i	0.931884	+	0.362756i	$0.118164\pi$
$233$			11.0745i			0.725512i	−0.931884	+	0.362756i	$0.881836\pi$
$234$	5.01577			0.327891
$235$	−5.48370	−	0.801583i	−0.357717	−	0.0522895i
$236$	−10.4792			−0.682139
$237$		−	1.02969i		−	0.0668855i
$238$		−	0.861288i		−	0.0558290i
$239$	10.6496			0.688865			0.344433	−	0.938811i	$-0.388071\pi$
$239$	10.6496			0.688865			0.344433	+	0.938811i	$0.388071\pi$
$240$	15.4904	+	2.26432i	0.999903	+	0.146161i
$241$	−5.01271			−0.322897			−0.161448	−	0.986881i	$-0.551617\pi$
$241$	−5.01271			−0.322897			−0.161448	+	0.986881i	$0.551617\pi$
$242$		−	13.2802i		−	0.853686i
$243$			8.85892i			0.568300i
$244$	−12.5511			−0.803503
$245$	−2.19018	+	14.9832i	−0.139925	+	0.957241i
$246$	28.2023			1.79811
$247$		0			0
$248$		−	5.90103i		−	0.374716i
$249$	−17.2758			−1.09481
$250$	18.7782	+	8.73609i	1.18764	+	0.552519i
$251$	−26.1721			−1.65197			−0.825986	−	0.563691i	$-0.809381\pi$
$251$	−26.1721			−1.65197			−0.825986	+	0.563691i	$0.809381\pi$
$252$		−	0.604892i		−	0.0381046i
$253$			10.9476i			0.688271i
$254$	17.1039			1.07319
$255$	0.457919	−	3.13266i	0.0286760	−	0.196175i
$256$	20.9546			1.30967
$257$			22.4024i			1.39742i	0.715403	+	0.698712i	$0.246243\pi$
$257$			22.4024i			1.39742i	−0.715403	+	0.698712i	$0.753757\pi$
$258$			16.7304i			1.04159i
$259$	2.70206			0.167898
$260$	−9.69339	−	1.41694i	−0.601159	−	0.0878747i
$261$	−9.00263			−0.557249
$262$		−	25.8074i		−	1.59438i
$263$		−	25.9338i		−	1.59915i	−0.600569	−	0.799573i	$-0.705059\pi$
$263$		−	25.9338i		−	1.59915i	0.600569	−	0.799573i	$-0.294941\pi$
$264$	−2.99772			−0.184497
$265$	−23.8317	−	3.48361i	−1.46397	−	0.213997i
$266$		0			0
$267$			3.12485i			0.191238i
$268$		−	12.6267i		−	0.771296i
$269$	−9.24978			−0.563969			−0.281985	−	0.959419i	$-0.590993\pi$
$269$	−9.24978			−0.563969			−0.281985	+	0.959419i	$0.590993\pi$
$270$	3.38498	−	23.1569i	0.206003	−	1.40929i
$271$	−22.4688			−1.36488			−0.682441	−	0.730941i	$-0.739082\pi$
$271$	−22.4688			−1.36488			−0.682441	+	0.730941i	$0.739082\pi$
$272$		−	4.68623i		−	0.284145i
$273$			2.12585i			0.128663i
$274$	−7.11958			−0.430110
$275$	−9.37693	−	2.80121i	−0.565450	−	0.168919i
$276$	11.6452			0.700961
$277$			9.16598i			0.550730i	0.961340	+	0.275365i	$0.0887987\pi$
$277$			9.16598i			0.550730i	−0.961340	+	0.275365i	$0.911201\pi$
$278$			34.9611i			2.09683i
$279$	−4.95774			−0.296812
$280$	0.162664	−	1.11280i	0.00972103	−	0.0665025i
$281$	19.3577			1.15479			0.577393	−	0.816467i	$-0.304070\pi$
$281$	19.3577			1.15479			0.577393	+	0.816467i	$0.304070\pi$
$282$		−	6.67738i		−	0.397632i
$283$		−	8.72514i		−	0.518656i	−0.965789	−	0.259328i	$-0.916499\pi$
$283$		−	8.72514i		−	0.518656i	0.965789	−	0.259328i	$-0.0835010\pi$
$284$	−18.8741			−1.11997
$285$		0			0
$286$	11.0963			0.656140
$287$		−	4.99950i		−	0.295111i
$288$		−	6.02600i		−	0.355085i
$289$	16.0523			0.944253
$290$	41.7057	+	6.09636i	2.44905	+	0.357990i
$291$	−8.57427			−0.502632
$292$			7.11641i			0.416456i
$293$		−	16.7749i		−	0.980002i	−0.871722	−	0.490001i	$-0.836996\pi$
$293$		−	16.7749i		−	0.980002i	0.871722	−	0.490001i	$-0.163004\pi$
$294$	−18.2447			−1.06405
$295$	−2.36755	+	16.1966i	−0.137844	+	0.943002i
$296$	5.95776			0.346287
$297$			11.0585i			0.641680i
$298$			44.3230i			2.56756i
$299$	17.1179			0.989952
$300$	−2.97971	+	9.97446i	−0.172034	+	0.575876i
$301$	2.96584			0.170948
$302$			10.9350i			0.629236i
$303$			0.375542i			0.0215743i
$304$		0			0
$305$	−2.83565	+	19.3989i	−0.162369	+	1.11078i
$306$	−1.59548			−0.0912076
$307$			6.40893i			0.365777i	0.983134	+	0.182889i	$0.0585448\pi$
$307$			6.40893i			0.365777i	−0.983134	+	0.182889i	$0.941455\pi$
$308$		−	1.33819i		−	0.0762507i
$309$	20.9017			1.18905
$310$	22.9673	+	3.35726i	1.30446	+	0.190680i
$311$	10.6248			0.602477			0.301238	−	0.953549i	$-0.402600\pi$
$311$	10.6248			0.602477			0.301238	+	0.953549i	$0.402600\pi$
$312$			4.68728i			0.265365i
$313$			4.75656i			0.268857i	0.990923	+	0.134428i	$0.0429198\pi$
$313$			4.75656i			0.268857i	−0.990923	+	0.134428i	$0.957080\pi$
$314$	−19.5815			−1.10505
$315$	−0.934917	−	0.136662i	−0.0526766	−	0.00770003i
$316$	1.01350			0.0570136
$317$			0.0612218i			0.00343856i	0.999999	+	0.00171928i	$0.000547264\pi$
$317$			0.0612218i			0.00343856i	−0.999999	+	0.00171928i	$0.999453\pi$
$318$		−	29.0194i		−	1.62732i
$319$	−19.9164			−1.11510
$320$	−0.966894	+	6.61461i	−0.0540510	+	0.369768i
$321$	8.33536			0.465235
$322$		−	4.94855i		−	0.275772i
$323$		0			0
$324$	7.96366			0.442425
$325$	−4.38002	+	14.6619i	−0.242960	+	0.813297i
$326$	−34.4720			−1.90923
$327$		−	8.40368i		−	0.464724i
$328$		−	11.0234i		−	0.608663i
$329$	−1.18372			−0.0652603
$330$	1.70548	−	11.6674i	0.0938838	−	0.642268i
$331$	−17.6067			−0.967752			−0.483876	−	0.875137i	$-0.660771\pi$
$331$	−17.6067			−0.967752			−0.483876	+	0.875137i	$0.660771\pi$
$332$		−	17.0041i		−	0.933224i
$333$		−	5.00540i		−	0.274294i
$334$	−5.14478			−0.281510
$335$	−19.5157	−	2.85271i	−1.06625	−	0.155860i
$336$	3.34378			0.182418
$337$			6.90874i			0.376343i	0.982136	+	0.188171i	$0.0602560\pi$
$337$			6.90874i			0.376343i	−0.982136	+	0.188171i	$0.939744\pi$
$338$			6.73129i			0.366134i
$339$	−20.3270			−1.10401
$340$	3.08340	+	0.450718i	0.167221	+	0.0244436i
$341$	−10.9680			−0.593948
$342$		0			0
$343$			6.57751i			0.355152i
$344$	6.53935			0.352578
$345$	2.63098	−	17.9988i	0.141647	−	0.969023i
$346$	−16.5251			−0.888396
$347$			7.32576i			0.393267i	0.980477	+	0.196634i	$0.0630010\pi$
$347$			7.32576i			0.393267i	−0.980477	+	0.196634i	$0.936999\pi$
$348$			21.1856i			1.13567i
$349$	2.16127			0.115690			0.0578452	−	0.998326i	$-0.481577\pi$
$349$	2.16127			0.115690			0.0578452	+	0.998326i	$0.481577\pi$
$350$	4.23857	+	1.26620i	0.226561	+	0.0676815i
$351$	17.2913			0.922939
$352$		−	13.3312i		−	0.710557i
$353$			16.6022i			0.883644i	0.897103	+	0.441822i	$0.145668\pi$
$353$			16.6022i			0.883644i	−0.897103	+	0.441822i	$0.854332\pi$
$354$	−19.7222			−1.04822
$355$	−4.26418	+	29.1716i	−0.226319	+	1.54827i
$356$	−3.07571			−0.163012
$357$		−	0.676219i		−	0.0357893i
$358$			28.2768i			1.49448i
$359$	−17.0830			−0.901608			−0.450804	−	0.892623i	$-0.648863\pi$
$359$	−17.0830			−0.901608			−0.450804	+	0.892623i	$0.648863\pi$
$360$	−2.06139	−	0.301325i	−0.108645	−	0.0158812i
$361$		0			0
$362$			15.8217i			0.831569i
$363$		−	10.4267i		−	0.547257i
$364$	−2.09242			−0.109673
$365$	10.9991	+	1.60779i	0.575717	+	0.0841558i
$366$	−23.6216			−1.23472
$367$			19.5631i			1.02119i	0.859822	+	0.510594i	$0.170574\pi$
$367$			19.5631i			1.02119i	−0.859822	+	0.510594i	$0.829426\pi$
$368$		−	26.9249i		−	1.40356i
$369$	−9.26125			−0.482122
$370$	−3.38953	+	23.1881i	−0.176213	+	1.20549i
$371$	−5.14433			−0.267080
$372$			11.6669i			0.604899i
$373$		−	6.59700i		−	0.341580i	−0.985307	−	0.170790i	$-0.945368\pi$
$373$		−	6.59700i		−	0.341580i	0.985307	−	0.170790i	$-0.0546320\pi$
$374$	−3.52966			−0.182515
$375$	14.7433	+	6.85893i	0.761339	+	0.354194i
$376$	−2.60997			−0.134599
$377$			31.1416i			1.60387i
$378$		−	4.99868i		−	0.257104i
$379$	21.6574			1.11246			0.556232	−	0.831027i	$-0.312247\pi$
$379$	21.6574			1.11246			0.556232	+	0.831027i	$0.312247\pi$
$380$		0			0
$381$	13.4287			0.687974
$382$		−	30.1886i		−	1.54458i
$383$		−	24.3214i		−	1.24277i	−0.783507	−	0.621383i	$-0.786571\pi$
$383$		−	24.3214i		−	1.24277i	0.783507	−	0.621383i	$-0.213429\pi$
$384$	11.7576			0.600005
$385$	−2.06830	−	0.302335i	−0.105411	−	0.0154084i
$386$	−30.5082			−1.55282
$387$		−	5.49403i		−	0.279277i
$388$		−	8.43943i		−	0.428447i
$389$	−15.8227			−0.802241			−0.401120	−	0.916025i	$-0.631379\pi$
$389$	−15.8227			−0.802241			−0.401120	+	0.916025i	$0.631379\pi$
$390$	−18.2433	−	2.66672i	−0.923785	−	0.135035i
$391$	−5.44507			−0.275369
$392$			7.13124i			0.360182i
$393$		−	20.2620i		−	1.02208i
$394$	18.5668			0.935381
$395$	0.228977	−	1.56645i	0.0115211	−	0.0788168i
$396$	−2.47892			−0.124571
$397$		−	35.4753i		−	1.78046i	−0.455515	−	0.890228i	$-0.650545\pi$
$397$		−	35.4753i		−	1.78046i	0.455515	−	0.890228i	$-0.349455\pi$
$398$			23.4598i			1.17593i
$399$		0			0
$400$	23.0619	+	6.88937i	1.15309	+	0.344468i
$401$	11.2107			0.559837			0.279919	−	0.960024i	$-0.409693\pi$
$401$	11.2107			0.559837			0.279919	+	0.960024i	$0.409693\pi$
$402$		−	23.7638i		−	1.18523i
$403$			17.1497i			0.854286i
$404$	−0.369636			−0.0183901
$405$	1.79921	−	12.3086i	0.0894035	−	0.611618i
$406$	9.00263			0.446793
$407$		−	11.0734i		−	0.548887i
$408$		−	1.49099i		−	0.0738150i
$409$	1.91450			0.0946660			0.0473330	−	0.998879i	$-0.484928\pi$
$409$	1.91450			0.0946660			0.0473330	+	0.998879i	$0.484928\pi$
$410$	42.9038	+	6.27149i	2.11887	+	0.309727i
$411$	−5.58977			−0.275723
$412$			20.5730i			1.01356i
$413$			3.49621i			0.172037i
$414$	−9.16688			−0.450528
$415$	−26.2815	−	3.84171i	−1.29011	−	0.188582i
$416$	−20.8449			−1.02201
$417$			27.4489i			1.34418i
$418$		0			0
$419$	22.1856			1.08384			0.541918	−	0.840431i	$-0.317698\pi$
$419$	22.1856			1.08384			0.541918	+	0.840431i	$0.317698\pi$
$420$	−0.321601	+	2.20010i	−0.0156925	+	0.107354i
$421$	−13.3793			−0.652069			−0.326034	−	0.945358i	$-0.605713\pi$
$421$	−13.3793			−0.652069			−0.326034	+	0.945358i	$0.605713\pi$
$422$		−	10.6257i		−	0.517253i
$423$			2.19276i			0.106616i
$424$	−11.3427			−0.550850
$425$	1.39325	−	4.66385i	0.0675826	−	0.226230i
$426$	−35.5216			−1.72103
$427$			4.18747i			0.202646i
$428$			8.20428i			0.396569i
$429$	8.71201			0.420620
$430$	−3.72042	+	25.4517i	−0.179415	+	1.22739i
$431$	37.1687			1.79035			0.895177	−	0.445711i	$-0.147049\pi$
$431$	37.1687			1.79035			0.895177	+	0.445711i	$0.147049\pi$
$432$		−	27.1976i		−	1.30855i
$433$		−	8.32630i		−	0.400137i	−0.979782	−	0.200068i	$-0.935884\pi$
$433$		−	8.32630i		−	0.400137i	0.979782	−	0.200068i	$-0.0641164\pi$
$434$	4.95774			0.237979
$435$	32.7443	+	4.78641i	1.56997	+	0.229491i
$436$	8.27152			0.396134
$437$		0			0
$438$			13.3933i			0.639957i
$439$	−17.0746			−0.814928			−0.407464	−	0.913221i	$-0.633587\pi$
$439$	−17.0746			−0.814928			−0.407464	+	0.913221i	$0.633587\pi$
$440$	−4.56039	−	0.666617i	−0.217408	−	0.0317797i
$441$	5.99131			0.285300
$442$			5.51904i			0.262514i
$443$			7.18135i			0.341196i	0.985341	+	0.170598i	$0.0545700\pi$
$443$			7.18135i			0.341196i	−0.985341	+	0.170598i	$0.945430\pi$
$444$	−11.7790			−0.559008
$445$	−0.694888	+	4.75379i	−0.0329409	+	0.225351i
$446$	−23.7998			−1.12695
$447$			34.7991i			1.64594i
$448$			1.42784i			0.0674589i
$449$	23.1024			1.09027			0.545134	−	0.838349i	$-0.316479\pi$
$449$	23.1024			1.09027			0.545134	+	0.838349i	$0.316479\pi$
$450$	2.34557	−	7.85168i	0.110571	−	0.370132i
$451$	−20.4886			−0.964768
$452$		−	20.0073i		−	0.941065i
$453$			8.58532i			0.403373i
$454$	28.8625			1.35458
$455$	−0.472737	+	3.23403i	−0.0221622	+	0.151614i
$456$		0			0
$457$			13.7430i			0.642872i	0.946931	+	0.321436i	$0.104166\pi$
$457$			13.7430i			0.642872i	−0.946931	+	0.321436i	$0.895834\pi$
$458$			7.00091i			0.327131i
$459$	−5.50023			−0.256729
$460$	17.7158	+	2.58961i	0.826001	+	0.120741i
$461$	−26.0522			−1.21337			−0.606686	−	0.794942i	$-0.707501\pi$
$461$	−26.0522			−1.21337			−0.606686	+	0.794942i	$0.707501\pi$
$462$		−	2.51853i		−	0.117173i
$463$			4.24698i			0.197374i	0.995119	+	0.0986869i	$0.0314642\pi$
$463$			4.24698i			0.197374i	−0.995119	+	0.0986869i	$0.968536\pi$
$464$	48.9830			2.27398
$465$	18.0322	+	2.63587i	0.836225	+	0.122236i
$466$	−20.5147			−0.950327
$467$		−	27.7571i		−	1.28444i	−0.766519	−	0.642222i	$-0.778013\pi$
$467$		−	27.7571i		−	1.28444i	0.766519	−	0.642222i	$-0.221987\pi$
$468$			3.87608i			0.179172i
$469$	−4.21267			−0.194523
$470$	1.48488	−	10.1582i	0.0684925	−	0.468563i
$471$	−15.3739			−0.708394
$472$			7.70877i			0.354825i
$473$		−	12.1544i		−	0.558858i
$474$	1.90744			0.0876114
$475$		0			0
$476$	0.665585			0.0305070
$477$			9.52956i			0.436328i
$478$			19.7277i			0.902325i
$479$	7.11883			0.325268			0.162634	−	0.986686i	$-0.448001\pi$
$479$	7.11883			0.325268			0.162634	+	0.986686i	$0.448001\pi$
$480$	−3.20383	+	21.9177i	−0.146234	+	1.00040i
$481$	−17.3145			−0.789474
$482$		−	9.28573i		−	0.422953i
$483$		−	3.88523i		−	0.176784i
$484$	10.2627			0.466486
$485$	−13.0439	−	1.90670i	−0.592294	−	0.0865789i
$486$	−16.4106			−0.744400
$487$		−	3.54621i		−	0.160694i	−0.996767	−	0.0803470i	$-0.974397\pi$
$487$		−	3.54621i		−	0.160694i	0.996767	−	0.0803470i	$-0.0256028\pi$
$488$			9.23291i			0.417954i
$489$	−27.0649			−1.22392
$490$	−27.7554	−	4.05716i	−1.25386	−	0.183284i
$491$	−32.1308			−1.45004			−0.725020	−	0.688727i	$-0.758170\pi$
$491$	−32.1308			−1.45004			−0.725020	+	0.688727i	$0.758170\pi$
$492$			21.7942i			0.982557i
$493$		−	9.90593i		−	0.446141i
$494$		0			0
$495$	−0.560057	+	3.83140i	−0.0251727	+	0.172209i
$496$	26.9749			1.21121
$497$			6.29701i			0.282459i
$498$		−	32.0024i		−	1.43406i
$499$	11.9147			0.533376			0.266688	−	0.963783i	$-0.414071\pi$
$499$	11.9147			0.533376			0.266688	+	0.963783i	$0.414071\pi$
$500$	−6.75107	+	14.5114i	−0.301917	+	0.648970i
$501$	−4.03930			−0.180463
$502$		−	48.4823i		−	2.16387i
$503$		−	0.239744i		−	0.0106896i	−0.999986	−	0.00534482i	$-0.998299\pi$
$503$		−	0.239744i		−	0.0106896i	0.999986	−	0.00534482i	$-0.00170132\pi$
$504$	−0.444973			−0.0198207
$505$	−0.0835111	+	0.571307i	−0.00371620	+	0.0254228i
$506$	−20.2798			−0.901546
$507$			5.28491i			0.234711i
$508$			13.2175i			0.586434i
$509$	−29.3663			−1.30164			−0.650819	−	0.759233i	$-0.725574\pi$
$509$	−29.3663			−1.30164			−0.650819	+	0.759233i	$0.725574\pi$
$510$	5.80306	+	0.848266i	0.256964	+	0.0375618i
$511$	2.37427			0.105031
$512$			22.6488i			1.00094i
$513$		0			0
$514$	−41.4991			−1.83045
$515$	31.7974	+	4.64801i	1.40116	+	0.204816i
$516$	−12.9289			−0.569163
$517$			4.85101i			0.213347i
$518$			5.00540i			0.219925i
$519$	−12.9743			−0.569509
$520$	−1.04233	+	7.13070i	−0.0457093	+	0.312702i
$521$	−12.1069			−0.530414			−0.265207	−	0.964191i	$-0.585440\pi$
$521$	−12.1069			−0.530414			−0.265207	+	0.964191i	$0.585440\pi$
$522$		−	16.6768i		−	0.729924i
$523$			6.43779i			0.281505i	0.990045	+	0.140752i	$0.0449522\pi$
$523$			6.43779i			0.281505i	−0.990045	+	0.140752i	$0.955048\pi$
$524$	19.9434			0.871231
$525$	3.32781	+	0.994130i	0.145237	+	0.0433874i
$526$	48.0407			2.09467
$527$		−	5.45519i		−	0.237632i
$528$		−	13.7032i		−	0.596356i
$529$	−8.28480			−0.360209
$530$	6.45318	−	44.1468i	0.280308	−	1.91761i
$531$	6.47651			0.281057
$532$		0			0
$533$			32.0362i			1.38764i
$534$	−5.78859			−0.250497
$535$	12.6805	+	1.85358i	0.548225	+	0.0801371i
$536$	−9.28848			−0.401201
$537$			22.2008i			0.958037i
$538$		−	17.1346i		−	0.738727i
$539$	13.2545			0.570911
$540$	17.8952	+	2.61584i	0.770087	+	0.112568i
$541$	−15.1179			−0.649969			−0.324985	−	0.945719i	$-0.605359\pi$
$541$	−15.1179			−0.649969			−0.324985	+	0.945719i	$0.605359\pi$
$542$		−	41.6220i		−	1.78782i
$543$			12.4220i			0.533079i
$544$	6.63063			0.284286
$545$	1.86877	−	12.7844i	0.0800492	−	0.547624i
$546$	−3.93801			−0.168531
$547$			36.1694i			1.54649i	0.634106	+	0.773246i	$0.281368\pi$
$547$			36.1694i			1.54649i	−0.634106	+	0.773246i	$0.718632\pi$
$548$		−	5.50186i		−	0.235028i
$549$	7.75702			0.331061
$550$	5.18906	−	17.3702i	0.221262	−	0.740667i
$551$		0			0
$552$		−	8.56652i		−	0.364615i
$553$		−	0.338136i		−	0.0143790i
$554$	−16.9794			−0.721386
$555$	−2.66121	+	18.2056i	−0.112962	+	0.772784i
$556$	−27.0172			−1.14579
$557$			37.0585i			1.57022i	0.619358	+	0.785109i	$0.287393\pi$
$557$			37.0585i			1.57022i	−0.619358	+	0.785109i	$0.712607\pi$
$558$		−	9.18391i		−	0.388786i
$559$	−19.0048			−0.803816
$560$	5.08685	+	0.743572i	0.214958	+	0.0314217i
$561$	−2.77123			−0.117001
$562$			35.8590i			1.51262i
$563$			12.9283i			0.544863i	0.962175	+	0.272432i	$0.0878279\pi$
$563$			12.9283i			0.544863i	−0.962175	+	0.272432i	$0.912172\pi$
$564$	5.16014			0.217281
$565$	−30.9232	−	4.52021i	−1.30095	−	0.190167i
$566$	16.1628			0.679372
$567$		−	2.65694i		−	0.111581i
$568$			13.8842i			0.582569i
$569$	18.5114			0.776038			0.388019	−	0.921651i	$-0.373159\pi$
$569$	18.5114			0.776038			0.388019	+	0.921651i	$0.373159\pi$
$570$		0			0
$571$	16.2207			0.678816			0.339408	−	0.940639i	$-0.389773\pi$
$571$	16.2207			0.678816			0.339408	+	0.940639i	$0.389773\pi$
$572$			8.57501i			0.358539i
$573$		−	23.7019i		−	0.990160i
$574$	9.26125			0.386557
$575$	8.00496	−	26.7963i	0.333830	−	1.11748i
$576$	2.64498			0.110207
$577$			17.7980i			0.740939i	0.928845	+	0.370470i	$0.120803\pi$
$577$			17.7980i			0.740939i	−0.928845	+	0.370470i	$0.879197\pi$
$578$			29.7359i			1.23685i
$579$	−23.9527			−0.995442
$580$	−4.71114	+	32.2293i	−0.195619	+	1.33825i
$581$	−5.67314			−0.235362
$582$		−	15.8833i		−	0.658384i
$583$			21.0821i			0.873132i
$584$	5.23500			0.216626
$585$	5.99085	+	0.875715i	0.247691	+	0.0362064i
$586$	31.0745			1.28368
$587$			35.8593i			1.48007i	0.672567	+	0.740036i	$0.265191\pi$
$587$			35.8593i			1.48007i	−0.672567	+	0.740036i	$0.734809\pi$
$588$		−	14.0991i		−	0.581438i
$589$		0			0
$590$	−30.0032	−	4.38573i	−1.23521	−	0.180558i
$591$	14.5773			0.599628
$592$			27.2342i			1.11932i
$593$		−	18.2848i		−	0.750868i	−0.926849	−	0.375434i	$-0.877494\pi$
$593$		−	18.2848i		−	0.750868i	0.926849	−	0.375434i	$-0.122506\pi$
$594$	−20.4852			−0.840518
$595$	0.150374	−	1.02872i	0.00616474	−	0.0421735i
$596$	−34.2519			−1.40301
$597$			18.4189i			0.753836i
$598$			31.7098i			1.29671i
$599$	−7.85141			−0.320800			−0.160400	−	0.987052i	$-0.551278\pi$
$599$	−7.85141			−0.320800			−0.160400	+	0.987052i	$0.551278\pi$
$600$	7.33746	+	2.19195i	0.299551	+	0.0894860i
$601$	−17.3527			−0.707833			−0.353917	−	0.935277i	$-0.615150\pi$
$601$	−17.3527			−0.707833			−0.353917	+	0.935277i	$0.615150\pi$
$602$			5.49403i			0.223920i
$603$			7.80370i			0.317791i
$604$	−8.45030			−0.343838
$605$	2.31863	−	15.8619i	0.0942656	−	0.644879i
$606$	−0.695668			−0.0282596
$607$		−	40.7364i		−	1.65344i	−0.562614	−	0.826720i	$-0.690204\pi$
$607$		−	40.7364i		−	1.65344i	0.562614	−	0.826720i	$-0.309796\pi$
$608$		0			0
$609$	7.06820			0.286418
$610$	−35.9353	−	5.25286i	−1.45498	−	0.212682i
$611$	7.58512			0.306861
$612$		−	1.23295i		−	0.0498392i
$613$			27.0535i			1.09268i	0.837564	+	0.546340i	$0.183979\pi$
$613$			27.0535i			1.09268i	−0.837564	+	0.546340i	$0.816021\pi$
$614$	−11.8721			−0.479121
$615$	33.6849	+	4.92391i	1.35831	+	0.198551i
$616$	−0.984409			−0.0396630
$617$		−	19.8932i		−	0.800871i	−0.916325	−	0.400436i	$-0.868859\pi$
$617$		−	19.8932i		−	0.800871i	0.916325	−	0.400436i	$-0.131141\pi$
$618$			38.7190i			1.55751i
$619$	−16.8447			−0.677044			−0.338522	−	0.940958i	$-0.609927\pi$
$619$	−16.8447			−0.677044			−0.338522	+	0.940958i	$0.609927\pi$
$620$	−2.59442	+	17.7487i	−0.104194	+	0.712804i
$621$	−31.6017			−1.26813
$622$			19.6818i			0.789167i
$623$			1.02616i			0.0411121i
$624$	−21.4266			−0.857749
$625$	20.9035	+	13.7129i	0.836139	+	0.548517i
$626$	−8.81123			−0.352168
$627$		0			0
$628$		−	15.1322i		−	0.603839i
$629$	5.50763			0.219603
$630$	0.253158	−	1.73187i	0.0100860	−	0.0689995i
$631$	27.2013			1.08287			0.541433	−	0.840744i	$-0.317882\pi$
$631$	27.2013			1.08287			0.541433	+	0.840744i	$0.317882\pi$
$632$		−	0.745553i		−	0.0296565i
$633$		−	8.34254i		−	0.331586i
$634$	−0.113410			−0.00450407
$635$	20.4289	+	2.98621i	0.810698	+	0.118504i
$636$	22.4255			0.889231
$637$		−	20.7249i		−	0.821152i
$638$		−	36.8939i		−	1.46064i
$639$	11.6648			0.461453
$640$	17.8867	+	2.61460i	0.707036	+	0.103351i
$641$	17.6090			0.695514			0.347757	−	0.937585i	$-0.386943\pi$
$641$	17.6090			0.695514			0.347757	+	0.937585i	$0.386943\pi$
$642$			15.4407i			0.609398i
$643$		−	8.95765i		−	0.353255i	−0.984278	−	0.176628i	$-0.943481\pi$
$643$		−	8.95765i		−	0.353255i	0.984278	−	0.176628i	$-0.0565188\pi$
$644$	3.82414			0.150692
$645$	−2.92100	+	19.9828i	−0.115014	+	0.786822i
$646$		0			0
$647$		−	49.1850i		−	1.93366i	−0.255416	−	0.966831i	$-0.582212\pi$
$647$		−	49.1850i		−	1.93366i	0.255416	−	0.966831i	$-0.417788\pi$
$648$		−	5.85826i		−	0.230134i
$649$	14.3279			0.562419
$650$	−27.1603	−	8.11371i	−1.06531	−	0.318246i
$651$	3.89245			0.152557
$652$		−	26.6393i		−	1.04327i
$653$			11.7035i			0.457993i	0.973427	+	0.228997i	$0.0735445\pi$
$653$			11.7035i			0.457993i	−0.973427	+	0.228997i	$0.926456\pi$
$654$	15.5673			0.608729
$655$	4.50576	−	30.8243i	0.176055	−	1.20441i
$656$	50.3901			1.96740
$657$		−	4.39818i		−	0.171589i
$658$		−	2.19276i		−	0.0854826i
$659$	34.7573			1.35395			0.676976	−	0.736005i	$-0.263290\pi$
$659$	34.7573			1.35395			0.676976	+	0.736005i	$0.263290\pi$
$660$	9.01630	+	1.31796i	0.350959	+	0.0513016i
$661$	17.9064			0.696477			0.348239	−	0.937406i	$-0.386780\pi$
$661$	17.9064			0.696477			0.348239	+	0.937406i	$0.386780\pi$
$662$		−	32.6153i		−	1.26763i
$663$			4.33314i			0.168285i
$664$	−12.5087			−0.485431
$665$		0			0
$666$	9.27219			0.359290
$667$		−	56.9148i		−	2.20375i
$668$		−	3.97578i		−	0.153828i
$669$	−18.6858			−0.722435
$670$	5.28447	−	36.1516i	0.204157	−	1.39666i
$671$	17.1607			0.662483
$672$			4.73117i			0.182509i
$673$			10.9828i			0.423355i	0.977340	+	0.211677i	$0.0678926\pi$
$673$			10.9828i			0.423355i	−0.977340	+	0.211677i	$0.932107\pi$
$674$	−12.7980			−0.492961
$675$	8.08605	−	27.0677i	0.311232	−	1.04184i
$676$	−5.20180			−0.200069
$677$		−	4.77520i		−	0.183526i	−0.995781	−	0.0917630i	$-0.970750\pi$
$677$		−	4.77520i		−	0.183526i	0.995781	−	0.0917630i	$-0.0292502\pi$
$678$		−	37.6544i		−	1.44611i
$679$	−2.81567			−0.108056
$680$	0.331559	−	2.26822i	0.0127147	−	0.0869824i
$681$	22.6607			0.868359
$682$		−	20.3175i		−	0.777995i
$683$		−	46.0853i		−	1.76341i	−0.471805	−	0.881703i	$-0.656397\pi$
$683$		−	46.0853i		−	1.76341i	0.471805	−	0.881703i	$-0.343603\pi$
$684$		0			0
$685$	−8.50364	−	1.24302i	−0.324907	−	0.0474935i
$686$	−12.1844			−0.465203
$687$			5.49660i			0.209708i
$688$			29.8928i			1.13965i
$689$	32.9643			1.25584
$690$	33.3417	+	4.87373i	1.26930	+	0.185540i
$691$	15.2699			0.580893			0.290447	−	0.956891i	$-0.406196\pi$
$691$	15.2699			0.580893			0.290447	+	0.956891i	$0.406196\pi$
$692$		−	12.7703i		−	0.485453i
$693$			0.827050i			0.0314170i
$694$	−13.5705			−0.515130
$695$	−6.10394	+	41.7576i	−0.231536	+	1.58396i
$696$	15.5846			0.590733
$697$		−	10.1905i		−	0.385993i
$698$			4.00362i			0.151539i
$699$	−16.1067			−0.609210
$700$	−0.978496	+	3.27548i	−0.0369837	+	0.123801i
$701$	−16.6852			−0.630191			−0.315096	−	0.949060i	$-0.602037\pi$
$701$	−16.6852			−0.630191			−0.315096	+	0.949060i	$0.602037\pi$
$702$			32.0310i			1.20893i
$703$		0			0
$704$	5.85144			0.220535
$705$	1.16582	−	7.97547i	0.0439073	−	0.300374i
$706$	−30.7545			−1.15746
$707$			0.123323i			0.00463803i
$708$		−	15.2409i		−	0.572789i
$709$	−1.95870			−0.0735604			−0.0367802	−	0.999323i	$-0.511710\pi$
$709$	−1.95870			−0.0735604			−0.0367802	+	0.999323i	$0.511710\pi$
$710$	−54.0386	−	7.89912i	−2.02803	−	0.296449i
$711$	−0.626375			−0.0234909
$712$			2.26257i			0.0847933i
$713$		−	31.3429i		−	1.17380i
$714$	1.25265			0.0468794
$715$	13.2535	+	1.93733i	0.495652	+	0.0724522i
$716$	−21.8517			−0.816637
$717$			15.4887i			0.578438i
$718$		−	31.6452i		−	1.18099i
$719$	23.0165			0.858370			0.429185	−	0.903217i	$-0.358801\pi$
$719$	23.0165			0.858370			0.429185	+	0.903217i	$0.358801\pi$
$720$	1.37742	−	9.42306i	0.0513334	−	0.351177i
$721$	6.86382			0.255622
$722$		0			0
$723$		−	7.29046i		−	0.271135i
$724$	−12.2267			−0.454400
$725$	48.7490	+	14.5630i	1.81049	+	0.540856i
$726$	19.3147			0.716837
$727$		−	10.3883i		−	0.385279i	−0.981270	−	0.192640i	$-0.938295\pi$
$727$		−	10.3883i		−	0.385279i	0.981270	−	0.192640i	$-0.0617048\pi$
$728$			1.53924i			0.0570479i
$729$	−29.5736			−1.09532
$730$	−2.97834	+	20.3751i	−0.110233	+	0.754116i
$731$	6.04528			0.223593
$732$		−	18.2543i		−	0.674698i
$733$		−	40.7900i		−	1.50661i	−0.657670	−	0.753306i	$-0.728458\pi$
$733$		−	40.7900i		−	1.50661i	0.657670	−	0.753306i	$-0.271542\pi$
$734$	−36.2395			−1.33762
$735$	−21.7915	−	3.18538i	−0.803791	−	0.117495i
$736$	38.0965			1.40425
$737$			17.2640i			0.635929i
$738$		−	17.1559i		−	0.631517i
$739$	7.92965			0.291697			0.145848	−	0.989307i	$-0.453409\pi$
$739$	7.92965			0.291697			0.145848	+	0.989307i	$0.453409\pi$
$740$	−17.9193	−	2.61936i	−0.658726	−	0.0962896i
$741$		0			0
$742$		−	9.52956i		−	0.349841i
$743$		−	7.27911i		−	0.267045i	−0.991046	−	0.133522i	$-0.957371\pi$
$743$		−	7.27911i		−	0.267045i	0.991046	−	0.133522i	$-0.0426288\pi$
$744$	8.58244			0.314648
$745$	−7.73845	+	52.9395i	−0.283515	+	1.93955i
$746$	12.2205			0.447426
$747$			10.5091i			0.384509i
$748$		−	2.72765i		−	0.0997327i
$749$	2.73722			0.100016
$750$	−12.7057	+	27.3110i	−0.463948	+	0.997255i
$751$	37.8815			1.38232			0.691158	−	0.722704i	$-0.257101\pi$
$751$	37.8815			1.38232			0.691158	+	0.722704i	$0.257101\pi$
$752$		−	11.9307i		−	0.435068i
$753$		−	38.0647i		−	1.38715i
$754$	−57.6879			−2.10087
$755$	−1.90916	+	13.0607i	−0.0694814	+	0.475329i
$756$	3.86287			0.140491
$757$			51.1527i			1.85917i	0.368602	+	0.929587i	$0.379837\pi$
$757$			51.1527i			1.85917i	−0.368602	+	0.929587i	$0.620163\pi$
$758$			40.1189i			1.45718i
$759$	−15.9222			−0.577938
$760$		0			0
$761$	−10.8749			−0.394213			−0.197107	−	0.980382i	$-0.563155\pi$
$761$	−10.8749			−0.394213			−0.197107	+	0.980382i	$0.563155\pi$
$762$			24.8759i			0.901158i
$763$		−	2.75965i		−	0.0999061i
$764$	23.3291			0.844019
$765$	−1.90565	−	0.278559i	−0.0688988	−	0.0100713i
$766$	45.0539			1.62786
$767$		−	22.4033i		−	0.808938i
$768$			30.4764i			1.09972i
$769$	18.8020			0.678016			0.339008	−	0.940783i	$-0.389909\pi$
$769$	18.8020			0.678016			0.339008	+	0.940783i	$0.389909\pi$
$770$	0.560057	−	3.83140i	0.0201831	−	0.138074i
$771$	−32.5820			−1.17341
$772$		−	23.5761i		−	0.848521i
$773$		−	24.3856i		−	0.877090i	−0.898709	−	0.438545i	$-0.855494\pi$
$773$		−	24.3856i		−	0.877090i	0.898709	−	0.438545i	$-0.144506\pi$
$774$	10.1773			0.365817
$775$	26.8461	+	8.01984i	0.964339	+	0.288081i
$776$	−6.20825			−0.222863
$777$			3.92987i			0.140983i
$778$		−	29.3105i		−	1.05083i
$779$		0			0
$780$	2.06079	−	14.0980i	0.0737880	−	0.504791i
$781$	25.8059			0.923408
$782$		−	10.0867i		−	0.360698i
$783$		−	57.4913i		−	2.05457i
$784$	−32.5985			−1.16423
$785$	−23.3882	−	3.41878i	−0.834760	−	0.122021i
$786$	37.5341			1.33880
$787$		−	9.17617i		−	0.327095i	−0.986535	−	0.163547i	$-0.947706\pi$
$787$		−	9.17617i		−	0.327095i	0.986535	−	0.163547i	$-0.0522937\pi$
$788$			14.3480i			0.511127i
$789$	37.7180			1.34280
$790$	2.90176	+	0.424166i	0.103240	+	0.0150911i
$791$	−6.67510			−0.237339
$792$			1.82356i			0.0647972i
$793$		−	26.8328i		−	0.952862i
$794$	65.7158			2.33217
$795$	5.06656	−	34.6608i	0.179692	−	1.22929i
$796$	−18.1293			−0.642574
$797$			46.8095i			1.65808i	0.559191	+	0.829039i	$0.311112\pi$
$797$			46.8095i			1.65808i	−0.559191	+	0.829039i	$0.688888\pi$
$798$		0			0
$799$	−2.41277			−0.0853578
$800$	−9.74789	+	32.6306i	−0.344640	+	1.15367i
$801$	1.90089			0.0671647
$802$			20.7672i			0.733314i
$803$		−	9.73004i		−	0.343366i
$804$	18.3642			0.647654
$805$	0.863979	−	5.91056i	0.0304512	−	0.208320i
$806$	−31.7687			−1.11900
$807$		−	13.4529i		−	0.473563i
$808$			0.271913i			0.00956588i
$809$	−11.7440			−0.412898			−0.206449	−	0.978457i	$-0.566191\pi$
$809$	−11.7440			−0.412898			−0.206449	+	0.978457i	$0.566191\pi$
$810$	22.8009	+	3.33293i	0.801141	+	0.117107i
$811$	−41.3856			−1.45324			−0.726622	−	0.687038i	$-0.758911\pi$
$811$	−41.3856			−1.45324			−0.726622	+	0.687038i	$0.758911\pi$
$812$			6.95704i			0.244144i
$813$		−	32.6785i		−	1.14609i
$814$	20.5127			0.718971
$815$	−41.1734	−	6.01855i	−1.44224	−	0.210821i
$816$	6.81564			0.238595
$817$		0			0
$818$			3.54650i			0.124000i
$819$	1.29319			0.0451877
$820$	−4.84648	+	33.1552i	−0.169246	+	1.15783i
$821$	−15.6567			−0.546424			−0.273212	−	0.961954i	$-0.588086\pi$
$821$	−15.6567			−0.546424			−0.273212	+	0.961954i	$0.588086\pi$
$822$		−	10.3547i		−	0.361161i
$823$		−	42.0847i		−	1.46698i	−0.679700	−	0.733490i	$-0.737890\pi$
$823$		−	42.0847i		−	1.46698i	0.679700	−	0.733490i	$-0.262110\pi$
$824$	15.1340			0.527217
$825$	4.07407	−	13.6378i	0.141841	−	0.474806i
$826$	−6.47651			−0.225347
$827$			23.0974i			0.803175i	0.915821	+	0.401588i	$0.131541\pi$
$827$			23.0974i			0.803175i	−0.915821	+	0.401588i	$0.868459\pi$
$828$		−	7.08397i		−	0.246185i
$829$	44.6607			1.55113			0.775566	−	0.631267i	$-0.217465\pi$
$829$	44.6607			1.55113			0.775566	+	0.631267i	$0.217465\pi$
$830$	7.11653	−	48.6848i	0.247018	−	1.68988i
$831$	−13.3310			−0.462446
$832$		−	9.14941i		−	0.317199i
$833$			6.59245i			0.228415i
$834$	−50.8473			−1.76070
$835$	−6.14494	−	0.898240i	−0.212654	−	0.0310849i
$836$		0			0
$837$		−	31.6604i		−	1.09434i
$838$			41.0974i			1.41969i
$839$	27.2641			0.941260			0.470630	−	0.882331i	$-0.344027\pi$
$839$	27.2641			0.941260			0.470630	+	0.882331i	$0.344027\pi$
$840$	1.61845	+	0.236578i	0.0558419	+	0.00816271i
$841$	74.5420			2.57041
$842$		−	24.7844i		−	0.854126i
$843$			28.1538i			0.969669i
$844$	8.21135			0.282646
$845$	−1.17523	+	8.03986i	−0.0404292	+	0.276580i
$846$	−4.06195			−0.139653
$847$		−	3.42397i		−	0.117649i
$848$		−	51.8499i		−	1.78053i
$849$	12.6898			0.435513
$850$	8.63949	+	2.58091i	0.296332	+	0.0885245i
$851$	31.6442			1.08475
$852$		−	27.4504i		−	0.940434i
$853$			6.64990i			0.227688i	0.993499	+	0.113844i	$0.0363165\pi$
$853$			6.64990i			0.227688i	−0.993499	+	0.113844i	$0.963684\pi$
$854$	−7.75702			−0.265440
$855$		0			0
$856$	6.03527			0.206281
$857$			47.5875i			1.62556i	0.582571	+	0.812780i	$0.302047\pi$
$857$			47.5875i			1.62556i	−0.582571	+	0.812780i	$0.697953\pi$
$858$			16.1385i			0.550958i
$859$	−47.5779			−1.62334			−0.811669	−	0.584118i	$-0.801441\pi$
$859$	−47.5779			−1.62334			−0.811669	+	0.584118i	$0.801441\pi$
$860$	−19.6686	−	2.87506i	−0.670692	−	0.0980388i
$861$	7.27125			0.247804
$862$			68.8527i			2.34513i
$863$		−	0.387407i		−	0.0131875i	−0.999978	−	0.00659374i	$-0.997901\pi$
$863$		−	0.387407i		−	0.0131875i	0.999978	−	0.00659374i	$-0.00209887\pi$
$864$	38.4823			1.30920
$865$	−19.7376	−	2.88516i	−0.671100	−	0.0980984i
$866$	15.4240			0.524127
$867$			23.3464i			0.792885i
$868$			3.83124i			0.130041i
$869$	−1.38572			−0.0470074
$870$	−8.86652	+	60.6567i	−0.300603	+	2.05645i
$871$	26.9943			0.914667
$872$		−	6.08473i		−	0.206055i
$873$			5.21585i			0.176530i
$874$		0			0
$875$	4.84148	+	2.25238i	0.163672	+	0.0761443i
$876$	−10.3501			−0.349697
$877$			39.0509i			1.31865i	0.751856	+	0.659327i	$0.229159\pi$
$877$			39.0509i			1.31865i	−0.751856	+	0.659327i	$0.770841\pi$
$878$		−	31.6297i		−	1.06745i
$879$	24.3974			0.822904
$880$	3.04725	−	20.8465i	0.102723	−	0.702736i
$881$	22.9067			0.771747			0.385873	−	0.922552i	$-0.373900\pi$
$881$	22.9067			0.771747			0.385873	+	0.922552i	$0.373900\pi$
$882$			11.0985i			0.373707i
$883$			28.5966i			0.962353i	0.876624	+	0.481176i	$0.159790\pi$
$883$			28.5966i			0.962353i	−0.876624	+	0.481176i	$0.840210\pi$
$884$	−4.26500			−0.143447
$885$	−23.5563	−	3.44335i	−0.791835	−	0.115747i
$886$	−13.3030			−0.446923
$887$		−	8.79919i		−	0.295448i	−0.989029	−	0.147724i	$-0.952805\pi$
$887$		−	8.79919i		−	0.295448i	0.989029	−	0.147724i	$-0.0471947\pi$
$888$			8.66494i			0.290776i
$889$	4.40981			0.147900
$890$	−8.80610	−	1.28724i	−0.295181	−	0.0431483i
$891$	−10.8885			−0.364777
$892$		−	18.3919i		−	0.615808i
$893$		0			0
$894$	−64.4632			−2.15597
$895$	−4.93691	+	33.7739i	−0.165023	+	1.12894i
$896$	3.86105			0.128989
$897$			24.8962i			0.831259i
$898$			42.7957i			1.42811i
$899$	57.0205			1.90174
$900$	6.06761	+	1.81260i	0.202254	+	0.0604201i
$901$	−10.4857			−0.349330
$902$		−	37.9538i		−	1.26372i
$903$			4.31350i			0.143544i
$904$	−14.7179			−0.489509
$905$	−2.76234	+	18.8974i	−0.0918234	+	0.628172i
$906$	−15.9038			−0.528367
$907$		−	23.7448i		−	0.788432i	−0.919018	−	0.394216i	$-0.871016\pi$
$907$		−	23.7448i		−	0.788432i	0.919018	−	0.394216i	$-0.128984\pi$
$908$			22.3043i			0.740194i
$909$	0.228448			0.00757713
$910$	−5.99085	−	0.875715i	−0.198595	−	0.0290297i
$911$	8.14760			0.269942			0.134971	−	0.990850i	$-0.456906\pi$
$911$	8.14760			0.269942			0.134971	+	0.990850i	$0.456906\pi$
$912$		0			0
$913$			23.2492i			0.769438i
$914$	−25.4581			−0.842080
$915$	−28.2137	−	4.12416i	−0.932717	−	0.136340i
$916$	−5.41016			−0.178757
$917$		−	6.65377i		−	0.219727i
$918$		−	10.1888i		−	0.336281i
$919$	4.38700			0.144714			0.0723569	−	0.997379i	$-0.476948\pi$
$919$	4.38700			0.144714			0.0723569	+	0.997379i	$0.476948\pi$
$920$	1.90498	−	13.0321i	0.0628053	−	0.429657i
$921$	−9.32113			−0.307142
$922$		−	48.2601i		−	1.58936i
$923$		−	40.3506i		−	1.32816i
$924$	1.94627			0.0640274
$925$	−8.09693	+	27.1041i	−0.266225	+	0.891178i
$926$	−7.86726			−0.258534
$927$		−	12.7148i		−	0.417609i
$928$			69.3068i			2.27511i
$929$	0.394075			0.0129292			0.00646459	−	0.999979i	$-0.497942\pi$
$929$	0.394075			0.0129292			0.00646459	+	0.999979i	$0.497942\pi$
$930$	−4.88279	+	33.4036i	−0.160113	+	1.09535i
$931$		0			0
$932$		−	15.8534i		−	0.519294i
$933$			15.4527i			0.505898i
$934$	51.4182			1.68246
$935$	−4.21584	−	0.616252i	−0.137873	−	0.0201536i
$936$	2.85134			0.0931990
$937$		−	28.6351i		−	0.935468i	−0.883869	−	0.467734i	$-0.845070\pi$
$937$		−	28.6351i		−	0.935468i	0.883869	−	0.467734i	$-0.154930\pi$
$938$		−	7.80370i		−	0.254800i
$939$	−6.91792			−0.225758
$940$	7.85005	+	1.14749i	0.256040	+	0.0374268i
$941$	26.6636			0.869208			0.434604	−	0.900622i	$-0.356888\pi$
$941$	26.6636			0.869208			0.434604	+	0.900622i	$0.356888\pi$
$942$		−	28.4793i		−	0.927904i
$943$		−	58.5498i		−	1.90664i
$944$	−35.2384			−1.14691
$945$	0.872730	−	5.97043i	0.0283899	−	0.194218i
$946$	22.5152			0.732032
$947$		−	18.0730i		−	0.587295i	−0.955914	−	0.293648i	$-0.905131\pi$
$947$		−	18.0730i		−	0.587295i	0.955914	−	0.293648i	$-0.0948692\pi$
$948$			1.47403i			0.0478741i
$949$	−15.2140			−0.493869
$950$		0			0
$951$	−0.0890408			−0.00288735
$952$		−	0.489621i		−	0.0158687i
$953$		−	23.2504i		−	0.753155i	−0.926385	−	0.376577i	$-0.877101\pi$
$953$		−	23.2504i		−	0.753155i	0.926385	−	0.376577i	$-0.122899\pi$
$954$	−17.6529			−0.571534
$955$	5.27070	−	36.0574i	0.170556	−	1.16679i
$956$	−15.2452			−0.493064
$957$		−	28.9663i		−	0.936349i
$958$			13.1872i			0.426059i
$959$	−1.83560			−0.0592747
$960$	−9.62027	−	1.40625i	−0.310493	−	0.0453864i
$961$	0.401173			0.0129411
$962$		−	32.0741i		−	1.03411i
$963$		−	5.07053i		−	0.163395i
$964$	7.17581			0.231117
$965$	−36.4390	−	5.32649i	−1.17301	−	0.171466i
$966$	7.19715			0.231565
$967$		−	38.9509i		−	1.25258i	−0.779591	−	0.626289i	$-0.784573\pi$
$967$		−	38.9509i		−	1.25258i	0.779591	−	0.626289i	$-0.215427\pi$
$968$		−	7.54948i		−	0.242650i
$969$		0			0
$970$	3.53205	−	24.1631i	0.113407	−	0.775829i
$971$	−11.0320			−0.354034			−0.177017	−	0.984208i	$-0.556645\pi$
$971$	−11.0320			−0.354034			−0.177017	+	0.984208i	$0.556645\pi$
$972$		−	12.6818i		−	0.406768i
$973$			9.01384i			0.288970i
$974$	6.56913			0.210488
$975$	−21.3242	−	6.37028i	−0.682922	−	0.204012i
$976$	−42.2056			−1.35097
$977$			26.3934i			0.844401i	0.906502	+	0.422201i	$0.138742\pi$
$977$			26.3934i			0.844401i	−0.906502	+	0.422201i	$0.861258\pi$
$978$		−	50.1360i		−	1.60317i
$979$	4.20532			0.134403
$980$	3.13529	−	21.4488i	0.100153	−	0.685157i
$981$	−5.11208			−0.163216
$982$		−	59.5202i		−	1.89937i
$983$			47.2339i			1.50653i	0.657719	+	0.753264i	$0.271522\pi$
$983$			47.2339i			1.50653i	−0.657719	+	0.753264i	$0.728478\pi$
$984$	16.0323			0.511092
$985$	22.1762	+	3.24162i	0.706593	+	0.103287i
$986$	18.3501			0.584387
$987$		−	1.72159i		−	0.0547989i
$988$		0			0
$989$	34.7333			1.10446
$990$	−7.09744	−	1.03747i	−0.225571	−	0.0329730i
$991$	45.6843			1.45121			0.725604	−	0.688112i	$-0.241560\pi$
$991$	45.6843			1.45121			0.725604	+	0.688112i	$0.241560\pi$
$992$			38.1672i			1.21181i
$993$		−	25.6071i		−	0.812618i
$994$	−11.6648			−0.369986
$995$	−4.09590	+	28.0205i	−0.129849	+	0.888308i
$996$	24.7308			0.783625
$997$			28.9871i			0.918031i	0.888428	+	0.459016i	$0.151798\pi$
$997$			28.9871i			0.918031i	−0.888428	+	0.459016i	$0.848202\pi$
$998$			22.0713i			0.698654i
$999$	31.9648			1.01132

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.j.1084.13	yes	16
5.2	odd	4		9025.2.a.ck.1.4		16
5.3	odd	4		9025.2.a.ck.1.13		16
5.4	even	2	inner	1805.2.b.j.1084.4	yes	16
19.18	odd	2		1805.2.b.i.1084.4	✓	16
95.18	even	4		9025.2.a.cl.1.4		16
95.37	even	4		9025.2.a.cl.1.13		16
95.94	odd	2		1805.2.b.i.1084.13	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.b.i.1084.4	✓	16	19.18	odd	2
1805.2.b.i.1084.13	yes	16	95.94	odd	2
1805.2.b.j.1084.4	yes	16	5.4	even	2	inner
1805.2.b.j.1084.13	yes	16	1.1	even	1	trivial
9025.2.a.ck.1.4		16	5.2	odd	4
9025.2.a.ck.1.13		16	5.3	odd	4
9025.2.a.cl.1.4		16	95.18	even	4
9025.2.a.cl.1.13		16	95.37	even	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.85244i q^{2} +1.45440i q^{3} -1.43152 q^{4} +(-0.323421 + 2.21255i) q^{5} -2.69418 q^{6} +0.477604i q^{7} +1.05306i q^{8} +0.884731 q^{9} +O(q^{10})\)	\(q+1.85244i q^{2} +1.45440i q^{3} -1.43152 q^{4} +(-0.323421 + 2.21255i) q^{5} -2.69418 q^{6} +0.477604i q^{7} +1.05306i q^{8} +0.884731 q^{9} +(-4.09862 - 0.599118i) q^{10} +1.95728 q^{11} -2.08200i q^{12} -3.06043i q^{13} -0.884731 q^{14} +(-3.21793 - 0.470383i) q^{15} -4.81379 q^{16} +0.973502i q^{17} +1.63891i q^{18} +(0.462986 - 3.16733i) q^{20} -0.694625 q^{21} +3.62574i q^{22} +5.59328i q^{23} -1.53157 q^{24} +(-4.79080 - 1.43117i) q^{25} +5.66926 q^{26} +5.64994i q^{27} -0.683702i q^{28} -10.1756 q^{29} +(0.871355 - 5.96102i) q^{30} -5.60367 q^{31} -6.81111i q^{32} +2.84666i q^{33} -1.80335 q^{34} +(-1.05672 - 0.154467i) q^{35} -1.26651 q^{36} -5.65754i q^{37} +4.45108 q^{39} +(-2.32996 - 0.340584i) q^{40} -10.4679 q^{41} -1.28675i q^{42} -6.20983i q^{43} -2.80189 q^{44} +(-0.286141 + 1.95752i) q^{45} -10.3612 q^{46} +2.47845i q^{47} -7.00115i q^{48} +6.77189 q^{49} +(2.65116 - 8.87465i) q^{50} -1.41586 q^{51} +4.38109i q^{52} +10.7711i q^{53} -10.4662 q^{54} +(-0.633026 + 4.33059i) q^{55} -0.502948 q^{56} -18.8496i q^{58} +7.32031 q^{59} +(4.60655 + 0.673365i) q^{60} +8.76766 q^{61} -10.3805i q^{62} +0.422551i q^{63} +2.98958 q^{64} +(6.77138 + 0.989809i) q^{65} -5.27326 q^{66} +8.82042i q^{67} -1.39359i q^{68} -8.13485 q^{69} +(0.286141 - 1.95752i) q^{70} +13.1846 q^{71} +0.931679i q^{72} -4.97121i q^{73} +10.4802 q^{74} +(2.08150 - 6.96772i) q^{75} +0.934804i q^{77} +8.24535i q^{78} -0.707984 q^{79} +(1.55688 - 10.6508i) q^{80} -5.56306 q^{81} -19.3911i q^{82} +11.8783i q^{83} +0.994373 q^{84} +(-2.15393 - 0.314851i) q^{85} +11.5033 q^{86} -14.7993i q^{87} +2.06114i q^{88} +2.14855 q^{89} +(-3.62618 - 0.530058i) q^{90} +1.46167 q^{91} -8.00692i q^{92} -8.14996i q^{93} -4.59117 q^{94} +9.90605 q^{96} +5.89541i q^{97} +12.5445i q^{98} +1.73167 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9}+O(q^{10}) \) 16 * q - 12 * q^4 + 4 * q^5 - 10 * q^6 - 6 * q^9	\( 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9} + 16 q^{10} - 22 q^{11} + 6 q^{14} - 10 q^{15} + 8 q^{16} - 14 q^{20} + 20 q^{21} + 14 q^{24} + 4 q^{25} - 16 q^{26} + 2 q^{29} - 12 q^{30} - 16 q^{31} - 8 q^{34} - 10 q^{35} + 18 q^{36} + 36 q^{39} - 38 q^{40} - 26 q^{41} + 64 q^{44} - 2 q^{45} - 2 q^{46} + 20 q^{49} + 48 q^{50} + 38 q^{51} + 12 q^{54} - 10 q^{55} - 6 q^{56} + 10 q^{59} + 10 q^{60} - 30 q^{61} + 16 q^{64} + 36 q^{65} + 4 q^{66} + 68 q^{69} + 2 q^{70} + 20 q^{71} + 40 q^{74} + 32 q^{75} + 12 q^{79} + 40 q^{80} - 48 q^{81} - 2 q^{84} - 2 q^{85} + 20 q^{86} - 30 q^{90} + 86 q^{91} - 38 q^{94} + 22 q^{96} + 32 q^{99}+O(q^{100}) \) 16 * q - 12 * q^4 + 4 * q^5 - 10 * q^6 - 6 * q^9 + 16 * q^10 - 22 * q^11 + 6 * q^14 - 10 * q^15 + 8 * q^16 - 14 * q^20 + 20 * q^21 + 14 * q^24 + 4 * q^25 - 16 * q^26 + 2 * q^29 - 12 * q^30 - 16 * q^31 - 8 * q^34 - 10 * q^35 + 18 * q^36 + 36 * q^39 - 38 * q^40 - 26 * q^41 + 64 * q^44 - 2 * q^45 - 2 * q^46 + 20 * q^49 + 48 * q^50 + 38 * q^51 + 12 * q^54 - 10 * q^55 - 6 * q^56 + 10 * q^59 + 10 * q^60 - 30 * q^61 + 16 * q^64 + 36 * q^65 + 4 * q^66 + 68 * q^69 + 2 * q^70 + 20 * q^71 + 40 * q^74 + 32 * q^75 + 12 * q^79 + 40 * q^80 - 48 * q^81 - 2 * q^84 - 2 * q^85 + 20 * q^86 - 30 * q^90 + 86 * q^91 - 38 * q^94 + 22 * q^96 + 32 * q^99

Introduction

L-functions

Modular forms

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Database

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