LMFDB - Embedded newform 225.2.e.c.76.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(76,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("225.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.e (of order $3$, degree $2$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1223810289.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 8x^{6} - 2x^{5} + 23x^{4} - 8x^{3} + 37x^{2} + 15x + 9 $ x^8 - 2x^7 + 8x^6 - 2x^5 + 23x^4 - 8x^3 + 37x^2 + 15*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			76.3
Root			$-0.236627 - 0.409850i$ of defining polynomial
Character	$\chi$	$=$	225.76
Dual form			225.2.e.c.151.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.236627 + 0.409850i) q^{2} +(-0.544899 + 1.64411i) q^{3} +(0.888015 - 1.53809i) q^{4} +(-0.802776 + 0.165713i) q^{6} +(1.28153 + 2.21967i) q^{7} +1.78702 q^{8} +(-2.40617 - 1.79175i) q^{9} +O(q^{10})$	\(q+(0.236627 + 0.409850i) q^{2} +(-0.544899 + 1.64411i) q^{3} +(0.888015 - 1.53809i) q^{4} +(-0.802776 + 0.165713i) q^{6} +(1.28153 + 2.21967i) q^{7} +1.78702 q^{8} +(-2.40617 - 1.79175i) q^{9} +(3.08430 + 5.34217i) q^{11} +(2.04490 + 2.29809i) q^{12} +(1.06615 - 1.84662i) q^{13} +(-0.606488 + 1.05047i) q^{14} +(-1.35317 - 2.34376i) q^{16} -3.16860 q^{17} +(0.164982 - 1.41015i) q^{18} +0.356267 q^{19} +(-4.34768 + 0.897469i) q^{21} +(-1.45966 + 2.52821i) q^{22} +(-2.10649 + 3.64854i) q^{23} +(-0.973748 + 2.93806i) q^{24} +1.00912 q^{26} +(4.25694 - 2.97968i) q^{27} +4.55206 q^{28} +(-0.843116 - 1.46032i) q^{29} +(4.12920 - 7.15199i) q^{31} +(2.42742 - 4.20441i) q^{32} +(-10.4637 + 2.15998i) q^{33} +(-0.749778 - 1.29865i) q^{34} +(-4.89257 + 2.10980i) q^{36} -3.63274 q^{37} +(0.0843024 + 0.146016i) q^{38} +(2.45510 + 2.75908i) q^{39} +(1.36677 - 2.36731i) q^{41} +(-1.39661 - 1.56953i) q^{42} +(-3.83908 - 6.64949i) q^{43} +10.9556 q^{44} -1.99381 q^{46} +(-5.71444 - 9.89770i) q^{47} +(4.59074 - 0.947643i) q^{48} +(0.215378 - 0.373046i) q^{49} +(1.72657 - 5.20952i) q^{51} +(-1.89351 - 3.27966i) q^{52} +9.43507 q^{53} +(2.22853 + 1.03964i) q^{54} +(2.29012 + 3.96660i) q^{56} +(-0.194129 + 0.585740i) q^{57} +(0.399008 - 0.691103i) q^{58} +(-5.10795 + 8.84723i) q^{59} +(0.00549659 + 0.00952038i) q^{61} +3.90833 q^{62} +(0.893512 - 7.63707i) q^{63} -3.11511 q^{64} +(-3.36127 - 3.77745i) q^{66} +(0.491409 - 0.851145i) q^{67} +(-2.81377 + 4.87359i) q^{68} +(-4.85077 - 5.45138i) q^{69} -6.43507 q^{71} +(-4.29988 - 3.20189i) q^{72} -6.61467 q^{73} +(-0.859605 - 1.48888i) q^{74} +(0.316370 - 0.547969i) q^{76} +(-7.90523 + 13.6923i) q^{77} +(-0.549868 + 1.65910i) q^{78} +(4.73569 + 8.20246i) q^{79} +(2.57930 + 8.62248i) q^{81} +1.29366 q^{82} +(-5.20988 - 9.02378i) q^{83} +(-2.48042 + 7.48407i) q^{84} +(1.81686 - 3.14690i) q^{86} +(2.86033 - 0.590444i) q^{87} +(5.51172 + 9.54658i) q^{88} -6.26940 q^{89} +5.46519 q^{91} +(3.74119 + 6.47993i) q^{92} +(9.50863 + 10.6860i) q^{93} +(2.70439 - 4.68413i) q^{94} +(5.58980 + 6.28191i) q^{96} +(3.60339 + 6.24126i) q^{97} +0.203858 q^{98} +(2.15045 - 18.3804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + q^{3} - 4 q^{4} + 8 q^{6} + q^{7} + 18 q^{8} + 5 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + q^3 - 4 * q^4 + 8 * q^6 + q^7 + 18 * q^8 + 5 * q^9	$ 8 q - 2 q^{2} + q^{3} - 4 q^{4} + 8 q^{6} + q^{7} + 18 q^{8} + 5 q^{9} + q^{11} + 11 q^{12} - 2 q^{13} - 3 q^{14} - 4 q^{16} + 22 q^{17} - 5 q^{18} + 4 q^{19} - 15 q^{21} - 3 q^{22} - 15 q^{23} - 33 q^{24} - 20 q^{26} - 2 q^{27} - 8 q^{28} - q^{29} + 4 q^{31} - 10 q^{32} - 28 q^{33} - 9 q^{34} - 14 q^{36} - 2 q^{37} - 23 q^{38} + 25 q^{39} + 5 q^{41} - 21 q^{42} + 10 q^{43} + 44 q^{44} - 20 q^{47} + 53 q^{48} + 3 q^{49} + 11 q^{51} - 17 q^{52} + 40 q^{53} + 26 q^{54} + 30 q^{56} - 8 q^{57} + 18 q^{58} - 17 q^{59} + 13 q^{61} - 12 q^{62} + 9 q^{63} + 38 q^{64} - 8 q^{66} - 17 q^{67} - 34 q^{68} - 27 q^{69} - 16 q^{71} + 18 q^{72} + 4 q^{73} - 40 q^{74} - 11 q^{76} - 12 q^{77} - 61 q^{78} + 7 q^{79} + 17 q^{81} + 24 q^{82} - 30 q^{83} + 27 q^{84} + 34 q^{86} - 23 q^{87} - 9 q^{88} - 18 q^{89} - 34 q^{91} + 12 q^{92} + 15 q^{93} - 3 q^{94} + 34 q^{96} + 19 q^{97} + 26 q^{98} - 17 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + q^3 - 4 * q^4 + 8 * q^6 + q^7 + 18 * q^8 + 5 * q^9 + q^11 + 11 * q^12 - 2 * q^13 - 3 * q^14 - 4 * q^16 + 22 * q^17 - 5 * q^18 + 4 * q^19 - 15 * q^21 - 3 * q^22 - 15 * q^23 - 33 * q^24 - 20 * q^26 - 2 * q^27 - 8 * q^28 - q^29 + 4 * q^31 - 10 * q^32 - 28 * q^33 - 9 * q^34 - 14 * q^36 - 2 * q^37 - 23 * q^38 + 25 * q^39 + 5 * q^41 - 21 * q^42 + 10 * q^43 + 44 * q^44 - 20 * q^47 + 53 * q^48 + 3 * q^49 + 11 * q^51 - 17 * q^52 + 40 * q^53 + 26 * q^54 + 30 * q^56 - 8 * q^57 + 18 * q^58 - 17 * q^59 + 13 * q^61 - 12 * q^62 + 9 * q^63 + 38 * q^64 - 8 * q^66 - 17 * q^67 - 34 * q^68 - 27 * q^69 - 16 * q^71 + 18 * q^72 + 4 * q^73 - 40 * q^74 - 11 * q^76 - 12 * q^77 - 61 * q^78 + 7 * q^79 + 17 * q^81 + 24 * q^82 - 30 * q^83 + 27 * q^84 + 34 * q^86 - 23 * q^87 - 9 * q^88 - 18 * q^89 - 34 * q^91 + 12 * q^92 + 15 * q^93 - 3 * q^94 + 34 * q^96 + 19 * q^97 + 26 * q^98 - 17 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.236627	+	0.409850i	0.167321	+	0.289808i	0.937477	−	0.348047i	$-0.113155\pi$
$2$	0.236627	+	0.409850i	0.167321	+	0.289808i	−0.770156	+	0.637855i	$0.779822\pi$
$3$	−0.544899	+	1.64411i	−0.314598	+	0.949225i
$3$	−0.544899	+	1.64411i	−0.314598	+	0.949225i
$4$	0.888015	−	1.53809i	0.444008	−	0.769044i
$5$		0			0
$5$		0			0
$6$	−0.802776	+	0.165713i	−0.327732	+	0.0676521i
$7$	1.28153	+	2.21967i	0.484372	+	0.838956i	0.999839	−	0.0179531i	$-0.00571495\pi$
$7$	1.28153	+	2.21967i	0.484372	+	0.838956i	−0.515467	+	0.856909i	$0.672382\pi$
$8$	1.78702			0.631808
$9$	−2.40617	−	1.79175i	−0.802056	−	0.597248i
$10$		0			0
$11$	3.08430	+	5.34217i	0.929952	+	1.61072i	0.783397	+	0.621522i	$0.213485\pi$
$11$	3.08430	+	5.34217i	0.929952	+	1.61072i	0.146555	+	0.989202i	$0.453181\pi$
$12$	2.04490	+	2.29809i	0.590312	+	0.663403i
$13$	1.06615	−	1.84662i	0.295696	−	0.512161i	−0.679450	−	0.733722i	$-0.737782\pi$
$13$	1.06615	−	1.84662i	0.295696	−	0.512161i	0.975147	+	0.221560i	$0.0711150\pi$
$14$	−0.606488	+	1.05047i	−0.162091	+	0.280750i
$15$		0			0
$16$	−1.35317	−	2.34376i	−0.338293	−	0.585941i
$17$	−3.16860			−0.768500			−0.384250	−	0.923229i	$-0.625540\pi$
$17$	−3.16860			−0.768500			−0.384250	+	0.923229i	$0.625540\pi$
$18$	0.164982	−	1.41015i	0.0388867	−	0.332374i
$19$	0.356267			0.0817332			0.0408666	−	0.999165i	$-0.486988\pi$
$19$	0.356267			0.0817332			0.0408666	+	0.999165i	$0.486988\pi$
$20$		0			0
$21$	−4.34768	+	0.897469i	−0.948740	+	0.195844i
$22$	−1.45966	+	2.52821i	−0.311201	+	0.539015i
$23$	−2.10649	+	3.64854i	−0.439233	+	0.760774i	−0.997631	−	0.0687995i	$-0.978083\pi$
$23$	−2.10649	+	3.64854i	−0.439233	+	0.760774i	0.558397	+	0.829574i	$0.311416\pi$
$24$	−0.973748	+	2.93806i	−0.198766	+	0.599728i
$25$		0			0
$26$	1.00912			0.197905
$27$	4.25694	−	2.97968i	0.819248	−	0.573439i
$28$	4.55206			0.860259
$29$	−0.843116	−	1.46032i	−0.156563	−	0.271174i	0.777064	−	0.629421i	$-0.216708\pi$
$29$	−0.843116	−	1.46032i	−0.156563	−	0.271174i	−0.933627	+	0.358247i	$0.883375\pi$
$30$		0			0
$31$	4.12920	−	7.15199i	0.741627	−	1.28453i	−0.210128	−	0.977674i	$-0.567388\pi$
$31$	4.12920	−	7.15199i	0.741627	−	1.28453i	0.951754	−	0.306861i	$-0.0992787\pi$
$32$	2.42742	−	4.20441i	0.429111	−	0.743242i
$33$	−10.4637	+	2.15998i	−1.82150	+	0.376003i
$34$	−0.749778	−	1.29865i	−0.128586	−	0.222717i
$35$		0			0
$36$	−4.89257	+	2.10980i	−0.815429	+	0.351634i
$37$	−3.63274			−0.597219			−0.298609	−	0.954375i	$-0.596523\pi$
$37$	−3.63274			−0.597219			−0.298609	+	0.954375i	$0.596523\pi$
$38$	0.0843024	+	0.146016i	0.0136757	+	0.0236869i
$39$	2.45510	+	2.75908i	0.393131	+	0.441807i
$40$		0			0
$41$	1.36677	−	2.36731i	0.213453	−	0.369711i	−0.739340	−	0.673332i	$-0.764862\pi$
$41$	1.36677	−	2.36731i	0.213453	−	0.369711i	0.952793	+	0.303621i	$0.0981956\pi$
$42$	−1.39661	−	1.56953i	−0.215501	−	0.242184i
$43$	−3.83908	−	6.64949i	−0.585455	−	1.01404i	−0.994819	−	0.101666i	$-0.967583\pi$
$43$	−3.83908	−	6.64949i	−0.585455	−	1.01404i	0.409364	−	0.912371i	$-0.365751\pi$
$44$	10.9556			1.65162
$45$		0			0
$46$	−1.99381			−0.293971
$47$	−5.71444	−	9.89770i	−0.833537	−	1.44373i	−0.895216	−	0.445632i	$-0.852979\pi$
$47$	−5.71444	−	9.89770i	−0.833537	−	1.44373i	0.0616792	−	0.998096i	$-0.480354\pi$
$48$	4.59074	−	0.947643i	0.662616	−	0.136780i
$49$	0.215378	−	0.373046i	0.0307683	−	0.0532923i
$50$		0			0
$51$	1.72657	−	5.20952i	0.241768	−	0.729479i
$52$	−1.89351	−	3.27966i	−0.262583	−	0.454807i
$53$	9.43507			1.29601			0.648003	−	0.761637i	$-0.275604\pi$
$53$	9.43507			1.29601			0.648003	+	0.761637i	$0.275604\pi$
$54$	2.22853	+	1.03964i	0.303264	+	0.141477i
$55$		0			0
$56$	2.29012	+	3.96660i	0.306030	+	0.530059i
$57$	−0.194129	+	0.585740i	−0.0257131	+	0.0775832i
$58$	0.399008	−	0.691103i	0.0523924	−	0.0907462i
$59$	−5.10795	+	8.84723i	−0.664999	+	1.15181i	0.314287	+	0.949328i	$0.398235\pi$
$59$	−5.10795	+	8.84723i	−0.664999	+	1.15181i	−0.979286	+	0.202484i	$0.935099\pi$
$60$		0			0
$61$	0.00549659	+	0.00952038i	0.000703767	+	0.00121896i	0.866377	−	0.499390i	$-0.166443\pi$
$61$	0.00549659	+	0.00952038i	0.000703767	+	0.00121896i	−0.865673	+	0.500609i	$0.833109\pi$
$62$	3.90833			0.496358
$63$	0.893512	−	7.63707i	0.112572	−	0.962180i
$64$	−3.11511			−0.389389
$65$		0			0
$66$	−3.36127	−	3.77745i	−0.413744	−	0.464972i
$67$	0.491409	−	0.851145i	0.0600351	−	0.103984i	−0.834446	−	0.551090i	$-0.814212\pi$
$67$	0.491409	−	0.851145i	0.0600351	−	0.103984i	0.894481	+	0.447106i	$0.147545\pi$
$68$	−2.81377	+	4.87359i	−0.341220	+	0.591010i
$69$	−4.85077	−	5.45138i	−0.583964	−	0.656269i
$70$		0			0
$71$	−6.43507			−0.763703			−0.381851	−	0.924224i	$-0.624713\pi$
$71$	−6.43507			−0.763703			−0.381851	+	0.924224i	$0.624713\pi$
$72$	−4.29988	−	3.20189i	−0.506746	−	0.377346i
$73$	−6.61467			−0.774189			−0.387094	−	0.922040i	$-0.626521\pi$
$73$	−6.61467			−0.774189			−0.387094	+	0.922040i	$0.626521\pi$
$74$	−0.859605	−	1.48888i	−0.0999271	−	0.173079i
$75$		0			0
$76$	0.316370	−	0.547969i	0.0362901	−	0.0628564i
$77$	−7.90523	+	13.6923i	−0.900885	+	1.56038i
$78$	−0.549868	+	1.65910i	−0.0622603	+	0.187856i
$79$	4.73569	+	8.20246i	0.532807	+	0.922848i	0.999266	+	0.0383057i	$0.0121961\pi$
$79$	4.73569	+	8.20246i	0.532807	+	0.922848i	−0.466459	+	0.884543i	$0.654471\pi$
$80$		0			0
$81$	2.57930	+	8.62248i	0.286589	+	0.958054i
$82$	1.29366			0.142860
$83$	−5.20988	−	9.02378i	−0.571859	−	0.990489i	−0.996375	−	0.0850682i	$-0.972889\pi$
$83$	−5.20988	−	9.02378i	−0.571859	−	0.990489i	0.424516	−	0.905420i	$-0.360444\pi$
$84$	−2.48042	+	7.48407i	−0.270636	+	0.816579i
$85$		0			0
$86$	1.81686	−	3.14690i	0.195917	−	0.339339i
$87$	2.86033	−	0.590444i	0.306660	−	0.0633023i
$88$	5.51172	+	9.54658i	0.587551	+	1.01767i
$89$	−6.26940			−0.664555			−0.332277	−	0.943182i	$-0.607817\pi$
$89$	−6.26940			−0.664555			−0.332277	+	0.943182i	$0.607817\pi$
$90$		0			0
$91$	5.46519			0.572908
$92$	3.74119	+	6.47993i	0.390046	+	0.675579i
$93$	9.50863	+	10.6860i	0.985999	+	1.10808i
$94$	2.70439	−	4.68413i	0.278936	−	0.483131i
$95$		0			0
$96$	5.58980	+	6.28191i	0.570506	+	0.641145i
$97$	3.60339	+	6.24126i	0.365869	+	0.633704i	0.988915	−	0.148481i	$-0.0474384\pi$
$97$	3.60339	+	6.24126i	0.365869	+	0.633704i	−0.623046	+	0.782185i	$0.714105\pi$
$98$	0.203858			0.0205927
$99$	2.15045	−	18.3804i	0.216128	−	1.84730i
$100$		0			0
$101$	−3.48547	−	6.03701i	−0.346817	−	0.600705i	0.638865	−	0.769319i	$-0.279404\pi$
$101$	−3.48547	−	6.03701i	−0.346817	−	0.600705i	−0.985682	+	0.168614i	$0.946071\pi$
$102$	2.54368	−	0.525079i	0.251862	−	0.0519906i
$103$	−3.05756	+	5.29584i	−0.301270	+	0.521815i	−0.976424	−	0.215862i	$-0.930744\pi$
$103$	−3.05756	+	5.29584i	−0.301270	+	0.521815i	0.675154	+	0.737677i	$0.264077\pi$
$104$	1.90523	−	3.29996i	0.186823	−	0.323588i
$105$		0			0
$106$	2.23260	+	3.86697i	0.216849	+	0.375593i
$107$	14.5349			1.40514			0.702570	−	0.711615i	$-0.252036\pi$
$107$	14.5349			1.40514			0.702570	+	0.711615i	$0.252036\pi$
$108$	−0.802776	−	9.19354i	−0.0772471	−	0.884649i
$109$	1.90214			0.182192			0.0910958	−	0.995842i	$-0.470963\pi$
$109$	1.90214			0.182192			0.0910958	+	0.995842i	$0.470963\pi$
$110$		0			0
$111$	1.97948	−	5.97261i	0.187884	−	0.566895i
$112$	3.46825	−	6.00719i	0.327719	−	0.567626i
$113$	−3.28962	+	5.69780i	−0.309462	+	0.536004i	−0.978245	−	0.207454i	$-0.933482\pi$
$113$	−3.28962	+	5.69780i	−0.309462	+	0.536004i	0.668783	+	0.743458i	$0.266816\pi$
$114$	−0.286002	+	0.0590380i	−0.0267866	+	0.00552942i
$115$		0			0
$116$	−2.99480			−0.278060
$117$	−5.87401	+	2.53302i	−0.543053	+	0.234178i
$118$	−4.83472			−0.445072
$119$	−4.06065	−	7.03326i	−0.372239	−	0.644737i
$120$		0			0
$121$	−13.5258	+	23.4274i	−1.22962	+	2.12977i
$122$	−0.00260129	+	0.00450556i	−0.000235509	+	0.000407914i
$123$	3.14736	+	3.53705i	0.283788	+	0.318925i
$124$	−7.33359	−	12.7021i	−0.658576	−	1.14069i
$125$		0			0
$126$	3.34149	−	1.44093i	0.297683	−	0.128368i
$127$	9.25840			0.821550			0.410775	−	0.911737i	$-0.365258\pi$
$127$	9.25840			0.821550			0.410775	+	0.911737i	$0.365258\pi$
$128$	−5.59196	−	9.68555i	−0.494264	−	0.856090i
$129$	13.0244	−	2.68856i	1.14673	−	0.236714i
$130$		0			0
$131$	−0.134698	+	0.233305i	−0.0117687	+	0.0203839i	−0.871850	−	0.489773i	$-0.837080\pi$
$131$	−0.134698	+	0.233305i	−0.0117687	+	0.0203839i	0.860081	+	0.510157i	$0.170413\pi$
$132$	−5.96972	+	18.0122i	−0.519597	+	1.56776i
$133$	0.456565	+	0.790794i	0.0395892	+	0.0685705i
$134$	0.465123			0.0401805
$135$		0			0
$136$	−5.66237			−0.485544
$137$	1.73809	+	3.01046i	0.148495	+	0.257201i	0.930671	−	0.365856i	$-0.119224\pi$
$137$	1.73809	+	3.01046i	0.148495	+	0.257201i	−0.782176	+	0.623057i	$0.785890\pi$
$138$	1.08643	−	3.27804i	0.0924827	−	0.279045i
$139$	−7.37393	+	12.7720i	−0.625448	+	1.08331i	0.363006	+	0.931787i	$0.381751\pi$
$139$	−7.37393	+	12.7720i	−0.625448	+	1.08331i	−0.988454	+	0.151521i	$0.951583\pi$
$140$		0			0
$141$	19.3867	−	4.00189i	1.63265	−	0.337020i
$142$	−1.52271	−	2.63742i	−0.127783	−	0.221327i
$143$	13.1533			1.09993
$144$	−0.943464	+	8.06403i	−0.0786220	+	0.672002i
$145$		0			0
$146$	−1.56521	−	2.71103i	−0.129538	−	0.224366i
$147$	0.495968	+	0.557378i	0.0409068	+	0.0459717i
$148$	−3.22593	+	5.58747i	−0.265170	+	0.459287i
$149$	5.07665	−	8.79301i	0.415895	−	0.720352i	−0.579627	−	0.814882i	$-0.696802\pi$
$149$	5.07665	−	8.79301i	0.415895	−	0.720352i	0.995522	+	0.0945305i	$0.0301350\pi$
$150$		0			0
$151$	5.15811	+	8.93410i	0.419761	+	0.727047i	0.995915	−	0.0902940i	$-0.0287807\pi$
$151$	5.15811	+	8.93410i	0.419761	+	0.727047i	−0.576155	+	0.817341i	$0.695447\pi$
$152$	0.636657			0.0516397
$153$	7.62420	+	5.67733i	0.616380	+	0.458985i
$154$	−7.48237			−0.602947
$155$		0			0
$156$	6.42388	−	1.32605i	0.514322	−	0.106169i
$157$	0.531305	−	0.920247i	0.0424028	−	0.0734437i	−0.844045	−	0.536272i	$-0.819832\pi$
$157$	0.531305	−	0.920247i	0.0424028	−	0.0734437i	0.886448	+	0.462828i	$0.153165\pi$
$158$	−2.24119	+	3.88185i	−0.178299	+	0.308823i
$159$	−5.14117	+	15.5123i	−0.407721	+	1.23020i
$160$		0			0
$161$	−10.7981			−0.851008
$162$	−2.92360	+	3.09744i	−0.229699	+	0.243358i
$163$	17.1386			1.34240			0.671198	−	0.741278i	$-0.265780\pi$
$163$	17.1386			1.34240			0.671198	+	0.741278i	$0.265780\pi$
$164$	−2.42742	−	4.20441i	−0.189549	−	0.328309i
$165$		0			0
$166$	2.46560	−	4.27054i	0.191368	−	0.331459i
$167$	−2.18672	+	3.78752i	−0.169214	+	0.293087i	−0.938144	−	0.346246i	$-0.887456\pi$
$167$	−2.18672	+	3.78752i	−0.169214	+	0.293087i	0.768930	+	0.639333i	$0.220790\pi$
$168$	−7.76940	+	1.60380i	−0.599422	+	0.123736i
$169$	4.22666	+	7.32078i	0.325127	+	0.563137i
$170$		0			0
$171$	−0.857238	−	0.638339i	−0.0655546	−	0.0488150i
$172$	−13.6367			−1.03979
$173$	−7.33005	−	12.6960i	−0.557293	−	0.965260i	−0.997721	−	0.0674723i	$-0.978507\pi$
$173$	−7.33005	−	12.6960i	−0.557293	−	0.965260i	0.440428	−	0.897788i	$-0.354827\pi$
$174$	0.918827	+	1.03259i	0.0696561	+	0.0782807i
$175$		0			0
$176$	8.34718	−	14.4577i	0.629192	−	1.08979i
$177$	−11.7625	−	13.2189i	−0.884121	−	0.993591i
$178$	−1.48351	−	2.56952i	−0.111194	−	0.192593i
$179$	−6.87014			−0.513499			−0.256749	−	0.966478i	$-0.582651\pi$
$179$	−6.87014			−0.513499			−0.256749	+	0.966478i	$0.582651\pi$
$180$		0			0
$181$	−10.9709			−0.815463			−0.407732	−	0.913102i	$-0.633680\pi$
$181$	−10.9709			−0.815463			−0.407732	+	0.913102i	$0.633680\pi$
$182$	1.29321	+	2.23991i	0.0958593	+	0.166033i
$183$	−0.0186476	+	0.00384933i	−0.00137847	+	0.000284551i
$184$	−3.76434	+	6.52003i	−0.277511	+	0.480663i
$185$		0			0
$186$	−2.12965	+	6.42570i	−0.156153	+	0.471155i
$187$	−9.77294	−	16.9272i	−0.714668	−	1.23784i
$188$	−20.2980			−1.48039
$189$	12.0693	+	5.63046i	0.877911	+	0.409556i
$190$		0			0
$191$	−6.86627	−	11.8927i	−0.496826	−	0.860528i	0.503167	−	0.864189i	$-0.332168\pi$
$191$	−6.86627	−	11.8927i	−0.496826	−	0.860528i	−0.999993	+	0.00366109i	$0.998835\pi$
$192$	1.69742	−	5.12158i	0.122501	−	0.369618i
$193$	−0.241187	+	0.417748i	−0.0173610	+	0.0300701i	−0.874575	−	0.484890i	$-0.838860\pi$
$193$	−0.241187	+	0.417748i	−0.0173610	+	0.0300701i	0.857214	+	0.514960i	$0.172193\pi$
$194$	−1.70532	+	2.95370i	−0.122435	+	0.212064i
$195$		0			0
$196$	−0.382518	−	0.662541i	−0.0273227	−	0.0473244i
$197$	−5.53488			−0.394344			−0.197172	−	0.980369i	$-0.563176\pi$
$197$	−5.53488			−0.394344			−0.197172	+	0.980369i	$0.563176\pi$
$198$	8.04209	−	3.46795i	0.571526	−	0.246457i
$199$	17.4590			1.23764			0.618818	−	0.785534i	$-0.287612\pi$
$199$	17.4590			1.23764			0.618818	+	0.785534i	$0.287612\pi$
$200$		0			0
$201$	1.13160	+	1.27172i	0.0798172	+	0.0896999i
$202$	1.64951	−	2.85704i	0.116059	−	0.201021i
$203$	2.16095	−	3.74288i	0.151669	−	0.262698i
$204$	−6.47948	−	7.28175i	−0.453654	−	0.509825i
$205$		0			0
$206$	−2.89401			−0.201635
$207$	11.6058	−	5.00473i	0.806661	−	0.347852i
$208$	−5.77073			−0.400128
$209$	1.09883	+	1.90324i	0.0760079	+	0.131650i
$210$		0			0
$211$	0.818328	−	1.41739i	0.0563360	−	0.0975769i	−0.836482	−	0.547994i	$-0.815392\pi$
$211$	0.818328	−	1.41739i	0.0563360	−	0.0975769i	0.892818	+	0.450417i	$0.148725\pi$
$212$	8.37849	−	14.5120i	0.575437	−	0.996686i
$213$	3.50647	−	10.5799i	0.240259	−	0.724926i
$214$	3.43935	+	5.95713i	0.235109	+	0.407221i
$215$		0			0
$216$	7.60725	−	5.32475i	0.517608	−	0.362303i
$217$	21.1667			1.43689
$218$	0.450098	+	0.779592i	0.0304844	+	0.0528006i
$219$	3.60433	−	10.8752i	0.243558	−	0.734879i
$220$		0			0
$221$	−3.37820	+	5.85122i	−0.227243	+	0.393596i
$222$	2.91628	−	0.601992i	0.195728	−	0.0404031i
$223$	3.87393	+	6.70984i	0.259417	+	0.449324i	0.966086	−	0.258221i	$-0.0831362\pi$
$223$	3.87393	+	6.70984i	0.259417	+	0.449324i	−0.706669	+	0.707545i	$0.749803\pi$
$224$	12.4432			0.831397
$225$		0			0
$226$	−3.11366			−0.207118
$227$	−5.63014	−	9.75169i	−0.373685	−	0.647242i	0.616444	−	0.787399i	$-0.288573\pi$
$227$	−5.63014	−	9.75169i	−0.373685	−	0.647242i	−0.990129	+	0.140157i	$0.955239\pi$
$228$	0.728529	+	0.818734i	0.0482480	+	0.0542220i
$229$	5.23879	−	9.07384i	0.346189	−	0.599616i	−0.639380	−	0.768891i	$-0.720809\pi$
$229$	5.23879	−	9.07384i	0.346189	−	0.599616i	0.985569	+	0.169274i	$0.0541424\pi$
$230$		0			0
$231$	−18.2040	−	20.4579i	−1.19773	−	1.34603i
$232$	−1.50667	−	2.60962i	−0.0989176	−	0.171330i
$233$	2.90214			0.190125			0.0950627	−	0.995471i	$-0.469695\pi$
$233$	2.90214			0.190125			0.0950627	+	0.995471i	$0.469695\pi$
$234$	−2.42811	−	1.80808i	−0.158731	−	0.118198i
$235$		0			0
$236$	9.07188	+	15.7130i	0.590529	+	1.02283i
$237$	−16.0662	+	3.31646i	−1.04361	+	0.215427i
$238$	1.92172	−	3.32852i	0.124567	−	0.215756i
$239$	−8.17723	+	14.1634i	−0.528941	+	0.916153i	0.470489	+	0.882406i	$0.344077\pi$
$239$	−8.17723	+	14.1634i	−0.528941	+	0.916153i	−0.999430	+	0.0337471i	$0.989256\pi$
$240$		0			0
$241$	−8.76194	−	15.1761i	−0.564406	−	0.977580i	−0.997105	−	0.0760416i	$-0.975772\pi$
$241$	−8.76194	−	15.1761i	−0.564406	−	0.977580i	0.432698	−	0.901539i	$-0.357562\pi$
$242$	−12.8023			−0.822965
$243$	−15.5817	−	0.457745i	−0.999569	−	0.0293644i
$244$	0.0195242			0.00124991
$245$		0			0
$246$	−0.704913	+	2.12691i	−0.0449436	+	0.135607i
$247$	0.379833	−	0.657890i	0.0241682	−	0.0418605i
$248$	7.37898	−	12.7808i	0.468566	−	0.811580i
$249$	17.6749	−	3.64854i	1.12010	−	0.231217i
$250$		0			0
$251$	8.46999			0.534621			0.267311	−	0.963610i	$-0.413865\pi$
$251$	8.46999			0.534621			0.267311	+	0.963610i	$0.413865\pi$
$252$	−10.9530	−	8.15613i	−0.689976	−	0.513788i
$253$	−25.9882			−1.63386
$254$	2.19079	+	3.79456i	0.137462	+	0.238092i
$255$		0			0
$256$	−0.468695	+	0.811804i	−0.0292934	+	0.0507377i
$257$	−1.43625	+	2.48766i	−0.0895910	+	0.155176i	−0.907338	−	0.420401i	$-0.861889\pi$
$257$	−1.43625	+	2.48766i	−0.0895910	+	0.155176i	0.817747	+	0.575577i	$0.195223\pi$
$258$	4.18383	+	4.70186i	0.260474	+	0.292725i
$259$	−4.65545	−	8.06348i	−0.289276	−	0.501040i
$260$		0			0
$261$	−0.587841	+	5.02442i	−0.0363864	+	0.311004i
$262$	−0.127493			−0.00787656
$263$	12.8119	+	22.1909i	0.790017	+	1.36835i	0.925955	+	0.377633i	$0.123262\pi$
$263$	12.8119	+	22.1909i	0.790017	+	1.36835i	−0.135938	+	0.990717i	$0.543405\pi$
$264$	−18.6989	+	3.85993i	−1.15084	+	0.237562i
$265$		0			0
$266$	−0.216072	+	0.374247i	−0.0132482	+	0.0229465i
$267$	3.41619	−	10.3076i	0.209068	−	0.630812i
$268$	−0.872756	−	1.51166i	−0.0533121	−	0.0923392i
$269$	0.337210			0.0205600			0.0102800	−	0.999947i	$-0.496728\pi$
$269$	0.337210			0.0205600			0.0102800	+	0.999947i	$0.496728\pi$
$270$		0			0
$271$	21.5927			1.31166			0.655831	−	0.754908i	$-0.272318\pi$
$271$	21.5927			1.31166			0.655831	+	0.754908i	$0.272318\pi$
$272$	4.28767	+	7.42646i	0.259978	+	0.450295i
$273$	−2.97798	+	8.98535i	−0.180236	+	0.543818i
$274$	−0.822560	+	1.42472i	−0.0496927	+	0.0860702i
$275$		0			0
$276$	−12.6923	+	2.62000i	−0.763984	+	0.157705i
$277$	12.0669	+	20.9004i	0.725028	+	1.25579i	0.958962	+	0.283533i	$0.0915067\pi$
$277$	12.0669	+	20.9004i	0.725028	+	1.25579i	−0.233934	+	0.972252i	$0.575160\pi$
$278$	−6.97949			−0.418602
$279$	−22.7501	+	9.81041i	−1.36201	+	0.587334i
$280$		0			0
$281$	−1.68363	−	2.91613i	−0.100437	−	0.173962i	0.811428	−	0.584453i	$-0.198691\pi$
$281$	−1.68363	−	2.91613i	−0.100437	−	0.173962i	−0.911865	+	0.410491i	$0.865357\pi$
$282$	6.22759	+	6.99868i	0.370848	+	0.416765i
$283$	10.9249	−	18.9224i	0.649415	−	1.12482i	−0.333848	−	0.942627i	$-0.608347\pi$
$283$	10.9249	−	18.9224i	0.649415	−	1.12482i	0.983263	−	0.182193i	$-0.0583195\pi$
$284$	−5.71444	+	9.89770i	−0.339090	+	0.587321i
$285$		0			0
$286$	3.11243	+	5.39088i	0.184042	+	0.318770i
$287$	7.00619			0.413562
$288$	−13.3740	+	5.76721i	−0.788071	+	0.339836i
$289$	−6.95994			−0.409408
$290$		0			0
$291$	−12.2248	+	2.52350i	−0.716629	+	0.147930i
$292$	−5.87393	+	10.1739i	−0.343746	+	0.595385i
$293$	6.87702	−	11.9114i	0.401760	−	0.695869i	−0.592179	−	0.805807i	$-0.701732\pi$
$293$	6.87702	−	11.9114i	0.401760	−	0.695869i	0.993938	+	0.109938i	$0.0350653\pi$
$294$	−0.111082	+	0.335163i	−0.00647843	+	0.0195471i
$295$		0			0
$296$	−6.49179			−0.377328
$297$	29.0476	+	13.5511i	1.68551	+	0.786312i
$298$	4.80509			0.278352
$299$	4.49166	+	7.77978i	0.259759	+	0.449916i
$300$		0			0
$301$	9.83978	−	17.0430i	0.567155	−	0.982342i
$302$	−2.44110	+	4.22810i	−0.140469	+	0.243300i
$303$	11.8247	−	2.44092i	0.679312	−	0.140227i
$304$	−0.482090	−	0.835004i	−0.0276498	−	0.0478908i
$305$		0			0
$306$	−0.522764	+	4.46819i	−0.0298844	+	0.255430i
$307$	−34.2183			−1.95294			−0.976472	−	0.215644i	$-0.930815\pi$
$307$	−34.2183			−1.95294			−0.976472	+	0.215644i	$0.930815\pi$
$308$	14.0399	+	24.3179i	0.799999	+	1.38564i
$309$	−7.04087	−	7.91265i	−0.400541	−	0.450135i
$310$		0			0
$311$	−11.5199	+	19.9530i	−0.653232	+	1.13143i	0.329102	+	0.944294i	$0.393254\pi$
$311$	−11.5199	+	19.9530i	−0.653232	+	1.13143i	−0.982334	+	0.187136i	$0.940079\pi$
$312$	4.38732	+	4.93055i	0.248383	+	0.279137i
$313$	−1.79565	−	3.11016i	−0.101496	−	0.175796i	0.810805	−	0.585316i	$-0.199030\pi$
$313$	−1.79565	−	3.11016i	−0.101496	−	0.175796i	−0.912301	+	0.409520i	$0.865696\pi$
$314$	0.502885			0.0283794
$315$		0			0
$316$	16.8215			0.946281
$317$	6.59033	+	11.4148i	0.370150	+	0.641118i	0.989588	−	0.143927i	$-0.0459731\pi$
$317$	6.59033	+	11.4148i	0.370150	+	0.641118i	−0.619439	+	0.785045i	$0.712640\pi$
$318$	−7.57425	+	1.56351i	−0.424743	+	0.0876775i
$319$	5.20085	−	9.00813i	0.291192	−	0.504359i
$320$		0			0
$321$	−7.92005	+	23.8969i	−0.442054	+	1.33379i
$322$	−2.55512	−	4.42560i	−0.142391	−	0.246629i
$323$	−1.12887			−0.0628119
$324$	15.5526	+	3.68971i	0.864033	+	0.204984i
$325$		0			0
$326$	4.05545	+	7.02424i	0.224611	+	0.389037i
$327$	−1.03647	+	3.12732i	−0.0573171	+	0.172941i
$328$	2.44244	−	4.23044i	0.134861	−	0.233587i
$329$	14.6464	−	25.3683i	0.807483	−	1.39860i
$330$		0			0
$331$	−0.591264	−	1.02410i	−0.0324988	−	0.0562896i	0.849319	−	0.527881i	$-0.177013\pi$
$331$	−0.591264	−	1.02410i	−0.0324988	−	0.0562896i	−0.881817	+	0.471591i	$0.843680\pi$
$332$	−18.5058			−1.01564
$333$	8.74099	+	6.50894i	0.479003	+	0.356688i
$334$	−2.06975			−0.113252
$335$		0			0
$336$	7.98661	+	8.97549i	0.435705	+	0.489653i
$337$	−12.3997	+	21.4770i	−0.675457	+	1.16993i	0.300879	+	0.953662i	$0.402720\pi$
$337$	−12.3997	+	21.4770i	−0.675457	+	1.16993i	−0.976335	+	0.216263i	$0.930613\pi$
$338$	−2.00028	+	3.46459i	−0.108801	+	0.188449i
$339$	−7.57527	−	8.51322i	−0.411432	−	0.462375i
$340$		0			0
$341$	50.9428			2.75871
$342$	0.0587777	−	0.502388i	0.00317833	−	0.0271660i
$343$	19.0454			1.02836
$344$	−6.86053	−	11.8828i	−0.369895	−	0.640677i
$345$		0			0
$346$	3.46898	−	6.00845i	0.186493	−	0.323016i
$347$	11.0846	−	19.1991i	0.595052	−	1.03066i	−0.398488	−	0.917174i	$-0.630465\pi$
$347$	11.0846	−	19.1991i	0.595052	−	1.03066i	0.993540	−	0.113486i	$-0.0362018\pi$
$348$	1.63186	−	4.92376i	0.0874771	−	0.263941i
$349$	−7.45925	−	12.9198i	−0.399285	−	0.691581i	0.594353	−	0.804204i	$-0.297408\pi$
$349$	−7.45925	−	12.9198i	−0.399285	−	0.691581i	−0.993638	+	0.112623i	$0.964075\pi$
$350$		0			0
$351$	−0.963810	−	11.0377i	−0.0514444	−	0.589151i
$352$	29.9476			1.59621
$353$	8.45726	+	14.6484i	0.450134	+	0.779656i	0.998394	−	0.0566525i	$-0.0180427\pi$
$353$	8.45726	+	14.6484i	0.450134	+	0.779656i	−0.548260	+	0.836308i	$0.684709\pi$
$354$	2.63444	−	7.94880i	0.140019	−	0.422474i
$355$		0			0
$356$	−5.56732	+	9.64288i	−0.295067	+	0.511072i
$357$	13.7761	−	2.84372i	0.729107	−	0.150506i
$358$	−1.62566	−	2.81573i	−0.0859190	−	0.148816i
$359$	0.636657			0.0336015			0.0168007	−	0.999859i	$-0.494652\pi$
$359$	0.636657			0.0336015			0.0168007	+	0.999859i	$0.494652\pi$
$360$		0			0
$361$	−18.8731			−0.993320
$362$	−2.59602	−	4.49644i	−0.136444	−	0.236328i
$363$	−31.1470	−	35.0035i	−1.63479	−	1.83721i
$364$	4.85317	−	8.40594i	0.254375	−	0.440591i
$365$		0			0
$366$	−0.00599018	−	0.00673187i	−0.000313112	−	0.000351880i
$367$	10.0490	+	17.4053i	0.524552	+	0.908550i	0.999591	+	0.0285858i	$0.00910039\pi$
$367$	10.0490	+	17.4053i	0.524552	+	0.908550i	−0.475040	+	0.879964i	$0.657566\pi$
$368$	11.4018			0.594358
$369$	−7.53028	+	3.24725i	−0.392011	+	0.169045i
$370$		0			0
$371$	12.0913	+	20.9427i	0.627749	+	1.08729i
$372$	24.8797	−	5.13580i	1.28995	−	0.266279i
$373$	−9.82146	+	17.0113i	−0.508536	+	0.880810i	0.491415	+	0.870925i	$0.336480\pi$
$373$	−9.82146	+	17.0113i	−0.508536	+	0.880810i	−0.999951	+	0.00988448i	$0.996854\pi$
$374$	4.62509	−	8.01088i	0.239157	−	0.414233i
$375$		0			0
$376$	−10.2118	−	17.6874i	−0.526635	−	0.912159i
$377$	−3.59555			−0.185180
$378$	0.548272	+	6.27892i	0.0282001	+	0.322953i
$379$	−7.94219			−0.407963			−0.203982	−	0.978975i	$-0.565388\pi$
$379$	−7.94219			−0.407963			−0.203982	+	0.978975i	$0.565388\pi$
$380$		0			0
$381$	−5.04490	+	15.2218i	−0.258458	+	0.779836i
$382$	3.24949	−	5.62829i	0.166259	−	0.287968i
$383$	−15.5944	+	27.0103i	−0.796836	+	1.38016i	0.124830	+	0.992178i	$0.460161\pi$
$383$	−15.5944	+	27.0103i	−0.796836	+	1.38016i	−0.921667	+	0.387983i	$0.873172\pi$
$384$	18.9711	−	3.91612i	0.968116	−	0.199843i
$385$		0			0
$386$	−0.228285			−0.0116194
$387$	−2.67670	+	22.8785i	−0.136064	+	1.16298i
$388$	12.7995			0.649795
$389$	15.7247	+	27.2360i	0.797274	+	1.38092i	0.921385	+	0.388650i	$0.127059\pi$
$389$	15.7247	+	27.2360i	0.797274	+	1.38092i	−0.124111	+	0.992268i	$0.539608\pi$
$390$		0			0
$391$	6.67463	−	11.5608i	0.337550	−	0.584655i
$392$	0.384886	−	0.666642i	0.0194397	−	0.0336705i
$393$	−0.310180	−	0.348586i	−0.0156465	−	0.0175838i
$394$	−1.30970	−	2.26847i	−0.0659819	−	0.114284i
$395$		0			0
$396$	−26.3611	−	19.6297i	−1.32469	−	0.986429i
$397$	−17.7174			−0.889211			−0.444606	−	0.895726i	$-0.646656\pi$
$397$	−17.7174			−0.889211			−0.444606	+	0.895726i	$0.646656\pi$
$398$	4.13128	+	7.15558i	0.207082	+	0.358677i
$399$	−1.54893	+	0.319738i	−0.0775436	+	0.0160069i
$400$		0			0
$401$	3.57124	−	6.18556i	0.178339	−	0.308892i	−0.762973	−	0.646431i	$-0.776261\pi$
$401$	3.57124	−	6.18556i	0.178339	−	0.308892i	0.941312	+	0.337538i	$0.109594\pi$
$402$	−0.253445	+	0.764711i	−0.0126407	+	0.0381403i
$403$	−8.80468	−	15.2502i	−0.438593	−	0.759665i
$404$	−12.3806			−0.615958
$405$		0			0
$406$	2.04536			0.101509
$407$	−11.2045	−	19.4067i	−0.555385	−	0.961955i
$408$	3.08542	−	9.30954i	0.152751	−	0.460891i
$409$	−12.3759	+	21.4357i	−0.611948	+	1.05993i	0.378964	+	0.925412i	$0.376281\pi$
$409$	−12.3759	+	21.4357i	−0.611948	+	1.05993i	−0.990912	+	0.134514i	$0.957053\pi$
$410$		0			0
$411$	−5.89661	+	1.21721i	−0.290858	+	0.0600404i
$412$	5.43031	+	9.40558i	0.267532	+	0.463380i
$413$	−26.1839			−1.28843
$414$	4.79744	+	3.57240i	0.235782	+	0.175574i
$415$		0			0
$416$	−5.17598	−	8.96505i	−0.253773	−	0.439548i
$417$	−16.9805	−	19.0830i	−0.831539	−	0.934498i
$418$	−0.520028	+	0.900715i	−0.0254354	+	0.0440554i
$419$	5.32956	−	9.23106i	0.260366	−	0.450967i	−0.705973	−	0.708238i	$-0.749490\pi$
$419$	5.32956	−	9.23106i	0.260366	−	0.450967i	0.966339	+	0.257272i	$0.0828235\pi$
$420$		0			0
$421$	4.08931	+	7.08288i	0.199301	+	0.345199i	0.948302	−	0.317370i	$-0.102800\pi$
$421$	4.08931	+	7.08288i	0.199301	+	0.345199i	−0.749001	+	0.662569i	$0.769466\pi$
$422$	0.774555			0.0377048
$423$	−3.98425	+	34.0544i	−0.193721	+	1.65578i
$424$	16.8607			0.818828
$425$		0			0
$426$	5.16592	−	1.06638i	0.250290	−	0.0516660i
$427$	−0.0140881	+	0.0244012i	−0.000681769	+	0.00118086i
$428$	12.9072	−	22.3559i	0.623893	−	1.08061i
$429$	−7.16722	+	21.6254i	−0.346037	+	1.04408i
$430$		0			0
$431$	1.67248			0.0805604			0.0402802	−	0.999188i	$-0.487175\pi$
$431$	1.67248			0.0805604			0.0402802	+	0.999188i	$0.487175\pi$
$432$	−12.7440	−	5.94524i	−0.613147	−	0.286040i
$433$	9.95994			0.478644			0.239322	−	0.970940i	$-0.423075\pi$
$433$	9.95994			0.478644			0.239322	+	0.970940i	$0.423075\pi$
$434$	5.00863	+	8.67519i	0.240422	+	0.416423i
$435$		0			0
$436$	1.68913	−	2.92565i	0.0808945	−	0.140113i
$437$	−0.750471	+	1.29985i	−0.0358999	+	0.0621805i
$438$	5.31010	−	1.09614i	0.253726	−	0.0523754i
$439$	−6.40788	−	11.0988i	−0.305832	−	0.529716i	0.671615	−	0.740901i	$-0.265601\pi$
$439$	−6.40788	−	11.0988i	−0.305832	−	0.529716i	−0.977446	+	0.211185i	$0.932268\pi$
$440$		0			0
$441$	−1.18664	+	0.511709i	−0.0565067	+	0.0243671i
$442$	−3.19750			−0.152090
$443$	−3.87702	−	6.71520i	−0.184203	−	0.319049i	0.759105	−	0.650968i	$-0.225637\pi$
$443$	−3.87702	−	6.71520i	−0.184203	−	0.319049i	−0.943308	+	0.331920i	$0.892304\pi$
$444$	−7.42859	−	8.34838i	−0.352545	−	0.396196i
$445$		0			0
$446$	−1.83335	+	3.17546i	−0.0868118	+	0.150362i
$447$	11.6904	+	13.1379i	0.552936	+	0.621399i
$448$	−3.99210	−	6.91452i	−0.188609	−	0.326681i
$449$	−33.3401			−1.57342			−0.786709	−	0.617324i	$-0.788217\pi$
$449$	−33.3401			−1.57342			−0.786709	+	0.617324i	$0.788217\pi$
$450$		0			0
$451$	16.8621			0.794004
$452$	5.84247	+	10.1195i	0.274807	+	0.475979i
$453$	−17.4993	+	3.61229i	−0.822187	+	0.169720i
$454$	2.66449	−	4.61503i	0.125051	−	0.216594i
$455$		0			0
$456$	−0.346914	+	1.04673i	−0.0162457	+	0.0490177i
$457$	−19.1096	−	33.0988i	−0.893910	−	1.54830i	−0.835148	−	0.550026i	$-0.814618\pi$
$457$	−19.1096	−	33.0988i	−0.893910	−	1.54830i	−0.0587626	−	0.998272i	$-0.518715\pi$
$458$	4.95856			0.231698
$459$	−13.4886	+	9.44142i	−0.629592	+	0.440688i
$460$		0			0
$461$	−15.6517	−	27.1095i	−0.728971	−	1.26261i	−0.957319	−	0.289035i	$-0.906666\pi$
$461$	−15.6517	−	27.1095i	−0.728971	−	1.26261i	0.228348	−	0.973580i	$-0.426668\pi$
$462$	4.07714	−	12.3018i	0.189686	−	0.572332i
$463$	6.04258	−	10.4661i	0.280823	−	0.486399i	−0.690765	−	0.723079i	$-0.742726\pi$
$463$	6.04258	−	10.4661i	0.280823	−	0.486399i	0.971588	+	0.236680i	$0.0760594\pi$
$464$	−2.28176	+	3.95212i	−0.105928	+	0.183473i
$465$		0			0
$466$	0.686725	+	1.18944i	0.0318119	+	0.0550998i
$467$	7.60466			0.351902			0.175951	−	0.984399i	$-0.443700\pi$
$467$	7.60466			0.351902			0.175951	+	0.984399i	$0.443700\pi$
$468$	−1.32020	+	11.2841i	−0.0610264	+	0.521608i
$469$	2.51901			0.116317
$470$		0			0
$471$	1.22348	+	1.37496i	0.0563748	+	0.0633550i
$472$	−9.12803	+	15.8102i	−0.420152	+	0.727724i
$473$	23.6818	−	41.0181i	1.08889	−	1.88601i
$474$	−5.16095	−	5.79997i	−0.237050	−	0.266401i
$475$		0			0
$476$	−14.4237			−0.661108
$477$	−22.7024	−	16.9052i	−1.03947	−	0.774038i
$478$	−7.73982			−0.354011
$479$	16.2417	+	28.1314i	0.742101	+	1.28536i	0.951537	+	0.307534i	$0.0995037\pi$
$479$	16.2417	+	28.1314i	0.742101	+	1.28536i	−0.209437	+	0.977822i	$0.567163\pi$
$480$		0			0
$481$	−3.87304	+	6.70830i	−0.176595	+	0.305872i
$482$	4.14663	−	7.18217i	0.188874	−	0.327139i
$483$	5.88387	−	17.7532i	0.267725	−	0.807798i
$484$	24.0223	+	41.6079i	1.09192	+	1.89127i
$485$		0			0
$486$	−3.49946	−	6.49450i	−0.158739	−	0.294596i
$487$	4.46121			0.202157			0.101078	−	0.994878i	$-0.467771\pi$
$487$	4.46121			0.202157			0.101078	+	0.994878i	$0.467771\pi$
$488$	0.00982254	+	0.0170131i	0.000444645	+	0.000770148i
$489$	−9.33879	+	28.1776i	−0.422315	+	1.27424i
$490$		0			0
$491$	−16.4210	+	28.4420i	−0.741070	+	1.28357i	0.210938	+	0.977499i	$0.432348\pi$
$491$	−16.4210	+	28.4420i	−0.741070	+	1.28357i	−0.952008	+	0.306072i	$0.900985\pi$
$492$	8.23520	−	1.69995i	0.371271	−	0.0766397i
$493$	2.67150	+	4.62717i	0.120318	+	0.208397i
$494$	0.359515			0.0161754
$495$		0			0
$496$	−22.3501			−1.00355
$497$	−8.24672	−	14.2837i	−0.369916	−	0.640713i
$498$	5.67772	+	6.38073i	0.254425	+	0.285927i
$499$	17.1010	−	29.6198i	0.765547	−	1.32597i	−0.174410	−	0.984673i	$-0.555802\pi$
$499$	17.1010	−	29.6198i	0.765547	−	1.32597i	0.939957	−	0.341293i	$-0.110865\pi$
$500$		0			0
$501$	−5.03554	−	5.65902i	−0.224971	−	0.252827i
$502$	2.00423	+	3.47143i	0.0894532	+	0.154938i
$503$	−22.1773			−0.988837			−0.494419	−	0.869224i	$-0.664619\pi$
$503$	−22.1773			−0.988837			−0.494419	+	0.869224i	$0.664619\pi$
$504$	1.59673	−	13.6476i	0.0711238	−	0.607913i
$505$		0			0
$506$	−6.14951	−	10.6513i	−0.273379	−	0.473507i
$507$	−14.3392	+	2.95998i	−0.636828	+	0.131457i
$508$	8.22160	−	14.2402i	0.364775	−	0.631808i
$509$	10.7816	−	18.6743i	0.477887	−	0.827724i	−0.521792	−	0.853073i	$-0.674736\pi$
$509$	10.7816	−	18.6743i	0.477887	−	0.827724i	0.999679	+	0.0253489i	$0.00806968\pi$
$510$		0			0
$511$	−8.47688	−	14.6824i	−0.374995	−	0.649510i
$512$	−22.8115			−1.00813
$513$	1.51661	−	1.06156i	0.0669598	−	0.0468690i
$514$	−1.35943			−0.0599617
$515$		0			0
$516$	7.43061	−	22.4201i	0.327114	−	0.986990i
$517$	35.2501	−	61.0550i	1.55030	−	2.68520i
$518$	2.20321	−	3.81608i	0.0968037	−	0.167669i
$519$	24.8677	−	5.13332i	1.09157	−	0.225328i
$520$		0			0
$521$	20.2626			0.887718			0.443859	−	0.896097i	$-0.353609\pi$
$521$	20.2626			0.887718			0.443859	+	0.896097i	$0.353609\pi$
$522$	−2.19836	+	0.947989i	−0.0962196	+	0.0414923i
$523$	−31.8114			−1.39101			−0.695507	−	0.718520i	$-0.744820\pi$
$523$	−31.8114			−1.39101			−0.695507	+	0.718520i	$0.744820\pi$
$524$	0.239229	+	0.414356i	0.0104507	+	0.0181012i
$525$		0			0
$526$	−6.06330	+	10.5019i	−0.264373	+	0.457907i
$527$	−13.0838	+	22.6618i	−0.569940	+	0.987164i
$528$	19.2217	+	21.6017i	0.836517	+	0.940092i
$529$	2.62541	+	4.54735i	0.114148	+	0.197711i
$530$		0			0
$531$	28.1426	−	12.1358i	1.22128	−	0.526649i
$532$	1.62175			0.0703117
$533$	−2.91435	−	5.04780i	−0.126235	−	0.218645i
$534$	5.03292	−	1.03892i	0.217796	−	0.0449585i
$535$		0			0
$536$	0.878159	−	1.52102i	0.0379307	−	0.0656978i
$537$	3.74354	−	11.2952i	0.161546	−	0.487426i
$538$	0.0797930	+	0.138205i	0.00344012	+	0.00595846i
$539$	2.65717			0.114452
$540$		0			0
$541$	−15.1315			−0.650553			−0.325277	−	0.945619i	$-0.605457\pi$
$541$	−15.1315			−0.650553			−0.325277	+	0.945619i	$0.605457\pi$
$542$	5.10942	+	8.84977i	0.219468	+	0.380130i
$543$	5.97806	−	18.0374i	0.256543	−	0.774058i
$544$	−7.69153	+	13.3221i	−0.329772	+	0.571181i
$545$		0			0
$546$	−4.38732	+	0.905653i	−0.187760	+	0.0387584i
$547$	−2.04372	−	3.53982i	−0.0873831	−	0.151352i	0.819021	−	0.573763i	$-0.194517\pi$
$547$	−2.04372	−	3.53982i	−0.0873831	−	0.151352i	−0.906404	+	0.422411i	$0.861184\pi$
$548$	6.17381			0.263732
$549$	0.00383236	−	0.0327561i	0.000163561	−	0.00139800i
$550$		0			0
$551$	−0.300374	−	0.520263i	−0.0127964	−	0.0221639i
$552$	−8.66844	−	9.74174i	−0.368953	−	0.414636i
$553$	−12.1378	+	21.0233i	−0.516153	+	0.894003i
$554$	−5.71070	+	9.89123i	−0.242625	+	0.420238i
$555$		0			0
$556$	13.0963	+	22.6835i	0.555408	+	0.961994i
$557$	13.1425			0.556864			0.278432	−	0.960456i	$-0.410185\pi$
$557$	13.1425			0.556864			0.278432	+	0.960456i	$0.410185\pi$
$558$	−9.40410	−	7.00273i	−0.398107	−	0.296449i
$559$	−16.3721			−0.692467
$560$		0			0
$561$	33.1554	−	6.84411i	1.39982	−	0.288958i
$562$	0.796785	−	1.38007i	0.0336104	−	0.0582149i
$563$	−12.2611	+	21.2368i	−0.516742	+	0.895023i	0.483069	+	0.875582i	$0.339522\pi$
$563$	−12.2611	+	21.2368i	−0.516742	+	0.895023i	−0.999811	+	0.0194410i	$0.993811\pi$
$564$	11.0604	−	33.3721i	0.465727	−	1.40522i
$565$		0			0
$566$	10.3405			0.434642
$567$	−15.8336	+	16.7751i	−0.664950	+	0.704489i
$568$	−11.4996			−0.482514
$569$	−11.3649	−	19.6846i	−0.476442	−	0.825223i	0.523193	−	0.852214i	$-0.324741\pi$
$569$	−11.3649	−	19.6846i	−0.476442	−	0.825223i	−0.999636	+	0.0269915i	$0.991407\pi$
$570$		0			0
$571$	0.247093	−	0.427977i	0.0103405	−	0.0179103i	−0.860809	−	0.508928i	$-0.830042\pi$
$571$	0.247093	−	0.427977i	0.0103405	−	0.0179103i	0.871149	+	0.491018i	$0.163375\pi$
$572$	11.6803	−	20.2309i	0.488379	−	0.845897i
$573$	23.2943	−	4.80854i	0.973135	−	0.200879i
$574$	1.65786	+	2.87149i	0.0691976	+	0.119854i
$575$		0			0
$576$	7.49549	+	5.58149i	0.312312	+	0.232562i
$577$	9.41187			0.391821			0.195911	−	0.980622i	$-0.437234\pi$
$577$	9.41187			0.391821			0.195911	+	0.980622i	$0.437234\pi$
$578$	−1.64691	−	2.85254i	−0.0685025	−	0.118650i
$579$	−0.555399	−	0.624167i	−0.0230816	−	0.0259395i
$580$		0			0
$581$	13.3532	−	23.1284i	0.553984	−	0.959529i
$582$	−3.92697	−	4.41320i	−0.162778	−	0.182933i
$583$	29.1006	+	50.4037i	1.20522	+	2.08751i
$584$	−11.8206			−0.489139
$585$		0			0
$586$	6.50916			0.268891
$587$	4.98661	+	8.63705i	0.205819	+	0.356489i	0.950393	−	0.311050i	$-0.100681\pi$
$587$	4.98661	+	8.63705i	0.205819	+	0.356489i	−0.744574	+	0.667540i	$0.767347\pi$
$588$	1.29772	−	0.267882i	0.0535172	−	0.0110473i
$589$	1.47110	−	2.54801i	0.0606155	−	0.104989i
$590$		0			0
$591$	3.01595	−	9.09993i	0.124060	−	0.374321i
$592$	4.91572	+	8.51428i	0.202035	+	0.349935i
$593$	−38.3421			−1.57452			−0.787260	−	0.616621i	$-0.788501\pi$
$593$	−38.3421			−1.57452			−0.787260	+	0.616621i	$0.788501\pi$
$594$	1.31955	+	15.1117i	0.0541418	+	0.620042i
$595$		0			0
$596$	−9.01628	−	15.6167i	−0.369321	−	0.639683i
$597$	−9.51340	+	28.7044i	−0.389358	+	1.17479i
$598$	−2.12570	+	3.68182i	−0.0869262	+	0.150561i
$599$	5.07665	−	8.79301i	0.207426	−	0.359273i	−0.743477	−	0.668762i	$-0.766825\pi$
$599$	5.07665	−	8.79301i	0.207426	−	0.359273i	0.950903	+	0.309489i	$0.100158\pi$
$600$		0			0
$601$	10.6371	+	18.4241i	0.433898	+	0.751533i	0.997205	−	0.0747146i	$-0.0238046\pi$
$601$	10.6371	+	18.4241i	0.433898	+	0.751533i	−0.563307	+	0.826248i	$0.690471\pi$
$602$	9.31344			0.379587
$603$	−2.70745	+	1.16752i	−0.110256	+	0.0475450i
$604$	18.3219			0.745508
$605$		0			0
$606$	3.79846	+	4.26878i	0.154302	+	0.173407i
$607$	−18.8678	+	32.6799i	−0.765819	+	1.32644i	0.173993	+	0.984747i	$0.444333\pi$
$607$	−18.8678	+	32.6799i	−0.765819	+	1.32644i	−0.939812	+	0.341691i	$0.889000\pi$
$608$	0.864808	−	1.49789i	0.0350726	−	0.0607475i
$609$	4.97618	+	5.59232i	0.201645	+	0.226612i
$610$		0			0
$611$	−24.3698			−0.985895
$612$	15.5026	−	6.68513i	0.626657	−	0.270230i
$613$	32.2633			1.30310			0.651551	−	0.758605i	$-0.274119\pi$
$613$	32.2633			1.30310			0.651551	+	0.758605i	$0.274119\pi$
$614$	−8.09699	−	14.0244i	−0.326768	−	0.565979i
$615$		0			0
$616$	−14.1268	+	24.4684i	−0.569186	+	0.985860i
$617$	−13.0089	+	22.5321i	−0.523719	+	0.907108i	0.475900	+	0.879499i	$0.342122\pi$
$617$	−13.0089	+	22.5321i	−0.523719	+	0.907108i	−0.999619	+	0.0276084i	$0.991211\pi$
$618$	1.57694	−	4.75805i	0.0634339	−	0.191397i
$619$	5.94077	+	10.2897i	0.238780	+	0.413578i	0.960364	−	0.278748i	$-0.0899193\pi$
$619$	5.94077	+	10.2897i	0.238780	+	0.413578i	−0.721585	+	0.692326i	$0.756586\pi$
$620$		0			0
$621$	1.90429	+	21.8083i	0.0764165	+	0.875136i
$622$	−10.9037			−0.437197
$623$	−8.03440	−	13.9160i	−0.321891	−	0.557532i
$624$	3.14447	−	9.48769i	0.125879	−	0.379811i
$625$		0			0
$626$	0.849799	−	1.47189i	0.0339648	−	0.0588288i
$627$	−3.72788	+	0.769527i	−0.148877	+	0.0307319i
$628$	−0.943614	−	1.63439i	−0.0376543	−	0.0652191i
$629$	11.5107			0.458962
$630$		0			0
$631$	−13.2726			−0.528372			−0.264186	−	0.964472i	$-0.585103\pi$
$631$	−13.2726			−0.528372			−0.264186	+	0.964472i	$0.585103\pi$
$632$	8.46279	+	14.6580i	0.336632	+	0.583063i
$633$	1.88443	+	2.11775i	0.0748992	+	0.0841731i
$634$	−3.11890	+	5.40210i	−0.123867	+	0.214545i
$635$		0			0
$636$	19.2938	+	21.6827i	0.765048	+	0.859774i
$637$	−0.459251	−	0.795445i	−0.0181962	−	0.0315167i
$638$	4.92265			0.194890
$639$	15.4839	+	11.5300i	0.612533	+	0.456120i
$640$		0			0
$641$	−22.4075	−	38.8109i	−0.885042	−	1.53294i	−0.845665	−	0.533713i	$-0.820796\pi$
$641$	−22.4075	−	38.8109i	−0.885042	−	1.53294i	−0.0393765	−	0.999224i	$-0.512537\pi$
$642$	−11.6682	+	2.40862i	−0.460509	+	0.0950606i
$643$	−7.46275	+	12.9259i	−0.294302	+	0.509747i	−0.974822	−	0.222983i	$-0.928421\pi$
$643$	−7.46275	+	12.9259i	−0.294302	+	0.509747i	0.680520	+	0.732729i	$0.261754\pi$
$644$	−9.58886	+	16.6084i	−0.377854	+	0.654462i
$645$		0			0
$646$	−0.267121	−	0.462667i	−0.0105097	−	0.0182034i
$647$	41.2684			1.62243			0.811214	−	0.584749i	$-0.198807\pi$
$647$	41.2684			1.62243			0.811214	+	0.584749i	$0.198807\pi$
$648$	4.60927	+	15.4086i	0.181069	+	0.605306i
$649$	−63.0179			−2.47367
$650$		0			0
$651$	−11.5337	+	34.8003i	−0.452043	+	1.36393i
$652$	15.2193	−	26.3606i	0.596034	−	1.03236i
$653$	13.8126	−	23.9241i	0.540528	−	0.936223i	−0.458345	−	0.888774i	$-0.651558\pi$
$653$	13.8126	−	23.9241i	0.540528	−	0.936223i	0.998874	−	0.0474484i	$-0.0151090\pi$
$654$	−1.52699	+	0.315209i	−0.0597100	+	0.0123256i
$655$		0			0
$656$	−7.39788			−0.288839
$657$	15.9160	+	11.8518i	0.620943	+	0.462383i
$658$	13.8630			0.540435
$659$	−20.0112	−	34.6605i	−0.779527	−	1.35018i	−0.932215	−	0.361905i	$-0.882126\pi$
$659$	−20.0112	−	34.6605i	−0.779527	−	1.35018i	0.152688	−	0.988274i	$-0.451207\pi$
$660$		0			0
$661$	−12.4965	+	21.6445i	−0.486056	+	0.841874i	−0.999872	−	0.0160270i	$-0.994898\pi$
$661$	−12.4965	+	21.6445i	−0.486056	+	0.841874i	0.513816	+	0.857901i	$0.328232\pi$
$662$	0.279818	−	0.484659i	0.0108754	−	0.0188368i
$663$	−7.77924	−	8.74245i	−0.302121	−	0.339529i
$664$	−9.31018	−	16.1257i	−0.361305	−	0.625799i
$665$		0			0
$666$	−0.599338	+	5.12269i	−0.0232239	+	0.198500i
$667$	7.10405			0.275070
$668$	3.88369	+	6.72675i	0.150264	+	0.260266i
$669$	−13.1426	+	2.71296i	−0.508122	+	0.104889i
$670$		0			0
$671$	−0.0339063	+	0.0587274i	−0.00130894	+	0.00226715i
$672$	−6.78030	+	20.4579i	−0.261556	+	0.789182i
$673$	−20.4024	−	35.3380i	−0.786454	−	1.36218i	−0.928126	−	0.372265i	$-0.878581\pi$
$673$	−20.4024	−	35.3380i	−0.786454	−	1.36218i	0.141672	−	0.989914i	$-0.454752\pi$
$674$	−11.7365			−0.452072
$675$		0			0
$676$	15.0133			0.577436
$677$	20.5947	+	35.6710i	0.791518	+	1.37095i	0.925027	+	0.379901i	$0.124042\pi$
$677$	20.5947	+	35.6710i	0.791518	+	1.37095i	−0.133509	+	0.991048i	$0.542625\pi$
$678$	1.69663	−	5.11919i	0.0651587	−	0.196601i
$679$	−9.23569	+	15.9967i	−0.354433	+	0.613896i
$680$		0			0
$681$	19.1007	−	3.94286i	0.731939	−	0.151091i
$682$	12.0545	+	20.8789i	0.461589	+	0.799496i
$683$	−1.33820			−0.0512047			−0.0256023	−	0.999672i	$-0.508150\pi$
$683$	−1.33820			−0.0512047			−0.0256023	+	0.999672i	$0.508150\pi$
$684$	−1.74306	+	0.751652i	−0.0666476	+	0.0287401i
$685$		0			0
$686$	4.50667	+	7.80578i	0.172065	+	0.298026i
$687$	12.0637	+	13.5574i	0.460261	+	0.517249i
$688$	−10.3899	+	17.9958i	−0.396110	+	0.686083i
$689$	10.0592	−	17.4230i	0.383225	−	0.663764i
$690$		0			0
$691$	12.6407	+	21.8943i	0.480874	+	0.832898i	0.999759	−	0.0219459i	$-0.00698617\pi$
$691$	12.6407	+	21.8943i	0.480874	+	0.832898i	−0.518885	+	0.854844i	$0.673653\pi$
$692$	−26.0368			−0.989770
$693$	43.5544	−	18.7817i	1.65449	−	0.713459i
$694$	10.4917			0.398258
$695$		0			0
$696$	5.11148	−	1.05514i	0.193750	−	0.0399949i
$697$	−4.33074	+	7.50106i	−0.164039	+	0.284123i
$698$	3.53012	−	6.11435i	0.133617	−	0.231432i
$699$	−1.58137	+	4.77142i	−0.0598130	+	0.180472i
$700$		0			0
$701$	−18.2064			−0.687645			−0.343822	−	0.939035i	$-0.611722\pi$
$701$	−18.2064			−0.687645			−0.343822	+	0.939035i	$0.611722\pi$
$702$	4.29576	−	3.00685i	0.162133	−	0.113486i
$703$	−1.29422			−0.0488126
$704$	−9.60795	−	16.6415i	−0.362113	−	0.627199i
$705$		0			0
$706$	−4.00244	+	6.93242i	−0.150634	+	0.260905i
$707$	8.93344	−	15.4732i	0.335977	−	0.581929i
$708$	−30.7770	+	6.35315i	−1.15667	+	0.238766i
$709$	−20.9103	−	36.2177i	−0.785304	−	1.36019i	−0.928818	−	0.370537i	$-0.879174\pi$
$709$	−20.9103	−	36.2177i	−0.785304	−	1.36019i	0.143514	−	0.989648i	$-0.454160\pi$
$710$		0			0
$711$	3.30184	−	28.2216i	0.123829	−	1.05839i
$712$	−11.2036			−0.419871
$713$	17.3962	+	30.1312i	0.651494	+	1.12842i
$714$	4.42529	+	4.97322i	0.165612	+	0.186118i
$715$		0			0
$716$	−6.10079	+	10.5669i	−0.227997	+	0.394903i
$717$	−18.8303	−	21.1619i	−0.703231	−	0.790304i
$718$	0.150650	+	0.260934i	0.00562222	+	0.00973797i
$719$	48.9786			1.82660			0.913298	−	0.407293i	$-0.133527\pi$
$719$	48.9786			1.82660			0.913298	+	0.407293i	$0.133527\pi$
$720$		0			0
$721$	−15.6734			−0.583707
$722$	−4.46588	−	7.73514i	−0.166203	−	0.287872i
$723$	29.7255	−	6.13610i	1.10550	−	0.228204i
$724$	−9.74236	+	16.8743i	−0.362072	+	0.627127i
$725$		0			0
$726$	6.97598	−	21.0484i	0.258903	−	0.781179i
$727$	−21.9005	−	37.9327i	−0.812243	−	1.40685i	−0.911291	−	0.411764i	$-0.864913\pi$
$727$	−21.9005	−	37.9327i	−0.812243	−	1.40685i	0.0990474	−	0.995083i	$-0.468420\pi$
$728$	9.76642			0.361968
$729$	9.24306	−	25.3686i	0.342336	−	0.939578i
$730$		0			0
$731$	12.1645	+	21.0696i	0.449922	+	0.779287i
$732$	−0.0106387	+	0.0320999i	−0.000393219	+	0.00118645i
$733$	−3.39332	+	5.87740i	−0.125335	+	0.217087i	−0.921864	−	0.387514i	$-0.873334\pi$
$733$	−3.39332	+	5.87740i	−0.125335	+	0.217087i	0.796529	+	0.604601i	$0.206667\pi$
$734$	−4.75572	+	8.23715i	−0.175537	+	0.304039i
$735$		0			0
$736$	10.2267	+	17.7131i	0.376960	+	0.652913i
$737$	6.06261			0.223319
$738$	−3.11276	−	2.31790i	−0.114582	−	0.0853232i
$739$	28.7245			1.05665			0.528324	−	0.849043i	$-0.322821\pi$
$739$	28.7245			1.05665			0.528324	+	0.849043i	$0.322821\pi$
$740$		0			0
$741$	0.874670	+	0.982970i	0.0321318	+	0.0361103i
$742$	−5.72226	+	9.91125i	−0.210071	+	0.363853i
$743$	−15.7262	+	27.2385i	−0.576937	+	0.999284i	0.418891	+	0.908036i	$0.362419\pi$
$743$	−15.7262	+	27.2385i	−0.576937	+	0.999284i	−0.995828	+	0.0912477i	$0.970915\pi$
$744$	16.9921	+	19.0961i	0.622962	+	0.700096i
$745$		0			0
$746$	−9.29610			−0.340354
$747$	−3.63246	+	31.0475i	−0.132905	+	1.13597i
$748$	−34.7141			−1.26927
$749$	18.6268	+	32.2626i	0.680610	+	1.17885i
$750$		0			0
$751$	−5.47659	+	9.48574i	−0.199844	+	0.346139i	−0.948478	−	0.316844i	$-0.897377\pi$
$751$	−5.47659	+	9.48574i	−0.199844	+	0.346139i	0.748634	+	0.662984i	$0.230710\pi$
$752$	−15.4652	+	26.7866i	−0.563959	+	0.976806i
$753$	−4.61530	+	13.9256i	−0.168191	+	0.507476i
$754$	−0.850804	−	1.47364i	−0.0309845	−	0.0536667i
$755$		0			0
$756$	19.3778	−	13.5637i	0.704765	−	0.493306i
$757$	45.7942			1.66442			0.832210	−	0.554461i	$-0.187075\pi$
$757$	45.7942			1.66442			0.832210	+	0.554461i	$0.187075\pi$
$758$	−1.87934	−	3.25511i	−0.0682607	−	0.118231i
$759$	14.1610	−	42.7273i	0.514010	−	1.55090i
$760$		0			0
$761$	16.9569	−	29.3702i	0.614687	−	1.06467i	−0.375753	−	0.926720i	$-0.622616\pi$
$761$	16.9569	−	29.3702i	0.614687	−	1.06467i	0.990439	−	0.137948i	$-0.0440508\pi$
$762$	−7.43242	+	1.53424i	−0.269248	+	0.0555796i
$763$	2.43764	+	4.22212i	0.0882485	+	0.152851i
$764$	−24.3894			−0.882378
$765$		0			0
$766$	−14.7602			−0.533309
$767$	10.8917	+	18.8649i	0.393275	+	0.681173i
$768$	−1.07930	−	1.21294i	−0.0389459	−	0.0437680i
$769$	−3.57986	+	6.20050i	−0.129093	+	0.223596i	−0.923325	−	0.384018i	$-0.874540\pi$
$769$	−3.57986	+	6.20050i	−0.129093	+	0.223596i	0.794232	+	0.607614i	$0.207873\pi$
$770$		0			0
$771$	−3.30737	−	3.71688i	−0.119112	−	0.133860i
$772$	0.428355	+	0.741933i	0.0154168	+	0.0267027i
$773$	14.5998			0.525117			0.262558	−	0.964916i	$-0.415434\pi$
$773$	14.5998			0.525117			0.262558	+	0.964916i	$0.415434\pi$
$774$	−10.0101	+	4.31662i	−0.359806	+	0.155158i
$775$		0			0
$776$	6.43935	+	11.1533i	0.231159	+	0.400379i

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.236627 + 0.409850i) q^{2} +(-0.544899 + 1.64411i) q^{3} +(0.888015 - 1.53809i) q^{4} +(-0.802776 + 0.165713i) q^{6} +(1.28153 + 2.21967i) q^{7} +1.78702 q^{8} +(-2.40617 - 1.79175i) q^{9} +O(q^{10})\)	\(q+(0.236627 + 0.409850i) q^{2} +(-0.544899 + 1.64411i) q^{3} +(0.888015 - 1.53809i) q^{4} +(-0.802776 + 0.165713i) q^{6} +(1.28153 + 2.21967i) q^{7} +1.78702 q^{8} +(-2.40617 - 1.79175i) q^{9} +(3.08430 + 5.34217i) q^{11} +(2.04490 + 2.29809i) q^{12} +(1.06615 - 1.84662i) q^{13} +(-0.606488 + 1.05047i) q^{14} +(-1.35317 - 2.34376i) q^{16} -3.16860 q^{17} +(0.164982 - 1.41015i) q^{18} +0.356267 q^{19} +(-4.34768 + 0.897469i) q^{21} +(-1.45966 + 2.52821i) q^{22} +(-2.10649 + 3.64854i) q^{23} +(-0.973748 + 2.93806i) q^{24} +1.00912 q^{26} +(4.25694 - 2.97968i) q^{27} +4.55206 q^{28} +(-0.843116 - 1.46032i) q^{29} +(4.12920 - 7.15199i) q^{31} +(2.42742 - 4.20441i) q^{32} +(-10.4637 + 2.15998i) q^{33} +(-0.749778 - 1.29865i) q^{34} +(-4.89257 + 2.10980i) q^{36} -3.63274 q^{37} +(0.0843024 + 0.146016i) q^{38} +(2.45510 + 2.75908i) q^{39} +(1.36677 - 2.36731i) q^{41} +(-1.39661 - 1.56953i) q^{42} +(-3.83908 - 6.64949i) q^{43} +10.9556 q^{44} -1.99381 q^{46} +(-5.71444 - 9.89770i) q^{47} +(4.59074 - 0.947643i) q^{48} +(0.215378 - 0.373046i) q^{49} +(1.72657 - 5.20952i) q^{51} +(-1.89351 - 3.27966i) q^{52} +9.43507 q^{53} +(2.22853 + 1.03964i) q^{54} +(2.29012 + 3.96660i) q^{56} +(-0.194129 + 0.585740i) q^{57} +(0.399008 - 0.691103i) q^{58} +(-5.10795 + 8.84723i) q^{59} +(0.00549659 + 0.00952038i) q^{61} +3.90833 q^{62} +(0.893512 - 7.63707i) q^{63} -3.11511 q^{64} +(-3.36127 - 3.77745i) q^{66} +(0.491409 - 0.851145i) q^{67} +(-2.81377 + 4.87359i) q^{68} +(-4.85077 - 5.45138i) q^{69} -6.43507 q^{71} +(-4.29988 - 3.20189i) q^{72} -6.61467 q^{73} +(-0.859605 - 1.48888i) q^{74} +(0.316370 - 0.547969i) q^{76} +(-7.90523 + 13.6923i) q^{77} +(-0.549868 + 1.65910i) q^{78} +(4.73569 + 8.20246i) q^{79} +(2.57930 + 8.62248i) q^{81} +1.29366 q^{82} +(-5.20988 - 9.02378i) q^{83} +(-2.48042 + 7.48407i) q^{84} +(1.81686 - 3.14690i) q^{86} +(2.86033 - 0.590444i) q^{87} +(5.51172 + 9.54658i) q^{88} -6.26940 q^{89} +5.46519 q^{91} +(3.74119 + 6.47993i) q^{92} +(9.50863 + 10.6860i) q^{93} +(2.70439 - 4.68413i) q^{94} +(5.58980 + 6.28191i) q^{96} +(3.60339 + 6.24126i) q^{97} +0.203858 q^{98} +(2.15045 - 18.3804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + q^{3} - 4 q^{4} + 8 q^{6} + q^{7} + 18 q^{8} + 5 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + q^3 - 4 * q^4 + 8 * q^6 + q^7 + 18 * q^8 + 5 * q^9	\( 8 q - 2 q^{2} + q^{3} - 4 q^{4} + 8 q^{6} + q^{7} + 18 q^{8} + 5 q^{9} + q^{11} + 11 q^{12} - 2 q^{13} - 3 q^{14} - 4 q^{16} + 22 q^{17} - 5 q^{18} + 4 q^{19} - 15 q^{21} - 3 q^{22} - 15 q^{23} - 33 q^{24} - 20 q^{26} - 2 q^{27} - 8 q^{28} - q^{29} + 4 q^{31} - 10 q^{32} - 28 q^{33} - 9 q^{34} - 14 q^{36} - 2 q^{37} - 23 q^{38} + 25 q^{39} + 5 q^{41} - 21 q^{42} + 10 q^{43} + 44 q^{44} - 20 q^{47} + 53 q^{48} + 3 q^{49} + 11 q^{51} - 17 q^{52} + 40 q^{53} + 26 q^{54} + 30 q^{56} - 8 q^{57} + 18 q^{58} - 17 q^{59} + 13 q^{61} - 12 q^{62} + 9 q^{63} + 38 q^{64} - 8 q^{66} - 17 q^{67} - 34 q^{68} - 27 q^{69} - 16 q^{71} + 18 q^{72} + 4 q^{73} - 40 q^{74} - 11 q^{76} - 12 q^{77} - 61 q^{78} + 7 q^{79} + 17 q^{81} + 24 q^{82} - 30 q^{83} + 27 q^{84} + 34 q^{86} - 23 q^{87} - 9 q^{88} - 18 q^{89} - 34 q^{91} + 12 q^{92} + 15 q^{93} - 3 q^{94} + 34 q^{96} + 19 q^{97} + 26 q^{98} - 17 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + q^3 - 4 * q^4 + 8 * q^6 + q^7 + 18 * q^8 + 5 * q^9 + q^11 + 11 * q^12 - 2 * q^13 - 3 * q^14 - 4 * q^16 + 22 * q^17 - 5 * q^18 + 4 * q^19 - 15 * q^21 - 3 * q^22 - 15 * q^23 - 33 * q^24 - 20 * q^26 - 2 * q^27 - 8 * q^28 - q^29 + 4 * q^31 - 10 * q^32 - 28 * q^33 - 9 * q^34 - 14 * q^36 - 2 * q^37 - 23 * q^38 + 25 * q^39 + 5 * q^41 - 21 * q^42 + 10 * q^43 + 44 * q^44 - 20 * q^47 + 53 * q^48 + 3 * q^49 + 11 * q^51 - 17 * q^52 + 40 * q^53 + 26 * q^54 + 30 * q^56 - 8 * q^57 + 18 * q^58 - 17 * q^59 + 13 * q^61 - 12 * q^62 + 9 * q^63 + 38 * q^64 - 8 * q^66 - 17 * q^67 - 34 * q^68 - 27 * q^69 - 16 * q^71 + 18 * q^72 + 4 * q^73 - 40 * q^74 - 11 * q^76 - 12 * q^77 - 61 * q^78 + 7 * q^79 + 17 * q^81 + 24 * q^82 - 30 * q^83 + 27 * q^84 + 34 * q^86 - 23 * q^87 - 9 * q^88 - 18 * q^89 - 34 * q^91 + 12 * q^92 + 15 * q^93 - 3 * q^94 + 34 * q^96 + 19 * q^97 + 26 * q^98 - 17 * q^99

Introduction

L-functions

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