LMFDB - Embedded newform 225.2.e.c.76.4

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			76.4
Root			$-0.816862 - 1.41485i$ of defining polynomial
Character	$\chi$	$=$	225.76
Dual form			225.2.e.c.151.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.816862 + 1.41485i) q^{2} +(1.06419 - 1.36657i) q^{3} +(-0.334526 + 0.579416i) q^{4} +(2.80278 + 0.389365i) q^{6} +(0.252674 + 0.437645i) q^{7} +2.17440 q^{8} +(-0.735010 - 2.90857i) q^{9} +O(q^{10})$	\(q+(0.816862 + 1.41485i) q^{2} +(1.06419 - 1.36657i) q^{3} +(-0.334526 + 0.579416i) q^{4} +(2.80278 + 0.389365i) q^{6} +(0.252674 + 0.437645i) q^{7} +2.17440 q^{8} +(-0.735010 - 2.90857i) q^{9} +(-1.55010 - 2.68485i) q^{11} +(0.435812 + 1.07376i) q^{12} +(-3.11964 + 5.40337i) q^{13} +(-0.412800 + 0.714990i) q^{14} +(2.44524 + 4.23527i) q^{16} +6.10020 q^{17} +(3.51477 - 3.41582i) q^{18} -5.57022 q^{19} +(0.866963 + 0.120440i) q^{21} +(2.53244 - 4.38631i) q^{22} +(-1.91280 + 3.31307i) q^{23} +(2.31397 - 2.97146i) q^{24} -10.1932 q^{26} +(-4.75694 - 2.09082i) q^{27} -0.338104 q^{28} +(-1.22966 - 2.12984i) q^{29} +(-2.11429 + 3.66206i) q^{31} +(-1.82044 + 3.15309i) q^{32} +(-5.31863 - 0.738871i) q^{33} +(4.98302 + 8.63085i) q^{34} +(1.93115 + 0.547115i) q^{36} -6.72677 q^{37} +(-4.55010 - 7.88101i) q^{38} +(4.06419 + 10.0134i) q^{39} +(2.72092 - 4.71278i) q^{41} +(0.537785 + 1.32500i) q^{42} +(0.663704 + 1.14957i) q^{43} +2.07420 q^{44} -6.24997 q^{46} +(-1.85396 - 3.21115i) q^{47} +(8.38998 + 1.16555i) q^{48} +(3.37231 - 5.84101i) q^{49} +(6.49176 - 8.33633i) q^{51} +(-2.08720 - 3.61514i) q^{52} -2.54205 q^{53} +(-0.927572 - 8.43825i) q^{54} +(0.549415 + 0.951614i) q^{56} +(-5.92776 + 7.61208i) q^{57} +(2.00893 - 3.47956i) q^{58} +(-1.44116 + 2.49616i) q^{59} +(1.42173 + 2.46250i) q^{61} -6.90833 q^{62} +(1.08720 - 1.05659i) q^{63} +3.83276 q^{64} +(-3.29920 - 8.12860i) q^{66} +(1.20326 - 2.08411i) q^{67} +(-2.04068 + 3.53456i) q^{68} +(2.49195 + 6.13969i) q^{69} +5.54205 q^{71} +(-1.59821 - 6.32439i) q^{72} +11.7988 q^{73} +(-5.49484 - 9.51734i) q^{74} +(1.86338 - 3.22748i) q^{76} +(0.783341 - 1.35679i) q^{77} +(-10.8475 + 13.9298i) q^{78} +(-1.70149 - 2.94707i) q^{79} +(-7.91952 + 4.27565i) q^{81} +8.89047 q^{82} +(-6.95059 - 12.0388i) q^{83} +(-0.359807 + 0.462042i) q^{84} +(-1.08431 + 1.87808i) q^{86} +(-4.21915 - 0.586130i) q^{87} +(-3.37054 - 5.83795i) q^{88} +3.38513 q^{89} -3.15301 q^{91} +(-1.27976 - 2.21661i) q^{92} +(2.75444 + 6.78643i) q^{93} +(3.02886 - 5.24614i) q^{94} +(2.37162 + 5.84324i) q^{96} +(5.53779 + 9.59173i) q^{97} +11.0188 q^{98} +(-6.66974 + 6.48197i) 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 $

$2$	0.816862	+	1.41485i	0.577608	+	1.00045i	0.995753	+	0.0920666i	$0.0293473\pi$
$2$	0.816862	+	1.41485i	0.577608	+	1.00045i	−0.418144	+	0.908381i	$0.637319\pi$
$3$	1.06419	−	1.36657i	0.614409	−	0.788988i
$3$	1.06419	−	1.36657i	0.614409	−	0.788988i
$4$	−0.334526	+	0.579416i	−0.167263	+	0.289708i
$5$		0			0
$5$		0			0
$6$	2.80278	+	0.389365i	1.14423	+	0.158958i
$7$	0.252674	+	0.437645i	0.0955019	+	0.165414i	0.909818	−	0.415008i	$-0.136221\pi$
$7$	0.252674	+	0.437645i	0.0955019	+	0.165414i	−0.814316	+	0.580422i	$0.802888\pi$
$8$	2.17440			0.768767
$9$	−0.735010	−	2.90857i	−0.245003	−	0.969522i
$10$		0			0
$11$	−1.55010	−	2.68485i	−0.467373	−	0.809514i	0.531932	−	0.846787i	$-0.321466\pi$
$11$	−1.55010	−	2.68485i	−0.467373	−	0.809514i	−0.999305	+	0.0372730i	$0.988133\pi$
$12$	0.435812	+	1.07376i	0.125808	+	0.309968i
$13$	−3.11964	+	5.40337i	−0.865232	+	1.49863i	0.00158518	+	0.999999i	$0.499495\pi$
$13$	−3.11964	+	5.40337i	−0.865232	+	1.49863i	−0.866817	+	0.498627i	$0.833838\pi$
$14$	−0.412800	+	0.714990i	−0.110325	+	0.191089i
$15$		0			0
$16$	2.44524	+	4.23527i	0.611309	+	1.05882i
$17$	6.10020			1.47952			0.739758	−	0.672873i	$-0.234940\pi$
$17$	6.10020			1.47952			0.739758	+	0.672873i	$0.234940\pi$
$18$	3.51477	−	3.41582i	0.828440	−	0.805117i
$19$	−5.57022			−1.27790			−0.638948	−	0.769250i	$-0.720630\pi$
$19$	−5.57022			−1.27790			−0.638948	+	0.769250i	$0.720630\pi$
$20$		0			0
$21$	0.866963	+	0.120440i	0.189187	+	0.0262821i
$22$	2.53244	−	4.38631i	0.539917	−	0.935164i
$23$	−1.91280	+	3.31307i	−0.398846	+	0.690822i	−0.993584	−	0.113098i	$-0.963923\pi$
$23$	−1.91280	+	3.31307i	−0.398846	+	0.690822i	0.594738	+	0.803920i	$0.297256\pi$
$24$	2.31397	−	2.97146i	0.472337	−	0.606547i
$25$		0			0
$26$	−10.1932			−1.99906
$27$	−4.75694	−	2.09082i	−0.915473	−	0.402379i
$28$	−0.338104			−0.0638957
$29$	−1.22966	−	2.12984i	−0.228342	−	0.395501i	0.728975	−	0.684541i	$-0.239997\pi$
$29$	−1.22966	−	2.12984i	−0.228342	−	0.395501i	−0.957317	+	0.289040i	$0.906664\pi$
$30$		0			0
$31$	−2.11429	+	3.66206i	−0.379738	+	0.657725i	−0.991024	−	0.133685i	$-0.957319\pi$
$31$	−2.11429	+	3.66206i	−0.379738	+	0.657725i	0.611286	+	0.791409i	$0.290652\pi$
$32$	−1.82044	+	3.15309i	−0.321811	+	0.557394i
$33$	−5.31863	−	0.738871i	−0.925855	−	0.128621i
$34$	4.98302	+	8.63085i	0.854581	+	1.48018i
$35$		0			0
$36$	1.93115	+	0.547115i	0.321858	+	0.0911858i
$37$	−6.72677			−1.10587			−0.552937	−	0.833223i	$-0.686493\pi$
$37$	−6.72677			−1.10587			−0.552937	+	0.833223i	$0.686493\pi$
$38$	−4.55010	−	7.88101i	−0.738124	−	1.27847i
$39$	4.06419	+	10.0134i	0.650791	+	1.60343i
$40$		0			0
$41$	2.72092	−	4.71278i	0.424937	−	0.736012i	−0.571478	−	0.820618i	$-0.693630\pi$
$41$	2.72092	−	4.71278i	0.424937	−	0.736012i	0.996415	+	0.0846053i	$0.0269630\pi$
$42$	0.537785	+	1.32500i	0.0829821	+	0.204452i
$43$	0.663704	+	1.14957i	0.101214	+	0.175308i	0.912185	−	0.409779i	$-0.134394\pi$
$43$	0.663704	+	1.14957i	0.101214	+	0.175308i	−0.810971	+	0.585086i	$0.801061\pi$
$44$	2.07420			0.312697
$45$		0			0
$46$	−6.24997			−0.921508
$47$	−1.85396	−	3.21115i	−0.270428	−	0.468395i	0.698544	−	0.715568i	$-0.253832\pi$
$47$	−1.85396	−	3.21115i	−0.270428	−	0.468395i	−0.968971	+	0.247173i	$0.920499\pi$
$48$	8.38998	+	1.16555i	1.21099	+	0.168232i
$49$	3.37231	−	5.84101i	0.481759	−	0.834431i
$50$		0			0
$51$	6.49176	−	8.33633i	0.909028	−	1.16732i
$52$	−2.08720	−	3.61514i	−0.289443	−	0.501329i
$53$	−2.54205			−0.349177			−0.174589	−	0.984641i	$-0.555860\pi$
$53$	−2.54205			−0.349177			−0.174589	+	0.984641i	$0.555860\pi$
$54$	−0.927572	−	8.43825i	−0.126227	−	1.14830i
$55$		0			0
$56$	0.549415	+	0.951614i	0.0734187	+	0.127165i
$57$	−5.92776	+	7.61208i	−0.785151	+	1.00824i
$58$	2.00893	−	3.47956i	0.263785	−	0.456889i
$59$	−1.44116	+	2.49616i	−0.187623	+	0.324973i	−0.944457	−	0.328634i	$-0.893412\pi$
$59$	−1.44116	+	2.49616i	−0.187623	+	0.324973i	0.756834	+	0.653607i	$0.226745\pi$
$60$		0			0
$61$	1.42173	+	2.46250i	0.182033	+	0.315291i	0.942573	−	0.334001i	$-0.108399\pi$
$61$	1.42173	+	2.46250i	0.182033	+	0.315291i	−0.760539	+	0.649292i	$0.775065\pi$
$62$	−6.90833			−0.877358
$63$	1.08720	−	1.05659i	0.136974	−	0.133118i
$64$	3.83276			0.479095
$65$		0			0
$66$	−3.29920	−	8.12860i	−0.406103	−	1.00056i
$67$	1.20326	−	2.08411i	0.147002	−	0.254614i	−0.783116	−	0.621875i	$-0.786371\pi$
$67$	1.20326	−	2.08411i	0.147002	−	0.254614i	0.930118	+	0.367261i	$0.119704\pi$
$68$	−2.04068	+	3.53456i	−0.247468	+	0.428628i
$69$	2.49195	+	6.13969i	0.299995	+	0.739132i
$70$		0			0
$71$	5.54205			0.657720			0.328860	−	0.944379i	$-0.393336\pi$
$71$	5.54205			0.657720			0.328860	+	0.944379i	$0.393336\pi$
$72$	−1.59821	−	6.32439i	−0.188350	−	0.745336i
$73$	11.7988			1.38095			0.690473	−	0.723359i	$-0.257403\pi$
$73$	11.7988			1.38095			0.690473	+	0.723359i	$0.257403\pi$
$74$	−5.49484	−	9.51734i	−0.638762	−	1.10637i
$75$		0			0
$76$	1.86338	−	3.22748i	0.213745	−	0.370217i
$77$	0.783341	−	1.35679i	0.0892700	−	0.154620i
$78$	−10.8475	+	13.9298i	−1.22824	+	1.57723i
$79$	−1.70149	−	2.94707i	−0.191433	−	0.331571i	0.754293	−	0.656538i	$-0.227980\pi$
$79$	−1.70149	−	2.94707i	−0.191433	−	0.331571i	−0.945725	+	0.324967i	$0.894647\pi$
$80$		0			0
$81$	−7.91952	+	4.27565i	−0.879947	+	0.475072i
$82$	8.89047			0.981789
$83$	−6.95059	−	12.0388i	−0.762926	−	1.32143i	−0.941336	−	0.337470i	$-0.890429\pi$
$83$	−6.95059	−	12.0388i	−0.762926	−	1.32143i	0.178410	−	0.983956i	$-0.442905\pi$
$84$	−0.359807	+	0.462042i	−0.0392581	+	0.0504129i
$85$		0			0
$86$	−1.08431	+	1.87808i	−0.116924	+	0.202518i
$87$	−4.21915	−	0.586130i	−0.452341	−	0.0628398i
$88$	−3.37054	−	5.83795i	−0.359301	−	0.622327i
$89$	3.38513			0.358823			0.179411	−	0.983774i	$-0.442581\pi$
$89$	3.38513			0.358823			0.179411	+	0.983774i	$0.442581\pi$
$90$		0			0
$91$	−3.15301			−0.330525
$92$	−1.27976	−	2.21661i	−0.133425	−	0.231098i
$93$	2.75444	+	6.78643i	0.285623	+	0.703720i
$94$	3.02886	−	5.24614i	0.312403	−	0.541098i
$95$		0			0
$96$	2.37162	+	5.84324i	0.242053	+	0.596373i
$97$	5.53779	+	9.59173i	0.562277	+	0.973892i	0.997297	+	0.0734716i	$0.0234078\pi$
$97$	5.53779	+	9.59173i	0.562277	+	0.973892i	−0.435020	+	0.900421i	$0.643259\pi$
$98$	11.0188			1.11307
$99$	−6.66974	+	6.48197i	−0.670334	+	0.651462i
$100$		0			0
$101$	8.68451	+	15.0420i	0.864141	+	1.49674i	0.867897	+	0.496744i	$0.165471\pi$
$101$	8.68451	+	15.0420i	0.864141	+	1.49674i	−0.00375621	+	0.999993i	$0.501196\pi$
$102$	17.0975	+	2.37521i	1.69290	+	0.235181i
$103$	0.416378	−	0.721188i	0.0410269	−	0.0710608i	−0.844783	−	0.535109i	$-0.820270\pi$
$103$	0.416378	−	0.721188i	0.0410269	−	0.0710608i	0.885810	+	0.464049i	$0.153604\pi$
$104$	−6.78334	+	11.7491i	−0.665161	+	1.15209i
$105$		0			0
$106$	−2.07650	−	3.59661i	−0.201688	−	0.349334i
$107$	11.0684			1.07002			0.535012	−	0.844844i	$-0.320307\pi$
$107$	11.0684			1.07002			0.535012	+	0.844844i	$0.320307\pi$
$108$	2.80278	−	2.05681i	0.269697	−	0.197917i
$109$	−4.65836			−0.446190			−0.223095	−	0.974797i	$-0.571616\pi$
$109$	−4.65836			−0.446190			−0.223095	+	0.974797i	$0.571616\pi$
$110$		0			0
$111$	−7.15854	+	9.19258i	−0.679459	+	0.872521i
$112$	−1.23570	+	2.14029i	−0.116762	+	0.202238i
$113$	−5.99711	+	10.3873i	−0.564160	+	0.977155i	0.432967	+	0.901410i	$0.357467\pi$
$113$	−5.99711	+	10.3873i	−0.564160	+	0.977155i	−0.997127	+	0.0757447i	$0.975867\pi$
$114$	−15.6121	−	2.16885i	−1.46221	−	0.203132i
$115$		0			0
$116$	1.64542			0.152773
$117$	18.0090	+	5.10214i	1.66494	+	0.471693i
$118$	−4.70892			−0.433491
$119$	1.54136	+	2.66972i	0.141297	+	0.244733i
$120$		0			0
$121$	0.694371	−	1.20269i	0.0631246	−	0.109335i
$122$	−2.32271	+	4.02305i	−0.210288	+	0.364230i
$123$	−3.54475	−	8.73360i	−0.319620	−	0.787483i
$124$	−1.41457	−	2.45011i	−0.127032	−	0.220026i
$125$		0			0
$126$	2.38301	+	0.675131i	0.212295	+	0.0601454i
$127$	−3.22858			−0.286490			−0.143245	−	0.989687i	$-0.545754\pi$
$127$	−3.22858			−0.286490			−0.143245	+	0.989687i	$0.545754\pi$
$128$	6.77171	+	11.7289i	0.598540	+	1.03670i
$129$	2.27727	+	0.316361i	0.200502	+	0.0278540i
$130$		0			0
$131$	4.69256	−	8.12776i	0.409991	−	0.710125i	−0.584897	−	0.811107i	$-0.698865\pi$
$131$	4.69256	−	8.12776i	0.409991	−	0.710125i	0.994888	+	0.100982i	$0.0321985\pi$
$132$	2.20734	−	2.83453i	0.192124	−	0.246714i
$133$	−1.40745	−	2.43778i	−0.122042	−	0.211382i
$134$	3.93159			0.339637
$135$		0			0
$136$	13.2643			1.13740
$137$	−1.15478	−	2.00013i	−0.0986593	−	0.170883i	0.812471	−	0.583002i	$-0.198122\pi$
$137$	−1.15478	−	2.00013i	−0.0986593	−	0.170883i	−0.911130	+	0.412119i	$0.864789\pi$
$138$	−6.65114	+	8.54100i	−0.566183	+	0.727059i
$139$	−5.44701	+	9.43449i	−0.462009	+	0.800223i	−0.999061	−	0.0433260i	$-0.986205\pi$
$139$	−5.44701	+	9.43449i	−0.462009	+	0.800223i	0.537052	+	0.843549i	$0.319538\pi$
$140$		0			0
$141$	−6.36122	−	0.883709i	−0.535711	−	0.0744217i
$142$	4.52709	+	7.84115i	0.379905	+	0.658014i
$143$	19.3430			1.61754
$144$	10.5213	−	10.2251i	0.876775	−	0.852092i
$145$		0			0
$146$	9.63799	+	16.6935i	0.797646	+	1.38156i
$147$	−4.39337	−	10.8244i	−0.362359	−	0.892783i
$148$	2.25028	−	3.89760i	0.184972	−	0.320381i
$149$	8.17151	−	14.1535i	0.669436	−	1.15950i	−0.308626	−	0.951183i	$-0.599869\pi$
$149$	8.17151	−	14.1535i	0.669436	−	1.15950i	0.978062	−	0.208314i	$-0.0667975\pi$
$150$		0			0
$151$	−11.3913	−	19.7304i	−0.927015	−	1.60564i	−0.788288	−	0.615306i	$-0.789032\pi$
$151$	−11.3913	−	19.7304i	−0.927015	−	1.60564i	−0.138727	−	0.990331i	$-0.544301\pi$
$152$	−12.1119			−0.982404
$153$	−4.48371	−	17.7428i	−0.362486	−	1.43442i
$154$	2.55953			0.206252
$155$		0			0
$156$	−7.16150	−	0.994885i	−0.573379	−	0.0796545i
$157$	−6.23035	+	10.7913i	−0.497236	+	0.861238i	−0.999995	−	0.00318877i	$-0.998985\pi$
$157$	−6.23035	+	10.7913i	−0.497236	+	0.861238i	0.502759	+	0.864427i	$0.332318\pi$
$158$	2.77976	−	4.81469i	0.221146	−	0.383036i
$159$	−2.70522	+	3.47388i	−0.214538	+	0.275497i
$160$		0			0
$161$	−1.93326			−0.152362
$162$	−12.5185	−	7.71229i	−0.983549	−	0.605935i
$163$	−7.57384			−0.593229			−0.296614	−	0.954997i	$-0.595858\pi$
$163$	−7.57384			−0.593229			−0.296614	+	0.954997i	$0.595858\pi$
$164$	1.82044	+	3.15309i	0.142152	+	0.246215i
$165$		0			0
$166$	11.3553	−	19.6680i	0.881345	−	1.52653i
$167$	1.48837	−	2.57793i	0.115174	−	0.199486i	−0.802676	−	0.596416i	$-0.796591\pi$
$167$	1.48837	−	2.57793i	0.115174	−	0.199486i	0.917849	+	0.396929i	$0.129924\pi$
$168$	1.88513	+	0.261884i	0.145441	+	0.0202048i
$169$	−12.9643	−	22.4548i	−0.997252	−	1.72729i
$170$		0			0
$171$	4.09417	+	16.2014i	0.313089	+	1.23895i
$172$	−0.888105			−0.0677174
$173$	7.92649	+	13.7291i	0.602640	+	1.04380i	0.992420	+	0.122895i	$0.0392177\pi$
$173$	7.92649	+	13.7291i	0.602640	+	1.04380i	−0.389780	+	0.920908i	$0.627449\pi$
$174$	−2.61718	−	6.44824i	−0.198408	−	0.488840i
$175$		0			0
$176$	7.58073	−	13.1302i	0.571419	−	0.989727i
$177$	1.87751	+	4.62583i	0.141122	+	0.347699i
$178$	2.76518	+	4.78943i	0.207259	+	0.358983i
$179$	17.0841			1.27693			0.638463	−	0.769653i	$-0.279571\pi$
$179$	17.0841			1.27693			0.638463	+	0.769653i	$0.279571\pi$
$180$		0			0
$181$	13.3690			0.993712			0.496856	−	0.867833i	$-0.334488\pi$
$181$	13.3690			0.993712			0.496856	+	0.867833i	$0.334488\pi$
$182$	−2.57557	−	4.46102i	−0.190914	−	0.330673i
$183$	4.87816	+	0.677680i	0.360604	+	0.0500956i
$184$	−4.15919	+	7.20393i	−0.306620	+	0.531081i
$185$		0			0
$186$	−7.35176	+	9.44069i	−0.539057	+	0.692225i
$187$	−9.45593	−	16.3782i	−0.691486	−	1.19769i
$188$	2.48079			0.180930
$189$	−0.286920	−	2.61014i	−0.0208703	−	0.189860i
$190$		0			0
$191$	−12.6686	−	21.9427i	−0.916669	−	1.58772i	−0.804439	−	0.594035i	$-0.797534\pi$
$191$	−12.6686	−	21.9427i	−0.916669	−	1.58772i	−0.112230	−	0.993682i	$-0.535799\pi$
$192$	4.07877	−	5.23772i	0.294360	−	0.378000i
$193$	4.77976	−	8.27879i	0.344055	−	0.595921i	−0.641127	−	0.767435i	$-0.721533\pi$
$193$	4.77976	−	8.27879i	0.344055	−	0.595921i	0.985182	+	0.171515i	$0.0548660\pi$
$194$	−9.04721	+	15.6702i	−0.649552	+	1.12506i
$195$		0			0
$196$	2.25625	+	3.90794i	0.161161	+	0.279139i
$197$	−2.06841			−0.147368			−0.0736842	−	0.997282i	$-0.523476\pi$
$197$	−2.06841			−0.147368			−0.0736842	+	0.997282i	$0.523476\pi$
$198$	−14.6192	−	4.14178i	−1.03894	−	0.294344i
$199$	13.0970			0.928419			0.464210	−	0.885725i	$-0.346338\pi$
$199$	13.0970			0.928419			0.464210	+	0.885725i	$0.346338\pi$
$200$		0			0
$201$	−1.56758	−	3.86221i	−0.110568	−	0.272420i
$202$	−14.1881	+	24.5745i	−0.998271	+	1.72906i
$203$	0.621407	−	1.07631i	0.0436142	−	0.0755421i
$204$	2.65854	+	6.55015i	0.186135	+	0.458602i
$205$		0			0
$206$	1.36049			0.0947900
$207$	11.0422	+	3.12837i	0.767486	+	0.217437i
$208$	−30.5130			−2.11570
$209$	8.63441	+	14.9552i	0.597255	+	1.03448i
$210$		0			0
$211$	−5.55595	+	9.62318i	−0.382487	+	0.662487i	−0.991417	−	0.130737i	$-0.958266\pi$
$211$	−5.55595	+	9.62318i	−0.382487	+	0.662487i	0.608930	+	0.793224i	$0.291599\pi$
$212$	0.850382	−	1.47291i	0.0584045	−	0.101160i
$213$	5.89778	−	7.57358i	0.404109	−	0.518933i
$214$	9.04136	+	15.6601i	0.618055	+	1.07050i
$215$		0			0
$216$	−10.3435	−	4.54628i	−0.703785	−	0.309335i
$217$	−2.13690			−0.145063
$218$	−3.80523	−	6.59086i	−0.257723	−	0.446389i
$219$	12.5561	−	16.1238i	0.848465	−	1.08955i
$220$		0			0
$221$	−19.0304	+	32.9617i	−1.28012	+	2.21724i
$222$	−18.8536	−	2.61917i	−1.26537	−	0.175787i
$223$	1.94701	+	3.37231i	0.130381	+	0.225827i	0.923824	−	0.382819i	$-0.125047\pi$
$223$	1.94701	+	3.37231i	0.130381	+	0.225827i	−0.793442	+	0.608645i	$0.791713\pi$
$224$	−1.83991			−0.122934
$225$		0			0
$226$	−19.5952			−1.30346
$227$	−6.40406	−	11.0922i	−0.425053	−	0.736213i	0.571373	−	0.820691i	$-0.306411\pi$
$227$	−6.40406	−	11.0922i	−0.425053	−	0.736213i	−0.996425	+	0.0844781i	$0.973078\pi$
$228$	−2.42757	−	5.98108i	−0.160770	−	0.396107i
$229$	−3.32647	+	5.76162i	−0.219820	+	0.380739i	−0.954753	−	0.297401i	$-0.903880\pi$
$229$	−3.32647	+	5.76162i	−0.219820	+	0.380739i	0.734933	+	0.678140i	$0.237214\pi$
$230$		0			0
$231$	−1.02052	−	2.51436i	−0.0671451	−	0.165433i
$232$	−2.67378	−	4.63112i	−0.175542	−	0.304048i
$233$	−3.65836			−0.239667			−0.119833	−	0.992794i	$-0.538236\pi$
$233$	−3.65836			−0.239667			−0.119833	+	0.992794i	$0.538236\pi$
$234$	7.49214	+	29.6477i	0.489776	+	1.93813i
$235$		0			0
$236$	−0.964212	−	1.67006i	−0.0627648	−	0.108712i
$237$	−5.83807	−	0.811032i	−0.379223	−	0.0526822i
$238$	−2.51816	+	4.36158i	−0.163228	+	0.282720i
$239$	7.84576	−	13.5893i	0.507500	−	0.879016i	−0.492462	−	0.870334i	$-0.663903\pi$
$239$	7.84576	−	13.5893i	0.507500	−	0.879016i	0.999962	−	0.00868195i	$-0.00276358\pi$
$240$		0			0
$241$	−5.61248	−	9.72110i	−0.361532	−	0.626191i	0.626681	−	0.779276i	$-0.284413\pi$
$241$	−5.61248	−	9.72110i	−0.361532	−	0.626191i	−0.988213	+	0.153084i	$0.951079\pi$
$242$	2.26882			0.145845
$243$	−2.58489	+	15.3726i	−0.165821	+	0.986156i
$244$	−1.90242			−0.121790
$245$		0			0
$246$	9.46113	−	12.1494i	0.603220	−	0.774619i
$247$	17.3771	−	30.0980i	1.10568	−	1.91509i
$248$	−4.59731	+	7.96278i	−0.291930	+	0.505637i
$249$	−23.8485	−	3.31307i	−1.51134	−	0.209957i
$250$		0			0
$251$	6.94042			0.438075			0.219038	−	0.975716i	$-0.429708\pi$
$251$	6.94042			0.438075			0.219038	+	0.975716i	$0.429708\pi$
$252$	0.248510	+	0.983399i	0.0156547	+	0.0619483i
$253$	11.8601			0.745640
$254$	−2.63730	−	4.56794i	−0.165479	−	0.286618i
$255$		0			0
$256$	−7.23035	+	12.5233i	−0.451897	+	0.782708i
$257$	−9.16635	+	15.8766i	−0.571781	+	0.990354i	0.424602	+	0.905380i	$0.360414\pi$
$257$	−9.16635	+	15.8766i	−0.571781	+	0.990354i	−0.996383	+	0.0849739i	$0.972919\pi$
$258$	1.41261	+	3.48041i	0.0879453	+	0.216681i
$259$	−1.69968	−	2.94393i	−0.105613	−	0.182927i
$260$		0			0
$261$	−5.29096	+	5.14200i	−0.327502	+	0.318282i
$262$	15.3327			0.947257
$263$	−8.03832	−	13.9228i	−0.495664	−	0.858515i	0.504323	−	0.863515i	$-0.331742\pi$
$263$	−8.03832	−	13.9228i	−0.495664	−	0.858515i	−0.999988	+	0.00499942i	$0.998409\pi$
$264$	−11.5648	−	1.60660i	−0.711766	−	0.0988795i
$265$		0			0
$266$	2.29939	−	3.98265i	0.140984	−	0.244192i
$267$	3.60241	−	4.62600i	0.220464	−	0.283107i
$268$	0.805043	+	1.39438i	0.0491758	+	0.0851751i
$269$	−18.2004			−1.10970			−0.554849	−	0.831951i	$-0.687224\pi$
$269$	−18.2004			−1.10970			−0.554849	+	0.831951i	$0.687224\pi$
$270$		0			0
$271$	−2.48571			−0.150996			−0.0754979	−	0.997146i	$-0.524055\pi$
$271$	−2.48571			−0.150996			−0.0754979	+	0.997146i	$0.524055\pi$
$272$	14.9164	+	25.8360i	0.904442	+	1.56654i
$273$	−3.35539	+	4.30879i	−0.203077	+	0.260780i
$274$	1.88659	−	3.26766i	0.113973	−	0.197407i
$275$		0			0
$276$	−4.39106	−	0.610012i	−0.264311	−	0.0367184i
$277$	−3.83363	−	6.64004i	−0.230341	−	0.398962i	0.727568	−	0.686036i	$-0.240651\pi$
$277$	−3.83363	−	6.64004i	−0.230341	−	0.398962i	−0.957908	+	0.287074i	$0.907317\pi$
$278$	−17.7978			−1.06744
$279$	12.2054	+	3.45790i	0.730716	+	0.207019i
$280$		0			0
$281$	−0.136615	−	0.236624i	−0.00814978	−	0.0141158i	0.861922	−	0.507041i	$-0.169261\pi$
$281$	−0.136615	−	0.236624i	−0.00814978	−	0.0141158i	−0.870072	+	0.492925i	$0.835928\pi$
$282$	−3.94592	−	9.72201i	−0.234976	−	0.578937i
$283$	−1.68544	+	2.91928i	−0.100189	+	0.173533i	−0.911763	−	0.410718i	$-0.865278\pi$
$283$	−1.68544	+	2.91928i	−0.100189	+	0.173533i	0.811573	+	0.584251i	$0.198611\pi$
$284$	−1.85396	+	3.21115i	−0.110012	+	0.190547i
$285$		0			0
$286$	15.8006	+	27.3674i	0.934307	+	1.61827i
$287$	2.75003			0.162329
$288$	10.5090	+	2.97732i	0.619250	+	0.175440i
$289$	20.2125			1.18897
$290$		0			0
$291$	19.0010	+	2.63964i	1.11386	+	0.154739i
$292$	−3.94701	+	6.83642i	−0.230981	+	0.400071i
$293$	2.82202	−	4.88788i	0.164864	−	0.285553i	−0.771743	−	0.635935i	$-0.780615\pi$
$293$	2.82202	−	4.88788i	0.164864	−	0.285553i	0.936607	+	0.350382i	$0.113948\pi$
$294$	11.7261	−	15.0580i	0.683881	−	0.878200i
$295$		0			0
$296$	−14.6267			−0.850159
$297$	1.76019	+	16.0127i	0.102137	+	0.929150i
$298$	26.7000			1.54669
$299$	−11.9345	−	20.6711i	−0.690189	−	1.19544i
$300$		0			0
$301$	−0.335402	+	0.580933i	−0.0193322	+	0.0334844i
$302$	18.6103	−	32.2340i	1.07090	−	1.85486i
$303$	29.7979	+	4.13956i	1.71184	+	0.237811i
$304$	−13.6205	−	23.5914i	−0.781190	−	1.35306i
$305$		0			0
$306$	21.4408	−	20.8372i	1.22569	−	1.19118i
$307$	5.44105			0.310537			0.155269	−	0.987872i	$-0.450376\pi$
$307$	5.44105			0.310537			0.155269	+	0.987872i	$0.450376\pi$
$308$	0.524096	+	0.907761i	0.0298632	+	0.0517245i
$309$	−0.542447	−	1.33649i	−0.0308587	−	0.0760301i
$310$		0			0
$311$	9.53985	−	16.5235i	0.540955	−	0.936962i	−0.457895	−	0.889007i	$-0.651396\pi$
$311$	9.53985	−	16.5235i	0.540955	−	0.936962i	0.998849	−	0.0479550i	$-0.0152704\pi$
$312$	8.83717	+	21.7731i	0.500306	+	1.23266i
$313$	4.57116	+	7.91747i	0.258377	+	0.447522i	0.965807	−	0.259261i	$-0.0834790\pi$
$313$	4.57116	+	7.91747i	0.258377	+	0.447522i	−0.707430	+	0.706783i	$0.750146\pi$
$314$	−20.3573			−1.14883
$315$		0			0
$316$	2.27677			0.128078
$317$	−7.11836	−	12.3294i	−0.399807	−	0.692486i	0.593895	−	0.804543i	$-0.297590\pi$
$317$	−7.11836	−	12.3294i	−0.399807	−	0.692486i	−0.993702	+	0.112056i	$0.964256\pi$
$318$	−7.12480	−	0.989786i	−0.399539	−	0.0555045i
$319$	−3.81220	+	6.60292i	−0.213442	+	0.369693i
$320$		0			0
$321$	11.7789	−	15.1257i	0.657432	−	0.844236i
$322$	−1.57921	−	2.73527i	−0.0880057	−	0.152430i
$323$	−33.9795			−1.89067
$324$	0.171906	−	6.01902i	0.00955032	−	0.334390i
$325$		0			0
$326$	−6.18678	−	10.7158i	−0.342654	−	0.593494i
$327$	−4.95736	+	6.36595i	−0.274143	+	0.352038i
$328$	5.91638	−	10.2475i	0.326677	−	0.565822i
$329$	0.936896	−	1.62275i	0.0516527	−	0.0894652i
$330$		0			0
$331$	6.10001	+	10.5655i	0.335287	+	0.580734i	0.983540	−	0.180691i	$-0.0578334\pi$
$331$	6.10001	+	10.5655i	0.335287	+	0.580734i	−0.648253	+	0.761425i	$0.724500\pi$
$332$	9.30061			0.510437
$333$	4.94424	+	19.5653i	0.270943	+	1.07217i
$334$	4.86317			0.266101
$335$		0			0
$336$	1.60984	+	3.96633i	0.0878237	+	0.216381i
$337$	−2.29493	+	3.97494i	−0.125013	+	0.216529i	−0.921738	−	0.387813i	$-0.873231\pi$
$337$	−2.29493	+	3.97494i	−0.125013	+	0.216529i	0.796725	+	0.604342i	$0.206564\pi$
$338$	21.1800	−	36.6849i	1.15204	−	1.99540i
$339$	7.81289	+	19.2495i	0.424338	+	1.04549i
$340$		0			0
$341$	13.1094			0.709917
$342$	−19.5781	+	19.0269i	−1.05866	+	1.02886i
$343$	6.94582			0.375039
$344$	1.44316	+	2.49962i	0.0778099	+	0.134771i
$345$		0			0
$346$	−12.9497	+	22.4295i	−0.696180	+	1.20582i
$347$	−16.7301	+	28.9775i	−0.898121	+	1.55559i	−0.0682272	+	0.997670i	$0.521734\pi$
$347$	−16.7301	+	28.9775i	−0.898121	+	1.55559i	−0.829894	+	0.557921i	$0.811599\pi$
$348$	1.75103	−	2.24857i	0.0938651	−	0.120536i
$349$	14.0408	+	24.3193i	0.751586	+	1.30178i	0.947054	+	0.321074i	$0.104044\pi$
$349$	14.0408	+	24.3193i	0.751586	+	1.30178i	−0.195468	+	0.980710i	$0.562623\pi$
$350$		0			0
$351$	26.1374	−	19.1809i	1.39511	−	1.02380i
$352$	11.2875			0.601624
$353$	0.920851	+	1.59496i	0.0490119	+	0.0848912i	0.889491	−	0.456954i	$-0.151059\pi$
$353$	0.920851	+	1.59496i	0.0490119	+	0.0848912i	−0.840479	+	0.541845i	$0.817726\pi$
$354$	−5.01117	+	6.43505i	−0.266341	+	0.342019i
$355$		0			0
$356$	−1.13241	+	1.96140i	−0.0600178	+	0.103954i
$357$	5.28865	+	0.734707i	0.279905	+	0.0388848i
$358$	13.9553	+	24.1714i	0.737563	+	1.27750i
$359$	−12.1119			−0.639241			−0.319621	−	0.947546i	$-0.603555\pi$
$359$	−12.1119			−0.639241			−0.319621	+	0.947546i	$0.603555\pi$
$360$		0			0
$361$	12.0274			0.633020
$362$	10.9206	+	18.9151i	0.573976	+	0.994156i
$363$	−0.904610	−	2.22879i	−0.0474797	−	0.116981i
$364$	1.05476	−	1.82690i	0.0552846	−	0.0957558i
$365$		0			0
$366$	3.02597	+	7.45541i	0.158170	+	0.389701i
$367$	7.28688	+	12.6212i	0.380372	+	0.658824i	0.991115	−	0.133005i	$-0.0424626\pi$
$367$	7.28688	+	12.6212i	0.380372	+	0.658824i	−0.610743	+	0.791829i	$0.709129\pi$
$368$	−18.7090			−0.975274
$369$	−15.7073	−	4.45005i	−0.817691	−	0.231660i
$370$		0			0
$371$	−0.642310	−	1.11251i	−0.0333471	−	0.0577589i
$372$	−4.85360	−	0.674269i	−0.251648	−	0.0349592i
$373$	4.72323	−	8.18087i	0.244560	−	0.423590i	−0.717448	−	0.696612i	$-0.754690\pi$
$373$	4.72323	−	8.18087i	0.244560	−	0.423590i	0.962008	+	0.273022i	$0.0880233\pi$
$374$	15.4484	−	26.7574i	0.798817	−	1.38359i
$375$		0			0
$376$	−4.03125	−	6.98233i	−0.207896	−	0.360086i
$377$	15.3444			0.790276
$378$	3.45858	−	2.53807i	0.177890	−	0.130544i
$379$	−28.5541			−1.46673			−0.733363	−	0.679837i	$-0.762051\pi$
$379$	−28.5541			−1.46673			−0.733363	+	0.679837i	$0.762051\pi$
$380$		0			0
$381$	−3.43581	+	4.41207i	−0.176022	+	0.226037i
$382$	20.6970	−	35.8483i	1.05895	−	1.83416i
$383$	−0.732704	+	1.26908i	−0.0374394	+	0.0648470i	−0.884138	−	0.467226i	$-0.845253\pi$
$383$	−0.732704	+	1.26908i	−0.0374394	+	0.0648470i	0.846699	+	0.532073i	$0.178587\pi$
$384$	23.2348	+	3.22780i	1.18569	+	0.164718i
$385$		0			0
$386$	15.6176			0.794916
$387$	2.85577	−	2.77537i	0.145167	−	0.141080i
$388$	−7.41014			−0.376193
$389$	6.45506	+	11.1805i	0.327284	+	0.566873i	0.981972	−	0.189026i	$-0.0605331\pi$
$389$	6.45506	+	11.1805i	0.327284	+	0.566873i	−0.654688	+	0.755900i	$0.727200\pi$
$390$		0			0
$391$	−11.6685	+	20.2104i	−0.590100	+	1.02208i
$392$	7.33276	−	12.7007i	0.370360	−	0.641483i
$393$	−6.11336	−	15.0622i	−0.308378	−	0.759785i
$394$	−1.68961	−	2.92649i	−0.0851212	−	0.147434i
$395$		0			0
$396$	−1.52456	−	6.03294i	−0.0766118	−	0.303167i
$397$	−0.868386			−0.0435831			−0.0217915	−	0.999763i	$-0.506937\pi$
$397$	−0.868386			−0.0435831			−0.0217915	+	0.999763i	$0.506937\pi$
$398$	10.6984	+	18.5302i	0.536263	+	0.928834i
$399$	−4.82918	−	0.670876i	−0.241761	−	0.0335858i
$400$		0			0
$401$	−16.7063	+	28.9361i	−0.834270	+	1.44500i	0.0603527	+	0.998177i	$0.480777\pi$
$401$	−16.7063	+	28.9361i	−0.834270	+	1.44500i	−0.894623	+	0.446822i	$0.852556\pi$
$402$	4.18394	−	5.37277i	0.208676	−	0.267970i
$403$	−13.1916	−	22.8486i	−0.657122	−	1.13817i
$404$	−11.6208			−0.578156
$405$		0			0
$406$	2.03042			0.100768
$407$	10.4272	+	18.0604i	0.516856	+	0.895221i
$408$	14.1157	−	18.1265i	0.698831	−	0.897397i
$409$	−2.52767	+	4.37806i	−0.124985	+	0.216481i	−0.921727	−	0.387839i	$-0.873222\pi$
$409$	−2.52767	+	4.37806i	−0.124985	+	0.216481i	0.796742	+	0.604320i	$0.206555\pi$
$410$		0			0
$411$	−3.96221	−	0.550436i	−0.195442	−	0.0271510i
$412$	0.278579	+	0.482512i	0.0137246	+	0.0237717i
$413$	−1.45658			−0.0716734
$414$	4.59379	+	18.1785i	0.225772	+	0.893423i
$415$		0			0
$416$	−11.3582	−	19.6730i	−0.556883	−	0.964549i
$417$	7.09623	+	17.4838i	0.347504	+	0.856184i
$418$	−14.1062	+	24.4327i	−0.689959	+	1.19504i
$419$	−5.47880	+	9.48955i	−0.267657	+	0.463595i	−0.968256	−	0.249960i	$-0.919583\pi$
$419$	−5.47880	+	9.48955i	−0.267657	+	0.463595i	0.700600	+	0.713555i	$0.252916\pi$
$420$		0			0
$421$	5.31932	+	9.21333i	0.259248	+	0.449030i	0.966041	−	0.258390i	$-0.0831921\pi$
$421$	5.31932	+	9.21333i	0.259248	+	0.449030i	−0.706793	+	0.707421i	$0.749859\pi$
$422$	−18.1538			−0.883711
$423$	−7.97718	+	7.75260i	−0.387864	+	0.376944i
$424$	−5.52744			−0.268436
$425$		0			0
$426$	15.5331	+	2.15788i	0.752582	+	0.104550i
$427$	−0.718467	+	1.24442i	−0.0347691	+	0.0602218i
$428$	−3.70267	+	6.41322i	−0.178975	+	0.309995i
$429$	20.5846	−	26.4335i	0.993834	−	1.27622i
$430$		0			0
$431$	−37.3529			−1.79923			−0.899613	−	0.436687i	$-0.856152\pi$
$431$	−37.3529			−1.79923			−0.899613	+	0.436687i	$0.856152\pi$
$432$	−2.77664	−	25.2595i	−0.133591	−	1.21530i
$433$	−17.2125			−0.827179			−0.413589	−	0.910464i	$-0.635725\pi$
$433$	−17.2125			−0.827179			−0.413589	+	0.910464i	$0.635725\pi$
$434$	−1.74556	−	3.02339i	−0.0837894	−	0.145127i
$435$		0			0
$436$	1.55834	−	2.69913i	0.0746310	−	0.129265i
$437$	10.6547	−	18.4545i	0.509684	−	0.882799i
$438$	33.0694	+	4.59404i	1.58012	+	0.219512i
$439$	15.8744	+	27.4952i	0.757642	+	1.31228i	0.944050	+	0.329803i	$0.106982\pi$
$439$	15.8744	+	27.4952i	0.757642	+	1.31228i	−0.186408	+	0.982473i	$0.559684\pi$
$440$		0			0
$441$	−19.4677	−	5.51539i	−0.927032	−	0.262638i
$442$	−62.1809			−2.95764
$443$	0.177979	+	0.308268i	0.00845603	+	0.0146463i	0.870222	−	0.492659i	$-0.163975\pi$
$443$	0.177979	+	0.308268i	0.00845603	+	0.0146463i	−0.861766	+	0.507305i	$0.830642\pi$
$444$	−2.93161	−	7.22293i	−0.139128	−	0.342785i
$445$		0			0
$446$	−3.18087	+	5.50943i	−0.150619	+	0.260879i
$447$	−10.6456	−	26.2289i	−0.503522	−	1.24058i
$448$	0.968438	+	1.67738i	0.0457544	+	0.0792490i
$449$	−7.85632			−0.370762			−0.185381	−	0.982667i	$-0.559352\pi$
$449$	−7.85632			−0.370762			−0.185381	+	0.982667i	$0.559352\pi$
$450$		0			0
$451$	−16.8708			−0.794416
$452$	−4.01238	−	6.94964i	−0.188726	−	0.326884i
$453$	−39.0854	−	5.42980i	−1.83639	−	0.255114i
$454$	10.4625	−	18.1215i	0.491028	−	0.850485i
$455$		0			0
$456$	−12.8893	+	16.5517i	−0.603598	+	0.775105i
$457$	−10.7455	−	18.6118i	−0.502654	−	0.870622i	−0.999995	−	0.00306742i	$-0.999024\pi$
$457$	−10.7455	−	18.6118i	−0.502654	−	0.870622i	0.497341	−	0.867555i	$-0.334310\pi$
$458$	−10.8691			−0.507879
$459$	−29.0183	−	12.7544i	−1.35446	−	0.595326i
$460$		0			0
$461$	−20.4964	−	35.5007i	−0.954611	−	1.65343i	−0.735256	−	0.677789i	$-0.762938\pi$
$461$	−20.4964	−	35.5007i	−0.954611	−	1.65343i	−0.219355	−	0.975645i	$-0.570395\pi$
$462$	2.72382	−	3.49776i	0.126723	−	0.162731i
$463$	−21.0669	+	36.4890i	−0.979063	+	1.69579i	−0.313248	+	0.949671i	$0.601417\pi$
$463$	−21.0669	+	36.4890i	−0.979063	+	1.69579i	−0.665816	+	0.746116i	$0.731916\pi$
$464$	6.01363	−	10.4159i	0.279176	−	0.483546i
$465$		0			0
$466$	−2.98837	−	5.17601i	−0.138434	−	0.239774i
$467$	−22.5376			−1.04292			−0.521459	−	0.853276i	$-0.674612\pi$
$467$	−22.5376			−1.04292			−0.521459	+	0.853276i	$0.674612\pi$
$468$	−8.98075	+	8.72792i	−0.415136	+	0.403448i
$469$	1.21613			0.0561557
$470$		0			0
$471$	8.11675	+	19.9981i	0.374000	+	0.921465i
$472$	−3.13366	+	5.42766i	−0.144238	+	0.249828i
$473$	2.05762	−	3.56390i	0.0946093	−	0.163868i
$474$	−3.62141	−	8.92247i	−0.166337	−	0.409822i
$475$		0			0
$476$	−2.06251			−0.0945348
$477$	1.86843	+	7.39372i	0.0855496	+	0.338535i
$478$	25.6356			1.17255
$479$	16.6440	+	28.8282i	0.760483	+	1.31720i	0.942602	+	0.333919i	$0.108371\pi$
$479$	16.6440	+	28.8282i	0.760483	+	1.31720i	−0.182119	+	0.983277i	$0.558296\pi$
$480$		0			0
$481$	20.9851	−	36.3472i	0.956837	−	1.65729i
$482$	9.16924	−	15.8816i	0.417647	−	0.723387i
$483$	−2.05735	+	2.64193i	−0.0936127	+	0.120212i
$484$	0.464570	+	0.804660i	0.0211168	+	0.0365754i
$485$		0			0
$486$	−23.8614	+	8.90010i	−1.08238	+	0.403717i
$487$	23.7703			1.07713			0.538566	−	0.842583i	$-0.318966\pi$
$487$	23.7703			1.07713			0.538566	+	0.842583i	$0.318966\pi$
$488$	3.09140	+	5.35447i	0.139941	+	0.242385i
$489$	−8.05999	+	10.3502i	−0.364485	+	0.468050i
$490$		0			0
$491$	2.30281	−	3.98859i	0.103925	−	0.180003i	−0.809374	−	0.587294i	$-0.800193\pi$
$491$	2.30281	−	3.98859i	0.103925	−	0.180003i	0.913298	+	0.407291i	$0.133527\pi$
$492$	6.24620	+	0.867731i	0.281601	+	0.0391203i
$493$	−7.50118	−	12.9924i	−0.337836	−	0.585150i
$494$	56.7787			2.55459
$495$		0			0
$496$	−20.6797			−0.928548
$497$	1.40033	+	2.42545i	0.0628135	+	0.108796i
$498$	−14.7935	−	36.4483i	−0.662910	−	1.63329i
$499$	9.44878	−	16.3658i	0.422985	−	0.732632i	−0.573245	−	0.819384i	$-0.694316\pi$
$499$	9.44878	−	16.3658i	0.422985	−	0.732632i	0.996230	+	0.0867522i	$0.0276488\pi$
$500$		0			0
$501$	−1.93901	−	4.77736i	−0.0866287	−	0.213437i
$502$	5.66936	+	9.81962i	0.253036	+	0.438271i
$503$	35.7581			1.59438			0.797188	−	0.603731i	$-0.206320\pi$
$503$	35.7581			1.59438			0.797188	+	0.603731i	$0.206320\pi$
$504$	2.36401	−	2.29746i	0.105301	−	0.102337i
$505$		0			0
$506$	9.68809	+	16.7803i	0.430688	+	0.745974i
$507$	−44.4824	−	6.17955i	−1.97553	−	0.274444i
$508$	1.08004	−	1.87069i	0.0479192	−	0.0829985i
$509$	−12.2034	+	21.1368i	−0.540904	+	0.936874i	0.457948	+	0.888979i	$0.348585\pi$
$509$	−12.2034	+	21.1368i	−0.540904	+	0.936874i	−0.998852	+	0.0478949i	$0.984749\pi$
$510$		0			0
$511$	2.98125	+	5.16368i	0.131883	+	0.228428i
$512$	3.46207			0.153003
$513$	26.4972	+	11.6463i	1.16988	+	0.514198i
$514$	−29.9506			−1.32106
$515$		0			0
$516$	−0.945110	+	1.21365i	−0.0416062	+	0.0534282i
$517$	−5.74765	+	9.95523i	−0.252782	+	0.437830i
$518$	2.77681	−	4.80957i	0.122006	−	0.211321i
$519$	27.1970	+	3.77824i	1.19381	+	0.165846i
$520$		0			0
$521$	33.3968			1.46314			0.731571	−	0.681766i	$-0.238788\pi$
$521$	33.3968			1.46314			0.731571	+	0.681766i	$0.238788\pi$
$522$	−11.5971	−	3.28558i	−0.507592	−	0.143806i
$523$	−37.3654			−1.63388			−0.816938	−	0.576726i	$-0.804330\pi$
$523$	−37.3654			−1.63388			−0.816938	+	0.576726i	$0.804330\pi$
$524$	3.13957	+	5.43789i	0.137153	+	0.237555i
$525$		0			0
$526$	13.1324	−	22.7460i	0.572600	−	0.991772i
$527$	−12.8976	+	22.3393i	−0.561828	+	0.973115i
$528$	−9.87599	−	24.3326i	−0.429797	−	1.05894i
$529$	4.18239	+	7.24412i	0.181843	+	0.314962i
$530$		0			0
$531$	8.31953	+	2.35701i	0.361037	+	0.102285i
$532$	1.88332			0.0816521
$533$	16.9766	+	29.4043i	0.735338	+	1.27364i
$534$	9.48775	+	1.31805i	0.410575	+	0.0570376i
$535$		0			0
$536$	2.61637	−	4.53168i	0.113010	−	0.195739i
$537$	18.1807	−	23.3466i	0.784555	−	1.00748i
$538$	−14.8672	−	25.7508i	−0.640971	−	1.11019i
$539$	−20.9097			−0.900645
$540$		0			0
$541$	28.2560			1.21482			0.607409	−	0.794389i	$-0.292209\pi$
$541$	28.2560			1.21482			0.607409	+	0.794389i	$0.292209\pi$
$542$	−2.03048	−	3.51689i	−0.0872165	−	0.151063i
$543$	14.2271	−	18.2697i	0.610545	−	0.784026i
$544$	−11.1051	+	19.2345i	−0.476125	+	0.824673i
$545$		0			0
$546$	−8.83717	−	1.22767i	−0.378196	−	0.0525395i
$547$	19.2726	+	33.3811i	0.824036	+	1.42727i	0.902654	+	0.430368i	$0.141616\pi$
$547$	19.2726	+	33.3811i	0.824036	+	1.42727i	−0.0786172	+	0.996905i	$0.525050\pi$
$548$	1.54521			0.0660082
$549$	6.11737	−	5.94515i	0.261083	−	0.253733i
$550$		0			0
$551$	6.84949	+	11.8637i	0.291798	+	0.505409i
$552$	5.41850	+	13.3502i	0.230626	+	0.568220i
$553$	0.859845	−	1.48929i	0.0365643	−	0.0633313i
$554$	6.26309	−	10.8480i	0.266093	−	0.460887i
$555$		0			0
$556$	−3.64433	−	6.31217i	−0.154554	−	0.267696i
$557$	−27.4125			−1.16151			−0.580753	−	0.814080i	$-0.697242\pi$
$557$	−27.4125			−1.16151			−0.580753	+	0.814080i	$0.697242\pi$
$558$	5.07769	+	20.0933i	0.214956	+	0.850618i
$559$	−8.28206			−0.350294
$560$		0			0
$561$	−32.4447	−	4.50727i	−1.36982	−	0.190297i
$562$	0.223191	−	0.386579i	0.00941476	−	0.0163068i
$563$	13.8196	−	23.9363i	0.582427	−	1.00879i	−0.412764	−	0.910838i	$-0.635437\pi$
$563$	13.8196	−	23.9363i	0.582427	−	1.00879i	0.995191	−	0.0979551i	$-0.0312302\pi$
$564$	2.64003	−	3.39017i	0.111165	−	0.142752i
$565$		0			0
$566$	−5.50710			−0.231481
$567$	−3.87227	−	2.38559i	−0.162620	−	0.100185i
$568$	12.0506			0.505634
$569$	7.35807	+	12.7446i	0.308467	+	0.534280i	0.978027	−	0.208478i	$-0.0668509\pi$
$569$	7.35807	+	12.7446i	0.308467	+	0.534280i	−0.669561	+	0.742757i	$0.733518\pi$
$570$		0			0
$571$	14.1503	−	24.5090i	0.592172	−	1.02567i	−0.401768	−	0.915742i	$-0.631604\pi$
$571$	14.1503	−	24.5090i	0.592172	−	1.02567i	0.993939	−	0.109930i	$-0.0350627\pi$
$572$	−6.47074	+	11.2077i	−0.270555	+	0.468616i
$573$	−43.4679	−	6.03862i	−1.81590	−	0.252267i
$574$	2.24639	+	3.89087i	0.0937626	+	0.162402i
$575$		0			0
$576$	−2.81711	−	11.1478i	−0.117380	−	0.464493i
$577$	−40.7976			−1.69843			−0.849214	−	0.528049i	$-0.822924\pi$
$577$	−40.7976			−1.69843			−0.849214	+	0.528049i	$0.822924\pi$
$578$	16.5108	+	28.5975i	0.686759	+	1.18950i
$579$	−6.22696	−	15.3421i	−0.258784	−	0.637594i
$580$		0			0
$581$	3.51247	−	6.08377i	0.145722	−	0.252397i
$582$	11.7865	+	29.0397i	0.488565	+	1.20373i
$583$	3.94044	+	6.82504i	0.163196	+	0.282664i
$584$	25.6553			1.06162
$585$		0			0
$586$	9.22080			0.380908
$587$	−1.39016	−	2.40784i	−0.0573782	−	0.0993820i	0.835910	−	0.548867i	$-0.184941\pi$
$587$	−1.39016	−	2.40784i	−0.0573782	−	0.0993820i	−0.893288	+	0.449485i	$0.851607\pi$
$588$	7.74154	+	1.07547i	0.319256	+	0.0443514i
$589$	11.7771	−	20.3985i	0.485265	−	0.840504i
$590$		0			0
$591$	−2.20118	+	2.82663i	−0.0905445	+	0.116272i
$592$	−16.4485	−	28.4897i	−0.676031	−	1.17092i
$593$	−14.8084			−0.608109			−0.304055	−	0.952655i	$-0.598341\pi$
$593$	−14.8084			−0.608109			−0.304055	+	0.952655i	$0.598341\pi$
$594$	−21.2176	+	15.5705i	−0.870570	+	0.638867i
$595$		0			0
$596$	5.46717	+	9.46941i	0.223944	+	0.387882i
$597$	13.9376	−	17.8979i	0.570429	−	0.732511i
$598$	19.4976	−	33.7709i	0.797318	−	1.38100i
$599$	8.17151	−	14.1535i	0.333879	−	0.578295i	−0.649390	−	0.760456i	$-0.724976\pi$
$599$	8.17151	−	14.1535i	0.333879	−	0.578295i	0.983269	+	0.182160i	$0.0583090\pi$
$600$		0			0
$601$	3.31185	+	5.73630i	0.135093	+	0.233988i	0.925633	−	0.378422i	$-0.123533\pi$
$601$	3.31185	+	5.73630i	0.135093	+	0.233988i	−0.790540	+	0.612411i	$0.790200\pi$
$602$	−1.09591			−0.0446658
$603$	−6.94617	−	1.96792i	−0.282870	−	0.0801400i
$604$	15.2428			0.620221
$605$		0			0
$606$	18.4839	+	45.5408i	0.750857	+	1.84997i
$607$	−15.1547	+	26.2487i	−0.615110	+	1.06540i	0.375256	+	0.926921i	$0.377555\pi$
$607$	−15.1547	+	26.2487i	−0.615110	+	1.06540i	−0.990365	+	0.138480i	$0.955778\pi$
$608$	10.1403	−	17.5634i	0.411242	−	0.712291i
$609$	−0.809554	−	1.99459i	−0.0328048	−	0.0808248i
$610$		0			0
$611$	23.1347			0.935931
$612$	11.7804	+	3.33751i	0.476195	+	0.134911i
$613$	14.7803			0.596969			0.298484	−	0.954415i	$-0.403519\pi$
$613$	14.7803			0.596969			0.298484	+	0.954415i	$0.403519\pi$
$614$	4.44459	+	7.69825i	0.179369	+	0.310676i
$615$		0			0
$616$	1.70330	−	2.95020i	0.0686278	−	0.118867i
$617$	16.9256	−	29.3160i	0.681399	−	1.18022i	−0.293155	−	0.956065i	$-0.594705\pi$
$617$	16.9256	−	29.3160i	0.681399	−	1.18022i	0.974554	−	0.224152i	$-0.0719614\pi$
$618$	1.44782	−	1.85920i	0.0582399	−	0.0747882i
$619$	−5.84433	−	10.1227i	−0.234903	−	0.406865i	0.724341	−	0.689442i	$-0.242144\pi$
$619$	−5.84433	−	10.1227i	−0.234903	−	0.406865i	−0.959245	+	0.282577i	$0.908811\pi$
$620$		0			0
$621$	16.0261	−	11.7607i	0.643105	−	0.471942i
$622$	31.1709			1.24984
$623$	0.855334	+	1.48148i	0.0342682	+	0.0593543i
$624$	−32.4716	+	41.6981i	−1.29990	+	1.66926i
$625$		0			0
$626$	−7.46800	+	12.9350i	−0.298481	+	0.516985i
$627$	29.6260	+	4.11568i	1.18315	+	0.164364i
$628$	−4.16843	−	7.21993i	−0.166338	−	0.288107i
$629$	−41.0347			−1.63616
$630$		0			0
$631$	−38.1357			−1.51816			−0.759078	−	0.650999i	$-0.774350\pi$
$631$	−38.1357			−1.51816			−0.759078	+	0.650999i	$0.774350\pi$
$632$	−3.69972	−	6.40810i	−0.147167	−	0.254901i
$633$	7.23815	+	17.8334i	0.287691	+	0.708816i
$634$	11.6294	−	20.1428i	0.461864	−	0.799972i
$635$		0			0
$636$	−1.10786	−	2.72955i	−0.0439294	−	0.108234i
$637$	21.0408	+	36.4437i	0.833666	+	1.44395i
$638$	−12.4562			−0.493144
$639$	−4.07346	−	16.1194i	−0.161144	−	0.637675i
$640$		0			0
$641$	17.3827	+	30.1077i	0.686576	+	1.18918i	0.972939	+	0.231063i	$0.0742204\pi$
$641$	17.3827	+	30.1077i	0.686576	+	1.18918i	−0.286363	+	0.958121i	$0.592446\pi$
$642$	31.0223	+	4.30966i	1.22435	+	0.170089i
$643$	−1.34258	+	2.32541i	−0.0529461	+	0.0917053i	−0.891284	−	0.453446i	$-0.850194\pi$
$643$	−1.34258	+	2.32541i	−0.0529461	+	0.0917053i	0.838338	+	0.545151i	$0.183528\pi$
$644$	0.646726	−	1.12016i	0.0254846	−	0.0441406i
$645$		0			0
$646$	−27.7565	−	48.0757i	−1.09207	−	1.89151i
$647$	40.5103			1.59262			0.796311	−	0.604887i	$-0.206782\pi$
$647$	40.5103			1.59262			0.796311	+	0.604887i	$0.206782\pi$
$648$	−17.2202	+	9.29698i	−0.676474	+	0.365220i
$649$	8.93578			0.350760
$650$		0			0
$651$	−2.27407	+	2.92022i	−0.0891277	+	0.114453i
$652$	2.53365	−	4.38841i	0.0992253	−	0.171863i
$653$	−6.66772	+	11.5488i	−0.260928	+	0.451941i	−0.966489	−	0.256709i	$-0.917362\pi$
$653$	−6.66772	+	11.5488i	−0.260928	+	0.451941i	0.705561	+	0.708650i	$0.250695\pi$
$654$	−13.0563	−	1.81380i	−0.510543	−	0.0709253i
$655$		0			0
$656$	26.6132			1.03907
$657$	−8.67223	−	34.3176i	−0.338336	−	1.33886i
$658$	3.06126			0.119340
$659$	−15.5772	−	26.9804i	−0.606800	−	1.05101i	−0.991764	−	0.128077i	$-0.959120\pi$
$659$	−15.5772	−	26.9804i	−0.606800	−	1.05101i	0.384965	−	0.922931i	$-0.374214\pi$
$660$		0			0
$661$	−3.15894	+	5.47145i	−0.122869	+	0.212815i	−0.920898	−	0.389804i	$-0.872543\pi$
$661$	−3.15894	+	5.47145i	−0.122869	+	0.212815i	0.798029	+	0.602619i	$0.205876\pi$
$662$	−9.96574	+	17.2612i	−0.387329	+	0.670874i
$663$	24.7924	+	61.0837i	0.962856	+	2.37230i
$664$	−15.1134	−	26.1771i	−0.586512	−	1.01587i
$665$		0			0
$666$	−23.6431	+	22.9775i	−0.916150	+	0.890358i
$667$	9.40838			0.364294
$668$	0.995798	+	1.72477i	0.0385286	+	0.0667334i
$669$	6.68047	+	0.928060i	0.258282	+	0.0358809i
$670$		0			0
$671$	4.40764	−	7.63426i	0.170155	−	0.294717i
$672$	−1.95801	+	2.51436i	−0.0755320	+	0.0969937i
$673$	3.29610	+	5.70901i	0.127055	+	0.220066i	0.922534	−	0.385915i	$-0.126114\pi$
$673$	3.29610	+	5.70901i	0.127055	+	0.220066i	−0.795479	+	0.605981i	$0.792781\pi$
$674$	−7.49857			−0.288834
$675$		0			0
$676$	17.3476			0.667214
$677$	−17.4473	−	30.2197i	−0.670556	−	1.16144i	−0.977747	−	0.209788i	$-0.932722\pi$
$677$	−17.4473	−	30.2197i	−0.670556	−	1.16144i	0.307191	−	0.951648i	$-0.400611\pi$
$678$	−20.8530	+	26.7782i	−0.800855	+	1.02841i
$679$	−2.79851	+	4.84716i	−0.107397	+	0.186017i
$680$		0			0
$681$	−21.9733	−	3.05256i	−0.842019	−	0.116974i
$682$	10.7086	+	18.5479i	0.410054	+	0.710234i
$683$	26.0958			0.998528			0.499264	−	0.866450i	$-0.333604\pi$
$683$	26.0958			0.998528			0.499264	+	0.866450i	$0.333604\pi$
$684$	−10.7569	−	3.04755i	−0.411302	−	0.116526i
$685$		0			0
$686$	5.67378	+	9.82727i	0.216626	+	0.375207i
$687$	4.33365	+	10.6773i	0.165339	+	0.407364i
$688$	−3.24583	+	5.62194i	−0.123746	+	0.214334i
$689$	7.93028	−	13.7356i	0.302119	−	0.523286i
$690$		0			0
$691$	14.6529	+	25.3796i	0.557423	+	0.965485i	0.997711	+	0.0676282i	$0.0215432\pi$
$691$	14.6529	+	25.3796i	0.557423	+	0.965485i	−0.440288	+	0.897857i	$0.645124\pi$
$692$	−10.6065			−0.403197
$693$	−4.52207	−	1.28115i	−0.171779	−	0.0486668i
$694$	−54.6648			−2.07505
$695$		0			0
$696$	−9.17413	−	1.27448i	−0.347745	−	0.0483091i
$697$	16.5982	−	28.7489i	0.628701	−	1.08894i
$698$	−22.9387	+	39.7311i	−0.868244	+	1.50384i
$699$	−3.89318	+	4.99939i	−0.147253	+	0.189094i
$700$		0			0
$701$	15.3891			0.581239			0.290620	−	0.956839i	$-0.406139\pi$
$701$	15.3891			0.581239			0.290620	+	0.956839i	$0.406139\pi$
$702$	48.4887	+	21.3123i	1.83009	+	0.804379i
$703$	37.4696			1.41319
$704$	−5.94116	−	10.2904i	−0.223916	−	0.387834i
$705$		0			0
$706$	−1.50442	+	2.60572i	−0.0566194	+	0.0980677i
$707$	−4.38870	+	7.60146i	−0.165054	+	0.285882i
$708$	−3.30836	−	0.459601i	−0.124336	−	0.0172729i
$709$	3.86996	+	6.70296i	0.145339	+	0.251735i	0.929499	−	0.368823i	$-0.120239\pi$
$709$	3.86996	+	6.70296i	0.145339	+	0.251735i	−0.784160	+	0.620558i	$0.786906\pi$
$710$		0			0
$711$	−7.32113	+	7.11502i	−0.274564	+	0.266834i
$712$	7.36062			0.275851
$713$	−8.08842	−	14.0096i	−0.302914	−	0.524662i
$714$	3.28060	+	8.08278i	0.122773	+	0.302490i
$715$		0			0
$716$	−5.71508	+	9.89880i	−0.213582	+	0.369936i
$717$	−10.2213	−	25.1833i	−0.381720	−	0.940486i
$718$	−9.89374	−	17.1365i	−0.369231	−	0.639527i
$719$	−15.1316			−0.564313			−0.282156	−	0.959368i	$-0.591050\pi$
$719$	−15.1316			−0.564313			−0.282156	+	0.959368i	$0.591050\pi$
$720$		0			0
$721$	0.420832			0.0156726
$722$	9.82470	+	17.0169i	0.365638	+	0.633303i
$723$	−19.2573	−	2.67525i	−0.716185	−	0.0994934i
$724$	−4.47229	+	7.74623i	−0.166211	+	0.287886i
$725$		0			0
$726$	2.41445	−	3.10049i	0.0896086	−	0.115070i
$727$	−0.0809381	−	0.140189i	−0.00300183	−	0.00519932i	0.864521	−	0.502597i	$-0.167622\pi$
$727$	−0.0809381	−	0.140189i	−0.00300183	−	0.00519932i	−0.867522	+	0.497398i	$0.834289\pi$
$728$	−6.85590			−0.254097
$729$	18.2569	+	19.8918i	0.676183	+	0.736734i
$730$		0			0
$731$	4.04873	+	7.01260i	0.149748	+	0.259370i
$732$	−2.02453	+	2.59978i	−0.0748288	+	0.0960907i
$733$	25.0166	−	43.3300i	0.924009	−	1.60043i	0.130861	−	0.991401i	$-0.458226\pi$
$733$	25.0166	−	43.3300i	0.924009	−	1.60043i	0.793148	−	0.609029i	$-0.208441\pi$
$734$	−11.9047	+	20.6196i	−0.439412	+	0.761084i
$735$		0			0
$736$	−6.96427	−	12.0625i	−0.256707	−	0.444629i
$737$	−7.46070			−0.274818
$738$	−6.53458	−	25.8585i	−0.240541	−	0.951866i
$739$	30.5505			1.12382			0.561909	−	0.827199i	$-0.310067\pi$
$739$	30.5505			1.12382			0.561909	+	0.827199i	$0.310067\pi$
$740$		0			0
$741$	−22.6384	−	55.7768i	−0.831643	−	2.04901i
$742$	1.04936	−	1.81754i	0.0385231	−	0.0667240i
$743$	−2.98342	+	5.16743i	−0.109451	+	0.189575i	−0.915548	−	0.402209i	$-0.868243\pi$
$743$	−2.98342	+	5.16743i	−0.109451	+	0.189575i	0.806097	+	0.591783i	$0.201576\pi$
$744$	5.98927	+	14.7564i	0.219577	+	0.540997i
$745$		0			0
$746$	15.4329			0.565039
$747$	−29.9068	+	29.0649i	−1.09423	+	1.06343i
$748$	12.6530			0.462640
$749$	2.79670	+	4.84403i	0.102189	+	0.176997i
$750$		0			0
$751$	−17.1988	+	29.7892i	−0.627593	+	1.08702i	0.360441	+	0.932782i	$0.382626\pi$
$751$	−17.1988	+	29.7892i	−0.627593	+	1.08702i	−0.988033	+	0.154240i	$0.950707\pi$
$752$	9.06674	−	15.7041i	0.330630	−	0.572668i
$753$	7.38591	−	9.48454i	0.269157	−	0.345636i
$754$	12.5342	+	21.7099i	0.456470	+	0.790630i
$755$		0			0
$756$	1.60834	+	0.706916i	0.0584948	+	0.0257103i
$757$	40.6873			1.47881			0.739403	−	0.673263i	$-0.235108\pi$
$757$	40.6873			1.47881			0.739403	+	0.673263i	$0.235108\pi$
$758$	−23.3248	−	40.3997i	−0.847194	−	1.46738i
$759$	12.6214	−	16.2077i	0.458128	−	0.588301i
$760$		0			0
$761$	−14.1298	+	24.4735i	−0.512204	+	0.887164i	0.487696	+	0.873014i	$0.337838\pi$
$761$	−14.1298	+	24.4735i	−0.512204	+	0.887164i	−0.999900	+	0.0141502i	$0.995496\pi$
$762$	−9.04898	−	1.25710i	−0.327810	−	0.0455398i
$763$	−1.17705	−	2.03870i	−0.0426119	−	0.0738060i
$764$	16.9519			0.613299
$765$		0			0
$766$	−2.39407			−0.0865013
$767$	−8.99180	−	15.5743i	−0.324675	−	0.562354i
$768$	9.41952	+	23.2079i	0.339898	+	0.837444i
$769$	23.4518	−	40.6197i	0.845694	−	1.46478i	−0.0393235	−	0.999227i	$-0.512520\pi$
$769$	23.4518	−	40.6197i	0.845694	−	1.46478i	0.885017	−	0.465558i	$-0.154146\pi$
$770$		0			0
$771$	11.9417	+	29.4221i	0.430070	+	1.05961i
$772$	3.19791	+	5.53894i	0.115095	+	0.199351i
$773$	9.19641			0.330772			0.165386	−	0.986229i	$-0.447113\pi$
$773$	9.19641			0.330772			0.165386	+	0.986229i	$0.447113\pi$
$774$	6.25949	+	1.77338i	0.224993	+	0.0637428i
$775$		0			0

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)

\(f(q)\)	\(=\)	\(q+(0.816862 + 1.41485i) q^{2} +(1.06419 - 1.36657i) q^{3} +(-0.334526 + 0.579416i) q^{4} +(2.80278 + 0.389365i) q^{6} +(0.252674 + 0.437645i) q^{7} +2.17440 q^{8} +(-0.735010 - 2.90857i) q^{9} +O(q^{10})\)	\(q+(0.816862 + 1.41485i) q^{2} +(1.06419 - 1.36657i) q^{3} +(-0.334526 + 0.579416i) q^{4} +(2.80278 + 0.389365i) q^{6} +(0.252674 + 0.437645i) q^{7} +2.17440 q^{8} +(-0.735010 - 2.90857i) q^{9} +(-1.55010 - 2.68485i) q^{11} +(0.435812 + 1.07376i) q^{12} +(-3.11964 + 5.40337i) q^{13} +(-0.412800 + 0.714990i) q^{14} +(2.44524 + 4.23527i) q^{16} +6.10020 q^{17} +(3.51477 - 3.41582i) q^{18} -5.57022 q^{19} +(0.866963 + 0.120440i) q^{21} +(2.53244 - 4.38631i) q^{22} +(-1.91280 + 3.31307i) q^{23} +(2.31397 - 2.97146i) q^{24} -10.1932 q^{26} +(-4.75694 - 2.09082i) q^{27} -0.338104 q^{28} +(-1.22966 - 2.12984i) q^{29} +(-2.11429 + 3.66206i) q^{31} +(-1.82044 + 3.15309i) q^{32} +(-5.31863 - 0.738871i) q^{33} +(4.98302 + 8.63085i) q^{34} +(1.93115 + 0.547115i) q^{36} -6.72677 q^{37} +(-4.55010 - 7.88101i) q^{38} +(4.06419 + 10.0134i) q^{39} +(2.72092 - 4.71278i) q^{41} +(0.537785 + 1.32500i) q^{42} +(0.663704 + 1.14957i) q^{43} +2.07420 q^{44} -6.24997 q^{46} +(-1.85396 - 3.21115i) q^{47} +(8.38998 + 1.16555i) q^{48} +(3.37231 - 5.84101i) q^{49} +(6.49176 - 8.33633i) q^{51} +(-2.08720 - 3.61514i) q^{52} -2.54205 q^{53} +(-0.927572 - 8.43825i) q^{54} +(0.549415 + 0.951614i) q^{56} +(-5.92776 + 7.61208i) q^{57} +(2.00893 - 3.47956i) q^{58} +(-1.44116 + 2.49616i) q^{59} +(1.42173 + 2.46250i) q^{61} -6.90833 q^{62} +(1.08720 - 1.05659i) q^{63} +3.83276 q^{64} +(-3.29920 - 8.12860i) q^{66} +(1.20326 - 2.08411i) q^{67} +(-2.04068 + 3.53456i) q^{68} +(2.49195 + 6.13969i) q^{69} +5.54205 q^{71} +(-1.59821 - 6.32439i) q^{72} +11.7988 q^{73} +(-5.49484 - 9.51734i) q^{74} +(1.86338 - 3.22748i) q^{76} +(0.783341 - 1.35679i) q^{77} +(-10.8475 + 13.9298i) q^{78} +(-1.70149 - 2.94707i) q^{79} +(-7.91952 + 4.27565i) q^{81} +8.89047 q^{82} +(-6.95059 - 12.0388i) q^{83} +(-0.359807 + 0.462042i) q^{84} +(-1.08431 + 1.87808i) q^{86} +(-4.21915 - 0.586130i) q^{87} +(-3.37054 - 5.83795i) q^{88} +3.38513 q^{89} -3.15301 q^{91} +(-1.27976 - 2.21661i) q^{92} +(2.75444 + 6.78643i) q^{93} +(3.02886 - 5.24614i) q^{94} +(2.37162 + 5.84324i) q^{96} +(5.53779 + 9.59173i) q^{97} +11.0188 q^{98} +(-6.66974 + 6.48197i) 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

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L-functions

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