LMFDB - Embedded newform 729.2.c.e.244.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(244,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("729.244");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.c (of order $3$, degree $2$, not 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			244.3
Root			$0.500000 - 0.258654i$ of defining polynomial
Character	$\chi$	$=$	729.244
Dual form			729.2.c.e.487.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207733 + 0.359804i) q^{2} +(0.913694 - 1.58256i) q^{4} +(-1.10759 + 1.91841i) q^{5} +(0.659815 + 1.14283i) q^{7} +1.59015 q^{8} +O(q^{10})$	\(q+(0.207733 + 0.359804i) q^{2} +(0.913694 - 1.58256i) q^{4} +(-1.10759 + 1.91841i) q^{5} +(0.659815 + 1.14283i) q^{7} +1.59015 q^{8} -0.920335 q^{10} +(2.60759 + 4.51648i) q^{11} +(0.00902926 - 0.0156391i) q^{13} +(-0.274131 + 0.474808i) q^{14} +(-1.49706 - 2.59299i) q^{16} -3.13280 q^{17} +0.417352 q^{19} +(2.02400 + 3.50568i) q^{20} +(-1.08337 + 1.87645i) q^{22} +(0.517193 - 0.895805i) q^{23} +(0.0464738 + 0.0804949i) q^{25} +0.00750270 q^{26} +2.41147 q^{28} +(3.90361 + 6.76125i) q^{29} +(-1.86483 + 3.22998i) q^{31} +(2.21213 - 3.83152i) q^{32} +(-0.650785 - 1.12719i) q^{34} -2.92322 q^{35} +4.42476 q^{37} +(0.0866979 + 0.150165i) q^{38} +(-1.76124 + 3.05056i) q^{40} +(1.83747 - 3.18259i) q^{41} +(4.15394 + 7.19483i) q^{43} +9.53017 q^{44} +0.429753 q^{46} +(3.54895 + 6.14697i) q^{47} +(2.62929 - 4.55406i) q^{49} +(-0.0193083 + 0.0334429i) q^{50} +(-0.0165000 - 0.0285788i) q^{52} -1.30057 q^{53} -11.5526 q^{55} +(1.04920 + 1.81728i) q^{56} +(-1.62182 + 2.80907i) q^{58} +(1.85091 - 3.20586i) q^{59} +(-3.45712 - 5.98791i) q^{61} -1.54955 q^{62} -4.15011 q^{64} +(0.0200015 + 0.0346436i) q^{65} +(5.51340 - 9.54949i) q^{67} +(-2.86242 + 4.95785i) q^{68} +(-0.607251 - 1.05179i) q^{70} -6.08428 q^{71} -0.546973 q^{73} +(0.919169 + 1.59205i) q^{74} +(0.381332 - 0.660487i) q^{76} +(-3.44106 + 5.96008i) q^{77} +(-0.244572 - 0.423611i) q^{79} +6.63254 q^{80} +1.52681 q^{82} +(-2.30684 - 3.99556i) q^{83} +(3.46986 - 6.00998i) q^{85} +(-1.72582 + 2.98921i) q^{86} +(4.14647 + 7.18189i) q^{88} -3.37307 q^{89} +0.0238305 q^{91} +(-0.945113 - 1.63698i) q^{92} +(-1.47447 + 2.55386i) q^{94} +(-0.462257 + 0.800652i) q^{95} +(-4.97068 - 8.60947i) q^{97} +2.18476 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 - 12 * q^8	$ 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8} + 6 q^{10} + 12 q^{11} + 6 q^{14} + 3 q^{16} - 18 q^{17} + 6 q^{19} + 6 q^{20} - 6 q^{22} + 15 q^{23} + 6 q^{25} - 30 q^{26} - 12 q^{28} + 12 q^{29} - 24 q^{35} + 6 q^{37} - 3 q^{38} - 6 q^{40} + 15 q^{41} - 6 q^{44} + 6 q^{46} + 21 q^{47} + 12 q^{49} + 3 q^{50} - 12 q^{52} - 18 q^{53} - 12 q^{55} - 6 q^{56} + 12 q^{58} + 24 q^{59} + 9 q^{61} + 24 q^{62} - 24 q^{64} - 6 q^{65} + 9 q^{67} - 9 q^{68} - 15 q^{70} - 54 q^{71} - 12 q^{73} - 12 q^{74} - 6 q^{76} - 12 q^{77} + 42 q^{80} - 12 q^{82} + 12 q^{83} - 21 q^{86} - 12 q^{88} - 18 q^{89} - 12 q^{91} + 6 q^{92} - 6 q^{94} + 12 q^{95} + 90 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 - 12 * q^8 + 6 * q^10 + 12 * q^11 + 6 * q^14 + 3 * q^16 - 18 * q^17 + 6 * q^19 + 6 * q^20 - 6 * q^22 + 15 * q^23 + 6 * q^25 - 30 * q^26 - 12 * q^28 + 12 * q^29 - 24 * q^35 + 6 * q^37 - 3 * q^38 - 6 * q^40 + 15 * q^41 - 6 * q^44 + 6 * q^46 + 21 * q^47 + 12 * q^49 + 3 * q^50 - 12 * q^52 - 18 * q^53 - 12 * q^55 - 6 * q^56 + 12 * q^58 + 24 * q^59 + 9 * q^61 + 24 * q^62 - 24 * q^64 - 6 * q^65 + 9 * q^67 - 9 * q^68 - 15 * q^70 - 54 * q^71 - 12 * q^73 - 12 * q^74 - 6 * q^76 - 12 * q^77 + 42 * q^80 - 12 * q^82 + 12 * q^83 - 21 * q^86 - 12 * q^88 - 18 * q^89 - 12 * q^91 + 6 * q^92 - 6 * q^94 + 12 * q^95 + 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.207733	+	0.359804i	0.146889	+	0.254420i	0.930076	−	0.367366i	$-0.119740\pi$
$2$	0.207733	+	0.359804i	0.146889	+	0.254420i	−0.783187	+	0.621786i	$0.786407\pi$
$3$		0			0
$3$		0			0
$4$	0.913694	−	1.58256i	0.456847	−	0.791282i
$5$	−1.10759	+	1.91841i	−0.495331	+	0.857938i	−0.999986	−	0.00538314i	$-0.998286\pi$
$5$	−1.10759	+	1.91841i	−0.495331	+	0.857938i	0.504655	+	0.863321i	$0.331620\pi$
$6$		0			0
$7$	0.659815	+	1.14283i	0.249386	+	0.431950i	0.963356	−	0.268227i	$-0.0864377\pi$
$7$	0.659815	+	1.14283i	0.249386	+	0.431950i	−0.713969	+	0.700177i	$0.753104\pi$
$8$	1.59015			0.562203
$9$		0			0
$10$	−0.920335			−0.291036
$11$	2.60759	+	4.51648i	0.786219	+	1.36177i	0.928268	+	0.371912i	$0.121298\pi$
$11$	2.60759	+	4.51648i	0.786219	+	1.36177i	−0.142049	+	0.989860i	$0.545369\pi$
$12$		0			0
$13$	0.00902926	−	0.0156391i	0.00250427	−	0.00433752i	−0.864771	−	0.502167i	$-0.832536\pi$
$13$	0.00902926	−	0.0156391i	0.00250427	−	0.00433752i	0.867275	+	0.497830i	$0.165870\pi$
$14$	−0.274131	+	0.474808i	−0.0732645	+	0.126898i
$15$		0			0
$16$	−1.49706	−	2.59299i	−0.374265	−	0.648246i
$17$	−3.13280			−0.759814			−0.379907	−	0.925025i	$-0.624044\pi$
$17$	−3.13280			−0.759814			−0.379907	+	0.925025i	$0.624044\pi$
$18$		0			0
$19$	0.417352			0.0957472			0.0478736	−	0.998853i	$-0.484756\pi$
$19$	0.417352			0.0957472			0.0478736	+	0.998853i	$0.484756\pi$
$20$	2.02400	+	3.50568i	0.452581	+	0.783893i
$21$		0			0
$22$	−1.08337	+	1.87645i	−0.230975	+	0.400060i
$23$	0.517193	−	0.895805i	0.107842	−	0.186788i	−0.807054	−	0.590478i	$-0.798939\pi$
$23$	0.517193	−	0.895805i	0.107842	−	0.186788i	0.914896	+	0.403690i	$0.132273\pi$
$24$		0			0
$25$	0.0464738	+	0.0804949i	0.00929475	+	0.0160990i
$26$	0.00750270			0.00147140
$27$		0			0
$28$	2.41147			0.455726
$29$	3.90361	+	6.76125i	0.724882	+	1.25553i	0.959022	+	0.283330i	$0.0914393\pi$
$29$	3.90361	+	6.76125i	0.724882	+	1.25553i	−0.234140	+	0.972203i	$0.575227\pi$
$30$		0			0
$31$	−1.86483	+	3.22998i	−0.334934	+	0.580122i	−0.983472	−	0.181060i	$-0.942047\pi$
$31$	−1.86483	+	3.22998i	−0.334934	+	0.580122i	0.648538	+	0.761182i	$0.275381\pi$
$32$	2.21213	−	3.83152i	0.391053	−	0.677323i
$33$		0			0
$34$	−0.650785	−	1.12719i	−0.111609	−	0.193312i
$35$	−2.92322			−0.494115
$36$		0			0
$37$	4.42476			0.727426			0.363713	−	0.931511i	$-0.381509\pi$
$37$	4.42476			0.727426			0.363713	+	0.931511i	$0.381509\pi$
$38$	0.0866979	+	0.150165i	0.0140643	+	0.0243600i
$39$		0			0
$40$	−1.76124	+	3.05056i	−0.278477	+	0.482335i
$41$	1.83747	−	3.18259i	0.286965	−	0.497037i	−0.686119	−	0.727489i	$-0.740687\pi$
$41$	1.83747	−	3.18259i	0.286965	−	0.497037i	0.973084	+	0.230452i	$0.0740205\pi$
$42$		0			0
$43$	4.15394	+	7.19483i	0.633469	+	1.09720i	0.986837	+	0.161717i	$0.0517031\pi$
$43$	4.15394	+	7.19483i	0.633469	+	1.09720i	−0.353368	+	0.935484i	$0.614964\pi$
$44$	9.53017			1.43673
$45$		0			0
$46$	0.429753			0.0633636
$47$	3.54895	+	6.14697i	0.517668	+	0.896628i	0.999789	+	0.0205231i	$0.00653317\pi$
$47$	3.54895	+	6.14697i	0.517668	+	0.896628i	−0.482121	+	0.876105i	$0.660133\pi$
$48$		0			0
$49$	2.62929	−	4.55406i	0.375613	−	0.650580i
$50$	−0.0193083	+	0.0334429i	−0.00273060	+	0.00472954i
$51$		0			0
$52$	−0.0165000	−	0.0285788i	−0.00228813	−	0.00396316i
$53$	−1.30057			−0.178648			−0.0893238	−	0.996003i	$-0.528471\pi$
$53$	−1.30057			−0.178648			−0.0893238	+	0.996003i	$0.528471\pi$
$54$		0			0
$55$	−11.5526			−1.55775
$56$	1.04920	+	1.81728i	0.140206	+	0.242844i
$57$		0			0
$58$	−1.62182	+	2.80907i	−0.212955	+	0.368849i
$59$	1.85091	−	3.20586i	0.240967	−	0.417368i	−0.720023	−	0.693950i	$-0.755869\pi$
$59$	1.85091	−	3.20586i	0.240967	−	0.417368i	0.960990	+	0.276583i	$0.0892020\pi$
$60$		0			0
$61$	−3.45712	−	5.98791i	−0.442639	−	0.766673i	0.555246	−	0.831686i	$-0.312624\pi$
$61$	−3.45712	−	5.98791i	−0.442639	−	0.766673i	−0.997884	+	0.0650137i	$0.979291\pi$
$62$	−1.54955			−0.196793
$63$		0			0
$64$	−4.15011			−0.518764
$65$	0.0200015	+	0.0346436i	0.00248088	+	0.00429701i
$66$		0			0
$67$	5.51340	−	9.54949i	0.673569	−	1.16666i	−0.303316	−	0.952890i	$-0.598094\pi$
$67$	5.51340	−	9.54949i	0.673569	−	1.16666i	0.976885	−	0.213765i	$-0.0685728\pi$
$68$	−2.86242	+	4.95785i	−0.347119	+	0.601228i
$69$		0			0
$70$	−0.607251	−	1.05179i	−0.0725803	−	0.125713i
$71$	−6.08428			−0.722071			−0.361035	−	0.932552i	$-0.617577\pi$
$71$	−6.08428			−0.722071			−0.361035	+	0.932552i	$0.617577\pi$
$72$		0			0
$73$	−0.546973			−0.0640183			−0.0320092	−	0.999488i	$-0.510191\pi$
$73$	−0.546973			−0.0640183			−0.0320092	+	0.999488i	$0.510191\pi$
$74$	0.919169	+	1.59205i	0.106851	+	0.185072i
$75$		0			0
$76$	0.381332	−	0.660487i	0.0437418	−	0.0757630i
$77$	−3.44106	+	5.96008i	−0.392145	+	0.679215i
$78$		0			0
$79$	−0.244572	−	0.423611i	−0.0275165	−	0.0476600i	0.851939	−	0.523641i	$-0.175427\pi$
$79$	−0.244572	−	0.423611i	−0.0275165	−	0.0476600i	−0.879456	+	0.475981i	$0.842093\pi$
$80$	6.63254			0.741540
$81$		0			0
$82$	1.52681			0.168608
$83$	−2.30684	−	3.99556i	−0.253208	−	0.438569i	0.711199	−	0.702991i	$-0.248152\pi$
$83$	−2.30684	−	3.99556i	−0.253208	−	0.438569i	−0.964407	+	0.264421i	$0.914819\pi$
$84$		0			0
$85$	3.46986	−	6.00998i	0.376360	−	0.651874i
$86$	−1.72582	+	2.98921i	−0.186100	+	0.322335i
$87$		0			0
$88$	4.14647	+	7.18189i	0.442015	+	0.765592i
$89$	−3.37307			−0.357544			−0.178772	−	0.983891i	$-0.557212\pi$
$89$	−3.37307			−0.357544			−0.178772	+	0.983891i	$0.557212\pi$
$90$		0			0
$91$	0.0238305			0.00249812
$92$	−0.945113	−	1.63698i	−0.0985348	−	0.170667i
$93$		0			0
$94$	−1.47447	+	2.55386i	−0.152080	+	0.263410i
$95$	−0.462257	+	0.800652i	−0.0474265	+	0.0821452i
$96$		0			0
$97$	−4.97068	−	8.60947i	−0.504696	−	0.874159i	−0.999985	−	0.00543103i	$-0.998271\pi$
$97$	−4.97068	−	8.60947i	−0.504696	−	0.874159i	0.495289	−	0.868728i	$-0.335062\pi$
$98$	2.18476			0.220694
$99$		0			0
$100$	0.169851			0.0169851
$101$	−6.89974	−	11.9507i	−0.686550	−	1.18914i	−0.972947	−	0.231029i	$-0.925791\pi$
$101$	−6.89974	−	11.9507i	−0.686550	−	1.18914i	0.286397	−	0.958111i	$-0.407542\pi$
$102$		0			0
$103$	−2.28256	+	3.95351i	−0.224907	+	0.389551i	−0.956292	−	0.292415i	$-0.905541\pi$
$103$	−2.28256	+	3.95351i	−0.224907	+	0.389551i	0.731384	+	0.681966i	$0.238875\pi$
$104$	0.0143579	−	0.0248686i	0.00140791	−	0.00243856i
$105$		0			0
$106$	−0.270172	−	0.467952i	−0.0262415	−	0.0454515i
$107$	−11.2965			−1.09207			−0.546035	−	0.837762i	$-0.683864\pi$
$107$	−11.2965			−1.09207			−0.546035	+	0.837762i	$0.683864\pi$
$108$		0			0
$109$	14.5032			1.38915			0.694577	−	0.719419i	$-0.255592\pi$
$109$	14.5032			1.38915			0.694577	+	0.719419i	$0.255592\pi$
$110$	−2.39986	−	4.15668i	−0.228818	−	0.396324i
$111$		0			0
$112$	1.97557	−	3.42178i	0.186673	−	0.323328i
$113$	−6.27921	+	10.8759i	−0.590699	+	1.02312i	0.403440	+	0.915006i	$0.367814\pi$
$113$	−6.27921	+	10.8759i	−0.590699	+	1.02312i	−0.994139	+	0.108114i	$0.965519\pi$
$114$		0			0
$115$	1.14568	+	1.98438i	0.106835	+	0.185044i
$116$	14.2668			1.32464
$117$		0			0
$118$	1.53798			0.141582
$119$	−2.06706	−	3.58026i	−0.189487	−	0.328202i
$120$		0			0
$121$	−8.09909	+	14.0280i	−0.736281	+	1.27528i
$122$	1.43632	−	2.48777i	0.130038	−	0.225232i
$123$		0			0
$124$	3.40777	+	5.90243i	0.306027	+	0.530054i
$125$	−11.2818			−1.00908
$126$		0			0
$127$	−8.39499			−0.744935			−0.372467	−	0.928045i	$-0.621488\pi$
$127$	−8.39499			−0.744935			−0.372467	+	0.928045i	$0.621488\pi$
$128$	−5.28637	−	9.15627i	−0.467254	−	0.809307i
$129$		0			0
$130$	−0.00830995	+	0.0143932i	−0.000728831	+	0.00126237i
$131$	7.76745	−	13.4536i	0.678645	−	1.17545i	−0.296744	−	0.954957i	$-0.595901\pi$
$131$	7.76745	−	13.4536i	0.678645	−	1.17545i	0.975389	−	0.220491i	$-0.0707659\pi$
$132$		0			0
$133$	0.275375	+	0.476964i	0.0238781	+	0.0413580i
$134$	4.58126			0.395761
$135$		0			0
$136$	−4.98162			−0.427170
$137$	−6.00370	−	10.3987i	−0.512930	−	0.888421i	−0.999888	−	0.0149956i	$-0.995227\pi$
$137$	−6.00370	−	10.3987i	−0.512930	−	0.888421i	0.486957	−	0.873426i	$-0.338107\pi$
$138$		0			0
$139$	−3.07256	+	5.32183i	−0.260611	+	0.451392i	−0.966404	−	0.257026i	$-0.917257\pi$
$139$	−3.07256	+	5.32183i	−0.260611	+	0.451392i	0.705793	+	0.708418i	$0.250591\pi$
$140$	−2.67093	+	4.62619i	−0.225735	+	0.390985i
$141$		0			0
$142$	−1.26391	−	2.18915i	−0.106065	−	0.183709i
$143$	0.0941785			0.00787561
$144$		0			0
$145$	−17.2945			−1.43623
$146$	−0.113624	−	0.196803i	−0.00940362	−	0.0162876i
$147$		0			0
$148$	4.04287	−	7.00246i	0.332322	−	0.575599i
$149$	−0.441410	+	0.764545i	−0.0361617	+	0.0626340i	−0.883540	−	0.468356i	$-0.844846\pi$
$149$	−0.441410	+	0.764545i	−0.0361617	+	0.0626340i	0.847378	+	0.530990i	$0.178180\pi$
$150$		0			0
$151$	−4.11274	−	7.12347i	−0.334690	−	0.579700i	0.648735	−	0.761014i	$-0.275298\pi$
$151$	−4.11274	−	7.12347i	−0.334690	−	0.579700i	−0.983425	+	0.181314i	$0.941965\pi$
$152$	0.663653			0.0538294
$153$		0			0
$154$	−2.85929			−0.230408
$155$	−4.13095	−	7.15502i	−0.331806	−	0.574705i
$156$		0			0
$157$	−6.27991	+	10.8771i	−0.501192	+	0.868089i	0.498808	+	0.866713i	$0.333771\pi$
$157$	−6.27991	+	10.8771i	−0.501192	+	0.868089i	−0.999999	+	0.00137640i	$0.999562\pi$
$158$	0.101611	−	0.175996i	0.00808377	−	0.0140015i
$159$		0			0
$160$	4.90028	+	8.48753i	0.387401	+	0.670998i
$161$	1.36501			0.107578
$162$		0			0
$163$	3.31466			0.259624			0.129812	−	0.991539i	$-0.458563\pi$
$163$	3.31466			0.259624			0.129812	+	0.991539i	$0.458563\pi$
$164$	−3.35777	−	5.81583i	−0.262198	−	0.454140i
$165$		0			0
$166$	0.958412	−	1.66002i	0.0743872	−	0.128842i
$167$	10.2815	−	17.8081i	0.795606	−	1.37803i	−0.126848	−	0.991922i	$-0.540486\pi$
$167$	10.2815	−	17.8081i	0.795606	−	1.37803i	0.922454	−	0.386107i	$-0.126180\pi$
$168$		0			0
$169$	6.49984	+	11.2580i	0.499987	+	0.866004i
$170$	2.88322			0.221133
$171$		0			0
$172$	15.1817			1.15759
$173$	−7.01663	−	12.1532i	−0.533465	−	0.923988i	−0.999236	−	0.0390830i	$-0.987556\pi$
$173$	−7.01663	−	12.1532i	−0.533465	−	0.923988i	0.465771	−	0.884905i	$-0.345777\pi$
$174$		0			0
$175$	−0.0613281	+	0.106223i	−0.00463597	+	0.00802974i
$176$	7.80745	−	13.5229i	0.588509	−	1.01933i
$177$		0			0
$178$	−0.700697	−	1.21364i	−0.0525195	−	0.0909664i
$179$	10.1900			0.761636			0.380818	−	0.924650i	$-0.375642\pi$
$179$	10.1900			0.761636			0.380818	+	0.924650i	$0.375642\pi$
$180$		0			0
$181$	24.0547			1.78797			0.893987	−	0.448093i	$-0.147897\pi$
$181$	24.0547			1.78797			0.893987	+	0.448093i	$0.147897\pi$
$182$	0.00495039	+	0.00857433i	0.000366948	+	0.000635572i
$183$		0			0
$184$	0.822415	−	1.42446i	0.0606292	−	0.105013i
$185$	−4.90083	+	8.48849i	−0.360316	+	0.624086i
$186$		0			0
$187$	−8.16906	−	14.1492i	−0.597381	−	1.03469i
$188$	12.9706			0.945981
$189$		0			0
$190$	−0.384104			−0.0278658
$191$	−5.47318	−	9.47983i	−0.396026	−	0.685937i	0.597206	−	0.802088i	$-0.296278\pi$
$191$	−5.47318	−	9.47983i	−0.396026	−	0.685937i	−0.993232	+	0.116151i	$0.962944\pi$
$192$		0			0
$193$	5.40298	−	9.35824i	0.388915	−	0.673621i	−0.603389	−	0.797447i	$-0.706183\pi$
$193$	5.40298	−	9.35824i	0.388915	−	0.673621i	0.992304	+	0.123826i	$0.0395166\pi$
$194$	2.06515	−	3.57694i	0.148269	−	0.256810i
$195$		0			0
$196$	−4.80473	−	8.32204i	−0.343195	−	0.594431i
$197$	−22.0734			−1.57266			−0.786331	−	0.617806i	$-0.788022\pi$
$197$	−22.0734			−1.57266			−0.786331	+	0.617806i	$0.788022\pi$
$198$		0			0
$199$	12.8868			0.913518			0.456759	−	0.889590i	$-0.349010\pi$
$199$	12.8868			0.913518			0.456759	+	0.889590i	$0.349010\pi$
$200$	0.0739003	+	0.127999i	0.00522554	+	0.00905090i
$201$		0			0
$202$	2.86661	−	4.96512i	0.201694	−	0.349344i
$203$	−5.15132	+	8.92235i	−0.361552	+	0.626226i
$204$		0			0
$205$	4.07034	+	7.05003i	0.284285	+	0.492396i
$206$	−1.89665			−0.132146
$207$		0			0
$208$	−0.0540694			−0.00374904
$209$	1.08829	+	1.88497i	0.0752783	+	0.130386i
$210$		0			0
$211$	11.9978	−	20.7808i	0.825964	−	1.43061i	−0.0752168	−	0.997167i	$-0.523965\pi$
$211$	11.9978	−	20.7808i	0.825964	−	1.43061i	0.901181	−	0.433444i	$-0.142702\pi$
$212$	−1.18833	+	2.05824i	−0.0816146	+	0.141361i
$213$		0			0
$214$	−2.34665	−	4.06452i	−0.160414	−	0.277845i
$215$	−18.4035			−1.25511
$216$		0			0
$217$	−4.92177			−0.334112
$218$	3.01279	+	5.21831i	0.204052	+	0.353428i
$219$		0			0
$220$	−10.5556	+	18.2828i	−0.711655	+	1.23262i
$221$	−0.0282868	+	0.0489942i	−0.00190278	+	0.00329571i
$222$		0			0
$223$	−10.8311	−	18.7600i	−0.725303	−	1.25626i	−0.958849	−	0.283916i	$-0.908366\pi$
$223$	−10.8311	−	18.7600i	−0.725303	−	1.25626i	0.233546	−	0.972346i	$-0.424967\pi$
$224$	5.83838			0.390093
$225$		0			0
$226$	−5.21760			−0.347070
$227$	−10.8209	−	18.7424i	−0.718211	−	1.24398i	−0.961708	−	0.274076i	$-0.911628\pi$
$227$	−10.8209	−	18.7424i	−0.718211	−	1.24398i	0.243497	−	0.969902i	$-0.421705\pi$
$228$		0			0
$229$	5.40268	−	9.35772i	0.357019	−	0.618375i	−0.630442	−	0.776236i	$-0.717126\pi$
$229$	5.40268	−	9.35772i	0.357019	−	0.618375i	0.987461	+	0.157861i	$0.0504598\pi$
$230$	−0.475991	+	0.824441i	−0.0313859	+	0.0543620i
$231$		0			0
$232$	6.20733	+	10.7514i	0.407531	+	0.705865i
$233$	7.63900			0.500447			0.250224	−	0.968188i	$-0.419496\pi$
$233$	7.63900			0.500447			0.250224	+	0.968188i	$0.419496\pi$
$234$		0			0
$235$	−15.7232			−1.02567
$236$	−3.38232	−	5.85835i	−0.220170	−	0.381346i
$237$		0			0
$238$	0.858795	−	1.48748i	0.0556674	−	0.0964188i
$239$	1.61575	−	2.79855i	0.104514	−	0.181023i	−0.809026	−	0.587773i	$-0.800005\pi$
$239$	1.61575	−	2.79855i	0.104514	−	0.181023i	0.913540	+	0.406750i	$0.133338\pi$
$240$		0			0
$241$	13.2725	+	22.9886i	0.854955	+	1.48083i	0.876687	+	0.481062i	$0.159749\pi$
$241$	13.2725	+	22.9886i	0.854955	+	1.48083i	−0.0217316	+	0.999764i	$0.506918\pi$
$242$	−6.72979			−0.432608
$243$		0			0
$244$	−12.6350			−0.808873
$245$	5.82437	+	10.0881i	0.372105	+	0.644505i
$246$		0			0
$247$	0.00376838	−	0.00652703i	0.000239776	−	0.000415305i
$248$	−2.96536	+	5.13616i	−0.188301	+	0.326147i
$249$		0			0
$250$	−2.34361	−	4.05925i	−0.148223	−	0.256730i
$251$	−4.49930			−0.283993			−0.141997	−	0.989867i	$-0.545352\pi$
$251$	−4.49930			−0.283993			−0.141997	+	0.989867i	$0.545352\pi$
$252$		0			0
$253$	5.39452			0.339150
$254$	−1.74392	−	3.02055i	−0.109423	−	0.189526i
$255$		0			0
$256$	−1.95380	+	3.38409i	−0.122113	+	0.211506i
$257$	−6.86771	+	11.8952i	−0.428396	+	0.742003i	−0.996731	−	0.0807940i	$-0.974254\pi$
$257$	−6.86771	+	11.8952i	−0.428396	+	0.742003i	0.568335	+	0.822797i	$0.307588\pi$
$258$		0			0
$259$	2.91952	+	5.05676i	0.181410	+	0.314211i
$260$	0.0731010			0.00453353
$261$		0			0
$262$	6.45423			0.398743
$263$	12.1013	+	20.9600i	0.746197	+	1.29245i	0.949634	+	0.313363i	$0.101456\pi$
$263$	12.1013	+	20.9600i	0.746197	+	1.29245i	−0.203437	+	0.979088i	$0.565211\pi$
$264$		0			0
$265$	1.44051	−	2.49503i	0.0884897	−	0.153269i
$266$	−0.114409	+	0.198162i	−0.00701487	+	0.0121501i
$267$		0			0
$268$	−10.0751	−	17.4506i	−0.615436	−	1.06597i
$269$	12.0062			0.732032			0.366016	−	0.930609i	$-0.380722\pi$
$269$	12.0062			0.732032			0.366016	+	0.930609i	$0.380722\pi$
$270$		0			0
$271$	3.71777			0.225839			0.112919	−	0.993604i	$-0.463980\pi$
$271$	3.71777			0.225839			0.112919	+	0.993604i	$0.463980\pi$
$272$	4.68999	+	8.12329i	0.284372	+	0.492547i
$273$		0			0
$274$	2.49433	−	4.32031i	0.150688	−	0.261000i
$275$	−0.242369	+	0.419796i	−0.0146154	+	0.0253146i
$276$		0			0
$277$	11.7416	+	20.3370i	0.705482	+	1.22193i	0.966517	+	0.256601i	$0.0826027\pi$
$277$	11.7416	+	20.3370i	0.705482	+	1.22193i	−0.261035	+	0.965329i	$0.584064\pi$
$278$	−2.55309			−0.153124
$279$		0			0
$280$	−4.64837			−0.277793
$281$	10.1859	+	17.6424i	0.607638	+	1.05246i	0.991629	+	0.129123i	$0.0412162\pi$
$281$	10.1859	+	17.6424i	0.607638	+	1.05246i	−0.383991	+	0.923337i	$0.625451\pi$
$282$		0			0
$283$	−5.79997	+	10.0458i	−0.344772	+	0.597163i	−0.985312	−	0.170761i	$-0.945377\pi$
$283$	−5.79997	+	10.0458i	−0.344772	+	0.597163i	0.640540	+	0.767925i	$0.278711\pi$
$284$	−5.55917	+	9.62876i	−0.329876	+	0.571362i
$285$		0			0
$286$	0.0195640	+	0.0338858i	0.00115684	+	0.00200371i
$287$	4.84956			0.286260
$288$		0			0
$289$	−7.18559			−0.422682
$290$	−3.59263	−	6.22262i	−0.210967	−	0.365405i
$291$		0			0
$292$	−0.499766	+	0.865620i	−0.0292466	+	0.0506566i
$293$	−15.7871	+	27.3440i	−0.922291	+	1.59745i	−0.126430	+	0.991976i	$0.540352\pi$
$293$	−15.7871	+	27.3440i	−0.922291	+	1.59745i	−0.795861	+	0.605479i	$0.792981\pi$
$294$		0			0
$295$	4.10010	+	7.10158i	0.238717	+	0.413470i
$296$	7.03603			0.408961
$297$		0			0
$298$	−0.366782			−0.0212471
$299$	−0.00933974	−	0.0161769i	−0.000540131	−	0.000935535i
$300$		0			0
$301$	−5.48166	+	9.49451i	−0.315957	+	0.547254i
$302$	1.70870	−	2.95956i	0.0983248	−	0.170304i
$303$		0			0
$304$	−0.624802	−	1.08219i	−0.0358348	−	0.0620678i
$305$	15.3163			0.877010
$306$		0			0
$307$	−8.12054			−0.463464			−0.231732	−	0.972780i	$-0.574439\pi$
$307$	−8.12054			−0.463464			−0.231732	+	0.972780i	$0.574439\pi$
$308$	6.28814	+	10.8914i	0.358300	+	0.620594i
$309$		0			0
$310$	1.71627	−	2.97267i	0.0974776	−	0.168836i
$311$	11.9243	−	20.6535i	0.676164	−	1.17115i	−0.299963	−	0.953951i	$-0.596974\pi$
$311$	11.9243	−	20.6535i	0.676164	−	1.17115i	0.976127	−	0.217199i	$-0.0696922\pi$
$312$		0			0
$313$	−13.4552	−	23.3051i	−0.760535	−	1.31728i	−0.942575	−	0.333994i	$-0.891604\pi$
$313$	−13.4552	−	23.3051i	−0.760535	−	1.31728i	0.182040	−	0.983291i	$-0.441730\pi$
$314$	−5.21818			−0.294479
$315$		0			0
$316$	−0.893856			−0.0502833
$317$	4.16617	+	7.21601i	0.233995	+	0.405292i	0.958980	−	0.283473i	$-0.0914867\pi$
$317$	4.16617	+	7.21601i	0.233995	+	0.405292i	−0.724985	+	0.688765i	$0.758153\pi$
$318$		0			0
$319$	−20.3581	+	35.2612i	−1.13983	+	1.97425i
$320$	4.59664	−	7.96161i	0.256960	−	0.445068i
$321$		0			0
$322$	0.283557	+	0.491135i	0.0158020	+	0.0273699i
$323$	−1.30748			−0.0727501
$324$		0			0
$325$	0.00167849			9.31061e−5
$326$	0.688565	+	1.19263i	0.0381361	+	0.0660536i
$327$		0			0
$328$	2.92185	−	5.06080i	0.161332	−	0.279436i
$329$	−4.68330	+	8.11172i	−0.258199	+	0.447214i
$330$		0			0
$331$	3.21013	+	5.56011i	0.176445	+	0.305611i	0.940660	−	0.339350i	$-0.110207\pi$
$331$	3.21013	+	5.56011i	0.176445	+	0.305611i	−0.764216	+	0.644961i	$0.776874\pi$
$332$	−8.43096			−0.462709
$333$		0			0
$334$	8.54322			0.467464
$335$	12.2132	+	21.1539i	0.667279	+	1.15576i
$336$		0			0
$337$	−3.73745	+	6.47345i	−0.203592	+	0.352631i	−0.949683	−	0.313212i	$-0.898595\pi$
$337$	−3.73745	+	6.47345i	−0.203592	+	0.352631i	0.746091	+	0.665844i	$0.231928\pi$
$338$	−2.70046	+	4.67734i	−0.146886	+	0.254414i
$339$		0			0
$340$	−6.34079	−	10.9826i	−0.343877	−	0.595613i
$341$	−19.4509			−1.05333
$342$		0			0
$343$	16.1768			0.873464
$344$	6.60538	+	11.4409i	0.356138	+	0.616850i
$345$		0			0
$346$	2.91517	−	5.04923i	0.156721	−	0.271448i
$347$	15.7272	−	27.2404i	0.844283	−	1.46234i	−0.0419596	−	0.999119i	$-0.513360\pi$
$347$	15.7272	−	27.2404i	0.844283	−	1.46234i	0.886243	−	0.463222i	$-0.153307\pi$
$348$		0			0
$349$	−5.92647	−	10.2650i	−0.317237	−	0.549470i	0.662674	−	0.748908i	$-0.269422\pi$
$349$	−5.92647	−	10.2650i	−0.317237	−	0.549470i	−0.979910	+	0.199438i	$0.936088\pi$
$350$	−0.0509595			−0.00272390
$351$		0			0
$352$	23.0733			1.22981
$353$	4.10354	+	7.10754i	0.218409	+	0.378296i	0.954322	−	0.298780i	$-0.0965798\pi$
$353$	4.10354	+	7.10754i	0.218409	+	0.378296i	−0.735912	+	0.677077i	$0.763246\pi$
$354$		0			0
$355$	6.73891	−	11.6721i	0.357664	−	0.619492i
$356$	−3.08195	+	5.33809i	−0.163343	+	0.282918i
$357$		0			0
$358$	2.11680	+	3.66640i	0.111876	+	0.193775i
$359$	17.7273			0.935611			0.467806	−	0.883831i	$-0.345045\pi$
$359$	17.7273			0.935611			0.467806	+	0.883831i	$0.345045\pi$
$360$		0			0
$361$	−18.8258			−0.990832
$362$	4.99696	+	8.65499i	0.262635	+	0.454896i
$363$		0			0
$364$	0.0217738	−	0.0377134i	0.00114126	−	0.00197672i
$365$	0.605824	−	1.04932i	0.0317103	−	0.0549238i
$366$		0			0
$367$	10.1598	+	17.5972i	0.530335	+	0.918568i	0.999374	+	0.0353899i	$0.0112673\pi$
$367$	10.1598	+	17.5972i	0.530335	+	0.918568i	−0.469038	+	0.883178i	$0.655399\pi$
$368$	−3.09708			−0.161446
$369$		0			0
$370$	−4.07226			−0.211707
$371$	−0.858138	−	1.48634i	−0.0445523	−	0.0771668i
$372$		0			0
$373$	4.84072	−	8.38437i	0.250643	−	0.434126i	−0.713060	−	0.701103i	$-0.752691\pi$
$373$	4.84072	−	8.38437i	0.250643	−	0.434126i	0.963703	+	0.266977i	$0.0860247\pi$
$374$	3.39397	−	5.87852i	0.175498	−	0.303971i
$375$		0			0
$376$	5.64337	+	9.77461i	0.291035	+	0.504087i
$377$	0.140987			0.00726119
$378$		0			0
$379$	−4.12905			−0.212095			−0.106048	−	0.994361i	$-0.533820\pi$
$379$	−4.12905			−0.212095			−0.106048	+	0.994361i	$0.533820\pi$
$380$	0.844722	+	1.46310i	0.0433333	+	0.0750555i
$381$		0			0
$382$	2.27392	−	3.93855i	0.116344	−	0.201514i
$383$	−2.37509	+	4.11378i	−0.121362	+	0.210204i	−0.920305	−	0.391202i	$-0.872059\pi$
$383$	−2.37509	+	4.11378i	−0.121362	+	0.210204i	0.798943	+	0.601406i	$0.205393\pi$
$384$		0			0
$385$	−7.62258	−	13.2027i	−0.388483	−	0.672872i
$386$	4.48951			0.228510
$387$		0			0
$388$	−18.1667			−0.922275
$389$	10.9067	+	18.8909i	0.552990	+	0.957806i	0.998057	+	0.0623089i	$0.0198464\pi$
$389$	10.9067	+	18.8909i	0.552990	+	0.957806i	−0.445067	+	0.895497i	$0.646820\pi$
$390$		0			0
$391$	−1.62026	+	2.80637i	−0.0819401	+	0.141924i
$392$	4.18097	−	7.24165i	0.211171	−	0.365758i
$393$		0			0
$394$	−4.58537	−	7.94209i	−0.231007	−	0.400117i
$395$	1.08355			0.0545191
$396$		0			0
$397$	−34.8490			−1.74902			−0.874512	−	0.485005i	$-0.838818\pi$
$397$	−34.8490			−1.74902			−0.874512	+	0.485005i	$0.838818\pi$
$398$	2.67701	+	4.63671i	0.134186	+	0.232417i
$399$		0			0
$400$	0.139148	−	0.241012i	0.00695740	−	0.0120506i
$401$	9.41304	−	16.3039i	0.470065	−	0.814176i	−0.529349	−	0.848404i	$-0.677564\pi$
$401$	9.41304	−	16.3039i	0.470065	−	0.814176i	0.999414	+	0.0342279i	$0.0108972\pi$
$402$		0			0
$403$	0.0336761	+	0.0583287i	0.00167753	+	0.00290556i
$404$	−25.2170			−1.25459
$405$		0			0
$406$	−4.28040			−0.212433
$407$	11.5380	+	19.9843i	0.571916	+	0.990587i
$408$		0			0
$409$	3.17998	−	5.50788i	0.157240	−	0.272347i	−0.776633	−	0.629954i	$-0.783074\pi$
$409$	3.17998	−	5.50788i	0.157240	−	0.272347i	0.933872	+	0.357607i	$0.116407\pi$
$410$	−1.69109	+	2.92905i	−0.0835169	+	0.144656i
$411$		0			0
$412$	4.17112	+	7.22459i	0.205496	+	0.355930i
$413$	4.88502			0.240376
$414$		0			0
$415$	10.2201			0.501687
$416$	−0.0399478	−	0.0691916i	−0.00195860	−	0.00339240i
$417$		0			0
$418$	−0.452146	+	0.783139i	−0.0221152	+	0.0383046i
$419$	12.1590	−	21.0600i	0.594005	−	1.02885i	−0.399681	−	0.916654i	$-0.630879\pi$
$419$	12.1590	−	21.0600i	0.594005	−	1.02885i	0.993686	−	0.112193i	$-0.0357875\pi$
$420$		0			0
$421$	3.99502	+	6.91957i	0.194705	+	0.337239i	0.946804	−	0.321811i	$-0.104292\pi$
$421$	3.99502	+	6.91957i	0.194705	+	0.337239i	−0.752099	+	0.659051i	$0.770958\pi$
$422$	9.96937			0.485302
$423$		0			0
$424$	−2.06811			−0.100436
$425$	−0.145593	−	0.252174i	−0.00706229	−	0.0122322i
$426$		0			0
$427$	4.56211	−	7.90181i	0.220776	−	0.382396i
$428$	−10.3215	+	17.8774i	−0.498909	+	0.864136i
$429$		0			0
$430$	−3.82301	−	6.62166i	−0.184362	−	0.319325i
$431$	9.87124			0.475481			0.237740	−	0.971329i	$-0.423593\pi$
$431$	9.87124			0.475481			0.237740	+	0.971329i	$0.423593\pi$
$432$		0			0
$433$	−6.10369			−0.293325			−0.146662	−	0.989187i	$-0.546853\pi$
$433$	−6.10369			−0.293325			−0.146662	+	0.989187i	$0.546853\pi$
$434$	−1.02242	−	1.77088i	−0.0490775	−	0.0850047i
$435$		0			0
$436$	13.2515	−	22.9522i	0.634630	−	1.09921i
$437$	0.215852	−	0.373866i	0.0103256	−	0.0178844i
$438$		0			0
$439$	7.56701	+	13.1064i	0.361154	+	0.625537i	0.988151	−	0.153485i	$-0.0490496\pi$
$439$	7.56701	+	13.1064i	0.361154	+	0.625537i	−0.626997	+	0.779021i	$0.715716\pi$
$440$	−18.3704			−0.875774
$441$		0			0
$442$	−0.0235044			−0.00111799
$443$	0.361397	+	0.625957i	0.0171705	+	0.0297401i	0.874483	−	0.485056i	$-0.161201\pi$
$443$	0.361397	+	0.625957i	0.0171705	+	0.0297401i	−0.857312	+	0.514796i	$0.827868\pi$
$444$		0			0
$445$	3.73598	−	6.47092i	0.177103	−	0.306751i
$446$	4.49995	−	7.79414i	0.213079	−	0.369063i
$447$		0			0
$448$	−2.73831	−	4.74288i	−0.129373	−	0.224080i
$449$	1.66845			0.0787389			0.0393695	−	0.999225i	$-0.487465\pi$
$449$	1.66845			0.0787389			0.0393695	+	0.999225i	$0.487465\pi$
$450$		0			0
$451$	19.1655			0.902468
$452$	11.4746	+	19.8745i	0.539718	+	0.934819i
$453$		0			0
$454$	4.49573	−	7.78684i	0.210995	−	0.365455i
$455$	−0.0263946	+	0.0457167i	−0.00123740	+	0.00214323i
$456$		0			0
$457$	−5.54172	−	9.59855i	−0.259231	−	0.449001i	0.706805	−	0.707408i	$-0.250136\pi$
$457$	−5.54172	−	9.59855i	−0.259231	−	0.449001i	−0.966036	+	0.258407i	$0.916802\pi$
$458$	4.48926			0.209769
$459$		0			0
$460$	4.18720			0.195229
$461$	10.9422	+	18.9524i	0.509629	+	0.882703i	0.999938	+	0.0111543i	$0.00355060\pi$
$461$	10.9422	+	18.9524i	0.509629	+	0.882703i	−0.490309	+	0.871549i	$0.663116\pi$
$462$		0			0
$463$	−12.4259	+	21.5222i	−0.577479	+	1.00022i	0.418289	+	0.908314i	$0.362630\pi$
$463$	−12.4259	+	21.5222i	−0.577479	+	1.00022i	−0.995767	+	0.0919086i	$0.970703\pi$
$464$	11.6879	−	20.2440i	0.542597	−	0.939805i
$465$		0			0
$466$	1.58687	+	2.74854i	0.0735105	+	0.127324i
$467$	−11.8355			−0.547683			−0.273842	−	0.961775i	$-0.588294\pi$
$467$	−11.8355			−0.547683			−0.273842	+	0.961775i	$0.588294\pi$
$468$		0			0
$469$	14.5513			0.671916
$470$	−3.26623	−	5.65727i	−0.150660	−	0.260951i
$471$		0			0
$472$	2.94322	−	5.09780i	0.135473	−	0.234645i
$473$	−21.6636	+	37.5224i	−0.996091	+	1.72528i
$474$		0			0
$475$	0.0193959	+	0.0335947i	0.000889946	+	0.00154143i
$476$	−7.55465			−0.346267
$477$		0			0
$478$	1.34258			0.0614080
$479$	−1.44368	−	2.50052i	−0.0659632	−	0.114252i	0.831158	−	0.556037i	$-0.187679\pi$
$479$	−1.44368	−	2.50052i	−0.0659632	−	0.114252i	−0.897121	+	0.441785i	$0.854345\pi$
$480$		0			0
$481$	0.0399523	−	0.0691994i	0.00182167	−	0.00315522i
$482$	−5.51426	+	9.55099i	−0.251168	+	0.435035i
$483$		0			0
$484$	14.8002	+	25.6347i	0.672735	+	1.16521i
$485$	22.0220			0.999966
$486$		0			0
$487$	8.75903			0.396910			0.198455	−	0.980110i	$-0.436408\pi$
$487$	8.75903			0.396910			0.198455	+	0.980110i	$0.436408\pi$
$488$	−5.49734	−	9.52167i	−0.248853	−	0.431026i
$489$		0			0
$490$	−2.41983	+	4.19127i	−0.109317	+	0.189342i
$491$	11.2865	−	19.5488i	0.509354	−	0.882226i	−0.490588	−	0.871392i	$-0.663218\pi$
$491$	11.2865	−	19.5488i	0.509354	−	0.882226i	0.999941	−	0.0108346i	$-0.00344882\pi$
$492$		0			0
$493$	−12.2292	−	21.1816i	−0.550776	−	0.953972i
$494$	0.00313127			0.000140883
$495$		0			0
$496$	11.1671			0.501416
$497$	−4.01449	−	6.95331i	−0.180075	−	0.311899i
$498$		0			0
$499$	12.6664	−	21.9389i	0.567026	−	0.982118i	−0.429832	−	0.902909i	$-0.641427\pi$
$499$	12.6664	−	21.9389i	0.567026	−	0.982118i	0.996858	−	0.0792092i	$-0.0252395\pi$
$500$	−10.3081	+	17.8542i	−0.460994	+	0.798465i
$501$		0			0
$502$	−0.934653	−	1.61887i	−0.0417156	−	0.0722536i
$503$	3.74414			0.166943			0.0834714	−	0.996510i	$-0.473399\pi$
$503$	3.74414			0.166943			0.0834714	+	0.996510i	$0.473399\pi$
$504$		0			0
$505$	30.5684			1.36028
$506$	1.12062	+	1.94097i	0.0498176	+	0.0862867i
$507$		0			0
$508$	−7.67045	+	13.2856i	−0.340321	+	0.589454i
$509$	−12.1749	+	21.0876i	−0.539645	+	0.934692i	0.459278	+	0.888292i	$0.348108\pi$
$509$	−12.1749	+	21.0876i	−0.539645	+	0.934692i	−0.998923	+	0.0463997i	$0.985225\pi$
$510$		0			0
$511$	−0.360901	−	0.625098i	−0.0159653	−	0.0276527i
$512$	−22.7690			−1.00626
$513$		0			0
$514$	−5.70660			−0.251707
$515$	−5.05630	−	8.75776i	−0.222807	−	0.385913i
$516$		0			0
$517$	−18.5085	+	32.0576i	−0.814001	+	1.40989i
$518$	−1.21296	+	2.10091i	−0.0532945	+	0.0923087i
$519$		0			0
$520$	0.0318054	+	0.0550885i	0.00139476	+	0.00241579i
$521$	19.6209			0.859608			0.429804	−	0.902922i	$-0.358583\pi$
$521$	19.6209			0.859608			0.429804	+	0.902922i	$0.358583\pi$
$522$		0			0
$523$	20.8154			0.910194			0.455097	−	0.890442i	$-0.349605\pi$
$523$	20.8154			0.910194			0.455097	+	0.890442i	$0.349605\pi$
$524$	−14.1941	−	24.5850i	−0.620074	−	1.07400i
$525$		0			0
$526$	−5.02767	+	8.70819i	−0.219217	+	0.379695i
$527$	5.84214	−	10.1189i	0.254488	−	0.440785i
$528$		0			0
$529$	10.9650	+	18.9920i	0.476740	+	0.825738i
$530$	1.19696			0.0519928
$531$		0			0
$532$	1.00643			0.0436345
$533$	−0.0331820	−	0.0574729i	−0.00143727	−	0.00248943i
$534$		0			0
$535$	12.5119	−	21.6712i	0.540936	−	0.936929i
$536$	8.76713	−	15.1851i	0.378682	−	0.655897i
$537$		0			0
$538$	2.49409	+	4.31989i	0.107528	+	0.186244i
$539$	27.4245			1.18126
$540$		0			0
$541$	−30.6272			−1.31676			−0.658382	−	0.752684i	$-0.728759\pi$
$541$	−30.6272			−1.31676			−0.658382	+	0.752684i	$0.728759\pi$
$542$	0.772305	+	1.33767i	0.0331733	+	0.0574579i
$543$		0			0
$544$	−6.93015	+	12.0034i	−0.297128	+	0.514640i
$545$	−16.0636	+	27.8230i	−0.688090	+	1.19181i
$546$		0			0
$547$	−11.3238	−	19.6135i	−0.484172	−	0.838611i	0.515662	−	0.856792i	$-0.327546\pi$
$547$	−11.3238	−	19.6135i	−0.484172	−	0.838611i	−0.999835	+	0.0181808i	$0.994213\pi$
$548$	−21.9422			−0.937323
$549$		0			0
$550$	−0.201393			−0.00858741
$551$	1.62918	+	2.82182i	0.0694055	+	0.120214i
$552$		0			0
$553$	0.322744	−	0.559010i	0.0137245	−	0.0237715i
$554$	−4.87822	+	8.44933i	−0.207256	+	0.358978i
$555$		0			0
$556$	5.61476	+	9.72504i	0.238119	+	0.412434i
$557$	36.4518			1.54451			0.772256	−	0.635311i	$-0.219128\pi$
$557$	36.4518			1.54451			0.772256	+	0.635311i	$0.219128\pi$
$558$		0			0
$559$	0.150028			0.00634550
$560$	4.37625	+	7.57988i	0.184930	+	0.320308i
$561$		0			0
$562$	−4.23188	+	7.32984i	−0.178511	+	0.309191i
$563$	−13.2581	+	22.9637i	−0.558763	+	0.967806i	0.438837	+	0.898567i	$0.355391\pi$
$563$	−13.2581	+	22.9637i	−0.558763	+	0.967806i	−0.997600	+	0.0692393i	$0.977943\pi$
$564$		0			0
$565$	−13.9096	−	24.0922i	−0.585183	−	1.01357i
$566$	−4.81938			−0.202574
$567$		0			0
$568$	−9.67492			−0.405950
$569$	−11.4837	−	19.8904i	−0.481422	−	0.833847i	0.518351	−	0.855168i	$-0.326546\pi$
$569$	−11.4837	−	19.8904i	−0.481422	−	0.833847i	−0.999773	+	0.0213210i	$0.993213\pi$
$570$		0			0
$571$	2.39900	−	4.15519i	0.100395	−	0.173889i	−0.811452	−	0.584419i	$-0.801323\pi$
$571$	2.39900	−	4.15519i	0.100395	−	0.173889i	0.911848	+	0.410529i	$0.134656\pi$
$572$	0.0860504	−	0.149044i	0.00359795	−	0.00623183i
$573$		0			0
$574$	1.00741	+	1.74489i	0.0420486	+	0.0728304i
$575$	0.0961436			0.00400947
$576$		0			0
$577$	−4.31333			−0.179566			−0.0897831	−	0.995961i	$-0.528617\pi$
$577$	−4.31333			−0.179566			−0.0897831	+	0.995961i	$0.528617\pi$
$578$	−1.49269	−	2.58541i	−0.0620876	−	0.107539i
$579$		0			0
$580$	−15.8018	+	27.3696i	−0.656136	+	1.13646i
$581$	3.04417	−	5.27265i	0.126293	−	0.218746i
$582$		0			0
$583$	−3.39137	−	5.87402i	−0.140456	−	0.243277i
$584$	−0.869769			−0.0359913
$585$		0			0
$586$	−13.1180			−0.541899
$587$	−20.9111	−	36.2191i	−0.863094	−	1.49492i	−0.868928	−	0.494939i	$-0.835190\pi$
$587$	−20.9111	−	36.2191i	−0.863094	−	1.49492i	0.00583407	−	0.999983i	$-0.498143\pi$
$588$		0			0
$589$	−0.778292	+	1.34804i	−0.0320690	+	0.0555451i
$590$	−1.70345	+	2.95047i	−0.0701301	+	0.121469i
$591$		0			0
$592$	−6.62413	−	11.4733i	−0.272250	−	0.471551i
$593$	−31.5370			−1.29507			−0.647536	−	0.762035i	$-0.724200\pi$
$593$	−31.5370			−1.29507			−0.647536	+	0.762035i	$0.724200\pi$
$594$		0			0
$595$	9.15786			0.375436
$596$	0.806628	+	1.39712i	0.0330408	+	0.0572283i
$597$		0			0
$598$	0.00388035	−	0.00672096i	0.000158679	−	0.000274840i
$599$	6.31515	−	10.9382i	0.258030	−	0.446921i	−0.707684	−	0.706529i	$-0.750260\pi$
$599$	6.31515	−	10.9382i	0.258030	−	0.446921i	0.965714	+	0.259608i	$0.0835933\pi$
$600$		0			0
$601$	−10.2715	−	17.7907i	−0.418983	−	0.725699i	0.576855	−	0.816847i	$-0.304280\pi$
$601$	−10.2715	−	17.7907i	−0.418983	−	0.725699i	−0.995837	+	0.0911474i	$0.970947\pi$
$602$	−4.55489			−0.185643
$603$		0			0
$604$	−15.0311			−0.611608
$605$	−17.9410	−	31.0747i	−0.729405	−	1.26337i
$606$		0			0
$607$	−6.45628	+	11.1826i	−0.262052	+	0.453888i	−0.966787	−	0.255583i	$-0.917733\pi$
$607$	−6.45628	+	11.1826i	−0.262052	+	0.453888i	0.704735	+	0.709471i	$0.251066\pi$
$608$	0.923237	−	1.59909i	0.0374422	−	0.0648518i
$609$		0			0
$610$	3.18171	+	5.51088i	0.128824	+	0.223129i
$611$	0.128178			0.00518552
$612$		0			0
$613$	−31.1598			−1.25853			−0.629265	−	0.777191i	$-0.716644\pi$
$613$	−31.1598			−1.25853			−0.629265	+	0.777191i	$0.716644\pi$
$614$	−1.68690	−	2.92180i	−0.0680779	−	0.117914i
$615$		0			0
$616$	−5.47180	+	9.47743i	−0.220465	+	0.381857i
$617$	3.57039	−	6.18410i	0.143739	−	0.248962i	−0.785163	−	0.619289i	$-0.787421\pi$
$617$	3.57039	−	6.18410i	0.143739	−	0.248962i	0.928902	+	0.370327i	$0.120754\pi$
$618$		0			0
$619$	5.01545	+	8.68702i	0.201588	+	0.349161i	0.949040	−	0.315155i	$-0.102056\pi$
$619$	5.01545	+	8.68702i	0.201588	+	0.349161i	−0.747452	+	0.664316i	$0.768723\pi$
$620$	−15.0977			−0.606338
$621$		0			0
$622$	9.90827			0.397285
$623$	−2.22560	−	3.85485i	−0.0891667	−	0.154441i
$624$		0			0
$625$	12.2633	−	21.2407i	0.490532	−	0.849627i
$626$	5.59020	−	9.68250i	0.223429	−	0.386991i
$627$		0			0
$628$	11.4758	+	19.8767i	0.457936	+	0.793168i
$629$	−13.8619			−0.552708
$630$		0			0
$631$	−7.07560			−0.281675			−0.140838	−	0.990033i	$-0.544980\pi$
$631$	−7.07560			−0.281675			−0.140838	+	0.990033i	$0.544980\pi$
$632$	−0.388906	−	0.673606i	−0.0154699	−	0.0267946i
$633$		0			0
$634$	−1.73090	+	2.99801i	−0.0687429	+	0.119066i
$635$	9.29823	−	16.1050i	0.368989	−	0.639108i
$636$		0			0
$637$	−0.0474811	−	0.0822396i	−0.00188127	−	0.00325845i
$638$	−16.9162			−0.669718
$639$		0			0
$640$	23.4206			0.925781
$641$	2.50561	+	4.33984i	0.0989655	+	0.171413i	0.911257	−	0.411839i	$-0.135113\pi$
$641$	2.50561	+	4.33984i	0.0989655	+	0.171413i	−0.812291	+	0.583252i	$0.801780\pi$
$642$		0			0
$643$	−0.819202	+	1.41890i	−0.0323062	+	0.0559559i	−0.881726	−	0.471761i	$-0.843618\pi$
$643$	−0.819202	+	1.41890i	−0.0323062	+	0.0559559i	0.849420	+	0.527717i	$0.176952\pi$
$644$	1.24720	−	2.16021i	0.0491465	−	0.0851242i
$645$		0			0
$646$	−0.271607	−	0.470437i	−0.0106862	−	0.0185091i
$647$	34.4927			1.35605			0.678024	−	0.735040i	$-0.262836\pi$
$647$	34.4927			1.35605			0.678024	+	0.735040i	$0.262836\pi$
$648$		0			0
$649$	19.3056			0.757813
$650$	0.000348679	0	0.000603929i	1.36763e−5	0	2.36881e-5i
$651$		0			0
$652$	3.02858	−	5.24566i	0.118609	−	0.205436i
$653$	−19.3803	+	33.5677i	−0.758410	+	1.31360i	0.185252	+	0.982691i	$0.440690\pi$
$653$	−19.3803	+	33.5677i	−0.758410	+	1.31360i	−0.943661	+	0.330913i	$0.892643\pi$
$654$		0			0
$655$	17.2064	+	29.8023i	0.672308	+	1.16447i
$656$	−11.0032			−0.429604
$657$		0			0
$658$	−3.89151			−0.151707
$659$	−4.69596	−	8.13364i	−0.182929	−	0.316842i	0.759948	−	0.649984i	$-0.225224\pi$
$659$	−4.69596	−	8.13364i	−0.182929	−	0.316842i	−0.942877	+	0.333142i	$0.891891\pi$
$660$		0			0
$661$	12.0737	−	20.9123i	0.469613	−	0.813394i	−0.529783	−	0.848133i	$-0.677727\pi$
$661$	12.0737	−	20.9123i	0.469613	−	0.813394i	0.999396	+	0.0347394i	$0.0110601\pi$
$662$	−1.33370	+	2.31004i	−0.0518357	+	0.0897821i
$663$		0			0
$664$	−3.66821	−	6.35353i	−0.142354	−	0.246565i
$665$	−1.22001			−0.0473101
$666$		0			0
$667$	8.07569			0.312692
$668$	−18.7883	−	32.5422i	−0.726940	−	1.25910i
$669$		0			0
$670$	−5.07417	+	8.78873i	−0.196032	+	0.339538i
$671$	18.0295	−	31.2280i	0.696022	−	1.20555i
$672$		0			0
$673$	13.2331	+	22.9203i	0.510097	+	0.883514i	0.999932	+	0.0116988i	$0.00372393\pi$
$673$	13.2331	+	22.9203i	0.510097	+	0.883514i	−0.489834	+	0.871816i	$0.662943\pi$
$674$	−3.10557			−0.119622
$675$		0			0
$676$	23.7554			0.913671
$677$	−15.5334	−	26.9047i	−0.596998	−	1.03403i	−0.993262	−	0.115894i	$-0.963027\pi$
$677$	−15.5334	−	26.9047i	−0.596998	−	1.03403i	0.396264	−	0.918137i	$-0.370307\pi$
$678$		0			0
$679$	6.55945	−	11.3613i	0.251729	−	0.436007i
$680$	5.51760	−	9.55677i	0.211590	−	0.366485i
$681$		0			0
$682$	−4.04060	−	6.99852i	−0.154722	−	0.267987i
$683$	38.1361			1.45924			0.729619	−	0.683854i	$-0.239697\pi$
$683$	38.1361			1.45924			0.729619	+	0.683854i	$0.239697\pi$
$684$		0			0
$685$	26.5986			1.01628
$686$	3.36045	+	5.82047i	0.128303	+	0.222227i
$687$		0			0
$688$	12.4374	−	21.5422i	0.474171	−	0.821288i
$689$	−0.0117432	+	0.0203399i	−0.000447381	+	0.000774887i
$690$		0			0
$691$	−16.4648	−	28.5178i	−0.626349	−	1.08487i	−0.988278	−	0.152663i	$-0.951215\pi$
$691$	−16.4648	−	28.5178i	−0.626349	−	1.08487i	0.361929	−	0.932206i	$-0.382118\pi$
$692$	−25.6442			−0.974847
$693$		0			0
$694$	13.0683			0.496065
$695$	−6.80629	−	11.7888i	−0.258177	−	0.447176i
$696$		0			0
$697$	−5.75642	+	9.97041i	−0.218040	+	0.377656i
$698$	2.46225	−	4.26474i	0.0931975	−	0.161423i
$699$		0			0
$700$	0.112070	+	0.194111i	0.00423586	+	0.00733672i
$701$	−2.30710			−0.0871381			−0.0435690	−	0.999050i	$-0.513873\pi$
$701$	−2.30710			−0.0871381			−0.0435690	+	0.999050i	$0.513873\pi$
$702$		0			0
$703$	1.84668			0.0696490
$704$	−10.8218	−	18.7439i	−0.407862	−	0.706438i
$705$		0			0
$706$	−1.70488	+	2.95294i	−0.0641641	+	0.111136i
$707$	9.10510	−	15.7705i	0.342433	−	0.593111i
$708$		0			0
$709$	5.57603	+	9.65797i	0.209412	+	0.362713i	0.951530	−	0.307557i	$-0.0995116\pi$
$709$	5.57603	+	9.65797i	0.209412	+	0.362713i	−0.742117	+	0.670270i	$0.766178\pi$
$710$	5.59958			0.210148
$711$		0			0
$712$	−5.36368			−0.201012
$713$	1.92896	+	3.34105i	0.0722400	+	0.125123i
$714$		0			0
$715$	−0.104312	+	0.180673i	−0.00390103	+	0.00675678i
$716$	9.31053	−	16.1263i	0.347951	−	0.602669i
$717$		0			0
$718$	3.68255	+	6.37836i	0.137431	+	0.238038i
$719$	−32.1700			−1.19974			−0.599869	−	0.800098i	$-0.704781\pi$
$719$	−32.1700			−1.19974			−0.599869	+	0.800098i	$0.704781\pi$
$720$		0			0
$721$	−6.02426			−0.224355
$722$	−3.91075	−	6.77361i	−0.145543	−	0.252088i
$723$		0			0
$724$	21.9787	−	38.0681i	0.816830	−	1.41479i
$725$	−0.362831	+	0.628442i	−0.0134752	+	0.0233397i
$726$		0			0
$727$	2.68275	+	4.64667i	0.0994979	+	0.172335i	0.911477	−	0.411351i	$-0.134943\pi$
$727$	2.68275	+	4.64667i	0.0994979	+	0.172335i	−0.811979	+	0.583687i	$0.801610\pi$
$728$	0.0378942			0.00140445
$729$		0			0
$730$	0.503399			0.0186316
$731$	−13.0134	−	22.5399i	−0.481319	−	0.833669i
$732$		0			0
$733$	7.29818	−	12.6408i	0.269564	−	0.466899i	−0.699185	−	0.714941i	$-0.746454\pi$
$733$	7.29818	−	12.6408i	0.269564	−	0.466899i	0.968749	+	0.248042i	$0.0797870\pi$
$734$	−4.22104	+	7.31105i	−0.155801	+	0.269856i
$735$		0			0
$736$	−2.28820	−	3.96327i	−0.0843440	−	0.146088i
$737$	57.5068			2.11829
$738$		0			0
$739$	−43.2165			−1.58975			−0.794873	−	0.606776i	$-0.792463\pi$
$739$	−43.2165			−1.58975			−0.794873	+	0.606776i	$0.792463\pi$
$740$	8.95572	+	15.5118i	0.329219	+	0.570224i
$741$		0			0
$742$	0.356527	−	0.617523i	0.0130885	−	0.0226700i
$743$	−4.05610	+	7.02538i	−0.148804	+	0.257736i	−0.930786	−	0.365565i	$-0.880876\pi$
$743$	−4.05610	+	7.02538i	−0.148804	+	0.257736i	0.781982	+	0.623301i	$0.214209\pi$
$744$		0			0
$745$	−0.977806	−	1.69361i	−0.0358240	−	0.0620491i
$746$	4.02231			0.147267
$747$		0			0
$748$	−29.8561			−1.09165
$749$	−7.45357	−	12.9100i	−0.272348	−	0.471720i
$750$		0			0
$751$	−4.37773	+	7.58245i	−0.159746	+	0.276687i	−0.934777	−	0.355235i	$-0.884401\pi$
$751$	−4.37773	+	7.58245i	−0.159746	+	0.276687i	0.775031	+	0.631923i	$0.217734\pi$
$752$	10.6260	−	18.4048i	0.387490	−	0.671153i
$753$		0			0
$754$	0.0292876	+	0.0507277i	0.00106659	+	0.00184739i
$755$	18.2210			0.663129
$756$		0			0
$757$	−32.1511			−1.16855			−0.584276	−	0.811555i	$-0.698622\pi$
$757$	−32.1511			−1.16855			−0.584276	+	0.811555i	$0.698622\pi$
$758$	−0.857741	−	1.48565i	−0.0311546	−	0.0539613i
$759$		0			0
$760$	−0.735058	+	1.27316i	−0.0266633	+	0.0461823i
$761$	12.2730	−	21.2574i	0.444894	−	0.770580i	−0.553151	−	0.833081i	$-0.686575\pi$
$761$	12.2730	−	21.2574i	0.444894	−	0.770580i	0.998045	+	0.0625018i	$0.0199079\pi$
$762$		0			0
$763$	9.56941	+	16.5747i	0.346436	+	0.600045i
$764$	−20.0033			−0.723693
$765$		0			0
$766$	−1.97354			−0.0713069
$767$	−0.0334246	−	0.0578931i	−0.00120689	−	0.00209040i
$768$		0			0
$769$	−15.7072	+	27.2057i	−0.566416	+	0.981061i	0.430500	+	0.902590i	$0.358337\pi$
$769$	−15.7072	+	27.2057i	−0.566416	+	0.981061i	−0.996916	+	0.0784710i	$0.974996\pi$
$770$	3.16693	−	5.48528i	0.114128	−	0.197676i
$771$		0			0
$772$	−9.87335	−	17.1011i	−0.355349	−	0.615483i
$773$	28.7145			1.03279			0.516395	−	0.856351i	$-0.327274\pi$
$773$	28.7145			1.03279			0.516395	+	0.856351i	$0.327274\pi$
$774$		0			0
$775$	−0.346663			−0.0124525
$776$	−7.90413	−	13.6904i	−0.283742	−	0.491455i
$777$		0			0
$778$	−4.53135	+	7.84853i	−0.162457	+	0.281383i
$779$	0.766872	−	1.32826i	0.0274761	−	0.0475899i
$780$		0			0
$781$	−15.8653	−	27.4795i	−0.567706	−	0.983295i
$782$	−1.34633			−0.0481446
$783$		0			0
$784$	−15.7448			−0.562315
$785$	−13.9112	−	24.0949i	−0.496511	−	0.859983i
$786$		0			0
$787$	19.4080	−	33.6157i	0.691821	−	1.19827i	−0.279420	−	0.960169i	$-0.590142\pi$
$787$	19.4080	−	33.6157i	0.691821	−	1.19827i	0.971241	−	0.238100i	$-0.0765246\pi$
$788$	−20.1683	+	34.9325i	−0.718466	+	1.24442i
$789$		0			0
$790$	0.225088	+	0.389864i	0.00800828	+	0.0138708i
$791$	−16.5725			−0.589249
$792$		0			0
$793$	−0.124861			−0.00443394
$794$	−7.23930	−	12.5388i	−0.256913	−	0.444987i
$795$		0			0
$796$	11.7746	−	20.3941i	0.417338	−	0.722851i
$797$	2.01705	−	3.49363i	0.0714476	−	0.123751i	−0.828088	−	0.560598i	$-0.810571\pi$
$797$	2.01705	−	3.49363i	0.0714476	−	0.123751i	0.899536	+	0.436847i	$0.143905\pi$
$798$		0			0
$799$	−11.1181	−	19.2572i	−0.393332	−	0.681271i
$800$	0.411224			0.0145390
$801$		0			0
$802$	7.82160			0.276190
$803$	−1.42628	−	2.47039i	−0.0503324	−	0.0871783i
$804$		0			0
$805$	−1.51187	+	2.61864i	−0.0532865	+	0.0922949i
$806$	−0.0139913	+	0.0242336i	−0.000492822	+	0.000853593i
$807$		0			0
$808$	−10.9716	−	19.0034i	−0.385981	−	0.668538i
$809$	−29.9454			−1.05283			−0.526413	−	0.850229i	$-0.676463\pi$
$809$	−29.9454			−1.05283			−0.526413	+	0.850229i	$0.676463\pi$
$810$		0			0
$811$	20.2173			0.709927			0.354963	−	0.934880i	$-0.384493\pi$
$811$	20.2173			0.709927			0.354963	+	0.934880i	$0.384493\pi$
$812$	9.41346	+	16.3046i	0.330348	+	0.572179i
$813$		0			0
$814$	−4.79364	+	8.30282i	−0.168017	+	0.291014i
$815$	−3.67129	+	6.35887i	−0.128600	+	0.222741i
$816$		0			0
$817$	1.73365	+	3.00278i	0.0606529	+	0.105054i
$818$	2.64235			0.0923875
$819$		0			0
$820$	14.8762			0.519499
$821$	−13.4368	−	23.2733i	−0.468948	−	0.812242i	0.530422	−	0.847734i	$-0.322034\pi$
$821$	−13.4368	−	23.2733i	−0.468948	−	0.812242i	−0.999370	+	0.0354918i	$0.988700\pi$
$822$		0			0
$823$	−11.5272	+	19.9656i	−0.401812	+	0.695958i	−0.993945	−	0.109882i	$-0.964953\pi$
$823$	−11.5272	+	19.9656i	−0.401812	+	0.695958i	0.592133	+	0.805840i	$0.298286\pi$
$824$	−3.62961	+	6.28667i	−0.126444	+	0.219007i
$825$		0			0
$826$	1.01478	+	1.75765i	0.0353087	+	0.0611565i
$827$	−5.10953			−0.177676			−0.0888378	−	0.996046i	$-0.528315\pi$
$827$	−5.10953			−0.177676			−0.0888378	+	0.996046i	$0.528315\pi$
$828$		0			0
$829$	−30.5982			−1.06272			−0.531360	−	0.847146i	$-0.678319\pi$
$829$	−30.5982			−1.06272			−0.531360	+	0.847146i	$0.678319\pi$
$830$	2.12306	+	3.67725i	0.0736926	+	0.127639i
$831$		0			0
$832$	−0.0374725	+	0.0649042i	−0.00129912	+	0.00225015i
$833$	−8.23703	+	14.2669i	−0.285396	+	0.494320i
$834$		0			0
$835$	22.7754	+	39.4482i	0.788176	+	1.36516i
$836$	3.97744			0.137563
$837$		0			0
$838$	10.1033			0.349013
$839$	28.1543	+	48.7648i	0.971996	+	1.68355i	0.689512	+	0.724275i	$0.257825\pi$
$839$	28.1543	+	48.7648i	0.971996	+	1.68355i	0.282485	+	0.959272i	$0.408841\pi$
$840$		0			0
$841$	−15.9764	+	27.6719i	−0.550909	+	0.954203i
$842$	−1.65980	+	2.87485i	−0.0572003	+	0.0990739i
$843$		0			0
$844$	−21.9247	−	37.9746i	−0.754678	−	1.30714i
$845$	−28.7967			−0.990637
$846$		0			0
$847$	−21.3756			−0.734474
$848$	1.94704	+	3.37237i	0.0668616	+	0.115808i
$849$		0			0
$850$	0.0604889	−	0.104770i	0.00207475	−	0.00359357i
$851$	2.28845	−	3.96372i	0.0784472	−	0.135875i
$852$		0			0
$853$	22.7725	+	39.4431i	0.779715	+	1.35051i	0.932106	+	0.362186i	$0.117970\pi$
$853$	22.7725	+	39.4431i	0.779715	+	1.35051i	−0.152390	+	0.988320i	$0.548697\pi$
$854$	3.79081			0.129719
$855$		0			0
$856$	−17.9631			−0.613966
$857$	8.74459	+	15.1461i	0.298709	+	0.517380i	0.975841	−	0.218482i	$-0.0701105\pi$
$857$	8.74459	+	15.1461i	0.298709	+	0.517380i	−0.677131	+	0.735862i	$0.736777\pi$
$858$		0			0
$859$	−9.17301	+	15.8881i	−0.312979	+	0.542096i	−0.979006	−	0.203832i	$-0.934660\pi$
$859$	−9.17301	+	15.8881i	−0.312979	+	0.542096i	0.666027	+	0.745928i	$0.267994\pi$
$860$	−16.8152	+	29.1247i	−0.573392	+	0.993144i
$861$		0			0
$862$	2.05058	+	3.55171i	0.0698431	+	0.120972i
$863$	4.65373			0.158415			0.0792073	−	0.996858i	$-0.474761\pi$
$863$	4.65373			0.158415			0.0792073	+	0.996858i	$0.474761\pi$
$864$		0			0
$865$	31.0863			1.05697
$866$	−1.26794	−	2.19613i	−0.0430863	−	0.0746277i
$867$		0			0
$868$	−4.49699	+	7.78902i	−0.152638	+	0.264377i
$869$	1.27549	−	2.20921i	0.0432680	−	0.0749424i
$870$		0			0
$871$	−0.0995638	−	0.172450i	−0.00337359	−	0.00584323i
$872$	23.0622			0.780986
$873$		0			0
$874$	0.179358			0.00606688
$875$	−7.44392	−	12.8932i	−0.251650	−	0.435871i
$876$		0			0
$877$	1.83355	−	3.17580i	0.0619145	−	0.107239i	−0.833407	−	0.552660i	$-0.813613\pi$
$877$	1.83355	−	3.17580i	0.0619145	−	0.107239i	0.895321	+	0.445421i	$0.146946\pi$
$878$	−3.14384	+	5.44529i	−0.106099	+	0.183770i
$879$		0			0
$880$	17.2950	+	29.9558i	0.583013	+	1.00981i
$881$	38.3008			1.29039			0.645193	−	0.764020i	$-0.276777\pi$
$881$	38.3008			1.29039			0.645193	+	0.764020i	$0.276777\pi$
$882$		0			0
$883$	22.6142			0.761027			0.380513	−	0.924775i	$-0.375747\pi$
$883$	22.6142			0.761027			0.380513	+	0.924775i	$0.375747\pi$
$884$	0.0516910	+	0.0895314i	0.00173856	+	0.00301127i
$885$		0			0
$886$	−0.150148	+	0.260064i	−0.00504433	+	0.00873703i
$887$	0.948279	−	1.64247i	0.0318401	−	0.0551486i	−0.849666	−	0.527321i	$-0.823197\pi$
$887$	0.948279	−	1.64247i	0.0318401	−	0.0551486i	0.881506	+	0.472172i	$0.156530\pi$
$888$		0			0
$889$	−5.53914	−	9.59406i	−0.185777	−	0.321775i
$890$	3.10435			0.104058
$891$		0			0
$892$	−39.5852			−1.32541
$893$	1.48116	+	2.56545i	0.0495653	+	0.0858496i
$894$		0			0
$895$	−11.2864	+	19.5486i	−0.377262	+	0.653436i
$896$	6.97605	−	12.0829i	0.233054	−	0.403661i
$897$		0			0
$898$	0.346592	+	0.600315i	0.0115659	+	0.0200328i
$899$	−29.1183			−0.971150
$900$		0			0
$901$	4.07443			0.135739
$902$	3.98131	+	6.89583i	0.132563	+	0.229606i
$903$		0			0
$904$	−9.98489	+	17.2943i	−0.332093	+	0.575201i
$905$	−26.6429	+	46.1468i	−0.885638	+	1.53397i
$906$		0			0
$907$	−3.26547	−	5.65596i	−0.108428	−	0.187803i	0.806705	−	0.590954i	$-0.201248\pi$
$907$	−3.26547	−	5.65596i	−0.108428	−	0.187803i	−0.915134	+	0.403151i	$0.867915\pi$
$908$	−39.5481			−1.31245
$909$		0			0
$910$	−0.0219321			−0.000727042
$911$	21.5186	+	37.2712i	0.712942	+	1.23485i	0.963748	+	0.266814i	$0.0859709\pi$
$911$	21.5186	+	37.2712i	0.712942	+	1.23485i	−0.250806	+	0.968037i	$0.580696\pi$
$912$		0			0
$913$	12.0306	−	20.8376i	0.398154	−	0.689623i
$914$	2.30240	−	3.98787i	0.0761566	−	0.131907i
$915$		0			0
$916$	−9.87279	−	17.1002i	−0.326206	−	0.565006i
$917$	20.5003			0.676980
$918$		0			0
$919$	−16.7911			−0.553887			−0.276943	−	0.960886i	$-0.589321\pi$
$919$	−16.7911			−0.553887			−0.276943	+	0.960886i	$0.589321\pi$
$920$	1.82180	+	3.15545i	0.0600631	+	0.104032i
$921$		0			0
$922$	−4.54611	+	7.87410i	−0.149718	+	0.259320i
$923$	−0.0549365	+	0.0951528i	−0.00180826	+	0.00313199i
$924$		0			0
$925$	0.205635	+	0.356170i	0.00676124	+	0.0117108i
$926$	−10.3251			−0.339302
$927$		0			0
$928$	34.5412			1.13387
$929$	5.80000	+	10.0459i	0.190292	+	0.329595i	0.945347	−	0.326066i	$-0.105723\pi$
$929$	5.80000	+	10.0459i	0.190292	+	0.329595i	−0.755055	+	0.655661i	$0.772390\pi$
$930$		0			0
$931$	1.09734	−	1.90065i	0.0359639	−	0.0622912i
$932$	6.97971	−	12.0892i	0.228628	−	0.395995i
$933$		0			0
$934$	−2.45863	−	4.25848i	−0.0804489	−	0.139342i
$935$	36.1920			1.18360
$936$		0			0
$937$	47.7953			1.56140			0.780702	−	0.624904i	$-0.214862\pi$
$937$	47.7953			1.56140			0.780702	+	0.624904i	$0.214862\pi$
$938$	3.02278	+	5.23561i	0.0986974	+	0.170949i
$939$		0			0
$940$	−14.3662	+	24.8830i	−0.468573	+	0.811593i
$941$	−5.63018	+	9.75175i	−0.183538	+	0.317898i	−0.943083	−	0.332557i	$-0.892089\pi$
$941$	−5.63018	+	9.75175i	−0.183538	+	0.317898i	0.759545	+	0.650455i	$0.225422\pi$
$942$		0			0
$943$	−1.90065	−	3.29203i	−0.0618938	−	0.107203i
$944$	−11.0837			−0.360743
$945$		0			0
$946$	−18.0010			−0.585261
$947$	−3.66595	−	6.34961i	−0.119127	−	0.206335i	0.800295	−	0.599607i	$-0.204676\pi$
$947$	−3.66595	−	6.34961i	−0.119127	−	0.206335i	−0.919422	+	0.393272i	$0.871343\pi$
$948$		0			0
$949$	−0.00493876	+	0.00855418i	−0.000160319	+	0.000277681i
$950$	−0.00805835	+	0.0139575i	−0.000261447	+	0.000452840i
$951$		0			0
$952$	−3.28694	−	5.69315i	−0.106530	−	0.184516i
$953$	−24.8753			−0.805791			−0.402895	−	0.915246i	$-0.631996\pi$
$953$	−24.8753			−0.805791			−0.402895	+	0.915246i	$0.631996\pi$
$954$		0			0
$955$	24.2483			0.784655
$956$	−2.95259	−	5.11404i	−0.0954937	−	0.165400i
$957$		0			0
$958$	0.599799	−	1.03888i	0.0193786	−	0.0335647i
$959$	7.92265	−	13.7224i	0.255836	−	0.443121i
$960$		0			0
$961$	8.54480	+	14.8000i	0.275639	+	0.477420i
$962$	0.0331976			0.00107034
$963$		0			0
$964$	48.5079			1.56233
$965$	11.9686	+	20.7303i	0.385283	+	0.667330i
$966$		0			0
$967$	17.0150	−	29.4708i	0.547165	−	0.947718i	−0.451302	−	0.892371i	$-0.649040\pi$
$967$	17.0150	−	29.4708i	0.547165	−	0.947718i	0.998467	−	0.0553465i	$-0.0176264\pi$
$968$	−12.8788	+	22.3067i	−0.413939	+	0.716964i
$969$		0			0
$970$	4.57469	+	7.92360i	0.146885	+	0.254411i
$971$	−34.2476			−1.09906			−0.549530	−	0.835474i	$-0.685193\pi$
$971$	−34.2476			−1.09906			−0.549530	+	0.835474i	$0.685193\pi$
$972$		0			0
$973$	−8.10928			−0.259971
$974$	1.81954	+	3.15154i	0.0583018	+	0.100982i
$975$		0			0
$976$	−10.3510	+	17.9285i	−0.331329	+	0.573878i
$977$	11.7087	−	20.2800i	0.374593	−	0.648814i	−0.615673	−	0.788002i	$-0.711116\pi$
$977$	11.7087	−	20.2800i	0.374593	−	0.648814i	0.990266	+	0.139188i	$0.0444491\pi$
$978$		0			0
$979$	−8.79558	−	15.2344i	−0.281108	−	0.486893i
$980$	21.2868			0.679980
$981$		0			0
$982$	9.37834			0.299275
$983$	16.6016	+	28.7547i	0.529508	+	0.917134i	0.999408	+	0.0344144i	$0.0109566\pi$
$983$	16.6016	+	28.7547i	0.529508	+	0.917134i	−0.469900	+	0.882720i	$0.655710\pi$
$984$		0			0
$985$	24.4483	−	42.3457i	0.778988	−	1.34925i
$986$	5.08083	−	8.80025i	0.161806	−	0.280257i
$987$		0			0
$988$	−0.00688630	−	0.0119274i	−0.000219082	−	0.000379462i
$989$	8.59355			0.273259
$990$		0			0
$991$	−28.1806			−0.895187			−0.447594	−	0.894237i	$-0.647719\pi$
$991$	−28.1806			−0.895187			−0.447594	+	0.894237i	$0.647719\pi$
$992$	8.25050	+	14.2903i	0.261954	+	0.453717i
$993$		0			0
$994$	1.66789	−	2.88887i	0.0529022	−	0.0916292i
$995$	−14.2733	+	24.7221i	−0.452494	+	0.783742i
$996$		0			0
$997$	22.4754	+	38.9285i	0.711802	+	1.23288i	0.964180	+	0.265248i	$0.0854538\pi$
$997$	22.4754	+	38.9285i	0.711802	+	1.23288i	−0.252379	+	0.967629i	$0.581213\pi$
$998$	10.5249			0.333161
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.c.e.244.3		12
3.2	odd	2		729.2.c.b.244.4		12
9.2	odd	6		729.2.c.b.487.4		12
9.4	even	3		729.2.a.a.1.4		6
9.5	odd	6		729.2.a.d.1.3		6
9.7	even	3	inner	729.2.c.e.487.3		12
27.2	odd	18		243.2.e.a.28.1		12
27.4	even	9		243.2.e.d.217.2		12
27.5	odd	18		243.2.e.b.55.2		12
27.7	even	9		243.2.e.c.190.1		12
27.11	odd	18		81.2.e.a.37.1		12
27.13	even	9		27.2.e.a.16.2	✓	12
27.14	odd	18		81.2.e.a.46.1		12
27.16	even	9		27.2.e.a.22.2	yes	12
27.20	odd	18		243.2.e.b.190.2		12
27.22	even	9		243.2.e.c.55.1		12
27.23	odd	18		243.2.e.a.217.1		12
27.25	even	9		243.2.e.d.28.2		12
108.43	odd	18		432.2.u.c.49.1		12
108.67	odd	18		432.2.u.c.97.1		12
135.13	odd	36		675.2.u.b.124.2		24
135.43	odd	36		675.2.u.b.49.3		24
135.67	odd	36		675.2.u.b.124.3		24
135.94	even	18		675.2.l.c.151.1		12
135.97	odd	36		675.2.u.b.49.2		24
135.124	even	18		675.2.l.c.76.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.16.2	✓	12	27.13	even	9
27.2.e.a.22.2	yes	12	27.16	even	9
81.2.e.a.37.1		12	27.11	odd	18
81.2.e.a.46.1		12	27.14	odd	18
243.2.e.a.28.1		12	27.2	odd	18
243.2.e.a.217.1		12	27.23	odd	18
243.2.e.b.55.2		12	27.5	odd	18
243.2.e.b.190.2		12	27.20	odd	18
243.2.e.c.55.1		12	27.22	even	9
243.2.e.c.190.1		12	27.7	even	9
243.2.e.d.28.2		12	27.25	even	9
243.2.e.d.217.2		12	27.4	even	9
432.2.u.c.49.1		12	108.43	odd	18
432.2.u.c.97.1		12	108.67	odd	18
675.2.l.c.76.1		12	135.124	even	18
675.2.l.c.151.1		12	135.94	even	18
675.2.u.b.49.2		24	135.97	odd	36
675.2.u.b.49.3		24	135.43	odd	36
675.2.u.b.124.2		24	135.13	odd	36
675.2.u.b.124.3		24	135.67	odd	36
729.2.a.a.1.4		6	9.4	even	3
729.2.a.d.1.3		6	9.5	odd	6
729.2.c.b.244.4		12	3.2	odd	2
729.2.c.b.487.4		12	9.2	odd	6
729.2.c.e.244.3		12	1.1	even	1	trivial
729.2.c.e.487.3		12	9.7	even	3	inner

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.207733 + 0.359804i) q^{2} +(0.913694 - 1.58256i) q^{4} +(-1.10759 + 1.91841i) q^{5} +(0.659815 + 1.14283i) q^{7} +1.59015 q^{8} +O(q^{10})\)	\(q+(0.207733 + 0.359804i) q^{2} +(0.913694 - 1.58256i) q^{4} +(-1.10759 + 1.91841i) q^{5} +(0.659815 + 1.14283i) q^{7} +1.59015 q^{8} -0.920335 q^{10} +(2.60759 + 4.51648i) q^{11} +(0.00902926 - 0.0156391i) q^{13} +(-0.274131 + 0.474808i) q^{14} +(-1.49706 - 2.59299i) q^{16} -3.13280 q^{17} +0.417352 q^{19} +(2.02400 + 3.50568i) q^{20} +(-1.08337 + 1.87645i) q^{22} +(0.517193 - 0.895805i) q^{23} +(0.0464738 + 0.0804949i) q^{25} +0.00750270 q^{26} +2.41147 q^{28} +(3.90361 + 6.76125i) q^{29} +(-1.86483 + 3.22998i) q^{31} +(2.21213 - 3.83152i) q^{32} +(-0.650785 - 1.12719i) q^{34} -2.92322 q^{35} +4.42476 q^{37} +(0.0866979 + 0.150165i) q^{38} +(-1.76124 + 3.05056i) q^{40} +(1.83747 - 3.18259i) q^{41} +(4.15394 + 7.19483i) q^{43} +9.53017 q^{44} +0.429753 q^{46} +(3.54895 + 6.14697i) q^{47} +(2.62929 - 4.55406i) q^{49} +(-0.0193083 + 0.0334429i) q^{50} +(-0.0165000 - 0.0285788i) q^{52} -1.30057 q^{53} -11.5526 q^{55} +(1.04920 + 1.81728i) q^{56} +(-1.62182 + 2.80907i) q^{58} +(1.85091 - 3.20586i) q^{59} +(-3.45712 - 5.98791i) q^{61} -1.54955 q^{62} -4.15011 q^{64} +(0.0200015 + 0.0346436i) q^{65} +(5.51340 - 9.54949i) q^{67} +(-2.86242 + 4.95785i) q^{68} +(-0.607251 - 1.05179i) q^{70} -6.08428 q^{71} -0.546973 q^{73} +(0.919169 + 1.59205i) q^{74} +(0.381332 - 0.660487i) q^{76} +(-3.44106 + 5.96008i) q^{77} +(-0.244572 - 0.423611i) q^{79} +6.63254 q^{80} +1.52681 q^{82} +(-2.30684 - 3.99556i) q^{83} +(3.46986 - 6.00998i) q^{85} +(-1.72582 + 2.98921i) q^{86} +(4.14647 + 7.18189i) q^{88} -3.37307 q^{89} +0.0238305 q^{91} +(-0.945113 - 1.63698i) q^{92} +(-1.47447 + 2.55386i) q^{94} +(-0.462257 + 0.800652i) q^{95} +(-4.97068 - 8.60947i) q^{97} +2.18476 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 - 12 * q^8	\( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8} + 6 q^{10} + 12 q^{11} + 6 q^{14} + 3 q^{16} - 18 q^{17} + 6 q^{19} + 6 q^{20} - 6 q^{22} + 15 q^{23} + 6 q^{25} - 30 q^{26} - 12 q^{28} + 12 q^{29} - 24 q^{35} + 6 q^{37} - 3 q^{38} - 6 q^{40} + 15 q^{41} - 6 q^{44} + 6 q^{46} + 21 q^{47} + 12 q^{49} + 3 q^{50} - 12 q^{52} - 18 q^{53} - 12 q^{55} - 6 q^{56} + 12 q^{58} + 24 q^{59} + 9 q^{61} + 24 q^{62} - 24 q^{64} - 6 q^{65} + 9 q^{67} - 9 q^{68} - 15 q^{70} - 54 q^{71} - 12 q^{73} - 12 q^{74} - 6 q^{76} - 12 q^{77} + 42 q^{80} - 12 q^{82} + 12 q^{83} - 21 q^{86} - 12 q^{88} - 18 q^{89} - 12 q^{91} + 6 q^{92} - 6 q^{94} + 12 q^{95} + 90 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 - 12 * q^8 + 6 * q^10 + 12 * q^11 + 6 * q^14 + 3 * q^16 - 18 * q^17 + 6 * q^19 + 6 * q^20 - 6 * q^22 + 15 * q^23 + 6 * q^25 - 30 * q^26 - 12 * q^28 + 12 * q^29 - 24 * q^35 + 6 * q^37 - 3 * q^38 - 6 * q^40 + 15 * q^41 - 6 * q^44 + 6 * q^46 + 21 * q^47 + 12 * q^49 + 3 * q^50 - 12 * q^52 - 18 * q^53 - 12 * q^55 - 6 * q^56 + 12 * q^58 + 24 * q^59 + 9 * q^61 + 24 * q^62 - 24 * q^64 - 6 * q^65 + 9 * q^67 - 9 * q^68 - 15 * q^70 - 54 * q^71 - 12 * q^73 - 12 * q^74 - 6 * q^76 - 12 * q^77 + 42 * q^80 - 12 * q^82 + 12 * q^83 - 21 * q^86 - 12 * q^88 - 18 * q^89 - 12 * q^91 + 6 * q^92 - 6 * q^94 + 12 * q^95 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more