LMFDB - Embedded newform 819.2.o.e.757.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(568,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("819.568");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.o (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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			757.2
Root			$0.900969 + 1.56052i$ of defining polynomial
Character	$\chi$	$=$	819.757
Dual form			819.2.o.e.568.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.277479 - 0.480608i) q^{2} +(0.846011 - 1.46533i) q^{4} -1.35690 q^{5} +(-0.500000 + 0.866025i) q^{7} -2.04892 q^{8} +O(q^{10})$	\(q+(-0.277479 - 0.480608i) q^{2} +(0.846011 - 1.46533i) q^{4} -1.35690 q^{5} +(-0.500000 + 0.866025i) q^{7} -2.04892 q^{8} +(0.376510 + 0.652135i) q^{10} +(0.568532 + 0.984726i) q^{11} +(1.37047 - 3.33494i) q^{13} +0.554958 q^{14} +(-1.12349 - 1.94594i) q^{16} +(-0.277479 + 0.480608i) q^{17} +(2.05496 - 3.55929i) q^{19} +(-1.14795 + 1.98831i) q^{20} +(0.315511 - 0.546482i) q^{22} +(-3.39493 - 5.88019i) q^{23} -3.15883 q^{25} +(-1.98307 + 0.266717i) q^{26} +(0.846011 + 1.46533i) q^{28} +(-4.51842 - 7.82613i) q^{29} -8.63102 q^{31} +(-2.67241 + 4.62874i) q^{32} +0.307979 q^{34} +(0.678448 - 1.17511i) q^{35} +(2.59030 + 4.48653i) q^{37} -2.28083 q^{38} +2.78017 q^{40} +(0.109916 + 0.190381i) q^{41} +(-1.94989 + 3.37730i) q^{43} +1.92394 q^{44} +(-1.88404 + 3.26326i) q^{46} +8.13706 q^{47} +(-0.500000 - 0.866025i) q^{49} +(0.876510 + 1.51816i) q^{50} +(-3.72737 - 4.82959i) q^{52} -7.98792 q^{53} +(-0.771438 - 1.33617i) q^{55} +(1.02446 - 1.77441i) q^{56} +(-2.50753 + 4.34317i) q^{58} +(1.94989 - 3.37730i) q^{59} +(-5.46077 + 9.45833i) q^{61} +(2.39493 + 4.14814i) q^{62} -1.52781 q^{64} +(-1.85958 + 4.52516i) q^{65} +(-0.381355 - 0.660525i) q^{67} +(0.469501 + 0.813199i) q^{68} -0.753020 q^{70} +(2.25182 - 3.90027i) q^{71} +8.50365 q^{73} +(1.43751 - 2.48984i) q^{74} +(-3.47703 - 6.02240i) q^{76} -1.13706 q^{77} -3.74094 q^{79} +(1.52446 + 2.64044i) q^{80} +(0.0609989 - 0.105653i) q^{82} +11.0586 q^{83} +(0.376510 - 0.652135i) q^{85} +2.16421 q^{86} +(-1.16487 - 2.01762i) q^{88} +(-4.30194 - 7.45117i) q^{89} +(2.20291 + 2.85433i) q^{91} -11.4886 q^{92} +(-2.25786 - 3.91074i) q^{94} +(-2.78836 + 4.82959i) q^{95} +(7.47434 - 12.9459i) q^{97} +(-0.277479 + 0.480608i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 3 q^{7} + 6 q^{8}+O(q^{10}) $ 6 * q - 2 * q^2 - 3 * q^7 + 6 * q^8	$ 6 q - 2 q^{2} - 3 q^{7} + 6 q^{8} + 7 q^{10} - 2 q^{11} - 6 q^{13} + 4 q^{14} - 2 q^{16} - 2 q^{17} + 13 q^{19} + 7 q^{20} - 13 q^{22} + 3 q^{23} - 2 q^{25} + 4 q^{26} + q^{29} - 22 q^{31} + 7 q^{32} + 12 q^{34} + 4 q^{37} - 36 q^{38} + 14 q^{40} + 2 q^{41} + 11 q^{43} + 42 q^{44} + 9 q^{46} + 38 q^{47} - 3 q^{49} + 10 q^{50} - 10 q^{53} + 14 q^{55} - 3 q^{56} + 10 q^{58} - 11 q^{59} - 7 q^{61} - 9 q^{62} - 22 q^{64} + 15 q^{67} - 7 q^{68} - 14 q^{70} - 18 q^{71} - 12 q^{73} + 33 q^{74} + 14 q^{76} + 4 q^{77} + 6 q^{79} + 20 q^{82} + 4 q^{83} + 7 q^{85} - 10 q^{86} - 9 q^{88} - 17 q^{89} - 56 q^{92} - q^{94} - 14 q^{95} + 13 q^{97} - 2 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 - 3 * q^7 + 6 * q^8 + 7 * q^10 - 2 * q^11 - 6 * q^13 + 4 * q^14 - 2 * q^16 - 2 * q^17 + 13 * q^19 + 7 * q^20 - 13 * q^22 + 3 * q^23 - 2 * q^25 + 4 * q^26 + q^29 - 22 * q^31 + 7 * q^32 + 12 * q^34 + 4 * q^37 - 36 * q^38 + 14 * q^40 + 2 * q^41 + 11 * q^43 + 42 * q^44 + 9 * q^46 + 38 * q^47 - 3 * q^49 + 10 * q^50 - 10 * q^53 + 14 * q^55 - 3 * q^56 + 10 * q^58 - 11 * q^59 - 7 * q^61 - 9 * q^62 - 22 * q^64 + 15 * q^67 - 7 * q^68 - 14 * q^70 - 18 * q^71 - 12 * q^73 + 33 * q^74 + 14 * q^76 + 4 * q^77 + 6 * q^79 + 20 * q^82 + 4 * q^83 + 7 * q^85 - 10 * q^86 - 9 * q^88 - 17 * q^89 - 56 * q^92 - q^94 - 14 * q^95 + 13 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.277479	−	0.480608i	−0.196207	−	0.339841i	0.751088	−	0.660202i	$-0.229529\pi$
$2$	−0.277479	−	0.480608i	−0.196207	−	0.339841i	−0.947296	+	0.320361i	$0.896196\pi$
$3$		0			0
$3$		0			0
$4$	0.846011	−	1.46533i	0.423005	−	0.732667i
$5$	−1.35690			−0.606822			−0.303411	−	0.952860i	$-0.598126\pi$
$5$	−1.35690			−0.606822			−0.303411	+	0.952860i	$0.598126\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	−2.04892			−0.724402
$9$		0			0
$10$	0.376510	+	0.652135i	0.119063	+	0.206223i
$11$	0.568532	+	0.984726i	0.171419	+	0.296906i	0.938916	−	0.344146i	$-0.111832\pi$
$11$	0.568532	+	0.984726i	0.171419	+	0.296906i	−0.767497	+	0.641052i	$0.778498\pi$
$12$		0			0
$13$	1.37047	−	3.33494i	0.380100	−	0.924945i
$13$	1.37047	−	3.33494i	0.380100	−	0.924945i
$14$	0.554958			0.148319
$15$		0			0
$16$	−1.12349	−	1.94594i	−0.280872	−	0.486485i
$17$	−0.277479	+	0.480608i	−0.0672986	+	0.116565i	−0.897711	−	0.440584i	$-0.854771\pi$
$17$	−0.277479	+	0.480608i	−0.0672986	+	0.116565i	0.830413	+	0.557149i	$0.188105\pi$
$18$		0			0
$19$	2.05496	−	3.55929i	0.471440	−	0.816558i	−0.528026	−	0.849228i	$-0.677068\pi$
$19$	2.05496	−	3.55929i	0.471440	−	0.816558i	0.999466	+	0.0326704i	$0.0104011\pi$
$20$	−1.14795	+	1.98831i	−0.256689	+	0.444599i
$21$		0			0
$22$	0.315511	−	0.546482i	0.0672672	−	0.116510i
$23$	−3.39493	−	5.88019i	−0.707891	−	1.22610i	−0.965638	−	0.259891i	$-0.916313\pi$
$23$	−3.39493	−	5.88019i	−0.707891	−	1.22610i	0.257746	−	0.966213i	$-0.417020\pi$
$24$		0			0
$25$	−3.15883			−0.631767
$26$	−1.98307	+	0.266717i	−0.388913	+	0.0523076i
$27$		0			0
$28$	0.846011	+	1.46533i	0.159881	+	0.276922i
$29$	−4.51842	−	7.82613i	−0.839049	−	1.45328i	−0.890691	−	0.454610i	$-0.849779\pi$
$29$	−4.51842	−	7.82613i	−0.839049	−	1.45328i	0.0516414	−	0.998666i	$-0.483555\pi$
$30$		0			0
$31$	−8.63102			−1.55018			−0.775089	−	0.631852i	$-0.782295\pi$
$31$	−8.63102			−1.55018			−0.775089	+	0.631852i	$0.782295\pi$
$32$	−2.67241	+	4.62874i	−0.472419	+	0.818254i
$33$		0			0
$34$	0.307979			0.0528179
$35$	0.678448	−	1.17511i	0.114679	−	0.198629i
$36$		0			0
$37$	2.59030	+	4.48653i	0.425843	+	0.737582i	0.996499	−	0.0836077i	$-0.0266442\pi$
$37$	2.59030	+	4.48653i	0.425843	+	0.737582i	−0.570656	+	0.821189i	$0.693311\pi$
$38$	−2.28083			−0.370000
$39$		0			0
$40$	2.78017			0.439583
$41$	0.109916	+	0.190381i	0.0171660	+	0.0297324i	0.874481	−	0.485060i	$-0.161202\pi$
$41$	0.109916	+	0.190381i	0.0171660	+	0.0297324i	−0.857315	+	0.514793i	$0.827869\pi$
$42$		0			0
$43$	−1.94989	+	3.37730i	−0.297355	+	0.515034i	−0.975530	−	0.219867i	$-0.929438\pi$
$43$	−1.94989	+	3.37730i	−0.297355	+	0.515034i	0.678175	+	0.734900i	$0.262771\pi$
$44$	1.92394			0.290044
$45$		0			0
$46$	−1.88404	+	3.26326i	−0.277787	+	0.481141i
$47$	8.13706			1.18691			0.593456	−	0.804866i	$-0.297763\pi$
$47$	8.13706			1.18691			0.593456	+	0.804866i	$0.297763\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	0.876510	+	1.51816i	0.123957	+	0.214700i
$51$		0			0
$52$	−3.72737	−	4.82959i	−0.516893	−	0.669743i
$53$	−7.98792			−1.09722			−0.548612	−	0.836077i	$-0.684844\pi$
$53$	−7.98792			−1.09722			−0.548612	+	0.836077i	$0.684844\pi$
$54$		0			0
$55$	−0.771438	−	1.33617i	−0.104021	−	0.180169i
$56$	1.02446	−	1.77441i	0.136899	−	0.237116i
$57$		0			0
$58$	−2.50753	+	4.34317i	−0.329255	+	0.570287i
$59$	1.94989	−	3.37730i	0.253854	−	0.439687i	−0.710730	−	0.703465i	$-0.751635\pi$
$59$	1.94989	−	3.37730i	0.253854	−	0.439687i	0.964583	+	0.263778i	$0.0849685\pi$
$60$		0			0
$61$	−5.46077	+	9.45833i	−0.699180	+	1.21102i	0.269571	+	0.962981i	$0.413118\pi$
$61$	−5.46077	+	9.45833i	−0.699180	+	1.21102i	−0.968751	+	0.248035i	$0.920215\pi$
$62$	2.39493	+	4.14814i	0.304156	+	0.526814i
$63$		0			0
$64$	−1.52781			−0.190976
$65$	−1.85958	+	4.52516i	−0.230653	+	0.561278i
$66$		0			0
$67$	−0.381355	−	0.660525i	−0.0465899	−	0.0806960i	0.841790	−	0.539805i	$-0.181502\pi$
$67$	−0.381355	−	0.660525i	−0.0465899	−	0.0806960i	−0.888380	+	0.459109i	$0.848169\pi$
$68$	0.469501	+	0.813199i	0.0569353	+	0.0986148i
$69$		0			0
$70$	−0.753020			−0.0900032
$71$	2.25182	−	3.90027i	0.267242	−	0.462877i	−0.700906	−	0.713253i	$-0.747221\pi$
$71$	2.25182	−	3.90027i	0.267242	−	0.462877i	0.968149	+	0.250376i	$0.0805542\pi$
$72$		0			0
$73$	8.50365			0.995277			0.497638	−	0.867385i	$-0.334201\pi$
$73$	8.50365			0.995277			0.497638	+	0.867385i	$0.334201\pi$
$74$	1.43751	−	2.48984i	0.167107	−	0.289438i
$75$		0			0
$76$	−3.47703	−	6.02240i	−0.398843	−	0.690816i
$77$	−1.13706			−0.129580
$78$		0			0
$79$	−3.74094			−0.420888			−0.210444	−	0.977606i	$-0.567491\pi$
$79$	−3.74094			−0.420888			−0.210444	+	0.977606i	$0.567491\pi$
$80$	1.52446	+	2.64044i	0.170440	+	0.295210i
$81$		0			0
$82$	0.0609989	−	0.105653i	0.00673620	−	0.0116674i
$83$	11.0586			1.21384			0.606920	−	0.794763i	$-0.292405\pi$
$83$	11.0586			1.21384			0.606920	+	0.794763i	$0.292405\pi$
$84$		0			0
$85$	0.376510	−	0.652135i	0.0408383	−	0.0707339i
$86$	2.16421			0.233373
$87$		0			0
$88$	−1.16487	−	2.01762i	−0.124176	−	0.215079i
$89$	−4.30194	−	7.45117i	−0.456004	−	0.789823i	0.542741	−	0.839900i	$-0.317387\pi$
$89$	−4.30194	−	7.45117i	−0.456004	−	0.789823i	−0.998745	+	0.0500773i	$0.984053\pi$
$90$		0			0
$91$	2.20291	+	2.85433i	0.230927	+	0.299215i
$92$	−11.4886			−1.19777
$93$		0			0
$94$	−2.25786	−	3.91074i	−0.232881	−	0.403362i
$95$	−2.78836	+	4.82959i	−0.286080	+	0.495505i
$96$		0			0
$97$	7.47434	−	12.9459i	0.758905	−	1.31446i	−0.184505	−	0.982832i	$-0.559068\pi$
$97$	7.47434	−	12.9459i	0.758905	−	1.31446i	0.943410	−	0.331630i	$-0.107599\pi$
$98$	−0.277479	+	0.480608i	−0.0280296	+	0.0485487i
$99$		0			0
$100$	−2.67241	+	4.62874i	−0.267241	+	0.462874i
$101$	2.12618	+	3.68265i	0.211563	+	0.366437i	0.952204	−	0.305464i	$-0.0988114\pi$
$101$	2.12618	+	3.68265i	0.211563	+	0.366437i	−0.740641	+	0.671901i	$0.765478\pi$
$102$		0			0
$103$	6.08575			0.599647			0.299824	−	0.953995i	$-0.403072\pi$
$103$	6.08575			0.599647			0.299824	+	0.953995i	$0.403072\pi$
$104$	−2.80798	+	6.83301i	−0.275345	+	0.670032i
$105$		0			0
$106$	2.21648	+	3.83906i	0.215284	+	0.372882i
$107$	−6.42812	−	11.1338i	−0.621429	−	1.07635i	−0.989220	−	0.146439i	$-0.953219\pi$
$107$	−6.42812	−	11.1338i	−0.621429	−	1.07635i	0.367790	−	0.929909i	$-0.380114\pi$
$108$		0			0
$109$	−6.84117			−0.655265			−0.327632	−	0.944805i	$-0.606251\pi$
$109$	−6.84117			−0.655265			−0.327632	+	0.944805i	$0.606251\pi$
$110$	−0.428116	+	0.741519i	−0.0408193	+	0.0707010i
$111$		0			0
$112$	2.24698			0.212320
$113$	9.31551	−	16.1349i	0.876330	−	1.51785i	0.0209900	−	0.999780i	$-0.493318\pi$
$113$	9.31551	−	16.1349i	0.876330	−	1.51785i	0.855340	−	0.518068i	$-0.173348\pi$
$114$		0			0
$115$	4.60656	+	7.97880i	0.429564	+	0.744027i
$116$	−15.2905			−1.41969
$117$		0			0
$118$	−2.16421			−0.199232
$119$	−0.277479	−	0.480608i	−0.0254365	−	0.0440572i
$120$		0			0
$121$	4.85354	−	8.40658i	0.441231	−	0.764235i
$122$	6.06100			0.548737
$123$		0			0
$124$	−7.30194	+	12.6473i	−0.655733	+	1.13576i
$125$	11.0707			0.990192
$126$		0			0
$127$	−2.30947	−	4.00012i	−0.204932	−	0.354953i	0.745179	−	0.666865i	$-0.232364\pi$
$127$	−2.30947	−	4.00012i	−0.204932	−	0.354953i	−0.950111	+	0.311911i	$0.899031\pi$
$128$	5.76875	+	9.99177i	0.509890	+	0.883156i
$129$		0			0
$130$	2.69083	−	0.361908i	0.236001	−	0.0317414i
$131$	3.35690			0.293293			0.146647	−	0.989189i	$-0.453152\pi$
$131$	3.35690			0.293293			0.146647	+	0.989189i	$0.453152\pi$
$132$		0			0
$133$	2.05496	+	3.55929i	0.178187	+	0.308630i
$134$	−0.211636	+	0.366564i	−0.0182825	+	0.0316663i
$135$		0			0
$136$	0.568532	−	0.984726i	0.0487512	−	0.0844395i
$137$	−10.7567	+	18.6311i	−0.919004	+	1.59176i	−0.118074	+	0.993005i	$0.537672\pi$
$137$	−10.7567	+	18.6311i	−0.919004	+	1.59176i	−0.800931	+	0.598757i	$0.795661\pi$
$138$		0			0
$139$	4.04623	−	7.00827i	0.343197	−	0.594434i	−0.641828	−	0.766849i	$-0.721824\pi$
$139$	4.04623	−	7.00827i	0.343197	−	0.594434i	0.985024	+	0.172415i	$0.0551569\pi$
$140$	−1.14795	−	1.98831i	−0.0970194	−	0.168042i
$141$		0			0
$142$	−2.49934			−0.209740
$143$	4.06315	−	0.546482i	0.339778	−	0.0456991i
$144$		0			0
$145$	6.13102	+	10.6192i	0.509154	+	0.881880i
$146$	−2.35958	−	4.08692i	−0.195281	−	0.338236i
$147$		0			0
$148$	8.76569			0.720536
$149$	1.62953	−	2.82243i	0.133496	−	0.231222i	−0.791526	−	0.611136i	$-0.790713\pi$
$149$	1.62953	−	2.82243i	0.133496	−	0.231222i	0.925022	+	0.379913i	$0.124046\pi$
$150$		0			0
$151$	−6.81163			−0.554322			−0.277161	−	0.960823i	$-0.589394\pi$
$151$	−6.81163			−0.554322			−0.277161	+	0.960823i	$0.589394\pi$
$152$	−4.21044	+	7.29269i	−0.341512	+	0.591516i
$153$		0			0
$154$	0.315511	+	0.546482i	0.0254246	+	0.0440367i
$155$	11.7114			0.940682
$156$		0			0
$157$	24.4306			1.94977			0.974886	−	0.222705i	$-0.0714888\pi$
$157$	24.4306			1.94977			0.974886	+	0.222705i	$0.0714888\pi$
$158$	1.03803	+	1.79792i	0.0825814	+	0.143035i
$159$		0			0
$160$	3.62618	−	6.28072i	0.286675	−	0.496535i
$161$	6.78986			0.535116
$162$		0			0
$163$	5.77413	−	10.0011i	0.452265	−	0.783345i	−0.546262	−	0.837614i	$-0.683950\pi$
$163$	5.77413	−	10.0011i	0.452265	−	0.783345i	0.998526	+	0.0542694i	$0.0172830\pi$
$164$	0.371961			0.0290453
$165$		0			0
$166$	−3.06853	−	5.31485i	−0.238164	−	0.412513i
$167$	2.41185	+	4.17745i	0.186635	+	0.323261i	0.944126	−	0.329584i	$-0.106909\pi$
$167$	2.41185	+	4.17745i	0.186635	+	0.323261i	−0.757491	+	0.652845i	$0.773575\pi$
$168$		0			0
$169$	−9.24363	−	9.14086i	−0.711048	−	0.703143i
$170$	−0.417895			−0.0320511
$171$		0			0
$172$	3.29925	+	5.71447i	0.251565	+	0.435724i
$173$	−10.8128	+	18.7284i	−0.822084	+	1.42389i	0.0820441	+	0.996629i	$0.473855\pi$
$173$	−10.8128	+	18.7284i	−0.822084	+	1.42389i	−0.904128	+	0.427262i	$0.859478\pi$
$174$		0			0
$175$	1.57942	−	2.73563i	0.119393	−	0.206794i
$176$	1.27748	−	2.21266i	0.0962936	−	0.166785i
$177$		0			0
$178$	−2.38740	+	4.13509i	−0.178943	+	0.309938i
$179$	12.7044	+	22.0047i	0.949571	+	1.64471i	0.746329	+	0.665577i	$0.231815\pi$
$179$	12.7044	+	22.0047i	0.949571	+	1.64471i	0.203242	+	0.979128i	$0.434852\pi$
$180$		0			0
$181$	−7.67994			−0.570845			−0.285423	−	0.958402i	$-0.592134\pi$
$181$	−7.67994			−0.570845			−0.285423	+	0.958402i	$0.592134\pi$
$182$	0.760553	−	1.85075i	0.0563759	−	0.137187i
$183$		0			0
$184$	6.95593	+	12.0480i	0.512798	+	0.888192i
$185$	−3.51477	−	6.08776i	−0.258411	−	0.447581i
$186$		0			0
$187$	−0.631023			−0.0461449
$188$	6.88404	−	11.9235i	0.502070	−	0.869611i
$189$		0			0
$190$	3.09485			0.224524
$191$	4.75182	−	8.23040i	0.343830	−	0.595531i	−0.641311	−	0.767281i	$-0.721609\pi$
$191$	4.75182	−	8.23040i	0.343830	−	0.595531i	0.985140	+	0.171751i	$0.0549423\pi$
$192$		0			0
$193$	4.67576	+	8.09865i	0.336569	+	0.582954i	0.983785	−	0.179353i	$-0.0574003\pi$
$193$	4.67576	+	8.09865i	0.336569	+	0.582954i	−0.647216	+	0.762306i	$0.724067\pi$
$194$	−8.29590			−0.595611
$195$		0			0
$196$	−1.69202			−0.120859
$197$	8.75786	+	15.1691i	0.623972	+	1.08075i	0.988739	+	0.149652i	$0.0478154\pi$
$197$	8.75786	+	15.1691i	0.623972	+	1.08075i	−0.364767	+	0.931099i	$0.618851\pi$
$198$		0			0
$199$	8.79470	−	15.2329i	0.623440	−	1.07983i	−0.365401	−	0.930850i	$-0.619068\pi$
$199$	8.79470	−	15.2329i	0.623440	−	1.07983i	0.988840	−	0.148979i	$-0.0475987\pi$
$200$	6.47219			0.457653
$201$		0			0
$202$	1.17994	−	2.04372i	0.0830203	−	0.143795i
$203$	9.03684			0.634262
$204$		0			0
$205$	−0.149145	−	0.258327i	−0.0104167	−	0.0180423i
$206$	−1.68867	−	2.92486i	−0.117655	−	0.203785i
$207$		0			0
$208$	−8.02930	+	1.07992i	−0.556732	+	0.0748787i
$209$	4.67324			0.323254
$210$		0			0
$211$	−0.681136	−	1.17976i	−0.0468914	−	0.0812182i	0.841627	−	0.540059i	$-0.181598\pi$
$211$	−0.681136	−	1.17976i	−0.0468914	−	0.0812182i	−0.888518	+	0.458841i	$0.848265\pi$
$212$	−6.75786	+	11.7050i	−0.464132	+	0.803900i
$213$		0			0
$214$	−3.56734	+	6.17881i	−0.243858	+	0.422374i
$215$	2.64579	−	4.58265i	0.180442	−	0.312534i
$216$		0			0
$217$	4.31551	−	7.47468i	0.292956	−	0.507415i
$218$	1.89828	+	3.28792i	0.128568	+	0.222686i
$219$		0			0
$220$	−2.61058			−0.176005
$221$	1.22252	+	1.58403i	0.0822357	+	0.106554i
$222$		0			0
$223$	5.14310	+	8.90812i	0.344408	+	0.596532i	0.985246	−	0.171144i	$-0.0547464\pi$
$223$	5.14310	+	8.90812i	0.344408	+	0.596532i	−0.640838	+	0.767676i	$0.721413\pi$
$224$	−2.67241	−	4.62874i	−0.178558	−	0.309271i
$225$		0			0
$226$	−10.3394			−0.687769
$227$	2.80409	−	4.85683i	0.186114	−	0.322359i	−0.757837	−	0.652444i	$-0.773744\pi$
$227$	2.80409	−	4.85683i	0.186114	−	0.322359i	0.943951	+	0.330084i	$0.107077\pi$
$228$		0			0
$229$	−1.88040			−0.124260			−0.0621300	−	0.998068i	$-0.519789\pi$
$229$	−1.88040			−0.124260			−0.0621300	+	0.998068i	$0.519789\pi$
$230$	2.55645	−	4.42790i	0.168567	−	0.291967i
$231$		0			0
$232$	9.25786	+	16.0351i	0.607809	+	1.05276i
$233$	6.38404			0.418233			0.209116	−	0.977891i	$-0.432941\pi$
$233$	6.38404			0.418233			0.209116	+	0.977891i	$0.432941\pi$
$234$		0			0
$235$	−11.0411			−0.720245
$236$	−3.29925	−	5.71447i	−0.214763	−	0.371980i
$237$		0			0
$238$	−0.153989	+	0.266717i	−0.00998164	+	0.0172887i
$239$	−1.90217			−0.123041			−0.0615204	−	0.998106i	$-0.519595\pi$
$239$	−1.90217			−0.123041			−0.0615204	+	0.998106i	$0.519595\pi$
$240$		0			0
$241$	−6.60603	+	11.4420i	−0.425532	+	0.737043i	−0.996470	−	0.0839503i	$-0.973246\pi$
$241$	−6.60603	+	11.4420i	−0.425532	+	0.737043i	0.570938	+	0.820993i	$0.306580\pi$
$242$	−5.38703			−0.346291
$243$		0			0
$244$	9.23974	+	16.0037i	0.591514	+	1.02453i
$245$	0.678448	+	1.17511i	0.0433444	+	0.0750748i
$246$		0			0
$247$	−9.05376	−	11.7311i	−0.576077	−	0.746429i
$248$	17.6843			1.12295
$249$		0			0
$250$	−3.07188	−	5.32066i	−0.194283	−	0.336508i
$251$	3.77024	−	6.53025i	0.237976	−	0.412186i	−0.722158	−	0.691728i	$-0.756850\pi$
$251$	3.77024	−	6.53025i	0.237976	−	0.412186i	0.960133	+	0.279543i	$0.0901829\pi$
$252$		0			0
$253$	3.86025	−	6.68615i	0.242692	−	0.420354i
$254$	−1.28166	+	2.21990i	−0.0804185	+	0.139289i
$255$		0			0
$256$	1.67360	−	2.89877i	0.104600	−	0.181173i
$257$	6.70895	+	11.6202i	0.418493	+	0.724851i	0.995788	−	0.0916848i	$-0.0292252\pi$
$257$	6.70895	+	11.6202i	0.418493	+	0.724851i	−0.577295	+	0.816535i	$0.695892\pi$
$258$		0			0
$259$	−5.18060			−0.321907
$260$	5.05765	+	6.55325i	0.313662	+	0.406415i
$261$		0			0
$262$	−0.931468	−	1.61335i	−0.0575463	−	0.0996731i
$263$	−5.59903	−	9.69781i	−0.345251	−	0.597992i	0.640148	−	0.768251i	$-0.278873\pi$
$263$	−5.59903	−	9.69781i	−0.345251	−	0.597992i	−0.985399	+	0.170259i	$0.945540\pi$
$264$		0			0
$265$	10.8388			0.665821
$266$	1.14042	−	1.97526i	0.0699234	−	0.121111i
$267$		0			0
$268$	−1.29052			−0.0788311
$269$	6.95862	−	12.0527i	0.424274	−	0.734865i	−0.572078	−	0.820199i	$-0.693863\pi$
$269$	6.95862	−	12.0527i	0.424274	−	0.734865i	0.996352	+	0.0853346i	$0.0271959\pi$
$270$		0			0
$271$	−0.991271	−	1.71693i	−0.0602154	−	0.104296i	0.834346	−	0.551241i	$-0.185845\pi$
$271$	−0.991271	−	1.71693i	−0.0602154	−	0.104296i	−0.894562	+	0.446945i	$0.852512\pi$
$272$	1.24698			0.0756092
$273$		0			0
$274$	11.9390			0.721261
$275$	−1.79590	−	3.11058i	−0.108297	−	0.187575i
$276$		0			0
$277$	−4.89977	+	8.48665i	−0.294399	+	0.509914i	−0.974845	−	0.222884i	$-0.928453\pi$
$277$	−4.89977	+	8.48665i	−0.294399	+	0.509914i	0.680446	+	0.732798i	$0.261786\pi$
$278$	−4.49098			−0.269351
$279$		0			0
$280$	−1.39008	+	2.40770i	−0.0830734	+	0.143887i
$281$	25.7603			1.53673			0.768366	−	0.640011i	$-0.221070\pi$
$281$	25.7603			1.53673			0.768366	+	0.640011i	$0.221070\pi$
$282$		0			0
$283$	0.0244587	+	0.0423637i	0.00145392	+	0.00251826i	0.866751	−	0.498740i	$-0.166204\pi$
$283$	0.0244587	+	0.0423637i	0.00145392	+	0.00251826i	−0.865298	+	0.501259i	$0.832871\pi$
$284$	−3.81013	−	6.59935i	−0.226090	−	0.391599i
$285$		0			0
$286$	−1.39008	−	1.80115i	−0.0821974	−	0.106504i
$287$	−0.219833			−0.0129763
$288$		0			0
$289$	8.34601	+	14.4557i	0.490942	+	0.850336i
$290$	3.40246	−	5.89324i	0.199799	−	0.346063i
$291$		0			0
$292$	7.19418	−	12.4607i	0.421007	−	0.729206i
$293$	10.6610	−	18.4654i	0.622822	−	1.07876i	−0.366136	−	0.930561i	$-0.619320\pi$
$293$	10.6610	−	18.4654i	0.622822	−	1.07876i	0.988958	−	0.148197i	$-0.0473471\pi$
$294$		0			0
$295$	−2.64579	+	4.58265i	−0.154044	+	0.266812i
$296$	−5.30731	−	9.19254i	−0.308481	−	0.534305i
$297$		0			0
$298$	−1.80864			−0.104772
$299$	−24.2627	+	3.26326i	−1.40315	+	0.188719i
$300$		0			0
$301$	−1.94989	−	3.37730i	−0.112390	−	0.194664i
$302$	1.89008	+	3.27372i	0.108762	+	0.188381i
$303$		0			0
$304$	−9.23490			−0.529658
$305$	7.40970	−	12.8340i	0.424278	−	0.734871i
$306$		0			0
$307$	−23.6528			−1.34994			−0.674968	−	0.737847i	$-0.735843\pi$
$307$	−23.6528			−1.34994			−0.674968	+	0.737847i	$0.735843\pi$
$308$	−0.961968	+	1.66618i	−0.0548132	+	0.0949393i
$309$		0			0
$310$	−3.24967	−	5.62859i	−0.184569	−	0.319682i
$311$	−16.5851			−0.940454			−0.470227	−	0.882545i	$-0.655828\pi$
$311$	−16.5851			−0.940454			−0.470227	+	0.882545i	$0.655828\pi$
$312$		0			0
$313$	−6.90648			−0.390377			−0.195189	−	0.980766i	$-0.562532\pi$
$313$	−6.90648			−0.390377			−0.195189	+	0.980766i	$0.562532\pi$
$314$	−6.77897	−	11.7415i	−0.382559	−	0.662612i
$315$		0			0
$316$	−3.16487	+	5.48172i	−0.178038	+	0.308371i
$317$	−26.0562			−1.46346			−0.731731	−	0.681593i	$-0.761287\pi$
$317$	−26.0562			−1.46346			−0.731731	+	0.681593i	$0.761287\pi$
$318$		0			0
$319$	5.13773	−	8.89880i	0.287658	−	0.498237i
$320$	2.07308			0.115889
$321$		0			0
$322$	−1.88404	−	3.26326i	−0.104994	−	0.181854i
$323$	1.14042	+	1.97526i	0.0634544	+	0.109906i
$324$		0			0
$325$	−4.32908	+	10.5345i	−0.240134	+	0.584350i
$326$	−6.40880			−0.354950
$327$		0			0
$328$	−0.225209	−	0.390074i	−0.0124351	−	0.0215382i
$329$	−4.06853	+	7.04690i	−0.224305	+	0.388508i
$330$		0			0
$331$	1.75033	−	3.03166i	0.0962069	−	0.166635i	−0.813905	−	0.580998i	$-0.802662\pi$
$331$	1.75033	−	3.03166i	0.0962069	−	0.166635i	0.910112	+	0.414363i	$0.135996\pi$
$332$	9.35570	−	16.2045i	0.513461	−	0.889340i
$333$		0			0
$334$	1.33848	−	2.31831i	0.0732383	−	0.126852i
$335$	0.517458	+	0.896264i	0.0282718	+	0.0489681i
$336$		0			0
$337$	−4.14782			−0.225946			−0.112973	−	0.993598i	$-0.536037\pi$
$337$	−4.14782			−0.225946			−0.112973	+	0.993598i	$0.536037\pi$
$338$	−1.82826	+	6.97896i	−0.0994441	+	0.379605i
$339$		0			0
$340$	−0.637063	−	1.10343i	−0.0345496	−	0.0598417i
$341$	−4.90701	−	8.49919i	−0.265729	−	0.460257i
$342$		0			0
$343$	1.00000			0.0539949
$344$	3.99516	−	6.91981i	0.215404	−	0.373091i
$345$		0			0
$346$	12.0013			0.645195
$347$	−5.78717	+	10.0237i	−0.310671	+	0.538099i	−0.978508	−	0.206209i	$-0.933887\pi$
$347$	−5.78717	+	10.0237i	−0.310671	+	0.538099i	0.667836	+	0.744308i	$0.267221\pi$
$348$		0			0
$349$	6.50634	+	11.2693i	0.348276	+	0.603232i	0.985943	−	0.167080i	$-0.0534338\pi$
$349$	6.50634	+	11.2693i	0.348276	+	0.603232i	−0.637667	+	0.770312i	$0.720100\pi$
$350$	−1.75302			−0.0937029
$351$		0			0
$352$	−6.07739			−0.323926
$353$	13.0957	+	22.6824i	0.697013	+	1.20726i	0.969497	+	0.245101i	$0.0788212\pi$
$353$	13.0957	+	22.6824i	0.697013	+	1.20726i	−0.272485	+	0.962160i	$0.587845\pi$
$354$		0			0
$355$	−3.05549	+	5.29226i	−0.162169	+	0.280884i
$356$	−14.5579			−0.771569
$357$		0			0
$358$	7.05041	−	12.2117i	0.372626	−	0.645407i
$359$	−11.0750			−0.584516			−0.292258	−	0.956339i	$-0.594407\pi$
$359$	−11.0750			−0.584516			−0.292258	+	0.956339i	$0.594407\pi$
$360$		0			0
$361$	1.05429	+	1.82609i	0.0554892	+	0.0961101i
$362$	2.13102	+	3.69104i	0.112004	+	0.193997i
$363$		0			0
$364$	6.04623	−	0.813199i	0.316909	−	0.0426232i
$365$	−11.5386			−0.603956
$366$		0			0
$367$	6.68545	+	11.5795i	0.348978	+	0.604447i	0.986068	−	0.166342i	$-0.0531956\pi$
$367$	6.68545	+	11.5795i	0.348978	+	0.604447i	−0.637091	+	0.770789i	$0.719862\pi$
$368$	−7.62833	+	13.2127i	−0.397654	+	0.688758i
$369$		0			0
$370$	−1.95055	+	3.37845i	−0.101404	+	0.175637i
$371$	3.99396	−	6.91774i	0.207356	−	0.359151i
$372$		0			0
$373$	18.3654	−	31.8098i	0.950924	−	1.64705i	0.207492	−	0.978237i	$-0.433470\pi$
$373$	18.3654	−	31.8098i	0.950924	−	1.64705i	0.743432	−	0.668811i	$-0.233197\pi$
$374$	0.175096	+	0.303274i	0.00905398	+	0.0156819i
$375$		0			0
$376$	−16.6722			−0.859802
$377$	−32.2920	+	4.34317i	−1.66312	+	0.223685i
$378$		0			0
$379$	−16.6407	−	28.8226i	−0.854776	−	1.48052i	−0.876853	−	0.480759i	$-0.840361\pi$
$379$	−16.6407	−	28.8226i	−0.854776	−	1.48052i	0.0220768	−	0.999756i	$-0.492972\pi$
$380$	4.71797	+	8.17177i	0.242027	+	0.419203i
$381$		0			0
$382$	−5.27413			−0.269848
$383$	−8.81163	+	15.2622i	−0.450253	+	0.779861i	−0.998401	−	0.0565199i	$-0.982000\pi$
$383$	−8.81163	+	15.2622i	−0.450253	+	0.779861i	0.548148	+	0.836381i	$0.315333\pi$
$384$		0			0
$385$	1.54288			0.0786323
$386$	2.59485	−	4.49441i	0.132074	−	0.228760i
$387$		0			0
$388$	−12.6468	−	21.9048i	−0.642042	−	1.11205i
$389$	−29.6340			−1.50250			−0.751252	−	0.660016i	$-0.770550\pi$
$389$	−29.6340			−1.50250			−0.751252	+	0.660016i	$0.770550\pi$
$390$		0			0
$391$	3.76809			0.190560
$392$	1.02446	+	1.77441i	0.0517430	+	0.0896215i
$393$		0			0
$394$	4.86025	−	8.41820i	0.244856	−	0.424103i
$395$	5.07606			0.255405
$396$		0			0
$397$	−9.59999	+	16.6277i	−0.481810	+	0.834519i	−0.999782	−	0.0208785i	$-0.993354\pi$
$397$	−9.59999	+	16.6277i	−0.481810	+	0.834519i	0.517972	+	0.855397i	$0.326687\pi$
$398$	−9.76138			−0.489294
$399$		0			0
$400$	3.54892	+	6.14691i	0.177446	+	0.307345i
$401$	6.24967	+	10.8247i	0.312094	+	0.540562i	0.978815	−	0.204745i	$-0.0656364\pi$
$401$	6.24967	+	10.8247i	0.312094	+	0.540562i	−0.666722	+	0.745307i	$0.732303\pi$
$402$		0			0
$403$	−11.8286	+	28.7839i	−0.589222	+	1.43383i
$404$	7.19508			0.357969
$405$		0			0
$406$	−2.50753	−	4.34317i	−0.124447	−	0.215548i
$407$	−2.94534	+	5.10147i	−0.145995	+	0.252871i
$408$		0			0
$409$	8.39104	−	14.5337i	0.414910	−	0.718646i	−0.580509	−	0.814254i	$-0.697146\pi$
$409$	8.39104	−	14.5337i	0.414910	−	0.718646i	0.995419	+	0.0956082i	$0.0304796\pi$
$410$	−0.0827692	+	0.143360i	−0.00408768	+	0.00708007i
$411$		0			0
$412$	5.14861	−	8.91766i	0.253654	−	0.439341i
$413$	1.94989	+	3.37730i	0.0959476	+	0.166186i
$414$		0			0
$415$	−15.0054			−0.736585
$416$	11.7741	+	15.2559i	0.577274	+	0.747980i
$417$		0			0
$418$	−1.29672	−	2.24599i	−0.0634249	−	0.109855i
$419$	−7.18210	−	12.4398i	−0.350868	−	0.607722i	0.635533	−	0.772073i	$-0.280780\pi$
$419$	−7.18210	−	12.4398i	−0.350868	−	0.607722i	−0.986402	+	0.164352i	$0.947447\pi$
$420$		0			0
$421$	−22.5526			−1.09914			−0.549572	−	0.835446i	$-0.685209\pi$
$421$	−22.5526			−1.09914			−0.549572	+	0.835446i	$0.685209\pi$
$422$	−0.378002	+	0.654719i	−0.0184009	+	0.0318712i
$423$		0			0
$424$	16.3666			0.794832
$425$	0.876510	−	1.51816i	0.0425170	−	0.0736416i
$426$		0			0
$427$	−5.46077	−	9.45833i	−0.264265	−	0.457721i
$428$	−21.7530			−1.05147
$429$		0			0
$430$	−2.93661			−0.141616
$431$	2.24482	+	3.88815i	0.108129	+	0.187286i	0.915012	−	0.403426i	$-0.132181\pi$
$431$	2.24482	+	3.88815i	0.108129	+	0.187286i	−0.806883	+	0.590711i	$0.798847\pi$
$432$		0			0
$433$	−9.68060	+	16.7673i	−0.465220	+	0.805785i	−0.999211	−	0.0397051i	$-0.987358\pi$
$433$	−9.68060	+	16.7673i	−0.465220	+	0.805785i	0.533991	+	0.845490i	$0.320691\pi$
$434$	−4.78986			−0.229920
$435$		0			0
$436$	−5.78770	+	10.0246i	−0.277181	+	0.480091i
$437$	−27.9057			−1.33491
$438$		0			0
$439$	−13.6434	−	23.6311i	−0.651164	−	1.12785i	−0.982841	−	0.184456i	$-0.940948\pi$
$439$	−13.6434	−	23.6311i	−0.651164	−	1.12785i	0.331677	−	0.943393i	$-0.392386\pi$
$440$	1.58061	+	2.73770i	0.0753528	+	0.130515i
$441$		0			0
$442$	0.422075	−	1.02709i	0.0200761	−	0.0488537i
$443$	16.2319			0.771202			0.385601	−	0.922666i	$-0.373994\pi$
$443$	16.2319			0.771202			0.385601	+	0.922666i	$0.373994\pi$
$444$		0			0
$445$	5.83728	+	10.1105i	0.276714	+	0.479282i
$446$	2.85421	−	4.94363i	0.135151	−	0.234088i
$447$		0			0
$448$	0.763906	−	1.32312i	0.0360911	−	0.0625117i
$449$	−12.1235	+	20.9985i	−0.572143	+	0.990980i	0.424203	+	0.905567i	$0.360554\pi$
$449$	−12.1235	+	20.9985i	−0.572143	+	0.990980i	−0.996346	+	0.0854133i	$0.972779\pi$
$450$		0			0
$451$	−0.124982	+	0.216475i	−0.00588516	+	0.0101934i
$452$	−15.7620	−	27.3007i	−0.741384	−	1.28412i
$453$		0			0
$454$	−3.11231			−0.146068
$455$	−2.98911	−	3.87303i	−0.140132	−	0.181570i
$456$		0			0
$457$	15.7451	+	27.2713i	0.736526	+	1.27570i	0.954051	+	0.299645i	$0.0968683\pi$
$457$	15.7451	+	27.2713i	0.736526	+	1.27570i	−0.217525	+	0.976055i	$0.569798\pi$
$458$	0.521770	+	0.903733i	0.0243807	+	0.0422287i
$459$		0			0
$460$	15.5888			0.726832
$461$	20.4284	−	35.3830i	0.951446	−	1.64795i	0.209147	−	0.977884i	$-0.432931\pi$
$461$	20.4284	−	35.3830i	0.951446	−	1.64795i	0.742299	−	0.670068i	$-0.233735\pi$
$462$		0			0
$463$	39.0941			1.81686			0.908429	−	0.418040i	$-0.137283\pi$
$463$	39.0941			1.81686			0.908429	+	0.418040i	$0.137283\pi$
$464$	−10.1528	+	17.5852i	−0.471332	+	0.816370i
$465$		0			0
$466$	−1.77144	−	3.06822i	−0.0820603	−	0.142133i
$467$	−9.39804			−0.434890			−0.217445	−	0.976073i	$-0.569772\pi$
$467$	−9.39804			−0.434890			−0.217445	+	0.976073i	$0.569772\pi$
$468$		0			0
$469$	0.762709			0.0352186
$470$	3.06369	+	5.30646i	0.141317	+	0.244769i
$471$		0			0
$472$	−3.99516	+	6.91981i	−0.183892	+	0.318510i
$473$	−4.43429			−0.203889
$474$		0			0
$475$	−6.49127	+	11.2432i	−0.297840	+	0.515874i
$476$	−0.939001			−0.0430390
$477$		0			0
$478$	0.527811	+	0.914196i	0.0241415	+	0.0418143i
$479$	−1.01693	−	1.76137i	−0.0464645	−	0.0804789i	0.841858	−	0.539699i	$-0.181462\pi$
$479$	−1.01693	−	1.76137i	−0.0464645	−	0.0804789i	−0.888322	+	0.459221i	$0.848129\pi$
$480$		0			0
$481$	18.5122	−	2.48984i	0.844086	−	0.113527i
$482$	7.33214			0.333970
$483$		0			0
$484$	−8.21230	−	14.2241i	−0.373286	−	0.646551i
$485$	−10.1419	+	17.5663i	−0.460520	+	0.797645i
$486$		0			0
$487$	15.1441	−	26.2303i	0.686243	−	1.18861i	−0.286801	−	0.957990i	$-0.592592\pi$
$487$	15.1441	−	26.2303i	0.686243	−	1.18861i	0.973044	−	0.230618i	$-0.0740747\pi$
$488$	11.1887	−	19.3793i	0.506487	−	0.877262i
$489$		0			0
$490$	0.376510	−	0.652135i	0.0170090	−	0.0294604i
$491$	−14.5945	−	25.2784i	−0.658640	−	1.14080i	−0.980968	−	0.194170i	$-0.937799\pi$
$491$	−14.5945	−	25.2784i	−0.658640	−	1.14080i	0.322328	−	0.946628i	$-0.395535\pi$
$492$		0			0
$493$	5.01507			0.225867
$494$	−3.12581	+	7.60643i	−0.140637	+	0.342230i
$495$		0			0
$496$	9.69687	+	16.7955i	0.435402	+	0.754139i
$497$	2.25182	+	3.90027i	0.101008	+	0.174951i
$498$		0			0
$499$	1.24937			0.0559296			0.0279648	−	0.999609i	$-0.491097\pi$
$499$	1.24937			0.0559296			0.0279648	+	0.999609i	$0.491097\pi$
$500$	9.36592	−	16.2223i	0.418857	−	0.725481i
$501$		0			0
$502$	−4.18465			−0.186770
$503$	10.5097	−	18.2033i	0.468604	−	0.811646i	−0.530752	−	0.847527i	$-0.678091\pi$
$503$	10.5097	−	18.2033i	0.468604	−	0.811646i	0.999356	+	0.0358814i	$0.0114238\pi$
$504$		0			0
$505$	−2.88500	−	4.99697i	−0.128381	−	0.222362i
$506$	−4.28455			−0.190472
$507$		0			0
$508$	−7.81535			−0.346750
$509$	11.8388	+	20.5054i	0.524744	+	0.908884i	0.999585	+	0.0288121i	$0.00917244\pi$
$509$	11.8388	+	20.5054i	0.524744	+	0.908884i	−0.474840	+	0.880072i	$0.657494\pi$
$510$		0			0
$511$	−4.25182	+	7.36438i	−0.188090	+	0.325781i
$512$	21.2174			0.937687
$513$		0			0
$514$	3.72318	−	6.44875i	0.164223	−	0.284442i
$515$	−8.25773			−0.363879
$516$		0			0
$517$	4.62618	+	8.01278i	0.203459	+	0.352401i
$518$	1.43751	+	2.48984i	0.0631605	+	0.109397i
$519$		0			0
$520$	3.81013	−	9.27169i	0.167085	−	0.406590i
$521$	−2.47783			−0.108556			−0.0542778	−	0.998526i	$-0.517286\pi$
$521$	−2.47783			−0.108556			−0.0542778	+	0.998526i	$0.517286\pi$
$522$		0			0
$523$	−3.55280	−	6.15363i	−0.155353	−	0.269080i	0.777834	−	0.628469i	$-0.216318\pi$
$523$	−3.55280	−	6.15363i	−0.155353	−	0.269080i	−0.933188	+	0.359390i	$0.882985\pi$
$524$	2.83997	−	4.91897i	0.124065	−	0.214886i
$525$		0			0
$526$	−3.10723	+	5.38188i	−0.135482	+	0.234661i
$527$	2.39493	−	4.14814i	0.104325	−	0.180696i
$528$		0			0
$529$	−11.5511	+	20.0070i	−0.502221	+	0.869872i
$530$	−3.00753	−	5.20920i	−0.130639	−	0.226273i
$531$		0			0
$532$	6.95407			0.301497
$533$	0.785544	−	0.105653i	0.0340257	−	0.00457635i
$534$		0			0
$535$	8.72228	+	15.1074i	0.377097	+	0.653152i
$536$	0.781364	+	1.35336i	0.0337498	+	0.0584563i
$537$		0			0
$538$	−7.72348			−0.332983
$539$	0.568532	−	0.984726i	0.0244884	−	0.0424151i
$540$		0			0
$541$	−35.7157			−1.53554			−0.767769	−	0.640727i	$-0.778633\pi$
$541$	−35.7157			−1.53554			−0.767769	+	0.640727i	$0.778633\pi$
$542$	−0.550114	+	0.952825i	−0.0236294	+	0.0409273i
$543$		0			0
$544$	−1.48307	−	2.56876i	−0.0635863	−	0.110135i
$545$	9.28275			0.397629
$546$		0			0
$547$	10.1395			0.433532			0.216766	−	0.976224i	$-0.430449\pi$
$547$	10.1395			0.433532			0.216766	+	0.976224i	$0.430449\pi$
$548$	18.2005	+	31.5242i	0.777487	+	1.34665i
$549$		0			0
$550$	−0.996648	+	1.72624i	−0.0424972	+	0.0736073i
$551$	−37.1406			−1.58224
$552$		0			0
$553$	1.87047	−	3.23975i	0.0795404	−	0.137768i
$554$	5.43834			0.231053
$555$		0			0
$556$	−6.84631	−	11.8582i	−0.290348	−	0.502898i
$557$	1.81671	+	3.14663i	0.0769764	+	0.133327i	0.901944	−	0.431853i	$-0.142140\pi$
$557$	1.81671	+	3.14663i	0.0769764	+	0.133327i	−0.824968	+	0.565180i	$0.808807\pi$
$558$		0			0
$559$	8.59083	+	11.1312i	0.363354	+	0.470801i
$560$	−3.04892			−0.128840
$561$		0			0
$562$	−7.14795	−	12.3806i	−0.301518	−	0.522245i
$563$	19.9182	−	34.4993i	0.839452	−	1.45397i	−0.0509022	−	0.998704i	$-0.516210\pi$
$563$	19.9182	−	34.4993i	0.839452	−	1.45397i	0.890354	−	0.455269i	$-0.150457\pi$
$564$		0			0
$565$	−12.6402	+	21.8934i	−0.531776	+	0.921064i
$566$	0.0135735	−	0.0235101i	0.000570538	−	0.000988201i
$567$		0			0
$568$	−4.61380	+	7.99134i	−0.193591	+	0.335309i
$569$	1.34063	+	2.32205i	0.0562023	+	0.0973452i	0.892758	−	0.450537i	$-0.148767\pi$
$569$	1.34063	+	2.32205i	0.0562023	+	0.0973452i	−0.836555	+	0.547882i	$0.815434\pi$
$570$		0			0
$571$	−6.76138			−0.282955			−0.141477	−	0.989941i	$-0.545185\pi$
$571$	−6.76138			−0.282955			−0.141477	+	0.989941i	$0.545185\pi$
$572$	2.63669	−	6.41621i	0.110246	−	0.268275i
$573$		0			0
$574$	0.0609989	+	0.105653i	0.00254605	+	0.00440988i
$575$	10.7240	+	18.5745i	0.447222	+	0.774612i
$576$		0			0
$577$	−6.73556			−0.280405			−0.140203	−	0.990123i	$-0.544775\pi$
$577$	−6.73556			−0.280405			−0.140203	+	0.990123i	$0.544775\pi$
$578$	4.63169	−	8.02232i	0.192653	−	0.333684i
$579$		0			0
$580$	20.7476			0.861499
$581$	−5.52930	+	9.57703i	−0.229394	+	0.397322i
$582$		0			0
$583$	−4.54138	−	7.86591i	−0.188085	−	0.325773i
$584$	−17.4233			−0.720980
$585$		0			0
$586$	−11.8328			−0.488809
$587$	−11.6265	−	20.1376i	−0.479876	−	0.831169i	0.519858	−	0.854253i	$-0.325985\pi$
$587$	−11.6265	−	20.1376i	−0.479876	−	0.831169i	−0.999734	+	0.0230834i	$0.992652\pi$
$588$		0			0
$589$	−17.7364	+	30.7203i	−0.730815	+	1.26581i
$590$	2.93661			0.120898
$591$		0			0
$592$	5.82036	−	10.0812i	0.239215	−	0.414333i
$593$	25.4717			1.04600			0.522999	−	0.852333i	$-0.324813\pi$
$593$	25.4717			1.04600			0.522999	+	0.852333i	$0.324813\pi$
$594$		0			0
$595$	0.376510	+	0.652135i	0.0154354	+	0.0267349i
$596$	−2.75720	−	4.77561i	−0.112939	−	0.195617i
$597$		0			0
$598$	8.30074	+	10.7554i	0.339443	+	0.439819i
$599$	16.7453			0.684192			0.342096	−	0.939665i	$-0.388863\pi$
$599$	16.7453			0.684192			0.342096	+	0.939665i	$0.388863\pi$
$600$		0			0
$601$	−0.206259	−	0.357251i	−0.00841348	−	0.0145726i	0.861788	−	0.507269i	$-0.169345\pi$
$601$	−0.206259	−	0.357251i	−0.00841348	−	0.0145726i	−0.870201	+	0.492696i	$0.836011\pi$
$602$	−1.08211	+	1.87426i	−0.0441033	+	0.0763892i
$603$		0			0
$604$	−5.76271	+	9.98130i	−0.234481	+	0.406134i
$605$	−6.58575	+	11.4069i	−0.267749	+	0.463755i
$606$		0			0
$607$	20.5057	−	35.5169i	0.832300	−	1.44159i	−0.0639107	−	0.997956i	$-0.520357\pi$
$607$	20.5057	−	35.5169i	0.832300	−	1.44159i	0.896210	−	0.443630i	$-0.146309\pi$
$608$	10.9834	+	19.0238i	0.445434	+	0.771515i
$609$		0			0
$610$	−8.22414			−0.332986
$611$	11.1516	−	27.1366i	0.451145	−	1.09783i
$612$		0			0
$613$	−14.4248	−	24.9844i	−0.582611	−	1.00911i	−0.995169	−	0.0981800i	$-0.968698\pi$
$613$	−14.4248	−	24.9844i	−0.582611	−	1.00911i	0.412558	−	0.910931i	$-0.364635\pi$
$614$	6.56315	+	11.3677i	0.264867	+	0.458764i
$615$		0			0
$616$	2.32975			0.0938683
$617$	−1.65428	+	2.86531i	−0.0665990	+	0.115353i	−0.897402	−	0.441213i	$-0.854548\pi$
$617$	−1.65428	+	2.86531i	−0.0665990	+	0.115353i	0.830803	+	0.556566i	$0.187881\pi$
$618$		0			0
$619$	−36.0737			−1.44992			−0.724962	−	0.688789i	$-0.758143\pi$
$619$	−36.0737			−1.44992			−0.724962	+	0.688789i	$0.758143\pi$
$620$	9.90797	−	17.1611i	0.397914	−	0.689207i
$621$		0			0
$622$	4.60202	+	7.97092i	0.184524	+	0.319605i
$623$	8.60388			0.344707
$624$		0			0
$625$	0.772398			0.0308959
$626$	1.91640	+	3.31931i	0.0765949	+	0.132666i
$627$		0			0
$628$	20.6685	−	35.7989i	0.824764	−	1.42853i
$629$	−2.87502			−0.114634
$630$		0			0
$631$	19.2315	−	33.3100i	0.765596	−	1.32605i	−0.174335	−	0.984686i	$-0.555778\pi$
$631$	19.2315	−	33.3100i	0.765596	−	1.32605i	0.939931	−	0.341364i	$-0.110889\pi$
$632$	7.66487			0.304892
$633$		0			0
$634$	7.23005	+	12.5228i	0.287142	+	0.497345i
$635$	3.13371	+	5.42775i	0.124358	+	0.215394i
$636$		0			0
$637$	−3.57338	+	0.480608i	−0.141582	+	0.0190424i
$638$	−5.70245			−0.225762
$639$		0			0
$640$	−7.82759	−	13.5578i	−0.309413	−	0.535919i
$641$	−2.13049	+	3.69012i	−0.0841493	+	0.145751i	−0.905028	−	0.425351i	$-0.860151\pi$
$641$	−2.13049	+	3.69012i	−0.0841493	+	0.145751i	0.820879	+	0.571102i	$0.193484\pi$
$642$		0			0
$643$	1.79829	−	3.11473i	0.0709176	−	0.122833i	−0.828386	−	0.560158i	$-0.810741\pi$
$643$	1.79829	−	3.11473i	0.0709176	−	0.122833i	0.899304	+	0.437325i	$0.144074\pi$
$644$	5.74429	−	9.94940i	0.226357	−	0.392061i
$645$		0			0
$646$	0.632883	−	1.09619i	0.0249004	−	0.0431288i
$647$	−22.3572	−	38.7238i	−0.878952	−	1.52239i	−0.852493	−	0.522739i	$-0.824910\pi$
$647$	−22.3572	−	38.7238i	−0.878952	−	1.52239i	−0.0264594	−	0.999650i	$-0.508423\pi$
$648$		0			0
$649$	4.43429			0.174061
$650$	6.26420	−	0.842515i	0.245702	−	0.0330462i
$651$		0			0
$652$	−9.76995	−	16.9220i	−0.382621	−	0.662718i
$653$	−16.5978	−	28.7483i	−0.649523	−	1.12501i	−0.983237	−	0.182333i	$-0.941635\pi$
$653$	−16.5978	−	28.7483i	−0.649523	−	1.12501i	0.333713	−	0.942675i	$-0.391698\pi$
$654$		0			0
$655$	−4.55496			−0.177977
$656$	0.246980	−	0.427781i	0.00964293	−	0.0167021i
$657$		0			0
$658$	4.51573			0.176041
$659$	23.8735	−	41.3500i	0.929978	−	1.61077i	0.146624	−	0.989192i	$-0.453159\pi$
$659$	23.8735	−	41.3500i	0.929978	−	1.61077i	0.783354	−	0.621576i	$-0.213507\pi$
$660$		0			0
$661$	−3.64526	−	6.31378i	−0.141784	−	0.245577i	0.786384	−	0.617738i	$-0.211951\pi$
$661$	−3.64526	−	6.31378i	−0.141784	−	0.245577i	−0.928169	+	0.372160i	$0.878617\pi$
$662$	−1.94272			−0.0755060
$663$		0			0
$664$	−22.6582			−0.879308
$665$	−2.78836	−	4.82959i	−0.108128	−	0.187283i
$666$		0			0
$667$	−30.6794	+	53.1383i	−1.18791	+	2.05752i
$668$	8.16182			0.315790
$669$		0			0
$670$	0.287168	−	0.497389i	0.0110943	−	0.0192158i
$671$	−12.4185			−0.479410
$672$		0			0
$673$	16.9421	+	29.3446i	0.653071	+	1.13115i	0.982374	+	0.186927i	$0.0598529\pi$
$673$	16.9421	+	29.3446i	0.653071	+	1.13115i	−0.329303	+	0.944224i	$0.606814\pi$
$674$	1.15093	+	1.99347i	0.0443323	+	0.0767857i
$675$		0			0
$676$	−21.2146	+	5.81173i	−0.815947	+	0.223528i
$677$	36.2989			1.39508			0.697540	−	0.716546i	$-0.254278\pi$
$677$	36.2989			1.39508			0.697540	+	0.716546i	$0.254278\pi$
$678$		0			0
$679$	7.47434	+	12.9459i	0.286839	+	0.496820i
$680$	−0.771438	+	1.33617i	−0.0295833	+	0.0512398i
$681$		0			0
$682$	−2.72318	+	4.71669i	−0.104276	+	0.180612i
$683$	−0.568236	+	0.984214i	−0.0217430	+	0.0376599i	−0.876692	−	0.481052i	$-0.840255\pi$
$683$	−0.568236	+	0.984214i	−0.0217430	+	0.0376599i	0.854949	+	0.518712i	$0.173588\pi$
$684$		0			0
$685$	14.5957	−	25.2805i	0.557672	−	0.965917i
$686$	−0.277479	−	0.480608i	−0.0105942	−	0.0183497i
$687$		0			0
$688$	8.76271			0.334075
$689$	−10.9472	+	26.6392i	−0.417055	+	1.01487i
$690$		0			0
$691$	17.7301	+	30.7094i	0.674483	+	1.16824i	0.976620	+	0.214974i	$0.0689668\pi$
$691$	17.7301	+	30.7094i	0.674483	+	1.16824i	−0.302137	+	0.953265i	$0.597700\pi$
$692$	18.2955	+	31.6888i	0.695492	+	1.20463i
$693$		0			0
$694$	6.42327			0.243824
$695$	−5.49031	+	9.50950i	−0.208259	+	0.360716i
$696$		0			0
$697$	−0.121998			−0.00462100
$698$	3.61074	−	6.25399i	0.136669	−	0.236717i
$699$		0			0
$700$	−2.67241	−	4.62874i	−0.101007	−	0.174950i
$701$	−31.7265			−1.19829			−0.599146	−	0.800640i	$-0.704493\pi$
$701$	−31.7265			−1.19829			−0.599146	+	0.800640i	$0.704493\pi$
$702$		0			0
$703$	21.2918			0.803037
$704$	−0.868609	−	1.50447i	−0.0327369	−	0.0567020i
$705$		0			0
$706$	7.26755	−	12.5878i	0.273518	−	0.473747i
$707$	−4.25236			−0.159926
$708$		0			0
$709$	17.5913	−	30.4690i	0.660654	−	1.14429i	−0.319790	−	0.947488i	$-0.603613\pi$
$709$	17.5913	−	30.4690i	0.660654	−	1.14429i	0.980444	−	0.196797i	$-0.0630541\pi$
$710$	3.39134			0.127275
$711$		0			0
$712$	8.81431	+	15.2668i	0.330330	+	0.572149i
$713$	29.3017	+	50.7520i	1.09736	+	1.90068i
$714$		0			0
$715$	−5.51328	+	0.741519i	−0.206185	+	0.0277312i
$716$	42.9922			1.60670
$717$		0			0
$718$	3.07308	+	5.32273i	0.114686	+	0.198643i
$719$	−0.970992	+	1.68181i	−0.0362119	+	0.0627209i	−0.883563	−	0.468312i	$-0.844862\pi$
$719$	−0.970992	+	1.68181i	−0.0362119	+	0.0627209i	0.847351	+	0.531033i	$0.178196\pi$
$720$		0			0
$721$	−3.04288	+	5.27042i	−0.113323	+	0.196281i
$722$	0.585089	−	1.01340i	0.0217748	−	0.0377150i
$723$		0			0
$724$	−6.49731	+	11.2537i	−0.241471	+	0.418239i
$725$	14.2729	+	24.7214i	0.530083	+	0.918131i
$726$		0			0
$727$	8.95838			0.332248			0.166124	−	0.986105i	$-0.446875\pi$
$727$	8.95838			0.332248			0.166124	+	0.986105i	$0.446875\pi$
$728$	−4.51357	−	5.84829i	−0.167284	−	0.216752i
$729$		0			0
$730$	3.20171	+	5.54552i	0.118501	+	0.205249i
$731$	−1.08211	−	1.87426i	−0.0400231	−	0.0693221i
$732$		0			0
$733$	9.11662			0.336730			0.168365	−	0.985725i	$-0.446151\pi$
$733$	9.11662			0.336730			0.168365	+	0.985725i	$0.446151\pi$
$734$	3.71014	−	6.42616i	0.136944	−	0.237194i
$735$		0			0
$736$	36.2905			1.33769
$737$	0.433624	−	0.751059i	0.0159728	−	0.0276656i
$738$		0			0
$739$	14.4167	+	24.9705i	0.530327	+	0.918553i	0.999374	+	0.0353799i	$0.0112641\pi$
$739$	14.4167	+	24.9705i	0.530327	+	0.918553i	−0.469047	+	0.883173i	$0.655403\pi$
$740$	−11.8941			−0.437237
$741$		0			0
$742$	−4.43296			−0.162739
$743$	25.1005	+	43.4754i	0.920849	+	1.59496i	0.798105	+	0.602519i	$0.205836\pi$
$743$	25.1005	+	43.4754i	0.920849	+	1.59496i	0.122744	+	0.992438i	$0.460831\pi$
$744$		0			0
$745$	−2.21110	+	3.82974i	−0.0810086	+	0.140311i
$746$	−20.3840			−0.746313
$747$		0			0
$748$	−0.533852	+	0.924659i	−0.0195196	+	0.0338089i
$749$	12.8562			0.469756
$750$		0			0
$751$	4.01477	+	6.95379i	0.146501	+	0.253747i	0.929932	−	0.367732i	$-0.119865\pi$
$751$	4.01477	+	6.95379i	0.146501	+	0.253747i	−0.783431	+	0.621479i	$0.786532\pi$
$752$	−9.14191	−	15.8342i	−0.333371	−	0.577416i
$753$		0			0
$754$	11.0477	+	14.3147i	0.402334	+	0.521309i
$755$	9.24267			0.336375
$756$		0			0
$757$	−23.3751	−	40.4868i	−0.849582	−	1.47152i	−0.881582	−	0.472031i	$-0.843521\pi$
$757$	−23.3751	−	40.4868i	−0.849582	−	1.47152i	0.0320005	−	0.999488i	$-0.489812\pi$
$758$	−9.23490	+	15.9953i	−0.335427	+	0.580976i
$759$		0			0
$760$	5.71313	−	9.89543i	0.207237	−	0.358945i
$761$	3.15668	−	5.46753i	0.114429	−	0.198198i	−0.803122	−	0.595815i	$-0.796829\pi$
$761$	3.15668	−	5.46753i	0.114429	−	0.198198i	0.917552	+	0.397617i	$0.130163\pi$
$762$		0			0
$763$	3.42058	−	5.92462i	0.123833	−	0.214486i
$764$	−8.04019	−	13.9260i	−0.290884	−	0.503826i
$765$		0			0
$766$	9.78017			0.353372
$767$	−8.59083	−	11.1312i	−0.310197	−	0.401926i
$768$		0			0
$769$	−20.9366	−	36.2633i	−0.754993	−	1.30769i	−0.945378	−	0.325977i	$-0.894307\pi$
$769$	−20.9366	−	36.2633i	−0.754993	−	1.30769i	0.190384	−	0.981710i	$-0.439027\pi$
$770$	−0.428116	−	0.741519i	−0.0154282	−	0.0267225i
$771$		0			0
$772$	15.8230			0.569481
$773$	−19.6320	+	34.0036i	−0.706113	+	1.22302i	0.260175	+	0.965561i	$0.416220\pi$
$773$	−19.6320	+	34.0036i	−0.706113	+	1.22302i	−0.966288	+	0.257463i	$0.917114\pi$
$774$		0			0
$775$	27.2640			0.979350
$776$	−15.3143	+	26.5252i	−0.549752	+	0.952198i
$777$		0			0
$778$	8.22282	+	14.2423i	0.294802	+	0.510612i
$779$	0.903493			0.0323710
$780$		0			0
$781$	5.12093			0.183241
$782$	−1.04556	−	1.81097i	−0.0373893	−	0.0647602i
$783$		0			0
$784$	−1.12349	+	1.94594i	−0.0401246	+	0.0694979i
$785$	−33.1497			−1.18316
$786$		0			0
$787$	18.0027	−	31.1816i	0.641727	−	1.11150i	−0.343321	−	0.939218i	$-0.611552\pi$
$787$	18.0027	−	31.1816i	0.641727	−	1.11150i	0.985047	−	0.172285i	$-0.0551149\pi$
$788$	29.6370			1.05577
$789$		0			0
$790$	−1.40850	−	2.43960i	−0.0501122	−	0.0867969i
$791$	9.31551	+	16.1349i	0.331221	+	0.573692i
$792$		0			0
$793$	24.0591	+	31.1737i	0.854365	+	1.10701i
$794$	10.6552			0.378138
$795$		0			0
$796$	−14.8808	−	25.7743i	−0.527437	−	0.913547i
$797$	−9.07553	+	15.7193i	−0.321472	+	0.556806i	−0.980792	−	0.195057i	$-0.937511\pi$
$797$	−9.07553	+	15.7193i	−0.321472	+	0.556806i	0.659320	+	0.751862i	$0.270844\pi$
$798$		0			0
$799$	−2.25786	+	3.91074i	−0.0798775	+	0.138352i
$800$	8.44169	−	14.6214i	0.298459	−	0.516946i
$801$		0			0
$802$	3.46830	−	6.00728i	0.122470	−	0.212124i
$803$	4.83459	+	8.37376i	0.170609	+	0.295504i
$804$		0			0
$805$	−9.21313			−0.324720
$806$	17.1160	−	2.30204i	0.602884	−	0.0810860i
$807$		0			0
$808$	−4.35636	−	7.54544i	−0.153256	−	0.265448i
$809$	18.6417	+	32.2883i	0.655406	+	1.13520i	0.981792	+	0.189960i	$0.0608359\pi$
$809$	18.6417	+	32.2883i	0.655406	+	1.13520i	−0.326386	+	0.945237i	$0.605831\pi$
$810$		0			0
$811$	37.7657			1.32613			0.663066	−	0.748561i	$-0.269255\pi$
$811$	37.7657			1.32613			0.663066	+	0.748561i	$0.269255\pi$
$812$	7.64526	−	13.2420i	0.268296	−	0.464702i
$813$		0			0
$814$	3.26908			0.114581
$815$	−7.83489	+	13.5704i	−0.274444	+	0.475351i
$816$		0			0
$817$	8.01387	+	13.8804i	0.280370	+	0.485615i
$818$	−9.31336			−0.325634
$819$		0			0
$820$	−0.504713			−0.0176253
$821$	0.807315	+	1.39831i	0.0281755	+	0.0488013i	0.879769	−	0.475401i	$-0.157697\pi$
$821$	0.807315	+	1.39831i	0.0281755	+	0.0488013i	−0.851594	+	0.524202i	$0.824364\pi$
$822$		0			0
$823$	−17.0550	+	29.5401i	−0.594498	+	1.02970i	0.399119	+	0.916899i	$0.369316\pi$
$823$	−17.0550	+	29.5401i	−0.594498	+	1.02970i	−0.993617	+	0.112802i	$0.964017\pi$
$824$	−12.4692			−0.434385
$825$		0			0
$826$	1.08211	−	1.87426i	0.0376513	−	0.0652139i
$827$	−23.1360			−0.804517			−0.402259	−	0.915526i	$-0.631775\pi$
$827$	−23.1360			−0.804517			−0.402259	+	0.915526i	$0.631775\pi$
$828$		0			0
$829$	−0.195669	−	0.338909i	−0.00679588	−	0.0117708i	0.862607	−	0.505874i	$-0.168830\pi$
$829$	−0.195669	−	0.338909i	−0.00679588	−	0.0117708i	−0.869403	+	0.494103i	$0.835497\pi$
$830$	4.16368	+	7.21170i	0.144523	+	0.250322i
$831$		0			0
$832$	−2.09382	+	5.09516i	−0.0725901	+	0.176643i
$833$	0.554958			0.0192282
$834$		0			0
$835$	−3.27263	−	5.66837i	−0.113254	−	0.196162i
$836$	3.95361	−	6.84785i	0.136738	−	0.236838i
$837$		0			0
$838$	−3.98576	+	6.90354i	−0.137686	+	0.238479i
$839$	−12.2690	+	21.2506i	−0.423574	+	0.733653i	−0.996286	−	0.0861044i	$-0.972558\pi$
$839$	−12.2690	+	21.2506i	−0.423574	+	0.733653i	0.572712	+	0.819757i	$0.305891\pi$
$840$		0			0
$841$	−26.3322	+	45.6087i	−0.908007	+	1.57271i
$842$	6.25786	+	10.8389i	0.215660	+	0.373535i
$843$		0			0
$844$	−2.30499			−0.0793412
$845$	12.5426	+	12.4032i	0.431480	+	0.426683i
$846$		0			0
$847$	4.85354	+	8.40658i	0.166770	+	0.288854i
$848$	8.97434	+	15.5440i	0.308180	+	0.533784i
$849$		0			0
$850$	−0.972853			−0.0333686
$851$	17.5878	−	30.4629i	0.602901	−	1.04426i
$852$		0			0
$853$	−19.6786			−0.673783			−0.336891	−	0.941544i	$-0.609376\pi$
$853$	−19.6786			−0.673783			−0.336891	+	0.941544i	$0.609376\pi$
$854$	−3.03050	+	5.24898i	−0.103702	+	0.179616i
$855$		0			0
$856$	13.1707	+	22.8123i	0.450165	+	0.779708i
$857$	22.5429			0.770050			0.385025	−	0.922906i	$-0.374193\pi$
$857$	22.5429			0.770050			0.385025	+	0.922906i	$0.374193\pi$
$858$		0			0
$859$	−23.8931			−0.815221			−0.407610	−	0.913156i	$-0.633638\pi$
$859$	−23.8931			−0.815221			−0.407610	+	0.913156i	$0.633638\pi$
$860$	−4.47674	−	7.75394i	−0.152655	−	0.264407i
$861$		0			0
$862$	1.24578	−	2.15776i	0.0424315	−	0.0734936i
$863$	−15.5821			−0.530421			−0.265211	−	0.964191i	$-0.585441\pi$
$863$	−15.5821			−0.530421			−0.265211	+	0.964191i	$0.585441\pi$
$864$		0			0
$865$	14.6719	−	25.4124i	0.498859	−	0.864049i
$866$	10.7447			0.365118
$867$		0			0
$868$	−7.30194	−	12.6473i	−0.247844	−	0.429278i
$869$	−2.12684	−	3.68380i	−0.0721482	−	0.124964i
$870$		0			0
$871$	−2.72545	+	0.366564i	−0.0923482	+	0.0124205i
$872$	14.0170			0.474675
$873$		0			0
$874$	7.74326	+	13.4117i	0.261920	+	0.453658i
$875$	−5.53534	+	9.58750i	−0.187129	+	0.324117i
$876$		0			0
$877$	−8.83848	+	15.3087i	−0.298454	+	0.516938i	−0.975782	−	0.218743i	$-0.929804\pi$
$877$	−8.83848	+	15.3087i	−0.298454	+	0.516938i	0.677328	+	0.735681i	$0.263138\pi$
$878$	−7.57152	+	13.1142i	−0.255526	+	0.442584i
$879$		0			0
$880$	−1.73341	+	3.00235i	−0.0584331	+	0.101209i
$881$	22.7684	+	39.4360i	0.767086	+	1.32863i	0.939137	+	0.343544i	$0.111628\pi$
$881$	22.7684	+	39.4360i	0.767086	+	1.32863i	−0.172050	+	0.985088i	$0.555039\pi$
$882$		0			0
$883$	7.13361			0.240065			0.120032	−	0.992770i	$-0.461700\pi$
$883$	7.13361			0.240065			0.120032	+	0.992770i	$0.461700\pi$
$884$	3.35540	−	0.451291i	0.112854	−	0.0151786i
$885$		0			0
$886$	−4.50402	−	7.80119i	−0.151315	−	0.262086i
$887$	−21.4590	−	37.1682i	−0.720524	−	1.24798i	−0.960790	−	0.277277i	$-0.910568\pi$
$887$	−21.4590	−	37.1682i	−0.720524	−	1.24798i	0.240266	−	0.970707i	$-0.422765\pi$
$888$		0			0
$889$	4.61894			0.154914
$890$	3.23945	−	5.61089i	0.108587	−	0.188077i
$891$		0			0
$892$	17.4045			0.582745
$893$	16.7213	−	28.9622i	0.559558	−	0.969183i
$894$		0			0
$895$	−17.2385	−	29.8580i	−0.576221	−	0.998044i
$896$	−11.5375			−0.385441
$897$		0			0
$898$	13.4561			0.449034
$899$	38.9986	+	67.5475i	1.30068	+	2.25284i
$900$		0			0
$901$	2.21648	−	3.83906i	0.0738417	−	0.127898i
$902$	0.138719			0.00461885
$903$		0			0
$904$	−19.0867	+	33.0592i	−0.634815	+	1.09953i
$905$	10.4209			0.346402
$906$		0			0
$907$	−17.4629	−	30.2467i	−0.579847	−	1.00432i	−0.995496	−	0.0947995i	$-0.969779\pi$
$907$	−17.4629	−	30.2467i	−0.579847	−	1.00432i	0.415649	−	0.909525i	$-0.363554\pi$
$908$	−4.74459	−	8.21787i	−0.157455	−	0.272719i
$909$		0			0
$910$	−1.03199	+	2.51128i	−0.0342102	+	0.0832480i
$911$	−56.0810			−1.85805			−0.929023	−	0.370023i	$-0.879350\pi$
$911$	−56.0810			−1.85805			−0.929023	+	0.370023i	$0.879350\pi$
$912$		0			0
$913$	6.28717	+	10.8897i	0.208075	+	0.360396i
$914$	8.73788	−	15.1345i	0.289023	−	0.500603i
$915$		0			0
$916$	−1.59083	+	2.75541i	−0.0525626	+	0.0910412i
$917$	−1.67845	+	2.90716i	−0.0554272	+	0.0960028i
$918$		0			0
$919$	15.8041	−	27.3735i	0.521329	−	0.902968i	−0.478363	−	0.878162i	$-0.658770\pi$
$919$	15.8041	−	27.3735i	0.521329	−	0.902968i	0.999692	−	0.0248062i	$-0.00789687\pi$
$920$	−9.43847	−	16.3479i	−0.311177	−	0.538975i
$921$		0			0
$922$	−22.6738			−0.746723
$923$	−9.92112	−	12.8549i	−0.326557	−	0.423124i
$924$		0			0
$925$	−8.18233	−	14.1722i	−0.269033	−	0.465980i
$926$	−10.8478	−	18.7889i	−0.356481	−	0.617443i
$927$		0			0
$928$	48.3002			1.58553
$929$	12.2615	−	21.2376i	0.402287	−	0.696782i	−0.591714	−	0.806148i	$-0.701549\pi$
$929$	12.2615	−	21.2376i	0.402287	−	0.696782i	0.994002	+	0.109366i	$0.0348820\pi$
$930$		0			0
$931$	−4.10992			−0.134697
$932$	5.40097	−	9.35475i	0.176915	−	0.306425i
$933$		0			0
$934$	2.60776	+	4.51677i	0.0853285	+	0.147793i
$935$	0.856232			0.0280018
$936$		0			0
$937$	−11.1943			−0.365703			−0.182852	−	0.983141i	$-0.558533\pi$
$937$	−11.1943			−0.365703			−0.182852	+	0.983141i	$0.558533\pi$
$938$	−0.211636	−	0.366564i	−0.00691015	−	0.0119687i
$939$		0			0
$940$	−9.34093	+	16.1790i	−0.304668	+	0.527700i
$941$	−9.92931			−0.323686			−0.161843	−	0.986816i	$-0.551744\pi$
$941$	−9.92931			−0.323686			−0.161843	+	0.986816i	$0.551744\pi$
$942$		0			0
$943$	0.746316	−	1.29266i	0.0243034	−	0.0420947i
$944$	−8.76271			−0.285202
$945$		0			0
$946$	1.23042	+	2.13115i	0.0400045	+	0.0692898i
$947$	−22.1301	−	38.3305i	−0.719132	−	1.24557i	−0.961344	−	0.275350i	$-0.911206\pi$
$947$	−22.1301	−	38.3305i	−0.719132	−	1.24557i	0.242212	−	0.970223i	$-0.422127\pi$
$948$		0			0
$949$	11.6540	−	28.3591i	0.378305	−	0.920577i
$950$	7.20477			0.233754
$951$		0			0
$952$	0.568532	+	0.984726i	0.0184262	+	0.0319151i
$953$	15.5656	−	26.9604i	0.504219	−	0.873334i	−0.495769	−	0.868455i	$-0.665114\pi$
$953$	15.5656	−	26.9604i	0.504219	−	0.873334i	0.999988	−	0.00487907i	$-0.00155306\pi$
$954$		0			0
$955$	−6.44773	+	11.1678i	−0.208644	+	0.361381i
$956$	−1.60925	+	2.78731i	−0.0520469	+	0.0901479i
$957$		0			0
$958$	−0.564351	+	0.977485i	−0.0182334	+	0.0315811i
$959$	−10.7567	−	18.6311i	−0.347351	−	0.601629i
$960$		0			0
$961$	43.4946			1.40305
$962$	−6.33340	−	8.20625i	−0.204197	−	0.264580i
$963$		0			0
$964$	11.1775	+	19.3601i	0.360005	+	0.623546i
$965$	−6.34452	−	10.9890i	−0.204237	−	0.353749i
$966$		0			0
$967$	−15.9745			−0.513706			−0.256853	−	0.966451i	$-0.582686\pi$
$967$	−15.9745			−0.513706			−0.256853	+	0.966451i	$0.582686\pi$
$968$	−9.94451	+	17.2244i	−0.319629	+	0.553613i
$969$		0			0
$970$	11.2567			0.361430
$971$	−18.9263	+	32.7812i	−0.607372	+	1.05200i	0.384299	+	0.923209i	$0.374443\pi$
$971$	−18.9263	+	32.7812i	−0.607372	+	1.05200i	−0.991672	+	0.128791i	$0.958890\pi$
$972$		0			0
$973$	4.04623	+	7.00827i	0.129716	+	0.224675i
$974$	−16.8086			−0.538584
$975$		0			0
$976$	24.5405			0.785522
$977$	−0.961968	−	1.66618i	−0.0307761	−	0.0533057i	0.850227	−	0.526416i	$-0.176465\pi$
$977$	−0.961968	−	1.66618i	−0.0307761	−	0.0533057i	−0.881003	+	0.473110i	$0.843131\pi$
$978$		0			0
$979$	4.89158	−	8.47246i	0.156335	−	0.270781i
$980$	2.29590			0.0733397
$981$		0			0
$982$	−8.09933	+	14.0284i	−0.258460	+	0.447666i
$983$	−47.7922			−1.52434			−0.762168	−	0.647379i	$-0.775865\pi$
$983$	−47.7922			−1.52434			−0.762168	+	0.647379i	$0.775865\pi$
$984$		0			0
$985$	−11.8835	−	20.5828i	−0.378640	−	0.655824i
$986$	−1.39158	−	2.41028i	−0.0443168	−	0.0767589i
$987$		0			0
$988$	−24.8495	+	3.34218i	−0.790568	+	0.106329i
$989$	26.4789			0.841980
$990$		0			0
$991$	−22.0341	−	38.1643i	−0.699938	−	1.21233i	−0.968488	−	0.249062i	$-0.919878\pi$
$991$	−22.0341	−	38.1643i	−0.699938	−	1.21233i	0.268550	−	0.963266i	$-0.413456\pi$
$992$	23.0656	−	39.9508i	0.732334	−	1.26844i
$993$		0			0
$994$	1.24967	−	2.16449i	0.0396371	−	0.0686534i
$995$	−11.9335	+	20.6694i	−0.378317	+	0.655265i
$996$		0			0
$997$	−24.1172	+	41.7722i	−0.763800	+	1.32294i	0.177079	+	0.984197i	$0.443335\pi$
$997$	−24.1172	+	41.7722i	−0.763800	+	1.32294i	−0.940879	+	0.338743i	$0.889998\pi$
$998$	−0.346675	−	0.600458i	−0.0109738	−	0.0190072i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.o.e.757.2		6
3.2	odd	2		273.2.k.c.211.2	yes	6
13.9	even	3	inner	819.2.o.e.568.2		6
39.23	odd	6		3549.2.a.u.1.2		3
39.29	odd	6		3549.2.a.i.1.2		3
39.35	odd	6		273.2.k.c.22.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.c.22.2	✓	6	39.35	odd	6
273.2.k.c.211.2	yes	6	3.2	odd	2
819.2.o.e.568.2		6	13.9	even	3	inner
819.2.o.e.757.2		6	1.1	even	1	trivial
3549.2.a.i.1.2		3	39.29	odd	6
3549.2.a.u.1.2		3	39.23	odd	6

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.o (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.277479 - 0.480608i) q^{2} +(0.846011 - 1.46533i) q^{4} -1.35690 q^{5} +(-0.500000 + 0.866025i) q^{7} -2.04892 q^{8} +O(q^{10})\)	\(q+(-0.277479 - 0.480608i) q^{2} +(0.846011 - 1.46533i) q^{4} -1.35690 q^{5} +(-0.500000 + 0.866025i) q^{7} -2.04892 q^{8} +(0.376510 + 0.652135i) q^{10} +(0.568532 + 0.984726i) q^{11} +(1.37047 - 3.33494i) q^{13} +0.554958 q^{14} +(-1.12349 - 1.94594i) q^{16} +(-0.277479 + 0.480608i) q^{17} +(2.05496 - 3.55929i) q^{19} +(-1.14795 + 1.98831i) q^{20} +(0.315511 - 0.546482i) q^{22} +(-3.39493 - 5.88019i) q^{23} -3.15883 q^{25} +(-1.98307 + 0.266717i) q^{26} +(0.846011 + 1.46533i) q^{28} +(-4.51842 - 7.82613i) q^{29} -8.63102 q^{31} +(-2.67241 + 4.62874i) q^{32} +0.307979 q^{34} +(0.678448 - 1.17511i) q^{35} +(2.59030 + 4.48653i) q^{37} -2.28083 q^{38} +2.78017 q^{40} +(0.109916 + 0.190381i) q^{41} +(-1.94989 + 3.37730i) q^{43} +1.92394 q^{44} +(-1.88404 + 3.26326i) q^{46} +8.13706 q^{47} +(-0.500000 - 0.866025i) q^{49} +(0.876510 + 1.51816i) q^{50} +(-3.72737 - 4.82959i) q^{52} -7.98792 q^{53} +(-0.771438 - 1.33617i) q^{55} +(1.02446 - 1.77441i) q^{56} +(-2.50753 + 4.34317i) q^{58} +(1.94989 - 3.37730i) q^{59} +(-5.46077 + 9.45833i) q^{61} +(2.39493 + 4.14814i) q^{62} -1.52781 q^{64} +(-1.85958 + 4.52516i) q^{65} +(-0.381355 - 0.660525i) q^{67} +(0.469501 + 0.813199i) q^{68} -0.753020 q^{70} +(2.25182 - 3.90027i) q^{71} +8.50365 q^{73} +(1.43751 - 2.48984i) q^{74} +(-3.47703 - 6.02240i) q^{76} -1.13706 q^{77} -3.74094 q^{79} +(1.52446 + 2.64044i) q^{80} +(0.0609989 - 0.105653i) q^{82} +11.0586 q^{83} +(0.376510 - 0.652135i) q^{85} +2.16421 q^{86} +(-1.16487 - 2.01762i) q^{88} +(-4.30194 - 7.45117i) q^{89} +(2.20291 + 2.85433i) q^{91} -11.4886 q^{92} +(-2.25786 - 3.91074i) q^{94} +(-2.78836 + 4.82959i) q^{95} +(7.47434 - 12.9459i) q^{97} +(-0.277479 + 0.480608i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) 6 * q - 2 * q^2 - 3 * q^7 + 6 * q^8	\( 6 q - 2 q^{2} - 3 q^{7} + 6 q^{8} + 7 q^{10} - 2 q^{11} - 6 q^{13} + 4 q^{14} - 2 q^{16} - 2 q^{17} + 13 q^{19} + 7 q^{20} - 13 q^{22} + 3 q^{23} - 2 q^{25} + 4 q^{26} + q^{29} - 22 q^{31} + 7 q^{32} + 12 q^{34} + 4 q^{37} - 36 q^{38} + 14 q^{40} + 2 q^{41} + 11 q^{43} + 42 q^{44} + 9 q^{46} + 38 q^{47} - 3 q^{49} + 10 q^{50} - 10 q^{53} + 14 q^{55} - 3 q^{56} + 10 q^{58} - 11 q^{59} - 7 q^{61} - 9 q^{62} - 22 q^{64} + 15 q^{67} - 7 q^{68} - 14 q^{70} - 18 q^{71} - 12 q^{73} + 33 q^{74} + 14 q^{76} + 4 q^{77} + 6 q^{79} + 20 q^{82} + 4 q^{83} + 7 q^{85} - 10 q^{86} - 9 q^{88} - 17 q^{89} - 56 q^{92} - q^{94} - 14 q^{95} + 13 q^{97} - 2 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 - 3 * q^7 + 6 * q^8 + 7 * q^10 - 2 * q^11 - 6 * q^13 + 4 * q^14 - 2 * q^16 - 2 * q^17 + 13 * q^19 + 7 * q^20 - 13 * q^22 + 3 * q^23 - 2 * q^25 + 4 * q^26 + q^29 - 22 * q^31 + 7 * q^32 + 12 * q^34 + 4 * q^37 - 36 * q^38 + 14 * q^40 + 2 * q^41 + 11 * q^43 + 42 * q^44 + 9 * q^46 + 38 * q^47 - 3 * q^49 + 10 * q^50 - 10 * q^53 + 14 * q^55 - 3 * q^56 + 10 * q^58 - 11 * q^59 - 7 * q^61 - 9 * q^62 - 22 * q^64 + 15 * q^67 - 7 * q^68 - 14 * q^70 - 18 * q^71 - 12 * q^73 + 33 * q^74 + 14 * q^76 + 4 * q^77 + 6 * q^79 + 20 * q^82 + 4 * q^83 + 7 * q^85 - 10 * q^86 - 9 * q^88 - 17 * q^89 - 56 * q^92 - q^94 - 14 * q^95 + 13 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more