LMFDB - Embedded newform 1386.2.bu.a.827.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(701,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("1386.701");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bu (of order $10$, degree $4$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			827.4
Character	$\chi$	$=$	1386.827
Dual form			1386.2.bu.a.1205.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.81910 + 0.591063i) q^{5} +(0.587785 - 0.809017i) q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.81910 + 0.591063i) q^{5} +(0.587785 - 0.809017i) q^{7} +(-0.809017 + 0.587785i) q^{8} +1.91272i q^{10} +(2.51938 + 2.15702i) q^{11} +(-2.40385 - 0.781057i) q^{13} +(-0.587785 - 0.809017i) q^{14} +(0.309017 + 0.951057i) q^{16} +(1.61414 + 4.96780i) q^{17} +(-1.99024 - 2.73933i) q^{19} +(1.81910 + 0.591063i) q^{20} +(2.82998 - 1.72952i) q^{22} -0.978876i q^{23} +(-1.08530 + 0.788518i) q^{25} +(-1.48566 + 2.04483i) q^{26} +(-0.951057 + 0.309017i) q^{28} +(6.64433 + 4.82739i) q^{29} +(-1.58538 + 4.87928i) q^{31} +1.00000 q^{32} +5.22345 q^{34} +(-0.591063 + 1.81910i) q^{35} +(3.15240 + 2.29035i) q^{37} +(-3.22027 + 1.04633i) q^{38} +(1.12427 - 1.54742i) q^{40} +(3.37971 - 2.45550i) q^{41} +3.26590i q^{43} +(-0.770356 - 3.22592i) q^{44} +(-0.930967 - 0.302489i) q^{46} +(2.86808 + 3.94757i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(0.414549 + 1.27585i) q^{50} +(1.48566 + 2.04483i) q^{52} +(11.8470 + 3.84933i) q^{53} +(-5.85794 - 2.43473i) q^{55} +1.00000i q^{56} +(6.64433 - 4.82739i) q^{58} +(2.71698 - 3.73961i) q^{59} +(0.970903 - 0.315465i) q^{61} +(4.15057 + 3.01556i) q^{62} +(0.309017 - 0.951057i) q^{64} +4.83450 q^{65} +1.31842 q^{67} +(1.61414 - 4.96780i) q^{68} +(1.54742 + 1.12427i) q^{70} +(-4.69625 + 1.52590i) q^{71} +(2.95616 - 4.06881i) q^{73} +(3.15240 - 2.29035i) q^{74} +3.38599i q^{76} +(3.22592 - 0.770356i) q^{77} +(12.9644 + 4.21238i) q^{79} +(-1.12427 - 1.54742i) q^{80} +(-1.29093 - 3.97309i) q^{82} +(1.38607 + 4.26588i) q^{83} +(-5.87256 - 8.08288i) q^{85} +(3.10606 + 1.00922i) q^{86} +(-3.30608 - 0.264212i) q^{88} +5.41698i q^{89} +(-2.04483 + 1.48566i) q^{91} +(-0.575369 + 0.791928i) q^{92} +(4.64065 - 1.50784i) q^{94} +(5.23956 + 3.80676i) q^{95} +(0.223141 - 0.686757i) q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8}+O(q^{10}) $ 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8	$ 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8} + 4 q^{11} - 12 q^{16} + 24 q^{17} + 4 q^{22} + 24 q^{25} + 40 q^{26} - 16 q^{29} + 40 q^{31} + 48 q^{32} - 16 q^{34} - 12 q^{35} + 16 q^{37} - 40 q^{38} + 24 q^{41} + 4 q^{44} - 40 q^{46} - 40 q^{47} + 12 q^{49} + 4 q^{50} - 40 q^{52} - 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} - 40 q^{62} - 12 q^{64} + 48 q^{67} + 24 q^{68} + 8 q^{70} + 40 q^{73} + 16 q^{74} + 32 q^{77} + 40 q^{79} - 16 q^{82} - 16 q^{83} - 20 q^{85} + 4 q^{88} - 20 q^{92} - 52 q^{95} - 8 q^{97} - 48 q^{98}+O(q^{100}) $ 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8 + 4 * q^11 - 12 * q^16 + 24 * q^17 + 4 * q^22 + 24 * q^25 + 40 * q^26 - 16 * q^29 + 40 * q^31 + 48 * q^32 - 16 * q^34 - 12 * q^35 + 16 * q^37 - 40 * q^38 + 24 * q^41 + 4 * q^44 - 40 * q^46 - 40 * q^47 + 12 * q^49 + 4 * q^50 - 40 * q^52 - 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^64 + 48 * q^67 + 24 * q^68 + 8 * q^70 + 40 * q^73 + 16 * q^74 + 32 * q^77 + 40 * q^79 - 16 * q^82 - 16 * q^83 - 20 * q^85 + 4 * q^88 - 20 * q^92 - 52 * q^95 - 8 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−1.81910	+	0.591063i	−0.813528	+	0.264331i	−0.686091	−	0.727515i	$-0.740675\pi$
$5$	−1.81910	+	0.591063i	−0.813528	+	0.264331i	−0.127437	+	0.991847i	$0.540675\pi$
$6$		0			0
$7$	0.587785	−	0.809017i	0.222162	−	0.305780i
$7$	0.587785	−	0.809017i	0.222162	−	0.305780i
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$		0			0
$10$			1.91272i			0.604855i
$11$	2.51938	+	2.15702i	0.759621	+	0.650366i
$11$	2.51938	+	2.15702i	0.759621	+	0.650366i
$12$		0			0
$13$	−2.40385	−	0.781057i	−0.666707	−	0.216626i	−0.0439409	−	0.999034i	$-0.513991\pi$
$13$	−2.40385	−	0.781057i	−0.666707	−	0.216626i	−0.622766	+	0.782408i	$0.713991\pi$
$14$	−0.587785	−	0.809017i	−0.157092	−	0.216219i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	1.61414	+	4.96780i	0.391485	+	1.20487i	0.931665	+	0.363318i	$0.118356\pi$
$17$	1.61414	+	4.96780i	0.391485	+	1.20487i	−0.540180	+	0.841550i	$0.681644\pi$
$18$		0			0
$19$	−1.99024	−	2.73933i	−0.456592	−	0.628445i	0.517206	−	0.855861i	$-0.326972\pi$
$19$	−1.99024	−	2.73933i	−0.456592	−	0.628445i	−0.973798	+	0.227416i	$0.926972\pi$
$20$	1.81910	+	0.591063i	0.406764	+	0.132166i
$21$		0			0
$22$	2.82998	−	1.72952i	0.603353	−	0.368734i
$23$		−	0.978876i		−	0.204110i	−0.994779	−	0.102055i	$-0.967458\pi$
$23$		−	0.978876i		−	0.204110i	0.994779	−	0.102055i	$-0.0325417\pi$
$24$		0			0
$25$	−1.08530	+	0.788518i	−0.217060	+	0.157704i
$26$	−1.48566	+	2.04483i	−0.291362	+	0.401025i
$27$		0			0
$28$	−0.951057	+	0.309017i	−0.179733	+	0.0583987i
$29$	6.64433	+	4.82739i	1.23382	+	0.896424i	0.997171	−	0.0751709i	$-0.0239502\pi$
$29$	6.64433	+	4.82739i	1.23382	+	0.896424i	0.236651	+	0.971595i	$0.423950\pi$
$30$		0			0
$31$	−1.58538	+	4.87928i	−0.284742	+	0.876345i	0.701734	+	0.712439i	$0.252409\pi$
$31$	−1.58538	+	4.87928i	−0.284742	+	0.876345i	−0.986476	+	0.163906i	$0.947591\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	5.22345			0.895815
$35$	−0.591063	+	1.81910i	−0.0999078	+	0.307485i
$36$		0			0
$37$	3.15240	+	2.29035i	0.518251	+	0.376531i	0.815945	−	0.578130i	$-0.196217\pi$
$37$	3.15240	+	2.29035i	0.518251	+	0.376531i	−0.297694	+	0.954661i	$0.596217\pi$
$38$	−3.22027	+	1.04633i	−0.522397	+	0.169737i
$39$		0			0
$40$	1.12427	−	1.54742i	0.177762	−	0.244669i
$41$	3.37971	−	2.45550i	0.527822	−	0.383485i	−0.291720	−	0.956504i	$-0.594228\pi$
$41$	3.37971	−	2.45550i	0.527822	−	0.383485i	0.819543	+	0.573018i	$0.194228\pi$
$42$		0			0
$43$			3.26590i			0.498045i	0.968498	+	0.249023i	$0.0801094\pi$
$43$			3.26590i			0.498045i	−0.968498	+	0.249023i	$0.919891\pi$
$44$	−0.770356	−	3.22592i	−0.116136	−	0.486326i
$45$		0			0
$46$	−0.930967	−	0.302489i	−0.137264	−	0.0445996i
$47$	2.86808	+	3.94757i	0.418353	+	0.575813i	0.965231	−	0.261399i	$-0.0841839\pi$
$47$	2.86808	+	3.94757i	0.418353	+	0.575813i	−0.546878	+	0.837212i	$0.684184\pi$
$48$		0			0
$49$	−0.309017	−	0.951057i	−0.0441453	−	0.135865i
$50$	0.414549	+	1.27585i	0.0586260	+	0.180432i
$51$		0			0
$52$	1.48566	+	2.04483i	0.206024	+	0.283568i
$53$	11.8470	+	3.84933i	1.62732	+	0.528747i	0.973652	−	0.228039i	$-0.0732313\pi$
$53$	11.8470	+	3.84933i	1.62732	+	0.528747i	0.653663	+	0.756786i	$0.273231\pi$
$54$		0			0
$55$	−5.85794	−	2.43473i	−0.789885	−	0.328299i
$56$			1.00000i			0.133631i
$57$		0			0
$58$	6.64433	−	4.82739i	0.872444	−	0.633867i
$59$	2.71698	−	3.73961i	0.353721	−	0.486855i	−0.594665	−	0.803974i	$-0.702715\pi$
$59$	2.71698	−	3.73961i	0.353721	−	0.486855i	0.948386	+	0.317118i	$0.102715\pi$
$60$		0			0
$61$	0.970903	−	0.315465i	0.124311	−	0.0403912i	−0.246201	−	0.969219i	$-0.579182\pi$
$61$	0.970903	−	0.315465i	0.124311	−	0.0403912i	0.370512	+	0.928828i	$0.379182\pi$
$62$	4.15057	+	3.01556i	0.527123	+	0.382977i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	4.83450			0.599646
$66$		0			0
$67$	1.31842			0.161071			0.0805353	−	0.996752i	$-0.474337\pi$
$67$	1.31842			0.161071			0.0805353	+	0.996752i	$0.474337\pi$
$68$	1.61414	−	4.96780i	0.195743	−	0.602434i
$69$		0			0
$70$	1.54742	+	1.12427i	0.184952	+	0.134376i
$71$	−4.69625	+	1.52590i	−0.557342	+	0.181092i	−0.574125	−	0.818768i	$-0.694658\pi$
$71$	−4.69625	+	1.52590i	−0.557342	+	0.181092i	0.0167826	+	0.999859i	$0.494658\pi$
$72$		0			0
$73$	2.95616	−	4.06881i	0.345993	−	0.476218i	−0.600187	−	0.799860i	$-0.704907\pi$
$73$	2.95616	−	4.06881i	0.345993	−	0.476218i	0.946180	+	0.323642i	$0.104907\pi$
$74$	3.15240	−	2.29035i	0.366459	−	0.266248i
$75$		0			0
$76$			3.38599i			0.388400i
$77$	3.22592	−	0.770356i	0.367628	−	0.0877902i
$78$		0			0
$79$	12.9644	+	4.21238i	1.45860	+	0.473929i	0.927644	−	0.373467i	$-0.121831\pi$
$79$	12.9644	+	4.21238i	1.45860	+	0.473929i	0.530961	+	0.847396i	$0.321831\pi$
$80$	−1.12427	−	1.54742i	−0.125697	−	0.173007i
$81$		0			0
$82$	−1.29093	−	3.97309i	−0.142560	−	0.438754i
$83$	1.38607	+	4.26588i	0.152141	+	0.468242i	0.997860	−	0.0653868i	$-0.0208281\pi$
$83$	1.38607	+	4.26588i	0.152141	+	0.468242i	−0.845719	+	0.533628i	$0.820828\pi$
$84$		0			0
$85$	−5.87256	−	8.08288i	−0.636968	−	0.876712i
$86$	3.10606	+	1.00922i	0.334935	+	0.108827i
$87$		0			0
$88$	−3.30608	−	0.264212i	−0.352430	−	0.0281651i
$89$			5.41698i			0.574198i	0.957901	+	0.287099i	$0.0926909\pi$
$89$			5.41698i			0.574198i	−0.957901	+	0.287099i	$0.907309\pi$
$90$		0			0
$91$	−2.04483	+	1.48566i	−0.214357	+	0.155739i
$92$	−0.575369	+	0.791928i	−0.0599864	+	0.0825642i
$93$		0			0
$94$	4.64065	−	1.50784i	0.478647	−	0.155522i
$95$	5.23956	+	3.80676i	0.537568	+	0.390566i
$96$		0			0
$97$	0.223141	−	0.686757i	0.0226565	−	0.0697296i	−0.939089	−	0.343674i	$-0.888328\pi$
$97$	0.223141	−	0.686757i	0.0226565	−	0.0697296i	0.961746	+	0.273944i	$0.0883285\pi$
$98$	−1.00000			−0.101015
$99$		0			0
$100$	1.34151			0.134151
$101$	−4.24111	+	13.0528i	−0.422006	+	1.29880i	0.483825	+	0.875165i	$0.339247\pi$
$101$	−4.24111	+	13.0528i	−0.422006	+	1.29880i	−0.905832	+	0.423638i	$0.860753\pi$
$102$		0			0
$103$	−3.30656	−	2.40235i	−0.325805	−	0.236711i	0.412844	−	0.910802i	$-0.364536\pi$
$103$	−3.30656	−	2.40235i	−0.325805	−	0.236711i	−0.738648	+	0.674091i	$0.764536\pi$
$104$	2.40385	−	0.781057i	0.235717	−	0.0765890i
$105$		0			0
$106$	7.32187	−	10.0777i	0.711163	−	0.978832i
$107$	−10.2841	+	7.47183i	−0.994200	+	0.722329i	−0.960837	−	0.277114i	$-0.910622\pi$
$107$	−10.2841	+	7.47183i	−0.994200	+	0.722329i	−0.0333634	+	0.999443i	$0.510622\pi$
$108$		0			0
$109$		−	8.30166i		−	0.795155i	−0.917569	−	0.397577i	$-0.869851\pi$
$109$		−	8.30166i		−	0.795155i	0.917569	−	0.397577i	$-0.130149\pi$
$110$	−4.12577	+	4.81886i	−0.393377	+	0.459460i
$111$		0			0
$112$	0.951057	+	0.309017i	0.0898664	+	0.0291994i
$113$	1.32328	+	1.82134i	0.124483	+	0.171337i	0.866710	−	0.498812i	$-0.166230\pi$
$113$	1.32328	+	1.82134i	0.124483	+	0.171337i	−0.742227	+	0.670149i	$0.766230\pi$
$114$		0			0
$115$	0.578577	+	1.78068i	0.0539526	+	0.166049i
$116$	−2.53791	−	7.81088i	−0.235639	−	0.725222i
$117$		0			0
$118$	−2.71698	−	3.73961i	−0.250119	−	0.344259i
$119$	4.96780	+	1.61414i	0.455397	+	0.147968i
$120$		0			0
$121$	1.69454	+	10.8687i	0.154049	+	0.988063i
$122$		−	1.02087i		−	0.0924250i
$123$		0			0
$124$	4.15057	−	3.01556i	0.372732	−	0.270806i
$125$	7.12955	−	9.81299i	0.637687	−	0.877700i
$126$		0			0
$127$	6.93827	−	2.25438i	0.615672	−	0.200044i	0.0154542	−	0.999881i	$-0.495081\pi$
$127$	6.93827	−	2.25438i	0.615672	−	0.200044i	0.600218	+	0.799837i	$0.295081\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$		0			0
$130$	1.49394	−	4.59788i	0.131027	−	0.403261i
$131$	−14.2499			−1.24502			−0.622509	−	0.782613i	$-0.713887\pi$
$131$	−14.2499			−1.24502			−0.622509	+	0.782613i	$0.713887\pi$
$132$		0			0
$133$	−3.38599			−0.293603
$134$	0.407414	−	1.25389i	0.0351952	−	0.108320i
$135$		0			0
$136$	−4.22586	−	3.07027i	−0.362365	−	0.263273i
$137$	−17.0872	+	5.55197i	−1.45986	+	0.474337i	−0.928027	−	0.372514i	$-0.878496\pi$
$137$	−17.0872	+	5.55197i	−1.45986	+	0.474337i	−0.531831	+	0.846850i	$0.678496\pi$
$138$		0			0
$139$	9.52863	−	13.1150i	0.808208	−	1.11240i	−0.183390	−	0.983040i	$-0.558707\pi$
$139$	9.52863	−	13.1150i	0.808208	−	1.11240i	0.991597	−	0.129362i	$-0.0412929\pi$
$140$	1.54742	−	1.12427i	0.130781	−	0.0950180i
$141$		0			0
$142$			4.93793i			0.414382i
$143$	−4.37145	−	7.15293i	−0.365559	−	0.598158i
$144$		0			0
$145$	−14.9400	−	4.85431i	−1.24070	−	0.403128i
$146$	−2.95616	−	4.06881i	−0.244654	−	0.336737i
$147$		0			0
$148$	−1.20411	−	3.70586i	−0.0989771	−	0.304620i
$149$	0.374369	+	1.15219i	0.0306695	+	0.0943909i	0.965220	−	0.261441i	$-0.0841976\pi$
$149$	0.374369	+	1.15219i	0.0306695	+	0.0943909i	−0.934550	+	0.355832i	$0.884198\pi$
$150$		0			0
$151$	5.13618	+	7.06935i	0.417976	+	0.575295i	0.965141	−	0.261730i	$-0.0842929\pi$
$151$	5.13618	+	7.06935i	0.417976	+	0.575295i	−0.547165	+	0.837025i	$0.684293\pi$
$152$	3.22027	+	1.04633i	0.261199	+	0.0848685i
$153$		0			0
$154$	0.264212	−	3.30608i	0.0212908	−	0.266412i
$155$		−	9.81298i		−	0.788197i
$156$		0			0
$157$	−13.3509	+	9.70002i	−1.06552	+	0.774146i	−0.975102	−	0.221758i	$-0.928821\pi$
$157$	−13.3509	+	9.70002i	−1.06552	+	0.774146i	−0.0904187	+	0.995904i	$0.528821\pi$
$158$	8.01242	−	11.0281i	0.637434	−	0.877352i
$159$		0			0
$160$	−1.81910	+	0.591063i	−0.143813	+	0.0467276i
$161$	−0.791928	−	0.575369i	−0.0624126	−	0.0453454i
$162$		0			0
$163$	−4.30587	+	13.2521i	−0.337262	+	1.03798i	0.628336	+	0.777942i	$0.283736\pi$
$163$	−4.30587	+	13.2521i	−0.337262	+	1.03798i	−0.965597	+	0.260042i	$0.916264\pi$
$164$	−4.17755			−0.326212
$165$		0			0
$166$	4.48542			0.348136
$167$	−0.603258	+	1.85664i	−0.0466815	+	0.143671i	−0.971680	−	0.236299i	$-0.924066\pi$
$167$	−0.603258	+	1.85664i	−0.0466815	+	0.143671i	0.924999	+	0.379970i	$0.124066\pi$
$168$		0			0
$169$	−5.34879	−	3.88612i	−0.411445	−	0.298932i
$170$	−9.50200	+	3.08739i	−0.728770	+	0.236792i
$171$		0			0
$172$	1.91965	−	2.64217i	0.146372	−	0.201464i
$173$	−17.2221	+	12.5126i	−1.30938	+	0.951317i	−0.309375	+	0.950940i	$0.600120\pi$
$173$	−17.2221	+	12.5126i	−1.30938	+	0.951317i	−1.00000		0.000376806i	$0.999880\pi$
$174$		0			0
$175$			1.34151i			0.101408i
$176$	−1.27292	+	3.06263i	−0.0959497	+	0.230854i
$177$		0			0
$178$	5.15185	+	1.67394i	0.386148	+	0.125467i
$179$	1.89804	+	2.61242i	0.141866	+	0.195262i	0.874037	−	0.485859i	$-0.161493\pi$
$179$	1.89804	+	2.61242i	0.141866	+	0.195262i	−0.732172	+	0.681120i	$0.761493\pi$
$180$		0			0
$181$	−6.30995	−	19.4200i	−0.469015	−	1.44348i	−0.853862	−	0.520499i	$-0.825746\pi$
$181$	−6.30995	−	19.4200i	−0.469015	−	1.44348i	0.384848	−	0.922980i	$-0.374254\pi$
$182$	0.781057	+	2.40385i	0.0578958	+	0.178185i
$183$		0			0
$184$	0.575369	+	0.791928i	0.0424168	+	0.0583817i
$185$	−7.08828	−	2.30312i	−0.521140	−	0.169329i
$186$		0			0
$187$	−6.64902	+	15.9975i	−0.486224	+	1.16985i
$188$		−	4.87947i		−	0.355872i
$189$		0			0
$190$	5.23956	−	3.80676i	0.380118	−	0.276172i
$191$	8.38091	−	11.5353i	0.606422	−	0.834668i	−0.389855	−	0.920876i	$-0.627475\pi$
$191$	8.38091	−	11.5353i	0.606422	−	0.834668i	0.996277	+	0.0862082i	$0.0274750\pi$
$192$		0			0
$193$	10.6613	−	3.46406i	0.767415	−	0.249348i	0.100957	−	0.994891i	$-0.467809\pi$
$193$	10.6613	−	3.46406i	0.767415	−	0.249348i	0.666458	+	0.745542i	$0.267809\pi$
$194$	−0.584191	−	0.424439i	−0.0419424	−	0.0304730i
$195$		0			0
$196$	−0.309017	+	0.951057i	−0.0220726	+	0.0679326i
$197$	9.39169			0.669130			0.334565	−	0.942373i	$-0.391411\pi$
$197$	9.39169			0.669130			0.334565	+	0.942373i	$0.391411\pi$
$198$		0			0
$199$	−4.12932			−0.292720			−0.146360	−	0.989231i	$-0.546756\pi$
$199$	−4.12932			−0.292720			−0.146360	+	0.989231i	$0.546756\pi$
$200$	0.414549	−	1.27585i	0.0293130	−	0.0902162i
$201$		0			0
$202$	11.1034	+	8.06707i	0.781231	+	0.567597i
$203$	7.81088	−	2.53791i	0.548216	−	0.178126i
$204$		0			0
$205$	−4.69669	+	6.46444i	−0.328031	+	0.451496i
$206$	−3.30656	+	2.40235i	−0.230379	+	0.167380i
$207$		0			0
$208$		−	2.52756i		−	0.175254i
$209$	0.894620	−	11.1944i	0.0618821	−	0.774332i
$210$		0			0
$211$	−18.4953	−	6.00950i	−1.27327	−	0.413711i	−0.407066	−	0.913399i	$-0.633448\pi$
$211$	−18.4953	−	6.00950i	−1.27327	−	0.413711i	−0.866206	+	0.499688i	$0.833448\pi$
$212$	−7.32187	−	10.0777i	−0.502868	−	0.692138i
$213$		0			0
$214$	3.92817	+	12.0897i	0.268524	+	0.826433i
$215$	−1.93035	−	5.94101i	−0.131649	−	0.405174i
$216$		0			0
$217$	3.01556	+	4.15057i	0.204710	+	0.281759i
$218$	−7.89535	−	2.56535i	−0.534740	−	0.173748i
$219$		0			0
$220$	3.30808	+	5.41295i	0.223030	+	0.364941i
$221$		−	13.2026i		−	0.888100i
$222$		0			0
$223$	18.2910	−	13.2892i	1.22485	−	0.889909i	0.228361	−	0.973576i	$-0.426663\pi$
$223$	18.2910	−	13.2892i	1.22485	−	0.889909i	0.996494	+	0.0836673i	$0.0266633\pi$
$224$	0.587785	−	0.809017i	0.0392731	−	0.0540547i
$225$		0			0
$226$	2.14111	−	0.695688i	0.142424	−	0.0462765i
$227$	−17.7997	−	12.9322i	−1.18141	−	0.858341i	−0.189076	−	0.981963i	$-0.560549\pi$
$227$	−17.7997	−	12.9322i	−1.18141	−	0.858341i	−0.992329	+	0.123621i	$0.960549\pi$
$228$		0			0
$229$	−1.70328	+	5.24217i	−0.112556	+	0.346412i	−0.991429	−	0.130643i	$-0.958296\pi$
$229$	−1.70328	+	5.24217i	−0.112556	+	0.346412i	0.878873	+	0.477055i	$0.158296\pi$
$230$	1.87232			0.123457
$231$		0			0
$232$	−8.21285			−0.539200
$233$	−5.22868	+	16.0922i	−0.342542	+	1.05424i	0.620344	+	0.784330i	$0.286993\pi$
$233$	−5.22868	+	16.0922i	−0.342542	+	1.05424i	−0.962886	+	0.269907i	$0.913007\pi$
$234$		0			0
$235$	−7.55060	−	5.48583i	−0.492547	−	0.357856i
$236$	−4.39617	+	1.42840i	−0.286166	+	0.0929811i
$237$		0			0
$238$	3.07027	−	4.22586i	0.199016	−	0.273922i
$239$	18.9448	−	13.7642i	1.22544	−	0.890333i	0.228899	−	0.973450i	$-0.426487\pi$
$239$	18.9448	−	13.7642i	1.22544	−	0.890333i	0.996540	+	0.0831169i	$0.0264875\pi$
$240$		0			0
$241$			28.3450i			1.82586i	0.408115	+	0.912931i	$0.366186\pi$
$241$			28.3450i			1.82586i	−0.408115	+	0.912931i	$0.633814\pi$
$242$	10.8604	+	1.74701i	0.698132	+	0.112302i
$243$		0			0
$244$	−0.970903	−	0.315465i	−0.0621557	−	0.0201956i
$245$	1.12427	+	1.54742i	0.0718268	+	0.0988612i
$246$		0			0
$247$	2.64466	+	8.13941i	0.168275	+	0.517898i
$248$	−1.58538	−	4.87928i	−0.100671	−	0.309835i
$249$		0			0
$250$	−7.12955	−	9.81299i	−0.450912	−	0.620628i
$251$	−7.90201	−	2.56752i	−0.498770	−	0.162060i	0.0488189	−	0.998808i	$-0.484454\pi$
$251$	−7.90201	−	2.56752i	−0.498770	−	0.162060i	−0.547589	+	0.836747i	$0.684454\pi$
$252$		0			0
$253$	2.11146	−	2.46616i	0.132746	−	0.155046i
$254$		−	7.29533i		−	0.457750i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−0.390175	+	0.537030i	−0.0243385	+	0.0334990i	−0.821013	−	0.570910i	$-0.806591\pi$
$257$	−0.390175	+	0.537030i	−0.0243385	+	0.0334990i	0.796674	+	0.604409i	$0.206591\pi$
$258$		0			0
$259$	3.70586	−	1.20411i	0.230271	−	0.0748197i
$260$	−3.91119	−	2.84165i	−0.242562	−	0.176232i
$261$		0			0
$262$	−4.40345	+	13.5524i	−0.272046	+	0.837272i
$263$	26.7624			1.65024			0.825120	−	0.564957i	$-0.191107\pi$
$263$	26.7624			1.65024			0.825120	+	0.564957i	$0.191107\pi$
$264$		0			0
$265$	−23.8262			−1.46363
$266$	−1.04633	+	3.22027i	−0.0641546	+	0.197448i
$267$		0			0
$268$	−1.06662	−	0.774948i	−0.0651544	−	0.0473375i
$269$	−26.5586	+	8.62941i	−1.61931	+	0.526145i	−0.971778	−	0.235897i	$-0.924197\pi$
$269$	−26.5586	+	8.62941i	−1.61931	+	0.526145i	−0.647529	+	0.762041i	$0.724197\pi$
$270$		0			0
$271$	14.9804	−	20.6188i	0.909996	−	1.25250i	−0.0571719	−	0.998364i	$-0.518208\pi$
$271$	14.9804	−	20.6188i	0.909996	−	1.25250i	0.967168	−	0.254138i	$-0.0817917\pi$
$272$	−4.22586	+	3.07027i	−0.256230	+	0.186162i
$273$		0			0
$274$			17.9665i			1.08540i
$275$	−4.43514	−	0.354442i	−0.267449	−	0.0213737i
$276$		0			0
$277$	−17.6581	−	5.73745i	−1.06097	−	0.344730i	−0.274005	−	0.961728i	$-0.588349\pi$
$277$	−17.6581	−	5.73745i	−1.06097	−	0.344730i	−0.786965	+	0.616998i	$0.788349\pi$
$278$	−9.52863	−	13.1150i	−0.571489	−	0.786587i
$279$		0			0
$280$	−0.591063	−	1.81910i	−0.0353227	−	0.108712i
$281$	5.31780	+	16.3665i	0.317233	+	0.976343i	0.974825	+	0.222969i	$0.0715750\pi$
$281$	5.31780	+	16.3665i	0.317233	+	0.976343i	−0.657592	+	0.753374i	$0.728425\pi$
$282$		0			0
$283$	3.74234	+	5.15088i	0.222459	+	0.306188i	0.905629	−	0.424071i	$-0.139399\pi$
$283$	3.74234	+	5.15088i	0.222459	+	0.306188i	−0.683170	+	0.730259i	$0.739399\pi$
$284$	4.69625	+	1.52590i	0.278671	+	0.0905458i
$285$		0			0
$286$	−8.15369	+	1.94712i	−0.482138	+	0.115135i
$287$		−	4.17755i		−	0.246593i
$288$		0			0
$289$	−8.32029	+	6.04504i	−0.489429	+	0.355591i
$290$	−9.23344	+	12.7087i	−0.542206	+	0.746283i
$291$		0			0
$292$	−4.78317	+	1.55415i	−0.279914	+	0.0909496i
$293$	9.58104	+	6.96103i	0.559730	+	0.406668i	0.831360	−	0.555734i	$-0.187563\pi$
$293$	9.58104	+	6.96103i	0.559730	+	0.406668i	−0.271630	+	0.962402i	$0.587563\pi$
$294$		0			0
$295$	−2.73213	+	8.40864i	−0.159071	+	0.489570i
$296$	−3.89658			−0.226484
$297$		0			0
$298$	1.21148			0.0701793
$299$	−0.764559	+	2.35307i	−0.0442156	+	0.136082i
$300$		0			0
$301$	2.64217	+	1.91965i	0.152292	+	0.110647i
$302$	8.31052	−	2.70025i	0.478216	−	0.155382i
$303$		0			0
$304$	1.99024	−	2.73933i	0.114148	−	0.157111i
$305$	−1.57971	+	1.14773i	−0.0904541	+	0.0657187i
$306$		0			0
$307$			9.52739i			0.543757i	0.962332	+	0.271879i	$0.0876449\pi$
$307$			9.52739i			0.543757i	−0.962332	+	0.271879i	$0.912355\pi$
$308$	−3.06263	−	1.27292i	−0.174509	−	0.0725312i
$309$		0			0
$310$	−9.33270	−	3.03238i	−0.530062	−	0.172227i
$311$	−5.93596	−	8.17014i	−0.336597	−	0.463286i	0.606846	−	0.794819i	$-0.292434\pi$
$311$	−5.93596	−	8.17014i	−0.336597	−	0.463286i	−0.943444	+	0.331533i	$0.892434\pi$
$312$		0			0
$313$	1.69856	+	5.22764i	0.0960085	+	0.295484i	0.987515	−	0.157524i	$-0.0503511\pi$
$313$	1.69856	+	5.22764i	0.0960085	+	0.295484i	−0.891507	+	0.453007i	$0.850351\pi$
$314$	5.09960	+	15.6950i	0.287787	+	0.885718i
$315$		0			0
$316$	−8.01242	−	11.0281i	−0.450734	−	0.620382i
$317$	7.26109	+	2.35927i	0.407823	+	0.132510i	0.505742	−	0.862685i	$-0.331219\pi$
$317$	7.26109	+	2.35927i	0.407823	+	0.132510i	−0.0979191	+	0.995194i	$0.531219\pi$
$318$		0			0
$319$	6.32681	+	26.4940i	0.354234	+	1.48338i
$320$			1.91272i			0.106924i
$321$		0			0
$322$	−0.791928	+	0.575369i	−0.0441324	+	0.0320641i
$323$	10.3959	−	14.3087i	0.578444	−	0.796160i
$324$		0			0
$325$	3.22478	−	1.04779i	0.178879	−	0.0581212i
$326$	11.2729	+	8.19025i	0.624349	+	0.453616i
$327$		0			0
$328$	−1.29093	+	3.97309i	−0.0712800	+	0.219377i
$329$	4.87947			0.269014
$330$		0			0
$331$	−20.5239			−1.12809			−0.564047	−	0.825743i	$-0.690756\pi$
$331$	−20.5239			−1.12809			−0.564047	+	0.825743i	$0.690756\pi$
$332$	1.38607	−	4.26588i	0.0760704	−	0.234121i
$333$		0			0
$334$	1.57935	+	1.14746i	0.0864182	+	0.0627865i
$335$	−2.39834	+	0.779269i	−0.131035	+	0.0425760i
$336$		0			0
$337$	−12.6125	+	17.3596i	−0.687045	+	0.945636i	−0.999991	−	0.00413453i	$-0.998684\pi$
$337$	−12.6125	+	17.3596i	−0.687045	+	0.945636i	0.312947	+	0.949771i	$0.398684\pi$
$338$	−5.34879	+	3.88612i	−0.290936	+	0.211377i
$339$		0			0
$340$			9.99099i			0.541838i
$341$	−14.5189	+	8.87308i	−0.786241	+	0.480504i
$342$		0			0
$343$	−0.951057	−	0.309017i	−0.0513522	−	0.0166853i
$344$	−1.91965	−	2.64217i	−0.103501	−	0.142456i
$345$		0			0
$346$	6.57827	+	20.2458i	0.353650	+	1.08842i
$347$	−8.04394	−	24.7567i	−0.431821	−	1.32901i	−0.896309	−	0.443430i	$-0.853762\pi$
$347$	−8.04394	−	24.7567i	−0.431821	−	1.32901i	0.464488	−	0.885579i	$-0.346238\pi$
$348$		0			0
$349$	−2.47717	−	3.40953i	−0.132600	−	0.182508i	0.737554	−	0.675288i	$-0.235981\pi$
$349$	−2.47717	−	3.40953i	−0.132600	−	0.182508i	−0.870154	+	0.492780i	$0.835981\pi$
$350$	1.27585	+	0.414549i	0.0681970	+	0.0221586i
$351$		0			0
$352$	2.51938	+	2.15702i	0.134283	+	0.114970i
$353$		−	23.9953i		−	1.27714i	−0.769564	−	0.638569i	$-0.779526\pi$
$353$		−	23.9953i		−	1.27714i	0.769564	−	0.638569i	$-0.220474\pi$
$354$		0			0
$355$	7.64106	−	5.55156i	0.405545	−	0.294646i
$356$	3.18402	−	4.38243i	0.168753	−	0.232268i
$357$		0			0
$358$	3.07109	−	0.997856i	0.162312	−	0.0527383i
$359$	−8.04179	−	5.84271i	−0.424430	−	0.308366i	0.354988	−	0.934871i	$-0.384485\pi$
$359$	−8.04179	−	5.84271i	−0.424430	−	0.308366i	−0.779418	+	0.626505i	$0.784485\pi$
$360$		0			0
$361$	2.32846	−	7.16625i	0.122550	−	0.377171i
$362$	−20.4194			−1.07322
$363$		0			0
$364$	2.52756			0.132480
$365$	−2.97265	+	9.14886i	−0.155595	+	0.478873i
$366$		0			0
$367$	25.2504	+	18.3455i	1.31806	+	0.957626i	0.999954	+	0.00957100i	$0.00304659\pi$
$367$	25.2504	+	18.3455i	1.31806	+	0.957626i	0.318105	+	0.948055i	$0.396953\pi$
$368$	0.930967	−	0.302489i	0.0485300	−	0.0157684i
$369$		0			0
$370$	−4.38080	+	6.02965i	−0.227747	+	0.313466i
$371$	10.0777	−	7.32187i	0.523208	−	0.380133i
$372$		0			0
$373$			3.52287i			0.182407i	0.995832	+	0.0912037i	$0.0290714\pi$
$373$			3.52287i			0.182407i	−0.995832	+	0.0912037i	$0.970929\pi$
$374$	13.1599	+	11.2671i	0.680480	+	0.582607i
$375$		0			0
$376$	−4.64065	−	1.50784i	−0.239323	−	0.0777609i
$377$	−12.2015	−	16.7939i	−0.628409	−	0.864931i
$378$		0			0
$379$	−5.94760	−	18.3048i	−0.305508	−	0.940256i	−0.979487	−	0.201506i	$-0.935416\pi$
$379$	−5.94760	−	18.3048i	−0.305508	−	0.940256i	0.673980	−	0.738750i	$-0.264584\pi$
$380$	−2.00133	−	6.15947i	−0.102666	−	0.315974i
$381$		0			0
$382$	−8.38091	−	11.5353i	−0.428805	−	0.590199i
$383$	17.7722	+	5.77453i	0.908115	+	0.295064i	0.725582	−	0.688135i	$-0.241570\pi$
$383$	17.7722	+	5.77453i	0.908115	+	0.295064i	0.182533	+	0.983200i	$0.441570\pi$
$384$		0			0
$385$	−5.41295	+	3.30808i	−0.275870	+	0.168595i
$386$		−	11.2099i		−	0.570570i
$387$		0			0
$388$	−0.584191	+	0.424439i	−0.0296578	+	0.0215476i
$389$	15.6893	−	21.5945i	0.795480	−	1.09488i	−0.197924	−	0.980217i	$-0.563420\pi$
$389$	15.6893	−	21.5945i	0.795480	−	1.09488i	0.993404	−	0.114667i	$-0.0365802\pi$
$390$		0			0
$391$	4.86286	−	1.58004i	0.245925	−	0.0799060i
$392$	0.809017	+	0.587785i	0.0408615	+	0.0296876i
$393$		0			0
$394$	2.90219	−	8.93203i	0.146210	−	0.449989i
$395$	−26.0733			−1.31189
$396$		0			0
$397$	5.59545			0.280827			0.140414	−	0.990093i	$-0.455157\pi$
$397$	5.59545			0.280827			0.140414	+	0.990093i	$0.455157\pi$
$398$	−1.27603	+	3.92722i	−0.0639616	+	0.196854i
$399$		0			0
$400$	−1.08530	−	0.788518i	−0.0542651	−	0.0394259i
$401$	−2.35271	+	0.764442i	−0.117489	+	0.0381744i	−0.367171	−	0.930153i	$-0.619674\pi$
$401$	−2.35271	+	0.764442i	−0.117489	+	0.0381744i	0.249683	+	0.968328i	$0.419674\pi$
$402$		0			0
$403$	7.62200	−	10.4908i	0.379679	−	0.522583i
$404$	11.1034	−	8.06707i	0.552414	−	0.401352i
$405$		0			0
$406$		−	8.21285i		−	0.407597i
$407$	3.00175	+	12.5700i	0.148791	+	0.623074i
$408$		0			0
$409$	−18.1003	−	5.88115i	−0.895002	−	0.290804i	−0.174830	−	0.984599i	$-0.555937\pi$
$409$	−18.1003	−	5.88115i	−0.895002	−	0.290804i	−0.720173	+	0.693795i	$0.755937\pi$
$410$	4.69669	+	6.46444i	0.231953	+	0.319256i
$411$		0			0
$412$	1.26299	+	3.88709i	0.0622232	+	0.191503i
$413$	−1.42840	−	4.39617i	−0.0702871	−	0.216321i
$414$		0			0
$415$	−5.04281	−	6.94083i	−0.247542	−	0.340712i
$416$	−2.40385	−	0.781057i	−0.117858	−	0.0382945i
$417$		0			0
$418$	−10.3700	−	4.31009i	−0.507215	−	0.210813i
$419$			19.0625i			0.931263i	0.884979	+	0.465632i	$0.154173\pi$
$419$			19.0625i			0.931263i	−0.884979	+	0.465632i	$0.845827\pi$
$420$		0			0
$421$	27.8933	−	20.2657i	1.35944	−	0.987690i	0.360958	−	0.932582i	$-0.382450\pi$
$421$	27.8933	−	20.2657i	1.35944	−	0.987690i	0.998480	−	0.0551072i	$-0.0175501\pi$
$422$	−11.4307	+	15.7331i	−0.556440	+	0.765874i
$423$		0			0
$424$	−11.8470	+	3.84933i	−0.575343	+	0.186940i
$425$	−5.66902	−	4.11879i	−0.274988	−	0.199790i
$426$		0			0
$427$	0.315465	−	0.970903i	0.0152664	−	0.0469853i
$428$	12.7118			0.614450
$429$		0			0
$430$	−6.24675			−0.301245
$431$	−3.43503	+	10.5719i	−0.165460	+	0.509232i	−0.999070	−	0.0431207i	$-0.986270\pi$
$431$	−3.43503	+	10.5719i	−0.165460	+	0.509232i	0.833610	+	0.552353i	$0.186270\pi$
$432$		0			0
$433$	−20.9188	−	15.1984i	−1.00529	−	0.730389i	−0.0420776	−	0.999114i	$-0.513398\pi$
$433$	−20.9188	−	15.1984i	−1.00529	−	0.730389i	−0.963217	+	0.268725i	$0.913398\pi$
$434$	4.87928	−	1.58538i	0.234213	−	0.0761005i
$435$		0			0
$436$	−4.87959	+	6.71618i	−0.233690	+	0.321647i
$437$	−2.68146	+	1.94820i	−0.128272	+	0.0931949i
$438$		0			0
$439$			30.6630i			1.46347i	0.681591	+	0.731734i	$0.261289\pi$
$439$			30.6630i			1.46347i	−0.681591	+	0.731734i	$0.738711\pi$
$440$	6.17028	−	1.47347i	0.294156	−	0.0702451i
$441$		0			0
$442$	−12.5564	−	4.07982i	−0.597246	−	0.194057i
$443$	−2.86164	−	3.93871i	−0.135961	−	0.187134i	0.735608	−	0.677408i	$-0.236897\pi$
$443$	−2.86164	−	3.93871i	−0.135961	−	0.187134i	−0.871568	+	0.490274i	$0.836897\pi$
$444$		0			0
$445$	−3.20177	−	9.85404i	−0.151779	−	0.467126i
$446$	−6.98653	−	21.5023i	−0.330822	−	1.01817i
$447$		0			0
$448$	−0.587785	−	0.809017i	−0.0277702	−	0.0382225i
$449$	15.2316	+	4.94905i	0.718825	+	0.233560i	0.645513	−	0.763749i	$-0.276643\pi$
$449$	15.2316	+	4.94905i	0.718825	+	0.233560i	0.0733110	+	0.997309i	$0.476643\pi$
$450$		0			0
$451$	13.8113	+	1.10376i	0.650351	+	0.0519740i
$452$		−	2.25129i		−	0.105892i
$453$		0			0
$454$	−17.7997	+	12.9322i	−0.835380	+	0.606939i
$455$	2.84165	−	3.91119i	0.133219	−	0.183360i
$456$		0			0
$457$	−19.1059	+	6.20788i	−0.893735	+	0.290392i	−0.719649	−	0.694338i	$-0.755697\pi$
$457$	−19.1059	+	6.20788i	−0.893735	+	0.290392i	−0.174087	+	0.984730i	$0.555697\pi$
$458$	4.45926	+	3.23984i	0.208367	+	0.151388i
$459$		0			0
$460$	0.578577	−	1.78068i	0.0269763	−	0.0830245i
$461$	−18.8576			−0.878288			−0.439144	−	0.898417i	$-0.644718\pi$
$461$	−18.8576			−0.878288			−0.439144	+	0.898417i	$0.644718\pi$
$462$		0			0
$463$	0.113096			0.00525602			0.00262801	−	0.999997i	$-0.499163\pi$
$463$	0.113096			0.00525602			0.00262801	+	0.999997i	$0.499163\pi$
$464$	−2.53791	+	7.81088i	−0.117819	+	0.362611i
$465$		0			0
$466$	13.6889	+	9.94554i	0.634124	+	0.460718i
$467$	26.4307	−	8.58785i	1.22307	−	0.397398i	0.374868	−	0.927078i	$-0.377688\pi$
$467$	26.4307	−	8.58785i	1.22307	−	0.397398i	0.848198	+	0.529680i	$0.177688\pi$
$468$		0			0
$469$	0.774948	−	1.06662i	0.0357838	−	0.0492521i
$470$	−7.55060	+	5.48583i	−0.348283	+	0.253043i
$471$		0			0
$472$			4.62241i			0.212764i
$473$	−7.04461	+	8.22804i	−0.323912	+	0.378326i
$474$		0			0
$475$	4.32002	+	1.40366i	0.198216	+	0.0644043i
$476$	−3.07027	−	4.22586i	−0.140725	−	0.193692i
$477$		0			0
$478$	−7.23628	−	22.2710i	−0.330980	−	1.01865i
$479$	3.42776	+	10.5496i	0.156618	+	0.482022i	0.998321	−	0.0579193i	$-0.0184466\pi$
$479$	3.42776	+	10.5496i	0.156618	+	0.482022i	−0.841703	+	0.539941i	$0.818447\pi$
$480$		0			0
$481$	−5.78899	−	7.96786i	−0.263955	−	0.363303i
$482$	26.9577	+	8.75908i	1.22789	+	0.398965i
$483$		0			0
$484$	5.01755	−	9.78898i	0.228071	−	0.444954i
$485$			1.38117i			0.0627158i
$486$		0			0
$487$	9.42200	−	6.84549i	0.426952	−	0.310199i	−0.353477	−	0.935443i	$-0.615001\pi$
$487$	9.42200	−	6.84549i	0.426952	−	0.310199i	0.780429	+	0.625245i	$0.215001\pi$
$488$	−0.600051	+	0.825899i	−0.0271630	+	0.0373867i
$489$		0			0
$490$	1.81910	−	0.591063i	0.0821787	−	0.0267015i
$491$	−7.33613	−	5.33001i	−0.331075	−	0.240540i	0.409812	−	0.912170i	$-0.365594\pi$
$491$	−7.33613	−	5.33001i	−0.331075	−	0.240540i	−0.740887	+	0.671630i	$0.765594\pi$
$492$		0			0
$493$	−13.2566	+	40.7998i	−0.597049	+	1.83753i
$494$	8.55829			0.385055
$495$		0			0
$496$	−5.13038			−0.230361
$497$	−1.52590	+	4.69625i	−0.0684462	+	0.210656i
$498$		0			0
$499$	31.3314	+	22.7636i	1.40258	+	1.01904i	0.994349	+	0.106160i	$0.0338557\pi$
$499$	31.3314	+	22.7636i	1.40258	+	1.01904i	0.408235	+	0.912877i	$0.366144\pi$
$500$	−11.5359	+	3.74823i	−0.515899	+	0.167626i
$501$		0			0
$502$	−4.88371	+	6.72185i	−0.217971	+	0.300011i
$503$	−13.2513	+	9.62763i	−0.590846	+	0.429275i	−0.842618	−	0.538512i	$-0.818987\pi$
$503$	−13.2513	+	9.62763i	−0.590846	+	0.429275i	0.251772	+	0.967787i	$0.418987\pi$
$504$		0			0
$505$		−	26.2512i		−	1.16816i
$506$	−1.69298	−	2.77020i	−0.0752622	−	0.123150i
$507$		0			0
$508$	−6.93827	−	2.25438i	−0.307836	−	0.100022i
$509$	−21.4805	−	29.5654i	−0.952107	−	1.31046i	−0.950585	−	0.310463i	$-0.899516\pi$
$509$	−21.4805	−	29.5654i	−0.952107	−	1.31046i	−0.00152118	−	0.999999i	$-0.500484\pi$
$510$		0			0
$511$	−1.55415	−	4.78317i	−0.0687514	−	0.211595i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$		0			0
$514$	0.390175	+	0.537030i	0.0172099	+	0.0236874i
$515$	7.43491	+	2.41575i	0.327621	+	0.106451i
$516$		0			0
$517$	−1.28921	+	16.1319i	−0.0566996	+	0.709482i
$518$		−	3.89658i		−	0.171206i
$519$		0			0
$520$	−3.91119	+	2.84165i	−0.171517	+	0.124615i
$521$	−23.4422	+	32.2654i	−1.02702	+	1.41358i	−0.119862	+	0.992791i	$0.538245\pi$
$521$	−23.4422	+	32.2654i	−1.02702	+	1.41358i	−0.907161	+	0.420784i	$0.861755\pi$
$522$		0			0
$523$	−10.9125	+	3.54569i	−0.477171	+	0.155042i	−0.537721	−	0.843123i	$-0.680715\pi$
$523$	−10.9125	+	3.54569i	−0.477171	+	0.155042i	0.0605497	+	0.998165i	$0.480715\pi$
$524$	11.5284	+	8.37587i	0.503620	+	0.365901i
$525$		0			0
$526$	8.27004	−	25.4526i	0.360591	−	1.10978i
$527$	−26.7983			−1.16735
$528$		0			0
$529$	22.0418			0.958339
$530$	−7.36269	+	22.6600i	−0.319815	+	0.984289i
$531$		0			0
$532$	2.73933	+	1.99024i	0.118765	+	0.0862877i
$533$	−10.0422	+	3.26291i	−0.434976	+	0.141332i
$534$		0			0
$535$	14.2915	−	19.6706i	0.617876	−	0.850433i
$536$	−1.06662	+	0.774948i	−0.0460711	+	0.0334726i
$537$		0			0
$538$			27.9254i			1.20395i
$539$	1.27292	−	3.06263i	0.0548284	−	0.131917i
$540$		0			0
$541$	−13.0010	−	4.22427i	−0.558955	−	0.181615i	0.0158960	−	0.999874i	$-0.494940\pi$
$541$	−13.0010	−	4.22427i	−0.558955	−	0.181615i	−0.574851	+	0.818258i	$0.694940\pi$
$542$	−14.9804	−	20.6188i	−0.643464	−	0.885653i
$543$		0			0
$544$	1.61414	+	4.96780i	0.0692055	+	0.212993i
$545$	4.90680	+	15.1016i	0.210184	+	0.646881i
$546$		0			0
$547$	2.55494	+	3.51657i	0.109241	+	0.150358i	0.860137	−	0.510063i	$-0.170378\pi$
$547$	2.55494	+	3.51657i	0.109241	+	0.150358i	−0.750896	+	0.660421i	$0.770378\pi$
$548$	17.0872	+	5.55197i	0.729929	+	0.237168i
$549$		0			0
$550$	−1.70763	+	4.10854i	−0.0728134	+	0.175189i
$551$		−	27.8086i		−	1.18469i
$552$		0			0
$553$	11.0281	−	8.01242i	0.468964	−	0.340723i
$554$	−10.9133	+	15.0208i	−0.463661	+	0.638175i
$555$		0			0
$556$	−15.4176	+	5.00950i	−0.653854	+	0.212450i
$557$	−7.52986	−	5.47076i	−0.319050	−	0.231804i	0.416720	−	0.909035i	$-0.363180\pi$
$557$	−7.52986	−	5.47076i	−0.319050	−	0.231804i	−0.735770	+	0.677231i	$0.763180\pi$
$558$		0			0
$559$	2.55086	−	7.85073i	0.107890	−	0.332051i
$560$	−1.91272			−0.0808271
$561$		0			0
$562$	17.2088			0.725907
$563$	−3.64937	+	11.2316i	−0.153803	+	0.473356i	−0.998038	−	0.0626174i	$-0.980055\pi$
$563$	−3.64937	+	11.2316i	−0.153803	+	0.473356i	0.844235	+	0.535973i	$0.180055\pi$
$564$		0			0
$565$	−3.48370	−	2.53106i	−0.146560	−	0.106482i
$566$	6.05523	−	1.96746i	0.254520	−	0.0826986i
$567$		0			0
$568$	2.90244	−	3.99487i	0.121784	−	0.167621i
$569$	8.32897	−	6.05135i	0.349169	−	0.253686i	−0.399352	−	0.916798i	$-0.630765\pi$
$569$	8.32897	−	6.05135i	0.349169	−	0.253686i	0.748520	+	0.663112i	$0.230765\pi$
$570$		0			0
$571$		−	30.9466i		−	1.29508i	−0.762033	−	0.647538i	$-0.775799\pi$
$571$		−	30.9466i		−	1.29508i	0.762033	−	0.647538i	$-0.224201\pi$
$572$	−0.667810	+	8.35631i	−0.0279225	+	0.349395i
$573$		0			0
$574$	−3.97309	−	1.29093i	−0.165834	−	0.0538826i
$575$	0.771862	+	1.06238i	0.0321889	+	0.0443042i
$576$		0			0
$577$	4.19088	+	12.8982i	0.174468	+	0.536959i	0.999609	−	0.0279691i	$-0.00890401\pi$
$577$	4.19088	+	12.8982i	0.174468	+	0.536959i	−0.825140	+	0.564928i	$0.808904\pi$
$578$	3.17807	+	9.78109i	0.132190	+	0.406840i
$579$		0			0
$580$	9.23344	+	12.7087i	0.383398	+	0.527702i
$581$	4.26588	+	1.38607i	0.176979	+	0.0575039i
$582$		0			0
$583$	21.5441	+	35.2522i	0.892264	+	1.46000i
$584$			5.02932i			0.208115i
$585$		0			0
$586$	9.58104	−	6.96103i	0.395789	−	0.287558i
$587$	14.6685	−	20.1894i	0.605432	−	0.833306i	−0.390760	−	0.920493i	$-0.627788\pi$
$587$	14.6685	−	20.1894i	0.605432	−	0.833306i	0.996192	+	0.0871865i	$0.0277876\pi$
$588$		0			0
$589$	16.5212	−	5.36807i	0.680745	−	0.221188i
$590$	7.15282	+	5.19682i	0.294477	+	0.213950i
$591$		0			0
$592$	−1.20411	+	3.70586i	−0.0494886	+	0.152310i
$593$	31.1565			1.27944			0.639721	−	0.768607i	$-0.279050\pi$
$593$	31.1565			1.27944			0.639721	+	0.768607i	$0.279050\pi$
$594$		0			0
$595$	−9.99099			−0.409591
$596$	0.374369	−	1.15219i	0.0153347	−	0.0471955i
$597$		0			0
$598$	2.00164	+	1.45428i	0.0818532	+	0.0594698i
$599$	17.2811	−	5.61497i	0.706086	−	0.229421i	0.0661059	−	0.997813i	$-0.478942\pi$
$599$	17.2811	−	5.61497i	0.706086	−	0.229421i	0.639980	+	0.768391i	$0.278942\pi$
$600$		0			0
$601$	25.2390	−	34.7385i	1.02952	−	1.41701i	0.124213	−	0.992256i	$-0.460359\pi$
$601$	25.2390	−	34.7385i	1.02952	−	1.41701i	0.905307	−	0.424758i	$-0.139641\pi$
$602$	2.64217	−	1.91965i	0.107687	−	0.0782390i
$603$		0			0
$604$		−	8.73819i		−	0.355552i
$605$	−9.50661	−	18.7697i	−0.386499	−	0.763097i
$606$		0			0
$607$	30.4736	+	9.90146i	1.23688	+	0.401888i	0.853204	−	0.521578i	$-0.174656\pi$
$607$	30.4736	+	9.90146i	1.23688	+	0.401888i	0.383681	+	0.923466i	$0.374656\pi$
$608$	−1.99024	−	2.73933i	−0.0807148	−	0.111094i
$609$		0			0
$610$	0.603397	+	1.85706i	0.0244308	+	0.0751903i
$611$	−3.81115	−	11.7295i	−0.154183	−	0.474525i
$612$		0			0
$613$	−14.6531	−	20.1683i	−0.591834	−	0.814590i	0.403096	−	0.915158i	$-0.367934\pi$
$613$	−14.6531	−	20.1683i	−0.591834	−	0.814590i	−0.994930	+	0.100568i	$0.967934\pi$
$614$	9.06109	+	2.94413i	0.365676	+	0.118815i
$615$		0			0
$616$	−2.15702	+	2.51938i	−0.0869088	+	0.101509i
$617$		−	22.9711i		−	0.924782i	−0.886676	−	0.462391i	$-0.846992\pi$
$617$		−	22.9711i		−	0.924782i	0.886676	−	0.462391i	$-0.153008\pi$
$618$		0			0
$619$	26.2410	−	19.0652i	1.05472	−	0.766296i	0.0816126	−	0.996664i	$-0.473993\pi$
$619$	26.2410	−	19.0652i	1.05472	−	0.766296i	0.973104	+	0.230368i	$0.0739930\pi$
$620$	−5.76792	+	7.93887i	−0.231645	+	0.318833i
$621$		0			0
$622$	−9.60458	+	3.12072i	−0.385109	+	0.125129i
$623$	4.38243	+	3.18402i	0.175578	+	0.127565i
$624$		0			0
$625$	−5.09656	+	15.6856i	−0.203862	+	0.627424i
$626$	5.49667			0.219691
$627$		0			0
$628$	16.5027			0.658528
$629$	−6.28960	+	19.3574i	−0.250783	+	0.771830i
$630$		0			0
$631$	5.53510	+	4.02148i	0.220349	+	0.160093i	0.692484	−	0.721434i	$-0.256516\pi$
$631$	5.53510	+	4.02148i	0.220349	+	0.160093i	−0.472135	+	0.881526i	$0.656516\pi$
$632$	−12.9644	+	4.21238i	−0.515695	+	0.167559i
$633$		0			0
$634$	4.48760	−	6.17665i	0.178225	−	0.245306i
$635$	−11.2890	+	8.20190i	−0.447988	+	0.325483i
$636$		0			0
$637$			2.52756i			0.100145i
$638$	27.1524	+	2.16993i	1.07497	+	0.0859084i
$639$		0			0
$640$	1.81910	+	0.591063i	0.0719064	+	0.0233638i
$641$	14.8995	+	20.5074i	0.588496	+	0.809995i	0.994595	−	0.103834i	$-0.0331111\pi$
$641$	14.8995	+	20.5074i	0.588496	+	0.809995i	−0.406099	+	0.913829i	$0.633111\pi$
$642$		0			0
$643$	−5.10129	−	15.7002i	−0.201175	−	0.619154i	−0.999849	−	0.0173895i	$-0.994464\pi$
$643$	−5.10129	−	15.7002i	−0.201175	−	0.619154i	0.798673	−	0.601765i	$-0.205536\pi$
$644$	0.302489	+	0.930967i	0.0119198	+	0.0366852i
$645$		0			0
$646$	−10.3959	−	14.3087i	−0.409022	−	0.562970i
$647$	−4.04411	−	1.31401i	−0.158990	−	0.0516591i	0.228440	−	0.973558i	$-0.426637\pi$
$647$	−4.04411	−	1.31401i	−0.158990	−	0.0516591i	−0.387431	+	0.921899i	$0.626637\pi$
$648$		0			0
$649$	14.9115	−	3.56090i	0.585328	−	0.139778i
$650$		−	3.39073i		−	0.132996i
$651$		0			0
$652$	11.2729	−	8.19025i	0.441481	−	0.320755i
$653$	13.7685	−	18.9507i	0.538804	−	0.741600i	−0.449636	−	0.893212i	$-0.648446\pi$
$653$	13.7685	−	18.9507i	0.538804	−	0.741600i	0.988440	+	0.151612i	$0.0484464\pi$
$654$		0			0
$655$	25.9220	−	8.42257i	1.01286	−	0.329097i
$656$	3.37971	+	2.45550i	0.131956	+	0.0958713i
$657$		0			0
$658$	1.50784	−	4.64065i	0.0587817	−	0.180911i
$659$	42.8398			1.66880			0.834400	−	0.551159i	$-0.185814\pi$
$659$	42.8398			1.66880			0.834400	+	0.551159i	$0.185814\pi$
$660$		0			0
$661$	32.6658			1.27055			0.635277	−	0.772284i	$-0.280886\pi$
$661$	32.6658			1.27055			0.635277	+	0.772284i	$0.280886\pi$
$662$	−6.34222	+	19.5194i	−0.246497	+	0.758641i
$663$		0			0
$664$	−3.62878	−	2.63646i	−0.140824	−	0.102315i
$665$	6.15947	−	2.00133i	0.238854	−	0.0776084i
$666$		0			0
$667$	4.72542	−	6.50398i	0.182969	−	0.251835i
$668$	1.57935	−	1.14746i	0.0611069	−	0.0443967i
$669$		0			0
$670$			2.52177i			0.0974243i
$671$	3.12654	+	1.29948i	0.120699	+	0.0501658i
$672$		0			0
$673$	−32.7889	−	10.6538i	−1.26392	−	0.410672i	−0.401030	−	0.916065i	$-0.631348\pi$
$673$	−32.7889	−	10.6538i	−1.26392	−	0.410672i	−0.862889	+	0.505393i	$0.831348\pi$
$674$	12.6125	+	17.3596i	0.485814	+	0.668666i
$675$		0			0
$676$	2.04306	+	6.28788i	0.0785790	+	0.241841i
$677$	6.23872	+	19.2008i	0.239773	+	0.737947i	0.996452	+	0.0841599i	$0.0268207\pi$
$677$	6.23872	+	19.2008i	0.239773	+	0.737947i	−0.756679	+	0.653787i	$0.773179\pi$
$678$		0			0
$679$	−0.424439	−	0.584191i	−0.0162885	−	0.0224192i
$680$	9.50200	+	3.08739i	0.364385	+	0.118396i
$681$		0			0
$682$	3.95222	+	16.5502i	0.151338	+	0.633740i
$683$		−	7.14702i		−	0.273473i	−0.990607	−	0.136736i	$-0.956339\pi$
$683$		−	7.14702i		−	0.273473i	0.990607	−	0.136736i	$-0.0436614\pi$
$684$		0			0
$685$	27.8018	−	20.1992i	1.06225	−	0.771772i
$686$	−0.587785	+	0.809017i	−0.0224417	+	0.0308884i
$687$		0			0
$688$	−3.10606	+	1.00922i	−0.118417	+	0.0384761i
$689$	−25.4719	−	18.5064i	−0.970403	−	0.705039i
$690$		0			0
$691$	7.14323	−	21.9846i	0.271741	−	0.836334i	−0.718322	−	0.695711i	$-0.755090\pi$
$691$	7.14323	−	21.9846i	0.271741	−	0.836334i	0.990063	−	0.140623i	$-0.0449105\pi$
$692$	21.2877			0.809238
$693$		0			0
$694$	−26.0307			−0.988113
$695$	−9.58176	+	29.4896i	−0.363457	+	1.11860i
$696$		0			0
$697$	17.6538	+	12.8262i	0.668684	+	0.485827i
$698$	−4.00814	+	1.30232i	−0.151710	+	0.0492937i
$699$		0			0
$700$	0.788518	−	1.08530i	0.0298032	−	0.0410206i
$701$	27.1549	−	19.7292i	1.02563	−	0.745161i	0.0581978	−	0.998305i	$-0.481465\pi$
$701$	27.1549	−	19.7292i	1.02563	−	0.745161i	0.967429	+	0.253144i	$0.0814646\pi$
$702$		0			0
$703$		−	13.1938i		−	0.497613i
$704$	2.82998	−	1.72952i	0.106659	−	0.0651836i
$705$		0			0
$706$	−22.8209	−	7.41494i	−0.858874	−	0.279065i
$707$	8.06707	+	11.1034i	0.303394	+	0.417585i
$708$		0			0
$709$	−13.6620	−	42.0473i	−0.513087	−	1.57912i	−0.786736	−	0.617290i	$-0.788231\pi$
$709$	−13.6620	−	42.0473i	−0.513087	−	1.57912i	0.273649	−	0.961830i	$-0.411769\pi$
$710$	−2.91863	−	8.98261i	−0.109534	−	0.337111i
$711$		0			0
$712$	−3.18402	−	4.38243i	−0.119326	−	0.164238i
$713$	4.77622	+	1.55189i	0.178871	+	0.0581186i
$714$		0			0
$715$	12.1799	+	10.4281i	0.455504	+	0.389989i
$716$		−	3.22913i		−	0.120678i
$717$		0			0
$718$	−8.04179	+	5.84271i	−0.300117	+	0.218048i
$719$	0.700685	−	0.964410i	0.0261311	−	0.0359664i	−0.795752	−	0.605623i	$-0.792924\pi$
$719$	0.700685	−	0.964410i	0.0261311	−	0.0359664i	0.821883	+	0.569657i	$0.192924\pi$
$720$		0			0
$721$	−3.88709	+	1.26299i	−0.144763	+	0.0470363i
$722$	−6.09598	−	4.42899i	−0.226869	−	0.164830i
$723$		0			0
$724$	−6.30995	+	19.4200i	−0.234507	+	0.721739i
$725$	−11.0176			−0.409183
$726$		0			0
$727$	47.9531			1.77848			0.889240	−	0.457440i	$-0.151234\pi$
$727$	47.9531			1.77848			0.889240	+	0.457440i	$0.151234\pi$
$728$	0.781057	−	2.40385i	0.0289479	−	0.0890925i
$729$		0			0
$730$	7.78249	+	5.65431i	0.288043	+	0.209275i
$731$	−16.2243	+	5.27161i	−0.600079	+	0.194977i
$732$		0			0
$733$	−25.0145	+	34.4294i	−0.923930	+	1.27168i	0.0382508	+	0.999268i	$0.487821\pi$
$733$	−25.0145	+	34.4294i	−0.923930	+	1.27168i	−0.962181	+	0.272412i	$0.912179\pi$
$734$	25.2504	−	18.3455i	0.932009	−	0.677144i
$735$		0			0
$736$		−	0.978876i		−	0.0360819i
$737$	3.32160	+	2.84386i	0.122353	+	0.104755i
$738$		0			0
$739$	−41.7792	−	13.5749i	−1.53687	−	0.499360i	−0.586360	−	0.810050i	$-0.699440\pi$
$739$	−41.7792	−	13.5749i	−1.53687	−	0.499360i	−0.950511	+	0.310691i	$0.899440\pi$
$740$	4.38080	+	6.02965i	0.161041	+	0.221654i
$741$		0			0
$742$	−3.84933	−	11.8470i	−0.141314	−	0.434918i
$743$	13.2834	+	40.8822i	0.487322	+	1.49982i	0.828589	+	0.559857i	$0.189144\pi$
$743$	13.2834	+	40.8822i	0.487322	+	1.49982i	−0.341267	+	0.939967i	$0.610856\pi$
$744$		0			0
$745$	−1.36203	−	1.87467i	−0.0499009	−	0.0686827i
$746$	3.35045	+	1.08863i	0.122669	+	0.0398575i
$747$		0			0
$748$	14.7823	−	9.03404i	0.540493	−	0.330317i
$749$			12.7118i			0.464480i
$750$		0			0
$751$	11.2638	−	8.18361i	0.411021	−	0.298624i	−0.362994	−	0.931791i	$-0.618245\pi$
$751$	11.2638	−	8.18361i	0.411021	−	0.298624i	0.774015	+	0.633167i	$0.218245\pi$
$752$	−2.86808	+	3.94757i	−0.104588	+	0.143953i
$753$		0			0
$754$	−19.7424	+	6.41470i	−0.718977	+	0.233610i
$755$	−13.5217	−	9.82407i	−0.492104	−	0.357534i
$756$		0			0
$757$	−5.19049	+	15.9747i	−0.188652	+	0.580610i	−0.999992	−	0.00396391i	$-0.998738\pi$
$757$	−5.19049	+	15.9747i	−0.188652	+	0.580610i	0.811341	+	0.584574i	$0.198738\pi$
$758$	−19.2468			−0.699077
$759$		0			0
$760$	−6.47645			−0.234926
$761$	−13.8588	+	42.6530i	−0.502381	+	1.54617i	0.302749	+	0.953070i	$0.402096\pi$
$761$	−13.8588	+	42.6530i	−0.502381	+	1.54617i	−0.805130	+	0.593099i	$0.797904\pi$
$762$		0			0
$763$	−6.71618	−	4.87959i	−0.243142	−	0.176653i
$764$	−13.5606	+	4.40611i	−0.490605	+	0.159407i
$765$		0			0
$766$	10.9838	−	15.1179i	0.396861	−	0.546232i
$767$	−9.45206	+	6.86732i	−0.341294	+	0.247965i
$768$		0			0
$769$		−	42.5105i		−	1.53297i	−0.642264	−	0.766483i	$-0.722005\pi$
$769$		−	42.5105i		−	1.53297i	0.642264	−	0.766483i	$-0.277995\pi$
$770$	1.47347	+	6.17028i	0.0531003	+	0.222361i
$771$		0			0
$772$	−10.6613	−	3.46406i	−0.383708	−	0.124674i
$773$	26.9174	+	37.0487i	0.968153	+	1.33255i	0.942974	+	0.332866i	$0.108016\pi$
$773$	26.9174	+	37.0487i	0.968153	+	1.33255i	0.0251789	+	0.999683i	$0.491984\pi$
$774$		0			0
$775$	−2.12679	−	6.54559i	−0.0763966	−	0.235125i
$776$	0.223141	+	0.686757i	0.00801029	+	0.0246531i
$777$		0			0
$778$	−15.6893	−	21.5945i	−0.562490	−	0.774200i
$779$	−13.4529	−	4.37110i	−0.481999	−	0.156611i
$780$		0			0
$781$	−15.1230	−	6.28557i	−0.541145	−	0.224916i
$782$		−	5.11311i		−	0.182845i
$783$		0			0
$784$	0.809017	−	0.587785i	0.0288935	−	0.0209923i
$785$	18.5534	−	25.5366i	0.662200	−	0.911440i
$786$		0			0
$787$	24.4324	−	7.93858i	0.870923	−	0.282980i	0.160739	−	0.986997i	$-0.448612\pi$
$787$	24.4324	−	7.93858i	0.870923	−	0.282980i	0.710183	+	0.704017i	$0.248612\pi$
$788$	−7.59804	−	5.52030i	−0.270669	−	0.196653i
$789$		0			0
$790$	−8.05709	+	24.7972i	−0.286658	+	0.882244i
$791$	2.25129			0.0800468
$792$		0			0
$793$	−2.58030			−0.0916291
$794$	1.72909	−	5.32159i	0.0613631	−	0.188856i
$795$		0			0
$796$	3.34069	+	2.42715i	0.118408	+	0.0860282i
$797$	−17.7416	+	5.76458i	−0.628438	+	0.204192i	−0.605883	−	0.795554i	$-0.707180\pi$
$797$	−17.7416	+	5.76458i	−0.628438	+	0.204192i	−0.0225552	+	0.999746i	$0.507180\pi$
$798$		0			0
$799$	−14.9813	+	20.6200i	−0.530000	+	0.729482i
$800$	−1.08530	+	0.788518i	−0.0383712	+	0.0278783i
$801$		0			0
$802$			2.47379i			0.0873524i
$803$	16.2242	−	3.87437i	0.572539	−	0.136724i
$804$		0			0
$805$	1.78068	+	0.578577i	0.0627606	+	0.0203922i
$806$	−7.62200	−	10.4908i	−0.268474	−	0.369522i
$807$		0			0
$808$	−4.24111	−	13.0528i	−0.149202	−	0.459196i
$809$	10.0523	+	30.9378i	0.353421	+	1.08772i	0.956920	+	0.290353i	$0.0937727\pi$
$809$	10.0523	+	30.9378i	0.353421	+	1.08772i	−0.603499	+	0.797364i	$0.706227\pi$
$810$		0			0
$811$	−7.84833	−	10.8023i	−0.275592	−	0.379320i	0.648676	−	0.761065i	$-0.275323\pi$
$811$	−7.84833	−	10.8023i	−0.275592	−	0.379320i	−0.924268	+	0.381745i	$0.875323\pi$
$812$	−7.81088	−	2.53791i	−0.274108	−	0.0890631i
$813$		0			0
$814$	12.8824	+	1.02952i	0.451528	+	0.0360847i
$815$		−	26.6520i		−	0.933578i
$816$		0			0
$817$	8.94637	−	6.49992i	0.312994	−	0.227403i
$818$	−11.1866	+	15.3970i	−0.391130	+	0.538345i
$819$		0			0
$820$	7.59940	−	2.46920i	0.265383	−	0.0862280i
$821$	−10.8695	−	7.89716i	−0.379348	−	0.275613i	0.381728	−	0.924275i	$-0.375329\pi$
$821$	−10.8695	−	7.89716i	−0.379348	−	0.275613i	−0.761077	+	0.648662i	$0.775329\pi$
$822$		0			0
$823$	6.20701	−	19.1032i	0.216363	−	0.665896i	−0.782691	−	0.622410i	$-0.786154\pi$
$823$	6.20701	−	19.1032i	0.216363	−	0.665896i	0.999054	−	0.0434862i	$-0.0138464\pi$
$824$	4.08713			0.142382
$825$		0			0
$826$	−4.62241			−0.160834
$827$	2.20313	−	6.78055i	0.0766104	−	0.235783i	−0.905416	−	0.424525i	$-0.860441\pi$
$827$	2.20313	−	6.78055i	0.0766104	−	0.235783i	0.982027	+	0.188742i	$0.0604411\pi$
$828$		0			0
$829$	−39.3754	−	28.6079i	−1.36756	−	0.993592i	−0.997923	−	0.0644171i	$-0.979481\pi$
$829$	−39.3754	−	28.6079i	−1.36756	−	0.993592i	−0.369639	−	0.929175i	$-0.620519\pi$
$830$	−8.15943	+	2.65116i	−0.283218	+	0.0920231i
$831$		0			0
$832$	−1.48566	+	2.04483i	−0.0515060	+	0.0708919i
$833$	4.22586	−	3.07027i	0.146417	−	0.106378i
$834$		0			0
$835$		−	3.73398i		−	0.129220i
$836$	−7.30365	+	8.53060i	−0.252602	+	0.295037i
$837$		0			0
$838$	18.1295	+	5.89063i	0.626273	+	0.203489i
$839$	−10.9923	−	15.1297i	−0.379498	−	0.522334i	0.575954	−	0.817482i	$-0.304631\pi$
$839$	−10.9923	−	15.1297i	−0.379498	−	0.522334i	−0.955451	+	0.295149i	$0.904631\pi$
$840$		0			0
$841$	11.8820	+	36.5689i	0.409723	+	1.26100i
$842$	−10.6543	−	32.7906i	−0.367172	−	1.13004i
$843$		0			0
$844$	11.4307	+	15.7331i	0.393463	+	0.541555i
$845$	12.0269	+	3.90779i	0.413739	+	0.134432i
$846$		0			0
$847$	9.78898	+	5.01755i	0.336353	+	0.172405i
$848$			12.4567i			0.427765i
$849$		0			0
$850$	−5.66902	+	4.11879i	−0.194446	+	0.141273i
$851$	2.24197	−	3.08581i	0.0768537	−	0.105780i
$852$		0			0
$853$	22.1836	−	7.20788i	0.759551	−	0.246793i	0.0964649	−	0.995336i	$-0.469246\pi$
$853$	22.1836	−	7.20788i	0.759551	−	0.246793i	0.663086	+	0.748543i	$0.269246\pi$
$854$	−0.825899	−	0.600051i	−0.0282617	−	0.0205333i
$855$		0			0
$856$	3.92817	−	12.0897i	0.134262	−	0.413216i
$857$	0.991384			0.0338650			0.0169325	−	0.999857i	$-0.494610\pi$
$857$	0.991384			0.0338650			0.0169325	+	0.999857i	$0.494610\pi$
$858$		0			0
$859$	23.2008			0.791601			0.395800	−	0.918337i	$-0.370467\pi$
$859$	23.2008			0.791601			0.395800	+	0.918337i	$0.370467\pi$
$860$	−1.93035	+	5.94101i	−0.0658245	+	0.202587i
$861$		0			0
$862$	8.99303	+	6.53382i	0.306304	+	0.222543i
$863$	44.2135	−	14.3658i	1.50505	−	0.489019i	0.563561	−	0.826074i	$-0.309431\pi$
$863$	44.2135	−	14.3658i	1.50505	−	0.489019i	0.941485	+	0.337055i	$0.109431\pi$
$864$		0			0
$865$	23.9331	−	32.9411i	0.813751	−	1.12003i
$866$	−20.9188	+	15.1984i	−0.710851	+	0.516463i
$867$		0			0
$868$		−	5.13038i		−	0.174137i
$869$	23.5760	+	38.5770i	0.799760	+	1.30863i
$870$		0			0
$871$	−3.16928	−	1.02976i	−0.107387	−	0.0348921i
$872$	4.87959	+	6.71618i	0.165244	+	0.227439i
$873$		0			0
$874$	1.02423	+	3.15225i	0.0346450	+	0.106626i
$875$	−3.74823	−	11.5359i	−0.126713	−	0.389983i
$876$		0			0
$877$	−0.973067	−	1.33931i	−0.0328581	−	0.0452253i	0.792272	−	0.610168i	$-0.208898\pi$
$877$	−0.973067	−	1.33931i	−0.0328581	−	0.0452253i	−0.825130	+	0.564943i	$0.808898\pi$
$878$	29.1623	+	9.47540i	0.984180	+	0.319779i
$879$		0			0
$880$	0.505363	−	6.32361i	0.0170358	−	0.213169i
$881$		−	7.73809i		−	0.260703i	−0.991468	−	0.130351i	$-0.958389\pi$
$881$		−	7.73809i		−	0.260703i	0.991468	−	0.130351i	$-0.0416105\pi$
$882$		0			0
$883$	35.6322	−	25.8883i	1.19912	−	0.871210i	0.204920	−	0.978779i	$-0.434306\pi$
$883$	35.6322	−	25.8883i	1.19912	−	0.871210i	0.994198	+	0.107568i	$0.0343064\pi$
$884$	−7.76027	+	10.6811i	−0.261006	+	0.359244i
$885$		0			0
$886$	−4.63023	+	1.50445i	−0.155556	+	0.0505431i
$887$	−31.6552	−	22.9988i	−1.06288	−	0.772225i	−0.0882581	−	0.996098i	$-0.528130\pi$
$887$	−31.6552	−	22.9988i	−1.06288	−	0.772225i	−0.974618	+	0.223873i	$0.928130\pi$
$888$		0			0
$889$	2.25438	−	6.93827i	0.0756095	−	0.232702i
$890$	−10.3612			−0.347307
$891$		0			0
$892$	−22.6089			−0.757002
$893$	5.10554	−	15.7132i	0.170850	−	0.525823i
$894$		0			0
$895$	−4.99683	−	3.63041i	−0.167026	−	0.121351i
$896$	−0.951057	+	0.309017i	−0.0317726	+	0.0103235i
$897$		0			0
$898$	9.41366	−	12.9568i	0.314138	−	0.432374i
$899$	−34.0880	+	24.7664i	−1.13690	+	0.826004i
$900$		0			0
$901$			65.0670i			2.16770i
$902$	5.31768	−	12.7943i	0.177059	−	0.426003i
$903$		0			0
$904$	−2.14111	−	0.695688i	−0.0712122	−	0.0231382i
$905$	22.9569	+	31.5975i	0.763113	+	1.05033i
$906$		0			0
$907$	−6.95828	−	21.4154i	−0.231046	−	0.711086i	−0.997621	−	0.0689320i	$-0.978041\pi$
$907$	−6.95828	−	21.4154i	−0.231046	−	0.711086i	0.766575	−	0.642154i	$-0.221959\pi$
$908$	6.79887	+	20.9248i	0.225628	+	0.694413i
$909$		0			0
$910$	−2.84165	−	3.91119i	−0.0941997	−	0.129655i
$911$	28.5483	+	9.27591i	0.945848	+	0.307325i	0.741027	−	0.671475i	$-0.234339\pi$
$911$	28.5483	+	9.27591i	0.945848	+	0.307325i	0.204821	+	0.978799i	$0.434339\pi$
$912$		0			0
$913$	−5.70956	+	13.7372i	−0.188959	+	0.454633i
$914$			20.0891i			0.664489i
$915$		0			0
$916$	4.45926	−	3.23984i	0.147338	−	0.107047i
$917$	−8.37587	+	11.5284i	−0.276596	+	0.380701i
$918$		0			0
$919$	3.18329	−	1.03431i	0.105007	−	0.0341188i	−0.256042	−	0.966666i	$-0.582419\pi$
$919$	3.18329	−	1.03431i	0.105007	−	0.0341188i	0.361049	+	0.932547i	$0.382419\pi$
$920$	−1.51473	−	1.10052i	−0.0499393	−	0.0362830i
$921$		0			0
$922$	−5.82733	+	17.9347i	−0.191913	+	0.590647i
$923$	12.4809			0.410814
$924$		0			0
$925$	−5.22729			−0.171872
$926$	0.0349486	−	0.107561i	0.00114848	−	0.00353466i
$927$		0			0
$928$	6.64433	+	4.82739i	0.218111	+	0.158467i
$929$	52.2370	−	16.9728i	1.71384	−	0.556861i	0.722875	−	0.690979i	$-0.242820\pi$
$929$	52.2370	−	16.9728i	1.71384	−	0.556861i	0.990965	+	0.134118i	$0.0428202\pi$
$930$		0			0
$931$	−1.99024	+	2.73933i	−0.0652274	+	0.0897778i
$932$	13.6889	−	9.94554i	0.448393	−	0.325777i
$933$		0			0
$934$		−	27.7909i		−	0.909344i
$935$	2.63974	−	33.0311i	0.0863287	−	1.08023i
$936$		0			0
$937$	−4.39734	−	1.42878i	−0.143655	−	0.0466763i	0.236307	−	0.971678i	$-0.424063\pi$
$937$	−4.39734	−	1.42878i	−0.143655	−	0.0466763i	−0.379962	+	0.925002i	$0.624063\pi$
$938$	−0.774948	−	1.06662i	−0.0253029	−	0.0348265i
$939$		0			0
$940$	2.88407	+	8.87626i	0.0940681	+	0.289512i
$941$	14.3549	+	44.1798i	0.467956	+	1.44022i	0.855226	+	0.518255i	$0.173418\pi$
$941$	14.3549	+	44.1798i	0.467956	+	1.44022i	−0.387270	+	0.921966i	$0.626582\pi$
$942$		0			0
$943$	−2.40364	−	3.30832i	−0.0782731	−	0.107734i
$944$	4.39617	+	1.42840i	0.143083	+	0.0464905i
$945$		0			0
$946$	5.64843	+	9.24243i	0.183646	+	0.300497i
$947$			17.4661i			0.567573i	0.958887	+	0.283786i	$0.0915907\pi$
$947$			17.4661i			0.567573i	−0.958887	+	0.283786i	$0.908409\pi$
$948$		0			0
$949$	−10.2841	+	7.47186i	−0.333837	+	0.242547i
$950$	2.66992	−	3.67483i	0.0866236	−	0.119227i
$951$		0			0
$952$	−4.96780	+	1.61414i	−0.161007	+	0.0523144i
$953$	−39.6043	−	28.7742i	−1.28291	−	0.932089i	−0.283274	−	0.959039i	$-0.591421\pi$
$953$	−39.6043	−	28.7742i	−1.28291	−	0.932089i	−0.999637	+	0.0269499i	$0.991421\pi$
$954$		0			0
$955$	−8.42764	+	25.9376i	−0.272712	+	0.839322i
$956$	−23.4171			−0.757363
$957$		0			0
$958$	11.0925			0.358381
$959$	−5.55197	+	17.0872i	−0.179282	+	0.551774i
$960$		0			0
$961$	3.78553	+	2.75035i	0.122114	+	0.0887209i
$962$	−9.36678	+	3.04345i	−0.301997	+	0.0981248i
$963$		0			0
$964$	16.6608	−	22.9316i	0.536607	−	0.738576i
$965$	−17.3465	+	12.6030i	−0.558403	+	0.405704i
$966$		0			0
$967$			61.6392i			1.98218i	0.133181	+	0.991092i	$0.457481\pi$
$967$			61.6392i			1.98218i	−0.133181	+	0.991092i	$0.542519\pi$
$968$	−7.75937	−	7.79694i	−0.249396	−	0.250603i
$969$		0			0
$970$	1.31357	+	0.426806i	0.0421763	+	0.0137039i
$971$	−11.9515	−	16.4498i	−0.383541	−	0.527899i	0.572977	−	0.819571i	$-0.305788\pi$
$971$	−11.9515	−	16.4498i	−0.383541	−	0.527899i	−0.956518	+	0.291672i	$0.905788\pi$
$972$		0			0
$973$	−5.00950	−	15.4176i	−0.160597	−	0.494267i
$974$	−3.59888	−	11.0762i	−0.115316	−	0.354905i
$975$		0			0
$976$	0.600051	+	0.825899i	0.0192072	+	0.0264364i
$977$	−47.7725	−	15.5222i	−1.52838	−	0.496600i	−0.580237	−	0.814448i	$-0.697040\pi$
$977$	−47.7725	−	15.5222i	−1.52838	−	0.496600i	−0.948142	+	0.317847i	$0.897040\pi$
$978$		0			0
$979$	−11.6845	+	13.6474i	−0.373439	+	0.436173i
$980$		−	1.91272i		−	0.0610996i
$981$		0			0
$982$	−7.33613	+	5.33001i	−0.234105	+	0.170087i
$983$	24.0749	−	33.1363i	0.767871	−	1.05688i	−0.228647	−	0.973509i	$-0.573430\pi$
$983$	24.0749	−	33.1363i	0.767871	−	1.05688i	0.996518	−	0.0833747i	$-0.0265698\pi$
$984$		0			0
$985$	−17.0845	+	5.55108i	−0.544356	+	0.176872i
$986$	34.7063	+	25.2156i	1.10528	+	0.803029i
$987$		0			0
$988$	2.64466	−	8.13941i	0.0841377	−	0.258949i
$989$	3.19691			0.101656
$990$		0			0
$991$	−30.2387			−0.960562			−0.480281	−	0.877115i	$-0.659465\pi$
$991$	−30.2387			−0.960562			−0.480281	+	0.877115i	$0.659465\pi$
$992$	−1.58538	+	4.87928i	−0.0503357	+	0.154917i
$993$		0			0
$994$	3.99487	+	2.90244i	0.126710	+	0.0920599i
$995$	7.51166	−	2.44069i	0.238136	−	0.0773750i
$996$		0			0
$997$	−31.8042	+	43.7748i	−1.00725	+	1.38636i	−0.0864805	+	0.996254i	$0.527562\pi$
$997$	−31.8042	+	43.7748i	−1.00725	+	1.38636i	−0.920769	+	0.390107i	$0.872438\pi$
$998$	31.3314	−	22.7636i	0.991777	−	0.720568i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bu.a.827.4	✓	48
3.2	odd	2		1386.2.bu.b.827.9	yes	48
11.6	odd	10		1386.2.bu.b.1205.9	yes	48
33.17	even	10	inner	1386.2.bu.a.1205.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bu.a.827.4	✓	48	1.1	even	1	trivial
1386.2.bu.a.1205.4	yes	48	33.17	even	10	inner
1386.2.bu.b.827.9	yes	48	3.2	odd	2
1386.2.bu.b.1205.9	yes	48	11.6	odd	10

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bu (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.81910 + 0.591063i) q^{5} +(0.587785 - 0.809017i) q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.81910 + 0.591063i) q^{5} +(0.587785 - 0.809017i) q^{7} +(-0.809017 + 0.587785i) q^{8} +1.91272i q^{10} +(2.51938 + 2.15702i) q^{11} +(-2.40385 - 0.781057i) q^{13} +(-0.587785 - 0.809017i) q^{14} +(0.309017 + 0.951057i) q^{16} +(1.61414 + 4.96780i) q^{17} +(-1.99024 - 2.73933i) q^{19} +(1.81910 + 0.591063i) q^{20} +(2.82998 - 1.72952i) q^{22} -0.978876i q^{23} +(-1.08530 + 0.788518i) q^{25} +(-1.48566 + 2.04483i) q^{26} +(-0.951057 + 0.309017i) q^{28} +(6.64433 + 4.82739i) q^{29} +(-1.58538 + 4.87928i) q^{31} +1.00000 q^{32} +5.22345 q^{34} +(-0.591063 + 1.81910i) q^{35} +(3.15240 + 2.29035i) q^{37} +(-3.22027 + 1.04633i) q^{38} +(1.12427 - 1.54742i) q^{40} +(3.37971 - 2.45550i) q^{41} +3.26590i q^{43} +(-0.770356 - 3.22592i) q^{44} +(-0.930967 - 0.302489i) q^{46} +(2.86808 + 3.94757i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(0.414549 + 1.27585i) q^{50} +(1.48566 + 2.04483i) q^{52} +(11.8470 + 3.84933i) q^{53} +(-5.85794 - 2.43473i) q^{55} +1.00000i q^{56} +(6.64433 - 4.82739i) q^{58} +(2.71698 - 3.73961i) q^{59} +(0.970903 - 0.315465i) q^{61} +(4.15057 + 3.01556i) q^{62} +(0.309017 - 0.951057i) q^{64} +4.83450 q^{65} +1.31842 q^{67} +(1.61414 - 4.96780i) q^{68} +(1.54742 + 1.12427i) q^{70} +(-4.69625 + 1.52590i) q^{71} +(2.95616 - 4.06881i) q^{73} +(3.15240 - 2.29035i) q^{74} +3.38599i q^{76} +(3.22592 - 0.770356i) q^{77} +(12.9644 + 4.21238i) q^{79} +(-1.12427 - 1.54742i) q^{80} +(-1.29093 - 3.97309i) q^{82} +(1.38607 + 4.26588i) q^{83} +(-5.87256 - 8.08288i) q^{85} +(3.10606 + 1.00922i) q^{86} +(-3.30608 - 0.264212i) q^{88} +5.41698i q^{89} +(-2.04483 + 1.48566i) q^{91} +(-0.575369 + 0.791928i) q^{92} +(4.64065 - 1.50784i) q^{94} +(5.23956 + 3.80676i) q^{95} +(0.223141 - 0.686757i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8}+O(q^{10}) \) 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8	\( 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8} + 4 q^{11} - 12 q^{16} + 24 q^{17} + 4 q^{22} + 24 q^{25} + 40 q^{26} - 16 q^{29} + 40 q^{31} + 48 q^{32} - 16 q^{34} - 12 q^{35} + 16 q^{37} - 40 q^{38} + 24 q^{41} + 4 q^{44} - 40 q^{46} - 40 q^{47} + 12 q^{49} + 4 q^{50} - 40 q^{52} - 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} - 40 q^{62} - 12 q^{64} + 48 q^{67} + 24 q^{68} + 8 q^{70} + 40 q^{73} + 16 q^{74} + 32 q^{77} + 40 q^{79} - 16 q^{82} - 16 q^{83} - 20 q^{85} + 4 q^{88} - 20 q^{92} - 52 q^{95} - 8 q^{97} - 48 q^{98}+O(q^{100}) \) 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8 + 4 * q^11 - 12 * q^16 + 24 * q^17 + 4 * q^22 + 24 * q^25 + 40 * q^26 - 16 * q^29 + 40 * q^31 + 48 * q^32 - 16 * q^34 - 12 * q^35 + 16 * q^37 - 40 * q^38 + 24 * q^41 + 4 * q^44 - 40 * q^46 - 40 * q^47 + 12 * q^49 + 4 * q^50 - 40 * q^52 - 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^64 + 48 * q^67 + 24 * q^68 + 8 * q^70 + 40 * q^73 + 16 * q^74 + 32 * q^77 + 40 * q^79 - 16 * q^82 - 16 * q^83 - 20 * q^85 + 4 * q^88 - 20 * q^92 - 52 * q^95 - 8 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more