LMFDB - Embedded newform 448.2.ba.c.81.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,2,Mod(81,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("448.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.ba (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			81.3
Character	$\chi$	$=$	448.81
Dual form			448.2.ba.c.177.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95279 + 0.523249i) q^{3} +(0.959072 + 0.256983i) q^{5} +(-0.292831 - 2.62950i) q^{7} +(0.941530 - 0.543593i) q^{9} +O(q^{10})$	\(q+(-1.95279 + 0.523249i) q^{3} +(0.959072 + 0.256983i) q^{5} +(-0.292831 - 2.62950i) q^{7} +(0.941530 - 0.543593i) q^{9} +(0.505816 + 1.88773i) q^{11} +(-2.10314 - 2.10314i) q^{13} -2.00733 q^{15} +(2.83885 - 4.91704i) q^{17} +(0.165210 - 0.616573i) q^{19} +(1.94772 + 4.98163i) q^{21} +(5.92691 - 3.42190i) q^{23} +(-3.47635 - 2.00707i) q^{25} +(2.73445 - 2.73445i) q^{27} +(-0.207295 - 0.207295i) q^{29} +(3.94693 - 6.83628i) q^{31} +(-1.97551 - 3.42168i) q^{33} +(0.394889 - 2.59713i) q^{35} +(9.60533 + 2.57374i) q^{37} +(5.20747 + 3.00653i) q^{39} -2.40202i q^{41} +(-3.65586 + 3.65586i) q^{43} +(1.04269 - 0.279388i) q^{45} +(0.144593 + 0.250442i) q^{47} +(-6.82850 + 1.53999i) q^{49} +(-2.97086 + 11.0874i) q^{51} +(-2.04376 - 7.62740i) q^{53} +1.94045i q^{55} +1.29048i q^{57} +(-3.60507 - 13.4543i) q^{59} +(-0.969174 + 3.61701i) q^{61} +(-1.70508 - 2.31657i) q^{63} +(-1.47659 - 2.55754i) q^{65} +(-10.0468 + 2.69202i) q^{67} +(-9.78352 + 9.78352i) q^{69} +11.5947i q^{71} +(-0.310772 - 0.179424i) q^{73} +(7.83878 + 2.10040i) q^{75} +(4.81566 - 1.88283i) q^{77} +(3.84953 + 6.66758i) q^{79} +(-5.53979 + 9.59520i) q^{81} +(0.424001 + 0.424001i) q^{83} +(3.98626 - 3.98626i) q^{85} +(0.513270 + 0.296337i) q^{87} +(-15.2323 + 8.79437i) q^{89} +(-4.91434 + 6.14607i) q^{91} +(-4.13045 + 15.4150i) q^{93} +(0.316897 - 0.548881i) q^{95} +12.2678 q^{97} +(1.50240 + 1.50240i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{5}+O(q^{10}) $ 48 * q + 4 * q^5	$ 48 q + 4 q^{5} + 4 q^{11} - 24 q^{13} + 40 q^{15} + 8 q^{17} + 4 q^{19} - 8 q^{21} + 24 q^{27} + 24 q^{29} - 28 q^{31} + 16 q^{33} - 28 q^{35} - 24 q^{37} + 40 q^{43} - 28 q^{45} + 20 q^{47} - 24 q^{51} - 16 q^{53} + 20 q^{59} + 8 q^{61} + 16 q^{63} + 8 q^{65} - 48 q^{67} - 40 q^{69} + 4 q^{75} - 20 q^{77} + 36 q^{79} + 8 q^{83} - 64 q^{91} + 8 q^{93} + 4 q^{95} - 48 q^{97} + 24 q^{99}+O(q^{100}) $ 48 * q + 4 * q^5 + 4 * q^11 - 24 * q^13 + 40 * q^15 + 8 * q^17 + 4 * q^19 - 8 * q^21 + 24 * q^27 + 24 * q^29 - 28 * q^31 + 16 * q^33 - 28 * q^35 - 24 * q^37 + 40 * q^43 - 28 * q^45 + 20 * q^47 - 24 * q^51 - 16 * q^53 + 20 * q^59 + 8 * q^61 + 16 * q^63 + 8 * q^65 - 48 * q^67 - 40 * q^69 + 4 * q^75 - 20 * q^77 + 36 * q^79 + 8 * q^83 - 64 * q^91 + 8 * q^93 + 4 * q^95 - 48 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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			0
$2$		0			0
$3$	−1.95279	+	0.523249i	−1.12744	+	0.302098i	−0.773893	−	0.633317i	$-0.781693\pi$
$3$	−1.95279	+	0.523249i	−1.12744	+	0.302098i	−0.353552	+	0.935415i	$0.615026\pi$
$4$		0			0
$5$	0.959072	+	0.256983i	0.428910	+	0.114926i	0.466814	−	0.884355i	$-0.345402\pi$
$5$	0.959072	+	0.256983i	0.428910	+	0.114926i	−0.0379045	+	0.999281i	$0.512068\pi$
$6$		0			0
$7$	−0.292831	−	2.62950i	−0.110680	−	0.993856i
$7$	−0.292831	−	2.62950i	−0.110680	−	0.993856i
$8$		0			0
$9$	0.941530	−	0.543593i	0.313843	−	0.181198i
$10$		0			0
$11$	0.505816	+	1.88773i	0.152509	+	0.569172i	0.999306	+	0.0372551i	$0.0118614\pi$
$11$	0.505816	+	1.88773i	0.152509	+	0.569172i	−0.846797	+	0.531917i	$0.821472\pi$
$12$		0			0
$13$	−2.10314	−	2.10314i	−0.583307	−	0.583307i	0.352504	−	0.935810i	$-0.385330\pi$
$13$	−2.10314	−	2.10314i	−0.583307	−	0.583307i	−0.935810	+	0.352504i	$0.885330\pi$
$14$		0			0
$15$	−2.00733			−0.518291
$16$		0			0
$17$	2.83885	−	4.91704i	0.688523	−	1.19256i	−0.283792	−	0.958886i	$-0.591593\pi$
$17$	2.83885	−	4.91704i	0.688523	−	1.19256i	0.972316	−	0.233672i	$-0.0750741\pi$
$18$		0			0
$19$	0.165210	−	0.616573i	0.0379018	−	0.141451i	−0.944382	−	0.328850i	$-0.893339\pi$
$19$	0.165210	−	0.616573i	0.0379018	−	0.141451i	0.982284	+	0.187399i	$0.0600056\pi$
$20$		0			0
$21$	1.94772	+	4.98163i	0.425027	+	1.08708i
$22$		0			0
$23$	5.92691	−	3.42190i	1.23585	−	0.713516i	0.267604	−	0.963529i	$-0.413768\pi$
$23$	5.92691	−	3.42190i	1.23585	−	0.713516i	0.968243	+	0.250013i	$0.0804348\pi$
$24$		0			0
$25$	−3.47635	−	2.00707i	−0.695270	−	0.401414i
$26$		0			0
$27$	2.73445	−	2.73445i	0.526245	−	0.526245i
$28$		0			0
$29$	−0.207295	−	0.207295i	−0.0384937	−	0.0384937i	0.687598	−	0.726092i	$-0.258665\pi$
$29$	−0.207295	−	0.207295i	−0.0384937	−	0.0384937i	−0.726092	+	0.687598i	$0.758665\pi$
$30$		0			0
$31$	3.94693	−	6.83628i	0.708889	−	1.22783i	−0.256381	−	0.966576i	$-0.582530\pi$
$31$	3.94693	−	6.83628i	0.708889	−	1.22783i	0.965270	−	0.261255i	$-0.0841365\pi$
$32$		0			0
$33$	−1.97551	−	3.42168i	−0.343891	−	0.595637i
$34$		0			0
$35$	0.394889	−	2.59713i	0.0667484	−	0.438995i
$36$		0			0
$37$	9.60533	+	2.57374i	1.57911	+	0.423120i	0.938649	−	0.344873i	$-0.112078\pi$
$37$	9.60533	+	2.57374i	1.57911	+	0.423120i	0.640457	+	0.767994i	$0.278745\pi$
$38$		0			0
$39$	5.20747	+	3.00653i	0.833862	+	0.481430i
$40$		0			0
$41$		−	2.40202i		−	0.375132i	−0.982252	−	0.187566i	$-0.939940\pi$
$41$		−	2.40202i		−	0.375132i	0.982252	−	0.187566i	$-0.0600599\pi$
$42$		0			0
$43$	−3.65586	+	3.65586i	−0.557514	+	0.557514i	−0.928599	−	0.371085i	$-0.878986\pi$
$43$	−3.65586	+	3.65586i	−0.557514	+	0.557514i	0.371085	+	0.928599i	$0.378986\pi$
$44$		0			0
$45$	1.04269	−	0.279388i	0.155435	−	0.0416486i
$46$		0			0
$47$	0.144593	+	0.250442i	0.0210910	+	0.0365307i	0.876378	−	0.481623i	$-0.159953\pi$
$47$	0.144593	+	0.250442i	0.0210910	+	0.0365307i	−0.855287	+	0.518154i	$0.826619\pi$
$48$		0			0
$49$	−6.82850	+	1.53999i	−0.975500	+	0.219999i
$50$		0			0
$51$	−2.97086	+	11.0874i	−0.416003	+	1.55254i
$52$		0			0
$53$	−2.04376	−	7.62740i	−0.280732	−	1.04770i	−0.951902	−	0.306402i	$-0.900875\pi$
$53$	−2.04376	−	7.62740i	−0.280732	−	1.04770i	0.671171	−	0.741303i	$-0.265792\pi$
$54$		0			0
$55$			1.94045i			0.261651i
$56$		0			0
$57$			1.29048i			0.170929i
$58$		0			0
$59$	−3.60507	−	13.4543i	−0.469340	−	1.75160i	−0.642084	−	0.766634i	$-0.721930\pi$
$59$	−3.60507	−	13.4543i	−0.469340	−	1.75160i	0.172744	−	0.984967i	$-0.444737\pi$
$60$		0			0
$61$	−0.969174	+	3.61701i	−0.124090	+	0.463110i	−0.999806	−	0.0197171i	$-0.993723\pi$
$61$	−0.969174	+	3.61701i	−0.124090	+	0.463110i	0.875716	+	0.482827i	$0.160390\pi$
$62$		0			0
$63$	−1.70508	−	2.31657i	−0.214820	−	0.291860i
$64$		0			0
$65$	−1.47659	−	2.55754i	−0.183149	−	0.317223i
$66$		0			0
$67$	−10.0468	+	2.69202i	−1.22741	+	0.328883i	−0.813570	−	0.581467i	$-0.802479\pi$
$67$	−10.0468	+	2.69202i	−1.22741	+	0.328883i	−0.413838	+	0.910350i	$0.635812\pi$
$68$		0			0
$69$	−9.78352	+	9.78352i	−1.17780	+	1.17780i
$70$		0			0
$71$			11.5947i			1.37603i	0.725695	+	0.688017i	$0.241518\pi$
$71$			11.5947i			1.37603i	−0.725695	+	0.688017i	$0.758482\pi$
$72$		0			0
$73$	−0.310772	−	0.179424i	−0.0363731	−	0.0210000i	0.481703	−	0.876334i	$-0.340018\pi$
$73$	−0.310772	−	0.179424i	−0.0363731	−	0.0210000i	−0.518076	+	0.855334i	$0.673352\pi$
$74$		0			0
$75$	7.83878	+	2.10040i	0.905145	+	0.242533i
$76$		0			0
$77$	4.81566	−	1.88283i	0.548795	−	0.214568i
$78$		0			0
$79$	3.84953	+	6.66758i	0.433106	+	0.750161i	0.997139	−	0.0755910i	$-0.0240843\pi$
$79$	3.84953	+	6.66758i	0.433106	+	0.750161i	−0.564033	+	0.825752i	$0.690751\pi$
$80$		0			0
$81$	−5.53979	+	9.59520i	−0.615532	+	1.06613i
$82$		0			0
$83$	0.424001	+	0.424001i	0.0465402	+	0.0465402i	0.729994	−	0.683454i	$-0.239523\pi$
$83$	0.424001	+	0.424001i	0.0465402	+	0.0465402i	−0.683454	+	0.729994i	$0.739523\pi$
$84$		0			0
$85$	3.98626	−	3.98626i	0.432371	−	0.432371i
$86$		0			0
$87$	0.513270	+	0.296337i	0.0550283	+	0.0317706i
$88$		0			0
$89$	−15.2323	+	8.79437i	−1.61462	+	0.932201i	−0.626340	+	0.779550i	$0.715448\pi$
$89$	−15.2323	+	8.79437i	−1.61462	+	0.932201i	−0.988280	+	0.152652i	$0.951219\pi$
$90$		0			0
$91$	−4.91434	+	6.14607i	−0.515163	+	0.644283i
$92$		0			0
$93$	−4.13045	+	15.4150i	−0.428308	+	1.59847i
$94$		0			0
$95$	0.316897	−	0.548881i	0.0325129	−	0.0563140i
$96$		0			0
$97$	12.2678			1.24560			0.622802	−	0.782379i	$-0.285994\pi$
$97$	12.2678			1.24560			0.622802	+	0.782379i	$0.285994\pi$
$98$		0			0
$99$	1.50240	+	1.50240i	0.150997	+	0.150997i
$100$		0			0
$101$	−0.313118	−	1.16857i	−0.0311564	−	0.116277i	0.948596	−	0.316488i	$-0.102504\pi$
$101$	−0.313118	−	1.16857i	−0.0311564	−	0.116277i	−0.979753	+	0.200211i	$0.935837\pi$
$102$		0			0
$103$	−5.06181	+	2.92244i	−0.498755	+	0.287956i	−0.728199	−	0.685365i	$-0.759643\pi$
$103$	−5.06181	+	2.92244i	−0.498755	+	0.287956i	0.229444	+	0.973322i	$0.426309\pi$
$104$		0			0
$105$	0.587809	+	5.27828i	0.0573643	+	0.515107i
$106$		0			0
$107$	−3.62492	−	0.971295i	−0.350435	−	0.0938987i	0.0793079	−	0.996850i	$-0.474729\pi$
$107$	−3.62492	−	0.971295i	−0.350435	−	0.0938987i	−0.429742	+	0.902952i	$0.641396\pi$
$108$		0			0
$109$	9.67656	−	2.59283i	0.926846	−	0.248348i	0.236337	−	0.971671i	$-0.424053\pi$
$109$	9.67656	−	2.59283i	0.926846	−	0.248348i	0.690509	+	0.723323i	$0.257386\pi$
$110$		0			0
$111$	−20.1039			−1.90818
$112$		0			0
$113$	5.07461			0.477379			0.238689	−	0.971096i	$-0.423282\pi$
$113$	5.07461			0.477379			0.238689	+	0.971096i	$0.423282\pi$
$114$		0			0
$115$	6.56370	−	1.75874i	0.612069	−	0.164003i
$116$		0			0
$117$	−3.12342	−	0.836919i	−0.288761	−	0.0773732i
$118$		0			0
$119$	−13.7606	−	6.02490i	−1.26144	−	0.552301i
$120$		0			0
$121$	6.21861	−	3.59031i	0.565328	−	0.326392i
$122$		0			0
$123$	1.25685	+	4.69064i	0.113327	+	0.422941i
$124$		0			0
$125$	−6.32873	−	6.32873i	−0.566059	−	0.566059i
$126$		0			0
$127$	11.1710			0.991270			0.495635	−	0.868531i	$-0.334935\pi$
$127$	11.1710			0.991270			0.495635	+	0.868531i	$0.334935\pi$
$128$		0			0
$129$	5.22621	−	9.05207i	0.460142	−	0.796990i
$130$		0			0
$131$	3.26332	−	12.1789i	0.285118	−	1.06407i	−0.663636	−	0.748056i	$-0.730988\pi$
$131$	3.26332	−	12.1789i	0.285118	−	1.06407i	0.948753	−	0.316017i	$-0.102346\pi$
$132$		0			0
$133$	−1.66965	−	0.253868i	−0.144777	−	0.0220131i
$134$		0			0
$135$	3.32524	−	1.91983i	0.286191	−	0.165233i
$136$		0			0
$137$	14.0325	+	8.10166i	1.19888	+	0.692172i	0.960305	−	0.278953i	$-0.0899874\pi$
$137$	14.0325	+	8.10166i	1.19888	+	0.692172i	0.238572	+	0.971125i	$0.423321\pi$
$138$		0			0
$139$	−10.5018	+	10.5018i	−0.890748	+	0.890748i	−0.994593	−	0.103846i	$-0.966885\pi$
$139$	−10.5018	+	10.5018i	−0.890748	+	0.890748i	0.103846	+	0.994593i	$0.466885\pi$
$140$		0			0
$141$	−0.413403	−	0.413403i	−0.0348148	−	0.0348148i
$142$		0			0
$143$	2.90636	−	5.03397i	0.243042	−	0.420961i
$144$		0			0
$145$	−0.145539	−	0.252082i	−0.0120864	−	0.0209342i
$146$		0			0
$147$	12.5288	−	6.58030i	1.03336	−	0.542734i
$148$		0			0
$149$	−9.61931	−	2.57749i	−0.788045	−	0.211156i	−0.157716	−	0.987484i	$-0.550413\pi$
$149$	−9.61931	−	2.57749i	−0.788045	−	0.211156i	−0.630329	+	0.776328i	$0.717080\pi$
$150$		0			0
$151$	−8.97638	−	5.18252i	−0.730487	−	0.421747i	0.0881130	−	0.996110i	$-0.471916\pi$
$151$	−8.97638	−	5.18252i	−0.730487	−	0.421747i	−0.818600	+	0.574363i	$0.805250\pi$
$152$		0			0
$153$		−	6.17272i		−	0.499035i
$154$		0			0
$155$	5.54219	−	5.54219i	0.445159	−	0.445159i
$156$		0			0
$157$	3.98512	−	1.06781i	0.318047	−	0.0852205i	−0.0962637	−	0.995356i	$-0.530689\pi$
$157$	3.98512	−	1.06781i	0.318047	−	0.0852205i	0.414311	+	0.910135i	$0.364023\pi$
$158$		0			0
$159$	7.98206	+	13.8253i	0.633019	+	1.09642i
$160$		0			0
$161$	−10.7335	−	14.5828i	−0.845916	−	1.14928i
$162$		0			0
$163$	−2.13899	+	7.98280i	−0.167538	+	0.625261i	0.830165	+	0.557518i	$0.188246\pi$
$163$	−2.13899	+	7.98280i	−0.167538	+	0.625261i	−0.997703	+	0.0677429i	$0.978420\pi$
$164$		0			0
$165$	−1.01534	−	3.78930i	−0.0790442	−	0.294997i
$166$		0			0
$167$		−	8.92669i		−	0.690768i	−0.938462	−	0.345384i	$-0.887749\pi$
$167$		−	8.92669i		−	0.690768i	0.938462	−	0.345384i	$-0.112251\pi$
$168$		0			0
$169$		−	4.15359i		−	0.319507i
$170$		0			0
$171$	−0.179614	−	0.670329i	−0.0137354	−	0.0512613i
$172$		0			0
$173$	1.41044	−	5.26383i	0.107234	−	0.400202i	−0.891355	−	0.453305i	$-0.850245\pi$
$173$	1.41044	−	5.26383i	0.107234	−	0.400202i	0.998589	+	0.0531037i	$0.0169114\pi$
$174$		0			0
$175$	−4.25960	+	9.72878i	−0.321996	+	0.735426i
$176$		0			0
$177$	14.0799	+	24.3871i	1.05831	+	1.83305i
$178$		0			0
$179$	9.42440	−	2.52526i	0.704413	−	0.188747i	0.111207	−	0.993797i	$-0.464528\pi$
$179$	9.42440	−	2.52526i	0.704413	−	0.188747i	0.593206	+	0.805050i	$0.297862\pi$
$180$		0			0
$181$	−8.42976	+	8.42976i	−0.626579	+	0.626579i	−0.947206	−	0.320627i	$-0.896106\pi$
$181$	−8.42976	+	8.42976i	−0.626579	+	0.626579i	0.320627	+	0.947206i	$0.396106\pi$
$182$		0			0
$183$		−	7.57038i		−	0.559619i
$184$		0			0
$185$	8.55080	+	4.93680i	0.628667	+	0.362961i
$186$		0			0
$187$	10.7180	+	2.87187i	0.783776	+	0.210012i
$188$		0			0
$189$	−7.99096	−	6.38950i	−0.581257	−	0.464767i
$190$		0			0
$191$	−2.46522	−	4.26989i	−0.178377	−	0.308958i	0.762948	−	0.646460i	$-0.223751\pi$
$191$	−2.46522	−	4.26989i	−0.178377	−	0.308958i	−0.941325	+	0.337502i	$0.890418\pi$
$192$		0			0
$193$	−10.9543	+	18.9735i	−0.788510	+	1.36574i	0.138370	+	0.990381i	$0.455814\pi$
$193$	−10.9543	+	18.9735i	−0.788510	+	1.36574i	−0.926880	+	0.375358i	$0.877520\pi$
$194$		0			0
$195$	4.22171	+	4.22171i	0.302323	+	0.302323i
$196$		0			0
$197$	7.61984	−	7.61984i	0.542891	−	0.542891i	−0.381484	−	0.924375i	$-0.624587\pi$
$197$	7.61984	−	7.61984i	0.542891	−	0.542891i	0.924375	+	0.381484i	$0.124587\pi$
$198$		0			0
$199$	3.09710	+	1.78811i	0.219547	+	0.126756i	0.605741	−	0.795662i	$-0.292877\pi$
$199$	3.09710	+	1.78811i	0.219547	+	0.126756i	−0.386193	+	0.922418i	$0.626210\pi$
$200$		0			0
$201$	18.2106	−	10.5139i	1.28448	−	0.741595i
$202$		0			0
$203$	−0.484378	+	0.605783i	−0.0339967	+	0.0425176i
$204$		0			0
$205$	0.617276	−	2.30371i	0.0431125	−	0.160898i
$206$		0			0
$207$	3.72024	−	6.44365i	0.258575	−	0.447865i
$208$		0			0
$209$	1.24749			0.0862906
$210$		0			0
$211$	−7.33737	−	7.33737i	−0.505126	−	0.505126i	0.407901	−	0.913026i	$-0.366261\pi$
$211$	−7.33737	−	7.33737i	−0.505126	−	0.505126i	−0.913026	+	0.407901i	$0.866261\pi$
$212$		0			0
$213$	−6.06690	−	22.6420i	−0.415697	−	1.55140i
$214$		0			0
$215$	−4.44573	+	2.56674i	−0.303196	+	0.175050i
$216$		0			0
$217$	−19.1317	−	8.37655i	−1.29875	−	0.568637i
$218$		0			0
$219$	0.700757	+	0.187767i	0.0473528	+	0.0126881i
$220$		0			0
$221$	−16.3117	+	4.37072i	−1.09725	+	0.294006i
$222$		0			0
$223$	−4.26037			−0.285295			−0.142648	−	0.989774i	$-0.545562\pi$
$223$	−4.26037			−0.285295			−0.142648	+	0.989774i	$0.545562\pi$
$224$		0			0
$225$	−4.36411			−0.290941
$226$		0			0
$227$	4.67340	−	1.25223i	0.310184	−	0.0831136i	−0.100369	−	0.994950i	$-0.532002\pi$
$227$	4.67340	−	1.25223i	0.310184	−	0.0831136i	0.410553	+	0.911837i	$0.365336\pi$
$228$		0			0
$229$	18.9490	+	5.07737i	1.25218	+	0.335522i	0.823180	−	0.567781i	$-0.192198\pi$
$229$	18.9490	+	5.07737i	1.25218	+	0.335522i	0.429005	+	0.903302i	$0.358864\pi$
$230$		0			0
$231$	−8.41879	+	6.19656i	−0.553916	+	0.407703i
$232$		0			0
$233$	4.38681	−	2.53273i	0.287390	−	0.165925i	−0.349374	−	0.936983i	$-0.613606\pi$
$233$	4.38681	−	2.53273i	0.287390	−	0.165925i	0.636764	+	0.771059i	$0.280273\pi$
$234$		0			0
$235$	0.0743155	+	0.277349i	0.00484781	+	0.0180923i
$236$		0			0
$237$	−11.0061	−	11.0061i	−0.714925	−	0.714925i
$238$		0			0
$239$	9.32494			0.603181			0.301590	−	0.953438i	$-0.402483\pi$
$239$	9.32494			0.603181			0.301590	+	0.953438i	$0.402483\pi$
$240$		0			0
$241$	−12.8663	+	22.2850i	−0.828789	+	1.43550i	0.0702006	+	0.997533i	$0.477636\pi$
$241$	−12.8663	+	22.2850i	−0.828789	+	1.43550i	−0.898989	+	0.437971i	$0.855697\pi$
$242$		0			0
$243$	2.79475	−	10.4301i	0.179283	−	0.669093i
$244$		0			0
$245$	−6.94477	−	0.277839i	−0.443685	−	0.0177505i
$246$		0			0
$247$	−1.64420	+	0.949280i	−0.104618	+	0.0604012i
$248$		0			0
$249$	−1.04984	−	0.606128i	−0.0665312	−	0.0384118i
$250$		0			0
$251$	3.64372	−	3.64372i	0.229990	−	0.229990i	−0.582699	−	0.812688i	$-0.698003\pi$
$251$	3.64372	−	3.64372i	0.229990	−	0.229990i	0.812688	+	0.582699i	$0.198003\pi$
$252$		0			0
$253$	9.45755	+	9.45755i	0.594591	+	0.594591i
$254$		0			0
$255$	−5.69853	+	9.87014i	−0.356856	+	0.618092i
$256$		0			0
$257$	1.87774	+	3.25234i	0.117130	+	0.202875i	0.918629	−	0.395121i	$-0.129297\pi$
$257$	1.87774	+	3.25234i	0.117130	+	0.202875i	−0.801499	+	0.597996i	$0.795964\pi$
$258$		0			0
$259$	3.95490	−	26.0108i	0.245746	−	1.61624i
$260$		0			0
$261$	−0.307858	−	0.0824903i	−0.0190559	−	0.00510602i
$262$		0			0
$263$	16.3252	+	9.42534i	1.00665	+	0.581191i	0.910210	−	0.414147i	$-0.135920\pi$
$263$	16.3252	+	9.42534i	1.00665	+	0.581191i	0.0964430	+	0.995339i	$0.469253\pi$
$264$		0			0
$265$		−	7.84044i		−	0.481634i
$266$		0			0
$267$	25.1439	−	25.1439i	1.53878	−	1.53878i
$268$		0			0
$269$	16.5643	−	4.43839i	1.00994	−	0.270614i	0.284338	−	0.958724i	$-0.408226\pi$
$269$	16.5643	−	4.43839i	1.00994	−	0.270614i	0.725606	+	0.688111i	$0.241560\pi$
$270$		0			0
$271$	2.65608	+	4.60046i	0.161345	+	0.279458i	0.935351	−	0.353720i	$-0.115083\pi$
$271$	2.65608	+	4.60046i	0.161345	+	0.279458i	−0.774006	+	0.633178i	$0.781750\pi$
$272$		0			0
$273$	6.38076	−	14.5734i	0.386181	−	0.882023i
$274$		0			0
$275$	2.03042	−	7.57761i	0.122439	−	0.456947i
$276$		0			0
$277$	−3.93434	−	14.6832i	−0.236392	−	0.882226i	−0.977517	−	0.210859i	$-0.932374\pi$
$277$	−3.93434	−	14.6832i	−0.236392	−	0.882226i	0.741125	−	0.671367i	$-0.234293\pi$
$278$		0			0
$279$		−	8.58208i		−	0.513795i
$280$		0			0
$281$			3.15786i			0.188382i	0.995554	+	0.0941910i	$0.0300264\pi$
$281$			3.15786i			0.188382i	−0.995554	+	0.0941910i	$0.969974\pi$
$282$		0			0
$283$	3.65368	+	13.6357i	0.217189	+	0.810559i	0.985385	+	0.170344i	$0.0544879\pi$
$283$	3.65368	+	13.6357i	0.217189	+	0.810559i	−0.768196	+	0.640215i	$0.778845\pi$
$284$		0			0
$285$	−0.331632	+	1.23767i	−0.0196442	+	0.0733131i
$286$		0			0
$287$	−6.31609	+	0.703385i	−0.372827	+	0.0415195i
$288$		0			0
$289$	−7.61819	−	13.1951i	−0.448129	−	0.776182i
$290$		0			0
$291$	−23.9564	+	6.41911i	−1.40435	+	0.376295i
$292$		0			0
$293$	−10.9335	+	10.9335i	−0.638743	+	0.638743i	−0.950245	−	0.311502i	$-0.899168\pi$
$293$	−10.9335	+	10.9335i	−0.638743	+	0.638743i	0.311502	+	0.950245i	$0.399168\pi$
$294$		0			0
$295$		−	13.8301i		−	0.805219i
$296$		0			0
$297$	6.54503	+	3.77878i	0.379781	+	0.219267i
$298$		0			0
$299$	−19.6619	−	5.26839i	−1.13708	−	0.304679i
$300$		0			0
$301$	10.6836	+	8.54253i	0.615794	+	0.492383i
$302$		0			0
$303$	1.22291	+	2.11814i	0.0702543	+	0.121684i
$304$		0			0
$305$	−1.85902	+	3.21991i	−0.106447	+	0.184371i
$306$		0			0
$307$	14.7735	+	14.7735i	0.843170	+	0.843170i	0.989270	−	0.146100i	$-0.0466721\pi$
$307$	14.7735	+	14.7735i	0.843170	+	0.843170i	−0.146100	+	0.989270i	$0.546672\pi$
$308$		0			0
$309$	8.35550	−	8.35550i	0.475328	−	0.475328i
$310$		0			0
$311$	7.56549	+	4.36794i	0.429000	+	0.247683i	0.698920	−	0.715199i	$-0.253664\pi$
$311$	7.56549	+	4.36794i	0.429000	+	0.247683i	−0.269921	+	0.962883i	$0.586998\pi$
$312$		0			0
$313$	3.56615	−	2.05892i	0.201571	−	0.116377i	−0.395817	−	0.918329i	$-0.629539\pi$
$313$	3.56615	−	2.05892i	0.201571	−	0.116377i	0.597388	+	0.801952i	$0.296205\pi$
$314$		0			0
$315$	−1.03998	−	2.65993i	−0.0585962	−	0.149870i
$316$		0			0
$317$	6.32257	−	23.5962i	0.355111	−	1.32529i	−0.525234	−	0.850958i	$-0.676022\pi$
$317$	6.32257	−	23.5962i	0.355111	−	1.32529i	0.880345	−	0.474335i	$-0.157311\pi$
$318$		0			0
$319$	0.286463	−	0.496169i	0.0160389	−	0.0277801i
$320$		0			0
$321$	7.58695			0.423462
$322$		0			0
$323$	−2.56271	−	2.56271i	−0.142593	−	0.142593i
$324$		0			0
$325$	3.09010	+	11.5324i	0.171408	+	0.639703i
$326$		0			0
$327$	−17.5396	+	10.1265i	−0.969943	+	0.559997i
$328$		0			0
$329$	0.616194	−	0.453543i	0.0339719	−	0.0250046i
$330$		0			0
$331$	7.05503	+	1.89039i	0.387780	+	0.103905i	0.447441	−	0.894313i	$-0.352335\pi$
$331$	7.05503	+	1.89039i	0.387780	+	0.103905i	−0.0596615	+	0.998219i	$0.519002\pi$
$332$		0			0
$333$	10.4428	−	2.79813i	0.572260	−	0.153337i
$334$		0			0
$335$	−10.3274			−0.564245
$336$		0			0
$337$	−9.53985			−0.519669			−0.259834	−	0.965653i	$-0.583668\pi$
$337$	−9.53985			−0.519669			−0.259834	+	0.965653i	$0.583668\pi$
$338$		0			0
$339$	−9.90965	+	2.65528i	−0.538218	+	0.144215i
$340$		0			0
$341$	14.9015	+	3.99283i	0.806959	+	0.216224i
$342$		0			0
$343$	6.04901	+	17.5046i	0.326616	+	0.945157i
$344$		0			0
$345$	−11.8973	+	6.86890i	−0.640528	+	0.369809i
$346$		0			0
$347$	−2.36483	−	8.82567i	−0.126951	−	0.473787i	0.872951	−	0.487808i	$-0.162203\pi$
$347$	−2.36483	−	8.82567i	−0.126951	−	0.473787i	−0.999902	+	0.0140212i	$0.995537\pi$
$348$		0			0
$349$	24.4862	+	24.4862i	1.31072	+	1.31072i	0.920887	+	0.389831i	$0.127467\pi$
$349$	24.4862	+	24.4862i	1.31072	+	1.31072i	0.389831	+	0.920887i	$0.372533\pi$
$350$		0			0
$351$	−11.5019			−0.613925
$352$		0			0
$353$	13.0352	−	22.5776i	0.693793	−	1.20168i	−0.276793	−	0.960930i	$-0.589272\pi$
$353$	13.0352	−	22.5776i	0.693793	−	1.20168i	0.970586	−	0.240755i	$-0.0773950\pi$
$354$		0			0
$355$	−2.97963	+	11.1201i	−0.158142	+	0.590194i
$356$		0			0
$357$	30.0242	+	4.56513i	1.58905	+	0.241612i
$358$		0			0
$359$	3.01740	−	1.74210i	0.159252	−	0.0919443i	−0.418256	−	0.908329i	$-0.637358\pi$
$359$	3.01740	−	1.74210i	0.159252	−	0.0919443i	0.577508	+	0.816385i	$0.304025\pi$
$360$		0			0
$361$	16.1016	+	9.29627i	0.847453	+	0.489277i
$362$		0			0
$363$	−10.2650	+	10.2650i	−0.538773	+	0.538773i
$364$		0			0
$365$	−0.251944	−	0.251944i	−0.0131873	−	0.0131873i
$366$		0			0
$367$	12.2280	−	21.1796i	0.638298	−	1.10556i	−0.347508	−	0.937677i	$-0.612972\pi$
$367$	12.2280	−	21.1796i	0.638298	−	1.10556i	0.985806	−	0.167888i	$-0.0536946\pi$
$368$		0			0
$369$	−1.30572	−	2.26157i	−0.0679730	−	0.117733i
$370$		0			0
$371$	−19.4578	+	7.60759i	−1.01020	+	0.394966i
$372$		0			0
$373$	−35.4993	−	9.51200i	−1.83808	−	0.492513i	−0.839385	−	0.543537i	$-0.817085\pi$
$373$	−35.4993	−	9.51200i	−1.83808	−	0.492513i	−0.998697	+	0.0510246i	$0.983751\pi$
$374$		0			0
$375$	15.6702	+	9.04719i	0.809206	+	0.467195i
$376$		0			0
$377$			0.871940i			0.0449072i
$378$		0			0
$379$	−18.5183	+	18.5183i	−0.951222	+	0.951222i	−0.998864	−	0.0476420i	$-0.984829\pi$
$379$	−18.5183	+	18.5183i	−0.951222	+	0.951222i	0.0476420	+	0.998864i	$0.484829\pi$
$380$		0			0
$381$	−21.8147	+	5.84524i	−1.11760	+	0.299461i
$382$		0			0
$383$	−7.89785	−	13.6795i	−0.403562	−	0.698989i	0.590591	−	0.806971i	$-0.298895\pi$
$383$	−7.89785	−	13.6795i	−0.403562	−	0.698989i	−0.994153	+	0.107982i	$0.965561\pi$
$384$		0			0
$385$	5.10242	−	0.568225i	0.260043	−	0.0289594i
$386$		0			0
$387$	−1.45480	+	5.42940i	−0.0739519	+	0.275992i
$388$		0			0
$389$	1.47562	+	5.50707i	0.0748167	+	0.279220i	0.993192	−	0.116492i	$-0.0371648\pi$
$389$	1.47562	+	5.50707i	0.0748167	+	0.279220i	−0.918375	+	0.395711i	$0.870498\pi$
$390$		0			0
$391$		−	38.8572i		−	1.96509i
$392$		0			0
$393$			25.4903i			1.28582i
$394$		0			0
$395$	1.97852	+	7.38395i	0.0995503	+	0.371527i
$396$		0			0
$397$	0.260427	−	0.971927i	0.0130705	−	0.0487796i	−0.959083	−	0.283126i	$-0.908628\pi$
$397$	0.260427	−	0.971927i	0.0130705	−	0.0487796i	0.972153	+	0.234347i	$0.0752951\pi$
$398$		0			0
$399$	3.39332	−	0.377894i	0.169879	−	0.0189183i
$400$		0			0
$401$	8.70318	+	15.0744i	0.434616	+	0.752777i	0.997264	−	0.0739192i	$-0.0235507\pi$
$401$	8.70318	+	15.0744i	0.434616	+	0.752777i	−0.562648	+	0.826697i	$0.690217\pi$
$402$		0			0
$403$	−22.6786	+	6.07671i	−1.12970	+	0.302703i
$404$		0			0
$405$	−7.77886	+	7.77886i	−0.386535	+	0.386535i
$406$		0			0
$407$			19.4341i			0.963313i
$408$		0			0
$409$	−33.0605	−	19.0875i	−1.63474	−	0.943815i	−0.982605	−	0.185709i	$-0.940542\pi$
$409$	−33.0605	−	19.0875i	−1.63474	−	0.943815i	−0.652131	−	0.758106i	$-0.726125\pi$
$410$		0			0
$411$	−31.6417	−	8.47837i	−1.56077	−	0.418207i
$412$		0			0
$413$	−34.3224	+	13.4194i	−1.68889	+	0.660323i
$414$		0			0
$415$	0.297687	+	0.515608i	0.0146129	+	0.0253102i
$416$		0			0
$417$	15.0127	−	26.0028i	0.735176	−	1.27336i
$418$		0			0
$419$	27.0004	+	27.0004i	1.31905	+	1.31905i	0.914525	+	0.404529i	$0.132565\pi$
$419$	27.0004	+	27.0004i	1.31905	+	1.31905i	0.404529	+	0.914525i	$0.367435\pi$
$420$		0			0
$421$	−19.1472	+	19.1472i	−0.933175	+	0.933175i	−0.997903	−	0.0647277i	$-0.979382\pi$
$421$	−19.1472	+	19.1472i	−0.933175	+	0.933175i	0.0647277	+	0.997903i	$0.479382\pi$
$422$		0			0
$423$	0.272276	+	0.157199i	0.0132385	+	0.00764327i
$424$		0			0
$425$	−19.7377	+	11.3956i	−0.957419	+	0.552766i
$426$		0			0
$427$	9.79471	+	1.48927i	0.473999	+	0.0720708i
$428$		0			0
$429$	−3.04150	+	11.3510i	−0.146845	+	0.548033i
$430$		0			0
$431$	0.628555	−	1.08869i	0.0302764	−	0.0524403i	−0.850490	−	0.525991i	$-0.823695\pi$
$431$	0.628555	−	1.08869i	0.0302764	−	0.0524403i	0.880767	+	0.473551i	$0.157028\pi$
$432$		0			0
$433$	−9.16885			−0.440627			−0.220313	−	0.975429i	$-0.570708\pi$
$433$	−9.16885			−0.440627			−0.220313	+	0.975429i	$0.570708\pi$
$434$		0			0
$435$	0.416110	+	0.416110i	0.0199509	+	0.0199509i
$436$		0			0
$437$	−1.13067	−	4.21971i	−0.0540871	−	0.201856i
$438$		0			0
$439$	6.89864	−	3.98293i	0.329254	−	0.190095i	−0.326256	−	0.945282i	$-0.605787\pi$
$439$	6.89864	−	3.98293i	0.329254	−	0.190095i	0.655510	+	0.755187i	$0.272454\pi$
$440$		0			0
$441$	−5.59211	+	5.16187i	−0.266291	+	0.245803i
$442$		0			0
$443$	24.1691	+	6.47610i	1.14831	+	0.307689i	0.782288	−	0.622918i	$-0.214053\pi$
$443$	24.1691	+	6.47610i	1.14831	+	0.307689i	0.366022	+	0.930606i	$0.380719\pi$
$444$		0			0
$445$	−16.8689	+	4.52000i	−0.799661	+	0.214269i
$446$		0			0
$447$	20.1332			0.952267
$448$		0			0
$449$	−8.33038			−0.393135			−0.196567	−	0.980490i	$-0.562979\pi$
$449$	−8.33038			−0.393135			−0.196567	+	0.980490i	$0.562979\pi$
$450$		0			0
$451$	4.53436	−	1.21498i	0.213515	−	0.0572111i
$452$		0			0
$453$	20.2407	+	5.42349i	0.950993	+	0.254818i
$454$		0			0
$455$	−6.29264	+	4.63162i	−0.295003	+	0.217134i
$456$		0			0
$457$	−12.5338	+	7.23641i	−0.586308	+	0.338505i	−0.763636	−	0.645647i	$-0.776588\pi$
$457$	−12.5338	+	7.23641i	−0.586308	+	0.338505i	0.177328	+	0.984152i	$0.443255\pi$
$458$		0			0
$459$	−5.68270	−	21.2081i	−0.265246	−	0.989910i
$460$		0			0
$461$	−4.23021	−	4.23021i	−0.197020	−	0.197020i	0.601701	−	0.798721i	$-0.294490\pi$
$461$	−4.23021	−	4.23021i	−0.197020	−	0.197020i	−0.798721	+	0.601701i	$0.794490\pi$
$462$		0			0
$463$	25.1987			1.17108			0.585542	−	0.810642i	$-0.300882\pi$
$463$	25.1987			1.17108			0.585542	+	0.810642i	$0.300882\pi$
$464$		0			0
$465$	−7.92280	+	13.7227i	−0.367411	+	0.636374i
$466$		0			0
$467$	−3.97667	+	14.8411i	−0.184018	+	0.686766i	0.810820	+	0.585295i	$0.199021\pi$
$467$	−3.97667	+	14.8411i	−0.184018	+	0.686766i	−0.994839	+	0.101470i	$0.967645\pi$
$468$		0			0
$469$	10.0207	+	25.6296i	0.462711	+	1.18347i
$470$		0			0
$471$	−7.22338	+	4.17042i	−0.332836	+	0.192163i
$472$		0			0
$473$	−8.75047	−	5.05209i	−0.402347	−	0.232295i
$474$		0			0
$475$	−1.81183	+	1.81183i	−0.0831326	+	0.0831326i
$476$		0			0
$477$	−6.07046	−	6.07046i	−0.277947	−	0.277947i
$478$		0			0
$479$	−10.4147	+	18.0387i	−0.475859	+	0.824211i	−0.999618	−	0.0276553i	$-0.991196\pi$
$479$	−10.4147	+	18.0387i	−0.475859	+	0.824211i	0.523759	+	0.851867i	$0.324529\pi$
$480$		0			0
$481$	−14.7884	−	25.6143i	−0.674294	−	1.16791i
$482$		0			0
$483$	28.5906	+	22.8608i	1.30092	+	1.04020i
$484$		0			0
$485$	11.7657	+	3.15261i	0.534252	+	0.143152i
$486$		0			0
$487$	0.192631	+	0.111216i	0.00872895	+	0.00503966i	0.504358	−	0.863495i	$-0.331729\pi$
$487$	0.192631	+	0.111216i	0.00872895	+	0.00503966i	−0.495629	+	0.868534i	$0.665062\pi$
$488$		0			0
$489$		−	16.7080i		−	0.755561i
$490$		0			0
$491$	−18.1586	+	18.1586i	−0.819486	+	0.819486i	−0.986033	−	0.166547i	$-0.946738\pi$
$491$	−18.1586	+	18.1586i	−0.819486	+	0.819486i	0.166547	+	0.986033i	$0.446738\pi$
$492$		0			0
$493$	−1.60776	+	0.430797i	−0.0724097	+	0.0194021i
$494$		0			0
$495$	1.05482	+	1.82700i	0.0474105	+	0.0821173i
$496$		0			0
$497$	30.4881	−	3.39527i	1.36758	−	0.152299i
$498$		0			0
$499$	−0.908747	+	3.39149i	−0.0406811	+	0.151824i	−0.983279	−	0.182107i	$-0.941708\pi$
$499$	−0.908747	+	3.39149i	−0.0406811	+	0.151824i	0.942598	+	0.333930i	$0.108375\pi$
$500$		0			0
$501$	4.67088	+	17.4320i	0.208680	+	0.778802i
$502$		0			0
$503$		−	7.65278i		−	0.341220i	−0.985339	−	0.170610i	$-0.945426\pi$
$503$		−	7.65278i		−	0.341220i	0.985339	−	0.170610i	$-0.0545739\pi$
$504$		0			0
$505$		−	1.20121i		−	0.0534532i
$506$		0			0
$507$	2.17336	+	8.11109i	0.0965223	+	0.360226i
$508$		0			0
$509$	−8.27238	+	30.8730i	−0.366667	+	1.36842i	0.498480	+	0.866901i	$0.333892\pi$
$509$	−8.27238	+	30.8730i	−0.366667	+	1.36842i	−0.865147	+	0.501519i	$0.832775\pi$
$510$		0			0
$511$	−0.380792	+	0.869715i	−0.0168452	+	0.0384739i
$512$		0			0
$513$	−1.23423	−	2.13775i	−0.0544925	−	0.0943838i
$514$		0			0
$515$	−5.60566	+	1.50203i	−0.247015	+	0.0661874i
$516$		0			0
$517$	−0.399629	+	0.399629i	−0.0175757	+	0.0175757i
$518$		0			0
$519$			11.0172i			0.483600i
$520$		0			0
$521$	2.39816	+	1.38458i	0.105065	+	0.0606595i	0.551612	−	0.834101i	$-0.314013\pi$
$521$	2.39816	+	1.38458i	0.105065	+	0.0606595i	−0.446547	+	0.894760i	$0.647346\pi$
$522$		0			0
$523$	21.3583	+	5.72293i	0.933932	+	0.250246i	0.693530	−	0.720427i	$-0.256054\pi$
$523$	21.3583	+	5.72293i	0.933932	+	0.250246i	0.240401	+	0.970674i	$0.422721\pi$
$524$		0			0
$525$	3.22754	−	21.2271i	0.140862	−	0.926427i
$526$		0			0
$527$	−22.4095	−	38.8144i	−0.976173	−	1.69078i
$528$		0			0
$529$	11.9189	−	20.6441i	0.518211	−	0.897568i
$530$		0			0
$531$	−10.7079	−	10.7079i	−0.464685	−	0.464685i
$532$		0			0
$533$	−5.05178	+	5.05178i	−0.218817	+	0.218817i
$534$		0			0
$535$	−3.22696	−	1.86308i	−0.139513	−	0.0805481i
$536$		0			0
$537$	−17.0826	+	9.86262i	−0.737167	+	0.425603i
$538$		0			0
$539$	−6.36106	−	12.1114i	−0.273990	−	0.521675i
$540$		0			0
$541$	8.64497	−	32.2635i	0.371676	−	1.38711i	−0.486465	−	0.873700i	$-0.661714\pi$
$541$	8.64497	−	32.2635i	0.371676	−	1.38711i	0.858141	−	0.513414i	$-0.171619\pi$
$542$		0			0
$543$	12.0507	−	20.8724i	0.517145	−	0.895721i
$544$		0			0
$545$	9.94683			0.426075
$546$		0			0
$547$	−3.45137	−	3.45137i	−0.147570	−	0.147570i	0.629462	−	0.777032i	$-0.283276\pi$
$547$	−3.45137	−	3.45137i	−0.147570	−	0.147570i	−0.777032	+	0.629462i	$0.783276\pi$
$548$		0			0
$549$	1.05367	+	3.93236i	0.0449696	+	0.167829i
$550$		0			0
$551$	−0.162059	+	0.0935651i	−0.00690396	+	0.00398601i
$552$		0			0
$553$	16.4051	−	12.0748i	0.697616	−	0.513472i
$554$		0			0
$555$	−19.2811	−	5.16636i	−0.818437	−	0.219300i
$556$		0			0
$557$	21.3055	−	5.70879i	0.902742	−	0.241889i	0.222549	−	0.974922i	$-0.428562\pi$
$557$	21.3055	−	5.70879i	0.902742	−	0.241889i	0.680194	+	0.733032i	$0.261896\pi$
$558$		0			0
$559$	15.3776			0.650403
$560$		0			0
$561$	−22.4327			−0.947109
$562$		0			0
$563$	−26.6690	+	7.14593i	−1.12396	+	0.301165i	−0.772486	−	0.635031i	$-0.780987\pi$
$563$	−26.6690	+	7.14593i	−1.12396	+	0.301165i	−0.351477	+	0.936196i	$0.614321\pi$
$564$		0			0
$565$	4.86691	+	1.30408i	0.204752	+	0.0548633i
$566$		0			0
$567$	26.8528	+	11.7571i	1.12771	+	0.493751i
$568$		0			0
$569$	30.3657	−	17.5317i	1.27300	−	0.734965i	0.297446	−	0.954739i	$-0.403865\pi$
$569$	30.3657	−	17.5317i	1.27300	−	0.734965i	0.975551	+	0.219773i	$0.0705318\pi$
$570$		0			0
$571$	0.334280	+	1.24755i	0.0139892	+	0.0522083i	0.972568	−	0.232620i	$-0.0747300\pi$
$571$	0.334280	+	1.24755i	0.0139892	+	0.0522083i	−0.958578	+	0.284829i	$0.908063\pi$
$572$		0			0
$573$	7.04827	+	7.04827i	0.294446	+	0.294446i
$574$		0			0
$575$	−27.4720			−1.14566
$576$		0			0
$577$	−7.66470	+	13.2757i	−0.319086	+	0.552673i	−0.980298	−	0.197527i	$-0.936709\pi$
$577$	−7.66470	+	13.2757i	−0.319086	+	0.552673i	0.661212	+	0.750199i	$0.270042\pi$
$578$		0			0
$579$	11.4637	−	42.7830i	0.476414	−	1.77800i
$580$		0			0
$581$	0.990749	−	1.23907i	0.0411032	−	0.0514053i
$582$		0			0
$583$	13.3647	−	7.71612i	0.553510	−	0.319569i
$584$		0			0
$585$	−2.78051	−	1.60533i	−0.114960	−	0.0663722i
$586$		0			0
$587$	27.8270	−	27.8270i	1.14854	−	1.14854i	0.161702	−	0.986840i	$-0.448302\pi$
$587$	27.8270	−	27.8270i	1.14854	−	1.14854i	0.986840	−	0.161702i	$-0.0516982\pi$
$588$		0			0
$589$	−3.56299	−	3.56299i	−0.146810	−	0.146810i
$590$		0			0
$591$	−10.8929	+	18.8670i	−0.448074	+	0.776087i
$592$		0			0
$593$	−8.89810	−	15.4120i	−0.365401	−	0.632894i	0.623439	−	0.781872i	$-0.285735\pi$
$593$	−8.89810	−	15.4120i	−0.365401	−	0.632894i	−0.988840	+	0.148978i	$0.952402\pi$
$594$		0			0
$595$	−11.6492	−	9.31455i	−0.477569	−	0.381859i
$596$		0			0
$597$	−6.98361	−	1.87125i	−0.285820	−	0.0765853i
$598$		0			0
$599$	16.6221	+	9.59676i	0.679159	+	0.392113i	0.799538	−	0.600615i	$-0.205078\pi$
$599$	16.6221	+	9.59676i	0.679159	+	0.392113i	−0.120379	+	0.992728i	$0.538411\pi$
$600$		0			0
$601$			26.9530i			1.09944i	0.835351	+	0.549718i	$0.185265\pi$
$601$			26.9530i			1.09944i	−0.835351	+	0.549718i	$0.814735\pi$
$602$		0			0
$603$	−7.99597	+	7.99597i	−0.325621	+	0.325621i
$604$		0			0
$605$	6.88674	−	1.84530i	0.279986	−	0.0750219i
$606$		0			0
$607$	−14.7276	−	25.5089i	−0.597773	−	1.03537i	−0.993149	−	0.116854i	$-0.962719\pi$
$607$	−14.7276	−	25.5089i	−0.597773	−	1.03537i	0.395376	−	0.918519i	$-0.370614\pi$
$608$		0			0
$609$	0.628915	−	1.43642i	0.0254849	−	0.0582066i
$610$		0			0
$611$	0.222616	−	0.830813i	0.00900607	−	0.0336111i
$612$		0			0
$613$	−6.46001	−	24.1091i	−0.260917	−	0.973756i	−0.964702	−	0.263343i	$-0.915175\pi$
$613$	−6.46001	−	24.1091i	−0.260917	−	0.973756i	0.703785	−	0.710413i	$-0.251492\pi$
$614$		0			0
$615$			4.82165i			0.194428i
$616$		0			0
$617$		−	10.8407i		−	0.436431i	−0.975901	−	0.218216i	$-0.929976\pi$
$617$		−	10.8407i		−	0.436431i	0.975901	−	0.218216i	$-0.0700236\pi$
$618$		0			0
$619$	−5.19721	−	19.3962i	−0.208893	−	0.779601i	−0.988227	−	0.152992i	$-0.951109\pi$
$619$	−5.19721	−	19.3962i	−0.208893	−	0.779601i	0.779334	−	0.626609i	$-0.215558\pi$
$620$		0			0
$621$	6.84982	−	25.5639i	0.274874	−	1.02584i
$622$		0			0
$623$	27.5853	+	37.4780i	1.10518	+	1.50152i
$624$		0			0
$625$	5.59202	+	9.68566i	0.223681	+	0.387426i
$626$		0			0
$627$	−2.43609	+	0.652747i	−0.0972879	+	0.0260682i
$628$		0			0
$629$	39.9233	−	39.9233i	1.59185	−	1.59185i
$630$		0			0
$631$		−	5.71697i		−	0.227589i	−0.993504	−	0.113794i	$-0.963699\pi$
$631$		−	5.71697i		−	0.227589i	0.993504	−	0.113794i	$-0.0363005\pi$
$632$		0			0
$633$	18.1676	+	10.4891i	0.722099	+	0.416904i
$634$		0			0
$635$	10.7138	+	2.87076i	0.425166	+	0.113923i
$636$		0			0
$637$	17.6001	+	11.1225i	0.697343	+	0.440689i
$638$		0			0
$639$	6.30277	+	10.9167i	0.249334	+	0.431859i
$640$		0			0
$641$	−14.8475	+	25.7166i	−0.586441	+	1.01575i	0.408253	+	0.912869i	$0.366138\pi$
$641$	−14.8475	+	25.7166i	−0.586441	+	1.01575i	−0.994694	+	0.102877i	$0.967195\pi$
$642$		0			0
$643$	−3.53512	−	3.53512i	−0.139412	−	0.139412i	0.633957	−	0.773368i	$-0.281430\pi$
$643$	−3.53512	−	3.53512i	−0.139412	−	0.139412i	−0.773368	+	0.633957i	$0.781430\pi$
$644$		0			0
$645$	7.33854	−	7.33854i	0.288955	−	0.288955i
$646$		0			0
$647$	−12.7788	−	7.37782i	−0.502385	−	0.290052i	0.227313	−	0.973822i	$-0.427006\pi$
$647$	−12.7788	−	7.37782i	−0.502385	−	0.290052i	−0.729698	+	0.683770i	$0.760339\pi$
$648$		0			0
$649$	23.5746	−	13.6108i	0.925384	−	0.534270i
$650$		0			0
$651$	41.7433	+	6.34700i	1.63605	+	0.248759i
$652$		0			0
$653$	−2.56350	+	9.56710i	−0.100317	+	0.374390i	−0.997772	−	0.0667174i	$-0.978747\pi$
$653$	−2.56350	+	9.56710i	−0.100317	+	0.374390i	0.897455	+	0.441107i	$0.145414\pi$
$654$		0			0
$655$	6.25952	−	10.8418i	0.244580	−	0.423624i
$656$		0			0
$657$	−0.390135			−0.0152206
$658$		0			0
$659$	−5.68205	−	5.68205i	−0.221341	−	0.221341i	0.587722	−	0.809063i	$-0.300025\pi$
$659$	−5.68205	−	5.68205i	−0.221341	−	0.221341i	−0.809063	+	0.587722i	$0.800025\pi$
$660$		0			0
$661$	−2.48266	−	9.26542i	−0.0965643	−	0.360383i	0.900688	−	0.434467i	$-0.143063\pi$
$661$	−2.48266	−	9.26542i	−0.0965643	−	0.360383i	−0.997252	+	0.0740843i	$0.976397\pi$
$662$		0			0
$663$	29.5665	−	17.0702i	1.14827	−	0.662952i
$664$		0			0
$665$	−1.53608	−	0.672550i	−0.0595666	−	0.0260804i
$666$		0			0
$667$	−1.93796	−	0.519275i	−0.0750381	−	0.0201064i
$668$		0			0
$669$	8.31961	−	2.22923i	0.321655	−	0.0861871i
$670$		0			0
$671$	−7.31815			−0.282514
$672$		0			0
$673$	3.24280			0.125001			0.0625004	−	0.998045i	$-0.480093\pi$
$673$	3.24280			0.125001			0.0625004	+	0.998045i	$0.480093\pi$
$674$		0			0
$675$	−14.9941	+	4.01767i	−0.577125	+	0.154640i
$676$		0			0
$677$	−32.3879	−	8.67832i	−1.24477	−	0.333535i	−0.424455	−	0.905449i	$-0.639534\pi$
$677$	−32.3879	−	8.67832i	−1.24477	−	0.333535i	−0.820314	+	0.571914i	$0.806201\pi$
$678$		0			0
$679$	−3.59239	−	32.2581i	−0.137863	−	1.23795i
$680$		0			0
$681$	−8.47094	+	4.89070i	−0.324607	+	0.187412i
$682$		0			0
$683$	−4.81432	−	17.9673i	−0.184215	−	0.687499i	−0.994797	−	0.101874i	$-0.967516\pi$
$683$	−4.81432	−	17.9673i	−0.184215	−	0.687499i	0.810583	−	0.585624i	$-0.199151\pi$
$684$		0			0
$685$	11.3762	+	11.3762i	0.434662	+	0.434662i
$686$		0			0
$687$	−39.6602			−1.51313
$688$		0			0
$689$	−11.7432	+	20.3398i	−0.447380	+	0.774886i
$690$		0			0
$691$	−5.60826	+	20.9303i	−0.213348	+	0.796227i	0.773393	+	0.633927i	$0.218558\pi$
$691$	−5.60826	+	20.9303i	−0.213348	+	0.796227i	−0.986741	+	0.162300i	$0.948109\pi$
$692$		0			0
$693$	3.51060	−	4.39049i	0.133357	−	0.166781i
$694$		0			0
$695$	−12.7707	+	7.37317i	−0.484421	+	0.279680i
$696$		0			0
$697$	−11.8108	−	6.81898i	−0.447367	−	0.258287i
$698$		0			0
$699$	−7.24128	+	7.24128i	−0.273891	+	0.273891i
$700$		0			0
$701$	4.96023	+	4.96023i	0.187345	+	0.187345i	0.794547	−	0.607202i	$-0.207708\pi$
$701$	4.96023	+	4.96023i	0.187345	+	0.187345i	−0.607202	+	0.794547i	$0.707708\pi$
$702$		0			0
$703$	3.17380	−	5.49718i	0.119702	−	0.207330i
$704$		0			0
$705$	−0.290246	−	0.502720i	−0.0109313	−	0.0189335i
$706$		0			0
$707$	−2.98107	+	1.16554i	−0.112115	+	0.0438345i
$708$		0			0
$709$	13.9774	+	3.74523i	0.524932	+	0.140655i	0.511547	−	0.859255i	$-0.329073\pi$
$709$	13.9774	+	3.74523i	0.524932	+	0.140655i	0.0133851	+	0.999910i	$0.495739\pi$
$710$		0			0
$711$	7.24889	+	4.18515i	0.271855	+	0.156955i
$712$		0			0
$713$		−	54.0240i		−	2.02321i
$714$		0			0
$715$	4.08105	−	4.08105i	0.152623	−	0.152623i
$716$		0			0
$717$	−18.2097	+	4.87927i	−0.680053	+	0.182220i
$718$		0			0
$719$	16.5646	+	28.6908i	0.617756	+	1.06998i	0.989894	+	0.141808i	$0.0452914\pi$
$719$	16.5646	+	28.6908i	0.617756	+	1.06998i	−0.372138	+	0.928177i	$0.621375\pi$
$720$		0			0
$721$	9.16680	+	12.4542i	0.341389	+	0.463820i
$722$		0			0
$723$	13.4645	−	50.2502i	0.500751	−	1.86883i
$724$		0			0
$725$	0.304573	+	1.13668i	0.0113116	+	0.0422154i
$726$		0			0
$727$			23.5496i			0.873406i	0.899606	+	0.436703i	$0.143854\pi$
$727$			23.5496i			0.873406i	−0.899606	+	0.436703i	$0.856146\pi$
$728$		0			0
$729$		−	11.4085i		−	0.422538i
$730$		0			0
$731$	7.59756	+	28.3545i	0.281006	+	1.04873i
$732$		0			0
$733$	0.462947	−	1.72774i	0.0170993	−	0.0638156i	−0.956849	−	0.290586i	$-0.906150\pi$
$733$	0.462947	−	1.72774i	0.0170993	−	0.0638156i	0.973948	+	0.226770i	$0.0728166\pi$
$734$		0			0
$735$	13.7071	−	3.09128i	0.505593	−	0.114024i
$736$		0			0
$737$	−10.1636	−	17.6039i	−0.374382	−	0.648448i
$738$		0			0
$739$	22.6228	−	6.06175i	0.832192	−	0.222985i	0.182522	−	0.983202i	$-0.441574\pi$
$739$	22.6228	−	6.06175i	0.832192	−	0.222985i	0.649670	+	0.760217i	$0.274907\pi$
$740$		0			0
$741$	2.71407	−	2.71407i	0.0997039	−	0.0997039i
$742$		0			0
$743$		−	13.9219i		−	0.510747i	−0.966843	−	0.255373i	$-0.917802\pi$
$743$		−	13.9219i		−	0.510747i	0.966843	−	0.255373i	$-0.0821984\pi$
$744$		0			0
$745$	−8.56324	−	4.94399i	−0.313733	−	0.181134i
$746$		0			0
$747$	0.629693	+	0.168726i	0.0230393	+	0.00617336i
$748$		0			0
$749$	−1.49253	+	9.81615i	−0.0545358	+	0.358674i
$750$		0			0
$751$	−4.53854	−	7.86098i	−0.165614	−	0.286851i	0.771259	−	0.636521i	$-0.219627\pi$
$751$	−4.53854	−	7.86098i	−0.165614	−	0.286851i	−0.936873	+	0.349670i	$0.886294\pi$
$752$		0			0
$753$	−5.20885	+	9.02200i	−0.189821	+	0.328780i
$754$		0			0
$755$	−7.27718	−	7.27718i	−0.264844	−	0.264844i
$756$		0			0
$757$	−1.14043	+	1.14043i	−0.0414496	+	0.0414496i	−0.727528	−	0.686078i	$-0.759331\pi$
$757$	−1.14043	+	1.14043i	−0.0414496	+	0.0414496i	0.686078	+	0.727528i	$0.259331\pi$
$758$		0			0
$759$	−23.4173	−	13.5200i	−0.849994	−	0.490744i
$760$		0			0
$761$	−7.60476	+	4.39061i	−0.275672	+	0.159159i	−0.631463	−	0.775406i	$-0.717545\pi$
$761$	−7.60476	+	4.39061i	−0.275672	+	0.159159i	0.355790	+	0.934566i	$0.384212\pi$
$762$		0			0
$763$	−9.65142	−	24.6852i	−0.349405	−	0.893665i
$764$		0			0
$765$	1.58628	−	5.92008i	0.0573521	−	0.214041i
$766$		0			0
$767$	−20.7143	+	35.8783i	−0.747951	+	1.29549i
$768$		0			0
$769$	29.8204			1.07535			0.537676	−	0.843152i	$-0.319303\pi$
$769$	29.8204			1.07535			0.537676	+	0.843152i	$0.319303\pi$
$770$		0			0
$771$	−5.36862	−	5.36862i	−0.193346	−	0.193346i
$772$		0			0
$773$	11.9365	+	44.5476i	0.429326	+	1.60227i	0.754291	+	0.656540i	$0.227981\pi$
$773$	11.9365	+	44.5476i	0.429326	+	1.60227i	−0.324965	+	0.945726i	$0.605352\pi$
$774$		0			0
$775$	−27.4418	+	15.8435i	−0.985738	+	0.569116i
$776$		0			0
$777$	5.88705	+	52.8632i	0.211197	+	1.89646i
$778$		0			0
$779$	−1.48102	−	0.396838i	−0.0530630	−	0.0142182i
$780$		0			0
$781$	−21.8876	+	5.86476i	−0.783199	+	0.209858i
$782$		0			0
$783$	−1.13367			−0.0405142
$784$		0			0
$785$	4.09643			0.146208
$786$		0			0
$787$	25.3091	−	6.78154i	0.902170	−	0.241736i	0.222222	−	0.974996i	$-0.428669\pi$
$787$	25.3091	−	6.78154i	0.902170	−	0.241736i	0.679948	+	0.733260i	$0.262002\pi$
$788$		0			0
$789$	−36.8115	−	9.86360i	−1.31052	−	0.351153i
$790$		0			0
$791$	−1.48600	−	13.3437i	−0.0528361	−	0.474446i
$792$		0			0
$793$	9.64539	−	5.56877i	0.342518	−	0.197753i
$794$		0			0
$795$	4.10250	+	15.3107i	0.145501	+	0.543016i
$796$		0			0
$797$	−16.7419	−	16.7419i	−0.593028	−	0.593028i	0.345420	−	0.938448i	$-0.387736\pi$
$797$	−16.7419	−	16.7419i	−0.593028	−	0.593028i	−0.938448	+	0.345420i	$0.887736\pi$
$798$		0			0
$799$	1.64191			0.0580866
$800$		0			0
$801$	−9.56111	+	16.5603i	−0.337825	+	0.585130i
$802$		0			0
$803$	0.181511	−	0.677409i	0.00640540	−	0.0239053i
$804$		0			0
$805$	−6.54665	−	16.7442i	−0.230739	−	0.590156i
$806$		0			0
$807$	−30.0243	+	17.3345i	−1.05690	+	0.610204i
$808$		0			0
$809$	30.7720	+	17.7662i	1.08189	+	0.624628i	0.931405	−	0.363985i	$-0.118584\pi$
$809$	30.7720	+	17.7662i	1.08189	+	0.624628i	0.150482	+	0.988613i	$0.451917\pi$
$810$		0			0
$811$	−29.5602	+	29.5602i	−1.03800	+	1.03800i	−0.0387507	+	0.999249i	$0.512338\pi$
$811$	−29.5602	+	29.5602i	−1.03800	+	1.03800i	−0.999249	+	0.0387507i	$0.987662\pi$
$812$		0			0
$813$	−7.59395	−	7.59395i	−0.266331	−	0.266331i
$814$		0			0
$815$	−4.10288	+	7.10640i	−0.143718	+	0.248926i
$816$		0			0
$817$	1.65012	+	2.85809i	0.0577304	+	0.0999920i
$818$		0			0
$819$	−1.28604	+	8.45811i	−0.0449379	+	0.295550i
$820$		0			0
$821$	−7.63653	−	2.04620i	−0.266517	−	0.0714129i	0.123086	−	0.992396i	$-0.460721\pi$
$821$	−7.63653	−	2.04620i	−0.266517	−	0.0714129i	−0.389602	+	0.920983i	$0.627388\pi$
$822$		0			0
$823$	−43.2107	−	24.9477i	−1.50623	−	0.869623i	−0.999974	−	0.00724096i	$-0.997695\pi$
$823$	−43.2107	−	24.9477i	−1.50623	−	0.869623i	−0.506258	−	0.862382i	$-0.668972\pi$
$824$		0			0
$825$			15.8599i			0.552171i
$826$		0			0
$827$	8.11672	−	8.11672i	0.282246	−	0.282246i	−0.551758	−	0.834004i	$-0.686043\pi$
$827$	8.11672	−	8.11672i	0.282246	−	0.282246i	0.834004	+	0.551758i	$0.186043\pi$
$828$		0			0
$829$	6.87035	−	1.84091i	0.238617	−	0.0639373i	−0.137528	−	0.990498i	$-0.543916\pi$
$829$	6.87035	−	1.84091i	0.238617	−	0.0639373i	0.376146	+	0.926561i	$0.377249\pi$
$830$		0			0
$831$	15.3659	+	26.6145i	0.533037	+	0.923248i
$832$		0			0
$833$	−11.8129	+	37.9478i	−0.409293	+	1.31481i
$834$		0			0
$835$	2.29400	−	8.56133i	0.0793872	−	0.296277i
$836$		0			0
$837$	−7.90079	−	29.4861i	−0.273091	−	1.01919i
$838$		0			0
$839$		−	3.57060i		−	0.123271i	−0.998099	−	0.0616354i	$-0.980368\pi$
$839$		−	3.57060i		−	0.123271i	0.998099	−	0.0616354i	$-0.0196316\pi$
$840$		0			0
$841$		−	28.9141i		−	0.997036i
$842$		0			0
$843$	−1.65235	−	6.16664i	−0.0569098	−	0.212390i
$844$		0			0
$845$	1.06740	−	3.98359i	0.0367197	−	0.137040i
$846$		0			0
$847$	−11.2617	−	15.3004i	−0.386957	−	0.525730i
$848$		0			0
$849$	−14.2697	−	24.7159i	−0.489736	−	0.848248i
$850$		0			0
$851$	65.7370	−	17.6142i	2.25344	−	0.603806i
$852$		0			0
$853$	13.8958	−	13.8958i	0.475784	−	0.475784i	−0.427996	−	0.903780i	$-0.640780\pi$
$853$	13.8958	−	13.8958i	0.475784	−	0.475784i	0.903780	+	0.427996i	$0.140780\pi$
$854$		0			0
$855$		−	0.689051i		−	0.0235650i
$856$		0			0
$857$	34.8241	+	20.1057i	1.18957	+	0.686798i	0.958209	−	0.286070i	$-0.0923490\pi$
$857$	34.8241	+	20.1057i	1.18957	+	0.686798i	0.231360	+	0.972868i	$0.425682\pi$
$858$		0			0
$859$	25.0429	+	6.71022i	0.854452	+	0.228950i	0.659353	−	0.751834i	$-0.270830\pi$
$859$	25.0429	+	6.71022i	0.854452	+	0.228950i	0.195099	+	0.980784i	$0.437497\pi$
$860$		0			0
$861$	11.9660	−	4.67845i	0.407799	−	0.159441i
$862$		0			0
$863$	8.22908	+	14.2532i	0.280121	+	0.485184i	0.971414	−	0.237390i	$-0.0762920\pi$
$863$	8.22908	+	14.2532i	0.280121	+	0.485184i	−0.691293	+	0.722574i	$0.742959\pi$
$864$		0			0
$865$	2.70543	−	4.68593i	0.0919872	−	0.159327i
$866$		0			0
$867$	21.7811	+	21.7811i	0.739724	+	0.739724i
$868$		0			0
$869$	−10.6394	+	10.6394i	−0.360918	+	0.360918i
$870$		0			0
$871$	26.7915	+	15.4681i	0.907795	+	0.524116i
$872$		0			0
$873$	11.5505	−	6.66868i	0.390925	−	0.225700i
$874$		0			0
$875$	−14.7881	+	18.4946i	−0.499930	+	0.625232i
$876$		0			0
$877$	5.90884	−	22.0521i	0.199527	−	0.744646i	−0.791521	−	0.611142i	$-0.790710\pi$
$877$	5.90884	−	22.0521i	0.199527	−	0.744646i	0.991048	−	0.133504i	$-0.0426228\pi$
$878$		0			0
$879$	15.6299	−	27.0718i	0.527185	−	0.913111i
$880$		0			0
$881$	5.29761			0.178481			0.0892405	−	0.996010i	$-0.471556\pi$
$881$	5.29761			0.178481			0.0892405	+	0.996010i	$0.471556\pi$
$882$		0			0
$883$	30.7426	+	30.7426i	1.03457	+	1.03457i	0.999381	+	0.0351900i	$0.0112036\pi$
$883$	30.7426	+	30.7426i	1.03457	+	1.03457i	0.0351900	+	0.999381i	$0.488796\pi$
$884$		0			0
$885$	7.23658	+	27.0073i	0.243255	+	0.907840i
$886$		0			0
$887$	−5.04199	+	2.91100i	−0.169294	+	0.0977417i	−0.582253	−	0.813008i	$-0.697829\pi$
$887$	−5.04199	+	2.91100i	−0.169294	+	0.0977417i	0.412959	+	0.910750i	$0.364495\pi$
$888$		0			0
$889$	−3.27123	−	29.3742i	−0.109713	−	0.985180i
$890$		0			0
$891$	−20.9153	−	5.60423i	−0.700688	−	0.187749i
$892$		0			0
$893$	0.178304	−	0.0477763i	0.00596671	−	0.00159877i
$894$		0			0
$895$	9.68763			0.323822
$896$		0			0
$897$	41.1522			1.37403
$898$		0			0
$899$	−2.23530	+	0.598947i	−0.0745514	+	0.0199760i
$900$		0			0
$901$	−43.3062	−	11.6039i	−1.44274	−	0.386581i
$902$		0			0
$903$	−25.3328	−	11.0916i	−0.843022	−	0.369105i
$904$		0			0
$905$	−10.2510	+	5.91844i	−0.340756	+	0.196736i
$906$		0			0
$907$	5.44791	+	20.3319i	0.180895	+	0.675108i	0.995472	+	0.0950536i	$0.0303022\pi$
$907$	5.44791	+	20.3319i	0.180895	+	0.675108i	−0.814577	+	0.580055i	$0.803031\pi$
$908$		0			0
$909$	−0.930037	−	0.930037i	−0.0308474	−	0.0308474i
$910$		0			0
$911$	46.3231			1.53475			0.767376	−	0.641197i	$-0.221562\pi$
$911$	46.3231			1.53475			0.767376	+	0.641197i	$0.221562\pi$
$912$		0			0
$913$	−0.585933	+	1.01487i	−0.0193916	+	0.0335872i
$914$		0			0
$915$	1.94546	−	7.26054i	0.0643148	−	0.240026i
$916$		0			0
$917$	−32.9799	−	5.01454i	−1.08909	−	0.165595i
$918$		0			0
$919$	−12.8775	+	7.43484i	−0.424790	+	0.245253i	−0.697125	−	0.716950i	$-0.745538\pi$
$919$	−12.8775	+	7.43484i	−0.424790	+	0.245253i	0.272335	+	0.962203i	$0.412204\pi$
$920$		0			0
$921$	−36.5799	−	21.1194i	−1.20535	−	0.695908i
$922$		0			0
$923$	24.3852	−	24.3852i	0.802649	−	0.802649i
$924$		0			0
$925$	−28.2258	−	28.2258i	−0.928058	−	0.928058i
$926$		0			0
$927$	−3.17723	+	5.50313i	−0.104354	+	0.180746i
$928$		0			0
$929$	25.8504	+	44.7742i	0.848124	+	1.46899i	0.882881	+	0.469598i	$0.155601\pi$
$929$	25.8504	+	44.7742i	0.848124	+	1.46899i	−0.0347569	+	0.999396i	$0.511066\pi$
$930$		0			0
$931$	−0.178619	+	4.46469i	−0.00585399	+	0.146324i
$932$		0			0
$933$	−17.0593	−	4.57104i	−0.558498	−	0.149649i
$934$		0			0
$935$	9.54129	+	5.50867i	0.312034	+	0.180153i
$936$		0			0
$937$			50.1408i			1.63803i	0.573773	+	0.819014i	$0.305479\pi$
$937$			50.1408i			1.63803i	−0.573773	+	0.819014i	$0.694521\pi$
$938$		0			0
$939$	−5.88663	+	5.88663i	−0.192103	+	0.192103i
$940$		0			0
$941$	−43.3123	+	11.6055i	−1.41194	+	0.378328i	−0.882617	−	0.470093i	$-0.844220\pi$
$941$	−43.3123	+	11.6055i	−1.41194	+	0.378328i	−0.529322	+	0.848421i	$0.677554\pi$
$942$		0			0
$943$	−8.21947	−	14.2365i	−0.267663	−	0.463606i
$944$		0			0
$945$	−6.02192	−	8.18152i	−0.195893	−	0.266145i
$946$		0			0
$947$	−0.427149	+	1.59414i	−0.0138805	+	0.0518027i	−0.972519	−	0.232825i	$-0.925203\pi$
$947$	−0.427149	+	1.59414i	−0.0138805	+	0.0518027i	0.958638	+	0.284627i	$0.0918698\pi$
$948$		0			0
$949$	0.276243	+	1.03095i	0.00896723	+	0.0334661i
$950$		0			0
$951$			49.3867i			1.60147i
$952$		0			0
$953$			40.9510i			1.32653i	0.748384	+	0.663266i	$0.230830\pi$
$953$			40.9510i			1.32653i	−0.748384	+	0.663266i	$0.769170\pi$
$954$		0			0
$955$	−1.26704	−	4.72865i	−0.0410003	−	0.153015i
$956$		0			0
$957$	−0.299783	+	1.11881i	−0.00969062	+	0.0361659i
$958$		0			0
$959$	17.1941	−	39.2708i	0.555228	−	1.26812i
$960$		0			0
$961$	−15.6564	−	27.1177i	−0.505046	−	0.874766i
$962$		0			0
$963$	−3.94096	+	1.05598i	−0.126996	+	0.0340284i
$964$		0			0
$965$	−15.3818	+	15.3818i	−0.495159	+	0.495159i
$966$		0			0
$967$			14.6315i			0.470518i	0.971933	+	0.235259i	$0.0755938\pi$
$967$			14.6315i			0.470518i	−0.971933	+	0.235259i	$0.924406\pi$
$968$		0			0
$969$	6.34536	+	3.66350i	0.203842	+	0.117688i
$970$		0			0
$971$	23.5944	+	6.32211i	0.757181	+	0.202886i	0.616701	−	0.787197i	$-0.288469\pi$
$971$	23.5944	+	6.32211i	0.757181	+	0.202886i	0.140480	+	0.990084i	$0.455135\pi$
$972$		0			0
$973$	30.6896	+	24.5391i	0.983863	+	0.786687i
$974$		0			0
$975$	−12.0686	−	20.9035i	−0.386506	−	0.669448i
$976$		0			0
$977$	2.85781	−	4.94988i	0.0914295	−	0.158361i	−0.816683	−	0.577086i	$-0.804190\pi$
$977$	2.85781	−	4.94988i	0.0914295	−	0.158361i	0.908113	+	0.418725i	$0.137523\pi$
$978$		0			0
$979$	−24.3061	−	24.3061i	−0.776827	−	0.776827i
$980$		0			0
$981$	7.70133	−	7.70133i	0.245885	−	0.245885i
$982$		0			0
$983$	−18.6714	−	10.7799i	−0.595525	−	0.343827i	0.171754	−	0.985140i	$-0.445057\pi$
$983$	−18.6714	−	10.7799i	−0.595525	−	0.343827i	−0.767279	+	0.641313i	$0.778390\pi$
$984$		0			0
$985$	9.26615	−	5.34981i	0.295244	−	0.170459i
$986$		0			0
$987$	−0.965983	+	1.20810i	−0.0307476	+	0.0384542i
$988$		0			0
$989$	−9.15796	+	34.1780i	−0.291206	+	1.08680i
$990$		0			0
$991$	−17.3811	+	30.1049i	−0.552128	+	0.956314i	0.445993	+	0.895037i	$0.352851\pi$
$991$	−17.3811	+	30.1049i	−0.552128	+	0.956314i	−0.998121	+	0.0612772i	$0.980483\pi$
$992$		0			0
$993$	−14.7661			−0.468590
$994$		0			0
$995$	2.51082	+	2.51082i	0.0795985	+	0.0795985i
$996$		0			0
$997$	1.32792	+	4.95586i	0.0420556	+	0.156954i	0.983760	−	0.179487i	$-0.0574436\pi$
$997$	1.32792	+	4.95586i	0.0420556	+	0.156954i	−0.941705	+	0.336440i	$0.890777\pi$
$998$		0			0
$999$	33.3031	−	19.2275i	1.05366	−	0.608332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.ba.c.81.3		48
4.3	odd	2		112.2.w.c.109.3	yes	48
7.2	even	3	inner	448.2.ba.c.401.10		48
8.3	odd	2		896.2.ba.f.417.3		48
8.5	even	2		896.2.ba.e.417.10		48
16.3	odd	4		896.2.ba.f.865.10		48
16.5	even	4	inner	448.2.ba.c.305.10		48
16.11	odd	4		112.2.w.c.53.7	yes	48
16.13	even	4		896.2.ba.e.865.3		48
28.3	even	6		784.2.m.k.589.10		24
28.11	odd	6		784.2.m.j.589.10		24
28.19	even	6		784.2.x.o.765.7		48
28.23	odd	6		112.2.w.c.93.7	yes	48
28.27	even	2		784.2.x.o.557.3		48
56.37	even	6		896.2.ba.e.289.3		48
56.51	odd	6		896.2.ba.f.289.10		48
112.11	odd	12		784.2.m.j.197.10		24
112.27	even	4		784.2.x.o.165.7		48
112.37	even	12	inner	448.2.ba.c.177.3		48
112.51	odd	12		896.2.ba.f.737.3		48
112.59	even	12		784.2.m.k.197.10		24
112.75	even	12		784.2.x.o.373.3		48
112.93	even	12		896.2.ba.e.737.10		48
112.107	odd	12		112.2.w.c.37.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.3	✓	48	112.107	odd	12
112.2.w.c.53.7	yes	48	16.11	odd	4
112.2.w.c.93.7	yes	48	28.23	odd	6
112.2.w.c.109.3	yes	48	4.3	odd	2
448.2.ba.c.81.3		48	1.1	even	1	trivial
448.2.ba.c.177.3		48	112.37	even	12	inner
448.2.ba.c.305.10		48	16.5	even	4	inner
448.2.ba.c.401.10		48	7.2	even	3	inner
784.2.m.j.197.10		24	112.11	odd	12
784.2.m.j.589.10		24	28.11	odd	6
784.2.m.k.197.10		24	112.59	even	12
784.2.m.k.589.10		24	28.3	even	6
784.2.x.o.165.7		48	112.27	even	4
784.2.x.o.373.3		48	112.75	even	12
784.2.x.o.557.3		48	28.27	even	2
784.2.x.o.765.7		48	28.19	even	6
896.2.ba.e.289.3		48	56.37	even	6
896.2.ba.e.417.10		48	8.5	even	2
896.2.ba.e.737.10		48	112.93	even	12
896.2.ba.e.865.3		48	16.13	even	4
896.2.ba.f.289.10		48	56.51	odd	6
896.2.ba.f.417.3		48	8.3	odd	2
896.2.ba.f.737.3		48	112.51	odd	12
896.2.ba.f.865.10		48	16.3	odd	4

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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.ba (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.95279 + 0.523249i) q^{3} +(0.959072 + 0.256983i) q^{5} +(-0.292831 - 2.62950i) q^{7} +(0.941530 - 0.543593i) q^{9} +O(q^{10})\)	\(q+(-1.95279 + 0.523249i) q^{3} +(0.959072 + 0.256983i) q^{5} +(-0.292831 - 2.62950i) q^{7} +(0.941530 - 0.543593i) q^{9} +(0.505816 + 1.88773i) q^{11} +(-2.10314 - 2.10314i) q^{13} -2.00733 q^{15} +(2.83885 - 4.91704i) q^{17} +(0.165210 - 0.616573i) q^{19} +(1.94772 + 4.98163i) q^{21} +(5.92691 - 3.42190i) q^{23} +(-3.47635 - 2.00707i) q^{25} +(2.73445 - 2.73445i) q^{27} +(-0.207295 - 0.207295i) q^{29} +(3.94693 - 6.83628i) q^{31} +(-1.97551 - 3.42168i) q^{33} +(0.394889 - 2.59713i) q^{35} +(9.60533 + 2.57374i) q^{37} +(5.20747 + 3.00653i) q^{39} -2.40202i q^{41} +(-3.65586 + 3.65586i) q^{43} +(1.04269 - 0.279388i) q^{45} +(0.144593 + 0.250442i) q^{47} +(-6.82850 + 1.53999i) q^{49} +(-2.97086 + 11.0874i) q^{51} +(-2.04376 - 7.62740i) q^{53} +1.94045i q^{55} +1.29048i q^{57} +(-3.60507 - 13.4543i) q^{59} +(-0.969174 + 3.61701i) q^{61} +(-1.70508 - 2.31657i) q^{63} +(-1.47659 - 2.55754i) q^{65} +(-10.0468 + 2.69202i) q^{67} +(-9.78352 + 9.78352i) q^{69} +11.5947i q^{71} +(-0.310772 - 0.179424i) q^{73} +(7.83878 + 2.10040i) q^{75} +(4.81566 - 1.88283i) q^{77} +(3.84953 + 6.66758i) q^{79} +(-5.53979 + 9.59520i) q^{81} +(0.424001 + 0.424001i) q^{83} +(3.98626 - 3.98626i) q^{85} +(0.513270 + 0.296337i) q^{87} +(-15.2323 + 8.79437i) q^{89} +(-4.91434 + 6.14607i) q^{91} +(-4.13045 + 15.4150i) q^{93} +(0.316897 - 0.548881i) q^{95} +12.2678 q^{97} +(1.50240 + 1.50240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{5}+O(q^{10}) \) 48 * q + 4 * q^5	\( 48 q + 4 q^{5} + 4 q^{11} - 24 q^{13} + 40 q^{15} + 8 q^{17} + 4 q^{19} - 8 q^{21} + 24 q^{27} + 24 q^{29} - 28 q^{31} + 16 q^{33} - 28 q^{35} - 24 q^{37} + 40 q^{43} - 28 q^{45} + 20 q^{47} - 24 q^{51} - 16 q^{53} + 20 q^{59} + 8 q^{61} + 16 q^{63} + 8 q^{65} - 48 q^{67} - 40 q^{69} + 4 q^{75} - 20 q^{77} + 36 q^{79} + 8 q^{83} - 64 q^{91} + 8 q^{93} + 4 q^{95} - 48 q^{97} + 24 q^{99}+O(q^{100}) \) 48 * q + 4 * q^5 + 4 * q^11 - 24 * q^13 + 40 * q^15 + 8 * q^17 + 4 * q^19 - 8 * q^21 + 24 * q^27 + 24 * q^29 - 28 * q^31 + 16 * q^33 - 28 * q^35 - 24 * q^37 + 40 * q^43 - 28 * q^45 + 20 * q^47 - 24 * q^51 - 16 * q^53 + 20 * q^59 + 8 * q^61 + 16 * q^63 + 8 * q^65 - 48 * q^67 - 40 * q^69 + 4 * q^75 - 20 * q^77 + 36 * q^79 + 8 * q^83 - 64 * q^91 + 8 * q^93 + 4 * q^95 - 48 * q^97 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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