LMFDB - Embedded newform 1078.2.i.c.901.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(901,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1078.901");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.3
Root			$1.60599 + 0.430324i$ of defining polynomial
Character	$\chi$	$=$	1078.901
Dual form			1078.2.i.c.1011.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.889740 - 0.513691i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.09005 - 0.629341i) q^{5} -1.02738 q^{6} -1.00000i q^{8} +(-0.972242 + 1.68397i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.889740 - 0.513691i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.09005 - 0.629341i) q^{5} -1.02738 q^{6} -1.00000i q^{8} +(-0.972242 + 1.68397i) q^{9} +(0.629341 + 1.09005i) q^{10} +(1.85817 + 2.74722i) q^{11} +(0.889740 + 0.513691i) q^{12} -4.08338 q^{13} -1.29315 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.60096 - 2.77294i) q^{17} +(1.68397 - 0.972242i) q^{18} +(3.81407 - 6.60616i) q^{19} -1.25868i q^{20} +(-0.235617 - 3.30824i) q^{22} +(4.12636 - 7.14707i) q^{23} +(-0.513691 - 0.889740i) q^{24} +(-1.70786 - 2.95810i) q^{25} +(3.53631 + 2.04169i) q^{26} +5.07988i q^{27} -3.54386i q^{29} +(1.11990 + 0.646574i) q^{30} +(7.95304 - 4.59169i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.06451 + 1.48978i) q^{33} +3.20191i q^{34} -1.94448 q^{36} +(0.154122 - 0.266948i) q^{37} +(-6.60616 + 3.81407i) q^{38} +(-3.63315 + 2.09760i) q^{39} +(-0.629341 + 1.09005i) q^{40} -6.05276 q^{41} -7.57607i q^{43} +(-1.45007 + 2.98283i) q^{44} +(2.11959 - 1.22374i) q^{45} +(-7.14707 + 4.12636i) q^{46} +(-4.07263 - 2.35133i) q^{47} +1.02738i q^{48} +3.41572i q^{50} +(-2.84887 - 1.64480i) q^{51} +(-2.04169 - 3.53631i) q^{52} +(2.39830 + 4.15397i) q^{53} +(2.53994 - 4.39930i) q^{54} +(-0.296567 - 4.16403i) q^{55} -7.83701i q^{57} +(-1.77193 + 3.06907i) q^{58} +(-2.36710 + 1.36664i) q^{59} +(-0.646574 - 1.11990i) q^{60} +(-0.755050 + 1.30779i) q^{61} -9.18338 q^{62} -1.00000 q^{64} +(4.45110 + 2.56984i) q^{65} +(-1.90905 - 2.82244i) q^{66} +(-1.69044 - 2.92792i) q^{67} +(1.60096 - 2.77294i) q^{68} -8.47871i q^{69} +3.50810 q^{71} +(1.68397 + 0.972242i) q^{72} +(0.483428 + 0.837321i) q^{73} +(-0.266948 + 0.154122i) q^{74} +(-3.03910 - 1.75463i) q^{75} +7.62813 q^{76} +4.19520 q^{78} +(13.5212 + 7.80647i) q^{79} +(1.09005 - 0.629341i) q^{80} +(-0.307237 - 0.532150i) q^{81} +(5.24185 + 3.02638i) q^{82} -1.32998 q^{83} +4.03019i q^{85} +(-3.78804 + 6.56107i) q^{86} +(-1.82045 - 3.15311i) q^{87} +(2.74722 - 1.85817i) q^{88} +(-9.22296 - 5.32488i) q^{89} -2.44749 q^{90} +8.25273 q^{92} +(4.71742 - 8.17082i) q^{93} +(2.35133 + 4.07263i) q^{94} +(-8.31505 + 4.80070i) q^{95} +(0.513691 - 0.889740i) q^{96} -10.6748i q^{97} +(-6.43283 + 0.458154i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 12 q^{5} + 16 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^9	$ 16 q + 8 q^{4} + 12 q^{5} + 16 q^{9} + 8 q^{11} - 8 q^{15} - 8 q^{16} - 8 q^{22} + 16 q^{23} + 36 q^{26} + 12 q^{31} + 24 q^{33} + 32 q^{36} - 16 q^{37} - 12 q^{38} - 8 q^{44} + 108 q^{45} - 24 q^{47} - 28 q^{53} - 12 q^{58} - 60 q^{59} - 4 q^{60} - 16 q^{64} - 48 q^{66} + 12 q^{67} + 8 q^{71} - 60 q^{75} - 16 q^{78} - 12 q^{80} - 8 q^{81} + 20 q^{86} - 4 q^{88} - 96 q^{89} + 32 q^{92} - 44 q^{93} + 56 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^9 + 8 * q^11 - 8 * q^15 - 8 * q^16 - 8 * q^22 + 16 * q^23 + 36 * q^26 + 12 * q^31 + 24 * q^33 + 32 * q^36 - 16 * q^37 - 12 * q^38 - 8 * q^44 + 108 * q^45 - 24 * q^47 - 28 * q^53 - 12 * q^58 - 60 * q^59 - 4 * q^60 - 16 * q^64 - 48 * q^66 + 12 * q^67 + 8 * q^71 - 60 * q^75 - 16 * q^78 - 12 * q^80 - 8 * q^81 + 20 * q^86 - 4 * q^88 - 96 * q^89 + 32 * q^92 - 44 * q^93 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.889740	−	0.513691i	0.513691	−	0.296580i	−0.220658	−	0.975351i	$-0.570821\pi$
$3$	0.889740	−	0.513691i	0.513691	−	0.296580i	0.734350	+	0.678771i	$0.237487\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.09005	−	0.629341i	−0.487486	−	0.281450i	0.236045	−	0.971742i	$-0.424149\pi$
$5$	−1.09005	−	0.629341i	−0.487486	−	0.281450i	−0.723531	+	0.690292i	$0.757482\pi$
$6$	−1.02738			−0.419427
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−0.972242	+	1.68397i	−0.324081	+	0.561324i
$10$	0.629341	+	1.09005i	0.199015	+	0.344704i
$11$	1.85817	+	2.74722i	0.560260	+	0.828317i
$11$	1.85817	+	2.74722i	0.560260	+	0.828317i
$12$	0.889740	+	0.513691i	0.256846	+	0.148290i
$13$	−4.08338			−1.13253			−0.566263	−	0.824224i	$-0.691612\pi$
$13$	−4.08338			−1.13253			−0.566263	+	0.824224i	$0.691612\pi$
$14$		0			0
$15$	−1.29315			−0.333890
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.60096	−	2.77294i	−0.388289	−	0.672537i	0.603930	−	0.797037i	$-0.293600\pi$
$17$	−1.60096	−	2.77294i	−0.388289	−	0.672537i	−0.992220	+	0.124501i	$0.960267\pi$
$18$	1.68397	−	0.972242i	0.396916	−	0.229160i
$19$	3.81407	−	6.60616i	0.875007	−	1.51556i	0.0182510	−	0.999833i	$-0.494190\pi$
$19$	3.81407	−	6.60616i	0.875007	−	1.51556i	0.856756	−	0.515723i	$-0.172476\pi$
$20$		−	1.25868i		−	0.281450i
$21$		0			0
$22$	−0.235617	−	3.30824i	−0.0502337	−	0.705320i
$23$	4.12636	−	7.14707i	0.860407	−	1.49027i	−0.0111305	−	0.999938i	$-0.503543\pi$
$23$	4.12636	−	7.14707i	0.860407	−	1.49027i	0.871537	−	0.490330i	$-0.163124\pi$
$24$	−0.513691	−	0.889740i	−0.104857	−	0.181617i
$25$	−1.70786	−	2.95810i	−0.341572	−	0.591620i
$26$	3.53631	+	2.04169i	0.693528	+	0.400409i
$27$			5.07988i			0.977623i
$28$		0			0
$29$		−	3.54386i		−	0.658079i	−0.944316	−	0.329039i	$-0.893275\pi$
$29$		−	3.54386i		−	0.658079i	0.944316	−	0.329039i	$-0.106725\pi$
$30$	1.11990	+	0.646574i	0.204465	+	0.118048i
$31$	7.95304	−	4.59169i	1.42841	−	0.824692i	0.431413	−	0.902155i	$-0.358015\pi$
$31$	7.95304	−	4.59169i	1.42841	−	0.824692i	0.996995	+	0.0774626i	$0.0246818\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	3.06451	+	1.48978i	0.533463	+	0.259337i
$34$			3.20191i			0.549124i
$35$		0			0
$36$	−1.94448			−0.324081
$37$	0.154122	−	0.266948i	0.0253376	−	0.0438860i	−0.853079	−	0.521782i	$-0.825267\pi$
$37$	0.154122	−	0.266948i	0.0253376	−	0.0438860i	0.878416	+	0.477896i	$0.158601\pi$
$38$	−6.60616	+	3.81407i	−1.07166	+	0.618723i
$39$	−3.63315	+	2.09760i	−0.581769	+	0.335885i
$40$	−0.629341	+	1.09005i	−0.0995076	+	0.172352i
$41$	−6.05276			−0.945283			−0.472641	−	0.881255i	$-0.656699\pi$
$41$	−6.05276			−0.945283			−0.472641	+	0.881255i	$0.656699\pi$
$42$		0			0
$43$		−	7.57607i		−	1.15534i	−0.816270	−	0.577670i	$-0.803962\pi$
$43$		−	7.57607i		−	1.15534i	0.816270	−	0.577670i	$-0.196038\pi$
$44$	−1.45007	+	2.98283i	−0.218607	+	0.449679i
$45$	2.11959	−	1.22374i	0.315969	−	0.182425i
$46$	−7.14707	+	4.12636i	−1.05378	+	0.608399i
$47$	−4.07263	−	2.35133i	−0.594054	−	0.342977i	0.172645	−	0.984984i	$-0.444769\pi$
$47$	−4.07263	−	2.35133i	−0.594054	−	0.342977i	−0.766699	+	0.642007i	$0.778102\pi$
$48$			1.02738i			0.148290i
$49$		0			0
$50$			3.41572i			0.483056i
$51$	−2.84887	−	1.64480i	−0.398922	−	0.230317i
$52$	−2.04169	−	3.53631i	−0.283132	−	0.490399i
$53$	2.39830	+	4.15397i	0.329431	+	0.570592i	0.982399	−	0.186794i	$-0.0598097\pi$
$53$	2.39830	+	4.15397i	0.329431	+	0.570592i	−0.652968	+	0.757386i	$0.726476\pi$
$54$	2.53994	−	4.39930i	0.345642	−	0.598669i
$55$	−0.296567	−	4.16403i	−0.0399891	−	0.561478i
$56$		0			0
$57$		−	7.83701i		−	1.03804i
$58$	−1.77193	+	3.06907i	−0.232666	+	0.402989i
$59$	−2.36710	+	1.36664i	−0.308170	+	0.177922i	−0.646107	−	0.763247i	$-0.723604\pi$
$59$	−2.36710	+	1.36664i	−0.308170	+	0.177922i	0.337938	+	0.941169i	$0.390271\pi$
$60$	−0.646574	−	1.11990i	−0.0834724	−	0.144578i
$61$	−0.755050	+	1.30779i	−0.0966743	+	0.167445i	−0.910306	−	0.413936i	$-0.864154\pi$
$61$	−0.755050	+	1.30779i	−0.0966743	+	0.167445i	0.813632	+	0.581380i	$0.197487\pi$
$62$	−9.18338			−1.16629
$63$		0			0
$64$	−1.00000			−0.125000
$65$	4.45110	+	2.56984i	0.552090	+	0.318750i
$66$	−1.90905	−	2.82244i	−0.234988	−	0.347419i
$67$	−1.69044	−	2.92792i	−0.206520	−	0.357703i	0.744096	−	0.668073i	$-0.232880\pi$
$67$	−1.69044	−	2.92792i	−0.206520	−	0.357703i	−0.950616	+	0.310370i	$0.899547\pi$
$68$	1.60096	−	2.77294i	0.194145	−	0.336268i
$69$		−	8.47871i		−	1.02072i
$70$		0			0
$71$	3.50810			0.416334			0.208167	−	0.978093i	$-0.433250\pi$
$71$	3.50810			0.416334			0.208167	+	0.978093i	$0.433250\pi$
$72$	1.68397	+	0.972242i	0.198458	+	0.114580i
$73$	0.483428	+	0.837321i	0.0565809	+	0.0980011i	0.892929	−	0.450198i	$-0.148647\pi$
$73$	0.483428	+	0.837321i	0.0565809	+	0.0980011i	−0.836348	+	0.548200i	$0.815313\pi$
$74$	−0.266948	+	0.154122i	−0.0310321	+	0.0179164i
$75$	−3.03910	−	1.75463i	−0.350925	−	0.202607i
$76$	7.62813			0.875007
$77$		0			0
$78$	4.19520			0.475013
$79$	13.5212	+	7.80647i	1.52125	+	0.878296i	0.999685	+	0.0250865i	$0.00798611\pi$
$79$	13.5212	+	7.80647i	1.52125	+	0.878296i	0.521568	+	0.853210i	$0.325347\pi$
$80$	1.09005	−	0.629341i	0.121871	−	0.0703625i
$81$	−0.307237	−	0.532150i	−0.0341374	−	0.0591278i
$82$	5.24185	+	3.02638i	0.578865	+	0.334208i
$83$	−1.32998			−0.145984			−0.0729921	−	0.997333i	$-0.523255\pi$
$83$	−1.32998			−0.145984			−0.0729921	+	0.997333i	$0.523255\pi$
$84$		0			0
$85$			4.03019i			0.437136i
$86$	−3.78804	+	6.56107i	−0.408474	+	0.707498i
$87$	−1.82045	−	3.15311i	−0.195173	−	0.338049i
$88$	2.74722	−	1.85817i	0.292854	−	0.198082i
$89$	−9.22296	−	5.32488i	−0.977631	−	0.564436i	−0.0760772	−	0.997102i	$-0.524240\pi$
$89$	−9.22296	−	5.32488i	−0.977631	−	0.564436i	−0.901554	+	0.432666i	$0.857573\pi$
$90$	−2.44749			−0.257988
$91$		0			0
$92$	8.25273			0.860407
$93$	4.71742	−	8.17082i	0.489174	−	0.847274i
$94$	2.35133	+	4.07263i	0.242521	+	0.420059i
$95$	−8.31505	+	4.80070i	−0.853106	+	0.492541i
$96$	0.513691	−	0.889740i	0.0524284	−	0.0908087i
$97$		−	10.6748i		−	1.08386i	−0.840424	−	0.541930i	$-0.817694\pi$
$97$		−	10.6748i		−	1.08386i	0.840424	−	0.541930i	$-0.182306\pi$
$98$		0			0
$99$	−6.43283	+	0.458154i	−0.646524	+	0.0460462i
$100$	1.70786	−	2.95810i	0.170786	−	0.295810i
$101$	5.03242	+	8.71642i	0.500745	+	0.867316i	1.00000		0.000860457i	$0.000273892\pi$
$101$	5.03242	+	8.71642i	0.500745	+	0.867316i	−0.499255	+	0.866455i	$0.666393\pi$
$102$	1.64480	+	2.84887i	0.162859	+	0.282080i
$103$	−2.49868	−	1.44261i	−0.246202	−	0.142145i	0.371822	−	0.928304i	$-0.378733\pi$
$103$	−2.49868	−	1.44261i	−0.246202	−	0.142145i	−0.618024	+	0.786159i	$0.712067\pi$
$104$			4.08338i			0.400409i
$105$		0			0
$106$		−	4.79659i		−	0.465886i
$107$	−14.1162	−	8.15002i	−1.36467	−	0.787892i	−0.374428	−	0.927256i	$-0.622161\pi$
$107$	−14.1162	−	8.15002i	−1.36467	−	0.787892i	−0.990241	+	0.139364i	$0.955494\pi$
$108$	−4.39930	+	2.53994i	−0.423323	+	0.244406i
$109$	9.96227	−	5.75172i	0.954213	−	0.550915i	0.0598257	−	0.998209i	$-0.480946\pi$
$109$	9.96227	−	5.75172i	0.954213	−	0.550915i	0.894387	+	0.447294i	$0.147612\pi$
$110$	−1.82518	+	3.75444i	−0.174024	+	0.357972i
$111$		−	0.316686i		−	0.0300585i
$112$		0			0
$113$	0.558958			0.0525824			0.0262912	−	0.999654i	$-0.491630\pi$
$113$	0.558958			0.0525824			0.0262912	+	0.999654i	$0.491630\pi$
$114$	−3.91851	+	6.78705i	−0.367002	+	0.635666i
$115$	−8.99589	+	5.19378i	−0.838872	+	0.484323i
$116$	3.06907	−	1.77193i	0.284956	−	0.164520i
$117$	3.97004	−	6.87631i	0.367030	−	0.635715i
$118$	2.73329			0.251619
$119$		0			0
$120$			1.29315i			0.118048i
$121$	−4.09439	+	10.2096i	−0.372217	+	0.928146i
$122$	1.30779	−	0.755050i	0.118401	−	0.0683590i
$123$	−5.38538	+	3.10925i	−0.485584	+	0.280352i
$124$	7.95304	+	4.59169i	0.714204	+	0.412346i
$125$			10.5927i			0.947441i
$126$		0			0
$127$			11.2829i			1.00120i	0.865679	+	0.500599i	$0.166887\pi$
$127$			11.2829i			1.00120i	−0.865679	+	0.500599i	$0.833113\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−3.89176	−	6.74073i	−0.342651	−	0.593488i
$130$	−2.56984	−	4.45110i	−0.225390	−	0.390387i
$131$	−3.51694	+	6.09152i	−0.307276	+	0.532218i	−0.977766	−	0.209701i	$-0.932751\pi$
$131$	−3.51694	+	6.09152i	−0.307276	+	0.532218i	0.670489	+	0.741919i	$0.266084\pi$
$132$	0.242069	+	3.39883i	0.0210694	+	0.295831i
$133$		0			0
$134$			3.38087i			0.292063i
$135$	3.19698	−	5.53733i	0.275152	−	0.476577i
$136$	−2.77294	+	1.60096i	−0.237778	+	0.137281i
$137$	−4.54487	−	7.87195i	−0.388294	−	0.672546i	0.603926	−	0.797041i	$-0.293602\pi$
$137$	−4.54487	−	7.87195i	−0.388294	−	0.672546i	−0.992220	+	0.124495i	$0.960269\pi$
$138$	−4.23936	+	7.34278i	−0.360878	+	0.625059i
$139$	7.86546			0.667140			0.333570	−	0.942725i	$-0.391747\pi$
$139$	7.86546			0.667140			0.333570	+	0.942725i	$0.391747\pi$
$140$		0			0
$141$	−4.83144			−0.406880
$142$	−3.03810	−	1.75405i	−0.254952	−	0.147196i
$143$	−7.58763	−	11.2179i	−0.634510	−	0.938091i
$144$	−0.972242	−	1.68397i	−0.0810202	−	0.140331i
$145$	−2.23030	+	3.86299i	−0.185216	+	0.320804i
$146$		−	0.966855i		−	0.0800175i
$147$		0			0
$148$	0.308245			0.0253376
$149$	−5.39617	−	3.11548i	−0.442072	−	0.255230i	0.262404	−	0.964958i	$-0.415485\pi$
$149$	−5.39617	−	3.11548i	−0.442072	−	0.255230i	−0.704476	+	0.709728i	$0.748818\pi$
$150$	1.75463	+	3.03910i	0.143265	+	0.248142i
$151$	15.1642	−	8.75506i	1.23405	−	0.712476i	0.266175	−	0.963925i	$-0.414240\pi$
$151$	15.1642	−	8.75506i	1.23405	−	0.712476i	0.967871	+	0.251448i	$0.0809069\pi$
$152$	−6.60616	−	3.81407i	−0.535830	−	0.309362i
$153$	6.22607			0.503348
$154$		0			0
$155$	−11.5590			−0.928438
$156$	−3.63315	−	2.09760i	−0.290885	−	0.167942i
$157$	6.73252	−	3.88702i	0.537314	−	0.310218i	−0.206676	−	0.978409i	$-0.566265\pi$
$157$	6.73252	−	3.88702i	0.537314	−	0.310218i	0.743989	+	0.668191i	$0.232931\pi$
$158$	−7.80647	−	13.5212i	−0.621049	−	1.07569i
$159$	4.26772	+	2.46397i	0.338452	+	0.195405i
$160$	−1.25868			−0.0995076
$161$		0			0
$162$			0.614474i			0.0482776i
$163$	9.10616	−	15.7723i	0.713249	−	1.23538i	−0.250382	−	0.968147i	$-0.580556\pi$
$163$	9.10616	−	15.7723i	0.713249	−	1.23538i	0.963631	−	0.267237i	$-0.0861105\pi$
$164$	−3.02638	−	5.24185i	−0.236321	−	0.409319i
$165$	−2.40289	−	3.55256i	−0.187065	−	0.276566i
$166$	1.15180	+	0.664990i	0.0893967	+	0.0516132i
$167$	−14.3653			−1.11162			−0.555809	−	0.831310i	$-0.687591\pi$
$167$	−14.3653			−1.11162			−0.555809	+	0.831310i	$0.687591\pi$
$168$		0			0
$169$	3.67402			0.282617
$170$	2.01510	−	3.49025i	0.154551	−	0.267690i
$171$	7.41639	+	12.8456i	0.567146	+	0.982325i
$172$	6.56107	−	3.78804i	0.500277	−	0.288835i
$173$	−2.38160	+	4.12505i	−0.181069	+	0.313621i	−0.942245	−	0.334924i	$-0.891289\pi$
$173$	−2.38160	+	4.12505i	−0.181069	+	0.313621i	0.761176	+	0.648546i	$0.224623\pi$
$174$			3.64090i			0.276016i
$175$		0			0
$176$	−3.30824	+	0.235617i	−0.249368	+	0.0177603i
$177$	−1.40407	+	2.43191i	−0.105536	+	0.182794i
$178$	5.32488	+	9.22296i	0.399116	+	0.691290i
$179$	1.94526	+	3.36928i	0.145395	+	0.251832i	0.929520	−	0.368771i	$-0.120221\pi$
$179$	1.94526	+	3.36928i	0.145395	+	0.251832i	−0.784125	+	0.620603i	$0.786888\pi$
$180$	2.11959	+	1.22374i	0.157985	+	0.0912125i
$181$		−	13.0698i		−	0.971474i	−0.874105	−	0.485737i	$-0.838551\pi$
$181$		−	13.0698i		−	0.971474i	0.874105	−	0.485737i	$-0.161449\pi$
$182$		0			0
$183$			1.55145i			0.114687i
$184$	−7.14707	−	4.12636i	−0.526889	−	0.304200i
$185$	−0.336003	+	0.193991i	−0.0247034	+	0.0142625i
$186$	−8.17082	+	4.71742i	−0.599113	+	0.345898i
$187$	4.64301	−	9.55077i	0.339530	−	0.698422i
$188$		−	4.70267i		−	0.342977i
$189$		0			0
$190$	9.60139			0.696558
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	−0.953912	−	0.300088i	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$	−0.889740	+	0.513691i	−0.0642114	+	0.0370725i
$193$	−8.12582	+	4.69144i	−0.584909	+	0.337698i	−0.763082	−	0.646302i	$-0.776315\pi$
$193$	−8.12582	+	4.69144i	−0.584909	+	0.337698i	0.178173	+	0.983999i	$0.442981\pi$
$194$	−5.33739	+	9.24463i	−0.383202	+	0.663726i
$195$	5.28042			0.378139
$196$		0			0
$197$			17.3471i			1.23593i	0.786205	+	0.617966i	$0.212043\pi$
$197$			17.3471i			1.23593i	−0.786205	+	0.617966i	$0.787957\pi$
$198$	5.80007	+	2.81964i	0.412193	+	0.200383i
$199$	−2.53353	+	1.46273i	−0.179597	+	0.103690i	−0.587103	−	0.809512i	$-0.699732\pi$
$199$	−2.53353	+	1.46273i	−0.179597	+	0.103690i	0.407506	+	0.913202i	$0.366398\pi$
$200$	−2.95810	+	1.70786i	−0.209169	+	0.120764i
$201$	−3.00810	−	1.73673i	−0.212175	−	0.122499i
$202$		−	10.0648i		−	0.708160i
$203$		0			0
$204$		−	3.28959i		−	0.230317i
$205$	6.59782	+	3.80925i	0.460812	+	0.266050i
$206$	1.44261	+	2.49868i	0.100512	+	0.174091i
$207$	8.02365	+	13.8974i	0.557682	+	0.965934i
$208$	2.04169	−	3.53631i	0.141566	−	0.245199i
$209$	25.2357	−	1.79732i	1.74559	−	0.124323i
$210$		0			0
$211$			0.252729i			0.0173986i	0.999962	+	0.00869931i	$0.00276911\pi$
$211$			0.252729i			0.0173986i	−0.999962	+	0.00869931i	$0.997231\pi$
$212$	−2.39830	+	4.15397i	−0.164716	+	0.285296i
$213$	3.12129	−	1.80208i	0.213867	−	0.123476i
$214$	8.15002	+	14.1162i	0.557124	+	0.964967i
$215$	−4.76793	+	8.25830i	−0.325170	+	0.563212i
$216$	5.07988			0.345642
$217$		0			0
$218$	−11.5034			−0.779111
$219$	0.860250	+	0.496665i	0.0581303	+	0.0335615i
$220$	3.45787	−	2.33885i	0.233130	−	0.157685i
$221$	6.53732	+	11.3230i	0.439748	+	0.761666i
$222$	−0.158343	+	0.274258i	−0.0106273	+	0.0184070i
$223$			19.0370i			1.27482i	0.770527	+	0.637408i	$0.219993\pi$
$223$			19.0370i			1.27482i	−0.770527	+	0.637408i	$0.780007\pi$
$224$		0			0
$225$	6.64181			0.442788
$226$	−0.484072	−	0.279479i	−0.0322000	−	0.0185907i
$227$	9.20350	+	15.9409i	0.610858	+	1.05804i	0.991096	+	0.133148i	$0.0425086\pi$
$227$	9.20350	+	15.9409i	0.610858	+	1.05804i	−0.380238	+	0.924888i	$0.624158\pi$
$228$	6.78705	−	3.91851i	0.449483	−	0.259509i
$229$	4.59674	+	2.65393i	0.303761	+	0.175377i	0.644131	−	0.764915i	$-0.277219\pi$
$229$	4.59674	+	2.65393i	0.303761	+	0.175377i	−0.340370	+	0.940292i	$0.610552\pi$
$230$	10.3876			0.684936
$231$		0			0
$232$	−3.54386			−0.232666
$233$	−18.4629	−	10.6596i	−1.20955	−	0.698332i	−0.246887	−	0.969044i	$-0.579408\pi$
$233$	−18.4629	−	10.6596i	−1.20955	−	0.698332i	−0.962660	+	0.270712i	$0.912741\pi$
$234$	−6.87631	+	3.97004i	−0.449518	+	0.259530i
$235$	2.95958	+	5.12614i	0.193062	+	0.334393i
$236$	−2.36710	−	1.36664i	−0.154085	−	0.0889609i
$237$	16.0405			1.04194
$238$		0			0
$239$			7.25163i			0.469069i	0.972108	+	0.234535i	$0.0753566\pi$
$239$			7.25163i			0.469069i	−0.972108	+	0.234535i	$0.924643\pi$
$240$	0.646574	−	1.11990i	0.0417362	−	0.0722892i
$241$	−1.77705	−	3.07794i	−0.114470	−	0.198267i	0.803098	−	0.595847i	$-0.203184\pi$
$241$	−1.77705	−	3.07794i	−0.114470	−	0.198267i	−0.917568	+	0.397580i	$0.869850\pi$
$242$	8.65064	−	6.79458i	0.556084	−	0.436772i
$243$	−13.7446	−	7.93547i	−0.881719	−	0.509060i
$244$	−1.51010			−0.0966743
$245$		0			0
$246$	6.21850			0.396477
$247$	−15.5743	+	26.9755i	−0.990968	+	1.71641i
$248$	−4.59169	−	7.95304i	−0.291573	−	0.505019i
$249$	−1.18334	+	0.683199i	−0.0749908	+	0.0432960i
$250$	5.29636	−	9.17356i	0.334971	−	0.580187i
$251$			0.735728i			0.0464387i	0.999730	+	0.0232194i	$0.00739162\pi$
$251$			0.735728i			0.0464387i	−0.999730	+	0.0232194i	$0.992608\pi$
$252$		0			0
$253$	27.3021	−	1.94448i	1.71647	−	0.122249i
$254$	5.64146	−	9.77130i	0.353977	−	0.613106i
$255$	2.07028	+	3.58582i	0.129646	+	0.224553i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	14.0352	+	8.10325i	0.875494	+	0.505467i	0.869170	−	0.494513i	$-0.164654\pi$
$257$	14.0352	+	8.10325i	0.875494	+	0.505467i	0.00632378	+	0.999980i	$0.497987\pi$
$258$			7.78352i			0.484581i
$259$		0			0
$260$			5.13968i			0.318750i
$261$	5.96777	+	3.44549i	0.369396	+	0.213271i
$262$	6.09152	−	3.51694i	0.376335	−	0.217277i
$263$	21.0462	−	12.1510i	1.29776	−	0.749264i	0.317746	−	0.948176i	$-0.397074\pi$
$263$	21.0462	−	12.1510i	1.29776	−	0.749264i	0.980017	+	0.198911i	$0.0637406\pi$
$264$	1.48978	−	3.06451i	0.0916896	−	0.188608i
$265$		−	6.03738i		−	0.370874i
$266$		0			0
$267$	−10.9414			−0.669601
$268$	1.69044	−	2.92792i	0.103260	−	0.178851i
$269$	23.4246	−	13.5242i	1.42822	−	0.824586i	0.431244	−	0.902236i	$-0.358075\pi$
$269$	23.4246	−	13.5242i	1.42822	−	0.824586i	0.996981	+	0.0776498i	$0.0247416\pi$
$270$	−5.53733	+	3.19698i	−0.336991	+	0.194562i
$271$	−5.22166	+	9.04417i	−0.317193	+	0.549394i	−0.979901	−	0.199483i	$-0.936074\pi$
$271$	−5.22166	+	9.04417i	−0.317193	+	0.549394i	0.662708	+	0.748878i	$0.269407\pi$
$272$	3.20191			0.194145
$273$		0			0
$274$			9.08974i			0.549131i
$275$	4.95304	−	10.1885i	0.298679	−	0.614391i
$276$	7.34278	−	4.23936i	0.441983	−	0.255179i
$277$	−17.6675	+	10.2003i	−1.06153	+	0.612877i	−0.925856	−	0.377876i	$-0.876655\pi$
$277$	−17.6675	+	10.2003i	−1.06153	+	0.612877i	−0.135678	+	0.990753i	$0.543321\pi$
$278$	−6.81169	−	3.93273i	−0.408538	−	0.235869i
$279$			17.8569i			1.06907i
$280$		0			0
$281$			9.99535i			0.596272i	0.954523	+	0.298136i	$0.0963650\pi$
$281$			9.99535i			0.596272i	−0.954523	+	0.298136i	$0.903635\pi$
$282$	4.18415	+	2.41572i	0.249162	+	0.143854i
$283$	−1.74448	−	3.02153i	−0.103699	−	0.179611i	0.809507	−	0.587110i	$-0.199734\pi$
$283$	−1.74448	−	3.02153i	−0.103699	−	0.179611i	−0.913206	+	0.407499i	$0.866401\pi$
$284$	1.75405	+	3.03810i	0.104084	+	0.180278i
$285$	−4.93215	+	8.54274i	−0.292156	+	0.506028i
$286$	0.962115	+	13.5088i	0.0568911	+	0.798794i
$287$		0			0
$288$			1.94448i			0.114580i
$289$	3.37387	−	5.84372i	0.198463	−	0.343748i
$290$	3.86299	−	2.23030i	0.226843	−	0.130968i
$291$	−5.48354	−	9.49778i	−0.321451	−	0.556770i
$292$	−0.483428	+	0.837321i	−0.0282905	+	0.0490005i
$293$	−17.3549			−1.01388			−0.506942	−	0.861980i	$-0.669224\pi$
$293$	−17.3549			−1.01388			−0.506942	+	0.861980i	$0.669224\pi$
$294$		0			0
$295$	3.44034			0.200304
$296$	−0.266948	−	0.154122i	−0.0155160	−	0.00895819i
$297$	−13.9555	+	9.43929i	−0.809781	+	0.547723i
$298$	3.11548	+	5.39617i	0.180475	+	0.312592i
$299$	−16.8495	+	29.1842i	−0.974433	+	1.68777i
$300$		−	3.50925i		−	0.202607i
$301$		0			0
$302$	−17.5101			−1.00759
$303$	8.95510	+	5.17023i	0.514457	+	0.297022i
$304$	3.81407	+	6.60616i	0.218752	+	0.378889i
$305$	1.64609	−	0.950368i	0.0942546	−	0.0544179i
$306$	−5.39194	−	3.11304i	−0.308237	−	0.177960i
$307$	22.6829			1.29458			0.647290	−	0.762244i	$-0.275902\pi$
$307$	22.6829			1.29458			0.647290	+	0.762244i	$0.275902\pi$
$308$		0			0
$309$	−2.96423			−0.168629
$310$	10.0104	+	5.77948i	0.568550	+	0.328252i
$311$	−5.75141	+	3.32058i	−0.326133	+	0.188293i	−0.654123	−	0.756388i	$-0.726962\pi$
$311$	−5.75141	+	3.32058i	−0.326133	+	0.188293i	0.327990	+	0.944681i	$0.393629\pi$
$312$	2.09760	+	3.63315i	0.118753	+	0.205687i
$313$	0.435583	+	0.251484i	0.0246206	+	0.0142147i	0.512260	−	0.858831i	$-0.328809\pi$
$313$	0.435583	+	0.251484i	0.0246206	+	0.0142147i	−0.487639	+	0.873045i	$0.662142\pi$
$314$	−7.77404			−0.438715
$315$		0			0
$316$			15.6129i			0.878296i
$317$	5.27437	−	9.13547i	0.296238	−	0.513099i	−0.679034	−	0.734107i	$-0.737601\pi$
$317$	5.27437	−	9.13547i	0.296238	−	0.513099i	0.975272	+	0.221008i	$0.0709345\pi$
$318$	−2.46397	−	4.26772i	−0.138172	−	0.239322i
$319$	9.73575	−	6.58511i	0.545098	−	0.368695i
$320$	1.09005	+	0.629341i	0.0609357	+	0.0351812i
$321$	−16.7464			−0.934692
$322$		0			0
$323$	−24.4246			−1.35902
$324$	0.307237	−	0.532150i	0.0170687	−	0.0295639i
$325$	6.97385	+	12.0791i	0.386839	+	0.670025i
$326$	−15.7723	+	9.10616i	−0.873548	+	0.504343i
$327$	5.90922	−	10.2351i	0.326781	−	0.566001i
$328$			6.05276i			0.334208i
$329$		0			0
$330$	0.304688	+	4.27805i	0.0167725	+	0.235499i
$331$	2.89029	−	5.00613i	0.158865	−	0.275162i	−0.775595	−	0.631231i	$-0.782550\pi$
$331$	2.89029	−	5.00613i	0.158865	−	0.275162i	0.934460	+	0.356069i	$0.115883\pi$
$332$	−0.664990	−	1.15180i	−0.0364960	−	0.0632130i
$333$	0.299689	+	0.519076i	0.0164228	+	0.0284452i
$334$	12.4407	+	7.18264i	0.680724	+	0.393016i
$335$			4.25544i			0.232500i
$336$		0			0
$337$			11.1226i			0.605885i	0.953009	+	0.302943i	$0.0979690\pi$
$337$			11.1226i			0.605885i	−0.953009	+	0.302943i	$0.902031\pi$
$338$	−3.18180	−	1.83701i	−0.173067	−	0.0999202i
$339$	0.497327	−	0.287132i	0.0270111	−	0.0155949i
$340$	−3.49025	+	2.01510i	−0.189285	+	0.109284i
$341$	27.3925	+	13.3166i	1.48339	+	0.721132i
$342$		−	14.8328i		−	0.802065i
$343$		0			0
$344$	−7.57607			−0.408474
$345$	−5.33600	+	9.24223i	−0.287281	+	0.497585i
$346$	4.12505	−	2.38160i	0.221764	−	0.128035i
$347$	12.7058	−	7.33569i	0.682083	−	0.393801i	−0.118557	−	0.992947i	$-0.537827\pi$
$347$	12.7058	−	7.33569i	0.682083	−	0.393801i	0.800639	+	0.599147i	$0.204493\pi$
$348$	1.82045	−	3.15311i	0.0975864	−	0.169025i
$349$	24.6769			1.32093			0.660463	−	0.750859i	$-0.270360\pi$
$349$	24.6769			1.32093			0.660463	+	0.750859i	$0.270360\pi$
$350$		0			0
$351$		−	20.7431i		−	1.10718i
$352$	2.98283	+	1.45007i	0.158986	+	0.0772891i
$353$	16.6664	−	9.62237i	0.887065	−	0.512147i	0.0140834	−	0.999901i	$-0.495517\pi$
$353$	16.6664	−	9.62237i	0.887065	−	0.512147i	0.872981	+	0.487754i	$0.162184\pi$
$354$	2.43191	−	1.40407i	0.129255	−	0.0746252i
$355$	−3.82400	−	2.20779i	−0.202957	−	0.117177i
$356$		−	10.6498i		−	0.564436i
$357$		0			0
$358$		−	3.89051i		−	0.205620i
$359$	−2.85275	−	1.64703i	−0.150562	−	0.0869271i	0.422826	−	0.906211i	$-0.361038\pi$
$359$	−2.85275	−	1.64703i	−0.150562	−	0.0869271i	−0.573388	+	0.819284i	$0.694371\pi$
$360$	−1.22374	−	2.11959i	−0.0644970	−	0.111712i
$361$	−19.5942	−	33.9381i	−1.03127	−	1.78622i
$362$	−6.53492	+	11.3188i	−0.343468	+	0.594904i
$363$	1.60165	+	11.1871i	0.0840647	+	0.587173i
$364$		0			0
$365$		−	1.21696i		−	0.0636988i
$366$	0.775726	−	1.34360i	0.0405478	−	0.0702309i
$367$	−26.7957	+	15.4705i	−1.39873	+	0.807555i	−0.994259	−	0.106998i	$-0.965876\pi$
$367$	−26.7957	+	15.4705i	−1.39873	+	0.807555i	−0.404467	+	0.914553i	$0.632543\pi$
$368$	4.12636	+	7.14707i	0.215102	+	0.372567i
$369$	5.88475	−	10.1927i	0.306348	−	0.530610i
$370$	0.387982			0.0201702
$371$		0			0
$372$	9.43485			0.489174
$373$	−0.832767	−	0.480798i	−0.0431191	−	0.0248948i	0.478286	−	0.878204i	$-0.341258\pi$
$373$	−0.832767	−	0.480798i	−0.0431191	−	0.0248948i	−0.521405	+	0.853310i	$0.674592\pi$
$374$	−8.79635	+	5.94971i	−0.454848	+	0.307652i
$375$	5.44139	+	9.42476i	0.280992	+	0.486692i
$376$	−2.35133	+	4.07263i	−0.121261	+	0.210030i
$377$			14.4709i			0.745292i
$378$		0			0
$379$	−1.41216			−0.0725379			−0.0362689	−	0.999342i	$-0.511547\pi$
$379$	−1.41216			−0.0725379			−0.0362689	+	0.999342i	$0.511547\pi$
$380$	−8.31505	−	4.80070i	−0.426553	−	0.246271i
$381$	5.79594	+	10.0389i	0.296935	+	0.514307i
$382$	5.19615	−	3.00000i	0.265858	−	0.153493i
$383$	−3.27426	−	1.89039i	−0.167307	−	0.0965946i	0.414009	−	0.910273i	$-0.364128\pi$
$383$	−3.27426	−	1.89039i	−0.167307	−	0.0965946i	−0.581315	+	0.813678i	$0.697462\pi$
$384$	1.02738			0.0524284
$385$		0			0
$386$	9.38289			0.477576
$387$	12.7579	+	7.36578i	0.648520	+	0.374423i
$388$	9.24463	−	5.33739i	0.469325	−	0.270965i
$389$	1.68943	+	2.92618i	0.0856574	+	0.148363i	0.905671	−	0.423981i	$-0.139368\pi$
$389$	1.68943	+	2.92618i	0.0856574	+	0.148363i	−0.820014	+	0.572344i	$0.806034\pi$
$390$	−4.57298	−	2.64021i	−0.231562	−	0.133692i
$391$	−26.4245			−1.33635
$392$		0			0
$393$			7.22649i			0.364528i
$394$	8.67356	−	15.0230i	0.436968	−	0.756850i
$395$	−9.82586	−	17.0189i	−0.494393	−	0.856313i
$396$	−3.61319	−	5.34192i	−0.181570	−	0.268441i
$397$	9.98525	+	5.76499i	0.501145	+	0.289336i	0.729186	−	0.684315i	$-0.239899\pi$
$397$	9.98525	+	5.76499i	0.501145	+	0.289336i	−0.228041	+	0.973652i	$0.573232\pi$
$398$	2.92547			0.146640
$399$		0			0
$400$	3.41572			0.170786
$401$	−13.0261	+	22.5619i	−0.650494	+	1.12669i	0.332509	+	0.943100i	$0.392105\pi$
$401$	−13.0261	+	22.5619i	−0.650494	+	1.12669i	−0.983003	+	0.183588i	$0.941229\pi$
$402$	1.73673	+	3.00810i	0.0866200	+	0.150030i
$403$	−32.4753	+	18.7496i	−1.61771	+	0.933986i
$404$	−5.03242	+	8.71642i	−0.250372	+	0.433658i
$405$			0.773427i			0.0384319i
$406$		0			0
$407$	1.01975	−	0.0726278i	0.0505471	−	0.00360003i
$408$	−1.64480	+	2.84887i	−0.0814295	+	0.141040i
$409$	17.5109	+	30.3297i	0.865856	+	1.49971i	0.866194	+	0.499707i	$0.166559\pi$
$409$	17.5109	+	30.3297i	0.865856	+	1.49971i	−0.000338063		1.00000i	$0.500108\pi$
$410$	−3.80925	−	6.59782i	−0.188126	−	0.325843i
$411$	−8.08750	−	4.66932i	−0.398927	−	0.230321i
$412$		−	2.88523i		−	0.142145i
$413$		0			0
$414$		−	16.0473i		−	0.788682i
$415$	1.44974	+	0.837011i	0.0711652	+	0.0410872i
$416$	−3.53631	+	2.04169i	−0.173382	+	0.100102i
$417$	6.99821	−	4.04042i	0.342704	−	0.197860i
$418$	−22.7534	−	11.0613i	−1.11291	−	0.541028i
$419$		−	12.1242i		−	0.592307i	−0.955140	−	0.296154i	$-0.904296\pi$
$419$		−	12.1242i		−	0.592307i	0.955140	−	0.296154i	$-0.0957040\pi$
$420$		0			0
$421$	18.6940			0.911089			0.455545	−	0.890213i	$-0.349445\pi$
$421$	18.6940			0.911089			0.455545	+	0.890213i	$0.349445\pi$
$422$	0.126365	−	0.218870i	0.00615134	−	0.0106544i
$423$	7.91916	−	4.57213i	0.385043	−	0.222305i
$424$	4.15397	−	2.39830i	0.201735	−	0.116472i
$425$	−5.46842	+	9.47158i	−0.265257	+	0.459439i
$426$	−3.60416			−0.174622
$427$		0			0
$428$		−	16.3000i		−	0.787892i
$429$	−12.5136	−	6.08334i	−0.604161	−	0.293706i
$430$	8.25830	−	4.76793i	0.398251	−	0.229930i
$431$	−29.3945	+	16.9709i	−1.41588	+	0.817461i	−0.995934	−	0.0900869i	$-0.971286\pi$
$431$	−29.3945	+	16.9709i	−1.41588	+	0.817461i	−0.419949	+	0.907548i	$0.637952\pi$
$432$	−4.39930	−	2.53994i	−0.211662	−	0.122203i
$433$		−	27.0949i		−	1.30210i	−0.759037	−	0.651048i	$-0.774330\pi$
$433$		−	27.0949i		−	1.30210i	0.759037	−	0.651048i	$-0.225670\pi$
$434$		0			0
$435$			4.58274i			0.219726i
$436$	9.96227	+	5.75172i	0.477106	+	0.275458i
$437$	−31.4765	−	54.5188i	−1.50572	−	2.60799i
$438$	−0.496665	−	0.860250i	−0.0237316	−	0.0411043i
$439$	10.2269	−	17.7135i	0.488104	−	0.845421i	−0.511802	−	0.859103i	$-0.671022\pi$
$439$	10.2269	−	17.7135i	0.488104	−	0.845421i	0.999906	+	0.0136821i	$0.00435529\pi$
$440$	−4.16403	+	0.296567i	−0.198512	+	0.0141383i
$441$		0			0
$442$		−	13.0746i		−	0.621897i
$443$	1.79868	−	3.11541i	0.0854579	−	0.148017i	−0.820128	−	0.572180i	$-0.806098\pi$
$443$	1.79868	−	3.11541i	0.0854579	−	0.148017i	0.905586	+	0.424162i	$0.139431\pi$
$444$	0.274258	−	0.158343i	0.0130157	−	0.00751462i
$445$	6.70233	+	11.6088i	0.317721	+	0.550309i
$446$	9.51852	−	16.4866i	0.450715	−	0.780662i
$447$	−6.40159			−0.302785
$448$		0			0
$449$	37.0664			1.74927			0.874637	−	0.484779i	$-0.161100\pi$
$449$	37.0664			1.74927			0.874637	+	0.484779i	$0.161100\pi$
$450$	−5.75198	−	3.32091i	−0.271151	−	0.156549i
$451$	−11.2471	−	16.6282i	−0.529604	−	0.782993i
$452$	0.279479	+	0.484072i	0.0131456	+	0.0227688i
$453$	8.99479	−	15.5794i	0.422612	−	0.731986i
$454$		−	18.4070i		−	0.863883i
$455$		0			0
$456$	−7.83701			−0.367002
$457$	−15.7194	−	9.07561i	−0.735323	−	0.424539i	0.0850431	−	0.996377i	$-0.472897\pi$
$457$	−15.7194	−	9.07561i	−0.735323	−	0.424539i	−0.820366	+	0.571838i	$0.806231\pi$
$458$	−2.65393	−	4.59674i	−0.124010	−	0.214792i
$459$	14.0862	−	8.13267i	0.657487	−	0.379600i
$460$	−8.99589	−	5.19378i	−0.419436	−	0.242161i
$461$	−22.4278			−1.04457			−0.522284	−	0.852772i	$-0.674920\pi$
$461$	−22.4278			−1.04457			−0.522284	+	0.852772i	$0.674920\pi$
$462$		0			0
$463$	−15.6274			−0.726267			−0.363134	−	0.931737i	$-0.618293\pi$
$463$	−15.6274			−0.726267			−0.363134	+	0.931737i	$0.618293\pi$
$464$	3.06907	+	1.77193i	0.142478	+	0.0822598i
$465$	−10.2845	+	5.93774i	−0.476931	+	0.275356i
$466$	10.6596	+	18.4629i	0.493796	+	0.855279i
$467$	5.27860	+	3.04760i	0.244264	+	0.141026i	0.617135	−	0.786857i	$-0.288293\pi$
$467$	5.27860	+	3.04760i	0.244264	+	0.141026i	−0.372871	+	0.927883i	$0.621626\pi$
$468$	7.94008			0.367030
$469$		0			0
$470$		−	5.91916i		−	0.273031i
$471$	3.99346	−	6.91688i	0.184009	−	0.318713i
$472$	1.36664	+	2.36710i	0.0629048	+	0.108954i
$473$	20.8131	−	14.0776i	0.956987	−	0.647291i
$474$	−13.8914	−	8.02023i	−0.638055	−	0.368381i
$475$	−26.0556			−1.19551
$476$		0			0
$477$	−9.32690			−0.427049
$478$	3.62582	−	6.28010i	0.165841	−	0.287245i
$479$	−15.3138	−	26.5242i	−0.699704	−	1.21192i	−0.968569	−	0.248745i	$-0.919982\pi$
$479$	−15.3138	−	26.5242i	−0.699704	−	1.21192i	0.268865	−	0.963178i	$-0.413352\pi$
$480$	−1.11990	+	0.646574i	−0.0511162	+	0.0295119i
$481$	−0.629341	+	1.09005i	−0.0286955	+	0.0497020i
$482$			3.55410i			0.161885i
$483$		0			0
$484$	−10.8890	+	1.55896i	−0.494953	+	0.0708617i
$485$	−6.71808	+	11.6361i	−0.305052	+	0.528366i
$486$	7.93547	+	13.7446i	0.359960	+	0.623469i
$487$	1.58726	+	2.74922i	0.0719258	+	0.124579i	0.899745	−	0.436415i	$-0.143752\pi$
$487$	1.58726	+	2.74922i	0.0719258	+	0.124579i	−0.827819	+	0.560995i	$0.810419\pi$
$488$	1.30779	+	0.755050i	0.0592007	+	0.0341795i
$489$		−	18.7110i		−	0.846141i
$490$		0			0
$491$		−	32.6507i		−	1.47351i	−0.676162	−	0.736753i	$-0.736358\pi$
$491$		−	32.6507i		−	1.47351i	0.676162	−	0.736753i	$-0.263642\pi$
$492$	−5.38538	−	3.10925i	−0.242792	−	0.140176i
$493$	−9.82691	+	5.67357i	−0.442582	+	0.255525i
$494$	26.9755	−	15.5743i	1.21368	−	0.700721i
$495$	7.30045	+	3.54903i	0.328131	+	0.159517i
$496$			9.18338i			0.412346i
$497$		0			0
$498$	1.36640			0.0612297
$499$	−14.2274	+	24.6426i	−0.636906	+	1.10315i	0.349202	+	0.937048i	$0.386453\pi$
$499$	−14.2274	+	24.6426i	−0.636906	+	1.10315i	−0.986108	+	0.166106i	$0.946881\pi$
$500$	−9.17356	+	5.29636i	−0.410254	+	0.236860i
$501$	−12.7814	+	7.37932i	−0.571029	+	0.329684i
$502$	0.367864	−	0.637159i	0.0164186	−	0.0284378i
$503$	22.5058			1.00348			0.501741	−	0.865018i	$-0.332693\pi$
$503$	22.5058			1.00348			0.501741	+	0.865018i	$0.332693\pi$
$504$		0			0
$505$		−	12.6684i		−	0.563739i
$506$	−24.6165	−	11.9671i	−1.09434	−	0.532000i
$507$	3.26892	−	1.88731i	0.145178	−	0.0838185i
$508$	−9.77130	+	5.64146i	−0.433531	+	0.250299i
$509$	11.6437	+	6.72249i	0.516098	+	0.297969i	0.735337	−	0.677702i	$-0.237024\pi$
$509$	11.6437	+	6.72249i	0.516098	+	0.297969i	−0.219239	+	0.975671i	$0.570357\pi$
$510$		−	4.14055i		−	0.183347i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	33.5585	+	19.3750i	1.48164	+	0.855427i
$514$	−8.10325	−	14.0352i	−0.357419	−	0.619068i
$515$	1.81579	+	3.14505i	0.0800134	+	0.138587i
$516$	3.89176	−	6.74073i	0.171325	−	0.296744i
$517$	−1.10803	−	15.5576i	−0.0487310	−	0.684221i
$518$		0			0
$519$			4.89362i			0.214806i
$520$	2.56984	−	4.45110i	0.112695	−	0.195193i
$521$	−34.2339	+	19.7649i	−1.49981	+	0.865918i	−1.00000		0.000215610i	$-0.999931\pi$
$521$	−34.2339	+	19.7649i	−1.49981	+	0.865918i	−0.499813	+	0.866133i	$0.666598\pi$
$522$	−3.44549	−	5.96777i	−0.150805	−	0.261202i
$523$	14.8061	−	25.6449i	0.647425	−	1.12137i	−0.336310	−	0.941751i	$-0.609179\pi$
$523$	14.8061	−	25.6449i	0.647425	−	1.12137i	0.983736	−	0.179622i	$-0.0574875\pi$
$524$	−7.03388			−0.307276
$525$		0			0
$526$	−24.3021			−1.05962
$527$	−25.4650	−	14.7022i	−1.10927	−	0.640438i
$528$	−2.82244	+	1.90905i	−0.122831	+	0.0830810i
$529$	−22.5538	−	39.0643i	−0.980599	−	1.69845i
$530$	−3.01869	+	5.22853i	−0.131124	+	0.227113i
$531$		−	5.31483i		−	0.230644i
$532$		0			0
$533$	24.7158			1.07056
$534$	9.47551	+	5.47069i	0.410045	+	0.236740i
$535$	10.2583	+	17.7679i	0.443504	+	0.768172i
$536$	−2.92792	+	1.69044i	−0.126467	+	0.0730157i
$537$	3.46154	+	1.99852i	0.149377	+	0.0862426i
$538$	−27.0484			−1.16614
$539$		0			0
$540$	6.39395			0.275152
$541$	15.1111	+	8.72442i	0.649679	+	0.375092i	0.788333	−	0.615249i	$-0.210944\pi$
$541$	15.1111	+	8.72442i	0.649679	+	0.375092i	−0.138654	+	0.990341i	$0.544278\pi$
$542$	9.04417	−	5.22166i	0.388480	−	0.224289i
$543$	−6.71387	−	11.6288i	−0.288120	−	0.499038i
$544$	−2.77294	−	1.60096i	−0.118889	−	0.0686405i
$545$	−14.4792			−0.620220
$546$		0			0
$547$		−	1.16878i		−	0.0499734i	−0.999688	−	0.0249867i	$-0.992046\pi$
$547$		−	1.16878i		−	0.0499734i	0.999688	−	0.0249867i	$-0.00795434\pi$
$548$	4.54487	−	7.87195i	0.194147	−	0.336273i
$549$	−1.46818	−	2.54297i	−0.0626605	−	0.108531i
$550$	−9.38372	+	6.34700i	−0.400123	+	0.270637i
$551$	−23.4113	−	13.5165i	−0.997355	−	0.575823i
$552$	−8.47871			−0.360878
$553$		0			0
$554$	20.4006			0.866739
$555$	−0.199303	+	0.345203i	−0.00845995	+	0.0146531i
$556$	3.93273	+	6.81169i	0.166785	+	0.288880i
$557$	4.20151	−	2.42574i	0.178024	−	0.102782i	−0.408340	−	0.912830i	$-0.633892\pi$
$557$	4.20151	−	2.42574i	0.178024	−	0.102782i	0.586364	+	0.810048i	$0.300559\pi$
$558$	8.92847	−	15.4646i	0.377972	−	0.654667i
$559$			30.9360i			1.30845i
$560$		0			0
$561$	−0.775084	−	10.8828i	−0.0327241	−	0.459471i
$562$	4.99767	−	8.65622i	0.210814	−	0.365141i
$563$	13.0572	+	22.6158i	0.550297	+	0.953143i	0.998253	+	0.0590869i	$0.0188189\pi$
$563$	13.0572	+	22.6158i	0.550297	+	0.953143i	−0.447956	+	0.894056i	$0.647848\pi$
$564$	−2.41572	−	4.18415i	−0.101720	−	0.176184i
$565$	−0.609293	−	0.351776i	−0.0256332	−	0.0147993i
$566$			3.48896i			0.146652i
$567$		0			0
$568$		−	3.50810i		−	0.147196i
$569$	−6.47913	−	3.74073i	−0.271619	−	0.156820i	0.358004	−	0.933720i	$-0.383457\pi$
$569$	−6.47913	−	3.74073i	−0.271619	−	0.156820i	−0.629623	+	0.776901i	$0.716791\pi$
$570$	8.54274	−	4.93215i	0.357816	−	0.206585i
$571$	−28.5249	+	16.4688i	−1.19373	+	0.689199i	−0.959150	−	0.282898i	$-0.908704\pi$
$571$	−28.5249	+	16.4688i	−1.19373	+	0.689199i	−0.234578	+	0.972097i	$0.575371\pi$
$572$	5.92120	−	12.1801i	0.247578	−	0.509273i
$573$			6.16430i			0.257517i
$574$		0			0
$575$	−28.1890			−1.17556
$576$	0.972242	−	1.68397i	0.0405101	−	0.0701655i
$577$	−1.34703	+	0.777711i	−0.0560778	+	0.0323765i	−0.527777	−	0.849383i	$-0.676974\pi$
$577$	−1.34703	+	0.777711i	−0.0560778	+	0.0323765i	0.471699	+	0.881760i	$0.343641\pi$
$578$	−5.84372	+	3.37387i	−0.243067	+	0.140335i
$579$	−4.81991	+	8.34833i	−0.200309	+	0.346945i
$580$	−4.46060			−0.185216
$581$		0			0
$582$			10.9671i			0.454600i
$583$	−6.95540	+	14.3074i	−0.288063	+	0.592553i
$584$	0.837321	−	0.483428i	0.0346486	−	0.0200044i
$585$	−8.65509	+	4.99702i	−0.357844	+	0.206601i
$586$	15.0298	+	8.67744i	0.620874	+	0.358462i
$587$			42.8124i			1.76706i	0.468376	+	0.883529i	$0.344839\pi$
$587$			42.8124i			1.76706i	−0.468376	+	0.883529i	$0.655161\pi$
$588$		0			0
$589$		−	70.0520i		−	2.88644i
$590$	−2.97942	−	1.72017i	−0.122661	−	0.0708183i
$591$	8.91107	+	15.4344i	0.366552	+	0.634887i
$592$	0.154122	+	0.266948i	0.00633439	+	0.0109715i
$593$	16.7711	−	29.0484i	0.688707	−	1.19288i	−0.283549	−	0.958958i	$-0.591512\pi$
$593$	16.7711	−	29.0484i	0.688707	−	1.19288i	0.972256	−	0.233918i	$-0.0751549\pi$
$594$	16.8055	−	1.19691i	0.689537	−	0.0491097i
$595$		0			0
$596$		−	6.23096i		−	0.255230i
$597$	−1.50279	+	2.60290i	−0.0615050	+	0.106530i
$598$	29.1842	−	16.8495i	1.19343	−	0.689029i
$599$	−7.00856	−	12.1392i	−0.286362	−	0.495993i	0.686577	−	0.727057i	$-0.259113\pi$
$599$	−7.00856	−	12.1392i	−0.286362	−	0.495993i	−0.972939	+	0.231064i	$0.925779\pi$
$600$	−1.75463	+	3.03910i	−0.0716323	+	0.124071i
$601$	−36.1513			−1.47464			−0.737322	−	0.675542i	$-0.763910\pi$
$601$	−36.1513			−1.47464			−0.737322	+	0.675542i	$0.763910\pi$
$602$		0			0
$603$	6.57405			0.267716
$604$	15.1642	+	8.75506i	0.617023	+	0.356238i
$605$	10.8884	−	8.55222i	0.442677	−	0.347697i
$606$	−5.17023	−	8.95510i	−0.210026	−	0.363776i
$607$	14.8196	−	25.6684i	0.601511	−	1.04185i	−0.391082	−	0.920356i	$-0.627899\pi$
$607$	14.8196	−	25.6684i	0.601511	−	1.04185i	0.992593	−	0.121491i	$-0.0387676\pi$
$608$		−	7.62813i		−	0.309362i
$609$		0			0
$610$	−1.90074			−0.0769586
$611$	16.6301	+	9.60139i	0.672782	+	0.388431i
$612$	3.11304	+	5.39194i	0.125837	+	0.217956i
$613$	28.9964	−	16.7411i	1.17115	−	0.676166i	0.217202	−	0.976127i	$-0.430307\pi$
$613$	28.9964	−	16.7411i	1.17115	−	0.676166i	0.953951	+	0.299961i	$0.0969737\pi$
$614$	−19.6439	−	11.3414i	−0.792765	−	0.457703i
$615$	7.82712			0.315620
$616$		0			0
$617$	8.79395			0.354031			0.177016	−	0.984208i	$-0.443356\pi$
$617$	8.79395			0.354031			0.177016	+	0.984208i	$0.443356\pi$
$618$	2.56710	+	1.48212i	0.103264	+	0.0596195i
$619$	−24.2445	+	13.9976i	−0.974469	+	0.562610i	−0.900596	−	0.434657i	$-0.856869\pi$
$619$	−24.2445	+	13.9976i	−0.974469	+	0.562610i	−0.0738736	+	0.997268i	$0.523536\pi$
$620$	−5.77948	−	10.0104i	−0.232109	−	0.402025i
$621$	36.3063	+	20.9614i	1.45692	+	0.841153i
$622$	6.64116			0.266286
$623$		0			0
$624$		−	4.19520i		−	0.167942i
$625$	−1.87286	+	3.24390i	−0.0749146	+	0.129756i
$626$	−0.251484	−	0.435583i	−0.0100513	−	0.0174094i
$627$	21.5300	−	14.5625i	0.859824	−	0.581571i
$628$	6.73252	+	3.88702i	0.268657	+	0.155109i
$629$	−0.986974			−0.0393532
$630$		0			0
$631$	−0.154087			−0.00613412			−0.00306706	−	0.999995i	$-0.500976\pi$
$631$	−0.154087			−0.00613412			−0.00306706	+	0.999995i	$0.500976\pi$
$632$	7.80647	−	13.5212i	0.310525	−	0.537844i
$633$	0.129825	+	0.224863i	0.00516008	+	0.00893752i
$634$	−9.13547	+	5.27437i	−0.362816	+	0.209472i
$635$	7.10081	−	12.2990i	0.281787	−	0.488069i
$636$			4.92794i			0.195405i
$637$		0			0
$638$	−11.7240	+	0.834995i	−0.464156	+	0.0330578i
$639$	−3.41072	+	5.90754i	−0.134926	+	0.233699i
$640$	−0.629341	−	1.09005i	−0.0248769	−	0.0430880i
$641$	9.92017	+	17.1822i	0.391823	+	0.678658i	0.992690	−	0.120691i	$-0.0385112\pi$
$641$	9.92017	+	17.1822i	0.391823	+	0.678658i	−0.600867	+	0.799349i	$0.705178\pi$
$642$	14.5028	+	8.37319i	0.572379	+	0.330463i
$643$		−	25.2948i		−	0.997529i	−0.866737	−	0.498765i	$-0.833787\pi$
$643$		−	25.2948i		−	0.997529i	0.866737	−	0.498765i	$-0.166213\pi$
$644$		0			0
$645$			9.79699i			0.385756i
$646$	21.1523	+	12.2123i	0.832228	+	0.480487i
$647$	−0.813596	+	0.469730i	−0.0319857	+	0.0184670i	−0.515908	−	0.856644i	$-0.672545\pi$
$647$	−0.813596	+	0.469730i	−0.0319857	+	0.0184670i	0.483922	+	0.875111i	$0.339212\pi$
$648$	−0.532150	+	0.307237i	−0.0209048	+	0.0120694i
$649$	−8.15293	−	3.96346i	−0.320031	−	0.155579i
$650$		−	13.9477i		−	0.547073i
$651$		0			0
$652$	18.2123			0.713249
$653$	5.50375	−	9.53278i	0.215379	−	0.373047i	−0.738011	−	0.674789i	$-0.764235\pi$
$653$	5.50375	−	9.53278i	0.215379	−	0.373047i	0.953390	+	0.301742i	$0.0975681\pi$
$654$	−10.2351	+	5.90922i	−0.400223	+	0.231069i
$655$	7.66729	−	4.42671i	0.299586	−	0.172966i
$656$	3.02638	−	5.24185i	0.118160	−	0.204660i
$657$	−1.88004			−0.0733472
$658$		0			0
$659$			29.9068i			1.16500i	0.812830	+	0.582501i	$0.197926\pi$
$659$			29.9068i			1.16500i	−0.812830	+	0.582501i	$0.802074\pi$
$660$	1.87516	−	3.85725i	0.0729904	−	0.150143i
$661$	−2.32896	+	1.34463i	−0.0905861	+	0.0522999i	−0.544609	−	0.838690i	$-0.683322\pi$
$661$	−2.32896	+	1.34463i	−0.0905861	+	0.0522999i	0.454023	+	0.890990i	$0.349989\pi$
$662$	−5.00613	+	2.89029i	−0.194569	+	0.112334i
$663$	11.6330	+	6.71633i	0.451789	+	0.260841i
$664$			1.32998i			0.0516132i
$665$		0			0
$666$		−	0.599378i		−	0.0232254i
$667$	−25.3282	−	14.6233i	−0.980713	−	0.566215i
$668$	−7.18264	−	12.4407i	−0.277905	−	0.481345i
$669$	9.77917	+	16.9380i	0.378084	+	0.654862i
$670$	2.12772	−	3.68532i	0.0822011	−	0.142376i
$671$	−4.99578	+	0.355806i	−0.192860	+	0.0137357i
$672$		0			0
$673$		−	3.56361i		−	0.137367i	−0.997638	−	0.0686836i	$-0.978120\pi$
$673$		−	3.56361i		−	0.137367i	0.997638	−	0.0686836i	$-0.0218799\pi$
$674$	5.56129	−	9.63243i	0.214213	−	0.371027i
$675$	15.0268	−	8.67572i	0.578381	−	0.333929i
$676$	1.83701	+	3.18180i	0.0706543	+	0.122377i
$677$	−15.5901	+	27.0029i	−0.599178	+	1.03781i	0.393765	+	0.919211i	$0.371172\pi$
$677$	−15.5901	+	27.0029i	−0.599178	+	1.03781i	−0.992943	+	0.118595i	$0.962161\pi$
$678$	−0.574264			−0.0220545
$679$		0			0
$680$	4.03019			0.154551
$681$	16.3774	+	9.45552i	0.627585	+	0.362336i
$682$	−17.0643	−	25.2287i	−0.653426	−	0.966058i
$683$	7.79993	+	13.5099i	0.298456	+	0.516941i	0.975783	−	0.218741i	$-0.0701951\pi$
$683$	7.79993	+	13.5099i	0.298456	+	0.516941i	−0.677327	+	0.735682i	$0.736862\pi$
$684$	−7.41639	+	12.8456i	−0.283573	+	0.491163i
$685$			11.4411i			0.437142i
$686$		0			0
$687$	5.45320			0.208053
$688$	6.56107	+	3.78804i	0.250138	+	0.144417i
$689$	−9.79316	−	16.9623i	−0.373090	−	0.646210i
$690$	9.24223	−	5.33600i	0.351846	−	0.203138i
$691$	31.8902	+	18.4118i	1.21316	+	0.700419i	0.963447	−	0.267901i	$-0.0863299\pi$
$691$	31.8902	+	18.4118i	1.21316	+	0.700419i	0.249714	+	0.968320i	$0.419663\pi$
$692$	−4.76319			−0.181069
$693$		0			0
$694$	−14.6714			−0.556918
$695$	−8.57375	−	4.95006i	−0.325221	−	0.187766i
$696$	−3.15311	+	1.82045i	−0.119518	+	0.0690040i
$697$	9.69021	+	16.7839i	0.367043	+	0.635737i
$698$	−21.3708	−	12.3385i	−0.808899	−	0.467018i
$699$	−21.9029			−0.828445
$700$		0			0
$701$		−	15.6940i		−	0.592754i	−0.955071	−	0.296377i	$-0.904222\pi$
$701$		−	15.6940i		−	0.592754i	0.955071	−	0.296377i	$-0.0957784\pi$
$702$	−10.3715	+	17.9640i	−0.391449	+	0.678009i
$703$	−1.17567	−	2.03631i	−0.0443411	−	0.0768010i
$704$	−1.85817	−	2.74722i	−0.0700325	−	0.103540i
$705$	5.26651	+	3.04062i	0.198348	+	0.114516i
$706$	−19.2447			−0.724285
$707$		0			0
$708$	−2.80813			−0.105536
$709$	12.1733	−	21.0847i	0.457176	−	0.791852i	−0.541634	−	0.840614i	$-0.682194\pi$
$709$	12.1733	−	21.0847i	0.457176	−	0.791852i	0.998810	+	0.0487621i	$0.0155276\pi$
$710$	2.20779	+	3.82400i	0.0828569	+	0.143512i
$711$	−26.2918	+	15.1796i	−0.986018	+	0.569278i
$712$	−5.32488	+	9.22296i	−0.199558	+	0.345645i
$713$		−	75.7880i		−	2.83828i
$714$		0			0
$715$	1.21100	+	17.0033i	0.0452887	+	0.635888i
$716$	−1.94526	+	3.36928i	−0.0726976	+	0.125916i
$717$	3.72510	+	6.45207i	0.139116	+	0.240957i
$718$	1.64703	+	2.85275i	0.0614668	+	0.106464i
$719$	−36.9070	−	21.3083i	−1.37640	−	0.794665i	−0.384676	−	0.923051i	$-0.625687\pi$
$719$	−36.9070	−	21.3083i	−1.37640	−	0.794665i	−0.991724	+	0.128386i	$0.959020\pi$
$720$			2.44749i			0.0912125i
$721$		0			0
$722$			39.1884i			1.45844i
$723$	−3.16222	−	1.82571i	−0.117604	−	0.0678988i
$724$	11.3188	−	6.53492i	0.420661	−	0.242868i
$725$	−10.4831	+	6.05242i	−0.389332	+	0.224781i
$726$	4.20650	−	10.4892i	0.156118	−	0.389290i
$727$			23.2698i			0.863031i	0.902106	+	0.431515i	$0.142021\pi$
$727$			23.2698i			0.863031i	−0.902106	+	0.431515i	$0.857979\pi$
$728$		0			0
$729$	−14.4621			−0.535633
$730$	−0.608482	+	1.05392i	−0.0225209	+	0.0390074i
$731$	−21.0080	+	12.1290i	−0.777008	+	0.448606i
$732$	−1.34360	+	0.775726i	−0.0496607	+	0.0286716i
$733$	−18.8378	+	32.6281i	−0.695791	+	1.20515i	0.274122	+	0.961695i	$0.411613\pi$
$733$	−18.8378	+	32.6281i	−0.695791	+	1.20515i	−0.969913	+	0.243450i	$0.921721\pi$
$734$	30.9410			1.14205
$735$		0			0
$736$		−	8.25273i		−	0.304200i
$737$	4.90251	−	10.0846i	0.180586	−	0.371470i
$738$	−10.1927	+	5.88475i	−0.375198	+	0.216621i
$739$	−0.479784	+	0.277003i	−0.0176491	+	0.0101897i	−0.508799	−	0.860886i	$-0.669910\pi$
$739$	−0.479784	+	0.277003i	−0.0176491	+	0.0101897i	0.491149	+	0.871075i	$0.336577\pi$
$740$	−0.336003	−	0.193991i	−0.0123517	−	0.00713126i
$741$			32.0015i			1.17561i
$742$		0			0
$743$		−	20.1974i		−	0.740972i	−0.928838	−	0.370486i	$-0.879191\pi$
$743$		−	20.1974i		−	0.740972i	0.928838	−	0.370486i	$-0.120809\pi$
$744$	−8.17082	−	4.71742i	−0.299557	−	0.172949i
$745$	3.92140	+	6.79207i	0.143669	+	0.248842i
$746$	0.480798	+	0.832767i	0.0176033	+	0.0304898i
$747$	1.29306	−	2.23965i	0.0473107	−	0.0819445i
$748$	10.5927	−	0.754426i	0.387308	−	0.0275845i
$749$		0			0
$750$		−	10.8828i		−	0.397383i
$751$	−3.70031	+	6.40913i	−0.135026	+	0.233872i	−0.925607	−	0.378485i	$-0.876445\pi$
$751$	−3.70031	+	6.40913i	−0.135026	+	0.233872i	0.790581	+	0.612357i	$0.209779\pi$
$752$	4.07263	−	2.35133i	0.148513	−	0.0857443i
$753$	0.377937	+	0.654606i	0.0137728	+	0.0238552i
$754$	7.23547	−	12.5322i	0.263500	−	0.456396i
$755$	−22.0397			−0.802106
$756$		0			0
$757$	−29.1994			−1.06127			−0.530636	−	0.847600i	$-0.678047\pi$
$757$	−29.1994			−1.06127			−0.530636	+	0.847600i	$0.678047\pi$
$758$	1.22297	+	0.706081i	0.0444202	+	0.0256460i
$759$	23.2929	−	15.7549i	0.845477	−	0.571867i
$760$	4.80070	+	8.31505i	0.174140	+	0.301619i
$761$	−25.4831	+	44.1380i	−0.923761	+	1.60000i	−0.130220	+	0.991485i	$0.541568\pi$
$761$	−25.4831	+	44.1380i	−0.923761	+	1.60000i	−0.793541	+	0.608517i	$0.791765\pi$
$762$		−	11.5919i		−	0.419930i
$763$		0			0
$764$	−6.00000			−0.217072
$765$	−6.78674	−	3.91832i	−0.245375	−	0.141667i
$766$	1.89039	+	3.27426i	0.0683027	+	0.118304i
$767$	9.66576	−	5.58053i	0.349010	−	0.201501i
$768$	−0.889740	−	0.513691i	−0.0321057	−	0.0185362i
$769$	32.9963			1.18988			0.594938	−	0.803771i	$-0.297176\pi$
$769$	32.9963			1.18988			0.594938	+	0.803771i	$0.297176\pi$
$770$		0			0
$771$	16.6503			0.599645
$772$	−8.12582	−	4.69144i	−0.292455	−	0.168849i
$773$	28.1797	−	16.2696i	1.01355	−	0.585175i	0.101323	−	0.994854i	$-0.467692\pi$
$773$	28.1797	−	16.2696i	1.01355	−	0.585175i	0.912230	+	0.409678i	$0.134359\pi$
$774$	−7.36578	−	12.7579i	−0.264757	−	0.458573i
$775$	−27.1654	−	15.6839i	−0.975808	−	0.563383i
$776$	−10.6748			−0.383202
$777$		0			0
$778$		−	3.37886i		−	0.121138i
$779$	−23.0856	+	39.9855i	−0.827129	+	1.43263i
$780$	2.64021	+	4.57298i	0.0945347	+	0.163739i
$781$	6.51865	+	9.63750i	0.233256	+	0.344857i
$782$	22.8843	+	13.2123i	0.818341	+	0.472470i
$783$	18.0024			0.643353
$784$		0			0
$785$	−9.78505			−0.349243
$786$	3.61324	−	6.25832i	0.128880	−	0.223227i
$787$	−10.0577	−	17.4205i	−0.358519	−	0.620973i	0.629195	−	0.777248i	$-0.283385\pi$
$787$	−10.0577	−	17.4205i	−0.358519	−	0.620973i	−0.987714	+	0.156275i	$0.950051\pi$
$788$	−15.0230	+	8.67356i	−0.535174	+	0.308983i
$789$	12.4838	−	21.6225i	0.444433	−	0.769781i
$790$			19.6517i			0.699177i
$791$		0			0
$792$	0.458154	+	6.43283i	0.0162798	+	0.228581i
$793$	3.08316	−	5.34019i	0.109486	−	0.189636i
$794$	−5.76499	−	9.98525i	−0.204592	−	0.354363i
$795$	−3.10135	−	5.37170i	−0.109994	−	0.190515i
$796$	−2.53353	−	1.46273i	−0.0897985	−	0.0518452i
$797$			31.1568i			1.10363i	0.833966	+	0.551816i	$0.186065\pi$
$797$			31.1568i			1.10363i	−0.833966	+	0.551816i	$0.813935\pi$
$798$		0			0
$799$			15.0575i			0.532697i
$800$	−2.95810	−	1.70786i	−0.104585	−	0.0603819i
$801$	17.9339	−	10.3541i	0.633663	−	0.365846i
$802$	22.5619	−	13.0261i	0.796689	−	0.459969i
$803$	−1.40201	+	2.88397i	−0.0494759	+	0.101773i
$804$		−	3.47345i		−	0.122499i
$805$		0			0
$806$	37.4993			1.32086
$807$	13.8945	−	24.0661i	0.489111	−	0.847165i
$808$	8.71642	−	5.03242i	0.306642	−	0.177040i
$809$	−12.6960	+	7.33001i	−0.446366	+	0.257709i	−0.706294	−	0.707918i	$-0.749634\pi$
$809$	−12.6960	+	7.33001i	−0.446366	+	0.257709i	0.259928	+	0.965628i	$0.416301\pi$
$810$	0.386714	−	0.669808i	0.0135877	−	0.0235346i
$811$	45.7501			1.60650			0.803251	−	0.595640i	$-0.203102\pi$
$811$	45.7501			1.60650			0.803251	+	0.595640i	$0.203102\pi$
$812$		0			0
$813$			10.7293i			0.376292i
$814$	−0.919443	−	0.446977i	−0.0322265	−	0.0156665i
$815$	−19.8523	+	11.4618i	−0.695397	+	0.401488i
$816$	2.84887	−	1.64480i	0.0997304	−	0.0575794i
$817$	−50.0487	−	28.8956i	−1.75098	−	1.01093i
$818$		−	35.0217i		−	1.22451i
$819$		0			0
$820$			7.61851i			0.266050i
$821$	6.11121	+	3.52831i	0.213283	+	0.123139i	0.602836	−	0.797865i	$-0.294037\pi$
$821$	6.11121	+	3.52831i	0.213283	+	0.123139i	−0.389553	+	0.921004i	$0.627371\pi$
$822$	4.66932	+	8.08750i	0.162861	+	0.282084i
$823$	14.2038	+	24.6016i	0.495112	+	0.857559i	0.999984	−	0.00563530i	$-0.00179378\pi$
$823$	14.2038	+	24.6016i	0.495112	+	0.857559i	−0.504872	+	0.863194i	$0.668460\pi$
$824$	−1.44261	+	2.49868i	−0.0502559	+	0.0870457i
$825$	−0.826840	−	11.6095i	−0.0287869	−	0.404190i
$826$		0			0
$827$			0.161893i			0.00562957i	0.999996	+	0.00281478i	$0.000895975\pi$
$827$			0.161893i			0.00562957i	−0.999996	+	0.00281478i	$0.999104\pi$
$828$	−8.02365	+	13.8974i	−0.278841	+	0.482967i
$829$	21.0966	−	12.1801i	0.732715	−	0.423033i	−0.0866997	−	0.996234i	$-0.527632\pi$
$829$	21.0966	−	12.1801i	0.732715	−	0.423033i	0.819415	+	0.573201i	$0.194299\pi$
$830$	−0.837011	−	1.44974i	−0.0290531	−	0.0503214i
$831$	−10.4796	+	18.1512i	−0.363534	+	0.629660i
$832$	4.08338			0.141566
$833$		0			0
$834$	−8.08084			−0.279817
$835$	15.6589	+	9.04066i	0.541898	+	0.312865i
$836$	14.1744	+	20.9561i	0.490231	+	0.724783i
$837$	23.3252	+	40.4005i	0.806238	+	1.39644i
$838$	−6.06211	+	10.4999i	−0.209412	+	0.362713i
$839$			3.31341i			0.114392i	0.998363	+	0.0571958i	$0.0182159\pi$
$839$			3.31341i			0.114392i	−0.998363	+	0.0571958i	$0.981784\pi$
$840$		0			0
$841$	16.4410			0.566932
$842$	−16.1895	−	9.34699i	−0.557926	−	0.322119i
$843$	5.13452	+	8.89326i	0.176842	+	0.306300i
$844$	−0.218870	+	0.126365i	−0.00753382	+	0.00434965i
$845$	−4.00487	−	2.31221i	−0.137772	−	0.0795425i
$846$	−9.14426			−0.314386
$847$		0			0
$848$	−4.79659			−0.164716
$849$	−3.10427	−	1.79225i	−0.106538	−	0.0615098i
$850$	9.47158	−	5.46842i	0.324873	−	0.187565i
$851$	−1.27193	−	2.20305i	−0.0436012	−	0.0755196i
$852$	3.12129	+	1.80208i	0.106934	+	0.0617382i
$853$	17.0905			0.585169			0.292584	−	0.956240i	$-0.405485\pi$
$853$	17.0905			0.585169			0.292584	+	0.956240i	$0.405485\pi$
$854$		0			0
$855$		−	18.6698i		−	0.638492i
$856$	−8.15002	+	14.1162i	−0.278562	+	0.482483i
$857$	−11.2484	−	19.4827i	−0.384237	−	0.665517i	0.607426	−	0.794376i	$-0.292202\pi$
$857$	−11.2484	−	19.4827i	−0.384237	−	0.665517i	−0.991663	+	0.128859i	$0.958869\pi$
$858$	7.79540	+	11.5251i	0.266131	+	0.393461i
$859$	33.3698	+	19.2661i	1.13856	+	0.657350i	0.946074	−	0.323950i	$-0.105011\pi$
$859$	33.3698	+	19.2661i	1.13856	+	0.657350i	0.192489	+	0.981299i	$0.438344\pi$
$860$	−9.53587			−0.325170
$861$		0			0
$862$	33.9418			1.15606
$863$	12.8730	−	22.2967i	0.438202	−	0.758989i	−0.559348	−	0.828933i	$-0.688949\pi$
$863$	12.8730	−	22.2967i	0.438202	−	0.758989i	0.997551	+	0.0699437i	$0.0222820\pi$
$864$	2.53994	+	4.39930i	0.0864105	+	0.149667i
$865$	5.19212	−	2.99767i	0.176537	−	0.101924i
$866$	−13.5474	+	23.4648i	−0.460360	+	0.797368i
$867$		−	6.93252i		−	0.235441i
$868$		0			0
$869$	3.67867	+	51.6514i	0.124790	+	1.75215i
$870$	2.29137	−	3.96877i	0.0776847	−	0.134554i
$871$	6.90270	+	11.9558i	0.233889	+	0.405108i
$872$	−5.75172	−	9.96227i	−0.194778	−	0.337365i
$873$	17.9760	+	10.3785i	0.608397	+	0.351258i
$874$			62.9529i			2.12941i
$875$		0			0
$876$			0.993331i			0.0335615i
$877$	14.7676	+	8.52609i	0.498667	+	0.287906i	0.728163	−	0.685404i	$-0.240374\pi$
$877$	14.7676	+	8.52609i	0.498667	+	0.287906i	−0.229496	+	0.973310i	$0.573708\pi$
$878$	−17.7135	+	10.2269i	−0.597803	+	0.345142i
$879$	−15.4413	+	8.91506i	−0.520823	+	0.300697i
$880$	3.75444	+	1.82518i	0.126562	+	0.0615268i
$881$			38.3968i			1.29362i	0.762651	+	0.646811i	$0.223898\pi$
$881$			38.3968i			1.29362i	−0.762651	+	0.646811i	$0.776102\pi$
$882$		0			0
$883$	−35.3727			−1.19038			−0.595192	−	0.803583i	$-0.702924\pi$
$883$	−35.3727			−1.19038			−0.595192	+	0.803583i	$0.702924\pi$
$884$	−6.53732	+	11.3230i	−0.219874	+	0.380833i
$885$	3.06101	−	1.76727i	0.102895	−	0.0594062i
$886$	−3.11541	+	1.79868i	−0.104664	+	0.0604279i
$887$	1.05289	−	1.82365i	0.0353525	−	0.0612322i	−0.847808	−	0.530304i	$-0.822078\pi$
$887$	1.05289	−	1.82365i	0.0353525	−	0.0612322i	0.883160	+	0.469071i	$0.155411\pi$
$888$	−0.316686			−0.0106273
$889$		0			0
$890$		−	13.4047i		−	0.449325i
$891$	0.891031	−	1.83287i	0.0298507	−	0.0614036i
$892$	−16.4866	+	9.51852i	−0.552011	+	0.318704i
$893$	−31.0665	+	17.9363i	−1.03960	+	0.600215i
$894$	5.54394	+	3.20079i	0.185417	+	0.107051i
$895$		−	4.89692i		−	0.163686i
$896$		0			0
$897$			34.6218i			1.15599i
$898$	−32.1005	−	18.5332i	−1.07121	−	0.618461i
$899$	−16.2723	−	28.1845i	−0.542712	−	0.940005i
$900$	3.32091	+	5.75198i	0.110697	+	0.191733i
$901$	7.67914	−	13.3007i	0.255829	−	0.443109i
$902$	1.42613	+	20.0240i	0.0474851	+	0.666727i
$903$		0			0
$904$		−	0.558958i		−	0.0185907i
$905$	−8.22539	+	14.2468i	−0.273421	+	0.473579i
$906$	−15.5794	+	8.99479i	−0.517592	+	0.298832i
$907$	−25.2204	−	43.6831i	−0.837431	−	1.45047i	−0.892035	−	0.451965i	$-0.850723\pi$
$907$	−25.2204	−	43.6831i	−0.837431	−	1.45047i	0.0546043	−	0.998508i	$-0.482610\pi$
$908$	−9.20350	+	15.9409i	−0.305429	+	0.529018i
$909$	−19.5709			−0.649127
$910$		0			0
$911$	−1.24825			−0.0413565			−0.0206782	−	0.999786i	$-0.506583\pi$
$911$	−1.24825			−0.0413565			−0.0206782	+	0.999786i	$0.506583\pi$
$912$	6.78705	+	3.91851i	0.224742	+	0.129755i
$913$	−2.47133	−	3.65374i	−0.0817891	−	0.120921i
$914$	9.07561	+	15.7194i	0.300195	+	0.519952i
$915$	0.976392	−	1.69116i	0.0322785	−	0.0559080i
$916$			5.30786i			0.175377i
$917$		0			0
$918$	−16.2653			−0.536836
$919$	14.0660	+	8.12103i	0.463996	+	0.267888i	0.713723	−	0.700428i	$-0.247008\pi$
$919$	14.0660	+	8.12103i	0.463996	+	0.267888i	−0.249727	+	0.968316i	$0.580341\pi$
$920$	5.19378	+	8.99589i	0.171234	+	0.296586i
$921$	20.1818	−	11.6520i	0.665014	−	0.383946i
$922$	19.4231	+	11.2139i	0.639665	+	0.369311i
$923$	−14.3249			−0.471510
$924$		0			0
$925$	−1.05288			−0.0346184
$926$	13.5337	+	7.81370i	0.444746	+	0.256774i
$927$	4.85865	−	2.80514i	0.159579	−	0.0921329i
$928$	−1.77193	−	3.06907i	−0.0581665	−	0.100747i
$929$	20.7072	+	11.9553i	0.679382	+	0.392242i	0.799622	−	0.600503i	$-0.205033\pi$
$929$	20.7072	+	11.9553i	0.679382	+	0.392242i	−0.120240	+	0.992745i	$0.538366\pi$
$930$	11.8755			0.389412
$931$		0			0
$932$		−	21.3192i		−	0.698332i
$933$	−3.41151	+	5.90890i	−0.111688	+	0.193449i
$934$	−3.04760	−	5.27860i	−0.0997206	−	0.172721i
$935$	−11.0718	+	7.48879i	−0.362087	+	0.244910i
$936$	−6.87631	−	3.97004i	−0.224759	−	0.129765i
$937$	28.2482			0.922827			0.461414	−	0.887185i	$-0.347342\pi$
$937$	28.2482			0.922827			0.461414	+	0.887185i	$0.347342\pi$
$938$		0			0
$939$	0.516740			0.0168632
$940$	−2.95958	+	5.12614i	−0.0965309	+	0.167196i
$941$	29.3512	+	50.8377i	0.956821	+	1.65726i	0.730144	+	0.683293i	$0.239453\pi$
$941$	29.3512	+	50.8377i	0.956821	+	1.65726i	0.226677	+	0.973970i	$0.427214\pi$
$942$	−6.91688	+	3.99346i	−0.225364	+	0.130114i
$943$	−24.9759	+	43.2595i	−0.813327	+	1.40872i
$944$		−	2.73329i		−	0.0889609i
$945$		0			0
$946$	−25.0635	+	1.78505i	−0.814885	+	0.0580371i
$947$	22.1672	−	38.3948i	0.720338	−	1.24766i	−0.240526	−	0.970643i	$-0.577320\pi$
$947$	22.1672	−	38.3948i	0.720338	−	1.24766i	0.960864	−	0.277020i	$-0.0893468\pi$
$948$	8.02023	+	13.8914i	0.260485	+	0.451173i
$949$	−1.97402	−	3.41910i	−0.0640794	−	0.110989i
$950$	22.5648	+	13.0278i	0.732098	+	0.422677i
$951$		−	10.8376i		−	0.351433i
$952$		0			0
$953$		−	13.9238i		−	0.451037i	−0.974239	−	0.225518i	$-0.927592\pi$
$953$		−	13.9238i		−	0.451037i	0.974239	−	0.225518i	$-0.0724075\pi$
$954$	8.07733	+	4.66345i	0.261513	+	0.150985i
$955$	6.54031	−	3.77605i	0.211639	−	0.122190i
$956$	−6.28010	+	3.62582i	−0.203113	+	0.117267i
$957$	5.27957	−	10.8602i	0.170664	−	0.351061i
$958$			30.6275i			0.989531i
$959$		0			0
$960$	1.29315			0.0417362
$961$	26.6672	−	46.1890i	0.860233	−	1.48997i
$962$	1.09005	−	0.629341i	0.0351447	−	0.0202908i
$963$	27.4488	−	15.8476i	0.884526	−	0.510681i
$964$	1.77705	−	3.07794i	0.0572349	−	0.0991337i
$965$	11.8101			0.380180
$966$		0			0
$967$			29.3085i			0.942499i	0.882000	+	0.471250i	$0.156197\pi$
$967$			29.3085i			0.942499i	−0.882000	+	0.471250i	$0.843803\pi$
$968$	10.2096	+	4.09439i	0.328149	+	0.131599i
$969$	−21.7316	+	12.5467i	−0.698118	+	0.403059i
$970$	11.6361	−	6.71808i	0.373611	−	0.215705i
$971$	0.0286574	+	0.0165453i	0.000919659	+	0.000530965i	0.500460	−	0.865760i	$-0.333164\pi$
$971$	0.0286574	+	0.0165453i	0.000919659	+	0.000530965i	−0.499540	+	0.866291i	$0.666498\pi$
$972$		−	15.8709i		−	0.509060i
$973$		0			0
$974$		−	3.17453i		−	0.101718i
$975$	12.4098	+	7.16481i	0.397432	+	0.229458i
$976$	−0.755050	−	1.30779i	−0.0241686	−	0.0418612i
$977$	−21.0948	−	36.5373i	−0.674883	−	1.16893i	−0.976503	−	0.215503i	$-0.930861\pi$
$977$	−21.0948	−	36.5373i	−0.674883	−	1.16893i	0.301620	−	0.953428i	$-0.402473\pi$
$978$	−9.35551	+	16.2042i	−0.299156	+	0.518154i
$979$	−2.50926	−	35.2320i	−0.0801964	−	1.12602i
$980$		0			0
$981$			22.3683i			0.714164i
$982$	−16.3254	+	28.2763i	−0.520963	+	0.902335i
$983$	44.0056	−	25.4067i	1.40356	−	0.810347i	0.408806	−	0.912621i	$-0.365945\pi$
$983$	44.0056	−	25.4067i	1.40356	−	0.810347i	0.994756	+	0.102274i	$0.0326120\pi$
$984$	3.10925	+	5.38538i	0.0991193	+	0.171680i
$985$	10.9173	−	18.9092i	0.347853	−	0.602499i
$986$	11.3471			0.361367
$987$		0			0
$988$	−31.1486			−0.990968
$989$	−54.1467	−	31.2616i	−1.72177	−	0.994062i
$990$	−4.54786	−	6.72378i	−0.144540	−	0.213696i
$991$	−23.2614	−	40.2899i	−0.738923	−	1.27985i	−0.952981	−	0.303030i	$-0.902002\pi$
$991$	−23.2614	−	40.2899i	−0.738923	−	1.27985i	0.214058	−	0.976821i	$-0.431332\pi$
$992$	4.59169	−	7.95304i	0.145786	−	0.252509i
$993$		−	5.93886i		−	0.188464i
$994$		0			0
$995$	3.68223			0.116735
$996$	−1.18334	−	0.683199i	−0.0374954	−	0.0216480i
$997$	2.26888	+	3.92981i	0.0718560	+	0.124458i	0.899715	−	0.436478i	$-0.143774\pi$
$997$	2.26888	+	3.92981i	0.0718560	+	0.124458i	−0.827859	+	0.560937i	$0.810441\pi$
$998$	24.6426	−	14.2274i	0.780048	−	0.450361i
$999$	1.35606	+	0.782923i	0.0429039	+	0.0247706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.i.c.901.3		16
7.2	even	3		1078.2.c.b.1077.13		16
7.3	odd	6	inner	1078.2.i.c.1011.7		16
7.4	even	3		154.2.i.a.87.6	yes	16
7.5	odd	6		1078.2.c.b.1077.12		16
7.6	odd	2		154.2.i.a.131.2	yes	16
11.10	odd	2	inner	1078.2.i.c.901.7		16
21.11	odd	6		1386.2.bk.c.703.1		16
21.20	even	2		1386.2.bk.c.901.5		16
28.11	odd	6		1232.2.bn.b.241.5		16
28.27	even	2		1232.2.bn.b.593.6		16
77.10	even	6	inner	1078.2.i.c.1011.3		16
77.32	odd	6		154.2.i.a.87.2	✓	16
77.54	even	6		1078.2.c.b.1077.4		16
77.65	odd	6		1078.2.c.b.1077.5		16
77.76	even	2		154.2.i.a.131.6	yes	16
231.32	even	6		1386.2.bk.c.703.5		16
231.230	odd	2		1386.2.bk.c.901.1		16
308.263	even	6		1232.2.bn.b.241.6		16
308.307	odd	2		1232.2.bn.b.593.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.i.a.87.2	✓	16	77.32	odd	6
154.2.i.a.87.6	yes	16	7.4	even	3
154.2.i.a.131.2	yes	16	7.6	odd	2
154.2.i.a.131.6	yes	16	77.76	even	2
1078.2.c.b.1077.4		16	77.54	even	6
1078.2.c.b.1077.5		16	77.65	odd	6
1078.2.c.b.1077.12		16	7.5	odd	6
1078.2.c.b.1077.13		16	7.2	even	3
1078.2.i.c.901.3		16	1.1	even	1	trivial
1078.2.i.c.901.7		16	11.10	odd	2	inner
1078.2.i.c.1011.3		16	77.10	even	6	inner
1078.2.i.c.1011.7		16	7.3	odd	6	inner
1232.2.bn.b.241.5		16	28.11	odd	6
1232.2.bn.b.241.6		16	308.263	even	6
1232.2.bn.b.593.5		16	308.307	odd	2
1232.2.bn.b.593.6		16	28.27	even	2
1386.2.bk.c.703.1		16	21.11	odd	6
1386.2.bk.c.703.5		16	231.32	even	6
1386.2.bk.c.901.1		16	231.230	odd	2
1386.2.bk.c.901.5		16	21.20	even	2

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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.889740 - 0.513691i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.09005 - 0.629341i) q^{5} -1.02738 q^{6} -1.00000i q^{8} +(-0.972242 + 1.68397i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.889740 - 0.513691i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.09005 - 0.629341i) q^{5} -1.02738 q^{6} -1.00000i q^{8} +(-0.972242 + 1.68397i) q^{9} +(0.629341 + 1.09005i) q^{10} +(1.85817 + 2.74722i) q^{11} +(0.889740 + 0.513691i) q^{12} -4.08338 q^{13} -1.29315 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.60096 - 2.77294i) q^{17} +(1.68397 - 0.972242i) q^{18} +(3.81407 - 6.60616i) q^{19} -1.25868i q^{20} +(-0.235617 - 3.30824i) q^{22} +(4.12636 - 7.14707i) q^{23} +(-0.513691 - 0.889740i) q^{24} +(-1.70786 - 2.95810i) q^{25} +(3.53631 + 2.04169i) q^{26} +5.07988i q^{27} -3.54386i q^{29} +(1.11990 + 0.646574i) q^{30} +(7.95304 - 4.59169i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.06451 + 1.48978i) q^{33} +3.20191i q^{34} -1.94448 q^{36} +(0.154122 - 0.266948i) q^{37} +(-6.60616 + 3.81407i) q^{38} +(-3.63315 + 2.09760i) q^{39} +(-0.629341 + 1.09005i) q^{40} -6.05276 q^{41} -7.57607i q^{43} +(-1.45007 + 2.98283i) q^{44} +(2.11959 - 1.22374i) q^{45} +(-7.14707 + 4.12636i) q^{46} +(-4.07263 - 2.35133i) q^{47} +1.02738i q^{48} +3.41572i q^{50} +(-2.84887 - 1.64480i) q^{51} +(-2.04169 - 3.53631i) q^{52} +(2.39830 + 4.15397i) q^{53} +(2.53994 - 4.39930i) q^{54} +(-0.296567 - 4.16403i) q^{55} -7.83701i q^{57} +(-1.77193 + 3.06907i) q^{58} +(-2.36710 + 1.36664i) q^{59} +(-0.646574 - 1.11990i) q^{60} +(-0.755050 + 1.30779i) q^{61} -9.18338 q^{62} -1.00000 q^{64} +(4.45110 + 2.56984i) q^{65} +(-1.90905 - 2.82244i) q^{66} +(-1.69044 - 2.92792i) q^{67} +(1.60096 - 2.77294i) q^{68} -8.47871i q^{69} +3.50810 q^{71} +(1.68397 + 0.972242i) q^{72} +(0.483428 + 0.837321i) q^{73} +(-0.266948 + 0.154122i) q^{74} +(-3.03910 - 1.75463i) q^{75} +7.62813 q^{76} +4.19520 q^{78} +(13.5212 + 7.80647i) q^{79} +(1.09005 - 0.629341i) q^{80} +(-0.307237 - 0.532150i) q^{81} +(5.24185 + 3.02638i) q^{82} -1.32998 q^{83} +4.03019i q^{85} +(-3.78804 + 6.56107i) q^{86} +(-1.82045 - 3.15311i) q^{87} +(2.74722 - 1.85817i) q^{88} +(-9.22296 - 5.32488i) q^{89} -2.44749 q^{90} +8.25273 q^{92} +(4.71742 - 8.17082i) q^{93} +(2.35133 + 4.07263i) q^{94} +(-8.31505 + 4.80070i) q^{95} +(0.513691 - 0.889740i) q^{96} -10.6748i q^{97} +(-6.43283 + 0.458154i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 12 q^{5} + 16 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^9	\( 16 q + 8 q^{4} + 12 q^{5} + 16 q^{9} + 8 q^{11} - 8 q^{15} - 8 q^{16} - 8 q^{22} + 16 q^{23} + 36 q^{26} + 12 q^{31} + 24 q^{33} + 32 q^{36} - 16 q^{37} - 12 q^{38} - 8 q^{44} + 108 q^{45} - 24 q^{47} - 28 q^{53} - 12 q^{58} - 60 q^{59} - 4 q^{60} - 16 q^{64} - 48 q^{66} + 12 q^{67} + 8 q^{71} - 60 q^{75} - 16 q^{78} - 12 q^{80} - 8 q^{81} + 20 q^{86} - 4 q^{88} - 96 q^{89} + 32 q^{92} - 44 q^{93} + 56 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^9 + 8 * q^11 - 8 * q^15 - 8 * q^16 - 8 * q^22 + 16 * q^23 + 36 * q^26 + 12 * q^31 + 24 * q^33 + 32 * q^36 - 16 * q^37 - 12 * q^38 - 8 * q^44 + 108 * q^45 - 24 * q^47 - 28 * q^53 - 12 * q^58 - 60 * q^59 - 4 * q^60 - 16 * q^64 - 48 * q^66 + 12 * q^67 + 8 * q^71 - 60 * q^75 - 16 * q^78 - 12 * q^80 - 8 * q^81 + 20 * q^86 - 4 * q^88 - 96 * q^89 + 32 * q^92 - 44 * q^93 + 56 * q^99

Introduction

L-functions

Modular forms

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