LMFDB - Embedded newform 756.2.bi.c.307.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(307,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("756.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bi (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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			307.1
Character	$\chi$	$=$	756.307
Dual form			756.2.bi.c.559.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40431 - 0.167104i) q^{2} +(1.94415 + 0.469331i) q^{4} +(-1.39056 - 0.802839i) q^{5} +(0.686390 - 2.55517i) q^{7} +(-2.65176 - 0.983961i) q^{8} +O(q^{10})$	\(q+(-1.40431 - 0.167104i) q^{2} +(1.94415 + 0.469331i) q^{4} +(-1.39056 - 0.802839i) q^{5} +(0.686390 - 2.55517i) q^{7} +(-2.65176 - 0.983961i) q^{8} +(1.81861 + 1.35980i) q^{10} +(4.25491 - 2.45657i) q^{11} +(2.86262 + 1.65273i) q^{13} +(-1.39088 + 3.47354i) q^{14} +(3.55946 + 1.82490i) q^{16} +2.99090i q^{17} -6.50880 q^{19} +(-2.32666 - 2.21347i) q^{20} +(-6.38570 + 2.73877i) q^{22} +(-1.26402 - 0.729782i) q^{23} +(-1.21090 - 2.09734i) q^{25} +(-3.74381 - 2.79930i) q^{26} +(2.53367 - 4.64549i) q^{28} +(-0.0999499 - 0.173118i) q^{29} +(4.60497 - 7.97605i) q^{31} +(-4.69362 - 3.15752i) q^{32} +(0.499792 - 4.20013i) q^{34} +(-3.00585 + 3.00204i) q^{35} -6.44730 q^{37} +(9.14035 + 1.08765i) q^{38} +(2.89746 + 3.49719i) q^{40} +(-3.27157 - 1.88884i) q^{41} +(6.76071 - 3.90330i) q^{43} +(9.42514 - 2.77899i) q^{44} +(1.65312 + 1.23606i) q^{46} +(0.564684 + 0.978061i) q^{47} +(-6.05774 - 3.50768i) q^{49} +(1.35000 + 3.14766i) q^{50} +(4.78968 + 4.55668i) q^{52} +7.11643 q^{53} -7.88893 q^{55} +(-4.33432 + 6.10030i) q^{56} +(0.111431 + 0.259813i) q^{58} +(3.50075 - 6.06347i) q^{59} +(1.64302 - 0.948597i) q^{61} +(-7.79962 + 10.4313i) q^{62} +(6.06364 + 5.21845i) q^{64} +(-2.65375 - 4.59644i) q^{65} +(-4.72658 - 2.72889i) q^{67} +(-1.40372 + 5.81476i) q^{68} +(4.72279 - 3.71350i) q^{70} -8.96538i q^{71} +1.20449i q^{73} +(9.05398 + 1.07737i) q^{74} +(-12.6541 - 3.05479i) q^{76} +(-3.35642 - 12.5582i) q^{77} +(8.32279 - 4.80516i) q^{79} +(-3.48452 - 5.39530i) q^{80} +(4.27865 + 3.19921i) q^{82} +(-6.94130 - 12.0227i) q^{83} +(2.40121 - 4.15901i) q^{85} +(-10.1464 + 4.35168i) q^{86} +(-13.7002 + 2.32757i) q^{88} -8.07848i q^{89} +(6.18787 - 6.18004i) q^{91} +(-2.11494 - 2.01205i) q^{92} +(-0.629551 - 1.46786i) q^{94} +(9.05086 + 5.22552i) q^{95} +(-13.6407 + 7.87544i) q^{97} +(7.92077 + 5.93813i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8}+O(q^{10}) $ 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8	$ 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8} - 10 q^{14} - 18 q^{16} - 14 q^{22} + 32 q^{25} + 28 q^{28} - 8 q^{29} + 16 q^{32} - 16 q^{37} + 84 q^{44} + 24 q^{46} - 24 q^{49} + 12 q^{50} + 48 q^{53} - 32 q^{56} - 14 q^{58} - 8 q^{64} + 40 q^{65} - 22 q^{70} - 64 q^{74} + 12 q^{77} + 40 q^{85} + 52 q^{86} + 6 q^{88} - 30 q^{92} - 20 q^{98}+O(q^{100}) $ 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8 - 10 * q^14 - 18 * q^16 - 14 * q^22 + 32 * q^25 + 28 * q^28 - 8 * q^29 + 16 * q^32 - 16 * q^37 + 84 * q^44 + 24 * q^46 - 24 * q^49 + 12 * q^50 + 48 * q^53 - 32 * q^56 - 14 * q^58 - 8 * q^64 + 40 * q^65 - 22 * q^70 - 64 * q^74 + 12 * q^77 + 40 * q^85 + 52 * q^86 + 6 * q^88 - 30 * q^92 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$

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 $

$2$	−1.40431	−	0.167104i	−0.992994	−	0.118161i
$2$	−1.40431	−	0.167104i	−0.992994	−	0.118161i
$3$		0			0
$3$		0			0
$4$	1.94415	+	0.469331i	0.972076	+	0.234666i
$5$	−1.39056	−	0.802839i	−0.621876	−	0.359040i	0.155723	−	0.987801i	$-0.450229\pi$
$5$	−1.39056	−	0.802839i	−0.621876	−	0.359040i	−0.777599	+	0.628760i	$0.783563\pi$
$6$		0			0
$7$	0.686390	−	2.55517i	0.259431	−	0.965762i
$7$	0.686390	−	2.55517i	0.259431	−	0.965762i
$8$	−2.65176	−	0.983961i	−0.937538	−	0.347883i
$9$		0			0
$10$	1.81861	+	1.35980i	0.575095	+	0.430006i
$11$	4.25491	−	2.45657i	1.28290	−	0.740685i	0.305526	−	0.952184i	$-0.401168\pi$
$11$	4.25491	−	2.45657i	1.28290	−	0.740685i	0.977378	+	0.211499i	$0.0678344\pi$
$12$		0			0
$13$	2.86262	+	1.65273i	0.793947	+	0.458385i	0.841350	−	0.540490i	$-0.181761\pi$
$13$	2.86262	+	1.65273i	0.793947	+	0.458385i	−0.0474033	+	0.998876i	$0.515095\pi$
$14$	−1.39088	+	3.47354i	−0.371729	+	0.928341i
$15$		0			0
$16$	3.55946	+	1.82490i	0.889864	+	0.456226i
$17$			2.99090i			0.725399i	0.931906	+	0.362699i	$0.118145\pi$
$17$			2.99090i			0.725399i	−0.931906	+	0.362699i	$0.881855\pi$
$18$		0			0
$19$	−6.50880			−1.49322			−0.746611	−	0.665261i	$-0.768320\pi$
$19$	−6.50880			−1.49322			−0.746611	+	0.665261i	$0.768320\pi$
$20$	−2.32666	−	2.21347i	−0.520256	−	0.494948i
$21$		0			0
$22$	−6.38570	+	2.73877i	−1.36144	+	0.583907i
$23$	−1.26402	−	0.729782i	−0.263566	−	0.152170i	0.362394	−	0.932025i	$-0.381959\pi$
$23$	−1.26402	−	0.729782i	−0.263566	−	0.152170i	−0.625960	+	0.779855i	$0.715293\pi$
$24$		0			0
$25$	−1.21090	−	2.09734i	−0.242180	−	0.419468i
$26$	−3.74381	−	2.79930i	−0.734222	−	0.548987i
$27$		0			0
$28$	2.53367	−	4.64549i	0.478818	−	0.877914i
$29$	−0.0999499	−	0.173118i	−0.0185602	−	0.0321473i	0.856596	−	0.515987i	$-0.172575\pi$
$29$	−0.0999499	−	0.173118i	−0.0185602	−	0.0321473i	−0.875156	+	0.483840i	$0.839242\pi$
$30$		0			0
$31$	4.60497	−	7.97605i	0.827077	−	1.43254i	−0.0732437	−	0.997314i	$-0.523335\pi$
$31$	4.60497	−	7.97605i	0.827077	−	1.43254i	0.900321	−	0.435226i	$-0.143332\pi$
$32$	−4.69362	−	3.15752i	−0.829722	−	0.558177i
$33$		0			0
$34$	0.499792	−	4.20013i	0.0857136	−	0.720317i
$35$	−3.00585	+	3.00204i	−0.508081	+	0.507438i
$36$		0			0
$37$	−6.44730			−1.05993			−0.529965	−	0.848020i	$-0.677795\pi$
$37$	−6.44730			−1.05993			−0.529965	+	0.848020i	$0.677795\pi$
$38$	9.14035	+	1.08765i	1.48276	+	0.176440i
$39$		0			0
$40$	2.89746	+	3.49719i	0.458129	+	0.552954i
$41$	−3.27157	−	1.88884i	−0.510933	−	0.294988i	0.222284	−	0.974982i	$-0.428649\pi$
$41$	−3.27157	−	1.88884i	−0.510933	−	0.294988i	−0.733217	+	0.679994i	$0.761982\pi$
$42$		0			0
$43$	6.76071	−	3.90330i	1.03100	−	0.595248i	0.113729	−	0.993512i	$-0.463721\pi$
$43$	6.76071	−	3.90330i	1.03100	−	0.595248i	0.917271	+	0.398264i	$0.130387\pi$
$44$	9.42514	−	2.77899i	1.42089	−	0.418949i
$45$		0			0
$46$	1.65312	+	1.23606i	0.243739	+	0.182247i
$47$	0.564684	+	0.978061i	0.0823676	+	0.142665i	0.904266	−	0.426969i	$-0.140419\pi$
$47$	0.564684	+	0.978061i	0.0823676	+	0.142665i	−0.821899	+	0.569633i	$0.807085\pi$
$48$		0			0
$49$	−6.05774	−	3.50768i	−0.865391	−	0.501097i
$50$	1.35000	+	3.14766i	0.190919	+	0.445146i
$51$		0			0
$52$	4.78968	+	4.55668i	0.664209	+	0.631898i
$53$	7.11643			0.977517			0.488758	−	0.872419i	$-0.337450\pi$
$53$	7.11643			0.977517			0.488758	+	0.872419i	$0.337450\pi$
$54$		0			0
$55$	−7.88893			−1.06374
$56$	−4.33432	+	6.10030i	−0.579198	+	0.815187i
$57$		0			0
$58$	0.111431	+	0.259813i	0.0146317	+	0.0341151i
$59$	3.50075	−	6.06347i	0.455758	−	0.789396i	−0.542973	−	0.839750i	$-0.682702\pi$
$59$	3.50075	−	6.06347i	0.455758	−	0.789396i	0.998731	+	0.0503536i	$0.0160348\pi$
$60$		0			0
$61$	1.64302	−	0.948597i	0.210367	−	0.121455i	−0.391115	−	0.920342i	$-0.627911\pi$
$61$	1.64302	−	0.948597i	0.210367	−	0.121455i	0.601482	+	0.798886i	$0.294577\pi$
$62$	−7.79962	+	10.4313i	−0.990553	+	1.32478i
$63$		0			0
$64$	6.06364	+	5.21845i	0.757955	+	0.652307i
$65$	−2.65375	−	4.59644i	−0.329158	−	0.570118i
$66$		0			0
$67$	−4.72658	−	2.72889i	−0.577444	−	0.333387i	0.182673	−	0.983174i	$-0.441525\pi$
$67$	−4.72658	−	2.72889i	−0.577444	−	0.333387i	−0.760117	+	0.649786i	$0.774858\pi$
$68$	−1.40372	+	5.81476i	−0.170226	+	0.705143i
$69$		0			0
$70$	4.72279	−	3.71350i	0.564481	−	0.443848i
$71$		−	8.96538i		−	1.06400i	−0.846746	−	0.531998i	$-0.821442\pi$
$71$		−	8.96538i		−	1.06400i	0.846746	−	0.531998i	$-0.178558\pi$
$72$		0			0
$73$			1.20449i			0.140975i	0.997513	+	0.0704877i	$0.0224556\pi$
$73$			1.20449i			0.140975i	−0.997513	+	0.0704877i	$0.977544\pi$
$74$	9.05398	+	1.07737i	1.05250	+	0.125242i
$75$		0			0
$76$	−12.6541	−	3.05479i	−1.45153	−	0.350408i
$77$	−3.35642	−	12.5582i	−0.382500	−	1.43114i
$78$		0			0
$79$	8.32279	−	4.80516i	0.936387	−	0.540623i	0.0475610	−	0.998868i	$-0.484855\pi$
$79$	8.32279	−	4.80516i	0.936387	−	0.540623i	0.888826	+	0.458245i	$0.151522\pi$
$80$	−3.48452	−	5.39530i	−0.389582	−	0.603213i
$81$		0			0
$82$	4.27865	+	3.19921i	0.472498	+	0.353293i
$83$	−6.94130	−	12.0227i	−0.761907	−	1.31966i	−0.941866	−	0.335988i	$-0.890930\pi$
$83$	−6.94130	−	12.0227i	−0.761907	−	1.31966i	0.179959	−	0.983674i	$-0.442403\pi$
$84$		0			0
$85$	2.40121	−	4.15901i	0.260447	−	0.451108i
$86$	−10.1464	+	4.35168i	−1.09411	+	0.469254i
$87$		0			0
$88$	−13.7002	+	2.32757i	−1.46044	+	0.248120i
$89$		−	8.07848i		−	0.856317i	−0.903704	−	0.428159i	$-0.859162\pi$
$89$		−	8.07848i		−	0.856317i	0.903704	−	0.428159i	$-0.140838\pi$
$90$		0			0
$91$	6.18787	−	6.18004i	0.648666	−	0.647844i
$92$	−2.11494	−	2.01205i	−0.220497	−	0.209771i
$93$		0			0
$94$	−0.629551	−	1.46786i	−0.0649332	−	0.151398i
$95$	9.05086	+	5.22552i	0.928599	+	0.536127i
$96$		0			0
$97$	−13.6407	+	7.87544i	−1.38500	+	0.799630i	−0.992746	−	0.120228i	$-0.961638\pi$
$97$	−13.6407	+	7.87544i	−1.38500	+	0.799630i	−0.392253	+	0.919857i	$0.628304\pi$
$98$	7.92077	+	5.93813i	0.800119	+	0.599842i
$99$		0			0
$100$	−1.36983	−	4.64586i	−0.136983	−	0.464586i
$101$	3.85659	−	2.22660i	0.383745	−	0.221555i	−0.295701	−	0.955280i	$-0.595553\pi$
$101$	3.85659	−	2.22660i	0.383745	−	0.221555i	0.679446	+	0.733725i	$0.262220\pi$
$102$		0			0
$103$	−2.89379	+	5.01219i	−0.285134	+	0.493866i	−0.972642	−	0.232311i	$-0.925371\pi$
$103$	−2.89379	+	5.01219i	−0.285134	+	0.493866i	0.687508	+	0.726177i	$0.258705\pi$
$104$	−5.96474	−	7.19935i	−0.584891	−	0.705954i
$105$		0			0
$106$	−9.99364	−	1.18919i	−0.970669	−	0.115504i
$107$			12.1900i			1.17845i	0.807970	+	0.589224i	$0.200567\pi$
$107$			12.1900i			1.17845i	−0.807970	+	0.589224i	$0.799433\pi$
$108$		0			0
$109$	−2.95669			−0.283200			−0.141600	−	0.989924i	$-0.545225\pi$
$109$	−2.95669			−0.283200			−0.141600	+	0.989924i	$0.545225\pi$
$110$	11.0785	+	1.31827i	1.05629	+	0.125693i
$111$		0			0
$112$	7.10610	−	7.84240i	0.671464	−	0.741037i
$113$	−3.60818	+	6.24954i	−0.339429	+	0.587908i	−0.984325	−	0.176362i	$-0.943567\pi$
$113$	−3.60818	+	6.24954i	−0.339429	+	0.587908i	0.644897	+	0.764270i	$0.276900\pi$
$114$		0			0
$115$	1.17179	+	2.02961i	0.109270	+	0.189262i
$116$	−0.113068	−	0.383478i	−0.0104981	−	0.0356050i
$117$		0			0
$118$	−5.92935	+	7.92998i	−0.545841	+	0.730014i
$119$	7.64223	+	2.05292i	0.700562	+	0.188191i
$120$		0			0
$121$	6.56951	−	11.3787i	0.597229	−	1.03443i
$122$	−2.46581	+	1.05756i	−0.223244	+	0.0957474i
$123$		0			0
$124$	12.6962	−	13.3454i	1.14015	−	1.19845i
$125$			11.9170i			1.06589i
$126$		0			0
$127$			7.53945i			0.669018i	0.942393	+	0.334509i	$0.108570\pi$
$127$			7.53945i			0.669018i	−0.942393	+	0.334509i	$0.891430\pi$
$128$	−7.64318	−	8.34157i	−0.675568	−	0.737298i
$129$		0			0
$130$	2.95860	+	6.89826i	0.259486	+	0.605017i
$131$	−0.168472	+	0.291803i	−0.0147195	+	0.0254949i	−0.873291	−	0.487198i	$-0.838019\pi$
$131$	−0.168472	+	0.291803i	−0.0147195	+	0.0254949i	0.858572	+	0.512693i	$0.171352\pi$
$132$		0			0
$133$	−4.46758	+	16.6311i	−0.387388	+	1.44210i
$134$	6.18156	+	4.62203i	0.534005	+	0.399283i
$135$		0			0
$136$	2.94293	−	7.93113i	0.252354	−	0.680089i
$137$	−7.88278	−	13.6534i	−0.673472	−	1.16649i	−0.976913	−	0.213637i	$-0.931469\pi$
$137$	−7.88278	−	13.6534i	−0.673472	−	1.16649i	0.303442	−	0.952850i	$-0.401864\pi$
$138$		0			0
$139$	2.27775	−	3.94519i	0.193197	−	0.334626i	−0.753111	−	0.657893i	$-0.771448\pi$
$139$	2.27775	−	3.94519i	0.193197	−	0.334626i	0.946308	+	0.323267i	$0.104781\pi$
$140$	−7.25278	+	4.42569i	−0.612972	+	0.374039i
$141$		0			0
$142$	−1.49815	+	12.5901i	−0.125722	+	1.05654i
$143$	16.2402			1.35808
$144$		0			0
$145$			0.320974i			0.0266555i
$146$	0.201276	−	1.69148i	0.0166577	−	0.139988i
$147$		0			0
$148$	−12.5345	−	3.02592i	−1.03033	−	0.248729i
$149$	−5.27890	+	9.14333i	−0.432464	+	0.749050i	−0.997085	−	0.0763003i	$-0.975689\pi$
$149$	−5.27890	+	9.14333i	−0.432464	+	0.749050i	0.564620	+	0.825351i	$0.309023\pi$
$150$		0			0
$151$	−10.1964	+	5.88688i	−0.829769	+	0.479067i	−0.853773	−	0.520645i	$-0.825692\pi$
$151$	−10.1964	+	5.88688i	−0.829769	+	0.479067i	0.0240048	+	0.999712i	$0.492358\pi$
$152$	17.2598	+	6.40441i	1.39995	+	0.519466i
$153$		0			0
$154$	2.61492	+	18.1964i	0.210716	+	1.46631i
$155$	−12.8070	+	7.39410i	−1.02868	+	0.593908i
$156$		0			0
$157$	19.4681	+	11.2399i	1.55372	+	0.897043i	0.997834	+	0.0657878i	$0.0209561\pi$
$157$	19.4681	+	11.2399i	1.55372	+	0.897043i	0.555891	+	0.831255i	$0.312377\pi$
$158$	−12.4907	+	5.35715i	−0.993707	+	0.426192i
$159$		0			0
$160$	3.99176	+	8.15893i	0.315576	+	0.645020i
$161$	−2.73232	+	2.72886i	−0.215337	+	0.215064i
$162$		0			0
$163$			13.0725i			1.02392i	0.859009	+	0.511961i	$0.171081\pi$
$163$			13.0725i			1.02392i	−0.859009	+	0.511961i	$0.828919\pi$
$164$	−5.47394	−	5.20765i	−0.427443	−	0.406649i
$165$		0			0
$166$	7.73867	+	18.0435i	0.600637	+	1.40044i
$167$	2.34440	−	4.06062i	0.181415	−	0.314220i	−0.760948	−	0.648813i	$-0.775266\pi$
$167$	2.34440	−	4.06062i	0.181415	−	0.314220i	0.942363	+	0.334593i	$0.108599\pi$
$168$		0			0
$169$	−1.03695	−	1.79606i	−0.0797656	−	0.138158i
$170$	−4.06702	+	5.43927i	−0.311926	+	0.417173i
$171$		0			0
$172$	14.9758	−	4.41559i	1.14189	−	0.336686i
$173$	21.1644	−	12.2193i	1.60910	−	0.929014i	0.619528	−	0.784975i	$-0.287324\pi$
$173$	21.1644	−	12.2193i	1.60910	−	0.929014i	0.989572	−	0.144039i	$-0.0460091\pi$
$174$		0			0
$175$	−6.19020	+	1.65446i	−0.467935	+	0.125065i
$176$	19.6282	−	0.979266i	1.47953	−	0.0738150i
$177$		0			0
$178$	−1.34995	+	11.3447i	−0.101183	+	0.850319i
$179$			4.85575i			0.362936i	0.983397	+	0.181468i	$0.0580849\pi$
$179$			4.85575i			0.362936i	−0.983397	+	0.181468i	$0.941915\pi$
$180$		0			0
$181$		−	9.77729i		−	0.726740i	−0.931645	−	0.363370i	$-0.881626\pi$
$181$		−	9.77729i		−	0.726740i	0.931645	−	0.363370i	$-0.118374\pi$
$182$	−9.72238	+	7.64465i	−0.720671	+	0.566659i
$183$		0			0
$184$	2.63380	+	3.17895i	0.194166	+	0.234355i
$185$	8.96534	+	5.17614i	0.659145	+	0.380557i
$186$		0			0
$187$	7.34736	+	12.7260i	0.537292	+	0.930617i
$188$	0.638797	+	2.16652i	0.0465890	+	0.158010i
$189$		0			0
$190$	−11.8370	−	8.85067i	−0.858744	−	0.642095i
$191$	3.45030	−	1.99203i	0.249655	−	0.144138i	−0.369951	−	0.929051i	$-0.620626\pi$
$191$	3.45030	−	1.99203i	0.249655	−	0.144138i	0.619606	+	0.784913i	$0.287292\pi$
$192$		0			0
$193$	−6.37596	+	11.0435i	−0.458952	+	0.794927i	−0.998906	−	0.0467669i	$-0.985108\pi$
$193$	−6.37596	+	11.0435i	−0.458952	+	0.794927i	0.539954	+	0.841694i	$0.318442\pi$
$194$	20.4717	−	8.78012i	1.46978	−	0.630376i
$195$		0			0
$196$	−10.1309	−	9.66255i	−0.723636	−	0.690182i
$197$	7.28071			0.518729			0.259365	−	0.965779i	$-0.416487\pi$
$197$	7.28071			0.518729			0.259365	+	0.965779i	$0.416487\pi$
$198$		0			0
$199$	3.59409			0.254778			0.127389	−	0.991853i	$-0.459340\pi$
$199$	3.59409			0.254778			0.127389	+	0.991853i	$0.459340\pi$
$200$	1.14731	+	6.75312i	0.0811272	+	0.477518i
$201$		0			0
$202$	−5.78791	+	2.48238i	−0.407236	+	0.174660i
$203$	−0.510950	+	0.136562i	−0.0358617	+	0.00958476i
$204$		0			0
$205$	3.03287	+	5.25309i	0.211825	+	0.366891i
$206$	4.90133	−	6.55509i	0.341492	−	0.456715i
$207$		0			0
$208$	7.17328	+	11.1068i	0.497377	+	0.770120i
$209$	−27.6944	+	15.9894i	−1.91566	+	1.10601i
$210$		0			0
$211$	13.5070	+	7.79829i	0.929863	+	0.536857i	0.886768	−	0.462214i	$-0.152945\pi$
$211$	13.5070	+	7.79829i	0.929863	+	0.536857i	0.0430948	+	0.999071i	$0.486278\pi$
$212$	13.8354	+	3.33996i	0.950220	+	0.229390i
$213$		0			0
$214$	2.03700	−	17.1184i	0.139246	−	1.17019i
$215$	−12.5349			−0.854872
$216$		0			0
$217$	−17.2193	−	17.2411i	−1.16892	−	1.17041i
$218$	4.15210	+	0.494076i	0.281216	+	0.0334631i
$219$		0			0
$220$	−15.3373	−	3.70252i	−1.03404	−	0.249624i
$221$	−4.94315	+	8.56179i	−0.332512	+	0.575928i
$222$		0			0
$223$	−4.34831	−	7.53150i	−0.291184	−	0.504346i	0.682906	−	0.730507i	$-0.260716\pi$
$223$	−4.34831	−	7.53150i	−0.291184	−	0.504346i	−0.974090	+	0.226160i	$0.927383\pi$
$224$	−11.2896	+	9.82567i	−0.754321	+	0.656505i
$225$		0			0
$226$	6.11131	−	8.17333i	0.406518	−	0.543682i
$227$	14.0714	+	24.3724i	0.933951	+	1.61765i	0.776494	+	0.630125i	$0.216996\pi$
$227$	14.0714	+	24.3724i	0.933951	+	1.61765i	0.157457	+	0.987526i	$0.449670\pi$
$228$		0			0
$229$	15.9707	+	9.22071i	1.05538	+	0.609322i	0.924150	−	0.382031i	$-0.124775\pi$
$229$	15.9707	+	9.22071i	1.05538	+	0.609322i	0.131226	+	0.991352i	$0.458109\pi$
$230$	−1.30640	−	3.04600i	−0.0861416	−	0.200847i
$231$		0			0
$232$	0.0947012	+	0.557415i	0.00621744	+	0.0365961i
$233$	−0.923263			−0.0604850			−0.0302425	−	0.999543i	$-0.509628\pi$
$233$	−0.923263			−0.0604850			−0.0302425	+	0.999543i	$0.509628\pi$
$234$		0			0
$235$		−	1.81340i		−	0.118293i
$236$	9.65176	−	10.1453i	0.628276	−	0.660403i
$237$		0			0
$238$	−10.3890	−	4.15998i	−0.673418	−	0.269651i
$239$	1.11018	+	0.640964i	0.0718117	+	0.0414605i	0.535476	−	0.844550i	$-0.320132\pi$
$239$	1.11018	+	0.640964i	0.0718117	+	0.0414605i	−0.463664	+	0.886011i	$0.653466\pi$
$240$		0			0
$241$	16.1798	−	9.34142i	1.04223	−	0.601734i	0.121769	−	0.992559i	$-0.461143\pi$
$241$	16.1798	−	9.34142i	1.04223	−	0.601734i	0.920465	+	0.390825i	$0.127810\pi$
$242$	−11.1270	+	14.8814i	−0.715274	+	0.956615i
$243$		0			0
$244$	3.63948	−	1.07310i	0.232994	−	0.0686980i
$245$	5.60753	+	9.74102i	0.358252	+	0.622331i
$246$		0			0
$247$	−18.6322	−	10.7573i	−1.18554	−	0.684471i
$248$	−20.0594	+	16.6194i	−1.27377	+	1.05533i
$249$		0			0
$250$	1.99139	−	16.7351i	0.125946	−	1.05842i
$251$	−2.71363			−0.171283			−0.0856413	−	0.996326i	$-0.527294\pi$
$251$	−2.71363			−0.171283			−0.0856413	+	0.996326i	$0.527294\pi$
$252$		0			0
$253$	−7.17105			−0.450840
$254$	1.25988	−	10.5877i	0.0790516	−	0.664331i
$255$		0			0
$256$	9.33946	+	12.9913i	0.583716	+	0.811958i
$257$	−4.68736	−	2.70625i	−0.292390	−	0.168811i	0.346629	−	0.938002i	$-0.387326\pi$
$257$	−4.68736	−	2.70625i	−0.292390	−	0.168811i	−0.639019	+	0.769191i	$0.720659\pi$
$258$		0			0
$259$	−4.42536	+	16.4739i	−0.274979	+	1.02364i
$260$	−3.00205	−	10.1817i	−0.186179	−	0.631440i
$261$		0			0
$262$	0.285348	−	0.381628i	0.0176289	−	0.0235770i
$263$	0.738091	−	0.426137i	0.0455126	−	0.0262767i	−0.477071	−	0.878865i	$-0.658302\pi$
$263$	0.738091	−	0.426137i	0.0455126	−	0.0262767i	0.522584	+	0.852588i	$0.324968\pi$
$264$		0			0
$265$	−9.89580	−	5.71334i	−0.607894	−	0.350968i
$266$	9.05297	−	22.6086i	0.555073	−	1.38622i
$267$		0			0
$268$	−7.90844	−	7.52371i	−0.483085	−	0.459584i
$269$			19.2701i			1.17492i	0.809254	+	0.587459i	$0.199872\pi$
$269$			19.2701i			1.17492i	−0.809254	+	0.587459i	$0.800128\pi$
$270$		0			0
$271$	5.94449			0.361102			0.180551	−	0.983566i	$-0.442212\pi$
$271$	5.94449			0.361102			0.180551	+	0.983566i	$0.442212\pi$
$272$	−5.45810	+	10.6460i	−0.330946	+	0.645506i
$273$		0			0
$274$	8.78830	+	20.4908i	0.530921	+	1.23789i
$275$	−10.3045	−	5.94933i	−0.621388	−	0.358758i
$276$		0			0
$277$	1.71326	+	2.96745i	0.102940	+	0.178297i	0.912895	−	0.408195i	$-0.133842\pi$
$277$	1.71326	+	2.96745i	0.102940	+	0.178297i	−0.809955	+	0.586492i	$0.800508\pi$
$278$	−3.85792	+	5.15963i	−0.231383	+	0.309454i
$279$		0			0
$280$	10.9247	−	5.00305i	0.652875	−	0.298989i
$281$	4.58768	+	7.94609i	0.273678	+	0.474024i	0.969801	−	0.243899i	$-0.0784264\pi$
$281$	4.58768	+	7.94609i	0.273678	+	0.474024i	−0.696123	+	0.717923i	$0.745093\pi$
$282$		0			0
$283$	6.29463	−	10.9026i	0.374177	−	0.648094i	−0.616026	−	0.787726i	$-0.711259\pi$
$283$	6.29463	−	10.9026i	0.374177	−	0.648094i	0.990204	+	0.139632i	$0.0445918\pi$
$284$	4.20774	−	17.4301i	0.249683	−	1.03428i
$285$		0			0
$286$	−22.8063	−	2.71381i	−1.34856	−	0.160471i
$287$	−7.07188	+	7.06292i	−0.417440	+	0.416911i
$288$		0			0
$289$	8.05454			0.473797
$290$	0.0536362	−	0.450746i	0.00314963	−	0.0264687i
$291$		0			0
$292$	−0.565307	+	2.34172i	−0.0330821	+	0.137039i
$293$	15.0422	+	8.68459i	0.878772	+	0.507359i	0.870253	−	0.492605i	$-0.163955\pi$
$293$	15.0422	+	8.68459i	0.878772	+	0.507359i	0.00851854	+	0.999964i	$0.497288\pi$
$294$		0			0
$295$	−9.73597	+	5.62107i	−0.566850	+	0.327271i
$296$	17.0967	+	6.34389i	0.993724	+	0.368731i
$297$		0			0
$298$	8.94108	−	11.9579i	0.517943	−	0.692703i
$299$	−2.41227	−	4.17817i	−0.139505	−	0.241630i
$300$		0			0
$301$	−5.33309	−	19.9539i	−0.307394	−	1.15013i
$302$	15.3025	−	6.56312i	0.880562	−	0.377665i
$303$		0			0
$304$	−23.1678	−	11.8779i	−1.32876	−	0.681246i
$305$	−3.04628			−0.174429
$306$		0			0
$307$	5.65422			0.322704			0.161352	−	0.986897i	$-0.448415\pi$
$307$	5.65422			0.322704			0.161352	+	0.986897i	$0.448415\pi$
$308$	−0.631456	−	25.9903i	−0.0359806	−	1.48093i
$309$		0			0
$310$	19.2205	−	8.24348i	1.09165	−	0.468198i
$311$	−1.96633	+	3.40578i	−0.111500	+	0.193124i	−0.916375	−	0.400320i	$-0.868899\pi$
$311$	−1.96633	+	3.40578i	−0.111500	+	0.193124i	0.804875	+	0.593444i	$0.202232\pi$
$312$		0			0
$313$	−8.58846	+	4.95855i	−0.485449	+	0.280274i	−0.722684	−	0.691178i	$-0.757092\pi$
$313$	−8.58846	+	4.95855i	−0.485449	+	0.280274i	0.237236	+	0.971452i	$0.423759\pi$
$314$	−25.4610	−	19.0375i	−1.43684	−	1.07435i
$315$		0			0
$316$	18.4360	−	5.43582i	1.03710	−	0.305789i
$317$	4.26914	+	7.39437i	0.239779	+	0.415309i	0.960651	−	0.277759i	$-0.0895917\pi$
$317$	4.26914	+	7.39437i	0.239779	+	0.415309i	−0.720872	+	0.693068i	$0.756258\pi$
$318$		0			0
$319$	−0.850556	−	0.491069i	−0.0476220	−	0.0274946i
$320$	−4.24226	−	12.1247i	−0.237150	−	0.677790i
$321$		0			0
$322$	4.29302	−	3.37558i	0.239241	−	0.188113i
$323$		−	19.4671i		−	1.08318i
$324$		0			0
$325$		−	8.00518i		−	0.444047i
$326$	2.18448	−	18.3579i	0.120987	−	1.01675i
$327$		0			0
$328$	6.81687	+	8.22785i	0.376398	+	0.454307i
$329$	2.88670	−	0.771529i	0.159149	−	0.0425358i
$330$		0			0
$331$	2.38726	−	1.37829i	0.131216	−	0.0757575i	−0.432955	−	0.901415i	$-0.642529\pi$
$331$	2.38726	−	1.37829i	0.131216	−	0.0757575i	0.564171	+	0.825658i	$0.309196\pi$
$332$	−7.85232	−	26.6317i	−0.430952	−	1.46161i
$333$		0			0
$334$	−3.97080	+	5.31059i	−0.217273	+	0.290583i
$335$	4.38172	+	7.58936i	0.239399	+	0.414651i
$336$		0			0
$337$	15.6413	−	27.0916i	0.852038	−	1.47577i	−0.0273287	−	0.999627i	$-0.508700\pi$
$337$	15.6413	−	27.0916i	0.852038	−	1.47577i	0.879366	−	0.476146i	$-0.157967\pi$
$338$	1.15607	+	2.69549i	0.0628820	+	0.146615i
$339$		0			0
$340$	6.62027	−	6.95879i	0.359034	−	0.377393i
$341$		−	45.2498i		−	2.45042i
$342$		0			0
$343$	−13.1207	+	13.0709i	−0.708450	+	0.705761i
$344$	−21.7685	+	3.69833i	−1.17368	+	0.199400i
$345$		0			0
$346$	−31.7632	+	13.6229i	−1.70760	+	0.732374i
$347$	−27.6946	−	15.9895i	−1.48673	−	0.858361i	−0.486840	−	0.873491i	$-0.661850\pi$
$347$	−27.6946	−	15.9895i	−1.48673	−	0.858361i	−0.999886	+	0.0151303i	$0.995184\pi$
$348$		0			0
$349$	20.3530	−	11.7508i	1.08947	−	0.629007i	0.156037	−	0.987751i	$-0.450128\pi$
$349$	20.3530	−	11.7508i	1.08947	−	0.629007i	0.933436	+	0.358744i	$0.116795\pi$
$350$	8.96941	−	1.28895i	0.479435	−	0.0688975i
$351$		0			0
$352$	−27.7276	−	1.90476i	−1.47789	−	0.101524i
$353$	0.600459	−	0.346675i	0.0319592	−	0.0184516i	−0.483935	−	0.875104i	$-0.660793\pi$
$353$	0.600459	−	0.346675i	0.0319592	−	0.0184516i	0.515894	+	0.856652i	$0.327460\pi$
$354$		0			0
$355$	−7.19776	+	12.4669i	−0.382017	+	0.661673i
$356$	3.79149	−	15.7058i	0.200948	−	0.832406i
$357$		0			0
$358$	0.811418	−	6.81897i	0.0428848	−	0.360394i
$359$		−	32.6380i		−	1.72257i	−0.508123	−	0.861285i	$-0.669660\pi$
$359$		−	32.6380i		−	1.72257i	0.508123	−	0.861285i	$-0.330340\pi$
$360$		0			0
$361$	23.3645			1.22971
$362$	−1.63383	+	13.7303i	−0.0858721	+	0.721649i
$363$		0			0
$364$	14.9307	−	9.11077i	0.782579	−	0.477534i
$365$	0.967014	−	1.67492i	0.0506159	−	0.0876692i
$366$		0			0
$367$	−2.78726	−	4.82767i	−0.145494	−	0.252002i	0.784063	−	0.620681i	$-0.213144\pi$
$367$	−2.78726	−	4.82767i	−0.145494	−	0.252002i	−0.929557	+	0.368678i	$0.879810\pi$
$368$	−3.16744	−	4.90434i	−0.165114	−	0.255656i
$369$		0			0
$370$	−11.7251	−	8.76703i	−0.609560	−	0.455776i
$371$	4.88465	−	18.1836i	0.253598	−	0.944048i
$372$		0			0
$373$	−11.0409	+	19.1233i	−0.571674	+	0.990169i	0.424720	+	0.905325i	$0.360373\pi$
$373$	−11.0409	+	19.1233i	−0.571674	+	0.990169i	−0.996394	+	0.0848444i	$0.972961\pi$
$374$	−8.19137	−	19.0990i	−0.423566	−	0.987584i
$375$		0			0
$376$	−0.535031	−	3.14921i	−0.0275921	−	0.162408i
$377$		−	0.660761i		−	0.0340309i
$378$		0			0
$379$		−	22.4005i		−	1.15064i	−0.817929	−	0.575319i	$-0.804878\pi$
$379$		−	22.4005i		−	1.15064i	0.817929	−	0.575319i	$-0.195122\pi$
$380$	15.1438	+	14.4071i	0.776858	+	0.739066i
$381$		0			0
$382$	−5.17815	+	2.22086i	−0.264937	+	0.113629i
$383$	−16.6413	+	28.8236i	−0.850331	+	1.47282i	0.0305787	+	0.999532i	$0.490265\pi$
$383$	−16.6413	+	28.8236i	−0.850331	+	1.47282i	−0.880910	+	0.473284i	$0.843068\pi$
$384$		0			0
$385$	−5.41488	+	20.1575i	−0.275968	+	1.02732i
$386$	10.7992	−	14.4430i	0.549666	−	0.735129i
$387$		0			0
$388$	−30.2157	+	8.90906i	−1.53397	+	0.452289i
$389$	13.6469	+	23.6372i	0.691927	+	1.19845i	0.971206	+	0.238243i	$0.0765714\pi$
$389$	13.6469	+	23.6372i	0.691927	+	1.19845i	−0.279279	+	0.960210i	$0.590095\pi$
$390$		0			0
$391$	2.18270	−	3.78055i	0.110384	−	0.191191i
$392$	12.6122	+	15.2621i	0.637014	+	0.770852i
$393$		0			0
$394$	−10.2244	−	1.21664i	−0.515095	−	0.0612934i
$395$	−15.4311			−0.776422
$396$		0			0
$397$		−	0.475116i		−	0.0238454i	−0.999929	−	0.0119227i	$-0.996205\pi$
$397$		−	0.475116i		−	0.0238454i	0.999929	−	0.0119227i	$-0.00379520\pi$
$398$	−5.04720	−	0.600588i	−0.252993	−	0.0301047i
$399$		0			0
$400$	−0.482702	−	9.67517i	−0.0241351	−	0.483758i
$401$	4.44710	−	7.70260i	0.222078	−	0.384650i	−0.733361	−	0.679839i	$-0.762050\pi$
$401$	4.44710	−	7.70260i	0.222078	−	0.384650i	0.955439	+	0.295190i	$0.0953828\pi$
$402$		0			0
$403$	26.3645	−	15.2216i	1.31331	−	0.758241i
$404$	8.54281	−	2.51884i	0.425021	−	0.125317i
$405$		0			0
$406$	0.740351	−	0.106393i	0.0367430	−	0.00528017i
$407$	−27.4327	+	15.8383i	−1.35979	+	0.785074i
$408$		0			0
$409$	23.7466	+	13.7101i	1.17419	+	0.677921i	0.954664	−	0.297685i	$-0.0962146\pi$
$409$	23.7466	+	13.7101i	1.17419	+	0.677921i	0.219529	+	0.975606i	$0.429548\pi$
$410$	−3.38127	−	7.88375i	−0.166989	−	0.389351i
$411$		0			0
$412$	−7.97835	+	8.38632i	−0.393065	+	0.413164i
$413$	−13.0903	−	13.1069i	−0.644131	−	0.644948i
$414$		0			0
$415$			22.2910i			1.09422i
$416$	−8.21748	−	16.7961i	−0.402895	−	0.823495i
$417$		0			0
$418$	41.5633	−	17.8261i	2.03293	−	0.871903i
$419$	−11.0927	+	19.2131i	−0.541913	+	0.938622i	0.456881	+	0.889528i	$0.348967\pi$
$419$	−11.0927	+	19.2131i	−0.541913	+	0.938622i	−0.998794	+	0.0490936i	$0.984367\pi$
$420$		0			0
$421$	15.8247	+	27.4092i	0.771249	+	1.33584i	0.936879	+	0.349654i	$0.113701\pi$
$421$	15.8247	+	27.4092i	0.771249	+	1.33584i	−0.165630	+	0.986188i	$0.552966\pi$
$422$	−17.6649	−	13.2083i	−0.859914	−	0.642969i
$423$		0			0
$424$	−18.8710	−	7.00229i	−0.916459	−	0.340061i
$425$	6.27293	−	3.62168i	0.304282	−	0.175677i
$426$		0			0
$427$	−1.29607	−	4.84929i	−0.0627212	−	0.234673i
$428$	−5.72113	+	23.6991i	−0.276541	+	1.14554i
$429$		0			0
$430$	17.6028	+	2.09463i	0.848883	+	0.101012i
$431$			18.9813i			0.914298i	0.889390	+	0.457149i	$0.151129\pi$
$431$			18.9813i			0.914298i	−0.889390	+	0.457149i	$0.848871\pi$
$432$		0			0
$433$			1.83792i			0.0883248i	0.999024	+	0.0441624i	$0.0140619\pi$
$433$			1.83792i			0.0883248i	−0.999024	+	0.0441624i	$0.985938\pi$
$434$	21.3001	+	27.0893i	1.02244	+	1.30033i
$435$		0			0
$436$	−5.74826	−	1.38767i	−0.275292	−	0.0664573i
$437$	8.22725	+	4.75001i	0.393563	+	0.227224i
$438$		0			0
$439$	6.48634	+	11.2347i	0.309576	+	0.536201i	0.978270	−	0.207337i	$-0.0664796\pi$
$439$	6.48634	+	11.2347i	0.309576	+	0.536201i	−0.668694	+	0.743538i	$0.733146\pi$
$440$	20.9195	+	7.76240i	0.997300	+	0.370058i
$441$		0			0
$442$	8.37241	−	11.1973i	0.398235	−	0.532604i
$443$	−7.31594	+	4.22386i	−0.347591	+	0.200682i	−0.663624	−	0.748067i	$-0.730982\pi$
$443$	−7.31594	+	4.22386i	−0.347591	+	0.200682i	0.316033	+	0.948748i	$0.397649\pi$
$444$		0			0
$445$	−6.48572	+	11.2336i	−0.307453	+	0.532523i
$446$	4.84781	+	11.3031i	0.229551	+	0.535220i
$447$		0			0
$448$	17.4960	−	11.9117i	0.826610	−	0.562775i
$449$	−34.5071			−1.62849			−0.814245	−	0.580521i	$-0.802849\pi$
$449$	−34.5071			−1.62849			−0.814245	+	0.580521i	$0.802849\pi$
$450$		0			0
$451$	−18.5603			−0.873972
$452$	−9.94795	+	10.4566i	−0.467912	+	0.491839i
$453$		0			0
$454$	−15.6878	−	36.5777i	−0.736266	−	1.71667i
$455$	−13.5662	+	3.62583i	−0.635992	+	0.169982i
$456$		0			0
$457$	−2.19998	−	3.81048i	−0.102911	−	0.178247i	0.809972	−	0.586469i	$-0.199482\pi$
$457$	−2.19998	−	3.81048i	−0.102911	−	0.178247i	−0.912883	+	0.408222i	$0.866149\pi$
$458$	−20.8870	−	15.6175i	−0.975985	−	0.729757i
$459$		0			0
$460$	1.32559	+	4.49582i	0.0618058	+	0.209619i
$461$	21.1414	−	12.2060i	0.984654	−	0.568491i	0.0809823	−	0.996716i	$-0.474194\pi$
$461$	21.1414	−	12.2060i	0.984654	−	0.568491i	0.903672	+	0.428225i	$0.140861\pi$
$462$		0			0
$463$	6.05752	+	3.49731i	0.281517	+	0.162534i	0.634110	−	0.773243i	$-0.281367\pi$
$463$	6.05752	+	3.49731i	0.281517	+	0.162534i	−0.352593	+	0.935777i	$0.614700\pi$
$464$	−0.0398431	−	0.798606i	−0.00184967	−	0.0370743i
$465$		0			0
$466$	1.29654	+	0.154281i	0.0600613	+	0.00714694i
$467$	15.2449			0.705450			0.352725	−	0.935727i	$-0.385255\pi$
$467$	15.2449			0.705450			0.352725	+	0.935727i	$0.385255\pi$
$468$		0			0
$469$	−10.2170	+	10.2041i	−0.471779	+	0.471182i
$470$	−0.303027	+	2.54657i	−0.0139776	+	0.117464i
$471$		0			0
$472$	−15.2493	+	12.6343i	−0.701908	+	0.581539i
$473$	19.1775	−	33.2164i	0.881782	−	1.52729i
$474$		0			0
$475$	7.88151	+	13.6512i	0.361629	+	0.626359i
$476$	13.8942	+	7.57793i	0.636838	+	0.347334i
$477$		0			0
$478$	−1.45193	−	1.08563i	−0.0664096	−	0.0496554i
$479$	−16.6451	−	28.8302i	−0.760535	−	1.31729i	−0.942575	−	0.333994i	$-0.891603\pi$
$479$	−16.6451	−	28.8302i	−0.760535	−	1.31729i	0.182040	−	0.983291i	$-0.441730\pi$
$480$		0			0
$481$	−18.4561	−	10.6557i	−0.841528	−	0.485856i
$482$	−24.2824	+	10.4145i	−1.10603	+	0.474368i
$483$		0			0
$484$	18.1125	−	19.0387i	0.823297	−	0.865396i
$485$	25.2908			1.14840
$486$		0			0
$487$		−	3.11001i		−	0.140928i	−0.997514	−	0.0704640i	$-0.977552\pi$
$487$		−	3.11001i		−	0.140928i	0.997514	−	0.0704640i	$-0.0224480\pi$
$488$	−5.29027	+	0.898783i	−0.239479	+	0.0406860i
$489$		0			0
$490$	−6.24692	−	14.6164i	−0.282207	−	0.660302i
$491$	22.5966	+	13.0462i	1.01977	+	0.588766i	0.914038	−	0.405629i	$-0.132947\pi$
$491$	22.5966	+	13.0462i	1.01977	+	0.588766i	0.105734	+	0.994394i	$0.466281\pi$
$492$		0			0
$493$	0.517779	−	0.298940i	0.0233196	−	0.0134636i
$494$	24.3677	+	18.2201i	1.09636	+	0.819760i
$495$		0			0
$496$	30.9467	−	19.9868i	1.38955	−	0.897432i
$497$	−22.9080	−	6.15375i	−1.02757	−	0.276033i
$498$		0			0
$499$	1.61303	+	0.931283i	0.0722091	+	0.0416899i	0.535670	−	0.844428i	$-0.320059\pi$
$499$	1.61303	+	0.931283i	0.0722091	+	0.0416899i	−0.463461	+	0.886117i	$0.653392\pi$
$500$	−5.59303	+	23.1685i	−0.250128	+	1.03613i
$501$		0			0
$502$	3.81076	+	0.453459i	0.170083	+	0.0202389i
$503$	32.3227			1.44120			0.720599	−	0.693352i	$-0.243867\pi$
$503$	32.3227			1.44120			0.720599	+	0.693352i	$0.243867\pi$
$504$		0			0
$505$	−7.15041			−0.318189
$506$	10.0704	+	1.19831i	0.447682	+	0.0532716i
$507$		0			0
$508$	−3.53850	+	14.6578i	−0.156996	+	0.650337i
$509$	13.5012	+	7.79490i	0.598429	+	0.345503i	0.768423	−	0.639942i	$-0.221042\pi$
$509$	13.5012	+	7.79490i	0.598429	+	0.345503i	−0.169994	+	0.985445i	$0.554375\pi$
$510$		0			0
$511$	3.07768	+	0.826753i	0.136149	+	0.0365734i
$512$	−10.9445	−	19.8045i	−0.483685	−	0.875242i
$513$		0			0
$514$	6.13026	+	4.58368i	0.270394	+	0.202178i
$515$	8.04797	−	4.64649i	0.354636	−	0.204749i
$516$		0			0
$517$	4.80536	+	2.77438i	0.211339	+	0.122017i
$518$	8.96743	−	22.3949i	0.394006	−	0.983976i
$519$		0			0
$520$	2.51440	+	14.7998i	0.110264	+	0.649016i
$521$			40.1427i			1.75869i	0.476189	+	0.879343i	$0.342018\pi$
$521$			40.1427i			1.75869i	−0.476189	+	0.879343i	$0.657982\pi$
$522$		0			0
$523$	−4.17022			−0.182351			−0.0911755	−	0.995835i	$-0.529062\pi$
$523$	−4.17022			−0.182351			−0.0911755	+	0.995835i	$0.529062\pi$
$524$	−0.464488	+	0.488239i	−0.0202912	+	0.0213288i
$525$		0			0
$526$	−1.10771	+	0.475088i	−0.0482987	+	0.0207148i
$527$	23.8555	+	13.7730i	1.03916	+	0.599961i
$528$		0			0
$529$	−10.4348	−	18.0737i	−0.453689	−	0.785812i
$530$	12.9420	+	9.67691i	0.562165	+	0.420338i
$531$		0			0
$532$	−16.4911	+	30.2365i	−0.714981	+	1.31092i
$533$	−6.24350	−	10.8141i	−0.270436	−	0.468409i
$534$		0			0
$535$	9.78658	−	16.9508i	0.423111	−	0.732849i
$536$	9.84862	+	11.8871i	0.425396	+	0.513446i
$537$		0			0
$538$	3.22011	−	27.0611i	0.138829	−	1.16669i
$539$	−34.3920	−	0.0435855i	−1.48137	−	0.00187736i
$540$		0			0
$541$	0.600133			0.0258017			0.0129009	−	0.999917i	$-0.495893\pi$
$541$	0.600133			0.0258017			0.0129009	+	0.999917i	$0.495893\pi$
$542$	−8.34788	−	0.993350i	−0.358572	−	0.0426680i
$543$		0			0
$544$	9.44382	−	14.0381i	0.404901	−	0.601879i
$545$	4.11145	+	2.37375i	0.176115	+	0.101680i
$546$		0			0
$547$	−29.9910	+	17.3153i	−1.28232	+	0.740349i	−0.977272	−	0.211988i	$-0.932006\pi$
$547$	−29.9910	+	17.3153i	−1.28232	+	0.740349i	−0.305049	+	0.952337i	$0.598673\pi$
$548$	−8.91737	−	30.2439i	−0.380931	−	1.29195i
$549$		0			0
$550$	13.4766	+	10.0766i	0.574643	+	0.429669i
$551$	0.650554	+	1.12679i	0.0277145	+	0.0480030i
$552$		0			0
$553$	−6.56531	−	24.5643i	−0.279185	−	1.04458i
$554$	−1.91007	−	4.45351i	−0.0811510	−	0.189211i
$555$		0			0
$556$	6.27990	−	6.60102i	0.266327	−	0.279946i
$557$	−29.2218			−1.23817			−0.619084	−	0.785325i	$-0.712496\pi$
$557$	−29.2218			−1.23817			−0.619084	+	0.785325i	$0.712496\pi$
$558$		0			0
$559$	25.8044			1.09141
$560$	−16.1776	+	5.20025i	−0.683630	+	0.219751i
$561$		0			0
$562$	−5.11468	−	11.9254i	−0.215750	−	0.503041i
$563$	22.8977	−	39.6601i	0.965025	−	1.67147i	0.255477	−	0.966815i	$-0.417768\pi$
$563$	22.8977	−	39.6601i	0.965025	−	1.67147i	0.709548	−	0.704657i	$-0.248899\pi$
$564$		0			0
$565$	10.0348	−	5.79357i	0.422165	−	0.243737i
$566$	−10.6615	+	14.2588i	−0.448135	+	0.599341i
$567$		0			0
$568$	−8.82159	+	23.7740i	−0.370146	+	0.997536i
$569$	−2.29224	−	3.97027i	−0.0960956	−	0.166443i	0.813970	−	0.580907i	$-0.197302\pi$
$569$	−2.29224	−	3.97027i	−0.0960956	−	0.166443i	−0.910065	+	0.414465i	$0.863969\pi$
$570$		0			0
$571$	−0.314130	−	0.181363i	−0.0131460	−	0.00758982i	0.493413	−	0.869795i	$-0.335749\pi$
$571$	−0.314130	−	0.181363i	−0.0131460	−	0.00758982i	−0.506559	+	0.862206i	$0.669083\pi$
$572$	31.5735	+	7.62205i	1.32015	+	0.318694i
$573$		0			0
$574$	11.1113	−	8.73676i	0.463778	−	0.364665i
$575$			3.53477i			0.147410i
$576$		0			0
$577$			17.4574i			0.726760i	0.931641	+	0.363380i	$0.118377\pi$
$577$			17.4574i			0.726760i	−0.931641	+	0.363380i	$0.881623\pi$
$578$	−11.3110	−	1.34595i	−0.470477	−	0.0559841i
$579$		0			0
$580$	−0.150643	+	0.624023i	−0.00625513	+	0.0259112i
$581$	−35.4844	+	9.48392i	−1.47214	+	0.393459i
$582$		0			0
$583$	30.2798	−	17.4820i	1.25406	−	0.724032i
$584$	1.18518	−	3.19403i	0.0490429	−	0.132170i
$585$		0			0
$586$	−19.6726	−	14.7094i	−0.812666	−	0.607641i
$587$	9.60046	+	16.6285i	0.396253	+	0.686331i	0.993260	−	0.115905i	$-0.0369769\pi$
$587$	9.60046	+	16.6285i	0.396253	+	0.686331i	−0.597007	+	0.802236i	$0.703644\pi$
$588$		0			0
$589$	−29.9729	+	51.9145i	−1.23501	+	2.13910i
$590$	14.6116	−	6.26678i	0.601550	−	0.257999i
$591$		0			0
$592$	−22.9489	−	11.7657i	−0.943193	−	0.483567i
$593$			13.3399i			0.547805i	0.961758	+	0.273902i	$0.0883145\pi$
$593$			13.3399i			0.547805i	−0.961758	+	0.273902i	$0.911686\pi$
$594$		0			0
$595$	−8.97880	−	8.99018i	−0.368095	−	0.368562i
$596$	−14.5542	+	15.2985i	−0.596165	+	0.626649i
$597$		0			0
$598$	2.68937	+	6.27053i	0.109977	+	0.256421i
$599$	−19.4102	−	11.2065i	−0.793079	−	0.457884i	0.0479667	−	0.998849i	$-0.484726\pi$
$599$	−19.4102	−	11.2065i	−0.793079	−	0.457884i	−0.841045	+	0.540965i	$0.818059\pi$
$600$		0			0
$601$	−13.3727	+	7.72073i	−0.545484	+	0.314935i	−0.747299	−	0.664488i	$-0.768649\pi$
$601$	−13.3727	+	7.72073i	−0.545484	+	0.314935i	0.201815	+	0.979424i	$0.435316\pi$
$602$	4.15490	+	28.9126i	0.169341	+	1.17839i
$603$		0			0
$604$	−22.5862	+	6.65951i	−0.919019	+	0.270971i
$605$	−18.2706	+	10.5485i	−0.742804	+	0.428858i
$606$		0			0
$607$	−9.97738	+	17.2813i	−0.404969	+	0.701427i	−0.994318	−	0.106452i	$-0.966051\pi$
$607$	−9.97738	+	17.2813i	−0.404969	+	0.701427i	0.589349	+	0.807879i	$0.299384\pi$
$608$	30.5498	+	20.5517i	1.23896	+	0.833481i
$609$		0			0
$610$	4.27791	+	0.509047i	0.173207	+	0.0206107i
$611$			3.73308i			0.151024i
$612$		0			0
$613$	23.4679			0.947859			0.473929	−	0.880563i	$-0.342835\pi$
$613$	23.4679			0.947859			0.473929	+	0.880563i	$0.342835\pi$
$614$	−7.94026	−	0.944845i	−0.320443	−	0.0381309i
$615$		0			0
$616$	−3.45633	+	36.6038i	−0.139259	+	1.47481i
$617$	−5.44048	+	9.42319i	−0.219026	+	0.379363i	−0.954510	−	0.298178i	$-0.903621\pi$
$617$	−5.44048	+	9.42319i	−0.219026	+	0.379363i	0.735485	+	0.677541i	$0.236954\pi$
$618$		0			0
$619$	−17.5874	−	30.4622i	−0.706896	−	1.22438i	−0.966003	−	0.258531i	$-0.916761\pi$
$619$	−17.5874	−	30.4622i	−0.706896	−	1.22438i	0.259107	−	0.965849i	$-0.416572\pi$
$620$	−28.3690	+	8.36455i	−1.13932	+	0.335928i
$621$		0			0
$622$	3.33045	−	4.45418i	0.133539	−	0.178596i
$623$	−20.6419	−	5.54499i	−0.826999	−	0.222155i
$624$		0			0
$625$	3.51294	−	6.08459i	0.140518	−	0.243384i
$626$	12.8894	−	5.52815i	0.515165	−	0.220950i
$627$		0			0
$628$	32.5737	+	30.9891i	1.29983	+	1.23660i
$629$		−	19.2832i		−	0.768871i
$630$		0			0
$631$		−	14.3791i		−	0.572421i	−0.958167	−	0.286211i	$-0.907604\pi$
$631$		−	14.3791i		−	0.572421i	0.958167	−	0.286211i	$-0.0923957\pi$
$632$	−26.7981	+	4.55283i	−1.06597	+	0.181102i
$633$		0			0
$634$	−4.75955	−	11.0973i	−0.189026	−	0.440732i
$635$	6.05296	−	10.4840i	0.240205	−	0.416046i
$636$		0			0
$637$	−11.5437	−	20.0530i	−0.457379	−	0.794527i
$638$	1.11238	+	0.831742i	0.0440396	+	0.0329290i
$639$		0			0
$640$	3.93135	+	17.7357i	0.155400	+	0.701064i
$641$	12.4756	+	21.6083i	0.492755	+	0.853476i	0.999965	−	0.00834610i	$-0.00265668\pi$
$641$	12.4756	+	21.6083i	0.492755	+	0.853476i	−0.507211	+	0.861822i	$0.669323\pi$
$642$		0			0
$643$	11.9561	−	20.7086i	0.471504	−	0.816669i	−0.527964	−	0.849267i	$-0.677045\pi$
$643$	11.9561	−	20.7086i	0.471504	−	0.816669i	0.999469	+	0.0325973i	$0.0103779\pi$
$644$	−6.59279	+	4.02296i	−0.259792	+	0.158527i
$645$		0			0
$646$	−3.25305	+	27.3378i	−0.127989	+	1.07559i
$647$	41.4943			1.63131			0.815655	−	0.578539i	$-0.196377\pi$
$647$	41.4943			1.63131			0.815655	+	0.578539i	$0.196377\pi$
$648$		0			0
$649$		−	34.3994i		−	1.35029i
$650$	−1.33770	+	11.2417i	−0.0524689	+	0.440936i
$651$		0			0
$652$	−6.13536	+	25.4150i	−0.240279	+	0.995329i
$653$	6.12472	−	10.6083i	0.239679	−	0.415136i	−0.720943	−	0.692994i	$-0.756291\pi$
$653$	6.12472	−	10.6083i	0.239679	−	0.415136i	0.960622	+	0.277858i	$0.0896245\pi$
$654$		0			0
$655$	0.468541	−	0.270512i	0.0183074	−	0.0105698i
$656$	−8.19806	−	12.6936i	−0.320080	−	0.495600i
$657$		0			0
$658$	−4.18274	+	0.601083i	−0.163060	+	0.0234326i
$659$	32.0479	−	18.5029i	1.24841	−	0.720769i	0.277617	−	0.960692i	$-0.410455\pi$
$659$	32.0479	−	18.5029i	1.24841	−	0.720769i	0.970792	+	0.239923i	$0.0771220\pi$
$660$		0			0
$661$	25.4350	+	14.6849i	0.989308	+	0.571177i	0.905067	−	0.425268i	$-0.139820\pi$
$661$	25.4350	+	14.6849i	0.989308	+	0.571177i	0.0842406	+	0.996445i	$0.473154\pi$
$662$	−3.58277	+	1.53662i	−0.139248	+	0.0597223i
$663$		0			0
$664$	6.57679	+	38.7112i	0.255229	+	1.50229i
$665$	19.5645	−	19.5397i	0.758678	−	0.757717i
$666$		0			0
$667$			0.291766i			0.0112972i
$668$	6.46365	−	6.79416i	0.250086	−	0.262874i
$669$		0			0
$670$	−4.88506	−	11.3900i	−0.188726	−	0.440034i
$671$	4.66060	−	8.07239i	0.179920	−	0.311631i
$672$		0			0
$673$	−20.0641	−	34.7520i	−0.773413	−	1.33959i	−0.935682	−	0.352844i	$-0.885215\pi$
$673$	−20.0641	−	34.7520i	−0.773413	−	1.33959i	0.162269	−	0.986747i	$-0.448119\pi$
$674$	−26.4923	+	35.4311i	−1.02045	+	1.36476i
$675$		0			0
$676$	−1.17305	−	3.97848i	−0.0451173	−	0.153018i
$677$	−22.9867	+	13.2714i	−0.883450	+	0.510060i	−0.871794	−	0.489872i	$-0.837044\pi$
$677$	−22.9867	+	13.2714i	−0.883450	+	0.510060i	−0.0116558	+	0.999932i	$0.503710\pi$
$678$		0			0
$679$	10.7602	+	40.2598i	0.412940	+	1.54503i
$680$	−10.4597	+	8.66600i	−0.401112	+	0.332326i
$681$		0			0
$682$	−7.56144	+	63.5446i	−0.289543	+	2.43325i
$683$			18.8108i			0.719774i	0.932996	+	0.359887i	$0.117185\pi$
$683$			18.8108i			0.719774i	−0.932996	+	0.359887i	$0.882815\pi$
$684$		0			0
$685$			25.3144i			0.967214i
$686$	20.6096	−	16.1630i	0.786880	−	0.617106i
$687$		0			0
$688$	31.1876	−	1.55598i	1.18902	−	0.0593210i
$689$	20.3716	+	11.7615i	0.776096	+	0.448079i
$690$		0			0
$691$	−10.5275	−	18.2342i	−0.400485	−	0.693660i	0.593299	−	0.804982i	$-0.297825\pi$
$691$	−10.5275	−	18.2342i	−0.400485	−	0.693660i	−0.993784	+	0.111321i	$0.964492\pi$
$692$	46.8817	−	13.8230i	1.78217	−	0.525472i
$693$		0			0
$694$	36.2198	+	27.0820i	1.37489	+	1.02802i
$695$	−6.33469	+	3.65734i	−0.240289	+	0.138731i
$696$		0			0
$697$	5.64933	−	9.78493i	0.213984	−	0.370631i
$698$	−30.5455	+	13.1007i	−1.15616	+	0.495868i
$699$		0			0
$700$	−12.8112	+	0.311259i	−0.484217	+	0.0117645i
$701$	43.5613			1.64529			0.822644	−	0.568556i	$-0.192498\pi$
$701$	43.5613			1.64529			0.822644	+	0.568556i	$0.192498\pi$
$702$		0			0
$703$	41.9642			1.58271
$704$	38.6198	+	7.30828i	1.45554	+	0.275441i
$705$		0			0
$706$	−0.901159	+	0.386499i	−0.0339156	+	0.0145461i
$707$	−3.04221	−	11.3825i	−0.114414	−	0.428084i
$708$		0			0
$709$	3.49938	+	6.06110i	0.131422	+	0.227630i	0.924225	−	0.381849i	$-0.124712\pi$
$709$	3.49938	+	6.06110i	0.131422	+	0.227630i	−0.792803	+	0.609478i	$0.791379\pi$
$710$	12.1911	−	16.3045i	0.457525	−	0.611898i
$711$		0			0
$712$	−7.94891	+	21.4222i	−0.297898	+	0.802830i
$713$	−11.6415	+	6.72125i	−0.435979	+	0.251713i
$714$		0			0
$715$	−22.5830	−	13.0383i	−0.844556	−	0.487604i
$716$	−2.27896	+	9.44033i	−0.0851687	+	0.352802i
$717$		0			0
$718$	−5.45396	+	45.8338i	−0.203540	+	1.71050i
$719$	−24.7885			−0.924456			−0.462228	−	0.886761i	$-0.652950\pi$
$719$	−24.7885			−0.924456			−0.462228	+	0.886761i	$0.652950\pi$
$720$		0			0
$721$	10.8207	+	10.8344i	0.402984	+	0.403495i
$722$	−32.8109	−	3.90431i	−1.22110	−	0.145303i
$723$		0			0
$724$	4.58879	−	19.0085i	0.170541	−	0.706447i
$725$	−0.242059	+	0.419258i	−0.00898983	+	0.0155708i
$726$		0			0
$727$	0.647887	+	1.12217i	0.0240288	+	0.0416191i	0.877790	−	0.479046i	$-0.159017\pi$
$727$	0.647887	+	1.12217i	0.0240288	+	0.0416191i	−0.853761	+	0.520665i	$0.825684\pi$
$728$	−22.4897	+	10.2993i	−0.833522	+	0.381719i
$729$		0			0
$730$	−1.63787	+	2.19051i	−0.0606203	+	0.0810743i
$731$	11.6744	+	20.2206i	0.431792	+	0.747886i
$732$		0			0
$733$	−39.4400	−	22.7707i	−1.45675	−	0.841054i	−0.457899	−	0.889004i	$-0.651398\pi$
$733$	−39.4400	−	22.7707i	−1.45675	−	0.841054i	−0.998850	+	0.0479504i	$0.984731\pi$
$734$	3.10744	+	7.24529i	0.114698	+	0.267428i
$735$		0			0
$736$	3.62852	+	7.41649i	0.133749	+	0.273375i
$737$	−26.8149			−0.987740
$738$		0			0
$739$			35.7360i			1.31457i	0.753642	+	0.657285i	$0.228295\pi$
$739$			35.7360i			1.31457i	−0.753642	+	0.657285i	$0.771705\pi$
$740$	15.0007	+	14.2709i	0.551435	+	0.524609i
$741$		0			0
$742$	−9.89810	+	24.7192i	−0.363371	+	0.907469i
$743$	46.8515	+	27.0497i	1.71882	+	0.992358i	0.921102	+	0.389321i	$0.127290\pi$
$743$	46.8515	+	27.0497i	1.71882	+	0.992358i	0.797713	+	0.603037i	$0.206043\pi$
$744$		0			0
$745$	14.6812	−	8.47621i	0.537879	−	0.310544i
$746$	18.7004	−	25.0101i	0.684669	−	0.915683i
$747$		0			0
$748$	8.31167	+	28.1896i	0.303905	+	1.03071i
$749$	31.1474	+	8.36707i	1.13810	+	0.305726i
$750$		0			0
$751$	−42.0553	−	24.2807i	−1.53462	−	0.886014i	−0.999140	−	0.0414665i	$-0.986797\pi$
$751$	−42.0553	−	24.2807i	−1.53462	−	0.886014i	−0.535481	−	0.844547i	$-0.679870\pi$
$752$	0.225100	+	4.51186i	0.00820857	+	0.164531i
$753$		0			0
$754$	−0.110416	+	0.927911i	−0.00402112	+	0.0337925i
$755$	18.9048			0.688018
$756$		0			0
$757$	−14.5848			−0.530092			−0.265046	−	0.964236i	$-0.585387\pi$
$757$	−14.5848			−0.530092			−0.265046	+	0.964236i	$0.585387\pi$
$758$	−3.74323	+	31.4572i	−0.135960	+	1.14258i
$759$		0			0
$760$	−18.8590	−	22.7625i	−0.684087	−	0.825683i
$761$	−39.0860	−	22.5663i	−1.41687	−	0.818028i	−0.420844	−	0.907133i	$-0.638266\pi$
$761$	−39.0860	−	22.5663i	−1.41687	−	0.818028i	−0.996022	+	0.0891053i	$0.971599\pi$
$762$		0			0
$763$	−2.02945	+	7.55484i	−0.0734709	+	0.273504i
$764$	7.64283	−	2.25348i	0.276508	−	0.0815279i
$765$		0			0
$766$	28.1860	−	37.6963i	1.01840	−	1.36202i
$767$	20.0426	−	11.5716i	0.723696	−	0.417826i
$768$		0			0
$769$	5.99708	+	3.46241i	0.216260	+	0.124858i	0.604217	−	0.796820i	$-0.293486\pi$
$769$	5.99708	+	3.46241i	0.216260	+	0.124858i	−0.387957	+	0.921677i	$0.626819\pi$
$770$	10.9726	−	27.4025i	0.395424	−	0.987517i
$771$		0			0
$772$	−17.5789	+	18.4778i	−0.632678	+	0.665030i
$773$		−	21.4608i		−	0.771891i	−0.922522	−	0.385945i	$-0.873875\pi$
$773$		−	21.4608i		−	0.771891i	0.922522	−	0.385945i	$-0.126125\pi$
$774$		0			0
$775$	−22.3047			−0.801207
$776$	43.9209	−	7.46188i	1.57667	−	0.267866i
$777$		0			0
$778$	−15.2146	−	35.4743i	−0.545470	−	1.27182i
$779$	21.2940	+	12.2941i	0.762937	+	0.440482i
$780$		0			0
$781$	−22.0241	−	38.1469i	−0.788085	−	1.36500i
$782$	−3.69693	+	4.94431i	−0.132202	+	0.176808i
$783$		0			0
$784$	−15.1611	−	23.5402i	−0.541467	−	0.840722i
$785$	−18.0477	−	31.2595i	−0.644149	−	1.11570i
$786$		0			0
$787$	−13.3345	+	23.0961i	−0.475324	+	0.823285i	−0.999601	−	0.0282627i	$-0.991002\pi$
$787$	−13.3345	+	23.0961i	−0.475324	+	0.823285i	0.524277	+	0.851548i	$0.324336\pi$
$788$	14.1548	+	3.41707i	0.504244	+	0.121728i
$789$		0			0
$790$	21.6700	+	2.57860i	0.770983	+	0.0917425i
$791$	13.4920	+	13.5091i	0.479720	+	0.480329i
$792$		0			0
$793$	6.27110			0.222693
$794$	−0.0793939	+	0.667208i	−0.00281759	+	0.0236783i
$795$		0			0
$796$	6.98745	+	1.68682i	0.247664	+	0.0597877i
$797$	−8.30603	−	4.79549i	−0.294215	−	0.169865i	0.345626	−	0.938372i	$-0.387667\pi$
$797$	−8.30603	−	4.79549i	−0.294215	−	0.169865i	−0.639841	+	0.768507i	$0.721000\pi$
$798$		0			0
$799$	−2.92528	+	1.68891i	−0.103489	+	0.0597494i
$800$	−0.938901	+	13.6676i	−0.0331952	+	0.483221i
$801$		0			0
$802$	−7.53223	+	10.0737i	−0.265972	+	0.355714i
$803$	2.95893	+	5.12502i	0.104418	+	0.180858i
$804$		0			0
$805$	5.99029	−	1.60103i	0.211130	−	0.0564287i
$806$	−39.5675	+	16.9701i	−1.39370	+	0.597747i
$807$		0			0
$808$	−12.4176	+	2.10968i	−0.436851	+	0.0742182i
$809$	−17.5496			−0.617010			−0.308505	−	0.951223i	$-0.599829\pi$
$809$	−17.5496			−0.617010			−0.308505	+	0.951223i	$0.599829\pi$
$810$		0			0
$811$	−6.54554			−0.229845			−0.114922	−	0.993374i	$-0.536662\pi$
$811$	−6.54554			−0.229845			−0.114922	+	0.993374i	$0.536662\pi$
$812$	−1.05746	+	0.0256919i	−0.0371095	+	0.000901607i
$813$		0			0
$814$	41.1705	−	17.6577i	1.44303	−	0.618901i
$815$	10.4951	−	18.1781i	0.367629	−	0.636752i
$816$		0			0
$817$	−44.0042	+	25.4058i	−1.53951	+	0.888837i
$818$	−31.0565	−	23.2213i	−1.08586	−	0.811915i
$819$		0			0
$820$	3.43092	+	11.6362i	0.119813	+	0.406354i
$821$	−3.29785	−	5.71204i	−0.115096	−	0.199352i	0.802722	−	0.596353i	$-0.203384\pi$
$821$	−3.29785	−	5.71204i	−0.115096	−	0.199352i	−0.917818	+	0.397001i	$0.870051\pi$
$822$		0			0
$823$	31.8965	+	18.4154i	1.11184	+	0.641922i	0.939306	−	0.343081i	$-0.111471\pi$
$823$	31.8965	+	18.4154i	1.11184	+	0.641922i	0.172536	+	0.985003i	$0.444804\pi$
$824$	12.6054	−	10.4437i	0.439131	−	0.363825i
$825$		0			0
$826$	16.1926	+	20.5935i	0.563411	+	0.716540i
$827$			6.08634i			0.211643i	0.994385	+	0.105821i	$0.0337472\pi$
$827$			6.08634i			0.211643i	−0.994385	+	0.105821i	$0.966253\pi$
$828$		0			0
$829$			46.3749i			1.61067i	0.592822	+	0.805334i	$0.298014\pi$
$829$			46.3749i			1.61067i	−0.592822	+	0.805334i	$0.701986\pi$
$830$	3.72492	−	31.3034i	0.129294	−	1.08656i
$831$		0			0
$832$	8.73317	+	24.9600i	0.302768	+	0.865332i
$833$	10.4911	−	18.1181i	0.363495	−	0.627754i
$834$		0			0
$835$	−6.52004	+	3.76435i	−0.225635	+	0.130271i
$836$	−61.3464	+	18.0879i	−2.12171	+	0.625583i
$837$		0			0
$838$	18.7881	−	25.1274i	0.649025	−	0.868013i
$839$	−13.4516	−	23.2988i	−0.464401	−	0.804365i	0.534774	−	0.844995i	$-0.320397\pi$
$839$	−13.4516	−	23.2988i	−0.464401	−	0.804365i	−0.999174	+	0.0406299i	$0.987064\pi$
$840$		0			0
$841$	14.4800	−	25.0801i	0.499311	−	0.864832i
$842$	−17.6425	−	41.1353i	−0.608002	−	1.41762i
$843$		0			0
$844$	22.5998	+	21.5003i	0.777916	+	0.740073i
$845$			3.33002i			0.114556i
$846$		0			0
$847$	−24.5653	−	24.5964i	−0.844073	−	0.845144i
$848$	25.3306	+	12.9868i	0.869857	+	0.445968i
$849$		0			0
$850$	−9.41431	+	4.03771i	−0.322908	+	0.138492i
$851$	8.14951	+	4.70512i	0.279362	+	0.161289i
$852$		0			0
$853$	22.4430	−	12.9575i	0.768435	−	0.443656i	−0.0638813	−	0.997958i	$-0.520348\pi$
$853$	22.4430	−	12.9575i	0.768435	−	0.443656i	0.832316	+	0.554302i	$0.187015\pi$
$854$	1.00974	+	7.02646i	0.0345527	+	0.240441i
$855$		0			0
$856$	11.9945	−	32.3248i	0.409962	−	1.10484i
$857$	−26.1210	+	15.0809i	−0.892275	+	0.515155i	−0.874686	−	0.484690i	$-0.838932\pi$
$857$	−26.1210	+	15.0809i	−0.892275	+	0.515155i	−0.0175891	+	0.999845i	$0.505599\pi$
$858$		0			0
$859$	8.63542	−	14.9570i	0.294637	−	0.510326i	−0.680263	−	0.732968i	$-0.738135\pi$
$859$	8.63542	−	14.9570i	0.294637	−	0.510326i	0.974900	+	0.222642i	$0.0714680\pi$
$860$	−24.3697	−	5.88301i	−0.831000	−	0.200609i
$861$		0			0
$862$	3.17186	−	26.6556i	0.108034	−	0.907893i
$863$		−	6.23238i		−	0.212153i	−0.994358	−	0.106076i	$-0.966171\pi$
$863$		−	6.23238i		−	0.212153i	0.994358	−	0.106076i	$-0.0338288\pi$
$864$		0			0
$865$	−39.2404			−1.33421
$866$	0.307124	−	2.58100i	0.0104365	−	0.0877060i
$867$		0			0
$868$	−25.3851	−	41.6010i	−0.861628	−	1.41203i
$869$	23.6085	−	40.8911i	0.800863	−	1.38714i
$870$		0			0
$871$	−9.02026	−	15.6235i	−0.305640	−	0.529383i
$872$	7.84044	+	2.90927i	0.265511	+	0.0985204i
$873$		0			0
$874$	−10.7598	−	8.04527i	−0.363957	−	0.272135i
$875$	30.4499	+	8.17972i	1.02940	+	0.276525i
$876$		0			0
$877$	−6.98489	+	12.0982i	−0.235863	+	0.408527i	−0.959523	−	0.281630i	$-0.909125\pi$
$877$	−6.98489	+	12.0982i	−0.235863	+	0.408527i	0.723660	+	0.690156i	$0.242458\pi$
$878$	−7.23144	−	16.8608i	−0.244049	−	0.569025i
$879$		0			0
$880$	−28.0803	−	14.3965i	−0.946587	−	0.485307i
$881$			7.85378i			0.264601i	0.991210	+	0.132300i	$0.0422363\pi$
$881$			7.85378i			0.264601i	−0.991210	+	0.132300i	$0.957764\pi$
$882$		0			0
$883$		−	9.62415i		−	0.323878i	−0.986801	−	0.161939i	$-0.948225\pi$
$883$		−	9.62415i		−	0.323878i	0.986801	−	0.161939i	$-0.0517748\pi$
$884$	−13.6286	+	14.3254i	−0.458378	+	0.481817i
$885$		0			0
$886$	10.9797	−	4.70907i	0.368869	−	0.158204i
$887$	6.66329	−	11.5412i	0.223731	−	0.387514i	−0.732207	−	0.681083i	$-0.761509\pi$
$887$	6.66329	−	11.5412i	0.223731	−	0.387514i	0.955938	+	0.293568i	$0.0948428\pi$
$888$		0			0
$889$	19.2645	+	5.17500i	0.646112	+	0.173564i
$890$	10.9851	−	14.6916i	0.368222	−	0.492464i
$891$		0			0
$892$	−4.91901	−	16.6832i	−0.164701	−	0.558594i
$893$	−3.67542	−	6.36601i	−0.122993	−	0.213030i
$894$		0			0
$895$	3.89839	−	6.75220i	0.130309	−	0.225701i
$896$	−26.5603	+	13.8040i	−0.887317	+	0.461160i
$897$		0			0
$898$	48.4585	+	5.76629i	1.61708	+	0.192423i
$899$	−1.84107			−0.0614030
$900$		0			0
$901$			21.2845i			0.709089i
$902$	26.0644	+	3.10151i	0.867849	+	0.103269i
$903$		0			0
$904$	15.7173	−	13.0220i	0.522750	−	0.433104i
$905$	−7.84959	+	13.5959i	−0.260929	+	0.451943i
$906$		0			0
$907$	−24.2973	+	14.0281i	−0.806780	+	0.465795i	−0.845836	−	0.533442i	$-0.820898\pi$
$907$	−24.2973	+	14.0281i	−0.806780	+	0.465795i	0.0390564	+	0.999237i	$0.487565\pi$
$908$	15.9182	+	53.9877i	0.528264	+	1.79165i
$909$		0			0
$910$	19.6569	−	2.82481i	0.651621	−	0.0936416i
$911$	−22.4667	+	12.9711i	−0.744354	+	0.429753i	−0.823650	−	0.567098i	$-0.808066\pi$
$911$	−22.4667	+	12.9711i	−0.744354	+	0.429753i	0.0792961	+	0.996851i	$0.474733\pi$
$912$		0			0
$913$	−59.0693	−	34.1037i	−1.95491	−	1.12867i
$914$	2.45270	+	5.71871i	0.0811281	+	0.189158i
$915$		0			0
$916$	26.7220	+	25.4220i	0.882919	+	0.839968i
$917$	0.629966	+	0.630765i	0.0208033	+	0.0208297i
$918$		0			0
$919$		−	13.7527i		−	0.453661i	−0.973934	−	0.226830i	$-0.927164\pi$
$919$		−	13.7527i		−	0.453661i	0.973934	−	0.226830i	$-0.0728363\pi$
$920$	−1.11026	−	6.53503i	−0.0366042	−	0.215453i
$921$		0			0
$922$	−31.7287	+	13.6082i	−1.04493	+	0.448161i
$923$	14.8174	−	25.6644i	0.487720	−	0.844756i
$924$		0			0
$925$	7.80704	+	13.5222i	0.256694	+	0.444607i
$926$	−7.92220	−	5.92353i	−0.260340	−	0.194659i
$927$		0			0
$928$	−0.0774986	+	1.12814i	−0.00254402	+	0.0370332i
$929$	−18.9681	+	10.9512i	−0.622322	+	0.359298i	−0.777773	−	0.628546i	$-0.783650\pi$
$929$	−18.9681	+	10.9512i	−0.622322	+	0.359298i	0.155450	+	0.987844i	$0.450317\pi$
$930$		0			0
$931$	39.4286	+	22.8308i	1.29222	+	0.748249i
$932$	−1.79496	−	0.433316i	−0.0587960	−	0.0141938i
$933$		0			0
$934$	−21.4085	−	2.54749i	−0.700508	−	0.0833564i
$935$		−	23.5950i		−	0.771638i
$936$		0			0
$937$		−	11.7229i		−	0.382970i	−0.981496	−	0.191485i	$-0.938670\pi$
$937$		−	11.7229i		−	0.382970i	0.981496	−	0.191485i	$-0.0613304\pi$
$938$	16.0530	−	12.6224i	0.524150	−	0.412135i
$939$		0			0
$940$	0.851085	−	3.52553i	0.0277593	−	0.114990i
$941$	17.2190	+	9.94138i	0.561323	+	0.324080i	0.753676	−	0.657246i	$-0.228279\pi$
$941$	17.2190	+	9.94138i	0.561323	+	0.324080i	−0.192354	+	0.981326i	$0.561612\pi$
$942$		0			0
$943$	2.75689	+	4.77507i	0.0897765	+	0.155498i
$944$	23.5260	−	15.1941i	0.765706	−	0.494527i
$945$		0			0
$946$	−32.4817	+	43.4413i	−1.05607	+	1.41240i
$947$	−20.7634	+	11.9878i	−0.674721	+	0.389550i	−0.797863	−	0.602839i	$-0.794036\pi$
$947$	−20.7634	+	11.9878i	−0.674721	+	0.389550i	0.123142	+	0.992389i	$0.460703\pi$
$948$		0			0
$949$	−1.99071	+	3.44800i	−0.0646211	+	0.111927i
$950$	−8.78688	−	20.4875i	−0.285084	−	0.664701i
$951$		0			0
$952$	−18.2454	−	12.9635i	−0.591335	−	0.420150i
$953$	52.7537			1.70886			0.854431	−	0.519565i	$-0.173906\pi$
$953$	52.7537			1.70886			0.854431	+	0.519565i	$0.173906\pi$
$954$		0			0
$955$	−6.39712			−0.207006
$956$	1.85754	+	1.76718i	0.0600771	+	0.0571545i
$957$		0			0
$958$	18.5572	+	43.2679i	0.599556	+	1.39792i
$959$	−40.2973	+	10.7703i	−1.30127	+	0.347790i
$960$		0			0
$961$	−26.9115	−	46.6122i	−0.868114	−	1.50362i
$962$	24.1375	+	18.0479i	0.778223	+	0.581888i
$963$		0			0
$964$	35.8403	−	10.5675i	1.15434	−	0.340355i
$965$	17.7323	−	10.2377i	0.570822	−	0.329564i
$966$		0			0
$967$	34.6344	+	19.9962i	1.11377	+	0.643033i	0.939802	−	0.341719i	$-0.111009\pi$
$967$	34.6344	+	19.9962i	1.11377	+	0.643033i	0.173964	+	0.984752i	$0.444342\pi$
$968$	−28.6170	+	23.7095i	−0.919785	+	0.762052i
$969$		0			0
$970$	−35.5161	−	4.22621i	−1.14035	−	0.135695i
$971$	−20.2688			−0.650457			−0.325229	−	0.945635i	$-0.605441\pi$
$971$	−20.2688			−0.650457			−0.325229	+	0.945635i	$0.605441\pi$
$972$		0			0
$973$	−8.51717	−	8.52797i	−0.273048	−	0.273394i
$974$	−0.519696	+	4.36740i	−0.0166521	+	0.139941i
$975$		0			0
$976$	7.57935	−	0.378140i	0.242609	−	0.0121040i
$977$	−11.3142	+	19.5968i	−0.361974	+	0.626957i	−0.988286	−	0.152615i	$-0.951230\pi$
$977$	−11.3142	+	19.5968i	−0.361974	+	0.626957i	0.626312	+	0.779573i	$0.284564\pi$
$978$		0			0
$979$	−19.8454	−	34.3732i	−0.634262	−	1.09857i
$980$	6.33013	+	21.5698i	0.202209	+	0.689022i
$981$		0			0
$982$	−29.5525	−	22.0968i	−0.943059	−	0.705138i
$983$	−20.8965	−	36.1937i	−0.666494	−	1.15440i	−0.978878	−	0.204445i	$-0.934461\pi$
$983$	−20.8965	−	36.1937i	−0.666494	−	1.15440i	0.312384	−	0.949956i	$-0.398872\pi$
$984$		0			0
$985$	−10.1242	−	5.84524i	−0.322585	−	0.186245i
$986$	−0.777074	+	0.333280i	−0.0247471	+	0.0106138i
$987$		0			0
$988$	−31.1751	−	29.6585i	−0.991812	−	0.943563i
$989$	−11.3942			−0.362315
$990$		0			0
$991$		−	50.7785i		−	1.61303i	−0.591213	−	0.806515i	$-0.701351\pi$
$991$		−	50.7785i		−	1.61303i	0.591213	−	0.806515i	$-0.298649\pi$
$992$	−46.7985	+	22.8962i	−1.48585	+	0.726955i
$993$		0			0
$994$	31.1416	+	12.4698i	0.987751	+	0.395517i
$995$	−4.99778	−	2.88547i	−0.158440	−	0.0914756i
$996$		0			0
$997$	27.7940	−	16.0469i	0.880246	−	0.508210i	0.00950674	−	0.999955i	$-0.496974\pi$
$997$	27.7940	−	16.0469i	0.880246	−	0.508210i	0.870740	+	0.491744i	$0.163641\pi$
$998$	−2.10957	−	1.57735i	−0.0667771	−	0.0499302i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bi.c.307.1		80
3.2	odd	2		252.2.bi.c.139.39	yes	80
4.3	odd	2	inner	756.2.bi.c.307.23		80
7.6	odd	2	inner	756.2.bi.c.307.2		80
9.2	odd	6		252.2.bi.c.223.17	yes	80
9.7	even	3	inner	756.2.bi.c.559.24		80
12.11	even	2		252.2.bi.c.139.18	yes	80
21.20	even	2		252.2.bi.c.139.40	yes	80
28.27	even	2	inner	756.2.bi.c.307.24		80
36.7	odd	6	inner	756.2.bi.c.559.2		80
36.11	even	6		252.2.bi.c.223.40	yes	80
63.20	even	6		252.2.bi.c.223.18	yes	80
63.34	odd	6	inner	756.2.bi.c.559.23		80
84.83	odd	2		252.2.bi.c.139.17	✓	80
252.83	odd	6		252.2.bi.c.223.39	yes	80
252.223	even	6	inner	756.2.bi.c.559.1		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.17	✓	80	84.83	odd	2
252.2.bi.c.139.18	yes	80	12.11	even	2
252.2.bi.c.139.39	yes	80	3.2	odd	2
252.2.bi.c.139.40	yes	80	21.20	even	2
252.2.bi.c.223.17	yes	80	9.2	odd	6
252.2.bi.c.223.18	yes	80	63.20	even	6
252.2.bi.c.223.39	yes	80	252.83	odd	6
252.2.bi.c.223.40	yes	80	36.11	even	6
756.2.bi.c.307.1		80	1.1	even	1	trivial
756.2.bi.c.307.2		80	7.6	odd	2	inner
756.2.bi.c.307.23		80	4.3	odd	2	inner
756.2.bi.c.307.24		80	28.27	even	2	inner
756.2.bi.c.559.1		80	252.223	even	6	inner
756.2.bi.c.559.2		80	36.7	odd	6	inner
756.2.bi.c.559.23		80	63.34	odd	6	inner
756.2.bi.c.559.24		80	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.40431 - 0.167104i) q^{2} +(1.94415 + 0.469331i) q^{4} +(-1.39056 - 0.802839i) q^{5} +(0.686390 - 2.55517i) q^{7} +(-2.65176 - 0.983961i) q^{8} +O(q^{10})\)	\(q+(-1.40431 - 0.167104i) q^{2} +(1.94415 + 0.469331i) q^{4} +(-1.39056 - 0.802839i) q^{5} +(0.686390 - 2.55517i) q^{7} +(-2.65176 - 0.983961i) q^{8} +(1.81861 + 1.35980i) q^{10} +(4.25491 - 2.45657i) q^{11} +(2.86262 + 1.65273i) q^{13} +(-1.39088 + 3.47354i) q^{14} +(3.55946 + 1.82490i) q^{16} +2.99090i q^{17} -6.50880 q^{19} +(-2.32666 - 2.21347i) q^{20} +(-6.38570 + 2.73877i) q^{22} +(-1.26402 - 0.729782i) q^{23} +(-1.21090 - 2.09734i) q^{25} +(-3.74381 - 2.79930i) q^{26} +(2.53367 - 4.64549i) q^{28} +(-0.0999499 - 0.173118i) q^{29} +(4.60497 - 7.97605i) q^{31} +(-4.69362 - 3.15752i) q^{32} +(0.499792 - 4.20013i) q^{34} +(-3.00585 + 3.00204i) q^{35} -6.44730 q^{37} +(9.14035 + 1.08765i) q^{38} +(2.89746 + 3.49719i) q^{40} +(-3.27157 - 1.88884i) q^{41} +(6.76071 - 3.90330i) q^{43} +(9.42514 - 2.77899i) q^{44} +(1.65312 + 1.23606i) q^{46} +(0.564684 + 0.978061i) q^{47} +(-6.05774 - 3.50768i) q^{49} +(1.35000 + 3.14766i) q^{50} +(4.78968 + 4.55668i) q^{52} +7.11643 q^{53} -7.88893 q^{55} +(-4.33432 + 6.10030i) q^{56} +(0.111431 + 0.259813i) q^{58} +(3.50075 - 6.06347i) q^{59} +(1.64302 - 0.948597i) q^{61} +(-7.79962 + 10.4313i) q^{62} +(6.06364 + 5.21845i) q^{64} +(-2.65375 - 4.59644i) q^{65} +(-4.72658 - 2.72889i) q^{67} +(-1.40372 + 5.81476i) q^{68} +(4.72279 - 3.71350i) q^{70} -8.96538i q^{71} +1.20449i q^{73} +(9.05398 + 1.07737i) q^{74} +(-12.6541 - 3.05479i) q^{76} +(-3.35642 - 12.5582i) q^{77} +(8.32279 - 4.80516i) q^{79} +(-3.48452 - 5.39530i) q^{80} +(4.27865 + 3.19921i) q^{82} +(-6.94130 - 12.0227i) q^{83} +(2.40121 - 4.15901i) q^{85} +(-10.1464 + 4.35168i) q^{86} +(-13.7002 + 2.32757i) q^{88} -8.07848i q^{89} +(6.18787 - 6.18004i) q^{91} +(-2.11494 - 2.01205i) q^{92} +(-0.629551 - 1.46786i) q^{94} +(9.05086 + 5.22552i) q^{95} +(-13.6407 + 7.87544i) q^{97} +(7.92077 + 5.93813i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8}+O(q^{10}) \) 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8	\( 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8} - 10 q^{14} - 18 q^{16} - 14 q^{22} + 32 q^{25} + 28 q^{28} - 8 q^{29} + 16 q^{32} - 16 q^{37} + 84 q^{44} + 24 q^{46} - 24 q^{49} + 12 q^{50} + 48 q^{53} - 32 q^{56} - 14 q^{58} - 8 q^{64} + 40 q^{65} - 22 q^{70} - 64 q^{74} + 12 q^{77} + 40 q^{85} + 52 q^{86} + 6 q^{88} - 30 q^{92} - 20 q^{98}+O(q^{100}) \) 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8 - 10 * q^14 - 18 * q^16 - 14 * q^22 + 32 * q^25 + 28 * q^28 - 8 * q^29 + 16 * q^32 - 16 * q^37 + 84 * q^44 + 24 * q^46 - 24 * q^49 + 12 * q^50 + 48 * q^53 - 32 * q^56 - 14 * q^58 - 8 * q^64 + 40 * q^65 - 22 * q^70 - 64 * q^74 + 12 * q^77 + 40 * q^85 + 52 * q^86 + 6 * q^88 - 30 * q^92 - 20 * q^98

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