LMFDB - Embedded newform 784.2.x.p.165.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			165.10
Character	$\chi$	$=$	784.165
Dual form			784.2.x.p.765.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.646444 - 1.25782i) q^{2} +(0.729365 + 2.72203i) q^{3} +(-1.16422 + 1.62622i) q^{4} +(0.691444 - 2.58050i) q^{5} +(2.95233 - 2.67705i) q^{6} +(2.79809 + 0.413120i) q^{8} +(-4.27938 + 2.47070i) q^{9} +O(q^{10})$	\(q+(-0.646444 - 1.25782i) q^{2} +(0.729365 + 2.72203i) q^{3} +(-1.16422 + 1.62622i) q^{4} +(0.691444 - 2.58050i) q^{5} +(2.95233 - 2.67705i) q^{6} +(2.79809 + 0.413120i) q^{8} +(-4.27938 + 2.47070i) q^{9} +(-3.69279 + 0.798439i) q^{10} +(5.36650 - 1.43795i) q^{11} +(-5.27576 - 1.98293i) q^{12} +(-3.30151 + 3.30151i) q^{13} +7.52851 q^{15} +(-1.28918 - 3.78656i) q^{16} +(2.63692 - 4.56728i) q^{17} +(5.87408 + 3.78552i) q^{18} +(2.19147 + 0.587201i) q^{19} +(3.39147 + 4.12871i) q^{20} +(-5.27782 - 5.82053i) q^{22} +(3.73587 - 2.15691i) q^{23} +(0.916309 + 7.91781i) q^{24} +(-1.85077 - 1.06854i) q^{25} +(6.28695 + 2.01846i) q^{26} +(-3.86857 - 3.86857i) q^{27} +(1.07893 - 1.07893i) q^{29} +(-4.86676 - 9.46951i) q^{30} +(-2.24040 + 3.88049i) q^{31} +(-3.92942 + 4.06935i) q^{32} +(7.82827 + 13.5590i) q^{33} +(-7.44943 - 0.364280i) q^{34} +(0.964240 - 9.83566i) q^{36} +(-0.143285 + 0.534749i) q^{37} +(-0.678066 - 3.13606i) q^{38} +(-11.3948 - 6.57880i) q^{39} +(3.00078 - 6.93484i) q^{40} +7.35196i q^{41} +(1.67142 + 1.67142i) q^{43} +(-3.90937 + 10.4012i) q^{44} +(3.41670 + 12.7513i) q^{45} +(-5.12803 - 3.30474i) q^{46} +(0.245394 + 0.425035i) q^{47} +(9.36683 - 6.27097i) q^{48} +(-0.147615 + 3.01869i) q^{50} +(14.3555 + 3.84655i) q^{51} +(-1.52530 - 9.21267i) q^{52} +(7.90260 - 2.11750i) q^{53} +(-2.36515 + 7.36678i) q^{54} -14.8425i q^{55} +6.39351i q^{57} +(-2.05457 - 0.659634i) q^{58} +(-3.53183 + 0.946351i) q^{59} +(-8.76485 + 12.2430i) q^{60} +(7.30218 + 1.95661i) q^{61} +(6.32925 + 0.309503i) q^{62} +(7.65866 + 2.31190i) q^{64} +(6.23675 + 10.8024i) q^{65} +(11.9942 - 18.6117i) q^{66} +(3.33541 + 12.4479i) q^{67} +(4.35744 + 9.60553i) q^{68} +(8.59598 + 8.59598i) q^{69} -16.2570i q^{71} +(-12.9948 + 5.14536i) q^{72} +(6.89278 + 3.97955i) q^{73} +(0.765243 - 0.165458i) q^{74} +(1.55872 - 5.81721i) q^{75} +(-3.50627 + 2.88017i) q^{76} +(-0.908834 + 18.5854i) q^{78} +(-1.10561 - 1.91497i) q^{79} +(-10.6626 + 0.708545i) q^{80} +(0.296643 - 0.513800i) q^{81} +(9.24743 - 4.75263i) q^{82} +(3.81693 - 3.81693i) q^{83} +(-9.96259 - 9.96259i) q^{85} +(1.02187 - 3.18283i) q^{86} +(3.72382 + 2.14995i) q^{87} +(15.6100 - 1.80651i) q^{88} +(-9.66675 + 5.58110i) q^{89} +(13.8301 - 12.5406i) q^{90} +(-0.841775 + 8.58647i) q^{92} +(-12.1969 - 3.26814i) q^{93} +(0.375984 - 0.583423i) q^{94} +(3.03055 - 5.24907i) q^{95} +(-13.9429 - 7.72795i) q^{96} -2.26374 q^{97} +(-19.4126 + 19.4126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 4 q^{4}+O(q^{10}) $ 96 * q + 4 * q^4	$ 96 q + 4 q^{4} + 8 q^{11} + 64 q^{15} - 36 q^{16} - 20 q^{18} - 56 q^{22} - 32 q^{29} - 96 q^{30} - 40 q^{32} + 80 q^{36} + 16 q^{37} + 16 q^{43} - 4 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{53} + 20 q^{58} - 8 q^{60} + 88 q^{64} - 40 q^{67} + 196 q^{72} + 28 q^{74} + 112 q^{78} - 80 q^{79} + 48 q^{81} + 108 q^{86} + 100 q^{88} + 128 q^{95} - 80 q^{99}+O(q^{100}) $ 96 * q + 4 * q^4 + 8 * q^11 + 64 * q^15 - 36 * q^16 - 20 * q^18 - 56 * q^22 - 32 * q^29 - 96 * q^30 - 40 * q^32 + 80 * q^36 + 16 * q^37 + 16 * q^43 - 4 * q^44 - 64 * q^46 - 56 * q^50 - 16 * q^53 + 20 * q^58 - 8 * q^60 + 88 * q^64 - 40 * q^67 + 196 * q^72 + 28 * q^74 + 112 * q^78 - 80 * q^79 + 48 * q^81 + 108 * q^86 + 100 * q^88 + 128 * q^95 - 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.646444	−	1.25782i	−0.457105	−	0.889413i
$2$	−0.646444	−	1.25782i	−0.457105	−	0.889413i
$3$	0.729365	+	2.72203i	0.421099	+	1.57156i	0.772297	+	0.635262i	$0.219108\pi$
$3$	0.729365	+	2.72203i	0.421099	+	1.57156i	−0.351198	+	0.936301i	$0.614225\pi$
$4$	−1.16422	+	1.62622i	−0.582110	+	0.813110i
$5$	0.691444	−	2.58050i	0.309223	−	1.15404i	−0.620026	−	0.784581i	$-0.712878\pi$
$5$	0.691444	−	2.58050i	0.309223	−	1.15404i	0.929249	−	0.369454i	$-0.120455\pi$
$6$	2.95233	−	2.67705i	1.20528	−	1.09290i
$7$		0			0
$7$		0			0
$8$	2.79809	+	0.413120i	0.989276	+	0.146060i
$9$	−4.27938	+	2.47070i	−1.42646	+	0.823568i
$10$	−3.69279	+	0.798439i	−1.16776	+	0.252489i
$11$	5.36650	−	1.43795i	1.61806	−	0.433558i	0.667629	−	0.744494i	$-0.267309\pi$
$11$	5.36650	−	1.43795i	1.61806	−	0.433558i	0.950431	+	0.310936i	$0.100642\pi$
$12$	−5.27576	−	1.98293i	−1.52298	−	0.572423i
$13$	−3.30151	+	3.30151i	−0.915674	+	0.915674i	−0.996711	−	0.0810367i	$-0.974177\pi$
$13$	−3.30151	+	3.30151i	−0.915674	+	0.915674i	0.0810367	+	0.996711i	$0.474177\pi$
$14$		0			0
$15$	7.52851			1.94385
$16$	−1.28918	−	3.78656i	−0.322295	−	0.946639i
$17$	2.63692	−	4.56728i	0.639547	−	1.10773i	−0.345985	−	0.938240i	$-0.612455\pi$
$17$	2.63692	−	4.56728i	0.639547	−	1.10773i	0.985532	−	0.169488i	$-0.0542114\pi$
$18$	5.87408	+	3.78552i	1.38453	+	0.892256i
$19$	2.19147	+	0.587201i	0.502757	+	0.134713i	0.501279	−	0.865286i	$-0.332863\pi$
$19$	2.19147	+	0.587201i	0.502757	+	0.134713i	0.00147756	+	0.999999i	$0.499530\pi$
$20$	3.39147	+	4.12871i	0.758356	+	0.923208i
$21$		0			0
$22$	−5.27782	−	5.82053i	−1.12524	−	1.24094i
$23$	3.73587	−	2.15691i	0.778984	−	0.449746i	−0.0570864	−	0.998369i	$-0.518181\pi$
$23$	3.73587	−	2.15691i	0.778984	−	0.449746i	0.836070	+	0.548623i	$0.184848\pi$
$24$	0.916309	+	7.91781i	0.187041	+	1.61622i
$25$	−1.85077	−	1.06854i	−0.370155	−	0.213709i
$26$	6.28695	+	2.01846i	1.23297	+	0.395853i
$27$	−3.86857	−	3.86857i	−0.744507	−	0.744507i
$28$		0			0
$29$	1.07893	−	1.07893i	0.200353	−	0.200353i	−0.599798	−	0.800151i	$-0.704753\pi$
$29$	1.07893	−	1.07893i	0.200353	−	0.200353i	0.800151	+	0.599798i	$0.204753\pi$
$30$	−4.86676	−	9.46951i	−0.888545	−	1.72889i
$31$	−2.24040	+	3.88049i	−0.402388	+	0.696957i	−0.994014	−	0.109256i	$-0.965153\pi$
$31$	−2.24040	+	3.88049i	−0.402388	+	0.696957i	0.591625	+	0.806213i	$0.298486\pi$
$32$	−3.92942	+	4.06935i	−0.694630	+	0.719367i
$33$	7.82827	+	13.5590i	1.36273	+	2.36031i
$34$	−7.44943	−	0.364280i	−1.27757	−	0.0624735i
$35$		0			0
$36$	0.964240	−	9.83566i	0.160707	−	1.63928i
$37$	−0.143285	+	0.534749i	−0.0235560	+	0.0879121i	−0.976703	−	0.214595i	$-0.931157\pi$
$37$	−0.143285	+	0.534749i	−0.0235560	+	0.0879121i	0.953147	+	0.302507i	$0.0978236\pi$
$38$	−0.678066	−	3.13606i	−0.109997	−	0.508736i
$39$	−11.3948	−	6.57880i	−1.82463	−	1.05345i
$40$	3.00078	−	6.93484i	0.474465	−	1.09649i
$41$			7.35196i			1.14818i	0.818791	+	0.574091i	$0.194645\pi$
$41$			7.35196i			1.14818i	−0.818791	+	0.574091i	$0.805355\pi$
$42$		0			0
$43$	1.67142	+	1.67142i	0.254889	+	0.254889i	0.822972	−	0.568082i	$-0.192314\pi$
$43$	1.67142	+	1.67142i	0.254889	+	0.254889i	−0.568082	+	0.822972i	$0.692314\pi$
$44$	−3.90937	+	10.4012i	−0.589359	+	1.56804i
$45$	3.41670	+	12.7513i	0.509332	+	1.90085i
$46$	−5.12803	−	3.30474i	−0.756087	−	0.487257i
$47$	0.245394	+	0.425035i	0.0357944	+	0.0619978i	0.883368	−	0.468681i	$-0.155271\pi$
$47$	0.245394	+	0.425035i	0.0357944	+	0.0619978i	−0.847573	+	0.530678i	$0.821937\pi$
$48$	9.36683	−	6.27097i	1.35199	−	0.905136i
$49$		0			0
$50$	−0.147615	+	3.01869i	−0.0208759	+	0.426908i
$51$	14.3555	+	3.84655i	2.01018	+	0.538625i
$52$	−1.52530	−	9.21267i	−0.211520	−	1.27757i
$53$	7.90260	−	2.11750i	1.08551	−	0.290860i	0.328656	−	0.944450i	$-0.393404\pi$
$53$	7.90260	−	2.11750i	1.08551	−	0.290860i	0.756849	+	0.653589i	$0.226738\pi$
$54$	−2.36515	+	7.36678i	−0.321856	+	1.00249i
$55$		−	14.8425i		−	2.00137i
$56$		0			0
$57$			6.39351i			0.846842i
$58$	−2.05457	−	0.659634i	−0.269779	−	0.0866142i
$59$	−3.53183	+	0.946351i	−0.459805	+	0.123204i	−0.481284	−	0.876565i	$-0.659829\pi$
$59$	−3.53183	+	0.946351i	−0.459805	+	0.123204i	0.0214786	+	0.999769i	$0.493163\pi$
$60$	−8.76485	+	12.2430i	−1.13154	+	1.58057i
$61$	7.30218	+	1.95661i	0.934949	+	0.250519i	0.693964	−	0.720010i	$-0.255863\pi$
$61$	7.30218	+	1.95661i	0.934949	+	0.250519i	0.240985	+	0.970529i	$0.422530\pi$
$62$	6.32925	+	0.309503i	0.803816	+	0.0393069i
$63$		0			0
$64$	7.65866	+	2.31190i	0.957333	+	0.288987i
$65$	6.23675	+	10.8024i	0.773574	+	1.33987i
$66$	11.9942	−	18.6117i	1.47638	−	2.29094i
$67$	3.33541	+	12.4479i	0.407485	+	1.52076i	0.799425	+	0.600766i	$0.205137\pi$
$67$	3.33541	+	12.4479i	0.407485	+	1.52076i	−0.391940	+	0.919991i	$0.628196\pi$
$68$	4.35744	+	9.60553i	0.528418	+	1.16484i
$69$	8.59598	+	8.59598i	1.03483	+	1.03483i
$70$		0			0
$71$		−	16.2570i		−	1.92935i	−0.263442	−	0.964675i	$-0.584858\pi$
$71$		−	16.2570i		−	1.92935i	0.263442	−	0.964675i	$-0.415142\pi$
$72$	−12.9948	+	5.14536i	−1.53145	+	0.606387i
$73$	6.89278	+	3.97955i	0.806739	+	0.465771i	0.845822	−	0.533465i	$-0.179110\pi$
$73$	6.89278	+	3.97955i	0.806739	+	0.465771i	−0.0390832	+	0.999236i	$0.512444\pi$
$74$	0.765243	−	0.165458i	0.0889577	−	0.0192341i
$75$	1.55872	−	5.81721i	0.179985	−	0.671714i
$76$	−3.50627	+	2.88017i	−0.402196	+	0.330378i
$77$		0			0
$78$	−0.908834	+	18.5854i	−0.102905	+	2.10439i
$79$	−1.10561	−	1.91497i	−0.124390	−	0.215451i	0.797104	−	0.603842i	$-0.206364\pi$
$79$	−1.10561	−	1.91497i	−0.124390	−	0.215451i	−0.921494	+	0.388391i	$0.873031\pi$
$80$	−10.6626	+	0.708545i	−1.19212	+	0.0792177i
$81$	0.296643	−	0.513800i	0.0329603	−	0.0570889i
$82$	9.24743	−	4.75263i	1.02121	−	0.524840i
$83$	3.81693	−	3.81693i	0.418963	−	0.418963i	−0.465883	−	0.884846i	$-0.654263\pi$
$83$	3.81693	−	3.81693i	0.418963	−	0.418963i	0.884846	+	0.465883i	$0.154263\pi$
$84$		0			0
$85$	−9.96259	−	9.96259i	−1.08060	−	1.08060i
$86$	1.02187	−	3.18283i	0.110191	−	0.343213i
$87$	3.72382	+	2.14995i	0.399236	+	0.230499i
$88$	15.6100	−	1.80651i	1.66403	−	0.192575i
$89$	−9.66675	+	5.58110i	−1.02467	+	0.591596i	−0.915454	−	0.402422i	$-0.868168\pi$
$89$	−9.66675	+	5.58110i	−1.02467	+	0.591596i	−0.109219	+	0.994018i	$0.534835\pi$
$90$	13.8301	−	12.5406i	1.45783	−	1.32190i
$91$		0			0
$92$	−0.841775	+	8.58647i	−0.0877611	+	0.895201i
$93$	−12.1969	−	3.26814i	−1.26476	−	0.338891i
$94$	0.375984	−	0.583423i	0.0387798	−	0.0601755i
$95$	3.03055	−	5.24907i	0.310928	−	0.538543i
$96$	−13.9429	−	7.72795i	−1.42304	−	0.788731i
$97$	−2.26374			−0.229848			−0.114924	−	0.993374i	$-0.536662\pi$
$97$	−2.26374			−0.229848			−0.114924	+	0.993374i	$0.536662\pi$
$98$		0			0
$99$	−19.4126	+	19.4126i	−1.95104	+	1.95104i
$100$	3.89240	−	1.76574i	0.389240	−	0.176574i
$101$	−12.2544	+	3.28356i	−1.21936	+	0.326727i	−0.810428	−	0.585838i	$-0.800765\pi$
$101$	−12.2544	+	3.28356i	−1.21936	+	0.326727i	−0.408932	+	0.912565i	$0.634099\pi$
$102$	−4.44178	−	20.5433i	−0.439802	−	2.03409i
$103$	−3.23781	+	1.86935i	−0.319031	+	0.184193i	−0.650961	−	0.759112i	$-0.725634\pi$
$103$	−3.23781	+	1.86935i	−0.319031	+	0.184193i	0.331930	+	0.943304i	$0.392300\pi$
$104$	−10.6019	+	7.87402i	−1.03960	+	0.772111i
$105$		0			0
$106$	−7.77201	−	8.57120i	−0.754885	−	0.832509i
$107$	2.13890	−	7.98249i	0.206775	−	0.771697i	−0.782126	−	0.623121i	$-0.785864\pi$
$107$	2.13890	−	7.98249i	0.206775	−	0.771697i	0.988901	−	0.148576i	$-0.0474689\pi$
$108$	10.7950	−	1.78728i	1.03875	−	0.171981i
$109$	−3.54589	−	13.2335i	−0.339635	−	1.26753i	−0.898756	−	0.438449i	$-0.855528\pi$
$109$	−3.54589	−	13.2335i	−0.339635	−	1.26753i	0.559121	−	0.829086i	$-0.311139\pi$
$110$	−18.6692	+	9.59486i	−1.78004	+	0.914834i
$111$	−1.56011			−0.148079
$112$		0			0
$113$	−8.11093			−0.763012			−0.381506	−	0.924366i	$-0.624594\pi$
$113$	−8.11093			−0.763012			−0.381506	+	0.924366i	$0.624594\pi$
$114$	8.04189	−	4.13305i	0.753192	−	0.387095i
$115$	−2.98276	−	11.1318i	−0.278144	−	1.03805i
$116$	0.498467	+	3.01070i	0.0462815	+	0.279537i
$117$	5.97138	−	22.2855i	0.552054	−	2.06029i
$118$	3.47347	+	3.83064i	0.319759	+	0.352639i
$119$		0			0
$120$	21.0655	+	3.11018i	1.92301	+	0.283919i
$121$	17.2053	−	9.93351i	1.56412	−	0.903046i
$122$	−2.25938	−	10.4497i	−0.204555	−	0.946068i
$123$	−20.0122	+	5.36226i	−1.80444	+	0.483499i
$124$	−3.70221	−	8.16113i	−0.332468	−	0.732892i
$125$	5.40821	−	5.40821i	0.483725	−	0.483725i
$126$		0			0
$127$	−0.238096			−0.0211276			−0.0105638	−	0.999944i	$-0.503363\pi$
$127$	−0.238096			−0.0211276			−0.0105638	+	0.999944i	$0.503363\pi$
$128$	−2.04295	−	11.1277i	−0.180573	−	0.983562i
$129$	−3.33058	+	5.76873i	−0.293241	+	0.507909i
$130$	9.55572	−	14.8278i	0.838092	−	1.30049i
$131$	−0.624805	−	0.167416i	−0.0545895	−	0.0146272i	0.231421	−	0.972854i	$-0.425663\pi$
$131$	−0.624805	−	0.167416i	−0.0545895	−	0.0146272i	−0.286010	+	0.958227i	$0.592329\pi$
$132$	−31.1637	−	3.05514i	−2.71245	−	0.265915i
$133$		0			0
$134$	13.5011	−	12.2422i	1.16632	−	1.05757i
$135$	−12.6578	+	7.30796i	−1.08941	+	0.628969i
$136$	9.26518	−	11.6903i	0.794483	−	1.00244i
$137$	3.51539	+	2.02961i	0.300340	+	0.173402i	0.642596	−	0.766205i	$-0.277857\pi$
$137$	3.51539	+	2.02961i	0.300340	+	0.173402i	−0.342255	+	0.939607i	$0.611191\pi$
$138$	5.25537	−	16.3690i	0.447367	−	1.39342i
$139$	−6.00840	−	6.00840i	−0.509626	−	0.509626i	0.404786	−	0.914411i	$-0.367346\pi$
$139$	−6.00840	−	6.00840i	−0.509626	−	0.509626i	−0.914411	+	0.404786i	$0.867346\pi$
$140$		0			0
$141$	−0.977976	+	0.977976i	−0.0823604	+	0.0823604i
$142$	−20.4484	+	10.5092i	−1.71599	+	0.881916i
$143$	−12.9702	+	22.4650i	−1.08462	+	1.87861i
$144$	14.8724	+	13.0189i	1.23936	+	1.08491i
$145$	−2.03817	−	3.53021i	−0.169261	−	0.293168i
$146$	0.549758	−	11.2424i	0.0454983	−	0.930430i
$147$		0			0
$148$	−0.702803	−	0.855579i	−0.0577700	−	0.0703281i
$149$	−0.773337	+	2.88613i	−0.0633542	+	0.236441i	−0.990341	−	0.138653i	$-0.955723\pi$
$149$	−0.773337	+	2.88613i	−0.0633542	+	0.236441i	0.926987	+	0.375094i	$0.122390\pi$
$150$	−8.32463	+	1.79992i	−0.679703	+	0.146963i
$151$	−13.1296	−	7.58036i	−1.06847	−	0.616881i	−0.140706	−	0.990051i	$-0.544937\pi$
$151$	−13.1296	−	7.58036i	−1.06847	−	0.616881i	−0.927763	+	0.373171i	$0.878271\pi$
$152$	5.88934	+	2.54838i	0.477689	+	0.206701i
$153$			26.0602i			2.10684i
$154$		0			0
$155$	8.46451	+	8.46451i	0.679885	+	0.679885i
$156$	23.9646	−	10.8713i	1.91871	−	0.870400i
$157$	−2.72507	−	10.1701i	−0.217484	−	0.811661i	−0.985277	−	0.170964i	$-0.945312\pi$
$157$	−2.72507	−	10.1701i	−0.217484	−	0.811661i	0.767793	−	0.640697i	$-0.221355\pi$
$158$	−1.69397	+	2.62857i	−0.134765	+	0.209118i
$159$	11.5278	+	19.9667i	0.914211	+	1.58346i
$160$	7.78401	+	12.9536i	0.615380	+	1.02407i
$161$		0			0
$162$	−0.838030	−	0.0409800i	−0.0658419	−	0.00321969i
$163$	6.46324	+	1.73182i	0.506240	+	0.135647i	0.502894	−	0.864348i	$-0.332268\pi$
$163$	6.46324	+	1.73182i	0.506240	+	0.135647i	0.00334537	+	0.999994i	$0.498935\pi$
$164$	−11.9559	−	8.55930i	−0.933599	−	0.668369i
$165$	40.4018	−	10.8256i	3.14527	−	0.842773i
$166$	−7.26844	−	2.33358i	−0.564141	−	0.181121i
$167$			13.8640i			1.07283i	0.843955	+	0.536414i	$0.180221\pi$
$167$			13.8640i			1.07283i	−0.843955	+	0.536414i	$0.819779\pi$
$168$		0			0
$169$		−	8.79995i		−	0.676919i
$170$	−6.09089	+	18.9714i	−0.467150	+	1.45504i
$171$	−10.8289	+	2.90160i	−0.828108	+	0.221891i
$172$	−4.66400	+	0.772196i	−0.355627	+	0.0588794i
$173$	−23.2018	−	6.21690i	−1.76400	−	0.472662i	−0.776477	−	0.630145i	$-0.782995\pi$
$173$	−23.2018	−	6.21690i	−1.76400	−	0.472662i	−0.987522	+	0.157483i	$0.949662\pi$
$174$	0.297007	−	6.07372i	0.0225160	−	0.460448i
$175$		0			0
$176$	−12.3633	−	18.4668i	−0.931916	−	1.39199i
$177$	−5.15199	−	8.92350i	−0.387247	−	0.670732i
$178$	13.2690	+	8.55116i	0.994556	+	0.640937i
$179$	−4.96759	−	18.5393i	−0.371295	−	1.38569i	−0.858683	−	0.512506i	$-0.828717\pi$
$179$	−4.96759	−	18.5393i	−0.371295	−	1.38569i	0.487389	−	0.873185i	$-0.337950\pi$
$180$	−24.7142	−	9.28903i	−1.84209	−	0.692363i
$181$	−4.76859	−	4.76859i	−0.354446	−	0.354446i	0.507315	−	0.861761i	$-0.330638\pi$
$181$	−4.76859	−	4.76859i	−0.354446	−	0.354446i	−0.861761	+	0.507315i	$0.830638\pi$
$182$		0			0
$183$			21.3038i			1.57482i
$184$	11.3444	−	4.49187i	0.836319	−	0.331145i
$185$	1.28085	+	0.739497i	0.0941697	+	0.0543689i
$186$	3.77386	+	17.4541i	0.276713	+	1.27980i
$187$	7.58351	−	28.3021i	0.554561	−	2.06965i
$188$	−0.976894	−	0.0957699i	−0.0712473	−	0.00698473i
$189$		0			0
$190$	−8.56146	−	0.418658i	−0.621113	−	0.0303726i
$191$	−1.71906	−	2.97750i	−0.124387	−	0.215444i	0.797106	−	0.603839i	$-0.206363\pi$
$191$	−1.71906	−	2.97750i	−0.124387	−	0.215444i	−0.921493	+	0.388395i	$0.873030\pi$
$192$	−0.707080	+	22.5333i	−0.0510291	+	1.62620i
$193$	−11.0060	+	19.0629i	−0.792227	+	1.37218i	0.132358	+	0.991202i	$0.457745\pi$
$193$	−11.0060	+	19.0629i	−0.792227	+	1.37218i	−0.924585	+	0.380976i	$0.875588\pi$
$194$	1.46338	+	2.84737i	0.105065	+	0.204430i
$195$	−24.8555	+	24.8555i	−1.77994	+	1.77994i
$196$		0			0
$197$	−6.02579	−	6.02579i	−0.429320	−	0.429320i	0.459077	−	0.888397i	$-0.348180\pi$
$197$	−6.02579	−	6.02579i	−0.429320	−	0.429320i	−0.888397	+	0.459077i	$0.848180\pi$
$198$	36.9666	+	11.8684i	2.62710	+	0.843448i
$199$	2.94240	+	1.69879i	0.208581	+	0.120424i	0.600652	−	0.799511i	$-0.294908\pi$
$199$	2.94240	+	1.69879i	0.208581	+	0.120424i	−0.392071	+	0.919935i	$0.628241\pi$
$200$	−4.73720	−	3.75448i	−0.334971	−	0.265482i
$201$	−31.4509	+	18.1582i	−2.21837	+	1.28078i
$202$	12.0519	+	13.2912i	0.847971	+	0.935167i
$203$		0			0
$204$	−22.9684	+	18.8670i	−1.60811	+	1.32096i
$205$	18.9717	+	5.08346i	1.32504	+	0.355044i
$206$	4.44437	+	2.86415i	0.309654	+	0.199555i
$207$	−10.6582	+	18.4605i	−0.740793	+	1.28309i
$208$	16.7576	+	8.24511i	1.16193	+	0.571696i
$209$	12.6049			0.871897
$210$		0			0
$211$	−3.23499	+	3.23499i	−0.222706	+	0.222706i	−0.809637	−	0.586931i	$-0.800336\pi$
$211$	−3.23499	+	3.23499i	−0.222706	+	0.222706i	0.586931	+	0.809637i	$0.300336\pi$
$212$	−5.75686	+	15.3166i	−0.395382	+	1.05195i
$213$	44.2520	−	11.8573i	3.03210	−	0.812448i
$214$	−11.4232	+	2.46988i	−0.780875	+	0.168838i
$215$	5.46880	−	3.15742i	0.372969	−	0.215334i
$216$	−9.22644	−	12.4228i	−0.627780	−	0.845265i
$217$		0			0
$218$	−14.3531	+	13.0148i	−0.972113	+	0.881472i
$219$	−5.80509	+	21.6649i	−0.392271	+	1.46398i
$220$	24.1372	+	17.2800i	1.62733	+	1.16502i
$221$	6.37310	+	23.7847i	0.428701	+	1.59993i
$222$	1.00852	+	1.96233i	0.0676876	+	0.131703i
$223$	0.464368			0.0310964			0.0155482	−	0.999879i	$-0.495051\pi$
$223$	0.464368			0.0310964			0.0155482	+	0.999879i	$0.495051\pi$
$224$		0			0
$225$	10.5602			0.704015
$226$	5.24326	+	10.2021i	0.348777	+	0.678633i
$227$	−5.02951	−	18.7704i	−0.333821	−	1.24584i	−0.905142	−	0.425109i	$-0.860236\pi$
$227$	−5.02951	−	18.7704i	−0.333821	−	1.24584i	0.571322	−	0.820726i	$-0.306431\pi$
$228$	−10.3973	−	7.44346i	−0.688575	−	0.492955i
$229$	0.288531	−	1.07681i	0.0190667	−	0.0711578i	−0.955737	−	0.294222i	$-0.904939\pi$
$229$	0.288531	−	1.07681i	0.0190667	−	0.0711578i	0.974804	+	0.223065i	$0.0716061\pi$
$230$	−12.0736	+	10.9479i	−0.796111	+	0.721881i
$231$		0			0
$232$	3.46469	−	2.57323i	0.227468	−	0.168941i
$233$	−9.11534	+	5.26274i	−0.597166	+	0.344774i	−0.767926	−	0.640539i	$-0.778711\pi$
$233$	−9.11534	+	5.26274i	−0.597166	+	0.344774i	0.170760	+	0.985313i	$0.445378\pi$
$234$	−31.8913	+	6.89540i	−2.08480	+	0.450767i
$235$	1.26648	−	0.339353i	0.0826161	−	0.0221369i
$236$	2.57285	−	6.84529i	0.167479	−	0.445591i
$237$	4.40620	−	4.40620i	0.286213	−	0.286213i
$238$		0			0
$239$	22.0909			1.42894			0.714469	−	0.699667i	$-0.246668\pi$
$239$	22.0909			1.42894			0.714469	+	0.699667i	$0.246668\pi$
$240$	−9.70562	−	28.5071i	−0.626495	−	1.84013i
$241$	1.74230	−	3.01775i	0.112231	−	0.194391i	−0.804438	−	0.594036i	$-0.797534\pi$
$241$	1.74230	−	3.01775i	0.112231	−	0.194391i	0.916670	+	0.399646i	$0.130867\pi$
$242$	−23.6168	−	15.2198i	−1.51815	−	0.978363i
$243$	−14.2388	−	3.81526i	−0.913417	−	0.244749i
$244$	−11.6832	+	9.59702i	−0.747942	+	0.614386i
$245$		0			0
$246$	19.6815	+	21.7054i	1.25485	+	1.38388i
$247$	−9.17380	+	5.29650i	−0.583715	+	0.337008i
$248$	−7.87197	+	9.93243i	−0.499870	+	0.630710i
$249$	13.1737	+	7.60586i	0.834851	+	0.482002i
$250$	−10.2987	−	3.30645i	−0.651344	−	0.209118i
$251$	−19.4610	−	19.4610i	−1.22837	−	1.22837i	−0.964582	−	0.263784i	$-0.915029\pi$
$251$	−19.4610	−	19.4610i	−1.22837	−	1.22837i	−0.263784	−	0.964582i	$-0.584971\pi$
$252$		0			0
$253$	16.9470	−	16.9470i	1.06545	−	1.06545i
$254$	0.153916	+	0.299482i	0.00965753	+	0.0187912i
$255$	19.8521	−	34.3848i	1.24319	−	2.15326i
$256$	−12.6760	+	9.76312i	−0.792251	+	0.610195i
$257$	10.9786	+	19.0155i	0.684827	+	1.18615i	0.973491	+	0.228724i	$0.0734555\pi$
$257$	10.9786	+	19.0155i	0.684827	+	1.18615i	−0.288664	+	0.957430i	$0.593211\pi$
$258$	9.40906	+	0.460106i	0.585783	+	0.0286450i
$259$		0			0
$260$	−24.8280	−	2.43401i	−1.53977	−	0.150951i
$261$	−1.95145	+	7.28290i	−0.120792	+	0.450800i
$262$	0.193322	+	0.894118i	0.0119435	+	0.0552388i
$263$	13.6351	+	7.87225i	0.840779	+	0.485424i	0.857529	−	0.514436i	$-0.171999\pi$
$263$	13.6351	+	7.87225i	0.840779	+	0.485424i	−0.0167499	+	0.999860i	$0.505332\pi$
$264$	16.3028	+	41.1733i	1.00337	+	2.53404i
$265$		−	21.8568i		−	1.34265i
$266$		0			0
$267$	−22.2425	−	22.2425i	−1.36122	−	1.36122i
$268$	−24.1262	−	9.06802i	−1.47374	−	0.553917i
$269$	0.435915	+	1.62686i	0.0265782	+	0.0991913i	0.977941	−	0.208882i	$-0.0669825\pi$
$269$	0.435915	+	1.62686i	0.0265782	+	0.0991913i	−0.951363	+	0.308073i	$0.900316\pi$
$270$	17.3746	+	11.1970i	1.05739	+	0.681427i
$271$	−6.14352	−	10.6409i	−0.373192	−	0.646388i	0.616863	−	0.787071i	$-0.288403\pi$
$271$	−6.14352	−	10.6409i	−0.373192	−	0.646388i	−0.990055	+	0.140683i	$0.955070\pi$
$272$	−20.6937	−	4.09680i	−1.25474	−	0.248405i
$273$		0			0
$274$	0.280383	−	5.73376i	0.0169385	−	0.346389i
$275$	−11.4687	−	3.07302i	−0.691588	−	0.185310i
$276$	−23.9866	+	3.97134i	−1.44382	+	0.239046i
$277$	−29.8378	+	7.99501i	−1.79278	+	0.480374i	−0.992813	−	0.119673i	$-0.961815\pi$
$277$	−29.8378	+	7.99501i	−1.79278	+	0.480374i	−0.799965	+	0.600046i	$0.795149\pi$
$278$	−3.67339	+	11.4416i	−0.220315	+	0.686220i
$279$		−	22.1415i		−	1.32558i
$280$		0			0
$281$			21.3934i			1.27622i	0.769944	+	0.638111i	$0.220284\pi$
$281$			21.3934i			1.27622i	−0.769944	+	0.638111i	$0.779716\pi$
$282$	1.86232	+	0.597911i	0.110900	+	0.0356051i
$283$	14.4807	−	3.88010i	0.860790	−	0.230648i	0.198689	−	0.980063i	$-0.436332\pi$
$283$	14.4807	−	3.88010i	0.860790	−	0.230648i	0.662101	+	0.749415i	$0.269665\pi$
$284$	26.4374	+	18.9267i	1.56877	+	1.12309i
$285$	16.4985	+	4.42075i	0.977285	+	0.261863i
$286$	36.6413	+	1.79177i	2.16665	+	0.105950i
$287$		0			0
$288$	6.76134	−	27.1228i	0.398416	−	1.59822i
$289$	−5.40669	−	9.36467i	−0.318041	−	0.550863i
$290$	−3.12281	+	4.84574i	−0.183378	+	0.284551i
$291$	−1.65109	−	6.16196i	−0.0967887	−	0.361220i
$292$	−14.4963	+	6.57610i	−0.848334	+	0.384837i
$293$	−21.0093	−	21.0093i	−1.22738	−	1.22738i	−0.964952	−	0.262428i	$-0.915477\pi$
$293$	−21.0093	−	21.0093i	−1.22738	−	1.22738i	−0.262428	−	0.964952i	$-0.584523\pi$
$294$		0			0
$295$			9.76825i			0.568729i
$296$	−0.621841	+	1.43708i	−0.0361438	+	0.0835287i
$297$	−26.3235	−	15.1979i	−1.52744	−	0.881870i
$298$	4.13015	−	0.893005i	0.239253	−	0.0517304i
$299$	−5.21297	+	19.4551i	−0.301474	+	1.12512i
$300$	7.64538	+	9.30734i	0.441406	+	0.537359i
$301$		0			0
$302$	−1.04720	+	21.4149i	−0.0602593	+	1.23229i
$303$	−17.8759	−	30.9620i	−1.02694	−	1.77872i
$304$	−0.601725	−	9.05512i	−0.0345113	−	0.519347i
$305$	10.0981	−	17.4904i	0.578215	−	1.00150i
$306$	32.7790	−	16.8465i	1.87385	−	0.963048i
$307$	0.818174	−	0.818174i	0.0466957	−	0.0466957i	−0.683373	−	0.730069i	$-0.739488\pi$
$307$	0.818174	−	0.818174i	0.0466957	−	0.0466957i	0.730069	+	0.683373i	$0.239488\pi$
$308$		0			0
$309$	−7.44997	−	7.44997i	−0.423814	−	0.423814i
$310$	5.17499	−	16.1187i	0.293920	−	0.915478i
$311$	−6.81671	−	3.93563i	−0.386540	−	0.223169i	0.294120	−	0.955769i	$-0.404974\pi$
$311$	−6.81671	−	3.93563i	−0.386540	−	0.223169i	−0.680660	+	0.732599i	$0.738307\pi$
$312$	−29.1659	−	23.1155i	−1.65120	−	1.30866i
$313$	4.43539	−	2.56077i	0.250703	−	0.144743i	−0.369383	−	0.929277i	$-0.620431\pi$
$313$	4.43539	−	2.56077i	0.250703	−	0.144743i	0.620086	+	0.784534i	$0.287098\pi$
$314$	−11.0305	+	10.0020i	−0.622489	+	0.564447i
$315$		0			0
$316$	4.40132	+	0.431484i	0.247594	+	0.0242729i
$317$	18.0167	+	4.82757i	1.01192	+	0.271144i	0.726432	−	0.687238i	$-0.241177\pi$
$317$	18.0167	+	4.82757i	1.01192	+	0.271144i	0.285489	+	0.958382i	$0.407844\pi$
$318$	17.6624	−	27.4072i	0.990459	−	1.53692i
$319$	4.23865	−	7.34155i	0.237319	−	0.411048i
$320$	11.2614	−	18.1647i	0.629531	−	1.01544i
$321$	23.2886			1.29984
$322$		0			0
$323$	8.46063	−	8.46063i	0.470762	−	0.470762i
$324$	0.490194	+	1.08058i	0.0272330	+	0.0600323i
$325$	9.63816	−	2.58254i	0.534629	−	0.143253i
$326$	−1.99980	−	9.24911i	−0.110759	−	0.512261i
$327$	33.4356	−	19.3040i	1.84899	−	1.06752i
$328$	−3.03724	+	20.5715i	−0.167703	+	1.13587i
$329$		0			0
$330$	−39.7342	−	43.8200i	−2.18729	−	2.41221i
$331$	3.37401	−	12.5920i	0.185453	−	0.692118i	−0.809081	−	0.587698i	$-0.800034\pi$
$331$	3.37401	−	12.5920i	0.185453	−	0.692118i	0.994533	−	0.104421i	$-0.0332989\pi$
$332$	1.76342	+	10.6509i	0.0967802	+	0.584545i
$333$	−0.708032	−	2.64241i	−0.0387999	−	0.144803i
$334$	17.4384	−	8.96229i	0.954186	−	0.490395i
$335$	34.4282			1.88101
$336$		0			0
$337$	13.5463			0.737913			0.368956	−	0.929447i	$-0.379715\pi$
$337$	13.5463			0.737913			0.368956	+	0.929447i	$0.379715\pi$
$338$	−11.0687	+	5.68867i	−0.602061	+	0.309423i
$339$	−5.91583	−	22.0782i	−0.321304	−	1.19912i
$340$	27.8000	−	4.60271i	1.50767	−	0.249617i
$341$	−6.44317	+	24.0462i	−0.348917	+	1.30218i
$342$	10.6500	+	11.7451i	0.575885	+	0.635103i
$343$		0			0
$344$	3.98630	+	5.36729i	0.214927	+	0.289385i
$345$	28.1256	−	16.2383i	1.51423	−	0.874241i
$346$	7.17891	+	33.2025i	0.385941	+	1.78498i
$347$	24.5626	−	6.58152i	1.31859	−	0.353314i	0.470139	−	0.882592i	$-0.344204\pi$
$347$	24.5626	−	6.58152i	1.31859	−	0.353314i	0.848448	+	0.529278i	$0.177537\pi$
$348$	−7.83165	+	3.55274i	−0.419820	+	0.190447i
$349$	−3.17376	+	3.17376i	−0.169887	+	0.169887i	−0.786930	−	0.617043i	$-0.788331\pi$
$349$	−3.17376	+	3.17376i	−0.169887	+	0.169887i	0.617043	+	0.786930i	$0.288331\pi$
$350$		0			0
$351$	25.5443			1.36345
$352$	−15.2357	+	27.4885i	−0.812066	+	1.46514i
$353$	3.29923	−	5.71444i	0.175600	−	0.304149i	−0.764769	−	0.644305i	$-0.777147\pi$
$353$	3.29923	−	5.71444i	0.175600	−	0.304149i	0.940369	+	0.340156i	$0.110480\pi$
$354$	−7.89369	+	12.2488i	−0.419545	+	0.651017i
$355$	−41.9512	−	11.2408i	−2.22654	−	0.596600i
$356$	2.17813	−	22.2179i	0.115441	−	1.17755i
$357$		0			0
$358$	−20.1078	+	18.2329i	−1.06273	+	0.963641i
$359$	−7.68624	+	4.43765i	−0.405664	+	0.234210i	−0.688925	−	0.724833i	$-0.741917\pi$
$359$	−7.68624	+	4.43765i	−0.405664	+	0.234210i	0.283261	+	0.959043i	$0.408584\pi$
$360$	4.29244	+	37.0909i	0.226232	+	1.95486i
$361$	−11.9968	−	6.92634i	−0.631409	−	0.364544i
$362$	−2.91540	+	9.08064i	−0.153230	+	0.477268i
$363$	39.5882	+	39.5882i	2.07784	+	2.07784i
$364$		0			0
$365$	15.0352	−	15.0352i	0.786979	−	0.786979i
$366$	26.7964	−	13.7717i	1.40067	−	0.719860i
$367$	−13.7984	+	23.8996i	−0.720273	+	1.24755i	0.240618	+	0.970620i	$0.422650\pi$
$367$	−13.7984	+	23.8996i	−0.720273	+	1.24755i	−0.960890	+	0.276929i	$0.910683\pi$
$368$	−12.9835	−	11.3655i	−0.676810	−	0.592465i
$369$	−18.1645	−	31.4618i	−0.945606	−	1.63784i
$370$	0.102158	−	2.08912i	0.00531097	−	0.108608i
$371$		0			0
$372$	19.5146	−	16.0300i	1.01178	−	0.831115i
$373$	−7.05779	+	26.3400i	−0.365439	+	1.36384i	0.501387	+	0.865223i	$0.332823\pi$
$373$	−7.05779	+	26.3400i	−0.365439	+	1.36384i	−0.866825	+	0.498612i	$0.833843\pi$
$374$	−40.5012	+	8.75700i	−2.09427	+	0.452814i
$375$	18.6659	+	10.7767i	0.963901	+	0.556508i
$376$	0.511046	+	1.29067i	0.0263552	+	0.0665610i
$377$			7.12422i			0.366916i
$378$		0			0
$379$	16.2102	+	16.2102i	0.832663	+	0.832663i	0.987880	−	0.155218i	$-0.0496079\pi$
$379$	16.2102	+	16.2102i	0.832663	+	0.832663i	−0.155218	+	0.987880i	$0.549608\pi$
$380$	5.00791	+	11.0394i	0.256900	+	0.566310i
$381$	−0.173659	−	0.648103i	−0.00889681	−	0.0332033i
$382$	−2.63388	+	4.08706i	−0.134761	+	0.209112i
$383$	0.993740	+	1.72121i	0.0507778	+	0.0879496i	0.890297	−	0.455380i	$-0.150497\pi$
$383$	0.993740	+	1.72121i	0.0507778	+	0.0879496i	−0.839519	+	0.543330i	$0.817163\pi$
$384$	28.7999	−	13.6771i	1.46969	−	0.697959i
$385$		0			0
$386$	31.0924	+	1.52043i	1.58256	+	0.0773879i
$387$	−11.2822	−	3.02307i	−0.573509	−	0.153671i
$388$	2.63549	−	3.68134i	0.133797	−	0.186892i
$389$	−19.8389	+	5.31582i	−1.00587	+	0.269523i	−0.723904	−	0.689901i	$-0.757654\pi$
$389$	−19.8389	+	5.31582i	−1.00587	+	0.269523i	−0.281969	+	0.959424i	$0.590988\pi$
$390$	47.3314	+	15.1960i	2.39672	+	0.769481i
$391$		−	22.7504i		−	1.15054i
$392$		0			0
$393$		−	1.82285i		−	0.0919504i
$394$	−3.68402	+	11.4747i	−0.185598	+	0.578087i
$395$	−5.70604	+	1.52893i	−0.287102	+	0.0769287i
$396$	−8.96859	−	54.1696i	−0.450689	−	2.72213i
$397$	32.5487	+	8.72141i	1.63357	+	0.437715i	0.954949	−	0.296770i	$-0.0959094\pi$
$397$	32.5487	+	8.72141i	1.63357	+	0.437715i	0.678625	+	0.734485i	$0.262576\pi$
$398$	0.234681	−	4.79918i	0.0117635	−	0.240561i
$399$		0			0
$400$	−1.66012	+	8.38560i	−0.0830061	+	0.419280i
$401$	−11.5351	−	19.9794i	−0.576037	−	0.997726i	−0.995928	−	0.0901513i	$-0.971265\pi$
$401$	−11.5351	−	19.9794i	−0.576037	−	0.997726i	0.419891	−	0.907575i	$-0.362068\pi$
$402$	43.1709	+	27.8213i	2.15317	+	1.38760i
$403$	−5.41477	−	20.2082i	−0.269729	−	1.00664i
$404$	8.92706	−	23.7512i	0.444138	−	1.18167i
$405$	−1.12075	−	1.12075i	−0.0556905	−	0.0556905i
$406$		0			0
$407$			3.07576i			0.152460i
$408$	38.5791	+	16.6936i	1.90995	+	0.826455i
$409$	−21.6470	−	12.4979i	−1.07038	−	0.617982i	−0.142092	−	0.989853i	$-0.545383\pi$
$409$	−21.6470	−	12.4979i	−1.07038	−	0.617982i	−0.928284	+	0.371872i	$0.878716\pi$
$410$	−5.87009	−	27.1492i	−0.289903	−	1.34080i
$411$	−2.96066	+	11.0493i	−0.146038	+	0.545023i
$412$	0.729550	−	7.44173i	0.0359424	−	0.366628i
$413$		0			0
$414$	30.1099	+	1.47238i	1.47982	+	0.0723636i
$415$	−7.21041	−	12.4888i	−0.353945	−	0.613051i
$416$	−0.461987	−	26.4080i	−0.0226508	−	1.29476i
$417$	11.9727	−	20.7373i	0.586306	−	1.01551i
$418$	−8.14834	−	15.8546i	−0.398548	−	0.775476i
$419$	11.0926	−	11.0926i	0.541911	−	0.541911i	−0.382178	−	0.924089i	$-0.624826\pi$
$419$	11.0926	−	11.0926i	0.541911	−	0.541911i	0.924089	+	0.382178i	$0.124826\pi$
$420$		0			0
$421$	0.513978	+	0.513978i	0.0250497	+	0.0250497i	0.719521	−	0.694471i	$-0.244362\pi$
$421$	0.513978	+	0.513978i	0.0250497	+	0.0250497i	−0.694471	+	0.719521i	$0.744362\pi$
$422$	6.16028	+	1.97779i	0.299878	+	0.0962776i
$423$	−2.10027	−	1.21259i	−0.102119	−	0.0589583i
$424$	22.9870	−	2.66023i	1.11635	−	0.129192i
$425$	−9.76068	+	5.63533i	−0.473463	+	0.273354i
$426$	−43.5208	−	47.9960i	−2.10859	−	2.32541i
$427$		0			0
$428$	10.4911	+	12.7717i	0.507108	+	0.617344i
$429$	−70.6102	−	18.9200i	−3.40909	−	0.913464i
$430$	−7.50673	−	4.83768i	−0.362007	−	0.233293i
$431$	−15.8660	+	27.4807i	−0.764238	+	1.32370i	0.176410	+	0.984317i	$0.443552\pi$
$431$	−15.8660	+	27.4807i	−0.764238	+	1.32370i	−0.940648	+	0.339383i	$0.889782\pi$
$432$	−9.66127	+	19.6358i	−0.464828	+	0.944730i
$433$	18.4117			0.884808			0.442404	−	0.896816i	$-0.354126\pi$
$433$	18.4117			0.884808			0.442404	+	0.896816i	$0.354126\pi$
$434$		0			0
$435$	8.12277	−	8.12277i	0.389457	−	0.389457i
$436$	25.6487	+	9.64025i	1.22835	+	0.461684i
$437$	9.45358	−	2.53308i	0.452226	−	0.121174i
$438$	31.0032	−	6.70338i	1.48139	−	0.320300i
$439$	7.67855	−	4.43321i	0.366477	−	0.211586i	−0.305441	−	0.952211i	$-0.598804\pi$
$439$	7.67855	−	4.43321i	0.366477	−	0.211586i	0.671918	+	0.740625i	$0.265471\pi$
$440$	6.13174	−	41.5308i	0.292319	−	1.97990i
$441$		0			0
$442$	25.7971	−	23.3917i	1.22704	−	1.11263i
$443$	−1.91253	+	7.13765i	−0.0908669	+	0.339120i	−0.996360	−	0.0852402i	$-0.972834\pi$
$443$	−1.91253	+	7.13765i	−0.0908669	+	0.339120i	0.905494	+	0.424360i	$0.139501\pi$
$444$	1.81631	−	2.53708i	0.0861982	−	0.120404i
$445$	7.71803	+	28.8041i	0.365870	+	1.36545i
$446$	−0.300188	−	0.584091i	−0.0142143	−	0.0276575i
$447$	−8.42018			−0.398261
$448$		0			0
$449$	−36.5402			−1.72444			−0.862218	−	0.506537i	$-0.830925\pi$
$449$	−36.5402			−1.72444			−0.862218	+	0.506537i	$0.830925\pi$
$450$	−6.82659	−	13.2829i	−0.321809	−	0.626160i
$451$	10.5717	+	39.4543i	0.497804	+	1.85783i
$452$	9.44291	−	13.1902i	0.444157	−	0.620413i
$453$	11.0577	−	41.2679i	0.519536	−	1.93893i
$454$	−20.3585	+	18.4602i	−0.955471	+	0.866382i
$455$		0			0
$456$	−2.64129	+	17.8897i	−0.123690	+	0.837760i
$457$	−13.7199	+	7.92121i	−0.641792	+	0.370539i	−0.785304	−	0.619110i	$-0.787494\pi$
$457$	−13.7199	+	7.92121i	−0.641792	+	0.370539i	0.143513	+	0.989648i	$0.454160\pi$
$458$	−1.54096	+	0.333179i	−0.0720041	+	0.0155684i
$459$	−27.8699	+	7.46773i	−1.30086	+	0.348564i
$460$	21.5754	+	8.10926i	1.00596	+	0.378096i
$461$	−3.07760	+	3.07760i	−0.143338	+	0.143338i	−0.775134	−	0.631796i	$-0.782318\pi$
$461$	−3.07760	+	3.07760i	−0.143338	+	0.143338i	0.631796	+	0.775134i	$0.282318\pi$
$462$		0			0
$463$	−26.2198			−1.21854			−0.609269	−	0.792964i	$-0.708537\pi$
$463$	−26.2198			−1.21854			−0.609269	+	0.792964i	$0.708537\pi$
$464$	−5.47639	−	2.69450i	−0.254235	−	0.125089i
$465$	−16.8669	+	29.2143i	−0.782184	+	1.35478i
$466$	12.5121	+	8.06339i	0.579614	+	0.373529i
$467$	−1.33886	−	0.358746i	−0.0619549	−	0.0166008i	0.227708	−	0.973729i	$-0.426877\pi$
$467$	−1.33886	−	0.358746i	−0.0619549	−	0.0166008i	−0.289663	+	0.957129i	$0.593543\pi$
$468$	29.2891	+	35.6560i	1.35389	+	1.64820i
$469$		0			0
$470$	−1.24555	−	1.37363i	−0.0574531	−	0.0633609i
$471$	25.6957	−	14.8354i	1.18399	−	0.683579i
$472$	−10.2734	+	1.18891i	−0.472869	+	0.0547241i
$473$	11.3731	+	6.56627i	0.522936	+	0.301917i
$474$	−8.39057	−	2.69384i	−0.385391	−	0.123732i
$475$	−3.42845	−	3.42845i	−0.157308	−	0.157308i
$476$		0			0
$477$	−28.5866	+	28.5866i	−1.30889	+	1.30889i
$478$	−14.2805	−	27.7863i	−0.653175	−	1.27092i
$479$	−3.71973	+	6.44276i	−0.169959	+	0.294377i	−0.938405	−	0.345537i	$-0.887697\pi$
$479$	−3.71973	+	6.44276i	−0.169959	+	0.294377i	0.768446	+	0.639914i	$0.221030\pi$
$480$	−29.5827	+	30.6362i	−1.35026	+	1.39834i
$481$	−1.29242	−	2.23854i	−0.0589293	−	0.102068i
$482$	−4.92209	−	0.240692i	−0.224195	−	0.0109632i
$483$		0			0
$484$	−3.87674	+	39.5444i	−0.176216	+	1.79747i
$485$	−1.56525	+	5.84158i	−0.0710742	+	0.265253i
$486$	4.40564	+	20.3761i	0.199844	+	0.924280i
$487$	25.8498	+	14.9244i	1.17137	+	0.676290i	0.954002	−	0.299800i	$-0.0969201\pi$
$487$	25.8498	+	14.9244i	1.17137	+	0.676290i	0.217366	+	0.976090i	$0.430253\pi$
$488$	19.6239	+	8.49146i	0.888331	+	0.384390i
$489$			18.8562i			0.852708i
$490$		0			0
$491$	−17.1830	−	17.1830i	−0.775457	−	0.775457i	0.203597	−	0.979055i	$-0.434737\pi$
$491$	−17.1830	−	17.1830i	−0.775457	−	0.775457i	−0.979055	+	0.203597i	$0.934737\pi$
$492$	14.5784	−	38.7871i	0.657246	−	1.74866i
$493$	−2.08273	−	7.77285i	−0.0938014	−	0.350072i
$494$	12.5924	+	8.11510i	0.566558	+	0.365115i
$495$	36.6715	+	63.5169i	1.64826	+	2.85487i
$496$	17.5820	+	3.48076i	0.789454	+	0.156291i
$497$		0			0
$498$	1.05072	−	21.4869i	0.0470838	−	0.962853i
$499$	11.6949	+	3.13364i	0.523536	+	0.140281i	0.510902	−	0.859639i	$-0.329312\pi$
$499$	11.6949	+	3.13364i	0.523536	+	0.140281i	0.0126341	+	0.999920i	$0.495978\pi$
$500$	2.49859	+	15.0913i	0.111740	+	0.674903i
$501$	−37.7381	+	10.1119i	−1.68602	+	0.451767i
$502$	−11.8980	+	37.0588i	−0.531032	+	1.65402i
$503$			16.3203i			0.727686i	0.931460	+	0.363843i	$0.118535\pi$
$503$			16.3203i			0.727686i	−0.931460	+	0.363843i	$0.881465\pi$
$504$		0			0
$505$			33.8930i			1.50822i
$506$	−32.2716	−	10.3610i	−1.43465	−	0.460603i
$507$	23.9537	−	6.41838i	1.06382	−	0.285050i
$508$	0.277196	−	0.387196i	0.0122986	−	0.0171791i
$509$	3.29918	+	0.884013i	0.146234	+	0.0391832i	0.331193	−	0.943563i	$-0.392549\pi$
$509$	3.29918	+	0.884013i	0.146234	+	0.0391832i	−0.184960	+	0.982746i	$0.559215\pi$
$510$	−56.0832	−	2.74249i	−2.48340	−	0.121439i
$511$		0			0
$512$	20.4746	+	9.63285i	0.904857	+	0.425716i
$513$	−6.20621	−	10.7495i	−0.274011	−	0.474601i
$514$	16.8210	−	26.1016i	0.741944	−	1.15129i
$515$	2.58510	+	9.64773i	0.113913	+	0.425130i
$516$	−5.50370	−	12.1323i	−0.242287	−	0.534096i
$517$	1.92809	+	1.92809i	0.0847972	+	0.0847972i
$518$		0			0
$519$		−	67.6903i		−	2.97127i
$520$	12.9883	+	32.8026i	0.569577	+	1.43849i
$521$	24.8133	+	14.3260i	1.08709	+	0.627633i	0.932801	−	0.360393i	$-0.117357\pi$
$521$	24.8133	+	14.3260i	1.08709	+	0.627633i	0.154291	+	0.988025i	$0.450691\pi$
$522$	10.4221	−	2.25342i	0.456162	−	0.0986294i
$523$	−0.216091	+	0.806464i	−0.00944902	+	0.0352642i	−0.970489	−	0.241144i	$-0.922477\pi$
$523$	−0.216091	+	0.806464i	−0.00944902	+	0.0352642i	0.961040	+	0.276408i	$0.0891441\pi$
$524$	0.999667	−	0.821162i	0.0436706	−	0.0358726i
$525$		0			0
$526$	1.08752	−	22.2395i	0.0474181	−	0.969689i
$527$	11.8155	+	20.4651i	0.514692	+	0.891473i
$528$	41.2497	−	47.1222i	1.79516	−	2.05073i
$529$	−2.19550	+	3.80271i	−0.0954564	+	0.165335i
$530$	−27.4919	+	14.1292i	−1.19417	+	0.613733i
$531$	12.7759	−	12.7759i	0.554427	−	0.554427i
$532$		0			0
$533$	−24.2726	−	24.2726i	−1.05136	−	1.05136i
$534$	−13.5985	+	42.3556i	−0.588466	+	1.83291i
$535$	−19.1199	−	11.0389i	−0.826626	−	0.477253i
$536$	4.19032	+	36.2084i	0.180994	+	1.56396i
$537$	46.8413	−	27.0438i	2.02135	−	1.16703i
$538$	1.76450	−	1.59998i	0.0760730	−	0.0689799i
$539$		0			0
$540$	2.85207	−	29.0924i	0.122734	−	1.25194i
$541$	−12.2532	−	3.28325i	−0.526808	−	0.141158i	−0.0143942	−	0.999896i	$-0.504582\pi$
$541$	−12.2532	−	3.28325i	−0.526808	−	0.141158i	−0.512414	+	0.858739i	$0.671249\pi$
$542$	−9.41287	+	14.6062i	−0.404318	+	0.627389i
$543$	9.50218	−	16.4583i	0.407778	−	0.706292i
$544$	8.22430	+	28.6773i	0.352614	+	1.22953i
$545$	−36.6007			−1.56780
$546$		0			0
$547$	−15.6827	+	15.6827i	−0.670546	+	0.670546i	−0.957842	−	0.287296i	$-0.907244\pi$
$547$	−15.6827	+	15.6827i	−0.670546	+	0.670546i	0.287296	+	0.957842i	$0.407244\pi$
$548$	−7.39329	+	3.35388i	−0.315826	+	0.143271i
$549$	−36.0831	+	9.66842i	−1.53999	+	0.412638i
$550$	3.54855	+	16.4121i	0.151311	+	0.699813i
$551$	2.99800	−	1.73089i	0.127719	−	0.0737386i
$552$	20.5012	+	27.6035i	0.872589	+	1.17488i
$553$		0			0
$554$	29.3447	+	32.3622i	1.24674	+	1.37494i
$555$	−1.07873	+	4.02586i	−0.0457894	+	0.170888i
$556$	16.7661	−	2.77587i	0.711040	−	0.117723i
$557$	−4.28460	−	15.9904i	−0.181544	−	0.677533i	−0.995344	−	0.0963873i	$-0.969271\pi$
$557$	−4.28460	−	15.9904i	−0.181544	−	0.677533i	0.813799	−	0.581146i	$-0.197395\pi$
$558$	−27.8500	+	14.3132i	−1.17898	+	0.605927i
$559$	−11.0364			−0.466792
$560$		0			0
$561$	82.5701			3.48611
$562$	26.9090	−	13.8296i	1.13509	−	0.583367i
$563$	5.52415	+	20.6164i	0.232815	+	0.868878i	0.979122	+	0.203275i	$0.0651587\pi$
$563$	5.52415	+	20.6164i	0.232815	+	0.868878i	−0.746306	+	0.665602i	$0.768175\pi$
$564$	−0.451824	−	2.72898i	−0.0190252	−	0.114911i
$565$	−5.60825	+	20.9303i	−0.235941	+	0.880544i
$566$	−14.2414	−	15.7059i	−0.598613	−	0.660168i
$567$		0			0
$568$	6.71608	−	45.4886i	0.281801	−	1.90866i
$569$	−23.3737	+	13.4948i	−0.979875	+	0.565731i	−0.902232	−	0.431250i	$-0.858073\pi$
$569$	−23.3737	+	13.4948i	−0.979875	+	0.565731i	−0.0776423	+	0.996981i	$0.524739\pi$
$570$	−5.10483	−	23.6099i	−0.213818	−	0.988909i
$571$	−8.98941	+	2.40871i	−0.376195	+	0.100801i	−0.441962	−	0.897034i	$-0.645717\pi$
$571$	−8.98941	+	2.40871i	−0.376195	+	0.100801i	0.0657667	+	0.997835i	$0.479051\pi$
$572$	−21.4328	−	47.2465i	−0.896152	−	1.97547i
$573$	6.85102	−	6.85102i	0.286205	−	0.286205i
$574$		0			0
$575$	−9.21901			−0.384459
$576$	−38.4864	+	9.02880i	−1.60360	+	0.376200i
$577$	−0.726967	+	1.25914i	−0.0302640	+	0.0524188i	−0.880761	−	0.473562i	$-0.842968\pi$
$577$	−0.726967	+	1.25914i	−0.0302640	+	0.0524188i	0.850497	+	0.525980i	$0.176301\pi$
$578$	−8.28394	+	12.8544i	−0.344566	+	0.534672i
$579$	−59.9171	−	16.0547i	−2.49007	−	0.667212i
$580$	8.11378	+	0.795435i	0.336906	+	0.0330287i
$581$		0			0
$582$	−6.68329	+	6.06014i	−0.277031	+	0.251201i
$583$	39.3644	−	22.7271i	1.63031	−	0.941259i
$584$	17.6426	+	13.9827i	0.730057	+	0.578608i
$585$	−53.3789	−	30.8183i	−2.20695	−	1.27418i
$586$	−12.8446	+	40.0073i	−0.530606	+	1.65269i
$587$	−10.3785	−	10.3785i	−0.428367	−	0.428367i	0.459705	−	0.888072i	$-0.347955\pi$
$587$	−10.3785	−	10.3785i	−0.428367	−	0.428367i	−0.888072	+	0.459705i	$0.847955\pi$
$588$		0			0
$589$	−7.18839	+	7.18839i	−0.296193	+	0.296193i
$590$	12.2867	−	6.31462i	0.505835	−	0.259969i
$591$	12.0074	−	20.7974i	0.493917	−	0.855489i
$592$	2.20958	−	0.146829i	0.0908130	−	0.00603465i
$593$	−4.32233	−	7.48650i	−0.177497	−	0.307434i	0.763526	−	0.645777i	$-0.223467\pi$
$593$	−4.32233	−	7.48650i	−0.177497	−	0.307434i	−0.941023	+	0.338344i	$0.890133\pi$
$594$	−2.09952	+	42.9348i	−0.0861445	+	1.76163i
$595$		0			0
$596$	−3.79315	−	4.61771i	−0.155374	−	0.189149i
$597$	−2.47808	+	9.24833i	−0.101421	+	0.378509i
$598$	27.8409	−	6.01964i	1.13850	−	0.246161i
$599$	25.5370	+	14.7438i	1.04341	+	0.602415i	0.920798	−	0.390039i	$-0.127539\pi$
$599$	25.5370	+	14.7438i	1.04341	+	0.602415i	0.122615	+	0.992454i	$0.460872\pi$
$600$	6.76464	−	15.6332i	0.276165	−	0.638222i
$601$		−	21.8149i		−	0.889849i	−0.895568	−	0.444925i	$-0.853231\pi$
$601$		−	21.8149i		−	0.889849i	0.895568	−	0.444925i	$-0.146769\pi$
$602$		0			0
$603$	−45.0287	−	45.0287i	−1.83371	−	1.83371i
$604$	27.6130	−	12.5263i	1.12356	−	0.509690i
$605$	−13.7369	−	51.2669i	−0.558485	−	2.08429i
$606$	−27.3888	+	42.4998i	−1.11259	+	1.72644i
$607$	−7.17791	−	12.4325i	−0.291342	−	0.504620i	0.682785	−	0.730619i	$-0.260769\pi$
$607$	−7.17791	−	12.4325i	−0.291342	−	0.504620i	−0.974127	+	0.225999i	$0.927435\pi$
$608$	−11.0007	+	6.61049i	−0.446138	+	0.268091i
$609$		0			0
$610$	−28.5276	−	1.39501i	−1.15505	−	0.0564823i
$611$	−2.21343	−	0.593087i	−0.0895458	−	0.0239937i
$612$	−42.3796	−	30.3398i	−1.71309	−	1.22641i
$613$	−3.04073	+	0.814761i	−0.122814	+	0.0329079i	−0.319702	−	0.947518i	$-0.603583\pi$
$613$	−3.04073	+	0.814761i	−0.122814	+	0.0329079i	0.196889	+	0.980426i	$0.436916\pi$
$614$	−1.55802	−	0.500212i	−0.0628765	−	0.0201869i
$615$			55.3493i			2.23190i
$616$		0			0
$617$			35.3166i			1.42179i	0.703296	+	0.710897i	$0.251711\pi$
$617$			35.3166i			1.42179i	−0.703296	+	0.710897i	$0.748289\pi$
$618$	−4.55473	+	14.1867i	−0.183218	+	0.570673i
$619$	32.0875	−	8.59783i	1.28971	−	0.345576i	0.452158	−	0.891938i	$-0.350654\pi$
$619$	32.0875	−	8.59783i	1.28971	−	0.345576i	0.837549	+	0.546362i	$0.183988\pi$
$620$	−23.6197	+	3.91060i	−0.948590	+	0.157053i
$621$	−22.7966	−	6.10834i	−0.914798	−	0.245119i
$622$	−0.543692	+	11.1184i	−0.0218000	+	0.445806i
$623$		0			0
$624$	−10.2210	+	51.6284i	−0.409168	+	2.06679i
$625$	−15.5591	−	26.9492i	−0.622366	−	1.07797i
$626$	−6.08822	−	3.92352i	−0.243334	−	0.156815i
$627$	9.19355	+	34.3108i	0.367155	+	1.37024i
$628$	19.7114	+	7.40866i	0.786569	+	0.295638i
$629$	2.06451	+	2.06451i	0.0823175	+	0.0823175i
$630$		0			0
$631$			16.7508i			0.666841i	0.942778	+	0.333420i	$0.108203\pi$
$631$			16.7508i			0.666841i	−0.942778	+	0.333420i	$0.891797\pi$
$632$	−2.30248	−	5.81500i	−0.0915878	−	0.231308i
$633$	−11.1652	−	6.44625i	−0.443778	−	0.256215i
$634$	−5.57460	−	25.7826i	−0.221396	−	1.02396i
$635$	−0.164630	+	0.614407i	−0.00653314	+	0.0243820i
$636$	−45.8910	−	4.49893i	−1.81970	−	0.178394i
$637$		0			0
$638$	−11.9744	−	0.585552i	−0.474071	−	0.0231822i
$639$	40.1662	+	69.5699i	1.58895	+	2.75214i
$640$	−30.1277	−	2.42236i	−1.19090	−	0.0957522i
$641$	−11.6917	+	20.2506i	−0.461795	+	0.799852i	−0.999050	−	0.0435673i	$-0.986128\pi$
$641$	−11.6917	+	20.2506i	−0.461795	+	0.799852i	0.537256	+	0.843419i	$0.319461\pi$
$642$	−15.0548	−	29.2929i	−0.594165	−	1.15610i
$643$	2.10371	−	2.10371i	0.0829620	−	0.0829620i	−0.664408	−	0.747370i	$-0.731316\pi$
$643$	2.10371	−	2.10371i	0.0829620	−	0.0829620i	0.747370	+	0.664408i	$0.231316\pi$
$644$		0			0
$645$	12.5833	+	12.5833i	0.495468	+	0.495468i
$646$	−16.1113	−	5.17262i	−0.633889	−	0.203514i
$647$	5.68625	+	3.28296i	0.223550	+	0.129066i	0.607593	−	0.794249i	$-0.292135\pi$
$647$	5.68625	+	3.28296i	0.223550	+	0.129066i	−0.384043	+	0.923315i	$0.625469\pi$
$648$	1.04229	−	1.31511i	0.0409452	−	0.0516625i
$649$	−17.5928	+	10.1572i	−0.690576	+	0.398704i
$650$	−9.47889	−	10.4536i	−0.371793	−	0.410024i
$651$		0			0
$652$	−10.3410	+	8.49442i	−0.404983	+	0.332667i
$653$	37.3783	+	10.0155i	1.46273	+	0.391936i	0.900430	−	0.435000i	$-0.143252\pi$
$653$	37.3783	+	10.0155i	1.46273	+	0.391936i	0.562295	+	0.826937i	$0.309918\pi$
$654$	−45.8952	−	29.5769i	−1.79464	−	1.15655i
$655$	−0.864035	+	1.49655i	−0.0337607	+	0.0584752i
$656$	27.8386	−	9.47800i	1.08691	−	0.370054i
$657$	−39.3291			−1.53438
$658$		0			0
$659$	20.7559	−	20.7559i	0.808533	−	0.808533i	−0.175879	−	0.984412i	$-0.556277\pi$
$659$	20.7559	−	20.7559i	0.808533	−	0.808533i	0.984412	+	0.175879i	$0.0562766\pi$
$660$	−29.4317	+	78.3056i	−1.14563	+	3.04804i
$661$	−42.5471	+	11.4005i	−1.65489	+	0.443426i	−0.960976	−	0.276632i	$-0.910782\pi$
$661$	−42.5471	+	11.4005i	−1.65489	+	0.443426i	−0.693913	+	0.720059i	$0.744115\pi$
$662$	−18.0196	+	3.89612i	−0.700350	+	0.151427i
$663$	−60.0944	+	34.6955i	−2.33387	+	1.34746i
$664$	12.2570	−	9.10329i	0.475663	−	0.353276i
$665$		0			0
$666$	−2.86597	+	2.59875i	−0.111054	+	0.100699i
$667$	1.70360	−	6.35792i	0.0659637	−	0.246180i
$668$	−22.5459	−	16.1407i	−0.872326	−	0.624504i
$669$	0.338694	+	1.26402i	0.0130947	+	0.0488699i
$670$	−22.2559	−	43.3044i	−0.859819	−	1.67300i
$671$	42.0007			1.62142
$672$		0			0
$673$	26.5908			1.02500			0.512500	−	0.858687i	$-0.328720\pi$
$673$	26.5908			1.02500			0.512500	+	0.858687i	$0.328720\pi$
$674$	−8.75691	−	17.0388i	−0.337304	−	0.656309i
$675$	3.02611	+	11.2936i	0.116475	+	0.434690i
$676$	14.3107	+	10.2451i	0.550410	+	0.394042i
$677$	8.26024	−	30.8276i	0.317467	−	1.18480i	−0.604204	−	0.796830i	$-0.706509\pi$
$677$	8.26024	−	30.8276i	0.317467	−	1.18480i	0.921671	−	0.387973i	$-0.126825\pi$
$678$	−23.9461	+	21.7134i	−0.919645	+	0.833896i
$679$		0			0
$680$	−23.7605	−	31.9920i	−0.911175	−	1.22684i
$681$	47.4252	−	27.3810i	1.81734	−	1.04924i
$682$	34.4110	−	7.44020i	1.31766	−	0.284900i
$683$	24.5538	−	6.57917i	0.939525	−	0.251745i	0.243614	−	0.969872i	$-0.421667\pi$
$683$	24.5538	−	6.57917i	0.939525	−	0.251745i	0.695912	+	0.718127i	$0.255000\pi$
$684$	7.88861	−	20.9883i	0.301629	−	0.802508i
$685$	7.66812	−	7.66812i	0.292984	−	0.292984i
$686$		0			0
$687$	3.14156			0.119858
$688$	4.17417	−	8.48370i	0.159139	−	0.323438i
$689$	−19.0996	+	33.0815i	−0.727636	+	1.26030i
$690$	−38.6065	−	24.8798i	−1.46972	−	0.947156i
$691$	33.4013	+	8.94986i	1.27065	+	0.340469i	0.830279	−	0.557349i	$-0.188181\pi$
$691$	33.4013	+	8.94986i	1.27065	+	0.340469i	0.440368	+	0.897817i	$0.354848\pi$
$692$	37.1220	−	30.4934i	1.41117	−	1.15918i
$693$		0			0
$694$	−24.1567	−	26.6407i	−0.916975	−	1.01127i
$695$	−19.6591	+	11.3502i	−0.745714	+	0.430538i
$696$	9.53143	+	7.55415i	0.361288	+	0.286339i
$697$	33.5784	+	19.3865i	1.27187	+	0.734317i
$698$	6.04367	+	1.94036i	0.228756	+	0.0734436i
$699$	−20.9737	−	20.9737i	−0.793300	−	0.793300i
$700$		0			0
$701$	−31.0840	+	31.0840i	−1.17403	+	1.17403i	−0.192785	+	0.981241i	$0.561752\pi$
$701$	−31.0840	+	31.0840i	−1.17403	+	1.17403i	−0.981241	+	0.192785i	$0.938248\pi$
$702$	−16.5129	−	32.1301i	−0.623240	−	1.21267i
$703$	−0.628010	+	1.08775i	−0.0236858	+	0.0410251i
$704$	44.4246	+	1.39401i	1.67432	+	0.0525389i
$705$	1.84745	+	3.19988i	0.0695791	+	0.120515i
$706$	−9.32050	−	0.455775i	−0.350782	−	0.0171533i
$707$		0			0
$708$	20.5096	+	2.01066i	0.770799	+	0.0755653i
$709$	10.1162	−	37.7540i	0.379921	−	1.41788i	−0.466100	−	0.884732i	$-0.654341\pi$
$709$	10.1162	−	37.7540i	0.379921	−	1.41788i	0.846020	−	0.533151i	$-0.178992\pi$
$710$	12.9802	+	60.0336i	0.487139	+	2.25302i
$711$	9.46263	+	5.46325i	0.354876	+	0.204888i
$712$	−29.3541	+	11.6229i	−1.10009	+	0.435588i
$713$			19.3294i			0.723891i
$714$		0			0
$715$	49.0028	+	49.0028i	1.83260	+	1.83260i
$716$	35.9323	+	13.5054i	1.34285	+	0.504722i
$717$	16.1123	+	60.1319i	0.601725	+	2.24567i
$718$	10.5505	+	6.79921i	0.393741	+	0.253744i
$719$	−1.34884	−	2.33625i	−0.0503031	−	0.0871276i	0.839777	−	0.542931i	$-0.182685\pi$
$719$	−1.34884	−	2.33625i	−0.0503031	−	0.0871276i	−0.890081	+	0.455803i	$0.849352\pi$
$720$	43.8788	−	29.3763i	1.63527	−	1.09479i
$721$		0			0
$722$	−0.956845	+	19.5673i	−0.0356101	+	0.728218i
$723$	9.48518	+	2.54155i	0.352758	+	0.0945211i
$724$	13.3065	−	2.20308i	0.494530	−	0.0818769i
$725$	−3.14975	+	0.843973i	−0.116979	+	0.0313444i
$726$	24.2033	−	75.3865i	0.898269	−	2.79785i
$727$			29.4609i			1.09264i	0.837576	+	0.546321i	$0.183972\pi$
$727$			29.4609i			1.09264i	−0.837576	+	0.546321i	$0.816028\pi$
$728$		0			0
$729$		−	43.3209i		−	1.60448i
$730$	−28.6310	−	9.19216i	−1.05968	−	0.340217i
$731$	12.0413	−	3.22645i	0.445362	−	0.119334i
$732$	−34.6447	−	24.8023i	−1.28050	−	0.916721i
$733$	22.6627	+	6.07246i	0.837067	+	0.224291i	0.651794	−	0.758396i	$-0.274016\pi$
$733$	22.6627	+	6.07246i	0.837067	+	0.224291i	0.185273	+	0.982687i	$0.440683\pi$
$734$	38.9813	+	1.90620i	1.43883	+	0.0703591i
$735$		0			0
$736$	−5.90260	+	23.6780i	−0.217573	+	0.872783i
$737$	35.7990	+	62.0056i	1.31867	+	2.28401i
$738$	−27.8310	+	43.1860i	−1.02447	+	1.58970i
$739$	−11.0520	−	41.2466i	−0.406555	−	1.51728i	−0.801171	−	0.598436i	$-0.795789\pi$
$739$	−11.0520	−	41.2466i	−0.406555	−	1.51728i	0.394616	−	0.918846i	$-0.370878\pi$
$740$	−2.69377	+	1.22200i	−0.0990250	+	0.0449216i
$741$	−21.1083	−	21.1083i	−0.775431	−	0.775431i
$742$		0			0
$743$		−	15.9080i		−	0.583606i	−0.956478	−	0.291803i	$-0.905745\pi$
$743$		−	15.9080i		−	0.583606i	0.956478	−	0.291803i	$-0.0942552\pi$
$744$	−32.7779	−	14.1833i	−1.20170	−	0.519986i
$745$	6.91296	+	3.99120i	0.253271	+	0.146226i
$746$	37.6935	−	8.14993i	1.38006	−	0.298390i
$747$	−6.90361	+	25.7646i	−0.252590	+	0.942678i
$748$	37.1965	+	45.2823i	1.36004	+	1.65568i
$749$		0			0
$750$	1.48876	−	30.4448i	0.0543619	−	1.11169i
$751$	−17.0414	−	29.5165i	−0.621848	−	1.07707i	−0.989141	−	0.146967i	$-0.953049\pi$
$751$	−17.0414	−	29.5165i	−0.621848	−	1.07707i	0.367294	−	0.930105i	$-0.380284\pi$
$752$	1.29306	−	1.47715i	0.0471531	−	0.0538660i
$753$	38.7792	−	67.1675i	1.41319	−	2.44772i
$754$	8.96099	−	4.60541i	0.326340	−	0.167719i
$755$	−28.6395	+	28.6395i	−1.04230	+	1.04230i
$756$		0			0
$757$	15.8161	+	15.8161i	0.574845	+	0.574845i	0.933478	−	0.358634i	$-0.116757\pi$
$757$	15.8161	+	15.8161i	0.574845	+	0.574845i	−0.358634	+	0.933478i	$0.616757\pi$
$758$	9.91053	−	30.8685i	0.359967	−	1.12119i
$759$	58.4909	+	33.7697i	2.12308	+	1.22576i
$760$	10.6483	−	13.4354i	0.386253	−	0.487353i
$761$	14.7507	−	8.51630i	0.534711	−	0.308716i	−0.208222	−	0.978082i	$-0.566768\pi$
$761$	14.7507	−	8.51630i	0.534711	−	0.308716i	0.742933	+	0.669366i	$0.233434\pi$
$762$	−0.702937	+	0.637394i	−0.0254647	+	0.0230903i
$763$		0			0
$764$	6.84344	+	0.670897i	0.247587	+	0.0242722i
$765$	67.2484	+	18.0192i	2.43137	+	0.651484i
$766$	1.52257	−	2.36261i	0.0550128	−	0.0853646i
$767$	8.53599	−	14.7848i	0.308217	−	0.533847i
$768$	−35.8209	−	27.3836i	−1.29258	−	0.988121i
$769$	−29.7823			−1.07398			−0.536989	−	0.843590i	$-0.680438\pi$
$769$	−29.7823			−1.07398			−0.536989	+	0.843590i	$0.680438\pi$
$770$		0			0
$771$	−43.7533	+	43.7533i	−1.57574	+	1.57574i
$772$	−18.1871	−	40.0915i	−0.654568	−	1.44293i
$773$	50.1642	−	13.4415i	1.80428	−	0.483456i	0.809649	−	0.586915i	$-0.199658\pi$
$773$	50.1642	−	13.4415i	1.80428	−	0.483456i	0.994634	+	0.103459i	$0.0329910\pi$
$774$	3.49086	+	16.1453i	0.125477	+	0.580330i
$775$	8.29295	−	4.78794i	0.297892	−	0.171988i
$776$	−6.33415	−	0.935195i	−0.227383	−	0.0335715i
$777$		0			0
$778$	19.5111	+	21.5174i	0.699507	+	0.771436i
$779$	−4.31708	+	16.1116i	−0.154675	+	0.577256i
$780$	−11.4832	−	69.3577i	−0.411165	−	2.48340i
$781$	−23.3767	−	87.2432i	−0.836485	−	3.12181i
$782$	−28.6159	+	14.7068i	−1.02330	+	0.525916i
$783$	−8.34786			−0.298328
$784$		0			0
$785$	−28.1282			−1.00394
$786$	−2.29281	+	1.17837i	−0.0817818	+	0.0420310i
$787$	−4.56538	−	17.0382i	−0.162738	−	0.607347i	−0.998318	−	0.0579780i	$-0.981535\pi$
$787$	−4.56538	−	17.0382i	−0.162738	−	0.607347i	0.835580	−	0.549369i	$-0.185132\pi$
$788$	16.8146	−	2.78391i	0.598996	−	0.0991727i
$789$	−11.4835	+	42.8570i	−0.408823	+	1.52575i
$790$	5.61175	+	6.18880i	0.199657	+	0.220188i
$791$		0			0
$792$	−62.3379	+	46.2985i	−2.21508	+	1.64514i
$793$	−30.5680	+	17.6485i	−1.08550	+	0.626715i
$794$	−10.0710	−	46.5783i	−0.357406	−	1.65300i
$795$	59.4948	−	15.9416i	2.11006	−	0.565390i
$796$	−6.18821	+	2.80721i	−0.219335	+	0.0994990i
$797$	−22.0887	+	22.0887i	−0.782423	+	0.782423i	−0.980239	−	0.197816i	$-0.936615\pi$
$797$	−22.0887	+	22.0887i	−0.782423	+	0.782423i	0.197816	+	0.980239i	$0.436615\pi$
$798$		0			0
$799$	2.58834			0.0915689
$800$	11.6208	−	3.33269i	0.410856	−	0.117828i
$801$	27.5785	−	47.7674i	0.974438	−	1.68778i
$802$	−17.6737	+	27.4247i	−0.624081	+	0.968400i
$803$	42.7125	+	11.4448i	1.50729	+	0.403877i
$804$	7.08658	−	72.2861i	0.249924	−	2.54934i
$805$		0			0
$806$	−21.9179	+	19.8743i	−0.772026	+	0.700041i
$807$	−4.11041	+	2.37315i	−0.144693	+	0.0835388i
$808$	−35.6455	+	4.12518i	−1.25401	+	0.145123i
$809$	−13.6366	−	7.87312i	−0.479439	−	0.276804i	0.240744	−	0.970589i	$-0.422609\pi$
$809$	−13.6366	−	7.87312i	−0.479439	−	0.276804i	−0.720183	+	0.693785i	$0.755942\pi$
$810$	−0.685200	+	2.13420i	−0.0240755	+	0.0749883i
$811$	6.94480	+	6.94480i	0.243865	+	0.243865i	0.818447	−	0.574582i	$-0.194835\pi$
$811$	6.94480	+	6.94480i	0.243865	+	0.243865i	−0.574582	+	0.818447i	$0.694835\pi$
$812$		0			0
$813$	24.4839	−	24.4839i	0.858688	−	0.858688i
$814$	3.86876	−	1.98831i	0.135600	−	0.0696902i
$815$	8.93793	−	15.4809i	0.313082	−	0.542274i
$816$	−3.94169	−	59.3170i	−0.137987	−	2.07651i
$817$	2.68140	+	4.64433i	0.0938104	+	0.162484i
$818$	−1.72654	+	35.3072i	−0.0603669	+	1.23449i
$819$		0			0
$820$	−30.3541	+	24.9339i	−1.06001	+	0.870731i
$821$	−2.42598	+	9.05390i	−0.0846674	+	0.315983i	−0.995251	−	0.0973418i	$-0.968966\pi$
$821$	−2.42598	+	9.05390i	−0.0846674	+	0.315983i	0.910584	+	0.413325i	$0.135633\pi$
$822$	15.8120	−	3.41880i	0.551505	−	0.119244i
$823$	−28.2638	−	16.3181i	−0.985213	−	0.568813i	−0.0813732	−	0.996684i	$-0.525931\pi$
$823$	−28.2638	−	16.3181i	−0.985213	−	0.568813i	−0.903840	+	0.427871i	$0.859264\pi$
$824$	−9.83196	+	3.89302i	−0.342513	+	0.135620i
$825$		−	33.4594i		−	1.16491i
$826$		0			0
$827$	4.84782	+	4.84782i	0.168575	+	0.168575i	0.786353	−	0.617778i	$-0.211967\pi$
$827$	4.84782	+	4.84782i	0.168575	+	0.168575i	−0.617778	+	0.786353i	$0.711967\pi$
$828$	−17.6123	−	38.8246i	−0.612071	−	1.34925i
$829$	13.3049	+	49.6545i	0.462098	+	1.72457i	0.666336	+	0.745652i	$0.267862\pi$
$829$	13.3049	+	49.6545i	0.462098	+	1.72457i	−0.204238	+	0.978921i	$0.565472\pi$
$830$	−11.0475	+	17.1427i	−0.383465	+	0.595032i
$831$	−43.5253	−	75.3880i	−1.50988	−	2.61518i
$832$	−32.9179	+	17.6524i	−1.14122	+	0.611987i
$833$		0			0
$834$	−33.8235	−	1.65398i	−1.17121	−	0.0572727i
$835$	35.7760	+	9.58616i	1.23808	+	0.331743i
$836$	−14.6748	+	20.4983i	−0.507540	+	0.708948i
$837$	23.6791	−	6.34480i	0.818470	−	0.219308i
$838$	−21.1233	−	6.78177i	−0.729693	−	0.234272i
$839$		−	28.0971i		−	0.970020i	−0.874509	−	0.485010i	$-0.838816\pi$
$839$		−	28.0971i		−	0.970020i	0.874509	−	0.485010i	$-0.161184\pi$
$840$		0			0
$841$			26.6718i			0.919717i
$842$	0.314233	−	0.978749i	0.0108292	−	0.0337299i
$843$	−58.2334	+	15.6036i	−2.00566	+	0.537416i
$844$	−1.49456	−	9.02705i	−0.0514450	−	0.310724i
$845$	−22.7083	−	6.08467i	−0.781189	−	0.209319i
$846$	−0.167515	+	3.42564i	−0.00575928	+	0.117776i
$847$		0			0
$848$	−18.2059	−	27.1938i	−0.625193	−	0.933839i
$849$	21.1235	+	36.5869i	0.724956	+	1.25566i
$850$	13.3980	+	8.63425i	0.459546	+	0.296152i
$851$	0.618107	+	2.30681i	0.0211884	+	0.0790763i
$852$	−32.2365	+	85.7680i	−1.10441	+	2.93836i
$853$	−20.9925	−	20.9925i	−0.718769	−	0.718769i	0.249584	−	0.968353i	$-0.419706\pi$
$853$	−20.9925	−	20.9925i	−0.718769	−	0.718769i	−0.968353	+	0.249584i	$0.919706\pi$
$854$		0			0
$855$			29.9504i			1.02428i
$856$	9.28257	−	21.4521i	0.317272	−	0.733219i
$857$	−15.6359	−	9.02739i	−0.534112	−	0.308370i	0.208577	−	0.978006i	$-0.433117\pi$
$857$	−15.6359	−	9.02739i	−0.534112	−	0.308370i	−0.742689	+	0.669636i	$0.766450\pi$
$858$	21.8477	+	101.046i	0.745867	+	3.44964i
$859$	3.85776	−	14.3973i	0.131625	−	0.491231i	−0.868364	−	0.495927i	$-0.834828\pi$
$859$	3.85776	−	14.3973i	0.131625	−	0.491231i	0.999989	+	0.00469633i	$0.00149489\pi$
$860$	−1.23224	+	12.5694i	−0.0420191	+	0.428613i
$861$		0			0
$862$	44.8223	+	2.19182i	1.52665	+	0.0746538i
$863$	−19.4024	−	33.6060i	−0.660467	−	1.14396i	−0.980493	−	0.196554i	$-0.937025\pi$
$863$	−19.4024	−	33.6060i	−0.660467	−	1.14396i	0.320026	−	0.947409i	$-0.396308\pi$
$864$	30.9438	−	0.541336i	1.05273	−	0.0184166i
$865$	−32.0854	+	55.5736i	−1.09094	+	1.88956i
$866$	−11.9021	−	23.1585i	−0.404450	−	0.786959i
$867$	21.5474	−	21.5474i	0.731789	−	0.731789i
$868$		0			0
$869$	−8.68686	−	8.68686i	−0.294681	−	0.294681i
$870$	−15.4679	−	4.96606i	−0.524411	−	0.168365i
$871$	−52.1089	−	30.0851i	−1.76564	−	1.01939i
$872$	−4.45474	−	38.4933i	−0.150857	−	1.30355i
$873$	9.68741	−	5.59303i	0.327869	−	0.189295i
$874$	−9.29736	−	10.2534i	−0.314488	−	0.346827i
$875$		0			0
$876$	−28.4735	−	34.6630i	−0.962029	−	1.17116i
$877$	−1.32758	−	0.355724i	−0.0448291	−	0.0120119i	0.236335	−	0.971672i	$-0.424054\pi$
$877$	−1.32758	−	0.355724i	−0.0448291	−	0.0120119i	−0.281164	+	0.959660i	$0.590720\pi$
$878$	−10.5399	−	6.79241i	−0.355706	−	0.229233i
$879$	41.8645	−	72.5115i	1.41206	−	2.44575i
$880$	−56.2021	+	19.1347i	−1.89457	+	0.645031i
$881$	−13.5748			−0.457347			−0.228673	−	0.973503i	$-0.573439\pi$
$881$	−13.5748			−0.457347			−0.228673	+	0.973503i	$0.573439\pi$
$882$		0			0
$883$	15.1719	−	15.1719i	0.510576	−	0.510576i	−0.404127	−	0.914703i	$-0.632425\pi$
$883$	15.1719	−	15.1719i	0.510576	−	0.510576i	0.914703	+	0.404127i	$0.132425\pi$
$884$	−46.0989	−	17.3266i	−1.55047	−	0.582757i
$885$	−26.5894	+	7.12462i	−0.893794	+	0.239491i
$886$	10.2142	−	2.20847i	0.343153	−	0.0741952i
$887$	25.9694	−	14.9934i	0.871966	−	0.503430i	0.00396485	−	0.999992i	$-0.498738\pi$
$887$	25.9694	−	14.9934i	0.871966	−	0.503430i	0.868001	+	0.496562i	$0.165405\pi$
$888$	−4.36533	−	0.644511i	−0.146491	−	0.0216284i
$889$		0			0
$890$	31.2411	−	28.3281i	1.04720	−	0.949561i
$891$	0.853114	−	3.18386i	0.0285804	−	0.106663i
$892$	−0.540627	+	0.755164i	−0.0181015	+	0.0252848i
$893$	0.288192	+	1.07555i	0.00964397	+	0.0359918i
$894$	5.44317	+	10.5911i	0.182047	+	0.354218i
$895$	−51.2755			−1.71395
$896$		0			0
$897$	−56.7594			−1.89514
$898$	23.6212	+	45.9609i	0.788248	+	1.53374i
$899$	1.76955	+	6.60404i	0.0590177	+	0.220257i
$900$	−12.2944	+	17.1732i	−0.409814	+	0.572442i
$901$	11.1673	−	41.6770i	0.372038	−	1.38846i
$902$	42.7923	−	38.8023i	1.42483	−	1.29198i
$903$		0			0
$904$	−22.6952	−	3.35078i	−0.754830	−	0.111445i
$905$	−15.6026	+	9.00814i	−0.518647	+	0.299441i
$906$	−59.0557	+	12.7688i	−1.96200	+	0.424214i
$907$	−20.5407	+	5.50387i	−0.682043	+	0.182753i	−0.583174	−	0.812347i	$-0.698189\pi$
$907$	−20.5407	+	5.50387i	−0.682043	+	0.182753i	−0.0988696	+	0.995100i	$0.531523\pi$
$908$	36.3803	+	13.6738i	1.20732	+	0.453781i
$909$	44.3287	−	44.3287i	1.47029	−	1.47029i
$910$		0			0
$911$	15.3180			0.507506			0.253753	−	0.967269i	$-0.418335\pi$
$911$	15.3180			0.507506			0.253753	+	0.967269i	$0.418335\pi$
$912$	24.2094	−	8.24240i	0.801653	−	0.272933i
$913$	14.9950	−	25.9721i	0.496262	−	0.859552i
$914$	18.8326	+	12.1366i	0.622928	+	0.401443i
$915$	54.9746	+	14.7304i	1.81740	+	0.486972i
$916$	1.41522	+	1.72286i	0.0467602	+	0.0569250i
$917$		0			0
$918$	27.4094	+	30.2279i	0.904645	+	0.997669i
$919$	−30.8775	+	17.8272i	−1.01856	+	0.588064i	−0.913685	−	0.406422i	$-0.866776\pi$
$919$	−30.8775	+	17.8272i	−1.01856	+	0.588064i	−0.104871	+	0.994486i	$0.533443\pi$
$920$	−3.74728	−	32.3801i	−0.123544	−	1.06754i
$921$	2.82384	+	1.63035i	0.0930487	+	0.0537217i
$922$	5.86055	+	1.88157i	0.193007	+	0.0619661i
$923$	53.6727	+	53.6727i	1.76666	+	1.76666i
$924$		0			0
$925$	0.836591	−	0.836591i	0.0275069	−	0.0275069i
$926$	16.9496	+	32.9798i	0.556999	+	1.08378i
$927$	9.23722	−	15.9993i	0.303390	−	0.525487i
$928$	0.150977	+	8.63015i	0.00495607	+	0.283299i
$929$	−12.6992	−	21.9956i	−0.416647	−	0.721653i	0.578953	−	0.815361i	$-0.303461\pi$
$929$	−12.6992	−	21.9956i	−0.416647	−	0.721653i	−0.995600	+	0.0937078i	$0.970128\pi$
$930$	47.6499	+	2.33009i	1.56250	+	0.0764068i
$931$		0			0
$932$	2.05389	−	20.9505i	0.0672773	−	0.686258i
$933$	5.74103	−	21.4258i	0.187953	−	0.701449i
$934$	0.414259	+	1.91595i	0.0135550	+	0.0626918i
$935$	−67.7900	−	39.1386i	−2.21697	−	1.27997i
$936$	25.9151	−	59.8900i	0.847060	−	1.95757i
$937$		−	58.1917i		−	1.90104i	−0.310664	−	0.950520i	$-0.600551\pi$
$937$		−	58.1917i		−	1.90104i	0.310664	−	0.950520i	$-0.399449\pi$
$938$		0			0
$939$	10.2055	+	10.2055i	0.333044	+	0.333044i
$940$	−0.922601	+	2.45466i	−0.0300919	+	0.0800621i
$941$	−10.4802	−	39.1126i	−0.341645	−	1.27504i	−0.896483	−	0.443078i	$-0.853887\pi$
$941$	−10.4802	−	39.1126i	−0.341645	−	1.27504i	0.554838	−	0.831958i	$-0.312780\pi$
$942$	−35.2711	−	22.7303i	−1.14919	−	0.740592i
$943$	15.8575	+	27.4660i	0.516391	+	0.894415i
$944$	8.13658	+	12.1535i	0.264823	+	0.395561i
$945$		0			0
$946$	0.907103	−	18.5500i	0.0294925	−	0.603114i
$947$	−54.7515	−	14.6706i	−1.77918	−	0.476731i	−0.788750	−	0.614714i	$-0.789271\pi$
$947$	−54.7515	−	14.6706i	−1.77918	−	0.476731i	−0.990435	+	0.137983i	$0.955938\pi$
$948$	2.03566	+	12.2952i	0.0661152	+	0.399331i
$949$	−35.8951	+	9.61807i	−1.16520	+	0.312216i
$950$	−2.09607	+	6.52868i	−0.0680056	+	0.211818i
$951$			52.5632i			1.70448i
$952$		0			0
$953$			9.65307i			0.312694i	0.987702	+	0.156347i	$0.0499718\pi$
$953$			9.65307i			0.312694i	−0.987702	+	0.156347i	$0.950028\pi$
$954$	54.4363	+	17.4771i	1.76244	+	0.565843i
$955$	−8.87209	+	2.37727i	−0.287094	+	0.0769266i
$956$	−25.7186	+	35.9246i	−0.831800	+	1.16188i
$957$	23.0754	+	6.18304i	0.745922	+	0.199869i
$958$	10.5084	+	0.513865i	0.339512	+	0.0166022i
$959$		0			0
$960$	57.6584	+	17.4051i	1.86092	+	0.561748i
$961$	5.46119	+	9.45906i	0.176167	+	0.305131i
$962$	−1.98020	+	3.07272i	−0.0638442	+	0.0990684i
$963$	10.5692	+	39.4447i	0.340587	+	1.27109i
$964$	2.87911	+	6.34669i	0.0927298	+	0.204413i
$965$	41.5819	+	41.5819i	1.33857	+	1.33857i
$966$		0			0
$967$		−	29.5949i		−	0.951706i	−0.879525	−	0.475853i	$-0.842139\pi$
$967$		−	29.5949i		−	0.951706i	0.879525	−	0.475853i	$-0.157861\pi$
$968$	52.2459	−	20.6870i	1.67925	−	0.664906i
$969$	29.2010	+	16.8592i	0.938070	+	0.541595i
$970$	8.35950	−	1.80746i	0.268407	−	0.0580339i
$971$	−10.3789	+	38.7346i	−0.333075	+	1.24305i	0.572867	+	0.819648i	$0.305831\pi$
$971$	−10.3789	+	38.7346i	−0.333075	+	1.24305i	−0.905942	+	0.423403i	$0.860836\pi$
$972$	22.7815	−	18.7135i	0.730717	−	0.600237i
$973$		0			0
$974$	2.06175	−	42.1622i	0.0660626	−	1.35097i
$975$	14.0595	+	24.3517i	0.450263	+	0.779879i
$976$	−2.00501	−	30.1726i	−0.0641787	−	0.965800i
$977$	−10.8910	+	18.8638i	−0.348434	+	0.603505i	−0.985971	−	0.166914i	$-0.946620\pi$
$977$	−10.8910	+	18.8638i	−0.348434	+	0.603505i	0.637538	+	0.770419i	$0.279953\pi$
$978$	23.7177	−	12.1895i	0.758410	−	0.389777i
$979$	−43.8513	+	43.8513i	−1.40149	+	1.40149i
$980$		0			0
$981$	47.8702	+	47.8702i	1.52838	+	1.52838i
$982$	−10.5053	+	32.7209i	−0.335236	+	1.04417i
$983$	38.5006	+	22.2283i	1.22798	+	0.708973i	0.966607	−	0.256265i	$-0.0824920\pi$
$983$	38.5006	+	22.2283i	1.22798	+	0.708973i	0.261371	+	0.965238i	$0.415825\pi$
$984$	−58.2114	+	6.73667i	−1.85571	+	0.214757i
$985$	−19.7161	+	11.3831i	−0.628206	+	0.362695i
$986$	−8.43048	+	7.64441i	−0.268481	+	0.243448i
$987$		0			0
$988$	2.06706	−	21.0849i	0.0657619	−	0.670800i
$989$	9.84933	+	2.63912i	0.313190	+	0.0839191i
$990$	56.1867	−	87.1862i	1.78573	−	2.77096i
$991$	−13.3978	+	23.2057i	−0.425596	+	0.737154i	−0.996476	−	0.0838794i	$-0.973269\pi$
$991$	−13.3978	+	23.2057i	−0.425596	+	0.737154i	0.570880	+	0.821034i	$0.306602\pi$
$992$	−6.98760	−	24.3651i	−0.221857	−	0.773592i
$993$	36.7366			1.16580
$994$		0			0
$995$	6.41824	−	6.41824i	0.203472	−	0.203472i
$996$	−27.7059	+	12.5685i	−0.877896	+	0.398248i
$997$	−43.4209	+	11.6346i	−1.37515	+	0.368471i	−0.869358	−	0.494183i	$-0.835467\pi$
$997$	−43.4209	+	11.6346i	−1.37515	+	0.368471i	−0.505795	+	0.862654i	$0.668801\pi$
$998$	−3.61854	−	16.7358i	−0.114543	−	0.529762i
$999$	2.62302	−	1.51440i	0.0829887	−	0.0479136i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.p.165.10		96
7.2	even	3	inner	784.2.x.p.373.7		96
7.3	odd	6		784.2.m.l.197.23	✓	48
7.4	even	3		784.2.m.l.197.24	yes	48
7.5	odd	6	inner	784.2.x.p.373.8		96
7.6	odd	2	inner	784.2.x.p.165.9		96
16.13	even	4	inner	784.2.x.p.557.7		96
112.13	odd	4	inner	784.2.x.p.557.8		96
112.45	odd	12		784.2.m.l.589.23	yes	48
112.61	odd	12	inner	784.2.x.p.765.9		96
112.93	even	12	inner	784.2.x.p.765.10		96
112.109	even	12		784.2.m.l.589.24	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.m.l.197.23	✓	48	7.3	odd	6
784.2.m.l.197.24	yes	48	7.4	even	3
784.2.m.l.589.23	yes	48	112.45	odd	12
784.2.m.l.589.24	yes	48	112.109	even	12
784.2.x.p.165.9		96	7.6	odd	2	inner
784.2.x.p.165.10		96	1.1	even	1	trivial
784.2.x.p.373.7		96	7.2	even	3	inner
784.2.x.p.373.8		96	7.5	odd	6	inner
784.2.x.p.557.7		96	16.13	even	4	inner
784.2.x.p.557.8		96	112.13	odd	4	inner
784.2.x.p.765.9		96	112.61	odd	12	inner
784.2.x.p.765.10		96	112.93	even	12	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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.646444 - 1.25782i) q^{2} +(0.729365 + 2.72203i) q^{3} +(-1.16422 + 1.62622i) q^{4} +(0.691444 - 2.58050i) q^{5} +(2.95233 - 2.67705i) q^{6} +(2.79809 + 0.413120i) q^{8} +(-4.27938 + 2.47070i) q^{9} +O(q^{10})\)	\(q+(-0.646444 - 1.25782i) q^{2} +(0.729365 + 2.72203i) q^{3} +(-1.16422 + 1.62622i) q^{4} +(0.691444 - 2.58050i) q^{5} +(2.95233 - 2.67705i) q^{6} +(2.79809 + 0.413120i) q^{8} +(-4.27938 + 2.47070i) q^{9} +(-3.69279 + 0.798439i) q^{10} +(5.36650 - 1.43795i) q^{11} +(-5.27576 - 1.98293i) q^{12} +(-3.30151 + 3.30151i) q^{13} +7.52851 q^{15} +(-1.28918 - 3.78656i) q^{16} +(2.63692 - 4.56728i) q^{17} +(5.87408 + 3.78552i) q^{18} +(2.19147 + 0.587201i) q^{19} +(3.39147 + 4.12871i) q^{20} +(-5.27782 - 5.82053i) q^{22} +(3.73587 - 2.15691i) q^{23} +(0.916309 + 7.91781i) q^{24} +(-1.85077 - 1.06854i) q^{25} +(6.28695 + 2.01846i) q^{26} +(-3.86857 - 3.86857i) q^{27} +(1.07893 - 1.07893i) q^{29} +(-4.86676 - 9.46951i) q^{30} +(-2.24040 + 3.88049i) q^{31} +(-3.92942 + 4.06935i) q^{32} +(7.82827 + 13.5590i) q^{33} +(-7.44943 - 0.364280i) q^{34} +(0.964240 - 9.83566i) q^{36} +(-0.143285 + 0.534749i) q^{37} +(-0.678066 - 3.13606i) q^{38} +(-11.3948 - 6.57880i) q^{39} +(3.00078 - 6.93484i) q^{40} +7.35196i q^{41} +(1.67142 + 1.67142i) q^{43} +(-3.90937 + 10.4012i) q^{44} +(3.41670 + 12.7513i) q^{45} +(-5.12803 - 3.30474i) q^{46} +(0.245394 + 0.425035i) q^{47} +(9.36683 - 6.27097i) q^{48} +(-0.147615 + 3.01869i) q^{50} +(14.3555 + 3.84655i) q^{51} +(-1.52530 - 9.21267i) q^{52} +(7.90260 - 2.11750i) q^{53} +(-2.36515 + 7.36678i) q^{54} -14.8425i q^{55} +6.39351i q^{57} +(-2.05457 - 0.659634i) q^{58} +(-3.53183 + 0.946351i) q^{59} +(-8.76485 + 12.2430i) q^{60} +(7.30218 + 1.95661i) q^{61} +(6.32925 + 0.309503i) q^{62} +(7.65866 + 2.31190i) q^{64} +(6.23675 + 10.8024i) q^{65} +(11.9942 - 18.6117i) q^{66} +(3.33541 + 12.4479i) q^{67} +(4.35744 + 9.60553i) q^{68} +(8.59598 + 8.59598i) q^{69} -16.2570i q^{71} +(-12.9948 + 5.14536i) q^{72} +(6.89278 + 3.97955i) q^{73} +(0.765243 - 0.165458i) q^{74} +(1.55872 - 5.81721i) q^{75} +(-3.50627 + 2.88017i) q^{76} +(-0.908834 + 18.5854i) q^{78} +(-1.10561 - 1.91497i) q^{79} +(-10.6626 + 0.708545i) q^{80} +(0.296643 - 0.513800i) q^{81} +(9.24743 - 4.75263i) q^{82} +(3.81693 - 3.81693i) q^{83} +(-9.96259 - 9.96259i) q^{85} +(1.02187 - 3.18283i) q^{86} +(3.72382 + 2.14995i) q^{87} +(15.6100 - 1.80651i) q^{88} +(-9.66675 + 5.58110i) q^{89} +(13.8301 - 12.5406i) q^{90} +(-0.841775 + 8.58647i) q^{92} +(-12.1969 - 3.26814i) q^{93} +(0.375984 - 0.583423i) q^{94} +(3.03055 - 5.24907i) q^{95} +(-13.9429 - 7.72795i) q^{96} -2.26374 q^{97} +(-19.4126 + 19.4126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 4 q^{4}+O(q^{10}) \) 96 * q + 4 * q^4	\( 96 q + 4 q^{4} + 8 q^{11} + 64 q^{15} - 36 q^{16} - 20 q^{18} - 56 q^{22} - 32 q^{29} - 96 q^{30} - 40 q^{32} + 80 q^{36} + 16 q^{37} + 16 q^{43} - 4 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{53} + 20 q^{58} - 8 q^{60} + 88 q^{64} - 40 q^{67} + 196 q^{72} + 28 q^{74} + 112 q^{78} - 80 q^{79} + 48 q^{81} + 108 q^{86} + 100 q^{88} + 128 q^{95} - 80 q^{99}+O(q^{100}) \) 96 * q + 4 * q^4 + 8 * q^11 + 64 * q^15 - 36 * q^16 - 20 * q^18 - 56 * q^22 - 32 * q^29 - 96 * q^30 - 40 * q^32 + 80 * q^36 + 16 * q^37 + 16 * q^43 - 4 * q^44 - 64 * q^46 - 56 * q^50 - 16 * q^53 + 20 * q^58 - 8 * q^60 + 88 * q^64 - 40 * q^67 + 196 * q^72 + 28 * q^74 + 112 * q^78 - 80 * q^79 + 48 * q^81 + 108 * q^86 + 100 * q^88 + 128 * q^95 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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