LMFDB - Embedded newform 775.2.f.c.743.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(557,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("775.557");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.f (of order $4$, degree $2$, 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:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.3317760000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 25x^{4} + 625 $ x^8 - 25*x^4 + 625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			743.2
Root			$-2.15988 - 0.578737i$ of defining polynomial
Character	$\chi$	$=$	775.743
Dual form			775.2.f.c.557.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 + 1.73205i) q^{2} +(1.58114 - 1.58114i) q^{3} -4.00000i q^{4} +5.47723i q^{6} +(1.73205 - 1.73205i) q^{7} +(3.46410 + 3.46410i) q^{8} -2.00000i q^{9} +O(q^{10})$	\(q+(-1.73205 + 1.73205i) q^{2} +(1.58114 - 1.58114i) q^{3} -4.00000i q^{4} +5.47723i q^{6} +(1.73205 - 1.73205i) q^{7} +(3.46410 + 3.46410i) q^{8} -2.00000i q^{9} +5.47723i q^{11} +(-6.32456 - 6.32456i) q^{12} +6.00000i q^{14} -4.00000 q^{16} +(1.58114 + 1.58114i) q^{17} +(3.46410 + 3.46410i) q^{18} +7.00000i q^{19} -5.47723i q^{21} +(-9.48683 - 9.48683i) q^{22} +(3.16228 - 3.16228i) q^{23} +10.9545 q^{24} +(1.58114 + 1.58114i) q^{27} +(-6.92820 - 6.92820i) q^{28} +5.47723 q^{29} +(-1.00000 - 5.47723i) q^{31} +(8.66025 + 8.66025i) q^{33} -5.47723 q^{34} -8.00000 q^{36} +(-4.74342 - 4.74342i) q^{37} +(-12.1244 - 12.1244i) q^{38} +9.00000 q^{41} +(9.48683 + 9.48683i) q^{42} +(4.74342 - 4.74342i) q^{43} +21.9089 q^{44} +10.9545i q^{46} +(-6.32456 + 6.32456i) q^{48} +1.00000i q^{49} +5.00000 q^{51} +(7.90569 - 7.90569i) q^{53} -5.47723 q^{54} +12.0000 q^{56} +(11.0680 + 11.0680i) q^{57} +(-9.48683 + 9.48683i) q^{58} +3.00000i q^{59} -10.9545i q^{61} +(11.2189 + 7.75478i) q^{62} +(-3.46410 - 3.46410i) q^{63} -8.00000i q^{64} -30.0000 q^{66} +(8.66025 - 8.66025i) q^{67} +(6.32456 - 6.32456i) q^{68} -10.0000i q^{69} -9.00000 q^{71} +(6.92820 - 6.92820i) q^{72} +(-4.74342 + 4.74342i) q^{73} +16.4317 q^{74} +28.0000 q^{76} +(9.48683 + 9.48683i) q^{77} -5.47723 q^{79} +11.0000 q^{81} +(-15.5885 + 15.5885i) q^{82} +(-7.90569 + 7.90569i) q^{83} -21.9089 q^{84} +16.4317i q^{86} +(8.66025 - 8.66025i) q^{87} +(-18.9737 + 18.9737i) q^{88} -5.47723 q^{89} +(-12.6491 - 12.6491i) q^{92} +(-10.2414 - 7.07912i) q^{93} +(-10.3923 + 10.3923i) q^{97} +(-1.73205 - 1.73205i) q^{98} +10.9545 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 32 q^{16} - 8 q^{31} - 64 q^{36} + 72 q^{41} + 40 q^{51} + 96 q^{56} - 240 q^{66} - 72 q^{71} + 224 q^{76} + 88 q^{81}+O(q^{100}) $ 8 * q - 32 * q^16 - 8 * q^31 - 64 * q^36 + 72 * q^41 + 40 * q^51 + 96 * q^56 - 240 * q^66 - 72 * q^71 + 224 * q^76 + 88 * q^81

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.73205	+	1.73205i	−1.22474	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$2$	−1.73205	+	1.73205i	−1.22474	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$3$	1.58114	−	1.58114i	0.912871	−	0.912871i	−0.0836263	−	0.996497i	$-0.526650\pi$
$3$	1.58114	−	1.58114i	0.912871	−	0.912871i	0.996497	+	0.0836263i	$0.0266502\pi$
$4$		−	4.00000i		−	2.00000i
$5$		0			0
$5$		0			0
$6$			5.47723i			2.23607i
$7$	1.73205	−	1.73205i	0.654654	−	0.654654i	−0.299456	−	0.954110i	$-0.596805\pi$
$7$	1.73205	−	1.73205i	0.654654	−	0.654654i	0.954110	+	0.299456i	$0.0968053\pi$
$8$	3.46410	+	3.46410i	1.22474	+	1.22474i
$9$		−	2.00000i		−	0.666667i
$10$		0			0
$11$			5.47723i			1.65145i	0.564076	+	0.825723i	$0.309232\pi$
$11$			5.47723i			1.65145i	−0.564076	+	0.825723i	$0.690768\pi$
$12$	−6.32456	−	6.32456i	−1.82574	−	1.82574i
$13$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$13$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$14$			6.00000i			1.60357i
$15$		0			0
$16$	−4.00000			−1.00000
$17$	1.58114	+	1.58114i	0.383482	+	0.383482i	0.872355	−	0.488873i	$-0.162592\pi$
$17$	1.58114	+	1.58114i	0.383482	+	0.383482i	−0.488873	+	0.872355i	$0.662592\pi$
$18$	3.46410	+	3.46410i	0.816497	+	0.816497i
$19$			7.00000i			1.60591i	0.596040	+	0.802955i	$0.296740\pi$
$19$			7.00000i			1.60591i	−0.596040	+	0.802955i	$0.703260\pi$
$20$		0			0
$21$		−	5.47723i		−	1.19523i
$22$	−9.48683	−	9.48683i	−2.02260	−	2.02260i
$23$	3.16228	−	3.16228i	0.659380	−	0.659380i	−0.295853	−	0.955233i	$-0.595604\pi$
$23$	3.16228	−	3.16228i	0.659380	−	0.659380i	0.955233	+	0.295853i	$0.0956039\pi$
$24$	10.9545			2.23607
$25$		0			0
$26$		0			0
$27$	1.58114	+	1.58114i	0.304290	+	0.304290i
$28$	−6.92820	−	6.92820i	−1.30931	−	1.30931i
$29$	5.47723			1.01710			0.508548	−	0.861034i	$-0.330183\pi$
$29$	5.47723			1.01710			0.508548	+	0.861034i	$0.330183\pi$
$30$		0			0
$31$	−1.00000	−	5.47723i	−0.179605	−	0.983739i
$31$	−1.00000	−	5.47723i	−0.179605	−	0.983739i
$32$		0			0
$33$	8.66025	+	8.66025i	1.50756	+	1.50756i
$34$	−5.47723			−0.939336
$35$		0			0
$36$	−8.00000			−1.33333
$37$	−4.74342	−	4.74342i	−0.779813	−	0.779813i	0.199986	−	0.979799i	$-0.435910\pi$
$37$	−4.74342	−	4.74342i	−0.779813	−	0.779813i	−0.979799	+	0.199986i	$0.935910\pi$
$38$	−12.1244	−	12.1244i	−1.96683	−	1.96683i
$39$		0			0
$40$		0			0
$41$	9.00000			1.40556			0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000			1.40556			0.702782	+	0.711405i	$0.251941\pi$
$42$	9.48683	+	9.48683i	1.46385	+	1.46385i
$43$	4.74342	−	4.74342i	0.723364	−	0.723364i	−0.245925	−	0.969289i	$-0.579092\pi$
$43$	4.74342	−	4.74342i	0.723364	−	0.723364i	0.969289	+	0.245925i	$0.0790916\pi$
$44$	21.9089			3.30289
$45$		0			0
$46$			10.9545i			1.61515i
$47$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$47$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$48$	−6.32456	+	6.32456i	−0.912871	+	0.912871i
$49$			1.00000i			0.142857i
$50$		0			0
$51$	5.00000			0.700140
$52$		0			0
$53$	7.90569	−	7.90569i	1.08593	−	1.08593i	0.0899877	−	0.995943i	$-0.471317\pi$
$53$	7.90569	−	7.90569i	1.08593	−	1.08593i	0.995943	−	0.0899877i	$-0.0286828\pi$
$54$	−5.47723			−0.745356
$55$		0			0
$56$	12.0000			1.60357
$57$	11.0680	+	11.0680i	1.46599	+	1.46599i
$58$	−9.48683	+	9.48683i	−1.24568	+	1.24568i
$59$			3.00000i			0.390567i	0.980747	+	0.195283i	$0.0625627\pi$
$59$			3.00000i			0.390567i	−0.980747	+	0.195283i	$0.937437\pi$
$60$		0			0
$61$		−	10.9545i		−	1.40257i	−0.712879	−	0.701287i	$-0.752609\pi$
$61$		−	10.9545i		−	1.40257i	0.712879	−	0.701287i	$-0.247391\pi$
$62$	11.2189	+	7.75478i	1.42480	+	0.984858i
$63$	−3.46410	−	3.46410i	−0.436436	−	0.436436i
$64$		−	8.00000i		−	1.00000i
$65$		0			0
$66$	−30.0000			−3.69274
$67$	8.66025	−	8.66025i	1.05802	−	1.05802i	0.0598086	−	0.998210i	$-0.480951\pi$
$67$	8.66025	−	8.66025i	1.05802	−	1.05802i	0.998210	−	0.0598086i	$-0.0190490\pi$
$68$	6.32456	−	6.32456i	0.766965	−	0.766965i
$69$		−	10.0000i		−	1.20386i
$70$		0			0
$71$	−9.00000			−1.06810			−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000			−1.06810			−0.534052	+	0.845452i	$0.679331\pi$
$72$	6.92820	−	6.92820i	0.816497	−	0.816497i
$73$	−4.74342	+	4.74342i	−0.555175	+	0.555175i	−0.927930	−	0.372755i	$-0.878413\pi$
$73$	−4.74342	+	4.74342i	−0.555175	+	0.555175i	0.372755	+	0.927930i	$0.378413\pi$
$74$	16.4317			1.91014
$75$		0			0
$76$	28.0000			3.21182
$77$	9.48683	+	9.48683i	1.08112	+	1.08112i
$78$		0			0
$79$	−5.47723			−0.616236			−0.308118	−	0.951348i	$-0.599699\pi$
$79$	−5.47723			−0.616236			−0.308118	+	0.951348i	$0.599699\pi$
$80$		0			0
$81$	11.0000			1.22222
$82$	−15.5885	+	15.5885i	−1.72146	+	1.72146i
$83$	−7.90569	+	7.90569i	−0.867763	+	0.867763i	−0.992224	−	0.124462i	$-0.960280\pi$
$83$	−7.90569	+	7.90569i	−0.867763	+	0.867763i	0.124462	+	0.992224i	$0.460280\pi$
$84$	−21.9089			−2.39046
$85$		0			0
$86$			16.4317i			1.77187i
$87$	8.66025	−	8.66025i	0.928477	−	0.928477i
$88$	−18.9737	+	18.9737i	−2.02260	+	2.02260i
$89$	−5.47723			−0.580585			−0.290292	−	0.956938i	$-0.593753\pi$
$89$	−5.47723			−0.580585			−0.290292	+	0.956938i	$0.593753\pi$
$90$		0			0
$91$		0			0
$92$	−12.6491	−	12.6491i	−1.31876	−	1.31876i
$93$	−10.2414	−	7.07912i	−1.06198	−	0.734070i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−10.3923	+	10.3923i	−1.05518	+	1.05518i	−0.0567927	+	0.998386i	$0.518087\pi$
$97$	−10.3923	+	10.3923i	−1.05518	+	1.05518i	−0.998386	+	0.0567927i	$0.981913\pi$
$98$	−1.73205	−	1.73205i	−0.174964	−	0.174964i
$99$	10.9545			1.10096
$100$		0			0
$101$	−9.00000			−0.895533			−0.447767	−	0.894150i	$-0.647781\pi$
$101$	−9.00000			−0.895533			−0.447767	+	0.894150i	$0.647781\pi$
$102$	−8.66025	+	8.66025i	−0.857493	+	0.857493i
$103$	3.46410	+	3.46410i	0.341328	+	0.341328i	0.856866	−	0.515538i	$-0.172408\pi$
$103$	3.46410	+	3.46410i	0.341328	+	0.341328i	−0.515538	+	0.856866i	$0.672408\pi$
$104$		0			0
$105$		0			0
$106$			27.3861i			2.65998i
$107$	−10.3923	+	10.3923i	−1.00466	+	1.00466i	−0.00467295	+	0.999989i	$0.501487\pi$
$107$	−10.3923	+	10.3923i	−1.00466	+	1.00466i	−0.999989	+	0.00467295i	$0.998513\pi$
$108$	6.32456	−	6.32456i	0.608581	−	0.608581i
$109$			7.00000i			0.670478i	0.942133	+	0.335239i	$0.108817\pi$
$109$			7.00000i			0.670478i	−0.942133	+	0.335239i	$0.891183\pi$
$110$		0			0
$111$	−15.0000			−1.42374
$112$	−6.92820	+	6.92820i	−0.654654	+	0.654654i
$113$	5.19615	+	5.19615i	0.488813	+	0.488813i	0.907931	−	0.419119i	$-0.137661\pi$
$113$	5.19615	+	5.19615i	0.488813	+	0.488813i	−0.419119	+	0.907931i	$0.637661\pi$
$114$	−38.3406			−3.59092
$115$		0			0
$116$		−	21.9089i		−	2.03419i
$117$		0			0
$118$	−5.19615	−	5.19615i	−0.478345	−	0.478345i
$119$	5.47723			0.502096
$120$		0			0
$121$	−19.0000			−1.72727
$122$	18.9737	+	18.9737i	1.71780	+	1.71780i
$123$	14.2302	−	14.2302i	1.28310	−	1.28310i
$124$	−21.9089	+	4.00000i	−1.96748	+	0.359211i
$125$		0			0
$126$	12.0000			1.06904
$127$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$127$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$128$	13.8564	+	13.8564i	1.22474	+	1.22474i
$129$		−	15.0000i		−	1.32068i
$130$		0			0
$131$	3.00000			0.262111			0.131056	−	0.991375i	$-0.458163\pi$
$131$	3.00000			0.262111			0.131056	+	0.991375i	$0.458163\pi$
$132$	34.6410	−	34.6410i	3.01511	−	3.01511i
$133$	12.1244	+	12.1244i	1.05131	+	1.05131i
$134$			30.0000i			2.59161i
$135$		0			0
$136$			10.9545i			0.939336i
$137$	−11.0680	−	11.0680i	−0.945601	−	0.945601i	0.0529942	−	0.998595i	$-0.483124\pi$
$137$	−11.0680	−	11.0680i	−0.945601	−	0.945601i	−0.998595	+	0.0529942i	$0.983124\pi$
$138$	17.3205	+	17.3205i	1.47442	+	1.47442i
$139$	16.4317			1.39372			0.696858	−	0.717209i	$-0.254581\pi$
$139$	16.4317			1.39372			0.696858	+	0.717209i	$0.254581\pi$
$140$		0			0
$141$		0			0
$142$	15.5885	−	15.5885i	1.30815	−	1.30815i
$143$		0			0
$144$			8.00000i			0.666667i
$145$		0			0
$146$		−	16.4317i		−	1.35990i
$147$	1.58114	+	1.58114i	0.130410	+	0.130410i
$148$	−18.9737	+	18.9737i	−1.55963	+	1.55963i
$149$			9.00000i			0.737309i	0.929567	+	0.368654i	$0.120181\pi$
$149$			9.00000i			0.737309i	−0.929567	+	0.368654i	$0.879819\pi$
$150$		0			0
$151$		−	16.4317i		−	1.33719i	−0.743626	−	0.668595i	$-0.766896\pi$
$151$		−	16.4317i		−	1.33719i	0.743626	−	0.668595i	$-0.233104\pi$
$152$	−24.2487	+	24.2487i	−1.96683	+	1.96683i
$153$	3.16228	−	3.16228i	0.255655	−	0.255655i
$154$	−32.8634			−2.64820
$155$		0			0
$156$		0			0
$157$	1.73205	−	1.73205i	0.138233	−	0.138233i	−0.634604	−	0.772837i	$-0.718837\pi$
$157$	1.73205	−	1.73205i	0.138233	−	0.138233i	0.772837	+	0.634604i	$0.218837\pi$
$158$	9.48683	−	9.48683i	0.754732	−	0.754732i
$159$		−	25.0000i		−	1.98263i
$160$		0			0
$161$		−	10.9545i		−	0.863332i
$162$	−19.0526	+	19.0526i	−1.49691	+	1.49691i
$163$	−13.8564	−	13.8564i	−1.08532	−	1.08532i	−0.996004	−	0.0893140i	$-0.971533\pi$
$163$	−13.8564	−	13.8564i	−1.08532	−	1.08532i	−0.0893140	−	0.996004i	$-0.528467\pi$
$164$		−	36.0000i		−	2.81113i
$165$		0			0
$166$		−	27.3861i		−	2.12558i
$167$	−1.58114	−	1.58114i	−0.122352	−	0.122352i	0.643279	−	0.765632i	$-0.277573\pi$
$167$	−1.58114	−	1.58114i	−0.122352	−	0.122352i	−0.765632	+	0.643279i	$0.777573\pi$
$168$	18.9737	−	18.9737i	1.46385	−	1.46385i
$169$			13.0000i			1.00000i
$170$		0			0
$171$	14.0000			1.07061
$172$	−18.9737	−	18.9737i	−1.44673	−	1.44673i
$173$	8.66025	+	8.66025i	0.658427	+	0.658427i	0.955008	−	0.296581i	$-0.0958464\pi$
$173$	8.66025	+	8.66025i	0.658427	+	0.658427i	−0.296581	+	0.955008i	$0.595846\pi$
$174$			30.0000i			2.27429i
$175$		0			0
$176$		−	21.9089i		−	1.65145i
$177$	4.74342	+	4.74342i	0.356537	+	0.356537i
$178$	9.48683	−	9.48683i	0.711068	−	0.711068i
$179$	16.4317			1.22816			0.614081	−	0.789243i	$-0.289527\pi$
$179$	16.4317			1.22816			0.614081	+	0.789243i	$0.289527\pi$
$180$		0			0
$181$			10.9545i			0.814238i	0.913375	+	0.407119i	$0.133467\pi$
$181$			10.9545i			0.814238i	−0.913375	+	0.407119i	$0.866533\pi$
$182$		0			0
$183$	−17.3205	−	17.3205i	−1.28037	−	1.28037i
$184$	21.9089			1.61515
$185$		0			0
$186$	30.0000	−	5.47723i	2.19971	−	0.401610i
$187$	−8.66025	+	8.66025i	−0.633300	+	0.633300i
$188$		0			0
$189$	5.47723			0.398410
$190$		0			0
$191$	−6.00000			−0.434145			−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000			−0.434145			−0.217072	+	0.976156i	$0.569651\pi$
$192$	−12.6491	−	12.6491i	−0.912871	−	0.912871i
$193$	−3.46410	−	3.46410i	−0.249351	−	0.249351i	0.571353	−	0.820704i	$-0.306419\pi$
$193$	−3.46410	−	3.46410i	−0.249351	−	0.249351i	−0.820704	+	0.571353i	$0.806419\pi$
$194$		−	36.0000i		−	2.58465i
$195$		0			0
$196$	4.00000			0.285714
$197$	−6.32456	−	6.32456i	−0.450606	−	0.450606i	0.444950	−	0.895556i	$-0.353222\pi$
$197$	−6.32456	−	6.32456i	−0.450606	−	0.450606i	−0.895556	+	0.444950i	$0.853222\pi$
$198$	−18.9737	+	18.9737i	−1.34840	+	1.34840i
$199$	16.4317			1.16481			0.582405	−	0.812899i	$-0.302112\pi$
$199$	16.4317			1.16481			0.582405	+	0.812899i	$0.302112\pi$
$200$		0			0
$201$		−	27.3861i		−	1.93167i
$202$	15.5885	−	15.5885i	1.09680	−	1.09680i
$203$	9.48683	−	9.48683i	0.665845	−	0.665845i
$204$		−	20.0000i		−	1.40028i
$205$		0			0
$206$	−12.0000			−0.836080
$207$	−6.32456	−	6.32456i	−0.439587	−	0.439587i
$208$		0			0
$209$	−38.3406			−2.65207
$210$		0			0
$211$	16.0000			1.10149			0.550743	−	0.834675i	$-0.314345\pi$
$211$	16.0000			1.10149			0.550743	+	0.834675i	$0.314345\pi$
$212$	−31.6228	−	31.6228i	−2.17186	−	2.17186i
$213$	−14.2302	+	14.2302i	−0.975041	+	0.975041i
$214$		−	36.0000i		−	2.46091i
$215$		0			0
$216$			10.9545i			0.745356i
$217$	−11.2189	−	7.75478i	−0.761587	−	0.526429i
$218$	−12.1244	−	12.1244i	−0.821165	−	0.821165i
$219$			15.0000i			1.01361i
$220$		0			0
$221$		0			0
$222$	25.9808	−	25.9808i	1.74371	−	1.74371i
$223$	−14.2302	+	14.2302i	−0.952928	+	0.952928i	−0.998941	−	0.0460129i	$-0.985348\pi$
$223$	−14.2302	+	14.2302i	−0.952928	+	0.952928i	0.0460129	+	0.998941i	$0.485348\pi$
$224$		0			0
$225$		0			0
$226$	−18.0000			−1.19734
$227$	8.66025	−	8.66025i	0.574801	−	0.574801i	−0.358665	−	0.933466i	$-0.616768\pi$
$227$	8.66025	−	8.66025i	0.574801	−	0.574801i	0.933466	+	0.358665i	$0.116768\pi$
$228$	44.2719	−	44.2719i	2.93198	−	2.93198i
$229$	−5.47723			−0.361945			−0.180973	−	0.983488i	$-0.557925\pi$
$229$	−5.47723			−0.361945			−0.180973	+	0.983488i	$0.557925\pi$
$230$		0			0
$231$	30.0000			1.97386
$232$	18.9737	+	18.9737i	1.24568	+	1.24568i
$233$	−5.19615	−	5.19615i	−0.340411	−	0.340411i	0.516111	−	0.856522i	$-0.327379\pi$
$233$	−5.19615	−	5.19615i	−0.340411	−	0.340411i	−0.856522	+	0.516111i	$0.827379\pi$
$234$		0			0
$235$		0			0
$236$	12.0000			0.781133
$237$	−8.66025	+	8.66025i	−0.562544	+	0.562544i
$238$	−9.48683	+	9.48683i	−0.614940	+	0.614940i
$239$	10.9545			0.708585			0.354292	−	0.935135i	$-0.384722\pi$
$239$	10.9545			0.708585			0.354292	+	0.935135i	$0.384722\pi$
$240$		0			0
$241$			5.47723i			0.352819i	0.984317	+	0.176410i	$0.0564483\pi$
$241$			5.47723i			0.352819i	−0.984317	+	0.176410i	$0.943552\pi$
$242$	32.9090	−	32.9090i	2.11547	−	2.11547i
$243$	12.6491	−	12.6491i	0.811441	−	0.811441i
$244$	−43.8178			−2.80515
$245$		0			0
$246$			49.2950i			3.14294i
$247$		0			0
$248$	15.5096	−	22.4378i	0.984858	−	1.42480i
$249$			25.0000i			1.58431i
$250$		0			0
$251$		−	10.9545i		−	0.691439i	−0.938338	−	0.345719i	$-0.887635\pi$
$251$		−	10.9545i		−	0.691439i	0.938338	−	0.345719i	$-0.112365\pi$
$252$	−13.8564	+	13.8564i	−0.872872	+	0.872872i
$253$	17.3205	+	17.3205i	1.08893	+	1.08893i
$254$		0			0
$255$		0			0
$256$	−32.0000			−2.00000
$257$	1.73205	−	1.73205i	0.108042	−	0.108042i	−0.651019	−	0.759061i	$-0.725658\pi$
$257$	1.73205	−	1.73205i	0.108042	−	0.108042i	0.759061	+	0.651019i	$0.225658\pi$
$258$	25.9808	+	25.9808i	1.61749	+	1.61749i
$259$	−16.4317			−1.02101
$260$		0			0
$261$		−	10.9545i		−	0.678064i
$262$	−5.19615	+	5.19615i	−0.321019	+	0.321019i
$263$	−1.58114	+	1.58114i	−0.0974972	+	0.0974972i	−0.754173	−	0.656676i	$-0.771962\pi$
$263$	−1.58114	+	1.58114i	−0.0974972	+	0.0974972i	0.656676	+	0.754173i	$0.271962\pi$
$264$			60.0000i			3.69274i
$265$		0			0
$266$	−42.0000			−2.57519
$267$	−8.66025	+	8.66025i	−0.529999	+	0.529999i
$268$	−34.6410	−	34.6410i	−2.11604	−	2.11604i
$269$	−5.47723			−0.333952			−0.166976	−	0.985961i	$-0.553400\pi$
$269$	−5.47723			−0.333952			−0.166976	+	0.985961i	$0.553400\pi$
$270$		0			0
$271$			27.3861i			1.66359i	0.555084	+	0.831794i	$0.312686\pi$
$271$			27.3861i			1.66359i	−0.555084	+	0.831794i	$0.687314\pi$
$272$	−6.32456	−	6.32456i	−0.383482	−	0.383482i
$273$		0			0
$274$	38.3406			2.31624
$275$		0			0
$276$	−40.0000			−2.40772
$277$	−4.74342	−	4.74342i	−0.285004	−	0.285004i	0.550097	−	0.835101i	$-0.314591\pi$
$277$	−4.74342	−	4.74342i	−0.285004	−	0.285004i	−0.835101	+	0.550097i	$0.814591\pi$
$278$	−28.4605	+	28.4605i	−1.70695	+	1.70695i
$279$	−10.9545	+	2.00000i	−0.655826	+	0.119737i
$280$		0			0
$281$	21.0000			1.25275			0.626377	−	0.779520i	$-0.284537\pi$
$281$	21.0000			1.25275			0.626377	+	0.779520i	$0.284537\pi$
$282$		0			0
$283$	−17.3205	−	17.3205i	−1.02960	−	1.02960i	−0.999548	−	0.0300489i	$-0.990434\pi$
$283$	−17.3205	−	17.3205i	−1.02960	−	1.02960i	−0.0300489	−	0.999548i	$-0.509566\pi$
$284$			36.0000i			2.13621i
$285$		0			0
$286$		0			0
$287$	15.5885	−	15.5885i	0.920158	−	0.920158i
$288$		0			0
$289$		−	12.0000i		−	0.705882i
$290$		0			0
$291$			32.8634i			1.92648i
$292$	18.9737	+	18.9737i	1.11035	+	1.11035i
$293$	−8.66025	−	8.66025i	−0.505937	−	0.505937i	0.407339	−	0.913277i	$-0.366457\pi$
$293$	−8.66025	−	8.66025i	−0.505937	−	0.505937i	−0.913277	+	0.407339i	$0.866457\pi$
$294$	−5.47723			−0.319438
$295$		0			0
$296$		−	32.8634i		−	1.91014i
$297$	−8.66025	+	8.66025i	−0.502519	+	0.502519i
$298$	−15.5885	−	15.5885i	−0.903015	−	0.903015i
$299$		0			0
$300$		0			0
$301$		−	16.4317i		−	0.947106i
$302$	28.4605	+	28.4605i	1.63772	+	1.63772i
$303$	−14.2302	+	14.2302i	−0.817506	+	0.817506i
$304$		−	28.0000i		−	1.60591i
$305$		0			0
$306$			10.9545i			0.626224i
$307$	−1.73205	+	1.73205i	−0.0988534	+	0.0988534i	−0.754804	−	0.655951i	$-0.772268\pi$
$307$	−1.73205	+	1.73205i	−0.0988534	+	0.0988534i	0.655951	+	0.754804i	$0.272268\pi$
$308$	37.9473	−	37.9473i	2.16225	−	2.16225i
$309$	10.9545			0.623177
$310$		0			0
$311$	−21.0000			−1.19080			−0.595400	−	0.803429i	$-0.703007\pi$
$311$	−21.0000			−1.19080			−0.595400	+	0.803429i	$0.703007\pi$
$312$		0			0
$313$	4.74342	−	4.74342i	0.268114	−	0.268114i	−0.560226	−	0.828340i	$-0.689286\pi$
$313$	4.74342	−	4.74342i	0.268114	−	0.268114i	0.828340	+	0.560226i	$0.189286\pi$
$314$			6.00000i			0.338600i
$315$		0			0
$316$			21.9089i			1.23247i
$317$	−24.2487	+	24.2487i	−1.36194	+	1.36194i	−0.490505	+	0.871438i	$0.663188\pi$
$317$	−24.2487	+	24.2487i	−1.36194	+	1.36194i	−0.871438	+	0.490505i	$0.836812\pi$
$318$	43.3013	+	43.3013i	2.42821	+	2.42821i
$319$			30.0000i			1.67968i
$320$		0			0
$321$			32.8634i			1.83425i
$322$	18.9737	+	18.9737i	1.05736	+	1.05736i
$323$	−11.0680	+	11.0680i	−0.615838	+	0.615838i
$324$		−	44.0000i		−	2.44444i
$325$		0			0
$326$	48.0000			2.65847
$327$	11.0680	+	11.0680i	0.612060	+	0.612060i
$328$	31.1769	+	31.1769i	1.72146	+	1.72146i
$329$		0			0
$330$		0			0
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	31.6228	+	31.6228i	1.73553	+	1.73553i
$333$	−9.48683	+	9.48683i	−0.519875	+	0.519875i
$334$	5.47723			0.299700
$335$		0			0
$336$			21.9089i			1.19523i
$337$	−14.2302	−	14.2302i	−0.775171	−	0.775171i	0.203834	−	0.979005i	$-0.434660\pi$
$337$	−14.2302	−	14.2302i	−0.775171	−	0.775171i	−0.979005	+	0.203834i	$0.934660\pi$
$338$	−22.5167	−	22.5167i	−1.22474	−	1.22474i
$339$	16.4317			0.892446
$340$		0			0
$341$	30.0000	−	5.47723i	1.62459	−	0.296608i
$342$	−24.2487	+	24.2487i	−1.31122	+	1.31122i
$343$	13.8564	+	13.8564i	0.748176	+	0.748176i
$344$	32.8634			1.77187
$345$		0			0
$346$	−30.0000			−1.61281
$347$	22.1359	+	22.1359i	1.18832	+	1.18832i	0.977532	+	0.210788i	$0.0676029\pi$
$347$	22.1359	+	22.1359i	1.18832	+	1.18832i	0.210788	+	0.977532i	$0.432397\pi$
$348$	−34.6410	−	34.6410i	−1.85695	−	1.85695i
$349$		−	1.00000i		−	0.0535288i	−0.999642	−	0.0267644i	$-0.991480\pi$
$349$		−	1.00000i		−	0.0535288i	0.999642	−	0.0267644i	$-0.00852039\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.32456	+	6.32456i	−0.336622	+	0.336622i	−0.855094	−	0.518472i	$-0.826501\pi$
$353$	−6.32456	+	6.32456i	−0.336622	+	0.336622i	0.518472	+	0.855094i	$0.326501\pi$
$354$	−16.4317			−0.873334
$355$		0			0
$356$			21.9089i			1.16117i
$357$	8.66025	−	8.66025i	0.458349	−	0.458349i
$358$	−28.4605	+	28.4605i	−1.50418	+	1.50418i
$359$		−	18.0000i		−	0.950004i	−0.879985	−	0.475002i	$-0.842447\pi$
$359$		−	18.0000i		−	0.950004i	0.879985	−	0.475002i	$-0.157553\pi$
$360$		0			0
$361$	−30.0000			−1.57895
$362$	−18.9737	−	18.9737i	−0.997234	−	0.997234i
$363$	−30.0416	+	30.0416i	−1.57678	+	1.57678i
$364$		0			0
$365$		0			0
$366$	60.0000			3.13625
$367$	−23.7171	−	23.7171i	−1.23802	−	1.23802i	−0.960808	−	0.277213i	$-0.910589\pi$
$367$	−23.7171	−	23.7171i	−1.23802	−	1.23802i	−0.277213	−	0.960808i	$-0.589411\pi$
$368$	−12.6491	+	12.6491i	−0.659380	+	0.659380i
$369$		−	18.0000i		−	0.937043i
$370$		0			0
$371$		−	27.3861i		−	1.42182i
$372$	−28.3165	+	40.9656i	−1.46814	+	2.12397i
$373$	−5.19615	−	5.19615i	−0.269047	−	0.269047i	0.559669	−	0.828716i	$-0.310928\pi$
$373$	−5.19615	−	5.19615i	−0.269047	−	0.269047i	−0.828716	+	0.559669i	$0.810928\pi$
$374$		−	30.0000i		−	1.55126i
$375$		0			0
$376$		0			0
$377$		0			0
$378$	−9.48683	+	9.48683i	−0.487950	+	0.487950i
$379$		−	11.0000i		−	0.565032i	−0.959263	−	0.282516i	$-0.908831\pi$
$379$		−	11.0000i		−	0.565032i	0.959263	−	0.282516i	$-0.0911690\pi$
$380$		0			0
$381$		0			0
$382$	10.3923	−	10.3923i	0.531717	−	0.531717i
$383$	−17.3925	+	17.3925i	−0.888717	+	0.888717i	−0.994400	−	0.105683i	$-0.966297\pi$
$383$	−17.3925	+	17.3925i	−0.888717	+	0.888717i	0.105683	+	0.994400i	$0.466297\pi$
$384$	43.8178			2.23607
$385$		0			0
$386$	12.0000			0.610784
$387$	−9.48683	−	9.48683i	−0.482243	−	0.482243i
$388$	41.5692	+	41.5692i	2.11036	+	2.11036i
$389$	−21.9089			−1.11083			−0.555413	−	0.831575i	$-0.687440\pi$
$389$	−21.9089			−1.11083			−0.555413	+	0.831575i	$0.687440\pi$
$390$		0			0
$391$	10.0000			0.505722
$392$	−3.46410	+	3.46410i	−0.174964	+	0.174964i
$393$	4.74342	−	4.74342i	0.239274	−	0.239274i
$394$	21.9089			1.10375
$395$		0			0
$396$		−	43.8178i		−	2.20193i
$397$	6.92820	−	6.92820i	0.347717	−	0.347717i	−0.511542	−	0.859258i	$-0.670925\pi$
$397$	6.92820	−	6.92820i	0.347717	−	0.347717i	0.859258	+	0.511542i	$0.170925\pi$
$398$	−28.4605	+	28.4605i	−1.42660	+	1.42660i
$399$	38.3406			1.91943
$400$		0			0
$401$		−	16.4317i		−	0.820559i	−0.911960	−	0.410279i	$-0.865431\pi$
$401$		−	16.4317i		−	0.820559i	0.911960	−	0.410279i	$-0.134569\pi$
$402$	47.4342	+	47.4342i	2.36580	+	2.36580i
$403$		0			0
$404$			36.0000i			1.79107i
$405$		0			0
$406$			32.8634i			1.63098i
$407$	25.9808	−	25.9808i	1.28782	−	1.28782i
$408$	17.3205	+	17.3205i	0.857493	+	0.857493i
$409$	5.47723			0.270831			0.135416	−	0.990789i	$-0.456763\pi$
$409$	5.47723			0.270831			0.135416	+	0.990789i	$0.456763\pi$
$410$		0			0
$411$	−35.0000			−1.72642
$412$	13.8564	−	13.8564i	0.682656	−	0.682656i
$413$	5.19615	+	5.19615i	0.255686	+	0.255686i
$414$	21.9089			1.07676
$415$		0			0
$416$		0			0
$417$	25.9808	−	25.9808i	1.27228	−	1.27228i
$418$	66.4078	−	66.4078i	3.24811	−	3.24811i
$419$			3.00000i			0.146560i	0.997311	+	0.0732798i	$0.0233466\pi$
$419$			3.00000i			0.146560i	−0.997311	+	0.0732798i	$0.976653\pi$
$420$		0			0
$421$	−1.00000			−0.0487370			−0.0243685	−	0.999703i	$-0.507758\pi$
$421$	−1.00000			−0.0487370			−0.0243685	+	0.999703i	$0.507758\pi$
$422$	−27.7128	+	27.7128i	−1.34904	+	1.34904i
$423$		0			0
$424$	54.7723			2.65998
$425$		0			0
$426$		−	49.2950i		−	2.38835i
$427$	−18.9737	−	18.9737i	−0.918200	−	0.918200i
$428$	41.5692	+	41.5692i	2.00932	+	2.00932i
$429$		0			0
$430$		0			0
$431$	−27.0000			−1.30054			−0.650272	−	0.759701i	$-0.725345\pi$
$431$	−27.0000			−1.30054			−0.650272	+	0.759701i	$0.725345\pi$
$432$	−6.32456	−	6.32456i	−0.304290	−	0.304290i
$433$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$433$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$434$	32.8634	−	6.00000i	1.57749	−	0.288009i
$435$		0			0
$436$	28.0000			1.34096
$437$	22.1359	+	22.1359i	1.05891	+	1.05891i
$438$	−25.9808	−	25.9808i	−1.24141	−	1.24141i
$439$		−	17.0000i		−	0.811366i	−0.914014	−	0.405683i	$-0.867034\pi$
$439$		−	17.0000i		−	0.811366i	0.914014	−	0.405683i	$-0.132966\pi$
$440$		0			0
$441$	2.00000			0.0952381
$442$		0			0
$443$	−3.46410	−	3.46410i	−0.164584	−	0.164584i	0.620010	−	0.784594i	$-0.287129\pi$
$443$	−3.46410	−	3.46410i	−0.164584	−	0.164584i	−0.784594	+	0.620010i	$0.787129\pi$
$444$			60.0000i			2.84747i
$445$		0			0
$446$		−	49.2950i		−	2.33419i
$447$	14.2302	+	14.2302i	0.673068	+	0.673068i
$448$	−13.8564	−	13.8564i	−0.654654	−	0.654654i
$449$	−21.9089			−1.03395			−0.516973	−	0.856002i	$-0.672941\pi$
$449$	−21.9089			−1.03395			−0.516973	+	0.856002i	$0.672941\pi$
$450$		0			0
$451$			49.2950i			2.32121i
$452$	20.7846	−	20.7846i	0.977626	−	0.977626i
$453$	−25.9808	−	25.9808i	−1.22068	−	1.22068i
$454$			30.0000i			1.40797i
$455$		0			0
$456$			76.6812i			3.59092i
$457$	−18.9737	−	18.9737i	−0.887551	−	0.887551i	0.106737	−	0.994287i	$-0.465960\pi$
$457$	−18.9737	−	18.9737i	−0.887551	−	0.887551i	−0.994287	+	0.106737i	$0.965960\pi$
$458$	9.48683	−	9.48683i	0.443291	−	0.443291i
$459$			5.00000i			0.233380i
$460$		0			0
$461$		−	38.3406i		−	1.78570i	−0.450355	−	0.892849i	$-0.648703\pi$
$461$		−	38.3406i		−	1.78570i	0.450355	−	0.892849i	$-0.351297\pi$
$462$	−51.9615	+	51.9615i	−2.41747	+	2.41747i
$463$	9.48683	−	9.48683i	0.440891	−	0.440891i	−0.451421	−	0.892311i	$-0.649083\pi$
$463$	9.48683	−	9.48683i	0.440891	−	0.440891i	0.892311	+	0.451421i	$0.149083\pi$
$464$	−21.9089			−1.01710
$465$		0			0
$466$	18.0000			0.833834
$467$	−24.2487	+	24.2487i	−1.12210	+	1.12210i	−0.130671	+	0.991426i	$0.541713\pi$
$467$	−24.2487	+	24.2487i	−1.12210	+	1.12210i	−0.991426	+	0.130671i	$0.958287\pi$
$468$		0			0
$469$		−	30.0000i		−	1.38527i
$470$		0			0
$471$		−	5.47723i		−	0.252377i
$472$	−10.3923	+	10.3923i	−0.478345	+	0.478345i
$473$	25.9808	+	25.9808i	1.19460	+	1.19460i
$474$		−	30.0000i		−	1.37795i
$475$		0			0
$476$		−	21.9089i		−	1.00419i
$477$	−15.8114	−	15.8114i	−0.723954	−	0.723954i
$478$	−18.9737	+	18.9737i	−0.867835	+	0.867835i
$479$			18.0000i			0.822441i	0.911536	+	0.411220i	$0.134897\pi$
$479$			18.0000i			0.822441i	−0.911536	+	0.411220i	$0.865103\pi$
$480$		0			0
$481$		0			0
$482$	−9.48683	−	9.48683i	−0.432113	−	0.432113i
$483$	−17.3205	−	17.3205i	−0.788110	−	0.788110i
$484$			76.0000i			3.45455i
$485$		0			0
$486$			43.8178i			1.98762i
$487$	14.2302	+	14.2302i	0.644834	+	0.644834i	0.951740	−	0.306906i	$-0.0992936\pi$
$487$	14.2302	+	14.2302i	0.644834	+	0.644834i	−0.306906	+	0.951740i	$0.599294\pi$
$488$	37.9473	−	37.9473i	1.71780	−	1.71780i
$489$	−43.8178			−1.98151
$490$		0			0
$491$		−	10.9545i		−	0.494367i	−0.968969	−	0.247184i	$-0.920495\pi$
$491$		−	10.9545i		−	0.494367i	0.968969	−	0.247184i	$-0.0795051\pi$
$492$	−56.9210	−	56.9210i	−2.56620	−	2.56620i
$493$	8.66025	+	8.66025i	0.390038	+	0.390038i
$494$		0			0
$495$		0			0
$496$	4.00000	+	21.9089i	0.179605	+	0.983739i
$497$	−15.5885	+	15.5885i	−0.699238	+	0.699238i
$498$	−43.3013	−	43.3013i	−1.94038	−	1.94038i
$499$	−5.47723			−0.245194			−0.122597	−	0.992457i	$-0.539122\pi$
$499$	−5.47723			−0.245194			−0.122597	+	0.992457i	$0.539122\pi$
$500$		0			0
$501$	−5.00000			−0.223384
$502$	18.9737	+	18.9737i	0.846836	+	0.846836i
$503$	12.1244	+	12.1244i	0.540598	+	0.540598i	0.923704	−	0.383106i	$-0.125146\pi$
$503$	12.1244	+	12.1244i	0.540598	+	0.540598i	−0.383106	+	0.923704i	$0.625146\pi$
$504$		−	24.0000i		−	1.06904i
$505$		0			0
$506$	−60.0000			−2.66733
$507$	20.5548	+	20.5548i	0.912871	+	0.912871i
$508$		0			0
$509$	−10.9545			−0.485548			−0.242774	−	0.970083i	$-0.578057\pi$
$509$	−10.9545			−0.485548			−0.242774	+	0.970083i	$0.578057\pi$
$510$		0			0
$511$			16.4317i			0.726895i
$512$	27.7128	−	27.7128i	1.22474	−	1.22474i
$513$	−11.0680	+	11.0680i	−0.488663	+	0.488663i
$514$			6.00000i			0.264649i
$515$		0			0
$516$	−60.0000			−2.64135
$517$		0			0
$518$	28.4605	−	28.4605i	1.25048	−	1.25048i
$519$	27.3861			1.20212
$520$		0			0
$521$	−27.0000			−1.18289			−0.591446	−	0.806345i	$-0.701443\pi$
$521$	−27.0000			−1.18289			−0.591446	+	0.806345i	$0.701443\pi$
$522$	18.9737	+	18.9737i	0.830455	+	0.830455i
$523$	23.7171	−	23.7171i	1.03708	−	1.03708i	0.0377899	−	0.999286i	$-0.487968\pi$
$523$	23.7171	−	23.7171i	1.03708	−	1.03708i	0.999286	−	0.0377899i	$-0.0120318\pi$
$524$		−	12.0000i		−	0.524222i
$525$		0			0
$526$		−	5.47723i		−	0.238818i
$527$	7.07912	−	10.2414i	0.308371	−	0.446122i
$528$	−34.6410	−	34.6410i	−1.50756	−	1.50756i
$529$			3.00000i			0.130435i
$530$		0			0
$531$	6.00000			0.260378
$532$	48.4974	−	48.4974i	2.10263	−	2.10263i
$533$		0			0
$534$		−	30.0000i		−	1.29823i
$535$		0			0
$536$	60.0000			2.59161
$537$	25.9808	−	25.9808i	1.12115	−	1.12115i
$538$	9.48683	−	9.48683i	0.409006	−	0.409006i
$539$	−5.47723			−0.235921
$540$		0			0
$541$	−4.00000			−0.171973			−0.0859867	−	0.996296i	$-0.527404\pi$
$541$	−4.00000			−0.171973			−0.0859867	+	0.996296i	$0.527404\pi$
$542$	−47.4342	−	47.4342i	−2.03747	−	2.03747i
$543$	17.3205	+	17.3205i	0.743294	+	0.743294i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−15.5885	+	15.5885i	−0.666514	+	0.666514i	−0.956907	−	0.290393i	$-0.906214\pi$
$547$	−15.5885	+	15.5885i	−0.666514	+	0.666514i	0.290393	+	0.956907i	$0.406214\pi$
$548$	−44.2719	+	44.2719i	−1.89120	+	1.89120i
$549$	−21.9089			−0.935049
$550$		0			0
$551$			38.3406i			1.63336i
$552$	34.6410	−	34.6410i	1.47442	−	1.47442i
$553$	−9.48683	+	9.48683i	−0.403421	+	0.403421i
$554$	16.4317			0.698115
$555$		0			0
$556$		−	65.7267i		−	2.78743i
$557$	−3.16228	−	3.16228i	−0.133990	−	0.133990i	0.636931	−	0.770921i	$-0.280204\pi$
$557$	−3.16228	−	3.16228i	−0.133990	−	0.133990i	−0.770921	+	0.636931i	$0.780204\pi$
$558$	15.5096	−	22.4378i	0.656572	−	0.949866i
$559$		0			0
$560$		0			0
$561$			27.3861i			1.15624i
$562$	−36.3731	+	36.3731i	−1.53431	+	1.53431i
$563$	5.19615	+	5.19615i	0.218992	+	0.218992i	0.808073	−	0.589082i	$-0.200510\pi$
$563$	5.19615	+	5.19615i	0.218992	+	0.218992i	−0.589082	+	0.808073i	$0.700510\pi$
$564$		0			0
$565$		0			0
$566$	60.0000			2.52199
$567$	19.0526	−	19.0526i	0.800132	−	0.800132i
$568$	−31.1769	−	31.1769i	−1.30815	−	1.30815i
$569$	−21.9089			−0.918469			−0.459234	−	0.888315i	$-0.651876\pi$
$569$	−21.9089			−0.918469			−0.459234	+	0.888315i	$0.651876\pi$
$570$		0			0
$571$		−	5.47723i		−	0.229215i	−0.993411	−	0.114607i	$-0.963439\pi$
$571$		−	5.47723i		−	0.229215i	0.993411	−	0.114607i	$-0.0365610\pi$
$572$		0			0
$573$	−9.48683	+	9.48683i	−0.396318	+	0.396318i
$574$			54.0000i			2.25392i
$575$		0			0
$576$	−16.0000			−0.666667
$577$	8.66025	−	8.66025i	0.360531	−	0.360531i	−0.503477	−	0.864008i	$-0.667946\pi$
$577$	8.66025	−	8.66025i	0.360531	−	0.360531i	0.864008	+	0.503477i	$0.167946\pi$
$578$	20.7846	+	20.7846i	0.864526	+	0.864526i
$579$	−10.9545			−0.455251
$580$		0			0
$581$			27.3861i			1.13617i
$582$	−56.9210	−	56.9210i	−2.35945	−	2.35945i
$583$	43.3013	+	43.3013i	1.79336	+	1.79336i
$584$	−32.8634			−1.35990
$585$		0			0
$586$	30.0000			1.23929
$587$	−22.1359	−	22.1359i	−0.913648	−	0.913648i	0.0829090	−	0.996557i	$-0.473579\pi$
$587$	−22.1359	−	22.1359i	−0.913648	−	0.913648i	−0.996557	+	0.0829090i	$0.973579\pi$
$588$	6.32456	−	6.32456i	0.260820	−	0.260820i
$589$	38.3406	−	7.00000i	1.57980	−	0.288430i
$590$		0			0
$591$	−20.0000			−0.822690
$592$	18.9737	+	18.9737i	0.779813	+	0.779813i
$593$	−13.8564	−	13.8564i	−0.569014	−	0.569014i	0.362838	−	0.931852i	$-0.381808\pi$
$593$	−13.8564	−	13.8564i	−0.569014	−	0.569014i	−0.931852	+	0.362838i	$0.881808\pi$
$594$		−	30.0000i		−	1.23091i
$595$		0			0
$596$	36.0000			1.47462
$597$	25.9808	−	25.9808i	1.06332	−	1.06332i
$598$		0			0
$599$			12.0000i			0.490307i	0.969484	+	0.245153i	$0.0788383\pi$
$599$			12.0000i			0.490307i	−0.969484	+	0.245153i	$0.921162\pi$
$600$		0			0
$601$			5.47723i			0.223421i	0.993741	+	0.111710i	$0.0356329\pi$
$601$			5.47723i			0.223421i	−0.993741	+	0.111710i	$0.964367\pi$
$602$	28.4605	+	28.4605i	1.15996	+	1.15996i
$603$	−17.3205	−	17.3205i	−0.705346	−	0.705346i
$604$	−65.7267			−2.67438
$605$		0			0
$606$		−	49.2950i		−	2.00247i
$607$	25.9808	−	25.9808i	1.05453	−	1.05453i	0.0561015	−	0.998425i	$-0.482133\pi$
$607$	25.9808	−	25.9808i	1.05453	−	1.05453i	0.998425	−	0.0561015i	$-0.0178671\pi$
$608$		0			0
$609$		−	30.0000i		−	1.21566i
$610$		0			0
$611$		0			0
$612$	−12.6491	−	12.6491i	−0.511310	−	0.511310i
$613$	23.7171	−	23.7171i	0.957924	−	0.957924i	−0.0412259	−	0.999150i	$-0.513126\pi$
$613$	23.7171	−	23.7171i	0.957924	−	0.957924i	0.999150	+	0.0412259i	$0.0131263\pi$
$614$		−	6.00000i		−	0.242140i
$615$		0			0
$616$			65.7267i			2.64820i
$617$	−8.66025	+	8.66025i	−0.348649	+	0.348649i	−0.859606	−	0.510957i	$-0.829291\pi$
$617$	−8.66025	+	8.66025i	−0.348649	+	0.348649i	0.510957	+	0.859606i	$0.329291\pi$
$618$	−18.9737	+	18.9737i	−0.763233	+	0.763233i
$619$	32.8634			1.32089			0.660445	−	0.750875i	$-0.270368\pi$
$619$	32.8634			1.32089			0.660445	+	0.750875i	$0.270368\pi$
$620$		0			0
$621$	10.0000			0.401286
$622$	36.3731	−	36.3731i	1.45843	−	1.45843i
$623$	−9.48683	+	9.48683i	−0.380082	+	0.380082i
$624$		0			0
$625$		0			0
$626$			16.4317i			0.656742i
$627$	−60.6218	+	60.6218i	−2.42100	+	2.42100i
$628$	−6.92820	−	6.92820i	−0.276465	−	0.276465i
$629$		−	15.0000i		−	0.598089i
$630$		0			0
$631$			21.9089i			0.872180i	0.899903	+	0.436090i	$0.143637\pi$
$631$			21.9089i			0.872180i	−0.899903	+	0.436090i	$0.856363\pi$
$632$	−18.9737	−	18.9737i	−0.754732	−	0.754732i
$633$	25.2982	−	25.2982i	1.00551	−	1.00551i
$634$		−	84.0000i		−	3.33607i
$635$		0			0
$636$	−100.000			−3.96526
$637$		0			0
$638$	−51.9615	−	51.9615i	−2.05718	−	2.05718i
$639$			18.0000i			0.712069i
$640$		0			0
$641$			32.8634i			1.29802i	0.760778	+	0.649012i	$0.224818\pi$
$641$			32.8634i			1.29802i	−0.760778	+	0.649012i	$0.775182\pi$
$642$	−56.9210	−	56.9210i	−2.24649	−	2.24649i
$643$	33.2039	−	33.2039i	1.30943	−	1.30943i	0.387612	−	0.921823i	$-0.373300\pi$
$643$	33.2039	−	33.2039i	1.30943	−	1.30943i	0.921823	−	0.387612i	$-0.126700\pi$
$644$	−43.8178			−1.72666
$645$		0			0
$646$		−	38.3406i		−	1.50849i
$647$	−1.58114	−	1.58114i	−0.0621610	−	0.0621610i	0.675343	−	0.737504i	$-0.263996\pi$
$647$	−1.58114	−	1.58114i	−0.0621610	−	0.0621610i	−0.737504	+	0.675343i	$0.763996\pi$
$648$	38.1051	+	38.1051i	1.49691	+	1.49691i
$649$	−16.4317			−0.645000
$650$		0			0
$651$	−30.0000	+	5.47723i	−1.17579	+	0.214669i
$652$	−55.4256	+	55.4256i	−2.17064	+	2.17064i
$653$	−17.3205	−	17.3205i	−0.677804	−	0.677804i	0.281699	−	0.959503i	$-0.409102\pi$
$653$	−17.3205	−	17.3205i	−0.677804	−	0.677804i	−0.959503	+	0.281699i	$0.909102\pi$
$654$	−38.3406			−1.49924
$655$		0			0
$656$	−36.0000			−1.40556
$657$	9.48683	+	9.48683i	0.370117	+	0.370117i
$658$		0			0
$659$		−	33.0000i		−	1.28550i	−0.766077	−	0.642749i	$-0.777794\pi$
$659$		−	33.0000i		−	1.28550i	0.766077	−	0.642749i	$-0.222206\pi$
$660$		0			0
$661$	41.0000			1.59472			0.797358	−	0.603507i	$-0.206231\pi$
$661$	41.0000			1.59472			0.797358	+	0.603507i	$0.206231\pi$
$662$		0			0
$663$		0			0
$664$	−54.7723			−2.12558
$665$		0			0
$666$		−	32.8634i		−	1.27343i
$667$	17.3205	−	17.3205i	0.670653	−	0.670653i
$668$	−6.32456	+	6.32456i	−0.244704	+	0.244704i
$669$			45.0000i			1.73980i
$670$		0			0
$671$	60.0000			2.31627
$672$		0			0
$673$	4.74342	−	4.74342i	0.182845	−	0.182845i	−0.609749	−	0.792594i	$-0.708730\pi$
$673$	4.74342	−	4.74342i	0.182845	−	0.182845i	0.792594	+	0.609749i	$0.208730\pi$
$674$	49.2950			1.89877
$675$		0			0
$676$	52.0000			2.00000
$677$	1.58114	+	1.58114i	0.0607681	+	0.0607681i	0.736838	−	0.676070i	$-0.236318\pi$
$677$	1.58114	+	1.58114i	0.0607681	+	0.0607681i	−0.676070	+	0.736838i	$0.736318\pi$
$678$	−28.4605	+	28.4605i	−1.09302	+	1.09302i
$679$			36.0000i			1.38155i
$680$		0			0
$681$		−	27.3861i		−	1.04944i
$682$	−42.4747	+	61.4484i	−1.62644	+	2.35298i
$683$	22.5167	+	22.5167i	0.861576	+	0.861576i	0.991521	−	0.129945i	$-0.0414801\pi$
$683$	22.5167	+	22.5167i	0.861576	+	0.861576i	−0.129945	+	0.991521i	$0.541480\pi$
$684$		−	56.0000i		−	2.14121i
$685$		0			0
$686$	−48.0000			−1.83265
$687$	−8.66025	+	8.66025i	−0.330409	+	0.330409i
$688$	−18.9737	+	18.9737i	−0.723364	+	0.723364i
$689$		0			0
$690$		0			0
$691$	19.0000			0.722794			0.361397	−	0.932412i	$-0.382300\pi$
$691$	19.0000			0.722794			0.361397	+	0.932412i	$0.382300\pi$
$692$	34.6410	−	34.6410i	1.31685	−	1.31685i
$693$	18.9737	−	18.9737i	0.720750	−	0.720750i
$694$	−76.6812			−2.91078
$695$		0			0
$696$	60.0000			2.27429
$697$	14.2302	+	14.2302i	0.539009	+	0.539009i
$698$	1.73205	+	1.73205i	0.0655591	+	0.0655591i
$699$	−16.4317			−0.621503
$700$		0			0
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$		0			0
$703$	33.2039	−	33.2039i	1.25231	−	1.25231i
$704$	43.8178			1.65145
$705$		0			0
$706$		−	21.9089i		−	0.824552i
$707$	−15.5885	+	15.5885i	−0.586264	+	0.586264i
$708$	18.9737	−	18.9737i	0.713074	−	0.713074i
$709$		0			0			−	1.00000i	$-0.5\pi$
$709$		0			0				1.00000i	$0.5\pi$
$710$		0			0
$711$			10.9545i			0.410824i
$712$	−18.9737	−	18.9737i	−0.711068	−	0.711068i
$713$	−20.4828	−	14.1582i	−0.767086	−	0.530230i
$714$			30.0000i			1.12272i
$715$		0			0
$716$		−	65.7267i		−	2.45632i
$717$	17.3205	−	17.3205i	0.646846	−	0.646846i
$718$	31.1769	+	31.1769i	1.16351	+	1.16351i
$719$	−10.9545			−0.408532			−0.204266	−	0.978915i	$-0.565481\pi$
$719$	−10.9545			−0.408532			−0.204266	+	0.978915i	$0.565481\pi$
$720$		0			0
$721$	12.0000			0.446903
$722$	51.9615	−	51.9615i	1.93381	−	1.93381i
$723$	8.66025	+	8.66025i	0.322078	+	0.322078i
$724$	43.8178			1.62848
$725$		0			0
$726$		−	104.067i		−	3.86230i
$727$	24.2487	−	24.2487i	0.899335	−	0.899335i	−0.0960423	−	0.995377i	$-0.530618\pi$
$727$	24.2487	−	24.2487i	0.899335	−	0.899335i	0.995377	+	0.0960423i	$0.0306184\pi$
$728$		0			0
$729$		−	7.00000i		−	0.259259i
$730$		0			0
$731$	15.0000			0.554795
$732$	−69.2820	+	69.2820i	−2.56074	+	2.56074i
$733$	−3.46410	−	3.46410i	−0.127950	−	0.127950i	0.640232	−	0.768182i	$-0.278838\pi$
$733$	−3.46410	−	3.46410i	−0.127950	−	0.127950i	−0.768182	+	0.640232i	$0.778838\pi$
$734$	82.1584			3.03252
$735$		0			0
$736$		0			0
$737$	47.4342	+	47.4342i	1.74726	+	1.74726i
$738$	31.1769	+	31.1769i	1.14764	+	1.14764i
$739$	−43.8178			−1.61186			−0.805932	−	0.592008i	$-0.798335\pi$
$739$	−43.8178			−1.61186			−0.805932	+	0.592008i	$0.798335\pi$
$740$		0			0
$741$		0			0
$742$	47.4342	+	47.4342i	1.74136	+	1.74136i
$743$	−20.5548	+	20.5548i	−0.754083	+	0.754083i	−0.975238	−	0.221156i	$-0.929017\pi$
$743$	−20.5548	+	20.5548i	−0.754083	+	0.754083i	0.221156	+	0.975238i	$0.429017\pi$
$744$	−10.9545	−	60.0000i	−0.401610	−	2.19971i
$745$		0			0
$746$	18.0000			0.659027
$747$	15.8114	+	15.8114i	0.578508	+	0.578508i
$748$	34.6410	+	34.6410i	1.26660	+	1.26660i
$749$			36.0000i			1.31541i
$750$		0			0
$751$	−14.0000			−0.510867			−0.255434	−	0.966827i	$-0.582218\pi$
$751$	−14.0000			−0.510867			−0.255434	+	0.966827i	$0.582218\pi$
$752$		0			0
$753$	−17.3205	−	17.3205i	−0.631194	−	0.631194i
$754$		0			0
$755$		0			0
$756$		−	21.9089i		−	0.796819i
$757$	−14.2302	−	14.2302i	−0.517207	−	0.517207i	0.399518	−	0.916725i	$-0.369177\pi$
$757$	−14.2302	−	14.2302i	−0.517207	−	0.517207i	−0.916725	+	0.399518i	$0.869177\pi$
$758$	19.0526	+	19.0526i	0.692020	+	0.692020i
$759$	54.7723			1.98811
$760$		0			0
$761$			32.8634i			1.19130i	0.803246	+	0.595648i	$0.203105\pi$
$761$			32.8634i			1.19130i	−0.803246	+	0.595648i	$0.796895\pi$
$762$		0			0
$763$	12.1244	+	12.1244i	0.438931	+	0.438931i
$764$			24.0000i			0.868290i
$765$		0			0
$766$		−	60.2495i		−	2.17690i
$767$		0			0
$768$	−50.5964	+	50.5964i	−1.82574	+	1.82574i
$769$		−	47.0000i		−	1.69486i	−0.530904	−	0.847432i	$-0.678148\pi$
$769$		−	47.0000i		−	1.69486i	0.530904	−	0.847432i	$-0.321852\pi$
$770$		0			0
$771$		−	5.47723i		−	0.197257i
$772$	−13.8564	+	13.8564i	−0.498703	+	0.498703i
$773$	22.1359	−	22.1359i	0.796175	−	0.796175i	−0.186315	−	0.982490i	$-0.559655\pi$
$773$	22.1359	−	22.1359i	0.796175	−	0.796175i	0.982490	+	0.186315i	$0.0596546\pi$
$774$	32.8634			1.18125
$775$		0			0
$776$	−72.0000			−2.58465
$777$	−25.9808	+	25.9808i	−0.932055	+	0.932055i
$778$	37.9473	−	37.9473i	1.36048	−	1.36048i
$779$			63.0000i			2.25721i
$780$		0			0
$781$		−	49.2950i		−	1.76391i
$782$	−17.3205	+	17.3205i	−0.619380	+	0.619380i
$783$	8.66025	+	8.66025i	0.309492	+	0.309492i
$784$		−	4.00000i		−	0.142857i
$785$		0			0
$786$			16.4317i			0.586098i
$787$	9.48683	+	9.48683i	0.338169	+	0.338169i	0.855678	−	0.517509i	$-0.173141\pi$
$787$	9.48683	+	9.48683i	0.338169	+	0.338169i	−0.517509	+	0.855678i	$0.673141\pi$
$788$	−25.2982	+	25.2982i	−0.901212	+	0.901212i
$789$			5.00000i			0.178005i
$790$		0			0
$791$	18.0000			0.640006
$792$	37.9473	+	37.9473i	1.34840	+	1.34840i
$793$		0			0
$794$			24.0000i			0.851728i
$795$		0			0
$796$		−	65.7267i		−	2.32962i
$797$	−3.16228	−	3.16228i	−0.112014	−	0.112014i	0.648878	−	0.760892i	$-0.275238\pi$
$797$	−3.16228	−	3.16228i	−0.112014	−	0.112014i	−0.760892	+	0.648878i	$0.775238\pi$
$798$	−66.4078	+	66.4078i	−2.35081	+	2.35081i
$799$		0			0
$800$		0			0
$801$			10.9545i			0.387056i
$802$	28.4605	+	28.4605i	1.00498	+	1.00498i
$803$	−25.9808	−	25.9808i	−0.916841	−	0.916841i
$804$	−109.545			−3.86334
$805$		0			0
$806$		0			0
$807$	−8.66025	+	8.66025i	−0.304855	+	0.304855i
$808$	−31.1769	−	31.1769i	−1.09680	−	1.09680i
$809$	−16.4317			−0.577707			−0.288853	−	0.957373i	$-0.593274\pi$
$809$	−16.4317			−0.577707			−0.288853	+	0.957373i	$0.593274\pi$
$810$		0			0
$811$	−13.0000			−0.456492			−0.228246	−	0.973604i	$-0.573299\pi$
$811$	−13.0000			−0.456492			−0.228246	+	0.973604i	$0.573299\pi$
$812$	−37.9473	−	37.9473i	−1.33169	−	1.33169i
$813$	43.3013	+	43.3013i	1.51864	+	1.51864i
$814$			90.0000i			3.15450i
$815$		0			0
$816$	−20.0000			−0.700140
$817$	33.2039	+	33.2039i	1.16166	+	1.16166i
$818$	−9.48683	+	9.48683i	−0.331699	+	0.331699i
$819$		0			0
$820$		0			0
$821$		−	49.2950i		−	1.72041i	−0.509950	−	0.860204i	$-0.670336\pi$
$821$		−	49.2950i		−	1.72041i	0.509950	−	0.860204i	$-0.329664\pi$
$822$	60.6218	−	60.6218i	2.11443	−	2.11443i
$823$	−14.2302	+	14.2302i	−0.496035	+	0.496035i	−0.910201	−	0.414166i	$-0.864073\pi$
$823$	−14.2302	+	14.2302i	−0.496035	+	0.496035i	0.414166	+	0.910201i	$0.364073\pi$
$824$			24.0000i			0.836080i
$825$		0			0
$826$	−18.0000			−0.626300
$827$	7.90569	+	7.90569i	0.274908	+	0.274908i	0.831072	−	0.556164i	$-0.187728\pi$
$827$	7.90569	+	7.90569i	0.274908	+	0.274908i	−0.556164	+	0.831072i	$0.687728\pi$
$828$	−25.2982	+	25.2982i	−0.879174	+	0.879174i
$829$	−32.8634			−1.14139			−0.570696	−	0.821162i	$-0.693326\pi$
$829$	−32.8634			−1.14139			−0.570696	+	0.821162i	$0.693326\pi$
$830$		0			0
$831$	−15.0000			−0.520344
$832$		0			0
$833$	−1.58114	+	1.58114i	−0.0547832	+	0.0547832i
$834$			90.0000i			3.11645i
$835$		0			0
$836$			153.362i			5.30415i
$837$	7.07912	−	10.2414i	0.244690	−	0.353994i
$838$	−5.19615	−	5.19615i	−0.179498	−	0.179498i
$839$		−	39.0000i		−	1.34643i	−0.739447	−	0.673215i	$-0.764913\pi$
$839$		−	39.0000i		−	1.34643i	0.739447	−	0.673215i	$-0.235087\pi$
$840$		0			0
$841$	1.00000			0.0344828
$842$	1.73205	−	1.73205i	0.0596904	−	0.0596904i
$843$	33.2039	−	33.2039i	1.14360	−	1.14360i
$844$		−	64.0000i		−	2.20297i
$845$		0			0
$846$		0			0
$847$	−32.9090	+	32.9090i	−1.13077	+	1.13077i
$848$	−31.6228	+	31.6228i	−1.08593	+	1.08593i
$849$	−54.7723			−1.87978
$850$		0			0
$851$	−30.0000			−1.02839
$852$	56.9210	+	56.9210i	1.95008	+	1.95008i
$853$	−17.3205	−	17.3205i	−0.593043	−	0.593043i	0.345409	−	0.938452i	$-0.387740\pi$
$853$	−17.3205	−	17.3205i	−0.593043	−	0.593043i	−0.938452	+	0.345409i	$0.887740\pi$
$854$	65.7267			2.24912
$855$		0			0
$856$	−72.0000			−2.46091
$857$	−8.66025	+	8.66025i	−0.295829	+	0.295829i	−0.839378	−	0.543549i	$-0.817080\pi$
$857$	−8.66025	+	8.66025i	−0.295829	+	0.295829i	0.543549	+	0.839378i	$0.317080\pi$
$858$		0			0
$859$	38.3406			1.30816			0.654082	−	0.756424i	$-0.273055\pi$
$859$	38.3406			1.30816			0.654082	+	0.756424i	$0.273055\pi$
$860$		0			0
$861$		−	49.2950i		−	1.67997i
$862$	46.7654	−	46.7654i	1.59283	−	1.59283i
$863$	−30.0416	+	30.0416i	−1.02263	+	1.02263i	−0.0228913	+	0.999738i	$0.507287\pi$
$863$	−30.0416	+	30.0416i	−1.02263	+	1.02263i	−0.999738	+	0.0228913i	$0.992713\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−18.9737	−	18.9737i	−0.644379	−	0.644379i
$868$	−31.0191	+	44.8755i	−1.05286	+	1.52317i
$869$		−	30.0000i		−	1.01768i
$870$		0			0
$871$		0			0
$872$	−24.2487	+	24.2487i	−0.821165	+	0.821165i
$873$	20.7846	+	20.7846i	0.703452	+	0.703452i
$874$	−76.6812			−2.59378
$875$		0			0
$876$	60.0000			2.02721
$877$	−36.3731	+	36.3731i	−1.22823	+	1.22823i	−0.263599	+	0.964632i	$0.584909\pi$
$877$	−36.3731	+	36.3731i	−1.22823	+	1.22823i	−0.964632	+	0.263599i	$0.915091\pi$
$878$	29.4449	+	29.4449i	0.993716	+	0.993716i
$879$	−27.3861			−0.923711
$880$		0			0
$881$			38.3406i			1.29173i	0.763453	+	0.645863i	$0.223502\pi$
$881$			38.3406i			1.29173i	−0.763453	+	0.645863i	$0.776498\pi$
$882$	−3.46410	+	3.46410i	−0.116642	+	0.116642i
$883$	−23.7171	+	23.7171i	−0.798143	+	0.798143i	−0.982803	−	0.184659i	$-0.940882\pi$
$883$	−23.7171	+	23.7171i	−0.798143	+	0.798143i	0.184659	+	0.982803i	$0.440882\pi$
$884$		0			0
$885$		0			0
$886$	12.0000			0.403148
$887$	−19.0526	+	19.0526i	−0.639722	+	0.639722i	−0.950487	−	0.310765i	$-0.899415\pi$
$887$	−19.0526	+	19.0526i	−0.639722	+	0.639722i	0.310765	+	0.950487i	$0.399415\pi$
$888$	−51.9615	−	51.9615i	−1.74371	−	1.74371i
$889$		0			0
$890$		0			0
$891$			60.2495i			2.01843i
$892$	56.9210	+	56.9210i	1.90586	+	1.90586i
$893$		0			0
$894$	−49.2950			−1.64867
$895$		0			0
$896$	48.0000			1.60357
$897$		0			0
$898$	37.9473	−	37.9473i	1.26632	−	1.26632i
$899$	−5.47723	−	30.0000i	−0.182676	−	1.00056i
$900$		0			0
$901$	25.0000			0.832871
$902$	−85.3815	−	85.3815i	−2.84289	−	2.84289i
$903$	−25.9808	−	25.9808i	−0.864586	−	0.864586i
$904$			36.0000i			1.19734i
$905$		0			0
$906$	90.0000			2.99005
$907$	−6.92820	+	6.92820i	−0.230047	+	0.230047i	−0.812712	−	0.582665i	$-0.802010\pi$
$907$	−6.92820	+	6.92820i	−0.230047	+	0.230047i	0.582665	+	0.812712i	$0.302010\pi$
$908$	−34.6410	−	34.6410i	−1.14960	−	1.14960i
$909$			18.0000i			0.597022i
$910$		0			0
$911$			5.47723i			0.181469i	0.995875	+	0.0907343i	$0.0289214\pi$
$911$			5.47723i			0.181469i	−0.995875	+	0.0907343i	$0.971079\pi$
$912$	−44.2719	−	44.2719i	−1.46599	−	1.46599i
$913$	−43.3013	−	43.3013i	−1.43306	−	1.43306i
$914$	65.7267			2.17405
$915$		0			0
$916$			21.9089i			0.723891i
$917$	5.19615	−	5.19615i	0.171592	−	0.171592i
$918$	−8.66025	−	8.66025i	−0.285831	−	0.285831i
$919$			31.0000i			1.02260i	0.859404	+	0.511298i	$0.170835\pi$
$919$			31.0000i			1.02260i	−0.859404	+	0.511298i	$0.829165\pi$
$920$		0			0
$921$			5.47723i			0.180481i
$922$	66.4078	+	66.4078i	2.18703	+	2.18703i
$923$		0			0
$924$		−	120.000i		−	3.94771i
$925$		0			0
$926$			32.8634i			1.07996i
$927$	6.92820	−	6.92820i	0.227552	−	0.227552i
$928$		0			0
$929$	10.9545			0.359404			0.179702	−	0.983721i	$-0.442487\pi$
$929$	10.9545			0.359404			0.179702	+	0.983721i	$0.442487\pi$
$930$		0			0
$931$	−7.00000			−0.229416
$932$	−20.7846	+	20.7846i	−0.680823	+	0.680823i
$933$	−33.2039	+	33.2039i	−1.08705	+	1.08705i
$934$		−	84.0000i		−	2.74856i
$935$		0			0
$936$		0			0
$937$	8.66025	−	8.66025i	0.282918	−	0.282918i	−0.551354	−	0.834272i	$-0.685888\pi$
$937$	8.66025	−	8.66025i	0.282918	−	0.282918i	0.834272	+	0.551354i	$0.185888\pi$
$938$	51.9615	+	51.9615i	1.69660	+	1.69660i
$939$		−	15.0000i		−	0.489506i
$940$		0			0
$941$		0			0		1.00000			$0$
$941$		0			0		−1.00000			$\pi$
$942$	9.48683	+	9.48683i	0.309098	+	0.309098i
$943$	28.4605	−	28.4605i	0.926801	−	0.926801i
$944$		−	12.0000i		−	0.390567i
$945$		0			0
$946$	−90.0000			−2.92615
$947$	−17.3925	−	17.3925i	−0.565181	−	0.565181i	0.365593	−	0.930775i	$-0.380866\pi$
$947$	−17.3925	−	17.3925i	−0.565181	−	0.565181i	−0.930775	+	0.365593i	$0.880866\pi$
$948$	34.6410	+	34.6410i	1.12509	+	1.12509i
$949$		0			0
$950$		0			0
$951$			76.6812i			2.48656i
$952$	18.9737	+	18.9737i	0.614940	+	0.614940i
$953$	1.58114	−	1.58114i	0.0512181	−	0.0512181i	−0.681034	−	0.732252i	$-0.738469\pi$
$953$	1.58114	−	1.58114i	0.0512181	−	0.0512181i	0.732252	+	0.681034i	$0.238469\pi$
$954$	54.7723			1.77332
$955$		0			0
$956$		−	43.8178i		−	1.41717i
$957$	47.4342	+	47.4342i	1.53333	+	1.53333i
$958$	−31.1769	−	31.1769i	−1.00728	−	1.00728i
$959$	−38.3406			−1.23808
$960$		0			0
$961$	−29.0000	+	10.9545i	−0.935484	+	0.353369i
$962$		0			0
$963$	20.7846	+	20.7846i	0.669775	+	0.669775i
$964$	21.9089			0.705638
$965$		0			0
$966$	60.0000			1.93047
$967$	−37.9473	−	37.9473i	−1.22030	−	1.22030i	−0.967524	−	0.252780i	$-0.918655\pi$
$967$	−37.9473	−	37.9473i	−1.22030	−	1.22030i	−0.252780	−	0.967524i	$-0.581345\pi$
$968$	−65.8179	−	65.8179i	−2.11547	−	2.11547i
$969$			35.0000i			1.12436i
$970$		0			0
$971$	−33.0000			−1.05902			−0.529510	−	0.848304i	$-0.677624\pi$
$971$	−33.0000			−1.05902			−0.529510	+	0.848304i	$0.677624\pi$
$972$	−50.5964	−	50.5964i	−1.62288	−	1.62288i
$973$	28.4605	−	28.4605i	0.912402	−	0.912402i
$974$	−49.2950			−1.57951
$975$		0			0
$976$			43.8178i			1.40257i
$977$	15.5885	−	15.5885i	0.498719	−	0.498719i	−0.412320	−	0.911039i	$-0.635281\pi$
$977$	15.5885	−	15.5885i	0.498719	−	0.498719i	0.911039	+	0.412320i	$0.135281\pi$
$978$	75.8947	−	75.8947i	2.42684	−	2.42684i
$979$		−	30.0000i		−	0.958804i
$980$		0			0
$981$	14.0000			0.446986
$982$	18.9737	+	18.9737i	0.605474	+	0.605474i
$983$	34.7851	−	34.7851i	1.10947	−	1.10947i	0.116251	−	0.993220i	$-0.462912\pi$
$983$	34.7851	−	34.7851i	1.10947	−	1.10947i	0.993220	−	0.116251i	$-0.0370877\pi$
$984$	98.5901			3.14294
$985$		0			0
$986$	−30.0000			−0.955395
$987$		0			0
$988$		0			0
$989$		−	30.0000i		−	0.953945i
$990$		0			0
$991$			5.47723i			0.173990i	0.996209	+	0.0869949i	$0.0277264\pi$
$991$			5.47723i			0.173990i	−0.996209	+	0.0869949i	$0.972274\pi$
$992$		0			0
$993$		0			0
$994$		−	54.0000i		−	1.71278i
$995$		0			0
$996$	100.000			3.16862
$997$	−6.92820	+	6.92820i	−0.219418	+	0.219418i	−0.808253	−	0.588835i	$-0.799587\pi$
$997$	−6.92820	+	6.92820i	−0.219418	+	0.219418i	0.588835	+	0.808253i	$0.299587\pi$
$998$	9.48683	−	9.48683i	0.300300	−	0.300300i
$999$		−	15.0000i		−	0.474579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.f.c.743.2	yes	8
5.2	odd	4	inner	775.2.f.c.557.1	✓	8
5.3	odd	4	inner	775.2.f.c.557.4	yes	8
5.4	even	2	inner	775.2.f.c.743.3	yes	8
31.30	odd	2	inner	775.2.f.c.743.1	yes	8
155.92	even	4	inner	775.2.f.c.557.2	yes	8
155.123	even	4	inner	775.2.f.c.557.3	yes	8
155.154	odd	2	inner	775.2.f.c.743.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
775.2.f.c.557.1	✓	8	5.2	odd	4	inner
775.2.f.c.557.2	yes	8	155.92	even	4	inner
775.2.f.c.557.3	yes	8	155.123	even	4	inner
775.2.f.c.557.4	yes	8	5.3	odd	4	inner
775.2.f.c.743.1	yes	8	31.30	odd	2	inner
775.2.f.c.743.2	yes	8	1.1	even	1	trivial
775.2.f.c.743.3	yes	8	5.4	even	2	inner
775.2.f.c.743.4	yes	8	155.154	odd	2	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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 + 1.73205i) q^{2} +(1.58114 - 1.58114i) q^{3} -4.00000i q^{4} +5.47723i q^{6} +(1.73205 - 1.73205i) q^{7} +(3.46410 + 3.46410i) q^{8} -2.00000i q^{9} +O(q^{10})\)	\(q+(-1.73205 + 1.73205i) q^{2} +(1.58114 - 1.58114i) q^{3} -4.00000i q^{4} +5.47723i q^{6} +(1.73205 - 1.73205i) q^{7} +(3.46410 + 3.46410i) q^{8} -2.00000i q^{9} +5.47723i q^{11} +(-6.32456 - 6.32456i) q^{12} +6.00000i q^{14} -4.00000 q^{16} +(1.58114 + 1.58114i) q^{17} +(3.46410 + 3.46410i) q^{18} +7.00000i q^{19} -5.47723i q^{21} +(-9.48683 - 9.48683i) q^{22} +(3.16228 - 3.16228i) q^{23} +10.9545 q^{24} +(1.58114 + 1.58114i) q^{27} +(-6.92820 - 6.92820i) q^{28} +5.47723 q^{29} +(-1.00000 - 5.47723i) q^{31} +(8.66025 + 8.66025i) q^{33} -5.47723 q^{34} -8.00000 q^{36} +(-4.74342 - 4.74342i) q^{37} +(-12.1244 - 12.1244i) q^{38} +9.00000 q^{41} +(9.48683 + 9.48683i) q^{42} +(4.74342 - 4.74342i) q^{43} +21.9089 q^{44} +10.9545i q^{46} +(-6.32456 + 6.32456i) q^{48} +1.00000i q^{49} +5.00000 q^{51} +(7.90569 - 7.90569i) q^{53} -5.47723 q^{54} +12.0000 q^{56} +(11.0680 + 11.0680i) q^{57} +(-9.48683 + 9.48683i) q^{58} +3.00000i q^{59} -10.9545i q^{61} +(11.2189 + 7.75478i) q^{62} +(-3.46410 - 3.46410i) q^{63} -8.00000i q^{64} -30.0000 q^{66} +(8.66025 - 8.66025i) q^{67} +(6.32456 - 6.32456i) q^{68} -10.0000i q^{69} -9.00000 q^{71} +(6.92820 - 6.92820i) q^{72} +(-4.74342 + 4.74342i) q^{73} +16.4317 q^{74} +28.0000 q^{76} +(9.48683 + 9.48683i) q^{77} -5.47723 q^{79} +11.0000 q^{81} +(-15.5885 + 15.5885i) q^{82} +(-7.90569 + 7.90569i) q^{83} -21.9089 q^{84} +16.4317i q^{86} +(8.66025 - 8.66025i) q^{87} +(-18.9737 + 18.9737i) q^{88} -5.47723 q^{89} +(-12.6491 - 12.6491i) q^{92} +(-10.2414 - 7.07912i) q^{93} +(-10.3923 + 10.3923i) q^{97} +(-1.73205 - 1.73205i) q^{98} +10.9545 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 32 q^{16} - 8 q^{31} - 64 q^{36} + 72 q^{41} + 40 q^{51} + 96 q^{56} - 240 q^{66} - 72 q^{71} + 224 q^{76} + 88 q^{81}+O(q^{100}) \) 8 * q - 32 * q^16 - 8 * q^31 - 64 * q^36 + 72 * q^41 + 40 * q^51 + 96 * q^56 - 240 * q^66 - 72 * q^71 + 224 * q^76 + 88 * q^81

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more