LMFDB - Embedded newform 775.2.o.b.749.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(149,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("775.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			749.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	775.749
Dual form			775.2.o.b.149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} +(1.73205 + 1.00000i) q^{3} -2.00000 q^{4} +(2.00000 - 3.46410i) q^{6} +(-3.46410 - 2.00000i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-2.00000i q^{2} +(1.73205 + 1.00000i) q^{3} -2.00000 q^{4} +(2.00000 - 3.46410i) q^{6} +(-3.46410 - 2.00000i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-2.50000 - 4.33013i) q^{11} +(-3.46410 - 2.00000i) q^{12} +(-5.19615 + 3.00000i) q^{13} +(-4.00000 + 6.92820i) q^{14} -4.00000 q^{16} +(3.46410 + 2.00000i) q^{17} +(1.73205 - 1.00000i) q^{18} +(2.00000 - 3.46410i) q^{19} +(-4.00000 - 6.92820i) q^{21} +(-8.66025 + 5.00000i) q^{22} +2.00000i q^{23} +(6.00000 + 10.3923i) q^{26} -4.00000i q^{27} +(6.92820 + 4.00000i) q^{28} +3.00000 q^{29} +(5.50000 - 0.866025i) q^{31} +8.00000i q^{32} -10.0000i q^{33} +(4.00000 - 6.92820i) q^{34} +(-1.00000 - 1.73205i) q^{36} +(-6.92820 - 4.00000i) q^{37} +(-6.92820 - 4.00000i) q^{38} -12.0000 q^{39} +(1.50000 + 2.59808i) q^{41} +(-13.8564 + 8.00000i) q^{42} +(5.00000 + 8.66025i) q^{44} +4.00000 q^{46} -8.00000i q^{47} +(-6.92820 - 4.00000i) q^{48} +(4.50000 + 7.79423i) q^{49} +(4.00000 + 6.92820i) q^{51} +(10.3923 - 6.00000i) q^{52} +(-5.19615 + 3.00000i) q^{53} -8.00000 q^{54} +(6.92820 - 4.00000i) q^{57} -6.00000i q^{58} +(6.50000 - 11.2583i) q^{59} +1.00000 q^{61} +(-1.73205 - 11.0000i) q^{62} -4.00000i q^{63} +8.00000 q^{64} -20.0000 q^{66} +(1.73205 - 1.00000i) q^{67} +(-6.92820 - 4.00000i) q^{68} +(-2.00000 + 3.46410i) q^{69} +(-1.50000 - 2.59808i) q^{71} +(3.46410 - 2.00000i) q^{73} +(-8.00000 + 13.8564i) q^{74} +(-4.00000 + 6.92820i) q^{76} +20.0000i q^{77} +24.0000i q^{78} +(1.50000 - 2.59808i) q^{79} +(5.50000 - 9.52628i) q^{81} +(5.19615 - 3.00000i) q^{82} +(-3.46410 + 2.00000i) q^{83} +(8.00000 + 13.8564i) q^{84} +(5.19615 + 3.00000i) q^{87} +11.0000 q^{89} +24.0000 q^{91} -4.00000i q^{92} +(10.3923 + 4.00000i) q^{93} -16.0000 q^{94} +(-8.00000 + 13.8564i) q^{96} +(15.5885 - 9.00000i) q^{98} +(2.50000 - 4.33013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{4} + 8 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q - 8 * q^4 + 8 * q^6 + 2 * q^9	$ 4 q - 8 q^{4} + 8 q^{6} + 2 q^{9} - 10 q^{11} - 16 q^{14} - 16 q^{16} + 8 q^{19} - 16 q^{21} + 24 q^{26} + 12 q^{29} + 22 q^{31} + 16 q^{34} - 4 q^{36} - 48 q^{39} + 6 q^{41} + 20 q^{44} + 16 q^{46} + 18 q^{49} + 16 q^{51} - 32 q^{54} + 26 q^{59} + 4 q^{61} + 32 q^{64} - 80 q^{66} - 8 q^{69} - 6 q^{71} - 32 q^{74} - 16 q^{76} + 6 q^{79} + 22 q^{81} + 32 q^{84} + 44 q^{89} + 96 q^{91} - 64 q^{94} - 32 q^{96} + 10 q^{99}+O(q^{100}) $ 4 * q - 8 * q^4 + 8 * q^6 + 2 * q^9 - 10 * q^11 - 16 * q^14 - 16 * q^16 + 8 * q^19 - 16 * q^21 + 24 * q^26 + 12 * q^29 + 22 * q^31 + 16 * q^34 - 4 * q^36 - 48 * q^39 + 6 * q^41 + 20 * q^44 + 16 * q^46 + 18 * q^49 + 16 * q^51 - 32 * q^54 + 26 * q^59 + 4 * q^61 + 32 * q^64 - 80 * q^66 - 8 * q^69 - 6 * q^71 - 32 * q^74 - 16 * q^76 + 6 * q^79 + 22 * q^81 + 32 * q^84 + 44 * q^89 + 96 * q^91 - 64 * q^94 - 32 * q^96 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$		−	2.00000i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$2$		−	2.00000i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$3$	1.73205	+	1.00000i	1.00000	+	0.577350i	0.908248	−	0.418432i	$-0.137420\pi$
$3$	1.73205	+	1.00000i	1.00000	+	0.577350i	0.0917517	+	0.995782i	$0.470753\pi$
$4$	−2.00000			−1.00000
$5$		0			0
$5$		0			0
$6$	2.00000	−	3.46410i	0.816497	−	1.41421i
$7$	−3.46410	−	2.00000i	−1.30931	−	0.755929i	−0.327327	−	0.944911i	$-0.606148\pi$
$7$	−3.46410	−	2.00000i	−1.30931	−	0.755929i	−0.981981	+	0.188982i	$0.939481\pi$
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	−0.945979	−	0.324227i	$-0.894896\pi$
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	0.192201	−	0.981356i	$-0.438437\pi$
$12$	−3.46410	−	2.00000i	−1.00000	−	0.577350i
$13$	−5.19615	+	3.00000i	−1.44115	+	0.832050i	−0.997927	−	0.0643593i	$-0.979500\pi$
$13$	−5.19615	+	3.00000i	−1.44115	+	0.832050i	−0.443227	+	0.896410i	$0.646166\pi$
$14$	−4.00000	+	6.92820i	−1.06904	+	1.85164i
$15$		0			0
$16$	−4.00000			−1.00000
$17$	3.46410	+	2.00000i	0.840168	+	0.485071i	0.857321	−	0.514782i	$-0.172127\pi$
$17$	3.46410	+	2.00000i	0.840168	+	0.485071i	−0.0171533	+	0.999853i	$0.505460\pi$
$18$	1.73205	−	1.00000i	0.408248	−	0.235702i
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$		0			0
$21$	−4.00000	−	6.92820i	−0.872872	−	1.51186i
$22$	−8.66025	+	5.00000i	−1.84637	+	1.06600i
$23$			2.00000i			0.417029i	0.978019	+	0.208514i	$0.0668628\pi$
$23$			2.00000i			0.417029i	−0.978019	+	0.208514i	$0.933137\pi$
$24$		0			0
$25$		0			0
$26$	6.00000	+	10.3923i	1.17670	+	2.03810i
$27$		−	4.00000i		−	0.769800i
$28$	6.92820	+	4.00000i	1.30931	+	0.755929i
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$		0			0
$31$	5.50000	−	0.866025i	0.987829	−	0.155543i
$31$	5.50000	−	0.866025i	0.987829	−	0.155543i
$32$			8.00000i			1.41421i
$33$		−	10.0000i		−	1.74078i
$34$	4.00000	−	6.92820i	0.685994	−	1.18818i
$35$		0			0
$36$	−1.00000	−	1.73205i	−0.166667	−	0.288675i
$37$	−6.92820	−	4.00000i	−1.13899	−	0.657596i	−0.192809	−	0.981236i	$-0.561760\pi$
$37$	−6.92820	−	4.00000i	−1.13899	−	0.657596i	−0.946180	+	0.323640i	$0.895093\pi$
$38$	−6.92820	−	4.00000i	−1.12390	−	0.648886i
$39$	−12.0000			−1.92154
$40$		0			0
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$	−13.8564	+	8.00000i	−2.13809	+	1.23443i
$43$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$43$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$44$	5.00000	+	8.66025i	0.753778	+	1.30558i
$45$		0			0
$46$	4.00000			0.589768
$47$		−	8.00000i		−	1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$		−	8.00000i		−	1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$	−6.92820	−	4.00000i	−1.00000	−	0.577350i
$49$	4.50000	+	7.79423i	0.642857	+	1.11346i
$50$		0			0
$51$	4.00000	+	6.92820i	0.560112	+	0.970143i
$52$	10.3923	−	6.00000i	1.44115	−	0.832050i
$53$	−5.19615	+	3.00000i	−0.713746	+	0.412082i	−0.812447	−	0.583036i	$-0.801865\pi$
$53$	−5.19615	+	3.00000i	−0.713746	+	0.412082i	0.0987002	+	0.995117i	$0.468532\pi$
$54$	−8.00000			−1.08866
$55$		0			0
$56$		0			0
$57$	6.92820	−	4.00000i	0.917663	−	0.529813i
$58$		−	6.00000i		−	0.787839i
$59$	6.50000	−	11.2583i	0.846228	−	1.46571i	−0.0383226	−	0.999265i	$-0.512201\pi$
$59$	6.50000	−	11.2583i	0.846228	−	1.46571i	0.884551	−	0.466444i	$-0.154465\pi$
$60$		0			0
$61$	1.00000			0.128037			0.0640184	−	0.997949i	$-0.479608\pi$
$61$	1.00000			0.128037			0.0640184	+	0.997949i	$0.479608\pi$
$62$	−1.73205	−	11.0000i	−0.219971	−	1.39700i
$63$		−	4.00000i		−	0.503953i
$64$	8.00000			1.00000
$65$		0			0
$66$	−20.0000			−2.46183
$67$	1.73205	−	1.00000i	0.211604	−	0.122169i	−0.390453	−	0.920623i	$-0.627682\pi$
$67$	1.73205	−	1.00000i	0.211604	−	0.122169i	0.602056	+	0.798454i	$0.294348\pi$
$68$	−6.92820	−	4.00000i	−0.840168	−	0.485071i
$69$	−2.00000	+	3.46410i	−0.240772	+	0.417029i
$70$		0			0
$71$	−1.50000	−	2.59808i	−0.178017	−	0.308335i	0.763184	−	0.646181i	$-0.223635\pi$
$71$	−1.50000	−	2.59808i	−0.178017	−	0.308335i	−0.941201	+	0.337846i	$0.890302\pi$
$72$		0			0
$73$	3.46410	−	2.00000i	0.405442	−	0.234082i	−0.283387	−	0.959006i	$-0.591458\pi$
$73$	3.46410	−	2.00000i	0.405442	−	0.234082i	0.688830	+	0.724923i	$0.258125\pi$
$74$	−8.00000	+	13.8564i	−0.929981	+	1.61077i
$75$		0			0
$76$	−4.00000	+	6.92820i	−0.458831	+	0.794719i
$77$			20.0000i			2.27921i
$78$			24.0000i			2.71746i
$79$	1.50000	−	2.59808i	0.168763	−	0.292306i	−0.769222	−	0.638982i	$-0.779356\pi$
$79$	1.50000	−	2.59808i	0.168763	−	0.292306i	0.937985	+	0.346675i	$0.112689\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	5.19615	−	3.00000i	0.573819	−	0.331295i
$83$	−3.46410	+	2.00000i	−0.380235	+	0.219529i	−0.677920	−	0.735135i	$-0.737119\pi$
$83$	−3.46410	+	2.00000i	−0.380235	+	0.219529i	0.297686	+	0.954664i	$0.403785\pi$
$84$	8.00000	+	13.8564i	0.872872	+	1.51186i
$85$		0			0
$86$		0			0
$87$	5.19615	+	3.00000i	0.557086	+	0.321634i
$88$		0			0
$89$	11.0000			1.16600			0.582999	−	0.812473i	$-0.301879\pi$
$89$	11.0000			1.16600			0.582999	+	0.812473i	$0.301879\pi$
$90$		0			0
$91$	24.0000			2.51588
$92$		−	4.00000i		−	0.417029i
$93$	10.3923	+	4.00000i	1.07763	+	0.414781i
$94$	−16.0000			−1.65027
$95$		0			0
$96$	−8.00000	+	13.8564i	−0.816497	+	1.41421i
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	15.5885	−	9.00000i	1.57467	−	0.909137i
$99$	2.50000	−	4.33013i	0.251259	−	0.435194i
$100$		0			0
$101$	−10.0000			−0.995037			−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000			−0.995037			−0.497519	+	0.867453i	$0.665755\pi$
$102$	13.8564	−	8.00000i	1.37199	−	0.792118i
$103$	8.66025	−	5.00000i	0.853320	−	0.492665i	−0.00844953	−	0.999964i	$-0.502690\pi$
$103$	8.66025	−	5.00000i	0.853320	−	0.492665i	0.861770	+	0.507300i	$0.169356\pi$
$104$		0			0
$105$		0			0
$106$	6.00000	+	10.3923i	0.582772	+	1.00939i
$107$	12.1244	+	7.00000i	1.17211	+	0.676716i	0.954175	−	0.299249i	$-0.0967360\pi$
$107$	12.1244	+	7.00000i	1.17211	+	0.676716i	0.217931	+	0.975964i	$0.430069\pi$
$108$			8.00000i			0.769800i
$109$	5.00000			0.478913			0.239457	−	0.970907i	$-0.423031\pi$
$109$	5.00000			0.478913			0.239457	+	0.970907i	$0.423031\pi$
$110$		0			0
$111$	−8.00000	−	13.8564i	−0.759326	−	1.31519i
$112$	13.8564	+	8.00000i	1.30931	+	0.755929i
$113$	5.19615	−	3.00000i	0.488813	−	0.282216i	−0.235269	−	0.971930i	$-0.575597\pi$
$113$	5.19615	−	3.00000i	0.488813	−	0.282216i	0.724082	+	0.689714i	$0.242264\pi$
$114$	−8.00000	−	13.8564i	−0.749269	−	1.29777i
$115$		0			0
$116$	−6.00000			−0.557086
$117$	−5.19615	−	3.00000i	−0.480384	−	0.277350i
$118$	−22.5167	−	13.0000i	−2.07283	−	1.19675i
$119$	−8.00000	−	13.8564i	−0.733359	−	1.27021i
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$		−	2.00000i		−	0.181071i
$123$			6.00000i			0.541002i
$124$	−11.0000	+	1.73205i	−0.987829	+	0.155543i
$125$		0			0
$126$	−8.00000			−0.712697
$127$	8.66025	+	5.00000i	0.768473	+	0.443678i	0.832330	−	0.554281i	$-0.187007\pi$
$127$	8.66025	+	5.00000i	0.768473	+	0.443678i	−0.0638564	+	0.997959i	$0.520340\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.50000	+	11.2583i	−0.567908	+	0.983645i	0.428865	+	0.903369i	$0.358914\pi$
$131$	−6.50000	+	11.2583i	−0.567908	+	0.983645i	−0.996773	+	0.0802763i	$0.974420\pi$
$132$			20.0000i			1.74078i
$133$	−13.8564	+	8.00000i	−1.20150	+	0.693688i
$134$	−2.00000	−	3.46410i	−0.172774	−	0.299253i
$135$		0			0
$136$		0			0
$137$	−15.5885	+	9.00000i	−1.33181	+	0.768922i	−0.985577	−	0.169226i	$-0.945873\pi$
$137$	−15.5885	+	9.00000i	−1.33181	+	0.768922i	−0.346235	+	0.938148i	$0.612540\pi$
$138$	6.92820	+	4.00000i	0.589768	+	0.340503i
$139$	−9.00000			−0.763370			−0.381685	−	0.924292i	$-0.624656\pi$
$139$	−9.00000			−0.763370			−0.381685	+	0.924292i	$0.624656\pi$
$140$		0			0
$141$	8.00000	−	13.8564i	0.673722	−	1.16692i
$142$	−5.19615	+	3.00000i	−0.436051	+	0.251754i
$143$	25.9808	+	15.0000i	2.17262	+	1.25436i
$144$	−2.00000	−	3.46410i	−0.166667	−	0.288675i
$145$		0			0
$146$	−4.00000	−	6.92820i	−0.331042	−	0.573382i
$147$			18.0000i			1.48461i
$148$	13.8564	+	8.00000i	1.13899	+	0.657596i
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	−0.798019	−	0.602632i	$-0.794119\pi$
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	0.920904	+	0.389789i	$0.127452\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$		0			0
$153$			4.00000i			0.323381i
$154$	40.0000			3.22329
$155$		0			0
$156$	24.0000			1.92154
$157$		−	10.0000i		−	0.798087i	−0.916932	−	0.399043i	$-0.869342\pi$
$157$		−	10.0000i		−	0.798087i	0.916932	−	0.399043i	$-0.130658\pi$
$158$	−5.19615	−	3.00000i	−0.413384	−	0.238667i
$159$	−12.0000			−0.951662
$160$		0			0
$161$	4.00000	−	6.92820i	0.315244	−	0.546019i
$162$	−19.0526	−	11.0000i	−1.49691	−	0.864242i
$163$		−	2.00000i		−	0.156652i	−0.996928	−	0.0783260i	$-0.975042\pi$
$163$		−	2.00000i		−	0.156652i	0.996928	−	0.0783260i	$-0.0249575\pi$
$164$	−3.00000	−	5.19615i	−0.234261	−	0.405751i
$165$		0			0
$166$	4.00000	+	6.92820i	0.310460	+	0.537733i
$167$	−3.46410	−	2.00000i	−0.268060	−	0.154765i	0.359946	−	0.932973i	$-0.382795\pi$
$167$	−3.46410	−	2.00000i	−0.268060	−	0.154765i	−0.628006	+	0.778209i	$0.716129\pi$
$168$		0			0
$169$	11.5000	−	19.9186i	0.884615	−	1.53220i
$170$		0			0
$171$	4.00000			0.305888
$172$		0			0
$173$	−5.19615	+	3.00000i	−0.395056	+	0.228086i	−0.684349	−	0.729155i	$-0.739913\pi$
$173$	−5.19615	+	3.00000i	−0.395056	+	0.228086i	0.289292	+	0.957241i	$0.406580\pi$
$174$	6.00000	−	10.3923i	0.454859	−	0.787839i
$175$		0			0
$176$	10.0000	+	17.3205i	0.753778	+	1.30558i
$177$	22.5167	−	13.0000i	1.69246	−	0.977140i
$178$		−	22.0000i		−	1.64897i
$179$	−9.50000	+	16.4545i	−0.710063	+	1.22987i	0.254770	+	0.967002i	$0.418000\pi$
$179$	−9.50000	+	16.4545i	−0.710063	+	1.22987i	−0.964833	+	0.262864i	$0.915333\pi$
$180$		0			0
$181$	3.00000	+	5.19615i	0.222988	+	0.386227i	0.955714	−	0.294297i	$-0.0950855\pi$
$181$	3.00000	+	5.19615i	0.222988	+	0.386227i	−0.732726	+	0.680524i	$0.761752\pi$
$182$		−	48.0000i		−	3.55800i
$183$	1.73205	+	1.00000i	0.128037	+	0.0739221i
$184$		0			0
$185$		0			0
$186$	8.00000	−	20.7846i	0.586588	−	1.52400i
$187$		−	20.0000i		−	1.46254i
$188$			16.0000i			1.16692i
$189$	−8.00000	+	13.8564i	−0.581914	+	1.00791i
$190$		0			0
$191$	−3.50000	−	6.06218i	−0.253251	−	0.438644i	0.711168	−	0.703022i	$-0.248167\pi$
$191$	−3.50000	−	6.06218i	−0.253251	−	0.438644i	−0.964419	+	0.264378i	$0.914833\pi$
$192$	13.8564	+	8.00000i	1.00000	+	0.577350i
$193$	−20.7846	−	12.0000i	−1.49611	−	0.863779i	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	−20.7846	−	12.0000i	−1.49611	−	0.863779i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$		0			0
$195$		0			0
$196$	−9.00000	−	15.5885i	−0.642857	−	1.11346i
$197$	1.73205	−	1.00000i	0.123404	−	0.0712470i	−0.437028	−	0.899448i	$-0.643969\pi$
$197$	1.73205	−	1.00000i	0.123404	−	0.0712470i	0.560431	+	0.828201i	$0.310635\pi$
$198$	−8.66025	−	5.00000i	−0.615457	−	0.355335i
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	0.996850	+	0.0793045i	$0.0252700\pi$
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	−0.429745	+	0.902950i	$0.641397\pi$
$200$		0			0
$201$	4.00000			0.282138
$202$			20.0000i			1.40720i
$203$	−10.3923	−	6.00000i	−0.729397	−	0.421117i
$204$	−8.00000	−	13.8564i	−0.560112	−	0.970143i
$205$		0			0
$206$	−10.0000	−	17.3205i	−0.696733	−	1.20678i
$207$	−1.73205	+	1.00000i	−0.120386	+	0.0695048i
$208$	20.7846	−	12.0000i	1.44115	−	0.832050i
$209$	−20.0000			−1.38343
$210$		0			0
$211$	9.50000	−	16.4545i	0.654007	−	1.13277i	−0.328135	−	0.944631i	$-0.606420\pi$
$211$	9.50000	−	16.4545i	0.654007	−	1.13277i	0.982142	−	0.188142i	$-0.0602466\pi$
$212$	10.3923	−	6.00000i	0.713746	−	0.412082i
$213$		−	6.00000i		−	0.411113i
$214$	14.0000	−	24.2487i	0.957020	−	1.65761i
$215$		0			0
$216$		0			0
$217$	−20.7846	−	8.00000i	−1.41095	−	0.543075i
$218$		−	10.0000i		−	0.677285i
$219$	8.00000			0.540590
$220$		0			0
$221$	−24.0000			−1.61441
$222$	−27.7128	+	16.0000i	−1.85996	+	1.07385i
$223$	24.2487	+	14.0000i	1.62381	+	0.937509i	0.985887	+	0.167412i	$0.0535411\pi$
$223$	24.2487	+	14.0000i	1.62381	+	0.937509i	0.637927	+	0.770097i	$0.279792\pi$
$224$	16.0000	−	27.7128i	1.06904	−	1.85164i
$225$		0			0
$226$	−6.00000	−	10.3923i	−0.399114	−	0.691286i
$227$	−17.3205	+	10.0000i	−1.14960	+	0.663723i	−0.948790	−	0.315906i	$-0.897691\pi$
$227$	−17.3205	+	10.0000i	−1.14960	+	0.663723i	−0.200812	+	0.979630i	$0.564358\pi$
$228$	−13.8564	+	8.00000i	−0.917663	+	0.529813i
$229$	4.50000	−	7.79423i	0.297368	−	0.515057i	−0.678165	−	0.734910i	$-0.737224\pi$
$229$	4.50000	−	7.79423i	0.297368	−	0.515057i	0.975533	+	0.219853i	$0.0705577\pi$
$230$		0			0
$231$	−20.0000	+	34.6410i	−1.31590	+	2.27921i
$232$		0			0
$233$		−	24.0000i		−	1.57229i	−0.618041	−	0.786146i	$-0.712073\pi$
$233$		−	24.0000i		−	1.57229i	0.618041	−	0.786146i	$-0.287927\pi$
$234$	−6.00000	+	10.3923i	−0.392232	+	0.679366i
$235$		0			0
$236$	−13.0000	+	22.5167i	−0.846228	+	1.46571i
$237$	5.19615	−	3.00000i	0.337526	−	0.194871i
$238$	−27.7128	+	16.0000i	−1.79635	+	1.03713i
$239$	−5.50000	−	9.52628i	−0.355765	−	0.616204i	0.631483	−	0.775390i	$-0.282446\pi$
$239$	−5.50000	−	9.52628i	−0.355765	−	0.616204i	−0.987249	+	0.159186i	$0.949113\pi$
$240$		0			0
$241$	11.0000	−	19.0526i	0.708572	−	1.22728i	−0.256814	−	0.966461i	$-0.582673\pi$
$241$	11.0000	−	19.0526i	0.708572	−	1.22728i	0.965387	−	0.260822i	$-0.0839937\pi$
$242$	24.2487	+	14.0000i	1.55877	+	0.899954i
$243$	8.66025	−	5.00000i	0.555556	−	0.320750i
$244$	−2.00000			−0.128037
$245$		0			0
$246$	12.0000			0.765092
$247$			24.0000i			1.52708i
$248$		0			0
$249$	−8.00000			−0.506979
$250$		0			0
$251$	8.00000	−	13.8564i	0.504956	−	0.874609i	−0.495028	−	0.868877i	$-0.664842\pi$
$251$	8.00000	−	13.8564i	0.504956	−	0.874609i	0.999984	−	0.00573163i	$-0.00182444\pi$
$252$			8.00000i			0.503953i
$253$	8.66025	−	5.00000i	0.544466	−	0.314347i
$254$	10.0000	−	17.3205i	0.627456	−	1.08679i
$255$		0			0
$256$	16.0000			1.00000
$257$	20.7846	−	12.0000i	1.29651	−	0.748539i	0.316709	−	0.948523i	$-0.397422\pi$
$257$	20.7846	−	12.0000i	1.29651	−	0.748539i	0.979799	+	0.199983i	$0.0640888\pi$
$258$		0			0
$259$	16.0000	+	27.7128i	0.994192	+	1.72199i
$260$		0			0
$261$	1.50000	+	2.59808i	0.0928477	+	0.160817i
$262$	22.5167	+	13.0000i	1.39108	+	0.803143i
$263$			6.00000i			0.369976i	0.982741	+	0.184988i	$0.0592246\pi$
$263$			6.00000i			0.369976i	−0.982741	+	0.184988i	$0.940775\pi$
$264$		0			0
$265$		0			0
$266$	16.0000	+	27.7128i	0.981023	+	1.69918i
$267$	19.0526	+	11.0000i	1.16600	+	0.673189i
$268$	−3.46410	+	2.00000i	−0.211604	+	0.122169i
$269$	1.50000	+	2.59808i	0.0914566	+	0.158408i	0.908124	−	0.418701i	$-0.137514\pi$
$269$	1.50000	+	2.59808i	0.0914566	+	0.158408i	−0.816668	+	0.577108i	$0.804181\pi$
$270$		0			0
$271$	−31.0000			−1.88312			−0.941558	−	0.336851i	$-0.890638\pi$
$271$	−31.0000			−1.88312			−0.941558	+	0.336851i	$0.890638\pi$
$272$	−13.8564	−	8.00000i	−0.840168	−	0.485071i
$273$	41.5692	+	24.0000i	2.51588	+	1.45255i
$274$	18.0000	+	31.1769i	1.08742	+	1.88347i
$275$		0			0
$276$	4.00000	−	6.92820i	0.240772	−	0.417029i
$277$			2.00000i			0.120168i	0.998193	+	0.0600842i	$0.0191369\pi$
$277$			2.00000i			0.120168i	−0.998193	+	0.0600842i	$0.980863\pi$
$278$			18.0000i			1.07957i
$279$	3.50000	+	4.33013i	0.209540	+	0.259238i
$280$		0			0
$281$	−3.00000			−0.178965			−0.0894825	−	0.995988i	$-0.528521\pi$
$281$	−3.00000			−0.178965			−0.0894825	+	0.995988i	$0.528521\pi$
$282$	−27.7128	−	16.0000i	−1.65027	−	0.952786i
$283$			8.00000i			0.475551i	0.971320	+	0.237775i	$0.0764182\pi$
$283$			8.00000i			0.475551i	−0.971320	+	0.237775i	$0.923582\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$		0			0
$286$	30.0000	−	51.9615i	1.77394	−	3.07255i
$287$		−	12.0000i		−	0.708338i
$288$	−6.92820	+	4.00000i	−0.408248	+	0.235702i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$		0			0
$291$		0			0
$292$	−6.92820	+	4.00000i	−0.405442	+	0.234082i
$293$	−13.8564	−	8.00000i	−0.809500	−	0.467365i	0.0372823	−	0.999305i	$-0.488130\pi$
$293$	−13.8564	−	8.00000i	−0.809500	−	0.467365i	−0.846782	+	0.531940i	$0.821463\pi$
$294$	36.0000			2.09956
$295$		0			0
$296$		0			0
$297$	−17.3205	+	10.0000i	−1.00504	+	0.580259i
$298$	−5.19615	−	3.00000i	−0.301005	−	0.173785i
$299$	−6.00000	−	10.3923i	−0.346989	−	0.601003i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−17.3205	−	10.0000i	−0.995037	−	0.574485i
$304$	−8.00000	+	13.8564i	−0.458831	+	0.794719i
$305$		0			0
$306$	8.00000			0.457330
$307$	12.1244	+	7.00000i	0.691974	+	0.399511i	0.804351	−	0.594154i	$-0.202513\pi$
$307$	12.1244	+	7.00000i	0.691974	+	0.399511i	−0.112377	+	0.993666i	$0.535847\pi$
$308$		−	40.0000i		−	2.27921i
$309$	20.0000			1.13776
$310$		0			0
$311$	−33.0000			−1.87126			−0.935629	−	0.352985i	$-0.885167\pi$
$311$	−33.0000			−1.87126			−0.935629	+	0.352985i	$0.885167\pi$
$312$		0			0
$313$	24.2487	+	14.0000i	1.37062	+	0.791327i	0.991006	−	0.133819i	$-0.0427240\pi$
$313$	24.2487	+	14.0000i	1.37062	+	0.791327i	0.379612	+	0.925146i	$0.376057\pi$
$314$	−20.0000			−1.12867
$315$		0			0
$316$	−3.00000	+	5.19615i	−0.168763	+	0.292306i
$317$	−5.19615	−	3.00000i	−0.291845	−	0.168497i	0.346929	−	0.937892i	$-0.387225\pi$
$317$	−5.19615	−	3.00000i	−0.291845	−	0.168497i	−0.638774	+	0.769395i	$0.720558\pi$
$318$			24.0000i			1.34585i
$319$	−7.50000	−	12.9904i	−0.419919	−	0.727322i
$320$		0			0
$321$	14.0000	+	24.2487i	0.781404	+	1.35343i
$322$	−13.8564	−	8.00000i	−0.772187	−	0.445823i
$323$	13.8564	−	8.00000i	0.770991	−	0.445132i
$324$	−11.0000	+	19.0526i	−0.611111	+	1.05848i
$325$		0			0
$326$	−4.00000			−0.221540
$327$	8.66025	+	5.00000i	0.478913	+	0.276501i
$328$		0			0
$329$	−16.0000	+	27.7128i	−0.882109	+	1.52786i
$330$		0			0
$331$	3.50000	+	6.06218i	0.192377	+	0.333207i	0.946038	−	0.324057i	$-0.105047\pi$
$331$	3.50000	+	6.06218i	0.192377	+	0.333207i	−0.753660	+	0.657264i	$0.771714\pi$
$332$	6.92820	−	4.00000i	0.380235	−	0.219529i
$333$		−	8.00000i		−	0.438397i
$334$	−4.00000	+	6.92820i	−0.218870	+	0.379094i
$335$		0			0
$336$	16.0000	+	27.7128i	0.872872	+	1.51186i
$337$			22.0000i			1.19842i	0.800593	+	0.599208i	$0.204518\pi$
$337$			22.0000i			1.19842i	−0.800593	+	0.599208i	$0.795482\pi$
$338$	−39.8372	−	23.0000i	−2.16686	−	1.25104i
$339$	12.0000			0.651751
$340$		0			0
$341$	−17.5000	−	21.6506i	−0.947678	−	1.17245i
$342$		−	8.00000i		−	0.432590i
$343$		−	8.00000i		−	0.431959i
$344$		0			0
$345$		0			0
$346$	6.00000	+	10.3923i	0.322562	+	0.558694i
$347$	−15.5885	−	9.00000i	−0.836832	−	0.483145i	0.0193540	−	0.999813i	$-0.493839\pi$
$347$	−15.5885	−	9.00000i	−0.836832	−	0.483145i	−0.856186	+	0.516667i	$0.827172\pi$
$348$	−10.3923	−	6.00000i	−0.557086	−	0.321634i
$349$	−13.0000			−0.695874			−0.347937	−	0.937518i	$-0.613118\pi$
$349$	−13.0000			−0.695874			−0.347937	+	0.937518i	$0.613118\pi$
$350$		0			0
$351$	12.0000	+	20.7846i	0.640513	+	1.10940i
$352$	34.6410	−	20.0000i	1.84637	−	1.06600i
$353$	13.8564	+	8.00000i	0.737502	+	0.425797i	0.821160	−	0.570697i	$-0.193327\pi$
$353$	13.8564	+	8.00000i	0.737502	+	0.425797i	−0.0836583	+	0.996495i	$0.526660\pi$
$354$	−26.0000	−	45.0333i	−1.38188	−	2.39349i
$355$		0			0
$356$	−22.0000			−1.16600
$357$		−	32.0000i		−	1.69362i
$358$	32.9090	+	19.0000i	1.73929	+	1.00418i
$359$	8.50000	+	14.7224i	0.448613	+	0.777020i	0.998296	−	0.0583530i	$-0.0185849\pi$
$359$	8.50000	+	14.7224i	0.448613	+	0.777020i	−0.549683	+	0.835373i	$0.685252\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	10.3923	−	6.00000i	0.546207	−	0.315353i
$363$	−24.2487	+	14.0000i	−1.27273	+	0.734809i
$364$	−48.0000			−2.51588
$365$		0			0
$366$	2.00000	−	3.46410i	0.104542	−	0.181071i
$367$	13.8564	−	8.00000i	0.723299	−	0.417597i	−0.0926670	−	0.995697i	$-0.529539\pi$
$367$	13.8564	−	8.00000i	0.723299	−	0.417597i	0.815966	+	0.578101i	$0.196206\pi$
$368$		−	8.00000i		−	0.417029i
$369$	−1.50000	+	2.59808i	−0.0780869	+	0.135250i
$370$		0			0
$371$	24.0000			1.24602
$372$	−20.7846	−	8.00000i	−1.07763	−	0.414781i
$373$		−	32.0000i		−	1.65690i	−0.560065	−	0.828449i	$-0.689224\pi$
$373$		−	32.0000i		−	1.65690i	0.560065	−	0.828449i	$-0.310776\pi$
$374$	−40.0000			−2.06835
$375$		0			0
$376$		0			0
$377$	−15.5885	+	9.00000i	−0.802846	+	0.463524i
$378$	27.7128	+	16.0000i	1.42539	+	0.822951i
$379$	−4.00000	+	6.92820i	−0.205466	+	0.355878i	−0.950281	−	0.311393i	$-0.899204\pi$
$379$	−4.00000	+	6.92820i	−0.205466	+	0.355878i	0.744815	+	0.667271i	$0.232538\pi$
$380$		0			0
$381$	10.0000	+	17.3205i	0.512316	+	0.887357i
$382$	−12.1244	+	7.00000i	−0.620336	+	0.358151i
$383$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$383$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$384$		0			0
$385$		0			0
$386$	−24.0000	+	41.5692i	−1.22157	+	2.11582i
$387$		0			0
$388$		0			0
$389$	−8.50000	+	14.7224i	−0.430967	+	0.746457i	−0.996957	−	0.0779554i	$-0.975161\pi$
$389$	−8.50000	+	14.7224i	−0.430967	+	0.746457i	0.565990	+	0.824412i	$0.308494\pi$
$390$		0			0
$391$	−4.00000	+	6.92820i	−0.202289	+	0.350374i
$392$		0			0
$393$	−22.5167	+	13.0000i	−1.13582	+	0.655763i
$394$	−2.00000	−	3.46410i	−0.100759	−	0.174519i
$395$		0			0
$396$	−5.00000	+	8.66025i	−0.251259	+	0.435194i
$397$	−12.1244	−	7.00000i	−0.608504	−	0.351320i	0.163876	−	0.986481i	$-0.447600\pi$
$397$	−12.1244	−	7.00000i	−0.608504	−	0.351320i	−0.772380	+	0.635161i	$0.780934\pi$
$398$	27.7128	−	16.0000i	1.38912	−	0.802008i
$399$	−32.0000			−1.60200
$400$		0			0
$401$	19.0000			0.948815			0.474407	−	0.880305i	$-0.342662\pi$
$401$	19.0000			0.948815			0.474407	+	0.880305i	$0.342662\pi$
$402$		−	8.00000i		−	0.399004i
$403$	−25.9808	+	21.0000i	−1.29419	+	1.04608i
$404$	20.0000			0.995037
$405$		0			0
$406$	−12.0000	+	20.7846i	−0.595550	+	1.03152i
$407$			40.0000i			1.98273i
$408$		0			0
$409$	−3.00000	+	5.19615i	−0.148340	+	0.256933i	−0.930614	−	0.366002i	$-0.880726\pi$
$409$	−3.00000	+	5.19615i	−0.148340	+	0.256933i	0.782274	+	0.622935i	$0.214060\pi$
$410$		0			0
$411$	−36.0000			−1.77575
$412$	−17.3205	+	10.0000i	−0.853320	+	0.492665i
$413$	−45.0333	+	26.0000i	−2.21594	+	1.27938i
$414$	2.00000	+	3.46410i	0.0982946	+	0.170251i
$415$		0			0
$416$	−24.0000	−	41.5692i	−1.17670	−	2.03810i
$417$	−15.5885	−	9.00000i	−0.763370	−	0.440732i
$418$			40.0000i			1.95646i
$419$	25.0000			1.22133			0.610665	−	0.791889i	$-0.290902\pi$
$419$	25.0000			1.22133			0.610665	+	0.791889i	$0.290902\pi$
$420$		0			0
$421$	7.50000	+	12.9904i	0.365528	+	0.633112i	0.988861	−	0.148844i	$-0.0475552\pi$
$421$	7.50000	+	12.9904i	0.365528	+	0.633112i	−0.623333	+	0.781956i	$0.714222\pi$
$422$	−32.9090	−	19.0000i	−1.60198	−	0.924906i
$423$	6.92820	−	4.00000i	0.336861	−	0.194487i
$424$		0			0
$425$		0			0
$426$	−12.0000			−0.581402
$427$	−3.46410	−	2.00000i	−0.167640	−	0.0967868i
$428$	−24.2487	−	14.0000i	−1.17211	−	0.676716i
$429$	30.0000	+	51.9615i	1.44841	+	2.50873i
$430$		0			0
$431$	−5.50000	+	9.52628i	−0.264926	+	0.458865i	−0.967544	−	0.252702i	$-0.918681\pi$
$431$	−5.50000	+	9.52628i	−0.264926	+	0.458865i	0.702618	+	0.711567i	$0.252014\pi$
$432$			16.0000i			0.769800i
$433$		−	30.0000i		−	1.44171i	−0.693087	−	0.720854i	$-0.743750\pi$
$433$		−	30.0000i		−	1.44171i	0.693087	−	0.720854i	$-0.256250\pi$
$434$	−16.0000	+	41.5692i	−0.768025	+	1.99539i
$435$		0			0
$436$	−10.0000			−0.478913
$437$	6.92820	+	4.00000i	0.331421	+	0.191346i
$438$		−	16.0000i		−	0.764510i
$439$	−10.5000	−	18.1865i	−0.501138	−	0.867996i	−0.999999	−	0.00131415i	$-0.999582\pi$
$439$	−10.5000	−	18.1865i	−0.501138	−	0.867996i	0.498861	−	0.866682i	$-0.333752\pi$
$440$		0			0
$441$	−4.50000	+	7.79423i	−0.214286	+	0.371154i
$442$			48.0000i			2.28313i
$443$	6.92820	−	4.00000i	0.329169	−	0.190046i	−0.326303	−	0.945265i	$-0.605803\pi$
$443$	6.92820	−	4.00000i	0.329169	−	0.190046i	0.655472	+	0.755219i	$0.272470\pi$
$444$	16.0000	+	27.7128i	0.759326	+	1.31519i
$445$		0			0
$446$	28.0000	−	48.4974i	1.32584	−	2.29642i
$447$	5.19615	−	3.00000i	0.245770	−	0.141895i
$448$	−27.7128	−	16.0000i	−1.30931	−	0.755929i
$449$	2.00000			0.0943858			0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000			0.0943858			0.0471929	+	0.998886i	$0.484972\pi$
$450$		0			0
$451$	7.50000	−	12.9904i	0.353161	−	0.611693i
$452$	−10.3923	+	6.00000i	−0.488813	+	0.282216i
$453$		0			0
$454$	20.0000	+	34.6410i	0.938647	+	1.62578i
$455$		0			0
$456$		0			0
$457$		−	32.0000i		−	1.49690i	−0.663193	−	0.748448i	$-0.730799\pi$
$457$		−	32.0000i		−	1.49690i	0.663193	−	0.748448i	$-0.269201\pi$
$458$	−15.5885	−	9.00000i	−0.728401	−	0.420542i
$459$	8.00000	−	13.8564i	0.373408	−	0.646762i
$460$		0			0
$461$	−6.00000			−0.279448			−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000			−0.279448			−0.139724	+	0.990190i	$0.544622\pi$
$462$	69.2820	+	40.0000i	3.22329	+	1.86097i
$463$			34.0000i			1.58011i	0.613033	+	0.790057i	$0.289949\pi$
$463$			34.0000i			1.58011i	−0.613033	+	0.790057i	$0.710051\pi$
$464$	−12.0000			−0.557086
$465$		0			0
$466$	−48.0000			−2.22356
$467$		−	32.0000i		−	1.48078i	−0.672176	−	0.740392i	$-0.734640\pi$
$467$		−	32.0000i		−	1.48078i	0.672176	−	0.740392i	$-0.265360\pi$
$468$	10.3923	+	6.00000i	0.480384	+	0.277350i
$469$	−8.00000			−0.369406
$470$		0			0
$471$	10.0000	−	17.3205i	0.460776	−	0.798087i
$472$		0			0
$473$		0			0
$474$	−6.00000	−	10.3923i	−0.275589	−	0.477334i
$475$		0			0
$476$	16.0000	+	27.7128i	0.733359	+	1.27021i
$477$	−5.19615	−	3.00000i	−0.237915	−	0.137361i
$478$	−19.0526	+	11.0000i	−0.871444	+	0.503128i
$479$	−12.5000	+	21.6506i	−0.571140	+	0.989243i	0.425310	+	0.905048i	$0.360165\pi$
$479$	−12.5000	+	21.6506i	−0.571140	+	0.989243i	−0.996449	+	0.0841949i	$0.973168\pi$
$480$		0			0
$481$	48.0000			2.18861
$482$	−38.1051	−	22.0000i	−1.73564	−	1.00207i
$483$	13.8564	−	8.00000i	0.630488	−	0.364013i
$484$	14.0000	−	24.2487i	0.636364	−	1.10221i
$485$		0			0
$486$	−10.0000	−	17.3205i	−0.453609	−	0.785674i
$487$	22.5167	−	13.0000i	1.02033	−	0.589086i	0.106129	−	0.994352i	$-0.466154\pi$
$487$	22.5167	−	13.0000i	1.02033	−	0.589086i	0.914199	+	0.405266i	$0.132821\pi$
$488$		0			0
$489$	2.00000	−	3.46410i	0.0904431	−	0.156652i
$490$		0			0
$491$	7.50000	+	12.9904i	0.338470	+	0.586248i	0.984145	−	0.177365i	$-0.0567572\pi$
$491$	7.50000	+	12.9904i	0.338470	+	0.586248i	−0.645675	+	0.763612i	$0.723424\pi$
$492$		−	12.0000i		−	0.541002i
$493$	10.3923	+	6.00000i	0.468046	+	0.270226i
$494$	48.0000			2.15962
$495$		0			0
$496$	−22.0000	+	3.46410i	−0.987829	+	0.155543i
$497$			12.0000i			0.538274i
$498$			16.0000i			0.716977i
$499$	21.5000	−	37.2391i	0.962472	−	1.66705i	0.246214	−	0.969216i	$-0.420813\pi$
$499$	21.5000	−	37.2391i	0.962472	−	1.66705i	0.716258	−	0.697835i	$-0.245853\pi$
$500$		0			0
$501$	−4.00000	−	6.92820i	−0.178707	−	0.309529i
$502$	−27.7128	−	16.0000i	−1.23688	−	0.714115i
$503$	5.19615	+	3.00000i	0.231685	+	0.133763i	0.611349	−	0.791361i	$-0.290627\pi$
$503$	5.19615	+	3.00000i	0.231685	+	0.133763i	−0.379664	+	0.925124i	$0.623960\pi$
$504$		0			0
$505$		0			0
$506$	−10.0000	−	17.3205i	−0.444554	−	0.769991i
$507$	39.8372	−	23.0000i	1.76923	−	1.02147i
$508$	−17.3205	−	10.0000i	−0.768473	−	0.443678i
$509$	8.50000	+	14.7224i	0.376756	+	0.652560i	0.990588	−	0.136876i	$-0.0437062\pi$
$509$	8.50000	+	14.7224i	0.376756	+	0.652560i	−0.613832	+	0.789436i	$0.710373\pi$
$510$		0			0
$511$	−16.0000			−0.707798
$512$		−	32.0000i		−	1.41421i
$513$	−13.8564	−	8.00000i	−0.611775	−	0.353209i
$514$	−24.0000	−	41.5692i	−1.05859	−	1.83354i
$515$		0			0
$516$		0			0
$517$	−34.6410	+	20.0000i	−1.52351	+	0.879599i
$518$	55.4256	−	32.0000i	2.43526	−	1.40600i
$519$	−12.0000			−0.526742
$520$		0			0
$521$	−7.50000	+	12.9904i	−0.328581	+	0.569119i	−0.982231	−	0.187678i	$-0.939904\pi$
$521$	−7.50000	+	12.9904i	−0.328581	+	0.569119i	0.653650	+	0.756797i	$0.273237\pi$
$522$	5.19615	−	3.00000i	0.227429	−	0.131306i
$523$		−	10.0000i		−	0.437269i	−0.975807	−	0.218635i	$-0.929840\pi$
$523$		−	10.0000i		−	0.437269i	0.975807	−	0.218635i	$-0.0701603\pi$
$524$	13.0000	−	22.5167i	0.567908	−	0.983645i
$525$		0			0
$526$	12.0000			0.523225
$527$	20.7846	+	8.00000i	0.905392	+	0.348485i
$528$			40.0000i			1.74078i
$529$	19.0000			0.826087
$530$		0			0
$531$	13.0000			0.564152
$532$	27.7128	−	16.0000i	1.20150	−	0.693688i
$533$	−15.5885	−	9.00000i	−0.675211	−	0.389833i
$534$	22.0000	−	38.1051i	0.952033	−	1.64897i
$535$		0			0
$536$		0			0
$537$	−32.9090	+	19.0000i	−1.42013	+	0.819911i
$538$	5.19615	−	3.00000i	0.224022	−	0.129339i
$539$	22.5000	−	38.9711i	0.969144	−	1.67861i
$540$		0			0
$541$	14.5000	−	25.1147i	0.623404	−	1.07977i	−0.365444	−	0.930834i	$-0.619083\pi$
$541$	14.5000	−	25.1147i	0.623404	−	1.07977i	0.988847	−	0.148933i	$-0.0475840\pi$
$542$			62.0000i			2.66313i
$543$			12.0000i			0.514969i
$544$	−16.0000	+	27.7128i	−0.685994	+	1.18818i
$545$		0			0
$546$	48.0000	−	83.1384i	2.05421	−	3.55800i
$547$	1.73205	−	1.00000i	0.0740571	−	0.0427569i	−0.462514	−	0.886612i	$-0.653053\pi$
$547$	1.73205	−	1.00000i	0.0740571	−	0.0427569i	0.536571	+	0.843855i	$0.319719\pi$
$548$	31.1769	−	18.0000i	1.33181	−	0.768922i
$549$	0.500000	+	0.866025i	0.0213395	+	0.0369611i
$550$		0			0
$551$	6.00000	−	10.3923i	0.255609	−	0.442727i
$552$		0			0
$553$	−10.3923	+	6.00000i	−0.441926	+	0.255146i
$554$	4.00000			0.169944
$555$		0			0
$556$	18.0000			0.763370
$557$			4.00000i			0.169485i	0.996403	+	0.0847427i	$0.0270068\pi$
$557$			4.00000i			0.169485i	−0.996403	+	0.0847427i	$0.972993\pi$
$558$	8.66025	−	7.00000i	0.366618	−	0.296334i
$559$		0			0
$560$		0			0
$561$	20.0000	−	34.6410i	0.844401	−	1.46254i
$562$			6.00000i			0.253095i
$563$	20.7846	−	12.0000i	0.875967	−	0.505740i	0.00664037	−	0.999978i	$-0.497886\pi$
$563$	20.7846	−	12.0000i	0.875967	−	0.505740i	0.869326	+	0.494238i	$0.164553\pi$
$564$	−16.0000	+	27.7128i	−0.673722	+	1.16692i
$565$		0			0
$566$	16.0000			0.672530
$567$	−38.1051	+	22.0000i	−1.60026	+	0.923913i
$568$		0			0
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	0.979313	−	0.202350i	$-0.0648579\pi$
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	−0.664897	+	0.746935i	$0.731525\pi$
$570$		0			0
$571$	−3.50000	−	6.06218i	−0.146470	−	0.253694i	0.783450	−	0.621455i	$-0.213458\pi$
$571$	−3.50000	−	6.06218i	−0.146470	−	0.253694i	−0.929921	+	0.367760i	$0.880125\pi$
$572$	−51.9615	−	30.0000i	−2.17262	−	1.25436i
$573$		−	14.0000i		−	0.584858i
$574$	−24.0000			−1.00174
$575$		0			0
$576$	4.00000	+	6.92820i	0.166667	+	0.288675i
$577$	−39.8372	−	23.0000i	−1.65844	−	0.957503i	−0.973434	−	0.228968i	$-0.926465\pi$
$577$	−39.8372	−	23.0000i	−1.65844	−	0.957503i	−0.685009	−	0.728535i	$-0.740202\pi$
$578$	−1.73205	+	1.00000i	−0.0720438	+	0.0415945i
$579$	−24.0000	−	41.5692i	−0.997406	−	1.72756i
$580$		0			0
$581$	16.0000			0.663792
$582$		0			0
$583$	25.9808	+	15.0000i	1.07601	+	0.621237i
$584$		0			0
$585$		0			0
$586$	−16.0000	+	27.7128i	−0.660954	+	1.14481i
$587$		−	18.0000i		−	0.742940i	−0.928445	−	0.371470i	$-0.878854\pi$
$587$		−	18.0000i		−	0.742940i	0.928445	−	0.371470i	$-0.121146\pi$
$588$		−	36.0000i		−	1.48461i
$589$	8.00000	−	20.7846i	0.329634	−	0.856415i
$590$		0			0
$591$	4.00000			0.164538
$592$	27.7128	+	16.0000i	1.13899	+	0.657596i
$593$			6.00000i			0.246390i	0.992382	+	0.123195i	$0.0393141\pi$
$593$			6.00000i			0.246390i	−0.992382	+	0.123195i	$0.960686\pi$
$594$	20.0000	+	34.6410i	0.820610	+	1.42134i
$595$		0			0
$596$	−3.00000	+	5.19615i	−0.122885	+	0.212843i
$597$			32.0000i			1.30967i
$598$	−20.7846	+	12.0000i	−0.849946	+	0.490716i
$599$	9.50000	+	16.4545i	0.388159	+	0.672312i	0.992202	−	0.124640i	$-0.0397776\pi$
$599$	9.50000	+	16.4545i	0.388159	+	0.672312i	−0.604043	+	0.796952i	$0.706444\pi$
$600$		0			0
$601$	−2.50000	+	4.33013i	−0.101977	+	0.176630i	−0.912499	−	0.409079i	$-0.865850\pi$
$601$	−2.50000	+	4.33013i	−0.101977	+	0.176630i	0.810522	+	0.585708i	$0.199184\pi$
$602$		0			0
$603$	1.73205	+	1.00000i	0.0705346	+	0.0407231i
$604$		0			0
$605$		0			0
$606$	−20.0000	+	34.6410i	−0.812444	+	1.40720i
$607$	38.1051	−	22.0000i	1.54664	−	0.892952i	0.548244	−	0.836318i	$-0.315297\pi$
$607$	38.1051	−	22.0000i	1.54664	−	0.892952i	0.998395	−	0.0566340i	$-0.0180368\pi$
$608$	27.7128	+	16.0000i	1.12390	+	0.648886i
$609$	−12.0000	−	20.7846i	−0.486265	−	0.842235i
$610$		0			0
$611$	24.0000	+	41.5692i	0.970936	+	1.68171i
$612$		−	8.00000i		−	0.323381i
$613$	39.8372	+	23.0000i	1.60901	+	0.928961i	0.989593	+	0.143898i	$0.0459637\pi$
$613$	39.8372	+	23.0000i	1.60901	+	0.928961i	0.619416	+	0.785063i	$0.287370\pi$
$614$	14.0000	−	24.2487i	0.564994	−	0.978598i
$615$		0			0
$616$		0			0
$617$	17.3205	+	10.0000i	0.697297	+	0.402585i	0.806340	−	0.591452i	$-0.201445\pi$
$617$	17.3205	+	10.0000i	0.697297	+	0.402585i	−0.109043	+	0.994037i	$0.534779\pi$
$618$		−	40.0000i		−	1.60904i
$619$	−35.0000			−1.40677			−0.703384	−	0.710810i	$-0.748329\pi$
$619$	−35.0000			−1.40677			−0.703384	+	0.710810i	$0.748329\pi$
$620$		0			0
$621$	8.00000			0.321029
$622$			66.0000i			2.64636i
$623$	−38.1051	−	22.0000i	−1.52665	−	0.881411i
$624$	48.0000			1.92154
$625$		0			0
$626$	28.0000	−	48.4974i	1.11911	−	1.93835i
$627$	−34.6410	−	20.0000i	−1.38343	−	0.798723i
$628$			20.0000i			0.798087i
$629$	−16.0000	−	27.7128i	−0.637962	−	1.10498i
$630$		0			0
$631$	−2.50000	−	4.33013i	−0.0995234	−	0.172380i	0.811964	−	0.583707i	$-0.198398\pi$
$631$	−2.50000	−	4.33013i	−0.0995234	−	0.172380i	−0.911487	+	0.411328i	$0.865065\pi$
$632$		0			0
$633$	32.9090	−	19.0000i	1.30801	−	0.755182i
$634$	−6.00000	+	10.3923i	−0.238290	+	0.412731i
$635$		0			0
$636$	24.0000			0.951662
$637$	−46.7654	−	27.0000i	−1.85291	−	1.06978i
$638$	−25.9808	+	15.0000i	−1.02859	+	0.593856i
$639$	1.50000	−	2.59808i	0.0593391	−	0.102778i
$640$		0			0
$641$	−5.00000	−	8.66025i	−0.197488	−	0.342059i	0.750225	−	0.661182i	$-0.229945\pi$
$641$	−5.00000	−	8.66025i	−0.197488	−	0.342059i	−0.947713	+	0.319123i	$0.896612\pi$
$642$	48.4974	−	28.0000i	1.91404	−	1.10507i
$643$		−	22.0000i		−	0.867595i	−0.901010	−	0.433798i	$-0.857173\pi$
$643$		−	22.0000i		−	0.867595i	0.901010	−	0.433798i	$-0.142827\pi$
$644$	−8.00000	+	13.8564i	−0.315244	+	0.546019i
$645$		0			0
$646$	−16.0000	−	27.7128i	−0.629512	−	1.09035i
$647$			14.0000i			0.550397i	0.961387	+	0.275198i	$0.0887435\pi$
$647$			14.0000i			0.550397i	−0.961387	+	0.275198i	$0.911256\pi$
$648$		0			0
$649$	−65.0000			−2.55147
$650$		0			0
$651$	−28.0000	−	34.6410i	−1.09741	−	1.35769i
$652$			4.00000i			0.156652i
$653$		−	34.0000i		−	1.33052i	−0.746611	−	0.665261i	$-0.768320\pi$
$653$		−	34.0000i		−	1.33052i	0.746611	−	0.665261i	$-0.231680\pi$
$654$	10.0000	−	17.3205i	0.391031	−	0.677285i
$655$		0			0
$656$	−6.00000	−	10.3923i	−0.234261	−	0.405751i
$657$	3.46410	+	2.00000i	0.135147	+	0.0780274i
$658$	55.4256	+	32.0000i	2.16072	+	1.24749i
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		0			0
$661$	13.0000	+	22.5167i	0.505641	+	0.875797i	0.999979	+	0.00652642i	$0.00207744\pi$
$661$	13.0000	+	22.5167i	0.505641	+	0.875797i	−0.494337	+	0.869270i	$0.664589\pi$
$662$	12.1244	−	7.00000i	0.471226	−	0.272063i
$663$	−41.5692	−	24.0000i	−1.61441	−	0.932083i
$664$		0			0
$665$		0			0
$666$	−16.0000			−0.619987
$667$			6.00000i			0.232321i
$668$	6.92820	+	4.00000i	0.268060	+	0.154765i
$669$	28.0000	+	48.4974i	1.08254	+	1.87502i
$670$		0			0
$671$	−2.50000	−	4.33013i	−0.0965114	−	0.167163i
$672$	55.4256	−	32.0000i	2.13809	−	1.23443i
$673$	−24.2487	+	14.0000i	−0.934719	+	0.539660i	−0.888301	−	0.459262i	$-0.848114\pi$
$673$	−24.2487	+	14.0000i	−0.934719	+	0.539660i	−0.0464181	+	0.998922i	$0.514781\pi$
$674$	44.0000			1.69482
$675$		0			0
$676$	−23.0000	+	39.8372i	−0.884615	+	1.53220i
$677$	3.46410	−	2.00000i	0.133136	−	0.0768662i	−0.431953	−	0.901896i	$-0.642175\pi$
$677$	3.46410	−	2.00000i	0.133136	−	0.0768662i	0.565089	+	0.825030i	$0.308842\pi$
$678$		−	24.0000i		−	0.921714i
$679$		0			0
$680$		0			0
$681$	−40.0000			−1.53280
$682$	−43.3013	+	35.0000i	−1.65809	+	1.34022i
$683$			16.0000i			0.612223i	0.951996	+	0.306111i	$0.0990280\pi$
$683$			16.0000i			0.612223i	−0.951996	+	0.306111i	$0.900972\pi$
$684$	−8.00000			−0.305888
$685$		0			0
$686$	−16.0000			−0.610883
$687$	15.5885	−	9.00000i	0.594737	−	0.343371i
$688$		0			0
$689$	18.0000	−	31.1769i	0.685745	−	1.18775i
$690$		0			0
$691$	4.50000	+	7.79423i	0.171188	+	0.296506i	0.938835	−	0.344366i	$-0.111906\pi$
$691$	4.50000	+	7.79423i	0.171188	+	0.296506i	−0.767647	+	0.640872i	$0.778573\pi$
$692$	10.3923	−	6.00000i	0.395056	−	0.228086i
$693$	−17.3205	+	10.0000i	−0.657952	+	0.379869i
$694$	−18.0000	+	31.1769i	−0.683271	+	1.18346i
$695$		0			0
$696$		0			0
$697$			12.0000i			0.454532i
$698$			26.0000i			0.984115i
$699$	24.0000	−	41.5692i	0.907763	−	1.57229i
$700$		0			0
$701$	−22.5000	+	38.9711i	−0.849813	+	1.47192i	0.0315614	+	0.999502i	$0.489952\pi$
$701$	−22.5000	+	38.9711i	−0.849813	+	1.47192i	−0.881375	+	0.472418i	$0.843381\pi$
$702$	41.5692	−	24.0000i	1.56893	−	0.905822i
$703$	−27.7128	+	16.0000i	−1.04521	+	0.603451i
$704$	−20.0000	−	34.6410i	−0.753778	−	1.30558i
$705$		0			0
$706$	16.0000	−	27.7128i	0.602168	−	1.04299i
$707$	34.6410	+	20.0000i	1.30281	+	0.752177i
$708$	−45.0333	+	26.0000i	−1.69246	+	0.977140i
$709$	6.00000			0.225335			0.112667	−	0.993633i	$-0.464061\pi$
$709$	6.00000			0.225335			0.112667	+	0.993633i	$0.464061\pi$
$710$		0			0
$711$	3.00000			0.112509
$712$		0			0
$713$	1.73205	+	11.0000i	0.0648658	+	0.411953i
$714$	−64.0000			−2.39514
$715$		0			0
$716$	19.0000	−	32.9090i	0.710063	−	1.22987i
$717$		−	22.0000i		−	0.821605i
$718$	29.4449	−	17.0000i	1.09887	−	0.634434i
$719$	−4.00000	+	6.92820i	−0.149175	+	0.258378i	−0.930923	−	0.365216i	$-0.880995\pi$
$719$	−4.00000	+	6.92820i	−0.149175	+	0.258378i	0.781748	+	0.623595i	$0.214328\pi$
$720$		0			0
$721$	−40.0000			−1.48968
$722$	5.19615	−	3.00000i	0.193381	−	0.111648i
$723$	38.1051	−	22.0000i	1.41714	−	0.818189i
$724$	−6.00000	−	10.3923i	−0.222988	−	0.386227i
$725$		0			0
$726$	28.0000	+	48.4974i	1.03918	+	1.79991i
$727$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$727$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$		0			0
$732$	−3.46410	−	2.00000i	−0.128037	−	0.0739221i
$733$	−45.0333	+	26.0000i	−1.66334	+	0.960332i	−0.692242	+	0.721665i	$0.743377\pi$
$733$	−45.0333	+	26.0000i	−1.66334	+	0.960332i	−0.971102	+	0.238667i	$0.923290\pi$
$734$	−16.0000	−	27.7128i	−0.590571	−	1.02290i
$735$		0			0
$736$	−16.0000			−0.589768
$737$	−8.66025	−	5.00000i	−0.319005	−	0.184177i
$738$	5.19615	+	3.00000i	0.191273	+	0.110432i
$739$	15.5000	+	26.8468i	0.570177	+	0.987575i	0.996547	+	0.0830265i	$0.0264586\pi$
$739$	15.5000	+	26.8468i	0.570177	+	0.987575i	−0.426371	+	0.904549i	$0.640208\pi$
$740$		0			0
$741$	−24.0000	+	41.5692i	−0.881662	+	1.52708i
$742$		−	48.0000i		−	1.76214i
$743$		−	6.00000i		−	0.220119i	−0.993925	−	0.110059i	$-0.964896\pi$
$743$		−	6.00000i		−	0.220119i	0.993925	−	0.110059i	$-0.0351041\pi$
$744$		0			0
$745$		0			0
$746$	−64.0000			−2.34321
$747$	−3.46410	−	2.00000i	−0.126745	−	0.0731762i
$748$			40.0000i			1.46254i
$749$	−28.0000	−	48.4974i	−1.02310	−	1.77206i
$750$		0			0
$751$	4.00000	−	6.92820i	0.145962	−	0.252814i	−0.783769	−	0.621052i	$-0.786706\pi$
$751$	4.00000	−	6.92820i	0.145962	−	0.252814i	0.929731	+	0.368238i	$0.120039\pi$
$752$			32.0000i			1.16692i
$753$	27.7128	−	16.0000i	1.00991	−	0.583072i
$754$	18.0000	+	31.1769i	0.655521	+	1.13540i
$755$		0			0
$756$	16.0000	−	27.7128i	0.581914	−	1.00791i
$757$	19.0526	−	11.0000i	0.692477	−	0.399802i	−0.112062	−	0.993701i	$-0.535746\pi$
$757$	19.0526	−	11.0000i	0.692477	−	0.399802i	0.804539	+	0.593899i	$0.202412\pi$
$758$	13.8564	+	8.00000i	0.503287	+	0.290573i
$759$	20.0000			0.725954
$760$		0			0
$761$	−15.0000	+	25.9808i	−0.543750	+	0.941802i	0.454935	+	0.890525i	$0.349663\pi$
$761$	−15.0000	+	25.9808i	−0.543750	+	0.941802i	−0.998684	+	0.0512772i	$0.983671\pi$
$762$	34.6410	−	20.0000i	1.25491	−	0.724524i
$763$	−17.3205	−	10.0000i	−0.627044	−	0.362024i
$764$	7.00000	+	12.1244i	0.253251	+	0.438644i
$765$		0			0
$766$		0			0
$767$			78.0000i			2.81642i
$768$	27.7128	+	16.0000i	1.00000	+	0.577350i
$769$	0.500000	−	0.866025i	0.0180305	−	0.0312297i	−0.856869	−	0.515534i	$-0.827594\pi$
$769$	0.500000	−	0.866025i	0.0180305	−	0.0312297i	0.874900	+	0.484304i	$0.160927\pi$
$770$		0			0
$771$	48.0000			1.72868
$772$	41.5692	+	24.0000i	1.49611	+	0.863779i
$773$			24.0000i			0.863220i	0.902060	+	0.431610i	$0.142054\pi$
$773$			24.0000i			0.863220i	−0.902060	+	0.431610i	$0.857946\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$			64.0000i			2.29599i
$778$	29.4449	+	17.0000i	1.05565	+	0.609480i
$779$	12.0000			0.429945
$780$		0			0
$781$	−7.50000	+	12.9904i	−0.268371	+	0.464832i
$782$	13.8564	+	8.00000i	0.495504	+	0.286079i
$783$		−	12.0000i		−	0.428845i
$784$	−18.0000	−	31.1769i	−0.642857	−	1.11346i
$785$		0			0
$786$	26.0000	+	45.0333i	0.927389	+	1.60629i
$787$	−24.2487	−	14.0000i	−0.864373	−	0.499046i	0.00110111	−	0.999999i	$-0.499650\pi$
$787$	−24.2487	−	14.0000i	−0.864373	−	0.499046i	−0.865474	+	0.500953i	$0.832983\pi$
$788$	−3.46410	+	2.00000i	−0.123404	+	0.0712470i
$789$	−6.00000	+	10.3923i	−0.213606	+	0.369976i
$790$		0			0
$791$	−24.0000			−0.853342
$792$		0			0
$793$	−5.19615	+	3.00000i	−0.184521	+	0.106533i
$794$	−14.0000	+	24.2487i	−0.496841	+	0.860555i
$795$		0			0
$796$	−16.0000	−	27.7128i	−0.567105	−	0.982255i
$797$	15.5885	−	9.00000i	0.552171	−	0.318796i	−0.197826	−	0.980237i	$-0.563388\pi$
$797$	15.5885	−	9.00000i	0.552171	−	0.318796i	0.749997	+	0.661441i	$0.230055\pi$
$798$			64.0000i			2.26558i
$799$	16.0000	−	27.7128i	0.566039	−	0.980409i
$800$		0			0
$801$	5.50000	+	9.52628i	0.194333	+	0.336595i
$802$		−	38.0000i		−	1.34183i
$803$	−17.3205	−	10.0000i	−0.611227	−	0.352892i
$804$	−8.00000			−0.282138
$805$		0			0
$806$	42.0000	+	51.9615i	1.47939	+	1.83027i
$807$			6.00000i			0.211210i
$808$		0			0
$809$	−15.0000	+	25.9808i	−0.527372	+	0.913435i	0.472119	+	0.881535i	$0.343489\pi$
$809$	−15.0000	+	25.9808i	−0.527372	+	0.913435i	−0.999491	+	0.0319002i	$0.989844\pi$
$810$		0			0
$811$	−5.50000	−	9.52628i	−0.193131	−	0.334513i	0.753155	−	0.657843i	$-0.228531\pi$
$811$	−5.50000	−	9.52628i	−0.193131	−	0.334513i	−0.946286	+	0.323330i	$0.895198\pi$
$812$	20.7846	+	12.0000i	0.729397	+	0.421117i
$813$	−53.6936	−	31.0000i	−1.88312	−	1.08722i
$814$	80.0000			2.80400
$815$		0			0
$816$	−16.0000	−	27.7128i	−0.560112	−	0.970143i
$817$		0			0
$818$	10.3923	+	6.00000i	0.363358	+	0.209785i
$819$	12.0000	+	20.7846i	0.419314	+	0.726273i
$820$		0			0
$821$	9.00000			0.314102			0.157051	−	0.987590i	$-0.449801\pi$
$821$	9.00000			0.314102			0.157051	+	0.987590i	$0.449801\pi$
$822$			72.0000i			2.51129i
$823$	−27.7128	−	16.0000i	−0.966008	−	0.557725i	−0.0679910	−	0.997686i	$-0.521659\pi$
$823$	−27.7128	−	16.0000i	−0.966008	−	0.557725i	−0.898017	+	0.439961i	$0.854992\pi$
$824$		0			0
$825$		0			0
$826$	52.0000	+	90.0666i	1.80931	+	3.13382i
$827$	41.5692	−	24.0000i	1.44550	−	0.834562i	0.447295	−	0.894387i	$-0.352388\pi$
$827$	41.5692	−	24.0000i	1.44550	−	0.834562i	0.998209	+	0.0598250i	$0.0190543\pi$
$828$	3.46410	−	2.00000i	0.120386	−	0.0695048i
$829$	−23.0000			−0.798823			−0.399412	−	0.916772i	$-0.630786\pi$
$829$	−23.0000			−0.798823			−0.399412	+	0.916772i	$0.630786\pi$
$830$		0			0
$831$	−2.00000	+	3.46410i	−0.0693792	+	0.120168i
$832$	−41.5692	+	24.0000i	−1.44115	+	0.832050i
$833$			36.0000i			1.24733i
$834$	−18.0000	+	31.1769i	−0.623289	+	1.07957i
$835$		0			0
$836$	40.0000			1.38343
$837$	−3.46410	−	22.0000i	−0.119737	−	0.760431i
$838$		−	50.0000i		−	1.72722i
$839$	51.0000			1.76072			0.880358	−	0.474310i	$-0.157302\pi$
$839$	51.0000			1.76072			0.880358	+	0.474310i	$0.157302\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$	25.9808	−	15.0000i	0.895356	−	0.516934i
$843$	−5.19615	−	3.00000i	−0.178965	−	0.103325i
$844$	−19.0000	+	32.9090i	−0.654007	+	1.13277i
$845$		0			0
$846$	−8.00000	−	13.8564i	−0.275046	−	0.476393i
$847$	48.4974	−	28.0000i	1.66639	−	0.962091i
$848$	20.7846	−	12.0000i	0.713746	−	0.412082i
$849$	−8.00000	+	13.8564i	−0.274559	+	0.475551i
$850$		0			0
$851$	8.00000	−	13.8564i	0.274236	−	0.474991i
$852$			12.0000i			0.411113i
$853$		−	4.00000i		−	0.136957i	−0.997653	−	0.0684787i	$-0.978185\pi$
$853$		−	4.00000i		−	0.136957i	0.997653	−	0.0684787i	$-0.0218145\pi$
$854$	−4.00000	+	6.92820i	−0.136877	+	0.237078i
$855$		0			0
$856$		0			0
$857$	−31.1769	+	18.0000i	−1.06498	+	0.614868i	−0.926806	−	0.375539i	$-0.877458\pi$
$857$	−31.1769	+	18.0000i	−1.06498	+	0.614868i	−0.138177	+	0.990408i	$0.544124\pi$
$858$	103.923	−	60.0000i	3.54787	−	2.04837i
$859$	−2.50000	−	4.33013i	−0.0852989	−	0.147742i	0.820220	−	0.572049i	$-0.193851\pi$
$859$	−2.50000	−	4.33013i	−0.0852989	−	0.147742i	−0.905519	+	0.424307i	$0.860518\pi$
$860$		0			0
$861$	12.0000	−	20.7846i	0.408959	−	0.708338i
$862$	19.0526	+	11.0000i	0.648933	+	0.374661i
$863$	−48.4974	+	28.0000i	−1.65087	+	0.953131i	−0.674157	+	0.738588i	$0.735493\pi$
$863$	−48.4974	+	28.0000i	−1.65087	+	0.953131i	−0.976715	+	0.214543i	$0.931174\pi$
$864$	32.0000			1.08866
$865$		0			0
$866$	−60.0000			−2.03888
$867$		−	2.00000i		−	0.0679236i
$868$	41.5692	+	16.0000i	1.41095	+	0.543075i
$869$	−15.0000			−0.508840
$870$		0			0
$871$	−6.00000	+	10.3923i	−0.203302	+	0.352130i
$872$		0			0
$873$		0			0
$874$	8.00000	−	13.8564i	0.270604	−	0.468700i
$875$		0			0
$876$	−16.0000			−0.540590
$877$	−5.19615	+	3.00000i	−0.175462	+	0.101303i	−0.585159	−	0.810919i	$-0.698968\pi$
$877$	−5.19615	+	3.00000i	−0.175462	+	0.101303i	0.409697	+	0.912222i	$0.365634\pi$
$878$	−36.3731	+	21.0000i	−1.22753	+	0.708716i
$879$	−16.0000	−	27.7128i	−0.539667	−	0.934730i
$880$		0			0
$881$	−1.00000	−	1.73205i	−0.0336909	−	0.0583543i	0.848688	−	0.528893i	$-0.177393\pi$
$881$	−1.00000	−	1.73205i	−0.0336909	−	0.0583543i	−0.882379	+	0.470539i	$0.844059\pi$
$882$	15.5885	+	9.00000i	0.524891	+	0.303046i
$883$		−	16.0000i		−	0.538443i	−0.963078	−	0.269221i	$-0.913234\pi$
$883$		−	16.0000i		−	0.538443i	0.963078	−	0.269221i	$-0.0867663\pi$
$884$	48.0000			1.61441
$885$		0			0
$886$	−8.00000	−	13.8564i	−0.268765	−	0.465515i
$887$	−5.19615	−	3.00000i	−0.174470	−	0.100730i	0.410222	−	0.911986i	$-0.365451\pi$
$887$	−5.19615	−	3.00000i	−0.174470	−	0.100730i	−0.584692	+	0.811256i	$0.698785\pi$
$888$		0			0
$889$	−20.0000	−	34.6410i	−0.670778	−	1.16182i
$890$		0			0
$891$	−55.0000			−1.84257
$892$	−48.4974	−	28.0000i	−1.62381	−	0.937509i
$893$	−27.7128	−	16.0000i	−0.927374	−	0.535420i
$894$	−6.00000	−	10.3923i	−0.200670	−	0.347571i
$895$		0			0
$896$		0			0
$897$		−	24.0000i		−	0.801337i
$898$		−	4.00000i		−	0.133482i
$899$	16.5000	−	2.59808i	0.550306	−	0.0866507i
$900$		0			0
$901$	−24.0000			−0.799556
$902$	−25.9808	−	15.0000i	−0.865065	−	0.499445i
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		−	36.0000i		−	1.19536i	−0.801735	−	0.597680i	$-0.796089\pi$
$907$		−	36.0000i		−	1.19536i	0.801735	−	0.597680i	$-0.203911\pi$
$908$	34.6410	−	20.0000i	1.14960	−	0.663723i
$909$	−5.00000	−	8.66025i	−0.165840	−	0.287242i
$910$		0			0
$911$	2.50000	−	4.33013i	0.0828287	−	0.143464i	−0.821635	−	0.570014i	$-0.806938\pi$
$911$	2.50000	−	4.33013i	0.0828287	−	0.143464i	0.904464	+	0.426550i	$0.140271\pi$
$912$	−27.7128	+	16.0000i	−0.917663	+	0.529813i
$913$	17.3205	+	10.0000i	0.573225	+	0.330952i
$914$	−64.0000			−2.11693
$915$		0			0
$916$	−9.00000	+	15.5885i	−0.297368	+	0.515057i
$917$	45.0333	−	26.0000i	1.48713	−	0.858596i
$918$	−27.7128	−	16.0000i	−0.914659	−	0.528079i
$919$	5.50000	+	9.52628i	0.181428	+	0.314243i	0.942367	−	0.334581i	$-0.108595\pi$
$919$	5.50000	+	9.52628i	0.181428	+	0.314243i	−0.760939	+	0.648824i	$0.775261\pi$
$920$		0			0
$921$	14.0000	+	24.2487i	0.461316	+	0.799022i
$922$			12.0000i			0.395199i
$923$	15.5885	+	9.00000i	0.513100	+	0.296239i
$924$	40.0000	−	69.2820i	1.31590	−	2.27921i
$925$		0			0
$926$	68.0000			2.23462
$927$	8.66025	+	5.00000i	0.284440	+	0.164222i
$928$			24.0000i			0.787839i
$929$	−19.0000			−0.623370			−0.311685	−	0.950186i	$-0.600893\pi$
$929$	−19.0000			−0.623370			−0.311685	+	0.950186i	$0.600893\pi$
$930$		0			0
$931$	36.0000			1.17985
$932$			48.0000i			1.57229i
$933$	−57.1577	−	33.0000i	−1.87126	−	1.08037i
$934$	−64.0000			−2.09414
$935$		0			0
$936$		0			0
$937$	41.5692	+	24.0000i	1.35801	+	0.784046i	0.989355	−	0.145522i	$-0.0464860\pi$
$937$	41.5692	+	24.0000i	1.35801	+	0.784046i	0.368652	+	0.929567i	$0.379819\pi$
$938$			16.0000i			0.522419i
$939$	28.0000	+	48.4974i	0.913745	+	1.58265i
$940$		0			0
$941$	3.00000	+	5.19615i	0.0977972	+	0.169390i	0.910773	−	0.412908i	$-0.135487\pi$
$941$	3.00000	+	5.19615i	0.0977972	+	0.169390i	−0.812975	+	0.582298i	$0.802154\pi$
$942$	−34.6410	−	20.0000i	−1.12867	−	0.651635i
$943$	−5.19615	+	3.00000i	−0.169210	+	0.0976934i
$944$	−26.0000	+	45.0333i	−0.846228	+	1.46571i
$945$		0			0
$946$		0			0
$947$	15.5885	+	9.00000i	0.506557	+	0.292461i	0.731417	−	0.681930i	$-0.238859\pi$
$947$	15.5885	+	9.00000i	0.506557	+	0.292461i	−0.224860	+	0.974391i	$0.572193\pi$
$948$	−10.3923	+	6.00000i	−0.337526	+	0.194871i
$949$	−12.0000	+	20.7846i	−0.389536	+	0.674697i
$950$		0			0
$951$	−6.00000	−	10.3923i	−0.194563	−	0.336994i
$952$		0			0
$953$			6.00000i			0.194359i	0.995267	+	0.0971795i	$0.0309821\pi$
$953$			6.00000i			0.194359i	−0.995267	+	0.0971795i	$0.969018\pi$
$954$	−6.00000	+	10.3923i	−0.194257	+	0.336463i
$955$		0			0
$956$	11.0000	+	19.0526i	0.355765	+	0.616204i
$957$		−	30.0000i		−	0.969762i
$958$	43.3013	+	25.0000i	1.39900	+	0.807713i
$959$	72.0000			2.32500
$960$		0			0
$961$	29.5000	−	9.52628i	0.951613	−	0.307299i
$962$		−	96.0000i		−	3.09516i
$963$			14.0000i			0.451144i
$964$	−22.0000	+	38.1051i	−0.708572	+	1.22728i
$965$		0			0
$966$	−16.0000	−	27.7128i	−0.514792	−	0.891645i
$967$	−10.3923	−	6.00000i	−0.334194	−	0.192947i	0.323508	−	0.946226i	$-0.395138\pi$
$967$	−10.3923	−	6.00000i	−0.334194	−	0.192947i	−0.657702	+	0.753279i	$0.728471\pi$
$968$		0			0
$969$	32.0000			1.02799
$970$		0			0
$971$	30.0000	+	51.9615i	0.962746	+	1.66752i	0.715553	+	0.698558i	$0.246175\pi$
$971$	30.0000	+	51.9615i	0.962746	+	1.66752i	0.247193	+	0.968966i	$0.420492\pi$
$972$	−17.3205	+	10.0000i	−0.555556	+	0.320750i
$973$	31.1769	+	18.0000i	0.999486	+	0.577054i
$974$	−26.0000	−	45.0333i	−0.833094	−	1.44296i
$975$		0			0
$976$	−4.00000			−0.128037
$977$		−	6.00000i		−	0.191957i	−0.995383	−	0.0959785i	$-0.969402\pi$
$977$		−	6.00000i		−	0.191957i	0.995383	−	0.0959785i	$-0.0305980\pi$
$978$	−6.92820	−	4.00000i	−0.221540	−	0.127906i
$979$	−27.5000	−	47.6314i	−0.878904	−	1.52231i
$980$		0			0
$981$	2.50000	+	4.33013i	0.0798189	+	0.138250i
$982$	25.9808	−	15.0000i	0.829079	−	0.478669i
$983$	27.7128	−	16.0000i	0.883901	−	0.510321i	0.0119587	−	0.999928i	$-0.496193\pi$
$983$	27.7128	−	16.0000i	0.883901	−	0.510321i	0.871943	+	0.489608i	$0.162860\pi$
$984$		0			0
$985$		0			0
$986$	12.0000	−	20.7846i	0.382158	−	0.661917i
$987$	−55.4256	+	32.0000i	−1.76422	+	1.01857i
$988$		−	48.0000i		−	1.52708i
$989$		0			0
$990$		0			0
$991$	25.0000			0.794151			0.397076	−	0.917786i	$-0.370025\pi$
$991$	25.0000			0.794151			0.397076	+	0.917786i	$0.370025\pi$
$992$	6.92820	+	44.0000i	0.219971	+	1.39700i
$993$			14.0000i			0.444277i
$994$	24.0000			0.761234
$995$		0			0
$996$	16.0000			0.506979
$997$	5.19615	−	3.00000i	0.164564	−	0.0950110i	−0.415456	−	0.909613i	$-0.636378\pi$
$997$	5.19615	−	3.00000i	0.164564	−	0.0950110i	0.580020	+	0.814602i	$0.303045\pi$
$998$	−74.4782	−	43.0000i	−2.35757	−	1.36114i
$999$	−16.0000	+	27.7128i	−0.506218	+	0.876795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.o.b.749.1		4
5.2	odd	4		775.2.e.b.501.1		2
5.3	odd	4		155.2.e.a.36.1	✓	2
5.4	even	2	inner	775.2.o.b.749.2		4
31.25	even	3	inner	775.2.o.b.149.1		4
155.87	odd	12		775.2.e.b.676.1		2
155.88	even	12		4805.2.a.a.1.1		1
155.98	odd	12		4805.2.a.c.1.1		1
155.118	odd	12		155.2.e.a.56.1	yes	2
155.149	even	6	inner	775.2.o.b.149.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.e.a.36.1	✓	2	5.3	odd	4
155.2.e.a.56.1	yes	2	155.118	odd	12
775.2.e.b.501.1		2	5.2	odd	4
775.2.e.b.676.1		2	155.87	odd	12
775.2.o.b.149.1		4	31.25	even	3	inner
775.2.o.b.149.2		4	155.149	even	6	inner
775.2.o.b.749.1		4	1.1	even	1	trivial
775.2.o.b.749.2		4	5.4	even	2	inner
4805.2.a.a.1.1		1	155.88	even	12
4805.2.a.c.1.1		1	155.98	odd	12

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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +(1.73205 + 1.00000i) q^{3} -2.00000 q^{4} +(2.00000 - 3.46410i) q^{6} +(-3.46410 - 2.00000i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} +(1.73205 + 1.00000i) q^{3} -2.00000 q^{4} +(2.00000 - 3.46410i) q^{6} +(-3.46410 - 2.00000i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-2.50000 - 4.33013i) q^{11} +(-3.46410 - 2.00000i) q^{12} +(-5.19615 + 3.00000i) q^{13} +(-4.00000 + 6.92820i) q^{14} -4.00000 q^{16} +(3.46410 + 2.00000i) q^{17} +(1.73205 - 1.00000i) q^{18} +(2.00000 - 3.46410i) q^{19} +(-4.00000 - 6.92820i) q^{21} +(-8.66025 + 5.00000i) q^{22} +2.00000i q^{23} +(6.00000 + 10.3923i) q^{26} -4.00000i q^{27} +(6.92820 + 4.00000i) q^{28} +3.00000 q^{29} +(5.50000 - 0.866025i) q^{31} +8.00000i q^{32} -10.0000i q^{33} +(4.00000 - 6.92820i) q^{34} +(-1.00000 - 1.73205i) q^{36} +(-6.92820 - 4.00000i) q^{37} +(-6.92820 - 4.00000i) q^{38} -12.0000 q^{39} +(1.50000 + 2.59808i) q^{41} +(-13.8564 + 8.00000i) q^{42} +(5.00000 + 8.66025i) q^{44} +4.00000 q^{46} -8.00000i q^{47} +(-6.92820 - 4.00000i) q^{48} +(4.50000 + 7.79423i) q^{49} +(4.00000 + 6.92820i) q^{51} +(10.3923 - 6.00000i) q^{52} +(-5.19615 + 3.00000i) q^{53} -8.00000 q^{54} +(6.92820 - 4.00000i) q^{57} -6.00000i q^{58} +(6.50000 - 11.2583i) q^{59} +1.00000 q^{61} +(-1.73205 - 11.0000i) q^{62} -4.00000i q^{63} +8.00000 q^{64} -20.0000 q^{66} +(1.73205 - 1.00000i) q^{67} +(-6.92820 - 4.00000i) q^{68} +(-2.00000 + 3.46410i) q^{69} +(-1.50000 - 2.59808i) q^{71} +(3.46410 - 2.00000i) q^{73} +(-8.00000 + 13.8564i) q^{74} +(-4.00000 + 6.92820i) q^{76} +20.0000i q^{77} +24.0000i q^{78} +(1.50000 - 2.59808i) q^{79} +(5.50000 - 9.52628i) q^{81} +(5.19615 - 3.00000i) q^{82} +(-3.46410 + 2.00000i) q^{83} +(8.00000 + 13.8564i) q^{84} +(5.19615 + 3.00000i) q^{87} +11.0000 q^{89} +24.0000 q^{91} -4.00000i q^{92} +(10.3923 + 4.00000i) q^{93} -16.0000 q^{94} +(-8.00000 + 13.8564i) q^{96} +(15.5885 - 9.00000i) q^{98} +(2.50000 - 4.33013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{4} + 8 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q - 8 * q^4 + 8 * q^6 + 2 * q^9	\( 4 q - 8 q^{4} + 8 q^{6} + 2 q^{9} - 10 q^{11} - 16 q^{14} - 16 q^{16} + 8 q^{19} - 16 q^{21} + 24 q^{26} + 12 q^{29} + 22 q^{31} + 16 q^{34} - 4 q^{36} - 48 q^{39} + 6 q^{41} + 20 q^{44} + 16 q^{46} + 18 q^{49} + 16 q^{51} - 32 q^{54} + 26 q^{59} + 4 q^{61} + 32 q^{64} - 80 q^{66} - 8 q^{69} - 6 q^{71} - 32 q^{74} - 16 q^{76} + 6 q^{79} + 22 q^{81} + 32 q^{84} + 44 q^{89} + 96 q^{91} - 64 q^{94} - 32 q^{96} + 10 q^{99}+O(q^{100}) \) 4 * q - 8 * q^4 + 8 * q^6 + 2 * q^9 - 10 * q^11 - 16 * q^14 - 16 * q^16 + 8 * q^19 - 16 * q^21 + 24 * q^26 + 12 * q^29 + 22 * q^31 + 16 * q^34 - 4 * q^36 - 48 * q^39 + 6 * q^41 + 20 * q^44 + 16 * q^46 + 18 * q^49 + 16 * q^51 - 32 * q^54 + 26 * q^59 + 4 * q^61 + 32 * q^64 - 80 * q^66 - 8 * q^69 - 6 * q^71 - 32 * q^74 - 16 * q^76 + 6 * q^79 + 22 * q^81 + 32 * q^84 + 44 * q^89 + 96 * q^91 - 64 * q^94 - 32 * q^96 + 10 * q^99

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