LMFDB - Embedded newform 380.2.i.b.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(121,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("380.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.i (of order $3$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1783323.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 $ x^6 - x^5 + 5x^4 - 2x^3 + 19x^2 - 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.3
Root			$0.356769 - 0.617942i$ of defining polynomial
Character	$\chi$	$=$	380.121
Dual form			380.2.i.b.201.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60220 + 2.77509i) q^{3} +(0.500000 + 0.866025i) q^{5} -2.20440 q^{7} +(-3.63409 + 6.29444i) q^{9} +O(q^{10})$	\(q+(1.60220 + 2.77509i) q^{3} +(0.500000 + 0.866025i) q^{5} -2.20440 q^{7} +(-3.63409 + 6.29444i) q^{9} -1.20440 q^{11} +(0.500000 - 0.866025i) q^{13} +(-1.60220 + 2.77509i) q^{15} +(1.07031 + 1.85383i) q^{17} +(4.30660 - 0.673184i) q^{19} +(-3.53189 - 6.11742i) q^{21} +(4.63409 - 8.02649i) q^{23} +(-0.500000 + 0.866025i) q^{25} -13.6770 q^{27} +(-4.16599 + 7.21570i) q^{29} +8.26819 q^{31} +(-1.92969 - 3.34233i) q^{33} +(-1.10220 - 1.90907i) q^{35} -2.20440 q^{37} +3.20440 q^{39} +(3.30660 + 5.72720i) q^{41} +(-1.17251 - 2.03084i) q^{43} -7.26819 q^{45} +(4.16599 - 7.21570i) q^{47} -2.14061 q^{49} +(-3.42969 + 5.94040i) q^{51} +(-0.134095 + 0.232259i) q^{53} +(-0.602201 - 1.04304i) q^{55} +(8.76819 + 10.8726i) q^{57} +(4.16599 + 7.21570i) q^{59} +(1.70440 - 2.95211i) q^{61} +(8.01100 - 13.8755i) q^{63} +1.00000 q^{65} +(1.06379 - 1.84253i) q^{67} +29.6990 q^{69} +(5.23630 + 9.06953i) q^{71} +(2.42969 + 4.20835i) q^{73} -3.20440 q^{75} +2.65498 q^{77} +(-8.20440 - 14.2104i) q^{79} +(-11.0110 - 19.0716i) q^{81} -5.73181 q^{83} +(-1.07031 + 1.85383i) q^{85} -26.6990 q^{87} +(5.40880 - 9.36832i) q^{89} +(-1.10220 + 1.90907i) q^{91} +(13.2473 + 22.9450i) q^{93} +(2.73630 + 3.39304i) q^{95} +(-7.87039 - 13.6319i) q^{97} +(4.37691 - 7.58103i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} + 3 q^{5} + 4 q^{7} - 8 q^{9}+O(q^{10}) $ 6 * q + q^3 + 3 * q^5 + 4 * q^7 - 8 * q^9	$ 6 q + q^{3} + 3 q^{5} + 4 q^{7} - 8 q^{9} + 10 q^{11} + 3 q^{13} - q^{15} + 3 q^{17} - 16 q^{21} + 14 q^{23} - 3 q^{25} - 20 q^{27} - 6 q^{29} + 22 q^{31} - 15 q^{33} + 2 q^{35} + 4 q^{37} + 2 q^{39} - 6 q^{41} + 5 q^{43} - 16 q^{45} + 6 q^{47} - 6 q^{49} - 24 q^{51} + 13 q^{53} + 5 q^{55} + 25 q^{57} + 6 q^{59} - 7 q^{61} + 5 q^{63} + 6 q^{65} - 4 q^{67} + 30 q^{69} + 9 q^{71} + 18 q^{73} - 2 q^{75} + 40 q^{77} - 32 q^{79} - 23 q^{81} - 62 q^{83} - 3 q^{85} - 12 q^{87} - 2 q^{89} + 2 q^{91} + 14 q^{93} - 6 q^{95} - 11 q^{97} - 3 q^{99}+O(q^{100}) $ 6 * q + q^3 + 3 * q^5 + 4 * q^7 - 8 * q^9 + 10 * q^11 + 3 * q^13 - q^15 + 3 * q^17 - 16 * q^21 + 14 * q^23 - 3 * q^25 - 20 * q^27 - 6 * q^29 + 22 * q^31 - 15 * q^33 + 2 * q^35 + 4 * q^37 + 2 * q^39 - 6 * q^41 + 5 * q^43 - 16 * q^45 + 6 * q^47 - 6 * q^49 - 24 * q^51 + 13 * q^53 + 5 * q^55 + 25 * q^57 + 6 * q^59 - 7 * q^61 + 5 * q^63 + 6 * q^65 - 4 * q^67 + 30 * q^69 + 9 * q^71 + 18 * q^73 - 2 * q^75 + 40 * q^77 - 32 * q^79 - 23 * q^81 - 62 * q^83 - 3 * q^85 - 12 * q^87 - 2 * q^89 + 2 * q^91 + 14 * q^93 - 6 * q^95 - 11 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.60220	+	2.77509i	0.925031	+	1.60220i	0.791511	+	0.611155i	$0.209295\pi$
$3$	1.60220	+	2.77509i	0.925031	+	1.60220i	0.133520	+	0.991046i	$0.457372\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−2.20440			−0.833185			−0.416593	−	0.909093i	$-0.636776\pi$
$7$	−2.20440			−0.833185			−0.416593	+	0.909093i	$0.636776\pi$
$8$		0			0
$9$	−3.63409	+	6.29444i	−1.21136	+	2.09815i
$10$		0			0
$11$	−1.20440			−0.363141			−0.181570	−	0.983378i	$-0.558118\pi$
$11$	−1.20440			−0.363141			−0.181570	+	0.983378i	$0.558118\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	0.926995	+	0.375073i	$0.122382\pi$
$14$		0			0
$15$	−1.60220	+	2.77509i	−0.413686	+	0.716526i
$16$		0			0
$17$	1.07031	+	1.85383i	0.259588	+	0.449619i	0.966131	−	0.258050i	$-0.0830801\pi$
$17$	1.07031	+	1.85383i	0.259588	+	0.449619i	−0.706544	+	0.707669i	$0.749747\pi$
$18$		0			0
$19$	4.30660	−	0.673184i	0.988002	−	0.154439i
$19$	4.30660	−	0.673184i	0.988002	−	0.154439i
$20$		0			0
$21$	−3.53189	−	6.11742i	−0.770722	−	1.33493i
$22$		0			0
$23$	4.63409	−	8.02649i	0.966276	−	1.67364i	0.260127	−	0.965574i	$-0.416235\pi$
$23$	4.63409	−	8.02649i	0.966276	−	1.67364i	0.706148	−	0.708064i	$-0.250431\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−13.6770			−2.63214
$28$		0			0
$29$	−4.16599	+	7.21570i	−0.773605	+	1.33992i	0.161971	+	0.986796i	$0.448215\pi$
$29$	−4.16599	+	7.21570i	−0.773605	+	1.33992i	−0.935575	+	0.353127i	$0.885118\pi$
$30$		0			0
$31$	8.26819			1.48501			0.742505	−	0.669840i	$-0.233637\pi$
$31$	8.26819			1.48501			0.742505	+	0.669840i	$0.233637\pi$
$32$		0			0
$33$	−1.92969	−	3.34233i	−0.335916	−	0.581824i
$34$		0			0
$35$	−1.10220	−	1.90907i	−0.186306	−	0.322691i
$36$		0			0
$37$	−2.20440			−0.362401			−0.181201	−	0.983446i	$-0.557998\pi$
$37$	−2.20440			−0.362401			−0.181201	+	0.983446i	$0.557998\pi$
$38$		0			0
$39$	3.20440			0.513115
$40$		0			0
$41$	3.30660	+	5.72720i	0.516405	+	0.894439i	0.999819	+	0.0190471i	$0.00606323\pi$
$41$	3.30660	+	5.72720i	0.516405	+	0.894439i	−0.483414	+	0.875392i	$0.660603\pi$
$42$		0			0
$43$	−1.17251	−	2.03084i	−0.178806	−	0.309701i	0.762666	−	0.646793i	$-0.223890\pi$
$43$	−1.17251	−	2.03084i	−0.178806	−	0.309701i	−0.941472	+	0.337092i	$0.890557\pi$
$44$		0			0
$45$	−7.26819			−1.08348
$46$		0			0
$47$	4.16599	−	7.21570i	0.607672	−	1.05252i	−0.383951	−	0.923353i	$-0.625437\pi$
$47$	4.16599	−	7.21570i	0.607672	−	1.05252i	0.991623	−	0.129165i	$-0.0412297\pi$
$48$		0			0
$49$	−2.14061			−0.305802
$50$		0			0
$51$	−3.42969	+	5.94040i	−0.480253	+	0.831823i
$52$		0			0
$53$	−0.134095	+	0.232259i	−0.0184193	+	0.0319032i	−0.875088	−	0.483964i	$-0.839197\pi$
$53$	−0.134095	+	0.232259i	−0.0184193	+	0.0319032i	0.856669	+	0.515867i	$0.172530\pi$
$54$		0			0
$55$	−0.602201	−	1.04304i	−0.0812007	−	0.140644i
$56$		0			0
$57$	8.76819	+	10.8726i	1.16138	+	1.44012i
$58$		0			0
$59$	4.16599	+	7.21570i	0.542366	+	0.939405i	0.998768	+	0.0496310i	$0.0158045\pi$
$59$	4.16599	+	7.21570i	0.542366	+	0.939405i	−0.456402	+	0.889774i	$0.650862\pi$
$60$		0			0
$61$	1.70440	−	2.95211i	0.218226	−	0.377979i	−0.736040	−	0.676939i	$-0.763306\pi$
$61$	1.70440	−	2.95211i	0.218226	−	0.377979i	0.954266	+	0.298960i	$0.0966396\pi$
$62$		0			0
$63$	8.01100	−	13.8755i	1.00929	−	1.74814i
$64$		0			0
$65$	1.00000			0.124035
$66$		0			0
$67$	1.06379	−	1.84253i	0.129962	−	0.225101i	−0.793699	−	0.608310i	$-0.791848\pi$
$67$	1.06379	−	1.84253i	0.129962	−	0.225101i	0.923662	+	0.383209i	$0.125181\pi$
$68$		0			0
$69$	29.6990			3.57534
$70$		0			0
$71$	5.23630	+	9.06953i	0.621434	+	1.07636i	0.989219	+	0.146444i	$0.0467829\pi$
$71$	5.23630	+	9.06953i	0.621434	+	1.07636i	−0.367785	+	0.929911i	$0.619884\pi$
$72$		0			0
$73$	2.42969	+	4.20835i	0.284374	+	0.492550i	0.972457	−	0.233082i	$-0.0748809\pi$
$73$	2.42969	+	4.20835i	0.284374	+	0.492550i	−0.688083	+	0.725632i	$0.741548\pi$
$74$		0			0
$75$	−3.20440			−0.370012
$76$		0			0
$77$	2.65498			0.302564
$78$		0			0
$79$	−8.20440	−	14.2104i	−0.923067	−	1.59880i	−0.794640	−	0.607080i	$-0.792341\pi$
$79$	−8.20440	−	14.2104i	−0.923067	−	1.59880i	−0.128427	−	0.991719i	$-0.540993\pi$
$80$		0			0
$81$	−11.0110	−	19.0716i	−1.22344	−	2.11907i
$82$		0			0
$83$	−5.73181			−0.629148			−0.314574	−	0.949233i	$-0.601862\pi$
$83$	−5.73181			−0.629148			−0.314574	+	0.949233i	$0.601862\pi$
$84$		0			0
$85$	−1.07031	+	1.85383i	−0.116091	+	0.201076i
$86$		0			0
$87$	−26.6990			−2.86243
$88$		0			0
$89$	5.40880	−	9.36832i	0.573332	−	0.993040i	−0.422889	−	0.906182i	$-0.638984\pi$
$89$	5.40880	−	9.36832i	0.573332	−	0.993040i	0.996221	−	0.0868585i	$-0.0276828\pi$
$90$		0			0
$91$	−1.10220	+	1.90907i	−0.115542	+	0.200125i
$92$		0			0
$93$	13.2473	+	22.9450i	1.37368	+	2.37929i
$94$		0			0
$95$	2.73630	+	3.39304i	0.280738	+	0.348118i
$96$		0			0
$97$	−7.87039	−	13.6319i	−0.799117	−	1.38411i	−0.920192	−	0.391468i	$-0.871967\pi$
$97$	−7.87039	−	13.6319i	−0.799117	−	1.38411i	0.121075	−	0.992643i	$-0.461366\pi$
$98$		0			0
$99$	4.37691	−	7.58103i	0.439896	−	0.761922i
$100$		0			0
$101$	5.27471	−	9.13606i	0.524853	−	0.909072i	−0.474728	−	0.880133i	$-0.657454\pi$
$101$	5.27471	−	9.13606i	0.524853	−	0.909072i	0.999581	−	0.0289397i	$-0.00921308\pi$
$102$		0			0
$103$	−0.731811			−0.0721075			−0.0360537	−	0.999350i	$-0.511479\pi$
$103$	−0.731811			−0.0721075			−0.0360537	+	0.999350i	$0.511479\pi$
$104$		0			0
$105$	3.53189	−	6.11742i	0.344678	−	0.596999i
$106$		0			0
$107$	−13.3958			−1.29502			−0.647509	−	0.762058i	$-0.724189\pi$
$107$	−13.3958			−1.29502			−0.647509	+	0.762058i	$0.724189\pi$
$108$		0			0
$109$	−2.96811	−	5.14091i	−0.284293	−	0.492410i	0.688144	−	0.725574i	$-0.258426\pi$
$109$	−2.96811	−	5.14091i	−0.284293	−	0.492410i	−0.972437	+	0.233164i	$0.925092\pi$
$110$		0			0
$111$	−3.53189	−	6.11742i	−0.335233	−	0.580640i
$112$		0			0
$113$	15.6132			1.46877			0.734383	−	0.678735i	$-0.237471\pi$
$113$	15.6132			1.46877			0.734383	+	0.678735i	$0.237471\pi$
$114$		0			0
$115$	9.26819			0.864263
$116$		0			0
$117$	3.63409	+	6.29444i	0.335972	+	0.581921i
$118$		0			0
$119$	−2.35939	−	4.08658i	−0.216285	−	0.374616i
$120$		0			0
$121$	−9.54942			−0.868129
$122$		0			0
$123$	−10.5957	+	18.3523i	−0.955380	+	1.65477i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	7.67699	−	13.2969i	0.681223	−	1.17991i	−0.293385	−	0.955994i	$-0.594782\pi$
$127$	7.67699	−	13.2969i	0.681223	−	1.17991i	0.974608	−	0.223918i	$-0.0718849\pi$
$128$		0			0
$129$	3.75719	−	6.50764i	0.330802	−	0.572965i
$130$		0			0
$131$	3.89780	+	6.75119i	0.340552	+	0.589854i	0.984535	−	0.175186i	$-0.0560526\pi$
$131$	3.89780	+	6.75119i	0.340552	+	0.589854i	−0.643983	+	0.765040i	$0.722719\pi$
$132$		0			0
$133$	−9.49348	+	1.48397i	−0.823189	+	0.128676i
$134$		0			0
$135$	−6.83850	−	11.8446i	−0.588564	−	1.01942i
$136$		0			0
$137$	−8.23630	+	14.2657i	−0.703674	+	1.21880i	0.263494	+	0.964661i	$0.415125\pi$
$137$	−8.23630	+	14.2657i	−0.703674	+	1.21880i	−0.967168	+	0.254138i	$0.918208\pi$
$138$		0			0
$139$	9.76819	−	16.9190i	0.828527	−	1.43505i	−0.0706667	−	0.997500i	$-0.522513\pi$
$139$	9.76819	−	16.9190i	0.828527	−	1.43505i	0.899194	−	0.437551i	$-0.144154\pi$
$140$		0			0
$141$	26.6990			2.24846
$142$		0			0
$143$	−0.602201	+	1.04304i	−0.0503586	+	0.0872236i
$144$		0			0
$145$	−8.33198			−0.691933
$146$		0			0
$147$	−3.42969	−	5.94040i	−0.282876	−	0.489956i
$148$		0			0
$149$	2.83850	+	4.91642i	0.232539	+	0.402769i	0.958555	−	0.284909i	$-0.0919634\pi$
$149$	2.83850	+	4.91642i	0.232539	+	0.402769i	−0.726016	+	0.687678i	$0.758630\pi$
$150$		0			0
$151$	−14.2264			−1.15773			−0.578864	−	0.815424i	$-0.696504\pi$
$151$	−14.2264			−1.15773			−0.578864	+	0.815424i	$0.696504\pi$
$152$		0			0
$153$	−15.5584			−1.25782
$154$		0			0
$155$	4.13409	+	7.16046i	0.332058	+	0.575142i
$156$		0			0
$157$	0.327492	+	0.567233i	0.0261367	+	0.0452701i	0.878798	−	0.477194i	$-0.158346\pi$
$157$	0.327492	+	0.567233i	0.0261367	+	0.0452701i	−0.852661	+	0.522464i	$0.825013\pi$
$158$		0			0
$159$	−0.859386			−0.0681538
$160$		0			0
$161$	−10.2154	+	17.6936i	−0.805087	+	1.39445i
$162$		0			0
$163$	−12.6770			−0.992939			−0.496469	−	0.868054i	$-0.665370\pi$
$163$	−12.6770			−0.992939			−0.496469	+	0.868054i	$0.665370\pi$
$164$		0			0
$165$	1.92969	−	3.34233i	0.150226	−	0.260200i
$166$		0			0
$167$	3.89780	−	6.75119i	0.301621	−	0.522422i	−0.674882	−	0.737925i	$-0.735806\pi$
$167$	3.89780	−	6.75119i	0.301621	−	0.522422i	0.976503	+	0.215503i	$0.0691390\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$		0			0
$171$	−11.4133	+	29.5540i	−0.872796	+	2.26005i
$172$		0			0
$173$	5.37039	+	9.30179i	0.408303	+	0.707202i	0.994700	−	0.102822i	$-0.0327873\pi$
$173$	5.37039	+	9.30179i	0.408303	+	0.707202i	−0.586397	+	0.810024i	$0.699454\pi$
$174$		0			0
$175$	1.10220	−	1.90907i	0.0833185	−	0.144312i
$176$		0			0
$177$	−13.3495	+	23.1220i	−1.00341	+	1.73796i
$178$		0			0
$179$	−1.54942			−0.115809			−0.0579044	−	0.998322i	$-0.518442\pi$
$179$	−1.54942			−0.115809			−0.0579044	+	0.998322i	$0.518442\pi$
$180$		0			0
$181$	4.11320	−	7.12428i	0.305732	−	0.529544i	−0.671692	−	0.740831i	$-0.734432\pi$
$181$	4.11320	−	7.12428i	0.305732	−	0.529544i	0.977424	+	0.211287i	$0.0677655\pi$
$182$		0			0
$183$	10.9232			0.807464
$184$		0			0
$185$	−1.10220	−	1.90907i	−0.0810354	−	0.140357i
$186$		0			0
$187$	−1.28908	−	2.23275i	−0.0942668	−	0.163275i
$188$		0			0
$189$	30.1496			2.19306
$190$		0			0
$191$	16.2812			1.17807			0.589034	−	0.808108i	$-0.299508\pi$
$191$	16.2812			1.17807			0.589034	+	0.808108i	$0.299508\pi$
$192$		0			0
$193$	−8.60669	−	14.9072i	−0.619523	−	1.07304i	−0.989573	−	0.144033i	$-0.953993\pi$
$193$	−8.60669	−	14.9072i	−0.619523	−	1.07304i	0.370050	−	0.929012i	$-0.379341\pi$
$194$		0			0
$195$	1.60220	+	2.77509i	0.114736	+	0.198729i
$196$		0			0
$197$	−10.2044			−0.727034			−0.363517	−	0.931588i	$-0.618424\pi$
$197$	−10.2044			−0.727034			−0.363517	+	0.931588i	$0.618424\pi$
$198$		0			0
$199$	−5.03189	+	8.71550i	−0.356701	+	0.617825i	−0.987408	−	0.158197i	$-0.949432\pi$
$199$	−5.03189	+	8.71550i	−0.356701	+	0.617825i	0.630706	+	0.776022i	$0.282765\pi$
$200$		0			0
$201$	6.81761			0.480877
$202$		0			0
$203$	9.18351	−	15.9063i	0.644556	−	1.11640i
$204$		0			0
$205$	−3.30660	+	5.72720i	−0.230943	+	0.400005i
$206$		0			0
$207$	33.6815	+	58.3380i	2.34102	+	4.05477i
$208$		0			0
$209$	−5.18688	+	0.810784i	−0.358784	+	0.0560831i
$210$		0			0
$211$	6.12758	+	10.6133i	0.421840	+	0.730648i	0.996119	−	0.0880113i	$-0.0280512\pi$
$211$	6.12758	+	10.6133i	0.421840	+	0.730648i	−0.574280	+	0.818659i	$0.694718\pi$
$212$		0			0
$213$	−16.7792	+	29.0624i	−1.14969	+	1.99132i
$214$		0			0
$215$	1.17251	−	2.03084i	0.0799644	−	0.138502i
$216$		0			0
$217$	−18.2264			−1.23729
$218$		0			0
$219$	−7.78571	+	13.4852i	−0.526110	+	0.911249i
$220$		0			0
$221$	2.14061			0.143993
$222$		0			0
$223$	10.0748	+	17.4501i	0.674658	+	1.16854i	0.976569	+	0.215206i	$0.0690422\pi$
$223$	10.0748	+	17.4501i	0.674658	+	1.16854i	−0.301911	+	0.953336i	$0.597624\pi$
$224$		0			0
$225$	−3.63409	−	6.29444i	−0.242273	−	0.419629i
$226$		0			0
$227$	−8.25515			−0.547914			−0.273957	−	0.961742i	$-0.588333\pi$
$227$	−8.25515			−0.547914			−0.273957	+	0.961742i	$0.588333\pi$
$228$		0			0
$229$	−26.6860			−1.76346			−0.881729	−	0.471756i	$-0.843620\pi$
$229$	−26.6860			−1.76346			−0.881729	+	0.471756i	$0.843620\pi$
$230$		0			0
$231$	4.25382	+	7.36783i	0.279881	+	0.484768i
$232$		0			0
$233$	−7.00448	−	12.1321i	−0.458879	−	0.794802i	0.540023	−	0.841650i	$-0.318416\pi$
$233$	−7.00448	−	12.1321i	−0.458879	−	0.794802i	−0.998902	+	0.0468485i	$0.985082\pi$
$234$		0			0
$235$	8.33198			0.543518
$236$		0			0
$237$	26.2902	−	45.5360i	1.70773	−	2.95788i
$238$		0			0
$239$	−12.2682			−0.793563			−0.396782	−	0.917913i	$-0.629873\pi$
$239$	−12.2682			−0.793563			−0.396782	+	0.917913i	$0.629873\pi$
$240$		0			0
$241$	−4.93621	+	8.54977i	−0.317969	+	0.550739i	−0.980064	−	0.198681i	$-0.936334\pi$
$241$	−4.93621	+	8.54977i	−0.317969	+	0.550739i	0.662095	+	0.749420i	$0.269668\pi$
$242$		0			0
$243$	14.7682	−	25.5793i	0.947380	−	1.64091i
$244$		0			0
$245$	−1.07031	−	1.85383i	−0.0683794	−	0.118437i
$246$		0			0
$247$	1.57031	−	4.06622i	0.0999162	−	0.258727i
$248$		0			0
$249$	−9.18351	−	15.9063i	−0.581981	−	1.00802i
$250$		0			0
$251$	−14.4198	+	24.9758i	−0.910170	+	1.57646i	−0.0963474	+	0.995348i	$0.530716\pi$
$251$	−14.4198	+	24.9758i	−0.910170	+	1.57646i	−0.813823	+	0.581113i	$0.802617\pi$
$252$		0			0
$253$	−5.58131	+	9.66711i	−0.350894	+	0.607766i
$254$		0			0
$255$	−6.85939			−0.429551
$256$		0			0
$257$	2.39780	−	4.15311i	0.149571	−	0.259064i	−0.781498	−	0.623907i	$-0.785544\pi$
$257$	2.39780	−	4.15311i	0.149571	−	0.259064i	0.931069	+	0.364844i	$0.118878\pi$
$258$		0			0
$259$	4.85939			0.301948
$260$		0			0
$261$	−30.2792	−	52.4451i	−1.87424	−	3.24627i
$262$		0			0
$263$	−10.2044	−	17.6745i	−0.629230	−	1.08986i	−0.987706	−	0.156320i	$-0.950037\pi$
$263$	−10.2044	−	17.6745i	−0.629230	−	1.08986i	0.358476	−	0.933539i	$-0.383296\pi$
$264$		0			0
$265$	−0.268189			−0.0164747
$266$		0			0
$267$	34.6640			2.12140
$268$		0			0
$269$	−0.563788	−	0.976509i	−0.0343747	−	0.0595388i	0.848326	−	0.529474i	$-0.177611\pi$
$269$	−0.563788	−	0.976509i	−0.0343747	−	0.0595388i	−0.882701	+	0.469935i	$0.844277\pi$
$270$		0			0
$271$	−9.83850	−	17.0408i	−0.597646	−	1.03515i	−0.993168	−	0.116697i	$-0.962769\pi$
$271$	−9.83850	−	17.0408i	−0.597646	−	1.03515i	0.395522	−	0.918457i	$-0.370564\pi$
$272$		0			0
$273$	−7.06379			−0.427520
$274$		0			0
$275$	0.602201	−	1.04304i	0.0363141	−	0.0628978i
$276$		0			0
$277$	7.35398			0.441858			0.220929	−	0.975290i	$-0.429091\pi$
$277$	7.35398			0.441858			0.220929	+	0.975290i	$0.429091\pi$
$278$		0			0
$279$	−30.0474	+	52.0436i	−1.79889	+	3.11577i
$280$		0			0
$281$	−6.73630	+	11.6676i	−0.401854	+	0.696031i	−0.993950	−	0.109836i	$-0.964967\pi$
$281$	−6.73630	+	11.6676i	−0.401854	+	0.696031i	0.592096	+	0.805867i	$0.298301\pi$
$282$		0			0
$283$	−10.6595	−	18.4627i	−0.633640	−	1.09750i	−0.986802	−	0.161934i	$-0.948227\pi$
$283$	−10.6595	−	18.4627i	−0.633640	−	1.09750i	0.353162	−	0.935562i	$-0.385106\pi$
$284$		0			0
$285$	−5.03189	+	13.0298i	−0.298064	+	0.771819i
$286$		0			0
$287$	−7.28908	−	12.6251i	−0.430261	−	0.745233i
$288$		0			0
$289$	6.20889	−	10.7541i	0.365229	−	0.632594i
$290$		0			0
$291$	25.2199	−	43.6821i	1.47842	−	2.56069i
$292$		0			0
$293$	8.08580			0.472377			0.236189	−	0.971707i	$-0.424102\pi$
$293$	8.08580			0.472377			0.236189	+	0.971707i	$0.424102\pi$
$294$		0			0
$295$	−4.16599	+	7.21570i	−0.242553	+	0.420115i
$296$		0			0
$297$	16.4726			0.955837
$298$		0			0
$299$	−4.63409	−	8.02649i	−0.267997	−	0.464184i
$300$		0			0
$301$	2.58468	+	4.47679i	0.148978	+	0.258038i
$302$		0			0
$303$	33.8046			1.94202
$304$		0			0
$305$	3.40880			0.195187
$306$		0			0
$307$	−14.2922	−	24.7549i	−0.815701	−	1.41284i	−0.908824	−	0.417180i	$-0.863018\pi$
$307$	−14.2922	−	24.7549i	−0.815701	−	1.41284i	0.0931229	−	0.995655i	$-0.470315\pi$
$308$		0			0
$309$	−1.17251	−	2.03084i	−0.0667016	−	0.115531i
$310$		0			0
$311$	−10.7408			−0.609054			−0.304527	−	0.952504i	$-0.598498\pi$
$311$	−10.7408			−0.609054			−0.304527	+	0.952504i	$0.598498\pi$
$312$		0			0
$313$	−5.71092	+	9.89160i	−0.322800	+	0.559107i	−0.981065	−	0.193680i	$-0.937958\pi$
$313$	−5.71092	+	9.89160i	−0.322800	+	0.559107i	0.658264	+	0.752787i	$0.271291\pi$
$314$		0			0
$315$	16.0220			0.902738
$316$		0			0
$317$	−1.62309	+	2.81128i	−0.0911619	+	0.157897i	−0.908000	−	0.418970i	$-0.862391\pi$
$317$	−1.62309	+	2.81128i	−0.0911619	+	0.157897i	0.816838	+	0.576867i	$0.195725\pi$
$318$		0			0
$319$	5.01752	−	8.69060i	0.280927	−	0.486580i
$320$		0			0
$321$	−21.4627	−	37.1745i	−1.19793	−	2.07488i
$322$		0			0
$323$	5.85735	+	7.26318i	0.325912	+	0.404134i
$324$		0			0
$325$	0.500000	+	0.866025i	0.0277350	+	0.0480384i
$326$		0			0
$327$	9.51100	−	16.4735i	0.525960	−	0.910989i
$328$		0			0
$329$	−9.18351	+	15.9063i	−0.506303	+	0.876943i
$330$		0			0
$331$	35.1208			1.93042			0.965208	−	0.261483i	$-0.0842116\pi$
$331$	35.1208			1.93042			0.965208	+	0.261483i	$0.0842116\pi$
$332$		0			0
$333$	8.01100	−	13.8755i	0.439000	−	0.760371i
$334$		0			0
$335$	2.12758			0.116242
$336$		0			0
$337$	−7.93621	−	13.7459i	−0.432313	−	0.748788i	0.564759	−	0.825256i	$-0.308969\pi$
$337$	−7.93621	−	13.7459i	−0.432313	−	0.748788i	−0.997072	+	0.0764677i	$0.975636\pi$
$338$		0			0
$339$	25.0155	+	43.3281i	1.35865	+	2.35326i
$340$		0			0
$341$	−9.95822			−0.539268
$342$		0			0
$343$	20.1496			1.08798
$344$		0			0
$345$	14.8495	+	25.7201i	0.799470	+	1.38472i
$346$		0			0
$347$	16.3221	+	28.2707i	0.876216	+	1.51765i	0.855462	+	0.517866i	$0.173273\pi$
$347$	16.3221	+	28.2707i	0.876216	+	1.51765i	0.0207537	+	0.999785i	$0.493393\pi$
$348$		0			0
$349$	−21.7538			−1.16446			−0.582228	−	0.813026i	$-0.697819\pi$
$349$	−21.7538			−1.16446			−0.582228	+	0.813026i	$0.697819\pi$
$350$		0			0
$351$	−6.83850	+	11.8446i	−0.365012	+	0.632219i
$352$		0			0
$353$	8.67699			0.461830			0.230915	−	0.972974i	$-0.425828\pi$
$353$	8.67699			0.461830			0.230915	+	0.972974i	$0.425828\pi$
$354$		0			0
$355$	−5.23630	+	9.06953i	−0.277914	+	0.481361i
$356$		0			0
$357$	7.56042	−	13.0950i	0.400140	−	0.693063i
$358$		0			0
$359$	−5.81109	−	10.0651i	−0.306697	−	0.531216i	0.670940	−	0.741511i	$-0.265891\pi$
$359$	−5.81109	−	10.0651i	−0.306697	−	0.531216i	−0.977638	+	0.210296i	$0.932557\pi$
$360$		0			0
$361$	18.0936	−	5.79827i	0.952297	−	0.305172i
$362$		0			0
$363$	−15.3001	−	26.5005i	−0.803046	−	1.39092i
$364$		0			0
$365$	−2.42969	+	4.20835i	−0.127176	+	0.220275i
$366$		0			0
$367$	−15.3046	+	26.5083i	−0.798892	+	1.38372i	0.121446	+	0.992598i	$0.461247\pi$
$367$	−15.3046	+	26.5083i	−0.798892	+	1.38372i	−0.920338	+	0.391123i	$0.872087\pi$
$368$		0			0
$369$	−48.0660			−2.50222
$370$		0			0
$371$	0.295598	−	0.511992i	0.0153467	−	0.0265813i
$372$		0			0
$373$	4.70980			0.243864			0.121932	−	0.992538i	$-0.461091\pi$
$373$	4.70980			0.243864			0.121932	+	0.992538i	$0.461091\pi$
$374$		0			0
$375$	−1.60220	−	2.77509i	−0.0827373	−	0.143305i
$376$		0			0
$377$	4.16599	+	7.21570i	0.214559	+	0.371628i
$378$		0			0
$379$	10.0638			0.516942			0.258471	−	0.966019i	$-0.416781\pi$
$379$	10.0638			0.516942			0.258471	+	0.966019i	$0.416781\pi$
$380$		0			0
$381$	49.2003			2.52061
$382$		0			0
$383$	−13.7219	−	23.7671i	−0.701158	−	1.21444i	−0.968060	−	0.250717i	$-0.919334\pi$
$383$	−13.7219	−	23.7671i	−0.701158	−	1.21444i	0.266903	−	0.963723i	$-0.414000\pi$
$384$		0			0
$385$	1.32749	+	2.29928i	0.0676553	+	0.117182i
$386$		0			0
$387$	17.0440			0.866396
$388$		0			0
$389$	−0.257185	+	0.445458i	−0.0130398	+	0.0225856i	−0.872472	−	0.488665i	$-0.837484\pi$
$389$	−0.257185	+	0.445458i	−0.0130398	+	0.0225856i	0.859432	+	0.511250i	$0.170817\pi$
$390$		0			0
$391$	19.8396			1.00333
$392$		0			0
$393$	−12.4901	+	21.6335i	−0.630043	+	1.09127i
$394$		0			0
$395$	8.20440	−	14.2104i	0.412808	−	0.715005i
$396$		0			0
$397$	−1.55278	−	2.68950i	−0.0779320	−	0.134982i	0.824426	−	0.565970i	$-0.191498\pi$
$397$	−1.55278	−	2.68950i	−0.0779320	−	0.134982i	−0.902358	+	0.430988i	$0.858165\pi$
$398$		0			0
$399$	−19.3286	−	23.9677i	−0.967641	−	1.19988i
$400$		0			0
$401$	6.51752	+	11.2887i	0.325470	+	0.563730i	0.981607	−	0.190911i	$-0.0611443\pi$
$401$	6.51752	+	11.2887i	0.325470	+	0.563730i	−0.656138	+	0.754641i	$0.727811\pi$
$402$		0			0
$403$	4.13409	−	7.16046i	0.205934	−	0.356688i
$404$		0			0
$405$	11.0110	−	19.0716i	0.547141	−	0.947676i
$406$		0			0
$407$	2.65498			0.131603
$408$		0			0
$409$	−13.7747	+	23.8585i	−0.681115	+	1.17973i	0.293525	+	0.955951i	$0.405172\pi$
$409$	−13.7747	+	23.8585i	−0.681115	+	1.17973i	−0.974641	+	0.223775i	$0.928162\pi$
$410$		0			0
$411$	−52.7848			−2.60368
$412$		0			0
$413$	−9.18351	−	15.9063i	−0.451891	−	0.782698i
$414$		0			0
$415$	−2.86591	−	4.96389i	−0.140682	−	0.243668i
$416$		0			0
$417$	62.6024			3.06565
$418$		0			0
$419$	16.5494			0.808492			0.404246	−	0.914650i	$-0.367534\pi$
$419$	16.5494			0.808492			0.404246	+	0.914650i	$0.367534\pi$
$420$		0			0
$421$	7.93418	+	13.7424i	0.386688	+	0.669764i	0.992002	−	0.126223i	$-0.0402856\pi$
$421$	7.93418	+	13.7424i	0.386688	+	0.669764i	−0.605314	+	0.795987i	$0.706952\pi$
$422$		0			0
$423$	30.2792	+	52.4451i	1.47222	+	2.54997i
$424$		0			0
$425$	−2.14061			−0.103835
$426$		0			0
$427$	−3.75719	+	6.50764i	−0.181823	+	0.314927i
$428$		0			0
$429$	−3.85939			−0.186333
$430$		0			0
$431$	−11.4472	+	19.8272i	−0.551393	+	0.955041i	0.446781	+	0.894643i	$0.352570\pi$
$431$	−11.4472	+	19.8272i	−0.551393	+	0.955041i	−0.998174	+	0.0603975i	$0.980763\pi$
$432$		0			0
$433$	10.6660	−	18.4740i	0.512575	−	0.887805i	−0.487319	−	0.873224i	$-0.662025\pi$
$433$	10.6660	−	18.4740i	0.512575	−	0.887805i	0.999894	−	0.0145814i	$-0.00464157\pi$
$434$		0			0
$435$	−13.3495	−	23.1220i	−0.640060	−	1.10862i
$436$		0			0
$437$	14.5539	−	37.6865i	0.696208	−	1.80279i
$438$		0			0
$439$	5.08783	+	8.81238i	0.242829	+	0.420592i	0.961519	−	0.274739i	$-0.0885913\pi$
$439$	5.08783	+	8.81238i	0.242829	+	0.420592i	−0.718690	+	0.695331i	$0.755258\pi$
$440$		0			0
$441$	7.77919	−	13.4740i	0.370438	−	0.641617i
$442$		0			0
$443$	3.30660	−	5.72720i	0.157101	−	0.272108i	−0.776721	−	0.629845i	$-0.783118\pi$
$443$	3.30660	−	5.72720i	0.157101	−	0.272108i	0.933822	+	0.357737i	$0.116452\pi$
$444$		0			0
$445$	10.8176			0.512804
$446$		0			0
$447$	−9.09568	+	15.7542i	−0.430211	+	0.745147i
$448$		0			0
$449$	10.9870			0.518507			0.259253	−	0.965809i	$-0.416524\pi$
$449$	10.9870			0.518507			0.259253	+	0.965809i	$0.416524\pi$
$450$		0			0
$451$	−3.98248	−	6.89785i	−0.187528	−	0.324807i
$452$		0			0
$453$	−22.7936	−	39.4796i	−1.07094	−	1.85491i
$454$		0			0
$455$	−2.20440			−0.103344
$456$		0			0
$457$	12.5494			0.587037			0.293518	−	0.955953i	$-0.405174\pi$
$457$	12.5494			0.587037			0.293518	+	0.955953i	$0.405174\pi$
$458$		0			0
$459$	−14.6386	−	25.3548i	−0.683270	−	1.18346i
$460$		0			0
$461$	11.6386	+	20.1586i	0.542063	+	0.938880i	0.998785	+	0.0492710i	$0.0156898\pi$
$461$	11.6386	+	20.1586i	0.542063	+	0.938880i	−0.456723	+	0.889609i	$0.650977\pi$
$462$		0			0
$463$	−23.3958			−1.08729			−0.543647	−	0.839314i	$-0.682957\pi$
$463$	−23.3958			−1.08729			−0.543647	+	0.839314i	$0.682957\pi$
$464$		0			0
$465$	−13.2473	+	22.9450i	−0.614329	+	1.06405i
$466$		0			0
$467$	−12.6352			−0.584688			−0.292344	−	0.956313i	$-0.594435\pi$
$467$	−12.6352			−0.584688			−0.292344	+	0.956313i	$0.594435\pi$
$468$		0			0
$469$	−2.34502	+	4.06169i	−0.108283	+	0.187551i
$470$		0			0
$471$	−1.04942	+	1.81764i	−0.0483546	+	0.0837526i
$472$		0			0
$473$	1.41217	+	2.44595i	0.0649316	+	0.112465i
$474$		0			0
$475$	−1.57031	+	4.06622i	−0.0720506	+	0.186571i
$476$		0			0
$477$	−0.974625	−	1.68810i	−0.0446250	−	0.0772928i
$478$		0			0
$479$	−2.01752	+	3.49445i	−0.0921830	+	0.159666i	−0.908429	−	0.418038i	$-0.862718\pi$
$479$	−2.01752	+	3.49445i	−0.0921830	+	0.159666i	0.816246	+	0.577704i	$0.196051\pi$
$480$		0			0
$481$	−1.10220	+	1.90907i	−0.0502560	+	0.0870460i
$482$		0			0
$483$	−65.4685			−2.97892
$484$		0			0
$485$	7.87039	−	13.6319i	0.357376	−	0.618993i
$486$		0			0
$487$	6.54942			0.296782			0.148391	−	0.988929i	$-0.452591\pi$
$487$	6.54942			0.296782			0.148391	+	0.988929i	$0.452591\pi$
$488$		0			0
$489$	−20.3111	−	35.1798i	−0.918499	−	1.59089i
$490$		0			0
$491$	−1.04290	−	1.80635i	−0.0470653	−	0.0815195i	0.841533	−	0.540206i	$-0.181654\pi$
$491$	−1.04290	−	1.80635i	−0.0470653	−	0.0815195i	−0.888598	+	0.458686i	$0.848320\pi$
$492$		0			0
$493$	−17.8355			−0.803273
$494$		0			0
$495$	8.75382			0.393455
$496$		0			0
$497$	−11.5429	−	19.9929i	−0.517770	−	0.896803i
$498$		0			0
$499$	12.0539	+	20.8780i	0.539607	+	0.934626i	0.998925	+	0.0463546i	$0.0147604\pi$
$499$	12.0539	+	20.8780i	0.539607	+	0.934626i	−0.459318	+	0.888272i	$0.651906\pi$
$500$		0			0
$501$	24.9802			1.11603
$502$		0			0
$503$	4.13858	−	7.16823i	0.184530	−	0.319616i	−0.758888	−	0.651221i	$-0.774257\pi$
$503$	4.13858	−	7.16823i	0.184530	−	0.319616i	0.943418	+	0.331606i	$0.107590\pi$
$504$		0			0
$505$	10.5494			0.469443
$506$		0			0
$507$	−19.2264	+	33.3011i	−0.853875	+	1.47895i
$508$		0			0
$509$	2.86591	−	4.96389i	0.127029	−	0.220021i	−0.795495	−	0.605960i	$-0.792789\pi$
$509$	2.86591	−	4.96389i	0.127029	−	0.220021i	0.922524	+	0.385939i	$0.126123\pi$
$510$		0			0
$511$	−5.35602	−	9.27690i	−0.236936	−	0.410386i
$512$		0			0
$513$	−58.9014	+	9.20713i	−2.60056	+	0.406505i
$514$		0			0
$515$	−0.365905	−	0.633767i	−0.0161237	−	0.0279271i
$516$		0			0
$517$	−5.01752	+	8.69060i	−0.220670	+	0.382212i
$518$		0			0
$519$	−17.2089	+	29.8067i	−0.755386	+	1.30837i
$520$		0			0
$521$	14.8086			0.648778			0.324389	−	0.945924i	$-0.394841\pi$
$521$	14.8086			0.648778			0.324389	+	0.945924i	$0.394841\pi$
$522$		0			0
$523$	−7.79356	+	13.4988i	−0.340789	+	0.590263i	−0.984579	−	0.174938i	$-0.944027\pi$
$523$	−7.79356	+	13.4988i	−0.340789	+	0.590263i	0.643791	+	0.765202i	$0.277361\pi$
$524$		0			0
$525$	7.06379			0.308289
$526$		0			0
$527$	8.84950	+	15.3278i	0.385490	+	0.667689i
$528$		0			0
$529$	−31.4497	−	54.4724i	−1.36738	−	2.36837i
$530$		0			0
$531$	−60.5584			−2.62801
$532$		0			0
$533$	6.61320			0.286450
$534$		0			0
$535$	−6.69788	−	11.6011i	−0.289575	−	0.501558i
$536$		0			0
$537$	−2.48248	−	4.29978i	−0.107127	−	0.185549i
$538$		0			0
$539$	2.57816			0.111049
$540$		0			0
$541$	−14.0539	+	24.3421i	−0.604224	+	1.04655i	0.387949	+	0.921681i	$0.373184\pi$
$541$	−14.0539	+	24.3421i	−0.604224	+	1.04655i	−0.992174	+	0.124867i	$0.960150\pi$
$542$		0			0
$543$	26.3607			1.13125
$544$		0			0
$545$	2.96811	−	5.14091i	0.127140	−	0.220212i
$546$		0			0
$547$	21.6835	−	37.5569i	0.927120	−	1.60582i	0.139004	−	0.990292i	$-0.455610\pi$
$547$	21.6835	−	37.5569i	0.927120	−	1.60582i	0.788116	−	0.615527i	$-0.211057\pi$
$548$		0			0
$549$	12.3879	+	21.4565i	0.528703	+	0.915741i
$550$		0			0
$551$	−13.0838	+	33.8796i	−0.557387	+	1.44332i
$552$		0			0
$553$	18.0858	+	31.3255i	0.769086	+	1.33210i
$554$		0			0
$555$	3.53189	−	6.11742i	0.149921	−	0.259670i
$556$		0			0
$557$	−8.65814	+	14.9963i	−0.366857	+	0.635415i	−0.989072	−	0.147431i	$-0.952900\pi$
$557$	−8.65814	+	14.9963i	−0.366857	+	0.635415i	0.622215	+	0.782846i	$0.286233\pi$
$558$		0			0
$559$	−2.34502			−0.0991836
$560$		0			0
$561$	4.13073	−	7.15463i	0.174399	−	0.302069i
$562$		0			0
$563$	8.35398			0.352078			0.176039	−	0.984383i	$-0.443671\pi$
$563$	8.35398			0.352078			0.176039	+	0.984383i	$0.443671\pi$
$564$		0			0
$565$	7.80660	+	13.5214i	0.328426	+	0.568851i
$566$		0			0
$567$	24.2727	+	42.0415i	1.01936	+	1.76558i
$568$		0			0
$569$	−10.6640			−0.447056			−0.223528	−	0.974697i	$-0.571757\pi$
$569$	−10.6640			−0.447056			−0.223528	+	0.974697i	$0.571757\pi$
$570$		0			0
$571$	−2.56512			−0.107347			−0.0536735	−	0.998559i	$-0.517093\pi$
$571$	−2.56512			−0.107347			−0.0536735	+	0.998559i	$0.517093\pi$
$572$		0			0
$573$	26.0858	+	45.1819i	1.08975	+	1.88750i
$574$		0			0
$575$	4.63409	+	8.02649i	0.193255	+	0.334728i
$576$		0			0
$577$	20.4218			0.850172			0.425086	−	0.905153i	$-0.360244\pi$
$577$	20.4218			0.850172			0.425086	+	0.905153i	$0.360244\pi$
$578$		0			0
$579$	27.5793	−	47.7687i	1.14616	−	1.98520i
$580$		0			0
$581$	12.6352			0.524197
$582$		0			0
$583$	0.161504	−	0.279733i	0.00668880	−	0.0115853i
$584$		0			0
$585$	−3.63409	+	6.29444i	−0.150251	+	0.260243i
$586$		0			0
$587$	4.40432	+	7.62850i	0.181786	+	0.314862i	0.942489	−	0.334238i	$-0.108479\pi$
$587$	4.40432	+	7.62850i	0.181786	+	0.314862i	−0.760703	+	0.649100i	$0.775146\pi$
$588$		0			0
$589$	35.6078	−	5.56601i	1.46719	−	0.229343i
$590$		0			0
$591$	−16.3495	−	28.3182i	−0.672529	−	1.16485i
$592$		0			0
$593$	−16.4726	+	28.5314i	−0.676448	+	1.17164i	0.299595	+	0.954066i	$0.403148\pi$
$593$	−16.4726	+	28.5314i	−0.676448	+	1.17164i	−0.976043	+	0.217576i	$0.930185\pi$
$594$		0			0
$595$	2.35939	−	4.08658i	0.0967254	−	0.167533i
$596$		0			0
$597$	−32.2484			−1.31984
$598$		0			0
$599$	9.56379	−	16.5650i	0.390766	−	0.676826i	−0.601785	−	0.798658i	$-0.705544\pi$
$599$	9.56379	−	16.5650i	0.390766	−	0.676826i	0.992551	+	0.121832i	$0.0388769\pi$
$600$		0			0
$601$	19.3100			0.787670			0.393835	−	0.919181i	$-0.371148\pi$
$601$	19.3100			0.787670			0.393835	+	0.919181i	$0.371148\pi$
$602$		0			0
$603$	7.73181	+	13.3919i	0.314864	+	0.545360i
$604$		0			0
$605$	−4.77471	−	8.27004i	−0.194120	−	0.336225i
$606$		0			0
$607$	36.8773			1.49680			0.748402	−	0.663245i	$-0.230821\pi$
$607$	36.8773			1.49680			0.748402	+	0.663245i	$0.230821\pi$
$608$		0			0
$609$	58.8553			2.38494
$610$		0			0
$611$	−4.16599	−	7.21570i	−0.168538	−	0.291916i
$612$		0			0
$613$	14.2603	+	24.6996i	0.575970	+	0.997609i	0.995936	+	0.0900688i	$0.0287087\pi$
$613$	14.2603	+	24.6996i	0.575970	+	0.997609i	−0.419966	+	0.907540i	$0.637958\pi$
$614$		0			0
$615$	−21.1914			−0.854518
$616$		0			0
$617$	5.64713	−	9.78112i	0.227345	−	0.393773i	−0.729675	−	0.683794i	$-0.760329\pi$
$617$	5.64713	−	9.78112i	0.227345	−	0.393773i	0.957020	+	0.290021i	$0.0936622\pi$
$618$		0			0
$619$	27.2044			1.09344			0.546719	−	0.837316i	$-0.315877\pi$
$619$	27.2044			1.09344			0.546719	+	0.837316i	$0.315877\pi$
$620$		0			0
$621$	−63.3805	+	109.778i	−2.54337	+	4.40525i
$622$		0			0
$623$	−11.9232	+	20.6515i	−0.477692	+	0.827387i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−10.5604	−	13.0950i	−0.421743	−	0.522965i
$628$		0			0
$629$	−2.35939	−	4.08658i	−0.0940749	−	0.162942i
$630$		0			0
$631$	−4.19136	+	7.25965i	−0.166856	+	0.289002i	−0.937313	−	0.348490i	$-0.886695\pi$
$631$	−4.19136	+	7.25965i	−0.166856	+	0.289002i	0.770457	+	0.637492i	$0.220028\pi$
$632$		0			0
$633$	−19.6352	+	34.0092i	−0.780430	+	1.35174i
$634$		0			0
$635$	15.3540			0.609304
$636$		0			0
$637$	−1.07031	+	1.85383i	−0.0424071	+	0.0734513i
$638$		0			0
$639$	−76.1168			−3.01113
$640$		0			0
$641$	−9.55594	−	16.5514i	−0.377437	−	0.653740i	0.613252	−	0.789888i	$-0.289861\pi$
$641$	−9.55594	−	16.5514i	−0.377437	−	0.653740i	−0.990689	+	0.136148i	$0.956528\pi$
$642$		0			0
$643$	24.1112	+	41.7618i	0.950852	+	1.64692i	0.743588	+	0.668638i	$0.233123\pi$
$643$	24.1112	+	41.7618i	0.950852	+	1.64692i	0.207264	+	0.978285i	$0.433544\pi$
$644$		0			0
$645$	7.51437			0.295878
$646$		0			0
$647$	−30.0817			−1.18263			−0.591317	−	0.806439i	$-0.701392\pi$
$647$	−30.0817			−1.18263			−0.591317	+	0.806439i	$0.701392\pi$
$648$		0			0
$649$	−5.01752	−	8.69060i	−0.196955	−	0.341136i
$650$		0			0
$651$	−29.2024	−	50.5800i	−1.14453	−	1.98239i
$652$		0			0
$653$	41.9124			1.64016			0.820079	−	0.572250i	$-0.193929\pi$
$653$	41.9124			1.64016			0.820079	+	0.572250i	$0.193929\pi$
$654$		0			0
$655$	−3.89780	+	6.75119i	−0.152300	+	0.263791i
$656$		0			0
$657$	−35.3189			−1.37792
$658$		0			0
$659$	20.0936	−	34.8032i	0.782737	−	1.35574i	−0.147604	−	0.989047i	$-0.547156\pi$
$659$	20.0936	−	34.8032i	0.782737	−	1.35574i	0.930341	−	0.366694i	$-0.119511\pi$
$660$		0			0
$661$	0.757185	−	1.31148i	0.0294511	−	0.0510108i	−0.850924	−	0.525289i	$-0.823957\pi$
$661$	0.757185	−	1.31148i	0.0294511	−	0.0510108i	0.880375	+	0.474278i	$0.157291\pi$
$662$		0			0
$663$	3.42969	+	5.94040i	0.133198	+	0.230706i
$664$		0			0
$665$	−6.03189	−	7.47961i	−0.233907	−	0.290047i
$666$		0			0
$667$	38.6112	+	66.8765i	1.49503	+	2.58947i
$668$		0			0
$669$	−32.2837	+	55.9170i	−1.24816	+	2.16187i
$670$		0			0
$671$	−2.05278	+	3.55553i	−0.0792468	+	0.137260i
$672$		0			0
$673$	−7.76686			−0.299390			−0.149695	−	0.988732i	$-0.547829\pi$
$673$	−7.76686			−0.299390			−0.149695	+	0.988732i	$0.547829\pi$
$674$		0			0
$675$	6.83850	−	11.8446i	0.263214	−	0.455900i
$676$		0			0
$677$	6.19136			0.237953			0.118977	−	0.992897i	$-0.462039\pi$
$677$	6.19136			0.237953			0.118977	+	0.992897i	$0.462039\pi$
$678$		0			0
$679$	17.3495	+	30.0502i	0.665813	+	1.15322i
$680$		0			0
$681$	−13.2264	−	22.9088i	−0.506837	−	0.877868i
$682$		0			0
$683$	2.92317			0.111852			0.0559261	−	0.998435i	$-0.482189\pi$
$683$	2.92317			0.111852			0.0559261	+	0.998435i	$0.482189\pi$
$684$		0			0
$685$	−16.4726			−0.629385
$686$		0			0
$687$	−42.7563	−	74.0560i	−1.63125	−	2.82541i
$688$		0			0
$689$	0.134095	+	0.232259i	0.00510860	+	0.00884835i
$690$		0			0
$691$	−2.35805			−0.0897046			−0.0448523	−	0.998994i	$-0.514282\pi$
$691$	−2.35805			−0.0897046			−0.0448523	+	0.998994i	$0.514282\pi$
$692$		0			0
$693$	−9.64847	+	16.7116i	−0.366515	+	0.634822i
$694$		0			0
$695$	19.5364			0.741057
$696$		0			0
$697$	−7.07816	+	12.2597i	−0.268104	+	0.464370i
$698$		0			0
$699$	22.4452	−	38.8762i	0.848955	−	1.47043i
$700$		0			0
$701$	−12.2792	−	21.2682i	−0.463779	−	0.803288i	0.535367	−	0.844620i	$-0.320173\pi$
$701$	−12.2792	−	21.2682i	−0.463779	−	0.803288i	−0.999145	+	0.0413314i	$0.986840\pi$
$702$		0			0
$703$	−9.49348	+	1.48397i	−0.358053	+	0.0559689i
$704$		0			0
$705$	13.3495	+	23.1220i	0.502771	+	0.870825i
$706$		0			0
$707$	−11.6276	+	20.1396i	−0.437300	+	0.757426i
$708$		0			0
$709$	−3.63858	+	6.30220i	−0.136650	+	0.236684i	−0.926226	−	0.376968i	$-0.876967\pi$
$709$	−3.63858	+	6.30220i	−0.136650	+	0.236684i	0.789577	+	0.613652i	$0.210300\pi$
$710$		0			0
$711$	119.262			4.47269
$712$		0			0
$713$	38.3156	−	66.3645i	1.43493	−	2.48537i
$714$		0			0
$715$	−1.20440			−0.0450421
$716$		0			0
$717$	−19.6561	−	34.0454i	−0.734071	−	1.27145i
$718$		0			0
$719$	−16.4452	−	28.4839i	−0.613302	−	1.06227i	−0.990680	−	0.136211i	$-0.956508\pi$
$719$	−16.4452	−	28.4839i	−0.613302	−	1.06227i	0.377378	−	0.926059i	$-0.376826\pi$
$720$		0			0
$721$	1.61320			0.0600789
$722$		0			0
$723$	−31.6352			−1.17653
$724$		0			0
$725$	−4.16599	−	7.21570i	−0.154721	−	0.267985i
$726$		0			0
$727$	−13.9551	−	24.1709i	−0.517565	−	0.896449i	−0.999792	−	0.0204023i	$-0.993505\pi$
$727$	−13.9551	−	24.1709i	−0.517565	−	0.896449i	0.482227	−	0.876046i	$-0.339828\pi$
$728$		0			0
$729$	28.5804			1.05853
$730$		0			0
$731$	2.50989	−	4.34725i	0.0928315	−	0.160789i
$732$		0			0
$733$	−4.89710			−0.180878			−0.0904392	−	0.995902i	$-0.528827\pi$
$733$	−4.89710			−0.180878			−0.0904392	+	0.995902i	$0.528827\pi$
$734$		0			0
$735$	3.42969	−	5.94040i	0.126506	−	0.219115i
$736$		0			0
$737$	−1.28123	+	2.21915i	−0.0471946	+	0.0817435i
$738$		0			0
$739$	11.5936	+	20.0808i	0.426479	+	0.738684i	0.996557	−	0.0829069i	$-0.0264204\pi$
$739$	11.5936	+	20.0808i	0.426479	+	0.738684i	−0.570078	+	0.821591i	$0.693087\pi$
$740$		0			0
$741$	13.8001	−	2.15715i	0.506959	−	0.0792449i
$742$		0			0
$743$	−19.9901	−	34.6239i	−0.733366	−	1.27023i	−0.955436	−	0.295197i	$-0.904615\pi$
$743$	−19.9901	−	34.6239i	−0.733366	−	1.27023i	0.222070	−	0.975031i	$-0.428719\pi$
$744$		0			0
$745$	−2.83850	+	4.91642i	−0.103994	+	0.180124i
$746$		0			0
$747$	20.8299	−	36.0785i	0.762128	−	1.32004i
$748$		0			0
$749$	29.5296			1.07899
$750$		0			0
$751$	10.2936	−	17.8290i	0.375617	−	0.650589i	−0.614802	−	0.788682i	$-0.710764\pi$
$751$	10.2936	−	17.8290i	0.375617	−	0.650589i	0.990419	+	0.138093i	$0.0440973\pi$
$752$		0			0
$753$	−92.4137			−3.36774
$754$		0			0
$755$	−7.11320	−	12.3204i	−0.258876	−	0.448386i
$756$		0			0
$757$	17.3176	+	29.9950i	0.629419	+	1.09019i	0.987668	+	0.156560i	$0.0500404\pi$
$757$	17.3176	+	29.9950i	0.629419	+	1.09019i	−0.358249	+	0.933626i	$0.616626\pi$
$758$		0			0
$759$	−35.7695			−1.29835
$760$		0			0
$761$	24.3890			0.884102			0.442051	−	0.896990i	$-0.354251\pi$
$761$	24.3890			0.884102			0.442051	+	0.896990i	$0.354251\pi$
$762$		0			0
$763$	6.54290	+	11.3326i	0.236869	+	0.410269i
$764$		0			0
$765$	−7.77919	−	13.4740i	−0.281257	−	0.487152i
$766$		0			0
$767$	8.33198			0.300850
$768$		0			0
$769$	−3.27471	+	5.67196i	−0.118089	+	0.204536i	−0.919010	−	0.394233i	$-0.871010\pi$
$769$	−3.27471	+	5.67196i	−0.118089	+	0.204536i	0.800921	+	0.598770i	$0.204343\pi$
$770$		0			0
$771$	15.3670			0.553430
$772$		0			0
$773$	18.7363	−	32.4522i	0.673898	−	1.16723i	−0.302892	−	0.953025i	$-0.597952\pi$
$773$	18.7363	−	32.4522i	0.673898	−	1.16723i	0.976790	−	0.214200i	$-0.0687145\pi$
$774$		0			0
$775$	−4.13409	+	7.16046i	−0.148501	+	0.257211i
$776$		0			0
$777$	7.78571	+	13.4852i	0.279311	+	0.483781i
$778$		0			0
$779$	18.0957	+	22.4388i	0.648345	+	0.803955i
$780$		0			0
$781$	−6.30660	−	10.9234i	−0.225668	−	0.390868i
$782$		0			0
$783$	56.9782	−	98.6891i	2.03623	−	3.52686i
$784$		0			0
$785$	−0.327492	+	0.567233i	−0.0116887	+	0.0202454i
$786$		0			0
$787$	−12.8306			−0.457363			−0.228682	−	0.973501i	$-0.573441\pi$
$787$	−12.8306			−0.457363			−0.228682	+	0.973501i	$0.573441\pi$
$788$		0			0
$789$	32.6990	−	56.6363i	1.16412	−	2.01631i
$790$		0			0
$791$	−34.4178			−1.22376
$792$		0			0
$793$	−1.70440	−	2.95211i	−0.0605251	−	0.104833i
$794$		0			0
$795$	−0.429693	−	0.744250i	−0.0152396	−	0.0263958i
$796$		0			0
$797$	−28.3032			−1.00255			−0.501276	−	0.865287i	$-0.667136\pi$
$797$	−28.3032			−1.00255			−0.501276	+	0.865287i	$0.667136\pi$
$798$		0			0
$799$	17.8355			0.630976
$800$		0			0
$801$	39.3122	+	68.0907i	1.38903	+	2.40587i
$802$		0			0
$803$	−2.92633	−	5.06855i	−0.103268	−	0.178865i
$804$		0			0
$805$	−20.4308			−0.720091
$806$		0			0
$807$	1.80660	−	3.12913i	0.0635954	−	0.110150i
$808$		0			0
$809$	−55.4946			−1.95109			−0.975543	−	0.219808i	$-0.929457\pi$
$809$	−55.4946			−1.95109			−0.975543	+	0.219808i	$0.929457\pi$
$810$		0			0
$811$	11.8540	−	20.5317i	0.416250	−	0.720966i	−0.579309	−	0.815108i	$-0.696678\pi$
$811$	11.8540	−	20.5317i	0.416250	−	0.720966i	0.995559	+	0.0941424i	$0.0300109\pi$
$812$		0			0
$813$	31.5265	−	54.6055i	1.10568	−	1.91510i
$814$		0			0
$815$	−6.33850	−	10.9786i	−0.222028	−	0.384563i
$816$		0			0
$817$	−6.41665	−	7.95672i	−0.224490	−	0.278370i
$818$		0			0
$819$	−8.01100	−	13.8755i	−0.279927	−	0.484848i
$820$		0			0
$821$	−11.3625	+	19.6805i	−0.396555	+	0.686854i	−0.993298	−	0.115578i	$-0.963128\pi$
$821$	−11.3625	+	19.6805i	−0.396555	+	0.686854i	0.596743	+	0.802432i	$0.296461\pi$
$822$		0			0
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	−0.692240	−	0.721668i	$-0.743376\pi$
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	0.971102	+	0.238664i	$0.0767093\pi$
$824$		0			0
$825$	3.85939			0.134367
$826$		0			0
$827$	−9.94722	+	17.2291i	−0.345899	+	0.599114i	−0.985517	−	0.169579i	$-0.945759\pi$
$827$	−9.94722	+	17.2291i	−0.345899	+	0.599114i	0.639618	+	0.768693i	$0.279093\pi$
$828$		0			0
$829$	4.37109			0.151814			0.0759071	−	0.997115i	$-0.475815\pi$
$829$	4.37109			0.151814			0.0759071	+	0.997115i	$0.475815\pi$
$830$		0			0
$831$	11.7826	+	20.4080i	0.408732	+	0.707945i
$832$		0			0
$833$	−2.29111	−	3.96833i	−0.0793824	−	0.137494i
$834$		0			0
$835$	7.79560			0.269778
$836$		0			0
$837$	−113.084			−3.90875
$838$		0			0
$839$	−1.22396	−	2.11996i	−0.0422558	−	0.0731891i	0.844124	−	0.536148i	$-0.180121\pi$
$839$	−1.22396	−	2.11996i	−0.0422558	−	0.0731891i	−0.886380	+	0.462959i	$0.846788\pi$
$840$		0			0
$841$	−20.2109	−	35.0063i	−0.696928	−	1.20712i
$842$		0			0
$843$	−43.1716			−1.48691
$844$		0			0
$845$	−6.00000	+	10.3923i	−0.206406	+	0.357506i
$846$		0			0
$847$	21.0507			0.723312
$848$		0			0
$849$	34.1572	−	59.1620i	1.17227	−	2.03044i
$850$		0			0
$851$	−10.2154	+	17.6936i	−0.350180	+	0.606529i
$852$		0			0
$853$	8.96607	+	15.5297i	0.306992	+	0.531727i	0.977703	−	0.209993i	$-0.0673440\pi$
$853$	8.96607	+	15.5297i	0.306992	+	0.531727i	−0.670711	+	0.741719i	$0.734011\pi$
$854$		0			0
$855$	−31.3012	+	4.89283i	−1.07048	+	0.167331i
$856$		0			0
$857$	29.0474	+	50.3115i	0.992240	+	1.71861i	0.603801	+	0.797135i	$0.293652\pi$
$857$	29.0474	+	50.3115i	0.992240	+	1.71861i	0.388438	+	0.921475i	$0.373015\pi$
$858$		0			0
$859$	−10.0409	+	17.3913i	−0.342590	+	0.593383i	−0.984913	−	0.173051i	$-0.944637\pi$
$859$	−10.0409	+	17.3913i	−0.342590	+	0.593383i	0.642323	+	0.766434i	$0.277971\pi$
$860$		0			0
$861$	23.3571	−	40.4557i	0.796009	−	1.37873i
$862$		0			0
$863$	−28.6262			−0.974449			−0.487224	−	0.873277i	$-0.661991\pi$
$863$	−28.6262			−0.974449			−0.487224	+	0.873277i	$0.661991\pi$
$864$		0			0
$865$	−5.37039	+	9.30179i	−0.182599	+	0.316270i
$866$		0			0
$867$	39.7915			1.35139
$868$		0			0
$869$	9.88139	+	17.1151i	0.335203	+	0.580589i
$870$		0			0
$871$	−1.06379	−	1.84253i	−0.0360451	−	0.0624319i
$872$		0			0
$873$	114.407			3.87209
$874$		0			0
$875$	2.20440			0.0745224
$876$		0			0
$877$	−25.5200	−	44.2019i	−0.861748	−	1.49259i	−0.870240	−	0.492628i	$-0.836036\pi$
$877$	−25.5200	−	44.2019i	−0.861748	−	1.49259i	0.00849182	−	0.999964i	$-0.497297\pi$
$878$		0			0
$879$	12.9551	+	22.4388i	0.436964	+	0.756843i
$880$		0			0
$881$	−14.2992			−0.481751			−0.240876	−	0.970556i	$-0.577435\pi$
$881$	−14.2992			−0.481751			−0.240876	+	0.970556i	$0.577435\pi$
$882$		0			0
$883$	−14.6999	+	25.4610i	−0.494692	+	0.856831i	−0.999981	−	0.00611882i	$-0.998052\pi$
$883$	−14.6999	+	25.4610i	−0.494692	+	0.856831i	0.505290	+	0.862950i	$0.331386\pi$
$884$		0			0
$885$	−26.6990			−0.897477
$886$		0			0
$887$	−6.46811	+	11.2031i	−0.217178	+	0.376163i	−0.953944	−	0.299985i	$-0.903018\pi$
$887$	−6.46811	+	11.2031i	−0.217178	+	0.376163i	0.736766	+	0.676147i	$0.236352\pi$
$888$		0			0
$889$	−16.9232	+	29.3118i	−0.567585	+	0.983086i
$890$		0			0
$891$	13.2617	+	22.9699i	0.444283	+	0.769520i
$892$		0			0
$893$	13.0838	−	33.8796i	0.437831	−	1.13374i
$894$		0			0
$895$	−0.774708	−	1.34183i	−0.0258956	−	0.0448526i
$896$		0			0
$897$	14.8495	−	25.7201i	0.495810	−	0.858769i
$898$		0			0
$899$	−34.4452	+	59.6608i	−1.14881	+	1.98980i
$900$		0			0
$901$	−0.574090			−0.0191257
$902$		0			0
$903$	−8.28235	+	14.3454i	−0.275619	+	0.477386i
$904$		0			0
$905$	8.22641			0.273455
$906$		0			0
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	0.937018	−	0.349281i	$-0.113574\pi$
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	−0.770996	+	0.636841i	$0.780241\pi$
$908$		0			0
$909$	38.3376	+	66.4026i	1.27158	+	2.20244i
$910$		0			0
$911$	−3.10964			−0.103027			−0.0515134	−	0.998672i	$-0.516404\pi$
$911$	−3.10964			−0.103027			−0.0515134	+	0.998672i	$0.516404\pi$
$912$		0			0
$913$	6.90340			0.228469
$914$		0			0
$915$	5.46159	+	9.45975i	0.180554	+	0.312730i
$916$		0			0
$917$	−8.59231	−	14.8823i	−0.283743	−	0.491458i
$918$		0			0
$919$	23.4987			0.775150			0.387575	−	0.921838i	$-0.373313\pi$
$919$	23.4987			0.775150			0.387575	+	0.921838i	$0.373313\pi$
$920$		0			0
$921$	45.7980	−	79.3245i	1.50910	−	2.61383i
$922$		0			0
$923$	10.4726			0.344710
$924$		0			0
$925$	1.10220	−	1.90907i	0.0362401	−	0.0627698i
$926$		0			0
$927$	2.65947	−	4.60634i	0.0873484	−	0.151292i
$928$		0			0
$929$	22.3221	+	38.6630i	0.732364	+	1.26849i	0.955870	+	0.293789i	$0.0949164\pi$
$929$	22.3221	+	38.6630i	0.732364	+	1.26849i	−0.223506	+	0.974703i	$0.571750\pi$
$930$		0			0
$931$	−9.21877	+	1.44103i	−0.302133	+	0.0472277i
$932$		0			0
$933$	−17.2089	−	29.8067i	−0.563394	−	0.975826i
$934$		0			0
$935$	1.28908	−	2.23275i	0.0421574	−	0.0730188i
$936$		0			0
$937$	11.7363	−	20.3279i	0.383408	−	0.664082i	−0.608139	−	0.793831i	$-0.708084\pi$
$937$	11.7363	−	20.3279i	0.383408	−	0.664082i	0.991547	+	0.129748i	$0.0414170\pi$
$938$		0			0
$939$	−36.6002			−1.19440
$940$		0			0
$941$	−20.0858	+	34.7896i	−0.654778	+	1.13411i	0.327171	+	0.944965i	$0.393905\pi$
$941$	−20.0858	+	34.7896i	−0.654778	+	1.13411i	−0.981949	+	0.189144i	$0.939429\pi$
$942$		0			0
$943$	61.2924			1.99596
$944$		0			0
$945$	15.0748	+	26.1103i	0.490383	+	0.849368i
$946$		0			0
$947$	−9.68148	−	16.7688i	−0.314606	−	0.544913i	0.664748	−	0.747068i	$-0.268539\pi$
$947$	−9.68148	−	16.7688i	−0.314606	−	0.544913i	−0.979354	+	0.202155i	$0.935206\pi$
$948$		0			0
$949$	4.85939			0.157742
$950$		0			0
$951$	−10.4021			−0.337310
$952$		0			0
$953$	−2.41981	−	4.19123i	−0.0783852	−	0.135767i	0.824168	−	0.566345i	$-0.191643\pi$
$953$	−2.41981	−	4.19123i	−0.0783852	−	0.135767i	−0.902553	+	0.430578i	$0.858310\pi$
$954$		0			0
$955$	8.14061	+	14.1000i	0.263424	+	0.456264i
$956$		0			0
$957$	32.1563			1.03947
$958$		0			0
$959$	18.1561	−	31.4473i	0.586291	−	1.01549i
$960$		0			0
$961$	37.3630			1.20526
$962$		0			0
$963$	48.6815	−	84.3188i	1.56874	−	2.71714i
$964$		0			0
$965$	8.60669	−	14.9072i	0.277059	−	0.479880i
$966$		0			0
$967$	−13.5364	−	23.4457i	−0.435301	−	0.753963i	0.562020	−	0.827124i	$-0.310025\pi$
$967$	−13.5364	−	23.4457i	−0.435301	−	0.753963i	−0.997320	+	0.0731612i	$0.976691\pi$
$968$		0			0
$969$	−10.7713	+	27.8918i	−0.346025	+	0.896013i
$970$		0			0
$971$	−1.61769	−	2.80192i	−0.0519141	−	0.0899179i	0.838901	−	0.544285i	$-0.183199\pi$
$971$	−1.61769	−	2.80192i	−0.0519141	−	0.0899179i	−0.890815	+	0.454367i	$0.849866\pi$
$972$		0			0
$973$	−21.5330	+	37.2963i	−0.690317	+	1.19566i
$974$		0			0
$975$	−1.60220	+	2.77509i	−0.0513115	+	0.0888741i
$976$		0			0
$977$	−1.93214			−0.0618147			−0.0309074	−	0.999522i	$-0.509840\pi$
$977$	−1.93214			−0.0618147			−0.0309074	+	0.999522i	$0.509840\pi$
$978$		0			0
$979$	−6.51437	+	11.2832i	−0.208200	+	0.360613i
$980$		0			0
$981$	43.1455			1.37753
$982$		0			0
$983$	7.18555	+	12.4457i	0.229183	+	0.396957i	0.957566	−	0.288213i	$-0.0930611\pi$
$983$	7.18555	+	12.4457i	0.229183	+	0.396957i	−0.728383	+	0.685170i	$0.759728\pi$
$984$		0			0
$985$	−5.10220	−	8.83727i	−0.162570	−	0.281579i
$986$		0			0
$987$	−58.8553			−1.87339
$988$		0			0
$989$	−21.7340			−0.691102
$990$		0			0
$991$	−17.7956	−	30.8229i	−0.565296	−	0.979121i	−0.997022	−	0.0771164i	$-0.975429\pi$
$991$	−17.7956	−	30.8229i	−0.565296	−	0.979121i	0.431726	−	0.902005i	$-0.357905\pi$
$992$		0			0
$993$	56.2706	+	97.4636i	1.78569	+	3.09291i
$994$		0			0
$995$	−10.0638			−0.319044
$996$		0			0
$997$	−23.7902	+	41.2058i	−0.753443	+	1.30500i	0.192702	+	0.981257i	$0.438275\pi$
$997$	−23.7902	+	41.2058i	−0.753443	+	1.30500i	−0.946145	+	0.323744i	$0.895058\pi$
$998$		0			0
$999$	30.1496			0.953891

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.i.b.121.3	✓	6
3.2	odd	2		3420.2.t.v.1261.1		6
4.3	odd	2		1520.2.q.i.881.1		6
5.2	odd	4		1900.2.s.c.349.6		12
5.3	odd	4		1900.2.s.c.349.1		12
5.4	even	2		1900.2.i.c.501.1		6
19.7	even	3		7220.2.a.n.1.1		3
19.11	even	3	inner	380.2.i.b.201.3	yes	6
19.12	odd	6		7220.2.a.o.1.3		3
57.11	odd	6		3420.2.t.v.3241.1		6
76.11	odd	6		1520.2.q.i.961.1		6
95.49	even	6		1900.2.i.c.201.1		6
95.68	odd	12		1900.2.s.c.49.6		12
95.87	odd	12		1900.2.s.c.49.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.i.b.121.3	✓	6	1.1	even	1	trivial
380.2.i.b.201.3	yes	6	19.11	even	3	inner
1520.2.q.i.881.1		6	4.3	odd	2
1520.2.q.i.961.1		6	76.11	odd	6
1900.2.i.c.201.1		6	95.49	even	6
1900.2.i.c.501.1		6	5.4	even	2
1900.2.s.c.49.1		12	95.87	odd	12
1900.2.s.c.49.6		12	95.68	odd	12
1900.2.s.c.349.1		12	5.3	odd	4
1900.2.s.c.349.6		12	5.2	odd	4
3420.2.t.v.1261.1		6	3.2	odd	2
3420.2.t.v.3241.1		6	57.11	odd	6
7220.2.a.n.1.1		3	19.7	even	3
7220.2.a.o.1.3		3	19.12	odd	6

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.60220 + 2.77509i) q^{3} +(0.500000 + 0.866025i) q^{5} -2.20440 q^{7} +(-3.63409 + 6.29444i) q^{9} +O(q^{10})\)	\(q+(1.60220 + 2.77509i) q^{3} +(0.500000 + 0.866025i) q^{5} -2.20440 q^{7} +(-3.63409 + 6.29444i) q^{9} -1.20440 q^{11} +(0.500000 - 0.866025i) q^{13} +(-1.60220 + 2.77509i) q^{15} +(1.07031 + 1.85383i) q^{17} +(4.30660 - 0.673184i) q^{19} +(-3.53189 - 6.11742i) q^{21} +(4.63409 - 8.02649i) q^{23} +(-0.500000 + 0.866025i) q^{25} -13.6770 q^{27} +(-4.16599 + 7.21570i) q^{29} +8.26819 q^{31} +(-1.92969 - 3.34233i) q^{33} +(-1.10220 - 1.90907i) q^{35} -2.20440 q^{37} +3.20440 q^{39} +(3.30660 + 5.72720i) q^{41} +(-1.17251 - 2.03084i) q^{43} -7.26819 q^{45} +(4.16599 - 7.21570i) q^{47} -2.14061 q^{49} +(-3.42969 + 5.94040i) q^{51} +(-0.134095 + 0.232259i) q^{53} +(-0.602201 - 1.04304i) q^{55} +(8.76819 + 10.8726i) q^{57} +(4.16599 + 7.21570i) q^{59} +(1.70440 - 2.95211i) q^{61} +(8.01100 - 13.8755i) q^{63} +1.00000 q^{65} +(1.06379 - 1.84253i) q^{67} +29.6990 q^{69} +(5.23630 + 9.06953i) q^{71} +(2.42969 + 4.20835i) q^{73} -3.20440 q^{75} +2.65498 q^{77} +(-8.20440 - 14.2104i) q^{79} +(-11.0110 - 19.0716i) q^{81} -5.73181 q^{83} +(-1.07031 + 1.85383i) q^{85} -26.6990 q^{87} +(5.40880 - 9.36832i) q^{89} +(-1.10220 + 1.90907i) q^{91} +(13.2473 + 22.9450i) q^{93} +(2.73630 + 3.39304i) q^{95} +(-7.87039 - 13.6319i) q^{97} +(4.37691 - 7.58103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} + 3 q^{5} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) 6 * q + q^3 + 3 * q^5 + 4 * q^7 - 8 * q^9	\( 6 q + q^{3} + 3 q^{5} + 4 q^{7} - 8 q^{9} + 10 q^{11} + 3 q^{13} - q^{15} + 3 q^{17} - 16 q^{21} + 14 q^{23} - 3 q^{25} - 20 q^{27} - 6 q^{29} + 22 q^{31} - 15 q^{33} + 2 q^{35} + 4 q^{37} + 2 q^{39} - 6 q^{41} + 5 q^{43} - 16 q^{45} + 6 q^{47} - 6 q^{49} - 24 q^{51} + 13 q^{53} + 5 q^{55} + 25 q^{57} + 6 q^{59} - 7 q^{61} + 5 q^{63} + 6 q^{65} - 4 q^{67} + 30 q^{69} + 9 q^{71} + 18 q^{73} - 2 q^{75} + 40 q^{77} - 32 q^{79} - 23 q^{81} - 62 q^{83} - 3 q^{85} - 12 q^{87} - 2 q^{89} + 2 q^{91} + 14 q^{93} - 6 q^{95} - 11 q^{97} - 3 q^{99}+O(q^{100}) \) 6 * q + q^3 + 3 * q^5 + 4 * q^7 - 8 * q^9 + 10 * q^11 + 3 * q^13 - q^15 + 3 * q^17 - 16 * q^21 + 14 * q^23 - 3 * q^25 - 20 * q^27 - 6 * q^29 + 22 * q^31 - 15 * q^33 + 2 * q^35 + 4 * q^37 + 2 * q^39 - 6 * q^41 + 5 * q^43 - 16 * q^45 + 6 * q^47 - 6 * q^49 - 24 * q^51 + 13 * q^53 + 5 * q^55 + 25 * q^57 + 6 * q^59 - 7 * q^61 + 5 * q^63 + 6 * q^65 - 4 * q^67 + 30 * q^69 + 9 * q^71 + 18 * q^73 - 2 * q^75 + 40 * q^77 - 32 * q^79 - 23 * q^81 - 62 * q^83 - 3 * q^85 - 12 * q^87 - 2 * q^89 + 2 * q^91 + 14 * q^93 - 6 * q^95 - 11 * q^97 - 3 * q^99

Introduction

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