LMFDB - Embedded newform 380.2.i.c.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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 9x^{6} + 2x^{5} + 65x^{4} - 20x^{3} + 25x^{2} + 6x + 4 $ x^8 - x^7 + 9x^6 + 2x^5 + 65x^4 - 20x^3 + 25x^2 + 6x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.3
Root			$-0.176725 - 0.306096i$ of defining polynomial
Character	$\chi$	$=$	380.121
Dual form			380.2.i.c.201.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.176725 + 0.306096i) q^{3} +(-0.500000 - 0.866025i) q^{5} -4.30507 q^{7} +(1.43754 - 2.48989i) q^{9} +O(q^{10})$	\(q+(0.176725 + 0.306096i) q^{3} +(-0.500000 - 0.866025i) q^{5} -4.30507 q^{7} +(1.43754 - 2.48989i) q^{9} +6.01196 q^{11} +(2.97581 - 5.15425i) q^{13} +(0.176725 - 0.306096i) q^{15} +(-1.93754 - 3.35591i) q^{17} +(4.19835 - 1.17212i) q^{19} +(-0.760812 - 1.31776i) q^{21} +(-0.391721 + 0.678480i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.07654 q^{27} +(-3.98179 + 6.89666i) q^{29} -4.49034 q^{31} +(1.06246 + 1.84024i) q^{33} +(2.15253 + 3.72830i) q^{35} -0.988035 q^{37} +2.10360 q^{39} +(-3.15253 - 5.46035i) q^{41} +(0.785004 + 1.35967i) q^{43} -2.87507 q^{45} +(0.630909 - 1.09277i) q^{47} +11.5336 q^{49} +(0.684822 - 1.18615i) q^{51} +(4.07443 - 7.05712i) q^{53} +(-3.00598 - 5.20651i) q^{55} +(1.10073 + 1.07796i) q^{57} +(-2.62834 - 4.55242i) q^{59} +(-2.80507 + 4.85852i) q^{61} +(-6.18869 + 10.7191i) q^{63} -5.95162 q^{65} +(-3.52162 + 6.09963i) q^{67} -0.276907 q^{69} +(2.90736 + 5.03570i) q^{71} +(4.62024 + 8.00250i) q^{73} -0.353450 q^{75} -25.8819 q^{77} +(6.99743 + 12.1199i) q^{79} +(-3.94563 - 6.83404i) q^{81} +6.58197 q^{83} +(-1.93754 + 3.35591i) q^{85} -2.81472 q^{87} +(1.69237 - 2.93126i) q^{89} +(-12.8110 + 22.1894i) q^{91} +(-0.793555 - 1.37448i) q^{93} +(-3.11426 - 3.04982i) q^{95} +(3.69835 + 6.40573i) q^{97} +(8.64242 - 14.9691i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{3} - 4 q^{5} - 5 q^{9}+O(q^{10}) $ 8 * q - q^3 - 4 * q^5 - 5 * q^9	$ 8 q - q^{3} - 4 q^{5} - 5 q^{9} + 4 q^{11} + 9 q^{13} - q^{15} + q^{17} + 3 q^{19} + 8 q^{21} - 4 q^{25} + 20 q^{27} + 5 q^{29} - 20 q^{31} + 25 q^{33} - 52 q^{37} - 54 q^{39} - 8 q^{41} + 7 q^{43} + 10 q^{45} + 16 q^{47} + 20 q^{49} + 12 q^{51} + 5 q^{53} - 2 q^{55} + 27 q^{57} + 11 q^{59} + 12 q^{61} - 3 q^{63} - 18 q^{65} + 6 q^{69} + 14 q^{71} - 4 q^{73} + 2 q^{75} - 44 q^{77} + 13 q^{79} - 24 q^{81} + 10 q^{83} + q^{85} - 4 q^{87} + 5 q^{89} - 46 q^{91} - 28 q^{93} - 6 q^{95} - q^{97} + 24 q^{99}+O(q^{100}) $ 8 * q - q^3 - 4 * q^5 - 5 * q^9 + 4 * q^11 + 9 * q^13 - q^15 + q^17 + 3 * q^19 + 8 * q^21 - 4 * q^25 + 20 * q^27 + 5 * q^29 - 20 * q^31 + 25 * q^33 - 52 * q^37 - 54 * q^39 - 8 * q^41 + 7 * q^43 + 10 * q^45 + 16 * q^47 + 20 * q^49 + 12 * q^51 + 5 * q^53 - 2 * q^55 + 27 * q^57 + 11 * q^59 + 12 * q^61 - 3 * q^63 - 18 * q^65 + 6 * q^69 + 14 * q^71 - 4 * q^73 + 2 * q^75 - 44 * q^77 + 13 * q^79 - 24 * q^81 + 10 * q^83 + q^85 - 4 * q^87 + 5 * q^89 - 46 * q^91 - 28 * q^93 - 6 * q^95 - q^97 + 24 * 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
$3$	0.176725	+	0.306096i	0.102032	+	0.176725i	0.912522	−	0.409028i	$-0.134132\pi$
$3$	0.176725	+	0.306096i	0.102032	+	0.176725i	−0.810490	+	0.585753i	$0.800799\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−4.30507			−1.62716			−0.813581	−	0.581452i	$-0.802485\pi$
$7$	−4.30507			−1.62716			−0.813581	+	0.581452i	$0.802485\pi$
$8$		0			0
$9$	1.43754	−	2.48989i	0.479179	−	0.829962i
$10$		0			0
$11$	6.01196			1.81268			0.906338	−	0.422554i	$-0.138866\pi$
$11$	6.01196			1.81268			0.906338	+	0.422554i	$0.138866\pi$
$12$		0			0
$13$	2.97581	−	5.15425i	0.825341	−	1.42953i	−0.0763181	−	0.997084i	$-0.524316\pi$
$13$	2.97581	−	5.15425i	0.825341	−	1.42953i	0.901659	−	0.432448i	$-0.142350\pi$
$14$		0			0
$15$	0.176725	−	0.306096i	0.0456301	−	0.0790337i
$16$		0			0
$17$	−1.93754	−	3.35591i	−0.469922	−	0.813928i	0.529487	−	0.848318i	$-0.322385\pi$
$17$	−1.93754	−	3.35591i	−0.469922	−	0.813928i	−0.999408	+	0.0343900i	$0.989051\pi$
$18$		0			0
$19$	4.19835	−	1.17212i	0.963167	−	0.268903i
$19$	4.19835	−	1.17212i	0.963167	−	0.268903i
$20$		0			0
$21$	−0.760812	−	1.31776i	−0.166023	−	0.287560i
$22$		0			0
$23$	−0.391721	+	0.678480i	−0.0816794	+	0.141473i	−0.903971	−	0.427593i	$-0.859362\pi$
$23$	−0.391721	+	0.678480i	−0.0816794	+	0.141473i	0.822292	+	0.569066i	$0.192695\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	2.07654			0.399631
$28$		0			0
$29$	−3.98179	+	6.89666i	−0.739400	+	1.28068i	0.213366	+	0.976972i	$0.431557\pi$
$29$	−3.98179	+	6.89666i	−0.739400	+	1.28068i	−0.952766	+	0.303706i	$0.901776\pi$
$30$		0			0
$31$	−4.49034			−0.806489			−0.403245	−	0.915092i	$-0.632118\pi$
$31$	−4.49034			−0.806489			−0.403245	+	0.915092i	$0.632118\pi$
$32$		0			0
$33$	1.06246	+	1.84024i	0.184951	+	0.320345i
$34$		0			0
$35$	2.15253	+	3.72830i	0.363844	+	0.630197i
$36$		0			0
$37$	−0.988035			−0.162432			−0.0812160	−	0.996697i	$-0.525880\pi$
$37$	−0.988035			−0.162432			−0.0812160	+	0.996697i	$0.525880\pi$
$38$		0			0
$39$	2.10360			0.336845
$40$		0			0
$41$	−3.15253	−	5.46035i	−0.492343	−	0.852763i	0.507618	−	0.861582i	$-0.330526\pi$
$41$	−3.15253	−	5.46035i	−0.492343	−	0.852763i	−0.999961	+	0.00881921i	$0.997193\pi$
$42$		0			0
$43$	0.785004	+	1.35967i	0.119712	+	0.207347i	0.919654	−	0.392731i	$-0.128470\pi$
$43$	0.785004	+	1.35967i	0.119712	+	0.207347i	−0.799942	+	0.600078i	$0.795136\pi$
$44$		0			0
$45$	−2.87507			−0.428591
$46$		0			0
$47$	0.630909	−	1.09277i	0.0920275	−	0.159396i	−0.816337	−	0.577576i	$-0.803999\pi$
$47$	0.630909	−	1.09277i	0.0920275	−	0.159396i	0.908364	+	0.418180i	$0.137332\pi$
$48$		0			0
$49$	11.5336			1.64766
$50$		0			0
$51$	0.684822	−	1.18615i	0.0958942	−	0.166094i
$52$		0			0
$53$	4.07443	−	7.05712i	0.559666	−	0.969369i	−0.437858	−	0.899044i	$-0.644263\pi$
$53$	4.07443	−	7.05712i	0.559666	−	0.969369i	0.997524	−	0.0703255i	$-0.0224038\pi$
$54$		0			0
$55$	−3.00598	−	5.20651i	−0.405327	−	0.702046i
$56$		0			0
$57$	1.10073	+	1.07796i	0.145796	+	0.142779i
$58$		0			0
$59$	−2.62834	−	4.55242i	−0.342181	−	0.592675i	0.642657	−	0.766154i	$-0.277832\pi$
$59$	−2.62834	−	4.55242i	−0.342181	−	0.592675i	−0.984837	+	0.173480i	$0.944499\pi$
$60$		0			0
$61$	−2.80507	+	4.85852i	−0.359152	+	0.622069i	−0.987819	−	0.155605i	$-0.950267\pi$
$61$	−2.80507	+	4.85852i	−0.359152	+	0.622069i	0.628668	+	0.777674i	$0.283601\pi$
$62$		0			0
$63$	−6.18869	+	10.7191i	−0.779702	+	1.35048i
$64$		0			0
$65$	−5.95162			−0.738207
$66$		0			0
$67$	−3.52162	+	6.09963i	−0.430235	+	0.745189i	−0.996893	−	0.0787642i	$-0.974903\pi$
$67$	−3.52162	+	6.09963i	−0.430235	+	0.745189i	0.566658	+	0.823953i	$0.308236\pi$
$68$		0			0
$69$	−0.276907			−0.0333357
$70$		0			0
$71$	2.90736	+	5.03570i	0.345040	+	0.597628i	0.985361	−	0.170480i	$-0.0545319\pi$
$71$	2.90736	+	5.03570i	0.345040	+	0.597628i	−0.640321	+	0.768108i	$0.721199\pi$
$72$		0			0
$73$	4.62024	+	8.00250i	0.540759	+	0.936621i	0.998861	+	0.0477218i	$0.0151961\pi$
$73$	4.62024	+	8.00250i	0.540759	+	0.936621i	−0.458102	+	0.888900i	$0.651471\pi$
$74$		0			0
$75$	−0.353450			−0.0408128
$76$		0			0
$77$	−25.8819			−2.94952
$78$		0			0
$79$	6.99743	+	12.1199i	0.787273	+	1.36360i	0.927632	+	0.373495i	$0.121841\pi$
$79$	6.99743	+	12.1199i	0.787273	+	1.36360i	−0.140359	+	0.990101i	$0.544826\pi$
$80$		0			0
$81$	−3.94563	−	6.83404i	−0.438404	−	0.759338i
$82$		0			0
$83$	6.58197			0.722465			0.361233	−	0.932476i	$-0.382356\pi$
$83$	6.58197			0.722465			0.361233	+	0.932476i	$0.382356\pi$
$84$		0			0
$85$	−1.93754	+	3.35591i	−0.210155	+	0.364000i
$86$		0			0
$87$	−2.81472			−0.301770
$88$		0			0
$89$	1.69237	−	2.93126i	0.179390	−	0.310713i	−0.762281	−	0.647246i	$-0.775921\pi$
$89$	1.69237	−	2.93126i	0.179390	−	0.310713i	0.941672	+	0.336532i	$0.109254\pi$
$90$		0			0
$91$	−12.8110	+	22.1894i	−1.34296	+	2.32608i
$92$		0			0
$93$	−0.793555	−	1.37448i	−0.0822878	−	0.142527i
$94$		0			0
$95$	−3.11426	−	3.04982i	−0.319516	−	0.312904i
$96$		0			0
$97$	3.69835	+	6.40573i	0.375510	+	0.650403i	0.990403	−	0.138208i	$-0.0441341\pi$
$97$	3.69835	+	6.40573i	0.375510	+	0.650403i	−0.614893	+	0.788611i	$0.710801\pi$
$98$		0			0
$99$	8.64242	−	14.9691i	0.868596	−	1.50445i
$100$		0			0
$101$	4.90369	−	8.49343i	0.487935	−	0.845128i	−0.511969	−	0.859004i	$-0.671084\pi$
$101$	4.90369	−	8.49343i	0.487935	−	0.845128i	0.999904	+	0.0138759i	$0.00441699\pi$
$102$		0			0
$103$	14.4368			1.42250			0.711251	−	0.702938i	$-0.248129\pi$
$103$	14.4368			1.42250			0.711251	+	0.702938i	$0.248129\pi$
$104$		0			0
$105$	−0.760812	+	1.31776i	−0.0742476	+	0.128601i
$106$		0			0
$107$	−9.49034			−0.917466			−0.458733	−	0.888574i	$-0.651697\pi$
$107$	−9.49034			−0.917466			−0.458733	+	0.888574i	$0.651697\pi$
$108$		0			0
$109$	1.30920	+	2.26759i	0.125398	+	0.217196i	0.921889	−	0.387455i	$-0.126646\pi$
$109$	1.30920	+	2.26759i	0.125398	+	0.217196i	−0.796490	+	0.604651i	$0.793312\pi$
$110$		0			0
$111$	−0.174610	−	0.302434i	−0.0165733	−	0.0287058i
$112$		0			0
$113$	−13.6705			−1.28601			−0.643005	−	0.765862i	$-0.722313\pi$
$113$	−13.6705			−1.28601			−0.643005	+	0.765862i	$0.722313\pi$
$114$		0			0
$115$	0.783442			0.0730563
$116$		0			0
$117$	−8.55567	−	14.8188i	−0.790972	−	1.37000i
$118$		0			0
$119$	8.34122	+	14.4474i	0.764639	+	1.32439i
$120$		0			0
$121$	25.1437			2.28579
$122$		0			0
$123$	1.11426	−	1.92996i	0.100470	−	0.174018i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−6.53359	+	11.3165i	−0.579762	+	1.00418i	0.415744	+	0.909482i	$0.363521\pi$
$127$	−6.53359	+	11.3165i	−0.579762	+	1.00418i	−0.995506	+	0.0946960i	$0.969812\pi$
$128$		0			0
$129$	−0.277459	+	0.480574i	−0.0244289	+	0.0423122i
$130$		0			0
$131$	3.75070	+	6.49640i	0.327700	+	0.567593i	0.982055	−	0.188594i	$-0.0603931\pi$
$131$	3.75070	+	6.49640i	0.327700	+	0.567593i	−0.654355	+	0.756188i	$0.727060\pi$
$132$		0			0
$133$	−18.0742	+	5.04606i	−1.56723	+	0.437549i
$134$		0			0
$135$	−1.03827	−	1.79834i	−0.0893602	−	0.154776i
$136$		0			0
$137$	4.21500	−	7.30059i	0.360111	−	0.623731i	−0.627867	−	0.778320i	$-0.716072\pi$
$137$	4.21500	−	7.30059i	0.360111	−	0.623731i	0.987979	+	0.154589i	$0.0494053\pi$
$138$		0			0
$139$	−4.38961	+	7.60302i	−0.372322	+	0.644880i	−0.989922	−	0.141612i	$-0.954771\pi$
$139$	−4.38961	+	7.60302i	−0.372322	+	0.644880i	0.617601	+	0.786492i	$0.288105\pi$
$140$		0			0
$141$	0.445989			0.0375591
$142$		0			0
$143$	17.8905	−	30.9872i	1.49607	−	2.59128i
$144$		0			0
$145$	7.96358			0.661339
$146$		0			0
$147$	2.03827	+	3.53039i	0.168114	+	0.291182i
$148$		0			0
$149$	0.915913	+	1.58641i	0.0750345	+	0.129964i	0.901101	−	0.433609i	$-0.142760\pi$
$149$	0.915913	+	1.58641i	0.0750345	+	0.129964i	−0.826067	+	0.563572i	$0.809427\pi$
$150$		0			0
$151$	−0.389869			−0.0317271			−0.0158635	−	0.999874i	$-0.505050\pi$
$151$	−0.389869			−0.0317271			−0.0158635	+	0.999874i	$0.505050\pi$
$152$		0			0
$153$	−11.1411			−0.900706
$154$		0			0
$155$	2.24517	+	3.88875i	0.180336	+	0.312352i
$156$		0			0
$157$	1.37608	+	2.38344i	0.109823	+	0.190219i	0.915698	−	0.401866i	$-0.131638\pi$
$157$	1.37608	+	2.38344i	0.109823	+	0.190219i	−0.805875	+	0.592085i	$0.798305\pi$
$158$		0			0
$159$	2.88021			0.228416
$160$		0			0
$161$	1.68638	−	2.92090i	0.132906	−	0.230199i
$162$		0			0
$163$	−15.0953			−1.18236			−0.591179	−	0.806540i	$-0.701337\pi$
$163$	−15.0953			−1.18236			−0.591179	+	0.806540i	$0.701337\pi$
$164$		0			0
$165$	1.06246	−	1.84024i	0.0827127	−	0.143263i
$166$		0			0
$167$	−1.49402	+	2.58771i	−0.115611	+	0.200243i	−0.918024	−	0.396526i	$-0.870216\pi$
$167$	−1.49402	+	2.58771i	−0.115611	+	0.200243i	0.802413	+	0.596769i	$0.203549\pi$
$168$		0			0
$169$	−11.2109	−	19.4178i	−0.862374	−	1.49368i
$170$		0			0
$171$	3.11683	−	12.1384i	0.238350	−	0.928245i
$172$		0			0
$173$	11.5945	+	20.0822i	0.881513	+	1.52682i	0.849659	+	0.527332i	$0.176808\pi$
$173$	11.5945	+	20.0822i	0.881513	+	1.52682i	0.0318535	+	0.999493i	$0.489859\pi$
$174$		0			0
$175$	2.15253	−	3.72830i	0.162716	−	0.281833i
$176$		0			0
$177$	0.928986	−	1.60905i	0.0698269	−	0.120944i
$178$		0			0
$179$	−13.5091			−1.00972			−0.504860	−	0.863201i	$-0.668456\pi$
$179$	−13.5091			−1.00972			−0.504860	+	0.863201i	$0.668456\pi$
$180$		0			0
$181$	10.1559	−	17.5906i	0.754886	−	1.30750i	−0.190546	−	0.981678i	$-0.561026\pi$
$181$	10.1559	−	17.5906i	0.754886	−	1.30750i	0.945431	−	0.325822i	$-0.105641\pi$
$182$		0			0
$183$	−1.98290			−0.146580
$184$		0			0
$185$	0.494018	+	0.855664i	0.0363209	+	0.0629096i
$186$		0			0
$187$	−11.6484	−	20.1756i	−0.851816	−	1.47539i
$188$		0			0
$189$	−8.93965			−0.650264
$190$		0			0
$191$	−7.04838			−0.510003			−0.255002	−	0.966941i	$-0.582076\pi$
$191$	−7.04838			−0.510003			−0.255002	+	0.966941i	$0.582076\pi$
$192$		0			0
$193$	11.8892	+	20.5926i	0.855800	+	1.48229i	0.875901	+	0.482491i	$0.160268\pi$
$193$	11.8892	+	20.5926i	0.855800	+	1.48229i	−0.0201010	+	0.999798i	$0.506399\pi$
$194$		0			0
$195$	−1.05180	−	1.82177i	−0.0753208	−	0.130460i
$196$		0			0
$197$	23.7428			1.69160			0.845802	−	0.533497i	$-0.179122\pi$
$197$	23.7428			1.69160			0.845802	+	0.533497i	$0.179122\pi$
$198$		0			0
$199$	11.4893	−	19.9001i	0.814457	−	1.41068i	−0.0952595	−	0.995452i	$-0.530368\pi$
$199$	11.4893	−	19.9001i	0.814457	−	1.41068i	0.909717	−	0.415229i	$-0.136299\pi$
$200$		0			0
$201$	−2.48943			−0.175591
$202$		0			0
$203$	17.1419	−	29.6906i	1.20312	−	2.08387i
$204$		0			0
$205$	−3.15253	+	5.46035i	−0.220182	+	0.381367i
$206$		0			0
$207$	1.12623	+	1.95068i	0.0782781	+	0.135582i
$208$		0			0
$209$	25.2403	−	7.04675i	1.74591	−	0.487434i
$210$		0			0
$211$	0.692366	+	1.19921i	0.0476645	+	0.0825573i	0.888873	−	0.458153i	$-0.151489\pi$
$211$	0.692366	+	1.19921i	0.0476645	+	0.0825573i	−0.841209	+	0.540710i	$0.818156\pi$
$212$		0			0
$213$	−1.02761	+	1.77987i	−0.0704104	+	0.121954i
$214$		0			0
$215$	0.785004	−	1.35967i	0.0535368	−	0.0927285i
$216$		0			0
$217$	19.3312			1.31229
$218$		0			0
$219$	−1.63302	+	2.82848i	−0.110349	+	0.191131i
$220$		0			0
$221$	−23.0629			−1.55138
$222$		0			0
$223$	11.6500	+	20.1783i	0.780139	+	1.35124i	0.931860	+	0.362818i	$0.118185\pi$
$223$	11.6500	+	20.1783i	0.780139	+	1.35124i	−0.151721	+	0.988423i	$0.548481\pi$
$224$		0			0
$225$	1.43754	+	2.48989i	0.0958358	+	0.165992i
$226$		0			0
$227$	−4.48943			−0.297974			−0.148987	−	0.988839i	$-0.547601\pi$
$227$	−4.48943			−0.297974			−0.148987	+	0.988839i	$0.547601\pi$
$228$		0			0
$229$	9.20830			0.608501			0.304251	−	0.952592i	$-0.401594\pi$
$229$	9.20830			0.608501			0.304251	+	0.952592i	$0.401594\pi$
$230$		0			0
$231$	−4.57397	−	7.92236i	−0.300945	−	0.521253i
$232$		0			0
$233$	2.16265	+	3.74581i	0.141680	+	0.245396i	0.928129	−	0.372258i	$-0.121416\pi$
$233$	2.16265	+	3.74581i	0.141680	+	0.245396i	−0.786450	+	0.617654i	$0.788083\pi$
$234$		0			0
$235$	−1.26182			−0.0823119
$236$		0			0
$237$	−2.47324	+	4.28378i	−0.160654	+	0.278261i
$238$		0			0
$239$	−14.8267			−0.959059			−0.479529	−	0.877526i	$-0.659193\pi$
$239$	−14.8267			−0.959059			−0.479529	+	0.877526i	$0.659193\pi$
$240$		0			0
$241$	−1.44453	+	2.50199i	−0.0930500	+	0.161167i	−0.908793	−	0.417247i	$-0.862995\pi$
$241$	−1.44453	+	2.50199i	−0.0930500	+	0.161167i	0.815743	+	0.578414i	$0.196328\pi$
$242$		0			0
$243$	4.50940	−	7.81050i	0.289278	−	0.501044i
$244$		0			0
$245$	−5.76679	−	9.98838i	−0.368427	−	0.638134i
$246$		0			0
$247$	6.45207	−	25.1273i	0.410535	−	1.59881i
$248$		0			0
$249$	1.16320	+	2.01472i	0.0737147	+	0.127678i
$250$		0			0
$251$	−7.65253	+	13.2546i	−0.483024	+	0.836621i	−0.999810	−	0.0194930i	$-0.993795\pi$
$251$	−7.65253	+	13.2546i	−0.483024	+	0.836621i	0.516786	+	0.856114i	$0.327128\pi$
$252$		0			0
$253$	−2.35501	+	4.07900i	−0.148058	+	0.256445i
$254$		0			0
$255$	−1.36964			−0.0857704
$256$		0			0
$257$	−6.54214	+	11.3313i	−0.408087	+	0.706828i	−0.994675	−	0.103057i	$-0.967137\pi$
$257$	−6.54214	+	11.3313i	−0.408087	+	0.706828i	0.586588	+	0.809886i	$0.300471\pi$
$258$		0			0
$259$	4.25356			0.264303
$260$		0			0
$261$	11.4479	+	19.8284i	0.708610	+	1.22735i
$262$		0			0
$263$	−9.68980	−	16.7832i	−0.597499	−	1.03490i	−0.993189	−	0.116514i	$-0.962828\pi$
$263$	−9.68980	−	16.7832i	−0.597499	−	1.03490i	0.395691	−	0.918384i	$-0.370505\pi$
$264$		0			0
$265$	−8.14886			−0.500580
$266$		0			0
$267$	1.19633			0.0732144
$268$		0			0
$269$	0.728523	+	1.26184i	0.0444188	+	0.0769357i	0.887380	−	0.461039i	$-0.152523\pi$
$269$	0.728523	+	1.26184i	0.0444188	+	0.0769357i	−0.842961	+	0.537974i	$0.819190\pi$
$270$		0			0
$271$	−6.28133	−	10.8796i	−0.381563	−	0.660887i	0.609722	−	0.792615i	$-0.291281\pi$
$271$	−6.28133	−	10.8796i	−0.381563	−	0.660887i	−0.991286	+	0.131728i	$0.957948\pi$
$272$		0			0
$273$	−9.05612			−0.548101
$274$		0			0
$275$	−3.00598	+	5.20651i	−0.181268	+	0.313965i
$276$		0			0
$277$	−4.39448			−0.264039			−0.132019	−	0.991247i	$-0.542146\pi$
$277$	−4.39448			−0.264039			−0.132019	+	0.991247i	$0.542146\pi$
$278$		0			0
$279$	−6.45503	+	11.1804i	−0.386453	+	0.669355i
$280$		0			0
$281$	−2.16265	+	3.74581i	−0.129013	+	0.223456i	−0.923294	−	0.384093i	$-0.874514\pi$
$281$	−2.16265	+	3.74581i	−0.129013	+	0.223456i	0.794282	+	0.607550i	$0.207847\pi$
$282$		0			0
$283$	−3.74885	−	6.49319i	−0.222846	−	0.385980i	0.732825	−	0.680417i	$-0.238201\pi$
$283$	−3.74885	−	6.49319i	−0.222846	−	0.385980i	−0.955671	+	0.294437i	$0.904868\pi$
$284$		0			0
$285$	0.383170	−	1.49224i	0.0226970	−	0.0883928i
$286$		0			0
$287$	13.5719	+	23.5072i	0.801122	+	1.38758i
$288$		0			0
$289$	0.991903	−	1.71803i	0.0583472	−	0.101060i
$290$		0			0
$291$	−1.30718	+	2.26410i	−0.0766282	+	0.132724i
$292$		0			0
$293$	−22.2837			−1.30183			−0.650915	−	0.759151i	$-0.725615\pi$
$293$	−22.2837			−1.30183			−0.650915	+	0.759151i	$0.725615\pi$
$294$		0			0
$295$	−2.62834	+	4.55242i	−0.153028	+	0.265052i
$296$		0			0
$297$	12.4841			0.724401
$298$		0			0
$299$	2.33137	+	4.03805i	0.134827	+	0.233527i
$300$		0			0
$301$	−3.37949	−	5.85345i	−0.194791	−	0.337387i
$302$		0			0
$303$	3.46641			0.199140
$304$		0			0
$305$	5.61013			0.321235
$306$		0			0
$307$	15.1403	+	26.2238i	0.864103	+	1.49667i	0.867935	+	0.496677i	$0.165447\pi$
$307$	15.1403	+	26.2238i	0.864103	+	1.49667i	−0.00383236	+	0.999993i	$0.501220\pi$
$308$		0			0
$309$	2.55134	+	4.41906i	0.145141	+	0.251391i
$310$		0			0
$311$	−5.37224			−0.304632			−0.152316	−	0.988332i	$-0.548673\pi$
$311$	−5.37224			−0.304632			−0.152316	+	0.988332i	$0.548673\pi$
$312$		0			0
$313$	2.40369	−	4.16331i	0.135864	−	0.235324i	−0.790063	−	0.613026i	$-0.789952\pi$
$313$	2.40369	−	4.16331i	0.135864	−	0.235324i	0.925927	+	0.377702i	$0.123286\pi$
$314$		0			0
$315$	12.3774			0.697386
$316$		0			0
$317$	14.8855	−	25.7824i	0.836052	−	1.44808i	−0.0571197	−	0.998367i	$-0.518192\pi$
$317$	14.8855	−	25.7824i	0.836052	−	1.44808i	0.893171	−	0.449717i	$-0.148475\pi$
$318$		0			0
$319$	−23.9384	+	41.4625i	−1.34029	+	2.32145i
$320$		0			0
$321$	−1.67718	−	2.90496i	−0.0936110	−	0.162139i
$322$		0			0
$323$	−12.0680	−	11.8183i	−0.671481	−	0.657586i
$324$		0			0
$325$	2.97581	+	5.15425i	0.165068	+	0.285906i
$326$		0			0
$327$	−0.462735	+	0.801480i	−0.0255893	+	0.0443220i
$328$		0			0
$329$	−2.71610	+	4.70443i	−0.149744	+	0.259364i
$330$		0			0
$331$	30.8042			1.69315			0.846577	−	0.532266i	$-0.178659\pi$
$331$	30.8042			1.69315			0.846577	+	0.532266i	$0.178659\pi$
$332$		0			0
$333$	−1.42034	+	2.46010i	−0.0778340	+	0.134812i
$334$		0			0
$335$	7.04325			0.384814
$336$		0			0
$337$	3.32529	+	5.75957i	0.181140	+	0.313744i	0.942269	−	0.334857i	$-0.108688\pi$
$337$	3.32529	+	5.75957i	0.181140	+	0.313744i	−0.761129	+	0.648601i	$0.775355\pi$
$338$		0			0
$339$	−2.41591	−	4.18448i	−0.131214	−	0.227270i
$340$		0			0
$341$	−26.9958			−1.46190
$342$		0			0
$343$	−19.5174			−1.05384
$344$		0			0
$345$	0.138454	+	0.239809i	0.00745409	+	0.0129109i
$346$		0			0
$347$	−7.70534	−	13.3460i	−0.413644	−	0.716453i	0.581641	−	0.813446i	$-0.302411\pi$
$347$	−7.70534	−	13.3460i	−0.413644	−	0.716453i	−0.995285	+	0.0969930i	$0.969078\pi$
$348$		0			0
$349$	−27.0157			−1.44612			−0.723058	−	0.690788i	$-0.757264\pi$
$349$	−27.0157			−1.44612			−0.723058	+	0.690788i	$0.757264\pi$
$350$		0			0
$351$	6.17939	−	10.7030i	0.329832	−	0.571285i
$352$		0			0
$353$	19.7783			1.05269			0.526346	−	0.850270i	$-0.323561\pi$
$353$	19.7783			1.05269			0.526346	+	0.850270i	$0.323561\pi$
$354$		0			0
$355$	2.90736	−	5.03570i	0.154307	−	0.267267i
$356$		0			0
$357$	−2.94820	+	5.10644i	−0.156035	+	0.270261i
$358$		0			0
$359$	−17.8408	−	30.9011i	−0.941600	−	1.63090i	−0.762420	−	0.647082i	$-0.775989\pi$
$359$	−17.8408	−	30.9011i	−0.941600	−	1.63090i	−0.179179	−	0.983816i	$-0.557344\pi$
$360$		0			0
$361$	16.2523	−	9.84195i	0.855382	−	0.517997i
$362$		0			0
$363$	4.44352	+	7.69640i	0.233224	+	0.403956i
$364$		0			0
$365$	4.62024	−	8.00250i	0.241835	−	0.418870i
$366$		0			0
$367$	1.05235	−	1.82272i	0.0549322	−	0.0951454i	−0.837252	−	0.546818i	$-0.815839\pi$
$367$	1.05235	−	1.82272i	0.0549322	−	0.0951454i	0.892184	+	0.451672i	$0.149172\pi$
$368$		0			0
$369$	−18.1275			−0.943681
$370$		0			0
$371$	−17.5407	+	30.3813i	−0.910667	+	1.57732i
$372$		0			0
$373$	−32.0208			−1.65797			−0.828987	−	0.559268i	$-0.811082\pi$
$373$	−32.0208			−1.65797			−0.828987	+	0.559268i	$0.811082\pi$
$374$		0			0
$375$	0.176725	+	0.306096i	0.00912603	+	0.0158067i
$376$		0			0
$377$	23.6981	+	41.0463i	1.22051	+	2.11399i
$378$		0			0
$379$	−2.24784			−0.115464			−0.0577319	−	0.998332i	$-0.518387\pi$
$379$	−2.24784			−0.115464			−0.0577319	+	0.998332i	$0.518387\pi$
$380$		0			0
$381$	−4.61859			−0.236617
$382$		0			0
$383$	−1.33479	−	2.31192i	−0.0682044	−	0.118133i	0.829907	−	0.557902i	$-0.188394\pi$
$383$	−1.33479	−	2.31192i	−0.0682044	−	0.118133i	−0.898111	+	0.439769i	$0.855060\pi$
$384$		0			0
$385$	12.9410	+	22.4144i	0.659532	+	1.14234i
$386$		0			0
$387$	4.51389			0.229454
$388$		0			0
$389$	−7.76036	+	13.4413i	−0.393466	+	0.681503i	−0.992904	−	0.118918i	$-0.962057\pi$
$389$	−7.76036	+	13.4413i	−0.393466	+	0.681503i	0.599438	+	0.800421i	$0.295391\pi$
$390$		0			0
$391$	3.03589			0.153532
$392$		0			0
$393$	−1.32568	+	2.29615i	−0.0668719	+	0.115825i
$394$		0			0
$395$	6.99743	−	12.1199i	0.352079	−	0.609819i
$396$		0			0
$397$	−1.24839	−	2.16228i	−0.0626551	−	0.108522i	0.832996	−	0.553278i	$-0.186623\pi$
$397$	−1.24839	−	2.16228i	−0.0626551	−	0.108522i	−0.895651	+	0.444757i	$0.853290\pi$
$398$		0			0
$399$	−4.73873	−	4.64067i	−0.237233	−	0.232324i
$400$		0			0
$401$	10.8590	+	18.8083i	0.542271	+	0.939242i	0.998773	+	0.0495192i	$0.0157689\pi$
$401$	10.8590	+	18.8083i	0.542271	+	0.939242i	−0.456502	+	0.889723i	$0.650898\pi$
$402$		0			0
$403$	−13.3624	+	23.1443i	−0.665628	+	1.15290i
$404$		0			0
$405$	−3.94563	+	6.83404i	−0.196060	+	0.339586i
$406$		0			0
$407$	−5.94003			−0.294437
$408$		0			0
$409$	−12.1200	+	20.9924i	−0.599294	+	1.03801i	0.393631	+	0.919269i	$0.371219\pi$
$409$	−12.1200	+	20.9924i	−0.599294	+	1.03801i	−0.992925	+	0.118740i	$0.962115\pi$
$410$		0			0
$411$	2.97958			0.146972
$412$		0			0
$413$	11.3152	+	19.5985i	0.556784	+	0.964377i
$414$		0			0
$415$	−3.29099	−	5.70016i	−0.161548	−	0.279810i
$416$		0			0
$417$	−3.10301			−0.151955
$418$		0			0
$419$	−37.6543			−1.83953			−0.919766	−	0.392467i	$-0.871622\pi$
$419$	−37.6543			−1.83953			−0.919766	+	0.392467i	$0.871622\pi$
$420$		0			0
$421$	18.6884	+	32.3693i	0.910818	+	1.57758i	0.812911	+	0.582388i	$0.197881\pi$
$421$	18.6884	+	32.3693i	0.910818	+	1.57758i	0.0979071	+	0.995196i	$0.468785\pi$
$422$		0			0
$423$	−1.81391	−	3.14178i	−0.0881953	−	0.152759i
$424$		0			0
$425$	3.87507			0.187969
$426$		0			0
$427$	12.0760	−	20.9162i	0.584398	−	1.01221i
$428$		0			0
$429$	12.6467			0.610591
$430$		0			0
$431$	−5.41491	+	9.37889i	−0.260827	+	0.451765i	−0.966462	−	0.256810i	$-0.917329\pi$
$431$	−5.41491	+	9.37889i	−0.260827	+	0.451765i	0.705635	+	0.708576i	$0.250662\pi$
$432$		0			0
$433$	−5.71031	+	9.89055i	−0.274420	+	0.475310i	−0.969989	−	0.243150i	$-0.921819\pi$
$433$	−5.71031	+	9.89055i	−0.274420	+	0.475310i	0.695569	+	0.718460i	$0.255153\pi$
$434$		0			0
$435$	1.40736	+	2.43762i	0.0674779	+	0.116875i
$436$		0			0
$437$	−0.849319	+	3.30764i	−0.0406284	+	0.158226i
$438$		0			0
$439$	−15.0612	−	26.0868i	−0.718832	−	1.24505i	−0.961463	−	0.274934i	$-0.911344\pi$
$439$	−15.0612	−	26.0868i	−0.718832	−	1.24505i	0.242631	−	0.970119i	$-0.421989\pi$
$440$		0			0
$441$	16.5800	−	28.7173i	0.789522	−	1.36749i
$442$		0			0
$443$	10.3045	−	17.8479i	0.489582	−	0.847981i	−0.510346	−	0.859969i	$-0.670483\pi$
$443$	10.3045	−	17.8479i	0.489582	−	0.847981i	0.999928	+	0.0119880i	$0.00381598\pi$
$444$		0			0
$445$	−3.38473			−0.160452
$446$		0			0
$447$	−0.323729	+	0.560715i	−0.0153119	+	0.0265209i
$448$		0			0
$449$	−3.61436			−0.170572			−0.0852861	−	0.996357i	$-0.527180\pi$
$449$	−3.61436			−0.170572			−0.0852861	+	0.996357i	$0.527180\pi$
$450$		0			0
$451$	−18.9529	−	32.8274i	−0.892458	−	1.54578i
$452$		0			0
$453$	−0.0688995	−	0.119338i	−0.00323718	−	0.00560697i
$454$		0			0
$455$	25.6221			1.20118
$456$		0			0
$457$	5.50452			0.257491			0.128745	−	0.991678i	$-0.458905\pi$
$457$	5.50452			0.257491			0.128745	+	0.991678i	$0.458905\pi$
$458$		0			0
$459$	−4.02338	−	6.96869i	−0.187795	−	0.325271i
$460$		0			0
$461$	−9.66053	−	16.7325i	−0.449936	−	0.779312i	0.548446	−	0.836186i	$-0.315220\pi$
$461$	−9.66053	−	16.7325i	−0.449936	−	0.779312i	−0.998381	+	0.0568746i	$0.981886\pi$
$462$		0			0
$463$	1.05722			0.0491334			0.0245667	−	0.999698i	$-0.492179\pi$
$463$	1.05722			0.0491334			0.0245667	+	0.999698i	$0.492179\pi$
$464$		0			0
$465$	−0.793555	+	1.37448i	−0.0368002	+	0.0637398i
$466$		0			0
$467$	21.9413			1.01532			0.507662	−	0.861556i	$-0.330510\pi$
$467$	21.9413			1.01532			0.507662	+	0.861556i	$0.330510\pi$
$468$		0			0
$469$	15.1608	−	26.2593i	0.700062	−	1.21254i
$470$		0			0
$471$	−0.486375	+	0.842426i	−0.0224110	+	0.0388169i
$472$		0			0
$473$	4.71942	+	8.17427i	0.216999	+	0.375853i
$474$		0			0
$475$	−1.08409	+	4.22194i	−0.0497413	+	0.193716i
$476$		0			0
$477$	−11.7143	−	20.2897i	−0.536360	−	0.929003i
$478$		0			0
$479$	6.60203	−	11.4351i	0.301655	−	0.522481i	−0.674856	−	0.737949i	$-0.735794\pi$
$479$	6.60203	−	11.4351i	0.301655	−	0.522481i	0.976511	+	0.215468i	$0.0691277\pi$
$480$		0			0
$481$	−2.94020	+	5.09258i	−0.134062	+	0.232202i
$482$		0			0
$483$	1.19210			0.0542426
$484$		0			0
$485$	3.69835	−	6.40573i	0.167933	−	0.290869i
$486$		0			0
$487$	15.5627			0.705211			0.352606	−	0.935772i	$-0.385296\pi$
$487$	15.5627			0.705211			0.352606	+	0.935772i	$0.385296\pi$
$488$		0			0
$489$	−2.66772	−	4.62063i	−0.120638	−	0.208952i
$490$		0			0
$491$	14.7978	+	25.6306i	0.667816	+	1.15669i	0.978514	+	0.206182i	$0.0661040\pi$
$491$	14.7978	+	25.6306i	0.667816	+	1.15669i	−0.310698	+	0.950509i	$0.600563\pi$
$492$		0			0
$493$	30.8595			1.38984
$494$		0			0
$495$	−17.2848			−0.776896
$496$		0			0
$497$	−12.5164	−	21.6790i	−0.561437	−	0.972437i
$498$		0			0
$499$	2.92190	+	5.06087i	0.130802	+	0.226556i	0.923986	−	0.382426i	$-0.124911\pi$
$499$	2.92190	+	5.06087i	0.130802	+	0.226556i	−0.793184	+	0.608982i	$0.791578\pi$
$500$		0			0
$501$	−1.05612			−0.0471840
$502$		0			0
$503$	−3.14544	+	5.44807i	−0.140248	+	0.242917i	−0.927590	−	0.373600i	$-0.878123\pi$
$503$	−3.14544	+	5.44807i	−0.140248	+	0.242917i	0.787342	+	0.616517i	$0.211457\pi$
$504$		0			0
$505$	−9.80737			−0.436422
$506$		0			0
$507$	3.96248	−	6.86321i	0.175980	−	0.304806i
$508$		0			0
$509$	1.84591	−	3.19720i	0.0818183	−	0.141713i	−0.822213	−	0.569180i	$-0.807261\pi$
$509$	1.84591	−	3.19720i	0.0818183	−	0.141713i	0.904031	+	0.427467i	$0.140594\pi$
$510$		0			0
$511$	−19.8905	−	34.4513i	−0.879902	−	1.52403i
$512$		0			0
$513$	8.71805	−	2.43396i	0.384911	−	0.107462i
$514$		0			0
$515$	−7.21841	−	12.5027i	−0.318081	−	0.550933i
$516$		0			0
$517$	3.79300	−	6.56967i	0.166816	−	0.288934i
$518$		0			0
$519$	−4.09807	+	7.09806i	−0.179885	+	0.311570i
$520$		0			0
$521$	29.0510			1.27275			0.636373	−	0.771381i	$-0.280434\pi$
$521$	29.0510			1.27275			0.636373	+	0.771381i	$0.280434\pi$
$522$		0			0
$523$	−9.21685	+	15.9640i	−0.403025	+	0.698059i	−0.994089	−	0.108565i	$-0.965374\pi$
$523$	−9.21685	+	15.9640i	−0.403025	+	0.698059i	0.591065	+	0.806624i	$0.298708\pi$
$524$		0			0
$525$	1.52162			0.0664091
$526$		0			0
$527$	8.70020	+	15.0692i	0.378987	+	0.656424i
$528$		0			0
$529$	11.1931	+	19.3870i	0.486657	+	0.842915i
$530$		0			0
$531$	−15.1133			−0.655863
$532$		0			0
$533$	−37.5253			−1.62540
$534$		0			0
$535$	4.74517	+	8.21888i	0.205152	+	0.355333i
$536$		0			0
$537$	−2.38740	−	4.13510i	−0.103024	−	0.178443i
$538$		0			0
$539$	69.3395			2.98666
$540$		0			0
$541$	21.0875	−	36.5246i	0.906622	−	1.57032i	0.0878981	−	0.996129i	$-0.471985\pi$
$541$	21.0875	−	36.5246i	0.906622	−	1.57032i	0.818724	−	0.574187i	$-0.194682\pi$
$542$		0			0
$543$	7.17923			0.308090
$544$		0			0
$545$	1.30920	−	2.26759i	0.0560798	−	0.0971331i
$546$		0			0
$547$	−7.87719	+	13.6437i	−0.336804	+	0.583362i	−0.983830	−	0.179106i	$-0.942679\pi$
$547$	−7.87719	+	13.6437i	−0.336804	+	0.583362i	0.647025	+	0.762468i	$0.276013\pi$
$548$		0			0
$549$	8.06477	+	13.9686i	0.344196	+	0.596165i
$550$		0			0
$551$	−8.63321	+	33.6217i	−0.367787	+	1.43233i
$552$		0			0
$553$	−30.1244	−	52.1770i	−1.28102	−	2.21879i
$554$		0			0
$555$	−0.174610	+	0.302434i	−0.00741180	+	0.0128376i
$556$		0			0
$557$	−11.5924	+	20.0786i	−0.491185	+	0.850757i	−0.999948	−	0.0101493i	$-0.996769\pi$
$557$	−11.5924	+	20.0786i	−0.491185	+	0.850757i	0.508764	+	0.860906i	$0.330103\pi$
$558$		0			0
$559$	9.34408			0.395213
$560$		0			0
$561$	4.11712	−	7.13107i	0.173825	−	0.301074i
$562$		0			0
$563$	−0.970934			−0.0409200			−0.0204600	−	0.999791i	$-0.506513\pi$
$563$	−0.970934			−0.0409200			−0.0204600	+	0.999791i	$0.506513\pi$
$564$		0			0
$565$	6.83524	+	11.8390i	0.287561	+	0.498070i
$566$		0			0
$567$	16.9862	+	29.4210i	0.713354	+	1.23556i
$568$		0			0
$569$	−30.1395			−1.26351			−0.631757	−	0.775167i	$-0.717666\pi$
$569$	−30.1395			−1.26351			−0.631757	+	0.775167i	$0.717666\pi$
$570$		0			0
$571$	−31.8976			−1.33487			−0.667436	−	0.744667i	$-0.732608\pi$
$571$	−31.8976			−1.33487			−0.667436	+	0.744667i	$0.732608\pi$
$572$		0			0
$573$	−1.24562	−	2.15748i	−0.0520367	−	0.0901302i
$574$		0			0
$575$	−0.391721	−	0.678480i	−0.0163359	−	0.0282946i
$576$		0			0
$577$	23.2889			0.969528			0.484764	−	0.874645i	$-0.338905\pi$
$577$	23.2889			0.969528			0.484764	+	0.874645i	$0.338905\pi$
$578$		0			0
$579$	−4.20222	+	7.27845i	−0.174638	+	0.302482i
$580$		0			0
$581$	−28.3358			−1.17557
$582$		0			0
$583$	24.4953	−	42.4271i	1.01449	−	1.75715i
$584$		0			0
$585$	−8.55567	+	14.8188i	−0.353733	+	0.612684i
$586$		0			0
$587$	−4.74059	−	8.21094i	−0.195665	−	0.338902i	0.751453	−	0.659786i	$-0.229353\pi$
$587$	−4.74059	−	8.21094i	−0.195665	−	0.338902i	−0.947118	+	0.320885i	$0.896020\pi$
$588$		0			0
$589$	−18.8520	+	5.26323i	−0.776784	+	0.216867i
$590$		0			0
$591$	4.19594	+	7.26758i	0.172598	+	0.298948i
$592$		0			0
$593$	21.2234	−	36.7600i	0.871540	−	1.50955i	0.0111366	−	0.999938i	$-0.496455\pi$
$593$	21.2234	−	36.7600i	0.871540	−	1.50955i	0.860403	−	0.509614i	$-0.170212\pi$
$594$		0			0
$595$	8.34122	−	14.4474i	0.341957	−	0.592287i
$596$		0			0
$597$	8.12180			0.332403
$598$		0			0
$599$	12.8961	−	22.3368i	0.526922	−	0.912656i	−0.472586	−	0.881285i	$-0.656679\pi$
$599$	12.8961	−	22.3368i	0.526922	−	0.912656i	0.999508	−	0.0313711i	$-0.00998736\pi$
$600$		0			0
$601$	0.206080			0.00840619			0.00420310	−	0.999991i	$-0.498662\pi$
$601$	0.206080			0.00840619			0.00420310	+	0.999991i	$0.498662\pi$
$602$		0			0
$603$	10.1249	+	17.5369i	0.412319	+	0.714157i
$604$		0			0
$605$	−12.5719	−	21.7751i	−0.511119	−	0.885284i
$606$		0			0
$607$	0.100472			0.00407802			0.00203901	−	0.999998i	$-0.499351\pi$
$607$	0.100472			0.00407802			0.00203901	+	0.999998i	$0.499351\pi$
$608$		0			0
$609$	12.1176			0.491029
$610$		0			0
$611$	−3.75493	−	6.50373i	−0.151908	−	0.263113i
$612$		0			0
$613$	19.7400	+	34.1907i	0.797292	+	1.38095i	0.921373	+	0.388679i	$0.127068\pi$
$613$	19.7400	+	34.1907i	0.797292	+	1.38095i	−0.124081	+	0.992272i	$0.539598\pi$
$614$		0			0
$615$	−2.22852			−0.0898627
$616$		0			0
$617$	14.1658	−	24.5359i	0.570294	−	0.987777i	−0.426242	−	0.904609i	$-0.640163\pi$
$617$	14.1658	−	24.5359i	0.570294	−	0.987777i	0.996536	−	0.0831682i	$-0.0265039\pi$
$618$		0			0
$619$	−1.39670			−0.0561380			−0.0280690	−	0.999606i	$-0.508936\pi$
$619$	−1.39670			−0.0561380			−0.0280690	+	0.999606i	$0.508936\pi$
$620$		0			0
$621$	−0.813425	+	1.40889i	−0.0326416	+	0.0565369i
$622$		0			0
$623$	−7.28575	+	12.6193i	−0.291897	+	0.505581i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	6.61758	+	6.48063i	0.264281	+	0.258812i
$628$		0			0
$629$	1.91435	+	3.31576i	0.0763303	+	0.132208i
$630$		0			0
$631$	−4.07397	+	7.05633i	−0.162182	+	0.280908i	−0.935651	−	0.352926i	$-0.885187\pi$
$631$	−4.07397	+	7.05633i	−0.162182	+	0.280908i	0.773469	+	0.633834i	$0.218520\pi$
$632$		0			0
$633$	−0.244717	+	0.423862i	−0.00972661	+	0.0168470i
$634$		0			0
$635$	13.0672			0.518555
$636$		0			0
$637$	34.3217	−	59.4470i	1.35988	−	2.35538i
$638$		0			0
$639$	16.7178			0.661344
$640$		0			0
$641$	−9.76367	−	16.9112i	−0.385642	−	0.667951i	0.606216	−	0.795300i	$-0.292687\pi$
$641$	−9.76367	−	16.9112i	−0.385642	−	0.667951i	−0.991858	+	0.127349i	$0.959353\pi$
$642$		0			0
$643$	−21.5945	−	37.4028i	−0.851604	−	1.47502i	−0.879761	−	0.475417i	$-0.842297\pi$
$643$	−21.5945	−	37.4028i	−0.851604	−	1.47502i	0.0281570	−	0.999604i	$-0.491036\pi$
$644$		0			0
$645$	0.554919			0.0218499
$646$		0			0
$647$	27.4390			1.07874			0.539370	−	0.842069i	$-0.318662\pi$
$647$	27.4390			1.07874			0.539370	+	0.842069i	$0.318662\pi$
$648$		0			0
$649$	−15.8015	−	27.3690i	−0.620263	−	1.07433i
$650$		0			0
$651$	3.41630	+	5.91721i	0.133896	+	0.231914i
$652$		0			0
$653$	−3.40515			−0.133254			−0.0666270	−	0.997778i	$-0.521224\pi$
$653$	−3.40515			−0.133254			−0.0666270	+	0.997778i	$0.521224\pi$
$654$		0			0
$655$	3.75070	−	6.49640i	0.146552	−	0.253835i
$656$		0			0
$657$	26.5671			1.03648
$658$		0			0
$659$	−6.09862	+	10.5631i	−0.237569	+	0.411481i	−0.960016	−	0.279945i	$-0.909684\pi$
$659$	−6.09862	+	10.5631i	−0.237569	+	0.411481i	0.722448	+	0.691426i	$0.243017\pi$
$660$		0			0
$661$	19.0683	−	33.0272i	0.741670	−	1.28461i	−0.210064	−	0.977688i	$-0.567367\pi$
$661$	19.0683	−	33.0272i	0.741670	−	1.28461i	0.951734	−	0.306923i	$-0.0992994\pi$
$662$		0			0
$663$	−4.07580	−	7.05948i	−0.158291	−	0.274168i
$664$		0			0
$665$	13.4071	+	13.1297i	0.519905	+	0.509146i
$666$		0			0
$667$	−3.11950	−	5.40313i	−0.120788	−	0.209210i
$668$		0			0
$669$	−4.11768	+	7.13202i	−0.159199	+	0.275740i
$670$		0			0
$671$	−16.8640	+	29.2092i	−0.651026	+	1.12761i
$672$		0			0
$673$	−37.9505			−1.46288			−0.731442	−	0.681903i	$-0.761152\pi$
$673$	−37.9505			−1.46288			−0.731442	+	0.681903i	$0.761152\pi$
$674$		0			0
$675$	−1.03827	+	1.79834i	−0.0399631	+	0.0692181i
$676$		0			0
$677$	−32.4499			−1.24715			−0.623575	−	0.781763i	$-0.714321\pi$
$677$	−32.4499			−1.24715			−0.623575	+	0.781763i	$0.714321\pi$
$678$		0			0
$679$	−15.9216	−	27.5771i	−0.611016	−	1.05831i
$680$		0			0
$681$	−0.793394	−	1.37420i	−0.0304029	−	0.0526594i
$682$		0			0
$683$	40.5283			1.55077			0.775385	−	0.631488i	$-0.217556\pi$
$683$	40.5283			1.55077			0.775385	+	0.631488i	$0.217556\pi$
$684$		0			0
$685$	−8.42999			−0.322093
$686$		0			0
$687$	1.62733	+	2.81863i	0.0620867	+	0.107537i
$688$		0			0
$689$	−24.2494	−	42.0012i	−0.923830	−	1.60012i
$690$		0			0
$691$	1.78657			0.0679642			0.0339821	−	0.999422i	$-0.489181\pi$
$691$	1.78657			0.0679642			0.0339821	+	0.999422i	$0.489181\pi$
$692$		0			0
$693$	−37.2062	+	64.4430i	−1.41335	+	2.44799i
$694$		0			0
$695$	8.77921			0.333015
$696$		0			0
$697$	−12.2163	+	21.1592i	−0.462725	+	0.801464i
$698$		0			0
$699$	−0.764386	+	1.32396i	−0.0289117	+	0.0500766i
$700$		0			0
$701$	21.8614	+	37.8650i	0.825693	+	1.43014i	0.901388	+	0.433011i	$0.142549\pi$
$701$	21.8614	+	37.8650i	0.825693	+	1.43014i	−0.0756952	+	0.997131i	$0.524118\pi$
$702$		0			0
$703$	−4.14812	+	1.15810i	−0.156449	+	0.0436785i
$704$		0			0
$705$	−0.222995	−	0.386238i	−0.00839846	−	0.0145466i
$706$		0			0
$707$	−21.1107	+	36.5648i	−0.793949	+	1.37516i
$708$		0			0
$709$	−7.32015	+	12.6789i	−0.274914	+	0.476165i	−0.970113	−	0.242652i	$-0.921983\pi$
$709$	−7.32015	+	12.6789i	−0.274914	+	0.476165i	0.695199	+	0.718817i	$0.255316\pi$
$710$		0			0
$711$	40.2363			1.50898
$712$		0			0
$713$	1.75896	−	3.04661i	0.0658736	−	0.114096i
$714$		0			0
$715$	−35.7809			−1.33813
$716$		0			0
$717$	−2.62024	−	4.53840i	−0.0978548	−	0.169489i
$718$		0			0
$719$	11.1778	+	19.3606i	0.416863	+	0.722028i	0.995622	−	0.0934709i	$-0.0297962\pi$
$719$	11.1778	+	19.3606i	0.416863	+	0.722028i	−0.578759	+	0.815499i	$0.696463\pi$
$720$		0			0
$721$	−62.1515			−2.31464
$722$		0			0
$723$	−1.02113			−0.0379764
$724$		0			0
$725$	−3.98179	−	6.89666i	−0.147880	−	0.256136i
$726$		0			0
$727$	−4.15042	−	7.18874i	−0.153930	−	0.266615i	0.778739	−	0.627349i	$-0.215860\pi$
$727$	−4.15042	−	7.18874i	−0.153930	−	0.266615i	−0.932669	+	0.360733i	$0.882527\pi$
$728$		0			0
$729$	−20.4861			−0.758745
$730$		0			0
$731$	3.04195	−	5.26881i	0.112511	−	0.194874i
$732$		0			0
$733$	35.7912			1.32198			0.660989	−	0.750396i	$-0.270137\pi$
$733$	35.7912			1.32198			0.660989	+	0.750396i	$0.270137\pi$
$734$		0			0
$735$	2.03827	−	3.53039i	0.0751828	−	0.130220i
$736$		0			0
$737$	−21.1719	+	36.6708i	−0.779876	+	1.35079i
$738$		0			0
$739$	16.6216	+	28.7895i	0.611437	+	1.05904i	0.990998	+	0.133873i	$0.0427415\pi$
$739$	16.6216	+	28.7895i	0.611437	+	1.05904i	−0.379561	+	0.925167i	$0.623925\pi$
$740$		0			0
$741$	8.83163	−	2.46567i	0.324438	−	0.0905787i
$742$		0			0
$743$	9.27444	+	16.0638i	0.340246	+	0.589324i	0.984478	−	0.175506i	$-0.0561563\pi$
$743$	9.27444	+	16.0638i	0.340246	+	0.589324i	−0.644232	+	0.764830i	$0.722823\pi$
$744$		0			0
$745$	0.915913	−	1.58641i	0.0335565	−	0.0581215i
$746$		0			0
$747$	9.46183	−	16.3884i	0.346190	−	0.599619i
$748$		0			0
$749$	40.8565			1.49287
$750$		0			0
$751$	−21.5748	+	37.3687i	−0.787276	+	1.36360i	0.140353	+	0.990101i	$0.455176\pi$
$751$	−21.5748	+	37.3687i	−0.787276	+	1.36360i	−0.927630	+	0.373501i	$0.878157\pi$
$752$		0			0
$753$	−5.40957			−0.197136
$754$		0			0
$755$	0.194935	+	0.337637i	0.00709440	+	0.0122879i
$756$		0			0
$757$	−4.77434	−	8.26940i	−0.173526	−	0.300556i	0.766124	−	0.642693i	$-0.222183\pi$
$757$	−4.77434	−	8.26940i	−0.173526	−	0.300556i	−0.939650	+	0.342136i	$0.888849\pi$
$758$		0			0
$759$	−1.66476			−0.0604268
$760$		0			0
$761$	35.8512			1.29960			0.649802	−	0.760103i	$-0.274852\pi$
$761$	35.8512			1.29960			0.649802	+	0.760103i	$0.274852\pi$
$762$		0			0
$763$	−5.63617	−	9.76214i	−0.204043	−	0.353413i
$764$		0			0
$765$	5.57056	+	9.64849i	0.201404	+	0.348842i
$766$		0			0
$767$	−31.2857			−1.12966
$768$		0			0
$769$	8.93698	−	15.4793i	0.322276	−	0.558198i	−0.658681	−	0.752422i	$-0.728886\pi$
$769$	8.93698	−	15.4793i	0.322276	−	0.558198i	0.980957	+	0.194224i	$0.0622188\pi$
$770$		0			0
$771$	−4.62463			−0.166552
$772$		0			0
$773$	−0.926769	+	1.60521i	−0.0333336	+	0.0577354i	−0.882211	−	0.470854i	$-0.843946\pi$
$773$	−0.926769	+	1.60521i	−0.0333336	+	0.0577354i	0.848877	+	0.528590i	$0.177279\pi$
$774$		0			0
$775$	2.24517	−	3.88875i	0.0806489	−	0.139688i
$776$		0			0
$777$	0.751709	+	1.30200i	0.0269674	+	0.0467089i
$778$		0			0
$779$	−19.6356	−	19.2293i	−0.703519	−	0.688961i
$780$		0			0
$781$	17.4790	+	30.2744i	0.625446	+	1.08330i
$782$		0			0
$783$	−8.26836	+	14.3212i	−0.295487	+	0.511798i
$784$		0			0
$785$	1.37608	−	2.38344i	0.0491144	−	0.0850686i
$786$		0			0
$787$	−53.8501			−1.91955			−0.959774	−	0.280773i	$-0.909409\pi$
$787$	−53.8501			−1.91955			−0.959774	+	0.280773i	$0.909409\pi$
$788$		0			0
$789$	3.42486	−	5.93202i	0.121928	−	0.211186i
$790$		0			0
$791$	58.8523			2.09255
$792$		0			0
$793$	16.6947	+	28.9160i	0.592845	+	1.02684i
$794$		0			0
$795$	−1.44011	−	2.49434i	−0.0510753	−	0.0884649i
$796$		0			0
$797$	−44.2766			−1.56836			−0.784179	−	0.620535i	$-0.786915\pi$
$797$	−44.2766			−1.56836			−0.784179	+	0.620535i	$0.786915\pi$
$798$		0			0
$799$	−4.88964			−0.172983
$800$		0			0
$801$	−4.86568	−	8.42760i	−0.171920	−	0.297775i
$802$		0			0
$803$	27.7767	+	48.1107i	0.980220	+	1.69779i
$804$		0			0
$805$	−3.37277			−0.118874
$806$		0			0
$807$	−0.257496	+	0.445996i	−0.00906429	+	0.0156998i
$808$		0			0
$809$	−16.7641			−0.589395			−0.294698	−	0.955591i	$-0.595219\pi$
$809$	−16.7641			−0.589395			−0.294698	+	0.955591i	$0.595219\pi$
$810$		0			0
$811$	13.7203	−	23.7642i	0.481784	−	0.834474i	−0.517998	−	0.855382i	$-0.673322\pi$
$811$	13.7203	−	23.7642i	0.481784	−	0.834474i	0.999781	+	0.0209083i	$0.00665581\pi$
$812$		0			0
$813$	2.22013	−	3.84538i	0.0778635	−	0.134863i
$814$		0			0
$815$	7.54767	+	13.0729i	0.264383	+	0.457925i
$816$		0			0
$817$	4.88942	+	4.78823i	0.171059	+	0.167519i
$818$		0			0
$819$	36.8327	+	63.7961i	1.28704	+	2.22922i
$820$		0			0
$821$	11.9404	−	20.6814i	0.416723	−	0.721785i	−0.578885	−	0.815409i	$-0.696512\pi$
$821$	11.9404	−	20.6814i	0.416723	−	0.721785i	0.995608	+	0.0936244i	$0.0298453\pi$
$822$		0			0
$823$	11.3410	−	19.6431i	0.395321	−	0.684716i	−0.597821	−	0.801630i	$-0.703967\pi$
$823$	11.3410	−	19.6431i	0.395321	−	0.684716i	0.993142	+	0.116913i	$0.0373000\pi$
$824$		0			0
$825$	−2.12493			−0.0739804
$826$		0			0
$827$	−16.1121	+	27.9071i	−0.560274	+	0.970423i	0.437198	+	0.899365i	$0.355971\pi$
$827$	−16.1121	+	27.9071i	−0.560274	+	0.970423i	−0.997472	+	0.0710581i	$0.977362\pi$
$828$		0			0
$829$	−0.593350			−0.0206079			−0.0103040	−	0.999947i	$-0.503280\pi$
$829$	−0.593350			−0.0206079			−0.0103040	+	0.999947i	$0.503280\pi$
$830$		0			0
$831$	−0.776614	−	1.34513i	−0.0269404	−	0.0466622i
$832$		0			0
$833$	−22.3468	−	38.7057i	−0.774269	−	1.34107i
$834$		0			0
$835$	2.98804			0.103405
$836$		0			0
$837$	−9.32438			−0.322298
$838$		0			0
$839$	10.9777	+	19.0139i	0.378991	+	0.656431i	0.990916	−	0.134484i	$-0.0429378\pi$
$839$	10.9777	+	19.0139i	0.378991	+	0.656431i	−0.611925	+	0.790916i	$0.709604\pi$
$840$		0			0
$841$	−17.2093	−	29.8074i	−0.593424	−	1.02784i
$842$		0			0
$843$	−1.52877			−0.0526537
$844$		0			0
$845$	−11.2109	+	19.4178i	−0.385665	+	0.667992i
$846$		0			0
$847$	−108.245			−3.71935
$848$		0			0
$849$	1.32503	−	2.29502i	0.0454749	−	0.0787648i
$850$		0			0
$851$	0.387034	−	0.670363i	0.0132674	−	0.0229797i
$852$		0			0
$853$	−9.76396	−	16.9117i	−0.334312	−	0.579045i	0.649041	−	0.760754i	$-0.275171\pi$
$853$	−9.76396	−	16.9117i	−0.334312	−	0.579045i	−0.983352	+	0.181709i	$0.941837\pi$
$854$		0			0
$855$	−12.0706	+	3.36994i	−0.412804	+	0.115249i
$856$		0			0
$857$	0.421704	+	0.730413i	0.0144051	+	0.0249504i	0.873138	−	0.487473i	$-0.162081\pi$
$857$	0.421704	+	0.730413i	0.0144051	+	0.0249504i	−0.858733	+	0.512423i	$0.828748\pi$
$858$		0			0
$859$	−16.7147	+	28.9508i	−0.570299	+	0.987787i	0.426236	+	0.904612i	$0.359839\pi$
$859$	−16.7147	+	28.9508i	−0.570299	+	0.987787i	−0.996535	+	0.0831752i	$0.973494\pi$
$860$		0			0
$861$	−4.79697	+	8.30859i	−0.163480	+	0.283156i
$862$		0			0
$863$	−7.13064			−0.242730			−0.121365	−	0.992608i	$-0.538727\pi$
$863$	−7.13064			−0.242730			−0.121365	+	0.992608i	$0.538727\pi$
$864$		0			0
$865$	11.5945	−	20.0822i	0.394224	−	0.682817i
$866$		0			0
$867$	0.701176			0.0238132
$868$		0			0
$869$	42.0683	+	72.8645i	1.42707	+	2.47176i
$870$		0			0
$871$	20.9594	+	36.3027i	0.710181	+	1.23007i
$872$		0			0
$873$	21.2660			0.719747
$874$		0			0
$875$	−4.30507			−0.145538
$876$		0			0
$877$	−8.01564	−	13.8835i	−0.270669	−	0.468812i	0.698364	−	0.715742i	$-0.253912\pi$
$877$	−8.01564	−	13.8835i	−0.270669	−	0.468812i	−0.969033	+	0.246930i	$0.920578\pi$
$878$		0			0
$879$	−3.93809	−	6.82097i	−0.132828	−	0.230066i
$880$		0			0
$881$	−23.0319			−0.775963			−0.387982	−	0.921667i	$-0.626828\pi$
$881$	−23.0319			−0.775963			−0.387982	+	0.921667i	$0.626828\pi$
$882$		0			0
$883$	−20.5300	+	35.5590i	−0.690890	+	1.19666i	0.280657	+	0.959808i	$0.409448\pi$
$883$	−20.5300	+	35.5590i	−0.690890	+	1.19666i	−0.971547	+	0.236848i	$0.923886\pi$
$884$		0			0
$885$	−1.85797			−0.0624550
$886$		0			0
$887$	−5.06900	+	8.77977i	−0.170200	+	0.294796i	−0.938490	−	0.345307i	$-0.887775\pi$
$887$	−5.06900	+	8.77977i	−0.170200	+	0.294796i	0.768289	+	0.640103i	$0.221108\pi$
$888$		0			0
$889$	28.1275	−	48.7183i	0.943367	−	1.63396i
$890$		0			0
$891$	−23.7210	−	41.0860i	−0.794684	−	1.37643i
$892$		0			0
$893$	1.36792	−	5.32732i	0.0457757	−	0.178272i
$894$		0			0
$895$	6.75457	+	11.6993i	0.225780	+	0.391063i
$896$		0			0
$897$	−0.824023	+	1.42725i	−0.0275133	+	0.0476545i
$898$		0			0
$899$	17.8796	−	30.9684i	0.596318	−	1.03285i
$900$		0			0
$901$	−31.5774			−1.05200
$902$		0			0
$903$	1.19448	−	2.06890i	0.0397498	−	0.0688487i
$904$		0			0
$905$	−20.3119			−0.675190
$906$		0			0
$907$	−19.0916	−	33.0677i	−0.633927	−	1.09799i	−0.986741	−	0.162301i	$-0.948109\pi$
$907$	−19.0916	−	33.0677i	−0.633927	−	1.09799i	0.352814	−	0.935693i	$-0.385225\pi$
$908$		0			0
$909$	−14.0985	−	24.4192i	−0.467616	−	0.809935i
$910$		0			0
$911$	−14.4138			−0.477550			−0.238775	−	0.971075i	$-0.576746\pi$
$911$	−14.4138			−0.477550			−0.238775	+	0.971075i	$0.576746\pi$
$912$		0			0
$913$	39.5706			1.30960
$914$		0			0
$915$	0.991449	+	1.71724i	0.0327763	+	0.0567702i
$916$		0			0
$917$	−16.1470	−	27.9674i	−0.533221	−	0.923566i
$918$		0			0
$919$	5.20920			0.171836			0.0859179	−	0.996302i	$-0.472618\pi$
$919$	5.20920			0.171836			0.0859179	+	0.996302i	$0.472618\pi$
$920$		0			0
$921$	−5.35134	+	9.26878i	−0.176332	+	0.305417i
$922$		0			0
$923$	34.6070			1.13910
$924$		0			0
$925$	0.494018	−	0.855664i	0.0162432	−	0.0281340i
$926$		0			0
$927$	20.7535	−	35.9460i	0.681633	−	1.18062i
$928$		0			0
$929$	19.1769	+	33.2154i	0.629174	+	1.08976i	0.987718	+	0.156249i	$0.0499401\pi$
$929$	19.1769	+	33.2154i	0.629174	+	1.08976i	−0.358544	+	0.933513i	$0.616727\pi$
$930$		0			0
$931$	48.4220	−	13.5188i	1.58697	−	0.443060i
$932$		0			0
$933$	−0.949408	−	1.64442i	−0.0310822	−	0.0538360i
$934$		0			0
$935$	−11.6484	+	20.1756i	−0.380943	+	0.659813i
$936$		0			0
$937$	−30.2289	+	52.3580i	−0.987536	+	1.71046i	−0.357459	+	0.933929i	$0.616357\pi$
$937$	−30.2289	+	52.3580i	−0.987536	+	1.71046i	−0.630077	+	0.776533i	$0.716977\pi$
$938$		0			0
$939$	1.69916			0.0554501
$940$		0			0
$941$	12.0859	−	20.9335i	0.393990	−	0.682411i	−0.598981	−	0.800763i	$-0.704428\pi$
$941$	12.0859	−	20.9335i	0.393990	−	0.682411i	0.992972	+	0.118352i	$0.0377610\pi$
$942$		0			0
$943$	4.93965			0.160857
$944$		0			0
$945$	4.46983	+	7.74196i	0.145403	+	0.251846i
$946$		0			0
$947$	−4.91390	−	8.51112i	−0.159680	−	0.276574i	0.775073	−	0.631872i	$-0.217713\pi$
$947$	−4.91390	−	8.51112i	−0.159680	−	0.276574i	−0.934753	+	0.355297i	$0.884380\pi$
$948$		0			0
$949$	54.9958			1.78524
$950$		0			0
$951$	10.5225			0.341216
$952$		0			0
$953$	1.04867	+	1.81636i	0.0339699	+	0.0588375i	0.882511	−	0.470293i	$-0.155852\pi$
$953$	1.04867	+	1.81636i	0.0339699	+	0.0588375i	−0.848541	+	0.529130i	$0.822518\pi$
$954$		0			0
$955$	3.52419	+	6.10408i	0.114040	+	0.197523i
$956$		0			0
$957$	−16.9220			−0.547011
$958$		0			0
$959$	−18.1458	+	31.4295i	−0.585960	+	1.01491i
$960$		0			0
$961$	−10.8368			−0.349575
$962$		0			0
$963$	−13.6427	+	23.6299i	−0.439630	+	0.761462i
$964$		0			0
$965$	11.8892	−	20.5926i	0.382725	−	0.662900i
$966$		0			0
$967$	19.1770	+	33.2156i	0.616691	+	1.06814i	0.990085	+	0.140468i	$0.0448606\pi$
$967$	19.1770	+	33.2156i	0.616691	+	1.06814i	−0.373394	+	0.927673i	$0.621806\pi$
$968$		0			0
$969$	1.48481	−	5.78255i	0.0476990	−	0.185762i
$970$		0			0
$971$	−9.56818	−	16.5726i	−0.307058	−	0.531839i	0.670660	−	0.741765i	$-0.266011\pi$
$971$	−9.56818	−	16.5726i	−0.307058	−	0.531839i	−0.977717	+	0.209926i	$0.932678\pi$
$972$		0			0
$973$	18.8975	−	32.7315i	0.605827	−	1.04932i
$974$		0			0
$975$	−1.05180	+	1.82177i	−0.0336845	+	0.0583433i
$976$		0			0
$977$	19.8444			0.634878			0.317439	−	0.948279i	$-0.397177\pi$
$977$	19.8444			0.634878			0.317439	+	0.948279i	$0.397177\pi$
$978$		0			0
$979$	10.1744	−	17.6227i	0.325177	−	0.563223i
$980$		0			0
$981$	7.52807			0.240353
$982$		0			0
$983$	−20.8080	−	36.0406i	−0.663673	−	1.14952i	−0.979643	−	0.200746i	$-0.935663\pi$
$983$	−20.8080	−	36.0406i	−0.663673	−	1.14952i	0.315970	−	0.948769i	$-0.397670\pi$
$984$		0			0
$985$	−11.8714	−	20.5619i	−0.378254	−	0.655155i
$986$		0			0
$987$	−1.92001			−0.0611147
$988$		0			0
$989$	−1.23001			−0.0391120
$990$		0			0
$991$	5.96872	+	10.3381i	0.189603	+	0.328401i	0.945118	−	0.326730i	$-0.105947\pi$
$991$	5.96872	+	10.3381i	0.189603	+	0.328401i	−0.755515	+	0.655131i	$0.772613\pi$
$992$		0			0
$993$	5.44387	+	9.42907i	0.172756	+	0.299222i
$994$		0			0
$995$	−22.9787			−0.728473
$996$		0			0
$997$	9.63745	−	16.6925i	0.305221	−	0.528658i	−0.672089	−	0.740470i	$-0.734603\pi$
$997$	9.63745	−	16.6925i	0.305221	−	0.528658i	0.977311	+	0.211812i	$0.0679363\pi$
$998$		0			0
$999$	−2.05170			−0.0649128

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.i.c.121.3	✓	8
3.2	odd	2		3420.2.t.w.1261.1		8
4.3	odd	2		1520.2.q.m.881.2		8
5.2	odd	4		1900.2.s.d.349.5		16
5.3	odd	4		1900.2.s.d.349.4		16
5.4	even	2		1900.2.i.d.501.2		8
19.7	even	3		7220.2.a.r.1.2		4
19.11	even	3	inner	380.2.i.c.201.3	yes	8
19.12	odd	6		7220.2.a.p.1.3		4
57.11	odd	6		3420.2.t.w.3241.1		8
76.11	odd	6		1520.2.q.m.961.2		8
95.49	even	6		1900.2.i.d.201.2		8
95.68	odd	12		1900.2.s.d.49.5		16
95.87	odd	12		1900.2.s.d.49.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.i.c.121.3	✓	8	1.1	even	1	trivial
380.2.i.c.201.3	yes	8	19.11	even	3	inner
1520.2.q.m.881.2		8	4.3	odd	2
1520.2.q.m.961.2		8	76.11	odd	6
1900.2.i.d.201.2		8	95.49	even	6
1900.2.i.d.501.2		8	5.4	even	2
1900.2.s.d.49.4		16	95.87	odd	12
1900.2.s.d.49.5		16	95.68	odd	12
1900.2.s.d.349.4		16	5.3	odd	4
1900.2.s.d.349.5		16	5.2	odd	4
3420.2.t.w.1261.1		8	3.2	odd	2
3420.2.t.w.3241.1		8	57.11	odd	6
7220.2.a.p.1.3		4	19.12	odd	6
7220.2.a.r.1.2		4	19.7	even	3

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)

\(f(q)\)	\(=\)	\(q+(0.176725 + 0.306096i) q^{3} +(-0.500000 - 0.866025i) q^{5} -4.30507 q^{7} +(1.43754 - 2.48989i) q^{9} +O(q^{10})\)	\(q+(0.176725 + 0.306096i) q^{3} +(-0.500000 - 0.866025i) q^{5} -4.30507 q^{7} +(1.43754 - 2.48989i) q^{9} +6.01196 q^{11} +(2.97581 - 5.15425i) q^{13} +(0.176725 - 0.306096i) q^{15} +(-1.93754 - 3.35591i) q^{17} +(4.19835 - 1.17212i) q^{19} +(-0.760812 - 1.31776i) q^{21} +(-0.391721 + 0.678480i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.07654 q^{27} +(-3.98179 + 6.89666i) q^{29} -4.49034 q^{31} +(1.06246 + 1.84024i) q^{33} +(2.15253 + 3.72830i) q^{35} -0.988035 q^{37} +2.10360 q^{39} +(-3.15253 - 5.46035i) q^{41} +(0.785004 + 1.35967i) q^{43} -2.87507 q^{45} +(0.630909 - 1.09277i) q^{47} +11.5336 q^{49} +(0.684822 - 1.18615i) q^{51} +(4.07443 - 7.05712i) q^{53} +(-3.00598 - 5.20651i) q^{55} +(1.10073 + 1.07796i) q^{57} +(-2.62834 - 4.55242i) q^{59} +(-2.80507 + 4.85852i) q^{61} +(-6.18869 + 10.7191i) q^{63} -5.95162 q^{65} +(-3.52162 + 6.09963i) q^{67} -0.276907 q^{69} +(2.90736 + 5.03570i) q^{71} +(4.62024 + 8.00250i) q^{73} -0.353450 q^{75} -25.8819 q^{77} +(6.99743 + 12.1199i) q^{79} +(-3.94563 - 6.83404i) q^{81} +6.58197 q^{83} +(-1.93754 + 3.35591i) q^{85} -2.81472 q^{87} +(1.69237 - 2.93126i) q^{89} +(-12.8110 + 22.1894i) q^{91} +(-0.793555 - 1.37448i) q^{93} +(-3.11426 - 3.04982i) q^{95} +(3.69835 + 6.40573i) q^{97} +(8.64242 - 14.9691i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{3} - 4 q^{5} - 5 q^{9}+O(q^{10}) \) 8 * q - q^3 - 4 * q^5 - 5 * q^9	\( 8 q - q^{3} - 4 q^{5} - 5 q^{9} + 4 q^{11} + 9 q^{13} - q^{15} + q^{17} + 3 q^{19} + 8 q^{21} - 4 q^{25} + 20 q^{27} + 5 q^{29} - 20 q^{31} + 25 q^{33} - 52 q^{37} - 54 q^{39} - 8 q^{41} + 7 q^{43} + 10 q^{45} + 16 q^{47} + 20 q^{49} + 12 q^{51} + 5 q^{53} - 2 q^{55} + 27 q^{57} + 11 q^{59} + 12 q^{61} - 3 q^{63} - 18 q^{65} + 6 q^{69} + 14 q^{71} - 4 q^{73} + 2 q^{75} - 44 q^{77} + 13 q^{79} - 24 q^{81} + 10 q^{83} + q^{85} - 4 q^{87} + 5 q^{89} - 46 q^{91} - 28 q^{93} - 6 q^{95} - q^{97} + 24 q^{99}+O(q^{100}) \) 8 * q - q^3 - 4 * q^5 - 5 * q^9 + 4 * q^11 + 9 * q^13 - q^15 + q^17 + 3 * q^19 + 8 * q^21 - 4 * q^25 + 20 * q^27 + 5 * q^29 - 20 * q^31 + 25 * q^33 - 52 * q^37 - 54 * q^39 - 8 * q^41 + 7 * q^43 + 10 * q^45 + 16 * q^47 + 20 * q^49 + 12 * q^51 + 5 * q^53 - 2 * q^55 + 27 * q^57 + 11 * q^59 + 12 * q^61 - 3 * q^63 - 18 * q^65 + 6 * q^69 + 14 * q^71 - 4 * q^73 + 2 * q^75 - 44 * q^77 + 13 * q^79 - 24 * q^81 + 10 * q^83 + q^85 - 4 * q^87 + 5 * q^89 - 46 * q^91 - 28 * q^93 - 6 * q^95 - q^97 + 24 * q^99

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