LMFDB - Embedded newform 308.2.j.c.113.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(113,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("308.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.j (of order $5$, degree $4$, 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:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{11} + 11x^{10} - 18x^{9} + 48x^{8} - 22x^{7} + 80x^{6} + 68x^{5} + 26x^{4} - 24x^{3} + 9x^{2} + 1 $ x^12 - 4x^11 + 11x^10 - 18x^9 + 48x^8 - 22x^7 + 80x^6 + 68x^5 + 26x^4 - 24x^3 + 9x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			113.1
Root			$0.348189 + 0.252974i$ of defining polynomial
Character	$\chi$	$=$	308.113
Dual form			308.2.j.c.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.585004 - 1.80046i) q^{3} +(-1.81637 - 1.31967i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-0.472365 + 0.343194i) q^{9} +O(q^{10})$	\(q+(-0.585004 - 1.80046i) q^{3} +(-1.81637 - 1.31967i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-0.472365 + 0.343194i) q^{9} +(-3.20325 + 0.859769i) q^{11} +(-3.19331 + 2.32008i) q^{13} +(-1.31342 + 4.04230i) q^{15} +(0.797479 + 0.579403i) q^{17} +(-1.91513 - 5.89415i) q^{19} -1.89311 q^{21} -1.77681 q^{23} +(0.0125818 + 0.0387229i) q^{25} +(-3.70044 - 2.68853i) q^{27} +(-2.39279 + 7.36426i) q^{29} +(7.41972 - 5.39074i) q^{31} +(3.42189 + 5.26434i) q^{33} +(-1.81637 + 1.31967i) q^{35} +(0.976908 - 3.00661i) q^{37} +(6.04529 + 4.39216i) q^{39} +(-0.554225 - 1.70573i) q^{41} +9.78510 q^{43} +1.31089 q^{45} +(-3.48381 - 10.7221i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(0.576661 - 1.77478i) q^{51} +(0.624955 - 0.454056i) q^{53} +(6.95289 + 2.66557i) q^{55} +(-9.49181 + 6.89620i) q^{57} +(1.80044 - 5.54119i) q^{59} +(4.31337 + 3.13385i) q^{61} +(0.180428 + 0.555299i) q^{63} +8.86195 q^{65} -5.97196 q^{67} +(1.03944 + 3.19907i) q^{69} +(5.73285 + 4.16516i) q^{71} +(2.71268 - 8.34877i) q^{73} +(0.0623585 - 0.0453061i) q^{75} +(-0.172169 + 3.31215i) q^{77} +(8.06846 - 5.86208i) q^{79} +(-3.21709 + 9.90118i) q^{81} +(-0.515819 - 0.374765i) q^{83} +(-0.683896 - 2.10482i) q^{85} +14.6588 q^{87} +9.73855 q^{89} +(1.21974 + 3.75396i) q^{91} +(-14.0464 - 10.2053i) q^{93} +(-4.29975 + 13.2333i) q^{95} +(-3.27720 + 2.38102i) q^{97} +(1.21804 - 1.50546i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + q^{5} - 3 q^{7} + q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 + q^5 - 3 * q^7 + q^9	$ 12 q + 6 q^{3} + q^{5} - 3 q^{7} + q^{9} + 2 q^{11} - 7 q^{13} - 4 q^{15} + 3 q^{17} - 23 q^{19} - 4 q^{21} - 38 q^{23} + 2 q^{25} - 18 q^{27} + 29 q^{29} + 9 q^{31} - 4 q^{33} + q^{35} + 3 q^{37} + 25 q^{39} - 18 q^{41} + 34 q^{43} + 14 q^{45} + 9 q^{47} - 3 q^{49} + 35 q^{51} + 13 q^{53} + 16 q^{55} + 9 q^{57} - 17 q^{59} - 19 q^{61} - 9 q^{63} + 8 q^{65} - 20 q^{67} - 14 q^{69} + 15 q^{71} + 9 q^{73} - 47 q^{75} - 8 q^{77} - 14 q^{79} - 49 q^{81} + 41 q^{83} - 66 q^{85} + 40 q^{87} + 34 q^{89} + 13 q^{91} - 40 q^{93} + 42 q^{95} - 10 q^{97} - 24 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 + q^5 - 3 * q^7 + q^9 + 2 * q^11 - 7 * q^13 - 4 * q^15 + 3 * q^17 - 23 * q^19 - 4 * q^21 - 38 * q^23 + 2 * q^25 - 18 * q^27 + 29 * q^29 + 9 * q^31 - 4 * q^33 + q^35 + 3 * q^37 + 25 * q^39 - 18 * q^41 + 34 * q^43 + 14 * q^45 + 9 * q^47 - 3 * q^49 + 35 * q^51 + 13 * q^53 + 16 * q^55 + 9 * q^57 - 17 * q^59 - 19 * q^61 - 9 * q^63 + 8 * q^65 - 20 * q^67 - 14 * q^69 + 15 * q^71 + 9 * q^73 - 47 * q^75 - 8 * q^77 - 14 * q^79 - 49 * q^81 + 41 * q^83 - 66 * q^85 + 40 * q^87 + 34 * q^89 + 13 * q^91 - 40 * q^93 + 42 * q^95 - 10 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.585004	−	1.80046i	−0.337752	−	1.03949i	−0.965350	−	0.260957i	$-0.915962\pi$
$3$	−0.585004	−	1.80046i	−0.337752	−	1.03949i	0.627598	−	0.778537i	$-0.284038\pi$
$4$		0			0
$5$	−1.81637	−	1.31967i	−0.812304	−	0.590174i	0.102193	−	0.994765i	$-0.467414\pi$
$5$	−1.81637	−	1.31967i	−0.812304	−	0.590174i	−0.914498	+	0.404591i	$0.867414\pi$
$6$		0			0
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$		0			0
$9$	−0.472365	+	0.343194i	−0.157455	+	0.114398i
$10$		0			0
$11$	−3.20325	+	0.859769i	−0.965816	+	0.259230i
$11$	−3.20325	+	0.859769i	−0.965816	+	0.259230i
$12$		0			0
$13$	−3.19331	+	2.32008i	−0.885665	+	0.643473i	−0.934744	−	0.355322i	$-0.884371\pi$
$13$	−3.19331	+	2.32008i	−0.885665	+	0.643473i	0.0490793	+	0.998795i	$0.484371\pi$
$14$		0			0
$15$	−1.31342	+	4.04230i	−0.339125	+	1.04372i
$16$		0			0
$17$	0.797479	+	0.579403i	0.193417	+	0.140526i	0.680279	−	0.732953i	$-0.261859\pi$
$17$	0.797479	+	0.579403i	0.193417	+	0.140526i	−0.486862	+	0.873479i	$0.661859\pi$
$18$		0			0
$19$	−1.91513	−	5.89415i	−0.439360	−	1.35221i	−0.888552	−	0.458776i	$-0.848288\pi$
$19$	−1.91513	−	5.89415i	−0.439360	−	1.35221i	0.449192	−	0.893435i	$-0.351712\pi$
$20$		0			0
$21$	−1.89311			−0.413111
$22$		0			0
$23$	−1.77681			−0.370491			−0.185245	−	0.982692i	$-0.559308\pi$
$23$	−1.77681			−0.370491			−0.185245	+	0.982692i	$0.559308\pi$
$24$		0			0
$25$	0.0125818	+	0.0387229i	0.00251637	+	0.00774459i
$26$		0			0
$27$	−3.70044	−	2.68853i	−0.712150	−	0.517407i
$28$		0			0
$29$	−2.39279	+	7.36426i	−0.444330	+	1.36751i	0.438886	+	0.898543i	$0.355373\pi$
$29$	−2.39279	+	7.36426i	−0.444330	+	1.36751i	−0.883216	+	0.468966i	$0.844627\pi$
$30$		0			0
$31$	7.41972	−	5.39074i	1.33262	−	0.968206i	0.332941	−	0.942948i	$-0.391959\pi$
$31$	7.41972	−	5.39074i	1.33262	−	0.968206i	0.999681	−	0.0252584i	$-0.00804086\pi$
$32$		0			0
$33$	3.42189	+	5.26434i	0.595675	+	0.916404i
$34$		0			0
$35$	−1.81637	+	1.31967i	−0.307022	+	0.223065i
$36$		0			0
$37$	0.976908	−	3.00661i	0.160603	−	0.494284i	−0.838083	−	0.545543i	$-0.816323\pi$
$37$	0.976908	−	3.00661i	0.160603	−	0.494284i	0.998685	+	0.0512589i	$0.0163234\pi$
$38$		0			0
$39$	6.04529	+	4.39216i	0.968022	+	0.703309i
$40$		0			0
$41$	−0.554225	−	1.70573i	−0.0865554	−	0.266390i	0.898406	−	0.439167i	$-0.144726\pi$
$41$	−0.554225	−	1.70573i	−0.0865554	−	0.266390i	−0.984961	+	0.172776i	$0.944726\pi$
$42$		0			0
$43$	9.78510			1.49221			0.746107	−	0.665826i	$-0.231921\pi$
$43$	9.78510			1.49221			0.746107	+	0.665826i	$0.231921\pi$
$44$		0			0
$45$	1.31089			0.195416
$46$		0			0
$47$	−3.48381	−	10.7221i	−0.508166	−	1.56397i	−0.795382	−	0.606108i	$-0.792730\pi$
$47$	−3.48381	−	10.7221i	−0.508166	−	1.56397i	0.287217	−	0.957866i	$-0.407270\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$		0			0
$51$	0.576661	−	1.77478i	0.0807487	−	0.248519i
$52$		0			0
$53$	0.624955	−	0.454056i	0.0858441	−	0.0623694i	−0.544035	−	0.839062i	$-0.683104\pi$
$53$	0.624955	−	0.454056i	0.0858441	−	0.0623694i	0.629879	+	0.776693i	$0.283104\pi$
$54$		0			0
$55$	6.95289	+	2.66557i	0.937527	+	0.359425i
$56$		0			0
$57$	−9.49181	+	6.89620i	−1.25722	+	0.913424i
$58$		0			0
$59$	1.80044	−	5.54119i	0.234397	−	0.721401i	−0.762803	−	0.646631i	$-0.776178\pi$
$59$	1.80044	−	5.54119i	0.234397	−	0.721401i	0.997201	−	0.0747706i	$-0.0238225\pi$
$60$		0			0
$61$	4.31337	+	3.13385i	0.552271	+	0.401248i	0.828622	−	0.559809i	$-0.189125\pi$
$61$	4.31337	+	3.13385i	0.552271	+	0.401248i	−0.276351	+	0.961057i	$0.589125\pi$
$62$		0			0
$63$	0.180428	+	0.555299i	0.0227317	+	0.0699611i
$64$		0			0
$65$	8.86195			1.09919
$66$		0			0
$67$	−5.97196			−0.729591			−0.364796	−	0.931088i	$-0.618861\pi$
$67$	−5.97196			−0.729591			−0.364796	+	0.931088i	$0.618861\pi$
$68$		0			0
$69$	1.03944	+	3.19907i	0.125134	+	0.385123i
$70$		0			0
$71$	5.73285	+	4.16516i	0.680364	+	0.494314i	0.873479	−	0.486863i	$-0.161859\pi$
$71$	5.73285	+	4.16516i	0.680364	+	0.494314i	−0.193114	+	0.981176i	$0.561859\pi$
$72$		0			0
$73$	2.71268	−	8.34877i	0.317495	−	0.977149i	−0.657220	−	0.753699i	$-0.728268\pi$
$73$	2.71268	−	8.34877i	0.317495	−	0.977149i	0.974715	−	0.223451i	$-0.0717322\pi$
$74$		0			0
$75$	0.0623585	−	0.0453061i	0.00720054	−	0.00523150i
$76$		0			0
$77$	−0.172169	+	3.31215i	−0.0196204	+	0.377455i
$78$		0			0
$79$	8.06846	−	5.86208i	0.907773	−	0.659536i	−0.0326775	−	0.999466i	$-0.510403\pi$
$79$	8.06846	−	5.86208i	0.907773	−	0.659536i	0.940451	+	0.339930i	$0.110403\pi$
$80$		0			0
$81$	−3.21709	+	9.90118i	−0.357454	+	1.10013i
$82$		0			0
$83$	−0.515819	−	0.374765i	−0.0566185	−	0.0411358i	0.559116	−	0.829089i	$-0.311141\pi$
$83$	−0.515819	−	0.374765i	−0.0566185	−	0.0411358i	−0.615735	+	0.787954i	$0.711141\pi$
$84$		0			0
$85$	−0.683896	−	2.10482i	−0.0741790	−	0.228299i
$86$		0			0
$87$	14.6588			1.57159
$88$		0			0
$89$	9.73855			1.03228			0.516142	−	0.856503i	$-0.327368\pi$
$89$	9.73855			1.03228			0.516142	+	0.856503i	$0.327368\pi$
$90$		0			0
$91$	1.21974	+	3.75396i	0.127863	+	0.393522i
$92$		0			0
$93$	−14.0464	−	10.2053i	−1.45654	−	1.05824i
$94$		0			0
$95$	−4.29975	+	13.2333i	−0.441145	+	1.35771i
$96$		0			0
$97$	−3.27720	+	2.38102i	−0.332749	+	0.241756i	−0.741596	−	0.670847i	$-0.765931\pi$
$97$	−3.27720	+	2.38102i	−0.332749	+	0.241756i	0.408847	+	0.912603i	$0.365931\pi$
$98$		0			0
$99$	1.21804	−	1.50546i	0.122417	−	0.151304i
$100$		0			0
$101$	−8.15171	+	5.92256i	−0.811126	+	0.589317i	−0.914157	−	0.405361i	$-0.867146\pi$
$101$	−8.15171	+	5.92256i	−0.811126	+	0.589317i	0.103031	+	0.994678i	$0.467146\pi$
$102$		0			0
$103$	−5.11751	+	15.7501i	−0.504243	+	1.55190i	0.297797	+	0.954629i	$0.403748\pi$
$103$	−5.11751	+	15.7501i	−0.504243	+	1.55190i	−0.802040	+	0.597271i	$0.796252\pi$
$104$		0			0
$105$	3.43859	+	2.49828i	0.335572	+	0.243807i
$106$		0			0
$107$	−3.32393	−	10.2300i	−0.321336	−	0.988970i	−0.973067	−	0.230521i	$-0.925957\pi$
$107$	−3.32393	−	10.2300i	−0.321336	−	0.988970i	0.651731	−	0.758450i	$-0.274043\pi$
$108$		0			0
$109$	6.44750			0.617558			0.308779	−	0.951134i	$-0.400080\pi$
$109$	6.44750			0.617558			0.308779	+	0.951134i	$0.400080\pi$
$110$		0			0
$111$	−5.98478			−0.568050
$112$		0			0
$113$	−2.01772	−	6.20992i	−0.189812	−	0.584180i	0.810186	−	0.586172i	$-0.199366\pi$
$113$	−2.01772	−	6.20992i	−0.189812	−	0.584180i	−0.999998	+	0.00199235i	$0.999366\pi$
$114$		0			0
$115$	3.22734	+	2.34480i	0.300951	+	0.218654i
$116$		0			0
$117$	0.712174	−	2.19185i	0.0658405	−	0.202636i
$118$		0			0
$119$	0.797479	−	0.579403i	0.0731048	−	0.0531138i
$120$		0			0
$121$	9.52159	−	5.50811i	0.865599	−	0.500737i
$122$		0			0
$123$	−2.74687	+	1.99572i	−0.247677	+	0.179948i
$124$		0			0
$125$	−3.44071	+	10.5894i	−0.307746	+	0.947145i
$126$		0			0
$127$	−12.6750	−	9.20890i	−1.12472	−	0.817158i	−0.139803	−	0.990179i	$-0.544647\pi$
$127$	−12.6750	−	9.20890i	−1.12472	−	0.817158i	−0.984918	+	0.173022i	$0.944647\pi$
$128$		0			0
$129$	−5.72432	−	17.6177i	−0.503999	−	1.55115i
$130$		0			0
$131$	−5.26440			−0.459952			−0.229976	−	0.973196i	$-0.573865\pi$
$131$	−5.26440			−0.459952			−0.229976	+	0.973196i	$0.573865\pi$
$132$		0			0
$133$	−6.19748			−0.537389
$134$		0			0
$135$	3.17340	+	9.76671i	0.273122	+	0.840584i
$136$		0			0
$137$	−17.5693	−	12.7649i	−1.50105	−	1.09058i	−0.969962	−	0.243258i	$-0.921784\pi$
$137$	−17.5693	−	12.7649i	−1.50105	−	1.09058i	−0.531087	−	0.847317i	$-0.678216\pi$
$138$		0			0
$139$	0.252180	−	0.776130i	0.0213896	−	0.0658305i	−0.939792	−	0.341747i	$-0.888981\pi$
$139$	0.252180	−	0.776130i	0.0213896	−	0.0658305i	0.961182	+	0.275917i	$0.0889814\pi$
$140$		0			0
$141$	−17.2666	+	12.5449i	−1.45411	+	1.05647i
$142$		0			0
$143$	8.23423	−	10.1773i	0.688581	−	0.851067i
$144$		0			0
$145$	14.0646	−	10.2185i	1.16800	−	0.848601i
$146$		0			0
$147$	−0.585004	+	1.80046i	−0.0482503	+	0.148499i
$148$		0			0
$149$	10.2408	+	7.44036i	0.838957	+	0.609538i	0.922079	−	0.387002i	$-0.126489\pi$
$149$	10.2408	+	7.44036i	0.838957	+	0.609538i	−0.0831223	+	0.996539i	$0.526489\pi$
$150$		0			0
$151$	3.67746	+	11.3181i	0.299268	+	0.921051i	0.981754	+	0.190153i	$0.0608985\pi$
$151$	3.67746	+	11.3181i	0.299268	+	0.921051i	−0.682487	+	0.730898i	$0.739102\pi$
$152$		0			0
$153$	−0.575549			−0.0465304
$154$		0			0
$155$	−20.5909			−1.65390
$156$		0			0
$157$	−4.72615	−	14.5456i	−0.377188	−	1.16086i	−0.941991	−	0.335639i	$-0.891048\pi$
$157$	−4.72615	−	14.5456i	−0.377188	−	1.16086i	0.564803	−	0.825226i	$-0.308952\pi$
$158$		0			0
$159$	−1.18311	−	0.859580i	−0.0938267	−	0.0681691i
$160$		0			0
$161$	−0.549065	+	1.68985i	−0.0432724	+	0.133179i
$162$		0			0
$163$	7.68888	−	5.58630i	0.602239	−	0.437552i	−0.244434	−	0.969666i	$-0.578602\pi$
$163$	7.68888	−	5.58630i	0.602239	−	0.437552i	0.846673	+	0.532114i	$0.178602\pi$
$164$		0			0
$165$	0.731773	−	14.0777i	0.0569685	−	1.09595i
$166$		0			0
$167$	−0.917176	+	0.666368i	−0.0709732	+	0.0515651i	−0.622706	−	0.782456i	$-0.713967\pi$
$167$	−0.917176	+	0.666368i	−0.0709732	+	0.0515651i	0.551733	+	0.834021i	$0.313967\pi$
$168$		0			0
$169$	0.797256	−	2.45370i	0.0613274	−	0.188746i
$170$		0			0
$171$	2.92747	+	2.12693i	0.223870	+	0.162651i
$172$		0			0
$173$	1.05264	+	3.23970i	0.0800310	+	0.246310i	0.983064	−	0.183260i	$-0.0586651\pi$
$173$	1.05264	+	3.23970i	0.0800310	+	0.246310i	−0.903033	+	0.429570i	$0.858665\pi$
$174$		0			0
$175$	0.0407157			0.00307782
$176$		0			0
$177$	−11.0299			−0.829061
$178$		0			0
$179$	−6.57879	−	20.2474i	−0.491722	−	1.51336i	−0.822004	−	0.569482i	$-0.807144\pi$
$179$	−6.57879	−	20.2474i	−0.491722	−	1.51336i	0.330282	−	0.943882i	$-0.392856\pi$
$180$		0			0
$181$	10.6066	+	7.70614i	0.788382	+	0.572793i	0.907483	−	0.420089i	$-0.138001\pi$
$181$	10.6066	+	7.70614i	0.788382	+	0.572793i	−0.119101	+	0.992882i	$0.538001\pi$
$182$		0			0
$183$	3.11902	−	9.59936i	0.230565	−	0.709605i
$184$		0			0
$185$	−5.74216	+	4.17192i	−0.422172	+	0.306726i
$186$		0			0
$187$	−3.05268	−	1.17032i	−0.223234	−	0.0855824i
$188$		0			0
$189$	−3.70044	+	2.68853i	−0.269167	+	0.195562i
$190$		0			0
$191$	−6.75963	+	20.8040i	−0.489110	+	1.50532i	0.336830	+	0.941566i	$0.390645\pi$
$191$	−6.75963	+	20.8040i	−0.489110	+	1.50532i	−0.825939	+	0.563759i	$0.809355\pi$
$192$		0			0
$193$	14.5888	+	10.5994i	1.05012	+	0.762960i	0.972236	−	0.234002i	$-0.0751822\pi$
$193$	14.5888	+	10.5994i	1.05012	+	0.762960i	0.0778883	+	0.996962i	$0.475182\pi$
$194$		0			0
$195$	−5.18428	−	15.9556i	−0.371254	−	1.14260i
$196$		0			0
$197$	12.9818			0.924916			0.462458	−	0.886641i	$-0.346968\pi$
$197$	12.9818			0.924916			0.462458	+	0.886641i	$0.346968\pi$
$198$		0			0
$199$	−19.3539			−1.37196			−0.685982	−	0.727618i	$-0.740627\pi$
$199$	−19.3539			−1.37196			−0.685982	+	0.727618i	$0.740627\pi$
$200$		0			0
$201$	3.49362	+	10.7523i	0.246421	+	0.758406i
$202$		0			0
$203$	6.26441	+	4.55136i	0.439676	+	0.319443i
$204$		0			0
$205$	−1.24432	+	3.82962i	−0.0869071	+	0.267473i
$206$		0			0
$207$	0.839304	−	0.609790i	0.0583357	−	0.0423833i
$208$		0			0
$209$	11.2022	+	17.2339i	0.774875	+	1.19209i
$210$		0			0
$211$	−1.79852	+	1.30670i	−0.123815	+	0.0899570i	−0.647969	−	0.761666i	$-0.724382\pi$
$211$	−1.79852	+	1.30670i	−0.123815	+	0.0899570i	0.524154	+	0.851623i	$0.324382\pi$
$212$		0			0
$213$	4.14545	−	12.7584i	0.284042	−	0.874191i
$214$		0			0
$215$	−17.7733	−	12.9131i	−1.21213	−	0.880665i
$216$		0			0
$217$	−2.83408	−	8.72241i	−0.192390	−	0.592116i
$218$		0			0
$219$	−16.6185			−1.12298
$220$		0			0
$221$	−3.89086			−0.261727
$222$		0			0
$223$	6.33045	+	19.4831i	0.423918	+	1.30469i	0.904026	+	0.427477i	$0.140597\pi$
$223$	6.33045	+	19.4831i	0.423918	+	1.30469i	−0.480108	+	0.877209i	$0.659403\pi$
$224$		0			0
$225$	−0.0192327	−	0.0139734i	−0.00128218	−	0.000931558i
$226$		0			0
$227$	1.77072	−	5.44972i	0.117527	−	0.361711i	−0.874939	−	0.484234i	$-0.839099\pi$
$227$	1.77072	−	5.44972i	0.117527	−	0.361711i	0.992466	+	0.122523i	$0.0390985\pi$
$228$		0			0
$229$	3.35034	−	2.43416i	0.221396	−	0.160854i	−0.471559	−	0.881835i	$-0.656308\pi$
$229$	3.35034	−	2.43416i	0.221396	−	0.160854i	0.692955	+	0.720981i	$0.256308\pi$
$230$		0			0
$231$	6.06411	−	1.62764i	0.398989	−	0.107091i
$232$		0			0
$233$	−2.45586	+	1.78428i	−0.160888	+	0.116892i	−0.665316	−	0.746561i	$-0.731703\pi$
$233$	−2.45586	+	1.78428i	−0.160888	+	0.116892i	0.504428	+	0.863454i	$0.331703\pi$
$234$		0			0
$235$	−7.82169	+	24.0727i	−0.510231	+	1.57033i
$236$		0			0
$237$	−15.2745	−	11.0976i	−0.992186	−	0.720866i
$238$		0			0
$239$	4.31463	+	13.2791i	0.279090	+	0.858952i	0.988108	+	0.153761i	$0.0491387\pi$
$239$	4.31463	+	13.2791i	0.279090	+	0.858952i	−0.709018	+	0.705191i	$0.750861\pi$
$240$		0			0
$241$	1.47197			0.0948178			0.0474089	−	0.998876i	$-0.484904\pi$
$241$	1.47197			0.0948178			0.0474089	+	0.998876i	$0.484904\pi$
$242$		0			0
$243$	5.98667			0.384045
$244$		0			0
$245$	0.693791	+	2.13527i	0.0443247	+	0.136417i
$246$		0			0
$247$	19.7905	+	14.3786i	1.25924	+	0.914889i
$248$		0			0
$249$	−0.372991	+	1.14795i	−0.0236374	+	0.0727483i
$250$		0			0
$251$	12.3246	−	8.95431i	0.777919	−	0.565191i	−0.126435	−	0.991975i	$-0.540353\pi$
$251$	12.3246	−	8.95431i	0.777919	−	0.565191i	0.904354	+	0.426784i	$0.140353\pi$
$252$		0			0
$253$	5.69157	−	1.52765i	0.357826	−	0.0960424i
$254$		0			0
$255$	−3.38955	+	2.46265i	−0.212262	+	0.154217i
$256$		0			0
$257$	−7.62710	+	23.4738i	−0.475765	+	1.46426i	0.369157	+	0.929367i	$0.379646\pi$
$257$	−7.62710	+	23.4738i	−0.475765	+	1.46426i	−0.844923	+	0.534888i	$0.820354\pi$
$258$		0			0
$259$	−2.55758	−	1.85819i	−0.158920	−	0.115462i
$260$		0			0
$261$	−1.39709	−	4.29981i	−0.0864779	−	0.266152i
$262$		0			0
$263$	−13.5834			−0.837589			−0.418795	−	0.908081i	$-0.637547\pi$
$263$	−13.5834			−0.837589			−0.418795	+	0.908081i	$0.637547\pi$
$264$		0			0
$265$	−1.73435			−0.106540
$266$		0			0
$267$	−5.69709	−	17.5338i	−0.348656	−	1.07305i
$268$		0			0
$269$	10.5015	+	7.62978i	0.640287	+	0.465196i	0.859949	−	0.510380i	$-0.170495\pi$
$269$	10.5015	+	7.62978i	0.640287	+	0.465196i	−0.219662	+	0.975576i	$0.570495\pi$
$270$		0			0
$271$	6.12885	−	18.8627i	0.372301	−	1.14583i	−0.572980	−	0.819569i	$-0.694213\pi$
$271$	6.12885	−	18.8627i	0.372301	−	1.14583i	0.945281	−	0.326256i	$-0.105787\pi$
$272$		0			0
$273$	6.04529	−	4.39216i	0.365878	−	0.265826i
$274$		0			0
$275$	−0.0735955	−	0.113222i	−0.00443798	−	0.00682752i
$276$		0			0
$277$	23.7092	−	17.2258i	1.42455	−	1.03500i	0.433551	−	0.901129i	$-0.357261\pi$
$277$	23.7092	−	17.2258i	1.42455	−	1.03500i	0.990999	−	0.133867i	$-0.0427395\pi$
$278$		0			0
$279$	−1.65475	+	5.09280i	−0.0990674	+	0.304898i
$280$		0			0
$281$	18.7423	+	13.6171i	1.11807	+	0.812328i	0.983916	−	0.178632i	$-0.0571671\pi$
$281$	18.7423	+	13.6171i	1.11807	+	0.812328i	0.134158	+	0.990960i	$0.457167\pi$
$282$		0			0
$283$	7.74490	+	23.8364i	0.460387	+	1.41692i	0.864693	+	0.502301i	$0.167513\pi$
$283$	7.74490	+	23.8364i	0.460387	+	1.41692i	−0.404306	+	0.914624i	$0.632487\pi$
$284$		0			0
$285$	26.3413			1.56032
$286$		0			0
$287$	−1.79351			−0.105868
$288$		0			0
$289$	−4.95302	−	15.2438i	−0.291354	−	0.896696i
$290$		0			0
$291$	6.20410	+	4.50754i	0.363691	+	0.264237i
$292$		0			0
$293$	8.38794	−	25.8154i	0.490029	−	1.50815i	−0.334534	−	0.942384i	$-0.608579\pi$
$293$	8.38794	−	25.8154i	0.490029	−	1.50815i	0.824563	−	0.565770i	$-0.191421\pi$
$294$		0			0
$295$	−10.5828	+	7.68885i	−0.616154	+	0.447662i
$296$		0			0
$297$	14.1649	+	5.43049i	0.821933	+	0.315109i
$298$		0			0
$299$	5.67391	−	4.12234i	0.328131	−	0.238401i
$300$		0			0
$301$	3.02376	−	9.30619i	0.174287	−	0.536400i
$302$		0			0
$303$	15.4321	+	11.2121i	0.886551	+	0.644117i
$304$		0			0
$305$	−3.69903	−	11.3844i	−0.211806	−	0.651871i
$306$		0			0
$307$	−2.36692			−0.135087			−0.0675437	−	0.997716i	$-0.521516\pi$
$307$	−2.36692			−0.135087			−0.0675437	+	0.997716i	$0.521516\pi$
$308$		0			0
$309$	31.3511			1.78350
$310$		0			0
$311$	4.74503	+	14.6037i	0.269066	+	0.828099i	0.990729	+	0.135855i	$0.0433780\pi$
$311$	4.74503	+	14.6037i	0.269066	+	0.828099i	−0.721663	+	0.692244i	$0.756622\pi$
$312$		0			0
$313$	−11.8807	−	8.63185i	−0.671538	−	0.487901i	0.199001	−	0.979999i	$-0.436230\pi$
$313$	−11.8807	−	8.63185i	−0.671538	−	0.487901i	−0.870540	+	0.492098i	$0.836230\pi$
$314$		0			0
$315$	0.405088	−	1.24673i	0.0228241	−	0.0702454i
$316$		0			0
$317$	16.9415	−	12.3087i	0.951528	−	0.691326i	0.000360416	−	1.00000i	$-0.499885\pi$
$317$	16.9415	−	12.3087i	0.951528	−	0.691326i	0.951168	+	0.308674i	$0.0998853\pi$
$318$		0			0
$319$	1.33314	−	25.6468i	0.0746417	−	1.43595i
$320$		0			0
$321$	−16.4741	+	11.9692i	−0.919497	+	0.668054i
$322$		0			0
$323$	1.88781	−	5.81009i	0.105041	−	0.323282i
$324$		0			0
$325$	−0.130018	−	0.0944635i	−0.00721209	−	0.00523989i
$326$		0			0
$327$	−3.77181	−	11.6084i	−0.208582	−	0.641948i
$328$		0			0
$329$	−11.2738			−0.621547
$330$		0			0
$331$	−1.37426			−0.0755359			−0.0377680	−	0.999287i	$-0.512025\pi$
$331$	−1.37426			−0.0755359			−0.0377680	+	0.999287i	$0.512025\pi$
$332$		0			0
$333$	0.570393	+	1.75549i	0.0312573	+	0.0962002i
$334$		0			0
$335$	10.8473	+	7.88101i	0.592650	+	0.430585i
$336$		0			0
$337$	7.29145	−	22.4408i	0.397191	−	1.22243i	−0.530052	−	0.847965i	$-0.677828\pi$
$337$	7.29145	−	22.4408i	0.397191	−	1.22243i	0.927242	−	0.374462i	$-0.122172\pi$
$338$		0			0
$339$	−10.0003	+	7.26565i	−0.543142	+	0.394616i
$340$		0			0
$341$	−19.1324	+	23.6471i	−1.03608	+	1.28056i
$342$		0			0
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$		0			0
$345$	2.33371	−	7.18241i	0.125643	−	0.386688i
$346$		0			0
$347$	30.0910	+	21.8624i	1.61537	+	1.17363i	0.841408	+	0.540400i	$0.181727\pi$
$347$	30.0910	+	21.8624i	1.61537	+	1.17363i	0.773961	+	0.633234i	$0.218273\pi$
$348$		0			0
$349$	1.44120	+	4.43557i	0.0771458	+	0.237430i	0.982191	−	0.187885i	$-0.0601632\pi$
$349$	1.44120	+	4.43557i	0.0771458	+	0.237430i	−0.905045	+	0.425315i	$0.860163\pi$
$350$		0			0
$351$	18.0542			0.963664
$352$		0			0
$353$	−9.07613			−0.483074			−0.241537	−	0.970392i	$-0.577651\pi$
$353$	−9.07613			−0.483074			−0.241537	+	0.970392i	$0.577651\pi$
$354$		0			0
$355$	−4.91634	−	15.1309i	−0.260932	−	0.803066i
$356$		0			0
$357$	−1.50972	−	1.09687i	−0.0799028	−	0.0580528i
$358$		0			0
$359$	−5.49080	+	16.8989i	−0.289793	+	0.891892i	0.695128	+	0.718886i	$0.255348\pi$
$359$	−5.49080	+	16.8989i	−0.289793	+	0.891892i	−0.984921	+	0.173006i	$0.944652\pi$
$360$		0			0
$361$	−15.7020	+	11.4082i	−0.826420	+	0.600429i
$362$		0			0
$363$	−15.4873	−	13.9210i	−0.812872	−	0.730661i
$364$		0			0
$365$	−15.9448	+	11.5846i	−0.834590	+	0.606365i
$366$		0			0
$367$	−4.45799	+	13.7203i	−0.232705	+	0.716193i	0.764712	+	0.644372i	$0.222881\pi$
$367$	−4.45799	+	13.7203i	−0.232705	+	0.716193i	−0.997418	+	0.0718213i	$0.977119\pi$
$368$		0			0
$369$	0.847192	+	0.615521i	0.0441030	+	0.0320427i
$370$		0			0
$371$	−0.238711	−	0.734678i	−0.0123933	−	0.0381426i
$372$		0			0
$373$	−31.1926			−1.61509			−0.807546	−	0.589805i	$-0.799205\pi$
$373$	−31.1926			−1.61509			−0.807546	+	0.589805i	$0.799205\pi$
$374$		0			0
$375$	21.0786			1.08849
$376$		0			0
$377$	−9.44471	−	29.0678i	−0.486427	−	1.49707i
$378$		0			0
$379$	12.7346	+	9.25222i	0.654132	+	0.475255i	0.864676	−	0.502330i	$-0.167524\pi$
$379$	12.7346	+	9.25222i	0.654132	+	0.475255i	−0.210544	+	0.977584i	$0.567524\pi$
$380$		0			0
$381$	−9.16532	+	28.2080i	−0.469554	+	1.44514i
$382$		0			0
$383$	−6.88745	+	5.00403i	−0.351932	+	0.255694i	−0.749679	−	0.661801i	$-0.769792\pi$
$383$	−6.88745	+	5.00403i	−0.351932	+	0.255694i	0.397747	+	0.917495i	$0.369792\pi$
$384$		0			0
$385$	4.68366	−	5.78888i	0.238702	−	0.295029i
$386$		0			0
$387$	−4.62214	+	3.35818i	−0.234957	+	0.170706i
$388$		0			0
$389$	11.5596	−	35.5768i	0.586096	−	1.80382i	−0.00872949	−	0.999962i	$-0.502779\pi$
$389$	11.5596	−	35.5768i	0.586096	−	1.80382i	0.594825	−	0.803855i	$-0.297221\pi$
$390$		0			0
$391$	−1.41697	−	1.02949i	−0.0716593	−	0.0520635i
$392$		0			0
$393$	3.07969	+	9.47832i	0.155350	+	0.478118i
$394$		0			0
$395$	−22.3913			−1.12663
$396$		0			0
$397$	−7.11042			−0.356862			−0.178431	−	0.983952i	$-0.557102\pi$
$397$	−7.11042			−0.356862			−0.178431	+	0.983952i	$0.557102\pi$
$398$		0			0
$399$	3.62555	+	11.1583i	0.181504	+	0.558613i
$400$		0			0
$401$	−15.0678	−	10.9474i	−0.752449	−	0.546686i	0.144136	−	0.989558i	$-0.453960\pi$
$401$	−15.0678	−	10.9474i	−0.752449	−	0.546686i	−0.896585	+	0.442872i	$0.853960\pi$
$402$		0			0
$403$	−11.1865	+	34.4286i	−0.557241	+	1.71501i
$404$		0			0
$405$	18.9097	−	13.7387i	0.939630	−	0.682681i
$406$		0			0
$407$	−0.544284	+	10.4708i	−0.0269792	+	0.519021i
$408$		0			0
$409$	−25.9657	+	18.8652i	−1.28392	+	0.932823i	−0.999664	−	0.0259253i	$-0.991747\pi$
$409$	−25.9657	+	18.8652i	−1.28392	+	0.932823i	−0.284257	+	0.958748i	$0.591747\pi$
$410$		0			0
$411$	−12.7045	+	39.1003i	−0.626665	+	1.92868i
$412$		0			0
$413$	−4.71362	−	3.42464i	−0.231942	−	0.168516i
$414$		0			0
$415$	0.442352	+	1.36142i	0.0217142	+	0.0668295i
$416$		0			0
$417$	−1.54492			−0.0756548
$418$		0			0
$419$	−9.04218			−0.441739			−0.220870	−	0.975303i	$-0.570890\pi$
$419$	−9.04218			−0.441739			−0.220870	+	0.975303i	$0.570890\pi$
$420$		0			0
$421$	0.102030	+	0.314015i	0.00497261	+	0.0153041i	0.953512	−	0.301355i	$-0.0974389\pi$
$421$	0.102030	+	0.314015i	0.00497261	+	0.0153041i	−0.948539	+	0.316659i	$0.897439\pi$
$422$		0			0
$423$	5.32537	+	3.86911i	0.258929	+	0.188123i
$424$		0			0
$425$	−0.0124024	+	0.0381707i	−0.000601605	+	0.00185155i
$426$		0			0
$427$	4.31337	−	3.13385i	0.208739	−	0.151658i
$428$		0			0
$429$	−23.1408	−	8.87163i	−1.11725	−	0.428326i
$430$		0			0
$431$	26.1819	−	19.0223i	1.26114	−	0.916270i	0.262324	−	0.964980i	$-0.415511\pi$
$431$	26.1819	−	19.0223i	1.26114	−	0.916270i	0.998813	+	0.0487099i	$0.0155110\pi$
$432$		0			0
$433$	6.29909	−	19.3866i	0.302715	−	0.931661i	−0.677805	−	0.735242i	$-0.737069\pi$
$433$	6.29909	−	19.3866i	0.302715	−	0.931661i	0.980520	−	0.196419i	$-0.0629313\pi$
$434$		0			0
$435$	−26.6258	−	19.3448i	−1.27661	−	0.927512i
$436$		0			0
$437$	3.40282	+	10.4728i	0.162779	+	0.500982i
$438$		0			0
$439$	−9.26436			−0.442164			−0.221082	−	0.975255i	$-0.570959\pi$
$439$	−9.26436			−0.442164			−0.221082	+	0.975255i	$0.570959\pi$
$440$		0			0
$441$	0.583876			0.0278036
$442$		0			0
$443$	−5.30548	−	16.3286i	−0.252071	−	0.775795i	−0.994393	−	0.105751i	$-0.966275\pi$
$443$	−5.30548	−	16.3286i	−0.252071	−	0.775795i	0.742322	−	0.670044i	$-0.233725\pi$
$444$		0			0
$445$	−17.6888	−	12.8517i	−0.838529	−	0.609227i
$446$		0			0
$447$	7.40515	−	22.7907i	0.350252	−	1.07796i
$448$		0			0
$449$	21.7760	−	15.8212i	1.02767	−	0.746648i	0.0598308	−	0.998209i	$-0.480944\pi$
$449$	21.7760	−	15.8212i	1.02767	−	0.746648i	0.967841	+	0.251561i	$0.0809439\pi$
$450$		0			0
$451$	3.24185	+	4.98737i	0.152653	+	0.234846i
$452$		0			0
$453$	18.2264	−	13.2422i	0.856349	−	0.622174i
$454$		0			0
$455$	2.73849	−	8.42822i	0.128383	−	0.395121i
$456$		0			0
$457$	0.549840	+	0.399482i	0.0257204	+	0.0186870i	0.600571	−	0.799571i	$-0.294940\pi$
$457$	0.549840	+	0.399482i	0.0257204	+	0.0186870i	−0.574851	+	0.818258i	$0.694940\pi$
$458$		0			0
$459$	−1.39328	−	4.28809i	−0.0650330	−	0.200151i
$460$		0			0
$461$	5.47763			0.255119			0.127559	−	0.991831i	$-0.459286\pi$
$461$	5.47763			0.255119			0.127559	+	0.991831i	$0.459286\pi$
$462$		0			0
$463$	−9.69706			−0.450661			−0.225330	−	0.974282i	$-0.572346\pi$
$463$	−9.69706			−0.450661			−0.225330	+	0.974282i	$0.572346\pi$
$464$		0			0
$465$	12.0458	+	37.0731i	0.558610	+	1.71922i
$466$		0			0
$467$	−11.6226	−	8.44428i	−0.537828	−	0.390755i	0.285450	−	0.958394i	$-0.407857\pi$
$467$	−11.6226	−	8.44428i	−0.537828	−	0.390755i	−0.823278	+	0.567639i	$0.807857\pi$
$468$		0			0
$469$	−1.84544	+	5.67967i	−0.0852144	+	0.262263i
$470$		0			0
$471$	−23.4239	+	17.0185i	−1.07932	+	0.784169i
$472$		0			0
$473$	−31.3441	+	8.41293i	−1.44120	+	0.386827i
$474$		0			0
$475$	0.204143	−	0.148319i	0.00936672	−	0.00680532i
$476$		0			0
$477$	−0.139378	+	0.428961i	−0.00638167	+	0.0196408i
$478$		0			0
$479$	−8.91219	−	6.47508i	−0.407208	−	0.295854i	0.365262	−	0.930905i	$-0.380979\pi$
$479$	−8.91219	−	6.47508i	−0.407208	−	0.295854i	−0.772471	+	0.635050i	$0.780979\pi$
$480$		0			0
$481$	3.85600	+	11.8676i	0.175819	+	0.541114i
$482$		0			0
$483$	3.36370			0.153054
$484$		0			0
$485$	9.09475			0.412971
$486$		0			0
$487$	0.311875	+	0.959852i	0.0141324	+	0.0434951i	0.957874	−	0.287189i	$-0.0927207\pi$
$487$	0.311875	+	0.959852i	0.0141324	+	0.0434951i	−0.943742	+	0.330684i	$0.892721\pi$
$488$		0			0
$489$	−14.5559	−	10.5755i	−0.658241	−	0.478240i
$490$		0			0
$491$	9.41221	−	28.9678i	0.424767	−	1.30730i	−0.478450	−	0.878115i	$-0.658801\pi$
$491$	9.41221	−	28.9678i	0.424767	−	1.30730i	0.903217	−	0.429184i	$-0.141199\pi$
$492$		0			0
$493$	−6.17507	+	4.48645i	−0.278111	+	0.202060i
$494$		0			0
$495$	−4.19911	+	1.12706i	−0.188736	+	0.0506578i
$496$		0			0
$497$	5.73285	−	4.16516i	0.257154	−	0.186833i
$498$		0			0
$499$	12.0976	−	37.2326i	0.541563	−	1.66676i	−0.187460	−	0.982272i	$-0.560026\pi$
$499$	12.0976	−	37.2326i	0.541563	−	1.66676i	0.729024	−	0.684489i	$-0.239974\pi$
$500$		0			0
$501$	1.73632	+	1.26151i	0.0775730	+	0.0563601i
$502$		0			0
$503$	−2.23497	−	6.87854i	−0.0996526	−	0.306699i	0.888786	−	0.458323i	$-0.151550\pi$
$503$	−2.23497	−	6.87854i	−0.0996526	−	0.306699i	−0.988438	+	0.151624i	$0.951550\pi$
$504$		0			0
$505$	22.6223			1.00668
$506$		0			0
$507$	−4.88418			−0.216914
$508$		0			0
$509$	0.947379	+	2.91573i	0.0419918	+	0.129238i	0.969855	−	0.243684i	$-0.0783560\pi$
$509$	0.947379	+	2.91573i	0.0419918	+	0.129238i	−0.927863	+	0.372922i	$0.878356\pi$
$510$		0			0
$511$	−7.10189	−	5.15982i	−0.314169	−	0.228257i
$512$		0			0
$513$	−8.75978	+	26.9598i	−0.386754	+	1.19031i
$514$		0			0
$515$	30.0801	−	21.8545i	1.32549	−	0.963024i
$516$		0			0
$517$	20.3780	+	31.3502i	0.896224	+	1.37878i
$518$		0			0
$519$	5.21715	−	3.79048i	0.229007	−	0.166384i
$520$		0			0
$521$	11.7653	−	36.2098i	0.515446	−	1.58638i	−0.267022	−	0.963690i	$-0.586040\pi$
$521$	11.7653	−	36.2098i	0.515446	−	1.58638i	0.782469	−	0.622690i	$-0.213960\pi$
$522$		0			0
$523$	−33.5942	−	24.4076i	−1.46897	−	1.06727i	−0.980910	−	0.194461i	$-0.937704\pi$
$523$	−33.5942	−	24.4076i	−1.46897	−	1.06727i	−0.488061	−	0.872809i	$-0.662296\pi$
$524$		0			0
$525$	−0.0238188	−	0.0733069i	−0.00103954	−	0.00319937i
$526$		0			0
$527$	9.04049			0.393810
$528$		0			0
$529$	−19.8429			−0.862737
$530$		0			0
$531$	1.05123	+	3.23537i	0.0456197	+	0.140403i
$532$		0			0
$533$	5.72723	+	4.16108i	0.248074	+	0.180236i
$534$		0			0
$535$	−7.46272	+	22.9679i	−0.322642	+	0.992989i
$536$		0			0
$537$	−32.6060	+	23.6897i	−1.40705	+	1.02228i
$538$		0			0
$539$	3.09684	+	1.18725i	0.133390	+	0.0511386i
$540$		0			0
$541$	−19.6828	+	14.3004i	−0.846229	+	0.614821i	−0.924104	−	0.382142i	$-0.875187\pi$
$541$	−19.6828	+	14.3004i	−0.846229	+	0.614821i	0.0778746	+	0.996963i	$0.475187\pi$
$542$		0			0
$543$	7.66968	−	23.6048i	0.329137	−	1.01298i
$544$		0			0
$545$	−11.7110	−	8.50856i	−0.501645	−	0.364467i
$546$		0			0
$547$	−5.42287	−	16.6899i	−0.231865	−	0.713608i	−0.997522	−	0.0703584i	$-0.977586\pi$
$547$	−5.42287	−	16.6899i	−0.231865	−	0.713608i	0.765656	−	0.643250i	$-0.222414\pi$
$548$		0			0
$549$	−3.11300			−0.132860
$550$		0			0
$551$	47.9886			2.04438
$552$		0			0
$553$	−3.08188	−	9.48505i	−0.131055	−	0.403345i
$554$		0			0
$555$	10.8706	+	7.89792i	0.461429	+	0.335248i
$556$		0			0
$557$	−4.42235	+	13.6106i	−0.187381	+	0.576699i	−0.999981	−	0.00612208i	$-0.998051\pi$
$557$	−4.42235	+	13.6106i	−0.187381	+	0.576699i	0.812600	+	0.582821i	$0.198051\pi$
$558$		0			0
$559$	−31.2469	+	22.7022i	−1.32160	+	0.960200i
$560$		0			0
$561$	−0.321286	+	6.18086i	−0.0135647	+	0.260956i
$562$		0			0
$563$	−20.0015	+	14.5320i	−0.842964	+	0.612449i	−0.923197	−	0.384327i	$-0.874433\pi$
$563$	−20.0015	+	14.5320i	−0.842964	+	0.612449i	0.0802333	+	0.996776i	$0.474433\pi$
$564$		0			0
$565$	−4.53010	+	13.9422i	−0.190583	+	0.586554i
$566$		0			0
$567$	8.42245	+	6.11927i	0.353710	+	0.256985i
$568$		0			0
$569$	12.1694	+	37.4536i	0.510169	+	1.57014i	0.791904	+	0.610646i	$0.209090\pi$
$569$	12.1694	+	37.4536i	0.510169	+	1.57014i	−0.281735	+	0.959492i	$0.590910\pi$
$570$		0			0
$571$	−14.8585			−0.621809			−0.310905	−	0.950441i	$-0.600632\pi$
$571$	−14.8585			−0.621809			−0.310905	+	0.950441i	$0.600632\pi$
$572$		0			0
$573$	41.4111			1.72997
$574$		0			0
$575$	−0.0223556	−	0.0688033i	−0.000932291	−	0.00286930i
$576$		0			0
$577$	−12.5170	−	9.09416i	−0.521091	−	0.378595i	0.295924	−	0.955212i	$-0.404373\pi$
$577$	−12.5170	−	9.09416i	−0.521091	−	0.378595i	−0.817015	+	0.576617i	$0.804373\pi$
$578$		0			0
$579$	10.5492	−	32.4672i	0.438411	−	1.34929i
$580$		0			0
$581$	−0.515819	+	0.374765i	−0.0213998	+	0.0155479i
$582$		0			0
$583$	−1.61150	+	1.99177i	−0.0667416	+	0.0824908i
$584$		0			0
$585$	−4.18608	+	3.04137i	−0.173073	+	0.125745i
$586$		0			0
$587$	5.96693	−	18.3643i	0.246282	−	0.757977i	−0.749142	−	0.662410i	$-0.769534\pi$
$587$	5.96693	−	18.3643i	0.246282	−	0.757977i	0.995423	−	0.0955666i	$-0.0304663\pi$
$588$		0			0
$589$	−45.9836	−	33.4090i	−1.89472	−	1.37659i
$590$		0			0
$591$	−7.59441	−	23.3732i	−0.312392	−	0.961445i
$592$		0			0
$593$	30.7857			1.26422			0.632109	−	0.774880i	$-0.282190\pi$
$593$	30.7857			1.26422			0.632109	+	0.774880i	$0.282190\pi$
$594$		0			0
$595$	−2.21314			−0.0907297
$596$		0			0
$597$	11.3221	+	34.8459i	0.463384	+	1.42615i
$598$		0			0
$599$	−12.4569	−	9.05049i	−0.508976	−	0.369793i	0.303459	−	0.952845i	$-0.401859\pi$
$599$	−12.4569	−	9.05049i	−0.508976	−	0.369793i	−0.812435	+	0.583052i	$0.801859\pi$
$600$		0			0
$601$	−12.2565	+	37.7218i	−0.499955	+	1.53870i	0.309135	+	0.951018i	$0.399961\pi$
$601$	−12.2565	+	37.7218i	−0.499955	+	1.53870i	−0.809090	+	0.587685i	$0.800039\pi$
$602$		0			0
$603$	2.82095	−	2.04954i	0.114878	−	0.0834637i
$604$		0			0
$605$	−24.5636	−	2.56059i	−0.998652	−	0.104103i
$606$		0			0
$607$	19.7222	−	14.3290i	0.800498	−	0.581596i	−0.110562	−	0.993869i	$-0.535265\pi$
$607$	19.7222	−	14.3290i	0.800498	−	0.581596i	0.911060	+	0.412273i	$0.135265\pi$
$608$		0			0
$609$	4.52983	−	13.9414i	0.183558	−	0.564933i
$610$		0			0
$611$	36.0009	+	26.1562i	1.45644	+	1.05817i
$612$		0			0
$613$	3.20901	+	9.87632i	0.129611	+	0.398901i	0.994713	−	0.102695i	$-0.0327465\pi$
$613$	3.20901	+	9.87632i	0.129611	+	0.398901i	−0.865102	+	0.501596i	$0.832747\pi$
$614$		0			0
$615$	7.62301			0.307389
$616$		0			0
$617$	19.6562			0.791328			0.395664	−	0.918395i	$-0.370514\pi$
$617$	19.6562			0.791328			0.395664	+	0.918395i	$0.370514\pi$
$618$		0			0
$619$	10.4438	+	32.1428i	0.419773	+	1.29193i	0.907911	+	0.419163i	$0.137676\pi$
$619$	10.4438	+	32.1428i	0.419773	+	1.29193i	−0.488138	+	0.872767i	$0.662324\pi$
$620$		0			0
$621$	6.57498	+	4.77701i	0.263845	+	0.191695i
$622$		0			0
$623$	3.00938	−	9.26191i	0.120568	−	0.371071i
$624$		0			0
$625$	20.3888	−	14.8133i	0.815551	−	0.592533i
$626$		0			0
$627$	24.4755	−	30.2510i	0.977456	−	1.20811i
$628$		0			0
$629$	2.52110	−	1.83169i	0.100523	−	0.0730343i
$630$		0			0
$631$	6.50116	−	20.0085i	0.258807	−	0.796526i	−0.734249	−	0.678881i	$-0.762465\pi$
$631$	6.50116	−	20.0085i	0.258807	−	0.796526i	0.993056	−	0.117645i	$-0.0375346\pi$
$632$		0			0
$633$	3.40480	+	2.47373i	0.135329	+	0.0983221i
$634$		0			0
$635$	10.8697	+	33.4535i	0.431351	+	1.32756i
$636$		0			0
$637$	3.94715			0.156392
$638$		0			0
$639$	−4.13746			−0.163675
$640$		0			0
$641$	3.66665	+	11.2848i	0.144824	+	0.445723i	0.996988	−	0.0775517i	$-0.0247103\pi$
$641$	3.66665	+	11.2848i	0.144824	+	0.445723i	−0.852164	+	0.523274i	$0.824710\pi$
$642$		0			0
$643$	22.0460	+	16.0173i	0.869408	+	0.631662i	0.930428	−	0.366475i	$-0.119435\pi$
$643$	22.0460	+	16.0173i	0.869408	+	0.631662i	−0.0610200	+	0.998137i	$0.519435\pi$
$644$		0			0
$645$	−12.8520	+	39.5544i	−0.506047	+	1.55745i
$646$		0			0
$647$	20.7065	−	15.0441i	0.814055	−	0.591446i	−0.100948	−	0.994892i	$-0.532188\pi$
$647$	20.7065	−	15.0441i	0.814055	−	0.591446i	0.915004	+	0.403446i	$0.132188\pi$
$648$		0			0
$649$	−1.00311	+	19.2978i	−0.0393757	+	0.757503i
$650$		0			0
$651$	−14.0464	+	10.2053i	−0.550521	+	0.399977i
$652$		0			0
$653$	−3.77689	+	11.6241i	−0.147801	+	0.454885i	−0.997361	−	0.0726080i	$-0.976868\pi$
$653$	−3.77689	+	11.6241i	−0.147801	+	0.454885i	0.849560	+	0.527493i	$0.176868\pi$
$654$		0			0
$655$	9.56208	+	6.94726i	0.373621	+	0.271452i
$656$		0			0
$657$	1.58387	+	4.87464i	0.0617926	+	0.190178i
$658$		0			0
$659$	−29.2427			−1.13913			−0.569567	−	0.821945i	$-0.692889\pi$
$659$	−29.2427			−1.13913			−0.569567	+	0.821945i	$0.692889\pi$
$660$		0			0
$661$	4.97634			0.193557			0.0967785	−	0.995306i	$-0.469146\pi$
$661$	4.97634			0.193557			0.0967785	+	0.995306i	$0.469146\pi$
$662$		0			0
$663$	2.27617	+	7.00532i	0.0883990	+	0.272064i
$664$		0			0
$665$	11.2569	+	8.17861i	0.436524	+	0.317153i
$666$		0			0
$667$	4.25154	−	13.0849i	0.164620	−	0.506649i
$668$		0			0
$669$	31.3752	−	22.7954i	1.21303	−	0.881321i
$670$		0			0
$671$	−16.5112	−	6.32999i	−0.637407	−	0.244366i
$672$		0			0
$673$	37.5778	−	27.3019i	1.44852	−	1.05241i	0.462342	−	0.886702i	$-0.347009\pi$
$673$	37.5778	−	27.3019i	1.44852	−	1.05241i	0.986175	−	0.165707i	$-0.0529908\pi$
$674$		0			0
$675$	0.0575493	−	0.177118i	0.00221507	−	0.00681729i
$676$		0			0
$677$	−21.5589	−	15.6635i	−0.828577	−	0.601997i	0.0905791	−	0.995889i	$-0.471128\pi$
$677$	−21.5589	−	15.6635i	−0.828577	−	0.601997i	−0.919157	+	0.393893i	$0.871128\pi$
$678$		0			0
$679$	1.25178	+	3.85257i	0.0480388	+	0.147848i
$680$		0			0
$681$	−10.8479			−0.415691
$682$		0			0
$683$	13.7432			0.525870			0.262935	−	0.964814i	$-0.415310\pi$
$683$	13.7432			0.525870			0.262935	+	0.964814i	$0.415310\pi$
$684$		0			0
$685$	15.0670	+	46.3714i	0.575679	+	1.77176i
$686$		0			0
$687$	−6.34256	−	4.60814i	−0.241984	−	0.175812i
$688$		0			0
$689$	−0.942230	+	2.89988i	−0.0358961	+	0.110477i
$690$		0			0
$691$	−23.4634	+	17.0472i	−0.892590	+	0.648505i	−0.936552	−	0.350529i	$-0.886002\pi$
$691$	−23.4634	+	17.0472i	−0.892590	+	0.648505i	0.0439619	+	0.999033i	$0.486002\pi$
$692$		0			0
$693$	−1.05538	−	1.62363i	−0.0400907	−	0.0616767i
$694$		0			0
$695$	−1.48229	+	1.07694i	−0.0562263	+	0.0408508i
$696$		0			0
$697$	0.546321	−	1.68140i	0.0206934	−	0.0636877i
$698$		0			0
$699$	4.64921	+	3.37785i	0.175849	+	0.127762i
$700$		0			0
$701$	−6.79011	−	20.8978i	−0.256459	−	0.789299i	−0.993539	−	0.113494i	$-0.963796\pi$
$701$	−6.79011	−	20.8978i	−0.256459	−	0.789299i	0.737080	−	0.675806i	$-0.236204\pi$
$702$		0			0
$703$	−19.5923			−0.738939
$704$		0			0
$705$	47.9176			1.80468
$706$		0			0
$707$	3.11368	+	9.58291i	0.117102	+	0.360402i
$708$		0			0
$709$	−35.8959	−	26.0799i	−1.34810	−	0.979451i	−0.999104	−	0.0423260i	$-0.986523\pi$
$709$	−35.8959	−	26.0799i	−1.34810	−	0.979451i	−0.348995	−	0.937125i	$-0.613477\pi$
$710$		0			0
$711$	−1.79943	+	5.53809i	−0.0674841	+	0.207695i
$712$		0			0
$713$	−13.1834	+	9.57833i	−0.493724	+	0.358711i
$714$		0			0
$715$	−28.3870	+	7.61924i	−1.06161	+	0.284943i
$716$		0			0
$717$	21.3843	−	15.5366i	0.798613	−	0.580226i
$718$		0			0
$719$	13.0859	−	40.2741i	0.488020	−	1.50197i	−0.339538	−	0.940592i	$-0.610271\pi$
$719$	13.0859	−	40.2741i	0.488020	−	1.50197i	0.827559	−	0.561379i	$-0.189729\pi$
$720$		0			0
$721$	13.3978	+	9.73408i	0.498960	+	0.362516i
$722$		0			0
$723$	−0.861107	−	2.65022i	−0.0320249	−	0.0985626i
$724$		0			0
$725$	−0.315271			−0.0117089
$726$		0			0
$727$	−4.93516			−0.183035			−0.0915175	−	0.995803i	$-0.529172\pi$
$727$	−4.93516			−0.183035			−0.0915175	+	0.995803i	$0.529172\pi$
$728$		0			0
$729$	6.14904	+	18.9248i	0.227742	+	0.700918i
$730$		0			0
$731$	7.80342	+	5.66951i	0.288620	+	0.209695i
$732$		0			0
$733$	−8.06276	+	24.8146i	−0.297805	+	0.916549i	0.684460	+	0.729050i	$0.260038\pi$
$733$	−8.06276	+	24.8146i	−0.297805	+	0.916549i	−0.982265	+	0.187499i	$0.939962\pi$
$734$		0			0
$735$	3.43859	−	2.49828i	0.126834	−	0.0921505i
$736$		0			0
$737$	19.1297	−	5.13451i	0.704650	−	0.189132i
$738$		0			0
$739$	15.6373	−	11.3612i	0.575228	−	0.417927i	−0.261773	−	0.965130i	$-0.584307\pi$
$739$	15.6373	−	11.3612i	0.575228	−	0.417927i	0.837001	+	0.547202i	$0.184307\pi$
$740$		0			0
$741$	14.3106	−	44.0434i	0.525712	−	1.61798i
$742$		0			0
$743$	−9.11808	−	6.62467i	−0.334510	−	0.243036i	0.407832	−	0.913057i	$-0.366285\pi$
$743$	−9.11808	−	6.62467i	−0.334510	−	0.243036i	−0.742342	+	0.670021i	$0.766285\pi$
$744$		0			0
$745$	−8.78220	−	27.0288i	−0.321755	−	0.990260i
$746$		0			0
$747$	0.372272			0.0136207
$748$		0			0
$749$	−10.7564			−0.393032
$750$		0			0
$751$	14.5063	+	44.6458i	0.529343	+	1.62915i	0.755565	+	0.655073i	$0.227362\pi$
$751$	14.5063	+	44.6458i	0.529343	+	1.62915i	−0.226223	+	0.974076i	$0.572638\pi$
$752$		0			0
$753$	−23.3318	−	16.9515i	−0.850257	−	0.617748i
$754$		0			0
$755$	8.25647	−	25.4108i	0.300484	−	0.924794i
$756$		0			0
$757$	10.5053	−	7.63256i	0.381822	−	0.277410i	−0.380274	−	0.924874i	$-0.624170\pi$
$757$	10.5053	−	7.63256i	0.381822	−	0.277410i	0.762096	+	0.647464i	$0.224170\pi$
$758$		0			0
$759$	−6.08005	−	9.35374i	−0.220692	−	0.339519i
$760$		0			0
$761$	−15.5968	+	11.3317i	−0.565382	+	0.410774i	−0.833425	−	0.552633i	$-0.813623\pi$
$761$	−15.5968	+	11.3317i	−0.565382	+	0.410774i	0.268043	+	0.963407i	$0.413623\pi$
$762$		0			0
$763$	1.99239	−	6.13194i	0.0721292	−	0.221991i
$764$		0			0
$765$	1.04541	+	0.759534i	0.0377968	+	0.0274610i
$766$		0			0
$767$	7.10661	+	21.8719i	0.256605	+	0.789748i
$768$		0			0
$769$	9.39699			0.338864			0.169432	−	0.985542i	$-0.445807\pi$
$769$	9.39699			0.338864			0.169432	+	0.985542i	$0.445807\pi$
$770$		0			0
$771$	46.7255			1.68278
$772$		0			0
$773$	−9.70591	−	29.8717i	−0.349097	−	1.07441i	−0.959354	−	0.282207i	$-0.908934\pi$
$773$	−9.70591	−	29.8717i	−0.349097	−	1.07441i	0.610256	−	0.792204i	$-0.291066\pi$
$774$		0			0
$775$	0.302099	+	0.219488i	0.0108517	+	0.00788424i
$776$		0			0
$777$	−1.84940	+	5.69186i	−0.0663468	+	0.204194i
$778$		0			0
$779$	−8.99241	+	6.53337i	−0.322187	+	0.234082i
$780$		0			0
$781$	−21.9448	−	8.41311i	−0.785248	−	0.301045i
$782$		0			0
$783$	28.6534	−	20.8179i	1.02399	−	0.743972i
$784$		0			0
$785$	−10.6109	+	32.6571i	−0.378720	+	1.16558i
$786$		0			0
$787$	17.6201	+	12.8017i	0.628087	+	0.456332i	0.855737	−	0.517411i	$-0.173104\pi$
$787$	17.6201	+	12.8017i	0.628087	+	0.456332i	−0.227650	+	0.973743i	$0.573104\pi$
$788$		0			0
$789$	7.94635	+	24.4564i	0.282898	+	0.870669i
$790$		0			0
$791$	−6.52949			−0.232162
$792$		0			0
$793$	−21.0447			−0.747319
$794$		0			0
$795$	1.01460	+	3.12263i	0.0359842	+	0.110748i
$796$		0			0
$797$	21.0512	+	15.2946i	0.745672	+	0.541762i	0.894482	−	0.447103i	$-0.147544\pi$
$797$	21.0512	+	15.2946i	0.745672	+	0.541762i	−0.148810	+	0.988866i	$0.547544\pi$
$798$		0			0
$799$	3.43413	−	10.5692i	0.121491	−	0.373910i
$800$		0			0
$801$	−4.60015	+	3.34221i	−0.162538	+	0.118091i
$802$		0			0
$803$	−1.51137	+	29.0754i	−0.0533350	+	1.02605i
$804$		0			0
$805$	3.22734	−	2.34480i	0.113749	−	0.0826434i
$806$		0			0
$807$	7.59367	−	23.3709i	0.267310	−	0.822696i
$808$		0			0
$809$	18.7769	+	13.6422i	0.660160	+	0.479635i	0.866717	−	0.498800i	$-0.166226\pi$
$809$	18.7769	+	13.6422i	0.660160	+	0.479635i	−0.206557	+	0.978435i	$0.566226\pi$
$810$		0			0
$811$	12.1169	+	37.2921i	0.425484	+	1.30950i	0.902531	+	0.430626i	$0.141707\pi$
$811$	12.1169	+	37.2921i	0.425484	+	1.30950i	−0.477047	+	0.878878i	$0.658293\pi$
$812$		0			0
$813$	−37.5468			−1.31682
$814$		0			0
$815$	−21.3379			−0.747433
$816$		0			0
$817$	−18.7397	−	57.6749i	−0.655619	−	2.01779i
$818$		0			0
$819$	−1.86450	−	1.35464i	−0.0651508	−	0.0473348i
$820$		0			0
$821$	−6.62499	+	20.3896i	−0.231214	+	0.711602i	0.766388	+	0.642378i	$0.222052\pi$
$821$	−6.62499	+	20.3896i	−0.231214	+	0.711602i	−0.997601	+	0.0692238i	$0.977948\pi$
$822$		0			0
$823$	−14.9717	+	10.8776i	−0.521880	+	0.379168i	−0.817312	−	0.576196i	$-0.804537\pi$
$823$	−14.9717	+	10.8776i	−0.521880	+	0.379168i	0.295432	+	0.955364i	$0.404537\pi$
$824$		0			0
$825$	−0.160797	+	0.198741i	−0.00559823	+	0.00691926i
$826$		0			0
$827$	4.88913	−	3.55216i	0.170012	−	0.123521i	−0.499526	−	0.866299i	$-0.666492\pi$
$827$	4.88913	−	3.55216i	0.170012	−	0.123521i	0.669537	+	0.742778i	$0.266492\pi$
$828$		0			0
$829$	3.60815	−	11.1048i	0.125316	−	0.385684i	−0.868642	−	0.495440i	$-0.835007\pi$
$829$	3.60815	−	11.1048i	0.125316	−	0.385684i	0.993959	+	0.109756i	$0.0350069\pi$
$830$		0			0
$831$	−44.8843	−	32.6103i	−1.55702	−	1.13124i
$832$		0			0
$833$	−0.304610	−	0.937493i	−0.0105541	−	0.0324822i
$834$		0			0
$835$	2.54531			0.0880842
$836$		0			0
$837$	−41.9494			−1.44998
$838$		0			0
$839$	−12.4482	−	38.3115i	−0.429758	−	1.32266i	−0.898364	−	0.439252i	$-0.855244\pi$
$839$	−12.4482	−	38.3115i	−0.429758	−	1.32266i	0.468606	−	0.883407i	$-0.344756\pi$
$840$		0			0
$841$	−25.0454	−	18.1965i	−0.863633	−	0.627466i
$842$		0			0
$843$	13.5527	−	41.7108i	0.466779	−	1.43660i
$844$		0			0
$845$	−4.68618	+	3.40471i	−0.161210	+	0.117126i
$846$		0			0
$847$	−2.29619	−	10.7577i	−0.0788980	−	0.369638i
$848$		0			0
$849$	38.3856	−	27.8887i	1.31739	−	0.957139i
$850$		0			0
$851$	−1.73578	+	5.34219i	−0.0595018	+	0.183128i
$852$		0			0
$853$	−28.8497	−	20.9606i	−0.987796	−	0.717676i	−0.0283590	−	0.999598i	$-0.509028\pi$
$853$	−28.8497	−	20.9606i	−0.987796	−	0.717676i	−0.959437	+	0.281922i	$0.909028\pi$
$854$		0			0
$855$	−2.51052	−	7.72659i	−0.0858580	−	0.264244i
$856$		0			0
$857$	−0.493095			−0.0168438			−0.00842191	−	0.999965i	$-0.502681\pi$
$857$	−0.493095			−0.0168438			−0.00842191	+	0.999965i	$0.502681\pi$
$858$		0			0
$859$	54.1552			1.84775			0.923875	−	0.382694i	$-0.125004\pi$
$859$	54.1552			1.84775			0.923875	+	0.382694i	$0.125004\pi$
$860$		0			0
$861$	1.04921	+	3.22914i	0.0357570	+	0.110049i
$862$		0			0
$863$	16.1186	+	11.7109i	0.548685	+	0.398643i	0.827300	−	0.561760i	$-0.189876\pi$
$863$	16.1186	+	11.7109i	0.548685	+	0.398643i	−0.278616	+	0.960403i	$0.589876\pi$
$864$		0			0
$865$	2.36335	−	7.27363i	0.0803562	−	0.247311i
$866$		0			0
$867$	−24.5483	+	17.8354i	−0.833705	+	0.605722i
$868$		0			0
$869$	−20.8053	+	25.7147i	−0.705770	+	0.872312i
$870$		0			0
$871$	19.0703	−	13.8554i	0.646173	−	0.469472i
$872$		0			0
$873$	0.730882	−	2.24942i	0.0247366	−	0.0761315i
$874$		0			0
$875$	9.00788	+	6.54461i	0.304522	+	0.221248i
$876$		0			0
$877$	0.260378	+	0.801360i	0.00879233	+	0.0270600i	0.955356	−	0.295456i	$-0.0954715\pi$
$877$	0.260378	+	0.801360i	0.00879233	+	0.0270600i	−0.946564	+	0.322516i	$0.895471\pi$
$878$		0			0
$879$	−51.3866			−1.73323
$880$		0			0
$881$	10.1511			0.341998			0.170999	−	0.985271i	$-0.445301\pi$
$881$	10.1511			0.341998			0.170999	+	0.985271i	$0.445301\pi$
$882$		0			0
$883$	8.88415	+	27.3426i	0.298976	+	0.920152i	0.981857	+	0.189623i	$0.0607265\pi$
$883$	8.88415	+	27.3426i	0.298976	+	0.920152i	−0.682881	+	0.730529i	$0.739273\pi$
$884$		0			0
$885$	20.0344	+	14.5559i	0.673450	+	0.489290i
$886$		0			0
$887$	−1.20571	+	3.71079i	−0.0404837	+	0.124596i	−0.969256	−	0.246055i	$-0.920866\pi$
$887$	−1.20571	+	3.71079i	−0.0404837	+	0.124596i	0.928772	+	0.370651i	$0.120866\pi$
$888$		0			0
$889$	−12.6750	+	9.20890i	−0.425105	+	0.308857i
$890$		0			0
$891$	1.79240	−	34.4819i	0.0600476	−	1.15519i
$892$		0			0
$893$	−56.5255	+	41.0682i	−1.89155	+	1.37429i
$894$		0			0
$895$	−14.7704	+	45.4586i	−0.493720	+	1.51951i
$896$		0			0
$897$	−10.7413	−	7.80405i	−0.358643	−	0.260570i
$898$		0			0
$899$	21.9450	+	67.5397i	0.731906	+	2.25258i
$900$		0			0
$901$	0.761470			0.0253682
$902$		0			0
$903$	−18.5243			−0.616450
$904$		0			0
$905$	−9.09592	−	27.9944i	−0.302359	−	0.930564i
$906$		0			0
$907$	29.7233	+	21.5952i	0.986945	+	0.717058i	0.959250	−	0.282559i	$-0.0911832\pi$
$907$	29.7233	+	21.5952i	0.986945	+	0.717058i	0.0276952	+	0.999616i	$0.491183\pi$
$908$		0			0
$909$	1.81800	−	5.59523i	0.0602993	−	0.185582i
$910$		0			0
$911$	−18.0100	+	13.0850i	−0.596699	+	0.433527i	−0.844706	−	0.535231i	$-0.820224\pi$
$911$	−18.0100	+	13.0850i	−0.596699	+	0.433527i	0.248007	+	0.968758i	$0.420224\pi$
$912$		0			0
$913$	1.97451	+	0.756978i	0.0653467	+	0.0250523i
$914$		0			0
$915$	−18.3333	+	13.3199i	−0.606079	+	0.440342i
$916$		0			0
$917$	−1.62679	+	5.00674i	−0.0537213	+	0.165337i
$918$		0			0
$919$	−35.9620	−	26.1279i	−1.18628	−	0.861880i	−0.193411	−	0.981118i	$-0.561955\pi$
$919$	−35.9620	−	26.1279i	−1.18628	−	0.861880i	−0.992866	+	0.119237i	$0.961955\pi$
$920$		0			0
$921$	1.38466	+	4.26154i	0.0456261	+	0.140423i
$922$		0			0
$923$	−27.9703			−0.920652
$924$		0			0
$925$	0.128716			0.00423216
$926$		0			0
$927$	−2.98799	−	9.19608i	−0.0981384	−	0.302039i
$928$		0			0
$929$	48.2299	+	35.0411i	1.58237	+	1.14966i	0.913913	+	0.405911i	$0.133046\pi$
$929$	48.2299	+	35.0411i	1.58237	+	1.14966i	0.668459	+	0.743749i	$0.266954\pi$
$930$		0			0
$931$	−1.91513	+	5.89415i	−0.0627657	+	0.193173i
$932$		0			0
$933$	23.5175	−	17.0864i	0.769927	−	0.559385i
$934$		0			0
$935$	4.00035	+	6.15426i	0.130825	+	0.201266i
$936$		0			0
$937$	−37.7199	+	27.4051i	−1.23226	+	0.895287i	−0.997057	−	0.0766604i	$-0.975574\pi$
$937$	−37.7199	+	27.4051i	−1.23226	+	0.895287i	−0.235199	+	0.971947i	$0.575574\pi$
$938$		0			0
$939$	−8.59101	+	26.4404i	−0.280357	+	0.862850i
$940$		0			0
$941$	10.6852	+	7.76327i	0.348328	+	0.253075i	0.748167	−	0.663510i	$-0.230934\pi$
$941$	10.6852	+	7.76327i	0.348328	+	0.253075i	−0.399839	+	0.916585i	$0.630934\pi$
$942$		0			0
$943$	0.984753	+	3.03076i	0.0320680	+	0.0986951i
$944$		0			0
$945$	10.2693			0.334061
$946$		0			0
$947$	−49.9115			−1.62191			−0.810954	−	0.585110i	$-0.801051\pi$
$947$	−49.9115			−1.62191			−0.810954	+	0.585110i	$0.801051\pi$
$948$		0			0
$949$	10.7073	+	32.9538i	0.347575	+	1.06973i
$950$		0			0
$951$	−32.0721	−	23.3018i	−1.04001	−	0.755612i
$952$		0			0
$953$	9.79667	−	30.1511i	0.317345	−	0.976688i	−0.657433	−	0.753513i	$-0.728358\pi$
$953$	9.79667	−	30.1511i	0.317345	−	0.976688i	0.974778	−	0.223175i	$-0.0716423\pi$
$954$		0			0
$955$	39.7323	−	28.8672i	1.28571	−	0.934122i
$956$		0			0
$957$	−46.9559	+	12.6032i	−1.51787	+	0.407404i
$958$		0			0
$959$	−17.5693	+	12.7649i	−0.567343	+	0.412199i
$960$		0			0
$961$	16.4126	−	50.5129i	0.529440	−	1.62945i
$962$		0			0
$963$	5.08097	+	3.69154i	0.163732	+	0.118958i
$964$		0			0
$965$	−12.5109	−	38.5047i	−0.402742	−	1.23951i
$966$		0			0
$967$	−15.5126			−0.498852			−0.249426	−	0.968394i	$-0.580242\pi$
$967$	−15.5126			−0.498852			−0.249426	+	0.968394i	$0.580242\pi$
$968$		0			0
$969$	−11.5652			−0.371528
$970$		0			0
$971$	−18.3101	−	56.3525i	−0.587597	−	1.80844i	−0.588579	−	0.808440i	$-0.700312\pi$
$971$	−18.3101	−	56.3525i	−0.587597	−	1.80844i	0.000981627	−	1.00000i	$-0.499688\pi$
$972$		0			0
$973$	−0.660216	−	0.479675i	−0.0211655	−	0.0153777i
$974$		0			0
$975$	−0.0940165	+	0.289353i	−0.00301094	+	0.00926671i
$976$		0			0
$977$	20.7490	−	15.0750i	0.663820	−	0.482293i	−0.204131	−	0.978944i	$-0.565437\pi$
$977$	20.7490	−	15.0750i	0.663820	−	0.482293i	0.867951	+	0.496650i	$0.165437\pi$
$978$		0			0
$979$	−31.1950	+	8.37291i	−0.996996	+	0.267599i
$980$		0			0
$981$	−3.04558	+	2.21274i	−0.0972377	+	0.0706473i
$982$		0			0
$983$	7.08062	−	21.7919i	0.225837	−	0.695054i	−0.772369	−	0.635174i	$-0.780928\pi$
$983$	7.08062	−	21.7919i	0.225837	−	0.695054i	0.998206	−	0.0598799i	$-0.0190718\pi$
$984$		0			0
$985$	−23.5797	−	17.1317i	−0.751313	−	0.545861i
$986$		0			0
$987$	6.59524	+	20.2981i	0.209929	+	0.646095i
$988$		0			0
$989$	−17.3863			−0.552852
$990$		0			0
$991$	−17.1427			−0.544557			−0.272278	−	0.962218i	$-0.587777\pi$
$991$	−17.1427			−0.544557			−0.272278	+	0.962218i	$0.587777\pi$
$992$		0			0
$993$	0.803945	+	2.47429i	0.0255124	+	0.0785192i
$994$		0			0
$995$	35.1539	+	25.5408i	1.11445	+	0.809697i
$996$		0			0
$997$	−7.55874	+	23.2634i	−0.239388	+	0.736760i	0.757121	+	0.653274i	$0.226605\pi$
$997$	−7.55874	+	23.2634i	−0.239388	+	0.736760i	−0.996509	+	0.0834852i	$0.973395\pi$
$998$		0			0
$999$	−11.6984	+	8.49935i	−0.370120	+	0.268908i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.j.c.113.1	✓	12
11.2	odd	10		3388.2.a.t.1.2		6
11.4	even	5	inner	308.2.j.c.169.1	yes	12
11.9	even	5		3388.2.a.u.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.j.c.113.1	✓	12	1.1	even	1	trivial
308.2.j.c.169.1	yes	12	11.4	even	5	inner
3388.2.a.t.1.2		6	11.2	odd	10
3388.2.a.u.1.2		6	11.9	even	5

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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.585004 - 1.80046i) q^{3} +(-1.81637 - 1.31967i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-0.472365 + 0.343194i) q^{9} +O(q^{10})\)	\(q+(-0.585004 - 1.80046i) q^{3} +(-1.81637 - 1.31967i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-0.472365 + 0.343194i) q^{9} +(-3.20325 + 0.859769i) q^{11} +(-3.19331 + 2.32008i) q^{13} +(-1.31342 + 4.04230i) q^{15} +(0.797479 + 0.579403i) q^{17} +(-1.91513 - 5.89415i) q^{19} -1.89311 q^{21} -1.77681 q^{23} +(0.0125818 + 0.0387229i) q^{25} +(-3.70044 - 2.68853i) q^{27} +(-2.39279 + 7.36426i) q^{29} +(7.41972 - 5.39074i) q^{31} +(3.42189 + 5.26434i) q^{33} +(-1.81637 + 1.31967i) q^{35} +(0.976908 - 3.00661i) q^{37} +(6.04529 + 4.39216i) q^{39} +(-0.554225 - 1.70573i) q^{41} +9.78510 q^{43} +1.31089 q^{45} +(-3.48381 - 10.7221i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(0.576661 - 1.77478i) q^{51} +(0.624955 - 0.454056i) q^{53} +(6.95289 + 2.66557i) q^{55} +(-9.49181 + 6.89620i) q^{57} +(1.80044 - 5.54119i) q^{59} +(4.31337 + 3.13385i) q^{61} +(0.180428 + 0.555299i) q^{63} +8.86195 q^{65} -5.97196 q^{67} +(1.03944 + 3.19907i) q^{69} +(5.73285 + 4.16516i) q^{71} +(2.71268 - 8.34877i) q^{73} +(0.0623585 - 0.0453061i) q^{75} +(-0.172169 + 3.31215i) q^{77} +(8.06846 - 5.86208i) q^{79} +(-3.21709 + 9.90118i) q^{81} +(-0.515819 - 0.374765i) q^{83} +(-0.683896 - 2.10482i) q^{85} +14.6588 q^{87} +9.73855 q^{89} +(1.21974 + 3.75396i) q^{91} +(-14.0464 - 10.2053i) q^{93} +(-4.29975 + 13.2333i) q^{95} +(-3.27720 + 2.38102i) q^{97} +(1.21804 - 1.50546i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + q^{5} - 3 q^{7} + q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 + q^5 - 3 * q^7 + q^9	\( 12 q + 6 q^{3} + q^{5} - 3 q^{7} + q^{9} + 2 q^{11} - 7 q^{13} - 4 q^{15} + 3 q^{17} - 23 q^{19} - 4 q^{21} - 38 q^{23} + 2 q^{25} - 18 q^{27} + 29 q^{29} + 9 q^{31} - 4 q^{33} + q^{35} + 3 q^{37} + 25 q^{39} - 18 q^{41} + 34 q^{43} + 14 q^{45} + 9 q^{47} - 3 q^{49} + 35 q^{51} + 13 q^{53} + 16 q^{55} + 9 q^{57} - 17 q^{59} - 19 q^{61} - 9 q^{63} + 8 q^{65} - 20 q^{67} - 14 q^{69} + 15 q^{71} + 9 q^{73} - 47 q^{75} - 8 q^{77} - 14 q^{79} - 49 q^{81} + 41 q^{83} - 66 q^{85} + 40 q^{87} + 34 q^{89} + 13 q^{91} - 40 q^{93} + 42 q^{95} - 10 q^{97} - 24 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 + q^5 - 3 * q^7 + q^9 + 2 * q^11 - 7 * q^13 - 4 * q^15 + 3 * q^17 - 23 * q^19 - 4 * q^21 - 38 * q^23 + 2 * q^25 - 18 * q^27 + 29 * q^29 + 9 * q^31 - 4 * q^33 + q^35 + 3 * q^37 + 25 * q^39 - 18 * q^41 + 34 * q^43 + 14 * q^45 + 9 * q^47 - 3 * q^49 + 35 * q^51 + 13 * q^53 + 16 * q^55 + 9 * q^57 - 17 * q^59 - 19 * q^61 - 9 * q^63 + 8 * q^65 - 20 * q^67 - 14 * q^69 + 15 * q^71 + 9 * q^73 - 47 * q^75 - 8 * q^77 - 14 * q^79 - 49 * q^81 + 41 * q^83 - 66 * q^85 + 40 * q^87 + 34 * q^89 + 13 * q^91 - 40 * q^93 + 42 * q^95 - 10 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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