LMFDB - Embedded newform 819.2.y.h.811.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(307,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("819.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.y (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
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} + 35x^{8} + 295x^{4} + 169 $ x^12 + 35x^8 + 295x^4 + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			811.3
Root			$-1.52891 + 1.52891i$ of defining polynomial
Character	$\chi$	$=$	819.811
Dual form			819.2.y.h.307.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.403032 - 0.403032i) q^{2} +1.67513i q^{4} +(-1.03221 - 1.03221i) q^{5} +(2.60707 - 0.450747i) q^{7} +(1.48119 + 1.48119i) q^{8} +O(q^{10})$	\(q+(0.403032 - 0.403032i) q^{2} +1.67513i q^{4} +(-1.03221 - 1.03221i) q^{5} +(2.60707 - 0.450747i) q^{7} +(1.48119 + 1.48119i) q^{8} -0.832030 q^{10} +(0.596968 + 0.596968i) q^{11} +(-3.59334 - 0.296512i) q^{13} +(0.869067 - 1.23240i) q^{14} -2.15633 q^{16} +7.34804 q^{17} +(3.59334 + 3.59334i) q^{19} +(1.72909 - 1.72909i) q^{20} +0.481194 q^{22} +4.44358i q^{23} -2.86907i q^{25} +(-1.56773 + 1.32873i) q^{26} +(0.755061 + 4.36719i) q^{28} +3.54420 q^{29} +(-1.27122 - 1.27122i) q^{31} +(-3.83146 + 3.83146i) q^{32} +(2.96149 - 2.96149i) q^{34} +(-3.15633 - 2.22579i) q^{35} +(2.88423 + 2.88423i) q^{37} +2.89646 q^{38} -3.05782i q^{40} +(-1.23240 - 1.23240i) q^{41} +8.66291i q^{43} +(-1.00000 + 1.00000i) q^{44} +(1.79090 + 1.79090i) q^{46} +(-2.52230 + 2.52230i) q^{47} +(6.59365 - 2.35026i) q^{49} +(-1.15633 - 1.15633i) q^{50} +(0.496696 - 6.01931i) q^{52} +9.79384 q^{53} -1.23240i q^{55} +(4.52923 + 3.19394i) q^{56} +(1.42842 - 1.42842i) q^{58} +(1.08972 - 1.08972i) q^{59} +7.10903i q^{61} -1.02469 q^{62} -1.22425i q^{64} +(3.40303 + 4.01516i) q^{65} +(8.76845 - 8.76845i) q^{67} +12.3089i q^{68} +(-2.16916 + 0.375035i) q^{70} +(1.46604 - 1.46604i) q^{71} +(-0.103857 + 0.103857i) q^{73} +2.32487 q^{74} +(-6.01931 + 6.01931i) q^{76} +(1.82542 + 1.28726i) q^{77} -4.79877 q^{79} +(2.22579 + 2.22579i) q^{80} -0.993391 q^{82} +(-12.3165 - 12.3165i) q^{83} +(-7.58475 - 7.58475i) q^{85} +(3.49143 + 3.49143i) q^{86} +1.76845i q^{88} +(6.89017 - 6.89017i) q^{89} +(-9.50175 + 0.846661i) q^{91} -7.44358 q^{92} +2.03313i q^{94} -7.41819i q^{95} +(-6.05814 - 6.05814i) q^{97} +(1.71022 - 3.60468i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} - 8 q^{7} - 4 q^{8}+O(q^{10}) $ 12 * q + 4 * q^2 - 8 * q^7 - 4 * q^8	$ 12 q + 4 q^{2} - 8 q^{7} - 4 q^{8} + 8 q^{11} - 8 q^{14} + 16 q^{16} - 16 q^{22} - 20 q^{28} + 4 q^{29} + 16 q^{32} + 4 q^{35} + 12 q^{37} - 12 q^{44} + 24 q^{46} + 28 q^{50} + 12 q^{53} - 44 q^{58} + 40 q^{65} + 60 q^{67} + 4 q^{70} + 48 q^{74} - 4 q^{79} + 12 q^{85} - 36 q^{86} - 32 q^{91} - 24 q^{92} + 28 q^{98}+O(q^{100}) $ 12 * q + 4 * q^2 - 8 * q^7 - 4 * q^8 + 8 * q^11 - 8 * q^14 + 16 * q^16 - 16 * q^22 - 20 * q^28 + 4 * q^29 + 16 * q^32 + 4 * q^35 + 12 * q^37 - 12 * q^44 + 24 * q^46 + 28 * q^50 + 12 * q^53 - 44 * q^58 + 40 * q^65 + 60 * q^67 + 4 * q^70 + 48 * q^74 - 4 * q^79 + 12 * q^85 - 36 * q^86 - 32 * q^91 - 24 * q^92 + 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	0.403032	−	0.403032i	0.284986	−	0.284986i	−0.550107	−	0.835094i	$-0.685413\pi$
$2$	0.403032	−	0.403032i	0.284986	−	0.284986i	0.835094	+	0.550107i	$0.185413\pi$
$3$		0			0
$3$		0			0
$4$			1.67513i			0.837565i
$5$	−1.03221	−	1.03221i	−0.461620	−	0.461620i	0.437566	−	0.899186i	$-0.355841\pi$
$5$	−1.03221	−	1.03221i	−0.461620	−	0.461620i	−0.899186	+	0.437566i	$0.855841\pi$
$6$		0			0
$7$	2.60707	−	0.450747i	0.985381	−	0.170366i
$7$	2.60707	−	0.450747i	0.985381	−	0.170366i
$8$	1.48119	+	1.48119i	0.523681	+	0.523681i
$9$		0			0
$10$	−0.832030			−0.263111
$11$	0.596968	+	0.596968i	0.179993	+	0.179993i	0.791353	−	0.611360i	$-0.209377\pi$
$11$	0.596968	+	0.596968i	0.179993	+	0.179993i	−0.611360	+	0.791353i	$0.709377\pi$
$12$		0			0
$13$	−3.59334	−	0.296512i	−0.996613	−	0.0822375i
$13$	−3.59334	−	0.296512i	−0.996613	−	0.0822375i
$14$	0.869067	−	1.23240i	0.232268	−	0.329372i
$15$		0			0
$16$	−2.15633			−0.539081
$17$	7.34804			1.78216			0.891080	−	0.453845i	$-0.149948\pi$
$17$	7.34804			1.78216			0.891080	+	0.453845i	$0.149948\pi$
$18$		0			0
$19$	3.59334	+	3.59334i	0.824368	+	0.824368i	0.986731	−	0.162363i	$-0.0519115\pi$
$19$	3.59334	+	3.59334i	0.824368	+	0.824368i	−0.162363	+	0.986731i	$0.551911\pi$
$20$	1.72909	−	1.72909i	0.386637	−	0.386637i
$21$		0			0
$22$	0.481194			0.102591
$23$			4.44358i			0.926551i	0.886214	+	0.463276i	$0.153326\pi$
$23$			4.44358i			0.926551i	−0.886214	+	0.463276i	$0.846674\pi$
$24$		0			0
$25$		−	2.86907i		−	0.573813i
$26$	−1.56773	+	1.32873i	−0.307458	+	0.260585i
$27$		0			0
$28$	0.755061	+	4.36719i	0.142693	+	0.825321i
$29$	3.54420			0.658141			0.329071	−	0.944305i	$-0.393265\pi$
$29$	3.54420			0.658141			0.329071	+	0.944305i	$0.393265\pi$
$30$		0			0
$31$	−1.27122	−	1.27122i	−0.228318	−	0.228318i	0.583672	−	0.811990i	$-0.301616\pi$
$31$	−1.27122	−	1.27122i	−0.228318	−	0.228318i	−0.811990	+	0.583672i	$0.801616\pi$
$32$	−3.83146	+	3.83146i	−0.677312	+	0.677312i
$33$		0			0
$34$	2.96149	−	2.96149i	0.507892	−	0.507892i
$35$	−3.15633	−	2.22579i	−0.533516	−	0.376227i
$36$		0			0
$37$	2.88423	+	2.88423i	0.474164	+	0.474164i	0.903259	−	0.429095i	$-0.141168\pi$
$37$	2.88423	+	2.88423i	0.474164	+	0.474164i	−0.429095	+	0.903259i	$0.641168\pi$
$38$	2.89646			0.469868
$39$		0			0
$40$		−	3.05782i		−	0.483484i
$41$	−1.23240	−	1.23240i	−0.192468	−	0.192468i	0.604294	−	0.796762i	$-0.293455\pi$
$41$	−1.23240	−	1.23240i	−0.192468	−	0.192468i	−0.796762	+	0.604294i	$0.793455\pi$
$42$		0			0
$43$			8.66291i			1.32108i	0.750790	+	0.660541i	$0.229673\pi$
$43$			8.66291i			1.32108i	−0.750790	+	0.660541i	$0.770327\pi$
$44$	−1.00000	+	1.00000i	−0.150756	+	0.150756i
$45$		0			0
$46$	1.79090	+	1.79090i	0.264055	+	0.264055i
$47$	−2.52230	+	2.52230i	−0.367915	+	0.367915i	−0.866717	−	0.498801i	$-0.833774\pi$
$47$	−2.52230	+	2.52230i	−0.367915	+	0.367915i	0.498801	+	0.866717i	$0.333774\pi$
$48$		0			0
$49$	6.59365	−	2.35026i	0.941951	−	0.335752i
$50$	−1.15633	−	1.15633i	−0.163529	−	0.163529i
$51$		0			0
$52$	0.496696	−	6.01931i	0.0688793	−	0.834728i
$53$	9.79384			1.34529			0.672644	−	0.739966i	$-0.265159\pi$
$53$	9.79384			1.34529			0.672644	+	0.739966i	$0.265159\pi$
$54$		0			0
$55$		−	1.23240i		−	0.166177i
$56$	4.52923	+	3.19394i	0.605243	+	0.426808i
$57$		0			0
$58$	1.42842	−	1.42842i	0.187561	−	0.187561i
$59$	1.08972	−	1.08972i	0.141869	−	0.141869i	−0.632605	−	0.774474i	$-0.718014\pi$
$59$	1.08972	−	1.08972i	0.141869	−	0.141869i	0.774474	+	0.632605i	$0.218014\pi$
$60$		0			0
$61$			7.10903i			0.910218i	0.890436	+	0.455109i	$0.150400\pi$
$61$			7.10903i			0.910218i	−0.890436	+	0.455109i	$0.849600\pi$
$62$	−1.02469			−0.130135
$63$		0			0
$64$		−	1.22425i		−	0.153032i
$65$	3.40303	+	4.01516i	0.422094	+	0.498019i
$66$		0			0
$67$	8.76845	−	8.76845i	1.07124	−	1.07124i	0.0739770	−	0.997260i	$-0.476431\pi$
$67$	8.76845	−	8.76845i	1.07124	−	1.07124i	0.997260	−	0.0739770i	$-0.0235691\pi$
$68$			12.3089i			1.49268i
$69$		0			0
$70$	−2.16916	+	0.375035i	−0.259265	+	0.0448253i
$71$	1.46604	−	1.46604i	0.173986	−	0.173986i	−0.614742	−	0.788728i	$-0.710740\pi$
$71$	1.46604	−	1.46604i	0.173986	−	0.173986i	0.788728	+	0.614742i	$0.210740\pi$
$72$		0			0
$73$	−0.103857	+	0.103857i	−0.0121555	+	0.0121555i	−0.713158	−	0.701003i	$-0.752736\pi$
$73$	−0.103857	+	0.103857i	−0.0121555	+	0.0121555i	0.701003	+	0.713158i	$0.252736\pi$
$74$	2.32487			0.270261
$75$		0			0
$76$	−6.01931	+	6.01931i	−0.690462	+	0.690462i
$77$	1.82542	+	1.28726i	0.208026	+	0.146697i
$78$		0			0
$79$	−4.79877			−0.539904			−0.269952	−	0.962874i	$-0.587008\pi$
$79$	−4.79877			−0.539904			−0.269952	+	0.962874i	$0.587008\pi$
$80$	2.22579	+	2.22579i	0.248851	+	0.248851i
$81$		0			0
$82$	−0.993391			−0.109702
$83$	−12.3165	−	12.3165i	−1.35191	−	1.35191i	−0.883528	−	0.468379i	$-0.844838\pi$
$83$	−12.3165	−	12.3165i	−1.35191	−	1.35191i	−0.468379	−	0.883528i	$-0.655162\pi$
$84$		0			0
$85$	−7.58475	−	7.58475i	−0.822682	−	0.822682i
$86$	3.49143	+	3.49143i	0.376490	+	0.376490i
$87$		0			0
$88$			1.76845i			0.188518i
$89$	6.89017	−	6.89017i	0.730356	−	0.730356i	−0.240334	−	0.970690i	$-0.577257\pi$
$89$	6.89017	−	6.89017i	0.730356	−	0.730356i	0.970690	+	0.240334i	$0.0772570\pi$
$90$		0			0
$91$	−9.50175	+	0.846661i	−0.996054	+	0.0887541i
$92$	−7.44358			−0.776047
$93$		0			0
$94$			2.03313i			0.209702i
$95$		−	7.41819i		−	0.761090i
$96$		0			0
$97$	−6.05814	−	6.05814i	−0.615110	−	0.615110i	0.329163	−	0.944273i	$-0.393234\pi$
$97$	−6.05814	−	6.05814i	−0.615110	−	0.615110i	−0.944273	+	0.329163i	$0.893234\pi$
$98$	1.71022	−	3.60468i	0.172758	−	0.364128i
$99$		0			0
$100$	4.80606			0.480606
$101$	−12.8707			−1.28068			−0.640339	−	0.768092i	$-0.721206\pi$
$101$	−12.8707			−1.28068			−0.640339	+	0.768092i	$0.721206\pi$
$102$		0			0
$103$	−6.11564			−0.602592			−0.301296	−	0.953531i	$-0.597419\pi$
$103$	−6.11564			−0.602592			−0.301296	+	0.953531i	$0.597419\pi$
$104$	−4.88324	−	5.76162i	−0.478841	−	0.564974i
$105$		0			0
$106$	3.94723	−	3.94723i	0.383389	−	0.383389i
$107$	−8.86907			−0.857405			−0.428703	−	0.903446i	$-0.641029\pi$
$107$	−8.86907			−0.857405			−0.428703	+	0.903446i	$0.641029\pi$
$108$		0			0
$109$	−4.59697	+	4.59697i	−0.440310	+	0.440310i	−0.892116	−	0.451806i	$-0.850780\pi$
$109$	−4.59697	+	4.59697i	−0.440310	+	0.440310i	0.451806	+	0.892116i	$0.350780\pi$
$110$	−0.496696	−	0.496696i	−0.0473581	−	0.0473581i
$111$		0			0
$112$	−5.62170	+	0.971958i	−0.531200	+	0.0918414i
$113$	−1.60720			−0.151193			−0.0755964	−	0.997138i	$-0.524086\pi$
$113$	−1.60720			−0.151193			−0.0755964	+	0.997138i	$0.524086\pi$
$114$		0			0
$115$	4.58673	−	4.58673i	0.427715	−	0.427715i
$116$			5.93700i			0.551236i
$117$		0			0
$118$		−	0.878382i		−	0.0808617i
$119$	19.1569	−	3.31211i	1.75611	−	0.303620i
$120$		0			0
$121$		−	10.2873i		−	0.935205i
$122$	2.86516	+	2.86516i	0.259400	+	0.259400i
$123$		0			0
$124$	2.12946	−	2.12946i	0.191231	−	0.191231i
$125$	−8.12256	+	8.12256i	−0.726504	+	0.726504i
$126$		0			0
$127$			1.54912i			0.137462i	0.997635	+	0.0687312i	$0.0218951\pi$
$127$			1.54912i			0.137462i	−0.997635	+	0.0687312i	$0.978105\pi$
$128$	−8.15633	−	8.15633i	−0.720924	−	0.720924i
$129$		0			0
$130$	2.98977	+	0.246707i	0.262220	+	0.0216376i
$131$		−	5.31490i		−	0.464365i	−0.972672	−	0.232183i	$-0.925413\pi$
$131$		−	5.31490i		−	0.464365i	0.972672	−	0.232183i	$-0.0745867\pi$
$132$		0			0
$133$	10.9878	+	7.74841i	0.952761	+	0.671872i
$134$		−	7.06793i		−	0.610576i
$135$		0			0
$136$	10.8839	+	10.8839i	0.933284	+	0.933284i
$137$	−12.7157	−	12.7157i	−1.08637	−	1.08637i	−0.995899	−	0.0904753i	$-0.971161\pi$
$137$	−12.7157	−	12.7157i	−1.08637	−	1.08637i	−0.0904753	−	0.995899i	$-0.528839\pi$
$138$		0			0
$139$		−	6.94767i		−	0.589294i	−0.955606	−	0.294647i	$-0.904798\pi$
$139$		−	6.94767i		−	0.589294i	0.955606	−	0.294647i	$-0.0952020\pi$
$140$	3.72849	−	5.28726i	0.315115	−	0.446855i
$141$		0			0
$142$		−	1.18172i		−	0.0991676i
$143$	−1.96810	−	2.32212i	−0.164581	−	0.194185i
$144$		0			0
$145$	−3.65837	−	3.65837i	−0.303811	−	0.303811i
$146$			0.0837150i			0.00692831i
$147$		0			0
$148$	−4.83146	+	4.83146i	−0.397143	+	0.397143i
$149$	10.9653	−	10.9653i	0.898315	−	0.898315i	−0.0969724	−	0.995287i	$-0.530916\pi$
$149$	10.9653	−	10.9653i	0.898315	−	0.898315i	0.995287	+	0.0969724i	$0.0309158\pi$
$150$		0			0
$151$	6.14117	+	6.14117i	0.499761	+	0.499761i	0.911363	−	0.411602i	$-0.135031\pi$
$151$	6.14117	+	6.14117i	0.499761	+	0.499761i	−0.411602	+	0.911363i	$0.635031\pi$
$152$			10.6449i			0.863413i
$153$		0			0
$154$	1.25451	−	0.216897i	0.101091	−	0.0174781i
$155$			2.62435i			0.210793i
$156$		0			0
$157$			9.69783i			0.773971i	0.922086	+	0.386985i	$0.126484\pi$
$157$			9.69783i			0.773971i	−0.922086	+	0.386985i	$0.873516\pi$
$158$	−1.93406	+	1.93406i	−0.153865	+	0.153865i
$159$		0			0
$160$	7.90977			0.625322
$161$	2.00293	+	11.5847i	0.157853	+	0.913006i
$162$		0			0
$163$	−5.41327	−	5.41327i	−0.424000	−	0.424000i	0.462579	−	0.886578i	$-0.346924\pi$
$163$	−5.41327	−	5.41327i	−0.424000	−	0.424000i	−0.886578	+	0.462579i	$0.846924\pi$
$164$	2.06443	−	2.06443i	0.161205	−	0.161205i
$165$		0			0
$166$	−9.92784			−0.770550
$167$	−8.90824	+	8.90824i	−0.689340	+	0.689340i	−0.962086	−	0.272746i	$-0.912068\pi$
$167$	−8.90824	+	8.90824i	−0.689340	+	0.689340i	0.272746	+	0.962086i	$0.412068\pi$
$168$		0			0
$169$	12.8242	+	2.13093i	0.986474	+	0.163918i
$170$	−6.11379			−0.468906
$171$		0			0
$172$	−14.5115			−1.10649
$173$	−7.15538			−0.544014			−0.272007	−	0.962295i	$-0.587687\pi$
$173$	−7.15538			−0.544014			−0.272007	+	0.962295i	$0.587687\pi$
$174$		0			0
$175$	−1.29322	−	7.47987i	−0.0977586	−	0.565425i
$176$	−1.28726	−	1.28726i	−0.0970307	−	0.0970307i
$177$		0			0
$178$		−	5.55391i		−	0.416283i
$179$			13.8119i			1.03235i	0.856482	+	0.516177i	$0.172645\pi$
$179$			13.8119i			1.03235i	−0.856482	+	0.516177i	$0.827355\pi$
$180$		0			0
$181$	−4.56052			−0.338981			−0.169490	−	0.985532i	$-0.554212\pi$
$181$	−4.56052			−0.338981			−0.169490	+	0.985532i	$0.554212\pi$
$182$	−3.48827	+	4.17074i	−0.258568	+	0.309156i
$183$		0			0
$184$	−6.58181	+	6.58181i	−0.485217	+	0.485217i
$185$		−	5.95428i		−	0.437767i
$186$		0			0
$187$	4.38655	+	4.38655i	0.320776	+	0.320776i
$188$	−4.22518	−	4.22518i	−0.308153	−	0.308153i
$189$		0			0
$190$	−2.98977	−	2.98977i	−0.216900	−	0.216900i
$191$	−3.70545			−0.268117			−0.134058	−	0.990973i	$-0.542801\pi$
$191$	−3.70545			−0.268117			−0.134058	+	0.990973i	$0.542801\pi$
$192$		0			0
$193$	−17.0508	−	17.0508i	−1.22734	−	1.22734i	−0.964965	−	0.262377i	$-0.915494\pi$
$193$	−17.0508	−	17.0508i	−1.22734	−	1.22734i	−0.262377	−	0.964965i	$-0.584506\pi$
$194$	−4.88324			−0.350596
$195$		0			0
$196$	3.93700	+	11.0452i	0.281214	+	0.788945i
$197$	8.01810	−	8.01810i	0.571266	−	0.571266i	−0.361216	−	0.932482i	$-0.617638\pi$
$197$	8.01810	−	8.01810i	0.571266	−	0.571266i	0.932482	+	0.361216i	$0.117638\pi$
$198$		0			0
$199$	−4.57558			−0.324354			−0.162177	−	0.986762i	$-0.551852\pi$
$199$	−4.57558			−0.324354			−0.162177	+	0.986762i	$0.551852\pi$
$200$	4.24965	−	4.24965i	0.300495	−	0.300495i
$201$		0			0
$202$	−5.18728	+	5.18728i	−0.364976	+	0.364976i
$203$	9.23998	−	1.59754i	0.648520	−	0.112125i
$204$		0			0
$205$			2.54420i			0.177695i
$206$	−2.46480	+	2.46480i	−0.171731	+	0.171731i
$207$		0			0
$208$	7.74841	+	0.639375i	0.537255	+	0.0443327i
$209$			4.29022i			0.296761i
$210$		0			0
$211$	−0.594028			−0.0408946			−0.0204473	−	0.999791i	$-0.506509\pi$
$211$	−0.594028			−0.0408946			−0.0204473	+	0.999791i	$0.506509\pi$
$212$			16.4060i			1.12677i
$213$		0			0
$214$	−3.57452	+	3.57452i	−0.244349	+	0.244349i
$215$	8.94198	−	8.94198i	0.609838	−	0.609838i
$216$		0			0
$217$	−3.88717	−	2.74117i	−0.263878	−	0.186083i
$218$			3.70545i			0.250965i
$219$		0			0
$220$	2.06443			0.139184
$221$	−26.4040	−	2.17878i	−1.77612	−	0.146560i
$222$		0			0
$223$	2.85764	+	2.85764i	0.191361	+	0.191361i	0.796284	−	0.604923i	$-0.206796\pi$
$223$	2.85764	+	2.85764i	0.191361	+	0.191361i	−0.604923	+	0.796284i	$0.706796\pi$
$224$	−8.26187	+	11.7159i	−0.552019	+	0.782802i
$225$		0			0
$226$	−0.647754	+	0.647754i	−0.0430879	+	0.0430879i
$227$	19.6570	+	19.6570i	1.30468	+	1.30468i	0.925201	+	0.379477i	$0.123896\pi$
$227$	19.6570	+	19.6570i	1.30468	+	1.30468i	0.379477	+	0.925201i	$0.376104\pi$
$228$		0			0
$229$	−13.2060	+	13.2060i	−0.872676	+	0.872676i	−0.992763	−	0.120087i	$-0.961683\pi$
$229$	−13.2060	+	13.2060i	−0.872676	+	0.872676i	0.120087	+	0.992763i	$0.461683\pi$
$230$		−	3.69720i		−	0.243786i
$231$		0			0
$232$	5.24965	+	5.24965i	0.344656	+	0.344656i
$233$		−	16.2243i		−	1.06289i	−0.847094	−	0.531443i	$-0.821650\pi$
$233$		−	16.2243i		−	1.06289i	0.847094	−	0.531443i	$-0.178350\pi$
$234$		0			0
$235$	5.20711			0.339674
$236$	1.82542	+	1.82542i	0.118825	+	0.118825i
$237$		0			0
$238$	6.38594	−	9.05571i	0.413939	−	0.586994i
$239$	0.843675	−	0.843675i	0.0545728	−	0.0545728i	−0.679294	−	0.733867i	$-0.737714\pi$
$239$	0.843675	−	0.843675i	0.0545728	−	0.0545728i	0.733867	+	0.679294i	$0.237714\pi$
$240$		0			0
$241$	15.2966	−	15.2966i	0.985342	−	0.985342i	−0.0145517	−	0.999894i	$-0.504632\pi$
$241$	15.2966	−	15.2966i	0.985342	−	0.985342i	0.999894	+	0.0145517i	$0.00463211\pi$
$242$	−4.14609	−	4.14609i	−0.266521	−	0.266521i
$243$		0			0
$244$	−11.9086			−0.762367
$245$	−9.23204	−	4.38009i	−0.589813	−	0.279834i
$246$		0			0
$247$	−11.8466	−	13.9775i	−0.753782	−	0.889370i
$248$		−	3.76585i		−	0.239132i
$249$		0			0
$250$			6.54730i			0.414088i
$251$	−27.4367			−1.73179			−0.865893	−	0.500229i	$-0.833249\pi$
$251$	−27.4367			−1.73179			−0.865893	+	0.500229i	$0.833249\pi$
$252$		0			0
$253$	−2.65268	+	2.65268i	−0.166772	+	0.166772i
$254$	0.624346	+	0.624346i	0.0391749	+	0.0391749i
$255$		0			0
$256$	−4.12601			−0.257876
$257$	−20.5727			−1.28329			−0.641645	−	0.767002i	$-0.721748\pi$
$257$	−20.5727			−1.28329			−0.641645	+	0.767002i	$0.721748\pi$
$258$		0			0
$259$	8.81944	+	6.21933i	0.548014	+	0.386450i
$260$	−6.72592	+	5.70052i	−0.417124	+	0.353531i
$261$		0			0
$262$	−2.14207	−	2.14207i	−0.132338	−	0.132338i
$263$	23.8568			1.47108			0.735538	−	0.677483i	$-0.236929\pi$
$263$	23.8568			1.47108			0.735538	+	0.677483i	$0.236929\pi$
$264$		0			0
$265$	−10.1093	−	10.1093i	−0.621012	−	0.621012i
$266$	7.55128	−	1.30557i	0.462999	−	0.0800497i
$267$		0			0
$268$	14.6883	+	14.6883i	0.897231	+	0.897231i
$269$		−	1.10840i		−	0.0675803i	−0.999429	−	0.0337902i	$-0.989242\pi$
$269$		−	1.10840i		−	0.0675803i	0.999429	−	0.0337902i	$-0.0107578\pi$
$270$		0			0
$271$	20.8894	−	20.8894i	1.26894	−	1.26894i	0.322301	−	0.946637i	$-0.395544\pi$
$271$	20.8894	−	20.8894i	1.26894	−	1.26894i	0.946637	−	0.322301i	$-0.104456\pi$
$272$	−15.8448			−0.960730
$273$		0			0
$274$	−10.2496			−0.619204
$275$	1.71274	−	1.71274i	0.103282	−	0.103282i
$276$		0			0
$277$			25.8265i			1.55177i	0.630877	+	0.775883i	$0.282695\pi$
$277$			25.8265i			1.55177i	−0.630877	+	0.775883i	$0.717305\pi$
$278$	−2.80013	−	2.80013i	−0.167941	−	0.167941i
$279$		0			0
$280$	−1.37830	−	7.97196i	−0.0823694	−	0.476416i
$281$	−12.0782	−	12.0782i	−0.720523	−	0.720523i	0.248189	−	0.968712i	$-0.420165\pi$
$281$	−12.0782	−	12.0782i	−0.720523	−	0.720523i	−0.968712	+	0.248189i	$0.920165\pi$
$282$		0			0
$283$	−15.3667			−0.913458			−0.456729	−	0.889606i	$-0.650979\pi$
$283$	−15.3667			−0.913458			−0.456729	+	0.889606i	$0.650979\pi$
$284$	2.45580	+	2.45580i	0.145725	+	0.145725i
$285$		0			0
$286$	−1.72909	−	0.142680i	−0.102243	−	0.00843683i
$287$	−3.76845	−	2.65745i	−0.222445	−	0.156864i
$288$		0			0
$289$	36.9937			2.17610
$290$	−2.94888			−0.173164
$291$		0			0
$292$	−0.173973	−	0.173973i	−0.0101810	−	0.0101810i
$293$	9.78662	−	9.78662i	0.571741	−	0.571741i	−0.360874	−	0.932615i	$-0.617522\pi$
$293$	9.78662	−	9.78662i	0.571741	−	0.571741i	0.932615	+	0.360874i	$0.117522\pi$
$294$		0			0
$295$	−2.24965			−0.130979
$296$			8.54420i			0.496621i
$297$		0			0
$298$		−	8.83875i		−	0.512015i
$299$	1.31757	−	15.9673i	0.0761972	−	0.923413i
$300$		0			0
$301$	3.90478	+	22.5848i	0.225068	+	1.30177i
$302$	4.95017			0.284850
$303$		0			0
$304$	−7.74841	−	7.74841i	−0.444402	−	0.444402i
$305$	7.33804	−	7.33804i	0.420175	−	0.420175i
$306$		0			0
$307$	−8.14125	+	8.14125i	−0.464645	+	0.464645i	−0.900175	−	0.435529i	$-0.856561\pi$
$307$	−8.14125	+	8.14125i	−0.464645	+	0.464645i	0.435529	+	0.900175i	$0.356561\pi$
$308$	−2.15633	+	3.05782i	−0.122868	+	0.174235i
$309$		0			0
$310$	1.05769	+	1.05769i	0.0600730	+	0.0600730i
$311$	32.4813			1.84184			0.920922	−	0.389747i	$-0.127438\pi$
$311$	32.4813			1.84184			0.920922	+	0.389747i	$0.127438\pi$
$312$		0			0
$313$		−	19.7346i		−	1.11547i	−0.830020	−	0.557733i	$-0.811671\pi$
$313$		−	19.7346i		−	1.11547i	0.830020	−	0.557733i	$-0.188329\pi$
$314$	3.90853	+	3.90853i	0.220571	+	0.220571i
$315$		0			0
$316$		−	8.03857i		−	0.452205i
$317$	8.11871	−	8.11871i	0.455992	−	0.455992i	−0.441345	−	0.897337i	$-0.645499\pi$
$317$	8.11871	−	8.11871i	0.455992	−	0.455992i	0.897337	+	0.441345i	$0.145499\pi$
$318$		0			0
$319$	2.11577	+	2.11577i	0.118461	+	0.118461i
$320$	−1.26369	+	1.26369i	−0.0706425	+	0.0706425i
$321$		0			0
$322$	5.47626	+	3.86177i	0.305180	+	0.215208i
$323$	26.4040	+	26.4040i	1.46916	+	1.46916i
$324$		0			0
$325$	−0.850712	+	10.3095i	−0.0471890	+	0.571870i
$326$	−4.36344			−0.241668
$327$		0			0
$328$		−	3.65084i		−	0.201584i
$329$	−5.43890	+	7.71274i	−0.299856	+	0.425217i
$330$		0			0
$331$	−0.806063	+	0.806063i	−0.0443053	+	0.0443053i	−0.728912	−	0.684607i	$-0.759974\pi$
$331$	−0.806063	+	0.806063i	−0.0443053	+	0.0443053i	0.684607	+	0.728912i	$0.259974\pi$
$332$	20.6317	−	20.6317i	1.13231	−	1.13231i
$333$		0			0
$334$			7.18061i			0.392905i
$335$	−18.1018			−0.989009
$336$		0			0
$337$		−	26.6058i		−	1.44931i	−0.689112	−	0.724655i	$-0.741999\pi$
$337$		−	26.6058i		−	1.44931i	0.689112	−	0.724655i	$-0.258001\pi$
$338$	6.02738	−	4.30971i	0.327846	−	0.234417i
$339$		0			0
$340$	12.7054	−	12.7054i	0.689050	−	0.689050i
$341$		−	1.51776i		−	0.0821912i
$342$		0			0
$343$	16.1308	−	9.09937i	0.870979	−	0.491320i
$344$	−12.8315	+	12.8315i	−0.691826	+	0.691826i
$345$		0			0
$346$	−2.88385	+	2.88385i	−0.155037	+	0.155037i
$347$	20.2071			1.08477			0.542387	−	0.840129i	$-0.317521\pi$
$347$	20.2071			1.08477			0.542387	+	0.840129i	$0.317521\pi$
$348$		0			0
$349$	−2.31459	+	2.31459i	−0.123897	+	0.123897i	−0.766336	−	0.642439i	$-0.777922\pi$
$349$	−2.31459	+	2.31459i	−0.123897	+	0.123897i	0.642439	+	0.766336i	$0.277922\pi$
$350$	−3.53583	−	2.49341i	−0.188998	−	0.133279i
$351$		0			0
$352$	−4.57452			−0.243822
$353$	10.7412	+	10.7412i	0.571696	+	0.571696i	0.932602	−	0.360906i	$-0.117533\pi$
$353$	10.7412	+	10.7412i	0.571696	+	0.571696i	−0.360906	+	0.932602i	$0.617533\pi$
$354$		0			0
$355$	−3.02653			−0.160631
$356$	11.5419	+	11.5419i	0.611721	+	0.611721i
$357$		0			0
$358$	5.56665	+	5.56665i	0.294207	+	0.294207i
$359$	16.9726	+	16.9726i	0.895781	+	0.895781i	0.995060	−	0.0992789i	$-0.0316536\pi$
$359$	16.9726	+	16.9726i	0.895781	+	0.895781i	−0.0992789	+	0.995060i	$0.531654\pi$
$360$		0			0
$361$			6.82416i			0.359166i
$362$	−1.83803	+	1.83803i	−0.0966049	+	0.0966049i
$363$		0			0
$364$	−1.41827	−	15.9167i	−0.0743374	−	0.834260i
$365$	0.214405			0.0112225
$366$		0			0
$367$			9.79778i			0.511440i	0.966751	+	0.255720i	$0.0823125\pi$
$367$			9.79778i			0.511440i	−0.966751	+	0.255720i	$0.917688\pi$
$368$		−	9.58181i		−	0.499486i
$369$		0			0
$370$	−2.39976	−	2.39976i	−0.124758	−	0.124758i
$371$	25.5333	−	4.41455i	1.32562	−	0.229192i
$372$		0			0
$373$	−5.96731			−0.308976			−0.154488	−	0.987995i	$-0.549373\pi$
$373$	−5.96731			−0.308976			−0.154488	+	0.987995i	$0.549373\pi$
$374$	3.53583			0.182834
$375$		0			0
$376$	−7.47204			−0.385341
$377$	−12.7355	−	1.05090i	−0.655912	−	0.0541239i
$378$		0			0
$379$	2.14117	−	2.14117i	0.109984	−	0.109984i	−0.649973	−	0.759957i	$-0.725220\pi$
$379$	2.14117	−	2.14117i	0.109984	−	0.109984i	0.759957	+	0.649973i	$0.225220\pi$
$380$	12.4264			0.637463
$381$		0			0
$382$	−1.49341	+	1.49341i	−0.0764097	+	0.0764097i
$383$	−2.91152	−	2.91152i	−0.148772	−	0.148772i	0.628798	−	0.777569i	$-0.283547\pi$
$383$	−2.91152	−	2.91152i	−0.148772	−	0.148772i	−0.777569	+	0.628798i	$0.783547\pi$
$384$		0			0
$385$	−0.555500	−	3.21295i	−0.0283109	−	0.163747i
$386$	−13.7440			−0.699552
$387$		0			0
$388$	10.1482	−	10.1482i	0.515195	−	0.515195i
$389$			17.4436i			0.884425i	0.896910	+	0.442212i	$0.145806\pi$
$389$			17.4436i			0.884425i	−0.896910	+	0.442212i	$0.854194\pi$
$390$		0			0
$391$			32.6516i			1.65126i
$392$	13.2477	+	6.28529i	0.669109	+	0.317455i
$393$		0			0
$394$		−	6.46310i		−	0.325606i
$395$	4.95336	+	4.95336i	0.249230	+	0.249230i
$396$		0			0
$397$	10.1870	−	10.1870i	0.511270	−	0.511270i	−0.403645	−	0.914916i	$-0.632257\pi$
$397$	10.1870	−	10.1870i	0.511270	−	0.511270i	0.914916	+	0.403645i	$0.132257\pi$
$398$	−1.84410	+	1.84410i	−0.0924365	+	0.0924365i
$399$		0			0
$400$			6.18664i			0.309332i
$401$	−15.5950	−	15.5950i	−0.778776	−	0.778776i	0.200846	−	0.979623i	$-0.435631\pi$
$401$	−15.5950	−	15.5950i	−0.778776	−	0.778776i	−0.979623	+	0.200846i	$0.935631\pi$
$402$		0			0
$403$	4.19100	+	4.94486i	0.208768	+	0.246321i
$404$		−	21.5600i		−	1.07265i
$405$		0			0
$406$	3.08015	−	4.36786i	0.152865	−	0.216773i
$407$			3.44358i			0.170692i
$408$		0			0
$409$	1.79921	+	1.79921i	0.0889652	+	0.0889652i	0.750189	−	0.661224i	$-0.229963\pi$
$409$	1.79921	+	1.79921i	0.0889652	+	0.0889652i	−0.661224	+	0.750189i	$0.729963\pi$
$410$	1.02539	+	1.02539i	0.0506405	+	0.0506405i
$411$		0			0
$412$		−	10.2445i		−	0.504710i
$413$	2.34979	−	3.33216i	0.115626	−	0.163965i
$414$		0			0
$415$			25.4264i			1.24813i
$416$	14.9038	−	12.6316i	0.730718	−	0.619317i
$417$		0			0
$418$	1.72909	+	1.72909i	0.0845728	+	0.0845728i
$419$			16.5064i			0.806392i	0.915114	+	0.403196i	$0.132101\pi$
$419$			16.5064i			0.806392i	−0.915114	+	0.403196i	$0.867899\pi$
$420$		0			0
$421$	−8.53492	+	8.53492i	−0.415967	+	0.415967i	−0.883811	−	0.467844i	$-0.845031\pi$
$421$	−8.53492	+	8.53492i	−0.415967	+	0.415967i	0.467844	+	0.883811i	$0.345031\pi$
$422$	−0.239412	+	0.239412i	−0.0116544	+	0.0116544i
$423$		0			0
$424$	14.5066	+	14.5066i	0.704502	+	0.704502i
$425$		−	21.0820i		−	1.02263i
$426$		0			0
$427$	3.20438	+	18.5338i	0.155071	+	0.896911i
$428$		−	14.8568i		−	0.718133i
$429$		0			0
$430$		−	7.20780i		−	0.347591i
$431$	−24.2071	+	24.2071i	−1.16602	+	1.16602i	−0.182880	+	0.983135i	$0.558542\pi$
$431$	−24.2071	+	24.2071i	−1.16602	+	1.16602i	−0.983135	+	0.182880i	$0.941458\pi$
$432$		0			0
$433$	−35.8708			−1.72384			−0.861920	−	0.507044i	$-0.830738\pi$
$433$	−35.8708			−1.72384			−0.861920	+	0.507044i	$0.830738\pi$
$434$	−2.67143	+	0.461874i	−0.128233	+	0.0221707i
$435$		0			0
$436$	−7.70052	−	7.70052i	−0.368788	−	0.368788i
$437$	−15.9673	+	15.9673i	−0.763819	+	0.763819i
$438$		0			0
$439$	10.5299			0.502563			0.251281	−	0.967914i	$-0.419148\pi$
$439$	10.5299			0.502563			0.251281	+	0.967914i	$0.419148\pi$
$440$	1.82542	−	1.82542i	0.0870236	−	0.0870236i
$441$		0			0
$442$	−11.5198	+	9.76353i	−0.547939	+	0.464404i
$443$	−12.8618			−0.611081			−0.305541	−	0.952179i	$-0.598837\pi$
$443$	−12.8618			−0.611081			−0.305541	+	0.952179i	$0.598837\pi$
$444$		0			0
$445$	−14.2243			−0.674294
$446$	2.30344			0.109071
$447$		0			0
$448$	−0.551829	−	3.19172i	−0.0260715	−	0.150795i
$449$	−9.65069	−	9.65069i	−0.455444	−	0.455444i	0.441712	−	0.897157i	$-0.354371\pi$
$449$	−9.65069	−	9.65069i	−0.455444	−	0.455444i	−0.897157	+	0.441712i	$0.854371\pi$
$450$		0			0
$451$		−	1.47141i		−	0.0692858i
$452$		−	2.69227i		−	0.126634i
$453$		0			0
$454$	15.8448			0.743631
$455$	10.6818	+	8.93390i	0.500769	+	0.418828i
$456$		0			0
$457$	−22.1217	+	22.1217i	−1.03481	+	1.03481i	−0.0354353	+	0.999372i	$0.511282\pi$
$457$	−22.1217	+	22.1217i	−1.03481	+	1.03481i	−0.999372	+	0.0354353i	$0.988718\pi$
$458$			10.6449i			0.497402i
$459$		0			0
$460$	7.68337	+	7.68337i	0.358239	+	0.358239i
$461$	−0.593023	−	0.593023i	−0.0276198	−	0.0276198i	0.693162	−	0.720782i	$-0.256217\pi$
$461$	−0.593023	−	0.593023i	−0.0276198	−	0.0276198i	−0.720782	+	0.693162i	$0.756217\pi$
$462$		0			0
$463$	2.47096	+	2.47096i	0.114835	+	0.114835i	0.762189	−	0.647354i	$-0.224124\pi$
$463$	2.47096	+	2.47096i	0.114835	+	0.114835i	−0.647354	+	0.762189i	$0.724124\pi$
$464$	−7.64244			−0.354792
$465$		0			0
$466$	−6.53889	−	6.53889i	−0.302908	−	0.302908i
$467$	13.3860			0.619432			0.309716	−	0.950829i	$-0.399766\pi$
$467$	13.3860			0.619432			0.309716	+	0.950829i	$0.399766\pi$
$468$		0			0
$469$	18.9076	−	26.8123i	0.873073	−	1.23808i
$470$	2.09863	−	2.09863i	0.0968026	−	0.0968026i
$471$		0			0
$472$	3.22817			0.148589
$473$	−5.17148	+	5.17148i	−0.237785	+	0.237785i
$474$		0			0
$475$	10.3095	−	10.3095i	0.473034	−	0.473034i
$476$	5.54821	+	32.0903i	0.254302	+	1.47085i
$477$		0			0
$478$		−	0.680055i		−	0.0311050i
$479$	8.85827	−	8.85827i	0.404745	−	0.404745i	−0.475157	−	0.879901i	$-0.657609\pi$
$479$	8.85827	−	8.85827i	0.404745	−	0.404745i	0.879901	+	0.475157i	$0.157609\pi$
$480$		0			0
$481$	−9.50879	−	11.2192i	−0.433564	−	0.511552i
$482$		−	12.3301i		−	0.561619i
$483$		0			0
$484$	17.2325			0.783296
$485$			12.5066i			0.567895i
$486$		0			0
$487$	17.9805	−	17.9805i	0.814774	−	0.814774i	−0.170572	−	0.985345i	$-0.554561\pi$
$487$	17.9805	−	17.9805i	0.814774	−	0.814774i	0.985345	+	0.170572i	$0.0545614\pi$
$488$	−10.5299	+	10.5299i	−0.476664	+	0.476664i
$489$		0			0
$490$	−5.48612	+	1.95549i	−0.247838	+	0.0883400i
$491$			19.4944i			0.879769i	0.898054	+	0.439884i	$0.144981\pi$
$491$			19.4944i			0.879769i	−0.898054	+	0.439884i	$0.855019\pi$
$492$		0			0
$493$	26.0429			1.17291
$494$	−10.4080	−	0.858833i	−0.468276	−	0.0386407i
$495$		0			0
$496$	2.74117	+	2.74117i	0.123082	+	0.123082i
$497$	3.16125	−	4.48287i	0.141801	−	0.201084i
$498$		0			0
$499$	10.2150	−	10.2150i	0.457285	−	0.457285i	−0.440478	−	0.897763i	$-0.645191\pi$
$499$	10.2150	−	10.2150i	0.457285	−	0.457285i	0.897763	+	0.440478i	$0.145191\pi$
$500$	−13.6064	−	13.6064i	−0.608495	−	0.608495i
$501$		0			0
$502$	−11.0578	+	11.0578i	−0.493536	+	0.493536i
$503$		−	31.8196i		−	1.41877i	−0.704824	−	0.709383i	$-0.748974\pi$
$503$		−	31.8196i		−	1.41877i	0.704824	−	0.709383i	$-0.251026\pi$
$504$		0			0
$505$	13.2853	+	13.2853i	0.591187	+	0.591187i
$506$			2.13823i			0.0950558i
$507$		0			0
$508$	−2.59498			−0.115134
$509$	13.6139	+	13.6139i	0.603425	+	0.603425i	0.941220	−	0.337795i	$-0.109681\pi$
$509$	13.6139	+	13.6139i	0.603425	+	0.603425i	−0.337795	+	0.941220i	$0.609681\pi$
$510$		0			0
$511$	−0.223949	+	0.317575i	−0.00990691	+	0.0140487i
$512$	14.6497	−	14.6497i	0.647433	−	0.647433i
$513$		0			0
$514$	−8.29145	+	8.29145i	−0.365720	+	0.365720i
$515$	6.31265	+	6.31265i	0.278169	+	0.278169i
$516$		0			0
$517$	−3.01147			−0.132444
$518$	6.06110	−	1.04793i	0.266310	−	0.0460433i
$519$		0			0
$520$	−0.906679	+	10.9878i	−0.0397605	+	0.481846i
$521$			21.6750i			0.949601i	0.880094	+	0.474800i	$0.157480\pi$
$521$			21.6750i			0.949601i	−0.880094	+	0.474800i	$0.842520\pi$
$522$		0			0
$523$		−	8.77309i		−	0.383620i	−0.981432	−	0.191810i	$-0.938564\pi$
$523$		−	8.77309i		−	0.383620i	0.981432	−	0.191810i	$-0.0614358\pi$
$524$	8.90316			0.388936
$525$		0			0
$526$	9.61507	−	9.61507i	0.419237	−	0.419237i
$527$	−9.34098	−	9.34098i	−0.406900	−	0.406900i
$528$		0			0
$529$	3.25457			0.141503
$530$	−8.14877			−0.353960
$531$		0			0
$532$	−12.9796	+	18.4060i	−0.562737	+	0.798000i
$533$	4.06300	+	4.79384i	0.175988	+	0.207644i
$534$		0			0
$535$	9.15478	+	9.15478i	0.395796	+	0.395796i
$536$	25.9756			1.12197
$537$		0			0
$538$	−0.446720	−	0.446720i	−0.0192595	−	0.0192595i
$539$	5.33923	+	2.53317i	0.229977	+	0.109111i
$540$		0			0
$541$	−23.2853	−	23.2853i	−1.00111	−	1.00111i	−0.999999	−	0.00111270i	$-0.999646\pi$
$541$	−23.2853	−	23.2853i	−1.00111	−	1.00111i	−0.00111270	−	0.999999i	$-0.500354\pi$
$542$		−	16.8382i		−	0.723260i
$543$		0			0
$544$	−28.1537	+	28.1537i	−1.20708	+	1.20708i
$545$	9.49011			0.406512
$546$		0			0
$547$	−15.1744			−0.648812			−0.324406	−	0.945918i	$-0.605164\pi$
$547$	−15.1744			−0.648812			−0.324406	+	0.945918i	$0.605164\pi$
$548$	21.3004	−	21.3004i	0.909909	−	0.909909i
$549$		0			0
$550$		−	1.38058i		−	0.0588681i
$551$	12.7355	+	12.7355i	0.542551	+	0.542551i
$552$		0			0
$553$	−12.5107	+	2.16303i	−0.532011	+	0.0919815i
$554$	10.4089	+	10.4089i	0.442232	+	0.442232i
$555$		0			0
$556$	11.6383			0.493572
$557$	−8.45676	−	8.45676i	−0.358324	−	0.358324i	0.504871	−	0.863195i	$-0.331540\pi$
$557$	−8.45676	−	8.45676i	−0.358324	−	0.358324i	−0.863195	+	0.504871i	$0.831540\pi$
$558$		0			0
$559$	2.56865	−	31.1288i	0.108642	−	1.31661i
$560$	6.80606	+	4.79953i	0.287609	+	0.202817i
$561$		0			0
$562$	−9.73577			−0.410678
$563$	−6.34858			−0.267561			−0.133780	−	0.991011i	$-0.542712\pi$
$563$	−6.34858			−0.267561			−0.133780	+	0.991011i	$0.542712\pi$
$564$		0			0
$565$	1.65898	+	1.65898i	0.0697937	+	0.0697937i
$566$	−6.19329	+	6.19329i	−0.260323	+	0.260323i
$567$		0			0
$568$	4.34297			0.182227
$569$			36.6140i			1.53494i	0.641085	+	0.767470i	$0.278485\pi$
$569$			36.6140i			1.53494i	−0.641085	+	0.767470i	$0.721515\pi$
$570$		0			0
$571$			18.8070i			0.787049i	0.919314	+	0.393525i	$0.128744\pi$
$571$			18.8070i			0.787049i	−0.919314	+	0.393525i	$0.871256\pi$
$572$	3.88985	−	3.29683i	0.162643	−	0.137847i
$573$		0			0
$574$	−2.58984	+	0.447768i	−0.108098	+	0.0186895i
$575$	12.7489			0.531668
$576$		0			0
$577$	31.3416	+	31.3416i	1.30477	+	1.30477i	0.925140	+	0.379627i	$0.123948\pi$
$577$	31.3416	+	31.3416i	1.30477	+	1.30477i	0.379627	+	0.925140i	$0.376052\pi$
$578$	14.9096	−	14.9096i	0.620158	−	0.620158i
$579$		0			0
$580$	6.12825	−	6.12825i	0.254462	−	0.254462i
$581$	−37.6615	−	26.5583i	−1.56246	−	1.10182i
$582$		0			0
$583$	5.84661	+	5.84661i	0.242142	+	0.242142i
$584$	−0.307664			−0.0127312
$585$		0			0
$586$		−	7.88864i		−	0.325877i
$587$	−3.36694	−	3.36694i	−0.138969	−	0.138969i	0.634200	−	0.773169i	$-0.281329\pi$
$587$	−3.36694	−	3.36694i	−0.138969	−	0.138969i	−0.773169	+	0.634200i	$0.781329\pi$
$588$		0			0
$589$		−	9.13586i		−	0.376436i
$590$	−0.906679	+	0.906679i	−0.0373274	+	0.0373274i
$591$		0			0
$592$	−6.21933	−	6.21933i	−0.255613	−	0.255613i
$593$	−10.6837	+	10.6837i	−0.438726	+	0.438726i	−0.891583	−	0.452857i	$-0.850405\pi$
$593$	−10.6837	+	10.6837i	−0.438726	+	0.438726i	0.452857	+	0.891583i	$0.350405\pi$
$594$		0			0
$595$	−23.1928	−	16.3552i	−0.950812	−	0.670497i
$596$	18.3684	+	18.3684i	0.752397	+	0.752397i
$597$		0			0
$598$	−5.90430	−	6.96635i	−0.241445	−	0.284875i
$599$	12.8437			0.524778			0.262389	−	0.964962i	$-0.415490\pi$
$599$	12.8437			0.524778			0.262389	+	0.964962i	$0.415490\pi$
$600$		0			0
$601$			19.5732i			0.798409i	0.916862	+	0.399205i	$0.130714\pi$
$601$			19.5732i			0.798409i	−0.916862	+	0.399205i	$0.869286\pi$
$602$	10.6762	+	7.52865i	0.435128	+	0.306845i
$603$		0			0
$604$	−10.2873	+	10.2873i	−0.418583	+	0.418583i
$605$	−10.6187	+	10.6187i	−0.431710	+	0.431710i
$606$		0			0
$607$		−	41.9804i		−	1.70393i	−0.523598	−	0.851965i	$-0.675411\pi$
$607$		−	41.9804i		−	1.70393i	0.523598	−	0.851965i	$-0.324589\pi$
$608$	−27.5354			−1.11671
$609$		0			0
$610$		−	5.91493i		−	0.239488i
$611$	9.81137	−	8.31559i	0.396926	−	0.336413i
$612$		0			0
$613$	20.4993	−	20.4993i	0.827959	−	0.827959i	−0.159276	−	0.987234i	$-0.550916\pi$
$613$	20.4993	−	20.4993i	0.827959	−	0.827959i	0.987234	+	0.159276i	$0.0509158\pi$
$614$			6.56236i			0.264835i
$615$		0			0
$616$	0.797125	+	4.61048i	0.0321171	+	0.185762i
$617$	−8.21440	+	8.21440i	−0.330699	+	0.330699i	−0.852852	−	0.522153i	$-0.825129\pi$
$617$	−8.21440	+	8.21440i	−0.330699	+	0.330699i	0.522153	+	0.852852i	$0.325129\pi$
$618$		0			0
$619$	26.6973	−	26.6973i	1.07306	−	1.07306i	0.0759445	−	0.997112i	$-0.475803\pi$
$619$	26.6973	−	26.6973i	1.07306	−	1.07306i	0.997112	−	0.0759445i	$-0.0241972\pi$
$620$	−4.39612			−0.176553
$621$		0			0
$622$	13.0910	−	13.0910i	0.524900	−	0.524900i
$623$	14.8574	−	21.0689i	0.595251	−	0.844107i
$624$		0			0
$625$	2.42311			0.0969246
$626$	−7.95367	−	7.95367i	−0.317893	−	0.317893i
$627$		0			0
$628$	−16.2451			−0.648251
$629$	21.1934	+	21.1934i	0.845036	+	0.845036i
$630$		0			0
$631$	5.13093	+	5.13093i	0.204259	+	0.204259i	0.801822	−	0.597563i	$-0.203864\pi$
$631$	5.13093	+	5.13093i	0.204259	+	0.204259i	−0.597563	+	0.801822i	$0.703864\pi$
$632$	−7.10791	−	7.10791i	−0.282737	−	0.282737i
$633$		0			0
$634$		−	6.54420i		−	0.259903i
$635$	1.59903	−	1.59903i	0.0634554	−	0.0634554i
$636$		0			0
$637$	−24.3901	+	6.49019i	−0.966371	+	0.257151i
$638$	1.70545			0.0675193
$639$		0			0
$640$			16.8382i			0.665586i
$641$		−	16.3357i		−	0.645220i	−0.946532	−	0.322610i	$-0.895440\pi$
$641$		−	16.3357i		−	0.645220i	0.946532	−	0.322610i	$-0.104560\pi$
$642$		0			0
$643$	28.1910	+	28.1910i	1.11175	+	1.11175i	0.992914	+	0.118832i	$0.0379150\pi$
$643$	28.1910	+	28.1910i	1.11175	+	1.11175i	0.118832	+	0.992914i	$0.462085\pi$
$644$	−19.4060	+	3.35517i	−0.764702	+	0.132212i
$645$		0			0
$646$	21.2833			0.837380
$647$	−11.1139			−0.436932			−0.218466	−	0.975845i	$-0.570105\pi$
$647$	−11.1139			−0.436932			−0.218466	+	0.975845i	$0.570105\pi$
$648$		0			0
$649$	1.30105			0.0510709
$650$	3.81220	+	4.49793i	0.149527	+	0.176423i
$651$		0			0
$652$	9.06793	−	9.06793i	0.355127	−	0.355127i
$653$	−4.95651			−0.193963			−0.0969816	−	0.995286i	$-0.530919\pi$
$653$	−4.95651			−0.193963			−0.0969816	+	0.995286i	$0.530919\pi$
$654$		0			0
$655$	−5.48612	+	5.48612i	−0.214360	+	0.214360i
$656$	2.65745	+	2.65745i	0.103756	+	0.103756i
$657$		0			0
$658$	0.916430	+	5.30053i	0.0357262	+	0.206636i
$659$	−26.1514			−1.01871			−0.509357	−	0.860555i	$-0.670117\pi$
$659$	−26.1514			−1.01871			−0.509357	+	0.860555i	$0.670117\pi$
$660$		0			0
$661$	−22.2906	+	22.2906i	−0.867006	+	0.867006i	−0.992140	−	0.125134i	$-0.960064\pi$
$661$	−22.2906	+	22.2906i	−0.867006	+	0.867006i	0.125134	+	0.992140i	$0.460064\pi$
$662$			0.649738i			0.0252528i
$663$		0			0
$664$		−	36.4861i		−	1.41594i
$665$	−3.34373	−	19.3398i	−0.129664	−	0.749964i
$666$		0			0
$667$			15.7489i			0.609801i
$668$	−14.9225	−	14.9225i	−0.577368	−	0.577368i
$669$		0			0
$670$	−7.29562	+	7.29562i	−0.281854	+	0.281854i
$671$	−4.24387	+	4.24387i	−0.163833	+	0.163833i
$672$		0			0
$673$		−	1.38550i		−	0.0534072i	−0.999643	−	0.0267036i	$-0.991499\pi$
$673$		−	1.38550i		−	0.0534072i	0.999643	−	0.0267036i	$-0.00850104\pi$
$674$	−10.7230	−	10.7230i	−0.413034	−	0.413034i
$675$		0			0
$676$	−3.56959	+	21.4821i	−0.137292	+	0.826237i
$677$			14.1868i			0.545242i	0.962122	+	0.272621i	$0.0878905\pi$
$677$			14.1868i			0.545242i	−0.962122	+	0.272621i	$0.912110\pi$
$678$		0			0
$679$	−18.5247	−	13.0633i	−0.710912	−	0.501324i
$680$		−	22.4690i		−	0.861646i
$681$		0			0
$682$	−0.611704	−	0.611704i	−0.0234234	−	0.0234234i
$683$	−27.2882	−	27.2882i	−1.04415	−	1.04415i	−0.998979	−	0.0451754i	$-0.985615\pi$
$683$	−27.2882	−	27.2882i	−1.04415	−	1.04415i	−0.0451754	−	0.998979i	$-0.514385\pi$
$684$		0			0
$685$			26.2506i			1.00298i
$686$	2.83387	−	10.1685i	0.108198	−	0.388237i
$687$		0			0
$688$		−	18.6801i		−	0.712170i
$689$	−35.1926	−	2.90399i	−1.34073	−	0.110633i
$690$		0			0
$691$	16.1937	+	16.1937i	0.616037	+	0.616037i	0.944513	−	0.328475i	$-0.106535\pi$
$691$	16.1937	+	16.1937i	0.616037	+	0.616037i	−0.328475	+	0.944513i	$0.606535\pi$
$692$		−	11.9862i		−	0.455647i
$693$		0			0
$694$	8.14411	−	8.14411i	0.309146	−	0.309146i
$695$	−7.17148	+	7.17148i	−0.272030	+	0.272030i
$696$		0			0
$697$	−9.05571	−	9.05571i	−0.343009	−	0.343009i
$698$			1.86570i			0.0706180i
$699$		0			0
$700$	12.5298	−	2.16632i	0.473580	−	0.0818792i
$701$		−	15.2981i		−	0.577800i	−0.957359	−	0.288900i	$-0.906711\pi$
$701$		−	15.2981i		−	0.577800i	0.957359	−	0.288900i	$-0.0932895\pi$
$702$		0			0
$703$			20.7280i			0.781771i
$704$	0.730841	−	0.730841i	0.0275446	−	0.0275446i
$705$		0			0
$706$	8.65808			0.325851
$707$	−33.5547	+	5.80141i	−1.26196	+	0.218185i
$708$		0			0
$709$	−2.74107	−	2.74107i	−0.102943	−	0.102943i	0.653759	−	0.756703i	$-0.273191\pi$
$709$	−2.74107	−	2.74107i	−0.102943	−	0.102943i	−0.756703	+	0.653759i	$0.773191\pi$
$710$	−1.21979	+	1.21979i	−0.0457778	+	0.0457778i
$711$		0			0
$712$	20.4113			0.764948
$713$	5.64878	−	5.64878i	0.211548	−	0.211548i
$714$		0			0
$715$	−0.365420	+	4.42842i	−0.0136659	+	0.165614i
$716$	−23.1368			−0.864663
$717$		0			0
$718$	13.6810			0.510571
$719$	5.99456			0.223559			0.111780	−	0.993733i	$-0.464345\pi$
$719$	5.99456			0.223559			0.111780	+	0.993733i	$0.464345\pi$
$720$		0			0
$721$	−15.9439	+	2.75661i	−0.593782	+	0.102661i
$722$	2.75035	+	2.75035i	0.102358	+	0.102358i
$723$		0			0
$724$		−	7.63947i		−	0.283919i
$725$		−	10.1685i		−	0.377650i
$726$		0			0
$727$	14.6184			0.542168			0.271084	−	0.962556i	$-0.412618\pi$
$727$	14.6184			0.542168			0.271084	+	0.962556i	$0.412618\pi$
$728$	−15.3280	−	12.8199i	−0.568093	−	0.475136i
$729$		0			0
$730$	0.0864119	−	0.0864119i	0.00319825	−	0.00319825i
$731$			63.6554i			2.35438i
$732$		0			0
$733$	−28.0685	−	28.0685i	−1.03673	−	1.03673i	−0.999299	−	0.0374350i	$-0.988081\pi$
$733$	−28.0685	−	28.0685i	−1.03673	−	1.03673i	−0.0374350	−	0.999299i	$-0.511919\pi$
$734$	3.94881	+	3.94881i	0.145753	+	0.145753i
$735$		0			0
$736$	−17.0254	−	17.0254i	−0.627564	−	0.627564i
$737$	10.4690			0.385630
$738$		0			0
$739$	−16.6028	−	16.6028i	−0.610746	−	0.610746i	0.332395	−	0.943140i	$-0.392143\pi$
$739$	−16.6028	−	16.6028i	−0.610746	−	0.610746i	−0.943140	+	0.332395i	$0.892143\pi$
$740$	9.97420			0.366659
$741$		0			0
$742$	8.51151	−	12.0699i	0.312467	−	0.443101i
$743$	2.87636	−	2.87636i	0.105523	−	0.105523i	−0.652374	−	0.757897i	$-0.726227\pi$
$743$	2.87636	−	2.87636i	0.105523	−	0.105523i	0.757897	+	0.652374i	$0.226227\pi$
$744$		0			0
$745$	−22.6371			−0.829361
$746$	−2.40502	+	2.40502i	−0.0880539	+	0.0880539i
$747$		0			0
$748$	−7.34804	+	7.34804i	−0.268671	+	0.268671i
$749$	−23.1223	+	3.99771i	−0.844871	+	0.146073i
$750$		0			0
$751$			45.9438i			1.67651i	0.545275	+	0.838257i	$0.316425\pi$
$751$			45.9438i			1.67651i	−0.545275	+	0.838257i	$0.683575\pi$
$752$	5.43890	−	5.43890i	0.198336	−	0.198336i
$753$		0			0
$754$	−5.55636	+	4.70927i	−0.202351	+	0.171501i
$755$		−	12.6780i		−	0.461400i
$756$		0			0
$757$	−24.7889			−0.900969			−0.450484	−	0.892784i	$-0.648749\pi$
$757$	−24.7889			−0.900969			−0.450484	+	0.892784i	$0.648749\pi$
$758$		−	1.72592i		−	0.0626881i
$759$		0			0
$760$	10.9878	−	10.9878i	0.398569	−	0.398569i
$761$	−10.8450	+	10.8450i	−0.393133	+	0.393133i	−0.875802	−	0.482670i	$-0.839667\pi$
$761$	−10.8450	+	10.8450i	−0.393133	+	0.393133i	0.482670	+	0.875802i	$0.339667\pi$
$762$		0			0
$763$	−9.91256	+	14.0567i	−0.358859	+	0.508887i
$764$		−	6.20711i		−	0.224565i
$765$		0			0
$766$	−2.34687			−0.0847958
$767$	−4.23884	+	3.59261i	−0.153056	+	0.129722i
$768$		0			0
$769$	−4.63670	−	4.63670i	−0.167204	−	0.167204i	0.618545	−	0.785749i	$-0.287722\pi$
$769$	−4.63670	−	4.63670i	−0.167204	−	0.167204i	−0.785749	+	0.618545i	$0.787722\pi$
$770$	−1.51881	−	1.07104i	−0.0547340	−	0.0385975i
$771$		0			0
$772$	28.5623	−	28.5623i	1.02798	−	1.02798i
$773$	5.68398	+	5.68398i	0.204438	+	0.204438i	0.801899	−	0.597460i	$-0.203823\pi$
$773$	5.68398	+	5.68398i	0.204438	+	0.204438i	−0.597460	+	0.801899i	$0.703823\pi$
$774$		0			0
$775$	−3.64722	+	3.64722i	−0.131012	+	0.131012i
$776$		−	17.9466i		−	0.644244i
$777$		0			0
$778$	7.03032	+	7.03032i	0.252049	+	0.252049i
$779$		−	8.85685i		−	0.317330i
$780$		0			0
$781$	1.75035			0.0626326
$782$	13.1596	+	13.1596i	0.470588	+	0.470588i
$783$		0			0
$784$	−14.2181	+	5.06793i	−0.507788	+	0.180997i
$785$	10.0102	−	10.0102i	0.357281	−	0.357281i
$786$		0			0
$787$	−8.65662	+	8.65662i	−0.308575	+	0.308575i	−0.844357	−	0.535781i	$-0.820017\pi$
$787$	−8.65662	+	8.65662i	−0.308575	+	0.308575i	0.535781	+	0.844357i	$0.320017\pi$
$788$	13.4314	+	13.4314i	0.478473	+	0.478473i
$789$		0			0
$790$	3.99272			0.142055
$791$	−4.19009	+	0.724442i	−0.148983	+	0.0257582i
$792$		0			0
$793$	2.10791	−	25.5452i	0.0748541	−	0.907135i
$794$		−	8.21136i		−	0.291410i
$795$		0			0
$796$		−	7.66469i		−	0.271668i
$797$	28.1163			0.995931			0.497966	−	0.867197i	$-0.334081\pi$
$797$	28.1163			0.995931			0.497966	+	0.867197i	$0.334081\pi$
$798$		0			0
$799$	−18.5340	+	18.5340i	−0.655685	+	0.655685i
$800$	10.9927	+	10.9927i	0.388651	+	0.388651i
$801$		0			0
$802$	−12.5705			−0.443881
$803$	−0.123998			−0.00437580
$804$		0			0
$805$	9.89048	−	14.0254i	0.348594	−	0.494330i
$806$	3.68204	+	0.303831i	0.129694	+	0.0107020i
$807$		0			0
$808$	−19.0639	−	19.0639i	−0.670667	−	0.670667i
$809$	−0.687350			−0.0241659			−0.0120830	−	0.999927i	$-0.503846\pi$
$809$	−0.687350			−0.0241659			−0.0120830	+	0.999927i	$0.503846\pi$
$810$		0			0
$811$	−0.354016	−	0.354016i	−0.0124312	−	0.0124312i	0.700864	−	0.713295i	$-0.252798\pi$
$811$	−0.354016	−	0.354016i	−0.0124312	−	0.0124312i	−0.713295	+	0.700864i	$0.752798\pi$
$812$	2.67608	+	15.4782i	0.0939122	+	0.543178i
$813$		0			0
$814$	1.38787	+	1.38787i	0.0486449	+	0.0486449i
$815$			11.1753i			0.391454i
$816$		0			0
$817$	−31.1288	+	31.1288i	−1.08906	+	1.08906i
$818$	1.45028			0.0507078
$819$		0			0
$820$	−4.26187			−0.148831
$821$	−20.8773	+	20.8773i	−0.728623	+	0.728623i	−0.970346	−	0.241722i	$-0.922288\pi$
$821$	−20.8773	+	20.8773i	−0.728623	+	0.728623i	0.241722	+	0.970346i	$0.422288\pi$
$822$		0			0
$823$		−	10.3611i		−	0.361164i	−0.983560	−	0.180582i	$-0.942202\pi$
$823$		−	10.3611i		−	0.361164i	0.983560	−	0.180582i	$-0.0577981\pi$
$824$	−9.05845	−	9.05845i	−0.315566	−	0.315566i
$825$		0			0
$826$	−0.395928	−	2.29001i	−0.0137761	−	0.0796795i
$827$	−33.3235	−	33.3235i	−1.15877	−	1.15877i	−0.984740	−	0.174030i	$-0.944321\pi$
$827$	−33.3235	−	33.3235i	−1.15877	−	1.15877i	−0.174030	−	0.984740i	$-0.555679\pi$
$828$		0			0
$829$	−19.8647			−0.689929			−0.344964	−	0.938616i	$-0.612109\pi$
$829$	−19.8647			−0.689929			−0.344964	+	0.938616i	$0.612109\pi$
$830$	10.2477	+	10.2477i	0.355702	+	0.355702i
$831$		0			0
$832$	−0.363005	+	4.39916i	−0.0125849	+	0.152513i
$833$	48.4504	−	17.2698i	1.67871	−	0.598364i
$834$		0			0
$835$	18.3904			0.636427
$836$	−7.18668			−0.248556
$837$		0			0
$838$	6.65262	+	6.65262i	0.229811	+	0.229811i
$839$	16.2048	−	16.2048i	0.559453	−	0.559453i	−0.369698	−	0.929152i	$-0.620539\pi$
$839$	16.2048	−	16.2048i	0.559453	−	0.559453i	0.929152	+	0.369698i	$0.120539\pi$
$840$		0			0
$841$	−16.4387			−0.566850
$842$			6.87969i			0.237090i
$843$		0			0
$844$		−	0.995075i		−	0.0342519i
$845$	−11.0377	−	15.4369i	−0.379709	−	0.531044i
$846$		0			0
$847$	−4.63695	−	26.8196i	−0.159328	−	0.921533i
$848$	−21.1187			−0.725220
$849$		0			0
$850$	−8.49672	−	8.49672i	−0.291435	−	0.291435i
$851$	−12.8163	+	12.8163i	−0.439337	+	0.439337i
$852$		0			0
$853$	−12.4778	+	12.4778i	−0.427232	+	0.427232i	−0.887684	−	0.460452i	$-0.847687\pi$
$853$	−12.4778	+	12.4778i	−0.427232	+	0.427232i	0.460452	+	0.887684i	$0.347687\pi$
$854$	8.76116	+	6.17823i	0.299801	+	0.211415i
$855$		0			0
$856$	−13.1368	−	13.1368i	−0.449007	−	0.449007i
$857$	−27.2501			−0.930845			−0.465422	−	0.885089i	$-0.654098\pi$
$857$	−27.2501			−0.930845			−0.465422	+	0.885089i	$0.654098\pi$
$858$		0			0
$859$			22.7834i			0.777361i	0.921373	+	0.388680i	$0.127069\pi$
$859$			22.7834i			0.777361i	−0.921373	+	0.388680i	$0.872931\pi$
$860$	14.9790	+	14.9790i	0.510779	+	0.510779i
$861$		0			0
$862$			19.5125i			0.664597i
$863$	21.1187	−	21.1187i	0.718889	−	0.718889i	−0.249488	−	0.968378i	$-0.580262\pi$
$863$	21.1187	−	21.1187i	0.718889	−	0.718889i	0.968378	+	0.249488i	$0.0802624\pi$
$864$		0			0
$865$	7.38589	+	7.38589i	0.251128	+	0.251128i
$866$	−14.4571	+	14.4571i	−0.491271	+	0.491271i
$867$		0			0
$868$	4.59181	−	6.51151i	0.155856	−	0.221015i
$869$	−2.86471	−	2.86471i	−0.0971787	−	0.0971787i
$870$		0			0
$871$	−34.1080	+	28.9081i	−1.15570	+	0.979513i
$872$	−13.6180			−0.461164
$873$		0			0
$874$			12.8707i			0.435356i
$875$	−17.5149	+	24.8373i	−0.592111	+	0.839655i
$876$		0			0
$877$	14.0455	−	14.0455i	0.474282	−	0.474282i	−0.429015	−	0.903297i	$-0.641139\pi$
$877$	14.0455	−	14.0455i	0.474282	−	0.474282i	0.903297	+	0.429015i	$0.141139\pi$
$878$	4.24387	−	4.24387i	0.143224	−	0.143224i
$879$		0			0
$880$			2.65745i			0.0895827i
$881$	13.3800			0.450782			0.225391	−	0.974268i	$-0.427634\pi$
$881$	13.3800			0.450782			0.225391	+	0.974268i	$0.427634\pi$
$882$		0			0
$883$		−	1.63893i		−	0.0551545i	−0.999620	−	0.0275773i	$-0.991221\pi$
$883$		−	1.63893i		−	0.0551545i	0.999620	−	0.0275773i	$-0.00877923\pi$
$884$	3.64974	−	44.2301i	0.122754	−	1.48762i
$885$		0			0
$886$	−5.18370	+	5.18370i	−0.174150	+	0.174150i
$887$			21.4198i			0.719206i	0.933105	+	0.359603i	$0.117088\pi$
$887$			21.4198i			0.719206i	−0.933105	+	0.359603i	$0.882912\pi$
$888$		0			0
$889$	0.698263	+	4.03868i	0.0234190	+	0.135453i
$890$	−5.73283	+	5.73283i	−0.192165	+	0.192165i
$891$		0			0
$892$	−4.78691	+	4.78691i	−0.160278	+	0.160278i
$893$	−18.1270			−0.606596
$894$		0			0
$895$	14.2569	−	14.2569i	0.476555	−	0.476555i
$896$	−24.9406	−	17.5877i	−0.833206	−	0.587563i
$897$		0			0
$898$	−7.77907			−0.259591
$899$	−4.50546	−	4.50546i	−0.150266	−	0.150266i
$900$		0			0
$901$	71.9655			2.39752
$902$	−0.593023	−	0.593023i	−0.0197455	−	0.0197455i
$903$		0			0
$904$	−2.38058	−	2.38058i	−0.0791769	−	0.0791769i
$905$	4.70743	+	4.70743i	0.156480	+	0.156480i
$906$		0			0
$907$			2.59991i			0.0863285i	0.999068	+	0.0431643i	$0.0137439\pi$
$907$			2.59991i			0.0863285i	−0.999068	+	0.0431643i	$0.986256\pi$
$908$	−32.9280	+	32.9280i	−1.09275	+	1.09275i
$909$		0			0
$910$	7.90574	−	0.704447i	0.262073	−	0.0233522i
$911$	−41.2579			−1.36694			−0.683468	−	0.729981i	$-0.739529\pi$
$911$	−41.2579			−1.36694			−0.683468	+	0.729981i	$0.739529\pi$
$912$		0			0
$913$		−	14.7051i		−	0.486667i
$914$			17.8315i			0.589812i
$915$		0			0
$916$	−22.1218	−	22.1218i	−0.730924	−	0.730924i
$917$	−2.39568	−	13.8563i	−0.0791123	−	0.457577i
$918$		0			0
$919$	−48.3039			−1.59340			−0.796700	−	0.604375i	$-0.793423\pi$
$919$	−48.3039			−1.59340			−0.796700	+	0.604375i	$0.793423\pi$
$920$	13.5877			0.447972
$921$		0			0
$922$	−0.478014			−0.0157426
$923$	−5.70266	+	4.83327i	−0.187705	+	0.159089i
$924$		0			0
$925$	8.27504	−	8.27504i	0.272082	−	0.272082i
$926$	1.99175			0.0654530
$927$		0			0
$928$	−13.5794	+	13.5794i	−0.445767	+	0.445767i
$929$	−19.1804	−	19.1804i	−0.629289	−	0.629289i	0.318600	−	0.947889i	$-0.396787\pi$
$929$	−19.1804	−	19.1804i	−0.629289	−	0.629289i	−0.947889	+	0.318600i	$0.896787\pi$
$930$		0			0
$931$	32.1385	+	15.2479i	1.05330	+	0.499731i
$932$	27.1777			0.890237
$933$		0			0
$934$	5.39500	−	5.39500i	0.176530	−	0.176530i
$935$		−	9.05571i		−	0.296153i
$936$		0			0
$937$		−	2.66644i		−	0.0871088i	−0.999051	−	0.0435544i	$-0.986132\pi$
$937$		−	2.66644i		−	0.0871088i	0.999051	−	0.0435544i	$-0.0138682\pi$
$938$	−3.18585	−	18.4266i	−0.104022	−	0.601650i
$939$		0			0
$940$			8.72259i			0.284500i
$941$	31.9331	+	31.9331i	1.04099	+	1.04099i	0.999123	+	0.0418672i	$0.0133307\pi$
$941$	31.9331	+	31.9331i	1.04099	+	1.04099i	0.0418672	+	0.999123i	$0.486669\pi$
$942$		0			0
$943$	5.47626	−	5.47626i	0.178332	−	0.178332i
$944$	−2.34979	+	2.34979i	−0.0764791	+	0.0764791i
$945$		0			0
$946$			4.16854i			0.135531i
$947$	8.43041	+	8.43041i	0.273951	+	0.273951i	0.830689	−	0.556737i	$-0.187947\pi$
$947$	8.43041	+	8.43041i	0.273951	+	0.273951i	−0.556737	+	0.830689i	$0.687947\pi$
$948$		0			0
$949$	0.403987	−	0.342397i	0.0131140	−	0.0111147i
$950$		−	8.31014i		−	0.269616i
$951$		0			0
$952$	33.2809	+	23.4692i	1.07864	+	0.760640i
$953$		−	20.8846i		−	0.676519i	−0.941053	−	0.338259i	$-0.890162\pi$
$953$		−	20.8846i		−	0.676519i	0.941053	−	0.338259i	$-0.109838\pi$
$954$		0			0
$955$	3.82482	+	3.82482i	0.123768	+	0.123768i
$956$	1.41327	+	1.41327i	0.0457083	+	0.0457083i
$957$		0			0
$958$		−	7.14032i		−	0.230693i
$959$	−38.8823	−	27.4191i	−1.25557	−	0.885410i
$960$		0			0
$961$		−	27.7680i		−	0.895742i
$962$	−8.35404	−	0.689351i	−0.269345	−	0.0222256i
$963$		0			0
$964$	25.6239	+	25.6239i	0.825289	+	0.825289i
$965$			35.2001i			1.13313i
$966$		0			0
$967$	20.9628	−	20.9628i	0.674117	−	0.674117i	−0.284545	−	0.958663i	$-0.591843\pi$
$967$	20.9628	−	20.9628i	0.674117	−	0.674117i	0.958663	+	0.284545i	$0.0918426\pi$
$968$	15.2374	−	15.2374i	0.489749	−	0.489749i
$969$		0			0
$970$	5.04055	+	5.04055i	0.161842	+	0.161842i
$971$		−	12.7719i		−	0.409869i	−0.978776	−	0.204935i	$-0.934302\pi$
$971$		−	12.7719i		−	0.409869i	0.978776	−	0.204935i	$-0.0656982\pi$
$972$		0			0
$973$	−3.13164	−	18.1131i	−0.100396	−	0.580679i
$974$		−	14.4934i		−	0.464399i
$975$		0			0
$976$		−	15.3294i		−	0.490682i
$977$	27.8222	−	27.8222i	0.890110	−	0.890110i	−0.104423	−	0.994533i	$-0.533299\pi$
$977$	27.8222	−	27.8222i	0.890110	−	0.890110i	0.994533	+	0.104423i	$0.0332995\pi$
$978$		0			0
$979$	8.22642			0.262918
$980$	7.33722	−	15.4649i	0.234379	−	0.494007i
$981$		0			0
$982$	7.85685	+	7.85685i	0.250722	+	0.250722i
$983$	35.8970	−	35.8970i	1.14494	−	1.14494i	0.157402	−	0.987535i	$-0.449688\pi$
$983$	35.8970	−	35.8970i	1.14494	−	1.14494i	0.987535	−	0.157402i	$-0.0503119\pi$
$984$		0			0
$985$	−16.5528			−0.527416
$986$	10.4961	−	10.4961i	0.334264	−	0.334264i
$987$		0			0
$988$	23.4142	−	19.8446i	0.744906	−	0.631342i
$989$	−38.4944			−1.22405
$990$		0			0
$991$	−8.69418			−0.276180			−0.138090	−	0.990420i	$-0.544096\pi$
$991$	−8.69418			−0.276180			−0.138090	+	0.990420i	$0.544096\pi$
$992$	9.74126			0.309285
$993$		0			0
$994$	−0.532656	−	3.08082i	−0.0168948	−	0.0977178i
$995$	4.72298	+	4.72298i	0.149728	+	0.149728i
$996$		0			0
$997$		−	26.5673i		−	0.841394i	−0.907201	−	0.420697i	$-0.861786\pi$
$997$		−	26.5673i		−	0.841394i	0.907201	−	0.420697i	$-0.138214\pi$
$998$		−	8.23392i		−	0.260640i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.y.h.811.3		12
3.2	odd	2		91.2.i.a.83.3	yes	12
7.6	odd	2	inner	819.2.y.h.811.4		12
13.8	odd	4	inner	819.2.y.h.307.4		12
21.2	odd	6		637.2.bc.a.31.4		24
21.5	even	6		637.2.bc.a.31.3		24
21.11	odd	6		637.2.bc.a.460.3		24
21.17	even	6		637.2.bc.a.460.4		24
21.20	even	2		91.2.i.a.83.4	yes	12
39.8	even	4		91.2.i.a.34.3	✓	12
91.34	even	4	inner	819.2.y.h.307.3		12
273.47	odd	12		637.2.bc.a.619.3		24
273.86	even	12		637.2.bc.a.619.4		24
273.125	odd	4		91.2.i.a.34.4	yes	12
273.164	odd	12		637.2.bc.a.411.4		24
273.242	even	12		637.2.bc.a.411.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.i.a.34.3	✓	12	39.8	even	4
91.2.i.a.34.4	yes	12	273.125	odd	4
91.2.i.a.83.3	yes	12	3.2	odd	2
91.2.i.a.83.4	yes	12	21.20	even	2
637.2.bc.a.31.3		24	21.5	even	6
637.2.bc.a.31.4		24	21.2	odd	6
637.2.bc.a.411.3		24	273.242	even	12
637.2.bc.a.411.4		24	273.164	odd	12
637.2.bc.a.460.3		24	21.11	odd	6
637.2.bc.a.460.4		24	21.17	even	6
637.2.bc.a.619.3		24	273.47	odd	12
637.2.bc.a.619.4		24	273.86	even	12
819.2.y.h.307.3		12	91.34	even	4	inner
819.2.y.h.307.4		12	13.8	odd	4	inner
819.2.y.h.811.3		12	1.1	even	1	trivial
819.2.y.h.811.4		12	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.y (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.403032 - 0.403032i) q^{2} +1.67513i q^{4} +(-1.03221 - 1.03221i) q^{5} +(2.60707 - 0.450747i) q^{7} +(1.48119 + 1.48119i) q^{8} +O(q^{10})\)	\(q+(0.403032 - 0.403032i) q^{2} +1.67513i q^{4} +(-1.03221 - 1.03221i) q^{5} +(2.60707 - 0.450747i) q^{7} +(1.48119 + 1.48119i) q^{8} -0.832030 q^{10} +(0.596968 + 0.596968i) q^{11} +(-3.59334 - 0.296512i) q^{13} +(0.869067 - 1.23240i) q^{14} -2.15633 q^{16} +7.34804 q^{17} +(3.59334 + 3.59334i) q^{19} +(1.72909 - 1.72909i) q^{20} +0.481194 q^{22} +4.44358i q^{23} -2.86907i q^{25} +(-1.56773 + 1.32873i) q^{26} +(0.755061 + 4.36719i) q^{28} +3.54420 q^{29} +(-1.27122 - 1.27122i) q^{31} +(-3.83146 + 3.83146i) q^{32} +(2.96149 - 2.96149i) q^{34} +(-3.15633 - 2.22579i) q^{35} +(2.88423 + 2.88423i) q^{37} +2.89646 q^{38} -3.05782i q^{40} +(-1.23240 - 1.23240i) q^{41} +8.66291i q^{43} +(-1.00000 + 1.00000i) q^{44} +(1.79090 + 1.79090i) q^{46} +(-2.52230 + 2.52230i) q^{47} +(6.59365 - 2.35026i) q^{49} +(-1.15633 - 1.15633i) q^{50} +(0.496696 - 6.01931i) q^{52} +9.79384 q^{53} -1.23240i q^{55} +(4.52923 + 3.19394i) q^{56} +(1.42842 - 1.42842i) q^{58} +(1.08972 - 1.08972i) q^{59} +7.10903i q^{61} -1.02469 q^{62} -1.22425i q^{64} +(3.40303 + 4.01516i) q^{65} +(8.76845 - 8.76845i) q^{67} +12.3089i q^{68} +(-2.16916 + 0.375035i) q^{70} +(1.46604 - 1.46604i) q^{71} +(-0.103857 + 0.103857i) q^{73} +2.32487 q^{74} +(-6.01931 + 6.01931i) q^{76} +(1.82542 + 1.28726i) q^{77} -4.79877 q^{79} +(2.22579 + 2.22579i) q^{80} -0.993391 q^{82} +(-12.3165 - 12.3165i) q^{83} +(-7.58475 - 7.58475i) q^{85} +(3.49143 + 3.49143i) q^{86} +1.76845i q^{88} +(6.89017 - 6.89017i) q^{89} +(-9.50175 + 0.846661i) q^{91} -7.44358 q^{92} +2.03313i q^{94} -7.41819i q^{95} +(-6.05814 - 6.05814i) q^{97} +(1.71022 - 3.60468i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} - 8 q^{7} - 4 q^{8}+O(q^{10}) \) 12 * q + 4 * q^2 - 8 * q^7 - 4 * q^8	\( 12 q + 4 q^{2} - 8 q^{7} - 4 q^{8} + 8 q^{11} - 8 q^{14} + 16 q^{16} - 16 q^{22} - 20 q^{28} + 4 q^{29} + 16 q^{32} + 4 q^{35} + 12 q^{37} - 12 q^{44} + 24 q^{46} + 28 q^{50} + 12 q^{53} - 44 q^{58} + 40 q^{65} + 60 q^{67} + 4 q^{70} + 48 q^{74} - 4 q^{79} + 12 q^{85} - 36 q^{86} - 32 q^{91} - 24 q^{92} + 28 q^{98}+O(q^{100}) \) 12 * q + 4 * q^2 - 8 * q^7 - 4 * q^8 + 8 * q^11 - 8 * q^14 + 16 * q^16 - 16 * q^22 - 20 * q^28 + 4 * q^29 + 16 * q^32 + 4 * q^35 + 12 * q^37 - 12 * q^44 + 24 * q^46 + 28 * q^50 + 12 * q^53 - 44 * q^58 + 40 * q^65 + 60 * q^67 + 4 * q^70 + 48 * q^74 - 4 * q^79 + 12 * q^85 - 36 * q^86 - 32 * q^91 - 24 * q^92 + 28 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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