LMFDB - Embedded newform 819.2.y.h.307.1

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			307.1
Root			$1.33026 + 1.33026i$ of defining polynomial
Character	$\chi$	$=$	819.307
Dual form			819.2.y.h.811.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.854638 - 0.854638i) q^{2} -0.539189i q^{4} +(-0.612999 + 0.612999i) q^{5} +(-2.64571 - 0.0148122i) q^{7} +(-2.17009 + 2.17009i) q^{8} +O(q^{10})$	\(q+(-0.854638 - 0.854638i) q^{2} -0.539189i q^{4} +(-0.612999 + 0.612999i) q^{5} +(-2.64571 - 0.0148122i) q^{7} +(-2.17009 + 2.17009i) q^{8} +1.04778 q^{10} +(1.85464 - 1.85464i) q^{11} +(0.104263 - 3.60404i) q^{13} +(2.24846 + 2.27378i) q^{14} +2.63090 q^{16} -3.04726 q^{17} +(-0.104263 + 0.104263i) q^{19} +(0.330522 + 0.330522i) q^{20} -3.17009 q^{22} +6.51026i q^{23} +4.24846i q^{25} +(-3.16926 + 2.99104i) q^{26} +(-0.00798659 + 1.42654i) q^{28} +3.78765 q^{29} +(-6.77330 + 6.77330i) q^{31} +(2.09171 + 2.09171i) q^{32} +(2.60430 + 2.60430i) q^{34} +(1.63090 - 1.61274i) q^{35} +(-2.02472 + 2.02472i) q^{37} +0.178214 q^{38} -2.66052i q^{40} +(-2.27378 + 2.27378i) q^{41} +3.18342i q^{43} +(-1.00000 - 1.00000i) q^{44} +(5.56391 - 5.56391i) q^{46} +(5.21678 + 5.21678i) q^{47} +(6.99956 + 0.0783777i) q^{49} +(3.63090 - 3.63090i) q^{50} +(-1.94326 - 0.0562174i) q^{52} -3.43188 q^{53} +2.27378i q^{55} +(5.77356 - 5.70928i) q^{56} +(-3.23707 - 3.23707i) q^{58} +(-9.15135 - 9.15135i) q^{59} +9.20756i q^{61} +11.5774 q^{62} -8.83710i q^{64} +(2.14536 + 2.27319i) q^{65} +(-1.04945 - 1.04945i) q^{67} +1.64305i q^{68} +(-2.77213 - 0.0155200i) q^{70} +(4.10310 + 4.10310i) q^{71} +(-6.92561 - 6.92561i) q^{73} +3.46081 q^{74} +(0.0562174 + 0.0562174i) q^{76} +(-4.93430 + 4.87936i) q^{77} +17.5958 q^{79} +(-1.61274 + 1.61274i) q^{80} +3.88652 q^{82} +(-10.5474 + 10.5474i) q^{83} +(1.86797 - 1.86797i) q^{85} +(2.72067 - 2.72067i) q^{86} +8.04945i q^{88} +(3.39552 + 3.39552i) q^{89} +(-0.329233 + 9.53371i) q^{91} +3.51026 q^{92} -8.91692i q^{94} -0.127826i q^{95} +(-4.44330 + 4.44330i) q^{97} +(-5.91510 - 6.04907i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.854638	−	0.854638i	−0.604320	−	0.604320i	0.337136	−	0.941456i	$-0.390542\pi$
$2$	−0.854638	−	0.854638i	−0.604320	−	0.604320i	−0.941456	+	0.337136i	$0.890542\pi$
$3$		0			0
$3$		0			0
$4$		−	0.539189i		−	0.269594i
$5$	−0.612999	+	0.612999i	−0.274142	+	0.274142i	−0.830765	−	0.556623i	$-0.812097\pi$
$5$	−0.612999	+	0.612999i	−0.274142	+	0.274142i	0.556623	+	0.830765i	$0.312097\pi$
$6$		0			0
$7$	−2.64571	−	0.0148122i	−0.999984	−	0.00559850i
$7$	−2.64571	−	0.0148122i	−0.999984	−	0.00559850i
$8$	−2.17009	+	2.17009i	−0.767241	+	0.767241i
$9$		0			0
$10$	1.04778			0.331338
$11$	1.85464	−	1.85464i	0.559194	−	0.559194i	−0.369884	−	0.929078i	$-0.620602\pi$
$11$	1.85464	−	1.85464i	0.559194	−	0.559194i	0.929078	+	0.369884i	$0.120602\pi$
$12$		0			0
$13$	0.104263	−	3.60404i	0.0289173	−	0.999582i
$13$	0.104263	−	3.60404i	0.0289173	−	0.999582i
$14$	2.24846	+	2.27378i	0.600927	+	0.607694i
$15$		0			0
$16$	2.63090			0.657724
$17$	−3.04726			−0.739070			−0.369535	−	0.929217i	$-0.620483\pi$
$17$	−3.04726			−0.739070			−0.369535	+	0.929217i	$0.620483\pi$
$18$		0			0
$19$	−0.104263	+	0.104263i	−0.0239195	+	0.0239195i	−0.718965	−	0.695046i	$-0.755384\pi$
$19$	−0.104263	+	0.104263i	−0.0239195	+	0.0239195i	0.695046	+	0.718965i	$0.255384\pi$
$20$	0.330522	+	0.330522i	0.0739070	+	0.0739070i
$21$		0			0
$22$	−3.17009			−0.675865
$23$			6.51026i			1.35748i	0.734377	+	0.678741i	$0.237474\pi$
$23$			6.51026i			1.35748i	−0.734377	+	0.678741i	$0.762526\pi$
$24$		0			0
$25$			4.24846i			0.849693i
$26$	−3.16926	+	2.99104i	−0.621543	+	0.586592i
$27$		0			0
$28$	−0.00798659	+	1.42654i	−0.00150932	+	0.269590i
$29$	3.78765			0.703350			0.351675	−	0.936122i	$-0.385612\pi$
$29$	3.78765			0.703350			0.351675	+	0.936122i	$0.385612\pi$
$30$		0			0
$31$	−6.77330	+	6.77330i	−1.21652	+	1.21652i	−0.247679	+	0.968842i	$0.579668\pi$
$31$	−6.77330	+	6.77330i	−1.21652	+	1.21652i	−0.968842	+	0.247679i	$0.920332\pi$
$32$	2.09171	+	2.09171i	0.369765	+	0.369765i
$33$		0			0
$34$	2.60430	+	2.60430i	0.446635	+	0.446635i
$35$	1.63090	−	1.61274i	0.275672	−	0.272602i
$36$		0			0
$37$	−2.02472	+	2.02472i	−0.332863	+	0.332863i	−0.853673	−	0.520810i	$-0.825630\pi$
$37$	−2.02472	+	2.02472i	−0.332863	+	0.332863i	0.520810	+	0.853673i	$0.325630\pi$
$38$	0.178214			0.0289101
$39$		0			0
$40$		−	2.66052i		−	0.420665i
$41$	−2.27378	+	2.27378i	−0.355105	+	0.355105i	−0.862005	−	0.506900i	$-0.830791\pi$
$41$	−2.27378	+	2.27378i	−0.355105	+	0.355105i	0.506900	+	0.862005i	$0.330791\pi$
$42$		0			0
$43$			3.18342i			0.485467i	0.970093	+	0.242733i	$0.0780440\pi$
$43$			3.18342i			0.485467i	−0.970093	+	0.242733i	$0.921956\pi$
$44$	−1.00000	−	1.00000i	−0.150756	−	0.150756i
$45$		0			0
$46$	5.56391	−	5.56391i	0.820354	−	0.820354i
$47$	5.21678	+	5.21678i	0.760946	+	0.760946i	0.976493	−	0.215548i	$-0.0691536\pi$
$47$	5.21678	+	5.21678i	0.760946	+	0.760946i	−0.215548	+	0.976493i	$0.569154\pi$
$48$		0			0
$49$	6.99956	+	0.0783777i	0.999937	+	0.0111968i
$50$	3.63090	−	3.63090i	0.513486	−	0.513486i
$51$		0			0
$52$	−1.94326	−	0.0562174i	−0.269482	−	0.00779595i
$53$	−3.43188			−0.471405			−0.235703	−	0.971825i	$-0.575739\pi$
$53$	−3.43188			−0.471405			−0.235703	+	0.971825i	$0.575739\pi$
$54$		0			0
$55$			2.27378i			0.306597i
$56$	5.77356	−	5.70928i	0.771525	−	0.762934i
$57$		0			0
$58$	−3.23707	−	3.23707i	−0.425048	−	0.425048i
$59$	−9.15135	−	9.15135i	−1.19140	−	1.19140i	−0.976673	−	0.214731i	$-0.931113\pi$
$59$	−9.15135	−	9.15135i	−1.19140	−	1.19140i	−0.214731	−	0.976673i	$-0.568887\pi$
$60$		0			0
$61$			9.20756i			1.17891i	0.807802	+	0.589454i	$0.200657\pi$
$61$			9.20756i			1.17891i	−0.807802	+	0.589454i	$0.799343\pi$
$62$	11.5774			1.47034
$63$		0			0
$64$		−	8.83710i		−	1.10464i
$65$	2.14536	+	2.27319i	0.266099	+	0.281954i
$66$		0			0
$67$	−1.04945	−	1.04945i	−0.128211	−	0.128211i	0.640090	−	0.768300i	$-0.278897\pi$
$67$	−1.04945	−	1.04945i	−0.128211	−	0.128211i	−0.768300	+	0.640090i	$0.778897\pi$
$68$			1.64305i			0.199249i
$69$		0			0
$70$	−2.77213	−	0.0155200i	−0.331333	−	0.00185500i
$71$	4.10310	+	4.10310i	0.486949	+	0.486949i	0.907342	−	0.420393i	$-0.138108\pi$
$71$	4.10310	+	4.10310i	0.486949	+	0.486949i	−0.420393	+	0.907342i	$0.638108\pi$
$72$		0			0
$73$	−6.92561	−	6.92561i	−0.810581	−	0.810581i	0.174140	−	0.984721i	$-0.444286\pi$
$73$	−6.92561	−	6.92561i	−0.810581	−	0.810581i	−0.984721	+	0.174140i	$0.944286\pi$
$74$	3.46081			0.402311
$75$		0			0
$76$	0.0562174	+	0.0562174i	0.00644858	+	0.00644858i
$77$	−4.93430	+	4.87936i	−0.562316	+	0.556055i
$78$		0			0
$79$	17.5958			1.97968			0.989842	−	0.142168i	$-0.0454074\pi$
$79$	17.5958			1.97968			0.989842	+	0.142168i	$0.0454074\pi$
$80$	−1.61274	+	1.61274i	−0.180310	+	0.180310i
$81$		0			0
$82$	3.88652			0.429194
$83$	−10.5474	+	10.5474i	−1.15773	+	1.15773i	−0.172763	+	0.984963i	$0.555269\pi$
$83$	−10.5474	+	10.5474i	−1.15773	+	1.15773i	−0.984963	+	0.172763i	$0.944731\pi$
$84$		0			0
$85$	1.86797	−	1.86797i	0.202610	−	0.202610i
$86$	2.72067	−	2.72067i	0.293377	−	0.293377i
$87$		0			0
$88$			8.04945i			0.858074i
$89$	3.39552	+	3.39552i	0.359924	+	0.359924i	0.863785	−	0.503861i	$-0.168088\pi$
$89$	3.39552	+	3.39552i	0.359924	+	0.359924i	−0.503861	+	0.863785i	$0.668088\pi$
$90$		0			0
$91$	−0.329233	+	9.53371i	−0.0345130	+	0.999404i
$92$	3.51026			0.365970
$93$		0			0
$94$		−	8.91692i		−	0.919710i
$95$		−	0.127826i		−	0.0131147i
$96$		0			0
$97$	−4.44330	+	4.44330i	−0.451149	+	0.451149i	−0.895736	−	0.444587i	$-0.853351\pi$
$97$	−4.44330	+	4.44330i	−0.451149	+	0.451149i	0.444587	+	0.895736i	$0.353351\pi$
$98$	−5.91510	−	6.04907i	−0.597516	−	0.611049i
$99$		0			0
$100$	2.29072			0.229072
$101$	1.16022			0.115446			0.0577231	−	0.998333i	$-0.481616\pi$
$101$	1.16022			0.115446			0.0577231	+	0.998333i	$0.481616\pi$
$102$		0			0
$103$	5.32104			0.524298			0.262149	−	0.965027i	$-0.415569\pi$
$103$	5.32104			0.524298			0.262149	+	0.965027i	$0.415569\pi$
$104$	7.59483	+	8.04735i	0.744734	+	0.789107i
$105$		0			0
$106$	2.93302	+	2.93302i	0.284880	+	0.284880i
$107$	−10.2485			−0.990756			−0.495378	−	0.868677i	$-0.664971\pi$
$107$	−10.2485			−0.990756			−0.495378	+	0.868677i	$0.664971\pi$
$108$		0			0
$109$	−5.85464	−	5.85464i	−0.560773	−	0.560773i	0.368754	−	0.929527i	$-0.379784\pi$
$109$	−5.85464	−	5.85464i	−0.560773	−	0.560773i	−0.929527	+	0.368754i	$0.879784\pi$
$110$	1.94326	−	1.94326i	0.185283	−	0.185283i
$111$		0			0
$112$	−6.96059	−	0.0389695i	−0.657714	−	0.00368227i
$113$	−5.74539			−0.540481			−0.270241	−	0.962793i	$-0.587103\pi$
$113$	−5.74539			−0.540481			−0.270241	+	0.962793i	$0.587103\pi$
$114$		0			0
$115$	−3.99078	−	3.99078i	−0.372142	−	0.372142i
$116$		−	2.04226i		−	0.189619i
$117$		0			0
$118$			15.6422i			1.43998i
$119$	8.06217	+	0.0451368i	0.739058	+	0.00413768i
$120$		0			0
$121$			4.12064i			0.374603i
$122$	7.86913	−	7.86913i	0.712438	−	0.712438i
$123$		0			0
$124$	3.65209	+	3.65209i	0.327967	+	0.327967i
$125$	−5.66930	−	5.66930i	−0.507078	−	0.507078i
$126$		0			0
$127$			7.37629i			0.654540i	0.944931	+	0.327270i	$0.106129\pi$
$127$			7.37629i			0.654540i	−0.944931	+	0.327270i	$0.893871\pi$
$128$	−3.36910	+	3.36910i	−0.297789	+	0.297789i
$129$		0			0
$130$	0.109245	−	3.77626i	0.00958142	−	0.331200i
$131$		−	11.9642i		−	1.04532i	−0.852543	−	0.522658i	$-0.824941\pi$
$131$		−	11.9642i		−	1.04532i	0.852543	−	0.522658i	$-0.175059\pi$
$132$		0			0
$133$	0.277394	−	0.274305i	0.0240531	−	0.0237853i
$134$			1.79380i			0.154960i
$135$		0			0
$136$	6.61282	−	6.61282i	0.567045	−	0.567045i
$137$	−1.88357	+	1.88357i	−0.160924	+	0.160924i	−0.782976	−	0.622052i	$-0.786299\pi$
$137$	−1.88357	+	1.88357i	−0.160924	+	0.160924i	0.622052	+	0.782976i	$0.286299\pi$
$138$		0			0
$139$		−	6.36883i		−	0.540197i	−0.962833	−	0.270098i	$-0.912944\pi$
$139$		−	6.36883i		−	0.540197i	0.962833	−	0.270098i	$-0.0870563\pi$
$140$	−0.869570	−	0.879362i	−0.0734921	−	0.0743196i
$141$		0			0
$142$		−	7.01333i		−	0.588546i
$143$	−6.49082	−	6.87756i	−0.542790	−	0.575131i
$144$		0			0
$145$	−2.32183	+	2.32183i	−0.192817	+	0.192817i
$146$			11.8378i			0.979701i
$147$		0			0
$148$	1.09171	+	1.09171i	0.0897379	+	0.0897379i
$149$	−13.3360	−	13.3360i	−1.09253	−	1.09253i	−0.995258	−	0.0972667i	$-0.968990\pi$
$149$	−13.3360	−	13.3360i	−1.09253	−	1.09253i	−0.0972667	−	0.995258i	$-0.531010\pi$
$150$		0			0
$151$	7.64229	−	7.64229i	0.621921	−	0.621921i	−0.324102	−	0.946022i	$-0.605062\pi$
$151$	7.64229	−	7.64229i	0.621921	−	0.621921i	0.946022	+	0.324102i	$0.105062\pi$
$152$		−	0.452519i		−	0.0367041i
$153$		0			0
$154$	8.38713	+	0.0469561i	0.675854	+	0.00378383i
$155$		−	8.30406i		−	0.666998i
$156$		0			0
$157$		−	21.0290i		−	1.67830i	−0.543903	−	0.839148i	$-0.683054\pi$
$157$		−	21.0290i		−	1.67830i	0.543903	−	0.839148i	$-0.316946\pi$
$158$	−15.0381	−	15.0381i	−1.19636	−	1.19636i
$159$		0			0
$160$	−2.56443			−0.202736
$161$	0.0964315	−	17.2243i	0.00759987	−	1.35746i
$162$		0			0
$163$	−7.03612	+	7.03612i	−0.551111	+	0.551111i	−0.926762	−	0.375650i	$-0.877419\pi$
$163$	−7.03612	+	7.03612i	−0.551111	+	0.551111i	0.375650	+	0.926762i	$0.377419\pi$
$164$	1.22600	+	1.22600i	0.0957344	+	0.0957344i
$165$		0			0
$166$	18.0284			1.39927
$167$	12.0684	+	12.0684i	0.933884	+	0.933884i	0.997946	−	0.0640620i	$-0.0204055\pi$
$167$	12.0684	+	12.0684i	0.933884	+	0.933884i	−0.0640620	+	0.997946i	$0.520406\pi$
$168$		0			0
$169$	−12.9783	−	0.751536i	−0.998328	−	0.0578104i
$170$	−3.19287			−0.244882
$171$		0			0
$172$	1.71646			0.130879
$173$	−7.48239			−0.568876			−0.284438	−	0.958694i	$-0.591807\pi$
$173$	−7.48239			−0.568876			−0.284438	+	0.958694i	$0.591807\pi$
$174$		0			0
$175$	0.0629292	−	11.2402i	0.00475700	−	0.849680i
$176$	4.87936	−	4.87936i	0.367796	−	0.367796i
$177$		0			0
$178$		−	5.80387i		−	0.435019i
$179$			22.7009i			1.69674i	0.529402	+	0.848371i	$0.322416\pi$
$179$			22.7009i			1.69674i	−0.529402	+	0.848371i	$0.677584\pi$
$180$		0			0
$181$	1.91735			0.142516			0.0712579	−	0.997458i	$-0.477299\pi$
$181$	1.91735			0.142516			0.0712579	+	0.997458i	$0.477299\pi$
$182$	8.42924	−	7.86649i	0.624817	−	0.583103i
$183$		0			0
$184$	−14.1278	−	14.1278i	−1.04152	−	1.04152i
$185$		−	2.48231i		−	0.182503i
$186$		0			0
$187$	−5.65157	+	5.65157i	−0.413283	+	0.413283i
$188$	2.81283	−	2.81283i	0.205147	−	0.205147i
$189$		0			0
$190$	−0.109245	+	0.109245i	−0.00792546	+	0.00792546i
$191$	10.0072			0.724095			0.362047	−	0.932160i	$-0.382078\pi$
$191$	10.0072			0.724095			0.362047	+	0.932160i	$0.382078\pi$
$192$		0			0
$193$	−10.2351	+	10.2351i	−0.736741	+	0.736741i	−0.971946	−	0.235205i	$-0.924424\pi$
$193$	−10.2351	+	10.2351i	−0.736741	+	0.736741i	0.235205	+	0.971946i	$0.424424\pi$
$194$	7.59483			0.545277
$195$		0			0
$196$	0.0422604	−	3.77409i	0.00301860	−	0.269578i
$197$	−15.2690	−	15.2690i	−1.08787	−	1.08787i	−0.995748	−	0.0921223i	$-0.970635\pi$
$197$	−15.2690	−	15.2690i	−1.08787	−	1.08787i	−0.0921223	−	0.995748i	$-0.529365\pi$
$198$		0			0
$199$	−22.4635			−1.59240			−0.796198	−	0.605036i	$-0.793159\pi$
$199$	−22.4635			−1.59240			−0.796198	+	0.605036i	$0.793159\pi$
$200$	−9.21953	−	9.21953i	−0.651920	−	0.651920i
$201$		0			0
$202$	−0.991567	−	0.991567i	−0.0697664	−	0.0697664i
$203$	−10.0210	−	0.0561036i	−0.703339	−	0.00393770i
$204$		0			0
$205$		−	2.78765i		−	0.194698i
$206$	−4.54756	−	4.54756i	−0.316844	−	0.316844i
$207$		0			0
$208$	0.274305	−	9.48187i	0.0190196	−	0.657449i
$209$			0.386740i			0.0267513i
$210$		0			0
$211$	−18.8504			−1.29772			−0.648859	−	0.760909i	$-0.724753\pi$
$211$	−18.8504			−1.29772			−0.648859	+	0.760909i	$0.724753\pi$
$212$			1.85043i			0.127088i
$213$		0			0
$214$	8.75872	+	8.75872i	0.598734	+	0.598734i
$215$	−1.95143	−	1.95143i	−0.133087	−	0.133087i
$216$		0			0
$217$	18.0205	−	17.8199i	1.22331	−	1.20969i
$218$			10.0072i			0.677772i
$219$		0			0
$220$	1.22600			0.0826568
$221$	−0.317716	+	10.9825i	−0.0213719	+	0.738760i
$222$		0			0
$223$	−4.32131	+	4.32131i	−0.289376	+	0.289376i	−0.836833	−	0.547457i	$-0.815596\pi$
$223$	−4.32131	+	4.32131i	−0.289376	+	0.289376i	0.547457	+	0.836833i	$0.315596\pi$
$224$	−5.50307	−	5.56504i	−0.367689	−	0.371830i
$225$		0			0
$226$	4.91023	+	4.91023i	0.326624	+	0.326624i
$227$	−4.69031	+	4.69031i	−0.311307	+	0.311307i	−0.845416	−	0.534109i	$-0.820647\pi$
$227$	−4.69031	+	4.69031i	−0.311307	+	0.311307i	0.534109	+	0.845416i	$0.320647\pi$
$228$		0			0
$229$	0.264743	+	0.264743i	0.0174947	+	0.0174947i	0.715800	−	0.698305i	$-0.246062\pi$
$229$	0.264743	+	0.264743i	0.0174947	+	0.0174947i	−0.698305	+	0.715800i	$0.746062\pi$
$230$			6.82135i			0.449786i
$231$		0			0
$232$	−8.21953	+	8.21953i	−0.539639	+	0.539639i
$233$			6.16290i			0.403745i	0.979412	+	0.201872i	$0.0647026\pi$
$233$			6.16290i			0.403745i	−0.979412	+	0.201872i	$0.935297\pi$
$234$		0			0
$235$	−6.39576			−0.417214
$236$	−4.93430	+	4.93430i	−0.321196	+	0.321196i
$237$		0			0
$238$	−6.85166	−	6.92881i	−0.444127	−	0.449128i
$239$	5.63090	+	5.63090i	0.364232	+	0.364232i	0.865369	−	0.501136i	$-0.167084\pi$
$239$	5.63090	+	5.63090i	0.364232	+	0.364232i	−0.501136	+	0.865369i	$0.667084\pi$
$240$		0			0
$241$	−1.11217	−	1.11217i	−0.0716414	−	0.0716414i	0.670378	−	0.742020i	$-0.266132\pi$
$241$	−1.11217	−	1.11217i	−0.0716414	−	0.0716414i	−0.742020	+	0.670378i	$0.766132\pi$
$242$	3.52165	−	3.52165i	0.226380	−	0.226380i
$243$		0			0
$244$	4.96462			0.317827
$245$	−4.33877	+	4.24268i	−0.277194	+	0.271055i
$246$		0			0
$247$	0.364897	+	0.386639i	0.0232178	+	0.0246012i
$248$		−	29.3973i		−	1.86673i
$249$		0			0
$250$			9.69040i			0.612874i
$251$	12.1069			0.764182			0.382091	−	0.924125i	$-0.375204\pi$
$251$	12.1069			0.764182			0.382091	+	0.924125i	$0.375204\pi$
$252$		0			0
$253$	12.0742	+	12.0742i	0.759097	+	0.759097i
$254$	6.30406	−	6.30406i	0.395552	−	0.395552i
$255$		0			0
$256$	−11.9155			−0.744717
$257$	17.5759			1.09635			0.548176	−	0.836363i	$-0.315322\pi$
$257$	17.5759			1.09635			0.548176	+	0.836363i	$0.315322\pi$
$258$		0			0
$259$	5.38682	−	5.32684i	0.334721	−	0.330994i
$260$	1.22568	−	1.15676i	0.0760133	−	0.0717389i
$261$		0			0
$262$	−10.2250	+	10.2250i	−0.631705	+	0.631705i
$263$	14.5259			0.895703			0.447851	−	0.894108i	$-0.352189\pi$
$263$	14.5259			0.895703			0.447851	+	0.894108i	$0.352189\pi$
$264$		0			0
$265$	2.10374	−	2.10374i	0.129232	−	0.129232i
$266$	−0.471502	−	0.00263975i	−0.0289097	−	0.000161853i
$267$		0			0
$268$	−0.565851	+	0.565851i	−0.0345648	+	0.0345648i
$269$		−	23.4152i		−	1.42765i	−0.700324	−	0.713825i	$-0.746961\pi$
$269$		−	23.4152i		−	1.42765i	0.700324	−	0.713825i	$-0.253039\pi$
$270$		0			0
$271$	−2.41653	−	2.41653i	−0.146794	−	0.146794i	0.629890	−	0.776684i	$-0.283100\pi$
$271$	−2.41653	−	2.41653i	−0.146794	−	0.146794i	−0.776684	+	0.629890i	$0.783100\pi$
$272$	−8.01703			−0.486104
$273$		0			0
$274$	3.21953			0.194499
$275$	7.87936	+	7.87936i	0.475143	+	0.475143i
$276$		0			0
$277$		−	29.0722i		−	1.74678i	−0.487020	−	0.873391i	$-0.661916\pi$
$277$		−	29.0722i		−	1.74678i	0.487020	−	0.873391i	$-0.338084\pi$
$278$	−5.44304	+	5.44304i	−0.326452	+	0.326452i
$279$		0			0
$280$	−0.0394083	+	7.03897i	−0.00235509	+	0.420659i
$281$	−9.68455	+	9.68455i	−0.577732	+	0.577732i	−0.934278	−	0.356546i	$-0.883954\pi$
$281$	−9.68455	+	9.68455i	−0.577732	+	0.577732i	0.356546	+	0.934278i	$0.383954\pi$
$282$		0			0
$283$	4.30357			0.255821			0.127910	−	0.991786i	$-0.459173\pi$
$283$	4.30357			0.255821			0.127910	+	0.991786i	$0.459173\pi$
$284$	2.21235	−	2.21235i	0.131279	−	0.131279i
$285$		0			0
$286$	−0.330522	+	11.4251i	−0.0195442	+	0.675582i
$287$	6.04945	−	5.98209i	0.357088	−	0.353112i
$288$		0			0
$289$	−7.71420			−0.453776
$290$	3.96864			0.233047
$291$		0			0
$292$	−3.73421	+	3.73421i	−0.218528	+	0.218528i
$293$	3.57373	+	3.57373i	0.208780	+	0.208780i	0.803749	−	0.594969i	$-0.202836\pi$
$293$	3.57373	+	3.57373i	0.208780	+	0.208780i	−0.594969	+	0.803749i	$0.702836\pi$
$294$		0			0
$295$	11.2195			0.653227
$296$		−	8.78765i		−	0.510772i
$297$		0			0
$298$			22.7948i			1.32047i
$299$	23.4633	+	0.678778i	1.35692	+	0.0392548i
$300$		0			0
$301$	0.0471535	−	8.42240i	0.00271788	−	0.485459i
$302$	−13.0628			−0.751678
$303$		0			0
$304$	−0.274305	+	0.274305i	−0.0157325	+	0.0157325i
$305$	−5.64423	−	5.64423i	−0.323188	−	0.323188i
$306$		0			0
$307$	8.59457	+	8.59457i	0.490518	+	0.490518i	0.908469	−	0.417952i	$-0.137252\pi$
$307$	8.59457	+	8.59457i	0.490518	+	0.490518i	−0.417952	+	0.908469i	$0.637252\pi$
$308$	2.63090	+	2.66052i	0.149909	+	0.151597i
$309$		0			0
$310$	−7.09696	+	7.09696i	−0.403080	+	0.403080i
$311$	−22.5405			−1.27815			−0.639077	−	0.769143i	$-0.720683\pi$
$311$	−22.5405			−1.27815			−0.639077	+	0.769143i	$0.720683\pi$
$312$		0			0
$313$			4.30873i			0.243544i	0.992558	+	0.121772i	$0.0388576\pi$
$313$			4.30873i			0.243544i	−0.992558	+	0.121772i	$0.961142\pi$
$314$	−17.9722	+	17.9722i	−1.01423	+	1.01423i
$315$		0			0
$316$		−	9.48747i		−	0.533712i
$317$	−3.97107	−	3.97107i	−0.223038	−	0.223038i	0.586739	−	0.809776i	$-0.300412\pi$
$317$	−3.97107	−	3.97107i	−0.223038	−	0.223038i	−0.809776	+	0.586739i	$0.800412\pi$
$318$		0			0
$319$	7.02472	−	7.02472i	0.393309	−	0.393309i
$320$	5.41714	+	5.41714i	0.302827	+	0.302827i
$321$		0			0
$322$	−14.8029	+	14.6381i	−0.824934	+	0.815749i
$323$	0.317716	−	0.317716i	0.0176782	−	0.0176782i
$324$		0			0
$325$	15.3116	+	0.442957i	0.849338	+	0.0245708i
$326$	12.0267			0.666095
$327$		0			0
$328$		−	9.86861i		−	0.544903i
$329$	−13.7248	−	13.8794i	−0.756674	−	0.765194i
$330$		0			0
$331$	1.70928	+	1.70928i	0.0939503	+	0.0939503i	0.752520	−	0.658570i	$-0.228838\pi$
$331$	1.70928	+	1.70928i	0.0939503	+	0.0939503i	−0.658570	+	0.752520i	$0.728838\pi$
$332$	5.68703	+	5.68703i	0.312117	+	0.312117i
$333$		0			0
$334$		−	20.6283i		−	1.12873i
$335$	1.28662			0.0702957
$336$		0			0
$337$		−	23.1327i		−	1.26012i	−0.776546	−	0.630061i	$-0.783030\pi$
$337$		−	23.1327i		−	1.26012i	0.776546	−	0.630061i	$-0.216970\pi$
$338$	10.4494	+	11.7340i	0.568373	+	0.638245i
$339$		0			0
$340$	−1.00719	−	1.00719i	−0.0546224	−	0.0546224i
$341$			25.1240i			1.36054i
$342$		0			0
$343$	−18.5176	−	0.311044i	−0.999859	−	0.0167948i
$344$	−6.90829	−	6.90829i	−0.372470	−	0.372470i
$345$		0			0
$346$	6.39473	+	6.39473i	0.343783	+	0.343783i
$347$	8.60424			0.461900			0.230950	−	0.972966i	$-0.425817\pi$
$347$	8.60424			0.461900			0.230950	+	0.972966i	$0.425817\pi$
$348$		0			0
$349$	19.0680	+	19.0680i	1.02069	+	1.02069i	0.999781	+	0.0209053i	$0.00665484\pi$
$349$	19.0680	+	19.0680i	1.02069	+	1.02069i	0.0209053	+	0.999781i	$0.493345\pi$
$350$	−9.66008	+	9.55252i	−0.516353	+	0.510604i
$351$		0			0
$352$	7.75872			0.413541
$353$	−4.81231	+	4.81231i	−0.256133	+	0.256133i	−0.823479	−	0.567346i	$-0.807970\pi$
$353$	−4.81231	+	4.81231i	−0.256133	+	0.256133i	0.567346	+	0.823479i	$0.307970\pi$
$354$		0			0
$355$	−5.03040			−0.266986
$356$	1.83083	−	1.83083i	0.0970336	−	0.0970336i
$357$		0			0
$358$	19.4010	−	19.4010i	1.02538	−	1.02538i
$359$	12.5506	−	12.5506i	0.662394	−	0.662394i	−0.293549	−	0.955944i	$-0.594837\pi$
$359$	12.5506	−	12.5506i	0.662394	−	0.662394i	0.955944	+	0.293549i	$0.0948365\pi$
$360$		0			0
$361$			18.9783i			0.998856i
$362$	−1.63864	−	1.63864i	−0.0861252	−	0.0861252i
$363$		0			0
$364$	5.14047	+	0.177519i	0.269434	+	0.00930452i
$365$	8.49079			0.444428
$366$		0			0
$367$			22.8806i			1.19436i	0.802109	+	0.597178i	$0.203711\pi$
$367$			22.8806i			1.19436i	−0.802109	+	0.597178i	$0.796289\pi$
$368$			17.1278i			0.892850i
$369$		0			0
$370$	−2.12147	+	2.12147i	−0.110290	+	0.110290i
$371$	9.07976	+	0.0508338i	0.471398	+	0.00263916i
$372$		0			0
$373$	10.5041			0.543883			0.271941	−	0.962314i	$-0.412334\pi$
$373$	10.5041			0.543883			0.271941	+	0.962314i	$0.412334\pi$
$374$	9.66008			0.499511
$375$		0			0
$376$	−22.6417			−1.16766
$377$	0.394912	−	13.6509i	0.0203390	−	0.703055i
$378$		0			0
$379$	3.64229	+	3.64229i	0.187092	+	0.187092i	0.794438	−	0.607346i	$-0.207766\pi$
$379$	3.64229	+	3.64229i	0.187092	+	0.187092i	−0.607346	+	0.794438i	$0.707766\pi$
$380$	−0.0689224			−0.00353564
$381$		0			0
$382$	−8.55252	−	8.55252i	−0.437585	−	0.437585i
$383$	−24.5591	+	24.5591i	−1.25491	+	1.25491i	−0.301419	+	0.953492i	$0.597460\pi$
$383$	−24.5591	+	24.5591i	−1.25491	+	1.25491i	−0.953492	+	0.301419i	$0.902540\pi$
$384$		0			0
$385$	0.0336798	−	6.01577i	0.00171648	−	0.306592i
$386$	17.4947			0.890455
$387$		0			0
$388$	2.39578	+	2.39578i	0.121627	+	0.121627i
$389$		−	6.48974i		−	0.329043i	−0.986374	−	0.164521i	$-0.947392\pi$
$389$		−	6.48974i		−	0.329043i	0.986374	−	0.164521i	$-0.0526080\pi$
$390$		0			0
$391$		−	19.8385i		−	1.00327i
$392$	−15.3597	+	15.0196i	−0.775784	+	0.758603i
$393$		0			0
$394$			26.0989i			1.31484i
$395$	−10.7862	+	10.7862i	−0.542714	+	0.542714i
$396$		0			0
$397$	6.89530	+	6.89530i	0.346065	+	0.346065i	0.858642	−	0.512576i	$-0.171309\pi$
$397$	6.89530	+	6.89530i	0.346065	+	0.346065i	−0.512576	+	0.858642i	$0.671309\pi$
$398$	19.1982	+	19.1982i	0.962317	+	0.962317i
$399$		0			0
$400$			11.1773i			0.558864i
$401$	−9.02279	+	9.02279i	−0.450576	+	0.450576i	−0.895546	−	0.444969i	$-0.853215\pi$
$401$	−9.02279	+	9.02279i	−0.450576	+	0.450576i	0.444969	+	0.895546i	$0.353215\pi$
$402$		0			0
$403$	23.7051	+	25.1175i	1.18083	+	1.25119i
$404$		−	0.625577i		−	0.0311236i
$405$		0			0
$406$	8.51640	+	8.61230i	0.422662	+	0.427421i
$407$			7.51026i			0.372270i
$408$		0			0
$409$	−2.86088	+	2.86088i	−0.141461	+	0.141461i	−0.774291	−	0.632830i	$-0.781893\pi$
$409$	−2.86088	+	2.86088i	−0.141461	+	0.141461i	0.632830	+	0.774291i	$0.281893\pi$
$410$	−2.38243	+	2.38243i	−0.117660	+	0.117660i
$411$		0			0
$412$		−	2.86905i		−	0.141348i
$413$	24.0763	+	24.3474i	1.18472	+	1.19806i
$414$		0			0
$415$		−	12.9311i		−	0.634762i
$416$	7.75670	−	7.32052i	0.380303	−	0.358918i
$417$		0			0
$418$	0.330522	−	0.330522i	0.0161664	−	0.0161664i
$419$			35.4097i			1.72988i	0.501878	+	0.864939i	$0.332643\pi$
$419$			35.4097i			1.72988i	−0.501878	+	0.864939i	$0.667357\pi$
$420$		0			0
$421$	18.9307	+	18.9307i	0.922628	+	0.922628i	0.997215	−	0.0745864i	$-0.0237636\pi$
$421$	18.9307	+	18.9307i	0.922628	+	0.922628i	−0.0745864	+	0.997215i	$0.523764\pi$
$422$	16.1103	+	16.1103i	0.784237	+	0.784237i
$423$		0			0
$424$	7.44748	−	7.44748i	0.361682	−	0.361682i
$425$		−	12.9462i		−	0.627982i
$426$		0			0
$427$	0.136385	−	24.3605i	0.00660011	−	1.17889i
$428$			5.52586i			0.267102i
$429$		0			0
$430$			3.33553i			0.160854i
$431$	−12.6042	−	12.6042i	−0.607125	−	0.607125i	0.335069	−	0.942194i	$-0.391240\pi$
$431$	−12.6042	−	12.6042i	−0.607125	−	0.607125i	−0.942194	+	0.335069i	$0.891240\pi$
$432$		0			0
$433$	−14.3392			−0.689098			−0.344549	−	0.938768i	$-0.611968\pi$
$433$	−14.3392			−0.689098			−0.344549	+	0.938768i	$0.611968\pi$
$434$	−30.6305	−	0.171488i	−1.47031	−	0.00823167i
$435$		0			0
$436$	−3.15676	+	3.15676i	−0.151181	+	0.151181i
$437$	−0.678778	−	0.678778i	−0.0324704	−	0.0324704i
$438$		0			0
$439$	19.9812			0.953651			0.476826	−	0.878998i	$-0.341787\pi$
$439$	19.9812			0.953651			0.476826	+	0.878998i	$0.341787\pi$
$440$	−4.93430	−	4.93430i	−0.235234	−	0.235234i
$441$		0			0
$442$	9.65756	−	9.11450i	0.459363	−	0.433532i
$443$	5.63809			0.267874			0.133937	−	0.990990i	$-0.457238\pi$
$443$	5.63809			0.267874			0.133937	+	0.990990i	$0.457238\pi$
$444$		0			0
$445$	−4.16290			−0.197340
$446$	7.38630			0.349751
$447$		0			0
$448$	−0.130897	+	23.3804i	−0.00618431	+	1.10462i
$449$	12.9060	−	12.9060i	0.609073	−	0.609073i	−0.333631	−	0.942704i	$-0.608274\pi$
$449$	12.9060	−	12.9060i	0.609073	−	0.609073i	0.942704	+	0.333631i	$0.108274\pi$
$450$		0			0
$451$			8.43409i			0.397146i
$452$			3.09785i			0.145711i
$453$		0			0
$454$	8.01703			0.376258
$455$	−5.64234	−	6.04597i	−0.264517	−	0.283440i
$456$		0			0
$457$	6.96687	+	6.96687i	0.325896	+	0.325896i	0.851024	−	0.525127i	$-0.175982\pi$
$457$	6.96687	+	6.96687i	0.325896	+	0.325896i	−0.525127	+	0.851024i	$0.675982\pi$
$458$		−	0.452519i		−	0.0211448i
$459$		0			0
$460$	−2.15179	+	2.15179i	−0.100328	+	0.100328i
$461$	7.20809	−	7.20809i	0.335714	−	0.335714i	−0.519037	−	0.854752i	$-0.673709\pi$
$461$	7.20809	−	7.20809i	0.335714	−	0.335714i	0.854752	+	0.519037i	$0.173709\pi$
$462$		0			0
$463$	−4.06084	+	4.06084i	−0.188723	+	0.188723i	−0.795144	−	0.606421i	$-0.792605\pi$
$463$	−4.06084	+	4.06084i	−0.188723	+	0.188723i	0.606421	+	0.795144i	$0.292605\pi$
$464$	9.96493			0.462610
$465$		0			0
$466$	5.26705	−	5.26705i	0.243991	−	0.243991i
$467$	−17.3673			−0.803665			−0.401832	−	0.915713i	$-0.631627\pi$
$467$	−17.3673			−0.803665			−0.401832	+	0.915713i	$0.631627\pi$
$468$		0			0
$469$	2.76099	+	2.79208i	0.127491	+	0.128926i
$470$	5.46606	+	5.46606i	0.252131	+	0.252131i
$471$		0			0
$472$	39.7184			1.82819
$473$	5.90409	+	5.90409i	0.271470	+	0.271470i
$474$		0			0
$475$	−0.442957	−	0.442957i	−0.0203243	−	0.0203243i
$476$	0.0243372	−	4.34703i	0.00111550	−	0.199246i
$477$		0			0
$478$		−	9.62475i		−	0.440226i
$479$	9.88634	+	9.88634i	0.451719	+	0.451719i	0.895925	−	0.444206i	$-0.146514\pi$
$479$	9.88634	+	9.88634i	0.451719	+	0.451719i	−0.444206	+	0.895925i	$0.646514\pi$
$480$		0			0
$481$	7.08609	+	7.50830i	0.323098	+	0.342349i
$482$			1.90101i			0.0865887i
$483$		0			0
$484$	2.22180			0.100991
$485$		−	5.44748i		−	0.247357i
$486$		0			0
$487$	−12.6092	−	12.6092i	−0.571375	−	0.571375i	0.361137	−	0.932513i	$-0.382389\pi$
$487$	−12.6092	−	12.6092i	−0.571375	−	0.571375i	−0.932513	+	0.361137i	$0.882389\pi$
$488$	−19.9812	−	19.9812i	−0.904507	−	0.904507i
$489$		0			0
$490$	7.33403	+	0.0821230i	0.331318	+	0.00370994i
$491$		−	1.72487i		−	0.0778425i	−0.999242	−	0.0389212i	$-0.987608\pi$
$491$		−	1.72487i		−	0.0778425i	0.999242	−	0.0389212i	$-0.0123921\pi$
$492$		0			0
$493$	−11.5420			−0.519824
$494$	0.0185811	−	0.642291i	0.000836003	−	0.0288980i
$495$		0			0
$496$	−17.8199	+	17.8199i	−0.800135	+	0.800135i
$497$	−10.7948	−	10.9164i	−0.484215	−	0.489667i
$498$		0			0
$499$	−27.5555	−	27.5555i	−1.23355	−	1.23355i	−0.962589	−	0.270964i	$-0.912657\pi$
$499$	−27.5555	−	27.5555i	−1.23355	−	1.23355i	−0.270964	−	0.962589i	$-0.587343\pi$
$500$	−3.05682	+	3.05682i	−0.136705	+	0.136705i
$501$		0			0
$502$	−10.3470	−	10.3470i	−0.461811	−	0.461811i
$503$			20.8862i			0.931272i	0.884976	+	0.465636i	$0.154174\pi$
$503$			20.8862i			0.931272i	−0.884976	+	0.465636i	$0.845826\pi$
$504$		0			0
$505$	−0.711213	+	0.711213i	−0.0316486	+	0.0316486i
$506$		−	20.6381i		−	0.917475i
$507$		0			0
$508$	3.97721			0.176460
$509$	15.2473	−	15.2473i	0.675823	−	0.675823i	−0.283229	−	0.959052i	$-0.591406\pi$
$509$	15.2473	−	15.2473i	0.675823	−	0.675823i	0.959052	+	0.283229i	$0.0914057\pi$
$510$		0			0
$511$	18.2206	+	18.4257i	0.806031	+	0.815107i
$512$	16.9216	+	16.9216i	0.747837	+	0.747837i
$513$		0			0
$514$	−15.0210	−	15.0210i	−0.662548	−	0.662548i
$515$	−3.26180	+	3.26180i	−0.143732	+	0.143732i
$516$		0			0
$517$	19.3505			0.851033
$518$	−9.15630	−	0.0512623i	−0.402305	−	0.00225234i
$519$		0			0
$520$	−9.58864	−	0.277394i	−0.420490	−	0.0121645i
$521$			20.1543i			0.882975i	0.897268	+	0.441487i	$0.145549\pi$
$521$			20.1543i			0.882975i	−0.897268	+	0.441487i	$0.854451\pi$
$522$		0			0
$523$		−	11.3031i		−	0.494251i	−0.968983	−	0.247126i	$-0.920514\pi$
$523$		−	11.3031i		−	0.494251i	0.968983	−	0.247126i	$-0.0794861\pi$
$524$	−6.45095			−0.281811
$525$		0			0
$526$	−12.4143	−	12.4143i	−0.541291	−	0.541291i
$527$	20.6400	−	20.6400i	0.899094	−	0.899094i
$528$		0			0
$529$	−19.3835			−0.842760
$530$	−3.59587			−0.156195
$531$		0			0
$532$	−0.147902	−	0.149568i	−0.00641237	−	0.00648458i
$533$	7.95774	+	8.43188i	0.344688	+	0.365225i
$534$		0			0
$535$	6.28230	−	6.28230i	0.271607	−	0.271607i
$536$	4.55479			0.196737
$537$		0			0
$538$	−20.0115	+	20.0115i	−0.862758	+	0.862758i
$539$	13.1270	−	12.8363i	0.565420	−	0.552898i
$540$		0			0
$541$	−9.28879	+	9.28879i	−0.399356	+	0.399356i	−0.878006	−	0.478650i	$-0.841126\pi$
$541$	−9.28879	+	9.28879i	−0.399356	+	0.399356i	0.478650	+	0.878006i	$0.341126\pi$
$542$			4.13051i			0.177421i
$543$		0			0
$544$	−6.37398	−	6.37398i	−0.273282	−	0.273282i
$545$	7.17778			0.307462
$546$		0			0
$547$	12.8999			0.551559			0.275780	−	0.961221i	$-0.411064\pi$
$547$	12.8999			0.551559			0.275780	+	0.961221i	$0.411064\pi$
$548$	1.01560	+	1.01560i	0.0433842	+	0.0433842i
$549$		0			0
$550$		−	13.4680i		−	0.574277i
$551$	−0.394912	+	0.394912i	−0.0168238	+	0.0168238i
$552$		0			0
$553$	−46.5534	−	0.260633i	−1.97965	−	0.0110833i
$554$	−24.8462	+	24.8462i	−1.05562	+	1.05562i
$555$		0			0
$556$	−3.43400			−0.145634
$557$	16.6153	−	16.6153i	0.704013	−	0.704013i	−0.261257	−	0.965269i	$-0.584137\pi$
$557$	16.6153	−	16.6153i	0.704013	−	0.704013i	0.965269	+	0.261257i	$0.0841369\pi$
$558$		0			0
$559$	11.4732	+	0.331912i	0.485264	+	0.0140384i
$560$	4.29072	−	4.24295i	0.181316	−	0.179297i
$561$		0			0
$562$	16.5536			0.698270
$563$	−21.6761			−0.913538			−0.456769	−	0.889585i	$-0.650993\pi$
$563$	−21.6761			−0.913538			−0.456769	+	0.889585i	$0.650993\pi$
$564$		0			0
$565$	3.52192	−	3.52192i	0.148168	−	0.148168i
$566$	−3.67799	−	3.67799i	−0.154598	−	0.154598i
$567$		0			0
$568$	−17.8082			−0.747214
$569$			18.0738i			0.757695i	0.925459	+	0.378847i	$0.123679\pi$
$569$			18.0738i			0.757695i	−0.925459	+	0.378847i	$0.876321\pi$
$570$		0			0
$571$			8.53692i			0.357259i	0.983916	+	0.178630i	$0.0571664\pi$
$571$			8.53692i			0.357259i	−0.983916	+	0.178630i	$0.942834\pi$
$572$	−3.70831	+	3.49978i	−0.155052	+	0.146333i
$573$		0			0
$574$	−10.2826	−	0.0575680i	−0.429188	−	0.00240284i
$575$	−27.6586			−1.15344
$576$		0			0
$577$	8.56564	−	8.56564i	0.356592	−	0.356592i	−0.505963	−	0.862555i	$-0.668863\pi$
$577$	8.56564	−	8.56564i	0.356592	−	0.356592i	0.862555	+	0.505963i	$0.168863\pi$
$578$	6.59284	+	6.59284i	0.274226	+	0.274226i
$579$		0			0
$580$	1.25190	+	1.25190i	0.0519825	+	0.0519825i
$581$	28.0616	−	27.7491i	1.16419	−	1.15123i
$582$		0			0
$583$	−6.36490	+	6.36490i	−0.263607	+	0.263607i
$584$	30.0583			1.24382
$585$		0			0
$586$		−	6.10849i		−	0.252339i
$587$	−0.308382	+	0.308382i	−0.0127283	+	0.0127283i	−0.713442	−	0.700714i	$-0.752865\pi$
$587$	−0.308382	+	0.308382i	−0.0127283	+	0.0127283i	0.700714	+	0.713442i	$0.252865\pi$
$588$		0			0
$589$		−	1.41241i		−	0.0581972i
$590$	−9.58864	−	9.58864i	−0.394758	−	0.394758i
$591$		0			0
$592$	−5.32684	+	5.32684i	−0.218932	+	0.218932i
$593$	−4.95204	−	4.95204i	−0.203356	−	0.203356i	0.598080	−	0.801436i	$-0.295930\pi$
$593$	−4.95204	−	4.95204i	−0.203356	−	0.203356i	−0.801436	+	0.598080i	$0.795930\pi$
$594$		0			0
$595$	−4.96977	+	4.91443i	−0.203741	+	0.201472i
$596$	−7.19061	+	7.19061i	−0.294539	+	0.294539i
$597$		0			0
$598$	−19.4725	−	20.6327i	−0.796289	−	0.843734i
$599$	17.6309			0.720379			0.360189	−	0.932879i	$-0.382712\pi$
$599$	17.6309			0.720379			0.360189	+	0.932879i	$0.382712\pi$
$600$		0			0
$601$		−	7.14746i		−	0.291551i	−0.989318	−	0.145776i	$-0.953432\pi$
$601$		−	7.14746i		−	0.291551i	0.989318	−	0.145776i	$-0.0465677\pi$
$602$	−7.23840	+	7.15780i	−0.295015	+	0.291730i
$603$		0			0
$604$	−4.12064	−	4.12064i	−0.167666	−	0.167666i
$605$	−2.52595	−	2.52595i	−0.102694	−	0.102694i
$606$		0			0
$607$			29.8550i			1.21178i	0.795550	+	0.605888i	$0.207182\pi$
$607$			29.8550i			1.21178i	−0.795550	+	0.605888i	$0.792818\pi$
$608$	−0.436175			−0.0176892
$609$		0			0
$610$			9.64754i			0.390618i
$611$	19.3454	−	18.2576i	0.782632	−	0.738623i
$612$		0			0
$613$	−6.43907	−	6.43907i	−0.260072	−	0.260072i	0.565011	−	0.825083i	$-0.308872\pi$
$613$	−6.43907	−	6.43907i	−0.260072	−	0.260072i	−0.825083	+	0.565011i	$0.808872\pi$
$614$		−	14.6905i		−	0.592859i
$615$		0			0
$616$	0.119230	−	21.2965i	0.00480393	−	0.858061i
$617$	−16.4908	−	16.4908i	−0.663894	−	0.663894i	0.292402	−	0.956296i	$-0.405546\pi$
$617$	−16.4908	−	16.4908i	−0.663894	−	0.663894i	−0.956296	+	0.292402i	$0.905546\pi$
$618$		0			0
$619$	22.3208	+	22.3208i	0.897148	+	0.897148i	0.995183	−	0.0980353i	$-0.0312558\pi$
$619$	22.3208	+	22.3208i	0.897148	+	0.897148i	−0.0980353	+	0.995183i	$0.531256\pi$
$620$	−4.47745			−0.179819
$621$		0			0
$622$	19.2639	+	19.2639i	0.772414	+	0.772414i
$623$	−8.93326	−	9.03385i	−0.357903	−	0.361934i
$624$		0			0
$625$	−14.2918			−0.571671
$626$	3.68240	−	3.68240i	0.147178	−	0.147178i
$627$		0			0
$628$	−11.3386			−0.452459
$629$	6.16986	−	6.16986i	0.246009	−	0.246009i
$630$		0			0
$631$	3.75154	−	3.75154i	0.149346	−	0.149346i	−0.628480	−	0.777826i	$-0.716322\pi$
$631$	3.75154	−	3.75154i	0.149346	−	0.149346i	0.777826	+	0.628480i	$0.216322\pi$
$632$	−38.1845	+	38.1845i	−1.51890	+	1.51890i
$633$		0			0
$634$			6.78765i			0.269572i
$635$	−4.52166	−	4.52166i	−0.179437	−	0.179437i
$636$		0			0
$637$	1.01227	−	25.2186i	0.0401076	−	0.999195i
$638$	−12.0072			−0.475369
$639$		0			0
$640$		−	4.13051i		−	0.163273i
$641$		−	25.6947i		−	1.01488i	−0.861687	−	0.507440i	$-0.830592\pi$
$641$		−	25.6947i		−	1.01488i	0.861687	−	0.507440i	$-0.169408\pi$
$642$		0			0
$643$	−22.1537	+	22.1537i	−0.873658	+	0.873658i	−0.992869	−	0.119211i	$-0.961964\pi$
$643$	−22.1537	+	22.1537i	−0.873658	+	0.873658i	0.119211	+	0.992869i	$0.461964\pi$
$644$	−9.28713	−	0.0519948i	−0.365964	−	0.00204888i
$645$		0			0
$646$	−0.543065			−0.0213666
$647$	32.4446			1.27553			0.637764	−	0.770232i	$-0.279860\pi$
$647$	32.4446			1.27553			0.637764	+	0.770232i	$0.279860\pi$
$648$		0			0
$649$	−33.9449			−1.33245
$650$	−12.7073	−	13.4645i	−0.498423	−	0.528120i
$651$		0			0
$652$	3.79380	+	3.79380i	0.148577	+	0.148577i
$653$	−31.6514			−1.23862			−0.619308	−	0.785148i	$-0.712587\pi$
$653$	−31.6514			−1.23862			−0.619308	+	0.785148i	$0.712587\pi$
$654$		0			0
$655$	7.33403	+	7.33403i	0.286564	+	0.286564i
$656$	−5.98209	+	5.98209i	−0.233561	+	0.233561i
$657$		0			0
$658$	−0.132079	+	23.5916i	−0.00514899	+	0.919695i
$659$	−30.5330			−1.18940			−0.594699	−	0.803948i	$-0.702729\pi$
$659$	−30.5330			−1.18940			−0.594699	+	0.803948i	$0.702729\pi$
$660$		0			0
$661$	−9.20895	−	9.20895i	−0.358187	−	0.358187i	0.504957	−	0.863144i	$-0.331508\pi$
$661$	−9.20895	−	9.20895i	−0.358187	−	0.358187i	−0.863144	+	0.504957i	$0.831508\pi$
$662$		−	2.92162i		−	0.113552i
$663$		0			0
$664$		−	45.7775i		−	1.77651i
$665$	−0.00189339	+	0.338191i	−7.34225e−5	+	0.0131145i
$666$		0			0
$667$			24.6586i			0.954785i
$668$	6.50717	−	6.50717i	0.251770	−	0.251770i
$669$		0			0
$670$	−1.09960	−	1.09960i	−0.0424811	−	0.0424811i
$671$	17.0767	+	17.0767i	0.659239	+	0.659239i
$672$		0			0
$673$		−	22.6319i		−	0.872397i	−0.899850	−	0.436199i	$-0.856325\pi$
$673$		−	22.6319i		−	0.872397i	0.899850	−	0.436199i	$-0.143675\pi$
$674$	−19.7701	+	19.7701i	−0.761516	+	0.761516i
$675$		0			0
$676$	−0.405220	+	6.99773i	−0.0155854	+	0.269144i
$677$			10.7242i			0.412165i	0.978535	+	0.206082i	$0.0660715\pi$
$677$			10.7242i			0.412165i	−0.978535	+	0.206082i	$0.933928\pi$
$678$		0			0
$679$	11.8215	−	11.6899i	0.453668	−	0.448616i
$680$			8.10731i			0.310901i
$681$		0			0
$682$	21.4720	−	21.4720i	0.822204	−	0.822204i
$683$	3.70701	−	3.70701i	0.141845	−	0.141845i	−0.632619	−	0.774463i	$-0.718020\pi$
$683$	3.70701	−	3.70701i	0.141845	−	0.141845i	0.774463	+	0.632619i	$0.218020\pi$
$684$		0			0
$685$		−	2.30925i		−	0.0882319i
$686$	15.5600	+	16.0917i	0.594085	+	0.614384i
$687$		0			0
$688$			8.37525i			0.319303i
$689$	−0.357818	+	12.3687i	−0.0136318	+	0.471208i
$690$		0			0
$691$	0.266133	−	0.266133i	0.0101242	−	0.0101242i	−0.702027	−	0.712151i	$-0.747721\pi$
$691$	0.266133	−	0.266133i	0.0101242	−	0.0101242i	0.712151	+	0.702027i	$0.247721\pi$
$692$			4.03442i			0.153366i
$693$		0			0
$694$	−7.35350	−	7.35350i	−0.279135	−	0.279135i
$695$	3.90409	+	3.90409i	0.148090	+	0.148090i
$696$		0			0
$697$	6.92881	−	6.92881i	0.262447	−	0.262447i
$698$		−	32.5925i		−	1.23364i
$699$		0			0
$700$	−6.06059	−	0.0339307i	−0.229069	−	0.00128246i
$701$		−	34.0349i		−	1.28548i	−0.766084	−	0.642740i	$-0.777798\pi$
$701$		−	34.0349i		−	1.28548i	0.766084	−	0.642740i	$-0.222202\pi$
$702$		0			0
$703$		−	0.422207i		−	0.0159238i
$704$	−16.3896	−	16.3896i	−0.617707	−	0.617707i
$705$		0			0
$706$	8.22556			0.309573
$707$	−3.06960	−	0.0171854i	−0.115444	−	0.000646325i
$708$		0			0
$709$	11.4989	−	11.4989i	0.431849	−	0.431849i	−0.457408	−	0.889257i	$-0.651222\pi$
$709$	11.4989	−	11.4989i	0.431849	−	0.431849i	0.889257	+	0.457408i	$0.151222\pi$
$710$	4.29917	+	4.29917i	0.161345	+	0.161345i
$711$		0			0
$712$	−14.7371			−0.552297
$713$	−44.0960	−	44.0960i	−1.65141	−	1.65141i
$714$		0			0
$715$	8.19481	+	0.237071i	0.306469	+	0.00886596i
$716$	12.2401			0.457432
$717$		0			0
$718$	−21.4524			−0.800596
$719$	35.0445			1.30694			0.653469	−	0.756953i	$-0.273313\pi$
$719$	35.0445			1.30694			0.653469	+	0.756953i	$0.273313\pi$
$720$		0			0
$721$	−14.0779	−	0.0788166i	−0.524290	−	0.00293528i
$722$	16.2195	−	16.2195i	0.603629	−	0.603629i
$723$		0			0
$724$		−	1.03382i		−	0.0384215i
$725$			16.0917i			0.597631i
$726$		0			0
$727$	−15.0936			−0.559789			−0.279895	−	0.960031i	$-0.590300\pi$
$727$	−15.0936			−0.559789			−0.279895	+	0.960031i	$0.590300\pi$
$728$	−19.9745	−	21.4034i	−0.740305	−	0.793264i
$729$		0			0
$730$	−7.25655	−	7.25655i	−0.268577	−	0.268577i
$731$		−	9.70071i		−	0.358794i
$732$		0			0
$733$	14.8155	−	14.8155i	0.547223	−	0.547223i	−0.378414	−	0.925637i	$-0.623530\pi$
$733$	14.8155	−	14.8155i	0.547223	−	0.547223i	0.925637	+	0.378414i	$0.123530\pi$
$734$	19.5546	−	19.5546i	0.721773	−	0.721773i
$735$		0			0
$736$	−13.6176	+	13.6176i	−0.501950	+	0.501950i
$737$	−3.89269			−0.143389
$738$		0			0
$739$	16.1370	−	16.1370i	0.593607	−	0.593607i	−0.344997	−	0.938604i	$-0.612120\pi$
$739$	16.1370	−	16.1370i	0.593607	−	0.593607i	0.938604	+	0.344997i	$0.112120\pi$
$740$	−1.33843			−0.0492018
$741$		0			0
$742$	−7.71646	−	7.80335i	−0.283280	−	0.286470i
$743$	24.1350	+	24.1350i	0.885428	+	0.885428i	0.994080	−	0.108652i	$-0.0346534\pi$
$743$	24.1350	+	24.1350i	0.885428	+	0.885428i	−0.108652	+	0.994080i	$0.534653\pi$
$744$		0			0
$745$	16.3499			0.599013
$746$	−8.97721	−	8.97721i	−0.328679	−	0.328679i
$747$		0			0
$748$	3.04726	+	3.04726i	0.111419	+	0.111419i
$749$	27.1145	+	0.151803i	0.990741	+	0.00554675i
$750$		0			0
$751$			16.7770i			0.612201i	0.951999	+	0.306100i	$0.0990243\pi$
$751$			16.7770i			0.612201i	−0.951999	+	0.306100i	$0.900976\pi$
$752$	13.7248	+	13.7248i	0.500493	+	0.500493i
$753$		0			0
$754$	−12.0041	+	11.3290i	−0.437162	+	0.412579i
$755$			9.36943i			0.340989i
$756$		0			0
$757$	−20.7321			−0.753520			−0.376760	−	0.926311i	$-0.622962\pi$
$757$	−20.7321			−0.753520			−0.376760	+	0.926311i	$0.622962\pi$
$758$		−	6.22568i		−	0.226127i
$759$		0			0
$760$	0.277394	+	0.277394i	0.0100621	+	0.0100621i
$761$	−2.11330	−	2.11330i	−0.0766071	−	0.0766071i	0.667765	−	0.744372i	$-0.267251\pi$
$761$	−2.11330	−	2.11330i	−0.0766071	−	0.0766071i	−0.744372	+	0.667765i	$0.767251\pi$
$762$		0			0
$763$	15.4030	+	15.5764i	0.557624	+	0.563903i
$764$		−	5.39576i		−	0.195212i
$765$		0			0
$766$	41.9782			1.51674
$767$	−33.9360	+	32.0277i	−1.22536	+	1.15645i
$768$		0			0
$769$	25.9456	−	25.9456i	0.935621	−	0.935621i	−0.0624284	−	0.998049i	$-0.519885\pi$
$769$	25.9456	−	25.9456i	0.935621	−	0.935621i	0.998049	+	0.0624284i	$0.0198845\pi$
$770$	−5.17009	+	5.11252i	−0.186317	+	0.184242i
$771$		0			0
$772$	5.51867	+	5.51867i	0.198621	+	0.198621i
$773$	−0.951693	+	0.951693i	−0.0342300	+	0.0342300i	−0.724015	−	0.689785i	$-0.757705\pi$
$773$	−0.951693	+	0.951693i	−0.0342300	+	0.0342300i	0.689785	+	0.724015i	$0.257705\pi$
$774$		0			0
$775$	−28.7761	−	28.7761i	−1.03367	−	1.03367i
$776$		−	19.2847i		−	0.692280i
$777$		0			0
$778$	−5.54638	+	5.54638i	−0.198847	+	0.198847i
$779$		−	0.474142i		−	0.0169879i
$780$		0			0
$781$	15.2195			0.544598
$782$	−16.9547	+	16.9547i	−0.606299	+	0.606299i
$783$		0			0
$784$	18.4151	+	0.206204i	0.657683	+	0.00736442i
$785$	12.8908	+	12.8908i	0.460091	+	0.460091i
$786$		0			0
$787$	24.8017	+	24.8017i	0.884085	+	0.884085i	0.993947	−	0.109862i	$-0.0350409\pi$
$787$	24.8017	+	24.8017i	0.884085	+	0.884085i	−0.109862	+	0.993947i	$0.535041\pi$
$788$	−8.23287	+	8.23287i	−0.293284	+	0.293284i
$789$		0			0
$790$	18.4366			0.655946
$791$	15.2006	+	0.0851021i	0.540473	+	0.00302588i
$792$		0			0
$793$	33.1845	+	0.960007i	1.17841	+	0.0340908i
$794$		−	11.7860i		−	0.418268i
$795$		0			0
$796$			12.1121i			0.429301i
$797$	34.9017			1.23628			0.618141	−	0.786067i	$-0.287886\pi$
$797$	34.9017			1.23628			0.618141	+	0.786067i	$0.287886\pi$
$798$		0			0
$799$	−15.8969	−	15.8969i	−0.562392	−	0.562392i
$800$	−8.88655	+	8.88655i	−0.314187	+	0.314187i
$801$		0			0
$802$	15.4224			0.544585
$803$	−25.6890			−0.906545
$804$		0			0
$805$	10.4993	+	10.6176i	0.370053	+	0.374220i
$806$	1.20710	−	41.7256i	0.0425182	−	1.46972i
$807$		0			0
$808$	−2.51778	+	2.51778i	−0.0885750	+	0.0885750i
$809$	−10.2618			−0.360786			−0.180393	−	0.983595i	$-0.557737\pi$
$809$	−10.2618			−0.360786			−0.180393	+	0.983595i	$0.557737\pi$
$810$		0			0
$811$	13.3684	−	13.3684i	0.469428	−	0.469428i	−0.432301	−	0.901729i	$-0.642298\pi$
$811$	13.3684	−	13.3684i	0.469428	−	0.469428i	0.901729	+	0.432301i	$0.142298\pi$
$812$	−0.0302504	+	5.40323i	−0.00106158	+	0.189616i
$813$		0			0
$814$	6.41855	−	6.41855i	0.224970	−	0.224970i
$815$		−	8.62627i		−	0.302165i
$816$		0			0
$817$	−0.331912	−	0.331912i	−0.0116121	−	0.0116121i
$818$	4.89002			0.170976
$819$		0			0
$820$	−1.50307			−0.0524895
$821$	−17.3074	−	17.3074i	−0.604031	−	0.604031i	0.337349	−	0.941380i	$-0.390470\pi$
$821$	−17.3074	−	17.3074i	−0.604031	−	0.604031i	−0.941380	+	0.337349i	$0.890470\pi$
$822$		0			0
$823$		−	35.0772i		−	1.22271i	−0.791355	−	0.611356i	$-0.790624\pi$
$823$		−	35.0772i		−	1.22271i	0.791355	−	0.611356i	$-0.209376\pi$
$824$	−11.5471	+	11.5471i	−0.402263	+	0.402263i
$825$		0			0
$826$	0.231696	−	41.3846i	0.00806172	−	1.43996i
$827$	19.4173	−	19.4173i	0.675207	−	0.675207i	−0.283705	−	0.958912i	$-0.591564\pi$
$827$	19.4173	−	19.4173i	0.675207	−	0.675207i	0.958912	+	0.283705i	$0.0915636\pi$
$828$		0			0
$829$	−9.16091			−0.318172			−0.159086	−	0.987265i	$-0.550855\pi$
$829$	−9.16091			−0.318172			−0.159086	+	0.987265i	$0.550855\pi$
$830$	−11.0514	+	11.0514i	−0.383599	+	0.383599i
$831$		0			0
$832$	−31.8493	−	0.921381i	−1.10418	−	0.0319432i
$833$	−21.3295	−	0.238838i	−0.739023	−	0.00827523i
$834$		0			0
$835$	−14.7959			−0.512033
$836$	0.208526			0.00721201
$837$		0			0
$838$	30.2625	−	30.2625i	1.04540	−	1.04540i
$839$	−26.1882	−	26.1882i	−0.904116	−	0.904116i	0.0916731	−	0.995789i	$-0.470779\pi$
$839$	−26.1882	−	26.1882i	−0.904116	−	0.904116i	−0.995789	+	0.0916731i	$0.970779\pi$
$840$		0			0
$841$	−14.6537			−0.505299
$842$		−	32.3579i		−	1.11513i
$843$		0			0
$844$			10.1639i			0.349857i
$845$	8.41635	−	7.49497i	0.289531	−	0.257835i
$846$		0			0
$847$	0.0610359	−	10.9020i	0.00209722	−	0.374598i
$848$	−9.02893			−0.310055
$849$		0			0
$850$	−11.0643	+	11.0643i	−0.379502	+	0.379502i
$851$	−13.1815	−	13.1815i	−0.451855	−	0.451855i
$852$		0			0
$853$	−7.70865	−	7.70865i	−0.263939	−	0.263939i	0.562713	−	0.826652i	$-0.309758\pi$
$853$	−7.70865	−	7.70865i	−0.263939	−	0.263939i	−0.826652	+	0.562713i	$0.809758\pi$
$854$	−20.9360	+	20.7029i	−0.716415	+	0.708438i
$855$		0			0
$856$	22.2401	−	22.2401i	0.760149	−	0.760149i
$857$	22.4141			0.765651			0.382825	−	0.923821i	$-0.374951\pi$
$857$	22.4141			0.765651			0.382825	+	0.923821i	$0.374951\pi$
$858$		0			0
$859$			43.5695i			1.48657i	0.668974	+	0.743286i	$0.266734\pi$
$859$			43.5695i			1.48657i	−0.668974	+	0.743286i	$0.733266\pi$
$860$	−1.05219	+	1.05219i	−0.0358794	+	0.0358794i
$861$		0			0
$862$			21.5441i			0.733795i
$863$	9.02893	+	9.02893i	0.307348	+	0.307348i	0.843880	−	0.536532i	$-0.180266\pi$
$863$	9.02893	+	9.02893i	0.307348	+	0.307348i	−0.536532	+	0.843880i	$0.680266\pi$
$864$		0			0
$865$	4.58670	−	4.58670i	0.155952	−	0.155952i
$866$	12.2548	+	12.2548i	0.416436	+	0.416436i
$867$		0			0
$868$	−9.60827	−	9.71646i	−0.326126	−	0.329798i
$869$	32.6339	−	32.6339i	1.10703	−	1.10703i
$870$		0			0
$871$	−3.89168	+	3.67284i	−0.131864	+	0.124449i
$872$	25.4101			0.860496
$873$		0			0
$874$			1.16022i			0.0392450i
$875$	14.9153	+	15.0833i	0.504231	+	0.509909i
$876$		0			0
$877$	−4.81957	−	4.81957i	−0.162745	−	0.162745i	0.621036	−	0.783782i	$-0.286712\pi$
$877$	−4.81957	−	4.81957i	−0.162745	−	0.162745i	−0.783782	+	0.621036i	$0.786712\pi$
$878$	−17.0767	−	17.0767i	−0.576311	−	0.576311i
$879$		0			0
$880$			5.98209i			0.201656i
$881$	3.46947			0.116889			0.0584447	−	0.998291i	$-0.481386\pi$
$881$	3.46947			0.116889			0.0584447	+	0.998291i	$0.481386\pi$
$882$		0			0
$883$			47.0772i			1.58427i	0.610344	+	0.792136i	$0.291031\pi$
$883$			47.0772i			1.58427i	−0.610344	+	0.792136i	$0.708969\pi$
$884$	5.92162	+	0.171309i	0.199166	+	0.00576175i
$885$		0			0
$886$	−4.81852	−	4.81852i	−0.161881	−	0.161881i
$887$		−	5.75722i		−	0.193309i	−0.995318	−	0.0966543i	$-0.969186\pi$
$887$		−	5.75722i		−	0.193309i	0.995318	−	0.0966543i	$-0.0308141\pi$
$888$		0			0
$889$	0.109259	−	19.5155i	0.00366444	−	0.654530i
$890$	3.55777	+	3.55777i	0.119257	+	0.119257i
$891$		0			0
$892$	2.33000	+	2.33000i	0.0780142	+	0.0780142i
$893$	−1.08783			−0.0364029
$894$		0			0
$895$	−13.9156	−	13.9156i	−0.465148	−	0.465148i
$896$	8.96357	−	8.86376i	0.299452	−	0.296118i
$897$		0			0
$898$	−22.0599			−0.736150
$899$	−25.6549	+	25.6549i	−0.855639	+	0.855639i
$900$		0			0
$901$	10.4578			0.348401
$902$	7.20809	−	7.20809i	0.240003	−	0.240003i
$903$		0			0
$904$	12.4680	−	12.4680i	0.414679	−	0.414679i
$905$	−1.17534	+	1.17534i	−0.0390695	+	0.0390695i
$906$		0			0
$907$			13.1412i			0.436345i	0.975910	+	0.218172i	$0.0700095\pi$
$907$			13.1412i			0.436345i	−0.975910	+	0.218172i	$0.929990\pi$
$908$	2.52896	+	2.52896i	0.0839266	+	0.0839266i
$909$		0			0
$910$	−0.344965	+	9.98927i	−0.0114355	+	0.331141i
$911$	−22.8394			−0.756702			−0.378351	−	0.925662i	$-0.623509\pi$
$911$	−22.8394			−0.756702			−0.378351	+	0.925662i	$0.623509\pi$
$912$		0			0
$913$			39.1232i			1.29479i
$914$		−	11.9083i		−	0.393891i
$915$		0			0
$916$	0.142747	−	0.142747i	0.00471648	−	0.00471648i
$917$	−0.177216	+	31.6537i	−0.00585219	+	1.04530i
$918$		0			0
$919$	35.0265			1.15542			0.577709	−	0.816243i	$-0.303947\pi$
$919$	35.0265			1.15542			0.577709	+	0.816243i	$0.303947\pi$
$920$	17.3207			0.571046
$921$		0			0
$922$	−12.3206			−0.405758
$923$	15.2156	−	14.3600i	0.500826	−	0.472664i
$924$		0			0
$925$	−8.60197	−	8.60197i	−0.282831	−	0.282831i
$926$	6.94110			0.228099
$927$		0			0
$928$	7.92267	+	7.92267i	0.260074	+	0.260074i
$929$	−16.0163	+	16.0163i	−0.525479	+	0.525479i	−0.919221	−	0.393742i	$-0.871180\pi$
$929$	−16.0163	+	16.0163i	−0.525479	+	0.525479i	0.393742	+	0.919221i	$0.371180\pi$
$930$		0			0
$931$	−0.737966	+	0.721622i	−0.0241859	+	0.0236502i
$932$	3.32297			0.108847
$933$		0			0
$934$	14.8428	+	14.8428i	0.485671	+	0.485671i
$935$		−	6.92881i		−	0.226596i
$936$		0			0
$937$			39.2356i			1.28177i	0.767636	+	0.640886i	$0.221433\pi$
$937$			39.2356i			1.28177i	−0.767636	+	0.640886i	$0.778567\pi$
$938$	0.0265701	−	4.74586i	0.000867545	−	0.154958i
$939$		0			0
$940$			3.44852i			0.112478i
$941$	−31.6697	+	31.6697i	−1.03240	+	1.03240i	−0.0329454	+	0.999457i	$0.510489\pi$
$941$	−31.6697	+	31.6697i	−1.03240	+	1.03240i	−0.999457	+	0.0329454i	$0.989511\pi$
$942$		0			0
$943$	−14.8029	−	14.8029i	−0.482049	−	0.482049i
$944$	−24.0763	−	24.0763i	−0.783615	−	0.783615i
$945$		0			0
$946$		−	10.0917i		−	0.328110i
$947$	11.5948	−	11.5948i	0.376780	−	0.376780i	−0.493159	−	0.869939i	$-0.664158\pi$
$947$	11.5948	−	11.5948i	0.376780	−	0.376780i	0.869939	+	0.493159i	$0.164158\pi$
$948$		0			0
$949$	−25.6823	+	24.2381i	−0.833682	+	0.786803i
$950$			0.757136i			0.0245647i
$951$		0			0
$952$	−17.5936	+	17.3977i	−0.570210	+	0.563861i
$953$			37.1939i			1.20483i	0.798183	+	0.602415i	$0.205795\pi$
$953$			37.1939i			1.20483i	−0.798183	+	0.602415i	$0.794205\pi$
$954$		0			0
$955$	−6.13440	+	6.13440i	−0.198504	+	0.198504i
$956$	3.03612	−	3.03612i	0.0981951	−	0.0981951i
$957$		0			0
$958$		−	16.8985i		−	0.545965i
$959$	5.01127	−	4.95547i	0.161822	−	0.160021i
$960$		0			0
$961$		−	60.7552i		−	1.95985i
$962$	0.360834	−	12.4729i	0.0116338	−	0.402143i
$963$		0			0
$964$	−0.599672	+	0.599672i	−0.0193141	+	0.0193141i
$965$		−	12.5483i		−	0.403943i
$966$		0			0
$967$	34.8785	+	34.8785i	1.12162	+	1.12162i	0.991499	+	0.130117i	$0.0415354\pi$
$967$	34.8785	+	34.8785i	1.12162	+	1.12162i	0.130117	+	0.991499i	$0.458465\pi$
$968$	−8.94214	−	8.94214i	−0.287411	−	0.287411i
$969$		0			0
$970$	−4.65562	+	4.65562i	−0.149483	+	0.149483i
$971$		−	13.7033i		−	0.439760i	−0.975527	−	0.219880i	$-0.929433\pi$
$971$		−	13.7033i		−	0.439760i	0.975527	−	0.219880i	$-0.0705666\pi$
$972$		0			0
$973$	−0.0943366	+	16.8501i	−0.00302429	+	0.540189i
$974$			21.5525i			0.690587i
$975$		0			0
$976$			24.2242i			0.775396i
$977$	−5.81011	−	5.81011i	−0.185882	−	0.185882i	0.608031	−	0.793913i	$-0.291960\pi$
$977$	−5.81011	−	5.81011i	−0.185882	−	0.185882i	−0.793913	+	0.608031i	$0.791960\pi$
$978$		0			0
$979$	12.5949			0.402535
$980$	2.28761	+	2.33942i	0.0730749	+	0.0747299i
$981$		0			0
$982$	−1.47414	+	1.47414i	−0.0470418	+	0.0470418i
$983$	12.2658	+	12.2658i	0.391218	+	0.391218i	0.875121	−	0.483904i	$-0.160782\pi$
$983$	12.2658	+	12.2658i	0.391218	+	0.391218i	−0.483904	+	0.875121i	$0.660782\pi$
$984$		0			0
$985$	18.7197			0.596461
$986$	9.86420	+	9.86420i	0.314140	+	0.314140i
$987$		0			0
$988$	0.208471	−	0.196748i	0.00663235	−	0.00625940i
$989$	−20.7249			−0.659013
$990$		0			0
$991$	40.5574			1.28835			0.644175	−	0.764878i	$-0.277201\pi$
$991$	40.5574			1.28835			0.644175	+	0.764878i	$0.277201\pi$
$992$	−28.3355			−0.899655
$993$		0			0
$994$	−0.103883	+	18.5552i	−0.00329497	+	0.588536i
$995$	13.7701	−	13.7701i	0.436542	−	0.436542i
$996$		0			0
$997$			17.4686i			0.553236i	0.960980	+	0.276618i	$0.0892136\pi$
$997$			17.4686i			0.553236i	−0.960980	+	0.276618i	$0.910786\pi$
$998$			47.0999i			1.49092i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.y.h.307.1		12
3.2	odd	2		91.2.i.a.34.6	yes	12
7.6	odd	2	inner	819.2.y.h.307.2		12
13.5	odd	4	inner	819.2.y.h.811.2		12
21.2	odd	6		637.2.bc.a.619.5		24
21.5	even	6		637.2.bc.a.619.6		24
21.11	odd	6		637.2.bc.a.411.2		24
21.17	even	6		637.2.bc.a.411.1		24
21.20	even	2		91.2.i.a.34.5	✓	12
39.5	even	4		91.2.i.a.83.6	yes	12
91.83	even	4	inner	819.2.y.h.811.1		12
273.5	odd	12		637.2.bc.a.31.2		24
273.44	even	12		637.2.bc.a.31.1		24
273.83	odd	4		91.2.i.a.83.5	yes	12
273.122	odd	12		637.2.bc.a.460.5		24
273.200	even	12		637.2.bc.a.460.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.i.a.34.5	✓	12	21.20	even	2
91.2.i.a.34.6	yes	12	3.2	odd	2
91.2.i.a.83.5	yes	12	273.83	odd	4
91.2.i.a.83.6	yes	12	39.5	even	4
637.2.bc.a.31.1		24	273.44	even	12
637.2.bc.a.31.2		24	273.5	odd	12
637.2.bc.a.411.1		24	21.17	even	6
637.2.bc.a.411.2		24	21.11	odd	6
637.2.bc.a.460.5		24	273.122	odd	12
637.2.bc.a.460.6		24	273.200	even	12
637.2.bc.a.619.5		24	21.2	odd	6
637.2.bc.a.619.6		24	21.5	even	6
819.2.y.h.307.1		12	1.1	even	1	trivial
819.2.y.h.307.2		12	7.6	odd	2	inner
819.2.y.h.811.1		12	91.83	even	4	inner
819.2.y.h.811.2		12	13.5	odd	4	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)

\(f(q)\)	\(=\)	\(q+(-0.854638 - 0.854638i) q^{2} -0.539189i q^{4} +(-0.612999 + 0.612999i) q^{5} +(-2.64571 - 0.0148122i) q^{7} +(-2.17009 + 2.17009i) q^{8} +O(q^{10})\)	\(q+(-0.854638 - 0.854638i) q^{2} -0.539189i q^{4} +(-0.612999 + 0.612999i) q^{5} +(-2.64571 - 0.0148122i) q^{7} +(-2.17009 + 2.17009i) q^{8} +1.04778 q^{10} +(1.85464 - 1.85464i) q^{11} +(0.104263 - 3.60404i) q^{13} +(2.24846 + 2.27378i) q^{14} +2.63090 q^{16} -3.04726 q^{17} +(-0.104263 + 0.104263i) q^{19} +(0.330522 + 0.330522i) q^{20} -3.17009 q^{22} +6.51026i q^{23} +4.24846i q^{25} +(-3.16926 + 2.99104i) q^{26} +(-0.00798659 + 1.42654i) q^{28} +3.78765 q^{29} +(-6.77330 + 6.77330i) q^{31} +(2.09171 + 2.09171i) q^{32} +(2.60430 + 2.60430i) q^{34} +(1.63090 - 1.61274i) q^{35} +(-2.02472 + 2.02472i) q^{37} +0.178214 q^{38} -2.66052i q^{40} +(-2.27378 + 2.27378i) q^{41} +3.18342i q^{43} +(-1.00000 - 1.00000i) q^{44} +(5.56391 - 5.56391i) q^{46} +(5.21678 + 5.21678i) q^{47} +(6.99956 + 0.0783777i) q^{49} +(3.63090 - 3.63090i) q^{50} +(-1.94326 - 0.0562174i) q^{52} -3.43188 q^{53} +2.27378i q^{55} +(5.77356 - 5.70928i) q^{56} +(-3.23707 - 3.23707i) q^{58} +(-9.15135 - 9.15135i) q^{59} +9.20756i q^{61} +11.5774 q^{62} -8.83710i q^{64} +(2.14536 + 2.27319i) q^{65} +(-1.04945 - 1.04945i) q^{67} +1.64305i q^{68} +(-2.77213 - 0.0155200i) q^{70} +(4.10310 + 4.10310i) q^{71} +(-6.92561 - 6.92561i) q^{73} +3.46081 q^{74} +(0.0562174 + 0.0562174i) q^{76} +(-4.93430 + 4.87936i) q^{77} +17.5958 q^{79} +(-1.61274 + 1.61274i) q^{80} +3.88652 q^{82} +(-10.5474 + 10.5474i) q^{83} +(1.86797 - 1.86797i) q^{85} +(2.72067 - 2.72067i) q^{86} +8.04945i q^{88} +(3.39552 + 3.39552i) q^{89} +(-0.329233 + 9.53371i) q^{91} +3.51026 q^{92} -8.91692i q^{94} -0.127826i q^{95} +(-4.44330 + 4.44330i) q^{97} +(-5.91510 - 6.04907i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} - 8 q^{7} - 4 q^{8}+O(q^{10}) \) 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

Related objects

Downloads

Learn more