LMFDB - Embedded newform 819.2.y.h.811.1

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			811.1
Root			$1.33026 - 1.33026i$ of defining polynomial
Character	$\chi$	$=$	819.811
Dual form			819.2.y.h.307.1

$q$-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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.854638	+	0.854638i	−0.604320	+	0.604320i	−0.941456	−	0.337136i	$-0.890542\pi$
$2$	−0.854638	+	0.854638i	−0.604320	+	0.604320i	0.337136	+	0.941456i	$0.390542\pi$
$3$		0			0
$3$		0			0
$4$			0.539189i			0.269594i
$5$	−0.612999	−	0.612999i	−0.274142	−	0.274142i	0.556623	−	0.830765i	$-0.312097\pi$
$5$	−0.612999	−	0.612999i	−0.274142	−	0.274142i	−0.830765	+	0.556623i	$0.812097\pi$
$6$		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	0.929078	−	0.369884i	$-0.120602\pi$
$11$	1.85464	+	1.85464i	0.559194	+	0.559194i	−0.369884	+	0.929078i	$0.620602\pi$
$12$		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	0.695046	−	0.718965i	$-0.255384\pi$
$19$	−0.104263	−	0.104263i	−0.0239195	−	0.0239195i	−0.718965	+	0.695046i	$0.755384\pi$
$20$	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	$-0.762526\pi$
$23$		−	6.51026i		−	1.35748i	0.734377	−	0.678741i	$-0.237474\pi$
$24$		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	−0.968842	−	0.247679i	$-0.920332\pi$
$31$	−6.77330	−	6.77330i	−1.21652	−	1.21652i	−0.247679	−	0.968842i	$-0.579668\pi$
$32$	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	0.520810	−	0.853673i	$-0.325630\pi$
$37$	−2.02472	−	2.02472i	−0.332863	−	0.332863i	−0.853673	+	0.520810i	$0.825630\pi$
$38$	0.178214			0.0289101
$39$		0			0
$40$			2.66052i			0.420665i
$41$	−2.27378	−	2.27378i	−0.355105	−	0.355105i	0.506900	−	0.862005i	$-0.330791\pi$
$41$	−2.27378	−	2.27378i	−0.355105	−	0.355105i	−0.862005	+	0.506900i	$0.830791\pi$
$42$		0			0
$43$		−	3.18342i		−	0.485467i	−0.970093	−	0.242733i	$-0.921956\pi$
$43$		−	3.18342i		−	0.485467i	0.970093	−	0.242733i	$-0.0780440\pi$
$44$	−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	−0.215548	−	0.976493i	$-0.569154\pi$
$47$	5.21678	−	5.21678i	0.760946	−	0.760946i	0.976493	+	0.215548i	$0.0691536\pi$
$48$		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	−0.214731	+	0.976673i	$0.568887\pi$
$59$	−9.15135	+	9.15135i	−1.19140	+	1.19140i	−0.976673	+	0.214731i	$0.931113\pi$
$60$		0			0
$61$		−	9.20756i		−	1.17891i	−0.807802	−	0.589454i	$-0.799343\pi$
$61$		−	9.20756i		−	1.17891i	0.807802	−	0.589454i	$-0.200657\pi$
$62$	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	−0.768300	−	0.640090i	$-0.778897\pi$
$67$	−1.04945	+	1.04945i	−0.128211	+	0.128211i	0.640090	+	0.768300i	$0.278897\pi$
$68$		−	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	−0.420393	−	0.907342i	$-0.638108\pi$
$71$	4.10310	−	4.10310i	0.486949	−	0.486949i	0.907342	+	0.420393i	$0.138108\pi$
$72$		0			0
$73$	−6.92561	+	6.92561i	−0.810581	+	0.810581i	−0.984721	−	0.174140i	$-0.944286\pi$
$73$	−6.92561	+	6.92561i	−0.810581	+	0.810581i	0.174140	+	0.984721i	$0.444286\pi$
$74$	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	−0.984963	−	0.172763i	$-0.944731\pi$
$83$	−10.5474	−	10.5474i	−1.15773	−	1.15773i	−0.172763	−	0.984963i	$-0.555269\pi$
$84$		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	−0.503861	−	0.863785i	$-0.668088\pi$
$89$	3.39552	−	3.39552i	0.359924	−	0.359924i	0.863785	+	0.503861i	$0.168088\pi$
$90$		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	0.444587	−	0.895736i	$-0.353351\pi$
$97$	−4.44330	−	4.44330i	−0.451149	−	0.451149i	−0.895736	+	0.444587i	$0.853351\pi$
$98$	−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	−0.929527	−	0.368754i	$-0.879784\pi$
$109$	−5.85464	+	5.85464i	−0.560773	+	0.560773i	0.368754	+	0.929527i	$0.379784\pi$
$110$	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	$-0.893871\pi$
$127$		−	7.37629i		−	0.654540i	0.944931	−	0.327270i	$-0.106129\pi$
$128$	−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	$0.175059\pi$
$131$			11.9642i			1.04532i	−0.852543	+	0.522658i	$0.824941\pi$
$132$		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	0.622052	−	0.782976i	$-0.286299\pi$
$137$	−1.88357	−	1.88357i	−0.160924	−	0.160924i	−0.782976	+	0.622052i	$0.786299\pi$
$138$		0			0
$139$			6.36883i			0.540197i	0.962833	+	0.270098i	$0.0870563\pi$
$139$			6.36883i			0.540197i	−0.962833	+	0.270098i	$0.912944\pi$
$140$	−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	−0.0972667	+	0.995258i	$0.531010\pi$
$149$	−13.3360	+	13.3360i	−1.09253	+	1.09253i	−0.995258	+	0.0972667i	$0.968990\pi$
$150$		0			0
$151$	7.64229	+	7.64229i	0.621921	+	0.621921i	0.946022	−	0.324102i	$-0.105062\pi$
$151$	7.64229	+	7.64229i	0.621921	+	0.621921i	−0.324102	+	0.946022i	$0.605062\pi$
$152$			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	$0.316946\pi$
$157$			21.0290i			1.67830i	−0.543903	+	0.839148i	$0.683054\pi$
$158$	−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	0.375650	−	0.926762i	$-0.377419\pi$
$163$	−7.03612	−	7.03612i	−0.551111	−	0.551111i	−0.926762	+	0.375650i	$0.877419\pi$
$164$	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	−0.0640620	−	0.997946i	$-0.520406\pi$
$167$	12.0684	−	12.0684i	0.933884	−	0.933884i	0.997946	+	0.0640620i	$0.0204055\pi$
$168$		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	$-0.677584\pi$
$179$		−	22.7009i		−	1.69674i	0.529402	−	0.848371i	$-0.322416\pi$
$180$		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	0.235205	−	0.971946i	$-0.424424\pi$
$193$	−10.2351	−	10.2351i	−0.736741	−	0.736741i	−0.971946	+	0.235205i	$0.924424\pi$
$194$	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	−0.0921223	+	0.995748i	$0.529365\pi$
$197$	−15.2690	+	15.2690i	−1.08787	+	1.08787i	−0.995748	+	0.0921223i	$0.970635\pi$
$198$		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	0.547457	−	0.836833i	$-0.315596\pi$
$223$	−4.32131	−	4.32131i	−0.289376	−	0.289376i	−0.836833	+	0.547457i	$0.815596\pi$
$224$	−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	0.534109	−	0.845416i	$-0.320647\pi$
$227$	−4.69031	−	4.69031i	−0.311307	−	0.311307i	−0.845416	+	0.534109i	$0.820647\pi$
$228$		0			0
$229$	0.264743	−	0.264743i	0.0174947	−	0.0174947i	−0.698305	−	0.715800i	$-0.746062\pi$
$229$	0.264743	−	0.264743i	0.0174947	−	0.0174947i	0.715800	+	0.698305i	$0.246062\pi$
$230$		−	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	$-0.935297\pi$
$233$		−	6.16290i		−	0.403745i	0.979412	−	0.201872i	$-0.0647026\pi$
$234$		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	−0.501136	−	0.865369i	$-0.667084\pi$
$239$	5.63090	−	5.63090i	0.364232	−	0.364232i	0.865369	+	0.501136i	$0.167084\pi$
$240$		0			0
$241$	−1.11217	+	1.11217i	−0.0716414	+	0.0716414i	−0.742020	−	0.670378i	$-0.766132\pi$
$241$	−1.11217	+	1.11217i	−0.0716414	+	0.0716414i	0.670378	+	0.742020i	$0.266132\pi$
$242$	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	$0.253039\pi$
$269$			23.4152i			1.42765i	−0.700324	+	0.713825i	$0.746961\pi$
$270$		0			0
$271$	−2.41653	+	2.41653i	−0.146794	+	0.146794i	−0.776684	−	0.629890i	$-0.783100\pi$
$271$	−2.41653	+	2.41653i	−0.146794	+	0.146794i	0.629890	+	0.776684i	$0.283100\pi$
$272$	−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	$0.338084\pi$
$277$			29.0722i			1.74678i	−0.487020	+	0.873391i	$0.661916\pi$
$278$	−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	0.356546	−	0.934278i	$-0.383954\pi$
$281$	−9.68455	−	9.68455i	−0.577732	−	0.577732i	−0.934278	+	0.356546i	$0.883954\pi$
$282$		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	−0.594969	−	0.803749i	$-0.702836\pi$
$293$	3.57373	−	3.57373i	0.208780	−	0.208780i	0.803749	+	0.594969i	$0.202836\pi$
$294$		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	−0.417952	−	0.908469i	$-0.637252\pi$
$307$	8.59457	−	8.59457i	0.490518	−	0.490518i	0.908469	+	0.417952i	$0.137252\pi$
$308$	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	$-0.961142\pi$
$313$		−	4.30873i		−	0.243544i	0.992558	−	0.121772i	$-0.0388576\pi$
$314$	−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	−0.809776	−	0.586739i	$-0.800412\pi$
$317$	−3.97107	+	3.97107i	−0.223038	+	0.223038i	0.586739	+	0.809776i	$0.300412\pi$
$318$		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	−0.658570	−	0.752520i	$-0.728838\pi$
$331$	1.70928	−	1.70928i	0.0939503	−	0.0939503i	0.752520	+	0.658570i	$0.228838\pi$
$332$	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	$0.216970\pi$
$337$			23.1327i			1.26012i	−0.776546	+	0.630061i	$0.783030\pi$
$338$	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	0.0209053	−	0.999781i	$-0.493345\pi$
$349$	19.0680	−	19.0680i	1.02069	−	1.02069i	0.999781	−	0.0209053i	$-0.00665484\pi$
$350$	−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	0.567346	−	0.823479i	$-0.307970\pi$
$353$	−4.81231	−	4.81231i	−0.256133	−	0.256133i	−0.823479	+	0.567346i	$0.807970\pi$
$354$		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	0.955944	−	0.293549i	$-0.0948365\pi$
$359$	12.5506	+	12.5506i	0.662394	+	0.662394i	−0.293549	+	0.955944i	$0.594837\pi$
$360$		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	$-0.796289\pi$
$367$		−	22.8806i		−	1.19436i	0.802109	−	0.597178i	$-0.203711\pi$
$368$		−	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	−0.607346	−	0.794438i	$-0.707766\pi$
$379$	3.64229	−	3.64229i	0.187092	−	0.187092i	0.794438	+	0.607346i	$0.207766\pi$
$380$	−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	−0.953492	−	0.301419i	$-0.902540\pi$
$383$	−24.5591	−	24.5591i	−1.25491	−	1.25491i	−0.301419	−	0.953492i	$-0.597460\pi$
$384$		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	$0.0526080\pi$
$389$			6.48974i			0.329043i	−0.986374	+	0.164521i	$0.947392\pi$
$390$		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	−0.512576	−	0.858642i	$-0.671309\pi$
$397$	6.89530	−	6.89530i	0.346065	−	0.346065i	0.858642	+	0.512576i	$0.171309\pi$
$398$	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	0.444969	−	0.895546i	$-0.353215\pi$
$401$	−9.02279	−	9.02279i	−0.450576	−	0.450576i	−0.895546	+	0.444969i	$0.853215\pi$
$402$		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	0.632830	−	0.774291i	$-0.281893\pi$
$409$	−2.86088	−	2.86088i	−0.141461	−	0.141461i	−0.774291	+	0.632830i	$0.781893\pi$
$410$	−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	$-0.667357\pi$
$419$		−	35.4097i		−	1.72988i	0.501878	−	0.864939i	$-0.332643\pi$
$420$		0			0
$421$	18.9307	−	18.9307i	0.922628	−	0.922628i	−0.0745864	−	0.997215i	$-0.523764\pi$
$421$	18.9307	−	18.9307i	0.922628	−	0.922628i	0.997215	+	0.0745864i	$0.0237636\pi$
$422$	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	−0.942194	−	0.335069i	$-0.891240\pi$
$431$	−12.6042	+	12.6042i	−0.607125	+	0.607125i	0.335069	+	0.942194i	$0.391240\pi$
$432$		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	0.942704	−	0.333631i	$-0.108274\pi$
$449$	12.9060	+	12.9060i	0.609073	+	0.609073i	−0.333631	+	0.942704i	$0.608274\pi$
$450$		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	−0.525127	−	0.851024i	$-0.675982\pi$
$457$	6.96687	−	6.96687i	0.325896	−	0.325896i	0.851024	+	0.525127i	$0.175982\pi$
$458$			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	0.854752	−	0.519037i	$-0.173709\pi$
$461$	7.20809	+	7.20809i	0.335714	+	0.335714i	−0.519037	+	0.854752i	$0.673709\pi$
$462$		0			0
$463$	−4.06084	−	4.06084i	−0.188723	−	0.188723i	0.606421	−	0.795144i	$-0.292605\pi$
$463$	−4.06084	−	4.06084i	−0.188723	−	0.188723i	−0.795144	+	0.606421i	$0.792605\pi$
$464$	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	−0.444206	−	0.895925i	$-0.646514\pi$
$479$	9.88634	−	9.88634i	0.451719	−	0.451719i	0.895925	+	0.444206i	$0.146514\pi$
$480$		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	−0.932513	−	0.361137i	$-0.882389\pi$
$487$	−12.6092	+	12.6092i	−0.571375	+	0.571375i	0.361137	+	0.932513i	$0.382389\pi$
$488$	−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	$0.0123921\pi$
$491$			1.72487i			0.0778425i	−0.999242	+	0.0389212i	$0.987608\pi$
$492$		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	−0.270964	+	0.962589i	$0.587343\pi$
$499$	−27.5555	+	27.5555i	−1.23355	+	1.23355i	−0.962589	+	0.270964i	$0.912657\pi$
$500$	−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	$-0.845826\pi$
$503$		−	20.8862i		−	0.931272i	0.884976	−	0.465636i	$-0.154174\pi$
$504$		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	0.959052	−	0.283229i	$-0.0914057\pi$
$509$	15.2473	+	15.2473i	0.675823	+	0.675823i	−0.283229	+	0.959052i	$0.591406\pi$
$510$		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	$-0.854451\pi$
$521$		−	20.1543i		−	0.882975i	0.897268	−	0.441487i	$-0.145549\pi$
$522$		0			0
$523$			11.3031i			0.494251i	0.968983	+	0.247126i	$0.0794861\pi$
$523$			11.3031i			0.494251i	−0.968983	+	0.247126i	$0.920514\pi$
$524$	−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	0.478650	−	0.878006i	$-0.341126\pi$
$541$	−9.28879	−	9.28879i	−0.399356	−	0.399356i	−0.878006	+	0.478650i	$0.841126\pi$
$542$		−	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	0.965269	−	0.261257i	$-0.0841369\pi$
$557$	16.6153	+	16.6153i	0.704013	+	0.704013i	−0.261257	+	0.965269i	$0.584137\pi$
$558$		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	$-0.876321\pi$
$569$		−	18.0738i		−	0.757695i	0.925459	−	0.378847i	$-0.123679\pi$
$570$		0			0
$571$		−	8.53692i		−	0.357259i	−0.983916	−	0.178630i	$-0.942834\pi$
$571$		−	8.53692i		−	0.357259i	0.983916	−	0.178630i	$-0.0571664\pi$
$572$	−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	0.862555	−	0.505963i	$-0.168863\pi$
$577$	8.56564	+	8.56564i	0.356592	+	0.356592i	−0.505963	+	0.862555i	$0.668863\pi$
$578$	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	0.700714	−	0.713442i	$-0.252865\pi$
$587$	−0.308382	−	0.308382i	−0.0127283	−	0.0127283i	−0.713442	+	0.700714i	$0.752865\pi$
$588$		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	−0.801436	−	0.598080i	$-0.795930\pi$
$593$	−4.95204	+	4.95204i	−0.203356	+	0.203356i	0.598080	+	0.801436i	$0.295930\pi$
$594$		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	$0.0465677\pi$
$601$			7.14746i			0.291551i	−0.989318	+	0.145776i	$0.953432\pi$
$602$	−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	$-0.792818\pi$
$607$		−	29.8550i		−	1.21178i	0.795550	−	0.605888i	$-0.207182\pi$
$608$	−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	−0.825083	−	0.565011i	$-0.808872\pi$
$613$	−6.43907	+	6.43907i	−0.260072	+	0.260072i	0.565011	+	0.825083i	$0.308872\pi$
$614$			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	−0.956296	−	0.292402i	$-0.905546\pi$
$617$	−16.4908	+	16.4908i	−0.663894	+	0.663894i	0.292402	+	0.956296i	$0.405546\pi$
$618$		0			0
$619$	22.3208	−	22.3208i	0.897148	−	0.897148i	−0.0980353	−	0.995183i	$-0.531256\pi$
$619$	22.3208	−	22.3208i	0.897148	−	0.897148i	0.995183	+	0.0980353i	$0.0312558\pi$
$620$	−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	0.777826	−	0.628480i	$-0.216322\pi$
$631$	3.75154	+	3.75154i	0.149346	+	0.149346i	−0.628480	+	0.777826i	$0.716322\pi$
$632$	−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	$0.169408\pi$
$641$			25.6947i			1.01488i	−0.861687	+	0.507440i	$0.830592\pi$
$642$		0			0
$643$	−22.1537	−	22.1537i	−0.873658	−	0.873658i	0.119211	−	0.992869i	$-0.461964\pi$
$643$	−22.1537	−	22.1537i	−0.873658	−	0.873658i	−0.992869	+	0.119211i	$0.961964\pi$
$644$	−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	−0.863144	−	0.504957i	$-0.831508\pi$
$661$	−9.20895	+	9.20895i	−0.358187	+	0.358187i	0.504957	+	0.863144i	$0.331508\pi$
$662$			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	$0.143675\pi$
$673$			22.6319i			0.872397i	−0.899850	+	0.436199i	$0.856325\pi$
$674$	−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	$-0.933928\pi$
$677$		−	10.7242i		−	0.412165i	0.978535	−	0.206082i	$-0.0660715\pi$
$678$		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	0.774463	−	0.632619i	$-0.218020\pi$
$683$	3.70701	+	3.70701i	0.141845	+	0.141845i	−0.632619	+	0.774463i	$0.718020\pi$
$684$		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	0.712151	−	0.702027i	$-0.247721\pi$
$691$	0.266133	+	0.266133i	0.0101242	+	0.0101242i	−0.702027	+	0.712151i	$0.747721\pi$
$692$		−	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	$0.222202\pi$
$701$			34.0349i			1.28548i	−0.766084	+	0.642740i	$0.777798\pi$
$702$		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	0.889257	−	0.457408i	$-0.151222\pi$
$709$	11.4989	+	11.4989i	0.431849	+	0.431849i	−0.457408	+	0.889257i	$0.651222\pi$
$710$	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	0.925637	−	0.378414i	$-0.123530\pi$
$733$	14.8155	+	14.8155i	0.547223	+	0.547223i	−0.378414	+	0.925637i	$0.623530\pi$
$734$	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	0.938604	−	0.344997i	$-0.112120\pi$
$739$	16.1370	+	16.1370i	0.593607	+	0.593607i	−0.344997	+	0.938604i	$0.612120\pi$
$740$	−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	−0.108652	−	0.994080i	$-0.534653\pi$
$743$	24.1350	−	24.1350i	0.885428	−	0.885428i	0.994080	+	0.108652i	$0.0346534\pi$
$744$		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	$-0.900976\pi$
$751$		−	16.7770i		−	0.612201i	0.951999	−	0.306100i	$-0.0990243\pi$
$752$	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	−0.744372	−	0.667765i	$-0.767251\pi$
$761$	−2.11330	+	2.11330i	−0.0766071	+	0.0766071i	0.667765	+	0.744372i	$0.267251\pi$
$762$		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	0.998049	−	0.0624284i	$-0.0198845\pi$
$769$	25.9456	+	25.9456i	0.935621	+	0.935621i	−0.0624284	+	0.998049i	$0.519885\pi$
$770$	−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	0.689785	−	0.724015i	$-0.257705\pi$
$773$	−0.951693	−	0.951693i	−0.0342300	−	0.0342300i	−0.724015	+	0.689785i	$0.757705\pi$
$774$		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	−0.109862	−	0.993947i	$-0.535041\pi$
$787$	24.8017	−	24.8017i	0.884085	−	0.884085i	0.993947	+	0.109862i	$0.0350409\pi$
$788$	−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	0.901729	−	0.432301i	$-0.142298\pi$
$811$	13.3684	+	13.3684i	0.469428	+	0.469428i	−0.432301	+	0.901729i	$0.642298\pi$
$812$	−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	−0.941380	−	0.337349i	$-0.890470\pi$
$821$	−17.3074	+	17.3074i	−0.604031	+	0.604031i	0.337349	+	0.941380i	$0.390470\pi$
$822$		0			0
$823$			35.0772i			1.22271i	0.791355	+	0.611356i	$0.209376\pi$
$823$			35.0772i			1.22271i	−0.791355	+	0.611356i	$0.790624\pi$
$824$	−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	0.958912	−	0.283705i	$-0.0915636\pi$
$827$	19.4173	+	19.4173i	0.675207	+	0.675207i	−0.283705	+	0.958912i	$0.591564\pi$
$828$		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	−0.995789	−	0.0916731i	$-0.970779\pi$
$839$	−26.1882	+	26.1882i	−0.904116	+	0.904116i	0.0916731	+	0.995789i	$0.470779\pi$
$840$		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	−0.826652	−	0.562713i	$-0.809758\pi$
$853$	−7.70865	+	7.70865i	−0.263939	+	0.263939i	0.562713	+	0.826652i	$0.309758\pi$
$854$	−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	$-0.733266\pi$
$859$		−	43.5695i		−	1.48657i	0.668974	−	0.743286i	$-0.266734\pi$
$860$	−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	−0.536532	−	0.843880i	$-0.680266\pi$
$863$	9.02893	−	9.02893i	0.307348	−	0.307348i	0.843880	+	0.536532i	$0.180266\pi$
$864$		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	−0.783782	−	0.621036i	$-0.786712\pi$
$877$	−4.81957	+	4.81957i	−0.162745	+	0.162745i	0.621036	+	0.783782i	$0.286712\pi$
$878$	−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	$-0.708969\pi$
$883$		−	47.0772i		−	1.58427i	0.610344	−	0.792136i	$-0.291031\pi$
$884$	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	$0.0308141\pi$
$887$			5.75722i			0.193309i	−0.995318	+	0.0966543i	$0.969186\pi$
$888$		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	$-0.929990\pi$
$907$		−	13.1412i		−	0.436345i	0.975910	−	0.218172i	$-0.0700095\pi$
$908$	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	0.393742	−	0.919221i	$-0.371180\pi$
$929$	−16.0163	−	16.0163i	−0.525479	−	0.525479i	−0.919221	+	0.393742i	$0.871180\pi$
$930$		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	$-0.778567\pi$
$937$		−	39.2356i		−	1.28177i	0.767636	−	0.640886i	$-0.221433\pi$
$938$	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	−0.999457	−	0.0329454i	$-0.989511\pi$
$941$	−31.6697	−	31.6697i	−1.03240	−	1.03240i	−0.0329454	−	0.999457i	$-0.510489\pi$
$942$		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	0.869939	−	0.493159i	$-0.164158\pi$
$947$	11.5948	+	11.5948i	0.376780	+	0.376780i	−0.493159	+	0.869939i	$0.664158\pi$
$948$		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	$-0.794205\pi$
$953$		−	37.1939i		−	1.20483i	0.798183	−	0.602415i	$-0.205795\pi$
$954$		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	0.130117	−	0.991499i	$-0.458465\pi$
$967$	34.8785	−	34.8785i	1.12162	−	1.12162i	0.991499	−	0.130117i	$-0.0415354\pi$
$968$	−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	$0.0705666\pi$
$971$			13.7033i			0.439760i	−0.975527	+	0.219880i	$0.929433\pi$
$972$		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	−0.793913	−	0.608031i	$-0.791960\pi$
$977$	−5.81011	+	5.81011i	−0.185882	+	0.185882i	0.608031	+	0.793913i	$0.291960\pi$
$978$		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	−0.483904	−	0.875121i	$-0.660782\pi$
$983$	12.2658	−	12.2658i	0.391218	−	0.391218i	0.875121	+	0.483904i	$0.160782\pi$
$984$		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	$-0.910786\pi$
$997$		−	17.4686i		−	0.553236i	0.960980	−	0.276618i	$-0.0892136\pi$
$998$		−	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.811.1		12
3.2	odd	2		91.2.i.a.83.5	yes	12
7.6	odd	2	inner	819.2.y.h.811.2		12
13.8	odd	4	inner	819.2.y.h.307.2		12
21.2	odd	6		637.2.bc.a.31.2		24
21.5	even	6		637.2.bc.a.31.1		24
21.11	odd	6		637.2.bc.a.460.5		24
21.17	even	6		637.2.bc.a.460.6		24
21.20	even	2		91.2.i.a.83.6	yes	12
39.8	even	4		91.2.i.a.34.5	✓	12
91.34	even	4	inner	819.2.y.h.307.1		12
273.47	odd	12		637.2.bc.a.619.5		24
273.86	even	12		637.2.bc.a.619.6		24
273.125	odd	4		91.2.i.a.34.6	yes	12
273.164	odd	12		637.2.bc.a.411.2		24
273.242	even	12		637.2.bc.a.411.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.i.a.34.5	✓	12	39.8	even	4
91.2.i.a.34.6	yes	12	273.125	odd	4
91.2.i.a.83.5	yes	12	3.2	odd	2
91.2.i.a.83.6	yes	12	21.20	even	2
637.2.bc.a.31.1		24	21.5	even	6
637.2.bc.a.31.2		24	21.2	odd	6
637.2.bc.a.411.1		24	273.242	even	12
637.2.bc.a.411.2		24	273.164	odd	12
637.2.bc.a.460.5		24	21.11	odd	6
637.2.bc.a.460.6		24	21.17	even	6
637.2.bc.a.619.5		24	273.47	odd	12
637.2.bc.a.619.6		24	273.86	even	12
819.2.y.h.307.1		12	91.34	even	4	inner
819.2.y.h.307.2		12	13.8	odd	4	inner
819.2.y.h.811.1		12	1.1	even	1	trivial
819.2.y.h.811.2		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)

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

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Representations

Groups

Database

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