LMFDB - Embedded newform 832.2.bu.n.319.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [832,2,Mod(63,832)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(832, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 7]))

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

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

chi := DirichletCharacter("832.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 832 = 2^{6} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	832.bu (of order $12$, degree $4$, not 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:	$6.64355344817$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.102930383934669717504.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 5 x^{14} - 2 x^{13} + 5 x^{12} - 8 x^{11} - 12 x^{10} + 32 x^{9} - 36 x^{8} + \cdots + 256 $ x^16 - 4x^15 + 5x^14 - 2x^13 + 5x^12 - 8x^11 - 12x^10 + 32x^9 - 36x^8 + 64x^7 - 48x^6 - 64x^5 + 80x^4 - 64x^3 + 320x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			319.2
Root			$1.08916 + 0.902074i$ of defining polynomial
Character	$\chi$	$=$	832.319
Dual form			832.2.bu.n.639.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.736159 - 0.425021i) q^{3} +(0.166404 + 0.166404i) q^{5} +(-0.684384 + 2.55416i) q^{7} +(-1.13871 - 1.97231i) q^{9} +(-1.39298 + 0.373247i) q^{11} +(0.406663 - 3.58254i) q^{13} +(-0.0517744 - 0.193225i) q^{15} +(1.21178 - 0.699622i) q^{17} +(5.39188 + 1.44475i) q^{19} +(1.58939 - 1.58939i) q^{21} +(4.37216 - 7.57279i) q^{23} -4.94462i q^{25} +4.48604i q^{27} +(2.11023 - 3.65503i) q^{29} +(-3.88100 + 3.88100i) q^{31} +(1.18409 + 0.317276i) q^{33} +(-0.538906 + 0.311137i) q^{35} +(0.133975 + 0.500000i) q^{37} +(-1.82203 + 2.46448i) q^{39} +(5.59808 - 1.50000i) q^{41} +(-4.59362 - 7.95638i) q^{43} +(0.138714 - 0.517686i) q^{45} +(2.80318 + 2.80318i) q^{47} +(0.00684229 + 0.00395040i) q^{49} -1.18942 q^{51} +5.94462 q^{53} +(-0.293906 - 0.169687i) q^{55} +(-3.35523 - 3.35523i) q^{57} +(2.20512 - 8.22961i) q^{59} +(-3.61102 - 6.25448i) q^{61} +(5.81691 - 1.55864i) q^{63} +(0.663819 - 0.528479i) q^{65} +(-0.652790 - 2.43624i) q^{67} +(-6.43720 + 3.71652i) q^{69} +(-10.5002 - 2.81352i) q^{71} +(5.05407 - 5.05407i) q^{73} +(-2.10157 + 3.64002i) q^{75} -3.81333i q^{77} -8.51654i q^{79} +(-1.50948 + 2.61449i) q^{81} +(-6.91195 + 6.91195i) q^{83} +(0.318065 + 0.0852251i) q^{85} +(-3.10694 + 1.79379i) q^{87} +(-1.71941 - 6.41693i) q^{89} +(8.87207 + 3.49052i) q^{91} +(4.50653 - 1.20752i) q^{93} +(0.656818 + 1.13764i) q^{95} +(-4.00474 + 14.9459i) q^{97} +(2.32236 + 2.32236i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5} + 4 q^{9} + 12 q^{13} + 12 q^{17} + 28 q^{21} + 8 q^{29} - 20 q^{33} + 16 q^{37} + 48 q^{41} - 20 q^{45} + 60 q^{49} + 32 q^{53} + 12 q^{57} - 4 q^{61} - 8 q^{65} + 12 q^{69} + 20 q^{73}+ \cdots - 28 q^{97}+O(q^{100}) $ 16 * q + 12 * q^5 + 4 * q^9 + 12 * q^13 + 12 * q^17 + 28 * q^21 + 8 * q^29 - 20 * q^33 + 16 * q^37 + 48 * q^41 - 20 * q^45 + 60 * q^49 + 32 * q^53 + 12 * q^57 - 4 * q^61 - 8 * q^65 + 12 * q^69 + 20 * q^73 + 48 * q^81 - 20 * q^85 - 52 * q^89 + 92 * q^93 - 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/832\mathbb{Z}\right)^\times$.

$n$	$261$	$703$	$769$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.736159	−	0.425021i	−0.425021	−	0.245386i	0.272202	−	0.962240i	$-0.412248\pi$
$3$	−0.736159	−	0.425021i	−0.425021	−	0.245386i	−0.697223	+	0.716854i	$0.745581\pi$
$4$		0			0
$5$	0.166404	+	0.166404i	0.0744180	+	0.0744180i	0.743336	−	0.668918i	$-0.233242\pi$
$5$	0.166404	+	0.166404i	0.0744180	+	0.0744180i	−0.668918	+	0.743336i	$0.733242\pi$
$6$		0			0
$7$	−0.684384	+	2.55416i	−0.258673	+	0.965381i	0.707337	+	0.706876i	$0.249896\pi$
$7$	−0.684384	+	2.55416i	−0.258673	+	0.965381i	−0.966010	+	0.258504i	$0.916770\pi$
$8$		0			0
$9$	−1.13871	−	1.97231i	−0.379571	−	0.657437i
$10$		0			0
$11$	−1.39298	+	0.373247i	−0.419998	+	0.112538i	−0.462628	−	0.886553i	$-0.653093\pi$
$11$	−1.39298	+	0.373247i	−0.419998	+	0.112538i	0.0426292	+	0.999091i	$0.486427\pi$
$12$		0			0
$13$	0.406663	−	3.58254i	0.112788	−	0.993619i
$13$	0.406663	−	3.58254i	0.112788	−	0.993619i
$14$		0			0
$15$	−0.0517744	−	0.193225i	−0.0133681	−	0.0498904i
$16$		0			0
$17$	1.21178	−	0.699622i	0.293900	−	0.169683i	−0.345799	−	0.938308i	$-0.612392\pi$
$17$	1.21178	−	0.699622i	0.293900	−	0.169683i	0.639699	+	0.768625i	$0.279059\pi$
$18$		0			0
$19$	5.39188	+	1.44475i	1.23698	+	0.331449i	0.817295	−	0.576220i	$-0.195473\pi$
$19$	5.39188	+	1.44475i	1.23698	+	0.331449i	0.419688	+	0.907668i	$0.362139\pi$
$20$		0			0
$21$	1.58939	−	1.58939i	0.346833	−	0.346833i
$22$		0			0
$23$	4.37216	−	7.57279i	0.911657	−	1.57904i	0.0999345	−	0.994994i	$-0.468137\pi$
$23$	4.37216	−	7.57279i	0.911657	−	1.57904i	0.811723	−	0.584043i	$-0.198530\pi$
$24$		0			0
$25$		−	4.94462i		−	0.988924i
$26$		0			0
$27$			4.48604i			0.863339i
$28$		0			0
$29$	2.11023	−	3.65503i	0.391861	−	0.678723i	−0.600834	−	0.799374i	$-0.705165\pi$
$29$	2.11023	−	3.65503i	0.391861	−	0.678723i	0.992695	+	0.120651i	$0.0384982\pi$
$30$		0			0
$31$	−3.88100	+	3.88100i	−0.697047	+	0.697047i	−0.963773	−	0.266725i	$-0.914058\pi$
$31$	−3.88100	+	3.88100i	−0.697047	+	0.697047i	0.266725	+	0.963773i	$0.414058\pi$
$32$		0			0
$33$	1.18409	+	0.317276i	0.206124	+	0.0552307i
$34$		0			0
$35$	−0.538906	+	0.311137i	−0.0910917	+	0.0525918i
$36$		0			0
$37$	0.133975	+	0.500000i	0.0220253	+	0.0821995i	0.976064	−	0.217485i	$-0.0697853\pi$
$37$	0.133975	+	0.500000i	0.0220253	+	0.0821995i	−0.954038	+	0.299684i	$0.903119\pi$
$38$		0			0
$39$	−1.82203	+	2.46448i	−0.291758	+	0.394633i
$40$		0			0
$41$	5.59808	−	1.50000i	0.874273	−	0.234261i	0.206338	−	0.978481i	$-0.433845\pi$
$41$	5.59808	−	1.50000i	0.874273	−	0.234261i	0.667934	+	0.744220i	$0.267179\pi$
$42$		0			0
$43$	−4.59362	−	7.95638i	−0.700520	−	1.21334i	−0.968284	−	0.249852i	$-0.919618\pi$
$43$	−4.59362	−	7.95638i	−0.700520	−	1.21334i	0.267764	−	0.963484i	$-0.413715\pi$
$44$		0			0
$45$	0.138714	−	0.517686i	0.0206782	−	0.0771721i
$46$		0			0
$47$	2.80318	+	2.80318i	0.408886	+	0.408886i	0.881350	−	0.472464i	$-0.156635\pi$
$47$	2.80318	+	2.80318i	0.408886	+	0.408886i	−0.472464	+	0.881350i	$0.656635\pi$
$48$		0			0
$49$	0.00684229	+	0.00395040i	0.000977470	+	0.000564343i
$50$		0			0
$51$	−1.18942			−0.166552
$52$		0			0
$53$	5.94462			0.816556			0.408278	−	0.912858i	$-0.366129\pi$
$53$	5.94462			0.816556			0.408278	+	0.912858i	$0.366129\pi$
$54$		0			0
$55$	−0.293906	−	0.169687i	−0.0396303	−	0.0228806i
$56$		0			0
$57$	−3.35523	−	3.35523i	−0.444411	−	0.444411i
$58$		0			0
$59$	2.20512	−	8.22961i	0.287082	−	1.07140i	−0.660223	−	0.751070i	$-0.729538\pi$
$59$	2.20512	−	8.22961i	0.287082	−	1.07140i	0.947305	−	0.320334i	$-0.103795\pi$
$60$		0			0
$61$	−3.61102	−	6.25448i	−0.462344	−	0.800804i	0.536733	−	0.843752i	$-0.319658\pi$
$61$	−3.61102	−	6.25448i	−0.462344	−	0.800804i	−0.999077	+	0.0429485i	$0.986325\pi$
$62$		0			0
$63$	5.81691	−	1.55864i	0.732861	−	0.196370i
$64$		0			0
$65$	0.663819	−	0.528479i	0.0823366	−	0.0655497i
$66$		0			0
$67$	−0.652790	−	2.43624i	−0.0797510	−	0.297635i	0.914518	−	0.404546i	$-0.132571\pi$
$67$	−0.652790	−	2.43624i	−0.0797510	−	0.297635i	−0.994269	+	0.106912i	$0.965904\pi$
$68$		0			0
$69$	−6.43720	+	3.71652i	−0.774948	+	0.447416i
$70$		0			0
$71$	−10.5002	−	2.81352i	−1.24614	−	0.333903i	−0.425298	−	0.905053i	$-0.639831\pi$
$71$	−10.5002	−	2.81352i	−1.24614	−	0.333903i	−0.820846	+	0.571150i	$0.806498\pi$
$72$		0			0
$73$	5.05407	−	5.05407i	0.591534	−	0.591534i	−0.346512	−	0.938046i	$-0.612634\pi$
$73$	5.05407	−	5.05407i	0.591534	−	0.591534i	0.938046	+	0.346512i	$0.112634\pi$
$74$		0			0
$75$	−2.10157	+	3.64002i	−0.242668	+	0.420314i
$76$		0			0
$77$		−	3.81333i		−	0.434569i
$78$		0			0
$79$		−	8.51654i		−	0.958186i	−0.877764	−	0.479093i	$-0.840966\pi$
$79$		−	8.51654i		−	0.958186i	0.877764	−	0.479093i	$-0.159034\pi$
$80$		0			0
$81$	−1.50948	+	2.61449i	−0.167720	+	0.290499i
$82$		0			0
$83$	−6.91195	+	6.91195i	−0.758685	+	0.758685i	−0.976083	−	0.217398i	$-0.930243\pi$
$83$	−6.91195	+	6.91195i	−0.758685	+	0.758685i	0.217398	+	0.976083i	$0.430243\pi$
$84$		0			0
$85$	0.318065	+	0.0852251i	0.0344989	+	0.00924396i
$86$		0			0
$87$	−3.10694	+	1.79379i	−0.333098	+	0.192314i
$88$		0			0
$89$	−1.71941	−	6.41693i	−0.182257	−	0.680193i	−0.995201	−	0.0978511i	$-0.968803\pi$
$89$	−1.71941	−	6.41693i	−0.182257	−	0.680193i	0.812944	−	0.582342i	$-0.197864\pi$
$90$		0			0
$91$	8.87207	+	3.49052i	0.930045	+	0.365906i
$92$		0			0
$93$	4.50653	−	1.20752i	0.467306	−	0.125214i
$94$		0			0
$95$	0.656818	+	1.13764i	0.0673881	+	0.116720i
$96$		0			0
$97$	−4.00474	+	14.9459i	−0.406620	+	1.51753i	0.394429	+	0.918926i	$0.370942\pi$
$97$	−4.00474	+	14.9459i	−0.406620	+	1.51753i	−0.801049	+	0.598599i	$0.795724\pi$
$98$		0			0
$99$	2.32236	+	2.32236i	0.233406	+	0.233406i
$100$		0			0
$101$	7.94541	+	4.58728i	0.790598	+	0.456452i	0.840173	−	0.542319i	$-0.182453\pi$
$101$	7.94541	+	4.58728i	0.790598	+	0.456452i	−0.0495752	+	0.998770i	$0.515787\pi$
$102$		0			0
$103$	10.9080			1.07480			0.537398	−	0.843329i	$-0.319407\pi$
$103$	10.9080			1.07480			0.537398	+	0.843329i	$0.319407\pi$
$104$		0			0
$105$	0.528960			0.0516212
$106$		0			0
$107$	8.53605	+	4.92829i	0.825211	+	0.476436i	0.852210	−	0.523200i	$-0.175262\pi$
$107$	8.53605	+	4.92829i	0.825211	+	0.476436i	−0.0269990	+	0.999635i	$0.508595\pi$
$108$		0			0
$109$	−0.0243171	−	0.0243171i	−0.00232916	−	0.00232916i	0.705941	−	0.708270i	$-0.250524\pi$
$109$	−0.0243171	−	0.0243171i	−0.00232916	−	0.00232916i	−0.708270	+	0.705941i	$0.750524\pi$
$110$		0			0
$111$	0.113884	−	0.425021i	0.0108094	−	0.0403412i
$112$		0			0
$113$	−2.27664	−	3.94325i	−0.214168	−	0.370950i	0.738847	−	0.673873i	$-0.235371\pi$
$113$	−2.27664	−	3.94325i	−0.214168	−	0.370950i	−0.953015	+	0.302923i	$0.902037\pi$
$114$		0			0
$115$	1.98769	−	0.532599i	0.185353	−	0.0496651i
$116$		0			0
$117$	−7.52896	+	3.27743i	−0.696053	+	0.302998i
$118$		0			0
$119$	0.957620	+	3.57389i	0.0877849	+	0.327618i
$120$		0			0
$121$	−7.72521	+	4.46015i	−0.702292	+	0.405468i
$122$		0			0
$123$	−4.75860	−	1.27506i	−0.429069	−	0.114969i
$124$		0			0
$125$	1.65482	−	1.65482i	0.148012	−	0.148012i
$126$		0			0
$127$	−2.67207	+	4.62816i	−0.237108	+	0.410683i	−0.959883	−	0.280400i	$-0.909533\pi$
$127$	−2.67207	+	4.62816i	−0.237108	+	0.410683i	0.722775	+	0.691083i	$0.242866\pi$
$128$		0			0
$129$			7.80954i			0.687592i
$130$		0			0
$131$		−	11.2254i		−	0.980764i	−0.871508	−	0.490382i	$-0.836857\pi$
$131$		−	11.2254i		−	0.980764i	0.871508	−	0.490382i	$-0.163143\pi$
$132$		0			0
$133$	−7.38024	+	12.7830i	−0.639948	+	1.10842i
$134$		0			0
$135$	−0.746494	+	0.746494i	−0.0642480	+	0.0642480i
$136$		0			0
$137$	4.64424	+	1.24442i	0.396784	+	0.106318i	0.451693	−	0.892173i	$-0.350820\pi$
$137$	4.64424	+	1.24442i	0.396784	+	0.106318i	−0.0549089	+	0.998491i	$0.517487\pi$
$138$		0			0
$139$	−6.01080	+	3.47034i	−0.509830	+	0.294350i	−0.732764	−	0.680483i	$-0.761770\pi$
$139$	−6.01080	+	3.47034i	−0.509830	+	0.294350i	0.222934	+	0.974834i	$0.428437\pi$
$140$		0			0
$141$	−0.872175	−	3.25500i	−0.0734504	−	0.274121i
$142$		0			0
$143$	0.770702	+	5.14219i	0.0644494	+	0.430011i
$144$		0			0
$145$	0.959363	−	0.257060i	0.0796707	−	0.0213477i
$146$		0			0
$147$	−0.00335801	−	0.00581624i	−0.000276964	−	0.000479715i
$148$		0			0
$149$	−3.92298	+	14.6408i	−0.321383	+	1.19942i	0.596515	+	0.802602i	$0.296552\pi$
$149$	−3.92298	+	14.6408i	−0.321383	+	1.19942i	−0.917898	+	0.396817i	$0.870115\pi$
$150$		0			0
$151$	0.480824	+	0.480824i	0.0391289	+	0.0391289i	0.726401	−	0.687272i	$-0.241192\pi$
$151$	0.480824	+	0.480824i	0.0391289	+	0.0391289i	−0.687272	+	0.726401i	$0.741192\pi$
$152$		0			0
$153$	−2.75974	−	1.59334i	−0.223112	−	0.128814i
$154$		0			0
$155$	−1.29162			−0.103746
$156$		0			0
$157$	−5.90408			−0.471197			−0.235598	−	0.971851i	$-0.575705\pi$
$157$	−5.90408			−0.471197			−0.235598	+	0.971851i	$0.575705\pi$
$158$		0			0
$159$	−4.37618	−	2.52659i	−0.347054	−	0.200372i
$160$		0			0
$161$	16.3499	+	16.3499i	1.28855	+	1.28855i
$162$		0			0
$163$	−4.07194	+	15.1967i	−0.318939	+	1.19030i	0.601327	+	0.799003i	$0.294639\pi$
$163$	−4.07194	+	15.1967i	−0.318939	+	1.19030i	−0.920266	+	0.391294i	$0.872028\pi$
$164$		0			0
$165$	0.144241	+	0.249833i	0.0112292	+	0.0194495i
$166$		0			0
$167$	−5.41542	+	1.45106i	−0.419058	+	0.112286i	−0.462185	−	0.886783i	$-0.652935\pi$
$167$	−5.41542	+	1.45106i	−0.419058	+	0.112286i	0.0431274	+	0.999070i	$0.486268\pi$
$168$		0			0
$169$	−12.6693	−	2.91377i	−0.974558	−	0.224137i
$170$		0			0
$171$	−3.29032	−	12.2796i	−0.251617	−	0.939046i
$172$		0			0
$173$	−1.87129	+	1.08039i	−0.142272	+	0.0821405i	−0.569446	−	0.822029i	$-0.692842\pi$
$173$	−1.87129	+	1.08039i	−0.142272	+	0.0821405i	0.427175	+	0.904169i	$0.359509\pi$
$174$		0			0
$175$	12.6293	+	3.38402i	0.954688	+	0.255808i
$176$		0			0
$177$	−5.12108	+	5.12108i	−0.384924	+	0.384924i
$178$		0			0
$179$	5.06638	−	8.77523i	0.378679	−	0.655892i	−0.612191	−	0.790710i	$-0.709712\pi$
$179$	5.06638	−	8.77523i	0.378679	−	0.655892i	0.990870	+	0.134818i	$0.0430450\pi$
$180$		0			0
$181$			13.8528i			1.02967i	0.857289	+	0.514836i	$0.172147\pi$
$181$			13.8528i			1.02967i	−0.857289	+	0.514836i	$0.827853\pi$
$182$		0			0
$183$			6.13905i			0.453812i
$184$		0			0
$185$	−0.0609080	+	0.105496i	−0.00447805	+	0.00775620i
$186$		0			0
$187$	−1.42685	+	1.42685i	−0.104342	+	0.104342i
$188$		0			0
$189$	−11.4580	−	3.07017i	−0.833450	−	0.223322i
$190$		0			0
$191$	3.35193	−	1.93524i	0.242537	−	0.140029i	−0.373805	−	0.927507i	$-0.621947\pi$
$191$	3.35193	−	1.93524i	0.242537	−	0.140029i	0.616342	+	0.787478i	$0.288614\pi$
$192$		0			0
$193$	2.12861	+	7.94409i	0.153221	+	0.571828i	0.999251	+	0.0386934i	$0.0123196\pi$
$193$	2.12861	+	7.94409i	0.153221	+	0.571828i	−0.846030	+	0.533135i	$0.821014\pi$
$194$		0			0
$195$	−0.713291	+	0.106907i	−0.0510798	+	0.00765576i
$196$		0			0
$197$	11.9588	−	3.20436i	0.852032	−	0.228301i	0.193730	−	0.981055i	$-0.437942\pi$
$197$	11.9588	−	3.20436i	0.852032	−	0.228301i	0.658302	+	0.752754i	$0.271275\pi$
$198$		0			0
$199$	−1.21698	−	2.10788i	−0.0862696	−	0.149423i	0.819662	−	0.572848i	$-0.194161\pi$
$199$	−1.21698	−	2.10788i	−0.0862696	−	0.149423i	−0.905932	+	0.423424i	$0.860828\pi$
$200$		0			0
$201$	−0.554899	+	2.07091i	−0.0391396	+	0.146071i
$202$		0			0
$203$	7.89132	+	7.89132i	0.553862	+	0.553862i
$204$		0			0
$205$	1.18115	+	0.681935i	0.0824949	+	0.0476284i
$206$		0			0
$207$	−19.9145			−1.38416
$208$		0			0
$209$	−8.05002			−0.556831
$210$		0			0
$211$	−3.62910	−	2.09526i	−0.249838	−	0.144244i	0.369852	−	0.929091i	$-0.379408\pi$
$211$	−3.62910	−	2.09526i	−0.249838	−	0.144244i	−0.619690	+	0.784847i	$0.712742\pi$
$212$		0			0
$213$	6.53401	+	6.53401i	0.447703	+	0.447703i
$214$		0			0
$215$	0.559576	−	2.08837i	0.0381628	−	0.142425i
$216$		0			0
$217$	−7.25658	−	12.5688i	−0.492609	−	0.853223i
$218$		0			0
$219$	−5.86868	+	1.57251i	−0.396569	+	0.106260i
$220$		0			0
$221$	−2.01364	−	4.62577i	−0.135452	−	0.311163i
$222$		0			0
$223$	−4.87316	−	18.1869i	−0.326331	−	1.21788i	−0.912967	−	0.408033i	$-0.866215\pi$
$223$	−4.87316	−	18.1869i	−0.326331	−	1.21788i	0.586636	−	0.809850i	$-0.300452\pi$
$224$		0			0
$225$	−9.75232	+	5.63051i	−0.650155	+	0.375367i
$226$		0			0
$227$	−7.18635	−	1.92558i	−0.476974	−	0.127805i	0.0123190	−	0.999924i	$-0.496079\pi$
$227$	−7.18635	−	1.92558i	−0.476974	−	0.127805i	−0.489293	+	0.872119i	$0.662745\pi$
$228$		0			0
$229$	3.17720	−	3.17720i	0.209955	−	0.209955i	−0.594293	−	0.804248i	$-0.702568\pi$
$229$	3.17720	−	3.17720i	0.209955	−	0.209955i	0.804248	+	0.594293i	$0.202568\pi$
$230$		0			0
$231$	−1.62075	+	2.80721i	−0.106637	+	0.184701i
$232$		0			0
$233$			13.3205i			0.872655i	0.899788	+	0.436328i	$0.143721\pi$
$233$			13.3205i			0.872655i	−0.899788	+	0.436328i	$0.856279\pi$
$234$		0			0
$235$			0.932921i			0.0608571i
$236$		0			0
$237$	−3.61971	+	6.26953i	−0.235126	+	0.407250i
$238$		0			0
$239$	5.96641	−	5.96641i	0.385935	−	0.385935i	−0.487300	−	0.873235i	$-0.662018\pi$
$239$	5.96641	−	5.96641i	0.385935	−	0.385935i	0.873235	+	0.487300i	$0.162018\pi$
$240$		0			0
$241$	−14.9406	−	4.00333i	−0.962410	−	0.257877i	−0.256790	−	0.966467i	$-0.582665\pi$
$241$	−14.9406	−	4.00333i	−0.962410	−	0.257877i	−0.705620	+	0.708590i	$0.749332\pi$
$242$		0			0
$243$	13.8775	−	8.01218i	0.890242	−	0.513982i
$244$		0			0
$245$	0.000481222		0.00179594i	3.07441e−5		0.000114739i
$246$		0			0
$247$	7.36856	−	18.7291i	0.468851	−	1.19171i
$248$		0			0
$249$	8.02602	−	2.15056i	0.508628	−	0.136287i
$250$		0			0
$251$	13.7387	+	23.7962i	0.867182	+	1.50200i	0.864865	+	0.502005i	$0.167404\pi$
$251$	13.7387	+	23.7962i	0.867182	+	1.50200i	0.00231697	+	0.999997i	$0.499262\pi$
$252$		0			0
$253$	−3.26379	+	12.1806i	−0.205193	+	0.765789i
$254$		0			0
$255$	−0.197923	−	0.197923i	−0.0123944	−	0.0123944i
$256$		0			0
$257$	24.1060	+	13.9176i	1.50369	+	0.868157i	0.999991	+	0.00427985i	$0.00136232\pi$
$257$	24.1060	+	13.9176i	1.50369	+	0.868157i	0.503702	+	0.863878i	$0.331971\pi$
$258$		0			0
$259$	−1.36877			−0.0850511
$260$		0			0
$261$	−9.61181			−0.594956
$262$		0			0
$263$	20.6166	+	11.9030i	1.27128	+	0.733972i	0.975228	−	0.221201i	$-0.0709978\pi$
$263$	20.6166	+	11.9030i	1.27128	+	0.733972i	0.296048	+	0.955173i	$0.404331\pi$
$264$		0			0
$265$	0.989207	+	0.989207i	0.0607665	+	0.0607665i
$266$		0			0
$267$	−1.46157	+	5.45466i	−0.0894468	+	0.333820i
$268$		0			0
$269$	−10.3559	−	17.9370i	−0.631412	−	1.09364i	−0.987263	−	0.159095i	$-0.949142\pi$
$269$	−10.3559	−	17.9370i	−0.631412	−	1.09364i	0.355851	−	0.934543i	$-0.384191\pi$
$270$		0			0
$271$	−13.3489	+	3.57684i	−0.810890	+	0.217277i	−0.640360	−	0.768075i	$-0.721215\pi$
$271$	−13.3489	+	3.57684i	−0.810890	+	0.217277i	−0.170530	+	0.985352i	$0.554548\pi$
$272$		0			0
$273$	−5.04770	−	6.34039i	−0.305501	−	0.383738i
$274$		0			0
$275$	1.84556	+	6.88774i	0.111292	+	0.415346i
$276$		0			0
$277$	−11.0276	+	6.36681i	−0.662587	+	0.382545i	−0.793262	−	0.608880i	$-0.791619\pi$
$277$	−11.0276	+	6.36681i	−0.662587	+	0.382545i	0.130675	+	0.991425i	$0.458286\pi$
$278$		0			0
$279$	12.0739	+	3.23518i	0.722844	+	0.193685i
$280$		0			0
$281$	15.4454	−	15.4454i	0.921396	−	0.921396i	−0.0757324	−	0.997128i	$-0.524129\pi$
$281$	15.4454	−	15.4454i	0.921396	−	0.921396i	0.997128	+	0.0757324i	$0.0241295\pi$
$282$		0			0
$283$	10.3449	−	17.9178i	0.614939	−	1.06511i	−0.375456	−	0.926840i	$-0.622514\pi$
$283$	10.3449	−	17.9178i	0.614939	−	1.06511i	0.990395	−	0.138265i	$-0.0441527\pi$
$284$		0			0
$285$		−	1.11665i		−	0.0661445i
$286$		0			0
$287$			15.3249i			0.904603i
$288$		0			0
$289$	−7.52106	+	13.0269i	−0.442415	+	0.766286i
$290$		0			0
$291$	9.30045	−	9.30045i	0.545202	−	0.545202i
$292$		0			0
$293$	22.2734	+	5.96815i	1.30123	+	0.348663i	0.841914	−	0.539611i	$-0.181429\pi$
$293$	22.2734	+	5.96815i	1.30123	+	0.348663i	0.459314	+	0.888274i	$0.348095\pi$
$294$		0			0
$295$	1.73638	−	1.00250i	0.101096	−	0.0583677i
$296$		0			0
$297$	−1.67440	−	6.24895i	−0.0971586	−	0.362601i
$298$		0			0
$299$	−25.3519	−	18.7430i	−1.46614	−	1.08394i
$300$		0			0
$301$	23.4656	−	6.28760i	1.35254	−	0.362411i
$302$		0			0
$303$	−3.89939	−	6.75394i	−0.224014	−	0.388004i
$304$		0			0
$305$	0.439881	−	1.64166i	0.0251875	−	0.0940010i
$306$		0			0
$307$	−16.3164	−	16.3164i	−0.931228	−	0.931228i	0.0665547	−	0.997783i	$-0.478799\pi$
$307$	−16.3164	−	16.3164i	−0.931228	−	0.931228i	−0.997783	+	0.0665547i	$0.978799\pi$
$308$		0			0
$309$	−8.03001	−	4.63613i	−0.456811	−	0.263740i
$310$		0			0
$311$	−8.54527			−0.484558			−0.242279	−	0.970207i	$-0.577895\pi$
$311$	−8.54527			−0.484558			−0.242279	+	0.970207i	$0.577895\pi$
$312$		0			0
$313$	5.88378			0.332571			0.166285	−	0.986078i	$-0.446823\pi$
$313$	5.88378			0.332571			0.166285	+	0.986078i	$0.446823\pi$
$314$		0			0
$315$	1.22732	+	0.708592i	0.0691515	+	0.0399247i
$316$		0			0
$317$	16.5045	+	16.5045i	0.926984	+	0.926984i	0.997510	−	0.0705258i	$-0.0224677\pi$
$317$	16.5045	+	16.5045i	0.926984	+	0.926984i	−0.0705258	+	0.997510i	$0.522468\pi$
$318$		0			0
$319$	−1.57528	+	5.87902i	−0.0881986	+	0.329162i
$320$		0			0
$321$	−4.18926	−	7.25601i	−0.233822	−	0.404991i
$322$		0			0
$323$	7.54456	−	2.02156i	0.419790	−	0.112483i
$324$		0			0
$325$	−17.7143	−	2.01079i	−0.982614	−	0.111539i
$326$		0			0
$327$	0.00756596	+	0.0282365i	0.000418399	+	0.00156148i
$328$		0			0
$329$	−9.07823	+	5.24132i	−0.500499	+	0.288963i
$330$		0			0
$331$	−13.8768	−	3.71829i	−0.762740	−	0.204375i	−0.143578	−	0.989639i	$-0.545861\pi$
$331$	−13.8768	−	3.71829i	−0.762740	−	0.204375i	−0.619162	+	0.785264i	$0.712527\pi$
$332$		0			0
$333$	0.833596	−	0.833596i	0.0456808	−	0.0456808i
$334$		0			0
$335$	0.296774	−	0.514027i	0.0162145	−	0.0280843i
$336$		0			0
$337$		−	14.3427i		−	0.781297i	−0.920540	−	0.390649i	$-0.872251\pi$
$337$		−	14.3427i		−	0.781297i	0.920540	−	0.390649i	$-0.127749\pi$
$338$		0			0
$339$			3.87048i			0.210216i
$340$		0			0
$341$	3.95757	−	6.85471i	0.214314	−	0.371203i
$342$		0			0
$343$	−13.1032	+	13.1032i	−0.707505	+	0.707505i
$344$		0			0
$345$	−1.68962	−	0.452732i	−0.0909659	−	0.0243743i
$346$		0			0
$347$	0.407300	−	0.235155i	0.0218650	−	0.0126238i	−0.489028	−	0.872268i	$-0.662648\pi$
$347$	0.407300	−	0.235155i	0.0218650	−	0.0126238i	0.510893	+	0.859645i	$0.329315\pi$
$348$		0			0
$349$	−7.32017	−	27.3192i	−0.391840	−	1.46237i	−0.827097	−	0.562059i	$-0.810009\pi$
$349$	−7.32017	−	27.3192i	−0.391840	−	1.46237i	0.435257	−	0.900306i	$-0.356657\pi$
$350$		0			0
$351$	16.0714	+	1.82431i	0.857830	+	0.0973742i
$352$		0			0
$353$	34.7270	−	9.30507i	1.84833	−	0.495259i	0.848887	−	0.528574i	$-0.177273\pi$
$353$	34.7270	−	9.30507i	1.84833	−	0.495259i	0.999445	+	0.0333153i	$0.0106066\pi$
$354$		0			0
$355$	−1.27909	−	2.21545i	−0.0678872	−	0.117584i
$356$		0			0
$357$	0.814018	−	3.03796i	0.0430824	−	0.160786i
$358$		0			0
$359$	−11.7167	−	11.7167i	−0.618383	−	0.618383i	0.326733	−	0.945117i	$-0.394052\pi$
$359$	−11.7167	−	11.7167i	−0.618383	−	0.618383i	−0.945117	+	0.326733i	$0.894052\pi$
$360$		0			0
$361$	10.5306	+	6.07986i	0.554244	+	0.319993i
$362$		0			0
$363$	7.58264			0.397985
$364$		0			0
$365$	1.68203			0.0880416
$366$		0			0
$367$	8.79501	+	5.07780i	0.459096	+	0.265059i	0.711664	−	0.702520i	$-0.247942\pi$
$367$	8.79501	+	5.07780i	0.459096	+	0.265059i	−0.252568	+	0.967579i	$0.581275\pi$
$368$		0			0
$369$	−9.33307	−	9.33307i	−0.485860	−	0.485860i
$370$		0			0
$371$	−4.06840	+	15.1835i	−0.211221	+	0.788288i
$372$		0			0
$373$	−7.50790	−	13.0041i	−0.388744	−	0.673325i	0.603537	−	0.797335i	$-0.293758\pi$
$373$	−7.50790	−	13.0041i	−0.388744	−	0.673325i	−0.992281	+	0.124010i	$0.960424\pi$
$374$		0			0
$375$	−1.92155	+	0.514877i	−0.0992283	+	0.0265881i
$376$		0			0
$377$	−12.2362	−	9.04638i	−0.630195	−	0.465912i
$378$		0			0
$379$	8.63337	+	32.2202i	0.443467	+	1.65504i	0.719953	+	0.694022i	$0.244163\pi$
$379$	8.63337	+	32.2202i	0.443467	+	1.65504i	−0.276487	+	0.961018i	$0.589170\pi$
$380$		0			0
$381$	3.93413	−	2.27137i	0.201552	−	0.116366i
$382$		0			0
$383$	−20.2216	−	5.41837i	−1.03328	−	0.276866i	−0.297953	−	0.954581i	$-0.596304\pi$
$383$	−20.2216	−	5.41837i	−1.03328	−	0.276866i	−0.735325	+	0.677715i	$0.762970\pi$
$384$		0			0
$385$	0.634552	−	0.634552i	0.0323398	−	0.0323398i
$386$		0			0
$387$	−10.4616	+	18.1201i	−0.531794	+	0.921095i
$388$		0			0
$389$		−	9.60410i		−	0.486947i	−0.969908	−	0.243474i	$-0.921713\pi$
$389$		−	9.60410i		−	0.486947i	0.969908	−	0.243474i	$-0.0782870\pi$
$390$		0			0
$391$		−	12.2354i		−	0.618772i
$392$		0			0
$393$	−4.77101	+	8.26364i	−0.240666	+	0.416846i
$394$		0			0
$395$	1.41718	−	1.41718i	0.0713063	−	0.0713063i
$396$		0			0
$397$	−2.49473	−	0.668462i	−0.125207	−	0.0335492i	0.195671	−	0.980670i	$-0.437311\pi$
$397$	−2.49473	−	0.668462i	−0.125207	−	0.0335492i	−0.320878	+	0.947120i	$0.603978\pi$
$398$		0			0
$399$	10.8661	−	6.27352i	0.543983	−	0.314069i
$400$		0			0
$401$	−7.00137	−	26.1295i	−0.349632	−	1.30484i	−0.887107	−	0.461563i	$-0.847289\pi$
$401$	−7.00137	−	26.1295i	−0.349632	−	1.30484i	0.537476	−	0.843279i	$-0.319378\pi$
$402$		0			0
$403$	12.3256	+	15.4821i	0.613981	+	0.771218i
$404$		0			0
$405$	−0.686244	+	0.183879i	−0.0340998	+	0.00913700i
$406$		0			0
$407$	−0.373247	−	0.646483i	−0.0185012	−	0.0320450i
$408$		0			0
$409$	1.24095	−	4.63129i	0.0613611	−	0.229003i	−0.928435	−	0.371496i	$-0.878845\pi$
$409$	1.24095	−	4.63129i	0.0613611	−	0.229003i	0.989796	+	0.142493i	$0.0455118\pi$
$410$		0			0
$411$	−2.88999	−	2.88999i	−0.142553	−	0.142553i
$412$		0			0
$413$	19.5106	+	11.2644i	0.960053	+	0.554287i
$414$		0			0
$415$	−2.30035			−0.112920
$416$		0			0
$417$	5.89987			0.288918
$418$		0			0
$419$	−4.85410	−	2.80251i	−0.237138	−	0.136912i	0.376723	−	0.926326i	$-0.377051\pi$
$419$	−4.85410	−	2.80251i	−0.237138	−	0.136912i	−0.613861	+	0.789414i	$0.710384\pi$
$420$		0			0
$421$	−3.55354	−	3.55354i	−0.173189	−	0.173189i	0.615190	−	0.788379i	$-0.289079\pi$
$421$	−3.55354	−	3.55354i	−0.173189	−	0.173189i	−0.788379	+	0.615190i	$0.789079\pi$
$422$		0			0
$423$	2.33672	−	8.72077i	0.113615	−	0.424018i
$424$		0			0
$425$	−3.45936	−	5.99179i	−0.167804	−	0.290645i
$426$		0			0
$427$	18.4462	−	4.94266i	0.892676	−	0.239192i
$428$		0			0
$429$	1.61818	−	4.11303i	0.0781265	−	0.198579i
$430$		0			0
$431$	0.894922	+	3.33989i	0.0431069	+	0.160877i	0.984124	−	0.177482i	$-0.0567950\pi$
$431$	0.894922	+	3.33989i	0.0431069	+	0.160877i	−0.941017	+	0.338359i	$0.890128\pi$
$432$		0			0
$433$	−4.73943	+	2.73631i	−0.227762	+	0.131499i	−0.609539	−	0.792756i	$-0.708646\pi$
$433$	−4.73943	+	2.73631i	−0.227762	+	0.131499i	0.381777	+	0.924254i	$0.375312\pi$
$434$		0			0
$435$	−0.815499	−	0.218512i	−0.0391002	−	0.0104769i
$436$		0			0
$437$	34.5150	−	34.5150i	1.65107	−	1.65107i
$438$		0			0
$439$	−15.2532	+	26.4193i	−0.727994	+	1.26092i	0.229736	+	0.973253i	$0.426214\pi$
$439$	−15.2532	+	26.4193i	−0.727994	+	1.26092i	−0.957730	+	0.287669i	$0.907120\pi$
$440$		0			0
$441$		−	0.0179935i		−	0.000856833i
$442$		0			0
$443$		−	12.8994i		−	0.612869i	−0.951892	−	0.306434i	$-0.900864\pi$
$443$		−	12.8994i		−	0.612869i	0.951892	−	0.306434i	$-0.0991360\pi$
$444$		0			0
$445$	0.781685	−	1.35392i	0.0370554	−	0.0641819i
$446$		0			0
$447$	9.11058	−	9.11058i	0.430916	−	0.430916i
$448$		0			0
$449$	9.53370	+	2.55455i	0.449923	+	0.120557i	0.476663	−	0.879086i	$-0.341846\pi$
$449$	9.53370	+	2.55455i	0.449923	+	0.120557i	−0.0267403	+	0.999642i	$0.508513\pi$
$450$		0			0
$451$	−7.23812	+	4.17893i	−0.340830	+	0.196778i
$452$		0			0
$453$	−0.149602	−	0.558323i	−0.00702893	−	0.0262323i
$454$		0			0
$455$	0.895510	+	2.05718i	0.0419822	+	0.0964421i
$456$		0			0
$457$	10.0284	−	2.68710i	0.469108	−	0.125697i	−0.0165184	−	0.999864i	$-0.505258\pi$
$457$	10.0284	−	2.68710i	0.469108	−	0.125697i	0.485626	+	0.874166i	$0.338592\pi$
$458$		0			0
$459$	3.13853	+	5.43609i	0.146494	+	0.253735i
$460$		0			0
$461$	−7.43710	+	27.7556i	−0.346380	+	1.29271i	0.544611	+	0.838689i	$0.316677\pi$
$461$	−7.43710	+	27.7556i	−0.346380	+	1.29271i	−0.890991	+	0.454021i	$0.849989\pi$
$462$		0			0
$463$	5.89061	+	5.89061i	0.273760	+	0.273760i	0.830612	−	0.556852i	$-0.187991\pi$
$463$	5.89061	+	5.89061i	0.273760	+	0.273760i	−0.556852	+	0.830612i	$0.687991\pi$
$464$		0			0
$465$	0.950841	+	0.548968i	0.0440942	+	0.0254578i
$466$		0			0
$467$	3.30334			0.152860			0.0764301	−	0.997075i	$-0.475648\pi$
$467$	3.30334			0.152860			0.0764301	+	0.997075i	$0.475648\pi$
$468$		0			0
$469$	6.66931			0.307960
$470$		0			0
$471$	4.34634	+	2.50936i	0.200269	+	0.115625i
$472$		0			0
$473$	9.36849	+	9.36849i	0.430764	+	0.430764i
$474$		0			0
$475$	7.14374	−	26.6608i	0.327777	−	1.22328i
$476$		0			0
$477$	−6.76922	−	11.7246i	−0.309941	−	0.536834i
$478$		0			0
$479$	26.8650	−	7.19847i	1.22750	−	0.328906i	0.413892	−	0.910326i	$-0.364169\pi$
$479$	26.8650	−	7.19847i	1.22750	−	0.328906i	0.813604	+	0.581420i	$0.197503\pi$
$480$		0			0
$481$	1.84575	−	0.276639i	0.0841592	−	0.0126136i
$482$		0			0
$483$	−5.08705	−	18.9851i	−0.231469	−	0.863854i
$484$		0			0
$485$	−3.15346	+	1.82065i	−0.143191	+	0.0826714i
$486$		0			0
$487$	9.96577	+	2.67032i	0.451592	+	0.121004i	0.477444	−	0.878662i	$-0.341563\pi$
$487$	9.96577	+	2.67032i	0.451592	+	0.121004i	−0.0258522	+	0.999666i	$0.508230\pi$
$488$		0			0
$489$	9.45652	−	9.45652i	0.427638	−	0.427638i
$490$		0			0
$491$	−6.81243	+	11.7995i	−0.307441	+	0.532503i	−0.977802	−	0.209532i	$-0.932806\pi$
$491$	−6.81243	+	11.7995i	−0.307441	+	0.532503i	0.670361	+	0.742035i	$0.266139\pi$
$492$		0			0
$493$		−	5.90546i		−	0.265969i
$494$		0			0
$495$			0.772899i			0.0347392i
$496$		0			0
$497$	14.3723	−	24.8936i	0.644688	−	1.11663i
$498$		0			0
$499$	11.2288	−	11.2288i	0.502670	−	0.502670i	−0.409597	−	0.912267i	$-0.634331\pi$
$499$	11.2288	−	11.2288i	0.502670	−	0.502670i	0.912267	+	0.409597i	$0.134331\pi$
$500$		0			0
$501$	4.60334	+	1.23346i	0.205662	+	0.0551070i
$502$		0			0
$503$	−19.7978	+	11.4303i	−0.882739	+	0.509650i	−0.871561	−	0.490288i	$-0.836892\pi$
$503$	−19.7978	+	11.4303i	−0.882739	+	0.509650i	−0.0111787	+	0.999938i	$0.503558\pi$
$504$		0			0
$505$	0.558805	+	2.08549i	0.0248665	+	0.0928030i
$506$		0			0
$507$	8.08816	+	7.52970i	0.359208	+	0.334406i
$508$		0			0
$509$	9.52759	−	2.55291i	0.422303	−	0.113156i	−0.0414078	−	0.999142i	$-0.513184\pi$
$509$	9.52759	−	2.55291i	0.422303	−	0.113156i	0.463711	+	0.885987i	$0.346518\pi$
$510$		0			0
$511$	9.44995	+	16.3678i	0.418041	+	0.724069i
$512$		0			0
$513$	−6.48121	+	24.1882i	−0.286152	+	1.06794i
$514$		0			0
$515$	1.81513	+	1.81513i	0.0799842	+	0.0799842i
$516$		0			0
$517$	−4.95105	−	2.85849i	−0.217747	−	0.125716i
$518$		0			0
$519$	1.83676			0.0806246
$520$		0			0
$521$	15.9204			0.697486			0.348743	−	0.937218i	$-0.386609\pi$
$521$	15.9204			0.697486			0.348743	+	0.937218i	$0.386609\pi$
$522$		0			0
$523$	1.86869	+	1.07889i	0.0817122	+	0.0471766i	0.540299	−	0.841473i	$-0.318311\pi$
$523$	1.86869	+	1.07889i	0.0817122	+	0.0471766i	−0.458587	+	0.888649i	$0.651644\pi$
$524$		0			0
$525$	−7.85891	−	7.85891i	−0.342991	−	0.342991i
$526$		0			0
$527$	−1.98769	+	7.41814i	−0.0865849	+	0.323139i
$528$		0			0
$529$	−26.7315	−	46.3003i	−1.16224	−	2.01306i
$530$		0			0
$531$	−18.7423	+	5.02200i	−0.813348	+	0.217936i
$532$		0			0
$533$	−3.09729	−	20.6654i	−0.134158	−	0.895116i
$534$		0			0
$535$	0.600345	+	2.24052i	0.0259552	+	0.0968660i
$536$		0			0
$537$	−7.45933	+	4.30664i	−0.321894	+	0.185845i
$538$		0			0
$539$	−0.0110056	−	0.00294895i	−0.000474046	−	0.000127020i
$540$		0			0
$541$	−8.15947	+	8.15947i	−0.350803	+	0.350803i	−0.860408	−	0.509605i	$-0.829791\pi$
$541$	−8.15947	+	8.15947i	−0.350803	+	0.350803i	0.509605	+	0.860408i	$0.329791\pi$
$542$		0			0
$543$	5.88774	−	10.1979i	0.252667	−	0.437632i
$544$		0			0
$545$		−	0.00809292i		−	0.000346663i
$546$		0			0
$547$			8.11076i			0.346791i	0.984852	+	0.173396i	$0.0554739\pi$
$547$			8.11076i			0.346791i	−0.984852	+	0.173396i	$0.944526\pi$
$548$		0			0
$549$	−8.22384	+	14.2441i	−0.350985	+	0.607924i
$550$		0			0
$551$	16.6588	−	16.6588i	0.709687	−	0.709687i
$552$		0			0
$553$	21.7526	+	5.82859i	0.925014	+	0.247857i
$554$		0			0
$555$	0.0896759	−	0.0517744i	0.00380653	−	0.00219770i
$556$		0			0
$557$	0.887873	+	3.31359i	0.0376204	+	0.140401i	0.982182	−	0.187934i	$-0.0601791\pi$
$557$	0.887873	+	3.31359i	0.0376204	+	0.140401i	−0.944561	+	0.328335i	$0.893512\pi$
$558$		0			0
$559$	−30.3721	+	13.2213i	−1.28460	+	0.559200i
$560$		0			0
$561$	1.65683	−	0.443946i	0.0699514	−	0.0187434i
$562$		0			0
$563$	−3.12130	−	5.40625i	−0.131547	−	0.227846i	0.792726	−	0.609578i	$-0.208661\pi$
$563$	−3.12130	−	5.40625i	−0.131547	−	0.227846i	−0.924273	+	0.381732i	$0.875328\pi$
$564$		0			0
$565$	0.277331	−	1.03501i	0.0116674	−	0.0435434i
$566$		0			0
$567$	−5.64476	−	5.64476i	−0.237058	−	0.237058i
$568$		0			0
$569$	−27.8969	−	16.1063i	−1.16950	−	0.675211i	−0.215937	−	0.976407i	$-0.569281\pi$
$569$	−27.8969	−	16.1063i	−1.16950	−	0.675211i	−0.953562	+	0.301197i	$0.902614\pi$
$570$		0			0
$571$	−41.4189			−1.73333			−0.866663	−	0.498894i	$-0.833740\pi$
$571$	−41.4189			−1.73333			−0.866663	+	0.498894i	$0.833740\pi$
$572$		0			0
$573$	−3.29007			−0.137445
$574$		0			0
$575$	−37.4446	−	21.6186i	−1.56155	−	0.901560i
$576$		0			0
$577$	12.3408	+	12.3408i	0.513753	+	0.513753i	0.915674	−	0.401921i	$-0.131657\pi$
$577$	12.3408	+	12.3408i	0.513753	+	0.513753i	−0.401921	+	0.915674i	$0.631657\pi$
$578$		0			0
$579$	1.80941	−	6.75282i	0.0751966	−	0.280638i
$580$		0			0
$581$	−12.9238	−	22.3846i	−0.536168	−	0.928671i
$582$		0			0
$583$	−8.28072	+	2.21881i	−0.342952	+	0.0918938i
$584$		0			0
$585$	−1.79822	−	0.707471i	−0.0743474	−	0.0292503i
$586$		0			0
$587$	−5.98011	−	22.3181i	−0.246825	−	0.921165i	−0.972457	−	0.233082i	$-0.925119\pi$
$587$	−5.98011	−	22.3181i	−0.246825	−	0.921165i	0.725632	−	0.688083i	$-0.241548\pi$
$588$		0			0
$589$	−26.5330	+	15.3188i	−1.09327	+	0.631200i
$590$		0			0
$591$	−10.1655	−	2.72384i	−0.418154	−	0.112044i
$592$		0			0
$593$	11.0244	−	11.0244i	0.452717	−	0.452717i	−0.443538	−	0.896255i	$-0.646277\pi$
$593$	11.0244	−	11.0244i	0.452717	−	0.452717i	0.896255	+	0.443538i	$0.146277\pi$
$594$		0			0
$595$	−0.435357	+	0.754060i	−0.0178479	+	0.0309134i
$596$		0			0
$597$			2.06898i			0.0846775i
$598$		0			0
$599$		−	10.6090i		−	0.433471i	−0.976230	−	0.216735i	$-0.930459\pi$
$599$		−	10.6090i		−	0.433471i	0.976230	−	0.216735i	$-0.0695409\pi$
$600$		0			0
$601$	−14.1251	+	24.4655i	−0.576177	+	0.997967i	0.419736	+	0.907646i	$0.362123\pi$
$601$	−14.1251	+	24.4655i	−0.576177	+	0.997967i	−0.995913	+	0.0903210i	$0.971211\pi$
$602$		0			0
$603$	−4.06169	+	4.06169i	−0.165405	+	0.165405i
$604$		0			0
$605$	−2.02769	−	0.543318i	−0.0824373	−	0.0220890i
$606$		0			0
$607$	8.89476	−	5.13539i	0.361027	−	0.208439i	−0.308504	−	0.951223i	$-0.599828\pi$
$607$	8.89476	−	5.13539i	0.361027	−	0.208439i	0.669531	+	0.742784i	$0.266495\pi$
$608$		0			0
$609$	−2.45528	−	9.16324i	−0.0994931	−	0.371313i
$610$		0			0
$611$	11.1825	−	8.90258i	0.452395	−	0.360160i
$612$		0			0
$613$	34.2262	−	9.17089i	1.38238	−	0.370409i	0.510397	−	0.859939i	$-0.329498\pi$
$613$	34.2262	−	9.17089i	1.38238	−	0.370409i	0.871986	+	0.489530i	$0.162832\pi$
$614$		0			0
$615$	−0.579674	−	1.00403i	−0.0233747	−	0.0404862i
$616$		0			0
$617$	−10.8473	+	40.4828i	−0.436697	+	1.62978i	0.300275	+	0.953853i	$0.402922\pi$
$617$	−10.8473	+	40.4828i	−0.436697	+	1.62978i	−0.736972	+	0.675923i	$0.763745\pi$
$618$		0			0
$619$	12.0880	+	12.0880i	0.485858	+	0.485858i	0.906996	−	0.421138i	$-0.138369\pi$
$619$	12.0880	+	12.0880i	0.485858	+	0.485858i	−0.421138	+	0.906996i	$0.638369\pi$
$620$		0			0
$621$	33.9719	+	19.6137i	1.36324	+	0.787069i
$622$		0			0
$623$	17.5666			0.703790
$624$		0			0
$625$	−24.1724			−0.966894
$626$		0			0
$627$	5.92609	+	3.42143i	0.236665	+	0.136639i
$628$		0			0
$629$	0.512159	+	0.512159i	0.0204211	+	0.0204211i
$630$		0			0
$631$	3.12081	−	11.6470i	0.124237	−	0.463660i	−0.875574	−	0.483084i	$-0.839517\pi$
$631$	3.12081	−	11.6470i	0.124237	−	0.463660i	0.999811	+	0.0194238i	$0.00618318\pi$
$632$		0			0
$633$	1.78106	+	3.08489i	0.0707909	+	0.122613i
$634$		0			0
$635$	−1.21479	+	0.325501i	−0.0482073	+	0.0129171i
$636$		0			0
$637$	0.0169350	−	0.0229063i	0.000670988	−	0.000907582i
$638$		0			0
$639$	6.40759	+	23.9134i	0.253480	+	0.946001i
$640$		0			0
$641$	−1.81632	+	1.04865i	−0.0717404	+	0.0414193i	−0.535441	−	0.844573i	$-0.679855\pi$
$641$	−1.81632	+	1.04865i	−0.0717404	+	0.0414193i	0.463701	+	0.885992i	$0.346521\pi$
$642$		0			0
$643$	40.9391	+	10.9696i	1.61448	+	0.432599i	0.949374	−	0.314148i	$-0.101719\pi$
$643$	40.9391	+	10.9696i	1.61448	+	0.432599i	0.665108	+	0.746747i	$0.268386\pi$
$644$		0			0
$645$	−1.29954	+	1.29954i	−0.0511692	+	0.0511692i
$646$		0			0
$647$	21.5400	−	37.3083i	0.846824	−	1.46674i	−0.0372042	−	0.999308i	$-0.511845\pi$
$647$	21.5400	−	37.3083i	0.846824	−	1.46674i	0.884028	−	0.467434i	$-0.154821\pi$
$648$		0			0
$649$			12.2867i			0.482296i
$650$		0			0
$651$			12.3368i			0.483518i
$652$		0			0
$653$	−5.56059	+	9.63123i	−0.217603	+	0.376899i	−0.954075	−	0.299569i	$-0.903157\pi$
$653$	−5.56059	+	9.63123i	−0.217603	+	0.376899i	0.736472	+	0.676468i	$0.236490\pi$
$654$		0			0
$655$	1.86794	−	1.86794i	0.0729865	−	0.0729865i
$656$		0			0
$657$	−15.7233	−	4.21305i	−0.613425	−	0.164367i
$658$		0			0
$659$	−13.2010	+	7.62162i	−0.514239	+	0.296896i	−0.734575	−	0.678528i	$-0.762618\pi$
$659$	−13.2010	+	7.62162i	−0.514239	+	0.296896i	0.220335	+	0.975424i	$0.429285\pi$
$660$		0			0
$661$	2.67284	+	9.97516i	0.103961	+	0.387989i	0.998225	−	0.0595512i	$-0.0189669\pi$
$661$	2.67284	+	9.97516i	0.103961	+	0.387989i	−0.894264	+	0.447540i	$0.852300\pi$
$662$		0			0
$663$	−0.483691	+	4.26114i	−0.0187850	+	0.165489i
$664$		0			0
$665$	−3.35523	+	0.899032i	−0.130110	+	0.0348630i
$666$		0			0
$667$	−18.4525	−	31.9607i	−0.714485	−	1.23753i
$668$		0			0
$669$	−4.14239	+	15.4596i	−0.160154	+	0.597704i
$670$		0			0
$671$	7.36454	+	7.36454i	0.284305	+	0.284305i
$672$		0			0
$673$	25.8030	+	14.8974i	0.994631	+	0.574251i	0.906655	−	0.421872i	$-0.138627\pi$
$673$	25.8030	+	14.8974i	0.994631	+	0.574251i	0.0879759	+	0.996123i	$0.471960\pi$
$674$		0			0
$675$	22.1818			0.853776
$676$		0			0
$677$	29.1021			1.11849			0.559243	−	0.829004i	$-0.311092\pi$
$677$	29.1021			1.11849			0.559243	+	0.829004i	$0.311092\pi$
$678$		0			0
$679$	−35.4334	−	20.4575i	−1.35981	−	0.785085i
$680$		0			0
$681$	4.47188	+	4.47188i	0.171363	+	0.171363i
$682$		0			0
$683$	−1.30625	+	4.87499i	−0.0499823	+	0.186536i	−0.986404	−	0.164342i	$-0.947450\pi$
$683$	−1.30625	+	4.87499i	−0.0499823	+	0.186536i	0.936421	+	0.350878i	$0.114117\pi$
$684$		0			0
$685$	0.565743	+	0.979896i	0.0216159	+	0.0374399i
$686$		0			0
$687$	−3.68930	+	0.988544i	−0.140755	+	0.0377153i
$688$		0			0
$689$	2.41746	−	21.2969i	0.0920977	−	0.811346i
$690$		0			0
$691$	2.89268	+	10.7956i	0.110043	+	0.410685i	0.998868	−	0.0475604i	$-0.0151447\pi$
$691$	2.89268	+	10.7956i	0.110043	+	0.410685i	−0.888826	+	0.458246i	$0.848478\pi$
$692$		0			0
$693$	−7.52106	+	4.34229i	−0.285701	+	0.164950i
$694$		0			0
$695$	−1.57770	−	0.422743i	−0.0598455	−	0.0160355i
$696$		0			0
$697$	5.73421	−	5.73421i	0.217199	−	0.217199i
$698$		0			0
$699$	5.66150	−	9.80601i	0.214138	−	0.370897i
$700$		0			0
$701$			27.1476i			1.02535i	0.858582	+	0.512676i	$0.171346\pi$
$701$			27.1476i			1.02535i	−0.858582	+	0.512676i	$0.828654\pi$
$702$		0			0
$703$			2.88950i			0.108980i
$704$		0			0
$705$	0.396511	−	0.686778i	0.0149335	−	0.0258656i
$706$		0			0
$707$	−17.1544	+	17.1544i	−0.645156	+	0.645156i
$708$		0			0
$709$	−40.9857	−	10.9821i	−1.53925	−	0.412441i	−0.613228	−	0.789906i	$-0.710129\pi$
$709$	−40.9857	−	10.9821i	−1.53925	−	0.412441i	−0.926024	+	0.377465i	$0.876796\pi$
$710$		0			0
$711$	−16.7973	+	9.69790i	−0.629946	+	0.363700i
$712$		0			0
$713$	12.4217	+	46.3583i	0.465195	+	1.73613i
$714$		0			0
$715$	−0.727432	+	0.983927i	−0.0272044	+	0.0367968i
$716$		0			0
$717$	−6.92808	+	1.85637i	−0.258734	+	0.0693275i
$718$		0			0
$719$	8.21566	+	14.2299i	0.306392	+	0.530687i	0.977570	−	0.210609i	$-0.0675447\pi$
$719$	8.21566	+	14.2299i	0.306392	+	0.530687i	−0.671178	+	0.741296i	$0.734211\pi$
$720$		0			0
$721$	−7.46526	+	27.8607i	−0.278021	+	1.03759i
$722$		0			0
$723$	9.29717	+	9.29717i	0.345765	+	0.345765i
$724$		0			0
$725$	−18.0728	−	10.4343i	−0.671205	−	0.387520i
$726$		0			0
$727$	32.1429			1.19211			0.596057	−	0.802942i	$-0.296733\pi$
$727$	32.1429			1.19211			0.596057	+	0.802942i	$0.296733\pi$
$728$		0			0
$729$	−4.56452			−0.169056
$730$		0			0
$731$	−11.1329	−	6.42759i	−0.411765	−	0.237733i
$732$		0			0
$733$	19.2047	+	19.2047i	0.709343	+	0.709343i	0.966397	−	0.257054i	$-0.0827518\pi$
$733$	19.2047	+	19.2047i	0.709343	+	0.709343i	−0.257054	+	0.966397i	$0.582752\pi$
$734$		0			0
$735$	0.000409059	−	0.00152663i	1.50884e−5	−	5.63106e-5i
$736$		0			0
$737$	1.81864	+	3.14998i	0.0669905	+	0.116031i
$738$		0			0
$739$	−22.4404	+	6.01290i	−0.825485	+	0.221188i	−0.646743	−	0.762708i	$-0.723869\pi$
$739$	−22.4404	+	6.01290i	−0.825485	+	0.221188i	−0.178742	+	0.983896i	$0.557203\pi$
$740$		0			0
$741$	−13.3847	+	10.6558i	−0.491700	+	0.391451i
$742$		0			0
$743$	9.98778	+	37.2749i	0.366416	+	1.36748i	0.865491	+	0.500925i	$0.167007\pi$
$743$	9.98778	+	37.2749i	0.366416	+	1.36748i	−0.499075	+	0.866559i	$0.666327\pi$
$744$		0			0
$745$	−3.08908	+	1.78348i	−0.113175	+	0.0653417i
$746$		0			0
$747$	21.5032	+	5.76177i	0.786762	+	0.210812i
$748$		0			0
$749$	−18.4296	+	18.4296i	−0.673402	+	0.673402i
$750$		0			0
$751$	0.646973	−	1.12059i	0.0236084	−	0.0408909i	−0.853980	−	0.520306i	$-0.825818\pi$
$751$	0.646973	−	1.12059i	0.0236084	−	0.0408909i	0.877588	+	0.479415i	$0.159151\pi$
$752$		0			0
$753$		−	23.3570i		−	0.851178i
$754$		0			0
$755$			0.160022i			0.00582380i
$756$		0			0
$757$	−11.2800	+	19.5376i	−0.409979	+	0.710104i	−0.994887	−	0.100995i	$-0.967797\pi$
$757$	−11.2800	+	19.5376i	−0.409979	+	0.710104i	0.584908	+	0.811100i	$0.301131\pi$
$758$		0			0
$759$	7.57969	−	7.57969i	0.275125	−	0.275125i
$760$		0			0
$761$	8.40241	+	2.25142i	0.304587	+	0.0816138i	0.407875	−	0.913038i	$-0.366270\pi$
$761$	8.40241	+	2.25142i	0.304587	+	0.0816138i	−0.103288	+	0.994651i	$0.532936\pi$
$762$		0			0
$763$	0.0787520	−	0.0454675i	0.00285101	−	0.00164603i
$764$		0			0
$765$	−0.194094	−	0.724369i	−0.00701748	−	0.0261896i
$766$		0			0
$767$	−28.5862	−	11.2466i	−1.03219	−	0.406092i
$768$		0			0
$769$	−9.35018	+	2.50537i	−0.337176	+	0.0903461i	−0.423434	−	0.905927i	$-0.639176\pi$
$769$	−9.35018	+	2.50537i	−0.337176	+	0.0903461i	0.0862584	+	0.996273i	$0.472509\pi$
$770$		0			0
$771$	−11.8306	−	20.4912i	−0.426068	−	0.737971i
$772$		0			0
$773$	4.96928	−	18.5456i	0.178732	−	0.667039i	−0.817153	−	0.576420i	$-0.804449\pi$
$773$	4.96928	−	18.5456i	0.178732	−	0.667039i	0.995886	−	0.0906182i	$-0.0288843\pi$
$774$		0			0
$775$	19.1900	+	19.1900i	0.689327	+	0.689327i
$776$		0			0
$777$	1.00763	+	0.581756i	0.0361486	+	0.0208704i
$778$		0			0
$779$	32.3513			1.15911
$780$		0			0
$781$	15.6767			0.560955
$782$		0			0
$783$	16.3966	+	9.46660i	0.585968	+	0.338309i
$784$		0			0
$785$	−0.982461	−	0.982461i	−0.0350655	−	0.0350655i
$786$		0			0
$787$	7.73737	−	28.8763i	0.275808	−	1.02933i	−0.679491	−	0.733684i	$-0.737799\pi$
$787$	7.73737	−	28.8763i	0.275808	−	1.02933i	0.955298	−	0.295644i	$-0.0955341\pi$
$788$		0			0
$789$	−10.1181	−	17.5250i	−0.360213	−	0.623907i
$790$		0			0
$791$	11.6298	−	3.11619i	0.413508	−	0.110799i
$792$		0			0
$793$	−23.8754	+	10.3932i	−0.847841	+	0.369073i
$794$		0			0
$795$	−0.307779	−	1.14865i	−0.0109158	−	0.0407383i
$796$		0			0
$797$	−32.2562	+	18.6231i	−1.14257	+	0.659665i	−0.947067	−	0.321037i	$-0.895969\pi$
$797$	−32.2562	+	18.6231i	−1.14257	+	0.659665i	−0.195507	+	0.980702i	$0.562635\pi$
$798$		0			0
$799$	5.35801	+	1.43567i	0.189553	+	0.0507905i
$800$		0			0
$801$	−10.6983	+	10.6983i	−0.378004	+	0.378004i
$802$		0			0
$803$	−5.15378	+	8.92661i	−0.181873	+	0.315013i
$804$		0			0
$805$			5.44136i			0.191783i
$806$		0			0
$807$			17.6060i			0.619759i
$808$		0			0
$809$	−20.9090	+	36.2154i	−0.735121	+	1.27327i	0.219550	+	0.975601i	$0.429541\pi$
$809$	−20.9090	+	36.2154i	−0.735121	+	1.27327i	−0.954670	+	0.297665i	$0.903792\pi$
$810$		0			0
$811$	−4.29617	+	4.29617i	−0.150859	+	0.150859i	−0.778502	−	0.627643i	$-0.784020\pi$
$811$	−4.29617	+	4.29617i	−0.150859	+	0.150859i	0.627643	+	0.778502i	$0.284020\pi$
$812$		0			0
$813$	11.3472	+	3.04046i	0.397962	+	0.106634i
$814$		0			0
$815$	−3.20637	+	1.85120i	−0.112314	+	0.0648447i
$816$		0			0
$817$	−13.2733	−	49.5365i	−0.464373	−	1.73306i
$818$		0			0
$819$	−3.21836	−	21.4732i	−0.112459	−	0.750333i
$820$		0			0
$821$	−18.2378	+	4.88681i	−0.636505	+	0.170551i	−0.562620	−	0.826716i	$-0.690207\pi$
$821$	−18.2378	+	4.88681i	−0.636505	+	0.170551i	−0.0738852	+	0.997267i	$0.523540\pi$
$822$		0			0
$823$	−6.80437	−	11.7855i	−0.237185	−	0.410817i	0.722720	−	0.691141i	$-0.242892\pi$
$823$	−6.80437	−	11.7855i	−0.237185	−	0.410817i	−0.959906	+	0.280324i	$0.909558\pi$
$824$		0			0
$825$	1.56881	−	5.85487i	0.0546189	−	0.203841i
$826$		0			0
$827$	−17.0815	−	17.0815i	−0.593982	−	0.593982i	0.344723	−	0.938705i	$-0.387973\pi$
$827$	−17.0815	−	17.0815i	−0.593982	−	0.593982i	−0.938705	+	0.344723i	$0.887973\pi$
$828$		0			0
$829$	23.8014	+	13.7417i	0.826657	+	0.477270i	0.852707	−	0.522390i	$-0.174960\pi$
$829$	23.8014	+	13.7417i	0.826657	+	0.477270i	−0.0260500	+	0.999661i	$0.508293\pi$
$830$		0			0
$831$	10.8241			0.375485
$832$		0			0
$833$	0.0110551			0.000383038
$834$		0			0
$835$	−1.14261	−	0.659685i	−0.0395416	−	0.0228294i
$836$		0			0
$837$	−17.4103	−	17.4103i	−0.601788	−	0.601788i
$838$		0			0
$839$	−10.3356	+	38.5731i	−0.356825	+	1.33169i	0.521347	+	0.853345i	$0.325430\pi$
$839$	−10.3356	+	38.5731i	−0.356825	+	1.33169i	−0.878172	+	0.478345i	$0.841237\pi$
$840$		0			0
$841$	5.59382	+	9.68878i	0.192890	+	0.334096i
$842$		0			0
$843$	−17.9349	+	4.80564i	−0.617711	+	0.165515i
$844$		0			0
$845$	−1.62335	−	2.59307i	−0.0558449	−	0.0892045i
$846$		0			0
$847$	−6.10491	−	22.7839i	−0.209767	−	0.782862i
$848$		0			0
$849$	−15.2309	+	8.79359i	−0.522725	+	0.301795i
$850$		0			0
$851$	4.37216	+	1.17152i	0.149876	+	0.0401590i
$852$		0			0
$853$	6.78242	−	6.78242i	0.232226	−	0.232226i	−0.581395	−	0.813621i	$-0.697493\pi$
$853$	6.78242	−	6.78242i	0.232226	−	0.232226i	0.813621	+	0.581395i	$0.197493\pi$
$854$		0			0
$855$	1.49586	−	2.59090i	0.0511572	−	0.0886068i
$856$		0			0
$857$			25.7579i			0.879872i	0.898029	+	0.439936i	$0.144999\pi$
$857$			25.7579i			0.879872i	−0.898029	+	0.439936i	$0.855001\pi$
$858$		0			0
$859$			51.8251i			1.76825i	0.467252	+	0.884124i	$0.345244\pi$
$859$			51.8251i			1.76825i	−0.467252	+	0.884124i	$0.654756\pi$
$860$		0			0
$861$	6.51343	−	11.2816i	0.221977	−	0.384476i
$862$		0			0
$863$	−35.1233	+	35.1233i	−1.19561	+	1.19561i	−0.220144	+	0.975467i	$0.570653\pi$
$863$	−35.1233	+	35.1233i	−1.19561	+	1.19561i	−0.975467	+	0.220144i	$0.929347\pi$
$864$		0			0
$865$	−0.491171	−	0.131609i	−0.0167003	−	0.00447483i
$866$		0			0
$867$	11.0734	−	6.39322i	0.376072	−	0.217125i
$868$		0			0
$869$	3.17877	+	11.8633i	0.107833	+	0.402436i
$870$		0			0
$871$	−8.99342	+	1.34792i	−0.304730	+	0.0456725i
$872$		0			0
$873$	34.0382	−	9.12050i	1.15202	−	0.308682i
$874$		0			0
$875$	3.09414	+	5.35921i	0.104601	+	0.181174i
$876$		0			0
$877$	−9.61256	+	35.8746i	−0.324593	+	1.21140i	0.590127	+	0.807310i	$0.299078\pi$
$877$	−9.61256	+	35.8746i	−0.324593	+	1.21140i	−0.914720	+	0.404088i	$0.867589\pi$
$878$		0			0
$879$	−13.8602	−	13.8602i	−0.467493	−	0.467493i
$880$		0			0
$881$	−1.73014	−	0.998897i	−0.0582899	−	0.0336537i	0.470572	−	0.882362i	$-0.344048\pi$
$881$	−1.73014	−	0.998897i	−0.0582899	−	0.0336537i	−0.528862	+	0.848708i	$0.677381\pi$
$882$		0			0
$883$	−16.1625			−0.543913			−0.271956	−	0.962310i	$-0.587671\pi$
$883$	−16.1625			−0.543913			−0.271956	+	0.962310i	$0.587671\pi$
$884$		0			0
$885$	−1.70433			−0.0572906
$886$		0			0
$887$	−15.2472	−	8.80298i	−0.511951	−	0.295575i	0.221684	−	0.975119i	$-0.428845\pi$
$887$	−15.2472	−	8.80298i	−0.511951	−	0.295575i	−0.733635	+	0.679543i	$0.762178\pi$
$888$		0			0
$889$	−9.99232	−	9.99232i	−0.335132	−	0.335132i
$890$		0			0
$891$	1.12682	−	4.20534i	0.0377498	−	0.140884i
$892$		0			0
$893$	11.0645	+	19.1644i	0.370261	+	0.641311i
$894$		0			0
$895$	2.30330	−	0.617167i	0.0769908	−	0.0206296i
$896$		0			0
$897$	10.6968	+	24.5729i	0.357157	+	0.820466i
$898$		0			0
$899$	5.99536	+	22.3750i	0.199956	+	0.746247i
$900$		0			0
$901$	7.20357	−	4.15898i	0.239986	−	0.138556i
$902$		0			0
$903$	−19.9468	−	5.34473i	−0.663788	−	0.177861i
$904$		0			0
$905$	−2.30516	+	2.30516i	−0.0766261	+	0.0766261i
$906$		0			0
$907$	−14.7054	+	25.4704i	−0.488283	+	0.845731i	−0.999909	−	0.0134769i	$-0.995710\pi$
$907$	−14.7054	+	25.4704i	−0.488283	+	0.845731i	0.511626	+	0.859208i	$0.329043\pi$
$908$		0			0
$909$		−	20.8944i		−	0.693024i
$910$		0			0
$911$		−	20.5091i		−	0.679495i	−0.940517	−	0.339748i	$-0.889658\pi$
$911$		−	20.5091i		−	0.679495i	0.940517	−	0.339748i	$-0.110342\pi$
$912$		0			0
$913$	7.04832	−	12.2080i	0.233265	−	0.404027i
$914$		0			0
$915$	−1.02156	+	1.02156i	−0.0337718	+	0.0337718i
$916$		0			0
$917$	28.6713	+	7.68245i	0.946810	+	0.253697i
$918$		0			0
$919$	42.4137	−	24.4876i	1.39910	−	0.807770i	0.404800	−	0.914405i	$-0.367341\pi$
$919$	42.4137	−	24.4876i	1.39910	−	0.807770i	0.994298	+	0.106635i	$0.0340077\pi$
$920$		0			0
$921$	5.07665	+	18.9463i	0.167281	+	0.624302i
$922$		0			0
$923$	−14.3496	+	36.4733i	−0.472323	+	1.20053i
$924$		0			0
$925$	2.47231	−	0.662453i	0.0812890	−	0.0217813i
$926$		0			0
$927$	−12.4211	−	21.5139i	−0.407962	−	0.706610i
$928$		0			0
$929$	−1.77316	+	6.61751i	−0.0581754	+	0.217113i	−0.988894	−	0.148623i	$-0.952516\pi$
$929$	−1.77316	+	6.61751i	−0.0581754	+	0.217113i	0.930719	+	0.365736i	$0.119183\pi$
$930$		0			0
$931$	0.0311855	+	0.0311855i	0.00102206	+	0.00102206i
$932$		0			0
$933$	6.29067	+	3.63192i	0.205947	+	0.118904i
$934$		0			0
$935$	−0.474867			−0.0155298
$936$		0			0
$937$	11.1107			0.362970			0.181485	−	0.983394i	$-0.441910\pi$
$937$	11.1107			0.362970			0.181485	+	0.983394i	$0.441910\pi$
$938$		0			0
$939$	−4.33139	−	2.50073i	−0.141350	−	0.0816083i
$940$		0			0
$941$	20.5970	+	20.5970i	0.671442	+	0.671442i	0.958048	−	0.286606i	$-0.0925272\pi$
$941$	20.5970	+	20.5970i	0.671442	+	0.671442i	−0.286606	+	0.958048i	$0.592527\pi$
$942$		0			0
$943$	13.1165	−	48.9513i	0.427131	−	1.59407i
$944$		0			0
$945$	−1.39577	−	2.41755i	−0.0454045	−	0.0786430i
$946$		0			0
$947$	28.3374	−	7.59297i	0.920841	−	0.246739i	0.232896	−	0.972502i	$-0.425180\pi$
$947$	28.3374	−	7.59297i	0.920841	−	0.246739i	0.687945	+	0.725763i	$0.258513\pi$
$948$		0			0
$949$	−16.0511	−	20.1617i	−0.521041	−	0.654477i
$950$		0			0
$951$	−5.13516	−	19.1647i	−0.166519	−	0.621457i
$952$		0			0
$953$	−11.3638	+	6.56091i	−0.368110	+	0.212529i	−0.672633	−	0.739977i	$-0.734837\pi$
$953$	−11.3638	+	6.56091i	−0.368110	+	0.212529i	0.304522	+	0.952505i	$0.401503\pi$
$954$		0			0
$955$	0.879806	+	0.235743i	0.0284699	+	0.00762847i
$956$		0			0
$957$	3.65836	−	3.65836i	0.118258	−	0.118258i
$958$		0			0
$959$	−6.35689	+	11.0105i	−0.205275	+	0.355546i
$960$		0			0
$961$			0.875747i			0.0282499i
$962$		0			0
$963$		−	22.4477i		−	0.723365i
$964$		0			0
$965$	−0.967718	+	1.67614i	−0.0311519	+	0.0539568i
$966$		0			0
$967$	−13.0476	+	13.0476i	−0.419581	+	0.419581i	−0.885059	−	0.465478i	$-0.845882\pi$
$967$	−13.0476	+	13.0476i	−0.419581	+	0.419581i	0.465478	+	0.885059i	$0.345882\pi$
$968$		0			0
$969$	−6.41320	−	1.71841i	−0.206022	−	0.0552033i
$970$		0			0
$971$	38.3512	−	22.1421i	1.23075	−	0.710573i	0.263562	−	0.964642i	$-0.415103\pi$
$971$	38.3512	−	22.1421i	1.23075	−	0.710573i	0.967186	+	0.254070i	$0.0817692\pi$
$972$		0			0
$973$	−4.75009	−	17.7276i	−0.152281	−	0.568320i
$974$		0			0
$975$	12.1859	+	9.00923i	0.390262	+	0.288526i
$976$		0			0
$977$	0.239374	−	0.0641402i	0.00765826	−	0.00205203i	−0.254988	−	0.966944i	$-0.582071\pi$
$977$	0.239374	−	0.0641402i	0.00765826	−	0.00205203i	0.262646	+	0.964892i	$0.415405\pi$
$978$		0			0
$979$	4.79020	+	8.29687i	0.153095	+	0.265169i
$980$		0			0
$981$	−0.0202707	+	0.0756511i	−0.000647192	+	0.00241535i
$982$		0			0
$983$	−8.44991	−	8.44991i	−0.269510	−	0.269510i	0.559393	−	0.828903i	$-0.311034\pi$
$983$	−8.44991	−	8.44991i	−0.269510	−	0.269510i	−0.828903	+	0.559393i	$0.811034\pi$
$984$		0			0
$985$	2.52321	+	1.45678i	0.0803963	+	0.0464168i
$986$		0			0
$987$	8.91069			0.283630
$988$		0			0
$989$	−80.3360			−2.55454
$990$		0			0
$991$	36.2254	+	20.9147i	1.15074	+	0.664379i	0.949067	−	0.315074i	$-0.102029\pi$
$991$	36.2254	+	20.9147i	1.15074	+	0.664379i	0.201671	+	0.979453i	$0.435363\pi$
$992$		0			0
$993$	8.63520	+	8.63520i	0.274030	+	0.274030i
$994$		0			0
$995$	0.148248	−	0.553269i	0.00469978	−	0.0175398i
$996$		0			0
$997$	6.38088	+	11.0520i	0.202085	+	0.350021i	0.949200	−	0.314674i	$-0.101895\pi$
$997$	6.38088	+	11.0520i	0.202085	+	0.350021i	−0.747115	+	0.664694i	$0.768562\pi$
$998$		0			0
$999$	−2.24302	+	0.601015i	−0.0709660	+	0.0190153i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	832.2.bu.n.319.2		16
4.3	odd	2	inner	832.2.bu.n.319.3		16
8.3	odd	2		52.2.l.b.7.4	yes	16
8.5	even	2		52.2.l.b.7.3	✓	16
13.2	odd	12	inner	832.2.bu.n.639.3		16
24.5	odd	2		468.2.cb.f.163.2		16
24.11	even	2		468.2.cb.f.163.1		16
52.15	even	12	inner	832.2.bu.n.639.2		16
104.3	odd	6		676.2.l.m.427.1		16
104.5	odd	4		676.2.l.m.19.1		16
104.11	even	12		676.2.l.k.587.2		16
104.19	even	12		676.2.f.h.239.1		16
104.21	odd	4		676.2.l.i.19.4		16
104.29	even	6		676.2.l.m.427.3		16
104.35	odd	6		676.2.f.h.99.6		16
104.37	odd	12		676.2.l.k.587.1		16
104.43	odd	6		676.2.f.i.99.3		16
104.45	odd	12		676.2.f.h.239.6		16
104.51	odd	2		676.2.l.k.319.1		16
104.59	even	12		676.2.f.i.239.8		16
104.61	even	6		676.2.f.h.99.1		16
104.67	even	12		52.2.l.b.15.3	yes	16
104.69	even	6		676.2.f.i.99.8		16
104.75	odd	6		676.2.l.i.427.4		16
104.77	even	2		676.2.l.k.319.2		16
104.83	even	4		676.2.l.m.19.3		16
104.85	odd	12		676.2.f.i.239.3		16
104.93	odd	12		52.2.l.b.15.4	yes	16
104.99	even	4		676.2.l.i.19.2		16
104.101	even	6		676.2.l.i.427.2		16
312.197	even	12		468.2.cb.f.379.1		16
312.275	odd	12		468.2.cb.f.379.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.l.b.7.3	✓	16	8.5	even	2
52.2.l.b.7.4	yes	16	8.3	odd	2
52.2.l.b.15.3	yes	16	104.67	even	12
52.2.l.b.15.4	yes	16	104.93	odd	12
468.2.cb.f.163.1		16	24.11	even	2
468.2.cb.f.163.2		16	24.5	odd	2
468.2.cb.f.379.1		16	312.197	even	12
468.2.cb.f.379.2		16	312.275	odd	12
676.2.f.h.99.1		16	104.61	even	6
676.2.f.h.99.6		16	104.35	odd	6
676.2.f.h.239.1		16	104.19	even	12
676.2.f.h.239.6		16	104.45	odd	12
676.2.f.i.99.3		16	104.43	odd	6
676.2.f.i.99.8		16	104.69	even	6
676.2.f.i.239.3		16	104.85	odd	12
676.2.f.i.239.8		16	104.59	even	12
676.2.l.i.19.2		16	104.99	even	4
676.2.l.i.19.4		16	104.21	odd	4
676.2.l.i.427.2		16	104.101	even	6
676.2.l.i.427.4		16	104.75	odd	6
676.2.l.k.319.1		16	104.51	odd	2
676.2.l.k.319.2		16	104.77	even	2
676.2.l.k.587.1		16	104.37	odd	12
676.2.l.k.587.2		16	104.11	even	12
676.2.l.m.19.1		16	104.5	odd	4
676.2.l.m.19.3		16	104.83	even	4
676.2.l.m.427.1		16	104.3	odd	6
676.2.l.m.427.3		16	104.29	even	6
832.2.bu.n.319.2		16	1.1	even	1	trivial
832.2.bu.n.319.3		16	4.3	odd	2	inner
832.2.bu.n.639.2		16	52.15	even	12	inner
832.2.bu.n.639.3		16	13.2	odd	12	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:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	832.bu (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.736159 - 0.425021i) q^{3} +(0.166404 + 0.166404i) q^{5} +(-0.684384 + 2.55416i) q^{7} +(-1.13871 - 1.97231i) q^{9} +(-1.39298 + 0.373247i) q^{11} +(0.406663 - 3.58254i) q^{13} +(-0.0517744 - 0.193225i) q^{15} +(1.21178 - 0.699622i) q^{17} +(5.39188 + 1.44475i) q^{19} +(1.58939 - 1.58939i) q^{21} +(4.37216 - 7.57279i) q^{23} -4.94462i q^{25} +4.48604i q^{27} +(2.11023 - 3.65503i) q^{29} +(-3.88100 + 3.88100i) q^{31} +(1.18409 + 0.317276i) q^{33} +(-0.538906 + 0.311137i) q^{35} +(0.133975 + 0.500000i) q^{37} +(-1.82203 + 2.46448i) q^{39} +(5.59808 - 1.50000i) q^{41} +(-4.59362 - 7.95638i) q^{43} +(0.138714 - 0.517686i) q^{45} +(2.80318 + 2.80318i) q^{47} +(0.00684229 + 0.00395040i) q^{49} -1.18942 q^{51} +5.94462 q^{53} +(-0.293906 - 0.169687i) q^{55} +(-3.35523 - 3.35523i) q^{57} +(2.20512 - 8.22961i) q^{59} +(-3.61102 - 6.25448i) q^{61} +(5.81691 - 1.55864i) q^{63} +(0.663819 - 0.528479i) q^{65} +(-0.652790 - 2.43624i) q^{67} +(-6.43720 + 3.71652i) q^{69} +(-10.5002 - 2.81352i) q^{71} +(5.05407 - 5.05407i) q^{73} +(-2.10157 + 3.64002i) q^{75} -3.81333i q^{77} -8.51654i q^{79} +(-1.50948 + 2.61449i) q^{81} +(-6.91195 + 6.91195i) q^{83} +(0.318065 + 0.0852251i) q^{85} +(-3.10694 + 1.79379i) q^{87} +(-1.71941 - 6.41693i) q^{89} +(8.87207 + 3.49052i) q^{91} +(4.50653 - 1.20752i) q^{93} +(0.656818 + 1.13764i) q^{95} +(-4.00474 + 14.9459i) q^{97} +(2.32236 + 2.32236i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} + 4 q^{9} + 12 q^{13} + 12 q^{17} + 28 q^{21} + 8 q^{29} - 20 q^{33} + 16 q^{37} + 48 q^{41} - 20 q^{45} + 60 q^{49} + 32 q^{53} + 12 q^{57} - 4 q^{61} - 8 q^{65} + 12 q^{69} + 20 q^{73}+ \cdots - 28 q^{97}+O(q^{100}) \) 16 * q + 12 * q^5 + 4 * q^9 + 12 * q^13 + 12 * q^17 + 28 * q^21 + 8 * q^29 - 20 * q^33 + 16 * q^37 + 48 * q^41 - 20 * q^45 + 60 * q^49 + 32 * q^53 + 12 * q^57 - 4 * q^61 - 8 * q^65 + 12 * q^69 + 20 * q^73 + 48 * q^81 - 20 * q^85 - 52 * q^89 + 92 * q^93 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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