LMFDB - Embedded newform 1232.2.q.o.177.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(177,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1232.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.q (of order $3$, degree $2$, 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:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.939795628203.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - 9x^{7} + 10x^{6} - 26x^{5} + 87x^{4} - 48x^{3} - 65x^{2} + 30x + 36 $ x^10 - x^9 + x^8 - 9x^7 + 10x^6 - 26x^5 + 87x^4 - 48x^3 - 65x^2 + 30*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 616)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.2
Root			$1.13198 + 0.475002i$ of defining polynomial
Character	$\chi$	$=$	1232.177
Dual form			1232.2.q.o.529.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.746498 - 1.29297i) q^{3} +(0.631979 - 1.09462i) q^{5} +(2.25927 + 1.37685i) q^{7} +(0.385481 - 0.667672i) q^{9} +O(q^{10})$	\(q+(-0.746498 - 1.29297i) q^{3} +(0.631979 - 1.09462i) q^{5} +(2.25927 + 1.37685i) q^{7} +(0.385481 - 0.667672i) q^{9} +(-0.500000 - 0.866025i) q^{11} +6.62065 q^{13} -1.88708 q^{15} +(0.512769 + 0.888141i) q^{17} +(-1.05106 + 1.82049i) q^{19} +(0.0936894 - 3.94899i) q^{21} +(-0.923770 + 1.60002i) q^{23} +(1.70121 + 2.94657i) q^{25} -5.63003 q^{27} +4.86370 q^{29} +(0.804560 + 1.39354i) q^{31} +(-0.746498 + 1.29297i) q^{33} +(2.93493 - 1.60290i) q^{35} +(1.08021 - 1.87098i) q^{37} +(-4.94230 - 8.56032i) q^{39} -6.49373 q^{41} +12.3528 q^{43} +(-0.487231 - 0.843909i) q^{45} +(2.51277 - 4.35224i) q^{47} +(3.20857 + 6.22134i) q^{49} +(0.765562 - 1.32599i) q^{51} +(-1.26087 - 2.18389i) q^{53} -1.26396 q^{55} +3.13845 q^{57} +(-1.77025 - 3.06617i) q^{59} +(1.47483 - 2.55448i) q^{61} +(1.79019 - 0.977701i) q^{63} +(4.18411 - 7.24709i) q^{65} +(-4.92253 - 8.52608i) q^{67} +2.75837 q^{69} -8.86228 q^{71} +(-7.61257 - 13.1854i) q^{73} +(2.53989 - 4.39922i) q^{75} +(0.0627526 - 2.64501i) q^{77} +(-4.15752 + 7.20103i) q^{79} +(3.04637 + 5.27646i) q^{81} +4.54870 q^{83} +1.29624 q^{85} +(-3.63074 - 6.28863i) q^{87} +(-3.31156 + 5.73580i) q^{89} +(14.9578 + 9.11563i) q^{91} +(1.20121 - 2.08055i) q^{93} +(1.32849 + 2.30102i) q^{95} +1.10674 q^{97} -0.770961 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{3} - 4 q^{5} + 2 q^{7}+O(q^{10}) $ 10 * q - q^3 - 4 * q^5 + 2 * q^7	$ 10 q - q^{3} - 4 q^{5} + 2 q^{7} - 5 q^{11} + 2 q^{13} - 14 q^{15} - 9 q^{17} + q^{19} - 12 q^{21} - 8 q^{23} - 5 q^{25} + 8 q^{27} + 18 q^{29} + 3 q^{31} - q^{33} + 15 q^{35} - 2 q^{37} - 7 q^{39} + 30 q^{41} - 28 q^{43} - 19 q^{45} + 11 q^{47} - 18 q^{49} - 14 q^{51} + 9 q^{53} + 8 q^{55} + 8 q^{57} + 4 q^{59} + 2 q^{61} + 28 q^{63} - 7 q^{65} - 8 q^{67} + 22 q^{69} - 30 q^{71} - 26 q^{73} + 27 q^{75} + 2 q^{77} - 3 q^{79} + 19 q^{81} + 2 q^{83} + 26 q^{85} + 14 q^{87} - 41 q^{89} + 39 q^{91} - 10 q^{93} - 19 q^{95} + 14 q^{97}+O(q^{100}) $ 10 * q - q^3 - 4 * q^5 + 2 * q^7 - 5 * q^11 + 2 * q^13 - 14 * q^15 - 9 * q^17 + q^19 - 12 * q^21 - 8 * q^23 - 5 * q^25 + 8 * q^27 + 18 * q^29 + 3 * q^31 - q^33 + 15 * q^35 - 2 * q^37 - 7 * q^39 + 30 * q^41 - 28 * q^43 - 19 * q^45 + 11 * q^47 - 18 * q^49 - 14 * q^51 + 9 * q^53 + 8 * q^55 + 8 * q^57 + 4 * q^59 + 2 * q^61 + 28 * q^63 - 7 * q^65 - 8 * q^67 + 22 * q^69 - 30 * q^71 - 26 * q^73 + 27 * q^75 + 2 * q^77 - 3 * q^79 + 19 * q^81 + 2 * q^83 + 26 * q^85 + 14 * q^87 - 41 * q^89 + 39 * q^91 - 10 * q^93 - 19 * q^95 + 14 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.746498	−	1.29297i	−0.430991	−	0.746498i	0.565968	−	0.824427i	$-0.308503\pi$
$3$	−0.746498	−	1.29297i	−0.430991	−	0.746498i	−0.996959	+	0.0779290i	$0.975169\pi$
$4$		0			0
$5$	0.631979	−	1.09462i	0.282630	−	0.489529i	−0.689402	−	0.724379i	$-0.742127\pi$
$5$	0.631979	−	1.09462i	0.282630	−	0.489529i	0.972032	+	0.234850i	$0.0754600\pi$
$6$		0			0
$7$	2.25927	+	1.37685i	0.853923	+	0.520400i
$7$	2.25927	+	1.37685i	0.853923	+	0.520400i
$8$		0			0
$9$	0.385481	−	0.667672i	0.128494	−	0.222557i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	6.62065			1.83624			0.918119	−	0.396305i	$-0.129708\pi$
$13$	6.62065			1.83624			0.918119	+	0.396305i	$0.129708\pi$
$14$		0			0
$15$	−1.88708			−0.487243
$16$		0			0
$17$	0.512769	+	0.888141i	0.124365	+	0.215406i	0.921484	−	0.388415i	$-0.126977\pi$
$17$	0.512769	+	0.888141i	0.124365	+	0.215406i	−0.797120	+	0.603821i	$0.793644\pi$
$18$		0			0
$19$	−1.05106	+	1.82049i	−0.241129	+	0.417648i	−0.961036	−	0.276422i	$-0.910851\pi$
$19$	−1.05106	+	1.82049i	−0.241129	+	0.417648i	0.719907	+	0.694071i	$0.244184\pi$
$20$		0			0
$21$	0.0936894	−	3.94899i	0.0204447	−	0.861739i
$22$		0			0
$23$	−0.923770	+	1.60002i	−0.192619	+	0.333627i	−0.946118	−	0.323823i	$-0.895032\pi$
$23$	−0.923770	+	1.60002i	−0.192619	+	0.333627i	0.753498	+	0.657450i	$0.228365\pi$
$24$		0			0
$25$	1.70121	+	2.94657i	0.340241	+	0.589315i
$26$		0			0
$27$	−5.63003			−1.08350
$28$		0			0
$29$	4.86370			0.903166			0.451583	−	0.892229i	$-0.350860\pi$
$29$	4.86370			0.903166			0.451583	+	0.892229i	$0.350860\pi$
$30$		0			0
$31$	0.804560	+	1.39354i	0.144503	+	0.250287i	0.929188	−	0.369609i	$-0.120508\pi$
$31$	0.804560	+	1.39354i	0.144503	+	0.250287i	−0.784684	+	0.619896i	$0.787175\pi$
$32$		0			0
$33$	−0.746498	+	1.29297i	−0.129949	+	0.225078i
$34$		0			0
$35$	2.93493	−	1.60290i	0.496095	−	0.270939i
$36$		0			0
$37$	1.08021	−	1.87098i	0.177586	−	0.307588i	−0.763467	−	0.645846i	$-0.776505\pi$
$37$	1.08021	−	1.87098i	0.177586	−	0.307588i	0.941053	+	0.338259i	$0.109838\pi$
$38$		0			0
$39$	−4.94230	−	8.56032i	−0.791402	−	1.37075i
$40$		0			0
$41$	−6.49373			−1.01415			−0.507075	−	0.861902i	$-0.669273\pi$
$41$	−6.49373			−1.01415			−0.507075	+	0.861902i	$0.669273\pi$
$42$		0			0
$43$	12.3528			1.88378			0.941892	−	0.335916i	$-0.109046\pi$
$43$	12.3528			1.88378			0.941892	+	0.335916i	$0.109046\pi$
$44$		0			0
$45$	−0.487231	−	0.843909i	−0.0726322	−	0.125803i
$46$		0			0
$47$	2.51277	−	4.35224i	0.366525	−	0.634840i	−0.622495	−	0.782624i	$-0.713881\pi$
$47$	2.51277	−	4.35224i	0.366525	−	0.634840i	0.989020	+	0.147784i	$0.0472141\pi$
$48$		0			0
$49$	3.20857	+	6.22134i	0.458368	+	0.888763i
$50$		0			0
$51$	0.765562	−	1.32599i	0.107200	−	0.185676i
$52$		0			0
$53$	−1.26087	−	2.18389i	−0.173194	−	0.299981i	0.766341	−	0.642434i	$-0.222075\pi$
$53$	−1.26087	−	2.18389i	−0.173194	−	0.299981i	−0.939535	+	0.342454i	$0.888742\pi$
$54$		0			0
$55$	−1.26396			−0.170432
$56$		0			0
$57$	3.13845			0.415698
$58$		0			0
$59$	−1.77025	−	3.06617i	−0.230467	−	0.399181i	0.727478	−	0.686131i	$-0.240692\pi$
$59$	−1.77025	−	3.06617i	−0.230467	−	0.399181i	−0.957946	+	0.286950i	$0.907359\pi$
$60$		0			0
$61$	1.47483	−	2.55448i	0.188832	−	0.327067i	−0.756029	−	0.654538i	$-0.772863\pi$
$61$	1.47483	−	2.55448i	0.188832	−	0.327067i	0.944861	+	0.327471i	$0.106196\pi$
$62$		0			0
$63$	1.79019	−	0.977701i	0.225542	−	0.123179i
$64$		0			0
$65$	4.18411	−	7.24709i	0.518975	−	0.898891i
$66$		0			0
$67$	−4.92253	−	8.52608i	−0.601383	−	1.04163i	−0.992612	−	0.121333i	$-0.961283\pi$
$67$	−4.92253	−	8.52608i	−0.601383	−	1.04163i	0.391229	−	0.920293i	$-0.372050\pi$
$68$		0			0
$69$	2.75837			0.332069
$70$		0			0
$71$	−8.86228			−1.05176			−0.525880	−	0.850559i	$-0.676264\pi$
$71$	−8.86228			−1.05176			−0.525880	+	0.850559i	$0.676264\pi$
$72$		0			0
$73$	−7.61257	−	13.1854i	−0.890984	−	1.54323i	−0.838697	−	0.544598i	$-0.816682\pi$
$73$	−7.61257	−	13.1854i	−0.890984	−	1.54323i	−0.0522869	−	0.998632i	$-0.516651\pi$
$74$		0			0
$75$	2.53989	−	4.39922i	0.293282	−	0.507979i
$76$		0			0
$77$	0.0627526	−	2.64501i	0.00715132	−	0.301427i
$78$		0			0
$79$	−4.15752	+	7.20103i	−0.467757	+	0.810179i	−0.999321	−	0.0368390i	$-0.988271\pi$
$79$	−4.15752	+	7.20103i	−0.467757	+	0.810179i	0.531564	+	0.847018i	$0.321604\pi$
$80$		0			0
$81$	3.04637	+	5.27646i	0.338485	+	0.586274i
$82$		0			0
$83$	4.54870			0.499284			0.249642	−	0.968338i	$-0.419687\pi$
$83$	4.54870			0.499284			0.249642	+	0.968338i	$0.419687\pi$
$84$		0			0
$85$	1.29624			0.140597
$86$		0			0
$87$	−3.63074	−	6.28863i	−0.389256	−	0.674212i
$88$		0			0
$89$	−3.31156	+	5.73580i	−0.351025	+	0.607993i	−0.986429	−	0.164186i	$-0.947500\pi$
$89$	−3.31156	+	5.73580i	−0.351025	+	0.607993i	0.635404	+	0.772180i	$0.280833\pi$
$90$		0			0
$91$	14.9578	+	9.11563i	1.56801	+	0.955578i
$92$		0			0
$93$	1.20121	−	2.08055i	0.124559	−	0.215743i
$94$		0			0
$95$	1.32849	+	2.30102i	0.136301	+	0.236079i
$96$		0			0
$97$	1.10674			0.112373			0.0561863	−	0.998420i	$-0.482106\pi$
$97$	1.10674			0.112373			0.0561863	+	0.998420i	$0.482106\pi$
$98$		0			0
$99$	−0.770961			−0.0774845
$100$		0			0
$101$	−9.79526	−	16.9659i	−0.974665	−	1.68817i	−0.681037	−	0.732249i	$-0.738471\pi$
$101$	−9.79526	−	16.9659i	−0.974665	−	1.68817i	−0.293628	−	0.955920i	$-0.594863\pi$
$102$		0			0
$103$	3.34019	−	5.78537i	0.329118	−	0.570050i	−0.653219	−	0.757169i	$-0.726582\pi$
$103$	3.34019	−	5.78537i	0.329118	−	0.570050i	0.982337	+	0.187119i	$0.0599151\pi$
$104$		0			0
$105$	−4.26343	−	2.59823i	−0.416068	−	0.253561i
$106$		0			0
$107$	2.92147	−	5.06014i	0.282430	−	0.489182i	−0.689553	−	0.724235i	$-0.742193\pi$
$107$	2.92147	−	5.06014i	0.282430	−	0.489182i	0.971983	+	0.235053i	$0.0755263\pi$
$108$		0			0
$109$	0.135349	+	0.234432i	0.0129641	+	0.0224545i	0.872435	−	0.488731i	$-0.162540\pi$
$109$	0.135349	+	0.234432i	0.0129641	+	0.0224545i	−0.859471	+	0.511185i	$0.829207\pi$
$110$		0			0
$111$	−3.22551			−0.306151
$112$		0			0
$113$	−11.2445			−1.05779			−0.528897	−	0.848686i	$-0.677394\pi$
$113$	−11.2445			−1.05779			−0.528897	+	0.848686i	$0.677394\pi$
$114$		0			0
$115$	1.16761	+	2.02235i	0.108880	+	0.188585i
$116$		0			0
$117$	2.55213	−	4.42042i	0.235945	−	0.408668i
$118$		0			0
$119$	−0.0643551	+	2.71255i	−0.00589942	+	0.248659i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	4.84756	+	8.39621i	0.437089	+	0.757061i
$124$		0			0
$125$	10.6203			0.949908
$126$		0			0
$127$	−3.26643			−0.289849			−0.144925	−	0.989443i	$-0.546294\pi$
$127$	−3.26643			−0.289849			−0.144925	+	0.989443i	$0.546294\pi$
$128$		0			0
$129$	−9.22134	−	15.9718i	−0.811894	−	1.40624i
$130$		0			0
$131$	7.64173	−	13.2359i	0.667661	−	1.15642i	−0.310896	−	0.950444i	$-0.600629\pi$
$131$	7.64173	−	13.2359i	0.667661	−	1.15642i	0.978557	−	0.205978i	$-0.0660376\pi$
$132$		0			0
$133$	−4.88116	+	2.66582i	−0.423250	+	0.231156i
$134$		0			0
$135$	−3.55806	+	6.16274i	−0.306229	+	0.530405i
$136$		0			0
$137$	7.59804	+	13.1602i	0.649144	+	1.12435i	0.983328	+	0.181843i	$0.0582061\pi$
$137$	7.59804	+	13.1602i	0.649144	+	1.12435i	−0.334183	+	0.942508i	$0.608461\pi$
$138$		0			0
$139$	17.3356			1.47039			0.735193	−	0.677858i	$-0.237092\pi$
$139$	17.3356			1.47039			0.735193	+	0.677858i	$0.237092\pi$
$140$		0			0
$141$	−7.50311			−0.631876
$142$		0			0
$143$	−3.31033	−	5.73365i	−0.276823	−	0.479472i
$144$		0			0
$145$	3.07375	−	5.32390i	0.255261	−	0.442126i
$146$		0			0
$147$	5.64883	−	8.79282i	0.465907	−	0.725219i
$148$		0			0
$149$	−11.4794	+	19.8828i	−0.940425	+	1.62886i	−0.175764	+	0.984432i	$0.556240\pi$
$149$	−11.4794	+	19.8828i	−0.940425	+	1.62886i	−0.764661	+	0.644432i	$0.777094\pi$
$150$		0			0
$151$	4.69616	+	8.13398i	0.382168	+	0.661934i	0.991372	−	0.131080i	$-0.0418443\pi$
$151$	4.69616	+	8.13398i	0.382168	+	0.661934i	−0.609204	+	0.793013i	$0.708511\pi$
$152$		0			0
$153$	0.790650			0.0639202
$154$		0			0
$155$	2.03386			0.163364
$156$		0			0
$157$	0.507369	+	0.878789i	0.0404925	+	0.0701350i	0.885561	−	0.464522i	$-0.153774\pi$
$157$	0.507369	+	0.878789i	0.0404925	+	0.0701350i	−0.845069	+	0.534657i	$0.820441\pi$
$158$		0			0
$159$	−1.88248	+	3.26054i	−0.149290	+	0.258578i
$160$		0			0
$161$	−4.29002	+	2.34297i	−0.338101	+	0.184652i
$162$		0			0
$163$	−8.45686	+	14.6477i	−0.662392	+	1.14730i	0.317593	+	0.948227i	$0.397125\pi$
$163$	−8.45686	+	14.6477i	−0.662392	+	1.14730i	−0.979985	+	0.199070i	$0.936208\pi$
$164$		0			0
$165$	0.943542	+	1.63426i	0.0734547	+	0.127227i
$166$		0			0
$167$	3.48220			0.269461			0.134730	−	0.990882i	$-0.456983\pi$
$167$	3.48220			0.269461			0.134730	+	0.990882i	$0.456983\pi$
$168$		0			0
$169$	30.8330			2.37177
$170$		0			0
$171$	0.810325	+	1.40352i	0.0619671	+	0.107330i
$172$		0			0
$173$	−12.1054	+	20.9672i	−0.920357	+	1.59411i	−0.121494	+	0.992592i	$0.538769\pi$
$173$	−12.1054	+	20.9672i	−0.920357	+	1.59411i	−0.798863	+	0.601513i	$0.794565\pi$
$174$		0			0
$175$	−0.213510	+	8.99940i	−0.0161398	+	0.680291i
$176$		0			0
$177$	−2.64298	+	4.57778i	−0.198659	+	0.344087i
$178$		0			0
$179$	7.88532	+	13.6578i	0.589376	+	1.02083i	0.994314	+	0.106485i	$0.0339598\pi$
$179$	7.88532	+	13.6578i	0.589376	+	1.02083i	−0.404938	+	0.914344i	$0.632707\pi$
$180$		0			0
$181$	−13.5710			−1.00873			−0.504364	−	0.863491i	$-0.668273\pi$
$181$	−13.5710			−1.00873			−0.504364	+	0.863491i	$0.668273\pi$
$182$		0			0
$183$	−4.40383			−0.325540
$184$		0			0
$185$	−1.36534	−	2.36484i	−0.100382	−	0.173867i
$186$		0			0
$187$	0.512769	−	0.888141i	0.0374974	−	0.0649473i
$188$		0			0
$189$	−12.7197	−	7.75170i	−0.925225	−	0.563853i
$190$		0			0
$191$	9.53043	−	16.5072i	0.689598	−	1.19442i	−0.282370	−	0.959305i	$-0.591121\pi$
$191$	9.53043	−	16.5072i	0.689598	−	1.19442i	0.971968	−	0.235113i	$-0.0755460\pi$
$192$		0			0
$193$	3.70068	+	6.40976i	0.266381	+	0.461385i	0.967924	−	0.251242i	$-0.0808389\pi$
$193$	3.70068	+	6.40976i	0.266381	+	0.461385i	−0.701544	+	0.712626i	$0.747506\pi$
$194$		0			0
$195$	−12.4937			−0.894694
$196$		0			0
$197$	2.01629			0.143655			0.0718273	−	0.997417i	$-0.477117\pi$
$197$	2.01629			0.143655			0.0718273	+	0.997417i	$0.477117\pi$
$198$		0			0
$199$	1.14873	+	1.98966i	0.0814313	+	0.141043i	0.903865	−	0.427818i	$-0.140718\pi$
$199$	1.14873	+	1.98966i	0.0814313	+	0.141043i	−0.822434	+	0.568861i	$0.807384\pi$
$200$		0			0
$201$	−7.34932	+	12.7294i	−0.518381	+	0.897863i
$202$		0			0
$203$	10.9884	+	6.69657i	0.771234	+	0.470007i
$204$		0			0
$205$	−4.10390	+	7.10816i	−0.286629	+	0.496456i
$206$		0			0
$207$	0.712191	+	1.23355i	0.0495007	+	0.0857377i
$208$		0			0
$209$	2.10212			0.145406
$210$		0			0
$211$	−20.3438			−1.40052			−0.700262	−	0.713886i	$-0.746933\pi$
$211$	−20.3438			−1.40052			−0.700262	+	0.713886i	$0.746933\pi$
$212$		0			0
$213$	6.61568	+	11.4587i	0.453299	+	0.785136i
$214$		0			0
$215$	7.80671	−	13.5216i	0.532413	−	0.922167i
$216$		0			0
$217$	−0.100976	+	4.25613i	−0.00685473	+	0.288925i
$218$		0			0
$219$	−11.3655	+	19.6857i	−0.768012	+	1.33024i
$220$		0			0
$221$	3.39486	+	5.88007i	0.228363	+	0.395537i
$222$		0			0
$223$	−18.0165			−1.20648			−0.603238	−	0.797561i	$-0.706123\pi$
$223$	−18.0165			−1.20648			−0.603238	+	0.797561i	$0.706123\pi$
$224$		0			0
$225$	2.62313			0.174875
$226$		0			0
$227$	3.90846	+	6.76965i	0.259414	+	0.449317i	0.966085	−	0.258224i	$-0.0831374\pi$
$227$	3.90846	+	6.76965i	0.259414	+	0.449317i	−0.706671	+	0.707542i	$0.749804\pi$
$228$		0			0
$229$	1.63429	−	2.83068i	0.107997	−	0.187056i	−0.806962	−	0.590604i	$-0.798890\pi$
$229$	1.63429	−	2.83068i	0.107997	−	0.187056i	0.914959	+	0.403547i	$0.132223\pi$
$230$		0			0
$231$	−3.46677	+	1.89336i	−0.228097	+	0.124574i
$232$		0			0
$233$	−13.5549	+	23.4778i	−0.888014	+	1.53809i	−0.0457939	+	0.998951i	$0.514582\pi$
$233$	−13.5549	+	23.4778i	−0.888014	+	1.53809i	−0.842220	+	0.539134i	$0.818752\pi$
$234$		0			0
$235$	−3.17603	−	5.50105i	−0.207182	−	0.358849i
$236$		0			0
$237$	12.4143			0.806396
$238$		0			0
$239$	−23.3429			−1.50992			−0.754962	−	0.655769i	$-0.772345\pi$
$239$	−23.3429			−1.50992			−0.754962	+	0.655769i	$0.772345\pi$
$240$		0			0
$241$	−9.91287	−	17.1696i	−0.638544	−	1.10599i	−0.985752	−	0.168203i	$-0.946204\pi$
$241$	−9.91287	−	17.1696i	−0.638544	−	1.10599i	0.347209	−	0.937788i	$-0.387130\pi$
$242$		0			0
$243$	−3.89683	+	6.74951i	−0.249982	+	0.432981i
$244$		0			0
$245$	8.83775	+	0.419586i	0.564623	+	0.0268064i
$246$		0			0
$247$	−6.95869	+	12.0528i	−0.442771	+	0.766902i
$248$		0			0
$249$	−3.39559	−	5.88134i	−0.215187	−	0.372715i
$250$		0			0
$251$	23.7297			1.49780			0.748902	−	0.662681i	$-0.230581\pi$
$251$	23.7297			1.49780			0.748902	+	0.662681i	$0.230581\pi$
$252$		0			0
$253$	1.84754			0.116154
$254$		0			0
$255$	−0.967638	−	1.67600i	−0.0605958	−	0.104955i
$256$		0			0
$257$	−9.68322	+	16.7718i	−0.604022	+	1.04620i	0.388183	+	0.921582i	$0.373103\pi$
$257$	−9.68322	+	16.7718i	−0.604022	+	1.04620i	−0.992205	+	0.124615i	$0.960230\pi$
$258$		0			0
$259$	5.01655	−	2.73976i	0.311713	−	0.170240i
$260$		0			0
$261$	1.87486	−	3.24735i	0.116051	−	0.201006i
$262$		0			0
$263$	0.682737	+	1.18254i	0.0420994	+	0.0729182i	0.886307	−	0.463098i	$-0.153262\pi$
$263$	0.682737	+	1.18254i	0.0420994	+	0.0729182i	−0.844208	+	0.536016i	$0.819929\pi$
$264$		0			0
$265$	−3.18738			−0.195799
$266$		0			0
$267$	9.88831			0.605154
$268$		0			0
$269$	−5.75563	−	9.96905i	−0.350927	−	0.607824i	0.635485	−	0.772113i	$-0.280800\pi$
$269$	−5.75563	−	9.96905i	−0.350927	−	0.607824i	−0.986412	+	0.164290i	$0.947467\pi$
$270$		0			0
$271$	−4.38134	+	7.58870i	−0.266147	+	0.460980i	−0.967864	−	0.251476i	$-0.919084\pi$
$271$	−4.38134	+	7.58870i	−0.266147	+	0.460980i	0.701716	+	0.712456i	$0.252417\pi$
$272$		0			0
$273$	0.620285	−	26.1449i	0.0375413	−	1.58236i
$274$		0			0
$275$	1.70121	−	2.94657i	0.102587	−	0.177685i
$276$		0			0
$277$	−5.16903	−	8.95302i	−0.310577	−	0.537935i	0.667910	−	0.744242i	$-0.267189\pi$
$277$	−5.16903	−	8.95302i	−0.310577	−	0.537935i	−0.978487	+	0.206307i	$0.933856\pi$
$278$		0			0
$279$	1.24057			0.0742709
$280$		0			0
$281$	19.2331			1.14735			0.573676	−	0.819083i	$-0.305517\pi$
$281$	19.2331			1.14735			0.573676	+	0.819083i	$0.305517\pi$
$282$		0			0
$283$	−5.80041	−	10.0466i	−0.344799	−	0.597209i	0.640518	−	0.767943i	$-0.278720\pi$
$283$	−5.80041	−	10.0466i	−0.344799	−	0.597209i	−0.985317	+	0.170734i	$0.945386\pi$
$284$		0			0
$285$	1.98344	−	3.43541i	0.117489	−	0.203496i
$286$		0			0
$287$	−14.6711	−	8.94088i	−0.866006	−	0.527764i
$288$		0			0
$289$	7.97414	−	13.8116i	0.469067	−	0.812448i
$290$		0			0
$291$	−0.826181	−	1.43099i	−0.0484316	−	0.0838859i
$292$		0			0
$293$	−0.737833			−0.0431047			−0.0215523	−	0.999768i	$-0.506861\pi$
$293$	−0.737833			−0.0431047			−0.0215523	+	0.999768i	$0.506861\pi$
$294$		0			0
$295$	−4.47505			−0.260547
$296$		0			0
$297$	2.81502	+	4.87575i	0.163344	+	0.282920i
$298$		0			0
$299$	−6.11596	+	10.5932i	−0.353695	+	0.612618i
$300$		0			0
$301$	27.9083	+	17.0079i	1.60861	+	0.980321i
$302$		0			0
$303$	−14.6243	+	25.3300i	−0.840144	+	1.45517i
$304$		0			0
$305$	−1.86412	−	3.22875i	−0.106739	−	0.184878i
$306$		0			0
$307$	15.0009			0.856144			0.428072	−	0.903745i	$-0.359193\pi$
$307$	15.0009			0.856144			0.428072	+	0.903745i	$0.359193\pi$
$308$		0			0
$309$	−9.97378			−0.567388
$310$		0			0
$311$	−7.97466	−	13.8125i	−0.452202	−	0.783236i	0.546321	−	0.837576i	$-0.316028\pi$
$311$	−7.97466	−	13.8125i	−0.452202	−	0.783236i	−0.998523	+	0.0543396i	$0.982695\pi$
$312$		0			0
$313$	−11.3806	+	19.7118i	−0.643271	+	1.11418i	0.341427	+	0.939908i	$0.389090\pi$
$313$	−11.3806	+	19.7118i	−0.643271	+	1.11418i	−0.984698	+	0.174270i	$0.944244\pi$
$314$		0			0
$315$	0.0611500	−	2.57746i	0.00344541	−	0.145223i
$316$		0			0
$317$	3.67878	−	6.37183i	0.206621	−	0.357878i	−0.744027	−	0.668149i	$-0.767087\pi$
$317$	3.67878	−	6.37183i	0.206621	−	0.357878i	0.950648	+	0.310272i	$0.100420\pi$
$318$		0			0
$319$	−2.43185	−	4.21208i	−0.136157	−	0.235831i
$320$		0			0
$321$	−8.72350			−0.486898
$322$		0			0
$323$	−2.15580			−0.119952
$324$		0			0
$325$	11.2631	+	19.5082i	0.624764	+	1.08212i
$326$		0			0
$327$	0.202076	−	0.350006i	0.0111748	−	0.0193554i
$328$		0			0
$329$	11.6694	−	6.37318i	0.643355	−	0.351365i
$330$		0			0
$331$	−13.4602	+	23.3137i	−0.739839	+	1.28144i	0.212728	+	0.977111i	$0.431765\pi$
$331$	−13.4602	+	23.3137i	−0.739839	+	1.28144i	−0.952567	+	0.304328i	$0.901568\pi$
$332$		0			0
$333$	−0.832802	−	1.44245i	−0.0456373	−	0.0790460i
$334$		0			0
$335$	−12.4437			−0.679874
$336$		0			0
$337$	24.4273			1.33064			0.665319	−	0.746559i	$-0.268296\pi$
$337$	24.4273			1.33064			0.665319	+	0.746559i	$0.268296\pi$
$338$		0			0
$339$	8.39401	+	14.5388i	0.455900	+	0.789642i
$340$		0			0
$341$	0.804560	−	1.39354i	0.0435694	−	0.0754644i
$342$		0			0
$343$	−1.31682	+	18.4734i	−0.0711014	+	0.997469i
$344$		0			0
$345$	1.74323	−	3.01937i	0.0938525	−	0.162557i
$346$		0			0
$347$	−17.4242	−	30.1796i	−0.935381	−	1.62013i	−0.773953	−	0.633243i	$-0.781723\pi$
$347$	−17.4242	−	30.1796i	−0.935381	−	1.62013i	−0.161428	−	0.986884i	$-0.551610\pi$
$348$		0			0
$349$	9.58943			0.513311			0.256655	−	0.966503i	$-0.417380\pi$
$349$	9.58943			0.513311			0.256655	+	0.966503i	$0.417380\pi$
$350$		0			0
$351$	−37.2745			−1.98956
$352$		0			0
$353$	−7.11025	−	12.3153i	−0.378441	−	0.655478i	0.612395	−	0.790552i	$-0.290206\pi$
$353$	−7.11025	−	12.3153i	−0.378441	−	0.655478i	−0.990836	+	0.135074i	$0.956873\pi$
$354$		0			0
$355$	−5.60077	+	9.70082i	−0.297258	+	0.514866i
$356$		0			0
$357$	3.55530	−	1.94171i	0.188166	−	0.102766i
$358$		0			0
$359$	−6.23358	+	10.7969i	−0.328996	+	0.569838i	−0.982313	−	0.187247i	$-0.940044\pi$
$359$	−6.23358	+	10.7969i	−0.328996	+	0.569838i	0.653317	+	0.757084i	$0.273377\pi$
$360$		0			0
$361$	7.29055	+	12.6276i	0.383713	+	0.664611i
$362$		0			0
$363$	1.49300			0.0783620
$364$		0			0
$365$	−19.2439			−1.00727
$366$		0			0
$367$	−3.47704	−	6.02241i	−0.181500	−	0.314367i	0.760892	−	0.648879i	$-0.224762\pi$
$367$	−3.47704	−	6.02241i	−0.181500	−	0.314367i	−0.942392	+	0.334512i	$0.891429\pi$
$368$		0			0
$369$	−2.50321	+	4.33568i	−0.130312	+	0.225707i
$370$		0			0
$371$	0.158246	−	6.67003i	0.00821571	−	0.346290i
$372$		0			0
$373$	−6.78808	+	11.7573i	−0.351473	+	0.608770i	−0.986508	−	0.163714i	$-0.947653\pi$
$373$	−6.78808	+	11.7573i	−0.351473	+	0.608770i	0.635034	+	0.772484i	$0.280986\pi$
$374$		0			0
$375$	−7.92803	−	13.7318i	−0.409402	−	0.709105i
$376$		0			0
$377$	32.2008			1.65843
$378$		0			0
$379$	18.6650			0.958757			0.479378	−	0.877608i	$-0.340862\pi$
$379$	18.6650			0.958757			0.479378	+	0.877608i	$0.340862\pi$
$380$		0			0
$381$	2.43839	+	4.22341i	0.124922	+	0.216372i
$382$		0			0
$383$	2.14012	−	3.70680i	0.109355	−	0.189409i	−0.806154	−	0.591706i	$-0.798455\pi$
$383$	2.14012	−	3.70680i	0.109355	−	0.189409i	0.915509	+	0.402297i	$0.131788\pi$
$384$		0			0
$385$	−2.85562	−	1.74028i	−0.145536	−	0.0886928i
$386$		0			0
$387$	4.76177	−	8.24762i	0.242054	−	0.419250i
$388$		0			0
$389$	−1.94414	−	3.36734i	−0.0985716	−	0.170731i	0.812522	−	0.582931i	$-0.198094\pi$
$389$	−1.94414	−	3.36734i	−0.0985716	−	0.170731i	−0.911094	+	0.412199i	$0.864761\pi$
$390$		0			0
$391$	−1.89472			−0.0958202
$392$		0			0
$393$	−22.8181			−1.15102
$394$		0			0
$395$	5.25493	+	9.10180i	0.264404	+	0.457961i
$396$		0			0
$397$	−18.2367	+	31.5868i	−0.915273	+	1.58530i	−0.108771	+	0.994067i	$0.534691\pi$
$397$	−18.2367	+	31.5868i	−0.915273	+	1.58530i	−0.806502	+	0.591232i	$0.798642\pi$
$398$		0			0
$399$	7.09060	+	4.32117i	0.354974	+	0.216329i
$400$		0			0
$401$	0.372532	−	0.645244i	0.0186033	−	0.0322219i	−0.856574	−	0.516024i	$-0.827411\pi$
$401$	0.372532	−	0.645244i	0.0186033	−	0.0322219i	0.875177	+	0.483803i	$0.160745\pi$
$402$		0			0
$403$	5.32671	+	9.22613i	0.265342	+	0.459586i
$404$		0			0
$405$	7.70096			0.382664
$406$		0			0
$407$	−2.16042			−0.107088
$408$		0			0
$409$	−4.27886	−	7.41120i	−0.211576	−	0.366460i	0.740632	−	0.671911i	$-0.234526\pi$
$409$	−4.27886	−	7.41120i	−0.211576	−	0.366460i	−0.952208	+	0.305451i	$0.901193\pi$
$410$		0			0
$411$	11.3438	−	19.6481i	0.559551	−	0.969170i
$412$		0			0
$413$	0.222176	−	9.36466i	0.0109326	−	0.460805i
$414$		0			0
$415$	2.87468	−	4.97909i	0.141113	−	0.244414i
$416$		0			0
$417$	−12.9410	−	22.4144i	−0.633723	−	1.09764i
$418$		0			0
$419$	−12.1216			−0.592181			−0.296091	−	0.955160i	$-0.595683\pi$
$419$	−12.1216			−0.592181			−0.296091	+	0.955160i	$0.595683\pi$
$420$		0			0
$421$	3.61874			0.176367			0.0881833	−	0.996104i	$-0.471894\pi$
$421$	3.61874			0.176367			0.0881833	+	0.996104i	$0.471894\pi$
$422$		0			0
$423$	−1.93725	−	3.35541i	−0.0941922	−	0.163146i
$424$		0			0
$425$	−1.74465	+	3.02182i	−0.0846279	+	0.146580i
$426$		0			0
$427$	6.84916	−	3.74063i	0.331454	−	0.181022i
$428$		0			0
$429$	−4.94230	+	8.56032i	−0.238617	+	0.413296i
$430$		0			0
$431$	15.6263	+	27.0655i	0.752692	+	1.30370i	0.946513	+	0.322665i	$0.104579\pi$
$431$	15.6263	+	27.0655i	0.752692	+	1.30370i	−0.193821	+	0.981037i	$0.562088\pi$
$432$		0			0
$433$	2.21202			0.106303			0.0531514	−	0.998586i	$-0.483073\pi$
$433$	2.21202			0.106303			0.0531514	+	0.998586i	$0.483073\pi$
$434$		0			0
$435$	−9.17821			−0.440061
$436$		0			0
$437$	−1.94187	−	3.36342i	−0.0928924	−	0.160894i
$438$		0			0
$439$	8.22539	−	14.2468i	0.392577	−	0.679962i	−0.600212	−	0.799841i	$-0.704917\pi$
$439$	8.22539	−	14.2468i	0.392577	−	0.679962i	0.992789	+	0.119878i	$0.0382505\pi$
$440$		0			0
$441$	5.39066	+	0.255930i	0.256698	+	0.0121871i
$442$		0			0
$443$	13.8395	−	23.9707i	0.657534	−	1.13888i	−0.323718	−	0.946153i	$-0.604933\pi$
$443$	13.8395	−	23.9707i	0.657534	−	1.13888i	0.981252	−	0.192728i	$-0.0617336\pi$
$444$		0			0
$445$	4.18568	+	7.24980i	0.198420	+	0.343674i
$446$		0			0
$447$	34.2773			1.62126
$448$		0			0
$449$	7.75897			0.366169			0.183084	−	0.983097i	$-0.441392\pi$
$449$	7.75897			0.366169			0.183084	+	0.983097i	$0.441392\pi$
$450$		0			0
$451$	3.24686	+	5.62373i	0.152889	+	0.264811i
$452$		0			0
$453$	7.01134	−	12.1440i	0.329422	−	0.570575i
$454$		0			0
$455$	19.4312	−	10.6122i	0.910948	−	0.497509i
$456$		0			0
$457$	−18.2740	+	31.6515i	−0.854823	+	1.48060i	0.0219868	+	0.999758i	$0.493001\pi$
$457$	−18.2740	+	31.6515i	−0.854823	+	1.48060i	−0.876809	+	0.480838i	$0.840333\pi$
$458$		0			0
$459$	−2.88690	−	5.00026i	−0.134749	−	0.233392i
$460$		0			0
$461$	−15.1821			−0.707099			−0.353550	−	0.935416i	$-0.615025\pi$
$461$	−15.1821			−0.707099			−0.353550	+	0.935416i	$0.615025\pi$
$462$		0			0
$463$	−20.5267			−0.953958			−0.476979	−	0.878915i	$-0.658268\pi$
$463$	−20.5267			−0.953958			−0.476979	+	0.878915i	$0.658268\pi$
$464$		0			0
$465$	−1.51827	−	2.62973i	−0.0704082	−	0.121951i
$466$		0			0
$467$	7.36936	−	12.7641i	0.341013	−	0.590652i	−0.643608	−	0.765355i	$-0.722563\pi$
$467$	7.36936	−	12.7641i	0.341013	−	0.590652i	0.984621	+	0.174703i	$0.0558966\pi$
$468$		0			0
$469$	0.617803	−	26.0403i	0.0285275	−	1.20243i
$470$		0			0
$471$	0.757501	−	1.31203i	0.0349038	−	0.0604551i
$472$		0			0
$473$	−6.17640	−	10.6978i	−0.283991	−	0.491887i
$474$		0			0
$475$	−7.15226			−0.328168
$476$		0			0
$477$	−1.94417			−0.0890172
$478$		0			0
$479$	−12.3953	−	21.4692i	−0.566353	−	0.980953i	−0.996922	−	0.0783953i	$-0.975020\pi$
$479$	−12.3953	−	21.4692i	−0.566353	−	0.980953i	0.430569	−	0.902558i	$-0.358313\pi$
$480$		0			0
$481$	7.15171	−	12.3871i	0.326090	−	0.564804i
$482$		0			0
$483$	6.23190	+	3.79786i	0.283561	+	0.172809i
$484$		0			0
$485$	0.699437	−	1.21146i	0.0317598	−	0.0550096i
$486$		0			0
$487$	13.5453	+	23.4612i	0.613796	+	1.06313i	0.990594	+	0.136831i	$0.0436918\pi$
$487$	13.5453	+	23.4612i	0.613796	+	1.06313i	−0.376798	+	0.926296i	$0.622975\pi$
$488$		0			0
$489$	25.2521			1.14194
$490$		0			0
$491$	23.3679			1.05458			0.527289	−	0.849686i	$-0.323208\pi$
$491$	23.3679			1.05458			0.527289	+	0.849686i	$0.323208\pi$
$492$		0			0
$493$	2.49395	+	4.31965i	0.112322	+	0.194547i
$494$		0			0
$495$	−0.487231	+	0.843909i	−0.0218994	+	0.0379309i
$496$		0			0
$497$	−20.0223	−	12.2020i	−0.898121	−	0.547335i
$498$		0			0
$499$	−0.866434	+	1.50071i	−0.0387869	+	0.0671809i	−0.884767	−	0.466033i	$-0.845683\pi$
$499$	−0.866434	+	1.50071i	−0.0387869	+	0.0671809i	0.845980	+	0.533214i	$0.179016\pi$
$500$		0			0
$501$	−2.59945	−	4.50239i	−0.116135	−	0.201152i
$502$		0			0
$503$	−17.9511			−0.800399			−0.400199	−	0.916428i	$-0.631059\pi$
$503$	−17.9511			−0.800399			−0.400199	+	0.916428i	$0.631059\pi$
$504$		0			0
$505$	−24.7616			−1.10188
$506$		0			0
$507$	−23.0168	−	39.8663i	−1.02221	−	1.77052i
$508$		0			0
$509$	13.4071	−	23.2218i	0.594260	−	1.02929i	−0.399390	−	0.916781i	$-0.630778\pi$
$509$	13.4071	−	23.2218i	0.594260	−	1.02929i	0.993651	−	0.112508i	$-0.0358885\pi$
$510$		0			0
$511$	0.955417	−	40.2706i	0.0422652	−	1.78147i
$512$		0			0
$513$	5.91749	−	10.2494i	0.261264	−	0.452522i
$514$		0			0
$515$	−4.22186	−	7.31247i	−0.186037	−	0.322226i
$516$		0			0
$517$	−5.02554			−0.221023
$518$		0			0
$519$	36.1467			1.58666
$520$		0			0
$521$	−5.12152	−	8.87074i	−0.224378	−	0.388634i	0.731755	−	0.681568i	$-0.238702\pi$
$521$	−5.12152	−	8.87074i	−0.224378	−	0.388634i	−0.956133	+	0.292934i	$0.905368\pi$
$522$		0			0
$523$	−20.1716	+	34.9383i	−0.882043	+	1.52774i	−0.0329771	+	0.999456i	$0.510499\pi$
$523$	−20.1716	+	34.9383i	−0.882043	+	1.52774i	−0.849066	+	0.528287i	$0.822834\pi$
$524$		0			0
$525$	11.7954	−	6.44197i	0.514792	−	0.281151i
$526$		0			0
$527$	−0.825106	+	1.42913i	−0.0359422	+	0.0622537i
$528$		0			0
$529$	9.79330	+	16.9625i	0.425796	+	0.737499i
$530$		0			0
$531$	−2.72959			−0.118454
$532$		0			0
$533$	−42.9927			−1.86222
$534$		0			0
$535$	−3.69262	−	6.39581i	−0.159646	−	0.276515i
$536$		0			0
$537$	11.7728	−	20.3910i	0.508032	−	0.879937i
$538$		0			0
$539$	3.78355	−	5.88938i	0.162969	−	0.253673i
$540$		0			0
$541$	8.26753	−	14.3198i	0.355449	−	0.615656i	−0.631746	−	0.775176i	$-0.717661\pi$
$541$	8.26753	−	14.3198i	0.355449	−	0.615656i	0.987195	+	0.159520i	$0.0509947\pi$
$542$		0			0
$543$	10.1308	+	17.5470i	0.434752	+	0.753013i
$544$		0			0
$545$	0.342152			0.0146562
$546$		0			0
$547$	−28.5561			−1.22097			−0.610486	−	0.792027i	$-0.709026\pi$
$547$	−28.5561			−1.22097			−0.610486	+	0.792027i	$0.709026\pi$
$548$		0			0
$549$	−1.13704	−	1.96940i	−0.0485275	−	0.0840521i
$550$		0			0
$551$	−5.11203	+	8.85429i	−0.217780	+	0.377206i
$552$		0			0
$553$	−19.3077	+	10.5448i	−0.821046	+	0.448410i
$554$		0			0
$555$	−2.03845	+	3.53070i	−0.0865275	+	0.149870i
$556$		0			0
$557$	16.8790	+	29.2353i	0.715187	+	1.23874i	0.962887	+	0.269904i	$0.0869920\pi$
$557$	16.8790	+	29.2353i	0.715187	+	1.23874i	−0.247700	+	0.968837i	$0.579675\pi$
$558$		0			0
$559$	81.7836			3.45908
$560$		0			0
$561$	−1.53112			−0.0646441
$562$		0			0
$563$	2.62260	+	4.54247i	0.110529	+	0.191442i	0.915984	−	0.401215i	$-0.131412\pi$
$563$	2.62260	+	4.54247i	0.110529	+	0.191442i	−0.805455	+	0.592658i	$0.798079\pi$
$564$		0			0
$565$	−7.10629	+	12.3085i	−0.298964	+	0.517821i
$566$		0			0
$567$	−0.382335	+	16.1153i	−0.0160566	+	0.676780i
$568$		0			0
$569$	−1.98165	+	3.43232i	−0.0830752	+	0.143890i	−0.904569	−	0.426326i	$-0.859808\pi$
$569$	−1.98165	+	3.43232i	−0.0830752	+	0.143890i	0.821494	+	0.570217i	$0.193141\pi$
$570$		0			0
$571$	12.3459	+	21.3837i	0.516660	+	0.894882i	0.999813	+	0.0193457i	$0.00615830\pi$
$571$	12.3459	+	21.3837i	0.516660	+	0.894882i	−0.483153	+	0.875536i	$0.660508\pi$
$572$		0			0
$573$	−28.4578			−1.18884
$574$		0			0
$575$	−6.28609			−0.262148
$576$		0			0
$577$	−4.71901	−	8.17357i	−0.196455	−	0.340270i	0.750921	−	0.660392i	$-0.229610\pi$
$577$	−4.71901	−	8.17357i	−0.196455	−	0.340270i	−0.947377	+	0.320121i	$0.896276\pi$
$578$		0			0
$579$	5.52510	−	9.56975i	0.229615	−	0.397705i
$580$		0			0
$581$	10.2767	+	6.26287i	0.426350	+	0.259828i
$582$		0			0
$583$	−1.26087	+	2.18389i	−0.0522199	+	0.0904476i
$584$		0			0
$585$	−3.22579	−	5.58723i	−0.133370	−	0.231003i
$586$		0			0
$587$	−18.7860			−0.775383			−0.387691	−	0.921789i	$-0.626727\pi$
$587$	−18.7860			−0.775383			−0.387691	+	0.921789i	$0.626727\pi$
$588$		0			0
$589$	−3.38256			−0.139376
$590$		0			0
$591$	−1.50515	−	2.60700i	−0.0619138	−	0.107238i
$592$		0			0
$593$	1.77684	−	3.07758i	0.0729661	−	0.126381i	−0.827234	−	0.561858i	$-0.810087\pi$
$593$	1.77684	−	3.07758i	0.0729661	−	0.126381i	0.900200	+	0.435477i	$0.143420\pi$
$594$		0			0
$595$	2.92854	+	1.78472i	0.120059	+	0.0731664i
$596$		0			0
$597$	1.71505	−	2.97055i	0.0701923	−	0.121577i
$598$		0			0
$599$	8.11845	+	14.0616i	0.331711	+	0.574540i	0.982847	−	0.184420i	$-0.0590408\pi$
$599$	8.11845	+	14.0616i	0.331711	+	0.574540i	−0.651136	+	0.758961i	$0.725707\pi$
$600$		0			0
$601$	45.1827			1.84304			0.921521	−	0.388329i	$-0.126948\pi$
$601$	45.1827			1.84304			0.921521	+	0.388329i	$0.126948\pi$
$602$		0			0
$603$	−7.59016			−0.309095
$604$		0			0
$605$	0.631979	+	1.09462i	0.0256936	+	0.0445026i
$606$		0			0
$607$	3.32923	−	5.76639i	0.135129	−	0.234050i	−0.790518	−	0.612439i	$-0.790188\pi$
$607$	3.32923	−	5.76639i	0.135129	−	0.234050i	0.925647	+	0.378389i	$0.123522\pi$
$608$		0			0
$609$	0.455677	−	19.2067i	0.0184649	−	0.778294i
$610$		0			0
$611$	16.6362	−	28.8147i	0.673027	−	1.16572i
$612$		0			0
$613$	−13.7933	−	23.8907i	−0.557106	−	0.964935i	−0.997736	−	0.0672470i	$-0.978578\pi$
$613$	−13.7933	−	23.8907i	−0.557106	−	0.964935i	0.440631	−	0.897689i	$-0.354755\pi$
$614$		0			0
$615$	12.2542			0.494138
$616$		0			0
$617$	2.16360			0.0871032			0.0435516	−	0.999051i	$-0.486133\pi$
$617$	2.16360			0.0871032			0.0435516	+	0.999051i	$0.486133\pi$
$618$		0			0
$619$	10.9123	+	18.9006i	0.438602	+	0.759681i	0.997582	−	0.0695001i	$-0.0221404\pi$
$619$	10.9123	+	18.9006i	0.438602	+	0.759681i	−0.558980	+	0.829181i	$0.688807\pi$
$620$		0			0
$621$	5.20086	−	9.00815i	0.208703	−	0.361484i
$622$		0			0
$623$	−15.3790	+	8.39917i	−0.616148	+	0.336506i
$624$		0			0
$625$	−1.79423	+	3.10769i	−0.0717690	+	0.124308i
$626$		0			0
$627$	−1.56923	−	2.71798i	−0.0626689	−	0.108546i
$628$		0			0
$629$	2.21560			0.0883416
$630$		0			0
$631$	35.8552			1.42737			0.713687	−	0.700465i	$-0.247024\pi$
$631$	35.8552			1.42737			0.713687	+	0.700465i	$0.247024\pi$
$632$		0			0
$633$	15.1866	+	26.3040i	0.603613	+	1.04549i
$634$		0			0
$635$	−2.06432	+	3.57550i	−0.0819199	+	0.141890i
$636$		0			0
$637$	21.2429	+	41.1893i	0.841672	+	1.63198i
$638$		0			0
$639$	−3.41624	+	5.91710i	−0.135144	+	0.234077i
$640$		0			0
$641$	10.1374	+	17.5585i	0.400403	+	0.693519i	0.993775	−	0.111410i	$-0.0355367\pi$
$641$	10.1374	+	17.5585i	0.400403	+	0.693519i	−0.593371	+	0.804929i	$0.702203\pi$
$642$		0			0
$643$	10.2348			0.403620			0.201810	−	0.979425i	$-0.435318\pi$
$643$	10.2348			0.403620			0.201810	+	0.979425i	$0.435318\pi$
$644$		0			0
$645$	−23.3108			−0.917861
$646$		0			0
$647$	10.4984	+	18.1838i	0.412735	+	0.714879i	0.995188	−	0.0979862i	$-0.0312401\pi$
$647$	10.4984	+	18.1838i	0.412735	+	0.714879i	−0.582452	+	0.812865i	$0.697907\pi$
$648$		0			0
$649$	−1.77025	+	3.06617i	−0.0694885	+	0.120358i
$650$		0			0
$651$	5.57844	−	3.04664i	0.218636	−	0.119407i
$652$		0			0
$653$	−3.68809	+	6.38795i	−0.144326	+	0.249980i	−0.929121	−	0.369775i	$-0.879435\pi$
$653$	−3.68809	+	6.38795i	−0.144326	+	0.249980i	0.784795	+	0.619755i	$0.212768\pi$
$654$		0			0
$655$	−9.65882	−	16.7296i	−0.377401	−	0.653678i
$656$		0			0
$657$	−11.7380			−0.457943
$658$		0			0
$659$	13.0961			0.510152			0.255076	−	0.966921i	$-0.417900\pi$
$659$	13.0961			0.510152			0.255076	+	0.966921i	$0.417900\pi$
$660$		0			0
$661$	−23.7475	−	41.1319i	−0.923671	−	1.59985i	−0.793684	−	0.608330i	$-0.791840\pi$
$661$	−23.7475	−	41.1319i	−0.923671	−	1.59985i	−0.129987	−	0.991516i	$-0.541494\pi$
$662$		0			0
$663$	5.06852	−	8.77893i	0.196845	−	0.340945i
$664$		0			0
$665$	−0.166733	+	7.02775i	−0.00646562	+	0.272524i
$666$		0			0
$667$	−4.49294	+	7.78200i	−0.173967	+	0.301320i
$668$		0			0
$669$	13.4493	+	23.2949i	0.519980	+	0.900632i
$670$		0			0
$671$	−2.94966			−0.113870
$672$		0			0
$673$	−13.9244			−0.536745			−0.268372	−	0.963315i	$-0.586486\pi$
$673$	−13.9244			−0.536745			−0.268372	+	0.963315i	$0.586486\pi$
$674$		0			0
$675$	−9.57784	−	16.5893i	−0.368651	−	0.638523i
$676$		0			0
$677$	25.6977	−	44.5097i	0.987642	−	1.71065i	0.358090	−	0.933687i	$-0.383428\pi$
$677$	25.6977	−	44.5097i	0.987642	−	1.71065i	0.629552	−	0.776959i	$-0.283239\pi$
$678$		0			0
$679$	2.50042	+	1.52382i	0.0959575	+	0.0584787i
$680$		0			0
$681$	5.83532	−	10.1071i	0.223610	−	0.387304i
$682$		0			0
$683$	−13.5937	−	23.5450i	−0.520149	−	0.900924i	−0.999726	−	0.0234244i	$-0.992543\pi$
$683$	−13.5937	−	23.5450i	−0.520149	−	0.900924i	0.479577	−	0.877500i	$-0.340790\pi$
$684$		0			0
$685$	19.2072			0.733869
$686$		0			0
$687$	−4.87998			−0.186183
$688$		0			0
$689$	−8.34779	−	14.4588i	−0.318025	−	0.550836i
$690$		0			0
$691$	−12.1131	+	20.9805i	−0.460805	+	0.798137i	−0.999001	−	0.0446821i	$-0.985772\pi$
$691$	−12.1131	+	20.9805i	−0.460805	+	0.798137i	0.538196	+	0.842819i	$0.319106\pi$
$692$		0			0
$693$	−1.74181	−	1.06150i	−0.0661658	−	0.0403229i
$694$		0			0
$695$	10.9557	−	18.9759i	0.415574	−	0.719796i
$696$		0			0
$697$	−3.32978	−	5.76735i	−0.126124	−	0.218454i
$698$		0			0
$699$	40.4750			1.53090
$700$		0			0
$701$	−50.4982			−1.90729			−0.953645	−	0.300935i	$-0.902701\pi$
$701$	−50.4982			−1.90729			−0.953645	+	0.300935i	$0.902701\pi$
$702$		0			0
$703$	2.27073	+	3.93302i	0.0856423	+	0.148337i
$704$		0			0
$705$	−4.74181	+	8.21305i	−0.178587	+	0.309321i
$706$		0			0
$707$	1.22936	−	51.8171i	0.0462347	−	1.94878i
$708$		0			0
$709$	15.6971	−	27.1881i	0.589516	−	1.02107i	−0.404780	−	0.914414i	$-0.632652\pi$
$709$	15.6971	−	27.1881i	0.589516	−	1.02107i	0.994296	−	0.106657i	$-0.0340147\pi$
$710$		0			0
$711$	3.20528	+	5.55172i	0.120208	+	0.208206i
$712$		0			0
$713$	−2.97291			−0.111337
$714$		0			0
$715$	−8.36822			−0.312954
$716$		0			0
$717$	17.4254	+	30.1817i	0.650763	+	1.12716i
$718$		0			0
$719$	−8.53053	+	14.7753i	−0.318135	+	0.551026i	−0.980099	−	0.198510i	$-0.936390\pi$
$719$	−8.53053	+	14.7753i	−0.318135	+	0.551026i	0.661964	+	0.749536i	$0.269723\pi$
$720$		0			0
$721$	15.5120	−	8.47177i	0.577696	−	0.315505i
$722$		0			0
$723$	−14.7999	+	25.6341i	−0.550413	+	0.953344i
$724$		0			0
$725$	8.27415	+	14.3312i	0.307294	+	0.532249i
$726$		0			0
$727$	24.4693			0.907517			0.453758	−	0.891125i	$-0.350083\pi$
$727$	24.4693			0.907517			0.453758	+	0.891125i	$0.350083\pi$
$728$		0			0
$729$	29.9141			1.10793
$730$		0			0
$731$	6.33413	+	10.9710i	0.234276	+	0.405778i
$732$		0			0
$733$	12.4630	−	21.5866i	0.460332	−	0.797319i	−0.538645	−	0.842533i	$-0.681064\pi$
$733$	12.4630	−	21.5866i	0.460332	−	0.797319i	0.998977	+	0.0452140i	$0.0143970\pi$
$734$		0			0
$735$	−6.05485	−	11.7402i	−0.223337	−	0.433044i
$736$		0			0
$737$	−4.92253	+	8.52608i	−0.181324	+	0.314062i
$738$		0			0
$739$	0.916467	+	1.58737i	0.0337128	+	0.0583922i	0.882390	−	0.470520i	$-0.155934\pi$
$739$	0.916467	+	1.58737i	0.0337128	+	0.0583922i	−0.848677	+	0.528912i	$0.822600\pi$
$740$		0			0
$741$	20.7786			0.763321
$742$		0			0
$743$	18.5966			0.682242			0.341121	−	0.940019i	$-0.389193\pi$
$743$	18.5966			0.682242			0.341121	+	0.940019i	$0.389193\pi$
$744$		0			0
$745$	14.5094	+	25.1311i	0.531584	+	0.920731i
$746$		0			0
$747$	1.75343	−	3.03704i	0.0641548	−	0.111119i
$748$		0			0
$749$	13.5674	−	7.40978i	0.495743	−	0.270748i
$750$		0			0
$751$	23.5821	−	40.8454i	0.860523	−	1.49047i	−0.0109013	−	0.999941i	$-0.503470\pi$
$751$	23.5821	−	40.8454i	0.860523	−	1.49047i	0.871425	−	0.490530i	$-0.163197\pi$
$752$		0			0
$753$	−17.7142	−	30.6818i	−0.645540	−	1.11811i
$754$		0			0
$755$	11.8715			0.432048
$756$		0			0
$757$	−14.8217			−0.538703			−0.269351	−	0.963042i	$-0.586809\pi$
$757$	−14.8217			−0.538703			−0.269351	+	0.963042i	$0.586809\pi$
$758$		0			0
$759$	−1.37919	−	2.38882i	−0.0500613	−	0.0867087i
$760$		0			0
$761$	3.88323	−	6.72596i	0.140767	−	0.243816i	−0.787019	−	0.616929i	$-0.788376\pi$
$761$	3.88323	−	6.72596i	0.140767	−	0.243816i	0.927786	+	0.373113i	$0.121710\pi$
$762$		0			0
$763$	−0.0169870	+	0.716000i	−0.000614972	+	0.0259209i
$764$		0			0
$765$	0.499674	−	0.865461i	0.0180657	−	0.0312908i
$766$		0			0
$767$	−11.7202	−	20.3000i	−0.423193	−	0.732991i
$768$		0			0
$769$	−22.0677			−0.795783			−0.397891	−	0.917432i	$-0.630258\pi$
$769$	−22.0677			−0.795783			−0.397891	+	0.917432i	$0.630258\pi$
$770$		0			0
$771$	28.9140			1.04131
$772$		0			0
$773$	−14.8473	−	25.7163i	−0.534020	−	0.924950i	−0.999210	−	0.0397391i	$-0.987347\pi$
$773$	−14.8473	−	25.7163i	−0.534020	−	0.924950i	0.465190	−	0.885211i	$-0.345986\pi$
$774$		0			0
$775$	−2.73744	+	4.74139i	−0.0983319	+	0.170316i
$776$		0			0
$777$	−7.28728	−	4.44103i	−0.261430	−	0.159321i
$778$		0			0
$779$	6.82529	−	11.8217i	0.244541	−	0.423558i
$780$		0			0
$781$	4.43114	+	7.67496i	0.158559	+	0.274632i
$782$		0			0
$783$	−27.3828			−0.978580
$784$		0			0
$785$	1.28259			0.0457775
$786$		0			0
$787$	6.27310	+	10.8653i	0.223612	+	0.387307i	0.955902	−	0.293686i	$-0.0948819\pi$
$787$	6.27310	+	10.8653i	0.223612	+	0.387307i	−0.732290	+	0.680993i	$0.761549\pi$
$788$		0			0
$789$	1.01932	−	1.76552i	0.0362889	−	0.0628542i
$790$		0			0
$791$	−25.4043	−	15.4820i	−0.903275	−	0.550476i
$792$		0			0
$793$	9.76432	−	16.9123i	0.346741	−	0.600574i
$794$		0			0
$795$	2.37937	+	4.12119i	0.0843876	+	0.146164i
$796$		0			0
$797$	2.10555			0.0745825			0.0372913	−	0.999304i	$-0.488127\pi$
$797$	2.10555			0.0745825			0.0372913	+	0.999304i	$0.488127\pi$
$798$		0			0
$799$	5.15388			0.182331
$800$		0			0
$801$	2.55309	+	4.42208i	0.0902089	+	0.156246i
$802$		0			0
$803$	−7.61257	+	13.1854i	−0.268642	+	0.465301i
$804$		0			0
$805$	−0.146541	+	6.17666i	−0.00516488	+	0.217698i
$806$		0			0
$807$	−8.59314	+	14.8838i	−0.302493	+	0.523933i
$808$		0			0
$809$	10.0647	+	17.4326i	0.353857	+	0.612898i	0.986922	−	0.161201i	$-0.0515368\pi$
$809$	10.0647	+	17.4326i	0.353857	+	0.612898i	−0.633065	+	0.774099i	$0.718203\pi$
$810$		0			0
$811$	−46.7505			−1.64163			−0.820817	−	0.571192i	$-0.806481\pi$
$811$	−46.7505			−1.64163			−0.820817	+	0.571192i	$0.806481\pi$
$812$		0			0
$813$	13.0826			0.458828
$814$		0			0
$815$	10.6891	+	18.5141i	0.374423	+	0.648520i
$816$		0			0
$817$	−12.9835	+	22.4881i	−0.454236	+	0.786759i
$818$		0			0
$819$	11.8522	−	6.47302i	0.414150	−	0.226185i
$820$		0			0
$821$	11.5668	−	20.0342i	0.403683	−	0.699200i	−0.590484	−	0.807049i	$-0.701063\pi$
$821$	11.5668	−	20.0342i	0.403683	−	0.699200i	0.994167	+	0.107850i	$0.0343965\pi$
$822$		0			0
$823$	5.16958	+	8.95397i	0.180200	+	0.312116i	0.941949	−	0.335757i	$-0.108992\pi$
$823$	5.16958	+	8.95397i	0.180200	+	0.312116i	−0.761749	+	0.647873i	$0.775659\pi$
$824$		0			0
$825$	−5.07979			−0.176855
$826$		0			0
$827$	−48.1690			−1.67500			−0.837500	−	0.546437i	$-0.815984\pi$
$827$	−48.1690			−1.67500			−0.837500	+	0.546437i	$0.815984\pi$
$828$		0			0
$829$	22.8948	+	39.6550i	0.795170	+	1.37728i	0.922731	+	0.385445i	$0.125952\pi$
$829$	22.8948	+	39.6550i	0.795170	+	1.37728i	−0.127560	+	0.991831i	$0.540715\pi$
$830$		0			0
$831$	−7.71734	+	13.3668i	−0.267712	+	0.463690i
$832$		0			0
$833$	−3.88017	+	6.03978i	−0.134440	+	0.209266i
$834$		0			0
$835$	2.20068	−	3.81168i	0.0761575	−	0.131909i
$836$		0			0
$837$	−4.52970	−	7.84567i	−0.156569	−	0.271186i
$838$		0			0
$839$	−15.4999			−0.535116			−0.267558	−	0.963542i	$-0.586217\pi$
$839$	−15.4999			−0.535116			−0.267558	+	0.963542i	$0.586217\pi$
$840$		0			0
$841$	−5.34446			−0.184292
$842$		0			0
$843$	−14.3575	−	24.8679i	−0.494498	−	0.856496i
$844$		0			0
$845$	19.4858	−	33.7504i	0.670332	−	1.16105i
$846$		0			0
$847$	−2.32202	+	1.26816i	−0.0797855	+	0.0435744i
$848$		0			0
$849$	−8.66000	+	14.9996i	−0.297210	+	0.514783i
$850$		0			0
$851$	1.99574	+	3.45672i	0.0684129	+	0.118495i
$852$		0			0
$853$	−21.4586			−0.734729			−0.367364	−	0.930077i	$-0.619740\pi$
$853$	−21.4586			−0.734729			−0.367364	+	0.930077i	$0.619740\pi$
$854$		0			0
$855$	2.04843			0.0700550
$856$		0			0
$857$	−6.65476	−	11.5264i	−0.227322	−	0.393734i	0.729691	−	0.683777i	$-0.239664\pi$
$857$	−6.65476	−	11.5264i	−0.227322	−	0.393734i	−0.957014	+	0.290043i	$0.906330\pi$
$858$		0			0
$859$	−18.4726	+	31.9955i	−0.630277	+	1.09167i	0.357218	+	0.934021i	$0.383725\pi$
$859$	−18.4726	+	31.9955i	−0.630277	+	1.09167i	−0.987495	+	0.157650i	$0.949608\pi$
$860$		0			0
$861$	−0.608393	+	25.6436i	−0.0207340	+	0.873933i
$862$		0			0
$863$	3.67116	−	6.35864i	0.124968	−	0.216451i	−0.796753	−	0.604306i	$-0.793451\pi$
$863$	3.67116	−	6.35864i	0.124968	−	0.216451i	0.921720	+	0.387855i	$0.126784\pi$
$864$		0			0
$865$	15.3007	+	26.5016i	0.520240	+	0.901083i
$866$		0			0
$867$	−23.8107			−0.808654
$868$		0			0
$869$	8.31503			0.282068
$870$		0			0
$871$	−32.5904	−	56.4482i	−1.10428	−	1.91267i
$872$		0			0
$873$	0.426628	−	0.738941i	0.0144392	−	0.0250093i
$874$		0			0
$875$	23.9941	+	14.6225i	0.811148	+	0.494332i
$876$		0			0
$877$	−5.17260	+	8.95920i	−0.174666	+	0.302531i	−0.940046	−	0.341049i	$-0.889218\pi$
$877$	−5.17260	+	8.95920i	−0.174666	+	0.302531i	0.765380	+	0.643579i	$0.222551\pi$
$878$		0			0
$879$	0.550791	+	0.953998i	0.0185777	+	0.0321776i
$880$		0			0
$881$	−17.0322			−0.573830			−0.286915	−	0.957956i	$-0.592630\pi$
$881$	−17.0322			−0.573830			−0.286915	+	0.957956i	$0.592630\pi$
$882$		0			0
$883$	2.22157			0.0747618			0.0373809	−	0.999301i	$-0.488099\pi$
$883$	2.22157			0.0747618			0.0373809	+	0.999301i	$0.488099\pi$
$884$		0			0
$885$	3.34062	+	5.78612i	0.112294	+	0.194498i
$886$		0			0
$887$	−6.88591	+	11.9267i	−0.231206	+	0.400461i	−0.958163	−	0.286222i	$-0.907600\pi$
$887$	−6.88591	+	11.9267i	−0.231206	+	0.400461i	0.726957	+	0.686683i	$0.240934\pi$
$888$		0			0
$889$	−7.37975	−	4.49739i	−0.247509	−	0.150837i
$890$		0			0
$891$	3.04637	−	5.27646i	0.102057	−	0.176768i
$892$		0			0
$893$	5.28213	+	9.14892i	0.176760	+	0.306157i
$894$		0			0
$895$	19.9334			0.666301
$896$		0			0
$897$	18.2622			0.609758
$898$		0			0
$899$	3.91314	+	6.77775i	0.130510	+	0.226051i
$900$		0			0
$901$	1.29307	−	2.23966i	0.0430784	−	0.0746140i
$902$		0			0
$903$	1.15733	−	48.7810i	0.0385134	−	1.62333i
$904$		0			0
$905$	−8.57661	+	14.8551i	−0.285096	+	0.493801i
$906$		0			0
$907$	−20.4790	−	35.4707i	−0.679995	−	1.17779i	−0.974982	−	0.222285i	$-0.928649\pi$
$907$	−20.4790	−	35.4707i	−0.679995	−	1.17779i	0.294987	−	0.955501i	$-0.404685\pi$
$908$		0			0
$909$	−15.1035			−0.500953
$910$		0			0
$911$	−15.9473			−0.528359			−0.264180	−	0.964474i	$-0.585101\pi$
$911$	−15.9473			−0.528359			−0.264180	+	0.964474i	$0.585101\pi$
$912$		0			0
$913$	−2.27435	−	3.93929i	−0.0752699	−	0.130371i
$914$		0			0
$915$	−2.78313	+	4.82052i	−0.0920073	+	0.159361i
$916$		0			0
$917$	35.4885	−	19.3818i	1.17193	−	0.640045i
$918$		0			0
$919$	18.8566	−	32.6606i	0.622022	−	1.07737i	−0.367087	−	0.930187i	$-0.619645\pi$
$919$	18.8566	−	32.6606i	0.622022	−	1.07737i	0.989109	−	0.147187i	$-0.0470219\pi$
$920$		0			0
$921$	−11.1981	−	19.3957i	−0.368991	−	0.639110i
$922$		0			0
$923$	−58.6741			−1.93128
$924$		0			0
$925$	7.35065			0.241688
$926$		0			0
$927$	−2.57516	−	4.46030i	−0.0845792	−	0.146495i
$928$		0			0
$929$	14.4517	−	25.0311i	0.474145	−	0.821244i	−0.525417	−	0.850845i	$-0.676091\pi$
$929$	14.4517	−	25.0311i	0.474145	−	0.821244i	0.999562	+	0.0296015i	$0.00942384\pi$
$930$		0			0
$931$	−14.6983	−	0.697823i	−0.481716	−	0.0228702i
$932$		0			0
$933$	−11.9061	+	20.6221i	−0.389790	+	0.675136i
$934$		0			0
$935$	−0.648118	−	1.12257i	−0.0211957	−	0.0367121i
$936$		0			0
$937$	14.8484			0.485075			0.242538	−	0.970142i	$-0.422020\pi$
$937$	14.8484			0.485075			0.242538	+	0.970142i	$0.422020\pi$
$938$		0			0
$939$	33.9825			1.10898
$940$		0			0
$941$	−21.6252	−	37.4559i	−0.704960	−	1.22103i	−0.966706	−	0.255890i	$-0.917631\pi$
$941$	−21.6252	−	37.4559i	−0.704960	−	1.22103i	0.261745	−	0.965137i	$-0.415702\pi$
$942$		0			0
$943$	5.99871	−	10.3901i	0.195345	−	0.338347i
$944$		0			0
$945$	−16.5238	+	9.02437i	−0.537519	+	0.293563i
$946$		0			0
$947$	−3.96072	+	6.86018i	−0.128706	+	0.222926i	−0.923176	−	0.384378i	$-0.874416\pi$
$947$	−3.96072	+	6.86018i	−0.128706	+	0.222926i	0.794469	+	0.607304i	$0.207749\pi$
$948$		0			0
$949$	−50.4002	−	87.2957i	−1.63606	−	2.83374i
$950$		0			0
$951$	−10.9848			−0.356207
$952$		0			0
$953$	−13.5952			−0.440390			−0.220195	−	0.975456i	$-0.570669\pi$
$953$	−13.5952			−0.440390			−0.220195	+	0.975456i	$0.570669\pi$
$954$		0			0
$955$	−12.0461	−	20.8644i	−0.389801	−	0.675156i
$956$		0			0
$957$	−3.63074	+	6.28863i	−0.117365	+	0.203282i
$958$		0			0
$959$	−0.953593	+	40.1937i	−0.0307931	+	1.29792i
$960$		0			0
$961$	14.2054	−	24.6044i	0.458238	−	0.793691i
$962$		0			0
$963$	−2.25234	−	3.90117i	−0.0725808	−	0.125714i
$964$		0			0
$965$	9.35500			0.301148
$966$		0			0
$967$	−19.1495			−0.615807			−0.307903	−	0.951418i	$-0.599627\pi$
$967$	−19.1495			−0.615807			−0.307903	+	0.951418i	$0.599627\pi$
$968$		0			0
$969$	1.60930	+	2.78739i	0.0516982	+	0.0895439i
$970$		0			0
$971$	−16.3213	+	28.2694i	−0.523777	+	0.907208i	0.475840	+	0.879532i	$0.342144\pi$
$971$	−16.3213	+	28.2694i	−0.523777	+	0.907208i	−0.999617	+	0.0276759i	$0.991189\pi$
$972$		0			0
$973$	39.1657	+	23.8685i	1.25560	+	0.765188i
$974$		0			0
$975$	16.8157	−	29.1257i	0.538535	−	0.932770i
$976$		0			0
$977$	18.1997	+	31.5228i	0.582259	+	1.00850i	0.995211	+	0.0977500i	$0.0311645\pi$
$977$	18.1997	+	31.5228i	0.582259	+	1.00850i	−0.412952	+	0.910753i	$0.635502\pi$
$978$		0			0
$979$	6.62313			0.211676
$980$		0			0
$981$	0.208698			0.00666322
$982$		0			0
$983$	12.2319	+	21.1862i	0.390136	+	0.675735i	0.992467	−	0.122511i	$-0.0390947\pi$
$983$	12.2319	+	21.1862i	0.390136	+	0.675735i	−0.602331	+	0.798246i	$0.705761\pi$
$984$		0			0
$985$	1.27425	−	2.20707i	0.0406010	−	0.0703230i
$986$		0			0
$987$	−16.9515	−	10.3306i	−0.539573	−	0.328828i
$988$		0			0
$989$	−11.4111	+	19.7647i	−0.362853	+	0.628481i
$990$		0			0
$991$	14.5125	+	25.1364i	0.461005	+	0.798484i	0.999011	−	0.0444567i	$-0.0141557\pi$
$991$	14.5125	+	25.1364i	0.461005	+	0.798484i	−0.538006	+	0.842941i	$0.680822\pi$
$992$		0			0
$993$	40.1921			1.27546
$994$		0			0
$995$	2.90389			0.0920596
$996$		0			0
$997$	27.7240	+	48.0195i	0.878029	+	1.52079i	0.853500	+	0.521092i	$0.174475\pi$
$997$	27.7240	+	48.0195i	0.878029	+	1.52079i	0.0245290	+	0.999699i	$0.492191\pi$
$998$		0			0
$999$	−6.08163	+	10.5337i	−0.192414	+	0.333271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.q.o.177.2		10
4.3	odd	2		616.2.q.f.177.4	✓	10
7.2	even	3		8624.2.a.dc.1.4		5
7.4	even	3	inner	1232.2.q.o.529.2		10
7.5	odd	6		8624.2.a.db.1.2		5
28.11	odd	6		616.2.q.f.529.4	yes	10
28.19	even	6		4312.2.a.bg.1.4		5
28.23	odd	6		4312.2.a.bf.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.q.f.177.4	✓	10	4.3	odd	2
616.2.q.f.529.4	yes	10	28.11	odd	6
1232.2.q.o.177.2		10	1.1	even	1	trivial
1232.2.q.o.529.2		10	7.4	even	3	inner
4312.2.a.bf.1.2		5	28.23	odd	6
4312.2.a.bg.1.4		5	28.19	even	6
8624.2.a.db.1.2		5	7.5	odd	6
8624.2.a.dc.1.4		5	7.2	even	3

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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.746498 - 1.29297i) q^{3} +(0.631979 - 1.09462i) q^{5} +(2.25927 + 1.37685i) q^{7} +(0.385481 - 0.667672i) q^{9} +O(q^{10})\)	\(q+(-0.746498 - 1.29297i) q^{3} +(0.631979 - 1.09462i) q^{5} +(2.25927 + 1.37685i) q^{7} +(0.385481 - 0.667672i) q^{9} +(-0.500000 - 0.866025i) q^{11} +6.62065 q^{13} -1.88708 q^{15} +(0.512769 + 0.888141i) q^{17} +(-1.05106 + 1.82049i) q^{19} +(0.0936894 - 3.94899i) q^{21} +(-0.923770 + 1.60002i) q^{23} +(1.70121 + 2.94657i) q^{25} -5.63003 q^{27} +4.86370 q^{29} +(0.804560 + 1.39354i) q^{31} +(-0.746498 + 1.29297i) q^{33} +(2.93493 - 1.60290i) q^{35} +(1.08021 - 1.87098i) q^{37} +(-4.94230 - 8.56032i) q^{39} -6.49373 q^{41} +12.3528 q^{43} +(-0.487231 - 0.843909i) q^{45} +(2.51277 - 4.35224i) q^{47} +(3.20857 + 6.22134i) q^{49} +(0.765562 - 1.32599i) q^{51} +(-1.26087 - 2.18389i) q^{53} -1.26396 q^{55} +3.13845 q^{57} +(-1.77025 - 3.06617i) q^{59} +(1.47483 - 2.55448i) q^{61} +(1.79019 - 0.977701i) q^{63} +(4.18411 - 7.24709i) q^{65} +(-4.92253 - 8.52608i) q^{67} +2.75837 q^{69} -8.86228 q^{71} +(-7.61257 - 13.1854i) q^{73} +(2.53989 - 4.39922i) q^{75} +(0.0627526 - 2.64501i) q^{77} +(-4.15752 + 7.20103i) q^{79} +(3.04637 + 5.27646i) q^{81} +4.54870 q^{83} +1.29624 q^{85} +(-3.63074 - 6.28863i) q^{87} +(-3.31156 + 5.73580i) q^{89} +(14.9578 + 9.11563i) q^{91} +(1.20121 - 2.08055i) q^{93} +(1.32849 + 2.30102i) q^{95} +1.10674 q^{97} -0.770961 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{3} - 4 q^{5} + 2 q^{7}+O(q^{10}) \) 10 * q - q^3 - 4 * q^5 + 2 * q^7	\( 10 q - q^{3} - 4 q^{5} + 2 q^{7} - 5 q^{11} + 2 q^{13} - 14 q^{15} - 9 q^{17} + q^{19} - 12 q^{21} - 8 q^{23} - 5 q^{25} + 8 q^{27} + 18 q^{29} + 3 q^{31} - q^{33} + 15 q^{35} - 2 q^{37} - 7 q^{39} + 30 q^{41} - 28 q^{43} - 19 q^{45} + 11 q^{47} - 18 q^{49} - 14 q^{51} + 9 q^{53} + 8 q^{55} + 8 q^{57} + 4 q^{59} + 2 q^{61} + 28 q^{63} - 7 q^{65} - 8 q^{67} + 22 q^{69} - 30 q^{71} - 26 q^{73} + 27 q^{75} + 2 q^{77} - 3 q^{79} + 19 q^{81} + 2 q^{83} + 26 q^{85} + 14 q^{87} - 41 q^{89} + 39 q^{91} - 10 q^{93} - 19 q^{95} + 14 q^{97}+O(q^{100}) \) 10 * q - q^3 - 4 * q^5 + 2 * q^7 - 5 * q^11 + 2 * q^13 - 14 * q^15 - 9 * q^17 + q^19 - 12 * q^21 - 8 * q^23 - 5 * q^25 + 8 * q^27 + 18 * q^29 + 3 * q^31 - q^33 + 15 * q^35 - 2 * q^37 - 7 * q^39 + 30 * q^41 - 28 * q^43 - 19 * q^45 + 11 * q^47 - 18 * q^49 - 14 * q^51 + 9 * q^53 + 8 * q^55 + 8 * q^57 + 4 * q^59 + 2 * q^61 + 28 * q^63 - 7 * q^65 - 8 * q^67 + 22 * q^69 - 30 * q^71 - 26 * q^73 + 27 * q^75 + 2 * q^77 - 3 * q^79 + 19 * q^81 + 2 * q^83 + 26 * q^85 + 14 * q^87 - 41 * q^89 + 39 * q^91 - 10 * q^93 - 19 * q^95 + 14 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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