LMFDB - Embedded newform 1232.2.q.o.177.4

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			177.4
Root			$-0.0561490 + 2.08099i$ of defining polynomial
Character	$\chi$	$=$	1232.177
Dual form			1232.2.q.o.529.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.666828 + 1.15498i) q^{3} +(-0.556149 + 0.963278i) q^{5} +(2.01243 - 1.71759i) q^{7} +(0.610680 - 1.05773i) q^{9} +O(q^{10})$	\(q+(0.666828 + 1.15498i) q^{3} +(-0.556149 + 0.963278i) q^{5} +(2.01243 - 1.71759i) q^{7} +(0.610680 - 1.05773i) q^{9} +(-0.500000 - 0.866025i) q^{11} -0.380391 q^{13} -1.48342 q^{15} +(1.67926 + 2.90856i) q^{17} +(2.20262 - 3.81506i) q^{19} +(3.32573 + 1.17898i) q^{21} +(3.27120 - 5.66589i) q^{23} +(1.88140 + 3.25867i) q^{25} +5.62984 q^{27} +3.06556 q^{29} +(-1.03580 - 1.79405i) q^{31} +(0.666828 - 1.15498i) q^{33} +(0.535311 + 2.89377i) q^{35} +(-2.43916 + 4.22476i) q^{37} +(-0.253656 - 0.439344i) q^{39} +6.56428 q^{41} -12.4155 q^{43} +(0.679258 + 1.17651i) q^{45} +(3.67926 - 6.37266i) q^{47} +(1.09974 - 6.91307i) q^{49} +(-2.23955 + 3.87902i) q^{51} +(-0.385173 - 0.667140i) q^{53} +1.11230 q^{55} +5.87509 q^{57} +(3.36428 + 5.82710i) q^{59} +(-5.97383 + 10.3470i) q^{61} +(-0.587798 - 3.17750i) q^{63} +(0.211554 - 0.366422i) q^{65} +(3.75926 + 6.51123i) q^{67} +8.72532 q^{69} +4.10572 q^{71} +(2.68438 + 4.64947i) q^{73} +(-2.50914 + 4.34595i) q^{75} +(-2.49369 - 0.884018i) q^{77} +(-5.30237 + 9.18397i) q^{79} +(1.92210 + 3.32918i) q^{81} +16.3001 q^{83} -3.73567 q^{85} +(2.04421 + 3.54067i) q^{87} +(-4.29786 + 7.44411i) q^{89} +(-0.765510 + 0.653357i) q^{91} +(1.38140 - 2.39265i) q^{93} +(2.44997 + 4.24348i) q^{95} +4.51152 q^{97} -1.22136 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.666828	+	1.15498i	0.384994	+	0.666828i	0.991768	−	0.128045i	$-0.0408703\pi$
$3$	0.666828	+	1.15498i	0.384994	+	0.666828i	−0.606775	+	0.794874i	$0.707537\pi$
$4$		0			0
$5$	−0.556149	+	0.963278i	−0.248717	+	0.430791i	−0.963170	−	0.268892i	$-0.913342\pi$
$5$	−0.556149	+	0.963278i	−0.248717	+	0.430791i	0.714453	+	0.699684i	$0.246676\pi$
$6$		0			0
$7$	2.01243	−	1.71759i	0.760627	−	0.649190i
$7$	2.01243	−	1.71759i	0.760627	−	0.649190i
$8$		0			0
$9$	0.610680	−	1.05773i	0.203560	−	0.352576i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	−0.380391			−0.105501			−0.0527507	−	0.998608i	$-0.516799\pi$
$13$	−0.380391			−0.105501			−0.0527507	+	0.998608i	$0.516799\pi$
$14$		0			0
$15$	−1.48342			−0.383018
$16$		0			0
$17$	1.67926	+	2.90856i	0.407280	+	0.705429i	0.994584	−	0.103937i	$-0.0331441\pi$
$17$	1.67926	+	2.90856i	0.407280	+	0.705429i	−0.587304	+	0.809366i	$0.699811\pi$
$18$		0			0
$19$	2.20262	−	3.81506i	0.505317	−	0.875234i	−0.494664	−	0.869084i	$-0.664709\pi$
$19$	2.20262	−	3.81506i	0.505317	−	0.875234i	0.999981	−	0.00615015i	$-0.00195767\pi$
$20$		0			0
$21$	3.32573	+	1.17898i	0.725734	+	0.257274i
$22$		0			0
$23$	3.27120	−	5.66589i	0.682093	−	1.18142i	−0.292248	−	0.956343i	$-0.594403\pi$
$23$	3.27120	−	5.66589i	0.682093	−	1.18142i	0.974341	−	0.225077i	$-0.0722634\pi$
$24$		0			0
$25$	1.88140	+	3.25867i	0.376279	+	0.651735i
$26$		0			0
$27$	5.62984			1.08346
$28$		0			0
$29$	3.06556			0.569261			0.284630	−	0.958637i	$-0.408129\pi$
$29$	3.06556			0.569261			0.284630	+	0.958637i	$0.408129\pi$
$30$		0			0
$31$	−1.03580	−	1.79405i	−0.186034	−	0.322221i	0.757890	−	0.652382i	$-0.226230\pi$
$31$	−1.03580	−	1.79405i	−0.186034	−	0.322221i	−0.943925	+	0.330161i	$0.892897\pi$
$32$		0			0
$33$	0.666828	−	1.15498i	0.116080	−	0.201056i
$34$		0			0
$35$	0.535311	+	2.89377i	0.0904840	+	0.489136i
$36$		0			0
$37$	−2.43916	+	4.22476i	−0.400996	+	0.694546i	−0.993846	−	0.110767i	$-0.964669\pi$
$37$	−2.43916	+	4.22476i	−0.400996	+	0.694546i	0.592850	+	0.805313i	$0.298003\pi$
$38$		0			0
$39$	−0.253656	−	0.439344i	−0.0406174	−	0.0703514i
$40$		0			0
$41$	6.56428			1.02517			0.512584	−	0.858637i	$-0.328688\pi$
$41$	6.56428			1.02517			0.512584	+	0.858637i	$0.328688\pi$
$42$		0			0
$43$	−12.4155			−1.89334			−0.946672	−	0.322199i	$-0.895578\pi$
$43$	−12.4155			−1.89334			−0.946672	+	0.322199i	$0.895578\pi$
$44$		0			0
$45$	0.679258	+	1.17651i	0.101258	+	0.175384i
$46$		0			0
$47$	3.67926	−	6.37266i	0.536675	−	0.929548i	−0.462405	−	0.886669i	$-0.653014\pi$
$47$	3.67926	−	6.37266i	0.536675	−	0.929548i	0.999080	−	0.0428795i	$-0.0136532\pi$
$48$		0			0
$49$	1.09974	−	6.91307i	0.157106	−	0.987582i
$50$		0			0
$51$	−2.23955	+	3.87902i	−0.313600	+	0.543172i
$52$		0			0
$53$	−0.385173	−	0.667140i	−0.0529076	−	0.0916387i	0.838359	−	0.545119i	$-0.183516\pi$
$53$	−0.385173	−	0.667140i	−0.0529076	−	0.0916387i	−0.891266	+	0.453480i	$0.850182\pi$
$54$		0			0
$55$	1.11230			0.149982
$56$		0			0
$57$	5.87509			0.778175
$58$		0			0
$59$	3.36428	+	5.82710i	0.437992	+	0.758624i	0.997535	−	0.0701772i	$-0.0223565\pi$
$59$	3.36428	+	5.82710i	0.437992	+	0.758624i	−0.559543	+	0.828802i	$0.689023\pi$
$60$		0			0
$61$	−5.97383	+	10.3470i	−0.764870	+	1.32479i	0.175445	+	0.984489i	$0.443864\pi$
$61$	−5.97383	+	10.3470i	−0.764870	+	1.32479i	−0.940315	+	0.340305i	$0.889470\pi$
$62$		0			0
$63$	−0.587798	−	3.17750i	−0.0740556	−	0.400328i
$64$		0			0
$65$	0.211554	−	0.366422i	0.0262401	−	0.0454491i
$66$		0			0
$67$	3.75926	+	6.51123i	0.459267	+	0.795473i	0.998922	−	0.0464127i	$-0.0147789\pi$
$67$	3.75926	+	6.51123i	0.459267	+	0.795473i	−0.539656	+	0.841886i	$0.681446\pi$
$68$		0			0
$69$	8.72532			1.05041
$70$		0			0
$71$	4.10572			0.487259			0.243629	−	0.969868i	$-0.421662\pi$
$71$	4.10572			0.487259			0.243629	+	0.969868i	$0.421662\pi$
$72$		0			0
$73$	2.68438	+	4.64947i	0.314182	+	0.544180i	0.979263	−	0.202591i	$-0.0649363\pi$
$73$	2.68438	+	4.64947i	0.314182	+	0.544180i	−0.665081	+	0.746771i	$0.731603\pi$
$74$		0			0
$75$	−2.50914	+	4.34595i	−0.289730	+	0.501828i
$76$		0			0
$77$	−2.49369	−	0.884018i	−0.284183	−	0.100743i
$78$		0			0
$79$	−5.30237	+	9.18397i	−0.596563	+	1.03328i	0.396761	+	0.917922i	$0.370134\pi$
$79$	−5.30237	+	9.18397i	−0.596563	+	1.03328i	−0.993324	+	0.115355i	$0.963199\pi$
$80$		0			0
$81$	1.92210	+	3.32918i	0.213567	+	0.369909i
$82$		0			0
$83$	16.3001			1.78917			0.894586	−	0.446895i	$-0.147470\pi$
$83$	16.3001			1.78917			0.894586	+	0.446895i	$0.147470\pi$
$84$		0			0
$85$	−3.73567			−0.405190
$86$		0			0
$87$	2.04421	+	3.54067i	0.219162	+	0.379599i
$88$		0			0
$89$	−4.29786	+	7.44411i	−0.455572	+	0.789074i	−0.998721	−	0.0505622i	$-0.983899\pi$
$89$	−4.29786	+	7.44411i	−0.455572	+	0.789074i	0.543149	+	0.839637i	$0.317232\pi$
$90$		0			0
$91$	−0.765510	+	0.653357i	−0.0802472	+	0.0684905i
$92$		0			0
$93$	1.38140	−	2.39265i	0.143244	−	0.248106i
$94$		0			0
$95$	2.44997	+	4.24348i	0.251362	+	0.435372i
$96$		0			0
$97$	4.51152			0.458075			0.229038	−	0.973418i	$-0.426442\pi$
$97$	4.51152			0.458075			0.229038	+	0.973418i	$0.426442\pi$
$98$		0			0
$99$	−1.22136			−0.122751
$100$		0			0
$101$	−8.09182	−	14.0154i	−0.805166	−	1.39459i	−0.916179	−	0.400769i	$-0.868743\pi$
$101$	−8.09182	−	14.0154i	−0.805166	−	1.39459i	0.111013	−	0.993819i	$-0.464590\pi$
$102$		0			0
$103$	5.15890	−	8.93549i	0.508322	−	0.880440i	−0.491632	−	0.870803i	$-0.663599\pi$
$103$	5.15890	−	8.93549i	0.508322	−	0.880440i	0.999954	−	0.00963621i	$-0.00306735\pi$
$104$		0			0
$105$	−2.98529	+	2.54792i	−0.291334	+	0.248652i
$106$		0			0
$107$	1.69007	−	2.92728i	0.163385	−	0.282991i	−0.772696	−	0.634777i	$-0.781092\pi$
$107$	1.69007	−	2.92728i	0.163385	−	0.282991i	0.936081	+	0.351786i	$0.114425\pi$
$108$		0			0
$109$	−3.54709	−	6.14374i	−0.339750	−	0.588464i	0.644636	−	0.764490i	$-0.277009\pi$
$109$	−3.54709	−	6.14374i	−0.339750	−	0.588464i	−0.984386	+	0.176026i	$0.943676\pi$
$110$		0			0
$111$	−6.50602			−0.617524
$112$		0			0
$113$	4.01529			0.377727			0.188864	−	0.982003i	$-0.439520\pi$
$113$	4.01529			0.377727			0.188864	+	0.982003i	$0.439520\pi$
$114$		0			0
$115$	3.63855	+	6.30216i	0.339297	+	0.587679i
$116$		0			0
$117$	−0.232297	+	0.402350i	−0.0214759	+	0.0371973i
$118$		0			0
$119$	8.37511	+	2.96899i	0.767745	+	0.272167i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	4.37725	+	7.58162i	0.394683	+	0.683612i
$124$		0			0
$125$	−9.74684			−0.871784
$126$		0			0
$127$	−9.86381			−0.875272			−0.437636	−	0.899152i	$-0.644184\pi$
$127$	−9.86381			−0.875272			−0.437636	+	0.899152i	$0.644184\pi$
$128$		0			0
$129$	−8.27900	−	14.3396i	−0.728925	−	1.26254i
$130$		0			0
$131$	−2.92091	+	5.05917i	−0.255202	+	0.442022i	−0.964950	−	0.262433i	$-0.915475\pi$
$131$	−2.92091	+	5.05917i	−0.255202	+	0.442022i	0.709749	+	0.704455i	$0.248808\pi$
$132$		0			0
$133$	−2.12009	−	11.4607i	−0.183836	−	0.993773i
$134$		0			0
$135$	−3.13103	+	5.42311i	−0.269476	+	0.466747i
$136$		0			0
$137$	−1.99995	−	3.46401i	−0.170867	−	0.295950i	0.767856	−	0.640622i	$-0.221323\pi$
$137$	−1.99995	−	3.46401i	−0.170867	−	0.295950i	−0.938723	+	0.344672i	$0.887990\pi$
$138$		0			0
$139$	−1.31997			−0.111958			−0.0559790	−	0.998432i	$-0.517828\pi$
$139$	−1.31997			−0.111958			−0.0559790	+	0.998432i	$0.517828\pi$
$140$		0			0
$141$	9.81374			0.826466
$142$		0			0
$143$	0.190195	+	0.329428i	0.0159049	+	0.0275482i
$144$		0			0
$145$	−1.70491	+	2.95299i	−0.141585	+	0.245233i
$146$		0			0
$147$	8.71780	−	3.33965i	0.719032	−	0.275450i
$148$		0			0
$149$	2.11628	−	3.66551i	0.173373	−	0.300290i	−0.766224	−	0.642573i	$-0.777867\pi$
$149$	2.11628	−	3.66551i	0.173373	−	0.300290i	0.939597	+	0.342283i	$0.111200\pi$
$150$		0			0
$151$	−11.6145	−	20.1169i	−0.945173	−	1.63709i	−0.755404	−	0.655259i	$-0.772559\pi$
$151$	−11.6145	−	20.1169i	−0.945173	−	1.63709i	−0.189769	−	0.981829i	$-0.560774\pi$
$152$		0			0
$153$	4.10195			0.331623
$154$		0			0
$155$	2.30423			0.185080
$156$		0			0
$157$	−1.78166	−	3.08592i	−0.142192	−	0.246283i	0.786130	−	0.618061i	$-0.212082\pi$
$157$	−1.78166	−	3.08592i	−0.142192	−	0.246283i	−0.928322	+	0.371778i	$0.878748\pi$
$158$		0			0
$159$	0.513689	−	0.889736i	0.0407382	−	0.0705606i
$160$		0			0
$161$	−3.14863	−	17.0208i	−0.248147	−	1.34143i
$162$		0			0
$163$	−10.9889	+	19.0333i	−0.860716	+	1.49080i	0.0105238	+	0.999945i	$0.496650\pi$
$163$	−10.9889	+	19.0333i	−0.860716	+	1.49080i	−0.871239	+	0.490858i	$0.836683\pi$
$164$		0			0
$165$	0.741712	+	1.28468i	0.0577422	+	0.100012i
$166$		0			0
$167$	−6.25548			−0.484064			−0.242032	−	0.970268i	$-0.577814\pi$
$167$	−6.25548			−0.484064			−0.242032	+	0.970268i	$0.577814\pi$
$168$		0			0
$169$	−12.8553			−0.988869
$170$		0			0
$171$	−2.69020	−	4.65956i	−0.205724	−	0.356325i
$172$		0			0
$173$	−0.218399	+	0.378279i	−0.0166046	+	0.0287600i	−0.874208	−	0.485551i	$-0.838619\pi$
$173$	−0.218399	+	0.378279i	−0.0166046	+	0.0287600i	0.857604	+	0.514311i	$0.171952\pi$
$174$		0			0
$175$	9.38326	+	3.32638i	0.709308	+	0.251450i
$176$		0			0
$177$	−4.48680	+	7.77136i	−0.337248	+	0.584131i
$178$		0			0
$179$	4.09295	+	7.08920i	0.305922	+	0.529872i	0.977466	−	0.211093i	$-0.0677022\pi$
$179$	4.09295	+	7.08920i	0.305922	+	0.529872i	−0.671545	+	0.740964i	$0.734369\pi$
$180$		0			0
$181$	18.5587			1.37946			0.689728	−	0.724069i	$-0.257730\pi$
$181$	18.5587			1.37946			0.689728	+	0.724069i	$0.257730\pi$
$182$		0			0
$183$	−15.9341			−1.17788
$184$		0			0
$185$	−2.71308	−	4.69919i	−0.199469	−	0.345491i
$186$		0			0
$187$	1.67926	−	2.90856i	0.122799	−	0.212695i
$188$		0			0
$189$	11.3297	−	9.66979i	0.824112	−	0.703374i
$190$		0			0
$191$	0.600747	−	1.04052i	0.0434685	−	0.0752897i	−0.843473	−	0.537172i	$-0.819493\pi$
$191$	0.600747	−	1.04052i	0.0434685	−	0.0752897i	0.886941	+	0.461883i	$0.152826\pi$
$192$		0			0
$193$	10.2331	+	17.7243i	0.736598	+	1.27582i	0.954019	+	0.299747i	$0.0969021\pi$
$193$	10.2331	+	17.7243i	0.736598	+	1.27582i	−0.217421	+	0.976078i	$0.569765\pi$
$194$		0			0
$195$	0.564281			0.0404090
$196$		0			0
$197$	−15.4750			−1.10255			−0.551275	−	0.834324i	$-0.685858\pi$
$197$	−15.4750			−1.10255			−0.551275	+	0.834324i	$0.685858\pi$
$198$		0			0
$199$	−6.58726	−	11.4095i	−0.466958	−	0.808796i	0.532329	−	0.846537i	$-0.321317\pi$
$199$	−6.58726	−	11.4095i	−0.466958	−	0.808796i	−0.999288	+	0.0377419i	$0.987984\pi$
$200$		0			0
$201$	−5.01356	+	8.68374i	−0.353629	+	0.612504i
$202$		0			0
$203$	6.16923	−	5.26539i	0.432995	−	0.369558i
$204$		0			0
$205$	−3.65072	+	6.32323i	−0.254977	+	0.441633i
$206$		0			0
$207$	−3.99531	−	6.92009i	−0.277693	−	0.480979i
$208$		0			0
$209$	−4.40525			−0.304717
$210$		0			0
$211$	−13.2004			−0.908754			−0.454377	−	0.890809i	$-0.650138\pi$
$211$	−13.2004			−0.908754			−0.454377	+	0.890809i	$0.650138\pi$
$212$		0			0
$213$	2.73781	+	4.74202i	0.187592	+	0.324918i
$214$		0			0
$215$	6.90486	−	11.9596i	0.470907	−	0.815636i
$216$		0			0
$217$	−5.16592	−	1.83132i	−0.350685	−	0.124318i
$218$		0			0
$219$	−3.58004	+	6.20080i	−0.241916	+	0.419012i
$220$		0			0
$221$	−0.638774	−	1.10639i	−0.0429686	−	0.0744238i
$222$		0			0
$223$	9.49742			0.635994			0.317997	−	0.948092i	$-0.396990\pi$
$223$	9.49742			0.635994			0.317997	+	0.948092i	$0.396990\pi$
$224$		0			0
$225$	4.59572			0.306381
$226$		0			0
$227$	1.61492	+	2.79713i	0.107186	+	0.185652i	0.914629	−	0.404294i	$-0.132483\pi$
$227$	1.61492	+	2.79713i	0.107186	+	0.185652i	−0.807443	+	0.589945i	$0.799149\pi$
$228$		0			0
$229$	5.40224	−	9.35695i	0.356990	−	0.618324i	−0.630467	−	0.776216i	$-0.717136\pi$
$229$	5.40224	−	9.35695i	0.356990	−	0.618324i	0.987456	+	0.157892i	$0.0504698\pi$
$230$		0			0
$231$	−0.641843	−	3.46966i	−0.0422302	−	0.228287i
$232$		0			0
$233$	13.4722	−	23.3346i	0.882594	−	1.52870i	0.0341476	−	0.999417i	$-0.489128\pi$
$233$	13.4722	−	23.3346i	0.882594	−	1.52870i	0.848447	−	0.529281i	$-0.177538\pi$
$234$		0			0
$235$	4.09243	+	7.08830i	0.266961	+	0.462390i
$236$		0			0
$237$	−14.1431			−0.918691
$238$		0			0
$239$	−4.82091			−0.311839			−0.155919	−	0.987770i	$-0.549834\pi$
$239$	−4.82091			−0.311839			−0.155919	+	0.987770i	$0.549834\pi$
$240$		0			0
$241$	−6.48367	−	11.2300i	−0.417650	−	0.723391i	0.578053	−	0.815999i	$-0.303813\pi$
$241$	−6.48367	−	11.2300i	−0.417650	−	0.723391i	−0.995703	+	0.0926088i	$0.970479\pi$
$242$		0			0
$243$	5.88134	−	10.1868i	0.377288	−	0.653482i
$244$		0			0
$245$	6.04759	+	4.90406i	0.386366	+	0.313309i
$246$		0			0
$247$	−0.837859	+	1.45121i	−0.0533117	+	0.0923385i
$248$		0			0
$249$	10.8694	+	18.8264i	0.688820	+	1.19307i
$250$		0			0
$251$	−3.01121			−0.190066			−0.0950328	−	0.995474i	$-0.530296\pi$
$251$	−3.01121			−0.190066			−0.0950328	+	0.995474i	$0.530296\pi$
$252$		0			0
$253$	−6.54241			−0.411317
$254$		0			0
$255$	−2.49105	−	4.31463i	−0.155996	−	0.270192i
$256$		0			0
$257$	−11.9244	+	20.6538i	−0.743827	+	1.28835i	0.206914	+	0.978359i	$0.433658\pi$
$257$	−11.9244	+	20.6538i	−0.743827	+	1.28835i	−0.950741	+	0.309987i	$0.899675\pi$
$258$		0			0
$259$	2.34777	+	12.6915i	0.145883	+	0.788612i
$260$		0			0
$261$	1.87208	−	3.24253i	0.115879	−	0.200708i
$262$		0			0
$263$	−10.6850	−	18.5069i	−0.658863	−	1.14118i	−0.980910	−	0.194460i	$-0.937705\pi$
$263$	−10.6850	−	18.5069i	−0.658863	−	1.14118i	0.322048	−	0.946723i	$-0.395629\pi$
$264$		0			0
$265$	0.856855			0.0526362
$266$		0			0
$267$	−11.4637			−0.701570
$268$		0			0
$269$	−0.187829	−	0.325329i	−0.0114521	−	0.0198357i	0.860243	−	0.509885i	$-0.170312\pi$
$269$	−0.187829	−	0.325329i	−0.0114521	−	0.0198357i	−0.871695	+	0.490049i	$0.836979\pi$
$270$		0			0
$271$	−13.5575	+	23.4822i	−0.823558	+	1.42644i	0.0794581	+	0.996838i	$0.474681\pi$
$271$	−13.5575	+	23.4822i	−0.823558	+	1.42644i	−0.903016	+	0.429606i	$0.858652\pi$
$272$		0			0
$273$	−1.26508	−	0.448472i	−0.0765661	−	0.0271428i
$274$		0			0
$275$	1.88140	−	3.25867i	0.113452	−	0.196505i
$276$		0			0
$277$	4.92609	+	8.53223i	0.295980	+	0.512652i	0.975212	−	0.221271i	$-0.0710205\pi$
$277$	4.92609	+	8.53223i	0.295980	+	0.512652i	−0.679232	+	0.733923i	$0.737687\pi$
$278$		0			0
$279$	−2.53016			−0.151477
$280$		0			0
$281$	−16.7895			−1.00158			−0.500788	−	0.865570i	$-0.666956\pi$
$281$	−16.7895			−1.00158			−0.500788	+	0.865570i	$0.666956\pi$
$282$		0			0
$283$	−7.65684	−	13.2620i	−0.455152	−	0.788346i	0.543545	−	0.839380i	$-0.317082\pi$
$283$	−7.65684	−	13.2620i	−0.455152	−	0.788346i	−0.998697	+	0.0510337i	$0.983748\pi$
$284$		0			0
$285$	−3.26743	+	5.65935i	−0.193546	+	0.335231i
$286$		0			0
$287$	13.2102	−	11.2748i	0.779771	−	0.665529i
$288$		0			0
$289$	2.86019	−	4.95399i	0.168246	−	0.291411i
$290$		0			0
$291$	3.00841	+	5.21072i	0.176356	+	0.305458i
$292$		0			0
$293$	9.31349			0.544100			0.272050	−	0.962283i	$-0.412298\pi$
$293$	9.31349			0.544100			0.272050	+	0.962283i	$0.412298\pi$
$294$		0			0
$295$	−7.48416			−0.435745
$296$		0			0
$297$	−2.81492	−	4.87559i	−0.163338	−	0.282910i
$298$		0			0
$299$	−1.24434	+	2.15525i	−0.0719618	+	0.124642i
$300$		0			0
$301$	−24.9853	+	21.3248i	−1.44013	+	1.22914i
$302$		0			0
$303$	10.7917	−	18.6918i	0.619968	−	1.07382i
$304$		0			0
$305$	−6.64468	−	11.5089i	−0.380473	−	0.658999i
$306$		0			0
$307$	−19.3136			−1.10229			−0.551143	−	0.834411i	$-0.685808\pi$
$307$	−19.3136			−1.10229			−0.551143	+	0.834411i	$0.685808\pi$
$308$		0			0
$309$	13.7604			0.782803
$310$		0			0
$311$	3.49156	+	6.04755i	0.197988	+	0.342925i	0.947876	−	0.318640i	$-0.103226\pi$
$311$	3.49156	+	6.04755i	0.197988	+	0.342925i	−0.749888	+	0.661565i	$0.769893\pi$
$312$		0			0
$313$	−9.71768	+	16.8315i	−0.549276	+	0.951373i	0.449049	+	0.893507i	$0.351763\pi$
$313$	−9.71768	+	16.8315i	−0.549276	+	0.951373i	−0.998324	+	0.0578660i	$0.981570\pi$
$314$		0			0
$315$	3.38772	+	1.20095i	0.190877	+	0.0676659i
$316$		0			0
$317$	−15.7909	+	27.3506i	−0.886903	+	1.53616i	−0.0433855	+	0.999058i	$0.513814\pi$
$317$	−15.7909	+	27.3506i	−0.886903	+	1.53616i	−0.843517	+	0.537102i	$0.819519\pi$
$318$		0			0
$319$	−1.53278	−	2.65486i	−0.0858193	−	0.148643i
$320$		0			0
$321$	4.50794			0.251609
$322$		0			0
$323$	14.7951			0.823221
$324$		0			0
$325$	−0.715666	−	1.23957i	−0.0396980	−	0.0687590i
$326$		0			0
$327$	4.73060	−	8.19365i	0.261603	−	0.453110i
$328$		0			0
$329$	−3.54140	−	19.1440i	−0.195244	−	1.05544i
$330$		0			0
$331$	9.34862	−	16.1923i	0.513847	−	0.890009i	−0.486024	−	0.873945i	$-0.661553\pi$
$331$	9.34862	−	16.1923i	0.513847	−	0.890009i	0.999871	−	0.0160633i	$-0.00511331\pi$
$332$		0			0
$333$	2.97910	+	5.15994i	0.163253	+	0.282763i
$334$		0			0
$335$	−8.36283			−0.456910
$336$		0			0
$337$	5.71941			0.311556			0.155778	−	0.987792i	$-0.450212\pi$
$337$	5.71941			0.311556			0.155778	+	0.987792i	$0.450212\pi$
$338$		0			0
$339$	2.67751	+	4.63759i	0.145422	+	0.251879i
$340$		0			0
$341$	−1.03580	+	1.79405i	−0.0560915	+	0.0971533i
$342$		0			0
$343$	−9.66070	−	15.8010i	−0.521629	−	0.853173i
$344$		0			0
$345$	−4.85258	+	8.40492i	−0.261254	+	0.452505i
$346$		0			0
$347$	−3.99165	−	6.91373i	−0.214283	−	0.371149i	0.738768	−	0.673960i	$-0.235408\pi$
$347$	−3.99165	−	6.91373i	−0.214283	−	0.371149i	−0.953050	+	0.302812i	$0.902075\pi$
$348$		0			0
$349$	3.04781			0.163146			0.0815729	−	0.996667i	$-0.474006\pi$
$349$	3.04781			0.163146			0.0815729	+	0.996667i	$0.474006\pi$
$350$		0			0
$351$	−2.14154			−0.114307
$352$		0			0
$353$	−15.5932	−	27.0081i	−0.829940	−	1.43750i	−0.898084	−	0.439823i	$-0.855041\pi$
$353$	−15.5932	−	27.0081i	−0.829940	−	1.43750i	0.0681444	−	0.997675i	$-0.478292\pi$
$354$		0			0
$355$	−2.28339	+	3.95495i	−0.121190	+	0.209907i
$356$		0			0
$357$	2.15564	+	11.6529i	0.114089	+	0.616737i
$358$		0			0
$359$	−7.55584	+	13.0871i	−0.398782	+	0.690711i	−0.993576	−	0.113168i	$-0.963900\pi$
$359$	−7.55584	+	13.0871i	−0.398782	+	0.690711i	0.594794	+	0.803878i	$0.297234\pi$
$360$		0			0
$361$	−0.203110	−	0.351797i	−0.0106900	−	0.0185156i
$362$		0			0
$363$	−1.33366			−0.0699988
$364$		0			0
$365$	−5.97165			−0.312570
$366$		0			0
$367$	−13.9154	−	24.1022i	−0.726379	−	1.25812i	−0.958404	−	0.285415i	$-0.907869\pi$
$367$	−13.9154	−	24.1022i	−0.726379	−	1.25812i	0.232025	−	0.972710i	$-0.425465\pi$
$368$		0			0
$369$	4.00867	−	6.94322i	0.208683	−	0.361450i
$370$		0			0
$371$	−1.92101	−	0.681000i	−0.0997339	−	0.0353558i
$372$		0			0
$373$	4.42506	−	7.66443i	0.229121	−	0.396849i	−0.728427	−	0.685124i	$-0.759748\pi$
$373$	4.42506	−	7.66443i	0.229121	−	0.396849i	0.957548	+	0.288274i	$0.0930815\pi$
$374$		0			0
$375$	−6.49947	−	11.2574i	−0.335631	−	0.581330i
$376$		0			0
$377$	−1.16611			−0.0600579
$378$		0			0
$379$	−26.1533			−1.34341			−0.671703	−	0.740821i	$-0.734437\pi$
$379$	−26.1533			−1.34341			−0.671703	+	0.740821i	$0.734437\pi$
$380$		0			0
$381$	−6.57747	−	11.3925i	−0.336974	−	0.583656i
$382$		0			0
$383$	−7.79366	+	13.4990i	−0.398237	+	0.689767i	−0.993509	−	0.113757i	$-0.963711\pi$
$383$	−7.79366	+	13.4990i	−0.398237	+	0.689767i	0.595271	+	0.803525i	$0.297045\pi$
$384$		0			0
$385$	2.23842	−	1.91048i	0.114080	−	0.0973669i
$386$		0			0
$387$	−7.58188	+	13.1322i	−0.385409	+	0.667548i
$388$		0			0
$389$	16.6515	+	28.8413i	0.844266	+	1.46231i	0.886257	+	0.463194i	$0.153297\pi$
$389$	16.6515	+	28.8413i	0.844266	+	1.46231i	−0.0419912	+	0.999118i	$0.513370\pi$
$390$		0			0
$391$	21.9728			1.11121
$392$		0			0
$393$	−7.79100			−0.393004
$394$		0			0
$395$	−5.89781	−	10.2153i	−0.296751	−	0.513988i
$396$		0			0
$397$	5.67755	−	9.83380i	0.284948	−	0.493545i	−0.687649	−	0.726044i	$-0.741357\pi$
$397$	5.67755	−	9.83380i	0.284948	−	0.493545i	0.972597	+	0.232499i	$0.0746903\pi$
$398$		0			0
$399$	11.8232	−	10.0910i	0.591901	−	0.505183i
$400$		0			0
$401$	−12.5060	+	21.6610i	−0.624518	+	1.08170i	0.364116	+	0.931354i	$0.381371\pi$
$401$	−12.5060	+	21.6610i	−0.624518	+	1.08170i	−0.988634	+	0.150343i	$0.951962\pi$
$402$		0			0
$403$	0.394007	+	0.682441i	0.0196269	+	0.0339948i
$404$		0			0
$405$	−4.27590			−0.212471
$406$		0			0
$407$	4.87833			0.241810
$408$		0			0
$409$	−1.34212	−	2.32462i	−0.0663636	−	0.114945i	0.830934	−	0.556370i	$-0.187806\pi$
$409$	−1.34212	−	2.32462i	−0.0663636	−	0.114945i	−0.897298	+	0.441425i	$0.854473\pi$
$410$		0			0
$411$	2.66724	−	4.61980i	0.131565	−	0.227878i
$412$		0			0
$413$	16.7790	+	5.94817i	0.825639	+	0.292690i
$414$		0			0
$415$	−9.06531	+	15.7016i	−0.444998	+	0.770760i
$416$		0			0
$417$	−0.880191	−	1.52454i	−0.0431031	−	0.0746568i
$418$		0			0
$419$	−2.70453			−0.132125			−0.0660624	−	0.997815i	$-0.521044\pi$
$419$	−2.70453			−0.132125			−0.0660624	+	0.997815i	$0.521044\pi$
$420$		0			0
$421$	−14.3434			−0.699057			−0.349528	−	0.936926i	$-0.613658\pi$
$421$	−14.3434			−0.699057			−0.349528	+	0.936926i	$0.613658\pi$
$422$		0			0
$423$	−4.49369	−	7.78331i	−0.218491	−	0.378437i
$424$		0			0
$425$	−6.31870	+	10.9443i	−0.306502	+	0.530877i
$426$		0			0
$427$	5.74999	+	31.0832i	0.278262	+	1.50422i
$428$		0			0
$429$	−0.253656	+	0.439344i	−0.0122466	+	0.0212117i
$430$		0			0
$431$	−17.0137	−	29.4685i	−0.819520	−	1.41945i	−0.906037	−	0.423199i	$-0.860907\pi$
$431$	−17.0137	−	29.4685i	−0.819520	−	1.41945i	0.0865171	−	0.996250i	$-0.472426\pi$
$432$		0			0
$433$	29.4843			1.41692			0.708462	−	0.705749i	$-0.249389\pi$
$433$	29.4843			1.41692			0.708462	+	0.705749i	$0.249389\pi$
$434$		0			0
$435$	−4.54753			−0.218037
$436$		0			0
$437$	−14.4105	−	24.9597i	−0.689346	−	1.19398i
$438$		0			0
$439$	−12.4729	+	21.6036i	−0.595297	+	1.03109i	0.398208	+	0.917295i	$0.369632\pi$
$439$	−12.4729	+	21.6036i	−0.595297	+	1.03109i	−0.993505	+	0.113790i	$0.963701\pi$
$440$		0			0
$441$	−6.64056	−	5.38490i	−0.316217	−	0.256424i
$442$		0			0
$443$	−18.9168	+	32.7649i	−0.898765	+	1.55671i	−0.0696903	+	0.997569i	$0.522201\pi$
$443$	−18.9168	+	32.7649i	−0.898765	+	1.55671i	−0.829075	+	0.559138i	$0.811132\pi$
$444$		0			0
$445$	−4.78050	−	8.28007i	−0.226618	−	0.392513i
$446$		0			0
$447$	5.64479			0.266989
$448$		0			0
$449$	27.5777			1.30147			0.650736	−	0.759304i	$-0.274461\pi$
$449$	27.5777			1.30147			0.650736	+	0.759304i	$0.274461\pi$
$450$		0			0
$451$	−3.28214	−	5.68483i	−0.154550	−	0.267688i
$452$		0			0
$453$	15.4897	−	26.8290i	0.727771	−	1.26054i
$454$		0			0
$455$	−0.203627	−	1.10076i	−0.00954620	−	0.0516046i
$456$		0			0
$457$	−16.1146	+	27.9113i	−0.753810	+	1.30564i	0.192154	+	0.981365i	$0.438453\pi$
$457$	−16.1146	+	27.9113i	−0.753810	+	1.30564i	−0.945964	+	0.324272i	$0.894881\pi$
$458$		0			0
$459$	9.45396	+	16.3747i	0.441273	+	0.764307i
$460$		0			0
$461$	20.1755			0.939668			0.469834	−	0.882755i	$-0.344314\pi$
$461$	20.1755			0.939668			0.469834	+	0.882755i	$0.344314\pi$
$462$		0			0
$463$	5.41828			0.251809			0.125904	−	0.992042i	$-0.459817\pi$
$463$	5.41828			0.251809			0.125904	+	0.992042i	$0.459817\pi$
$464$		0			0
$465$	1.53652	+	2.66134i	0.0712546	+	0.123417i
$466$		0			0
$467$	16.8420	−	29.1712i	0.779356	−	1.34988i	−0.152958	−	0.988233i	$-0.548880\pi$
$467$	16.8420	−	29.1712i	0.779356	−	1.34988i	0.932314	−	0.361651i	$-0.117787\pi$
$468$		0			0
$469$	18.7489	+	6.64650i	0.865743	+	0.306907i
$470$		0			0
$471$	2.37612	−	4.11555i	0.109486	−	0.189635i
$472$		0			0
$473$	6.20774	+	10.7521i	0.285432	+	0.494383i
$474$		0			0
$475$	16.5760			0.760561
$476$		0			0
$477$	−0.940870			−0.0430795
$478$		0			0
$479$	12.5704	+	21.7725i	0.574354	+	0.994810i	0.996111	+	0.0881016i	$0.0280800\pi$
$479$	12.5704	+	21.7725i	0.574354	+	0.994810i	−0.421758	+	0.906709i	$0.638587\pi$
$480$		0			0
$481$	0.927836	−	1.60706i	0.0423057	−	0.0732756i
$482$		0			0
$483$	17.5591	−	14.9866i	0.798967	−	0.681912i
$484$		0			0
$485$	−2.50908	+	4.34585i	−0.113931	+	0.197335i
$486$		0			0
$487$	14.6173	+	25.3179i	0.662372	+	1.14726i	0.979991	+	0.199043i	$0.0637833\pi$
$487$	14.6173	+	25.3179i	0.662372	+	1.14726i	−0.317619	+	0.948218i	$0.602883\pi$
$488$		0			0
$489$	−29.3108			−1.32548
$490$		0			0
$491$	17.8960			0.807634			0.403817	−	0.914840i	$-0.367683\pi$
$491$	17.8960			0.807634			0.403817	+	0.914840i	$0.367683\pi$
$492$		0			0
$493$	5.14787	+	8.91637i	0.231848	+	0.401573i
$494$		0			0
$495$	0.679258	−	1.17651i	0.0305304	−	0.0528801i
$496$		0			0
$497$	8.26246	−	7.05195i	0.370622	−	0.316323i
$498$		0			0
$499$	−10.6031	+	18.3650i	−0.474658	+	0.822132i	−0.999579	−	0.0290191i	$-0.990762\pi$
$499$	−10.6031	+	18.3650i	−0.474658	+	0.822132i	0.524921	+	0.851151i	$0.324095\pi$
$500$		0			0
$501$	−4.17133	−	7.22496i	−0.186361	−	0.322787i
$502$		0			0
$503$	−14.2236			−0.634200			−0.317100	−	0.948392i	$-0.602709\pi$
$503$	−14.2236			−0.634200			−0.317100	+	0.948392i	$0.602709\pi$
$504$		0			0
$505$	18.0010			0.801035
$506$		0			0
$507$	−8.57228	−	14.8476i	−0.380708	−	0.659406i
$508$		0			0
$509$	−4.17820	+	7.23685i	−0.185195	+	0.320768i	−0.943642	−	0.330967i	$-0.892625\pi$
$509$	−4.17820	+	7.23685i	−0.185195	+	0.320768i	0.758447	+	0.651735i	$0.225958\pi$
$510$		0			0
$511$	13.3880	+	4.74607i	0.592251	+	0.209954i
$512$		0			0
$513$	12.4004	−	21.4782i	0.547493	−	0.948285i
$514$		0			0
$515$	5.73824	+	9.93892i	0.252857	+	0.437961i
$516$		0			0
$517$	−7.35852			−0.323627
$518$		0			0
$519$	−0.582540			−0.0255707
$520$		0			0
$521$	−7.72298	−	13.3766i	−0.338350	−	0.586039i	0.645773	−	0.763530i	$-0.276535\pi$
$521$	−7.72298	−	13.3766i	−0.338350	−	0.586039i	−0.984122	+	0.177491i	$0.943202\pi$
$522$		0			0
$523$	6.14224	−	10.6387i	0.268581	−	0.465197i	−0.699914	−	0.714227i	$-0.746779\pi$
$523$	6.14224	−	10.6387i	0.268581	−	0.465197i	0.968496	+	0.249030i	$0.0801118\pi$
$524$		0			0
$525$	2.41512	+	13.0556i	0.105405	+	0.569793i
$526$		0			0
$527$	3.47874	−	6.02535i	0.151536	−	0.262468i
$528$		0			0
$529$	−9.90153	−	17.1500i	−0.430501	−	0.745650i
$530$		0			0
$531$	8.21799			0.356630
$532$		0			0
$533$	−2.49699			−0.108157
$534$		0			0
$535$	1.87986	+	3.25601i	0.0812734	+	0.140770i
$536$		0			0
$537$	−5.45859	+	9.45456i	−0.235556	+	0.407994i
$538$		0			0
$539$	−6.53677	+	2.50413i	−0.281558	+	0.107861i
$540$		0			0
$541$	−5.73628	+	9.93553i	−0.246622	+	0.427162i	−0.962586	−	0.270975i	$-0.912654\pi$
$541$	−5.73628	+	9.93553i	−0.246622	+	0.427162i	0.715964	+	0.698137i	$0.245987\pi$
$542$		0			0
$543$	12.3754	+	21.4349i	0.531081	+	0.919860i
$544$		0			0
$545$	7.89085			0.338007
$546$		0			0
$547$	4.76618			0.203787			0.101893	−	0.994795i	$-0.467510\pi$
$547$	4.76618			0.203787			0.101893	+	0.994795i	$0.467510\pi$
$548$		0			0
$549$	7.29619	+	12.6374i	0.311394	+	0.539350i
$550$		0			0
$551$	6.75229	−	11.6953i	0.287657	−	0.498237i
$552$		0			0
$553$	5.10369	+	27.5894i	0.217031	+	1.17322i
$554$		0			0
$555$	3.61831	−	6.26710i	0.153589	−	0.266024i
$556$		0			0
$557$	−7.89099	−	13.6676i	−0.334352	−	0.579114i	0.649008	−	0.760781i	$-0.275184\pi$
$557$	−7.89099	−	13.6676i	−0.334352	−	0.579114i	−0.983360	+	0.181667i	$0.941851\pi$
$558$		0			0
$559$	4.72274			0.199751
$560$		0			0
$561$	4.47911			0.189108
$562$		0			0
$563$	5.69331	+	9.86109i	0.239944	+	0.415596i	0.960698	−	0.277596i	$-0.0895375\pi$
$563$	5.69331	+	9.86109i	0.239944	+	0.415596i	−0.720754	+	0.693191i	$0.756204\pi$
$564$		0			0
$565$	−2.23310	+	3.86784i	−0.0939473	+	0.162721i
$566$		0			0
$567$	9.58627	+	3.39835i	0.402586	+	0.142717i
$568$		0			0
$569$	9.32339	−	16.1486i	0.390857	−	0.676984i	−0.601706	−	0.798718i	$-0.705512\pi$
$569$	9.32339	−	16.1486i	0.390857	−	0.676984i	0.992563	+	0.121734i	$0.0388454\pi$
$570$		0			0
$571$	8.72974	+	15.1203i	0.365328	+	0.632767i	0.988829	−	0.149056i	$-0.0476235\pi$
$571$	8.72974	+	15.1203i	0.365328	+	0.632767i	−0.623501	+	0.781823i	$0.714290\pi$
$572$		0			0
$573$	1.60238			0.0669405
$574$		0			0
$575$	24.6177			1.02663
$576$		0			0
$577$	9.09904	+	15.7600i	0.378798	+	0.656097i	0.990888	−	0.134691i	$-0.0430042\pi$
$577$	9.09904	+	15.7600i	0.378798	+	0.656097i	−0.612090	+	0.790788i	$0.709671\pi$
$578$		0			0
$579$	−13.6475	+	23.6382i	−0.567171	+	0.982369i
$580$		0			0
$581$	32.8029	−	27.9970i	1.36089	−	1.16151i
$582$		0			0
$583$	−0.385173	+	0.667140i	−0.0159523	+	0.0276301i
$584$		0			0
$585$	−0.258383	−	0.447533i	−0.0106828	−	0.0185032i
$586$		0			0
$587$	35.2867			1.45644			0.728218	−	0.685346i	$-0.240349\pi$
$587$	35.2867			1.45644			0.728218	+	0.685346i	$0.240349\pi$
$588$		0			0
$589$	−9.12588			−0.376025
$590$		0			0
$591$	−10.3192	−	17.8734i	−0.424475	−	0.735211i
$592$		0			0
$593$	19.2917	−	33.4142i	0.792214	−	1.37216i	−0.132379	−	0.991199i	$-0.542262\pi$
$593$	19.2917	−	33.4142i	0.792214	−	1.37216i	0.924593	−	0.380956i	$-0.124405\pi$
$594$		0			0
$595$	−7.51777	+	6.41636i	−0.308199	+	0.263045i
$596$		0			0
$597$	8.78514	−	15.2163i	0.359552	−	0.622762i
$598$		0			0
$599$	20.1401	+	34.8837i	0.822902	+	1.42531i	0.903512	+	0.428563i	$0.140980\pi$
$599$	20.1401	+	34.8837i	0.822902	+	1.42531i	−0.0806096	+	0.996746i	$0.525687\pi$
$600$		0			0
$601$	2.55263			0.104124			0.0520620	−	0.998644i	$-0.483421\pi$
$601$	2.55263			0.104124			0.0520620	+	0.998644i	$0.483421\pi$
$602$		0			0
$603$	9.18281			0.373953
$604$		0			0
$605$	−0.556149	−	0.963278i	−0.0226107	−	0.0391628i
$606$		0			0
$607$	−5.78065	+	10.0124i	−0.234629	+	0.406390i	−0.959165	−	0.282848i	$-0.908721\pi$
$607$	−5.78065	+	10.0124i	−0.234629	+	0.406390i	0.724536	+	0.689237i	$0.242054\pi$
$608$		0			0
$609$	10.1952	+	3.61423i	0.413132	+	0.146456i
$610$		0			0
$611$	−1.39956	+	2.42410i	−0.0566200	+	0.0980687i
$612$		0			0
$613$	−17.8344	−	30.8901i	−0.720324	−	1.24764i	−0.960870	−	0.277000i	$-0.910660\pi$
$613$	−17.8344	−	30.8901i	−0.720324	−	1.24764i	0.240546	−	0.970638i	$-0.422674\pi$
$614$		0			0
$615$	−9.73761			−0.392658
$616$		0			0
$617$	−21.9721			−0.884565			−0.442283	−	0.896876i	$-0.645831\pi$
$617$	−21.9721			−0.884565			−0.442283	+	0.896876i	$0.645831\pi$
$618$		0			0
$619$	4.80648	+	8.32507i	0.193189	+	0.334613i	0.946305	−	0.323274i	$-0.104784\pi$
$619$	4.80648	+	8.32507i	0.193189	+	0.334613i	−0.753116	+	0.657887i	$0.771450\pi$
$620$		0			0
$621$	18.4164	−	31.8981i	0.739023	−	1.28003i
$622$		0			0
$623$	4.13682	+	22.3627i	0.165738	+	0.895944i
$624$		0			0
$625$	−3.98629	+	6.90446i	−0.159452	+	0.276178i
$626$		0			0
$627$	−2.93755	−	5.08798i	−0.117314	−	0.203194i
$628$		0			0
$629$	−16.3839			−0.653270
$630$		0			0
$631$	19.8407			0.789846			0.394923	−	0.918714i	$-0.370771\pi$
$631$	19.8407			0.789846			0.394923	+	0.918714i	$0.370771\pi$
$632$		0			0
$633$	−8.80241	−	15.2462i	−0.349864	−	0.605983i
$634$		0			0
$635$	5.48575	−	9.50160i	0.217695	−	0.377059i
$636$		0			0
$637$	−0.418332	+	2.62967i	−0.0165749	+	0.104191i
$638$		0			0
$639$	2.50728	−	4.34273i	0.0991863	−	0.171796i
$640$		0			0
$641$	−8.66566	−	15.0094i	−0.342273	−	0.592834i	0.642581	−	0.766217i	$-0.277863\pi$
$641$	−8.66566	−	15.0094i	−0.342273	−	0.592834i	−0.984854	+	0.173383i	$0.944530\pi$
$642$		0			0
$643$	−24.6406			−0.971731			−0.485865	−	0.874034i	$-0.661495\pi$
$643$	−24.6406			−0.971731			−0.485865	+	0.874034i	$0.661495\pi$
$644$		0			0
$645$	18.4174			0.725185
$646$		0			0
$647$	−9.94317	−	17.2221i	−0.390906	−	0.677070i	0.601663	−	0.798750i	$-0.294505\pi$
$647$	−9.94317	−	17.2221i	−0.390906	−	0.677070i	−0.992569	+	0.121680i	$0.961172\pi$
$648$		0			0
$649$	3.36428	−	5.82710i	0.132060	−	0.228734i
$650$		0			0
$651$	−1.32964	−	7.18772i	−0.0521126	−	0.281709i
$652$		0			0
$653$	−15.7371	+	27.2575i	−0.615841	+	1.06667i	0.374396	+	0.927269i	$0.377850\pi$
$653$	−15.7371	+	27.2575i	−0.615841	+	1.06667i	−0.990236	+	0.139398i	$0.955483\pi$
$654$		0			0
$655$	−3.24893	−	5.62731i	−0.126946	−	0.219877i
$656$		0			0
$657$	6.55717			0.255820
$658$		0			0
$659$	1.34601			0.0524332			0.0262166	−	0.999656i	$-0.491654\pi$
$659$	1.34601			0.0524332			0.0262166	+	0.999656i	$0.491654\pi$
$660$		0			0
$661$	1.15233	+	1.99590i	0.0448206	+	0.0776315i	0.887565	−	0.460682i	$-0.152395\pi$
$661$	1.15233	+	1.99590i	0.0448206	+	0.0776315i	−0.842745	+	0.538313i	$0.819062\pi$
$662$		0			0
$663$	0.851906	−	1.47554i	0.0330853	−	0.0573054i
$664$		0			0
$665$	12.2190	+	4.33164i	0.473832	+	0.167974i
$666$		0			0
$667$	10.0281	−	17.3691i	0.388289	−	0.672536i
$668$		0			0
$669$	6.33315	+	10.9693i	0.244854	+	0.424099i
$670$		0			0
$671$	11.9477			0.461234
$672$		0			0
$673$	13.3286			0.513779			0.256889	−	0.966441i	$-0.417302\pi$
$673$	13.3286			0.513779			0.256889	+	0.966441i	$0.417302\pi$
$674$		0			0
$675$	10.5920	+	18.3458i	0.407685	+	0.706131i
$676$		0			0
$677$	24.3546	−	42.1834i	0.936024	−	1.62124i	0.163226	−	0.986589i	$-0.447810\pi$
$677$	24.3546	−	42.1834i	0.936024	−	1.62124i	0.772798	−	0.634652i	$-0.218857\pi$
$678$		0			0
$679$	9.07911	−	7.74896i	0.348424	−	0.297378i
$680$		0			0
$681$	−2.15375	+	3.73041i	−0.0825320	+	0.142950i
$682$		0			0
$683$	4.24469	+	7.35202i	0.162419	+	0.281317i	0.935736	−	0.352702i	$-0.114737\pi$
$683$	4.24469	+	7.35202i	0.162419	+	0.281317i	−0.773317	+	0.634020i	$0.781404\pi$
$684$		0			0
$685$	4.44907			0.169990
$686$		0			0
$687$	14.4095			0.549755
$688$		0			0
$689$	0.146516	+	0.253774i	0.00558183	+	0.00966802i
$690$		0			0
$691$	−8.63770	+	14.9609i	−0.328593	+	0.569141i	−0.982233	−	0.187665i	$-0.939908\pi$
$691$	−8.63770	+	14.9609i	−0.328593	+	0.569141i	0.653640	+	0.756806i	$0.273241\pi$
$692$		0			0
$693$	−2.45790	+	2.09780i	−0.0933678	+	0.0796888i
$694$		0			0
$695$	0.734098	−	1.27149i	0.0278459	−	0.0482305i
$696$		0			0
$697$	11.0231	+	19.0926i	0.417530	+	0.723184i
$698$		0			0
$699$	35.9346			1.35917
$700$		0			0
$701$	−15.2340			−0.575382			−0.287691	−	0.957723i	$-0.592888\pi$
$701$	−15.2340			−0.575382			−0.287691	+	0.957723i	$0.592888\pi$
$702$		0			0
$703$	10.7451	+	18.6111i	0.405260	+	0.701931i
$704$		0			0
$705$	−5.45790	+	9.45336i	−0.205556	+	0.356034i
$706$		0			0
$707$	−40.3570	−	14.3066i	−1.51778	−	0.538056i
$708$		0			0
$709$	−4.16188	+	7.20859i	−0.156303	+	0.270724i	−0.933533	−	0.358492i	$-0.883291\pi$
$709$	−4.16188	+	7.20859i	−0.156303	+	0.270724i	0.777230	+	0.629217i	$0.216624\pi$
$710$		0			0
$711$	6.47609	+	11.2169i	0.242872	+	0.420667i
$712$		0			0
$713$	−13.5532			−0.507571
$714$		0			0
$715$	−0.423108			−0.0158233
$716$		0			0
$717$	−3.21472	−	5.56806i	−0.120056	−	0.207943i
$718$		0			0
$719$	−10.4058	+	18.0234i	−0.388071	+	0.672159i	−0.992190	−	0.124735i	$-0.960192\pi$
$719$	−10.4058	+	18.0234i	−0.388071	+	0.672159i	0.604119	+	0.796894i	$0.293525\pi$
$720$		0			0
$721$	−4.96561	−	26.8429i	−0.184929	−	0.999683i
$722$		0			0
$723$	8.64699	−	14.9770i	0.321585	−	0.557001i
$724$		0			0
$725$	5.76754	+	9.98968i	0.214201	+	0.371007i
$726$		0			0
$727$	28.0523			1.04040			0.520202	−	0.854043i	$-0.325857\pi$
$727$	28.0523			1.04040			0.520202	+	0.854043i	$0.325857\pi$
$728$		0			0
$729$	27.2200			1.00815
$730$		0			0
$731$	−20.8488	−	36.1112i	−0.771121	−	1.33562i
$732$		0			0
$733$	−14.4075	+	24.9545i	−0.532152	+	0.921715i	0.467143	+	0.884182i	$0.345283\pi$
$733$	−14.4075	+	24.9545i	−0.532152	+	0.921715i	−0.999295	+	0.0375330i	$0.988050\pi$
$734$		0			0
$735$	−1.63138	+	10.2550i	−0.0601745	+	0.378262i
$736$		0			0
$737$	3.75926	−	6.51123i	0.138474	−	0.239844i
$738$		0			0
$739$	−13.0310	−	22.5704i	−0.479355	−	0.830267i	0.520365	−	0.853944i	$-0.325796\pi$
$739$	−13.0310	−	22.5704i	−0.479355	−	0.830267i	−0.999720	+	0.0236773i	$0.992463\pi$
$740$		0			0
$741$	−2.23483			−0.0820986
$742$		0			0
$743$	−11.2002			−0.410894			−0.205447	−	0.978668i	$-0.565865\pi$
$743$	−11.2002			−0.410894			−0.205447	+	0.978668i	$0.565865\pi$
$744$		0			0
$745$	2.35394	+	4.07714i	0.0862416	+	0.149375i
$746$		0			0
$747$	9.95416	−	17.2411i	0.364204	−	0.630819i
$748$		0			0
$749$	−1.62674	−	8.79380i	−0.0594399	−	0.321319i
$750$		0			0
$751$	−17.5572	+	30.4100i	−0.640672	+	1.10968i	0.344611	+	0.938746i	$0.388011\pi$
$751$	−17.5572	+	30.4100i	−0.640672	+	1.10968i	−0.985283	+	0.170931i	$0.945323\pi$
$752$		0			0
$753$	−2.00796	−	3.47789i	−0.0731741	−	0.126741i
$754$		0			0
$755$	25.8375			0.940324
$756$		0			0
$757$	3.93638			0.143070			0.0715350	−	0.997438i	$-0.477210\pi$
$757$	3.93638			0.143070			0.0715350	+	0.997438i	$0.477210\pi$
$758$		0			0
$759$	−4.36266	−	7.55635i	−0.158355	−	0.274278i
$760$		0			0
$761$	−12.8892	+	22.3247i	−0.467233	+	0.809271i	−0.999299	−	0.0374313i	$-0.988082\pi$
$761$	−12.8892	+	22.3247i	−0.467233	+	0.809271i	0.532066	+	0.846703i	$0.321416\pi$
$762$		0			0
$763$	−17.6907	−	6.27138i	−0.640447	−	0.227039i
$764$		0			0
$765$	−2.28130	+	3.95132i	−0.0824805	+	0.142860i
$766$		0			0
$767$	−1.27974	−	2.21658i	−0.0462088	−	0.0800360i
$768$		0			0
$769$	14.3551			0.517657			0.258828	−	0.965923i	$-0.416664\pi$
$769$	14.3551			0.517657			0.258828	+	0.965923i	$0.416664\pi$
$770$		0			0
$771$	−31.8063			−1.14547
$772$		0			0
$773$	0.445542	+	0.771702i	0.0160250	+	0.0277562i	0.873927	−	0.486058i	$-0.161566\pi$
$773$	0.445542	+	0.771702i	0.0160250	+	0.0277562i	−0.857902	+	0.513814i	$0.828232\pi$
$774$		0			0
$775$	3.89749	−	6.75064i	0.140002	−	0.242490i
$776$		0			0
$777$	−13.0929	+	11.1747i	−0.469705	+	0.400890i
$778$		0			0
$779$	14.4586	−	25.0431i	0.518035	−	0.897263i
$780$		0			0
$781$	−2.05286	−	3.55565i	−0.0734570	−	0.127231i
$782$		0			0
$783$	17.2586			0.616774
$784$		0			0
$785$	3.96346			0.141462
$786$		0			0
$787$	−23.9936	−	41.5581i	−0.855278	−	1.48138i	−0.876387	−	0.481608i	$-0.840053\pi$
$787$	−23.9936	−	41.5581i	−0.855278	−	1.48138i	0.0211088	−	0.999777i	$-0.493280\pi$
$788$		0			0
$789$	14.2501	−	24.6818i	0.507316	−	0.878697i
$790$		0			0
$791$	8.08049	−	6.89664i	0.287309	−	0.245216i
$792$		0			0
$793$	2.27239	−	3.93590i	0.0806949	−	0.139768i
$794$		0			0
$795$	0.571375	+	0.989651i	0.0202646	+	0.0350993i
$796$		0			0
$797$	42.2980			1.49827			0.749136	−	0.662416i	$-0.230469\pi$
$797$	42.2980			1.49827			0.749136	+	0.662416i	$0.230469\pi$
$798$		0			0
$799$	24.7137			0.874307
$800$		0			0
$801$	5.24923	+	9.09194i	0.185472	+	0.321248i
$802$		0			0
$803$	2.68438	−	4.64947i	0.0947296	−	0.164076i
$804$		0			0
$805$	18.1469	+	6.43309i	0.639593	+	0.226737i
$806$		0			0
$807$	0.250499	−	0.433877i	0.00881799	−	0.0152732i
$808$		0			0
$809$	25.4997	+	44.1667i	0.896520	+	1.55282i	0.831912	+	0.554908i	$0.187246\pi$
$809$	25.4997	+	44.1667i	0.896520	+	1.55282i	0.0646083	+	0.997911i	$0.479420\pi$
$810$		0			0
$811$	−20.7203			−0.727589			−0.363794	−	0.931479i	$-0.618519\pi$
$811$	−20.7203			−0.727589			−0.363794	+	0.931479i	$0.618519\pi$
$812$		0			0
$813$	−36.1621			−1.26826
$814$		0			0
$815$	−12.2229	−	21.1707i	−0.428150	−	0.741577i
$816$		0			0
$817$	−27.3467	+	47.3658i	−0.956738	+	1.65712i
$818$		0			0
$819$	0.223593	+	1.20869i	0.00781297	+	0.0422352i
$820$		0			0
$821$	−11.8548	+	20.5332i	−0.413736	+	0.716613i	−0.995295	−	0.0968921i	$-0.969110\pi$
$821$	−11.8548	+	20.5332i	−0.413736	+	0.716613i	0.581558	+	0.813505i	$0.302443\pi$
$822$		0			0
$823$	−3.35818	−	5.81653i	−0.117059	−	0.202752i	0.801542	−	0.597938i	$-0.204013\pi$
$823$	−3.35818	−	5.81653i	−0.117059	−	0.202752i	−0.918601	+	0.395187i	$0.870680\pi$
$824$		0			0
$825$	5.01828			0.174714
$826$		0			0
$827$	32.4414			1.12810			0.564048	−	0.825742i	$-0.309243\pi$
$827$	32.4414			1.12810			0.564048	+	0.825742i	$0.309243\pi$
$828$		0			0
$829$	17.7520	+	30.7473i	0.616551	+	1.06790i	0.990110	+	0.140291i	$0.0448038\pi$
$829$	17.7520	+	30.7473i	0.616551	+	1.06790i	−0.373560	+	0.927606i	$0.621863\pi$
$830$		0			0
$831$	−6.56971	+	11.3791i	−0.227901	+	0.394736i
$832$		0			0
$833$	21.9538	−	8.41017i	0.760655	−	0.291395i
$834$		0			0
$835$	3.47898	−	6.02577i	0.120395	−	0.208530i
$836$		0			0
$837$	−5.83137	−	10.1002i	−0.201562	−	0.349115i
$838$		0			0
$839$	−46.9126			−1.61960			−0.809802	−	0.586704i	$-0.800425\pi$
$839$	−46.9126			−1.61960			−0.809802	+	0.586704i	$0.800425\pi$
$840$		0			0
$841$	−19.6023			−0.675942
$842$		0			0
$843$	−11.1957	−	19.3915i	−0.385601	−	0.667880i
$844$		0			0
$845$	7.14946	−	12.3832i	0.245949	−	0.425996i
$846$		0			0
$847$	0.481266	+	2.60161i	0.0165365	+	0.0893924i
$848$		0			0
$849$	10.2116	−	17.6870i	0.350461	−	0.607017i
$850$		0			0
$851$	15.9580	+	27.6401i	0.547033	+	0.947489i
$852$		0			0
$853$	−36.1884			−1.23907			−0.619533	−	0.784971i	$-0.712678\pi$
$853$	−36.1884			−1.23907			−0.619533	+	0.784971i	$0.712678\pi$
$854$		0			0
$855$	5.98460			0.204669
$856$		0			0
$857$	11.6548	+	20.1867i	0.398120	+	0.689564i	0.993494	−	0.113885i	$-0.0363295\pi$
$857$	11.6548	+	20.1867i	0.398120	+	0.689564i	−0.595374	+	0.803449i	$0.702996\pi$
$858$		0			0
$859$	−25.6819	+	44.4823i	−0.876254	+	1.51772i	−0.0208331	+	0.999783i	$0.506632\pi$
$859$	−25.6819	+	44.4823i	−0.876254	+	1.51772i	−0.855421	+	0.517933i	$0.826701\pi$
$860$		0			0
$861$	21.8310	+	7.73913i	0.744000	+	0.263749i
$862$		0			0
$863$	−13.4051	+	23.2183i	−0.456314	+	0.790360i	−0.998763	−	0.0497294i	$-0.984164\pi$
$863$	−13.4051	+	23.2183i	−0.456314	+	0.790360i	0.542448	+	0.840089i	$0.317497\pi$
$864$		0			0
$865$	−0.242925	−	0.420759i	−0.00825971	−	0.0143062i
$866$		0			0
$867$	7.62902			0.259095
$868$		0			0
$869$	10.6047			0.359741
$870$		0			0
$871$	−1.42999	−	2.47681i	−0.0484533	−	0.0839236i
$872$		0			0
$873$	2.75509	−	4.77196i	0.0932457	−	0.161506i
$874$		0			0
$875$	−19.6148	+	16.7411i	−0.663102	+	0.565953i
$876$		0			0
$877$	−7.18585	+	12.4463i	−0.242649	+	0.420280i	−0.961468	−	0.274917i	$-0.911350\pi$
$877$	−7.18585	+	12.4463i	−0.242649	+	0.420280i	0.718819	+	0.695197i	$0.244683\pi$
$878$		0			0
$879$	6.21050	+	10.7569i	0.209475	+	0.362821i
$880$		0			0
$881$	41.8248			1.40911			0.704557	−	0.709648i	$-0.251146\pi$
$881$	41.8248			1.40911			0.704557	+	0.709648i	$0.251146\pi$
$882$		0			0
$883$	27.4995			0.925431			0.462715	−	0.886507i	$-0.346875\pi$
$883$	27.4995			0.925431			0.462715	+	0.886507i	$0.346875\pi$
$884$		0			0
$885$	−4.99065	−	8.64407i	−0.167759	−	0.290567i
$886$		0			0
$887$	−13.6898	+	23.7114i	−0.459658	+	0.796151i	−0.998943	−	0.0459723i	$-0.985361\pi$
$887$	−13.6898	+	23.7114i	−0.459658	+	0.796151i	0.539285	+	0.842124i	$0.318695\pi$
$888$		0			0
$889$	−19.8502	+	16.9420i	−0.665755	+	0.568217i
$890$		0			0
$891$	1.92210	−	3.32918i	0.0643929	−	0.111532i
$892$		0			0
$893$	−16.2080	−	28.0732i	−0.542382	−	0.939432i
$894$		0			0
$895$	−9.10516			−0.304352
$896$		0			0
$897$	−3.31903			−0.110819
$898$		0			0
$899$	−3.17530	−	5.49978i	−0.105902	−	0.183428i
$900$		0			0
$901$	1.29361	−	2.24060i	0.0430964	−	0.0746452i
$902$		0			0
$903$	−41.2906	−	14.6376i	−1.37406	−	0.487108i
$904$		0			0
$905$	−10.3214	+	17.8772i	−0.343094	+	0.594257i
$906$		0			0
$907$	1.15174	+	1.99487i	0.0382429	+	0.0662387i	0.884513	−	0.466515i	$-0.154491\pi$
$907$	1.15174	+	1.99487i	0.0382429	+	0.0662387i	−0.846270	+	0.532754i	$0.821157\pi$
$908$		0			0
$909$	−19.7660			−0.655598
$910$		0			0
$911$	16.1674			0.535651			0.267826	−	0.963467i	$-0.413695\pi$
$911$	16.1674			0.535651			0.267826	+	0.963467i	$0.413695\pi$
$912$		0			0
$913$	−8.15007	−	14.1163i	−0.269728	−	0.467183i
$914$		0			0
$915$	8.86172	−	15.3489i	0.292959	−	0.507420i
$916$		0			0
$917$	2.81147	+	15.1982i	0.0928430	+	0.501888i
$918$		0			0
$919$	−20.3091	+	35.1763i	−0.669935	+	1.16036i	0.307987	+	0.951390i	$0.400345\pi$
$919$	−20.3091	+	35.1763i	−0.669935	+	1.16036i	−0.977922	+	0.208970i	$0.932989\pi$
$920$		0			0
$921$	−12.8789	−	22.3069i	−0.424373	−	0.735036i
$922$		0			0
$923$	−1.56178			−0.0514065
$924$		0			0
$925$	−18.3561			−0.603546
$926$		0			0
$927$	−6.30088	−	10.9134i	−0.206948	−	0.358444i
$928$		0			0
$929$	−10.3121	+	17.8610i	−0.338328	+	0.586001i	−0.984118	−	0.177514i	$-0.943195\pi$
$929$	−10.3121	+	17.8610i	−0.338328	+	0.586001i	0.645791	+	0.763515i	$0.276528\pi$
$930$		0			0
$931$	−23.9515	−	19.4225i	−0.784977	−	0.636546i
$932$		0			0
$933$	−4.65654	+	8.06536i	−0.152448	+	0.264048i
$934$		0			0
$935$	1.86783	+	3.23518i	0.0610847	+	0.105802i
$936$		0			0
$937$	−43.6953			−1.42746			−0.713732	−	0.700419i	$-0.752997\pi$
$937$	−43.6953			−1.42746			−0.713732	+	0.700419i	$0.752997\pi$
$938$		0			0
$939$	−25.9201			−0.845870
$940$		0			0
$941$	30.1857	+	52.2831i	0.984025	+	1.70438i	0.646193	+	0.763174i	$0.276360\pi$
$941$	30.1857	+	52.2831i	0.984025	+	1.70438i	0.337832	+	0.941206i	$0.390306\pi$
$942$		0			0
$943$	21.4731	−	37.1925i	0.699260	−	1.21115i
$944$		0			0
$945$	3.01372	+	16.2915i	0.0980362	+	0.529961i
$946$		0			0
$947$	19.9462	−	34.5478i	0.648165	−	1.12265i	−0.335396	−	0.942077i	$-0.608870\pi$
$947$	19.9462	−	34.5478i	0.648165	−	1.12265i	0.983561	−	0.180577i	$-0.0577964\pi$
$948$		0			0
$949$	−1.02111	−	1.76862i	−0.0331467	−	0.0574118i
$950$		0			0
$951$	−42.1192			−1.36581
$952$		0			0
$953$	27.3714			0.886648			0.443324	−	0.896362i	$-0.353799\pi$
$953$	27.3714			0.886648			0.443324	+	0.896362i	$0.353799\pi$
$954$		0			0
$955$	0.668210	+	1.15737i	0.0216228	+	0.0374517i
$956$		0			0
$957$	2.04421	−	3.54067i	0.0660798	−	0.114454i
$958$		0			0
$959$	−9.97451	−	3.53597i	−0.322094	−	0.114183i
$960$		0			0
$961$	13.3543	−	23.1302i	0.430782	−	0.746137i
$962$		0			0
$963$	−2.06418	−	3.57526i	−0.0665173	−	0.115211i
$964$		0			0
$965$	−22.7646			−0.732818
$966$		0			0
$967$	28.6973			0.922844			0.461422	−	0.887181i	$-0.347339\pi$
$967$	28.6973			0.922844			0.461422	+	0.887181i	$0.347339\pi$
$968$		0			0
$969$	9.86579	+	17.0881i	0.316935	+	0.548947i
$970$		0			0
$971$	7.88317	−	13.6540i	0.252983	−	0.438179i	−0.711363	−	0.702825i	$-0.751922\pi$
$971$	7.88317	−	13.6540i	0.252983	−	0.438179i	0.964346	+	0.264646i	$0.0852550\pi$
$972$		0			0
$973$	−2.65634	+	2.26717i	−0.0851583	+	0.0726820i
$974$		0			0
$975$	0.954453	−	1.65316i	0.0305670	−	0.0529435i
$976$		0			0
$977$	14.8868	+	25.7847i	0.476271	+	0.824926i	0.999630	−	0.0271861i	$-0.00865468\pi$
$977$	14.8868	+	25.7847i	0.476271	+	0.824926i	−0.523359	+	0.852112i	$0.675321\pi$
$978$		0			0
$979$	8.59572			0.274720
$980$		0			0
$981$	−8.66455			−0.276638
$982$		0			0
$983$	24.4485	+	42.3460i	0.779785	+	1.35063i	0.932066	+	0.362289i	$0.118005\pi$
$983$	24.4485	+	42.3460i	0.779785	+	1.35063i	−0.152281	+	0.988337i	$0.548662\pi$
$984$		0			0
$985$	8.60642	−	14.9068i	0.274223	−	0.474969i
$986$		0			0
$987$	19.7494	−	16.8560i	0.628632	−	0.536533i
$988$		0			0
$989$	−40.6136	+	70.3448i	−1.29144	+	2.23683i
$990$		0			0
$991$	0.856466	+	1.48344i	0.0272065	+	0.0471231i	0.879308	−	0.476253i	$-0.158005\pi$
$991$	0.856466	+	1.48344i	0.0272065	+	0.0471231i	−0.852102	+	0.523376i	$0.824672\pi$
$992$		0			0
$993$	24.9357			0.791311
$994$		0			0
$995$	14.6540			0.464563
$996$		0			0
$997$	10.8058	+	18.7162i	0.342223	+	0.592748i	0.984845	−	0.173435i	$-0.0554867\pi$
$997$	10.8058	+	18.7162i	0.342223	+	0.592748i	−0.642622	+	0.766183i	$0.722153\pi$
$998$		0			0
$999$	−13.7321	+	23.7847i	−0.434465	+	0.752515i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.666828 + 1.15498i) q^{3} +(-0.556149 + 0.963278i) q^{5} +(2.01243 - 1.71759i) q^{7} +(0.610680 - 1.05773i) q^{9} +O(q^{10})\)	\(q+(0.666828 + 1.15498i) q^{3} +(-0.556149 + 0.963278i) q^{5} +(2.01243 - 1.71759i) q^{7} +(0.610680 - 1.05773i) q^{9} +(-0.500000 - 0.866025i) q^{11} -0.380391 q^{13} -1.48342 q^{15} +(1.67926 + 2.90856i) q^{17} +(2.20262 - 3.81506i) q^{19} +(3.32573 + 1.17898i) q^{21} +(3.27120 - 5.66589i) q^{23} +(1.88140 + 3.25867i) q^{25} +5.62984 q^{27} +3.06556 q^{29} +(-1.03580 - 1.79405i) q^{31} +(0.666828 - 1.15498i) q^{33} +(0.535311 + 2.89377i) q^{35} +(-2.43916 + 4.22476i) q^{37} +(-0.253656 - 0.439344i) q^{39} +6.56428 q^{41} -12.4155 q^{43} +(0.679258 + 1.17651i) q^{45} +(3.67926 - 6.37266i) q^{47} +(1.09974 - 6.91307i) q^{49} +(-2.23955 + 3.87902i) q^{51} +(-0.385173 - 0.667140i) q^{53} +1.11230 q^{55} +5.87509 q^{57} +(3.36428 + 5.82710i) q^{59} +(-5.97383 + 10.3470i) q^{61} +(-0.587798 - 3.17750i) q^{63} +(0.211554 - 0.366422i) q^{65} +(3.75926 + 6.51123i) q^{67} +8.72532 q^{69} +4.10572 q^{71} +(2.68438 + 4.64947i) q^{73} +(-2.50914 + 4.34595i) q^{75} +(-2.49369 - 0.884018i) q^{77} +(-5.30237 + 9.18397i) q^{79} +(1.92210 + 3.32918i) q^{81} +16.3001 q^{83} -3.73567 q^{85} +(2.04421 + 3.54067i) q^{87} +(-4.29786 + 7.44411i) q^{89} +(-0.765510 + 0.653357i) q^{91} +(1.38140 - 2.39265i) q^{93} +(2.44997 + 4.24348i) q^{95} +4.51152 q^{97} -1.22136 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{3} - 4 q^{5} + 2 q^{7}+O(q^{10}) \) 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

Related objects

Downloads

Learn more