LMFDB - Embedded newform 1232.2.q.l.529.1

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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 308)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.1
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	1232.529
Dual form			1232.2.q.l.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.794182 + 1.37556i) q^{3} +(-1.64400 - 2.84748i) q^{5} +(-2.64400 - 0.0963576i) q^{7} +(0.238550 + 0.413181i) q^{9} +O(q^{10})$	\(q+(-0.794182 + 1.37556i) q^{3} +(-1.64400 - 2.84748i) q^{5} +(-2.64400 - 0.0963576i) q^{7} +(0.238550 + 0.413181i) q^{9} +(-0.500000 + 0.866025i) q^{11} -4.98762 q^{13} +5.22253 q^{15} +(1.84981 - 3.20397i) q^{17} +(2.84981 + 4.93602i) q^{19} +(2.23236 - 3.56046i) q^{21} +(0.349814 + 0.605896i) q^{23} +(-2.90545 + 5.03238i) q^{25} -5.52290 q^{27} +7.68725 q^{29} +(5.25526 - 9.10238i) q^{31} +(-0.794182 - 1.37556i) q^{33} +(4.07234 + 7.68715i) q^{35} +(5.28799 + 9.15907i) q^{37} +(3.96108 - 6.86079i) q^{39} +7.81089 q^{41} -1.63416 q^{43} +(0.784350 - 1.35853i) q^{45} +(1.15019 + 1.99218i) q^{47} +(6.98143 + 0.509538i) q^{49} +(2.93818 + 5.08907i) q^{51} +(1.60507 - 2.78007i) q^{53} +3.28799 q^{55} -9.05308 q^{57} +(3.88255 - 6.72477i) q^{59} +(-2.47710 - 4.29046i) q^{61} +(-0.590912 - 1.11543i) q^{63} +(8.19963 + 14.2022i) q^{65} +(-0.810892 + 1.40451i) q^{67} -1.11126 q^{69} +2.30037 q^{71} +(-2.70582 + 4.68661i) q^{73} +(-4.61491 - 7.99325i) q^{75} +(1.40545 - 2.24159i) q^{77} +(-1.36652 - 2.36689i) q^{79} +(3.67054 - 6.35756i) q^{81} -6.65383 q^{83} -12.1643 q^{85} +(-6.10507 + 10.5743i) q^{87} +(6.43199 + 11.1405i) q^{89} +(13.1872 + 0.480595i) q^{91} +(8.34727 + 14.4579i) q^{93} +(9.37017 - 16.2296i) q^{95} +18.6094 q^{97} -0.477100 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} + 2 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 6 * q + q^3 + 2 * q^5 - 4 * q^7 - 4 * q^9	$ 6 q + q^{3} + 2 q^{5} - 4 q^{7} - 4 q^{9} - 3 q^{11} + 6 q^{13} + 30 q^{15} + 5 q^{17} + 11 q^{19} - 10 q^{21} - 4 q^{23} - 11 q^{25} - 44 q^{27} - 2 q^{29} + 19 q^{31} + q^{33} + 17 q^{35} + 8 q^{37} + 17 q^{39} + 34 q^{41} - 20 q^{43} + 21 q^{45} + 13 q^{47} - 12 q^{49} - 9 q^{53} - 4 q^{55} + 4 q^{57} + 6 q^{59} - 4 q^{61} - 50 q^{63} + 37 q^{65} + 8 q^{67} - 6 q^{69} + 26 q^{71} - 22 q^{73} + 13 q^{75} + 2 q^{77} + 5 q^{79} - 19 q^{81} - 6 q^{83} - 14 q^{85} - 18 q^{87} + 3 q^{89} + 31 q^{91} - 14 q^{93} + 3 q^{95} + 50 q^{97} + 8 q^{99}+O(q^{100}) $ 6 * q + q^3 + 2 * q^5 - 4 * q^7 - 4 * q^9 - 3 * q^11 + 6 * q^13 + 30 * q^15 + 5 * q^17 + 11 * q^19 - 10 * q^21 - 4 * q^23 - 11 * q^25 - 44 * q^27 - 2 * q^29 + 19 * q^31 + q^33 + 17 * q^35 + 8 * q^37 + 17 * q^39 + 34 * q^41 - 20 * q^43 + 21 * q^45 + 13 * q^47 - 12 * q^49 - 9 * q^53 - 4 * q^55 + 4 * q^57 + 6 * q^59 - 4 * q^61 - 50 * q^63 + 37 * q^65 + 8 * q^67 - 6 * q^69 + 26 * q^71 - 22 * q^73 + 13 * q^75 + 2 * q^77 + 5 * q^79 - 19 * q^81 - 6 * q^83 - 14 * q^85 - 18 * q^87 + 3 * q^89 + 31 * q^91 - 14 * q^93 + 3 * q^95 + 50 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	−0.794182	+	1.37556i	−0.458521	+	0.794182i	−0.998883	−	0.0472507i	$-0.984954\pi$
$3$	−0.794182	+	1.37556i	−0.458521	+	0.794182i	0.540362	+	0.841433i	$0.318287\pi$
$4$		0			0
$5$	−1.64400	−	2.84748i	−0.735217	−	1.27343i	−0.954628	−	0.297801i	$-0.903747\pi$
$5$	−1.64400	−	2.84748i	−0.735217	−	1.27343i	0.219411	−	0.975633i	$-0.429587\pi$
$6$		0			0
$7$	−2.64400	−	0.0963576i	−0.999337	−	0.0364197i
$7$	−2.64400	−	0.0963576i	−0.999337	−	0.0364197i
$8$		0			0
$9$	0.238550	+	0.413181i	0.0795166	+	0.137727i
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$		0			0
$13$	−4.98762			−1.38332			−0.691658	−	0.722225i	$-0.743120\pi$
$13$	−4.98762			−1.38332			−0.691658	+	0.722225i	$0.743120\pi$
$14$		0			0
$15$	5.22253			1.34845
$16$		0			0
$17$	1.84981	−	3.20397i	0.448646	−	0.777077i	−0.549652	−	0.835393i	$-0.685240\pi$
$17$	1.84981	−	3.20397i	0.448646	−	0.777077i	0.998298	+	0.0583162i	$0.0185731\pi$
$18$		0			0
$19$	2.84981	+	4.93602i	0.653792	+	1.13240i	0.982195	+	0.187864i	$0.0601563\pi$
$19$	2.84981	+	4.93602i	0.653792	+	1.13240i	−0.328403	+	0.944538i	$0.606510\pi$
$20$		0			0
$21$	2.23236	−	3.56046i	0.487141	−	0.776956i
$22$		0			0
$23$	0.349814	+	0.605896i	0.0729413	+	0.126338i	0.900189	−	0.435499i	$-0.143428\pi$
$23$	0.349814	+	0.605896i	0.0729413	+	0.126338i	−0.827248	+	0.561837i	$0.810095\pi$
$24$		0			0
$25$	−2.90545	+	5.03238i	−0.581089	+	1.00648i
$26$		0			0
$27$	−5.52290			−1.06288
$28$		0			0
$29$	7.68725			1.42749			0.713743	−	0.700408i	$-0.246998\pi$
$29$	7.68725			1.42749			0.713743	+	0.700408i	$0.246998\pi$
$30$		0			0
$31$	5.25526	−	9.10238i	0.943873	−	1.63484i	0.185880	−	0.982573i	$-0.440487\pi$
$31$	5.25526	−	9.10238i	0.943873	−	1.63484i	0.757993	−	0.652263i	$-0.226180\pi$
$32$		0			0
$33$	−0.794182	−	1.37556i	−0.138249	−	0.239455i
$34$		0			0
$35$	4.07234	+	7.68715i	0.688351	+	1.29937i
$36$		0			0
$37$	5.28799	+	9.15907i	0.869341	+	1.50574i	0.862672	+	0.505764i	$0.168789\pi$
$37$	5.28799	+	9.15907i	0.869341	+	1.50574i	0.00666881	+	0.999978i	$0.497877\pi$
$38$		0			0
$39$	3.96108	−	6.86079i	0.634280	−	1.09861i
$40$		0			0
$41$	7.81089			1.21986			0.609928	−	0.792457i	$-0.291198\pi$
$41$	7.81089			1.21986			0.609928	+	0.792457i	$0.291198\pi$
$42$		0			0
$43$	−1.63416			−0.249208			−0.124604	−	0.992207i	$-0.539766\pi$
$43$	−1.63416			−0.249208			−0.124604	+	0.992207i	$0.539766\pi$
$44$		0			0
$45$	0.784350	−	1.35853i	0.116924	−	0.202518i
$46$		0			0
$47$	1.15019	+	1.99218i	0.167772	+	0.290589i	0.937636	−	0.347618i	$-0.113009\pi$
$47$	1.15019	+	1.99218i	0.167772	+	0.290589i	−0.769864	+	0.638208i	$0.779676\pi$
$48$		0			0
$49$	6.98143	+	0.509538i	0.997347	+	0.0727912i
$50$		0			0
$51$	2.93818	+	5.08907i	0.411427	+	0.712613i
$52$		0			0
$53$	1.60507	−	2.78007i	0.220474	−	0.381872i	−0.734478	−	0.678632i	$-0.762573\pi$
$53$	1.60507	−	2.78007i	0.220474	−	0.381872i	0.954952	+	0.296760i	$0.0959063\pi$
$54$		0			0
$55$	3.28799			0.443353
$56$		0			0
$57$	−9.05308			−1.19911
$58$		0			0
$59$	3.88255	−	6.72477i	0.505464	−	0.875490i	−0.494516	−	0.869169i	$-0.664655\pi$
$59$	3.88255	−	6.72477i	0.505464	−	0.875490i	0.999980	−	0.00632132i	$-0.00201215\pi$
$60$		0			0
$61$	−2.47710	−	4.29046i	−0.317160	−	0.549337i	0.662734	−	0.748855i	$-0.269396\pi$
$61$	−2.47710	−	4.29046i	−0.317160	−	0.549337i	−0.979894	+	0.199517i	$0.936063\pi$
$62$		0			0
$63$	−0.590912	−	1.11543i	−0.0744479	−	0.140531i
$64$		0			0
$65$	8.19963	+	14.2022i	1.01704	+	1.76156i
$66$		0			0
$67$	−0.810892	+	1.40451i	−0.0990663	+	0.171588i	−0.911298	−	0.411747i	$-0.864919\pi$
$67$	−0.810892	+	1.40451i	−0.0990663	+	0.171588i	0.812232	+	0.583334i	$0.198252\pi$
$68$		0			0
$69$	−1.11126			−0.133780
$70$		0			0
$71$	2.30037			0.273004			0.136502	−	0.990640i	$-0.456414\pi$
$71$	2.30037			0.273004			0.136502	+	0.990640i	$0.456414\pi$
$72$		0			0
$73$	−2.70582	+	4.68661i	−0.316692	+	0.548527i	−0.979796	−	0.200001i	$-0.935906\pi$
$73$	−2.70582	+	4.68661i	−0.316692	+	0.548527i	0.663104	+	0.748528i	$0.269239\pi$
$74$		0			0
$75$	−4.61491	−	7.99325i	−0.532883	−	0.922981i
$76$		0			0
$77$	1.40545	−	2.24159i	0.160165	−	0.255453i
$78$		0			0
$79$	−1.36652	−	2.36689i	−0.153746	−	0.266296i	0.778856	−	0.627203i	$-0.215800\pi$
$79$	−1.36652	−	2.36689i	−0.153746	−	0.266296i	−0.932602	+	0.360907i	$0.882467\pi$
$80$		0			0
$81$	3.67054	−	6.35756i	0.407838	−	0.706395i
$82$		0			0
$83$	−6.65383			−0.730352			−0.365176	−	0.930938i	$-0.618991\pi$
$83$	−6.65383			−0.730352			−0.365176	+	0.930938i	$0.618991\pi$
$84$		0			0
$85$	−12.1643			−1.31941
$86$		0			0
$87$	−6.10507	+	10.5743i	−0.654533	+	1.13368i
$88$		0			0
$89$	6.43199	+	11.1405i	0.681789	+	1.18089i	0.974434	+	0.224673i	$0.0721313\pi$
$89$	6.43199	+	11.1405i	0.681789	+	1.18089i	−0.292645	+	0.956221i	$0.594535\pi$
$90$		0			0
$91$	13.1872	+	0.480595i	1.38240	+	0.0503801i
$92$		0			0
$93$	8.34727	+	14.4579i	0.865571	+	1.49921i
$94$		0			0
$95$	9.37017	−	16.2296i	0.961359	−	1.66512i
$96$		0			0
$97$	18.6094			1.88950			0.944749	−	0.327794i	$-0.106305\pi$
$97$	18.6094			1.88950			0.944749	+	0.327794i	$0.106305\pi$
$98$		0			0
$99$	−0.477100			−0.0479503
$100$		0			0
$101$	−3.27197	+	5.66722i	−0.325573	+	0.563909i	−0.981628	−	0.190804i	$-0.938891\pi$
$101$	−3.27197	+	5.66722i	−0.325573	+	0.563909i	0.656055	+	0.754713i	$0.272224\pi$
$102$		0			0
$103$	1.01602	+	1.75980i	0.100112	+	0.173398i	0.911730	−	0.410789i	$-0.134747\pi$
$103$	1.01602	+	1.75980i	0.100112	+	0.173398i	−0.811619	+	0.584187i	$0.801413\pi$
$104$		0			0
$105$	−13.8083	−	0.503230i	−1.34756	−	0.0491102i
$106$		0			0
$107$	9.74288	+	16.8752i	0.941880	+	1.63138i	0.761881	+	0.647717i	$0.224276\pi$
$107$	9.74288	+	16.8752i	0.941880	+	1.63138i	0.179999	+	0.983667i	$0.442391\pi$
$108$		0			0
$109$	−4.53273	+	7.85092i	−0.434157	+	0.751982i	−0.997226	−	0.0744276i	$-0.976287\pi$
$109$	−4.53273	+	7.85092i	−0.434157	+	0.751982i	0.563069	+	0.826410i	$0.309620\pi$
$110$		0			0
$111$	−16.7985			−1.59444
$112$		0			0
$113$	−8.14468			−0.766187			−0.383094	−	0.923709i	$-0.625141\pi$
$113$	−8.14468			−0.766187			−0.383094	+	0.923709i	$0.625141\pi$
$114$		0			0
$115$	1.15019	−	1.99218i	0.107255	−	0.185772i
$116$		0			0
$117$	−1.18980	−	2.06079i	−0.109997	−	0.190520i
$118$		0			0
$119$	−5.19963	+	8.29305i	−0.476649	+	0.760222i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	−6.20327	+	10.7444i	−0.559330	+	0.968788i
$124$		0			0
$125$	2.66621			0.238473
$126$		0			0
$127$	7.98762			0.708787			0.354393	−	0.935096i	$-0.384687\pi$
$127$	7.98762			0.708787			0.354393	+	0.935096i	$0.384687\pi$
$128$		0			0
$129$	1.29782	−	2.24790i	0.114267	−	0.197916i
$130$		0			0
$131$	2.77816	+	4.81191i	0.242729	+	0.420419i	0.961491	−	0.274838i	$-0.0886241\pi$
$131$	2.77816	+	4.81191i	0.242729	+	0.420419i	−0.718762	+	0.695257i	$0.755291\pi$
$132$		0			0
$133$	−7.05927	−	13.3254i	−0.612117	−	1.15546i
$134$		0			0
$135$	9.07963	+	15.7264i	0.781450	+	1.35351i
$136$		0			0
$137$	0.105074	−	0.181994i	0.00897710	−	0.0155488i	−0.861502	−	0.507754i	$-0.830476\pi$
$137$	0.105074	−	0.181994i	0.00897710	−	0.0155488i	0.870479	+	0.492205i	$0.163809\pi$
$138$		0			0
$139$	−11.0000			−0.933008			−0.466504	−	0.884519i	$-0.654487\pi$
$139$	−11.0000			−0.933008			−0.466504	+	0.884519i	$0.654487\pi$
$140$		0			0
$141$	−3.65383			−0.307708
$142$		0			0
$143$	2.49381	−	4.31941i	0.208543	−	0.361207i
$144$		0			0
$145$	−12.6378	−	21.8893i	−1.04951	−	1.81781i
$146$		0			0
$147$	−6.24543	+	9.19874i	−0.515114	+	0.758699i
$148$		0			0
$149$	−6.18725	−	10.7166i	−0.506879	−	0.877940i	−0.999968	−	0.00796165i	$-0.997466\pi$
$149$	−6.18725	−	10.7166i	−0.506879	−	0.877940i	0.493089	−	0.869979i	$-0.335868\pi$
$150$		0			0
$151$	3.67054	−	6.35756i	0.298704	−	0.517371i	−0.677136	−	0.735858i	$-0.736779\pi$
$151$	3.67054	−	6.35756i	0.298704	−	0.517371i	0.975840	+	0.218487i	$0.0701123\pi$
$152$		0			0
$153$	1.76509			0.142699
$154$		0			0
$155$	−34.5585			−2.77581
$156$		0			0
$157$	4.68911	−	8.12177i	0.374232	−	0.648188i	−0.615980	−	0.787762i	$-0.711240\pi$
$157$	4.68911	−	8.12177i	0.374232	−	0.648188i	0.990212	+	0.139574i	$0.0445732\pi$
$158$		0			0
$159$	2.54944	+	4.41576i	0.202184	+	0.350193i
$160$		0			0
$161$	−0.866524	−	1.63569i	−0.0682917	−	0.128911i
$162$		0			0
$163$	−7.89926	−	13.6819i	−0.618718	−	1.07165i	−0.989720	−	0.143018i	$-0.954319\pi$
$163$	−7.89926	−	13.6819i	−0.618718	−	1.07165i	0.371003	−	0.928632i	$-0.379014\pi$
$164$		0			0
$165$	−2.61126	+	4.52284i	−0.203287	+	0.352103i
$166$		0			0
$167$	8.26323			0.639428			0.319714	−	0.947514i	$-0.396413\pi$
$167$	8.26323			0.639428			0.319714	+	0.947514i	$0.396413\pi$
$168$		0			0
$169$	11.8764			0.913566
$170$		0			0
$171$	−1.35965	+	2.35498i	−0.103975	+	0.180089i
$172$		0			0
$173$	5.30470	+	9.18801i	0.403309	+	0.698552i	0.994123	−	0.108256i	$-0.0345266\pi$
$173$	5.30470	+	9.18801i	0.403309	+	0.698552i	−0.590814	+	0.806808i	$0.701193\pi$
$174$		0			0
$175$	8.16690	−	13.0256i	0.617359	−	0.984645i
$176$		0			0
$177$	6.16690	+	10.6814i	0.463532	+	0.802862i
$178$		0			0
$179$	5.28180	−	9.14835i	0.394780	−	0.683780i	−0.598293	−	0.801278i	$-0.704154\pi$
$179$	5.28180	−	9.14835i	0.394780	−	0.683780i	0.993073	+	0.117498i	$0.0374873\pi$
$180$		0			0
$181$	−20.4079			−1.51691			−0.758454	−	0.651726i	$-0.774045\pi$
$181$	−20.4079			−1.51691			−0.758454	+	0.651726i	$0.774045\pi$
$182$		0			0
$183$	7.86907			0.581699
$184$		0			0
$185$	17.3869	−	30.1150i	1.27831	−	2.21410i
$186$		0			0
$187$	1.84981	+	3.20397i	0.135272	+	0.234298i
$188$		0			0
$189$	14.6025	+	0.532173i	1.06218	+	0.0387099i
$190$		0			0
$191$	11.1996	+	19.3983i	0.810377	+	1.40361i	0.912601	+	0.408852i	$0.134071\pi$
$191$	11.1996	+	19.3983i	0.810377	+	1.40361i	−0.102224	+	0.994761i	$0.532596\pi$
$192$		0			0
$193$	0.394926	−	0.684031i	0.0284274	−	0.0492377i	−0.851462	−	0.524417i	$-0.824283\pi$
$193$	0.394926	−	0.684031i	0.0284274	−	0.0492377i	0.879889	+	0.475179i	$0.157617\pi$
$194$		0			0
$195$	−26.0480			−1.86534
$196$		0			0
$197$	10.3214			0.735370			0.367685	−	0.929950i	$-0.380150\pi$
$197$	10.3214			0.735370			0.367685	+	0.929950i	$0.380150\pi$
$198$		0			0
$199$	6.81020	−	11.7956i	0.482763	−	0.836169i	−0.517042	−	0.855960i	$-0.672967\pi$
$199$	6.81020	−	11.7956i	0.482763	−	0.836169i	0.999804	+	0.0197910i	$0.00630009\pi$
$200$		0			0
$201$	−1.28799	−	2.23087i	−0.0908480	−	0.157353i
$202$		0			0
$203$	−20.3251	−	0.740725i	−1.42654	−	0.0519887i
$204$		0			0
$205$	−12.8411	−	22.2414i	−0.896860	−	1.55341i
$206$		0			0
$207$	−0.166896	+	0.289073i	−0.0116001	+	0.0200919i
$208$		0			0
$209$	−5.69963			−0.394252
$210$		0			0
$211$	26.7738			1.84318			0.921591	−	0.388163i	$-0.126890\pi$
$211$	26.7738			1.84318			0.921591	+	0.388163i	$0.126890\pi$
$212$		0			0
$213$	−1.82691	+	3.16431i	−0.125178	+	0.216815i
$214$		0			0
$215$	2.68656	+	4.65326i	0.183222	+	0.317350i
$216$		0			0
$217$	−14.7720	+	23.5603i	−1.00279	+	1.59938i
$218$		0			0
$219$	−4.29782	−	7.44405i	−0.290420	−	0.503022i
$220$		0			0
$221$	−9.22617	+	15.9802i	−0.620619	+	1.07494i
$222$		0			0
$223$	5.60074			0.375054			0.187527	−	0.982259i	$-0.439953\pi$
$223$	5.60074			0.375054			0.187527	+	0.982259i	$0.439953\pi$
$224$		0			0
$225$	−2.77238			−0.184825
$226$		0			0
$227$	6.89857	−	11.9487i	0.457874	−	0.793061i	−0.540974	−	0.841039i	$-0.681944\pi$
$227$	6.89857	−	11.9487i	0.457874	−	0.793061i	0.998848	+	0.0479780i	$0.0152777\pi$
$228$		0			0
$229$	−3.48762	−	6.04074i	−0.230468	−	0.399183i	0.727478	−	0.686131i	$-0.240693\pi$
$229$	−3.48762	−	6.04074i	−0.230468	−	0.399183i	−0.957946	+	0.286948i	$0.907359\pi$
$230$		0			0
$231$	1.96727	+	3.71351i	0.129437	+	0.244331i
$232$		0			0
$233$	−3.38874	−	5.86946i	−0.222003	−	0.384521i	0.733413	−	0.679784i	$-0.237926\pi$
$233$	−3.38874	−	5.86946i	−0.222003	−	0.384521i	−0.955416	+	0.295262i	$0.904593\pi$
$234$		0			0
$235$	3.78180	−	6.55027i	0.246698	−	0.427293i
$236$		0			0
$237$	4.34108			0.281983
$238$		0			0
$239$	−7.43996			−0.481251			−0.240626	−	0.970618i	$-0.577353\pi$
$239$	−7.43996			−0.481251			−0.240626	+	0.970618i	$0.577353\pi$
$240$		0			0
$241$	7.35965	−	12.7473i	0.474076	−	0.821125i	−0.525483	−	0.850804i	$-0.676115\pi$
$241$	7.35965	−	12.7473i	0.474076	−	0.821125i	0.999559	+	0.0296796i	$0.00944869\pi$
$242$		0			0
$243$	−2.45420	−	4.25080i	−0.157437	−	0.272689i
$244$		0			0
$245$	−10.0265	−	20.7172i	−0.640572	−	1.32357i
$246$		0			0
$247$	−14.2138	−	24.6190i	−0.904402	−	1.56647i
$248$		0			0
$249$	5.28435	−	9.15276i	0.334882	−	0.580033i
$250$		0			0
$251$	25.0741			1.58266			0.791332	−	0.611386i	$-0.209388\pi$
$251$	25.0741			1.58266			0.791332	+	0.611386i	$0.209388\pi$
$252$		0			0
$253$	−0.699628			−0.0439852
$254$		0			0
$255$	9.66071	−	16.7328i	0.604977	−	1.04785i
$256$		0			0
$257$	−5.65452	−	9.79391i	−0.352719	−	0.610927i	0.634006	−	0.773328i	$-0.281410\pi$
$257$	−5.65452	−	9.79391i	−0.352719	−	0.610927i	−0.986725	+	0.162401i	$0.948076\pi$
$258$		0			0
$259$	−13.0989	−	24.7261i	−0.813925	−	1.53640i
$260$		0			0
$261$	1.83379	+	3.17622i	0.113509	+	0.196603i
$262$		0			0
$263$	−2.16071	+	3.74245i	−0.133235	+	0.230770i	−0.924922	−	0.380157i	$-0.875870\pi$
$263$	−2.16071	+	3.74245i	−0.133235	+	0.230770i	0.791687	+	0.610927i	$0.209203\pi$
$264$		0			0
$265$	−10.5549			−0.648385
$266$		0			0
$267$	−20.4327			−1.25046
$268$		0			0
$269$	−2.32072	+	4.01961i	−0.141497	+	0.245080i	−0.928061	−	0.372429i	$-0.878525\pi$
$269$	−2.32072	+	4.01961i	−0.141497	+	0.245080i	0.786564	+	0.617509i	$0.211858\pi$
$270$		0			0
$271$	−5.88688	−	10.1964i	−0.357602	−	0.619385i	0.629957	−	0.776630i	$-0.283072\pi$
$271$	−5.88688	−	10.1964i	−0.357602	−	0.619385i	−0.987560	+	0.157244i	$0.949739\pi$
$272$		0			0
$273$	−11.1342	+	17.7582i	−0.673870	+	1.07478i
$274$		0			0
$275$	−2.90545	−	5.03238i	−0.175205	−	0.303464i
$276$		0			0
$277$	−6.28180	+	10.8804i	−0.377437	+	0.653740i	−0.990689	−	0.136148i	$-0.956528\pi$
$277$	−6.28180	+	10.8804i	−0.377437	+	0.653740i	0.613252	+	0.789888i	$0.289861\pi$
$278$		0			0
$279$	5.01457			0.300214
$280$		0			0
$281$	−17.9949			−1.07349			−0.536743	−	0.843746i	$-0.680346\pi$
$281$	−17.9949			−1.07349			−0.536743	+	0.843746i	$0.680346\pi$
$282$		0			0
$283$	−1.86033	+	3.22219i	−0.110585	+	0.191540i	−0.916006	−	0.401164i	$-0.868606\pi$
$283$	−1.86033	+	3.22219i	−0.110585	+	0.191540i	0.805421	+	0.592703i	$0.201939\pi$
$284$		0			0
$285$	14.8832	+	25.7785i	0.881607	+	1.52699i
$286$		0			0
$287$	−20.6520	−	0.752639i	−1.21905	−	0.0444269i
$288$		0			0
$289$	1.65638	+	2.86893i	0.0974339	+	0.168760i
$290$		0			0
$291$	−14.7793	+	25.5984i	−0.866375	+	1.50061i
$292$		0			0
$293$	25.8654			1.51107			0.755535	−	0.655108i	$-0.227377\pi$
$293$	25.8654			1.51107			0.755535	+	0.655108i	$0.227377\pi$
$294$		0			0
$295$	−25.5316			−1.48650
$296$		0			0
$297$	2.76145	−	4.78297i	0.160236	−	0.277536i
$298$		0			0
$299$	−1.74474	−	3.02198i	−0.100901	−	0.174765i
$300$		0			0
$301$	4.32072	+	0.157464i	0.249042	+	0.00907608i
$302$		0			0
$303$	−5.19708	−	9.00161i	−0.298564	−	0.517129i
$304$		0			0
$305$	−8.14468	+	14.1070i	−0.466363	+	0.807765i
$306$		0			0
$307$	−16.3090			−0.930806			−0.465403	−	0.885099i	$-0.654091\pi$
$307$	−16.3090			−0.930806			−0.465403	+	0.885099i	$0.654091\pi$
$308$		0			0
$309$	−3.22762			−0.183613
$310$		0			0
$311$	−0.244740	+	0.423902i	−0.0138779	+	0.0240373i	−0.872881	−	0.487933i	$-0.837751\pi$
$311$	−0.244740	+	0.423902i	−0.0138779	+	0.0240373i	0.859003	+	0.511970i	$0.171084\pi$
$312$		0			0
$313$	−6.91528	−	11.9776i	−0.390875	−	0.677015i	0.601691	−	0.798729i	$-0.294494\pi$
$313$	−6.91528	−	11.9776i	−0.390875	−	0.677015i	−0.992565	+	0.121715i	$0.961161\pi$
$314$		0			0
$315$	−2.20472	+	3.51638i	−0.124222	+	0.198126i
$316$		0			0
$317$	8.77128	+	15.1923i	0.492644	+	0.853285i	0.999964	−	0.00847294i	$-0.00269705\pi$
$317$	8.77128	+	15.1923i	0.492644	+	0.853285i	−0.507320	+	0.861758i	$0.669364\pi$
$318$		0			0
$319$	−3.84362	+	6.65735i	−0.215202	+	0.372740i
$320$		0			0
$321$	−30.9505			−1.72749
$322$		0			0
$323$	21.0865			1.17328
$324$		0			0
$325$	14.4913	−	25.0996i	0.803831	−	1.39228i
$326$		0			0
$327$	−7.19963	−	12.4701i	−0.398140	−	0.689599i
$328$		0			0
$329$	−2.84913	−	5.37815i	−0.157077	−	0.296507i
$330$		0			0
$331$	4.31089	+	7.46668i	0.236948	+	0.410406i	0.959837	−	0.280558i	$-0.0905195\pi$
$331$	4.31089	+	7.46668i	0.236948	+	0.410406i	−0.722889	+	0.690964i	$0.757186\pi$
$332$		0			0
$333$	−2.52290	+	4.36979i	−0.138254	+	0.239463i
$334$		0			0
$335$	5.33242			0.291341
$336$		0			0
$337$	25.0073			1.36223			0.681117	−	0.732175i	$-0.261495\pi$
$337$	25.0073			1.36223			0.681117	+	0.732175i	$0.261495\pi$
$338$		0			0
$339$	6.46836	−	11.2035i	0.351313	−	0.608492i
$340$		0			0
$341$	5.25526	+	9.10238i	0.284588	+	0.492921i
$342$		0			0
$343$	−18.4098	−	2.01993i	−0.994035	−	0.109066i
$344$		0			0
$345$	1.82691	+	3.16431i	0.0983577	+	0.170361i
$346$		0			0
$347$	−10.1774	+	17.6278i	−0.546352	+	0.946310i	0.452168	+	0.891933i	$0.350651\pi$
$347$	−10.1774	+	17.6278i	−0.546352	+	0.946310i	−0.998520	+	0.0543773i	$0.982683\pi$
$348$		0			0
$349$	−10.7775			−0.576905			−0.288452	−	0.957494i	$-0.593141\pi$
$349$	−10.7775			−0.576905			−0.288452	+	0.957494i	$0.593141\pi$
$350$		0			0
$351$	27.5461			1.47030
$352$		0			0
$353$	−11.4691	+	19.8650i	−0.610436	+	1.05731i	0.380731	+	0.924686i	$0.375672\pi$
$353$	−11.4691	+	19.8650i	−0.610436	+	1.05731i	−0.991167	+	0.132620i	$0.957661\pi$
$354$		0			0
$355$	−3.78180	−	6.55027i	−0.200717	−	0.347652i
$356$		0			0
$357$	−7.27816	−	13.7386i	−0.385201	−	0.727124i
$358$		0			0
$359$	9.42766	+	16.3292i	0.497573	+	0.861821i	0.999996	−	0.00280050i	$-0.000891427\pi$
$359$	9.42766	+	16.3292i	0.497573	+	0.861821i	−0.502423	+	0.864622i	$0.667558\pi$
$360$		0			0
$361$	−6.74288	+	11.6790i	−0.354888	+	0.614685i
$362$		0			0
$363$	1.58836			0.0833675
$364$		0			0
$365$	17.7934			0.931350
$366$		0			0
$367$	11.2553	−	19.4947i	0.587520	−	1.01761i	−0.407036	−	0.913412i	$-0.633438\pi$
$367$	11.2553	−	19.4947i	0.587520	−	1.01761i	0.994556	−	0.104202i	$-0.0332289\pi$
$368$		0			0
$369$	1.86329	+	3.22731i	0.0969989	+	0.168007i
$370$		0			0
$371$	−4.51169	+	7.19583i	−0.234235	+	0.373589i
$372$		0			0
$373$	−6.82141	−	11.8150i	−0.353199	−	0.611759i	0.633609	−	0.773654i	$-0.281573\pi$
$373$	−6.82141	−	11.8150i	−0.353199	−	0.611759i	−0.986808	+	0.161894i	$0.948240\pi$
$374$		0			0
$375$	−2.11745	+	3.66754i	−0.109345	+	0.189391i
$376$		0			0
$377$	−38.3411			−1.97467
$378$		0			0
$379$	7.69963			0.395503			0.197752	−	0.980252i	$-0.436636\pi$
$379$	7.69963			0.395503			0.197752	+	0.980252i	$0.436636\pi$
$380$		0			0
$381$	−6.34362	+	10.9875i	−0.324994	+	0.562906i
$382$		0			0
$383$	5.95853	+	10.3205i	0.304467	+	0.527352i	0.977142	−	0.212586i	$-0.0681884\pi$
$383$	5.95853	+	10.3205i	0.304467	+	0.527352i	−0.672676	+	0.739937i	$0.734855\pi$
$384$		0			0
$385$	−8.69344	−	0.316823i	−0.443059	−	0.0161468i
$386$		0			0
$387$	−0.389830	−	0.675205i	−0.0198162	−	0.0343226i
$388$		0			0
$389$	14.6545	−	25.3824i	0.743013	−	1.28694i	−0.208104	−	0.978107i	$-0.566729\pi$
$389$	14.6545	−	25.3824i	0.743013	−	1.28694i	0.951117	−	0.308830i	$-0.0999375\pi$
$390$		0			0
$391$	2.58836			0.130899
$392$		0			0
$393$	−8.82546			−0.445186
$394$		0			0
$395$	−4.49312	+	7.78231i	−0.226073	+	0.391571i
$396$		0			0
$397$	10.4647	+	18.1254i	0.525209	+	0.909689i	0.999569	+	0.0293580i	$0.00934628\pi$
$397$	10.4647	+	18.1254i	0.525209	+	0.909689i	−0.474360	+	0.880331i	$0.657320\pi$
$398$		0			0
$399$	23.9363	+	0.872333i	1.19831	+	0.0436713i
$400$		0			0
$401$	11.8578	+	20.5383i	0.592150	+	1.02563i	0.993942	+	0.109903i	$0.0350539\pi$
$401$	11.8578	+	20.5383i	0.592150	+	1.02563i	−0.401793	+	0.915731i	$0.631613\pi$
$402$		0			0
$403$	−26.2112	+	45.3992i	−1.30567	+	2.26150i
$404$		0			0
$405$	−24.1374			−1.19940
$406$		0			0
$407$	−10.5760			−0.524232
$408$		0			0
$409$	−10.9215	+	18.9165i	−0.540032	+	0.935363i	0.458870	+	0.888504i	$0.348254\pi$
$409$	−10.9215	+	18.9165i	−0.540032	+	0.935363i	−0.998902	+	0.0468590i	$0.985079\pi$
$410$		0			0
$411$	0.166896	+	0.289073i	0.00823238	+	0.0142589i
$412$		0			0
$413$	−10.9134	+	17.4061i	−0.537014	+	0.856500i
$414$		0			0
$415$	10.9389	+	18.9467i	0.536968	+	0.930056i
$416$		0			0
$417$	8.73600	−	15.1312i	0.427804	−	0.740978i
$418$		0			0
$419$	20.5970			1.00623			0.503115	−	0.864219i	$-0.332187\pi$
$419$	20.5970			1.00623			0.503115	+	0.864219i	$0.332187\pi$
$420$		0			0
$421$	38.3607			1.86959			0.934794	−	0.355190i	$-0.115584\pi$
$421$	38.3607			1.86959			0.934794	+	0.355190i	$0.115584\pi$
$422$		0			0
$423$	−0.548754	+	0.950469i	−0.0266813	+	0.0462134i
$424$		0			0
$425$	10.7491	+	18.6179i	0.521407	+	0.903103i
$426$		0			0
$427$	6.13602	+	11.5827i	0.296943	+	0.560524i
$428$		0			0
$429$	3.96108	+	6.86079i	0.191243	+	0.331242i
$430$		0			0
$431$	−17.8535	+	30.9231i	−0.859971	+	1.48951i	0.0119850	+	0.999928i	$0.496185\pi$
$431$	−17.8535	+	30.9231i	−0.859971	+	1.48951i	−0.871956	+	0.489585i	$0.837148\pi$
$432$		0			0
$433$	7.08513			0.340489			0.170245	−	0.985402i	$-0.445544\pi$
$433$	7.08513			0.340489			0.170245	+	0.985402i	$0.445544\pi$
$434$		0			0
$435$	40.1469			1.92490
$436$		0			0
$437$	−1.99381	+	3.45338i	−0.0953769	+	0.165198i
$438$		0			0
$439$	7.63781	+	13.2291i	0.364533	+	0.631389i	0.988701	−	0.149901i	$-0.0478954\pi$
$439$	7.63781	+	13.2291i	0.364533	+	0.631389i	−0.624168	+	0.781290i	$0.714562\pi$
$440$		0			0
$441$	1.45489	+	3.00614i	0.0692804	+	0.143150i
$442$		0			0
$443$	−13.9320	−	24.1309i	−0.661929	−	1.14649i	−0.980108	−	0.198464i	$-0.936405\pi$
$443$	−13.9320	−	24.1309i	−0.661929	−	1.14649i	0.318180	−	0.948030i	$-0.396929\pi$
$444$		0			0
$445$	21.1483	−	36.6300i	1.00253	−	1.73643i
$446$		0			0
$447$	19.6552			0.929659
$448$		0			0
$449$	−10.0879			−0.476077			−0.238038	−	0.971256i	$-0.576504\pi$
$449$	−10.0879			−0.476077			−0.238038	+	0.971256i	$0.576504\pi$
$450$		0			0
$451$	−3.90545	+	6.76443i	−0.183900	+	0.318525i
$452$		0			0
$453$	5.83015	+	10.0981i	0.273924	+	0.474451i
$454$		0			0
$455$	−20.3113	−	38.3406i	−0.952208	−	1.79743i
$456$		0			0
$457$	5.45056	+	9.44064i	0.254966	+	0.441615i	0.964886	−	0.262668i	$-0.0846023\pi$
$457$	5.45056	+	9.44064i	0.254966	+	0.441615i	−0.709920	+	0.704282i	$0.751269\pi$
$458$		0			0
$459$	−10.2163	+	17.6952i	−0.476858	+	0.825942i
$460$		0			0
$461$	−28.4313			−1.32418			−0.662089	−	0.749425i	$-0.730330\pi$
$461$	−28.4313			−1.32418			−0.662089	+	0.749425i	$0.730330\pi$
$462$		0			0
$463$	−2.11498			−0.0982916			−0.0491458	−	0.998792i	$-0.515650\pi$
$463$	−2.11498			−0.0982916			−0.0491458	+	0.998792i	$0.515650\pi$
$464$		0			0
$465$	27.4457	−	47.5374i	1.27277	−	2.20450i
$466$		0			0
$467$	−18.1483	−	31.4338i	−0.839804	−	1.45458i	−0.890058	−	0.455847i	$-0.849336\pi$
$467$	−18.1483	−	31.4338i	−0.839804	−	1.45458i	0.0502535	−	0.998736i	$-0.483997\pi$
$468$		0			0
$469$	2.27933	−	3.63537i	0.105250	−	0.167866i
$470$		0			0
$471$	7.44801	+	12.9003i	0.343186	+	0.594416i
$472$		0			0
$473$	0.817082	−	1.41523i	0.0375695	−	0.0650722i
$474$		0			0
$475$	−33.1199			−1.51965
$476$		0			0
$477$	1.53156			0.0701254
$478$		0			0
$479$	−7.49745	+	12.9860i	−0.342567	+	0.593344i	−0.984909	−	0.173075i	$-0.944630\pi$
$479$	−7.49745	+	12.9860i	−0.342567	+	0.593344i	0.642341	+	0.766419i	$0.277963\pi$
$480$		0			0
$481$	−26.3745	−	45.6820i	−1.20257	−	2.08292i
$482$		0			0
$483$	2.93818	+	0.107079i	0.133692	+	0.00487225i
$484$		0			0
$485$	−30.5938	−	52.9900i	−1.38919	−	2.40615i
$486$		0			0
$487$	3.77128	−	6.53205i	0.170893	−	0.295996i	−0.767839	−	0.640643i	$-0.778668\pi$
$487$	3.77128	−	6.53205i	0.170893	−	0.295996i	0.938732	+	0.344647i	$0.112001\pi$
$488$		0			0
$489$	25.0938			1.13478
$490$		0			0
$491$	18.5302			0.836255			0.418128	−	0.908388i	$-0.362686\pi$
$491$	18.5302			0.836255			0.418128	+	0.908388i	$0.362686\pi$
$492$		0			0
$493$	14.2200	−	24.6297i	0.640436	−	1.10927i
$494$		0			0
$495$	0.784350	+	1.35853i	0.0352539	+	0.0610616i
$496$		0			0
$497$	−6.08217	−	0.221658i	−0.272823	−	0.00994273i
$498$		0			0
$499$	4.99931	+	8.65906i	0.223800	+	0.387633i	0.955959	−	0.293501i	$-0.0948205\pi$
$499$	4.99931	+	8.65906i	0.223800	+	0.387633i	−0.732159	+	0.681134i	$0.761487\pi$
$500$		0			0
$501$	−6.56251	+	11.3666i	−0.293191	+	0.507822i
$502$		0			0
$503$	−4.34479			−0.193725			−0.0968624	−	0.995298i	$-0.530881\pi$
$503$	−4.34479			−0.193725			−0.0968624	+	0.995298i	$0.530881\pi$
$504$		0			0
$505$	21.5164			0.957468
$506$		0			0
$507$	−9.43199	+	16.3367i	−0.418889	+	0.725538i
$508$		0			0
$509$	19.0036	+	32.9153i	0.842322	+	1.45894i	0.887927	+	0.459984i	$0.152145\pi$
$509$	19.0036	+	32.9153i	0.842322	+	1.45894i	−0.0456054	+	0.998960i	$0.514522\pi$
$510$		0			0
$511$	7.60576	−	12.1307i	0.336459	−	0.536629i
$512$		0			0
$513$	−15.7392	−	27.2612i	−0.694904	−	1.20361i
$514$		0			0
$515$	3.34067	−	5.78621i	0.147208	−	0.254971i
$516$		0			0
$517$	−2.30037			−0.101170
$518$		0			0
$519$	−16.8516			−0.739703
$520$		0			0
$521$	5.40290	−	9.35809i	0.236705	−	0.409986i	−0.723062	−	0.690784i	$-0.757266\pi$
$521$	5.40290	−	9.35809i	0.236705	−	0.409986i	0.959767	+	0.280798i	$0.0905991\pi$
$522$		0			0
$523$	10.4134	+	18.0366i	0.455347	+	0.788684i	0.998708	−	0.0508150i	$-0.0161819\pi$
$523$	10.4134	+	18.0366i	0.455347	+	0.788684i	−0.543361	+	0.839499i	$0.682849\pi$
$524$		0			0
$525$	11.4316	+	21.5788i	0.498915	+	0.941776i
$526$		0			0
$527$	−19.4425	−	33.6754i	−0.846929	−	1.46692i
$528$		0			0
$529$	11.2553	−	19.4947i	0.489359	−	0.847595i
$530$		0			0
$531$	3.70472			0.160771
$532$		0			0
$533$	−38.9578			−1.68745
$534$		0			0
$535$	32.0345	−	55.4854i	1.38497	−	2.39884i
$536$		0			0
$537$	8.38942	+	14.5309i	0.362030	+	0.627055i
$538$		0			0
$539$	−3.93199	+	5.79133i	−0.169363	+	0.249450i
$540$		0			0
$541$	2.55563	+	4.42648i	0.109875	+	0.190309i	0.915720	−	0.401818i	$-0.131622\pi$
$541$	2.55563	+	4.42648i	0.109875	+	0.190309i	−0.805844	+	0.592127i	$0.798288\pi$
$542$		0			0
$543$	16.2076	−	28.0724i	0.695535	−	1.20470i
$544$		0			0
$545$	29.8072			1.27680
$546$		0			0
$547$	−2.04580			−0.0874721			−0.0437361	−	0.999043i	$-0.513926\pi$
$547$	−2.04580			−0.0874721			−0.0437361	+	0.999043i	$0.513926\pi$
$548$		0			0
$549$	1.18182	−	2.04698i	0.0504390	−	0.0873629i
$550$		0			0
$551$	21.9072	+	37.9444i	0.933279	+	1.61649i
$552$		0			0
$553$	3.38502	+	6.38972i	0.143946	+	0.271719i
$554$		0			0
$555$	27.6167	+	47.8335i	1.17226	+	2.03042i
$556$		0			0
$557$	−17.6316	+	30.5389i	−0.747076	+	1.29397i	0.202143	+	0.979356i	$0.435209\pi$
$557$	−17.6316	+	30.5389i	−0.747076	+	1.29397i	−0.949219	+	0.314617i	$0.898124\pi$
$558$		0			0
$559$	8.15059			0.344733
$560$		0			0
$561$	−5.87636			−0.248100
$562$		0			0
$563$	−7.77630	+	13.4689i	−0.327732	+	0.567649i	−0.982061	−	0.188561i	$-0.939618\pi$
$563$	−7.77630	+	13.4689i	−0.327732	+	0.567649i	0.654329	+	0.756210i	$0.272951\pi$
$564$		0			0
$565$	13.3898	+	23.1919i	0.563314	+	0.975689i
$566$		0			0
$567$	−10.3175	+	16.4557i	−0.433294	+	0.691073i
$568$		0			0
$569$	3.14833	+	5.45306i	0.131985	+	0.228604i	0.924442	−	0.381324i	$-0.124532\pi$
$569$	3.14833	+	5.45306i	0.131985	+	0.228604i	−0.792457	+	0.609928i	$0.791198\pi$
$570$		0			0
$571$	3.47160	−	6.01299i	0.145282	−	0.251636i	−0.784196	−	0.620513i	$-0.786924\pi$
$571$	3.47160	−	6.01299i	0.145282	−	0.251636i	0.929478	+	0.368877i	$0.120258\pi$
$572$		0			0
$573$	−35.5782			−1.48630
$574$		0			0
$575$	−4.06546			−0.169542
$576$		0			0
$577$	1.09201	−	1.89141i	0.0454608	−	0.0787404i	−0.842400	−	0.538853i	$-0.818858\pi$
$577$	1.09201	−	1.89141i	0.0454608	−	0.0787404i	0.887860	+	0.460113i	$0.152191\pi$
$578$		0			0
$579$	0.627286	+	1.08649i	0.0260691	+	0.0451530i
$580$		0			0
$581$	17.5927	+	0.641147i	0.729868	+	0.0265993i
$582$		0			0
$583$	1.60507	+	2.78007i	0.0664754	+	0.115139i
$584$		0			0
$585$	−3.91204	+	6.77585i	−0.161743	+	0.280147i
$586$		0			0
$587$	24.4574			1.00947			0.504733	−	0.863275i	$-0.331591\pi$
$587$	24.4574			1.00947			0.504733	+	0.863275i	$0.331591\pi$
$588$		0			0
$589$	59.9061			2.46839
$590$		0			0
$591$	−8.19708	+	14.1978i	−0.337183	+	0.584018i
$592$		0			0
$593$	−13.2095	−	22.8795i	−0.542448	−	0.939547i	−0.998763	−	0.0497285i	$-0.984164\pi$
$593$	−13.2095	−	22.8795i	−0.542448	−	0.939547i	0.456315	−	0.889818i	$-0.349169\pi$
$594$		0			0
$595$	32.1625	+	1.17213i	1.31853	+	0.0480525i
$596$		0			0
$597$	10.8171	+	18.7357i	0.442714	+	0.766803i
$598$		0			0
$599$	24.0679	−	41.6869i	0.983389	−	1.70328i	0.334503	−	0.942395i	$-0.391432\pi$
$599$	24.0679	−	41.6869i	0.983389	−	1.70328i	0.648887	−	0.760885i	$-0.275235\pi$
$600$		0			0
$601$	−5.00138			−0.204010			−0.102005	−	0.994784i	$-0.532526\pi$
$601$	−5.00138			−0.204010			−0.102005	+	0.994784i	$0.532526\pi$
$602$		0			0
$603$	−0.773753			−0.0315097
$604$		0			0
$605$	−1.64400	+	2.84748i	−0.0668379	+	0.115767i
$606$		0			0
$607$	0.839982	+	1.45489i	0.0340938	+	0.0590522i	0.882569	−	0.470183i	$-0.155812\pi$
$607$	0.839982	+	1.45489i	0.0340938	+	0.0590522i	−0.848475	+	0.529235i	$0.822479\pi$
$608$		0			0
$609$	17.1607	−	27.3701i	0.695387	−	1.10909i
$610$		0			0
$611$	−5.73669	−	9.93624i	−0.232082	−	0.401977i
$612$		0			0
$613$	9.52290	−	16.4941i	0.384626	−	0.666192i	−0.607091	−	0.794632i	$-0.707664\pi$
$613$	9.52290	−	16.4941i	0.384626	−	0.666192i	0.991717	+	0.128440i	$0.0409970\pi$
$614$		0			0
$615$	40.7926			1.64492
$616$		0			0
$617$	32.3955			1.30420			0.652098	−	0.758135i	$-0.273889\pi$
$617$	32.3955			1.30420			0.652098	+	0.758135i	$0.273889\pi$
$618$		0			0
$619$	4.98762	−	8.63881i	0.200469	−	0.347223i	−0.748210	−	0.663462i	$-0.769087\pi$
$619$	4.98762	−	8.63881i	0.200469	−	0.347223i	0.948680	+	0.316238i	$0.102420\pi$
$620$		0			0
$621$	−1.93199	−	3.34630i	−0.0775280	−	0.134282i
$622$		0			0
$623$	−15.9327	−	30.0753i	−0.638329	−	1.20494i
$624$		0			0
$625$	10.1440	+	17.5699i	0.405760	+	0.702797i
$626$		0			0
$627$	4.52654	−	7.84020i	0.180773	−	0.313107i
$628$		0			0
$629$	39.1272			1.56010
$630$		0			0
$631$	−29.4290			−1.17155			−0.585774	−	0.810474i	$-0.699209\pi$
$631$	−29.4290			−1.17155			−0.585774	+	0.810474i	$0.699209\pi$
$632$		0			0
$633$	−21.2632	+	36.8290i	−0.845138	+	1.46382i
$634$		0			0
$635$	−13.1316	−	22.7446i	−0.521112	−	0.902593i
$636$		0			0
$637$	−34.8207	−	2.54138i	−1.37965	−	0.100693i
$638$		0			0
$639$	0.548754	+	0.950469i	0.0217084	+	0.0376000i
$640$		0			0
$641$	−0.0116910	+	0.0202494i	−0.000461767	+	0.000799804i	−0.866256	−	0.499600i	$-0.833480\pi$
$641$	−0.0116910	+	0.0202494i	−0.000461767	+	0.000799804i	0.865794	+	0.500400i	$0.166814\pi$
$642$		0			0
$643$	10.9963			0.433651			0.216826	−	0.976210i	$-0.430430\pi$
$643$	10.9963			0.433651			0.216826	+	0.976210i	$0.430430\pi$
$644$		0			0
$645$	−8.53447			−0.336044
$646$		0			0
$647$	−8.20877	+	14.2180i	−0.322720	+	0.558968i	−0.981048	−	0.193763i	$-0.937931\pi$
$647$	−8.20877	+	14.2180i	−0.322720	+	0.558968i	0.658328	+	0.752731i	$0.271264\pi$
$648$		0			0
$649$	3.88255	+	6.72477i	0.152403	+	0.263970i
$650$		0			0
$651$	−20.6770	−	39.0309i	−0.810396	−	1.52974i
$652$		0			0
$653$	−6.90545	−	11.9606i	−0.270231	−	0.468054i	0.698690	−	0.715425i	$-0.253767\pi$
$653$	−6.90545	−	11.9606i	−0.270231	−	0.468054i	−0.968921	+	0.247371i	$0.920433\pi$
$654$		0			0
$655$	9.13457	−	15.8215i	0.356917	−	0.618199i
$656$		0			0
$657$	−2.58189			−0.100729
$658$		0			0
$659$	19.0283			0.741238			0.370619	−	0.928785i	$-0.379146\pi$
$659$	19.0283			0.741238			0.370619	+	0.928785i	$0.379146\pi$
$660$		0			0
$661$	−3.14214	+	5.44234i	−0.122215	+	0.211683i	−0.920641	−	0.390411i	$-0.872333\pi$
$661$	−3.14214	+	5.44234i	−0.122215	+	0.211683i	0.798426	+	0.602093i	$0.205666\pi$
$662$		0			0
$663$	−14.6545	−	25.3824i	−0.569134	−	0.985769i
$664$		0			0
$665$	−26.3385	+	42.0081i	−1.02136	+	1.62901i
$666$		0			0
$667$	2.68911	+	4.65767i	0.104123	+	0.180346i
$668$		0			0
$669$	−4.44801	+	7.70418i	−0.171970	+	0.297861i
$670$		0			0
$671$	4.95420			0.191255
$672$		0			0
$673$	37.3497			1.43973			0.719863	−	0.694116i	$-0.244204\pi$
$673$	37.3497			1.43973			0.719863	+	0.694116i	$0.244204\pi$
$674$		0			0
$675$	16.0465	−	27.7933i	0.617630	−	1.06977i
$676$		0			0
$677$	22.1451	+	38.3564i	0.851105	+	1.47416i	0.880212	+	0.474581i	$0.157400\pi$
$677$	22.1451	+	38.3564i	0.851105	+	1.47416i	−0.0291070	+	0.999576i	$0.509266\pi$
$678$		0			0
$679$	−49.2032	−	1.79316i	−1.88825	−	0.0688151i
$680$		0			0
$681$	10.9574	+	18.9788i	0.419890	+	0.727271i
$682$		0			0
$683$	2.59269	−	4.49068i	0.0992067	−	0.171831i	−0.812150	−	0.583449i	$-0.801703\pi$
$683$	2.59269	−	4.49068i	0.0992067	−	0.171831i	0.911357	+	0.411618i	$0.135036\pi$
$684$		0			0
$685$	−0.690967			−0.0264005
$686$		0			0
$687$	11.0792			0.422699
$688$		0			0
$689$	−8.00550	+	13.8659i	−0.304985	+	0.528250i
$690$		0			0
$691$	−1.02104	−	1.76849i	−0.0388422	−	0.0672767i	0.845951	−	0.533261i	$-0.179034\pi$
$691$	−1.02104	−	1.76849i	−0.0388422	−	0.0672767i	−0.884793	+	0.465984i	$0.845700\pi$
$692$		0			0
$693$	1.26145	+	0.0459722i	0.0479185	+	0.00174634i
$694$		0			0
$695$	18.0840	+	31.3223i	0.685964	+	1.18812i
$696$		0			0
$697$	14.4487	−	25.0259i	0.547283	−	0.947923i
$698$		0			0
$699$	10.7651			0.407173
$700$		0			0
$701$	−44.6291			−1.68562			−0.842808	−	0.538214i	$-0.819099\pi$
$701$	−44.6291			−1.68562			−0.842808	+	0.538214i	$0.819099\pi$
$702$		0			0
$703$	−30.1396	+	52.2033i	−1.13674	+	1.96888i
$704$		0			0
$705$	6.00688	+	10.4042i	0.226232	+	0.391846i
$706$		0			0
$707$	9.19716	−	14.6688i	0.345895	−	0.551678i
$708$		0			0
$709$	−19.9301	−	34.5200i	−0.748492	−	1.29643i	−0.948546	−	0.316641i	$-0.897445\pi$
$709$	−19.9301	−	34.5200i	−0.748492	−	1.29643i	0.200054	−	0.979785i	$-0.435888\pi$
$710$		0			0
$711$	0.651969	−	1.12924i	0.0244507	−	0.0423499i
$712$		0			0
$713$	7.35346			0.275389
$714$		0			0
$715$	−16.3993			−0.613297
$716$		0			0
$717$	5.90868	−	10.2341i	0.220664	−	0.382201i
$718$		0			0
$719$	8.99745	+	15.5840i	0.335548	+	0.581187i	0.983590	−	0.180418i	$-0.0577451\pi$
$719$	8.99745	+	15.5840i	0.335548	+	0.581187i	−0.648042	+	0.761605i	$0.724412\pi$
$720$		0			0
$721$	−2.51679	−	4.75081i	−0.0937300	−	0.176929i
$722$		0			0
$723$	11.6898	+	20.2473i	0.434748	+	0.753006i
$724$		0			0
$725$	−22.3349	+	38.6852i	−0.829497	+	1.43673i
$726$		0			0
$727$	−13.9491			−0.517344			−0.258672	−	0.965965i	$-0.583285\pi$
$727$	−13.9491			−0.517344			−0.258672	+	0.965965i	$0.583285\pi$
$728$		0			0
$729$	29.8196			1.10443
$730$		0			0
$731$	−3.02290	+	5.23582i	−0.111806	+	0.193654i
$732$		0			0
$733$	−9.88323	−	17.1183i	−0.365046	−	0.632278i	0.623738	−	0.781634i	$-0.285613\pi$
$733$	−9.88323	−	17.1183i	−0.365046	−	0.632278i	−0.988783	+	0.149356i	$0.952280\pi$
$734$		0			0
$735$	36.4607	+	2.66108i	1.34487	+	0.0981553i
$736$		0			0
$737$	−0.810892	−	1.40451i	−0.0298696	−	0.0517357i
$738$		0			0
$739$	−0.458530	+	0.794198i	−0.0168673	+	0.0292150i	−0.874336	−	0.485321i	$-0.838703\pi$
$739$	−0.458530	+	0.794198i	−0.0168673	+	0.0292150i	0.857469	+	0.514536i	$0.172036\pi$
$740$		0			0
$741$	45.1533			1.65875
$742$		0			0
$743$	−6.22391			−0.228333			−0.114166	−	0.993462i	$-0.536420\pi$
$743$	−6.22391			−0.228333			−0.114166	+	0.993462i	$0.536420\pi$
$744$		0			0
$745$	−20.3436	+	35.2362i	−0.745333	+	1.29095i
$746$		0			0
$747$	−1.58727	−	2.74923i	−0.0580752	−	0.100589i
$748$		0			0
$749$	−24.1341	−	45.5567i	−0.881840	−	1.66460i
$750$		0			0
$751$	−22.5400	−	39.0405i	−0.822497	−	1.42461i	−0.903817	−	0.427918i	$-0.859247\pi$
$751$	−22.5400	−	39.0405i	−0.822497	−	1.42461i	0.0813205	−	0.996688i	$-0.474086\pi$
$752$		0			0
$753$	−19.9134	+	34.4911i	−0.725685	+	1.25692i
$754$		0			0
$755$	−24.1374			−0.878450
$756$		0			0
$757$	3.46844			0.126063			0.0630313	−	0.998012i	$-0.479923\pi$
$757$	3.46844			0.126063			0.0630313	+	0.998012i	$0.479923\pi$
$758$		0			0
$759$	0.555632	−	0.962383i	0.0201682	−	0.0349323i
$760$		0			0
$761$	11.0371	+	19.1168i	0.400093	+	0.692982i	0.993737	−	0.111746i	$-0.0356444\pi$
$761$	11.0371	+	19.1168i	0.400093	+	0.692982i	−0.593644	+	0.804728i	$0.702311\pi$
$762$		0			0
$763$	12.7410	−	20.3210i	0.461256	−	0.735671i
$764$		0			0
$765$	−2.90180	−	5.02607i	−0.104915	−	0.181718i
$766$		0			0
$767$	−19.3647	+	33.5406i	−0.699218	+	1.21108i
$768$		0			0
$769$	−47.9468			−1.72900			−0.864502	−	0.502629i	$-0.832366\pi$
$769$	−47.9468			−1.72900			−0.864502	+	0.502629i	$0.832366\pi$
$770$		0			0
$771$	17.9629			0.646917
$772$		0			0
$773$	24.0796	−	41.7071i	0.866084	−	1.50010i	0.000117116	−	1.00000i	$-0.499963\pi$
$773$	24.0796	−	41.7071i	0.866084	−	1.50010i	0.865967	−	0.500101i	$-0.166704\pi$
$774$		0			0
$775$	30.5378	+	52.8929i	1.09695	+	1.89997i
$776$		0			0
$777$	44.4152	+	1.61866i	1.59339	+	0.0580693i
$778$		0			0
$779$	22.2596	+	38.5547i	0.797533	+	1.38137i
$780$		0			0
$781$	−1.15019	+	1.99218i	−0.0411569	+	0.0712858i
$782$		0			0
$783$	−42.4559			−1.51725
$784$		0			0
$785$	−30.8355			−1.10057
$786$		0			0
$787$	−12.4814	+	21.6185i	−0.444915	+	0.770615i	−0.998046	−	0.0624788i	$-0.980099\pi$
$787$	−12.4814	+	21.6185i	−0.444915	+	0.770615i	0.553131	+	0.833094i	$0.313433\pi$
$788$		0			0
$789$	−3.43199	−	5.94438i	−0.122182	−	0.211625i
$790$		0			0
$791$	21.5345	+	0.784802i	0.765679	+	0.0279044i
$792$		0			0
$793$	12.3548	+	21.3992i	0.438733	+	0.759908i
$794$		0			0
$795$	8.38255	−	14.5190i	0.297298	−	0.514936i
$796$		0			0
$797$	1.02832			0.0364251			0.0182126	−	0.999834i	$-0.494202\pi$
$797$	1.02832			0.0364251			0.0182126	+	0.999834i	$0.494202\pi$
$798$		0			0
$799$	8.51052			0.301081
$800$		0			0
$801$	−3.06870	+	5.31515i	−0.108427	+	0.187801i
$802$		0			0
$803$	−2.70582	−	4.68661i	−0.0954862	−	0.165387i
$804$		0			0
$805$	−3.23305	+	5.15649i	−0.113950	+	0.181742i
$806$		0			0
$807$	−3.68615	−	6.38461i	−0.129759	−	0.224749i
$808$		0			0
$809$	15.3516	−	26.5897i	0.539733	−	0.934846i	−0.459185	−	0.888341i	$-0.651858\pi$
$809$	15.3516	−	26.5897i	0.539733	−	0.934846i	0.998918	−	0.0465048i	$-0.0148083\pi$
$810$		0			0
$811$	−33.8887			−1.18999			−0.594997	−	0.803728i	$-0.702847\pi$
$811$	−33.8887			−1.18999			−0.594997	+	0.803728i	$0.702847\pi$
$812$		0			0
$813$	18.7010			0.655873
$814$		0			0
$815$	−25.9727	+	44.9860i	−0.909784	+	1.57579i
$816$		0			0
$817$	−4.65706	−	8.06627i	−0.162930	−	0.282203i
$818$		0			0
$819$	2.94724	+	5.56336i	0.102985	+	0.194400i
$820$		0			0
$821$	14.4759	+	25.0730i	0.505213	+	0.875055i	0.999982	+	0.00603043i	$0.00191956\pi$
$821$	14.4759	+	25.0730i	0.505213	+	0.875055i	−0.494768	+	0.869025i	$0.664747\pi$
$822$		0			0
$823$	−9.41961	+	16.3152i	−0.328347	+	0.568714i	−0.982184	−	0.187922i	$-0.939825\pi$
$823$	−9.41961	+	16.3152i	−0.328347	+	0.568714i	0.653837	+	0.756635i	$0.273158\pi$
$824$		0			0
$825$	9.22981			0.321341
$826$		0			0
$827$	43.7366			1.52087			0.760436	−	0.649413i	$-0.224986\pi$
$827$	43.7366			1.52087			0.760436	+	0.649413i	$0.224986\pi$
$828$		0			0
$829$	−21.8898	+	37.9143i	−0.760265	+	1.31682i	0.182449	+	0.983215i	$0.441598\pi$
$829$	−21.8898	+	37.9143i	−0.760265	+	1.31682i	−0.942714	+	0.333603i	$0.891736\pi$
$830$		0			0
$831$	−9.97779	−	17.2820i	−0.346126	−	0.599507i
$832$		0			0
$833$	14.5469	−	21.4258i	0.504020	−	0.742358i
$834$		0			0
$835$	−13.5847	−	23.5294i	−0.470119	−	0.814269i
$836$		0			0
$837$	−29.0243	+	50.2715i	−1.00323	+	1.73764i
$838$		0			0
$839$	−26.9766			−0.931336			−0.465668	−	0.884959i	$-0.654186\pi$
$839$	−26.9766			−0.931336			−0.465668	+	0.884959i	$0.654186\pi$
$840$		0			0
$841$	30.0938			1.03772
$842$		0			0
$843$	14.2912	−	24.7531i	0.492216	−	0.852543i
$844$		0			0
$845$	−19.5247	−	33.8177i	−0.671670	−	1.16337i
$846$		0			0
$847$	1.23855	+	2.33795i	0.0425571	+	0.0803328i
$848$		0			0
$849$	−2.95489	−	5.11802i	−0.101412	−	0.175650i
$850$		0			0
$851$	−3.69963	+	6.40794i	−0.126822	+	0.219661i
$852$		0			0
$853$	−35.5082			−1.21578			−0.607888	−	0.794022i	$-0.707983\pi$
$853$	−35.5082			−1.21578			−0.607888	+	0.794022i	$0.707983\pi$
$854$		0			0
$855$	8.94101			0.305776
$856$		0			0
$857$	16.2509	−	28.1474i	0.555121	−	0.961498i	−0.442773	−	0.896634i	$-0.646005\pi$
$857$	16.2509	−	28.1474i	0.555121	−	0.961498i	0.997894	−	0.0648643i	$-0.0206615\pi$
$858$		0			0
$859$	−1.75704	−	3.04329i	−0.0599495	−	0.103836i	0.834493	−	0.551019i	$-0.185761\pi$
$859$	−1.75704	−	3.04329i	−0.0599495	−	0.103836i	−0.894443	+	0.447183i	$0.852427\pi$
$860$		0			0
$861$	17.4367	−	27.8104i	0.594242	−	0.947775i
$862$		0			0
$863$	18.4549	+	31.9648i	0.628212	+	1.08809i	0.987910	+	0.155026i	$0.0495462\pi$
$863$	18.4549	+	31.9648i	0.628212	+	1.08809i	−0.359699	+	0.933069i	$0.617121\pi$
$864$		0			0
$865$	17.4418	−	30.2101i	0.593040	−	1.02717i
$866$		0			0
$867$	−5.26186			−0.178702
$868$		0			0
$869$	2.73305			0.0927123
$870$		0			0
$871$	4.04442	−	7.00515i	0.137040	−	0.237360i
$872$		0			0
$873$	4.43927	+	7.68904i	0.150247	+	0.260235i
$874$		0			0
$875$	−7.04944	−	0.256909i	−0.238315	−	0.00868512i
$876$		0			0
$877$	21.4672	+	37.1823i	0.724896	+	1.25556i	0.959017	+	0.283349i	$0.0914453\pi$
$877$	21.4672	+	37.1823i	0.724896	+	1.25556i	−0.234121	+	0.972207i	$0.575221\pi$
$878$		0			0
$879$	−20.5418	+	35.5794i	−0.692858	+	1.20006i
$880$		0			0
$881$	−34.2980			−1.15553			−0.577765	−	0.816203i	$-0.696075\pi$
$881$	−34.2980			−1.15553			−0.577765	+	0.816203i	$0.696075\pi$
$882$		0			0
$883$	−0.436395			−0.0146859			−0.00734294	−	0.999973i	$-0.502337\pi$
$883$	−0.436395			−0.0146859			−0.00734294	+	0.999973i	$0.502337\pi$
$884$		0			0
$885$	20.2767	−	35.1203i	0.681594	−	1.18056i
$886$		0			0
$887$	22.4789	+	38.9346i	0.754767	+	1.30729i	0.945490	+	0.325651i	$0.105583\pi$
$887$	22.4789	+	38.9346i	0.754767	+	1.30729i	−0.190723	+	0.981644i	$0.561083\pi$
$888$		0			0
$889$	−21.1192	−	0.769668i	−0.708316	−	0.0258138i
$890$		0			0
$891$	3.67054	+	6.35756i	0.122968	+	0.212986i
$892$		0			0
$893$	−6.55563	+	11.3547i	−0.219376	+	0.379970i
$894$		0			0
$895$	−34.7330			−1.16100
$896$		0			0
$897$	5.54256			0.185061
$898$		0			0
$899$	40.3985	−	69.9722i	1.34737	−	2.33370i
$900$		0			0
$901$	−5.93818	−	10.2852i	−0.197829	−	0.342651i
$902$		0			0
$903$	−3.64804	+	5.81838i	−0.121399	+	0.193623i
$904$		0			0
$905$	33.5505	+	58.1112i	1.11526	+	1.93168i
$906$		0			0
$907$	21.9079	−	37.9456i	0.727440	−	1.25996i	−0.230521	−	0.973067i	$-0.574043\pi$
$907$	21.9079	−	37.9456i	0.727440	−	1.25996i	0.957962	−	0.286897i	$-0.0926236\pi$
$908$		0			0
$909$	−3.12211			−0.103554
$910$		0			0
$911$	40.7046			1.34860			0.674301	−	0.738456i	$-0.264445\pi$
$911$	40.7046			1.34860			0.674301	+	0.738456i	$0.264445\pi$
$912$		0			0
$913$	3.32691	−	5.76238i	0.110105	−	0.190707i
$914$		0			0
$915$	−12.9367	−	22.4071i	−0.427675	−	0.740755i
$916$		0			0
$917$	−6.88178	−	12.9904i	−0.227256	−	0.428980i
$918$		0			0
$919$	2.66435	+	4.61479i	0.0878887	+	0.152228i	0.906619	−	0.421951i	$-0.138655\pi$
$919$	2.66435	+	4.61479i	0.0878887	+	0.152228i	−0.818730	+	0.574179i	$0.805321\pi$
$920$		0			0
$921$	12.9523	−	22.4341i	0.426794	−	0.739229i
$922$		0			0
$923$	−11.4734			−0.377651
$924$		0			0
$925$	−61.4559			−2.02066
$926$		0			0
$927$	−0.484744	+	0.839601i	−0.0159211	+	0.0275761i
$928$		0			0
$929$	6.25340	+	10.8312i	0.205167	+	0.355360i	0.950186	−	0.311683i	$-0.100893\pi$
$929$	6.25340	+	10.8312i	0.205167	+	0.355360i	−0.745019	+	0.667044i	$0.767559\pi$
$930$		0			0
$931$	17.3807	+	35.9126i	0.569629	+	1.17699i
$932$		0			0
$933$	−0.388736	−	0.673310i	−0.0127266	−	0.0220432i
$934$		0			0
$935$	6.08217	−	10.5346i	0.198908	−	0.344519i
$936$		0			0
$937$	41.4152			1.35298			0.676488	−	0.736454i	$-0.263501\pi$
$937$	41.4152			1.35298			0.676488	+	0.736454i	$0.263501\pi$
$938$		0			0
$939$	21.9680			0.716897
$940$		0			0
$941$	−7.82437	+	13.5522i	−0.255067	+	0.441789i	−0.964914	−	0.262567i	$-0.915431\pi$
$941$	−7.82437	+	13.5522i	−0.255067	+	0.441789i	0.709847	+	0.704356i	$0.248764\pi$
$942$		0			0
$943$	2.73236	+	4.73259i	0.0889779	+	0.154114i
$944$		0			0
$945$	−22.4911	−	42.4554i	−0.731637	−	1.38107i
$946$		0			0
$947$	−5.91095	−	10.2381i	−0.192080	−	0.332692i	0.753859	−	0.657036i	$-0.228190\pi$
$947$	−5.91095	−	10.2381i	−0.192080	−	0.332692i	−0.945939	+	0.324343i	$0.894857\pi$
$948$		0			0
$949$	13.4956	−	23.3751i	0.438085	−	0.758786i
$950$		0			0
$951$	−27.8640			−0.903551
$952$		0			0
$953$	−26.8946			−0.871203			−0.435601	−	0.900140i	$-0.643464\pi$
$953$	−26.8946			−0.871203			−0.435601	+	0.900140i	$0.643464\pi$
$954$		0			0
$955$	36.8243	−	63.7815i	1.19161	−	2.06392i
$956$		0			0
$957$	−6.10507	−	10.5743i	−0.197349	−	0.341819i
$958$		0			0
$959$	−0.295353	+	0.471067i	−0.00953743	+	0.0152115i
$960$		0			0
$961$	−39.7355	−	68.8239i	−1.28179	−	2.22013i
$962$		0			0
$963$	−4.64833	+	8.05114i	−0.149790	+	0.259444i
$964$		0			0
$965$	−2.59703			−0.0836012
$966$		0			0
$967$	4.21015			0.135389			0.0676946	−	0.997706i	$-0.478436\pi$
$967$	4.21015			0.135389			0.0676946	+	0.997706i	$0.478436\pi$
$968$		0			0
$969$	−16.7465	+	29.0058i	−0.537976	+	0.931801i
$970$		0			0
$971$	25.5883	+	44.3202i	0.821167	+	1.42230i	0.904814	+	0.425808i	$0.140010\pi$
$971$	25.5883	+	44.3202i	0.821167	+	1.42230i	−0.0836464	+	0.996495i	$0.526657\pi$
$972$		0			0
$973$	29.0840	+	1.05993i	0.932389	+	0.0339799i
$974$		0			0
$975$	23.0174	+	39.8673i	0.737147	+	1.27678i
$976$		0			0
$977$	23.0778	−	39.9719i	0.738323	−	1.27881i	−0.214927	−	0.976630i	$-0.568951\pi$
$977$	23.0778	−	39.9719i	0.738323	−	1.27881i	0.953250	−	0.302183i	$-0.0977154\pi$
$978$		0			0
$979$	−12.8640			−0.411134
$980$		0			0
$981$	−4.32513			−0.138091
$982$		0			0
$983$	−25.1792	+	43.6117i	−0.803092	+	1.39100i	0.114480	+	0.993426i	$0.463480\pi$
$983$	−25.1792	+	43.6117i	−0.803092	+	1.39100i	−0.917572	+	0.397570i	$0.869854\pi$
$984$		0			0
$985$	−16.9684	−	29.3901i	−0.540657	−	0.936445i
$986$		0			0
$987$	9.66071	+	0.352074i	0.307504	+	0.0112066i
$988$		0			0
$989$	−0.571654	−	0.990133i	−0.0181775	−	0.0314844i
$990$		0			0
$991$	−22.8003	+	39.4913i	−0.724275	+	1.25448i	0.234996	+	0.971996i	$0.424492\pi$
$991$	−22.8003	+	39.4913i	−0.724275	+	1.25448i	−0.959272	+	0.282485i	$0.908841\pi$
$992$		0			0
$993$	−13.6945			−0.434583
$994$		0			0
$995$	−44.7838			−1.41974
$996$		0			0
$997$	19.1811	−	33.2226i	0.607470	−	1.05217i	−0.384186	−	0.923256i	$-0.625518\pi$
$997$	19.1811	−	33.2226i	0.607470	−	1.05217i	0.991656	−	0.128913i	$-0.0411489\pi$
$998$		0			0
$999$	−29.2051	−	50.5846i	−0.924007	−	1.60043i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.q.l.529.1		6
4.3	odd	2		308.2.i.a.221.3	yes	6
7.2	even	3	inner	1232.2.q.l.177.1		6
7.3	odd	6		8624.2.a.cn.1.1		3
7.4	even	3		8624.2.a.ci.1.3		3
12.11	even	2		2772.2.s.f.2377.3		6
28.3	even	6		2156.2.a.h.1.3		3
28.11	odd	6		2156.2.a.i.1.1		3
28.19	even	6		2156.2.i.l.177.1		6
28.23	odd	6		308.2.i.a.177.3	✓	6
28.27	even	2		2156.2.i.l.1145.1		6
84.23	even	6		2772.2.s.f.793.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.i.a.177.3	✓	6	28.23	odd	6
308.2.i.a.221.3	yes	6	4.3	odd	2
1232.2.q.l.177.1		6	7.2	even	3	inner
1232.2.q.l.529.1		6	1.1	even	1	trivial
2156.2.a.h.1.3		3	28.3	even	6
2156.2.a.i.1.1		3	28.11	odd	6
2156.2.i.l.177.1		6	28.19	even	6
2156.2.i.l.1145.1		6	28.27	even	2
2772.2.s.f.793.3		6	84.23	even	6
2772.2.s.f.2377.3		6	12.11	even	2
8624.2.a.ci.1.3		3	7.4	even	3
8624.2.a.cn.1.1		3	7.3	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-0.794182 + 1.37556i) q^{3} +(-1.64400 - 2.84748i) q^{5} +(-2.64400 - 0.0963576i) q^{7} +(0.238550 + 0.413181i) q^{9} +O(q^{10})\)	\(q+(-0.794182 + 1.37556i) q^{3} +(-1.64400 - 2.84748i) q^{5} +(-2.64400 - 0.0963576i) q^{7} +(0.238550 + 0.413181i) q^{9} +(-0.500000 + 0.866025i) q^{11} -4.98762 q^{13} +5.22253 q^{15} +(1.84981 - 3.20397i) q^{17} +(2.84981 + 4.93602i) q^{19} +(2.23236 - 3.56046i) q^{21} +(0.349814 + 0.605896i) q^{23} +(-2.90545 + 5.03238i) q^{25} -5.52290 q^{27} +7.68725 q^{29} +(5.25526 - 9.10238i) q^{31} +(-0.794182 - 1.37556i) q^{33} +(4.07234 + 7.68715i) q^{35} +(5.28799 + 9.15907i) q^{37} +(3.96108 - 6.86079i) q^{39} +7.81089 q^{41} -1.63416 q^{43} +(0.784350 - 1.35853i) q^{45} +(1.15019 + 1.99218i) q^{47} +(6.98143 + 0.509538i) q^{49} +(2.93818 + 5.08907i) q^{51} +(1.60507 - 2.78007i) q^{53} +3.28799 q^{55} -9.05308 q^{57} +(3.88255 - 6.72477i) q^{59} +(-2.47710 - 4.29046i) q^{61} +(-0.590912 - 1.11543i) q^{63} +(8.19963 + 14.2022i) q^{65} +(-0.810892 + 1.40451i) q^{67} -1.11126 q^{69} +2.30037 q^{71} +(-2.70582 + 4.68661i) q^{73} +(-4.61491 - 7.99325i) q^{75} +(1.40545 - 2.24159i) q^{77} +(-1.36652 - 2.36689i) q^{79} +(3.67054 - 6.35756i) q^{81} -6.65383 q^{83} -12.1643 q^{85} +(-6.10507 + 10.5743i) q^{87} +(6.43199 + 11.1405i) q^{89} +(13.1872 + 0.480595i) q^{91} +(8.34727 + 14.4579i) q^{93} +(9.37017 - 16.2296i) q^{95} +18.6094 q^{97} -0.477100 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} + 2 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 6 * q + q^3 + 2 * q^5 - 4 * q^7 - 4 * q^9	\( 6 q + q^{3} + 2 q^{5} - 4 q^{7} - 4 q^{9} - 3 q^{11} + 6 q^{13} + 30 q^{15} + 5 q^{17} + 11 q^{19} - 10 q^{21} - 4 q^{23} - 11 q^{25} - 44 q^{27} - 2 q^{29} + 19 q^{31} + q^{33} + 17 q^{35} + 8 q^{37} + 17 q^{39} + 34 q^{41} - 20 q^{43} + 21 q^{45} + 13 q^{47} - 12 q^{49} - 9 q^{53} - 4 q^{55} + 4 q^{57} + 6 q^{59} - 4 q^{61} - 50 q^{63} + 37 q^{65} + 8 q^{67} - 6 q^{69} + 26 q^{71} - 22 q^{73} + 13 q^{75} + 2 q^{77} + 5 q^{79} - 19 q^{81} - 6 q^{83} - 14 q^{85} - 18 q^{87} + 3 q^{89} + 31 q^{91} - 14 q^{93} + 3 q^{95} + 50 q^{97} + 8 q^{99}+O(q^{100}) \) 6 * q + q^3 + 2 * q^5 - 4 * q^7 - 4 * q^9 - 3 * q^11 + 6 * q^13 + 30 * q^15 + 5 * q^17 + 11 * q^19 - 10 * q^21 - 4 * q^23 - 11 * q^25 - 44 * q^27 - 2 * q^29 + 19 * q^31 + q^33 + 17 * q^35 + 8 * q^37 + 17 * q^39 + 34 * q^41 - 20 * q^43 + 21 * q^45 + 13 * q^47 - 12 * q^49 - 9 * q^53 - 4 * q^55 + 4 * q^57 + 6 * q^59 - 4 * q^61 - 50 * q^63 + 37 * q^65 + 8 * q^67 - 6 * q^69 + 26 * q^71 - 22 * q^73 + 13 * q^75 + 2 * q^77 + 5 * q^79 - 19 * q^81 - 6 * q^83 - 14 * q^85 - 18 * q^87 + 3 * q^89 + 31 * q^91 - 14 * q^93 + 3 * q^95 + 50 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

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Database

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