LMFDB - Embedded newform 1386.2.bk.c.901.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(703,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("1386.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bk (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.2
Root			$-1.29724 - 0.347596i$ of defining polynomial
Character	$\chi$	$=$	1386.901
Dual form			1386.2.bk.c.703.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.882559 - 0.509546i) q^{5} +(-2.25578 - 1.38256i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.882559 - 0.509546i) q^{5} +(-2.25578 - 1.38256i) q^{7} -1.00000i q^{8} +(0.509546 + 0.882559i) q^{10} +(2.58273 + 2.08075i) q^{11} +0.167247 q^{13} +(1.26228 + 2.32522i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.47616 - 2.55678i) q^{17} +(0.155850 - 0.269940i) q^{19} -1.01909i q^{20} +(-1.19633 - 3.09335i) q^{22} +(-0.237719 + 0.411742i) q^{23} +(-1.98073 - 3.43072i) q^{25} +(-0.144840 - 0.0836233i) q^{26} +(0.0694427 - 2.64484i) q^{28} +1.89701i q^{29} +(-2.20834 + 1.27498i) q^{31} +(0.866025 - 0.500000i) q^{32} +2.95232i q^{34} +(1.28638 + 2.36961i) q^{35} +(-3.04667 + 5.27699i) q^{37} +(-0.269940 + 0.155850i) q^{38} +(-0.509546 + 0.882559i) q^{40} -10.2084 q^{41} -10.1222i q^{43} +(-0.510616 + 3.27708i) q^{44} +(0.411742 - 0.237719i) q^{46} +(3.28968 + 1.89930i) q^{47} +(3.17706 + 6.23749i) q^{49} +3.96145i q^{50} +(0.0836233 + 0.144840i) q^{52} +(4.21079 + 7.29330i) q^{53} +(-1.21917 - 3.15240i) q^{55} +(-1.38256 + 2.25578i) q^{56} +(0.948505 - 1.64286i) q^{58} +(-5.40617 + 3.12126i) q^{59} +(-5.93960 + 10.2877i) q^{61} +2.54997 q^{62} -1.00000 q^{64} +(-0.147605 - 0.0852198i) q^{65} +(5.19151 + 8.99196i) q^{67} +(1.47616 - 2.55678i) q^{68} +(0.0707684 - 2.69533i) q^{70} -14.5206 q^{71} +(4.85385 + 8.40712i) q^{73} +(5.27699 - 3.04667i) q^{74} +0.311700 q^{76} +(-2.94930 - 8.26448i) q^{77} +(-6.06709 - 3.50284i) q^{79} +(0.882559 - 0.509546i) q^{80} +(8.84069 + 5.10418i) q^{82} -14.6915 q^{83} +3.00868i q^{85} +(-5.06112 + 8.76612i) q^{86} +(2.08075 - 2.58273i) q^{88} +(-5.97639 - 3.45047i) q^{89} +(-0.377271 - 0.231228i) q^{91} -0.475438 q^{92} +(-1.89930 - 3.28968i) q^{94} +(-0.275094 + 0.158826i) q^{95} -11.0218i q^{97} +(0.367330 - 6.99036i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 12 q^{5}+O(q^{10}) $ 16 * q + 8 * q^4 + 12 * q^5	$ 16 q + 8 q^{4} + 12 q^{5} - 8 q^{11} + 8 q^{14} - 8 q^{16} - 8 q^{22} - 16 q^{23} + 36 q^{26} - 12 q^{31} - 16 q^{37} - 12 q^{38} + 8 q^{44} - 24 q^{47} + 8 q^{49} + 28 q^{53} + 4 q^{56} - 12 q^{58} - 60 q^{59} - 16 q^{64} + 12 q^{67} + 60 q^{70} - 8 q^{71} - 44 q^{77} - 12 q^{80} - 20 q^{86} - 4 q^{88} - 96 q^{89} - 36 q^{91} - 32 q^{92}+O(q^{100}) $ 16 * q + 8 * q^4 + 12 * q^5 - 8 * q^11 + 8 * q^14 - 8 * q^16 - 8 * q^22 - 16 * q^23 + 36 * q^26 - 12 * q^31 - 16 * q^37 - 12 * q^38 + 8 * q^44 - 24 * q^47 + 8 * q^49 + 28 * q^53 + 4 * q^56 - 12 * q^58 - 60 * q^59 - 16 * q^64 + 12 * q^67 + 60 * q^70 - 8 * q^71 - 44 * q^77 - 12 * q^80 - 20 * q^86 - 4 * q^88 - 96 * q^89 - 36 * q^91 - 32 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.882559	−	0.509546i	−0.394692	−	0.227876i	0.289499	−	0.957178i	$-0.406511\pi$
$5$	−0.882559	−	0.509546i	−0.394692	−	0.227876i	−0.684191	+	0.729303i	$0.739845\pi$
$6$		0			0
$7$	−2.25578	−	1.38256i	−0.852604	−	0.522558i
$7$	−2.25578	−	1.38256i	−0.852604	−	0.522558i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	0.509546	+	0.882559i	0.161132	+	0.279090i
$11$	2.58273	+	2.08075i	0.778722	+	0.627369i
$11$	2.58273	+	2.08075i	0.778722	+	0.627369i
$12$		0			0
$13$	0.167247			0.0463859			0.0231929	−	0.999731i	$-0.492617\pi$
$13$	0.167247			0.0463859			0.0231929	+	0.999731i	$0.492617\pi$
$14$	1.26228	+	2.32522i	0.337359	+	0.621441i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.47616	−	2.55678i	−0.358021	−	0.620111i	0.629609	−	0.776912i	$-0.283215\pi$
$17$	−1.47616	−	2.55678i	−0.358021	−	0.620111i	−0.987630	+	0.156801i	$0.949882\pi$
$18$		0			0
$19$	0.155850	−	0.269940i	0.0357545	−	0.0619286i	−0.847594	−	0.530645i	$-0.821950\pi$
$19$	0.155850	−	0.269940i	0.0357545	−	0.0619286i	0.883349	+	0.468716i	$0.155283\pi$
$20$		−	1.01909i		−	0.227876i
$21$		0			0
$22$	−1.19633	−	3.09335i	−0.255059	−	0.659503i
$23$	−0.237719	+	0.411742i	−0.0495679	+	0.0858541i	−0.889745	−	0.456458i	$-0.849118\pi$
$23$	−0.237719	+	0.411742i	−0.0495679	+	0.0858541i	0.840177	+	0.542312i	$0.182451\pi$
$24$		0			0
$25$	−1.98073	−	3.43072i	−0.396145	−	0.686144i
$26$	−0.144840	−	0.0836233i	−0.0284054	−	0.0163999i
$27$		0			0
$28$	0.0694427	−	2.64484i	0.0131234	−	0.499828i
$29$			1.89701i			0.352266i	0.984366	+	0.176133i	$0.0563589\pi$
$29$			1.89701i			0.352266i	−0.984366	+	0.176133i	$0.943641\pi$
$30$		0			0
$31$	−2.20834	+	1.27498i	−0.396629	+	0.228994i	−0.685028	−	0.728516i	$-0.740210\pi$
$31$	−2.20834	+	1.27498i	−0.396629	+	0.228994i	0.288400	+	0.957510i	$0.406877\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$			2.95232i			0.506318i
$35$	1.28638	+	2.36961i	0.217438	+	0.400537i
$36$		0			0
$37$	−3.04667	+	5.27699i	−0.500870	+	0.867532i	0.499130	+	0.866527i	$0.333653\pi$
$37$	−3.04667	+	5.27699i	−0.500870	+	0.867532i	−0.999999	+	0.00100474i	$0.999680\pi$
$38$	−0.269940	+	0.155850i	−0.0437901	+	0.0252822i
$39$		0			0
$40$	−0.509546	+	0.882559i	−0.0805662	+	0.139545i
$41$	−10.2084			−1.59428			−0.797138	−	0.603797i	$-0.793654\pi$
$41$	−10.2084			−1.59428			−0.797138	+	0.603797i	$0.793654\pi$
$42$		0			0
$43$		−	10.1222i		−	1.54363i	−0.635848	−	0.771814i	$-0.719350\pi$
$43$		−	10.1222i		−	1.54363i	0.635848	−	0.771814i	$-0.280650\pi$
$44$	−0.510616	+	3.27708i	−0.0769783	+	0.494039i
$45$		0			0
$46$	0.411742	−	0.237719i	0.0607080	−	0.0350498i
$47$	3.28968	+	1.89930i	0.479849	+	0.277041i	0.720354	−	0.693607i	$-0.243980\pi$
$47$	3.28968	+	1.89930i	0.479849	+	0.277041i	−0.240505	+	0.970648i	$0.577313\pi$
$48$		0			0
$49$	3.17706	+	6.23749i	0.453866	+	0.891070i
$50$			3.96145i			0.560234i
$51$		0			0
$52$	0.0836233	+	0.144840i	0.0115965	+	0.0200857i
$53$	4.21079	+	7.29330i	0.578396	+	1.00181i	0.995664	+	0.0930275i	$0.0296544\pi$
$53$	4.21079	+	7.29330i	0.578396	+	1.00181i	−0.417268	+	0.908784i	$0.637012\pi$
$54$		0			0
$55$	−1.21917	−	3.15240i	−0.164393	−	0.425070i
$56$	−1.38256	+	2.25578i	−0.184752	+	0.301441i
$57$		0			0
$58$	0.948505	−	1.64286i	0.124545	−	0.215718i
$59$	−5.40617	+	3.12126i	−0.703824	+	0.406353i	−0.808770	−	0.588125i	$-0.799866\pi$
$59$	−5.40617	+	3.12126i	−0.703824	+	0.406353i	0.104946	+	0.994478i	$0.466533\pi$
$60$		0			0
$61$	−5.93960	+	10.2877i	−0.760488	+	1.31720i	0.182111	+	0.983278i	$0.441707\pi$
$61$	−5.93960	+	10.2877i	−0.760488	+	1.31720i	−0.942599	+	0.333926i	$0.891626\pi$
$62$	2.54997			0.323846
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.147605	−	0.0852198i	−0.0183081	−	0.0105702i
$66$		0			0
$67$	5.19151	+	8.99196i	0.634244	+	1.09854i	0.986675	+	0.162705i	$0.0520219\pi$
$67$	5.19151	+	8.99196i	0.634244	+	1.09854i	−0.352431	+	0.935838i	$0.614645\pi$
$68$	1.47616	−	2.55678i	0.179011	−	0.310055i
$69$		0			0
$70$	0.0707684	−	2.69533i	0.00845845	−	0.322154i
$71$	−14.5206			−1.72328			−0.861639	−	0.507522i	$-0.830561\pi$
$71$	−14.5206			−1.72328			−0.861639	+	0.507522i	$0.830561\pi$
$72$		0			0
$73$	4.85385	+	8.40712i	0.568101	+	0.983979i	0.996754	+	0.0805099i	$0.0256549\pi$
$73$	4.85385	+	8.40712i	0.568101	+	0.983979i	−0.428653	+	0.903469i	$0.641012\pi$
$74$	5.27699	−	3.04667i	0.613438	−	0.354168i
$75$		0			0
$76$	0.311700			0.0357545
$77$	−2.94930	−	8.26448i	−0.336104	−	0.941825i
$78$		0			0
$79$	−6.06709	−	3.50284i	−0.682601	−	0.394100i	0.118233	−	0.992986i	$-0.462277\pi$
$79$	−6.06709	−	3.50284i	−0.682601	−	0.394100i	−0.800834	+	0.598886i	$0.795610\pi$
$80$	0.882559	−	0.509546i	0.0986731	−	0.0569689i
$81$		0			0
$82$	8.84069	+	5.10418i	0.976291	+	0.563662i
$83$	−14.6915			−1.61261			−0.806303	−	0.591502i	$-0.798535\pi$
$83$	−14.6915			−1.61261			−0.806303	+	0.591502i	$0.798535\pi$
$84$		0			0
$85$			3.00868i			0.326337i
$86$	−5.06112	+	8.76612i	−0.545755	+	0.945275i
$87$		0			0
$88$	2.08075	−	2.58273i	0.221808	−	0.275320i
$89$	−5.97639	−	3.45047i	−0.633496	−	0.365749i	0.148609	−	0.988896i	$-0.452520\pi$
$89$	−5.97639	−	3.45047i	−0.633496	−	0.365749i	−0.782105	+	0.623147i	$0.785854\pi$
$90$		0			0
$91$	−0.377271	−	0.231228i	−0.0395488	−	0.0242393i
$92$	−0.475438			−0.0495679
$93$		0			0
$94$	−1.89930	−	3.28968i	−0.195898	−	0.339305i
$95$	−0.275094	+	0.158826i	−0.0282240	+	0.0162952i
$96$		0			0
$97$		−	11.0218i		−	1.11909i	−0.828799	−	0.559547i	$-0.810975\pi$
$97$		−	11.0218i		−	1.11909i	0.828799	−	0.559547i	$-0.189025\pi$
$98$	0.367330	−	6.99036i	0.0371059	−	0.706133i
$99$		0			0
$100$	1.98073	−	3.43072i	0.198073	−	0.343072i
$101$	−2.66752	−	4.62028i	−0.265428	−	0.459735i	0.702248	−	0.711933i	$-0.252180\pi$
$101$	−2.66752	−	4.62028i	−0.265428	−	0.459735i	−0.967676	+	0.252198i	$0.918847\pi$
$102$		0			0
$103$	−10.7849	−	6.22664i	−1.06266	−	0.613529i	−0.136496	−	0.990641i	$-0.543584\pi$
$103$	−10.7849	−	6.22664i	−1.06266	−	0.613529i	−0.926168	+	0.377112i	$0.876917\pi$
$104$		−	0.167247i		−	0.0163999i
$105$		0			0
$106$		−	8.42157i		−	0.817975i
$107$	6.28227	+	3.62707i	0.607330	+	0.350642i	0.771920	−	0.635720i	$-0.219297\pi$
$107$	6.28227	+	3.62707i	0.607330	+	0.350642i	−0.164590	+	0.986362i	$0.552630\pi$
$108$		0			0
$109$	−1.01103	+	0.583716i	−0.0968387	+	0.0559098i	−0.547637	−	0.836716i	$-0.684473\pi$
$109$	−1.01103	+	0.583716i	−0.0968387	+	0.0559098i	0.450799	+	0.892626i	$0.351139\pi$
$110$	−0.520365	+	3.33965i	−0.0496148	+	0.318423i
$111$		0			0
$112$	2.32522	−	1.26228i	0.219713	−	0.119274i
$113$	8.40135			0.790333			0.395166	−	0.918610i	$-0.370687\pi$
$113$	8.40135			0.790333			0.395166	+	0.918610i	$0.370687\pi$
$114$		0			0
$115$	0.419602	−	0.242258i	0.0391281	−	0.0225906i
$116$	−1.64286	+	0.948505i	−0.152536	+	0.0880665i
$117$		0			0
$118$	6.24251			0.574670
$119$	−0.205017	+	7.80841i	−0.0187939	+	0.715796i
$120$		0			0
$121$	2.34098	+	10.7480i	0.212816	+	0.977092i
$122$	10.2877	−	5.93960i	0.931404	−	0.537746i
$123$		0			0
$124$	−2.20834	−	1.27498i	−0.198314	−	0.114497i
$125$			9.13254i			0.816839i
$126$		0			0
$127$			3.53324i			0.313525i	0.987636	+	0.156762i	$0.0501057\pi$
$127$			3.53324i			0.313525i	−0.987636	+	0.156762i	$0.949894\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	0.0852198	+	0.147605i	0.00747427	+	0.0129458i
$131$	−6.98984	+	12.1068i	−0.610705	+	1.05777i	0.380417	+	0.924815i	$0.375781\pi$
$131$	−6.98984	+	12.1068i	−0.610705	+	1.05777i	−0.991122	+	0.132957i	$0.957553\pi$
$132$		0			0
$133$	−0.724772	+	0.393453i	−0.0628457	+	0.0341167i
$134$		−	10.3830i		−	0.896957i
$135$		0			0
$136$	−2.55678	+	1.47616i	−0.219242	+	0.126580i
$137$	−3.50529	−	6.07134i	−0.299477	−	0.518709i	0.676539	−	0.736406i	$-0.263479\pi$
$137$	−3.50529	−	6.07134i	−0.299477	−	0.518709i	−0.976016	+	0.217697i	$0.930146\pi$
$138$		0			0
$139$	−11.4615			−0.972148			−0.486074	−	0.873918i	$-0.661571\pi$
$139$	−11.4615			−0.972148			−0.486074	+	0.873918i	$0.661571\pi$
$140$	−1.40895	+	2.29884i	−0.119078	+	0.194288i
$141$		0			0
$142$	12.5752	+	7.26030i	1.05529	+	0.609270i
$143$	0.431953	+	0.347998i	0.0361217	+	0.0291011i
$144$		0			0
$145$	0.966613	−	1.67422i	0.0802729	−	0.139037i
$146$		−	9.70771i		−	0.803416i
$147$		0			0
$148$	−6.09335			−0.500870
$149$	12.2602	+	7.07841i	1.00439	+	0.579886i	0.909545	−	0.415606i	$-0.136430\pi$
$149$	12.2602	+	7.07841i	1.00439	+	0.579886i	0.0948474	+	0.995492i	$0.469764\pi$
$150$		0			0
$151$	−20.1819	+	11.6520i	−1.64238	+	0.948228i	−0.662394	+	0.749156i	$0.730459\pi$
$151$	−20.1819	+	11.6520i	−1.64238	+	0.948228i	−0.979985	+	0.199072i	$0.936207\pi$
$152$	−0.269940	−	0.155850i	−0.0218951	−	0.0126411i
$153$		0			0
$154$	−1.57807	+	8.63190i	−0.127164	+	0.695578i
$155$	2.59865			0.208728
$156$		0			0
$157$	3.49234	−	2.01630i	0.278719	−	0.160919i	−0.354124	−	0.935198i	$-0.615221\pi$
$157$	3.49234	−	2.01630i	0.278719	−	0.160919i	0.632843	+	0.774280i	$0.281888\pi$
$158$	3.50284	+	6.06709i	0.278671	+	0.482672i
$159$		0			0
$160$	−1.01909			−0.0805662
$161$	1.10550	−	0.600137i	0.0871255	−	0.0472974i
$162$		0			0
$163$	2.76994	−	4.79768i	0.216958	−	0.375783i	−0.736918	−	0.675982i	$-0.763720\pi$
$163$	2.76994	−	4.79768i	0.216958	−	0.375783i	0.953877	+	0.300199i	$0.0970530\pi$
$164$	−5.10418	−	8.84069i	−0.398569	−	0.690342i
$165$		0			0
$166$	12.7233	+	7.34577i	0.987516	+	0.570143i
$167$	21.2252			1.64245			0.821226	−	0.570603i	$-0.193291\pi$
$167$	21.2252			1.64245			0.821226	+	0.570603i	$0.193291\pi$
$168$		0			0
$169$	−12.9720			−0.997848
$170$	1.50434	−	2.60560i	0.115378	−	0.199840i
$171$		0			0
$172$	8.76612	−	5.06112i	0.668411	−	0.385907i
$173$	−7.53277	+	13.0471i	−0.572706	+	0.991956i	0.423581	+	0.905858i	$0.360773\pi$
$173$	−7.53277	+	13.0471i	−0.572706	+	0.991956i	−0.996287	+	0.0860973i	$0.972560\pi$
$174$		0			0
$175$	−0.275094	+	10.4774i	−0.0207951	+	0.792018i
$176$	−3.09335	+	1.19633i	−0.233170	+	0.0901771i
$177$		0			0
$178$	3.45047	+	5.97639i	0.258623	+	0.447949i
$179$	−1.08088	−	1.87214i	−0.0807887	−	0.139930i	0.822800	−	0.568331i	$-0.192411\pi$
$179$	−1.08088	−	1.87214i	−0.0807887	−	0.139930i	−0.903589	+	0.428401i	$0.859077\pi$
$180$		0			0
$181$		−	5.39285i		−	0.400848i	−0.979709	−	0.200424i	$-0.935768\pi$
$181$		−	5.39285i		−	0.400848i	0.979709	−	0.200424i	$-0.0642319\pi$
$182$	0.211112	+	0.388885i	0.0156487	+	0.0288261i
$183$		0			0
$184$	0.411742	+	0.237719i	0.0303540	+	0.0175249i
$185$	5.37774	−	3.10484i	0.395379	−	0.228272i
$186$		0			0
$187$	1.50750	−	9.67499i	0.110239	−	0.707505i
$188$			3.79859i			0.277041i
$189$		0			0
$190$	0.317651			0.0230448
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	−0.736839	−	0.676068i	$-0.763683\pi$
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	0.953912	+	0.300088i	$0.0970159\pi$
$192$		0			0
$193$	−8.31348	+	4.79979i	−0.598417	+	0.345496i	−0.768419	−	0.639947i	$-0.778956\pi$
$193$	−8.31348	+	4.79979i	−0.598417	+	0.345496i	0.170001	+	0.985444i	$0.445623\pi$
$194$	−5.51090	+	9.54515i	−0.395659	+	0.685302i
$195$		0			0
$196$	−3.81329	+	5.87016i	−0.272378	+	0.419297i
$197$			14.8180i			1.05574i	0.849325	+	0.527870i	$0.177009\pi$
$197$			14.8180i			1.05574i	−0.849325	+	0.527870i	$0.822991\pi$
$198$		0			0
$199$	3.55962	−	2.05515i	0.252335	−	0.145686i	−0.368498	−	0.929629i	$-0.620128\pi$
$199$	3.55962	−	2.05515i	0.252335	−	0.145686i	0.620833	+	0.783943i	$0.286795\pi$
$200$	−3.43072	+	1.98073i	−0.242588	+	0.140059i
$201$		0			0
$202$			5.33504i			0.375372i
$203$	2.62273	−	4.27923i	0.184079	−	0.300343i
$204$		0			0
$205$	9.00947	+	5.20162i	0.629249	+	0.363297i
$206$	6.22664	+	10.7849i	0.433831	+	0.751417i
$207$		0			0
$208$	−0.0836233	+	0.144840i	−0.00579823	+	0.0100428i
$209$	0.964197	−	0.372898i	0.0666949	−	0.0257939i
$210$		0			0
$211$			7.52456i			0.518012i	0.965876	+	0.259006i	$0.0833950\pi$
$211$			7.52456i			0.518012i	−0.965876	+	0.259006i	$0.916605\pi$
$212$	−4.21079	+	7.29330i	−0.289198	+	0.500906i
$213$		0			0
$214$	−3.62707	−	6.28227i	−0.247941	−	0.429447i
$215$	−5.15775	+	8.93348i	−0.351755	+	0.609258i
$216$		0			0
$217$	6.74425	+	0.177076i	0.457830	+	0.0120207i
$218$	1.16743			0.0790685
$219$		0			0
$220$	2.12047	−	2.63204i	0.142962	−	0.177452i
$221$	−0.246883	−	0.427613i	−0.0166071	−	0.0287644i
$222$		0			0
$223$		−	13.5885i		−	0.909951i	−0.890504	−	0.454975i	$-0.849648\pi$
$223$		−	13.5885i		−	0.909951i	0.890504	−	0.454975i	$-0.150352\pi$
$224$	−2.64484	−	0.0694427i	−0.176716	−	0.00463983i
$225$		0			0
$226$	−7.27578	−	4.20068i	−0.483978	−	0.279425i
$227$	−10.8318	−	18.7611i	−0.718929	−	1.24522i	−0.961425	−	0.275069i	$-0.911299\pi$
$227$	−10.8318	−	18.7611i	−0.718929	−	1.24522i	0.242496	−	0.970152i	$-0.422034\pi$
$228$		0			0
$229$	26.0355	+	15.0316i	1.72047	+	0.993317i	0.917948	+	0.396700i	$0.129845\pi$
$229$	26.0355	+	15.0316i	1.72047	+	0.993317i	0.802527	+	0.596616i	$0.203489\pi$
$230$	−0.484515			−0.0319480
$231$		0			0
$232$	1.89701			0.124545
$233$	14.0223	+	8.09580i	0.918633	+	0.530373i	0.883199	−	0.468999i	$-0.155385\pi$
$233$	14.0223	+	8.09580i	0.918633	+	0.530373i	0.0354345	+	0.999372i	$0.488718\pi$
$234$		0			0
$235$	−1.93556	−	3.35248i	−0.126262	−	0.218692i
$236$	−5.40617	−	3.12126i	−0.351912	−	0.203176i
$237$		0			0
$238$	4.08175	−	6.65977i	0.264581	−	0.431689i
$239$		−	26.0701i		−	1.68633i	−0.537652	−	0.843167i	$-0.680689\pi$
$239$		−	26.0701i		−	1.68633i	0.537652	−	0.843167i	$-0.319311\pi$
$240$		0			0
$241$	−6.60221	−	11.4354i	−0.425286	−	0.736617i	0.571161	−	0.820838i	$-0.306493\pi$
$241$	−6.60221	−	11.4354i	−0.425286	−	0.736617i	−0.996447	+	0.0842210i	$0.973160\pi$
$242$	3.34666	−	10.4785i	0.215132	−	0.673586i
$243$		0			0
$244$	−11.8792			−0.760488
$245$	0.374342	−	7.12381i	0.0239159	−	0.455124i
$246$		0			0
$247$	0.0260654	−	0.0451466i	0.00165850	−	0.00287261i
$248$	1.27498	+	2.20834i	0.0809615	+	0.140229i
$249$		0			0
$250$	4.56627	−	7.90901i	0.288796	−	0.500210i
$251$		−	28.9829i		−	1.82939i	−0.404149	−	0.914693i	$-0.632432\pi$
$251$		−	28.9829i		−	1.82939i	0.404149	−	0.914693i	$-0.367568\pi$
$252$		0			0
$253$	−1.47070	+	0.568783i	−0.0924618	+	0.0357591i
$254$	1.76662	−	3.05988i	0.110848	−	0.191994i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.05007	−	3.49301i	−0.377393	−	0.217888i	0.299290	−	0.954162i	$-0.403250\pi$
$257$	−6.05007	−	3.49301i	−0.377393	−	0.217888i	−0.676683	+	0.736274i	$0.736583\pi$
$258$		0			0
$259$	14.1684	−	7.69151i	0.880379	−	0.477927i
$260$		−	0.170440i		−	0.0105702i
$261$		0			0
$262$	12.1068	−	6.98984i	0.747958	−	0.431834i
$263$	−3.87174	+	2.23535i	−0.238741	+	0.137837i	−0.614598	−	0.788840i	$-0.710682\pi$
$263$	−3.87174	+	2.23535i	−0.238741	+	0.137837i	0.375857	+	0.926678i	$0.377348\pi$
$264$		0			0
$265$		−	8.58235i		−	0.527210i
$266$	0.824397	+	0.0216453i	0.0505470	+	0.00132716i
$267$		0			0
$268$	−5.19151	+	8.99196i	−0.317122	+	0.549272i
$269$	−1.92024	+	1.10865i	−0.117079	+	0.0675956i	−0.557396	−	0.830247i	$-0.688199\pi$
$269$	−1.92024	+	1.10865i	−0.117079	+	0.0675956i	0.440317	+	0.897842i	$0.354866\pi$
$270$		0			0
$271$	−11.2561	+	19.4961i	−0.683759	+	1.18431i	0.290066	+	0.957007i	$0.406323\pi$
$271$	−11.2561	+	19.4961i	−0.683759	+	1.18431i	−0.973825	+	0.227299i	$0.927011\pi$
$272$	2.95232			0.179011
$273$		0			0
$274$			7.01058i			0.423524i
$275$	2.02278	−	12.9820i	0.121978	−	0.782845i
$276$		0			0
$277$	21.1880	−	12.2329i	1.27306	−	0.735004i	0.297500	−	0.954722i	$-0.403847\pi$
$277$	21.1880	−	12.2329i	1.27306	−	0.735004i	0.975563	+	0.219718i	$0.0705138\pi$
$278$	9.92591	+	5.73073i	0.595317	+	0.343706i
$279$		0			0
$280$	2.36961	−	1.28638i	0.141611	−	0.0768759i
$281$		−	11.3532i		−	0.677273i	−0.940917	−	0.338636i	$-0.890034\pi$
$281$		−	11.3532i		−	0.677273i	0.940917	−	0.338636i	$-0.109966\pi$
$282$		0			0
$283$	−10.8268	−	18.7526i	−0.643589	−	1.11473i	−0.984626	−	0.174679i	$-0.944111\pi$
$283$	−10.8268	−	18.7526i	−0.643589	−	1.11473i	0.341037	−	0.940050i	$-0.389222\pi$
$284$	−7.26030	−	12.5752i	−0.430819	−	0.746201i
$285$		0			0
$286$	−0.200083	−	0.517352i	−0.0118312	−	0.0305916i
$287$	23.0278	+	14.1137i	1.35929	+	0.833102i
$288$		0			0
$289$	4.14191	−	7.17400i	0.243642	−	0.422000i
$290$	−1.67422	+	0.966613i	−0.0983138	+	0.0567615i
$291$		0			0
$292$	−4.85385	+	8.40712i	−0.284050	+	0.491990i
$293$	12.1233			0.708249			0.354124	−	0.935198i	$-0.384779\pi$
$293$	12.1233			0.708249			0.354124	+	0.935198i	$0.384779\pi$
$294$		0			0
$295$	6.36169			0.370392
$296$	5.27699	+	3.04667i	0.306719	+	0.177084i
$297$		0			0
$298$	−7.07841	−	12.2602i	−0.410041	−	0.710213i
$299$	−0.0397577	+	0.0688624i	−0.00229925	+	0.00398242i
$300$		0			0
$301$	−13.9946	+	22.8335i	−0.806636	+	1.31610i
$302$	23.3040			1.34100
$303$		0			0
$304$	0.155850	+	0.269940i	0.00893862	+	0.0154821i
$305$	10.4841	−	6.05300i	0.600318	−	0.346594i
$306$		0			0
$307$	−9.65817			−0.551221			−0.275610	−	0.961269i	$-0.588880\pi$
$307$	−9.65817			−0.551221			−0.275610	+	0.961269i	$0.588880\pi$
$308$	5.68260	−	6.68641i	0.323796	−	0.380994i
$309$		0			0
$310$	−2.25050	−	1.29932i	−0.127820	−	0.0737967i
$311$	15.3094	−	8.83890i	0.868118	−	0.501208i	0.00139530	−	0.999999i	$-0.499556\pi$
$311$	15.3094	−	8.83890i	0.868118	−	0.501208i	0.866722	+	0.498791i	$0.166223\pi$
$312$		0			0
$313$	−24.9505	−	14.4052i	−1.41028	−	0.814228i	−0.414869	−	0.909881i	$-0.636173\pi$
$313$	−24.9505	−	14.4052i	−1.41028	−	0.814228i	−0.995415	+	0.0956530i	$0.969506\pi$
$314$	−4.03261			−0.227573
$315$		0			0
$316$		−	7.00567i		−	0.394100i
$317$	5.17280	−	8.95955i	0.290533	−	0.503218i	−0.683403	−	0.730042i	$-0.739501\pi$
$317$	5.17280	−	8.95955i	0.290533	−	0.503218i	0.973936	+	0.226823i	$0.0728340\pi$
$318$		0			0
$319$	−3.94720	+	4.89946i	−0.221001	+	0.274317i
$320$	0.882559	+	0.509546i	0.0493366	+	0.0284845i
$321$		0			0
$322$	−1.25746	−	0.0330157i	−0.0700754	−	0.00183989i
$323$	−0.920239			−0.0512034
$324$		0			0
$325$	−0.331270	−	0.573776i	−0.0183755	−	0.0318274i
$326$	−4.79768	+	2.76994i	−0.265719	+	0.153413i
$327$		0			0
$328$			10.2084i			0.563662i
$329$	−4.79489	−	8.83257i	−0.264351	−	0.486955i
$330$		0			0
$331$	13.4224	−	23.2483i	0.737763	−	1.27784i	−0.215737	−	0.976451i	$-0.569215\pi$
$331$	13.4224	−	23.2483i	0.737763	−	1.27784i	0.953500	−	0.301392i	$-0.0974512\pi$
$332$	−7.34577	−	12.7233i	−0.403152	−	0.698279i
$333$		0			0
$334$	−18.3815	−	10.6126i	−1.00579	−	0.580694i
$335$		−	10.5813i		−	0.578116i
$336$		0			0
$337$		−	14.5505i		−	0.792614i	−0.918118	−	0.396307i	$-0.870292\pi$
$337$		−	14.5505i		−	0.792614i	0.918118	−	0.396307i	$-0.129708\pi$
$338$	11.2341	+	6.48601i	0.611055	+	0.352793i
$339$		0			0
$340$	−2.60560	+	1.50434i	−0.141308	+	0.0815844i
$341$	−8.35645	−	1.30205i	−0.452527	−	0.0705102i
$342$		0			0
$343$	1.45696	−	18.4629i	0.0786683	−	0.996901i
$344$	−10.1222			−0.545755
$345$		0			0
$346$	13.0471	−	7.53277i	0.701418	−	0.404964i
$347$	−24.7179	+	14.2709i	−1.32693	+	0.766101i	−0.984823	−	0.173562i	$-0.944472\pi$
$347$	−24.7179	+	14.2709i	−1.32693	+	0.766101i	−0.342102	+	0.939663i	$0.611139\pi$
$348$		0			0
$349$	34.6026			1.85224			0.926118	−	0.377235i	$-0.123125\pi$
$349$	34.6026			1.85224			0.926118	+	0.377235i	$0.123125\pi$
$350$	5.47694	−	8.93615i	0.292755	−	0.477658i
$351$		0			0
$352$	3.27708	+	0.510616i	0.174669	+	0.0272159i
$353$	14.6534	−	8.46017i	0.779924	−	0.450289i	−0.0564792	−	0.998404i	$-0.517987\pi$
$353$	14.6534	−	8.46017i	0.779924	−	0.450289i	0.836403	+	0.548114i	$0.184654\pi$
$354$		0			0
$355$	12.8153	+	7.39891i	0.680164	+	0.392693i
$356$		−	6.90094i		−	0.365749i
$357$		0			0
$358$			2.16176i			0.114252i
$359$	26.2848	+	15.1755i	1.38726	+	0.800934i	0.993006	−	0.118067i	$-0.0376698\pi$
$359$	26.2848	+	15.1755i	1.38726	+	0.800934i	0.394254	+	0.919002i	$0.371003\pi$
$360$		0			0
$361$	9.45142	+	16.3703i	0.497443	+	0.861597i
$362$	−2.69643	+	4.67035i	−0.141721	+	0.245468i
$363$		0			0
$364$	0.0116141	−	0.442341i	0.000608742	−	0.0231849i
$365$		−	9.89304i		−	0.517825i
$366$		0			0
$367$	−15.0875	+	8.71075i	−0.787559	+	0.454698i	−0.839103	−	0.543973i	$-0.816919\pi$
$367$	−15.0875	+	8.71075i	−0.787559	+	0.454698i	0.0515432	+	0.998671i	$0.483586\pi$
$368$	−0.237719	−	0.411742i	−0.0123920	−	0.0214635i
$369$		0			0
$370$	−6.20968			−0.322826
$371$	0.584817	−	22.2737i	0.0303622	−	1.15639i
$372$		0			0
$373$	−7.92596	−	4.57606i	−0.410391	−	0.236939i	0.280567	−	0.959834i	$-0.409478\pi$
$373$	−7.92596	−	4.57606i	−0.410391	−	0.236939i	−0.690958	+	0.722895i	$0.742811\pi$
$374$	−6.14303	+	7.62504i	−0.317649	+	0.394281i
$375$		0			0
$376$	1.89930	−	3.28968i	0.0979488	−	0.169652i
$377$			0.317269i			0.0163402i
$378$		0			0
$379$	−6.15382			−0.316100			−0.158050	−	0.987431i	$-0.550521\pi$
$379$	−6.15382			−0.316100			−0.158050	+	0.987431i	$0.550521\pi$
$380$	−0.275094	−	0.158826i	−0.0141120	−	0.00814758i
$381$		0			0
$382$	−5.19615	+	3.00000i	−0.265858	+	0.153493i
$383$	−11.2281	−	6.48253i	−0.573728	−	0.331242i	0.184909	−	0.982756i	$-0.440801\pi$
$383$	−11.2281	−	6.48253i	−0.573728	−	0.331242i	−0.758637	+	0.651514i	$0.774134\pi$
$384$		0			0
$385$	−1.60820	+	8.79670i	−0.0819612	+	0.448321i
$386$	9.59958			0.488606
$387$		0			0
$388$	9.54515	−	5.51090i	0.484582	−	0.279773i
$389$	2.58323	+	4.47429i	0.130975	+	0.226856i	0.924053	−	0.382265i	$-0.124856\pi$
$389$	2.58323	+	4.47429i	0.130975	+	0.226856i	−0.793078	+	0.609121i	$0.791523\pi$
$390$		0			0
$391$	1.40365			0.0709854
$392$	6.23749	−	3.17706i	0.315041	−	0.160466i
$393$		0			0
$394$	7.40901	−	12.8328i	0.373261	−	0.646506i
$395$	3.56971	+	6.18292i	0.179612	+	0.311097i
$396$		0			0
$397$	8.01690	+	4.62856i	0.402357	+	0.232301i	0.687500	−	0.726184i	$-0.258708\pi$
$397$	8.01690	+	4.62856i	0.402357	+	0.232301i	−0.285144	+	0.958485i	$0.592041\pi$
$398$	−4.11030			−0.206030
$399$		0			0
$400$	3.96145			0.198073
$401$	−15.4624	+	26.7816i	−0.772155	+	1.33741i	0.164225	+	0.986423i	$0.447488\pi$
$401$	−15.4624	+	26.7816i	−0.772155	+	1.33741i	−0.936380	+	0.350988i	$0.885846\pi$
$402$		0			0
$403$	−0.369337	+	0.213237i	−0.0183980	+	0.0106221i
$404$	2.66752	−	4.62028i	0.132714	−	0.229867i
$405$		0			0
$406$	−4.41097	+	2.39456i	−0.218913	+	0.118840i
$407$	−18.8488	+	7.28968i	−0.934301	+	0.361336i
$408$		0			0
$409$	11.9198	+	20.6458i	0.589399	+	1.02087i	0.994311	+	0.106513i	$0.0339686\pi$
$409$	11.9198	+	20.6458i	0.589399	+	1.02087i	−0.404913	+	0.914355i	$0.632698\pi$
$410$	−5.20162	−	9.00947i	−0.256890	−	0.444946i
$411$		0			0
$412$		−	12.4533i		−	0.613529i
$413$	16.5104	+	0.433497i	0.812426	+	0.0213310i
$414$		0			0
$415$	12.9662	+	7.48601i	0.636484	+	0.367474i
$416$	0.144840	−	0.0836233i	0.00710136	−	0.00409997i
$417$		0			0
$418$	−1.02147	−	0.159159i	−0.0499616	−	0.00778473i
$419$		−	5.03426i		−	0.245940i	−0.992410	−	0.122970i	$-0.960758\pi$
$419$		−	5.03426i		−	0.245940i	0.992410	−	0.122970i	$-0.0392418\pi$
$420$		0			0
$421$	−16.9250			−0.824872			−0.412436	−	0.910987i	$-0.635322\pi$
$421$	−16.9250			−0.824872			−0.412436	+	0.910987i	$0.635322\pi$
$422$	3.76228	−	6.51646i	0.183145	−	0.317216i
$423$		0			0
$424$	7.29330	−	4.21079i	0.354194	−	0.204494i
$425$	−5.84773	+	10.1286i	−0.283657	+	0.491308i
$426$		0			0
$427$	27.6218	−	14.9949i	1.33671	−	0.725654i
$428$			7.25414i			0.350642i
$429$		0			0
$430$	8.93348	−	5.15775i	0.430811	−	0.248729i
$431$	−5.19535	+	2.99953i	−0.250251	+	0.144482i	−0.619879	−	0.784697i	$-0.712818\pi$
$431$	−5.19535	+	2.99953i	−0.250251	+	0.144482i	0.369628	+	0.929180i	$0.379485\pi$
$432$		0			0
$433$		−	36.1175i		−	1.73570i	−0.496829	−	0.867849i	$-0.665502\pi$
$433$		−	36.1175i		−	1.73570i	0.496829	−	0.867849i	$-0.334498\pi$
$434$	−5.75216	−	3.52548i	−0.276112	−	0.169228i
$435$		0			0
$436$	−1.01103	−	0.583716i	−0.0484193	−	0.0279549i
$437$	0.0740971	+	0.128340i	0.00354455	+	0.00613934i
$438$		0			0
$439$	−5.67481	+	9.82906i	−0.270844	+	0.469116i	−0.969078	−	0.246754i	$-0.920636\pi$
$439$	−5.67481	+	9.82906i	−0.270844	+	0.469116i	0.698234	+	0.715869i	$0.253969\pi$
$440$	−3.15240	+	1.21917i	−0.150285	+	0.0581219i
$441$		0			0
$442$			0.493765i			0.0234860i
$443$	−2.37538	+	4.11428i	−0.112858	+	0.195475i	−0.916921	−	0.399068i	$-0.869334\pi$
$443$	−2.37538	+	4.11428i	−0.112858	+	0.195475i	0.804064	+	0.594543i	$0.202667\pi$
$444$		0			0
$445$	3.51634	+	6.09048i	0.166691	+	0.288717i
$446$	−6.79423	+	11.7680i	−0.321716	+	0.557229i
$447$		0			0
$448$	2.25578	+	1.38256i	0.106575	+	0.0653198i
$449$	−7.33297			−0.346064			−0.173032	−	0.984916i	$-0.555356\pi$
$449$	−7.33297			−0.346064			−0.173032	+	0.984916i	$0.555356\pi$
$450$		0			0
$451$	−26.3654	−	21.2410i	−1.24150	−	1.00020i
$452$	4.20068	+	7.27578i	0.197583	+	0.342224i
$453$		0			0
$454$			21.6635i			1.01672i
$455$	0.215143	+	0.396310i	0.0100860	+	0.0185793i
$456$		0			0
$457$	11.7066	+	6.75879i	0.547610	+	0.316163i	0.748158	−	0.663521i	$-0.230939\pi$
$457$	11.7066	+	6.75879i	0.547610	+	0.316163i	−0.200547	+	0.979684i	$0.564272\pi$
$458$	−15.0316	−	26.0355i	−0.702381	−	1.21656i
$459$		0			0
$460$	0.419602	+	0.242258i	0.0195641	+	0.0112953i
$461$	−18.5730			−0.865033			−0.432516	−	0.901626i	$-0.642374\pi$
$461$	−18.5730			−0.865033			−0.432516	+	0.901626i	$0.642374\pi$
$462$		0			0
$463$	28.2849			1.31451			0.657256	−	0.753667i	$-0.271717\pi$
$463$	28.2849			1.31451			0.657256	+	0.753667i	$0.271717\pi$
$464$	−1.64286	−	0.948505i	−0.0762678	−	0.0440332i
$465$		0			0
$466$	−8.09580	−	14.0223i	−0.375030	−	0.649572i
$467$	18.6881	+	10.7896i	0.864782	+	0.499282i	0.865611	−	0.500717i	$-0.166930\pi$
$467$	18.6881	+	10.7896i	0.864782	+	0.499282i	−0.000828665		1.00000i	$0.500264\pi$
$468$		0			0
$469$	0.721025	−	27.4614i	0.0332938	−	1.26805i
$470$			3.87112i			0.178561i
$471$		0			0
$472$	3.12126	+	5.40617i	0.143667	+	0.248839i
$473$	21.0618	−	26.1430i	0.968425	−	1.20206i
$474$		0			0
$475$	−1.23479			−0.0566559
$476$	−6.86479	+	3.72665i	−0.314647	+	0.170811i
$477$		0			0
$478$	−13.0350	+	22.5774i	−0.596209	+	1.03266i
$479$	−3.46780	−	6.00641i	−0.158448	−	0.274440i	0.775861	−	0.630904i	$-0.217316\pi$
$479$	−3.46780	−	6.00641i	−0.158448	−	0.274440i	−0.934309	+	0.356464i	$0.883982\pi$
$480$		0			0
$481$	−0.509546	+	0.882559i	−0.0232333	+	0.0402412i
$482$			13.2044i			0.601445i
$483$		0			0
$484$	−8.13757	+	7.40135i	−0.369889	+	0.336425i
$485$	−5.61611	+	9.72738i	−0.255014	+	0.441698i
$486$		0			0
$487$	6.08702	+	10.5430i	0.275829	+	0.477750i	0.970344	−	0.241728i	$-0.0777143\pi$
$487$	6.08702	+	10.5430i	0.275829	+	0.477750i	−0.694515	+	0.719478i	$0.744381\pi$
$488$	10.2877	+	5.93960i	0.465702	+	0.268873i
$489$		0			0
$490$	−3.88610	+	5.98223i	−0.175556	+	0.270250i
$491$		−	2.37152i		−	0.107025i	−0.998567	−	0.0535125i	$-0.982958\pi$
$491$		−	2.37152i		−	0.107025i	0.998567	−	0.0535125i	$-0.0170417\pi$
$492$		0			0
$493$	4.85024	−	2.80029i	0.218444	−	0.126119i
$494$	−0.0451466	+	0.0260654i	−0.00203124	+	0.00117274i
$495$		0			0
$496$		−	2.54997i		−	0.114497i
$497$	32.7552	+	20.0756i	1.46927	+	0.900513i
$498$		0			0
$499$	1.96446	−	3.40255i	0.0879413	−	0.152319i	−0.818699	−	0.574222i	$-0.805305\pi$
$499$	1.96446	−	3.40255i	0.0879413	−	0.152319i	0.906641	+	0.421903i	$0.138638\pi$
$500$	−7.90901	+	4.56627i	−0.353702	+	0.204210i
$501$		0			0
$502$	−14.4915	+	25.1000i	−0.646786	+	1.12027i
$503$	−19.8703			−0.885971			−0.442986	−	0.896529i	$-0.646081\pi$
$503$	−19.8703			−0.885971			−0.442986	+	0.896529i	$0.646081\pi$
$504$		0			0
$505$			5.43689i			0.241938i
$506$	1.55805	+	0.242767i	0.0692638	+	0.0107923i
$507$		0			0
$508$	−3.05988	+	1.76662i	−0.135760	+	0.0783812i
$509$	−13.2438	−	7.64634i	−0.587023	−	0.338918i	0.176896	−	0.984229i	$-0.443394\pi$
$509$	−13.2438	−	7.64634i	−0.587023	−	0.338918i	−0.763920	+	0.645312i	$0.776728\pi$
$510$		0			0
$511$	0.674129	−	25.6753i	0.0298217	−	1.13581i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	3.49301	+	6.05007i	0.154070	+	0.266857i
$515$	6.34552	+	10.9908i	0.279617	+	0.484311i
$516$		0			0
$517$	4.54439	+	11.7504i	0.199862	+	0.516780i
$518$	−16.1159	−	0.423138i	−0.708093	−	0.0185916i
$519$		0			0
$520$	−0.0852198	+	0.147605i	−0.00373714	+	0.00647291i
$521$	0.121861	−	0.0703565i	0.00533883	−	0.00308237i	−0.497328	−	0.867562i	$-0.665686\pi$
$521$	0.121861	−	0.0703565i	0.00533883	−	0.00308237i	0.502667	+	0.864480i	$0.332352\pi$
$522$		0			0
$523$	4.56153	−	7.90081i	0.199462	−	0.345478i	−0.748892	−	0.662692i	$-0.769414\pi$
$523$	4.56153	−	7.90081i	0.199462	−	0.345478i	0.948354	+	0.317214i	$0.102747\pi$
$524$	−13.9797			−0.610705
$525$		0			0
$526$	4.47070			0.194932
$527$	6.51971	+	3.76416i	0.284003	+	0.163969i
$528$		0			0
$529$	11.3870	+	19.7228i	0.495086	+	0.857514i
$530$	−4.29118	+	7.43253i	−0.186397	+	0.322849i
$531$		0			0
$532$	−0.703126	−	0.430944i	−0.0304844	−	0.0186838i
$533$	−1.70731			−0.0739519
$534$		0			0
$535$	−3.69632	−	6.40221i	−0.159806	−	0.276792i
$536$	8.99196	−	5.19151i	0.388394	−	0.224239i
$537$		0			0
$538$	2.21730			0.0955946
$539$	−4.77316	+	22.7204i	−0.205595	+	0.978637i
$540$		0			0
$541$	21.6730	+	12.5129i	0.931797	+	0.537973i	0.887379	−	0.461040i	$-0.152524\pi$
$541$	21.6730	+	12.5129i	0.931797	+	0.537973i	0.0444172	+	0.999013i	$0.485857\pi$
$542$	19.4961	−	11.2561i	0.837430	−	0.483491i
$543$		0			0
$544$	−2.55678	−	1.47616i	−0.109621	−	0.0632898i
$545$	1.18972			0.0509620
$546$		0			0
$547$		−	36.7246i		−	1.57023i	−0.619348	−	0.785116i	$-0.712603\pi$
$547$		−	36.7246i		−	1.57023i	0.619348	−	0.785116i	$-0.287397\pi$
$548$	3.50529	−	6.07134i	0.149738	−	0.259355i
$549$		0			0
$550$	−8.24279	+	10.2314i	−0.351474	+	0.436267i
$551$	0.512080	+	0.295649i	0.0218153	+	0.0125951i
$552$		0			0
$553$	8.84313	+	16.2897i	0.376048	+	0.692710i
$554$	−24.4658			−1.03945
$555$		0			0
$556$	−5.73073	−	9.92591i	−0.243037	−	0.420952i
$557$	−33.5815	+	19.3883i	−1.42290	+	0.821509i	−0.996545	−	0.0830490i	$-0.973534\pi$
$557$	−33.5815	+	19.3883i	−1.42290	+	0.821509i	−0.426350	+	0.904558i	$0.640201\pi$
$558$		0			0
$559$		−	1.69291i		−	0.0716025i
$560$	−2.69533	−	0.0707684i	−0.113899	−	0.00299051i
$561$		0			0
$562$	−5.67658	+	9.83212i	−0.239452	+	0.414743i
$563$	−21.6247	−	37.4550i	−0.911371	−	1.57854i	−0.812129	−	0.583477i	$-0.801692\pi$
$563$	−21.6247	−	37.4550i	−0.911371	−	1.57854i	−0.0992415	−	0.995063i	$-0.531642\pi$
$564$		0			0
$565$	−7.41469	−	4.28087i	−0.311938	−	0.180098i
$566$			21.6537i			0.910172i
$567$		0			0
$568$			14.5206i			0.609270i
$569$	−18.4783	−	10.6685i	−0.774651	−	0.447245i	0.0598803	−	0.998206i	$-0.480928\pi$
$569$	−18.4783	−	10.6685i	−0.774651	−	0.447245i	−0.834531	+	0.550961i	$0.814261\pi$
$570$		0			0
$571$	−19.5677	+	11.2974i	−0.818883	+	0.472782i	−0.850031	−	0.526733i	$-0.823417\pi$
$571$	−19.5677	+	11.2974i	−0.818883	+	0.472782i	0.0311482	+	0.999515i	$0.490084\pi$
$572$	−0.0853989	+	0.548081i	−0.00357071	+	0.0229164i
$573$		0			0
$574$	−12.8858	−	23.7367i	−0.537843	−	0.990749i
$575$	1.88343			0.0785443
$576$		0			0
$577$	−29.3358	+	16.9370i	−1.22126	+	0.705097i	−0.965187	−	0.261559i	$-0.915763\pi$
$577$	−29.3358	+	16.9370i	−1.22126	+	0.705097i	−0.256077	+	0.966656i	$0.582430\pi$
$578$	−7.17400	+	4.14191i	−0.298399	+	0.172281i
$579$		0			0
$580$	1.93323			0.0802729
$581$	33.1409	+	20.3119i	1.37491	+	0.842681i
$582$		0			0
$583$	−4.30019	+	27.5982i	−0.178096	+	1.14300i
$584$	8.40712	−	4.85385i	0.347889	−	0.200854i
$585$		0			0
$586$	−10.4991	−	6.06163i	−0.433712	−	0.250404i
$587$		−	6.07819i		−	0.250874i	−0.992102	−	0.125437i	$-0.959967\pi$
$587$		−	6.07819i		−	0.250874i	0.992102	−	0.125437i	$-0.0400332\pi$
$588$		0			0
$589$			0.794825i			0.0327502i
$590$	−5.50939	−	3.18085i	−0.226818	−	0.130953i
$591$		0			0
$592$	−3.04667	−	5.27699i	−0.125217	−	0.216883i
$593$	−0.809196	+	1.40157i	−0.0332297	+	0.0575555i	−0.882162	−	0.470946i	$-0.843913\pi$
$593$	−0.809196	+	1.40157i	−0.0332297	+	0.0575555i	0.848932	+	0.528502i	$0.177246\pi$
$594$		0			0
$595$	4.15968	−	6.78692i	0.170530	−	0.278236i
$596$			14.1568i			0.579886i
$597$		0			0
$598$	0.0688624	−	0.0397577i	0.00281599	−	0.00162581i
$599$	2.63955	+	4.57184i	0.107849	+	0.186800i	0.914899	−	0.403684i	$-0.132270\pi$
$599$	2.63955	+	4.57184i	0.107849	+	0.186800i	−0.807050	+	0.590484i	$0.798937\pi$
$600$		0			0
$601$	32.7945			1.33771			0.668857	−	0.743391i	$-0.266784\pi$
$601$	32.7945			1.33771			0.668857	+	0.743391i	$0.266784\pi$
$602$	23.5365	−	12.7771i	0.959274	−	0.520756i
$603$		0			0
$604$	−20.1819	−	11.6520i	−0.821189	−	0.474114i
$605$	3.41056	−	10.6786i	0.138659	−	0.434147i
$606$		0			0
$607$	−0.332910	+	0.576616i	−0.0135124	+	0.0234041i	−0.872703	−	0.488252i	$-0.837635\pi$
$607$	−0.332910	+	0.576616i	−0.0135124	+	0.0234041i	0.859190	+	0.511656i	$0.170968\pi$
$608$		−	0.311700i		−	0.0126411i
$609$		0			0
$610$	−12.1060			−0.490158
$611$	0.550188	+	0.317651i	0.0222582	+	0.0128508i
$612$		0			0
$613$	−3.71908	+	2.14721i	−0.150212	+	0.0867251i	−0.573222	−	0.819400i	$-0.694307\pi$
$613$	−3.71908	+	2.14721i	−0.150212	+	0.0867251i	0.423010	+	0.906125i	$0.360973\pi$
$614$	8.36422	+	4.82908i	0.337552	+	0.194886i
$615$		0			0
$616$	−8.26448	+	2.94930i	−0.332985	+	0.118831i
$617$	30.9913			1.24766			0.623831	−	0.781559i	$-0.285575\pi$
$617$	30.9913			1.24766			0.623831	+	0.781559i	$0.285575\pi$
$618$		0			0
$619$	−0.685357	+	0.395691i	−0.0275468	+	0.0159042i	−0.513710	−	0.857964i	$-0.671729\pi$
$619$	−0.685357	+	0.395691i	−0.0275468	+	0.0159042i	0.486163	+	0.873868i	$0.338396\pi$
$620$	1.29932	+	2.25050i	0.0521821	+	0.0903821i
$621$		0			0
$622$	−17.6778			−0.708815
$623$	8.71092	+	16.0462i	0.348996	+	0.642877i
$624$		0			0
$625$	−5.25019	+	9.09359i	−0.210007	+	0.363744i
$626$	14.4052	+	24.9505i	0.575746	+	0.997222i
$627$		0			0
$628$	3.49234	+	2.01630i	0.139360	+	0.0804593i
$629$	17.9895			0.717288
$630$		0			0
$631$	−34.3677			−1.36816			−0.684078	−	0.729409i	$-0.739795\pi$
$631$	−34.3677			−1.36816			−0.684078	+	0.729409i	$0.739795\pi$
$632$	−3.50284	+	6.06709i	−0.139335	+	0.241336i
$633$		0			0
$634$	−8.95955	+	5.17280i	−0.355829	+	0.205438i
$635$	1.80035	−	3.11830i	0.0714447	−	0.123746i
$636$		0			0
$637$	0.531353	+	1.04320i	0.0210530	+	0.0413331i
$638$	5.86811	−	2.26946i	0.232321	−	0.0898488i
$639$		0			0
$640$	−0.509546	−	0.882559i	−0.0201416	−	0.0348862i
$641$	2.47939	+	4.29443i	0.0979301	+	0.169620i	0.910828	−	0.412787i	$-0.135444\pi$
$641$	2.47939	+	4.29443i	0.0979301	+	0.169620i	−0.812898	+	0.582407i	$0.802111\pi$
$642$		0			0
$643$			48.1404i			1.89847i	0.314562	+	0.949237i	$0.398142\pi$
$643$			48.1404i			1.89847i	−0.314562	+	0.949237i	$0.601858\pi$
$644$	1.07248	+	0.657322i	0.0422618	+	0.0259021i
$645$		0			0
$646$	0.796950	+	0.460119i	0.0313556	+	0.0181031i
$647$	2.74160	−	1.58286i	0.107783	−	0.0622287i	−0.445139	−	0.895461i	$-0.646846\pi$
$647$	2.74160	−	1.58286i	0.107783	−	0.0622287i	0.552923	+	0.833233i	$0.313513\pi$
$648$		0			0
$649$	−20.4572	−	3.18753i	−0.803016	−	0.125121i
$650$			0.662540i			0.0259869i
$651$		0			0
$652$	5.53988			0.216958
$653$	−11.0606	+	19.1575i	−0.432833	+	0.749689i	−0.997116	−	0.0758922i	$-0.975820\pi$
$653$	−11.0606	+	19.1575i	−0.432833	+	0.749689i	0.564283	+	0.825582i	$0.309153\pi$
$654$		0			0
$655$	12.3379	−	7.12329i	0.482081	−	0.278330i
$656$	5.10418	−	8.84069i	0.199285	−	0.345171i
$657$		0			0
$658$	−0.263785	+	10.0467i	−0.0102834	+	0.391660i
$659$		−	24.6258i		−	0.959286i	−0.877464	−	0.479643i	$-0.840766\pi$
$659$		−	24.6258i		−	0.959286i	0.877464	−	0.479643i	$-0.159234\pi$
$660$		0			0
$661$	24.0205	−	13.8682i	0.934289	−	0.539412i	0.0461236	−	0.998936i	$-0.485313\pi$
$661$	24.0205	−	13.8682i	0.934289	−	0.539412i	0.888166	+	0.459524i	$0.151980\pi$
$662$	−23.2483	+	13.4224i	−0.903572	+	0.521677i
$663$		0			0
$664$			14.6915i			0.570143i
$665$	0.840136	+	0.0220585i	0.0325791	+	0.000855394i
$666$		0			0
$667$	−0.781078	−	0.450956i	−0.0302435	−	0.0174611i
$668$	10.6126	+	18.3815i	0.410613	+	0.711202i
$669$		0			0
$670$	−5.29063	+	9.16363i	−0.204395	+	0.354022i
$671$	−36.7465	+	14.2115i	−1.41858	+	0.548629i
$672$		0			0
$673$			15.9518i			0.614897i	0.951565	+	0.307449i	$0.0994752\pi$
$673$			15.9518i			0.614897i	−0.951565	+	0.307449i	$0.900525\pi$
$674$	−7.27523	+	12.6011i	−0.280231	+	0.485375i
$675$		0			0
$676$	−6.48601	−	11.2341i	−0.249462	−	0.432081i
$677$	7.52574	−	13.0350i	0.289238	−	0.500974i	−0.684390	−	0.729116i	$-0.739932\pi$
$677$	7.52574	−	13.0350i	0.289238	−	0.500974i	0.973628	+	0.228141i	$0.0732649\pi$
$678$		0			0
$679$	−15.2383	+	24.8627i	−0.584792	+	0.954143i
$680$	3.00868			0.115378
$681$		0			0
$682$	6.58587	+	5.30584i	0.252186	+	0.203171i
$683$	−2.64673	−	4.58427i	−0.101274	−	0.175412i	0.810936	−	0.585135i	$-0.198959\pi$
$683$	−2.64673	−	4.58427i	−0.101274	−	0.175412i	−0.912210	+	0.409723i	$0.865625\pi$
$684$		0			0
$685$			7.14442i			0.272974i
$686$	−10.4932	+	15.2608i	−0.400632	+	0.582661i
$687$		0			0
$688$	8.76612	+	5.06112i	0.334205	+	0.192954i
$689$	0.704240	+	1.21978i	0.0268294	+	0.0464699i
$690$		0			0
$691$	−23.4089	−	13.5151i	−0.890517	−	0.514140i	−0.0164055	−	0.999865i	$-0.505222\pi$
$691$	−23.4089	−	13.5151i	−0.890517	−	0.514140i	−0.874112	+	0.485725i	$0.838556\pi$
$692$	−15.0655			−0.572706
$693$		0			0
$694$	28.5417			1.08343
$695$	10.1154	+	5.84014i	0.383699	+	0.221529i
$696$		0			0
$697$	15.0692	+	26.1005i	0.570785	+	0.988629i
$698$	−29.9667	−	17.3013i	−1.13426	−	0.654864i
$699$		0			0
$700$	−9.21125	+	5.00047i	−0.348152	+	0.189000i
$701$			19.9250i			0.752555i	0.926507	+	0.376278i	$0.122796\pi$
$701$			19.9250i			0.752555i	−0.926507	+	0.376278i	$0.877204\pi$
$702$		0			0
$703$	0.949649	+	1.64484i	0.0358167	+	0.0620363i
$704$	−2.58273	−	2.08075i	−0.0973403	−	0.0784211i
$705$		0			0
$706$	−16.9203			−0.636805
$707$	−0.370479	+	14.1103i	−0.0139333	+	0.530673i
$708$		0			0
$709$	−4.98412	+	8.63276i	−0.187183	+	0.324210i	−0.944310	−	0.329058i	$-0.893269\pi$
$709$	−4.98412	+	8.63276i	−0.187183	+	0.324210i	0.757127	+	0.653268i	$0.226602\pi$
$710$	−7.39891	−	12.8153i	−0.277676	−	0.480949i
$711$		0			0
$712$	−3.45047	+	5.97639i	−0.129312	+	0.223975i
$713$		−	1.21235i		−	0.0454029i
$714$		0			0
$715$	−0.203903	−	0.527228i	−0.00762553	−	0.0197172i
$716$	1.08088	−	1.87214i	0.0403943	−	0.0699650i
$717$		0			0
$718$	−15.1755	−	26.2848i	−0.566346	−	0.980940i
$719$	−35.6817	−	20.6008i	−1.33070	−	0.768282i	−0.345295	−	0.938494i	$-0.612221\pi$
$719$	−35.6817	−	20.6008i	−1.33070	−	0.768282i	−0.985407	+	0.170212i	$0.945555\pi$
$720$		0			0
$721$	15.7195	+	28.9566i	0.585426	+	1.07840i
$722$		−	18.9028i		−	0.703491i
$723$		0			0
$724$	4.67035	−	2.69643i	0.173572	−	0.100212i
$725$	6.50811	−	3.75746i	0.241705	−	0.139549i
$726$		0			0
$727$		−	0.0415718i		−	0.00154181i	−1.00000		0.000770906i	$-0.999755\pi$
$727$		−	0.0415718i		−	0.00154181i	1.00000		0.000770906i	$-0.000245387\pi$
$728$	−0.231228	+	0.377271i	−0.00856989	+	0.0139826i
$729$		0			0
$730$	−4.94652	+	8.56762i	−0.183079	+	0.317102i
$731$	−25.8804	+	14.9420i	−0.957221	+	0.552652i
$732$		0			0
$733$	−4.40404	+	7.62803i	−0.162667	+	0.281748i	−0.935824	−	0.352467i	$-0.885343\pi$
$733$	−4.40404	+	7.62803i	−0.162667	+	0.281748i	0.773157	+	0.634214i	$0.218676\pi$
$734$	17.4215			0.643040
$735$		0			0
$736$			0.475438i			0.0175249i
$737$	−5.30174	+	34.0260i	−0.195292	+	1.25336i
$738$		0			0
$739$	28.4003	−	16.3969i	1.04472	−	0.603170i	0.123555	−	0.992338i	$-0.460571\pi$
$739$	28.4003	−	16.3969i	1.04472	−	0.603170i	0.921167	+	0.389167i	$0.127237\pi$
$740$	5.37774	+	3.10484i	0.197690	+	0.114136i
$741$		0			0
$742$	−11.6433	+	18.9972i	−0.427440	+	0.697409i
$743$			25.7575i			0.944952i	0.881344	+	0.472476i	$0.156640\pi$
$743$			25.7575i			0.944952i	−0.881344	+	0.472476i	$0.843360\pi$
$744$		0			0
$745$	−7.21355	−	12.4942i	−0.264284	−	0.457753i
$746$	4.57606	+	7.92596i	0.167541	+	0.290190i
$747$		0			0
$748$	9.13254	−	3.53196i	0.333919	−	0.129141i
$749$	−9.15676	−	16.8675i	−0.334581	−	0.616324i
$750$		0			0
$751$	−5.73290	+	9.92967i	−0.209196	+	0.362339i	−0.951462	−	0.307767i	$-0.900418\pi$
$751$	−5.73290	+	9.92967i	−0.209196	+	0.362339i	0.742265	+	0.670106i	$0.233751\pi$
$752$	−3.28968	+	1.89930i	−0.119962	+	0.0692603i
$753$		0			0
$754$	0.158634	−	0.274763i	0.00577712	−	0.0100063i
$755$	23.7489			0.864313
$756$		0			0
$757$	21.9741			0.798661			0.399331	−	0.916807i	$-0.369243\pi$
$757$	21.9741			0.798661			0.399331	+	0.916807i	$0.369243\pi$
$758$	5.32936	+	3.07691i	0.193571	+	0.111758i
$759$		0			0
$760$	0.158826	+	0.275094i	0.00576121	+	0.00997871i
$761$	13.0047	−	22.5249i	0.471421	−	0.816526i	−0.528044	−	0.849217i	$-0.677074\pi$
$761$	13.0047	−	22.5249i	0.471421	−	0.816526i	0.999466	+	0.0326910i	$0.0104077\pi$
$762$		0			0
$763$	3.08767	+	0.0810696i	0.111781	+	0.00293492i
$764$	6.00000			0.217072
$765$		0			0
$766$	6.48253	+	11.2281i	0.234223	+	0.405687i
$767$	−0.904164	+	0.522020i	−0.0326475	+	0.0188490i
$768$		0			0
$769$	40.8753			1.47400			0.737001	−	0.675891i	$-0.236241\pi$
$769$	40.8753			1.47400			0.737001	+	0.675891i	$0.236241\pi$
$770$	5.79109	−	6.81406i	0.208696	−	0.245562i
$771$		0			0
$772$	−8.31348	−	4.79979i	−0.299209	−	0.172748i
$773$	−40.8229	+	23.5691i	−1.46830	+	0.847722i	−0.999369	−	0.0355144i	$-0.988693\pi$
$773$	−40.8229	+	23.5691i	−1.46830	+	0.847722i	−0.468928	+	0.883236i	$0.655360\pi$
$774$		0			0
$775$	8.74822	+	5.05078i	0.314245	+	0.181430i
$776$	−11.0218			−0.395659
$777$		0			0
$778$		−	5.16647i		−	0.185227i
$779$	−1.59097	+	2.75565i	−0.0570025	+	0.0987313i
$780$		0			0
$781$	−37.5027	−	30.2137i	−1.34195	−	1.08113i
$782$	−1.21559	−	0.701823i	−0.0434695	−	0.0250971i
$783$		0			0
$784$	−6.99036	−	0.367330i	−0.249656	−	0.0131189i
$785$	−4.10960			−0.146678
$786$		0			0
$787$	−12.0746	−	20.9137i	−0.430411	−	0.745494i	0.566497	−	0.824064i	$-0.308298\pi$
$787$	−12.0746	−	20.9137i	−0.430411	−	0.745494i	−0.996909	+	0.0785692i	$0.974965\pi$
$788$	−12.8328	+	7.40901i	−0.457149	+	0.263935i
$789$		0			0
$790$		−	7.13942i		−	0.254009i
$791$	−18.9516	−	11.6154i	−0.673840	−	0.412995i
$792$		0			0
$793$	−0.993379	+	1.72058i	−0.0352759	+	0.0610997i
$794$	−4.62856	−	8.01690i	−0.164261	−	0.284509i
$795$		0			0
$796$	3.55962	+	2.05515i	0.126167	+	0.0728428i
$797$		−	20.3073i		−	0.719321i	−0.933083	−	0.359660i	$-0.882893\pi$
$797$		−	20.3073i		−	0.719321i	0.933083	−	0.359660i	$-0.117107\pi$
$798$		0			0
$799$		−	11.2147i		−	0.396746i
$800$	−3.43072	−	1.98073i	−0.121294	−	0.0700293i
$801$		0			0
$802$	26.7816	−	15.4624i	0.945692	−	0.545996i
$803$	−4.95691	+	31.8130i	−0.174926	+	1.12265i
$804$		0			0
$805$	−1.28147	−	0.0336460i	−0.0451657	−	0.00118587i
$806$	0.426473			0.0150219
$807$		0			0
$808$	−4.62028	+	2.66752i	−0.162541	+	0.0938430i
$809$	−23.4501	+	13.5389i	−0.824461	+	0.476003i	−0.851953	−	0.523619i	$-0.824582\pi$
$809$	−23.4501	+	13.5389i	−0.824461	+	0.476003i	0.0274911	+	0.999622i	$0.491248\pi$
$810$		0			0
$811$	−23.5808			−0.828033			−0.414016	−	0.910269i	$-0.635874\pi$
$811$	−23.5808			−0.828033			−0.414016	+	0.910269i	$0.635874\pi$
$812$	5.01729	+	0.131733i	0.176072	+	0.00462294i
$813$		0			0
$814$	19.9684	+	3.11136i	0.699892	+	0.109053i
$815$	−4.88927	+	2.82282i	−0.171264	+	0.0988792i
$816$		0			0
$817$	−2.73240	−	1.57755i	−0.0955947	−	0.0551916i
$818$		−	23.8397i		−	0.833535i
$819$		0			0
$820$			10.4032i			0.363297i
$821$	29.4247	+	16.9884i	1.02693	+	0.592898i	0.916104	−	0.400942i	$-0.131317\pi$
$821$	29.4247	+	16.9884i	1.02693	+	0.592898i	0.110826	+	0.993840i	$0.464650\pi$
$822$		0			0
$823$	5.90033	+	10.2197i	0.205673	+	0.356235i	0.950347	−	0.311193i	$-0.100728\pi$
$823$	5.90033	+	10.2197i	0.205673	+	0.356235i	−0.744674	+	0.667428i	$0.767395\pi$
$824$	−6.22664	+	10.7849i	−0.216915	+	0.375708i
$825$		0			0
$826$	−14.0817	−	8.63064i	−0.489966	−	0.300298i
$827$		−	17.0595i		−	0.593217i	−0.954999	−	0.296609i	$-0.904144\pi$
$827$		−	17.0595i		−	0.593217i	0.954999	−	0.296609i	$-0.0958557\pi$
$828$		0			0
$829$	−21.7387	+	12.5508i	−0.755015	+	0.435908i	−0.827503	−	0.561461i	$-0.810239\pi$
$829$	−21.7387	+	12.5508i	−0.755015	+	0.435908i	0.0724880	+	0.997369i	$0.476906\pi$
$830$	−7.48601	−	12.9662i	−0.259843	−	0.450062i
$831$		0			0
$832$	−0.167247			−0.00579823
$833$	11.2581	−	17.3306i	0.390069	−	0.600469i
$834$		0			0
$835$	−18.7324	−	10.8152i	−0.648263	−	0.374275i
$836$	0.805037	+	0.648570i	0.0278428	+	0.0224313i
$837$		0			0
$838$	−2.51713	+	4.35980i	−0.0869528	+	0.150607i
$839$			41.1030i			1.41903i	0.704688	+	0.709517i	$0.251087\pi$
$839$			41.1030i			1.41903i	−0.704688	+	0.709517i	$0.748913\pi$
$840$		0			0
$841$	25.4014			0.875909
$842$	14.6574	+	8.46248i	0.505129	+	0.291636i
$843$		0			0
$844$	−6.51646	+	3.76228i	−0.224306	+	0.129503i
$845$	11.4486	+	6.60984i	0.393843	+	0.227385i
$846$		0			0
$847$	9.57905	−	27.4817i	0.329140	−	0.944281i
$848$	−8.42157			−0.289198
$849$		0			0
$850$	10.1286	−	5.84773i	0.347407	−	0.200576i
$851$	−1.44851	−	2.50888i	−0.0496541	−	0.0860035i
$852$		0			0
$853$	−52.7195			−1.80508			−0.902541	−	0.430605i	$-0.858300\pi$
$853$	−52.7195			−1.80508			−0.902541	+	0.430605i	$0.858300\pi$
$854$	−31.4186	−	0.824924i	−1.07512	−	0.0282283i
$855$		0			0
$856$	3.62707	−	6.28227i	0.123971	−	0.214724i
$857$	−10.9387	−	18.9464i	−0.373659	−	0.647197i	0.616466	−	0.787382i	$-0.288564\pi$
$857$	−10.9387	−	18.9464i	−0.373659	−	0.647197i	−0.990125	+	0.140184i	$0.955230\pi$
$858$		0			0
$859$	11.8529	+	6.84326i	0.404415	+	0.233489i	0.688387	−	0.725344i	$-0.258319\pi$
$859$	11.8529	+	6.84326i	0.404415	+	0.233489i	−0.283972	+	0.958832i	$0.591652\pi$
$860$	−10.3155			−0.351755
$861$		0			0
$862$	5.99907			0.204329
$863$	15.0240	−	26.0223i	0.511423	−	0.885810i	−0.488490	−	0.872570i	$-0.662452\pi$
$863$	15.0240	−	26.0223i	0.511423	−	0.885810i	0.999912	−	0.0132402i	$-0.00421461\pi$
$864$		0			0
$865$	13.2962	−	7.67658i	0.452085	−	0.261012i
$866$	−18.0588	+	31.2787i	−0.613662	+	1.06289i
$867$		0			0
$868$	3.21877	+	5.92923i	0.109252	+	0.201251i
$869$	−8.38113	−	21.6710i	−0.284310	−	0.735137i
$870$		0			0
$871$	0.868263	+	1.50388i	0.0294200	+	0.0509569i
$872$	0.583716	+	1.01103i	0.0197671	+	0.0342377i
$873$		0			0
$874$		−	0.148194i		−	0.00501275i
$875$	12.6263	−	20.6010i	0.426846	−	0.696440i
$876$		0			0
$877$	12.2786	+	7.08908i	0.414620	+	0.239381i	0.692773	−	0.721156i	$-0.256389\pi$
$877$	12.2786	+	7.08908i	0.414620	+	0.239381i	−0.278153	+	0.960537i	$0.589722\pi$
$878$	9.82906	−	5.67481i	0.331715	−	0.191516i
$879$		0			0
$880$	3.33965	+	0.520365i	0.112579	+	0.0175415i
$881$			22.3264i			0.752196i	0.926580	+	0.376098i	$0.122734\pi$
$881$			22.3264i			0.752196i	−0.926580	+	0.376098i	$0.877266\pi$
$882$		0			0
$883$	−4.45618			−0.149962			−0.0749812	−	0.997185i	$-0.523890\pi$
$883$	−4.45618			−0.149962			−0.0749812	+	0.997185i	$0.523890\pi$
$884$	0.246883	−	0.427613i	0.00830356	−	0.0143822i
$885$		0			0
$886$	4.11428	−	2.37538i	0.138222	−	0.0798025i
$887$	−4.50070	+	7.79545i	−0.151119	+	0.261746i	−0.931639	−	0.363385i	$-0.881621\pi$
$887$	−4.50070	+	7.79545i	−0.151119	+	0.261746i	0.780520	+	0.625131i	$0.214954\pi$
$888$		0			0
$889$	4.88492	−	7.97021i	0.163835	−	0.267312i
$890$		−	7.03268i		−	0.235736i
$891$		0			0
$892$	11.7680	−	6.79423i	0.394020	−	0.227488i
$893$	1.02539	−	0.592012i	0.0343135	−	0.0198109i
$894$		0			0
$895$			2.20303i			0.0736391i
$896$	−1.26228	−	2.32522i	−0.0421698	−	0.0776801i
$897$		0			0
$898$	6.35054	+	3.66649i	0.211920	+	0.122352i
$899$	−2.41866	−	4.18924i	−0.0806667	−	0.139719i
$900$		0			0
$901$	12.4316	−	21.5321i	0.414156	−	0.717339i
$902$	12.2126	+	31.5780i	0.406635	+	1.05143i
$903$		0			0
$904$		−	8.40135i		−	0.279425i
$905$	−2.74791	+	4.75951i	−0.0913435	+	0.158212i
$906$		0			0
$907$	−10.6872	−	18.5107i	−0.354862	−	0.614638i	0.632233	−	0.774779i	$-0.282139\pi$
$907$	−10.6872	−	18.5107i	−0.354862	−	0.614638i	−0.987094	+	0.160140i	$0.948805\pi$
$908$	10.8318	−	18.7611i	0.359464	−	0.622611i
$909$		0			0
$910$	0.0118358	−	0.450785i	0.000392352	−	0.0149434i
$911$	28.4299			0.941924			0.470962	−	0.882153i	$-0.343907\pi$
$911$	28.4299			0.941924			0.470962	+	0.882153i	$0.343907\pi$
$912$		0			0
$913$	−37.9443	−	30.5694i	−1.25577	−	1.01170i
$914$	−6.75879	−	11.7066i	−0.223561	−	0.387219i
$915$		0			0
$916$			30.0632i			0.993317i
$917$	32.5058	−	17.6463i	1.07344	−	0.582732i
$918$		0			0
$919$	−18.2320	−	10.5263i	−0.601419	−	0.347229i	0.168181	−	0.985756i	$-0.446211\pi$
$919$	−18.2320	−	10.5263i	−0.601419	−	0.347229i	−0.769600	+	0.638527i	$0.779544\pi$
$920$	−0.242258	−	0.419602i	−0.00798700	−	0.0138339i
$921$		0			0
$922$	16.0847	+	9.28652i	0.529722	+	0.305835i
$923$	−2.42852			−0.0799357
$924$		0			0
$925$	24.1385			0.793669
$926$	−24.4955	−	14.1425i	−0.804971	−	0.464750i
$927$		0			0
$928$	0.948505	+	1.64286i	0.0311362	+	0.0539295i
$929$	−10.8055	−	6.23858i	−0.354518	−	0.204681i	0.312155	−	0.950031i	$-0.398949\pi$
$929$	−10.8055	−	6.23858i	−0.354518	−	0.204681i	−0.666674	+	0.745350i	$0.732282\pi$
$930$		0			0
$931$	2.17890	+	0.114497i	0.0714104	+	0.00375248i
$932$			16.1916i			0.530373i
$933$		0			0
$934$	−10.7896	−	18.6881i	−0.353046	−	0.611493i
$935$	−6.26031	+	7.77061i	−0.204734	+	0.254126i
$936$		0			0
$937$	−43.2128			−1.41170			−0.705850	−	0.708362i	$-0.749435\pi$
$937$	−43.2128			−1.41170			−0.705850	+	0.708362i	$0.749435\pi$
$938$	−14.3551	+	23.4218i	−0.468712	+	0.764749i
$939$		0			0
$940$	1.93556	−	3.35248i	0.0631309	−	0.109346i
$941$	7.73754	+	13.4018i	0.252236	+	0.436886i	0.964141	−	0.265390i	$-0.0855006\pi$
$941$	7.73754	+	13.4018i	0.252236	+	0.436886i	−0.711905	+	0.702276i	$0.752167\pi$
$942$		0			0
$943$	2.42672	−	4.20321i	0.0790249	−	0.136875i
$944$		−	6.24251i		−	0.203176i
$945$		0			0
$946$	−31.3116	+	12.1096i	−1.01803	+	0.393717i
$947$	16.7488	−	29.0098i	0.544264	−	0.942693i	−0.454389	−	0.890803i	$-0.650142\pi$
$947$	16.7488	−	29.0098i	0.544264	−	0.942693i	0.998653	−	0.0518895i	$-0.0165244\pi$
$948$		0			0
$949$	0.811791	+	1.40606i	0.0263518	+	0.0456427i
$950$	1.06936	+	0.617393i	0.0346945	+	0.0200309i
$951$		0			0
$952$	7.80841	+	0.205017i	0.253072	+	0.00664464i
$953$		−	25.4820i		−	0.825444i	−0.910857	−	0.412722i	$-0.864578\pi$
$953$		−	25.4820i		−	0.825444i	0.910857	−	0.412722i	$-0.135422\pi$
$954$		0			0
$955$	−5.29535	+	3.05727i	−0.171354	+	0.0989311i
$956$	22.5774	−	13.0350i	0.730204	−	0.421583i
$957$		0			0
$958$			6.93560i			0.224079i
$959$	−0.486833	+	18.5419i	−0.0157207	+	0.598748i
$960$		0			0
$961$	−12.2488	+	21.2156i	−0.395124	+	0.684374i
$962$	0.882559	−	0.509546i	0.0284548	−	0.0164284i
$963$		0			0
$964$	6.60221	−	11.4354i	0.212643	−	0.368309i
$965$	9.78285			0.314921
$966$		0			0
$967$			39.6417i			1.27479i	0.770537	+	0.637395i	$0.219988\pi$
$967$			39.6417i			1.27479i	−0.770537	+	0.637395i	$0.780012\pi$
$968$	10.7480	−	2.34098i	0.345454	−	0.0752418i
$969$		0			0
$970$	9.72738	−	5.61611i	0.312327	−	0.180322i
$971$	16.5082	+	9.53101i	0.529773	+	0.305865i	0.740924	−	0.671589i	$-0.234388\pi$
$971$	16.5082	+	9.53101i	0.529773	+	0.305865i	−0.211151	+	0.977454i	$0.567721\pi$
$972$		0			0
$973$	25.8545	+	15.8461i	0.828857	+	0.508004i
$974$		−	12.1740i		−	0.390081i
$975$		0			0
$976$	−5.93960	−	10.2877i	−0.190122	−	0.329301i
$977$	23.8348	+	41.2832i	0.762544	+	1.32077i	0.941535	+	0.336915i	$0.109383\pi$
$977$	23.8348	+	41.2832i	0.762544	+	1.32077i	−0.178991	+	0.983851i	$0.557283\pi$
$978$		0			0
$979$	−8.25583	−	21.3470i	−0.263857	−	0.682252i
$980$	6.35657	−	3.23772i	0.203053	−	0.103425i
$981$		0			0
$982$	−1.18576	+	2.05379i	−0.0378391	+	0.0655392i
$983$	−40.2377	+	23.2312i	−1.28338	+	0.740961i	−0.977465	−	0.211097i	$-0.932296\pi$
$983$	−40.2377	+	23.2312i	−1.28338	+	0.740961i	−0.305917	+	0.952058i	$0.598963\pi$
$984$		0			0
$985$	7.55046	−	13.0778i	0.240578	−	0.416693i
$986$	−5.60058			−0.178359
$987$		0			0
$988$	0.0521308			0.00165850
$989$	4.16775	+	2.40625i	0.132527	+	0.0765144i
$990$		0			0
$991$	7.28588	+	12.6195i	0.231444	+	0.400872i	0.958233	−	0.285988i	$-0.0923218\pi$
$991$	7.28588	+	12.6195i	0.231444	+	0.400872i	−0.726790	+	0.686860i	$0.758988\pi$
$992$	−1.27498	+	2.20834i	−0.0404808	+	0.0701147i
$993$		0			0
$994$	−18.3291	−	33.7636i	−0.581363	−	1.07092i
$995$	−4.18877			−0.132793
$996$		0			0
$997$	2.05848	+	3.56539i	0.0651927	+	0.112917i	0.896779	−	0.442478i	$-0.145900\pi$
$997$	2.05848	+	3.56539i	0.0651927	+	0.112917i	−0.831587	+	0.555395i	$0.812567\pi$
$998$	−3.40255	+	1.96446i	−0.107706	+	0.0621839i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bk.c.901.2		16
3.2	odd	2		154.2.i.a.131.7	yes	16
7.3	odd	6	inner	1386.2.bk.c.703.6		16
11.10	odd	2	inner	1386.2.bk.c.901.6		16
12.11	even	2		1232.2.bn.b.593.4		16
21.2	odd	6		1078.2.c.b.1077.6		16
21.5	even	6		1078.2.c.b.1077.3		16
21.11	odd	6		1078.2.i.c.1011.2		16
21.17	even	6		154.2.i.a.87.3	✓	16
21.20	even	2		1078.2.i.c.901.6		16
33.32	even	2		154.2.i.a.131.3	yes	16
77.10	even	6	inner	1386.2.bk.c.703.2		16
84.59	odd	6		1232.2.bn.b.241.3		16
132.131	odd	2		1232.2.bn.b.593.3		16
231.32	even	6		1078.2.i.c.1011.6		16
231.65	even	6		1078.2.c.b.1077.14		16
231.131	odd	6		1078.2.c.b.1077.11		16
231.164	odd	6		154.2.i.a.87.7	yes	16
231.230	odd	2		1078.2.i.c.901.2		16
924.395	even	6		1232.2.bn.b.241.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.i.a.87.3	✓	16	21.17	even	6
154.2.i.a.87.7	yes	16	231.164	odd	6
154.2.i.a.131.3	yes	16	33.32	even	2
154.2.i.a.131.7	yes	16	3.2	odd	2
1078.2.c.b.1077.3		16	21.5	even	6
1078.2.c.b.1077.6		16	21.2	odd	6
1078.2.c.b.1077.11		16	231.131	odd	6
1078.2.c.b.1077.14		16	231.65	even	6
1078.2.i.c.901.2		16	231.230	odd	2
1078.2.i.c.901.6		16	21.20	even	2
1078.2.i.c.1011.2		16	21.11	odd	6
1078.2.i.c.1011.6		16	231.32	even	6
1232.2.bn.b.241.3		16	84.59	odd	6
1232.2.bn.b.241.4		16	924.395	even	6
1232.2.bn.b.593.3		16	132.131	odd	2
1232.2.bn.b.593.4		16	12.11	even	2
1386.2.bk.c.703.2		16	77.10	even	6	inner
1386.2.bk.c.703.6		16	7.3	odd	6	inner
1386.2.bk.c.901.2		16	1.1	even	1	trivial
1386.2.bk.c.901.6		16	11.10	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.882559 - 0.509546i) q^{5} +(-2.25578 - 1.38256i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.882559 - 0.509546i) q^{5} +(-2.25578 - 1.38256i) q^{7} -1.00000i q^{8} +(0.509546 + 0.882559i) q^{10} +(2.58273 + 2.08075i) q^{11} +0.167247 q^{13} +(1.26228 + 2.32522i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.47616 - 2.55678i) q^{17} +(0.155850 - 0.269940i) q^{19} -1.01909i q^{20} +(-1.19633 - 3.09335i) q^{22} +(-0.237719 + 0.411742i) q^{23} +(-1.98073 - 3.43072i) q^{25} +(-0.144840 - 0.0836233i) q^{26} +(0.0694427 - 2.64484i) q^{28} +1.89701i q^{29} +(-2.20834 + 1.27498i) q^{31} +(0.866025 - 0.500000i) q^{32} +2.95232i q^{34} +(1.28638 + 2.36961i) q^{35} +(-3.04667 + 5.27699i) q^{37} +(-0.269940 + 0.155850i) q^{38} +(-0.509546 + 0.882559i) q^{40} -10.2084 q^{41} -10.1222i q^{43} +(-0.510616 + 3.27708i) q^{44} +(0.411742 - 0.237719i) q^{46} +(3.28968 + 1.89930i) q^{47} +(3.17706 + 6.23749i) q^{49} +3.96145i q^{50} +(0.0836233 + 0.144840i) q^{52} +(4.21079 + 7.29330i) q^{53} +(-1.21917 - 3.15240i) q^{55} +(-1.38256 + 2.25578i) q^{56} +(0.948505 - 1.64286i) q^{58} +(-5.40617 + 3.12126i) q^{59} +(-5.93960 + 10.2877i) q^{61} +2.54997 q^{62} -1.00000 q^{64} +(-0.147605 - 0.0852198i) q^{65} +(5.19151 + 8.99196i) q^{67} +(1.47616 - 2.55678i) q^{68} +(0.0707684 - 2.69533i) q^{70} -14.5206 q^{71} +(4.85385 + 8.40712i) q^{73} +(5.27699 - 3.04667i) q^{74} +0.311700 q^{76} +(-2.94930 - 8.26448i) q^{77} +(-6.06709 - 3.50284i) q^{79} +(0.882559 - 0.509546i) q^{80} +(8.84069 + 5.10418i) q^{82} -14.6915 q^{83} +3.00868i q^{85} +(-5.06112 + 8.76612i) q^{86} +(2.08075 - 2.58273i) q^{88} +(-5.97639 - 3.45047i) q^{89} +(-0.377271 - 0.231228i) q^{91} -0.475438 q^{92} +(-1.89930 - 3.28968i) q^{94} +(-0.275094 + 0.158826i) q^{95} -11.0218i q^{97} +(0.367330 - 6.99036i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 12 q^{5}+O(q^{10}) \) 16 * q + 8 * q^4 + 12 * q^5	\( 16 q + 8 q^{4} + 12 q^{5} - 8 q^{11} + 8 q^{14} - 8 q^{16} - 8 q^{22} - 16 q^{23} + 36 q^{26} - 12 q^{31} - 16 q^{37} - 12 q^{38} + 8 q^{44} - 24 q^{47} + 8 q^{49} + 28 q^{53} + 4 q^{56} - 12 q^{58} - 60 q^{59} - 16 q^{64} + 12 q^{67} + 60 q^{70} - 8 q^{71} - 44 q^{77} - 12 q^{80} - 20 q^{86} - 4 q^{88} - 96 q^{89} - 36 q^{91} - 32 q^{92}+O(q^{100}) \) 16 * q + 8 * q^4 + 12 * q^5 - 8 * q^11 + 8 * q^14 - 8 * q^16 - 8 * q^22 - 16 * q^23 + 36 * q^26 - 12 * q^31 - 16 * q^37 - 12 * q^38 + 8 * q^44 - 24 * q^47 + 8 * q^49 + 28 * q^53 + 4 * q^56 - 12 * q^58 - 60 * q^59 - 16 * q^64 + 12 * q^67 + 60 * q^70 - 8 * q^71 - 44 * q^77 - 12 * q^80 - 20 * q^86 - 4 * q^88 - 96 * q^89 - 36 * q^91 - 32 * q^92

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