LMFDB - Embedded newform 1386.2.bk.c.703.4

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			703.4
Root			$2.24352 - 0.601150i$ of defining polynomial
Character	$\chi$	$=$	1386.703
Dual form			1386.2.bk.c.901.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(3.06486 - 1.76950i) q^{5} +(0.649221 - 2.56486i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(3.06486 - 1.76950i) q^{5} +(0.649221 - 2.56486i) q^{7} +1.00000i q^{8} +(-1.76950 + 3.06486i) q^{10} +(-3.22122 + 0.789769i) q^{11} -5.01680 q^{13} +(0.720188 + 2.54585i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.94681 - 3.37197i) q^{17} +(-2.32819 - 4.03254i) q^{19} -3.53900i q^{20} +(2.39477 - 2.29457i) q^{22} +(-0.779812 - 1.35067i) q^{23} +(3.76225 - 6.51641i) q^{25} +(4.34467 - 2.50840i) q^{26} +(-1.89662 - 1.84467i) q^{28} -0.100205i q^{29} +(-0.242252 - 0.139864i) q^{31} +(0.866025 + 0.500000i) q^{32} +3.89362i q^{34} +(-2.54874 - 9.00974i) q^{35} +(-0.352715 - 0.610920i) q^{37} +(4.03254 + 2.32819i) q^{38} +(1.76950 + 3.06486i) q^{40} -2.94809 q^{41} +9.03556i q^{43} +(-0.926651 + 3.18454i) q^{44} +(1.35067 + 0.779812i) q^{46} +(-5.68935 + 3.28475i) q^{47} +(-6.15702 - 3.33032i) q^{49} +7.52450i q^{50} +(-2.50840 + 4.34467i) q^{52} +(2.77029 - 4.79828i) q^{53} +(-8.47510 + 8.12048i) q^{55} +(2.56486 + 0.649221i) q^{56} +(0.0501023 + 0.0867797i) q^{58} +(-12.5871 - 7.26719i) q^{59} +(5.56360 + 9.63644i) q^{61} +0.279729 q^{62} -1.00000 q^{64} +(-15.3758 + 8.87721i) q^{65} +(-1.99196 + 3.45017i) q^{67} +(-1.94681 - 3.37197i) q^{68} +(6.71215 + 6.52829i) q^{70} +8.45381 q^{71} +(1.94885 - 3.37552i) q^{73} +(0.610920 + 0.352715i) q^{74} -4.65637 q^{76} +(-0.0656384 + 8.77472i) q^{77} +(6.66824 - 3.84991i) q^{79} +(-3.06486 - 1.76950i) q^{80} +(2.55312 - 1.47405i) q^{82} -2.87320 q^{83} -13.7795i q^{85} +(-4.51778 - 7.82503i) q^{86} +(-0.789769 - 3.22122i) q^{88} +(5.15200 - 2.97451i) q^{89} +(-3.25701 + 12.8674i) q^{91} -1.55962 q^{92} +(3.28475 - 5.68935i) q^{94} +(-14.2711 - 8.23945i) q^{95} -16.7587i q^{97} +(6.99730 - 0.194366i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

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

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
$5$	3.06486	−	1.76950i	1.37065	−	0.791344i	0.379638	−	0.925135i	$-0.376049\pi$
$5$	3.06486	−	1.76950i	1.37065	−	0.791344i	0.991010	+	0.133791i	$0.0427152\pi$
$6$		0			0
$7$	0.649221	−	2.56486i	0.245383	−	0.969426i
$7$	0.649221	−	2.56486i	0.245383	−	0.969426i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−1.76950	+	3.06486i	−0.559564	+	0.969194i
$11$	−3.22122	+	0.789769i	−0.971235	+	0.238124i
$11$	−3.22122	+	0.789769i	−0.971235	+	0.238124i
$12$		0			0
$13$	−5.01680			−1.39141			−0.695704	−	0.718328i	$-0.744908\pi$
$13$	−5.01680			−1.39141			−0.695704	+	0.718328i	$0.744908\pi$
$14$	0.720188	+	2.54585i	0.192478	+	0.680406i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.94681	−	3.37197i	0.472171	−	0.817824i	−0.527322	−	0.849665i	$-0.676804\pi$
$17$	1.94681	−	3.37197i	0.472171	−	0.817824i	0.999493	+	0.0318416i	$0.0101372\pi$
$18$		0			0
$19$	−2.32819	−	4.03254i	−0.534123	−	0.925128i	−0.999205	−	0.0398605i	$-0.987309\pi$
$19$	−2.32819	−	4.03254i	−0.534123	−	0.925128i	0.465082	−	0.885267i	$-0.346025\pi$
$20$		−	3.53900i		−	0.791344i
$21$		0			0
$22$	2.39477	−	2.29457i	0.510568	−	0.489204i
$23$	−0.779812	−	1.35067i	−0.162602	−	0.281635i	0.773199	−	0.634163i	$-0.218655\pi$
$23$	−0.779812	−	1.35067i	−0.162602	−	0.281635i	−0.935801	+	0.352528i	$0.885322\pi$
$24$		0			0
$25$	3.76225	−	6.51641i	0.752450	−	1.30328i
$26$	4.34467	−	2.50840i	0.852060	−	0.491937i
$27$		0			0
$28$	−1.89662	−	1.84467i	−0.358428	−	0.348610i
$29$		−	0.100205i		−	0.0186075i	−0.999957	−	0.00930376i	$-0.997038\pi$
$29$		−	0.100205i		−	0.0186075i	0.999957	−	0.00930376i	$-0.00296152\pi$
$30$		0			0
$31$	−0.242252	−	0.139864i	−0.0435098	−	0.0251204i	0.478087	−	0.878312i	$-0.341330\pi$
$31$	−0.242252	−	0.139864i	−0.0435098	−	0.0251204i	−0.521597	+	0.853192i	$0.674664\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			3.89362i			0.667750i
$35$	−2.54874	−	9.00974i	−0.430816	−	1.52292i
$36$		0			0
$37$	−0.352715	−	0.610920i	−0.0579860	−	0.100435i	0.835575	−	0.549376i	$-0.185135\pi$
$37$	−0.352715	−	0.610920i	−0.0579860	−	0.100435i	−0.893561	+	0.448941i	$0.851801\pi$
$38$	4.03254	+	2.32819i	0.654164	+	0.377682i
$39$		0			0
$40$	1.76950	+	3.06486i	0.279782	+	0.484597i
$41$	−2.94809			−0.460415			−0.230207	−	0.973142i	$-0.573940\pi$
$41$	−2.94809			−0.460415			−0.230207	+	0.973142i	$0.573940\pi$
$42$		0			0
$43$			9.03556i			1.37791i	0.724804	+	0.688955i	$0.241930\pi$
$43$			9.03556i			1.37791i	−0.724804	+	0.688955i	$0.758070\pi$
$44$	−0.926651	+	3.18454i	−0.139698	+	0.480088i
$45$		0			0
$46$	1.35067	+	0.779812i	0.199146	+	0.114977i
$47$	−5.68935	+	3.28475i	−0.829876	+	0.479129i	−0.853810	−	0.520584i	$-0.825714\pi$
$47$	−5.68935	+	3.28475i	−0.829876	+	0.479129i	0.0239340	+	0.999714i	$0.492381\pi$
$48$		0			0
$49$	−6.15702	−	3.33032i	−0.879575	−	0.475761i
$50$			7.52450i			1.06412i
$51$		0			0
$52$	−2.50840	+	4.34467i	−0.347852	+	0.602498i
$53$	2.77029	−	4.79828i	0.380529	−	0.659095i	−0.610609	−	0.791932i	$-0.709075\pi$
$53$	2.77029	−	4.79828i	0.380529	−	0.659095i	0.991138	+	0.132837i	$0.0424087\pi$
$54$		0			0
$55$	−8.47510	+	8.12048i	−1.14278	+	1.09496i
$56$	2.56486	+	0.649221i	0.342744	+	0.0867558i
$57$		0			0
$58$	0.0501023	+	0.0867797i	0.00657875	+	0.0113947i
$59$	−12.5871	−	7.26719i	−1.63871	−	0.946108i	−0.981279	−	0.192589i	$-0.938312\pi$
$59$	−12.5871	−	7.26719i	−1.63871	−	0.946108i	−0.657427	−	0.753518i	$-0.728355\pi$
$60$		0			0
$61$	5.56360	+	9.63644i	0.712346	+	1.23382i	0.963974	+	0.265996i	$0.0857006\pi$
$61$	5.56360	+	9.63644i	0.712346	+	1.23382i	−0.251628	+	0.967824i	$0.580966\pi$
$62$	0.279729			0.0355256
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−15.3758	+	8.87721i	−1.90713	+	1.10108i
$66$		0			0
$67$	−1.99196	+	3.45017i	−0.243356	+	0.421506i	−0.961668	−	0.274216i	$-0.911582\pi$
$67$	−1.99196	+	3.45017i	−0.243356	+	0.421506i	0.718312	+	0.695721i	$0.244915\pi$
$68$	−1.94681	−	3.37197i	−0.236085	−	0.408912i
$69$		0			0
$70$	6.71215	+	6.52829i	0.802255	+	0.780280i
$71$	8.45381			1.00328			0.501641	−	0.865076i	$-0.332730\pi$
$71$	8.45381			1.00328			0.501641	+	0.865076i	$0.332730\pi$
$72$		0			0
$73$	1.94885	−	3.37552i	0.228096	−	0.395074i	−0.729148	−	0.684356i	$-0.760083\pi$
$73$	1.94885	−	3.37552i	0.228096	−	0.395074i	0.957244	+	0.289282i	$0.0934166\pi$
$74$	0.610920	+	0.352715i	0.0710180	+	0.0410023i
$75$		0			0
$76$	−4.65637			−0.534123
$77$	−0.0656384	+	8.77472i	−0.00748019	+	0.999972i
$78$		0			0
$79$	6.66824	−	3.84991i	0.750236	−	0.433149i	−0.0755434	−	0.997143i	$-0.524069\pi$
$79$	6.66824	−	3.84991i	0.750236	−	0.433149i	0.825779	+	0.563994i	$0.190736\pi$
$80$	−3.06486	−	1.76950i	−0.342662	−	0.197836i
$81$		0			0
$82$	2.55312	−	1.47405i	0.281945	−	0.162781i
$83$	−2.87320			−0.315375			−0.157687	−	0.987489i	$-0.550404\pi$
$83$	−2.87320			−0.315375			−0.157687	+	0.987489i	$0.550404\pi$
$84$		0			0
$85$		−	13.7795i		−	1.49460i
$86$	−4.51778	−	7.82503i	−0.487165	−	0.843794i
$87$		0			0
$88$	−0.789769	−	3.22122i	−0.0841896	−	0.343383i
$89$	5.15200	−	2.97451i	0.546111	−	0.315297i	−0.201441	−	0.979501i	$-0.564562\pi$
$89$	5.15200	−	2.97451i	0.546111	−	0.315297i	0.747552	+	0.664203i	$0.231229\pi$
$90$		0			0
$91$	−3.25701	+	12.8674i	−0.341428	+	1.34887i
$92$	−1.55962			−0.162602
$93$		0			0
$94$	3.28475	−	5.68935i	0.338796	−	0.586811i
$95$	−14.2711	−	8.23945i	−1.46419	−	0.845349i
$96$		0			0
$97$		−	16.7587i		−	1.70159i	−0.525502	−	0.850793i	$-0.676122\pi$
$97$		−	16.7587i		−	1.70159i	0.525502	−	0.850793i	$-0.323878\pi$
$98$	6.99730	−	0.194366i	0.706834	−	0.0196339i
$99$		0			0
$100$	−3.76225	−	6.51641i	−0.376225	−	0.651641i
$101$	−0.701452	+	1.21495i	−0.0697971	+	0.120892i	−0.898812	−	0.438335i	$-0.855569\pi$
$101$	−0.701452	+	1.21495i	−0.0697971	+	0.120892i	0.829015	+	0.559227i	$0.188902\pi$
$102$		0			0
$103$	1.78653	−	1.03145i	0.176032	−	0.101632i	−0.409395	−	0.912357i	$-0.634260\pi$
$103$	1.78653	−	1.03145i	0.176032	−	0.101632i	0.585427	+	0.810725i	$0.300927\pi$
$104$		−	5.01680i		−	0.491937i
$105$		0			0
$106$			5.54058i			0.538149i
$107$	10.6222	−	6.13274i	1.02689	−	0.592875i	0.110797	−	0.993843i	$-0.464660\pi$
$107$	10.6222	−	6.13274i	1.02689	−	0.592875i	0.916092	+	0.400968i	$0.131326\pi$
$108$		0			0
$109$	5.82394	+	3.36245i	0.557832	+	0.322065i	0.752275	−	0.658849i	$-0.228957\pi$
$109$	5.82394	+	3.36245i	0.557832	+	0.322065i	−0.194443	+	0.980914i	$0.562290\pi$
$110$	3.27941	−	11.2701i	0.312680	−	1.07456i
$111$		0			0
$112$	−2.54585	+	0.720188i	−0.240560	+	0.0680514i
$113$	11.9900			1.12792			0.563960	−	0.825802i	$-0.309277\pi$
$113$	11.9900			1.12792			0.563960	+	0.825802i	$0.309277\pi$
$114$		0			0
$115$	−4.78003	−	2.75975i	−0.445740	−	0.257348i
$116$	−0.0867797	−	0.0501023i	−0.00805729	−	0.00465188i
$117$		0			0
$118$	14.5344			1.33800
$119$	−7.38473	−	7.18245i	−0.676957	−	0.658415i
$120$		0			0
$121$	9.75253	−	5.08804i	0.886594	−	0.462549i
$122$	−9.63644	−	5.56360i	−0.872442	−	0.503705i
$123$		0			0
$124$	−0.242252	+	0.139864i	−0.0217549	+	0.0125602i
$125$		−	8.93419i		−	0.799098i
$126$		0			0
$127$		−	13.2199i		−	1.17308i	−0.809922	−	0.586538i	$-0.800491\pi$
$127$		−	13.2199i		−	1.17308i	0.809922	−	0.586538i	$-0.199509\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	8.87721	−	15.3758i	0.778583	−	1.34855i
$131$	8.24931	+	14.2882i	0.720746	+	1.24837i	0.960701	+	0.277584i	$0.0895337\pi$
$131$	8.24931	+	14.2882i	0.720746	+	1.24837i	−0.239956	+	0.970784i	$0.577133\pi$
$132$		0			0
$133$	−11.8544	+	3.35347i	−1.02791	+	0.290782i
$134$		−	3.98392i		−	0.344158i
$135$		0			0
$136$	3.37197	+	1.94681i	0.289144	+	0.166938i
$137$	3.32187	−	5.75365i	0.283807	−	0.491568i	−0.688512	−	0.725225i	$-0.741736\pi$
$137$	3.32187	−	5.75365i	0.283807	−	0.491568i	0.972319	+	0.233657i	$0.0750693\pi$
$138$		0			0
$139$	−14.3533			−1.21743			−0.608716	−	0.793388i	$-0.708315\pi$
$139$	−14.3533			−1.21743			−0.608716	+	0.793388i	$0.708315\pi$
$140$	−9.07703	−	2.29759i	−0.767149	−	0.194182i
$141$		0			0
$142$	−7.32121	+	4.22690i	−0.614383	+	0.354714i
$143$	16.1602	−	3.96211i	1.35138	−	0.331328i
$144$		0			0
$145$	−0.177312	−	0.307113i	−0.0147249	−	0.0255044i
$146$			3.89771i			0.322577i
$147$		0			0
$148$	−0.705430			−0.0579860
$149$	2.30871	−	1.33294i	0.189137	−	0.109198i	−0.402441	−	0.915446i	$-0.631838\pi$
$149$	2.30871	−	1.33294i	0.189137	−	0.109198i	0.591579	+	0.806247i	$0.298505\pi$
$150$		0			0
$151$	−8.99830	−	5.19517i	−0.732271	−	0.422777i	0.0869812	−	0.996210i	$-0.472278\pi$
$151$	−8.99830	−	5.19517i	−0.732271	−	0.422777i	−0.819253	+	0.573433i	$0.805611\pi$
$152$	4.03254	−	2.32819i	0.327082	−	0.188841i
$153$		0			0
$154$	−4.33051	−	7.63195i	−0.348963	−	0.615000i
$155$	−0.989959			−0.0795154
$156$		0			0
$157$	7.25273	+	4.18736i	0.578831	+	0.334188i	0.760669	−	0.649140i	$-0.224871\pi$
$157$	7.25273	+	4.18736i	0.578831	+	0.334188i	−0.181838	+	0.983329i	$0.558205\pi$
$158$	−3.84991	+	6.66824i	−0.306282	+	0.530497i
$159$		0			0
$160$	3.53900			0.279782
$161$	−3.97056	+	1.12322i	−0.312924	+	0.0885223i
$162$		0			0
$163$	−1.53254	−	2.65444i	−0.120038	−	0.207911i	0.799745	−	0.600340i	$-0.204968\pi$
$163$	−1.53254	−	2.65444i	−0.120038	−	0.207911i	−0.919782	+	0.392429i	$0.871635\pi$
$164$	−1.47405	+	2.55312i	−0.115104	+	0.199365i
$165$		0			0
$166$	2.48826	−	1.43660i	0.193127	−	0.111502i
$167$	−10.0731			−0.779482			−0.389741	−	0.920925i	$-0.627435\pi$
$167$	−10.0731			−0.779482			−0.389741	+	0.920925i	$0.627435\pi$
$168$		0			0
$169$	12.1682			0.936018
$170$	6.88975	+	11.9334i	0.528420	+	0.915250i
$171$		0			0
$172$	7.82503	+	4.51778i	0.596653	+	0.344478i
$173$	0.0383013	+	0.0663398i	0.00291200	+	0.00504372i	0.867478	−	0.497476i	$-0.165740\pi$
$173$	0.0383013	+	0.0663398i	0.00291200	+	0.00504372i	−0.864566	+	0.502520i	$0.832406\pi$
$174$		0			0
$175$	−14.2711	−	13.8802i	−1.07880	−	1.04925i
$176$	2.29457	+	2.39477i	0.172960	+	0.180513i
$177$		0			0
$178$	−2.97451	+	5.15200i	−0.222949	+	0.386159i
$179$	−4.48746	+	7.77250i	−0.335408	+	0.580944i	−0.983563	−	0.180564i	$-0.942208\pi$
$179$	−4.48746	+	7.77250i	−0.335408	+	0.580944i	0.648155	+	0.761509i	$0.275541\pi$
$180$		0			0
$181$		−	15.1450i		−	1.12572i	−0.826554	−	0.562858i	$-0.809702\pi$
$181$		−	15.1450i		−	1.12572i	0.826554	−	0.562858i	$-0.190298\pi$
$182$	−3.61304	−	12.7720i	−0.267816	−	0.946723i
$183$		0			0
$184$	1.35067	−	0.779812i	0.0995730	−	0.0574885i
$185$	−2.16204	−	1.24826i	−0.158957	−	0.0917736i
$186$		0			0
$187$	−3.60803	+	12.3994i	−0.263845	+	0.906734i
$188$			6.56949i			0.479129i
$189$		0			0
$190$	16.4789			1.19550
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	0.953912	−	0.300088i	$-0.0970159\pi$
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	−0.736839	+	0.676068i	$0.763683\pi$
$192$		0			0
$193$	12.8415	+	7.41403i	0.924350	+	0.533674i	0.885020	−	0.465552i	$-0.154144\pi$
$193$	12.8415	+	7.41403i	0.924350	+	0.533674i	0.0393299	+	0.999226i	$0.487478\pi$
$194$	8.37933	+	14.5134i	0.601601	+	1.04200i
$195$		0			0
$196$	−5.96266	+	3.66698i	−0.425904	+	0.261927i
$197$		−	14.4745i		−	1.03126i	−0.856811	−	0.515631i	$-0.827557\pi$
$197$		−	14.4745i		−	1.03126i	0.856811	−	0.515631i	$-0.172443\pi$
$198$		0			0
$199$	−9.72188	−	5.61293i	−0.689166	−	0.397890i	0.114133	−	0.993465i	$-0.463591\pi$
$199$	−9.72188	−	5.61293i	−0.689166	−	0.397890i	−0.803300	+	0.595575i	$0.796924\pi$
$200$	6.51641	+	3.76225i	0.460779	+	0.266031i
$201$		0			0
$202$		−	1.40290i		−	0.0987080i
$203$	−0.257011	−	0.0650550i	−0.0180386	−	0.00456596i
$204$		0			0
$205$	−9.03550	+	5.21665i	−0.631066	+	0.364346i
$206$	−1.03145	+	1.78653i	−0.0718647	+	0.124473i
$207$		0			0
$208$	2.50840	+	4.34467i	0.173926	+	0.301249i
$209$	10.6844	+	11.1510i	0.739054	+	0.771329i
$210$		0			0
$211$		−	6.44038i		−	0.443374i	−0.975118	−	0.221687i	$-0.928844\pi$
$211$		−	6.44038i		−	0.443374i	0.975118	−	0.221687i	$-0.0711563\pi$
$212$	−2.77029	−	4.79828i	−0.190264	−	0.329548i
$213$		0			0
$214$	−6.13274	+	10.6222i	−0.419226	+	0.726120i
$215$	15.9884	+	27.6927i	1.09040	+	1.88863i
$216$		0			0
$217$	−0.516008	+	0.530540i	−0.0350289	+	0.0360154i
$218$	−6.72491			−0.455468
$219$		0			0
$220$	2.79499	+	11.3999i	0.188438	+	0.768580i
$221$	−9.76675	+	16.9165i	−0.656983	+	1.13793i
$222$		0			0
$223$		−	4.01793i		−	0.269061i	−0.990909	−	0.134530i	$-0.957047\pi$
$223$		−	4.01793i		−	0.269061i	0.990909	−	0.134530i	$-0.0429526\pi$
$224$	1.84467	−	1.89662i	0.123252	−	0.126724i
$225$		0			0
$226$	−10.3836	+	5.99498i	−0.690707	+	0.398780i
$227$	6.36466	−	11.0239i	0.422437	−	0.731682i	−0.573740	−	0.819037i	$-0.694508\pi$
$227$	6.36466	−	11.0239i	0.422437	−	0.731682i	0.996177	+	0.0873549i	$0.0278414\pi$
$228$		0			0
$229$	−5.20780	+	3.00672i	−0.344141	+	0.198690i	−0.662102	−	0.749414i	$-0.730335\pi$
$229$	−5.20780	+	3.00672i	−0.344141	+	0.198690i	0.317961	+	0.948104i	$0.397002\pi$
$230$	5.51950			0.363945
$231$		0			0
$232$	0.100205			0.00657875
$233$	5.60053	−	3.23347i	0.366903	−	0.211832i	−0.305202	−	0.952288i	$-0.598724\pi$
$233$	5.60053	−	3.23347i	0.366903	−	0.211832i	0.672105	+	0.740456i	$0.265391\pi$
$234$		0			0
$235$	−11.6247	+	20.1346i	−0.758312	+	1.31343i
$236$	−12.5871	+	7.26719i	−0.819353	+	0.473054i
$237$		0			0
$238$	9.98659	+	2.52782i	0.647335	+	0.163854i
$239$		−	15.5775i		−	1.00762i	−0.863813	−	0.503812i	$-0.831930\pi$
$239$		−	15.5775i		−	1.00762i	0.863813	−	0.503812i	$-0.168070\pi$
$240$		0			0
$241$	11.7381	−	20.3310i	0.756119	−	1.30964i	−0.188697	−	0.982035i	$-0.560427\pi$
$241$	11.7381	−	20.3310i	0.756119	−	1.30964i	0.944816	−	0.327601i	$-0.106240\pi$
$242$	−5.90192	+	9.28264i	−0.379390	+	0.596710i
$243$		0			0
$244$	11.1272			0.712346
$245$	−24.7634	+	0.687860i	−1.58208	+	0.0439457i
$246$		0			0
$247$	11.6800	+	20.2304i	0.743183	+	1.28723i
$248$	0.139864	−	0.242252i	0.00888140	−	0.0153830i
$249$		0			0
$250$	4.46709	+	7.73723i	0.282524	+	0.489345i
$251$		−	18.2818i		−	1.15394i	−0.816766	−	0.576968i	$-0.804236\pi$
$251$		−	18.2818i		−	1.15394i	0.816766	−	0.576968i	$-0.195764\pi$
$252$		0			0
$253$	3.57867	+	3.73495i	0.224989	+	0.234814i
$254$	6.60994	+	11.4488i	0.414745	+	0.718359i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.33087	−	4.80983i	0.519666	−	0.300029i	−0.217132	−	0.976142i	$-0.569670\pi$
$257$	8.33087	−	4.80983i	0.519666	−	0.300029i	0.736798	+	0.676113i	$0.236337\pi$
$258$		0			0
$259$	−1.79591	+	0.508042i	−0.111593	+	0.0315682i
$260$			17.7544i			1.10108i
$261$		0			0
$262$	−14.2882	−	8.24931i	−0.882729	−	0.509644i
$263$	0.501139	+	0.289333i	0.0309016	+	0.0178410i	0.515371	−	0.856967i	$-0.327654\pi$
$263$	0.501139	+	0.289333i	0.0309016	+	0.0178410i	−0.484470	+	0.874808i	$0.660987\pi$
$264$		0			0
$265$		−	19.6081i		−	1.20452i
$266$	8.58949	−	8.83139i	0.526655	−	0.541487i
$267$		0			0
$268$	1.99196	+	3.45017i	0.121678	+	0.210753i
$269$	−19.1302	−	11.0448i	−1.16639	−	0.673413i	−0.213560	−	0.976930i	$-0.568506\pi$
$269$	−19.1302	−	11.0448i	−1.16639	−	0.673413i	−0.952826	+	0.303517i	$0.901839\pi$
$270$		0			0
$271$	−2.13111	−	3.69119i	−0.129456	−	0.224224i	0.794010	−	0.607905i	$-0.207990\pi$
$271$	−2.13111	−	3.69119i	−0.129456	−	0.224224i	−0.923466	+	0.383681i	$0.874656\pi$
$272$	−3.89362			−0.236085
$273$		0			0
$274$			6.64374i			0.401363i
$275$	−6.97258	+	23.9621i	−0.420462	+	1.44497i
$276$		0			0
$277$	15.9048	+	9.18263i	0.955626	+	0.551731i	0.894824	−	0.446419i	$-0.147301\pi$
$277$	15.9048	+	9.18263i	0.955626	+	0.551731i	0.0608016	+	0.998150i	$0.480634\pi$
$278$	12.4303	−	7.17666i	0.745522	−	0.430427i
$279$		0			0
$280$	9.00974	−	2.54874i	0.538435	−	0.152317i
$281$		−	3.72890i		−	0.222448i	−0.993795	−	0.111224i	$-0.964523\pi$
$281$		−	3.72890i		−	0.222448i	0.993795	−	0.111224i	$-0.0354771\pi$
$282$		0			0
$283$	−6.36576	+	11.0258i	−0.378405	+	0.655417i	−0.990830	−	0.135111i	$-0.956861\pi$
$283$	−6.36576	+	11.0258i	−0.378405	+	0.655417i	0.612425	+	0.790529i	$0.290194\pi$
$284$	4.22690	−	7.32121i	0.250821	−	0.434434i
$285$		0			0
$286$	−12.0141	+	11.5114i	−0.710408	+	0.680683i
$287$	−1.91397	+	7.56145i	−0.112978	+	0.446338i
$288$		0			0
$289$	0.919861	+	1.59325i	0.0541094	+	0.0937203i
$290$	0.307113	+	0.177312i	0.0180343	+	0.0104121i
$291$		0			0
$292$	−1.94885	−	3.37552i	−0.114048	−	0.197537i
$293$	26.2251			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$293$	26.2251			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$294$		0			0
$295$	−51.4371			−2.99478
$296$	0.610920	−	0.352715i	0.0355090	−	0.0205011i
$297$		0			0
$298$	−1.33294	+	2.30871i	−0.0772149	+	0.133740i
$299$	3.91216	+	6.77605i	0.226246	+	0.391869i
$300$		0			0
$301$	23.1750	+	5.86608i	1.33578	+	0.338115i
$302$	10.3903			0.597897
$303$		0			0
$304$	−2.32819	+	4.03254i	−0.133531	+	0.231282i
$305$	34.1033	+	19.6896i	1.95275	+	1.12742i
$306$		0			0
$307$	25.5942			1.46074			0.730369	−	0.683053i	$-0.239348\pi$
$307$	25.5942			1.46074			0.730369	+	0.683053i	$0.239348\pi$
$308$	7.56631	+	4.44420i	0.431131	+	0.253232i
$309$		0			0
$310$	0.857330	−	0.494980i	0.0486931	−	0.0281129i
$311$	1.65385	+	0.954850i	0.0937811	+	0.0541446i	0.546157	−	0.837683i	$-0.316090\pi$
$311$	1.65385	+	0.954850i	0.0937811	+	0.0541446i	−0.452376	+	0.891827i	$0.649423\pi$
$312$		0			0
$313$	−26.3707	+	15.2251i	−1.49056	+	0.860576i	−0.999942	−	0.0107985i	$-0.996563\pi$
$313$	−26.3707	+	15.2251i	−1.49056	+	0.860576i	−0.490619	+	0.871374i	$0.663229\pi$
$314$	−8.37473			−0.472613
$315$		0			0
$316$		−	7.69982i		−	0.433149i
$317$	17.1971	+	29.7862i	0.965885	+	1.67296i	0.707220	+	0.706994i	$0.249949\pi$
$317$	17.1971	+	29.7862i	0.965885	+	1.67296i	0.258665	+	0.965967i	$0.416717\pi$
$318$		0			0
$319$	0.0791385	+	0.322781i	0.00443090	+	0.0180723i
$320$	−3.06486	+	1.76950i	−0.171331	+	0.0989180i
$321$		0			0
$322$	2.87699	−	2.95802i	0.160329	−	0.164844i
$323$	−18.1302			−1.00879
$324$		0			0
$325$	−18.8744	+	32.6915i	−1.04697	+	1.81340i
$326$	2.65444	+	1.53254i	0.147016	+	0.0848795i
$327$		0			0
$328$		−	2.94809i		−	0.162781i
$329$	4.73127	+	16.7249i	0.260843	+	0.922074i
$330$		0			0
$331$	−7.75642	−	13.4345i	−0.426332	−	0.738428i	0.570212	−	0.821497i	$-0.306861\pi$
$331$	−7.75642	−	13.4345i	−0.426332	−	0.738428i	−0.996544	+	0.0830696i	$0.973528\pi$
$332$	−1.43660	+	2.48826i	−0.0788436	+	0.136561i
$333$		0			0
$334$	8.72358	−	5.03656i	0.477333	−	0.275588i
$335$			14.0991i			0.770314i
$336$		0			0
$337$		−	7.70882i		−	0.419926i	−0.977709	−	0.209963i	$-0.932666\pi$
$337$		−	7.70882i		−	0.419926i	0.977709	−	0.209963i	$-0.0673344\pi$
$338$	−10.5380	+	6.08412i	−0.573192	+	0.330933i
$339$		0			0
$340$	−11.9334	−	6.88975i	−0.647180	−	0.373649i
$341$	0.890808	+	0.259211i	0.0482400	+	0.0140371i
$342$		0			0
$343$	−12.5391	+	13.6298i	−0.677047	+	0.735940i
$344$	−9.03556			−0.487165
$345$		0			0
$346$	−0.0663398	−	0.0383013i	−0.00356645	−	0.00205909i
$347$	18.8285	+	10.8706i	1.01077	+	0.583567i	0.911416	−	0.411485i	$-0.134990\pi$
$347$	18.8285	+	10.8706i	1.01077	+	0.583567i	0.0993513	+	0.995052i	$0.468323\pi$
$348$		0			0
$349$	13.4565			0.720307			0.360154	−	0.932893i	$-0.382724\pi$
$349$	13.4565			0.720307			0.360154	+	0.932893i	$0.382724\pi$
$350$	19.2993	+	4.88506i	1.03159	+	0.261118i
$351$		0			0
$352$	−3.18454	−	0.926651i	−0.169737	−	0.0493907i
$353$	−5.80903	−	3.35384i	−0.309183	−	0.178507i	0.337378	−	0.941369i	$-0.390460\pi$
$353$	−5.80903	−	3.35384i	−0.309183	−	0.178507i	−0.646561	+	0.762862i	$0.723793\pi$
$354$		0			0
$355$	25.9098	−	14.9590i	1.37515	−	0.793941i
$356$		−	5.94902i		−	0.315297i
$357$		0			0
$358$		−	8.97491i		−	0.474339i
$359$	−26.8869	+	15.5232i	−1.41904	+	0.819282i	−0.996214	−	0.0869306i	$-0.972294\pi$
$359$	−26.8869	+	15.5232i	−1.41904	+	0.819282i	−0.422823	+	0.906212i	$0.638961\pi$
$360$		0			0
$361$	−1.34091	+	2.32253i	−0.0705744	+	0.122238i
$362$	7.57248	+	13.1159i	0.398001	+	0.689358i
$363$		0			0
$364$	9.51498	+	9.25435i	0.498720	+	0.485060i
$365$		−	13.7940i		−	0.722010i
$366$		0			0
$367$	25.6770	+	14.8246i	1.34033	+	0.773838i	0.986855	−	0.161608i	$-0.0516679\pi$
$367$	25.6770	+	14.8246i	1.34033	+	0.773838i	0.353471	+	0.935445i	$0.385001\pi$
$368$	−0.779812	+	1.35067i	−0.0406505	+	0.0704087i
$369$		0			0
$370$	2.49651			0.129788
$371$	−10.5084	−	10.2206i	−0.545569	−	0.530625i
$372$		0			0
$373$	−7.60418	+	4.39027i	−0.393729	+	0.227320i	−0.683775	−	0.729693i	$-0.739663\pi$
$373$	−7.60418	+	4.39027i	−0.393729	+	0.227320i	0.290045	+	0.957013i	$0.406330\pi$
$374$	−3.07506	−	12.5422i	−0.159008	−	0.648542i
$375$		0			0
$376$	−3.28475	−	5.68935i	−0.169398	−	0.293406i
$377$			0.502706i			0.0258907i
$378$		0			0
$379$	30.8135			1.58278			0.791391	−	0.611311i	$-0.209358\pi$
$379$	30.8135			1.58278			0.791391	+	0.611311i	$0.209358\pi$
$380$	−14.2711	+	8.23945i	−0.732094	+	0.422675i
$381$		0			0
$382$	−5.19615	−	3.00000i	−0.265858	−	0.153493i
$383$	−4.58545	+	2.64741i	−0.234305	+	0.135276i	−0.612557	−	0.790427i	$-0.709859\pi$
$383$	−4.58545	+	2.64741i	−0.234305	+	0.135276i	0.378251	+	0.925703i	$0.376526\pi$
$384$		0			0
$385$	15.3257	+	27.0094i	0.781069	+	1.37653i
$386$	−14.8281			−0.754729
$387$		0			0
$388$	−14.5134	−	8.37933i	−0.736808	−	0.425396i
$389$	0.430119	−	0.744987i	0.0218079	−	0.0377724i	−0.854916	−	0.518767i	$-0.826391\pi$
$389$	0.430119	−	0.744987i	0.0218079	−	0.0377724i	0.876723	+	0.480995i	$0.159724\pi$
$390$		0			0
$391$	−6.07258			−0.307104
$392$	3.33032	−	6.15702i	0.168207	−	0.310977i
$393$		0			0
$394$	7.23723	+	12.5353i	0.364606	+	0.631517i
$395$	13.6248	−	23.5989i	0.685539	−	1.18739i
$396$		0			0
$397$	10.6931	−	6.17367i	0.536672	−	0.309847i	−0.207057	−	0.978329i	$-0.566389\pi$
$397$	10.6931	−	6.17367i	0.536672	−	0.309847i	0.743729	+	0.668481i	$0.233055\pi$
$398$	11.2259			0.562702
$399$		0			0
$400$	−7.52450			−0.376225
$401$	16.8626	+	29.2069i	0.842078	+	1.45852i	0.888134	+	0.459584i	$0.152001\pi$
$401$	16.8626	+	29.2069i	0.842078	+	1.45852i	−0.0460561	+	0.998939i	$0.514665\pi$
$402$		0			0
$403$	1.21533	+	0.701671i	0.0605399	+	0.0349527i
$404$	0.701452	+	1.21495i	0.0348985	+	0.0604461i
$405$		0			0
$406$	0.255105	−	0.0721662i	0.0126607	−	0.00358155i
$407$	1.61866	+	1.68935i	0.0802339	+	0.0837377i
$408$		0			0
$409$	19.1846	−	33.2287i	0.948616	−	1.64305i	0.200273	−	0.979740i	$-0.435817\pi$
$409$	19.1846	−	33.2287i	0.948616	−	1.64305i	0.748343	−	0.663312i	$-0.230850\pi$
$410$	5.21665	−	9.03550i	0.257632	−	0.446231i
$411$		0			0
$412$		−	2.06291i		−	0.101632i
$413$	−26.8112	+	27.5663i	−1.31929	+	1.35645i
$414$		0			0
$415$	−8.80595	+	5.08412i	−0.432267	+	0.249570i
$416$	−4.34467	−	2.50840i	−0.213015	−	0.122984i
$417$		0			0
$418$	−14.8284	−	4.31483i	−0.725282	−	0.211045i
$419$		−	33.5023i		−	1.63670i	−0.574723	−	0.818348i	$-0.694890\pi$
$419$		−	33.5023i		−	1.63670i	0.574723	−	0.818348i	$-0.305110\pi$
$420$		0			0
$421$	−23.0155			−1.12171			−0.560853	−	0.827915i	$-0.689527\pi$
$421$	−23.0155			−1.12171			−0.560853	+	0.827915i	$0.689527\pi$
$422$	3.22019	+	5.57753i	0.156756	+	0.271510i
$423$		0			0
$424$	4.79828	+	2.77029i	0.233025	+	0.134537i
$425$	−14.6488	−	25.3724i	−0.710570	−	1.23074i
$426$		0			0
$427$	28.3281	−	8.01368i	1.37089	−	0.387809i
$428$		−	12.2655i		−	0.592875i
$429$		0			0
$430$	−27.6927	−	15.9884i	−1.33546	−	0.771030i
$431$	−23.2425	−	13.4191i	−1.11955	−	0.646373i	−0.178265	−	0.983983i	$-0.557048\pi$
$431$	−23.2425	−	13.4191i	−1.11955	−	0.646373i	−0.941286	+	0.337609i	$0.890382\pi$
$432$		0			0
$433$			30.6912i			1.47493i	0.675387	+	0.737463i	$0.263976\pi$
$433$			30.6912i			1.47493i	−0.675387	+	0.737463i	$0.736024\pi$
$434$	0.181606	−	0.717465i	0.00871736	−	0.0344394i
$435$		0			0
$436$	5.82394	−	3.36245i	0.278916	−	0.161032i
$437$	−3.63110	+	6.28924i	−0.173699	+	0.300855i
$438$		0			0
$439$	8.42258	+	14.5883i	0.401988	+	0.696263i	0.993966	−	0.109691i	$-0.0349861\pi$
$439$	8.42258	+	14.5883i	0.401988	+	0.696263i	−0.591978	+	0.805954i	$0.701653\pi$
$440$	−8.12048	−	8.47510i	−0.387129	−	0.404035i
$441$		0			0
$442$		−	19.5335i		−	0.929114i
$443$	−0.395295	−	0.684671i	−0.0187810	−	0.0325297i	0.856482	−	0.516177i	$-0.172645\pi$
$443$	−0.395295	−	0.684671i	−0.0187810	−	0.0325297i	−0.875263	+	0.483647i	$0.839312\pi$
$444$		0			0
$445$	10.5268	−	18.2329i	0.499017	−	0.864323i
$446$	2.00897	+	3.47963i	0.0951273	+	0.164765i
$447$		0			0
$448$	−0.649221	+	2.56486i	−0.0306728	+	0.121178i
$449$	−15.9734			−0.753833			−0.376917	−	0.926247i	$-0.623016\pi$
$449$	−15.9734			−0.753833			−0.376917	+	0.926247i	$0.623016\pi$
$450$		0			0
$451$	9.49646	−	2.32831i	0.447171	−	0.109636i
$452$	5.99498	−	10.3836i	0.281980	−	0.488404i
$453$		0			0
$454$			12.7293i			0.597416i
$455$	12.7865	+	45.2000i	0.599442	+	2.11901i
$456$		0			0
$457$	−30.2530	+	17.4666i	−1.41517	+	0.817052i	−0.995870	−	0.0907937i	$-0.971060\pi$
$457$	−30.2530	+	17.4666i	−1.41517	+	0.817052i	−0.419305	+	0.907845i	$0.637726\pi$
$458$	3.00672	−	5.20780i	0.140495	−	0.243344i
$459$		0			0
$460$	−4.78003	+	2.75975i	−0.222870	+	0.128674i
$461$	−20.8346			−0.970364			−0.485182	−	0.874413i	$-0.661247\pi$
$461$	−20.8346			−0.970364			−0.485182	+	0.874413i	$0.661247\pi$
$462$		0			0
$463$	13.1724			0.612172			0.306086	−	0.952004i	$-0.400981\pi$
$463$	13.1724			0.612172			0.306086	+	0.952004i	$0.400981\pi$
$464$	−0.0867797	+	0.0501023i	−0.00402865	+	0.00232594i
$465$		0			0
$466$	−3.23347	+	5.60053i	−0.149788	+	0.259440i
$467$	14.5651	−	8.40919i	0.673995	−	0.389131i	−0.123594	−	0.992333i	$-0.539442\pi$
$467$	14.5651	−	8.40919i	0.673995	−	0.389131i	0.797589	+	0.603202i	$0.206109\pi$
$468$		0			0
$469$	7.55599	+	7.34902i	0.348903	+	0.339346i
$470$		−	23.2494i		−	1.07241i
$471$		0			0
$472$	7.26719	−	12.5871i	0.334500	−	0.579370i
$473$	−7.13600	−	29.1055i	−0.328114	−	1.33827i
$474$		0			0
$475$	−35.0369			−1.60760
$476$	−9.91256	+	2.80414i	−0.454341	+	0.128528i
$477$		0			0
$478$	7.78874	+	13.4905i	0.356249	+	0.617041i
$479$	−11.4291	+	19.7957i	−0.522208	+	0.904491i	0.477458	+	0.878654i	$0.341558\pi$
$479$	−11.4291	+	19.7957i	−0.522208	+	0.904491i	−0.999666	+	0.0258361i	$0.991775\pi$
$480$		0			0
$481$	1.76950	+	3.06486i	0.0806822	+	0.139746i
$482$			23.4762i			1.06931i
$483$		0			0
$484$	0.469894	−	10.9900i	0.0213588	−	0.499544i
$485$	−29.6544	−	51.3630i	−1.34654	−	2.33227i
$486$		0			0
$487$	−15.6314	+	27.0744i	−0.708327	+	1.22686i	0.257150	+	0.966371i	$0.417217\pi$
$487$	−15.6314	+	27.0744i	−0.708327	+	1.22686i	−0.965477	+	0.260487i	$0.916117\pi$
$488$	−9.63644	+	5.56360i	−0.436221	+	0.251852i
$489$		0			0
$490$	21.1018	−	12.9774i	0.953283	−	0.586260i
$491$			22.4979i			1.01532i	0.861558	+	0.507659i	$0.169489\pi$
$491$			22.4979i			1.01532i	−0.861558	+	0.507659i	$0.830511\pi$
$492$		0			0
$493$	−0.337887	−	0.195079i	−0.0152177	−	0.00878593i
$494$	−20.2304	−	11.6800i	−0.910210	−	0.525510i
$495$		0			0
$496$			0.279729i			0.0125602i
$497$	5.48839	−	21.6828i	0.246188	−	0.972609i
$498$		0			0
$499$	15.9548	+	27.6346i	0.714236	+	1.23709i	0.963253	+	0.268595i	$0.0865592\pi$
$499$	15.9548	+	27.6346i	0.714236	+	1.23709i	−0.249017	+	0.968499i	$0.580107\pi$
$500$	−7.73723	−	4.46709i	−0.346020	−	0.199774i
$501$		0			0
$502$	9.14090	+	15.8325i	0.407978	+	0.706639i
$503$	30.2687			1.34962			0.674808	−	0.737994i	$-0.264227\pi$
$503$	30.2687			1.34962			0.674808	+	0.737994i	$0.264227\pi$
$504$		0			0
$505$			4.96487i			0.220934i
$506$	−4.96669	−	1.44523i	−0.220796	−	0.0642481i
$507$		0			0
$508$	−11.4488	−	6.60994i	−0.507956	−	0.293269i
$509$	19.9655	−	11.5271i	0.884957	−	0.510930i	0.0126676	−	0.999920i	$-0.495968\pi$
$509$	19.9655	−	11.5271i	0.884957	−	0.510930i	0.872290	+	0.488989i	$0.162634\pi$
$510$		0			0
$511$	−7.39249	−	7.19000i	−0.327025	−	0.318067i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−4.80983	+	8.33087i	−0.212153	+	0.367459i
$515$	3.65031	−	6.32252i	0.160852	−	0.278603i
$516$		0			0
$517$	15.7325	−	15.0742i	0.691912	−	0.662961i
$518$	1.30129	−	1.33793i	0.0571753	−	0.0587855i
$519$		0			0
$520$	−8.87721	−	15.3758i	−0.389291	−	0.674273i
$521$	6.91351	+	3.99152i	0.302886	+	0.174872i	0.643739	−	0.765245i	$-0.277382\pi$
$521$	6.91351	+	3.99152i	0.302886	+	0.174872i	−0.340852	+	0.940117i	$0.610716\pi$
$522$		0			0
$523$	−2.79140	−	4.83485i	−0.122059	−	0.211413i	0.798520	−	0.601968i	$-0.205617\pi$
$523$	−2.79140	−	4.83485i	−0.122059	−	0.211413i	−0.920580	+	0.390555i	$0.872283\pi$
$524$	16.4986			0.720746
$525$		0			0
$526$	−0.578666			−0.0252310
$527$	−0.943238	+	0.544579i	−0.0410881	+	0.0237222i
$528$		0			0
$529$	10.2838	−	17.8120i	0.447121	−	0.774437i
$530$	9.80405	+	16.9811i	0.425861	+	0.737612i
$531$		0			0
$532$	−3.02302	+	11.9430i	−0.131064	+	0.517793i
$533$	14.7900			0.640625
$534$		0			0
$535$	21.7038	−	37.5920i	0.938335	−	1.62524i
$536$	−3.45017	−	1.99196i	−0.149025	−	0.0860395i
$537$		0			0
$538$	22.0896			0.952350
$539$	22.4633	+	5.86509i	0.967564	+	0.252627i
$540$		0			0
$541$	−11.6066	+	6.70108i	−0.499007	+	0.288102i	−0.728304	−	0.685255i	$-0.759691\pi$
$541$	−11.6066	+	6.70108i	−0.499007	+	0.288102i	0.229296	+	0.973357i	$0.426358\pi$
$542$	3.69119	+	2.13111i	0.158550	+	0.0915390i
$543$		0			0
$544$	3.37197	−	1.94681i	0.144572	−	0.0834688i
$545$	23.7994			1.01946
$546$		0			0
$547$			24.5161i			1.04823i	0.851647	+	0.524116i	$0.175604\pi$
$547$			24.5161i			1.04823i	−0.851647	+	0.524116i	$0.824396\pi$
$548$	−3.32187	−	5.75365i	−0.141903	−	0.245784i
$549$		0			0
$550$	−5.94261	−	24.2381i	−0.253394	−	1.03351i
$551$	−0.404079	+	0.233295i	−0.0172143	+	0.00993870i
$552$		0			0
$553$	−5.54532	−	19.6026i	−0.235811	−	0.833585i
$554$	−18.3653			−0.780265
$555$		0			0
$556$	−7.17666	+	12.4303i	−0.304358	+	0.527164i
$557$	3.12772	+	1.80579i	0.132526	+	0.0765137i	0.564797	−	0.825230i	$-0.308954\pi$
$557$	3.12772	+	1.80579i	0.132526	+	0.0765137i	−0.432271	+	0.901744i	$0.642288\pi$
$558$		0			0
$559$		−	45.3296i		−	1.91724i
$560$	−6.52829	+	6.71215i	−0.275871	+	0.283640i
$561$		0			0
$562$	1.86445	+	3.22933i	0.0786472	+	0.136221i
$563$	2.92902	−	5.07320i	0.123443	−	0.213810i	−0.797680	−	0.603081i	$-0.793940\pi$
$563$	2.92902	−	5.07320i	0.123443	−	0.213810i	0.921123	+	0.389271i	$0.127273\pi$
$564$		0			0
$565$	36.7476	−	21.2162i	1.54598	−	0.892573i
$566$		−	12.7315i		−	0.535146i
$567$		0			0
$568$			8.45381i			0.354714i
$569$	−29.9772	+	17.3073i	−1.25671	+	0.725561i	−0.972433	−	0.233182i	$-0.925086\pi$
$569$	−29.9772	+	17.3073i	−1.25671	+	0.725561i	−0.284275	+	0.958743i	$0.591753\pi$
$570$		0			0
$571$	6.89907	+	3.98318i	0.288717	+	0.166691i	0.637363	−	0.770564i	$-0.280025\pi$
$571$	6.89907	+	3.98318i	0.288717	+	0.166691i	−0.348646	+	0.937254i	$0.613358\pi$
$572$	4.64882	−	15.9762i	0.194377	−	0.667999i
$573$		0			0
$574$	−2.12318	−	7.50539i	−0.0886199	−	0.313269i
$575$	−11.7354			−0.489399
$576$		0			0
$577$	15.9144	+	9.18819i	0.662525	+	0.382509i	0.793239	−	0.608911i	$-0.208393\pi$
$577$	15.9144	+	9.18819i	0.662525	+	0.382509i	−0.130713	+	0.991420i	$0.541727\pi$
$578$	−1.59325	−	0.919861i	−0.0662703	−	0.0382612i
$579$		0			0
$580$	−0.354624			−0.0147249
$581$	−1.86534	+	7.36936i	−0.0773874	+	0.305732i
$582$		0			0
$583$	−5.13418	+	17.6442i	−0.212636	+	0.730749i
$584$	3.37552	+	1.94885i	0.139680	+	0.0806442i
$585$		0			0
$586$	−22.7116	+	13.1126i	−0.938209	+	0.541675i
$587$			17.2267i			0.711021i	0.934672	+	0.355511i	$0.115693\pi$
$587$			17.2267i			0.711021i	−0.934672	+	0.355511i	$0.884307\pi$
$588$		0			0
$589$			1.30252i			0.0536695i
$590$	44.5459	−	25.7186i	1.83392	−	1.05882i
$591$		0			0
$592$	−0.352715	+	0.610920i	−0.0144965	+	0.0251087i
$593$	20.6214	+	35.7172i	0.846817	+	1.46673i	0.884033	+	0.467424i	$0.154818\pi$
$593$	20.6214	+	35.7172i	0.846817	+	1.46673i	−0.0372161	+	0.999307i	$0.511849\pi$
$594$		0			0
$595$	−35.3425	−	8.94595i	−1.44890	−	0.366748i
$596$		−	2.66587i		−	0.109198i
$597$		0			0
$598$	−6.77605	−	3.91216i	−0.277093	−	0.159980i
$599$	4.97720	−	8.62076i	0.203363	−	0.352235i	−0.746247	−	0.665669i	$-0.768146\pi$
$599$	4.97720	−	8.62076i	0.203363	−	0.352235i	0.949610	+	0.313434i	$0.101480\pi$
$600$		0			0
$601$	−4.76767			−0.194477			−0.0972386	−	0.995261i	$-0.531001\pi$
$601$	−4.76767			−0.194477			−0.0972386	+	0.995261i	$0.531001\pi$
$602$	−23.0031	+	6.50731i	−0.937538	+	0.265218i
$603$		0			0
$604$	−8.99830	+	5.19517i	−0.366136	+	0.211389i
$605$	20.8869	−	32.8512i	0.849172	−	1.33559i
$606$		0			0
$607$	2.27672	+	3.94340i	0.0924094	+	0.160058i	0.908524	−	0.417832i	$-0.137210\pi$
$607$	2.27672	+	3.94340i	0.0924094	+	0.160058i	−0.816115	+	0.577889i	$0.803876\pi$
$608$		−	4.65637i		−	0.188841i
$609$		0			0
$610$	−39.3791			−1.59441
$611$	28.5423	−	16.4789i	1.15470	−	0.666665i
$612$		0			0
$613$	−1.25482	−	0.724472i	−0.0506818	−	0.0292611i	0.474445	−	0.880285i	$-0.342649\pi$
$613$	−1.25482	−	0.724472i	−0.0506818	−	0.0292611i	−0.525127	+	0.851024i	$0.675982\pi$
$614$	−22.1652	+	12.7971i	−0.894515	+	0.516449i
$615$		0			0
$616$	−8.77472	−	0.0656384i	−0.353543	−	0.00264465i
$617$	2.96752			0.119468			0.0597340	−	0.998214i	$-0.480975\pi$
$617$	2.96752			0.119468			0.0597340	+	0.998214i	$0.480975\pi$
$618$		0			0
$619$	−10.0004	−	5.77375i	−0.401951	−	0.232067i	0.285374	−	0.958416i	$-0.407882\pi$
$619$	−10.0004	−	5.77375i	−0.401951	−	0.232067i	−0.687326	+	0.726349i	$0.741215\pi$
$620$	−0.494980	+	0.857330i	−0.0198789	+	0.0344312i
$621$		0			0
$622$	−1.90970			−0.0765720
$623$	−4.28442	−	15.1453i	−0.171651	−	0.606783i
$624$		0			0
$625$	3.00222	+	5.19999i	0.120089	+	0.208000i
$626$	15.2251	−	26.3707i	0.608519	−	1.05399i
$627$		0			0
$628$	7.25273	−	4.18736i	0.289415	−	0.167094i
$629$	−2.74668			−0.109517
$630$		0			0
$631$	−27.5215			−1.09562			−0.547808	−	0.836604i	$-0.684537\pi$
$631$	−27.5215			−1.09562			−0.547808	+	0.836604i	$0.684537\pi$
$632$	3.84991	+	6.66824i	0.153141	+	0.265248i
$633$		0			0
$634$	−29.7862	−	17.1971i	−1.18296	−	0.682983i
$635$	−23.3926	−	40.5171i	−0.928306	−	1.60787i
$636$		0			0
$637$	30.8885	+	16.7076i	1.22385	+	0.661978i
$638$	−0.229926	−	0.239967i	−0.00910288	−	0.00950040i
$639$		0			0
$640$	1.76950	−	3.06486i	0.0699456	−	0.121149i
$641$	16.8273	−	29.1458i	0.664639	−	1.15119i	−0.314744	−	0.949177i	$-0.601919\pi$
$641$	16.8273	−	29.1458i	0.664639	−	1.15119i	0.979383	−	0.202013i	$-0.0647482\pi$
$642$		0			0
$643$			5.95261i			0.234748i	0.993088	+	0.117374i	$0.0374476\pi$
$643$			5.95261i			0.234748i	−0.993088	+	0.117374i	$0.962552\pi$
$644$	−1.01254	+	4.00022i	−0.0398997	+	0.157631i
$645$		0			0
$646$	15.7012	−	9.06508i	0.617754	−	0.356661i
$647$	−10.1963	−	5.88686i	−0.400860	−	0.231437i	0.285995	−	0.958231i	$-0.407676\pi$
$647$	−10.1963	−	5.88686i	−0.400860	−	0.231437i	−0.686855	+	0.726795i	$0.741009\pi$
$648$		0			0
$649$	46.2854	+	13.4683i	1.81686	+	0.528677i
$650$		−	37.7489i		−	1.48063i
$651$		0			0
$652$	−3.06508			−0.120038
$653$	14.4335	+	24.9996i	0.564827	+	0.978309i	0.997066	+	0.0765498i	$0.0243904\pi$
$653$	14.4335	+	24.9996i	0.564827	+	0.978309i	−0.432239	+	0.901759i	$0.642276\pi$
$654$		0			0
$655$	50.5660	+	29.1943i	1.97578	+	1.14071i
$656$	1.47405	+	2.55312i	0.0575519	+	0.0996827i
$657$		0			0
$658$	−12.4599	−	12.1186i	−0.485736	−	0.472431i
$659$			44.6812i			1.74053i	0.492581	+	0.870266i	$0.336053\pi$
$659$			44.6812i			1.74053i	−0.492581	+	0.870266i	$0.663947\pi$
$660$		0			0
$661$	−34.3242	−	19.8171i	−1.33505	−	0.770794i	−0.348985	−	0.937128i	$-0.613474\pi$
$661$	−34.3242	−	19.8171i	−1.33505	−	0.770794i	−0.986069	+	0.166334i	$0.946807\pi$
$662$	13.4345	+	7.75642i	0.522147	+	0.301462i
$663$		0			0
$664$		−	2.87320i		−	0.111502i
$665$	−30.3982	+	31.2543i	−1.17879	+	1.21199i
$666$		0			0
$667$	−0.135344	+	0.0781407i	−0.00524053	+	0.00302562i
$668$	−5.03656	+	8.72358i	−0.194870	+	0.337525i
$669$		0			0
$670$	−7.04953	−	12.2101i	−0.272347	−	0.471719i
$671$	−25.5321	−	26.6471i	−0.985657	−	1.02870i
$672$		0			0
$673$			2.71886i			0.104804i	0.998626	+	0.0524022i	$0.0166878\pi$
$673$			2.71886i			0.104804i	−0.998626	+	0.0524022i	$0.983312\pi$
$674$	3.85441	+	6.67604i	0.148466	+	0.257151i
$675$		0			0
$676$	6.08412	−	10.5380i	0.234005	−	0.405308i
$677$	−3.02973	−	5.24764i	−0.116442	−	0.201683i	0.801913	−	0.597440i	$-0.203816\pi$
$677$	−3.02973	−	5.24764i	−0.116442	−	0.201683i	−0.918355	+	0.395757i	$0.870482\pi$
$678$		0			0
$679$	−42.9837	−	10.8801i	−1.64956	−	0.417539i
$680$	13.7795			0.528420
$681$		0			0
$682$	−0.901068	+	0.220921i	−0.0345037	+	0.00845950i
$683$	−3.01704	+	5.22567i	−0.115444	+	0.199955i	−0.917957	−	0.396680i	$-0.870162\pi$
$683$	−3.01704	+	5.22567i	−0.115444	+	0.199955i	0.802513	+	0.596634i	$0.203496\pi$
$684$		0			0
$685$		−	23.5122i		−	0.898354i
$686$	4.04428	−	18.0733i	0.154411	−	0.690041i
$687$		0			0
$688$	7.82503	−	4.51778i	0.298326	−	0.172239i
$689$	−13.8980	+	24.0720i	−0.529471	+	0.917071i
$690$		0			0
$691$	−17.1519	+	9.90263i	−0.652487	+	0.376714i	−0.789409	−	0.613868i	$-0.789613\pi$
$691$	−17.1519	+	9.90263i	−0.652487	+	0.376714i	0.136921	+	0.990582i	$0.456279\pi$
$692$	0.0766026			0.00291200
$693$		0			0
$694$	−21.7413			−0.825288
$695$	−43.9909	+	25.3982i	−1.66867	+	0.963407i
$696$		0			0
$697$	−5.73938	+	9.94090i	−0.217394	+	0.376538i
$698$	−11.6536	+	6.72823i	−0.441096	+	0.254667i
$699$		0			0
$700$	−19.1562	+	5.41905i	−0.724037	+	0.204821i
$701$		−	26.0155i		−	0.982591i	−0.870993	−	0.491296i	$-0.836524\pi$
$701$		−	26.0155i		−	0.982591i	0.870993	−	0.491296i	$-0.163476\pi$
$702$		0			0
$703$	−1.64237	+	2.84467i	−0.0619433	+	0.107289i
$704$	3.22122	−	0.789769i	0.121404	−	0.0297655i
$705$		0			0
$706$	6.70769			0.252447
$707$	2.66078	+	2.58790i	0.100069	+	0.0973280i
$708$		0			0
$709$	12.4458	+	21.5568i	0.467413	+	0.809583i	0.999307	−	0.0372278i	$-0.0118527\pi$
$709$	12.4458	+	21.5568i	0.467413	+	0.809583i	−0.531894	+	0.846811i	$0.678519\pi$
$710$	−14.9590	+	25.9098i	−0.561401	+	0.972376i
$711$		0			0
$712$	2.97451	+	5.15200i	0.111474	+	0.193079i
$713$			0.436271i			0.0163385i
$714$		0			0
$715$	42.5178	−	40.7388i	1.59008	−	1.52354i
$716$	4.48746	+	7.77250i	0.167704	+	0.290472i
$717$		0			0
$718$	15.5232	−	26.8869i	0.579320	−	1.00341i
$719$	11.5156	−	6.64851i	0.429458	−	0.247948i	−0.269658	−	0.962956i	$-0.586911\pi$
$719$	11.5156	−	6.64851i	0.429458	−	0.247948i	0.699116	+	0.715009i	$0.253577\pi$
$720$		0			0
$721$	−1.48568	−	5.25184i	−0.0553296	−	0.195589i
$722$		−	2.68183i		−	0.0998073i
$723$		0			0
$724$	−13.1159	−	7.57248i	−0.487449	−	0.281429i
$725$	−0.652974	−	0.376995i	−0.0242508	−	0.0140012i
$726$		0			0
$727$			5.67083i			0.210319i	0.994455	+	0.105160i	$0.0335354\pi$
$727$			5.67083i			0.210319i	−0.994455	+	0.105160i	$0.966465\pi$
$728$	−12.8674	−	3.25701i	−0.476897	−	0.120713i
$729$		0			0
$730$	6.89699	+	11.9459i	0.255269	+	0.442139i
$731$	30.4677	+	17.5905i	1.12689	+	0.650609i
$732$		0			0
$733$	−20.6879	−	35.8326i	−0.764127	−	1.32351i	−0.940707	−	0.339220i	$-0.889837\pi$
$733$	−20.6879	−	35.8326i	−0.764127	−	1.32351i	0.176580	−	0.984286i	$-0.443496\pi$
$734$	−29.6492			−1.09437
$735$		0			0
$736$		−	1.55962i		−	0.0574885i
$737$	3.69170	−	12.6870i	0.135985	−	0.467330i
$738$		0			0
$739$	−35.9749	−	20.7701i	−1.32336	−	0.764042i	−0.339097	−	0.940752i	$-0.610121\pi$
$739$	−35.9749	−	20.7701i	−1.32336	−	0.764042i	−0.984263	+	0.176710i	$0.943455\pi$
$740$	−2.16204	+	1.24826i	−0.0794783	+	0.0458868i
$741$		0			0
$742$	14.2108	+	3.59706i	0.521696	+	0.132052i
$743$		−	39.7404i		−	1.45793i	−0.684549	−	0.728967i	$-0.740001\pi$
$743$		−	39.7404i		−	1.45793i	0.684549	−	0.728967i	$-0.259999\pi$
$744$		0			0
$745$	4.71725	−	8.17053i	0.172827	−	0.299345i
$746$	4.39027	−	7.60418i	0.160739	−	0.278409i
$747$		0			0
$748$	8.93419	+	9.32434i	0.326666	+	0.340932i
$749$	−8.83346	−	31.2260i	−0.322768	−	1.14097i
$750$		0			0
$751$	−2.68263	−	4.64645i	−0.0978905	−	0.169551i	0.812921	−	0.582374i	$-0.197876\pi$
$751$	−2.68263	−	4.64645i	−0.0978905	−	0.169551i	−0.910811	+	0.412823i	$0.864543\pi$
$752$	5.68935	+	3.28475i	0.207469	+	0.119782i
$753$		0			0
$754$	−0.251353	−	0.435356i	−0.00915374	−	0.0158547i
$755$	−36.7714			−1.33825
$756$		0			0
$757$	25.8962			0.941215			0.470607	−	0.882343i	$-0.344035\pi$
$757$	25.8962			0.941215			0.470607	+	0.882343i	$0.344035\pi$
$758$	−26.6852	+	15.4067i	−0.969251	+	0.559598i
$759$		0			0
$760$	8.23945	−	14.2711i	0.298876	−	0.517669i
$761$	−7.61030	−	13.1814i	−0.275873	−	0.477827i	0.694482	−	0.719510i	$-0.255634\pi$
$761$	−7.61030	−	13.1814i	−0.275873	−	0.477827i	−0.970355	+	0.241684i	$0.922300\pi$
$762$		0			0
$763$	12.4053	−	12.7546i	0.449100	−	0.461748i
$764$	6.00000			0.217072
$765$		0			0
$766$	2.64741	−	4.58545i	0.0956548	−	0.165679i
$767$	63.1471	+	36.4580i	2.28011	+	1.31642i
$768$		0			0
$769$	−22.5146			−0.811898			−0.405949	−	0.913896i	$-0.633059\pi$
$769$	−22.5146			−0.811898			−0.405949	+	0.913896i	$0.633059\pi$
$770$	−26.7771	−	15.7280i	−0.964981	−	0.566799i
$771$		0			0
$772$	12.8415	−	7.41403i	0.462175	−	0.266837i
$773$	−24.2776	−	14.0167i	−0.873204	−	0.504144i	−0.00479213	−	0.999989i	$-0.501525\pi$
$773$	−24.2776	−	14.0167i	−0.873204	−	0.504144i	−0.868412	+	0.495844i	$0.834859\pi$
$774$		0			0
$775$	−1.82283	+	1.05241i	−0.0654778	+	0.0378036i
$776$	16.7587			0.601601
$777$		0			0
$778$			0.860237i			0.0308410i
$779$	6.86371	+	11.8883i	0.245918	+	0.425943i
$780$		0			0
$781$	−27.2316	+	6.67655i	−0.974423	+	0.238906i
$782$	5.25901	−	3.03629i	0.188062	−	0.108578i
$783$		0			0
$784$	0.194366	+	6.99730i	0.00694163	+	0.249904i
$785$	29.6381			1.05783
$786$		0			0
$787$	6.37160	−	11.0359i	0.227123	−	0.393388i	−0.729831	−	0.683627i	$-0.760401\pi$
$787$	6.37160	−	11.0359i	0.227123	−	0.393388i	0.956954	+	0.290239i	$0.0937347\pi$
$788$	−12.5353	−	7.23723i	−0.446550	−	0.257816i
$789$		0			0
$790$			27.2496i			0.969499i
$791$	7.78414	−	30.7526i	0.276772	−	1.09344i
$792$		0			0
$793$	−27.9114	−	48.3440i	−0.991165	−	1.71675i
$794$	−6.17367	+	10.6931i	−0.219095	+	0.379484i
$795$		0			0
$796$	−9.72188	+	5.61293i	−0.344583	+	0.198945i
$797$		−	5.63488i		−	0.199598i	−0.995008	−	0.0997989i	$-0.968180\pi$
$797$		−	5.63488i		−	0.199598i	0.995008	−	0.0997989i	$-0.0318199\pi$
$798$		0			0
$799$			25.5791i			0.904923i
$800$	6.51641	−	3.76225i	0.230390	−	0.133016i
$801$		0			0
$802$	−29.2069	−	16.8626i	−1.03133	−	0.595439i
$803$	−3.61182	+	12.4124i	−0.127458	+	0.438025i
$804$		0			0
$805$	−10.1817	+	10.4684i	−0.358857	+	0.368963i
$806$	−1.40334			−0.0494306
$807$		0			0
$808$	−1.21495	−	0.701452i	−0.0427418	−	0.0246770i
$809$	−14.7572	−	8.52007i	−0.518835	−	0.299550i	0.217623	−	0.976033i	$-0.430170\pi$
$809$	−14.7572	−	8.52007i	−0.518835	−	0.299550i	−0.736458	+	0.676483i	$0.763503\pi$
$810$		0			0
$811$	−0.332109			−0.0116619			−0.00583097	−	0.999983i	$-0.501856\pi$
$811$	−0.332109			−0.0116619			−0.00583097	+	0.999983i	$0.501856\pi$
$812$	−0.184845	+	0.190050i	−0.00648678	+	0.00666946i
$813$		0			0
$814$	−2.24647	−	0.653687i	−0.0787388	−	0.0229117i
$815$	−9.39404	−	5.42365i	−0.329059	−	0.189982i
$816$		0			0
$817$	36.4363	−	21.0365i	1.27474	−	0.735973i
$818$			38.3692i			1.34155i
$819$		0			0
$820$			10.4333i			0.364346i
$821$	−1.97706	+	1.14146i	−0.0690000	+	0.0398372i	−0.534103	−	0.845419i	$-0.679351\pi$
$821$	−1.97706	+	1.14146i	−0.0690000	+	0.0398372i	0.465103	+	0.885257i	$0.346017\pi$
$822$		0			0
$823$	−5.04228	+	8.73348i	−0.175763	+	0.304430i	−0.940425	−	0.340001i	$-0.889572\pi$
$823$	−5.04228	+	8.73348i	−0.175763	+	0.304430i	0.764662	+	0.644431i	$0.222906\pi$
$824$	1.03145	+	1.78653i	0.0359324	+	0.0622367i
$825$		0			0
$826$	9.43603	−	37.2787i	0.328321	−	1.29709i
$827$		−	10.9337i		−	0.380204i	−0.981764	−	0.190102i	$-0.939118\pi$
$827$		−	10.9337i		−	0.380204i	0.981764	−	0.190102i	$-0.0608818\pi$
$828$		0			0
$829$	−10.0682	−	5.81287i	−0.349683	−	0.201889i	0.314863	−	0.949137i	$-0.398041\pi$
$829$	−10.0682	−	5.81287i	−0.349683	−	0.201889i	−0.664545	+	0.747248i	$0.731375\pi$
$830$	5.08412	−	8.80595i	0.176472	−	0.305659i
$831$		0			0
$832$	5.01680			0.173926
$833$	−23.2163	+	14.2778i	−0.804398	+	0.494697i
$834$		0			0
$835$	−30.8727	+	17.8244i	−1.06839	+	0.616838i
$836$	14.9992	−	3.67746i	0.518759	−	0.127188i
$837$		0			0
$838$	16.7512	+	29.0139i	0.578659	+	1.00227i
$839$		−	23.4571i		−	0.809828i	−0.914355	−	0.404914i	$-0.867301\pi$
$839$		−	23.4571i		−	0.809828i	0.914355	−	0.404914i	$-0.132699\pi$
$840$		0			0
$841$	28.9900			0.999654
$842$	19.9320	−	11.5077i	0.686902	−	0.396583i
$843$		0			0
$844$	−5.57753	−	3.22019i	−0.191986	−	0.110843i
$845$	37.2940	−	21.5317i	1.28295	−	0.740712i
$846$		0			0
$847$	−6.71856	−	28.3171i	−0.230853	−	0.972989i
$848$	−5.54058			−0.190264
$849$		0			0
$850$	25.3724	+	14.6488i	0.870266	+	0.502449i
$851$	−0.550102	+	0.952805i	−0.0188573	+	0.0326617i
$852$		0			0
$853$	−38.5870			−1.32119			−0.660597	−	0.750741i	$-0.729697\pi$
$853$	−38.5870			−1.32119			−0.660597	+	0.750741i	$0.729697\pi$
$854$	−20.5260	+	21.1041i	−0.702387	+	0.722168i
$855$		0			0
$856$	6.13274	+	10.6222i	0.209613	+	0.363060i
$857$	21.3007	−	36.8938i	0.727617	−	1.26027i	−0.230271	−	0.973126i	$-0.573961\pi$
$857$	21.3007	−	36.8938i	0.727617	−	1.26027i	0.957888	−	0.287142i	$-0.0927053\pi$
$858$		0			0
$859$	10.7344	−	6.19752i	0.366254	−	0.211457i	−0.305567	−	0.952171i	$-0.598846\pi$
$859$	10.7344	−	6.19752i	0.366254	−	0.211457i	0.671821	+	0.740714i	$0.265513\pi$
$860$	31.9768			1.09040
$861$		0			0
$862$	26.8381			0.914110
$863$	−19.6374	−	34.0130i	−0.668465	−	1.15781i	−0.978333	−	0.207036i	$-0.933618\pi$
$863$	−19.6374	−	34.0130i	−0.668465	−	1.15781i	0.309869	−	0.950779i	$-0.399715\pi$
$864$		0			0
$865$	0.234776	+	0.135548i	0.00798264	+	0.00460878i
$866$	−15.3456	−	26.5794i	−0.521465	−	0.903204i
$867$		0			0
$868$	0.201457	+	0.712146i	0.00683791	+	0.0241718i
$869$	−18.4393	+	17.6678i	−0.625512	+	0.599338i
$870$		0			0
$871$	9.99325	−	17.3088i	0.338608	−	0.586487i
$872$	−3.36245	+	5.82394i	−0.113867	+	0.197223i
$873$		0			0
$874$		−	7.26219i		−	0.245647i
$875$	−22.9149	−	5.80026i	−0.774666	−	0.196085i
$876$		0			0
$877$	39.9403	−	23.0595i	1.34869	−	0.778665i	0.360624	−	0.932711i	$-0.382564\pi$
$877$	39.9403	−	23.0595i	1.34869	−	0.778665i	0.988064	+	0.154046i	$0.0492304\pi$
$878$	−14.5883	−	8.42258i	−0.492332	−	0.284248i
$879$		0			0
$880$	11.2701	+	3.27941i	0.379915	+	0.110549i
$881$			14.9583i			0.503957i	0.967733	+	0.251978i	$0.0810812\pi$
$881$			14.9583i			0.503957i	−0.967733	+	0.251978i	$0.918919\pi$
$882$		0			0
$883$	−8.42386			−0.283485			−0.141743	−	0.989904i	$-0.545271\pi$
$883$	−8.42386			−0.283485			−0.141743	+	0.989904i	$0.545271\pi$
$884$	9.76675	+	16.9165i	0.328491	+	0.568964i
$885$		0			0
$886$	0.684671	+	0.395295i	0.0230020	+	0.0132802i
$887$	5.66022	+	9.80379i	0.190052	+	0.329179i	0.945267	−	0.326298i	$-0.105801\pi$
$887$	5.66022	+	9.80379i	0.190052	+	0.329179i	−0.755216	+	0.655477i	$0.772468\pi$
$888$		0			0
$889$	−33.9072	−	8.58263i	−1.13721	−	0.287852i
$890$			21.0536i			0.705717i
$891$		0			0
$892$	−3.47963	−	2.00897i	−0.116507	−	0.0672652i
$893$	26.4917	+	15.2950i	0.886512	+	0.511828i
$894$		0			0
$895$			31.7622i			1.06169i
$896$	−0.720188	−	2.54585i	−0.0240598	−	0.0850507i
$897$		0			0
$898$	13.8334	−	7.98672i	0.461627	−	0.266520i
$899$	−0.0140151	+	0.0242748i	−0.000467428	+	0.000809609i
$900$		0			0
$901$	−10.7865	−	18.6827i	−0.359349	−	0.622411i
$902$	−7.06002	+	6.76461i	−0.235073	+	0.225237i
$903$		0			0
$904$			11.9900i			0.398780i
$905$	−26.7990	−	46.4172i	−0.890828	−	1.54296i
$906$		0			0
$907$	−27.4033	+	47.4638i	−0.909910	+	1.57601i	−0.0957232	+	0.995408i	$0.530516\pi$
$907$	−27.4033	+	47.4638i	−0.909910	+	1.57601i	−0.814187	+	0.580603i	$0.802817\pi$
$908$	−6.36466	−	11.0239i	−0.211219	−	0.365841i
$909$		0			0
$910$	−33.6735	−	32.7511i	−1.11626	−	1.08569i
$911$	−46.5914			−1.54364			−0.771820	−	0.635841i	$-0.780653\pi$
$911$	−46.5914			−1.54364			−0.771820	+	0.635841i	$0.780653\pi$
$912$		0			0
$913$	9.25521	−	2.26916i	0.306303	−	0.0750983i
$914$	17.4666	−	30.2530i	0.577743	−	1.00068i
$915$		0			0
$916$			6.01345i			0.198690i
$917$	42.0029	−	11.8821i	1.38706	−	0.392382i
$918$		0			0
$919$	47.0315	−	27.1536i	1.55142	−	0.895716i	0.553399	−	0.832916i	$-0.313331\pi$
$919$	47.0315	−	27.1536i	1.55142	−	0.895716i	0.998026	−	0.0627991i	$-0.0200028\pi$
$920$	2.75975	−	4.78003i	0.0909863	−	0.157593i
$921$		0			0
$922$	18.0433	−	10.4173i	0.594224	−	0.343076i
$923$	−42.4110			−1.39598
$924$		0			0
$925$	−5.30800			−0.174526
$926$	−11.4076	+	6.58618i	−0.374877	+	0.216435i
$927$		0			0
$928$	0.0501023	−	0.0867797i	0.00164469	−	0.00284868i
$929$	18.6550	−	10.7704i	0.612049	−	0.353367i	−0.161718	−	0.986837i	$-0.551703\pi$
$929$	18.6550	−	10.7704i	0.612049	−	0.353367i	0.773767	+	0.633470i	$0.218370\pi$
$930$		0			0
$931$	0.905040	+	32.5821i	0.0296615	+	1.06783i
$932$		−	6.46694i		−	0.211832i
$933$		0			0
$934$	−8.40919	+	14.5651i	−0.275157	+	0.476586i
$935$	10.8826	+	44.3868i	0.355900	+	1.45161i
$936$		0			0
$937$	15.2663			0.498729			0.249364	−	0.968410i	$-0.419778\pi$
$937$	15.2663			0.498729			0.249364	+	0.968410i	$0.419778\pi$
$938$	−10.2182	−	2.58644i	−0.333636	−	0.0844504i
$939$		0			0
$940$	11.6247	+	20.1346i	0.379156	+	0.656717i
$941$	−18.0945	+	31.3405i	−0.589863	+	1.02167i	0.404387	+	0.914588i	$0.367485\pi$
$941$	−18.0945	+	31.3405i	−0.589863	+	1.02167i	−0.994250	+	0.107085i	$0.965848\pi$
$942$		0			0
$943$	2.29896	+	3.98191i	0.0748644	+	0.129669i
$944$			14.5344i			0.473054i
$945$		0			0
$946$	20.7327	+	21.6381i	0.674079	+	0.703516i
$947$	19.9609	+	34.5733i	0.648641	+	1.12348i	0.983448	+	0.181193i	$0.0579958\pi$
$947$	19.9609	+	34.5733i	0.648641	+	1.12348i	−0.334806	+	0.942287i	$0.608671\pi$
$948$		0			0
$949$	−9.77701	+	16.9343i	−0.317375	+	0.549710i
$950$	30.3428	−	17.5184i	0.984451	−	0.568373i
$951$		0			0
$952$	7.18245	−	7.38473i	0.232785	−	0.239341i
$953$		−	8.97831i		−	0.290836i	−0.989370	−	0.145418i	$-0.953547\pi$
$953$		−	8.97831i		−	0.290836i	0.989370	−	0.145418i	$-0.0464527\pi$
$954$		0			0
$955$	18.3892	+	10.6170i	0.595059	+	0.343558i
$956$	−13.4905	−	7.78874i	−0.436314	−	0.251906i
$957$		0			0
$958$		−	22.8582i		−	0.738513i
$959$	−12.6007	−	12.2555i	−0.406897	−	0.395752i
$960$		0			0
$961$	−15.4609	−	26.7790i	−0.498738	−	0.863839i
$962$	−3.06486	−	1.76950i	−0.0988151	−	0.0570509i
$963$		0			0
$964$	−11.7381	−	20.3310i	−0.378059	−	0.654818i
$965$	52.4765			1.68928
$966$		0			0
$967$			51.5738i			1.65850i	0.558877	+	0.829251i	$0.311232\pi$
$967$			51.5738i			1.65850i	−0.558877	+	0.829251i	$0.688768\pi$
$968$	5.08804	+	9.75253i	0.163536	+	0.313458i
$969$		0			0
$970$	51.3630	+	29.6544i	1.64917	+	0.952147i
$971$	29.0721	−	16.7848i	0.932967	−	0.538649i	0.0452186	−	0.998977i	$-0.485602\pi$
$971$	29.0721	−	16.7848i	0.932967	−	0.538649i	0.887749	+	0.460328i	$0.152268\pi$
$972$		0			0
$973$	−9.31848	+	36.8143i	−0.298737	+	1.18021i
$974$		−	31.2628i		−	1.00173i
$975$		0			0
$976$	5.56360	−	9.63644i	0.178087	−	0.308455i
$977$	−0.576295	+	0.998172i	−0.0184373	+	0.0319344i	−0.875097	−	0.483948i	$-0.839202\pi$
$977$	−0.576295	+	0.998172i	−0.0184373	+	0.0319344i	0.856660	+	0.515882i	$0.172536\pi$
$978$		0			0
$979$	−14.2466	+	13.6504i	−0.455322	+	0.436270i
$980$	−11.7860	+	21.7897i	−0.376490	+	0.696046i
$981$		0			0
$982$	−11.2490	−	19.4838i	−0.358969	−	0.621753i
$983$	14.3846	+	8.30496i	0.458798	+	0.264887i	0.711539	−	0.702647i	$-0.247999\pi$
$983$	14.3846	+	8.30496i	0.458798	+	0.264887i	−0.252741	+	0.967534i	$0.581332\pi$
$984$		0			0
$985$	−25.6125	−	44.3622i	−0.816083	−	1.41350i
$986$	0.390159			0.0124252
$987$		0			0
$988$	23.3601			0.743183
$989$	12.2041	−	7.04604i	0.388068	−	0.224051i
$990$		0			0
$991$	9.24571	−	16.0140i	0.293700	−	0.508703i	−0.680982	−	0.732300i	$-0.738447\pi$
$991$	9.24571	−	16.0140i	0.293700	−	0.508703i	0.974682	+	0.223598i	$0.0717801\pi$
$992$	−0.139864	−	0.242252i	−0.00444070	−	0.00769151i
$993$		0			0
$994$	6.08833	+	21.5221i	0.193110	+	0.682639i
$995$	−39.7283			−1.25947
$996$		0			0
$997$	−10.5865	+	18.3363i	−0.335277	+	0.580717i	−0.983538	−	0.180701i	$-0.942163\pi$
$997$	−10.5865	+	18.3363i	−0.335277	+	0.580717i	0.648261	+	0.761418i	$0.275497\pi$
$998$	−27.6346	−	15.9548i	−0.874757	−	0.505041i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bk.c.703.4		16
3.2	odd	2		154.2.i.a.87.8	yes	16
7.5	odd	6	inner	1386.2.bk.c.901.8		16
11.10	odd	2	inner	1386.2.bk.c.703.8		16
12.11	even	2		1232.2.bn.b.241.1		16
21.2	odd	6		1078.2.i.c.901.1		16
21.5	even	6		154.2.i.a.131.4	yes	16
21.11	odd	6		1078.2.c.b.1077.10		16
21.17	even	6		1078.2.c.b.1077.15		16
21.20	even	2		1078.2.i.c.1011.5		16
33.32	even	2		154.2.i.a.87.4	✓	16
77.54	even	6	inner	1386.2.bk.c.901.4		16
84.47	odd	6		1232.2.bn.b.593.2		16
132.131	odd	2		1232.2.bn.b.241.2		16
231.32	even	6		1078.2.c.b.1077.2		16
231.65	even	6		1078.2.i.c.901.5		16
231.131	odd	6		154.2.i.a.131.8	yes	16
231.164	odd	6		1078.2.c.b.1077.7		16
231.230	odd	2		1078.2.i.c.1011.1		16
924.131	even	6		1232.2.bn.b.593.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.i.a.87.4	✓	16	33.32	even	2
154.2.i.a.87.8	yes	16	3.2	odd	2
154.2.i.a.131.4	yes	16	21.5	even	6
154.2.i.a.131.8	yes	16	231.131	odd	6
1078.2.c.b.1077.2		16	231.32	even	6
1078.2.c.b.1077.7		16	231.164	odd	6
1078.2.c.b.1077.10		16	21.11	odd	6
1078.2.c.b.1077.15		16	21.17	even	6
1078.2.i.c.901.1		16	21.2	odd	6
1078.2.i.c.901.5		16	231.65	even	6
1078.2.i.c.1011.1		16	231.230	odd	2
1078.2.i.c.1011.5		16	21.20	even	2
1232.2.bn.b.241.1		16	12.11	even	2
1232.2.bn.b.241.2		16	132.131	odd	2
1232.2.bn.b.593.1		16	924.131	even	6
1232.2.bn.b.593.2		16	84.47	odd	6
1386.2.bk.c.703.4		16	1.1	even	1	trivial
1386.2.bk.c.703.8		16	11.10	odd	2	inner
1386.2.bk.c.901.4		16	77.54	even	6	inner
1386.2.bk.c.901.8		16	7.5	odd	6	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(3.06486 - 1.76950i) q^{5} +(0.649221 - 2.56486i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(3.06486 - 1.76950i) q^{5} +(0.649221 - 2.56486i) q^{7} +1.00000i q^{8} +(-1.76950 + 3.06486i) q^{10} +(-3.22122 + 0.789769i) q^{11} -5.01680 q^{13} +(0.720188 + 2.54585i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.94681 - 3.37197i) q^{17} +(-2.32819 - 4.03254i) q^{19} -3.53900i q^{20} +(2.39477 - 2.29457i) q^{22} +(-0.779812 - 1.35067i) q^{23} +(3.76225 - 6.51641i) q^{25} +(4.34467 - 2.50840i) q^{26} +(-1.89662 - 1.84467i) q^{28} -0.100205i q^{29} +(-0.242252 - 0.139864i) q^{31} +(0.866025 + 0.500000i) q^{32} +3.89362i q^{34} +(-2.54874 - 9.00974i) q^{35} +(-0.352715 - 0.610920i) q^{37} +(4.03254 + 2.32819i) q^{38} +(1.76950 + 3.06486i) q^{40} -2.94809 q^{41} +9.03556i q^{43} +(-0.926651 + 3.18454i) q^{44} +(1.35067 + 0.779812i) q^{46} +(-5.68935 + 3.28475i) q^{47} +(-6.15702 - 3.33032i) q^{49} +7.52450i q^{50} +(-2.50840 + 4.34467i) q^{52} +(2.77029 - 4.79828i) q^{53} +(-8.47510 + 8.12048i) q^{55} +(2.56486 + 0.649221i) q^{56} +(0.0501023 + 0.0867797i) q^{58} +(-12.5871 - 7.26719i) q^{59} +(5.56360 + 9.63644i) q^{61} +0.279729 q^{62} -1.00000 q^{64} +(-15.3758 + 8.87721i) q^{65} +(-1.99196 + 3.45017i) q^{67} +(-1.94681 - 3.37197i) q^{68} +(6.71215 + 6.52829i) q^{70} +8.45381 q^{71} +(1.94885 - 3.37552i) q^{73} +(0.610920 + 0.352715i) q^{74} -4.65637 q^{76} +(-0.0656384 + 8.77472i) q^{77} +(6.66824 - 3.84991i) q^{79} +(-3.06486 - 1.76950i) q^{80} +(2.55312 - 1.47405i) q^{82} -2.87320 q^{83} -13.7795i q^{85} +(-4.51778 - 7.82503i) q^{86} +(-0.789769 - 3.22122i) q^{88} +(5.15200 - 2.97451i) q^{89} +(-3.25701 + 12.8674i) q^{91} -1.55962 q^{92} +(3.28475 - 5.68935i) q^{94} +(-14.2711 - 8.23945i) q^{95} -16.7587i q^{97} +(6.99730 - 0.194366i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 12 q^{5}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more