LMFDB - Embedded newform 1386.2.bk.c.901.4

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			901.4
Root			$2.24352 + 0.601150i$ of defining polynomial
Character	$\chi$	$=$	1386.901
Dual form			1386.2.bk.c.703.4

$q$-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 $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

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

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
$5$	3.06486	+	1.76950i	1.37065	+	0.791344i	0.991010	−	0.133791i	$-0.0427152\pi$
$5$	3.06486	+	1.76950i	1.37065	+	0.791344i	0.379638	+	0.925135i	$0.376049\pi$
$6$		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	0.999493	−	0.0318416i	$-0.0101372\pi$
$17$	1.94681	+	3.37197i	0.472171	+	0.817824i	−0.527322	+	0.849665i	$0.676804\pi$
$18$		0			0
$19$	−2.32819	+	4.03254i	−0.534123	+	0.925128i	0.465082	+	0.885267i	$0.346025\pi$
$19$	−2.32819	+	4.03254i	−0.534123	+	0.925128i	−0.999205	+	0.0398605i	$0.987309\pi$
$20$			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	−0.935801	−	0.352528i	$-0.885322\pi$
$23$	−0.779812	+	1.35067i	−0.162602	+	0.281635i	0.773199	+	0.634163i	$0.218655\pi$
$24$		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	$0.00296152\pi$
$29$			0.100205i			0.0186075i	−0.999957	+	0.00930376i	$0.997038\pi$
$30$		0			0
$31$	−0.242252	+	0.139864i	−0.0435098	+	0.0251204i	−0.521597	−	0.853192i	$-0.674664\pi$
$31$	−0.242252	+	0.139864i	−0.0435098	+	0.0251204i	0.478087	+	0.878312i	$0.341330\pi$
$32$	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	−0.893561	−	0.448941i	$-0.851801\pi$
$37$	−0.352715	+	0.610920i	−0.0579860	+	0.100435i	0.835575	+	0.549376i	$0.185135\pi$
$38$	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	$-0.758070\pi$
$43$		−	9.03556i		−	1.37791i	0.724804	−	0.688955i	$-0.241930\pi$
$44$	−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	0.0239340	−	0.999714i	$-0.492381\pi$
$47$	−5.68935	−	3.28475i	−0.829876	−	0.479129i	−0.853810	+	0.520584i	$0.825714\pi$
$48$		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	0.991138	−	0.132837i	$-0.0424087\pi$
$53$	2.77029	+	4.79828i	0.380529	+	0.659095i	−0.610609	+	0.791932i	$0.709075\pi$
$54$		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	−0.657427	+	0.753518i	$0.728355\pi$
$59$	−12.5871	+	7.26719i	−1.63871	+	0.946108i	−0.981279	+	0.192589i	$0.938312\pi$
$60$		0			0
$61$	5.56360	−	9.63644i	0.712346	−	1.23382i	−0.251628	−	0.967824i	$-0.580966\pi$
$61$	5.56360	−	9.63644i	0.712346	−	1.23382i	0.963974	−	0.265996i	$-0.0857006\pi$
$62$	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	0.718312	−	0.695721i	$-0.244915\pi$
$67$	−1.99196	−	3.45017i	−0.243356	−	0.421506i	−0.961668	+	0.274216i	$0.911582\pi$
$68$	−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	0.957244	−	0.289282i	$-0.0934166\pi$
$73$	1.94885	+	3.37552i	0.228096	+	0.395074i	−0.729148	+	0.684356i	$0.760083\pi$
$74$	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	0.825779	−	0.563994i	$-0.190736\pi$
$79$	6.66824	+	3.84991i	0.750236	+	0.433149i	−0.0755434	+	0.997143i	$0.524069\pi$
$80$	−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	0.747552	−	0.664203i	$-0.231229\pi$
$89$	5.15200	+	2.97451i	0.546111	+	0.315297i	−0.201441	+	0.979501i	$0.564562\pi$
$90$		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	$0.323878\pi$
$97$			16.7587i			1.70159i	−0.525502	+	0.850793i	$0.676122\pi$
$98$	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	0.829015	−	0.559227i	$-0.188902\pi$
$101$	−0.701452	−	1.21495i	−0.0697971	−	0.120892i	−0.898812	+	0.438335i	$0.855569\pi$
$102$		0			0
$103$	1.78653	+	1.03145i	0.176032	+	0.101632i	0.585427	−	0.810725i	$-0.300927\pi$
$103$	1.78653	+	1.03145i	0.176032	+	0.101632i	−0.409395	+	0.912357i	$0.634260\pi$
$104$			5.01680i			0.491937i
$105$		0			0
$106$		−	5.54058i		−	0.538149i
$107$	10.6222	+	6.13274i	1.02689	+	0.592875i	0.916092	−	0.400968i	$-0.131326\pi$
$107$	10.6222	+	6.13274i	1.02689	+	0.592875i	0.110797	+	0.993843i	$0.464660\pi$
$108$		0			0
$109$	5.82394	−	3.36245i	0.557832	−	0.322065i	−0.194443	−	0.980914i	$-0.562290\pi$
$109$	5.82394	−	3.36245i	0.557832	−	0.322065i	0.752275	+	0.658849i	$0.228957\pi$
$110$	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	$0.199509\pi$
$127$			13.2199i			1.17308i	−0.809922	+	0.586538i	$0.800491\pi$
$128$	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	−0.239956	−	0.970784i	$-0.577133\pi$
$131$	8.24931	−	14.2882i	0.720746	−	1.24837i	0.960701	−	0.277584i	$-0.0895337\pi$
$132$		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	0.972319	−	0.233657i	$-0.0750693\pi$
$137$	3.32187	+	5.75365i	0.283807	+	0.491568i	−0.688512	+	0.725225i	$0.741736\pi$
$138$		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	0.591579	−	0.806247i	$-0.298505\pi$
$149$	2.30871	+	1.33294i	0.189137	+	0.109198i	−0.402441	+	0.915446i	$0.631838\pi$
$150$		0			0
$151$	−8.99830	+	5.19517i	−0.732271	+	0.422777i	−0.819253	−	0.573433i	$-0.805611\pi$
$151$	−8.99830	+	5.19517i	−0.732271	+	0.422777i	0.0869812	+	0.996210i	$0.472278\pi$
$152$	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	−0.181838	−	0.983329i	$-0.558205\pi$
$157$	7.25273	−	4.18736i	0.578831	−	0.334188i	0.760669	+	0.649140i	$0.224871\pi$
$158$	−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	−0.919782	−	0.392429i	$-0.871635\pi$
$163$	−1.53254	+	2.65444i	−0.120038	+	0.207911i	0.799745	+	0.600340i	$0.204968\pi$
$164$	−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	−0.864566	−	0.502520i	$-0.832406\pi$
$173$	0.0383013	−	0.0663398i	0.00291200	−	0.00504372i	0.867478	+	0.497476i	$0.165740\pi$
$174$		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	0.648155	−	0.761509i	$-0.275541\pi$
$179$	−4.48746	−	7.77250i	−0.335408	−	0.580944i	−0.983563	+	0.180564i	$0.942208\pi$
$180$		0			0
$181$			15.1450i			1.12572i	0.826554	+	0.562858i	$0.190298\pi$
$181$			15.1450i			1.12572i	−0.826554	+	0.562858i	$0.809702\pi$
$182$	−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	−0.736839	−	0.676068i	$-0.763683\pi$
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	0.953912	+	0.300088i	$0.0970159\pi$
$192$		0			0
$193$	12.8415	−	7.41403i	0.924350	−	0.533674i	0.0393299	−	0.999226i	$-0.487478\pi$
$193$	12.8415	−	7.41403i	0.924350	−	0.533674i	0.885020	+	0.465552i	$0.154144\pi$
$194$	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	$0.172443\pi$
$197$			14.4745i			1.03126i	−0.856811	+	0.515631i	$0.827557\pi$
$198$		0			0
$199$	−9.72188	+	5.61293i	−0.689166	+	0.397890i	−0.803300	−	0.595575i	$-0.796924\pi$
$199$	−9.72188	+	5.61293i	−0.689166	+	0.397890i	0.114133	+	0.993465i	$0.463591\pi$
$200$	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	$0.0711563\pi$
$211$			6.44038i			0.443374i	−0.975118	+	0.221687i	$0.928844\pi$
$212$	−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	$0.0429526\pi$
$223$			4.01793i			0.269061i	−0.990909	+	0.134530i	$0.957047\pi$
$224$	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	0.996177	−	0.0873549i	$-0.0278414\pi$
$227$	6.36466	+	11.0239i	0.422437	+	0.731682i	−0.573740	+	0.819037i	$0.694508\pi$
$228$		0			0
$229$	−5.20780	−	3.00672i	−0.344141	−	0.198690i	0.317961	−	0.948104i	$-0.397002\pi$
$229$	−5.20780	−	3.00672i	−0.344141	−	0.198690i	−0.662102	+	0.749414i	$0.730335\pi$
$230$	5.51950			0.363945
$231$		0			0
$232$	0.100205			0.00657875
$233$	5.60053	+	3.23347i	0.366903	+	0.211832i	0.672105	−	0.740456i	$-0.265391\pi$
$233$	5.60053	+	3.23347i	0.366903	+	0.211832i	−0.305202	+	0.952288i	$0.598724\pi$
$234$		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	$0.168070\pi$
$239$			15.5775i			1.00762i	−0.863813	+	0.503812i	$0.831930\pi$
$240$		0			0
$241$	11.7381	+	20.3310i	0.756119	+	1.30964i	0.944816	+	0.327601i	$0.106240\pi$
$241$	11.7381	+	20.3310i	0.756119	+	1.30964i	−0.188697	+	0.982035i	$0.560427\pi$
$242$	−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	$0.195764\pi$
$251$			18.2818i			1.15394i	−0.816766	+	0.576968i	$0.804236\pi$
$252$		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	0.736798	−	0.676113i	$-0.236337\pi$
$257$	8.33087	+	4.80983i	0.519666	+	0.300029i	−0.217132	+	0.976142i	$0.569670\pi$
$258$		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	−0.484470	−	0.874808i	$-0.660987\pi$
$263$	0.501139	−	0.289333i	0.0309016	−	0.0178410i	0.515371	+	0.856967i	$0.327654\pi$
$264$		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	−0.952826	−	0.303517i	$-0.901839\pi$
$269$	−19.1302	+	11.0448i	−1.16639	+	0.673413i	−0.213560	+	0.976930i	$0.568506\pi$
$270$		0			0
$271$	−2.13111	+	3.69119i	−0.129456	+	0.224224i	−0.923466	−	0.383681i	$-0.874656\pi$
$271$	−2.13111	+	3.69119i	−0.129456	+	0.224224i	0.794010	+	0.607905i	$0.207990\pi$
$272$	−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	0.0608016	−	0.998150i	$-0.480634\pi$
$277$	15.9048	−	9.18263i	0.955626	−	0.551731i	0.894824	+	0.446419i	$0.147301\pi$
$278$	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	$0.0354771\pi$
$281$			3.72890i			0.222448i	−0.993795	+	0.111224i	$0.964523\pi$
$282$		0			0
$283$	−6.36576	−	11.0258i	−0.378405	−	0.655417i	0.612425	−	0.790529i	$-0.290194\pi$
$283$	−6.36576	−	11.0258i	−0.378405	−	0.655417i	−0.990830	+	0.135111i	$0.956861\pi$
$284$	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	−0.452376	−	0.891827i	$-0.649423\pi$
$311$	1.65385	−	0.954850i	0.0937811	−	0.0541446i	0.546157	+	0.837683i	$0.316090\pi$
$312$		0			0
$313$	−26.3707	−	15.2251i	−1.49056	−	0.860576i	−0.490619	−	0.871374i	$-0.663229\pi$
$313$	−26.3707	−	15.2251i	−1.49056	−	0.860576i	−0.999942	+	0.0107985i	$0.996563\pi$
$314$	−8.37473			−0.472613
$315$		0			0
$316$			7.69982i			0.433149i
$317$	17.1971	−	29.7862i	0.965885	−	1.67296i	0.258665	−	0.965967i	$-0.416717\pi$
$317$	17.1971	−	29.7862i	0.965885	−	1.67296i	0.707220	−	0.706994i	$-0.249949\pi$
$318$		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	−0.996544	−	0.0830696i	$-0.973528\pi$
$331$	−7.75642	+	13.4345i	−0.426332	+	0.738428i	0.570212	+	0.821497i	$0.306861\pi$
$332$	−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	$0.0673344\pi$
$337$			7.70882i			0.419926i	−0.977709	+	0.209963i	$0.932666\pi$
$338$	−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	0.0993513	−	0.995052i	$-0.468323\pi$
$347$	18.8285	−	10.8706i	1.01077	−	0.583567i	0.911416	+	0.411485i	$0.134990\pi$
$348$		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	−0.646561	−	0.762862i	$-0.723793\pi$
$353$	−5.80903	+	3.35384i	−0.309183	+	0.178507i	0.337378	+	0.941369i	$0.390460\pi$
$354$		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	−0.422823	−	0.906212i	$-0.638961\pi$
$359$	−26.8869	−	15.5232i	−1.41904	−	0.819282i	−0.996214	+	0.0869306i	$0.972294\pi$
$360$		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	0.353471	−	0.935445i	$-0.385001\pi$
$367$	25.6770	−	14.8246i	1.34033	−	0.773838i	0.986855	+	0.161608i	$0.0516679\pi$
$368$	−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	0.290045	−	0.957013i	$-0.406330\pi$
$373$	−7.60418	−	4.39027i	−0.393729	−	0.227320i	−0.683775	+	0.729693i	$0.739663\pi$
$374$	−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	0.378251	−	0.925703i	$-0.376526\pi$
$383$	−4.58545	−	2.64741i	−0.234305	−	0.135276i	−0.612557	+	0.790427i	$0.709859\pi$
$384$		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	0.876723	−	0.480995i	$-0.159724\pi$
$389$	0.430119	+	0.744987i	0.0218079	+	0.0377724i	−0.854916	+	0.518767i	$0.826391\pi$
$390$		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	0.743729	−	0.668481i	$-0.233055\pi$
$397$	10.6931	+	6.17367i	0.536672	+	0.309847i	−0.207057	+	0.978329i	$0.566389\pi$
$398$	11.2259			0.562702
$399$		0			0
$400$	−7.52450			−0.376225
$401$	16.8626	−	29.2069i	0.842078	−	1.45852i	−0.0460561	−	0.998939i	$-0.514665\pi$
$401$	16.8626	−	29.2069i	0.842078	−	1.45852i	0.888134	−	0.459584i	$-0.152001\pi$
$402$		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	0.748343	+	0.663312i	$0.230850\pi$
$409$	19.1846	+	33.2287i	0.948616	+	1.64305i	0.200273	+	0.979740i	$0.435817\pi$
$410$	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	$0.305110\pi$
$419$			33.5023i			1.63670i	−0.574723	+	0.818348i	$0.694890\pi$
$420$		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	−0.941286	−	0.337609i	$-0.890382\pi$
$431$	−23.2425	+	13.4191i	−1.11955	+	0.646373i	−0.178265	+	0.983983i	$0.557048\pi$
$432$		0			0
$433$		−	30.6912i		−	1.47493i	−0.675387	−	0.737463i	$-0.736024\pi$
$433$		−	30.6912i		−	1.47493i	0.675387	−	0.737463i	$-0.263976\pi$
$434$	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	−0.591978	−	0.805954i	$-0.701653\pi$
$439$	8.42258	−	14.5883i	0.401988	−	0.696263i	0.993966	+	0.109691i	$0.0349861\pi$
$440$	−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	−0.875263	−	0.483647i	$-0.839312\pi$
$443$	−0.395295	+	0.684671i	−0.0187810	+	0.0325297i	0.856482	+	0.516177i	$0.172645\pi$
$444$		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	−0.419305	−	0.907845i	$-0.637726\pi$
$457$	−30.2530	−	17.4666i	−1.41517	−	0.817052i	−0.995870	+	0.0907937i	$0.971060\pi$
$458$	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	0.797589	−	0.603202i	$-0.206109\pi$
$467$	14.5651	+	8.40919i	0.673995	+	0.389131i	−0.123594	+	0.992333i	$0.539442\pi$
$468$		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	−0.999666	−	0.0258361i	$-0.991775\pi$
$479$	−11.4291	−	19.7957i	−0.522208	−	0.904491i	0.477458	−	0.878654i	$-0.341558\pi$
$480$		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	−0.965477	−	0.260487i	$-0.916117\pi$
$487$	−15.6314	−	27.0744i	−0.708327	−	1.22686i	0.257150	−	0.966371i	$-0.417217\pi$
$488$	−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	$-0.830511\pi$
$491$		−	22.4979i		−	1.01532i	0.861558	−	0.507659i	$-0.169489\pi$
$492$		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	−0.249017	−	0.968499i	$-0.580107\pi$
$499$	15.9548	−	27.6346i	0.714236	−	1.23709i	0.963253	−	0.268595i	$-0.0865592\pi$
$500$	−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	0.872290	−	0.488989i	$-0.162634\pi$
$509$	19.9655	+	11.5271i	0.884957	+	0.510930i	0.0126676	+	0.999920i	$0.495968\pi$
$510$		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	−0.340852	−	0.940117i	$-0.610716\pi$
$521$	6.91351	−	3.99152i	0.302886	−	0.174872i	0.643739	+	0.765245i	$0.277382\pi$
$522$		0			0
$523$	−2.79140	+	4.83485i	−0.122059	+	0.211413i	−0.920580	−	0.390555i	$-0.872283\pi$
$523$	−2.79140	+	4.83485i	−0.122059	+	0.211413i	0.798520	+	0.601968i	$0.205617\pi$
$524$	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	0.229296	−	0.973357i	$-0.426358\pi$
$541$	−11.6066	−	6.70108i	−0.499007	−	0.288102i	−0.728304	+	0.685255i	$0.759691\pi$
$542$	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	$-0.824396\pi$
$547$		−	24.5161i		−	1.04823i	0.851647	−	0.524116i	$-0.175604\pi$
$548$	−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	−0.432271	−	0.901744i	$-0.642288\pi$
$557$	3.12772	−	1.80579i	0.132526	−	0.0765137i	0.564797	+	0.825230i	$0.308954\pi$
$558$		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	0.921123	−	0.389271i	$-0.127273\pi$
$563$	2.92902	+	5.07320i	0.123443	+	0.213810i	−0.797680	+	0.603081i	$0.793940\pi$
$564$		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	−0.284275	−	0.958743i	$-0.591753\pi$
$569$	−29.9772	−	17.3073i	−1.25671	−	0.725561i	−0.972433	+	0.233182i	$0.925086\pi$
$570$		0			0
$571$	6.89907	−	3.98318i	0.288717	−	0.166691i	−0.348646	−	0.937254i	$-0.613358\pi$
$571$	6.89907	−	3.98318i	0.288717	−	0.166691i	0.637363	+	0.770564i	$0.280025\pi$
$572$	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	−0.130713	−	0.991420i	$-0.541727\pi$
$577$	15.9144	−	9.18819i	0.662525	−	0.382509i	0.793239	+	0.608911i	$0.208393\pi$
$578$	−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	$-0.884307\pi$
$587$		−	17.2267i		−	0.711021i	0.934672	−	0.355511i	$-0.115693\pi$
$588$		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	−0.0372161	−	0.999307i	$-0.511849\pi$
$593$	20.6214	−	35.7172i	0.846817	−	1.46673i	0.884033	−	0.467424i	$-0.154818\pi$
$594$		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	0.949610	−	0.313434i	$-0.101480\pi$
$599$	4.97720	+	8.62076i	0.203363	+	0.352235i	−0.746247	+	0.665669i	$0.768146\pi$
$600$		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	−0.816115	−	0.577889i	$-0.803876\pi$
$607$	2.27672	−	3.94340i	0.0924094	−	0.160058i	0.908524	+	0.417832i	$0.137210\pi$
$608$			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	−0.525127	−	0.851024i	$-0.675982\pi$
$613$	−1.25482	+	0.724472i	−0.0506818	+	0.0292611i	0.474445	+	0.880285i	$0.342649\pi$
$614$	−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	−0.687326	−	0.726349i	$-0.741215\pi$
$619$	−10.0004	+	5.77375i	−0.401951	+	0.232067i	0.285374	+	0.958416i	$0.407882\pi$
$620$	−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	0.979383	+	0.202013i	$0.0647482\pi$
$641$	16.8273	+	29.1458i	0.664639	+	1.15119i	−0.314744	+	0.949177i	$0.601919\pi$
$642$		0			0
$643$		−	5.95261i		−	0.234748i	−0.993088	−	0.117374i	$-0.962552\pi$
$643$		−	5.95261i		−	0.234748i	0.993088	−	0.117374i	$-0.0374476\pi$
$644$	−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	−0.686855	−	0.726795i	$-0.741009\pi$
$647$	−10.1963	+	5.88686i	−0.400860	+	0.231437i	0.285995	+	0.958231i	$0.407676\pi$
$648$		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	−0.432239	−	0.901759i	$-0.642276\pi$
$653$	14.4335	−	24.9996i	0.564827	−	0.978309i	0.997066	−	0.0765498i	$-0.0243904\pi$
$654$		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	$-0.663947\pi$
$659$		−	44.6812i		−	1.74053i	0.492581	−	0.870266i	$-0.336053\pi$
$660$		0			0
$661$	−34.3242	+	19.8171i	−1.33505	+	0.770794i	−0.986069	−	0.166334i	$-0.946807\pi$
$661$	−34.3242	+	19.8171i	−1.33505	+	0.770794i	−0.348985	+	0.937128i	$0.613474\pi$
$662$	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	$-0.983312\pi$
$673$		−	2.71886i		−	0.104804i	0.998626	−	0.0524022i	$-0.0166878\pi$
$674$	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	−0.918355	−	0.395757i	$-0.870482\pi$
$677$	−3.02973	+	5.24764i	−0.116442	+	0.201683i	0.801913	+	0.597440i	$0.203816\pi$
$678$		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	0.802513	−	0.596634i	$-0.203496\pi$
$683$	−3.01704	−	5.22567i	−0.115444	−	0.199955i	−0.917957	+	0.396680i	$0.870162\pi$
$684$		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	0.136921	−	0.990582i	$-0.456279\pi$
$691$	−17.1519	−	9.90263i	−0.652487	−	0.376714i	−0.789409	+	0.613868i	$0.789613\pi$
$692$	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	$0.163476\pi$
$701$			26.0155i			0.982591i	−0.870993	+	0.491296i	$0.836524\pi$
$702$		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	−0.531894	−	0.846811i	$-0.678519\pi$
$709$	12.4458	−	21.5568i	0.467413	−	0.809583i	0.999307	+	0.0372278i	$0.0118527\pi$
$710$	−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	0.699116	−	0.715009i	$-0.253577\pi$
$719$	11.5156	+	6.64851i	0.429458	+	0.247948i	−0.269658	+	0.962956i	$0.586911\pi$
$720$		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	$-0.966465\pi$
$727$		−	5.67083i		−	0.210319i	0.994455	−	0.105160i	$-0.0335354\pi$
$728$	−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	0.176580	+	0.984286i	$0.443496\pi$
$733$	−20.6879	+	35.8326i	−0.764127	+	1.32351i	−0.940707	+	0.339220i	$0.889837\pi$
$734$	−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	−0.984263	−	0.176710i	$-0.943455\pi$
$739$	−35.9749	+	20.7701i	−1.32336	+	0.764042i	−0.339097	+	0.940752i	$0.610121\pi$
$740$	−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	$0.259999\pi$
$743$			39.7404i			1.45793i	−0.684549	+	0.728967i	$0.740001\pi$
$744$		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	−0.910811	−	0.412823i	$-0.864543\pi$
$751$	−2.68263	+	4.64645i	−0.0978905	+	0.169551i	0.812921	+	0.582374i	$0.197876\pi$
$752$	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	−0.970355	−	0.241684i	$-0.922300\pi$
$761$	−7.61030	+	13.1814i	−0.275873	+	0.477827i	0.694482	+	0.719510i	$0.255634\pi$
$762$		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	−0.868412	−	0.495844i	$-0.834859\pi$
$773$	−24.2776	+	14.0167i	−0.873204	+	0.504144i	−0.00479213	+	0.999989i	$0.501525\pi$
$774$		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	0.956954	−	0.290239i	$-0.0937347\pi$
$787$	6.37160	+	11.0359i	0.227123	+	0.393388i	−0.729831	+	0.683627i	$0.760401\pi$
$788$	−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	$0.0318199\pi$
$797$			5.63488i			0.199598i	−0.995008	+	0.0997989i	$0.968180\pi$
$798$		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	−0.736458	−	0.676483i	$-0.763503\pi$
$809$	−14.7572	+	8.52007i	−0.518835	+	0.299550i	0.217623	+	0.976033i	$0.430170\pi$
$810$		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	0.465103	−	0.885257i	$-0.346017\pi$
$821$	−1.97706	−	1.14146i	−0.0690000	−	0.0398372i	−0.534103	+	0.845419i	$0.679351\pi$
$822$		0			0
$823$	−5.04228	−	8.73348i	−0.175763	−	0.304430i	0.764662	−	0.644431i	$-0.222906\pi$
$823$	−5.04228	−	8.73348i	−0.175763	−	0.304430i	−0.940425	+	0.340001i	$0.889572\pi$
$824$	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	$0.0608818\pi$
$827$			10.9337i			0.380204i	−0.981764	+	0.190102i	$0.939118\pi$
$828$		0			0
$829$	−10.0682	+	5.81287i	−0.349683	+	0.201889i	−0.664545	−	0.747248i	$-0.731375\pi$
$829$	−10.0682	+	5.81287i	−0.349683	+	0.201889i	0.314863	+	0.949137i	$0.398041\pi$
$830$	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	$0.132699\pi$
$839$			23.4571i			0.809828i	−0.914355	+	0.404914i	$0.867301\pi$
$840$		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	0.957888	+	0.287142i	$0.0927053\pi$
$857$	21.3007	+	36.8938i	0.727617	+	1.26027i	−0.230271	+	0.973126i	$0.573961\pi$
$858$		0			0
$859$	10.7344	+	6.19752i	0.366254	+	0.211457i	0.671821	−	0.740714i	$-0.265513\pi$
$859$	10.7344	+	6.19752i	0.366254	+	0.211457i	−0.305567	+	0.952171i	$0.598846\pi$
$860$	31.9768			1.09040
$861$		0			0
$862$	26.8381			0.914110
$863$	−19.6374	+	34.0130i	−0.668465	+	1.15781i	0.309869	+	0.950779i	$0.399715\pi$
$863$	−19.6374	+	34.0130i	−0.668465	+	1.15781i	−0.978333	+	0.207036i	$0.933618\pi$
$864$		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	0.988064	−	0.154046i	$-0.0492304\pi$
$877$	39.9403	+	23.0595i	1.34869	+	0.778665i	0.360624	+	0.932711i	$0.382564\pi$
$878$	−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	$-0.918919\pi$
$881$		−	14.9583i		−	0.503957i	0.967733	−	0.251978i	$-0.0810812\pi$
$882$		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	−0.755216	−	0.655477i	$-0.772468\pi$
$887$	5.66022	−	9.80379i	0.190052	−	0.329179i	0.945267	+	0.326298i	$0.105801\pi$
$888$		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	−0.814187	−	0.580603i	$-0.802817\pi$
$907$	−27.4033	−	47.4638i	−0.909910	−	1.57601i	−0.0957232	−	0.995408i	$-0.530516\pi$
$908$	−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	0.998026	+	0.0627991i	$0.0200028\pi$
$919$	47.0315	+	27.1536i	1.55142	+	0.895716i	0.553399	+	0.832916i	$0.313331\pi$
$920$	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	0.773767	−	0.633470i	$-0.218370\pi$
$929$	18.6550	+	10.7704i	0.612049	+	0.353367i	−0.161718	+	0.986837i	$0.551703\pi$
$930$		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	−0.994250	−	0.107085i	$-0.965848\pi$
$941$	−18.0945	−	31.3405i	−0.589863	−	1.02167i	0.404387	−	0.914588i	$-0.367485\pi$
$942$		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	−0.334806	−	0.942287i	$-0.608671\pi$
$947$	19.9609	−	34.5733i	0.648641	−	1.12348i	0.983448	−	0.181193i	$-0.0579958\pi$
$948$		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	$0.0464527\pi$
$953$			8.97831i			0.290836i	−0.989370	+	0.145418i	$0.953547\pi$
$954$		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	$-0.688768\pi$
$967$		−	51.5738i		−	1.65850i	0.558877	−	0.829251i	$-0.311232\pi$
$968$	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	0.887749	−	0.460328i	$-0.152268\pi$
$971$	29.0721	+	16.7848i	0.932967	+	0.538649i	0.0452186	+	0.998977i	$0.485602\pi$
$972$		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	0.856660	−	0.515882i	$-0.172536\pi$
$977$	−0.576295	−	0.998172i	−0.0184373	−	0.0319344i	−0.875097	+	0.483948i	$0.839202\pi$
$978$		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	−0.252741	−	0.967534i	$-0.581332\pi$
$983$	14.3846	−	8.30496i	0.458798	−	0.264887i	0.711539	+	0.702647i	$0.247999\pi$
$984$		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	0.974682	−	0.223598i	$-0.0717801\pi$
$991$	9.24571	+	16.0140i	0.293700	+	0.508703i	−0.680982	+	0.732300i	$0.738447\pi$
$992$	−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	0.648261	−	0.761418i	$-0.275497\pi$
$997$	−10.5865	−	18.3363i	−0.335277	−	0.580717i	−0.983538	+	0.180701i	$0.942163\pi$
$998$	−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.901.4		16
3.2	odd	2		154.2.i.a.131.8	yes	16
7.3	odd	6	inner	1386.2.bk.c.703.8		16
11.10	odd	2	inner	1386.2.bk.c.901.8		16
12.11	even	2		1232.2.bn.b.593.1		16
21.2	odd	6		1078.2.c.b.1077.7		16
21.5	even	6		1078.2.c.b.1077.2		16
21.11	odd	6		1078.2.i.c.1011.1		16
21.17	even	6		154.2.i.a.87.4	✓	16
21.20	even	2		1078.2.i.c.901.5		16
33.32	even	2		154.2.i.a.131.4	yes	16
77.10	even	6	inner	1386.2.bk.c.703.4		16
84.59	odd	6		1232.2.bn.b.241.2		16
132.131	odd	2		1232.2.bn.b.593.2		16
231.32	even	6		1078.2.i.c.1011.5		16
231.65	even	6		1078.2.c.b.1077.15		16
231.131	odd	6		1078.2.c.b.1077.10		16
231.164	odd	6		154.2.i.a.87.8	yes	16
231.230	odd	2		1078.2.i.c.901.1		16
924.395	even	6		1232.2.bn.b.241.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.i.a.87.4	✓	16	21.17	even	6
154.2.i.a.87.8	yes	16	231.164	odd	6
154.2.i.a.131.4	yes	16	33.32	even	2
154.2.i.a.131.8	yes	16	3.2	odd	2
1078.2.c.b.1077.2		16	21.5	even	6
1078.2.c.b.1077.7		16	21.2	odd	6
1078.2.c.b.1077.10		16	231.131	odd	6
1078.2.c.b.1077.15		16	231.65	even	6
1078.2.i.c.901.1		16	231.230	odd	2
1078.2.i.c.901.5		16	21.20	even	2
1078.2.i.c.1011.1		16	21.11	odd	6
1078.2.i.c.1011.5		16	231.32	even	6
1232.2.bn.b.241.1		16	924.395	even	6
1232.2.bn.b.241.2		16	84.59	odd	6
1232.2.bn.b.593.1		16	12.11	even	2
1232.2.bn.b.593.2		16	132.131	odd	2
1386.2.bk.c.703.4		16	77.10	even	6	inner
1386.2.bk.c.703.8		16	7.3	odd	6	inner
1386.2.bk.c.901.4		16	1.1	even	1	trivial
1386.2.bk.c.901.8		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)

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

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