LMFDB - Embedded newform 308.3.r.a.57.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,3,Mod(29,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("308.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	308.r (of order $10$, degree $4$, 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:	$8.39239214230$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			57.3
Character	$\chi$	$=$	308.57
Dual form			308.3.r.a.281.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.66310 + 1.93486i) q^{3} +(-0.225454 - 0.693877i) q^{5} +(1.55513 - 2.14046i) q^{7} +(0.567294 - 1.74595i) q^{9} +O(q^{10})$	\(q+(-2.66310 + 1.93486i) q^{3} +(-0.225454 - 0.693877i) q^{5} +(1.55513 - 2.14046i) q^{7} +(0.567294 - 1.74595i) q^{9} +(-7.28563 - 8.24133i) q^{11} +(-6.37237 - 2.07051i) q^{13} +(1.94296 + 1.41165i) q^{15} +(18.4502 - 5.99483i) q^{17} +(-0.295896 - 0.407265i) q^{19} +8.70923i q^{21} +13.2440 q^{23} +(19.7948 - 14.3818i) q^{25} +(-7.28753 - 22.4287i) q^{27} +(27.3013 - 37.5770i) q^{29} +(5.53315 - 17.0293i) q^{31} +(35.3482 + 7.85086i) q^{33} +(-1.83583 - 0.596496i) q^{35} +(9.01297 + 6.54831i) q^{37} +(20.9764 - 6.81566i) q^{39} +(29.0242 + 39.9484i) q^{41} -81.3678i q^{43} -1.33937 q^{45} +(-60.8620 + 44.2188i) q^{47} +(-2.16312 - 6.65740i) q^{49} +(-37.5356 + 51.6633i) q^{51} +(12.6965 - 39.0758i) q^{53} +(-4.07590 + 6.91338i) q^{55} +(1.57600 + 0.512074i) q^{57} +(35.1249 + 25.5198i) q^{59} +(26.0595 - 8.46725i) q^{61} +(-2.85492 - 3.92946i) q^{63} +4.88845i q^{65} -106.827 q^{67} +(-35.2701 + 25.6252i) q^{69} +(-25.2285 - 77.6454i) q^{71} +(-7.14333 + 9.83196i) q^{73} +(-24.8889 + 76.6002i) q^{75} +(-28.9704 + 2.77821i) q^{77} +(-80.4877 - 26.1520i) q^{79} +(76.1706 + 55.3412i) q^{81} +(-33.3722 + 10.8433i) q^{83} +(-8.31935 - 11.4506i) q^{85} +152.896i q^{87} -62.7799 q^{89} +(-14.3417 + 10.4199i) q^{91} +(18.2139 + 56.0567i) q^{93} +(-0.215881 + 0.297135i) q^{95} +(13.0924 - 40.2943i) q^{97} +(-18.5221 + 8.04510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9}+O(q^{10}) $ 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9	$ 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9} - 10 q^{11} + 30 q^{13} + 24 q^{15} + 60 q^{19} - 132 q^{23} - 186 q^{25} - 110 q^{27} - 90 q^{29} - 26 q^{31} + 46 q^{33} + 82 q^{37} + 290 q^{39} - 336 q^{45} + 84 q^{47} + 84 q^{49} - 20 q^{51} + 58 q^{53} + 370 q^{55} - 20 q^{57} + 436 q^{59} + 160 q^{61} + 276 q^{67} - 118 q^{69} - 150 q^{71} - 320 q^{73} - 692 q^{75} + 28 q^{77} - 560 q^{79} + 122 q^{81} - 630 q^{83} + 220 q^{85} - 444 q^{89} - 126 q^{91} + 500 q^{93} + 440 q^{95} - 80 q^{97} + 1034 q^{99}+O(q^{100}) $ 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9 - 10 * q^11 + 30 * q^13 + 24 * q^15 + 60 * q^19 - 132 * q^23 - 186 * q^25 - 110 * q^27 - 90 * q^29 - 26 * q^31 + 46 * q^33 + 82 * q^37 + 290 * q^39 - 336 * q^45 + 84 * q^47 + 84 * q^49 - 20 * q^51 + 58 * q^53 + 370 * q^55 - 20 * q^57 + 436 * q^59 + 160 * q^61 + 276 * q^67 - 118 * q^69 - 150 * q^71 - 320 * q^73 - 692 * q^75 + 28 * q^77 - 560 * q^79 + 122 * q^81 - 630 * q^83 + 220 * q^85 - 444 * q^89 - 126 * q^91 + 500 * q^93 + 440 * q^95 - 80 * q^97 + 1034 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$	$1$

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			0
$2$		0			0
$3$	−2.66310	+	1.93486i	−0.887701	+	0.644953i	−0.935278	−	0.353915i	$-0.884850\pi$
$3$	−2.66310	+	1.93486i	−0.887701	+	0.644953i	0.0475763	+	0.998868i	$0.484850\pi$
$4$		0			0
$5$	−0.225454	−	0.693877i	−0.0450909	−	0.138775i	0.925976	−	0.377581i	$-0.123244\pi$
$5$	−0.225454	−	0.693877i	−0.0450909	−	0.138775i	−0.971067	+	0.238806i	$0.923244\pi$
$6$		0			0
$7$	1.55513	−	2.14046i	0.222162	−	0.305780i
$7$	1.55513	−	2.14046i	0.222162	−	0.305780i
$8$		0			0
$9$	0.567294	−	1.74595i	0.0630327	−	0.193995i
$10$		0			0
$11$	−7.28563	−	8.24133i	−0.662330	−	0.749212i
$11$	−7.28563	−	8.24133i	−0.662330	−	0.749212i
$12$		0			0
$13$	−6.37237	−	2.07051i	−0.490182	−	0.159270i	0.0534884	−	0.998568i	$-0.482966\pi$
$13$	−6.37237	−	2.07051i	−0.490182	−	0.159270i	−0.543671	+	0.839299i	$0.682966\pi$
$14$		0			0
$15$	1.94296	+	1.41165i	0.129531	+	0.0941097i
$16$		0			0
$17$	18.4502	−	5.99483i	1.08530	−	0.352637i	0.288874	−	0.957367i	$-0.406719\pi$
$17$	18.4502	−	5.99483i	1.08530	−	0.352637i	0.796430	+	0.604730i	$0.206719\pi$
$18$		0			0
$19$	−0.295896	−	0.407265i	−0.0155734	−	0.0214350i	0.801159	−	0.598451i	$-0.204217\pi$
$19$	−0.295896	−	0.407265i	−0.0155734	−	0.0214350i	−0.816733	+	0.577016i	$0.804217\pi$
$20$		0			0
$21$			8.70923i			0.414725i
$22$		0			0
$23$	13.2440			0.575825			0.287913	−	0.957657i	$-0.407039\pi$
$23$	13.2440			0.575825			0.287913	+	0.957657i	$0.407039\pi$
$24$		0			0
$25$	19.7948	−	14.3818i	0.791792	−	0.575270i
$26$		0			0
$27$	−7.28753	−	22.4287i	−0.269909	−	0.830693i
$28$		0			0
$29$	27.3013	−	37.5770i	0.941424	−	1.29576i	−0.0138084	−	0.999905i	$-0.504395\pi$
$29$	27.3013	−	37.5770i	0.941424	−	1.29576i	0.955233	−	0.295855i	$-0.0956045\pi$
$30$		0			0
$31$	5.53315	−	17.0293i	0.178489	−	0.549332i	−0.821287	−	0.570516i	$-0.806743\pi$
$31$	5.53315	−	17.0293i	0.178489	−	0.549332i	0.999776	+	0.0211835i	$0.00674341\pi$
$32$		0			0
$33$	35.3482	+	7.85086i	1.07116	+	0.237905i
$34$		0			0
$35$	−1.83583	−	0.596496i	−0.0524522	−	0.0170428i
$36$		0			0
$37$	9.01297	+	6.54831i	0.243594	+	0.176981i	0.702883	−	0.711306i	$-0.251896\pi$
$37$	9.01297	+	6.54831i	0.243594	+	0.176981i	−0.459289	+	0.888287i	$0.651896\pi$
$38$		0			0
$39$	20.9764	−	6.81566i	0.537857	−	0.174760i
$40$		0			0
$41$	29.0242	+	39.9484i	0.707908	+	0.974352i	0.999840	+	0.0179124i	$0.00570200\pi$
$41$	29.0242	+	39.9484i	0.707908	+	0.974352i	−0.291932	+	0.956439i	$0.594298\pi$
$42$		0			0
$43$		−	81.3678i		−	1.89227i	−0.323768	−	0.946137i	$-0.604950\pi$
$43$		−	81.3678i		−	1.89227i	0.323768	−	0.946137i	$-0.395050\pi$
$44$		0			0
$45$	−1.33937			−0.0297639
$46$		0			0
$47$	−60.8620	+	44.2188i	−1.29494	+	0.940826i	−0.999893	−	0.0146582i	$-0.995334\pi$
$47$	−60.8620	+	44.2188i	−1.29494	+	0.940826i	−0.295043	+	0.955484i	$0.595334\pi$
$48$		0			0
$49$	−2.16312	−	6.65740i	−0.0441453	−	0.135865i
$50$		0			0
$51$	−37.5356	+	51.6633i	−0.735992	+	1.01301i
$52$		0			0
$53$	12.6965	−	39.0758i	0.239557	−	0.737280i	−0.756927	−	0.653499i	$-0.773300\pi$
$53$	12.6965	−	39.0758i	0.239557	−	0.737280i	0.996484	−	0.0837809i	$-0.0266996\pi$
$54$		0			0
$55$	−4.07590	+	6.91338i	−0.0741072	+	0.125698i
$56$		0			0
$57$	1.57600	+	0.512074i	0.0276491	+	0.00898375i
$58$		0			0
$59$	35.1249	+	25.5198i	0.595338	+	0.432538i	0.844221	−	0.535995i	$-0.180063\pi$
$59$	35.1249	+	25.5198i	0.595338	+	0.432538i	−0.248883	+	0.968534i	$0.580063\pi$
$60$		0			0
$61$	26.0595	−	8.46725i	0.427205	−	0.138807i	−0.0875196	−	0.996163i	$-0.527894\pi$
$61$	26.0595	−	8.46725i	0.427205	−	0.138807i	0.514725	+	0.857355i	$0.327894\pi$
$62$		0			0
$63$	−2.85492	−	3.92946i	−0.0453161	−	0.0623723i
$64$		0			0
$65$			4.88845i			0.0752069i
$66$		0			0
$67$	−106.827			−1.59443			−0.797216	−	0.603695i	$-0.793695\pi$
$67$	−106.827			−1.59443			−0.797216	+	0.603695i	$0.793695\pi$
$68$		0			0
$69$	−35.2701	+	25.6252i	−0.511161	+	0.371380i
$70$		0			0
$71$	−25.2285	−	77.6454i	−0.355331	−	1.09360i	−0.955817	−	0.293961i	$-0.905026\pi$
$71$	−25.2285	−	77.6454i	−0.355331	−	1.09360i	0.600486	−	0.799635i	$-0.294974\pi$
$72$		0			0
$73$	−7.14333	+	9.83196i	−0.0978539	+	0.134684i	−0.855136	−	0.518403i	$-0.826527\pi$
$73$	−7.14333	+	9.83196i	−0.0978539	+	0.134684i	0.757282	+	0.653088i	$0.226527\pi$
$74$		0			0
$75$	−24.8889	+	76.6002i	−0.331852	+	1.02134i
$76$		0			0
$77$	−28.9704	+	2.77821i	−0.376238	+	0.0360807i
$78$		0			0
$79$	−80.4877	−	26.1520i	−1.01883	−	0.331038i	−0.248466	−	0.968641i	$-0.579926\pi$
$79$	−80.4877	−	26.1520i	−1.01883	−	0.331038i	−0.770366	+	0.637602i	$0.779926\pi$
$80$		0			0
$81$	76.1706	+	55.3412i	0.940378	+	0.683225i
$82$		0			0
$83$	−33.3722	+	10.8433i	−0.402075	+	0.130642i	−0.503072	−	0.864245i	$-0.667797\pi$
$83$	−33.3722	+	10.8433i	−0.402075	+	0.130642i	0.100997	+	0.994887i	$0.467797\pi$
$84$		0			0
$85$	−8.31935	−	11.4506i	−0.0978747	−	0.134713i
$86$		0			0
$87$			152.896i			1.75742i
$88$		0			0
$89$	−62.7799			−0.705392			−0.352696	−	0.935738i	$-0.614735\pi$
$89$	−62.7799			−0.705392			−0.352696	+	0.935738i	$0.614735\pi$
$90$		0			0
$91$	−14.3417	+	10.4199i	−0.157601	+	0.114504i
$92$		0			0
$93$	18.2139	+	56.0567i	0.195849	+	0.602760i
$94$		0			0
$95$	−0.215881	+	0.297135i	−0.00227243	+	0.00312774i
$96$		0			0
$97$	13.0924	−	40.2943i	0.134973	−	0.415405i	−0.860613	−	0.509260i	$-0.829919\pi$
$97$	13.0924	−	40.2943i	0.134973	−	0.415405i	0.995586	+	0.0938551i	$0.0299190\pi$
$98$		0			0
$99$	−18.5221	+	8.04510i	−0.187092	+	0.0812636i
$100$		0			0
$101$	−29.7587	−	9.66918i	−0.294640	−	0.0957344i	0.157967	−	0.987444i	$-0.449506\pi$
$101$	−29.7587	−	9.66918i	−0.294640	−	0.0957344i	−0.452607	+	0.891710i	$0.649506\pi$
$102$		0			0
$103$	63.1875	+	45.9084i	0.613470	+	0.445712i	0.850635	−	0.525757i	$-0.176218\pi$
$103$	63.1875	+	45.9084i	0.613470	+	0.445712i	−0.237164	+	0.971470i	$0.576218\pi$
$104$		0			0
$105$	6.04313	−	1.96353i	0.0575537	−	0.0187003i
$106$		0			0
$107$	94.2221	+	129.686i	0.880580	+	1.21201i	0.976260	+	0.216602i	$0.0694975\pi$
$107$	94.2221	+	129.686i	0.880580	+	1.21201i	−0.0956797	+	0.995412i	$0.530502\pi$
$108$		0			0
$109$		−	168.661i		−	1.54735i	−0.633581	−	0.773676i	$-0.718416\pi$
$109$		−	168.661i		−	1.54735i	0.633581	−	0.773676i	$-0.281584\pi$
$110$		0			0
$111$	−36.6725			−0.330383
$112$		0			0
$113$	−15.9070	+	11.5571i	−0.140770	+	0.102275i	−0.655942	−	0.754812i	$-0.727728\pi$
$113$	−15.9070	+	11.5571i	−0.140770	+	0.102275i	0.515171	+	0.857087i	$0.327728\pi$
$114$		0			0
$115$	−2.98591	−	9.18970i	−0.0259645	−	0.0799104i
$116$		0			0
$117$	−7.23001	+	9.95126i	−0.0617950	+	0.0850535i
$118$		0			0
$119$	15.8608	−	48.8146i	0.133284	−	0.410207i
$120$		0			0
$121$	−14.8392	+	120.087i	−0.122638	+	0.992452i
$122$		0			0
$123$	−154.589	−	50.2290i	−1.25682	−	0.408366i
$124$		0			0
$125$	−29.1982	−	21.2137i	−0.233585	−	0.169710i
$126$		0			0
$127$	41.0642	−	13.3426i	0.323340	−	0.105060i	−0.142850	−	0.989744i	$-0.545627\pi$
$127$	41.0642	−	13.3426i	0.323340	−	0.105060i	0.466189	+	0.884685i	$0.345627\pi$
$128$		0			0
$129$	157.435	+	216.691i	1.22043	+	1.67977i
$130$		0			0
$131$		−	2.86365i		−	0.0218599i	−0.999940	−	0.0109300i	$-0.996521\pi$
$131$		−	2.86365i		−	0.0218599i	0.999940	−	0.0109300i	$-0.00347919\pi$
$132$		0			0
$133$	−1.33189			−0.0100142
$134$		0			0
$135$	−13.9198	+	10.1133i	−0.103109	+	0.0749134i
$136$		0			0
$137$	0.725590	+	2.23314i	0.00529628	+	0.0163003i	0.953670	−	0.300856i	$-0.0972722\pi$
$137$	0.725590	+	2.23314i	0.00529628	+	0.0163003i	−0.948373	+	0.317156i	$0.897272\pi$
$138$		0			0
$139$	14.7720	−	20.3320i	0.106274	−	0.146273i	−0.752568	−	0.658515i	$-0.771185\pi$
$139$	14.7720	−	20.3320i	0.106274	−	0.146273i	0.858841	+	0.512242i	$0.171185\pi$
$140$		0			0
$141$	76.5246	−	235.519i	0.542728	−	1.67034i
$142$		0			0
$143$	29.3630	+	67.6018i	0.205336	+	0.472740i
$144$		0			0
$145$	−32.2290	−	10.4719i	−0.222269	−	0.0722197i
$146$		0			0
$147$	18.6417	+	13.5440i	0.126814	+	0.0921361i
$148$		0			0
$149$	148.935	−	48.3921i	0.999567	−	0.324779i	0.236874	−	0.971540i	$-0.423877\pi$
$149$	148.935	−	48.3921i	0.999567	−	0.324779i	0.762692	+	0.646761i	$0.223877\pi$
$150$		0			0
$151$	−31.8256	−	43.8042i	−0.210766	−	0.290094i	0.690525	−	0.723308i	$-0.257379\pi$
$151$	−31.8256	−	43.8042i	−0.210766	−	0.290094i	−0.901291	+	0.433214i	$0.857379\pi$
$152$		0			0
$153$		−	35.6139i		−	0.232771i
$154$		0			0
$155$	−13.0637			−0.0842820
$156$		0			0
$157$	−206.749	+	150.212i	−1.31687	+	0.956763i	−0.316906	+	0.948457i	$0.602644\pi$
$157$	−206.749	+	150.212i	−1.31687	+	0.956763i	−0.999965	+	0.00830670i	$0.997356\pi$
$158$		0			0
$159$	41.7941	+	128.629i	0.262856	+	0.808987i
$160$		0			0
$161$	20.5962	−	28.3482i	0.127926	−	0.176076i
$162$		0			0
$163$	22.5758	−	69.4811i	0.138502	−	0.426265i	−0.857617	−	0.514290i	$-0.828056\pi$
$163$	22.5758	−	69.4811i	0.138502	−	0.426265i	0.996118	+	0.0880252i	$0.0280556\pi$
$164$		0			0
$165$	−2.52187	−	26.2973i	−0.0152841	−	0.159378i
$166$		0			0
$167$	−2.94291	−	0.956208i	−0.0176222	−	0.00572580i	0.300193	−	0.953879i	$-0.402949\pi$
$167$	−2.94291	−	0.956208i	−0.0176222	−	0.00572580i	−0.317815	+	0.948153i	$0.602949\pi$
$168$		0			0
$169$	−100.404	−	72.9476i	−0.594105	−	0.431643i
$170$		0			0
$171$	−0.878925	+	0.285580i	−0.00513991	+	0.00167006i
$172$		0			0
$173$	82.4676	+	113.507i	0.476691	+	0.656110i	0.977865	−	0.209237i	$-0.0670981\pi$
$173$	82.4676	+	113.507i	0.476691	+	0.656110i	−0.501173	+	0.865347i	$0.667098\pi$
$174$		0			0
$175$		−	64.7355i		−	0.369917i
$176$		0			0
$177$	−142.919			−0.807449
$178$		0			0
$179$	86.3255	−	62.7192i	0.482265	−	0.350386i	−0.319937	−	0.947439i	$-0.603662\pi$
$179$	86.3255	−	62.7192i	0.482265	−	0.350386i	0.802202	+	0.597053i	$0.203662\pi$
$180$		0			0
$181$	−87.8209	−	270.285i	−0.485198	−	1.49329i	−0.831694	−	0.555235i	$-0.812628\pi$
$181$	−87.8209	−	270.285i	−0.485198	−	1.49329i	0.346496	−	0.938052i	$-0.387372\pi$
$182$		0			0
$183$	−53.0163	+	72.9707i	−0.289707	+	0.398747i
$184$		0			0
$185$	2.51171	−	7.73024i	0.0135768	−	0.0417851i
$186$		0			0
$187$	−183.827	−	108.378i	−0.983030	−	0.579561i
$188$		0			0
$189$	−59.3408	−	19.2810i	−0.313973	−	0.102016i
$190$		0			0
$191$	101.360	+	73.6423i	0.530680	+	0.385562i	0.820612	−	0.571485i	$-0.193633\pi$
$191$	101.360	+	73.6423i	0.530680	+	0.385562i	−0.289932	+	0.957047i	$0.593633\pi$
$192$		0			0
$193$	87.8230	−	28.5354i	0.455042	−	0.147852i	−0.0725233	−	0.997367i	$-0.523105\pi$
$193$	87.8230	−	28.5354i	0.455042	−	0.147852i	0.527565	+	0.849515i	$0.323105\pi$
$194$		0			0
$195$	−9.45846	−	13.0184i	−0.0485049	−	0.0667613i
$196$		0			0
$197$			185.766i			0.942977i	0.881872	+	0.471488i	$0.156283\pi$
$197$			185.766i			0.942977i	−0.881872	+	0.471488i	$0.843717\pi$
$198$		0			0
$199$	215.136			1.08109			0.540543	−	0.841316i	$-0.318219\pi$
$199$	215.136			1.08109			0.540543	+	0.841316i	$0.318219\pi$
$200$		0			0
$201$	284.491	−	206.695i	1.41538	−	1.02833i
$202$		0			0
$203$	−37.9749	−	116.875i	−0.187068	−	0.575737i
$204$		0			0
$205$	21.1757	−	29.1458i	0.103296	−	0.142175i
$206$		0			0
$207$	7.51323	−	23.1233i	0.0362958	−	0.111707i
$208$		0			0
$209$	−1.20062	+	5.40576i	−0.00574461	+	0.0258649i
$210$		0			0
$211$	−299.166	−	97.2050i	−1.41785	−	0.460687i	−0.502931	−	0.864327i	$-0.667745\pi$
$211$	−299.166	−	97.2050i	−1.41785	−	0.460687i	−0.914918	+	0.403640i	$0.867745\pi$
$212$		0			0
$213$	217.419	+	157.964i	1.02075	+	0.741615i
$214$		0			0
$215$	−56.4592	+	18.3447i	−0.262601	+	0.0853243i
$216$		0			0
$217$	−27.8457	−	38.3263i	−0.128321	−	0.176619i
$218$		0			0
$219$		−	40.0049i		−	0.182671i
$220$		0			0
$221$	−129.984			−0.588162
$222$		0			0
$223$	233.270	−	169.480i	1.04605	−	0.760001i	0.0745940	−	0.997214i	$-0.476234\pi$
$223$	233.270	−	169.480i	1.04605	−	0.760001i	0.971458	+	0.237213i	$0.0762339\pi$
$224$		0			0
$225$	−13.8804	−	42.7194i	−0.0616906	−	0.189864i
$226$		0			0
$227$	−194.166	+	267.247i	−0.855358	+	1.17730i	0.127299	+	0.991864i	$0.459369\pi$
$227$	−194.166	+	267.247i	−0.855358	+	1.17730i	−0.982657	+	0.185434i	$0.940631\pi$
$228$		0			0
$229$	131.400	−	404.406i	0.573797	−	1.76597i	−0.0664412	−	0.997790i	$-0.521164\pi$
$229$	131.400	−	404.406i	0.573797	−	1.76597i	0.640239	−	0.768176i	$-0.278836\pi$
$230$		0			0
$231$	71.7756	−	63.4522i	0.310717	−	0.274685i
$232$		0			0
$233$	219.534	+	71.3308i	0.942204	+	0.306141i	0.739544	−	0.673108i	$-0.235041\pi$
$233$	219.534	+	71.3308i	0.942204	+	0.306141i	0.202660	+	0.979249i	$0.435041\pi$
$234$		0			0
$235$	44.4040	+	32.2614i	0.188953	+	0.137283i
$236$		0			0
$237$	264.948	−	86.0867i	1.11792	−	0.363235i
$238$		0			0
$239$	144.790	+	199.286i	0.605814	+	0.833832i	0.996225	−	0.0868090i	$-0.0276670\pi$
$239$	144.790	+	199.286i	0.605814	+	0.833832i	−0.390411	+	0.920641i	$0.627667\pi$
$240$		0			0
$241$			263.799i			1.09460i	0.836937	+	0.547300i	$0.184344\pi$
$241$			263.799i			1.09460i	−0.836937	+	0.547300i	$0.815656\pi$
$242$		0			0
$243$	−97.6811			−0.401980
$244$		0			0
$245$	−4.13173	+	3.00188i	−0.0168642	+	0.0122526i
$246$		0			0
$247$	1.04231	+	3.20790i	0.00421988	+	0.0129874i
$248$		0			0
$249$	67.8935	−	93.4474i	0.272665	−	0.375291i
$250$		0			0
$251$	146.511	−	450.914i	0.583708	−	1.79647i	−0.0206902	−	0.999786i	$-0.506586\pi$
$251$	146.511	−	450.914i	0.583708	−	1.79647i	0.604398	−	0.796682i	$-0.293414\pi$
$252$		0			0
$253$	−96.4908	−	109.148i	−0.381386	−	0.431415i
$254$		0			0
$255$	44.3106	+	14.3974i	0.173767	+	0.0564603i
$256$		0			0
$257$	196.658	+	142.881i	0.765207	+	0.555955i	0.900503	−	0.434850i	$-0.143199\pi$
$257$	196.658	+	142.881i	0.765207	+	0.555955i	−0.135296	+	0.990805i	$0.543199\pi$
$258$		0			0
$259$	28.0328	−	9.10839i	0.108235	−	0.0351675i
$260$		0			0
$261$	−50.1198	−	68.9840i	−0.192030	−	0.264306i
$262$		0			0
$263$		−	284.133i		−	1.08035i	−0.841551	−	0.540177i	$-0.818357\pi$
$263$		−	284.133i		−	1.08035i	0.841551	−	0.540177i	$-0.181643\pi$
$264$		0			0
$265$	−29.9763			−0.113118
$266$		0			0
$267$	167.189	−	121.470i	0.626178	−	0.454945i
$268$		0			0
$269$	108.406	+	333.640i	0.402998	+	1.24030i	0.922556	+	0.385864i	$0.126097\pi$
$269$	108.406	+	333.640i	0.402998	+	1.24030i	−0.519558	+	0.854435i	$0.673903\pi$
$270$		0			0
$271$	−30.1319	+	41.4730i	−0.111188	+	0.153037i	−0.860984	−	0.508632i	$-0.830151\pi$
$271$	−30.1319	+	41.4730i	−0.111188	+	0.153037i	0.749796	+	0.661669i	$0.230151\pi$
$272$		0			0
$273$	18.0325	−	55.4984i	0.0660532	−	0.203291i
$274$		0			0
$275$	−262.742	−	58.3553i	−0.955427	−	0.212201i
$276$		0			0
$277$	52.3293	+	17.0028i	0.188914	+	0.0613820i	0.401946	−	0.915663i	$-0.368334\pi$
$277$	52.3293	+	17.0028i	0.188914	+	0.0613820i	−0.213032	+	0.977045i	$0.568334\pi$
$278$		0			0
$279$	−26.5934	−	19.3212i	−0.0953168	−	0.0692517i
$280$		0			0
$281$	−0.570367	+	0.185323i	−0.00202977	+	0.000659514i	−0.310032	−	0.950726i	$-0.600340\pi$
$281$	−0.570367	+	0.185323i	−0.00202977	+	0.000659514i	0.308002	+	0.951386i	$0.400340\pi$
$282$		0			0
$283$	−36.0582	−	49.6298i	−0.127414	−	0.175370i	0.740544	−	0.672008i	$-0.234568\pi$
$283$	−36.0582	−	49.6298i	−0.127414	−	0.175370i	−0.867958	+	0.496637i	$0.834568\pi$
$284$		0			0
$285$		−	1.20900i		−	0.00424211i
$286$		0			0
$287$	130.644			0.455207
$288$		0			0
$289$	70.6652	−	51.3412i	0.244516	−	0.177651i
$290$		0			0
$291$	43.0973	+	132.640i	0.148101	+	0.455807i
$292$		0			0
$293$	−173.388	+	238.649i	−0.591769	+	0.814501i	−0.994924	−	0.100631i	$-0.967914\pi$
$293$	−173.388	+	238.649i	−0.591769	+	0.814501i	0.403154	+	0.915132i	$0.367914\pi$
$294$		0			0
$295$	9.78851	−	30.1259i	0.0331814	−	0.102122i
$296$		0			0
$297$	−131.748	+	223.466i	−0.443597	+	0.752412i
$298$		0			0
$299$	−84.3956	−	27.4218i	−0.282259	−	0.0917116i
$300$		0			0
$301$	−174.164	−	126.538i	−0.578619	−	0.420391i
$302$		0			0
$303$	97.9589	−	31.8288i	0.323297	−	0.105046i
$304$		0			0
$305$	−11.7505	−	16.1731i	−0.0385261	−	0.0530267i
$306$		0			0
$307$			505.221i			1.64567i	0.568281	+	0.822835i	$0.307609\pi$
$307$			505.221i			1.64567i	−0.568281	+	0.822835i	$0.692391\pi$
$308$		0			0
$309$	−257.101			−0.832042
$310$		0			0
$311$	339.283	−	246.504i	1.09094	−	0.792616i	0.111384	−	0.993777i	$-0.464472\pi$
$311$	339.283	−	246.504i	1.09094	−	0.792616i	0.979558	+	0.201162i	$0.0644717\pi$
$312$		0			0
$313$	−48.9289	−	150.588i	−0.156323	−	0.481111i	0.841970	−	0.539524i	$-0.181396\pi$
$313$	−48.9289	−	150.588i	−0.156323	−	0.481111i	−0.998292	+	0.0584132i	$0.981396\pi$
$314$		0			0
$315$	−2.08291	+	2.86688i	−0.00661240	+	0.00910119i
$316$		0			0
$317$	−113.275	+	348.626i	−0.357335	+	1.09977i	0.597307	+	0.802012i	$0.296237\pi$
$317$	−113.275	+	348.626i	−0.357335	+	1.09977i	−0.954643	+	0.297753i	$0.903763\pi$
$318$		0			0
$319$	−508.592	+	48.7732i	−1.59433	+	0.152894i
$320$		0			0
$321$	−501.846	−	163.060i	−1.56338	−	0.507974i
$322$		0			0
$323$	−7.90081	−	5.74027i	−0.0244607	−	0.0177717i
$324$		0			0
$325$	−155.917	+	50.6606i	−0.479746	+	0.155879i
$326$		0			0
$327$	326.336	+	449.163i	0.997970	+	1.37359i
$328$		0			0
$329$			199.039i			0.604981i
$330$		0			0
$331$	137.079			0.414136			0.207068	−	0.978327i	$-0.433608\pi$
$331$	137.079			0.414136			0.207068	+	0.978327i	$0.433608\pi$
$332$		0			0
$333$	16.5460	−	12.0214i	0.0496878	−	0.0361003i
$334$		0			0
$335$	24.0846	+	74.1248i	0.0718943	+	0.221268i
$336$		0			0
$337$	−75.7506	+	104.262i	−0.224779	+	0.309382i	−0.906480	−	0.422249i	$-0.861241\pi$
$337$	−75.7506	+	104.262i	−0.224779	+	0.309382i	0.681700	+	0.731631i	$0.261241\pi$
$338$		0			0
$339$	20.0006	−	61.5557i	0.0589990	−	0.181580i
$340$		0			0
$341$	−180.657	+	78.4686i	−0.529785	+	0.230113i
$342$		0			0
$343$	−17.6138	−	5.72307i	−0.0513522	−	0.0166853i
$344$		0			0
$345$	25.7326	+	18.6958i	0.0745871	+	0.0541907i
$346$		0			0
$347$	−416.223	+	135.239i	−1.19949	+	0.389738i	−0.839573	−	0.543247i	$-0.817195\pi$
$347$	−416.223	+	135.239i	−1.19949	+	0.389738i	−0.359917	+	0.932984i	$0.617195\pi$
$348$		0			0
$349$	−24.9915	−	34.3979i	−0.0716089	−	0.0985612i	0.771710	−	0.635974i	$-0.219402\pi$
$349$	−24.9915	−	34.3979i	−0.0716089	−	0.0985612i	−0.843319	+	0.537413i	$0.819402\pi$
$350$		0			0
$351$			158.013i			0.450180i
$352$		0			0
$353$	−322.723			−0.914230			−0.457115	−	0.889408i	$-0.651117\pi$
$353$	−322.723			−0.914230			−0.457115	+	0.889408i	$0.651117\pi$
$354$		0			0
$355$	−48.1885	+	35.0110i	−0.135742	+	0.0986225i
$356$		0			0
$357$	52.2103	+	160.687i	0.146247	+	0.450103i
$358$		0			0
$359$	−139.027	+	191.354i	−0.387262	+	0.533020i	−0.957490	−	0.288466i	$-0.906855\pi$
$359$	−139.027	+	191.354i	−0.387262	+	0.533020i	0.570228	+	0.821486i	$0.306855\pi$
$360$		0			0
$361$	111.477	−	343.090i	0.308800	−	0.950389i
$362$		0			0
$363$	−192.832	−	348.515i	−0.531219	−	0.960096i
$364$		0			0
$365$	8.43267	+	2.73994i	0.0231032	+	0.00750669i
$366$		0			0
$367$	−4.91666	−	3.57216i	−0.0133969	−	0.00973341i	0.581067	−	0.813856i	$-0.302636\pi$
$367$	−4.91666	−	3.57216i	−0.0133969	−	0.00973341i	−0.594464	+	0.804123i	$0.702636\pi$
$368$		0			0
$369$	86.2132	−	28.0124i	0.233640	−	0.0759143i
$370$		0			0
$371$	−63.8954	−	87.9445i	−0.172225	−	0.237047i
$372$		0			0
$373$			283.267i			0.759429i	0.925104	+	0.379714i	$0.123978\pi$
$373$			283.267i			0.759429i	−0.925104	+	0.379714i	$0.876022\pi$
$374$		0			0
$375$	118.803			0.316809
$376$		0			0
$377$	−251.778	+	182.927i	−0.667845	+	0.485218i
$378$		0			0
$379$	7.52767	+	23.1678i	0.0198619	+	0.0611287i	0.960496	−	0.278293i	$-0.0897686\pi$
$379$	7.52767	+	23.1678i	0.0198619	+	0.0611287i	−0.940634	+	0.339422i	$0.889769\pi$
$380$		0			0
$381$	−83.5422	+	114.986i	−0.219271	+	0.301800i
$382$		0			0
$383$	−116.650	+	359.011i	−0.304569	+	0.937366i	0.675269	+	0.737571i	$0.264027\pi$
$383$	−116.650	+	359.011i	−0.304569	+	0.937366i	−0.979838	+	0.199794i	$0.935973\pi$
$384$		0			0
$385$	8.45923	+	19.4755i	0.0219720	+	0.0505857i
$386$		0			0
$387$	−142.064	−	46.1594i	−0.367091	−	0.119275i
$388$		0			0
$389$	238.950	+	173.607i	0.614267	+	0.446291i	0.850914	−	0.525305i	$-0.176049\pi$
$389$	238.950	+	173.607i	0.614267	+	0.446291i	−0.236648	+	0.971596i	$0.576049\pi$
$390$		0			0
$391$	244.354	−	79.3953i	0.624946	−	0.203057i
$392$		0			0
$393$	5.54076	+	7.62620i	0.0140986	+	0.0194051i
$394$		0			0
$395$			61.7447i			0.156316i
$396$		0			0
$397$	−655.582			−1.65134			−0.825670	−	0.564153i	$-0.809203\pi$
$397$	−655.582			−1.65134			−0.825670	+	0.564153i	$0.809203\pi$
$398$		0			0
$399$	3.54696	−	2.57702i	0.00888964	−	0.00645870i
$400$		0			0
$401$	55.2535	+	170.053i	0.137789	+	0.424072i	0.996013	−	0.0892034i	$-0.0284321\pi$
$401$	55.2535	+	170.053i	0.137789	+	0.424072i	−0.858224	+	0.513275i	$0.828432\pi$
$402$		0			0
$403$	−70.5186	+	97.0605i	−0.174984	+	0.240845i
$404$		0			0
$405$	21.2270	−	65.3300i	0.0524123	−	0.161309i
$406$		0			0
$407$	−11.6984	−	121.987i	−0.0287430	−	0.299723i
$408$		0			0
$409$	−264.895	−	86.0698i	−0.647666	−	0.210439i	−0.0332813	−	0.999446i	$-0.510596\pi$
$409$	−264.895	−	86.0698i	−0.647666	−	0.210439i	−0.614385	+	0.789007i	$0.710596\pi$
$410$		0			0
$411$	−6.25313	−	4.54316i	−0.0152144	−	0.0110539i
$412$		0			0
$413$	109.248	−	35.4968i	0.264523	−	0.0859487i
$414$		0			0
$415$	15.0478	+	20.7116i	0.0362599	+	0.0499074i
$416$		0			0
$417$			82.7279i			0.198388i
$418$		0			0
$419$	334.946			0.799394			0.399697	−	0.916647i	$-0.369115\pi$
$419$	334.946			0.799394			0.399697	+	0.916647i	$0.369115\pi$
$420$		0			0
$421$	78.2137	−	56.8256i	0.185781	−	0.134978i	−0.491008	−	0.871155i	$-0.663371\pi$
$421$	78.2137	−	56.8256i	0.185781	−	0.134978i	0.676788	+	0.736178i	$0.263371\pi$
$422$		0			0
$423$	42.6773	+	131.347i	0.100892	+	0.310513i
$424$		0			0
$425$	279.001	−	384.012i	0.656473	−	0.903558i
$426$		0			0
$427$	22.4022	−	68.9470i	0.0524643	−	0.161468i
$428$		0			0
$429$	−208.997	−	123.217i	−0.487172	−	0.287220i
$430$		0			0
$431$	754.980	+	245.308i	1.75169	+	0.569160i	0.996287	−	0.0860960i	$-0.0274392\pi$
$431$	754.980	+	245.308i	1.75169	+	0.569160i	0.755407	+	0.655256i	$0.227439\pi$
$432$		0			0
$433$	−17.5353	−	12.7401i	−0.0404972	−	0.0294230i	0.567353	−	0.823475i	$-0.307968\pi$
$433$	−17.5353	−	12.7401i	−0.0404972	−	0.0294230i	−0.607850	+	0.794052i	$0.707968\pi$
$434$		0			0
$435$	106.091	−	34.4710i	0.243887	−	0.0792437i
$436$		0			0
$437$	−3.91883	−	5.39381i	−0.00896758	−	0.0123428i
$438$		0			0
$439$			367.714i			0.837618i	0.908074	+	0.418809i	$0.137552\pi$
$439$			367.714i			0.837618i	−0.908074	+	0.418809i	$0.862448\pi$
$440$		0			0
$441$	−12.8506			−0.0291397
$442$		0			0
$443$	303.071	−	220.194i	0.684134	−	0.497052i	−0.190593	−	0.981669i	$-0.561041\pi$
$443$	303.071	−	220.194i	0.684134	−	0.497052i	0.874726	+	0.484617i	$0.161041\pi$
$444$		0			0
$445$	14.1540	+	43.5616i	0.0318068	+	0.0978911i
$446$		0			0
$447$	−302.999	+	417.042i	−0.677850	+	0.932980i
$448$		0			0
$449$	147.460	−	453.836i	0.328419	−	1.01077i	−0.641455	−	0.767161i	$-0.721669\pi$
$449$	147.460	−	453.836i	0.328419	−	1.01077i	0.969874	−	0.243609i	$-0.0783313\pi$
$450$		0			0
$451$	117.768	−	530.248i	0.261127	−	1.17572i
$452$		0			0
$453$	169.510	+	55.0771i	0.374194	+	0.121583i
$454$		0			0
$455$	10.4635	+	7.60219i	0.0229967	+	0.0167081i
$456$		0			0
$457$	−469.254	+	152.470i	−1.02681	+	0.333632i	−0.773530	−	0.633760i	$-0.781511\pi$
$457$	−469.254	+	152.470i	−1.02681	+	0.333632i	−0.253284	+	0.967392i	$0.581511\pi$
$458$		0			0
$459$	−268.913	−	370.126i	−0.585866	−	0.806375i
$460$		0			0
$461$			329.275i			0.714263i	0.934054	+	0.357132i	$0.116245\pi$
$461$			329.275i			0.714263i	−0.934054	+	0.357132i	$0.883755\pi$
$462$		0			0
$463$	454.799			0.982287			0.491144	−	0.871079i	$-0.336579\pi$
$463$	454.799			0.982287			0.491144	+	0.871079i	$0.336579\pi$
$464$		0			0
$465$	34.7900	−	25.2764i	0.0748173	−	0.0543579i
$466$		0			0
$467$	−35.2630	−	108.528i	−0.0755096	−	0.232395i	0.906177	−	0.422899i	$-0.138988\pi$
$467$	−35.2630	−	108.528i	−0.0755096	−	0.232395i	−0.981686	+	0.190505i	$0.938988\pi$
$468$		0			0
$469$	−166.130	+	228.658i	−0.354222	+	0.487545i
$470$		0			0
$471$	259.955	−	800.060i	0.551922	−	1.69864i
$472$		0			0
$473$	−670.579	+	592.815i	−1.41771	+	1.25331i
$474$		0			0
$475$	−11.7144	−	3.80623i	−0.0246618	−	0.00801312i
$476$		0			0
$477$	−61.0218	−	44.3350i	−0.127928	−	0.0929454i
$478$		0			0
$479$	772.876	−	251.122i	1.61352	−	0.524264i	0.643119	−	0.765767i	$-0.277640\pi$
$479$	772.876	−	251.122i	1.61352	−	0.524264i	0.970400	+	0.241502i	$0.0776402\pi$
$480$		0			0
$481$	−43.8757	−	60.3897i	−0.0912176	−	0.125550i
$482$		0			0
$483$			115.345i			0.238809i
$484$		0			0
$485$	−30.9110			−0.0637341
$486$		0			0
$487$	617.567	−	448.689i	1.26811	−	0.921332i	0.268980	−	0.963146i	$-0.413313\pi$
$487$	617.567	−	448.689i	1.26811	−	0.921332i	0.999125	+	0.0418134i	$0.0133135\pi$
$488$		0			0
$489$	74.3145	+	228.716i	0.151972	+	0.467723i
$490$		0			0
$491$	105.460	−	145.153i	0.214785	−	0.295626i	−0.688007	−	0.725705i	$-0.741514\pi$
$491$	105.460	−	145.153i	0.214785	−	0.295626i	0.902792	+	0.430078i	$0.141514\pi$
$492$		0			0
$493$	278.446	−	856.969i	0.564800	−	1.73827i
$494$		0			0
$495$	9.75819	+	11.0382i	0.0197135	+	0.0222995i
$496$		0			0
$497$	−205.430	−	66.7484i	−0.413341	−	0.134303i
$498$		0			0
$499$	408.788	+	297.002i	0.819214	+	0.595194i	0.916487	−	0.400064i	$-0.131012\pi$
$499$	408.788	+	297.002i	0.819214	+	0.595194i	−0.0972729	+	0.995258i	$0.531012\pi$
$500$		0			0
$501$	9.68739	−	3.14762i	0.0193361	−	0.00628268i
$502$		0			0
$503$	212.952	+	293.103i	0.423364	+	0.582711i	0.966414	−	0.256990i	$-0.0827306\pi$
$503$	212.952	+	293.103i	0.423364	+	0.582711i	−0.543050	+	0.839700i	$0.682731\pi$
$504$		0			0
$505$			22.8288i			0.0452056i
$506$		0			0
$507$	408.529			0.805777
$508$		0			0
$509$	496.749	−	360.910i	0.975932	−	0.709056i	0.0191363	−	0.999817i	$-0.493908\pi$
$509$	496.749	−	360.910i	0.975932	−	0.709056i	0.956796	+	0.290761i	$0.0939083\pi$
$510$		0			0
$511$	9.93605	+	30.5800i	0.0194443	+	0.0598435i
$512$		0			0
$513$	−6.97809	+	9.60452i	−0.0136025	+	0.0187223i
$514$		0			0
$515$	17.6089	−	54.1946i	0.0341920	−	0.105232i
$516$		0			0
$517$	807.840	+	179.422i	1.56255	+	0.347044i
$518$		0			0
$519$	−439.240	−	142.718i	−0.846319	−	0.274986i
$520$		0			0
$521$	−785.840	−	570.946i	−1.50833	−	1.09587i	−0.966912	−	0.255112i	$-0.917888\pi$
$521$	−785.840	−	570.946i	−1.50833	−	1.09587i	−0.541418	−	0.840754i	$-0.682112\pi$
$522$		0			0
$523$	−897.086	+	291.481i	−1.71527	+	0.557325i	−0.991197	−	0.132398i	$-0.957732\pi$
$523$	−897.086	+	291.481i	−1.71527	+	0.557325i	−0.724074	+	0.689723i	$0.757732\pi$
$524$		0			0
$525$	125.254	+	172.397i	0.238579	+	0.328376i
$526$		0			0
$527$		−	347.364i		−	0.659134i
$528$		0			0
$529$	−353.597			−0.668425
$530$		0			0
$531$	64.4824	−	46.8492i	0.121436	−	0.0882283i
$532$		0			0
$533$	−102.240	−	314.661i	−0.191819	−	0.590358i
$534$		0			0
$535$	68.7431	−	94.6167i	0.128492	−	0.176854i
$536$		0			0
$537$	−108.541	+	334.055i	−0.202125	+	0.622077i
$538$		0			0
$539$	−39.1061	+	66.3303i	−0.0725531	+	0.123062i
$540$		0			0
$541$	−225.305	−	73.2060i	−0.416460	−	0.135316i	0.0932893	−	0.995639i	$-0.470262\pi$
$541$	−225.305	−	73.2060i	−0.416460	−	0.135316i	−0.509749	+	0.860323i	$0.670262\pi$
$542$		0			0
$543$	756.839	+	549.876i	1.39381	+	1.01266i
$544$		0			0
$545$	−117.030	+	38.0255i	−0.214735	+	0.0697715i
$546$		0			0
$547$	151.592	+	208.648i	0.277133	+	0.381440i	0.924781	−	0.380499i	$-0.124248\pi$
$547$	151.592	+	208.648i	0.277133	+	0.381440i	−0.647649	+	0.761939i	$0.724248\pi$
$548$		0			0
$549$		−	50.3021i		−	0.0916249i
$550$		0			0
$551$	−23.3822			−0.0424358
$552$		0			0
$553$	−181.146	+	131.611i	−0.327570	+	0.237994i
$554$		0			0
$555$	8.26798	+	25.4462i	0.0148973	+	0.0458491i
$556$		0			0
$557$	113.758	−	156.575i	0.204234	−	0.281104i	−0.694597	−	0.719399i	$-0.744417\pi$
$557$	113.758	−	156.575i	0.204234	−	0.281104i	0.898831	+	0.438295i	$0.144417\pi$
$558$		0			0
$559$	−168.473	+	518.506i	−0.301382	+	0.927559i
$560$		0			0
$561$	699.245	−	67.0565i	1.24643	−	0.119530i
$562$		0			0
$563$	−693.980	−	225.488i	−1.23265	−	0.400511i	−0.380974	−	0.924586i	$-0.624411\pi$
$563$	−693.980	−	225.488i	−1.23265	−	0.400511i	−0.851673	+	0.524074i	$0.824411\pi$
$564$		0			0
$565$	11.6055	+	8.43191i	0.0205408	+	0.0149237i
$566$		0			0
$567$	236.911	−	76.9770i	0.417832	−	0.135762i
$568$		0			0
$569$	−77.4343	−	106.579i	−0.136088	−	0.187310i	0.735534	−	0.677488i	$-0.236932\pi$
$569$	−77.4343	−	106.579i	−0.136088	−	0.187310i	−0.871622	+	0.490179i	$0.836932\pi$
$570$		0			0
$571$		−	947.206i		−	1.65885i	−0.558615	−	0.829427i	$-0.688667\pi$
$571$		−	947.206i		−	1.65885i	0.558615	−	0.829427i	$-0.311333\pi$
$572$		0			0
$573$	−412.420			−0.719755
$574$		0			0
$575$	262.162	−	190.472i	0.455934	−	0.331255i
$576$		0			0
$577$	−193.046	−	594.134i	−0.334568	−	1.02969i	−0.966934	−	0.255025i	$-0.917916\pi$
$577$	−193.046	−	594.134i	−0.334568	−	1.02969i	0.632367	−	0.774669i	$-0.282084\pi$
$578$		0			0
$579$	−178.670	+	245.918i	−0.308583	+	0.424729i
$580$		0			0
$581$	−28.6887	+	88.2947i	−0.0493781	+	0.151970i
$582$		0			0
$583$	−414.539	+	180.056i	−0.711045	+	0.308844i
$584$		0			0
$585$	8.53499	+	2.77319i	0.0145897	+	0.00474049i
$586$		0			0
$587$	−345.023	−	250.674i	−0.587773	−	0.427042i	0.253745	−	0.967271i	$-0.418338\pi$
$587$	−345.023	−	250.674i	−0.587773	−	0.427042i	−0.841518	+	0.540229i	$0.818338\pi$
$588$		0			0
$589$	−8.57268	+	2.78543i	−0.0145546	+	0.00472908i
$590$		0			0
$591$	−359.432	−	494.715i	−0.608176	−	0.837082i
$592$		0			0
$593$		−	822.209i		−	1.38652i	−0.720685	−	0.693262i	$-0.756173\pi$
$593$		−	822.209i		−	1.38652i	0.720685	−	0.693262i	$-0.243827\pi$
$594$		0			0
$595$	−37.4472			−0.0629365
$596$		0			0
$597$	−572.930	+	416.258i	−0.959682	+	0.697250i
$598$		0			0
$599$	−104.161	−	320.573i	−0.173891	−	0.535181i	0.825690	−	0.564124i	$-0.190786\pi$
$599$	−104.161	−	320.573i	−0.173891	−	0.535181i	−0.999581	+	0.0289431i	$0.990786\pi$
$600$		0			0
$601$	416.911	−	573.828i	0.693695	−	0.954789i	−0.306301	−	0.951935i	$-0.599091\pi$
$601$	416.911	−	573.828i	0.693695	−	0.954789i	0.999996	−	0.00285454i	$-0.000908629\pi$
$602$		0			0
$603$	−60.6023	+	186.515i	−0.100501	+	0.309311i
$604$		0			0
$605$	86.6709	−	16.7775i	0.143258	−	0.0277314i
$606$		0			0
$607$	788.025	+	256.045i	1.29823	+	0.421820i	0.874965	−	0.484186i	$-0.160884\pi$
$607$	788.025	+	256.045i	1.29823	+	0.421820i	0.423264	+	0.906006i	$0.360884\pi$
$608$		0			0
$609$	327.267	+	237.773i	0.537384	+	0.390432i
$610$		0			0
$611$	479.391	−	155.763i	0.784600	−	0.254932i
$612$		0			0
$613$	583.258	+	802.786i	0.951481	+	1.30960i	0.950866	+	0.309602i	$0.100196\pi$
$613$	583.258	+	802.786i	0.951481	+	1.30960i	0.000615062		1.00000i	$0.499804\pi$
$614$		0			0
$615$			118.590i			0.192830i
$616$		0			0
$617$	160.688			0.260435			0.130217	−	0.991485i	$-0.458433\pi$
$617$	160.688			0.260435			0.130217	+	0.991485i	$0.458433\pi$
$618$		0			0
$619$	−463.492	+	336.746i	−0.748775	+	0.544017i	−0.895447	−	0.445168i	$-0.853144\pi$
$619$	−463.492	+	336.746i	−0.748775	+	0.544017i	0.146672	+	0.989185i	$0.453144\pi$
$620$		0			0
$621$	−96.5159	−	297.045i	−0.155420	−	0.478334i
$622$		0			0
$623$	−97.6311	+	134.378i	−0.156711	+	0.215695i
$624$		0			0
$625$	180.887	−	556.712i	0.289418	−	0.890739i
$626$		0			0
$627$	−7.26199	−	16.7191i	−0.0115821	−	0.0266653i
$628$		0			0
$629$	205.547	+	66.7862i	0.326784	+	0.106178i
$630$		0			0
$631$	−229.414	−	166.679i	−0.363572	−	0.264150i	0.390968	−	0.920404i	$-0.372140\pi$
$631$	−229.414	−	166.679i	−0.363572	−	0.264150i	−0.754540	+	0.656254i	$0.772140\pi$
$632$		0			0
$633$	984.788	−	319.977i	1.55575	−	0.505493i
$634$		0			0
$635$	−18.5162	−	25.4854i	−0.0291594	−	0.0401344i
$636$		0			0
$637$			46.9022i			0.0736298i
$638$		0			0
$639$	−149.877			−0.234549
$640$		0			0
$641$	−920.309	+	668.644i	−1.43574	+	1.04313i	−0.446828	+	0.894620i	$0.647447\pi$
$641$	−920.309	+	668.644i	−1.43574	+	1.04313i	−0.988911	+	0.148506i	$0.952553\pi$
$642$		0			0
$643$	122.601	+	377.329i	0.190671	+	0.586825i	1.00000		0.000530746i	$-0.000168942\pi$
$643$	122.601	+	377.329i	0.190671	+	0.586825i	−0.809329	+	0.587356i	$0.800169\pi$
$644$		0			0
$645$	114.862	−	158.095i	0.178081	−	0.245108i
$646$		0			0
$647$	110.565	−	340.283i	0.170888	−	0.525940i	−0.828533	−	0.559940i	$-0.810824\pi$
$647$	110.565	−	340.283i	0.170888	−	0.525940i	0.999422	+	0.0339992i	$0.0108244\pi$
$648$		0			0
$649$	−45.5905	−	475.404i	−0.0702473	−	0.732518i
$650$		0			0
$651$	148.312	+	48.1895i	0.227822	+	0.0740238i
$652$		0			0
$653$	402.286	+	292.278i	0.616058	+	0.447593i	0.851542	−	0.524286i	$-0.175668\pi$
$653$	402.286	+	292.278i	0.616058	+	0.447593i	−0.235484	+	0.971878i	$0.575668\pi$
$654$		0			0
$655$	−1.98702	+	0.645623i	−0.00303362	+	0.000985684i
$656$		0			0
$657$	13.1137	+	18.0495i	0.0199600	+	0.0274726i
$658$		0			0
$659$			1037.01i			1.57362i	0.617198	+	0.786808i	$0.288268\pi$
$659$			1037.01i			1.57362i	−0.617198	+	0.786808i	$0.711732\pi$
$660$		0			0
$661$	784.234			1.18644			0.593218	−	0.805042i	$-0.297857\pi$
$661$	784.234			1.18644			0.593218	+	0.805042i	$0.297857\pi$
$662$		0			0
$663$	346.160	−	251.500i	0.522112	−	0.379336i
$664$		0			0
$665$	0.300281	+	0.924169i	0.000451550	+	0.00138973i
$666$		0			0
$667$	361.578	−	497.669i	0.542096	−	0.746131i
$668$		0			0
$669$	−293.301	+	902.687i	−0.438417	+	1.34931i
$670$		0			0
$671$	−259.642	−	153.076i	−0.386947	−	0.228131i
$672$		0			0
$673$	304.885	+	99.0633i	0.453024	+	0.147197i	0.526637	−	0.850090i	$-0.323453\pi$
$673$	304.885	+	99.0633i	0.453024	+	0.147197i	−0.0736125	+	0.997287i	$0.523453\pi$
$674$		0			0
$675$	−466.820	−	339.164i	−0.691584	−	0.502466i
$676$		0			0
$677$	33.9251	−	11.0229i	0.0501110	−	0.0162820i	−0.283854	−	0.958867i	$-0.591613\pi$
$677$	33.9251	−	11.0229i	0.0501110	−	0.0162820i	0.333965	+	0.942585i	$0.391613\pi$
$678$		0			0
$679$	−65.8878	−	90.6868i	−0.0970365	−	0.133559i
$680$		0			0
$681$		−	1087.39i		−	1.59676i
$682$		0			0
$683$	−508.266			−0.744167			−0.372084	−	0.928199i	$-0.621357\pi$
$683$	−508.266			−0.744167			−0.372084	+	0.928199i	$0.621357\pi$
$684$		0			0
$685$	1.38594	−	1.00694i	0.00202326	−	0.00146999i
$686$		0			0
$687$	432.538	+	1331.22i	0.629604	+	1.93772i
$688$		0			0
$689$	−161.814	+	222.717i	−0.234853	+	0.323247i
$690$		0			0
$691$	−253.662	+	780.691i	−0.367094	+	1.12980i	0.581566	+	0.813499i	$0.302440\pi$
$691$	−253.662	+	780.691i	−0.367094	+	1.12980i	−0.948660	+	0.316299i	$0.897560\pi$
$692$		0			0
$693$	−11.5841	+	52.1569i	−0.0167159	+	0.0752625i
$694$		0			0
$695$	−17.4383	−	5.66605i	−0.0250911	−	0.00815259i
$696$		0			0
$697$	774.986	+	563.060i	1.11189	+	0.807834i
$698$		0			0
$699$	−722.656	+	234.805i	−1.03384	+	0.335916i
$700$		0			0
$701$	416.293	+	572.978i	0.593856	+	0.817373i	0.995129	−	0.0985861i	$-0.0314320\pi$
$701$	416.293	+	572.978i	0.593856	+	0.817373i	−0.401273	+	0.915959i	$0.631432\pi$
$702$		0			0
$703$		−	5.60828i		−	0.00797765i
$704$		0			0
$705$	−180.674			−0.256275
$706$		0			0
$707$	−66.9752	+	48.6603i	−0.0947315	+	0.0688265i
$708$		0			0
$709$	−8.34205	−	25.6742i	−0.0117659	−	0.0362118i	0.945001	−	0.327067i	$-0.106060\pi$
$709$	−8.34205	−	25.6742i	−0.0117659	−	0.0362118i	−0.956767	+	0.290855i	$0.906060\pi$
$710$		0			0
$711$	−91.3203	+	125.692i	−0.128439	+	0.176782i
$712$		0			0
$713$	73.2810	−	225.536i	0.102778	−	0.316319i
$714$		0			0
$715$	40.2873	−	35.6154i	0.0563459	−	0.0498118i
$716$		0			0
$717$	−771.180	−	250.571i	−1.07556	−	0.349472i
$718$		0			0
$719$	−323.010	−	234.681i	−0.449249	−	0.326399i	0.340050	−	0.940407i	$-0.389556\pi$
$719$	−323.010	−	234.681i	−0.449249	−	0.326399i	−0.789299	+	0.614009i	$0.789556\pi$
$720$		0			0
$721$	196.530	−	63.8564i	0.272580	−	0.0885665i
$722$		0			0
$723$	−510.413	−	702.523i	−0.705965	−	0.971678i
$724$		0			0
$725$		−	1136.47i		−	1.56754i
$726$		0			0
$727$	555.398			0.763958			0.381979	−	0.924171i	$-0.375243\pi$
$727$	555.398			0.763958			0.381979	+	0.924171i	$0.375243\pi$
$728$		0			0
$729$	−425.401	+	309.072i	−0.583540	+	0.423967i
$730$		0			0
$731$	−487.786	−	1501.25i	−0.667285	−	2.05369i
$732$		0			0
$733$	731.615	−	1006.98i	0.998110	−	1.37378i	0.0716329	−	0.997431i	$-0.477179\pi$
$733$	731.615	−	1006.98i	0.998110	−	1.37378i	0.926478	−	0.376350i	$-0.122821\pi$
$734$		0			0
$735$	5.19502	−	15.9886i	0.00706806	−	0.0217532i
$736$		0			0
$737$	778.301	+	880.396i	1.05604	+	1.19457i
$738$		0			0
$739$	665.401	+	216.202i	0.900407	+	0.292560i	0.722405	−	0.691470i	$-0.243037\pi$
$739$	665.401	+	216.202i	0.900407	+	0.292560i	0.178002	+	0.984030i	$0.443037\pi$
$740$		0			0
$741$	−8.98261	−	6.52625i	−0.0121223	−	0.00880735i
$742$		0			0
$743$	−687.235	+	223.296i	−0.924946	+	0.300533i	−0.732494	−	0.680773i	$-0.761644\pi$
$743$	−687.235	+	223.296i	−0.924946	+	0.300533i	−0.192452	+	0.981306i	$0.561644\pi$
$744$		0			0
$745$	−67.1563	−	92.4327i	−0.0901427	−	0.124071i
$746$		0			0
$747$			64.4177i			0.0862352i
$748$		0			0
$749$	424.114			0.566241
$750$		0			0
$751$	−486.087	+	353.163i	−0.647253	+	0.470257i	−0.862334	−	0.506339i	$-0.830998\pi$
$751$	−486.087	+	353.163i	−0.647253	+	0.470257i	0.215081	+	0.976596i	$0.430998\pi$
$752$		0			0
$753$	482.281	+	1484.31i	0.640479	+	1.97119i
$754$		0			0
$755$	−23.2195	+	31.9589i	−0.0307543	+	0.0423297i
$756$		0			0
$757$	−372.124	+	1145.28i	−0.491577	+	1.51292i	0.330646	+	0.943755i	$0.392733\pi$
$757$	−372.124	+	1145.28i	−0.491577	+	1.51292i	−0.822223	+	0.569165i	$0.807267\pi$
$758$		0			0
$759$	468.151	+	103.977i	0.616800	+	0.136992i
$760$		0			0
$761$	−347.241	−	112.825i	−0.456296	−	0.148260i	0.0718459	−	0.997416i	$-0.477111\pi$
$761$	−347.241	−	112.825i	−0.456296	−	0.148260i	−0.528142	+	0.849156i	$0.677111\pi$
$762$		0			0
$763$	−361.013	−	262.291i	−0.473149	−	0.343763i
$764$		0			0
$765$	−24.7117	+	8.02932i	−0.0323029	+	0.0104958i
$766$		0			0
$767$	−170.990	−	235.348i	−0.222934	−	0.306842i
$768$		0			0
$769$			1046.99i			1.36149i	0.732519	+	0.680747i	$0.238345\pi$
$769$			1046.99i			1.36149i	−0.732519	+	0.680747i	$0.761655\pi$
$770$		0			0
$771$	−800.175			−1.03784
$772$		0			0
$773$	−564.311	+	409.996i	−0.730027	+	0.530396i	−0.889572	−	0.456795i	$-0.848997\pi$
$773$	−564.311	+	409.996i	−0.730027	+	0.530396i	0.159545	+	0.987191i	$0.448997\pi$
$774$		0			0
$775$	−135.384	−	416.668i	−0.174688	−	0.537636i
$776$		0			0
$777$	−57.0307	+	78.4960i	−0.0733986	+	0.101024i
$778$		0			0
$779$	7.68146	−	23.6411i	0.00986067	−	0.0303480i
$780$		0			0
$781$	−456.096	+	773.612i	−0.583989	+	0.990540i
$782$		0			0
$783$	−1041.76	−	338.490i	−1.33048	−	0.432298i
$784$		0			0
$785$	150.841	+	109.592i	0.192154	+	0.139608i
$786$		0			0
$787$	−994.963	+	323.283i	−1.26425	+	0.410779i	−0.863006	−	0.505193i	$-0.831421\pi$
$787$	−994.963	+	323.283i	−1.26425	+	0.410779i	−0.401242	+	0.915972i	$0.631421\pi$
$788$		0			0
$789$	549.758	+	756.677i	0.696778	+	0.959033i
$790$		0			0
$791$			52.0212i			0.0657663i
$792$		0			0
$793$	−183.592			−0.231516
$794$		0			0
$795$	79.8300	−	57.9999i	0.100415	−	0.0729559i
$796$		0			0
$797$	−293.265	−	902.578i	−0.367962	−	1.13247i	−0.948106	−	0.317956i	$-0.897004\pi$
$797$	−293.265	−	902.578i	−0.367962	−	1.13247i	0.580144	−	0.814514i	$-0.302996\pi$
$798$		0			0
$799$	−857.830	+	1180.70i	−1.07363	+	1.47772i
$800$		0			0
$801$	−35.6147	+	109.611i	−0.0444627	+	0.136842i
$802$		0			0
$803$	133.072	−	12.7614i	0.165719	−	0.0158922i
$804$		0			0
$805$	−24.3137	−	7.89998i	−0.0302033	−	0.00981365i
$806$		0			0
$807$	−934.244	−	678.768i	−1.15768	−	0.841101i
$808$		0			0
$809$	11.4970	−	3.73562i	0.0142114	−	0.00461757i	−0.301903	−	0.953339i	$-0.597622\pi$
$809$	11.4970	−	3.73562i	0.0142114	−	0.00461757i	0.316114	+	0.948721i	$0.397622\pi$
$810$		0			0
$811$	652.307	+	897.824i	0.804325	+	1.10706i	0.992174	+	0.124860i	$0.0398482\pi$
$811$	652.307	+	897.824i	0.804325	+	1.10706i	−0.187850	+	0.982198i	$0.560152\pi$
$812$		0			0
$813$		−	168.748i		−	0.207562i
$814$		0			0
$815$	−53.3012			−0.0654002
$816$		0			0
$817$	−33.1383	+	24.0764i	−0.0405609	+	0.0294692i
$818$		0			0
$819$	10.0566	+	30.9511i	0.0122791	+	0.0377913i
$820$		0			0
$821$	−170.139	+	234.176i	−0.207233	+	0.285232i	−0.899964	−	0.435964i	$-0.856407\pi$
$821$	−170.139	+	234.176i	−0.207233	+	0.285232i	0.692731	+	0.721196i	$0.256407\pi$
$822$		0			0
$823$	−235.124	+	723.639i	−0.285692	+	0.879269i	0.700498	+	0.713654i	$0.252961\pi$
$823$	−235.124	+	723.639i	−0.285692	+	0.879269i	−0.986190	+	0.165615i	$0.947039\pi$
$824$		0			0
$825$	812.620	−	352.963i	0.984993	−	0.427834i
$826$		0			0
$827$	606.549	+	197.080i	0.733433	+	0.238307i	0.651838	−	0.758359i	$-0.273998\pi$
$827$	606.549	+	197.080i	0.733433	+	0.238307i	0.0815956	+	0.996666i	$0.473998\pi$
$828$		0			0
$829$	270.269	+	196.362i	0.326019	+	0.236866i	0.738739	−	0.673991i	$-0.235421\pi$
$829$	270.269	+	196.362i	0.326019	+	0.236866i	−0.412721	+	0.910858i	$0.635421\pi$
$830$		0			0
$831$	−172.256	+	55.9695i	−0.207288	+	0.0673519i
$832$		0			0
$833$	−79.8199	−	109.863i	−0.0958222	−	0.131888i
$834$		0			0
$835$			2.25760i			0.00270371i
$836$		0			0
$837$	−422.268			−0.504502
$838$		0			0
$839$	−673.488	+	489.318i	−0.802727	+	0.583215i	−0.911713	−	0.410828i	$-0.865240\pi$
$839$	−673.488	+	489.318i	−0.802727	+	0.583215i	0.108986	+	0.994043i	$0.465240\pi$
$840$		0			0
$841$	−406.788	−	1251.97i	−0.483696	−	1.48866i
$842$		0			0
$843$	1.16037	−	1.59711i	0.00137648	−	0.00189456i
$844$		0			0
$845$	−27.9802	+	86.1143i	−0.0331127	+	0.101910i
$846$		0			0
$847$	233.964	+	218.513i	0.276226	+	0.257985i
$848$		0			0
$849$	192.053	+	62.4019i	0.226211	+	0.0735005i
$850$		0			0
$851$	119.368	+	86.7256i	0.140267	+	0.101910i
$852$		0			0
$853$	1409.56	−	457.995i	1.65248	−	0.536922i	0.673203	−	0.739458i	$-0.264918\pi$
$853$	1409.56	−	457.995i	1.65248	−	0.536922i	0.979275	+	0.202536i	$0.0649182\pi$
$854$		0			0
$855$	0.396315	+	0.545481i	0.000463526	+	0.000637989i
$856$		0			0
$857$		−	55.4569i		−	0.0647105i	−0.999476	−	0.0323553i	$-0.989699\pi$
$857$		−	55.4569i		−	0.0647105i	0.999476	−	0.0323553i	$-0.0103008\pi$
$858$		0			0
$859$	−1652.01			−1.92318			−0.961590	−	0.274491i	$-0.911491\pi$
$859$	−1652.01			−1.92318			−0.961590	+	0.274491i	$0.911491\pi$
$860$		0			0
$861$	−347.920	+	252.778i	−0.404088	+	0.293587i
$862$		0			0
$863$	−100.362	−	308.882i	−0.116294	−	0.357916i	0.875921	−	0.482455i	$-0.160255\pi$
$863$	−100.362	−	308.882i	−0.116294	−	0.357916i	−0.992215	+	0.124539i	$0.960255\pi$
$864$		0			0
$865$	60.1672	−	82.8131i	0.0695575	−	0.0957376i
$866$		0			0
$867$	−88.8507	+	273.454i	−0.102481	+	0.315403i
$868$		0			0
$869$	370.876	+	853.860i	0.426785	+	0.982577i
$870$		0			0
$871$	680.741	+	221.186i	0.781562	+	0.253945i
$872$		0			0
$873$	−62.9246	−	45.7174i	−0.0720786	−	0.0523682i
$874$		0			0
$875$	−90.8141	+	29.5073i	−0.103788	+	0.0337226i
$876$		0			0
$877$	−703.860	−	968.780i	−0.802577	−	1.10465i	−0.992427	−	0.122839i	$-0.960800\pi$
$877$	−703.860	−	968.780i	−0.802577	−	1.10465i	0.189849	−	0.981813i	$-0.439200\pi$
$878$		0			0
$879$		−	971.029i		−	1.10470i
$880$		0			0
$881$	266.596			0.302606			0.151303	−	0.988487i	$-0.451653\pi$
$881$	266.596			0.302606			0.151303	+	0.988487i	$0.451653\pi$
$882$		0			0
$883$	−1137.53	+	826.466i	−1.28826	+	0.935975i	−0.999769	−	0.0215075i	$-0.993153\pi$
$883$	−1137.53	+	826.466i	−1.28826	+	0.935975i	−0.288491	+	0.957483i	$0.593153\pi$
$884$		0			0
$885$	32.2216	+	99.1679i	0.0364086	+	0.112054i
$886$		0			0
$887$	−47.3199	+	65.1303i	−0.0533483	+	0.0734276i	−0.834858	−	0.550466i	$-0.814450\pi$
$887$	−47.3199	+	65.1303i	−0.0533483	+	0.0734276i	0.781509	+	0.623894i	$0.214450\pi$
$888$		0			0
$889$	35.3011	−	108.646i	0.0397088	−	0.122211i
$890$		0			0
$891$	−98.8658	−	1030.94i	−0.110961	−	1.15706i
$892$		0			0
$893$	36.0176	+	11.7028i	0.0403332	+	0.0131051i
$894$		0			0
$895$	−62.9819	−	45.7590i	−0.0703708	−	0.0511274i
$896$		0			0
$897$	277.811	−	90.2664i	0.309712	−	0.100631i
$898$		0			0
$899$	−488.848	−	672.842i	−0.543769	−	0.748433i
$900$		0			0
$901$		−	797.069i		−	0.884650i
$902$		0			0
$903$	708.650			0.784773
$904$		0			0
$905$	−167.745	+	121.874i	−0.185353	+	0.134667i
$906$		0			0
$907$	481.906	+	1483.15i	0.531319	+	1.63523i	0.751472	+	0.659765i	$0.229344\pi$
$907$	481.906	+	1483.15i	0.531319	+	1.63523i	−0.220153	+	0.975465i	$0.570656\pi$
$908$		0			0
$909$	−33.7638	+	46.4719i	−0.0371439	+	0.0511242i
$910$		0			0
$911$	−144.613	+	445.072i	−0.158741	+	0.488553i	−0.998521	−	0.0543735i	$-0.982684\pi$
$911$	−144.613	+	445.072i	−0.158741	+	0.488553i	0.839780	+	0.542927i	$0.182684\pi$
$912$		0			0
$913$	332.501	+	196.032i	0.364185	+	0.214711i
$914$		0			0
$915$	62.5855	+	20.3352i	0.0683994	+	0.0222243i
$916$		0			0
$917$	−6.12953	−	4.45336i	−0.00668432	−	0.00485645i
$918$		0			0
$919$	28.2909	−	9.19226i	0.0307844	−	0.0100025i	−0.293584	−	0.955933i	$-0.594848\pi$
$919$	28.2909	−	9.19226i	0.0307844	−	0.0100025i	0.324369	+	0.945931i	$0.394848\pi$
$920$		0			0
$921$	−977.530	−	1345.46i	−1.06138	−	1.46086i
$922$		0			0
$923$			547.021i			0.592655i
$924$		0			0
$925$	272.586			0.294688
$926$		0			0
$927$	116.000	−	84.2787i	0.125134	−	0.0909155i
$928$		0			0
$929$	−264.447	−	813.885i	−0.284658	−	0.876087i	−0.986501	−	0.163755i	$-0.947639\pi$
$929$	−264.447	−	813.885i	−0.284658	−	0.876087i	0.701843	−	0.712332i	$-0.252361\pi$
$930$		0			0
$931$	−2.07127	+	2.85086i	−0.00222478	+	0.00306214i
$932$		0			0
$933$	−426.597	+	1312.93i	−0.457231	+	1.40721i
$934$		0			0
$935$	−33.7565	+	151.987i	−0.0361032	+	0.162553i
$936$		0			0
$937$	797.282	+	259.053i	0.850888	+	0.276470i	0.701818	−	0.712356i	$-0.252372\pi$
$937$	797.282	+	259.053i	0.850888	+	0.276470i	0.149070	+	0.988827i	$0.452372\pi$
$938$		0			0
$939$	421.669	+	306.360i	0.449062	+	0.326262i
$940$		0			0
$941$	−6.62900	+	2.15389i	−0.00704463	+	0.00228894i	−0.312537	−	0.949906i	$-0.601179\pi$
$941$	−6.62900	+	2.15389i	−0.00704463	+	0.00228894i	0.305493	+	0.952194i	$0.401179\pi$
$942$		0			0
$943$	384.396	+	529.076i	0.407631	+	0.561056i
$944$		0			0
$945$			45.5222i			0.0481717i
$946$		0			0
$947$	1691.21			1.78586			0.892931	−	0.450193i	$-0.148645\pi$
$947$	1691.21			1.78586			0.892931	+	0.450193i	$0.148645\pi$
$948$		0			0
$949$	65.8771	−	47.8625i	0.0694174	−	0.0504347i
$950$		0			0
$951$	−372.877	−	1147.60i	−0.392090	−	1.20673i
$952$		0			0
$953$	630.675	−	868.050i	0.661779	−	0.910861i	−0.337760	−	0.941232i	$-0.609669\pi$
$953$	630.675	−	868.050i	0.661779	−	0.910861i	0.999539	+	0.0303718i	$0.00966914\pi$
$954$		0			0
$955$	28.2467	−	86.9344i	0.0295777	−	0.0910307i
$956$		0			0
$957$	1260.06	−	1113.94i	1.31668	−	1.16399i
$958$		0			0
$959$	5.90832	+	1.91973i	0.00616092	+	0.00200180i
$960$		0			0
$961$	518.084	+	376.410i	0.539110	+	0.391686i
$962$		0			0
$963$	279.876	−	90.9373i	0.290630	−	0.0944313i
$964$		0			0
$965$	−39.6002	−	54.5050i	−0.0410364	−	0.0564818i
$966$		0			0
$967$			712.339i			0.736649i	0.929697	+	0.368324i	$0.120068\pi$
$967$			712.339i			0.736649i	−0.929697	+	0.368324i	$0.879932\pi$
$968$		0			0
$969$	32.1473			0.0331757
$970$		0			0
$971$	999.926	−	726.489i	1.02979	−	0.748186i	0.0615232	−	0.998106i	$-0.480404\pi$
$971$	999.926	−	726.489i	1.02979	−	0.748186i	0.968267	+	0.249920i	$0.0804042\pi$
$972$		0			0
$973$	−20.5472	−	63.2378i	−0.0211174	−	0.0649926i
$974$		0			0
$975$	317.203	−	436.592i	0.325336	−	0.447787i
$976$		0			0
$977$	−460.828	+	1418.28i	−0.471676	+	1.45167i	0.378712	+	0.925515i	$0.376367\pi$
$977$	−460.828	+	1418.28i	−0.471676	+	1.45167i	−0.850388	+	0.526156i	$0.823633\pi$
$978$		0			0
$979$	457.391	+	517.390i	0.467202	+	0.528488i
$980$		0			0
$981$	−294.475	−	95.6806i	−0.300178	−	0.0975338i
$982$		0			0
$983$	−1087.98	−	790.467i	−1.10680	−	0.804138i	−0.124644	−	0.992202i	$-0.539779\pi$
$983$	−1087.98	−	790.467i	−1.10680	−	0.804138i	−0.982157	+	0.188064i	$0.939779\pi$
$984$		0			0
$985$	128.899	−	41.8819i	0.130862	−	0.0425197i
$986$		0			0
$987$	−385.112	−	530.061i	−0.390184	−	0.537042i
$988$		0			0
$989$		−	1077.63i		−	1.08962i
$990$		0			0
$991$	1616.65			1.63134			0.815668	−	0.578520i	$-0.196370\pi$
$991$	1616.65			1.63134			0.815668	+	0.578520i	$0.196370\pi$
$992$		0			0
$993$	−365.056	+	265.228i	−0.367629	+	0.267098i
$994$		0			0
$995$	−48.5034	−	149.278i	−0.0487472	−	0.150028i
$996$		0			0
$997$	575.009	−	791.432i	0.576739	−	0.793813i	−0.416594	−	0.909093i	$-0.636776\pi$
$997$	575.009	−	791.432i	0.576739	−	0.793813i	0.993333	+	0.115279i	$0.0367764\pi$
$998$		0			0
$999$	81.1878	−	249.870i	0.0812691	−	0.250121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.3.r.a.57.3	✓	48
11.6	odd	10	inner	308.3.r.a.281.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.3.r.a.57.3	✓	48	1.1	even	1	trivial
308.3.r.a.281.3	yes	48	11.6	odd	10	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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	308.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.66310 + 1.93486i) q^{3} +(-0.225454 - 0.693877i) q^{5} +(1.55513 - 2.14046i) q^{7} +(0.567294 - 1.74595i) q^{9} +O(q^{10})\)	\(q+(-2.66310 + 1.93486i) q^{3} +(-0.225454 - 0.693877i) q^{5} +(1.55513 - 2.14046i) q^{7} +(0.567294 - 1.74595i) q^{9} +(-7.28563 - 8.24133i) q^{11} +(-6.37237 - 2.07051i) q^{13} +(1.94296 + 1.41165i) q^{15} +(18.4502 - 5.99483i) q^{17} +(-0.295896 - 0.407265i) q^{19} +8.70923i q^{21} +13.2440 q^{23} +(19.7948 - 14.3818i) q^{25} +(-7.28753 - 22.4287i) q^{27} +(27.3013 - 37.5770i) q^{29} +(5.53315 - 17.0293i) q^{31} +(35.3482 + 7.85086i) q^{33} +(-1.83583 - 0.596496i) q^{35} +(9.01297 + 6.54831i) q^{37} +(20.9764 - 6.81566i) q^{39} +(29.0242 + 39.9484i) q^{41} -81.3678i q^{43} -1.33937 q^{45} +(-60.8620 + 44.2188i) q^{47} +(-2.16312 - 6.65740i) q^{49} +(-37.5356 + 51.6633i) q^{51} +(12.6965 - 39.0758i) q^{53} +(-4.07590 + 6.91338i) q^{55} +(1.57600 + 0.512074i) q^{57} +(35.1249 + 25.5198i) q^{59} +(26.0595 - 8.46725i) q^{61} +(-2.85492 - 3.92946i) q^{63} +4.88845i q^{65} -106.827 q^{67} +(-35.2701 + 25.6252i) q^{69} +(-25.2285 - 77.6454i) q^{71} +(-7.14333 + 9.83196i) q^{73} +(-24.8889 + 76.6002i) q^{75} +(-28.9704 + 2.77821i) q^{77} +(-80.4877 - 26.1520i) q^{79} +(76.1706 + 55.3412i) q^{81} +(-33.3722 + 10.8433i) q^{83} +(-8.31935 - 11.4506i) q^{85} +152.896i q^{87} -62.7799 q^{89} +(-14.3417 + 10.4199i) q^{91} +(18.2139 + 56.0567i) q^{93} +(-0.215881 + 0.297135i) q^{95} +(13.0924 - 40.2943i) q^{97} +(-18.5221 + 8.04510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9}+O(q^{10}) \) 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9	\( 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9} - 10 q^{11} + 30 q^{13} + 24 q^{15} + 60 q^{19} - 132 q^{23} - 186 q^{25} - 110 q^{27} - 90 q^{29} - 26 q^{31} + 46 q^{33} + 82 q^{37} + 290 q^{39} - 336 q^{45} + 84 q^{47} + 84 q^{49} - 20 q^{51} + 58 q^{53} + 370 q^{55} - 20 q^{57} + 436 q^{59} + 160 q^{61} + 276 q^{67} - 118 q^{69} - 150 q^{71} - 320 q^{73} - 692 q^{75} + 28 q^{77} - 560 q^{79} + 122 q^{81} - 630 q^{83} + 220 q^{85} - 444 q^{89} - 126 q^{91} + 500 q^{93} + 440 q^{95} - 80 q^{97} + 1034 q^{99}+O(q^{100}) \) 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9 - 10 * q^11 + 30 * q^13 + 24 * q^15 + 60 * q^19 - 132 * q^23 - 186 * q^25 - 110 * q^27 - 90 * q^29 - 26 * q^31 + 46 * q^33 + 82 * q^37 + 290 * q^39 - 336 * q^45 + 84 * q^47 + 84 * q^49 - 20 * q^51 + 58 * q^53 + 370 * q^55 - 20 * q^57 + 436 * q^59 + 160 * q^61 + 276 * q^67 - 118 * q^69 - 150 * q^71 - 320 * q^73 - 692 * q^75 + 28 * q^77 - 560 * q^79 + 122 * q^81 - 630 * q^83 + 220 * q^85 - 444 * q^89 - 126 * q^91 + 500 * q^93 + 440 * q^95 - 80 * q^97 + 1034 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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