LMFDB - Embedded newform 1008.2.q.i.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(529,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))

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

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

chi := DirichletCharacter("1008.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.1
Root			$-0.335166 + 0.580525i$ of defining polynomial
Character	$\chi$	$=$	1008.529
Dual form			1008.2.q.i.625.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65263 + 0.518475i) q^{3} +(-0.712469 + 1.23403i) q^{5} +(2.36039 + 1.19522i) q^{7} +(2.46237 - 1.71369i) q^{9} +O(q^{10})$	\(q+(-1.65263 + 0.518475i) q^{3} +(-0.712469 + 1.23403i) q^{5} +(2.36039 + 1.19522i) q^{7} +(2.46237 - 1.71369i) q^{9} +(-2.46539 - 4.27018i) q^{11} +(-1.37730 - 2.38556i) q^{13} +(0.537632 - 2.40879i) q^{15} +(0.559839 - 0.969670i) q^{17} +(2.00752 + 3.47713i) q^{19} +(-4.52054 - 0.751449i) q^{21} +(2.71830 - 4.70824i) q^{23} +(1.48478 + 2.57171i) q^{25} +(-3.18087 + 4.10878i) q^{27} +(3.40555 - 5.89858i) q^{29} -2.50584 q^{31} +(6.28835 + 5.77878i) q^{33} +(-3.15664 + 2.06124i) q^{35} +(0.709787 + 1.22939i) q^{37} +(3.51302 + 3.22835i) q^{39} +(0.124384 + 0.215440i) q^{41} +(0.498313 - 0.863104i) q^{43} +(0.360392 + 4.25959i) q^{45} +9.47579 q^{47} +(4.14291 + 5.64237i) q^{49} +(-0.422457 + 1.89277i) q^{51} +(-0.410229 + 0.710537i) q^{53} +7.02604 q^{55} +(-5.12050 - 4.70556i) q^{57} +6.58407 q^{59} +0.0752645 q^{61} +(7.86039 - 1.10192i) q^{63} +3.92514 q^{65} +12.5877 q^{67} +(-2.05125 + 9.19035i) q^{69} -0.0804951 q^{71} +(5.34551 - 9.25869i) q^{73} +(-3.78715 - 3.48026i) q^{75} +(-0.715488 - 13.0260i) q^{77} +1.84491 q^{79} +(3.12651 - 8.43949i) q^{81} +(7.23583 - 12.5328i) q^{83} +(0.797736 + 1.38172i) q^{85} +(-2.56984 + 11.5139i) q^{87} +(6.76292 + 11.7137i) q^{89} +(-0.399711 - 7.27703i) q^{91} +(4.14122 - 1.29921i) q^{93} -5.72119 q^{95} +(2.70160 - 4.67930i) q^{97} +(-13.3885 - 6.28982i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} + 4 q^{5} + 4 q^{7} + 11 q^{9}+O(q^{10}) $ 10 * q + q^3 + 4 * q^5 + 4 * q^7 + 11 * q^9	$ 10 q + q^{3} + 4 q^{5} + 4 q^{7} + 11 q^{9} - 4 q^{11} - 8 q^{13} + 19 q^{15} + 12 q^{17} - q^{19} + 13 q^{21} - 3 q^{23} - q^{25} + 7 q^{27} + 7 q^{29} - 6 q^{31} + 14 q^{33} - 5 q^{35} - 2 q^{39} + 5 q^{41} + 7 q^{43} - 16 q^{45} + 54 q^{47} - 8 q^{49} + 9 q^{51} - 21 q^{53} - 4 q^{55} - 4 q^{57} + 60 q^{59} + 28 q^{61} + 59 q^{63} + 22 q^{65} - 4 q^{67} + 15 q^{69} + 6 q^{71} + 15 q^{73} + 14 q^{75} + 11 q^{77} - 8 q^{79} + 23 q^{81} - 9 q^{83} - 6 q^{85} - 2 q^{87} + 28 q^{89} + 4 q^{91} - 6 q^{93} - 28 q^{95} - 12 q^{97} - 35 q^{99}+O(q^{100}) $ 10 * q + q^3 + 4 * q^5 + 4 * q^7 + 11 * q^9 - 4 * q^11 - 8 * q^13 + 19 * q^15 + 12 * q^17 - q^19 + 13 * q^21 - 3 * q^23 - q^25 + 7 * q^27 + 7 * q^29 - 6 * q^31 + 14 * q^33 - 5 * q^35 - 2 * q^39 + 5 * q^41 + 7 * q^43 - 16 * q^45 + 54 * q^47 - 8 * q^49 + 9 * q^51 - 21 * q^53 - 4 * q^55 - 4 * q^57 + 60 * q^59 + 28 * q^61 + 59 * q^63 + 22 * q^65 - 4 * q^67 + 15 * q^69 + 6 * q^71 + 15 * q^73 + 14 * q^75 + 11 * q^77 - 8 * q^79 + 23 * q^81 - 9 * q^83 - 6 * q^85 - 2 * q^87 + 28 * q^89 + 4 * q^91 - 6 * q^93 - 28 * q^95 - 12 * q^97 - 35 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.65263	+	0.518475i	−0.954146	+	0.299342i
$3$	−1.65263	+	0.518475i	−0.954146	+	0.299342i
$4$		0			0
$5$	−0.712469	+	1.23403i	−0.318626	+	0.551876i	−0.980202	−	0.198002i	$-0.936555\pi$
$5$	−0.712469	+	1.23403i	−0.318626	+	0.551876i	0.661576	+	0.749878i	$0.269888\pi$
$6$		0			0
$7$	2.36039	+	1.19522i	0.892144	+	0.451750i
$7$	2.36039	+	1.19522i	0.892144	+	0.451750i
$8$		0			0
$9$	2.46237	−	1.71369i	0.820789	−	0.571231i
$10$		0			0
$11$	−2.46539	−	4.27018i	−0.743342	−	1.28751i	−0.950965	−	0.309297i	$-0.899906\pi$
$11$	−2.46539	−	4.27018i	−0.743342	−	1.28751i	0.207623	−	0.978209i	$-0.433427\pi$
$12$		0			0
$13$	−1.37730	−	2.38556i	−0.381995	−	0.661635i	0.609352	−	0.792900i	$-0.291429\pi$
$13$	−1.37730	−	2.38556i	−0.381995	−	0.661635i	−0.991347	+	0.131265i	$0.958096\pi$
$14$		0			0
$15$	0.537632	−	2.40879i	0.138816	−	0.621948i
$16$		0			0
$17$	0.559839	−	0.969670i	0.135781	−	0.235180i	−0.790115	−	0.612959i	$-0.789979\pi$
$17$	0.559839	−	0.969670i	0.135781	−	0.235180i	0.925896	+	0.377780i	$0.123312\pi$
$18$		0			0
$19$	2.00752	+	3.47713i	0.460557	+	0.797709i	0.998989	−	0.0449606i	$-0.0143162\pi$
$19$	2.00752	+	3.47713i	0.460557	+	0.797709i	−0.538431	+	0.842669i	$0.680983\pi$
$20$		0			0
$21$	−4.52054	−	0.751449i	−0.986464	−	0.163980i
$22$		0			0
$23$	2.71830	−	4.70824i	0.566806	−	0.981736i	−0.430073	−	0.902794i	$-0.641512\pi$
$23$	2.71830	−	4.70824i	0.566806	−	0.981736i	0.996879	−	0.0789424i	$-0.0251543\pi$
$24$		0			0
$25$	1.48478	+	2.57171i	0.296955	+	0.514342i
$26$		0			0
$27$	−3.18087	+	4.10878i	−0.612160	+	0.790734i
$28$		0			0
$29$	3.40555	−	5.89858i	0.632394	−	1.09534i	−0.354667	−	0.934993i	$-0.615406\pi$
$29$	3.40555	−	5.89858i	0.632394	−	1.09534i	0.987061	−	0.160346i	$-0.0512611\pi$
$30$		0			0
$31$	−2.50584			−0.450061			−0.225031	−	0.974352i	$-0.572248\pi$
$31$	−2.50584			−0.450061			−0.225031	+	0.974352i	$0.572248\pi$
$32$		0			0
$33$	6.28835	+	5.77878i	1.09466	+	1.00596i
$34$		0			0
$35$	−3.15664	+	2.06124i	−0.533570	+	0.348414i
$36$		0			0
$37$	0.709787	+	1.22939i	0.116688	+	0.202110i	0.918453	−	0.395529i	$-0.129439\pi$
$37$	0.709787	+	1.22939i	0.116688	+	0.202110i	−0.801765	+	0.597639i	$0.796106\pi$
$38$		0			0
$39$	3.51302	+	3.22835i	0.562534	+	0.516949i
$40$		0			0
$41$	0.124384	+	0.215440i	0.0194256	+	0.0336460i	0.875575	−	0.483083i	$-0.160483\pi$
$41$	0.124384	+	0.215440i	0.0194256	+	0.0336460i	−0.856149	+	0.516729i	$0.827150\pi$
$42$		0			0
$43$	0.498313	−	0.863104i	0.0759921	−	0.131622i	−0.825525	−	0.564365i	$-0.809121\pi$
$43$	0.498313	−	0.863104i	0.0759921	−	0.131622i	0.901517	+	0.432743i	$0.142454\pi$
$44$		0			0
$45$	0.360392	+	4.25959i	0.0537241	+	0.634983i
$46$		0			0
$47$	9.47579			1.38219			0.691093	−	0.722766i	$-0.257129\pi$
$47$	9.47579			1.38219			0.691093	+	0.722766i	$0.257129\pi$
$48$		0			0
$49$	4.14291	+	5.64237i	0.591844	+	0.806053i
$50$		0			0
$51$	−0.422457	+	1.89277i	−0.0591559	+	0.265041i
$52$		0			0
$53$	−0.410229	+	0.710537i	−0.0563493	+	0.0975998i	−0.892824	−	0.450406i	$-0.851279\pi$
$53$	−0.410229	+	0.710537i	−0.0563493	+	0.0975998i	0.836475	+	0.548005i	$0.184613\pi$
$54$		0			0
$55$	7.02604			0.947392
$56$		0			0
$57$	−5.12050	−	4.70556i	−0.678226	−	0.623267i
$58$		0			0
$59$	6.58407			0.857173			0.428586	−	0.903501i	$-0.359012\pi$
$59$	6.58407			0.857173			0.428586	+	0.903501i	$0.359012\pi$
$60$		0			0
$61$	0.0752645			0.00963663			0.00481831	−	0.999988i	$-0.498466\pi$
$61$	0.0752645			0.00963663			0.00481831	+	0.999988i	$0.498466\pi$
$62$		0			0
$63$	7.86039	−	1.10192i	0.990316	−	0.138829i
$64$		0			0
$65$	3.92514			0.486854
$66$		0			0
$67$	12.5877			1.53783			0.768916	−	0.639350i	$-0.220796\pi$
$67$	12.5877			1.53783			0.768916	+	0.639350i	$0.220796\pi$
$68$		0			0
$69$	−2.05125	+	9.19035i	−0.246941	+	1.10639i
$70$		0			0
$71$	−0.0804951			−0.00955301			−0.00477651	−	0.999989i	$-0.501520\pi$
$71$	−0.0804951			−0.00955301			−0.00477651	+	0.999989i	$0.501520\pi$
$72$		0			0
$73$	5.34551	−	9.25869i	0.625644	−	1.08365i	−0.362772	−	0.931878i	$-0.618170\pi$
$73$	5.34551	−	9.25869i	0.625644	−	1.08365i	0.988416	−	0.151769i	$-0.0484971\pi$
$74$		0			0
$75$	−3.78715	−	3.48026i	−0.437303	−	0.401866i
$76$		0			0
$77$	−0.715488	−	13.0260i	−0.0815374	−	1.48445i
$78$		0			0
$79$	1.84491			0.207569			0.103785	−	0.994600i	$-0.466905\pi$
$79$	1.84491			0.207569			0.103785	+	0.994600i	$0.466905\pi$
$80$		0			0
$81$	3.12651	−	8.43949i	0.347390	−	0.937721i
$82$		0			0
$83$	7.23583	−	12.5328i	0.794236	−	1.37566i	−0.129088	−	0.991633i	$-0.541205\pi$
$83$	7.23583	−	12.5328i	0.794236	−	1.37566i	0.923323	−	0.384023i	$-0.125462\pi$
$84$		0			0
$85$	0.797736	+	1.38172i	0.0865266	+	0.149868i
$86$		0			0
$87$	−2.56984	+	11.5139i	−0.275516	+	1.23442i
$88$		0			0
$89$	6.76292	+	11.7137i	0.716868	+	1.24165i	0.962235	+	0.272222i	$0.0877584\pi$
$89$	6.76292	+	11.7137i	0.716868	+	1.24165i	−0.245366	+	0.969430i	$0.578908\pi$
$90$		0			0
$91$	−0.399711	−	7.27703i	−0.0419011	−	0.762840i
$92$		0			0
$93$	4.14122	−	1.29921i	0.429424	−	0.134722i
$94$		0			0
$95$	−5.72119			−0.586982
$96$		0			0
$97$	2.70160	−	4.67930i	0.274306	−	0.475111i	−0.695654	−	0.718377i	$-0.744885\pi$
$97$	2.70160	−	4.67930i	0.274306	−	0.475111i	0.969960	+	0.243266i	$0.0782187\pi$
$98$		0			0
$99$	−13.3885	−	6.28982i	−1.34559	−	0.632151i
$100$		0			0
$101$	2.56770	+	4.44739i	0.255496	+	0.442531i	0.965030	−	0.262139i	$-0.0844280\pi$
$101$	2.56770	+	4.44739i	0.255496	+	0.442531i	−0.709534	+	0.704671i	$0.751095\pi$
$102$		0			0
$103$	−7.10561	+	12.3073i	−0.700137	+	1.21267i	0.268282	+	0.963341i	$0.413544\pi$
$103$	−7.10561	+	12.3073i	−0.700137	+	1.21267i	−0.968418	+	0.249332i	$0.919789\pi$
$104$		0			0
$105$	4.14806	−	5.04311i	0.404809	−	0.492157i
$106$		0			0
$107$	−3.83015	−	6.63401i	−0.370274	−	0.641334i	0.619333	−	0.785128i	$-0.287403\pi$
$107$	−3.83015	−	6.63401i	−0.370274	−	0.641334i	−0.989608	+	0.143794i	$0.954070\pi$
$108$		0			0
$109$	−0.849394	+	1.47119i	−0.0813572	+	0.140915i	−0.903833	−	0.427885i	$-0.859259\pi$
$109$	−0.849394	+	1.47119i	−0.0813572	+	0.140915i	0.822476	+	0.568800i	$0.192592\pi$
$110$		0			0
$111$	−1.81042	−	1.66371i	−0.171838	−	0.157913i
$112$		0			0
$113$	−0.300351	−	0.520224i	−0.0282547	−	0.0489385i	0.851552	−	0.524270i	$-0.175662\pi$
$113$	−0.300351	−	0.520224i	−0.0282547	−	0.0489385i	−0.879807	+	0.475331i	$0.842328\pi$
$114$		0			0
$115$	3.87341	+	6.70895i	0.361198	+	0.625613i
$116$		0			0
$117$	−7.47954	−	3.51385i	−0.691484	−	0.324855i
$118$		0			0
$119$	2.48041	−	1.61967i	0.227379	−	0.148475i
$120$		0			0
$121$	−6.65626	+	11.5290i	−0.605115	+	1.04809i
$122$		0			0
$123$	−0.317261	−	0.291552i	−0.0286065	−	0.0262884i
$124$		0			0
$125$	−11.3561			−1.01572
$126$		0			0
$127$	−7.25977			−0.644200			−0.322100	−	0.946706i	$-0.604389\pi$
$127$	−7.25977			−0.644200			−0.322100	+	0.946706i	$0.604389\pi$
$128$		0			0
$129$	−0.376030	+	1.68475i	−0.0331076	+	0.148334i
$130$		0			0
$131$	−10.2265	+	17.7128i	−0.893492	+	1.54757i	−0.0578326	+	0.998326i	$0.518419\pi$
$131$	−10.2265	+	17.7128i	−0.893492	+	1.54757i	−0.835660	+	0.549248i	$0.814914\pi$
$132$		0			0
$133$	0.582610	+	10.6068i	0.0505187	+	0.919728i
$134$		0			0
$135$	−2.80409	−	6.85267i	−0.241337	−	0.589784i
$136$		0			0
$137$	−6.10581	−	10.5756i	−0.521655	−	0.903532i	−0.999683	−	0.0251879i	$-0.991982\pi$
$137$	−6.10581	−	10.5756i	−0.521655	−	0.903532i	0.478028	−	0.878345i	$-0.341352\pi$
$138$		0			0
$139$	1.24092	+	2.14933i	0.105253	+	0.182304i	0.913842	−	0.406071i	$-0.133101\pi$
$139$	1.24092	+	2.14933i	0.105253	+	0.182304i	−0.808588	+	0.588375i	$0.799768\pi$
$140$		0			0
$141$	−15.6600	+	4.91296i	−1.31881	+	0.413746i
$142$		0			0
$143$	−6.79117	+	11.7626i	−0.567906	+	0.983642i
$144$		0			0
$145$	4.85269	+	8.40511i	0.402994	+	0.698006i
$146$		0			0
$147$	−9.77211	−	7.17675i	−0.805990	−	0.591929i
$148$		0			0
$149$	4.27797	−	7.40966i	0.350465	−	0.607023i	−0.635866	−	0.771799i	$-0.719357\pi$
$149$	4.27797	−	7.40966i	0.350465	−	0.607023i	0.986331	+	0.164777i	$0.0526903\pi$
$150$		0			0
$151$	−8.82962	−	15.2933i	−0.718544	−	1.24455i	−0.961577	−	0.274537i	$-0.911476\pi$
$151$	−8.82962	−	15.2933i	−0.718544	−	1.24455i	0.243033	−	0.970018i	$-0.421858\pi$
$152$		0			0
$153$	−0.283187	−	3.34708i	−0.0228943	−	0.270595i
$154$		0			0
$155$	1.78533	−	3.09228i	0.143401	−	0.248378i
$156$		0			0
$157$	6.32149			0.504510			0.252255	−	0.967661i	$-0.418828\pi$
$157$	6.32149			0.504510			0.252255	+	0.967661i	$0.418828\pi$
$158$		0			0
$159$	0.309561	−	1.38695i	0.0245498	−	0.109992i
$160$		0			0
$161$	12.0436	−	7.86433i	0.949172	−	0.619796i
$162$		0			0
$163$	4.01134	+	6.94784i	0.314192	+	0.544197i	0.979265	−	0.202581i	$-0.0649331\pi$
$163$	4.01134	+	6.94784i	0.314192	+	0.544197i	−0.665073	+	0.746778i	$0.731600\pi$
$164$		0			0
$165$	−11.6114	+	3.64283i	−0.903950	+	0.283594i
$166$		0			0
$167$	−1.06038	−	1.83663i	−0.0820545	−	0.142123i	0.822078	−	0.569375i	$-0.192815\pi$
$167$	−1.06038	−	1.83663i	−0.0820545	−	0.142123i	−0.904132	+	0.427253i	$0.859482\pi$
$168$		0			0
$169$	2.70608	−	4.68706i	0.208160	−	0.360543i
$170$		0			0
$171$	10.9020	+	5.12170i	0.833697	+	0.391666i
$172$		0			0
$173$	−18.2881			−1.39042			−0.695208	−	0.718808i	$-0.744688\pi$
$173$	−18.2881			−1.39042			−0.695208	+	0.718808i	$0.744688\pi$
$174$		0			0
$175$	0.430902	+	7.84487i	0.0325731	+	0.593017i
$176$		0			0
$177$	−10.8810	+	3.41367i	−0.817868	+	0.256587i
$178$		0			0
$179$	−3.81276	+	6.60389i	−0.284979	+	0.493598i	−0.972604	−	0.232468i	$-0.925320\pi$
$179$	−3.81276	+	6.60389i	−0.284979	+	0.493598i	0.687625	+	0.726066i	$0.258653\pi$
$180$		0			0
$181$	15.5305			1.15438			0.577188	−	0.816611i	$-0.304150\pi$
$181$	15.5305			1.15438			0.577188	+	0.816611i	$0.304150\pi$
$182$		0			0
$183$	−0.124384	+	0.0390227i	−0.00919475	+	0.00288464i
$184$		0			0
$185$	−2.02280			−0.148719
$186$		0			0
$187$	−5.52088			−0.403727
$188$		0			0
$189$	−12.4190	+	5.89648i	−0.903349	+	0.428906i
$190$		0			0
$191$	−14.8325			−1.07324			−0.536620	−	0.843824i	$-0.680299\pi$
$191$	−14.8325			−1.07324			−0.536620	+	0.843824i	$0.680299\pi$
$192$		0			0
$193$	16.5677			1.19257			0.596286	−	0.802772i	$-0.296642\pi$
$193$	16.5677			1.19257			0.596286	+	0.802772i	$0.296642\pi$
$194$		0			0
$195$	−6.48680	+	2.03509i	−0.464529	+	0.145736i
$196$		0			0
$197$	−4.03740			−0.287653			−0.143826	−	0.989603i	$-0.545941\pi$
$197$	−4.03740			−0.287653			−0.143826	+	0.989603i	$0.545941\pi$
$198$		0			0
$199$	12.6407	−	21.8943i	0.896076	−	1.55205i	0.0636081	−	0.997975i	$-0.479739\pi$
$199$	12.6407	−	21.8943i	0.896076	−	1.55205i	0.832468	−	0.554074i	$-0.186927\pi$
$200$		0			0
$201$	−20.8028	+	6.52640i	−1.46732	+	0.460337i
$202$		0			0
$203$	15.0885	−	9.85259i	1.05901	−	0.691516i
$204$		0			0
$205$	−0.354480			−0.0247579
$206$		0			0
$207$	−1.37502	−	16.2518i	−0.0955703	−	1.12958i
$208$		0			0
$209$	9.89864	−	17.1449i	0.684703	−	1.18594i
$210$		0			0
$211$	3.76246	+	6.51678i	0.259019	+	0.448634i	0.965979	−	0.258619i	$-0.0832675\pi$
$211$	3.76246	+	6.51678i	0.259019	+	0.448634i	−0.706961	+	0.707253i	$0.749934\pi$
$212$		0			0
$213$	0.133029	−	0.0417347i	0.00911497	−	0.00285961i
$214$		0			0
$215$	0.710065	+	1.22987i	0.0484261	+	0.0838764i
$216$		0			0
$217$	−5.91476	−	2.99502i	−0.401520	−	0.203315i
$218$		0			0
$219$	−4.03374	+	18.0727i	−0.272575	+	1.22124i
$220$		0			0
$221$	−3.08427			−0.207471
$222$		0			0
$223$	−6.49230	+	11.2450i	−0.434757	+	0.753020i	−0.997276	−	0.0737638i	$-0.976499\pi$
$223$	−6.49230	+	11.2450i	−0.434757	+	0.753020i	0.562519	+	0.826784i	$0.309832\pi$
$224$		0			0
$225$	8.06319	+	3.78804i	0.537546	+	0.252536i
$226$		0			0
$227$	−14.4832	−	25.0857i	−0.961286	−	1.66500i	−0.719277	−	0.694723i	$-0.755527\pi$
$227$	−14.4832	−	25.0857i	−0.961286	−	1.66500i	−0.242009	−	0.970274i	$-0.577806\pi$
$228$		0			0
$229$	−7.71790	+	13.3678i	−0.510013	+	0.883369i	0.489919	+	0.871768i	$0.337026\pi$
$229$	−7.71790	+	13.3678i	−0.510013	+	0.883369i	−0.999933	+	0.0116012i	$0.996307\pi$
$230$		0			0
$231$	7.93607	+	21.1561i	0.522155	+	1.39197i
$232$		0			0
$233$	−2.47324	−	4.28378i	−0.162027	−	0.280640i	0.773568	−	0.633713i	$-0.218470\pi$
$233$	−2.47324	−	4.28378i	−0.162027	−	0.280640i	−0.935596	+	0.353073i	$0.885137\pi$
$234$		0			0
$235$	−6.75121	+	11.6934i	−0.440400	+	0.762795i
$236$		0			0
$237$	−3.04896	+	0.956542i	−0.198051	+	0.0621341i
$238$		0			0
$239$	−6.51732	−	11.2883i	−0.421571	−	0.730182i	0.574523	−	0.818489i	$-0.305188\pi$
$239$	−6.51732	−	11.2883i	−0.421571	−	0.730182i	−0.996093	+	0.0883069i	$0.971854\pi$
$240$		0			0
$241$	−7.29123	−	12.6288i	−0.469670	−	0.813492i	0.529729	−	0.848167i	$-0.322294\pi$
$241$	−7.29123	−	12.6288i	−0.469670	−	0.813492i	−0.999399	+	0.0346754i	$0.988960\pi$
$242$		0			0
$243$	−0.791301	+	15.5684i	−0.0507620	+	0.998711i
$244$		0			0
$245$	−9.91456	+	1.09247i	−0.633418	+	0.0697951i
$246$		0			0
$247$	5.52993	−	9.57812i	0.351861	−	0.609441i
$248$		0			0
$249$	−5.46019	+	24.4637i	−0.346026	+	1.55032i
$250$		0			0
$251$	14.0715			0.888187			0.444094	−	0.895980i	$-0.353526\pi$
$251$	14.0715			0.888187			0.444094	+	0.895980i	$0.353526\pi$
$252$		0			0
$253$	−26.8067			−1.68532
$254$		0			0
$255$	−2.03475	−	1.86986i	−0.127421	−	0.117095i
$256$		0			0
$257$	4.18108	−	7.24184i	0.260808	−	0.451733i	−0.705649	−	0.708562i	$-0.749344\pi$
$257$	4.18108	−	7.24184i	0.260808	−	0.451733i	0.966457	+	0.256829i	$0.0826776\pi$
$258$		0			0
$259$	0.205989	+	3.75019i	0.0127996	+	0.233025i
$260$		0			0
$261$	−1.72265	−	20.3605i	−0.106629	−	1.26029i
$262$		0			0
$263$	1.63533	+	2.83247i	0.100839	+	0.174658i	0.912030	−	0.410122i	$-0.134514\pi$
$263$	1.63533	+	2.83247i	0.100839	+	0.174658i	−0.811192	+	0.584780i	$0.801181\pi$
$264$		0			0
$265$	−0.584551	−	1.01247i	−0.0359087	−	0.0621956i
$266$		0			0
$267$	−17.2499	−	15.8520i	−1.05568	−	0.970129i
$268$		0			0
$269$	−7.69349	+	13.3255i	−0.469081	+	0.812471i	−0.999375	−	0.0353420i	$-0.988748\pi$
$269$	−7.69349	+	13.3255i	−0.469081	+	0.812471i	0.530295	+	0.847813i	$0.322081\pi$
$270$		0			0
$271$	−4.06308	−	7.03747i	−0.246815	−	0.427496i	0.715825	−	0.698279i	$-0.246051\pi$
$271$	−4.06308	−	7.03747i	−0.246815	−	0.427496i	−0.962640	+	0.270783i	$0.912717\pi$
$272$		0			0
$273$	4.43353	+	11.8190i	0.268330	+	0.715318i
$274$		0			0
$275$	7.32110	−	12.6805i	0.441479	−	0.764664i
$276$		0			0
$277$	−6.42287	−	11.1247i	−0.385913	−	0.668421i	0.605982	−	0.795478i	$-0.292780\pi$
$277$	−6.42287	−	11.1247i	−0.385913	−	0.668421i	−0.991895	+	0.127057i	$0.959447\pi$
$278$		0			0
$279$	−6.17029	+	4.29423i	−0.369406	+	0.257089i
$280$		0			0
$281$	−0.724081	+	1.25415i	−0.0431951	+	0.0748161i	−0.886815	−	0.462125i	$-0.847087\pi$
$281$	−0.724081	+	1.25415i	−0.0431951	+	0.0748161i	0.843620	+	0.536941i	$0.180420\pi$
$282$		0			0
$283$	17.4385			1.03661			0.518306	−	0.855195i	$-0.326563\pi$
$283$	17.4385			1.03661			0.518306	+	0.855195i	$0.326563\pi$
$284$		0			0
$285$	9.45500	−	2.96629i	0.560066	−	0.175708i
$286$		0			0
$287$	0.0360979	+	0.657189i	0.00213079	+	0.0387926i
$288$		0			0
$289$	7.87316	+	13.6367i	0.463127	+	0.802160i
$290$		0			0
$291$	−2.03864	+	9.13386i	−0.119507	+	0.535437i
$292$		0			0
$293$	−0.900048	−	1.55893i	−0.0525814	−	0.0910736i	0.838537	−	0.544845i	$-0.183412\pi$
$293$	−0.900048	−	1.55893i	−0.0525814	−	0.0910736i	−0.891118	+	0.453772i	$0.850078\pi$
$294$		0			0
$295$	−4.69094	+	8.12495i	−0.273117	+	0.473053i
$296$		0			0
$297$	25.3873	+	3.45317i	1.47312	+	0.200373i
$298$		0			0
$299$	−14.9757			−0.866068
$300$		0			0
$301$	2.20781	−	1.44167i	0.127256	−	0.0830965i
$302$		0			0
$303$	−6.54931	−	6.01859i	−0.376248	−	0.345759i
$304$		0			0
$305$	−0.0536236	+	0.0928787i	−0.00307048	+	0.00531822i
$306$		0			0
$307$	−1.06478			−0.0607699			−0.0303850	−	0.999538i	$-0.509673\pi$
$307$	−1.06478			−0.0607699			−0.0303850	+	0.999538i	$0.509673\pi$
$308$		0			0
$309$	5.36193	−	24.0234i	0.305029	−	1.36665i
$310$		0			0
$311$	16.9293			0.959970			0.479985	−	0.877277i	$-0.340642\pi$
$311$	16.9293			0.959970			0.479985	+	0.877277i	$0.340642\pi$
$312$		0			0
$313$	−8.27856			−0.467932			−0.233966	−	0.972245i	$-0.575170\pi$
$313$	−8.27856			−0.467932			−0.233966	+	0.972245i	$0.575170\pi$
$314$		0			0
$315$	−4.24048	+	10.4851i	−0.238924	+	0.590766i
$316$		0			0
$317$	6.54741			0.367739			0.183870	−	0.982951i	$-0.441138\pi$
$317$	6.54741			0.367739			0.183870	+	0.982951i	$0.441138\pi$
$318$		0			0
$319$	−33.5840			−1.88034
$320$		0			0
$321$	9.76938	+	8.97773i	0.545274	+	0.501088i
$322$		0			0
$323$	4.49556			0.250140
$324$		0			0
$325$	4.08997	−	7.08404i	0.226871	−	0.392952i
$326$		0			0
$327$	0.640957	−	2.87173i	0.0354450	−	0.158807i
$328$		0			0
$329$	22.3666	+	11.3256i	1.23311	+	0.624403i
$330$		0			0
$331$	26.7258			1.46899			0.734493	−	0.678617i	$-0.237420\pi$
$331$	26.7258			1.46899			0.734493	+	0.678617i	$0.237420\pi$
$332$		0			0
$333$	3.85455	+	1.81085i	0.211228	+	0.0992337i
$334$		0			0
$335$	−8.96834	+	15.5336i	−0.489993	+	0.848692i
$336$		0			0
$337$	−4.76164	−	8.24740i	−0.259383	−	0.449264i	0.706694	−	0.707520i	$-0.250186\pi$
$337$	−4.76164	−	8.24740i	−0.259383	−	0.449264i	−0.966077	+	0.258255i	$0.916853\pi$
$338$		0			0
$339$	0.766092	+	0.704012i	0.0416084	+	0.0382367i
$340$		0			0
$341$	6.17786	+	10.7004i	0.334550	+	0.579457i
$342$		0			0
$343$	3.03502	+	18.2699i	0.163876	+	0.986481i
$344$		0			0
$345$	−9.87974	−	9.07914i	−0.531907	−	0.488805i
$346$		0			0
$347$	18.7031			1.00404			0.502018	−	0.864857i	$-0.332591\pi$
$347$	18.7031			1.00404			0.502018	+	0.864857i	$0.332591\pi$
$348$		0			0
$349$	−15.0542	+	26.0747i	−0.805834	+	1.39574i	0.109893	+	0.993943i	$0.464949\pi$
$349$	−15.0542	+	26.0747i	−0.805834	+	1.39574i	−0.915727	+	0.401801i	$0.868384\pi$
$350$		0			0
$351$	14.1827	+	1.92913i	0.757019	+	0.102970i
$352$		0			0
$353$	−3.12966	−	5.42074i	−0.166575	−	0.288517i	0.770638	−	0.637273i	$-0.219938\pi$
$353$	−3.12966	−	5.42074i	−0.166575	−	0.288517i	−0.937214	+	0.348756i	$0.886604\pi$
$354$		0			0
$355$	0.0573502	−	0.0993335i	0.00304383	−	0.00527208i
$356$		0			0
$357$	−3.25944	+	3.96275i	−0.172508	+	0.209731i
$358$		0			0
$359$	5.09755	+	8.82921i	0.269038	+	0.465988i	0.968614	−	0.248571i	$-0.0799608\pi$
$359$	5.09755	+	8.82921i	0.269038	+	0.465988i	−0.699575	+	0.714559i	$0.746628\pi$
$360$		0			0
$361$	1.43970	−	2.49364i	0.0757739	−	0.131244i
$362$		0			0
$363$	5.02285	−	22.5042i	0.263631	−	1.18117i
$364$		0			0
$365$	7.61701	+	13.1931i	0.398693	+	0.690556i
$366$		0			0
$367$	−14.3278	−	24.8165i	−0.747906	−	1.29541i	−0.948824	−	0.315804i	$-0.897726\pi$
$367$	−14.3278	−	24.8165i	−0.747906	−	1.29541i	0.200918	−	0.979608i	$-0.435608\pi$
$368$		0			0
$369$	0.675478	+	0.317336i	0.0351640	+	0.0165198i
$370$		0			0
$371$	−1.81755	+	1.18683i	−0.0943624	+	0.0616173i
$372$		0			0
$373$	8.03670	−	13.9200i	0.416124	−	0.720749i	−0.579421	−	0.815028i	$-0.696721\pi$
$373$	8.03670	−	13.9200i	0.416124	−	0.720749i	0.995546	+	0.0942796i	$0.0300548\pi$
$374$		0			0
$375$	18.7674	−	5.88786i	0.969147	−	0.304048i
$376$		0			0
$377$	−18.7619			−0.966286
$378$		0			0
$379$	1.01893			0.0523388			0.0261694	−	0.999658i	$-0.491669\pi$
$379$	1.01893			0.0523388			0.0261694	+	0.999658i	$0.491669\pi$
$380$		0			0
$381$	11.9977	−	3.76401i	0.614661	−	0.192836i
$382$		0			0
$383$	−5.79327	+	10.0342i	−0.296022	+	0.512725i	−0.975222	−	0.221228i	$-0.928994\pi$
$383$	−5.79327	+	10.0342i	−0.296022	+	0.512725i	0.679200	+	0.733953i	$0.262327\pi$
$384$		0			0
$385$	16.5842	+	8.39766i	0.845210	+	0.427984i
$386$		0			0
$387$	−0.252065	−	2.97924i	−0.0128132	−	0.151443i
$388$		0			0
$389$	−8.90675	−	15.4270i	−0.451590	−	0.782178i	0.546895	−	0.837201i	$-0.315810\pi$
$389$	−8.90675	−	15.4270i	−0.451590	−	0.782178i	−0.998485	+	0.0550239i	$0.982476\pi$
$390$		0			0
$391$	−3.04363	−	5.27172i	−0.153923	−	0.266602i
$392$		0			0
$393$	7.71695	−	34.5749i	0.389269	−	1.74407i
$394$		0			0
$395$	−1.31444	+	2.27668i	−0.0661369	+	0.114552i
$396$		0			0
$397$	−6.54229	−	11.3316i	−0.328348	−	0.568715i	0.653836	−	0.756636i	$-0.273159\pi$
$397$	−6.54229	−	11.3316i	−0.328348	−	0.568715i	−0.982184	+	0.187921i	$0.939825\pi$
$398$		0			0
$399$	−6.46221	−	17.2271i	−0.323515	−	0.862433i
$400$		0			0
$401$	−7.05165	+	12.2138i	−0.352143	+	0.609929i	−0.986625	−	0.163009i	$-0.947880\pi$
$401$	−7.05165	+	12.2138i	−0.352143	+	0.609929i	0.634482	+	0.772938i	$0.281213\pi$
$402$		0			0
$403$	3.45129	+	5.97782i	0.171921	+	0.297776i
$404$		0			0
$405$	8.18706	+	9.87108i	0.406818	+	0.490498i
$406$		0			0
$407$	3.49980	−	6.06183i	0.173479	−	0.300474i
$408$		0			0
$409$	−2.64599			−0.130836			−0.0654179	−	0.997858i	$-0.520838\pi$
$409$	−2.64599			−0.130836			−0.0654179	+	0.997858i	$0.520838\pi$
$410$		0			0
$411$	15.5738	+	14.3118i	0.768200	+	0.705949i
$412$		0			0
$413$	15.5410	+	7.86940i	0.764722	+	0.387228i
$414$		0			0
$415$	10.3106	+	17.8585i	0.506128	+	0.876639i
$416$		0			0
$417$	−3.16515	−	2.90866i	−0.154998	−	0.142438i
$418$		0			0
$419$	−16.7567	−	29.0235i	−0.818619	−	1.41789i	−0.906700	−	0.421776i	$-0.861407\pi$
$419$	−16.7567	−	29.0235i	−0.818619	−	1.41789i	0.0880816	−	0.996113i	$-0.471926\pi$
$420$		0			0
$421$	−2.41950	+	4.19071i	−0.117919	+	0.204242i	−0.918943	−	0.394390i	$-0.870956\pi$
$421$	−2.41950	+	4.19071i	−0.117919	+	0.204242i	0.801024	+	0.598633i	$0.204289\pi$
$422$		0			0
$423$	23.3329	−	16.2386i	1.13448	−	0.789548i
$424$		0			0
$425$	3.32495			0.161284
$426$		0			0
$427$	0.177654	+	0.0899575i	0.00859726	+	0.00435335i
$428$		0			0
$429$	5.12465	−	22.9603i	0.247420	−	1.10854i
$430$		0			0
$431$	−17.6643	+	30.5954i	−0.850858	+	1.47373i	0.0295774	+	0.999562i	$0.490584\pi$
$431$	−17.6643	+	30.5954i	−0.850858	+	1.47373i	−0.880435	+	0.474166i	$0.842749\pi$
$432$		0			0
$433$	5.47404			0.263066			0.131533	−	0.991312i	$-0.458010\pi$
$433$	5.47404			0.263066			0.131533	+	0.991312i	$0.458010\pi$
$434$		0			0
$435$	−12.3775	−	11.3745i	−0.593458	−	0.545367i
$436$		0			0
$437$	21.8282			1.04419
$438$		0			0
$439$	−6.39812			−0.305365			−0.152683	−	0.988275i	$-0.548791\pi$
$439$	−6.39812			−0.305365			−0.152683	+	0.988275i	$0.548791\pi$
$440$		0			0
$441$	19.8706	+	6.79392i	0.946221	+	0.323520i
$442$		0			0
$443$	6.38682			0.303447			0.151723	−	0.988423i	$-0.451518\pi$
$443$	6.38682			0.303447			0.151723	+	0.988423i	$0.451518\pi$
$444$		0			0
$445$	−19.2735			−0.913650
$446$		0			0
$447$	−3.22817	+	14.4634i	−0.152687	+	0.684097i
$448$		0			0
$449$	−11.7460			−0.554327			−0.277163	−	0.960823i	$-0.589394\pi$
$449$	−11.7460			−0.554327			−0.277163	+	0.960823i	$0.589394\pi$
$450$		0			0
$451$	0.613311	−	1.06229i	0.0288797	−	0.0500210i
$452$		0			0
$453$	22.5213	+	20.6963i	1.05814	+	0.972397i
$454$		0			0
$455$	9.26487	+	4.69140i	0.434344	+	0.219936i
$456$		0			0
$457$	10.5224			0.492217			0.246108	−	0.969242i	$-0.420848\pi$
$457$	10.5224			0.492217			0.246108	+	0.969242i	$0.420848\pi$
$458$		0			0
$459$	2.20338	+	5.38465i	0.102845	+	0.251334i
$460$		0			0
$461$	−3.54278	+	6.13627i	−0.165004	+	0.285794i	−0.936657	−	0.350249i	$-0.886097\pi$
$461$	−3.54278	+	6.13627i	−0.165004	+	0.285794i	0.771653	+	0.636044i	$0.219430\pi$
$462$		0			0
$463$	−16.3760	−	28.3641i	−0.761059	−	1.31819i	−0.942305	−	0.334755i	$-0.891346\pi$
$463$	−16.3760	−	28.3641i	−0.761059	−	1.31819i	0.181246	−	0.983438i	$-0.441987\pi$
$464$		0			0
$465$	−1.34722	+	6.03604i	−0.0624758	+	0.279915i
$466$		0			0
$467$	−1.96216	−	3.39856i	−0.0907978	−	0.157266i	0.817049	−	0.576568i	$-0.195608\pi$
$467$	−1.96216	−	3.39856i	−0.0907978	−	0.157266i	−0.907847	+	0.419301i	$0.862275\pi$
$468$		0			0
$469$	29.7119	+	15.0450i	1.37197	+	0.694716i
$470$		0			0
$471$	−10.4471	+	3.27753i	−0.481376	+	0.151021i
$472$		0			0
$473$	−4.91414			−0.225952
$474$		0			0
$475$	−5.96145	+	10.3255i	−0.273530	+	0.473768i
$476$		0			0
$477$	0.207509	+	2.45261i	0.00950117	+	0.112297i
$478$		0			0
$479$	8.04324	+	13.9313i	0.367505	+	0.636537i	0.989175	−	0.146742i	$-0.0468787\pi$
$479$	8.04324	+	13.9313i	0.367505	+	0.636537i	−0.621670	+	0.783279i	$0.713545\pi$
$480$		0			0
$481$	1.95518	−	3.38647i	0.0891486	−	0.154410i
$482$		0			0
$483$	−15.8262	+	19.2412i	−0.720118	+	0.875503i
$484$		0			0
$485$	3.84961	+	6.66771i	0.174802	+	0.302765i
$486$		0			0
$487$	1.75172	−	3.03407i	0.0793781	−	0.137487i	−0.823604	−	0.567166i	$-0.808040\pi$
$487$	1.75172	−	3.03407i	0.0793781	−	0.137487i	0.902982	+	0.429679i	$0.141373\pi$
$488$		0			0
$489$	−10.2315	−	9.40242i	−0.462686	−	0.425192i
$490$		0			0
$491$	20.5546	+	35.6017i	0.927618	+	1.60668i	0.787296	+	0.616575i	$0.211480\pi$
$491$	20.5546	+	35.6017i	0.927618	+	1.60668i	0.140321	+	0.990106i	$0.455186\pi$
$492$		0			0
$493$	−3.81312	−	6.60452i	−0.171734	−	0.297452i
$494$		0			0
$495$	17.3007	−	12.0405i	0.777609	−	0.541180i
$496$		0			0
$497$	−0.190000	−	0.0962092i	−0.00852267	−	0.00431557i
$498$		0			0
$499$	5.91486	−	10.2448i	0.264785	−	0.458622i	−0.702722	−	0.711465i	$-0.748032\pi$
$499$	5.91486	−	10.2448i	0.264785	−	0.458622i	0.967507	+	0.252843i	$0.0813655\pi$
$500$		0			0
$501$	2.70466	+	2.48549i	0.120835	+	0.111043i
$502$		0			0
$503$	−21.8595			−0.974665			−0.487332	−	0.873217i	$-0.662030\pi$
$503$	−21.8595			−0.974665			−0.487332	+	0.873217i	$0.662030\pi$
$504$		0			0
$505$	−7.31762			−0.325630
$506$		0			0
$507$	−2.04202	+	9.14901i	−0.0906892	+	0.406322i
$508$		0			0
$509$	−8.44831	+	14.6329i	−0.374465	+	0.648592i	−0.990247	−	0.139324i	$-0.955507\pi$
$509$	−8.44831	+	14.6329i	−0.374465	+	0.648592i	0.615782	+	0.787917i	$0.288840\pi$
$510$		0			0
$511$	23.6836	−	15.4651i	1.04770	−	0.684135i
$512$		0			0
$513$	−20.6724	−	2.81186i	−0.912710	−	0.124147i
$514$		0			0
$515$	−10.1250	−	17.5371i	−0.446163	−	0.772777i
$516$		0			0
$517$	−23.3615	−	40.4633i	−1.02744	−	1.77957i
$518$		0			0
$519$	30.2234	−	9.48190i	1.32666	−	0.416209i
$520$		0			0
$521$	−17.2466	+	29.8720i	−0.755587	+	1.30872i	0.189495	+	0.981882i	$0.439315\pi$
$521$	−17.2466	+	29.8720i	−0.755587	+	1.30872i	−0.945082	+	0.326834i	$0.894018\pi$
$522$		0			0
$523$	−0.995615	−	1.72445i	−0.0435352	−	0.0754051i	0.843437	−	0.537229i	$-0.180529\pi$
$523$	−0.995615	−	1.72445i	−0.0435352	−	0.0754051i	−0.886972	+	0.461823i	$0.847195\pi$
$524$		0			0
$525$	−4.77949	−	12.7413i	−0.208594	−	0.556074i
$526$		0			0
$527$	−1.40287	+	2.42983i	−0.0611098	+	0.105845i
$528$		0			0
$529$	−3.27836	−	5.67829i	−0.142538	−	0.246882i
$530$		0			0
$531$	16.2124	−	11.2831i	0.703558	−	0.489644i
$532$		0			0
$533$	0.342629	−	0.593452i	0.0148409	−	0.0257052i
$534$		0			0
$535$	10.9154			0.471916
$536$		0			0
$537$	2.87712	−	12.8906i	0.124157	−	0.556270i
$538$		0			0
$539$	13.8800	−	31.6016i	0.597856	−	1.36118i
$540$		0			0
$541$	−15.0681	−	26.0988i	−0.647830	−	1.12207i	−0.983640	−	0.180145i	$-0.942343\pi$
$541$	−15.0681	−	26.0988i	−0.647830	−	1.12207i	0.335810	−	0.941930i	$-0.390990\pi$
$542$		0			0
$543$	−25.6662	+	8.05220i	−1.10144	+	0.345553i
$544$		0			0
$545$	−1.21033	−	2.09636i	−0.0518450	−	0.0897982i
$546$		0			0
$547$	−7.68070	+	13.3034i	−0.328403	+	0.568810i	−0.982195	−	0.187864i	$-0.939844\pi$
$547$	−7.68070	+	13.3034i	−0.328403	+	0.568810i	0.653792	+	0.756674i	$0.273177\pi$
$548$		0			0
$549$	0.185329	−	0.128980i	0.00790964	−	0.00550474i
$550$		0			0
$551$	27.3469			1.16502
$552$		0			0
$553$	4.35472	+	2.20508i	0.185182	+	0.0937694i
$554$		0			0
$555$	3.34294	−	1.04877i	0.141900	−	0.0445179i
$556$		0			0
$557$	−11.6412	+	20.1631i	−0.493252	+	0.854338i	−0.999970	−	0.00777438i	$-0.997525\pi$
$557$	−11.6412	+	20.1631i	−0.493252	+	0.854338i	0.506718	+	0.862112i	$0.330859\pi$
$558$		0			0
$559$	−2.74531			−0.116114
$560$		0			0
$561$	9.12397	−	2.86244i	0.385214	−	0.120852i
$562$		0			0
$563$	−4.55885			−0.192133			−0.0960663	−	0.995375i	$-0.530626\pi$
$563$	−4.55885			−0.192133			−0.0960663	+	0.995375i	$0.530626\pi$
$564$		0			0
$565$	0.855964			0.0360107
$566$		0			0
$567$	17.4668	−	16.1836i	0.733538	−	0.679649i
$568$		0			0
$569$	18.1995			0.762963			0.381482	−	0.924376i	$-0.375414\pi$
$569$	18.1995			0.762963			0.381482	+	0.924376i	$0.375414\pi$
$570$		0			0
$571$	17.0455			0.713332			0.356666	−	0.934232i	$-0.383913\pi$
$571$	17.0455			0.713332			0.356666	+	0.934232i	$0.383913\pi$
$572$		0			0
$573$	24.5126	−	7.69027i	1.02403	−	0.321266i
$574$		0			0
$575$	16.1443			0.673264
$576$		0			0
$577$	−5.70473	+	9.88088i	−0.237491	+	0.411346i	−0.959994	−	0.280022i	$-0.909658\pi$
$577$	−5.70473	+	9.88088i	−0.237491	+	0.411346i	0.722503	+	0.691368i	$0.242992\pi$
$578$		0			0
$579$	−27.3803	+	8.58995i	−1.13789	+	0.356986i
$580$		0			0
$581$	32.0589	−	20.9340i	1.33003	−	0.868488i
$582$		0			0
$583$	4.04549			0.167547
$584$		0			0
$585$	9.66514	−	6.72649i	0.399604	−	0.278106i
$586$		0			0
$587$	−2.52544	+	4.37420i	−0.104236	+	0.180543i	−0.913426	−	0.407005i	$-0.866573\pi$
$587$	−2.52544	+	4.37420i	−0.104236	+	0.180543i	0.809190	+	0.587548i	$0.199906\pi$
$588$		0			0
$589$	−5.03052	−	8.71312i	−0.207279	−	0.359018i
$590$		0			0
$591$	6.67232	−	2.09329i	0.274463	−	0.0861064i
$592$		0			0
$593$	−9.98892	−	17.3013i	−0.410196	−	0.710480i	0.584715	−	0.811239i	$-0.301206\pi$
$593$	−9.98892	−	17.3013i	−0.410196	−	0.710480i	−0.994911	+	0.100759i	$0.967873\pi$
$594$		0			0
$595$	0.231513	+	4.21487i	0.00949113	+	0.172793i
$596$		0			0
$597$	−9.53873	+	42.7371i	−0.390394	+	1.74911i
$598$		0			0
$599$	−4.39321			−0.179502			−0.0897508	−	0.995964i	$-0.528607\pi$
$599$	−4.39321			−0.179502			−0.0897508	+	0.995964i	$0.528607\pi$
$600$		0			0
$601$	12.1778	−	21.0926i	0.496743	−	0.860385i	−0.503250	−	0.864141i	$-0.667862\pi$
$601$	12.1778	−	21.0926i	0.496743	−	0.860385i	0.999993	+	0.00375637i	$0.00119569\pi$
$602$		0			0
$603$	30.9955	−	21.5715i	1.26224	−	0.878457i
$604$		0			0
$605$	−9.48476	−	16.4281i	−0.385610	−	0.667897i
$606$		0			0
$607$	6.56281	−	11.3671i	0.266376	−	0.461377i	−0.701547	−	0.712623i	$-0.747507\pi$
$607$	6.56281	−	11.3671i	0.266376	−	0.461377i	0.967923	+	0.251246i	$0.0808403\pi$
$608$		0			0
$609$	−19.8274	+	24.1057i	−0.803447	+	0.976812i
$610$		0			0
$611$	−13.0510	−	22.6051i	−0.527988	−	0.914502i
$612$		0			0
$613$	−23.2403	+	40.2534i	−0.938667	+	1.62582i	−0.170707	+	0.985322i	$0.554605\pi$
$613$	−23.2403	+	40.2534i	−0.938667	+	1.62582i	−0.767960	+	0.640497i	$0.778728\pi$
$614$		0			0
$615$	0.585823	−	0.183789i	0.0236227	−	0.00741108i
$616$		0			0
$617$	14.1948	+	24.5862i	0.571463	+	0.989803i	0.996416	+	0.0845873i	$0.0269572\pi$
$617$	14.1948	+	24.5862i	0.571463	+	0.989803i	−0.424953	+	0.905215i	$0.639709\pi$
$618$		0			0
$619$	15.9606	+	27.6446i	0.641511	+	1.11113i	0.985096	+	0.172008i	$0.0550254\pi$
$619$	15.9606	+	27.6446i	0.641511	+	1.11113i	−0.343585	+	0.939122i	$0.611641\pi$
$620$		0			0
$621$	10.6985	+	26.1452i	0.429317	+	1.04917i
$622$		0			0
$623$	1.96269	+	35.7322i	0.0786335	+	1.43158i
$624$		0			0
$625$	0.666993	−	1.15527i	0.0266797	−	0.0462106i
$626$		0			0
$627$	−7.46956	+	33.4664i	−0.298306	+	1.33652i
$628$		0			0
$629$	1.58947			0.0633762
$630$		0			0
$631$	−38.7184			−1.54135			−0.770677	−	0.637226i	$-0.780082\pi$
$631$	−38.7184			−1.54135			−0.770677	+	0.637226i	$0.780082\pi$
$632$		0			0
$633$	−9.59675	−	8.81908i	−0.381436	−	0.350527i
$634$		0			0
$635$	5.17236	−	8.95878i	0.205259	−	0.355519i
$636$		0			0
$637$	7.75417	−	17.6544i	0.307231	−	0.699492i
$638$		0			0
$639$	−0.198209	+	0.137944i	−0.00784101	+	0.00545698i
$640$		0			0
$641$	20.2001	+	34.9875i	0.797854	+	1.38192i	0.921011	+	0.389537i	$0.127365\pi$
$641$	20.2001	+	34.9875i	0.797854	+	1.38192i	−0.123157	+	0.992387i	$0.539302\pi$
$642$		0			0
$643$	−6.27355	−	10.8661i	−0.247405	−	0.428517i	0.715400	−	0.698715i	$-0.246244\pi$
$643$	−6.27355	−	10.8661i	−0.247405	−	0.428517i	−0.962805	+	0.270198i	$0.912911\pi$
$644$		0			0
$645$	−1.81113	−	1.66437i	−0.0713132	−	0.0655344i
$646$		0			0
$647$	−17.2774	+	29.9253i	−0.679245	+	1.17649i	0.295964	+	0.955199i	$0.404359\pi$
$647$	−17.2774	+	29.9253i	−0.679245	+	1.17649i	−0.975209	+	0.221287i	$0.928974\pi$
$648$		0			0
$649$	−16.2323	−	28.1151i	−0.637173	−	1.10362i
$650$		0			0
$651$	11.3277	+	1.88301i	0.443969	+	0.0738009i
$652$		0			0
$653$	11.1472	−	19.3075i	0.436223	−	0.755560i	−0.561172	−	0.827699i	$-0.689649\pi$
$653$	11.1472	−	19.3075i	0.436223	−	0.755560i	0.997395	+	0.0721392i	$0.0229826\pi$
$654$		0			0
$655$	−14.5721	−	25.2396i	−0.569379	−	0.986194i
$656$		0			0
$657$	−2.70395	−	31.9589i	−0.105491	−	1.24683i
$658$		0			0
$659$	−3.57493	+	6.19196i	−0.139259	+	0.241204i	−0.927217	−	0.374526i	$-0.877806\pi$
$659$	−3.57493	+	6.19196i	−0.139259	+	0.241204i	0.787957	+	0.615730i	$0.211139\pi$
$660$		0			0
$661$	42.9060			1.66885			0.834425	−	0.551122i	$-0.185800\pi$
$661$	42.9060			1.66885			0.834425	+	0.551122i	$0.185800\pi$
$662$		0			0
$663$	5.09716	−	1.59912i	0.197957	−	0.0621046i
$664$		0			0
$665$	−13.5043	−	6.83807i	−0.523672	−	0.265169i
$666$		0			0
$667$	−18.5146	−	32.0683i	−0.716889	−	1.24169i
$668$		0			0
$669$	4.89912	−	21.9499i	0.189411	−	0.848632i
$670$		0			0
$671$	−0.185556	−	0.321392i	−0.00716331	−	0.0124072i
$672$		0			0
$673$	−18.8270	+	32.6094i	−0.725729	+	1.25700i	0.232944	+	0.972490i	$0.425164\pi$
$673$	−18.8270	+	32.6094i	−0.725729	+	1.25700i	−0.958673	+	0.284510i	$0.908169\pi$
$674$		0			0
$675$	−15.2895	−	2.07967i	−0.588492	−	0.0800465i
$676$		0			0
$677$	−26.3616			−1.01316			−0.506580	−	0.862193i	$-0.669090\pi$
$677$	−26.3616			−1.01316			−0.506580	+	0.862193i	$0.669090\pi$
$678$		0			0
$679$	11.9696	−	7.81599i	0.459352	−	0.299950i
$680$		0			0
$681$	36.9417	+	33.9482i	1.41561	+	1.30090i
$682$		0			0
$683$	−1.96588	+	3.40500i	−0.0752222	+	0.130289i	−0.901183	−	0.433439i	$-0.857300\pi$
$683$	−1.96588	+	3.40500i	−0.0752222	+	0.130289i	0.825961	+	0.563728i	$0.190633\pi$
$684$		0			0
$685$	17.4008			0.664850
$686$		0			0
$687$	5.82396	−	26.0936i	0.222198	−	0.995531i
$688$		0			0
$689$	2.26004			0.0861006
$690$		0			0
$691$	−19.9010			−0.757072			−0.378536	−	0.925587i	$-0.623572\pi$
$691$	−19.9010			−0.757072			−0.378536	+	0.925587i	$0.623572\pi$
$692$		0			0
$693$	−24.0843	−	30.8486i	−0.914887	−	1.17184i
$694$		0			0
$695$	−3.53645			−0.134145
$696$		0			0
$697$	0.278541			0.0105505
$698$		0			0
$699$	6.30838	+	5.79718i	0.238605	+	0.219270i
$700$		0			0
$701$	43.7908			1.65396			0.826979	−	0.562234i	$-0.190058\pi$
$701$	43.7908			1.65396			0.826979	+	0.562234i	$0.190058\pi$
$702$		0			0
$703$	−2.84983	+	4.93604i	−0.107483	+	0.186166i
$704$		0			0
$705$	5.09449	−	22.8252i	0.191870	−	0.859648i
$706$		0			0
$707$	0.745180	+	13.5665i	0.0280254	+	0.510222i
$708$		0			0
$709$	44.6344			1.67628			0.838139	−	0.545457i	$-0.183644\pi$
$709$	44.6344			1.67628			0.838139	+	0.545457i	$0.183644\pi$
$710$		0			0
$711$	4.54286	−	3.16162i	0.170371	−	0.118570i
$712$		0			0
$713$	−6.81163	+	11.7981i	−0.255097	+	0.441842i
$714$		0			0
$715$	−9.67699	−	16.7610i	−0.361899	−	0.626827i
$716$		0			0
$717$	16.6234	+	15.2764i	0.620814	+	0.570506i
$718$		0			0
$719$	19.5096	+	33.7917i	0.727586	+	1.26022i	0.957901	+	0.287100i	$0.0926912\pi$
$719$	19.5096	+	33.7917i	0.727586	+	1.26022i	−0.230315	+	0.973116i	$0.573976\pi$
$720$		0			0
$721$	−31.4819	+	20.5572i	−1.17245	+	0.765592i
$722$		0			0
$723$	18.5974	+	17.0904i	0.691645	+	0.635598i
$724$		0			0
$725$	20.2259			0.751171
$726$		0			0
$727$	11.2554	−	19.4949i	0.417439	−	0.723025i	−0.578242	−	0.815865i	$-0.696261\pi$
$727$	11.2554	−	19.4949i	0.417439	−	0.723025i	0.995681	+	0.0928402i	$0.0295946\pi$
$728$		0			0
$729$	−6.76407	−	26.1390i	−0.250521	−	0.968111i
$730$		0			0
$731$	−0.557951	−	0.966399i	−0.0206366	−	0.0357436i
$732$		0			0
$733$	0.448519	−	0.776858i	0.0165664	−	0.0286939i	−0.857623	−	0.514278i	$-0.828060\pi$
$733$	0.448519	−	0.776858i	0.0165664	−	0.0286939i	0.874190	+	0.485584i	$0.161393\pi$
$734$		0			0
$735$	15.8187	−	6.94589i	0.583480	−	0.256203i
$736$		0			0
$737$	−31.0335	−	53.7517i	−1.14314	−	1.97997i
$738$		0			0
$739$	−1.79032	+	3.10092i	−0.0658578	+	0.114069i	−0.897074	−	0.441880i	$-0.854312\pi$
$739$	−1.79032	+	3.10092i	−0.0658578	+	0.114069i	0.831216	+	0.555949i	$0.187645\pi$
$740$		0			0
$741$	−4.17291	+	18.6962i	−0.153296	+	0.686823i
$742$		0			0
$743$	24.7964	+	42.9486i	0.909691	+	1.57563i	0.814493	+	0.580173i	$0.197015\pi$
$743$	24.7964	+	42.9486i	0.909691	+	1.57563i	0.0951977	+	0.995458i	$0.469652\pi$
$744$		0			0
$745$	6.09583	+	10.5583i	0.223334	+	0.386826i
$746$		0			0
$747$	−3.66015	−	43.2604i	−0.133918	−	1.58282i
$748$		0			0
$749$	−1.11156	−	20.2367i	−0.0406155	−	0.739434i
$750$		0			0
$751$	−21.4515	+	37.1551i	−0.782776	+	1.35581i	0.147543	+	0.989056i	$0.452864\pi$
$751$	−21.4515	+	37.1551i	−0.782776	+	1.35581i	−0.930319	+	0.366752i	$0.880470\pi$
$752$		0			0
$753$	−23.2550	+	7.29574i	−0.847461	+	0.265871i
$754$		0			0
$755$	25.1633			0.915786
$756$		0			0
$757$	13.8029			0.501677			0.250838	−	0.968029i	$-0.419294\pi$
$757$	13.8029			0.501677			0.250838	+	0.968029i	$0.419294\pi$
$758$		0			0
$759$	44.3015	−	13.8986i	1.60804	−	0.504487i
$760$		0			0
$761$	−20.3599	+	35.2643i	−0.738044	+	1.27833i	0.215330	+	0.976541i	$0.430917\pi$
$761$	−20.3599	+	35.2643i	−0.738044	+	1.27833i	−0.953375	+	0.301789i	$0.902416\pi$
$762$		0			0
$763$	−3.76330	+	2.45738i	−0.136241	+	0.0889633i
$764$		0			0
$765$	4.33216	+	2.03523i	0.156630	+	0.0735838i
$766$		0			0
$767$	−9.06826	−	15.7067i	−0.327436	−	0.567135i
$768$		0			0
$769$	5.57381	+	9.65413i	0.200997	+	0.348137i	0.948850	−	0.315728i	$-0.102249\pi$
$769$	5.57381	+	9.65413i	0.200997	+	0.348137i	−0.747853	+	0.663864i	$0.768915\pi$
$770$		0			0
$771$	−3.15506	+	14.1359i	−0.113627	+	0.509090i
$772$		0			0
$773$	−0.462831	+	0.801647i	−0.0166469	+	0.0288332i	−0.874229	−	0.485514i	$-0.838632\pi$
$773$	−0.462831	+	0.801647i	−0.0166469	+	0.0288332i	0.857582	+	0.514347i	$0.171966\pi$
$774$		0			0
$775$	−3.72061	−	6.44428i	−0.133648	−	0.231485i
$776$		0			0
$777$	−2.28480	−	6.09087i	−0.0819668	−	0.218509i
$778$		0			0
$779$	−0.499408	+	0.865001i	−0.0178932	+	0.0309919i
$780$		0			0
$781$	0.198452	+	0.343728i	0.00710116	+	0.0122996i
$782$		0			0
$783$	13.4033	+	32.7553i	0.478996	+	1.17058i
$784$		0			0
$785$	−4.50386	+	7.80092i	−0.160750	+	0.278427i
$786$		0			0
$787$	−23.0240			−0.820716			−0.410358	−	0.911925i	$-0.634596\pi$
$787$	−23.0240			−0.820716			−0.410358	+	0.911925i	$0.634596\pi$
$788$		0			0
$789$	−4.17116	−	3.83315i	−0.148497	−	0.136464i
$790$		0			0
$791$	−0.0871659	−	1.58692i	−0.00309926	−	0.0564243i
$792$		0			0
$793$	−0.103662	−	0.179548i	−0.00368114	−	0.00637593i
$794$		0			0
$795$	1.49099	+	1.37017i	0.0528798	+	0.0485947i
$796$		0			0
$797$	11.3925	+	19.7325i	0.403544	+	0.698960i	0.994151	−	0.108000i	$-0.0344447\pi$
$797$	11.3925	+	19.7325i	0.403544	+	0.698960i	−0.590606	+	0.806960i	$0.701111\pi$
$798$		0			0
$799$	5.30492	−	9.18839i	0.187675	−	0.325062i
$800$		0			0
$801$	36.7265	+	17.2539i	1.29767	+	0.609637i
$802$		0			0
$803$	−52.7150			−1.86027
$804$		0			0
$805$	1.12412	+	20.4653i	0.0396199	+	0.721308i
$806$		0			0
$807$	5.80555	−	26.0110i	0.204365	−	0.915632i
$808$		0			0
$809$	6.73753	−	11.6697i	0.236879	−	0.410286i	−0.722938	−	0.690913i	$-0.757209\pi$
$809$	6.73753	−	11.6697i	0.236879	−	0.410286i	0.959817	+	0.280627i	$0.0905422\pi$
$810$		0			0
$811$	30.7348			1.07924			0.539622	−	0.841907i	$-0.318567\pi$
$811$	30.7348			1.07924			0.539622	+	0.841907i	$0.318567\pi$
$812$		0			0
$813$	10.3635	+	9.52372i	0.363465	+	0.334011i
$814$		0			0
$815$	−11.4318			−0.400439
$816$		0			0
$817$	4.00150			0.139995
$818$		0			0
$819$	−13.4548	−	17.2337i	−0.470150	−	0.602196i
$820$		0			0
$821$	−16.9864			−0.592829			−0.296414	−	0.955059i	$-0.595791\pi$
$821$	−16.9864			−0.592829			−0.296414	+	0.955059i	$0.595791\pi$
$822$		0			0
$823$	18.5831			0.647768			0.323884	−	0.946097i	$-0.395011\pi$
$823$	18.5831			0.647768			0.323884	+	0.946097i	$0.395011\pi$
$824$		0			0
$825$	−5.52453	+	24.7520i	−0.192340	+	0.861754i
$826$		0			0
$827$	−14.5419			−0.505670			−0.252835	−	0.967509i	$-0.581363\pi$
$827$	−14.5419			−0.505670			−0.252835	+	0.967509i	$0.581363\pi$
$828$		0			0
$829$	4.78717	−	8.29161i	0.166265	−	0.287980i	−0.770839	−	0.637030i	$-0.780163\pi$
$829$	4.78717	−	8.29161i	0.166265	−	0.287980i	0.937104	+	0.349051i	$0.113496\pi$
$830$		0			0
$831$	16.3825	+	15.0550i	0.568303	+	0.522251i
$832$		0			0
$833$	7.79060	−	0.858431i	0.269928	−	0.0297429i
$834$		0			0
$835$	3.02195			0.104579
$836$		0			0
$837$	7.97075	−	10.2959i	0.275509	−	0.355879i
$838$		0			0
$839$	−21.2303	+	36.7720i	−0.732952	+	1.26951i	0.222664	+	0.974895i	$0.428525\pi$
$839$	−21.2303	+	36.7720i	−0.732952	+	1.26951i	−0.955616	+	0.294615i	$0.904809\pi$
$840$		0			0
$841$	−8.69551	−	15.0611i	−0.299845	−	0.519347i
$842$		0			0
$843$	0.546395	−	2.44806i	0.0188189	−	0.0843155i
$844$		0			0
$845$	3.85599	+	6.67877i	0.132650	+	0.229757i
$846$		0			0
$847$	−29.4911	+	19.2572i	−1.01332	+	0.661687i
$848$		0			0
$849$	−28.8194	+	9.04143i	−0.989079	+	0.310301i
$850$		0			0
$851$	7.71767			0.264558
$852$		0			0
$853$	7.14039	−	12.3675i	0.244482	−	0.423456i	−0.717504	−	0.696555i	$-0.754715\pi$
$853$	7.14039	−	12.3675i	0.244482	−	0.423456i	0.961986	+	0.273099i	$0.0880486\pi$
$854$		0			0
$855$	−14.0877	+	9.80436i	−0.481788	+	0.335302i
$856$		0			0
$857$	−17.3895	−	30.1195i	−0.594013	−	1.02886i	−0.993685	−	0.112203i	$-0.964209\pi$
$857$	−17.3895	−	30.1195i	−0.594013	−	1.02886i	0.399672	−	0.916658i	$-0.369124\pi$
$858$		0			0
$859$	−6.32429	+	10.9540i	−0.215782	+	0.373745i	−0.953514	−	0.301348i	$-0.902563\pi$
$859$	−6.32429	+	10.9540i	−0.215782	+	0.373745i	0.737732	+	0.675093i	$0.235897\pi$
$860$		0			0
$861$	−0.400392	−	1.06737i	−0.0136453	−	0.0363760i
$862$		0			0
$863$	−13.2398	−	22.9321i	−0.450690	−	0.780617i	0.547739	−	0.836649i	$-0.315489\pi$
$863$	−13.2398	−	22.9321i	−0.450690	−	0.780617i	−0.998429	+	0.0560318i	$0.982155\pi$
$864$		0			0
$865$	13.0297	−	22.5681i	0.443022	−	0.767337i
$866$		0			0
$867$	−20.0817	−	18.4544i	−0.682011	−	0.626744i
$868$		0			0
$869$	−4.54843	−	7.87811i	−0.154295	−	0.267247i
$870$		0			0
$871$	−17.3371	−	30.0287i	−0.587444	−	1.01748i
$872$		0			0
$873$	−1.36657	−	16.1519i	−0.0462512	−	0.546658i
$874$		0			0
$875$	−26.8049	−	13.5730i	−0.906171	−	0.458852i
$876$		0			0
$877$	−14.2267	+	24.6414i	−0.480402	+	0.832081i	−0.999747	−	0.0224835i	$-0.992843\pi$
$877$	−14.2267	+	24.6414i	−0.480402	+	0.832081i	0.519345	+	0.854565i	$0.326176\pi$
$878$		0			0
$879$	2.29571	+	2.10968i	0.0774325	+	0.0711578i
$880$		0			0
$881$	−20.3637			−0.686071			−0.343036	−	0.939322i	$-0.611455\pi$
$881$	−20.3637			−0.686071			−0.343036	+	0.939322i	$0.611455\pi$
$882$		0			0
$883$	−49.1950			−1.65554			−0.827772	−	0.561065i	$-0.810392\pi$
$883$	−49.1950			−1.65554			−0.827772	+	0.561065i	$0.810392\pi$
$884$		0			0
$885$	3.53981	−	15.8597i	0.118989	−	0.533117i
$886$		0			0
$887$	−2.10846	+	3.65196i	−0.0707952	+	0.122621i	−0.899250	−	0.437435i	$-0.855887\pi$
$887$	−2.10846	+	3.65196i	−0.0707952	+	0.122621i	0.828455	+	0.560056i	$0.189220\pi$
$888$		0			0
$889$	−17.1359	−	8.67701i	−0.574720	−	0.291018i
$890$		0			0
$891$	−43.7461	+	7.45585i	−1.46555	+	0.249780i
$892$		0			0
$893$	19.0229	+	32.9486i	0.636576	+	1.10258i
$894$		0			0
$895$	−5.43294	−	9.41013i	−0.181603	−	0.314546i
$896$		0			0
$897$	24.7493	−	7.76453i	0.826355	−	0.259250i
$898$		0			0
$899$	−8.53374	+	14.7809i	−0.284616	+	0.492970i
$900$		0			0
$901$	0.459325	+	0.795574i	0.0153023	+	0.0265044i
$902$		0			0
$903$	−2.90123	+	3.52724i	−0.0965468	+	0.117379i
$904$		0			0
$905$	−11.0650	+	19.1652i	−0.367814	+	0.637072i
$906$		0			0
$907$	23.9925	+	41.5563i	0.796659	+	1.37985i	0.921780	+	0.387713i	$0.126735\pi$
$907$	23.9925	+	41.5563i	0.796659	+	1.37985i	−0.125121	+	0.992142i	$0.539932\pi$
$908$		0			0
$909$	13.9441	+	6.55085i	0.462496	+	0.217278i
$910$		0			0
$911$	12.8667	−	22.2858i	0.426294	−	0.738362i	−0.570247	−	0.821474i	$-0.693152\pi$
$911$	12.8667	−	22.2858i	0.426294	−	0.738362i	0.996540	+	0.0831113i	$0.0264857\pi$
$912$		0			0
$913$	−71.3565			−2.36155
$914$		0			0
$915$	0.0404646	−	0.181297i	0.00133772	−	0.00599348i
$916$		0			0
$917$	−45.3092	+	29.5863i	−1.49624	+	0.977024i
$918$		0			0
$919$	−1.13478	−	1.96550i	−0.0374330	−	0.0648359i	0.846702	−	0.532068i	$-0.178585\pi$
$919$	−1.13478	−	1.96550i	−0.0374330	−	0.0648359i	−0.884135	+	0.467232i	$0.845251\pi$
$920$		0			0
$921$	1.75968	−	0.552059i	0.0579834	−	0.0181910i
$922$		0			0
$923$	0.110866	+	0.192026i	0.00364920	+	0.00632060i
$924$		0			0
$925$	−2.10775	+	3.65073i	−0.0693024	+	0.120035i
$926$		0			0
$927$	3.59427	+	42.4819i	0.118051	+	1.39529i
$928$		0			0
$929$	45.8496			1.50428			0.752138	−	0.659006i	$-0.229023\pi$
$929$	45.8496			1.50428			0.752138	+	0.659006i	$0.229023\pi$
$930$		0			0
$931$	−11.3023	+	25.7326i	−0.370417	+	0.843352i
$932$		0			0
$933$	−27.9778	+	8.77739i	−0.915952	+	0.287359i
$934$		0			0
$935$	3.93346	−	6.81294i	0.128638	−	0.222807i
$936$		0			0
$937$	−56.2075			−1.83622			−0.918110	−	0.396325i	$-0.870285\pi$
$937$	−56.2075			−1.83622			−0.918110	+	0.396325i	$0.870285\pi$
$938$		0			0
$939$	13.6814	−	4.29222i	0.446475	−	0.140071i
$940$		0			0
$941$	−35.2803			−1.15011			−0.575053	−	0.818116i	$-0.695018\pi$
$941$	−35.2803			−1.15011			−0.575053	+	0.818116i	$0.695018\pi$
$942$		0			0
$943$	1.35246			0.0440421
$944$		0			0
$945$	1.57170	−	19.5265i	0.0511274	−	0.635197i
$946$		0			0
$947$	50.7130			1.64795			0.823976	−	0.566625i	$-0.191751\pi$
$947$	50.7130			1.64795			0.823976	+	0.566625i	$0.191751\pi$
$948$		0			0
$949$	−29.4495			−0.955972
$950$		0			0
$951$	−10.8204	+	3.39467i	−0.350877	+	0.110080i
$952$		0			0
$953$	25.9988			0.842184			0.421092	−	0.907018i	$-0.361647\pi$
$953$	25.9988			0.842184			0.421092	+	0.907018i	$0.361647\pi$
$954$		0			0
$955$	10.5677	−	18.3038i	0.341962	−	0.592296i
$956$		0			0
$957$	55.5019	−	17.4124i	1.79412	−	0.562864i
$958$		0			0
$959$	−1.77199	−	32.2603i	−0.0572204	−	1.04174i
$960$		0			0
$961$	−24.7208			−0.797445
$962$		0			0
$963$	−20.7999	−	9.77167i	−0.670267	−	0.314888i
$964$		0			0
$965$	−11.8040	+	20.4451i	−0.379984	+	0.658152i
$966$		0			0
$967$	12.9810	+	22.4838i	0.417442	+	0.723031i	0.995681	−	0.0928360i	$-0.0295932\pi$
$967$	12.9810	+	22.4838i	0.417442	+	0.723031i	−0.578239	+	0.815867i	$0.696260\pi$
$968$		0			0
$969$	−7.42950	+	2.33083i	−0.238670	+	0.0748772i
$970$		0			0
$971$	3.97206	+	6.87981i	0.127469	+	0.220783i	0.922696	−	0.385530i	$-0.125981\pi$
$971$	3.97206	+	6.87981i	0.127469	+	0.220783i	−0.795226	+	0.606313i	$0.792648\pi$
$972$		0			0
$973$	0.360130	+	6.55643i	0.0115452	+	0.210189i
$974$		0			0
$975$	−3.08631	+	13.8278i	−0.0988411	+	0.442845i
$976$		0			0
$977$	−52.2548			−1.67178			−0.835889	−	0.548898i	$-0.815048\pi$
$977$	−52.2548			−1.67178			−0.835889	+	0.548898i	$0.815048\pi$
$978$		0			0
$979$	33.3464	−	57.7577i	1.06576	−	1.84594i
$980$		0			0
$981$	0.429654	+	5.07822i	0.0137178	+	0.162135i
$982$		0			0
$983$	−19.4190	−	33.6346i	−0.619369	−	1.07278i	−0.989601	−	0.143839i	$-0.954055\pi$
$983$	−19.4190	−	33.6346i	−0.619369	−	1.07278i	0.370232	−	0.928939i	$-0.379278\pi$
$984$		0			0
$985$	2.87652	−	4.98228i	0.0916535	−	0.158749i
$986$		0			0
$987$	−42.8357	−	7.12058i	−1.36348	−	0.226651i
$988$		0			0
$989$	−2.70914	−	4.69236i	−0.0861455	−	0.149208i
$990$		0			0
$991$	15.4689	−	26.7929i	0.491385	−	0.851104i	−0.508565	−	0.861023i	$-0.669824\pi$
$991$	15.4689	−	26.7929i	0.491385	−	0.851104i	0.999951	+	0.00991892i	$0.00315734\pi$
$992$		0			0
$993$	−44.1679	+	13.8567i	−1.40163	+	0.439728i
$994$		0			0
$995$	18.0122	+	31.1981i	0.571025	+	0.989045i
$996$		0			0
$997$	−23.5335	−	40.7612i	−0.745313	−	1.29092i	−0.950048	−	0.312103i	$-0.898967\pi$
$997$	−23.5335	−	40.7612i	−0.745313	−	1.29092i	0.204735	−	0.978817i	$-0.434367\pi$
$998$		0			0
$999$	−7.30902	−	0.994170i	−0.231247	−	0.0314542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.q.i.529.1		10
3.2	odd	2		3024.2.q.i.2881.5		10
4.3	odd	2		63.2.h.b.25.4	yes	10
7.2	even	3		1008.2.t.i.961.4		10
9.4	even	3		1008.2.t.i.193.4		10
9.5	odd	6		3024.2.t.i.1873.1		10
12.11	even	2		189.2.h.b.46.2		10
21.2	odd	6		3024.2.t.i.289.1		10
28.3	even	6		441.2.f.f.295.2		10
28.11	odd	6		441.2.f.e.295.2		10
28.19	even	6		441.2.g.f.79.2		10
28.23	odd	6		63.2.g.b.16.2	yes	10
28.27	even	2		441.2.h.f.214.4		10
36.7	odd	6		567.2.e.f.487.2		10
36.11	even	6		567.2.e.e.487.4		10
36.23	even	6		189.2.g.b.172.4		10
36.31	odd	6		63.2.g.b.4.2	✓	10
63.23	odd	6		3024.2.q.i.2305.5		10
63.58	even	3	inner	1008.2.q.i.625.1		10
84.11	even	6		1323.2.f.e.883.4		10
84.23	even	6		189.2.g.b.100.4		10
84.47	odd	6		1323.2.g.f.667.4		10
84.59	odd	6		1323.2.f.f.883.4		10
84.83	odd	2		1323.2.h.f.802.2		10
252.11	even	6		3969.2.a.bc.1.2		5
252.23	even	6		189.2.h.b.37.2		10
252.31	even	6		441.2.f.f.148.2		10
252.59	odd	6		1323.2.f.f.442.4		10
252.67	odd	6		441.2.f.e.148.2		10
252.79	odd	6		567.2.e.f.163.2		10
252.95	even	6		1323.2.f.e.442.4		10
252.103	even	6		441.2.h.f.373.4		10
252.115	even	6		3969.2.a.ba.1.4		5
252.131	odd	6		1323.2.h.f.226.2		10
252.139	even	6		441.2.g.f.67.2		10
252.151	odd	6		3969.2.a.z.1.4		5
252.167	odd	6		1323.2.g.f.361.4		10
252.191	even	6		567.2.e.e.163.4		10
252.227	odd	6		3969.2.a.bb.1.2		5
252.247	odd	6		63.2.h.b.58.4	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.2	✓	10	36.31	odd	6
63.2.g.b.16.2	yes	10	28.23	odd	6
63.2.h.b.25.4	yes	10	4.3	odd	2
63.2.h.b.58.4	yes	10	252.247	odd	6
189.2.g.b.100.4		10	84.23	even	6
189.2.g.b.172.4		10	36.23	even	6
189.2.h.b.37.2		10	252.23	even	6
189.2.h.b.46.2		10	12.11	even	2
441.2.f.e.148.2		10	252.67	odd	6
441.2.f.e.295.2		10	28.11	odd	6
441.2.f.f.148.2		10	252.31	even	6
441.2.f.f.295.2		10	28.3	even	6
441.2.g.f.67.2		10	252.139	even	6
441.2.g.f.79.2		10	28.19	even	6
441.2.h.f.214.4		10	28.27	even	2
441.2.h.f.373.4		10	252.103	even	6
567.2.e.e.163.4		10	252.191	even	6
567.2.e.e.487.4		10	36.11	even	6
567.2.e.f.163.2		10	252.79	odd	6
567.2.e.f.487.2		10	36.7	odd	6
1008.2.q.i.529.1		10	1.1	even	1	trivial
1008.2.q.i.625.1		10	63.58	even	3	inner
1008.2.t.i.193.4		10	9.4	even	3
1008.2.t.i.961.4		10	7.2	even	3
1323.2.f.e.442.4		10	252.95	even	6
1323.2.f.e.883.4		10	84.11	even	6
1323.2.f.f.442.4		10	252.59	odd	6
1323.2.f.f.883.4		10	84.59	odd	6
1323.2.g.f.361.4		10	252.167	odd	6
1323.2.g.f.667.4		10	84.47	odd	6
1323.2.h.f.226.2		10	252.131	odd	6
1323.2.h.f.802.2		10	84.83	odd	2
3024.2.q.i.2305.5		10	63.23	odd	6
3024.2.q.i.2881.5		10	3.2	odd	2
3024.2.t.i.289.1		10	21.2	odd	6
3024.2.t.i.1873.1		10	9.5	odd	6
3969.2.a.z.1.4		5	252.151	odd	6
3969.2.a.ba.1.4		5	252.115	even	6
3969.2.a.bb.1.2		5	252.227	odd	6
3969.2.a.bc.1.2		5	252.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.65263 + 0.518475i) q^{3} +(-0.712469 + 1.23403i) q^{5} +(2.36039 + 1.19522i) q^{7} +(2.46237 - 1.71369i) q^{9} +O(q^{10})\)	\(q+(-1.65263 + 0.518475i) q^{3} +(-0.712469 + 1.23403i) q^{5} +(2.36039 + 1.19522i) q^{7} +(2.46237 - 1.71369i) q^{9} +(-2.46539 - 4.27018i) q^{11} +(-1.37730 - 2.38556i) q^{13} +(0.537632 - 2.40879i) q^{15} +(0.559839 - 0.969670i) q^{17} +(2.00752 + 3.47713i) q^{19} +(-4.52054 - 0.751449i) q^{21} +(2.71830 - 4.70824i) q^{23} +(1.48478 + 2.57171i) q^{25} +(-3.18087 + 4.10878i) q^{27} +(3.40555 - 5.89858i) q^{29} -2.50584 q^{31} +(6.28835 + 5.77878i) q^{33} +(-3.15664 + 2.06124i) q^{35} +(0.709787 + 1.22939i) q^{37} +(3.51302 + 3.22835i) q^{39} +(0.124384 + 0.215440i) q^{41} +(0.498313 - 0.863104i) q^{43} +(0.360392 + 4.25959i) q^{45} +9.47579 q^{47} +(4.14291 + 5.64237i) q^{49} +(-0.422457 + 1.89277i) q^{51} +(-0.410229 + 0.710537i) q^{53} +7.02604 q^{55} +(-5.12050 - 4.70556i) q^{57} +6.58407 q^{59} +0.0752645 q^{61} +(7.86039 - 1.10192i) q^{63} +3.92514 q^{65} +12.5877 q^{67} +(-2.05125 + 9.19035i) q^{69} -0.0804951 q^{71} +(5.34551 - 9.25869i) q^{73} +(-3.78715 - 3.48026i) q^{75} +(-0.715488 - 13.0260i) q^{77} +1.84491 q^{79} +(3.12651 - 8.43949i) q^{81} +(7.23583 - 12.5328i) q^{83} +(0.797736 + 1.38172i) q^{85} +(-2.56984 + 11.5139i) q^{87} +(6.76292 + 11.7137i) q^{89} +(-0.399711 - 7.27703i) q^{91} +(4.14122 - 1.29921i) q^{93} -5.72119 q^{95} +(2.70160 - 4.67930i) q^{97} +(-13.3885 - 6.28982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} + 4 q^{5} + 4 q^{7} + 11 q^{9}+O(q^{10}) \) 10 * q + q^3 + 4 * q^5 + 4 * q^7 + 11 * q^9	\( 10 q + q^{3} + 4 q^{5} + 4 q^{7} + 11 q^{9} - 4 q^{11} - 8 q^{13} + 19 q^{15} + 12 q^{17} - q^{19} + 13 q^{21} - 3 q^{23} - q^{25} + 7 q^{27} + 7 q^{29} - 6 q^{31} + 14 q^{33} - 5 q^{35} - 2 q^{39} + 5 q^{41} + 7 q^{43} - 16 q^{45} + 54 q^{47} - 8 q^{49} + 9 q^{51} - 21 q^{53} - 4 q^{55} - 4 q^{57} + 60 q^{59} + 28 q^{61} + 59 q^{63} + 22 q^{65} - 4 q^{67} + 15 q^{69} + 6 q^{71} + 15 q^{73} + 14 q^{75} + 11 q^{77} - 8 q^{79} + 23 q^{81} - 9 q^{83} - 6 q^{85} - 2 q^{87} + 28 q^{89} + 4 q^{91} - 6 q^{93} - 28 q^{95} - 12 q^{97} - 35 q^{99}+O(q^{100}) \) 10 * q + q^3 + 4 * q^5 + 4 * q^7 + 11 * q^9 - 4 * q^11 - 8 * q^13 + 19 * q^15 + 12 * q^17 - q^19 + 13 * q^21 - 3 * q^23 - q^25 + 7 * q^27 + 7 * q^29 - 6 * q^31 + 14 * q^33 - 5 * q^35 - 2 * q^39 + 5 * q^41 + 7 * q^43 - 16 * q^45 + 54 * q^47 - 8 * q^49 + 9 * q^51 - 21 * q^53 - 4 * q^55 - 4 * q^57 + 60 * q^59 + 28 * q^61 + 59 * q^63 + 22 * q^65 - 4 * q^67 + 15 * q^69 + 6 * q^71 + 15 * q^73 + 14 * q^75 + 11 * q^77 - 8 * q^79 + 23 * q^81 - 9 * q^83 - 6 * q^85 - 2 * q^87 + 28 * q^89 + 4 * q^91 - 6 * q^93 - 28 * q^95 - 12 * q^97 - 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more