LMFDB - Embedded newform 637.2.h.l.165.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(165,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("637.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.h (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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.6
Root			$0.217953 - 0.377506i$ of defining polynomial
Character	$\chi$	$=$	637.165
Dual form			637.2.h.l.471.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.85816 q^{2} +(1.14703 + 1.98672i) q^{3} +1.45276 q^{4} +(-0.0986811 - 0.170921i) q^{5} +(2.13137 + 3.69165i) q^{6} -1.01686 q^{8} +(-1.13137 + 1.95960i) q^{9} +O(q^{10})$	\(q+1.85816 q^{2} +(1.14703 + 1.98672i) q^{3} +1.45276 q^{4} +(-0.0986811 - 0.170921i) q^{5} +(2.13137 + 3.69165i) q^{6} -1.01686 q^{8} +(-1.13137 + 1.95960i) q^{9} +(-0.183365 - 0.317598i) q^{10} +(2.09137 + 3.62236i) q^{11} +(1.66637 + 2.88623i) q^{12} +(2.72221 + 2.36423i) q^{13} +(0.226381 - 0.392104i) q^{15} -4.79501 q^{16} -0.841305 q^{17} +(-2.10227 + 3.64125i) q^{18} +(0.675876 - 1.17065i) q^{19} +(-0.143360 - 0.248307i) q^{20} +(3.88610 + 6.73092i) q^{22} -4.11519 q^{23} +(-1.16637 - 2.02021i) q^{24} +(2.48052 - 4.29639i) q^{25} +(5.05830 + 4.39312i) q^{26} +1.69131 q^{27} +(4.11931 - 7.13485i) q^{29} +(0.420653 - 0.728592i) q^{30} +(-0.640350 + 1.10912i) q^{31} -6.87618 q^{32} +(-4.79774 + 8.30993i) q^{33} -1.56328 q^{34} +(-1.64362 + 2.84683i) q^{36} +3.04485 q^{37} +(1.25589 - 2.17526i) q^{38} +(-1.57459 + 8.12012i) q^{39} +(0.100344 + 0.173802i) q^{40} +(2.69848 - 4.67390i) q^{41} +(-2.66389 - 4.61399i) q^{43} +(3.03826 + 5.26242i) q^{44} +0.446581 q^{45} -7.64669 q^{46} +(-5.83204 - 10.1014i) q^{47} +(-5.50003 - 9.52634i) q^{48} +(4.60921 - 7.98339i) q^{50} +(-0.965006 - 1.67144i) q^{51} +(3.95472 + 3.43466i) q^{52} +(-2.32398 + 4.02525i) q^{53} +3.14272 q^{54} +(0.412757 - 0.714916i) q^{55} +3.10101 q^{57} +(7.65434 - 13.2577i) q^{58} -6.05811 q^{59} +(0.328878 - 0.569634i) q^{60} +(-5.68285 + 9.84298i) q^{61} +(-1.18987 + 2.06092i) q^{62} -3.18704 q^{64} +(0.135465 - 0.698587i) q^{65} +(-8.91498 + 15.4412i) q^{66} +(-6.69851 - 11.6022i) q^{67} -1.22222 q^{68} +(-4.72026 - 8.17574i) q^{69} +(2.98520 + 5.17051i) q^{71} +(1.15044 - 1.99263i) q^{72} +(1.94273 - 3.36491i) q^{73} +5.65782 q^{74} +11.3810 q^{75} +(0.981887 - 1.70068i) q^{76} +(-2.92585 + 15.0885i) q^{78} +(5.36669 + 9.29537i) q^{79} +(0.473177 + 0.819566i) q^{80} +(5.33411 + 9.23895i) q^{81} +(5.01421 - 8.68486i) q^{82} -3.07390 q^{83} +(0.0830210 + 0.143797i) q^{85} +(-4.94994 - 8.57354i) q^{86} +18.8999 q^{87} +(-2.12662 - 3.68341i) q^{88} +11.9841 q^{89} +0.829819 q^{90} -5.97840 q^{92} -2.93801 q^{93} +(-10.8369 - 18.7700i) q^{94} -0.266785 q^{95} +(-7.88721 - 13.6611i) q^{96} +(9.73637 + 16.8639i) q^{97} -9.46448 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9	$ 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} - 16 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + q^{20} - 5 q^{22} + 2 q^{23} + 11 q^{24} + 7 q^{25} + 16 q^{26} + 8 q^{27} + 3 q^{29} - 5 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 32 q^{34} - 21 q^{36} + 26 q^{37} + 17 q^{38} - 20 q^{39} + 5 q^{40} + 8 q^{41} - 11 q^{43} + 21 q^{44} - 14 q^{45} - 32 q^{46} + q^{47} - 21 q^{48} + 6 q^{50} - 20 q^{51} - 41 q^{52} - 2 q^{53} - 36 q^{54} - 9 q^{55} + 42 q^{57} - 8 q^{58} + 26 q^{59} + 20 q^{60} + 5 q^{61} - 5 q^{62} - 30 q^{64} - 5 q^{65} - 18 q^{66} - 11 q^{67} + 58 q^{68} - 23 q^{69} + 6 q^{71} + 25 q^{72} + 30 q^{73} + 6 q^{74} - 6 q^{75} + 9 q^{76} + 16 q^{78} + 7 q^{79} + 7 q^{80} - 6 q^{81} - q^{82} + 54 q^{83} - q^{85} - 7 q^{86} + 32 q^{87} + 8 q^{89} + 16 q^{90} + 54 q^{92} + 14 q^{93} - 45 q^{94} + 12 q^{95} - 19 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 - 16 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + q^20 - 5 * q^22 + 2 * q^23 + 11 * q^24 + 7 * q^25 + 16 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 + 26 * q^37 + 17 * q^38 - 20 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 - 14 * q^45 - 32 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 - 41 * q^52 - 2 * q^53 - 36 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 + 26 * q^59 + 20 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 5 * q^65 - 18 * q^66 - 11 * q^67 + 58 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 + 30 * q^73 + 6 * q^74 - 6 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 - 7 * q^86 + 32 * q^87 + 8 * q^89 + 16 * q^90 + 54 * q^92 + 14 * q^93 - 45 * q^94 + 12 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.85816			1.31392			0.656959	−	0.753926i	$-0.271842\pi$
$2$	1.85816			1.31392			0.656959	+	0.753926i	$0.271842\pi$
$3$	1.14703	+	1.98672i	0.662240	+	1.14703i	0.980026	+	0.198871i	$0.0637276\pi$
$3$	1.14703	+	1.98672i	0.662240	+	1.14703i	−0.317785	+	0.948163i	$0.602939\pi$
$4$	1.45276			0.726381
$5$	−0.0986811	−	0.170921i	−0.0441315	−	0.0764381i	0.843116	−	0.537732i	$-0.180719\pi$
$5$	−0.0986811	−	0.170921i	−0.0441315	−	0.0764381i	−0.887247	+	0.461294i	$0.847385\pi$
$6$	2.13137	+	3.69165i	0.870130	+	1.50711i
$7$		0			0
$7$		0			0
$8$	−1.01686			−0.359513
$9$	−1.13137	+	1.95960i	−0.377125	+	0.653199i
$10$	−0.183365	−	0.317598i	−0.0579852	−	0.100433i
$11$	2.09137	+	3.62236i	0.630571	+	1.09218i	0.987435	+	0.158025i	$0.0505127\pi$
$11$	2.09137	+	3.62236i	0.630571	+	1.09218i	−0.356864	+	0.934156i	$0.616154\pi$
$12$	1.66637	+	2.88623i	0.481039	+	0.833184i
$13$	2.72221	+	2.36423i	0.755005	+	0.655719i
$13$	2.72221	+	2.36423i	0.755005	+	0.655719i
$14$		0			0
$15$	0.226381	−	0.392104i	0.0584514	−	0.101241i
$16$	−4.79501			−1.19875
$17$	−0.841305			−0.204047			−0.102023	−	0.994782i	$-0.532532\pi$
$17$	−0.841305			−0.204047			−0.102023	+	0.994782i	$0.532532\pi$
$18$	−2.10227	+	3.64125i	−0.495511	+	0.858250i
$19$	0.675876	−	1.17065i	0.155057	−	0.268566i	−0.778023	−	0.628236i	$-0.783777\pi$
$19$	0.675876	−	1.17065i	0.155057	−	0.268566i	0.933080	+	0.359670i	$0.117111\pi$
$20$	−0.143360	−	0.248307i	−0.0320563	−	0.0555232i
$21$		0			0
$22$	3.88610	+	6.73092i	0.828519	+	1.43504i
$23$	−4.11519			−0.858077			−0.429038	−	0.903286i	$-0.641147\pi$
$23$	−4.11519			−0.858077			−0.429038	+	0.903286i	$0.641147\pi$
$24$	−1.16637	−	2.02021i	−0.238084	−	0.412373i
$25$	2.48052	−	4.29639i	0.496105	−	0.859279i
$26$	5.05830	+	4.39312i	0.992015	+	0.861561i
$27$	1.69131			0.325492
$28$		0			0
$29$	4.11931	−	7.13485i	0.764936	−	1.32491i	−0.175344	−	0.984507i	$-0.556104\pi$
$29$	4.11931	−	7.13485i	0.764936	−	1.32491i	0.940280	−	0.340401i	$-0.110563\pi$
$30$	0.420653	−	0.728592i	0.0768003	−	0.133022i
$31$	−0.640350	+	1.10912i	−0.115010	+	0.199203i	−0.917784	−	0.397080i	$-0.870023\pi$
$31$	−0.640350	+	1.10912i	−0.115010	+	0.199203i	0.802774	+	0.596284i	$0.203357\pi$
$32$	−6.87618			−1.21555
$33$	−4.79774	+	8.30993i	−0.835180	+	1.44657i
$34$	−1.56328			−0.268100
$35$		0			0
$36$	−1.64362	+	2.84683i	−0.273936	+	0.474471i
$37$	3.04485			0.500570			0.250285	−	0.968172i	$-0.419476\pi$
$37$	3.04485			0.500570			0.250285	+	0.968172i	$0.419476\pi$
$38$	1.25589	−	2.17526i	0.203732	−	0.352874i
$39$	−1.57459	+	8.12012i	−0.252137	+	1.30026i
$40$	0.100344	+	0.173802i	0.0158659	+	0.0274805i
$41$	2.69848	−	4.67390i	0.421431	−	0.729941i	−0.574648	−	0.818400i	$-0.694861\pi$
$41$	2.69848	−	4.67390i	0.421431	−	0.729941i	0.996080	+	0.0884599i	$0.0281945\pi$
$42$		0			0
$43$	−2.66389	−	4.61399i	−0.406239	−	0.703627i	0.588226	−	0.808697i	$-0.299827\pi$
$43$	−2.66389	−	4.61399i	−0.406239	−	0.703627i	−0.994465	+	0.105070i	$0.966493\pi$
$44$	3.03826	+	5.26242i	0.458035	+	0.793340i
$45$	0.446581			0.0665724
$46$	−7.64669			−1.12744
$47$	−5.83204	−	10.1014i	−0.850690	−	1.47344i	−0.880587	−	0.473885i	$-0.842851\pi$
$47$	−5.83204	−	10.1014i	−0.850690	−	1.47344i	0.0298969	−	0.999553i	$-0.490482\pi$
$48$	−5.50003	−	9.52634i	−0.793862	−	1.37501i
$49$		0			0
$50$	4.60921	−	7.98339i	0.651841	−	1.12902i
$51$	−0.965006	−	1.67144i	−0.135128	−	0.234048i
$52$	3.95472	+	3.43466i	0.548422	+	0.476302i
$53$	−2.32398	+	4.02525i	−0.319223	+	0.552911i	−0.980326	−	0.197384i	$-0.936755\pi$
$53$	−2.32398	+	4.02525i	−0.319223	+	0.552911i	0.661103	+	0.750295i	$0.270089\pi$
$54$	3.14272			0.427670
$55$	0.412757	−	0.714916i	0.0556562	−	0.0963993i
$56$		0			0
$57$	3.10101			0.410739
$58$	7.65434	−	13.2577i	1.00506	−	1.74082i
$59$	−6.05811			−0.788698			−0.394349	−	0.918961i	$-0.629030\pi$
$59$	−6.05811			−0.788698			−0.394349	+	0.918961i	$0.629030\pi$
$60$	0.328878	−	0.569634i	0.0424580	−	0.0735394i
$61$	−5.68285	+	9.84298i	−0.727614	+	1.26026i	0.230275	+	0.973126i	$0.426038\pi$
$61$	−5.68285	+	9.84298i	−0.727614	+	1.26026i	−0.957889	+	0.287139i	$0.907296\pi$
$62$	−1.18987	+	2.06092i	−0.151114	+	0.261737i
$63$		0			0
$64$	−3.18704			−0.398380
$65$	0.135465	−	0.698587i	0.0168023	−	0.0866490i
$66$	−8.91498	+	15.4412i	−1.09736	+	1.90068i
$67$	−6.69851	−	11.6022i	−0.818354	−	1.41743i	−0.906895	−	0.421357i	$-0.861554\pi$
$67$	−6.69851	−	11.6022i	−0.818354	−	1.41743i	0.0885411	−	0.996073i	$-0.471780\pi$
$68$	−1.22222			−0.148216
$69$	−4.72026	−	8.17574i	−0.568253	−	0.984243i
$70$		0			0
$71$	2.98520	+	5.17051i	0.354278	+	0.613627i	0.986994	−	0.160757i	$-0.0513934\pi$
$71$	2.98520	+	5.17051i	0.354278	+	0.613627i	−0.632716	+	0.774384i	$0.718060\pi$
$72$	1.15044	−	1.99263i	0.135581	−	0.234833i
$73$	1.94273	−	3.36491i	0.227380	−	0.393833i	−0.729651	−	0.683820i	$-0.760317\pi$
$73$	1.94273	−	3.36491i	0.227380	−	0.393833i	0.957031	+	0.289986i	$0.0936508\pi$
$74$	5.65782			0.657708
$75$	11.3810			1.31416
$76$	0.981887	−	1.70068i	0.112630	−	0.195081i
$77$		0			0
$78$	−2.92585	+	15.0885i	−0.331287	+	1.70844i
$79$	5.36669	+	9.29537i	0.603799	+	1.04581i	0.992240	+	0.124337i	$0.0396805\pi$
$79$	5.36669	+	9.29537i	0.603799	+	1.04581i	−0.388441	+	0.921474i	$0.626986\pi$
$80$	0.473177	+	0.819566i	0.0529028	+	0.0916303i
$81$	5.33411	+	9.23895i	0.592679	+	1.02655i
$82$	5.01421	−	8.68486i	0.553726	−	0.959082i
$83$	−3.07390			−0.337404			−0.168702	−	0.985667i	$-0.553958\pi$
$83$	−3.07390			−0.337404			−0.168702	+	0.985667i	$0.553958\pi$
$84$		0			0
$85$	0.0830210	+	0.143797i	0.00900489	+	0.0155969i
$86$	−4.94994	−	8.57354i	−0.533765	−	0.924509i
$87$	18.8999			2.02629
$88$	−2.12662	−	3.68341i	−0.226698	−	0.392653i
$89$	11.9841			1.27032			0.635159	−	0.772382i	$-0.280935\pi$
$89$	11.9841			1.27032			0.635159	+	0.772382i	$0.280935\pi$
$90$	0.829819			0.0874706
$91$		0			0
$92$	−5.97840			−0.623291
$93$	−2.93801			−0.304658
$94$	−10.8369	−	18.7700i	−1.11774	−	1.93598i
$95$	−0.266785			−0.0273715
$96$	−7.88721	−	13.6611i	−0.804986	−	1.39428i
$97$	9.73637	+	16.8639i	0.988578	+	1.71227i	0.624807	+	0.780779i	$0.285178\pi$
$97$	9.73637	+	16.8639i	0.988578	+	1.71227i	0.363771	+	0.931488i	$0.381489\pi$
$98$		0			0
$99$	−9.46448			−0.951216
$100$	3.60361	−	6.24164i	0.360361	−	0.624164i
$101$	−8.46697	−	14.6652i	−0.842495	−	1.45924i	−0.887779	−	0.460270i	$-0.847753\pi$
$101$	−8.46697	−	14.6652i	−0.842495	−	1.45924i	0.0452843	−	0.998974i	$-0.485581\pi$
$102$	−1.79314	−	3.10580i	−0.177547	−	0.307520i
$103$	−3.61712	−	6.26504i	−0.356406	−	0.617313i	0.630952	−	0.775822i	$-0.282665\pi$
$103$	−3.61712	−	6.26504i	−0.356406	−	0.617313i	−0.987357	+	0.158509i	$0.949331\pi$
$104$	−2.76809	−	2.40408i	−0.271434	−	0.235739i
$105$		0			0
$106$	−4.31833	+	7.47957i	−0.419434	+	0.726480i
$107$	−9.85249			−0.952477			−0.476238	−	0.879316i	$-0.658000\pi$
$107$	−9.85249			−0.952477			−0.476238	+	0.879316i	$0.658000\pi$
$108$	2.45707			0.236431
$109$	6.90796	−	11.9649i	0.661662	−	1.14603i	−0.318516	−	0.947917i	$-0.603185\pi$
$109$	6.90796	−	11.9649i	0.661662	−	1.14603i	0.980179	−	0.198115i	$-0.0634821\pi$
$110$	0.766969	−	1.32843i	0.0731277	−	0.126661i
$111$	3.49255	+	6.04927i	0.331498	+	0.574171i
$112$		0			0
$113$	2.13432	+	3.69675i	0.200780	+	0.347761i	0.948780	−	0.315938i	$-0.102319\pi$
$113$	2.13432	+	3.69675i	0.200780	+	0.347761i	−0.748000	+	0.663699i	$0.768986\pi$
$114$	5.76218			0.539677
$115$	0.406092	+	0.703371i	0.0378682	+	0.0655897i
$116$	5.98437	−	10.3652i	0.555635	−	0.962388i
$117$	−7.71277	+	2.65961i	−0.713046	+	0.245881i
$118$	−11.2569			−1.03629
$119$		0			0
$120$	−0.230197	+	0.398713i	−0.0210140	+	0.0363973i
$121$	−3.24765	+	5.62509i	−0.295240	+	0.511372i
$122$	−10.5596	+	18.2898i	−0.956026	+	1.65589i
$123$	12.3810			1.11636
$124$	−0.930276	+	1.61129i	−0.0835412	+	0.144698i
$125$	−1.96593			−0.175839
$126$		0			0
$127$	1.09512	−	1.89680i	0.0971761	−	0.168314i	−0.813339	−	0.581791i	$-0.802352\pi$
$127$	1.09512	−	1.89680i	0.0971761	−	0.168314i	0.910515	+	0.413477i	$0.135686\pi$
$128$	7.83033			0.692110
$129$	6.11114	−	10.5848i	0.538056	−	0.931941i
$130$	0.251715	−	1.29809i	0.0220769	−	0.113850i
$131$	1.13806	+	1.97117i	0.0994326	+	0.172222i	0.911450	−	0.411411i	$-0.134964\pi$
$131$	1.13806	+	1.97117i	0.0994326	+	0.172222i	−0.812017	+	0.583633i	$0.801631\pi$
$132$	−6.96998	+	12.0724i	−0.606659	+	1.05076i
$133$		0			0
$134$	−12.4469	−	21.5587i	−1.07525	−	1.86239i
$135$	−0.166900	−	0.289079i	−0.0143645	−	0.0248800i
$136$	0.855486			0.0733573
$137$	13.4480			1.14894			0.574469	−	0.818526i	$-0.305209\pi$
$137$	13.4480			1.14894			0.574469	+	0.818526i	$0.305209\pi$
$138$	−8.77101	−	15.1918i	−0.746638	−	1.29321i
$139$	2.02270	+	3.50342i	0.171563	+	0.297156i	0.938966	−	0.344009i	$-0.111785\pi$
$139$	2.02270	+	3.50342i	0.171563	+	0.297156i	−0.767403	+	0.641165i	$0.778452\pi$
$140$		0			0
$141$	13.3791	−	23.1733i	1.12672	−	1.95154i
$142$	5.54698	+	9.60765i	0.465492	+	0.806256i
$143$	−2.87093	+	14.8053i	−0.240079	+	1.23808i
$144$	5.42494	−	9.39628i	0.452079	−	0.783023i
$145$	−1.62599			−0.135031
$146$	3.60991	−	6.25255i	0.298758	−	0.517465i
$147$		0			0
$148$	4.42344			0.363605
$149$	−7.67596	+	13.2952i	−0.628840	+	1.08918i	0.358945	+	0.933359i	$0.383136\pi$
$149$	−7.67596	+	13.2952i	−0.628840	+	1.08918i	−0.987785	+	0.155823i	$0.950197\pi$
$150$	21.1477			1.72670
$151$	−3.06054	+	5.30101i	−0.249063	+	0.431390i	−0.963266	−	0.268548i	$-0.913456\pi$
$151$	−3.06054	+	5.30101i	−0.249063	+	0.431390i	0.714203	+	0.699939i	$0.246789\pi$
$152$	−0.687268	+	1.19038i	−0.0557448	+	0.0965528i
$153$	0.951831	−	1.64862i	0.0769510	−	0.133283i
$154$		0			0
$155$	0.252762			0.0203023
$156$	−2.28751	+	11.7966i	−0.183147	+	0.944484i
$157$	2.26834	−	3.92888i	0.181033	−	0.313559i	−0.761199	−	0.648518i	$-0.775389\pi$
$157$	2.26834	−	3.92888i	0.181033	−	0.313559i	0.942233	+	0.334959i	$0.108722\pi$
$158$	9.97217	+	17.2723i	0.793343	+	1.37411i
$159$	−10.6627			−0.845611
$160$	0.678549	+	1.17528i	0.0536440	+	0.0929142i
$161$		0			0
$162$	9.91163	+	17.1674i	0.778731	+	1.34880i
$163$	−0.911271	+	1.57837i	−0.0713762	+	0.123627i	−0.899505	−	0.436911i	$-0.856072\pi$
$163$	−0.911271	+	1.57837i	−0.0713762	+	0.123627i	0.828128	+	0.560538i	$0.189406\pi$
$164$	3.92025	−	6.79007i	0.306120	−	0.530215i
$165$	1.89379			0.147431
$166$	−5.71180			−0.443322
$167$	−5.35397	+	9.27336i	−0.414303	+	0.717594i	−0.995355	−	0.0962726i	$-0.969308\pi$
$167$	−5.35397	+	9.27336i	−0.414303	+	0.717594i	0.581052	+	0.813866i	$0.302641\pi$
$168$		0			0
$169$	1.82086	+	12.8718i	0.140066	+	0.990142i
$170$	0.154266	+	0.267197i	0.0118317	+	0.0204931i
$171$	1.52934	+	2.64889i	0.116951	+	0.202566i
$172$	−3.87000	−	6.70303i	−0.295085	−	0.511102i
$173$	−6.74634	+	11.6850i	−0.512915	+	0.888395i	0.486973	+	0.873417i	$0.338101\pi$
$173$	−6.74634	+	11.6850i	−0.512915	+	0.888395i	−0.999888	+	0.0149778i	$0.995232\pi$
$174$	35.1191			2.66237
$175$		0			0
$176$	−10.0281	−	17.3692i	−0.755898	−	1.30925i
$177$	−6.94886	−	12.0358i	−0.522308	−	0.904664i
$178$	22.2685			1.66909
$179$	−5.23458	−	9.06657i	−0.391251	−	0.677667i	0.601364	−	0.798975i	$-0.294624\pi$
$179$	−5.23458	−	9.06657i	−0.391251	−	0.677667i	−0.992615	+	0.121309i	$0.961291\pi$
$180$	0.648776			0.0483569
$181$	−12.5209			−0.930674			−0.465337	−	0.885133i	$-0.654067\pi$
$181$	−12.5209			−0.930674			−0.465337	+	0.885133i	$0.654067\pi$
$182$		0			0
$183$	−26.0737			−1.92742
$184$	4.18455			0.308489
$185$	−0.300469	−	0.520428i	−0.0220909	−	0.0382626i
$186$	−5.45930			−0.400295
$187$	−1.75948	−	3.04751i	−0.128666	−	0.222856i
$188$	−8.47256	−	14.6749i	−0.617925	−	1.07028i
$189$		0			0
$190$	−0.495729			−0.0359640
$191$	−6.55685	+	11.3568i	−0.474437	+	0.821749i	−0.999572	−	0.0292704i	$-0.990682\pi$
$191$	−6.55685	+	11.3568i	−0.474437	+	0.821749i	0.525135	+	0.851019i	$0.324015\pi$
$192$	−3.65565	−	6.33176i	−0.263823	−	0.456956i
$193$	−0.520786	−	0.902028i	−0.0374870	−	0.0649294i	0.846673	−	0.532113i	$-0.178602\pi$
$193$	−0.520786	−	0.902028i	−0.0374870	−	0.0649294i	−0.884160	+	0.467184i	$0.845269\pi$
$194$	18.0917	+	31.3358i	1.29891	+	2.24978i
$195$	1.54328	−	0.532172i	0.110517	−	0.0381096i
$196$		0			0
$197$	−0.739167	+	1.28027i	−0.0526635	+	0.0912158i	−0.891155	−	0.453698i	$-0.850104\pi$
$197$	−0.739167	+	1.28027i	−0.0526635	+	0.0912158i	0.838492	+	0.544914i	$0.183438\pi$
$198$	−17.5865			−1.24982
$199$	−14.0999			−0.999512			−0.499756	−	0.866166i	$-0.666577\pi$
$199$	−14.0999			−0.999512			−0.499756	+	0.866166i	$0.666577\pi$
$200$	−2.52233	+	4.36881i	−0.178356	+	0.308922i
$201$	15.3668	−	26.6162i	1.08389	−	1.87736i
$202$	−15.7330	−	27.2503i	−1.10697	−	1.91733i
$203$		0			0
$204$	−1.40192	−	2.42820i	−0.0981543	−	0.170008i
$205$	−1.06516			−0.0743937
$206$	−6.72120	−	11.6415i	−0.468288	−	0.811099i
$207$	4.65582	−	8.06412i	0.323602	−	0.560495i
$208$	−13.0530	−	11.3365i	−0.905064	−	0.786044i
$209$	5.65402			0.391097
$210$		0			0
$211$	−13.2346	+	22.9230i	−0.911108	+	1.57809i	−0.0986067	+	0.995126i	$0.531439\pi$
$211$	−13.2346	+	22.9230i	−0.911108	+	1.57809i	−0.812501	+	0.582959i	$0.801895\pi$
$212$	−3.37619	+	5.84774i	−0.231878	+	0.401624i
$213$	−6.84825	+	11.8615i	−0.469234	+	0.812737i
$214$	−18.3075			−1.25148
$215$	−0.525751	+	0.910628i	−0.0358559	+	0.0621043i
$216$	−1.71981			−0.117019
$217$		0			0
$218$	12.8361	−	22.2328i	0.869370	−	1.50579i
$219$	8.91352			0.602320
$220$	0.599638	−	1.03860i	0.0404276	−	0.0700227i
$221$	−2.29021	−	1.98904i	−0.154056	−	0.133797i
$222$	6.48971	+	11.2405i	0.435561	+	0.754414i
$223$	−0.364024	+	0.630508i	−0.0243769	+	0.0422219i	−0.877956	−	0.478740i	$-0.841093\pi$
$223$	−0.364024	+	0.630508i	−0.0243769	+	0.0422219i	0.853580	+	0.520962i	$0.174427\pi$
$224$		0			0
$225$	5.61280	+	9.72165i	0.374187	+	0.648110i
$226$	3.96591	+	6.86916i	0.263808	+	0.456929i
$227$	2.85195			0.189291			0.0946454	−	0.995511i	$-0.469828\pi$
$227$	2.85195			0.189291			0.0946454	+	0.995511i	$0.469828\pi$
$228$	4.50503			0.298353
$229$	1.58676	+	2.74835i	0.104856	+	0.181616i	0.913679	−	0.406436i	$-0.133228\pi$
$229$	1.58676	+	2.74835i	0.104856	+	0.181616i	−0.808823	+	0.588052i	$0.799895\pi$
$230$	0.754584	+	1.30698i	0.0497558	+	0.0861795i
$231$		0			0
$232$	−4.18874	+	7.25511i	−0.275004	+	0.476321i
$233$	−6.70354	−	11.6109i	−0.439163	−	0.760653i	0.558462	−	0.829530i	$-0.311392\pi$
$233$	−6.70354	−	11.6109i	−0.439163	−	0.760653i	−0.997625	+	0.0688769i	$0.978058\pi$
$234$	−14.3316	+	4.94198i	−0.936884	+	0.323068i
$235$	−1.15102	+	1.99363i	−0.0750845	+	0.130050i
$236$	−8.80099			−0.572896
$237$	−12.3115	+	21.3242i	−0.799721	+	1.38516i
$238$		0			0
$239$	−15.5538			−1.00609			−0.503046	−	0.864259i	$-0.667788\pi$
$239$	−15.5538			−1.00609			−0.503046	+	0.864259i	$0.667788\pi$
$240$	−1.08550	+	1.88014i	−0.0700687	+	0.121363i
$241$	7.57574			0.487996			0.243998	−	0.969776i	$-0.421541\pi$
$241$	7.57574			0.487996			0.243998	+	0.969776i	$0.421541\pi$
$242$	−6.03465	+	10.4523i	−0.387922	+	0.671900i
$243$	−9.69985	+	16.8006i	−0.622245	+	1.07776i
$244$	−8.25583	+	14.2995i	−0.528525	+	0.915433i
$245$		0			0
$246$	23.0059			1.46680
$247$	4.60756	−	1.58883i	0.293172	−	0.101095i
$248$	0.651143	−	1.12781i	0.0413476	−	0.0716162i
$249$	−3.52587	−	6.10698i	−0.223443	−	0.387014i
$250$	−3.65302			−0.231038
$251$	0.637382	+	1.10398i	0.0402312	+	0.0696825i	0.885440	−	0.464754i	$-0.153857\pi$
$251$	0.637382	+	1.10398i	0.0402312	+	0.0696825i	−0.845209	+	0.534436i	$0.820524\pi$
$252$		0			0
$253$	−8.60638	−	14.9067i	−0.541079	−	0.937176i
$254$	2.03491	−	3.52456i	0.127682	−	0.221151i
$255$	−0.190456	+	0.329879i	−0.0119268	+	0.0206578i
$256$	20.9241			1.30776
$257$	8.48019			0.528980			0.264490	−	0.964388i	$-0.414796\pi$
$257$	8.48019			0.528980			0.264490	+	0.964388i	$0.414796\pi$
$258$	11.3555	−	19.6683i	0.706962	−	1.22449i
$259$		0			0
$260$	0.196798	−	1.01488i	0.0122049	−	0.0629402i
$261$	9.32095	+	16.1444i	0.576952	+	0.999311i
$262$	2.11470	+	3.66276i	0.130646	+	0.226286i
$263$	−6.39415	−	11.0750i	−0.394280	−	0.682913i	0.598729	−	0.800952i	$-0.295673\pi$
$263$	−6.39415	−	11.0750i	−0.394280	−	0.682913i	−0.993009	+	0.118038i	$0.962339\pi$
$264$	4.87861	−	8.45000i	0.300258	−	0.520062i
$265$	0.917333			0.0563513
$266$		0			0
$267$	13.7462	+	23.8092i	0.841255	+	1.45710i
$268$	−9.73135	−	16.8552i	−0.594437	−	1.02959i
$269$	4.71172			0.287278			0.143639	−	0.989630i	$-0.454120\pi$
$269$	4.71172			0.287278			0.143639	+	0.989630i	$0.454120\pi$
$270$	−0.310127	−	0.537156i	−0.0188737	−	0.0326903i
$271$	18.0112			1.09410			0.547052	−	0.837098i	$-0.315750\pi$
$271$	18.0112			1.09410			0.547052	+	0.837098i	$0.315750\pi$
$272$	4.03407			0.244601
$273$		0			0
$274$	24.9885			1.50961
$275$	20.7508			1.25132
$276$	−6.85742	−	11.8774i	−0.412768	−	0.714936i
$277$	−26.1209			−1.56945			−0.784725	−	0.619844i	$-0.787196\pi$
$277$	−26.1209			−1.56945			−0.784725	+	0.619844i	$0.787196\pi$
$278$	3.75850	+	6.50991i	0.225420	+	0.390439i
$279$	−1.44895	−	2.50965i	−0.0867463	−	0.150249i
$280$		0			0
$281$	−3.66197			−0.218455			−0.109227	−	0.994017i	$-0.534838\pi$
$281$	−3.66197			−0.218455			−0.109227	+	0.994017i	$0.534838\pi$
$282$	24.8605	−	43.0596i	1.48042	−	2.56416i
$283$	3.82263	+	6.62099i	0.227232	+	0.393577i	0.956987	−	0.290132i	$-0.0936991\pi$
$283$	3.82263	+	6.62099i	0.227232	+	0.393577i	−0.729755	+	0.683709i	$0.760366\pi$
$284$	4.33678	+	7.51153i	0.257341	+	0.445727i
$285$	−0.306011	−	0.530027i	−0.0181265	−	0.0313961i
$286$	−5.33465	+	27.5106i	−0.315445	+	1.62674i
$287$		0			0
$288$	7.77953	−	13.4745i	0.458413	−	0.793995i
$289$	−16.2922			−0.958365
$290$	−3.02135			−0.177420
$291$	−22.3359	+	38.6869i	−1.30935	+	2.26787i
$292$	2.82233	−	4.88842i	0.165164	−	0.286073i
$293$	−8.57670	−	14.8553i	−0.501056	−	0.867855i	−0.999999	−	0.00122001i	$-0.999612\pi$
$293$	−8.57670	−	14.8553i	−0.501056	−	0.867855i	0.498943	−	0.866635i	$-0.333722\pi$
$294$		0			0
$295$	0.597821	+	1.03546i	0.0348065	+	0.0602866i
$296$	−3.09617			−0.179961
$297$	3.53715	+	6.12652i	0.205246	+	0.355497i
$298$	−14.2632	+	24.7045i	−0.826244	+	1.43110i
$299$	−11.2024	−	9.72925i	−0.647852	−	0.562657i
$300$	16.5339			0.954583
$301$		0			0
$302$	−5.68698	+	9.85014i	−0.327249	+	0.566812i
$303$	19.4238	−	33.6430i	1.11587	−	1.93274i
$304$	−3.24083	+	5.61328i	−0.185874	+	0.321944i
$305$	2.24316			0.128443
$306$	1.76866	−	3.06340i	0.101107	−	0.175123i
$307$	28.0696			1.60201			0.801007	−	0.598655i	$-0.204298\pi$
$307$	28.0696			1.60201			0.801007	+	0.598655i	$0.204298\pi$
$308$		0			0
$309$	8.29793	−	14.3724i	0.472052	−	0.817619i
$310$	0.469672			0.0266756
$311$	−11.7670	+	20.3811i	−0.667248	+	1.15571i	0.311423	+	0.950271i	$0.399194\pi$
$311$	−11.7670	+	20.3811i	−0.667248	+	1.15571i	−0.978671	+	0.205436i	$0.934139\pi$
$312$	1.60113	−	8.25699i	0.0906464	−	0.467460i
$313$	−1.67430	−	2.89997i	−0.0946370	−	0.163916i	0.814820	−	0.579714i	$-0.196836\pi$
$313$	−1.67430	−	2.89997i	−0.0946370	−	0.163916i	−0.909457	+	0.415798i	$0.863502\pi$
$314$	4.21494	−	7.30050i	0.237863	−	0.411991i
$315$		0			0
$316$	7.79652	+	13.5040i	0.438588	+	0.759658i
$317$	3.63917	+	6.30323i	0.204396	+	0.354025i	0.949940	−	0.312432i	$-0.101144\pi$
$317$	3.63917	+	6.30323i	0.204396	+	0.354025i	−0.745544	+	0.666456i	$0.767810\pi$
$318$	−19.8131			−1.11106
$319$	34.4600			1.92939
$320$	0.314501	+	0.544732i	0.0175811	+	0.0304514i
$321$	−11.3011	−	19.5742i	−0.630768	−	1.09252i
$322$		0			0
$323$	−0.568618	+	0.984875i	−0.0316388	+	0.0547999i
$324$	7.74919	+	13.4220i	0.430511	+	0.745666i
$325$	16.9102	−	5.83116i	0.938007	−	0.323455i
$326$	−1.69329	+	2.93286i	−0.0937826	+	0.162436i
$327$	31.6946			1.75272
$328$	−2.74396	+	4.75268i	−0.151510	+	0.262423i
$329$		0			0
$330$	3.51896			0.193712
$331$	7.16168	−	12.4044i	0.393642	−	0.681807i	−0.599285	−	0.800536i	$-0.704548\pi$
$331$	7.16168	−	12.4044i	0.393642	−	0.681807i	0.992927	+	0.118728i	$0.0378818\pi$
$332$	−4.46564			−0.245084
$333$	−3.44486	+	5.96668i	−0.188777	+	0.326972i
$334$	−9.94855	+	17.2314i	−0.544360	+	0.942860i
$335$	−1.32203	+	2.28983i	−0.0722304	+	0.125107i
$336$		0			0
$337$	17.1802			0.935868			0.467934	−	0.883764i	$-0.344999\pi$
$337$	17.1802			0.935868			0.467934	+	0.883764i	$0.344999\pi$
$338$	3.38344	+	23.9180i	0.184035	+	1.30097i
$339$	−4.89627	+	8.48060i	−0.265929	+	0.460603i
$340$	0.120610	+	0.208902i	0.00654098	+	0.0113293i
$341$	−5.35683			−0.290089
$342$	2.84175	+	4.92206i	0.153664	+	0.266155i
$343$		0			0
$344$	2.70879	+	4.69176i	0.146048	+	0.252963i
$345$	−0.931602	+	1.61358i	−0.0501558	+	0.0868723i
$346$	−12.5358	+	21.7126i	−0.673928	+	1.16728i
$347$	−7.70278			−0.413507			−0.206753	−	0.978393i	$-0.566290\pi$
$347$	−7.70278			−0.413507			−0.206753	+	0.978393i	$0.566290\pi$
$348$	27.4571			1.47186
$349$	11.1850	−	19.3730i	0.598721	−	1.03702i	−0.394289	−	0.918986i	$-0.629009\pi$
$349$	11.1850	−	19.3730i	0.598721	−	1.03702i	0.993010	−	0.118029i	$-0.0376575\pi$
$350$		0			0
$351$	4.60409	+	3.99863i	0.245748	+	0.213431i
$352$	−14.3806	−	24.9080i	−0.766490	−	1.32760i
$353$	−11.1311	−	19.2797i	−0.592451	−	1.02616i	−0.993901	−	0.110275i	$-0.964827\pi$
$353$	−11.1311	−	19.2797i	−0.592451	−	1.02616i	0.401450	−	0.915881i	$-0.368506\pi$
$354$	−12.9121	−	22.3644i	−0.686270	−	1.18865i
$355$	0.589165	−	1.02046i	0.0312697	−	0.0541606i
$356$	17.4101			0.922735
$357$		0			0
$358$	−9.72670	−	16.8471i	−0.514072	−	0.890399i
$359$	1.37921	+	2.38887i	0.0727920	+	0.126079i	0.900124	−	0.435634i	$-0.143476\pi$
$359$	1.37921	+	2.38887i	0.0727920	+	0.126079i	−0.827332	+	0.561713i	$0.810142\pi$
$360$	−0.454108			−0.0239336
$361$	8.58638	+	14.8721i	0.451915	+	0.782740i
$362$	−23.2659			−1.22283
$363$	−14.9006			−0.782081
$364$		0			0
$365$	−0.766844			−0.0401385
$366$	−48.4491			−2.53248
$367$	−7.07485	−	12.2540i	−0.369304	−	0.639654i	0.620153	−	0.784481i	$-0.287071\pi$
$367$	−7.07485	−	12.2540i	−0.369304	−	0.639654i	−0.989457	+	0.144827i	$0.953737\pi$
$368$	19.7324			1.02862
$369$	6.10597	+	10.5759i	0.317864	+	0.550557i
$370$	−0.558320	−	0.967039i	−0.0290257	−	0.0502740i
$371$		0			0
$372$	−4.26823			−0.221298
$373$	2.52142	−	4.36723i	0.130554	−	0.226127i	−0.793336	−	0.608784i	$-0.791658\pi$
$373$	2.52142	−	4.36723i	0.130554	−	0.226127i	0.923890	+	0.382657i	$0.124991\pi$
$374$	−3.26940	−	5.66276i	−0.169056	−	0.292814i
$375$	−2.25499	−	3.90576i	−0.116447	−	0.201693i
$376$	5.93034	+	10.2716i	0.305834	+	0.529720i
$377$	28.0820	−	9.68358i	1.44630	−	0.498730i
$378$		0			0
$379$	3.02982	−	5.24780i	0.155631	−	0.269561i	−0.777657	−	0.628688i	$-0.783592\pi$
$379$	3.02982	−	5.24780i	0.155631	−	0.269561i	0.933289	+	0.359127i	$0.116925\pi$
$380$	−0.387575			−0.0198822
$381$	5.02456			0.257416
$382$	−12.1837	+	21.1028i	−0.623371	+	1.07971i
$383$	−2.27052	+	3.93266i	−0.116018	+	0.200950i	−0.918186	−	0.396149i	$-0.870346\pi$
$383$	−2.27052	+	3.93266i	−0.116018	+	0.200950i	0.802168	+	0.597098i	$0.203680\pi$
$384$	8.98165	+	15.5567i	0.458343	+	0.793873i
$385$		0			0
$386$	−0.967705	−	1.67611i	−0.0492549	−	0.0853120i
$387$	12.0554			0.612811
$388$	14.1446	+	24.4992i	0.718085	+	1.24376i
$389$	−2.25383	+	3.90374i	−0.114273	+	0.197927i	−0.917489	−	0.397761i	$-0.869787\pi$
$389$	−2.25383	+	3.90374i	−0.114273	+	0.197927i	0.803216	+	0.595688i	$0.203121\pi$
$390$	2.86766	−	0.988862i	0.145210	−	0.0500730i
$391$	3.46213			0.175088
$392$		0			0
$393$	−2.61078	+	4.52201i	−0.131697	+	0.228105i
$394$	−1.37349	+	2.37896i	−0.0691955	+	0.119850i
$395$	1.05918	−	1.83456i	0.0532932	−	0.0923065i
$396$	−13.7496			−0.690945
$397$	2.00174	−	3.46712i	0.100465	−	0.174010i	−0.811412	−	0.584475i	$-0.801300\pi$
$397$	2.00174	−	3.46712i	0.100465	−	0.174010i	0.911876	+	0.410465i	$0.134634\pi$
$398$	−26.1998			−1.31328
$399$		0			0
$400$	−11.8941	+	20.6012i	−0.594706	+	1.03006i
$401$	12.6135			0.629887			0.314944	−	0.949110i	$-0.398014\pi$
$401$	12.6135			0.629887			0.314944	+	0.949110i	$0.398014\pi$
$402$	28.5541	−	49.4571i	1.42415	−	2.46670i
$403$	−4.36537	+	1.50532i	−0.217455	+	0.0749853i
$404$	−12.3005	−	21.3051i	−0.611972	−	1.05997i
$405$	1.05275	−	1.82342i	0.0523116	−	0.0906064i
$406$		0			0
$407$	6.36790	+	11.0295i	0.315645	+	0.546713i
$408$	0.981272	+	1.69961i	0.0485802	+	0.0841434i
$409$	−20.6952			−1.02331			−0.511657	−	0.859190i	$-0.670968\pi$
$409$	−20.6952			−1.02331			−0.511657	+	0.859190i	$0.670968\pi$
$410$	−1.97923			−0.0977472
$411$	15.4253	+	26.7174i	0.760873	+	1.31787i
$412$	−5.25482	−	9.10162i	−0.258886	−	0.448404i
$413$		0			0
$414$	8.65126	−	14.9844i	0.425186	−	0.736444i
$415$	0.303336	+	0.525393i	0.0148902	+	0.0257905i
$416$	−18.7184	−	16.2569i	−0.917746	−	0.797058i
$417$	−4.64021	+	8.03708i	−0.227232	+	0.393577i
$418$	10.5061			0.513869
$419$	−10.9088	+	18.8945i	−0.532928	+	0.923058i	0.466333	+	0.884609i	$0.345575\pi$
$419$	−10.9088	+	18.8945i	−0.532928	+	0.923058i	−0.999261	+	0.0384484i	$0.987758\pi$
$420$		0			0
$421$	9.42727			0.459457			0.229728	−	0.973255i	$-0.426216\pi$
$421$	9.42727			0.459457			0.229728	+	0.973255i	$0.426216\pi$
$422$	−24.5920	+	42.5947i	−1.19712	+	2.07348i
$423$	26.3928			1.28326
$424$	2.36315	−	4.09310i	0.114765	−	0.198779i
$425$	−2.08688	+	3.61458i	−0.101228	+	0.175333i
$426$	−12.7251	+	22.0406i	−0.616535	+	1.06787i
$427$		0			0
$428$	−14.3133			−0.691861
$429$	−32.7070	+	11.2784i	−1.57911	+	0.544528i
$430$	−0.976930	+	1.69209i	−0.0471118	+	0.0816000i
$431$	−10.2138	−	17.6908i	−0.491980	−	0.852134i	0.507977	−	0.861370i	$-0.330393\pi$
$431$	−10.2138	−	17.6908i	−0.491980	−	0.852134i	−0.999957	+	0.00923613i	$0.997060\pi$
$432$	−8.10983			−0.390184
$433$	13.1743	+	22.8186i	0.633117	+	1.09659i	0.986911	+	0.161267i	$0.0515581\pi$
$433$	13.1743	+	22.8186i	0.633117	+	1.09659i	−0.353794	+	0.935323i	$0.615109\pi$
$434$		0			0
$435$	−1.86507	−	3.23039i	−0.0894231	−	0.154885i
$436$	10.0356	−	17.3822i	0.480619	−	0.832457i
$437$	−2.78136	+	4.81745i	−0.133050	+	0.230450i
$438$	16.5628			0.791399
$439$	−25.1310			−1.19944			−0.599720	−	0.800210i	$-0.704721\pi$
$439$	−25.1310			−1.19944			−0.599720	+	0.800210i	$0.704721\pi$
$440$	−0.419714	+	0.726967i	−0.0200091	+	0.0346568i
$441$		0			0
$442$	−4.25558	−	3.69595i	−0.202417	−	0.175799i
$443$	−9.25995	−	16.0387i	−0.439953	−	0.762022i	0.557732	−	0.830021i	$-0.311672\pi$
$443$	−9.25995	−	16.0387i	−0.439953	−	0.762022i	−0.997685	+	0.0679994i	$0.978338\pi$
$444$	5.07384	+	8.78815i	0.240794	+	0.417067i
$445$	−1.18261	−	2.04834i	−0.0560611	−	0.0971006i
$446$	−0.676415	+	1.17159i	−0.0320292	+	0.0554762i
$447$	−35.2184			−1.66577
$448$		0			0
$449$	−5.82155	−	10.0832i	−0.274736	−	0.475856i	0.695333	−	0.718688i	$-0.255257\pi$
$449$	−5.82155	−	10.0832i	−0.274736	−	0.475856i	−0.970068	+	0.242832i	$0.921924\pi$
$450$	10.4295	+	18.0644i	0.491651	+	0.851564i
$451$	22.5740			1.06297
$452$	3.10066	+	5.37050i	0.145843	+	0.252607i
$453$	−14.0422			−0.659759
$454$	5.29939			0.248713
$455$		0			0
$456$	−3.15328			−0.147666
$457$	20.5184			0.959812			0.479906	−	0.877320i	$-0.340671\pi$
$457$	20.5184			0.959812			0.479906	+	0.877320i	$0.340671\pi$
$458$	2.94845	+	5.10687i	0.137772	+	0.238629i
$459$	−1.42291			−0.0664156
$460$	0.589955	+	1.02183i	0.0275068	+	0.0476431i
$461$	1.02038	+	1.76734i	0.0475236	+	0.0823134i	0.888809	−	0.458278i	$-0.151534\pi$
$461$	1.02038	+	1.76734i	0.0475236	+	0.0823134i	−0.841285	+	0.540592i	$0.818200\pi$
$462$		0			0
$463$	3.03155			0.140888			0.0704441	−	0.997516i	$-0.477558\pi$
$463$	3.03155			0.140888			0.0704441	+	0.997516i	$0.477558\pi$
$464$	−19.7521	+	34.2116i	−0.916968	+	1.58824i
$465$	0.289926	+	0.502167i	0.0134450	+	0.0232874i
$466$	−12.4563	−	21.5749i	−0.577025	−	0.999436i
$467$	−6.46371	−	11.1955i	−0.299105	−	0.518065i	0.676827	−	0.736142i	$-0.263355\pi$
$467$	−6.46371	−	11.1955i	−0.299105	−	0.518065i	−0.975931	+	0.218078i	$0.930021\pi$
$468$	−11.2048	+	3.86378i	−0.517943	+	0.178603i
$469$		0			0
$470$	−2.13879	+	3.70449i	−0.0986549	+	0.170875i
$471$	10.4075			0.479550
$472$	6.16022			0.283547
$473$	11.1423	−	19.2991i	0.512326	−	0.887374i
$474$	−22.8768	+	39.6238i	−1.05077	+	1.81998i
$475$	−3.35305	−	5.80766i	−0.153849	−	0.266474i
$476$		0			0
$477$	−5.25858	−	9.10814i	−0.240774	−	0.417033i
$478$	−28.9015			−1.32192
$479$	18.2911	+	31.6810i	0.835740	+	1.44754i	0.893427	+	0.449209i	$0.148294\pi$
$479$	18.2911	+	31.6810i	0.835740	+	1.44754i	−0.0576873	+	0.998335i	$0.518373\pi$
$480$	−1.55664	+	2.69618i	−0.0710505	+	0.123063i
$481$	8.28872	+	7.19872i	0.377933	+	0.328233i
$482$	14.0769			0.641187
$483$		0			0
$484$	−4.71806	+	8.17191i	−0.214457	+	0.371451i
$485$	1.92159	−	3.32829i	0.0872550	−	0.151130i
$486$	−18.0239	+	31.2183i	−0.817580	+	1.41609i
$487$	36.7496			1.66528			0.832642	−	0.553812i	$-0.186827\pi$
$487$	36.7496			1.66528			0.832642	+	0.553812i	$0.186827\pi$
$488$	5.77864	−	10.0089i	0.261587	−	0.453081i
$489$	−4.18103			−0.189073
$490$		0			0
$491$	4.09899	−	7.09965i	0.184985	−	0.320403i	−0.758587	−	0.651572i	$-0.774110\pi$
$491$	4.09899	−	7.09965i	0.184985	−	0.320403i	0.943571	+	0.331169i	$0.107443\pi$
$492$	17.9866			0.810900
$493$	−3.46560	+	6.00259i	−0.156083	+	0.270343i
$494$	8.56159	−	2.95231i	0.385204	−	0.132831i
$495$	0.933965	+	1.61768i	0.0419786	+	0.0727091i
$496$	3.07048	−	5.31823i	0.137869	−	0.238795i
$497$		0			0
$498$	−6.55163	−	11.3478i	−0.293585	−	0.508505i
$499$	21.6266	+	37.4584i	0.968141	+	1.67687i	0.700929	+	0.713231i	$0.252769\pi$
$499$	21.6266	+	37.4584i	0.968141	+	1.67687i	0.267211	+	0.963638i	$0.413898\pi$
$500$	−2.85604			−0.127726
$501$	−24.5648			−1.09747
$502$	1.18436	+	2.05137i	0.0528605	+	0.0915571i
$503$	0.00909609	+	0.0157549i	0.000405575	+	0.000702476i	0.866228	−	0.499649i	$-0.166538\pi$
$503$	0.00909609	+	0.0157549i	0.000405575	+	0.000702476i	−0.865823	+	0.500351i	$0.833204\pi$
$504$		0			0
$505$	−1.67106	+	2.89436i	−0.0743612	+	0.128797i
$506$	−15.9920	−	27.6990i	−0.710933	−	1.23137i
$507$	−23.4842	+	18.3820i	−1.04297	+	0.816372i
$508$	1.59095	−	2.75560i	0.0705869	−	0.122260i
$509$	−43.1006			−1.91040			−0.955200	−	0.295960i	$-0.904361\pi$
$509$	−43.1006			−1.91040			−0.955200	+	0.295960i	$0.904361\pi$
$510$	−0.353897	+	0.612968i	−0.0156708	+	0.0271427i
$511$		0			0
$512$	23.2197			1.02617
$513$	1.14311	−	1.97993i	0.0504697	−	0.0874161i
$514$	15.7576			0.695036
$515$	−0.713884	+	1.23648i	−0.0314575	+	0.0544859i
$516$	8.87804	−	15.3772i	0.390834	−	0.676944i
$517$	24.3939	−	42.2514i	1.07284	−	1.85822i
$518$		0			0
$519$	−30.9531			−1.35869
$520$	−0.137748	+	0.710362i	−0.00604065	+	0.0311514i
$521$	10.4770	−	18.1467i	0.459006	−	0.795022i	−0.539903	−	0.841727i	$-0.681539\pi$
$521$	10.4770	−	18.1467i	0.459006	−	0.795022i	0.998909	+	0.0467056i	$0.0148723\pi$
$522$	17.3198	+	29.9988i	0.758068	+	1.31301i
$523$	34.7403			1.51909			0.759543	−	0.650457i	$-0.225423\pi$
$523$	34.7403			1.51909			0.759543	+	0.650457i	$0.225423\pi$
$524$	1.65333	+	2.86365i	0.0722260	+	0.125099i
$525$		0			0
$526$	−11.8814	−	20.5791i	−0.518052	−	0.897292i
$527$	0.538730	−	0.933107i	0.0234674	−	0.0406468i
$528$	23.0052	−	39.8462i	1.00117	−	1.73408i
$529$	−6.06520			−0.263704
$530$	1.70455			0.0740410
$531$	6.85398	−	11.8714i	0.297438	−	0.515177i
$532$		0			0
$533$	18.3960	−	6.34352i	0.796819	−	0.274769i
$534$	25.5427	+	44.2413i	1.10534	+	1.91451i
$535$	0.972255	+	1.68400i	0.0420343	+	0.0728055i
$536$	6.81142	+	11.7977i	0.294209	+	0.509584i
$537$	12.0085	−	20.7993i	0.518205	−	0.897557i
$538$	8.75513			0.377460
$539$		0			0
$540$	−0.242466	−	0.419964i	−0.0104341	−	0.0180724i
$541$	1.64923	+	2.85655i	0.0709059	+	0.122813i	0.899299	−	0.437335i	$-0.144078\pi$
$541$	1.64923	+	2.85655i	0.0709059	+	0.122813i	−0.828393	+	0.560148i	$0.810744\pi$
$542$	33.4678			1.43756
$543$	−14.3619	−	24.8756i	−0.616330	−	1.06752i
$544$	5.78497			0.248029
$545$	−2.72674			−0.116801
$546$		0			0
$547$	21.9417			0.938161			0.469080	−	0.883155i	$-0.344585\pi$
$547$	21.9417			0.938161			0.469080	+	0.883155i	$0.344585\pi$
$548$	19.5367			0.834567
$549$	−12.8589	−	22.2722i	−0.548803	−	0.950554i
$550$	38.5583			1.64413
$551$	−5.56828	−	9.64455i	−0.237217	−	0.410871i
$552$	4.79983	+	8.31354i	0.204294	+	0.353848i
$553$		0			0
$554$	−48.5368			−2.06213
$555$	0.689297	−	1.19390i	0.0292590	−	0.0506781i
$556$	2.93850	+	5.08963i	0.124620	+	0.215848i
$557$	7.14329	+	12.3725i	0.302671	+	0.524241i	0.976740	−	0.214427i	$-0.0687884\pi$
$557$	7.14329	+	12.3725i	0.302671	+	0.524241i	−0.674069	+	0.738668i	$0.735455\pi$
$558$	−2.69238	−	4.66334i	−0.113978	−	0.197415i
$559$	3.65686	−	18.8583i	0.154669	−	0.797621i
$560$		0			0
$561$	4.03637	−	6.99119i	0.170416	−	0.295168i
$562$	−6.80453			−0.287032
$563$	−6.78784			−0.286073			−0.143037	−	0.989717i	$-0.545687\pi$
$563$	−6.78784			−0.286073			−0.143037	+	0.989717i	$0.545687\pi$
$564$	19.4366	−	33.6652i	0.818430	−	1.41756i
$565$	0.421234	−	0.729599i	0.0177215	−	0.0306945i
$566$	7.10307	+	12.3029i	0.298564	+	0.517128i
$567$		0			0
$568$	−3.03552	−	5.25767i	−0.127367	−	0.220607i
$569$	−17.3212			−0.726143			−0.363072	−	0.931761i	$-0.618272\pi$
$569$	−17.3212			−0.726143			−0.363072	+	0.931761i	$0.618272\pi$
$570$	−0.568618	−	0.984875i	−0.0238168	−	0.0412519i
$571$	6.50581	−	11.2684i	0.272260	−	0.471568i	−0.697180	−	0.716896i	$-0.745562\pi$
$571$	6.50581	−	11.2684i	0.272260	−	0.471568i	0.969440	+	0.245328i	$0.0788957\pi$
$572$	−4.17078	+	21.5086i	−0.174389	+	0.899318i
$573$	−30.0837			−1.25676
$574$		0			0
$575$	−10.2078	+	17.6805i	−0.425696	+	0.737327i
$576$	3.60574	−	6.24532i	0.150239	−	0.260222i
$577$	−0.365767	+	0.633528i	−0.0152271	+	0.0263741i	−0.873539	−	0.486755i	$-0.838180\pi$
$577$	−0.365767	+	0.633528i	−0.0152271	+	0.0263741i	0.858311	+	0.513129i	$0.171514\pi$
$578$	−30.2735			−1.25921
$579$	1.19472	−	2.06931i	0.0496508	−	0.0859978i
$580$	−2.36218			−0.0980842
$581$		0			0
$582$	−41.5037	+	71.8865i	−1.72038	+	2.97979i
$583$	−19.4412			−0.805173
$584$	−1.97548	+	3.42163i	−0.0817459	+	0.141588i
$585$	1.21569	+	1.05582i	0.0502625	+	0.0436527i
$586$	−15.9369	−	27.6035i	−0.658347	−	1.14029i
$587$	−4.26142	+	7.38099i	−0.175888	+	0.304646i	−0.940468	−	0.339882i	$-0.889613\pi$
$587$	−4.26142	+	7.38099i	−0.175888	+	0.304646i	0.764581	+	0.644528i	$0.222946\pi$
$588$		0			0
$589$	0.865594	+	1.49925i	0.0356662	+	0.0617756i
$590$	1.11085	+	1.92404i	0.0457329	+	0.0792117i
$591$	−3.39140			−0.139503
$592$	−14.6001			−0.600059
$593$	−15.6547	−	27.1147i	−0.642860	−	1.11347i	−0.984791	−	0.173741i	$-0.944415\pi$
$593$	−15.6547	−	27.1147i	−0.642860	−	1.11347i	0.341932	−	0.939725i	$-0.388919\pi$
$594$	6.57259	+	11.3841i	0.269677	+	0.467093i
$595$		0			0
$596$	−11.1514	+	19.3147i	−0.456777	+	0.791161i
$597$	−16.1730	−	28.0125i	−0.661917	−	1.14647i
$598$	−20.8159	−	18.0785i	−0.851225	−	0.739285i
$599$	0.375116	−	0.649720i	0.0153268	−	0.0265468i	−0.858260	−	0.513215i	$-0.828454\pi$
$599$	0.375116	−	0.649720i	0.0153268	−	0.0265468i	0.873587	+	0.486668i	$0.161788\pi$
$600$	−11.5728			−0.472458
$601$	−4.77652	+	8.27318i	−0.194838	+	0.337470i	−0.946848	−	0.321683i	$-0.895752\pi$
$601$	−4.77652	+	8.27318i	−0.194838	+	0.337470i	0.752009	+	0.659153i	$0.229085\pi$
$602$		0			0
$603$	30.3141			1.23449
$604$	−4.44624	+	7.70111i	−0.180915	+	0.313354i
$605$	1.28193			0.0521177
$606$	36.0925	−	62.5141i	1.46616	−	2.53946i
$607$	11.1197	−	19.2599i	0.451336	−	0.781737i	−0.547133	−	0.837045i	$-0.684281\pi$
$607$	11.1197	−	19.2599i	0.451336	−	0.781737i	0.998469	+	0.0553087i	$0.0176143\pi$
$608$	−4.64745	+	8.04961i	−0.188479	+	0.326455i
$609$		0			0
$610$	4.16815			0.168764
$611$	8.00594	−	41.2863i	0.323886	−	1.67027i
$612$	1.38278	−	2.39505i	0.0558957	−	0.0968143i
$613$	4.13993	+	7.17057i	0.167210	+	0.289617i	0.937438	−	0.348152i	$-0.113191\pi$
$613$	4.13993	+	7.17057i	0.167210	+	0.289617i	−0.770228	+	0.637769i	$0.779857\pi$
$614$	52.1578			2.10492
$615$	−1.22177	−	2.11617i	−0.0492665	−	0.0853321i
$616$		0			0
$617$	−10.1656	−	17.6073i	−0.409252	−	0.708845i	0.585554	−	0.810633i	$-0.300877\pi$
$617$	−10.1656	−	17.6073i	−0.409252	−	0.708845i	−0.994806	+	0.101789i	$0.967543\pi$
$618$	15.4189	−	26.7063i	0.620238	−	1.07428i
$619$	2.67049	−	4.62542i	0.107336	−	0.185911i	−0.807354	−	0.590067i	$-0.799101\pi$
$619$	2.67049	−	4.62542i	0.107336	−	0.185911i	0.914690	+	0.404156i	$0.132435\pi$
$620$	0.367203			0.0147472
$621$	−6.96005			−0.279297
$622$	−21.8651	+	37.8714i	−0.876709	+	1.51850i
$623$		0			0
$624$	7.55018	−	38.9360i	0.302249	−	1.55869i
$625$	−12.2086	−	21.1459i	−0.488345	−	0.845838i
$626$	−3.11112	−	5.38862i	−0.124345	−	0.215372i
$627$	6.48536	+	11.2330i	0.259000	+	0.448601i
$628$	3.29536	−	5.70773i	0.131499	−	0.227763i
$629$	−2.56165			−0.102140
$630$		0			0
$631$	−3.23331	−	5.60026i	−0.128716	−	0.222943i	0.794463	−	0.607312i	$-0.207752\pi$
$631$	−3.23331	−	5.60026i	−0.128716	−	0.222943i	−0.923179	+	0.384369i	$0.874419\pi$
$632$	−5.45714	−	9.45205i	−0.217074	−	0.375982i
$633$	−60.7222			−2.41349
$634$	6.76217	+	11.7124i	0.268560	+	0.465160i
$635$	−0.432271			−0.0171541
$636$	−15.4904			−0.614236
$637$		0			0
$638$	64.0322			2.53506
$639$	−13.5095			−0.534428
$640$	−0.772706	−	1.33837i	−0.0305439	−	0.0529035i
$641$	23.3289			0.921434			0.460717	−	0.887547i	$-0.347592\pi$
$641$	23.3289			0.921434			0.460717	+	0.887547i	$0.347592\pi$
$642$	−20.9993	−	36.3719i	−0.828778	−	1.43549i
$643$	−1.79439	−	3.10797i	−0.0707637	−	0.122566i	0.828472	−	0.560030i	$-0.189210\pi$
$643$	−1.79439	−	3.10797i	−0.0707637	−	0.122566i	−0.899236	+	0.437463i	$0.855877\pi$
$644$		0			0
$645$	−2.41222			−0.0949810
$646$	−1.05658	+	1.83006i	−0.0415707	+	0.0720026i
$647$	−19.8262	−	34.3400i	−0.779448	−	1.35004i	−0.932260	−	0.361788i	$-0.882166\pi$
$647$	−19.8262	−	34.3400i	−0.779448	−	1.35004i	0.152812	−	0.988255i	$-0.451167\pi$
$648$	−5.42402	−	9.39467i	−0.213076	−	0.369058i
$649$	−12.6697	−	21.9446i	−0.497331	−	0.861402i
$650$	31.4218	−	10.8352i	1.23246	−	0.424993i
$651$		0			0
$652$	−1.32386	+	2.29299i	−0.0518464	+	0.0898005i
$653$	18.1355			0.709699			0.354849	−	0.934923i	$-0.384532\pi$
$653$	18.1355			0.709699			0.354849	+	0.934923i	$0.384532\pi$
$654$	58.8938			2.30293
$655$	0.224610	−	0.389035i	0.00877623	−	0.0152009i
$656$	−12.9392	+	22.4114i	−0.505192	+	0.875017i
$657$	4.39592	+	7.61395i	0.171501	+	0.297048i
$658$		0			0
$659$	−6.74052	−	11.6749i	−0.262573	−	0.454791i	0.704352	−	0.709851i	$-0.251238\pi$
$659$	−6.74052	−	11.6749i	−0.262573	−	0.454791i	−0.966925	+	0.255061i	$0.917905\pi$
$660$	2.75122			0.107091
$661$	5.15611	+	8.93064i	0.200549	+	0.347362i	0.948706	−	0.316161i	$-0.102394\pi$
$661$	5.15611	+	8.93064i	0.200549	+	0.347362i	−0.748156	+	0.663523i	$0.769061\pi$
$662$	13.3076	−	23.0494i	0.517213	−	0.895839i
$663$	1.32471	−	6.83150i	0.0514476	−	0.265314i
$664$	3.12571			0.121301
$665$		0			0
$666$	−6.40111	+	11.0870i	−0.248038	+	0.429614i
$667$	−16.9517	+	29.3613i	−0.656374	+	1.13687i
$668$	−7.77805	+	13.4720i	−0.300942	+	0.521247i
$669$	−1.67019			−0.0645733
$670$	−2.45655	+	4.25487i	−0.0949049	+	0.164380i
$671$	−47.5397			−1.83525
$672$		0			0
$673$	4.61528	−	7.99390i	0.177906	−	0.308142i	−0.763257	−	0.646095i	$-0.776401\pi$
$673$	4.61528	−	7.99390i	0.177906	−	0.308142i	0.941163	+	0.337953i	$0.109734\pi$
$674$	31.9237			1.22965
$675$	4.19533	−	7.26652i	0.161478	−	0.279689i
$676$	2.64527	+	18.6997i	0.101741	+	0.719221i
$677$	−10.5467	−	18.2674i	−0.405343	−	0.702075i	0.589018	−	0.808120i	$-0.299515\pi$
$677$	−10.5467	−	18.2674i	−0.405343	−	0.702075i	−0.994361	+	0.106045i	$0.966181\pi$
$678$	−9.09807	+	15.7583i	−0.349409	+	0.605194i
$679$		0			0
$680$	−0.0844203	−	0.146220i	−0.00323737	−	0.00560729i
$681$	3.27129	+	5.66604i	0.125356	+	0.217123i
$682$	−9.95385			−0.381153
$683$	−38.2212			−1.46249			−0.731246	−	0.682113i	$-0.761061\pi$
$683$	−38.2212			−1.46249			−0.731246	+	0.682113i	$0.761061\pi$
$684$	2.22176	+	3.84821i	0.0849512	+	0.147140i
$685$	−1.32706	−	2.29854i	−0.0507044	−	0.0878226i
$686$		0			0
$687$	−3.64013	+	6.30490i	−0.138880	+	0.240547i
$688$	12.7734	+	22.1241i	0.486980	+	0.843474i
$689$	−15.8430	+	5.46317i	−0.603570	+	0.208130i
$690$	−1.73107	+	2.99830i	−0.0659006	+	0.114143i
$691$	26.2322			0.997920			0.498960	−	0.866625i	$-0.333715\pi$
$691$	26.2322			0.997920			0.498960	+	0.866625i	$0.333715\pi$
$692$	−9.80084	+	16.9755i	−0.372572	+	0.645313i
$693$		0			0
$694$	−14.3130			−0.543314
$695$	0.399204	−	0.691442i	0.0151427	−	0.0262279i
$696$	−19.2185			−0.728476
$697$	−2.27024	+	3.93218i	−0.0859916	+	0.148942i
$698$	20.7836	−	35.9982i	0.786670	−	1.36255i
$699$	15.3784	−	26.6361i	0.581664	−	1.00747i
$700$		0			0
$701$	−46.7346			−1.76514			−0.882570	−	0.470180i	$-0.844189\pi$
$701$	−46.7346			−1.76514			−0.882570	+	0.470180i	$0.844189\pi$
$702$	8.55515	+	7.43011i	0.322893	+	0.280431i
$703$	2.05794	−	3.56446i	0.0776167	−	0.134436i
$704$	−6.66528	−	11.5446i	−0.251207	−	0.435104i
$705$	−5.28105			−0.198896
$706$	−20.6835	−	35.8248i	−0.778433	−	1.34828i
$707$		0			0
$708$	−10.0950	−	17.4851i	−0.379395	−	0.657131i
$709$	23.7232	−	41.0898i	0.890944	−	1.54316i	0.0521988	−	0.998637i	$-0.483377\pi$
$709$	23.7232	−	41.0898i	0.890944	−	1.54316i	0.838745	−	0.544524i	$-0.183290\pi$
$710$	1.09476	−	1.89619i	0.0410858	−	0.0711626i
$711$	−24.2869			−0.910830
$712$	−12.1861			−0.456695
$713$	2.63516	−	4.56423i	0.0986876	−	0.170932i
$714$		0			0
$715$	2.81384	−	0.970301i	0.105232	−	0.0362872i
$716$	−7.60461	−	13.1716i	−0.284197	−	0.492244i
$717$	−17.8408	−	30.9011i	−0.666275	−	1.15402i
$718$	2.56280	+	4.43890i	0.0956428	+	0.165658i
$719$	−24.6190	+	42.6413i	−0.918133	+	1.59025i	−0.115884	+	0.993263i	$0.536970\pi$
$719$	−24.6190	+	42.6413i	−0.918133	+	1.59025i	−0.802249	+	0.596990i	$0.796363\pi$
$720$	−2.14136			−0.0798037
$721$		0			0
$722$	15.9549	+	27.6347i	0.593779	+	1.02846i
$723$	8.68963	+	15.0509i	0.323171	+	0.559748i
$724$	−18.1900			−0.676024
$725$	−20.4361	−	35.3963i	−0.758977	−	1.31459i
$726$	−27.6878			−1.02759
$727$	32.0495			1.18865			0.594325	−	0.804225i	$-0.297419\pi$
$727$	32.0495			1.18865			0.594325	+	0.804225i	$0.297419\pi$
$728$		0			0
$729$	−12.4996			−0.462947
$730$	−1.42492			−0.0527387
$731$	2.24114	+	3.88178i	0.0828917	+	0.143573i
$732$	−37.8789			−1.40004
$733$	14.1005	+	24.4228i	0.520813	+	0.902075i	0.999707	+	0.0242025i	$0.00770464\pi$
$733$	14.1005	+	24.4228i	0.520813	+	0.902075i	−0.478894	+	0.877873i	$0.658962\pi$
$734$	−13.1462	−	22.7699i	−0.485236	−	0.840453i
$735$		0			0
$736$	28.2968			1.04303
$737$	28.0181	−	48.5288i	1.03206	−	1.78758i
$738$	11.3459	+	19.6516i	0.417648	+	0.723387i
$739$	21.2685	+	36.8381i	0.782375	+	1.35511i	0.930555	+	0.366153i	$0.119325\pi$
$739$	21.2685	+	36.8381i	0.782375	+	1.35511i	−0.148180	+	0.988960i	$0.547342\pi$
$740$	−0.436510	−	0.756058i	−0.0160464	−	0.0277932i
$741$	8.44160	+	7.33149i	0.310110	+	0.269329i
$742$		0			0
$743$	−7.95711	+	13.7821i	−0.291918	+	0.505617i	−0.974263	−	0.225413i	$-0.927627\pi$
$743$	−7.95711	+	13.7821i	−0.291918	+	0.505617i	0.682345	+	0.731030i	$0.260960\pi$
$744$	2.98753			0.109528
$745$	3.02989			0.111007
$746$	4.68521	−	8.11502i	0.171538	−	0.297112i
$747$	3.47773	−	6.02360i	0.127243	−	0.220392i
$748$	−2.55611	−	4.42731i	−0.0934605	−	0.161878i
$749$		0			0
$750$	−4.19014	−	7.25754i	−0.153002	−	0.265008i
$751$	18.1996			0.664114			0.332057	−	0.943259i	$-0.392257\pi$
$751$	18.1996			0.664114			0.332057	+	0.943259i	$0.392257\pi$
$752$	27.9646	+	48.4362i	1.01977	+	1.76629i
$753$	−1.46220	+	2.53260i	−0.0532855	+	0.0922931i
$754$	52.1809	−	17.9937i	1.90032	−	0.655290i
$755$	1.20807			0.0439662
$756$		0			0
$757$	22.4502	−	38.8849i	0.815967	−	1.41330i	−0.0926649	−	0.995697i	$-0.529539\pi$
$757$	22.4502	−	38.8849i	0.815967	−	1.41330i	0.908632	−	0.417598i	$-0.137128\pi$
$758$	5.62989	−	9.75126i	0.204487	−	0.354182i
$759$	19.7436	−	34.1970i	0.716648	−	1.24127i
$760$	0.271282			0.00984042
$761$	−13.2444	+	22.9399i	−0.480108	+	0.831572i	−0.999740	−	0.0228184i	$-0.992736\pi$
$761$	−13.2444	+	22.9399i	−0.480108	+	0.831572i	0.519631	+	0.854391i	$0.326069\pi$
$762$	9.33644			0.338223
$763$		0			0
$764$	−9.52554	+	16.4987i	−0.344622	+	0.596903i
$765$	−0.375711			−0.0135839
$766$	−4.21900	+	7.30752i	−0.152439	+	0.264031i
$767$	−16.4914	−	14.3227i	−0.595471	−	0.517164i
$768$	24.0006	+	41.5703i	0.866049	+	1.50004i
$769$	6.98127	−	12.0919i	0.251751	−	0.436045i	−0.712257	−	0.701919i	$-0.752327\pi$
$769$	6.98127	−	12.0919i	0.251751	−	0.436045i	0.964008	+	0.265873i	$0.0856603\pi$
$770$		0			0
$771$	9.72707	+	16.8478i	0.350312	+	0.606758i
$772$	−0.756579	−	1.31043i	−0.0272299	−	0.0471635i
$773$	−12.8113			−0.460790			−0.230395	−	0.973097i	$-0.574002\pi$
$773$	−12.8113			−0.460790			−0.230395	+	0.973097i	$0.574002\pi$
$774$	22.4009			0.805184
$775$	3.17681	+

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.85816 q^{2} +(1.14703 + 1.98672i) q^{3} +1.45276 q^{4} +(-0.0986811 - 0.170921i) q^{5} +(2.13137 + 3.69165i) q^{6} -1.01686 q^{8} +(-1.13137 + 1.95960i) q^{9} +O(q^{10})\)	\(q+1.85816 q^{2} +(1.14703 + 1.98672i) q^{3} +1.45276 q^{4} +(-0.0986811 - 0.170921i) q^{5} +(2.13137 + 3.69165i) q^{6} -1.01686 q^{8} +(-1.13137 + 1.95960i) q^{9} +(-0.183365 - 0.317598i) q^{10} +(2.09137 + 3.62236i) q^{11} +(1.66637 + 2.88623i) q^{12} +(2.72221 + 2.36423i) q^{13} +(0.226381 - 0.392104i) q^{15} -4.79501 q^{16} -0.841305 q^{17} +(-2.10227 + 3.64125i) q^{18} +(0.675876 - 1.17065i) q^{19} +(-0.143360 - 0.248307i) q^{20} +(3.88610 + 6.73092i) q^{22} -4.11519 q^{23} +(-1.16637 - 2.02021i) q^{24} +(2.48052 - 4.29639i) q^{25} +(5.05830 + 4.39312i) q^{26} +1.69131 q^{27} +(4.11931 - 7.13485i) q^{29} +(0.420653 - 0.728592i) q^{30} +(-0.640350 + 1.10912i) q^{31} -6.87618 q^{32} +(-4.79774 + 8.30993i) q^{33} -1.56328 q^{34} +(-1.64362 + 2.84683i) q^{36} +3.04485 q^{37} +(1.25589 - 2.17526i) q^{38} +(-1.57459 + 8.12012i) q^{39} +(0.100344 + 0.173802i) q^{40} +(2.69848 - 4.67390i) q^{41} +(-2.66389 - 4.61399i) q^{43} +(3.03826 + 5.26242i) q^{44} +0.446581 q^{45} -7.64669 q^{46} +(-5.83204 - 10.1014i) q^{47} +(-5.50003 - 9.52634i) q^{48} +(4.60921 - 7.98339i) q^{50} +(-0.965006 - 1.67144i) q^{51} +(3.95472 + 3.43466i) q^{52} +(-2.32398 + 4.02525i) q^{53} +3.14272 q^{54} +(0.412757 - 0.714916i) q^{55} +3.10101 q^{57} +(7.65434 - 13.2577i) q^{58} -6.05811 q^{59} +(0.328878 - 0.569634i) q^{60} +(-5.68285 + 9.84298i) q^{61} +(-1.18987 + 2.06092i) q^{62} -3.18704 q^{64} +(0.135465 - 0.698587i) q^{65} +(-8.91498 + 15.4412i) q^{66} +(-6.69851 - 11.6022i) q^{67} -1.22222 q^{68} +(-4.72026 - 8.17574i) q^{69} +(2.98520 + 5.17051i) q^{71} +(1.15044 - 1.99263i) q^{72} +(1.94273 - 3.36491i) q^{73} +5.65782 q^{74} +11.3810 q^{75} +(0.981887 - 1.70068i) q^{76} +(-2.92585 + 15.0885i) q^{78} +(5.36669 + 9.29537i) q^{79} +(0.473177 + 0.819566i) q^{80} +(5.33411 + 9.23895i) q^{81} +(5.01421 - 8.68486i) q^{82} -3.07390 q^{83} +(0.0830210 + 0.143797i) q^{85} +(-4.94994 - 8.57354i) q^{86} +18.8999 q^{87} +(-2.12662 - 3.68341i) q^{88} +11.9841 q^{89} +0.829819 q^{90} -5.97840 q^{92} -2.93801 q^{93} +(-10.8369 - 18.7700i) q^{94} -0.266785 q^{95} +(-7.88721 - 13.6611i) q^{96} +(9.73637 + 16.8639i) q^{97} -9.46448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9	\( 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} - 16 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + q^{20} - 5 q^{22} + 2 q^{23} + 11 q^{24} + 7 q^{25} + 16 q^{26} + 8 q^{27} + 3 q^{29} - 5 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 32 q^{34} - 21 q^{36} + 26 q^{37} + 17 q^{38} - 20 q^{39} + 5 q^{40} + 8 q^{41} - 11 q^{43} + 21 q^{44} - 14 q^{45} - 32 q^{46} + q^{47} - 21 q^{48} + 6 q^{50} - 20 q^{51} - 41 q^{52} - 2 q^{53} - 36 q^{54} - 9 q^{55} + 42 q^{57} - 8 q^{58} + 26 q^{59} + 20 q^{60} + 5 q^{61} - 5 q^{62} - 30 q^{64} - 5 q^{65} - 18 q^{66} - 11 q^{67} + 58 q^{68} - 23 q^{69} + 6 q^{71} + 25 q^{72} + 30 q^{73} + 6 q^{74} - 6 q^{75} + 9 q^{76} + 16 q^{78} + 7 q^{79} + 7 q^{80} - 6 q^{81} - q^{82} + 54 q^{83} - q^{85} - 7 q^{86} + 32 q^{87} + 8 q^{89} + 16 q^{90} + 54 q^{92} + 14 q^{93} - 45 q^{94} + 12 q^{95} - 19 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 - 16 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + q^20 - 5 * q^22 + 2 * q^23 + 11 * q^24 + 7 * q^25 + 16 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 + 26 * q^37 + 17 * q^38 - 20 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 - 14 * q^45 - 32 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 - 41 * q^52 - 2 * q^53 - 36 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 + 26 * q^59 + 20 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 5 * q^65 - 18 * q^66 - 11 * q^67 + 58 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 + 30 * q^73 + 6 * q^74 - 6 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 - 7 * q^86 + 32 * q^87 + 8 * q^89 + 16 * q^90 + 54 * q^92 + 14 * q^93 - 45 * q^94 + 12 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Introduction

L-functions

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