LMFDB - Embedded newform 637.2.e.k.79.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(79,637)]

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([2, 0]))

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

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

chi := DirichletCharacter("637.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.e (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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.4406832.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 6x^{4} + 7x^{3} + 24x^{2} + 5x + 1 $ x^6 - x^5 + 6x^4 + 7x^3 + 24x^2 + 5x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.3
Root			$-0.827721 - 1.43366i$ of defining polynomial
Character	$\chi$	$=$	637.79
Dual form			637.2.e.k.508.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32772 - 2.29968i) q^{2} +(-1.19797 - 2.07494i) q^{3} +(-2.52569 - 4.37462i) q^{4} +(-1.82772 + 3.16571i) q^{5} -6.36226 q^{6} -8.10275 q^{8} +(-1.37024 + 2.37333i) q^{9} +O(q^{10})$	\(q+(1.32772 - 2.29968i) q^{2} +(-1.19797 - 2.07494i) q^{3} +(-2.52569 - 4.37462i) q^{4} +(-1.82772 + 3.16571i) q^{5} -6.36226 q^{6} -8.10275 q^{8} +(-1.37024 + 2.37333i) q^{9} +(4.85341 + 8.40635i) q^{10} +(-0.327721 - 0.567630i) q^{11} +(-6.05137 + 10.4813i) q^{12} -1.00000 q^{13} +8.75819 q^{15} +(-5.70682 + 9.88450i) q^{16} +(-1.19797 - 2.07494i) q^{17} +(3.63861 + 6.30225i) q^{18} +(1.35341 - 2.34417i) q^{19} +18.4650 q^{20} -1.74049 q^{22} +(-3.68113 + 6.37590i) q^{23} +(9.70682 + 16.8127i) q^{24} +(-4.18113 - 7.24193i) q^{25} +(-1.32772 + 2.29968i) q^{26} -0.621770 q^{27} -0.208136 q^{29} +(11.6284 - 20.1410i) q^{30} +(0.568211 + 0.984170i) q^{31} +(7.05137 + 12.2133i) q^{32} +(-0.785198 + 1.36000i) q^{33} -6.36226 q^{34} +13.8432 q^{36} +(3.72365 - 6.44956i) q^{37} +(-3.59390 - 6.22481i) q^{38} +(1.19797 + 2.07494i) q^{39} +(14.8096 - 25.6509i) q^{40} -10.2055 q^{41} -3.10275 q^{43} +(-1.65544 + 2.86731i) q^{44} +(-5.00885 - 8.67558i) q^{45} +(9.77503 + 16.9308i) q^{46} +(-2.30203 + 3.98724i) q^{47} +27.3463 q^{48} -22.2055 q^{50} +(-2.87024 + 4.97141i) q^{51} +(2.52569 + 4.37462i) q^{52} +(-2.62976 - 4.55487i) q^{53} +(-0.825537 + 1.42987i) q^{54} +2.39593 q^{55} -6.48535 q^{57} +(-0.276347 + 0.478647i) q^{58} +(-4.12976 - 7.15295i) q^{59} +(-22.1204 - 38.3137i) q^{60} +(0.948626 - 1.64307i) q^{61} +3.01770 q^{62} +14.6218 q^{64} +(1.82772 - 3.16571i) q^{65} +(2.08505 + 3.61141i) q^{66} +(6.44731 + 11.1671i) q^{67} +(-6.05137 + 10.4813i) q^{68} +17.6395 q^{69} -6.75819 q^{71} +(11.1027 - 19.2305i) q^{72} +(-6.26836 - 10.8571i) q^{73} +(-9.88795 - 17.1264i) q^{74} +(-10.0177 + 17.3512i) q^{75} -13.6731 q^{76} +6.36226 q^{78} +(0.759511 - 1.31551i) q^{79} +(-20.8609 - 36.1322i) q^{80} +(4.85559 + 8.41013i) q^{81} +(-13.5501 + 23.4694i) q^{82} +15.7582 q^{83} +8.75819 q^{85} +(-4.11958 + 7.13533i) q^{86} +(0.249340 + 0.431870i) q^{87} +(2.65544 + 4.59936i) q^{88} +(7.40478 - 12.8255i) q^{89} -26.6014 q^{90} +37.1895 q^{92} +(1.36139 - 2.35800i) q^{93} +(6.11292 + 10.5879i) q^{94} +(4.94731 + 8.56899i) q^{95} +(16.8946 - 29.2623i) q^{96} -10.0177 q^{97} +1.79623 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 5 q^{5} + 4 q^{6} - 12 q^{8} - 11 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 - 5 * q^5 + 4 * q^6 - 12 * q^8 - 11 * q^9	$ 6 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 5 q^{5} + 4 q^{6} - 12 q^{8} - 11 q^{9} + 14 q^{10} + 4 q^{11} - 18 q^{12} - 6 q^{13} + 4 q^{15} - 4 q^{16} - 4 q^{17} - 8 q^{18} - 7 q^{19} + 32 q^{20} - 16 q^{22} - q^{23} + 28 q^{24} - 4 q^{25} - 2 q^{26} + 44 q^{27} - 14 q^{29} + 24 q^{30} + 3 q^{31} + 24 q^{32} + 10 q^{33} + 4 q^{34} + 52 q^{36} + 10 q^{37} - 12 q^{38} + 4 q^{39} + 22 q^{40} + 12 q^{41} + 18 q^{43} + 2 q^{44} - 3 q^{45} + 28 q^{46} - 17 q^{47} + 32 q^{48} - 60 q^{50} - 20 q^{51} + 6 q^{52} - 13 q^{53} - 28 q^{54} + 8 q^{55} + 8 q^{57} - 14 q^{58} - 22 q^{59} - 42 q^{60} + 24 q^{61} - 36 q^{62} + 40 q^{64} + 5 q^{65} + 30 q^{66} + 14 q^{67} - 18 q^{68} + 4 q^{69} + 8 q^{71} + 30 q^{72} - 5 q^{73} - 8 q^{74} - 6 q^{75} - 16 q^{76} - 4 q^{78} - q^{79} - 40 q^{80} - 15 q^{81} - 20 q^{82} + 46 q^{83} + 4 q^{85} - 6 q^{86} - 20 q^{87} + 4 q^{88} + 11 q^{89} - 80 q^{90} + 60 q^{92} + 38 q^{93} + 16 q^{94} + 5 q^{95} + 52 q^{96} - 6 q^{97} - 60 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 - 5 * q^5 + 4 * q^6 - 12 * q^8 - 11 * q^9 + 14 * q^10 + 4 * q^11 - 18 * q^12 - 6 * q^13 + 4 * q^15 - 4 * q^16 - 4 * q^17 - 8 * q^18 - 7 * q^19 + 32 * q^20 - 16 * q^22 - q^23 + 28 * q^24 - 4 * q^25 - 2 * q^26 + 44 * q^27 - 14 * q^29 + 24 * q^30 + 3 * q^31 + 24 * q^32 + 10 * q^33 + 4 * q^34 + 52 * q^36 + 10 * q^37 - 12 * q^38 + 4 * q^39 + 22 * q^40 + 12 * q^41 + 18 * q^43 + 2 * q^44 - 3 * q^45 + 28 * q^46 - 17 * q^47 + 32 * q^48 - 60 * q^50 - 20 * q^51 + 6 * q^52 - 13 * q^53 - 28 * q^54 + 8 * q^55 + 8 * q^57 - 14 * q^58 - 22 * q^59 - 42 * q^60 + 24 * q^61 - 36 * q^62 + 40 * q^64 + 5 * q^65 + 30 * q^66 + 14 * q^67 - 18 * q^68 + 4 * q^69 + 8 * q^71 + 30 * q^72 - 5 * q^73 - 8 * q^74 - 6 * q^75 - 16 * q^76 - 4 * q^78 - q^79 - 40 * q^80 - 15 * q^81 - 20 * q^82 + 46 * q^83 + 4 * q^85 - 6 * q^86 - 20 * q^87 + 4 * q^88 + 11 * q^89 - 80 * q^90 + 60 * q^92 + 38 * q^93 + 16 * q^94 + 5 * q^95 + 52 * q^96 - 6 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.32772	−	2.29968i	0.938841	−	1.62612i	0.171203	−	0.985236i	$-0.445235\pi$
$2$	1.32772	−	2.29968i	0.938841	−	1.62612i	0.767638	−	0.640884i	$-0.221432\pi$
$3$	−1.19797	−	2.07494i	−0.691646	−	1.19797i	−0.971298	−	0.237865i	$-0.923553\pi$
$3$	−1.19797	−	2.07494i	−0.691646	−	1.19797i	0.279652	−	0.960101i	$-0.409781\pi$
$4$	−2.52569	−	4.37462i	−1.26284	−	2.18731i
$5$	−1.82772	+	3.16571i	−0.817382	+	1.41575i	0.0902232	+	0.995922i	$0.471242\pi$
$5$	−1.82772	+	3.16571i	−0.817382	+	1.41575i	−0.907605	+	0.419825i	$0.862091\pi$
$6$	−6.36226			−2.59738
$7$		0			0
$7$		0			0
$8$	−8.10275			−2.86475
$9$	−1.37024	+	2.37333i	−0.456748	+	0.791111i
$10$	4.85341	+	8.40635i	1.53478	+	2.65832i
$11$	−0.327721	−	0.567630i	−0.0988117	−	0.171147i	0.812381	−	0.583126i	$-0.198171\pi$
$11$	−0.327721	−	0.567630i	−0.0988117	−	0.171147i	−0.911193	+	0.411980i	$0.864837\pi$
$12$	−6.05137	+	10.4813i	−1.74688	+	3.02569i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	8.75819			2.26136
$16$	−5.70682	+	9.88450i	−1.42670	+	2.47112i
$17$	−1.19797	−	2.07494i	−0.290549	−	0.503246i	0.683390	−	0.730053i	$-0.260505\pi$
$17$	−1.19797	−	2.07494i	−0.290549	−	0.503246i	−0.973940	+	0.226807i	$0.927171\pi$
$18$	3.63861	+	6.30225i	0.857628	+	1.48545i
$19$	1.35341	−	2.34417i	0.310493	−	0.537790i	−0.667976	−	0.744183i	$-0.732839\pi$
$19$	1.35341	−	2.34417i	0.310493	−	0.537790i	0.978469	+	0.206393i	$0.0661725\pi$
$20$	18.4650			4.12890
$21$		0			0
$22$	−1.74049			−0.371074
$23$	−3.68113	+	6.37590i	−0.767569	+	1.32947i	0.171309	+	0.985217i	$0.445200\pi$
$23$	−3.68113	+	6.37590i	−0.767569	+	1.32947i	−0.938878	+	0.344250i	$0.888133\pi$
$24$	9.70682	+	16.8127i	1.98140	+	3.43188i
$25$	−4.18113	−	7.24193i	−0.836226	−	1.44839i
$26$	−1.32772	+	2.29968i	−0.260388	+	0.451004i
$27$	−0.621770			−0.119660
$28$		0			0
$29$	−0.208136			−0.0386499			−0.0193250	−	0.999813i	$-0.506152\pi$
$29$	−0.208136			−0.0386499			−0.0193250	+	0.999813i	$0.506152\pi$
$30$	11.6284	−	20.1410i	2.12305	−	3.67723i
$31$	0.568211	+	0.984170i	0.102054	+	0.176762i	0.912531	−	0.409008i	$-0.134125\pi$
$31$	0.568211	+	0.984170i	0.102054	+	0.176762i	−0.810477	+	0.585771i	$0.800792\pi$
$32$	7.05137	+	12.2133i	1.24652	+	2.15903i
$33$	−0.785198	+	1.36000i	−0.136685	+	0.236746i
$34$	−6.36226			−1.09112
$35$		0			0
$36$	13.8432			2.30721
$37$	3.72365	−	6.44956i	0.612165	−	1.06030i	−0.378710	−	0.925515i	$-0.623632\pi$
$37$	3.72365	−	6.44956i	0.612165	−	1.06030i	0.990875	−	0.134785i	$-0.0430344\pi$
$38$	−3.59390	−	6.22481i	−0.583007	−	1.00980i
$39$	1.19797	+	2.07494i	0.191828	+	0.332256i
$40$	14.8096	−	25.6509i	2.34160	−	4.05577i
$41$	−10.2055			−1.59383			−0.796915	−	0.604091i	$-0.793536\pi$
$41$	−10.2055			−1.59383			−0.796915	+	0.604091i	$0.793536\pi$
$42$		0			0
$43$	−3.10275			−0.473165			−0.236582	−	0.971611i	$-0.576027\pi$
$43$	−3.10275			−0.473165			−0.236582	+	0.971611i	$0.576027\pi$
$44$	−1.65544	+	2.86731i	−0.249567	+	0.432263i
$45$	−5.00885	−	8.67558i	−0.746675	−	1.29328i
$46$	9.77503	+	16.9308i	1.44125	+	2.49632i
$47$	−2.30203	+	3.98724i	−0.335786	+	0.581599i	−0.983636	−	0.180170i	$-0.942335\pi$
$47$	−2.30203	+	3.98724i	−0.335786	+	0.581599i	0.647849	+	0.761768i	$0.275669\pi$
$48$	27.3463			3.94710
$49$		0			0
$50$	−22.2055			−3.14033
$51$	−2.87024	+	4.97141i	−0.401915	+	0.696137i
$52$	2.52569	+	4.37462i	0.350250	+	0.606650i
$53$	−2.62976	−	4.55487i	−0.361225	−	0.625659i	0.626938	−	0.779069i	$-0.284308\pi$
$53$	−2.62976	−	4.55487i	−0.361225	−	0.625659i	−0.988163	+	0.153410i	$0.950975\pi$
$54$	−0.825537	+	1.42987i	−0.112341	+	0.194581i
$55$	2.39593			0.323067
$56$		0			0
$57$	−6.48535			−0.859005
$58$	−0.276347	+	0.478647i	−0.0362861	+	0.0628494i
$59$	−4.12976	−	7.15295i	−0.537648	−	0.931234i	−0.999030	−	0.0440325i	$-0.985979\pi$
$59$	−4.12976	−	7.15295i	−0.537648	−	0.931234i	0.461382	−	0.887202i	$-0.347354\pi$
$60$	−22.1204	−	38.3137i	−2.85574	−	4.94628i
$61$	0.948626	−	1.64307i	0.121459	−	0.210373i	−0.798884	−	0.601485i	$-0.794576\pi$
$61$	0.948626	−	1.64307i	0.121459	−	0.210373i	0.920343	+	0.391112i	$0.127909\pi$
$62$	3.01770			0.383248
$63$		0			0
$64$	14.6218			1.82772
$65$	1.82772	−	3.16571i	0.226701	−	0.392657i
$66$	2.08505	+	3.61141i	0.256652	+	0.444534i
$67$	6.44731	+	11.1671i	0.787664	+	1.36427i	0.927395	+	0.374084i	$0.122043\pi$
$67$	6.44731	+	11.1671i	0.787664	+	1.36427i	−0.139731	+	0.990190i	$0.544624\pi$
$68$	−6.05137	+	10.4813i	−0.733837	+	1.27104i
$69$	17.6395			2.12354
$70$		0			0
$71$	−6.75819			−0.802050			−0.401025	−	0.916067i	$-0.631346\pi$
$71$	−6.75819			−0.802050			−0.401025	+	0.916067i	$0.631346\pi$
$72$	11.1027	−	19.2305i	1.30847	−	2.26634i
$73$	−6.26836	−	10.8571i	−0.733656	−	1.27073i	−0.955310	−	0.295604i	$-0.904479\pi$
$73$	−6.26836	−	10.8571i	−0.733656	−	1.27073i	0.221654	−	0.975125i	$-0.428854\pi$
$74$	−9.88795	−	17.1264i	−1.14945	−	1.99091i
$75$	−10.0177	+	17.3512i	−1.15674	+	2.00354i
$76$	−13.6731			−1.56842
$77$		0			0
$78$	6.36226			0.720384
$79$	0.759511	−	1.31551i	0.0854516	−	0.148007i	−0.820132	−	0.572174i	$-0.806100\pi$
$79$	0.759511	−	1.31551i	0.0854516	−	0.148007i	0.905584	+	0.424168i	$0.139433\pi$
$80$	−20.8609	−	36.1322i	−2.33232	−	4.03970i
$81$	4.85559	+	8.41013i	0.539510	+	0.934459i
$82$	−13.5501	+	23.4694i	−1.49635	+	2.59176i
$83$	15.7582			1.72969			0.864843	−	0.502042i	$-0.167418\pi$
$83$	15.7582			1.72969			0.864843	+	0.502042i	$0.167418\pi$
$84$		0			0
$85$	8.75819			0.949959
$86$	−4.11958	+	7.13533i	−0.444226	+	0.769422i
$87$	0.249340	+	0.431870i	0.0267321	+	0.0463013i
$88$	2.65544	+	4.59936i	0.283071	+	0.490294i
$89$	7.40478	−	12.8255i	0.784905	−	1.35950i	−0.144150	−	0.989556i	$-0.546045\pi$
$89$	7.40478	−	12.8255i	0.784905	−	1.35950i	0.929056	−	0.369940i	$-0.120622\pi$
$90$	−26.6014			−2.80404
$91$		0			0
$92$	37.1895			3.87728
$93$	1.36139	−	2.35800i	0.141170	−	0.244514i
$94$	6.11292	+	10.5879i	0.630499	+	1.09206i
$95$	4.94731	+	8.56899i	0.507583	+	0.879159i
$96$	16.8946	−	29.2623i	1.72430	−	2.98657i
$97$	−10.0177			−1.01714			−0.508572	−	0.861020i	$-0.669826\pi$
$97$	−10.0177			−1.01714			−0.508572	+	0.861020i	$0.669826\pi$
$98$		0			0
$99$	1.79623			0.180528
$100$	−21.1204	+	36.5817i	−2.11204	+	3.65817i
$101$	1.50885	+	2.61341i	0.150136	+	0.260044i	0.931277	−	0.364311i	$-0.118695\pi$
$101$	1.50885	+	2.61341i	0.150136	+	0.260044i	−0.781141	+	0.624354i	$0.785362\pi$
$102$	7.62177	+	13.2013i	0.754668	+	1.30712i
$103$	2.51902	−	4.36307i	0.248207	−	0.429906i	−0.714822	−	0.699307i	$-0.753492\pi$
$103$	2.51902	−	4.36307i	0.248207	−	0.429906i	0.963028	+	0.269400i	$0.0868255\pi$
$104$	8.10275			0.794540
$105$		0			0
$106$	−13.9663			−1.35653
$107$	−5.92162	+	10.2565i	−0.572465	+	0.991538i	0.423848	+	0.905734i	$0.360679\pi$
$107$	−5.92162	+	10.2565i	−0.572465	+	0.991538i	−0.996312	+	0.0858041i	$0.972654\pi$
$108$	1.57040	+	2.72000i	0.151111	+	0.261733i
$109$	−1.77503	−	3.07444i	−0.170017	−	0.294478i	0.768409	−	0.639959i	$-0.221049\pi$
$109$	−1.77503	−	3.07444i	−0.170017	−	0.294478i	−0.938425	+	0.345482i	$0.887716\pi$
$110$	3.18113	−	5.50988i	0.303309	−	0.525346i
$111$	−17.8432			−1.69361
$112$		0			0
$113$	−9.46501			−0.890393			−0.445197	−	0.895433i	$-0.646866\pi$
$113$	−9.46501			−0.890393			−0.445197	+	0.895433i	$0.646866\pi$
$114$	−8.61073	+	14.9142i	−0.806469	+	1.39685i
$115$	−13.4562	−	23.3067i	−1.25479	−	2.17337i
$116$	0.525687	+	0.910517i	0.0488088	+	0.0845394i
$117$	1.37024	−	2.37333i	0.126679	−	0.219415i
$118$	−21.9327			−2.01906
$119$		0			0
$120$	−70.9654			−6.47823
$121$	5.28520	−	9.15423i	0.480473	−	0.832203i
$122$	−2.51902	−	4.36307i	−0.228061	−	0.395014i
$123$	12.2258	+	21.1758i	1.10237	+	1.90936i
$124$	2.87024	−	4.97141i	0.257756	−	0.446446i
$125$	12.2905			1.09930
$126$		0			0
$127$	5.46765			0.485175			0.242588	−	0.970130i	$-0.422004\pi$
$127$	5.46765			0.485175			0.242588	+	0.970130i	$0.422004\pi$
$128$	5.31088	−	9.19872i	0.469420	−	0.813060i
$129$	3.71699	+	6.43801i	0.327262	+	0.566835i
$130$	−4.85341	−	8.40635i	−0.425672	−	0.737286i
$131$	−4.91495	+	8.51295i	−0.429421	+	0.743780i	−0.996822	−	0.0796622i	$-0.974616\pi$
$131$	−4.91495	+	8.51295i	−0.429421	+	0.743780i	0.567400	+	0.823442i	$0.307949\pi$
$132$	7.93265			0.690449
$133$		0			0
$134$	34.2409			2.95796
$135$	1.13642	−	1.96834i	0.0978076	−	0.169408i
$136$	9.70682	+	16.8127i	0.832353	+	1.44168i
$137$	−8.77503	−	15.1988i	−0.749701	−	1.29852i	−0.947966	−	0.318372i	$-0.896864\pi$
$137$	−8.77503	−	15.1988i	−0.749701	−	1.29852i	0.198265	−	0.980149i	$-0.436469\pi$
$138$	23.4203	−	40.5651i	1.99367	−	3.45313i
$139$	−4.91495			−0.416881			−0.208440	−	0.978035i	$-0.566839\pi$
$139$	−4.91495			−0.416881			−0.208440	+	0.978035i	$0.566839\pi$
$140$		0			0
$141$	11.0310			0.928981
$142$	−8.97299	+	15.5417i	−0.752997	+	1.30423i
$143$	0.327721	+	0.567630i	0.0274054	+	0.0474676i
$144$	−15.6395	−	27.0884i	−1.30329	−	2.25736i
$145$	0.380415	−	0.658898i	0.0315918	−	0.0547185i
$146$	−33.2905			−2.75515
$147$		0			0
$148$	−37.6191			−3.09227
$149$	5.17096	−	8.95636i	0.423621	−	0.733734i	−0.572669	−	0.819787i	$-0.694092\pi$
$149$	5.17096	−	8.95636i	0.423621	−	0.733734i	0.996291	+	0.0860527i	$0.0274253\pi$
$150$	26.6014	+	46.0750i	2.17200	+	3.76201i
$151$	−2.53586	−	4.39223i	−0.206365	−	0.357435i	0.744202	−	0.667955i	$-0.232830\pi$
$151$	−2.53586	−	4.39223i	−0.206365	−	0.357435i	−0.950567	+	0.310520i	$0.899497\pi$
$152$	−10.9663	+	18.9942i	−0.889487	+	1.54064i
$153$	6.56603			0.530832
$154$		0			0
$155$	−4.15412			−0.333667
$156$	6.05137	−	10.4813i	0.484498	−	0.839175i
$157$	6.30071	+	10.9132i	0.502852	+	0.870965i	0.999995	+	0.00329606i	$0.00104917\pi$
$157$	6.30071	+	10.9132i	0.502852	+	0.870965i	−0.497143	+	0.867669i	$0.665617\pi$
$158$	−2.01684	−	3.49326i	−0.160451	−	0.277909i
$159$	−6.30071	+	10.9132i	−0.499679	+	0.865470i
$160$	−51.5518			−4.07553
$161$		0			0
$162$	25.7875			2.02606
$163$	−1.60407	+	2.77833i	−0.125640	+	0.217615i	−0.921983	−	0.387230i	$-0.873432\pi$
$163$	−1.60407	+	2.77833i	−0.125640	+	0.217615i	0.796343	+	0.604846i	$0.206765\pi$
$164$	25.7759	+	44.6452i	2.01276	+	3.48620i
$165$	−2.87024	−	4.97141i	−0.223448	−	0.387024i
$166$	20.9225	−	36.2388i	1.62390	−	2.81268i
$167$	8.12045			0.628379			0.314190	−	0.949360i	$-0.398267\pi$
$167$	8.12045			0.628379			0.314190	+	0.949360i	$0.398267\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	11.6284	−	20.1410i	0.891860	−	1.54475i
$171$	3.70900	+	6.42418i	0.283634	+	0.491269i
$172$	7.83657	+	13.5733i	0.597533	+	1.03496i
$173$	5.16429	−	8.94482i	0.392634	−	0.680062i	−0.600162	−	0.799878i	$-0.704897\pi$
$173$	5.16429	−	8.94482i	0.392634	−	0.680062i	0.992796	+	0.119816i	$0.0382306\pi$
$174$	1.32422			0.100389
$175$		0			0
$176$	7.48098			0.563900
$177$	−9.89461	+	17.1380i	−0.743725	+	1.28817i
$178$	−19.6630	−	34.0573i	−1.47380	−	2.55270i
$179$	1.18912	+	2.05961i	0.0888786	+	0.153942i	0.907037	−	0.421050i	$-0.138338\pi$
$179$	1.18912	+	2.05961i	0.0888786	+	0.153942i	−0.818159	+	0.574992i	$0.805005\pi$
$180$	−25.3016	+	43.8236i	−1.88587	+	3.26642i
$181$	21.8096			1.62109			0.810546	−	0.585675i	$-0.199170\pi$
$181$	21.8096			1.62109			0.810546	+	0.585675i	$0.199170\pi$
$182$		0			0
$183$	−4.54569			−0.336027
$184$	29.8273	−	51.6623i	2.19890	−	3.80860i
$185$	13.6116	+	23.5760i	1.00074	+	1.73334i
$186$	−3.61510	−	6.26154i	−0.265072	−	0.459119i
$187$	−0.785198	+	1.36000i	−0.0574193	+	0.0994532i
$188$	23.2569			1.69618
$189$		0			0
$190$	26.2746			1.90616
$191$	12.5434	−	21.7258i	0.907608	−	1.57202i	0.0902297	−	0.995921i	$-0.471240\pi$
$191$	12.5434	−	21.7258i	0.907608	−	1.57202i	0.817378	−	0.576102i	$-0.195427\pi$
$192$	−17.5164	−	30.3393i	−1.26414	−	2.18955i
$193$	−5.65544	−	9.79551i	−0.407088	−	0.705096i	0.587474	−	0.809243i	$-0.300122\pi$
$193$	−5.65544	−	9.79551i	−0.407088	−	0.705096i	−0.994562	+	0.104146i	$0.966789\pi$
$194$	−13.3007	+	23.0375i	−0.954936	+	1.65400i
$195$	−8.75819			−0.627187
$196$		0			0
$197$	−16.7919			−1.19637			−0.598185	−	0.801358i	$-0.704111\pi$
$197$	−16.7919			−1.19637			−0.598185	+	0.801358i	$0.704111\pi$
$198$	2.38490	−	4.13076i	0.169487	−	0.293560i
$199$	−10.2670	−	17.7830i	−0.727811	−	1.26061i	−0.957806	−	0.287414i	$-0.907204\pi$
$199$	−10.2670	−	17.7830i	−0.727811	−	1.26061i	0.229995	−	0.973192i	$-0.426129\pi$
$200$	33.8786	+	58.6795i	2.39558	+	4.14927i
$201$	15.4473	−	26.7555i	1.08957	−	1.88719i
$202$	8.01333			0.563816
$203$		0			0
$204$	28.9974			2.03022
$205$	18.6528	−	32.3076i	1.30277	−	2.25646i
$206$	−6.68912	−	11.5859i	−0.466053	−	0.807227i
$207$	−10.0881	−	17.4731i	−0.701171	−	1.21446i
$208$	5.70682	−	9.88450i	0.395697	−	0.685367i
$209$	−1.77416			−0.122721
$210$		0			0
$211$	−15.7785			−1.08624			−0.543119	−	0.839655i	$-0.682757\pi$
$211$	−15.7785			−1.08624			−0.543119	+	0.839655i	$0.682757\pi$
$212$	−13.2839	+	23.0084i	−0.912340	+	1.58022i
$213$	8.09608	+	14.0228i	0.554734	+	0.960828i
$214$	15.7245	+	27.2357i	1.07491	+	1.86179i
$215$	5.67096	−	9.82239i	0.386756	−	0.669881i
$216$	5.03804			0.342795
$217$		0			0
$218$	−9.42697			−0.638475
$219$	−15.0186	+	26.0129i	−1.01486	+	1.75779i
$220$	−6.05137	−	10.4813i	−0.407984	−	0.706648i
$221$	1.19797	+	2.07494i	0.0805839	+	0.139575i
$222$	−23.6908	+	41.0337i	−1.59003	+	2.75400i
$223$	−8.44731			−0.565673			−0.282837	−	0.959168i	$-0.591275\pi$
$223$	−8.44731			−0.565673			−0.282837	+	0.959168i	$0.591275\pi$
$224$		0			0
$225$	22.9167			1.52778
$226$	−12.5669	+	21.7665i	−0.835937	+	1.44789i
$227$	−3.34456	−	5.79294i	−0.221986	−	0.384491i	0.733425	−	0.679771i	$-0.237921\pi$
$227$	−3.34456	−	5.79294i	−0.221986	−	0.384491i	−0.955411	+	0.295279i	$0.904587\pi$
$228$	16.3800	+	28.3709i	1.08479	+	1.87891i
$229$	−4.31755	+	7.47822i	−0.285312	+	0.494175i	−0.972685	−	0.232130i	$-0.925430\pi$
$229$	−4.31755	+	7.47822i	−0.285312	+	0.494175i	0.687373	+	0.726305i	$0.258764\pi$
$230$	−71.4641			−4.71220
$231$		0			0
$232$	1.68648			0.110723
$233$	2.08373	−	3.60912i	0.136510	−	0.236441i	−0.789664	−	0.613540i	$-0.789745\pi$
$233$	2.08373	−	3.60912i	0.136510	−	0.236441i	0.926173	+	0.377099i	$0.123078\pi$
$234$	−3.63861	−	6.30225i	−0.237863	−	0.411991i
$235$	−8.41495	−	14.5751i	−0.548931	−	0.950776i
$236$	−20.8609	+	36.1322i	−1.35793	+	2.35201i
$237$	−3.63947			−0.236409
$238$		0			0
$239$	−1.79450			−0.116077			−0.0580384	−	0.998314i	$-0.518485\pi$
$239$	−1.79450			−0.116077			−0.0580384	+	0.998314i	$0.518485\pi$
$240$	−49.9814	+	86.5703i	−3.22628	+	5.58809i
$241$	−6.93047	−	12.0039i	−0.446431	−	0.773241i	0.551720	−	0.834029i	$-0.313972\pi$
$241$	−6.93047	−	12.0039i	−0.446431	−	0.773241i	−0.998151	+	0.0607887i	$0.980638\pi$
$242$	−14.0345	−	24.3085i	−0.902174	−	1.56261i
$243$	10.7010	−	18.5347i	0.686470	−	1.18900i
$244$	−9.58373			−0.613535
$245$		0			0
$246$	64.9300			4.13979
$247$	−1.35341	+	2.34417i	−0.0861153	+	0.149156i
$248$	−4.60407	−	7.97448i	−0.292359	−	0.506380i
$249$	−18.8778	−	32.6973i	−1.19633	−	2.07211i
$250$	16.3184	−	28.2643i	1.03207	−	1.78759i
$251$	14.7449			0.930687			0.465344	−	0.885130i	$-0.345931\pi$
$251$	14.7449			0.930687			0.465344	+	0.885130i	$0.345931\pi$
$252$		0			0
$253$	4.82554			0.303379
$254$	7.25951	−	12.5738i	0.455502	−	0.788953i
$255$	−10.4920	−	18.1727i	−0.657035	−	1.13802i
$256$	0.519021	+	0.898971i	0.0324388	+	0.0561857i
$257$	−11.8534	+	20.5307i	−0.739395	+	1.28067i	0.213373	+	0.976971i	$0.431555\pi$
$257$	−11.8534	+	20.5307i	−0.739395	+	1.28067i	−0.952768	+	0.303699i	$0.901778\pi$
$258$	19.7405			1.22899
$259$		0			0
$260$	−18.4650			−1.14515
$261$	0.285198	−	0.493977i	0.0176533	−	0.0305764i
$262$	13.0514	+	22.6056i	0.806317	+	1.39658i
$263$	−5.68780	−	9.85155i	−0.350725	−	0.607473i	0.635652	−	0.771976i	$-0.280731\pi$
$263$	−5.68780	−	9.85155i	−0.350725	−	0.607473i	−0.986377	+	0.164503i	$0.947398\pi$
$264$	6.36226	−	11.0198i	0.391570	−	0.678219i
$265$	19.2258			1.18103
$266$		0			0
$267$	−35.4827			−2.17151
$268$	32.5678	−	56.4090i	1.98939	−	3.44573i
$269$	5.55269	+	9.61755i	0.338554	+	0.586392i	0.984161	−	0.177277i	$-0.0567290\pi$
$269$	5.55269	+	9.61755i	0.338554	+	0.586392i	−0.645607	+	0.763670i	$0.723396\pi$
$270$	−3.01770	−	5.22681i	−0.183651	−	0.318094i
$271$	6.36226	−	11.0198i	0.386480	−	0.669402i	−0.605494	−	0.795850i	$-0.707024\pi$
$271$	6.36226	−	11.0198i	0.386480	−	0.669402i	0.991973	+	0.126448i	$0.0403576\pi$
$272$	27.3463			1.65811
$273$		0			0
$274$	−46.6032			−2.81540
$275$	−2.74049	+	4.74667i	−0.165258	+	0.286235i
$276$	−44.5518	−	77.1660i	−2.68170	−	4.64484i
$277$	1.50000	+	2.59808i	0.0901263	+	0.156103i	0.907564	−	0.419914i	$-0.137940\pi$
$277$	1.50000	+	2.59808i	0.0901263	+	0.156103i	−0.817438	+	0.576017i	$0.804606\pi$
$278$	−6.52569	+	11.3028i	−0.391385	+	0.677898i
$279$	−3.11435			−0.186451
$280$		0			0
$281$	3.44731			0.205649			0.102825	−	0.994700i	$-0.467212\pi$
$281$	3.44731			0.205649			0.102825	+	0.994700i	$0.467212\pi$
$282$	14.6461	−	25.3679i	0.872165	−	1.51063i
$283$	6.23917	+	10.8066i	0.370880	+	0.642383i	0.989701	−	0.143149i	$-0.0457227\pi$
$283$	6.23917	+	10.8066i	0.370880	+	0.642383i	−0.618821	+	0.785532i	$0.712389\pi$
$284$	17.0691	+	29.5645i	1.01286	+	1.75433i
$285$	11.8534	−	20.5307i	0.702135	−	1.21613i
$286$	1.74049			0.102917
$287$		0			0
$288$	−38.6484			−2.27738
$289$	5.62976	−	9.75102i	0.331162	−	0.573590i
$290$	−1.01017	−	1.74967i	−0.0593192	−	0.102744i
$291$	12.0009	+	20.7861i	0.703503	+	1.21850i
$292$	−31.6638	+	54.8434i	−1.85299	+	3.20947i
$293$	−13.5341			−0.790670			−0.395335	−	0.918537i	$-0.629371\pi$
$293$	−13.5341			−0.790670			−0.395335	+	0.918537i	$0.629371\pi$
$294$		0			0
$295$	30.1922			1.75786
$296$	−30.1718	+	52.2591i	−1.75370	+	3.03750i
$297$	0.203767	+	0.352935i	0.0118238	+	0.0204794i
$298$	−13.7312	−	23.7831i	−0.795426	−	1.37772i
$299$	3.68113	−	6.37590i	0.212885	−	0.368728i
$300$	101.206			5.84315
$301$		0			0
$302$	−13.4676			−0.774976
$303$	3.61510	−	6.26154i	0.207682	−	0.359716i
$304$	15.4473	+	26.7555i	0.885964	+	1.53453i
$305$	3.46765	+	6.00614i	0.198557	+	0.343911i
$306$	8.71785	−	15.0998i	0.498366	−	0.863196i
$307$	28.2365			1.61154			0.805772	−	0.592226i	$-0.201751\pi$
$307$	28.2365			1.61154			0.805772	+	0.592226i	$0.201751\pi$
$308$		0			0
$309$	−12.0708			−0.686684
$310$	−5.51552	+	9.55316i	−0.313260	+	0.542583i
$311$	12.3521	+	21.3944i	0.700423	+	1.21317i	0.968318	+	0.249720i	$0.0803385\pi$
$311$	12.3521	+	21.3944i	0.700423	+	1.21317i	−0.267895	+	0.963448i	$0.586328\pi$
$312$	−9.70682	−	16.8127i	−0.549540	−	0.951832i
$313$	10.4061	−	18.0239i	0.588188	−	1.01877i	−0.406282	−	0.913748i	$-0.633175\pi$
$313$	10.4061	−	18.0239i	0.588188	−	1.01877i	0.994470	−	0.105023i	$-0.0334917\pi$
$314$	33.4624			1.88839
$315$		0			0
$316$	−7.67314			−0.431648
$317$	−13.0691	+	22.6363i	−0.734032	+	1.27138i	0.221114	+	0.975248i	$0.429031\pi$
$317$	−13.0691	+	22.6363i	−0.734032	+	1.27138i	−0.955147	+	0.296134i	$0.904303\pi$
$318$	16.7312	+	28.9793i	0.938238	+	1.62508i
$319$	0.0682107	+	0.118144i	0.00381906	+	0.00661481i
$320$	−26.7245	+	46.2882i	−1.49395	+	2.58759i
$321$	28.3756			1.58377
$322$		0			0
$323$	−6.48535			−0.360854
$324$	24.5274	−	42.4827i	1.36263	−	2.36015i
$325$	4.18113	+	7.24193i	0.231927	+	0.401710i
$326$	4.25951	+	7.37769i	0.235912	+	0.408612i
$327$	−4.25284	+	7.36614i	−0.235183	+	0.407349i
$328$	82.6926			4.56593
$329$		0			0
$330$	−15.2435			−0.839129
$331$	12.0691	−	20.9043i	0.663376	−	1.14900i	−0.316346	−	0.948644i	$-0.602456\pi$
$331$	12.0691	−	20.9043i	0.663376	−	1.14900i	0.979723	−	0.200358i	$-0.0642105\pi$
$332$	−39.8003	−	68.9361i	−2.18432	−	3.78336i
$333$	10.2046	+	17.6749i	0.559210	+	0.968581i
$334$	10.7817	−	18.6744i	0.589948	−	1.02182i
$335$	−47.1355			−2.57529
$336$		0			0
$337$	−30.5297			−1.66306			−0.831530	−	0.555480i	$-0.812534\pi$
$337$	−30.5297			−1.66306			−0.831530	+	0.555480i	$0.812534\pi$
$338$	1.32772	−	2.29968i	0.0722185	−	0.125086i
$339$	11.3388	+	19.6393i	0.615837	+	1.06666i
$340$	−22.1204	−	38.3137i	−1.19965	−	2.07785i
$341$	0.372429	−	0.645067i	0.0201682	−	0.0349323i
$342$	19.6981			1.06515
$343$		0			0
$344$	25.1408			1.35550
$345$	−32.2400	+	55.8414i	−1.73575	+	3.00640i
$346$	−13.7135	−	23.7524i	−0.737241	−	1.27694i
$347$	12.4987	+	21.6483i	0.670964	+	1.16214i	0.977631	+	0.210327i	$0.0674530\pi$
$347$	12.4987	+	21.6483i	0.670964	+	1.16214i	−0.306667	+	0.951817i	$0.599214\pi$
$348$	1.25951	−	2.18154i	0.0675169	−	0.116943i
$349$	−1.83887			−0.0984324			−0.0492162	−	0.998788i	$-0.515672\pi$
$349$	−1.83887			−0.0984324			−0.0492162	+	0.998788i	$0.515672\pi$
$350$		0			0
$351$	0.621770			0.0331876
$352$	4.62177	−	8.00514i	0.246341	−	0.426675i
$353$	11.6284	+	20.1410i	0.618919	+	1.07200i	0.989683	+	0.143272i	$0.0457625\pi$
$353$	11.6284	+	20.1410i	0.618919	+	1.07200i	−0.370764	+	0.928727i	$0.620904\pi$
$354$	26.2746	+	45.5089i	1.39648	+	2.41877i
$355$	12.3521	−	21.3944i	0.655581	−	1.13550i
$356$	−74.8087			−3.96485
$357$		0			0
$358$	6.31525			0.333772
$359$	10.7237	−	18.5739i	0.565973	−	0.980294i	−0.430986	−	0.902359i	$-0.641834\pi$
$359$	10.7237	−	18.5739i	0.565973	−	0.980294i	0.996958	−	0.0779348i	$-0.0248326\pi$
$360$	40.5855	+	70.2961i	2.13904	+	3.70493i
$361$	5.83657	+	10.1092i	0.307188	+	0.532065i
$362$	28.9570	−	50.1550i	1.52195	−	2.63609i
$363$	−25.3259			−1.32927
$364$		0			0
$365$	45.8273			2.39871
$366$	−6.03540	+	10.4536i	−0.315476	+	0.546420i
$367$	0.560225	+	0.970338i	0.0292435	+	0.0506512i	0.880277	−	0.474461i	$-0.157357\pi$
$367$	0.560225	+	0.970338i	0.0292435	+	0.0506512i	−0.851033	+	0.525112i	$0.824024\pi$
$368$	−42.0151	−	72.7722i	−2.19019	−	3.79351i
$369$	13.9840	−	24.2210i	0.727979	−	1.26090i
$370$	72.2896			3.75816
$371$		0			0
$372$	−13.7538			−0.713102
$373$	−7.80290	+	13.5150i	−0.404019	+	0.699781i	−0.994207	−	0.107485i	$-0.965720\pi$
$373$	−7.80290	+	13.5150i	−0.404019	+	0.699781i	0.590188	+	0.807266i	$0.299054\pi$
$374$	2.08505	+	3.61141i	0.107815	+	0.186741i
$375$	−14.7237	−	25.5021i	−0.760326	−	1.31692i
$376$	18.6528	−	32.3076i	0.961945	−	1.66614i
$377$	0.208136			0.0107196
$378$		0			0
$379$	12.7849			0.656714			0.328357	−	0.944554i	$-0.393505\pi$
$379$	12.7849			0.656714			0.328357	+	0.944554i	$0.393505\pi$
$380$	24.9907	−	43.2852i	1.28200	−	2.22048i
$381$	−6.55005	−	11.3450i	−0.335569	−	0.581223i
$382$	−33.3082	−	57.6916i	−1.70420	−	2.95176i
$383$	−17.0177	+	29.4755i	−0.869564	+	1.50613i	−0.00712095	+	0.999975i	$0.502267\pi$
$383$	−17.0177	+	29.4755i	−0.869564	+	1.50613i	−0.862443	+	0.506154i	$0.831067\pi$
$384$	−25.4490			−1.29869
$385$		0			0
$386$	−30.0354			−1.52876
$387$	4.25152	−	7.36386i	0.216117	−	0.374326i
$388$	25.3016	+	43.8236i	1.28449	+	2.22481i
$389$	12.3353	+	21.3653i	0.625422	+	1.08326i	0.988459	+	0.151488i	$0.0484065\pi$
$389$	12.3353	+	21.3653i	0.625422	+	1.08326i	−0.363037	+	0.931775i	$0.618260\pi$
$390$	−11.6284	+	20.1410i	−0.588829	+	1.01988i
$391$	17.6395			0.892066
$392$		0			0
$393$	23.5518			1.18803
$394$	−22.2949	+	38.6159i	−1.12320	+	1.94544i
$395$	2.77635	+	4.80877i	0.139693	+	0.241956i
$396$	−4.53672	−	7.85783i	−0.227979	−	0.394871i
$397$	2.48983	−	4.31251i	0.124961	−	0.216439i	−0.796757	−	0.604300i	$-0.793453\pi$
$397$	2.48983	−	4.31251i	0.124961	−	0.216439i	0.921718	+	0.387861i	$0.126786\pi$
$398$	−54.5271			−2.73320
$399$		0			0
$400$	95.4438			4.77219
$401$	−0.344558	+	0.596791i	−0.0172064	+	0.0298023i	−0.874500	−	0.485025i	$-0.838811\pi$
$401$	−0.344558	+	0.596791i	−0.0172064	+	0.0298023i	0.857294	+	0.514827i	$0.172144\pi$
$402$	−41.0194	−	71.0477i	−2.04586	−	3.54354i
$403$	−0.568211	−	0.984170i	−0.0283046	−	0.0490250i
$404$	7.62177	−	13.2013i	0.379197	−	0.656789i
$405$	−35.4987			−1.76394
$406$		0			0
$407$	−4.88128			−0.241956
$408$	23.2569	−	40.2821i	1.15139	−	1.99426i
$409$	−9.98851	−	17.3006i	−0.493900	−	0.855460i	0.506075	−	0.862489i	$-0.331096\pi$
$409$	−9.98851	−	17.3006i	−0.493900	−	0.855460i	−0.999975	+	0.00702937i	$0.997762\pi$
$410$	−49.5314	−	85.7910i	−2.44618	−	4.23691i
$411$	−21.0244	+	36.4153i	−1.03706	+	1.79623i
$412$	−25.4490			−1.25378
$413$		0			0
$414$	−53.5767			−2.63315
$415$	−28.8016	+	49.8858i	−1.41381	+	2.44880i
$416$	−7.05137	−	12.2133i	−0.345722	−	0.598808i
$417$	5.88795	+	10.1982i	0.288334	+	0.499409i
$418$	−2.35559	+	4.08001i	−0.115216	+	0.199560i
$419$	19.6661			0.960754			0.480377	−	0.877062i	$-0.340500\pi$
$419$	19.6661			0.960754			0.480377	+	0.877062i	$0.340500\pi$
$420$		0			0
$421$	14.9283			0.727560			0.363780	−	0.931485i	$-0.381486\pi$
$421$	14.9283			0.727560			0.363780	+	0.931485i	$0.381486\pi$
$422$	−20.9495	+	36.2856i	−1.01981	+	1.76635i
$423$	−6.30870	−	10.9270i	−0.306739	−	0.531288i
$424$	21.3082	+	36.9070i	1.03482	+	1.79236i
$425$	−10.0177	+	17.3512i	−0.485930	+	0.841655i
$426$	42.9974			2.08323
$427$		0			0
$428$	59.8246			2.89173
$429$	0.785198	−	1.36000i	0.0379097	−	0.0656615i
$430$	−15.0589	−	26.0828i	−0.726205	−	1.25782i
$431$	16.3419	+	28.3050i	0.787163	+	1.36341i	0.927699	+	0.373330i	$0.121784\pi$
$431$	16.3419	+	28.3050i	0.787163	+	1.36341i	−0.140536	+	0.990076i	$0.544883\pi$
$432$	3.54832	−	6.14588i	0.170719	−	0.295694i
$433$	−8.96196			−0.430684			−0.215342	−	0.976539i	$-0.569087\pi$
$433$	−8.96196			−0.430684			−0.215342	+	0.976539i	$0.569087\pi$
$434$		0			0
$435$	−1.82290			−0.0874012
$436$	−8.96633	+	15.5301i	−0.429409	+	0.743759i
$437$	9.96414	+	17.2584i	0.476650	+	0.825581i
$438$	39.8809	+	69.0758i	1.90558	+	3.30057i
$439$	3.96633	−	6.86988i	0.189302	−	0.327881i	−0.755715	−	0.654900i	$-0.772711\pi$
$439$	3.96633	−	6.86988i	0.189302	−	0.327881i	0.945018	+	0.327019i	$0.106044\pi$
$440$	−19.4136			−0.925509
$441$		0			0
$442$	6.36226			0.302622
$443$	4.45529	−	7.71679i	0.211677	−	0.366636i	−0.740562	−	0.671988i	$-0.765441\pi$
$443$	4.45529	−	7.71679i	0.211677	−	0.366636i	0.952240	+	0.305352i	$0.0987741\pi$
$444$	45.0664	+	78.0574i	2.13876	+	3.70444i
$445$	27.0678	+	46.8827i	1.28313	+	2.22245i
$446$	−11.2157	+	19.4261i	−0.531077	+	0.919853i
$447$	−24.7785			−1.17198
$448$		0			0
$449$	−8.45168			−0.398859			−0.199430	−	0.979912i	$-0.563909\pi$
$449$	−8.45168			−0.398859			−0.199430	+	0.979912i	$0.563909\pi$
$450$	30.4270	−	52.7010i	1.43434	−	2.48435i
$451$	3.34456	+	5.79294i	0.157489	+	0.272779i
$452$	23.9056	+	41.4058i	1.12443	+	1.94756i
$453$	−6.07574	+	10.5235i	−0.285463	+	0.494437i
$454$	−17.7626			−0.833638
$455$		0			0
$456$	52.5491			2.46084
$457$	−11.5846	+	20.0651i	−0.541904	+	0.938606i	0.456890	+	0.889523i	$0.348963\pi$
$457$	−11.5846	+	20.0651i	−0.541904	+	0.938606i	−0.998795	+	0.0490829i	$0.984370\pi$
$458$	11.4650	+	19.8580i	0.535725	+	0.927902i
$459$	0.744859	+	1.29013i	0.0347670	+	0.0602183i
$460$	−67.9721	+	117.731i	−3.16921	+	5.48924i
$461$	2.27284			0.105857			0.0529284	−	0.998598i	$-0.483144\pi$
$461$	2.27284			0.105857			0.0529284	+	0.998598i	$0.483144\pi$
$462$		0			0
$463$	−4.10976			−0.190997			−0.0954983	−	0.995430i	$-0.530444\pi$
$463$	−4.10976			−0.190997			−0.0954983	+	0.995430i	$0.530444\pi$
$464$	1.18780	−	2.05732i	0.0551420	−	0.0955088i
$465$	4.97650	+	8.61955i	0.230780	+	0.399722i
$466$	−5.53322	−	9.58381i	−0.256321	−	0.443962i
$467$	−16.4575	+	28.5052i	−0.761561	+	1.31906i	0.180484	+	0.983578i	$0.442233\pi$
$467$	−16.4575	+	28.5052i	−0.761561	+	1.31906i	−0.942046	+	0.335485i	$0.891100\pi$
$468$	−13.8432			−0.639904
$469$		0			0
$470$	−44.6908			−2.06143
$471$	15.0961	−	26.1472i	0.695591	−	1.20480i
$472$	33.4624	+	57.9585i	1.54023	+	2.66776i
$473$	1.01684	+	1.76121i	0.0467542	+	0.0809806i
$474$	−4.83220	+	8.36962i	−0.221950	+	0.384429i
$475$	−22.6351			−1.03857
$476$		0			0
$477$	14.4136			0.659955
$478$	−2.38260	+	4.12678i	−0.108978	+	0.188755i
$479$	4.65763	+	8.06725i	0.212812	+	0.368602i	0.952594	−	0.304246i	$-0.0984043\pi$
$479$	4.65763	+	8.06725i	0.212812	+	0.368602i	−0.739781	+	0.672847i	$0.765071\pi$
$480$	61.7573	+	106.967i	2.81882	+	4.88234i
$481$	−3.72365	+	6.44956i	−0.169784	+	0.294074i
$482$	−36.8069			−1.67651
$483$		0			0
$484$	−53.3950			−2.42705
$485$	18.3096	−	31.7131i	0.831395	−	1.44002i
$486$	−28.4159	−	49.2178i	−1.28897	−	2.23257i
$487$	−10.1204	−	17.5291i	−0.458601	−	0.794321i	0.540286	−	0.841481i	$-0.318316\pi$
$487$	−10.1204	−	17.5291i	−0.458601	−	0.794321i	−0.998887	+	0.0471606i	$0.984983\pi$
$488$	−7.68648	+	13.3134i	−0.347950	+	0.602668i
$489$	7.68648			0.347594
$490$		0			0
$491$	−4.36226			−0.196866			−0.0984330	−	0.995144i	$-0.531383\pi$
$491$	−4.36226			−0.196866			−0.0984330	+	0.995144i	$0.531383\pi$
$492$	61.7573	−	106.967i	2.78423	−	4.82243i
$493$	0.249340	+	0.431870i	0.0112297	+	0.0194504i
$494$	3.59390	+	6.22481i	0.161697	+	0.280068i
$495$	−3.28301	+	5.68635i	−0.147560	+	0.255582i
$496$	−12.9707			−0.582401
$497$		0			0
$498$	−100.258			−4.49265
$499$	−4.84674	+	8.39480i	−0.216970	+	0.375803i	−0.953880	−	0.300188i	$-0.902951\pi$
$499$	−4.84674	+	8.39480i	−0.216970	+	0.375803i	0.736910	+	0.675991i	$0.236284\pi$
$500$	−31.0421	−	53.7664i	−1.38824	−	2.40451i
$501$	−9.72802	−	16.8494i	−0.434616	−	0.752777i
$502$	19.5771	−	33.9085i	0.873767	−	1.51341i
$503$	2.64843			0.118088			0.0590439	−	0.998255i	$-0.481195\pi$
$503$	2.64843			0.118088			0.0590439	+	0.998255i	$0.481195\pi$
$504$		0			0
$505$	−11.0310			−0.490875
$506$	6.40697	−	11.0972i	0.284824	−	0.493330i
$507$	−1.19797	−	2.07494i	−0.0532035	−	0.0921512i
$508$	−13.8096	−	23.9189i	−0.612700	−	1.06123i
$509$	6.97081	−	12.0738i	0.308976	−	0.535162i	−0.669163	−	0.743116i	$-0.733347\pi$
$509$	6.97081	−	12.0738i	0.308976	−	0.535162i	0.978139	+	0.207954i	$0.0666805\pi$
$510$	−55.7219			−2.46741
$511$		0			0
$512$	24.0000			1.06066
$513$	−0.841508	+	1.45753i	−0.0371535	+	0.0643517i
$514$	31.4760	+	54.5181i	1.38835	+	2.40469i
$515$	9.20814	+	15.9490i	0.405759	+	0.702795i
$516$	18.7759	−	32.5208i	0.826563	−	1.43165i
$517$	3.01770			0.132718
$518$		0			0
$519$	−24.7466			−1.08625
$520$	−14.8096	+	25.6509i	−0.649442	+	1.12487i
$521$	7.31088	+	12.6628i	0.320296	+	0.554768i	0.980549	−	0.196275i	$-0.0628844\pi$
$521$	7.31088	+	12.6628i	0.320296	+	0.554768i	−0.660253	+	0.751043i	$0.729551\pi$
$522$	−0.757326	−	1.31173i	−0.0331473	−	0.0574127i
$523$	−8.25951	+	14.3059i	−0.361163	+	0.625553i	−0.988153	−	0.153475i	$-0.950954\pi$
$523$	−8.25951	+	14.3059i	−0.361163	+	0.625553i	0.626989	+	0.779028i	$0.284287\pi$
$524$	49.6545			2.16917
$525$		0			0
$526$	−30.2072			−1.31710
$527$	1.36139	−	2.35800i	0.0593033	−	0.102716i
$528$	−8.96196	−	15.5226i	−0.390019	−	0.675533i
$529$	−15.6014	−	27.0225i	−0.678323	−	1.17489i
$530$	25.5266	−	44.2133i	1.10880	−	1.92050i
$531$	22.6351			0.982280
$532$		0			0
$533$	10.2055			0.442049
$534$	−47.1111	+	81.5989i	−2.03870	+	3.53113i
$535$	−21.6461	−	37.4922i	−0.935844	−	1.62093i
$536$	−52.2409	−	90.4839i	−2.25646	−	3.90831i
$537$	2.84904	−	4.93468i	0.122945	−	0.212947i
$538$	29.4897			1.27139
$539$		0			0
$540$	−11.4810			−0.494063
$541$	21.5509	−	37.3273i	0.926546	−	1.60483i	0.137491	−	0.990503i	$-0.456096\pi$
$541$	21.5509	−	37.3273i	0.926546	−	1.60483i	0.789055	−	0.614322i	$-0.210571\pi$
$542$	−16.8946	−	29.2623i	−0.725686	−	1.25692i
$543$	−26.1271	−	45.2535i	−1.12122	−	1.94201i
$544$	16.8946	−	29.2623i	0.724351	−	1.25461i
$545$	12.9770			0.555874
$546$		0			0
$547$	−13.5057			−0.577462			−0.288731	−	0.957410i	$-0.593233\pi$
$547$	−13.5057			−0.577462			−0.288731	+	0.957410i	$0.593233\pi$
$548$	−44.3259	+	76.7748i	−1.89351	+	3.27966i
$549$	2.59970	+	4.50281i	0.110952	+	0.192175i
$550$	7.27721	+	12.6045i	0.310301	+	0.537458i
$551$	−0.281693	+	0.487907i	−0.0120005	+	0.0207855i
$552$	−142.928			−6.08343
$553$		0			0
$554$	7.96633			0.338457
$555$	32.6125	−	56.4864i	1.38432	−	2.39772i
$556$	12.4136	+	21.5010i	0.526455	+	0.911847i
$557$	−0.675783	−	1.17049i	−0.0286338	−	0.0495953i	0.851353	−	0.524593i	$-0.175782\pi$
$557$	−0.675783	−	1.17049i	−0.0286338	−	0.0495953i	−0.879987	+	0.474997i	$0.842449\pi$
$558$	−4.13499	+	7.16201i	−0.175048	+	0.303192i
$559$	3.10275			0.131232
$560$		0			0
$561$	3.76256			0.158855
$562$	4.57706	−	7.92770i	0.193072	−	0.334410i
$563$	−15.8813	−	27.5072i	−0.669316	−	1.15929i	−0.978096	−	0.208156i	$-0.933254\pi$
$563$	−15.8813	−	27.5072i	−0.669316	−	1.15929i	0.308779	−	0.951134i	$-0.400079\pi$
$564$	−27.8609	−	48.2566i	−1.17316	−	2.03197i
$565$	17.2994	−	29.9634i	0.727791	−	1.26057i
$566$	33.1355			1.39279
$567$		0			0
$568$	54.7599			2.29768
$569$	−15.1865	+	26.3037i	−0.636650	+	1.10271i	0.349513	+	0.936932i	$0.386347\pi$
$569$	−15.1865	+	26.3037i	−0.636650	+	1.10271i	−0.986163	+	0.165779i	$0.946986\pi$
$570$	−31.4760	−	54.5181i	−1.31839	−	2.28351i
$571$	0.216122	+	0.374334i	0.00904442	+	0.0156654i	0.870512	−	0.492147i	$-0.163788\pi$
$571$	0.216122	+	0.374334i	0.00904442	+	0.0156654i	−0.861468	+	0.507812i	$0.830454\pi$
$572$	1.65544	−	2.86731i	0.0692175	−	0.119888i
$573$	−60.1062			−2.51097
$574$		0			0
$575$	61.5651			2.56744
$576$	−20.0354	+	34.7023i	−0.834808	+	1.44593i
$577$	−9.06908	−	15.7081i	−0.377551	−	0.653937i	0.613155	−	0.789963i	$-0.289900\pi$
$577$	−9.06908	−	15.7081i	−0.377551	−	0.653937i	−0.990705	+	0.136026i	$0.956567\pi$
$578$	−14.9495	−	25.8933i	−0.621817	−	1.07702i
$579$	−13.5501	+	23.4694i	−0.563121	+	0.975354i
$580$	−3.84324			−0.159582
$581$		0			0
$582$	63.7352			2.64191
$583$	−1.72365	+	2.98545i	−0.0713864	+	0.123645i
$584$	50.7910	+	87.9725i	2.10174	+	3.64033i
$585$	5.00885	+	8.67558i	0.207090	+	0.358691i
$586$	−17.9695	+	31.1241i	−0.742313	+	1.28572i
$587$	19.3065			0.796865			0.398433	−	0.917198i	$-0.369554\pi$
$587$	19.3065			0.796865			0.398433	+	0.917198i	$0.369554\pi$
$588$		0			0
$589$	3.07608			0.126748
$590$	40.0868	−	69.4323i	1.65035	−	2.85848i
$591$	20.1161	+	34.8421i	0.827465	+	1.43321i
$592$	42.5004	+	73.6129i	1.74676	+	3.02547i
$593$	−4.10056	+	7.10238i	−0.168390	+	0.291660i	−0.937854	−	0.347030i	$-0.887190\pi$
$593$	−4.10056	+	7.10238i	−0.168390	+	0.291660i	0.769464	+	0.638690i	$0.220523\pi$
$594$	1.08218			0.0444025
$595$		0			0
$596$	−52.2409			−2.13987
$597$	−24.5991	+	42.6069i	−1.00678	+	1.74379i
$598$	−9.77503	−	16.9308i	−0.399731	−	0.692354i
$599$	−11.7392	−	20.3328i	−0.479649	−	0.830777i	0.520078	−	0.854119i	$-0.325903\pi$
$599$	−11.7392	−	20.3328i	−0.479649	−	0.830777i	−0.999728	+	0.0233415i	$0.992570\pi$
$600$	81.1709	−	140.592i	3.31379	−	5.73965i
$601$	−8.96196			−0.365566			−0.182783	−	0.983153i	$-0.558511\pi$
$601$	−8.96196			−0.365566			−0.182783	+	0.983153i	$0.558511\pi$
$602$		0			0
$603$	−35.3375			−1.43906
$604$	−12.8096	+	22.1868i	−0.521214	+	0.902769i
$605$	19.3197	+	33.4628i	0.785459	+	1.36045i
$606$	−9.59970	−	16.6272i	−0.389961	−	0.675432i
$607$	−21.7320	+	37.6410i	−0.882077	+	1.52780i	−0.0330487	+	0.999454i	$0.510522\pi$
$607$	−21.7320	+	37.6410i	−0.882077	+	1.52780i	−0.849028	+	0.528348i	$0.822812\pi$
$608$	38.1736			1.54814
$609$		0			0
$610$	18.4163			0.745653
$611$	2.30203	−	3.98724i	0.0931303	−	0.161306i
$612$	−16.5837	−	28.7239i	−0.670357	−	1.16109i
$613$	10.7245	+	18.5754i	0.433159	+	0.750254i	0.997143	−	0.0755318i	$-0.0240655\pi$
$613$	10.7245	+	18.5754i	0.433159	+	0.750254i	−0.563984	+	0.825786i	$0.690732\pi$
$614$	37.4902	−	64.9350i	1.51298	−	2.62056i
$615$	−89.3817			−3.60422
$616$		0			0
$617$	−12.1294			−0.488312			−0.244156	−	0.969736i	$-0.578511\pi$
$617$	−12.1294			−0.488312			−0.244156	+	0.969736i	$0.578511\pi$
$618$	−16.0267	+	27.7590i	−0.644687	+	1.11663i
$619$	−6.36226	−	11.0198i	−0.255721	−	0.442921i	0.709370	−	0.704836i	$-0.248979\pi$
$619$	−6.36226	−	11.0198i	−0.255721	−	0.442921i	−0.965091	+	0.261915i	$0.915646\pi$
$620$	10.4920	+	18.1727i	0.421369	+	0.729833i
$621$	2.28881	−	3.96434i	0.0918469	−	0.159084i
$622$	65.6005			2.63034
$623$		0			0
$624$	−27.3463			−1.09473
$625$	−1.55804	+	2.69860i	−0.0623216	+	0.107944i
$626$	−27.6328	−	47.8614i	−1.10443	−	1.91293i
$627$	2.12539	+	3.68128i	0.0848797	+	0.147016i
$628$	31.8273	−	55.1264i	1.27005	−	2.19978i
$629$	−17.8432			−0.711456
$630$		0			0
$631$	−11.7538			−0.467912			−0.233956	−	0.972247i	$-0.575167\pi$
$631$	−11.7538			−0.467912			−0.233956	+	0.972247i	$0.575167\pi$
$632$	−6.15412	+	10.6593i	−0.244798	+	0.424002i
$633$	18.9021	+	32.7395i	0.751293	+	1.30128i
$634$	34.7042	+	60.1094i	1.37828	+	2.38725i
$635$	−9.99333	+	17.3090i	−0.396573	+	0.686885i
$636$	63.6545			2.52407
$637$		0			0
$638$	0.362259			0.0143420
$639$	9.26038	−	16.0394i	0.366335	−	0.634510i
$640$	19.4136	+	33.6254i	0.767391	+	1.32916i
$641$	−2.34324	−	4.05861i	−0.0925523	−	0.160305i	0.816032	−	0.578007i	$-0.196169\pi$
$641$	−2.34324	−	4.05861i	−0.0925523	−	0.160305i	−0.908584	+	0.417701i	$0.862836\pi$
$642$	37.6749	−	65.2548i	1.48691	−	2.57540i
$643$	−0.751182			−0.0296237			−0.0148119	−	0.999890i	$-0.504715\pi$
$643$	−0.751182			−0.0296237			−0.0148119	+	0.999890i	$0.504715\pi$
$644$		0			0
$645$	−27.1745			−1.06999
$646$	−8.61073	+	14.9142i	−0.338785	+	0.586792i
$647$	−20.4238	−	35.3751i	−0.802943	−	1.39074i	−0.917671	−	0.397340i	$-0.869933\pi$
$647$	−20.4238	−	35.3751i	−0.802943	−	1.39074i	0.114729	−	0.993397i	$-0.463400\pi$
$648$	−39.3436	−	68.1452i	−1.54556	−	2.67700i
$649$	−2.70682	+	4.68834i	−0.106252	+	0.184034i
$650$	22.2055			0.870971
$651$		0			0
$652$	16.2055			0.634656
$653$	23.2392	−	40.2514i	0.909419	−	1.57516i	0.0945459	−	0.995521i	$-0.469860\pi$
$653$	23.2392	−	40.2514i	0.909419	−	1.57516i	0.814873	−	0.579639i	$-0.196807\pi$
$654$	11.2932	+	19.5604i	0.441598	+	0.764871i
$655$	−17.9663	−	31.1186i	−0.702002	−	1.21590i
$656$	58.2409	−	100.876i	2.27393	−	3.93855i
$657$	34.3568			1.34038
$658$		0			0
$659$	30.3596			1.18264			0.591321	−	0.806436i	$-0.298606\pi$
$659$	30.3596			1.18264			0.591321	+	0.806436i	$0.298606\pi$
$660$	−14.4987	+	25.1125i	−0.564360	+	0.977501i
$661$	0.0535589	+	0.0927667i	0.00208320	+	0.00360820i	0.867065	−	0.498195i	$-0.166004\pi$
$661$	0.0535589	+	0.0927667i	0.00208320	+	0.00360820i	−0.864982	+	0.501803i	$0.832670\pi$
$662$	−32.0487	−	55.5100i	−1.24561	−	2.15746i
$663$	2.87024	−	4.97141i	0.111471	−	0.193074i
$664$	−127.685			−4.95513
$665$		0			0
$666$	54.1956			2.10004
$667$	0.766177	−	1.32706i	0.0296665	−	0.0513838i
$668$	−20.5097	−	35.5239i	−0.793545	−	1.37446i
$669$	10.1196	+	17.5276i	0.391246	+	0.677658i
$670$	−62.5828	+	108.397i	−2.41779	+	4.18773i
$671$	−1.24354			−0.0480063
$672$		0			0
$673$	38.5385			1.48555			0.742774	−	0.669542i	$-0.233510\pi$
$673$	38.5385			1.48555			0.742774	+	0.669542i	$0.233510\pi$
$674$	−40.5349	+	70.2086i	−1.56135	+	2.70433i
$675$	2.59970	+	4.50281i	0.100062	+	0.173313i
$676$	−2.52569	−	4.37462i	−0.0971418	−	0.168255i
$677$	10.3901	−	17.9962i	0.399325	−	0.691651i	−0.594318	−	0.804230i	$-0.702578\pi$
$677$	10.3901	−	17.9962i	0.399325	−	0.691651i	0.993643	+	0.112579i	$0.0359111\pi$
$678$	60.2188			2.31269
$679$		0			0
$680$	−70.9654			−2.72140
$681$	−8.01333	+	13.8795i	−0.307072	+	0.531864i
$682$	−0.988965	−	1.71294i	−0.0378694	−	0.0655918i
$683$	−13.7919	−	23.8882i	−0.527731	−	0.914057i	−0.999477	−	0.0323227i	$-0.989710\pi$
$683$	−13.7919	−	23.8882i	−0.527731	−	0.914057i	0.471746	−	0.881734i	$-0.343624\pi$
$684$	18.7356	−	32.4509i	0.716372	−	1.24079i
$685$	64.1532			2.45117
$686$		0			0
$687$	20.6891			0.789339
$688$	17.7068	−	30.6691i	0.675066	−	1.16925i
$689$	2.62976	+	4.55487i	0.100186	+	0.173527i
$690$	85.6116	+	148.284i	3.25918	+	5.64506i
$691$	−21.8388	+	37.8258i	−0.830785	+	1.43896i	0.0666308	+	0.997778i	$0.478775\pi$
$691$	−21.8388	+	37.8258i	−0.830785	+	1.43896i	−0.897416	+	0.441185i	$0.854558\pi$
$692$	−52.1736			−1.98334
$693$		0			0
$694$	66.3791			2.51971
$695$	8.98316	−	15.5593i	0.340751	−	0.590198i
$696$	−2.02034	−	3.49933i	−0.0765808	−	0.132642i
$697$	12.2258	+	21.1758i	0.463087	+	0.802090i
$698$	−2.44150	+	4.22881i	−0.0924123	+	0.160063i
$699$	−9.98494			−0.377665
$700$		0			0
$701$	−20.8973			−0.789278			−0.394639	−	0.918836i	$-0.629130\pi$
$701$	−20.8973			−0.789278			−0.394639	+	0.918836i	$0.629130\pi$
$702$	0.825537	−	1.42987i	0.0311579	−	0.0539670i
$703$	−10.0792	−	17.4578i	−0.380146	−	0.658432i
$704$	−4.79186	−	8.29975i	−0.180600	−	0.312809i
$705$	−20.1617	+	34.9210i	−0.759332	+	1.31520i
$706$	61.7573			2.32427
$707$		0			0
$708$	99.9628			3.75683
$709$	−4.96983	+	8.60800i	−0.186646	+	0.323280i	−0.944130	−	0.329574i	$-0.893095\pi$
$709$	−4.96983	+	8.60800i	−0.186646	+	0.323280i	0.757484	+	0.652854i	$0.226428\pi$
$710$	−32.8003	−	56.8117i	−1.23097	−	2.13211i
$711$	2.08143	+	3.60514i	0.0780597	+	0.135203i
$712$	−59.9991	+	103.921i	−2.24856	+	3.89462i
$713$	−8.36663			−0.313333
$714$		0			0
$715$	−2.39593			−0.0896028
$716$	6.00667	−	10.4039i	0.224480	−	0.388810i
$717$	2.14975	+	3.72348i	0.0802840	+	0.139056i
$718$	−28.4760	−	49.3220i	−1.06272	−	1.84068i
$719$	5.98983	−	10.3747i	0.223383	−	0.386911i	−0.732450	−	0.680821i	$-0.761623\pi$
$719$	5.98983	−	10.3747i	0.223383	−	0.386911i	0.955833	+	0.293910i	$0.0949566\pi$
$720$	114.338			4.26114
$721$		0			0
$722$	30.9974			1.15360
$723$	−16.6049	+	28.7606i	−0.617544	+	1.06962i
$724$	−55.0841	−	95.4085i	−2.04719	−	3.54583i
$725$	0.870245	+	1.50731i	0.0323201	+	0.0559800i
$726$	−33.6258	+	58.2416i	−1.24797	+	2.16155i
$727$	24.1736			0.896547			0.448274	−	0.893896i	$-0.352039\pi$
$727$	24.1736			0.896547			0.448274	+	0.893896i	$0.352039\pi$
$728$		0			0
$729$	−22.1443			−0.820157
$730$	60.8458	−	105.388i	2.25201	−	3.90059i
$731$	3.71699	+	6.43801i	0.137478	+	0.238118i
$732$	11.4810	+	19.8856i	0.424349	+	0.734994i
$733$	18.2237	−	31.5643i	0.673106	−	1.16585i	−0.303913	−	0.952700i	$-0.598293\pi$
$733$	18.2237	−	31.5643i	0.673106	−	1.16585i	0.977019	−	0.213154i	$-0.0683736\pi$
$734$	2.97529			0.109820
$735$		0			0
$736$	−103.828			−3.82715
$737$	4.22584	−	7.31937i	0.155661	−	0.269612i
$738$	−37.1338	−	64.3176i	−1.36691	−	2.36756i
$739$	−21.6386	−	37.4792i	−0.795989	−	1.37869i	−0.922209	−	0.386691i	$-0.873618\pi$
$739$	−21.6386	−	37.4792i	−0.795989	−	1.37869i	0.126220	−	0.992002i	$-0.459715\pi$
$740$	68.7573	−	119.091i	2.52757	−	4.37788i
$741$	6.48535			0.238245
$742$		0			0
$743$	22.6572			0.831211			0.415606	−	0.909545i	$-0.363570\pi$
$743$	22.6572			0.831211			0.415606	+	0.909545i	$0.363570\pi$
$744$	−11.0310	+	19.1063i	−0.404417	+	0.700471i
$745$	18.9021	+	32.7395i	0.692521	+	1.19948i
$746$	20.7201	+	35.8884i	0.758619	+	1.31397i
$747$	−21.5926	+	37.3994i	−0.790031	+	1.36837i
$748$	7.93265			0.290047
$749$		0			0
$750$	−78.1956			−2.85530
$751$	−14.9340	+	25.8664i	−0.544948	+	0.943878i	0.453662	+	0.891174i	$0.350117\pi$
$751$	−14.9340	+	25.8664i	−0.544948	+	0.943878i	−0.998610	+	0.0527044i	$0.983216\pi$
$752$	−26.2746	−	45.5089i	−0.958135	−	1.65954i
$753$	−17.6638	−	30.5947i	−0.643706	−	1.11493i
$754$	0.276347	−	0.478647i	0.0100640	−	0.0174313i
$755$	18.5394			0.674716
$756$		0			0
$757$	2.55706			0.0929380			0.0464690	−	0.998920i	$-0.485203\pi$
$757$	2.55706			0.0929380			0.0464690	+	0.998920i	$0.485203\pi$
$758$	16.9747	−	29.4011i	0.616550	−	1.06790i
$759$	−5.78083	−	10.0127i	−0.209831	−	0.363438i
$760$	−40.0868	−	69.4323i	−1.45410	−	2.51858i
$761$	−7.36444	+	12.7556i	−0.266961	+	0.462390i	−0.968075	−	0.250659i	$-0.919353\pi$
$761$	−7.36444	+	12.7556i	−0.266961	+	0.462390i	0.701115	+	0.713049i	$0.252686\pi$
$762$	−34.7866			−1.26019
$763$		0			0
$764$	−126.723			−4.58467
$765$	−12.0009	+	20.7861i	−0.433892	+	0.751523i
$766$	45.1895	+	78.2706i	1.63276	+	2.82803i
$767$	4.12976	+	7.15295i	0.149117	+	0.258278i
$768$	1.24354	−	2.15387i	0.0448724	−	0.0777212i
$769$	−36.1692			−1.30429			−0.652147	−	0.758092i	$-0.726132\pi$
$769$	−36.1692			−1.30429			−0.652147	+	0.758092i	$0.726132\pi$
$770$		0			0
$771$	56.7999			2.04560
$772$	−28.5678	+	49.4808i	−1.02818	+	1.78085i
$773$	−19.4783	−	33.7375i	−0.700587	−	1.21345i	−0.968261	−	0.249943i	$-0.919588\pi$
$773$	−19.4783	−	33.7375i	−0.700587	−	1.21345i	0.267673	−	0.963510i	$-0.413745\pi$
$774$	−11.2897	−	19.5543i	−0.405799	−	0.702865i
$775$	4.75152	−	8.22988i	0.170680	−	0.295626i </

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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.32772 - 2.29968i) q^{2} +(-1.19797 - 2.07494i) q^{3} +(-2.52569 - 4.37462i) q^{4} +(-1.82772 + 3.16571i) q^{5} -6.36226 q^{6} -8.10275 q^{8} +(-1.37024 + 2.37333i) q^{9} +O(q^{10})\)	\(q+(1.32772 - 2.29968i) q^{2} +(-1.19797 - 2.07494i) q^{3} +(-2.52569 - 4.37462i) q^{4} +(-1.82772 + 3.16571i) q^{5} -6.36226 q^{6} -8.10275 q^{8} +(-1.37024 + 2.37333i) q^{9} +(4.85341 + 8.40635i) q^{10} +(-0.327721 - 0.567630i) q^{11} +(-6.05137 + 10.4813i) q^{12} -1.00000 q^{13} +8.75819 q^{15} +(-5.70682 + 9.88450i) q^{16} +(-1.19797 - 2.07494i) q^{17} +(3.63861 + 6.30225i) q^{18} +(1.35341 - 2.34417i) q^{19} +18.4650 q^{20} -1.74049 q^{22} +(-3.68113 + 6.37590i) q^{23} +(9.70682 + 16.8127i) q^{24} +(-4.18113 - 7.24193i) q^{25} +(-1.32772 + 2.29968i) q^{26} -0.621770 q^{27} -0.208136 q^{29} +(11.6284 - 20.1410i) q^{30} +(0.568211 + 0.984170i) q^{31} +(7.05137 + 12.2133i) q^{32} +(-0.785198 + 1.36000i) q^{33} -6.36226 q^{34} +13.8432 q^{36} +(3.72365 - 6.44956i) q^{37} +(-3.59390 - 6.22481i) q^{38} +(1.19797 + 2.07494i) q^{39} +(14.8096 - 25.6509i) q^{40} -10.2055 q^{41} -3.10275 q^{43} +(-1.65544 + 2.86731i) q^{44} +(-5.00885 - 8.67558i) q^{45} +(9.77503 + 16.9308i) q^{46} +(-2.30203 + 3.98724i) q^{47} +27.3463 q^{48} -22.2055 q^{50} +(-2.87024 + 4.97141i) q^{51} +(2.52569 + 4.37462i) q^{52} +(-2.62976 - 4.55487i) q^{53} +(-0.825537 + 1.42987i) q^{54} +2.39593 q^{55} -6.48535 q^{57} +(-0.276347 + 0.478647i) q^{58} +(-4.12976 - 7.15295i) q^{59} +(-22.1204 - 38.3137i) q^{60} +(0.948626 - 1.64307i) q^{61} +3.01770 q^{62} +14.6218 q^{64} +(1.82772 - 3.16571i) q^{65} +(2.08505 + 3.61141i) q^{66} +(6.44731 + 11.1671i) q^{67} +(-6.05137 + 10.4813i) q^{68} +17.6395 q^{69} -6.75819 q^{71} +(11.1027 - 19.2305i) q^{72} +(-6.26836 - 10.8571i) q^{73} +(-9.88795 - 17.1264i) q^{74} +(-10.0177 + 17.3512i) q^{75} -13.6731 q^{76} +6.36226 q^{78} +(0.759511 - 1.31551i) q^{79} +(-20.8609 - 36.1322i) q^{80} +(4.85559 + 8.41013i) q^{81} +(-13.5501 + 23.4694i) q^{82} +15.7582 q^{83} +8.75819 q^{85} +(-4.11958 + 7.13533i) q^{86} +(0.249340 + 0.431870i) q^{87} +(2.65544 + 4.59936i) q^{88} +(7.40478 - 12.8255i) q^{89} -26.6014 q^{90} +37.1895 q^{92} +(1.36139 - 2.35800i) q^{93} +(6.11292 + 10.5879i) q^{94} +(4.94731 + 8.56899i) q^{95} +(16.8946 - 29.2623i) q^{96} -10.0177 q^{97} +1.79623 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 5 q^{5} + 4 q^{6} - 12 q^{8} - 11 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 - 5 * q^5 + 4 * q^6 - 12 * q^8 - 11 * q^9	\( 6 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 5 q^{5} + 4 q^{6} - 12 q^{8} - 11 q^{9} + 14 q^{10} + 4 q^{11} - 18 q^{12} - 6 q^{13} + 4 q^{15} - 4 q^{16} - 4 q^{17} - 8 q^{18} - 7 q^{19} + 32 q^{20} - 16 q^{22} - q^{23} + 28 q^{24} - 4 q^{25} - 2 q^{26} + 44 q^{27} - 14 q^{29} + 24 q^{30} + 3 q^{31} + 24 q^{32} + 10 q^{33} + 4 q^{34} + 52 q^{36} + 10 q^{37} - 12 q^{38} + 4 q^{39} + 22 q^{40} + 12 q^{41} + 18 q^{43} + 2 q^{44} - 3 q^{45} + 28 q^{46} - 17 q^{47} + 32 q^{48} - 60 q^{50} - 20 q^{51} + 6 q^{52} - 13 q^{53} - 28 q^{54} + 8 q^{55} + 8 q^{57} - 14 q^{58} - 22 q^{59} - 42 q^{60} + 24 q^{61} - 36 q^{62} + 40 q^{64} + 5 q^{65} + 30 q^{66} + 14 q^{67} - 18 q^{68} + 4 q^{69} + 8 q^{71} + 30 q^{72} - 5 q^{73} - 8 q^{74} - 6 q^{75} - 16 q^{76} - 4 q^{78} - q^{79} - 40 q^{80} - 15 q^{81} - 20 q^{82} + 46 q^{83} + 4 q^{85} - 6 q^{86} - 20 q^{87} + 4 q^{88} + 11 q^{89} - 80 q^{90} + 60 q^{92} + 38 q^{93} + 16 q^{94} + 5 q^{95} + 52 q^{96} - 6 q^{97} - 60 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 - 5 * q^5 + 4 * q^6 - 12 * q^8 - 11 * q^9 + 14 * q^10 + 4 * q^11 - 18 * q^12 - 6 * q^13 + 4 * q^15 - 4 * q^16 - 4 * q^17 - 8 * q^18 - 7 * q^19 + 32 * q^20 - 16 * q^22 - q^23 + 28 * q^24 - 4 * q^25 - 2 * q^26 + 44 * q^27 - 14 * q^29 + 24 * q^30 + 3 * q^31 + 24 * q^32 + 10 * q^33 + 4 * q^34 + 52 * q^36 + 10 * q^37 - 12 * q^38 + 4 * q^39 + 22 * q^40 + 12 * q^41 + 18 * q^43 + 2 * q^44 - 3 * q^45 + 28 * q^46 - 17 * q^47 + 32 * q^48 - 60 * q^50 - 20 * q^51 + 6 * q^52 - 13 * q^53 - 28 * q^54 + 8 * q^55 + 8 * q^57 - 14 * q^58 - 22 * q^59 - 42 * q^60 + 24 * q^61 - 36 * q^62 + 40 * q^64 + 5 * q^65 + 30 * q^66 + 14 * q^67 - 18 * q^68 + 4 * q^69 + 8 * q^71 + 30 * q^72 - 5 * q^73 - 8 * q^74 - 6 * q^75 - 16 * q^76 - 4 * q^78 - q^79 - 40 * q^80 - 15 * q^81 - 20 * q^82 + 46 * q^83 + 4 * q^85 - 6 * q^86 - 20 * q^87 + 4 * q^88 + 11 * q^89 - 80 * q^90 + 60 * q^92 + 38 * q^93 + 16 * q^94 + 5 * q^95 + 52 * q^96 - 6 * q^97 - 60 * q^99

Introduction

L-functions

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