LMFDB - Embedded newform 637.2.e.l.508.3

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			508.3
Root			$-0.827721 + 1.43366i$ of defining polynomial
Character	$\chi$	$=$	637.508
Dual form			637.2.e.l.79.3

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.32772	+	2.29968i	0.938841	+	1.62612i	0.767638	+	0.640884i	$0.221432\pi$
$2$	1.32772	+	2.29968i	0.938841	+	1.62612i	0.171203	+	0.985236i	$0.445235\pi$
$3$	1.19797	−	2.07494i	0.691646	−	1.19797i	−0.279652	−	0.960101i	$-0.590219\pi$
$3$	1.19797	−	2.07494i	0.691646	−	1.19797i	0.971298	−	0.237865i	$-0.0764475\pi$
$4$	−2.52569	+	4.37462i	−1.26284	+	2.18731i
$5$	1.82772	+	3.16571i	0.817382	+	1.41575i	0.907605	+	0.419825i	$0.137909\pi$
$5$	1.82772	+	3.16571i	0.817382	+	1.41575i	−0.0902232	+	0.995922i	$0.528758\pi$
$6$	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	−0.911193	−	0.411980i	$-0.864837\pi$
$11$	−0.327721	+	0.567630i	−0.0988117	+	0.171147i	0.812381	+	0.583126i	$0.198171\pi$
$12$	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	$-0.739495\pi$
$17$	1.19797	−	2.07494i	0.290549	−	0.503246i	0.973940	+	0.226807i	$0.0728286\pi$
$18$	3.63861	−	6.30225i	0.857628	−	1.48545i
$19$	−1.35341	−	2.34417i	−0.310493	−	0.537790i	0.667976	−	0.744183i	$-0.267161\pi$
$19$	−1.35341	−	2.34417i	−0.310493	−	0.537790i	−0.978469	+	0.206393i	$0.933828\pi$
$20$	−18.4650			−4.12890
$21$		0			0
$22$	−1.74049			−0.371074
$23$	−3.68113	−	6.37590i	−0.767569	−	1.32947i	−0.938878	−	0.344250i	$-0.888133\pi$
$23$	−3.68113	−	6.37590i	−0.767569	−	1.32947i	0.171309	−	0.985217i	$-0.445200\pi$
$24$	−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	$-0.865875\pi$
$31$	−0.568211	+	0.984170i	−0.102054	+	0.176762i	0.810477	+	0.585771i	$0.199208\pi$
$32$	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	0.990875	+	0.134785i	$0.0430344\pi$
$37$	3.72365	+	6.44956i	0.612165	+	1.06030i	−0.378710	+	0.925515i	$0.623632\pi$
$38$	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	$-0.206464\pi$
$41$	10.2055			1.59383			0.796915	+	0.604091i	$0.206464\pi$
$42$		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	$-0.0576647\pi$
$47$	2.30203	+	3.98724i	0.335786	+	0.581599i	−0.647849	+	0.761768i	$0.724331\pi$
$48$	−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	−0.988163	−	0.153410i	$-0.950975\pi$
$53$	−2.62976	+	4.55487i	−0.361225	+	0.625659i	0.626938	+	0.779069i	$0.284308\pi$
$54$	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	−0.461382	−	0.887202i	$-0.652646\pi$
$59$	4.12976	−	7.15295i	0.537648	−	0.931234i	0.999030	−	0.0440325i	$-0.0140205\pi$
$60$	−22.1204	+	38.3137i	−2.85574	+	4.94628i
$61$	−0.948626	−	1.64307i	−0.121459	−	0.210373i	0.798884	−	0.601485i	$-0.205424\pi$
$61$	−0.948626	−	1.64307i	−0.121459	−	0.210373i	−0.920343	+	0.391112i	$0.872091\pi$
$62$	−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	−0.139731	−	0.990190i	$-0.544624\pi$
$67$	6.44731	−	11.1671i	0.787664	−	1.36427i	0.927395	−	0.374084i	$-0.122043\pi$
$68$	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	−0.221654	−	0.975125i	$-0.571146\pi$
$73$	6.26836	−	10.8571i	0.733656	−	1.27073i	0.955310	−	0.295604i	$-0.0955210\pi$
$74$	−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	0.905584	−	0.424168i	$-0.139433\pi$
$79$	0.759511	+	1.31551i	0.0854516	+	0.148007i	−0.820132	+	0.572174i	$0.806100\pi$
$80$	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	$-0.832582\pi$
$83$	−15.7582			−1.72969			−0.864843	+	0.502042i	$0.832582\pi$
$84$		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	−0.929056	−	0.369940i	$-0.879378\pi$
$89$	−7.40478	−	12.8255i	−0.784905	−	1.35950i	0.144150	−	0.989556i	$-0.453955\pi$
$90$	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	$-0.330174\pi$
$97$	10.0177			1.01714			0.508572	+	0.861020i	$0.330174\pi$
$98$		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	$-0.881305\pi$
$101$	−1.50885	+	2.61341i	−0.150136	+	0.260044i	0.781141	+	0.624354i	$0.214638\pi$
$102$	7.62177	−	13.2013i	0.754668	−	1.30712i
$103$	−2.51902	−	4.36307i	−0.248207	−	0.429906i	0.714822	−	0.699307i	$-0.246508\pi$
$103$	−2.51902	−	4.36307i	−0.248207	−	0.429906i	−0.963028	+	0.269400i	$0.913174\pi$
$104$	−8.10275			−0.794540
$105$		0			0
$106$	−13.9663			−1.35653
$107$	−5.92162	−	10.2565i	−0.572465	−	0.991538i	−0.996312	−	0.0858041i	$-0.972654\pi$
$107$	−5.92162	−	10.2565i	−0.572465	−	0.991538i	0.423848	−	0.905734i	$-0.360679\pi$
$108$	−1.57040	+	2.72000i	−0.151111	+	0.261733i
$109$	−1.77503	+	3.07444i	−0.170017	+	0.294478i	−0.938425	−	0.345482i	$-0.887716\pi$
$109$	−1.77503	+	3.07444i	−0.170017	+	0.294478i	0.768409	+	0.639959i	$0.221049\pi$
$110$	−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	$-0.0253842\pi$
$131$	4.91495	+	8.51295i	0.429421	+	0.743780i	−0.567400	+	0.823442i	$0.692051\pi$
$132$	−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	0.198265	+	0.980149i	$0.436469\pi$
$137$	−8.77503	+	15.1988i	−0.749701	+	1.29852i	−0.947966	+	0.318372i	$0.896864\pi$
$138$	−23.4203	−	40.5651i	−1.99367	−	3.45313i
$139$	4.91495			0.416881			0.208440	−	0.978035i	$-0.433161\pi$
$139$	4.91495			0.416881			0.208440	+	0.978035i	$0.433161\pi$
$140$		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	0.996291	−	0.0860527i	$-0.0274253\pi$
$149$	5.17096	+	8.95636i	0.423621	+	0.733734i	−0.572669	+	0.819787i	$0.694092\pi$
$150$	−26.6014	+	46.0750i	−2.17200	+	3.76201i
$151$	−2.53586	+	4.39223i	−0.206365	+	0.357435i	−0.950567	−	0.310520i	$-0.899497\pi$
$151$	−2.53586	+	4.39223i	−0.206365	+	0.357435i	0.744202	+	0.667955i	$0.232830\pi$
$152$	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	0.497143	+	0.867669i	$0.334383\pi$
$157$	−6.30071	+	10.9132i	−0.502852	+	0.870965i	−0.999995	+	0.00329606i	$0.998951\pi$
$158$	−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	0.796343	−	0.604846i	$-0.206765\pi$
$163$	−1.60407	−	2.77833i	−0.125640	−	0.217615i	−0.921983	+	0.387230i	$0.873432\pi$
$164$	−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	$-0.601733\pi$
$167$	−8.12045			−0.628379			−0.314190	+	0.949360i	$0.601733\pi$
$168$		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	$-0.295103\pi$
$173$	−5.16429	−	8.94482i	−0.392634	−	0.680062i	−0.992796	+	0.119816i	$0.961769\pi$
$174$	−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	−0.818159	−	0.574992i	$-0.805005\pi$
$179$	1.18912	−	2.05961i	0.0888786	−	0.153942i	0.907037	+	0.421050i	$0.138338\pi$
$180$	25.3016	+	43.8236i	1.88587	+	3.26642i
$181$	−21.8096			−1.62109			−0.810546	−	0.585675i	$-0.800830\pi$
$181$	−21.8096			−1.62109			−0.810546	+	0.585675i	$0.800830\pi$
$182$		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	0.817378	+	0.576102i	$0.195427\pi$
$191$	12.5434	+	21.7258i	0.907608	+	1.57202i	0.0902297	+	0.995921i	$0.471240\pi$
$192$	17.5164	−	30.3393i	1.26414	−	2.18955i
$193$	−5.65544	+	9.79551i	−0.407088	+	0.705096i	−0.994562	−	0.104146i	$-0.966789\pi$
$193$	−5.65544	+	9.79551i	−0.407088	+	0.705096i	0.587474	+	0.809243i	$0.300122\pi$
$194$	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	−0.229995	−	0.973192i	$-0.573871\pi$
$199$	10.2670	−	17.7830i	0.727811	−	1.26061i	0.957806	−	0.287414i	$-0.0927957\pi$
$200$	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	$-0.408725\pi$
$223$	8.44731			0.565673			0.282837	+	0.959168i	$0.408725\pi$
$224$		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	$-0.762079\pi$
$227$	3.34456	−	5.79294i	0.221986	−	0.384491i	0.955411	+	0.295279i	$0.0954127\pi$
$228$	16.3800	−	28.3709i	1.08479	−	1.87891i
$229$	4.31755	+	7.47822i	0.285312	+	0.494175i	0.972685	−	0.232130i	$-0.0745695\pi$
$229$	4.31755	+	7.47822i	0.285312	+	0.494175i	−0.687373	+	0.726305i	$0.741236\pi$
$230$	71.4641			4.71220
$231$		0			0
$232$	1.68648			0.110723
$233$	2.08373	+	3.60912i	0.136510	+	0.236441i	0.926173	−	0.377099i	$-0.123078\pi$
$233$	2.08373	+	3.60912i	0.136510	+	0.236441i	−0.789664	+	0.613540i	$0.789745\pi$
$234$	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	$-0.686028\pi$
$241$	6.93047	−	12.0039i	0.446431	−	0.773241i	0.998151	+	0.0607887i	$0.0193616\pi$
$242$	−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	$-0.654069\pi$
$251$	−14.7449			−0.930687			−0.465344	+	0.885130i	$0.654069\pi$
$252$		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	0.952768	+	0.303699i	$0.0982218\pi$
$257$	11.8534	+	20.5307i	0.739395	+	1.28067i	−0.213373	+	0.976971i	$0.568445\pi$
$258$	−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	−0.986377	−	0.164503i	$-0.947398\pi$
$263$	−5.68780	+	9.85155i	−0.350725	+	0.607473i	0.635652	+	0.771976i	$0.280731\pi$
$264$	−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	$-0.943271\pi$
$269$	−5.55269	+	9.61755i	−0.338554	+	0.586392i	0.645607	+	0.763670i	$0.276604\pi$
$270$	−3.01770	+	5.22681i	−0.183651	+	0.318094i
$271$	−6.36226	−	11.0198i	−0.386480	−	0.669402i	0.605494	−	0.795850i	$-0.292976\pi$
$271$	−6.36226	−	11.0198i	−0.386480	−	0.669402i	−0.991973	+	0.126448i	$0.959642\pi$
$272$	−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	−0.817438	−	0.576017i	$-0.804606\pi$
$277$	1.50000	−	2.59808i	0.0901263	−	0.156103i	0.907564	+	0.419914i	$0.137940\pi$
$278$	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	$-0.954277\pi$
$283$	−6.23917	+	10.8066i	−0.370880	+	0.642383i	0.618821	+	0.785532i	$0.287611\pi$
$284$	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	$-0.370629\pi$
$293$	13.5341			0.790670			0.395335	+	0.918537i	$0.370629\pi$
$294$		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	$-0.798249\pi$
$307$	−28.2365			−1.61154			−0.805772	+	0.592226i	$0.798249\pi$
$308$		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	0.267895	+	0.963448i	$0.413672\pi$
$311$	−12.3521	+	21.3944i	−0.700423	+	1.21317i	−0.968318	+	0.249720i	$0.919662\pi$
$312$	−9.70682	+	16.8127i	−0.549540	+	0.951832i
$313$	−10.4061	−	18.0239i	−0.588188	−	1.01877i	−0.994470	−	0.105023i	$-0.966508\pi$
$313$	−10.4061	−	18.0239i	−0.588188	−	1.01877i	0.406282	−	0.913748i	$-0.366825\pi$
$314$	−33.4624			−1.88839
$315$		0			0
$316$	−7.67314			−0.431648
$317$	−13.0691	−	22.6363i	−0.734032	−	1.27138i	−0.955147	−	0.296134i	$-0.904303\pi$
$317$	−13.0691	−	22.6363i	−0.734032	−	1.27138i	0.221114	−	0.975248i	$-0.429031\pi$
$318$	−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	0.979723	+	0.200358i	$0.0642105\pi$
$331$	12.0691	+	20.9043i	0.663376	+	1.14900i	−0.316346	+	0.948644i	$0.602456\pi$
$332$	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	−0.306667	−	0.951817i	$-0.599214\pi$
$347$	12.4987	−	21.6483i	0.670964	−	1.16214i	0.977631	−	0.210327i	$-0.0674530\pi$
$348$	−1.25951	−	2.18154i	−0.0675169	−	0.116943i
$349$	1.83887			0.0984324			0.0492162	−	0.998788i	$-0.484328\pi$
$349$	1.83887			0.0984324			0.0492162	+	0.998788i	$0.484328\pi$
$350$		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	0.370764	+	0.928727i	$0.379096\pi$
$353$	−11.6284	+	20.1410i	−0.618919	+	1.07200i	−0.989683	+	0.143272i	$0.954238\pi$
$354$	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	0.996958	+	0.0779348i	$0.0248326\pi$
$359$	10.7237	+	18.5739i	0.565973	+	0.980294i	−0.430986	+	0.902359i	$0.641834\pi$
$360$	−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	$-0.842643\pi$
$367$	−0.560225	+	0.970338i	−0.0292435	+	0.0506512i	0.851033	+	0.525112i	$0.175976\pi$
$368$	−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	0.590188	−	0.807266i	$-0.299054\pi$
$373$	−7.80290	−	13.5150i	−0.404019	−	0.699781i	−0.994207	+	0.107485i	$0.965720\pi$
$374$	−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	0.862443	+	0.506154i	$0.168933\pi$
$383$	17.0177	+	29.4755i	0.869564	+	1.50613i	0.00712095	+	0.999975i	$0.497733\pi$
$384$	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	−0.363037	−	0.931775i	$-0.618260\pi$
$389$	12.3353	−	21.3653i	0.625422	−	1.08326i	0.988459	−	0.151488i	$-0.0484065\pi$
$390$	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	$-0.206547\pi$
$397$	−2.48983	−	4.31251i	−0.124961	−	0.216439i	−0.921718	+	0.387861i	$0.873214\pi$
$398$	54.5271			2.73320
$399$		0			0
$400$	95.4438			4.77219
$401$	−0.344558	−	0.596791i	−0.0172064	−	0.0298023i	0.857294	−	0.514827i	$-0.172144\pi$
$401$	−0.344558	−	0.596791i	−0.0172064	−	0.0298023i	−0.874500	+	0.485025i	$0.838811\pi$
$402$	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	$-0.668904\pi$
$409$	9.98851	−	17.3006i	0.493900	−	0.855460i	0.999975	+	0.00702937i	$0.00223754\pi$
$410$	−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	$-0.659500\pi$
$419$	−19.6661			−0.960754			−0.480377	+	0.877062i	$0.659500\pi$
$420$		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	−0.140536	−	0.990076i	$-0.544883\pi$
$431$	16.3419	−	28.3050i	0.787163	−	1.36341i	0.927699	−	0.373330i	$-0.121784\pi$
$432$	−3.54832	−	6.14588i	−0.170719	−	0.295694i
$433$	8.96196			0.430684			0.215342	−	0.976539i	$-0.430913\pi$
$433$	8.96196			0.430684			0.215342	+	0.976539i	$0.430913\pi$
$434$		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	$-0.227289\pi$
$439$	−3.96633	−	6.86988i	−0.189302	−	0.327881i	−0.945018	+	0.327019i	$0.893956\pi$
$440$	19.4136			0.925509
$441$		0			0
$442$	6.36226			0.302622
$443$	4.45529	+	7.71679i	0.211677	+	0.366636i	0.952240	−	0.305352i	$-0.0987741\pi$
$443$	4.45529	+	7.71679i	0.211677	+	0.366636i	−0.740562	+	0.671988i	$0.765441\pi$
$444$	−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	−0.998795	−	0.0490829i	$-0.984370\pi$
$457$	−11.5846	−	20.0651i	−0.541904	−	0.938606i	0.456890	−	0.889523i	$-0.348963\pi$
$458$	−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	$-0.516856\pi$
$461$	−2.27284			−0.105857			−0.0529284	+	0.998598i	$0.516856\pi$
$462$		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	0.942046	+	0.335485i	$0.108900\pi$
$467$	16.4575	+	28.5052i	0.761561	+	1.31906i	−0.180484	+	0.983578i	$0.557767\pi$
$468$	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	$-0.901596\pi$
$479$	−4.65763	+	8.06725i	−0.212812	+	0.368602i	0.739781	+	0.672847i	$0.234929\pi$
$480$	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	−0.998887	−	0.0471606i	$-0.984983\pi$
$487$	−10.1204	+	17.5291i	−0.458601	+	0.794321i	0.540286	+	0.841481i	$0.318316\pi$
$488$	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	0.736910	−	0.675991i	$-0.236284\pi$
$499$	−4.84674	−	8.39480i	−0.216970	−	0.375803i	−0.953880	+	0.300188i	$0.902951\pi$
$500$	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	$-0.518805\pi$
$503$	−2.64843			−0.118088			−0.0590439	+	0.998255i	$0.518805\pi$
$504$		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	$-0.266653\pi$
$509$	−6.97081	−	12.0738i	−0.308976	−	0.535162i	−0.978139	+	0.207954i	$0.933319\pi$
$510$	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	$-0.937116\pi$
$521$	−7.31088	+	12.6628i	−0.320296	+	0.554768i	0.660253	+	0.751043i	$0.270449\pi$
$522$	−0.757326	+	1.31173i	−0.0331473	+	0.0574127i
$523$	8.25951	+	14.3059i	0.361163	+	0.625553i	0.988153	−	0.153475i	$-0.0490464\pi$
$523$	8.25951	+	14.3059i	0.361163	+	0.625553i	−0.626989	+	0.779028i	$0.715713\pi$
$524$	−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	0.789055	+	0.614322i	$0.210571\pi$
$541$	21.5509	+	37.3273i	0.926546	+	1.60483i	0.137491	+	0.990503i	$0.456096\pi$
$542$	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	−0.879987	−	0.474997i	$-0.842449\pi$
$557$	−0.675783	+	1.17049i	−0.0286338	+	0.0495953i	0.851353	+	0.524593i	$0.175782\pi$
$558$	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	−0.308779	−	0.951134i	$-0.599921\pi$
$563$	15.8813	−	27.5072i	0.669316	−	1.15929i	0.978096	−	0.208156i	$-0.0667462\pi$
$564$	−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	−0.986163	−	0.165779i	$-0.946986\pi$
$569$	−15.1865	−	26.3037i	−0.636650	−	1.10271i	0.349513	−	0.936932i	$-0.386347\pi$
$570$	31.4760	−	54.5181i	1.31839	−	2.28351i
$571$	0.216122	−	0.374334i	0.00904442	−	0.0156654i	−0.861468	−	0.507812i	$-0.830454\pi$
$571$	0.216122	−	0.374334i	0.00904442	−	0.0156654i	0.870512	+	0.492147i	$0.163788\pi$
$572$	−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	$-0.710100\pi$
$577$	9.06908	−	15.7081i	0.377551	−	0.653937i	0.990705	+	0.136026i	$0.0434331\pi$
$578$	−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	$-0.630446\pi$
$587$	−19.3065			−0.796865			−0.398433	+	0.917198i	$0.630446\pi$
$588$		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	$-0.112810\pi$
$593$	4.10056	+	7.10238i	0.168390	+	0.291660i	−0.769464	+	0.638690i	$0.779477\pi$
$594$	−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	−0.999728	−	0.0233415i	$-0.992570\pi$
$599$	−11.7392	+	20.3328i	−0.479649	+	0.830777i	0.520078	+	0.854119i	$0.325903\pi$
$600$	−81.1709	−	140.592i	−3.31379	−	5.73965i
$601$	8.96196			0.365566			0.182783	−	0.983153i	$-0.441489\pi$
$601$	8.96196			0.365566			0.182783	+	0.983153i	$0.441489\pi$
$602$		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	0.849028	+	0.528348i	$0.177188\pi$
$607$	21.7320	+	37.6410i	0.882077	+	1.52780i	0.0330487	+	0.999454i	$0.489478\pi$
$608$	−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	−0.563984	−	0.825786i	$-0.690732\pi$
$613$	10.7245	−	18.5754i	0.433159	−	0.750254i	0.997143	+	0.0755318i	$0.0240655\pi$
$614$	−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	$-0.751021\pi$
$619$	6.36226	−	11.0198i	0.255721	−	0.442921i	0.965091	+	0.261915i	$0.0843539\pi$
$620$	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	−0.908584	−	0.417701i	$-0.862836\pi$
$641$	−2.34324	+	4.05861i	−0.0925523	+	0.160305i	0.816032	+	0.578007i	$0.196169\pi$
$642$	−37.6749	−	65.2548i	−1.48691	−	2.57540i
$643$	0.751182			0.0296237			0.0148119	−	0.999890i	$-0.495285\pi$
$643$	0.751182			0.0296237			0.0148119	+	0.999890i	$0.495285\pi$
$644$		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	−0.114729	−	0.993397i	$-0.536600\pi$
$647$	20.4238	−	35.3751i	0.802943	−	1.39074i	0.917671	−	0.397340i	$-0.130067\pi$
$648$	−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	0.814873	+	0.579639i	$0.196807\pi$
$653$	23.2392	+	40.2514i	0.909419	+	1.57516i	0.0945459	+	0.995521i	$0.469860\pi$
$654$	−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	$-0.833996\pi$
$661$	−0.0535589	+	0.0927667i	−0.00208320	+	0.00360820i	0.864982	+	0.501803i	$0.167330\pi$
$662$	−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	$-0.297422\pi$
$677$	−10.3901	−	17.9962i	−0.399325	−	0.691651i	−0.993643	+	0.112579i	$0.964089\pi$
$678$	−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	0.471746	+	0.881734i	$0.343624\pi$
$683$	−13.7919	+	23.8882i	−0.527731	+	0.914057i	−0.999477	+	0.0323227i	$0.989710\pi$
$684$	−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	0.897416	+	0.441185i	$0.145442\pi$
$691$	21.8388	+	37.8258i	0.830785	+	1.43896i	−0.0666308	+	0.997778i	$0.521225\pi$
$692$	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	0.757484	−	0.652854i	$-0.226428\pi$
$709$	−4.96983	−	8.60800i	−0.186646	−	0.323280i	−0.944130	+	0.329574i	$0.893095\pi$
$710$	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	$-0.238377\pi$
$719$	−5.98983	−	10.3747i	−0.223383	−	0.386911i	−0.955833	+	0.293910i	$0.905043\pi$
$720$	−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	$-0.647961\pi$
$727$	−24.1736			−0.896547			−0.448274	+	0.893896i	$0.647961\pi$
$728$		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	−0.977019	−	0.213154i	$-0.931626\pi$
$733$	−18.2237	−	31.5643i	−0.673106	−	1.16585i	0.303913	−	0.952700i	$-0.401707\pi$
$734$	−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	0.126220	+	0.992002i	$0.459715\pi$
$739$	−21.6386	+	37.4792i	−0.795989	+	1.37869i	−0.922209	+	0.386691i	$0.873618\pi$
$740$	−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	−0.998610	−	0.0527044i	$-0.983216\pi$
$751$	−14.9340	−	25.8664i	−0.544948	−	0.943878i	0.453662	−	0.891174i	$-0.350117\pi$
$752$	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	$-0.0806472\pi$
$761$	7.36444	+	12.7556i	0.266961	+	0.462390i	−0.701115	+	0.713049i	$0.747314\pi$
$762$	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	$-0.273868\pi$
$769$	36.1692			1.30429			0.652147	+	0.758092i	$0.273868\pi$
$770$		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	−0.267673	−	0.963510i	$-0.586255\pi$
$773$	19.4783	−	33.7375i	0.700587	−	1.21345i	0.968261	−	0.249943i	$-0.0804118\pi$
$774$	−11.2897	+	19.5543i	−0.405799	+	0.702865i
$775$	−4.75152	−	8.22988i	−0.170680	−	0.295626i
$776$	−81.1709			−2.91387
$777$		0			0
$778$	65.5111			2.34869
$779$	−13.8122	−	23.9234i	−0.494874	−	0.857146i
$780$	−22.1204	+	38.3137i	−0.792039	+	1.37185i
$781$	2.21480	−	3.83615i	0.0792519	−	0.137268i
$782$	−23.4203	−	40.5651i	−0.837508	−	1.45061i
$783$	−0.129413			−0.00462484
$784$		0			0
$785$	−46.0638			−1.64409
$786$	31.2702	+	54.1616i	1.11537	+	1.93188i
$787$	14.5522	−	25.2052i	0.518731	−	0.898469i	−0.481032	−	0.876703i	$-0.659738\pi$
$787$	14.5522	−	25.2052i	0.518731	−	0.898469i	0.999763	−	0.0217658i	$-0.00692882\pi$
$788$	42.4110	−	73.4580i	1.51083	−	2.61683i
$789$	13.6276	+	23.6036i	0.485154	+	0.840312i
$790$	−14.7449			−0.524599
$791$		0			0
$792$	−14.5544			−0.517169
$793$	−0.948626	−	1.64307i	−0.0336867	−	0.0583471i
$794$	6.61160	−	11.4516i	0.234637	−	0.406403i
$795$	−23.0319	+	39.8924i	−0.816857	+	1.41484i
$796$	51.8627	+	89.8288i	1.83822	+	3.18390i
$797$	17.8920			0.633766			0.316883	−	0.948465i	$-0.397364\pi$
$797$	17.8920			0.633766			0.316883	+	0.948465i	$0.397364\pi$
$798$		0			0
$799$	11.0310			0.390250
$800$	58.9654	+	102.131i	2.08474	+	3.61088i
$801$	−20.2927	+	35.1480i	−0.717008	+	1.24189i
$802$	0.914953	−	1.58474i	0.0323081	−	0.0559593i
$803$	4.10855	+	7.11622i	0.144988	+	0.251126i
$804$	156.060			5.50382
$805$		0			0
$806$	−3.01770			−0.106294
$807$	13.3039	+	23.0430i	0.468319	+	0.811152i
$808$	12.2258	−	21.1758i	0.430103	−	0.744961i
$809$	−10.2272	+	17.7140i	−0.359568	+	0.622790i	−0.987889	−	0.155165i	$-0.950409\pi$
$809$	−10.2272	+	17.7140i	−0.359568	+	0.622790i	0.628321	+	0.777954i	$0.283742\pi$
$810$	47.1324	+	81.6356i	1.65606	+	2.86838i
$811$	31.6458			1.11123			0.555617	−	0.831438i	$-0.312482\pi$
$811$	31.6458			1.11123			0.555617	+	0.831438i	$0.312482\pi$
$812$		0			0
$813$	−30.4871			−1.06923
$814$	−6.48098	−	11.2254i	−0.227158	−	0.393450i
$815$	5.86358	−	10.1560i	0.205392	−	0.355750i
$816$	−32.7599	+	56.7418i	−1.14683	+	1.98636i
$817$	4.19929	+	7.27338i	0.146914	+	0.254463i
$818$	53.0478			1.85477
$819$		0			0
$820$	−188.445			−6.58077
$821$	−9.03804	−	15.6543i	−0.315430	−	0.546341i	0.664099	−	0.747645i	$-0.268815\pi$
$821$	−9.03804	−	15.6543i	−0.315430	−	0.546341i	−0.979529	+	0.201304i	$0.935482\pi$
$822$	−55.8290	+	96.6987i	−1.94726	+	3.37275i
$823$	11.5257	−	19.9631i	0.401760	−	0.695869i	−0.592178	−	0.805807i	$-0.701732\pi$
$823$	11.5257	−	19.9631i	0.401760	−	0.695869i	0.993938	+	0.109938i	$0.0350652\pi$
$824$	20.4110	+	35.3529i	0.711051	+	1.23158i
$825$	−13.1321			−0.457199
$826$		0			0
$827$	−26.3756			−0.917169			−0.458585	−	0.888651i	$-0.651643\pi$
$827$	−26.3756			−0.917169			−0.458585	+	0.888651i	$0.651643\pi$
$828$	−50.9588	−	88.2631i	−1.77094	−	3.06736i
$829$	22.5576	−	39.0709i	0.783457	−	1.35699i	−0.146459	−	0.989217i	$-0.546788\pi$
$829$	22.5576	−	39.0709i	0.783457	−	1.35699i	0.929916	−	0.367771i	$-0.119879\pi$
$830$	76.4809	−	132.469i	2.65469	−	4.59806i
$831$	−3.59390	−	6.22481i	−0.124671	−	0.215936i
$832$	14.6218			0.506919
$833$		0			0
$834$	31.2702			1.08280
$835$	−14.8419	−	25.7070i	−0.513626	−	0.889626i
$836$	−4.48098	+	7.76128i	−0.154978	+	0.268430i
$837$	−0.353296	+	0.611927i	−0.0122117	+	0.0211513i
$838$	−26.1111	−	45.2258i	−0.901995	−	1.56230i
$839$	30.4871			1.05253			0.526265	−	0.850320i	$-0.323592\pi$
$839$	30.4871			1.05253			0.526265	+	0.850320i	$0.323592\pi$
$840$		0			0
$841$	−28.9567			−0.998506
$842$	19.8206	+	34.3303i	0.683063	+	1.18310i
$843$	4.12976	−	7.15295i	0.142236	−	0.246361i
$844$	39.8516	−	69.0251i	1.37175	−	2.37594i
$845$	1.82772	+	3.16571i	0.0628755	+	0.108904i
$846$	33.5048			1.15192
$847$		0			0
$848$	60.0301			2.06144
$849$	14.9486	+	25.8918i	0.513036	+	0.888604i
$850$	−26.6014	+	46.0750i	−0.912421	+	1.58036i
$851$	27.4145	−	47.4833i	0.939757	−	1.62771i
$852$	−40.8963	−	70.8345i	−1.40109	−	2.42675i
$853$	33.2746			1.13930			0.569650	−	0.821888i	$-0.307079\pi$
$853$	33.2746			1.13930			0.569650	+	0.821888i	$0.307079\pi$
$854$		0			0
$855$	−27.1161			−0.927350
$856$	47.9814	+	83.1062i	1.63997	+	2.84051i
$857$	22.8069	−	39.5028i	0.779070	−	1.34939i	−0.153409	−	0.988163i	$-0.549025\pi$
$857$	22.8069	−	39.5028i	0.779070	−	1.34939i	0.932478	−	0.361226i	$-0.117642\pi$
$858$	−2.08505	+	3.61141i	−0.0711823	+	0.123291i
$859$	10.4676	+	18.1305i	0.357151	+	0.618605i	0.987484	−	0.157721i	$-0.0504147\pi$
$859$	10.4676	+	18.1305i	0.357151	+	0.618605i	−0.630332	+	0.776326i	$0.717081\pi$
$860$	57.2923			1.95365
$861$		0			0
$862$	86.7900			2.95608
$863$	−1.48098	−	2.56513i	−0.0504131	−	0.0873181i	0.839718	−	0.543023i	$-0.182720\pi$
$863$	−1.48098	−	2.56513i	−0.0504131	−	0.0873181i	−0.890131	+	0.455705i	$0.849387\pi$
$864$	4.38433	−	7.59388i	0.149158	−	0.258349i
$865$	18.8778	−	32.6973i	0.641864	−	1.11174i
$866$	11.8990	+	20.6096i	0.404344	+	0.700344i
$867$	26.9770			0.916188
$868$		0			0
$869$	−0.995631			−0.0337745
$870$	−2.42030	−	4.19208i	−0.0820558	−	0.142125i
$871$	6.44731	−	11.1671i	0.218459	−	0.378381i
$872$	14.3826	−	24.9114i	0.487056	−	0.843606i
$873$	−13.7267	−	23.7753i	−0.464578	−	0.804674i
$874$	−52.9184			−1.78999
$875$		0			0
$876$	151.729			5.12644
$877$	18.4685	+	31.9884i	0.623637	+	1.08017i	0.988803	+	0.149229i	$0.0476791\pi$
$877$	18.4685	+	31.9884i	0.623637	+	1.08017i	−0.365165	+	0.930943i	$0.618988\pi$
$878$	10.5324	−	18.2426i	0.355450	−	0.615657i
$879$	16.2134	−	28.0824i	0.546863	−	0.947195i
$880$	13.6731	+	23.6826i	0.460922	+	0.798340i
$881$	−30.8946			−1.04087			−0.520433	−	0.853903i	$-0.674229\pi$
$881$	−30.8946			−1.04087			−0.520433	+	0.853903i	$0.674229\pi$
$882$		0			0
$883$	−9.64648			−0.324630			−0.162315	−	0.986739i	$-0.551896\pi$
$883$	−9.64648			−0.324630			−0.162315	+	0.986739i	$0.551896\pi$
$884$	6.05137	+	10.4813i	0.203530	+	0.352524i
$885$	36.1692	−	62.6469i	1.21581	−	2.10585i
$886$	−11.8308	+	20.4915i	−0.397463	+	0.688425i
$887$	−25.6528	−	44.4320i	−0.861337	−	1.49188i	−0.870639	−	0.491922i	$-0.836294\pi$
$887$	−25.6528	−	44.4320i	−0.861337	−	1.49188i	0.00930221	−	0.999957i	$-0.497039\pi$
$888$	−144.579			−4.85176
$889$		0			0
$890$	143.754			4.81864
$891$	3.18256	+	5.51236i	0.106620	+	0.184671i
$892$	−21.3353	+	36.9537i	−0.714357	+	1.23730i
$893$	6.23118	−	10.7927i	0.208519	−	0.361165i
$894$	32.8990	+	56.9827i	1.10031	+	1.90579i
$895$	8.69348			0.290591
$896$		0			0
$897$	−17.6395			−0.588965
$898$	−11.2215	−	19.4362i	−0.374465	−	0.648593i
$899$	0.118265	−	0.204841i	0.00394437	−	0.00683184i
$900$	−57.8804	+	100.252i	−1.92935	+	3.34172i
$901$	6.30071	+	10.9132i	0.209907	+	0.363570i
$902$	−17.7626			−0.591429
$903$		0			0
$904$	76.6926			2.55076
$905$	−39.8618	−	69.0427i	−1.32505	−	2.29506i
$906$	−16.1338	+	27.9445i	−0.536009	+	0.928395i
$907$	9.26923	−	16.0548i	0.307780	−	0.533090i	−0.670097	−	0.742274i	$-0.733747\pi$
$907$	9.26923	−	16.0548i	0.307780	−	0.533090i	0.977876	+	0.209184i	$0.0670807\pi$
$908$	16.8946	+	29.2623i	0.560667	+	0.971104i
$909$	8.26998			0.274298
$910$		0			0
$911$	20.7272			0.686721			0.343361	−	0.939204i	$-0.388435\pi$
$911$	20.7272			0.686721			0.343361	+	0.939204i	$0.388435\pi$
$912$	37.0107	+	64.1044i	1.22555	+	2.12271i
$913$	5.16429	−	8.94482i	0.170913	−	0.296030i
$914$	30.7622	−	53.2817i	1.01752	−	1.76240i
$915$	−8.30825	−	14.3903i	−0.274662	−	0.475729i
$916$	−43.6191			−1.44122
$917$		0			0
$918$	3.95586			0.130563
$919$	2.56603	+	4.44449i	0.0846454	+	0.146610i	0.905240	−	0.424901i	$-0.139691\pi$
$919$	2.56603	+	4.44449i	0.0846454	+	0.146610i	−0.820595	+	0.571511i	$0.806358\pi$
$920$	−109.032	+	188.849i	−3.59467	+	6.22616i
$921$	−33.8264	+	58.5890i	−1.11462	+	1.93057i
$922$	−3.01770	−	5.22681i	−0.0993827	−	0.172136i
$923$	−6.75819			−0.222449
$924$		0			0
$925$	−62.2763			−2.04763
$926$	−5.45661	−	9.45113i	−0.179315	−	0.310583i
$927$	−6.90335	+	11.9570i	−0.226736	+	0.392718i
$928$	−1.46765	+	2.54204i	−0.0481779	+	0.0834465i
$929$	9.96414	+	17.2584i	0.326913	+	0.566230i	0.981898	−	0.189412i	$-0.0606583\pi$
$929$	9.96414	+	17.2584i	0.326913	+	0.566230i	−0.654985	+	0.755642i	$0.727325\pi$
$930$	−26.4296			−0.866661
$931$		0			0
$932$	−21.0514			−0.689561
$933$	29.5948	+	51.2596i	0.968889	+	1.67817i
$934$	−43.7019	+	75.6939i	−1.42997	+	2.47678i
$935$	−2.87024	+	4.97141i	−0.0938670	+	0.162582i
$936$	11.1027	+	19.2305i	0.362905	+	0.628569i
$937$	1.64475			0.0537316			0.0268658	−	0.999639i	$-0.491447\pi$
$937$	1.64475			0.0537316			0.0268658	+	0.999639i	$0.491447\pi$
$938$		0			0
$939$	−49.8646			−1.62727
$940$	−42.5071	−	73.6244i	−1.38643	−	2.40136i
$941$	−8.89243	+	15.4021i	−0.289885	+	0.502095i	−0.973782	−	0.227483i	$-0.926950\pi$
$941$	−8.89243	+	15.4021i	−0.289885	+	0.502095i	0.683897	+	0.729578i	$0.260284\pi$
$942$	−40.0868	+	69.4323i	−1.30610	+	2.26223i
$943$	−37.5678	−	65.0693i	−1.22337	−	2.11895i
$944$	−94.2710			−3.06826
$945$		0			0
$946$	5.40030			0.175579
$947$	−5.32422	−	9.22181i	−0.173014	−	0.299669i	0.766458	−	0.642294i	$-0.222017\pi$
$947$	−5.32422	−	9.22181i	−0.173014	−	0.299669i	−0.939472	+	0.342625i	$0.888684\pi$
$948$	−9.19216	+	15.9213i	−0.298548	+	0.517100i
$949$	6.26836	−	10.8571i	0.203480	−	0.352437i
$950$	30.0531	+	52.0535i	0.975051	+	1.68884i
$951$	−62.6252			−2.03076
$952$		0			0
$953$	−41.5544			−1.34608			−0.673040	−	0.739606i	$-0.735012\pi$
$953$	−41.5544			−1.34608			−0.673040	+	0.739606i	$0.735012\pi$
$954$	19.1373	+	33.1468i	0.619593	+	1.07317i
$955$	−45.8516	+	79.4174i	−1.48372	+	2.56989i
$956$	4.53235	−	7.85027i	0.146587	−	0.253896i
$957$	−0.163428	−	0.283066i	−0.00528288	−	0.00915022i
$958$	−24.7361			−0.799188
$959$		0			0
$960$	128.060			4.13313
$961$	14.8543	+	25.7284i	0.479170	+	0.829947i
$962$	−9.88795	+	17.1264i	−0.318800	+	0.552178i
$963$	−16.2281	+	28.1080i	−0.522944	+	0.905766i
$964$	35.0084	+	60.6363i	1.12754	+	1.95296i
$965$	−41.3463			−1.33098
$966$		0			0
$967$	−5.51465			−0.177339			−0.0886696	−	0.996061i	$-0.528262\pi$
$967$	−5.51465			−0.177339			−0.0886696	+	0.996061i	$0.528262\pi$
$968$	−42.8246	−	74.1744i	−1.37644	−	2.38406i
$969$	−7.76923	+	13.4567i	−0.249584	+	0.432291i
$970$	−48.6200	+	84.2123i	−1.56109	+	2.70389i
$971$	19.9123	+	34.4891i	0.639017	+	1.10681i	0.985649	+	0.168808i	$0.0539918\pi$
$971$	19.9123	+	34.4891i	0.639017	+	1.10681i	−0.346632	+	0.938001i	$0.612675\pi$
$972$	108.110			3.46762
$973$		0			0
$974$	−53.7485			−1.72221
$975$	10.0177	+	17.3512i	0.320823	+	0.555682i
$976$	−10.8273	+	18.7534i	−0.346572	+	0.600281i
$977$	−0.965462	+	1.67223i	−0.0308879	+	0.0534994i	−0.881056	−	0.473012i	$-0.843167\pi$
$977$	−0.965462	+	1.67223i	−0.0308879	+	0.0534994i	0.850168	+	0.526511i	$0.176500\pi$
$978$	−10.2055	−	17.6764i	−0.326336	−	0.565230i
$979$	9.70682			0.310231
$980$		0			0
$981$	9.72889			0.310619
$982$	−5.79186	−	10.0318i	−0.184826	−	0.320128i
$983$	−21.5119	+	37.2597i	−0.686123	+	1.18840i	0.286959	+	0.957943i	$0.407356\pi$
$983$	−21.5119	+	37.2597i	−0.686123	+	1.18840i	−0.973082	+	0.230457i	$0.925978\pi$
$984$	−99.0629	+	171.582i	−3.15801	+	5.46983i
$985$	−30.6908	−	53.1581i	−0.977892	−	1.69376i
$986$	−1.32422			−0.0421717
$987$		0			0
$988$	13.6731			0.435001
$989$	11.4216	+	19.7828i	0.363186	+	0.629057i
$990$	−8.71785	+	15.0998i	−0.277072	+	0.479902i
$991$	8.80290	−	15.2471i	0.279633	−	0.484339i	−0.691660	−	0.722223i	$-0.743120\pi$
$991$	8.80290	−	15.2471i	0.279633	−	0.484339i	0.971294	+	0.237884i	$0.0764538\pi$
$992$	8.01333	+	13.8795i	0.254424	+	0.440675i
$993$	57.8334			1.83529
$994$		0			0
$995$	75.0612			2.37960
$996$	−95.3587	−	165.166i	−3.02156	−	5.23349i
$997$	−6.48535	+	11.2330i	−0.205393	+	0.355751i	−0.950258	−	0.311464i	$-0.899181\pi$
$997$	−6.48535	+	11.2330i	−0.205393	+	0.355751i	0.744865	+	0.667215i	$0.232514\pi$
$998$	12.8702	−	22.2919i	0.407400	−	0.705638i
$999$	2.31525	+	4.01014i	0.0732514	+	0.126875i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.e.l.508.3		6
7.2	even	3	inner	637.2.e.l.79.3		6
7.3	odd	6		637.2.a.i.1.1	yes	3
7.4	even	3		637.2.a.h.1.1	✓	3
7.5	odd	6		637.2.e.k.79.3		6
7.6	odd	2		637.2.e.k.508.3		6
21.11	odd	6		5733.2.a.be.1.3		3
21.17	even	6		5733.2.a.bd.1.3		3
91.25	even	6		8281.2.a.bh.1.3		3
91.38	odd	6		8281.2.a.bk.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.a.h.1.1	✓	3	7.4	even	3
637.2.a.i.1.1	yes	3	7.3	odd	6
637.2.e.k.79.3		6	7.5	odd	6
637.2.e.k.508.3		6	7.6	odd	2
637.2.e.l.79.3		6	7.2	even	3	inner
637.2.e.l.508.3		6	1.1	even	1	trivial
5733.2.a.bd.1.3		3	21.17	even	6
5733.2.a.be.1.3		3	21.11	odd	6
8281.2.a.bh.1.3		3	91.25	even	6
8281.2.a.bk.1.3		3	91.38	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
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

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