LMFDB - Embedded newform 637.2.e.k.508.2

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			508.2
Root			$-0.105378 + 0.182520i$ of defining polynomial
Character	$\chi$	$=$	637.508
Dual form			637.2.e.k.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.605378 + 1.04855i) q^{2} +(0.872413 - 1.51106i) q^{3} +(0.267035 - 0.462518i) q^{4} +(-1.10538 - 1.91457i) q^{5} +2.11256 q^{6} +3.06814 q^{8} +(-0.0222090 - 0.0384672i) q^{9} +O(q^{10})$	\(q+(0.605378 + 1.04855i) q^{2} +(0.872413 - 1.51106i) q^{3} +(0.267035 - 0.462518i) q^{4} +(-1.10538 - 1.91457i) q^{5} +2.11256 q^{6} +3.06814 q^{8} +(-0.0222090 - 0.0384672i) q^{9} +(1.33834 - 2.31808i) q^{10} +(0.394622 - 0.683505i) q^{11} +(-0.465930 - 0.807014i) q^{12} -1.00000 q^{13} -3.85738 q^{15} +(1.32331 + 2.29205i) q^{16} +(0.872413 - 1.51106i) q^{17} +(0.0268897 - 0.0465743i) q^{18} +(-2.16166 - 3.74410i) q^{19} -1.18070 q^{20} +0.955582 q^{22} +(0.556279 + 0.963504i) q^{23} +(2.67669 - 4.63616i) q^{24} +(0.0562792 - 0.0974785i) q^{25} +(-0.605378 - 1.04855i) q^{26} +5.15698 q^{27} -8.48965 q^{29} +(-2.33518 - 4.04464i) q^{30} +(-2.85020 + 4.93670i) q^{31} +(1.46593 - 2.53906i) q^{32} +(-0.688547 - 1.19260i) q^{33} +2.11256 q^{34} -0.0237224 q^{36} +(-1.13945 - 1.97358i) q^{37} +(2.61724 - 4.53319i) q^{38} +(-0.872413 + 1.51106i) q^{39} +(-3.39145 - 5.87417i) q^{40} +12.1363 q^{41} +8.06814 q^{43} +(-0.210756 - 0.365040i) q^{44} +(-0.0490987 + 0.0850415i) q^{45} +(-0.673518 + 1.16657i) q^{46} +(-4.37241 - 7.57324i) q^{47} +4.61791 q^{48} +0.136281 q^{50} +(-1.52221 - 2.63654i) q^{51} +(-0.267035 + 0.462518i) q^{52} +(-3.97779 + 6.88974i) q^{53} +(3.12192 + 5.40732i) q^{54} -1.74483 q^{55} -7.54343 q^{57} +(-5.13945 - 8.90179i) q^{58} +(-5.47779 + 9.48781i) q^{59} +(-1.03006 + 1.78411i) q^{60} +(6.53407 + 11.3173i) q^{61} -6.90180 q^{62} +8.84302 q^{64} +(1.10538 + 1.91457i) q^{65} +(0.833662 - 1.44395i) q^{66} +(-3.27890 + 5.67921i) q^{67} +(-0.465930 - 0.807014i) q^{68} +1.94122 q^{69} +5.85738 q^{71} +(-0.0681404 - 0.118023i) q^{72} +(-4.00468 + 6.93631i) q^{73} +(1.37959 - 2.38953i) q^{74} +(-0.0981974 - 0.170083i) q^{75} -2.30895 q^{76} -2.11256 q^{78} +(3.45558 + 5.98524i) q^{79} +(2.92552 - 5.06716i) q^{80} +(4.56564 - 7.90792i) q^{81} +(7.34704 + 12.7254i) q^{82} +3.14262 q^{83} -3.85738 q^{85} +(4.88427 + 8.45981i) q^{86} +(-7.40648 + 12.8284i) q^{87} +(1.21076 - 2.09709i) q^{88} +(-1.69573 - 2.93709i) q^{89} -0.118893 q^{90} +0.594184 q^{92} +(4.97311 + 8.61368i) q^{93} +(5.29392 - 9.16935i) q^{94} +(-4.77890 + 8.27729i) q^{95} +(-2.55779 - 4.43023i) q^{96} -0.0981974 q^{97} -0.0350567 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 $

$2$	0.605378	+	1.04855i	0.428067	+	0.741434i	0.996701	−	0.0811568i	$-0.0258614\pi$
$2$	0.605378	+	1.04855i	0.428067	+	0.741434i	−0.568635	+	0.822590i	$0.692528\pi$
$3$	0.872413	−	1.51106i	0.503688	−	0.872413i	−0.496303	−	0.868149i	$-0.665309\pi$
$3$	0.872413	−	1.51106i	0.503688	−	0.872413i	0.999991	−	0.00426367i	$-0.00135717\pi$
$4$	0.267035	−	0.462518i	0.133518	−	0.231259i
$5$	−1.10538	−	1.91457i	−0.494340	−	0.856222i	0.505639	−	0.862745i	$-0.331257\pi$
$5$	−1.10538	−	1.91457i	−0.494340	−	0.856222i	−0.999979	+	0.00652327i	$0.997924\pi$
$6$	2.11256			0.862448
$7$		0			0
$7$		0			0
$8$	3.06814			1.08475
$9$	−0.0222090	−	0.0384672i	−0.00740301	−	0.0128224i
$10$	1.33834	−	2.31808i	0.423221	−	0.733041i
$11$	0.394622	−	0.683505i	0.118983	−	0.206085i	−0.800382	−	0.599490i	$-0.795370\pi$
$11$	0.394622	−	0.683505i	0.118983	−	0.206085i	0.919365	+	0.393406i	$0.128703\pi$
$12$	−0.465930	−	0.807014i	−0.134502	−	0.232965i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	−3.85738			−0.995972
$16$	1.32331	+	2.29205i	0.330829	+	0.573012i
$17$	0.872413	−	1.51106i	0.211591	−	0.366487i	−0.740621	−	0.671923i	$-0.765469\pi$
$17$	0.872413	−	1.51106i	0.211591	−	0.366487i	0.952213	+	0.305436i	$0.0988021\pi$
$18$	0.0268897	−	0.0465743i	0.00633796	−	0.0109777i
$19$	−2.16166	−	3.74410i	−0.495918	−	0.858955i	0.504071	−	0.863662i	$-0.331835\pi$
$19$	−2.16166	−	3.74410i	−0.495918	−	0.858955i	−0.999989	+	0.00470690i	$0.998502\pi$
$20$	−1.18070			−0.264012
$21$		0			0
$22$	0.955582			0.203731
$23$	0.556279	+	0.963504i	0.115992	+	0.200904i	0.918176	−	0.396173i	$-0.129662\pi$
$23$	0.556279	+	0.963504i	0.115992	+	0.200904i	−0.802184	+	0.597077i	$0.796329\pi$
$24$	2.67669	−	4.63616i	0.546376	−	0.946351i
$25$	0.0562792	−	0.0974785i	0.0112558	−	0.0194957i
$26$	−0.605378	−	1.04855i	−0.118724	−	0.205637i
$27$	5.15698			0.992461
$28$		0			0
$29$	−8.48965			−1.57649			−0.788244	−	0.615362i	$-0.789010\pi$
$29$	−8.48965			−1.57649			−0.788244	+	0.615362i	$0.789010\pi$
$30$	−2.33518	−	4.04464i	−0.426343	−	0.738447i
$31$	−2.85020	+	4.93670i	−0.511912	+	0.886657i	0.487993	+	0.872848i	$0.337729\pi$
$31$	−2.85020	+	4.93670i	−0.511912	+	0.886657i	−0.999905	+	0.0138096i	$0.995604\pi$
$32$	1.46593	−	2.53906i	0.259142	−	0.448848i
$33$	−0.688547	−	1.19260i	−0.119861	−	0.207605i
$34$	2.11256			0.362301
$35$		0			0
$36$	−0.0237224			−0.00395373
$37$	−1.13945	−	1.97358i	−0.187324	−	0.324455i	0.757033	−	0.653377i	$-0.226648\pi$
$37$	−1.13945	−	1.97358i	−0.187324	−	0.324455i	−0.944357	+	0.328922i	$0.893315\pi$
$38$	2.61724	−	4.53319i	0.424572	−	0.735381i
$39$	−0.872413	+	1.51106i	−0.139698	+	0.241964i
$40$	−3.39145	−	5.87417i	−0.536236	−	0.928788i
$41$	12.1363			1.89537			0.947684	−	0.319209i	$-0.103417\pi$
$41$	12.1363			1.89537			0.947684	+	0.319209i	$0.103417\pi$
$42$		0			0
$43$	8.06814			1.23038			0.615190	−	0.788379i	$-0.289079\pi$
$43$	8.06814			1.23038			0.615190	+	0.788379i	$0.289079\pi$
$44$	−0.210756	−	0.365040i	−0.0317726	−	0.0550318i
$45$	−0.0490987	+	0.0850415i	−0.00731921	+	0.0126772i
$46$	−0.673518	+	1.16657i	−0.0993049	+	0.172001i
$47$	−4.37241	−	7.57324i	−0.637782	−	1.10467i	−0.985918	−	0.167227i	$-0.946519\pi$
$47$	−4.37241	−	7.57324i	−0.637782	−	1.10467i	0.348136	−	0.937444i	$-0.386815\pi$
$48$	4.61791			0.666537
$49$		0			0
$50$	0.136281			0.0192730
$51$	−1.52221	−	2.63654i	−0.213152	−	0.369190i
$52$	−0.267035	+	0.462518i	−0.0370311	+	0.0641398i
$53$	−3.97779	+	6.88974i	−0.546392	+	0.946378i	0.452126	+	0.891954i	$0.350666\pi$
$53$	−3.97779	+	6.88974i	−0.546392	+	0.946378i	−0.998518	+	0.0544241i	$0.982668\pi$
$54$	3.12192	+	5.40732i	0.424839	+	0.735844i
$55$	−1.74483			−0.235272
$56$		0			0
$57$	−7.54343			−0.999152
$58$	−5.13945	−	8.90179i	−0.674843	−	1.16886i
$59$	−5.47779	+	9.48781i	−0.713148	+	1.23521i	0.250522	+	0.968111i	$0.419398\pi$
$59$	−5.47779	+	9.48781i	−0.713148	+	1.23521i	−0.963670	+	0.267097i	$0.913936\pi$
$60$	−1.03006	+	1.78411i	−0.132980	+	0.230328i
$61$	6.53407	+	11.3173i	0.836602	+	1.44904i	0.892719	+	0.450613i	$0.148795\pi$
$61$	6.53407	+	11.3173i	0.836602	+	1.44904i	−0.0561175	+	0.998424i	$0.517872\pi$
$62$	−6.90180			−0.876530
$63$		0			0
$64$	8.84302			1.10538
$65$	1.10538	+	1.91457i	0.137105	+	0.237473i
$66$	0.833662	−	1.44395i	0.102617	−	0.177737i
$67$	−3.27890	+	5.67921i	−0.400581	+	0.693827i	−0.993796	−	0.111217i	$-0.964525\pi$
$67$	−3.27890	+	5.67921i	−0.400581	+	0.693827i	0.593215	+	0.805044i	$0.297858\pi$
$68$	−0.465930	−	0.807014i	−0.0565023	−	0.0978648i
$69$	1.94122			0.233696
$70$		0			0
$71$	5.85738			0.695144			0.347572	−	0.937653i	$-0.387006\pi$
$71$	5.85738			0.695144			0.347572	+	0.937653i	$0.387006\pi$
$72$	−0.0681404	−	0.118023i	−0.00803042	−	0.0139091i
$73$	−4.00468	+	6.93631i	−0.468712	+	0.811834i	−0.999360	−	0.0357585i	$-0.988615\pi$
$73$	−4.00468	+	6.93631i	−0.468712	+	0.811834i	0.530648	+	0.847592i	$0.321949\pi$
$74$	1.37959	−	2.38953i	0.160374	−	0.277777i
$75$	−0.0981974	−	0.170083i	−0.0113389	−	0.0196395i
$76$	−2.30895			−0.264855
$77$		0			0
$78$	−2.11256			−0.239200
$79$	3.45558	+	5.98524i	0.388783	+	0.673393i	0.992286	−	0.123968i	$-0.0395621\pi$
$79$	3.45558	+	5.98524i	0.388783	+	0.673393i	−0.603503	+	0.797361i	$0.706229\pi$
$80$	2.92552	−	5.06716i	0.327084	−	0.566525i
$81$	4.56564	−	7.90792i	0.507293	−	0.878658i
$82$	7.34704	+	12.7254i	0.811344	+	1.40529i
$83$	3.14262			0.344947			0.172473	−	0.985014i	$-0.444824\pi$
$83$	3.14262			0.344947			0.172473	+	0.985014i	$0.444824\pi$
$84$		0			0
$85$	−3.85738			−0.418392
$86$	4.88427	+	8.45981i	0.526685	+	0.912245i
$87$	−7.40648	+	12.8284i	−0.794058	+	1.37535i
$88$	1.21076	−	2.09709i	0.129067	−	0.223551i
$89$	−1.69573	−	2.93709i	−0.179747	−	0.311330i	0.762047	−	0.647522i	$-0.224194\pi$
$89$	−1.69573	−	2.93709i	−0.179747	−	0.311330i	−0.941794	+	0.336191i	$0.890861\pi$
$90$	−0.118893			−0.0125324
$91$		0			0
$92$	0.594184			0.0619480
$93$	4.97311	+	8.61368i	0.515688	+	0.893197i
$94$	5.29392	−	9.16935i	0.546027	−	0.945746i
$95$	−4.77890	+	8.27729i	−0.490304	+	0.849232i
$96$	−2.55779	−	4.43023i	−0.261054	−	0.452158i
$97$	−0.0981974			−0.00997044			−0.00498522	−	0.999988i	$-0.501587\pi$
$97$	−0.0981974			−0.00997044			−0.00498522	+	0.999988i	$0.501587\pi$
$98$		0			0
$99$	−0.0350567			−0.00352333
$100$	−0.0300571	−	0.0520603i	−0.00300571	−	0.00520603i
$101$	−3.45090	+	5.97714i	−0.343378	+	0.594747i	−0.985058	−	0.172225i	$-0.944904\pi$
$101$	−3.45090	+	5.97714i	−0.343378	+	0.594747i	0.641680	+	0.766972i	$0.278238\pi$
$102$	1.84302	−	3.19221i	0.182487	−	0.316076i
$103$	7.91116	+	13.7025i	0.779510	+	1.35015i	0.932224	+	0.361881i	$0.117865\pi$
$103$	7.91116	+	13.7025i	0.779510	+	1.35015i	−0.152714	+	0.988270i	$0.548801\pi$
$104$	−3.06814			−0.300856
$105$		0			0
$106$	−9.63227			−0.935569
$107$	1.01186	+	1.75259i	0.0978203	+	0.169430i	0.910782	−	0.412887i	$-0.135480\pi$
$107$	1.01186	+	1.75259i	0.0978203	+	0.169430i	−0.812962	+	0.582317i	$0.802146\pi$
$108$	1.37709	−	2.38520i	0.132511	−	0.229516i
$109$	8.67352	−	15.0230i	0.830772	−	1.43894i	−0.0666542	−	0.997776i	$-0.521232\pi$
$109$	8.67352	−	15.0230i	0.830772	−	1.43894i	0.897427	−	0.441164i	$-0.145434\pi$
$110$	−1.05628	−	1.82953i	−0.100712	−	0.174439i
$111$	−3.97628			−0.377412
$112$		0			0
$113$	10.1807			0.957720			0.478860	−	0.877891i	$-0.341050\pi$
$113$	10.1807			0.957720			0.478860	+	0.877891i	$0.341050\pi$
$114$	−4.56663	−	7.90963i	−0.427704	−	0.740805i
$115$	1.22980	−	2.13007i	0.114679	−	0.198630i
$116$	−2.26704	+	3.92662i	−0.210489	+	0.364578i
$117$	0.0222090	+	0.0384672i	0.00205322	+	0.00355629i
$118$	−13.2645			−1.22110
$119$		0			0
$120$	−11.8350			−1.08038
$121$	5.18855	+	8.98683i	0.471686	+	0.816984i
$122$	−7.91116	+	13.7025i	−0.716243	+	1.24057i
$123$	10.5878	−	18.3387i	0.954674	−	1.65354i
$124$	1.52221	+	2.63654i	0.136698	+	0.236769i
$125$	−11.3026			−1.01094
$126$		0			0
$127$	16.4452			1.45928			0.729639	−	0.683832i	$-0.239688\pi$
$127$	16.4452			1.45928			0.729639	+	0.683832i	$0.239688\pi$
$128$	2.42151	+	4.19418i	0.214033	+	0.370717i
$129$	7.03875	−	12.1915i	0.619727	−	1.07340i
$130$	−1.33834	+	2.31808i	−0.117380	+	0.203309i
$131$	−6.16634	−	10.6804i	−0.538755	−	0.933152i	−0.998971	−	0.0453448i	$-0.985561\pi$
$131$	−6.16634	−	10.6804i	−0.538755	−	0.933152i	0.460216	−	0.887807i	$-0.347772\pi$
$132$	−0.735465			−0.0640140
$133$		0			0
$134$	−7.93989			−0.685902
$135$	−5.70041	−	9.87340i	−0.490613	−	0.849767i
$136$	2.67669	−	4.63616i	0.229524	−	0.397547i
$137$	1.67352	−	2.89862i	0.142978	−	0.247646i	−0.785639	−	0.618686i	$-0.787665\pi$
$137$	1.67352	−	2.89862i	0.142978	−	0.247646i	0.928617	+	0.371040i	$0.120999\pi$
$138$	1.17517	+	2.03546i	0.100037	+	0.173270i
$139$	−6.16634			−0.523022			−0.261511	−	0.965201i	$-0.584221\pi$
$139$	−6.16634			−0.523022			−0.261511	+	0.965201i	$0.584221\pi$
$140$		0			0
$141$	−15.2582			−1.28497
$142$	3.54593	+	6.14173i	0.297568	+	0.515403i
$143$	−0.394622	+	0.683505i	−0.0330000	+	0.0571576i
$144$	0.0587790	−	0.101808i	0.00489825	−	0.00848402i
$145$	9.38427	+	16.2540i	0.779322	+	1.34982i
$146$	−9.69738			−0.802561
$147$		0			0
$148$	−1.21709			−0.100044
$149$	−9.41834	−	16.3131i	−0.771581	−	1.33642i	−0.936696	−	0.350143i	$-0.886133\pi$
$149$	−9.41834	−	16.3131i	−0.771581	−	1.33642i	0.165115	−	0.986274i	$-0.447200\pi$
$150$	0.118893	−	0.205929i	0.00970758	−	0.0168140i
$151$	−10.0950	+	17.4851i	−0.821522	+	1.42292i	0.0830268	+	0.996547i	$0.473541\pi$
$151$	−10.0950	+	17.4851i	−0.821522	+	1.42292i	−0.904549	+	0.426370i	$0.859792\pi$
$152$	−6.63227	−	11.4874i	−0.537948	−	0.931753i
$153$	−0.0775018			−0.00626565
$154$		0			0
$155$	12.6022			1.01223
$156$	0.465930	+	0.807014i	0.0373042	+	0.0646128i
$157$	−6.94055	+	12.0214i	−0.553916	+	0.959411i	0.444070	+	0.895992i	$0.353534\pi$
$157$	−6.94055	+	12.0214i	−0.553916	+	0.959411i	−0.997987	+	0.0634196i	$0.979799\pi$
$158$	−4.18387	+	7.24667i	−0.332851	+	0.576514i
$159$	6.94055	+	12.0214i	0.550422	+	0.953358i
$160$	−6.48163			−0.512418
$161$		0			0
$162$	11.0558			0.868622
$163$	−5.74483	−	9.95033i	−0.449970	−	0.779370i	0.548414	−	0.836207i	$-0.315232\pi$
$163$	−5.74483	−	9.95033i	−0.449970	−	0.779370i	−0.998383	+	0.0568369i	$0.981898\pi$
$164$	3.24081	−	5.61325i	0.253065	−	0.438321i
$165$	−1.52221	+	2.63654i	−0.118504	+	0.205255i
$166$	1.90247	+	3.29517i	0.147660	+	0.255755i
$167$	−12.9699			−1.00364			−0.501822	−	0.864971i	$-0.667337\pi$
$167$	−12.9699			−1.00364			−0.501822	+	0.864971i	$0.667337\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−2.33518	−	4.04464i	−0.179100	−	0.310210i
$171$	−0.0960166	+	0.166306i	−0.00734257	+	0.0127177i
$172$	2.15448	−	3.73166i	0.164277	−	0.284537i
$173$	−1.24015	−	2.14799i	−0.0942865	−	0.163309i	0.815024	−	0.579427i	$-0.196724\pi$
$173$	−1.24015	−	2.14799i	−0.0942865	−	0.163309i	−0.909311	+	0.416118i	$0.863390\pi$
$174$	−17.9349			−1.35964
$175$		0			0
$176$	2.08884			0.157452
$177$	9.55779	+	16.5546i	0.718408	+	1.24432i
$178$	2.05311	−	3.55609i	0.153887	−	0.266541i
$179$	4.07849	−	7.06415i	0.304841	−	0.527999i	−0.672385	−	0.740201i	$-0.734730\pi$
$179$	4.07849	−	7.06415i	0.304841	−	0.527999i	0.977226	+	0.212202i	$0.0680635\pi$
$180$	0.0262222	+	0.0454181i	0.00195448	+	0.00338527i
$181$	3.60855			0.268221			0.134111	−	0.990966i	$-0.457182\pi$
$181$	3.60855			0.268221			0.134111	+	0.990966i	$0.457182\pi$
$182$		0			0
$183$	22.8016			1.68555
$184$	1.70674	+	2.95617i	0.125823	+	0.217931i
$185$	−2.51904	+	4.36311i	−0.185204	+	0.320782i
$186$	−6.02122	+	10.4291i	−0.441497	+	0.764696i
$187$	−0.688547	−	1.19260i	−0.0503515	−	0.0872114i
$188$	−4.67035			−0.340620
$189$		0			0
$190$	−11.5722			−0.839532
$191$	−0.168838	−	0.292435i	−0.0122167	−	0.0211599i	0.859852	−	0.510543i	$-0.170555\pi$
$191$	−0.168838	−	0.292435i	−0.0122167	−	0.0211599i	−0.872069	+	0.489383i	$0.837222\pi$
$192$	7.71477	−	13.3624i	0.556765	−	0.964346i
$193$	−4.21076	+	7.29324i	−0.303097	+	0.524979i	−0.976836	−	0.213990i	$-0.931354\pi$
$193$	−4.21076	+	7.29324i	−0.303097	+	0.524979i	0.673739	+	0.738969i	$0.264687\pi$
$194$	−0.0594466	−	0.102964i	−0.00426801	−	0.00739242i
$195$	3.85738			0.276233
$196$		0			0
$197$	−8.51035			−0.606337			−0.303169	−	0.952937i	$-0.598045\pi$
$197$	−8.51035			−0.606337			−0.303169	+	0.952937i	$0.598045\pi$
$198$	−0.0212225	−	0.0367585i	−0.00150822	−	0.00261231i
$199$	7.30829	−	12.6583i	0.518071	−	0.897325i	−0.481709	−	0.876331i	$-0.659984\pi$
$199$	7.30829	−	12.6583i	0.518071	−	0.897325i	0.999780	−	0.0209934i	$-0.00668290\pi$
$200$	0.172673	−	0.299078i	0.0122098	−	0.0211480i
$201$	5.72110	+	9.90924i	0.403536	+	0.698944i
$202$	−8.35640			−0.587954
$203$		0			0
$204$	−1.62593			−0.113838
$205$	−13.4152	−	23.2358i	−0.936957	−	1.62286i
$206$	−9.57849	+	16.5904i	−0.667365	+	1.15591i
$207$	0.0247088	−	0.0427970i	0.00171738	−	0.00297459i
$208$	−1.32331	−	2.29205i	−0.0917553	−	0.158925i
$209$	−3.41215			−0.236023
$210$		0			0
$211$	−23.8667			−1.64305			−0.821527	−	0.570169i	$-0.806878\pi$
$211$	−23.8667			−1.64305			−0.821527	+	0.570169i	$0.806878\pi$
$212$	2.12442	+	3.67960i	0.145906	+	0.252716i
$213$	5.11006	−	8.85088i	0.350135	−	0.606452i
$214$	−1.22512	+	2.12196i	−0.0837473	+	0.145055i
$215$	−8.91834	−	15.4470i	−0.608226	−	1.05348i
$216$	15.8223			1.07657
$217$		0			0
$218$	21.0030			1.42250
$219$	6.98747	+	12.1027i	0.472170	+	0.817822i
$220$	−0.465930	+	0.807014i	−0.0314130	+	0.0544089i
$221$	−0.872413	+	1.51106i	−0.0586849	+	0.101645i
$222$	−2.40715	−	4.16931i	−0.161557	−	0.279826i
$223$	1.27890			0.0856412			0.0428206	−	0.999083i	$-0.486366\pi$
$223$	1.27890			0.0856412			0.0428206	+	0.999083i	$0.486366\pi$
$224$		0			0
$225$	−0.00499963			−0.000333308
$226$	6.16317	+	10.6749i	0.409968	+	0.710085i
$227$	−4.78924	+	8.29521i	−0.317873	+	0.550573i	−0.980044	−	0.198780i	$-0.936302\pi$
$227$	−4.78924	+	8.29521i	−0.317873	+	0.550573i	0.662171	+	0.749353i	$0.269635\pi$
$228$	−2.01436	+	3.48898i	−0.133404	+	0.231063i
$229$	6.75669	+	11.7029i	0.446494	+	0.773351i	0.998155	−	0.0607177i	$-0.0193389\pi$
$229$	6.75669	+	11.7029i	0.446494	+	0.773351i	−0.551661	+	0.834069i	$0.686006\pi$
$230$	2.97797			0.196361
$231$		0			0
$232$	−26.0474			−1.71010
$233$	−14.4793	−	25.0789i	−0.948571	−	1.64297i	−0.748439	−	0.663204i	$-0.769196\pi$
$233$	−14.4793	−	25.0789i	−0.948571	−	1.64297i	−0.200132	−	0.979769i	$-0.564137\pi$
$234$	−0.0268897	+	0.0465743i	−0.00175783	+	0.00304466i
$235$	−9.66634	+	16.7426i	−0.630562	+	1.09217i
$236$	2.92552	+	5.06716i	0.190435	+	0.329844i
$237$	12.0588			0.783302
$238$		0			0
$239$	−24.1363			−1.56125			−0.780623	−	0.625002i	$-0.785098\pi$
$239$	−24.1363			−1.56125			−0.780623	+	0.625002i	$0.785098\pi$
$240$	−5.10453	−	8.84131i	−0.329496	−	0.570704i
$241$	4.96276	−	8.59576i	0.319680	−	0.553701i	−0.660742	−	0.750614i	$-0.729758\pi$
$241$	4.96276	−	8.59576i	0.319680	−	0.553701i	0.980421	+	0.196912i	$0.0630914\pi$
$242$	−6.28206	+	10.8809i	−0.403826	+	0.699448i
$243$	−0.230784	−	0.399730i	−0.0148048	−	0.0256427i
$244$	6.97930			0.446804
$245$		0			0
$246$	25.6386			1.63466
$247$	2.16166	+	3.74410i	0.137543	+	0.238231i
$248$	−8.74483	+	15.1465i	−0.555297	+	0.961803i
$249$	2.74166	−	4.74869i	0.173746	−	0.300936i
$250$	−6.84236	−	11.8513i	−0.432749	−	0.749543i
$251$	18.4990			1.16765			0.583824	−	0.811880i	$-0.301556\pi$
$251$	18.4990			1.16765			0.583824	+	0.811880i	$0.301556\pi$
$252$		0			0
$253$	0.878080			0.0552044
$254$	9.95558	+	17.2436i	0.624669	+	1.08196i
$255$	−3.36523	+	5.82875i	−0.210739	+	0.365011i
$256$	5.91116	−	10.2384i	0.369448	−	0.639902i
$257$	−8.33834	−	14.4424i	−0.520132	−	0.900894i	−0.999726	−	0.0234040i	$-0.992550\pi$
$257$	−8.33834	−	14.4424i	−0.520132	−	0.900894i	0.479595	−	0.877490i	$-0.340784\pi$
$258$	17.0444			1.06114
$259$		0			0
$260$	1.18070			0.0732238
$261$	0.188547	+	0.326573i	0.0116708	+	0.0202143i
$262$	7.46593	−	12.9314i	0.461247	−	0.798903i
$263$	6.73448	−	11.6645i	0.415266	−	0.719261i	−0.580191	−	0.814481i	$-0.697022\pi$
$263$	6.73448	−	11.6645i	0.415266	−	0.719261i	0.995456	+	0.0952194i	$0.0303553\pi$
$264$	−2.11256	−	3.65906i	−0.130019	−	0.225199i
$265$	17.5878			1.08041
$266$		0			0
$267$	−5.91750			−0.362145
$268$	1.75116	+	3.03310i	0.106969	+	0.185276i
$269$	15.2789	−	26.4638i	0.931571	−	1.61353i	0.150933	−	0.988544i	$-0.451772\pi$
$269$	15.2789	−	26.4638i	0.931571	−	1.61353i	0.780638	−	0.624984i	$-0.214894\pi$
$270$	6.90180	−	11.9543i	0.420030	−	0.727514i
$271$	−2.11256	−	3.65906i	−0.128329	−	0.222272i	0.794700	−	0.607002i	$-0.207628\pi$
$271$	−2.11256	−	3.65906i	−0.128329	−	0.222272i	−0.923029	+	0.384730i	$0.874295\pi$
$272$	4.61791			0.280002
$273$		0			0
$274$	4.05244			0.244817
$275$	−0.0444180	−	0.0769343i	−0.00267851	−	0.00463931i
$276$	0.518374	−	0.897850i	0.0312025	−	0.0540442i
$277$	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	$0.137940\pi$
$278$	−3.73296	−	6.46568i	−0.223888	−	0.387786i
$279$	0.253201			0.0151587
$280$		0			0
$281$	−6.27890			−0.374568			−0.187284	−	0.982306i	$-0.559968\pi$
$281$	−6.27890			−0.374568			−0.187284	+	0.982306i	$0.559968\pi$
$282$	−9.23698	−	15.9989i	−0.550054	−	0.952722i
$283$	−11.7685	+	20.3837i	−0.699568	+	1.21169i	0.269049	+	0.963127i	$0.413291\pi$
$283$	−11.7685	+	20.3837i	−0.699568	+	1.21169i	−0.968616	+	0.248560i	$0.920043\pi$
$284$	1.56413	−	2.70915i	0.0928139	−	0.160758i
$285$	8.33834	+	14.4424i	0.493921	+	0.855496i
$286$	−0.955582			−0.0565047
$287$		0			0
$288$	−0.130227			−0.00767373
$289$	6.97779	+	12.0859i	0.410458	+	0.710935i
$290$	−11.3621	+	19.6797i	−0.667203	+	1.15563i
$291$	−0.0856687	+	0.148383i	−0.00502199	+	0.00869834i
$292$	2.13878	+	3.70448i	0.125163	+	0.216788i
$293$	21.6166			1.26285			0.631427	−	0.775435i	$-0.282470\pi$
$293$	21.6166			1.26285			0.631427	+	0.775435i	$0.282470\pi$
$294$		0			0
$295$	24.2201			1.41015
$296$	−3.49599	−	6.05523i	−0.203200	−	0.351953i
$297$	2.03506	−	3.52482i	0.118086	−	0.204531i
$298$	11.4033	−	19.7511i	0.660576	−	1.14415i
$299$	−0.556279	−	0.963504i	−0.0321705	−	0.0557209i
$300$	−0.104889			−0.00605575
$301$		0			0
$302$	−24.4452			−1.40667
$303$	6.02122	+	10.4291i	0.345910	+	0.599134i
$304$	5.72110	−	9.90924i	0.328128	−	0.568334i
$305$	14.4452	−	25.0199i	0.827132	−	1.43263i
$306$	−0.0469179	−	0.0812641i	−0.00268212	−	0.00464556i
$307$	−20.3945			−1.16397			−0.581987	−	0.813198i	$-0.697725\pi$
$307$	−20.3945			−1.16397			−0.581987	+	0.813198i	$0.697725\pi$
$308$		0			0
$309$	27.6072			1.57052
$310$	7.62910	+	13.2140i	0.433304	+	0.750504i
$311$	−6.47462	+	11.2144i	−0.367142	+	0.635909i	−0.989117	−	0.147128i	$-0.952997\pi$
$311$	−6.47462	+	11.2144i	−0.367142	+	0.635909i	0.621975	+	0.783037i	$0.286330\pi$
$312$	−2.67669	+	4.63616i	−0.151537	+	0.262471i
$313$	16.6172	+	28.7819i	0.939262	+	1.62685i	0.766852	+	0.641824i	$0.221822\pi$
$313$	16.6172	+	28.7819i	0.939262	+	1.62685i	0.172410	+	0.985025i	$0.444845\pi$
$314$	−16.8066			−0.948453
$315$		0			0
$316$	3.69105			0.207638
$317$	2.43587	+	4.21906i	0.136812	+	0.236966i	0.926288	−	0.376816i	$-0.122981\pi$
$317$	2.43587	+	4.21906i	0.136812	+	0.236966i	−0.789476	+	0.613781i	$0.789648\pi$
$318$	−8.40332	+	14.5550i	−0.471235	+	0.816202i
$319$	−3.35020	+	5.80272i	−0.187575	+	0.324890i
$320$	−9.77488	−	16.9306i	−0.546433	−	0.946449i
$321$	3.53104			0.197084
$322$		0			0
$323$	−7.54343			−0.419728
$324$	−2.43837	−	4.22339i	−0.135465	−	0.234633i
$325$	−0.0562792	+	0.0974785i	−0.00312181	+	0.00540713i
$326$	6.95558	−	12.0474i	0.385234	−	0.667245i
$327$	−15.1338	−	26.2125i	−0.836900	−	1.44955i
$328$	37.2358			2.05600
$329$		0			0
$330$	−3.68605			−0.202910
$331$	−3.43587	−	5.95111i	−0.188853	−	0.327102i	0.756015	−	0.654554i	$-0.227144\pi$
$331$	−3.43587	−	5.95111i	−0.188853	−	0.327102i	−0.944868	+	0.327452i	$0.893810\pi$
$332$	0.839189	−	1.45352i	0.0460565	−	0.0797721i
$333$	−0.0506121	+	0.0876626i	−0.00277352	+	0.00480388i
$334$	−7.85172	−	13.5996i	−0.429627	−	0.744136i
$335$	14.4977			0.792093
$336$		0			0
$337$	11.0712			0.603085			0.301542	−	0.953453i	$-0.402499\pi$
$337$	11.0712			0.603085			0.301542	+	0.953453i	$0.402499\pi$
$338$	0.605378	+	1.04855i	0.0329282	+	0.0570333i
$339$	8.88177	−	15.3837i	0.482392	−	0.835527i
$340$	−1.03006	+	1.78411i	−0.0558627	+	0.0967570i
$341$	2.24951	+	3.89626i	0.121818	+	0.210994i
$342$	−0.232505			−0.0125724
$343$		0			0
$344$	24.7542			1.33466
$345$	−2.14578	−	3.71660i	−0.115525	−	0.200095i
$346$	1.50151	−	2.60070i	0.0807219	−	0.139814i
$347$	−2.81297	+	4.87220i	−0.151008	+	0.261553i	−0.931598	−	0.363490i	$-0.881585\pi$
$347$	−2.81297	+	4.87220i	−0.151008	+	0.261553i	0.780590	+	0.625043i	$0.214919\pi$
$348$	3.95558	+	6.85127i	0.212041	+	0.367267i
$349$	18.4783			0.989122			0.494561	−	0.869143i	$-0.335329\pi$
$349$	18.4783			0.989122			0.494561	+	0.869143i	$0.335329\pi$
$350$		0			0
$351$	−5.15698			−0.275259
$352$	−1.15698	−	2.00394i	−0.0616671	−	0.106810i
$353$	−2.33518	+	4.04464i	−0.124289	+	0.215275i	−0.921455	−	0.388486i	$-0.872998\pi$
$353$	−2.33518	+	4.04464i	−0.124289	+	0.215275i	0.797166	+	0.603760i	$0.206332\pi$
$354$	−11.5722	+	20.0436i	−0.615053	+	1.06530i
$355$	−6.47462	−	11.2144i	−0.343637	−	0.595197i
$356$	−1.81127			−0.0959974
$357$		0			0
$358$	9.87611			0.521968
$359$	5.86055	+	10.1508i	0.309308	+	0.535737i	0.978211	−	0.207612i	$-0.0665692\pi$
$359$	5.86055	+	10.1508i	0.309308	+	0.535737i	−0.668903	+	0.743350i	$0.733236\pi$
$360$	−0.150642	+	0.260919i	−0.00793952	+	0.0137516i
$361$	0.154477	−	0.267561i	0.00813035	−	0.0140822i
$362$	2.18453	+	3.78372i	0.114817	+	0.198868i
$363$	18.1062			0.950330
$364$		0			0
$365$	17.7067			0.926813
$366$	13.8036	+	23.9085i	0.721526	+	1.24972i
$367$	−9.98497	+	17.2945i	−0.521211	+	0.902764i	0.478484	+	0.878096i	$0.341186\pi$
$367$	−9.98497	+	17.2945i	−0.521211	+	0.902764i	−0.999696	+	0.0246684i	$0.992147\pi$
$368$	−1.47226	+	2.55004i	−0.0767471	+	0.132930i
$369$	−0.269535	−	0.466848i	−0.0140314	−	0.0243031i
$370$	−6.09989			−0.317118
$371$		0			0
$372$	5.31198			0.275413
$373$	2.21326	+	3.83347i	0.114598	+	0.198490i	0.917619	−	0.397461i	$-0.130109\pi$
$373$	2.21326	+	3.83347i	0.114598	+	0.198490i	−0.803021	+	0.595951i	$0.796775\pi$
$374$	0.833662	−	1.44395i	0.0431076	−	0.0746646i
$375$	−9.86055	+	17.0790i	−0.509197	+	0.881955i
$376$	−13.4152	−	23.2358i	−0.691835	−	1.19829i
$377$	8.48965			0.437239
$378$		0			0
$379$	−32.5702			−1.67302			−0.836509	−	0.547953i	$-0.815407\pi$
$379$	−32.5702			−1.67302			−0.836509	+	0.547953i	$0.815407\pi$
$380$	2.55227	+	4.42065i	0.130928	+	0.226775i
$381$	14.3470	−	24.8498i	0.735021	−	1.27309i
$382$	0.204421	−	0.354068i	0.0104591	−	0.0181157i
$383$	−7.09820	−	12.2944i	−0.362701	−	0.628216i	0.625703	−	0.780061i	$-0.284812\pi$
$383$	−7.09820	−	12.2944i	−0.362701	−	0.628216i	−0.988404	+	0.151845i	$0.951479\pi$
$384$	8.45023			0.431224
$385$		0			0
$386$	−10.1964			−0.518983
$387$	−0.179185	−	0.310358i	−0.00910851	−	0.0157764i
$388$	−0.0262222	+	0.0454181i	−0.00133123	+	0.00230576i
$389$	−8.65849	+	14.9969i	−0.439003	+	0.760375i	−0.997613	−	0.0690552i	$-0.978002\pi$
$389$	−8.65849	+	14.9969i	−0.439003	+	0.760375i	0.558610	+	0.829430i	$0.311335\pi$
$390$	2.33518	+	4.04464i	0.118246	+	0.204808i
$391$	1.94122			0.0981718
$392$		0			0
$393$	−21.5184			−1.08546
$394$	−5.15198	−	8.92349i	−0.259553	−	0.449559i
$395$	7.63945	−	13.2319i	0.384382	−	0.665770i
$396$	−0.00936136	+	0.0162144i	−0.000470426	+	0.000814802i
$397$	−7.86207	−	13.6175i	−0.394586	−	0.683443i	0.598462	−	0.801151i	$-0.295779\pi$
$397$	−7.86207	−	13.6175i	−0.394586	−	0.683443i	−0.993048	+	0.117708i	$0.962445\pi$
$398$	17.6971			0.887075
$399$		0			0
$400$	0.297900			0.0148950
$401$	−1.78924	−	3.09906i	−0.0893506	−	0.154760i	0.817886	−	0.575380i	$-0.195146\pi$
$401$	−1.78924	−	3.09906i	−0.0893506	−	0.154760i	−0.907237	+	0.420620i	$0.861812\pi$
$402$	−6.92686	+	11.9977i	−0.345480	+	0.598390i
$403$	2.85020	−	4.93670i	0.141979	−	0.245914i
$404$	1.84302	+	3.19221i	0.0916938	+	0.158818i
$405$	−20.1870			−1.00310
$406$		0			0
$407$	−1.79861			−0.0891536
$408$	−4.67035	−	8.08929i	−0.231217	−	0.400479i
$409$	15.6750	−	27.1500i	0.775080	−	1.34248i	−0.159669	−	0.987171i	$-0.551043\pi$
$409$	15.6750	−	27.1500i	0.775080	−	1.34248i	0.934749	−	0.355308i	$-0.115624\pi$
$410$	16.2425	−	28.1328i	0.802160	−	1.38938i
$411$	−2.92000	−	5.05759i	−0.144033	−	0.249472i
$412$	8.45023			0.416313
$413$		0			0
$414$	0.0598327			0.00294062
$415$	−3.47378	−	6.01676i	−0.170521	−	0.295351i
$416$	−1.46593	+	2.53906i	−0.0718731	+	0.124488i
$417$	−5.37959	+	9.31773i	−0.263440	+	0.456291i
$418$	−2.06564	−	3.57779i	−0.101034	−	0.174996i
$419$	−28.7716			−1.40558			−0.702792	−	0.711396i	$-0.748063\pi$
$419$	−28.7716			−1.40558			−0.702792	+	0.711396i	$0.748063\pi$
$420$		0			0
$421$	−0.190060			−0.00926297			−0.00463148	−	0.999989i	$-0.501474\pi$
$421$	−0.190060			−0.00926297			−0.00463148	+	0.999989i	$0.501474\pi$
$422$	−14.4484	−	25.0254i	−0.703337	−	1.21822i
$423$	−0.194214	+	0.336389i	−0.00944301	+	0.0163558i
$424$	−12.2044	+	21.1387i	−0.592699	+	1.02658i
$425$	−0.0981974	−	0.170083i	−0.00476328	−	0.00825024i
$426$	12.3741			0.599526
$427$		0			0
$428$	1.08081			0.0522429
$429$	0.688547	+	1.19260i	0.0332434	+	0.0575792i
$430$	10.7979	−	18.7026i	0.520723	−	0.901918i
$431$	−12.8367	+	22.2338i	−0.618322	+	1.07096i	0.371470	+	0.928445i	$0.378854\pi$
$431$	−12.8367	+	22.2338i	−0.618322	+	1.07096i	−0.989792	+	0.142520i	$0.954480\pi$
$432$	6.82430	+	11.8200i	0.328334	+	0.568692i
$433$	1.82233			0.0875755			0.0437877	−	0.999041i	$-0.486057\pi$
$433$	1.82233			0.0875755			0.0437877	+	0.999041i	$0.486057\pi$
$434$		0			0
$435$	32.7479			1.57014
$436$	−4.63227	−	8.02332i	−0.221845	−	0.384247i
$437$	2.40497	−	4.16553i	0.115045	−	0.199264i
$438$	−8.46012	+	14.6534i	−0.404240	+	0.700165i
$439$	−0.367732	−	0.636931i	−0.0175509	−	0.0303991i	0.857117	−	0.515123i	$-0.172254\pi$
$439$	−0.367732	−	0.636931i	−0.0175509	−	0.0303991i	−0.874667	+	0.484723i	$0.838920\pi$
$440$	−5.35337			−0.255212
$441$		0			0
$442$	−2.11256			−0.100484
$443$	1.85587	+	3.21446i	0.0881751	+	0.152724i	0.906740	−	0.421691i	$-0.138563\pi$
$443$	1.85587	+	3.21446i	0.0881751	+	0.152724i	−0.818565	+	0.574414i	$0.805230\pi$
$444$	−1.06181	+	1.83910i	−0.0503911	+	0.0872799i
$445$	−3.74884	+	6.49318i	−0.177712	+	0.307806i
$446$	0.774216	+	1.34098i	0.0366602	+	0.0634973i
$447$	−32.8667			−1.55454
$448$		0			0
$449$	−5.17570			−0.244256			−0.122128	−	0.992514i	$-0.538972\pi$
$449$	−5.17570			−0.244256			−0.122128	+	0.992514i	$0.538972\pi$
$450$	−0.00302666	−	0.00524233i	−0.000142678	−	0.000247126i
$451$	4.78924	−	8.29521i	0.225517	−	0.390606i
$452$	2.71860	−	4.70876i	0.127872	−	0.221481i
$453$	17.6141	+	30.5085i	0.827581	+	1.43341i
$454$	−11.5972			−0.544284
$455$		0			0
$456$	−23.1443			−1.08383
$457$	17.0650	+	29.5574i	0.798266	+	1.38264i	0.920745	+	0.390166i	$0.127582\pi$
$457$	17.0650	+	29.5574i	0.798266	+	1.38264i	−0.122479	+	0.992471i	$0.539084\pi$
$458$	−8.18070	+	14.1694i	−0.382259	+	0.662092i
$459$	4.49901	−	7.79252i	0.209996	−	0.363724i
$460$	−0.656798	−	1.13761i	−0.0306234	−	0.0530412i
$461$	−11.4008			−0.530989			−0.265494	−	0.964112i	$-0.585535\pi$
$461$	−11.4008			−0.530989			−0.265494	+	0.964112i	$0.585535\pi$
$462$		0			0
$463$	−30.0124			−1.39479			−0.697397	−	0.716685i	$-0.745659\pi$
$463$	−30.0124			−1.39479			−0.697397	+	0.716685i	$0.745659\pi$
$464$	−11.2345	−	19.4587i	−0.521548	−	0.903347i
$465$	10.9943	−	19.0427i	0.509850	−	0.883086i
$466$	17.5309	−	30.3644i	0.812103	−	1.40660i
$467$	−17.0832	−	29.5889i	−0.790515	−	1.36921i	−0.925649	−	0.378384i	$-0.876480\pi$
$467$	−17.0832	−	29.5889i	−0.790515	−	1.36921i	0.135134	−	0.990827i	$-0.456854\pi$
$468$	0.0237224			0.00109657
$469$		0			0
$470$	−23.4072			−1.07969
$471$	12.1101	+	20.9752i	0.558002	+	0.966488i
$472$	−16.8066	+	29.1099i	−0.773588	+	1.33989i
$473$	3.18387	−	5.51462i	0.146394	−	0.253562i
$474$	7.30012	+	12.6442i	0.335306	+	0.580766i
$475$	−0.486625			−0.0223279
$476$		0			0
$477$	0.353371			0.0161798
$478$	−14.6116	−	25.3080i	−0.668318	−	1.15756i
$479$	6.43805	−	11.1510i	0.294162	−	0.509504i	−0.680627	−	0.732630i	$-0.738293\pi$
$479$	6.43805	−	11.1510i	0.294162	−	0.509504i	0.974790	+	0.223126i	$0.0716261\pi$
$480$	−5.65465	+	9.79415i	−0.258099	+	0.447040i
$481$	1.13945	+	1.97358i	0.0519544	+	0.0899876i
$482$	12.0174			0.547377
$483$		0			0
$484$	5.54210			0.251913
$485$	0.108545	+	0.188006i	0.00492879	+	0.00853691i
$486$	0.279423	−	0.483975i	0.0126749	−	0.0219536i
$487$	10.9699	−	19.0005i	0.497096	−	0.860995i	−0.502899	−	0.864345i	$-0.667733\pi$
$487$	10.9699	−	19.0005i	0.497096	−	0.860995i	0.999994	+	0.00335051i	$0.00106650\pi$
$488$	20.0474	+	34.7232i	0.907505	+	1.57185i
$489$	−20.0474			−0.906577
$490$		0			0
$491$	4.11256			0.185597			0.0927986	−	0.995685i	$-0.470419\pi$
$491$	4.11256			0.185597			0.0927986	+	0.995685i	$0.470419\pi$
$492$	−5.65465	−	9.79415i	−0.254932	−	0.441554i
$493$	−7.40648	+	12.8284i	−0.333571	+	0.577762i
$494$	−2.61724	+	4.53319i	−0.117755	+	0.203958i
$495$	0.0387509	+	0.0671185i	0.00174172	+	0.00301675i
$496$	−15.0869			−0.677420
$497$		0			0
$498$	6.63896			0.297499
$499$	−9.51654	−	16.4831i	−0.426019	−	0.737886i	0.570496	−	0.821300i	$-0.306751\pi$
$499$	−9.51654	−	16.4831i	−0.426019	−	0.737886i	−0.996515	+	0.0834139i	$0.973418\pi$
$500$	−3.01820	+	5.22767i	−0.134978	+	0.233788i
$501$	−11.3151	+	19.5984i	−0.505524	+	0.875592i
$502$	11.1989	+	19.3971i	0.499831	+	0.865733i
$503$	−35.8698			−1.59935			−0.799677	−	0.600430i	$-0.794996\pi$
$503$	−35.8698			−1.59935			−0.799677	+	0.600430i	$0.794996\pi$
$504$		0			0
$505$	15.2582			0.678981
$506$	0.531570	+	0.920707i	0.0236312	+	0.0409304i
$507$	0.872413	−	1.51106i	0.0387452	−	0.0671087i
$508$	4.39145	−	7.60622i	0.194839	−	0.337472i
$509$	−8.77323	−	15.1957i	−0.388867	−	0.673537i	0.603431	−	0.797415i	$-0.293800\pi$
$509$	−8.77323	−	15.1957i	−0.388867	−	0.673537i	−0.992297	+	0.123879i	$0.960467\pi$
$510$	−8.14895			−0.360842
$511$		0			0
$512$	24.0000			1.06066
$513$	−11.1476	−	19.3082i	−0.492179	−	0.852479i
$514$	10.0957	−	17.4863i	0.445302	−	0.771286i
$515$	17.4897	−	30.2930i	0.770686	−	1.33487i
$516$	−3.75919	−	6.51110i	−0.165489	−	0.286635i
$517$	−6.90180			−0.303541
$518$		0			0
$519$	−4.32768			−0.189964
$520$	3.39145	+	5.87417i	0.148725	+	0.257599i
$521$	4.42151	−	7.65828i	0.193710	−	0.335515i	−0.752767	−	0.658287i	$-0.771281\pi$
$521$	4.42151	−	7.65828i	0.193710	−	0.335515i	0.946477	+	0.322772i	$0.104615\pi$
$522$	−0.228284	+	0.395400i	−0.00999173	+	0.0173062i
$523$	−10.9556	−	18.9756i	−0.479054	−	0.829746i	0.520657	−	0.853766i	$-0.325687\pi$
$523$	−10.9556	−	18.9756i	−0.479054	−	0.829746i	−0.999711	+	0.0240196i	$0.992354\pi$
$524$	−6.58651			−0.287733
$525$		0			0
$526$	16.3076			0.711046
$527$	4.97311	+	8.61368i	0.216632	+	0.375218i
$528$	1.82233	−	3.15636i	0.0793066	−	0.137363i
$529$	10.8811	−	18.8466i	0.473092	−	0.819419i
$530$	10.6473	+	18.4417i	0.462489	+	0.801054i
$531$	0.486625			0.0211177
$532$		0			0
$533$	−12.1363			−0.525681
$534$	−3.58232	−	6.20477i	−0.155022	−	0.268506i
$535$	2.23698	−	3.87456i	0.0967130	−	0.167512i
$536$	−10.0601	+	17.4246i	−0.434531	+	0.752629i
$537$	−7.11625	−	12.3257i	−0.307089	−	0.531894i
$538$	36.9980			1.59510
$539$		0			0
$540$	−6.08884			−0.262022
$541$	−11.4327	−	19.8020i	−0.491530	−	0.851356i	0.508422	−	0.861108i	$-0.330229\pi$
$541$	−11.4327	−	19.8020i	−0.491530	−	0.851356i	−0.999952	+	0.00975240i	$0.996896\pi$
$542$	2.55779	−	4.43023i	0.109867	−	0.190295i
$543$	3.14814	−	5.45274i	0.135100	−	0.234000i
$544$	−2.55779	−	4.43023i	−0.109664	−	0.189944i
$545$	−38.3501			−1.64274
$546$		0			0
$547$	−35.2676			−1.50793			−0.753966	−	0.656913i	$-0.771862\pi$
$547$	−35.2676			−1.50793			−0.753966	+	0.656913i	$0.771862\pi$
$548$	−0.893776	−	1.54807i	−0.0381802	−	0.0661301i
$549$	0.290231	−	0.502694i	0.0123867	−	0.0214545i
$550$	0.0537794	−	0.0931487i	0.00229316	−	0.00397187i
$551$	18.3517	+	31.7861i	0.781809	+	1.35413i
$552$	5.95594			0.253502
$553$		0			0
$554$	3.63227			0.154320
$555$	4.39529	+	7.61286i	0.186570	+	0.323148i
$556$	−1.64663	+	2.85204i	−0.0698326	+	0.120954i
$557$	−19.9349	+	34.5282i	−0.844668	+	1.46301i	0.0412408	+	0.999149i	$0.486869\pi$
$557$	−19.9349	+	34.5282i	−0.844668	+	1.46301i	−0.885909	+	0.463859i	$0.846464\pi$
$558$	0.153282	+	0.265493i	0.00648896	+	0.0112392i
$559$	−8.06814			−0.341246
$560$		0			0
$561$	−2.40279			−0.101446
$562$	−3.80111	−	6.58371i	−0.160340	−	0.277717i
$563$	−12.7986	+	22.1678i	−0.539397	+	0.934263i	0.459540	+	0.888157i	$0.348014\pi$
$563$	−12.7986	+	22.1678i	−0.539397	+	0.934263i	−0.998937	+	0.0461056i	$0.985319\pi$
$564$	−4.07448	+	7.05720i	−0.171566	+	0.297162i
$565$	−11.2535	−	19.4917i	−0.473439	−	0.820021i
$566$	−28.4977			−1.19785
$567$		0			0
$568$	17.9713			0.754058
$569$	12.5474	+	21.7328i	0.526016	+	0.911087i	0.999541	+	0.0303062i	$0.00964823\pi$
$569$	12.5474	+	21.7328i	0.526016	+	0.911087i	−0.473524	+	0.880781i	$0.657018\pi$
$570$	−10.0957	+	17.4863i	−0.422862	+	0.732419i
$571$	15.6244	−	27.0623i	0.653862	−	1.13252i	−0.328316	−	0.944568i	$-0.606481\pi$
$571$	15.6244	−	27.0623i	0.653862	−	1.13252i	0.982178	−	0.187954i	$-0.0601855\pi$
$572$	0.210756	+	0.365040i	0.00881215	+	0.0152631i
$573$	−0.589185			−0.0246135
$574$		0			0
$575$	0.125228			0.00522236
$576$	−0.196395	−	0.340166i	−0.00818312	−	0.0141736i
$577$	6.43587	−	11.1473i	0.267929	−	0.464066i	−0.700398	−	0.713753i	$-0.746994\pi$
$577$	6.43587	−	11.1473i	0.267929	−	0.464066i	0.968327	+	0.249686i	$0.0803274\pi$
$578$	−8.44840	+	14.6331i	−0.351407	+	0.608655i
$579$	7.34704	+	12.7254i	0.305332	+	0.528851i
$580$	10.0237			0.416212
$581$		0			0
$582$	−0.207448			−0.00859899
$583$	3.13945	+	5.43768i	0.130023	+	0.225206i
$584$	−12.2869	+	21.2816i	−0.508436	+	0.880638i
$585$	0.0490987	−	0.0850415i	0.00202998	−	0.00351603i
$586$	13.0862	+	22.6660i	0.540586	+	0.936322i
$587$	9.96692			0.411379			0.205689	−	0.978617i	$-0.434056\pi$
$587$	9.96692			0.411379			0.205689	+	0.978617i	$0.434056\pi$
$588$		0			0
$589$	24.6447			1.01547
$590$	14.6623	+	25.3959i	0.603638	+	1.04553i
$591$	−7.42454	+	12.8597i	−0.305405	+	0.528976i
$592$	3.01570	−	5.22334i	0.123944	−	0.214678i
$593$	10.2954	+	17.8322i	0.422783	+	0.732282i	0.996211	−	0.0869747i	$-0.0277199\pi$
$593$	10.2954	+	17.8322i	0.422783	+	0.732282i	−0.573428	+	0.819256i	$0.694387\pi$
$594$	4.92791			0.202195
$595$		0			0
$596$	−10.0601			−0.412078
$597$	−12.7517	−	22.0866i	−0.521892	−	0.903943i
$598$	0.673518	−	1.16657i	0.0275422	−	0.0477045i
$599$	6.26855	−	10.8574i	0.256126	−	0.443623i	−0.709075	−	0.705133i	$-0.750887\pi$
$599$	6.26855	−	10.8574i	0.256126	−	0.443623i	0.965201	+	0.261510i	$0.0842205\pi$
$600$	−0.301284	−	0.521838i	−0.0122998	−	0.0213040i
$601$	1.82233			0.0743343			0.0371672	−	0.999309i	$-0.488167\pi$
$601$	1.82233			0.0743343			0.0371672	+	0.999309i	$0.488167\pi$
$602$		0			0
$603$	0.291284			0.0118620
$604$	5.39145	+	9.33827i	0.219375	+	0.379969i
$605$	11.4706	−	19.8677i	0.466347	−	0.807736i
$606$	−7.29023	+	12.6270i	−0.296145	+	0.512939i
$607$	15.4890	+	26.8277i	0.628678	+	1.08890i	0.987817	+	0.155619i	$0.0497372\pi$
$607$	15.4890	+	26.8277i	0.628678	+	1.08890i	−0.359139	+	0.933284i	$0.616929\pi$
$608$	−12.6754			−0.514053
$609$		0			0
$610$	34.9793			1.41627
$611$	4.37241	+	7.57324i	0.176889	+	0.306381i
$612$	−0.0206957	+	0.0358460i	−0.000836574	+	0.00144899i
$613$	−6.22512	+	10.7822i	−0.251430	+	0.435490i	−0.963920	−	0.266193i	$-0.914234\pi$
$613$	−6.22512	+	10.7822i	−0.251430	+	0.435490i	0.712490	+	0.701683i	$0.247568\pi$
$614$	−12.3464	−	21.3845i	−0.498259	−	0.863010i
$615$	−46.8143			−1.88773
$616$		0			0
$617$	31.7809			1.27945			0.639726	−	0.768603i	$-0.279048\pi$
$617$	31.7809			1.27945			0.639726	+	0.768603i	$0.279048\pi$
$618$	16.7128	+	28.9474i	0.672287	+	1.16444i
$619$	2.11256	−	3.65906i	0.0849109	−	0.147070i	−0.820442	−	0.571729i	$-0.806273\pi$
$619$	2.11256	−	3.65906i	0.0849109	−	0.147070i	0.905353	+	0.424659i	$0.139606\pi$
$620$	3.36523	−	5.82875i	0.135151	−	0.234088i
$621$	2.86872	+	4.96877i	0.115118	+	0.199390i
$622$	−15.6784			−0.628646
$623$		0			0
$624$	−4.61791			−0.184864
$625$	12.2123	+	21.1523i	0.488491	+	0.846091i
$626$	−20.1194	+	34.8479i	−0.804134	+	1.39280i
$627$	−2.97680	+	5.15598i	−0.118882	+	0.205910i
$628$	3.70674	+	6.42027i	0.147915	+	0.256197i
$629$	−3.97628			−0.158545
$630$		0			0
$631$	7.31198			0.291085			0.145543	−	0.989352i	$-0.453507\pi$
$631$	7.31198			0.291085			0.145543	+	0.989352i	$0.453507\pi$
$632$	10.6022	+	18.3636i	0.421733	+	0.730463i
$633$	−20.8217	+	36.0642i	−0.827587	+	1.43342i
$634$	−2.94925	+	5.10825i	−0.117130	+	0.202874i
$635$	−18.1782	−	31.4856i	−0.721380	−	1.24947i
$636$	7.41349			0.293964
$637$		0			0
$638$	−8.11256			−0.321179
$639$	−0.130087	−	0.225317i	−0.00514615	−	0.00891340i
$640$	5.35337	−	9.27231i	0.211611	−	0.366520i
$641$	11.5237	−	19.9597i	0.455160	−	0.788360i	−0.543538	−	0.839385i	$-0.682916\pi$
$641$	11.5237	−	19.9597i	0.455160	−	0.788360i	0.998697	+	0.0510251i	$0.0162488\pi$
$642$	2.13762	+	3.70246i	0.0843650	+	0.146124i
$643$	48.9379			1.92992			0.964961	−	0.262392i	$-0.0845113\pi$
$643$	48.9379			1.92992			0.964961	+	0.262392i	$0.0845113\pi$
$644$		0			0
$645$	−31.1219			−1.22542
$646$	−4.56663	−	7.90963i	−0.179672	−	0.311200i
$647$	−16.7154	+	28.9520i	−0.657152	+	1.13822i	0.324198	+	0.945989i	$0.394906\pi$
$647$	−16.7154	+	28.9520i	−0.657152	+	1.13822i	−0.981350	+	0.192231i	$0.938428\pi$
$648$	14.0080	−	24.2626i	0.550287	−	0.953125i
$649$	4.32331	+	7.48820i	0.169705	+	0.293938i
$650$	−0.136281			−0.00534537
$651$		0			0
$652$	−6.13628			−0.240315
$653$	5.23145	+	9.06114i	0.204723	+	0.354590i	0.950044	−	0.312115i	$-0.101037\pi$
$653$	5.23145	+	9.06114i	0.204723	+	0.354590i	−0.745322	+	0.666705i	$0.767704\pi$
$654$	18.3233	−	31.7369i	0.716498	−	1.24101i
$655$	−13.6323	+	23.6118i	−0.532657	+	0.922589i
$656$	16.0601	+	27.8169i	0.627042	+	1.08607i
$657$	0.355760			0.0138795
$658$		0			0
$659$	−8.73849			−0.340403			−0.170202	−	0.985409i	$-0.554442\pi$
$659$	−8.73849			−0.340403			−0.170202	+	0.985409i	$0.554442\pi$
$660$	0.812966	+	1.40810i	0.0316447	+	0.0548102i
$661$	−2.30677	+	3.99545i	−0.0897230	+	0.155405i	−0.907394	−	0.420281i	$-0.861932\pi$
$661$	−2.30677	+	3.99545i	−0.0897230	+	0.155405i	0.817671	+	0.575686i	$0.195265\pi$
$662$	4.16000	−	7.20534i	0.161683	−	0.280043i
$663$	1.52221	+	2.63654i	0.0591177	+	0.102395i
$664$	9.64199			0.374182
$665$		0			0
$666$	−0.122558			−0.00474901
$667$	−4.72262	−	8.17981i	−0.182860	−	0.316724i
$668$	−3.46343	+	5.99884i	−0.134004	+	0.232102i
$669$	1.11573	−	1.93249i	0.0431365	−	0.0747145i
$670$	8.77657	+	15.2015i	0.339069	+	0.587284i
$671$	10.3140			0.398166
$672$		0			0
$673$	9.83802			0.379228			0.189614	−	0.981859i	$-0.439276\pi$
$673$	9.83802			0.379228			0.189614	+	0.981859i	$0.439276\pi$
$674$	6.70224	+	11.6086i	0.258161	+	0.447147i
$675$	0.290231	−	0.502694i	0.0111710	−	0.0193487i
$676$	0.267035	−	0.462518i	0.0102706	−	0.0177892i
$677$	2.34770	+	4.06634i	0.0902296	+	0.156282i	0.907608	−	0.419819i	$-0.137907\pi$
$677$	2.34770	+	4.06634i	0.0902296	+	0.156282i	−0.817378	+	0.576102i	$0.804573\pi$
$678$	21.5073			0.825984
$679$		0			0
$680$	−11.8350			−0.453851
$681$	8.35640	+	14.4737i	0.320218	+	0.554634i
$682$	−2.72360	+	4.71742i	−0.104292	+	0.180639i
$683$	−5.51035	+	9.54420i	−0.210848	+	0.365199i	−0.951980	−	0.306160i	$-0.900956\pi$
$683$	−5.51035	+	9.54420i	−0.210848	+	0.365199i	0.741132	+	0.671359i	$0.234289\pi$
$684$	0.0512796	+	0.0888189i	0.00196072	+	0.00339607i
$685$	−7.39948			−0.282720
$686$		0			0
$687$	23.5785			0.899575
$688$	10.6767	+	18.4926i	0.407045	+	0.705022i
$689$	3.97779	−	6.88974i	0.151542	−	0.262478i
$690$	2.59802	−	4.49990i	0.0989049	−	0.171308i
$691$	−19.3818	−	33.5702i	−0.737317	−	1.27707i	−0.953699	−	0.300762i	$-0.902759\pi$
$691$	−19.3818	−	33.5702i	−0.737317	−	1.27707i	0.216382	−	0.976309i	$-0.430574\pi$
$692$	−1.32465			−0.0503556
$693$		0			0
$694$	−6.81163			−0.258566
$695$	6.81613	+	11.8059i	0.258551	+	0.447823i
$696$	−22.7241	+	39.3593i	−0.861356	+	1.49191i
$697$	10.5878	−	18.3387i	0.401043	−	0.694628i
$698$	11.1864	+	19.3754i	0.423410	+	0.733368i
$699$	−50.5277			−1.91113
$700$		0			0
$701$	−32.0681			−1.21120			−0.605598	−	0.795770i	$-0.707066\pi$
$701$	−32.0681			−1.21120			−0.605598	+	0.795770i	$0.707066\pi$
$702$	−3.12192	−	5.40732i	−0.117829	−	0.204086i
$703$	−4.92619	+	8.53242i	−0.185795	+	0.321806i
$704$	3.48965	−	6.04425i	0.131521	−	0.227801i
$705$	16.8661	+	29.2129i	0.635213	+	1.10022i
$706$	−5.65465			−0.212816
$707$		0			0
$708$	10.2091			0.383680
$709$	−19.1725	−	33.2078i	−0.720040	−	1.24715i	−0.960983	−	0.276606i	$-0.910790\pi$
$709$	−19.1725	−	33.2078i	−0.720040	−	1.24715i	0.240944	−	0.970539i	$-0.422543\pi$
$710$	7.83919	−	13.5779i	0.294200	−	0.509568i
$711$	0.153490	−	0.265853i	0.00575633	−	0.00997026i
$712$	−5.20273	−	9.01139i	−0.194981	−	0.337716i
$713$	−6.34204			−0.237511
$714$		0			0
$715$	1.74483			0.0652528
$716$	−2.17820	−	3.77275i	−0.0814031	−	0.140994i
$717$	−21.0568	+	36.4715i	−0.786381	+	1.36205i
$718$	−7.09570	+	12.2901i	−0.264809	+	0.458663i
$719$	−4.36207	−	7.55532i	−0.162678	−	0.281766i	0.773151	−	0.634223i	$-0.218680\pi$
$719$	−4.36207	−	7.55532i	−0.162678	−	0.281766i	−0.935828	+	0.352457i	$0.885346\pi$
$720$	−0.259892			−0.00968561
$721$		0			0
$722$	0.374067			0.0139213
$723$	−8.65916	−	14.9981i	−0.322038	−	0.557785i
$724$	0.963608	−	1.66902i	0.0358122	−	0.0620286i
$725$	−0.477791	+	0.827558i	−0.0177447	+	0.0307347i
$726$	10.9611	+	18.9852i	0.406805	+	0.704607i
$727$	−26.6754			−0.989334			−0.494667	−	0.869083i	$-0.664710\pi$
$727$	−26.6754			−0.989334			−0.494667	+	0.869083i	$0.664710\pi$
$728$		0			0
$729$	26.5885			0.984759
$730$	10.7193	+	18.5663i	0.396738	+	0.687170i
$731$	7.03875	−	12.1915i	0.260338	−	0.450918i
$732$	6.08884	−	10.5462i	0.225050	−	0.389798i
$733$	13.3606	+	23.1412i	0.493483	+	0.854738i	0.999972	−	0.00750863i	$-0.00239009\pi$
$733$	13.3606	+	23.1412i	0.493483	+	0.854738i	−0.506489	+	0.862247i	$0.669057\pi$
$734$	−24.1787			−0.892453
$735$		0			0
$736$	3.26187			0.120234
$737$	2.58785	+	4.48229i	0.0953247	+	0.165107i
$738$	0.326341	−	0.565239i	0.0120128	−	0.0208067i
$739$	−18.0269	+	31.2235i	−0.663130	+	1.14857i	0.316659	+	0.948539i	$0.397439\pi$
$739$	−18.0269	+	31.2235i	−0.663130	+	1.14857i	−0.979789	+	0.200035i	$0.935894\pi$
$740$	1.34535	+	2.33021i	0.0494559	+	0.0856601i
$741$	7.54343			0.277115
$742$		0			0
$743$	−2.96058			−0.108613			−0.0543066	−	0.998524i	$-0.517295\pi$
$743$	−2.96058			−0.108613			−0.0543066	+	0.998524i	$0.517295\pi$
$744$	15.2582	+	26.4280i	0.559393	+	0.968897i
$745$	−20.8217	+	36.0642i	−0.762847	+	1.32129i
$746$	−2.67971	+	4.64140i	−0.0981112	+	0.169934i
$747$	−0.0697944	−	0.120887i	−0.00255364	−	0.00442304i
$748$	−0.735465			−0.0268913
$749$		0			0
$750$	−23.8774			−0.871881
$751$	−21.5775	−	37.3733i	−0.787374	−	1.36377i	−0.927570	−	0.373648i	$-0.878107\pi$
$751$	−21.5775	−	37.3733i	−0.787374	−	1.36377i	0.140196	−	0.990124i	$-0.455227\pi$
$752$	11.5722	−	20.0436i	0.421993	−	0.730913i
$753$	16.1388	−	27.9532i	0.588130	−	1.01867i
$754$	5.13945	+	8.90179i	0.187168	+	0.324184i
$755$	44.6353			1.62444
$756$		0			0
$757$	18.7335			0.680880			0.340440	−	0.940266i	$-0.389424\pi$
$757$	18.7335			0.680880			0.340440	+	0.940266i	$0.389424\pi$
$758$	−19.7173	−	34.1513i	−0.716163	−	1.24043i
$759$	0.766049	−	1.32684i	0.0278058	−	0.0481611i
$760$	−14.6623	+	25.3959i	−0.531858	+	0.921206i
$761$	−2.11474	−	3.66284i	−0.0766592	−	0.132778i	0.825147	−	0.564918i	$-0.191092\pi$
$761$	−2.11474	−	3.66284i	−0.0766592	−	0.132778i	−0.901807	+	0.432140i	$0.857759\pi$
$762$	34.7415			1.25855
$763$		0			0
$764$	−0.180342			−0.00652456
$765$	0.0856687	+	0.148383i	0.00309736	+	0.00536478i
$766$	8.59418	−	14.8856i	0.310521	−	0.537837i
$767$	5.47779	−	9.48781i	0.197792	−	0.342585i
$768$	−10.3140	−	17.8643i	−0.372173	−	0.644622i
$769$	21.1299			0.761965			0.380983	−	0.924582i	$-0.375586\pi$
$769$	21.1299			0.761965			0.380983	+	0.924582i	$0.375586\pi$
$770$		0			0
$771$	−29.0979			−1.04794
$772$	2.24884	+	3.89510i	0.0809375	+	0.140188i
$773$	16.5371	−	28.6431i	0.594798	−	1.03022i	−0.398777	−	0.917048i	$-0.630565\pi$
$773$	16.5371	−	28.6431i	0.594798	−	1.03022i	0.993575	−	0.113173i	$-0.0361013\pi$
$774$	0.216950	−	0.375768i	0.00779810	−	0.0135067i

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)

\(f(q)\)	\(=\)	\(q+(0.605378 + 1.04855i) q^{2} +(0.872413 - 1.51106i) q^{3} +(0.267035 - 0.462518i) q^{4} +(-1.10538 - 1.91457i) q^{5} +2.11256 q^{6} +3.06814 q^{8} +(-0.0222090 - 0.0384672i) q^{9} +O(q^{10})\)	\(q+(0.605378 + 1.04855i) q^{2} +(0.872413 - 1.51106i) q^{3} +(0.267035 - 0.462518i) q^{4} +(-1.10538 - 1.91457i) q^{5} +2.11256 q^{6} +3.06814 q^{8} +(-0.0222090 - 0.0384672i) q^{9} +(1.33834 - 2.31808i) q^{10} +(0.394622 - 0.683505i) q^{11} +(-0.465930 - 0.807014i) q^{12} -1.00000 q^{13} -3.85738 q^{15} +(1.32331 + 2.29205i) q^{16} +(0.872413 - 1.51106i) q^{17} +(0.0268897 - 0.0465743i) q^{18} +(-2.16166 - 3.74410i) q^{19} -1.18070 q^{20} +0.955582 q^{22} +(0.556279 + 0.963504i) q^{23} +(2.67669 - 4.63616i) q^{24} +(0.0562792 - 0.0974785i) q^{25} +(-0.605378 - 1.04855i) q^{26} +5.15698 q^{27} -8.48965 q^{29} +(-2.33518 - 4.04464i) q^{30} +(-2.85020 + 4.93670i) q^{31} +(1.46593 - 2.53906i) q^{32} +(-0.688547 - 1.19260i) q^{33} +2.11256 q^{34} -0.0237224 q^{36} +(-1.13945 - 1.97358i) q^{37} +(2.61724 - 4.53319i) q^{38} +(-0.872413 + 1.51106i) q^{39} +(-3.39145 - 5.87417i) q^{40} +12.1363 q^{41} +8.06814 q^{43} +(-0.210756 - 0.365040i) q^{44} +(-0.0490987 + 0.0850415i) q^{45} +(-0.673518 + 1.16657i) q^{46} +(-4.37241 - 7.57324i) q^{47} +4.61791 q^{48} +0.136281 q^{50} +(-1.52221 - 2.63654i) q^{51} +(-0.267035 + 0.462518i) q^{52} +(-3.97779 + 6.88974i) q^{53} +(3.12192 + 5.40732i) q^{54} -1.74483 q^{55} -7.54343 q^{57} +(-5.13945 - 8.90179i) q^{58} +(-5.47779 + 9.48781i) q^{59} +(-1.03006 + 1.78411i) q^{60} +(6.53407 + 11.3173i) q^{61} -6.90180 q^{62} +8.84302 q^{64} +(1.10538 + 1.91457i) q^{65} +(0.833662 - 1.44395i) q^{66} +(-3.27890 + 5.67921i) q^{67} +(-0.465930 - 0.807014i) q^{68} +1.94122 q^{69} +5.85738 q^{71} +(-0.0681404 - 0.118023i) q^{72} +(-4.00468 + 6.93631i) q^{73} +(1.37959 - 2.38953i) q^{74} +(-0.0981974 - 0.170083i) q^{75} -2.30895 q^{76} -2.11256 q^{78} +(3.45558 + 5.98524i) q^{79} +(2.92552 - 5.06716i) q^{80} +(4.56564 - 7.90792i) q^{81} +(7.34704 + 12.7254i) q^{82} +3.14262 q^{83} -3.85738 q^{85} +(4.88427 + 8.45981i) q^{86} +(-7.40648 + 12.8284i) q^{87} +(1.21076 - 2.09709i) q^{88} +(-1.69573 - 2.93709i) q^{89} -0.118893 q^{90} +0.594184 q^{92} +(4.97311 + 8.61368i) q^{93} +(5.29392 - 9.16935i) q^{94} +(-4.77890 + 8.27729i) q^{95} +(-2.55779 - 4.43023i) q^{96} -0.0981974 q^{97} -0.0350567 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more