LMFDB - Embedded newform 325.2.n.e.251.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(101,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("325.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.n (of order $6$, degree $2$, 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:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 16x^{8} + 84x^{6} + 163x^{4} + 118x^{2} + 27 $ x^10 + 16x^8 + 84x^6 + 163x^4 + 118x^2 + 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.5
Root			$2.44399i$ of defining polynomial
Character	$\chi$	$=$	325.251
Dual form			325.2.n.e.101.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.11655 + 1.22199i) q^{2} +(-0.0609297 + 0.105533i) q^{3} +(1.98653 + 3.44078i) q^{4} +(-0.257922 + 0.148911i) q^{6} +(0.358632 - 0.207056i) q^{7} +4.82215i q^{8} +(1.49258 + 2.58522i) q^{9} +O(q^{10})$	\(q+(2.11655 + 1.22199i) q^{2} +(-0.0609297 + 0.105533i) q^{3} +(1.98653 + 3.44078i) q^{4} +(-0.257922 + 0.148911i) q^{6} +(0.358632 - 0.207056i) q^{7} +4.82215i q^{8} +(1.49258 + 2.58522i) q^{9} +(-3.97519 - 2.29507i) q^{11} -0.484156 q^{12} +(2.36255 - 2.72366i) q^{13} +1.01208 q^{14} +(-1.91956 + 3.32478i) q^{16} +(0.372098 + 0.644494i) q^{17} +7.29566i q^{18} +(-6.47544 + 3.73860i) q^{19} +0.0504635i q^{21} +(-5.60913 - 9.71530i) q^{22} +(3.17748 - 5.50356i) q^{23} +(-0.508897 - 0.293812i) q^{24} +(8.32877 - 2.87775i) q^{26} -0.729347 q^{27} +(1.42487 + 0.822647i) q^{28} +(2.80374 - 4.85623i) q^{29} +3.60934i q^{31} +(0.226492 - 0.130765i) q^{32} +(0.484414 - 0.279677i) q^{33} +1.81881i q^{34} +(-5.93010 + 10.2712i) q^{36} +(-5.57387 - 3.21808i) q^{37} -18.2742 q^{38} +(0.143488 + 0.415280i) q^{39} +(4.51661 + 2.60766i) q^{41} +(-0.0616660 + 0.106809i) q^{42} +(-4.96776 - 8.60441i) q^{43} -18.2370i q^{44} +(13.4506 - 7.76572i) q^{46} +1.52901i q^{47} +(-0.233917 - 0.405156i) q^{48} +(-3.41426 + 5.91366i) q^{49} -0.0906875 q^{51} +(14.0648 + 2.71838i) q^{52} +7.56847 q^{53} +(-1.54370 - 0.891257i) q^{54} +(0.998454 + 1.72937i) q^{56} -0.911167i q^{57} +(11.8685 - 6.85231i) q^{58} +(-3.15924 + 1.82399i) q^{59} +(-5.95805 - 10.3197i) q^{61} +(-4.41059 + 7.63937i) q^{62} +(1.07057 + 0.618093i) q^{63} +8.31742 q^{64} +1.36705 q^{66} +(5.67610 + 3.27710i) q^{67} +(-1.47837 + 2.56062i) q^{68} +(0.387206 + 0.670661i) q^{69} +(-5.89082 + 3.40107i) q^{71} +(-12.4663 + 7.19741i) q^{72} +3.08686i q^{73} +(-7.86493 - 13.6225i) q^{74} +(-25.7274 - 14.8537i) q^{76} -1.90084 q^{77} +(-0.203771 + 1.05430i) q^{78} +1.13034 q^{79} +(-4.43329 + 7.67868i) q^{81} +(6.37309 + 11.0385i) q^{82} +12.1541i q^{83} +(-0.173634 + 0.100247i) q^{84} -24.2823i q^{86} +(0.341663 + 0.591777i) q^{87} +(11.0672 - 19.1689i) q^{88} +(6.04168 + 3.48817i) q^{89} +(0.283336 - 1.46597i) q^{91} +25.2487 q^{92} +(-0.380906 - 0.219916i) q^{93} +(-1.86843 + 3.23622i) q^{94} +0.0318699i q^{96} +(-11.0122 + 6.35790i) q^{97} +(-14.4529 + 8.34439i) q^{98} -13.7023i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{3} + 6 q^{4} + 9 q^{6} - 6 q^{7} - 8 q^{9}+O(q^{10}) $ 10 * q - 3 * q^3 + 6 * q^4 + 9 * q^6 - 6 * q^7 - 8 * q^9	$ 10 q - 3 q^{3} + 6 q^{4} + 9 q^{6} - 6 q^{7} - 8 q^{9} - 9 q^{11} - 28 q^{12} + 8 q^{13} - 8 q^{14} - 12 q^{16} + 8 q^{17} - 12 q^{22} + 13 q^{23} + 42 q^{24} - 17 q^{26} + 30 q^{27} + 33 q^{28} + 7 q^{29} + 3 q^{32} - 6 q^{33} - 3 q^{36} + 3 q^{37} - 62 q^{38} + 8 q^{39} + 12 q^{41} + 32 q^{42} + 4 q^{43} + 39 q^{46} - 26 q^{48} - q^{49} + 16 q^{51} + 61 q^{52} + 24 q^{53} - 9 q^{54} - 21 q^{56} + 18 q^{58} - 48 q^{59} + 13 q^{61} + 17 q^{62} - 34 q^{64} - 42 q^{66} + 6 q^{67} - 13 q^{68} + 20 q^{69} - 27 q^{71} - 141 q^{72} - 26 q^{74} - 12 q^{76} - 48 q^{77} + 56 q^{78} + 4 q^{79} - 17 q^{81} - q^{82} - 90 q^{84} - 49 q^{87} - 6 q^{88} + 24 q^{89} + 13 q^{91} + 34 q^{92} - 63 q^{93} + 5 q^{94} - 15 q^{97} - 45 q^{98}+O(q^{100}) $ 10 * q - 3 * q^3 + 6 * q^4 + 9 * q^6 - 6 * q^7 - 8 * q^9 - 9 * q^11 - 28 * q^12 + 8 * q^13 - 8 * q^14 - 12 * q^16 + 8 * q^17 - 12 * q^22 + 13 * q^23 + 42 * q^24 - 17 * q^26 + 30 * q^27 + 33 * q^28 + 7 * q^29 + 3 * q^32 - 6 * q^33 - 3 * q^36 + 3 * q^37 - 62 * q^38 + 8 * q^39 + 12 * q^41 + 32 * q^42 + 4 * q^43 + 39 * q^46 - 26 * q^48 - q^49 + 16 * q^51 + 61 * q^52 + 24 * q^53 - 9 * q^54 - 21 * q^56 + 18 * q^58 - 48 * q^59 + 13 * q^61 + 17 * q^62 - 34 * q^64 - 42 * q^66 + 6 * q^67 - 13 * q^68 + 20 * q^69 - 27 * q^71 - 141 * q^72 - 26 * q^74 - 12 * q^76 - 48 * q^77 + 56 * q^78 + 4 * q^79 - 17 * q^81 - q^82 - 90 * q^84 - 49 * q^87 - 6 * q^88 + 24 * q^89 + 13 * q^91 + 34 * q^92 - 63 * q^93 + 5 * q^94 - 15 * q^97 - 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.11655	+	1.22199i	1.49663	+	0.864079i	0.999992	−	0.00387890i	$-0.00123470\pi$
$2$	2.11655	+	1.22199i	1.49663	+	0.864079i	0.496637	+	0.867958i	$0.334568\pi$
$3$	−0.0609297	+	0.105533i	−0.0351778	+	0.0609297i	−0.883078	−	0.469226i	$-0.844533\pi$
$3$	−0.0609297	+	0.105533i	−0.0351778	+	0.0609297i	0.847900	+	0.530155i	$0.177866\pi$
$4$	1.98653	+	3.44078i	0.993267	+	1.72039i
$5$		0			0
$5$		0			0
$6$	−0.257922	+	0.148911i	−0.105296	+	0.0607928i
$7$	0.358632	−	0.207056i	0.135550	−	0.0782598i	−0.430691	−	0.902499i	$-0.641730\pi$
$7$	0.358632	−	0.207056i	0.135550	−	0.0782598i	0.566241	+	0.824239i	$0.308397\pi$
$8$			4.82215i			1.70489i
$9$	1.49258	+	2.58522i	0.497525	+	0.861739i
$10$		0			0
$11$	−3.97519	−	2.29507i	−1.19856	−	0.691991i	−0.238329	−	0.971185i	$-0.576600\pi$
$11$	−3.97519	−	2.29507i	−1.19856	−	0.691991i	−0.960235	+	0.279194i	$0.909933\pi$
$12$	−0.484156			−0.139764
$13$	2.36255	−	2.72366i	0.655255	−	0.755408i
$13$	2.36255	−	2.72366i	0.655255	−	0.755408i
$14$	1.01208			0.270491
$15$		0			0
$16$	−1.91956	+	3.32478i	−0.479890	+	0.831194i
$17$	0.372098	+	0.644494i	0.0902471	+	0.156313i	0.907615	−	0.419803i	$-0.137901\pi$
$17$	0.372098	+	0.644494i	0.0902471	+	0.156313i	−0.817368	+	0.576116i	$0.804568\pi$
$18$			7.29566i			1.71960i
$19$	−6.47544	+	3.73860i	−1.48557	+	0.857693i	−0.999865	−	0.0164301i	$-0.994770\pi$
$19$	−6.47544	+	3.73860i	−1.48557	+	0.857693i	−0.485704	+	0.874124i	$0.661437\pi$
$20$		0			0
$21$			0.0504635i			0.0110120i
$22$	−5.60913	−	9.71530i	−1.19587	−	2.07131i
$23$	3.17748	−	5.50356i	0.662551	−	1.14757i	−0.317392	−	0.948294i	$-0.602807\pi$
$23$	3.17748	−	5.50356i	0.662551	−	1.14757i	0.979943	−	0.199278i	$-0.0638596\pi$
$24$	−0.508897	−	0.293812i	−0.103878	−	0.0599741i
$25$		0			0
$26$	8.32877	−	2.87775i	1.63341	−	0.564374i
$27$	−0.729347			−0.140363
$28$	1.42487	+	0.822647i	0.269275	+	0.155466i
$29$	2.80374	−	4.85623i	0.520642	−	0.901779i	−0.479070	−	0.877777i	$-0.659026\pi$
$29$	2.80374	−	4.85623i	0.520642	−	0.901779i	0.999712	−	0.0240019i	$-0.00764076\pi$
$30$		0			0
$31$			3.60934i			0.648257i	0.946013	+	0.324129i	$0.105071\pi$
$31$			3.60934i			0.648257i	−0.946013	+	0.324129i	$0.894929\pi$
$32$	0.226492	−	0.130765i	0.0400385	−	0.0231162i
$33$	0.484414	−	0.279677i	0.0843257	−	0.0486854i
$34$			1.81881i			0.311923i
$35$		0			0
$36$	−5.93010	+	10.2712i	−0.988350	+	1.71187i
$37$	−5.57387	−	3.21808i	−0.916339	−	0.529048i	−0.0338736	−	0.999426i	$-0.510784\pi$
$37$	−5.57387	−	3.21808i	−0.916339	−	0.529048i	−0.882465	+	0.470378i	$0.844118\pi$
$38$	−18.2742			−2.96446
$39$	0.143488	+	0.415280i	0.0229764	+	0.0664981i
$40$		0			0
$41$	4.51661	+	2.60766i	0.705375	+	0.407249i	0.809346	−	0.587332i	$-0.199822\pi$
$41$	4.51661	+	2.60766i	0.705375	+	0.407249i	−0.103971	+	0.994580i	$0.533155\pi$
$42$	−0.0616660	+	0.106809i	−0.00951527	+	0.0164809i
$43$	−4.96776	−	8.60441i	−0.757576	−	1.31216i	−0.944083	−	0.329707i	$-0.893050\pi$
$43$	−4.96776	−	8.60441i	−0.757576	−	1.31216i	0.186507	−	0.982454i	$-0.440283\pi$
$44$		−	18.2370i		−	2.74933i
$45$		0			0
$46$	13.4506	−	7.76572i	1.98319	−	1.14499i
$47$			1.52901i			0.223028i	0.993763	+	0.111514i	$0.0355701\pi$
$47$			1.52901i			0.223028i	−0.993763	+	0.111514i	$0.964430\pi$
$48$	−0.233917	−	0.405156i	−0.0337630	−	0.0584792i
$49$	−3.41426	+	5.91366i	−0.487751	+	0.844809i
$50$		0			0
$51$	−0.0906875			−0.0126988
$52$	14.0648	+	2.71838i	1.95044	+	0.376971i
$53$	7.56847			1.03961			0.519805	−	0.854285i	$-0.326005\pi$
$53$	7.56847			1.03961			0.519805	+	0.854285i	$0.326005\pi$
$54$	−1.54370	−	0.891257i	−0.210071	−	0.121285i
$55$		0			0
$56$	0.998454	+	1.72937i	0.133424	+	0.231097i
$57$		−	0.911167i		−	0.120687i
$58$	11.8685	−	6.85231i	1.55842	−	0.899752i
$59$	−3.15924	+	1.82399i	−0.411298	+	0.237463i	−0.691347	−	0.722523i	$-0.742982\pi$
$59$	−3.15924	+	1.82399i	−0.411298	+	0.237463i	0.280050	+	0.959986i	$0.409649\pi$
$60$		0			0
$61$	−5.95805	−	10.3197i	−0.762851	−	1.32130i	−0.941375	−	0.337361i	$-0.890466\pi$
$61$	−5.95805	−	10.3197i	−0.762851	−	1.32130i	0.178525	−	0.983935i	$-0.442868\pi$
$62$	−4.41059	+	7.63937i	−0.560146	+	0.970201i
$63$	1.07057	+	0.618093i	0.134879	+	0.0778725i
$64$	8.31742			1.03968
$65$		0			0
$66$	1.36705			0.168272
$67$	5.67610	+	3.27710i	0.693446	+	0.400361i	0.804902	−	0.593408i	$-0.202218\pi$
$67$	5.67610	+	3.27710i	0.693446	+	0.400361i	−0.111456	+	0.993769i	$0.535551\pi$
$68$	−1.47837	+	2.56062i	−0.179279	+	0.310520i
$69$	0.387206	+	0.670661i	0.0466142	+	0.0807381i
$70$		0			0
$71$	−5.89082	+	3.40107i	−0.699112	+	0.403633i	−0.807017	−	0.590529i	$-0.798919\pi$
$71$	−5.89082	+	3.40107i	−0.699112	+	0.403633i	0.107905	+	0.994161i	$0.465586\pi$
$72$	−12.4663	+	7.19741i	−1.46917	+	0.848223i
$73$			3.08686i			0.361290i	0.983548	+	0.180645i	$0.0578185\pi$
$73$			3.08686i			0.361290i	−0.983548	+	0.180645i	$0.942181\pi$
$74$	−7.86493	−	13.6225i	−0.914280	−	1.58358i
$75$		0			0
$76$	−25.7274	−	14.8537i	−2.95113	−	1.70384i
$77$	−1.90084			−0.216620
$78$	−0.203771	+	1.05430i	−0.0230725	+	0.119376i
$79$	1.13034			0.127173			0.0635864	−	0.997976i	$-0.479746\pi$
$79$	1.13034			0.127173			0.0635864	+	0.997976i	$0.479746\pi$
$80$		0			0
$81$	−4.43329	+	7.67868i	−0.492587	+	0.853186i
$82$	6.37309	+	11.0385i	0.703790	+	1.21900i
$83$			12.1541i			1.33409i	0.745019	+	0.667043i	$0.232440\pi$
$83$			12.1541i			1.33409i	−0.745019	+	0.667043i	$0.767560\pi$
$84$	−0.173634	+	0.100247i	−0.0189450	+	0.0109379i
$85$		0			0
$86$		−	24.2823i		−	2.61842i
$87$	0.341663	+	0.591777i	0.0366301	+	0.0634452i
$88$	11.0672	−	19.1689i	1.17977	−	2.04341i
$89$	6.04168	+	3.48817i	0.640417	+	0.369745i	0.784775	−	0.619781i	$-0.212778\pi$
$89$	6.04168	+	3.48817i	0.640417	+	0.369745i	−0.144358	+	0.989525i	$0.546112\pi$
$90$		0			0
$91$	0.283336	−	1.46597i	0.0297017	−	0.153676i
$92$	25.2487			2.63236
$93$	−0.380906	−	0.219916i	−0.0394981	−	0.0228043i
$94$	−1.86843	+	3.23622i	−0.192714	+	0.333791i
$95$		0			0
$96$			0.0318699i			0.00325271i
$97$	−11.0122	+	6.35790i	−1.11812	+	0.645547i	−0.940920	−	0.338628i	$-0.890037\pi$
$97$	−11.0122	+	6.35790i	−1.11812	+	0.645547i	−0.177199	+	0.984175i	$0.556704\pi$
$98$	−14.4529	+	8.34439i	−1.45996	+	0.842911i
$99$		−	13.7023i		−	1.37713i
$100$		0			0
$101$	−5.78481	+	10.0196i	−0.575610	+	0.996986i	0.420365	+	0.907355i	$0.361902\pi$
$101$	−5.78481	+	10.0196i	−0.575610	+	0.996986i	−0.995975	+	0.0896307i	$0.971431\pi$
$102$	−0.191945	−	0.110819i	−0.0190054	−	0.0109728i
$103$	4.48891			0.442305			0.221153	−	0.975239i	$-0.429018\pi$
$103$	4.48891			0.442305			0.221153	+	0.975239i	$0.429018\pi$
$104$	13.1339	+	11.3926i	1.28788	+	1.11713i
$105$		0			0
$106$	16.0191	+	9.24862i	1.55591	+	0.898305i
$107$	−3.89475	+	6.74590i	−0.376519	+	0.652151i	−0.990553	−	0.137129i	$-0.956213\pi$
$107$	−3.89475	+	6.74590i	−0.376519	+	0.652151i	0.614034	+	0.789280i	$0.289546\pi$
$108$	−1.44887	−	2.50952i	−0.139418	−	0.241479i
$109$			7.21948i			0.691501i	0.938327	+	0.345750i	$0.112376\pi$
$109$			7.21948i			0.691501i	−0.938327	+	0.345750i	$0.887624\pi$
$110$		0			0
$111$	0.679229	−	0.392153i	0.0644696	−	0.0372215i
$112$			1.58983i			0.150225i
$113$	−3.40533	−	5.89821i	−0.320347	−	0.554857i	0.660213	−	0.751079i	$-0.270466\pi$
$113$	−3.40533	−	5.89821i	−0.320347	−	0.554857i	−0.980560	+	0.196222i	$0.937133\pi$
$114$	1.11344	−	1.92853i	0.104283	−	0.180624i
$115$		0			0
$116$	22.2789			2.06855
$117$	10.5675	+	2.04244i	0.976970	+	0.188824i
$118$	−8.91559			−0.820747
$119$	0.266893	+	0.154090i	0.0244660	+	0.0141255i
$120$		0			0
$121$	5.03473	+	8.72041i	0.457703	+	0.792765i
$122$		−	29.1228i		−	2.63665i
$123$	−0.550391	+	0.317769i	−0.0496271	+	0.0286522i
$124$	−12.4189	+	7.17008i	−1.11525	+	0.643892i
$125$		0			0
$126$	1.51061	+	2.61646i	0.134576	+	0.233092i
$127$	1.69854	−	2.94195i	0.150721	−	0.261056i	−0.780772	−	0.624816i	$-0.785174\pi$
$127$	1.69854	−	2.94195i	0.150721	−	0.261056i	0.931493	+	0.363760i	$0.118507\pi$
$128$	17.1513	+	9.90230i	1.51597	+	0.875248i
$129$	1.21074			0.106599
$130$		0			0
$131$	6.51884			0.569554			0.284777	−	0.958594i	$-0.408080\pi$
$131$	6.51884			0.569554			0.284777	+	0.958594i	$0.408080\pi$
$132$	1.92461	+	1.11117i	0.167516	+	0.0967152i
$133$	−1.54820	+	2.68156i	−0.134246	+	0.232521i
$134$	8.00918	+	13.8723i	0.691888	+	1.19838i
$135$		0			0
$136$	−3.10784	+	1.79431i	−0.266495	+	0.153861i
$137$	3.67484	−	2.12167i	0.313963	−	0.181266i	−0.334736	−	0.942312i	$-0.608647\pi$
$137$	3.67484	−	2.12167i	0.313963	−	0.181266i	0.648698	+	0.761046i	$0.275314\pi$
$138$			1.89265i			0.161113i
$139$	−9.71433	−	16.8257i	−0.823959	−	1.42714i	−0.902712	−	0.430245i	$-0.858427\pi$
$139$	−9.71433	−	16.8257i	−0.823959	−	1.42714i	0.0787531	−	0.996894i	$-0.474906\pi$
$140$		0			0
$141$	−0.161361	−	0.0931619i	−0.0135891	−	0.00784565i
$142$	−16.6243			−1.39508
$143$	−15.6426	+	5.40482i	−1.30810	+	0.451974i
$144$	−11.4604			−0.955030
$145$		0			0
$146$	−3.77213	+	6.53351i	−0.312183	+	0.540717i
$147$	−0.416059	−	0.720636i	−0.0343160	−	0.0594371i
$148$		−	25.5713i		−	2.10194i
$149$	9.91182	−	5.72259i	0.812008	−	0.468813i	−0.0356447	−	0.999365i	$-0.511348\pi$
$149$	9.91182	−	5.72259i	0.812008	−	0.468813i	0.847653	+	0.530551i	$0.178015\pi$
$150$		0			0
$151$			4.88063i			0.397180i	0.980083	+	0.198590i	$0.0636362\pi$
$151$			4.88063i			0.397180i	−0.980083	+	0.198590i	$0.936364\pi$
$152$	−18.0281	−	31.2255i	−1.46227	−	2.53273i
$153$	−1.11077	+	1.92391i	−0.0898004	+	0.155539i
$154$	−4.02322	−	2.32281i	−0.324200	−	0.187177i
$155$		0			0
$156$	−1.14384	+	1.31868i	−0.0915808	+	0.105579i
$157$	−17.0352			−1.35956			−0.679779	−	0.733417i	$-0.737924\pi$
$157$	−17.0352			−1.35956			−0.679779	+	0.733417i	$0.737924\pi$
$158$	2.39242	+	1.38126i	0.190330	+	0.109887i
$159$	−0.461145	+	0.798726i	−0.0365712	+	0.0633431i
$160$		0			0
$161$		−	2.63167i		−	0.207405i
$162$	−18.7666	+	10.8349i	−1.47444	+	0.851269i
$163$	−9.44987	+	5.45588i	−0.740171	+	0.427338i	−0.822131	−	0.569298i	$-0.807215\pi$
$163$	−9.44987	+	5.45588i	−0.740171	+	0.427338i	0.0819607	+	0.996636i	$0.473882\pi$
$164$			20.7208i			1.61803i
$165$		0			0
$166$	−14.8522	+	25.7248i	−1.15276	+	1.99663i
$167$	−1.33382	−	0.770080i	−0.103214	−	0.0595905i	0.447505	−	0.894282i	$-0.352313\pi$
$167$	−1.33382	−	0.770080i	−0.103214	−	0.0595905i	−0.550718	+	0.834691i	$0.685646\pi$
$168$	−0.243342			−0.0187743
$169$	−1.83667	−	12.8696i	−0.141282	−	0.989969i
$170$		0			0
$171$	−19.3302	−	11.1603i	−1.47822	−	0.853448i
$172$	19.7372	−	34.1859i	1.50495	−	2.60665i
$173$	10.4124	+	18.0348i	0.791640	+	1.37116i	0.924951	+	0.380086i	$0.124106\pi$
$173$	10.4124	+	18.0348i	0.791640	+	1.37116i	−0.133311	+	0.991074i	$0.542561\pi$
$174$			1.67004i			0.126605i
$175$		0			0
$176$	15.2612	−	8.81107i	1.15036	−	0.664160i
$177$		−	0.444540i		−	0.0334137i
$178$	8.52503	+	14.7658i	0.638978	+	1.10674i
$179$	−8.39108	+	14.5338i	−0.627179	+	1.08631i	0.360936	+	0.932590i	$0.382457\pi$
$179$	−8.39108	+	14.5338i	−0.627179	+	1.08631i	−0.988115	+	0.153715i	$0.950876\pi$
$180$		0			0
$181$	15.7383			1.16982			0.584911	−	0.811098i	$-0.301130\pi$
$181$	15.7383			1.16982			0.584911	+	0.811098i	$0.301130\pi$
$182$	2.39110	−	2.75658i	0.177240	−	0.204331i
$183$	1.45209			0.107342
$184$	26.5390	+	15.3223i	1.95648	+	1.12957i
$185$		0			0
$186$	−0.537472	−	0.930929i	−0.0394094	−	0.0682590i
$187$		−	3.41597i		−	0.249801i
$188$	−5.26097	+	3.03742i	−0.383695	+	0.221527i
$189$	−0.261567	+	0.151016i	−0.0190262	+	0.0109848i
$190$		0			0
$191$	4.29028	+	7.43098i	0.310434	+	0.537687i	0.978456	−	0.206454i	$-0.0661924\pi$
$191$	4.29028	+	7.43098i	0.310434	+	0.537687i	−0.668023	+	0.744141i	$0.732859\pi$
$192$	−0.506778	+	0.877766i	−0.0365736	+	0.0633473i
$193$	12.8555	+	7.42213i	0.925359	+	0.534256i	0.885341	−	0.464942i	$-0.153925\pi$
$193$	12.8555	+	7.42213i	0.925359	+	0.534256i	0.0400185	+	0.999199i	$0.487258\pi$
$194$	−31.0772			−2.23121
$195$		0			0
$196$	−27.1301			−1.93787
$197$	−6.47111	−	3.73610i	−0.461047	−	0.266186i	0.251437	−	0.967874i	$-0.419097\pi$
$197$	−6.47111	−	3.73610i	−0.461047	−	0.266186i	−0.712485	+	0.701688i	$0.752430\pi$
$198$	16.7441	−	29.0016i	1.18995	−	2.06106i
$199$	−6.86341	−	11.8878i	−0.486534	−	0.842702i	0.513346	−	0.858182i	$-0.328406\pi$
$199$	−6.86341	−	11.8878i	−0.486534	−	0.842702i	−0.999880	+	0.0154796i	$0.995072\pi$
$200$		0			0
$201$	−0.691687	+	0.399345i	−0.0487878	+	0.0281677i
$202$	−24.4877	+	14.1380i	−1.72295	+	0.994745i
$203$		−	2.32213i		−	0.162981i
$204$	−0.180154	−	0.312035i	−0.0126133	−	0.0218468i
$205$		0			0
$206$	9.50102	+	5.48542i	0.661967	+	0.382187i
$207$	18.9705			1.31854
$208$	4.52050	+	13.0832i	0.313441	+	0.907157i
$209$	34.3215			2.37406
$210$		0			0
$211$	5.36355	−	9.28994i	0.369242	−	0.639546i	−0.620205	−	0.784440i	$-0.712951\pi$
$211$	5.36355	−	9.28994i	0.369242	−	0.639546i	0.989447	+	0.144894i	$0.0462840\pi$
$212$	15.0350	+	26.0414i	1.03261	+	1.78853i
$213$		−	0.828905i		−	0.0567956i
$214$	−16.4869	+	9.51871i	−1.12702	+	0.650685i
$215$		0			0
$216$		−	3.51702i		−	0.239303i
$217$	0.747336	+	1.29442i	0.0507325	+	0.0878712i
$218$	−8.82215	+	15.2804i	−0.597512	+	1.03492i
$219$	−0.325767	−	0.188082i	−0.0220133	−	0.0127094i
$220$		0			0
$221$	2.63449	+	0.509180i	0.177215	+	0.0342512i
$222$	1.91683			0.128649
$223$	−22.3213	−	12.8872i	−1.49474	−	0.862991i	−0.494762	−	0.869028i	$-0.664745\pi$
$223$	−22.3213	−	12.8872i	−1.49474	−	0.862991i	−0.999982	+	0.00603758i	$0.998078\pi$
$224$	0.0541514	−	0.0937930i	0.00361814	−	0.00626681i
$225$		0			0
$226$		−	16.6452i		−	1.10722i
$227$	25.1814	−	14.5385i	1.67135	−	0.964952i	0.704460	−	0.709743i	$-0.251189\pi$
$227$	25.1814	−	14.5385i	1.67135	−	0.964952i	0.966886	−	0.255209i	$-0.0821442\pi$
$228$	3.13512	−	1.81006i	0.207629	−	0.119874i
$229$			14.4689i			0.956131i	0.878324	+	0.478066i	$0.158662\pi$
$229$			14.4689i			0.956131i	−0.878324	+	0.478066i	$0.841338\pi$
$230$		0			0
$231$	0.115817	−	0.200602i	0.00762023	−	0.0131986i
$232$	23.4174	+	13.5201i	1.53743	+	0.887636i
$233$	10.8233			0.709059			0.354530	−	0.935045i	$-0.384641\pi$
$233$	10.8233			0.709059			0.354530	+	0.935045i	$0.384641\pi$
$234$	19.8709	+	17.2364i	1.29900	+	1.12678i
$235$		0			0
$236$	−12.5519	−	7.24682i	−0.817056	−	0.471728i
$237$	−0.0688711	+	0.119288i	−0.00447366	+	0.00774860i
$238$	0.376595	+	0.652282i	0.0244110	+	0.0422811i
$239$			13.8420i			0.895362i	0.894193	+	0.447681i	$0.147750\pi$
$239$			13.8420i			0.895362i	−0.894193	+	0.447681i	$0.852250\pi$
$240$		0			0
$241$	3.94528	−	2.27781i	0.254138	−	0.146726i	−0.367520	−	0.930016i	$-0.619793\pi$
$241$	3.94528	−	2.27781i	0.254138	−	0.146726i	0.621657	+	0.783289i	$0.286460\pi$
$242$			24.6096i			1.58197i
$243$	−1.63426	−	2.83062i	−0.104838	−	0.181584i
$244$	23.6717	−	41.0007i	1.51543	−	2.62480i
$245$		0			0
$246$	−1.55324			−0.0990312
$247$	−5.11591	+	26.4696i	−0.325517	+	1.68422i
$248$	−17.4048			−1.10520
$249$	−1.28266	−	0.740546i	−0.0812855	−	0.0469302i
$250$		0			0
$251$	−6.70194	−	11.6081i	−0.423022	−	0.732696i	0.573211	−	0.819408i	$-0.305698\pi$
$251$	−6.70194	−	11.6081i	−0.423022	−	0.732696i	−0.996233	+	0.0867115i	$0.972364\pi$
$252$			4.91145i			0.309392i
$253$	−25.2622	+	14.5851i	−1.58822	+	0.916959i
$254$	7.19009	−	4.15120i	0.451147	−	0.260470i
$255$		0			0
$256$	15.8837	+	27.5113i	0.992729	+	1.71946i
$257$	3.58101	−	6.20250i	0.223377	−	0.386901i	−0.732454	−	0.680817i	$-0.761625\pi$
$257$	3.58101	−	6.20250i	0.223377	−	0.386901i	0.955831	+	0.293916i	$0.0949584\pi$
$258$	2.56259	+	1.47951i	0.159540	+	0.0921104i
$259$	−2.66529			−0.165613
$260$		0			0
$261$	16.7392			1.03613
$262$	13.7975	+	7.96598i	0.852411	+	0.492140i
$263$	9.52678	−	16.5009i	0.587447	−	1.01749i	−0.407119	−	0.913375i	$-0.633467\pi$
$263$	9.52678	−	16.5009i	0.587447	−	1.01749i	0.994566	−	0.104112i	$-0.0332001\pi$
$264$	1.34864	+	2.33591i	0.0830031	+	0.143766i
$265$		0			0
$266$	−6.55369	+	3.78378i	−0.401833	+	0.231998i
$267$	−0.736236	+	0.425066i	−0.0450569	+	0.0260136i
$268$			26.0403i			1.59066i
$269$	5.94899	+	10.3039i	0.362716	+	0.628243i	0.988407	−	0.151828i	$-0.0485161\pi$
$269$	5.94899	+	10.3039i	0.362716	+	0.628243i	−0.625691	+	0.780071i	$0.715183\pi$
$270$		0			0
$271$	7.29977	+	4.21453i	0.443430	+	0.256014i	0.705051	−	0.709156i	$-0.250924\pi$
$271$	7.29977	+	4.21453i	0.443430	+	0.256014i	−0.261622	+	0.965171i	$0.584257\pi$
$272$	−2.85706			−0.173235
$273$	0.137445	+	0.119223i	0.00831858	+	0.00721569i
$274$	10.3707			0.626514
$275$		0			0
$276$	−1.53840	+	2.66458i	−0.0926006	+	0.160389i
$277$	0.0811749	+	0.140599i	0.00487733	+	0.00844778i	0.868454	−	0.495770i	$-0.165114\pi$
$277$	0.0811749	+	0.140599i	0.00487733	+	0.00844778i	−0.863576	+	0.504218i	$0.831781\pi$
$278$		−	47.4834i		−	2.84786i
$279$	−9.33093	+	5.38722i	−0.558628	+	0.322524i
$280$		0			0
$281$		−	22.4171i		−	1.33729i	−0.743581	−	0.668646i	$-0.766874\pi$
$281$		−	22.4171i		−	1.33729i	0.743581	−	0.668646i	$-0.233126\pi$
$282$	−0.227686	−	0.394364i	−0.0135585	−	0.0234841i
$283$	−3.87385	+	6.70971i	−0.230277	+	0.398851i	−0.957890	−	0.287137i	$-0.907296\pi$
$283$	−3.87385	+	6.70971i	−0.230277	+	0.398851i	0.727613	+	0.685988i	$0.240630\pi$
$284$	−23.4046	−	13.5127i	−1.38881	−	0.801830i
$285$		0			0
$286$	−39.7131	−	7.67554i	−2.34828	−	0.453864i
$287$	2.15973			0.127485
$288$	0.676112	+	0.390354i	0.0398403	+	0.0230018i
$289$	8.22309	−	14.2428i	0.483711	−	0.837812i
$290$		0			0
$291$		−	1.54954i		−	0.0908356i
$292$	−10.6212	+	6.13216i	−0.621559	+	0.358857i
$293$	21.5234	−	12.4265i	1.25741	−	0.725966i	0.284839	−	0.958575i	$-0.408060\pi$
$293$	21.5234	−	12.4265i	1.25741	−	0.725966i	0.972570	+	0.232610i	$0.0747265\pi$
$294$		−	2.03369i		−	0.118607i
$295$		0			0
$296$	15.5180	−	26.8780i	0.901967	−	1.56225i
$297$	2.89929	+	1.67391i	0.168234	+	0.0971299i
$298$	27.9719			1.62037
$299$	−7.48287	−	21.6569i	−0.432745	−	1.25245i
$300$		0			0
$301$	−3.56319	−	2.05721i	−0.205379	−	0.118576i
$302$	−5.96410	+	10.3301i	−0.343195	+	0.594431i
$303$	−0.704934	−	1.22098i	−0.0404974	−	0.0701435i
$304$		−	28.7059i		−	1.64640i
$305$		0			0
$306$	−4.70201	+	2.71471i	−0.268796	+	0.155189i
$307$		−	11.0390i		−	0.630029i	−0.949087	−	0.315014i	$-0.897991\pi$
$307$		−	11.0390i		−	0.630029i	0.949087	−	0.315014i	$-0.102009\pi$
$308$	−3.77607	−	6.54035i	−0.215162	−	0.372671i
$309$	−0.273508	+	0.473730i	−0.0155593	+	0.0269496i
$310$		0			0
$311$	−2.98906			−0.169494			−0.0847471	−	0.996402i	$-0.527008\pi$
$311$	−2.98906			−0.169494			−0.0847471	+	0.996402i	$0.527008\pi$
$312$	−2.00254	+	0.691918i	−0.113372	+	0.0391721i
$313$	16.1910			0.915169			0.457585	−	0.889166i	$-0.348715\pi$
$313$	16.1910			0.915169			0.457585	+	0.889166i	$0.348715\pi$
$314$	−36.0559	−	20.8169i	−2.03475	−	1.17477i
$315$		0			0
$316$	2.24545	+	3.88923i	0.126316	+	0.218786i
$317$		−	27.0057i		−	1.51679i	−0.651795	−	0.758396i	$-0.725984\pi$
$317$		−	27.0057i		−	1.51679i	0.651795	−	0.758396i	$-0.274016\pi$
$318$	−1.95208	+	1.12703i	−0.109467	+	0.0632008i
$319$	−22.2908	+	12.8696i	−1.24805	+	0.720559i
$320$		0			0
$321$	−0.474612	−	0.822052i	−0.0264902	−	0.0458825i
$322$	3.21588	−	5.57007i	0.179214	−	0.310408i
$323$	−4.81901	−	2.78225i	−0.268137	−	0.154809i
$324$	−35.2275			−1.95708
$325$		0			0
$326$	−26.6682			−1.47702
$327$	−0.761896	−	0.439881i	−0.0421330	−	0.0243255i
$328$	−12.5745	+	21.7797i	−0.694313	+	1.20258i
$329$	0.316590	+	0.548350i	0.0174542	+	0.0302315i
$330$		0			0
$331$	2.37093	−	1.36886i	0.130318	−	0.0752393i	−0.433424	−	0.901190i	$-0.642695\pi$
$331$	2.37093	−	1.36886i	0.130318	−	0.0752393i	0.563742	+	0.825951i	$0.309361\pi$
$332$	−41.8195	+	24.1445i	−2.29515	+	1.32510i
$333$		−	19.2129i		−	1.05286i
$334$	−1.88206	−	3.25983i	−0.102982	−	0.178370i
$335$		0			0
$336$	−0.167780	−	0.0968677i	−0.00915314	−	0.00528457i
$337$	−17.6945			−0.963879			−0.481940	−	0.876204i	$-0.660068\pi$
$337$	−17.6945			−0.963879			−0.481940	+	0.876204i	$0.660068\pi$
$338$	11.8391	−	29.4836i	0.643965	−	1.60370i
$339$	0.829944			0.0450764
$340$		0			0
$341$	8.28371	−	14.3478i	0.448588	−	0.776977i
$342$	−27.2756	−	47.2427i	−1.47489	−	2.55459i
$343$			5.72655i			0.309205i
$344$	41.4917	−	23.9553i	2.23708	−	1.29158i
$345$		0			0
$346$			50.8955i			2.73616i
$347$	−2.05669	−	3.56229i	−0.110409	−	0.191234i	0.805526	−	0.592560i	$-0.201883\pi$
$347$	−2.05669	−	3.56229i	−0.110409	−	0.191234i	−0.915935	+	0.401326i	$0.868549\pi$
$348$	−1.35745	+	2.35117i	−0.0727669	+	0.126036i
$349$	12.4657	+	7.19707i	0.667274	+	0.385251i	0.795043	−	0.606553i	$-0.207448\pi$
$349$	12.4657	+	7.19707i	0.667274	+	0.385251i	−0.127769	+	0.991804i	$0.540782\pi$
$350$		0			0
$351$	−1.72312	+	1.98650i	−0.0919735	+	0.106031i
$352$	−1.20046			−0.0639849
$353$	−21.5170	−	12.4229i	−1.14524	−	0.661202i	−0.197514	−	0.980300i	$-0.563287\pi$
$353$	−21.5170	−	12.4229i	−1.14524	−	0.661202i	−0.947722	+	0.319097i	$0.896620\pi$
$354$	0.543225	−	0.940893i	0.0288721	−	0.0500079i
$355$		0			0
$356$			27.7174i			1.46902i
$357$	−0.0325234	+	0.0187774i	−0.00172132	+	0.000993805i
$358$	−35.5204	+	20.5077i	−1.87731	+	1.08386i
$359$		−	21.1128i		−	1.11429i	−0.830416	−	0.557144i	$-0.811897\pi$
$359$		−	21.1128i		−	1.11429i	0.830416	−	0.557144i	$-0.188103\pi$
$360$		0			0
$361$	18.4542	−	31.9637i	0.971276	−	1.68230i
$362$	33.3110	+	19.2321i	1.75079	+	1.01082i
$363$	−1.22706			−0.0644039
$364$	5.60694	−	1.93731i	0.293884	−	0.101542i
$365$		0			0
$366$	3.07343	+	1.77444i	0.160651	+	0.0927517i
$367$	−4.27061	+	7.39691i	−0.222924	+	0.386115i	−0.955695	−	0.294360i	$-0.904893\pi$
$367$	−4.27061	+	7.39691i	−0.222924	+	0.386115i	0.732771	+	0.680476i	$0.238227\pi$
$368$	12.1987	+	21.1289i	0.635904	+	1.10142i
$369$			15.5685i			0.810466i
$370$		0			0
$371$	2.71429	−	1.56710i	0.140919	−	0.0813596i
$372$		−	1.74748i		−	0.0906028i
$373$	−6.40821	−	11.0994i	−0.331805	−	0.574703i	0.651061	−	0.759025i	$-0.274324\pi$
$373$	−6.40821	−	11.0994i	−0.331805	−	0.574703i	−0.982866	+	0.184323i	$0.940991\pi$
$374$	4.17430	−	7.23009i	0.215848	−	0.373859i
$375$		0			0
$376$	−7.37309			−0.380238
$377$	−6.60272	−	19.1096i	−0.340058	−	0.984192i
$378$	−0.738161			−0.0379669
$379$	10.3049	+	5.94956i	0.529329	+	0.305608i	0.740743	−	0.671788i	$-0.234474\pi$
$379$	10.3049	+	5.94956i	0.529329	+	0.305608i	−0.211414	+	0.977397i	$0.567807\pi$
$380$		0			0
$381$	0.206983	+	0.358505i	0.0106041	+	0.0183668i
$382$			20.9708i			1.07296i
$383$	1.40589	−	0.811694i	0.0718379	−	0.0414756i	−0.463651	−	0.886018i	$-0.653461\pi$
$383$	1.40589	−	0.811694i	0.0718379	−	0.0414756i	0.535489	+	0.844542i	$0.320127\pi$
$384$	−2.09005	+	1.20669i	−0.106657	+	0.0615786i
$385$		0			0
$386$	18.1396	+	31.4187i	0.923280	+	1.59917i
$387$	14.8295	−	25.6855i	0.753826	−	1.30567i
$388$	−43.7522	−	25.2603i	−2.22118	−	1.28240i
$389$	6.39483			0.324231			0.162115	−	0.986772i	$-0.448168\pi$
$389$	6.39483			0.324231			0.162115	+	0.986772i	$0.448168\pi$
$390$		0			0
$391$	4.72935			0.239173
$392$	−28.5165	−	16.4640i	−1.44030	−	0.831559i
$393$	−0.397191	+	0.687955i	−0.0200356	+	0.0347028i
$394$	−9.13097	−	15.8153i	−0.460012	−	0.796763i
$395$		0			0
$396$	47.1465	−	27.2200i	2.36920	−	1.36786i
$397$	28.7014	−	16.5707i	1.44048	−	0.831662i	0.442599	−	0.896720i	$-0.354057\pi$
$397$	28.7014	−	16.5707i	1.44048	−	0.831662i	0.997881	+	0.0650583i	$0.0207233\pi$
$398$		−	33.5482i		−	1.68162i
$399$	−0.188663	−	0.326773i	−0.00944495	−	0.0163591i
$400$		0			0
$401$	22.7880	+	13.1567i	1.13798	+	0.657013i	0.945929	−	0.324373i	$-0.105153\pi$
$401$	22.7880	+	13.1567i	1.13798	+	0.657013i	0.192050	+	0.981385i	$0.438486\pi$
$402$	−1.95199			−0.0973564
$403$	9.83063	+	8.52727i	0.489699	+	0.424774i
$404$	−45.9669			−2.28694
$405$		0			0
$406$	2.83762	−	4.91491i	0.140829	−	0.243923i
$407$	14.7714	+	25.5849i	0.732193	+	1.26820i
$408$		−	0.437308i		−	0.0216500i
$409$	−20.8366	+	12.0300i	−1.03031	+	0.594847i	−0.917072	−	0.398722i	$-0.869454\pi$
$409$	−20.8366	+	12.0300i	−1.03031	+	0.594847i	−0.113233	+	0.993568i	$0.536121\pi$
$410$		0			0
$411$			0.517091i			0.0255062i
$412$	8.91737	+	15.4453i	0.439327	+	0.760937i
$413$	−0.755335	+	1.30828i	−0.0371676	+	0.0643762i
$414$	40.1521	+	23.1819i	1.97337	+	1.13933i
$415$		0			0
$416$	0.178939	−	0.925827i	0.00877322	−	0.0453924i
$417$	2.36757			0.115940
$418$	72.6432	+	41.9406i	3.55309	+	2.05138i
$419$	1.26354	−	2.18852i	0.0617281	−	0.106916i	−0.833510	−	0.552505i	$-0.813672\pi$
$419$	1.26354	−	2.18852i	0.0617281	−	0.106916i	0.895238	+	0.445588i	$0.147005\pi$
$420$		0			0
$421$			36.7115i			1.78921i	0.446858	+	0.894605i	$0.352543\pi$
$421$			36.7115i			1.78921i	−0.446858	+	0.894605i	$0.647457\pi$
$422$	22.7045	−	13.1084i	1.10524	−	0.638109i
$423$	−3.95281	+	2.28216i	−0.192192	+	0.110962i
$424$			36.4963i			1.77242i
$425$		0			0
$426$	1.01292	−	1.75442i	0.0490759	−	0.0850020i
$427$	−4.27349	−	2.46730i	−0.206809	−	0.119401i
$428$	−30.9482			−1.49594
$429$	0.382710	−	1.98013i	0.0184774	−	0.0956016i
$430$		0			0
$431$	0.224956	+	0.129879i	0.0108358	+	0.00625604i	0.505408	−	0.862880i	$-0.331342\pi$
$431$	0.224956	+	0.129879i	0.0108358	+	0.00625604i	−0.494572	+	0.869136i	$0.664675\pi$
$432$	1.40003	−	2.42492i	0.0673588	−	0.116669i
$433$	−4.85471	−	8.40860i	−0.233302	−	0.404092i	0.725476	−	0.688248i	$-0.241620\pi$
$433$	−4.85471	−	8.40860i	−0.233302	−	0.404092i	−0.958778	+	0.284156i	$0.908287\pi$
$434$			3.65296i			0.175348i
$435$		0			0
$436$	−24.8406	+	14.3417i	−1.18965	+	0.686845i
$437$			47.5173i			2.27306i
$438$	−0.459669	−	0.796170i	−0.0219638	−	0.0380425i
$439$	−3.75018	+	6.49551i	−0.178986	+	0.310014i	−0.941534	−	0.336919i	$-0.890615\pi$
$439$	−3.75018	+	6.49551i	−0.178986	+	0.310014i	0.762547	+	0.646933i	$0.223948\pi$
$440$		0			0
$441$	−20.3841			−0.970673
$442$	4.95382	+	4.29703i	0.235629	+	0.204389i
$443$	28.5096			1.35453			0.677266	−	0.735739i	$-0.263165\pi$
$443$	28.5096			1.35453			0.677266	+	0.735739i	$0.263165\pi$
$444$	2.69862	+	1.55805i	0.128071	+	0.0739418i
$445$		0			0
$446$	−31.4961	−	54.5529i	−1.49139	−	2.58316i
$447$			1.39470i			0.0659672i
$448$	2.98289	−	1.72217i	0.140928	−	0.0813650i
$449$	−9.07159	+	5.23748i	−0.428115	+	0.247172i	−0.698543	−	0.715568i	$-0.746168\pi$
$449$	−9.07159	+	5.23748i	−0.428115	+	0.247172i	0.270428	+	0.962740i	$0.412835\pi$
$450$		0			0
$451$	−11.9696	−	20.7319i	−0.563625	−	0.976227i
$452$	13.5296	−	23.4340i	0.636379	−	1.10224i
$453$	−0.515070	−	0.297376i	−0.0242001	−	0.0139719i
$454$	71.0636			3.33518
$455$		0			0
$456$	4.39378			0.205758
$457$	−16.0887	−	9.28881i	−0.752597	−	0.434512i	0.0740342	−	0.997256i	$-0.476413\pi$
$457$	−16.0887	−	9.28881i	−0.752597	−	0.434512i	−0.826632	+	0.562743i	$0.809746\pi$
$458$	−17.6809	+	30.6242i	−0.826173	+	1.43097i
$459$	−0.271389	−	0.470060i	−0.0126674	−	0.0219405i
$460$		0			0
$461$	−12.1819	+	7.03325i	−0.567370	+	0.327571i	−0.756098	−	0.654458i	$-0.772897\pi$
$461$	−12.1819	+	7.03325i	−0.567370	+	0.327571i	0.188728	+	0.982029i	$0.439563\pi$
$462$	0.490268	−	0.283056i	0.0228093	−	0.0131690i
$463$		−	3.80329i		−	0.176754i	−0.996087	−	0.0883770i	$-0.971832\pi$
$463$		−	3.80329i		−	0.176754i	0.996087	−	0.0883770i	$-0.0281680\pi$
$464$	10.7639	+	18.6437i	0.499702	+	0.865510i
$465$		0			0
$466$	22.9081	+	13.2260i	1.06120	+	0.612683i
$467$	−30.6421			−1.41795			−0.708973	−	0.705236i	$-0.750841\pi$
$467$	−30.6421			−1.41795			−0.708973	+	0.705236i	$0.750841\pi$
$468$	13.9652	+	40.4179i	0.645541	+	1.86832i
$469$	2.71417			0.125329
$470$		0			0
$471$	1.03795	−	1.79778i	0.0478262	−	0.0828375i
$472$	−8.79553	−	15.2343i	−0.404847	−	0.701215i
$473$			45.6055i			2.09694i
$474$	−0.291539	+	0.168320i	−0.0133908	+	0.00773119i
$475$		0			0
$476$			1.22442i			0.0561214i
$477$	11.2965	+	19.5661i	0.517232	+	0.895872i
$478$	−16.9148	+	29.2972i	−0.773664	+	1.34002i
$479$	24.7749	+	14.3038i	1.13199	+	0.653557i	0.944436	−	0.328697i	$-0.106609\pi$
$479$	24.7749	+	14.3038i	1.13199	+	0.653557i	0.187558	+	0.982254i	$0.439943\pi$
$480$		0			0
$481$	−21.9335	+	7.57846i	−1.00008	+	0.345548i
$482$	11.1338			0.507133
$483$	0.277729	+	0.160347i	0.0126371	+	0.00729604i
$484$	−20.0033	+	34.6468i	−0.909242	+	1.57485i
$485$		0			0
$486$		−	7.98821i		−	0.362353i
$487$	1.60707	−	0.927840i	0.0728231	−	0.0420445i	−0.463146	−	0.886282i	$-0.653280\pi$
$487$	1.60707	−	0.927840i	0.0728231	−	0.0420445i	0.535969	+	0.844237i	$0.319946\pi$
$488$	49.7629	−	28.7306i	2.25266	−	1.30057i
$489$		−	1.32970i		−	0.0601312i
$490$		0			0
$491$	7.02539	−	12.1683i	0.317051	−	0.549149i	−0.662820	−	0.748779i	$-0.730641\pi$
$491$	7.02539	−	12.1683i	0.317051	−	0.549149i	0.979871	+	0.199630i	$0.0639739\pi$
$492$	−2.18674	−	1.26252i	−0.0985859	−	0.0569186i
$493$	4.17308			0.187946
$494$	−43.1737	+	49.7727i	−1.94248	+	2.23938i
$495$		0			0
$496$	−12.0003	−	6.92835i	−0.538828	−	0.311092i
$497$	−1.40842	+	2.43946i	−0.0631764	+	0.109425i
$498$	−1.80988	−	3.13481i	−0.0811029	−	0.140474i
$499$		−	3.21293i		−	0.143830i	−0.997411	−	0.0719152i	$-0.977089\pi$
$499$		−	3.21293i		−	0.143830i	0.997411	−	0.0719152i	$-0.0229111\pi$
$500$		0			0
$501$	0.162538	−	0.0938415i	0.00726167	−	0.00419253i
$502$		−	32.7589i		−	1.46210i
$503$	−17.7564	−	30.7550i	−0.791719	−	1.37130i	−0.924902	−	0.380205i	$-0.875853\pi$
$503$	−17.7564	−	30.7550i	−0.791719	−	1.37130i	0.133183	−	0.991091i	$-0.457480\pi$
$504$	−2.98054	+	5.16244i	−0.132764	+	0.229953i
$505$		0			0
$506$	−71.2917			−3.16930
$507$	1.47008	+	0.590311i	0.0652886	+	0.0262166i
$508$	13.4968			0.598824
$509$	−0.438602	−	0.253227i	−0.0194407	−	0.0112241i	0.490248	−	0.871583i	$-0.336906\pi$
$509$	−0.438602	−	0.253227i	−0.0194407	−	0.0112241i	−0.509689	+	0.860359i	$0.670239\pi$
$510$		0			0
$511$	0.639154	+	1.10705i	0.0282745	+	0.0489729i
$512$			38.0297i			1.68069i
$513$	4.72285	−	2.72674i	0.208519	−	0.120388i
$514$	15.1588	−	8.75194i	0.668626	−	0.386032i
$515$		0			0
$516$	2.40517	+	4.16588i	0.105882	+	0.183392i
$517$	3.50918	−	6.07808i	0.154334	−	0.267314i
$518$	−5.64123	−	3.25696i	−0.247861	−	0.143103i
$519$	−2.53770			−0.111393
$520$		0			0
$521$	−12.7770			−0.559769			−0.279885	−	0.960034i	$-0.590296\pi$
$521$	−12.7770			−0.559769			−0.279885	+	0.960034i	$0.590296\pi$
$522$	35.4294	+	20.4552i	1.55070	+	0.895299i
$523$	−9.48315	+	16.4253i	−0.414669	+	0.718228i	−0.995394	−	0.0958719i	$-0.969436\pi$
$523$	−9.48315	+	16.4253i	−0.414669	+	0.718228i	0.580724	+	0.814100i	$0.302769\pi$
$524$	12.9499	+	22.4299i	0.565719	+	0.979854i
$525$		0			0
$526$	40.3279	−	23.2833i	1.75838	−	1.01520i
$527$	−2.32620	+	1.34303i	−0.101331	+	0.0585033i
$528$			2.14743i			0.0934547i
$529$	−8.69280	−	15.0564i	−0.377948	−	0.654625i
$530$		0			0
$531$	−9.43079	−	5.44487i	−0.409262	−	0.236287i
$532$	−12.3022			−0.533368
$533$	17.7731	−	6.14096i	0.769839	−	0.265995i
$534$	−2.07771			−0.0899113
$535$		0			0
$536$	−15.8026	+	27.3710i	−0.682570	+	1.18225i
$537$	−1.02253	−	1.77108i	−0.0441255	−	0.0764277i
$538$			29.0785i			1.25366i
$539$	27.1446	−	15.6719i	1.16920	−	0.675038i
$540$		0			0
$541$			1.07070i			0.0460328i	0.999735	+	0.0230164i	$0.00732700\pi$
$541$			1.07070i			0.0460328i	−0.999735	+	0.0230164i	$0.992673\pi$
$542$	10.3002	+	17.8405i	0.442433	+	0.766317i
$543$	−0.958933	+	1.66092i	−0.0411518	+	0.0712769i
$544$	0.168555	+	0.0973150i	0.00722672	+	0.00417235i
$545$		0			0
$546$	0.145221	+	0.420299i	0.00621490	+	0.0179871i
$547$	−3.90950			−0.167158			−0.0835792	−	0.996501i	$-0.526635\pi$
$547$	−3.90950			−0.167158			−0.0835792	+	0.996501i	$0.526635\pi$
$548$	14.6004	+	8.42953i	0.623697	+	0.360092i
$549$	17.7857	−	30.8057i	0.759075	−	1.31476i
$550$		0			0
$551$			41.9283i			1.78621i
$552$	−3.23403	+	1.86717i	−0.137649	+	0.0794719i
$553$	0.405374	−	0.234043i	0.0172383	−	0.00995252i
$554$			0.396781i			0.0168576i
$555$		0			0
$556$	38.5957	−	66.8497i	1.63682	−	2.83506i
$557$	−28.4281	−	16.4130i	−1.20454	−	0.695440i	−0.242977	−	0.970032i	$-0.578124\pi$
$557$	−28.4281	−	16.4130i	−1.20454	−	0.695440i	−0.961561	+	0.274592i	$0.911457\pi$
$558$	−26.3326			−1.11475
$559$	−35.1721	−	6.79789i	−1.48762	−	0.287520i
$560$		0			0
$561$	0.360499	+	0.208134i	0.0152203	+	0.00878744i
$562$	27.3935	−	47.4470i	1.15553	−	2.00143i
$563$	12.1630	+	21.0670i	0.512611	+	0.887869i	0.999893	+	0.0146239i	$0.00465510\pi$
$563$	12.1630	+	21.0670i	0.512611	+	0.887869i	−0.487282	+	0.873245i	$0.662012\pi$
$564$		−	0.740277i		−	0.0311713i
$565$		0			0
$566$	−16.3984	+	9.46765i	−0.689278	+	0.397955i
$567$			3.67176i			0.154199i
$568$	−16.4004	−	28.4064i	−0.688148	−	1.19191i
$569$	−19.1183	+	33.1138i	−0.801480	+	1.38820i	0.117162	+	0.993113i	$0.462620\pi$
$569$	−19.1183	+	33.1138i	−0.801480	+	1.38820i	−0.918642	+	0.395092i	$0.870713\pi$
$570$		0			0
$571$	17.7041			0.740893			0.370446	−	0.928854i	$-0.379205\pi$
$571$	17.7041			0.740893			0.370446	+	0.928854i	$0.379205\pi$
$572$	−49.6713	−	43.0858i	−2.07686	−	1.80151i
$573$	−1.04562			−0.0436815
$574$	4.57119	+	2.63917i	0.190798	+	0.110157i
$575$		0			0
$576$	12.4144	+	21.5023i	0.517266	+	0.895930i
$577$			25.8925i			1.07792i	0.842332	+	0.538959i	$0.181182\pi$
$577$			25.8925i			1.07792i	−0.842332	+	0.538959i	$0.818818\pi$
$578$	34.8092	−	20.0971i	1.44787	−	0.835929i
$579$	−1.56656	+	0.904457i	−0.0651042	+	0.0375879i
$580$		0			0
$581$	2.51658	+	4.35885i	0.104405	+	0.180835i
$582$	1.89353	−	3.27968i	0.0784892	−	0.135947i
$583$	−30.0861	−	17.3702i	−1.24604	−	0.719400i
$584$	−14.8853			−0.615958
$585$		0			0
$586$	60.7405			2.50917
$587$	13.5106	+	7.80034i	0.557642	+	0.321955i	0.752198	−	0.658937i	$-0.228993\pi$
$587$	13.5106	+	7.80034i	0.557642	+	0.321955i	−0.194557	+	0.980891i	$0.562327\pi$
$588$	1.65303	−	2.86313i	0.0681699	−	0.118074i
$589$	−13.4939	−	23.3721i	−0.556006	−	0.963030i
$590$		0			0
$591$	0.788566	−	0.455279i	0.0324373	−	0.0187277i
$592$	21.3988	−	12.3546i	0.879484	−	0.507770i
$593$			21.8028i			0.895333i	0.894201	+	0.447667i	$0.147745\pi$
$593$			21.8028i			0.895333i	−0.894201	+	0.447667i	$0.852255\pi$
$594$	4.09100	+	7.08582i	0.167856	+	0.290735i
$595$		0			0
$596$	39.3803	+	22.7362i	1.61308	+	0.931313i
$597$	1.67274			0.0684608
$598$	10.6266	−	54.9819i	0.434555	−	2.24838i
$599$	20.7485			0.847760			0.423880	−	0.905718i	$-0.360668\pi$
$599$	20.7485			0.847760			0.423880	+	0.905718i	$0.360668\pi$
$600$		0			0
$601$	−17.0892	+	29.5994i	−0.697084	+	1.20739i	0.272389	+	0.962187i	$0.412186\pi$
$601$	−17.0892	+	29.5994i	−0.697084	+	1.20739i	−0.969473	+	0.245198i	$0.921147\pi$
$602$	−5.02779	−	8.70839i	−0.204917	−	0.354927i
$603$			19.5653i			0.796759i
$604$	−16.7932	+	9.69553i	−0.683304	+	0.394506i
$605$		0			0
$606$		−	3.44570i		−	0.139972i
$607$	4.56457	+	7.90607i	0.185270	+	0.320897i	0.943668	−	0.330895i	$-0.107351\pi$
$607$	4.56457	+	7.90607i	0.185270	+	0.320897i	−0.758397	+	0.651792i	$0.774017\pi$
$608$	−0.977757	+	1.69352i	−0.0396533	+	0.0686815i
$609$	0.245062	+	0.141487i	0.00993042	+	0.00573333i
$610$		0			0
$611$	4.16449	+	3.61236i	0.168477	+	0.146140i
$612$	−8.82632			−0.356783
$613$	−3.94882	−	2.27985i	−0.159491	−	0.0920823i	0.418130	−	0.908387i	$-0.362686\pi$
$613$	−3.94882	−	2.27985i	−0.159491	−	0.0920823i	−0.577621	+	0.816305i	$0.696019\pi$
$614$	13.4896	−	23.3646i	0.544395	−	0.942920i
$615$		0			0
$616$		−	9.16611i		−	0.369313i
$617$	6.85694	−	3.95886i	0.276050	−	0.159378i	−0.355584	−	0.934644i	$-0.615718\pi$
$617$	6.85694	−	3.95886i	0.276050	−	0.159378i	0.631634	+	0.775267i	$0.282385\pi$
$618$	−1.15779	+	0.668450i	−0.0465731	+	0.0268890i
$619$		−	5.98084i		−	0.240390i	−0.992750	−	0.120195i	$-0.961648\pi$
$619$		−	5.98084i		−	0.240390i	0.992750	−	0.120195i	$-0.0383520\pi$
$620$		0			0
$621$	−2.31749	+	4.01401i	−0.0929976	+	0.161077i
$622$	−6.32651	−	3.65261i	−0.253670	−	0.146456i
$623$	2.88898			0.115745
$624$	−1.65615	−	0.320092i	−0.0662990	−	0.0128139i
$625$		0			0
$626$	34.2691	+	19.7853i	1.36967	+	0.790779i
$627$	−2.09120	+	3.62206i	−0.0835144	+	0.144651i
$628$	−33.8410	−	58.6143i	−1.35040	−	2.33897i
$629$		−	4.78976i		−	0.190980i
$630$		0			0
$631$	−15.3843	+	8.88213i	−0.612440	+	0.353592i	−0.773920	−	0.633284i	$-0.781707\pi$
$631$	−15.3843	+	8.88213i	−0.612440	+	0.353592i	0.161480	+	0.986876i	$0.448373\pi$
$632$			5.45064i			0.216815i
$633$	0.653599	+	1.13207i	0.0259782	+	0.0449956i
$634$	33.0008	−	57.1590i	1.31063	−	2.27007i
$635$		0			0
$636$	−3.66432			−0.145300
$637$	8.04046	+	23.2706i	0.318575	+	0.922016i
$638$	−62.9062			−2.49048
$639$	−17.5850	−	10.1527i	−0.695652	−	0.401635i
$640$		0			0
$641$	−1.83334	−	3.17544i	−0.0724125	−	0.125422i	0.827546	−	0.561398i	$-0.189736\pi$
$641$	−1.83334	−	3.17544i	−0.0724125	−	0.125422i	−0.899958	+	0.435976i	$0.856403\pi$
$642$		−	2.31989i		−	0.0915587i
$643$	−26.0792	+	15.0568i	−1.02846	+	0.593782i	−0.916543	−	0.399935i	$-0.869033\pi$
$643$	−26.0792	+	15.0568i	−1.02846	+	0.593782i	−0.111918	+	0.993717i	$0.535699\pi$
$644$	9.05498	−	5.22790i	0.356816	−	0.206008i
$645$		0			0
$646$	−6.79979	−	11.7776i	−0.267534	−	0.463383i
$647$	−1.56841	+	2.71657i	−0.0616607	+	0.106799i	−0.895208	−	0.445649i	$-0.852973\pi$
$647$	−1.56841	+	2.71657i	−0.0616607	+	0.106799i	0.833547	+	0.552448i	$0.186306\pi$
$648$	−37.0277	−	21.3780i	−1.45459	−	0.839805i
$649$	16.7447			0.657288
$650$		0			0
$651$	−0.182140			−0.00713863
$652$	−37.5449	−	21.6766i	−1.47037	−	0.848921i
$653$	−15.1134	+	26.1771i	−0.591432	+	1.02439i	0.402608	+	0.915372i	$0.368104\pi$
$653$	−15.1134	+	26.1771i	−0.591432	+	1.02439i	−0.994040	+	0.109017i	$0.965230\pi$
$654$	−1.07506	−	1.86206i	−0.0420383	−	0.0728125i
$655$		0			0
$656$	−17.3398	+	10.0111i	−0.677006	+	0.390869i
$657$	−7.98021	+	4.60738i	−0.311338	+	0.179751i
$658$			1.54748i			0.0603271i
$659$	6.02408	+	10.4340i	0.234665	+	0.406451i	0.959175	−	0.282813i	$-0.0912674\pi$
$659$	6.02408	+	10.4340i	0.234665	+	0.406451i	−0.724510	+	0.689264i	$0.757934\pi$
$660$		0			0
$661$	−17.0845	−	9.86376i	−0.664511	−	0.383656i	0.129482	−	0.991582i	$-0.458668\pi$
$661$	−17.0845	−	9.86376i	−0.664511	−	0.383656i	−0.793994	+	0.607926i	$0.792002\pi$
$662$	6.69094			0.260051
$663$	−0.214254	+	0.247002i	−0.00832094	+	0.00959276i
$664$	−58.6089			−2.27446
$665$		0			0
$666$	23.4780	−	40.6651i	0.909754	−	1.57574i
$667$	−17.8177	−	30.8612i	−0.689904	−	1.19495i
$668$		−	6.11915i		−	0.236757i
$669$	2.72006	−	1.57043i	0.105164	−	0.0607162i
$670$		0			0
$671$			54.6967i			2.11154i
$672$	0.00659886	+	0.0114296i	0.000254557	+	0.000440905i
$673$	20.4220	−	35.3719i	0.787209	−	1.36349i	−0.140462	−	0.990086i	$-0.544859\pi$
$673$	20.4220	−	35.3719i	0.787209	−	1.36349i	0.927671	−	0.373399i	$-0.121808\pi$
$674$	−37.4513	−	21.6225i	−1.44257	−	0.832868i
$675$		0			0
$676$	40.6328	−	31.8855i	1.56280	−	1.22636i
$677$	−27.2536			−1.04744			−0.523720	−	0.851891i	$-0.675456\pi$
$677$	−27.2536			−1.04744			−0.523720	+	0.851891i	$0.675456\pi$
$678$	1.75662	+	1.01419i	0.0674626	+	0.0389496i
$679$	−2.63288	+	4.56029i	−0.101041	+	0.175008i
$680$		0			0
$681$			3.54330i			0.135780i
$682$	35.0658	−	20.2453i	1.34274	−	0.775231i
$683$	14.9820	−	8.64984i	0.573269	−	0.330977i	−0.185185	−	0.982704i	$-0.559288\pi$
$683$	14.9820	−	8.64984i	0.573269	−	0.330977i	0.758454	+	0.651727i	$0.225955\pi$
$684$		−	88.6811i		−	3.39081i
$685$		0			0
$686$	−6.99781	+	12.1206i	−0.267178	+	0.462765i
$687$	−1.52695	−	0.881586i	−0.0582568	−	0.0336346i
$688$	38.1437			1.45421
$689$	17.8809	−	20.6140i	0.681209	−	0.785329i
$690$		0			0
$691$	−30.1039	−	17.3805i	−1.14521	−	0.661186i	−0.197493	−	0.980304i	$-0.563280\pi$
$691$	−30.1039	−	17.3805i	−1.14521	−	0.661186i	−0.947715	+	0.319118i	$0.896613\pi$
$692$	−41.3691	+	71.6534i	−1.57262	+	2.72386i
$693$	−2.83714	−	4.91407i	−0.107774	−	0.186670i
$694$		−	10.0530i		−	0.381609i
$695$		0			0
$696$	−2.85364	+	1.64755i	−0.108167	+	0.0624501i
$697$			3.88123i			0.147012i
$698$	17.5895	+	30.4660i	0.665774	+	1.15315i
$699$	−0.659462	+	1.14222i	−0.0249431	+	0.0432028i
$700$		0			0
$701$	−2.33531			−0.0882035			−0.0441017	−	0.999027i	$-0.514043\pi$
$701$	−2.33531			−0.0882035			−0.0441017	+	0.999027i	$0.514043\pi$
$702$	−6.07457	+	2.09888i	−0.229270	+	0.0792172i
$703$	48.1244			1.81505
$704$	−33.0633	−	19.0891i	−1.24612	−	0.719448i
$705$		0			0
$706$	−30.3613	−	52.5873i	−1.14266	−	1.97915i
$707$			4.79112i			0.180189i
$708$	1.52956	−	0.883093i	0.0574845	−	0.0331887i
$709$	−19.7387	+	11.3961i	−0.741303	+	0.427991i	−0.822543	−	0.568703i	$-0.807445\pi$
$709$	−19.7387	+	11.3961i	−0.741303	+	0.427991i	0.0812401	+	0.996695i	$0.474112\pi$
$710$		0			0
$711$	1.68711	+	2.92216i	0.0632716	+	0.109590i
$712$	−16.8204	+	29.1339i	−0.630373	+	1.09184i
$713$	19.8642	+	11.4686i	0.743922	+	0.429503i
$714$	−0.0917833			−0.00343490
$715$		0			0
$716$	−66.6766			−2.49182
$717$	−1.46079	−	0.843387i	−0.0545542	−	0.0314969i
$718$	25.7996	−	44.6863i	0.962834	−	1.66768i
$719$	20.0615	+	34.7476i	0.748168	+	1.29587i	0.948700	+	0.316178i	$0.102400\pi$
$719$	20.0615	+	34.7476i	0.748168	+	1.29587i	−0.200532	+	0.979687i	$0.564267\pi$
$720$		0			0
$721$	1.60987	−	0.929456i	0.0599545	−	0.0346148i
$722$	78.1188	−	45.1019i	2.90728	−	1.67852i
$723$			0.555144i			0.0206460i
$724$	31.2647	+	54.1521i	1.16194	+	2.01255i
$725$		0			0
$726$	−2.59714	−	1.49946i	−0.0963888	−	0.0556501i
$727$	16.1408			0.598630			0.299315	−	0.954154i	$-0.403242\pi$
$727$	16.1408			0.598630			0.299315	+	0.954154i	$0.403242\pi$
$728$	7.06913	+	1.36629i	0.262000	+	0.0506380i
$729$	−26.2014			−0.970423
$730$		0			0
$731$	3.69699	−	6.40338i	0.136738	−	0.236838i
$732$	2.88463	+	4.99632i	0.106619	+	0.184669i
$733$		−	14.8283i		−	0.547697i	−0.961773	−	0.273848i	$-0.911703\pi$
$733$		−	14.8283i		−	0.547697i	0.961773	−	0.273848i	$-0.0882967\pi$
$734$	−18.0779	+	10.4373i	−0.667269	+	0.385248i
$735$		0			0
$736$		−	1.66202i		−	0.0612627i
$737$	−15.0424	−	26.0541i	−0.554093	−	0.959717i
$738$	−19.0246	+	32.9516i	−0.700307	+	1.21297i
$739$	−3.11391	−	1.79782i	−0.114547	−	0.0661338i	0.441632	−	0.897196i	$-0.354400\pi$
$739$	−3.11391	−	1.79782i	−0.114547	−	0.0661338i	−0.556179	+	0.831063i	$0.687733\pi$
$740$		0			0
$741$	−2.48171	−	2.15268i	−0.0911680	−	0.0790808i
$742$	7.65993			0.281205
$743$	−3.76018	−	2.17094i	−0.137947	−	0.0796440i	0.429438	−	0.903096i	$-0.358712\pi$
$743$	−3.76018	−	2.17094i	−0.137947	−	0.0796440i	−0.567385	+	0.823452i	$0.692045\pi$
$744$	1.06047	−	1.83679i	0.0388787	−	0.0673398i
$745$		0			0
$746$		−	31.3232i		−	1.14682i
$747$	−31.4210	+	18.1409i	−1.14963	+	0.663741i
$748$	11.7536	−	6.78595i	0.429754	−	0.248119i
$749$			3.22572i			0.117865i
$750$		0			0
$751$	−16.9961	+	29.4381i	−0.620195	+	1.07421i	0.369254	+	0.929329i	$0.379613\pi$
$751$	−16.9961	+	29.4381i	−0.620195	+	1.07421i	−0.989449	+	0.144881i	$0.953720\pi$
$752$	−5.08360	−	2.93502i	−0.185380	−	0.107029i
$753$	1.63339			0.0595240
$754$	9.37672	−	48.5149i	0.341480	−	1.76681i
$755$		0			0
$756$	−1.03922	−	0.599996i	−0.0377962	−	0.0218216i
$757$	−8.03385	+	13.9150i	−0.291995	+	0.505751i	−0.974281	−	0.225334i	$-0.927653\pi$
$757$	−8.03385	+	13.9150i	−0.291995	+	0.505751i	0.682286	+	0.731085i	$0.260986\pi$
$758$	14.5406	+	25.1851i	0.528140	+	0.914765i
$759$		−	3.55467i		−	0.129026i
$760$		0			0
$761$	0.122580	−	0.0707715i	0.00444351	−	0.00256546i	−0.497777	−	0.867305i	$-0.665850\pi$
$761$	0.122580	−	0.0707715i	0.00444351	−	0.00256546i	0.502220	+	0.864740i	$0.332517\pi$
$762$			1.01173i			0.0366510i
$763$	1.49484	+	2.58913i	0.0541167	+	0.0937329i
$764$	−17.0456	+	29.5238i	−0.616687	+	1.06813i
$765$		0			0
$766$	3.96753			0.143353
$767$	−2.49595	+	12.9140i	−0.0901234	+	0.466296i
$768$	−3.87115			−0.139688
$769$	12.1544	+	7.01732i	0.438297	+	0.253051i	0.702875	−	0.711313i	$-0.251899\pi$
$769$	12.1544	+	7.01732i	0.438297	+	0.253051i	−0.264578	+	0.964364i	$0.585233\pi$
$770$		0			0
$771$	0.436380	+	0.755833i	0.0157159	+	0.0272207i
$772$			58.9772i			2.12264i
$773$	−2.12867	+	1.22899i	−0.0765628	+	0.0442035i	−0.537793	−	0.843077i	$-0.680742\pi$
$773$	−2.12867	+	1.22899i	−0.0765628	+	0.0442035i	0.461230	+	0.887281i	$0.347408\pi$
$774$	62.7749	−	36.2431i	2.25640	−	1.30273i
$775$		0			0
$776$	−30.6587	−	53.1024i	−1.10058	−	1.90627i
$777$	0.162395	−	0.281277i	0.00582590	−	0.0100908i
$778$	13.5350	+	7.81443i	0.485253	+	0.280161i
$779$	−38.9960			−1.39718
$780$		0			0
$781$	31.2228			1.11724
$782$	10.0099	+	5.77923i	0.357954	+	0.206665i
$783$	−2.04490	+	3.54188i	−0.0730789	+	0.126576i
$784$	−13.1077	−	22.7033i	−0.468134	−	0.810832i
$785$		0			0
$786$	−1.68135	+	0.970730i	−0.0599719	+	0.0346248i
$787$	−11.3433	+	6.54905i	−0.404345	+	0.233449i	−0.688357	−	0.725372i	$-0.741668\pi$
$787$	−11.3433	+	6.54905i	−0.404345	+	0.233449i	0.284012	+	0.958821i	$0.408334\pi$
$788$		−	29.6875i		−	1.05757i
$789$	1.16093	+	2.01079i	0.0413302	+	0.0715859i
$790$		0			0
$791$	−2.44252	−	1.41019i	−0.0868460	−	0.0501406i
$792$	66.0744			2.34785
$793$	−42.1835	−	8.15301i	−1.49798	−	0.289522i
$794$	80.9973			2.87449
$795$		0			0
$796$	27.2688	−	47.2309i	0.966517	−	1.67406i
$797$	1.11943	+	1.93892i	0.0396524	+	0.0686800i	0.885171	−	0.465267i	$-0.154042\pi$
$797$	1.11943	+	1.93892i	0.0396524	+	0.0686800i	−0.845518	+	0.533947i	$0.820708\pi$
$798$		−	0.922178i		−	0.0326447i
$799$	−0.985434	+	0.568941i	−0.0348622	+	0.0201277i
$800$		0			0
$801$			20.8254i			0.735829i
$802$	32.1547	+	55.6936i	1.13542	+	1.96661i
$803$	7.08458	−	12.2709i	0.250009	−	0.433029i
$804$	−2.74812	−	1.58663i	−0.0969186	−	0.0559560i
$805$		0			0
$806$	10.3868	+	30.0614i	0.365859	+	1.05887i
$807$	−1.44988			−0.0510382
$808$	−48.3159	−	27.8952i	−1.69975	−	0.981349i
$809$	0.779435	−	1.35002i	0.0274035	−	0.0474642i	−0.851998	−	0.523544i	$-0.824609\pi$
$809$	0.779435	−	1.35002i	0.0274035	−	0.0474642i	0.879402	+	0.476080i	$0.157943\pi$
$810$		0			0
$811$		−	39.9267i		−	1.40202i	−0.713153	−	0.701008i	$-0.752734\pi$
$811$		−	39.9267i		−	1.40202i	0.713153	−	0.701008i	$-0.247266\pi$
$812$	7.98992	−	4.61299i	0.280391	−	0.161884i
$813$	−0.889547	+	0.513580i	−0.0311978	+	0.0180120i
$814$			72.2024i			2.53069i
$815$		0			0
$816$	0.174080	−	0.301516i	0.00609402	−	0.0105552i
$817$	64.3369	+	37.1449i	2.25086	+	1.29954i
$818$	−58.8025			−2.05598
$819$	4.21276	−	1.45559i	0.147206	−	0.0508624i
$820$		0			0
$821$	−25.1355	−	14.5120i	−0.877237	−	0.506473i	−0.00749029	−	0.999972i	$-0.502384\pi$
$821$	−25.1355	−	14.5120i	−0.877237	−	0.506473i	−0.869746	+	0.493499i	$0.835718\pi$
$822$	−0.631881	+	1.09445i	−0.0220394	+	0.0381734i
$823$	8.36535	+	14.4892i	0.291598	+	0.505062i	0.974188	−	0.225739i	$-0.0724798\pi$
$823$	8.36535	+	14.4892i	0.291598	+	0.505062i	−0.682590	+	0.730802i	$0.739146\pi$
$824$			21.6462i			0.754080i
$825$		0			0
$826$	−3.19741	+	1.84603i	−0.111252	+	0.0642315i
$827$		−	37.4382i		−	1.30185i	−0.759141	−	0.650926i	$-0.774381\pi$
$827$		−	37.4382i		−	1.30185i	0.759141	−	0.650926i	$-0.225619\pi$
$828$	37.6856	+	65.2734i	1.30966	+	2.26841i
$829$	−7.43017	+	12.8694i	−0.258060	+	0.446974i	−0.965722	−	0.259578i	$-0.916417\pi$
$829$	−7.43017	+	12.8694i	−0.258060	+	0.446974i	0.707662	+	0.706551i	$0.249750\pi$
$830$		0			0
$831$	−0.0197839			−0.000686295
$832$	19.6504	−	22.6538i	0.681254	−	0.785381i
$833$	−5.08176			−0.176072
$834$	5.01108	+	2.89315i	0.173520	+	0.100182i
$835$		0			0
$836$	68.1807	+	118.092i	2.35808	+	4.08431i
$837$		−	2.63246i		−	0.0909913i
$838$	5.34871	−	3.08808i	0.184768	−	0.106676i
$839$	11.8176	−	6.82287i	0.407987	−	0.235552i	−0.281937	−	0.959433i	$-0.590977\pi$
$839$	11.8176	−	6.82287i	0.407987	−	0.235552i	0.689925	+	0.723881i	$0.257644\pi$
$840$		0			0
$841$	−1.22196	−	2.11650i	−0.0421365	−	0.0729826i
$842$	−44.8612	+	77.7019i	−1.54602	+	2.67778i
$843$	2.36575	+	1.36587i	0.0814808	+	0.0470430i
$844$	42.6195			1.46702
$845$		0			0
$846$	−11.1551			−0.383521
$847$	3.61123	+	2.08494i	0.124083	+	0.0716395i
$848$	−14.5281	+	25.1635i	−0.498898	+	0.864117i
$849$	−0.472066	−	0.817642i	−0.0162013	−	0.0280614i
$850$		0			0
$851$	−35.4218	+	20.4508i	−1.21424	+	0.701043i
$852$	2.85208	−	1.64665i	0.0977105	−	0.0564132i
$853$			23.3227i			0.798554i	0.916830	+	0.399277i	$0.130739\pi$
$853$			23.3227i			0.798554i	−0.916830	+	0.399277i	$0.869261\pi$
$854$	−6.03005	−	10.4444i	−0.206344	−	0.357398i
$855$		0			0
$856$	−32.5297	−	18.7810i	−1.11184	−	0.641923i
$857$	46.7030			1.59534			0.797672	−	0.603091i	$-0.206064\pi$
$857$	46.7030			1.59534			0.797672	+	0.603091i	$0.206064\pi$
$858$	3.22973	−	3.72339i	0.110261	−	0.127114i
$859$	36.6191			1.24943			0.624713	−	0.780854i	$-0.285216\pi$
$859$	36.6191			1.24943			0.624713	+	0.780854i	$0.285216\pi$
$860$		0			0
$861$	−0.131592	+	0.227924i	−0.00448464	+	0.00776762i
$862$	0.317422	+	0.549790i	0.0108114	+	0.0187259i
$863$		−	28.8219i		−	0.981110i	−0.871410	−	0.490555i	$-0.836794\pi$
$863$		−	28.8219i		−	0.981110i	0.871410	−	0.490555i	$-0.163206\pi$
$864$	−0.165191	+	0.0953732i	−0.00561992	+	0.00324466i
$865$		0			0
$866$		−	23.7297i		−	0.806367i
$867$	1.00206	+	1.73562i	0.0340318	+	0.0589448i
$868$	−2.96922	+	5.14283i	−0.100782	+	0.174559i
$869$	−4.49329	−	2.59420i	−0.152425	−	0.0880024i
$870$		0			0
$871$	22.3358	−	7.71746i	0.756820	−	0.261496i
$872$	−34.8134			−1.17893
$873$	−32.8731	−	18.9793i	−1.11258	−	0.642351i
$874$	−58.0659	+	100.573i	−1.96411	+	3.40193i
$875$		0			0
$876$		−	1.49452i		−	0.0504952i
$877$	25.5639	−	14.7593i	0.863231	−	0.498387i	−0.00186162	−	0.999998i	$-0.500593\pi$
$877$	25.5639	−	14.7593i	0.863231	−	0.498387i	0.865093	+	0.501611i	$0.167259\pi$
$878$	−15.8749	+	9.16539i	−0.535753	+	0.309317i
$879$			3.02858i			0.102151i
$880$		0			0
$881$	14.5286	−	25.1642i	0.489480	−	0.847804i	−0.510447	−	0.859909i	$-0.670520\pi$
$881$	14.5286	−	25.1642i	0.489480	−	0.847804i	0.999927	+	0.0121052i	$0.00385331\pi$
$882$	−43.1441	−	24.9093i	−1.45274	−	0.838739i
$883$	54.1180			1.82122			0.910609	−	0.413270i	$-0.135613\pi$
$883$	54.1180			1.82122			0.910609	+	0.413270i	$0.135613\pi$
$884$	3.48152	+	10.0762i	0.117096	+	0.338899i
$885$		0			0
$886$	60.3421	+	34.8385i	2.02723	+	1.17042i
$887$	−9.46151	+	16.3878i	−0.317686	+	0.550249i	−0.980005	−	0.198973i	$-0.936239\pi$
$887$	−9.46151	+	16.3878i	−0.317686	+	0.550249i	0.662319	+	0.749222i	$0.269573\pi$
$888$	1.89102	+	3.27534i	0.0634584	+	0.109913i
$889$		−	1.40677i		−	0.0471816i
$890$		0			0
$891$	35.2463	−	20.3494i	1.18079	−	0.681732i
$892$		−	102.403i		−	3.42872i
$893$	−5.71634	−	9.90099i	−0.191290	−	0.331324i
$894$	−1.70432	+	2.95197i	−0.0570009	+	0.0987285i
$895$		0			0
$896$	8.20132			0.273987
$897$	2.74145	+	0.529854i	0.0915344	+	0.0176913i
$898$	−25.6007			−0.854306
$899$	17.5278	+	10.1197i	0.584584	+	0.337510i
$900$		0			0
$901$	2.81622	+	4.87783i	0.0938218	+	0.162504i
$902$		−	58.5069i		−	1.94807i
$903$	0.434209	−	0.250690i	0.0144496	−	0.00834246i
$904$	28.4420	−	16.4210i	0.945968	−	0.546155i
$905$		0			0
$906$	−0.726782	−	1.25882i	−0.0241457	−	0.0418216i
$907$	−0.194031	+	0.336072i	−0.00644270	+	0.0111591i	−0.869229	−	0.494410i	$-0.835384\pi$
$907$	−0.194031	+	0.336072i	−0.00644270	+	0.0111591i	0.862786	+	0.505569i	$0.168717\pi$
$908$	100.047	+	57.7623i	3.32018	+	1.91691i
$909$	−34.5370			−1.14552
$910$		0			0
$911$	23.5559			0.780443			0.390221	−	0.920721i	$-0.372398\pi$
$911$	23.5559			0.780443			0.390221	+	0.920721i	$0.372398\pi$
$912$	3.02943	+	1.74904i	0.100314	+	0.0579166i
$913$	27.8946	−	48.3148i	0.923175	−	1.59899i
$914$	−22.7017	−	39.3205i	−0.750906	−	1.30061i
$915$		0			0
$916$	−49.7842	+	28.7429i	−1.64492	+	0.949693i
$917$	2.33786	−	1.34977i	0.0772030	−	0.0445732i
$918$		−	1.32654i		−	0.0437824i
$919$	18.3292	+	31.7471i	0.604625	+	1.04724i	0.992111	+	0.125366i	$0.0400104\pi$
$919$	18.3292	+	31.7471i	0.604625	+	1.04724i	−0.387486	+	0.921876i	$0.626656\pi$
$920$		0			0
$921$	1.16498	+	0.672603i	0.0383875	+	0.0221630i
$922$	−34.3783			−1.13219
$923$	−4.65403	+	24.0798i	−0.153189	+	0.792597i
$924$	0.920301			0.0302757
$925$		0			0
$926$	4.64760	−	8.04987i	0.152729	−	0.264535i
$927$	6.70004	+	11.6048i	0.220058	+	0.381152i
$928$		−	1.46653i		−	0.0481411i
$929$	−3.50179	+	2.02176i	−0.114890	+	0.0663319i	−0.556344	−	0.830952i	$-0.687796\pi$
$929$	−3.50179	+	2.02176i	−0.114890	+	0.0663319i	0.441454	+	0.897284i	$0.354463\pi$
$930$		0			0
$931$		−	51.0581i		−	1.67336i
$932$	21.5009	+	37.2406i	0.704285	+	1.21986i
$933$	0.182123	−	0.315446i	0.00596243	−	0.0103272i
$934$	−64.8556	−	37.4444i	−2.12214	−	1.22522i
$935$		0			0
$936$	−9.84896	+	50.9582i	−0.321923	+	1.66562i
$937$	−9.43729			−0.308303			−0.154151	−	0.988047i	$-0.549264\pi$
$937$	−9.43729			−0.308303			−0.154151	+	0.988047i	$0.549264\pi$
$938$	5.74469	+	3.31670i	0.187571	+	0.108294i
$939$	−0.986513	+	1.70869i	−0.0321936	+	0.0557610i
$940$		0			0
$941$		−	43.9590i		−	1.43302i	−0.697575	−	0.716512i	$-0.745737\pi$
$941$		−	43.9590i		−	1.43302i	0.697575	−	0.716512i	$-0.254263\pi$
$942$	4.39376	−	2.53674i	0.143156	−	0.0826513i
$943$	28.7029	−	16.5716i	0.934694	−	0.539646i
$944$		−	14.0050i		−	0.455824i
$945$		0			0
$946$	−55.7296	+	96.5265i	−1.81193	+	3.13835i
$947$	−52.7410	−	30.4500i	−1.71385	−	0.989493i	−0.929216	−	0.369538i	$-0.879516\pi$
$947$	−52.7410	−	30.4500i	−1.71385	−	0.989493i	−0.784637	−	0.619955i	$-0.787151\pi$
$948$	−0.547259			−0.0177741
$949$	8.40757	+	7.29288i	0.272921	+	0.236737i
$950$		0			0
$951$	2.85000	+	1.64545i	0.0924177	+	0.0533574i
$952$	−0.743047	+	1.28699i	−0.0240823	+	0.0417117i
$953$	−16.4242	−	28.4476i	−0.532033	−	0.921508i	−0.999301	−	0.0373919i	$-0.988095\pi$
$953$	−16.4242	−	28.4476i	−0.532033	−	0.921508i	0.467268	−	0.884116i	$-0.345238\pi$
$954$			55.2170i			1.78772i
$955$		0			0
$956$	−47.6271	+	27.4975i	−1.54037	+	0.889333i
$957$		−	3.13657i		−	0.101391i
$958$	34.9583	+	60.5495i	1.12945	+	1.95626i
$959$	0.878609	−	1.52180i	0.0283718	−	0.0491413i
$960$		0			0
$961$	17.9726			0.579763
$962$	−55.6843	−	10.7624i	−1.79533	−	0.346993i
$963$	−23.2528			−0.749311
$964$	15.6748	+	9.04987i	0.504853	+	0.291477i
$965$		0			0
$966$	0.391885	+	0.678766i	0.0126087	+	0.0218389i
$967$		−	50.7651i		−	1.63250i	−0.577702	−	0.816248i	$-0.696050\pi$
$967$		−	50.7651i		−	1.63250i	0.577702	−	0.816248i	$-0.303950\pi$
$968$	−42.0511	+	24.2782i	−1.35157	+	0.780331i
$969$	0.587241	−	0.339044i	0.0188649	−	0.0108917i
$970$		0			0
$971$	−8.19371	−	14.1919i	−0.262949	−	0.455440i	0.704075	−	0.710125i	$-0.251362\pi$
$971$	−8.19371	−	14.1919i	−0.262949	−	0.455440i	−0.967024	+	0.254685i	$0.918028\pi$
$972$	6.49302	−	11.2462i	0.208264	−	0.360723i
$973$	−6.96773	−	4.02282i	−0.223375	−	0.128966i
$974$	4.53526			0.145319
$975$		0			0
$976$	45.7474			1.46434
$977$	−23.1517	−	13.3666i	−0.740688	−	0.427636i	0.0816313	−	0.996663i	$-0.473987\pi$
$977$	−23.1517	−	13.3666i	−0.740688	−	0.427636i	−0.822319	+	0.569026i	$0.807320\pi$
$978$	1.62489	−	2.81439i	0.0519581	−	0.0899941i
$979$	−16.0112	−	27.7322i	−0.511720	−	0.886325i
$980$		0			0
$981$	−18.6639	+	10.7756i	−0.595893	+	0.344039i
$982$	29.7392	−	17.1699i	0.949017	−	0.547915i
$983$		−	28.3499i		−	0.904222i	−0.891962	−	0.452111i	$-0.850671\pi$
$983$		−	28.3499i		−	0.904222i	0.891962	−	0.452111i	$-0.149329\pi$
$984$	−1.53233	−	2.65407i	−0.0488488	−	0.0846086i
$985$		0			0
$986$	8.83254	+	5.09947i	0.281285	+	0.162400i
$987$	−0.0771589			−0.00245600
$988$	−101.239	+	34.9800i	−3.22083	+	1.11286i
$989$	−63.1399			−2.00773
$990$		0			0
$991$	−28.2367	+	48.9073i	−0.896967	+	1.55359i	−0.0656162	+	0.997845i	$0.520901\pi$
$991$	−28.2367	+	48.9073i	−0.896967	+	1.55359i	−0.831351	+	0.555748i	$0.812432\pi$
$992$	0.471976	+	0.817487i	0.0149853	+	0.0259552i
$993$			0.333617i			0.0105870i
$994$	−5.96201	+	3.44217i	−0.189103	+	0.109179i
$995$		0			0
$996$		−	5.88448i		−	0.186457i
$997$	−19.6596	−	34.0513i	−0.622624	−	1.07842i	−0.988995	−	0.147948i	$-0.952733\pi$
$997$	−19.6596	−	34.0513i	−0.622624	−	1.07842i	0.366371	−	0.930469i	$-0.380600\pi$
$998$	3.92618	−	6.80034i	0.124281	−	0.215261i
$999$	4.06529	+	2.34709i	0.128620	+	0.0742588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.n.e.251.5	yes	10
5.2	odd	4		325.2.m.d.199.2		20
5.3	odd	4		325.2.m.d.199.9		20
5.4	even	2		325.2.n.f.251.1	yes	10
13.6	odd	12		4225.2.a.bv.1.2		10
13.7	odd	12		4225.2.a.bv.1.9		10
13.10	even	6	inner	325.2.n.e.101.5	✓	10
65.19	odd	12		4225.2.a.bu.1.9		10
65.23	odd	12		325.2.m.d.49.2		20
65.49	even	6		325.2.n.f.101.1	yes	10
65.59	odd	12		4225.2.a.bu.1.2		10
65.62	odd	12		325.2.m.d.49.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.m.d.49.2		20	65.23	odd	12
325.2.m.d.49.9		20	65.62	odd	12
325.2.m.d.199.2		20	5.2	odd	4
325.2.m.d.199.9		20	5.3	odd	4
325.2.n.e.101.5	✓	10	13.10	even	6	inner
325.2.n.e.251.5	yes	10	1.1	even	1	trivial
325.2.n.f.101.1	yes	10	65.49	even	6
325.2.n.f.251.1	yes	10	5.4	even	2
4225.2.a.bu.1.2		10	65.59	odd	12
4225.2.a.bu.1.9		10	65.19	odd	12
4225.2.a.bv.1.2		10	13.6	odd	12
4225.2.a.bv.1.9		10	13.7	odd	12

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.11655 + 1.22199i) q^{2} +(-0.0609297 + 0.105533i) q^{3} +(1.98653 + 3.44078i) q^{4} +(-0.257922 + 0.148911i) q^{6} +(0.358632 - 0.207056i) q^{7} +4.82215i q^{8} +(1.49258 + 2.58522i) q^{9} +O(q^{10})\)	\(q+(2.11655 + 1.22199i) q^{2} +(-0.0609297 + 0.105533i) q^{3} +(1.98653 + 3.44078i) q^{4} +(-0.257922 + 0.148911i) q^{6} +(0.358632 - 0.207056i) q^{7} +4.82215i q^{8} +(1.49258 + 2.58522i) q^{9} +(-3.97519 - 2.29507i) q^{11} -0.484156 q^{12} +(2.36255 - 2.72366i) q^{13} +1.01208 q^{14} +(-1.91956 + 3.32478i) q^{16} +(0.372098 + 0.644494i) q^{17} +7.29566i q^{18} +(-6.47544 + 3.73860i) q^{19} +0.0504635i q^{21} +(-5.60913 - 9.71530i) q^{22} +(3.17748 - 5.50356i) q^{23} +(-0.508897 - 0.293812i) q^{24} +(8.32877 - 2.87775i) q^{26} -0.729347 q^{27} +(1.42487 + 0.822647i) q^{28} +(2.80374 - 4.85623i) q^{29} +3.60934i q^{31} +(0.226492 - 0.130765i) q^{32} +(0.484414 - 0.279677i) q^{33} +1.81881i q^{34} +(-5.93010 + 10.2712i) q^{36} +(-5.57387 - 3.21808i) q^{37} -18.2742 q^{38} +(0.143488 + 0.415280i) q^{39} +(4.51661 + 2.60766i) q^{41} +(-0.0616660 + 0.106809i) q^{42} +(-4.96776 - 8.60441i) q^{43} -18.2370i q^{44} +(13.4506 - 7.76572i) q^{46} +1.52901i q^{47} +(-0.233917 - 0.405156i) q^{48} +(-3.41426 + 5.91366i) q^{49} -0.0906875 q^{51} +(14.0648 + 2.71838i) q^{52} +7.56847 q^{53} +(-1.54370 - 0.891257i) q^{54} +(0.998454 + 1.72937i) q^{56} -0.911167i q^{57} +(11.8685 - 6.85231i) q^{58} +(-3.15924 + 1.82399i) q^{59} +(-5.95805 - 10.3197i) q^{61} +(-4.41059 + 7.63937i) q^{62} +(1.07057 + 0.618093i) q^{63} +8.31742 q^{64} +1.36705 q^{66} +(5.67610 + 3.27710i) q^{67} +(-1.47837 + 2.56062i) q^{68} +(0.387206 + 0.670661i) q^{69} +(-5.89082 + 3.40107i) q^{71} +(-12.4663 + 7.19741i) q^{72} +3.08686i q^{73} +(-7.86493 - 13.6225i) q^{74} +(-25.7274 - 14.8537i) q^{76} -1.90084 q^{77} +(-0.203771 + 1.05430i) q^{78} +1.13034 q^{79} +(-4.43329 + 7.67868i) q^{81} +(6.37309 + 11.0385i) q^{82} +12.1541i q^{83} +(-0.173634 + 0.100247i) q^{84} -24.2823i q^{86} +(0.341663 + 0.591777i) q^{87} +(11.0672 - 19.1689i) q^{88} +(6.04168 + 3.48817i) q^{89} +(0.283336 - 1.46597i) q^{91} +25.2487 q^{92} +(-0.380906 - 0.219916i) q^{93} +(-1.86843 + 3.23622i) q^{94} +0.0318699i q^{96} +(-11.0122 + 6.35790i) q^{97} +(-14.4529 + 8.34439i) q^{98} -13.7023i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{3} + 6 q^{4} + 9 q^{6} - 6 q^{7} - 8 q^{9}+O(q^{10}) \) 10 * q - 3 * q^3 + 6 * q^4 + 9 * q^6 - 6 * q^7 - 8 * q^9	\( 10 q - 3 q^{3} + 6 q^{4} + 9 q^{6} - 6 q^{7} - 8 q^{9} - 9 q^{11} - 28 q^{12} + 8 q^{13} - 8 q^{14} - 12 q^{16} + 8 q^{17} - 12 q^{22} + 13 q^{23} + 42 q^{24} - 17 q^{26} + 30 q^{27} + 33 q^{28} + 7 q^{29} + 3 q^{32} - 6 q^{33} - 3 q^{36} + 3 q^{37} - 62 q^{38} + 8 q^{39} + 12 q^{41} + 32 q^{42} + 4 q^{43} + 39 q^{46} - 26 q^{48} - q^{49} + 16 q^{51} + 61 q^{52} + 24 q^{53} - 9 q^{54} - 21 q^{56} + 18 q^{58} - 48 q^{59} + 13 q^{61} + 17 q^{62} - 34 q^{64} - 42 q^{66} + 6 q^{67} - 13 q^{68} + 20 q^{69} - 27 q^{71} - 141 q^{72} - 26 q^{74} - 12 q^{76} - 48 q^{77} + 56 q^{78} + 4 q^{79} - 17 q^{81} - q^{82} - 90 q^{84} - 49 q^{87} - 6 q^{88} + 24 q^{89} + 13 q^{91} + 34 q^{92} - 63 q^{93} + 5 q^{94} - 15 q^{97} - 45 q^{98}+O(q^{100}) \) 10 * q - 3 * q^3 + 6 * q^4 + 9 * q^6 - 6 * q^7 - 8 * q^9 - 9 * q^11 - 28 * q^12 + 8 * q^13 - 8 * q^14 - 12 * q^16 + 8 * q^17 - 12 * q^22 + 13 * q^23 + 42 * q^24 - 17 * q^26 + 30 * q^27 + 33 * q^28 + 7 * q^29 + 3 * q^32 - 6 * q^33 - 3 * q^36 + 3 * q^37 - 62 * q^38 + 8 * q^39 + 12 * q^41 + 32 * q^42 + 4 * q^43 + 39 * q^46 - 26 * q^48 - q^49 + 16 * q^51 + 61 * q^52 + 24 * q^53 - 9 * q^54 - 21 * q^56 + 18 * q^58 - 48 * q^59 + 13 * q^61 + 17 * q^62 - 34 * q^64 - 42 * q^66 + 6 * q^67 - 13 * q^68 + 20 * q^69 - 27 * q^71 - 141 * q^72 - 26 * q^74 - 12 * q^76 - 48 * q^77 + 56 * q^78 + 4 * q^79 - 17 * q^81 - q^82 - 90 * q^84 - 49 * q^87 - 6 * q^88 + 24 * q^89 + 13 * q^91 + 34 * q^92 - 63 * q^93 + 5 * q^94 - 15 * q^97 - 45 * q^98

Introduction

L-functions

Modular forms

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Database

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