LMFDB - Embedded newform 507.2.j.g.316.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(316,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("507.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.j (of order $6$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1731891456.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 $ x^8 - 9x^6 + 65x^4 - 144*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			316.4
Root			$2.21837 + 1.28078i$ of defining polynomial
Character	$\chi$	$=$	507.316
Dual form			507.2.j.g.361.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.21837 + 1.28078i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(2.28078 + 3.95042i) q^{4} -0.561553i q^{5} +(-2.21837 + 1.28078i) q^{6} +(-3.08440 + 1.78078i) q^{7} +6.56155i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(2.21837 + 1.28078i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(2.28078 + 3.95042i) q^{4} -0.561553i q^{5} +(-2.21837 + 1.28078i) q^{6} +(-3.08440 + 1.78078i) q^{7} +6.56155i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.719224 - 1.24573i) q^{10} +(1.73205 + 1.00000i) q^{11} -4.56155 q^{12} -9.12311 q^{14} +(0.486319 + 0.280776i) q^{15} +(-3.84233 + 6.65511i) q^{16} +(1.28078 + 2.21837i) q^{17} -2.56155i q^{18} +(0.972638 - 0.561553i) q^{19} +(2.21837 - 1.28078i) q^{20} -3.56155i q^{21} +(2.56155 + 4.43674i) q^{22} +(1.00000 - 1.73205i) q^{23} +(-5.68247 - 3.28078i) q^{24} +4.68466 q^{25} +1.00000 q^{27} +(-14.0696 - 8.12311i) q^{28} +(2.84233 - 4.92306i) q^{29} +(0.719224 + 1.24573i) q^{30} +1.56155i q^{31} +(-5.68247 + 3.28078i) q^{32} +(-1.73205 + 1.00000i) q^{33} +6.56155i q^{34} +(1.00000 + 1.73205i) q^{35} +(2.28078 - 3.95042i) q^{36} +(-2.97778 - 1.71922i) q^{37} +2.87689 q^{38} +3.68466 q^{40} +(2.21837 + 1.28078i) q^{41} +(4.56155 - 7.90084i) q^{42} +(0.219224 + 0.379706i) q^{43} +9.12311i q^{44} +(-0.486319 + 0.280776i) q^{45} +(4.43674 - 2.56155i) q^{46} -8.24621i q^{47} +(-3.84233 - 6.65511i) q^{48} +(2.84233 - 4.92306i) q^{49} +(10.3923 + 6.00000i) q^{50} -2.56155 q^{51} +11.6847 q^{53} +(2.21837 + 1.28078i) q^{54} +(0.561553 - 0.972638i) q^{55} +(-11.6847 - 20.2384i) q^{56} +1.12311i q^{57} +(12.6107 - 7.28078i) q^{58} +(-9.63289 + 5.56155i) q^{59} +2.56155i q^{60} +(-6.06155 - 10.4989i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(3.08440 + 1.78078i) q^{63} -1.43845 q^{64} -5.12311 q^{66} +(0.379706 + 0.219224i) q^{67} +(-5.84233 + 10.1192i) q^{68} +(1.00000 + 1.73205i) q^{69} +5.12311i q^{70} +(-12.1244 + 7.00000i) q^{71} +(5.68247 - 3.28078i) q^{72} -1.87689i q^{73} +(-4.40388 - 7.62775i) q^{74} +(-2.34233 + 4.05703i) q^{75} +(4.43674 + 2.56155i) q^{76} -7.12311 q^{77} +9.56155 q^{79} +(3.73720 + 2.15767i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.28078 + 5.68247i) q^{82} +9.12311i q^{83} +(14.0696 - 8.12311i) q^{84} +(1.24573 - 0.719224i) q^{85} +1.12311i q^{86} +(2.84233 + 4.92306i) q^{87} +(-6.56155 + 11.3649i) q^{88} +(-11.3649 - 6.56155i) q^{89} -1.43845 q^{90} +9.12311 q^{92} +(-1.35234 - 0.780776i) q^{93} +(10.5616 - 18.2931i) q^{94} +(-0.315342 - 0.546188i) q^{95} -6.56155i q^{96} +(3.84381 - 2.21922i) q^{97} +(12.6107 - 7.28078i) q^{98} -2.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 10 q^{4} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 10 * q^4 - 4 * q^9	$ 8 q - 4 q^{3} + 10 q^{4} - 4 q^{9} + 14 q^{10} - 20 q^{12} - 40 q^{14} - 6 q^{16} + 2 q^{17} + 4 q^{22} + 8 q^{23} - 12 q^{25} + 8 q^{27} - 2 q^{29} + 14 q^{30} + 8 q^{35} + 10 q^{36} + 56 q^{38} - 20 q^{40} + 20 q^{42} + 10 q^{43} - 6 q^{48} - 2 q^{49} - 4 q^{51} + 44 q^{53} - 12 q^{55} - 44 q^{56} - 32 q^{61} - 16 q^{62} - 28 q^{64} - 8 q^{66} - 22 q^{68} + 8 q^{69} + 6 q^{74} + 6 q^{75} - 24 q^{77} + 60 q^{79} - 4 q^{81} + 18 q^{82} - 2 q^{87} - 36 q^{88} - 28 q^{90} + 40 q^{92} + 68 q^{94} - 52 q^{95}+O(q^{100}) $ 8 * q - 4 * q^3 + 10 * q^4 - 4 * q^9 + 14 * q^10 - 20 * q^12 - 40 * q^14 - 6 * q^16 + 2 * q^17 + 4 * q^22 + 8 * q^23 - 12 * q^25 + 8 * q^27 - 2 * q^29 + 14 * q^30 + 8 * q^35 + 10 * q^36 + 56 * q^38 - 20 * q^40 + 20 * q^42 + 10 * q^43 - 6 * q^48 - 2 * q^49 - 4 * q^51 + 44 * q^53 - 12 * q^55 - 44 * q^56 - 32 * q^61 - 16 * q^62 - 28 * q^64 - 8 * q^66 - 22 * q^68 + 8 * q^69 + 6 * q^74 + 6 * q^75 - 24 * q^77 + 60 * q^79 - 4 * q^81 + 18 * q^82 - 2 * q^87 - 36 * q^88 - 28 * q^90 + 40 * q^92 + 68 * q^94 - 52 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.21837	+	1.28078i	1.56862	+	0.905646i	0.996330	+	0.0855975i	$0.0272799\pi$
$2$	2.21837	+	1.28078i	1.56862	+	0.905646i	0.572295	+	0.820048i	$0.306053\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	2.28078	+	3.95042i	1.14039	+	1.97521i
$5$		−	0.561553i		−	0.251134i	−0.992085	−	0.125567i	$-0.959925\pi$
$5$		−	0.561553i		−	0.251134i	0.992085	−	0.125567i	$-0.0400750\pi$
$6$	−2.21837	+	1.28078i	−0.905646	+	0.522875i
$7$	−3.08440	+	1.78078i	−1.16579	+	0.673070i	−0.952685	−	0.303959i	$-0.901692\pi$
$7$	−3.08440	+	1.78078i	−1.16579	+	0.673070i	−0.213107	+	0.977029i	$0.568358\pi$
$8$			6.56155i			2.31986i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.719224	−	1.24573i	0.227438	−	0.393935i
$11$	1.73205	+	1.00000i	0.522233	+	0.301511i	0.737848	−	0.674967i	$-0.235842\pi$
$11$	1.73205	+	1.00000i	0.522233	+	0.301511i	−0.215615	+	0.976478i	$0.569176\pi$
$12$	−4.56155			−1.31681
$13$		0			0
$13$		0			0
$14$	−9.12311			−2.43825
$15$	0.486319	+	0.280776i	0.125567	+	0.0724962i
$16$	−3.84233	+	6.65511i	−0.960582	+	1.66378i
$17$	1.28078	+	2.21837i	0.310634	+	0.538034i	0.978500	−	0.206248i	$-0.0661254\pi$
$17$	1.28078	+	2.21837i	0.310634	+	0.538034i	−0.667866	+	0.744282i	$0.732792\pi$
$18$		−	2.56155i		−	0.603764i
$19$	0.972638	−	0.561553i	0.223138	−	0.128829i	−0.384264	−	0.923223i	$-0.625545\pi$
$19$	0.972638	−	0.561553i	0.223138	−	0.128829i	0.607403	+	0.794394i	$0.292211\pi$
$20$	2.21837	−	1.28078i	0.496043	−	0.286390i
$21$		−	3.56155i		−	0.777195i
$22$	2.56155	+	4.43674i	0.546125	+	0.945916i
$23$	1.00000	−	1.73205i	0.208514	−	0.361158i	−0.742732	−	0.669588i	$-0.766471\pi$
$23$	1.00000	−	1.73205i	0.208514	−	0.361158i	0.951247	+	0.308431i	$0.0998038\pi$
$24$	−5.68247	−	3.28078i	−1.15993	−	0.669686i
$25$	4.68466			0.936932
$26$		0			0
$27$	1.00000			0.192450
$28$	−14.0696	−	8.12311i	−2.65891	−	1.53512i
$29$	2.84233	−	4.92306i	0.527807	−	0.914189i	−0.471667	−	0.881777i	$-0.656348\pi$
$29$	2.84233	−	4.92306i	0.527807	−	0.914189i	0.999475	−	0.0324124i	$-0.0103190\pi$
$30$	0.719224	+	1.24573i	0.131312	+	0.227438i
$31$			1.56155i			0.280463i	0.990119	+	0.140232i	$0.0447847\pi$
$31$			1.56155i			0.280463i	−0.990119	+	0.140232i	$0.955215\pi$
$32$	−5.68247	+	3.28078i	−1.00453	+	0.579965i
$33$	−1.73205	+	1.00000i	−0.301511	+	0.174078i
$34$			6.56155i			1.12530i
$35$	1.00000	+	1.73205i	0.169031	+	0.292770i
$36$	2.28078	−	3.95042i	0.380129	−	0.658403i
$37$	−2.97778	−	1.71922i	−0.489544	−	0.282639i	0.234841	−	0.972034i	$-0.424543\pi$
$37$	−2.97778	−	1.71922i	−0.489544	−	0.282639i	−0.724385	+	0.689395i	$0.757876\pi$
$38$	2.87689			0.466694
$39$		0			0
$40$	3.68466			0.582596
$41$	2.21837	+	1.28078i	0.346451	+	0.200024i	0.663121	−	0.748512i	$-0.269231\pi$
$41$	2.21837	+	1.28078i	0.346451	+	0.200024i	−0.316670	+	0.948536i	$0.602565\pi$
$42$	4.56155	−	7.90084i	0.703863	−	1.21913i
$43$	0.219224	+	0.379706i	0.0334313	+	0.0579047i	0.882257	−	0.470768i	$-0.156023\pi$
$43$	0.219224	+	0.379706i	0.0334313	+	0.0579047i	−0.848826	+	0.528673i	$0.822690\pi$
$44$			9.12311i			1.37536i
$45$	−0.486319	+	0.280776i	−0.0724962	+	0.0418557i
$46$	4.43674	−	2.56155i	0.654162	−	0.377680i
$47$		−	8.24621i		−	1.20283i	−0.798935	−	0.601417i	$-0.794603\pi$
$47$		−	8.24621i		−	1.20283i	0.798935	−	0.601417i	$-0.205397\pi$
$48$	−3.84233	−	6.65511i	−0.554592	−	0.960582i
$49$	2.84233	−	4.92306i	0.406047	−	0.703294i
$50$	10.3923	+	6.00000i	1.46969	+	0.848528i
$51$	−2.56155			−0.358689
$52$		0			0
$53$	11.6847			1.60501			0.802506	−	0.596645i	$-0.203500\pi$
$53$	11.6847			1.60501			0.802506	+	0.596645i	$0.203500\pi$
$54$	2.21837	+	1.28078i	0.301882	+	0.174292i
$55$	0.561553	−	0.972638i	0.0757198	−	0.131150i
$56$	−11.6847	−	20.2384i	−1.56143	−	2.70447i
$57$			1.12311i			0.148759i
$58$	12.6107	−	7.28078i	1.65586	−	0.956013i
$59$	−9.63289	+	5.56155i	−1.25410	+	0.724053i	−0.971920	−	0.235310i	$-0.924389\pi$
$59$	−9.63289	+	5.56155i	−1.25410	+	0.724053i	−0.282175	+	0.959363i	$0.591056\pi$
$60$			2.56155i			0.330695i
$61$	−6.06155	−	10.4989i	−0.776102	−	1.34425i	−0.934173	−	0.356821i	$-0.883861\pi$
$61$	−6.06155	−	10.4989i	−0.776102	−	1.34425i	0.158071	−	0.987428i	$-0.449473\pi$
$62$	−2.00000	+	3.46410i	−0.254000	+	0.439941i
$63$	3.08440	+	1.78078i	0.388597	+	0.224357i
$64$	−1.43845			−0.179806
$65$		0			0
$66$	−5.12311			−0.630611
$67$	0.379706	+	0.219224i	0.0463885	+	0.0267824i	0.523015	−	0.852324i	$-0.324807\pi$
$67$	0.379706	+	0.219224i	0.0463885	+	0.0267824i	−0.476626	+	0.879106i	$0.658141\pi$
$68$	−5.84233	+	10.1192i	−0.708486	+	1.22713i
$69$	1.00000	+	1.73205i	0.120386	+	0.208514i
$70$			5.12311i			0.612328i
$71$	−12.1244	+	7.00000i	−1.43890	+	0.830747i	−0.997773	−	0.0666994i	$-0.978753\pi$
$71$	−12.1244	+	7.00000i	−1.43890	+	0.830747i	−0.441123	+	0.897447i	$0.645420\pi$
$72$	5.68247	−	3.28078i	0.669686	−	0.386643i
$73$		−	1.87689i		−	0.219674i	−0.993950	−	0.109837i	$-0.964967\pi$
$73$		−	1.87689i		−	0.219674i	0.993950	−	0.109837i	$-0.0350329\pi$
$74$	−4.40388	−	7.62775i	−0.511941	−	0.886708i
$75$	−2.34233	+	4.05703i	−0.270469	+	0.468466i
$76$	4.43674	+	2.56155i	0.508929	+	0.293830i
$77$	−7.12311			−0.811753
$78$		0			0
$79$	9.56155			1.07576			0.537879	−	0.843022i	$-0.319226\pi$
$79$	9.56155			1.07576			0.537879	+	0.843022i	$0.319226\pi$
$80$	3.73720	+	2.15767i	0.417831	+	0.241235i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.28078	+	5.68247i	0.362301	+	0.627524i
$83$			9.12311i			1.00139i	0.865624	+	0.500695i	$0.166922\pi$
$83$			9.12311i			1.00139i	−0.865624	+	0.500695i	$0.833078\pi$
$84$	14.0696	−	8.12311i	1.53512	−	0.886303i
$85$	1.24573	−	0.719224i	0.135119	−	0.0780108i
$86$			1.12311i			0.121108i
$87$	2.84233	+	4.92306i	0.304730	+	0.527807i
$88$	−6.56155	+	11.3649i	−0.699464	+	1.21151i
$89$	−11.3649	−	6.56155i	−1.20468	−	0.695523i	−0.243089	−	0.970004i	$-0.578161\pi$
$89$	−11.3649	−	6.56155i	−1.20468	−	0.695523i	−0.961593	+	0.274481i	$0.911494\pi$
$90$	−1.43845			−0.151626
$91$		0			0
$92$	9.12311			0.951150
$93$	−1.35234	−	0.780776i	−0.140232	−	0.0809627i
$94$	10.5616	−	18.2931i	1.08934	−	1.88679i
$95$	−0.315342	−	0.546188i	−0.0323534	−	0.0560377i
$96$		−	6.56155i		−	0.669686i
$97$	3.84381	−	2.21922i	0.390280	−	0.225328i	−0.292002	−	0.956418i	$-0.594321\pi$
$97$	3.84381	−	2.21922i	0.390280	−	0.225328i	0.682281	+	0.731090i	$0.260988\pi$
$98$	12.6107	−	7.28078i	1.27387	−	0.735469i
$99$		−	2.00000i		−	0.201008i
$100$	10.6847	+	18.5064i	1.06847	+	1.85064i
$101$	−1.71922	+	2.97778i	−0.171069	+	0.296300i	−0.938794	−	0.344479i	$-0.888055\pi$
$101$	−1.71922	+	2.97778i	−0.171069	+	0.296300i	0.767725	+	0.640780i	$0.221389\pi$
$102$	−5.68247	−	3.28078i	−0.562649	−	0.324845i
$103$	7.56155			0.745062			0.372531	−	0.928020i	$-0.378490\pi$
$103$	7.56155			0.745062			0.372531	+	0.928020i	$0.378490\pi$
$104$		0			0
$105$	−2.00000			−0.195180
$106$	25.9209	+	14.9654i	2.51766	+	1.45357i
$107$	−4.12311	+	7.14143i	−0.398596	+	0.690388i	−0.993553	−	0.113369i	$-0.963836\pi$
$107$	−4.12311	+	7.14143i	−0.398596	+	0.690388i	0.594957	+	0.803757i	$0.297169\pi$
$108$	2.28078	+	3.95042i	0.219468	+	0.380129i
$109$		−	17.8078i		−	1.70567i	−0.522177	−	0.852837i	$-0.674880\pi$
$109$		−	17.8078i		−	1.70567i	0.522177	−	0.852837i	$-0.325120\pi$
$110$	2.49146	−	1.43845i	0.237552	−	0.137151i
$111$	2.97778	−	1.71922i	0.282639	−	0.163181i
$112$		−	27.3693i		−	2.58616i
$113$	7.40388	+	12.8239i	0.696499	+	1.20637i	0.969673	+	0.244406i	$0.0785931\pi$
$113$	7.40388	+	12.8239i	0.696499	+	1.20637i	−0.273174	+	0.961965i	$0.588074\pi$
$114$	−1.43845	+	2.49146i	−0.134723	+	0.233347i
$115$	−0.972638	−	0.561553i	−0.0906990	−	0.0523651i
$116$	25.9309			2.40762
$117$		0			0
$118$	−28.4924			−2.62294
$119$	−7.90084	−	4.56155i	−0.724269	−	0.418157i
$120$	−1.84233	+	3.19101i	−0.168181	+	0.291298i
$121$	−3.50000	−	6.06218i	−0.318182	−	0.551107i
$122$		−	31.0540i		−	2.81149i
$123$	−2.21837	+	1.28078i	−0.200024	+	0.115484i
$124$	−6.16879	+	3.56155i	−0.553974	+	0.319837i
$125$		−	5.43845i		−	0.486430i
$126$	4.56155	+	7.90084i	0.406375	+	0.703863i
$127$	4.78078	−	8.28055i	0.424225	−	0.734780i	−0.572122	−	0.820168i	$-0.693880\pi$
$127$	4.78078	−	8.28055i	0.424225	−	0.734780i	0.996348	+	0.0853884i	$0.0272131\pi$
$128$	8.17394	+	4.71922i	0.722481	+	0.417124i
$129$	−0.438447			−0.0386031
$130$		0			0
$131$	−17.3693			−1.51756			−0.758782	−	0.651345i	$-0.774205\pi$
$131$	−17.3693			−1.51756			−0.758782	+	0.651345i	$0.774205\pi$
$132$	−7.90084	−	4.56155i	−0.687680	−	0.397032i
$133$	−2.00000	+	3.46410i	−0.173422	+	0.300376i
$134$	0.561553	+	0.972638i	0.0485108	+	0.0840231i
$135$		−	0.561553i		−	0.0483308i
$136$	−14.5560	+	8.40388i	−1.24816	+	0.720627i
$137$	−1.24573	+	0.719224i	−0.106430	+	0.0614474i	−0.552270	−	0.833665i	$-0.686238\pi$
$137$	−1.24573	+	0.719224i	−0.106430	+	0.0614474i	0.445840	+	0.895113i	$0.352905\pi$
$138$			5.12311i			0.436108i
$139$	−5.46543	−	9.46641i	−0.463572	−	0.802930i	0.535564	−	0.844495i	$-0.320099\pi$
$139$	−5.46543	−	9.46641i	−0.463572	−	0.802930i	−0.999136	+	0.0415643i	$0.986766\pi$
$140$	−4.56155	+	7.90084i	−0.385522	+	0.667743i
$141$	7.14143	+	4.12311i	0.601417	+	0.347228i
$142$	−35.8617			−3.00945
$143$		0			0
$144$	7.68466			0.640388
$145$	−2.76456	−	1.59612i	−0.229584	−	0.132550i
$146$	2.40388	−	4.16365i	0.198947	−	0.344586i
$147$	2.84233	+	4.92306i	0.234431	+	0.406047i
$148$		−	15.6847i		−	1.28927i
$149$	5.68247	−	3.28078i	0.465526	−	0.268772i	−0.248839	−	0.968545i	$-0.580049\pi$
$149$	5.68247	−	3.28078i	0.465526	−	0.268772i	0.714365	+	0.699773i	$0.246716\pi$
$150$	−10.3923	+	6.00000i	−0.848528	+	0.489898i
$151$			15.3693i			1.25074i	0.780329	+	0.625369i	$0.215051\pi$
$151$			15.3693i			1.25074i	−0.780329	+	0.625369i	$0.784949\pi$
$152$	3.68466	+	6.38202i	0.298865	+	0.517650i
$153$	1.28078	−	2.21837i	0.103545	−	0.179345i
$154$	−15.8017	−	9.12311i	−1.27334	−	0.735161i
$155$	0.876894			0.0704339
$156$		0			0
$157$	−4.36932			−0.348709			−0.174355	−	0.984683i	$-0.555784\pi$
$157$	−4.36932			−0.348709			−0.174355	+	0.984683i	$0.555784\pi$
$158$	21.2111	+	12.2462i	1.68746	+	0.974256i
$159$	−5.84233	+	10.1192i	−0.463327	+	0.802506i
$160$	1.84233	+	3.19101i	0.145649	+	0.252271i
$161$			7.12311i			0.561379i
$162$	−2.21837	+	1.28078i	−0.174292	+	0.100627i
$163$	13.6899	−	7.90388i	1.07228	−	0.619080i	0.143475	−	0.989654i	$-0.454172\pi$
$163$	13.6899	−	7.90388i	1.07228	−	0.619080i	0.928803	+	0.370574i	$0.120839\pi$
$164$			11.6847i			0.912419i
$165$	0.561553	+	0.972638i	0.0437168	+	0.0757198i
$166$	−11.6847	+	20.2384i	−0.906905	+	1.57081i
$167$	5.40938	+	3.12311i	0.418590	+	0.241673i	0.694474	−	0.719518i	$-0.255637\pi$
$167$	5.40938	+	3.12311i	0.418590	+	0.241673i	−0.275884	+	0.961191i	$0.588970\pi$
$168$	23.3693			1.80298
$169$		0			0
$170$	3.68466			0.282600
$171$	−0.972638	−	0.561553i	−0.0743795	−	0.0429430i
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	1.87689	+	3.25088i	0.142698	+	0.247160i	0.928512	−	0.371303i	$-0.121089\pi$
$173$	1.87689	+	3.25088i	0.142698	+	0.247160i	−0.785814	+	0.618463i	$0.787756\pi$
$174$			14.5616i			1.10391i
$175$	−14.4493	+	8.34233i	−1.09227	+	0.630621i
$176$	−13.3102	+	7.68466i	−1.00330	+	0.579253i
$177$		−	11.1231i		−	0.836064i
$178$	−16.8078	−	29.1119i	−1.25980	−	2.18203i
$179$	−6.56155	+	11.3649i	−0.490433	+	0.849456i	−0.999939	−	0.0110115i	$-0.996495\pi$
$179$	−6.56155	+	11.3649i	−0.490433	+	0.849456i	0.509506	+	0.860467i	$0.329828\pi$
$180$	−2.21837	−	1.28078i	−0.165348	−	0.0954634i
$181$	−9.68466			−0.719855			−0.359927	−	0.932980i	$-0.617199\pi$
$181$	−9.68466			−0.719855			−0.359927	+	0.932980i	$0.617199\pi$
$182$		0			0
$183$	12.1231			0.896166
$184$	11.3649	+	6.56155i	0.837835	+	0.483724i
$185$	−0.965435	+	1.67218i	−0.0709802	+	0.122941i
$186$	−2.00000	−	3.46410i	−0.146647	−	0.254000i
$187$			5.12311i			0.374639i
$188$	32.5760	−	18.8078i	2.37585	−	1.37170i
$189$	−3.08440	+	1.78078i	−0.224357	+	0.129532i
$190$		−	1.61553i		−	0.117203i
$191$	0.438447	+	0.759413i	0.0317249	+	0.0549492i	0.881452	−	0.472274i	$-0.156567\pi$
$191$	0.438447	+	0.759413i	0.0317249	+	0.0549492i	−0.849727	+	0.527223i	$0.823233\pi$
$192$	0.719224	−	1.24573i	0.0519055	−	0.0899029i
$193$	−16.8809	−	9.74621i	−1.21512	−	0.701548i	−0.251247	−	0.967923i	$-0.580841\pi$
$193$	−16.8809	−	9.74621i	−1.21512	−	0.701548i	−0.963869	+	0.266375i	$0.914174\pi$
$194$	11.3693			0.816269
$195$		0			0
$196$	25.9309			1.85220
$197$	−9.84612	−	5.68466i	−0.701507	−	0.405015i	0.106402	−	0.994323i	$-0.466067\pi$
$197$	−9.84612	−	5.68466i	−0.701507	−	0.405015i	−0.807908	+	0.589308i	$0.799400\pi$
$198$	2.56155	−	4.43674i	0.182042	−	0.315305i
$199$	−11.5885	−	20.0719i	−0.821490	−	1.42286i	−0.904573	−	0.426320i	$-0.859810\pi$
$199$	−11.5885	−	20.0719i	−0.821490	−	1.42286i	0.0830828	−	0.996543i	$-0.473523\pi$
$200$			30.7386i			2.17355i
$201$	−0.379706	+	0.219224i	−0.0267824	+	0.0154628i
$202$	−7.62775	+	4.40388i	−0.536686	+	0.309856i
$203$			20.2462i			1.42101i
$204$	−5.84233	−	10.1192i	−0.409045	−	0.708486i
$205$	0.719224	−	1.24573i	0.0502328	−	0.0870057i
$206$	16.7743	+	9.68466i	1.16872	+	0.674762i
$207$	−2.00000			−0.139010
$208$		0			0
$209$	2.24621			0.155374
$210$	−4.43674	−	2.56155i	−0.306164	−	0.176764i
$211$	−3.65767	+	6.33527i	−0.251804	+	0.436138i	−0.964023	−	0.265820i	$-0.914357\pi$
$211$	−3.65767	+	6.33527i	−0.251804	+	0.436138i	0.712218	+	0.701958i	$0.247691\pi$
$212$	26.6501	+	46.1593i	1.83034	+	3.17023i
$213$		−	14.0000i		−	0.959264i
$214$	−18.2931	+	10.5616i	−1.25049	+	0.721973i
$215$	0.213225	−	0.123106i	0.0145418	−	0.00839573i
$216$			6.56155i			0.446457i
$217$	−2.78078	−	4.81645i	−0.188771	−	0.326962i
$218$	22.8078	−	39.5042i	1.54474	−	2.67556i
$219$	1.62544	+	0.938447i	0.109837	+	0.0634144i
$220$	5.12311			0.345400
$221$		0			0
$222$	8.80776			0.591138
$223$	6.92820	+	4.00000i	0.463947	+	0.267860i	0.713702	−	0.700449i	$-0.247017\pi$
$223$	6.92820	+	4.00000i	0.463947	+	0.267860i	−0.249756	+	0.968309i	$0.580350\pi$
$224$	11.6847	−	20.2384i	0.780714	−	1.35224i
$225$	−2.34233	−	4.05703i	−0.156155	−	0.270469i
$226$			37.9309i			2.52312i
$227$	0.972638	−	0.561553i	0.0645563	−	0.0372716i	−0.467374	−	0.884059i	$-0.654800\pi$
$227$	0.972638	−	0.561553i	0.0645563	−	0.0372716i	0.531931	+	0.846788i	$0.321467\pi$
$228$	−4.43674	+	2.56155i	−0.293830	+	0.169643i
$229$			0.246211i			0.0162701i	0.999967	+	0.00813505i	$0.00258949\pi$
$229$			0.246211i			0.0162701i	−0.999967	+	0.00813505i	$0.997411\pi$
$230$	−1.43845	−	2.49146i	−0.0948484	−	0.164282i
$231$	3.56155	−	6.16879i	0.234333	−	0.405877i
$232$	32.3029	+	18.6501i	2.12079	+	1.22444i
$233$	−26.0000			−1.70332			−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−26.0000			−1.70332			−0.851658	+	0.524097i	$0.824403\pi$
$234$		0			0
$235$	−4.63068			−0.302072
$236$	−43.9409	−	25.3693i	−2.86031	−	1.65140i
$237$	−4.78078	+	8.28055i	−0.310545	+	0.537879i
$238$	−11.6847	−	20.2384i	−0.757404	−	1.31186i
$239$			0.630683i			0.0407955i	0.999792	+	0.0203977i	$0.00649326\pi$
$239$			0.630683i			0.0407955i	−0.999792	+	0.0203977i	$0.993507\pi$
$240$	−3.73720	+	2.15767i	−0.241235	+	0.139277i
$241$	2.43160	−	1.40388i	0.156633	−	0.0904320i	−0.419635	−	0.907693i	$-0.637842\pi$
$241$	2.43160	−	1.40388i	0.156633	−	0.0904320i	0.576268	+	0.817261i	$0.304509\pi$
$242$		−	17.9309i		−	1.15264i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	27.6501	−	47.8914i	1.77012	−	3.06593i
$245$	−2.76456	−	1.59612i	−0.176621	−	0.101972i
$246$	−6.56155			−0.418349
$247$		0			0
$248$	−10.2462			−0.650635
$249$	−7.90084	−	4.56155i	−0.500695	−	0.289077i
$250$	6.96543	−	12.0645i	0.440533	−	0.763025i
$251$	−15.3693	−	26.6204i	−0.970103	−	1.68027i	−0.695231	−	0.718786i	$-0.744698\pi$
$251$	−15.3693	−	26.6204i	−0.970103	−	1.68027i	−0.274871	−	0.961481i	$-0.588635\pi$
$252$			16.2462i			1.02342i
$253$	3.46410	−	2.00000i	0.217786	−	0.125739i
$254$	21.2111	−	12.2462i	1.33090	−	0.768396i
$255$			1.43845i			0.0900791i
$256$	13.5270	+	23.4294i	0.845437	+	1.46434i
$257$	−8.08854	+	14.0098i	−0.504549	+	0.873905i	0.495437	+	0.868644i	$0.335008\pi$
$257$	−8.08854	+	14.0098i	−0.504549	+	0.873905i	−0.999986	+	0.00526106i	$0.998325\pi$
$258$	−0.972638	−	0.561553i	−0.0605538	−	0.0349608i
$259$	12.2462			0.760943
$260$		0			0
$261$	−5.68466			−0.351872
$262$	−38.5316	−	22.2462i	−2.38049	−	1.37438i
$263$	7.68466	−	13.3102i	0.473856	−	0.820743i	−0.525696	−	0.850673i	$-0.676195\pi$
$263$	7.68466	−	13.3102i	0.473856	−	0.820743i	0.999552	+	0.0299295i	$0.00952826\pi$
$264$	−6.56155	−	11.3649i	−0.403836	−	0.699464i
$265$		−	6.56155i		−	0.403073i
$266$	−8.87348	+	5.12311i	−0.544068	+	0.314118i
$267$	11.3649	−	6.56155i	0.695523	−	0.401561i
$268$			2.00000i			0.122169i
$269$	−1.68466	−	2.91791i	−0.102715	−	0.177908i	0.810087	−	0.586310i	$-0.199420\pi$
$269$	−1.68466	−	2.91791i	−0.102715	−	0.177908i	−0.912803	+	0.408401i	$0.866086\pi$
$270$	0.719224	−	1.24573i	0.0437706	−	0.0758128i
$271$	0.925894	+	0.534565i	0.0562441	+	0.0324725i	0.527858	−	0.849332i	$-0.322995\pi$
$271$	0.925894	+	0.534565i	0.0562441	+	0.0324725i	−0.471614	+	0.881805i	$0.656329\pi$
$272$	−19.6847			−1.19356
$273$		0			0
$274$	−3.68466			−0.222598
$275$	8.11407	+	4.68466i	0.489297	+	0.282496i
$276$	−4.56155	+	7.90084i	−0.274573	+	0.475575i
$277$	8.84233	+	15.3154i	0.531284	+	0.920211i	0.999333	+	0.0365086i	$0.0116236\pi$
$277$	8.84233	+	15.3154i	0.531284	+	0.920211i	−0.468049	+	0.883702i	$0.655043\pi$
$278$		−	28.0000i		−	1.67933i
$279$	1.35234	−	0.780776i	0.0809627	−	0.0467439i
$280$	−11.3649	+	6.56155i	−0.679185	+	0.392128i
$281$		−	2.80776i		−	0.167497i	−0.996487	−	0.0837486i	$-0.973311\pi$
$281$		−	2.80776i		−	0.167497i	0.996487	−	0.0837486i	$-0.0266893\pi$
$282$	10.5616	+	18.2931i	0.628931	+	1.08934i
$283$	−0.657671	+	1.13912i	−0.0390945	+	0.0677136i	−0.884911	−	0.465761i	$-0.845781\pi$
$283$	−0.657671	+	1.13912i	−0.0390945	+	0.0677136i	0.845816	+	0.533475i	$0.179114\pi$
$284$	−55.3059	−	31.9309i	−3.28180	−	1.89475i
$285$	0.630683			0.0373584
$286$		0			0
$287$	−9.12311			−0.538520
$288$	5.68247	+	3.28078i	0.334843	+	0.193322i
$289$	5.21922	−	9.03996i	0.307013	−	0.531762i
$290$	−4.08854	−	7.08156i	−0.240087	−	0.415844i
$291$			4.43845i			0.260186i
$292$	7.41452	−	4.28078i	0.433902	−	0.250513i
$293$	21.2709	−	12.2808i	1.24266	−	0.717451i	0.273026	−	0.962007i	$-0.411976\pi$
$293$	21.2709	−	12.2808i	1.24266	−	0.717451i	0.969635	+	0.244556i	$0.0786422\pi$
$294$			14.5616i			0.849247i
$295$	3.12311	+	5.40938i	0.181834	+	0.314946i
$296$	11.2808	−	19.5389i	0.655682	−	1.13567i
$297$	1.73205	+	1.00000i	0.100504	+	0.0580259i
$298$	16.8078			0.973648
$299$		0			0
$300$	−21.3693			−1.23376
$301$	−1.35234	−	0.780776i	−0.0779478	−	0.0450032i
$302$	−19.6847	+	34.0948i	−1.13272	+	1.96194i
$303$	−1.71922	−	2.97778i	−0.0987668	−	0.171069i
$304$			8.63068i			0.495004i
$305$	−5.89570	+	3.40388i	−0.337587	+	0.194906i
$306$	5.68247	−	3.28078i	0.324845	−	0.187550i
$307$			10.1922i			0.581702i	0.956768	+	0.290851i	$0.0939383\pi$
$307$			10.1922i			0.581702i	−0.956768	+	0.290851i	$0.906062\pi$
$308$	−16.2462	−	28.1393i	−0.925714	−	1.60338i
$309$	−3.78078	+	6.54850i	−0.215081	+	0.372531i
$310$	1.94528	+	1.12311i	0.110484	+	0.0637881i
$311$	10.8769			0.616772			0.308386	−	0.951261i	$-0.400211\pi$
$311$	10.8769			0.616772			0.308386	+	0.951261i	$0.400211\pi$
$312$		0			0
$313$	−1.31534			−0.0743475			−0.0371738	−	0.999309i	$-0.511835\pi$
$313$	−1.31534			−0.0743475			−0.0371738	+	0.999309i	$0.511835\pi$
$314$	−9.69276	−	5.59612i	−0.546994	−	0.315807i
$315$	1.00000	−	1.73205i	0.0563436	−	0.0975900i
$316$	21.8078	+	37.7722i	1.22678	+	2.12485i
$317$			23.0540i			1.29484i	0.762133	+	0.647420i	$0.224152\pi$
$317$			23.0540i			1.29484i	−0.762133	+	0.647420i	$0.775848\pi$
$318$	−25.9209	+	14.9654i	−1.45357	+	0.839220i
$319$	9.84612	−	5.68466i	0.551277	−	0.318280i
$320$			0.807764i			0.0451554i
$321$	−4.12311	−	7.14143i	−0.230129	−	0.398596i
$322$	−9.12311	+	15.8017i	−0.508411	+	0.880593i
$323$	2.49146	+	1.43845i	0.138629	+	0.0800373i
$324$	−4.56155			−0.253420
$325$		0			0
$326$	40.4924			2.24267
$327$	15.4220	+	8.90388i	0.852837	+	0.492386i
$328$	−8.40388	+	14.5560i	−0.464027	+	0.803718i
$329$	14.6847	+	25.4346i	0.809591	+	1.40225i
$330$			2.87689i			0.158368i
$331$	20.6181	−	11.9039i	1.13327	−	0.654297i	0.188518	−	0.982070i	$-0.439631\pi$
$331$	20.6181	−	11.9039i	1.13327	−	0.654297i	0.944756	+	0.327773i	$0.106298\pi$
$332$	−36.0401	+	20.8078i	−1.97796	+	1.14197i
$333$			3.43845i			0.188426i
$334$	8.00000	+	13.8564i	0.437741	+	0.758189i
$335$	0.123106	−	0.213225i	0.00672598	−	0.0116497i
$336$	23.7025	+	13.6847i	1.29308	+	0.746559i
$337$	−2.12311			−0.115653			−0.0578265	−	0.998327i	$-0.518417\pi$
$337$	−2.12311			−0.115653			−0.0578265	+	0.998327i	$0.518417\pi$
$338$		0			0
$339$	−14.8078			−0.804247
$340$	5.68247	+	3.28078i	0.308175	+	0.177925i
$341$	−1.56155	+	2.70469i	−0.0845628	+	0.146467i
$342$	−1.43845	−	2.49146i	−0.0777823	−	0.134723i
$343$		−	4.68466i		−	0.252948i
$344$	−2.49146	+	1.43845i	−0.134331	+	0.0775559i
$345$	0.972638	−	0.561553i	0.0523651	−	0.0302330i
$346$			9.61553i			0.516934i
$347$	6.80776	+	11.7914i	0.365460	+	0.632995i	0.988850	−	0.148916i	$-0.0475784\pi$
$347$	6.80776	+	11.7914i	0.365460	+	0.632995i	−0.623390	+	0.781911i	$0.714245\pi$
$348$	−12.9654	+	22.4568i	−0.695020	+	1.20381i
$349$	11.9579	+	6.90388i	0.640090	+	0.369556i	0.784649	−	0.619940i	$-0.212843\pi$
$349$	11.9579	+	6.90388i	0.640090	+	0.369556i	−0.144559	+	0.989496i	$0.546176\pi$
$350$	−42.7386			−2.28448
$351$		0			0
$352$	−13.1231			−0.699464
$353$	15.3154	+	8.84233i	0.815155	+	0.470630i	0.848743	−	0.528806i	$-0.177360\pi$
$353$	15.3154	+	8.84233i	0.815155	+	0.470630i	−0.0335881	+	0.999436i	$0.510693\pi$
$354$	14.2462	−	24.6752i	0.757178	−	1.31147i
$355$	3.93087	+	6.80847i	0.208629	+	0.361356i
$356$		−	59.8617i		−	3.17267i
$357$	7.90084	−	4.56155i	0.418157	−	0.241423i
$358$	−29.1119	+	16.8078i	−1.53861	+	0.888318i
$359$			15.3693i			0.811162i	0.914059	+	0.405581i	$0.132931\pi$
$359$			15.3693i			0.811162i	−0.914059	+	0.405581i	$0.867069\pi$
$360$	−1.84233	−	3.19101i	−0.0970993	−	0.168181i
$361$	−8.86932	+	15.3621i	−0.466806	+	0.808532i
$362$	−21.4842	−	12.4039i	−1.12918	−	0.651934i
$363$	7.00000			0.367405
$364$		0			0
$365$	−1.05398			−0.0551676
$366$	26.8935	+	15.5270i	1.40575	+	0.811609i
$367$	−10.0270	+	17.3673i	−0.523404	+	0.906563i	0.476224	+	0.879324i	$0.342005\pi$
$367$	−10.0270	+	17.3673i	−0.523404	+	0.906563i	−0.999629	+	0.0272394i	$0.991328\pi$
$368$	7.68466	+	13.3102i	0.400591	+	0.693843i
$369$		−	2.56155i		−	0.133349i
$370$	−4.28338	+	2.47301i	−0.222682	+	0.128566i
$371$	−36.0401	+	20.8078i	−1.87111	+	1.08029i
$372$		−	7.12311i		−	0.369316i
$373$	−1.81534	−	3.14426i	−0.0939948	−	0.162804i	0.815194	−	0.579188i	$-0.196630\pi$
$373$	−1.81534	−	3.14426i	−0.0939948	−	0.162804i	−0.909189	+	0.416384i	$0.863297\pi$
$374$	−6.56155	+	11.3649i	−0.339290	+	0.587667i
$375$	4.70983	+	2.71922i	0.243215	+	0.140420i
$376$	54.1080			2.79040
$377$		0			0
$378$	−9.12311			−0.469242
$379$	9.79937	+	5.65767i	0.503360	+	0.290615i	0.730100	−	0.683340i	$-0.239473\pi$
$379$	9.79937	+	5.65767i	0.503360	+	0.290615i	−0.226740	+	0.973955i	$0.572807\pi$
$380$	1.43845	−	2.49146i	0.0737908	−	0.127809i
$381$	4.78078	+	8.28055i	0.244927	+	0.424225i
$382$			2.24621i			0.114926i
$383$	−23.1563	+	13.3693i	−1.18323	+	0.683140i	−0.956760	−	0.290877i	$-0.906053\pi$
$383$	−23.1563	+	13.3693i	−1.18323	+	0.683140i	−0.226473	+	0.974017i	$0.572720\pi$
$384$	−8.17394	+	4.71922i	−0.417124	+	0.240827i
$385$			4.00000i			0.203859i
$386$	−24.9654	−	43.2414i	−1.27071	−	2.20093i
$387$	0.219224	−	0.379706i	0.0111438	−	0.0193016i
$388$	17.5337	+	10.1231i	0.890140	+	0.513923i
$389$	3.05398			0.154843			0.0774213	−	0.996998i	$-0.475331\pi$
$389$	3.05398			0.154843			0.0774213	+	0.996998i	$0.475331\pi$
$390$		0			0
$391$	5.12311			0.259087
$392$	32.3029	+	18.6501i	1.63154	+	0.941972i
$393$	8.68466	−	15.0423i	0.438083	−	0.758782i
$394$	−14.5616	−	25.2213i	−0.733600	−	1.27063i
$395$		−	5.36932i		−	0.270160i
$396$	7.90084	−	4.56155i	0.397032	−	0.229227i
$397$	−10.4390	+	6.02699i	−0.523921	+	0.302486i	−0.738537	−	0.674213i	$-0.764483\pi$
$397$	−10.4390	+	6.02699i	−0.523921	+	0.302486i	0.214617	+	0.976698i	$0.431150\pi$
$398$		−	59.3693i		−	2.97591i
$399$	−2.00000	−	3.46410i	−0.100125	−	0.173422i
$400$	−18.0000	+	31.1769i	−0.900000	+	1.55885i
$401$	−16.0748	−	9.28078i	−0.802736	−	0.463460i	0.0416909	−	0.999131i	$-0.486726\pi$
$401$	−16.0748	−	9.28078i	−0.802736	−	0.463460i	−0.844427	+	0.535671i	$0.820059\pi$
$402$	−1.12311			−0.0560154
$403$		0			0
$404$	−15.6847			−0.780341
$405$	0.486319	+	0.280776i	0.0241654	+	0.0139519i
$406$	−25.9309	+	44.9136i	−1.28693	+	2.22902i
$407$	−3.43845	−	5.95557i	−0.170437	−	0.295206i
$408$		−	16.8078i		−	0.832108i
$409$	15.9083	−	9.18466i	0.786615	−	0.454152i	−0.0521548	−	0.998639i	$-0.516609\pi$
$409$	15.9083	−	9.18466i	0.786615	−	0.454152i	0.838769	+	0.544487i	$0.183276\pi$
$410$	3.19101	−	1.84233i	0.157593	−	0.0909862i
$411$		−	1.43845i		−	0.0709534i
$412$	17.2462	+	29.8713i	0.849660	+	1.47165i
$413$	19.8078	−	34.3081i	0.974676	−	1.68819i
$414$	−4.43674	−	2.56155i	−0.218054	−	0.125893i
$415$	5.12311			0.251483
$416$		0			0
$417$	10.9309			0.535287
$418$	4.98293	+	2.87689i	0.243723	+	0.140714i
$419$	8.87689	−	15.3752i	0.433665	−	0.751129i	−0.563521	−	0.826102i	$-0.690554\pi$
$419$	8.87689	−	15.3752i	0.433665	−	0.751129i	0.997186	+	0.0749725i	$0.0238869\pi$
$420$	−4.56155	−	7.90084i	−0.222581	−	0.385522i
$421$		−	14.7538i		−	0.719056i	−0.933134	−	0.359528i	$-0.882938\pi$
$421$		−	14.7538i		−	0.719056i	0.933134	−	0.359528i	$-0.117062\pi$
$422$	−16.2281	+	9.36932i	−0.789973	+	0.456091i
$423$	−7.14143	+	4.12311i	−0.347228	+	0.200472i
$424$			76.6695i			3.72340i
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$	17.9309	−	31.0572i	0.868753	−	1.50473i
$427$	37.3924	+	21.5885i	1.80955	+	1.04474i
$428$	−37.6155			−1.81822
$429$		0			0
$430$	0.630683			0.0304142
$431$	−2.49146	−	1.43845i	−0.120010	−	0.0692876i	0.438794	−	0.898588i	$-0.355406\pi$
$431$	−2.49146	−	1.43845i	−0.120010	−	0.0692876i	−0.558803	+	0.829300i	$0.688739\pi$
$432$	−3.84233	+	6.65511i	−0.184864	+	0.320194i
$433$	12.6231	+	21.8639i	0.606628	+	1.05071i	0.991792	+	0.127862i	$0.0408115\pi$
$433$	12.6231	+	21.8639i	0.606628	+	1.05071i	−0.385164	+	0.922848i	$0.625855\pi$
$434$		−	14.2462i		−	0.683840i
$435$	2.76456	−	1.59612i	0.132550	−	0.0765280i
$436$	70.3482	−	40.6155i	3.36907	−	1.94513i
$437$		−	2.24621i		−	0.107451i
$438$	2.40388	+	4.16365i	0.114862	+	0.198947i
$439$	−0.657671	+	1.13912i	−0.0313889	+	0.0543672i	−0.881293	−	0.472570i	$-0.843326\pi$
$439$	−0.657671	+	1.13912i	−0.0313889	+	0.0543672i	0.849904	+	0.526937i	$0.176660\pi$
$440$	6.38202	+	3.68466i	0.304251	+	0.175659i
$441$	−5.68466			−0.270698
$442$		0			0
$443$	14.7386			0.700254			0.350127	−	0.936702i	$-0.386138\pi$
$443$	14.7386			0.700254			0.350127	+	0.936702i	$0.386138\pi$
$444$	13.5833	+	7.84233i	0.644635	+	0.372180i
$445$	−3.68466	+	6.38202i	−0.174670	+	0.302537i
$446$	10.2462	+	17.7470i	0.485172	+	0.840343i
$447$			6.56155i			0.310351i
$448$	4.43674	−	2.56155i	0.209616	−	0.121022i
$449$	7.14143	−	4.12311i	0.337025	−	0.194581i	−0.321931	−	0.946763i	$-0.604332\pi$
$449$	7.14143	−	4.12311i	0.337025	−	0.194581i	0.658956	+	0.752182i	$0.270998\pi$
$450$		−	12.0000i		−	0.565685i
$451$	2.56155	+	4.43674i	0.120619	+	0.208918i
$452$	−33.7732	+	58.4969i	−1.58856	+	2.75146i
$453$	−13.3102	−	7.68466i	−0.625369	−	0.361057i
$454$	2.87689			0.135019
$455$		0			0
$456$	−7.36932			−0.345100
$457$	−24.7818	−	14.3078i	−1.15924	−	0.669289i	−0.208120	−	0.978103i	$-0.566735\pi$
$457$	−24.7818	−	14.3078i	−1.15924	−	0.669289i	−0.951122	+	0.308814i	$0.900068\pi$
$458$	−0.315342	+	0.546188i	−0.0147349	+	0.0255217i
$459$	1.28078	+	2.21837i	0.0597815	+	0.103545i
$460$		−	5.12311i		−	0.238866i
$461$	31.8765	−	18.4039i	1.48463	−	0.857154i	0.484787	−	0.874632i	$-0.338897\pi$
$461$	31.8765	−	18.4039i	1.48463	−	0.857154i	0.999847	+	0.0174778i	$0.00556363\pi$
$462$	15.8017	−	9.12311i	0.735161	−	0.424445i
$463$		−	26.6847i		−	1.24014i	−0.784546	−	0.620071i	$-0.787104\pi$
$463$		−	26.6847i		−	1.24014i	0.784546	−	0.620071i	$-0.212896\pi$
$464$	21.8423	+	37.8320i	1.01400	+	1.75631i
$465$	−0.438447	+	0.759413i	−0.0203325	+	0.0352169i
$466$	−57.6776	−	33.3002i	−2.67186	−	1.54260i
$467$	26.0000			1.20314			0.601568	−	0.798821i	$-0.294543\pi$
$467$	26.0000			1.20314			0.601568	+	0.798821i	$0.294543\pi$
$468$		0			0
$469$	−1.56155			−0.0721058
$470$	−10.2726	−	5.93087i	−0.473838	−	0.273571i
$471$	2.18466	−	3.78394i	0.100664	−	0.174355i
$472$	−36.4924	−	63.2067i	−1.67970	−	2.90933i
$473$			0.876894i			0.0403196i
$474$	−21.2111	+	12.2462i	−0.974256	+	0.562487i
$475$	4.55648	−	2.63068i	0.209065	−	0.120704i
$476$		−	41.6155i		−	1.90744i
$477$	−5.84233	−	10.1192i	−0.267502	−	0.463327i
$478$	−0.807764	+	1.39909i	−0.0369463	+	0.0639928i
$479$	5.40938	+	3.12311i	0.247161	+	0.142698i	0.618463	−	0.785814i	$-0.287755\pi$
$479$	5.40938	+	3.12311i	0.247161	+	0.142698i	−0.371303	+	0.928512i	$0.621089\pi$
$480$	−3.68466			−0.168181
$481$		0			0
$482$	7.19224			0.327597
$483$	−6.16879	−	3.56155i	−0.280690	−	0.162056i
$484$	15.9654	−	27.6529i	0.725702	−	1.25695i
$485$	−1.24621	−	2.15850i	−0.0565875	−	0.0980125i
$486$		−	2.56155i		−	0.116194i
$487$	0.972638	−	0.561553i	0.0440744	−	0.0254464i	−0.477801	−	0.878468i	$-0.658566\pi$
$487$	0.972638	−	0.561553i	0.0440744	−	0.0254464i	0.521875	+	0.853022i	$0.325233\pi$
$488$	68.8892	−	39.7732i	3.11847	−	1.80045i
$489$			15.8078i			0.714852i
$490$	−4.08854	−	7.08156i	−0.184701	−	0.319912i
$491$	−9.87689	+	17.1073i	−0.445738	+	0.772041i	−0.998103	−	0.0615613i	$-0.980392\pi$
$491$	−9.87689	+	17.1073i	−0.445738	+	0.772041i	0.552365	+	0.833602i	$0.313725\pi$
$492$	−10.1192	−	5.84233i	−0.456209	−	0.263393i
$493$	14.5616			0.655819
$494$		0			0
$495$	−1.12311			−0.0504798
$496$	−10.3923	−	6.00000i	−0.466628	−	0.269408i
$497$	24.9309	−	43.1815i	1.11830	−	1.93696i
$498$	−11.6847	−	20.2384i	−0.523602	−	0.906905i
$499$			28.4924i			1.27550i	0.770245	+	0.637748i	$0.220134\pi$
$499$			28.4924i			1.27550i	−0.770245	+	0.637748i	$0.779866\pi$
$500$	21.4842	−	12.4039i	0.960801	−	0.554718i
$501$	−5.40938	+	3.12311i	−0.241673	+	0.139530i
$502$		−	78.7386i		−	3.51428i
$503$	5.87689	+	10.1791i	0.262038	+	0.453863i	0.966783	−	0.255597i	$-0.0822722\pi$
$503$	5.87689	+	10.1791i	0.262038	+	0.453863i	−0.704746	+	0.709460i	$0.748939\pi$
$504$	−11.6847	+	20.2384i	−0.520476	+	0.901491i
$505$	1.67218	+	0.965435i	0.0744111	+	0.0429613i
$506$	10.2462			0.455500
$507$		0			0
$508$	43.6155			1.93513
$509$	5.89570	+	3.40388i	0.261322	+	0.150874i	0.624938	−	0.780675i	$-0.285124\pi$
$509$	5.89570	+	3.40388i	0.261322	+	0.150874i	−0.363615	+	0.931549i	$0.618458\pi$
$510$	−1.84233	+	3.19101i	−0.0815797	+	0.141300i
$511$	3.34233	+	5.78908i	0.147856	+	0.256094i
$512$			50.4233i			2.22842i
$513$	0.972638	−	0.561553i	0.0429430	−	0.0247932i
$514$	−35.8867	+	20.7192i	−1.58290	+	0.913886i
$515$		−	4.24621i		−	0.187110i
$516$	−1.00000	−	1.73205i	−0.0440225	−	0.0762493i
$517$	8.24621	−	14.2829i	0.362668	−	0.628159i
$518$	27.1666	+	15.6847i	1.19363	+	0.689144i
$519$	−3.75379			−0.164773
$520$		0			0
$521$	−37.9309			−1.66178			−0.830891	−	0.556436i	$-0.812169\pi$
$521$	−37.9309			−1.66178			−0.830891	+	0.556436i	$0.812169\pi$
$522$	−12.6107	−	7.28078i	−0.551954	−	0.318671i
$523$	11.9309	−	20.6649i	0.521701	−	0.903612i	−0.477981	−	0.878370i	$-0.658631\pi$
$523$	11.9309	−	20.6649i	0.521701	−	0.903612i	0.999681	−	0.0252415i	$-0.00803549\pi$
$524$	−39.6155	−	68.6161i	−1.73061	−	2.99751i
$525$		−	16.6847i		−	0.728178i
$526$	34.0948	−	19.6847i	1.48661	−	0.858292i
$527$	−3.46410	+	2.00000i	−0.150899	+	0.0871214i
$528$		−	15.3693i		−	0.668864i
$529$	9.50000	+	16.4545i	0.413043	+	0.715412i
$530$	8.40388	−	14.5560i	0.365041	−	0.632270i
$531$	9.63289	+	5.56155i	0.418032	+	0.241351i
$532$	−18.2462			−0.791074
$533$		0			0
$534$	33.6155			1.45469
$535$	4.01029	+	2.31534i	0.173380	+	0.100101i
$536$	−1.43845	+	2.49146i	−0.0621315	+	0.107615i
$537$	−6.56155	−	11.3649i	−0.283152	−	0.490433i
$538$		−	8.63068i		−	0.372095i
$539$	9.84612	−	5.68466i	0.424102	−	0.244856i
$540$	2.21837	−	1.28078i	0.0954634	−	0.0551158i
$541$		−	29.7386i		−	1.27856i	−0.768972	−	0.639282i	$-0.779232\pi$
$541$		−	29.7386i		−	1.27856i	0.768972	−	0.639282i	$-0.220768\pi$
$542$	1.36932	+	2.37173i	0.0588172	+	0.101874i
$543$	4.84233	−	8.38716i	0.207804	−	0.359927i
$544$	−14.5560	−	8.40388i	−0.624081	−	0.360313i
$545$	−10.0000			−0.428353
$546$		0			0
$547$	−24.9309			−1.06597			−0.532984	−	0.846126i	$-0.678929\pi$
$547$	−24.9309			−1.06597			−0.532984	+	0.846126i	$0.678929\pi$
$548$	−5.68247	−	3.28078i	−0.242743	−	0.140148i
$549$	−6.06155	+	10.4989i	−0.258701	+	0.448083i
$550$	12.0000	+	20.7846i	0.511682	+	0.886259i
$551$		−	6.38447i		−	0.271988i
$552$	−11.3649	+	6.56155i	−0.483724	+	0.279278i
$553$	−29.4916	+	17.0270i	−1.25411	+	0.724061i
$554$			45.3002i			1.92462i
$555$	−0.965435	−	1.67218i	−0.0409804	−	0.0709802i
$556$	24.9309	−	43.1815i	1.05730	−	1.83130i
$557$	12.1842	+	7.03457i	0.516262	+	0.298064i	0.735404	−	0.677629i	$-0.236992\pi$
$557$	12.1842	+	7.03457i	0.516262	+	0.298064i	−0.219142	+	0.975693i	$0.570326\pi$
$558$	4.00000			0.169334
$559$		0			0
$560$	−15.3693			−0.649472
$561$	−4.43674	−	2.56155i	−0.187319	−	0.108149i
$562$	3.59612	−	6.22866i	0.151693	−	0.262740i
$563$	0.684658	+	1.18586i	0.0288549	+	0.0499782i	0.880092	−	0.474803i	$-0.157481\pi$
$563$	0.684658	+	1.18586i	0.0288549	+	0.0499782i	−0.851237	+	0.524781i	$0.824147\pi$
$564$			37.6155i			1.58390i
$565$	7.20130	−	4.15767i	0.302961	−	0.174915i
$566$	−2.91791	+	1.68466i	−0.122649	+	0.0708115i
$567$		−	3.56155i		−	0.149571i
$568$	−45.9309	−	79.5546i	−1.92722	−	3.33804i
$569$	20.3693	−	35.2807i	0.853926	−	1.47904i	−0.0237115	−	0.999719i	$-0.507548\pi$
$569$	20.3693	−	35.2807i	0.853926	−	1.47904i	0.877638	−	0.479325i	$-0.159118\pi$
$570$	1.39909	+	0.807764i	0.0586014	+	0.0338335i
$571$	−19.3693			−0.810581			−0.405290	−	0.914188i	$-0.632830\pi$
$571$	−19.3693			−0.810581			−0.405290	+	0.914188i	$0.632830\pi$
$572$		0			0
$573$	−0.876894			−0.0366328
$574$	−20.2384	−	11.6847i	−0.844735	−	0.487708i
$575$	4.68466	−	8.11407i	0.195364	−	0.338380i
$576$	0.719224	+	1.24573i	0.0299676	+	0.0519055i
$577$			29.6847i			1.23579i	0.786261	+	0.617894i	$0.212014\pi$
$577$			29.6847i			1.23579i	−0.786261	+	0.617894i	$0.787986\pi$
$578$	23.1563	−	13.3693i	0.963177	−	0.556090i
$579$	16.8809	−	9.74621i	0.701548	−	0.405039i
$580$		−	14.5616i		−	0.604636i
$581$	−16.2462	−	28.1393i	−0.674006	−	1.16741i
$582$	−5.68466	+	9.84612i	−0.235637	+	0.408135i
$583$	20.2384	+	11.6847i	0.838190	+	0.483929i
$584$	12.3153			0.509612
$585$		0			0
$586$	62.9157			2.59902
$587$	12.6705	+	7.31534i	0.522969	+	0.301936i	0.738149	−	0.674638i	$-0.235700\pi$
$587$	12.6705	+	7.31534i	0.522969	+	0.301936i	−0.215179	+	0.976575i	$0.569034\pi$
$588$	−12.9654	+	22.4568i	−0.534686	+	0.926102i
$589$	0.876894	+	1.51883i	0.0361318	+	0.0625821i
$590$			16.0000i			0.658710i
$591$	9.84612	−	5.68466i	0.405015	−	0.233836i
$592$	22.8832	−	13.2116i	0.940495	−	0.542995i
$593$			44.4233i			1.82425i	0.409917	+	0.912123i	$0.365558\pi$
$593$			44.4233i			1.82425i	−0.409917	+	0.912123i	$0.634442\pi$
$594$	2.56155	+	4.43674i	0.105102	+	0.182042i
$595$	−2.56155	+	4.43674i	−0.105013	+	0.181889i
$596$	25.9209	+	14.9654i	1.06176	+	0.613008i
$597$	23.1771			0.948575
$598$		0			0
$599$	−0.384472			−0.0157091			−0.00785455	−	0.999969i	$-0.502500\pi$
$599$	−0.384472			−0.0157091			−0.00785455	+	0.999969i	$0.502500\pi$
$600$	−26.6204	−	15.3693i	−1.08677	−	0.627450i
$601$	17.9654	−	31.1170i	0.732825	−	1.26929i	−0.222846	−	0.974854i	$-0.571535\pi$
$601$	17.9654	−	31.1170i	0.732825	−	1.26929i	0.955671	−	0.294437i	$-0.0951321\pi$
$602$	−2.00000	−	3.46410i	−0.0815139	−	0.141186i
$603$		−	0.438447i		−	0.0178549i
$604$	−60.7153	+	35.0540i	−2.47047	+	1.42633i
$605$	−3.40423	+	1.96543i	−0.138402	+	0.0799063i
$606$		−	8.80776i		−	0.357791i
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	0.981454	−	0.191700i	$-0.0614000\pi$
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	−0.656744	+	0.754114i	$0.728067\pi$
$608$	−3.68466	+	6.38202i	−0.149433	+	0.258825i
$609$	−17.5337	−	10.1231i	−0.710503	−	0.410209i
$610$	−17.4384			−0.706062
$611$		0			0
$612$	11.6847			0.472324
$613$	19.7988	+	11.4309i	0.799668	+	0.461688i	0.843355	−	0.537357i	$-0.180577\pi$
$613$	19.7988	+	11.4309i	0.799668	+	0.461688i	−0.0436871	+	0.999045i	$0.513910\pi$
$614$	−13.0540	+	22.6101i	−0.526816	+	0.912471i
$615$	0.719224	+	1.24573i	0.0290019	+	0.0502328i
$616$		−	46.7386i		−	1.88315i
$617$	9.35980	−	5.40388i	0.376811	−	0.217552i	−0.299619	−	0.954059i	$-0.596859\pi$
$617$	9.35980	−	5.40388i	0.376811	−	0.217552i	0.676430	+	0.736507i	$0.263526\pi$
$618$	−16.7743	+	9.68466i	−0.674762	+	0.389574i
$619$		−	24.3002i		−	0.976707i	−0.872646	−	0.488353i	$-0.837598\pi$
$619$		−	24.3002i		−	0.976707i	0.872646	−	0.488353i	$-0.162402\pi$
$620$	2.00000	+	3.46410i	0.0803219	+	0.139122i
$621$	1.00000	−	1.73205i	0.0401286	−	0.0695048i
$622$	24.1290	+	13.9309i	0.967484	+	0.558577i
$623$	46.7386			1.87254
$624$		0			0
$625$	20.3693			0.814773
$626$	−2.91791	−	1.68466i	−0.116623	−	0.0673325i
$627$	−1.12311	+	1.94528i	−0.0448525	+	0.0776868i
$628$	−9.96543	−	17.2606i	−0.397664	−	0.688774i
$629$		−	8.80776i		−	0.351189i
$630$	4.43674	−	2.56155i	0.176764	−	0.102055i
$631$	−12.5041	+	7.21922i	−0.497779	+	0.287393i	−0.727796	−	0.685794i	$-0.759455\pi$
$631$	−12.5041	+	7.21922i	−0.497779	+	0.287393i	0.230017	+	0.973187i	$0.426122\pi$
$632$			62.7386i			2.49561i
$633$	−3.65767	−	6.33527i	−0.145379	−	0.251804i
$634$	−29.5270	+	51.1422i	−1.17267	+	2.03112i
$635$	−4.64996	−	2.68466i	−0.184528	−	0.106537i
$636$	−53.3002			−2.11349
$637$		0			0
$638$	29.1231			1.15299
$639$	12.1244	+	7.00000i	0.479632	+	0.276916i
$640$	2.65009	−	4.59010i	0.104754	−	0.181439i
$641$	13.0885	+	22.6700i	0.516966	+	0.895412i	0.999806	+	0.0197030i	$0.00627208\pi$
$641$	13.0885	+	22.6700i	0.516966	+	0.895412i	−0.482840	+	0.875709i	$0.660395\pi$
$642$		−	21.1231i		−	0.833662i
$643$	−33.3822	+	19.2732i	−1.31646	+	0.760061i	−0.983158	−	0.182758i	$-0.941498\pi$
$643$	−33.3822	+	19.2732i	−1.31646	+	0.760061i	−0.333306	+	0.942819i	$0.608164\pi$
$644$	−28.1393	+	16.2462i	−1.10884	+	0.640190i
$645$			0.246211i			0.00969456i
$646$	3.68466	+	6.38202i	0.144971	+	0.251097i
$647$	−23.8078	+	41.2363i	−0.935980	+	1.62116i	−0.163102	+	0.986609i	$0.552150\pi$
$647$	−23.8078	+	41.2363i	−0.935980	+	1.62116i	−0.772877	+	0.634555i	$0.781183\pi$
$648$	−5.68247	−	3.28078i	−0.223229	−	0.128881i
$649$	−22.2462			−0.873240
$650$		0			0
$651$	5.56155			0.217974
$652$	62.4473	+	36.0540i	2.44563	+	1.41198i
$653$	−7.43845	+	12.8838i	−0.291089	+	0.504181i	−0.974068	−	0.226258i	$-0.927351\pi$
$653$	−7.43845	+	12.8838i	−0.291089	+	0.504181i	0.682979	+	0.730438i	$0.260684\pi$
$654$	22.8078	+	39.5042i	0.891854	+	1.54474i
$655$			9.75379i			0.381112i
$656$	−17.0474	+	9.84233i	−0.665590	+	0.384278i
$657$	−1.62544	+	0.938447i	−0.0634144	+	0.0366123i
$658$			75.2311i			2.93281i
$659$	−7.12311	−	12.3376i	−0.277477	−	0.480604i	0.693280	−	0.720668i	$-0.256165\pi$
$659$	−7.12311	−	12.3376i	−0.277477	−	0.480604i	−0.970757	+	0.240064i	$0.922831\pi$
$660$	−2.56155	+	4.43674i	−0.0997083	+	0.172700i
$661$	−26.3006	−	15.1847i	−1.02297	−	0.590615i	−0.108011	−	0.994150i	$-0.534448\pi$
$661$	−26.3006	−	15.1847i	−1.02297	−	0.590615i	−0.914964	+	0.403535i	$0.867781\pi$
$662$	60.9848			2.37024
$663$		0			0
$664$	−59.8617			−2.32309
$665$	1.94528	+	1.12311i	0.0754346	+	0.0435522i
$666$	−4.40388	+	7.62775i	−0.170647	+	0.295569i
$667$	−5.68466	−	9.84612i	−0.220111	−	0.381243i
$668$			28.4924i			1.10240i
$669$	−6.92820	+	4.00000i	−0.267860	+	0.154649i
$670$	0.546188	−	0.315342i	0.0211011	−	0.0121827i
$671$		−	24.2462i		−	0.936015i
$672$	11.6847	+	20.2384i	0.450745	+	0.780714i
$673$	−3.37689	+	5.84895i	−0.130170	+	0.225461i	−0.923742	−	0.383016i	$-0.874886\pi$
$673$	−3.37689	+	5.84895i	−0.130170	+	0.225461i	0.793572	+	0.608476i	$0.208219\pi$
$674$	−4.70983	−	2.71922i	−0.181416	−	0.104741i
$675$	4.68466			0.180313
$676$		0			0
$677$	25.6155			0.984485			0.492242	−	0.870458i	$-0.336177\pi$
$677$	25.6155			0.984485			0.492242	+	0.870458i	$0.336177\pi$
$678$	−32.8491	−	18.9654i	−1.26156	−	0.728363i
$679$	−7.90388	+	13.6899i	−0.303323	+	0.525371i
$680$	4.71922	+	8.17394i	0.180974	+	0.313456i
$681$			1.12311i			0.0430375i
$682$	−6.92820	+	4.00000i	−0.265295	+	0.153168i
$683$	31.2704	−	18.0540i	1.19653	−	0.690816i	0.236749	−	0.971571i	$-0.423918\pi$
$683$	31.2704	−	18.0540i	1.19653	−	0.690816i	0.959780	+	0.280755i	$0.0905847\pi$
$684$		−	5.12311i		−	0.195887i
$685$	0.403882	+	0.699544i	0.0154315	+	0.0267282i
$686$	6.00000	−	10.3923i	0.229081	−	0.396780i
$687$	−0.213225	−	0.123106i	−0.00813505	−	0.00469677i
$688$	−3.36932			−0.128454
$689$		0			0
$690$	2.87689			0.109521
$691$	1.99202	+	1.15009i	0.0757800	+	0.0437516i	0.537411	−	0.843320i	$-0.319402\pi$
$691$	1.99202	+	1.15009i	0.0757800	+	0.0437516i	−0.461631	+	0.887072i	$0.652736\pi$
$692$	−8.56155	+	14.8290i	−0.325461	+	0.563716i
$693$	3.56155	+	6.16879i	0.135292	+	0.234333i
$694$			34.8769i			1.32391i
$695$	−5.31589	+	3.06913i	−0.201643	+	0.116419i
$696$	−32.3029	+	18.6501i	−1.22444	+	0.706930i
$697$			6.56155i			0.248537i
$698$	17.6847	+	30.6307i	0.669374	+	1.15939i
$699$	13.0000	−	22.5167i	0.491705	−	0.851658i
$700$	−65.9114	−	38.0540i	−2.49122	−	1.43831i
$701$	−19.3693			−0.731569			−0.365785	−	0.930700i	$-0.619199\pi$
$701$	−19.3693			−0.731569			−0.365785	+	0.930700i	$0.619199\pi$
$702$		0			0
$703$	−3.86174			−0.145648
$704$	−2.49146	−	1.43845i	−0.0939006	−	0.0542135i
$705$	2.31534	−	4.01029i	0.0872008	−	0.151036i
$706$	22.6501	+	39.2311i	0.852448	+	1.47648i
$707$		−	12.2462i		−	0.460566i
$708$	43.9409	−	25.3693i	1.65140	−	0.953437i
$709$	22.0771	−	12.7462i	0.829122	−	0.478694i	−0.0244297	−	0.999702i	$-0.507777\pi$
$709$	22.0771	−	12.7462i	0.829122	−	0.478694i	0.853552	+	0.521008i	$0.174444\pi$
$710$			20.1383i			0.755775i
$711$	−4.78078	−	8.28055i	−0.179293	−	0.310545i
$712$	43.0540	−	74.5717i	1.61352	−	2.79469i
$713$	2.70469	+	1.56155i	0.101291	+	0.0584806i
$714$	23.3693			0.874575
$715$		0			0
$716$	−59.8617			−2.23714
$717$	−0.546188	−	0.315342i	−0.0203977	−	0.0117766i
$718$	−19.6847	+	34.0948i	−0.734625	+	1.27241i
$719$	0.684658	+	1.18586i	0.0255335	+	0.0442252i	0.878510	−	0.477724i	$-0.158538\pi$
$719$	0.684658	+	1.18586i	0.0255335	+	0.0442252i	−0.852976	+	0.521950i	$0.825205\pi$
$720$		−	4.31534i		−	0.160823i
$721$	−23.3228	+	13.4654i	−0.868587	+	0.501479i
$722$	−39.3508	+	22.7192i	−1.46449	+	0.845522i
$723$			2.80776i			0.104422i
$724$	−22.0885	−	38.2585i	−0.820914	−	1.42187i
$725$	13.3153	−	23.0628i	0.494519	−	0.856533i
$726$	15.5286	+	8.96543i	0.576320	+	0.332738i
$727$	−39.6695			−1.47126			−0.735630	−	0.677383i	$-0.763114\pi$
$727$	−39.6695			−1.47126			−0.735630	+	0.677383i	$0.763114\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−2.33811	−	1.34991i	−0.0865372	−	0.0499623i
$731$	−0.561553	+	0.972638i	−0.0207698	+	0.0359743i
$732$	27.6501	+	47.8914i	1.02198	+	1.77012i
$733$		−	53.4924i		−	1.97579i	−0.155131	−	0.987894i	$-0.549580\pi$
$733$		−	53.4924i		−	1.97579i	0.155131	−	0.987894i	$-0.450420\pi$
$734$	−44.4871	+	25.6847i	−1.64205	+	0.948038i
$735$	2.76456	−	1.59612i	0.101972	−	0.0588737i
$736$			13.1231i			0.483724i
$737$	0.438447	+	0.759413i	0.0161504	+	0.0279733i
$738$	3.28078	−	5.68247i	0.120767	−	0.209175i
$739$	5.40938	+	3.12311i	0.198987	+	0.114885i	0.596183	−	0.802849i	$-0.296683\pi$
$739$	5.40938	+	3.12311i	0.198987	+	0.114885i	−0.397196	+	0.917734i	$0.630017\pi$
$740$	−8.80776			−0.323780
$741$		0			0
$742$	−106.600			−3.91342
$743$	−32.3628	−	18.6847i	−1.18728	−	0.685474i	−0.229589	−	0.973288i	$-0.573738\pi$
$743$	−32.3628	−	18.6847i	−1.18728	−	0.685474i	−0.957686	+	0.287814i	$0.907071\pi$
$744$	5.12311	−	8.87348i	0.187822	−	0.325318i
$745$	−1.84233	−	3.19101i	−0.0674977	−	0.116909i
$746$		−	9.30019i		−	0.340504i
$747$	7.90084	−	4.56155i	0.289077	−	0.166898i
$748$	−20.2384	+	11.6847i	−0.739990	+	0.427233i
$749$		−	29.3693i		−	1.07313i
$750$	6.96543	+	12.0645i	0.254342	+	0.440533i
$751$	−15.0540	+	26.0743i	−0.549327	+	0.951463i	0.448993	+	0.893535i	$0.351783\pi$
$751$	−15.0540	+	26.0743i	−0.549327	+	0.951463i	−0.998321	+	0.0579278i	$0.981551\pi$
$752$	54.8794	+	31.6847i	2.00125	+	1.15542i
$753$	30.7386			1.12018
$754$		0			0
$755$	8.63068			0.314103
$756$	−14.0696	−	8.12311i	−0.511708	−	0.295434i
$757$	−15.0000	+	25.9808i	−0.545184	+	0.944287i	0.453411	+	0.891302i	$0.350207\pi$
$757$	−15.0000	+	25.9808i	−0.545184	+	0.944287i	−0.998595	+	0.0529853i	$0.983126\pi$
$758$	14.4924	+	25.1016i	0.526388	+	0.911732i
$759$			4.00000i			0.145191i
$760$	3.58384	−	2.06913i	0.129999	−	0.0750552i
$761$	−13.3102	+	7.68466i	−0.482495	+	0.278569i	−0.721456	−	0.692461i	$-0.756527\pi$
$761$	−13.3102	+	7.68466i	−0.482495	+	0.278569i	0.238961	+	0.971029i	$0.423193\pi$
$762$			24.4924i			0.887267i
$763$	31.7116	+	54.9262i	1.14804	+	1.98846i
$764$	−2.00000	+	3.46410i	−0.0723575	+	0.125327i
$765$	−1.24573	−	0.719224i	−0.0450395	−	0.0260036i
$766$	−68.4924			−2.47473
$767$		0			0
$768$	−27.0540			−0.976226
$769$	−15.5885	−	9.00000i	−0.562134	−	0.324548i	0.191867	−	0.981421i	$-0.438546\pi$
$769$	−15.5885	−	9.00000i	−0.562134	−	0.324548i	−0.754002	+	0.656873i	$0.771879\pi$
$770$	−5.12311	+	8.87348i	−0.184624	+	0.319778i
$771$	−8.08854	−	14.0098i	−0.291302	−	0.504549i
$772$		−	88.9157i		−	3.20015i
$773$	6.71498	−	3.87689i	0.241521	−	0.139442i	−0.374355	−	0.927286i	$-0.622136\pi$ <

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.21837 + 1.28078i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(2.28078 + 3.95042i) q^{4} -0.561553i q^{5} +(-2.21837 + 1.28078i) q^{6} +(-3.08440 + 1.78078i) q^{7} +6.56155i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(2.21837 + 1.28078i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(2.28078 + 3.95042i) q^{4} -0.561553i q^{5} +(-2.21837 + 1.28078i) q^{6} +(-3.08440 + 1.78078i) q^{7} +6.56155i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.719224 - 1.24573i) q^{10} +(1.73205 + 1.00000i) q^{11} -4.56155 q^{12} -9.12311 q^{14} +(0.486319 + 0.280776i) q^{15} +(-3.84233 + 6.65511i) q^{16} +(1.28078 + 2.21837i) q^{17} -2.56155i q^{18} +(0.972638 - 0.561553i) q^{19} +(2.21837 - 1.28078i) q^{20} -3.56155i q^{21} +(2.56155 + 4.43674i) q^{22} +(1.00000 - 1.73205i) q^{23} +(-5.68247 - 3.28078i) q^{24} +4.68466 q^{25} +1.00000 q^{27} +(-14.0696 - 8.12311i) q^{28} +(2.84233 - 4.92306i) q^{29} +(0.719224 + 1.24573i) q^{30} +1.56155i q^{31} +(-5.68247 + 3.28078i) q^{32} +(-1.73205 + 1.00000i) q^{33} +6.56155i q^{34} +(1.00000 + 1.73205i) q^{35} +(2.28078 - 3.95042i) q^{36} +(-2.97778 - 1.71922i) q^{37} +2.87689 q^{38} +3.68466 q^{40} +(2.21837 + 1.28078i) q^{41} +(4.56155 - 7.90084i) q^{42} +(0.219224 + 0.379706i) q^{43} +9.12311i q^{44} +(-0.486319 + 0.280776i) q^{45} +(4.43674 - 2.56155i) q^{46} -8.24621i q^{47} +(-3.84233 - 6.65511i) q^{48} +(2.84233 - 4.92306i) q^{49} +(10.3923 + 6.00000i) q^{50} -2.56155 q^{51} +11.6847 q^{53} +(2.21837 + 1.28078i) q^{54} +(0.561553 - 0.972638i) q^{55} +(-11.6847 - 20.2384i) q^{56} +1.12311i q^{57} +(12.6107 - 7.28078i) q^{58} +(-9.63289 + 5.56155i) q^{59} +2.56155i q^{60} +(-6.06155 - 10.4989i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(3.08440 + 1.78078i) q^{63} -1.43845 q^{64} -5.12311 q^{66} +(0.379706 + 0.219224i) q^{67} +(-5.84233 + 10.1192i) q^{68} +(1.00000 + 1.73205i) q^{69} +5.12311i q^{70} +(-12.1244 + 7.00000i) q^{71} +(5.68247 - 3.28078i) q^{72} -1.87689i q^{73} +(-4.40388 - 7.62775i) q^{74} +(-2.34233 + 4.05703i) q^{75} +(4.43674 + 2.56155i) q^{76} -7.12311 q^{77} +9.56155 q^{79} +(3.73720 + 2.15767i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.28078 + 5.68247i) q^{82} +9.12311i q^{83} +(14.0696 - 8.12311i) q^{84} +(1.24573 - 0.719224i) q^{85} +1.12311i q^{86} +(2.84233 + 4.92306i) q^{87} +(-6.56155 + 11.3649i) q^{88} +(-11.3649 - 6.56155i) q^{89} -1.43845 q^{90} +9.12311 q^{92} +(-1.35234 - 0.780776i) q^{93} +(10.5616 - 18.2931i) q^{94} +(-0.315342 - 0.546188i) q^{95} -6.56155i q^{96} +(3.84381 - 2.21922i) q^{97} +(12.6107 - 7.28078i) q^{98} -2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 10 q^{4} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 10 * q^4 - 4 * q^9	\( 8 q - 4 q^{3} + 10 q^{4} - 4 q^{9} + 14 q^{10} - 20 q^{12} - 40 q^{14} - 6 q^{16} + 2 q^{17} + 4 q^{22} + 8 q^{23} - 12 q^{25} + 8 q^{27} - 2 q^{29} + 14 q^{30} + 8 q^{35} + 10 q^{36} + 56 q^{38} - 20 q^{40} + 20 q^{42} + 10 q^{43} - 6 q^{48} - 2 q^{49} - 4 q^{51} + 44 q^{53} - 12 q^{55} - 44 q^{56} - 32 q^{61} - 16 q^{62} - 28 q^{64} - 8 q^{66} - 22 q^{68} + 8 q^{69} + 6 q^{74} + 6 q^{75} - 24 q^{77} + 60 q^{79} - 4 q^{81} + 18 q^{82} - 2 q^{87} - 36 q^{88} - 28 q^{90} + 40 q^{92} + 68 q^{94} - 52 q^{95}+O(q^{100}) \) 8 * q - 4 * q^3 + 10 * q^4 - 4 * q^9 + 14 * q^10 - 20 * q^12 - 40 * q^14 - 6 * q^16 + 2 * q^17 + 4 * q^22 + 8 * q^23 - 12 * q^25 + 8 * q^27 - 2 * q^29 + 14 * q^30 + 8 * q^35 + 10 * q^36 + 56 * q^38 - 20 * q^40 + 20 * q^42 + 10 * q^43 - 6 * q^48 - 2 * q^49 - 4 * q^51 + 44 * q^53 - 12 * q^55 - 44 * q^56 - 32 * q^61 - 16 * q^62 - 28 * q^64 - 8 * q^66 - 22 * q^68 + 8 * q^69 + 6 * q^74 + 6 * q^75 - 24 * q^77 + 60 * q^79 - 4 * q^81 + 18 * q^82 - 2 * q^87 - 36 * q^88 - 28 * q^90 + 40 * q^92 + 68 * q^94 - 52 * q^95

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