LMFDB - Embedded newform 507.2.j.g.316.1

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			316.1
Root			$-2.21837 - 1.28078i$ of defining polynomial
Character	$\chi$	$=$	507.316
Dual form			507.2.j.g.361.1

$q$-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	$-0.972720\pi$
$2$	−2.21837	−	1.28078i	−1.56862	−	0.905646i	−0.572295	−	0.820048i	$-0.693947\pi$
$3$	−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	$0.0400750\pi$
$5$			0.561553i			0.251134i	−0.992085	+	0.125567i	$0.959925\pi$
$6$	2.21837	−	1.28078i	0.905646	−	0.522875i
$7$	3.08440	−	1.78078i	1.16579	−	0.673070i	0.213107	−	0.977029i	$-0.431642\pi$
$7$	3.08440	−	1.78078i	1.16579	−	0.673070i	0.952685	+	0.303959i	$0.0983085\pi$
$8$		−	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	0.215615	−	0.976478i	$-0.430824\pi$
$11$	−1.73205	−	1.00000i	−0.522233	−	0.301511i	−0.737848	+	0.674967i	$0.764158\pi$
$12$	−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	−0.607403	−	0.794394i	$-0.707789\pi$
$19$	−0.972638	+	0.561553i	−0.223138	+	0.128829i	0.384264	+	0.923223i	$0.374455\pi$
$20$	−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	$-0.955215\pi$
$31$		−	1.56155i		−	0.280463i	0.990119	−	0.140232i	$-0.0447847\pi$
$32$	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	0.724385	−	0.689395i	$-0.242124\pi$
$37$	2.97778	+	1.71922i	0.489544	+	0.282639i	−0.234841	+	0.972034i	$0.575457\pi$
$38$	2.87689			0.466694
$39$		0			0
$40$	3.68466			0.582596
$41$	−2.21837	−	1.28078i	−0.346451	−	0.200024i	0.316670	−	0.948536i	$-0.397435\pi$
$41$	−2.21837	−	1.28078i	−0.346451	−	0.200024i	−0.663121	+	0.748512i	$0.730769\pi$
$42$	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	$0.205397\pi$
$47$			8.24621i			1.20283i	−0.798935	+	0.601417i	$0.794603\pi$
$48$	−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	0.282175	−	0.959363i	$-0.408944\pi$
$59$	9.63289	−	5.56155i	1.25410	−	0.724053i	0.971920	+	0.235310i	$0.0756106\pi$
$60$		−	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	0.476626	−	0.879106i	$-0.341859\pi$
$67$	−0.379706	−	0.219224i	−0.0463885	−	0.0267824i	−0.523015	+	0.852324i	$0.675193\pi$
$68$	−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	0.441123	−	0.897447i	$-0.354580\pi$
$71$	12.1244	−	7.00000i	1.43890	−	0.830747i	0.997773	+	0.0666994i	$0.0212469\pi$
$72$	−5.68247	+	3.28078i	−0.669686	+	0.386643i
$73$			1.87689i			0.219674i	0.993950	+	0.109837i	$0.0350329\pi$
$73$			1.87689i			0.219674i	−0.993950	+	0.109837i	$0.964967\pi$
$74$	−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	$-0.833078\pi$
$83$		−	9.12311i		−	1.00139i	0.865624	−	0.500695i	$-0.166922\pi$
$84$	−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	0.961593	−	0.274481i	$-0.0885060\pi$
$89$	11.3649	+	6.56155i	1.20468	+	0.695523i	0.243089	+	0.970004i	$0.421839\pi$
$90$	−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	−0.682281	−	0.731090i	$-0.739012\pi$
$97$	−3.84381	+	2.21922i	−0.390280	+	0.225328i	0.292002	+	0.956418i	$0.405679\pi$
$98$	−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	$0.325120\pi$
$109$			17.8078i			1.70567i	−0.522177	+	0.852837i	$0.674880\pi$
$110$	−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	−0.445840	−	0.895113i	$-0.647095\pi$
$137$	1.24573	−	0.719224i	0.106430	−	0.0614474i	0.552270	+	0.833665i	$0.313762\pi$
$138$		−	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	−0.714365	−	0.699773i	$-0.753284\pi$
$149$	−5.68247	+	3.28078i	−0.465526	+	0.268772i	0.248839	+	0.968545i	$0.419951\pi$
$150$	10.3923	−	6.00000i	0.848528	−	0.489898i
$151$		−	15.3693i		−	1.25074i	−0.780329	−	0.625369i	$-0.784949\pi$
$151$		−	15.3693i		−	1.25074i	0.780329	−	0.625369i	$-0.215051\pi$
$152$	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	−0.928803	−	0.370574i	$-0.879161\pi$
$163$	−13.6899	+	7.90388i	−1.07228	+	0.619080i	−0.143475	+	0.989654i	$0.545828\pi$
$164$		−	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	0.275884	−	0.961191i	$-0.411030\pi$
$167$	−5.40938	−	3.12311i	−0.418590	−	0.241673i	−0.694474	+	0.719518i	$0.744363\pi$
$168$	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	0.963869	−	0.266375i	$-0.0858261\pi$
$193$	16.8809	+	9.74621i	1.21512	+	0.701548i	0.251247	+	0.967923i	$0.419159\pi$
$194$	11.3693			0.816269
$195$		0			0
$196$	25.9309			1.85220
$197$	9.84612	+	5.68466i	0.701507	+	0.405015i	0.807908	−	0.589308i	$-0.200600\pi$
$197$	9.84612	+	5.68466i	0.701507	+	0.405015i	−0.106402	+	0.994323i	$0.533933\pi$
$198$	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	0.249756	−	0.968309i	$-0.419650\pi$
$223$	−6.92820	−	4.00000i	−0.463947	−	0.267860i	−0.713702	+	0.700449i	$0.752983\pi$
$224$	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	−0.531931	−	0.846788i	$-0.678533\pi$
$227$	−0.972638	+	0.561553i	−0.0645563	+	0.0372716i	0.467374	+	0.884059i	$0.345200\pi$
$228$	4.43674	−	2.56155i	0.293830	−	0.169643i
$229$		−	0.246211i		−	0.0162701i	−0.999967	−	0.00813505i	$-0.997411\pi$
$229$		−	0.246211i		−	0.0162701i	0.999967	−	0.00813505i	$-0.00258949\pi$
$230$	−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	$-0.993507\pi$
$239$		−	0.630683i		−	0.0407955i	0.999792	−	0.0203977i	$-0.00649326\pi$
$240$	3.73720	−	2.15767i	0.241235	−	0.139277i
$241$	−2.43160	+	1.40388i	−0.156633	+	0.0904320i	−0.576268	−	0.817261i	$-0.695491\pi$
$241$	−2.43160	+	1.40388i	−0.156633	+	0.0904320i	0.419635	+	0.907693i	$0.362158\pi$
$242$			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	0.471614	−	0.881805i	$-0.343671\pi$
$271$	−0.925894	−	0.534565i	−0.0562441	−	0.0324725i	−0.527858	+	0.849332i	$0.677005\pi$
$272$	−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	$0.0266893\pi$
$281$			2.80776i			0.167497i	−0.996487	+	0.0837486i	$0.973311\pi$
$282$	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	−0.969635	−	0.244556i	$-0.921358\pi$
$293$	−21.2709	+	12.2808i	−1.24266	+	0.717451i	−0.273026	+	0.962007i	$0.588024\pi$
$294$		−	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	$-0.906062\pi$
$307$		−	10.1922i		−	0.581702i	0.956768	−	0.290851i	$-0.0939383\pi$
$308$	−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	$-0.775848\pi$
$317$		−	23.0540i		−	1.29484i	0.762133	−	0.647420i	$-0.224152\pi$
$318$	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	−0.944756	−	0.327773i	$-0.893702\pi$
$331$	−20.6181	+	11.9039i	−1.13327	+	0.654297i	−0.188518	+	0.982070i	$0.560369\pi$
$332$	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	0.144559	−	0.989496i	$-0.453824\pi$
$349$	−11.9579	−	6.90388i	−0.640090	−	0.369556i	−0.784649	+	0.619940i	$0.787157\pi$
$350$	−42.7386			−2.28448
$351$		0			0
$352$	−13.1231			−0.699464
$353$	−15.3154	−	8.84233i	−0.815155	−	0.470630i	0.0335881	−	0.999436i	$-0.489307\pi$
$353$	−15.3154	−	8.84233i	−0.815155	−	0.470630i	−0.848743	+	0.528806i	$0.822640\pi$
$354$	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	$-0.867069\pi$
$359$		−	15.3693i		−	0.811162i	0.914059	−	0.405581i	$-0.132931\pi$
$360$	−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	0.226740	−	0.973955i	$-0.427193\pi$
$379$	−9.79937	−	5.65767i	−0.503360	−	0.290615i	−0.730100	+	0.683340i	$0.760527\pi$
$380$	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	0.226473	−	0.974017i	$-0.427280\pi$
$383$	23.1563	−	13.3693i	1.18323	−	0.683140i	0.956760	+	0.290877i	$0.0939471\pi$
$384$	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	−0.214617	−	0.976698i	$-0.568850\pi$
$397$	10.4390	−	6.02699i	0.523921	−	0.302486i	0.738537	+	0.674213i	$0.235517\pi$
$398$			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	0.844427	−	0.535671i	$-0.179941\pi$
$401$	16.0748	+	9.28078i	0.802736	+	0.463460i	−0.0416909	+	0.999131i	$0.513274\pi$
$402$	−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	−0.838769	−	0.544487i	$-0.816724\pi$
$409$	−15.9083	+	9.18466i	−0.786615	+	0.454152i	0.0521548	+	0.998639i	$0.483391\pi$
$410$	−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	$0.117062\pi$
$421$			14.7538i			0.719056i	−0.933134	+	0.359528i	$0.882938\pi$
$422$	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	0.558803	−	0.829300i	$-0.311261\pi$
$431$	2.49146	+	1.43845i	0.120010	+	0.0692876i	−0.438794	+	0.898588i	$0.644594\pi$
$432$	−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	−0.658956	−	0.752182i	$-0.729002\pi$
$449$	−7.14143	+	4.12311i	−0.337025	+	0.194581i	0.321931	+	0.946763i	$0.395668\pi$
$450$			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	0.951122	−	0.308814i	$-0.0999322\pi$
$457$	24.7818	+	14.3078i	1.15924	+	0.669289i	0.208120	+	0.978103i	$0.433265\pi$
$458$	−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	−0.999847	−	0.0174778i	$-0.994436\pi$
$461$	−31.8765	+	18.4039i	−1.48463	+	0.857154i	−0.484787	+	0.874632i	$0.661103\pi$
$462$	−15.8017	+	9.12311i	−0.735161	+	0.424445i
$463$			26.6847i			1.24014i	0.784546	+	0.620071i	$0.212896\pi$
$463$			26.6847i			1.24014i	−0.784546	+	0.620071i	$0.787104\pi$
$464$	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	0.371303	−	0.928512i	$-0.378911\pi$
$479$	−5.40938	−	3.12311i	−0.247161	−	0.142698i	−0.618463	+	0.785814i	$0.712245\pi$
$480$	−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	−0.521875	−	0.853022i	$-0.674767\pi$
$487$	−0.972638	+	0.561553i	−0.0440744	+	0.0254464i	0.477801	+	0.878468i	$0.341434\pi$
$488$	−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	$-0.779866\pi$
$499$		−	28.4924i		−	1.27550i	0.770245	−	0.637748i	$-0.220134\pi$
$500$	−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	0.363615	−	0.931549i	$-0.381542\pi$
$509$	−5.89570	−	3.40388i	−0.261322	−	0.150874i	−0.624938	+	0.780675i	$0.714876\pi$
$510$	−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	$0.220768\pi$
$541$			29.7386i			1.27856i	−0.768972	+	0.639282i	$0.779232\pi$
$542$	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	0.219142	−	0.975693i	$-0.429674\pi$
$557$	−12.1842	−	7.03457i	−0.516262	−	0.298064i	−0.735404	+	0.677629i	$0.763008\pi$
$558$	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	$-0.787986\pi$
$577$		−	29.6847i		−	1.23579i	0.786261	−	0.617894i	$-0.212014\pi$
$578$	−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	0.215179	−	0.976575i	$-0.430966\pi$
$587$	−12.6705	−	7.31534i	−0.522969	−	0.301936i	−0.738149	+	0.674638i	$0.764300\pi$
$588$	−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	$-0.634442\pi$
$593$		−	44.4233i		−	1.82425i	0.409917	−	0.912123i	$-0.365558\pi$
$594$	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	0.0436871	−	0.999045i	$-0.486090\pi$
$613$	−19.7988	−	11.4309i	−0.799668	−	0.461688i	−0.843355	+	0.537357i	$0.819423\pi$
$614$	−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	−0.676430	−	0.736507i	$-0.736474\pi$
$617$	−9.35980	+	5.40388i	−0.376811	+	0.217552i	0.299619	+	0.954059i	$0.403141\pi$
$618$	16.7743	−	9.68466i	0.674762	−	0.389574i
$619$			24.3002i			0.976707i	0.872646	+	0.488353i	$0.162402\pi$
$619$			24.3002i			0.976707i	−0.872646	+	0.488353i	$0.837598\pi$
$620$	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	−0.230017	−	0.973187i	$-0.573878\pi$
$631$	12.5041	−	7.21922i	0.497779	−	0.287393i	0.727796	+	0.685794i	$0.240545\pi$
$632$		−	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	0.333306	−	0.942819i	$-0.391836\pi$
$643$	33.3822	−	19.2732i	1.31646	−	0.760061i	0.983158	+	0.182758i	$0.0585025\pi$
$644$	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	0.914964	−	0.403535i	$-0.132219\pi$
$661$	26.3006	+	15.1847i	1.02297	+	0.590615i	0.108011	+	0.994150i	$0.465552\pi$
$662$	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	−0.959780	−	0.280755i	$-0.909415\pi$
$683$	−31.2704	+	18.0540i	−1.19653	+	0.690816i	−0.236749	+	0.971571i	$0.576082\pi$
$684$			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	0.461631	−	0.887072i	$-0.347264\pi$
$691$	−1.99202	−	1.15009i	−0.0757800	−	0.0437516i	−0.537411	+	0.843320i	$0.680598\pi$
$692$	−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	−0.853552	−	0.521008i	$-0.825556\pi$
$709$	−22.0771	+	12.7462i	−0.829122	+	0.478694i	0.0244297	+	0.999702i	$0.492223\pi$
$710$		−	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	$0.450420\pi$
$733$			53.4924i			1.97579i	−0.155131	+	0.987894i	$0.549580\pi$
$734$	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	0.397196	−	0.917734i	$-0.369983\pi$
$739$	−5.40938	−	3.12311i	−0.198987	−	0.114885i	−0.596183	+	0.802849i	$0.703317\pi$
$740$	−8.80776			−0.323780
$741$		0			0
$742$	−106.600			−3.91342
$743$	32.3628	+	18.6847i	1.18728	+	0.685474i	0.957686	−	0.287814i	$-0.0929285\pi$
$743$	32.3628	+	18.6847i	1.18728	+	0.685474i	0.229589	+	0.973288i	$0.426262\pi$
$744$	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	−0.238961	−	0.971029i	$-0.576807\pi$
$761$	13.3102	−	7.68466i	0.482495	−	0.278569i	0.721456	+	0.692461i	$0.243473\pi$
$762$		−	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	0.754002	−	0.656873i	$-0.228121\pi$
$769$	15.5885	+	9.00000i	0.562134	+	0.324548i	−0.191867	+	0.981421i	$0.561454\pi$
$770$	−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	−0.615876	−	0.787843i	$-0.711198\pi$
$773$	−6.71498	+	3.87689i	−0.241521	+	0.139442i	0.374355	+	0.927286i	$0.377864\pi$
$774$	−0.972638	+	0.561553i	−0.0349608	+	0.0201846i
$775$		−	7.31534i		−	0.262775i
$776$	14.5616	+	25.2213i	0.522729	+	0.905394i
$777$	−6.12311	+	10.6055i	−0.219665	+	0.380471i
$778$	−6.77485	−	3.91146i	−0.242890	−	0.140233i
$779$	2.87689			0.103075
$780$		0			0
$781$	−28.0000			−1.00192
$782$	−11.3649	−	6.56155i	−0.406410	−	0.234641i
$783$	2.84233	−	4.92306i	0.101577	−	0.175936i
$784$	21.8423	+	37.8320i	0.780083	+	1.35114i
$785$		−	2.45360i		−	0.0875728i
$786$	−38.5316	+	22.2462i	−1.37438	+	0.793496i
$787$	1.01938	−	0.588540i	0.0363370	−	0.0209792i	−0.481721	−	0.876324i	$-0.659988\pi$
$787$	1.01938	−	0.588540i	0.0363370	−	0.0209792i	0.518058	+	0.855345i	$0.326655\pi$
$788$			51.8617i			1.84750i
$789$	7.68466	+	13.3102i	0.273581	+	0.473856i
$790$	6.87689	−	11.9111i	0.244669	−	0.423779i
$791$	45.6730	+	26.3693i	1.62394	+	0.937585i
$792$	13.1231			0.466309
$793$		0			0
$794$	−30.8769			−1.09578
$795$	−5.68247	−	3.28078i	−0.201536	−	0.116357i
$796$	52.8617	−	91.5592i	1.87363	−	3.24523i
$797$	−20.8078	−	36.0401i	−0.737049	−	1.27661i	−0.953819	−	0.300383i	$-0.902885\pi$
$797$	−20.8078	−	36.0401i	−0.737049	−	1.27661i	0.216770	−	0.976223i	$-0.430448\pi$
$798$			10.2462i			0.362712i
$799$	−18.2931	+	10.5616i	−0.647165	+	0.373641i
$800$	26.6204	−	15.3693i	0.941175	−	0.543387i
$801$		−	13.1231i		−	0.463682i
$802$	−23.7732	−	41.1764i	−0.839461	−	1.45399i
$803$	1.87689	−	3.25088i	0.0662342	−	0.114721i
$804$	1.73205	+	1.00000i	0.0610847	+	0.0352673i
$805$	4.00000			0.140981
$806$		0			0
$807$	3.36932			0.118606
$808$	19.5389	+	11.2808i	0.687375	+	0.396856i
$809$	−18.6501	+	32.3029i	−0.655702	+	1.13571i	0.326015	+	0.945365i	$0.394294\pi$
$809$	−18.6501	+	32.3029i	−0.655702	+	1.13571i	−0.981717	+	0.190345i	$0.939039\pi$
$810$	0.719224	+	1.24573i	0.0252709	+	0.0437706i
$811$		−	1.56155i		−	0.0548335i	−0.999624	−	0.0274168i	$-0.991272\pi$
$811$		−	1.56155i		−	0.0548335i	0.999624	−	0.0274168i	$-0.00872812\pi$
$812$	79.9811	−	46.1771i	2.80678	−	1.62050i
$813$	0.925894	−	0.534565i	0.0324725	−	0.0187480i
$814$			17.6155i			0.617424i
$815$	−4.43845	−	7.68762i	−0.155472	−	0.269285i
$816$	9.84233	−	17.0474i	0.344550	−	0.596779i
$817$	−0.426450	−	0.246211i	−0.0149196	−	0.00861384i
$818$	47.0540			1.64520
$819$		0			0
$820$	6.56155			0.229139
$821$	22.9431	+	13.2462i	0.800720	+	0.462296i	0.843723	−	0.536779i	$-0.180359\pi$
$821$	22.9431	+	13.2462i	0.800720	+	0.462296i	−0.0430028	+	0.999075i	$0.513692\pi$
$822$	1.84233	−	3.19101i	0.0642586	−	0.111299i
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	0.927281	−	0.374365i	$-0.122139\pi$
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	−0.787850	+	0.615867i	$0.788806\pi$
$824$		−	49.6155i		−	1.72844i
$825$	8.11407	−	4.68466i	0.282496	−	0.163099i
$826$	−87.8819	+	50.7386i	−3.05780	+	1.76542i
$827$		−	34.7386i		−	1.20798i	−0.796992	−	0.603990i	$-0.793577\pi$
$827$		−	34.7386i		−	1.20798i	0.796992	−	0.603990i	$-0.206423\pi$
$828$	−4.56155	−	7.90084i	−0.158525	−	0.274573i
$829$	−9.74621	+	16.8809i	−0.338500	+	0.586299i	−0.984151	−	0.177334i	$-0.943253\pi$
$829$	−9.74621	+	16.8809i	−0.338500	+	0.586299i	0.645651	+	0.763633i	$0.276586\pi$
$830$	−11.3649	−	6.56155i	−0.394483	−	0.227755i
$831$	−17.6847			−0.613474
$832$		0			0
$833$	14.5616			0.504528
$834$	−24.2487	−	14.0000i	−0.839664	−	0.484780i
$835$	1.75379	−	3.03765i	0.0606924	−	0.105122i
$836$	5.12311	+	8.87348i	0.177186	+	0.306896i
$837$		−	1.56155i		−	0.0539752i
$838$	−39.3845	+	22.7386i	−1.36051	+	0.785493i
$839$	16.9875	−	9.80776i	0.586475	−	0.338602i	−0.177227	−	0.984170i	$-0.556713\pi$
$839$	16.9875	−	9.80776i	0.586475	−	0.338602i	0.763703	+	0.645568i	$0.223379\pi$
$840$			13.1231i			0.452790i
$841$	−1.65767	−	2.87117i	−0.0571611	−	0.0990059i
$842$	18.8963	−	32.7294i	0.651210	−	1.12793i
$843$	−2.43160	−	1.40388i	−0.0837486	−	0.0483523i
$844$	−33.3693			−1.14862
$845$		0			0
$846$	−21.1231			−0.726227
$847$	−21.5908	−	12.4654i	−0.741868	−	0.428317i
$848$	−44.8963	+	77.7627i	−1.54175	+	2.67038i
$849$	−0.657671	−	1.13912i	−0.0225712	−	0.0390945i
$850$		−	30.7386i		−	1.05433i
$851$	5.95557	−	3.43845i	0.204154	−	0.117868i
$852$	−55.3059	+	31.9309i	−1.89475	+	1.09393i
$853$			6.12311i			0.209651i	0.994491	+	0.104826i	$0.0334284\pi$
$853$			6.12311i			0.209651i	−0.994491	+	0.104826i	$0.966572\pi$
$854$	55.3002	+	95.7827i	1.89233	+	3.27762i
$855$	−0.315342	+	0.546188i	−0.0107845	+	0.0186792i
$856$	46.8589	+	27.0540i	1.60160	+	0.924686i
$857$	−31.4384			−1.07392			−0.536958	−	0.843609i	$-0.680427\pi$
$857$	−31.4384			−1.07392			−0.536958	+	0.843609i	$0.680427\pi$
$858$		0			0
$859$	20.4384			0.697351			0.348675	−	0.937244i	$-0.386632\pi$
$859$	20.4384			0.697351			0.348675	+	0.937244i	$0.386632\pi$
$860$	−0.972638	−	0.561553i	−0.0331667	−	0.0191488i
$861$	4.56155	−	7.90084i	0.155457	−	0.269260i
$862$	−3.68466	−	6.38202i	−0.125500	−	0.217372i
$863$		−	2.49242i		−	0.0848430i	−0.999100	−	0.0424215i	$-0.986493\pi$
$863$		−	2.49242i		−	0.0848430i	0.999100	−	0.0424215i	$-0.0135072\pi$
$864$	5.68247	−	3.28078i	0.193322	−	0.111614i
$865$	−1.82554	+	1.05398i	−0.0620702	+	0.0358362i
$866$		−	64.6695i		−	2.19756i
$867$	5.21922	+	9.03996i	0.177254	+	0.307013i
$868$	12.6847	−	21.9705i	0.430545	−	0.745726i
$869$	−16.5611	−	9.56155i	−0.561797	−	0.324353i
$870$	8.17708			0.277229
$871$		0			0
$872$	116.847			3.95692
$873$	3.84381	+	2.21922i	0.130093	+	0.0751093i
$874$	2.87689	−	4.98293i	0.0973124	−	0.168550i
$875$	9.68466	+	16.7743i	0.327401	+	0.567076i
$876$		−	8.56155i		−	0.289268i
$877$	16.8342	−	9.71922i	0.568450	−	0.328195i	−0.188080	−	0.982154i	$-0.560226\pi$
$877$	16.8342	−	9.71922i	0.568450	−	0.328195i	0.756530	+	0.653959i	$0.226893\pi$
$878$	2.91791	−	1.68466i	0.0984748	−	0.0568545i
$879$		−	24.5616i		−	0.828441i
$880$	4.31534	+	7.47439i	0.145470	+	0.251962i
$881$	−18.9654	+	32.8491i	−0.638962	+	1.10671i	0.346699	+	0.937976i	$0.387302\pi$
$881$	−18.9654	+	32.8491i	−0.638962	+	1.10671i	−0.985661	+	0.168738i	$0.946031\pi$
$882$	12.6107	+	7.28078i	0.424624	+	0.245156i
$883$	11.8078			0.397363			0.198681	−	0.980064i	$-0.436334\pi$
$883$	11.8078			0.397363			0.198681	+	0.980064i	$0.436334\pi$
$884$		0			0
$885$	−6.24621			−0.209964
$886$	−32.6957	−	18.8769i	−1.09843	−	0.634182i
$887$	−24.6847	+	42.7551i	−0.828830	+	1.43558i	0.0701272	+	0.997538i	$0.477659\pi$
$887$	−24.6847	+	42.7551i	−0.828830	+	1.43558i	−0.898957	+	0.438037i	$0.855674\pi$
$888$	11.2808	+	19.5389i	0.378558	+	0.655682i
$889$		−	34.0540i		−	1.14213i
$890$	16.3479	−	9.43845i	0.547982	−	0.316377i
$891$	1.73205	−	1.00000i	0.0580259	−	0.0335013i
$892$		−	36.4924i		−	1.22186i
$893$	−4.63068	−	8.02058i	−0.154960	−	0.268398i
$894$	−8.40388	+	14.5560i	−0.281068	+	0.486824i
$895$	−6.38202	−	3.68466i	−0.213327	−	0.123165i
$896$	−33.6155			−1.12302
$897$		0			0
$898$	21.1231			0.704887
$899$	−7.68762	−	4.43845i	−0.256396	−	0.148031i
$900$	10.6847	−	18.5064i	0.356155	−	0.616879i
$901$	14.9654	+	25.9209i	0.498571	+	0.863550i
$902$		−	13.1231i		−	0.436952i
$903$	−1.35234	+	0.780776i	−0.0450032	+	0.0259826i
$904$	84.1447	−	48.5810i	2.79861	−	1.61578i
$905$		−	5.43845i		−	0.180780i
$906$	−19.6847	−	34.0948i	−0.653979	−	1.13272i
$907$	14.0000	−	24.2487i	0.464862	−	0.805165i	−0.534333	−	0.845274i	$-0.679437\pi$
$907$	14.0000	−	24.2487i	0.464862	−	0.805165i	0.999195	+	0.0401089i	$0.0127705\pi$
$908$	−4.43674	−	2.56155i	−0.147238	−	0.0850081i
$909$	3.43845			0.114046
$910$		0			0
$911$	−10.7386			−0.355787			−0.177893	−	0.984050i	$-0.556928\pi$
$911$	−10.7386			−0.355787			−0.177893	+	0.984050i	$0.556928\pi$
$912$	7.47439	+	4.31534i	0.247502	+	0.142895i
$913$	−9.12311	+	15.8017i	−0.301931	+	0.522959i
$914$	−36.6501	−	63.4798i	−1.21228	−	2.09973i
$915$			6.80776i			0.225058i
$916$	0.972638	−	0.561553i	0.0321369	−	0.0185542i
$917$	−53.5738	+	30.9309i	−1.76916	+	1.02143i
$918$		−	6.56155i		−	0.216564i
$919$	−22.2462	−	38.5316i	−0.733835	−	1.27104i	−0.955233	−	0.295856i	$-0.904395\pi$
$919$	−22.2462	−	38.5316i	−0.733835	−	1.27104i	0.221398	−	0.975184i	$-0.428938\pi$
$920$	3.68466	−	6.38202i	0.121480	−	0.210409i
$921$	8.82674	+	5.09612i	0.290851	+	0.167923i
$922$	94.2850			3.10511
$923$		0			0
$924$	32.4924			1.06892
$925$	13.9499	+	8.05398i	0.458670	+	0.264813i
$926$	34.1771	−	59.1964i	1.12313	−	1.94532i
$927$	−3.78078	−	6.54850i	−0.124177	−	0.215081i
$928$		−	37.3002i		−	1.22444i
$929$	11.0918	−	6.40388i	0.363912	−	0.210105i	−0.306884	−	0.951747i	$-0.599286\pi$
$929$	11.0918	−	6.40388i	0.363912	−	0.210105i	0.670795	+	0.741643i	$0.265953\pi$
$930$	1.94528	−	1.12311i	0.0637881	−	0.0368281i
$931$			6.38447i			0.209243i
$932$	−59.3002	−	102.711i	−1.94244	−	3.36441i
$933$	−5.43845	+	9.41967i	−0.178047	+	0.308386i
$934$	−57.6776	−	33.3002i	−1.88727	−	1.08962i
$935$	2.87689			0.0940845
$936$		0			0
$937$	−3.43845			−0.112329			−0.0561646	−	0.998422i	$-0.517887\pi$
$937$	−3.43845			−0.112329			−0.0561646	+	0.998422i	$0.517887\pi$
$938$	3.46410	+	2.00000i	0.113107	+	0.0653023i
$939$	0.657671	−	1.13912i	0.0214623	−	0.0371738i
$940$	−10.5616	−	18.2931i	−0.344480	−	0.596657i
$941$		−	2.49242i		−	0.0812507i	−0.999174	−	0.0406253i	$-0.987065\pi$
$941$		−	2.49242i		−	0.0812507i	0.999174	−	0.0406253i	$-0.0129350\pi$
$942$	−9.69276	+	5.59612i	−0.315807	+	0.182331i
$943$	−4.43674	+	2.56155i	−0.144480	+	0.0834156i
$944$			85.4773i			2.78205i
$945$	1.00000	+	1.73205i	0.0325300	+	0.0563436i
$946$	−1.12311	+	1.94528i	−0.0365153	+	0.0632464i
$947$	9.29993	+	5.36932i	0.302207	+	0.174479i	0.643434	−	0.765502i	$-0.277509\pi$
$947$	9.29993	+	5.36932i	0.302207	+	0.174479i	−0.341227	+	0.939981i	$0.610842\pi$
$948$	−43.6155			−1.41657
$949$		0			0
$950$	13.4773			0.437260
$951$	19.9653	+	11.5270i	0.647420	+	0.373788i
$952$	29.9309	−	51.8418i	0.970065	−	1.68020i
$953$	−17.4924	−	30.2978i	−0.566635	−	0.981441i	−0.996896	−	0.0787360i	$-0.974912\pi$
$953$	−17.4924	−	30.2978i	−0.566635	−	0.981441i	0.430260	−	0.902705i	$-0.358422\pi$
$954$			29.9309i			0.969048i
$955$	−0.426450	+	0.246211i	−0.0137996	+	0.00796721i
$956$	2.49146	−	1.43845i	0.0805797	−	0.0465227i
$957$		−	11.3693i		−	0.367518i
$958$	8.00000	+	13.8564i	0.258468	+	0.447680i
$959$	2.56155	−	4.43674i	0.0827169	−	0.143270i
$960$	0.699544	+	0.403882i	0.0225777	+	0.0130352i
$961$	28.5616			0.921340
$962$		0			0
$963$	8.24621			0.265730
$964$	−11.0918	−	6.40388i	−0.357244	−	0.206255i
$965$	−5.47301	+	9.47954i	−0.176183	+	0.305157i
$966$	−9.12311	−	15.8017i	−0.293531	−	0.508411i
$967$		−	9.12311i		−	0.293379i	−0.989183	−	0.146690i	$-0.953138\pi$
$967$		−	9.12311i		−	0.293379i	0.989183	−	0.146690i	$-0.0468619\pi$
$968$	−39.7773	+	22.9654i	−1.27849	+	0.738137i
$969$	2.49146	−	1.43845i	0.0800373	−	0.0462096i
$970$			6.38447i			0.204993i
$971$	−26.4924	−	45.8862i	−0.850182	−	1.47256i	−0.881043	−	0.473035i	$-0.843158\pi$
$971$	−26.4924	−	45.8862i	−0.850182	−	1.47256i	0.0308612	−	0.999524i	$-0.490175\pi$
$972$	2.28078	−	3.95042i	0.0731559	−	0.126710i
$973$	−33.7151	−	19.4654i	−1.08086	−	0.624033i
$974$	2.87689			0.0921816
$975$		0			0
$976$	93.1619			2.98204
$977$	−13.7030	−	7.91146i	−0.438399	−	0.253110i	0.264519	−	0.964380i	$-0.414787\pi$
$977$	−13.7030	−	7.91146i	−0.438399	−	0.253110i	−0.702918	+	0.711270i	$0.748120\pi$
$978$	−20.2462	+	35.0675i	−0.647402	+	1.12133i
$979$	−13.1231	−	22.7299i	−0.419416	−	0.726450i
$980$			14.5616i			0.465152i
$981$	15.4220	−	8.90388i	0.492386	−	0.284279i
$982$	43.8212	−	25.3002i	1.39839	−	0.807361i
$983$			27.6155i			0.880799i	0.897802	+	0.440399i	$0.145163\pi$
$983$			27.6155i			0.880799i	−0.897802	+	0.440399i	$0.854837\pi$
$984$	−8.40388	−	14.5560i	−0.267906	−	0.464027i
$985$	−3.19224	+	5.52911i	−0.101713	+	0.176172i
$986$	−32.3029	−	18.6501i	−1.02873	−	0.593940i
$987$	−29.3693			−0.934836
$988$		0			0
$989$	0.876894			0.0278836
$990$	2.49146	+	1.43845i	0.0791839	+	0.0457169i
$991$	−20.1771	+	34.9477i	−0.640946	+	1.11015i	0.344276	+	0.938869i	$0.388124\pi$
$991$	−20.1771	+	34.9477i	−0.640946	+	1.11015i	−0.985222	+	0.171283i	$0.945209\pi$
$992$	−5.12311	−	8.87348i	−0.162659	−	0.281733i
$993$		−	23.8078i		−	0.755517i
$994$	−110.612	+	63.8617i	−3.50839	+	2.02557i
$995$	11.2715	−	6.50758i	0.357329	−	0.206304i
$996$			41.6155i			1.31864i
$997$	−10.3078	−	17.8536i	−0.326450	−	0.565428i	0.655355	−	0.755321i	$-0.272519\pi$
$997$	−10.3078	−	17.8536i	−0.326450	−	0.565428i	−0.981805	+	0.189893i	$0.939186\pi$
$998$	−36.4924	+	63.2067i	−1.15515	+	2.00077i
$999$	2.97778	+	1.71922i	0.0942129	+	0.0543938i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.j.g.316.1		8
13.2	odd	12		39.2.e.b.16.1	✓	4
13.3	even	3	inner	507.2.j.g.361.4		8
13.4	even	6		507.2.b.d.337.1		4
13.5	odd	4		39.2.e.b.22.1	yes	4
13.6	odd	12		507.2.a.g.1.2		2
13.7	odd	12		507.2.a.d.1.1		2
13.8	odd	4		507.2.e.g.22.2		4
13.9	even	3		507.2.b.d.337.4		4
13.10	even	6	inner	507.2.j.g.361.1		8
13.11	odd	12		507.2.e.g.484.2		4
13.12	even	2	inner	507.2.j.g.316.4		8
39.2	even	12		117.2.g.c.55.2		4
39.5	even	4		117.2.g.c.100.2		4
39.17	odd	6		1521.2.b.h.1351.4		4
39.20	even	12		1521.2.a.m.1.2		2
39.32	even	12		1521.2.a.g.1.1		2
39.35	odd	6		1521.2.b.h.1351.1		4
52.7	even	12		8112.2.a.bo.1.1		2
52.15	even	12		624.2.q.h.289.2		4
52.19	even	12		8112.2.a.bk.1.2		2
52.31	even	4		624.2.q.h.529.2		4
65.2	even	12		975.2.bb.i.874.4		8
65.18	even	4		975.2.bb.i.724.4		8
65.28	even	12		975.2.bb.i.874.1		8
65.44	odd	4		975.2.i.k.451.2		4
65.54	odd	12		975.2.i.k.601.2		4
65.57	even	4		975.2.bb.i.724.1		8
156.83	odd	4		1872.2.t.r.1153.1		4
156.119	odd	12		1872.2.t.r.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.e.b.16.1	✓	4	13.2	odd	12
39.2.e.b.22.1	yes	4	13.5	odd	4
117.2.g.c.55.2		4	39.2	even	12
117.2.g.c.100.2		4	39.5	even	4
507.2.a.d.1.1		2	13.7	odd	12
507.2.a.g.1.2		2	13.6	odd	12
507.2.b.d.337.1		4	13.4	even	6
507.2.b.d.337.4		4	13.9	even	3
507.2.e.g.22.2		4	13.8	odd	4
507.2.e.g.484.2		4	13.11	odd	12
507.2.j.g.316.1		8	1.1	even	1	trivial
507.2.j.g.316.4		8	13.12	even	2	inner
507.2.j.g.361.1		8	13.10	even	6	inner
507.2.j.g.361.4		8	13.3	even	3	inner
624.2.q.h.289.2		4	52.15	even	12
624.2.q.h.529.2		4	52.31	even	4
975.2.i.k.451.2		4	65.44	odd	4
975.2.i.k.601.2		4	65.54	odd	12
975.2.bb.i.724.1		8	65.57	even	4
975.2.bb.i.724.4		8	65.18	even	4
975.2.bb.i.874.1		8	65.28	even	12
975.2.bb.i.874.4		8	65.2	even	12
1521.2.a.g.1.1		2	39.32	even	12
1521.2.a.m.1.2		2	39.20	even	12
1521.2.b.h.1351.1		4	39.35	odd	6
1521.2.b.h.1351.4		4	39.17	odd	6
1872.2.t.r.289.1		4	156.119	odd	12
1872.2.t.r.1153.1		4	156.83	odd	4
8112.2.a.bk.1.2		2	52.19	even	12
8112.2.a.bo.1.1		2	52.7	even	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
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

Introduction

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