LMFDB - Embedded newform 784.2.x.l.557.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.5
Character	$\chi$	$=$	784.557
Dual form			784.2.x.l.373.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13468 - 0.844095i) q^{2} +(2.80718 - 0.752181i) q^{3} +(0.575008 - 1.91556i) q^{4} +(-3.72606 - 0.998394i) q^{5} +(2.55034 - 3.22301i) q^{6} +(-0.964462 - 2.65891i) q^{8} +(4.71639 - 2.72301i) q^{9} +O(q^{10})$	\(q+(1.13468 - 0.844095i) q^{2} +(2.80718 - 0.752181i) q^{3} +(0.575008 - 1.91556i) q^{4} +(-3.72606 - 0.998394i) q^{5} +(2.55034 - 3.22301i) q^{6} +(-0.964462 - 2.65891i) q^{8} +(4.71639 - 2.72301i) q^{9} +(-5.07063 + 2.01229i) q^{10} +(0.336603 + 1.25622i) q^{11} +(0.173303 - 5.80982i) q^{12} +(-1.12607 - 1.12607i) q^{13} -11.2107 q^{15} +(-3.33873 - 2.20292i) q^{16} +(0.754426 - 1.30670i) q^{17} +(3.05313 - 7.07083i) q^{18} +(0.535390 - 1.99810i) q^{19} +(-4.05500 + 6.56340i) q^{20} +(1.44230 + 1.14128i) q^{22} +(4.13121 - 2.38515i) q^{23} +(-4.70740 - 6.73859i) q^{24} +(8.55659 + 4.94015i) q^{25} +(-2.22825 - 0.327223i) q^{26} +(5.02656 - 5.02656i) q^{27} +(4.10069 + 4.10069i) q^{29} +(-12.7206 + 9.46287i) q^{30} +(-2.05500 + 3.55936i) q^{31} +(-5.64788 + 0.318587i) q^{32} +(1.88981 + 3.27324i) q^{33} +(-0.246948 - 2.11950i) q^{34} +(-2.50412 - 10.6003i) q^{36} +(2.26031 + 0.605650i) q^{37} +(-1.07909 - 2.71913i) q^{38} +(-4.00810 - 2.31408i) q^{39} +(0.938997 + 10.8702i) q^{40} +7.45533i q^{41} +(5.68992 - 5.68992i) q^{43} +(2.59991 + 0.0775535i) q^{44} +(-20.2922 + 5.43727i) q^{45} +(2.67431 - 6.19352i) q^{46} +(-1.79874 - 3.11551i) q^{47} +(-11.0294 - 3.67267i) q^{48} +(13.8790 - 1.61707i) q^{50} +(1.13493 - 4.23561i) q^{51} +(-2.80456 + 1.50956i) q^{52} +(-0.247329 - 0.923043i) q^{53} +(1.46066 - 9.94644i) q^{54} -5.01680i q^{55} -6.01174i q^{57} +(8.11434 + 1.19161i) q^{58} +(0.416693 + 1.55512i) q^{59} +(-6.44623 + 21.4747i) q^{60} +(-1.17817 + 4.39698i) q^{61} +(0.672667 + 5.77335i) q^{62} +(-6.13963 + 5.12884i) q^{64} +(3.07155 + 5.32008i) q^{65} +(4.90726 + 2.11891i) q^{66} +(2.08511 - 0.558703i) q^{67} +(-2.06927 - 2.19651i) q^{68} +(9.80296 - 9.80296i) q^{69} +13.8202i q^{71} +(-11.7890 - 9.91423i) q^{72} +(12.5356 + 7.23744i) q^{73} +(3.07596 - 1.22070i) q^{74} +(27.7357 + 7.43177i) q^{75} +(-3.51963 - 2.17450i) q^{76} +(-6.50122 + 0.757473i) q^{78} +(0.889807 + 1.54119i) q^{79} +(10.2409 + 11.5416i) q^{80} +(2.16054 - 3.74216i) q^{81} +(6.29300 + 8.45943i) q^{82} +(-7.16133 - 7.16133i) q^{83} +(-4.11564 + 4.11564i) q^{85} +(1.65342 - 11.2591i) q^{86} +(14.5958 + 8.42689i) q^{87} +(3.01553 - 2.10657i) q^{88} +(-7.32570 + 4.22949i) q^{89} +(-18.4356 + 23.2981i) q^{90} +(-2.19342 - 9.28505i) q^{92} +(-3.09146 + 11.5375i) q^{93} +(-4.67078 - 2.01681i) q^{94} +(-3.98979 + 6.91052i) q^{95} +(-15.6150 + 5.14255i) q^{96} +16.2227 q^{97} +(5.00824 + 5.00824i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} - 4 q^{3} + 6 q^{4} - 4 q^{5} + 8 q^{6} - 8 q^{8}+O(q^{10}) $ 24 * q - 2 * q^2 - 4 * q^3 + 6 * q^4 - 4 * q^5 + 8 * q^6 - 8 * q^8	$ 24 q - 2 q^{2} - 4 q^{3} + 6 q^{4} - 4 q^{5} + 8 q^{6} - 8 q^{8} + 4 q^{10} - 8 q^{12} - 48 q^{15} - 10 q^{16} + 8 q^{17} - 40 q^{20} + 28 q^{22} + 8 q^{24} + 20 q^{26} + 8 q^{27} - 8 q^{29} + 28 q^{30} + 8 q^{31} - 12 q^{32} + 16 q^{34} - 32 q^{36} + 20 q^{37} - 16 q^{38} + 8 q^{40} + 32 q^{43} - 14 q^{44} - 40 q^{45} + 28 q^{46} - 16 q^{47} + 32 q^{48} + 88 q^{50} + 16 q^{51} + 16 q^{52} - 4 q^{53} - 64 q^{54} - 14 q^{58} + 16 q^{59} - 60 q^{60} + 20 q^{61} + 16 q^{62} - 36 q^{64} - 32 q^{65} - 12 q^{66} - 24 q^{67} + 28 q^{68} - 8 q^{69} - 6 q^{72} + 38 q^{74} + 40 q^{75} + 96 q^{76} - 152 q^{78} - 24 q^{79} - 24 q^{80} + 44 q^{81} + 16 q^{82} - 40 q^{83} - 16 q^{85} - 38 q^{86} + 14 q^{88} - 80 q^{90} + 64 q^{92} + 48 q^{93} + 24 q^{94} + 16 q^{96} + 96 q^{97} + 64 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 - 4 * q^3 + 6 * q^4 - 4 * q^5 + 8 * q^6 - 8 * q^8 + 4 * q^10 - 8 * q^12 - 48 * q^15 - 10 * q^16 + 8 * q^17 - 40 * q^20 + 28 * q^22 + 8 * q^24 + 20 * q^26 + 8 * q^27 - 8 * q^29 + 28 * q^30 + 8 * q^31 - 12 * q^32 + 16 * q^34 - 32 * q^36 + 20 * q^37 - 16 * q^38 + 8 * q^40 + 32 * q^43 - 14 * q^44 - 40 * q^45 + 28 * q^46 - 16 * q^47 + 32 * q^48 + 88 * q^50 + 16 * q^51 + 16 * q^52 - 4 * q^53 - 64 * q^54 - 14 * q^58 + 16 * q^59 - 60 * q^60 + 20 * q^61 + 16 * q^62 - 36 * q^64 - 32 * q^65 - 12 * q^66 - 24 * q^67 + 28 * q^68 - 8 * q^69 - 6 * q^72 + 38 * q^74 + 40 * q^75 + 96 * q^76 - 152 * q^78 - 24 * q^79 - 24 * q^80 + 44 * q^81 + 16 * q^82 - 40 * q^83 - 16 * q^85 - 38 * q^86 + 14 * q^88 - 80 * q^90 + 64 * q^92 + 48 * q^93 + 24 * q^94 + 16 * q^96 + 96 * q^97 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.13468	−	0.844095i	0.802342	−	0.596865i
$2$	1.13468	−	0.844095i	0.802342	−	0.596865i
$3$	2.80718	−	0.752181i	1.62072	−	0.434272i	0.669510	−	0.742803i	$-0.266504\pi$
$3$	2.80718	−	0.752181i	1.62072	−	0.434272i	0.951214	+	0.308531i	$0.0998374\pi$
$4$	0.575008	−	1.91556i	0.287504	−	0.957779i
$5$	−3.72606	−	0.998394i	−1.66634	−	0.446495i	−0.702222	−	0.711958i	$-0.747809\pi$
$5$	−3.72606	−	0.998394i	−1.66634	−	0.446495i	−0.964121	+	0.265462i	$0.914475\pi$
$6$	2.55034	−	3.22301i	1.04117	−	1.31579i
$7$		0			0
$7$		0			0
$8$	−0.964462	−	2.65891i	−0.340989	−	0.940067i
$9$	4.71639	−	2.72301i	1.57213	−	0.907670i
$10$	−5.07063	+	2.01229i	−1.60347	+	0.636341i
$11$	0.336603	+	1.25622i	0.101490	+	0.378764i	0.997923	−	0.0644137i	$-0.0205177\pi$
$11$	0.336603	+	1.25622i	0.101490	+	0.378764i	−0.896434	+	0.443178i	$0.853851\pi$
$12$	0.173303	−	5.80982i	0.0500282	−	1.67715i
$13$	−1.12607	−	1.12607i	−0.312316	−	0.312316i	0.533490	−	0.845806i	$-0.320880\pi$
$13$	−1.12607	−	1.12607i	−0.312316	−	0.312316i	−0.845806	+	0.533490i	$0.820880\pi$
$14$		0			0
$15$	−11.2107			−2.89458
$16$	−3.33873	−	2.20292i	−0.834683	−	0.550731i
$17$	0.754426	−	1.30670i	0.182975	−	0.316922i	−0.759917	−	0.650020i	$-0.774761\pi$
$17$	0.754426	−	1.30670i	0.182975	−	0.316922i	0.942892	+	0.333098i	$0.108094\pi$
$18$	3.05313	−	7.07083i	0.719629	−	1.66661i
$19$	0.535390	−	1.99810i	0.122827	−	0.458396i	−0.876926	−	0.480625i	$-0.840410\pi$
$19$	0.535390	−	1.99810i	0.122827	−	0.458396i	0.999753	+	0.0222291i	$0.00707632\pi$
$20$	−4.05500	+	6.56340i	−0.906725	+	1.46762i
$21$		0			0
$22$	1.44230	+	1.14128i	0.307500	+	0.243323i
$23$	4.13121	−	2.38515i	0.861416	−	0.497339i	−0.00307023	−	0.999995i	$-0.500977\pi$
$23$	4.13121	−	2.38515i	0.861416	−	0.497339i	0.864486	+	0.502657i	$0.167644\pi$
$24$	−4.70740	−	6.73859i	−0.960893	−	1.37551i
$25$	8.55659	+	4.94015i	1.71132	+	0.988030i
$26$	−2.22825	−	0.327223i	−0.436995	−	0.0641737i
$27$	5.02656	−	5.02656i	0.967362	−	0.967362i
$28$		0			0
$29$	4.10069	+	4.10069i	0.761478	+	0.761478i	0.976590	−	0.215111i	$-0.0690115\pi$
$29$	4.10069	+	4.10069i	0.761478	+	0.761478i	−0.215111	+	0.976590i	$0.569011\pi$
$30$	−12.7206	+	9.46287i	−2.32245	+	1.72768i
$31$	−2.05500	+	3.55936i	−0.369088	+	0.639280i	−0.989423	−	0.145057i	$-0.953663\pi$
$31$	−2.05500	+	3.55936i	−0.369088	+	0.639280i	0.620335	+	0.784337i	$0.286997\pi$
$32$	−5.64788	+	0.318587i	−0.998413	+	0.0563187i
$33$	1.88981	+	3.27324i	0.328973	+	0.569798i
$34$	−0.246948	−	2.11950i	−0.0423513	−	0.363491i
$35$		0			0
$36$	−2.50412	−	10.6003i	−0.417354	−	1.76671i
$37$	2.26031	+	0.605650i	0.371593	+	0.0995682i	0.439783	−	0.898104i	$-0.355055\pi$
$37$	2.26031	+	0.605650i	0.371593	+	0.0995682i	−0.0681892	+	0.997672i	$0.521722\pi$
$38$	−1.07909	−	2.71913i	−0.175052	−	0.441102i
$39$	−4.00810	−	2.31408i	−0.641809	−	0.370549i
$40$	0.938997	+	10.8702i	0.148469	+	1.71873i
$41$			7.45533i			1.16433i	0.813072	+	0.582163i	$0.197794\pi$
$41$			7.45533i			1.16433i	−0.813072	+	0.582163i	$0.802206\pi$
$42$		0			0
$43$	5.68992	−	5.68992i	0.867705	−	0.867705i	−0.124513	−	0.992218i	$-0.539737\pi$
$43$	5.68992	−	5.68992i	0.867705	−	0.867705i	0.992218	+	0.124513i	$0.0397369\pi$
$44$	2.59991	+	0.0775535i	0.391951	+	0.0116916i
$45$	−20.2922	+	5.43727i	−3.02498	+	0.810541i
$46$	2.67431	−	6.19352i	0.394306	−	0.913185i
$47$	−1.79874	−	3.11551i	−0.262373	−	0.454444i	0.704499	−	0.709705i	$-0.251172\pi$
$47$	−1.79874	−	3.11551i	−0.262373	−	0.454444i	−0.966872	+	0.255261i	$0.917838\pi$
$48$	−11.0294	−	3.67267i	−1.59196	−	0.530104i
$49$		0			0
$50$	13.8790	−	1.61707i	1.96278	−	0.228689i
$51$	1.13493	−	4.23561i	0.158922	−	0.593105i
$52$	−2.80456	+	1.50956i	−0.388923	+	0.209338i
$53$	−0.247329	−	0.923043i	−0.0339732	−	0.126790i	0.946857	−	0.321656i	$-0.104239\pi$
$53$	−0.247329	−	0.923043i	−0.0339732	−	0.126790i	−0.980830	+	0.194866i	$0.937573\pi$
$54$	1.46066	−	9.94644i	0.198770	−	1.35354i
$55$		−	5.01680i		−	0.676466i
$56$		0			0
$57$		−	6.01174i		−	0.796275i
$58$	8.11434	+	1.19161i	1.06547	+	0.156466i
$59$	0.416693	+	1.55512i	0.0542489	+	0.202459i	0.987731	−	0.156164i	$-0.0499129\pi$
$59$	0.416693	+	1.55512i	0.0542489	+	0.202459i	−0.933482	+	0.358624i	$0.883246\pi$
$60$	−6.44623	+	21.4747i	−0.832205	+	2.77237i
$61$	−1.17817	+	4.39698i	−0.150849	+	0.562975i	0.848576	+	0.529073i	$0.177460\pi$
$61$	−1.17817	+	4.39698i	−0.150849	+	0.562975i	−0.999425	+	0.0339025i	$0.989206\pi$
$62$	0.672667	+	5.77335i	0.0854288	+	0.733216i
$63$		0			0
$64$	−6.13963	+	5.12884i	−0.767453	+	0.641105i
$65$	3.07155	+	5.32008i	0.380979	+	0.659875i
$66$	4.90726	+	2.11891i	0.604041	+	0.260820i
$67$	2.08511	−	0.558703i	0.254736	−	0.0682564i	−0.129191	−	0.991620i	$-0.541238\pi$
$67$	2.08511	−	0.558703i	0.254736	−	0.0682564i	0.383927	+	0.923363i	$0.374571\pi$
$68$	−2.06927	−	2.19651i	−0.250936	−	0.266366i
$69$	9.80296	−	9.80296i	1.18014	−	1.18014i
$70$		0			0
$71$			13.8202i			1.64016i	0.572251	+	0.820079i	$0.306070\pi$
$71$			13.8202i			1.64016i	−0.572251	+	0.820079i	$0.693930\pi$
$72$	−11.7890	−	9.91423i	−1.38935	−	1.16840i
$73$	12.5356	+	7.23744i	1.46718	+	0.847078i	0.999325	−	0.0367258i	$-0.0116928\pi$
$73$	12.5356	+	7.23744i	1.46718	+	0.847078i	0.467857	+	0.883804i	$0.345026\pi$
$74$	3.07596	−	1.22070i	0.357574	−	0.141903i
$75$	27.7357	+	7.43177i	3.20265	+	0.858147i
$76$	−3.51963	−	2.17450i	−0.403729	−	0.249432i
$77$		0			0
$78$	−6.50122	+	0.757473i	−0.736118	+	0.0857669i
$79$	0.889807	+	1.54119i	0.100111	+	0.173397i	0.911730	−	0.410789i	$-0.134747\pi$
$79$	0.889807	+	1.54119i	0.100111	+	0.173397i	−0.811619	+	0.584187i	$0.801414\pi$
$80$	10.2409	+	11.5416i	1.14497	+	1.29039i
$81$	2.16054	−	3.74216i	0.240060	−	0.415795i
$82$	6.29300	+	8.45943i	0.694946	+	0.934188i
$83$	−7.16133	−	7.16133i	−0.786058	−	0.786058i	0.194787	−	0.980845i	$-0.437598\pi$
$83$	−7.16133	−	7.16133i	−0.786058	−	0.786058i	−0.980845	+	0.194787i	$0.937598\pi$
$84$		0			0
$85$	−4.11564	+	4.11564i	−0.446404	+	0.446404i
$86$	1.65342	−	11.2591i	0.178293	−	1.21410i
$87$	14.5958	+	8.42689i	1.56483	+	0.903458i
$88$	3.01553	−	2.10657i	0.321457	−	0.224561i
$89$	−7.32570	+	4.22949i	−0.776522	+	0.448325i	−0.835196	−	0.549952i	$-0.814646\pi$
$89$	−7.32570	+	4.22949i	−0.776522	+	0.448325i	0.0586740	+	0.998277i	$0.481313\pi$
$90$	−18.4356	+	23.2981i	−1.94328	+	2.45584i
$91$		0			0
$92$	−2.19342	−	9.28505i	−0.228680	−	0.968033i
$93$	−3.09146	+	11.5375i	−0.320569	+	1.19638i
$94$	−4.67078	−	2.01681i	−0.481755	−	0.208018i
$95$	−3.98979	+	6.91052i	−0.409344	+	0.709004i
$96$	−15.6150	+	5.14255i	−1.59369	+	0.524860i
$97$	16.2227			1.64717			0.823585	−	0.567194i	$-0.191971\pi$
$97$	16.2227			1.64717			0.823585	+	0.567194i	$0.191971\pi$
$98$		0			0
$99$	5.00824	+	5.00824i	0.503348	+	0.503348i
$100$	14.3833	−	13.5500i	1.43833	−	1.35500i
$101$	−4.23361	−	15.8001i	−0.421260	−	1.57216i	−0.771957	−	0.635675i	$-0.780722\pi$
$101$	−4.23361	−	15.8001i	−0.421260	−	1.57216i	0.350696	−	0.936489i	$-0.385945\pi$
$102$	−2.28748	−	5.76407i	−0.226494	−	0.570727i
$103$	14.8848	−	8.59375i	1.46664	−	0.846768i	0.467341	−	0.884077i	$-0.345212\pi$
$103$	14.8848	−	8.59375i	1.46664	−	0.846768i	0.999304	+	0.0373093i	$0.0118787\pi$
$104$	−1.90808	+	4.08018i	−0.187102	+	0.400095i
$105$		0			0
$106$	−1.05977	−	0.838591i	−0.102934	−	0.0814512i
$107$	−5.60266	−	1.50123i	−0.541630	−	0.145129i	−0.0223764	−	0.999750i	$-0.507123\pi$
$107$	−5.60266	−	1.50123i	−0.541630	−	0.145129i	−0.519253	+	0.854620i	$0.673790\pi$
$108$	−6.73836	−	12.5190i	−0.648399	−	1.20464i
$109$	4.47170	−	1.19819i	0.428311	−	0.114766i	−0.0382223	−	0.999269i	$-0.512169\pi$
$109$	4.47170	−	1.19819i	0.428311	−	0.114766i	0.466533	+	0.884504i	$0.345503\pi$
$110$	−4.23466	−	5.69248i	−0.403759	−	0.542757i
$111$	6.80066			0.645490
$112$		0			0
$113$	−9.17193			−0.862822			−0.431411	−	0.902155i	$-0.641984\pi$
$113$	−9.17193			−0.862822			−0.431411	+	0.902155i	$0.641984\pi$
$114$	−5.07448	−	6.82142i	−0.475269	−	0.638884i
$115$	−17.7744	+	4.76265i	−1.65747	+	0.444119i
$116$	10.2130	−	5.49718i	0.948256	−	0.510400i
$117$	−8.37731	−	2.24469i	−0.774483	−	0.207522i
$118$	1.78548	+	1.41284i	0.164367	+	0.130062i
$119$		0			0
$120$	10.8123	+	29.8082i	0.987021	+	2.72110i
$121$	8.06150	−	4.65431i	0.732863	−	0.423119i
$122$	2.37462	+	5.98366i	0.214988	+	0.541735i
$123$	5.60775	+	20.9284i	0.505634	+	1.88705i
$124$	5.63652	+	5.98313i	0.506174	+	0.537301i
$125$	−13.3118	−	13.3118i	−1.19064	−	1.19064i
$126$		0			0
$127$	−12.9787			−1.15167			−0.575835	−	0.817566i	$-0.695323\pi$
$127$	−12.9787			−1.15167			−0.575835	+	0.817566i	$0.695323\pi$
$128$	−2.63730	+	11.0020i	−0.233107	+	0.972451i
$129$	11.6928	−	20.2525i	1.02949	−	1.78313i
$130$	7.97588	+	3.44392i	0.699531	+	0.302052i
$131$	−2.49617	+	9.31582i	−0.218091	+	0.813927i	0.766964	+	0.641690i	$0.221766\pi$
$131$	−2.49617	+	9.31582i	−0.218091	+	0.813927i	−0.985055	+	0.172237i	$0.944900\pi$
$132$	7.35674	−	1.73790i	0.640322	−	0.151264i
$133$		0			0
$134$	1.89434	−	2.39398i	0.163646	−	0.206808i
$135$	−23.7477	+	13.7108i	−2.04388	+	1.18004i
$136$	−4.20203	−	0.745686i	−0.360321	−	0.0639421i
$137$	−19.6192	−	11.3271i	−1.67618	−	0.967742i	−0.964061	−	0.265682i	$-0.914403\pi$
$137$	−19.6192	−	11.3271i	−1.67618	−	0.967742i	−0.712118	−	0.702060i	$-0.752264\pi$
$138$	2.84862	−	19.3979i	0.242491	−	1.65126i
$139$	−6.64728	+	6.64728i	−0.563815	+	0.563815i	−0.930389	−	0.366574i	$-0.880531\pi$
$139$	−6.64728	+	6.64728i	−0.563815	+	0.563815i	0.366574	+	0.930389i	$0.380531\pi$
$140$		0			0
$141$	−7.39281	−	7.39281i	−0.622587	−	0.622587i
$142$	11.6656	+	15.6816i	0.978953	+	1.31597i
$143$	1.03555	−	1.79363i	0.0865974	−	0.149991i
$144$	−21.7453	−	1.29845i	−1.81211	−	0.108204i
$145$	−11.1853	−	19.3735i	−0.928888	−	1.60888i
$146$	20.3330	−	2.36905i	1.68277	−	0.196064i
$147$		0			0
$148$	2.45986	−	3.98151i	0.202199	−	0.327278i
$149$	−10.6144	−	2.84413i	−0.869568	−	0.233000i	−0.203667	−	0.979040i	$-0.565286\pi$
$149$	−10.6144	−	2.84413i	−0.869568	−	0.233000i	−0.665901	+	0.746040i	$0.731953\pi$
$150$	37.7444	−	14.9789i	3.08182	−	1.22302i
$151$	4.73568	+	2.73415i	0.385384	+	0.222502i	0.680158	−	0.733065i	$-0.261911\pi$
$151$	4.73568	+	2.73415i	0.385384	+	0.222502i	−0.294774	+	0.955567i	$0.595244\pi$
$152$	−5.82915	+	0.503539i	−0.472806	+	0.0408424i
$153$		−	8.21724i		−	0.664324i
$154$		0			0
$155$	11.2107	−	11.2107i	0.900463	−	0.900463i
$156$	−6.73744	+	6.34713i	−0.539427	+	0.508177i
$157$	7.67327	−	2.05605i	0.612393	−	0.164090i	0.0607259	−	0.998154i	$-0.480658\pi$
$157$	7.67327	−	2.05605i	0.612393	−	0.164090i	0.551667	+	0.834064i	$0.313992\pi$
$158$	2.31056	+	0.997680i	0.183818	+	0.0793712i
$159$	−1.38859	−	2.40511i	−0.110122	−	0.190737i
$160$	21.3624	+	4.45173i	1.68885	+	0.351940i
$161$		0			0
$162$	−0.707214	−	6.06986i	−0.0555640	−	0.476893i
$163$	−2.31239	+	8.62997i	−0.181121	+	0.675951i	0.814307	+	0.580434i	$0.197117\pi$
$163$	−2.31239	+	8.62997i	−0.181121	+	0.675951i	−0.995428	+	0.0955171i	$0.969550\pi$
$164$	14.2811	+	4.28687i	1.11517	+	0.334749i
$165$	−3.77354	−	14.0831i	−0.293770	−	1.09636i
$166$	−14.1707	−	2.08099i	−1.09986	−	0.161516i
$167$			11.8175i			0.914463i	0.889348	+	0.457231i	$0.151159\pi$
$167$			11.8175i			0.914463i	−0.889348	+	0.457231i	$0.848841\pi$
$168$		0			0
$169$		−	10.4639i		−	0.804917i
$170$	−1.19595	+	8.14394i	−0.0917255	+	0.624611i
$171$	−2.91575	−	10.8817i	−0.222973	−	0.832145i
$172$	−7.62763	−	14.1711i	−0.581601	−	1.08054i
$173$	2.06387	−	7.70245i	0.156913	−	0.585606i	−0.842021	−	0.539444i	$-0.818634\pi$
$173$	2.06387	−	7.70245i	0.156913	−	0.585606i	0.998934	−	0.0461620i	$-0.0146990\pi$
$174$	23.6747	−	2.75840i	1.79477	−	0.209114i
$175$		0			0
$176$	1.64353	−	4.93569i	0.123886	−	0.372041i
$177$	2.33946	+	4.05207i	0.175845	+	0.304572i
$178$	−4.74225	+	10.9827i	−0.355446	+	0.823189i
$179$	−16.0204	+	4.29266i	−1.19742	+	0.320849i	−0.801816	−	0.597571i	$-0.796133\pi$
$179$	−16.0204	+	4.29266i	−1.19742	+	0.320849i	−0.395608	+	0.918420i	$0.629466\pi$
$180$	−1.25275	+	41.9974i	−0.0933746	+	3.13030i
$181$	−4.18574	+	4.18574i	−0.311124	+	0.311124i	−0.845345	−	0.534221i	$-0.820605\pi$
$181$	−4.18574	+	4.18574i	−0.311124	+	0.311124i	0.534221	+	0.845345i	$0.320605\pi$
$182$		0			0
$183$			13.2293i			0.977937i
$184$	−10.3263	−	8.68413i	−0.761265	−	0.640202i
$185$	−7.81739	−	4.51337i	−0.574746	−	0.331830i
$186$	6.23090	+	15.7009i	0.456872	+	1.15124i
$187$	1.89545	+	0.507884i	0.138609	+	0.0371401i
$188$	−7.00223	+	1.65415i	−0.510690	+	0.120641i
$189$		0			0
$190$	1.30599	+	11.2090i	0.0947464	+	0.813187i
$191$	−6.18382	−	10.7107i	−0.447445	−	0.774998i	0.550774	−	0.834655i	$-0.314333\pi$
$191$	−6.18382	−	10.7107i	−0.447445	−	0.774998i	−0.998219	+	0.0596566i	$0.980999\pi$
$192$	−13.3772	+	19.0157i	−0.965417	+	1.37234i
$193$	−11.8419	+	20.5107i	−0.852395	+	1.47639i	0.0266452	+	0.999645i	$0.491518\pi$
$193$	−11.8419	+	20.5107i	−0.852395	+	1.47639i	−0.879041	+	0.476747i	$0.841816\pi$
$194$	18.4076	−	13.6935i	1.32159	−	0.983138i
$195$	12.6240	+	12.6240i	0.904026	+	0.904026i
$196$		0			0
$197$	−11.4195	+	11.4195i	−0.813606	+	0.813606i	−0.985173	−	0.171566i	$-0.945117\pi$
$197$	−11.4195	+	11.4195i	−0.813606	+	0.813606i	0.171566	+	0.985173i	$0.445117\pi$
$198$	9.91020	+	1.45533i	0.704287	+	0.103426i
$199$	4.76039	+	2.74841i	0.337455	+	0.194830i	0.659146	−	0.752015i	$-0.270918\pi$
$199$	4.76039	+	2.74841i	0.337455	+	0.194830i	−0.321691	+	0.946845i	$0.604251\pi$
$200$	4.88292	−	27.5158i	0.345275	−	1.94566i
$201$	5.43302	−	3.13675i	0.383216	−	0.221250i
$202$	−18.1406	−	14.3545i	−1.27636	−	1.00998i
$203$		0			0
$204$	−7.46098	−	4.60954i	−0.522373	−	0.322732i
$205$	7.44336	−	27.7790i	0.519867	−	1.94017i
$206$	9.63560	−	22.3154i	0.671344	−	1.55479i
$207$	12.9896	−	22.4986i	0.902839	−	1.56376i
$208$	1.27900	+	6.24031i	0.0886829	+	0.432688i
$209$	2.69027			0.186090
$210$		0			0
$211$	0.907874	+	0.907874i	0.0625007	+	0.0625007i	0.737666	−	0.675166i	$-0.235928\pi$
$211$	0.907874	+	0.907874i	0.0625007	+	0.0625007i	−0.675166	+	0.737666i	$0.735928\pi$
$212$	−1.91036	−	0.0569846i	−0.131204	−	0.00391372i
$213$	10.3953	+	38.7958i	0.712274	+	2.65824i
$214$	−7.62442	+	3.02576i	−0.521195	+	0.206837i
$215$	−26.8818	+	15.5202i	−1.83332	+	1.05847i
$216$	−18.2131	−	8.51726i	−1.23925	−	0.579526i
$217$		0			0
$218$	4.06257	−	5.13410i	0.275152	−	0.347725i
$219$	40.6336	+	10.8877i	2.74576	+	0.735724i
$220$	−9.60998	−	2.88470i	−0.647905	−	0.194487i
$221$	−2.32098	+	0.621906i	−0.156126	+	0.0418339i
$222$	7.71659	−	5.74040i	0.517904	−	0.385271i
$223$	−3.20318			−0.214501			−0.107250	−	0.994232i	$-0.534205\pi$
$223$	−3.20318			−0.214501			−0.107250	+	0.994232i	$0.534205\pi$
$224$		0			0
$225$	53.8083			3.58722
$226$	−10.4072	+	7.74197i	−0.692278	+	0.514988i
$227$	18.8417	−	5.04862i	1.25057	−	0.335089i	0.428012	−	0.903773i	$-0.359214\pi$
$227$	18.8417	−	5.04862i	1.25057	−	0.335089i	0.822556	+	0.568684i	$0.192547\pi$
$228$	−11.5158	−	3.45680i	−0.762655	−	0.228932i
$229$	−9.59192	−	2.57015i	−0.633852	−	0.169840i	−0.0724349	−	0.997373i	$-0.523077\pi$
$229$	−9.59192	−	2.57015i	−0.633852	−	0.169840i	−0.561417	+	0.827533i	$0.689744\pi$
$230$	−16.1482	+	20.4074i	−1.06478	+	1.34562i
$231$		0			0
$232$	6.94841	−	14.8583i	0.456185	−	0.975496i
$233$	−2.54488	+	1.46929i	−0.166720	+	0.0962561i	−0.581039	−	0.813876i	$-0.697353\pi$
$233$	−2.54488	+	1.46929i	−0.166720	+	0.0962561i	0.414318	+	0.910132i	$0.364020\pi$
$234$	−11.4003	+	4.52423i	−0.745262	+	0.295758i
$235$	3.59170	+	13.4044i	0.234297	+	0.874408i
$236$	3.21853	+	0.0960064i	0.209508	+	0.00624948i
$237$	3.65710	+	3.65710i	0.237554	+	0.237554i
$238$		0			0
$239$	16.2109			1.04859			0.524297	−	0.851536i	$-0.324328\pi$
$239$	16.2109			1.04859			0.524297	+	0.851536i	$0.324328\pi$
$240$	37.4294	+	24.6963i	2.41606	+	1.59414i
$241$	7.05829	−	12.2253i	0.454665	−	0.787502i	−0.544004	−	0.839082i	$-0.683092\pi$
$241$	7.05829	−	12.2253i	0.454665	−	0.787502i	0.998669	+	0.0515803i	$0.0164258\pi$
$242$	5.21856	−	12.0858i	0.335462	−	0.776906i
$243$	−2.26932	+	8.46922i	−0.145577	+	0.543301i
$244$	7.74522	+	4.78515i	0.495837	+	0.306338i
$245$		0			0
$246$	24.0286	+	19.0136i	1.53201	+	1.21227i
$247$	−2.85290	+	1.64712i	−0.181526	+	0.104804i
$248$	11.4460	+	2.03119i	0.726821	+	0.128981i
$249$	−25.4897	−	14.7165i	−1.61535	−	0.932621i
$250$	−26.3411	−	3.86825i	−1.66596	−	0.244649i
$251$	−14.1967	+	14.1967i	−0.896091	+	0.896091i	−0.995088	−	0.0989969i	$-0.968437\pi$
$251$	−14.1967	+	14.1967i	−0.896091	+	0.896091i	0.0989969	+	0.995088i	$0.468437\pi$
$252$		0			0
$253$	4.38685	+	4.38685i	0.275799	+	0.275799i
$254$	−14.7267	+	10.9552i	−0.924033	+	0.687392i
$255$	−8.45763	+	14.6490i	−0.529637	+	0.917358i
$256$	6.29425	+	14.7099i	0.393391	+	0.919371i
$257$	1.61839	+	2.80314i	0.100953	+	0.174855i	0.912077	−	0.410018i	$-0.134478\pi$
$257$	1.61839	+	2.80314i	0.100953	+	0.174855i	−0.811125	+	0.584873i	$0.801144\pi$
$258$	−3.82742	−	32.8499i	−0.238285	−	2.04515i
$259$		0			0
$260$	11.9571	−	2.82464i	0.741547	−	0.175177i
$261$	30.5066	+	8.17423i	1.88831	+	0.505972i
$262$	5.03108	+	12.6775i	0.310821	+	0.783218i
$263$	20.7985	+	12.0080i	1.28249	+	0.740448i	0.977304	−	0.211844i	$-0.0679468\pi$
$263$	20.7985	+	12.0080i	1.28249	+	0.740448i	0.305190	+	0.952292i	$0.401280\pi$
$264$	6.88061	−	8.18175i	0.423473	−	0.503552i
$265$			3.68624i			0.226444i
$266$		0			0
$267$	−17.3832	+	17.3832i	−1.06383	+	1.06383i
$268$	0.128725	−	4.31540i	0.00786316	−	0.263605i
$269$	0.119533	−	0.0320287i	0.00728804	−	0.00195282i	−0.255173	−	0.966895i	$-0.582132\pi$
$269$	0.119533	−	0.0320287i	0.00728804	−	0.00195282i	0.262461	+	0.964943i	$0.415466\pi$
$270$	−15.3730	+	35.6027i	−0.935569	+	2.16671i
$271$	5.05692	+	8.75884i	0.307186	+	0.532062i	0.977746	−	0.209794i	$-0.0672793\pi$
$271$	5.05692	+	8.75884i	0.307186	+	0.532062i	−0.670560	+	0.741856i	$0.733946\pi$
$272$	−5.39739	+	2.70079i	−0.327265	+	0.163760i
$273$		0			0
$274$	−31.8227	+	3.70774i	−1.92248	+	0.223993i
$275$	−3.32573	+	12.4118i	−0.200549	+	0.748460i
$276$	−13.1414	−	24.4149i	−0.791017	−	1.46961i
$277$	−4.02921	−	15.0372i	−0.242092	−	0.903498i	−0.974823	−	0.222980i	$-0.928422\pi$
$277$	−4.02921	−	15.0372i	−0.242092	−	0.903498i	0.732732	−	0.680518i	$-0.238245\pi$
$278$	−1.93162	+	13.1535i	−0.115851	+	0.788894i
$279$			22.3831i			1.34004i
$280$		0			0
$281$			4.21999i			0.251743i	0.992047	+	0.125872i	$0.0401727\pi$
$281$			4.21999i			0.251743i	−0.992047	+	0.125872i	$0.959827\pi$
$282$	−14.6287	−	2.14826i	−0.871128	−	0.127927i
$283$	−6.06995	−	22.6533i	−0.360821	−	1.34660i	−0.872999	−	0.487722i	$-0.837828\pi$
$283$	−6.06995	−	22.6533i	−0.360821	−	1.34660i	0.512178	−	0.858879i	$-0.328839\pi$
$284$	26.4734	+	7.94674i	1.57091	+	0.471552i
$285$	−6.00209	+	22.4001i	−0.355533	+	1.32687i
$286$	−0.338971	−	2.90931i	−0.0200438	−	0.172031i
$287$		0			0
$288$	−25.7701	+	16.8818i	−1.51852	+	0.994770i
$289$	7.36168	+	12.7508i	0.433040	+	0.750048i
$290$	−29.0448	−	12.5413i	−1.70557	−	0.736451i
$291$	45.5401	−	12.2024i	2.66961	−	0.715319i
$292$	21.0718	−	19.8511i	1.23314	−	1.16170i
$293$	−13.5242	+	13.5242i	−0.790093	+	0.790093i	−0.981509	−	0.191416i	$-0.938692\pi$
$293$	−13.5242	+	13.5242i	−0.790093	+	0.790093i	0.191416	+	0.981509i	$0.438692\pi$
$294$		0			0
$295$		−	6.21049i		−	0.361589i
$296$	−0.569618	−	6.59410i	−0.0331084	−	0.383275i
$297$	8.00641	+	4.62250i	0.464579	+	0.268225i
$298$	−14.4447	+	5.73241i	−0.836761	+	0.332069i
$299$	−7.33790	−	1.96618i	−0.424361	−	0.113707i
$300$	30.1843	−	48.8561i	1.74269	−	2.82071i
$301$		0			0
$302$	7.68137	−	0.894976i	0.442013	−	0.0515001i
$303$	−23.7690	−	41.1691i	−1.36549	−	2.36510i
$304$	−6.18919	+	5.49171i	−0.354975	+	0.314971i
$305$	8.77984	−	15.2071i	0.502732	−	0.870757i
$306$	−6.93613	−	9.32395i	−0.396512	−	0.533015i
$307$	−8.93389	−	8.93389i	−0.509884	−	0.509884i	0.404607	−	0.914491i	$-0.367408\pi$
$307$	−8.93389	−	8.93389i	−0.509884	−	0.509884i	−0.914491	+	0.404607i	$0.867408\pi$
$308$		0			0
$309$	35.3203	−	35.3203i	2.00930	−	2.00930i
$310$	3.25768	−	22.1834i	0.185024	−	1.25993i
$311$	17.1245	+	9.88684i	0.971042	+	0.560631i	0.899554	−	0.436810i	$-0.143892\pi$
$311$	17.1245	+	9.88684i	0.971042	+	0.560631i	0.0714882	+	0.997441i	$0.477225\pi$
$312$	−2.28727	+	12.8890i	−0.129491	+	0.729697i
$313$	−7.55817	+	4.36371i	−0.427213	+	0.246652i	−0.698159	−	0.715943i	$-0.745997\pi$
$313$	−7.55817	+	4.36371i	−0.427213	+	0.246652i	0.270945	+	0.962595i	$0.412664\pi$
$314$	6.97122	−	8.80992i	0.393409	−	0.497173i
$315$		0			0
$316$	3.46389	−	0.818280i	0.194859	−	0.0460319i
$317$	6.96171	−	25.9814i	0.391008	−	1.45926i	−0.437465	−	0.899235i	$-0.644124\pi$
$317$	6.96171	−	25.9814i	0.391008	−	1.45926i	0.828474	−	0.560028i	$-0.189210\pi$
$318$	−3.60575	−	1.55693i	−0.202200	−	0.0873084i
$319$	−3.77105	+	6.53166i	−0.211138	+	0.365703i
$320$	27.9972	−	12.9806i	1.56509	−	0.725636i
$321$	−16.8569			−0.940858
$322$		0			0
$323$	−2.20702	−	2.20702i	−0.122802	−	0.122802i
$324$	−5.92600	−	6.29040i	−0.329222	−	0.349467i
$325$	−4.07238	−	15.1983i	−0.225895	−	0.843051i
$326$	4.66068	+	11.7442i	0.258131	+	0.650448i
$327$	11.6516	−	6.72705i	0.644335	−	0.372007i
$328$	19.8231	−	7.19038i	1.09455	−	0.397022i
$329$		0			0
$330$	−16.1692	−	12.7946i	−0.890086	−	0.704318i
$331$	−30.5071	−	8.17436i	−1.67682	−	0.449303i	−0.709885	−	0.704317i	$-0.751253\pi$
$331$	−30.5071	−	8.17436i	−1.67682	−	0.449303i	−0.966937	+	0.255014i	$0.917920\pi$
$332$	−17.8358	+	9.60012i	−0.978865	+	0.526875i
$333$	12.3097	−	3.29838i	0.674568	−	0.180750i
$334$	9.97506	+	13.4091i	0.545811	+	0.733712i
$335$	−8.32703			−0.454954
$336$		0			0
$337$	−23.4825			−1.27918			−0.639588	−	0.768718i	$-0.720895\pi$
$337$	−23.4825			−1.27918			−0.639588	+	0.768718i	$0.720895\pi$
$338$	−8.83254	−	11.8732i	−0.480427	−	0.645818i
$339$	−25.7472	+	6.89895i	−1.39840	+	0.374699i
$340$	5.51722	+	10.2503i	0.299214	+	0.555899i
$341$	−5.16305	−	1.38343i	−0.279595	−	0.0749172i
$342$	−12.4936	−	9.88612i	−0.675579	−	0.534580i
$343$		0			0
$344$	−20.6167	−	9.64129i	−1.11158	−	0.519824i
$345$	−46.3136	+	26.7392i	−2.49344	+	1.43959i
$346$	−4.15977	−	10.4819i	−0.223630	−	0.563512i
$347$	−2.30492	−	8.60207i	−0.123735	−	0.461784i	0.876057	−	0.482208i	$-0.160165\pi$
$347$	−2.30492	−	8.60207i	−0.123735	−	0.461784i	−0.999791	+	0.0204242i	$0.993498\pi$
$348$	24.5349	−	23.1136i	1.31521	−	1.23902i
$349$	6.94033	+	6.94033i	0.371507	+	0.371507i	0.868026	−	0.496519i	$-0.165389\pi$
$349$	6.94033	+	6.94033i	0.371507	+	0.371507i	−0.496519	+	0.868026i	$0.665389\pi$
$350$		0			0
$351$	−11.3206			−0.604246
$352$	−2.30130	−	6.98773i	−0.122660	−	0.372447i
$353$	−15.0467	+	26.0617i	−0.800856	+	1.38712i	0.118198	+	0.992990i	$0.462288\pi$
$353$	−15.0467	+	26.0617i	−0.800856	+	1.38712i	−0.919054	+	0.394133i	$0.871045\pi$
$354$	6.07488	+	2.62308i	0.322876	+	0.139415i
$355$	13.7980	−	51.4949i	0.732323	−	2.73307i
$356$	3.88951	+	16.4648i	0.206144	+	0.872633i
$357$		0			0
$358$	−14.5547	+	18.3936i	−0.769239	+	0.972131i
$359$	−8.98209	+	5.18581i	−0.474057	+	0.273697i	−0.717936	−	0.696109i	$-0.754913\pi$
$359$	−8.98209	+	5.18581i	−0.474057	+	0.273697i	0.243880	+	0.969806i	$0.421580\pi$
$360$	34.0283	+	48.7111i	1.79345	+	2.56730i
$361$	12.7487	+	7.36047i	0.670985	+	0.387393i
$362$	−1.21632	+	8.28265i	−0.0639286	+	0.435326i
$363$	19.1292	−	19.1292i	1.00402	−	1.00402i
$364$		0			0
$365$	−39.4826	−	39.4826i	−2.06661	−	2.06661i
$366$	11.1668	+	15.0110i	0.583697	+	0.784640i
$367$	4.06486	−	7.04055i	0.212184	−	0.367514i	−0.740214	−	0.672372i	$-0.765276\pi$
$367$	4.06486	−	7.04055i	0.212184	−	0.367514i	0.952398	+	0.304858i	$0.0986090\pi$
$368$	−19.0473	−	1.13735i	−0.992909	−	0.0592883i
$369$	20.3009	+	35.1622i	1.05682	+	1.83047i
$370$	−12.6800	+	1.47737i	−0.659200	+	0.0768050i
$371$		0			0
$372$	20.3231	+	12.5560i	1.05370	+	0.650999i
$373$	4.35336	+	1.16648i	0.225408	+	0.0603980i	0.369755	−	0.929129i	$-0.379441\pi$
$373$	4.35336	+	1.16648i	0.225408	+	0.0603980i	−0.144347	+	0.989527i	$0.546108\pi$
$374$	2.57943	−	1.02365i	0.133379	−	0.0529317i
$375$	−47.3815	−	27.3557i	−2.44677	−	1.41264i
$376$	−6.54905	+	7.78748i	−0.337742	+	0.401609i
$377$		−	9.23534i		−	0.475644i
$378$		0			0
$379$	−0.839080	+	0.839080i	−0.0431006	+	0.0431006i	−0.728329	−	0.685228i	$-0.759703\pi$
$379$	−0.839080	+	0.839080i	−0.0431006	+	0.0431006i	0.685228	+	0.728329i	$0.259703\pi$
$380$	10.9433	+	11.6163i	0.561382	+	0.595903i
$381$	−36.4334	+	9.76231i	−1.86654	+	0.500138i
$382$	−16.0575	−	6.93350i	−0.821573	−	0.354749i
$383$	17.1874	+	29.7695i	0.878237	+	1.52115i	0.853274	+	0.521463i	$0.174614\pi$
$383$	17.1874	+	29.7695i	0.878237	+	1.52115i	0.0249634	+	0.999688i	$0.492053\pi$
$384$	0.872140	+	32.8684i	0.0445062	+	1.67731i
$385$		0			0
$386$	3.87623	+	33.2688i	0.197295	+	1.69334i
$387$	11.3422	−	42.3296i	0.576556	−	2.15173i
$388$	9.32820	−	31.0756i	0.473568	−	1.57762i
$389$	4.01283	+	14.9761i	0.203459	+	0.759319i	0.989914	+	0.141671i	$0.0452475\pi$
$389$	4.01283	+	14.9761i	0.203459	+	0.759319i	−0.786455	+	0.617648i	$0.788086\pi$
$390$	24.9802	+	3.66839i	1.26492	+	0.185756i
$391$		−	7.19768i		−	0.364003i
$392$		0			0
$393$			28.0287i			1.41386i
$394$	−3.31837	+	22.5967i	−0.167177	+	1.13840i
$395$	−1.77676	−	6.63094i	−0.0893983	−	0.333639i
$396$	12.4734	−	6.71381i	0.626810	−	0.337381i
$397$	9.67679	−	36.1143i	0.485664	−	1.81252i	−0.0913869	−	0.995815i	$-0.529130\pi$
$397$	9.67679	−	36.1143i	0.485664	−	1.81252i	0.577051	−	0.816708i	$-0.304203\pi$
$398$	7.72146	−	0.899646i	0.387042	−	0.0450952i
$399$		0			0
$400$	−17.6854	−	35.3433i	−0.884269	−	1.76717i
$401$	−2.48812	−	4.30956i	−0.124251	−	0.215209i	0.797189	−	0.603730i	$-0.206319\pi$
$401$	−2.48812	−	4.30956i	−0.124251	−	0.215209i	−0.921440	+	0.388521i	$0.872986\pi$
$402$	3.51703	−	8.14520i	0.175414	−	0.406246i
$403$	6.32217	−	1.69402i	0.314930	−	0.0843852i
$404$	−32.7003	−	0.975427i	−1.62690	−	0.0485293i
$405$	−11.7864	+	11.7864i	−0.585672	+	0.585672i
$406$		0			0
$407$			3.04331i			0.150851i
$408$	−12.3567	+	1.06741i	−0.611749	+	0.0528447i
$409$	3.51917	+	2.03180i	0.174012	+	0.100466i	0.584476	−	0.811411i	$-0.301300\pi$
$409$	3.51917	+	2.03180i	0.174012	+	0.100466i	−0.410464	+	0.911877i	$0.634633\pi$
$410$	−15.0022	−	37.8032i	−0.740908	−	1.86697i
$411$	−63.5945	−	17.0401i	−3.13689	−	0.840526i
$412$	−7.90295	−	33.4542i	−0.389350	−	1.64817i
$413$		0			0
$414$	−4.25192	−	36.4932i	−0.208970	−	1.79354i
$415$	19.5337	+	33.8334i	0.958871	+	1.66081i
$416$	6.71867	+	6.00117i	0.329410	+	0.294232i
$417$	−13.6601	+	23.6600i	−0.668940	+	1.15864i
$418$	3.05260	−	2.27084i	0.149308	−	0.111070i
$419$	0.552238	+	0.552238i	0.0269786	+	0.0269786i	0.720467	−	0.693489i	$-0.243927\pi$
$419$	0.552238	+	0.552238i	0.0269786	+	0.0269786i	−0.693489	+	0.720467i	$0.743927\pi$
$420$		0			0
$421$	−3.77763	+	3.77763i	−0.184110	+	0.184110i	−0.793144	−	0.609034i	$-0.791557\pi$
$421$	−3.77763	+	3.77763i	−0.184110	+	0.184110i	0.609034	+	0.793144i	$0.291557\pi$
$422$	1.79648	+	0.263817i	0.0874513	+	0.0128424i
$423$	−16.9671	−	9.79598i	−0.824970	−	0.476297i
$424$	−2.21575	+	1.54786i	−0.107606	+	0.0751709i
$425$	12.9106	−	7.45395i	0.626257	−	0.361570i
$426$	44.5427	+	35.2463i	2.15810	+	1.70769i
$427$		0			0
$428$	−6.09727	+	9.86901i	−0.294723	+	0.477037i
$429$	1.55785	−	5.81397i	0.0752136	−	0.280701i
$430$	−17.4017	+	40.3012i	−0.839187	+	1.94350i
$431$	−0.590931	+	1.02352i	−0.0284641	+	0.0493013i	−0.879907	−	0.475147i	$-0.842395\pi$
$431$	−0.590931	+	1.02352i	−0.0284641	+	0.0493013i	0.851442	+	0.524448i	$0.175728\pi$
$432$	−27.8555	+	5.70921i	−1.34020	+	0.274684i
$433$	−15.2584			−0.733273			−0.366637	−	0.930364i	$-0.619491\pi$
$433$	−15.2584			−0.733273			−0.366637	+	0.930364i	$0.619491\pi$
$434$		0			0
$435$	−45.9715	−	45.9715i	−2.20416	−	2.20416i
$436$	0.276063	−	9.25477i	0.0132210	−	0.443223i
$437$	−2.55398	−	9.53156i	−0.122173	−	0.455957i
$438$	55.2964	−	21.9445i	2.64217	−	1.04855i
$439$	−3.76290	+	2.17251i	−0.179593	+	0.103688i	−0.587102	−	0.809513i	$-0.699731\pi$
$439$	−3.76290	+	2.17251i	−0.179593	+	0.103688i	0.407508	+	0.913202i	$0.366398\pi$
$440$	−13.3392	+	4.83851i	−0.635923	+	0.230667i
$441$		0			0
$442$	−2.10863	+	2.66479i	−0.100297	+	0.126751i
$443$	5.89293	+	1.57901i	0.279981	+	0.0750208i	0.396077	−	0.918217i	$-0.370371\pi$
$443$	5.89293	+	1.57901i	0.279981	+	0.0750208i	−0.116096	+	0.993238i	$0.537038\pi$
$444$	3.91044	−	13.0271i	0.185581	−	0.618237i
$445$	31.5187	−	8.44540i	1.49413	−	0.400351i
$446$	−3.63459	+	2.70379i	−0.172103	+	0.128028i
$447$	−31.9359			−1.51052
$448$		0			0
$449$	3.72499			0.175793			0.0878967	−	0.996130i	$-0.471985\pi$
$449$	3.72499			0.175793			0.0878967	+	0.996130i	$0.471985\pi$
$450$	61.0553	−	45.4193i	2.87818	−	2.14109i
$451$	−9.36552	+	2.50948i	−0.441005	+	0.118167i
$452$	−5.27393	+	17.5694i	−0.248065	+	0.826393i
$453$	15.3505	+	4.11315i	0.721228	+	0.193252i
$454$	17.1178	−	21.6328i	0.803380	−	1.01528i
$455$		0			0
$456$	−15.9847	+	5.79809i	−0.748552	+	0.271521i
$457$	−9.30556	+	5.37257i	−0.435296	+	0.251318i	−0.701600	−	0.712571i	$-0.747531\pi$
$457$	−9.30556	+	5.37257i	−0.435296	+	0.251318i	0.266304	+	0.963889i	$0.414197\pi$
$458$	−13.0532	+	5.18019i	−0.609937	+	0.242054i
$459$	−2.77606	−	10.3604i	−0.129575	−	0.483582i
$460$	−1.09732	+	36.7865i	−0.0511626	+	1.71518i
$461$	7.88785	+	7.88785i	0.367374	+	0.367374i	0.866519	−	0.499145i	$-0.166352\pi$
$461$	7.88785	+	7.88785i	0.367374	+	0.367374i	−0.499145	+	0.866519i	$0.666352\pi$
$462$		0			0
$463$	27.3485			1.27099			0.635496	−	0.772104i	$-0.280796\pi$
$463$	27.3485			1.27099			0.635496	+	0.772104i	$0.280796\pi$
$464$	−4.65759	−	22.7246i	−0.216223	−	1.05496i
$465$	23.0379	−	39.9028i	1.06836	−	1.85045i
$466$	−1.64741	+	3.81529i	−0.0763148	+	0.176740i
$467$	4.16957	−	15.5610i	0.192945	−	0.720079i	−0.799845	−	0.600207i	$-0.795085\pi$
$467$	4.16957	−	15.5610i	0.192945	−	0.720079i	0.992789	−	0.119872i	$-0.0382485\pi$
$468$	−9.11686	+	14.7565i	−0.421427	+	0.682120i
$469$		0			0
$470$	15.3900	+	12.1780i	0.709890	+	0.561730i
$471$	19.9937	−	11.5434i	0.921261	−	0.531890i
$472$	3.73304	−	2.60781i	0.171827	−	0.120034i
$473$	9.06303	+	5.23254i	0.416718	+	0.240592i
$474$	7.23658	+	1.06271i	0.332387	+	0.0488118i
$475$	14.4520	−	14.4520i	0.663105	−	0.663105i
$476$		0			0
$477$	−3.67995	−	3.67995i	−0.168493	−	0.168493i
$478$	18.3942	−	13.6835i	0.841330	−	0.625869i
$479$	−5.69399	+	9.86229i	−0.260165	+	0.450619i	−0.966286	−	0.257472i	$-0.917110\pi$
$479$	−5.69399	+	9.86229i	−0.260165	+	0.450619i	0.706120	+	0.708092i	$0.250444\pi$
$480$	63.3165	−	3.57158i	2.88999	−	0.163019i
$481$	−1.86327	−	3.22729i	−0.0849580	−	0.147152i
$482$	−2.31041	−	19.8297i	−0.105236	−	0.903219i
$483$		0			0
$484$	−4.28017	−	18.1185i	−0.194553	−	0.823570i
$485$	−60.4468	−	16.1967i	−2.74475	−	0.735453i
$486$	4.57387	+	11.5254i	0.207475	+	0.522802i
$487$	−27.1526	−	15.6766i	−1.23040	−	0.710373i	−0.263288	−	0.964717i	$-0.584807\pi$
$487$	−27.1526	−	15.6766i	−1.23040	−	0.710373i	−0.967114	+	0.254344i	$0.918140\pi$
$488$	12.8275	−	1.10807i	0.580673	−	0.0501602i
$489$			25.9652i			1.17419i
$490$		0			0
$491$	20.2775	−	20.2775i	0.915112	−	0.915112i	−0.0815572	−	0.996669i	$-0.525989\pi$
$491$	20.2775	−	20.2775i	0.915112	−	0.915112i	0.996669	+	0.0815572i	$0.0259893\pi$
$492$	43.3141	+	1.29203i	1.95275	+	0.0582492i
$493$	8.45204	−	2.26472i	0.380661	−	0.101998i
$494$	−1.84681	+	4.27708i	−0.0830918	+	0.192435i
$495$	−13.6608	−	23.6612i	−0.614008	−	1.06349i
$496$	14.7021	−	7.35674i	0.660143	−	0.330327i
$497$		0			0
$498$	−41.3449	+	4.81719i	−1.85271	+	0.215864i
$499$	−6.77758	+	25.2943i	−0.303406	+	1.13233i	0.630902	+	0.775862i	$0.282685\pi$
$499$	−6.77758	+	25.2943i	−0.303406	+	1.13233i	−0.934309	+	0.356465i	$0.883982\pi$
$500$	−33.1540	+	17.8452i	−1.48269	+	0.798060i
$501$	8.88887	+	33.1737i	0.397126	+	1.48209i
$502$	−4.12540	+	28.0922i	−0.184126	+	1.25382i
$503$			31.9854i			1.42616i	0.701082	+	0.713080i	$0.252701\pi$
$503$			31.9854i			1.42616i	−0.701082	+	0.713080i	$0.747299\pi$
$504$		0			0
$505$			63.0987i			2.80786i
$506$	8.68059	+	1.27476i	0.385899	+	0.0566702i
$507$	−7.87076	−	29.3741i	−0.349553	−	1.30455i
$508$	−7.46284	+	24.8614i	−0.331110	+	1.10305i
$509$	4.45247	−	16.6168i	0.197352	−	0.736529i	−0.794293	−	0.607535i	$-0.792159\pi$
$509$	4.45247	−	16.6168i	0.197352	−	0.736529i	0.991645	−	0.128994i	$-0.0411748\pi$
$510$	2.76846	+	23.7610i	0.122589	+	1.05216i
$511$		0			0
$512$	19.5586	+	11.3782i	0.864375	+	0.502849i
$513$	−7.35242	−	12.7348i	−0.324617	−	0.562254i
$514$	4.20248	+	1.81460i	0.185363	+	0.0800384i
$515$	−64.0417	+	17.1599i	−2.82201	+	0.756156i
$516$	−32.0714	−	34.0435i	−1.41186	−	1.49868i
$517$	3.30830	−	3.30830i	0.145499	−	0.145499i
$518$		0			0
$519$		−	23.1745i		−	1.01725i
$520$	11.1832	−	13.2980i	0.490417	−	0.583155i
$521$	−29.8192	−	17.2161i	−1.30640	−	0.754251i	−0.324907	−	0.945746i	$-0.605333\pi$
$521$	−29.8192	−	17.2161i	−1.30640	−	0.754251i	−0.981494	+	0.191495i	$0.938666\pi$
$522$	41.5152	−	16.4753i	1.81707	−	0.721106i
$523$	21.0410	+	5.63792i	0.920060	+	0.246529i	0.687611	−	0.726079i	$-0.258660\pi$
$523$	21.0410	+	5.63792i	0.920060	+	0.246529i	0.232449	+	0.972609i	$0.425326\pi$
$524$	16.4097	+	10.1382i	0.716861	+	0.442890i
$525$		0			0
$526$	33.7357	−	3.93062i	1.47094	−	0.171383i
$527$	3.10069	+	5.37054i	0.135068	+	0.233945i
$528$	0.901144	−	15.0916i	0.0392173	−	0.656776i
$529$	−0.122092	+	0.211469i	−0.00530834	+	0.00919432i
$530$	3.11154	+	4.18271i	0.135157	+	0.181685i
$531$	6.19990	+	6.19990i	0.269053	+	0.269053i
$532$		0			0
$533$	8.39524	−	8.39524i	0.363638	−	0.363638i
$534$	−5.05134	+	34.3975i	−0.218593	+	1.48852i
$535$	19.3770	+	11.1873i	0.837742	+	0.483670i
$536$	−3.49655	−	5.00527i	−0.151028	−	0.216195i
$537$	−41.7433	+	24.1005i	−1.80136	+	1.04001i
$538$	0.108596	−	0.137239i	0.00468192	−	0.00591681i
$539$		0			0
$540$	12.6086	+	53.3740i	0.542589	+	2.29685i
$541$	−8.68080	+	32.3972i	−0.373217	+	1.39286i	0.482716	+	0.875777i	$0.339650\pi$
$541$	−8.68080	+	32.3972i	−0.373217	+	1.39286i	−0.855933	+	0.517087i	$0.827016\pi$
$542$	13.1313	+	5.66998i	0.564037	+	0.243547i
$543$	−8.60168	+	14.8985i	−0.369133	+	0.639358i
$544$	−3.84461	+	7.62045i	−0.164836	+	0.326724i
$545$	−17.8581			−0.764956
$546$		0			0
$547$	27.8819	+	27.8819i	1.19214	+	1.19214i	0.976464	+	0.215680i	$0.0691967\pi$
$547$	27.8819	+	27.8819i	1.19214	+	1.19214i	0.215680	+	0.976464i	$0.430803\pi$
$548$	−32.9790	+	31.0685i	−1.40879	+	1.32718i
$549$	6.41632	+	23.9460i	0.273842	+	1.02199i
$550$	6.70309	+	16.8907i	0.285821	+	0.720222i
$551$	10.3891	−	5.99813i	0.442589	−	0.255529i
$552$	−35.5198	−	16.6106i	−1.51182	−	0.706995i
$553$		0			0
$554$	−17.2647	−	13.6614i	−0.733506	−	0.580418i
$555$	−25.3397	−	6.78974i	−1.07561	−	0.288208i
$556$	8.91102	+	16.5555i	0.377911	+	0.702109i
$557$	−0.376946	+	0.101002i	−0.0159717	+	0.00427960i	−0.266796	−	0.963753i	$-0.585965\pi$
$557$	−0.376946	+	0.101002i	−0.0159717	+	0.00427960i	0.250824	+	0.968033i	$0.419298\pi$
$558$	18.8935	+	25.3977i	0.799824	+	1.07517i
$559$	−12.8145			−0.541997
$560$		0			0
$561$	5.70288			0.240776
$562$	3.56207	+	4.78834i	0.150257	+	0.201984i
$563$	18.9755	−	5.08448i	0.799724	−	0.214285i	0.164261	−	0.986417i	$-0.447476\pi$
$563$	18.9755	−	5.08448i	0.799724	−	0.214285i	0.635463	+	0.772132i	$0.280809\pi$
$564$	−18.4123	+	9.91044i	−0.775297	+	0.417305i
$565$	34.1751	+	9.15720i	1.43776	+	0.385246i
$566$	−26.0090	−	20.5807i	−1.09324	−	0.865073i
$567$		0			0
$568$	36.7467	−	13.3291i	1.54186	−	0.559275i
$569$	6.99814	−	4.04038i	0.293377	−	0.169381i	−0.346087	−	0.938203i	$-0.612490\pi$
$569$	6.99814	−	4.04038i	0.293377	−	0.169381i	0.639464	+	0.768821i	$0.279156\pi$
$570$	12.0973	+	30.4833i	0.506702	+	1.27681i
$571$	−2.76648	−	10.3246i	−0.115774	−	0.432073i	0.883570	−	0.468299i	$-0.155133\pi$
$571$	−2.76648	−	10.3246i	−0.115774	−	0.432073i	−0.999344	+	0.0362262i	$0.988466\pi$
$572$	−2.84036	−	3.01502i	−0.118761	−	0.126064i
$573$	−25.4154	−	25.4154i	−1.06175	−	1.06175i
$574$		0			0
$575$	47.1320			1.96554
$576$	−14.9910	+	40.9079i	−0.624626	+	1.70449i
$577$	−0.979847	+	1.69714i	−0.0407915	+	0.0706530i	−0.885700	−	0.464257i	$-0.846321\pi$
$577$	−0.979847	+	1.69714i	−0.0407915	+	0.0706530i	0.844909	+	0.534910i	$0.179655\pi$
$578$	19.1161	+	8.25416i	0.795123	+	0.343328i
$579$	−17.8144	+	66.4844i	−0.740343	+	2.76300i
$580$	−43.5427	+	10.2862i	−1.80801	+	0.427110i
$581$		0			0
$582$	41.3735	−	52.2860i	1.71499	−	2.16733i
$583$	1.07629	−	0.621397i	0.0445754	−	0.0257356i
$584$	7.15360	−	40.3113i	0.296018	−	1.66809i
$585$	28.9733	+	16.7277i	1.19790	+	0.691606i
$586$	−3.92997	+	26.7614i	−0.162346	+	1.10550i
$587$	24.6131	−	24.6131i	1.01589	−	1.01589i	0.0160192	−	0.999872i	$-0.494901\pi$
$587$	24.6131	−	24.6131i	1.01589	−	1.01589i	0.999872	−	0.0160192i	$-0.00509930\pi$
$588$		0			0
$589$	6.01174	+	6.01174i	0.247709	+	0.247709i
$590$	−5.24225	−	7.04694i	−0.215820	−	0.290118i
$591$	−23.4670	+	40.6461i	−0.965305	+	1.67196i
$592$	−6.21238	−	7.00140i	−0.255327	−	0.287756i
$593$	−8.27415	−	14.3313i	−0.339779	−	0.588514i	0.644612	−	0.764510i	$-0.277019\pi$
$593$	−8.27415	−	14.3313i	−0.339779	−	0.588514i	−0.984391	+	0.175996i	$0.943686\pi$
$594$	12.9866	−	1.51310i	0.532845	−	0.0620831i
$595$		0			0
$596$	−11.5515	+	18.6972i	−0.473167	+	0.765866i
$597$	15.4306	+	4.13461i	0.631531	+	0.169218i
$598$	−9.98583	+	3.96289i	−0.408351	+	0.162054i
$599$	8.88965	+	5.13244i	0.363221	+	0.209706i	0.670493	−	0.741916i	$-0.266083\pi$
$599$	8.88965	+	5.13244i	0.363221	+	0.209706i	−0.307272	+	0.951622i	$0.599416\pi$
$600$	−6.98964	−	80.9146i	−0.285351	−	3.30332i
$601$		−	35.6586i		−	1.45455i	−0.686348	−	0.727273i	$-0.740787\pi$
$601$		−	35.6586i		−	1.45455i	0.686348	−	0.727273i	$-0.259213\pi$
$602$		0			0
$603$	8.31283	−	8.31283i	0.338524	−	0.338524i
$604$	7.96048	−	7.49932i	0.323907	−	0.305143i
$605$	−34.6844	+	9.29367i	−1.41012	+	0.377841i
$606$	−61.7209	−	26.6506i	−2.50724	−	1.08261i
$607$	−11.5556	−	20.0148i	−0.469026	−	0.812377i	0.530347	−	0.847780i	$-0.322062\pi$
$607$	−11.5556	−	20.0148i	−0.469026	−	0.812377i	−0.999373	+	0.0354040i	$0.988728\pi$
$608$	−2.38725	+	11.4556i	−0.0968157	+	0.464586i
$609$		0			0
$610$	−2.87393	−	24.6663i	−0.116362	−	0.998708i
$611$	−1.48278	+	5.53381i	−0.0599868	+	0.223874i
$612$	−15.7406	−	4.72498i	−0.636276	−	0.190996i
$613$	−9.85340	−	36.7734i	−0.397975	−	1.48526i	−0.816653	−	0.577129i	$-0.804173\pi$
$613$	−9.85340	−	36.7734i	−0.397975	−	1.48526i	0.418678	−	0.908135i	$-0.362493\pi$
$614$	−17.6782	−	2.59608i	−0.713433	−	0.104769i
$615$		−	83.5793i		−	3.37024i
$616$		0			0
$617$		−	47.9337i		−	1.92974i	−0.262732	−	0.964869i	$-0.584623\pi$
$617$		−	47.9337i		−	1.92974i	0.262732	−	0.964869i	$-0.415377\pi$
$618$	10.2636	−	69.8909i	0.412864	−	2.81143i
$619$	1.48260	+	5.53313i	0.0595906	+	0.222395i	0.989299	−	0.145901i	$-0.0466080\pi$
$619$	1.48260	+	5.53313i	0.0595906	+	0.222395i	−0.929709	+	0.368296i	$0.879941\pi$
$620$	−15.0285	−	27.9209i	−0.603558	−	1.12133i
$621$	8.77664	−	32.7549i	0.352195	−	1.31441i
$622$	27.7763	−	3.23629i	1.11373	−	0.129763i
$623$		0			0
$624$	8.28423	+	16.5556i	0.331634	+	0.662755i
$625$	11.6094	+	20.1081i	0.464376	+	0.804323i
$626$	−4.89274	+	11.3312i	−0.195553	+	0.452888i
$627$	7.55206	−	2.02357i	0.301600	−	0.0808135i
$628$	0.473714	−	15.8808i	0.0189033	−	0.633714i
$629$	2.49664	−	2.49664i	0.0995477	−	0.0995477i
$630$		0			0
$631$		−	2.35784i		−	0.0938640i	−0.998898	−	0.0469320i	$-0.985056\pi$
$631$		−	2.35784i		−	0.0938640i	0.998898	−	0.0469320i	$-0.0149444\pi$
$632$	3.23971	−	3.85234i	0.128869	−	0.153238i
$633$	3.23145	+	1.86568i	0.128439	+	0.0741541i
$634$	−14.0315	−	35.3570i	−0.557261	−	1.40421i
$635$	48.3593	+	12.9578i	1.91908	+	0.514216i
$636$	−5.40558	+	1.27697i	−0.214345	+	0.0506351i
$637$		0			0
$638$	1.23439	+	10.5945i	0.0488699	+	0.419440i
$639$	37.6326	+	65.1815i	1.48872	+	2.57854i
$640$	20.8111	−	38.3611i	0.822631	−	1.51636i
$641$	24.9208	−	43.1640i	0.984311	−	1.70488i	0.339354	−	0.940659i	$-0.389791\pi$
$641$	24.9208	−	43.1640i	0.984311	−	1.70488i	0.644957	−	0.764219i	$-0.276875\pi$
$642$	−19.1272	+	14.2288i	−0.754890	+	0.561565i
$643$	−6.07975	−	6.07975i	−0.239762	−	0.239762i	0.576990	−	0.816751i	$-0.304227\pi$
$643$	−6.07975	−	6.07975i	−0.239762	−	0.239762i	−0.816751	+	0.576990i	$0.804227\pi$
$644$		0			0
$645$	−63.7879	+	63.7879i	−2.51165	+	2.51165i
$646$	−4.36720	−	0.641332i	−0.171825	−	0.0252329i
$647$	−0.401199	−	0.231632i	−0.0157727	−	0.00910640i	0.492093	−	0.870543i	$-0.336232\pi$
$647$	−0.401199	−	0.231632i	−0.0157727	−	0.00910640i	−0.507866	+	0.861436i	$0.669565\pi$
$648$	−12.0338	−	2.13551i	−0.472733	−	0.0838907i
$649$	−1.81331	+	1.04692i	−0.0711787	+	0.0410950i
$650$	−17.4497	−	13.8078i	−0.684432	−	0.541586i
$651$		0			0
$652$	15.2016	+	9.39183i	0.595339	+	0.367812i
$653$	2.42919	−	9.06587i	0.0950617	−	0.354775i	−0.901967	−	0.431805i	$-0.857877\pi$
$653$	2.42919	−	9.06587i	0.0950617	−	0.354775i	0.997029	+	0.0770297i	$0.0245436\pi$
$654$	7.54259	−	17.4681i	0.294939	−	0.683057i
$655$	18.6017	−	32.2191i	0.726829	−	1.25891i
$656$	16.4235	−	24.8913i	0.641231	−	0.971843i
$657$	78.8305			3.07547
$658$		0			0
$659$	−4.62922	−	4.62922i	−0.180329	−	0.180329i	0.611170	−	0.791499i	$-0.290699\pi$
$659$	−4.62922	−	4.62922i	−0.180329	−	0.180329i	−0.791499	+	0.611170i	$0.790699\pi$
$660$	−29.1467	−	0.869427i	−1.13454	−	0.0338424i
$661$	−0.826161	−	3.08328i	−0.0321339	−	0.119926i	0.947996	−	0.318283i	$-0.103106\pi$
$661$	−0.826161	−	3.08328i	−0.0321339	−	0.119926i	−0.980130	+	0.198357i	$0.936439\pi$
$662$	−41.5158	+	16.4756i	−1.61356	+	0.640342i
$663$	−6.04763	+	3.49160i	−0.234870	+	0.135602i
$664$	−12.1345	+	25.9482i	−0.470911	+	1.00698i
$665$		0			0
$666$	11.1835	−	14.1332i	0.433351	−	0.547650i
$667$	26.7215	+	7.16001i	1.03466	+	0.277237i
$668$	22.6371	+	6.79514i	0.875854	+	0.262912i
$669$	−8.99190	+	2.40937i	−0.347647	+	0.0931517i
$670$	−9.44854	+	7.02881i	−0.365029	+	0.271546i
$671$	−5.92014			−0.228544
$672$		0			0
$673$	6.82222			0.262977			0.131489	−	0.991318i	$-0.458024\pi$
$673$	6.82222			0.262977			0.131489	+	0.991318i	$0.458024\pi$
$674$	−26.6452	+	19.8215i	−1.02634	+	0.763495i
$675$	67.8422	−	18.1783i	2.61125	−	0.699682i
$676$	−20.0443	−	6.01684i	−0.770933	−	0.231417i
$677$	−6.52747	−	1.74903i	−0.250871	−	0.0672207i	0.131192	−	0.991357i	$-0.458120\pi$
$677$	−6.52747	−	1.74903i	−0.250871	−	0.0672207i	−0.382063	+	0.924136i	$0.624786\pi$
$678$	−23.3916	+	29.5612i	−0.898347	+	1.13529i
$679$		0			0
$680$	14.9125	+	6.97375i	0.571868	+	0.267431i
$681$	49.0946	−	28.3448i	1.88131	−	1.08617i
$682$	−7.02617	+	2.78834i	−0.269046	+	0.106771i
$683$	−10.7149	−	39.9884i	−0.409993	−	1.53012i	−0.794657	−	0.607059i	$-0.792349\pi$
$683$	−10.7149	−	39.9884i	−0.409993	−	1.53012i	0.384664	−	0.923057i	$-0.374317\pi$
$684$	−22.5211	−	0.671790i	−0.861117	−	0.0256865i
$685$	61.7932	+	61.7932i	2.36100	+	2.36100i
$686$		0			0
$687$	−28.8594			−1.10106
$688$	−31.5316	+	6.46266i	−1.20213	+	0.246386i
$689$	−0.760903	+	1.31792i	−0.0289881	+	0.0502089i
$690$	−29.9808	+	69.4336i	−1.14135	+	2.64329i
$691$	−1.70225	+	6.35289i	−0.0647567	+	0.241675i	−0.990716	−	0.135948i	$-0.956592\pi$
$691$	−1.70225	+	6.35289i	−0.0647567	+	0.241675i	0.925959	+	0.377624i	$0.123259\pi$
$692$	−13.5678	−	8.38243i	−0.515769	−	0.318652i
$693$		0			0
$694$	−9.87632	−	7.81505i	−0.374900	−	0.296655i
$695$	31.4048	−	18.1315i	1.19125	−	0.687769i
$696$	8.32927	−	46.9364i	0.315720	−	1.77912i
$697$	9.74191	+	5.62449i	0.369001	+	0.213043i
$698$	13.7334	+	2.01677i	0.519816	+	0.0763360i
$699$	−6.03875	+	6.03875i	−0.228407	+	0.228407i
$700$		0			0
$701$	−4.01206	−	4.01206i	−0.151533	−	0.151533i	0.627269	−	0.778802i	$-0.284173\pi$
$701$	−4.01206	−	4.01206i	−0.151533	−	0.151533i	−0.778802	+	0.627269i	$0.784173\pi$
$702$	−12.8452	+	9.55562i	−0.484812	+	0.360654i
$703$	2.42030	−	4.19208i	0.0912834	−	0.158107i
$704$	−8.50955	−	5.98633i	−0.320716	−	0.225618i
$705$	20.1651	+	34.9270i	0.759462	+	1.31543i
$706$	4.92528	+	42.2726i	0.185365	+	1.59095i
$707$		0			0
$708$	9.10719	−	2.15141i	0.342269	−	0.0808549i
$709$	−49.1929	−	13.1812i	−1.84748	−	0.495030i	−0.848085	−	0.529861i	$-0.822244\pi$
$709$	−49.1929	−	13.1812i	−1.84748	−	0.495030i	−0.999393	+	0.0348304i	$0.988911\pi$
$710$	−27.8102	−	70.0772i	−1.04370	−	2.62995i
$711$	8.39335	+	4.84590i	0.314775	+	0.181736i
$712$	18.3112	+	15.3992i	0.686241	+	0.577110i
$713$			19.6059i			0.734248i
$714$		0			0
$715$	−5.64929	+	5.64929i	−0.211271	+	0.211271i
$716$	−0.989032	+	33.1564i	−0.0369619	+	1.23911i
$717$	45.5068	−	12.1935i	1.69948	−	0.455375i
$718$	−5.81451	+	13.4660i	−0.216995	+	0.502546i
$719$	−3.81125	−	6.60127i	−0.142135	−	0.246186i	0.786165	−	0.618017i	$-0.212064\pi$
$719$	−3.81125	−	6.60127i	−0.142135	−	0.246186i	−0.928301	+	0.371831i	$0.878730\pi$
$720$	79.7281	+	26.5485i	2.97129	+	0.989406i
$721$		0			0
$722$	20.6787	−	2.40932i	0.769580	−	0.0896657i
$723$	10.6182	−	39.6278i	0.394896	−	1.47377i
$724$	5.61120	+	10.4249i	0.208538	+	0.387437i
$725$	14.8299	+	55.3459i	0.550768	+	2.05549i
$726$	5.55870	−	37.8524i	0.206303	−	1.40483i
$727$			25.4856i			0.945207i	0.881275	+	0.472604i	$0.156686\pi$
$727$			25.4856i			0.945207i	−0.881275	+	0.472604i	$0.843314\pi$
$728$		0			0
$729$			38.4448i			1.42388i
$730$	−78.1273	−	11.4732i	−2.89162	−	0.424641i
$731$	−3.14242	−	11.7277i	−0.116227	−	0.433763i
$732$	25.3415	+	7.60695i	0.936648	+	0.281161i
$733$	−5.48115	+	20.4559i	−0.202451	+	0.755557i	0.787761	+	0.615982i	$0.211240\pi$
$733$	−5.48115	+	20.4559i	−0.202451	+	0.755557i	−0.990211	+	0.139575i	$0.955426\pi$
$734$	−1.33056	−	11.4199i	−0.0491120	−	0.421517i
$735$		0			0
$736$	−22.5727	+	14.7872i	−0.832039	+	0.545063i
$737$	1.40371	+	2.43129i	0.0517061	+	0.0895577i
$738$	52.7154	+	22.7621i	1.94048	+	0.837883i
$739$	16.8591	−	4.51737i	0.620170	−	0.166174i	0.0649652	−	0.997888i	$-0.479306\pi$
$739$	16.8591	−	4.51737i	0.620170	−	0.166174i	0.555205	+	0.831713i	$0.312640\pi$
$740$	−13.1407	+	12.3794i	−0.483061	+	0.455077i
$741$	−6.76966	+	6.76966i	−0.248690	+	0.248690i
$742$		0			0
$743$		−	10.6724i		−	0.391531i	−0.980651	−	0.195766i	$-0.937281\pi$
$743$		−	10.6724i		−	0.391531i	0.980651	−	0.195766i	$-0.0627192\pi$
$744$	33.6587	−	2.90754i	1.23399	−	0.106596i
$745$	36.7104	+	21.1948i	1.34497	+	0.776517i
$746$	5.92430	−	2.35106i	0.216904	−	0.0860786i
$747$	−53.2760	−	14.2753i	−1.94927	−	0.522305i
$748$	2.06278	−	3.33880i	0.0754226	−	0.122079i
$749$		0			0
$750$	−76.8538	+	8.95442i	−2.80630	+	0.326969i
$751$	1.41476	+	2.45044i	0.0516254	+	0.0894178i	0.890683	−	0.454624i	$-0.150226\pi$
$751$	1.41476	+	2.45044i	0.0516254	+	0.0894178i	−0.839058	+	0.544042i	$0.816893\pi$
$752$	−0.857719	+	14.3643i	−0.0312778	+	0.523814i
$753$	−29.1743	+	50.5313i	−1.06317	+	1.84146i
$754$	−7.79550	−	10.4792i	−0.283896	−	0.381629i
$755$	−14.9157	−	14.9157i	−0.542837	−	0.542837i
$756$		0			0
$757$	15.6590	−	15.6590i	0.569136	−	0.569136i	−0.362750	−	0.931886i	$-0.618162\pi$
$757$	15.6590	−	15.6590i	0.569136	−	0.569136i	0.931886	+	0.362750i	$0.118162\pi$
$758$	−0.243826	+	1.66035i	−0.00885617	+	0.0603067i
$759$	15.6144	+	9.01496i	0.566765	+	0.327222i
$760$	22.2225	+	3.94357i	0.806093	+	0.143048i
$761$	−4.15144	+	2.39683i	−0.150490	+	0.0868852i	−0.573354	−	0.819308i	$-0.694358\pi$
$761$	−4.15144	+	2.39683i	−0.150490	+	0.0868852i	0.422864	+	0.906193i	$0.361025\pi$
$762$	−33.1001	+	41.8304i	−1.19909	+	1.51535i
$763$		0			0
$764$	−24.0727	+	5.68674i	−0.870920	+	0.205739i
$765$	−8.20404	+	30.6179i	−0.296618	+	1.10699i
$766$	44.6306	+	19.2711i	1.61257	+	0.696294i
$767$	1.28195	−	2.22041i	0.0462886	−	0.0801742i
$768$	28.7336	+	36.5590i	1.03684	+	1.31921i
$769$	13.5489			0.488585			0.244293	−	0.969702i	$-0.421444\pi$
$769$	13.5489			0.488585			0.244293	+	0.969702i	$0.421444\pi$
$770$		0			0
$771$	6.65159	+	6.65159i	0.239551	+	0.239551i
$772$	32.4803	+	34.4776i	1.16899	+	1.24088i
$773$	6.87406	+	25.6544i	0.247243	+	0.922723i	0.972243	+	0.233974i	$0.0751731\pi$
$773$	6.87406	+	25.6544i	0.247243	+	0.922723i	−0.725000	+	0.688749i	$0.758160\pi$
$774$	−22.8604	−	57.6045i	−0.821701	−	2.07055i
$775$	−35.1675	+	20.3040i	−1.26325	+	0.729340i
$776$	−15.6462	−	43.1348i	−0.561666	−	1.54845i
$777$		0			0
$778$	17.1945	+	13.6059i	0.616454	+	0.487795i
$779$	14.8965	+	3.99151i	0.533723	+	0.143011i
$780$	31.4410	−	16.9232i	1.12577	−	0.605947i
$781$	−17.3612	+	4.65192i	−0.621233	+	0.166459i
$782$	−6.07553	−	8.16709i	−0.217260	−	0.292054i
$783$	41.2247			1.47325
$784$		0			0
$785$	−30.6438			−1.09372
$786$	23.6589	+	31.8037i	0.843885	+	1.13440i
$787$	−33.4454	+	8.96168i	−1.19220	+	0.319449i	−0.799756	−	0.600326i	$-0.795038\pi$
$787$	−33.4454	+	8.96168i	−1.19220	+	0.319449i	−0.392446	+	0.919775i	$0.628371\pi$
$788$	15.3084	+	28.4410i	0.545340	+	1.01317i
$789$	67.4174	+	18.0644i	2.40012	+	0.643111i
$790$	−7.61320	−	6.02426i	−0.270865	−	0.214334i
$791$		0			0
$792$	8.48622	−	18.1467i	0.301545	−	0.644816i
$793$	6.27802	−	3.62462i	0.222939	−	0.128714i
$794$	−19.5038	−	49.1464i	−0.692163	−	1.74414i
$795$	2.77272	+	10.3479i	0.0983383	+	0.367003i
$796$	8.00201	−	7.53845i	0.283624	−	0.267193i
$797$	−17.6690	−	17.6690i	−0.625870	−	0.625870i	0.321157	−	0.947026i	$-0.395928\pi$
$797$	−17.6690	−	17.6690i	−0.625870	−	0.625870i	−0.947026	+	0.321157i	$0.895928\pi$
$798$		0			0
$799$	−5.42807			−0.192031
$800$	−49.9004	−	25.1753i	−1.76425	−	0.890082i
$801$	−23.0339	+	39.8959i	−0.813863	+	1.40965i
$802$	−6.46090	−	2.78977i	−0.228142	−	0.0985100i
$803$	−4.87228	+	18.1836i	−0.171939	+	0.641686i
$804$	−2.88461	−	12.2109i	−0.101732	−	0.430646i
$805$		0			0
$806$	5.74374	−	7.25869i	0.202315	−	0.255676i
$807$	0.311458	−	0.179820i	0.0109638	−	0.00632998i
$808$	−37.9278	+	26.4954i	−1.33430	+	0.932103i
$809$	−2.59269	−	1.49689i	−0.0911540	−	0.0526278i	0.453730	−	0.891139i	$-0.350093\pi$
$809$	−2.59269	−	1.49689i	−0.0911540	−	0.0526278i	−0.544884	+	0.838511i	$0.683426\pi$
$810$	−3.42499	+	23.3227i	−0.120342	+	0.819477i
$811$	−2.28628	+	2.28628i	−0.0802820	+	0.0802820i	−0.746108	−	0.665825i	$-0.768080\pi$
$811$	−2.28628	+	2.28628i	−0.0802820	+	0.0802820i	0.665825	+	0.746108i	$0.268080\pi$
$812$		0			0
$813$	20.7839	+	20.7839i	0.728923	+	0.728923i
$814$	2.56884	+	3.45319i	0.0900379	+	0.121034i
$815$	17.2322	−	29.8471i	0.603618	−	1.04550i
$816$	−13.1200	+	11.6414i	−0.459290	+	0.407531i
$817$	−8.32272	−	14.4154i	−0.291175	−	0.504330i
$818$	5.70817	−	0.665073i	0.199582	−	0.0232537i
$819$		0			0
$820$	−48.9323	−	30.2313i	−1.70879	−	1.05572i
$821$	39.1150	+	10.4808i	1.36512	+	0.365783i	0.865695	−	0.500572i	$-0.166877\pi$
$821$	39.1150	+	10.4808i	1.36512	+	0.365783i	0.499428	+	0.866356i	$0.333544\pi$
$822$	−86.5431	+	34.3447i	−3.01854	+	1.19791i
$823$	35.5496	+	20.5246i	1.23918	+	0.715442i	0.968927	−	0.247347i	$-0.0795588\pi$
$823$	35.5496	+	20.5246i	1.23918	+	0.715442i	0.270255	+	0.962789i	$0.412892\pi$
$824$	−37.2059	−	31.2891i	−1.29613	−	1.09001i
$825$			37.3437i			1.30014i
$826$		0			0
$827$	−20.3987	+	20.3987i	−0.709331	+	0.709331i	−0.966394	−	0.257064i	$-0.917245\pi$
$827$	−20.3987	+	20.3987i	−0.709331	+	0.709331i	0.257064	+	0.966394i	$0.417245\pi$
$828$	−35.6283	−	37.8192i	−1.23817	−	1.31431i
$829$	25.2567	−	6.76750i	0.877200	−	0.235045i	0.208001	−	0.978129i	$-0.433304\pi$
$829$	25.2567	−	6.76750i	0.877200	−	0.235045i	0.669199	+	0.743083i	$0.266637\pi$
$830$	50.7231	+	21.9018i	1.76062	+	0.760223i
$831$	−22.6214	−	39.1814i	−0.784727	−	1.35919i
$832$	12.6891	+	1.13822i	0.439916	+	0.0394608i
$833$		0			0
$834$	4.47141	+	38.3771i	0.154832	+	1.32889i
$835$	11.7985	−	44.0326i	0.408304	−	1.52381i
$836$	1.54693	−	5.15337i	0.0535016	−	0.178233i
$837$	7.56177	+	28.2209i	0.261373	+	0.975457i
$838$	1.09276	+	0.160473i	0.0377486	+	0.00554346i
$839$			41.9862i			1.44953i	0.688999	+	0.724763i	$0.258051\pi$
$839$			41.9862i			1.44953i	−0.688999	+	0.724763i	$0.741949\pi$
$840$		0			0
$841$			4.63123i			0.159698i
$842$	−1.09773	+	7.47508i	−0.0378303	+	0.257608i
$843$	3.17419	+	11.8462i	0.109325	+	0.408006i
$844$	2.26112	−	1.21705i	0.0778310	−	0.0418926i
$845$	−10.4471	+	38.9892i	−0.359392	+	1.34127i
$846$	−27.5210	+	3.20654i	−0.946193	+	0.110243i
$847$		0			0
$848$	−1.20763	+	3.62664i	−0.0414701	+	0.124539i
$849$	−34.0788	−	59.0263i	−1.16958	−	2.02578i
$850$	8.35762	−	19.3557i	0.286664	−	0.663894i
$851$	10.7824	−	2.88913i	0.369616	−	0.0990382i
$852$	80.2930	+	2.39508i	2.75079	+	0.0820542i
$853$	10.9845	−	10.9845i	0.376104	−	0.376104i	−0.493591	−	0.869694i	$-0.664316\pi$
$853$	10.9845	−	10.9845i	0.376104	−	0.376104i	0.869694	+	0.493591i	$0.164316\pi$
$854$		0			0
$855$			43.4570i			1.48620i
$856$	1.41192	+	16.3449i	0.0482583	+	0.558656i
$857$	40.9817	+	23.6608i	1.39991	+	0.808237i	0.994382	−	0.105848i	$-0.0337556\pi$
$857$	40.9817	+	23.6608i	1.39991	+	0.808237i	0.405524	+	0.914084i	$0.367089\pi$
$858$	−3.13988	−	7.91198i	−0.107194	−	0.270111i
$859$	−6.98214	−	1.87086i	−0.238228	−	0.0638329i	0.137730	−	0.990470i	$-0.456019\pi$
$859$	−6.98214	−	1.87086i	−0.238228	−	0.0638329i	−0.375957	+	0.926637i	$0.622686\pi$
$860$	14.2726	+	60.4178i	0.486692	+	2.06023i
$861$		0			0
$862$	0.193431	+	1.66017i	0.00658828	+	0.0565458i
$863$	−5.05527	−	8.75599i	−0.172084	−	0.298057i	0.767065	−	0.641570i	$-0.221717\pi$
$863$	−5.05527	−	8.75599i	−0.172084	−	0.298057i	−0.939148	+	0.343512i	$0.888383\pi$
$864$	−26.7880	+	29.9908i	−0.911346	+	1.02031i
$865$	−15.3802	+	26.6392i	−0.522941	+	0.905761i
$866$	−17.3135	+	12.8796i	−0.588335	+	0.437665i
$867$	30.2565	+	30.2565i	1.02756	+	1.02756i
$868$		0			0
$869$	−1.63656	+	1.63656i	−0.0555165	+	0.0555165i
$870$	−90.9673	−	13.3587i	−3.08408	−	0.452904i
$871$	−2.97712	−	1.71884i	−0.100876	−	0.0582408i
$872$	−7.49866	−	10.7342i	−0.253937	−	0.363507i
$873$	76.5128	−	44.1747i	2.58956	−	1.49509i
$874$	−10.9435	−	8.65950i	−0.370169	−	0.292912i
$875$		0			0
$876$	44.2207	−	71.5754i	1.49408	−	2.41831i
$877$	−13.9324	+	51.9964i	−0.470463	+	1.75579i	0.167646	+	0.985847i	$0.446384\pi$
$877$	−13.9324	+	51.9964i	−0.470463	+	1.75579i	−0.638109	+	0.769946i	$0.720283\pi$
$878$	−2.43589	+	5.64135i	−0.0822073	+	0.190386i
$879$	−27.7922	+	48.1375i	−0.937408	+	1.62364i
$880$	−11.0516	+	16.7498i	−0.372551	+	0.564634i
$881$	−21.5769			−0.726946			−0.363473	−	0.931605i	$-0.618409\pi$
$881$	−21.5769			−0.726946			−0.363473	+	0.931605i	$0.618409\pi$
$882$		0			0
$883$	21.5700	+	21.5700i	0.725888	+	0.725888i	0.969798	−	0.243910i	$-0.0784300\pi$
$883$	21.5700	+	21.5700i	0.725888	+	0.725888i	−0.243910	+	0.969798i	$0.578430\pi$
$884$	−0.143287	+	4.80358i	−0.00481928	+	0.161562i
$885$	−4.67141	−	17.4340i	−0.157028	−	0.586036i
$886$	8.01943	−	3.18252i	0.269418	−	0.106919i
$887$	−29.1946	+	16.8555i	−0.980260	+	0.565953i	−0.902348	−	0.431007i	$-0.858158\pi$
$887$	−29.1946	+	16.8555i	−0.980260	+	0.565953i	−0.0779110	+	0.996960i	$0.524825\pi$
$888$	−6.55898	−	18.0824i	−0.220105	−	0.606804i
$889$		0			0
$890$	28.6350	−	36.1876i	0.959846	−	1.21301i
$891$	5.42821	+	1.45448i	0.181852	+	0.0487271i
$892$	−1.84186	+	6.13588i	−0.0616699	+	0.205445i
$893$	−7.18814	+	1.92606i	−0.240542	+	0.0644530i
$894$	−36.2371	+	26.9569i	−1.21195	+	0.901574i
$895$	63.9788			2.13858
$896$		0			0
$897$	−22.0777			−0.737153
$898$	4.22668	−	3.14425i	0.141046	−	0.104925i
$899$	−23.0227	+	6.16891i	−0.767850	+	0.205745i
$900$	30.9402	−	103.073i	1.03134	−	3.43577i
$901$	−1.39273	−	0.373182i	−0.0463987	−	0.0124325i
$902$	−8.50865	+	10.7529i	−0.283307	+	0.358031i
$903$		0			0
$904$	8.84597	+	24.3873i	0.294213	+	0.811111i
$905$	19.7753	−	11.4173i	0.657354	−	0.379524i
$906$	20.8898	−	8.29014i	0.694017	−	0.275421i
$907$	0.338194	+	1.26216i	0.0112295	+	0.0419092i	0.971313	−	0.237804i	$-0.0764274\pi$
$907$	0.338194	+	1.26216i	0.0112295	+	0.0419092i	−0.960084	+	0.279713i	$0.909761\pi$
$908$	1.16321	−	38.9954i	0.0386023	−	1.29411i
$909$	−62.9911	−	62.9911i	−2.08928	−	2.08928i
$910$		0			0
$911$	−29.9873			−0.993522			−0.496761	−	0.867887i	$-0.665477\pi$
$911$	−29.9873			−0.993522			−0.496761	+	0.867887i	$0.665477\pi$
$912$	−13.2434	+	20.0716i	−0.438533	+	0.664637i
$913$	6.58567	−	11.4067i	0.217954	−	0.377507i
$914$	−6.02390	+	13.9509i	−0.199253	+	0.461456i
$915$	13.2080	−	49.2931i	0.436645	−	1.62958i
$916$	−10.4387	+	16.8960i	−0.344904	+	0.558261i
$917$		0			0
$918$	−11.8951	−	9.41250i	−0.392597	−	0.310659i
$919$	−11.3211	+	6.53623i	−0.373448	+	0.215610i	−0.674964	−	0.737851i	$-0.735841\pi$
$919$	−11.3211	+	6.53623i	−0.373448	+	0.215610i	0.301516	+	0.953461i	$0.402507\pi$
$920$	29.8062	+	42.6673i	0.982682	+	1.40670i
$921$	−31.7989	−	18.3591i	−1.04781	−	0.604953i
$922$	15.6083	+	2.29211i	0.514032	+	0.0754866i
$923$	15.5626	−	15.5626i	0.512248	−	0.512248i
$924$		0			0
$925$	16.3486	+	16.3486i	0.537538	+	0.537538i
$926$	31.0319	−	23.0847i	1.01977	−	0.758611i
$927$	46.8018	−	81.0630i	1.53717	−	2.66246i
$928$	−24.4666	−	21.8537i	−0.803155	−	0.717384i
$929$	10.3529	+	17.9317i	0.339667	+	0.588320i	0.984370	−	0.176113i	$-0.0563524\pi$
$929$	10.3529	+	17.9317i	0.339667	+	0.588320i	−0.644703	+	0.764433i	$0.723019\pi$
$930$	−7.54106	−	64.7232i	−0.247281	−	2.12236i
$931$		0			0
$932$	1.35118	+	5.71971i	0.0442593	+	0.187355i
$933$	55.5082	+	14.8734i	1.81726	+	0.486933i
$934$	−8.40386	−	21.1764i	−0.274983	−	0.692911i
$935$	−6.55548	−	3.78481i	−0.214387	−	0.123776i
$936$	2.11115	+	24.4395i	0.0690051	+	0.798828i
$937$		−	5.93799i		−	0.193986i	−0.995285	−	0.0969929i	$-0.969078\pi$
$937$		−	5.93799i		−	0.193986i	0.995285	−	0.0969929i	$-0.0309224\pi$
$938$		0			0
$939$	−17.9348	+	17.9348i	−0.585281	+	0.585281i
$940$	27.7422	+	0.827531i	0.904851	+	0.0269911i
$941$	19.1182	−	5.12272i	0.623237	−	0.166996i	0.0666382	−	0.997777i	$-0.478773\pi$
$941$	19.1182	−	5.12272i	0.623237	−	0.166996i	0.556599	+	0.830781i	$0.312106\pi$
$942$	12.9428	−	29.9746i	0.421699	−	0.976626i
$943$	17.7821	+	30.7995i	0.579065	+	1.00297i
$944$	2.03459	−	6.11007i	0.0662201	−	0.198866i
$945$		0			0
$946$	14.7004	−	1.71278i	0.477952	−	0.0556873i
$947$	−11.0792	+	41.3482i	−0.360027	+	1.34364i	0.514013	+	0.857782i	$0.328158\pi$
$947$	−11.0792	+	41.3482i	−0.360027	+	1.34364i	−0.874039	+	0.485855i	$0.838508\pi$
$948$	9.10825	−	4.90253i	0.295822	−	0.159227i
$949$	−5.96613	−	22.2659i	−0.193669	−	0.722782i
$950$	4.19958	−	28.5974i	0.136253	−	0.927821i
$951$		−	78.1710i		−	2.53487i
$952$		0			0
$953$			0.689500i			0.0223351i	0.999938	+	0.0111675i	$0.00355481\pi$
$953$			0.689500i			0.0223351i	−0.999938	+	0.0111675i	$0.996445\pi$
$954$	−7.28180	−	1.06935i	−0.235757	−	0.0346214i
$955$	12.3478	+	46.0825i	0.399565	+	1.49120i
$956$	9.32138	−	31.0529i	0.301475	−	1.00432i
$957$	−5.67303	+	21.1720i	−0.183383	+	0.684395i
$958$	1.86383	+	15.9968i	0.0602176	+	0.516834i
$959$		0			0
$960$	68.8294	−	57.4977i	2.22146	−	1.85573i
$961$	7.05398	+	12.2179i	0.227548	+	0.394124i
$962$	−4.83836	−	2.08916i	−0.155995	−	0.0673573i
$963$	−30.5122	+	8.17572i	−0.983242	+	0.263459i
$964$	−19.3597	−	20.5502i	−0.623535	−	0.661878i
$965$	64.6012	−	64.6012i	2.07959	−	2.07959i
$966$		0			0
$967$		−	14.1022i		−	0.453497i	−0.973953	−	0.226749i	$-0.927190\pi$
$967$		−	14.1022i		−	0.453497i	0.973953	−	0.226749i	$-0.0728096\pi$
$968$	−20.1504	−	16.9459i	−0.647658	−	0.544662i
$969$	−7.85557	−	4.53541i	−0.252357	−	0.145698i
$970$	−82.2595	+	32.6448i	−2.64119	+	1.04816i
$971$	0.348650	+	0.0934205i	0.0111887	+	0.00299801i	0.264409	−	0.964411i	$-0.414823\pi$
$971$	0.348650	+	0.0934205i	0.0111887	+	0.00299801i	−0.253220	+	0.967409i	$0.581490\pi$
$972$	14.9184	+	9.21689i	0.478508	+	0.295632i
$973$		0			0
$974$	−44.0421	+	5.13145i	−1.41120	+	0.164422i
$975$	−22.8638	−	39.6012i	−0.732226	−	1.26825i
$976$	13.6198	−	12.0849i	0.435959	−	0.386829i
$977$	4.91955	−	8.52091i	0.157390	−	0.272608i	−0.776536	−	0.630072i	$-0.783025\pi$
$977$	4.91955	−	8.52091i	0.157390	−	0.272608i	0.933927	+	0.357464i	$0.116359\pi$
$978$	21.9171	+	29.4622i	0.700831	+	0.942099i
$979$	−7.77902	−	7.77902i	−0.248618	−	0.248618i
$980$		0			0
$981$	17.8276	−	17.8276i	0.569191	−	0.569191i
$982$	5.89239	−	40.1247i	0.188034	−	1.28043i
$983$	−23.0786	−	13.3244i	−0.736094	−	0.424984i	0.0845537	−	0.996419i	$-0.473054\pi$
$983$	−23.0786	−	13.3244i	−0.736094	−	0.424984i	−0.820647	+	0.571435i	$0.806387\pi$
$984$	50.2384	−	35.0952i	1.60154	−	1.11879i
$985$	53.9509	−	31.1486i	1.71902	−	0.992476i
$986$	7.67875	−	9.70406i	0.244541	−	0.309040i
$987$		0			0
$988$	1.51472	+	6.41201i	0.0481896	+	0.203993i
$989$	9.93490	−	37.0776i	0.315912	−	1.17900i
$990$	−35.4730	−	15.3169i	−1.12741	−	0.486804i
$991$	−8.41437	+	14.5741i	−0.267291	+	0.462962i	−0.968161	−	0.250327i	$-0.919462\pi$
$991$	−8.41437	+	14.5741i	−0.267291	+	0.462962i	0.700870	+	0.713289i	$0.252795\pi$
$992$	10.4724	−	20.7575i	0.332499	−	0.659052i
$993$	−91.7875			−2.91279
$994$		0			0
$995$	−14.9935	−	14.9935i	−0.475326	−	0.475326i
$996$	−42.8471	+	40.3650i	−1.35766	+	1.27901i
$997$	−9.43672	−	35.2183i	−0.298864	−	1.11538i	−0.938100	−	0.346365i	$-0.887416\pi$
$997$	−9.43672	−	35.2183i	−0.298864	−	1.11538i	0.639236	−	0.769011i	$-0.279251\pi$
$998$	13.6604	+	34.4219i	0.432411	+	1.08961i
$999$	14.4059	−	8.31728i	0.455784	−	0.263147i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.l.557.5		24
7.2	even	3	inner	784.2.x.l.765.2		24
7.3	odd	6		784.2.m.h.589.3		12
7.4	even	3		112.2.m.d.29.3	✓	12
7.5	odd	6		784.2.x.m.765.2		24
7.6	odd	2		784.2.x.m.557.5		24
16.5	even	4	inner	784.2.x.l.165.2		24
28.11	odd	6		448.2.m.d.337.6		12
56.11	odd	6		896.2.m.h.673.1		12
56.53	even	6		896.2.m.g.673.6		12
112.5	odd	12		784.2.x.m.373.5		24
112.11	odd	12		448.2.m.d.113.6		12
112.37	even	12	inner	784.2.x.l.373.5		24
112.53	even	12		112.2.m.d.85.3	yes	12
112.67	odd	12		896.2.m.h.225.1		12
112.69	odd	4		784.2.x.m.165.2		24
112.101	odd	12		784.2.m.h.197.3		12
112.109	even	12		896.2.m.g.225.6		12
224.11	odd	24		7168.2.a.bi.1.11		12
224.53	even	24		7168.2.a.bj.1.2		12
224.123	odd	24		7168.2.a.bi.1.2		12
224.165	even	24		7168.2.a.bj.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.d.29.3	✓	12	7.4	even	3
112.2.m.d.85.3	yes	12	112.53	even	12
448.2.m.d.113.6		12	112.11	odd	12
448.2.m.d.337.6		12	28.11	odd	6
784.2.m.h.197.3		12	112.101	odd	12
784.2.m.h.589.3		12	7.3	odd	6
784.2.x.l.165.2		24	16.5	even	4	inner
784.2.x.l.373.5		24	112.37	even	12	inner
784.2.x.l.557.5		24	1.1	even	1	trivial
784.2.x.l.765.2		24	7.2	even	3	inner
784.2.x.m.165.2		24	112.69	odd	4
784.2.x.m.373.5		24	112.5	odd	12
784.2.x.m.557.5		24	7.6	odd	2
784.2.x.m.765.2		24	7.5	odd	6
896.2.m.g.225.6		12	112.109	even	12
896.2.m.g.673.6		12	56.53	even	6
896.2.m.h.225.1		12	112.67	odd	12
896.2.m.h.673.1		12	56.11	odd	6
7168.2.a.bi.1.2		12	224.123	odd	24
7168.2.a.bi.1.11		12	224.11	odd	24
7168.2.a.bj.1.2		12	224.53	even	24
7168.2.a.bj.1.11		12	224.165	even	24

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.13468 - 0.844095i) q^{2} +(2.80718 - 0.752181i) q^{3} +(0.575008 - 1.91556i) q^{4} +(-3.72606 - 0.998394i) q^{5} +(2.55034 - 3.22301i) q^{6} +(-0.964462 - 2.65891i) q^{8} +(4.71639 - 2.72301i) q^{9} +O(q^{10})\)	\(q+(1.13468 - 0.844095i) q^{2} +(2.80718 - 0.752181i) q^{3} +(0.575008 - 1.91556i) q^{4} +(-3.72606 - 0.998394i) q^{5} +(2.55034 - 3.22301i) q^{6} +(-0.964462 - 2.65891i) q^{8} +(4.71639 - 2.72301i) q^{9} +(-5.07063 + 2.01229i) q^{10} +(0.336603 + 1.25622i) q^{11} +(0.173303 - 5.80982i) q^{12} +(-1.12607 - 1.12607i) q^{13} -11.2107 q^{15} +(-3.33873 - 2.20292i) q^{16} +(0.754426 - 1.30670i) q^{17} +(3.05313 - 7.07083i) q^{18} +(0.535390 - 1.99810i) q^{19} +(-4.05500 + 6.56340i) q^{20} +(1.44230 + 1.14128i) q^{22} +(4.13121 - 2.38515i) q^{23} +(-4.70740 - 6.73859i) q^{24} +(8.55659 + 4.94015i) q^{25} +(-2.22825 - 0.327223i) q^{26} +(5.02656 - 5.02656i) q^{27} +(4.10069 + 4.10069i) q^{29} +(-12.7206 + 9.46287i) q^{30} +(-2.05500 + 3.55936i) q^{31} +(-5.64788 + 0.318587i) q^{32} +(1.88981 + 3.27324i) q^{33} +(-0.246948 - 2.11950i) q^{34} +(-2.50412 - 10.6003i) q^{36} +(2.26031 + 0.605650i) q^{37} +(-1.07909 - 2.71913i) q^{38} +(-4.00810 - 2.31408i) q^{39} +(0.938997 + 10.8702i) q^{40} +7.45533i q^{41} +(5.68992 - 5.68992i) q^{43} +(2.59991 + 0.0775535i) q^{44} +(-20.2922 + 5.43727i) q^{45} +(2.67431 - 6.19352i) q^{46} +(-1.79874 - 3.11551i) q^{47} +(-11.0294 - 3.67267i) q^{48} +(13.8790 - 1.61707i) q^{50} +(1.13493 - 4.23561i) q^{51} +(-2.80456 + 1.50956i) q^{52} +(-0.247329 - 0.923043i) q^{53} +(1.46066 - 9.94644i) q^{54} -5.01680i q^{55} -6.01174i q^{57} +(8.11434 + 1.19161i) q^{58} +(0.416693 + 1.55512i) q^{59} +(-6.44623 + 21.4747i) q^{60} +(-1.17817 + 4.39698i) q^{61} +(0.672667 + 5.77335i) q^{62} +(-6.13963 + 5.12884i) q^{64} +(3.07155 + 5.32008i) q^{65} +(4.90726 + 2.11891i) q^{66} +(2.08511 - 0.558703i) q^{67} +(-2.06927 - 2.19651i) q^{68} +(9.80296 - 9.80296i) q^{69} +13.8202i q^{71} +(-11.7890 - 9.91423i) q^{72} +(12.5356 + 7.23744i) q^{73} +(3.07596 - 1.22070i) q^{74} +(27.7357 + 7.43177i) q^{75} +(-3.51963 - 2.17450i) q^{76} +(-6.50122 + 0.757473i) q^{78} +(0.889807 + 1.54119i) q^{79} +(10.2409 + 11.5416i) q^{80} +(2.16054 - 3.74216i) q^{81} +(6.29300 + 8.45943i) q^{82} +(-7.16133 - 7.16133i) q^{83} +(-4.11564 + 4.11564i) q^{85} +(1.65342 - 11.2591i) q^{86} +(14.5958 + 8.42689i) q^{87} +(3.01553 - 2.10657i) q^{88} +(-7.32570 + 4.22949i) q^{89} +(-18.4356 + 23.2981i) q^{90} +(-2.19342 - 9.28505i) q^{92} +(-3.09146 + 11.5375i) q^{93} +(-4.67078 - 2.01681i) q^{94} +(-3.98979 + 6.91052i) q^{95} +(-15.6150 + 5.14255i) q^{96} +16.2227 q^{97} +(5.00824 + 5.00824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} - 4 q^{3} + 6 q^{4} - 4 q^{5} + 8 q^{6} - 8 q^{8}+O(q^{10}) \) 24 * q - 2 * q^2 - 4 * q^3 + 6 * q^4 - 4 * q^5 + 8 * q^6 - 8 * q^8	\( 24 q - 2 q^{2} - 4 q^{3} + 6 q^{4} - 4 q^{5} + 8 q^{6} - 8 q^{8} + 4 q^{10} - 8 q^{12} - 48 q^{15} - 10 q^{16} + 8 q^{17} - 40 q^{20} + 28 q^{22} + 8 q^{24} + 20 q^{26} + 8 q^{27} - 8 q^{29} + 28 q^{30} + 8 q^{31} - 12 q^{32} + 16 q^{34} - 32 q^{36} + 20 q^{37} - 16 q^{38} + 8 q^{40} + 32 q^{43} - 14 q^{44} - 40 q^{45} + 28 q^{46} - 16 q^{47} + 32 q^{48} + 88 q^{50} + 16 q^{51} + 16 q^{52} - 4 q^{53} - 64 q^{54} - 14 q^{58} + 16 q^{59} - 60 q^{60} + 20 q^{61} + 16 q^{62} - 36 q^{64} - 32 q^{65} - 12 q^{66} - 24 q^{67} + 28 q^{68} - 8 q^{69} - 6 q^{72} + 38 q^{74} + 40 q^{75} + 96 q^{76} - 152 q^{78} - 24 q^{79} - 24 q^{80} + 44 q^{81} + 16 q^{82} - 40 q^{83} - 16 q^{85} - 38 q^{86} + 14 q^{88} - 80 q^{90} + 64 q^{92} + 48 q^{93} + 24 q^{94} + 16 q^{96} + 96 q^{97} + 64 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 - 4 * q^3 + 6 * q^4 - 4 * q^5 + 8 * q^6 - 8 * q^8 + 4 * q^10 - 8 * q^12 - 48 * q^15 - 10 * q^16 + 8 * q^17 - 40 * q^20 + 28 * q^22 + 8 * q^24 + 20 * q^26 + 8 * q^27 - 8 * q^29 + 28 * q^30 + 8 * q^31 - 12 * q^32 + 16 * q^34 - 32 * q^36 + 20 * q^37 - 16 * q^38 + 8 * q^40 + 32 * q^43 - 14 * q^44 - 40 * q^45 + 28 * q^46 - 16 * q^47 + 32 * q^48 + 88 * q^50 + 16 * q^51 + 16 * q^52 - 4 * q^53 - 64 * q^54 - 14 * q^58 + 16 * q^59 - 60 * q^60 + 20 * q^61 + 16 * q^62 - 36 * q^64 - 32 * q^65 - 12 * q^66 - 24 * q^67 + 28 * q^68 - 8 * q^69 - 6 * q^72 + 38 * q^74 + 40 * q^75 + 96 * q^76 - 152 * q^78 - 24 * q^79 - 24 * q^80 + 44 * q^81 + 16 * q^82 - 40 * q^83 - 16 * q^85 - 38 * q^86 + 14 * q^88 - 80 * q^90 + 64 * q^92 + 48 * q^93 + 24 * q^94 + 16 * q^96 + 96 * q^97 + 64 * q^99

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