LMFDB - Embedded newform 784.2.x.l.765.2

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			765.2
Character	$\chi$	$=$	784.765
Dual form			784.2.x.l.165.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29835 - 0.560616i) q^{2} +(-0.752181 + 2.80718i) q^{3} +(1.37142 + 1.45575i) q^{4} +(0.998394 + 3.72606i) q^{5} +(2.55034 - 3.22301i) q^{6} +(-0.964462 - 2.65891i) q^{8} +(-4.71639 - 2.72301i) q^{9} +O(q^{10})$	\(q+(-1.29835 - 0.560616i) q^{2} +(-0.752181 + 2.80718i) q^{3} +(1.37142 + 1.45575i) q^{4} +(0.998394 + 3.72606i) q^{5} +(2.55034 - 3.22301i) q^{6} +(-0.964462 - 2.65891i) q^{8} +(-4.71639 - 2.72301i) q^{9} +(0.792625 - 5.39744i) q^{10} +(-1.25622 - 0.336603i) q^{11} +(-5.11811 + 2.75483i) q^{12} +(-1.12607 - 1.12607i) q^{13} -11.2107 q^{15} +(-0.238422 + 3.99289i) q^{16} +(0.754426 + 1.30670i) q^{17} +(4.59696 + 6.17950i) q^{18} +(-1.99810 + 0.535390i) q^{19} +(-4.05500 + 6.56340i) q^{20} +(1.44230 + 1.14128i) q^{22} +(-4.13121 - 2.38515i) q^{23} +(8.18949 - 0.707432i) q^{24} +(-8.55659 + 4.94015i) q^{25} +(0.830740 + 2.09333i) q^{26} +(5.02656 - 5.02656i) q^{27} +(4.10069 + 4.10069i) q^{29} +(14.5554 + 6.28489i) q^{30} +(-2.05500 - 3.55936i) q^{31} +(2.54803 - 5.05050i) q^{32} +(1.88981 - 3.27324i) q^{33} +(-0.246948 - 2.11950i) q^{34} +(-2.50412 - 10.6003i) q^{36} +(-0.605650 - 2.26031i) q^{37} +(2.89438 + 0.425046i) q^{38} +(4.00810 - 2.31408i) q^{39} +(8.94435 - 6.24828i) q^{40} +7.45533i q^{41} +(5.68992 - 5.68992i) q^{43} +(-1.23279 - 2.29036i) q^{44} +(5.43727 - 20.2922i) q^{45} +(4.02659 + 5.41278i) q^{46} +(-1.79874 + 3.11551i) q^{47} +(-11.0294 - 3.67267i) q^{48} +(13.8790 - 1.61707i) q^{50} +(-4.23561 + 1.13493i) q^{51} +(0.0949645 - 3.18360i) q^{52} +(0.923043 + 0.247329i) q^{53} +(-9.34420 + 3.70826i) q^{54} -5.01680i q^{55} -6.01174i q^{57} +(-3.02521 - 7.62303i) q^{58} +(-1.55512 - 0.416693i) q^{59} +(-15.3745 - 16.3200i) q^{60} +(4.39698 - 1.17817i) q^{61} +(0.672667 + 5.77335i) q^{62} +(-6.13963 + 5.12884i) q^{64} +(3.07155 - 5.32008i) q^{65} +(-4.28866 + 3.19035i) q^{66} +(-0.558703 + 2.08511i) q^{67} +(-0.867602 + 2.89029i) q^{68} +(9.80296 - 9.80296i) q^{69} +13.8202i q^{71} +(-2.69147 + 15.1667i) q^{72} +(-12.5356 + 7.23744i) q^{73} +(-0.480825 + 3.27421i) q^{74} +(-7.43177 - 27.7357i) q^{75} +(-3.51963 - 2.17450i) q^{76} +(-6.50122 + 0.757473i) q^{78} +(0.889807 - 1.54119i) q^{79} +(-15.1158 + 3.09810i) q^{80} +(2.16054 + 3.74216i) q^{81} +(4.17958 - 9.67961i) q^{82} +(-7.16133 - 7.16133i) q^{83} +(-4.11564 + 4.11564i) q^{85} +(-10.5774 + 4.19764i) q^{86} +(-14.5958 + 8.42689i) q^{87} +(0.316577 + 3.66481i) q^{88} +(7.32570 + 4.22949i) q^{89} +(-18.4356 + 23.2981i) q^{90} +(-2.19342 - 9.28505i) q^{92} +(11.5375 - 3.09146i) q^{93} +(4.08200 - 3.03661i) q^{94} +(-3.98979 - 6.91052i) q^{95} +(12.2611 + 10.9517i) 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 $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.29835	−	0.560616i	−0.918071	−	0.396416i
$2$	−1.29835	−	0.560616i	−0.918071	−	0.396416i
$3$	−0.752181	+	2.80718i	−0.434272	+	1.62072i	0.308531	+	0.951214i	$0.400163\pi$
$3$	−0.752181	+	2.80718i	−0.434272	+	1.62072i	−0.742803	+	0.669510i	$0.766504\pi$
$4$	1.37142	+	1.45575i	0.685709	+	0.727876i
$5$	0.998394	+	3.72606i	0.446495	+	1.66634i	0.711958	+	0.702222i	$0.247809\pi$
$5$	0.998394	+	3.72606i	0.446495	+	1.66634i	−0.265462	+	0.964121i	$0.585525\pi$
$6$	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
$10$	0.792625	−	5.39744i	0.250650	−	1.70682i
$11$	−1.25622	−	0.336603i	−0.378764	−	0.101490i	0.0644137	−	0.997923i	$-0.479482\pi$
$11$	−1.25622	−	0.336603i	−0.378764	−	0.101490i	−0.443178	+	0.896434i	$0.646149\pi$
$12$	−5.11811	+	2.75483i	−1.47747	+	0.795250i
$13$	−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
$16$	−0.238422	+	3.99289i	−0.0596056	+	0.998222i
$17$	0.754426	+	1.30670i	0.182975	+	0.316922i	0.942892	−	0.333098i	$-0.108094\pi$
$17$	0.754426	+	1.30670i	0.182975	+	0.316922i	−0.759917	+	0.650020i	$0.774761\pi$
$18$	4.59696	+	6.17950i	1.08351	+	1.45652i
$19$	−1.99810	+	0.535390i	−0.458396	+	0.122827i	−0.480625	−	0.876926i	$-0.659590\pi$
$19$	−1.99810	+	0.535390i	−0.458396	+	0.122827i	0.0222291	+	0.999753i	$0.492924\pi$
$20$	−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	$-0.499023\pi$
$23$	−4.13121	−	2.38515i	−0.861416	−	0.497339i	−0.864486	+	0.502657i	$0.832356\pi$
$24$	8.18949	−	0.707432i	1.67167	−	0.144404i
$25$	−8.55659	+	4.94015i	−1.71132	+	0.988030i
$26$	0.830740	+	2.09333i	0.162922	+	0.410536i
$27$	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	$0.569011\pi$
$30$	14.5554	+	6.28489i	2.65743	+	1.14746i
$31$	−2.05500	−	3.55936i	−0.369088	−	0.639280i	0.620335	−	0.784337i	$-0.286997\pi$
$31$	−2.05500	−	3.55936i	−0.369088	−	0.639280i	−0.989423	+	0.145057i	$0.953663\pi$
$32$	2.54803	−	5.05050i	0.450433	−	0.892810i
$33$	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
$37$	−0.605650	−	2.26031i	−0.0995682	−	0.371593i	0.898104	−	0.439783i	$-0.144945\pi$
$37$	−0.605650	−	2.26031i	−0.0995682	−	0.371593i	−0.997672	+	0.0681892i	$0.978278\pi$
$38$	2.89438	+	0.425046i	0.469531	+	0.0689516i
$39$	4.00810	−	2.31408i	0.641809	−	0.370549i
$40$	8.94435	−	6.24828i	1.41423	−	0.987940i
$41$			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	$0.0397369\pi$
$44$	−1.23279	−	2.29036i	−0.185850	−	0.345285i
$45$	5.43727	−	20.2922i	0.810541	−	3.02498i
$46$	4.02659	+	5.41278i	0.593688	+	0.798071i
$47$	−1.79874	+	3.11551i	−0.262373	+	0.454444i	−0.966872	−	0.255261i	$-0.917838\pi$
$47$	−1.79874	+	3.11551i	−0.262373	+	0.454444i	0.704499	+	0.709705i	$0.251172\pi$
$48$	−11.0294	−	3.67267i	−1.59196	−	0.530104i
$49$		0			0
$50$	13.8790	−	1.61707i	1.96278	−	0.228689i
$51$	−4.23561	+	1.13493i	−0.593105	+	0.158922i
$52$	0.0949645	−	3.18360i	0.0131692	−	0.441486i
$53$	0.923043	+	0.247329i	0.126790	+	0.0339732i	0.321656	−	0.946857i	$-0.395761\pi$
$53$	0.923043	+	0.247329i	0.126790	+	0.0339732i	−0.194866	+	0.980830i	$0.562427\pi$
$54$	−9.34420	+	3.70826i	−1.27158	+	0.504630i
$55$		−	5.01680i		−	0.676466i
$56$		0			0
$57$		−	6.01174i		−	0.796275i
$58$	−3.02521	−	7.62303i	−0.397229	−	1.00095i
$59$	−1.55512	−	0.416693i	−0.202459	−	0.0542489i	0.156164	−	0.987731i	$-0.450087\pi$
$59$	−1.55512	−	0.416693i	−0.202459	−	0.0542489i	−0.358624	+	0.933482i	$0.616754\pi$
$60$	−15.3745	−	16.3200i	−1.98484	−	2.10690i
$61$	4.39698	−	1.17817i	0.562975	−	0.150849i	0.0339025	−	0.999425i	$-0.489206\pi$
$61$	4.39698	−	1.17817i	0.562975	−	0.150849i	0.529073	+	0.848576i	$0.322540\pi$
$62$	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
$66$	−4.28866	+	3.19035i	−0.527898	+	0.392705i
$67$	−0.558703	+	2.08511i	−0.0682564	+	0.254736i	−0.991620	−	0.129191i	$-0.958762\pi$
$67$	−0.558703	+	2.08511i	−0.0682564	+	0.254736i	0.923363	+	0.383927i	$0.125429\pi$
$68$	−0.867602	+	2.89029i	−0.105212	+	0.350500i
$69$	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	$0.693930\pi$
$72$	−2.69147	+	15.1667i	−0.317192	+	1.78741i
$73$	−12.5356	+	7.23744i	−1.46718	+	0.847078i	−0.999325	−	0.0367258i	$-0.988307\pi$
$73$	−12.5356	+	7.23744i	−1.46718	+	0.847078i	−0.467857	+	0.883804i	$0.654974\pi$
$74$	−0.480825	+	3.27421i	−0.0558948	+	0.380620i
$75$	−7.43177	−	27.7357i	−0.858147	−	3.20265i
$76$	−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	−0.811619	−	0.584187i	$-0.801414\pi$
$79$	0.889807	−	1.54119i	0.100111	−	0.173397i	0.911730	+	0.410789i	$0.134747\pi$
$80$	−15.1158	+	3.09810i	−1.68999	+	0.346378i
$81$	2.16054	+	3.74216i	0.240060	+	0.415795i
$82$	4.17958	−	9.67961i	0.461557	−	1.06893i
$83$	−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
$86$	−10.5774	+	4.19764i	−1.14059	+	0.452643i
$87$	−14.5958	+	8.42689i	−1.56483	+	0.903458i
$88$	0.316577	+	3.66481i	0.0337473	+	0.390671i
$89$	7.32570	+	4.22949i	0.776522	+	0.448325i	0.835196	−	0.549952i	$-0.185354\pi$
$89$	7.32570	+	4.22949i	0.776522	+	0.448325i	−0.0586740	+	0.998277i	$0.518687\pi$
$90$	−18.4356	+	23.2981i	−1.94328	+	2.45584i
$91$		0			0
$92$	−2.19342	−	9.28505i	−0.228680	−	0.968033i
$93$	11.5375	−	3.09146i	1.19638	−	0.320569i
$94$	4.08200	−	3.03661i	0.421026	−	0.313203i
$95$	−3.98979	−	6.91052i	−0.409344	−	0.709004i
$96$	12.2611	+	10.9517i	1.25139	+	1.11775i
$97$	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
$100$	−18.9263	−	5.68125i	−1.89263	−	0.568125i
$101$	15.8001	+	4.23361i	1.57216	+	0.421260i	0.936489	−	0.350696i	$-0.114055\pi$
$101$	15.8001	+	4.23361i	1.57216	+	0.421260i	0.635675	+	0.771957i	$0.280722\pi$
$102$	6.13556	+	0.901021i	0.607511	+	0.0892143i
$103$	−14.8848	−	8.59375i	−1.46664	−	0.846768i	−0.467341	−	0.884077i	$-0.654788\pi$
$103$	−14.8848	−	8.59375i	−1.46664	−	0.846768i	−0.999304	+	0.0373093i	$0.988121\pi$
$104$	−1.90808	+	4.08018i	−0.187102	+	0.400095i
$105$		0			0
$106$	−1.05977	−	0.838591i	−0.102934	−	0.0814512i
$107$	1.50123	+	5.60266i	0.145129	+	0.541630i	0.999750	+	0.0223764i	$0.00712323\pi$
$107$	1.50123	+	5.60266i	0.145129	+	0.541630i	−0.854620	+	0.519253i	$0.826210\pi$
$108$	14.2109	+	0.423902i	1.36745	+	0.0407900i
$109$	−1.19819	+	4.47170i	−0.114766	+	0.428311i	−0.999269	−	0.0382223i	$-0.987831\pi$
$109$	−1.19819	+	4.47170i	−0.114766	+	0.428311i	0.884504	+	0.466533i	$0.154497\pi$
$110$	−2.81250	+	6.51356i	−0.268162	+	0.621044i
$111$	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	$0.641984\pi$
$114$	−3.37028	+	7.80534i	−0.315656	+	0.731037i
$115$	4.76265	−	17.7744i	0.444119	−	1.65747i
$116$	−0.345821	+	11.5933i	−0.0321087	+	1.07641i
$117$	2.24469	+	8.37731i	0.207522	+	0.774483i
$118$	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
$122$	−6.36931	−	0.935347i	−0.576650	−	0.0846823i
$123$	−20.9284	−	5.60775i	−1.88705	−	0.505634i
$124$	2.36328	−	7.87293i	0.212229	−	0.707010i
$125$	−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	$0.695323\pi$
$128$	10.8467	−	3.21704i	0.958721	−	0.284349i
$129$	11.6928	+	20.2525i	1.02949	+	1.78313i
$130$	−6.97046	+	5.18536i	−0.611350	+	0.454786i
$131$	9.31582	−	2.49617i	0.813927	−	0.218091i	0.172237	−	0.985055i	$-0.444900\pi$
$131$	9.31582	−	2.49617i	0.813927	−	0.218091i	0.641690	+	0.766964i	$0.278234\pi$
$132$	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
$136$	2.74680	−	3.26622i	0.235536	−	0.280076i
$137$	19.6192	−	11.3271i	1.67618	−	0.967742i	0.712118	−	0.702060i	$-0.247736\pi$
$137$	19.6192	−	11.3271i	1.67618	−	0.967742i	0.964061	−	0.265682i	$-0.0855973\pi$
$138$	−18.2234	+	7.23196i	−1.55128	+	0.615625i
$139$	−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
$142$	7.74784	−	17.9435i	0.650184	−	1.50578i
$143$	1.03555	+	1.79363i	0.0865974	+	0.149991i
$144$	11.9972	−	18.1828i	0.999764	−	1.51523i
$145$	−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
$149$	2.84413	+	10.6144i	0.233000	+	0.869568i	0.979040	+	0.203667i	$0.0652861\pi$
$149$	2.84413	+	10.6144i	0.233000	+	0.869568i	−0.746040	+	0.665901i	$0.768047\pi$
$150$	−5.90008	+	40.1770i	−0.481740	+	3.28044i
$151$	−4.73568	+	2.73415i	−0.385384	+	0.222502i	−0.680158	−	0.733065i	$-0.738089\pi$
$151$	−4.73568	+	2.73415i	−0.385384	+	0.222502i	0.294774	+	0.955567i	$0.404756\pi$
$152$	3.35065	+	4.79642i	0.271774	+	0.389041i
$153$		−	8.21724i		−	0.664324i
$154$		0			0
$155$	11.2107	−	11.2107i	0.900463	−	0.900463i
$156$	8.86550	+	2.66122i	0.709808	+	0.213069i
$157$	−2.05605	+	7.67327i	−0.164090	+	0.612393i	0.834064	+	0.551667i	$0.186008\pi$
$157$	−2.05605	+	7.67327i	−0.164090	+	0.612393i	−0.998154	+	0.0607259i	$0.980658\pi$
$158$	−2.01930	+	1.50216i	−0.160647	+	0.119506i
$159$	−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
$163$	8.62997	−	2.31239i	0.675951	−	0.181121i	0.0955171	−	0.995428i	$-0.469550\pi$
$163$	8.62997	−	2.31239i	0.675951	−	0.181121i	0.580434	+	0.814307i	$0.302883\pi$
$164$	−10.8531	+	10.2244i	−0.847485	+	0.798390i
$165$	14.0831	+	3.77354i	1.09636	+	0.293770i
$166$	5.28314	+	13.3127i	0.410051	+	1.03326i
$167$			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
$170$	7.65083	−	3.03624i	0.586792	−	0.232869i
$171$	10.8817	+	2.91575i	0.832145	+	0.222973i
$172$	16.0864	+	0.479845i	1.22657	+	0.0365879i
$173$	−7.70245	+	2.06387i	−0.585606	+	0.156913i	−0.539444	−	0.842021i	$-0.681366\pi$
$173$	−7.70245	+	2.06387i	−0.585606	+	0.156913i	−0.0461620	+	0.998934i	$0.514699\pi$
$174$	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
$178$	−7.14019	−	9.59826i	−0.535180	−	0.719420i
$179$	4.29266	−	16.0204i	0.320849	−	1.19742i	−0.597571	−	0.801816i	$-0.703867\pi$
$179$	4.29266	−	16.0204i	0.320849	−	1.19742i	0.918420	−	0.395608i	$-0.129466\pi$
$180$	36.9971	−	19.9138i	2.75760	−	1.48428i
$181$	−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
$184$	−2.35752	+	13.2849i	−0.173799	+	0.979376i
$185$	7.81739	−	4.51337i	0.574746	−	0.331830i
$186$	−16.7128	−	2.45431i	−1.22544	−	0.179959i
$187$	−0.507884	−	1.89545i	−0.0371401	−	0.138609i
$188$	−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	−0.998219	−	0.0596566i	$-0.980999\pi$
$191$	−6.18382	+	10.7107i	−0.447445	+	0.774998i	0.550774	+	0.834655i	$0.314333\pi$
$192$	−9.77944	−	21.0928i	−0.705771	−	1.52224i
$193$	−11.8419	−	20.5107i	−0.852395	−	1.47639i	−0.879041	−	0.476747i	$-0.841816\pi$
$193$	−11.8419	−	20.5107i	−0.852395	−	1.47639i	0.0266452	−	0.999645i	$-0.491518\pi$
$194$	−21.0628	−	9.09473i	−1.51222	−	0.652964i
$195$	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	$0.445117\pi$
$198$	−3.69474	−	9.31015i	−0.262574	−	0.661644i
$199$	−4.76039	+	2.74841i	−0.337455	+	0.194830i	−0.659146	−	0.752015i	$-0.729082\pi$
$199$	−4.76039	+	2.74841i	−0.337455	+	0.194830i	0.321691	+	0.946845i	$0.395749\pi$
$200$	21.3879	+	17.9866i	1.51235	+	1.27185i
$201$	−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
$205$	−27.7790	+	7.44336i	−1.94017	+	0.519867i
$206$	14.5079	+	19.5024i	1.01081	+	1.35879i
$207$	12.9896	+	22.4986i	0.902839	+	1.56376i
$208$	4.76476	−	4.22780i	0.330377	−	0.293145i
$209$	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	$0.735928\pi$
$212$	0.905829	+	1.68291i	0.0622126	+	0.115583i
$213$	−38.7958	−	10.3953i	−2.65824	−	0.712274i
$214$	1.19183	−	8.11582i	0.0814715	−	0.554786i
$215$	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
$219$	−10.8877	−	40.6336i	−0.735724	−	2.74576i
$220$	7.30322	−	6.88014i	0.492383	−	0.463859i
$221$	0.621906	−	2.32098i	0.0418339	−	0.156126i
$222$	−8.82963	−	3.81256i	−0.592606	−	0.255882i
$223$	−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
$226$	11.9084	+	5.14193i	0.792132	+	0.342036i
$227$	−5.04862	+	18.8417i	−0.335089	+	1.25057i	0.568684	+	0.822556i	$0.307453\pi$
$227$	−5.04862	+	18.8417i	−0.335089	+	1.25057i	−0.903773	+	0.428012i	$0.859214\pi$
$228$	8.75160	−	8.24461i	0.579589	−	0.546013i
$229$	2.57015	+	9.59192i	0.169840	+	0.633852i	0.997373	+	0.0724349i	$0.0230769\pi$
$229$	2.57015	+	9.59192i	0.169840	+	0.633852i	−0.827533	+	0.561417i	$0.810256\pi$
$230$	−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	$-0.302647\pi$
$233$	2.54488	+	1.46929i	0.166720	+	0.0962561i	−0.414318	+	0.910132i	$0.635980\pi$
$234$	1.78206	−	12.1351i	0.116497	−	0.793295i
$235$	−13.4044	−	3.59170i	−0.874408	−	0.234297i
$236$	−1.52612	−	2.83533i	−0.0993419	−	0.184564i
$237$	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	$0.324328\pi$
$240$	2.67287	−	44.7630i	0.172533	−	2.88944i
$241$	7.05829	+	12.2253i	0.454665	+	0.787502i	0.998669	−	0.0515803i	$-0.0164258\pi$
$241$	7.05829	+	12.2253i	0.454665	+	0.787502i	−0.544004	+	0.839082i	$0.683092\pi$
$242$	7.85735	+	10.5623i	0.505090	+	0.678972i
$243$	8.46922	−	2.26932i	0.543301	−	0.145577i
$244$	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
$248$	−7.48206	+	8.89692i	−0.475111	+	0.564955i
$249$	25.4897	−	14.7165i	1.61535	−	0.932621i
$250$	9.82055	+	24.7462i	0.621106	+	1.56509i
$251$	−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
$254$	16.8508	+	7.27605i	1.05732	+	0.456540i
$255$	−8.45763	−	14.6490i	−0.529637	−	0.917358i
$256$	−15.8863	−	1.90399i	−0.992894	−	0.118999i
$257$	1.61839	−	2.80314i	0.100953	−	0.174855i	−0.811125	−	0.584873i	$-0.801144\pi$
$257$	1.61839	−	2.80314i	0.100953	−	0.174855i	0.912077	+	0.410018i	$0.134478\pi$
$258$	−3.82742	−	32.8499i	−0.238285	−	2.04515i
$259$		0			0
$260$	11.9571	−	2.82464i	0.741547	−	0.175177i
$261$	−8.17423	−	30.5066i	−0.505972	−	1.88831i
$262$	−13.4946	−	1.98171i	−0.833698	−	0.122430i
$263$	−20.7985	+	12.0080i	−1.28249	+	0.740448i	−0.977304	−	0.211844i	$-0.932053\pi$
$263$	−20.7985	+	12.0080i	−1.28249	+	0.740448i	−0.305190	+	0.952292i	$0.598720\pi$
$264$	−10.5259	−	1.86791i	−0.647825	−	0.114962i
$265$			3.68624i			0.226444i
$266$		0			0
$267$	−17.3832	+	17.3832i	−1.06383	+	1.06383i
$268$	−3.80161	+	2.04622i	−0.232220	+	0.124993i
$269$	−0.0320287	+	0.119533i	−0.00195282	+	0.00728804i	−0.966895	−	0.255173i	$-0.917868\pi$
$269$	−0.0320287	+	0.119533i	−0.00195282	+	0.00728804i	0.964943	+	0.262461i	$0.0845342\pi$
$270$	−23.1464	−	31.1147i	−1.40864	−	1.89358i
$271$	5.05692	−	8.75884i	0.307186	−	0.532062i	−0.670560	−	0.741856i	$-0.733946\pi$
$271$	5.05692	−	8.75884i	0.307186	−	0.532062i	0.977746	+	0.209794i	$0.0672793\pi$
$272$	−5.39739	+	2.70079i	−0.327265	+	0.163760i
$273$		0			0
$274$	−31.8227	+	3.70774i	−1.92248	+	0.223993i
$275$	12.4118	−	3.32573i	0.748460	−	0.200549i
$276$	27.7146	+	0.826708i	1.66822	+	0.0497620i
$277$	15.0372	+	4.02921i	0.903498	+	0.242092i	0.680518	−	0.732732i	$-0.261755\pi$
$277$	15.0372	+	4.02921i	0.903498	+	0.242092i	0.222980	+	0.974823i	$0.428422\pi$
$278$	12.3571	−	4.90391i	0.741127	−	0.294117i
$279$			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	$0.959827\pi$
$282$	5.45391	+	13.7430i	0.324776	+	0.818382i
$283$	22.6533	+	6.06995i	1.34660	+	0.360821i	0.858879	−	0.512178i	$-0.171161\pi$
$283$	22.6533	+	6.06995i	1.34660	+	0.360821i	0.487722	+	0.872999i	$0.337828\pi$
$284$	−20.1188	+	18.9533i	−1.19383	+	1.12467i
$285$	22.4001	−	6.00209i	1.32687	−	0.355533i
$286$	−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
$290$	25.3835	−	18.8829i	1.49057	−	1.10884i
$291$	−12.2024	+	45.5401i	−0.715319	+	2.66961i
$292$	−27.7275	−	8.32317i	−1.62263	−	0.487077i
$293$	−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
$296$	−5.42585	+	3.79036i	−0.315371	+	0.220310i
$297$	−8.00641	+	4.62250i	−0.464579	+	0.268225i
$298$	2.25795	−	15.3757i	0.130800	−	0.890691i
$299$	1.96618	+	7.33790i	0.113707	+	0.424361i
$300$	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
$304$	−1.66136	−	8.10585i	−0.0952856	−	0.464903i
$305$	8.77984	+	15.2071i	0.502732	+	0.870757i
$306$	−4.60672	+	10.6688i	−0.263349	+	0.609897i
$307$	−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
$310$	−20.8403	+	8.27048i	−1.18365	+	0.469732i
$311$	−17.1245	+	9.88684i	−0.971042	+	0.560631i	−0.899554	−	0.436810i	$-0.856108\pi$
$311$	−17.1245	+	9.88684i	−0.971042	+	0.560631i	−0.0714882	+	0.997441i	$0.522775\pi$
$312$	−10.0186	−	8.42534i	−0.567190	−	0.476991i
$313$	7.55817	+	4.36371i	0.427213	+	0.246652i	0.698159	−	0.715943i	$-0.254003\pi$
$313$	7.55817	+	4.36371i	0.427213	+	0.246652i	−0.270945	+	0.962595i	$0.587336\pi$
$314$	6.97122	−	8.80992i	0.393409	−	0.497173i
$315$		0			0
$316$	3.46389	−	0.818280i	0.194859	−	0.0460319i
$317$	−25.9814	+	6.96171i	−1.45926	+	0.391008i	−0.899235	−	0.437465i	$-0.855876\pi$
$317$	−25.9814	+	6.96171i	−1.45926	+	0.391008i	−0.560028	+	0.828474i	$0.689210\pi$
$318$	3.15122	−	2.34420i	0.176711	−	0.131456i
$319$	−3.77105	−	6.53166i	−0.211138	−	0.365703i
$320$	−25.2401	−	17.7560i	−1.41097	−	0.992591i
$321$	−16.8569			−0.940858
$322$		0			0
$323$	−2.20702	−	2.20702i	−0.122802	−	0.122802i
$324$	−2.48465	+	8.27727i	−0.138036	+	0.459848i
$325$	15.1983	+	4.07238i	0.843051	+	0.225895i
$326$	−12.5011	−	1.83581i	−0.692370	−	0.101676i
$327$	−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
$331$	8.17436	+	30.5071i	0.449303	+	1.67682i	0.704317	+	0.709885i	$0.251253\pi$
$331$	8.17436	+	30.5071i	0.449303	+	1.67682i	−0.255014	+	0.966937i	$0.582080\pi$
$332$	0.603933	−	20.2463i	0.0331451	−	1.11116i
$333$	−3.29838	+	12.3097i	−0.180750	+	0.674568i
$334$	6.62507	−	15.3432i	0.362507	−	0.839542i
$335$	−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	$0.720895\pi$
$338$	−5.86624	+	13.5858i	−0.319082	+	0.738971i
$339$	6.89895	−	25.7472i	0.374699	−	1.39840i
$340$	−11.6356	−	0.347082i	−0.631030	−	0.0188232i
$341$	1.38343	+	5.16305i	0.0749172	+	0.279595i
$342$	−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
$346$	11.1575	+	1.63850i	0.599831	+	0.0880865i
$347$	8.60207	+	2.30492i	0.461784	+	0.123735i	0.482208	−	0.876057i	$-0.339835\pi$
$347$	8.60207	+	2.30492i	0.461784	+	0.123735i	−0.0204242	+	0.999791i	$0.506502\pi$
$348$	−32.2844	−	9.69106i	−1.73063	−	0.519496i
$349$	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
$352$	−4.90090	+	5.48685i	−0.261219	+	0.292450i
$353$	−15.0467	−	26.0617i	−0.800856	−	1.38712i	−0.919054	−	0.394133i	$-0.871045\pi$
$353$	−15.0467	−	26.0617i	−0.800856	−	1.38712i	0.118198	−	0.992990i	$-0.462288\pi$
$354$	−5.30910	+	3.94946i	−0.282175	+	0.209911i
$355$	−51.4949	+	13.7980i	−2.73307	+	0.732323i
$356$	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	$-0.245087\pi$
$359$	8.98209	+	5.18581i	0.474057	+	0.273697i	−0.243880	+	0.969806i	$0.578420\pi$
$360$	−59.1992	+	5.11380i	−3.12007	+	0.269521i
$361$	−12.7487	+	7.36047i	−0.670985	+	0.387393i
$362$	7.78114	−	3.08796i	0.408968	−	0.162299i
$363$	19.1292	−	19.1292i	1.00402	−	1.00402i
$364$		0			0
$365$	−39.4826	−	39.4826i	−2.06661	−	2.06661i
$366$	7.41656	−	17.1762i	0.387670	−	0.897816i
$367$	4.06486	+	7.04055i	0.212184	+	0.367514i	0.952398	−	0.304858i	$-0.0986090\pi$
$367$	4.06486	+	7.04055i	0.212184	+	0.367514i	−0.740214	+	0.672372i	$0.765276\pi$
$368$	10.5086	−	15.9268i	0.547800	−	0.830240i
$369$	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
$373$	−1.16648	−	4.35336i	−0.0603980	−	0.225408i	0.929129	−	0.369755i	$-0.120559\pi$
$373$	−1.16648	−	4.35336i	−0.0603980	−	0.225408i	−0.989527	+	0.144347i	$0.953892\pi$
$374$	−0.403209	+	2.74568i	−0.0208494	+	0.141976i
$375$	47.3815	−	27.3557i	2.44677	−	1.41264i
$376$	10.0187	+	1.77790i	0.516674	+	0.0916884i
$377$		−	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	$0.259703\pi$
$380$	4.58832	−	15.2854i	0.235376	−	0.784122i
$381$	9.76231	−	36.4334i	0.500138	−	1.86654i
$382$	14.0333	−	10.4395i	0.718008	−	0.534129i
$383$	17.1874	−	29.7695i	0.878237	−	1.52115i	0.0249634	−	0.999688i	$-0.492053\pi$
$383$	17.1874	−	29.7695i	0.878237	−	1.52115i	0.853274	−	0.521463i	$-0.174614\pi$
$384$	0.872140	+	32.8684i	0.0445062	+	1.67731i
$385$		0			0
$386$	3.87623	+	33.2688i	0.197295	+	1.69334i
$387$	−42.3296	+	11.3422i	−2.15173	+	0.576556i
$388$	22.2482	+	23.6163i	1.12948	+	1.19893i
$389$	−14.9761	−	4.01283i	−0.759319	−	0.203459i	−0.141671	−	0.989914i	$-0.545247\pi$
$389$	−14.9761	−	4.01283i	−0.759319	−	0.203459i	−0.617648	+	0.786455i	$0.711914\pi$
$390$	−9.31316	−	23.4677i	−0.471590	−	1.18833i
$391$		−	7.19768i		−	0.364003i
$392$		0			0
$393$			28.0287i			1.41386i
$394$	21.2285	−	8.42454i	1.06947	−	0.424422i
$395$	6.63094	+	1.77676i	0.333639	+	0.0893983i
$396$	−0.422358	+	14.1592i	−0.0212243	+	0.711524i
$397$	−36.1143	+	9.67679i	−1.81252	+	0.485664i	−0.995815	−	0.0913869i	$-0.970870\pi$
$397$	−36.1143	+	9.67679i	−1.81252	+	0.485664i	−0.816708	+	0.577051i	$0.804203\pi$
$398$	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	−0.921440	−	0.388521i	$-0.872986\pi$
$401$	−2.48812	+	4.30956i	−0.124251	+	0.215209i	0.797189	+	0.603730i	$0.206319\pi$
$402$	5.29544	+	7.11844i	0.264112	+	0.355036i
$403$	−1.69402	+	6.32217i	−0.0843852	+	0.314930i
$404$	15.5054	+	28.8070i	0.771423	+	1.43320i
$405$	−11.7864	+	11.7864i	−0.585672	+	0.585672i
$406$		0			0
$407$			3.04331i			0.150851i
$408$	7.10277	+	10.1675i	0.351639	+	0.503368i
$409$	−3.51917	+	2.03180i	−0.174012	+	0.100466i	−0.584476	−	0.811411i	$-0.698700\pi$
$409$	−3.51917	+	2.03180i	−0.174012	+	0.100466i	0.410464	+	0.911877i	$0.365367\pi$
$410$	40.2397	+	5.90928i	1.98730	+	0.291839i
$411$	17.0401	+	63.5945i	0.840526	+	3.13689i
$412$	−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
$416$	−8.55650	+	2.81796i	−0.419517	+	0.138162i
$417$	−13.6601	−	23.6600i	−0.668940	−	1.15864i
$418$	−3.49291	−	1.50821i	−0.170844	−	0.0737689i
$419$	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	$0.291557\pi$
$422$	−0.669768	−	1.68771i	−0.0326038	−	0.0821563i
$423$	16.9671	−	9.79598i	0.824970	−	0.476297i
$424$	−0.232614	−	2.69283i	−0.0112968	−	0.130775i
$425$	−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
$429$	−5.81397	+	1.55785i	−0.280701	+	0.0752136i
$430$	−26.2010	−	35.2210i	−1.26353	−	1.69851i
$431$	−0.590931	−	1.02352i	−0.0284641	−	0.0493013i	0.851442	−	0.524448i	$-0.175728\pi$
$431$	−0.590931	−	1.02352i	−0.0284641	−	0.0493013i	−0.879907	+	0.475147i	$0.842395\pi$
$432$	18.8721	+	21.2689i	0.907982	+	1.02330i
$433$	−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
$436$	−8.15290	+	4.38831i	−0.390453	+	0.210162i
$437$	9.53156	+	2.55398i	0.455957	+	0.122173i
$438$	−8.64377	+	58.8604i	−0.413015	+	2.81246i
$439$	3.76290	+	2.17251i	0.179593	+	0.103688i	0.587102	−	0.809513i	$-0.300269\pi$
$439$	3.76290	+	2.17251i	0.179593	+	0.103688i	−0.407508	+	0.913202i	$0.633602\pi$
$440$	−13.3392	+	4.83851i	−0.635923	+	0.230667i
$441$		0			0
$442$	−2.10863	+	2.66479i	−0.100297	+	0.126751i
$443$	−1.57901	−	5.89293i	−0.0750208	−	0.279981i	0.918217	−	0.396077i	$-0.129629\pi$
$443$	−1.57901	−	5.89293i	−0.0750208	−	0.279981i	−0.993238	+	0.116096i	$0.962962\pi$
$444$	9.32655	+	9.90007i	0.442619	+	0.469837i
$445$	−8.44540	+	31.5187i	−0.400351	+	1.49413i
$446$	4.15885	+	1.79576i	0.196927	+	0.0850315i
$447$	−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	$0.471985\pi$
$450$	−69.8619	−	30.1658i	−3.29332	−	1.42203i
$451$	2.50948	−	9.36552i	0.118167	−	0.441005i
$452$	−12.5785	−	13.3520i	−0.591645	−	0.628027i
$453$	−4.11315	−	15.3505i	−0.193252	−	0.721228i
$454$	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	$-0.252469\pi$
$457$	9.30556	+	5.37257i	0.435296	+	0.251318i	−0.266304	+	0.963889i	$0.585803\pi$
$458$	2.04044	−	13.8945i	0.0953435	−	0.649248i
$459$	10.3604	+	2.77606i	0.483582	+	0.129575i
$460$	32.4067	−	17.4430i	1.51097	−	0.813282i
$461$	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	$0.280796\pi$
$464$	−17.3513	+	15.3959i	−0.805513	+	0.714736i
$465$	23.0379	+	39.9028i	1.06836	+	1.85045i
$466$	−2.48043	−	3.33434i	−0.114904	−	0.154461i
$467$	−15.5610	+	4.16957i	−0.720079	+	0.192945i	−0.600207	−	0.799845i	$-0.704915\pi$
$467$	−15.5610	+	4.16957i	−0.720079	+	0.192945i	−0.119872	+	0.992789i	$0.538248\pi$
$468$	−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
$472$	0.391903	+	4.53681i	0.0180388	+	0.208824i
$473$	−9.06303	+	5.23254i	−0.416718	+	0.240592i
$474$	−2.69796	−	6.79842i	−0.123921	−	0.312262i
$475$	14.4520	−	14.4520i	0.663105	−	0.663105i
$476$		0			0
$477$	−3.67995	−	3.67995i	−0.168493	−	0.168493i
$478$	−21.0473	−	9.08807i	−0.962683	−	0.415679i
$479$	−5.69399	−	9.86229i	−0.260165	−	0.450619i	0.706120	−	0.708092i	$-0.250444\pi$
$479$	−5.69399	−	9.86229i	−0.260165	−	0.450619i	−0.966286	+	0.257472i	$0.917110\pi$
$480$	−28.5652	+	56.6195i	−1.30382	+	2.58431i
$481$	−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
$485$	16.1967	+	60.4468i	0.735453	+	2.74475i
$486$	−12.2682	−	1.80161i	−0.556498	−	0.0817229i
$487$	27.1526	−	15.6766i	1.23040	−	0.710373i	0.263288	−	0.964717i	$-0.415193\pi$
$487$	27.1526	−	15.6766i	1.23040	−	0.710373i	0.967114	+	0.254344i	$0.0818597\pi$
$488$	−7.37336	−	10.5549i	−0.333776	−	0.477797i
$489$			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	$0.0259893\pi$
$492$	−20.5381	−	38.1572i	−0.925931	−	1.72026i
$493$	−2.26472	+	8.45204i	−0.101998	+	0.380661i
$494$	−2.78065	−	3.73792i	−0.125108	−	0.168177i
$495$	−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
$499$	25.2943	−	6.77758i	1.13233	−	0.303406i	0.356465	−	0.934309i	$-0.383982\pi$
$499$	25.2943	−	6.77758i	1.13233	−	0.303406i	0.775862	+	0.630902i	$0.217315\pi$
$500$	1.12262	−	37.6348i	0.0502050	−	1.68308i
$501$	−33.1737	−	8.88887i	−1.48209	−	0.397126i
$502$	26.3913	−	10.4734i	1.17790	−	0.467451i
$503$			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
$506$	−3.23632	−	8.15500i	−0.143872	−	0.362534i
$507$	29.3741	+	7.87076i	1.30455	+	0.349553i
$508$	−17.7992	−	18.8937i	−0.789711	−	0.838273i
$509$	−16.6168	+	4.45247i	−0.736529	+	0.197352i	−0.607535	−	0.794293i	$-0.707841\pi$
$509$	−16.6168	+	4.45247i	−0.736529	+	0.197352i	−0.128994	+	0.991645i	$0.541175\pi$
$510$	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
$514$	−3.67273	+	2.73216i	−0.161997	+	0.120510i
$515$	17.1599	−	64.0417i	0.756156	−	2.82201i
$516$	−13.4469	+	44.7964i	−0.591966	+	1.97205i
$517$	3.30830	−	3.30830i	0.145499	−	0.145499i
$518$		0			0
$519$		−	23.1745i		−	1.01725i
$520$	−17.1080	−	3.03597i	−0.750236	−	0.133136i
$521$	29.8192	−	17.2161i	1.30640	−	0.754251i	0.324907	−	0.945746i	$-0.394667\pi$
$521$	29.8192	−	17.2161i	1.30640	−	0.754251i	0.981494	+	0.191495i	$0.0613336\pi$
$522$	−6.48952	+	44.1909i	−0.284039	+	1.93418i
$523$	−5.63792	−	21.0410i	−0.246529	−	0.920060i	−0.972609	−	0.232449i	$-0.925326\pi$
$523$	−5.63792	−	21.0410i	−0.246529	−	0.920060i	0.726079	−	0.687611i	$-0.241340\pi$
$524$	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
$528$	12.6191	+	8.32620i	0.549176	+	0.362351i
$529$	−0.122092	−	0.211469i	−0.00530834	−	0.00919432i
$530$	2.06657	−	4.78603i	0.0897659	−	0.207892i
$531$	6.19990	+	6.19990i	0.269053	+	0.269053i
$532$		0			0
$533$	8.39524	−	8.39524i	0.363638	−	0.363638i
$534$	32.3147	−	12.8241i	1.39840	−	0.554955i
$535$	−19.3770	+	11.1873i	−0.837742	+	0.483670i
$536$	6.08296	−	0.525464i	0.262744	−	0.0226966i
$537$	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
$541$	32.3972	−	8.68080i	1.39286	−	0.373217i	0.517087	−	0.855933i	$-0.327016\pi$
$541$	32.3972	−	8.68080i	1.39286	−	0.373217i	0.875777	+	0.482716i	$0.160350\pi$
$542$	−11.4760	+	8.53704i	−0.492936	+	0.366697i
$543$	−8.60168	−	14.8985i	−0.369133	−	0.639358i
$544$	8.52181	−	0.480700i	0.365370	−	0.0206099i
$545$	−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	$0.430803\pi$
$548$	43.3956	+	13.0264i	1.85377	+	0.556460i
$549$	−23.9460	−	6.41632i	−1.02199	−	0.273842i
$550$	−17.9793	−	2.64030i	−0.766641	−	0.112583i
$551$	−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
$555$	6.78974	+	25.3397i	0.288208	+	1.07561i
$556$	−18.7930	−	0.560582i	−0.797000	−	0.0237740i
$557$	0.101002	−	0.376946i	0.00427960	−	0.0159717i	−0.963753	−	0.266796i	$-0.914035\pi$
$557$	0.101002	−	0.376946i	0.00427960	−	0.0159717i	0.968033	+	0.250824i	$0.0807017\pi$
$558$	12.5483	−	29.0611i	0.531213	−	1.23025i
$559$	−12.8145			−0.541997
$560$		0			0
$561$	5.70288			0.240776
$562$	2.36579	−	5.47901i	0.0997949	−	0.231118i
$563$	−5.08448	+	18.9755i	−0.214285	+	0.799724i	0.772132	+	0.635463i	$0.219191\pi$
$563$	−5.08448	+	18.9755i	−0.214285	+	0.799724i	−0.986417	+	0.164261i	$0.947476\pi$
$564$	0.623454	−	20.9007i	0.0262521	−	0.880079i
$565$	−9.15720	−	34.1751i	−0.385246	−	1.43776i
$566$	−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	$-0.387510\pi$
$569$	−6.99814	−	4.04038i	−0.293377	−	0.169381i	−0.639464	+	0.768821i	$0.720844\pi$
$570$	−32.4480	−	4.76506i	−1.35910	−	0.199586i
$571$	10.3246	+	2.76648i	0.432073	+	0.115774i	0.468299	−	0.883570i	$-0.344867\pi$
$571$	10.3246	+	2.76648i	0.432073	+	0.115774i	−0.0362262	+	0.999344i	$0.511534\pi$
$572$	−1.19090	+	3.96733i	−0.0497942	+	0.165882i
$573$	−25.4154	−	25.4154i	−1.06175	−	1.06175i
$574$		0			0
$575$	47.1320			1.96554
$576$	42.9228	−	7.47134i	1.78845	−	0.311306i
$577$	−0.979847	−	1.69714i	−0.0407915	−	0.0706530i	0.844909	−	0.534910i	$-0.179655\pi$
$577$	−0.979847	−	1.69714i	−0.0407915	−	0.0706530i	−0.885700	+	0.464257i	$0.846321\pi$
$578$	−16.7063	+	12.4279i	−0.694892	+	0.516933i
$579$	66.4844	−	17.8144i	2.76300	−	0.740343i
$580$	−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
$584$	31.3338	+	26.3509i	1.29660	+	1.09041i
$585$	−28.9733	+	16.7277i	−1.19790	+	0.691606i
$586$	25.1410	−	9.97725i	1.03857	−	0.412156i
$587$	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
$590$	−3.48170	+	8.06339i	−0.143340	+	0.331964i
$591$	−23.4670	−	40.6461i	−0.965305	−	1.67196i
$592$	9.16958	−	1.87938i	0.376868	−	0.0772421i
$593$	−8.27415	+	14.3313i	−0.339779	+	0.588514i	−0.984391	−	0.175996i	$-0.943686\pi$
$593$	−8.27415	+	14.3313i	−0.339779	+	0.588514i	0.644612	+	0.764510i	$0.277019\pi$
$594$	12.9866	−	1.51310i	0.532845	−	0.0620831i
$595$		0			0
$596$	−11.5515	+	18.6972i	−0.473167	+	0.765866i
$597$	−4.13461	−	15.4306i	−0.169218	−	0.631531i
$598$	1.56095	−	10.6294i	0.0638321	−	0.434669i
$599$	−8.88965	+	5.13244i	−0.363221	+	0.209706i	−0.670493	−	0.741916i	$-0.733917\pi$
$599$	−8.88965	+	5.13244i	−0.363221	+	0.209706i	0.307272	+	0.951622i	$0.400584\pi$
$600$	−66.5793	+	46.5105i	−2.71809	+	1.89878i
$601$		−	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
$604$	−10.4748	−	3.14431i	−0.426215	−	0.127940i
$605$	9.29367	−	34.6844i	0.377841	−	1.41012i
$606$	53.9405	−	40.1266i	2.19118	−	1.63003i
$607$	−11.5556	+	20.0148i	−0.469026	+	0.812377i	−0.999373	−	0.0354040i	$-0.988728\pi$
$607$	−11.5556	+	20.0148i	−0.469026	+	0.812377i	0.530347	+	0.847780i	$0.322062\pi$
$608$	−2.38725	+	11.4556i	−0.0968157	+	0.464586i
$609$		0			0
$610$	−2.87393	−	24.6663i	−0.116362	−	0.998708i
$611$	5.53381	−	1.48278i	0.223874	−	0.0599868i
$612$	11.9623	−	11.2693i	0.483545	−	0.455533i
$613$	36.7734	+	9.85340i	1.48526	+	0.397975i	0.908135	−	0.418678i	$-0.137507\pi$
$613$	36.7734	+	9.85340i	1.48526	+	0.397975i	0.577129	+	0.816653i	$0.304173\pi$
$614$	6.59082	+	16.6078i	0.265984	+	0.670236i
$615$		−	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	$-0.415377\pi$
$618$	−65.6591	+	26.0569i	−2.64120	+	1.04816i
$619$	−5.53313	−	1.48260i	−0.222395	−	0.0595906i	0.145901	−	0.989299i	$-0.453392\pi$
$619$	−5.53313	−	1.48260i	−0.222395	−	0.0595906i	−0.368296	+	0.929709i	$0.620059\pi$
$620$	31.6945	+	0.945424i	1.27288	+	0.0379692i
$621$	−32.7549	+	8.77664i	−1.31441	+	0.352195i
$622$	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
$626$	−7.36678	−	9.90286i	−0.294436	−	0.395798i
$627$	−2.02357	+	7.55206i	−0.0808135	+	0.301600i
$628$	−13.9901	+	7.53017i	−0.558264	+	0.300486i
$629$	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	$-0.0149444\pi$
$632$	−4.95607	−	0.879499i	−0.197142	−	0.0349846i
$633$	−3.23145	+	1.86568i	−0.128439	+	0.0741541i
$634$	37.6358	+	5.52690i	1.49471	+	0.219501i
$635$	−12.9578	−	48.3593i	−0.514216	−	1.91908i
$636$	−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
$640$	22.8162	+	37.2035i	0.901888	+	1.47060i
$641$	24.9208	+	43.1640i	0.984311	+	1.70488i	0.644957	+	0.764219i	$0.276875\pi$
$641$	24.9208	+	43.1640i	0.984311	+	1.70488i	0.339354	+	0.940659i	$0.389791\pi$
$642$	21.8861	+	9.45023i	0.863775	+	0.372971i
$643$	−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
$646$	1.62819	+	4.10277i	0.0640602	+	0.161421i
$647$	0.401199	−	0.231632i	0.0157727	−	0.00910640i	−0.492093	−	0.870543i	$-0.663768\pi$
$647$	0.401199	−	0.231632i	0.0157727	−	0.00910640i	0.507866	+	0.861436i	$0.330435\pi$
$648$	7.86632	−	9.35384i	0.309018	−	0.367454i
$649$	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
$653$	−9.06587	+	2.42919i	−0.354775	+	0.0950617i	−0.431805	−	0.901967i	$-0.642123\pi$
$653$	−9.06587	+	2.42919i	−0.354775	+	0.0950617i	0.0770297	+	0.997029i	$0.475456\pi$
$654$	11.3565	+	15.2661i	0.444076	+	0.596953i
$655$	18.6017	+	32.2191i	0.726829	+	1.25891i
$656$	−29.7683	−	1.77752i	−1.16226	−	0.0694003i
$657$	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	$0.790699\pi$
$660$	13.8204	+	25.6765i	0.537959	+	0.999458i
$661$	3.08328	+	0.826161i	0.119926	+	0.0321339i	0.318283	−	0.947996i	$-0.396894\pi$
$661$	3.08328	+	0.826161i	0.119926	+	0.0321339i	−0.198357	+	0.980130i	$0.563561\pi$
$662$	6.48962	−	44.1916i	0.252226	−	1.71755i
$663$	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
$667$	−7.16001	−	26.7215i	−0.277237	−	1.03466i
$668$	−17.2033	+	16.2067i	−0.665615	+	0.627056i
$669$	2.40937	−	8.99190i	0.0931517	−	0.347647i
$670$	10.8114	+	4.66827i	0.417681	+	0.180351i
$671$	−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	$0.458024\pi$
$674$	30.4885	+	13.1647i	1.17437	+	0.507085i
$675$	−18.1783	+	67.8422i	−0.699682	+	2.61125i
$676$	15.2329	−	14.3504i	0.585879	−	0.551939i
$677$	1.74903	+	6.52747i	0.0672207	+	0.250871i	0.991357	−	0.131192i	$-0.0418804\pi$
$677$	1.74903	+	6.52747i	0.0672207	+	0.250871i	−0.924136	+	0.382063i	$0.875214\pi$
$678$	−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
$682$	1.09831	−	7.47901i	0.0420564	−	0.286386i
$683$	39.9884	+	10.7149i	1.53012	+	0.409993i	0.923057	−	0.384664i	$-0.125683\pi$
$683$	39.9884	+	10.7149i	1.53012	+	0.409993i	0.607059	+	0.794657i	$0.292349\pi$
$684$	10.6788	+	19.8398i	0.408313	+	0.758593i
$685$	61.7932	+	61.7932i	2.36100	+	2.36100i
$686$		0			0
$687$	−28.8594			−1.10106
$688$	21.3626	+	24.0758i	0.814442	+	0.917882i
$689$	−0.760903	−	1.31792i	−0.0289881	−	0.0502089i
$690$	−45.1408	−	60.6810i	−1.71848	−	2.31008i
$691$	6.35289	−	1.70225i	0.241675	−	0.0647567i	−0.135948	−	0.990716i	$-0.543408\pi$
$691$	6.35289	−	1.70225i	0.241675	−	0.0647567i	0.377624	+	0.925959i	$0.376741\pi$
$692$	−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
$696$	36.4835	+	30.6816i	1.38290	+	1.16298i
$697$	−9.74191	+	5.62449i	−0.369001	+	0.213043i
$698$	−5.12011	−	12.9018i	−0.193799	−	0.488341i
$699$	−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	$0.784173\pi$
$702$	14.6980	+	6.34649i	0.554741	+	0.239533i
$703$	2.42030	+	4.19208i	0.0912834	+	0.158107i
$704$	9.43909	−	4.37632i	0.355749	−	0.164939i
$705$	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
$709$	13.1812	+	49.1929i	0.495030	+	1.84748i	0.529861	+	0.848085i	$0.322244\pi$
$709$	13.1812	+	49.1929i	0.495030	+	1.84748i	−0.0348304	+	0.999393i	$0.511089\pi$
$710$	74.5938	+	10.9543i	2.79945	+	0.411106i
$711$	−8.39335	+	4.84590i	−0.314775	+	0.181736i
$712$	4.18050	−	23.5576i	0.156671	−	0.882857i
$713$			19.6059i			0.734248i
$714$		0			0
$715$	−5.64929	+	5.64929i	−0.211271	+	0.211271i
$716$	29.2088	−	15.7217i	1.09158	−	0.587547i
$717$	−12.1935	+	45.5068i	−0.455375	+	1.69948i
$718$	−8.75464	−	11.7685i	−0.326720	−	0.439197i
$719$	−3.81125	+	6.60127i	−0.142135	+	0.246186i	−0.928301	−	0.371831i	$-0.878730\pi$
$719$	−3.81125	+	6.60127i	−0.142135	+	0.246186i	0.786165	+	0.618017i	$0.212064\pi$
$720$	79.7281	+	26.5485i	2.97129	+	0.989406i
$721$		0			0
$722$	20.6787	−	2.40932i	0.769580	−	0.0896657i
$723$	−39.6278	+	10.6182i	−1.47377	+	0.394896i
$724$	−11.8338	−	0.352994i	−0.439800	−	0.0131189i
$725$	−55.3459	−	14.8299i	−2.05549	−	0.550768i
$726$	−35.5605	+	14.1122i	−1.31977	+	0.523753i
$727$			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
$730$	29.1276	+	73.3968i	1.07806	+	2.71654i
$731$	11.7277	+	3.14242i	0.433763	+	0.116227i
$732$	−19.2586	+	18.1429i	−0.711817	+	0.670581i
$733$	20.4559	−	5.48115i	0.755557	−	0.202451i	0.139575	−	0.990211i	$-0.455426\pi$
$733$	20.4559	−	5.48115i	0.755557	−	0.202451i	0.615982	+	0.787761i	$0.288760\pi$
$734$	−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
$738$	−46.0702	+	34.2718i	−1.69587	+	1.26156i
$739$	−4.51737	+	16.8591i	−0.166174	+	0.620170i	0.831713	+	0.555205i	$0.187360\pi$
$739$	−4.51737	+	16.8591i	−0.166174	+	0.620170i	−0.997888	+	0.0649652i	$0.979306\pi$
$740$	17.2913	+	5.19045i	0.635639	+	0.190805i
$741$	−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	$-0.0627192\pi$
$744$	−19.3474	−	27.6955i	−0.709309	−	1.01537i
$745$	−36.7104	+	21.1948i	−1.34497	+	0.776517i
$746$	−0.926068	+	6.30613i	−0.0339058	+	0.230884i
$747$	14.2753	+	53.2760i	0.522305	+	1.94927i
$748$	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	−0.839058	−	0.544042i	$-0.816893\pi$
$751$	1.41476	−	2.45044i	0.0516254	−	0.0894178i	0.890683	+	0.454624i	$0.150226\pi$
$752$	−12.0110	−	7.92498i	−0.437997	−	0.288994i
$753$	−29.1743	−	50.5313i	−1.06317	−	1.84146i
$754$	−5.17748	+	11.9907i	−0.188553	+	0.436675i
$755$	−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	$0.118162\pi$
$758$	1.55982	−	0.619016i	0.0566552	−	0.0224837i
$759$	−15.6144	+	9.01496i	−0.566765	+	0.327222i
$760$	−14.5265	+	17.2734i	−0.526930	+	0.626573i
$761$	4.15144	+	2.39683i	0.150490	+	0.0868852i	0.573354	−	0.819308i	$-0.305642\pi$
$761$	4.15144	+	2.39683i	0.150490	+	0.0868852i	−0.422864	+	0.906193i	$0.638975\pi$
$762$	−33.1001	+	41.8304i	−1.19909	+	1.51535i
$763$		0			0
$764$	−24.0727	+	5.68674i	−0.870920	+	0.205739i
$765$	30.6179	−	8.20404i	1.10699	−	0.296618i
$766$	−39.0046	+	29.0157i	−1.40929	+	1.04838i
$767$	1.28195	+	2.22041i	0.0462886	+	0.0801742i
$768$	17.2942	−	43.1635i	0.624051	−	1.55753i
$769$	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
$772$	13.6183	−	45.3675i	0.490134	−	1.63281i
$773$	−25.6544	−	6.87406i	−0.922723	−	0.247243i	−0.233974	−	0.972243i	$-0.575173\pi$
$773$	−25.6544	−	6.87406i	−0.922723	−	0.247243i	−0.688749	+	0.725000i	$0.741840\pi$
$774$	61.3172	+	9.00456i	2.20400	+	0.323662i
$775$	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
$779$	−3.99151	−	14.8965i	−0.143011	−	0.533723i
$780$	−1.06462	+	35.6903i	−0.0381194	+	1.27792i
$781$	4.65192	−	17.3612i	0.166459	−	0.621233i
$782$	−4.03514	+	9.34510i	−0.144296	+	0.334180i
$783$	41.2247			1.47325
$784$		0			0
$785$	−30.6438			−1.09372
$786$	15.7134	−	36.3911i	0.560477	−	1.29803i
$787$	8.96168	−	33.4454i	0.319449	−	1.19220i	−0.600326	−	0.799756i	$-0.704962\pi$
$787$	8.96168	−	33.4454i	0.319449	−	1.19220i	0.919775	−	0.392446i	$-0.128371\pi$
$788$	−32.2849	−	0.963035i	−1.15010	−	0.0343067i
$789$	−18.0644	−	67.4174i	−0.643111	−	2.40012i
$790$	−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
$794$	52.3139	+	7.68241i	1.85655	+	0.272638i
$795$	−10.3479	−	2.77272i	−0.367003	−	0.0983383i
$796$	−10.5295	−	3.16072i	−0.373208	−	0.112029i
$797$	−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
$800$	3.14773	+	55.8027i	0.111289	+	1.97292i
$801$	−23.0339	−	39.8959i	−0.813863	−	1.40965i
$802$	5.64646	−	4.20042i	0.199383	−	0.148322i
$803$	18.1836	−	4.87228i	0.641686	−	0.171939i
$804$	−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
$808$	−3.98174	−	46.0941i	−0.140077	−	1.62159i
$809$	2.59269	−	1.49689i	0.0911540	−	0.0526278i	−0.453730	−	0.891139i	$-0.649907\pi$
$809$	2.59269	−	1.49689i	0.0911540	−	0.0526278i	0.544884	+	0.838511i	$0.316574\pi$
$810$	21.9106	−	8.69523i	0.769859	−	0.305519i
$811$	−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
$814$	1.70613	−	3.95128i	0.0597998	−	0.138492i
$815$	17.2322	+	29.8471i	0.603618	+	1.04550i
$816$	−3.52178	−	17.1829i	−0.123287	−	0.601523i
$817$	−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
$821$	−10.4808	−	39.1150i	−0.365783	−	1.36512i	−0.866356	−	0.499428i	$-0.833544\pi$
$821$	−10.4808	−	39.1150i	−0.365783	−	1.36512i	0.500572	−	0.865695i	$-0.333123\pi$
$822$	13.5281	−	92.1208i	0.471848	−	3.21308i
$823$	−35.5496	+	20.5246i	−1.23918	+	0.715442i	−0.968927	−	0.247347i	$-0.920441\pi$
$823$	−35.5496	+	20.5246i	−1.23918	+	0.715442i	−0.270255	+	0.962789i	$0.587108\pi$
$824$	−8.49420	+	47.8658i	−0.295910	+	1.66748i
$825$			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	$0.417245\pi$
$828$	−14.9382	+	49.7646i	−0.519140	+	1.72944i
$829$	−6.76750	+	25.2567i	−0.235045	+	0.877200i	0.743083	+	0.669199i	$0.233363\pi$
$829$	−6.76750	+	25.2567i	−0.235045	+	0.877200i	−0.978129	+	0.208001i	$0.933304\pi$
$830$	−44.3291	+	32.9766i	−1.53868	+	1.14463i
$831$	−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
$835$	−44.0326	+	11.7985i	−1.52381	+	0.408304i
$836$	3.68948	+	3.91636i	0.127603	+	0.135450i
$837$	−28.2209	−	7.56177i	−0.975457	−	0.261373i
$838$	−0.407404	−	1.02659i	−0.0140735	−	0.0354630i
$839$			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
$842$	7.02247	−	2.78688i	0.242010	−	0.0960421i
$843$	−11.8462	−	3.17419i	−0.408006	−	0.109325i
$844$	−0.0765633	+	2.56672i	−0.00263542	+	0.0883500i
$845$	38.9892	−	10.4471i	1.34127	−	0.359392i
$846$	−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
$850$	12.5837	+	16.9157i	0.431617	+	0.580205i
$851$	−2.88913	+	10.7824i	−0.0990382	+	0.369616i
$852$	−38.0723	−	70.7333i	−1.30434	−	2.42328i
$853$	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
$856$	13.4491	−	9.39519i	0.459681	−	0.321121i
$857$	−40.9817	+	23.6608i	−1.39991	+	0.808237i	−0.994382	−	0.105848i	$-0.966244\pi$
$857$	−40.9817	+	23.6608i	−1.39991	+	0.808237i	−0.405524	+	0.914084i	$0.632911\pi$
$858$	8.42191	+	1.23678i	0.287519	+	0.0422228i
$859$	1.87086	+	6.98214i	0.0638329	+	0.238228i	0.990470	−	0.137730i	$-0.0439806\pi$
$859$	1.87086	+	6.98214i	0.0638329	+	0.238228i	−0.926637	+	0.375957i	$0.877314\pi$
$860$	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	−0.939148	−	0.343512i	$-0.888383\pi$
$863$	−5.05527	+	8.75599i	−0.172084	+	0.298057i	0.767065	+	0.641570i	$0.221717\pi$
$864$	−12.5788	−	38.1945i	−0.427939	−	1.29940i
$865$	−15.3802	−	26.6392i	−0.522941	−	0.905761i
$866$	19.8108	+	8.55412i	0.673197	+	0.290681i
$867$	30.2565	+	30.2565i	1.02756	+	1.02756i
$868$		0			0
$869$	−1.63656	+	1.63656i	−0.0555165	+	0.0555165i
$870$	33.9146	+	85.4593i	1.14981	+	2.89734i
$871$	2.97712	−	1.71884i	0.100876	−	0.0582408i
$872$	13.0455	−	1.12690i	0.441775	−	0.0381618i
$873$	−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
$877$	51.9964	−	13.9324i	1.75579	−	0.470463i	0.769946	−	0.638109i	$-0.220283\pi$
$877$	51.9964	−	13.9324i	1.75579	−	0.470463i	0.985847	+	0.167646i	$0.0536165\pi$
$878$	−3.66761	−	4.93022i	−0.123776	−	0.166387i
$879$	−27.7922	−	48.1375i	−0.937408	−	1.62364i
$880$	20.0315	+	1.19612i	0.675263	+	0.0403211i
$881$	−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	$0.578430\pi$
$884$	4.23167	−	2.27770i	0.142326	−	0.0766073i
$885$	17.4340	+	4.67141i	0.586036	+	0.157028i
$886$	−1.25357	+	8.53629i	−0.0421146	+	0.286782i
$887$	29.1946	+	16.8555i	0.980260	+	0.565953i	0.902348	−	0.431007i	$-0.141842\pi$
$887$	29.1946	+	16.8555i	0.980260	+	0.565953i	0.0779110	+	0.996960i	$0.475175\pi$
$888$	−6.55898	−	18.0824i	−0.220105	−	0.606804i
$889$		0			0
$890$	28.6350	−	36.1876i	0.959846	−	1.21301i
$891$	−1.45448	−	5.42821i	−0.0487271	−	0.181852i
$892$	−4.39290	−	4.66303i	−0.147085	−	0.156130i
$893$	1.92606	−	7.18814i	0.0644530	−	0.240542i
$894$	41.4639	+	17.9038i	1.38676	+	0.598792i
$895$	63.9788			2.13858
$896$		0			0
$897$	−22.0777			−0.737153
$898$	−4.83634	−	2.08829i	−0.161391	−	0.0696872i
$899$	6.16891	−	23.0227i	0.205745	−	0.767850i
$900$	73.7937	+	78.3315i	2.45979	+	2.61105i
$901$	0.373182	+	1.39273i	0.0124325	+	0.0463987i
$902$	−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
$906$	−3.26543	+	22.2362i	−0.108487	+	0.738747i
$907$	−1.26216	−	0.338194i	−0.0419092	−	0.0112295i	0.237804	−	0.971313i	$-0.423573\pi$
$907$	−1.26216	−	0.338194i	−0.0419092	−	0.0112295i	−0.279713	+	0.960084i	$0.590239\pi$
$908$	−34.3526	+	18.4903i	−1.14003	+	0.613624i
$909$	−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	$0.665477\pi$
$912$	24.0042	+	1.43333i	0.794859	+	0.0474624i
$913$	6.58567	+	11.4067i	0.217954	+	0.377507i
$914$	−9.06991	−	12.1923i	−0.300006	−	0.403286i
$915$	−49.2931	+	13.2080i	−1.62958	+	0.436645i
$916$	−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	$-0.264159\pi$
$919$	11.3211	+	6.53623i	0.373448	+	0.215610i	−0.301516	+	0.953461i	$0.597493\pi$
$920$	−51.8541	+	4.47930i	−1.70958	+	0.147678i
$921$	31.7989	−	18.3591i	1.04781	−	0.604953i
$922$	−5.81912	−	14.6632i	−0.191643	−	0.482908i
$923$	15.5626	−	15.5626i	0.512248	−	0.512248i
$924$		0			0
$925$	16.3486	+	16.3486i	0.537538	+	0.537538i
$926$	−35.5079	−	15.3320i	−1.16686	−	0.503841i
$927$	46.8018	+	81.0630i	1.53717	+	2.66246i
$928$	31.1592	−	10.2618i	1.02285	−	0.336861i
$929$	10.3529	−	17.9317i	0.339667	−	0.588320i	−0.644703	−	0.764433i	$-0.723019\pi$
$929$	10.3529	−	17.9317i	0.339667	−	0.588320i	0.984370	+	0.176113i	$0.0563524\pi$
$930$	−7.54106	−	64.7232i	−0.247281	−	2.12236i
$931$		0			0
$932$	1.35118	+	5.71971i	0.0442593	+	0.187355i
$933$	−14.8734	−	55.5082i	−0.486933	−	1.81726i
$934$	22.5412	+	3.31022i	0.737570	+	0.108314i
$935$	6.55548	−	3.78481i	0.214387	−	0.123776i
$936$	20.1096	−	14.0480i	0.657303	−	0.459174i
$937$		−	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
$940$	−13.1544	−	24.4392i	−0.429051	−	0.797120i
$941$	−5.12272	+	19.1182i	−0.166996	+	0.623237i	0.830781	+	0.556599i	$0.187894\pi$
$941$	−5.12272	+	19.1182i	−0.166996	+	0.623237i	−0.997777	+	0.0666382i	$0.978773\pi$
$942$	19.4874	+	26.1961i	0.634934	+	0.853516i
$943$	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
$947$	41.3482	−	11.0792i	1.34364	−	0.360027i	0.485855	−	0.874039i	$-0.338508\pi$
$947$	41.3482	−	11.0792i	1.34364	−	0.360027i	0.857782	+	0.514013i	$0.171842\pi$
$948$	−0.308412	+	10.3392i	−0.0100168	+	0.335803i
$949$	22.2659	+	5.96613i	0.722782	+	0.193669i
$950$	−26.8658	+	10.6617i	−0.871643	+	0.345913i
$951$		−	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	$0.996445\pi$
$954$	2.71482	+	6.84090i	0.0878955	+	0.221482i
$955$	−46.0825	−	12.3478i	−1.49120	−	0.399565i
$956$	22.2319	+	23.5990i	0.719030	+	0.763245i
$957$	21.1720	−	5.67303i	0.684395	−	0.183383i
$958$	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
$962$	4.22845	−	3.14556i	0.136331	−	0.101417i
$963$	8.17572	−	30.5122i	0.263459	−	0.983242i
$964$	−8.11715	+	27.0411i	−0.261436	+	0.870937i
$965$	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	$-0.0728096\pi$
$968$	−4.60039	+	25.9237i	−0.147862	+	0.833220i
$969$	7.85557	−	4.53541i	0.252357	−	0.145698i
$970$	12.8585	−	87.5612i	0.412863	−	2.81142i
$971$	−0.0934205	−	0.348650i	−0.00299801	−	0.0111887i	0.964411	−	0.264409i	$-0.0851769\pi$
$971$	−0.0934205	−	0.348650i	−0.00299801	−	0.0111887i	−0.967409	+	0.253220i	$0.918510\pi$
$972$	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
$976$	3.65595	+	17.8375i	0.117024	+	0.570966i
$977$	4.91955	+	8.52091i	0.157390	+	0.272608i	0.933927	−	0.357464i	$-0.116359\pi$
$977$	4.91955	+	8.52091i	0.157390	+	0.272608i	−0.776536	+	0.630072i	$0.783025\pi$
$978$	14.5565	−	33.7119i	0.465466	−	1.07799i
$979$	−7.77902	−	7.77902i	−0.248618	−	0.248618i
$980$		0			0
$981$	17.8276	−	17.8276i	0.569191	−	0.569191i
$982$	−37.6952	+	14.9594i	−1.20290	+	0.477373i
$983$	23.0786	−	13.3244i	0.736094	−	0.424984i	−0.0845537	−	0.996419i	$-0.526946\pi$
$983$	23.0786	−	13.3244i	0.736094	−	0.424984i	0.820647	+	0.571435i	$0.193613\pi$
$984$	5.27414	+	61.0553i	0.168133	+	1.94637i
$985$	−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
$989$	−37.0776	+	9.93490i	−1.17900	+	0.315912i
$990$	31.0014	−	23.0620i	0.985288	−	0.732959i
$991$	−8.41437	−	14.5741i	−0.267291	−	0.462962i	0.700870	−	0.713289i	$-0.252795\pi$
$991$	−8.41437	−	14.5741i	−0.267291	−	0.462962i	−0.968161	+	0.250327i	$0.919462\pi$
$992$	−23.2127	+	1.30939i	−0.737005	+	0.0415732i
$993$	−91.7875			−2.91279
$994$		0			0
$995$	−14.9935	−	14.9935i	−0.475326	−	0.475326i
$996$	56.3807	+	16.9242i	1.78649	+	0.536264i
$997$	35.2183	+	9.43672i	1.11538	+	0.298864i	0.769011	−	0.639236i	$-0.220749\pi$
$997$	35.2183	+	9.43672i	1.11538	+	0.298864i	0.346365	+	0.938100i	$0.387416\pi$
$998$	−36.6404	−	5.38072i	−1.15983	−	0.170324i
$999$	−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.765.2		24
7.2	even	3		112.2.m.d.29.3	✓	12
7.3	odd	6		784.2.x.m.557.5		24
7.4	even	3	inner	784.2.x.l.557.5		24
7.5	odd	6		784.2.m.h.589.3		12
7.6	odd	2		784.2.x.m.765.2		24
16.5	even	4	inner	784.2.x.l.373.5		24
28.23	odd	6		448.2.m.d.337.6		12
56.37	even	6		896.2.m.g.673.6		12
56.51	odd	6		896.2.m.h.673.1		12
112.5	odd	12		784.2.m.h.197.3		12
112.37	even	12		112.2.m.d.85.3	yes	12
112.51	odd	12		896.2.m.h.225.1		12
112.53	even	12	inner	784.2.x.l.165.2		24
112.69	odd	4		784.2.x.m.373.5		24
112.93	even	12		896.2.m.g.225.6		12
112.101	odd	12		784.2.x.m.165.2		24
112.107	odd	12		448.2.m.d.113.6		12
224.37	even	24		7168.2.a.bj.1.11		12
224.107	odd	24		7168.2.a.bi.1.11		12
224.149	even	24		7168.2.a.bj.1.2		12
224.219	odd	24		7168.2.a.bi.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.d.29.3	✓	12	7.2	even	3
112.2.m.d.85.3	yes	12	112.37	even	12
448.2.m.d.113.6		12	112.107	odd	12
448.2.m.d.337.6		12	28.23	odd	6
784.2.m.h.197.3		12	112.5	odd	12
784.2.m.h.589.3		12	7.5	odd	6
784.2.x.l.165.2		24	112.53	even	12	inner
784.2.x.l.373.5		24	16.5	even	4	inner
784.2.x.l.557.5		24	7.4	even	3	inner
784.2.x.l.765.2		24	1.1	even	1	trivial
784.2.x.m.165.2		24	112.101	odd	12
784.2.x.m.373.5		24	112.69	odd	4
784.2.x.m.557.5		24	7.3	odd	6
784.2.x.m.765.2		24	7.6	odd	2
896.2.m.g.225.6		12	112.93	even	12
896.2.m.g.673.6		12	56.37	even	6
896.2.m.h.225.1		12	112.51	odd	12
896.2.m.h.673.1		12	56.51	odd	6
7168.2.a.bi.1.2		12	224.219	odd	24
7168.2.a.bi.1.11		12	224.107	odd	24
7168.2.a.bj.1.2		12	224.149	even	24
7168.2.a.bj.1.11		12	224.37	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)

\(f(q)\)	\(=\)	\(q+(-1.29835 - 0.560616i) q^{2} +(-0.752181 + 2.80718i) q^{3} +(1.37142 + 1.45575i) q^{4} +(0.998394 + 3.72606i) q^{5} +(2.55034 - 3.22301i) q^{6} +(-0.964462 - 2.65891i) q^{8} +(-4.71639 - 2.72301i) q^{9} +O(q^{10})\)	\(q+(-1.29835 - 0.560616i) q^{2} +(-0.752181 + 2.80718i) q^{3} +(1.37142 + 1.45575i) q^{4} +(0.998394 + 3.72606i) q^{5} +(2.55034 - 3.22301i) q^{6} +(-0.964462 - 2.65891i) q^{8} +(-4.71639 - 2.72301i) q^{9} +(0.792625 - 5.39744i) q^{10} +(-1.25622 - 0.336603i) q^{11} +(-5.11811 + 2.75483i) q^{12} +(-1.12607 - 1.12607i) q^{13} -11.2107 q^{15} +(-0.238422 + 3.99289i) q^{16} +(0.754426 + 1.30670i) q^{17} +(4.59696 + 6.17950i) q^{18} +(-1.99810 + 0.535390i) q^{19} +(-4.05500 + 6.56340i) q^{20} +(1.44230 + 1.14128i) q^{22} +(-4.13121 - 2.38515i) q^{23} +(8.18949 - 0.707432i) q^{24} +(-8.55659 + 4.94015i) q^{25} +(0.830740 + 2.09333i) q^{26} +(5.02656 - 5.02656i) q^{27} +(4.10069 + 4.10069i) q^{29} +(14.5554 + 6.28489i) q^{30} +(-2.05500 - 3.55936i) q^{31} +(2.54803 - 5.05050i) q^{32} +(1.88981 - 3.27324i) q^{33} +(-0.246948 - 2.11950i) q^{34} +(-2.50412 - 10.6003i) q^{36} +(-0.605650 - 2.26031i) q^{37} +(2.89438 + 0.425046i) q^{38} +(4.00810 - 2.31408i) q^{39} +(8.94435 - 6.24828i) q^{40} +7.45533i q^{41} +(5.68992 - 5.68992i) q^{43} +(-1.23279 - 2.29036i) q^{44} +(5.43727 - 20.2922i) q^{45} +(4.02659 + 5.41278i) q^{46} +(-1.79874 + 3.11551i) q^{47} +(-11.0294 - 3.67267i) q^{48} +(13.8790 - 1.61707i) q^{50} +(-4.23561 + 1.13493i) q^{51} +(0.0949645 - 3.18360i) q^{52} +(0.923043 + 0.247329i) q^{53} +(-9.34420 + 3.70826i) q^{54} -5.01680i q^{55} -6.01174i q^{57} +(-3.02521 - 7.62303i) q^{58} +(-1.55512 - 0.416693i) q^{59} +(-15.3745 - 16.3200i) q^{60} +(4.39698 - 1.17817i) q^{61} +(0.672667 + 5.77335i) q^{62} +(-6.13963 + 5.12884i) q^{64} +(3.07155 - 5.32008i) q^{65} +(-4.28866 + 3.19035i) q^{66} +(-0.558703 + 2.08511i) q^{67} +(-0.867602 + 2.89029i) q^{68} +(9.80296 - 9.80296i) q^{69} +13.8202i q^{71} +(-2.69147 + 15.1667i) q^{72} +(-12.5356 + 7.23744i) q^{73} +(-0.480825 + 3.27421i) q^{74} +(-7.43177 - 27.7357i) q^{75} +(-3.51963 - 2.17450i) q^{76} +(-6.50122 + 0.757473i) q^{78} +(0.889807 - 1.54119i) q^{79} +(-15.1158 + 3.09810i) q^{80} +(2.16054 + 3.74216i) q^{81} +(4.17958 - 9.67961i) q^{82} +(-7.16133 - 7.16133i) q^{83} +(-4.11564 + 4.11564i) q^{85} +(-10.5774 + 4.19764i) q^{86} +(-14.5958 + 8.42689i) q^{87} +(0.316577 + 3.66481i) q^{88} +(7.32570 + 4.22949i) q^{89} +(-18.4356 + 23.2981i) q^{90} +(-2.19342 - 9.28505i) q^{92} +(11.5375 - 3.09146i) q^{93} +(4.08200 - 3.03661i) q^{94} +(-3.98979 - 6.91052i) q^{95} +(12.2611 + 10.9517i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more