LMFDB - Embedded newform 1218.2.m.b.307.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1218,2,Mod(307,1218)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1218.307"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1218, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1218 = 2 \cdot 3 \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1218.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,0,0,40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.72577896619$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.7
Character	$\chi$	$=$	1218.307
Dual form			1218.2.m.b.853.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +2.17708 q^{5} +1.00000 q^{6} +(-0.0332084 + 2.64554i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-1.53943 + 1.53943i) q^{10} +(-3.07581 + 3.07581i) q^{11} +(-0.707107 + 0.707107i) q^{12} -3.05148 q^{13} +(-1.84720 - 1.89416i) q^{14} +(-1.53943 - 1.53943i) q^{15} -1.00000 q^{16} +(-2.01832 - 2.01832i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(-2.09893 - 2.09893i) q^{19} -2.17708i q^{20} +(1.89416 - 1.84720i) q^{21} -4.34986i q^{22} -1.96734 q^{23} -1.00000i q^{24} -0.260314 q^{25} +(2.15772 - 2.15772i) q^{26} +(0.707107 - 0.707107i) q^{27} +(2.64554 + 0.0332084i) q^{28} +(-3.12402 - 4.38640i) q^{29} +2.17708 q^{30} +(1.89326 + 1.89326i) q^{31} +(0.707107 - 0.707107i) q^{32} +4.34986 q^{33} +2.85434 q^{34} +(-0.0722973 + 5.75956i) q^{35} +1.00000 q^{36} +(-5.99454 - 5.99454i) q^{37} +2.96834 q^{38} +(2.15772 + 2.15772i) q^{39} +(1.53943 + 1.53943i) q^{40} +(3.37850 - 3.37850i) q^{41} +(-0.0332084 + 2.64554i) q^{42} +(-2.06975 + 2.06975i) q^{43} +(3.07581 + 3.07581i) q^{44} +2.17708i q^{45} +(1.39112 - 1.39112i) q^{46} +(8.60874 - 8.60874i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-6.99779 - 0.175708i) q^{49} +(0.184070 - 0.184070i) q^{50} +2.85434i q^{51} +3.05148i q^{52} -10.9788 q^{53} +1.00000i q^{54} +(-6.69630 + 6.69630i) q^{55} +(-1.89416 + 1.84720i) q^{56} +2.96834i q^{57} +(5.31067 + 0.892636i) q^{58} +11.1746i q^{59} +(-1.53943 + 1.53943i) q^{60} +(3.08688 + 3.08688i) q^{61} -2.67747 q^{62} +(-2.64554 - 0.0332084i) q^{63} +1.00000i q^{64} -6.64333 q^{65} +(-3.07581 + 3.07581i) q^{66} +8.49928i q^{67} +(-2.01832 + 2.01832i) q^{68} +(1.39112 + 1.39112i) q^{69} +(-4.02150 - 4.12375i) q^{70} -13.7545i q^{71} +(-0.707107 + 0.707107i) q^{72} +(6.46121 - 6.46121i) q^{73} +8.47756 q^{74} +(0.184070 + 0.184070i) q^{75} +(-2.09893 + 2.09893i) q^{76} +(-8.03505 - 8.23934i) q^{77} -3.05148 q^{78} +(-10.6504 + 10.6504i) q^{79} -2.17708 q^{80} -1.00000 q^{81} +4.77792i q^{82} -7.41216i q^{83} +(-1.84720 - 1.89416i) q^{84} +(-4.39405 - 4.39405i) q^{85} -2.92707i q^{86} +(-0.892636 + 5.31067i) q^{87} -4.34986 q^{88} +(-12.7095 - 12.7095i) q^{89} +(-1.53943 - 1.53943i) q^{90} +(0.101335 - 8.07283i) q^{91} +1.96734i q^{92} -2.67747i q^{93} +12.1746i q^{94} +(-4.56955 - 4.56955i) q^{95} -1.00000 q^{96} +(-7.25077 + 7.25077i) q^{97} +(5.07243 - 4.82394i) q^{98} +(-3.07581 - 3.07581i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{6} - 4 q^{10} + 4 q^{14} - 4 q^{15} - 40 q^{16} - 8 q^{19} + 4 q^{21} + 24 q^{25} + 12 q^{28} + 8 q^{29} + 24 q^{31} + 12 q^{35} + 40 q^{36} - 16 q^{37} + 4 q^{40} - 16 q^{41} - 20 q^{43} + 4 q^{46}+ \cdots - 24 q^{98}+O(q^{100}) $ 40 * q + 40 * q^6 - 4 * q^10 + 4 * q^14 - 4 * q^15 - 40 * q^16 - 8 * q^19 + 4 * q^21 + 24 * q^25 + 12 * q^28 + 8 * q^29 + 24 * q^31 + 12 * q^35 + 40 * q^36 - 16 * q^37 + 4 * q^40 - 16 * q^41 - 20 * q^43 + 4 * q^46 + 16 * q^47 + 28 * q^49 + 32 * q^50 + 16 * q^53 + 24 * q^55 - 4 * q^56 - 20 * q^58 - 4 * q^60 + 44 * q^61 - 12 * q^63 + 4 * q^69 + 20 * q^70 + 52 * q^73 + 32 * q^75 - 8 * q^76 + 20 * q^77 + 4 * q^79 - 40 * q^81 + 4 * q^84 - 24 * q^85 + 12 * q^87 - 24 * q^89 - 4 * q^90 - 16 * q^95 - 40 * q^96 + 68 * q^97 - 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1218\mathbb{Z}\right)^\times$.

$n$	$379$	$407$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	2.17708			0.973621			0.486810	−	0.873508i	$-0.338160\pi$
$5$	2.17708			0.973621			0.486810	+	0.873508i	$0.338160\pi$
$6$	1.00000			0.408248
$7$	−0.0332084	+	2.64554i	−0.0125516	+	0.999921i
$7$	−0.0332084	+	2.64554i	−0.0125516	+	0.999921i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$			1.00000i			0.333333i
$10$	−1.53943	+	1.53943i	−0.486810	+	0.486810i
$11$	−3.07581	+	3.07581i	−0.927393	+	0.927393i	−0.997537	−	0.0701443i	$-0.977654\pi$
$11$	−3.07581	+	3.07581i	−0.927393	+	0.927393i	0.0701443	+	0.997537i	$0.477654\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−3.05148			−0.846329			−0.423165	−	0.906053i	$-0.639081\pi$
$13$	−3.05148			−0.846329			−0.423165	+	0.906053i	$0.639081\pi$
$14$	−1.84720	−	1.89416i	−0.493685	−	0.506236i
$15$	−1.53943	−	1.53943i	−0.397479	−	0.397479i
$16$	−1.00000			−0.250000
$17$	−2.01832	−	2.01832i	−0.489515	−	0.489515i	0.418638	−	0.908153i	$-0.362508\pi$
$17$	−2.01832	−	2.01832i	−0.489515	−	0.489515i	−0.908153	+	0.418638i	$0.862508\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	−2.09893	−	2.09893i	−0.481528	−	0.481528i	0.424091	−	0.905620i	$-0.360594\pi$
$19$	−2.09893	−	2.09893i	−0.481528	−	0.481528i	−0.905620	+	0.424091i	$0.860594\pi$
$20$		−	2.17708i		−	0.486810i
$21$	1.89416	−	1.84720i	0.413340	−	0.403092i
$22$		−	4.34986i		−	0.927393i
$23$	−1.96734			−0.410219			−0.205110	−	0.978739i	$-0.565755\pi$
$23$	−1.96734			−0.410219			−0.205110	+	0.978739i	$0.565755\pi$
$24$		−	1.00000i		−	0.204124i
$25$	−0.260314			−0.0520627
$26$	2.15772	−	2.15772i	0.423165	−	0.423165i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	2.64554	+	0.0332084i	0.499961	+	0.00627579i
$29$	−3.12402	−	4.38640i	−0.580116	−	0.814534i
$29$	−3.12402	−	4.38640i	−0.580116	−	0.814534i
$30$	2.17708			0.397479
$31$	1.89326	+	1.89326i	0.340040	+	0.340040i	0.856382	−	0.516343i	$-0.172707\pi$
$31$	1.89326	+	1.89326i	0.340040	+	0.340040i	−0.516343	+	0.856382i	$0.672707\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	4.34986			0.757213
$34$	2.85434			0.489515
$35$	−0.0722973	+	5.75956i	−0.0122205	+	0.973544i
$36$	1.00000			0.166667
$37$	−5.99454	−	5.99454i	−0.985496	−	0.985496i	0.0144003	−	0.999896i	$-0.495416\pi$
$37$	−5.99454	−	5.99454i	−0.985496	−	0.985496i	−0.999896	+	0.0144003i	$0.995416\pi$
$38$	2.96834			0.481528
$39$	2.15772	+	2.15772i	0.345512	+	0.345512i
$40$	1.53943	+	1.53943i	0.243405	+	0.243405i
$41$	3.37850	−	3.37850i	0.527633	−	0.527633i	−0.392233	−	0.919866i	$-0.628297\pi$
$41$	3.37850	−	3.37850i	0.527633	−	0.527633i	0.919866	+	0.392233i	$0.128297\pi$
$42$	−0.0332084	+	2.64554i	−0.00512416	+	0.408216i
$43$	−2.06975	+	2.06975i	−0.315634	+	0.315634i	−0.847088	−	0.531453i	$-0.821646\pi$
$43$	−2.06975	+	2.06975i	−0.315634	+	0.315634i	0.531453	+	0.847088i	$0.321646\pi$
$44$	3.07581	+	3.07581i	0.463696	+	0.463696i
$45$			2.17708i			0.324540i
$46$	1.39112	−	1.39112i	0.205110	−	0.205110i
$47$	8.60874	−	8.60874i	1.25571	−	1.25571i	0.302595	−	0.953119i	$-0.402147\pi$
$47$	8.60874	−	8.60874i	1.25571	−	1.25571i	0.953119	−	0.302595i	$-0.0978529\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$	−6.99779	−	0.175708i	−0.999685	−	0.0251012i
$50$	0.184070	−	0.184070i	0.0260314	−	0.0260314i
$51$			2.85434i			0.399687i
$52$			3.05148i			0.423165i
$53$	−10.9788			−1.50806			−0.754029	−	0.656841i	$-0.771892\pi$
$53$	−10.9788			−1.50806			−0.754029	+	0.656841i	$0.771892\pi$
$54$			1.00000i			0.136083i
$55$	−6.69630	+	6.69630i	−0.902929	+	0.902929i
$56$	−1.89416	+	1.84720i	−0.253118	+	0.246842i
$57$			2.96834i			0.393166i
$58$	5.31067	+	0.892636i	0.697325	+	0.117209i
$59$			11.1746i			1.45481i	0.686208	+	0.727406i	$0.259274\pi$
$59$			11.1746i			1.45481i	−0.686208	+	0.727406i	$0.740726\pi$
$60$	−1.53943	+	1.53943i	−0.198739	+	0.198739i
$61$	3.08688	+	3.08688i	0.395234	+	0.395234i	0.876548	−	0.481314i	$-0.159840\pi$
$61$	3.08688	+	3.08688i	0.395234	+	0.395234i	−0.481314	+	0.876548i	$0.659840\pi$
$62$	−2.67747			−0.340040
$63$	−2.64554	−	0.0332084i	−0.333307	−	0.00418386i
$64$			1.00000i			0.125000i
$65$	−6.64333			−0.824004
$66$	−3.07581	+	3.07581i	−0.378606	+	0.378606i
$67$			8.49928i			1.03835i	0.854667	+	0.519176i	$0.173761\pi$
$67$			8.49928i			1.03835i	−0.854667	+	0.519176i	$0.826239\pi$
$68$	−2.01832	+	2.01832i	−0.244758	+	0.244758i
$69$	1.39112	+	1.39112i	0.167471	+	0.167471i
$70$	−4.02150	−	4.12375i	−0.480662	−	0.492882i
$71$		−	13.7545i		−	1.63236i	−0.577798	−	0.816180i	$-0.696088\pi$
$71$		−	13.7545i		−	1.63236i	0.577798	−	0.816180i	$-0.303912\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	6.46121	−	6.46121i	0.756227	−	0.756227i	−0.219406	−	0.975634i	$-0.570412\pi$
$73$	6.46121	−	6.46121i	0.756227	−	0.756227i	0.975634	+	0.219406i	$0.0704121\pi$
$74$	8.47756			0.985496
$75$	0.184070	+	0.184070i	0.0212545	+	0.0212545i
$76$	−2.09893	+	2.09893i	−0.240764	+	0.240764i
$77$	−8.03505	−	8.23934i	−0.915679	−	0.938960i
$78$	−3.05148			−0.345512
$79$	−10.6504	+	10.6504i	−1.19826	+	1.19826i	−0.223575	+	0.974687i	$0.571773\pi$
$79$	−10.6504	+	10.6504i	−1.19826	+	1.19826i	−0.974687	+	0.223575i	$0.928227\pi$
$80$	−2.17708			−0.243405
$81$	−1.00000			−0.111111
$82$			4.77792i			0.527633i
$83$		−	7.41216i		−	0.813590i	−0.913520	−	0.406795i	$-0.866646\pi$
$83$		−	7.41216i		−	0.813590i	0.913520	−	0.406795i	$-0.133354\pi$
$84$	−1.84720	−	1.89416i	−0.201546	−	0.206670i
$85$	−4.39405	−	4.39405i	−0.476602	−	0.476602i
$86$		−	2.92707i		−	0.315634i
$87$	−0.892636	+	5.31067i	−0.0957006	+	0.569363i
$88$	−4.34986			−0.463696
$89$	−12.7095	−	12.7095i	−1.34720	−	1.34720i	−0.888685	−	0.458519i	$-0.848380\pi$
$89$	−12.7095	−	12.7095i	−1.34720	−	1.34720i	−0.458519	−	0.888685i	$-0.651620\pi$
$90$	−1.53943	−	1.53943i	−0.162270	−	0.162270i
$91$	0.101335	−	8.07283i	0.0106228	−	0.846262i
$92$			1.96734i			0.205110i
$93$		−	2.67747i		−	0.277641i
$94$			12.1746i			1.25571i
$95$	−4.56955	−	4.56955i	−0.468826	−	0.468826i
$96$	−1.00000			−0.102062
$97$	−7.25077	+	7.25077i	−0.736204	+	0.736204i	−0.971841	−	0.235637i	$-0.924282\pi$
$97$	−7.25077	+	7.25077i	−0.736204	+	0.736204i	0.235637	+	0.971841i	$0.424282\pi$
$98$	5.07243	−	4.82394i	0.512393	−	0.487292i
$99$	−3.07581	−	3.07581i	−0.309131	−	0.309131i
$100$			0.260314i			0.0260314i
$101$	4.72960	+	4.72960i	0.470612	+	0.470612i	0.902113	−	0.431500i	$-0.142016\pi$
$101$	4.72960	+	4.72960i	0.470612	+	0.470612i	−0.431500	+	0.902113i	$0.642016\pi$
$102$	−2.01832	−	2.01832i	−0.199844	−	0.199844i
$103$			2.63995i			0.260122i	0.991506	+	0.130061i	$0.0415173\pi$
$103$			2.63995i			0.260122i	−0.991506	+	0.130061i	$0.958483\pi$
$104$	−2.15772	−	2.15772i	−0.211582	−	0.211582i
$105$	4.12375	−	4.02150i	0.402437	−	0.392459i
$106$	7.76320	−	7.76320i	0.754029	−	0.754029i
$107$	−5.12152			−0.495116			−0.247558	−	0.968873i	$-0.579628\pi$
$107$	−5.12152			−0.495116			−0.247558	+	0.968873i	$0.579628\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$			7.14857i			0.684709i	0.939571	+	0.342354i	$0.111224\pi$
$109$			7.14857i			0.684709i	−0.939571	+	0.342354i	$0.888776\pi$
$110$		−	9.47000i		−	0.902929i
$111$			8.47756i			0.804654i
$112$	0.0332084	−	2.64554i	0.00313790	−	0.249980i
$113$	6.81615	+	6.81615i	0.641209	+	0.641209i	0.950853	−	0.309644i	$-0.100210\pi$
$113$	6.81615	+	6.81615i	0.641209	+	0.641209i	−0.309644	+	0.950853i	$0.600210\pi$
$114$	−2.09893	−	2.09893i	−0.196583	−	0.196583i
$115$	−4.28307			−0.399398
$116$	−4.38640	+	3.12402i	−0.407267	+	0.290058i
$117$		−	3.05148i		−	0.282110i
$118$	−7.90165	−	7.90165i	−0.727406	−	0.727406i
$119$	5.40659	−	5.27253i	0.495621	−	0.483332i
$120$		−	2.17708i		−	0.198739i
$121$		−	7.92125i		−	0.720114i
$122$	−4.36550			−0.395234
$123$	−4.77792			−0.430811
$124$	1.89326	−	1.89326i	0.170020	−	0.170020i
$125$	−11.4521			−1.02431
$126$	1.89416	−	1.84720i	0.168745	−	0.164562i
$127$	4.97865	−	4.97865i	0.441783	−	0.441783i	−0.450828	−	0.892611i	$-0.648871\pi$
$127$	4.97865	−	4.97865i	0.441783	−	0.441783i	0.892611	+	0.450828i	$0.148871\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	2.92707			0.257714
$130$	4.69754	−	4.69754i	0.412002	−	0.412002i
$131$	5.87709	−	5.87709i	0.513484	−	0.513484i	−0.402108	−	0.915592i	$-0.631723\pi$
$131$	5.87709	−	5.87709i	0.513484	−	0.513484i	0.915592	+	0.402108i	$0.131723\pi$
$132$		−	4.34986i		−	0.378606i
$133$	5.62252	−	5.48312i	0.487535	−	0.475447i
$134$	−6.00990	−	6.00990i	−0.519176	−	0.519176i
$135$	1.53943	−	1.53943i	0.132493	−	0.132493i
$136$		−	2.85434i		−	0.244758i
$137$	4.19336	−	4.19336i	0.358263	−	0.358263i	−0.504910	−	0.863172i	$-0.668474\pi$
$137$	4.19336	−	4.19336i	0.358263	−	0.358263i	0.863172	+	0.504910i	$0.168474\pi$
$138$	−1.96734			−0.167471
$139$			12.3931i			1.05117i	0.850740	+	0.525587i	$0.176154\pi$
$139$			12.3931i			1.05117i	−0.850740	+	0.525587i	$0.823846\pi$
$140$	5.75956	+	0.0722973i	0.486772	+	0.00611024i
$141$	−12.1746			−1.02529
$142$	9.72590	+	9.72590i	0.816180	+	0.816180i
$143$	9.38579	−	9.38579i	0.784879	−	0.784879i
$144$		−	1.00000i		−	0.0833333i
$145$	−6.80125	−	9.54955i	−0.564813	−	0.793047i
$146$			9.13753i			0.756227i
$147$	4.82394	+	5.07243i	0.397872	+	0.418367i
$148$	−5.99454	+	5.99454i	−0.492748	+	0.492748i
$149$		−	0.460829i		−	0.0377526i	−0.999822	−	0.0188763i	$-0.993991\pi$
$149$		−	0.460829i		−	0.0377526i	0.999822	−	0.0188763i	$-0.00600886\pi$
$150$	−0.260314			−0.0212545
$151$			20.7071i			1.68512i	0.538600	+	0.842562i	$0.318953\pi$
$151$			20.7071i			1.68512i	−0.538600	+	0.842562i	$0.681047\pi$
$152$		−	2.96834i		−	0.240764i
$153$	2.01832	−	2.01832i	0.163172	−	0.163172i
$154$	11.5077	+	0.144452i	0.927320	+	0.0116402i
$155$	4.12178	+	4.12178i	0.331070	+	0.331070i
$156$	2.15772	−	2.15772i	0.172756	−	0.172756i
$157$	−8.66060	+	8.66060i	−0.691191	+	0.691191i	−0.962494	−	0.271303i	$-0.912545\pi$
$157$	−8.66060	+	8.66060i	−0.691191	+	0.691191i	0.271303	+	0.962494i	$0.412545\pi$
$158$		−	15.0619i		−	1.19826i
$159$	7.76320	+	7.76320i	0.615662	+	0.615662i
$160$	1.53943	−	1.53943i	0.121703	−	0.121703i
$161$	0.0653322	−	5.20469i	0.00514890	−	0.410187i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−5.70229	−	5.70229i	−0.446638	−	0.446638i	0.447597	−	0.894235i	$-0.352280\pi$
$163$	−5.70229	−	5.70229i	−0.446638	−	0.446638i	−0.894235	+	0.447597i	$0.852280\pi$
$164$	−3.37850	−	3.37850i	−0.263817	−	0.263817i
$165$	9.47000			0.737238
$166$	5.24119	+	5.24119i	0.406795	+	0.406795i
$167$	−18.4936			−1.43108			−0.715541	−	0.698571i	$-0.753820\pi$
$167$	−18.4936			−1.43108			−0.715541	+	0.698571i	$0.753820\pi$
$168$	2.64554	+	0.0332084i	0.204108	+	0.00256208i
$169$	−3.68845			−0.283727
$170$	6.21413			0.476602
$171$	2.09893	−	2.09893i	0.160509	−	0.160509i
$172$	2.06975	+	2.06975i	0.157817	+	0.157817i
$173$	18.3070			1.39186			0.695928	−	0.718112i	$-0.254993\pi$
$173$	18.3070			1.39186			0.695928	+	0.718112i	$0.254993\pi$
$174$	−3.12402	−	4.38640i	−0.236831	−	0.332532i
$175$	0.00864459	−	0.688671i	0.000653470	−	0.0520586i
$176$	3.07581	−	3.07581i	0.231848	−	0.231848i
$177$	7.90165	−	7.90165i	0.593924	−	0.593924i
$178$	17.9739			1.34720
$179$			8.86359i			0.662496i	0.943544	+	0.331248i	$0.107470\pi$
$179$			8.86359i			0.662496i	−0.943544	+	0.331248i	$0.892530\pi$
$180$	2.17708			0.162270
$181$			20.0870i			1.49305i	0.665355	+	0.746527i	$0.268280\pi$
$181$			20.0870i			1.49305i	−0.665355	+	0.746527i	$0.731720\pi$
$182$	5.63670	+	5.78001i	0.417820	+	0.428443i
$183$		−	4.36550i		−	0.322707i
$184$	−1.39112	−	1.39112i	−0.102555	−	0.102555i
$185$	−13.0506	−	13.0506i	−0.959499	−	0.959499i
$186$	1.89326	+	1.89326i	0.138821	+	0.138821i
$187$	12.4160			0.907946
$188$	−8.60874	−	8.60874i	−0.627857	−	0.627857i
$189$	1.84720	+	1.89416i	0.134364	+	0.137780i
$190$	6.46232			0.468826
$191$	−6.39182	+	6.39182i	−0.462496	+	0.462496i	−0.899473	−	0.436977i	$-0.856049\pi$
$191$	−6.39182	+	6.39182i	−0.462496	+	0.462496i	0.436977	+	0.899473i	$0.356049\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	0.225289	−	0.225289i	0.0162166	−	0.0162166i	−0.698952	−	0.715169i	$-0.746350\pi$
$193$	0.225289	−	0.225289i	0.0162166	−	0.0162166i	0.715169	+	0.698952i	$0.246350\pi$
$194$		−	10.2541i		−	0.736204i
$195$	4.69754	+	4.69754i	0.336398	+	0.336398i
$196$	−0.175708	+	6.99779i	−0.0125506	+	0.499842i
$197$	−20.6557			−1.47166			−0.735830	−	0.677166i	$-0.763208\pi$
$197$	−20.6557			−1.47166			−0.735830	+	0.677166i	$0.763208\pi$
$198$	4.34986			0.309131
$199$			7.37290i			0.522651i	0.965251	+	0.261326i	$0.0841596\pi$
$199$			7.37290i			0.522651i	−0.965251	+	0.261326i	$0.915840\pi$
$200$	−0.184070	−	0.184070i	−0.0130157	−	0.0130157i
$201$	6.00990	−	6.00990i	0.423906	−	0.423906i
$202$	−6.68866			−0.470612
$203$	11.7081	−	8.11907i	0.821751	−	0.569847i
$204$	2.85434			0.199844
$205$	7.35528	−	7.35528i	0.513715	−	0.513715i
$206$	−1.86672	−	1.86672i	−0.130061	−	0.130061i
$207$		−	1.96734i		−	0.136740i
$208$	3.05148			0.211582
$209$	12.9119			0.893132
$210$	−0.0722973	+	5.75956i	−0.00498899	+	0.397448i
$211$	13.0824	+	13.0824i	0.900632	+	0.900632i	0.995491	−	0.0948586i	$-0.0302399\pi$
$211$	13.0824	+	13.0824i	0.900632	+	0.900632i	−0.0948586	+	0.995491i	$0.530240\pi$
$212$			10.9788i			0.754029i
$213$	−9.72590	+	9.72590i	−0.666408	+	0.666408i
$214$	3.62146	−	3.62146i	0.247558	−	0.247558i
$215$	−4.50602	+	4.50602i	−0.307308	+	0.307308i
$216$	1.00000			0.0680414
$217$	−5.07157	+	4.94583i	−0.344281	+	0.335745i
$218$	−5.05480	−	5.05480i	−0.342354	−	0.342354i
$219$	−9.13753			−0.617457
$220$	6.69630	+	6.69630i	0.451464	+	0.451464i
$221$	6.15888	+	6.15888i	0.414291	+	0.414291i
$222$	−5.99454	−	5.99454i	−0.402327	−	0.402327i
$223$		−	7.82250i		−	0.523834i	−0.965090	−	0.261917i	$-0.915645\pi$
$223$		−	7.82250i		−	0.523834i	0.965090	−	0.261917i	$-0.0843546\pi$
$224$	1.84720	+	1.89416i	0.123421	+	0.126559i
$225$		−	0.260314i		−	0.0173542i
$226$	−9.63949			−0.641209
$227$			23.3631i			1.55067i	0.631553	+	0.775333i	$0.282418\pi$
$227$			23.3631i			1.55067i	−0.631553	+	0.775333i	$0.717582\pi$
$228$	2.96834			0.196583
$229$	4.68182	−	4.68182i	0.309384	−	0.309384i	−0.535287	−	0.844670i	$-0.679796\pi$
$229$	4.68182	−	4.68182i	0.309384	−	0.309384i	0.844670	+	0.535287i	$0.179796\pi$
$230$	3.02859	−	3.02859i	0.199699	−	0.199699i
$231$	−0.144452	+	11.5077i	−0.00950422	+	0.757153i
$232$	0.892636	−	5.31067i	0.0586044	−	0.348662i
$233$	−0.533098			−0.0349244			−0.0174622	−	0.999848i	$-0.505559\pi$
$233$	−0.533098			−0.0349244			−0.0174622	+	0.999848i	$0.505559\pi$
$234$	2.15772	+	2.15772i	0.141055	+	0.141055i
$235$	18.7419	−	18.7419i	1.22259	−	1.22259i
$236$	11.1746			0.727406
$237$	15.0619			0.978376
$238$	−0.0947880	+	7.55128i	−0.00614419	+	0.489477i
$239$	22.8814			1.48007			0.740036	−	0.672567i	$-0.234808\pi$
$239$	22.8814			1.48007			0.740036	+	0.672567i	$0.234808\pi$
$240$	1.53943	+	1.53943i	0.0993697	+	0.0993697i
$241$	−7.01610			−0.451946			−0.225973	−	0.974134i	$-0.572556\pi$
$241$	−7.01610			−0.451946			−0.225973	+	0.974134i	$0.572556\pi$
$242$	5.60117	+	5.60117i	0.360057	+	0.360057i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	3.08688	−	3.08688i	0.197617	−	0.197617i
$245$	−15.2348	−	0.382531i	−0.973314	−	0.0244390i
$246$	3.37850	−	3.37850i	0.215405	−	0.215405i
$247$	6.40486	+	6.40486i	0.407532	+	0.407532i
$248$			2.67747i			0.170020i
$249$	−5.24119	+	5.24119i	−0.332147	+	0.332147i
$250$	8.09788	−	8.09788i	0.512155	−	0.512155i
$251$	−5.57436	−	5.57436i	−0.351851	−	0.351851i	0.508947	−	0.860798i	$-0.330035\pi$
$251$	−5.57436	−	5.57436i	−0.351851	−	0.351851i	−0.860798	+	0.508947i	$0.830035\pi$
$252$	−0.0332084	+	2.64554i	−0.00209193	+	0.166654i
$253$	6.05118	−	6.05118i	0.380434	−	0.380434i
$254$			7.04087i			0.441783i
$255$			6.21413i			0.389144i
$256$	1.00000			0.0625000
$257$			0.239239i			0.0149233i	0.999972	+	0.00746167i	$0.00237514\pi$
$257$			0.239239i			0.0149233i	−0.999972	+	0.00746167i	$0.997625\pi$
$258$	−2.06975	+	2.06975i	−0.128857	+	0.128857i
$259$	16.0579	−	15.6597i	0.997788	−	0.973049i
$260$			6.64333i			0.412002i
$261$	4.38640	−	3.12402i	0.271511	−	0.193372i
$262$			8.31146i			0.513484i
$263$	5.36523	−	5.36523i	0.330834	−	0.330834i	−0.522069	−	0.852903i	$-0.674840\pi$
$263$	5.36523	−	5.36523i	0.330834	−	0.330834i	0.852903	+	0.522069i	$0.174840\pi$
$264$	3.07581	+	3.07581i	0.189303	+	0.189303i
$265$	−23.9018			−1.46828
$266$	−0.0985738	+	7.85287i	−0.00604394	+	0.481491i
$267$			17.9739i			1.09999i
$268$	8.49928			0.519176
$269$	−1.49797	+	1.49797i	−0.0913331	+	0.0913331i	−0.751297	−	0.659964i	$-0.770571\pi$
$269$	−1.49797	+	1.49797i	−0.0913331	+	0.0913331i	0.659964	+	0.751297i	$0.270571\pi$
$270$			2.17708i			0.132493i
$271$	1.63211	−	1.63211i	0.0991433	−	0.0991433i	−0.655795	−	0.754939i	$-0.727667\pi$
$271$	1.63211	−	1.63211i	0.0991433	−	0.0991433i	0.754939	+	0.655795i	$0.227667\pi$
$272$	2.01832	+	2.01832i	0.122379	+	0.122379i
$273$	−5.78001	+	5.63670i	−0.349822	+	0.341148i
$274$			5.93030i			0.358263i
$275$	0.800676	−	0.800676i	0.0482826	−	0.0482826i
$276$	1.39112	−	1.39112i	0.0837357	−	0.0837357i
$277$	−16.2682			−0.977459			−0.488730	−	0.872435i	$-0.662540\pi$
$277$	−16.2682			−0.977459			−0.488730	+	0.872435i	$0.662540\pi$
$278$	−8.76328	−	8.76328i	−0.525587	−	0.525587i
$279$	−1.89326	+	1.89326i	−0.113347	+	0.113347i
$280$	−4.12375	+	4.02150i	−0.246441	+	0.240331i
$281$	−1.91319			−0.114132			−0.0570658	−	0.998370i	$-0.518174\pi$
$281$	−1.91319			−0.114132			−0.0570658	+	0.998370i	$0.518174\pi$
$282$	8.60874	−	8.60874i	0.512643	−	0.512643i
$283$	6.17983			0.367353			0.183676	−	0.982987i	$-0.441200\pi$
$283$	6.17983			0.367353			0.183676	+	0.982987i	$0.441200\pi$
$284$	−13.7545			−0.816180
$285$			6.46232i			0.382795i
$286$			13.2735i			0.784879i
$287$	8.82578	+	9.05017i	0.520969	+	0.534214i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$		−	8.85275i		−	0.520750i
$290$	11.5618	+	1.94334i	0.678930	+	0.114117i
$291$	10.2541			0.601108
$292$	−6.46121	−	6.46121i	−0.378114	−	0.378114i
$293$	14.1737	+	14.1737i	0.828037	+	0.828037i	0.987245	−	0.159208i	$-0.0508940\pi$
$293$	14.1737	+	14.1737i	0.828037	+	0.828037i	−0.159208	+	0.987245i	$0.550894\pi$
$294$	−6.99779	−	0.175708i	−0.408120	−	0.0102475i
$295$			24.3281i			1.41643i
$296$		−	8.47756i		−	0.492748i
$297$			4.34986i			0.252404i
$298$	0.325855	+	0.325855i	0.0188763	+	0.0188763i
$299$	6.00331			0.347181
$300$	0.184070	−	0.184070i	0.0106273	−	0.0106273i
$301$	−5.40688	−	5.54435i	−0.311648	−	0.319571i
$302$	−14.6422	−	14.6422i	−0.842562	−	0.842562i
$303$		−	6.68866i		−	0.384253i
$304$	2.09893	+	2.09893i	0.120382	+	0.120382i
$305$	6.72038	+	6.72038i	0.384808	+	0.384808i
$306$			2.85434i			0.163172i
$307$	−14.8118	−	14.8118i	−0.845355	−	0.845355i	0.144194	−	0.989549i	$-0.453941\pi$
$307$	−14.8118	−	14.8118i	−0.845355	−	0.845355i	−0.989549	+	0.144194i	$0.953941\pi$
$308$	−8.23934	+	8.03505i	−0.469480	+	0.457840i
$309$	1.86672	−	1.86672i	0.106194	−	0.106194i
$310$	−5.82908			−0.331070
$311$	−13.0106	−	13.0106i	−0.737764	−	0.737764i	0.234381	−	0.972145i	$-0.424694\pi$
$311$	−13.0106	−	13.0106i	−0.737764	−	0.737764i	−0.972145	+	0.234381i	$0.924694\pi$
$312$			3.05148i			0.172756i
$313$			5.84368i			0.330305i	0.986268	+	0.165152i	$0.0528116\pi$
$313$			5.84368i			0.330305i	−0.986268	+	0.165152i	$0.947188\pi$
$314$		−	12.2479i		−	0.691191i
$315$	−5.75956	−	0.0722973i	−0.324515	−	0.00407349i
$316$	10.6504	+	10.6504i	0.599131	+	0.599131i
$317$	9.59491	+	9.59491i	0.538904	+	0.538904i	0.923207	−	0.384303i	$-0.125558\pi$
$317$	9.59491	+	9.59491i	0.538904	+	0.538904i	−0.384303	+	0.923207i	$0.625558\pi$
$318$	−10.9788			−0.615662
$319$	23.1006	+	3.88284i	1.29339	+	0.217397i
$320$			2.17708i			0.121703i
$321$	3.62146	+	3.62146i	0.202130	+	0.202130i
$322$	3.63407	+	3.72647i	0.202519	+	0.207668i
$323$			8.47265i			0.471431i
$324$			1.00000i			0.0555556i
$325$	0.794342			0.0440622
$326$	8.06426			0.446638
$327$	5.05480	−	5.05480i	0.279531	−	0.279531i
$328$	4.77792			0.263817
$329$	22.4889	+	23.0607i	1.23985	+	1.27138i
$330$	−6.69630	+	6.69630i	−0.368619	+	0.368619i
$331$	22.4637	+	22.4637i	1.23472	+	1.23472i	0.962132	+	0.272584i	$0.0878781\pi$
$331$	22.4637	+	22.4637i	1.23472	+	1.23472i	0.272584	+	0.962132i	$0.412122\pi$
$332$	−7.41216			−0.406795
$333$	5.99454	−	5.99454i	0.328499	−	0.328499i
$334$	13.0770	−	13.0770i	0.715541	−	0.715541i
$335$			18.5036i			1.01096i
$336$	−1.89416	+	1.84720i	−0.103335	+	0.100773i
$337$	−0.981989	−	0.981989i	−0.0534923	−	0.0534923i	0.679855	−	0.733347i	$-0.262043\pi$
$337$	−0.981989	−	0.981989i	−0.0534923	−	0.0534923i	−0.733347	+	0.679855i	$0.762043\pi$
$338$	2.60813	−	2.60813i	0.141864	−	0.141864i
$339$		−	9.63949i		−	0.523545i
$340$	−4.39405	+	4.39405i	−0.238301	+	0.238301i
$341$	−11.6466			−0.630700
$342$			2.96834i			0.160509i
$343$	0.697229	−	18.5071i	0.0376468	−	0.999291i
$344$	−2.92707			−0.157817
$345$	3.02859	+	3.02859i	0.163054	+	0.163054i
$346$	−12.9450	+	12.9450i	−0.695928	+	0.695928i
$347$			2.91380i			0.156421i	0.996937	+	0.0782104i	$0.0249206\pi$
$347$			2.91380i			0.156421i	−0.996937	+	0.0782104i	$0.975079\pi$
$348$	5.31067	+	0.892636i	0.284682	+	0.0478503i
$349$			2.07742i			0.111202i	0.998453	+	0.0556010i	$0.0177075\pi$
$349$			2.07742i			0.111202i	−0.998453	+	0.0556010i	$0.982293\pi$
$350$	0.480851	+	0.493076i	0.0257026	+	0.0263560i
$351$	−2.15772	+	2.15772i	−0.115171	+	0.115171i
$352$			4.34986i			0.231848i
$353$	−9.78791			−0.520958			−0.260479	−	0.965480i	$-0.583880\pi$
$353$	−9.78791			−0.520958			−0.260479	+	0.965480i	$0.583880\pi$
$354$			11.1746i			0.593924i
$355$		−	29.9447i		−	1.58930i
$356$	−12.7095	+	12.7095i	−0.673602	+	0.673602i
$357$	−7.55128	−	0.0947880i	−0.399656	−	0.00501671i
$358$	−6.26751	−	6.26751i	−0.331248	−	0.331248i
$359$	−21.9678	+	21.9678i	−1.15942	+	1.15942i	−0.174814	+	0.984602i	$0.555932\pi$
$359$	−21.9678	+	21.9678i	−1.15942	+	1.15942i	−0.984602	+	0.174814i	$0.944068\pi$
$360$	−1.53943	+	1.53943i	−0.0811351	+	0.0811351i
$361$		−	10.1890i		−	0.536261i
$362$	−14.2037	−	14.2037i	−0.746527	−	0.746527i
$363$	−5.60117	+	5.60117i	−0.293985	+	0.293985i
$364$	−8.07283	−	0.101335i	−0.423131	−	0.00531138i
$365$	14.0666	−	14.0666i	0.736278	−	0.736278i
$366$	3.08688	+	3.08688i	0.161354	+	0.161354i
$367$	−20.6384	−	20.6384i	−1.07732	−	1.07732i	−0.996749	−	0.0805659i	$-0.974327\pi$
$367$	−20.6384	−	20.6384i	−1.07732	−	1.07732i	−0.0805659	−	0.996749i	$-0.525673\pi$
$368$	1.96734			0.102555
$369$	3.37850	+	3.37850i	0.175878	+	0.175878i
$370$	18.4563			0.959499
$371$	0.364589	−	29.0450i	0.0189285	−	1.50794i
$372$	−2.67747			−0.138821
$373$	26.7165			1.38333			0.691664	−	0.722219i	$-0.256878\pi$
$373$	26.7165			1.38333			0.691664	+	0.722219i	$0.256878\pi$
$374$	−8.77942	+	8.77942i	−0.453973	+	0.453973i
$375$	8.09788	+	8.09788i	0.418173	+	0.418173i
$376$	12.1746			0.627857
$377$	9.53290	+	13.3850i	0.490969	+	0.689364i
$378$	−2.64554	−	0.0332084i	−0.136072	−	0.00170805i
$379$	−14.3234	+	14.3234i	−0.735745	+	0.735745i	−0.971751	−	0.236007i	$-0.924161\pi$
$379$	−14.3234	+	14.3234i	−0.735745	+	0.735745i	0.236007	+	0.971751i	$0.424161\pi$
$380$	−4.56955	+	4.56955i	−0.234413	+	0.234413i
$381$	−7.04087			−0.360715
$382$		−	9.03940i		−	0.462496i
$383$	4.46904			0.228357			0.114179	−	0.993460i	$-0.463576\pi$
$383$	4.46904			0.228357			0.114179	+	0.993460i	$0.463576\pi$
$384$			1.00000i			0.0510310i
$385$	−17.4930	−	17.9377i	−0.891524	−	0.914191i
$386$			0.318606i			0.0162166i
$387$	−2.06975	−	2.06975i	−0.105211	−	0.105211i
$388$	7.25077	+	7.25077i	0.368102	+	0.368102i
$389$	−15.4546	−	15.4546i	−0.783578	−	0.783578i	0.196855	−	0.980433i	$-0.436927\pi$
$389$	−15.4546	−	15.4546i	−0.783578	−	0.783578i	−0.980433	+	0.196855i	$0.936927\pi$
$390$	−6.64333			−0.336398
$391$	3.97073	+	3.97073i	0.200809	+	0.200809i
$392$	−4.82394	−	5.07243i	−0.243646	−	0.256197i
$393$	−8.31146			−0.419258
$394$	14.6058	−	14.6058i	0.735830	−	0.735830i
$395$	−23.1868	+	23.1868i	−1.16665	+	1.16665i
$396$	−3.07581	+	3.07581i	−0.154565	+	0.154565i
$397$		−	9.25690i		−	0.464591i	−0.972645	−	0.232295i	$-0.925376\pi$
$397$		−	9.25690i		−	0.464591i	0.972645	−	0.232295i	$-0.0746236\pi$
$398$	−5.21343	−	5.21343i	−0.261326	−	0.261326i
$399$	−7.85287	−	0.0985738i	−0.393135	−	0.00493486i
$400$	0.260314			0.0130157
$401$	29.0745			1.45191			0.725956	−	0.687741i	$-0.241397\pi$
$401$	29.0745			1.45191			0.725956	+	0.687741i	$0.241397\pi$
$402$			8.49928i			0.423906i
$403$	−5.77725	−	5.77725i	−0.287785	−	0.287785i
$404$	4.72960	−	4.72960i	0.235306	−	0.235306i
$405$	−2.17708			−0.108180
$406$	−2.53786	+	14.0200i	−0.125952	+	0.695799i
$407$	36.8762			1.82788
$408$	−2.01832	+	2.01832i	−0.0999219	+	0.0999219i
$409$	−0.236472	−	0.236472i	−0.0116928	−	0.0116928i	0.701236	−	0.712929i	$-0.252632\pi$
$409$	−0.236472	−	0.236472i	−0.0116928	−	0.0116928i	−0.712929	+	0.701236i	$0.752632\pi$
$410$			10.4019i			0.513715i
$411$	−5.93030			−0.292520
$412$	2.63995			0.130061
$413$	−29.5629	−	0.371091i	−1.45470	−	0.0182602i
$414$	1.39112	+	1.39112i	0.0683699	+	0.0683699i
$415$		−	16.1369i		−	0.792128i
$416$	−2.15772	+	2.15772i	−0.105791	+	0.105791i
$417$	8.76328	−	8.76328i	0.429140	−	0.429140i
$418$	−9.13006	+	9.13006i	−0.446566	+	0.446566i
$419$	35.3605			1.72747			0.863737	−	0.503943i	$-0.168118\pi$
$419$	35.3605			1.72747			0.863737	+	0.503943i	$0.168118\pi$
$420$	−4.02150	−	4.12375i	−0.196229	−	0.201218i
$421$	14.1791	+	14.1791i	0.691048	+	0.691048i	0.962463	−	0.271414i	$-0.0874914\pi$
$421$	14.1791	+	14.1791i	0.691048	+	0.691048i	−0.271414	+	0.962463i	$0.587491\pi$
$422$	−18.5014			−0.900632
$423$	8.60874	+	8.60874i	0.418571	+	0.418571i
$424$	−7.76320	−	7.76320i	−0.377015	−	0.377015i
$425$	0.525397	+	0.525397i	0.0254855	+	0.0254855i
$426$		−	13.7545i		−	0.666408i
$427$	−8.26897	+	8.06395i	−0.400164	+	0.390242i
$428$			5.12152i			0.247558i
$429$	−13.2735			−0.640851
$430$		−	6.37247i		−	0.307308i
$431$	25.4595			1.22634			0.613172	−	0.789950i	$-0.289893\pi$
$431$	25.4595			1.22634			0.613172	+	0.789950i	$0.289893\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	16.9332	−	16.9332i	0.813756	−	0.813756i	−0.171438	−	0.985195i	$-0.554841\pi$
$433$	16.9332	−	16.9332i	0.813756	−	0.813756i	0.985195	+	0.171438i	$0.0548415\pi$
$434$	0.0889146	−	7.08337i	0.00426804	−	0.340013i
$435$	−1.94334	+	11.5618i	−0.0931761	+	0.554344i
$436$	7.14857			0.342354
$437$	4.12932	+	4.12932i	0.197532	+	0.197532i
$438$	6.46121	−	6.46121i	0.308728	−	0.308728i
$439$	−4.61793			−0.220402			−0.110201	−	0.993909i	$-0.535149\pi$
$439$	−4.61793			−0.220402			−0.110201	+	0.993909i	$0.535149\pi$
$440$	−9.47000			−0.451464
$441$	0.175708	−	6.99779i	0.00836706	−	0.333228i
$442$	−8.70997			−0.414291
$443$	−28.5522	−	28.5522i	−1.35656	−	1.35656i	−0.878124	−	0.478433i	$-0.841205\pi$
$443$	−28.5522	−	28.5522i	−1.35656	−	1.35656i	−0.478433	−	0.878124i	$-0.658795\pi$
$444$	8.47756			0.402327
$445$	−27.6696	−	27.6696i	−1.31167	−	1.31167i
$446$	5.53135	+	5.53135i	0.261917	+	0.261917i
$447$	−0.325855	+	0.325855i	−0.0154124	+	0.0154124i
$448$	−2.64554	−	0.0332084i	−0.124990	−	0.00156895i
$449$	17.6925	−	17.6925i	0.834961	−	0.834961i	−0.153230	−	0.988191i	$-0.548967\pi$
$449$	17.6925	−	17.6925i	0.834961	−	0.834961i	0.988191	+	0.153230i	$0.0489675\pi$
$450$	0.184070	+	0.184070i	0.00867712	+	0.00867712i
$451$			20.7833i			0.978647i
$452$	6.81615	−	6.81615i	0.320605	−	0.320605i
$453$	14.6422	−	14.6422i	0.687949	−	0.687949i
$454$	−16.5202	−	16.5202i	−0.775333	−	0.775333i
$455$	0.220614	−	17.5752i	0.0103425	−	0.823939i
$456$	−2.09893	+	2.09893i	−0.0982916	+	0.0982916i
$457$		−	32.0817i		−	1.50072i	−0.661031	−	0.750358i	$-0.729881\pi$
$457$		−	32.0817i		−	1.50072i	0.661031	−	0.750358i	$-0.270119\pi$
$458$			6.62110i			0.309384i
$459$	−2.85434			−0.133229
$460$			4.28307i			0.199699i
$461$	22.2104	−	22.2104i	1.03444	−	1.03444i	0.0350568	−	0.999385i	$-0.488839\pi$
$461$	22.2104	−	22.2104i	1.03444	−	1.03444i	0.999385	−	0.0350568i	$-0.0111612\pi$
$462$	−8.03505	−	8.23934i	−0.373825	−	0.383329i
$463$		−	19.9358i		−	0.926494i	−0.886229	−	0.463247i	$-0.846684\pi$
$463$		−	19.9358i		−	0.926494i	0.886229	−	0.463247i	$-0.153316\pi$
$464$	3.12402	+	4.38640i	0.145029	+	0.203633i
$465$		−	5.82908i		−	0.270317i
$466$	0.376957	−	0.376957i	0.0174622	−	0.0174622i
$467$	12.1462	+	12.1462i	0.562058	+	0.562058i	0.929892	−	0.367834i	$-0.119900\pi$
$467$	12.1462	+	12.1462i	0.562058	+	0.562058i	−0.367834	+	0.929892i	$0.619900\pi$
$468$	−3.05148			−0.141055
$469$	−22.4852	−	0.282247i	−1.03827	−	0.0130330i
$470$			26.5051i			1.22259i
$471$	12.2479			0.564355
$472$	−7.90165	+	7.90165i	−0.363703	+	0.363703i
$473$		−	12.7323i		−	0.585433i
$474$	−10.6504	+	10.6504i	−0.489188	+	0.489188i
$475$	0.546381	+	0.546381i	0.0250697	+	0.0250697i
$476$	−5.27253	−	5.40659i	−0.241666	−	0.247810i
$477$		−	10.9788i		−	0.502686i
$478$	−16.1796	+	16.1796i	−0.740036	+	0.740036i
$479$	−7.66087	+	7.66087i	−0.350034	+	0.350034i	−0.860122	−	0.510088i	$-0.829613\pi$
$479$	−7.66087	+	7.66087i	−0.350034	+	0.350034i	0.510088	+	0.860122i	$0.329613\pi$
$480$	−2.17708			−0.0993697
$481$	18.2922	+	18.2922i	0.834054	+	0.834054i
$482$	4.96113	−	4.96113i	0.225973	−	0.225973i
$483$	−3.72647	+	3.63407i	−0.169560	+	0.165356i
$484$	−7.92125			−0.360057
$485$	−15.7855	+	15.7855i	−0.716783	+	0.716783i
$486$	−1.00000			−0.0453609
$487$	−42.8321			−1.94091			−0.970454	−	0.241288i	$-0.922430\pi$
$487$	−42.8321			−1.94091			−0.970454	+	0.241288i	$0.922430\pi$
$488$			4.36550i			0.197617i
$489$			8.06426i			0.364679i
$490$	11.0431	−	10.5021i	0.498876	−	0.474437i
$491$	4.27185	+	4.27185i	0.192786	+	0.192786i	0.796899	−	0.604113i	$-0.206472\pi$
$491$	4.27185	+	4.27185i	0.192786	+	0.192786i	−0.604113	+	0.796899i	$0.706472\pi$
$492$			4.77792i			0.215405i
$493$	−2.54789	+	15.1585i	−0.114751	+	0.682702i
$494$	−9.05784			−0.407532
$495$	−6.69630	−	6.69630i	−0.300976	−	0.300976i
$496$	−1.89326	−	1.89326i	−0.0850099	−	0.0850099i
$497$	36.3881	+	0.456765i	1.63223	+	0.0204887i
$498$		−	7.41216i		−	0.332147i
$499$			10.2732i			0.459892i	0.973203	+	0.229946i	$0.0738550\pi$
$499$			10.2732i			0.459892i	−0.973203	+	0.229946i	$0.926145\pi$
$500$			11.4521i			0.512155i
$501$	13.0770	+	13.0770i	0.584237	+	0.584237i
$502$	7.88334			0.351851
$503$	9.86594	−	9.86594i	0.439900	−	0.439900i	−0.452078	−	0.891978i	$-0.649317\pi$
$503$	9.86594	−	9.86594i	0.439900	−	0.439900i	0.891978	+	0.452078i	$0.149317\pi$
$504$	−1.84720	−	1.89416i	−0.0822808	−	0.0843727i
$505$	10.2967	+	10.2967i	0.458198	+	0.458198i
$506$			8.55766i			0.380434i
$507$	2.60813	+	2.60813i	0.115831	+	0.115831i
$508$	−4.97865	−	4.97865i	−0.220892	−	0.220892i
$509$			14.1326i			0.626417i	0.949684	+	0.313209i	$0.101404\pi$
$509$			14.1326i			0.626417i	−0.949684	+	0.313209i	$0.898596\pi$
$510$	−4.39405	−	4.39405i	−0.194572	−	0.194572i
$511$	16.8788	+	17.3080i	0.746676	+	0.765659i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−2.96834			−0.131055
$514$	−0.169168	−	0.169168i	−0.00746167	−	0.00746167i
$515$			5.74738i			0.253260i
$516$		−	2.92707i		−	0.128857i
$517$			52.9578i			2.32908i
$518$	−0.281526	+	22.4277i	−0.0123695	+	0.985418i
$519$	−12.9450	−	12.9450i	−0.568223	−	0.568223i
$520$	−4.69754	−	4.69754i	−0.206001	−	0.206001i
$521$	16.4017			0.718569			0.359285	−	0.933228i	$-0.383021\pi$
$521$	16.4017			0.718569			0.359285	+	0.933228i	$0.383021\pi$
$522$	−0.892636	+	5.31067i	−0.0390696	+	0.232442i
$523$		−	31.8200i		−	1.39139i	−0.718336	−	0.695696i	$-0.755096\pi$
$523$		−	31.8200i		−	1.39139i	0.718336	−	0.695696i	$-0.244904\pi$
$524$	−5.87709	−	5.87709i	−0.256742	−	0.256742i
$525$	−0.493076	+	0.480851i	−0.0215196	+	0.0209861i
$526$			7.58758i			0.330834i
$527$		−	7.64242i		−	0.332909i
$528$	−4.34986			−0.189303
$529$	−19.1296			−0.831720
$530$	16.9011	−	16.9011i	0.734138	−	0.734138i
$531$	−11.1746			−0.484937
$532$	−5.48312	−	5.62252i	−0.237723	−	0.243767i
$533$	−10.3094	+	10.3094i	−0.446552	+	0.446552i
$534$	−12.7095	−	12.7095i	−0.549994	−	0.549994i
$535$	−11.1500			−0.482055
$536$	−6.00990	+	6.00990i	−0.259588	+	0.259588i
$537$	6.26751	−	6.26751i	0.270463	−	0.270463i
$538$		−	2.11846i		−	0.0913331i
$539$	22.0644	−	20.9835i	0.950379	−	0.903822i
$540$	−1.53943	−	1.53943i	−0.0662465	−	0.0662465i
$541$	16.5259	−	16.5259i	0.710505	−	0.710505i	−0.256136	−	0.966641i	$-0.582450\pi$
$541$	16.5259	−	16.5259i	0.710505	−	0.710505i	0.966641	+	0.256136i	$0.0824495\pi$
$542$			2.30815i			0.0991433i
$543$	14.2037	−	14.2037i	0.609537	−	0.609537i
$544$	−2.85434			−0.122379
$545$			15.5630i			0.666647i
$546$	0.101335	−	8.07283i	0.00433673	−	0.345485i
$547$	−7.07426			−0.302474			−0.151237	−	0.988498i	$-0.548326\pi$
$547$	−7.07426			−0.302474			−0.151237	+	0.988498i	$0.548326\pi$
$548$	−4.19336	−	4.19336i	−0.179131	−	0.179131i
$549$	−3.08688	+	3.08688i	−0.131745	+	0.131745i
$550$			1.13233i			0.0482826i
$551$	−2.64965	+	15.7639i	−0.112879	+	0.671564i
$552$			1.96734i			0.0837357i
$553$	−27.8224	−	28.5297i	−1.18313	−	1.21321i
$554$	11.5033	−	11.5033i	0.488730	−	0.488730i
$555$			18.4563i			0.783428i
$556$	12.3931			0.525587
$557$		−	31.9269i		−	1.35279i	−0.736541	−	0.676393i	$-0.763542\pi$
$557$		−	31.9269i		−	1.35279i	0.736541	−	0.676393i	$-0.236458\pi$
$558$		−	2.67747i		−	0.113347i
$559$	6.31581	−	6.31581i	0.267130	−	0.267130i
$560$	0.0722973	−	5.75956i	0.00305512	−	0.243386i
$561$	−8.77942	−	8.77942i	−0.370667	−	0.370667i
$562$	1.35283	−	1.35283i	0.0570658	−	0.0570658i
$563$	−25.1072	+	25.1072i	−1.05814	+	1.05814i	−0.0599417	+	0.998202i	$0.519091\pi$
$563$	−25.1072	+	25.1072i	−1.05814	+	1.05814i	−0.998202	+	0.0599417i	$0.980909\pi$
$564$			12.1746i			0.512643i
$565$	14.8393	+	14.8393i	0.624294	+	0.624294i
$566$	−4.36980	+	4.36980i	−0.183676	+	0.183676i
$567$	0.0332084	−	2.64554i	0.00139462	−	0.111102i
$568$	9.72590	−	9.72590i	0.408090	−	0.408090i
$569$	−14.1226	−	14.1226i	−0.592049	−	0.592049i	0.346136	−	0.938184i	$-0.387494\pi$
$569$	−14.1226	−	14.1226i	−0.592049	−	0.592049i	−0.938184	+	0.346136i	$0.887494\pi$
$570$	−4.56955	−	4.56955i	−0.191397	−	0.191397i
$571$	−27.0344			−1.13135			−0.565676	−	0.824627i	$-0.691385\pi$
$571$	−27.0344			−1.13135			−0.565676	+	0.824627i	$0.691385\pi$
$572$	−9.38579	−	9.38579i	−0.392440	−	0.392440i
$573$	9.03940			0.377626
$574$	−12.6402	−	0.158667i	−0.527592	−	0.00662263i
$575$	0.512126			0.0213571
$576$	−1.00000			−0.0416667
$577$	−8.06421	+	8.06421i	−0.335717	+	0.335717i	−0.854753	−	0.519035i	$-0.826291\pi$
$577$	−8.06421	+	8.06421i	−0.335717	+	0.335717i	0.519035	+	0.854753i	$0.326291\pi$
$578$	6.25984	+	6.25984i	0.260375	+	0.260375i
$579$	−0.318606			−0.0132408
$580$	−9.54955	+	6.80125i	−0.396523	+	0.282407i
$581$	19.6092	+	0.246146i	0.813526	+	0.0102118i
$582$	−7.25077	+	7.25077i	−0.300554	+	0.300554i
$583$	33.7688	−	33.7688i	1.39856	−	1.39856i
$584$	9.13753			0.378114
$585$		−	6.64333i		−	0.274668i
$586$	−20.0447			−0.828037
$587$			19.3031i			0.796723i	0.917229	+	0.398361i	$0.130421\pi$
$587$			19.3031i			0.796723i	−0.917229	+	0.398361i	$0.869579\pi$
$588$	5.07243	−	4.82394i	0.209184	−	0.198936i
$589$		−	7.94766i		−	0.327478i
$590$	−17.2025	−	17.2025i	−0.708217	−	0.708217i
$591$	14.6058	+	14.6058i	0.600803	+	0.600803i
$592$	5.99454	+	5.99454i	0.246374	+	0.246374i
$593$	4.83702			0.198633			0.0993163	−	0.995056i	$-0.468334\pi$
$593$	4.83702			0.198633			0.0993163	+	0.995056i	$0.468334\pi$
$594$	−3.07581	−	3.07581i	−0.126202	−	0.126202i
$595$	11.7706	−	11.4787i	0.482547	−	0.470582i
$596$	−0.460829			−0.0188763
$597$	5.21343	−	5.21343i	0.213371	−	0.213371i
$598$	−4.24498	+	4.24498i	−0.173590	+	0.173590i
$599$	−19.8884	+	19.8884i	−0.812617	+	0.812617i	−0.985025	−	0.172409i	$-0.944845\pi$
$599$	−19.8884	+	19.8884i	−0.812617	+	0.812617i	0.172409	+	0.985025i	$0.444845\pi$
$600$			0.260314i			0.0106273i
$601$	2.07799	+	2.07799i	0.0847630	+	0.0847630i	0.748217	−	0.663454i	$-0.230910\pi$
$601$	2.07799	+	2.07799i	0.0847630	+	0.0847630i	−0.663454	+	0.748217i	$0.730910\pi$
$602$	7.74369	+	0.0972032i	0.315609	+	0.00396171i
$603$	−8.49928			−0.346117
$604$	20.7071			0.842562
$605$		−	17.2452i		−	0.701118i
$606$	4.72960	+	4.72960i	0.192127	+	0.192127i
$607$	9.83290	−	9.83290i	0.399105	−	0.399105i	−0.478812	−	0.877917i	$-0.658933\pi$
$607$	9.83290	−	9.83290i	0.399105	−	0.399105i	0.877917	+	0.478812i	$0.158933\pi$
$608$	−2.96834			−0.120382
$609$	−14.0200	−	2.53786i	−0.568117	−	0.102839i
$610$	−9.50405			−0.384808
$611$	−26.2694	+	26.2694i	−1.06275	+	1.06275i
$612$	−2.01832	−	2.01832i	−0.0815859	−	0.0815859i
$613$			22.5792i			0.911967i	0.889988	+	0.455984i	$0.150712\pi$
$613$			22.5792i			0.911967i	−0.889988	+	0.455984i	$0.849288\pi$
$614$	20.9471			0.845355
$615$	−10.4019			−0.419446
$616$	0.144452	−	11.5077i	0.00582012	−	0.463660i
$617$	−26.6454	−	26.6454i	−1.07270	−	1.07270i	−0.997141	−	0.0755633i	$-0.975925\pi$
$617$	−26.6454	−	26.6454i	−1.07270	−	1.07270i	−0.0755633	−	0.997141i	$-0.524075\pi$
$618$			2.63995i			0.106194i
$619$	29.9664	−	29.9664i	1.20445	−	1.20445i	0.231655	−	0.972798i	$-0.425586\pi$
$619$	29.9664	−	29.9664i	1.20445	−	1.20445i	0.972798	−	0.231655i	$-0.0744141\pi$
$620$	4.12178	−	4.12178i	0.165535	−	0.165535i
$621$	−1.39112	+	1.39112i	−0.0558238	+	0.0558238i
$622$	18.3998			0.737764
$623$	34.0456	−	33.2014i	1.36401	−	1.33019i
$624$	−2.15772	−	2.15772i	−0.0863781	−	0.0863781i
$625$	−23.6307			−0.945227
$626$	−4.13211	−	4.13211i	−0.165152	−	0.165152i
$627$	−9.13006	−	9.13006i	−0.364620	−	0.364620i
$628$	8.66060	+	8.66060i	0.345596	+	0.345596i
$629$			24.1978i			0.964831i
$630$	4.12375	−	4.02150i	0.164294	−	0.160221i
$631$			38.6813i			1.53988i	0.638117	+	0.769940i	$0.279714\pi$
$631$			38.6813i			1.53988i	−0.638117	+	0.769940i	$0.720286\pi$
$632$	−15.0619			−0.599131
$633$		−	18.5014i		−	0.735363i
$634$	−13.5692			−0.538904
$635$	10.8389	−	10.8389i	0.430129	−	0.430129i
$636$	7.76320	−	7.76320i	0.307831	−	0.307831i
$637$	21.3537	+	0.536171i	0.846062	+	0.0212439i
$638$	−19.0802	+	13.5890i	−0.755393	+	0.537995i
$639$	13.7545			0.544120
$640$	−1.53943	−	1.53943i	−0.0608513	−	0.0608513i
$641$	9.68421	−	9.68421i	0.382503	−	0.382503i	−0.489500	−	0.872003i	$-0.662821\pi$
$641$	9.68421	−	9.68421i	0.382503	−	0.382503i	0.872003	+	0.489500i	$0.162821\pi$
$642$	−5.12152			−0.202130
$643$	−12.0757			−0.476221			−0.238111	−	0.971238i	$-0.576528\pi$
$643$	−12.0757			−0.476221			−0.238111	+	0.971238i	$0.576528\pi$
$644$	−5.20469	−	0.0653322i	−0.205094	−	0.00257445i
$645$	6.37247			0.250916
$646$	−5.99107	−	5.99107i	−0.235716	−	0.235716i
$647$	−43.9992			−1.72979			−0.864893	−	0.501956i	$-0.832614\pi$
$647$	−43.9992			−1.72979			−0.864893	+	0.501956i	$0.832614\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	−34.3710	−	34.3710i	−1.34918	−	1.34918i
$650$	−0.561685	+	0.561685i	−0.0220311	+	0.0220311i
$651$	7.08337	+	0.0889146i	0.277619	+	0.00348484i
$652$	−5.70229	+	5.70229i	−0.223319	+	0.223319i
$653$	−28.1024	−	28.1024i	−1.09973	−	1.09973i	−0.994442	−	0.105290i	$-0.966423\pi$
$653$	−28.1024	−	28.1024i	−1.09973	−	1.09973i	−0.105290	−	0.994442i	$-0.533577\pi$
$654$			7.14857i			0.279531i
$655$	12.7949	−	12.7949i	0.499938	−	0.499938i
$656$	−3.37850	+	3.37850i	−0.131908	+	0.131908i
$657$	6.46121	+	6.46121i	0.252076	+	0.252076i
$658$	−32.2084	−	0.404299i	−1.25562	−	0.0157612i
$659$	−7.04998	+	7.04998i	−0.274628	+	0.274628i	−0.830960	−	0.556332i	$-0.812208\pi$
$659$	−7.04998	+	7.04998i	−0.274628	+	0.274628i	0.556332	+	0.830960i	$0.312208\pi$
$660$		−	9.47000i		−	0.368619i
$661$		−	14.7475i		−	0.573611i	−0.957989	−	0.286805i	$-0.907407\pi$
$661$		−	14.7475i		−	0.573611i	0.957989	−	0.286805i	$-0.0925933\pi$
$662$	−31.7684			−1.23472
$663$		−	8.70997i		−	0.338267i
$664$	5.24119	−	5.24119i	0.203397	−	0.203397i
$665$	12.2407	−	11.9372i	0.474674	−	0.462905i
$666$			8.47756i			0.328499i
$667$	6.14602	+	8.62955i	0.237975	+	0.334138i
$668$			18.4936i			0.715541i
$669$	−5.53135	+	5.53135i	−0.213854	+	0.213854i
$670$	−13.0840	−	13.0840i	−0.505481	−	0.505481i
$671$	−18.9893			−0.733074
$672$	0.0332084	−	2.64554i	0.00128104	−	0.102054i
$673$			13.1967i			0.508694i	0.967113	+	0.254347i	$0.0818606\pi$
$673$			13.1967i			0.508694i	−0.967113	+	0.254347i	$0.918139\pi$
$674$	1.38874			0.0534923
$675$	−0.184070	+	0.184070i	−0.00708484	+	0.00708484i
$676$			3.68845i			0.141864i
$677$	−12.1125	+	12.1125i	−0.465520	+	0.465520i	−0.900460	−	0.434940i	$-0.856770\pi$
$677$	−12.1125	+	12.1125i	−0.465520	+	0.465520i	0.434940	+	0.900460i	$0.356770\pi$
$678$	6.81615	+	6.81615i	0.261772	+	0.261772i
$679$	−18.9414	−	19.4230i	−0.726905	−	0.745387i
$680$		−	6.21413i		−	0.238301i
$681$	16.5202	−	16.5202i	0.633057	−	0.633057i
$682$	8.23541	−	8.23541i	0.315350	−	0.315350i
$683$	−11.3921			−0.435905			−0.217952	−	0.975959i	$-0.569938\pi$
$683$	−11.3921			−0.435905			−0.217952	+	0.975959i	$0.569938\pi$
$684$	−2.09893	−	2.09893i	−0.0802547	−	0.0802547i
$685$	9.12929	−	9.12929i	0.348812	−	0.348812i
$686$	12.5935	+	13.5795i	0.480822	+	0.518469i
$687$	−6.62110			−0.252611
$688$	2.06975	−	2.06975i	0.0789085	−	0.0789085i
$689$	33.5017			1.27631
$690$	−4.28307			−0.163054
$691$		−	27.9978i		−	1.06509i	−0.846403	−	0.532543i	$-0.821236\pi$
$691$		−	27.9978i		−	1.06509i	0.846403	−	0.532543i	$-0.178764\pi$
$692$		−	18.3070i		−	0.695928i
$693$	8.23934	−	8.03505i	0.312987	−	0.305226i
$694$	−2.06037	−	2.06037i	−0.0782104	−	0.0782104i
$695$			26.9809i			1.02344i
$696$	−4.38640	+	3.12402i	−0.166266	+	0.118416i
$697$	−13.6378			−0.516569
$698$	−1.46896	−	1.46896i	−0.0556010	−	0.0556010i
$699$	0.376957	+	0.376957i	0.0142578	+	0.0142578i
$700$	−0.688671	−	0.00864459i	−0.0260293	−	0.000326735i
$701$		−	9.64404i		−	0.364250i	−0.983275	−	0.182125i	$-0.941702\pi$
$701$		−	9.64404i		−	0.364250i	0.983275	−	0.182125i	$-0.0582976\pi$
$702$		−	3.05148i		−	0.115171i
$703$			25.1643i			0.949089i
$704$	−3.07581	−	3.07581i	−0.115924	−	0.115924i
$705$	−26.5051			−0.998240
$706$	6.92109	−	6.92109i	0.260479	−	0.260479i
$707$	−12.6694	+	12.3553i	−0.476482	+	0.464668i
$708$	−7.90165	−	7.90165i	−0.296962	−	0.296962i
$709$			40.4212i			1.51805i	0.651061	+	0.759026i	$0.274324\pi$
$709$			40.4212i			1.51805i	−0.651061	+	0.759026i	$0.725676\pi$
$710$	21.1741	+	21.1741i	0.794649	+	0.794649i
$711$	−10.6504	−	10.6504i	−0.399420	−	0.399420i
$712$		−	17.9739i		−	0.673602i
$713$	−3.72469	−	3.72469i	−0.139491	−	0.139491i
$714$	5.40659	−	5.27253i	0.202336	−	0.197320i
$715$	20.4336	−	20.4336i	0.764175	−	0.764175i
$716$	8.86359			0.331248
$717$	−16.1796	−	16.1796i	−0.604237	−	0.604237i
$718$		−	31.0671i		−	1.15942i
$719$			18.2128i			0.679223i	0.940566	+	0.339612i	$0.110296\pi$
$719$			18.2128i			0.679223i	−0.940566	+	0.339612i	$0.889704\pi$
$720$		−	2.17708i		−	0.0811351i
$721$	−6.98409	−	0.0876683i	−0.260101	−	0.00326494i
$722$	7.20468	+	7.20468i	0.268130	+	0.268130i
$723$	4.96113	+	4.96113i	0.184506	+	0.184506i
$724$	20.0870			0.746527
$725$	0.813225	+	1.14184i	0.0302024	+	0.0424068i
$726$		−	7.92125i		−	0.293985i
$727$	−6.35224	−	6.35224i	−0.235592	−	0.235592i	0.579430	−	0.815022i	$-0.303275\pi$
$727$	−6.35224	−	6.35224i	−0.235592	−	0.235592i	−0.815022	+	0.579430i	$0.803275\pi$
$728$	5.78001	−	5.63670i	0.214221	−	0.208910i
$729$		−	1.00000i		−	0.0370370i
$730$			19.8931i			0.736278i
$731$	8.35485			0.309015
$732$	−4.36550			−0.161354
$733$	−29.8716	+	29.8716i	−1.10333	+	1.10333i	−0.109326	+	0.994006i	$0.534869\pi$
$733$	−29.8716	+	29.8716i	−1.10333	+	1.10333i	−0.994006	+	0.109326i	$0.965131\pi$
$734$	29.1871			1.07732
$735$	10.5021	+	11.0431i	0.387377	+	0.407331i
$736$	−1.39112	+	1.39112i	−0.0512774	+	0.0512774i
$737$	−26.1422	−	26.1422i	−0.962960	−	0.962960i
$738$	−4.77792			−0.175878
$739$	−1.09094	+	1.09094i	−0.0401309	+	0.0401309i	−0.726887	−	0.686757i	$-0.759034\pi$
$739$	−1.09094	+	1.09094i	−0.0401309	+	0.0401309i	0.686757	+	0.726887i	$0.259034\pi$
$740$	−13.0506	+	13.0506i	−0.479750	+	0.479750i
$741$		−	9.05784i		−	0.332748i
$742$	20.2801	+	20.7957i	0.744505	+	0.763434i
$743$	−6.63382	−	6.63382i	−0.243371	−	0.243371i	0.574872	−	0.818243i	$-0.305052\pi$
$743$	−6.63382	−	6.63382i	−0.243371	−	0.243371i	−0.818243	+	0.574872i	$0.805052\pi$
$744$	1.89326	−	1.89326i	0.0694103	−	0.0694103i
$745$		−	1.00326i		−	0.0367567i
$746$	−18.8914	+	18.8914i	−0.691664	+	0.691664i
$747$	7.41216			0.271197
$748$		−	12.4160i		−	0.453973i
$749$	0.170077	−	13.5492i	0.00621449	−	0.495077i
$750$	−11.4521			−0.418173
$751$	23.4865	+	23.4865i	0.857034	+	0.857034i	0.990988	−	0.133954i	$-0.0427674\pi$
$751$	23.4865	+	23.4865i	0.857034	+	0.857034i	−0.133954	+	0.990988i	$0.542767\pi$
$752$	−8.60874	+	8.60874i	−0.313929	+	0.313929i
$753$			7.88334i			0.287285i
$754$	−16.2054	−	2.72386i	−0.590166	−	0.0991972i
$755$			45.0811i			1.64067i
$756$	1.89416	−	1.84720i	0.0688900	−	0.0671820i
$757$	23.5159	−	23.5159i	0.854699	−	0.854699i	−0.136009	−	0.990708i	$-0.543427\pi$
$757$	23.5159	−	23.5159i	0.854699	−	0.854699i	0.990708	+	0.136009i	$0.0434275\pi$
$758$		−	20.2564i		−	0.735745i
$759$	−8.55766			−0.310623
$760$		−	6.46232i		−	0.234413i
$761$		−	44.2929i		−	1.60562i	−0.596237	−	0.802809i	$-0.703338\pi$
$761$		−	44.2929i		−	1.60562i	0.596237	−	0.802809i	$-0.296662\pi$
$762$	4.97865	−	4.97865i	0.180357	−	0.180357i
$763$	−18.9118	−	0.237392i	−0.684655	−	0.00859418i
$764$	6.39182	+	6.39182i	0.231248	+	0.231248i
$765$	4.39405	−	4.39405i	0.158867	−	0.158867i
$766$	−3.16009	+	3.16009i	−0.114179	+	0.114179i
$767$		−	34.0992i		−	1.23125i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−26.2261	+	26.2261i	−0.945737	+	0.945737i	−0.998602	−	0.0528650i	$-0.983165\pi$
$769$	−26.2261	+	26.2261i	−0.945737	+	0.945737i	0.0528650	+	0.998602i	$0.483165\pi$
$770$	25.0533	+	0.314483i	0.902857	+	0.0113332i
$771$	0.169168	−	0.169168i	0.00609243	−	0.00609243i
$772$	−0.225289	−	0.225289i	−0.00810831	−	0.00810831i
$773$	23.6859	+	23.6859i	0.851924	+	0.851924i	0.990370	−	0.138446i	$-0.0442107\pi$
$773$	23.6859	+	23.6859i	0.851924	+	0.851924i	−0.138446	+	0.990370i	$0.544211\pi$
$774$	2.92707			0.105211
$775$	−0.492841	−	0.492841i	−0.0177034	−	0.0177034i
$776$	−10.2541			−0.368102
$777$	−22.4277	−	0.281526i	−0.804591	−	0.0100997i
$778$	21.8561			0.783578
$779$	−14.1825			−0.508141
$780$	4.69754	−	4.69754i	0.168199	−	0.168199i
$781$	42.3063	+	42.3063i	1.51384	+	1.51384i
$782$	−5.61546			−0.200809
$783$	−5.31067	−	0.892636i	−0.189788	−	0.0319002i
$784$	6.99779	+	0.175708i	0.249921	+	0.00627530i
$785$	−18.8548	+	18.8548i	−0.672958	+	0.672958i
$786$	5.87709	−	5.87709i	0.209629	−	0.209629i
$787$	−55.0380			−1.96189			−0.980947	−	0.194276i	$-0.937764\pi$
$787$	−55.0380			−1.96189			−0.980947	+	0.194276i	$0.937764\pi$
$788$			20.6557i			0.735830i
$789$	−7.58758			−0.270125
$790$		−	32.7910i		−	1.16665i
$791$	−18.2588	+	17.8061i	−0.649207	+	0.633110i
$792$		−	4.34986i		−	0.154565i
$793$	−9.41955	−	9.41955i	−0.334498	−	0.334498i
$794$	6.54562	+	6.54562i	0.232295	+	0.232295i
$795$	16.9011	+	16.9011i	0.599421	+	0.599421i
$796$	7.37290			0.261326
$797$	−18.4450	−	18.4450i	−0.653355	−	0.653355i	0.300445	−	0.953799i	$-0.402865\pi$
$797$	−18.4450	−	18.4450i	−0.653355	−	0.653355i	−0.953799	+	0.300445i	$0.902865\pi$
$798$	5.62252	−	5.48312i	0.199035	−	0.194100i
$799$	−34.7504			−1.22938
$800$	−0.184070	+	0.184070i	−0.00650784	+	0.00650784i
$801$	12.7095	−	12.7095i	0.449068	−	0.449068i
$802$	−20.5588	+	20.5588i	−0.725956	+	0.725956i
$803$			39.7469i			1.40264i
$804$	−6.00990	−	6.00990i	−0.211953	−	0.211953i
$805$	0.142234	−	11.3310i	0.00501308	−	0.399367i
$806$	8.17027			0.287785
$807$	2.11846			0.0745732
$808$			6.68866i			0.235306i
$809$	4.73975	+	4.73975i	0.166641	+	0.166641i	0.785501	−	0.618860i	$-0.212405\pi$
$809$	4.73975	+	4.73975i	0.166641	+	0.166641i	−0.618860	+	0.785501i	$0.712405\pi$
$810$	1.53943	−	1.53943i	0.0540900	−	0.0540900i
$811$	−5.13193			−0.180206			−0.0901032	−	0.995932i	$-0.528720\pi$
$811$	−5.13193			−0.180206			−0.0901032	+	0.995932i	$0.528720\pi$
$812$	−8.11907	−	11.7081i	−0.284923	−	0.410875i
$813$	−2.30815			−0.0809502
$814$	−26.0754	+	26.0754i	−0.913942	+	0.913942i
$815$	−12.4144	−	12.4144i	−0.434856	−	0.434856i
$816$		−	2.85434i		−	0.0999219i
$817$	8.68854			0.303974
$818$	0.334422			0.0116928
$819$	8.07283	+	0.101335i	0.282087	+	0.00354092i
$820$	−7.35528	−	7.35528i	−0.256857	−	0.256857i
$821$			33.1076i			1.15546i	0.816227	+	0.577731i	$0.196062\pi$
$821$			33.1076i			1.15546i	−0.816227	+	0.577731i	$0.803938\pi$
$822$	4.19336	−	4.19336i	0.146260	−	0.146260i
$823$	11.8227	−	11.8227i	0.412115	−	0.412115i	−0.470360	−	0.882475i	$-0.655876\pi$
$823$	11.8227	−	11.8227i	0.412115	−	0.412115i	0.882475	+	0.470360i	$0.155876\pi$
$824$	−1.86672	+	1.86672i	−0.0650304	+	0.0650304i
$825$	−1.13233			−0.0394226
$826$	21.1666	−	20.6418i	0.736479	−	0.718218i
$827$	18.9709	+	18.9709i	0.659683	+	0.659683i	0.955305	−	0.295622i	$-0.0955268\pi$
$827$	18.9709	+	18.9709i	0.659683	+	0.659683i	−0.295622	+	0.955305i	$0.595527\pi$
$828$	−1.96734			−0.0683699
$829$	−12.3324	−	12.3324i	−0.428323	−	0.428323i	0.459734	−	0.888057i	$-0.347945\pi$
$829$	−12.3324	−	12.3324i	−0.428323	−	0.428323i	−0.888057	+	0.459734i	$0.847945\pi$
$830$	11.4105	+	11.4105i	0.396064	+	0.396064i
$831$	11.5033	+	11.5033i	0.399046	+	0.399046i
$832$		−	3.05148i		−	0.105791i
$833$	13.7692	+	14.4784i	0.477074	+	0.501648i
$834$			12.3931i			0.429140i
$835$	−40.2622			−1.39333
$836$		−	12.9119i		−	0.446566i
$837$	2.67747			0.0925471
$838$	−25.0036	+	25.0036i	−0.863737	+	0.863737i
$839$	−3.24044	+	3.24044i	−0.111872	+	0.111872i	−0.760827	−	0.648955i	$-0.775206\pi$
$839$	−3.24044	+	3.24044i	−0.111872	+	0.111872i	0.648955	+	0.760827i	$0.275206\pi$
$840$	5.75956	+	0.0722973i	0.198724	+	0.00249450i
$841$	−9.48098	+	27.4064i	−0.326930	+	0.945048i
$842$	−20.0523			−0.691048
$843$	1.35283	+	1.35283i	0.0465940	+	0.0465940i
$844$	13.0824	−	13.0824i	0.450316	−	0.450316i
$845$	−8.03006			−0.276243
$846$	−12.1746			−0.418571
$847$	20.9560	+	0.263052i	0.720057	+	0.00903857i
$848$	10.9788			0.377015
$849$	−4.36980	−	4.36980i	−0.149971	−	0.149971i
$850$	−0.743023			−0.0254855
$851$	11.7933	+	11.7933i	0.404270	+	0.404270i
$852$	9.72590	+	9.72590i	0.333204	+	0.333204i
$853$	15.8641	−	15.8641i	0.543178	−	0.543178i	−0.381281	−	0.924459i	$-0.624517\pi$
$853$	15.8641	−	15.8641i	0.543178	−	0.543178i	0.924459	+	0.381281i	$0.124517\pi$
$854$	0.144971	−	11.5491i	0.00496081	−	0.395203i
$855$	4.56955	−	4.56955i	0.156275	−	0.156275i
$856$	−3.62146	−	3.62146i	−0.123779	−	0.123779i
$857$			21.0071i			0.717589i	0.933417	+	0.358795i	$0.116812\pi$
$857$			21.0071i			0.717589i	−0.933417	+	0.358795i	$0.883188\pi$
$858$	9.38579	−	9.38579i	0.320426	−	0.320426i
$859$	−30.3830	+	30.3830i	−1.03665	+	1.03665i	−0.0373508	+	0.999302i	$0.511892\pi$
$859$	−30.3830	+	30.3830i	−1.03665	+	1.03665i	−0.999302	+	0.0373508i	$0.988108\pi$
$860$	4.50602	+	4.50602i	0.153654	+	0.153654i
$861$	0.158667	−	12.6402i	0.00540736	−	0.430777i
$862$	−18.0026	+	18.0026i	−0.613172	+	0.613172i
$863$			33.7270i			1.14808i	0.818827	+	0.574040i	$0.194625\pi$
$863$			33.7270i			1.14808i	−0.818827	+	0.574040i	$0.805375\pi$
$864$		−	1.00000i		−	0.0340207i
$865$	39.8558			1.35514
$866$			23.9471i			0.813756i
$867$	−6.25984	+	6.25984i	−0.212595	+	0.212595i
$868$	4.94583	+	5.07157i	0.167872	+	0.172140i
$869$		−	65.5172i		−	2.22252i
$870$	−6.80125	−	9.54955i	−0.230584	−	0.323760i
$871$		−	25.9354i		−	0.878788i
$872$	−5.05480	+	5.05480i	−0.171177	+	0.171177i
$873$	−7.25077	−	7.25077i	−0.245401	−	0.245401i
$874$	−5.83974			−0.197532
$875$	0.380307	−	30.2971i	0.0128567	−	1.02423i
$876$			9.13753i			0.308728i
$877$	38.1967			1.28981			0.644905	−	0.764263i	$-0.276897\pi$
$877$	38.1967			1.28981			0.644905	+	0.764263i	$0.276897\pi$
$878$	3.26537	−	3.26537i	0.110201	−	0.110201i
$879$		−	20.0447i		−	0.676089i
$880$	6.69630	−	6.69630i	0.225732	−	0.225732i
$881$	−10.4995	−	10.4995i	−0.353738	−	0.353738i	0.507760	−	0.861498i	$-0.330474\pi$
$881$	−10.4995	−	10.4995i	−0.353738	−	0.353738i	−0.861498	+	0.507760i	$0.830474\pi$
$882$	4.82394	+	5.07243i	0.162431	+	0.170798i
$883$		−	15.8354i		−	0.532904i	−0.963848	−	0.266452i	$-0.914149\pi$
$883$		−	15.8354i		−	0.532904i	0.963848	−	0.266452i	$-0.0858514\pi$
$884$	6.15888	−	6.15888i	0.207145	−	0.207145i
$885$	17.2025	−	17.2025i	0.578257	−	0.578257i
$886$	40.3789			1.35656
$887$	−0.0108862	−	0.0108862i	−0.000365523	−	0.000365523i	0.706924	−	0.707290i	$-0.250082\pi$
$887$	−0.0108862	−	0.0108862i	−0.000365523	−	0.000365523i	−0.707290	+	0.706924i	$0.750082\pi$
$888$	−5.99454	+	5.99454i	−0.201164	+	0.201164i
$889$	13.0059	+	13.3366i	0.436203	+	0.447294i
$890$	39.1307			1.31167
$891$	3.07581	−	3.07581i	0.103044	−	0.103044i
$892$	−7.82250			−0.261917
$893$	−36.1384			−1.20932
$894$		−	0.460829i		−	0.0154124i
$895$			19.2968i			0.645020i
$896$	1.89416	−	1.84720i	0.0632796	−	0.0617106i
$897$	−4.24498	−	4.24498i	−0.141736	−	0.141736i
$898$			25.0210i			0.834961i
$899$	2.39001	−	14.2192i	0.0797113	−	0.474236i
$900$	−0.260314			−0.00867712
$901$	22.1588	+	22.1588i	0.738217	+	0.738217i
$902$	−14.6960	−	14.6960i	−0.489323	−	0.489323i
$903$	−0.0972032	+	7.74369i	−0.00323472	+	0.257694i
$904$			9.63949i			0.320605i
$905$			43.7310i			1.45367i
$906$			20.7071i			0.687949i
$907$	−29.5935	−	29.5935i	−0.982636	−	0.982636i	0.0172156	−	0.999852i	$-0.494520\pi$
$907$	−29.5935	−	29.5935i	−0.982636	−	0.982636i	−0.999852	+	0.0172156i	$0.994520\pi$
$908$	23.3631			0.775333
$909$	−4.72960	+	4.72960i	−0.156871	+	0.156871i
$910$	12.2716	+	12.5835i	0.406798	+	0.417141i
$911$	−7.90665	−	7.90665i	−0.261959	−	0.261959i	0.563890	−	0.825850i	$-0.309304\pi$
$911$	−7.90665	−	7.90665i	−0.261959	−	0.261959i	−0.825850	+	0.563890i	$0.809304\pi$
$912$		−	2.96834i		−	0.0982916i
$913$	22.7984	+	22.7984i	0.754517	+	0.754517i
$914$	22.6852	+	22.6852i	0.750358	+	0.750358i
$915$		−	9.50405i		−	0.314194i
$916$	−4.68182	−	4.68182i	−0.154692	−	0.154692i
$917$	15.3529	+	15.7433i	0.506998	+	0.519888i
$918$	2.01832	−	2.01832i	0.0666146	−	0.0666146i
$919$	33.5692			1.10735			0.553673	−	0.832734i	$-0.313226\pi$
$919$	33.5692			1.10735			0.553673	+	0.832734i	$0.313226\pi$
$920$	−3.02859	−	3.02859i	−0.0998495	−	0.0998495i
$921$			20.9471i			0.690229i
$922$			31.4103i			1.03444i
$923$			41.9716i			1.38151i
$924$	11.5077	+	0.144452i	0.378577	+	0.00475211i
$925$	1.56046	+	1.56046i	0.0513076	+	0.0513076i
$926$	14.0967	+	14.0967i	0.463247	+	0.463247i
$927$	−2.63995			−0.0867072
$928$	−5.31067	−	0.892636i	−0.174331	−	0.0293022i
$929$			39.4514i			1.29436i	0.762339	+	0.647178i	$0.224051\pi$
$929$			39.4514i			1.29436i	−0.762339	+	0.647178i	$0.775949\pi$
$930$	4.12178	+	4.12178i	0.135159	+	0.135159i
$931$	14.3191	+	15.0567i	0.469290	+	0.493464i
$932$			0.533098i			0.0174622i
$933$			18.3998i			0.602382i
$934$	−17.1773			−0.562058
$935$	27.0306			0.883995
$936$	2.15772	−	2.15772i	0.0705274	−	0.0705274i
$937$	50.9693			1.66509			0.832547	−	0.553954i	$-0.186882\pi$
$937$	50.9693			1.66509			0.832547	+	0.553954i	$0.186882\pi$
$938$	16.0990	−	15.6999i	0.525652	−	0.512619i
$939$	4.13211	−	4.13211i	0.134846	−	0.134846i
$940$	−18.7419	−	18.7419i	−0.611295	−	0.611295i
$941$	26.7601			0.872354			0.436177	−	0.899861i	$-0.356332\pi$
$941$	26.7601			0.872354			0.436177	+	0.899861i	$0.356332\pi$
$942$	−8.66060	+	8.66060i	−0.282178	+	0.282178i
$943$	−6.64667	+	6.64667i	−0.216445	+	0.216445i
$944$		−	11.1746i		−	0.363703i
$945$	4.02150	+	4.12375i	0.130820	+	0.134146i
$946$	9.00312	+	9.00312i	0.292717	+	0.292717i
$947$	−30.6822	+	30.6822i	−0.997039	+	0.997039i	−0.999996	−	0.00295680i	$-0.999059\pi$
$947$	−30.6822	+	30.6822i	−0.997039	+	0.997039i	0.00295680	+	0.999996i	$0.499059\pi$
$948$		−	15.0619i		−	0.489188i
$949$	−19.7163	+	19.7163i	−0.640017	+	0.640017i
$950$	−0.772700			−0.0250697
$951$		−	13.5692i		−	0.440013i
$952$	7.55128	+	0.0947880i	0.244738	+	0.00307210i
$953$	37.2539			1.20677			0.603386	−	0.797450i	$-0.293818\pi$
$953$	37.2539			1.20677			0.603386	+	0.797450i	$0.293818\pi$
$954$	7.76320	+	7.76320i	0.251343	+	0.251343i
$955$	−13.9155	+	13.9155i	−0.450296	+	0.450296i
$956$		−	22.8814i		−	0.740036i
$957$	−13.5890	−	19.0802i	−0.439271	−	0.616775i
$958$		−	10.8341i		−	0.350034i
$959$	10.9545	+	11.2330i	0.353738	+	0.362731i
$960$	1.53943	−	1.53943i	0.0496849	−	0.0496849i
$961$		−	23.8311i		−	0.768746i
$962$	−25.8691			−0.834054
$963$		−	5.12152i		−	0.165039i
$964$			7.01610i			0.225973i
$965$	0.490472	−	0.490472i	0.0157888	−	0.0157888i
$966$	0.0653322	−	5.20469i	0.00210203	−	0.167458i
$967$	7.54886	+	7.54886i	0.242755	+	0.242755i	0.817989	−	0.575234i	$-0.195089\pi$
$967$	7.54886	+	7.54886i	0.242755	+	0.242755i	−0.575234	+	0.817989i	$0.695089\pi$
$968$	5.60117	−	5.60117i	0.180028	−	0.180028i
$969$	5.99107	−	5.99107i	0.192461	−	0.192461i
$970$		−	22.3241i		−	0.716783i
$971$	−25.3655	−	25.3655i	−0.814019	−	0.814019i	0.171215	−	0.985234i	$-0.445231\pi$
$971$	−25.3655	−	25.3655i	−0.814019	−	0.814019i	−0.985234	+	0.171215i	$0.945231\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	−32.7866	−	0.411556i	−1.05109	−	0.0131939i
$974$	30.2869	−	30.2869i	0.970454	−	0.970454i
$975$	−0.561685	−	0.561685i	−0.0179883	−	0.0179883i
$976$	−3.08688	−	3.08688i	−0.0988085	−	0.0988085i
$977$	−25.4162			−0.813138			−0.406569	−	0.913620i	$-0.633275\pi$
$977$	−25.4162			−0.813138			−0.406569	+	0.913620i	$0.633275\pi$
$978$	−5.70229	−	5.70229i	−0.182339	−	0.182339i
$979$	78.1841			2.49877
$980$	−0.382531	+	15.2348i	−0.0122195	+	0.486657i
$981$	−7.14857			−0.228236
$982$	−6.04131			−0.192786
$983$	13.7017	−	13.7017i	0.437018	−	0.437018i	−0.453989	−	0.891007i	$-0.650000\pi$
$983$	13.7017	−	13.7017i	0.437018	−	0.437018i	0.891007	+	0.453989i	$0.150000\pi$
$984$	−3.37850	−	3.37850i	−0.107703	−	0.107703i
$985$	−44.9693			−1.43284
$986$	−8.91702	−	12.5203i	−0.283976	−	0.398727i
$987$	0.404299	−	32.2084i	0.0128690	−	1.02521i
$988$	6.40486	−	6.40486i	0.203766	−	0.203766i
$989$	4.07191	−	4.07191i	0.129479	−	0.129479i
$990$	9.47000			0.300976
$991$			18.4180i			0.585066i	0.956255	+	0.292533i	$0.0944982\pi$
$991$			18.4180i			0.585066i	−0.956255	+	0.292533i	$0.905502\pi$
$992$	2.67747			0.0850099
$993$		−	31.7684i		−	1.00814i
$994$	−26.0533	+	25.4073i	−0.826360	+	0.805871i
$995$			16.0514i			0.508864i
$996$	5.24119	+	5.24119i	0.166073	+	0.166073i
$997$	1.78541	+	1.78541i	0.0565446	+	0.0565446i	0.734814	−	0.678269i	$-0.237270\pi$
$997$	1.78541	+	1.78541i	0.0565446	+	0.0565446i	−0.678269	+	0.734814i	$0.737270\pi$
$998$	−7.26426	−	7.26426i	−0.229946	−	0.229946i
$999$	−8.47756			−0.268218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1218.2.m.b.307.7	yes	40
7.6	odd	2		1218.2.m.a.307.7	✓	40
29.12	odd	4		1218.2.m.a.853.7	yes	40
203.41	even	4	inner	1218.2.m.b.853.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1218.2.m.a.307.7	✓	40	7.6	odd	2
1218.2.m.a.853.7	yes	40	29.12	odd	4
1218.2.m.b.307.7	yes	40	1.1	even	1	trivial
1218.2.m.b.853.7	yes	40	203.41	even	4	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1218 = 2 \cdot 3 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1218.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +2.17708 q^{5} +1.00000 q^{6} +(-0.0332084 + 2.64554i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-1.53943 + 1.53943i) q^{10} +(-3.07581 + 3.07581i) q^{11} +(-0.707107 + 0.707107i) q^{12} -3.05148 q^{13} +(-1.84720 - 1.89416i) q^{14} +(-1.53943 - 1.53943i) q^{15} -1.00000 q^{16} +(-2.01832 - 2.01832i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(-2.09893 - 2.09893i) q^{19} -2.17708i q^{20} +(1.89416 - 1.84720i) q^{21} -4.34986i q^{22} -1.96734 q^{23} -1.00000i q^{24} -0.260314 q^{25} +(2.15772 - 2.15772i) q^{26} +(0.707107 - 0.707107i) q^{27} +(2.64554 + 0.0332084i) q^{28} +(-3.12402 - 4.38640i) q^{29} +2.17708 q^{30} +(1.89326 + 1.89326i) q^{31} +(0.707107 - 0.707107i) q^{32} +4.34986 q^{33} +2.85434 q^{34} +(-0.0722973 + 5.75956i) q^{35} +1.00000 q^{36} +(-5.99454 - 5.99454i) q^{37} +2.96834 q^{38} +(2.15772 + 2.15772i) q^{39} +(1.53943 + 1.53943i) q^{40} +(3.37850 - 3.37850i) q^{41} +(-0.0332084 + 2.64554i) q^{42} +(-2.06975 + 2.06975i) q^{43} +(3.07581 + 3.07581i) q^{44} +2.17708i q^{45} +(1.39112 - 1.39112i) q^{46} +(8.60874 - 8.60874i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-6.99779 - 0.175708i) q^{49} +(0.184070 - 0.184070i) q^{50} +2.85434i q^{51} +3.05148i q^{52} -10.9788 q^{53} +1.00000i q^{54} +(-6.69630 + 6.69630i) q^{55} +(-1.89416 + 1.84720i) q^{56} +2.96834i q^{57} +(5.31067 + 0.892636i) q^{58} +11.1746i q^{59} +(-1.53943 + 1.53943i) q^{60} +(3.08688 + 3.08688i) q^{61} -2.67747 q^{62} +(-2.64554 - 0.0332084i) q^{63} +1.00000i q^{64} -6.64333 q^{65} +(-3.07581 + 3.07581i) q^{66} +8.49928i q^{67} +(-2.01832 + 2.01832i) q^{68} +(1.39112 + 1.39112i) q^{69} +(-4.02150 - 4.12375i) q^{70} -13.7545i q^{71} +(-0.707107 + 0.707107i) q^{72} +(6.46121 - 6.46121i) q^{73} +8.47756 q^{74} +(0.184070 + 0.184070i) q^{75} +(-2.09893 + 2.09893i) q^{76} +(-8.03505 - 8.23934i) q^{77} -3.05148 q^{78} +(-10.6504 + 10.6504i) q^{79} -2.17708 q^{80} -1.00000 q^{81} +4.77792i q^{82} -7.41216i q^{83} +(-1.84720 - 1.89416i) q^{84} +(-4.39405 - 4.39405i) q^{85} -2.92707i q^{86} +(-0.892636 + 5.31067i) q^{87} -4.34986 q^{88} +(-12.7095 - 12.7095i) q^{89} +(-1.53943 - 1.53943i) q^{90} +(0.101335 - 8.07283i) q^{91} +1.96734i q^{92} -2.67747i q^{93} +12.1746i q^{94} +(-4.56955 - 4.56955i) q^{95} -1.00000 q^{96} +(-7.25077 + 7.25077i) q^{97} +(5.07243 - 4.82394i) q^{98} +(-3.07581 - 3.07581i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{6} - 4 q^{10} + 4 q^{14} - 4 q^{15} - 40 q^{16} - 8 q^{19} + 4 q^{21} + 24 q^{25} + 12 q^{28} + 8 q^{29} + 24 q^{31} + 12 q^{35} + 40 q^{36} - 16 q^{37} + 4 q^{40} - 16 q^{41} - 20 q^{43} + 4 q^{46}+ \cdots - 24 q^{98}+O(q^{100}) \) 40 * q + 40 * q^6 - 4 * q^10 + 4 * q^14 - 4 * q^15 - 40 * q^16 - 8 * q^19 + 4 * q^21 + 24 * q^25 + 12 * q^28 + 8 * q^29 + 24 * q^31 + 12 * q^35 + 40 * q^36 - 16 * q^37 + 4 * q^40 - 16 * q^41 - 20 * q^43 + 4 * q^46 + 16 * q^47 + 28 * q^49 + 32 * q^50 + 16 * q^53 + 24 * q^55 - 4 * q^56 - 20 * q^58 - 4 * q^60 + 44 * q^61 - 12 * q^63 + 4 * q^69 + 20 * q^70 + 52 * q^73 + 32 * q^75 - 8 * q^76 + 20 * q^77 + 4 * q^79 - 40 * q^81 + 4 * q^84 - 24 * q^85 + 12 * q^87 - 24 * q^89 - 4 * q^90 - 16 * q^95 - 40 * q^96 + 68 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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