LMFDB - Embedded newform 930.2.j.d.683.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(497,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("930.497");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (of order $4$, degree $2$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			683.2
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	930.683
Dual form			930.2.j.d.497.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(1.22474 + 1.22474i) q^{3} +1.00000i q^{4} +(-2.12132 + 0.707107i) q^{5} -1.73205i q^{6} +(1.44949 - 1.44949i) q^{7} +(0.707107 - 0.707107i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.22474 + 1.22474i) q^{3} +1.00000i q^{4} +(-2.12132 + 0.707107i) q^{5} -1.73205i q^{6} +(1.44949 - 1.44949i) q^{7} +(0.707107 - 0.707107i) q^{8} +3.00000i q^{9} +(2.00000 + 1.00000i) q^{10} -0.635674i q^{11} +(-1.22474 + 1.22474i) q^{12} +(0.449490 + 0.449490i) q^{13} -2.04989 q^{14} +(-3.46410 - 1.73205i) q^{15} -1.00000 q^{16} +(3.14626 + 3.14626i) q^{17} +(2.12132 - 2.12132i) q^{18} +4.89898i q^{19} +(-0.707107 - 2.12132i) q^{20} +3.55051 q^{21} +(-0.449490 + 0.449490i) q^{22} +(-1.73205 + 1.73205i) q^{23} +1.73205 q^{24} +(4.00000 - 3.00000i) q^{25} -0.635674i q^{26} +(-3.67423 + 3.67423i) q^{27} +(1.44949 + 1.44949i) q^{28} -2.82843 q^{29} +(1.22474 + 3.67423i) q^{30} -1.00000 q^{31} +(0.707107 + 0.707107i) q^{32} +(0.778539 - 0.778539i) q^{33} -4.44949i q^{34} +(-2.04989 + 4.09978i) q^{35} -3.00000 q^{36} +(3.46410 - 3.46410i) q^{38} +1.10102i q^{39} +(-1.00000 + 2.00000i) q^{40} +2.82843i q^{41} +(-2.51059 - 2.51059i) q^{42} +(2.44949 + 2.44949i) q^{43} +0.635674 q^{44} +(-2.12132 - 6.36396i) q^{45} +2.44949 q^{46} +(5.65685 + 5.65685i) q^{47} +(-1.22474 - 1.22474i) q^{48} +2.79796i q^{49} +(-4.94975 - 0.707107i) q^{50} +7.70674i q^{51} +(-0.449490 + 0.449490i) q^{52} +(-4.24264 + 4.24264i) q^{53} +5.19615 q^{54} +(0.449490 + 1.34847i) q^{55} -2.04989i q^{56} +(-6.00000 + 6.00000i) q^{57} +(2.00000 + 2.00000i) q^{58} +3.60697 q^{59} +(1.73205 - 3.46410i) q^{60} -4.44949 q^{61} +(0.707107 + 0.707107i) q^{62} +(4.34847 + 4.34847i) q^{63} -1.00000i q^{64} +(-1.27135 - 0.635674i) q^{65} -1.10102 q^{66} +(-8.44949 + 8.44949i) q^{67} +(-3.14626 + 3.14626i) q^{68} -4.24264 q^{69} +(4.34847 - 1.44949i) q^{70} +9.12096i q^{71} +(2.12132 + 2.12132i) q^{72} +(-4.89898 - 4.89898i) q^{73} +(8.57321 + 1.22474i) q^{75} -4.89898 q^{76} +(-0.921404 - 0.921404i) q^{77} +(0.778539 - 0.778539i) q^{78} -8.89898i q^{79} +(2.12132 - 0.707107i) q^{80} -9.00000 q^{81} +(2.00000 - 2.00000i) q^{82} +(-0.635674 + 0.635674i) q^{83} +3.55051i q^{84} +(-8.89898 - 4.44949i) q^{85} -3.46410i q^{86} +(-3.46410 - 3.46410i) q^{87} +(-0.449490 - 0.449490i) q^{88} +18.2419 q^{89} +(-3.00000 + 6.00000i) q^{90} +1.30306 q^{91} +(-1.73205 - 1.73205i) q^{92} +(-1.22474 - 1.22474i) q^{93} -8.00000i q^{94} +(-3.46410 - 10.3923i) q^{95} +1.73205i q^{96} +(-3.00000 + 3.00000i) q^{97} +(1.97846 - 1.97846i) q^{98} +1.90702 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{7}+O(q^{10}) $ 8 * q - 8 * q^7	$ 8 q - 8 q^{7} + 16 q^{10} - 16 q^{13} - 8 q^{16} + 48 q^{21} + 16 q^{22} + 32 q^{25} - 8 q^{28} - 8 q^{31} - 24 q^{36} - 8 q^{40} + 16 q^{52} - 16 q^{55} - 48 q^{57} + 16 q^{58} - 16 q^{61} - 24 q^{63} - 48 q^{66} - 48 q^{67} - 24 q^{70} - 72 q^{81} + 16 q^{82} - 32 q^{85} + 16 q^{88} - 24 q^{90} + 128 q^{91} - 24 q^{97}+O(q^{100}) $ 8 * q - 8 * q^7 + 16 * q^10 - 16 * q^13 - 8 * q^16 + 48 * q^21 + 16 * q^22 + 32 * q^25 - 8 * q^28 - 8 * q^31 - 24 * q^36 - 8 * q^40 + 16 * q^52 - 16 * q^55 - 48 * q^57 + 16 * q^58 - 16 * q^61 - 24 * q^63 - 48 * q^66 - 48 * q^67 - 24 * q^70 - 72 * q^81 + 16 * q^82 - 32 * q^85 + 16 * q^88 - 24 * q^90 + 128 * q^91 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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
$3$	1.22474	+	1.22474i	0.707107	+	0.707107i
$3$	1.22474	+	1.22474i	0.707107	+	0.707107i
$4$			1.00000i			0.500000i
$5$	−2.12132	+	0.707107i	−0.948683	+	0.316228i
$5$	−2.12132	+	0.707107i	−0.948683	+	0.316228i
$6$		−	1.73205i		−	0.707107i
$7$	1.44949	−	1.44949i	0.547856	−	0.547856i	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	1.44949	−	1.44949i	0.547856	−	0.547856i	0.925820	+	0.377964i	$0.123376\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$			3.00000i			1.00000i
$10$	2.00000	+	1.00000i	0.632456	+	0.316228i
$11$		−	0.635674i		−	0.191663i	−0.995398	−	0.0958315i	$-0.969449\pi$
$11$		−	0.635674i		−	0.191663i	0.995398	−	0.0958315i	$-0.0305510\pi$
$12$	−1.22474	+	1.22474i	−0.353553	+	0.353553i
$13$	0.449490	+	0.449490i	0.124666	+	0.124666i	0.766687	−	0.642021i	$-0.221904\pi$
$13$	0.449490	+	0.449490i	0.124666	+	0.124666i	−0.642021	+	0.766687i	$0.721904\pi$
$14$	−2.04989			−0.547856
$15$	−3.46410	−	1.73205i	−0.894427	−	0.447214i
$16$	−1.00000			−0.250000
$17$	3.14626	+	3.14626i	0.763081	+	0.763081i	0.976878	−	0.213797i	$-0.0685831\pi$
$17$	3.14626	+	3.14626i	0.763081	+	0.763081i	−0.213797	+	0.976878i	$0.568583\pi$
$18$	2.12132	−	2.12132i	0.500000	−	0.500000i
$19$			4.89898i			1.12390i	0.827170	+	0.561951i	$0.189949\pi$
$19$			4.89898i			1.12390i	−0.827170	+	0.561951i	$0.810051\pi$
$20$	−0.707107	−	2.12132i	−0.158114	−	0.474342i
$21$	3.55051			0.774785
$22$	−0.449490	+	0.449490i	−0.0958315	+	0.0958315i
$23$	−1.73205	+	1.73205i	−0.361158	+	0.361158i	−0.864239	−	0.503081i	$-0.832200\pi$
$23$	−1.73205	+	1.73205i	−0.361158	+	0.361158i	0.503081	+	0.864239i	$0.332200\pi$
$24$	1.73205			0.353553
$25$	4.00000	−	3.00000i	0.800000	−	0.600000i
$26$		−	0.635674i		−	0.124666i
$27$	−3.67423	+	3.67423i	−0.707107	+	0.707107i
$28$	1.44949	+	1.44949i	0.273928	+	0.273928i
$29$	−2.82843			−0.525226			−0.262613	−	0.964901i	$-0.584584\pi$
$29$	−2.82843			−0.525226			−0.262613	+	0.964901i	$0.584584\pi$
$30$	1.22474	+	3.67423i	0.223607	+	0.670820i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	0.778539	−	0.778539i	0.135526	−	0.135526i
$34$		−	4.44949i		−	0.763081i
$35$	−2.04989	+	4.09978i	−0.346494	+	0.692989i
$36$	−3.00000			−0.500000
$37$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$37$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$38$	3.46410	−	3.46410i	0.561951	−	0.561951i
$39$			1.10102i			0.176304i
$40$	−1.00000	+	2.00000i	−0.158114	+	0.316228i
$41$			2.82843i			0.441726i	0.975305	+	0.220863i	$0.0708874\pi$
$41$			2.82843i			0.441726i	−0.975305	+	0.220863i	$0.929113\pi$
$42$	−2.51059	−	2.51059i	−0.387392	−	0.387392i
$43$	2.44949	+	2.44949i	0.373544	+	0.373544i	0.868766	−	0.495222i	$-0.164913\pi$
$43$	2.44949	+	2.44949i	0.373544	+	0.373544i	−0.495222	+	0.868766i	$0.664913\pi$
$44$	0.635674			0.0958315
$45$	−2.12132	−	6.36396i	−0.316228	−	0.948683i
$46$	2.44949			0.361158
$47$	5.65685	+	5.65685i	0.825137	+	0.825137i	0.986840	−	0.161703i	$-0.0516985\pi$
$47$	5.65685	+	5.65685i	0.825137	+	0.825137i	−0.161703	+	0.986840i	$0.551699\pi$
$48$	−1.22474	−	1.22474i	−0.176777	−	0.176777i
$49$			2.79796i			0.399708i
$50$	−4.94975	−	0.707107i	−0.700000	−	0.100000i
$51$			7.70674i			1.07916i
$52$	−0.449490	+	0.449490i	−0.0623330	+	0.0623330i
$53$	−4.24264	+	4.24264i	−0.582772	+	0.582772i	−0.935664	−	0.352892i	$-0.885198\pi$
$53$	−4.24264	+	4.24264i	−0.582772	+	0.582772i	0.352892	+	0.935664i	$0.385198\pi$
$54$	5.19615			0.707107
$55$	0.449490	+	1.34847i	0.0606092	+	0.181828i
$56$		−	2.04989i		−	0.273928i
$57$	−6.00000	+	6.00000i	−0.794719	+	0.794719i
$58$	2.00000	+	2.00000i	0.262613	+	0.262613i
$59$	3.60697			0.469587			0.234794	−	0.972045i	$-0.424559\pi$
$59$	3.60697			0.469587			0.234794	+	0.972045i	$0.424559\pi$
$60$	1.73205	−	3.46410i	0.223607	−	0.447214i
$61$	−4.44949			−0.569699			−0.284849	−	0.958572i	$-0.591944\pi$
$61$	−4.44949			−0.569699			−0.284849	+	0.958572i	$0.591944\pi$
$62$	0.707107	+	0.707107i	0.0898027	+	0.0898027i
$63$	4.34847	+	4.34847i	0.547856	+	0.547856i
$64$		−	1.00000i		−	0.125000i
$65$	−1.27135	−	0.635674i	−0.157691	−	0.0788457i
$66$	−1.10102			−0.135526
$67$	−8.44949	+	8.44949i	−1.03227	+	1.03227i	−0.0328078	+	0.999462i	$0.510445\pi$
$67$	−8.44949	+	8.44949i	−1.03227	+	1.03227i	−0.999462	+	0.0328078i	$0.989555\pi$
$68$	−3.14626	+	3.14626i	−0.381541	+	0.381541i
$69$	−4.24264			−0.510754
$70$	4.34847	−	1.44949i	0.519741	−	0.173247i
$71$			9.12096i			1.08246i	0.840875	+	0.541229i	$0.182041\pi$
$71$			9.12096i			1.08246i	−0.840875	+	0.541229i	$0.817959\pi$
$72$	2.12132	+	2.12132i	0.250000	+	0.250000i
$73$	−4.89898	−	4.89898i	−0.573382	−	0.573382i	0.359690	−	0.933072i	$-0.382883\pi$
$73$	−4.89898	−	4.89898i	−0.573382	−	0.573382i	−0.933072	+	0.359690i	$0.882883\pi$
$74$		0			0
$75$	8.57321	+	1.22474i	0.989949	+	0.141421i
$76$	−4.89898			−0.561951
$77$	−0.921404	−	0.921404i	−0.105004	−	0.105004i
$78$	0.778539	−	0.778539i	0.0881522	−	0.0881522i
$79$		−	8.89898i		−	1.00121i	−0.865675	−	0.500607i	$-0.833110\pi$
$79$		−	8.89898i		−	1.00121i	0.865675	−	0.500607i	$-0.166890\pi$
$80$	2.12132	−	0.707107i	0.237171	−	0.0790569i
$81$	−9.00000			−1.00000
$82$	2.00000	−	2.00000i	0.220863	−	0.220863i
$83$	−0.635674	+	0.635674i	−0.0697743	+	0.0697743i	−0.741133	−	0.671358i	$-0.765711\pi$
$83$	−0.635674	+	0.635674i	−0.0697743	+	0.0697743i	0.671358	+	0.741133i	$0.265711\pi$
$84$			3.55051i			0.387392i
$85$	−8.89898	−	4.44949i	−0.965230	−	0.482615i
$86$		−	3.46410i		−	0.373544i
$87$	−3.46410	−	3.46410i	−0.371391	−	0.371391i
$88$	−0.449490	−	0.449490i	−0.0479158	−	0.0479158i
$89$	18.2419			1.93364			0.966819	−	0.255461i	$-0.0822272\pi$
$89$	18.2419			1.93364			0.966819	+	0.255461i	$0.0822272\pi$
$90$	−3.00000	+	6.00000i	−0.316228	+	0.632456i
$91$	1.30306			0.136598
$92$	−1.73205	−	1.73205i	−0.180579	−	0.180579i
$93$	−1.22474	−	1.22474i	−0.127000	−	0.127000i
$94$		−	8.00000i		−	0.825137i
$95$	−3.46410	−	10.3923i	−0.355409	−	1.06623i
$96$			1.73205i			0.176777i
$97$	−3.00000	+	3.00000i	−0.304604	+	0.304604i	−0.842812	−	0.538208i	$-0.819101\pi$
$97$	−3.00000	+	3.00000i	−0.304604	+	0.304604i	0.538208	+	0.842812i	$0.319101\pi$
$98$	1.97846	−	1.97846i	0.199854	−	0.199854i
$99$	1.90702			0.191663
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$		−	9.89949i		−	0.985037i	−0.870302	−	0.492518i	$-0.836076\pi$
$101$		−	9.89949i		−	0.985037i	0.870302	−	0.492518i	$-0.163924\pi$
$102$	5.44949	−	5.44949i	0.539580	−	0.539580i
$103$	3.44949	+	3.44949i	0.339888	+	0.339888i	0.856325	−	0.516437i	$-0.172742\pi$
$103$	3.44949	+	3.44949i	0.339888	+	0.339888i	−0.516437	+	0.856325i	$0.672742\pi$
$104$	0.635674			0.0623330
$105$	−7.53177	+	2.51059i	−0.735025	+	0.245008i
$106$	6.00000			0.582772
$107$	−0.778539	−	0.778539i	−0.0752642	−	0.0752642i	0.668473	−	0.743737i	$-0.266948\pi$
$107$	−0.778539	−	0.778539i	−0.0752642	−	0.0752642i	−0.743737	+	0.668473i	$0.766948\pi$
$108$	−3.67423	−	3.67423i	−0.353553	−	0.353553i
$109$		−	6.89898i		−	0.660802i	−0.943841	−	0.330401i	$-0.892816\pi$
$109$		−	6.89898i		−	0.660802i	0.943841	−	0.330401i	$-0.107184\pi$
$110$	0.635674	−	1.27135i	0.0606092	−	0.121218i
$111$		0			0
$112$	−1.44949	+	1.44949i	−0.136964	+	0.136964i
$113$	−5.51399	+	5.51399i	−0.518713	+	0.518713i	−0.917182	−	0.398469i	$-0.869542\pi$
$113$	−5.51399	+	5.51399i	−0.518713	+	0.518713i	0.398469	+	0.917182i	$0.369542\pi$
$114$	8.48528			0.794719
$115$	2.44949	−	4.89898i	0.228416	−	0.456832i
$116$		−	2.82843i		−	0.262613i
$117$	−1.34847	+	1.34847i	−0.124666	+	0.124666i
$118$	−2.55051	−	2.55051i	−0.234794	−	0.234794i
$119$	9.12096			0.836117
$120$	−3.67423	+	1.22474i	−0.335410	+	0.111803i
$121$	10.5959			0.963265
$122$	3.14626	+	3.14626i	0.284849	+	0.284849i
$123$	−3.46410	+	3.46410i	−0.312348	+	0.312348i
$124$		−	1.00000i		−	0.0898027i
$125$	−6.36396	+	9.19239i	−0.569210	+	0.822192i
$126$		−	6.14966i		−	0.547856i
$127$	5.55051	−	5.55051i	0.492528	−	0.492528i	−0.416574	−	0.909102i	$-0.636769\pi$
$127$	5.55051	−	5.55051i	0.492528	−	0.492528i	0.909102	+	0.416574i	$0.136769\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$			6.00000i			0.528271i
$130$	0.449490	+	1.34847i	0.0394229	+	0.118269i
$131$		−	10.5352i		−	0.920462i	−0.887799	−	0.460231i	$-0.847767\pi$
$131$		−	10.5352i		−	0.920462i	0.887799	−	0.460231i	$-0.152233\pi$
$132$	0.778539	+	0.778539i	0.0677631	+	0.0677631i
$133$	7.10102	+	7.10102i	0.615737	+	0.615737i
$134$	11.9494			1.03227
$135$	5.19615	−	10.3923i	0.447214	−	0.894427i
$136$	4.44949			0.381541
$137$	13.5386	+	13.5386i	1.15668	+	1.15668i	0.985185	+	0.171493i	$0.0548590\pi$
$137$	13.5386	+	13.5386i	1.15668	+	1.15668i	0.171493	+	0.985185i	$0.445141\pi$
$138$	3.00000	+	3.00000i	0.255377	+	0.255377i
$139$		−	13.5505i		−	1.14934i	−0.818385	−	0.574670i	$-0.805131\pi$
$139$		−	13.5505i		−	1.14934i	0.818385	−	0.574670i	$-0.194869\pi$
$140$	−4.09978	−	2.04989i	−0.346494	−	0.173247i
$141$			13.8564i			1.16692i
$142$	6.44949	−	6.44949i	0.541229	−	0.541229i
$143$	0.285729	−	0.285729i	0.0238939	−	0.0238939i
$144$		−	3.00000i		−	0.250000i
$145$	6.00000	−	2.00000i	0.498273	−	0.166091i
$146$			6.92820i			0.573382i
$147$	−3.42679	+	3.42679i	−0.282637	+	0.282637i
$148$		0			0
$149$	6.78534			0.555877			0.277938	−	0.960599i	$-0.410349\pi$
$149$	6.78534			0.555877			0.277938	+	0.960599i	$0.410349\pi$
$150$	−5.19615	−	6.92820i	−0.424264	−	0.565685i
$151$	7.10102			0.577873			0.288936	−	0.957348i	$-0.406698\pi$
$151$	7.10102			0.577873			0.288936	+	0.957348i	$0.406698\pi$
$152$	3.46410	+	3.46410i	0.280976	+	0.280976i
$153$	−9.43879	+	9.43879i	−0.763081	+	0.763081i
$154$			1.30306i			0.105004i
$155$	2.12132	−	0.707107i	0.170389	−	0.0567962i
$156$	−1.10102			−0.0881522
$157$	16.8990	−	16.8990i	1.34869	−	1.34869i	0.461594	−	0.887091i	$-0.347278\pi$
$157$	16.8990	−	16.8990i	1.34869	−	1.34869i	0.887091	−	0.461594i	$-0.152722\pi$
$158$	−6.29253	+	6.29253i	−0.500607	+	0.500607i
$159$	−10.3923			−0.824163
$160$	−2.00000	−	1.00000i	−0.158114	−	0.0790569i
$161$			5.02118i			0.395724i
$162$	6.36396	+	6.36396i	0.500000	+	0.500000i
$163$	17.3485	+	17.3485i	1.35884	+	1.35884i	0.875353	+	0.483484i	$0.160629\pi$
$163$	17.3485	+	17.3485i	1.35884	+	1.35884i	0.483484	+	0.875353i	$0.339371\pi$
$164$	−2.82843			−0.220863
$165$	−1.10102	+	2.20204i	−0.0857143	+	0.171429i
$166$	0.898979			0.0697743
$167$	−12.1244	−	12.1244i	−0.938211	−	0.938211i	0.0599883	−	0.998199i	$-0.480894\pi$
$167$	−12.1244	−	12.1244i	−0.938211	−	0.938211i	−0.998199	+	0.0599883i	$0.980894\pi$
$168$	2.51059	−	2.51059i	0.193696	−	0.193696i
$169$		−	12.5959i		−	0.968917i
$170$	3.14626	+	9.43879i	0.241307	+	0.723922i
$171$	−14.6969			−1.12390
$172$	−2.44949	+	2.44949i	−0.186772	+	0.186772i
$173$	−0.142865	+	0.142865i	−0.0108618	+	0.0108618i	−0.712517	−	0.701655i	$-0.752445\pi$
$173$	−0.142865	+	0.142865i	−0.0108618	+	0.0108618i	0.701655	+	0.712517i	$0.252445\pi$
$174$			4.89898i			0.371391i
$175$	1.44949	−	10.1464i	0.109571	−	0.766998i
$176$			0.635674i			0.0479158i
$177$	4.41761	+	4.41761i	0.332048	+	0.332048i
$178$	−12.8990	−	12.8990i	−0.966819	−	0.966819i
$179$	3.74983			0.280276			0.140138	−	0.990132i	$-0.455245\pi$
$179$	3.74983			0.280276			0.140138	+	0.990132i	$0.455245\pi$
$180$	6.36396	−	2.12132i	0.474342	−	0.158114i
$181$	−3.55051			−0.263907			−0.131954	−	0.991256i	$-0.542125\pi$
$181$	−3.55051			−0.263907			−0.131954	+	0.991256i	$0.542125\pi$
$182$	−0.921404	−	0.921404i	−0.0682990	−	0.0682990i
$183$	−5.44949	−	5.44949i	−0.402838	−	0.402838i
$184$			2.44949i			0.180579i
$185$		0			0
$186$			1.73205i			0.127000i
$187$	2.00000	−	2.00000i	0.146254	−	0.146254i
$188$	−5.65685	+	5.65685i	−0.412568	+	0.412568i
$189$			10.6515i			0.774785i
$190$	−4.89898	+	9.79796i	−0.355409	+	0.710819i
$191$		−	21.7060i		−	1.57059i	−0.619120	−	0.785296i	$-0.712511\pi$
$191$		−	21.7060i		−	1.57059i	0.619120	−	0.785296i	$-0.287489\pi$
$192$	1.22474	−	1.22474i	0.0883883	−	0.0883883i
$193$	−7.00000	−	7.00000i	−0.503871	−	0.503871i	0.408768	−	0.912639i	$-0.365959\pi$
$193$	−7.00000	−	7.00000i	−0.503871	−	0.503871i	−0.912639	+	0.408768i	$0.865959\pi$
$194$	4.24264			0.304604
$195$	−0.778539	−	2.33562i	−0.0557523	−	0.167257i
$196$	−2.79796			−0.199854
$197$	−4.87832	−	4.87832i	−0.347566	−	0.347566i	0.511636	−	0.859202i	$-0.329039\pi$
$197$	−4.87832	−	4.87832i	−0.347566	−	0.347566i	−0.859202	+	0.511636i	$0.829039\pi$
$198$	−1.34847	−	1.34847i	−0.0958315	−	0.0958315i
$199$		−	10.6969i		−	0.758286i	−0.925338	−	0.379143i	$-0.876219\pi$
$199$		−	10.6969i		−	0.758286i	0.925338	−	0.379143i	$-0.123781\pi$
$200$	0.707107	−	4.94975i	0.0500000	−	0.350000i
$201$	−20.6969			−1.45985
$202$	−7.00000	+	7.00000i	−0.492518	+	0.492518i
$203$	−4.09978	+	4.09978i	−0.287748	+	0.287748i
$204$	−7.70674			−0.539580
$205$	−2.00000	−	6.00000i	−0.139686	−	0.419058i
$206$		−	4.87832i		−	0.339888i
$207$	−5.19615	−	5.19615i	−0.361158	−	0.361158i
$208$	−0.449490	−	0.449490i	−0.0311665	−	0.0311665i
$209$	3.11416			0.215411
$210$	7.10102	+	3.55051i	0.490017	+	0.245008i
$211$	−22.6969			−1.56252			−0.781261	−	0.624205i	$-0.785423\pi$
$211$	−22.6969			−1.56252			−0.781261	+	0.624205i	$0.785423\pi$
$212$	−4.24264	−	4.24264i	−0.291386	−	0.291386i
$213$	−11.1708	+	11.1708i	−0.765414	+	0.765414i
$214$			1.10102i			0.0752642i
$215$	−6.92820	−	3.46410i	−0.472500	−	0.236250i
$216$			5.19615i			0.353553i
$217$	−1.44949	+	1.44949i	−0.0983978	+	0.0983978i
$218$	−4.87832	+	4.87832i	−0.330401	+	0.330401i
$219$		−	12.0000i		−	0.810885i
$220$	−1.34847	+	0.449490i	−0.0909138	+	0.0303046i
$221$			2.82843i			0.190261i
$222$		0			0
$223$	8.44949	+	8.44949i	0.565820	+	0.565820i	0.930955	−	0.365135i	$-0.118977\pi$
$223$	8.44949	+	8.44949i	0.565820	+	0.565820i	−0.365135	+	0.930955i	$0.618977\pi$
$224$	2.04989			0.136964
$225$	9.00000	+	12.0000i	0.600000	+	0.800000i
$226$	7.79796			0.518713
$227$	−13.3636	−	13.3636i	−0.886973	−	0.886973i	0.107258	−	0.994231i	$-0.465793\pi$
$227$	−13.3636	−	13.3636i	−0.886973	−	0.886973i	−0.994231	+	0.107258i	$0.965793\pi$
$228$	−6.00000	−	6.00000i	−0.397360	−	0.397360i
$229$		−	11.5505i		−	0.763279i	−0.924311	−	0.381640i	$-0.875360\pi$
$229$		−	11.5505i		−	0.763279i	0.924311	−	0.381640i	$-0.124640\pi$
$230$	−5.19615	+	1.73205i	−0.342624	+	0.114208i
$231$		−	2.25697i		−	0.148498i
$232$	−2.00000	+	2.00000i	−0.131306	+	0.131306i
$233$	−0.778539	+	0.778539i	−0.0510038	+	0.0510038i	−0.732149	−	0.681145i	$-0.761482\pi$
$233$	−0.778539	+	0.778539i	−0.0510038	+	0.0510038i	0.681145	+	0.732149i	$0.261482\pi$
$234$	1.90702			0.124666
$235$	−16.0000	−	8.00000i	−1.04372	−	0.521862i
$236$			3.60697i			0.234794i
$237$	10.8990	−	10.8990i	0.707965	−	0.707965i
$238$	−6.44949	−	6.44949i	−0.418058	−	0.418058i
$239$	6.00680			0.388548			0.194274	−	0.980947i	$-0.437765\pi$
$239$	6.00680			0.388548			0.194274	+	0.980947i	$0.437765\pi$
$240$	3.46410	+	1.73205i	0.223607	+	0.111803i
$241$	22.8990			1.47505			0.737526	−	0.675318i	$-0.235994\pi$
$241$	22.8990			1.47505			0.737526	+	0.675318i	$0.235994\pi$
$242$	−7.49245	−	7.49245i	−0.481633	−	0.481633i
$243$	−11.0227	−	11.0227i	−0.707107	−	0.707107i
$244$		−	4.44949i		−	0.284849i
$245$	−1.97846	−	5.93537i	−0.126399	−	0.379197i
$246$	4.89898			0.312348
$247$	−2.20204	+	2.20204i	−0.140113	+	0.140113i
$248$	−0.707107	+	0.707107i	−0.0449013	+	0.0449013i
$249$	−1.55708			−0.0986758
$250$	11.0000	−	2.00000i	0.695701	−	0.126491i
$251$		−	18.8776i		−	1.19154i	−0.803154	−	0.595771i	$-0.796846\pi$
$251$		−	18.8776i		−	1.19154i	0.803154	−	0.595771i	$-0.203154\pi$
$252$	−4.34847	+	4.34847i	−0.273928	+	0.273928i
$253$	1.10102	+	1.10102i	0.0692206	+	0.0692206i
$254$	−7.84961			−0.492528
$255$	−5.44949	−	16.3485i	−0.341260	−	1.02378i
$256$	1.00000			0.0625000
$257$	13.3636	+	13.3636i	0.833598	+	0.833598i	0.988007	−	0.154409i	$-0.0493473\pi$
$257$	13.3636	+	13.3636i	0.833598	+	0.833598i	−0.154409	+	0.988007i	$0.549347\pi$
$258$	4.24264	−	4.24264i	0.264135	−	0.264135i
$259$		0			0
$260$	0.635674	−	1.27135i	0.0394229	−	0.0788457i
$261$		−	8.48528i		−	0.525226i
$262$	−7.44949	+	7.44949i	−0.460231	+	0.460231i
$263$	−19.9740	+	19.9740i	−1.23165	+	1.23165i	−0.268316	+	0.963331i	$0.586467\pi$
$263$	−19.9740	+	19.9740i	−1.23165	+	1.23165i	−0.963331	+	0.268316i	$0.913533\pi$
$264$		−	1.10102i		−	0.0677631i
$265$	6.00000	−	12.0000i	0.368577	−	0.737154i
$266$		−	10.0424i		−	0.615737i
$267$	22.3417	+	22.3417i	1.36729	+	1.36729i
$268$	−8.44949	−	8.44949i	−0.516135	−	0.516135i
$269$	5.65685			0.344904			0.172452	−	0.985018i	$-0.444831\pi$
$269$	5.65685			0.344904			0.172452	+	0.985018i	$0.444831\pi$
$270$	−11.0227	+	3.67423i	−0.670820	+	0.223607i
$271$	−13.7980			−0.838166			−0.419083	−	0.907948i	$-0.637648\pi$
$271$	−13.7980			−0.838166			−0.419083	+	0.907948i	$0.637648\pi$
$272$	−3.14626	−	3.14626i	−0.190770	−	0.190770i
$273$	1.59592	+	1.59592i	0.0965893	+	0.0965893i
$274$		−	19.1464i		−	1.15668i
$275$	−1.90702	−	2.54270i	−0.114998	−	0.153330i
$276$		−	4.24264i		−	0.255377i
$277$	−17.3485	+	17.3485i	−1.04237	+	1.04237i	−0.0433067	+	0.999062i	$0.513789\pi$
$277$	−17.3485	+	17.3485i	−1.04237	+	1.04237i	−0.999062	+	0.0433067i	$0.986211\pi$
$278$	−9.58166	+	9.58166i	−0.574670	+	0.574670i
$279$		−	3.00000i		−	0.179605i
$280$	1.44949	+	4.34847i	0.0866236	+	0.259871i
$281$		−	5.65685i		−	0.337460i	−0.985662	−	0.168730i	$-0.946033\pi$
$281$		−	5.65685i		−	0.337460i	0.985662	−	0.168730i	$-0.0539665\pi$
$282$	9.79796	−	9.79796i	0.583460	−	0.583460i
$283$	6.24745	+	6.24745i	0.371372	+	0.371372i	0.867977	−	0.496605i	$-0.165420\pi$
$283$	6.24745	+	6.24745i	0.371372	+	0.371372i	−0.496605	+	0.867977i	$0.665420\pi$
$284$	−9.12096			−0.541229
$285$	8.48528	−	16.9706i	0.502625	−	1.00525i
$286$	−0.404082			−0.0238939
$287$	4.09978	+	4.09978i	0.242002	+	0.242002i
$288$	−2.12132	+	2.12132i	−0.125000	+	0.125000i
$289$			2.79796i			0.164586i
$290$	−5.65685	−	2.82843i	−0.332182	−	0.166091i
$291$	−7.34847			−0.430775
$292$	4.89898	−	4.89898i	0.286691	−	0.286691i
$293$	12.7279	−	12.7279i	0.743573	−	0.743573i	−0.229691	−	0.973264i	$-0.573771\pi$
$293$	12.7279	−	12.7279i	0.743573	−	0.743573i	0.973264	+	0.229691i	$0.0737714\pi$
$294$	4.84621			0.282637
$295$	−7.65153	+	2.55051i	−0.445489	+	0.148496i
$296$		0			0
$297$	2.33562	+	2.33562i	0.135526	+	0.135526i
$298$	−4.79796	−	4.79796i	−0.277938	−	0.277938i
$299$	−1.55708			−0.0900482
$300$	−1.22474	+	8.57321i	−0.0707107	+	0.494975i
$301$	7.10102			0.409296
$302$	−5.02118	−	5.02118i	−0.288936	−	0.288936i
$303$	12.1244	−	12.1244i	0.696526	−	0.696526i
$304$		−	4.89898i		−	0.280976i
$305$	9.43879	−	3.14626i	0.540464	−	0.180155i
$306$	13.3485			0.763081
$307$	3.34847	−	3.34847i	0.191107	−	0.191107i	−0.605067	−	0.796174i	$-0.706854\pi$
$307$	3.34847	−	3.34847i	0.191107	−	0.191107i	0.796174	+	0.605067i	$0.206854\pi$
$308$	0.921404	−	0.921404i	0.0525018	−	0.0525018i
$309$			8.44949i			0.480675i
$310$	−2.00000	−	1.00000i	−0.113592	−	0.0567962i
$311$		−	26.0915i		−	1.47951i	−0.672874	−	0.739757i	$-0.734940\pi$
$311$		−	26.0915i		−	1.47951i	0.672874	−	0.739757i	$-0.265060\pi$
$312$	0.778539	+	0.778539i	0.0440761	+	0.0440761i
$313$	−14.8990	−	14.8990i	−0.842140	−	0.842140i	0.146997	−	0.989137i	$-0.453039\pi$
$313$	−14.8990	−	14.8990i	−0.842140	−	0.842140i	−0.989137	+	0.146997i	$0.953039\pi$
$314$	−23.8988			−1.34869
$315$	−12.2993	−	6.14966i	−0.692989	−	0.346494i
$316$	8.89898			0.500607
$317$	11.1708	+	11.1708i	0.627417	+	0.627417i	0.947417	−	0.320000i	$-0.103683\pi$
$317$	11.1708	+	11.1708i	0.627417	+	0.627417i	−0.320000	+	0.947417i	$0.603683\pi$
$318$	7.34847	+	7.34847i	0.412082	+	0.412082i
$319$			1.79796i			0.100666i
$320$	0.707107	+	2.12132i	0.0395285	+	0.118585i
$321$		−	1.90702i		−	0.106440i
$322$	3.55051	−	3.55051i	0.197862	−	0.197862i
$323$	−15.4135	+	15.4135i	−0.857629	+	0.857629i
$324$		−	9.00000i		−	0.500000i
$325$	3.14643	+	0.449490i	0.174532	+	0.0249332i
$326$		−	24.5344i		−	1.35884i
$327$	8.44949	−	8.44949i	0.467258	−	0.467258i
$328$	2.00000	+	2.00000i	0.110432	+	0.110432i
$329$	16.3991			0.904112
$330$	2.33562	−	0.778539i	0.128571	−	0.0428572i
$331$	−4.24745			−0.233461			−0.116730	−	0.993164i	$-0.537241\pi$
$331$	−4.24745			−0.233461			−0.116730	+	0.993164i	$0.537241\pi$
$332$	−0.635674	−	0.635674i	−0.0348872	−	0.0348872i
$333$		0			0
$334$			17.1464i			0.938211i
$335$	11.9494	−	23.8988i	0.652865	−	1.30573i
$336$	−3.55051			−0.193696
$337$	4.89898	−	4.89898i	0.266864	−	0.266864i	−0.560971	−	0.827835i	$-0.689572\pi$
$337$	4.89898	−	4.89898i	0.266864	−	0.266864i	0.827835	+	0.560971i	$0.189572\pi$
$338$	−8.90666	+	8.90666i	−0.484458	+	0.484458i
$339$	−13.5065			−0.733570
$340$	4.44949	−	8.89898i	0.241307	−	0.482615i
$341$			0.635674i			0.0344237i
$342$	10.3923	+	10.3923i	0.561951	+	0.561951i
$343$	14.2020	+	14.2020i	0.766838	+	0.766838i
$344$	3.46410			0.186772
$345$	9.00000	−	3.00000i	0.484544	−	0.161515i
$346$	0.202041			0.0108618
$347$	10.6780	+	10.6780i	0.573227	+	0.573227i	0.933029	−	0.359802i	$-0.117156\pi$
$347$	10.6780	+	10.6780i	0.573227	+	0.573227i	−0.359802	+	0.933029i	$0.617156\pi$
$348$	3.46410	−	3.46410i	0.185695	−	0.185695i
$349$			31.3939i			1.68048i	0.542218	+	0.840238i	$0.317585\pi$
$349$			31.3939i			1.68048i	−0.542218	+	0.840238i	$0.682415\pi$
$350$	−8.19955	+	6.14966i	−0.438285	+	0.328713i
$351$	−3.30306			−0.176304
$352$	0.449490	−	0.449490i	0.0239579	−	0.0239579i
$353$	−10.7101	+	10.7101i	−0.570043	+	0.570043i	−0.932140	−	0.362097i	$-0.882061\pi$
$353$	−10.7101	+	10.7101i	−0.570043	+	0.570043i	0.362097	+	0.932140i	$0.382061\pi$
$354$		−	6.24745i		−	0.332048i
$355$	−6.44949	−	19.3485i	−0.342303	−	1.02691i
$356$			18.2419i			0.966819i
$357$	11.1708	+	11.1708i	0.591224	+	0.591224i
$358$	−2.65153	−	2.65153i	−0.140138	−	0.140138i
$359$	−3.74983			−0.197908			−0.0989542	−	0.995092i	$-0.531550\pi$
$359$	−3.74983			−0.197908			−0.0989542	+	0.995092i	$0.531550\pi$
$360$	−6.00000	−	3.00000i	−0.316228	−	0.158114i
$361$	−5.00000			−0.263158
$362$	2.51059	+	2.51059i	0.131954	+	0.131954i
$363$	12.9773	+	12.9773i	0.681131	+	0.681131i
$364$			1.30306i			0.0682990i
$365$	13.8564	+	6.92820i	0.725277	+	0.362639i
$366$			7.70674i			0.402838i
$367$	3.55051	−	3.55051i	0.185335	−	0.185335i	−0.608341	−	0.793676i	$-0.708165\pi$
$367$	3.55051	−	3.55051i	0.185335	−	0.185335i	0.793676	+	0.608341i	$0.208165\pi$
$368$	1.73205	−	1.73205i	0.0902894	−	0.0902894i
$369$	−8.48528			−0.441726
$370$		0			0
$371$			12.2993i			0.638549i
$372$	1.22474	−	1.22474i	0.0635001	−	0.0635001i
$373$	−10.0000	−	10.0000i	−0.517780	−	0.517780i	0.399119	−	0.916899i	$-0.369316\pi$
$373$	−10.0000	−	10.0000i	−0.517780	−	0.517780i	−0.916899	+	0.399119i	$0.869316\pi$
$374$	−2.82843			−0.146254
$375$	−19.0526	+	3.46410i	−0.983870	+	0.178885i
$376$	8.00000			0.412568
$377$	−1.27135	−	1.27135i	−0.0654778	−	0.0654778i
$378$	7.53177	−	7.53177i	0.387392	−	0.387392i
$379$			12.0000i			0.616399i	0.951322	+	0.308199i	$0.0997264\pi$
$379$			12.0000i			0.616399i	−0.951322	+	0.308199i	$0.900274\pi$
$380$	10.3923	−	3.46410i	0.533114	−	0.177705i
$381$	13.5959			0.696540
$382$	−15.3485	+	15.3485i	−0.785296	+	0.785296i
$383$	−6.11756	+	6.11756i	−0.312593	+	0.312593i	−0.845913	−	0.533321i	$-0.820944\pi$
$383$	−6.11756	+	6.11756i	−0.312593	+	0.312593i	0.533321	+	0.845913i	$0.320944\pi$
$384$	−1.73205			−0.0883883
$385$	2.60612	+	1.30306i	0.132820	+	0.0664102i
$386$			9.89949i			0.503871i
$387$	−7.34847	+	7.34847i	−0.373544	+	0.373544i
$388$	−3.00000	−	3.00000i	−0.152302	−	0.152302i
$389$	21.0703			1.06831			0.534154	−	0.845387i	$-0.320630\pi$
$389$	21.0703			1.06831			0.534154	+	0.845387i	$0.320630\pi$
$390$	−1.10102	+	2.20204i	−0.0557523	+	0.111505i
$391$	−10.8990			−0.551185
$392$	1.97846	+	1.97846i	0.0999271	+	0.0999271i
$393$	12.9029	−	12.9029i	0.650865	−	0.650865i
$394$			6.89898i			0.347566i
$395$	6.29253	+	18.8776i	0.316611	+	0.949834i
$396$			1.90702i			0.0958315i
$397$	−16.6969	+	16.6969i	−0.837995	+	0.837995i	−0.988595	−	0.150600i	$-0.951880\pi$
$397$	−16.6969	+	16.6969i	−0.837995	+	0.837995i	0.150600	+	0.988595i	$0.451880\pi$
$398$	−7.56388	+	7.56388i	−0.379143	+	0.379143i
$399$			17.3939i			0.870783i
$400$	−4.00000	+	3.00000i	−0.200000	+	0.150000i
$401$			4.38551i			0.219002i	0.993987	+	0.109501i	$0.0349252\pi$
$401$			4.38551i			0.219002i	−0.993987	+	0.109501i	$0.965075\pi$
$402$	14.6349	+	14.6349i	0.729925	+	0.729925i
$403$	−0.449490	−	0.449490i	−0.0223907	−	0.0223907i
$404$	9.89949			0.492518
$405$	19.0919	−	6.36396i	0.948683	−	0.316228i
$406$	5.79796			0.287748
$407$		0			0
$408$	5.44949	+	5.44949i	0.269790	+	0.269790i
$409$			31.3939i			1.55233i	0.630532	+	0.776164i	$0.282837\pi$
$409$			31.3939i			1.55233i	−0.630532	+	0.776164i	$0.717163\pi$
$410$	−2.82843	+	5.65685i	−0.139686	+	0.279372i
$411$			33.1626i			1.63579i
$412$	−3.44949	+	3.44949i	−0.169944	+	0.169944i
$413$	5.22826	−	5.22826i	0.257266	−	0.257266i
$414$			7.34847i			0.361158i
$415$	0.898979	−	1.79796i	0.0441292	−	0.0882583i
$416$			0.635674i			0.0311665i
$417$	16.5959	−	16.5959i	0.812706	−	0.812706i
$418$	−2.20204	−	2.20204i	−0.107705	−	0.107705i
$419$	−35.9910			−1.75828			−0.879138	−	0.476567i	$-0.841881\pi$
$419$	−35.9910			−1.75828			−0.879138	+	0.476567i	$0.841881\pi$
$420$	−2.51059	−	7.53177i	−0.122504	−	0.367513i
$421$	−2.00000			−0.0974740			−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000			−0.0974740			−0.0487370	+	0.998812i	$0.515520\pi$
$422$	16.0492	+	16.0492i	0.781261	+	0.781261i
$423$	−16.9706	+	16.9706i	−0.825137	+	0.825137i
$424$			6.00000i			0.291386i
$425$	22.0239	+	3.14626i	1.06831	+	0.152616i
$426$	15.7980			0.765414
$427$	−6.44949	+	6.44949i	−0.312113	+	0.312113i
$428$	0.778539	−	0.778539i	0.0376321	−	0.0376321i
$429$	0.699891			0.0337910
$430$	2.44949	+	7.34847i	0.118125	+	0.354375i
$431$		−	27.6486i		−	1.33179i	−0.746047	−	0.665893i	$-0.768051\pi$
$431$		−	27.6486i		−	1.33179i	0.746047	−	0.665893i	$-0.231949\pi$
$432$	3.67423	−	3.67423i	0.176777	−	0.176777i
$433$	9.79796	+	9.79796i	0.470860	+	0.470860i	0.902193	−	0.431333i	$-0.141957\pi$
$433$	9.79796	+	9.79796i	0.470860	+	0.470860i	−0.431333	+	0.902193i	$0.641957\pi$
$434$	2.04989			0.0983978
$435$	9.79796	+	4.89898i	0.469776	+	0.234888i
$436$	6.89898			0.330401
$437$	−8.48528	−	8.48528i	−0.405906	−	0.405906i
$438$	−8.48528	+	8.48528i	−0.405442	+	0.405442i
$439$			6.89898i			0.329270i	0.986355	+	0.164635i	$0.0526447\pi$
$439$			6.89898i			0.329270i	−0.986355	+	0.164635i	$0.947355\pi$
$440$	1.27135	+	0.635674i	0.0606092	+	0.0303046i
$441$	−8.39388			−0.399708
$442$	2.00000	−	2.00000i	0.0951303	−	0.0951303i
$443$	12.0922	−	12.0922i	0.574520	−	0.574520i	−0.358868	−	0.933388i	$-0.616837\pi$
$443$	12.0922	−	12.0922i	0.574520	−	0.574520i	0.933388	+	0.358868i	$0.116837\pi$
$444$		0			0
$445$	−38.6969	+	12.8990i	−1.83441	+	0.611470i
$446$		−	11.9494i		−	0.565820i
$447$	8.31031	+	8.31031i	0.393064	+	0.393064i
$448$	−1.44949	−	1.44949i	−0.0684820	−	0.0684820i
$449$	10.0424			0.473928			0.236964	−	0.971518i	$-0.423848\pi$
$449$	10.0424			0.473928			0.236964	+	0.971518i	$0.423848\pi$
$450$	2.12132	−	14.8492i	0.100000	−	0.700000i
$451$	1.79796			0.0846626
$452$	−5.51399	−	5.51399i	−0.259356	−	0.259356i
$453$	8.69694	+	8.69694i	0.408618	+	0.408618i
$454$			18.8990i			0.886973i
$455$	−2.76421	+	0.921404i	−0.129588	+	0.0431961i
$456$			8.48528i			0.397360i
$457$	16.8990	−	16.8990i	0.790501	−	0.790501i	−0.191075	−	0.981576i	$-0.561197\pi$
$457$	16.8990	−	16.8990i	0.790501	−	0.790501i	0.981576	+	0.191075i	$0.0611972\pi$
$458$	−8.16744	+	8.16744i	−0.381640	+	0.381640i
$459$	−23.1202			−1.07916
$460$	4.89898	+	2.44949i	0.228416	+	0.114208i
$461$		−	3.11416i		−	0.145041i	−0.997367	−	0.0725204i	$-0.976896\pi$
$461$		−	3.11416i		−	0.145041i	0.997367	−	0.0725204i	$-0.0231042\pi$
$462$	−1.59592	+	1.59592i	−0.0742488	+	0.0742488i
$463$	11.3485	+	11.3485i	0.527408	+	0.527408i	0.919799	−	0.392391i	$-0.128352\pi$
$463$	11.3485	+	11.3485i	0.527408	+	0.527408i	−0.392391	+	0.919799i	$0.628352\pi$
$464$	2.82843			0.131306
$465$	3.46410	+	1.73205i	0.160644	+	0.0803219i
$466$	1.10102			0.0510038
$467$	−28.4914	−	28.4914i	−1.31842	−	1.31842i	−0.915025	−	0.403398i	$-0.867829\pi$
$467$	−28.4914	−	28.4914i	−1.31842	−	1.31842i	−0.403398	−	0.915025i	$-0.632171\pi$
$468$	−1.34847	−	1.34847i	−0.0623330	−	0.0623330i
$469$			24.4949i			1.13107i
$470$	5.65685	+	16.9706i	0.260931	+	0.782794i
$471$	41.3939			1.90733
$472$	2.55051	−	2.55051i	0.117397	−	0.117397i
$473$	1.55708	−	1.55708i	0.0715945	−	0.0715945i
$474$	−15.4135			−0.707965
$475$	14.6969	+	19.5959i	0.674342	+	0.899122i
$476$			9.12096i			0.418058i
$477$	−12.7279	−	12.7279i	−0.582772	−	0.582772i
$478$	−4.24745	−	4.24745i	−0.194274	−	0.194274i
$479$	26.0915			1.19215			0.596076	−	0.802928i	$-0.296726\pi$
$479$	26.0915			1.19215			0.596076	+	0.802928i	$0.296726\pi$
$480$	−1.22474	−	3.67423i	−0.0559017	−	0.167705i
$481$		0			0
$482$	−16.1920	−	16.1920i	−0.737526	−	0.737526i
$483$	−6.14966	+	6.14966i	−0.279819	+	0.279819i
$484$			10.5959i			0.481633i
$485$	4.24264	−	8.48528i	0.192648	−	0.385297i
$486$			15.5885i			0.707107i
$487$	17.1464	−	17.1464i	0.776979	−	0.776979i	−0.202337	−	0.979316i	$-0.564854\pi$
$487$	17.1464	−	17.1464i	0.776979	−	0.776979i	0.979316	+	0.202337i	$0.0648537\pi$
$488$	−3.14626	+	3.14626i	−0.142425	+	0.142425i
$489$			42.4949i			1.92169i
$490$	−2.79796	+	5.59592i	−0.126399	+	0.252798i
$491$		−	18.5919i		−	0.839039i	−0.907746	−	0.419519i	$-0.862199\pi$
$491$		−	18.5919i		−	0.839039i	0.907746	−	0.419519i	$-0.137801\pi$
$492$	−3.46410	−	3.46410i	−0.156174	−	0.156174i
$493$	−8.89898	−	8.89898i	−0.400790	−	0.400790i
$494$	3.11416			0.140113
$495$	−4.04541	+	1.34847i	−0.181828	+	0.0606092i
$496$	1.00000			0.0449013
$497$	13.2207	+	13.2207i	0.593031	+	0.593031i
$498$	1.10102	+	1.10102i	0.0493379	+	0.0493379i
$499$		−	5.55051i		−	0.248475i	−0.992253	−	0.124237i	$-0.960352\pi$
$499$		−	5.55051i		−	0.248475i	0.992253	−	0.124237i	$-0.0396485\pi$
$500$	−9.19239	−	6.36396i	−0.411096	−	0.284605i
$501$		−	29.6985i		−	1.32683i
$502$	−13.3485	+	13.3485i	−0.595771	+	0.595771i
$503$	24.2487	−	24.2487i	1.08120	−	1.08120i	0.0847985	−	0.996398i	$-0.472975\pi$
$503$	24.2487	−	24.2487i	1.08120	−	1.08120i	0.996398	−	0.0847985i	$-0.0270246\pi$
$504$	6.14966			0.273928
$505$	7.00000	+	21.0000i	0.311496	+	0.934488i
$506$		−	1.55708i		−	0.0692206i
$507$	15.4268	−	15.4268i	0.685128	−	0.685128i
$508$	5.55051	+	5.55051i	0.246264	+	0.246264i
$509$	17.9562			0.795894			0.397947	−	0.917408i	$-0.369723\pi$
$509$	17.9562			0.795894			0.397947	+	0.917408i	$0.369723\pi$
$510$	−7.70674	+	15.4135i	−0.341260	+	0.682521i
$511$	−14.2020			−0.628261
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−18.0000	−	18.0000i	−0.794719	−	0.794719i
$514$		−	18.8990i		−	0.833598i
$515$	−9.75663	−	4.87832i	−0.429929	−	0.214964i
$516$	−6.00000			−0.264135
$517$	3.59592	−	3.59592i	0.158148	−	0.158148i
$518$		0			0
$519$	−0.349945			−0.0153609
$520$	−1.34847	+	0.449490i	−0.0591343	+	0.0197114i
$521$			25.1701i			1.10272i	0.834267	+	0.551361i	$0.185891\pi$
$521$			25.1701i			1.10272i	−0.834267	+	0.551361i	$0.814109\pi$
$522$	−6.00000	+	6.00000i	−0.262613	+	0.262613i
$523$	31.5959	+	31.5959i	1.38159	+	1.38159i	0.841794	+	0.539799i	$0.181500\pi$
$523$	31.5959	+	31.5959i	1.38159	+	1.38159i	0.539799	+	0.841794i	$0.318500\pi$
$524$	10.5352			0.460231
$525$	14.2020	−	10.6515i	0.619828	−	0.464871i
$526$	28.2474			1.23165
$527$	−3.14626	−	3.14626i	−0.137053	−	0.137053i
$528$	−0.778539	+	0.778539i	−0.0338816	+	0.0338816i
$529$			17.0000i			0.739130i
$530$	−12.7279	+	4.24264i	−0.552866	+	0.184289i
$531$			10.8209i			0.469587i
$532$	−7.10102	+	7.10102i	−0.307868	+	0.307868i
$533$	−1.27135	+	1.27135i	−0.0550682	+	0.0550682i
$534$		−	31.5959i		−	1.36729i
$535$	2.20204	+	1.10102i	0.0952025	+	0.0476013i
$536$			11.9494i			0.516135i
$537$	4.59259	+	4.59259i	0.198185	+	0.198185i
$538$	−4.00000	−	4.00000i	−0.172452	−	0.172452i
$539$	1.77859			0.0766093
$540$	10.3923	+	5.19615i	0.447214	+	0.223607i
$541$	24.6969			1.06180			0.530902	−	0.847433i	$-0.321853\pi$
$541$	24.6969			1.06180			0.530902	+	0.847433i	$0.321853\pi$
$542$	9.75663	+	9.75663i	0.419083	+	0.419083i
$543$	−4.34847	−	4.34847i	−0.186611	−	0.186611i
$544$			4.44949i			0.190770i
$545$	4.87832	+	14.6349i	0.208964	+	0.626892i
$546$		−	2.25697i		−	0.0965893i
$547$	−8.24745	+	8.24745i	−0.352635	+	0.352635i	−0.861089	−	0.508454i	$-0.830217\pi$
$547$	−8.24745	+	8.24745i	−0.352635	+	0.352635i	0.508454	+	0.861089i	$0.330217\pi$
$548$	−13.5386	+	13.5386i	−0.578339	+	0.578339i
$549$		−	13.3485i		−	0.569699i
$550$	−0.449490	+	3.14643i	−0.0191663	+	0.134164i
$551$		−	13.8564i		−	0.590303i
$552$	−3.00000	+	3.00000i	−0.127688	+	0.127688i
$553$	−12.8990	−	12.8990i	−0.548520	−	0.548520i
$554$	24.5344			1.04237
$555$		0			0
$556$	13.5505			0.574670
$557$	−17.7491	−	17.7491i	−0.752054	−	0.752054i	0.222809	−	0.974862i	$-0.428477\pi$
$557$	−17.7491	−	17.7491i	−0.752054	−	0.752054i	−0.974862	+	0.222809i	$0.928477\pi$
$558$	−2.12132	+	2.12132i	−0.0898027	+	0.0898027i
$559$			2.20204i			0.0931364i
$560$	2.04989	−	4.09978i	0.0866236	−	0.173247i
$561$	4.89898			0.206835
$562$	−4.00000	+	4.00000i	−0.168730	+	0.168730i
$563$	−8.48528	+	8.48528i	−0.357612	+	0.357612i	−0.862932	−	0.505320i	$-0.831374\pi$
$563$	−8.48528	+	8.48528i	−0.357612	+	0.357612i	0.505320	+	0.862932i	$0.331374\pi$
$564$	−13.8564			−0.583460
$565$	7.79796	−	15.5959i	0.328063	−	0.656125i
$566$		−	8.83523i		−	0.371372i
$567$	−13.0454	+	13.0454i	−0.547856	+	0.547856i
$568$	6.44949	+	6.44949i	0.270615	+	0.270615i
$569$	34.5768			1.44953			0.724767	−	0.688994i	$-0.241947\pi$
$569$	34.5768			1.44953			0.724767	+	0.688994i	$0.241947\pi$
$570$	−18.0000	+	6.00000i	−0.753937	+	0.251312i
$571$	−18.9444			−0.792798			−0.396399	−	0.918078i	$-0.629740\pi$
$571$	−18.9444			−0.792798			−0.396399	+	0.918078i	$0.629740\pi$
$572$	0.285729	+	0.285729i	0.0119469	+	0.0119469i
$573$	26.5843	−	26.5843i	1.11058	−	1.11058i
$574$		−	5.79796i		−	0.242002i
$575$	−1.73205	+	12.1244i	−0.0722315	+	0.505621i
$576$	3.00000			0.125000
$577$	−10.7980	+	10.7980i	−0.449525	+	0.449525i	−0.895197	−	0.445672i	$-0.852965\pi$
$577$	−10.7980	+	10.7980i	−0.449525	+	0.449525i	0.445672	+	0.895197i	$0.352965\pi$
$578$	1.97846	−	1.97846i	0.0822929	−	0.0822929i
$579$		−	17.1464i		−	0.712581i
$580$	2.00000	+	6.00000i	0.0830455	+	0.249136i
$581$			1.84281i			0.0764525i
$582$	5.19615	+	5.19615i	0.215387	+	0.215387i
$583$	2.69694	+	2.69694i	0.111696	+	0.111696i
$584$	−6.92820			−0.286691
$585$	1.90702	−	3.81405i	0.0788457	−	0.157691i
$586$	−18.0000			−0.743573
$587$	−17.6062	−	17.6062i	−0.726687	−	0.726687i	0.243271	−	0.969958i	$-0.421780\pi$
$587$	−17.6062	−	17.6062i	−0.726687	−	0.726687i	−0.969958	+	0.243271i	$0.921780\pi$
$588$	−3.42679	−	3.42679i	−0.141318	−	0.141318i
$589$		−	4.89898i		−	0.201859i
$590$	7.21393	+	3.60697i	0.296993	+	0.148496i
$591$		−	11.9494i		−	0.491532i
$592$		0			0
$593$	21.5631	−	21.5631i	0.885492	−	0.885492i	−0.108594	−	0.994086i	$-0.534635\pi$
$593$	21.5631	−	21.5631i	0.885492	−	0.885492i	0.994086	+	0.108594i	$0.0346348\pi$
$594$		−	3.30306i		−	0.135526i
$595$	−19.3485	+	6.44949i	−0.793210	+	0.264403i
$596$			6.78534i			0.277938i
$597$	13.1010	−	13.1010i	0.536189	−	0.536189i
$598$	1.10102	+	1.10102i	0.0450241	+	0.0450241i
$599$	16.3349			0.667425			0.333713	−	0.942675i	$-0.391698\pi$
$599$	16.3349			0.667425			0.333713	+	0.942675i	$0.391698\pi$
$600$	6.92820	−	5.19615i	0.282843	−	0.212132i
$601$	−5.10102			−0.208075			−0.104037	−	0.994573i	$-0.533176\pi$
$601$	−5.10102			−0.208075			−0.104037	+	0.994573i	$0.533176\pi$
$602$	−5.02118	−	5.02118i	−0.204648	−	0.204648i
$603$	−25.3485	−	25.3485i	−1.03227	−	1.03227i
$604$			7.10102i			0.288936i
$605$	−22.4773	+	7.49245i	−0.913834	+	0.304611i
$606$	−17.1464			−0.696526
$607$	−1.44949	+	1.44949i	−0.0588330	+	0.0588330i	−0.735911	−	0.677078i	$-0.763246\pi$
$607$	−1.44949	+	1.44949i	−0.0588330	+	0.0588330i	0.677078	+	0.735911i	$0.263246\pi$
$608$	−3.46410	+	3.46410i	−0.140488	+	0.140488i
$609$	−10.0424			−0.406937
$610$	−8.89898	−	4.44949i	−0.360309	−	0.180155i
$611$			5.08540i			0.205733i
$612$	−9.43879	−	9.43879i	−0.381541	−	0.381541i
$613$	28.0454	+	28.0454i	1.13274	+	1.13274i	0.989719	+	0.143024i	$0.0456827\pi$
$613$	28.0454	+	28.0454i	1.13274	+	1.13274i	0.143024	+	0.989719i	$0.454317\pi$
$614$	−4.73545			−0.191107
$615$	4.89898	−	9.79796i	0.197546	−	0.395092i
$616$	−1.30306			−0.0525018
$617$	−18.7347	−	18.7347i	−0.754231	−	0.754231i	0.221034	−	0.975266i	$-0.429057\pi$
$617$	−18.7347	−	18.7347i	−0.754231	−	0.754231i	−0.975266	+	0.221034i	$0.929057\pi$
$618$	5.97469	−	5.97469i	0.240337	−	0.240337i
$619$			10.9444i			0.439892i	0.975512	+	0.219946i	$0.0705881\pi$
$619$			10.9444i			0.439892i	−0.975512	+	0.219946i	$0.929412\pi$
$620$	0.707107	+	2.12132i	0.0283981	+	0.0851943i
$621$		−	12.7279i		−	0.510754i
$622$	−18.4495	+	18.4495i	−0.739757	+	0.739757i
$623$	26.4415	−	26.4415i	1.05935	−	1.05935i
$624$		−	1.10102i		−	0.0440761i
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$			21.0703i			0.842140i
$627$	3.81405	+	3.81405i	0.152318	+	0.152318i
$628$	16.8990	+	16.8990i	0.674343	+	0.674343i
$629$		0			0
$630$	4.34847	+	13.0454i	0.173247	+	0.519741i
$631$	−28.0000			−1.11466			−0.557331	−	0.830290i	$-0.688175\pi$
$631$	−28.0000			−1.11466			−0.557331	+	0.830290i	$0.688175\pi$
$632$	−6.29253	−	6.29253i	−0.250303	−	0.250303i
$633$	−27.7980	−	27.7980i	−1.10487	−	1.10487i
$634$		−	15.7980i		−	0.627417i
$635$	−7.84961	+	15.6992i	−0.311502	+	0.623004i
$636$		−	10.3923i		−	0.412082i
$637$	−1.25765	+	1.25765i	−0.0498301	+	0.0498301i
$638$	1.27135	−	1.27135i	0.0503332	−	0.0503332i
$639$	−27.3629			−1.08246
$640$	1.00000	−	2.00000i	0.0395285	−	0.0790569i
$641$			13.2207i			0.522188i	0.965313	+	0.261094i	$0.0840832\pi$
$641$			13.2207i			0.522188i	−0.965313	+	0.261094i	$0.915917\pi$
$642$	−1.34847	+	1.34847i	−0.0532198	+	0.0532198i
$643$	−12.0000	−	12.0000i	−0.473234	−	0.473234i	0.429726	−	0.902959i	$-0.358610\pi$
$643$	−12.0000	−	12.0000i	−0.473234	−	0.473234i	−0.902959	+	0.429726i	$0.858610\pi$
$644$	−5.02118			−0.197862
$645$	−4.24264	−	12.7279i	−0.167054	−	0.501161i
$646$	21.7980			0.857629
$647$	9.93160	+	9.93160i	0.390452	+	0.390452i	0.874848	−	0.484397i	$-0.160961\pi$
$647$	9.93160	+	9.93160i	0.390452	+	0.390452i	−0.484397	+	0.874848i	$0.660961\pi$
$648$	−6.36396	+	6.36396i	−0.250000	+	0.250000i
$649$		−	2.29286i		−	0.0900025i
$650$	−1.90702	−	2.54270i	−0.0747996	−	0.0997328i
$651$	−3.55051			−0.139155
$652$	−17.3485	+	17.3485i	−0.679418	+	0.679418i
$653$	−30.8270	+	30.8270i	−1.20635	+	1.20635i	−0.234153	+	0.972200i	$0.575232\pi$
$653$	−30.8270	+	30.8270i	−1.20635	+	1.20635i	−0.972200	+	0.234153i	$0.924768\pi$
$654$	−11.9494			−0.467258
$655$	7.44949	+	22.3485i	0.291076	+	0.873227i
$656$		−	2.82843i		−	0.110432i
$657$	14.6969	−	14.6969i	0.573382	−	0.573382i
$658$	−11.5959	−	11.5959i	−0.452056	−	0.452056i
$659$	−17.4634			−0.680276			−0.340138	−	0.940375i	$-0.610474\pi$
$659$	−17.4634			−0.680276			−0.340138	+	0.940375i	$0.610474\pi$
$660$	−2.20204	−	1.10102i	−0.0857143	−	0.0428572i
$661$	−2.00000			−0.0777910			−0.0388955	−	0.999243i	$-0.512384\pi$
$661$	−2.00000			−0.0777910			−0.0388955	+	0.999243i	$0.512384\pi$
$662$	3.00340	+	3.00340i	0.116730	+	0.116730i
$663$	−3.46410	+	3.46410i	−0.134535	+	0.134535i
$664$			0.898979i			0.0348872i
$665$	−20.0847	−	10.0424i	−0.778852	−	0.389426i
$666$		0			0
$667$	4.89898	−	4.89898i	0.189689	−	0.189689i
$668$	12.1244	−	12.1244i	0.469105	−	0.469105i
$669$			20.6969i			0.800190i
$670$	−25.3485	+	8.44949i	−0.979297	+	0.326432i
$671$			2.82843i			0.109190i
$672$	2.51059	+	2.51059i	0.0968481	+	0.0968481i
$673$	15.7980	+	15.7980i	0.608967	+	0.608967i	0.942676	−	0.333709i	$-0.108300\pi$
$673$	15.7980	+	15.7980i	0.608967	+	0.608967i	−0.333709	+	0.942676i	$0.608300\pi$
$674$	−6.92820			−0.266864
$675$	−3.67423	+	25.7196i	−0.141421	+	0.989949i
$676$	12.5959			0.484458
$677$	12.7279	+	12.7279i	0.489174	+	0.489174i	0.908045	−	0.418872i	$-0.137574\pi$
$677$	12.7279	+	12.7279i	0.489174	+	0.489174i	−0.418872	+	0.908045i	$0.637574\pi$
$678$	9.55051	+	9.55051i	0.366785	+	0.366785i
$679$			8.69694i			0.333758i
$680$	−9.43879	+	3.14626i	−0.361961	+	0.120654i
$681$		−	32.7340i		−	1.25437i
$682$	0.449490	−	0.449490i	0.0172119	−	0.0172119i
$683$	−9.26382	+	9.26382i	−0.354470	+	0.354470i	−0.861770	−	0.507300i	$-0.830644\pi$
$683$	−9.26382	+	9.26382i	−0.354470	+	0.354470i	0.507300	+	0.861770i	$0.330644\pi$
$684$		−	14.6969i		−	0.561951i
$685$	−38.2929	−	19.1464i	−1.46309	−	0.731547i
$686$		−	20.0847i		−	0.766838i
$687$	14.1464	−	14.1464i	0.539720	−	0.539720i
$688$	−2.44949	−	2.44949i	−0.0933859	−	0.0933859i
$689$	−3.81405			−0.145304
$690$	−8.48528	−	4.24264i	−0.323029	−	0.161515i
$691$	−28.4949			−1.08400			−0.541998	−	0.840379i	$-0.682332\pi$
$691$	−28.4949			−1.08400			−0.541998	+	0.840379i	$0.682332\pi$
$692$	−0.142865	−	0.142865i	−0.00543090	−	0.00543090i
$693$	2.76421	−	2.76421i	0.105004	−	0.105004i
$694$		−	15.1010i		−	0.573227i
$695$	9.58166	+	28.7450i	0.363453	+	1.09036i
$696$	−4.89898			−0.185695
$697$	−8.89898	+	8.89898i	−0.337073	+	0.337073i
$698$	22.1988	−	22.1988i	0.840238	−	0.840238i
$699$	−1.90702			−0.0721303
$700$	10.1464	+	1.44949i	0.383499	+	0.0547856i
$701$		−	1.69994i		−	0.0642060i	−0.999485	−	0.0321030i	$-0.989780\pi$
$701$		−	1.69994i		−	0.0642060i	0.999485	−	0.0321030i	$-0.0102205\pi$
$702$	2.33562	+	2.33562i	0.0881522	+	0.0881522i
$703$		0			0
$704$	−0.635674			−0.0239579
$705$	−9.79796	−	29.3939i	−0.369012	−	1.10704i
$706$	15.1464			0.570043
$707$	−14.3492	−	14.3492i	−0.539658	−	0.539658i
$708$	−4.41761	+	4.41761i	−0.166024	+	0.166024i
$709$			32.0454i			1.20349i	0.798688	+	0.601745i	$0.205528\pi$
$709$			32.0454i			1.20349i	−0.798688	+	0.601745i	$0.794472\pi$
$710$	−9.12096	+	18.2419i	−0.342303	+	0.684607i
$711$	26.6969			1.00121
$712$	12.8990	−	12.8990i	0.483410	−	0.483410i
$713$	1.73205	−	1.73205i	0.0648658	−	0.0648658i
$714$		−	15.7980i		−	0.591224i
$715$	−0.404082	+	0.808164i	−0.0151118	+	0.0302236i
$716$			3.74983i			0.140138i
$717$	7.35680	+	7.35680i	0.274745	+	0.274745i
$718$	2.65153	+	2.65153i	0.0989542	+	0.0989542i
$719$	−0.921404			−0.0343626			−0.0171813	−	0.999852i	$-0.505469\pi$
$719$	−0.921404			−0.0343626			−0.0171813	+	0.999852i	$0.505469\pi$
$720$	2.12132	+	6.36396i	0.0790569	+	0.237171i
$721$	10.0000			0.372419
$722$	3.53553	+	3.53553i	0.131579	+	0.131579i
$723$	28.0454	+	28.0454i	1.04302	+	1.04302i
$724$		−	3.55051i		−	0.131954i
$725$	−11.3137	+	8.48528i	−0.420181	+	0.315135i
$726$		−	18.3527i		−	0.681131i
$727$	20.1464	−	20.1464i	0.747190	−	0.747190i	−0.226761	−	0.973950i	$-0.572814\pi$
$727$	20.1464	−	20.1464i	0.747190	−	0.747190i	0.973950	+	0.226761i	$0.0728136\pi$
$728$	0.921404	−	0.921404i	0.0341495	−	0.0341495i
$729$		−	27.0000i		−	1.00000i
$730$	−4.89898	−	14.6969i	−0.181319	−	0.543958i
$731$			15.4135i			0.570088i
$732$	5.44949	−	5.44949i	0.201419	−	0.201419i
$733$	−27.3939	−	27.3939i	−1.01182	−	1.01182i	−0.999929	−	0.0118866i	$-0.996216\pi$
$733$	−27.3939	−	27.3939i	−1.01182	−	1.01182i	−0.0118866	−	0.999929i	$-0.503784\pi$
$734$	−5.02118			−0.185335
$735$	4.84621	−	9.69241i	0.178755	−	0.357510i
$736$	−2.44949			−0.0902894
$737$	5.37113	+	5.37113i	0.197848	+	0.197848i
$738$	6.00000	+	6.00000i	0.220863	+	0.220863i
$739$		−	42.9444i		−	1.57973i	−0.613278	−	0.789867i	$-0.710149\pi$
$739$		−	42.9444i		−	1.57973i	0.613278	−	0.789867i	$-0.289851\pi$
$740$		0			0
$741$	−5.39388			−0.198149
$742$	8.69694	−	8.69694i	0.319275	−	0.319275i
$743$	3.92480	−	3.92480i	0.143987	−	0.143987i	−0.631439	−	0.775426i	$-0.717535\pi$
$743$	3.92480	−	3.92480i	0.143987	−	0.143987i	0.775426	+	0.631439i	$0.217535\pi$
$744$	−1.73205			−0.0635001
$745$	−14.3939	+	4.79796i	−0.527351	+	0.175784i
$746$			14.1421i			0.517780i
$747$	−1.90702	−	1.90702i	−0.0697743	−	0.0697743i
$748$	2.00000	+	2.00000i	0.0731272	+	0.0731272i
$749$	−2.25697			−0.0824678
$750$	15.9217	+	11.0227i	0.581378	+	0.402492i
$751$	−32.6969			−1.19313			−0.596564	−	0.802565i	$-0.703468\pi$
$751$	−32.6969			−1.19313			−0.596564	+	0.802565i	$0.703468\pi$
$752$	−5.65685	−	5.65685i	−0.206284	−	0.206284i
$753$	23.1202	−	23.1202i	0.842548	−	0.842548i
$754$			1.79796i			0.0654778i
$755$	−15.0635	+	5.02118i	−0.548218	+	0.182739i
$756$	−10.6515			−0.387392
$757$	13.3485	−	13.3485i	0.485158	−	0.485158i	−0.421616	−	0.906774i	$-0.638537\pi$
$757$	13.3485	−	13.3485i	0.485158	−	0.485158i	0.906774	+	0.421616i	$0.138537\pi$
$758$	8.48528	−	8.48528i	0.308199	−	0.308199i
$759$			2.69694i			0.0978927i
$760$	−9.79796	−	4.89898i	−0.355409	−	0.177705i
$761$			49.0689i			1.77875i	0.457183	+	0.889373i	$0.348859\pi$
$761$			49.0689i			1.77875i	−0.457183	+	0.889373i	$0.651141\pi$
$762$	−9.61377	−	9.61377i	−0.348270	−	0.348270i
$763$	−10.0000	−	10.0000i	−0.362024	−	0.362024i
$764$	21.7060			0.785296
$765$	13.3485	−	26.6969i	0.482615	−	0.965230i
$766$	8.65153			0.312593
$767$	1.62129	+	1.62129i	0.0585415	+	0.0585415i
$768$	1.22474	+	1.22474i	0.0441942	+	0.0441942i
$769$			27.5959i			0.995134i	0.867425	+	0.497567i	$0.165773\pi$
$769$			27.5959i			0.995134i	−0.867425	+	0.497567i	$0.834227\pi$
$770$	−0.921404	−	2.76421i	−0.0332051	−	0.0996152i
$771$			32.7340i			1.17889i
$772$	7.00000	−	7.00000i	0.251936	−	0.251936i
$773$	10.2494	−	10.2494i	0.368647	−	0.368647i	−0.498337	−	0.866984i	$-0.666056\pi$
$773$	10.2494	−	10.2494i	0.368647	−	0.368647i	0.866984	+	0.498337i	$0.166056\pi$
$774$	10.3923			0.373544
$775$	−4.00000	+	3.00000i	−0.143684	+	0.107763i
$776$			4.24264i			0.152302i
$777$		0			0
$778$	−14.8990	−	14.8990i	−0.534154	−	0.534154i
$779$	−13.8564			−0.496457
$780$	2.33562	−	0.778539i	0.0836285	−	0.0278762i
$781$	5.79796			0.207467
$782$	7.70674	+	7.70674i	0.275593	+	0.275593i
$783$	10.3923	−	10.3923i	0.371391	−	0.371391i
$784$		−	2.79796i		−	0.0999271i
$785$	−23.8988	+	47.7975i	−0.852984	+	1.70597i
$786$	−18.2474			−0.650865
$787$	8.65153	−	8.65153i	0.308394	−	0.308394i	−0.535892	−	0.844286i	$-0.680025\pi$
$787$	8.65153	−	8.65153i	0.308394	−	0.308394i	0.844286	+	0.535892i	$0.180025\pi$
$788$	4.87832	−	4.87832i	0.173783	−	0.173783i
$789$	−48.9260			−1.74181
$790$	8.89898	−	17.7980i	0.316611	−	0.633223i
$791$			15.9849i			0.568359i
$792$	1.34847	−	1.34847i	0.0479158	−	0.0479158i
$793$	−2.00000	−	2.00000i	−0.0710221	−	0.0710221i
$794$	23.6130			0.837995
$795$	22.0454	−	7.34847i	0.781870	−	0.260623i
$796$	10.6969			0.379143
$797$	16.4778	+	16.4778i	0.583672	+	0.583672i	0.935910	−	0.352238i	$-0.114579\pi$
$797$	16.4778	+	16.4778i	0.583672	+	0.583672i	−0.352238	+	0.935910i	$0.614579\pi$
$798$	12.2993	−	12.2993i	0.435392	−	0.435392i
$799$			35.5959i			1.25929i
$800$	4.94975	+	0.707107i	0.175000	+	0.0250000i
$801$			54.7257i			1.93364i
$802$	3.10102	−	3.10102i	0.109501	−	0.109501i
$803$	−3.11416	+	3.11416i	−0.109896	+	0.109896i
$804$		−	20.6969i		−	0.729925i
$805$	−3.55051	−	10.6515i	−0.125139	−	0.375417i
$806$			0.635674i			0.0223907i
$807$	6.92820	+	6.92820i	0.243884	+	0.243884i
$808$	−7.00000	−	7.00000i	−0.246259	−	0.246259i
$809$	−34.6410			−1.21791			−0.608957	−	0.793204i	$-0.708412\pi$
$809$	−34.6410			−1.21791			−0.608957	+	0.793204i	$0.708412\pi$
$810$	−18.0000	−	9.00000i	−0.632456	−	0.316228i
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$	−4.09978	−	4.09978i	−0.143874	−	0.143874i
$813$	−16.8990	−	16.8990i	−0.592673	−	0.592673i
$814$		0			0
$815$	−49.0689	−	24.5344i	−1.71881	−	0.859404i
$816$		−	7.70674i		−	0.269790i
$817$	−12.0000	+	12.0000i	−0.419827	+	0.419827i
$818$	22.1988	−	22.1988i	0.776164	−	0.776164i
$819$			3.90918i			0.136598i
$820$	6.00000	−	2.00000i	0.209529	−	0.0698430i
$821$		−	45.9547i		−	1.60383i	−0.597438	−	0.801915i	$-0.703814\pi$
$821$		−	45.9547i		−	1.60383i	0.597438	−	0.801915i	$-0.296186\pi$
$822$	23.4495	−	23.4495i	0.817895	−	0.817895i
$823$	−25.1464	−	25.1464i	−0.876549	−	0.876549i	0.116626	−	0.993176i	$-0.462792\pi$
$823$	−25.1464	−	25.1464i	−0.876549	−	0.876549i	−0.993176	+	0.116626i	$0.962792\pi$
$824$	4.87832			0.169944
$825$	0.778539	−	5.44977i	0.0271053	−	0.189737i
$826$	−7.39388			−0.257266
$827$	−37.1195	−	37.1195i	−1.29077	−	1.29077i	−0.934310	−	0.356461i	$-0.883983\pi$
$827$	−37.1195	−	37.1195i	−1.29077	−	1.29077i	−0.356461	−	0.934310i	$-0.616017\pi$
$828$	5.19615	−	5.19615i	0.180579	−	0.180579i
$829$		−	30.6515i		−	1.06457i	−0.846565	−	0.532286i	$-0.821333\pi$
$829$		−	30.6515i		−	1.06457i	0.846565	−	0.532286i	$-0.178667\pi$
$830$	−1.90702	+	0.635674i	−0.0661938	+	0.0220646i
$831$	−42.4949			−1.47413
$832$	0.449490	−	0.449490i	0.0155833	−	0.0155833i
$833$	−8.80312	+	8.80312i	−0.305010	+	0.305010i
$834$	−23.4702			−0.812706
$835$	34.2929	+	17.1464i	1.18675	+	0.593377i
$836$			3.11416i			0.107705i
$837$	3.67423	−	3.67423i	0.127000	−	0.127000i
$838$	25.4495	+	25.4495i	0.879138	+	0.879138i
$839$	−33.3055			−1.14983			−0.574916	−	0.818212i	$-0.694965\pi$
$839$	−33.3055			−1.14983			−0.574916	+	0.818212i	$0.694965\pi$
$840$	−3.55051	+	7.10102i	−0.122504	+	0.245008i
$841$	−21.0000			−0.724138
$842$	1.41421	+	1.41421i	0.0487370	+	0.0487370i
$843$	6.92820	−	6.92820i	0.238620	−	0.238620i
$844$		−	22.6969i		−	0.781261i
$845$	8.90666	+	26.7200i	0.306398	+	0.919195i
$846$	24.0000			0.825137
$847$	15.3587	−	15.3587i	0.527730	−	0.527730i
$848$	4.24264	−	4.24264i	0.145693	−	0.145693i
$849$			15.3031i			0.525200i
$850$	−13.3485	−	17.7980i	−0.457849	−	0.610465i
$851$		0			0
$852$	−11.1708	−	11.1708i	−0.382707	−	0.382707i
$853$	20.0000	+	20.0000i	0.684787	+	0.684787i	0.961075	−	0.276288i	$-0.0891043\pi$
$853$	20.0000	+	20.0000i	0.684787	+	0.684787i	−0.276288	+	0.961075i	$0.589104\pi$
$854$	9.12096			0.312113
$855$	31.1769	−	10.3923i	1.06623	−	0.355409i
$856$	−1.10102			−0.0376321
$857$	−11.1708	−	11.1708i	−0.381589	−	0.381589i	0.490086	−	0.871674i	$-0.336966\pi$
$857$	−11.1708	−	11.1708i	−0.381589	−	0.381589i	−0.871674	+	0.490086i	$0.836966\pi$
$858$	−0.494897	−	0.494897i	−0.0168955	−	0.0168955i
$859$		−	39.8434i		−	1.35944i	−0.733473	−	0.679719i	$-0.762102\pi$
$859$		−	39.8434i		−	1.35944i	0.733473	−	0.679719i	$-0.237898\pi$
$860$	3.46410	−	6.92820i	0.118125	−	0.236250i
$861$			10.0424i			0.342243i
$862$	−19.5505	+	19.5505i	−0.665893	+	0.665893i
$863$	39.4872	−	39.4872i	1.34416	−	1.34416i	0.452290	−	0.891871i	$-0.350607\pi$
$863$	39.4872	−	39.4872i	1.34416	−	1.34416i	0.891871	−	0.452290i	$-0.149393\pi$
$864$	−5.19615			−0.176777
$865$	0.202041	−	0.404082i	0.00686960	−	0.0137392i
$866$		−	13.8564i		−	0.470860i
$867$	−3.42679	+	3.42679i	−0.116380	+	0.116380i
$868$	−1.44949	−	1.44949i	−0.0491989	−	0.0491989i
$869$	−5.65685			−0.191896
$870$	−3.46410	−	10.3923i	−0.117444	−	0.352332i
$871$	−7.59592			−0.257378
$872$	−4.87832	−	4.87832i	−0.165201	−	0.165201i
$873$	−9.00000	−	9.00000i	−0.304604	−	0.304604i
$874$			12.0000i			0.405906i
$875$	4.09978	+	22.5488i	0.138598	+	0.762288i
$876$	12.0000			0.405442
$877$	20.8990	−	20.8990i	0.705708	−	0.705708i	−0.259921	−	0.965630i	$-0.583697\pi$
$877$	20.8990	−	20.8990i	0.705708	−	0.705708i	0.965630	+	0.259921i	$0.0836967\pi$
$878$	4.87832	−	4.87832i	0.164635	−	0.164635i
$879$	31.1769			1.05157
$880$	−0.449490	−	1.34847i	−0.0151523	−	0.0454569i
$881$		−	5.02118i		−	0.169168i	−0.996416	−	0.0845839i	$-0.973044\pi$
$881$		−	5.02118i		−	0.169168i	0.996416	−	0.0845839i	$-0.0269561\pi$
$882$	5.93537	+	5.93537i	0.199854	+	0.199854i
$883$	19.1010	+	19.1010i	0.642801	+	0.642801i	0.951243	−	0.308442i	$-0.0998077\pi$
$883$	19.1010	+	19.1010i	0.642801	+	0.642801i	−0.308442	+	0.951243i	$0.599808\pi$
$884$	−2.82843			−0.0951303
$885$	−12.4949	−	6.24745i	−0.420011	−	0.210006i
$886$	−17.1010			−0.574520
$887$	−23.8988	−	23.8988i	−0.802442	−	0.802442i	0.181035	−	0.983477i	$-0.442055\pi$
$887$	−23.8988	−	23.8988i	−0.802442	−	0.802442i	−0.983477	+	0.181035i	$0.942055\pi$
$888$		0			0
$889$		−	16.0908i		−	0.539669i
$890$	36.4838	+	18.2419i	1.22294	+	0.611470i
$891$			5.72107i			0.191663i
$892$	−8.44949	+	8.44949i	−0.282910	+	0.282910i
$893$	−27.7128	+	27.7128i	−0.927374	+	0.927374i
$894$		−	11.7526i		−	0.393064i
$895$	−7.95459	+	2.65153i	−0.265893	+	0.0886309i
$896$			2.04989i			0.0684820i
$897$	−1.90702	−	1.90702i	−0.0636737	−	0.0636737i
$898$	−7.10102	−	7.10102i	−0.236964	−	0.236964i
$899$	2.82843			0.0943333
$900$	−12.0000	+	9.00000i	−0.400000	+	0.300000i
$901$	−26.6969			−0.889404
$902$	−1.27135	−	1.27135i	−0.0423313	−	0.0423313i
$903$	8.69694	+	8.69694i	0.289416	+	0.289416i
$904$			7.79796i			0.259356i
$905$	7.53177	−	2.51059i	0.250364	−	0.0834548i
$906$		−	12.2993i		−	0.408618i
$907$	−26.9444	+	26.9444i	−0.894674	+	0.894674i	−0.994959	−	0.100285i	$-0.968025\pi$
$907$	−26.9444	+	26.9444i	−0.894674	+	0.894674i	0.100285	+	0.994959i	$0.468025\pi$
$908$	13.3636	−	13.3636i	0.443487	−	0.443487i
$909$	29.6985			0.985037
$910$	2.60612	+	1.30306i	0.0863921	+	0.0431961i
$911$			22.6274i			0.749680i	0.927090	+	0.374840i	$0.122302\pi$
$911$			22.6274i			0.749680i	−0.927090	+	0.374840i	$0.877698\pi$
$912$	6.00000	−	6.00000i	0.198680	−	0.198680i
$913$	0.404082	+	0.404082i	0.0133732	+	0.0133732i
$914$	−23.8988			−0.790501
$915$	15.4135	+	7.70674i	0.509554	+	0.254777i
$916$	11.5505			0.381640
$917$	−15.2706	−	15.2706i	−0.504280	−	0.504280i
$918$	16.3485	+	16.3485i	0.539580	+	0.539580i
$919$		−	47.1918i		−	1.55672i	−0.627821	−	0.778358i	$-0.716053\pi$
$919$		−	47.1918i		−	1.55672i	0.627821	−	0.778358i	$-0.283947\pi$
$920$	−1.73205	−	5.19615i	−0.0571040	−	0.171312i
$921$	8.20204			0.270266
$922$	−2.20204	+	2.20204i	−0.0725204	+	0.0725204i
$923$	−4.09978	+	4.09978i	−0.134946	+	0.134946i
$924$	2.25697			0.0742488
$925$		0			0
$926$		−	16.0492i		−	0.527408i
$927$	−10.3485	+	10.3485i	−0.339888	+	0.339888i
$928$	−2.00000	−	2.00000i	−0.0656532	−	0.0656532i
$929$	20.1489			0.661065			0.330533	−	0.943795i	$-0.392772\pi$
$929$	20.1489			0.661065			0.330533	+	0.943795i	$0.392772\pi$
$930$	−1.22474	−	3.67423i	−0.0401610	−	0.120483i
$931$	−13.7071			−0.449233
$932$	−0.778539	−	0.778539i	−0.0255019	−	0.0255019i
$933$	31.9555	−	31.9555i	1.04617	−	1.04617i
$934$			40.2929i			1.31842i
$935$	−2.82843	+	5.65685i	−0.0924995	+	0.184999i
$936$			1.90702i			0.0623330i
$937$	10.5959	−	10.5959i	0.346154	−	0.346154i	−0.512521	−	0.858675i	$-0.671288\pi$
$937$	10.5959	−	10.5959i	0.346154	−	0.346154i	0.858675	+	0.512521i	$0.171288\pi$
$938$	17.3205	−	17.3205i	0.565535	−	0.565535i
$939$		−	36.4949i		−	1.19097i
$940$	8.00000	−	16.0000i	0.260931	−	0.521862i
$941$			50.0545i			1.63173i	0.578242	+	0.815865i	$0.303739\pi$
$941$			50.0545i			1.63173i	−0.578242	+	0.815865i	$0.696261\pi$
$942$	−29.2699	−	29.2699i	−0.953665	−	0.953665i
$943$	−4.89898	−	4.89898i	−0.159533	−	0.159533i
$944$	−3.60697			−0.117397
$945$	−7.53177	−	22.5953i	−0.245008	−	0.735025i
$946$	−2.20204			−0.0715945
$947$	30.8270	+	30.8270i	1.00174	+	1.00174i	0.999998	+	0.00174342i	$0.000554948\pi$
$947$	30.8270	+	30.8270i	1.00174	+	1.00174i	0.00174342	+	0.999998i	$0.499445\pi$
$948$	10.8990	+	10.8990i	0.353982	+	0.353982i
$949$		−	4.40408i		−	0.142963i
$950$	3.46410	−	24.2487i	0.112390	−	0.786732i
$951$			27.3629i			0.887302i
$952$	6.44949	−	6.44949i	0.209029	−	0.209029i
$953$	−19.4812	+	19.4812i	−0.631056	+	0.631056i	−0.948333	−	0.317277i	$-0.897232\pi$
$953$	−19.4812	+	19.4812i	−0.631056	+	0.631056i	0.317277	+	0.948333i	$0.397232\pi$
$954$			18.0000i			0.582772i
$955$	15.3485	+	46.0454i	0.496665	+	1.48999i
$956$			6.00680i			0.194274i
$957$	−2.20204	+	2.20204i	−0.0711819	+	0.0711819i
$958$	−18.4495	−	18.4495i	−0.596076	−	0.596076i
$959$	39.2480			1.26739
$960$	−1.73205	+	3.46410i	−0.0559017	+	0.111803i
$961$	1.00000			0.0322581
$962$		0			0
$963$	2.33562	−	2.33562i	0.0752642	−	0.0752642i
$964$			22.8990i			0.737526i
$965$	19.7990	+	9.89949i	0.637352	+	0.318676i
$966$	8.69694			0.279819
$967$	−25.8434	+	25.8434i	−0.831067	+	0.831067i	−0.987663	−	0.156596i	$-0.949948\pi$
$967$	−25.8434	+	25.8434i	−0.831067	+	0.831067i	0.156596	+	0.987663i	$0.449948\pi$
$968$	7.49245	−	7.49245i	0.240816	−	0.240816i
$969$	−37.7552			−1.21287
$970$	−9.00000	+	3.00000i	−0.288973	+	0.0963242i
$971$			18.4490i			0.592056i	0.955179	+	0.296028i	$0.0956622\pi$
$971$			18.4490i			0.592056i	−0.955179	+	0.296028i	$0.904338\pi$
$972$	11.0227	−	11.0227i	0.353553	−	0.353553i
$973$	−19.6413	−	19.6413i	−0.629672	−	0.629672i
$974$	−24.2487			−0.776979
$975$	3.30306	+	4.40408i	0.105783	+	0.141044i
$976$	4.44949			0.142425
$977$	35.4196	+	35.4196i	1.13317	+	1.13317i	0.989647	+	0.143525i	$0.0458439\pi$
$977$	35.4196	+	35.4196i	1.13317	+	1.13317i	0.143525	+	0.989647i	$0.454156\pi$
$978$	30.0484	−	30.0484i	0.960843	−	0.960843i
$979$		−	11.5959i		−	0.370607i
$980$	5.93537	−	1.97846i	0.189598	−	0.0631995i
$981$	20.6969			0.660802
$982$	−13.1464	+	13.1464i	−0.419519	+	0.419519i
$983$	1.73205	−	1.73205i	0.0552438	−	0.0552438i	−0.678945	−	0.734189i	$-0.737563\pi$
$983$	1.73205	−	1.73205i	0.0552438	−	0.0552438i	0.734189	+	0.678945i	$0.237563\pi$
$984$			4.89898i			0.156174i
$985$	13.7980	+	6.89898i	0.439640	+	0.219820i
$986$			12.5851i			0.400790i
$987$	20.0847	+	20.0847i	0.639304	+	0.639304i
$988$	−2.20204	−	2.20204i	−0.0700563	−	0.0700563i
$989$	−8.48528			−0.269816
$990$	3.81405	+	1.90702i	0.121218	+	0.0606092i
$991$	35.1010			1.11502			0.557510	−	0.830170i	$-0.311757\pi$
$991$	35.1010			1.11502			0.557510	+	0.830170i	$0.311757\pi$
$992$	−0.707107	−	0.707107i	−0.0224507	−	0.0224507i
$993$	−5.20204	−	5.20204i	−0.165082	−	0.165082i
$994$		−	18.6969i		−	0.593031i
$995$	7.56388	+	22.6916i	0.239791	+	0.719373i
$996$		−	1.55708i		−	0.0493379i
$997$	3.30306	−	3.30306i	0.104609	−	0.104609i	−0.652865	−	0.757474i	$-0.726433\pi$
$997$	3.30306	−	3.30306i	0.104609	−	0.104609i	0.757474	+	0.652865i	$0.226433\pi$
$998$	−3.92480	+	3.92480i	−0.124237	+	0.124237i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.d.683.2	yes	8
3.2	odd	2	inner	930.2.j.d.683.4	yes	8
5.2	odd	4	inner	930.2.j.d.497.4	yes	8
15.2	even	4	inner	930.2.j.d.497.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.d.497.2	✓	8	15.2	even	4	inner
930.2.j.d.497.4	yes	8	5.2	odd	4	inner
930.2.j.d.683.2	yes	8	1.1	even	1	trivial
930.2.j.d.683.4	yes	8	3.2	odd	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.22474 + 1.22474i) q^{3} +1.00000i q^{4} +(-2.12132 + 0.707107i) q^{5} -1.73205i q^{6} +(1.44949 - 1.44949i) q^{7} +(0.707107 - 0.707107i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.22474 + 1.22474i) q^{3} +1.00000i q^{4} +(-2.12132 + 0.707107i) q^{5} -1.73205i q^{6} +(1.44949 - 1.44949i) q^{7} +(0.707107 - 0.707107i) q^{8} +3.00000i q^{9} +(2.00000 + 1.00000i) q^{10} -0.635674i q^{11} +(-1.22474 + 1.22474i) q^{12} +(0.449490 + 0.449490i) q^{13} -2.04989 q^{14} +(-3.46410 - 1.73205i) q^{15} -1.00000 q^{16} +(3.14626 + 3.14626i) q^{17} +(2.12132 - 2.12132i) q^{18} +4.89898i q^{19} +(-0.707107 - 2.12132i) q^{20} +3.55051 q^{21} +(-0.449490 + 0.449490i) q^{22} +(-1.73205 + 1.73205i) q^{23} +1.73205 q^{24} +(4.00000 - 3.00000i) q^{25} -0.635674i q^{26} +(-3.67423 + 3.67423i) q^{27} +(1.44949 + 1.44949i) q^{28} -2.82843 q^{29} +(1.22474 + 3.67423i) q^{30} -1.00000 q^{31} +(0.707107 + 0.707107i) q^{32} +(0.778539 - 0.778539i) q^{33} -4.44949i q^{34} +(-2.04989 + 4.09978i) q^{35} -3.00000 q^{36} +(3.46410 - 3.46410i) q^{38} +1.10102i q^{39} +(-1.00000 + 2.00000i) q^{40} +2.82843i q^{41} +(-2.51059 - 2.51059i) q^{42} +(2.44949 + 2.44949i) q^{43} +0.635674 q^{44} +(-2.12132 - 6.36396i) q^{45} +2.44949 q^{46} +(5.65685 + 5.65685i) q^{47} +(-1.22474 - 1.22474i) q^{48} +2.79796i q^{49} +(-4.94975 - 0.707107i) q^{50} +7.70674i q^{51} +(-0.449490 + 0.449490i) q^{52} +(-4.24264 + 4.24264i) q^{53} +5.19615 q^{54} +(0.449490 + 1.34847i) q^{55} -2.04989i q^{56} +(-6.00000 + 6.00000i) q^{57} +(2.00000 + 2.00000i) q^{58} +3.60697 q^{59} +(1.73205 - 3.46410i) q^{60} -4.44949 q^{61} +(0.707107 + 0.707107i) q^{62} +(4.34847 + 4.34847i) q^{63} -1.00000i q^{64} +(-1.27135 - 0.635674i) q^{65} -1.10102 q^{66} +(-8.44949 + 8.44949i) q^{67} +(-3.14626 + 3.14626i) q^{68} -4.24264 q^{69} +(4.34847 - 1.44949i) q^{70} +9.12096i q^{71} +(2.12132 + 2.12132i) q^{72} +(-4.89898 - 4.89898i) q^{73} +(8.57321 + 1.22474i) q^{75} -4.89898 q^{76} +(-0.921404 - 0.921404i) q^{77} +(0.778539 - 0.778539i) q^{78} -8.89898i q^{79} +(2.12132 - 0.707107i) q^{80} -9.00000 q^{81} +(2.00000 - 2.00000i) q^{82} +(-0.635674 + 0.635674i) q^{83} +3.55051i q^{84} +(-8.89898 - 4.44949i) q^{85} -3.46410i q^{86} +(-3.46410 - 3.46410i) q^{87} +(-0.449490 - 0.449490i) q^{88} +18.2419 q^{89} +(-3.00000 + 6.00000i) q^{90} +1.30306 q^{91} +(-1.73205 - 1.73205i) q^{92} +(-1.22474 - 1.22474i) q^{93} -8.00000i q^{94} +(-3.46410 - 10.3923i) q^{95} +1.73205i q^{96} +(-3.00000 + 3.00000i) q^{97} +(1.97846 - 1.97846i) q^{98} +1.90702 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{7}+O(q^{10}) \) 8 * q - 8 * q^7	\( 8 q - 8 q^{7} + 16 q^{10} - 16 q^{13} - 8 q^{16} + 48 q^{21} + 16 q^{22} + 32 q^{25} - 8 q^{28} - 8 q^{31} - 24 q^{36} - 8 q^{40} + 16 q^{52} - 16 q^{55} - 48 q^{57} + 16 q^{58} - 16 q^{61} - 24 q^{63} - 48 q^{66} - 48 q^{67} - 24 q^{70} - 72 q^{81} + 16 q^{82} - 32 q^{85} + 16 q^{88} - 24 q^{90} + 128 q^{91} - 24 q^{97}+O(q^{100}) \) 8 * q - 8 * q^7 + 16 * q^10 - 16 * q^13 - 8 * q^16 + 48 * q^21 + 16 * q^22 + 32 * q^25 - 8 * q^28 - 8 * q^31 - 24 * q^36 - 8 * q^40 + 16 * q^52 - 16 * q^55 - 48 * q^57 + 16 * q^58 - 16 * q^61 - 24 * q^63 - 48 * q^66 - 48 * q^67 - 24 * q^70 - 72 * q^81 + 16 * q^82 - 32 * q^85 + 16 * q^88 - 24 * q^90 + 128 * q^91 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more