LMFDB - Embedded newform 1050.2.j.a.407.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(407,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, 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("1050.407");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.40960000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{4} + 1 $ x^8 + 7*x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			407.4
Root			$-1.14412 - 1.14412i$ of defining polynomial
Character	$\chi$	$=$	1050.407
Dual form			1050.2.j.a.743.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.707107 + 1.58114i) q^{3} -1.00000i q^{4} +(1.61803 + 0.618034i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.00000 + 2.23607i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.707107 + 1.58114i) q^{3} -1.00000i q^{4} +(1.61803 + 0.618034i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.00000 + 2.23607i) q^{9} +3.23607i q^{11} +(1.58114 - 0.707107i) q^{12} +(-4.57649 + 4.57649i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(-1.41421 + 1.41421i) q^{17} +(0.166925 + 2.99535i) q^{18} -0.763932i q^{19} +(-0.618034 + 1.61803i) q^{21} +(2.28825 + 2.28825i) q^{22} +(1.74806 + 1.74806i) q^{23} +(0.618034 - 1.61803i) q^{24} +6.47214i q^{26} +(-4.94975 - 1.58114i) q^{27} +(0.707107 - 0.707107i) q^{28} +0.763932 q^{29} +5.23607 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-5.11667 + 2.28825i) q^{33} +2.00000i q^{34} +(2.23607 + 2.00000i) q^{36} +(5.11667 + 5.11667i) q^{37} +(-0.540182 - 0.540182i) q^{38} +(-10.4721 - 4.00000i) q^{39} -9.23607i q^{41} +(0.707107 + 1.58114i) q^{42} +(-2.28825 + 2.28825i) q^{43} +3.23607 q^{44} +2.47214 q^{46} +(7.19859 - 7.19859i) q^{47} +(-0.707107 - 1.58114i) q^{48} +1.00000i q^{49} +(-3.23607 - 1.23607i) q^{51} +(4.57649 + 4.57649i) q^{52} +(7.73877 + 7.73877i) q^{53} +(-4.61803 + 2.38197i) q^{54} -1.00000i q^{56} +(1.20788 - 0.540182i) q^{57} +(0.540182 - 0.540182i) q^{58} +0.291796 q^{59} -12.9443 q^{61} +(3.70246 - 3.70246i) q^{62} +(-2.99535 + 0.166925i) q^{63} +1.00000i q^{64} +(-2.00000 + 5.23607i) q^{66} +(6.19704 + 6.19704i) q^{67} +(1.41421 + 1.41421i) q^{68} +(-1.52786 + 4.00000i) q^{69} -11.4164i q^{71} +(2.99535 - 0.166925i) q^{72} +(-2.62210 + 2.62210i) q^{73} +7.23607 q^{74} -0.763932 q^{76} +(-2.28825 + 2.28825i) q^{77} +(-10.2333 + 4.57649i) q^{78} +12.9443i q^{79} +(-1.00000 - 8.94427i) q^{81} +(-6.53089 - 6.53089i) q^{82} +(-5.11667 - 5.11667i) q^{83} +(1.61803 + 0.618034i) q^{84} +3.23607i q^{86} +(0.540182 + 1.20788i) q^{87} +(2.28825 - 2.28825i) q^{88} +9.23607 q^{89} -6.47214 q^{91} +(1.74806 - 1.74806i) q^{92} +(3.70246 + 8.27895i) q^{93} -10.1803i q^{94} +(-1.61803 - 0.618034i) q^{96} +(10.0270 + 10.0270i) q^{97} +(0.707107 + 0.707107i) q^{98} +(-7.23607 - 6.47214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{6} - 16 q^{9}+O(q^{10}) $ 8 * q + 4 * q^6 - 16 * q^9	$ 8 q + 4 q^{6} - 16 q^{9} + 8 q^{14} - 8 q^{16} + 4 q^{21} - 4 q^{24} + 24 q^{29} + 24 q^{31} - 48 q^{39} + 8 q^{44} - 16 q^{46} - 8 q^{51} - 28 q^{54} + 56 q^{59} - 32 q^{61} - 16 q^{66} - 48 q^{69} + 40 q^{74} - 24 q^{76} - 8 q^{81} + 4 q^{84} + 56 q^{89} - 16 q^{91} - 4 q^{96} - 40 q^{99}+O(q^{100}) $ 8 * q + 4 * q^6 - 16 * q^9 + 8 * q^14 - 8 * q^16 + 4 * q^21 - 4 * q^24 + 24 * q^29 + 24 * q^31 - 48 * q^39 + 8 * q^44 - 16 * q^46 - 8 * q^51 - 28 * q^54 + 56 * q^59 - 32 * q^61 - 16 * q^66 - 48 * q^69 + 40 * q^74 - 24 * q^76 - 8 * q^81 + 4 * q^84 + 56 * q^89 - 16 * q^91 - 4 * q^96 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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	+	1.58114i	0.408248	+	0.912871i
$3$	0.707107	+	1.58114i	0.408248	+	0.912871i
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	1.61803	+	0.618034i	0.660560	+	0.252311i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.00000	+	2.23607i	−0.666667	+	0.745356i
$10$		0			0
$11$			3.23607i			0.975711i	0.872924	+	0.487856i	$0.162221\pi$
$11$			3.23607i			0.975711i	−0.872924	+	0.487856i	$0.837779\pi$
$12$	1.58114	−	0.707107i	0.456435	−	0.204124i
$13$	−4.57649	+	4.57649i	−1.26929	+	1.26929i	−0.322835	+	0.946455i	$0.604636\pi$
$13$	−4.57649	+	4.57649i	−1.26929	+	1.26929i	−0.946455	+	0.322835i	$0.895364\pi$
$14$	1.00000			0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−1.41421	+	1.41421i	−0.342997	+	0.342997i	−0.857493	−	0.514496i	$-0.827979\pi$
$17$	−1.41421	+	1.41421i	−0.342997	+	0.342997i	0.514496	+	0.857493i	$0.327979\pi$
$18$	0.166925	+	2.99535i	0.0393447	+	0.706011i
$19$		−	0.763932i		−	0.175258i	−0.996153	−	0.0876290i	$-0.972071\pi$
$19$		−	0.763932i		−	0.175258i	0.996153	−	0.0876290i	$-0.0279290\pi$
$20$		0			0
$21$	−0.618034	+	1.61803i	−0.134866	+	0.353084i
$22$	2.28825	+	2.28825i	0.487856	+	0.487856i
$23$	1.74806	+	1.74806i	0.364497	+	0.364497i	0.865465	−	0.500969i	$-0.167023\pi$
$23$	1.74806	+	1.74806i	0.364497	+	0.364497i	−0.500969	+	0.865465i	$0.667023\pi$
$24$	0.618034	−	1.61803i	0.126156	−	0.330280i
$25$		0			0
$26$			6.47214i			1.26929i
$27$	−4.94975	−	1.58114i	−0.952579	−	0.304290i
$28$	0.707107	−	0.707107i	0.133631	−	0.133631i
$29$	0.763932			0.141859			0.0709293	−	0.997481i	$-0.477404\pi$
$29$	0.763932			0.141859			0.0709293	+	0.997481i	$0.477404\pi$
$30$		0			0
$31$	5.23607			0.940426			0.470213	−	0.882553i	$-0.344177\pi$
$31$	5.23607			0.940426			0.470213	+	0.882553i	$0.344177\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−5.11667	+	2.28825i	−0.890698	+	0.398332i
$34$			2.00000i			0.342997i
$35$		0			0
$36$	2.23607	+	2.00000i	0.372678	+	0.333333i
$37$	5.11667	+	5.11667i	0.841176	+	0.841176i	0.989012	−	0.147836i	$-0.0472308\pi$
$37$	5.11667	+	5.11667i	0.841176	+	0.841176i	−0.147836	+	0.989012i	$0.547231\pi$
$38$	−0.540182	−	0.540182i	−0.0876290	−	0.0876290i
$39$	−10.4721	−	4.00000i	−1.67688	−	0.640513i
$40$		0			0
$41$		−	9.23607i		−	1.44243i	−0.692711	−	0.721216i	$-0.743584\pi$
$41$		−	9.23607i		−	1.44243i	0.692711	−	0.721216i	$-0.256416\pi$
$42$	0.707107	+	1.58114i	0.109109	+	0.243975i
$43$	−2.28825	+	2.28825i	−0.348954	+	0.348954i	−0.859720	−	0.510766i	$-0.829362\pi$
$43$	−2.28825	+	2.28825i	−0.348954	+	0.348954i	0.510766	+	0.859720i	$0.329362\pi$
$44$	3.23607			0.487856
$45$		0			0
$46$	2.47214			0.364497
$47$	7.19859	−	7.19859i	1.05002	−	1.05002i	0.0513407	−	0.998681i	$-0.483651\pi$
$47$	7.19859	−	7.19859i	1.05002	−	1.05002i	0.998681	−	0.0513407i	$-0.0163494\pi$
$48$	−0.707107	−	1.58114i	−0.102062	−	0.228218i
$49$			1.00000i			0.142857i
$50$		0			0
$51$	−3.23607	−	1.23607i	−0.453140	−	0.173084i
$52$	4.57649	+	4.57649i	0.634645	+	0.634645i
$53$	7.73877	+	7.73877i	1.06300	+	1.06300i	0.997877	+	0.0651245i	$0.0207445\pi$
$53$	7.73877	+	7.73877i	1.06300	+	1.06300i	0.0651245	+	0.997877i	$0.479256\pi$
$54$	−4.61803	+	2.38197i	−0.628435	+	0.324145i
$55$		0			0
$56$		−	1.00000i		−	0.133631i
$57$	1.20788	−	0.540182i	0.159988	−	0.0715488i
$58$	0.540182	−	0.540182i	0.0709293	−	0.0709293i
$59$	0.291796			0.0379886			0.0189943	−	0.999820i	$-0.493954\pi$
$59$	0.291796			0.0379886			0.0189943	+	0.999820i	$0.493954\pi$
$60$		0			0
$61$	−12.9443			−1.65734			−0.828672	−	0.559734i	$-0.810903\pi$
$61$	−12.9443			−1.65734			−0.828672	+	0.559734i	$0.810903\pi$
$62$	3.70246	−	3.70246i	0.470213	−	0.470213i
$63$	−2.99535	+	0.166925i	−0.377379	+	0.0210306i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−2.00000	+	5.23607i	−0.246183	+	0.644515i
$67$	6.19704	+	6.19704i	0.757088	+	0.757088i	0.975791	−	0.218703i	$-0.0701826\pi$
$67$	6.19704	+	6.19704i	0.757088	+	0.757088i	−0.218703	+	0.975791i	$0.570183\pi$
$68$	1.41421	+	1.41421i	0.171499	+	0.171499i
$69$	−1.52786	+	4.00000i	−0.183933	+	0.481543i
$70$		0			0
$71$		−	11.4164i		−	1.35488i	−0.735579	−	0.677439i	$-0.763090\pi$
$71$		−	11.4164i		−	1.35488i	0.735579	−	0.677439i	$-0.236910\pi$
$72$	2.99535	−	0.166925i	0.353006	−	0.0196723i
$73$	−2.62210	+	2.62210i	−0.306893	+	0.306893i	−0.843703	−	0.536810i	$-0.819629\pi$
$73$	−2.62210	+	2.62210i	−0.306893	+	0.306893i	0.536810	+	0.843703i	$0.319629\pi$
$74$	7.23607			0.841176
$75$		0			0
$76$	−0.763932			−0.0876290
$77$	−2.28825	+	2.28825i	−0.260770	+	0.260770i
$78$	−10.2333	+	4.57649i	−1.15870	+	0.518186i
$79$			12.9443i			1.45634i	0.685394	+	0.728172i	$0.259630\pi$
$79$			12.9443i			1.45634i	−0.685394	+	0.728172i	$0.740370\pi$
$80$		0			0
$81$	−1.00000	−	8.94427i	−0.111111	−	0.993808i
$82$	−6.53089	−	6.53089i	−0.721216	−	0.721216i
$83$	−5.11667	−	5.11667i	−0.561628	−	0.561628i	0.368142	−	0.929770i	$-0.379994\pi$
$83$	−5.11667	−	5.11667i	−0.561628	−	0.561628i	−0.929770	+	0.368142i	$0.879994\pi$
$84$	1.61803	+	0.618034i	0.176542	+	0.0674330i
$85$		0			0
$86$			3.23607i			0.348954i
$87$	0.540182	+	1.20788i	0.0579135	+	0.129499i
$88$	2.28825	−	2.28825i	0.243928	−	0.243928i
$89$	9.23607			0.979021			0.489511	−	0.871997i	$-0.337175\pi$
$89$	9.23607			0.979021			0.489511	+	0.871997i	$0.337175\pi$
$90$		0			0
$91$	−6.47214			−0.678464
$92$	1.74806	−	1.74806i	0.182248	−	0.182248i
$93$	3.70246	+	8.27895i	0.383927	+	0.858487i
$94$		−	10.1803i		−	1.05002i
$95$		0			0
$96$	−1.61803	−	0.618034i	−0.165140	−	0.0630778i
$97$	10.0270	+	10.0270i	1.01809	+	1.01809i	0.999833	+	0.0182557i	$0.00581130\pi$
$97$	10.0270	+	10.0270i	1.01809	+	1.01809i	0.0182557	+	0.999833i	$0.494189\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$	−7.23607	−	6.47214i	−0.727252	−	0.650474i
$100$		0			0
$101$		−	16.9443i		−	1.68602i	−0.537899	−	0.843009i	$-0.680782\pi$
$101$		−	16.9443i		−	1.68602i	0.537899	−	0.843009i	$-0.319218\pi$
$102$	−3.16228	+	1.41421i	−0.313112	+	0.140028i
$103$	−3.90879	+	3.90879i	−0.385145	+	0.385145i	−0.872952	−	0.487807i	$-0.837797\pi$
$103$	−3.90879	+	3.90879i	−0.385145	+	0.385145i	0.487807	+	0.872952i	$0.337797\pi$
$104$	6.47214			0.634645
$105$		0			0
$106$	10.9443			1.06300
$107$	−11.9814	+	11.9814i	−1.15829	+	1.15829i	−0.173443	+	0.984844i	$0.555489\pi$
$107$	−11.9814	+	11.9814i	−1.15829	+	1.15829i	−0.984844	+	0.173443i	$0.944511\pi$
$108$	−1.58114	+	4.94975i	−0.152145	+	0.476290i
$109$		−	2.94427i		−	0.282010i	−0.990009	−	0.141005i	$-0.954967\pi$
$109$		−	2.94427i		−	0.282010i	0.990009	−	0.141005i	$-0.0450334\pi$
$110$		0			0
$111$	−4.47214	+	11.7082i	−0.424476	+	1.11129i
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	2.49458	+	2.49458i	0.234670	+	0.234670i	0.814639	−	0.579969i	$-0.196935\pi$
$113$	2.49458	+	2.49458i	0.234670	+	0.234670i	−0.579969	+	0.814639i	$0.696935\pi$
$114$	0.472136	−	1.23607i	0.0442196	−	0.115768i
$115$		0			0
$116$		−	0.763932i		−	0.0709293i
$117$	−1.08036	−	19.3863i	−0.0998796	−	1.79227i
$118$	0.206331	−	0.206331i	0.0189943	−	0.0189943i
$119$	−2.00000			−0.183340
$120$		0			0
$121$	0.527864			0.0479876
$122$	−9.15298	+	9.15298i	−0.828672	+	0.828672i
$123$	14.6035	−	6.53089i	1.31675	−	0.588870i
$124$		−	5.23607i		−	0.470213i
$125$		0			0
$126$	−2.00000	+	2.23607i	−0.178174	+	0.199205i
$127$	−10.2333	−	10.2333i	−0.908063	−	0.908063i	0.0880532	−	0.996116i	$-0.471935\pi$
$127$	−10.2333	−	10.2333i	−0.908063	−	0.908063i	−0.996116	+	0.0880532i	$0.971935\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−5.23607	−	2.00000i	−0.461010	−	0.176090i
$130$		0			0
$131$		−	8.29180i		−	0.724458i	−0.932089	−	0.362229i	$-0.882016\pi$
$131$		−	8.29180i		−	0.724458i	0.932089	−	0.362229i	$-0.117984\pi$
$132$	2.28825	+	5.11667i	0.199166	+	0.445349i
$133$	0.540182	−	0.540182i	0.0468397	−	0.0468397i
$134$	8.76393			0.757088
$135$		0			0
$136$	2.00000			0.171499
$137$	9.89949	−	9.89949i	0.845771	−	0.845771i	−0.143831	−	0.989602i	$-0.545942\pi$
$137$	9.89949	−	9.89949i	0.845771	−	0.845771i	0.989602	+	0.143831i	$0.0459423\pi$
$138$	1.74806	+	3.90879i	0.148805	+	0.332738i
$139$			1.70820i			0.144888i	0.997372	+	0.0724440i	$0.0230799\pi$
$139$			1.70820i			0.144888i	−0.997372	+	0.0724440i	$0.976920\pi$
$140$		0			0
$141$	16.4721	+	6.29180i	1.38720	+	0.529865i
$142$	−8.07262	−	8.07262i	−0.677439	−	0.677439i
$143$	−14.8098	−	14.8098i	−1.23846	−	1.23846i
$144$	2.00000	−	2.23607i	0.166667	−	0.186339i
$145$		0			0
$146$			3.70820i			0.306893i
$147$	−1.58114	+	0.707107i	−0.130410	+	0.0583212i
$148$	5.11667	−	5.11667i	0.420588	−	0.420588i
$149$	20.1803			1.65324			0.826619	−	0.562762i	$-0.190261\pi$
$149$	20.1803			1.65324			0.826619	+	0.562762i	$0.190261\pi$
$150$		0			0
$151$	5.52786			0.449851			0.224926	−	0.974376i	$-0.427786\pi$
$151$	5.52786			0.449851			0.224926	+	0.974376i	$0.427786\pi$
$152$	−0.540182	+	0.540182i	−0.0438145	+	0.0438145i
$153$	−0.333851	−	5.99070i	−0.0269902	−	0.484320i
$154$			3.23607i			0.260770i
$155$		0			0
$156$	−4.00000	+	10.4721i	−0.320256	+	0.838442i
$157$	3.90879	+	3.90879i	0.311955	+	0.311955i	0.845667	−	0.533711i	$-0.179203\pi$
$157$	3.90879	+	3.90879i	0.311955	+	0.311955i	−0.533711	+	0.845667i	$0.679203\pi$
$158$	9.15298	+	9.15298i	0.728172	+	0.728172i
$159$	−6.76393	+	17.7082i	−0.536415	+	1.40435i
$160$		0			0
$161$			2.47214i			0.194832i
$162$	−7.03166	−	5.61745i	−0.552460	−	0.441348i
$163$	10.3609	−	10.3609i	0.811526	−	0.811526i	−0.173337	−	0.984863i	$-0.555455\pi$
$163$	10.3609	−	10.3609i	0.811526	−	0.811526i	0.984863	+	0.173337i	$0.0554550\pi$
$164$	−9.23607			−0.721216
$165$		0			0
$166$	−7.23607			−0.561628
$167$	0.206331	−	0.206331i	0.0159664	−	0.0159664i	−0.699079	−	0.715045i	$-0.746406\pi$
$167$	0.206331	−	0.206331i	0.0159664	−	0.0159664i	0.715045	+	0.699079i	$0.246406\pi$
$168$	1.58114	−	0.707107i	0.121988	−	0.0545545i
$169$		−	28.8885i		−	2.22220i
$170$		0			0
$171$	1.70820	+	1.52786i	0.130630	+	0.116839i
$172$	2.28825	+	2.28825i	0.174477	+	0.174477i
$173$	−6.32456	−	6.32456i	−0.480847	−	0.480847i	0.424555	−	0.905402i	$-0.360431\pi$
$173$	−6.32456	−	6.32456i	−0.480847	−	0.480847i	−0.905402	+	0.424555i	$0.860431\pi$
$174$	1.23607	+	0.472136i	0.0937061	+	0.0357925i
$175$		0			0
$176$		−	3.23607i		−	0.243928i
$177$	0.206331	+	0.461370i	0.0155088	+	0.0346787i
$178$	6.53089	−	6.53089i	0.489511	−	0.489511i
$179$	8.76393			0.655047			0.327524	−	0.944843i	$-0.393786\pi$
$179$	8.76393			0.655047			0.327524	+	0.944843i	$0.393786\pi$
$180$		0			0
$181$	−21.8885			−1.62696			−0.813481	−	0.581591i	$-0.802430\pi$
$181$	−21.8885			−1.62696			−0.813481	+	0.581591i	$0.802430\pi$
$182$	−4.57649	+	4.57649i	−0.339232	+	0.339232i
$183$	−9.15298	−	20.4667i	−0.676608	−	1.51294i
$184$		−	2.47214i		−	0.182248i
$185$		0			0
$186$	8.47214	+	3.23607i	0.621207	+	0.237280i
$187$	−4.57649	−	4.57649i	−0.334666	−	0.334666i
$188$	−7.19859	−	7.19859i	−0.525011	−	0.525011i
$189$	−2.38197	−	4.61803i	−0.173263	−	0.335913i
$190$		0			0
$191$		−	3.05573i		−	0.221105i	−0.993870	−	0.110552i	$-0.964738\pi$
$191$		−	3.05573i		−	0.221105i	0.993870	−	0.110552i	$-0.0352620\pi$
$192$	−1.58114	+	0.707107i	−0.114109	+	0.0510310i
$193$	5.24419	−	5.24419i	0.377485	−	0.377485i	−0.492709	−	0.870194i	$-0.663993\pi$
$193$	5.24419	−	5.24419i	0.377485	−	0.377485i	0.870194	+	0.492709i	$0.163993\pi$
$194$	14.1803			1.01809
$195$		0			0
$196$	1.00000			0.0714286
$197$	1.41421	−	1.41421i	0.100759	−	0.100759i	−0.654931	−	0.755689i	$-0.727302\pi$
$197$	1.41421	−	1.41421i	0.100759	−	0.100759i	0.755689	+	0.654931i	$0.227302\pi$
$198$	−9.69316	+	0.540182i	−0.688863	+	0.0383890i
$199$			2.18034i			0.154560i	0.997009	+	0.0772801i	$0.0246236\pi$
$199$			2.18034i			0.154560i	−0.997009	+	0.0772801i	$0.975376\pi$
$200$		0			0
$201$	−5.41641	+	14.1803i	−0.382044	+	1.00020i
$202$	−11.9814	−	11.9814i	−0.843009	−	0.843009i
$203$	0.540182	+	0.540182i	0.0379133	+	0.0379133i
$204$	−1.23607	+	3.23607i	−0.0865421	+	0.226570i
$205$		0			0
$206$			5.52786i			0.385145i
$207$	−7.40492	+	0.412662i	−0.514677	+	0.0286820i
$208$	4.57649	−	4.57649i	0.317323	−	0.317323i
$209$	2.47214			0.171001
$210$		0			0
$211$	26.8328			1.84725			0.923624	−	0.383301i	$-0.125213\pi$
$211$	26.8328			1.84725			0.923624	+	0.383301i	$0.125213\pi$
$212$	7.73877	−	7.73877i	0.531501	−	0.531501i
$213$	18.0509	−	8.07262i	1.23683	−	0.553127i
$214$			16.9443i			1.15829i
$215$		0			0
$216$	2.38197	+	4.61803i	0.162072	+	0.314217i
$217$	3.70246	+	3.70246i	0.251339	+	0.251339i
$218$	−2.08191	−	2.08191i	−0.141005	−	0.141005i
$219$	−6.00000	−	2.29180i	−0.405442	−	0.154865i
$220$		0			0
$221$		−	12.9443i		−	0.870726i
$222$	5.11667	+	11.4412i	0.343409	+	0.767885i
$223$	3.49613	−	3.49613i	0.234118	−	0.234118i	−0.580291	−	0.814409i	$-0.697061\pi$
$223$	3.49613	−	3.49613i	0.234118	−	0.234118i	0.814409	+	0.580291i	$0.197061\pi$
$224$	−1.00000			−0.0668153
$225$		0			0
$226$	3.52786			0.234670
$227$	−2.28825	+	2.28825i	−0.151876	+	0.151876i	−0.778955	−	0.627079i	$-0.784250\pi$
$227$	−2.28825	+	2.28825i	−0.151876	+	0.151876i	0.627079	+	0.778955i	$0.284250\pi$
$228$	−0.540182	−	1.20788i	−0.0357744	−	0.0799940i
$229$			8.94427i			0.591054i	0.955334	+	0.295527i	$0.0954953\pi$
$229$			8.94427i			0.591054i	−0.955334	+	0.295527i	$0.904505\pi$
$230$		0			0
$231$	−5.23607	−	2.00000i	−0.344508	−	0.131590i
$232$	−0.540182	−	0.540182i	−0.0354647	−	0.0354647i
$233$	5.99070	+	5.99070i	0.392464	+	0.392464i	0.875565	−	0.483101i	$-0.160489\pi$
$233$	5.99070	+	5.99070i	0.392464	+	0.392464i	−0.483101	+	0.875565i	$0.660489\pi$
$234$	−14.4721	−	12.9443i	−0.946073	−	0.846194i
$235$		0			0
$236$		−	0.291796i		−	0.0189943i
$237$	−20.4667	+	9.15298i	−1.32945	+	0.594550i
$238$	−1.41421	+	1.41421i	−0.0916698	+	0.0916698i
$239$	−30.8328			−1.99441			−0.997205	−	0.0747204i	$-0.976194\pi$
$239$	−30.8328			−1.99441			−0.997205	+	0.0747204i	$0.976194\pi$
$240$		0			0
$241$	27.8885			1.79646			0.898230	−	0.439527i	$-0.144854\pi$
$241$	27.8885			1.79646			0.898230	+	0.439527i	$0.144854\pi$
$242$	0.373256	−	0.373256i	0.0239938	−	0.0239938i
$243$	13.4350	−	7.90569i	0.861858	−	0.507151i
$244$			12.9443i			0.828672i
$245$		0			0
$246$	5.70820	−	14.9443i	0.363942	−	0.952812i
$247$	3.49613	+	3.49613i	0.222453	+	0.222453i
$248$	−3.70246	−	3.70246i	−0.235106	−	0.235106i
$249$	4.47214	−	11.7082i	0.283410	−	0.741977i
$250$		0			0
$251$			27.1246i			1.71209i	0.516901	+	0.856045i	$0.327086\pi$
$251$			27.1246i			1.71209i	−0.516901	+	0.856045i	$0.672914\pi$
$252$	0.166925	+	2.99535i	0.0105153	+	0.188689i
$253$	−5.65685	+	5.65685i	−0.355643	+	0.355643i
$254$	−14.4721			−0.908063
$255$		0			0
$256$	1.00000			0.0625000
$257$	1.41421	−	1.41421i	0.0882162	−	0.0882162i	−0.661622	−	0.749838i	$-0.730131\pi$
$257$	1.41421	−	1.41421i	0.0882162	−	0.0882162i	0.749838	+	0.661622i	$0.230131\pi$
$258$	−5.11667	+	2.28825i	−0.318550	+	0.142460i
$259$			7.23607i			0.449627i
$260$		0			0
$261$	−1.52786	+	1.70820i	−0.0945724	+	0.105735i
$262$	−5.86319	−	5.86319i	−0.362229	−	0.362229i
$263$	9.56564	+	9.56564i	0.589843	+	0.589843i	0.937589	−	0.347746i	$-0.113053\pi$
$263$	9.56564	+	9.56564i	0.589843	+	0.589843i	−0.347746	+	0.937589i	$0.613053\pi$
$264$	5.23607	+	2.00000i	0.322258	+	0.123091i
$265$		0			0
$266$		−	0.763932i		−	0.0468397i
$267$	6.53089	+	14.6035i	0.399684	+	0.893720i
$268$	6.19704	−	6.19704i	0.378544	−	0.378544i
$269$	26.4721			1.61403			0.807017	−	0.590528i	$-0.201080\pi$
$269$	26.4721			1.61403			0.807017	+	0.590528i	$0.201080\pi$
$270$		0			0
$271$	−14.7639			−0.896845			−0.448423	−	0.893822i	$-0.648014\pi$
$271$	−14.7639			−0.896845			−0.448423	+	0.893822i	$0.648014\pi$
$272$	1.41421	−	1.41421i	0.0857493	−	0.0857493i
$273$	−4.57649	−	10.2333i	−0.276982	−	0.619350i
$274$		−	14.0000i		−	0.845771i
$275$		0			0
$276$	4.00000	+	1.52786i	0.240772	+	0.0919666i
$277$	−22.3423	−	22.3423i	−1.34242	−	1.34242i	−0.893647	−	0.448770i	$-0.851862\pi$
$277$	−22.3423	−	22.3423i	−1.34242	−	1.34242i	−0.448770	−	0.893647i	$-0.648138\pi$
$278$	1.20788	+	1.20788i	0.0724440	+	0.0724440i
$279$	−10.4721	+	11.7082i	−0.626950	+	0.700952i
$280$		0			0
$281$		−	12.3607i		−	0.737376i	−0.929553	−	0.368688i	$-0.879807\pi$
$281$		−	12.3607i		−	0.737376i	0.929553	−	0.368688i	$-0.120193\pi$
$282$	16.0965	−	7.19859i	0.958534	−	0.428670i
$283$	−11.1074	+	11.1074i	−0.660265	+	0.660265i	−0.955442	−	0.295177i	$-0.904621\pi$
$283$	−11.1074	+	11.1074i	−0.660265	+	0.660265i	0.295177	+	0.955442i	$0.404621\pi$
$284$	−11.4164			−0.677439
$285$		0			0
$286$	−20.9443			−1.23846
$287$	6.53089	−	6.53089i	0.385506	−	0.385506i
$288$	−0.166925	−	2.99535i	−0.00983617	−	0.176503i
$289$			13.0000i			0.764706i
$290$		0			0
$291$	−8.76393	+	22.9443i	−0.513751	+	1.34502i
$292$	2.62210	+	2.62210i	0.153447	+	0.153447i
$293$	2.16073	+	2.16073i	0.126231	+	0.126231i	0.767400	−	0.641169i	$-0.221550\pi$
$293$	2.16073	+	2.16073i	0.126231	+	0.126231i	−0.641169	+	0.767400i	$0.721550\pi$
$294$	−0.618034	+	1.61803i	−0.0360445	+	0.0943657i
$295$		0			0
$296$		−	7.23607i		−	0.420588i
$297$	5.11667	−	16.0177i	0.296899	−	0.929442i
$298$	14.2697	−	14.2697i	0.826619	−	0.826619i
$299$	−16.0000			−0.925304
$300$		0			0
$301$	−3.23607			−0.186524
$302$	3.90879	−	3.90879i	0.224926	−	0.224926i
$303$	26.7912	−	11.9814i	1.53912	−	0.688314i
$304$			0.763932i			0.0438145i
$305$		0			0
$306$	−4.47214	−	4.00000i	−0.255655	−	0.228665i
$307$	−12.1877	−	12.1877i	−0.695591	−	0.695591i	0.267865	−	0.963456i	$-0.413682\pi$
$307$	−12.1877	−	12.1877i	−0.695591	−	0.695591i	−0.963456	+	0.267865i	$0.913682\pi$
$308$	2.28825	+	2.28825i	0.130385	+	0.130385i
$309$	−8.94427	−	3.41641i	−0.508822	−	0.194353i
$310$		0			0
$311$			8.00000i			0.453638i	0.973937	+	0.226819i	$0.0728326\pi$
$311$			8.00000i			0.453638i	−0.973937	+	0.226819i	$0.927167\pi$
$312$	4.57649	+	10.2333i	0.259093	+	0.579349i
$313$	6.53089	−	6.53089i	0.369148	−	0.369148i	−0.498019	−	0.867166i	$-0.665939\pi$
$313$	6.53089	−	6.53089i	0.369148	−	0.369148i	0.867166	+	0.498019i	$0.165939\pi$
$314$	5.52786			0.311955
$315$		0			0
$316$	12.9443			0.728172
$317$	−19.0525	+	19.0525i	−1.07009	+	1.07009i	−0.0727430	+	0.997351i	$0.523175\pi$
$317$	−19.0525	+	19.0525i	−1.07009	+	1.07009i	−0.997351	+	0.0727430i	$0.976825\pi$
$318$	7.73877	+	17.3044i	0.433969	+	0.970383i
$319$			2.47214i			0.138413i
$320$		0			0
$321$	−27.4164	−	10.4721i	−1.53023	−	0.584498i
$322$	1.74806	+	1.74806i	0.0974158	+	0.0974158i
$323$	1.08036	+	1.08036i	0.0601130	+	0.0601130i
$324$	−8.94427	+	1.00000i	−0.496904	+	0.0555556i
$325$		0			0
$326$		−	14.6525i		−	0.811526i
$327$	4.65530	−	2.08191i	0.257439	−	0.115130i
$328$	−6.53089	+	6.53089i	−0.360608	+	0.360608i
$329$	10.1803			0.561260
$330$		0			0
$331$	−26.4721			−1.45504			−0.727520	−	0.686086i	$-0.759327\pi$
$331$	−26.4721			−1.45504			−0.727520	+	0.686086i	$0.759327\pi$
$332$	−5.11667	+	5.11667i	−0.280814	+	0.280814i
$333$	−21.6746	+	1.20788i	−1.18776	+	0.0661916i
$334$		−	0.291796i		−	0.0159664i
$335$		0			0
$336$	0.618034	−	1.61803i	0.0337165	−	0.0882710i
$337$	15.8902	+	15.8902i	0.865594	+	0.865594i	0.991981	−	0.126387i	$-0.0403380\pi$
$337$	15.8902	+	15.8902i	0.865594	+	0.865594i	−0.126387	+	0.991981i	$0.540338\pi$
$338$	−20.4273	−	20.4273i	−1.11110	−	1.11110i
$339$	−2.18034	+	5.70820i	−0.118420	+	0.310027i
$340$		0			0
$341$			16.9443i			0.917584i
$342$	2.28825	−	0.127520i	0.123734	−	0.00689547i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	3.23607			0.174477
$345$		0			0
$346$	−8.94427			−0.480847
$347$	10.9010	−	10.9010i	0.585199	−	0.585199i	−0.351128	−	0.936327i	$-0.614202\pi$
$347$	10.9010	−	10.9010i	0.585199	−	0.585199i	0.936327	+	0.351128i	$0.114202\pi$
$348$	1.20788	−	0.540182i	0.0647493	−	0.0289568i
$349$			4.00000i			0.214115i	0.994253	+	0.107058i	$0.0341429\pi$
$349$			4.00000i			0.214115i	−0.994253	+	0.107058i	$0.965857\pi$
$350$		0			0
$351$	29.8885	−	15.4164i	1.59533	−	0.822867i
$352$	−2.28825	−	2.28825i	−0.121964	−	0.121964i
$353$	−24.0416	−	24.0416i	−1.27961	−	1.27961i	−0.940887	−	0.338719i	$-0.890006\pi$
$353$	−24.0416	−	24.0416i	−1.27961	−	1.27961i	−0.338719	−	0.940887i	$-0.609994\pi$
$354$	0.472136	+	0.180340i	0.0250937	+	0.00958496i
$355$		0			0
$356$		−	9.23607i		−	0.489511i
$357$	−1.41421	−	3.16228i	−0.0748481	−	0.167365i
$358$	6.19704	−	6.19704i	0.327524	−	0.327524i
$359$	−11.4164			−0.602535			−0.301267	−	0.953540i	$-0.597410\pi$
$359$	−11.4164			−0.602535			−0.301267	+	0.953540i	$0.597410\pi$
$360$		0			0
$361$	18.4164			0.969285
$362$	−15.4775	+	15.4775i	−0.813481	+	0.813481i
$363$	0.373256	+	0.834626i	0.0195909	+	0.0438065i
$364$			6.47214i			0.339232i
$365$		0			0
$366$	−20.9443	−	8.00000i	−1.09477	−	0.418167i
$367$	−14.8098	−	14.8098i	−0.773067	−	0.773067i	0.205574	−	0.978642i	$-0.434094\pi$
$367$	−14.8098	−	14.8098i	−0.773067	−	0.773067i	−0.978642	+	0.205574i	$0.934094\pi$
$368$	−1.74806	−	1.74806i	−0.0911241	−	0.0911241i
$369$	20.6525	+	18.4721i	1.07512	+	0.961621i
$370$		0			0
$371$			10.9443i			0.568198i
$372$	8.27895	−	3.70246i	0.429244	−	0.191964i
$373$	−16.4304	+	16.4304i	−0.850733	+	0.850733i	−0.990223	−	0.139491i	$-0.955454\pi$
$373$	−16.4304	+	16.4304i	−0.850733	+	0.850733i	0.139491	+	0.990223i	$0.455454\pi$
$374$	−6.47214			−0.334666
$375$		0			0
$376$	−10.1803			−0.525011
$377$	−3.49613	+	3.49613i	−0.180060	+	0.180060i
$378$	−4.94975	−	1.58114i	−0.254588	−	0.0813250i
$379$		−	28.3607i		−	1.45679i	−0.685157	−	0.728395i	$-0.740267\pi$
$379$		−	28.3607i		−	1.45679i	0.685157	−	0.728395i	$-0.259733\pi$
$380$		0			0
$381$	8.94427	−	23.4164i	0.458229	−	1.19966i
$382$	−2.16073	−	2.16073i	−0.110552	−	0.110552i
$383$	8.94665	+	8.94665i	0.457153	+	0.457153i	0.897720	−	0.440567i	$-0.145223\pi$
$383$	8.94665	+	8.94665i	0.457153	+	0.457153i	−0.440567	+	0.897720i	$0.645223\pi$
$384$	−0.618034	+	1.61803i	−0.0315389	+	0.0825700i
$385$		0			0
$386$		−	7.41641i		−	0.377485i
$387$	−0.540182	−	9.69316i	−0.0274590	−	0.492731i
$388$	10.0270	−	10.0270i	0.509045	−	0.509045i
$389$	−23.2361			−1.17812			−0.589058	−	0.808091i	$-0.700501\pi$
$389$	−23.2361			−1.17812			−0.589058	+	0.808091i	$0.700501\pi$
$390$		0			0
$391$	−4.94427			−0.250043
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$	13.1105	−	5.86319i	0.661336	−	0.295759i
$394$		−	2.00000i		−	0.100759i
$395$		0			0
$396$	−6.47214	+	7.23607i	−0.325237	+	0.363626i
$397$	0.412662	+	0.412662i	0.0207109	+	0.0207109i	0.717386	−	0.696675i	$-0.245338\pi$
$397$	0.412662	+	0.412662i	0.0207109	+	0.0207109i	−0.696675	+	0.717386i	$0.745338\pi$
$398$	1.54173	+	1.54173i	0.0772801	+	0.0772801i
$399$	1.23607	+	0.472136i	0.0618808	+	0.0236364i
$400$		0			0
$401$		−	3.05573i		−	0.152596i	−0.997085	−	0.0762979i	$-0.975690\pi$
$401$		−	3.05573i		−	0.152596i	0.997085	−	0.0762979i	$-0.0243100\pi$
$402$	6.19704	+	13.8570i	0.309080	+	0.691124i
$403$	−23.9628	+	23.9628i	−1.19367	+	1.19367i
$404$	−16.9443			−0.843009
$405$		0			0
$406$	0.763932			0.0379133
$407$	−16.5579	+	16.5579i	−0.820745	+	0.820745i
$408$	1.41421	+	3.16228i	0.0700140	+	0.156556i
$409$			4.11146i			0.203298i	0.994820	+	0.101649i	$0.0324119\pi$
$409$			4.11146i			0.203298i	−0.994820	+	0.101649i	$0.967588\pi$
$410$		0			0
$411$	22.6525	+	8.65248i	1.11736	+	0.426795i
$412$	3.90879	+	3.90879i	0.192572	+	0.192572i
$413$	0.206331	+	0.206331i	0.0101529	+	0.0101529i
$414$	−4.94427	+	5.52786i	−0.242998	+	0.271680i
$415$		0			0
$416$		−	6.47214i		−	0.317323i
$417$	−2.70091	+	1.20788i	−0.132264	+	0.0591503i
$418$	1.74806	−	1.74806i	0.0855006	−	0.0855006i
$419$	19.1246			0.934298			0.467149	−	0.884178i	$-0.345281\pi$
$419$	19.1246			0.934298			0.467149	+	0.884178i	$0.345281\pi$
$420$		0			0
$421$	10.9443			0.533391			0.266696	−	0.963781i	$-0.414068\pi$
$421$	10.9443			0.533391			0.266696	+	0.963781i	$0.414068\pi$
$422$	18.9737	−	18.9737i	0.923624	−	0.923624i
$423$	1.69936	+	30.4937i	0.0826255	+	1.48265i
$424$		−	10.9443i		−	0.531501i
$425$		0			0
$426$	7.05573	−	18.4721i	0.341851	−	0.894978i
$427$	−9.15298	−	9.15298i	−0.442944	−	0.442944i
$428$	11.9814	+	11.9814i	0.579143	+	0.579143i
$429$	12.9443	−	33.8885i	0.624955	−	1.63615i
$430$		0			0
$431$			12.5836i			0.606130i	0.952970	+	0.303065i	$0.0980100\pi$
$431$			12.5836i			0.606130i	−0.952970	+	0.303065i	$0.901990\pi$
$432$	4.94975	+	1.58114i	0.238145	+	0.0760726i
$433$	4.78282	−	4.78282i	0.229848	−	0.229848i	−0.582781	−	0.812629i	$-0.698036\pi$
$433$	4.78282	−	4.78282i	0.229848	−	0.229848i	0.812629	+	0.582781i	$0.198036\pi$
$434$	5.23607			0.251339
$435$		0			0
$436$	−2.94427			−0.141005
$437$	1.33540	−	1.33540i	0.0638809	−	0.0638809i
$438$	−5.86319	+	2.62210i	−0.280154	+	0.125289i
$439$		−	9.81966i		−	0.468667i	−0.972156	−	0.234333i	$-0.924709\pi$
$439$		−	9.81966i		−	0.468667i	0.972156	−	0.234333i	$-0.0752907\pi$
$440$		0			0
$441$	−2.23607	−	2.00000i	−0.106479	−	0.0952381i
$442$	−9.15298	−	9.15298i	−0.435363	−	0.435363i
$443$	6.32456	+	6.32456i	0.300489	+	0.300489i	0.841205	−	0.540716i	$-0.181847\pi$
$443$	6.32456	+	6.32456i	0.300489	+	0.300489i	−0.540716	+	0.841205i	$0.681847\pi$
$444$	11.7082	+	4.47214i	0.555647	+	0.212238i
$445$		0			0
$446$		−	4.94427i		−	0.234118i
$447$	14.2697	+	31.9079i	0.674932	+	1.50919i
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$	35.4164			1.67140			0.835702	−	0.549183i	$-0.185061\pi$
$449$	35.4164			1.67140			0.835702	+	0.549183i	$0.185061\pi$
$450$		0			0
$451$	29.8885			1.40740
$452$	2.49458	−	2.49458i	0.117335	−	0.117335i
$453$	3.90879	+	8.74032i	0.183651	+	0.410656i
$454$			3.23607i			0.151876i
$455$		0			0
$456$	−1.23607	−	0.472136i	−0.0578842	−	0.0221098i
$457$	3.08347	+	3.08347i	0.144238	+	0.144238i	0.775539	−	0.631300i	$-0.217478\pi$
$457$	3.08347	+	3.08347i	0.144238	+	0.144238i	−0.631300	+	0.775539i	$0.717478\pi$
$458$	6.32456	+	6.32456i	0.295527	+	0.295527i
$459$	9.23607	−	4.76393i	0.431103	−	0.222361i
$460$		0			0
$461$			20.3607i			0.948291i	0.880446	+	0.474146i	$0.157243\pi$
$461$			20.3607i			0.948291i	−0.880446	+	0.474146i	$0.842757\pi$
$462$	−5.11667	+	2.28825i	−0.238049	+	0.106459i
$463$	−14.8098	+	14.8098i	−0.688271	+	0.688271i	−0.961850	−	0.273578i	$-0.911793\pi$
$463$	−14.8098	+	14.8098i	−0.688271	+	0.688271i	0.273578	+	0.961850i	$0.411793\pi$
$464$	−0.763932			−0.0354647
$465$		0			0
$466$	8.47214			0.392464
$467$	−5.11667	+	5.11667i	−0.236771	+	0.236771i	−0.815512	−	0.578740i	$-0.803544\pi$
$467$	−5.11667	+	5.11667i	−0.236771	+	0.236771i	0.578740	+	0.815512i	$0.303544\pi$
$468$	−19.3863	+	1.08036i	−0.896133	+	0.0499398i
$469$			8.76393i			0.404681i
$470$		0			0
$471$	−3.41641	+	8.94427i	−0.157420	+	0.412130i
$472$	−0.206331	−	0.206331i	−0.00949715	−	0.00949715i
$473$	−7.40492	−	7.40492i	−0.340479	−	0.340479i
$474$	−8.00000	+	20.9443i	−0.367452	+	0.962002i
$475$		0			0
$476$			2.00000i			0.0916698i
$477$	−32.7820	+	1.82688i	−1.50098	+	0.0836469i
$478$	−21.8021	+	21.8021i	−0.997205	+	0.997205i
$479$	−5.52786			−0.252575			−0.126287	−	0.991994i	$-0.540306\pi$
$479$	−5.52786			−0.252575			−0.126287	+	0.991994i	$0.540306\pi$
$480$		0			0
$481$	−46.8328			−2.13539
$482$	19.7202	−	19.7202i	0.898230	−	0.898230i
$483$	−3.90879	+	1.74806i	−0.177856	+	0.0795397i
$484$		−	0.527864i		−	0.0239938i
$485$		0			0
$486$	3.90983	−	15.0902i	0.177353	−	0.684504i
$487$	11.5687	+	11.5687i	0.524230	+	0.524230i	0.918846	−	0.394616i	$-0.129122\pi$
$487$	11.5687	+	11.5687i	0.524230	+	0.524230i	−0.394616	+	0.918846i	$0.629122\pi$
$488$	9.15298	+	9.15298i	0.414336	+	0.414336i
$489$	23.7082	+	9.05573i	1.07212	+	0.409514i
$490$		0			0
$491$			21.7082i			0.979678i	0.871813	+	0.489839i	$0.162944\pi$
$491$			21.7082i			0.979678i	−0.871813	+	0.489839i	$0.837056\pi$
$492$	−6.53089	−	14.6035i	−0.294435	−	0.658377i
$493$	−1.08036	+	1.08036i	−0.0486571	+	0.0486571i
$494$	4.94427			0.222453
$495$		0			0
$496$	−5.23607			−0.235106
$497$	8.07262	−	8.07262i	0.362106	−	0.362106i
$498$	−5.11667	−	11.4412i	−0.229284	−	0.512694i
$499$			12.0000i			0.537194i	0.963253	+	0.268597i	$0.0865599\pi$
$499$			12.0000i			0.537194i	−0.963253	+	0.268597i	$0.913440\pi$
$500$		0			0
$501$	0.472136	+	0.180340i	0.0210935	+	0.00805699i
$502$	19.1800	+	19.1800i	0.856045	+	0.856045i
$503$	28.3330	+	28.3330i	1.26331	+	1.26331i	0.949481	+	0.313824i	$0.101610\pi$
$503$	28.3330	+	28.3330i	1.26331	+	1.26331i	0.313824	+	0.949481i	$0.398390\pi$
$504$	2.23607	+	2.00000i	0.0996024	+	0.0890871i
$505$		0			0
$506$			8.00000i			0.355643i
$507$	45.6768	−	20.4273i	2.02858	−	0.907208i
$508$	−10.2333	+	10.2333i	−0.454031	+	0.454031i
$509$	37.3050			1.65351			0.826756	−	0.562560i	$-0.190183\pi$
$509$	37.3050			1.65351			0.826756	+	0.562560i	$0.190183\pi$
$510$		0			0
$511$	−3.70820			−0.164041
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−1.20788	+	3.78127i	−0.0533293	+	0.166947i
$514$		−	2.00000i		−	0.0882162i
$515$		0			0
$516$	−2.00000	+	5.23607i	−0.0880451	+	0.230505i
$517$	23.2951	+	23.2951i	1.02452	+	1.02452i
$518$	5.11667	+	5.11667i	0.224814	+	0.224814i
$519$	5.52786	−	14.4721i	0.242646	−	0.635256i
$520$		0			0
$521$			12.2918i			0.538513i	0.963068	+	0.269257i	$0.0867780\pi$
$521$			12.2918i			0.538513i	−0.963068	+	0.269257i	$0.913222\pi$
$522$	0.127520	+	2.28825i	0.00558138	+	0.100154i
$523$	−19.8477	+	19.8477i	−0.867879	+	0.867879i	−0.992237	−	0.124358i	$-0.960313\pi$
$523$	−19.8477	+	19.8477i	−0.867879	+	0.867879i	0.124358	+	0.992237i	$0.460313\pi$
$524$	−8.29180			−0.362229
$525$		0			0
$526$	13.5279			0.589843
$527$	−7.40492	+	7.40492i	−0.322563	+	0.322563i
$528$	5.11667	−	2.28825i	0.222675	−	0.0995831i
$529$		−	16.8885i		−	0.734285i
$530$		0			0
$531$	−0.583592	+	0.652476i	−0.0253257	+	0.0283150i
$532$	−0.540182	−	0.540182i	−0.0234198	−	0.0234198i
$533$	42.2688	+	42.2688i	1.83086	+	1.83086i
$534$	14.9443	+	5.70820i	0.646702	+	0.247018i
$535$		0			0
$536$		−	8.76393i		−	0.378544i
$537$	6.19704	+	13.8570i	0.267422	+	0.597973i
$538$	18.7186	−	18.7186i	0.807017	−	0.807017i
$539$	−3.23607			−0.139387
$540$		0			0
$541$	6.00000			0.257960			0.128980	−	0.991647i	$-0.458830\pi$
$541$	6.00000			0.257960			0.128980	+	0.991647i	$0.458830\pi$
$542$	−10.4397	+	10.4397i	−0.448423	+	0.448423i
$543$	−15.4775	−	34.6088i	−0.664205	−	1.48521i
$544$		−	2.00000i		−	0.0857493i
$545$		0			0
$546$	−10.4721	−	4.00000i	−0.448166	−	0.171184i
$547$	18.4335	+	18.4335i	0.788159	+	0.788159i	0.981192	−	0.193033i	$-0.0618325\pi$
$547$	18.4335	+	18.4335i	0.788159	+	0.788159i	−0.193033	+	0.981192i	$0.561833\pi$
$548$	−9.89949	−	9.89949i	−0.422885	−	0.422885i
$549$	25.8885	−	28.9443i	1.10490	−	1.23531i
$550$		0			0
$551$		−	0.583592i		−	0.0248619i
$552$	3.90879	−	1.74806i	0.166369	−	0.0744025i
$553$	−9.15298	+	9.15298i	−0.389224	+	0.389224i
$554$	−31.5967			−1.34242
$555$		0			0
$556$	1.70820			0.0724440
$557$	26.0447	−	26.0447i	1.10355	−	1.10355i	0.109572	−	0.993979i	$-0.465052\pi$
$557$	26.0447	−	26.0447i	1.10355	−	1.10355i	0.993979	−	0.109572i	$-0.0349480\pi$
$558$	0.874032	+	15.6839i	0.0370007	+	0.663951i
$559$		−	20.9443i		−	0.885848i
$560$		0			0
$561$	4.00000	−	10.4721i	0.168880	−	0.442134i
$562$	−8.74032	−	8.74032i	−0.368688	−	0.368688i
$563$	−26.6637	−	26.6637i	−1.12374	−	1.12374i	−0.991174	−	0.132568i	$-0.957678\pi$
$563$	−26.6637	−	26.6637i	−1.12374	−	1.12374i	−0.132568	−	0.991174i	$-0.542322\pi$
$564$	6.29180	−	16.4721i	0.264932	−	0.693602i
$565$		0			0
$566$			15.7082i			0.660265i
$567$	5.61745	−	7.03166i	0.235911	−	0.295302i
$568$	−8.07262	+	8.07262i	−0.338720	+	0.338720i
$569$	−11.0557			−0.463480			−0.231740	−	0.972778i	$-0.574442\pi$
$569$	−11.0557			−0.463480			−0.231740	+	0.972778i	$0.574442\pi$
$570$		0			0
$571$	23.4164			0.979946			0.489973	−	0.871738i	$-0.337007\pi$
$571$	23.4164			0.979946			0.489973	+	0.871738i	$0.337007\pi$
$572$	−14.8098	+	14.8098i	−0.619230	+	0.619230i
$573$	4.83153	−	2.16073i	0.201840	−	0.0902656i
$574$		−	9.23607i		−	0.385506i
$575$		0			0
$576$	−2.23607	−	2.00000i	−0.0931695	−	0.0833333i
$577$	10.4397	+	10.4397i	0.434609	+	0.434609i	0.890193	−	0.455584i	$-0.150569\pi$
$577$	10.4397	+	10.4397i	0.434609	+	0.434609i	−0.455584	+	0.890193i	$0.650569\pi$
$578$	9.19239	+	9.19239i	0.382353	+	0.382353i
$579$	12.0000	+	4.58359i	0.498703	+	0.190488i
$580$		0			0
$581$		−	7.23607i		−	0.300203i
$582$	10.0270	+	22.4211i	0.415633	+	0.929384i
$583$	−25.0432	+	25.0432i	−1.03718	+	1.03718i
$584$	3.70820			0.153447
$585$		0			0
$586$	3.05573			0.126231
$587$	16.4304	−	16.4304i	0.678154	−	0.678154i	−0.281428	−	0.959582i	$-0.590808\pi$
$587$	16.4304	−	16.4304i	0.678154	−	0.678154i	0.959582	+	0.281428i	$0.0908080\pi$
$588$	0.707107	+	1.58114i	0.0291606	+	0.0652051i
$589$		−	4.00000i		−	0.164817i
$590$		0			0
$591$	3.23607	+	1.23607i	0.133114	+	0.0508450i
$592$	−5.11667	−	5.11667i	−0.210294	−	0.210294i
$593$	−24.7093	−	24.7093i	−1.01469	−	1.01469i	−0.999890	−	0.0148002i	$-0.995289\pi$
$593$	−24.7093	−	24.7093i	−1.01469	−	1.01469i	−0.0148002	−	0.999890i	$-0.504711\pi$
$594$	−7.70820	−	14.9443i	−0.316271	−	0.613171i
$595$		0			0
$596$		−	20.1803i		−	0.826619i
$597$	−3.44742	+	1.54173i	−0.141094	+	0.0630989i
$598$	−11.3137	+	11.3137i	−0.462652	+	0.462652i
$599$	−20.9443			−0.855760			−0.427880	−	0.903836i	$-0.640739\pi$
$599$	−20.9443			−0.855760			−0.427880	+	0.903836i	$0.640739\pi$
$600$		0			0
$601$	18.0000			0.734235			0.367118	−	0.930175i	$-0.380345\pi$
$601$	18.0000			0.734235			0.367118	+	0.930175i	$0.380345\pi$
$602$	−2.28825	+	2.28825i	−0.0932619	+	0.0932619i
$603$	−26.2511	+	1.46292i	−1.06903	+	0.0595748i
$604$		−	5.52786i		−	0.224926i
$605$		0			0
$606$	10.4721	−	27.4164i	0.425401	−	1.11372i
$607$	22.6274	+	22.6274i	0.918419	+	0.918419i	0.996914	−	0.0784959i	$-0.0250118\pi$
$607$	22.6274	+	22.6274i	0.918419	+	0.918419i	−0.0784959	+	0.996914i	$0.525012\pi$
$608$	0.540182	+	0.540182i	0.0219073	+	0.0219073i
$609$	−0.472136	+	1.23607i	−0.0191319	+	0.0500880i
$610$		0			0
$611$			65.8885i			2.66557i
$612$	−5.99070	+	0.333851i	−0.242160	+	0.0134951i
$613$	11.8539	−	11.8539i	0.478774	−	0.478774i	−0.425965	−	0.904739i	$-0.640065\pi$
$613$	11.8539	−	11.8539i	0.478774	−	0.478774i	0.904739	+	0.425965i	$0.140065\pi$
$614$	−17.2361			−0.695591
$615$		0			0
$616$	3.23607			0.130385
$617$	22.9613	−	22.9613i	0.924386	−	0.924386i	−0.0729498	−	0.997336i	$-0.523241\pi$
$617$	22.9613	−	22.9613i	0.924386	−	0.924386i	0.997336	+	0.0729498i	$0.0232413\pi$
$618$	−8.74032	+	3.90879i	−0.351587	+	0.157235i
$619$			7.23607i			0.290842i	0.989370	+	0.145421i	$0.0464537\pi$
$619$			7.23607i			0.290842i	−0.989370	+	0.145421i	$0.953546\pi$
$620$		0			0
$621$	−5.88854	−	11.4164i	−0.236299	−	0.458125i
$622$	5.65685	+	5.65685i	0.226819	+	0.226819i
$623$	6.53089	+	6.53089i	0.261654	+	0.261654i
$624$	10.4721	+	4.00000i	0.419221	+	0.160128i
$625$		0			0
$626$		−	9.23607i		−	0.369148i
$627$	1.74806	+	3.90879i	0.0698110	+	0.156102i
$628$	3.90879	−	3.90879i	0.155978	−	0.155978i
$629$	−14.4721			−0.577042
$630$		0			0
$631$	7.41641			0.295243			0.147621	−	0.989044i	$-0.452838\pi$
$631$	7.41641			0.295243			0.147621	+	0.989044i	$0.452838\pi$
$632$	9.15298	−	9.15298i	0.364086	−	0.364086i
$633$	18.9737	+	42.4264i	0.754136	+	1.68630i
$634$			26.9443i			1.07009i
$635$		0			0
$636$	17.7082	+	6.76393i	0.702176	+	0.268207i
$637$	−4.57649	−	4.57649i	−0.181327	−	0.181327i
$638$	1.74806	+	1.74806i	0.0692065	+	0.0692065i
$639$	25.5279	+	22.8328i	1.00987	+	0.903252i
$640$		0			0
$641$		−	11.0557i		−	0.436675i	−0.975873	−	0.218338i	$-0.929937\pi$
$641$		−	11.0557i		−	0.436675i	0.975873	−	0.218338i	$-0.0700634\pi$
$642$	−26.7912	+	11.9814i	−1.05737	+	0.472869i
$643$	1.12907	−	1.12907i	0.0445262	−	0.0445262i	−0.684493	−	0.729019i	$-0.739976\pi$
$643$	1.12907	−	1.12907i	0.0445262	−	0.0445262i	0.729019	+	0.684493i	$0.239976\pi$
$644$	2.47214			0.0974158
$645$		0			0
$646$	1.52786			0.0601130
$647$	−0.618993	+	0.618993i	−0.0243351	+	0.0243351i	−0.719170	−	0.694835i	$-0.755478\pi$
$647$	−0.618993	+	0.618993i	−0.0243351	+	0.0243351i	0.694835	+	0.719170i	$0.255478\pi$
$648$	−5.61745	+	7.03166i	−0.220674	+	0.276230i
$649$			0.944272i			0.0370659i
$650$		0			0
$651$	−3.23607	+	8.47214i	−0.126832	+	0.332049i
$652$	−10.3609	−	10.3609i	−0.405763	−	0.405763i
$653$	−20.5455	−	20.5455i	−0.804008	−	0.804008i	0.179712	−	0.983719i	$-0.442484\pi$
$653$	−20.5455	−	20.5455i	−0.804008	−	0.804008i	−0.983719	+	0.179712i	$0.942484\pi$
$654$	1.81966	−	4.76393i	0.0711543	−	0.186284i
$655$		0			0
$656$			9.23607i			0.360608i
$657$	−0.618993	−	11.1074i	−0.0241492	−	0.433340i
$658$	7.19859	−	7.19859i	0.280630	−	0.280630i
$659$	−19.2361			−0.749331			−0.374665	−	0.927160i	$-0.622242\pi$
$659$	−19.2361			−0.749331			−0.374665	+	0.927160i	$0.622242\pi$
$660$		0			0
$661$	−8.00000			−0.311164			−0.155582	−	0.987823i	$-0.549725\pi$
$661$	−8.00000			−0.311164			−0.155582	+	0.987823i	$0.549725\pi$
$662$	−18.7186	+	18.7186i	−0.727520	+	0.727520i
$663$	20.4667	−	9.15298i	0.794860	−	0.355472i
$664$			7.23607i			0.280814i
$665$		0			0
$666$	−14.4721	+	16.1803i	−0.560784	+	0.626975i
$667$	1.33540	+	1.33540i	0.0517070	+	0.0517070i
$668$	−0.206331	−	0.206331i	−0.00798319	−	0.00798319i
$669$	8.00000	+	3.05573i	0.309298	+	0.118141i
$670$		0			0
$671$		−	41.8885i		−	1.61709i
$672$	−0.707107	−	1.58114i	−0.0272772	−	0.0609938i
$673$	24.6305	−	24.6305i	0.949437	−	0.949437i	−0.0493450	−	0.998782i	$-0.515713\pi$
$673$	24.6305	−	24.6305i	0.949437	−	0.949437i	0.998782	+	0.0493450i	$0.0157134\pi$
$674$	22.4721			0.865594
$675$		0			0
$676$	−28.8885			−1.11110
$677$	−21.1344	+	21.1344i	−0.812261	+	0.812261i	−0.984972	−	0.172712i	$-0.944747\pi$
$677$	−21.1344	+	21.1344i	−0.812261	+	0.812261i	0.172712	+	0.984972i	$0.444747\pi$
$678$	2.49458	+	5.57804i	0.0958036	+	0.214223i
$679$			14.1803i			0.544191i
$680$		0			0
$681$	−5.23607	−	2.00000i	−0.200647	−	0.0766402i
$682$	11.9814	+	11.9814i	0.458792	+	0.458792i
$683$	−13.3168	−	13.3168i	−0.509554	−	0.509554i	0.404836	−	0.914389i	$-0.367329\pi$
$683$	−13.3168	−	13.3168i	−0.509554	−	0.509554i	−0.914389	+	0.404836i	$0.867329\pi$
$684$	1.52786	−	1.70820i	0.0584193	−	0.0653148i
$685$		0			0
$686$			1.00000i			0.0381802i
$687$	−14.1421	+	6.32456i	−0.539556	+	0.241297i
$688$	2.28825	−	2.28825i	0.0872385	−	0.0872385i
$689$	−70.8328			−2.69852
$690$		0			0
$691$	−2.87539			−0.109385			−0.0546925	−	0.998503i	$-0.517418\pi$
$691$	−2.87539			−0.109385			−0.0546925	+	0.998503i	$0.517418\pi$
$692$	−6.32456	+	6.32456i	−0.240424	+	0.240424i
$693$	−0.540182	−	9.69316i	−0.0205198	−	0.368213i
$694$		−	15.4164i		−	0.585199i
$695$		0			0
$696$	0.472136	−	1.23607i	0.0178963	−	0.0468530i
$697$	13.0618	+	13.0618i	0.494750	+	0.494750i
$698$	2.82843	+	2.82843i	0.107058	+	0.107058i
$699$	−5.23607	+	13.7082i	−0.198046	+	0.518492i
$700$		0			0
$701$			6.87539i			0.259680i	0.991535	+	0.129840i	$0.0414463\pi$
$701$			6.87539i			0.259680i	−0.991535	+	0.129840i	$0.958554\pi$
$702$	10.2333	−	32.0354i	0.386233	−	1.20910i
$703$	3.90879	−	3.90879i	0.147423	−	0.147423i
$704$	−3.23607			−0.121964
$705$		0			0
$706$	−34.0000			−1.27961
$707$	11.9814	−	11.9814i	0.450607	−	0.450607i
$708$	0.461370	−	0.206331i	0.0173393	−	0.00775439i
$709$			9.05573i			0.340095i	0.985436	+	0.170048i	$0.0543921\pi$
$709$			9.05573i			0.340095i	−0.985436	+	0.170048i	$0.945608\pi$
$710$		0			0
$711$	−28.9443	−	25.8885i	−1.08550	−	0.970896i
$712$	−6.53089	−	6.53089i	−0.244755	−	0.244755i
$713$	9.15298	+	9.15298i	0.342782	+	0.342782i
$714$	−3.23607	−	1.23607i	−0.121107	−	0.0462587i
$715$		0			0
$716$		−	8.76393i		−	0.327524i
$717$	−21.8021	−	48.7510i	−0.814214	−	1.82064i
$718$	−8.07262	+	8.07262i	−0.301267	+	0.301267i
$719$	−23.4164			−0.873285			−0.436642	−	0.899635i	$-0.643832\pi$
$719$	−23.4164			−0.873285			−0.436642	+	0.899635i	$0.643832\pi$
$720$		0			0
$721$	−5.52786			−0.205868
$722$	13.0224	−	13.0224i	0.484642	−	0.484642i
$723$	19.7202	+	44.0957i	0.733401	+	1.63994i
$724$			21.8885i			0.813481i
$725$		0			0
$726$	0.854102	+	0.326238i	0.0316987	+	0.0121078i
$727$	−22.2148	−	22.2148i	−0.823900	−	0.823900i	0.162765	−	0.986665i	$-0.447959\pi$
$727$	−22.2148	−	22.2148i	−0.823900	−	0.823900i	−0.986665	+	0.162765i	$0.947959\pi$
$728$	4.57649	+	4.57649i	0.169616	+	0.169616i
$729$	22.0000	+	15.6525i	0.814815	+	0.579721i
$730$		0			0
$731$		−	6.47214i		−	0.239381i
$732$	−20.4667	+	9.15298i	−0.756471	+	0.338304i
$733$	4.32145	−	4.32145i	0.159616	−	0.159616i	−0.622780	−	0.782397i	$-0.713997\pi$
$733$	4.32145	−	4.32145i	0.159616	−	0.159616i	0.782397	+	0.622780i	$0.213997\pi$
$734$	−20.9443			−0.773067
$735$		0			0
$736$	−2.47214			−0.0911241
$737$	−20.0540	+	20.0540i	−0.738700	+	0.738700i
$738$	27.6653	−	1.54173i	1.01837	−	0.0567520i
$739$			44.3607i			1.63183i	0.578169	+	0.815917i	$0.303767\pi$
$739$			44.3607i			1.63183i	−0.578169	+	0.815917i	$0.696233\pi$
$740$		0			0
$741$	−3.05573	+	8.00000i	−0.112255	+	0.293887i
$742$	7.73877	+	7.73877i	0.284099	+	0.284099i
$743$	13.4744	+	13.4744i	0.494329	+	0.494329i	0.909667	−	0.415338i	$-0.136337\pi$
$743$	13.4744	+	13.4744i	0.494329	+	0.494329i	−0.415338	+	0.909667i	$0.636337\pi$
$744$	3.23607	−	8.47214i	0.118640	−	0.310604i
$745$		0			0
$746$			23.2361i			0.850733i
$747$	21.6746	−	1.20788i	0.793031	−	0.0441941i
$748$	−4.57649	+	4.57649i	−0.167333	+	0.167333i
$749$	−16.9443			−0.619130
$750$		0			0
$751$	−15.4164			−0.562553			−0.281276	−	0.959627i	$-0.590758\pi$
$751$	−15.4164			−0.562553			−0.281276	+	0.959627i	$0.590758\pi$
$752$	−7.19859	+	7.19859i	−0.262505	+	0.262505i
$753$	−42.8878	+	19.1800i	−1.56292	+	0.698958i
$754$			4.94427i			0.180060i
$755$		0			0
$756$	−4.61803	+	2.38197i	−0.167956	+	0.0866313i
$757$	8.35776	+	8.35776i	0.303768	+	0.303768i	0.842486	−	0.538718i	$-0.181091\pi$
$757$	8.35776	+	8.35776i	0.303768	+	0.303768i	−0.538718	+	0.842486i	$0.681091\pi$
$758$	−20.0540	−	20.0540i	−0.728395	−	0.728395i
$759$	−12.9443	−	4.94427i	−0.469847	−	0.179466i
$760$		0			0
$761$			14.7639i			0.535192i	0.963531	+	0.267596i	$0.0862293\pi$
$761$			14.7639i			0.535192i	−0.963531	+	0.267596i	$0.913771\pi$
$762$	−10.2333	−	22.8825i	−0.370715	−	0.828944i
$763$	2.08191	−	2.08191i	0.0753704	−	0.0753704i
$764$	−3.05573			−0.110552
$765$		0			0
$766$	12.6525			0.457153
$767$	−1.33540	+	1.33540i	−0.0482186	+	0.0482186i
$768$	0.707107	+	1.58114i	0.0255155	+	0.0570544i
$769$		−	29.0557i		−	1.04778i	−0.851787	−	0.523888i	$-0.824481\pi$
$769$		−	29.0557i		−	1.04778i	0.851787	−	0.523888i	$-0.175519\pi$
$770$		0			0
$771$	3.23607	+	1.23607i	0.116544	+	0.0445159i
$772$	−5.24419	−	5.24419i	−0.188743	−	0.188743i
$773$	−2.16073	−	2.16073i	−0.0777159	−	0.0777159i	0.667180	−	0.744896i	$-0.267501\pi$
$773$	−2.16073	−	2.16073i	−0.0777159	−	0.0777159i	−0.744896	+	0.667180i	$0.767501\pi$
$774$	−7.23607	−	6.47214i	−0.260095	−	0.232636i
$775$		0			0
$776$		−	14.1803i		−	0.509045i
$777$	−11.4412	+	5.11667i	−0.410452	+	0.183560i
$778$	−16.4304	+	16.4304i	−0.589058	+	0.589058i
$779$	−7.05573			−0.252798
$780$		0			0
$781$	36.9443			1.32197
$782$	−3.49613	+	3.49613i	−0.125021	+	0.125021i
$783$	−3.78127	−	1.20788i	−0.135132	−	0.0431662i
$784$		−	1.00000i		−	0.0357143i
$785$		0			0
$786$	5.12461	−	13.4164i	0.182789	−	0.478547i
$787$	−13.5231	−	13.5231i	−0.482048	−	0.482048i	0.423737	−	0.905785i	$-0.360718\pi$
$787$	−13.5231	−	13.5231i	−0.482048	−	0.482048i	−0.905785	+	0.423737i	$0.860718\pi$
$788$	−1.41421	−	1.41421i	−0.0503793	−	0.0503793i
$789$	−8.36068	+	21.8885i	−0.297648	+	0.779253i
$790$		0			0
$791$			3.52786i			0.125436i
$792$	0.540182	+	9.69316i	0.0191945	+	0.344432i
$793$	59.2393	−	59.2393i	2.10365	−	2.10365i
$794$	0.583592			0.0207109
$795$		0			0
$796$	2.18034			0.0772801
$797$	−32.4481	+	32.4481i	−1.14937	+	1.14937i	−0.162694	+	0.986677i	$0.552018\pi$
$797$	−32.4481	+	32.4481i	−1.14937	+	1.14937i	−0.986677	+	0.162694i	$0.947982\pi$
$798$	1.20788	−	0.540182i	0.0427586	−	0.0191222i
$799$			20.3607i			0.720309i
$800$		0			0
$801$	−18.4721	+	20.6525i	−0.652681	+	0.729719i
$802$	−2.16073	−	2.16073i	−0.0762979	−	0.0762979i
$803$	−8.48528	−	8.48528i	−0.299439	−	0.299439i
$804$	14.1803	+	5.41641i	0.500102	+	0.191022i
$805$		0			0
$806$			33.8885i			1.19367i
$807$	18.7186	+	41.8561i	0.658927	+	1.47341i
$808$	−11.9814	+	11.9814i	−0.421505	+	0.421505i
$809$	39.4164			1.38581			0.692904	−	0.721030i	$-0.256331\pi$
$809$	39.4164			1.38581			0.692904	+	0.721030i	$0.256331\pi$
$810$		0			0
$811$	32.5410			1.14267			0.571335	−	0.820717i	$-0.306426\pi$
$811$	32.5410			1.14267			0.571335	+	0.820717i	$0.306426\pi$
$812$	0.540182	−	0.540182i	0.0189567	−	0.0189567i
$813$	−10.4397	−	23.3438i	−0.366135	−	0.818704i
$814$			23.4164i			0.820745i
$815$		0			0
$816$	3.23607	+	1.23607i	0.113285	+	0.0432710i
$817$	1.74806	+	1.74806i	0.0611570	+	0.0611570i
$818$	2.90724	+	2.90724i	0.101649	+	0.101649i
$819$	12.9443	−	14.4721i	0.452309	−	0.505697i
$820$		0			0
$821$		−	47.5967i		−	1.66114i	−0.556916	−	0.830569i	$-0.688015\pi$
$821$		−	47.5967i		−	1.66114i	0.556916	−	0.830569i	$-0.311985\pi$
$822$	22.1359	−	9.89949i	0.772080	−	0.345285i
$823$	−19.6414	+	19.6414i	−0.684655	+	0.684655i	−0.961045	−	0.276390i	$-0.910862\pi$
$823$	−19.6414	+	19.6414i	−0.684655	+	0.684655i	0.276390	+	0.961045i	$0.410862\pi$
$824$	5.52786			0.192572
$825$		0			0
$826$	0.291796			0.0101529
$827$	7.14988	−	7.14988i	0.248626	−	0.248626i	−0.571781	−	0.820406i	$-0.693747\pi$
$827$	7.14988	−	7.14988i	0.248626	−	0.248626i	0.820406	+	0.571781i	$0.193747\pi$
$828$	0.412662	+	7.40492i	0.0143410	+	0.257339i
$829$		−	25.8885i		−	0.899146i	−0.893244	−	0.449573i	$-0.851576\pi$
$829$		−	25.8885i		−	0.899146i	0.893244	−	0.449573i	$-0.148424\pi$
$830$		0			0
$831$	19.5279	−	51.1246i	0.677414	−	1.77349i
$832$	−4.57649	−	4.57649i	−0.158661	−	0.158661i
$833$	−1.41421	−	1.41421i	−0.0489996	−	0.0489996i
$834$	−1.05573	+	2.76393i	−0.0365569	+	0.0957071i
$835$		0			0
$836$		−	2.47214i		−	0.0855006i
$837$	−25.9172	−	8.27895i	−0.895830	−	0.286162i
$838$	13.5231	−	13.5231i	0.467149	−	0.467149i
$839$	−52.3607			−1.80769			−0.903846	−	0.427859i	$-0.859268\pi$
$839$	−52.3607			−1.80769			−0.903846	+	0.427859i	$0.859268\pi$
$840$		0			0
$841$	−28.4164			−0.979876
$842$	7.73877	−	7.73877i	0.266696	−	0.266696i
$843$	19.5440	−	8.74032i	0.673129	−	0.301033i
$844$		−	26.8328i		−	0.923624i
$845$		0			0
$846$	22.7639	+	20.3607i	0.782640	+	0.700015i
$847$	0.373256	+	0.373256i	0.0128252	+	0.0128252i
$848$	−7.73877	−	7.73877i	−0.265750	−	0.265750i
$849$	−25.4164	−	9.70820i	−0.872289	−	0.333185i
$850$		0			0
$851$			17.8885i			0.613211i
$852$	−8.07262	−	18.0509i	−0.276563	−	0.618415i
$853$	−16.5579	+	16.5579i	−0.566932	+	0.566932i	−0.931268	−	0.364336i	$-0.881296\pi$
$853$	−16.5579	+	16.5579i	−0.566932	+	0.566932i	0.364336	+	0.931268i	$0.381296\pi$
$854$	−12.9443			−0.442944
$855$		0			0
$856$	16.9443			0.579143
$857$	17.5595	−	17.5595i	0.599819	−	0.599819i	−0.340445	−	0.940264i	$-0.610578\pi$
$857$	17.5595	−	17.5595i	0.599819	−	0.599819i	0.940264	+	0.340445i	$0.110578\pi$
$858$	−14.8098	−	33.1158i	−0.505599	−	1.13055i
$859$		−	32.5410i		−	1.11029i	−0.831755	−	0.555143i	$-0.812664\pi$
$859$		−	32.5410i		−	1.11029i	0.831755	−	0.555143i	$-0.187336\pi$
$860$		0			0
$861$	14.9443	+	5.70820i	0.509299	+	0.194535i
$862$	8.89794	+	8.89794i	0.303065	+	0.303065i
$863$	−9.15298	−	9.15298i	−0.311571	−	0.311571i	0.533947	−	0.845518i	$-0.320708\pi$
$863$	−9.15298	−	9.15298i	−0.311571	−	0.311571i	−0.845518	+	0.533947i	$0.820708\pi$
$864$	4.61803	−	2.38197i	0.157109	−	0.0810361i
$865$		0			0
$866$		−	6.76393i		−	0.229848i
$867$	−20.5548	+	9.19239i	−0.698078	+	0.312190i
$868$	3.70246	−	3.70246i	0.125670	−	0.125670i
$869$	−41.8885			−1.42097
$870$		0			0
$871$	−56.7214			−1.92193
$872$	−2.08191	+	2.08191i	−0.0705025	+	0.0705025i
$873$	−42.4751	+	2.36706i	−1.43756	+	0.0801127i
$874$		−	1.88854i		−	0.0638809i
$875$		0			0
$876$	−2.29180	+	6.00000i	−0.0774326	+	0.202721i
$877$	16.4304	+	16.4304i	0.554815	+	0.554815i	0.927827	−	0.373012i	$-0.121675\pi$
$877$	16.4304	+	16.4304i	0.554815	+	0.554815i	−0.373012	+	0.927827i	$0.621675\pi$
$878$	−6.94355	−	6.94355i	−0.234333	−	0.234333i
$879$	−1.88854	+	4.94427i	−0.0636990	+	0.166766i
$880$		0			0
$881$			36.2918i			1.22270i	0.791360	+	0.611351i	$0.209374\pi$
$881$			36.2918i			1.22270i	−0.791360	+	0.611351i	$0.790626\pi$
$882$	−2.99535	+	0.166925i	−0.100859	+	0.00562067i
$883$	36.8971	−	36.8971i	1.24169	−	1.24169i	0.282384	−	0.959301i	$-0.408875\pi$
$883$	36.8971	−	36.8971i	1.24169	−	1.24169i	0.959301	−	0.282384i	$-0.0911252\pi$
$884$	−12.9443			−0.435363
$885$		0			0
$886$	8.94427			0.300489
$887$	24.1692	−	24.1692i	0.811521	−	0.811521i	−0.173341	−	0.984862i	$-0.555456\pi$
$887$	24.1692	−	24.1692i	0.811521	−	0.811521i	0.984862	+	0.173341i	$0.0554563\pi$
$888$	11.4412	−	5.11667i	0.383942	−	0.171704i
$889$		−	14.4721i		−	0.485380i
$890$		0			0
$891$	28.9443	−	3.23607i	0.969670	−	0.108412i
$892$	−3.49613	−	3.49613i	−0.117059	−	0.117059i
$893$	−5.49923	−	5.49923i	−0.184025	−	0.184025i
$894$	32.6525	+	12.4721i	1.09206	+	0.417131i
$895$		0			0
$896$			1.00000i			0.0334077i
$897$	−11.3137	−	25.2982i	−0.377754	−	0.844683i
$898$	25.0432	−	25.0432i	0.835702	−	0.835702i
$899$	4.00000			0.133407
$900$		0			0
$901$	−21.8885			−0.729213
$902$	21.1344	−	21.1344i	0.703698	−	0.703698i
$903$	−2.28825	−	5.11667i	−0.0761480	−	0.170272i
$904$		−	3.52786i		−	0.117335i
$905$		0			0
$906$	8.94427	+	3.41641i	0.297154	+	0.113503i
$907$	−17.5107	−	17.5107i	−0.581435	−	0.581435i	0.353863	−	0.935297i	$-0.384868\pi$
$907$	−17.5107	−	17.5107i	−0.581435	−	0.581435i	−0.935297	+	0.353863i	$0.884868\pi$
$908$	2.28825	+	2.28825i	0.0759381	+	0.0759381i
$909$	37.8885	+	33.8885i	1.25668	+	1.12401i
$910$		0			0
$911$		−	35.0557i		−	1.16145i	−0.814100	−	0.580724i	$-0.802770\pi$
$911$		−	35.0557i		−	1.16145i	0.814100	−	0.580724i	$-0.197230\pi$
$912$	−1.20788	+	0.540182i	−0.0399970	+	0.0178872i
$913$	16.5579	−	16.5579i	0.547987	−	0.547987i
$914$	4.36068			0.144238
$915$		0			0
$916$	8.94427			0.295527
$917$	5.86319	−	5.86319i	0.193619	−	0.193619i
$918$	3.16228	−	9.89949i	0.104371	−	0.326732i
$919$			20.3607i			0.671637i	0.941927	+	0.335818i	$0.109013\pi$
$919$			20.3607i			0.671637i	−0.941927	+	0.335818i	$0.890987\pi$
$920$		0			0
$921$	10.6525	−	27.8885i	0.351011	−	0.918959i
$922$	14.3972	+	14.3972i	0.474146	+	0.474146i
$923$	52.2471	+	52.2471i	1.71973	+	1.71973i
$924$	−2.00000	+	5.23607i	−0.0657952	+	0.172254i
$925$		0			0
$926$			20.9443i			0.688271i
$927$	−0.922740	−	16.5579i	−0.0303068	−	0.543833i
$928$	−0.540182	+	0.540182i	−0.0177323	+	0.0177323i
$929$	−14.1803			−0.465242			−0.232621	−	0.972567i	$-0.574730\pi$
$929$	−14.1803			−0.465242			−0.232621	+	0.972567i	$0.574730\pi$
$930$		0			0
$931$	0.763932			0.0250369
$932$	5.99070	−	5.99070i	0.196232	−	0.196232i
$933$	−12.6491	+	5.65685i	−0.414113	+	0.185197i
$934$			7.23607i			0.236771i
$935$		0			0
$936$	−12.9443	+	14.4721i	−0.423097	+	0.473037i
$937$	−8.27895	−	8.27895i	−0.270462	−	0.270462i	0.558824	−	0.829286i	$-0.311253\pi$
$937$	−8.27895	−	8.27895i	−0.270462	−	0.270462i	−0.829286	+	0.558824i	$0.811253\pi$
$938$	6.19704	+	6.19704i	0.202340	+	0.202340i
$939$	14.9443	+	5.70820i	0.487688	+	0.186280i
$940$		0			0
$941$		−	7.05573i		−	0.230010i	−0.993365	−	0.115005i	$-0.963312\pi$
$941$		−	7.05573i		−	0.230010i	0.993365	−	0.115005i	$-0.0366884\pi$
$942$	3.90879	+	8.74032i	0.127355	+	0.284775i
$943$	16.1452	−	16.1452i	0.525761	−	0.525761i
$944$	−0.291796			−0.00949715
$945$		0			0
$946$	−10.4721			−0.340479
$947$	−18.7186	+	18.7186i	−0.608274	+	0.608274i	−0.942495	−	0.334221i	$-0.891527\pi$
$947$	−18.7186	+	18.7186i	−0.608274	+	0.608274i	0.334221	+	0.942495i	$0.391527\pi$
$948$	9.15298	+	20.4667i	0.297275	+	0.664727i
$949$		−	24.0000i		−	0.779073i
$950$		0			0
$951$	−43.5967	−	16.6525i	−1.41372	−	0.539994i
$952$	1.41421	+	1.41421i	0.0458349	+	0.0458349i
$953$	22.9613	+	22.9613i	0.743788	+	0.743788i	0.973305	−	0.229516i	$-0.0737144\pi$
$953$	22.9613	+	22.9613i	0.743788	+	0.743788i	−0.229516	+	0.973305i	$0.573714\pi$
$954$	−21.8885	+	24.4721i	−0.708668	+	0.792315i
$955$		0			0
$956$			30.8328i			0.997205i
$957$	−3.90879	+	1.74806i	−0.126353	+	0.0565069i
$958$	−3.90879	+	3.90879i	−0.126287	+	0.126287i
$959$	14.0000			0.452084
$960$		0			0
$961$	−3.58359			−0.115600
$962$	−33.1158	+	33.1158i	−1.06770	+	1.06770i
$963$	−2.82843	−	50.7541i	−0.0911448	−	1.63553i
$964$		−	27.8885i		−	0.898230i
$965$		0			0
$966$	−1.52786	+	4.00000i	−0.0491582	+	0.128698i
$967$	−16.9706	−	16.9706i	−0.545737	−	0.545737i	0.379468	−	0.925205i	$-0.376107\pi$
$967$	−16.9706	−	16.9706i	−0.545737	−	0.545737i	−0.925205	+	0.379468i	$0.876107\pi$
$968$	−0.373256	−	0.373256i	−0.0119969	−	0.0119969i
$969$	−0.944272	+	2.47214i	−0.0303344	+	0.0794164i
$970$		0			0
$971$			48.6525i			1.56133i	0.624948	+	0.780666i	$0.285120\pi$
$971$			48.6525i			1.56133i	−0.624948	+	0.780666i	$0.714880\pi$
$972$	−7.90569	−	13.4350i	−0.253575	−	0.430929i
$973$	−1.20788	+	1.20788i	−0.0387229	+	0.0387229i
$974$	16.3607			0.524230
$975$		0			0
$976$	12.9443			0.414336
$977$	−27.7928	+	27.7928i	−0.889170	+	0.889170i	−0.994443	−	0.105273i	$-0.966428\pi$
$977$	−27.7928	+	27.7928i	−0.889170	+	0.889170i	0.105273	+	0.994443i	$0.466428\pi$
$978$	23.1676	−	10.3609i	0.740818	−	0.331304i
$979$			29.8885i			0.955242i
$980$		0			0
$981$	6.58359	+	5.88854i	0.210198	+	0.188007i
$982$	15.3500	+	15.3500i	0.489839	+	0.489839i
$983$	−29.8260	−	29.8260i	−0.951302	−	0.951302i	0.0475663	−	0.998868i	$-0.484853\pi$
$983$	−29.8260	−	29.8260i	−0.951302	−	0.951302i	−0.998868	+	0.0475663i	$0.984853\pi$
$984$	−14.9443	−	5.70820i	−0.476406	−	0.181971i
$985$		0			0
$986$			1.52786i			0.0486571i
$987$	7.19859	+	16.0965i	0.229134	+	0.512358i
$988$	3.49613	−	3.49613i	0.111227	−	0.111227i
$989$	−8.00000			−0.254385
$990$		0			0
$991$	−43.1935			−1.37209			−0.686043	−	0.727561i	$-0.740654\pi$
$991$	−43.1935			−1.37209			−0.686043	+	0.727561i	$0.740654\pi$
$992$	−3.70246	+	3.70246i	−0.117553	+	0.117553i
$993$	−18.7186	−	41.8561i	−0.594018	−	1.32826i
$994$		−	11.4164i		−	0.362106i
$995$		0			0
$996$	−11.7082	−	4.47214i	−0.370989	−	0.141705i
$997$	−6.99226	−	6.99226i	−0.221447	−	0.221447i	0.587661	−	0.809108i	$-0.300049\pi$
$997$	−6.99226	−	6.99226i	−0.221447	−	0.221447i	−0.809108	+	0.587661i	$0.800049\pi$
$998$	8.48528	+	8.48528i	0.268597	+	0.268597i
$999$	−17.2361	−	33.4164i	−0.545325	−	1.05725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.j.a.407.4	yes	8
3.2	odd	2		1050.2.j.b.407.1	yes	8
5.2	odd	4		1050.2.j.b.743.4	yes	8
5.3	odd	4		1050.2.j.b.743.1	yes	8
5.4	even	2	inner	1050.2.j.a.407.1	✓	8
15.2	even	4	inner	1050.2.j.a.743.2	yes	8
15.8	even	4	inner	1050.2.j.a.743.3	yes	8
15.14	odd	2		1050.2.j.b.407.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.j.a.407.1	✓	8	5.4	even	2	inner
1050.2.j.a.407.4	yes	8	1.1	even	1	trivial
1050.2.j.a.743.2	yes	8	15.2	even	4	inner
1050.2.j.a.743.3	yes	8	15.8	even	4	inner
1050.2.j.b.407.1	yes	8	3.2	odd	2
1050.2.j.b.407.4	yes	8	15.14	odd	2
1050.2.j.b.743.1	yes	8	5.3	odd	4
1050.2.j.b.743.4	yes	8	5.2	odd	4

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.707107 + 1.58114i) q^{3} -1.00000i q^{4} +(1.61803 + 0.618034i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.00000 + 2.23607i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.707107 + 1.58114i) q^{3} -1.00000i q^{4} +(1.61803 + 0.618034i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.00000 + 2.23607i) q^{9} +3.23607i q^{11} +(1.58114 - 0.707107i) q^{12} +(-4.57649 + 4.57649i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(-1.41421 + 1.41421i) q^{17} +(0.166925 + 2.99535i) q^{18} -0.763932i q^{19} +(-0.618034 + 1.61803i) q^{21} +(2.28825 + 2.28825i) q^{22} +(1.74806 + 1.74806i) q^{23} +(0.618034 - 1.61803i) q^{24} +6.47214i q^{26} +(-4.94975 - 1.58114i) q^{27} +(0.707107 - 0.707107i) q^{28} +0.763932 q^{29} +5.23607 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-5.11667 + 2.28825i) q^{33} +2.00000i q^{34} +(2.23607 + 2.00000i) q^{36} +(5.11667 + 5.11667i) q^{37} +(-0.540182 - 0.540182i) q^{38} +(-10.4721 - 4.00000i) q^{39} -9.23607i q^{41} +(0.707107 + 1.58114i) q^{42} +(-2.28825 + 2.28825i) q^{43} +3.23607 q^{44} +2.47214 q^{46} +(7.19859 - 7.19859i) q^{47} +(-0.707107 - 1.58114i) q^{48} +1.00000i q^{49} +(-3.23607 - 1.23607i) q^{51} +(4.57649 + 4.57649i) q^{52} +(7.73877 + 7.73877i) q^{53} +(-4.61803 + 2.38197i) q^{54} -1.00000i q^{56} +(1.20788 - 0.540182i) q^{57} +(0.540182 - 0.540182i) q^{58} +0.291796 q^{59} -12.9443 q^{61} +(3.70246 - 3.70246i) q^{62} +(-2.99535 + 0.166925i) q^{63} +1.00000i q^{64} +(-2.00000 + 5.23607i) q^{66} +(6.19704 + 6.19704i) q^{67} +(1.41421 + 1.41421i) q^{68} +(-1.52786 + 4.00000i) q^{69} -11.4164i q^{71} +(2.99535 - 0.166925i) q^{72} +(-2.62210 + 2.62210i) q^{73} +7.23607 q^{74} -0.763932 q^{76} +(-2.28825 + 2.28825i) q^{77} +(-10.2333 + 4.57649i) q^{78} +12.9443i q^{79} +(-1.00000 - 8.94427i) q^{81} +(-6.53089 - 6.53089i) q^{82} +(-5.11667 - 5.11667i) q^{83} +(1.61803 + 0.618034i) q^{84} +3.23607i q^{86} +(0.540182 + 1.20788i) q^{87} +(2.28825 - 2.28825i) q^{88} +9.23607 q^{89} -6.47214 q^{91} +(1.74806 - 1.74806i) q^{92} +(3.70246 + 8.27895i) q^{93} -10.1803i q^{94} +(-1.61803 - 0.618034i) q^{96} +(10.0270 + 10.0270i) q^{97} +(0.707107 + 0.707107i) q^{98} +(-7.23607 - 6.47214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{6} - 16 q^{9}+O(q^{10}) \) 8 * q + 4 * q^6 - 16 * q^9	\( 8 q + 4 q^{6} - 16 q^{9} + 8 q^{14} - 8 q^{16} + 4 q^{21} - 4 q^{24} + 24 q^{29} + 24 q^{31} - 48 q^{39} + 8 q^{44} - 16 q^{46} - 8 q^{51} - 28 q^{54} + 56 q^{59} - 32 q^{61} - 16 q^{66} - 48 q^{69} + 40 q^{74} - 24 q^{76} - 8 q^{81} + 4 q^{84} + 56 q^{89} - 16 q^{91} - 4 q^{96} - 40 q^{99}+O(q^{100}) \) 8 * q + 4 * q^6 - 16 * q^9 + 8 * q^14 - 8 * q^16 + 4 * q^21 - 4 * q^24 + 24 * q^29 + 24 * q^31 - 48 * q^39 + 8 * q^44 - 16 * q^46 - 8 * q^51 - 28 * q^54 + 56 * q^59 - 32 * q^61 - 16 * q^66 - 48 * q^69 + 40 * q^74 - 24 * q^76 - 8 * q^81 + 4 * q^84 + 56 * q^89 - 16 * q^91 - 4 * q^96 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more