LMFDB - Embedded newform 350.2.j.e.249.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(149,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("350.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	350.249
Dual form			350.2.j.e.149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.00000 q^{6} +(0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.00000 q^{6} +(0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.73205 - 1.00000i) q^{12} +2.00000i q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.59808 - 1.50000i) q^{17} +(0.866025 + 0.500000i) q^{18} +(4.00000 + 6.92820i) q^{19} +(4.00000 - 3.46410i) q^{21} +(-7.79423 + 4.50000i) q^{23} +(1.00000 - 1.73205i) q^{24} +(1.00000 + 1.73205i) q^{26} -4.00000i q^{27} +(-1.73205 - 2.00000i) q^{28} +6.00000 q^{29} +(-2.50000 + 4.33013i) q^{31} +(-0.866025 - 0.500000i) q^{32} -3.00000 q^{34} +1.00000 q^{36} +(-6.92820 + 4.00000i) q^{37} +(6.92820 + 4.00000i) q^{38} +(-2.00000 + 3.46410i) q^{39} -3.00000 q^{41} +(1.73205 - 5.00000i) q^{42} -10.0000i q^{43} +(-4.50000 + 7.79423i) q^{46} +(2.59808 - 1.50000i) q^{47} -2.00000i q^{48} +(-5.50000 - 4.33013i) q^{49} +(-3.00000 - 5.19615i) q^{51} +(1.73205 + 1.00000i) q^{52} +(-5.19615 - 3.00000i) q^{53} +(-2.00000 - 3.46410i) q^{54} +(-2.50000 - 0.866025i) q^{56} +16.0000i q^{57} +(5.19615 - 3.00000i) q^{58} +(6.00000 - 10.3923i) q^{59} +(2.00000 + 3.46410i) q^{61} +5.00000i q^{62} +(2.59808 - 0.500000i) q^{63} -1.00000 q^{64} +(1.73205 + 1.00000i) q^{67} +(-2.59808 + 1.50000i) q^{68} -18.0000 q^{69} -9.00000 q^{71} +(0.866025 - 0.500000i) q^{72} +(8.66025 + 5.00000i) q^{73} +(-4.00000 + 6.92820i) q^{74} +8.00000 q^{76} +4.00000i q^{78} +(2.50000 + 4.33013i) q^{79} +(5.50000 - 9.52628i) q^{81} +(-2.59808 + 1.50000i) q^{82} -6.00000i q^{83} +(-1.00000 - 5.19615i) q^{84} +(-5.00000 - 8.66025i) q^{86} +(10.3923 + 6.00000i) q^{87} +(1.50000 + 2.59808i) q^{89} +(5.00000 + 1.73205i) q^{91} +9.00000i q^{92} +(-8.66025 + 5.00000i) q^{93} +(1.50000 - 2.59808i) q^{94} +(-1.00000 - 1.73205i) q^{96} -5.00000i q^{97} +(-6.92820 - 1.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 8 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 8 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} + 8 q^{6} + 2 q^{9} - 2 q^{14} - 2 q^{16} + 16 q^{19} + 16 q^{21} + 4 q^{24} + 4 q^{26} + 24 q^{29} - 10 q^{31} - 12 q^{34} + 4 q^{36} - 8 q^{39} - 12 q^{41} - 18 q^{46} - 22 q^{49} - 12 q^{51} - 8 q^{54} - 10 q^{56} + 24 q^{59} + 8 q^{61} - 4 q^{64} - 72 q^{69} - 36 q^{71} - 16 q^{74} + 32 q^{76} + 10 q^{79} + 22 q^{81} - 4 q^{84} - 20 q^{86} + 6 q^{89} + 20 q^{91} + 6 q^{94} - 4 q^{96}+O(q^{100}) $ 4 * q + 2 * q^4 + 8 * q^6 + 2 * q^9 - 2 * q^14 - 2 * q^16 + 16 * q^19 + 16 * q^21 + 4 * q^24 + 4 * q^26 + 24 * q^29 - 10 * q^31 - 12 * q^34 + 4 * q^36 - 8 * q^39 - 12 * q^41 - 18 * q^46 - 22 * q^49 - 12 * q^51 - 8 * q^54 - 10 * q^56 + 24 * q^59 + 8 * q^61 - 4 * q^64 - 72 * q^69 - 36 * q^71 - 16 * q^74 + 32 * q^76 + 10 * q^79 + 22 * q^81 - 4 * q^84 - 20 * q^86 + 6 * q^89 + 20 * q^91 + 6 * q^94 - 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	1.73205	+	1.00000i	1.00000	+	0.577350i	0.908248	−	0.418432i	$-0.137420\pi$
$3$	1.73205	+	1.00000i	1.00000	+	0.577350i	0.0917517	+	0.995782i	$0.470753\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	2.00000			0.816497
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	1.73205	−	1.00000i	0.500000	−	0.288675i
$13$			2.00000i			0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$			2.00000i			0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$	−0.500000	−	2.59808i	−0.133631	−	0.694365i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.59808	−	1.50000i	−0.630126	−	0.363803i	0.150675	−	0.988583i	$-0.451855\pi$
$17$	−2.59808	−	1.50000i	−0.630126	−	0.363803i	−0.780801	+	0.624780i	$0.785189\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	4.00000	+	6.92820i	0.917663	+	1.58944i	0.802955	+	0.596040i	$0.203260\pi$
$19$	4.00000	+	6.92820i	0.917663	+	1.58944i	0.114708	+	0.993399i	$0.463407\pi$
$20$		0			0
$21$	4.00000	−	3.46410i	0.872872	−	0.755929i
$22$		0			0
$23$	−7.79423	+	4.50000i	−1.62521	+	0.938315i	−0.639713	+	0.768613i	$0.720947\pi$
$23$	−7.79423	+	4.50000i	−1.62521	+	0.938315i	−0.985496	+	0.169701i	$0.945720\pi$
$24$	1.00000	−	1.73205i	0.204124	−	0.353553i
$25$		0			0
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$		−	4.00000i		−	0.769800i
$28$	−1.73205	−	2.00000i	−0.327327	−	0.377964i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	−0.998322	−	0.0579057i	$-0.981558\pi$
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	0.549309	+	0.835619i	$0.314891\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−3.00000			−0.514496
$35$		0			0
$36$	1.00000			0.166667
$37$	−6.92820	+	4.00000i	−1.13899	+	0.657596i	−0.946180	−	0.323640i	$-0.895093\pi$
$37$	−6.92820	+	4.00000i	−1.13899	+	0.657596i	−0.192809	+	0.981236i	$0.561760\pi$
$38$	6.92820	+	4.00000i	1.12390	+	0.648886i
$39$	−2.00000	+	3.46410i	−0.320256	+	0.554700i
$40$		0			0
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$	1.73205	−	5.00000i	0.267261	−	0.771517i
$43$		−	10.0000i		−	1.52499i	−0.646997	−	0.762493i	$-0.723975\pi$
$43$		−	10.0000i		−	1.52499i	0.646997	−	0.762493i	$-0.276025\pi$
$44$		0			0
$45$		0			0
$46$	−4.50000	+	7.79423i	−0.663489	+	1.14920i
$47$	2.59808	−	1.50000i	0.378968	−	0.218797i	−0.298401	−	0.954441i	$-0.596453\pi$
$47$	2.59808	−	1.50000i	0.378968	−	0.218797i	0.677369	+	0.735643i	$0.263120\pi$
$48$		−	2.00000i		−	0.288675i
$49$	−5.50000	−	4.33013i	−0.785714	−	0.618590i
$50$		0			0
$51$	−3.00000	−	5.19615i	−0.420084	−	0.727607i
$52$	1.73205	+	1.00000i	0.240192	+	0.138675i
$53$	−5.19615	−	3.00000i	−0.713746	−	0.412082i	0.0987002	−	0.995117i	$-0.468532\pi$
$53$	−5.19615	−	3.00000i	−0.713746	−	0.412082i	−0.812447	+	0.583036i	$0.801865\pi$
$54$	−2.00000	−	3.46410i	−0.272166	−	0.471405i
$55$		0			0
$56$	−2.50000	−	0.866025i	−0.334077	−	0.115728i
$57$			16.0000i			2.11925i
$58$	5.19615	−	3.00000i	0.682288	−	0.393919i
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$		0			0
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	0.965187	−	0.261562i	$-0.0842377\pi$
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	−0.709113	+	0.705095i	$0.750904\pi$
$62$			5.00000i			0.635001i
$63$	2.59808	−	0.500000i	0.327327	−	0.0629941i
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	1.73205	+	1.00000i	0.211604	+	0.122169i	0.602056	−	0.798454i	$-0.294348\pi$
$67$	1.73205	+	1.00000i	0.211604	+	0.122169i	−0.390453	+	0.920623i	$0.627682\pi$
$68$	−2.59808	+	1.50000i	−0.315063	+	0.181902i
$69$	−18.0000			−2.16695
$70$		0			0
$71$	−9.00000			−1.06810			−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000			−1.06810			−0.534052	+	0.845452i	$0.679331\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	8.66025	+	5.00000i	1.01361	+	0.585206i	0.912245	−	0.409644i	$-0.134347\pi$
$73$	8.66025	+	5.00000i	1.01361	+	0.585206i	0.101361	+	0.994850i	$0.467680\pi$
$74$	−4.00000	+	6.92820i	−0.464991	+	0.805387i
$75$		0			0
$76$	8.00000			0.917663
$77$		0			0
$78$			4.00000i			0.452911i
$79$	2.50000	+	4.33013i	0.281272	+	0.487177i	0.971698	−	0.236225i	$-0.0759104\pi$
$79$	2.50000	+	4.33013i	0.281272	+	0.487177i	−0.690426	+	0.723403i	$0.742577\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	−2.59808	+	1.50000i	−0.286910	+	0.165647i
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$	−1.00000	−	5.19615i	−0.109109	−	0.566947i
$85$		0			0
$86$	−5.00000	−	8.66025i	−0.539164	−	0.933859i
$87$	10.3923	+	6.00000i	1.11417	+	0.643268i
$88$		0			0
$89$	1.50000	+	2.59808i	0.159000	+	0.275396i	0.934508	−	0.355942i	$-0.115840\pi$
$89$	1.50000	+	2.59808i	0.159000	+	0.275396i	−0.775509	+	0.631337i	$0.782506\pi$
$90$		0			0
$91$	5.00000	+	1.73205i	0.524142	+	0.181568i
$92$			9.00000i			0.938315i
$93$	−8.66025	+	5.00000i	−0.898027	+	0.518476i
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$		0			0
$96$	−1.00000	−	1.73205i	−0.102062	−	0.176777i
$97$		−	5.00000i		−	0.507673i	−0.967247	−	0.253837i	$-0.918307\pi$
$97$		−	5.00000i		−	0.507673i	0.967247	−	0.253837i	$-0.0816925\pi$
$98$	−6.92820	−	1.00000i	−0.699854	−	0.101015i
$99$		0			0
$100$		0			0
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$	−5.19615	−	3.00000i	−0.514496	−	0.297044i
$103$	9.52628	−	5.50000i	0.938652	−	0.541931i	0.0491146	−	0.998793i	$-0.484360\pi$
$103$	9.52628	−	5.50000i	0.938652	−	0.541931i	0.889538	+	0.456862i	$0.151027\pi$
$104$	2.00000			0.196116
$105$		0			0
$106$	−6.00000			−0.582772
$107$	−10.3923	+	6.00000i	−1.00466	+	0.580042i	−0.909624	−	0.415432i	$-0.863630\pi$
$107$	−10.3923	+	6.00000i	−1.00466	+	0.580042i	−0.0950377	+	0.995474i	$0.530297\pi$
$108$	−3.46410	−	2.00000i	−0.333333	−	0.192450i
$109$	−5.00000	+	8.66025i	−0.478913	+	0.829502i	−0.999708	−	0.0241802i	$-0.992302\pi$
$109$	−5.00000	+	8.66025i	−0.478913	+	0.829502i	0.520794	+	0.853682i	$0.325636\pi$
$110$		0			0
$111$	−16.0000			−1.51865
$112$	−2.59808	+	0.500000i	−0.245495	+	0.0472456i
$113$			15.0000i			1.41108i	0.708669	+	0.705541i	$0.249296\pi$
$113$			15.0000i			1.41108i	−0.708669	+	0.705541i	$0.750704\pi$
$114$	8.00000	+	13.8564i	0.749269	+	1.29777i
$115$		0			0
$116$	3.00000	−	5.19615i	0.278543	−	0.482451i
$117$	−1.73205	+	1.00000i	−0.160128	+	0.0924500i
$118$		−	12.0000i		−	1.10469i
$119$	−6.00000	+	5.19615i	−0.550019	+	0.476331i
$120$		0			0
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	3.46410	+	2.00000i	0.313625	+	0.181071i
$123$	−5.19615	−	3.00000i	−0.468521	−	0.270501i
$124$	2.50000	+	4.33013i	0.224507	+	0.388857i
$125$		0			0
$126$	2.00000	−	1.73205i	0.178174	−	0.154303i
$127$		−	8.00000i		−	0.709885i	−0.934888	−	0.354943i	$-0.884500\pi$
$127$		−	8.00000i		−	0.709885i	0.934888	−	0.354943i	$-0.115500\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	10.0000	−	17.3205i	0.880451	−	1.52499i
$130$		0			0
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$		0			0
$133$	20.7846	−	4.00000i	1.80225	−	0.346844i
$134$	2.00000			0.172774
$135$		0			0
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	7.79423	+	4.50000i	0.665906	+	0.384461i	0.794524	−	0.607233i	$-0.207721\pi$
$137$	7.79423	+	4.50000i	0.665906	+	0.384461i	−0.128618	+	0.991694i	$0.541054\pi$
$138$	−15.5885	+	9.00000i	−1.32698	+	0.766131i
$139$	−2.00000			−0.169638			−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000			−0.169638			−0.0848189	+	0.996396i	$0.527031\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$	−7.79423	+	4.50000i	−0.654077	+	0.377632i
$143$		0			0
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$		0			0
$146$	10.0000			0.827606
$147$	−5.19615	−	13.0000i	−0.428571	−	1.07222i
$148$			8.00000i			0.657596i
$149$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$149$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$150$		0			0
$151$	2.00000	−	3.46410i	0.162758	−	0.281905i	−0.773099	−	0.634285i	$-0.781294\pi$
$151$	2.00000	−	3.46410i	0.162758	−	0.281905i	0.935857	+	0.352381i	$0.114628\pi$
$152$	6.92820	−	4.00000i	0.561951	−	0.324443i
$153$		−	3.00000i		−	0.242536i
$154$		0			0
$155$		0			0
$156$	2.00000	+	3.46410i	0.160128	+	0.277350i
$157$	1.73205	+	1.00000i	0.138233	+	0.0798087i	0.567521	−	0.823359i	$-0.307902\pi$
$157$	1.73205	+	1.00000i	0.138233	+	0.0798087i	−0.429289	+	0.903167i	$0.641236\pi$
$158$	4.33013	+	2.50000i	0.344486	+	0.198889i
$159$	−6.00000	−	10.3923i	−0.475831	−	0.824163i
$160$		0			0
$161$	4.50000	+	23.3827i	0.354650	+	1.84281i
$162$		−	11.0000i		−	0.864242i
$163$	6.92820	−	4.00000i	0.542659	−	0.313304i	−0.203497	−	0.979076i	$-0.565231\pi$
$163$	6.92820	−	4.00000i	0.542659	−	0.313304i	0.746156	+	0.665771i	$0.231897\pi$
$164$	−1.50000	+	2.59808i	−0.117130	+	0.202876i
$165$		0			0
$166$	−3.00000	−	5.19615i	−0.232845	−	0.403300i
$167$		−	24.0000i		−	1.85718i	−0.371113	−	0.928588i	$-0.621024\pi$
$167$		−	24.0000i		−	1.85718i	0.371113	−	0.928588i	$-0.378976\pi$
$168$	−3.46410	−	4.00000i	−0.267261	−	0.308607i
$169$	9.00000			0.692308
$170$		0			0
$171$	−4.00000	+	6.92820i	−0.305888	+	0.529813i
$172$	−8.66025	−	5.00000i	−0.660338	−	0.381246i
$173$	−10.3923	+	6.00000i	−0.790112	+	0.456172i	−0.840002	−	0.542583i	$-0.817446\pi$
$173$	−10.3923	+	6.00000i	−0.790112	+	0.456172i	0.0498898	+	0.998755i	$0.484113\pi$
$174$	12.0000			0.909718
$175$		0			0
$176$		0			0
$177$	20.7846	−	12.0000i	1.56227	−	0.901975i
$178$	2.59808	+	1.50000i	0.194734	+	0.112430i
$179$	12.0000	−	20.7846i	0.896922	−	1.55351i	0.0655145	−	0.997852i	$-0.479131\pi$
$179$	12.0000	−	20.7846i	0.896922	−	1.55351i	0.831408	−	0.555663i	$-0.187536\pi$
$180$		0			0
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$	5.19615	−	1.00000i	0.385164	−	0.0741249i
$183$			8.00000i			0.591377i
$184$	4.50000	+	7.79423i	0.331744	+	0.574598i
$185$		0			0
$186$	−5.00000	+	8.66025i	−0.366618	+	0.635001i
$187$		0			0
$188$		−	3.00000i		−	0.218797i
$189$	−10.0000	−	3.46410i	−0.727393	−	0.251976i
$190$		0			0
$191$	−7.50000	−	12.9904i	−0.542681	−	0.939951i	−0.998749	−	0.0500060i	$-0.984076\pi$
$191$	−7.50000	−	12.9904i	−0.542681	−	0.939951i	0.456068	−	0.889945i	$-0.349257\pi$
$192$	−1.73205	−	1.00000i	−0.125000	−	0.0721688i
$193$	−4.33013	−	2.50000i	−0.311689	−	0.179954i	0.335993	−	0.941865i	$-0.390928\pi$
$193$	−4.33013	−	2.50000i	−0.311689	−	0.179954i	−0.647682	+	0.761911i	$0.724262\pi$
$194$	−2.50000	−	4.33013i	−0.179490	−	0.310885i
$195$		0			0
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$		−	18.0000i		−	1.28245i	−0.767354	−	0.641223i	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$		0			0
$199$	8.50000	−	14.7224i	0.602549	−	1.04365i	−0.389885	−	0.920864i	$-0.627485\pi$
$199$	8.50000	−	14.7224i	0.602549	−	1.04365i	0.992434	−	0.122782i	$-0.0391815\pi$
$200$		0			0
$201$	2.00000	+	3.46410i	0.141069	+	0.244339i
$202$		0			0
$203$	5.19615	−	15.0000i	0.364698	−	1.05279i
$204$	−6.00000			−0.420084
$205$		0			0
$206$	5.50000	−	9.52628i	0.383203	−	0.663727i
$207$	−7.79423	−	4.50000i	−0.541736	−	0.312772i
$208$	1.73205	−	1.00000i	0.120096	−	0.0693375i
$209$		0			0
$210$		0			0
$211$	2.00000			0.137686			0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000			0.137686			0.0688428	+	0.997628i	$0.478069\pi$
$212$	−5.19615	+	3.00000i	−0.356873	+	0.206041i
$213$	−15.5885	−	9.00000i	−1.06810	−	0.616670i
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$		0			0
$216$	−4.00000			−0.272166
$217$	8.66025	+	10.0000i	0.587896	+	0.678844i
$218$			10.0000i			0.677285i
$219$	10.0000	+	17.3205i	0.675737	+	1.17041i
$220$		0			0
$221$	3.00000	−	5.19615i	0.201802	−	0.349531i
$222$	−13.8564	+	8.00000i	−0.929981	+	0.536925i
$223$			23.0000i			1.54019i	0.637927	+	0.770097i	$0.279792\pi$
$223$			23.0000i			1.54019i	−0.637927	+	0.770097i	$0.720208\pi$
$224$	−2.00000	+	1.73205i	−0.133631	+	0.115728i
$225$		0			0
$226$	7.50000	+	12.9904i	0.498893	+	0.864107i
$227$	15.5885	+	9.00000i	1.03464	+	0.597351i	0.918311	−	0.395860i	$-0.129553\pi$
$227$	15.5885	+	9.00000i	1.03464	+	0.597351i	0.116331	+	0.993210i	$0.462887\pi$
$228$	13.8564	+	8.00000i	0.917663	+	0.529813i
$229$	10.0000	+	17.3205i	0.660819	+	1.14457i	0.980401	+	0.197013i	$0.0631241\pi$
$229$	10.0000	+	17.3205i	0.660819	+	1.14457i	−0.319582	+	0.947559i	$0.603543\pi$
$230$		0			0
$231$		0			0
$232$		−	6.00000i		−	0.393919i
$233$	−5.19615	+	3.00000i	−0.340411	+	0.196537i	−0.660454	−	0.750867i	$-0.729636\pi$
$233$	−5.19615	+	3.00000i	−0.340411	+	0.196537i	0.320043	+	0.947403i	$0.396303\pi$
$234$	−1.00000	+	1.73205i	−0.0653720	+	0.113228i
$235$		0			0
$236$	−6.00000	−	10.3923i	−0.390567	−	0.676481i
$237$			10.0000i			0.649570i
$238$	−2.59808	+	7.50000i	−0.168408	+	0.486153i
$239$	−15.0000			−0.970269			−0.485135	−	0.874439i	$-0.661229\pi$
$239$	−15.0000			−0.970269			−0.485135	+	0.874439i	$0.661229\pi$
$240$		0			0
$241$	11.0000	−	19.0526i	0.708572	−	1.22728i	−0.256814	−	0.966461i	$-0.582673\pi$
$241$	11.0000	−	19.0526i	0.708572	−	1.22728i	0.965387	−	0.260822i	$-0.0839937\pi$
$242$	9.52628	+	5.50000i	0.612372	+	0.353553i
$243$	8.66025	−	5.00000i	0.555556	−	0.320750i
$244$	4.00000			0.256074
$245$		0			0
$246$	−6.00000			−0.382546
$247$	−13.8564	+	8.00000i	−0.881662	+	0.509028i
$248$	4.33013	+	2.50000i	0.274963	+	0.158750i
$249$	6.00000	−	10.3923i	0.380235	−	0.658586i
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	0.866025	−	2.50000i	0.0545545	−	0.157485i
$253$		0			0
$254$	−4.00000	−	6.92820i	−0.250982	−	0.434714i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−15.5885	+	9.00000i	−0.972381	+	0.561405i	−0.899961	−	0.435970i	$-0.856405\pi$
$257$	−15.5885	+	9.00000i	−0.972381	+	0.561405i	−0.0724199	+	0.997374i	$0.523072\pi$
$258$		−	20.0000i		−	1.24515i
$259$	4.00000	+	20.7846i	0.248548	+	1.29149i
$260$		0			0
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$		0			0
$263$	−7.79423	−	4.50000i	−0.480613	−	0.277482i	0.240059	−	0.970758i	$-0.422833\pi$
$263$	−7.79423	−	4.50000i	−0.480613	−	0.277482i	−0.720672	+	0.693276i	$0.756167\pi$
$264$		0			0
$265$		0			0
$266$	16.0000	−	13.8564i	0.981023	−	0.849591i
$267$			6.00000i			0.367194i
$268$	1.73205	−	1.00000i	0.105802	−	0.0610847i
$269$	−15.0000	+	25.9808i	−0.914566	+	1.58408i	−0.107031	+	0.994256i	$0.534134\pi$
$269$	−15.0000	+	25.9808i	−0.914566	+	1.58408i	−0.807535	+	0.589819i	$0.799199\pi$
$270$		0			0
$271$	−5.50000	−	9.52628i	−0.334101	−	0.578680i	0.649211	−	0.760609i	$-0.275099\pi$
$271$	−5.50000	−	9.52628i	−0.334101	−	0.578680i	−0.983312	+	0.181928i	$0.941766\pi$
$272$			3.00000i			0.181902i
$273$	6.92820	+	8.00000i	0.419314	+	0.484182i
$274$	9.00000			0.543710
$275$		0			0
$276$	−9.00000	+	15.5885i	−0.541736	+	0.938315i
$277$	−3.46410	−	2.00000i	−0.208138	−	0.120168i	0.392308	−	0.919834i	$-0.371677\pi$
$277$	−3.46410	−	2.00000i	−0.208138	−	0.120168i	−0.600446	+	0.799666i	$0.705010\pi$
$278$	−1.73205	+	1.00000i	−0.103882	+	0.0599760i
$279$	−5.00000			−0.299342
$280$		0			0
$281$	3.00000			0.178965			0.0894825	−	0.995988i	$-0.471479\pi$
$281$	3.00000			0.178965			0.0894825	+	0.995988i	$0.471479\pi$
$282$	5.19615	−	3.00000i	0.309426	−	0.178647i
$283$	−1.73205	−	1.00000i	−0.102960	−	0.0594438i	0.447636	−	0.894216i	$-0.352266\pi$
$283$	−1.73205	−	1.00000i	−0.102960	−	0.0594438i	−0.550596	+	0.834772i	$0.685599\pi$
$284$	−4.50000	+	7.79423i	−0.267026	+	0.462502i
$285$		0			0
$286$		0			0
$287$	−2.59808	+	7.50000i	−0.153360	+	0.442711i
$288$		−	1.00000i		−	0.0589256i
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$		0			0
$291$	5.00000	−	8.66025i	0.293105	−	0.507673i
$292$	8.66025	−	5.00000i	0.506803	−	0.292603i
$293$			6.00000i			0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$			6.00000i			0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$	−11.0000	−	8.66025i	−0.641533	−	0.505076i
$295$		0			0
$296$	4.00000	+	6.92820i	0.232495	+	0.402694i
$297$		0			0
$298$		0			0
$299$	−9.00000	−	15.5885i	−0.520483	−	0.901504i
$300$		0			0
$301$	−25.0000	−	8.66025i	−1.44098	−	0.499169i
$302$		−	4.00000i		−	0.230174i
$303$		0			0
$304$	4.00000	−	6.92820i	0.229416	−	0.397360i
$305$		0			0
$306$	−1.50000	−	2.59808i	−0.0857493	−	0.148522i
$307$			16.0000i			0.913168i	0.889680	+	0.456584i	$0.150927\pi$
$307$			16.0000i			0.913168i	−0.889680	+	0.456584i	$0.849073\pi$
$308$		0			0
$309$	22.0000			1.25154
$310$		0			0
$311$	−10.5000	+	18.1865i	−0.595400	+	1.03126i	0.398090	+	0.917346i	$0.369673\pi$
$311$	−10.5000	+	18.1865i	−0.595400	+	1.03126i	−0.993490	+	0.113917i	$0.963660\pi$
$312$	3.46410	+	2.00000i	0.196116	+	0.113228i
$313$	14.7224	−	8.50000i	0.832161	−	0.480448i	−0.0224310	−	0.999748i	$-0.507141\pi$
$313$	14.7224	−	8.50000i	0.832161	−	0.480448i	0.854592	+	0.519300i	$0.173807\pi$
$314$	2.00000			0.112867
$315$		0			0
$316$	5.00000			0.281272
$317$	10.3923	−	6.00000i	0.583690	−	0.336994i	−0.178908	−	0.983866i	$-0.557257\pi$
$317$	10.3923	−	6.00000i	0.583690	−	0.336994i	0.762598	+	0.646872i	$0.223923\pi$
$318$	−10.3923	−	6.00000i	−0.582772	−	0.336463i
$319$		0			0
$320$		0			0
$321$	−24.0000			−1.33955
$322$	15.5885	+	18.0000i	0.868711	+	1.00310i
$323$		−	24.0000i		−	1.33540i
$324$	−5.50000	−	9.52628i	−0.305556	−	0.529238i
$325$		0			0
$326$	4.00000	−	6.92820i	0.221540	−	0.383718i
$327$	−17.3205	+	10.0000i	−0.957826	+	0.553001i
$328$			3.00000i			0.165647i
$329$	−1.50000	−	7.79423i	−0.0826977	−	0.429710i
$330$		0			0
$331$	−7.00000	−	12.1244i	−0.384755	−	0.666415i	0.606980	−	0.794717i	$-0.292381\pi$
$331$	−7.00000	−	12.1244i	−0.384755	−	0.666415i	−0.991735	+	0.128302i	$0.959047\pi$
$332$	−5.19615	−	3.00000i	−0.285176	−	0.164646i
$333$	−6.92820	−	4.00000i	−0.379663	−	0.219199i
$334$	−12.0000	−	20.7846i	−0.656611	−	1.13728i
$335$		0			0
$336$	−5.00000	−	1.73205i	−0.272772	−	0.0944911i
$337$			13.0000i			0.708155i	0.935216	+	0.354078i	$0.115205\pi$
$337$			13.0000i			0.708155i	−0.935216	+	0.354078i	$0.884795\pi$
$338$	7.79423	−	4.50000i	0.423950	−	0.244768i
$339$	−15.0000	+	25.9808i	−0.814688	+	1.41108i
$340$		0			0
$341$		0			0
$342$			8.00000i			0.432590i
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$	−10.0000			−0.539164
$345$		0			0
$346$	−6.00000	+	10.3923i	−0.322562	+	0.558694i
$347$	−5.19615	−	3.00000i	−0.278944	−	0.161048i	0.354001	−	0.935245i	$-0.384821\pi$
$347$	−5.19615	−	3.00000i	−0.278944	−	0.161048i	−0.632945	+	0.774197i	$0.718154\pi$
$348$	10.3923	−	6.00000i	0.557086	−	0.321634i
$349$	−26.0000			−1.39175			−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000			−1.39175			−0.695874	+	0.718164i	$0.744983\pi$
$350$		0			0
$351$	8.00000			0.427008
$352$		0			0
$353$	7.79423	+	4.50000i	0.414845	+	0.239511i	0.692869	−	0.721063i	$-0.256346\pi$
$353$	7.79423	+	4.50000i	0.414845	+	0.239511i	−0.278024	+	0.960574i	$0.589680\pi$
$354$	12.0000	−	20.7846i	0.637793	−	1.10469i
$355$		0			0
$356$	3.00000			0.159000
$357$	−15.5885	+	3.00000i	−0.825029	+	0.158777i
$358$		−	24.0000i		−	1.26844i
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	−0.986865	−	0.161546i	$-0.948352\pi$
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	0.353529	−	0.935423i	$-0.384981\pi$
$360$		0			0
$361$	−22.5000	+	38.9711i	−1.18421	+	2.05111i
$362$	17.3205	−	10.0000i	0.910346	−	0.525588i
$363$			22.0000i			1.15470i
$364$	4.00000	−	3.46410i	0.209657	−	0.181568i
$365$		0			0
$366$	4.00000	+	6.92820i	0.209083	+	0.362143i
$367$	6.92820	+	4.00000i	0.361649	+	0.208798i	0.669804	−	0.742538i	$-0.266378\pi$
$367$	6.92820	+	4.00000i	0.361649	+	0.208798i	−0.308155	+	0.951336i	$0.599711\pi$
$368$	7.79423	+	4.50000i	0.406302	+	0.234579i
$369$	−1.50000	−	2.59808i	−0.0780869	−	0.135250i
$370$		0			0
$371$	−12.0000	+	10.3923i	−0.623009	+	0.539542i
$372$			10.0000i			0.518476i
$373$	1.73205	−	1.00000i	0.0896822	−	0.0517780i	−0.454488	−	0.890753i	$-0.650178\pi$
$373$	1.73205	−	1.00000i	0.0896822	−	0.0517780i	0.544170	+	0.838975i	$0.316844\pi$
$374$		0			0
$375$		0			0
$376$	−1.50000	−	2.59808i	−0.0773566	−	0.133986i
$377$			12.0000i			0.618031i
$378$	−10.3923	+	2.00000i	−0.534522	+	0.102869i
$379$	−8.00000			−0.410932			−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000			−0.410932			−0.205466	+	0.978664i	$0.565871\pi$
$380$		0			0
$381$	8.00000	−	13.8564i	0.409852	−	0.709885i
$382$	−12.9904	−	7.50000i	−0.664646	−	0.383733i
$383$	7.79423	−	4.50000i	0.398266	−	0.229939i	−0.287469	−	0.957790i	$-0.592814\pi$
$383$	7.79423	−	4.50000i	0.398266	−	0.229939i	0.685736	+	0.727851i	$0.259481\pi$
$384$	−2.00000			−0.102062
$385$		0			0
$386$	−5.00000			−0.254493
$387$	8.66025	−	5.00000i	0.440225	−	0.254164i
$388$	−4.33013	−	2.50000i	−0.219829	−	0.126918i
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	−0.998763	−	0.0497253i	$-0.984165\pi$
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	0.542445	+	0.840091i	$0.317499\pi$
$390$		0			0
$391$	27.0000			1.36545
$392$	−4.33013	+	5.50000i	−0.218704	+	0.277792i
$393$		0			0
$394$	−9.00000	−	15.5885i	−0.453413	−	0.785335i
$395$		0			0
$396$		0			0
$397$	−1.73205	+	1.00000i	−0.0869291	+	0.0501886i	−0.542834	−	0.839840i	$-0.682649\pi$
$397$	−1.73205	+	1.00000i	−0.0869291	+	0.0501886i	0.455905	+	0.890028i	$0.349316\pi$
$398$		−	17.0000i		−	0.852133i
$399$	40.0000	+	13.8564i	2.00250	+	0.693688i
$400$		0			0
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$	3.46410	+	2.00000i	0.172774	+	0.0997509i
$403$	−8.66025	−	5.00000i	−0.431398	−	0.249068i
$404$		0			0
$405$		0			0
$406$	−3.00000	−	15.5885i	−0.148888	−	0.773642i
$407$		0			0
$408$	−5.19615	+	3.00000i	−0.257248	+	0.148522i
$409$	−3.50000	+	6.06218i	−0.173064	+	0.299755i	−0.939490	−	0.342578i	$-0.888700\pi$
$409$	−3.50000	+	6.06218i	−0.173064	+	0.299755i	0.766426	+	0.642333i	$0.222033\pi$
$410$		0			0
$411$	9.00000	+	15.5885i	0.443937	+	0.768922i
$412$		−	11.0000i		−	0.541931i
$413$	−20.7846	−	24.0000i	−1.02274	−	1.18096i
$414$	−9.00000			−0.442326
$415$		0			0
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$	−3.46410	−	2.00000i	−0.169638	−	0.0979404i
$418$		0			0
$419$	30.0000			1.46560			0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000			1.46560			0.732798	+	0.680446i	$0.238214\pi$
$420$		0			0
$421$	−4.00000			−0.194948			−0.0974740	−	0.995238i	$-0.531076\pi$
$421$	−4.00000			−0.194948			−0.0974740	+	0.995238i	$0.531076\pi$
$422$	1.73205	−	1.00000i	0.0843149	−	0.0486792i
$423$	2.59808	+	1.50000i	0.126323	+	0.0729325i
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$		0			0
$426$	−18.0000			−0.872103
$427$	10.3923	−	2.00000i	0.502919	−	0.0967868i
$428$			12.0000i			0.580042i
$429$		0			0
$430$		0			0
$431$	1.50000	−	2.59808i	0.0722525	−	0.125145i	−0.827636	−	0.561266i	$-0.810315\pi$
$431$	1.50000	−	2.59808i	0.0722525	−	0.125145i	0.899888	+	0.436121i	$0.143648\pi$
$432$	−3.46410	+	2.00000i	−0.166667	+	0.0962250i
$433$			29.0000i			1.39365i	0.717241	+	0.696826i	$0.245405\pi$
$433$			29.0000i			1.39365i	−0.717241	+	0.696826i	$0.754595\pi$
$434$	12.5000	+	4.33013i	0.600019	+	0.207853i
$435$		0			0
$436$	5.00000	+	8.66025i	0.239457	+	0.414751i
$437$	−62.3538	−	36.0000i	−2.98279	−	1.72211i
$438$	17.3205	+	10.0000i	0.827606	+	0.477818i
$439$	11.5000	+	19.9186i	0.548865	+	0.950662i	0.998353	+	0.0573756i	$0.0182733\pi$
$439$	11.5000	+	19.9186i	0.548865	+	0.950662i	−0.449488	+	0.893287i	$0.648393\pi$
$440$		0			0
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$		−	6.00000i		−	0.285391i
$443$	−10.3923	+	6.00000i	−0.493753	+	0.285069i	−0.726130	−	0.687557i	$-0.758683\pi$
$443$	−10.3923	+	6.00000i	−0.493753	+	0.285069i	0.232377	+	0.972626i	$0.425350\pi$
$444$	−8.00000	+	13.8564i	−0.379663	+	0.657596i
$445$		0			0
$446$	11.5000	+	19.9186i	0.544541	+	0.943172i
$447$		0			0
$448$	−0.866025	+	2.50000i	−0.0409159	+	0.118114i
$449$	27.0000			1.27421			0.637104	−	0.770778i	$-0.280132\pi$
$449$	27.0000			1.27421			0.637104	+	0.770778i	$0.280132\pi$
$450$		0			0
$451$		0			0
$452$	12.9904	+	7.50000i	0.611016	+	0.352770i
$453$	6.92820	−	4.00000i	0.325515	−	0.187936i
$454$	18.0000			0.844782
$455$		0			0
$456$	16.0000			0.749269
$457$	19.0526	−	11.0000i	0.891241	−	0.514558i	0.0168929	−	0.999857i	$-0.494623\pi$
$457$	19.0526	−	11.0000i	0.891241	−	0.514558i	0.874348	+	0.485299i	$0.161289\pi$
$458$	17.3205	+	10.0000i	0.809334	+	0.467269i
$459$	−6.00000	+	10.3923i	−0.280056	+	0.485071i
$460$		0			0
$461$	−24.0000			−1.11779			−0.558896	−	0.829238i	$-0.688775\pi$
$461$	−24.0000			−1.11779			−0.558896	+	0.829238i	$0.688775\pi$
$462$		0			0
$463$		−	25.0000i		−	1.16185i	−0.813958	−	0.580924i	$-0.802691\pi$
$463$		−	25.0000i		−	1.16185i	0.813958	−	0.580924i	$-0.197309\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	5.19615	−	3.00000i	0.240449	−	0.138823i	−0.374934	−	0.927052i	$-0.622335\pi$
$467$	5.19615	−	3.00000i	0.240449	−	0.138823i	0.615383	+	0.788228i	$0.289001\pi$
$468$			2.00000i			0.0924500i
$469$	4.00000	−	3.46410i	0.184703	−	0.159957i
$470$		0			0
$471$	2.00000	+	3.46410i	0.0921551	+	0.159617i
$472$	−10.3923	−	6.00000i	−0.478345	−	0.276172i
$473$		0			0
$474$	5.00000	+	8.66025i	0.229658	+	0.397779i
$475$		0			0
$476$	1.50000	+	7.79423i	0.0687524	+	0.357248i
$477$		−	6.00000i		−	0.274721i
$478$	−12.9904	+	7.50000i	−0.594166	+	0.343042i
$479$	−13.5000	+	23.3827i	−0.616831	+	1.06838i	0.373230	+	0.927739i	$0.378250\pi$
$479$	−13.5000	+	23.3827i	−0.616831	+	1.06838i	−0.990060	+	0.140643i	$0.955083\pi$
$480$		0			0
$481$	−8.00000	−	13.8564i	−0.364769	−	0.631798i
$482$		−	22.0000i		−	1.00207i
$483$	−15.5885	+	45.0000i	−0.709299	+	2.04757i
$484$	11.0000			0.500000
$485$		0			0
$486$	5.00000	−	8.66025i	0.226805	−	0.392837i
$487$	9.52628	+	5.50000i	0.431677	+	0.249229i	0.700061	−	0.714083i	$-0.253156\pi$
$487$	9.52628	+	5.50000i	0.431677	+	0.249229i	−0.268384	+	0.963312i	$0.586490\pi$
$488$	3.46410	−	2.00000i	0.156813	−	0.0905357i
$489$	16.0000			0.723545
$490$		0			0
$491$	42.0000			1.89543			0.947717	−	0.319113i	$-0.103385\pi$
$491$	42.0000			1.89543			0.947717	+	0.319113i	$0.103385\pi$
$492$	−5.19615	+	3.00000i	−0.234261	+	0.135250i
$493$	−15.5885	−	9.00000i	−0.702069	−	0.405340i
$494$	−8.00000	+	13.8564i	−0.359937	+	0.623429i
$495$		0			0
$496$	5.00000			0.224507
$497$	−7.79423	+	22.5000i	−0.349619	+	1.00926i
$498$		−	12.0000i		−	0.537733i
$499$	−17.0000	−	29.4449i	−0.761025	−	1.31813i	−0.942323	−	0.334705i	$-0.891363\pi$
$499$	−17.0000	−	29.4449i	−0.761025	−	1.31813i	0.181298	−	0.983428i	$-0.441970\pi$
$500$		0			0
$501$	24.0000	−	41.5692i	1.07224	−	1.85718i
$502$		0			0
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$	−0.500000	−	2.59808i	−0.0222718	−	0.115728i
$505$		0			0
$506$		0			0
$507$	15.5885	+	9.00000i	0.692308	+	0.399704i
$508$	−6.92820	−	4.00000i	−0.307389	−	0.177471i
$509$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$509$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$510$		0			0
$511$	20.0000	−	17.3205i	0.884748	−	0.766214i
$512$			1.00000i			0.0441942i
$513$	27.7128	−	16.0000i	1.22355	−	0.706417i
$514$	−9.00000	+	15.5885i	−0.396973	+	0.687577i
$515$		0			0
$516$	−10.0000	−	17.3205i	−0.440225	−	0.762493i
$517$		0			0
$518$	13.8564	+	16.0000i	0.608816	+	0.703000i
$519$	−24.0000			−1.05348
$520$		0			0
$521$	1.50000	−	2.59808i	0.0657162	−	0.113824i	−0.831295	−	0.555831i	$-0.812400\pi$
$521$	1.50000	−	2.59808i	0.0657162	−	0.113824i	0.897011	+	0.442007i	$0.145733\pi$
$522$	5.19615	+	3.00000i	0.227429	+	0.131306i
$523$	−29.4449	+	17.0000i	−1.28753	+	0.743358i	−0.978214	−	0.207600i	$-0.933435\pi$
$523$	−29.4449	+	17.0000i	−1.28753	+	0.743358i	−0.309320	+	0.950958i	$0.600101\pi$
$524$		0			0
$525$		0			0
$526$	−9.00000			−0.392419
$527$	12.9904	−	7.50000i	0.565870	−	0.326705i
$528$		0			0
$529$	29.0000	−	50.2295i	1.26087	−	2.18389i
$530$		0			0
$531$	12.0000			0.520756
$532$	6.92820	−	20.0000i	0.300376	−	0.867110i
$533$		−	6.00000i		−	0.259889i
$534$	3.00000	+	5.19615i	0.129823	+	0.224860i
$535$		0			0
$536$	1.00000	−	1.73205i	0.0431934	−	0.0748132i
$537$	41.5692	−	24.0000i	1.79384	−	1.03568i
$538$			30.0000i			1.29339i
$539$		0			0
$540$		0			0
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	0.953262	−	0.302144i	$-0.0977023\pi$
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	−0.738296	+	0.674477i	$0.764369\pi$
$542$	−9.52628	−	5.50000i	−0.409189	−	0.236245i
$543$	34.6410	+	20.0000i	1.48659	+	0.858282i
$544$	1.50000	+	2.59808i	0.0643120	+	0.111392i
$545$		0			0
$546$	10.0000	+	3.46410i	0.427960	+	0.148250i
$547$		−	8.00000i		−	0.342055i	−0.985266	−	0.171028i	$-0.945291\pi$
$547$		−	8.00000i		−	0.342055i	0.985266	−	0.171028i	$-0.0547087\pi$
$548$	7.79423	−	4.50000i	0.332953	−	0.192230i
$549$	−2.00000	+	3.46410i	−0.0853579	+	0.147844i
$550$		0			0
$551$	24.0000	+	41.5692i	1.02243	+	1.77091i
$552$			18.0000i			0.766131i
$553$	12.9904	−	2.50000i	0.552407	−	0.106311i
$554$	−4.00000			−0.169944
$555$		0			0
$556$	−1.00000	+	1.73205i	−0.0424094	+	0.0734553i
$557$	20.7846	+	12.0000i	0.880672	+	0.508456i	0.870880	−	0.491496i	$-0.163550\pi$
$557$	20.7846	+	12.0000i	0.880672	+	0.508456i	0.00979220	+	0.999952i	$0.496883\pi$
$558$	−4.33013	+	2.50000i	−0.183309	+	0.105833i
$559$	20.0000			0.845910
$560$		0			0
$561$		0			0
$562$	2.59808	−	1.50000i	0.109593	−	0.0632737i
$563$	5.19615	+	3.00000i	0.218992	+	0.126435i	0.605483	−	0.795858i	$-0.292980\pi$
$563$	5.19615	+	3.00000i	0.218992	+	0.126435i	−0.386492	+	0.922293i	$0.626313\pi$
$564$	3.00000	−	5.19615i	0.126323	−	0.218797i
$565$		0			0
$566$	−2.00000			−0.0840663
$567$	−19.0526	−	22.0000i	−0.800132	−	0.923913i
$568$			9.00000i			0.377632i
$569$	−1.50000	−	2.59808i	−0.0628833	−	0.108917i	0.832870	−	0.553469i	$-0.186696\pi$
$569$	−1.50000	−	2.59808i	−0.0628833	−	0.108917i	−0.895753	+	0.444552i	$0.853363\pi$
$570$		0			0
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$		0			0
$573$		−	30.0000i		−	1.25327i
$574$	1.50000	+	7.79423i	0.0626088	+	0.325325i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−29.4449	−	17.0000i	−1.22581	−	0.707719i	−0.259656	−	0.965701i	$-0.583609\pi$
$577$	−29.4449	−	17.0000i	−1.22581	−	0.707719i	−0.966150	+	0.257982i	$0.916942\pi$
$578$	−6.92820	−	4.00000i	−0.288175	−	0.166378i
$579$	−5.00000	−	8.66025i	−0.207793	−	0.359908i
$580$		0			0
$581$	−15.0000	−	5.19615i	−0.622305	−	0.215573i
$582$		−	10.0000i		−	0.414513i
$583$		0			0
$584$	5.00000	−	8.66025i	0.206901	−	0.358364i
$585$		0			0
$586$	3.00000	+	5.19615i	0.123929	+	0.214651i
$587$		−	12.0000i		−	0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$		−	12.0000i		−	0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$	−13.8564	−	2.00000i	−0.571429	−	0.0824786i
$589$	−40.0000			−1.64817
$590$		0			0
$591$	18.0000	−	31.1769i	0.740421	−	1.28245i
$592$	6.92820	+	4.00000i	0.284747	+	0.164399i
$593$	2.59808	−	1.50000i	0.106690	−	0.0615976i	−0.445705	−	0.895180i	$-0.647047\pi$
$593$	2.59808	−	1.50000i	0.106690	−	0.0615976i	0.552396	+	0.833582i	$0.313714\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	29.4449	−	17.0000i	1.20510	−	0.695764i
$598$	−15.5885	−	9.00000i	−0.637459	−	0.368037i
$599$	10.5000	−	18.1865i	0.429018	−	0.743082i	−0.567768	−	0.823189i	$-0.692193\pi$
$599$	10.5000	−	18.1865i	0.429018	−	0.743082i	0.996786	+	0.0801071i	$0.0255262\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$	−25.9808	+	5.00000i	−1.05890	+	0.203785i
$603$			2.00000i			0.0814463i
$604$	−2.00000	−	3.46410i	−0.0813788	−	0.140952i
$605$		0			0
$606$		0			0
$607$	21.6506	−	12.5000i	0.878772	−	0.507359i	0.00851879	−	0.999964i	$-0.497288\pi$
$607$	21.6506	−	12.5000i	0.878772	−	0.507359i	0.870253	+	0.492604i	$0.163955\pi$
$608$		−	8.00000i		−	0.324443i
$609$	24.0000	−	20.7846i	0.972529	−	0.842235i
$610$		0			0
$611$	3.00000	+	5.19615i	0.121367	+	0.210214i
$612$	−2.59808	−	1.50000i	−0.105021	−	0.0606339i
$613$	−1.73205	−	1.00000i	−0.0699569	−	0.0403896i	0.464614	−	0.885514i	$-0.346193\pi$
$613$	−1.73205	−	1.00000i	−0.0699569	−	0.0403896i	−0.534570	+	0.845124i	$0.679527\pi$
$614$	8.00000	+	13.8564i	0.322854	+	0.559199i
$615$		0			0
$616$		0			0
$617$		−	15.0000i		−	0.603877i	−0.953327	−	0.301939i	$-0.902366\pi$
$617$		−	15.0000i		−	0.603877i	0.953327	−	0.301939i	$-0.0976338\pi$
$618$	19.0526	−	11.0000i	0.766406	−	0.442485i
$619$	−5.00000	+	8.66025i	−0.200967	+	0.348085i	−0.948840	−	0.315757i	$-0.897742\pi$
$619$	−5.00000	+	8.66025i	−0.200967	+	0.348085i	0.747873	+	0.663842i	$0.231075\pi$
$620$		0			0
$621$	18.0000	+	31.1769i	0.722315	+	1.25109i
$622$			21.0000i			0.842023i
$623$	7.79423	−	1.50000i	0.312269	−	0.0600962i
$624$	4.00000			0.160128
$625$		0			0
$626$	8.50000	−	14.7224i	0.339728	−	0.588427i
$627$		0			0
$628$	1.73205	−	1.00000i	0.0691164	−	0.0399043i
$629$	24.0000			0.956943
$630$		0			0
$631$	−19.0000			−0.756378			−0.378189	−	0.925728i	$-0.623453\pi$
$631$	−19.0000			−0.756378			−0.378189	+	0.925728i	$0.623453\pi$
$632$	4.33013	−	2.50000i	0.172243	−	0.0994447i
$633$	3.46410	+	2.00000i	0.137686	+	0.0794929i
$634$	6.00000	−	10.3923i	0.238290	−	0.412731i
$635$		0			0
$636$	−12.0000			−0.475831
$637$	8.66025	−	11.0000i	0.343132	−	0.435836i
$638$		0			0
$639$	−4.50000	−	7.79423i	−0.178017	−	0.308335i
$640$		0			0
$641$	−22.5000	+	38.9711i	−0.888697	+	1.53927i	−0.0472793	+	0.998882i	$0.515055\pi$
$641$	−22.5000	+	38.9711i	−0.888697	+	1.53927i	−0.841417	+	0.540386i	$0.818278\pi$
$642$	−20.7846	+	12.0000i	−0.820303	+	0.473602i
$643$			20.0000i			0.788723i	0.918955	+	0.394362i	$0.129034\pi$
$643$			20.0000i			0.788723i	−0.918955	+	0.394362i	$0.870966\pi$
$644$	22.5000	+	7.79423i	0.886624	+	0.307136i
$645$		0			0
$646$	−12.0000	−	20.7846i	−0.472134	−	0.817760i
$647$	20.7846	+	12.0000i	0.817127	+	0.471769i	0.849425	−	0.527710i	$-0.176949\pi$
$647$	20.7846	+	12.0000i	0.817127	+	0.471769i	−0.0322975	+	0.999478i	$0.510282\pi$
$648$	−9.52628	−	5.50000i	−0.374228	−	0.216060i
$649$		0			0
$650$		0			0
$651$	5.00000	+	25.9808i	0.195965	+	1.01827i
$652$		−	8.00000i		−	0.313304i
$653$	15.5885	−	9.00000i	0.610023	−	0.352197i	−0.162951	−	0.986634i	$-0.552101\pi$
$653$	15.5885	−	9.00000i	0.610023	−	0.352197i	0.772975	+	0.634437i	$0.218768\pi$
$654$	−10.0000	+	17.3205i	−0.391031	+	0.677285i
$655$		0			0
$656$	1.50000	+	2.59808i	0.0585652	+	0.101438i
$657$			10.0000i			0.390137i
$658$	−5.19615	−	6.00000i	−0.202567	−	0.233904i
$659$	−30.0000			−1.16863			−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000			−1.16863			−0.584317	+	0.811525i	$0.698638\pi$
$660$		0			0
$661$	8.00000	−	13.8564i	0.311164	−	0.538952i	−0.667451	−	0.744654i	$-0.732615\pi$
$661$	8.00000	−	13.8564i	0.311164	−	0.538952i	0.978615	+	0.205702i	$0.0659478\pi$
$662$	−12.1244	−	7.00000i	−0.471226	−	0.272063i
$663$	10.3923	−	6.00000i	0.403604	−	0.233021i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	−8.00000			−0.309994
$667$	−46.7654	+	27.0000i	−1.81076	+	1.04544i
$668$	−20.7846	−	12.0000i	−0.804181	−	0.464294i
$669$	−23.0000	+	39.8372i	−0.889231	+	1.54019i
$670$		0			0
$671$		0			0
$672$	−5.19615	+	1.00000i	−0.200446	+	0.0385758i
$673$			5.00000i			0.192736i	0.995346	+	0.0963679i	$0.0307225\pi$
$673$			5.00000i			0.192736i	−0.995346	+	0.0963679i	$0.969277\pi$
$674$	6.50000	+	11.2583i	0.250371	+	0.433655i
$675$		0			0
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	−36.3731	+	21.0000i	−1.39793	+	0.807096i	−0.994176	−	0.107772i	$-0.965628\pi$
$677$	−36.3731	+	21.0000i	−1.39793	+	0.807096i	−0.403755	+	0.914867i	$0.632295\pi$
$678$			30.0000i			1.15214i
$679$	−12.5000	−	4.33013i	−0.479706	−	0.166175i
$680$		0			0
$681$	18.0000	+	31.1769i	0.689761	+	1.19470i
$682$		0			0
$683$	25.9808	+	15.0000i	0.994126	+	0.573959i	0.906505	−	0.422195i	$-0.138740\pi$
$683$	25.9808	+	15.0000i	0.994126	+	0.573959i	0.0876211	+	0.996154i	$0.472074\pi$
$684$	4.00000	+	6.92820i	0.152944	+	0.264906i
$685$		0			0
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$			40.0000i			1.52610i
$688$	−8.66025	+	5.00000i	−0.330169	+	0.190623i
$689$	6.00000	−	10.3923i	0.228582	−	0.395915i
$690$		0			0
$691$	−25.0000	−	43.3013i	−0.951045	−	1.64726i	−0.743170	−	0.669102i	$-0.766679\pi$
$691$	−25.0000	−	43.3013i	−0.951045	−	1.64726i	−0.207875	−	0.978155i	$-0.566655\pi$
$692$			12.0000i			0.456172i
$693$		0			0
$694$	−6.00000			−0.227757
$695$		0			0
$696$	6.00000	−	10.3923i	0.227429	−	0.393919i
$697$	7.79423	+	4.50000i	0.295227	+	0.170450i
$698$	−22.5167	+	13.0000i	−0.852268	+	0.492057i
$699$	−12.0000			−0.453882
$700$		0			0
$701$	−36.0000			−1.35970			−0.679851	−	0.733351i	$-0.737955\pi$
$701$	−36.0000			−1.35970			−0.679851	+	0.733351i	$0.737955\pi$
$702$	6.92820	−	4.00000i	0.261488	−	0.150970i
$703$	−55.4256	−	32.0000i	−2.09042	−	1.20690i
$704$		0			0
$705$		0			0
$706$	9.00000			0.338719
$707$		0			0
$708$		−	24.0000i		−	0.901975i
$709$	−2.00000	−	3.46410i	−0.0751116	−	0.130097i	0.826023	−	0.563636i	$-0.190598\pi$
$709$	−2.00000	−	3.46410i	−0.0751116	−	0.130097i	−0.901135	+	0.433539i	$0.857265\pi$
$710$		0			0
$711$	−2.50000	+	4.33013i	−0.0937573	+	0.162392i
$712$	2.59808	−	1.50000i	0.0973670	−	0.0562149i
$713$		−	45.0000i		−	1.68526i
$714$	−12.0000	+	10.3923i	−0.449089	+	0.388922i
$715$		0			0
$716$	−12.0000	−	20.7846i	−0.448461	−	0.776757i
$717$	−25.9808	−	15.0000i	−0.970269	−	0.560185i
$718$	−20.7846	−	12.0000i	−0.775675	−	0.447836i
$719$	−7.50000	−	12.9904i	−0.279703	−	0.484459i	0.691608	−	0.722273i	$-0.256903\pi$
$719$	−7.50000	−	12.9904i	−0.279703	−	0.484459i	−0.971311	+	0.237814i	$0.923569\pi$
$720$		0			0
$721$	−5.50000	−	28.5788i	−0.204831	−	1.06433i
$722$			45.0000i			1.67473i
$723$	38.1051	−	22.0000i	1.41714	−	0.818189i
$724$	10.0000	−	17.3205i	0.371647	−	0.643712i
$725$		0			0
$726$	11.0000	+	19.0526i	0.408248	+	0.707107i
$727$			31.0000i			1.14973i	0.818250	+	0.574863i	$0.194945\pi$
$727$			31.0000i			1.14973i	−0.818250	+	0.574863i	$0.805055\pi$
$728$	1.73205	−	5.00000i	0.0641941	−	0.185312i
$729$	−13.0000			−0.481481
$730$		0			0
$731$	−15.0000	+	25.9808i	−0.554795	+	0.960933i
$732$	6.92820	+	4.00000i	0.256074	+	0.147844i
$733$	−29.4449	+	17.0000i	−1.08757	+	0.627909i	−0.932929	−	0.360061i	$-0.882756\pi$
$733$	−29.4449	+	17.0000i	−1.08757	+	0.627909i	−0.154642	+	0.987971i	$0.549422\pi$
$734$	8.00000			0.295285
$735$		0			0
$736$	9.00000			0.331744
$737$		0			0
$738$	−2.59808	−	1.50000i	−0.0956365	−	0.0552158i
$739$	4.00000	−	6.92820i	0.147142	−	0.254858i	−0.783028	−	0.621987i	$-0.786326\pi$
$739$	4.00000	−	6.92820i	0.147142	−	0.254858i	0.930170	+	0.367129i	$0.119659\pi$
$740$		0			0
$741$	−32.0000			−1.17555
$742$	−5.19615	+	15.0000i	−0.190757	+	0.550667i
$743$			33.0000i			1.21065i	0.795977	+	0.605326i	$0.206957\pi$
$743$			33.0000i			1.21065i	−0.795977	+	0.605326i	$0.793043\pi$
$744$	5.00000	+	8.66025i	0.183309	+	0.317500i
$745$		0			0
$746$	1.00000	−	1.73205i	0.0366126	−	0.0634149i
$747$	5.19615	−	3.00000i	0.190117	−	0.109764i
$748$		0			0
$749$	6.00000	+	31.1769i	0.219235	+	1.13918i
$750$		0			0
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	0.974265	−	0.225407i	$-0.0723712\pi$
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	−0.682341	+	0.731034i	$0.739038\pi$
$752$	−2.59808	−	1.50000i	−0.0947421	−	0.0546994i
$753$		0			0
$754$	6.00000	+	10.3923i	0.218507	+	0.378465i
$755$		0			0
$756$	−8.00000	+	6.92820i	−0.290957	+	0.251976i
$757$		−	26.0000i		−	0.944986i	−0.881334	−	0.472493i	$-0.843354\pi$
$757$		−	26.0000i		−	0.944986i	0.881334	−	0.472493i	$-0.156646\pi$
$758$	−6.92820	+	4.00000i	−0.251644	+	0.145287i
$759$		0			0
$760$		0			0
$761$	−22.5000	−	38.9711i	−0.815624	−	1.41270i	−0.908879	−	0.417061i	$-0.863060\pi$
$761$	−22.5000	−	38.9711i	−0.815624	−	1.41270i	0.0932544	−	0.995642i	$-0.470273\pi$
$762$		−	16.0000i		−	0.579619i
$763$	17.3205	+	20.0000i	0.627044	+	0.724049i
$764$	−15.0000			−0.542681
$765$		0			0
$766$	4.50000	−	7.79423i	0.162592	−	0.281617i
$767$	20.7846	+	12.0000i	0.750489	+	0.433295i
$768$	−1.73205	+	1.00000i	−0.0625000	+	0.0360844i
$769$	−14.0000			−0.504853			−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$		0			0
$771$	−36.0000			−1.29651
$772$	−4.33013	+	2.50000i	−0.155845	+	0.0899770i
$773$	10.3923	+	6.00000i	0.373785	+	0.215805i	0.675111	−	0.737716i	$-0.264096\pi$
$773$	10.3923	+	6.00000i	0.373785	+	0.215805i	−0.301326	+	0.953521i	$0.597429\pi$
$774$	5.00000	−	8.66025i	0.179721	−	0.311286i
$775$		0			0
$776$	−5.00000			−0.179490
$777$	−13.8564	+	40.0000i	−0.497096	+	1.43499i
$778$			18.0000i			0.645331i
$779$	−12.0000	−	20.7846i	−0.429945	−	0.744686i
$780$		0			0
$781$		0			0
$782$	23.3827	−	13.5000i	0.836163	−	0.482759i
$783$		−	24.0000i		−	0.857690i
$784$	−1.00000	+	6.92820i	−0.0357143	+	0.247436i
$785$		0			0
$786$		0			0
$787$	−13.8564	−	8.00000i	−0.493928	−	0.285169i	0.232275	−	0.972650i	$-0.425383\pi$
$787$	−13.8564	−	8.00000i	−0.493928	−	0.285169i	−0.726202	+	0.687481i	$0.758716\pi$
$788$	−15.5885	−	9.00000i	−0.555316	−	0.320612i
$789$	−9.00000	−	15.5885i	−0.320408	−	0.554964i
$790$		0			0
$791$	37.5000	+	12.9904i	1.33335	+	0.461885i
$792$		0			0
$793$	−6.92820	+	4.00000i	−0.246028	+	0.142044i
$794$	−1.00000	+	1.73205i	−0.0354887	+	0.0614682i
$795$		0			0
$796$	−8.50000	−	14.7224i	−0.301275	−	0.521823i
$797$			12.0000i			0.425062i	0.977154	+	0.212531i	$0.0681706\pi$
$797$			12.0000i			0.425062i	−0.977154	+	0.212531i	$0.931829\pi$
$798$	41.5692	−	8.00000i	1.47153	−	0.283197i
$799$	−9.00000			−0.318397
$800$		0			0
$801$	−1.50000	+	2.59808i	−0.0529999	+	0.0917985i
$802$	−15.5885	−	9.00000i	−0.550448	−	0.317801i
$803$		0			0
$804$	4.00000			0.141069
$805$		0			0
$806$	−10.0000			−0.352235
$807$	−51.9615	+	30.0000i	−1.82913	+	1.05605i
$808$		0			0
$809$	−15.0000	+	25.9808i	−0.527372	+	0.913435i	0.472119	+	0.881535i	$0.343489\pi$
$809$	−15.0000	+	25.9808i	−0.527372	+	0.913435i	−0.999491	+	0.0319002i	$0.989844\pi$
$810$		0			0
$811$	26.0000			0.912983			0.456492	−	0.889728i	$-0.349106\pi$
$811$	26.0000			0.912983			0.456492	+	0.889728i	$0.349106\pi$
$812$	−10.3923	−	12.0000i	−0.364698	−	0.421117i
$813$		−	22.0000i		−	0.771574i
$814$		0			0
$815$		0			0
$816$	−3.00000	+	5.19615i	−0.105021	+	0.181902i
$817$	69.2820	−	40.0000i	2.42387	−	1.39942i
$818$			7.00000i			0.244749i
$819$	1.00000	+	5.19615i	0.0349428	+	0.181568i
$820$		0			0
$821$	6.00000	+	10.3923i	0.209401	+	0.362694i	0.951526	−	0.307568i	$-0.0995151\pi$
$821$	6.00000	+	10.3923i	0.209401	+	0.362694i	−0.742125	+	0.670262i	$0.766182\pi$
$822$	15.5885	+	9.00000i	0.543710	+	0.313911i
$823$	−17.3205	−	10.0000i	−0.603755	−	0.348578i	0.166762	−	0.985997i	$-0.446669\pi$
$823$	−17.3205	−	10.0000i	−0.603755	−	0.348578i	−0.770517	+	0.637419i	$0.780002\pi$
$824$	−5.50000	−	9.52628i	−0.191602	−	0.331864i
$825$		0			0
$826$	−30.0000	−	10.3923i	−1.04383	−	0.361595i
$827$			18.0000i			0.625921i	0.949766	+	0.312961i	$0.101321\pi$
$827$			18.0000i			0.625921i	−0.949766	+	0.312961i	$0.898679\pi$
$828$	−7.79423	+	4.50000i	−0.270868	+	0.156386i
$829$	22.0000	−	38.1051i	0.764092	−	1.32345i	−0.176634	−	0.984277i	$-0.556521\pi$
$829$	22.0000	−	38.1051i	0.764092	−	1.32345i	0.940726	−	0.339169i	$-0.110146\pi$
$830$		0			0
$831$	−4.00000	−	6.92820i	−0.138758	−	0.240337i
$832$		−	2.00000i		−	0.0693375i
$833$	7.79423	+	19.5000i	0.270054	+	0.675635i
$834$	−4.00000			−0.138509
$835$		0			0
$836$		0			0
$837$	17.3205	+	10.0000i	0.598684	+	0.345651i
$838$	25.9808	−	15.0000i	0.897491	−	0.518166i
$839$	33.0000			1.13929			0.569643	−	0.821892i	$-0.307081\pi$
$839$	33.0000			1.13929			0.569643	+	0.821892i	$0.307081\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	−3.46410	+	2.00000i	−0.119381	+	0.0689246i
$843$	5.19615	+	3.00000i	0.178965	+	0.103325i
$844$	1.00000	−	1.73205i	0.0344214	−	0.0596196i
$845$		0			0
$846$	3.00000			0.103142
$847$	28.5788	−	5.50000i	0.981981	−	0.188982i
$848$			6.00000i			0.206041i
$849$	−2.00000	−	3.46410i	−0.0686398	−	0.118888i
$850$		0			0
$851$	36.0000	−	62.3538i	1.23406	−	2.13746i
$852$	−15.5885	+	9.00000i	−0.534052	+	0.308335i
$853$		−	10.0000i		−	0.342393i	−0.985237	−	0.171197i	$-0.945237\pi$
$853$		−	10.0000i		−	0.342393i	0.985237	−	0.171197i	$-0.0547634\pi$
$854$	8.00000	−	6.92820i	0.273754	−	0.237078i
$855$		0			0
$856$	6.00000	+	10.3923i	0.205076	+	0.355202i
$857$	46.7654	+	27.0000i	1.59747	+	0.922302i	0.991972	+	0.126459i	$0.0403613\pi$
$857$	46.7654	+	27.0000i	1.59747	+	0.922302i	0.605503	+	0.795843i	$0.292972\pi$
$858$		0			0
$859$	−20.0000	−	34.6410i	−0.682391	−	1.18194i	−0.974249	−	0.225475i	$-0.927607\pi$
$859$	−20.0000	−	34.6410i	−0.682391	−	1.18194i	0.291858	−	0.956462i	$-0.405727\pi$
$860$		0			0
$861$	−12.0000	+	10.3923i	−0.408959	+	0.354169i
$862$		−	3.00000i		−	0.102180i
$863$	18.1865	−	10.5000i	0.619077	−	0.357424i	−0.157433	−	0.987530i	$-0.550322\pi$
$863$	18.1865	−	10.5000i	0.619077	−	0.357424i	0.776509	+	0.630106i	$0.216988\pi$
$864$	−2.00000	+	3.46410i	−0.0680414	+	0.117851i
$865$		0			0
$866$	14.5000	+	25.1147i	0.492730	+	0.853433i
$867$		−	16.0000i		−	0.543388i
$868$	12.9904	−	2.50000i	0.440922	−	0.0848555i
$869$		0			0
$870$		0			0
$871$	−2.00000	+	3.46410i	−0.0677674	+	0.117377i
$872$	8.66025	+	5.00000i	0.293273	+	0.169321i
$873$	4.33013	−	2.50000i	0.146553	−	0.0846122i
$874$	−72.0000			−2.43544
$875$		0			0
$876$	20.0000			0.675737
$877$	13.8564	−	8.00000i	0.467898	−	0.270141i	−0.247462	−	0.968898i	$-0.579596\pi$
$877$	13.8564	−	8.00000i	0.467898	−	0.270141i	0.715359	+	0.698757i	$0.246263\pi$
$878$	19.9186	+	11.5000i	0.672220	+	0.388106i
$879$	−6.00000	+	10.3923i	−0.202375	+	0.350524i
$880$		0			0
$881$	27.0000			0.909653			0.454827	−	0.890580i	$-0.349701\pi$
$881$	27.0000			0.909653			0.454827	+	0.890580i	$0.349701\pi$
$882$	−2.59808	−	6.50000i	−0.0874818	−	0.218866i
$883$			26.0000i			0.874970i	0.899226	+	0.437485i	$0.144131\pi$
$883$			26.0000i			0.874970i	−0.899226	+	0.437485i	$0.855869\pi$
$884$	−3.00000	−	5.19615i	−0.100901	−	0.174766i
$885$		0			0
$886$	−6.00000	+	10.3923i	−0.201574	+	0.349136i
$887$	−31.1769	+	18.0000i	−1.04682	+	0.604381i	−0.921757	−	0.387768i	$-0.873246\pi$
$887$	−31.1769	+	18.0000i	−1.04682	+	0.604381i	−0.125061	+	0.992149i	$0.539913\pi$
$888$			16.0000i			0.536925i
$889$	−20.0000	−	6.92820i	−0.670778	−	0.232364i
$890$		0			0
$891$		0			0
$892$	19.9186	+	11.5000i	0.666924	+	0.385048i
$893$	20.7846	+	12.0000i	0.695530	+	0.401565i
$894$		0			0
$895$		0			0
$896$	0.500000	+	2.59808i	0.0167038	+	0.0867956i
$897$		−	36.0000i		−	1.20201i
$898$	23.3827	−	13.5000i	0.780290	−	0.450501i
$899$	−15.0000	+	25.9808i	−0.500278	+	0.866507i
$900$		0			0
$901$	9.00000	+	15.5885i	0.299833	+	0.519327i
$902$		0			0
$903$	−34.6410	−	40.0000i	−1.15278	−	1.33112i
$904$	15.0000			0.498893
$905$		0			0
$906$	4.00000	−	6.92820i	0.132891	−	0.230174i
$907$	−34.6410	−	20.0000i	−1.15024	−	0.664089i	−0.201291	−	0.979531i	$-0.564514\pi$
$907$	−34.6410	−	20.0000i	−1.15024	−	0.664089i	−0.948945	+	0.315442i	$0.897847\pi$
$908$	15.5885	−	9.00000i	0.517321	−	0.298675i
$909$		0			0
$910$		0			0
$911$	3.00000			0.0993944			0.0496972	−	0.998764i	$-0.484174\pi$
$911$	3.00000			0.0993944			0.0496972	+	0.998764i	$0.484174\pi$
$912$	13.8564	−	8.00000i	0.458831	−	0.264906i
$913$		0			0
$914$	11.0000	−	19.0526i	0.363848	−	0.630203i
$915$		0			0
$916$	20.0000			0.660819
$917$		0			0
$918$			12.0000i			0.396059i
$919$	5.50000	+	9.52628i	0.181428	+	0.314243i	0.942367	−	0.334581i	$-0.108595\pi$
$919$	5.50000	+	9.52628i	0.181428	+	0.314243i	−0.760939	+	0.648824i	$0.775261\pi$
$920$		0			0
$921$	−16.0000	+	27.7128i	−0.527218	+	0.913168i
$922$	−20.7846	+	12.0000i	−0.684505	+	0.395199i
$923$		−	18.0000i		−	0.592477i
$924$		0			0
$925$		0			0
$926$	−12.5000	−	21.6506i	−0.410775	−	0.711484i
$927$	9.52628	+	5.50000i	0.312884	+	0.180644i
$928$	−5.19615	−	3.00000i	−0.170572	−	0.0984798i
$929$	21.0000	+	36.3731i	0.688988	+	1.19336i	0.972166	+	0.234294i	$0.0752779\pi$
$929$	21.0000	+	36.3731i	0.688988	+	1.19336i	−0.283178	+	0.959067i	$0.591389\pi$
$930$		0			0
$931$	8.00000	−	55.4256i	0.262189	−	1.81650i
$932$			6.00000i			0.196537i
$933$	−36.3731	+	21.0000i	−1.19080	+	0.687509i
$934$	3.00000	−	5.19615i	0.0981630	−	0.170023i
$935$		0			0
$936$	1.00000	+	1.73205i	0.0326860	+	0.0566139i
$937$			34.0000i			1.11073i	0.831606	+	0.555366i	$0.187422\pi$
$937$			34.0000i			1.11073i	−0.831606	+	0.555366i	$0.812578\pi$
$938$	1.73205	−	5.00000i	0.0565535	−	0.163256i
$939$	34.0000			1.10955
$940$		0			0
$941$	3.00000	−	5.19615i	0.0977972	−	0.169390i	−0.812975	−	0.582298i	$-0.802154\pi$
$941$	3.00000	−	5.19615i	0.0977972	−	0.169390i	0.910773	+	0.412908i	$0.135487\pi$
$942$	3.46410	+	2.00000i	0.112867	+	0.0651635i
$943$	23.3827	−	13.5000i	0.761445	−	0.439620i
$944$	−12.0000			−0.390567
$945$		0			0
$946$		0			0
$947$	10.3923	−	6.00000i	0.337705	−	0.194974i	−0.321552	−	0.946892i	$-0.604204\pi$
$947$	10.3923	−	6.00000i	0.337705	−	0.194974i	0.659256	+	0.751918i	$0.270871\pi$
$948$	8.66025	+	5.00000i	0.281272	+	0.162392i
$949$	−10.0000	+	17.3205i	−0.324614	+	0.562247i
$950$		0			0
$951$	24.0000			0.778253
$952$	5.19615	+	6.00000i	0.168408	+	0.194461i
$953$			54.0000i			1.74923i	0.484817	+	0.874616i	$0.338886\pi$
$953$			54.0000i			1.74923i	−0.484817	+	0.874616i	$0.661114\pi$
$954$	−3.00000	−	5.19615i	−0.0971286	−	0.168232i
$955$		0			0
$956$	−7.50000	+	12.9904i	−0.242567	+	0.420139i
$957$		0			0
$958$			27.0000i			0.872330i
$959$	18.0000	−	15.5885i	0.581250	−	0.503378i
$960$		0			0
$961$	3.00000	+	5.19615i	0.0967742	+	0.167618i
$962$	−13.8564	−	8.00000i	−0.446748	−	0.257930i
$963$	−10.3923	−	6.00000i	−0.334887	−	0.193347i
$964$	−11.0000	−	19.0526i	−0.354286	−	0.613642i
$965$		0			0
$966$	9.00000	+	46.7654i	0.289570	+	1.50465i
$967$			7.00000i			0.225105i	0.993646	+	0.112552i	$0.0359026\pi$
$967$			7.00000i			0.225105i	−0.993646	+	0.112552i	$0.964097\pi$
$968$	9.52628	−	5.50000i	0.306186	−	0.176777i
$969$	24.0000	−	41.5692i	0.770991	−	1.33540i
$970$		0			0
$971$	−15.0000	−	25.9808i	−0.481373	−	0.833762i	0.518399	−	0.855139i	$-0.326528\pi$
$971$	−15.0000	−	25.9808i	−0.481373	−	0.833762i	−0.999771	+	0.0213768i	$0.993195\pi$
$972$		−	10.0000i		−	0.320750i
$973$	−1.73205	+	5.00000i	−0.0555270	+	0.160293i
$974$	11.0000			0.352463
$975$		0			0
$976$	2.00000	−	3.46410i	0.0640184	−	0.110883i
$977$	−44.1673	−	25.5000i	−1.41304	−	0.815817i	−0.417364	−	0.908740i	$-0.637046\pi$
$977$	−44.1673	−	25.5000i	−1.41304	−	0.815817i	−0.995673	+	0.0929223i	$0.970379\pi$
$978$	13.8564	−	8.00000i	0.443079	−	0.255812i
$979$		0			0
$980$		0			0
$981$	−10.0000			−0.319275
$982$	36.3731	−	21.0000i	1.16071	−	0.670137i
$983$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$983$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$984$	−3.00000	+	5.19615i	−0.0956365	+	0.165647i
$985$		0			0
$986$	−18.0000			−0.573237
$987$	5.19615	−	15.0000i	0.165395	−	0.477455i
$988$			16.0000i			0.509028i
$989$	45.0000	+	77.9423i	1.43092	+	2.47842i
$990$		0			0
$991$	−14.5000	+	25.1147i	−0.460608	+	0.797796i	−0.998991	−	0.0449040i	$-0.985702\pi$
$991$	−14.5000	+	25.1147i	−0.460608	+	0.797796i	0.538384	+	0.842700i	$0.319035\pi$
$992$	4.33013	−	2.50000i	0.137482	−	0.0793751i
$993$		−	28.0000i		−	0.888553i
$994$	4.50000	+	23.3827i	0.142731	+	0.741654i
$995$		0			0
$996$	−6.00000	−	10.3923i	−0.190117	−	0.329293i
$997$	−3.46410	−	2.00000i	−0.109709	−	0.0633406i	0.444141	−	0.895957i	$-0.353509\pi$
$997$	−3.46410	−	2.00000i	−0.109709	−	0.0633406i	−0.553851	+	0.832616i	$0.686842\pi$
$998$	−29.4449	−	17.0000i	−0.932061	−	0.538126i
$999$	16.0000	+	27.7128i	0.506218	+	0.876795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.j.e.249.2		4
5.2	odd	4		350.2.e.k.151.1	yes	2
5.3	odd	4		350.2.e.a.151.1	yes	2
5.4	even	2	inner	350.2.j.e.249.1		4
7.2	even	3	inner	350.2.j.e.149.1		4
7.3	odd	6		2450.2.c.d.99.2		2
7.4	even	3		2450.2.c.o.99.2		2
35.2	odd	12		350.2.e.k.51.1	yes	2
35.3	even	12		2450.2.a.u.1.1		1
35.4	even	6		2450.2.c.o.99.1		2
35.9	even	6	inner	350.2.j.e.149.2		4
35.17	even	12		2450.2.a.o.1.1		1
35.18	odd	12		2450.2.a.be.1.1		1
35.23	odd	12		350.2.e.a.51.1	✓	2
35.24	odd	6		2450.2.c.d.99.1		2
35.32	odd	12		2450.2.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.e.a.51.1	✓	2	35.23	odd	12
350.2.e.a.151.1	yes	2	5.3	odd	4
350.2.e.k.51.1	yes	2	35.2	odd	12
350.2.e.k.151.1	yes	2	5.2	odd	4
350.2.j.e.149.1		4	7.2	even	3	inner
350.2.j.e.149.2		4	35.9	even	6	inner
350.2.j.e.249.1		4	5.4	even	2	inner
350.2.j.e.249.2		4	1.1	even	1	trivial
2450.2.a.e.1.1		1	35.32	odd	12
2450.2.a.o.1.1		1	35.17	even	12
2450.2.a.u.1.1		1	35.3	even	12
2450.2.a.be.1.1		1	35.18	odd	12
2450.2.c.d.99.1		2	35.24	odd	6
2450.2.c.d.99.2		2	7.3	odd	6
2450.2.c.o.99.1		2	35.4	even	6
2450.2.c.o.99.2		2	7.4	even	3

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.00000 q^{6} +(0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.00000 q^{6} +(0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.73205 - 1.00000i) q^{12} +2.00000i q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.59808 - 1.50000i) q^{17} +(0.866025 + 0.500000i) q^{18} +(4.00000 + 6.92820i) q^{19} +(4.00000 - 3.46410i) q^{21} +(-7.79423 + 4.50000i) q^{23} +(1.00000 - 1.73205i) q^{24} +(1.00000 + 1.73205i) q^{26} -4.00000i q^{27} +(-1.73205 - 2.00000i) q^{28} +6.00000 q^{29} +(-2.50000 + 4.33013i) q^{31} +(-0.866025 - 0.500000i) q^{32} -3.00000 q^{34} +1.00000 q^{36} +(-6.92820 + 4.00000i) q^{37} +(6.92820 + 4.00000i) q^{38} +(-2.00000 + 3.46410i) q^{39} -3.00000 q^{41} +(1.73205 - 5.00000i) q^{42} -10.0000i q^{43} +(-4.50000 + 7.79423i) q^{46} +(2.59808 - 1.50000i) q^{47} -2.00000i q^{48} +(-5.50000 - 4.33013i) q^{49} +(-3.00000 - 5.19615i) q^{51} +(1.73205 + 1.00000i) q^{52} +(-5.19615 - 3.00000i) q^{53} +(-2.00000 - 3.46410i) q^{54} +(-2.50000 - 0.866025i) q^{56} +16.0000i q^{57} +(5.19615 - 3.00000i) q^{58} +(6.00000 - 10.3923i) q^{59} +(2.00000 + 3.46410i) q^{61} +5.00000i q^{62} +(2.59808 - 0.500000i) q^{63} -1.00000 q^{64} +(1.73205 + 1.00000i) q^{67} +(-2.59808 + 1.50000i) q^{68} -18.0000 q^{69} -9.00000 q^{71} +(0.866025 - 0.500000i) q^{72} +(8.66025 + 5.00000i) q^{73} +(-4.00000 + 6.92820i) q^{74} +8.00000 q^{76} +4.00000i q^{78} +(2.50000 + 4.33013i) q^{79} +(5.50000 - 9.52628i) q^{81} +(-2.59808 + 1.50000i) q^{82} -6.00000i q^{83} +(-1.00000 - 5.19615i) q^{84} +(-5.00000 - 8.66025i) q^{86} +(10.3923 + 6.00000i) q^{87} +(1.50000 + 2.59808i) q^{89} +(5.00000 + 1.73205i) q^{91} +9.00000i q^{92} +(-8.66025 + 5.00000i) q^{93} +(1.50000 - 2.59808i) q^{94} +(-1.00000 - 1.73205i) q^{96} -5.00000i q^{97} +(-6.92820 - 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 8 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 8 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} + 8 q^{6} + 2 q^{9} - 2 q^{14} - 2 q^{16} + 16 q^{19} + 16 q^{21} + 4 q^{24} + 4 q^{26} + 24 q^{29} - 10 q^{31} - 12 q^{34} + 4 q^{36} - 8 q^{39} - 12 q^{41} - 18 q^{46} - 22 q^{49} - 12 q^{51} - 8 q^{54} - 10 q^{56} + 24 q^{59} + 8 q^{61} - 4 q^{64} - 72 q^{69} - 36 q^{71} - 16 q^{74} + 32 q^{76} + 10 q^{79} + 22 q^{81} - 4 q^{84} - 20 q^{86} + 6 q^{89} + 20 q^{91} + 6 q^{94} - 4 q^{96}+O(q^{100}) \) 4 * q + 2 * q^4 + 8 * q^6 + 2 * q^9 - 2 * q^14 - 2 * q^16 + 16 * q^19 + 16 * q^21 + 4 * q^24 + 4 * q^26 + 24 * q^29 - 10 * q^31 - 12 * q^34 + 4 * q^36 - 8 * q^39 - 12 * q^41 - 18 * q^46 - 22 * q^49 - 12 * q^51 - 8 * q^54 - 10 * q^56 + 24 * q^59 + 8 * q^61 - 4 * q^64 - 72 * q^69 - 36 * q^71 - 16 * q^74 + 32 * q^76 + 10 * q^79 + 22 * q^81 - 4 * q^84 - 20 * q^86 + 6 * q^89 + 20 * q^91 + 6 * q^94 - 4 * q^96

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