LMFDB - Embedded newform 350.2.j.c.249.1

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			249.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	350.249
Dual form			350.2.j.c.149.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.59808 - 0.500000i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.59808 - 0.500000i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(1.00000 - 1.73205i) q^{11} +(2.50000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-6.06218 - 3.50000i) q^{17} +(2.59808 + 1.50000i) q^{18} +2.00000i q^{22} +(2.59808 - 1.50000i) q^{23} +(-1.73205 + 2.00000i) q^{28} -6.00000 q^{29} +(3.50000 - 6.06218i) q^{31} +(0.866025 + 0.500000i) q^{32} +7.00000 q^{34} -3.00000 q^{36} +(3.46410 - 2.00000i) q^{37} -7.00000 q^{41} -8.00000i q^{43} +(-1.00000 - 1.73205i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(6.06218 - 3.50000i) q^{47} +(6.50000 + 2.59808i) q^{49} +(-3.46410 - 2.00000i) q^{53} +(0.500000 - 2.59808i) q^{56} +(5.19615 - 3.00000i) q^{58} +(-7.00000 + 12.1244i) q^{59} +(7.00000 + 12.1244i) q^{61} +7.00000i q^{62} +(2.59808 + 7.50000i) q^{63} -1.00000 q^{64} +(10.3923 + 6.00000i) q^{67} +(-6.06218 + 3.50000i) q^{68} -1.00000 q^{71} +(2.59808 - 1.50000i) q^{72} +(-12.1244 - 7.00000i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(-3.46410 + 4.00000i) q^{77} +(-5.50000 - 9.52628i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(6.06218 - 3.50000i) q^{82} +14.0000i q^{83} +(4.00000 + 6.92820i) q^{86} +(1.73205 + 1.00000i) q^{88} +(3.50000 + 6.06218i) q^{89} -3.00000i q^{92} +(-3.50000 + 6.06218i) q^{94} +7.00000i q^{97} +(-6.92820 + 1.00000i) q^{98} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 6 * q^9	$ 4 q + 2 q^{4} - 6 q^{9} + 4 q^{11} + 10 q^{14} - 2 q^{16} - 24 q^{29} + 14 q^{31} + 28 q^{34} - 12 q^{36} - 28 q^{41} - 4 q^{44} - 6 q^{46} + 26 q^{49} + 2 q^{56} - 28 q^{59} + 28 q^{61} - 4 q^{64} - 4 q^{71} - 8 q^{74} - 22 q^{79} - 18 q^{81} + 16 q^{86} + 14 q^{89} - 14 q^{94} - 24 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 6 * q^9 + 4 * q^11 + 10 * q^14 - 2 * q^16 - 24 * q^29 + 14 * q^31 + 28 * q^34 - 12 * q^36 - 28 * q^41 - 4 * q^44 - 6 * q^46 + 26 * q^49 + 2 * q^56 - 28 * q^59 + 28 * q^61 - 4 * q^64 - 4 * q^71 - 8 * q^74 - 22 * q^79 - 18 * q^81 + 16 * q^86 + 14 * q^89 - 14 * q^94 - 24 * q^99

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
$3$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$3$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.59808	−	0.500000i	−0.981981	−	0.188982i
$7$	−2.59808	−	0.500000i	−0.981981	−	0.188982i
$8$			1.00000i			0.353553i
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$		0			0
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$		0			0
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$	2.50000	−	0.866025i	0.668153	−	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−6.06218	−	3.50000i	−1.47029	−	0.848875i	−0.470850	−	0.882213i	$-0.656053\pi$
$17$	−6.06218	−	3.50000i	−1.47029	−	0.848875i	−0.999444	+	0.0333386i	$0.989386\pi$
$18$	2.59808	+	1.50000i	0.612372	+	0.353553i
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$		0			0
$21$		0			0
$22$			2.00000i			0.426401i
$23$	2.59808	−	1.50000i	0.541736	−	0.312772i	−0.204046	−	0.978961i	$-0.565409\pi$
$23$	2.59808	−	1.50000i	0.541736	−	0.312772i	0.745782	+	0.666190i	$0.232076\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		0			0
$28$	−1.73205	+	2.00000i	−0.327327	+	0.377964i
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$	3.50000	−	6.06218i	0.628619	−	1.08880i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	3.50000	−	6.06218i	0.628619	−	1.08880i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	7.00000			1.20049
$35$		0			0
$36$	−3.00000			−0.500000
$37$	3.46410	−	2.00000i	0.569495	−	0.328798i	−0.187453	−	0.982274i	$-0.560023\pi$
$37$	3.46410	−	2.00000i	0.569495	−	0.328798i	0.756948	+	0.653476i	$0.226690\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−7.00000			−1.09322			−0.546608	−	0.837389i	$-0.684081\pi$
$41$	−7.00000			−1.09322			−0.546608	+	0.837389i	$0.684081\pi$
$42$		0			0
$43$		−	8.00000i		−	1.21999i	−0.792406	−	0.609994i	$-0.791172\pi$
$43$		−	8.00000i		−	1.21999i	0.792406	−	0.609994i	$-0.208828\pi$
$44$	−1.00000	−	1.73205i	−0.150756	−	0.261116i
$45$		0			0
$46$	−1.50000	+	2.59808i	−0.221163	+	0.383065i
$47$	6.06218	−	3.50000i	0.884260	−	0.510527i	0.0121990	−	0.999926i	$-0.496117\pi$
$47$	6.06218	−	3.50000i	0.884260	−	0.510527i	0.872060	+	0.489398i	$0.162783\pi$
$48$		0			0
$49$	6.50000	+	2.59808i	0.928571	+	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.46410	−	2.00000i	−0.475831	−	0.274721i	0.242846	−	0.970065i	$-0.421919\pi$
$53$	−3.46410	−	2.00000i	−0.475831	−	0.274721i	−0.718677	+	0.695344i	$0.755252\pi$
$54$		0			0
$55$		0			0
$56$	0.500000	−	2.59808i	0.0668153	−	0.347183i
$57$		0			0
$58$	5.19615	−	3.00000i	0.682288	−	0.393919i
$59$	−7.00000	+	12.1244i	−0.911322	+	1.57846i	−0.0991242	+	0.995075i	$0.531604\pi$
$59$	−7.00000	+	12.1244i	−0.911322	+	1.57846i	−0.812198	+	0.583382i	$0.801729\pi$
$60$		0			0
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.832240	+	0.554416i	$0.187058\pi$
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.0640184	+	0.997949i	$0.479608\pi$
$62$			7.00000i			0.889001i
$63$	2.59808	+	7.50000i	0.327327	+	0.944911i
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	10.3923	+	6.00000i	1.26962	+	0.733017i	0.974916	−	0.222571i	$-0.0714450\pi$
$67$	10.3923	+	6.00000i	1.26962	+	0.733017i	0.294706	+	0.955588i	$0.404778\pi$
$68$	−6.06218	+	3.50000i	−0.735147	+	0.424437i
$69$		0			0
$70$		0			0
$71$	−1.00000			−0.118678			−0.0593391	−	0.998238i	$-0.518899\pi$
$71$	−1.00000			−0.118678			−0.0593391	+	0.998238i	$0.518899\pi$
$72$	2.59808	−	1.50000i	0.306186	−	0.176777i
$73$	−12.1244	−	7.00000i	−1.41905	−	0.819288i	−0.422833	−	0.906208i	$-0.638964\pi$
$73$	−12.1244	−	7.00000i	−1.41905	−	0.819288i	−0.996215	+	0.0869195i	$0.972298\pi$
$74$	−2.00000	+	3.46410i	−0.232495	+	0.402694i
$75$		0			0
$76$		0			0
$77$	−3.46410	+	4.00000i	−0.394771	+	0.455842i
$78$		0			0
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	−0.989705	−	0.143120i	$-0.954286\pi$
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	0.370907	−	0.928670i	$-0.379047\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	6.06218	−	3.50000i	0.669456	−	0.386510i
$83$			14.0000i			1.53670i	0.640030	+	0.768350i	$0.278922\pi$
$83$			14.0000i			1.53670i	−0.640030	+	0.768350i	$0.721078\pi$
$84$		0			0
$85$		0			0
$86$	4.00000	+	6.92820i	0.431331	+	0.747087i
$87$		0			0
$88$	1.73205	+	1.00000i	0.184637	+	0.106600i
$89$	3.50000	+	6.06218i	0.370999	+	0.642590i	0.989720	−	0.143022i	$-0.0456819\pi$
$89$	3.50000	+	6.06218i	0.370999	+	0.642590i	−0.618720	+	0.785611i	$0.712349\pi$
$90$		0			0
$91$		0			0
$92$		−	3.00000i		−	0.312772i
$93$		0			0
$94$	−3.50000	+	6.06218i	−0.360997	+	0.625266i
$95$		0			0
$96$		0			0
$97$			7.00000i			0.710742i	0.934725	+	0.355371i	$0.115646\pi$
$97$			7.00000i			0.710742i	−0.934725	+	0.355371i	$0.884354\pi$
$98$	−6.92820	+	1.00000i	−0.699854	+	0.101015i
$99$	−6.00000			−0.603023
$100$		0			0
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	6.06218	−	3.50000i	0.597324	−	0.344865i	−0.170664	−	0.985329i	$-0.554591\pi$
$103$	6.06218	−	3.50000i	0.597324	−	0.344865i	0.767988	+	0.640464i	$0.221258\pi$
$104$		0			0
$105$		0			0
$106$	4.00000			0.388514
$107$	5.19615	−	3.00000i	0.502331	−	0.290021i	−0.227345	−	0.973814i	$-0.573004\pi$
$107$	5.19615	−	3.00000i	0.502331	−	0.290021i	0.729676	+	0.683793i	$0.239671\pi$
$108$		0			0
$109$	6.00000	−	10.3923i	0.574696	−	0.995402i	−0.421379	−	0.906885i	$-0.638454\pi$
$109$	6.00000	−	10.3923i	0.574696	−	0.995402i	0.996075	−	0.0885176i	$-0.0282129\pi$
$110$		0			0
$111$		0			0
$112$	0.866025	+	2.50000i	0.0818317	+	0.236228i
$113$		−	1.00000i		−	0.0940721i	−0.998893	−	0.0470360i	$-0.985022\pi$
$113$		−	1.00000i		−	0.0940721i	0.998893	−	0.0470360i	$-0.0149776\pi$
$114$		0			0
$115$		0			0
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$		0			0
$118$		−	14.0000i		−	1.28880i
$119$	14.0000	+	12.1244i	1.28338	+	1.11144i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−12.1244	−	7.00000i	−1.09769	−	0.633750i
$123$		0			0
$124$	−3.50000	−	6.06218i	−0.314309	−	0.544400i
$125$		0			0
$126$	−6.00000	−	5.19615i	−0.534522	−	0.462910i
$127$			8.00000i			0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$			8.00000i			0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$		0			0
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	−0.990972	−	0.134069i	$-0.957196\pi$
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	0.379379	−	0.925241i	$-0.376138\pi$
$132$		0			0
$133$		0			0
$134$	−12.0000			−1.03664
$135$		0			0
$136$	3.50000	−	6.06218i	0.300123	−	0.519827i
$137$	−2.59808	−	1.50000i	−0.221969	−	0.128154i	0.384893	−	0.922961i	$-0.374238\pi$
$137$	−2.59808	−	1.50000i	−0.221969	−	0.128154i	−0.606861	+	0.794808i	$0.707572\pi$
$138$		0			0
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$		0			0
$141$		0			0
$142$	0.866025	−	0.500000i	0.0726752	−	0.0419591i
$143$		0			0
$144$	−1.50000	+	2.59808i	−0.125000	+	0.216506i
$145$		0			0
$146$	14.0000			1.15865
$147$		0			0
$148$		−	4.00000i		−	0.328798i
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$		0			0
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$		0			0
$153$			21.0000i			1.69775i
$154$	1.00000	−	5.19615i	0.0805823	−	0.418718i
$155$		0			0
$156$		0			0
$157$	−12.1244	−	7.00000i	−0.967629	−	0.558661i	−0.0691164	−	0.997609i	$-0.522018\pi$
$157$	−12.1244	−	7.00000i	−0.967629	−	0.558661i	−0.898513	+	0.438948i	$0.855351\pi$
$158$	9.52628	+	5.50000i	0.757870	+	0.437557i
$159$		0			0
$160$		0			0
$161$	−7.50000	+	2.59808i	−0.591083	+	0.204757i
$162$		−	9.00000i		−	0.707107i
$163$	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	$0.231897\pi$
$164$	−3.50000	+	6.06218i	−0.273304	+	0.473377i
$165$		0			0
$166$	−7.00000	−	12.1244i	−0.543305	−	0.941033i
$167$		0			0		1.00000			$0$
$167$		0			0		−1.00000			$\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$		0			0
$171$		0			0
$172$	−6.92820	−	4.00000i	−0.528271	−	0.304997i
$173$	12.1244	−	7.00000i	0.921798	−	0.532200i	0.0375896	−	0.999293i	$-0.488032\pi$
$173$	12.1244	−	7.00000i	0.921798	−	0.532200i	0.884208	+	0.467093i	$0.154699\pi$
$174$		0			0
$175$		0			0
$176$	−2.00000			−0.150756
$177$		0			0
$178$	−6.06218	−	3.50000i	−0.454379	−	0.262336i
$179$	9.00000	−	15.5885i	0.672692	−	1.16514i	−0.304446	−	0.952529i	$-0.598471\pi$
$179$	9.00000	−	15.5885i	0.672692	−	1.16514i	0.977138	−	0.212607i	$-0.0681952\pi$
$180$		0			0
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$		0			0
$183$		0			0
$184$	1.50000	+	2.59808i	0.110581	+	0.191533i
$185$		0			0
$186$		0			0
$187$	−12.1244	+	7.00000i	−0.886621	+	0.511891i
$188$		−	7.00000i		−	0.510527i
$189$		0			0
$190$		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	$-0.349257\pi$
$192$		0			0
$193$	−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	$0.724262\pi$
$194$	−3.50000	−	6.06218i	−0.251285	−	0.435239i
$195$		0			0
$196$	5.50000	−	4.33013i	0.392857	−	0.309295i
$197$		−	20.0000i		−	1.42494i	−0.701702	−	0.712470i	$-0.747576\pi$
$197$		−	20.0000i		−	1.42494i	0.701702	−	0.712470i	$-0.252424\pi$
$198$	5.19615	−	3.00000i	0.369274	−	0.213201i
$199$	−3.50000	+	6.06218i	−0.248108	+	0.429736i	−0.963001	−	0.269498i	$-0.913142\pi$
$199$	−3.50000	+	6.06218i	−0.248108	+	0.429736i	0.714893	+	0.699234i	$0.246476\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	15.5885	+	3.00000i	1.09410	+	0.210559i
$204$		0			0
$205$		0			0
$206$	−3.50000	+	6.06218i	−0.243857	+	0.422372i
$207$	−7.79423	−	4.50000i	−0.541736	−	0.312772i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	16.0000			1.10149			0.550743	−	0.834675i	$-0.314345\pi$
$211$	16.0000			1.10149			0.550743	+	0.834675i	$0.314345\pi$
$212$	−3.46410	+	2.00000i	−0.237915	+	0.137361i
$213$		0			0
$214$	−3.00000	+	5.19615i	−0.205076	+	0.355202i
$215$		0			0
$216$		0			0
$217$	−12.1244	+	14.0000i	−0.823055	+	0.950382i
$218$			12.0000i			0.812743i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$			7.00000i			0.468755i	0.972146	+	0.234377i	$0.0753051\pi$
$223$			7.00000i			0.468755i	−0.972146	+	0.234377i	$0.924695\pi$
$224$	−2.00000	−	1.73205i	−0.133631	−	0.115728i
$225$		0			0
$226$	0.500000	+	0.866025i	0.0332595	+	0.0576072i
$227$	12.1244	+	7.00000i	0.804722	+	0.464606i	0.845120	−	0.534577i	$-0.179529\pi$
$227$	12.1244	+	7.00000i	0.804722	+	0.464606i	−0.0403978	+	0.999184i	$0.512863\pi$
$228$		0			0
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	0.536515	−	0.843891i	$-0.319740\pi$
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	−0.999088	+	0.0426906i	$0.986407\pi$
$230$		0			0
$231$		0			0
$232$		−	6.00000i		−	0.393919i
$233$	−15.5885	+	9.00000i	−1.02123	+	0.589610i	−0.914461	−	0.404674i	$-0.867385\pi$
$233$	−15.5885	+	9.00000i	−1.02123	+	0.589610i	−0.106773	+	0.994283i	$0.534052\pi$
$234$		0			0
$235$		0			0
$236$	7.00000	+	12.1244i	0.455661	+	0.789228i
$237$		0			0
$238$	−18.1865	−	3.50000i	−1.17886	−	0.226871i
$239$	5.00000			0.323423			0.161712	−	0.986838i	$-0.448299\pi$
$239$	5.00000			0.323423			0.161712	+	0.986838i	$0.448299\pi$
$240$		0			0
$241$	7.00000	−	12.1244i	0.450910	−	0.780998i	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	7.00000	−	12.1244i	0.450910	−	0.780998i	0.998443	+	0.0557856i	$0.0177663\pi$
$242$	−6.06218	−	3.50000i	−0.389692	−	0.224989i
$243$		0			0
$244$	14.0000			0.896258
$245$		0			0
$246$		0			0
$247$		0			0
$248$	6.06218	+	3.50000i	0.384949	+	0.222250i
$249$		0			0
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	7.79423	+	1.50000i	0.490990	+	0.0944911i
$253$		−	6.00000i		−	0.377217i
$254$	−4.00000	−	6.92820i	−0.250982	−	0.434714i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.1244	+	7.00000i	−0.756297	+	0.436648i	−0.827964	−	0.560781i	$-0.810501\pi$
$257$	−12.1244	+	7.00000i	−0.756297	+	0.436648i	0.0716680	+	0.997429i	$0.477168\pi$
$258$		0			0
$259$	−10.0000	+	3.46410i	−0.621370	+	0.215249i
$260$		0			0
$261$	9.00000	+	15.5885i	0.557086	+	0.964901i
$262$	12.1244	+	7.00000i	0.749045	+	0.432461i
$263$	−4.33013	−	2.50000i	−0.267007	−	0.154157i	0.360520	−	0.932752i	$-0.382599\pi$
$263$	−4.33013	−	2.50000i	−0.267007	−	0.154157i	−0.627527	+	0.778595i	$0.715933\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	10.3923	−	6.00000i	0.634811	−	0.366508i
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$		0			0
$271$	10.5000	+	18.1865i	0.637830	+	1.10475i	0.985908	+	0.167288i	$0.0535009\pi$
$271$	10.5000	+	18.1865i	0.637830	+	1.10475i	−0.348079	+	0.937465i	$0.613166\pi$
$272$			7.00000i			0.424437i
$273$		0			0
$274$	3.00000			0.181237
$275$		0			0
$276$		0			0
$277$	15.5885	+	9.00000i	0.936620	+	0.540758i	0.888899	−	0.458103i	$-0.151471\pi$
$277$	15.5885	+	9.00000i	0.936620	+	0.540758i	0.0477206	+	0.998861i	$0.484804\pi$
$278$	−12.1244	+	7.00000i	−0.727171	+	0.419832i
$279$	−21.0000			−1.25724
$280$		0			0
$281$	−1.00000			−0.0596550			−0.0298275	−	0.999555i	$-0.509496\pi$
$281$	−1.00000			−0.0596550			−0.0298275	+	0.999555i	$0.509496\pi$
$282$		0			0
$283$	−12.1244	−	7.00000i	−0.720718	−	0.416107i	0.0942988	−	0.995544i	$-0.469939\pi$
$283$	−12.1244	−	7.00000i	−0.720718	−	0.416107i	−0.815017	+	0.579437i	$0.803272\pi$
$284$	−0.500000	+	0.866025i	−0.0296695	+	0.0513892i
$285$		0			0
$286$		0			0
$287$	18.1865	+	3.50000i	1.07352	+	0.206598i
$288$		−	3.00000i		−	0.176777i
$289$	16.0000	+	27.7128i	0.941176	+	1.63017i
$290$		0			0
$291$		0			0
$292$	−12.1244	+	7.00000i	−0.709524	+	0.409644i
$293$		−	14.0000i		−	0.817889i	−0.912559	−	0.408944i	$-0.865897\pi$
$293$		−	14.0000i		−	0.817889i	0.912559	−	0.408944i	$-0.134103\pi$
$294$		0			0
$295$		0			0
$296$	2.00000	+	3.46410i	0.116248	+	0.201347i
$297$		0			0
$298$	15.5885	+	9.00000i	0.903015	+	0.521356i
$299$		0			0
$300$		0			0
$301$	−4.00000	+	20.7846i	−0.230556	+	1.19800i
$302$			16.0000i			0.920697i
$303$		0			0
$304$		0			0
$305$		0			0
$306$	−10.5000	−	18.1865i	−0.600245	−	1.03965i
$307$		−	28.0000i		−	1.59804i	−0.601302	−	0.799022i	$-0.705351\pi$
$307$		−	28.0000i		−	1.59804i	0.601302	−	0.799022i	$-0.294649\pi$
$308$	1.73205	+	5.00000i	0.0986928	+	0.284901i
$309$		0			0
$310$		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	$0.963660\pi$
$312$		0			0
$313$	−6.06218	+	3.50000i	−0.342655	+	0.197832i	−0.661445	−	0.749993i	$-0.730057\pi$
$313$	−6.06218	+	3.50000i	−0.342655	+	0.197832i	0.318791	+	0.947825i	$0.396723\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	−11.0000			−0.618798
$317$	27.7128	−	16.0000i	1.55651	−	0.898650i	0.558920	−	0.829222i	$-0.311216\pi$
$317$	27.7128	−	16.0000i	1.55651	−	0.898650i	0.997587	−	0.0694277i	$-0.0221173\pi$
$318$		0			0
$319$	−6.00000	+	10.3923i	−0.335936	+	0.581857i
$320$		0			0
$321$		0			0
$322$	5.19615	−	6.00000i	0.289570	−	0.334367i
$323$		0			0
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$		0			0
$326$	−4.00000	+	6.92820i	−0.221540	+	0.383718i
$327$		0			0
$328$		−	7.00000i		−	0.386510i
$329$	−17.5000	+	6.06218i	−0.964806	+	0.334219i
$330$		0			0
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	0.695266	−	0.718752i	$-0.255287\pi$
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	−0.970091	+	0.242742i	$0.921953\pi$
$332$	12.1244	+	7.00000i	0.665410	+	0.384175i
$333$	−10.3923	−	6.00000i	−0.569495	−	0.328798i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			5.00000i			0.272367i	0.990684	+	0.136184i	$0.0434837\pi$
$337$			5.00000i			0.272367i	−0.990684	+	0.136184i	$0.956516\pi$
$338$	−11.2583	+	6.50000i	−0.612372	+	0.353553i
$339$		0			0
$340$		0			0
$341$	−7.00000	−	12.1244i	−0.379071	−	0.656571i
$342$		0			0
$343$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$344$	8.00000			0.431331
$345$		0			0
$346$	−7.00000	+	12.1244i	−0.376322	+	0.651809i
$347$	−1.73205	−	1.00000i	−0.0929814	−	0.0536828i	0.452788	−	0.891618i	$-0.350429\pi$
$347$	−1.73205	−	1.00000i	−0.0929814	−	0.0536828i	−0.545770	+	0.837935i	$0.683763\pi$
$348$		0			0
$349$	−28.0000			−1.49881			−0.749403	−	0.662114i	$-0.769659\pi$
$349$	−28.0000			−1.49881			−0.749403	+	0.662114i	$0.769659\pi$
$350$		0			0
$351$		0			0
$352$	1.73205	−	1.00000i	0.0923186	−	0.0533002i
$353$	18.1865	+	10.5000i	0.967972	+	0.558859i	0.898617	−	0.438733i	$-0.144573\pi$
$353$	18.1865	+	10.5000i	0.967972	+	0.558859i	0.0693543	+	0.997592i	$0.477906\pi$
$354$		0			0
$355$		0			0
$356$	7.00000			0.370999
$357$		0			0
$358$			18.0000i			0.951330i
$359$	−2.00000	−	3.46410i	−0.105556	−	0.182828i	0.808409	−	0.588621i	$-0.200329\pi$
$359$	−2.00000	−	3.46410i	−0.105556	−	0.182828i	−0.913965	+	0.405793i	$0.866996\pi$
$360$		0			0
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$	12.1244	−	7.00000i	0.637242	−	0.367912i
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	24.2487	+	14.0000i	1.26577	+	0.730794i	0.974185	−	0.225750i	$-0.0724833\pi$
$367$	24.2487	+	14.0000i	1.26577	+	0.730794i	0.291587	+	0.956544i	$0.405817\pi$
$368$	−2.59808	−	1.50000i	−0.135434	−	0.0781929i
$369$	10.5000	+	18.1865i	0.546608	+	0.946753i
$370$		0			0
$371$	8.00000	+	6.92820i	0.415339	+	0.359694i
$372$		0			0
$373$	−3.46410	+	2.00000i	−0.179364	+	0.103556i	−0.586994	−	0.809591i	$-0.699689\pi$
$373$	−3.46410	+	2.00000i	−0.179364	+	0.103556i	0.407630	+	0.913147i	$0.366355\pi$
$374$	7.00000	−	12.1244i	0.361961	−	0.626936i
$375$		0			0
$376$	3.50000	+	6.06218i	0.180499	+	0.312633i
$377$		0			0
$378$		0			0
$379$	−6.00000			−0.308199			−0.154100	−	0.988055i	$-0.549248\pi$
$379$	−6.00000			−0.308199			−0.154100	+	0.988055i	$0.549248\pi$
$380$		0			0
$381$		0			0
$382$	12.9904	+	7.50000i	0.664646	+	0.383733i
$383$	18.1865	−	10.5000i	0.929288	−	0.536525i	0.0427020	−	0.999088i	$-0.486403\pi$
$383$	18.1865	−	10.5000i	0.929288	−	0.536525i	0.886586	+	0.462563i	$0.153070\pi$
$384$		0			0
$385$		0			0
$386$	5.00000			0.254493
$387$	−20.7846	+	12.0000i	−1.05654	+	0.609994i
$388$	6.06218	+	3.50000i	0.307760	+	0.177686i
$389$	−8.00000	+	13.8564i	−0.405616	+	0.702548i	−0.994393	−	0.105748i	$-0.966276\pi$
$389$	−8.00000	+	13.8564i	−0.405616	+	0.702548i	0.588777	+	0.808296i	$0.299610\pi$
$390$		0			0
$391$	−21.0000			−1.06202
$392$	−2.59808	+	6.50000i	−0.131223	+	0.328300i
$393$		0			0
$394$	10.0000	+	17.3205i	0.503793	+	0.872595i
$395$		0			0
$396$	−3.00000	+	5.19615i	−0.150756	+	0.261116i
$397$	12.1244	−	7.00000i	0.608504	−	0.351320i	−0.163876	−	0.986481i	$-0.552400\pi$
$397$	12.1244	−	7.00000i	0.608504	−	0.351320i	0.772380	+	0.635161i	$0.219066\pi$
$398$		−	7.00000i		−	0.350878i
$399$		0			0
$400$		0			0
$401$	−5.00000	−	8.66025i	−0.249688	−	0.432472i	0.713751	−	0.700399i	$-0.246995\pi$
$401$	−5.00000	−	8.66025i	−0.249688	−	0.432472i	−0.963439	+	0.267927i	$0.913661\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−15.0000	+	5.19615i	−0.744438	+	0.257881i
$407$		−	8.00000i		−	0.396545i
$408$		0			0
$409$	10.5000	−	18.1865i	0.519192	−	0.899266i	−0.480560	−	0.876962i	$-0.659566\pi$
$409$	10.5000	−	18.1865i	0.519192	−	0.899266i	0.999751	−	0.0223042i	$-0.00710022\pi$
$410$		0			0
$411$		0			0
$412$		−	7.00000i		−	0.344865i
$413$	24.2487	−	28.0000i	1.19320	−	1.37779i
$414$	9.00000			0.442326
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	20.0000			0.974740			0.487370	−	0.873195i	$-0.337956\pi$
$421$	20.0000			0.974740			0.487370	+	0.873195i	$0.337956\pi$
$422$	−13.8564	+	8.00000i	−0.674519	+	0.389434i
$423$	−18.1865	−	10.5000i	−0.884260	−	0.510527i
$424$	2.00000	−	3.46410i	0.0971286	−	0.168232i
$425$		0			0
$426$		0			0
$427$	−12.1244	−	35.0000i	−0.586739	−	1.69377i
$428$		−	6.00000i		−	0.290021i
$429$		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	$0.143648\pi$
$432$		0			0
$433$		−	7.00000i		−	0.336399i	−0.985753	−	0.168199i	$-0.946205\pi$
$433$		−	7.00000i		−	0.336399i	0.985753	−	0.168199i	$-0.0537952\pi$
$434$	3.50000	−	18.1865i	0.168005	−	0.872982i
$435$		0			0
$436$	−6.00000	−	10.3923i	−0.287348	−	0.497701i
$437$		0			0
$438$		0			0
$439$	3.50000	+	6.06218i	0.167046	+	0.289332i	0.937380	−	0.348309i	$-0.113244\pi$
$439$	3.50000	+	6.06218i	0.167046	+	0.289332i	−0.770334	+	0.637641i	$0.779911\pi$
$440$		0			0
$441$	−3.00000	−	20.7846i	−0.142857	−	0.989743i
$442$		0			0
$443$	−17.3205	+	10.0000i	−0.822922	+	0.475114i	−0.851423	−	0.524479i	$-0.824260\pi$
$443$	−17.3205	+	10.0000i	−0.822922	+	0.475114i	0.0285009	+	0.999594i	$0.490927\pi$
$444$		0			0
$445$		0			0
$446$	−3.50000	−	6.06218i	−0.165730	−	0.287052i
$447$		0			0
$448$	2.59808	+	0.500000i	0.122748	+	0.0236228i
$449$	15.0000			0.707894			0.353947	−	0.935266i	$-0.384839\pi$
$449$	15.0000			0.707894			0.353947	+	0.935266i	$0.384839\pi$
$450$		0			0
$451$	−7.00000	+	12.1244i	−0.329617	+	0.570914i
$452$	−0.866025	−	0.500000i	−0.0407344	−	0.0235180i
$453$		0			0
$454$	−14.0000			−0.657053
$455$		0			0
$456$		0			0
$457$	−8.66025	+	5.00000i	−0.405110	+	0.233890i	−0.688686	−	0.725059i	$-0.741812\pi$
$457$	−8.66025	+	5.00000i	−0.405110	+	0.233890i	0.283577	+	0.958950i	$0.408479\pi$
$458$	12.1244	+	7.00000i	0.566534	+	0.327089i
$459$		0			0
$460$		0			0
$461$	28.0000			1.30409			0.652045	−	0.758180i	$-0.273911\pi$
$461$	28.0000			1.30409			0.652045	+	0.758180i	$0.273911\pi$
$462$		0			0
$463$			23.0000i			1.06890i	0.845200	+	0.534450i	$0.179481\pi$
$463$			23.0000i			1.06890i	−0.845200	+	0.534450i	$0.820519\pi$
$464$	3.00000	+	5.19615i	0.139272	+	0.241225i
$465$		0			0
$466$	9.00000	−	15.5885i	0.416917	−	0.722121i
$467$	−12.1244	+	7.00000i	−0.561048	+	0.323921i	−0.753566	−	0.657372i	$-0.771668\pi$
$467$	−12.1244	+	7.00000i	−0.561048	+	0.323921i	0.192518	+	0.981293i	$0.438335\pi$
$468$		0			0
$469$	−24.0000	−	20.7846i	−1.10822	−	0.959744i
$470$		0			0
$471$		0			0
$472$	−12.1244	−	7.00000i	−0.558069	−	0.322201i
$473$	−13.8564	−	8.00000i	−0.637118	−	0.367840i
$474$		0			0
$475$		0			0
$476$	17.5000	−	6.06218i	0.802111	−	0.277859i
$477$			12.0000i			0.549442i
$478$	−4.33013	+	2.50000i	−0.198055	+	0.114347i
$479$	10.5000	−	18.1865i	0.479757	−	0.830964i	−0.519973	−	0.854183i	$-0.674058\pi$
$479$	10.5000	−	18.1865i	0.479757	−	0.830964i	0.999730	+	0.0232187i	$0.00739140\pi$
$480$		0			0
$481$		0			0
$482$			14.0000i			0.637683i
$483$		0			0
$484$	7.00000			0.318182
$485$		0			0
$486$		0			0
$487$	−32.0429	−	18.5000i	−1.45200	−	0.838315i	−0.453409	−	0.891303i	$-0.649792\pi$
$487$	−32.0429	−	18.5000i	−1.45200	−	0.838315i	−0.998595	+	0.0529875i	$0.983126\pi$
$488$	−12.1244	+	7.00000i	−0.548844	+	0.316875i
$489$		0			0
$490$		0			0
$491$	−36.0000			−1.62466			−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000			−1.62466			−0.812329	+	0.583200i	$0.801800\pi$
$492$		0			0
$493$	36.3731	+	21.0000i	1.63816	+	0.945792i
$494$		0			0
$495$		0			0
$496$	−7.00000			−0.314309
$497$	2.59808	+	0.500000i	0.116540	+	0.0224281i
$498$		0			0
$499$	−3.00000	−	5.19615i	−0.134298	−	0.232612i	0.791031	−	0.611776i	$-0.209545\pi$
$499$	−3.00000	−	5.19615i	−0.134298	−	0.232612i	−0.925329	+	0.379165i	$0.876211\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$	−7.50000	+	2.59808i	−0.334077	+	0.115728i
$505$		0			0
$506$	3.00000	+	5.19615i	0.133366	+	0.230997i
$507$		0			0
$508$	6.92820	+	4.00000i	0.307389	+	0.177471i
$509$	−7.00000	−	12.1244i	−0.310270	−	0.537403i	0.668151	−	0.744026i	$-0.267086\pi$
$509$	−7.00000	−	12.1244i	−0.310270	−	0.537403i	−0.978421	+	0.206623i	$0.933753\pi$
$510$		0			0
$511$	28.0000	+	24.2487i	1.23865	+	1.07270i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	7.00000	−	12.1244i	0.308757	−	0.534782i
$515$		0			0
$516$		0			0
$517$		−	14.0000i		−	0.615719i
$518$	6.92820	−	8.00000i	0.304408	−	0.351500i
$519$		0			0
$520$		0			0
$521$	3.50000	−	6.06218i	0.153338	−	0.265589i	−0.779115	−	0.626881i	$-0.784331\pi$
$521$	3.50000	−	6.06218i	0.153338	−	0.265589i	0.932453	+	0.361293i	$0.117664\pi$
$522$	−15.5885	−	9.00000i	−0.682288	−	0.393919i
$523$	−12.1244	+	7.00000i	−0.530161	+	0.306089i	−0.741082	−	0.671414i	$-0.765687\pi$
$523$	−12.1244	+	7.00000i	−0.530161	+	0.306089i	0.210921	+	0.977503i	$0.432354\pi$
$524$	−14.0000			−0.611593
$525$		0			0
$526$	5.00000			0.218010
$527$	−42.4352	+	24.5000i	−1.84851	+	1.06724i
$528$		0			0
$529$	−7.00000	+	12.1244i	−0.304348	+	0.527146i
$530$		0			0
$531$	42.0000			1.82264
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−6.00000	+	10.3923i	−0.259161	+	0.448879i
$537$		0			0
$538$		0			0
$539$	11.0000	−	8.66025i	0.473804	−	0.373024i
$540$		0			0
$541$	−12.0000	−	20.7846i	−0.515920	−	0.893600i	−0.999829	−	0.0184818i	$-0.994117\pi$
$541$	−12.0000	−	20.7846i	−0.515920	−	0.893600i	0.483909	−	0.875118i	$-0.339217\pi$
$542$	−18.1865	−	10.5000i	−0.781179	−	0.451014i
$543$		0			0
$544$	−3.50000	−	6.06218i	−0.150061	−	0.259914i
$545$		0			0
$546$		0			0
$547$			36.0000i			1.53925i	0.638497	+	0.769624i	$0.279557\pi$
$547$			36.0000i			1.53925i	−0.638497	+	0.769624i	$0.720443\pi$
$548$	−2.59808	+	1.50000i	−0.110984	+	0.0640768i
$549$	21.0000	−	36.3731i	0.896258	−	1.55236i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	9.52628	+	27.5000i	0.405099	+	1.16942i
$554$	−18.0000			−0.764747
$555$		0			0
$556$	7.00000	−	12.1244i	0.296866	−	0.514187i
$557$	−1.73205	−	1.00000i	−0.0733893	−	0.0423714i	0.462856	−	0.886433i	$-0.346825\pi$
$557$	−1.73205	−	1.00000i	−0.0733893	−	0.0423714i	−0.536246	+	0.844062i	$0.680158\pi$
$558$	18.1865	−	10.5000i	0.769897	−	0.444500i
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.866025	−	0.500000i	0.0365311	−	0.0210912i
$563$	24.2487	+	14.0000i	1.02196	+	0.590030i	0.914671	−	0.404198i	$-0.132449\pi$
$563$	24.2487	+	14.0000i	1.02196	+	0.590030i	0.107290	+	0.994228i	$0.465783\pi$
$564$		0			0
$565$		0			0
$566$	14.0000			0.588464
$567$	15.5885	−	18.0000i	0.654654	−	0.755929i
$568$		−	1.00000i		−	0.0419591i
$569$	22.5000	+	38.9711i	0.943249	+	1.63376i	0.759220	+	0.650835i	$0.225581\pi$
$569$	22.5000	+	38.9711i	0.943249	+	1.63376i	0.184030	+	0.982921i	$0.441086\pi$
$570$		0			0
$571$	−6.00000	+	10.3923i	−0.251092	+	0.434904i	−0.963827	−	0.266529i	$-0.914123\pi$
$571$	−6.00000	+	10.3923i	−0.251092	+	0.434904i	0.712735	+	0.701434i	$0.247456\pi$
$572$		0			0
$573$		0			0
$574$	−17.5000	+	6.06218i	−0.730436	+	0.253030i
$575$		0			0
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	−12.1244	−	7.00000i	−0.504744	−	0.291414i	0.225927	−	0.974144i	$-0.427459\pi$
$577$	−12.1244	−	7.00000i	−0.504744	−	0.291414i	−0.730670	+	0.682730i	$0.760792\pi$
$578$	−27.7128	−	16.0000i	−1.15270	−	0.665512i
$579$		0			0
$580$		0			0
$581$	7.00000	−	36.3731i	0.290409	−	1.50901i
$582$		0			0
$583$	−6.92820	+	4.00000i	−0.286937	+	0.165663i
$584$	7.00000	−	12.1244i	0.289662	−	0.501709i
$585$		0			0
$586$	7.00000	+	12.1244i	0.289167	+	0.500853i
$587$		−	14.0000i		−	0.577842i	−0.957353	−	0.288921i	$-0.906704\pi$
$587$		−	14.0000i		−	0.577842i	0.957353	−	0.288921i	$-0.0932965\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−3.46410	−	2.00000i	−0.142374	−	0.0821995i
$593$	−18.1865	+	10.5000i	−0.746831	+	0.431183i	−0.824548	−	0.565792i	$-0.808570\pi$
$593$	−18.1865	+	10.5000i	−0.746831	+	0.431183i	0.0777165	+	0.996976i	$0.475237\pi$
$594$		0			0
$595$		0			0
$596$	−18.0000			−0.737309
$597$		0			0
$598$		0			0
$599$	16.5000	−	28.5788i	0.674172	−	1.16770i	−0.302539	−	0.953137i	$-0.597834\pi$
$599$	16.5000	−	28.5788i	0.674172	−	1.16770i	0.976710	−	0.214563i	$-0.0688326\pi$
$600$		0			0
$601$	−42.0000			−1.71322			−0.856608	−	0.515968i	$-0.827432\pi$
$601$	−42.0000			−1.71322			−0.856608	+	0.515968i	$0.827432\pi$
$602$	−6.92820	−	20.0000i	−0.282372	−	0.815139i
$603$		−	36.0000i		−	1.46603i
$604$	−8.00000	−	13.8564i	−0.325515	−	0.563809i
$605$		0			0
$606$		0			0
$607$	−6.06218	+	3.50000i	−0.246056	+	0.142061i	−0.617957	−	0.786212i	$-0.712039\pi$
$607$	−6.06218	+	3.50000i	−0.246056	+	0.142061i	0.371901	+	0.928272i	$0.378706\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	18.1865	+	10.5000i	0.735147	+	0.424437i
$613$	25.9808	+	15.0000i	1.04935	+	0.605844i	0.922468	−	0.386073i	$-0.126169\pi$
$613$	25.9808	+	15.0000i	1.04935	+	0.605844i	0.126885	+	0.991917i	$0.459502\pi$
$614$	14.0000	+	24.2487i	0.564994	+	0.978598i
$615$		0			0
$616$	−4.00000	−	3.46410i	−0.161165	−	0.139573i
$617$			1.00000i			0.0402585i	0.999797	+	0.0201292i	$0.00640777\pi$
$617$			1.00000i			0.0402585i	−0.999797	+	0.0201292i	$0.993592\pi$
$618$		0			0
$619$	7.00000	−	12.1244i	0.281354	−	0.487319i	−0.690365	−	0.723462i	$-0.742550\pi$
$619$	7.00000	−	12.1244i	0.281354	−	0.487319i	0.971718	+	0.236143i	$0.0758832\pi$
$620$		0			0
$621$		0			0
$622$		−	21.0000i		−	0.842023i
$623$	−6.06218	−	17.5000i	−0.242876	−	0.701123i
$624$		0			0
$625$		0			0
$626$	3.50000	−	6.06218i	0.139888	−	0.242293i
$627$		0			0
$628$	−12.1244	+	7.00000i	−0.483814	+	0.279330i
$629$	−28.0000			−1.11643
$630$		0			0
$631$	−43.0000			−1.71180			−0.855901	−	0.517139i	$-0.826997\pi$
$631$	−43.0000			−1.71180			−0.855901	+	0.517139i	$0.826997\pi$
$632$	9.52628	−	5.50000i	0.378935	−	0.218778i
$633$		0			0
$634$	−16.0000	+	27.7128i	−0.635441	+	1.10062i
$635$		0			0
$636$		0			0
$637$		0			0
$638$		−	12.0000i		−	0.475085i
$639$	1.50000	+	2.59808i	0.0593391	+	0.102778i
$640$		0			0
$641$	−2.50000	+	4.33013i	−0.0987441	+	0.171030i	−0.911165	−	0.412042i	$-0.864816\pi$
$641$	−2.50000	+	4.33013i	−0.0987441	+	0.171030i	0.812421	+	0.583071i	$0.198149\pi$
$642$		0			0
$643$		−	14.0000i		−	0.552106i	−0.961142	−	0.276053i	$-0.910973\pi$
$643$		−	14.0000i		−	0.552106i	0.961142	−	0.276053i	$-0.0890266\pi$
$644$	−1.50000	+	7.79423i	−0.0591083	+	0.307136i
$645$		0			0
$646$		0			0
$647$	24.2487	+	14.0000i	0.953315	+	0.550397i	0.894109	−	0.447849i	$-0.147810\pi$
$647$	24.2487	+	14.0000i	0.953315	+	0.550397i	0.0592060	+	0.998246i	$0.481143\pi$
$648$	−7.79423	−	4.50000i	−0.306186	−	0.176777i
$649$	14.0000	+	24.2487i	0.549548	+	0.951845i
$650$		0			0
$651$		0			0
$652$		−	8.00000i		−	0.313304i
$653$	6.92820	−	4.00000i	0.271122	−	0.156532i	−0.358276	−	0.933616i	$-0.616635\pi$
$653$	6.92820	−	4.00000i	0.271122	−	0.156532i	0.629397	+	0.777084i	$0.283302\pi$
$654$		0			0
$655$		0			0
$656$	3.50000	+	6.06218i	0.136652	+	0.236688i
$657$			42.0000i			1.63858i
$658$	12.1244	−	14.0000i	0.472657	−	0.545777i
$659$	26.0000			1.01282			0.506408	−	0.862294i	$-0.330973\pi$
$659$	26.0000			1.01282			0.506408	+	0.862294i	$0.330973\pi$
$660$		0			0
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	−0.697174	−	0.716902i	$-0.745559\pi$
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	0.969442	+	0.245319i	$0.0788928\pi$
$662$	8.66025	+	5.00000i	0.336590	+	0.194331i
$663$		0			0
$664$	−14.0000			−0.543305
$665$		0			0
$666$	12.0000			0.464991
$667$	−15.5885	+	9.00000i	−0.603587	+	0.348481i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	28.0000			1.08093
$672$		0			0
$673$			37.0000i			1.42625i	0.701039	+	0.713123i	$0.252720\pi$
$673$			37.0000i			1.42625i	−0.701039	+	0.713123i	$0.747280\pi$
$674$	−2.50000	−	4.33013i	−0.0962964	−	0.166790i
$675$		0			0
$676$	6.50000	−	11.2583i	0.250000	−	0.433013i
$677$	36.3731	−	21.0000i	1.39793	−	0.807096i	0.403755	−	0.914867i	$-0.367705\pi$
$677$	36.3731	−	21.0000i	1.39793	−	0.807096i	0.994176	+	0.107772i	$0.0343715\pi$
$678$		0			0
$679$	3.50000	−	18.1865i	0.134318	−	0.697935i
$680$		0			0
$681$		0			0
$682$	12.1244	+	7.00000i	0.464266	+	0.268044i
$683$	−22.5167	−	13.0000i	−0.861576	−	0.497431i	0.00296369	−	0.999996i	$-0.499057\pi$
$683$	−22.5167	−	13.0000i	−0.861576	−	0.497431i	−0.864540	+	0.502564i	$0.832390\pi$
$684$		0			0
$685$		0			0
$686$	18.5000	+	0.866025i	0.706333	+	0.0330650i
$687$		0			0
$688$	−6.92820	+	4.00000i	−0.264135	+	0.152499i
$689$		0			0
$690$		0			0
$691$	7.00000	+	12.1244i	0.266293	+	0.461232i	0.967901	−	0.251330i	$-0.0808679\pi$
$691$	7.00000	+	12.1244i	0.266293	+	0.461232i	−0.701609	+	0.712562i	$0.747535\pi$
$692$		−	14.0000i		−	0.532200i
$693$	15.5885	+	3.00000i	0.592157	+	0.113961i
$694$	2.00000			0.0759190
$695$		0			0
$696$		0			0
$697$	42.4352	+	24.5000i	1.60735	+	0.928004i
$698$	24.2487	−	14.0000i	0.917827	−	0.529908i
$699$		0			0
$700$		0			0
$701$	16.0000			0.604312			0.302156	−	0.953259i	$-0.402294\pi$
$701$	16.0000			0.604312			0.302156	+	0.953259i	$0.402294\pi$
$702$		0			0
$703$		0			0
$704$	−1.00000	+	1.73205i	−0.0376889	+	0.0652791i
$705$		0			0
$706$	−21.0000			−0.790345
$707$		0			0
$708$		0			0
$709$	11.0000	+	19.0526i	0.413114	+	0.715534i	0.995228	−	0.0975728i	$-0.0311079\pi$
$709$	11.0000	+	19.0526i	0.413114	+	0.715534i	−0.582115	+	0.813107i	$0.697775\pi$
$710$		0			0
$711$	−16.5000	+	28.5788i	−0.618798	+	1.07179i
$712$	−6.06218	+	3.50000i	−0.227190	+	0.131168i
$713$		−	21.0000i		−	0.786456i
$714$		0			0
$715$		0			0
$716$	−9.00000	−	15.5885i	−0.336346	−	0.582568i
$717$		0			0
$718$	3.46410	+	2.00000i	0.129279	+	0.0746393i
$719$	10.5000	+	18.1865i	0.391584	+	0.678243i	0.992659	−	0.120950i	$-0.0385939\pi$
$719$	10.5000	+	18.1865i	0.391584	+	0.678243i	−0.601075	+	0.799193i	$0.705261\pi$
$720$		0			0
$721$	−17.5000	+	6.06218i	−0.651734	+	0.225767i
$722$			19.0000i			0.707107i
$723$		0			0
$724$	−7.00000	+	12.1244i	−0.260153	+	0.450598i
$725$		0			0
$726$		0			0
$727$		−	21.0000i		−	0.778847i	−0.921059	−	0.389423i	$-0.872674\pi$
$727$		−	21.0000i		−	0.778847i	0.921059	−	0.389423i	$-0.127326\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$	−28.0000	+	48.4974i	−1.03562	+	1.79374i
$732$		0			0
$733$	−12.1244	+	7.00000i	−0.447823	+	0.258551i	−0.706910	−	0.707303i	$-0.749912\pi$
$733$	−12.1244	+	7.00000i	−0.447823	+	0.258551i	0.259087	+	0.965854i	$0.416578\pi$
$734$	−28.0000			−1.03350
$735$		0			0
$736$	3.00000			0.110581
$737$	20.7846	−	12.0000i	0.765611	−	0.442026i
$738$	−18.1865	−	10.5000i	−0.669456	−	0.386510i
$739$	−22.0000	+	38.1051i	−0.809283	+	1.40172i	0.104078	+	0.994569i	$0.466811\pi$
$739$	−22.0000	+	38.1051i	−0.809283	+	1.40172i	−0.913361	+	0.407150i	$0.866523\pi$
$740$		0			0
$741$		0			0
$742$	−10.3923	−	2.00000i	−0.381514	−	0.0734223i
$743$			9.00000i			0.330178i	0.986279	+	0.165089i	$0.0527911\pi$
$743$			9.00000i			0.330178i	−0.986279	+	0.165089i	$0.947209\pi$
$744$		0			0
$745$		0			0
$746$	2.00000	−	3.46410i	0.0732252	−	0.126830i
$747$	36.3731	−	21.0000i	1.33082	−	0.768350i
$748$			14.0000i			0.511891i
$749$	−15.0000	+	5.19615i	−0.548088	+	0.189863i
$750$		0			0
$751$	−4.00000	−	6.92820i	−0.145962	−	0.252814i	0.783769	−	0.621052i	$-0.213294\pi$
$751$	−4.00000	−	6.92820i	−0.145962	−	0.252814i	−0.929731	+	0.368238i	$0.879961\pi$
$752$	−6.06218	−	3.50000i	−0.221065	−	0.127632i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$			8.00000i			0.290765i	0.989376	+	0.145382i	$0.0464413\pi$
$757$			8.00000i			0.290765i	−0.989376	+	0.145382i	$0.953559\pi$
$758$	5.19615	−	3.00000i	0.188733	−	0.108965i
$759$		0			0
$760$		0			0
$761$	−10.5000	−	18.1865i	−0.380625	−	0.659261i	0.610527	−	0.791995i	$-0.290958\pi$
$761$	−10.5000	−	18.1865i	−0.380625	−	0.659261i	−0.991152	+	0.132734i	$0.957624\pi$
$762$		0			0
$763$	−20.7846	+	24.0000i	−0.752453	+	0.868858i
$764$	−15.0000			−0.542681
$765$		0			0
$766$	−10.5000	+	18.1865i	−0.379380	+	0.657106i
$767$		0			0
$768$		0			0
$769$	14.0000			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$770$		0			0
$771$		0			0
$772$	−4.33013	+	2.50000i	−0.155845	+	0.0899770i
$773$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$773$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$774$	12.0000	−	20.7846i	0.431331	−	0.747087i
$775$		0			0
$776$	−7.00000			−0.251285
$777$		0			0
$778$		−	16.0000i		−	0.573628i
$779$		0			0
$780$		0			0
$781$	−1.00000	+	1.73205i	−0.0357828	+	0.0619777i
$782$	18.1865	−	10.5000i	0.650349	−	0.375479i
$783$		0			0
$784$	−1.00000	−	6.92820i	−0.0357143	−	0.247436i
$785$		0			0
$786$		0			0
$787$	24.2487	+	14.0000i	0.864373	+	0.499046i	0.865474	−	0.500953i	$-0.167017\pi$
$787$	24.2487	+	14.0000i	0.864373	+	0.499046i	−0.00110111	+	0.999999i	$0.500350\pi$
$788$	−17.3205	−	10.0000i	−0.617018	−	0.356235i
$789$		0			0
$790$		0			0
$791$	−0.500000	+	2.59808i	−0.0177780	+	0.0923770i
$792$		−	6.00000i		−	0.213201i
$793$		0			0
$794$	−7.00000	+	12.1244i	−0.248421	+	0.430277i
$795$		0			0
$796$	3.50000	+	6.06218i	0.124054	+	0.214868i
$797$			42.0000i			1.48772i	0.668338	+	0.743858i	$0.267006\pi$
$797$			42.0000i			1.48772i	−0.668338	+	0.743858i	$0.732994\pi$
$798$		0			0
$799$	−49.0000			−1.73350
$800$		0			0
$801$	10.5000	−	18.1865i	0.370999	−	0.642590i
$802$	8.66025	+	5.00000i	0.305804	+	0.176556i
$803$	−24.2487	+	14.0000i	−0.855718	+	0.494049i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		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
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	10.3923	−	12.0000i	0.364698	−	0.421117i
$813$		0			0
$814$	4.00000	+	6.92820i	0.140200	+	0.242833i
$815$		0			0
$816$		0			0
$817$		0			0
$818$			21.0000i			0.734248i
$819$		0			0
$820$		0			0
$821$	24.0000	+	41.5692i	0.837606	+	1.45078i	0.891891	+	0.452250i	$0.149379\pi$
$821$	24.0000	+	41.5692i	0.837606	+	1.45078i	−0.0542853	+	0.998525i	$0.517288\pi$
$822$		0			0
$823$	38.1051	+	22.0000i	1.32826	+	0.766872i	0.985031	−	0.172379i	$-0.0551455\pi$
$823$	38.1051	+	22.0000i	1.32826	+	0.766872i	0.343230	+	0.939251i	$0.388479\pi$
$824$	3.50000	+	6.06218i	0.121928	+	0.211186i
$825$		0			0
$826$	−7.00000	+	36.3731i	−0.243561	+	1.26558i
$827$			22.0000i			0.765015i	0.923952	+	0.382507i	$0.124939\pi$
$827$			22.0000i			0.765015i	−0.923952	+	0.382507i	$0.875061\pi$
$828$	−7.79423	+	4.50000i	−0.270868	+	0.156386i
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	−0.718481	−	0.695546i	$-0.755162\pi$
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	0.961601	+	0.274450i	$0.0884958\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−30.3109	−	38.5000i	−1.05021	−	1.33395i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$	49.0000			1.69167			0.845834	−	0.533446i	$-0.179103\pi$
$839$	49.0000			1.69167			0.845834	+	0.533446i	$0.179103\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	−17.3205	+	10.0000i	−0.596904	+	0.344623i
$843$		0			0
$844$	8.00000	−	13.8564i	0.275371	−	0.476957i
$845$		0			0
$846$	21.0000			0.721995
$847$	−6.06218	−	17.5000i	−0.208299	−	0.601307i
$848$			4.00000i			0.137361i
$849$		0			0
$850$		0			0
$851$	6.00000	−	10.3923i	0.205677	−	0.356244i
$852$		0			0
$853$		−	28.0000i		−	0.958702i	−0.877623	−	0.479351i	$-0.840872\pi$
$853$		−	28.0000i		−	0.958702i	0.877623	−	0.479351i	$-0.159128\pi$
$854$	28.0000	+	24.2487i	0.958140	+	0.829774i
$855$		0			0
$856$	3.00000	+	5.19615i	0.102538	+	0.177601i
$857$	−36.3731	−	21.0000i	−1.24248	−	0.717346i	−0.272882	−	0.962048i	$-0.587977\pi$
$857$	−36.3731	−	21.0000i	−1.24248	−	0.717346i	−0.969599	+	0.244701i	$0.921310\pi$
$858$		0			0
$859$	−21.0000	−	36.3731i	−0.716511	−	1.24103i	−0.962374	−	0.271728i	$-0.912405\pi$
$859$	−21.0000	−	36.3731i	−0.716511	−	1.24103i	0.245863	−	0.969305i	$-0.420929\pi$
$860$		0			0
$861$		0			0
$862$			3.00000i			0.102180i
$863$	−9.52628	+	5.50000i	−0.324278	+	0.187222i	−0.653298	−	0.757101i	$-0.726615\pi$
$863$	−9.52628	+	5.50000i	−0.324278	+	0.187222i	0.329020	+	0.944323i	$0.393282\pi$
$864$		0			0
$865$		0			0
$866$	3.50000	+	6.06218i	0.118935	+	0.206001i
$867$		0			0
$868$	6.06218	+	17.5000i	0.205764	+	0.593989i
$869$	−22.0000			−0.746299
$870$		0			0
$871$		0			0
$872$	10.3923	+	6.00000i	0.351928	+	0.203186i
$873$	18.1865	−	10.5000i	0.615521	−	0.355371i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	29.4449	−	17.0000i	0.994282	−	0.574049i	0.0877308	−	0.996144i	$-0.472038\pi$
$877$	29.4449	−	17.0000i	0.994282	−	0.574049i	0.906552	+	0.422095i	$0.138705\pi$
$878$	−6.06218	−	3.50000i	−0.204589	−	0.118119i
$879$		0			0
$880$		0			0
$881$	35.0000			1.17918			0.589590	−	0.807703i	$-0.299289\pi$
$881$	35.0000			1.17918			0.589590	+	0.807703i	$0.299289\pi$
$882$	12.9904	+	16.5000i	0.437409	+	0.555584i
$883$			6.00000i			0.201916i	0.994891	+	0.100958i	$0.0321908\pi$
$883$			6.00000i			0.201916i	−0.994891	+	0.100958i	$0.967809\pi$
$884$		0			0
$885$		0			0
$886$	10.0000	−	17.3205i	0.335957	−	0.581894i
$887$	−48.4974	+	28.0000i	−1.62838	+	0.940148i	−0.643809	+	0.765186i	$0.722647\pi$
$887$	−48.4974	+	28.0000i	−1.62838	+	0.940148i	−0.984575	+	0.174962i	$0.944020\pi$
$888$		0			0
$889$	4.00000	−	20.7846i	0.134156	−	0.697093i
$890$		0			0
$891$	9.00000	+	15.5885i	0.301511	+	0.522233i
$892$	6.06218	+	3.50000i	0.202977	+	0.117189i
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−2.50000	+	0.866025i	−0.0835191	+	0.0289319i
$897$		0			0
$898$	−12.9904	+	7.50000i	−0.433495	+	0.250278i
$899$	−21.0000	+	36.3731i	−0.700389	+	1.21311i
$900$		0			0
$901$	14.0000	+	24.2487i	0.466408	+	0.807842i
$902$		−	14.0000i		−	0.466149i
$903$		0			0
$904$	1.00000			0.0332595
$905$		0			0
$906$		0			0
$907$	−8.66025	−	5.00000i	−0.287559	−	0.166022i	0.349281	−	0.937018i	$-0.386426\pi$
$907$	−8.66025	−	5.00000i	−0.287559	−	0.166022i	−0.636841	+	0.770996i	$0.719759\pi$
$908$	12.1244	−	7.00000i	0.402361	−	0.232303i
$909$		0			0
$910$		0			0
$911$	27.0000			0.894550			0.447275	−	0.894397i	$-0.352395\pi$
$911$	27.0000			0.894550			0.447275	+	0.894397i	$0.352395\pi$
$912$		0			0
$913$	24.2487	+	14.0000i	0.802515	+	0.463332i
$914$	5.00000	−	8.66025i	0.165385	−	0.286456i
$915$		0			0
$916$	−14.0000			−0.462573
$917$	12.1244	+	35.0000i	0.400381	+	1.15580i
$918$		0			0
$919$	−12.5000	−	21.6506i	−0.412337	−	0.714189i	0.582808	−	0.812610i	$-0.301954\pi$
$919$	−12.5000	−	21.6506i	−0.412337	−	0.714189i	−0.995145	+	0.0984214i	$0.968621\pi$
$920$		0			0
$921$		0			0
$922$	−24.2487	+	14.0000i	−0.798589	+	0.461065i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−11.5000	−	19.9186i	−0.377913	−	0.654565i
$927$	−18.1865	−	10.5000i	−0.597324	−	0.344865i
$928$	−5.19615	−	3.00000i	−0.170572	−	0.0984798i
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	0.728046	−	0.685529i	$-0.240429\pi$
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	−0.957708	+	0.287742i	$0.907096\pi$
$930$		0			0
$931$		0			0
$932$			18.0000i			0.589610i
$933$		0			0
$934$	7.00000	−	12.1244i	0.229047	−	0.396721i
$935$		0			0
$936$		0			0
$937$		−	14.0000i		−	0.457360i	−0.973502	−	0.228680i	$-0.926559\pi$
$937$		−	14.0000i		−	0.457360i	0.973502	−	0.228680i	$-0.0734410\pi$
$938$	31.1769	+	6.00000i	1.01796	+	0.195907i
$939$		0			0
$940$		0			0
$941$	14.0000	−	24.2487i	0.456387	−	0.790485i	−0.542380	−	0.840133i	$-0.682477\pi$
$941$	14.0000	−	24.2487i	0.456387	−	0.790485i	0.998767	+	0.0496480i	$0.0158099\pi$
$942$		0			0
$943$	−18.1865	+	10.5000i	−0.592235	+	0.341927i
$944$	14.0000			0.455661
$945$		0			0
$946$	16.0000			0.520205
$947$	−6.92820	+	4.00000i	−0.225136	+	0.129983i	−0.608326	−	0.793687i	$-0.708159\pi$
$947$	−6.92820	+	4.00000i	−0.225136	+	0.129983i	0.383190	+	0.923670i	$0.374825\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$	−12.1244	+	14.0000i	−0.392953	+	0.453743i
$953$			6.00000i			0.194359i	0.995267	+	0.0971795i	$0.0309821\pi$
$953$			6.00000i			0.194359i	−0.995267	+	0.0971795i	$0.969018\pi$
$954$	−6.00000	−	10.3923i	−0.194257	−	0.336463i
$955$		0			0
$956$	2.50000	−	4.33013i	0.0808558	−	0.140046i
$957$		0			0
$958$			21.0000i			0.678479i
$959$	6.00000	+	5.19615i	0.193750	+	0.167793i
$960$		0			0
$961$	−9.00000	−	15.5885i	−0.290323	−	0.502853i
$962$		0			0
$963$	−15.5885	−	9.00000i	−0.502331	−	0.290021i
$964$	−7.00000	−	12.1244i	−0.225455	−	0.390499i
$965$		0			0
$966$		0			0
$967$		−	37.0000i		−	1.18984i	−0.803785	−	0.594920i	$-0.797184\pi$
$967$		−	37.0000i		−	1.18984i	0.803785	−	0.594920i	$-0.202816\pi$
$968$	−6.06218	+	3.50000i	−0.194846	+	0.112494i
$969$		0			0
$970$		0			0
$971$	−21.0000	−	36.3731i	−0.673922	−	1.16727i	−0.976783	−	0.214232i	$-0.931275\pi$
$971$	−21.0000	−	36.3731i	−0.673922	−	1.16727i	0.302861	−	0.953035i	$-0.402058\pi$
$972$		0			0
$973$	−36.3731	−	7.00000i	−1.16607	−	0.224410i
$974$	37.0000			1.18556
$975$		0			0
$976$	7.00000	−	12.1244i	0.224065	−	0.388091i
$977$	−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	$0.970379\pi$
$978$		0			0
$979$	14.0000			0.447442
$980$		0			0
$981$	−36.0000			−1.14939
$982$	31.1769	−	18.0000i	0.994895	−	0.574403i
$983$	−48.4974	−	28.0000i	−1.54683	−	0.893061i	−0.998381	−	0.0568755i	$-0.981886\pi$
$983$	−48.4974	−	28.0000i	−1.54683	−	0.893061i	−0.548446	−	0.836186i	$-0.684780\pi$
$984$		0			0
$985$		0			0
$986$	−42.0000			−1.33755
$987$		0			0
$988$		0			0
$989$	−12.0000	−	20.7846i	−0.381578	−	0.660912i
$990$		0			0
$991$	11.5000	−	19.9186i	0.365310	−	0.632735i	−0.623516	−	0.781810i	$-0.714296\pi$
$991$	11.5000	−	19.9186i	0.365310	−	0.632735i	0.988826	+	0.149076i	$0.0476298\pi$
$992$	6.06218	−	3.50000i	0.192474	−	0.111125i
$993$		0			0
$994$	−2.50000	+	0.866025i	−0.0792952	+	0.0274687i
$995$		0			0
$996$		0			0
$997$	−24.2487	−	14.0000i	−0.767964	−	0.443384i	0.0641836	−	0.997938i	$-0.479556\pi$
$997$	−24.2487	−	14.0000i	−0.767964	−	0.443384i	−0.832148	+	0.554554i	$0.812889\pi$
$998$	5.19615	+	3.00000i	0.164481	+	0.0949633i
$999$		0			0

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.59808 - 0.500000i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.59808 - 0.500000i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(1.00000 - 1.73205i) q^{11} +(2.50000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-6.06218 - 3.50000i) q^{17} +(2.59808 + 1.50000i) q^{18} +2.00000i q^{22} +(2.59808 - 1.50000i) q^{23} +(-1.73205 + 2.00000i) q^{28} -6.00000 q^{29} +(3.50000 - 6.06218i) q^{31} +(0.866025 + 0.500000i) q^{32} +7.00000 q^{34} -3.00000 q^{36} +(3.46410 - 2.00000i) q^{37} -7.00000 q^{41} -8.00000i q^{43} +(-1.00000 - 1.73205i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(6.06218 - 3.50000i) q^{47} +(6.50000 + 2.59808i) q^{49} +(-3.46410 - 2.00000i) q^{53} +(0.500000 - 2.59808i) q^{56} +(5.19615 - 3.00000i) q^{58} +(-7.00000 + 12.1244i) q^{59} +(7.00000 + 12.1244i) q^{61} +7.00000i q^{62} +(2.59808 + 7.50000i) q^{63} -1.00000 q^{64} +(10.3923 + 6.00000i) q^{67} +(-6.06218 + 3.50000i) q^{68} -1.00000 q^{71} +(2.59808 - 1.50000i) q^{72} +(-12.1244 - 7.00000i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(-3.46410 + 4.00000i) q^{77} +(-5.50000 - 9.52628i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(6.06218 - 3.50000i) q^{82} +14.0000i q^{83} +(4.00000 + 6.92820i) q^{86} +(1.73205 + 1.00000i) q^{88} +(3.50000 + 6.06218i) q^{89} -3.00000i q^{92} +(-3.50000 + 6.06218i) q^{94} +7.00000i q^{97} +(-6.92820 + 1.00000i) q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 6 * q^9	\( 4 q + 2 q^{4} - 6 q^{9} + 4 q^{11} + 10 q^{14} - 2 q^{16} - 24 q^{29} + 14 q^{31} + 28 q^{34} - 12 q^{36} - 28 q^{41} - 4 q^{44} - 6 q^{46} + 26 q^{49} + 2 q^{56} - 28 q^{59} + 28 q^{61} - 4 q^{64} - 4 q^{71} - 8 q^{74} - 22 q^{79} - 18 q^{81} + 16 q^{86} + 14 q^{89} - 14 q^{94} - 24 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 6 * q^9 + 4 * q^11 + 10 * q^14 - 2 * q^16 - 24 * q^29 + 14 * q^31 + 28 * q^34 - 12 * q^36 - 28 * q^41 - 4 * q^44 - 6 * q^46 + 26 * q^49 + 2 * q^56 - 28 * q^59 + 28 * q^61 - 4 * q^64 - 4 * q^71 - 8 * q^74 - 22 * q^79 - 18 * q^81 + 16 * q^86 + 14 * q^89 - 14 * q^94 - 24 * q^99

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