LMFDB - Embedded newform 350.2.e.i.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(51,350)]

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([0, 2]))

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

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

chi := DirichletCharacter("350.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	350.151
Dual form			350.2.e.i.51.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.00000 - 1.73205i) q^{11} +(-2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.50000 + 6.06218i) q^{17} +(-1.50000 + 2.59808i) q^{18} +2.00000 q^{22} +(1.50000 + 2.59808i) q^{23} +(-2.00000 - 1.73205i) q^{28} +6.00000 q^{29} +(3.50000 - 6.06218i) q^{31} +(0.500000 - 0.866025i) q^{32} -7.00000 q^{34} -3.00000 q^{36} +(-2.00000 - 3.46410i) q^{37} -7.00000 q^{41} +8.00000 q^{43} +(1.00000 + 1.73205i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(-3.50000 - 6.06218i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(2.00000 - 3.46410i) q^{53} +(0.500000 - 2.59808i) q^{56} +(3.00000 + 5.19615i) q^{58} +(7.00000 - 12.1244i) q^{59} +(7.00000 + 12.1244i) q^{61} +7.00000 q^{62} +(-7.50000 + 2.59808i) q^{63} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{67} +(-3.50000 - 6.06218i) q^{68} -1.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} +(7.00000 - 12.1244i) q^{73} +(2.00000 - 3.46410i) q^{74} +(4.00000 + 3.46410i) q^{77} +(5.50000 + 9.52628i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-3.50000 - 6.06218i) q^{82} -14.0000 q^{83} +(4.00000 + 6.92820i) q^{86} +(-1.00000 + 1.73205i) q^{88} +(-3.50000 - 6.06218i) q^{89} -3.00000 q^{92} +(3.50000 - 6.06218i) q^{94} +7.00000 q^{97} +(-1.00000 - 6.92820i) q^{98} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + q^2 - q^4 - q^7 - 2 * q^8 + 3 * q^9	$ 2 q + q^{2} - q^{4} - q^{7} - 2 q^{8} + 3 q^{9} + 2 q^{11} - 5 q^{14} - q^{16} - 7 q^{17} - 3 q^{18} + 4 q^{22} + 3 q^{23} - 4 q^{28} + 12 q^{29} + 7 q^{31} + q^{32} - 14 q^{34} - 6 q^{36} - 4 q^{37} - 14 q^{41} + 16 q^{43} + 2 q^{44} - 3 q^{46} - 7 q^{47} - 13 q^{49} + 4 q^{53} + q^{56} + 6 q^{58} + 14 q^{59} + 14 q^{61} + 14 q^{62} - 15 q^{63} + 2 q^{64} + 12 q^{67} - 7 q^{68} - 2 q^{71} - 3 q^{72} + 14 q^{73} + 4 q^{74} + 8 q^{77} + 11 q^{79} - 9 q^{81} - 7 q^{82} - 28 q^{83} + 8 q^{86} - 2 q^{88} - 7 q^{89} - 6 q^{92} + 7 q^{94} + 14 q^{97} - 2 q^{98} + 12 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^4 - q^7 - 2 * q^8 + 3 * q^9 + 2 * q^11 - 5 * q^14 - q^16 - 7 * q^17 - 3 * q^18 + 4 * q^22 + 3 * q^23 - 4 * q^28 + 12 * q^29 + 7 * q^31 + q^32 - 14 * q^34 - 6 * q^36 - 4 * q^37 - 14 * q^41 + 16 * q^43 + 2 * q^44 - 3 * q^46 - 7 * q^47 - 13 * q^49 + 4 * q^53 + q^56 + 6 * q^58 + 14 * q^59 + 14 * q^61 + 14 * q^62 - 15 * q^63 + 2 * q^64 + 12 * q^67 - 7 * q^68 - 2 * q^71 - 3 * q^72 + 14 * q^73 + 4 * q^74 + 8 * q^77 + 11 * q^79 - 9 * q^81 - 7 * q^82 - 28 * q^83 + 8 * q^86 - 2 * q^88 - 7 * q^89 - 6 * q^92 + 7 * q^94 + 14 * q^97 - 2 * q^98 + 12 * 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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$3$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$	−1.00000			−0.353553
$9$	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			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	−2.50000	+	0.866025i	−0.668153	+	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.50000	+	6.06218i	−0.848875	+	1.47029i	0.0333386	+	0.999444i	$0.489386\pi$
$17$	−3.50000	+	6.06218i	−0.848875	+	1.47029i	−0.882213	+	0.470850i	$0.843947\pi$
$18$	−1.50000	+	2.59808i	−0.353553	+	0.612372i
$19$		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
$22$	2.00000			0.426401
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		0			0
$28$	−2.00000	−	1.73205i	−0.377964	−	0.327327i
$29$	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
$31$	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	$-0.0497126\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−7.00000			−1.20049
$35$		0			0
$36$	−3.00000			−0.500000
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	0.653476	−	0.756948i	$-0.273310\pi$
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	−0.982274	+	0.187453i	$0.939977\pi$
$38$		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
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$		0			0
$46$	−1.50000	+	2.59808i	−0.221163	+	0.383065i
$47$	−3.50000	−	6.06218i	−0.510527	−	0.884260i	−0.999926	−	0.0121990i	$-0.996117\pi$
$47$	−3.50000	−	6.06218i	−0.510527	−	0.884260i	0.489398	−	0.872060i	$-0.337217\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	−0.695344	−	0.718677i	$-0.744748\pi$
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	0.970065	+	0.242846i	$0.0780811\pi$
$54$		0			0
$55$		0			0
$56$	0.500000	−	2.59808i	0.0668153	−	0.347183i
$57$		0			0
$58$	3.00000	+	5.19615i	0.393919	+	0.682288i
$59$	7.00000	−	12.1244i	0.911322	−	1.57846i	0.0991242	−	0.995075i	$-0.468396\pi$
$59$	7.00000	−	12.1244i	0.911322	−	1.57846i	0.812198	−	0.583382i	$-0.198271\pi$
$60$		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	$0.479608\pi$
$62$	7.00000			0.889001
$63$	−7.50000	+	2.59808i	−0.944911	+	0.327327i
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	−0.222571	−	0.974916i	$-0.571445\pi$
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	0.955588	−	0.294706i	$-0.0952216\pi$
$68$	−3.50000	−	6.06218i	−0.424437	−	0.735147i
$69$		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	$0.518899\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	−0.0869195	−	0.996215i	$-0.527702\pi$
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	0.906208	−	0.422833i	$-0.138964\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$		0			0
$76$		0			0
$77$	4.00000	+	3.46410i	0.455842	+	0.394771i
$78$		0			0
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	0.989705	+	0.143120i	$0.0457135\pi$
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	−0.370907	+	0.928670i	$0.620953\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−3.50000	−	6.06218i	−0.386510	−	0.669456i
$83$	−14.0000			−1.53670			−0.768350	−	0.640030i	$-0.778922\pi$
$83$	−14.0000			−1.53670			−0.768350	+	0.640030i	$0.778922\pi$
$84$		0			0
$85$		0			0
$86$	4.00000	+	6.92820i	0.431331	+	0.747087i
$87$		0			0
$88$	−1.00000	+	1.73205i	−0.106600	+	0.184637i
$89$	−3.50000	−	6.06218i	−0.370999	−	0.642590i	0.618720	−	0.785611i	$-0.287651\pi$
$89$	−3.50000	−	6.06218i	−0.370999	−	0.642590i	−0.989720	+	0.143022i	$0.954318\pi$
$90$		0			0
$91$		0			0
$92$	−3.00000			−0.312772
$93$		0			0
$94$	3.50000	−	6.06218i	0.360997	−	0.625266i
$95$		0			0
$96$		0			0
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$	−1.00000	−	6.92820i	−0.101015	−	0.699854i
$99$	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
$103$	3.50000	+	6.06218i	0.344865	+	0.597324i	0.985329	−	0.170664i	$-0.0545913\pi$
$103$	3.50000	+	6.06218i	0.344865	+	0.597324i	−0.640464	+	0.767988i	$0.721258\pi$
$104$		0			0
$105$		0			0
$106$	4.00000			0.388514
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	0.683793	−	0.729676i	$-0.260329\pi$
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	−0.973814	+	0.227345i	$0.926996\pi$
$108$		0			0
$109$	−6.00000	+	10.3923i	−0.574696	+	0.995402i	0.421379	+	0.906885i	$0.361546\pi$
$109$	−6.00000	+	10.3923i	−0.574696	+	0.995402i	−0.996075	+	0.0885176i	$0.971787\pi$
$110$		0			0
$111$		0			0
$112$	2.50000	−	0.866025i	0.236228	−	0.0818317i
$113$	1.00000			0.0940721			0.0470360	−	0.998893i	$-0.485022\pi$
$113$	1.00000			0.0940721			0.0470360	+	0.998893i	$0.485022\pi$
$114$		0			0
$115$		0			0
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$		0			0
$118$	14.0000			1.28880
$119$	−14.0000	−	12.1244i	−1.28338	−	1.11144i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−7.00000	+	12.1244i	−0.633750	+	1.09769i
$123$		0			0
$124$	3.50000	+	6.06218i	0.314309	+	0.544400i
$125$		0			0
$126$	−6.00000	−	5.19615i	−0.534522	−	0.462910i
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		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
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	−0.922961	−	0.384893i	$-0.874238\pi$
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	0.794808	+	0.606861i	$0.207572\pi$
$138$		0			0
$139$	−14.0000			−1.18746			−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000			−1.18746			−0.593732	+	0.804663i	$0.702346\pi$
$140$		0			0
$141$		0			0
$142$	−0.500000	−	0.866025i	−0.0419591	−	0.0726752i
$143$		0			0
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$		0			0
$146$	14.0000			1.15865
$147$		0			0
$148$	4.00000			0.328798
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	0.953703	+	0.300750i	$0.0972370\pi$
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	−0.216394	+	0.976306i	$0.569430\pi$
$150$		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
$153$	−21.0000			−1.69775
$154$	−1.00000	+	5.19615i	−0.0805823	+	0.418718i
$155$		0			0
$156$		0			0
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	−5.50000	+	9.52628i	−0.437557	+	0.757870i
$159$		0			0
$160$		0			0
$161$	−7.50000	+	2.59808i	−0.591083	+	0.204757i
$162$	−9.00000			−0.707107
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	0.979076	−	0.203497i	$-0.0652307\pi$
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	−0.665771	+	0.746156i	$0.731897\pi$
$164$	3.50000	−	6.06218i	0.273304	−	0.473377i
$165$		0			0
$166$	−7.00000	−	12.1244i	−0.543305	−	0.941033i
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$		0			0
$171$		0			0
$172$	−4.00000	+	6.92820i	−0.304997	+	0.528271i
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	0.999293	+	0.0375896i	$0.0119679\pi$
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	−0.467093	+	0.884208i	$0.654699\pi$
$174$		0			0
$175$		0			0
$176$	−2.00000			−0.150756
$177$		0			0
$178$	3.50000	−	6.06218i	0.262336	−	0.454379i
$179$	−9.00000	+	15.5885i	−0.672692	+	1.16514i	0.304446	+	0.952529i	$0.401529\pi$
$179$	−9.00000	+	15.5885i	−0.672692	+	1.16514i	−0.977138	+	0.212607i	$0.931805\pi$
$180$		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
$187$	7.00000	+	12.1244i	0.511891	+	0.886621i
$188$	7.00000			0.510527
$189$		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
$193$	2.50000	−	4.33013i	0.179954	−	0.311689i	−0.761911	−	0.647682i	$-0.775738\pi$
$193$	2.50000	−	4.33013i	0.179954	−	0.311689i	0.941865	+	0.335993i	$0.109072\pi$
$194$	3.50000	+	6.06218i	0.251285	+	0.435239i
$195$		0			0
$196$	5.50000	−	4.33013i	0.392857	−	0.309295i
$197$	−20.0000			−1.42494			−0.712470	−	0.701702i	$-0.752424\pi$
$197$	−20.0000			−1.42494			−0.712470	+	0.701702i	$0.752424\pi$
$198$	3.00000	+	5.19615i	0.213201	+	0.369274i
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	−0.714893	−	0.699234i	$-0.753524\pi$
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	0.963001	+	0.269498i	$0.0868577\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.00000	+	15.5885i	−0.210559	+	1.09410i
$204$		0			0
$205$		0			0
$206$	−3.50000	+	6.06218i	−0.243857	+	0.422372i
$207$	−4.50000	+	7.79423i	−0.312772	+	0.541736i
$208$		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	$0.314345\pi$
$212$	2.00000	+	3.46410i	0.137361	+	0.237915i
$213$		0			0
$214$	3.00000	−	5.19615i	0.205076	−	0.355202i
$215$		0			0
$216$		0			0
$217$	14.0000	+	12.1244i	0.950382	+	0.823055i
$218$	−12.0000			−0.812743
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−7.00000			−0.468755			−0.234377	−	0.972146i	$-0.575305\pi$
$223$	−7.00000			−0.468755			−0.234377	+	0.972146i	$0.575305\pi$
$224$	2.00000	+	1.73205i	0.133631	+	0.115728i
$225$		0			0
$226$	0.500000	+	0.866025i	0.0332595	+	0.0576072i
$227$	7.00000	−	12.1244i	0.464606	−	0.804722i	−0.534577	−	0.845120i	$-0.679529\pi$
$227$	7.00000	−	12.1244i	0.464606	−	0.804722i	0.999184	+	0.0403978i	$0.0128625\pi$
$228$		0			0
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	0.999088	−	0.0426906i	$-0.0135930\pi$
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	−0.536515	+	0.843891i	$0.680260\pi$
$230$		0			0
$231$		0			0
$232$	−6.00000			−0.393919
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	−0.994283	−	0.106773i	$-0.965948\pi$
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	0.404674	−	0.914461i	$-0.367385\pi$
$234$		0			0
$235$		0			0
$236$	7.00000	+	12.1244i	0.455661	+	0.789228i
$237$		0			0
$238$	3.50000	−	18.1865i	0.226871	−	1.17886i
$239$	−5.00000			−0.323423			−0.161712	−	0.986838i	$-0.551701\pi$
$239$	−5.00000			−0.323423			−0.161712	+	0.986838i	$0.551701\pi$
$240$		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	$0.0177663\pi$
$242$	−3.50000	+	6.06218i	−0.224989	+	0.389692i
$243$		0			0
$244$	−14.0000			−0.896258
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−3.50000	+	6.06218i	−0.222250	+	0.384949i
$249$		0			0
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	1.50000	−	7.79423i	0.0944911	−	0.490990i
$253$	6.00000			0.377217
$254$	4.00000	+	6.92820i	0.250982	+	0.434714i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.00000	+	12.1244i	0.436648	+	0.756297i	0.997429	−	0.0716680i	$-0.0228322\pi$
$257$	7.00000	+	12.1244i	0.436648	+	0.756297i	−0.560781	+	0.827964i	$0.689499\pi$
$258$		0			0
$259$	10.0000	−	3.46410i	0.621370	−	0.215249i
$260$		0			0
$261$	9.00000	+	15.5885i	0.557086	+	0.964901i
$262$	7.00000	−	12.1244i	0.432461	−	0.749045i
$263$	2.50000	−	4.33013i	0.154157	−	0.267007i	−0.778595	−	0.627527i	$-0.784067\pi$
$263$	2.50000	−	4.33013i	0.154157	−	0.267007i	0.932752	+	0.360520i	$0.117401\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	6.00000	+	10.3923i	0.366508	+	0.634811i
$269$		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	$0.613166\pi$
$272$	7.00000			0.424437
$273$		0			0
$274$	−3.00000			−0.181237
$275$		0			0
$276$		0			0
$277$	9.00000	−	15.5885i	0.540758	−	0.936620i	−0.458103	−	0.888899i	$-0.651471\pi$
$277$	9.00000	−	15.5885i	0.540758	−	0.936620i	0.998861	−	0.0477206i	$-0.0151957\pi$
$278$	−7.00000	−	12.1244i	−0.419832	−	0.727171i
$279$	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
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	−0.579437	−	0.815017i	$-0.696728\pi$
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	0.995544	+	0.0942988i	$0.0300609\pi$
$284$	0.500000	−	0.866025i	0.0296695	−	0.0513892i
$285$		0			0
$286$		0			0
$287$	3.50000	−	18.1865i	0.206598	−	1.07352i
$288$	3.00000			0.176777
$289$	−16.0000	−	27.7128i	−0.941176	−	1.63017i
$290$		0			0
$291$		0			0
$292$	7.00000	+	12.1244i	0.409644	+	0.709524i
$293$	14.0000			0.817889			0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000			0.817889			0.408944	+	0.912559i	$0.365897\pi$
$294$		0			0
$295$		0			0
$296$	2.00000	+	3.46410i	0.116248	+	0.201347i
$297$		0			0
$298$	−9.00000	+	15.5885i	−0.521356	+	0.903015i
$299$		0			0
$300$		0			0
$301$	−4.00000	+	20.7846i	−0.230556	+	1.19800i
$302$	16.0000			0.920697
$303$		0			0
$304$		0			0
$305$		0			0
$306$	−10.5000	−	18.1865i	−0.600245	−	1.03965i
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	−5.00000	+	1.73205i	−0.284901	+	0.0986928i
$309$		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
$313$	−3.50000	−	6.06218i	−0.197832	−	0.342655i	0.749993	−	0.661445i	$-0.230057\pi$
$313$	−3.50000	−	6.06218i	−0.197832	−	0.342655i	−0.947825	+	0.318791i	$0.896723\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$	−11.0000			−0.618798
$317$	−16.0000	−	27.7128i	−0.898650	−	1.55651i	−0.829222	−	0.558920i	$-0.811216\pi$
$317$	−16.0000	−	27.7128i	−0.898650	−	1.55651i	−0.0694277	−	0.997587i	$-0.522117\pi$
$318$		0			0
$319$	6.00000	−	10.3923i	0.335936	−	0.581857i
$320$		0			0
$321$		0			0
$322$	−6.00000	−	5.19615i	−0.334367	−	0.289570i
$323$		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
$328$	7.00000			0.386510
$329$	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	$0.921953\pi$
$332$	7.00000	−	12.1244i	0.384175	−	0.665410i
$333$	6.00000	−	10.3923i	0.328798	−	0.569495i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	5.00000			0.272367			0.136184	−	0.990684i	$-0.456516\pi$
$337$	5.00000			0.272367			0.136184	+	0.990684i	$0.456516\pi$
$338$	−6.50000	−	11.2583i	−0.353553	−	0.612372i
$339$		0			0
$340$		0			0
$341$	−7.00000	−	12.1244i	−0.379071	−	0.656571i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−8.00000			−0.431331
$345$		0			0
$346$	−7.00000	+	12.1244i	−0.376322	+	0.651809i
$347$	−1.00000	+	1.73205i	−0.0536828	+	0.0929814i	−0.891618	−	0.452788i	$-0.850429\pi$
$347$	−1.00000	+	1.73205i	−0.0536828	+	0.0929814i	0.837935	+	0.545770i	$0.183763\pi$
$348$		0			0
$349$	28.0000			1.49881			0.749403	−	0.662114i	$-0.230341\pi$
$349$	28.0000			1.49881			0.749403	+	0.662114i	$0.230341\pi$
$350$		0			0
$351$		0			0
$352$	−1.00000	−	1.73205i	−0.0533002	−	0.0923186i
$353$	−10.5000	+	18.1865i	−0.558859	+	0.967972i	0.438733	+	0.898617i	$0.355427\pi$
$353$	−10.5000	+	18.1865i	−0.558859	+	0.967972i	−0.997592	+	0.0693543i	$0.977906\pi$
$354$		0			0
$355$		0			0
$356$	7.00000			0.370999
$357$		0			0
$358$	−18.0000			−0.951330
$359$	2.00000	+	3.46410i	0.105556	+	0.182828i	0.913965	−	0.405793i	$-0.133004\pi$
$359$	2.00000	+	3.46410i	0.105556	+	0.182828i	−0.808409	+	0.588621i	$0.799671\pi$
$360$		0			0
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$	−7.00000	−	12.1244i	−0.367912	−	0.637242i
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	−0.225750	−	0.974185i	$-0.572483\pi$
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	0.956544	−	0.291587i	$-0.0941834\pi$
$368$	1.50000	−	2.59808i	0.0781929	−	0.135434i
$369$	−10.5000	−	18.1865i	−0.546608	−	0.946753i
$370$		0			0
$371$	8.00000	+	6.92820i	0.415339	+	0.359694i
$372$		0			0
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	0.809591	−	0.586994i	$-0.199689\pi$
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	−0.913147	+	0.407630i	$0.866355\pi$
$374$	−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	$-0.450752\pi$
$379$	6.00000			0.308199			0.154100	+	0.988055i	$0.450752\pi$
$380$		0			0
$381$		0			0
$382$	7.50000	−	12.9904i	0.383733	−	0.664646i
$383$	10.5000	+	18.1865i	0.536525	+	0.929288i	0.999088	+	0.0427020i	$0.0135966\pi$
$383$	10.5000	+	18.1865i	0.536525	+	0.929288i	−0.462563	+	0.886586i	$0.653070\pi$
$384$		0			0
$385$		0			0
$386$	5.00000			0.254493
$387$	12.0000	+	20.7846i	0.609994	+	1.05654i
$388$	−3.50000	+	6.06218i	−0.177686	+	0.307760i
$389$	8.00000	−	13.8564i	0.405616	−	0.702548i	−0.588777	−	0.808296i	$-0.700390\pi$
$389$	8.00000	−	13.8564i	0.405616	−	0.702548i	0.994393	+	0.105748i	$0.0337237\pi$
$390$		0			0
$391$	−21.0000			−1.06202
$392$	6.50000	+	2.59808i	0.328300	+	0.131223i
$393$		0			0
$394$	−10.0000	−	17.3205i	−0.503793	−	0.872595i
$395$		0			0
$396$	−3.00000	+	5.19615i	−0.150756	+	0.261116i
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	0.635161	−	0.772380i	$-0.280934\pi$
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	−0.986481	+	0.163876i	$0.947600\pi$
$398$	7.00000			0.350878
$399$		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
$407$	−8.00000			−0.396545
$408$		0			0
$409$	−10.5000	+	18.1865i	−0.519192	+	0.899266i	0.480560	+	0.876962i	$0.340434\pi$
$409$	−10.5000	+	18.1865i	−0.519192	+	0.899266i	−0.999751	+	0.0223042i	$0.992900\pi$
$410$		0			0
$411$		0			0
$412$	−7.00000			−0.344865
$413$	28.0000	+	24.2487i	1.37779	+	1.19320i
$414$	−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	$0.337956\pi$
$422$	8.00000	+	13.8564i	0.389434	+	0.674519i
$423$	10.5000	−	18.1865i	0.510527	−	0.884260i
$424$	−2.00000	+	3.46410i	−0.0971286	+	0.168232i
$425$		0			0
$426$		0			0
$427$	−35.0000	+	12.1244i	−1.69377	+	0.586739i
$428$	6.00000			0.290021
$429$		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
$433$	7.00000			0.336399			0.168199	−	0.985753i	$-0.446205\pi$
$433$	7.00000			0.336399			0.168199	+	0.985753i	$0.446205\pi$
$434$	−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	0.770334	−	0.637641i	$-0.220089\pi$
$439$	−3.50000	−	6.06218i	−0.167046	−	0.289332i	−0.937380	+	0.348309i	$0.886756\pi$
$440$		0			0
$441$	−3.00000	−	20.7846i	−0.142857	−	0.989743i
$442$		0			0
$443$	−10.0000	−	17.3205i	−0.475114	−	0.822922i	0.524479	−	0.851423i	$-0.324260\pi$
$443$	−10.0000	−	17.3205i	−0.475114	−	0.822922i	−0.999594	+	0.0285009i	$0.990927\pi$
$444$		0			0
$445$		0			0
$446$	−3.50000	−	6.06218i	−0.165730	−	0.287052i
$447$		0			0
$448$	−0.500000	+	2.59808i	−0.0236228	+	0.122748i
$449$	−15.0000			−0.707894			−0.353947	−	0.935266i	$-0.615161\pi$
$449$	−15.0000			−0.707894			−0.353947	+	0.935266i	$0.615161\pi$
$450$		0			0
$451$	−7.00000	+	12.1244i	−0.329617	+	0.570914i
$452$	−0.500000	+	0.866025i	−0.0235180	+	0.0407344i
$453$		0			0
$454$	14.0000			0.657053
$455$		0			0
$456$		0			0
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	0.958950	−	0.283577i	$-0.0915211\pi$
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	−0.725059	+	0.688686i	$0.758188\pi$
$458$	−7.00000	+	12.1244i	−0.327089	+	0.566534i
$459$		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
$463$	−23.0000			−1.06890			−0.534450	−	0.845200i	$-0.679481\pi$
$463$	−23.0000			−1.06890			−0.534450	+	0.845200i	$0.679481\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$		0			0
$466$	9.00000	−	15.5885i	0.416917	−	0.722121i
$467$	7.00000	+	12.1244i	0.323921	+	0.561048i	0.981293	−	0.192518i	$-0.0616653\pi$
$467$	7.00000	+	12.1244i	0.323921	+	0.561048i	−0.657372	+	0.753566i	$0.728332\pi$
$468$		0			0
$469$	24.0000	+	20.7846i	1.10822	+	0.959744i
$470$		0			0
$471$		0			0
$472$	−7.00000	+	12.1244i	−0.322201	+	0.558069i
$473$	8.00000	−	13.8564i	0.367840	−	0.637118i
$474$		0			0
$475$		0			0
$476$	17.5000	−	6.06218i	0.802111	−	0.277859i
$477$	12.0000			0.549442
$478$	−2.50000	−	4.33013i	−0.114347	−	0.198055i
$479$	−10.5000	+	18.1865i	−0.479757	+	0.830964i	−0.999730	−	0.0232187i	$-0.992609\pi$
$479$	−10.5000	+	18.1865i	−0.479757	+	0.830964i	0.519973	+	0.854183i	$0.325942\pi$
$480$		0			0
$481$		0			0
$482$	14.0000			0.637683
$483$		0			0
$484$	−7.00000			−0.318182
$485$		0			0
$486$		0			0
$487$	−18.5000	+	32.0429i	−0.838315	+	1.45200i	0.0529875	+	0.998595i	$0.483126\pi$
$487$	−18.5000	+	32.0429i	−0.838315	+	1.45200i	−0.891303	+	0.453409i	$0.850208\pi$
$488$	−7.00000	−	12.1244i	−0.316875	−	0.548844i
$489$		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
$493$	−21.0000	+	36.3731i	−0.945792	+	1.63816i
$494$		0			0
$495$		0			0
$496$	−7.00000			−0.314309
$497$	0.500000	−	2.59808i	0.0224281	−	0.116540i
$498$		0			0
$499$	3.00000	+	5.19615i	0.134298	+	0.232612i	0.925329	−	0.379165i	$-0.123789\pi$
$499$	3.00000	+	5.19615i	0.134298	+	0.232612i	−0.791031	+	0.611776i	$0.790455\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	7.50000	−	2.59808i	0.334077	−	0.115728i
$505$		0			0
$506$	3.00000	+	5.19615i	0.133366	+	0.230997i
$507$		0			0
$508$	−4.00000	+	6.92820i	−0.177471	+	0.307389i
$509$	7.00000	+	12.1244i	0.310270	+	0.537403i	0.978421	−	0.206623i	$-0.0662474\pi$
$509$	7.00000	+	12.1244i	0.310270	+	0.537403i	−0.668151	+	0.744026i	$0.732914\pi$
$510$		0			0
$511$	28.0000	+	24.2487i	1.23865	+	1.07270i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−7.00000	+	12.1244i	−0.308757	+	0.534782i
$515$		0			0
$516$		0			0
$517$	−14.0000			−0.615719
$518$	8.00000	+	6.92820i	0.351500	+	0.304408i
$519$		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	$0.117664\pi$
$522$	−9.00000	+	15.5885i	−0.393919	+	0.682288i
$523$	−7.00000	−	12.1244i	−0.306089	−	0.530161i	0.671414	−	0.741082i	$-0.265687\pi$
$523$	−7.00000	−	12.1244i	−0.306089	−	0.530161i	−0.977503	+	0.210921i	$0.932354\pi$
$524$	14.0000			0.611593
$525$		0			0
$526$	5.00000			0.218010
$527$	24.5000	+	42.4352i	1.06724	+	1.84851i
$528$		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	$-0.339217\pi$
$542$	−10.5000	+	18.1865i	−0.451014	+	0.781179i
$543$		0			0
$544$	3.50000	+	6.06218i	0.150061	+	0.259914i
$545$		0			0
$546$		0			0
$547$	36.0000			1.53925			0.769624	−	0.638497i	$-0.220443\pi$
$547$	36.0000			1.53925			0.769624	+	0.638497i	$0.220443\pi$
$548$	−1.50000	−	2.59808i	−0.0640768	−	0.110984i
$549$	−21.0000	+	36.3731i	−0.896258	+	1.55236i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−27.5000	+	9.52628i	−1.16942	+	0.405099i
$554$	18.0000			0.764747
$555$		0			0
$556$	7.00000	−	12.1244i	0.296866	−	0.514187i
$557$	−1.00000	+	1.73205i	−0.0423714	+	0.0733893i	−0.886433	−	0.462856i	$-0.846825\pi$
$557$	−1.00000	+	1.73205i	−0.0423714	+	0.0733893i	0.844062	+	0.536246i	$0.180158\pi$
$558$	10.5000	+	18.1865i	0.444500	+	0.769897i
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.500000	−	0.866025i	−0.0210912	−	0.0365311i
$563$	−14.0000	+	24.2487i	−0.590030	+	1.02196i	0.404198	+	0.914671i	$0.367551\pi$
$563$	−14.0000	+	24.2487i	−0.590030	+	1.02196i	−0.994228	+	0.107290i	$0.965783\pi$
$564$		0			0
$565$		0			0
$566$	14.0000			0.588464
$567$	−18.0000	−	15.5885i	−0.755929	−	0.654654i
$568$	1.00000			0.0419591
$569$	−22.5000	−	38.9711i	−0.943249	−	1.63376i	−0.759220	−	0.650835i	$-0.774419\pi$
$569$	−22.5000	−	38.9711i	−0.943249	−	1.63376i	−0.184030	−	0.982921i	$-0.558914\pi$
$570$		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
$577$	−7.00000	+	12.1244i	−0.291414	+	0.504744i	−0.974144	−	0.225927i	$-0.927459\pi$
$577$	−7.00000	+	12.1244i	−0.291414	+	0.504744i	0.682730	+	0.730670i	$0.260792\pi$
$578$	16.0000	−	27.7128i	0.665512	−	1.15270i
$579$		0			0
$580$		0			0
$581$	7.00000	−	36.3731i	0.290409	−	1.50901i
$582$		0			0
$583$	−4.00000	−	6.92820i	−0.165663	−	0.286937i
$584$	−7.00000	+	12.1244i	−0.289662	+	0.501709i
$585$		0			0
$586$	7.00000	+	12.1244i	0.289167	+	0.500853i
$587$	−14.0000			−0.577842			−0.288921	−	0.957353i	$-0.593296\pi$
$587$	−14.0000			−0.577842			−0.288921	+	0.957353i	$0.593296\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−2.00000	+	3.46410i	−0.0821995	+	0.142374i
$593$	−10.5000	−	18.1865i	−0.431183	−	0.746831i	0.565792	−	0.824548i	$-0.308570\pi$
$593$	−10.5000	−	18.1865i	−0.431183	−	0.746831i	−0.996976	+	0.0777165i	$0.975237\pi$
$594$		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	$0.402166\pi$
$599$	−16.5000	+	28.5788i	−0.674172	+	1.16770i	−0.976710	+	0.214563i	$0.931167\pi$
$600$		0			0
$601$	−42.0000			−1.71322			−0.856608	−	0.515968i	$-0.827432\pi$
$601$	−42.0000			−1.71322			−0.856608	+	0.515968i	$0.827432\pi$
$602$	−20.0000	+	6.92820i	−0.815139	+	0.282372i
$603$	36.0000			1.46603
$604$	8.00000	+	13.8564i	0.325515	+	0.563809i
$605$		0			0
$606$		0			0
$607$	3.50000	+	6.06218i	0.142061	+	0.246056i	0.928272	−	0.371901i	$-0.121294\pi$
$607$	3.50000	+	6.06218i	0.142061	+	0.246056i	−0.786212	+	0.617957i	$0.787961\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	10.5000	−	18.1865i	0.424437	−	0.735147i
$613$	−15.0000	+	25.9808i	−0.605844	+	1.04935i	0.386073	+	0.922468i	$0.373831\pi$
$613$	−15.0000	+	25.9808i	−0.605844	+	1.04935i	−0.991917	+	0.126885i	$0.959502\pi$
$614$	−14.0000	−	24.2487i	−0.564994	−	0.978598i
$615$		0			0
$616$	−4.00000	−	3.46410i	−0.161165	−	0.139573i
$617$	1.00000			0.0402585			0.0201292	−	0.999797i	$-0.493592\pi$
$617$	1.00000			0.0402585			0.0201292	+	0.999797i	$0.493592\pi$
$618$		0			0
$619$	−7.00000	+	12.1244i	−0.281354	+	0.487319i	−0.971718	−	0.236143i	$-0.924117\pi$
$619$	−7.00000	+	12.1244i	−0.281354	+	0.487319i	0.690365	+	0.723462i	$0.257450\pi$
$620$		0			0
$621$		0			0
$622$	−21.0000			−0.842023
$623$	17.5000	−	6.06218i	0.701123	−	0.242876i
$624$		0			0
$625$		0			0
$626$	3.50000	−	6.06218i	0.139888	−	0.242293i
$627$		0			0
$628$	−7.00000	−	12.1244i	−0.279330	−	0.483814i
$629$	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	$0.826997\pi$
$632$	−5.50000	−	9.52628i	−0.218778	−	0.378935i
$633$		0			0
$634$	16.0000	−	27.7128i	0.635441	−	1.10062i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	12.0000			0.475085
$639$	−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
$643$	14.0000			0.552106			0.276053	−	0.961142i	$-0.410973\pi$
$643$	14.0000			0.552106			0.276053	+	0.961142i	$0.410973\pi$
$644$	1.50000	−	7.79423i	0.0591083	−	0.307136i
$645$		0			0
$646$		0			0
$647$	14.0000	−	24.2487i	0.550397	−	0.953315i	−0.447849	−	0.894109i	$-0.647810\pi$
$647$	14.0000	−	24.2487i	0.550397	−	0.953315i	0.998246	−	0.0592060i	$-0.0188569\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	−14.0000	−	24.2487i	−0.549548	−	0.951845i
$650$		0			0
$651$		0			0
$652$	−8.00000			−0.313304
$653$	4.00000	+	6.92820i	0.156532	+	0.271122i	0.933616	−	0.358276i	$-0.116635\pi$
$653$	4.00000	+	6.92820i	0.156532	+	0.271122i	−0.777084	+	0.629397i	$0.783302\pi$
$654$		0			0
$655$		0			0
$656$	3.50000	+	6.06218i	0.136652	+	0.236688i
$657$	42.0000			1.63858
$658$	14.0000	+	12.1244i	0.545777	+	0.472657i
$659$	−26.0000			−1.01282			−0.506408	−	0.862294i	$-0.669027\pi$
$659$	−26.0000			−1.01282			−0.506408	+	0.862294i	$0.669027\pi$
$660$		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	$0.0788928\pi$
$662$	5.00000	−	8.66025i	0.194331	−	0.336590i
$663$		0			0
$664$	14.0000			0.543305
$665$		0			0
$666$	12.0000			0.464991
$667$	9.00000	+	15.5885i	0.348481	+	0.603587i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	28.0000			1.08093
$672$		0			0
$673$	−37.0000			−1.42625			−0.713123	−	0.701039i	$-0.752720\pi$
$673$	−37.0000			−1.42625			−0.713123	+	0.701039i	$0.752720\pi$
$674$	2.50000	+	4.33013i	0.0962964	+	0.166790i
$675$		0			0
$676$	6.50000	−	11.2583i	0.250000	−	0.433013i
$677$	−21.0000	−	36.3731i	−0.807096	−	1.39793i	−0.914867	−	0.403755i	$-0.867705\pi$
$677$	−21.0000	−	36.3731i	−0.807096	−	1.39793i	0.107772	−	0.994176i	$-0.465628\pi$
$678$		0			0
$679$	−3.50000	+	18.1865i	−0.134318	+	0.697935i
$680$		0			0
$681$		0			0
$682$	7.00000	−	12.1244i	0.268044	−	0.464266i
$683$	13.0000	−	22.5167i	0.497431	−	0.861576i	−0.502564	−	0.864540i	$-0.667610\pi$
$683$	13.0000	−	22.5167i	0.497431	−	0.861576i	0.999996	+	0.00296369i	$0.000943372\pi$
$684$		0			0
$685$		0			0
$686$	18.5000	+	0.866025i	0.706333	+	0.0330650i
$687$		0			0
$688$	−4.00000	−	6.92820i	−0.152499	−	0.264135i
$689$		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	$0.747535\pi$
$692$	−14.0000			−0.532200
$693$	−3.00000	+	15.5885i	−0.113961	+	0.592157i
$694$	−2.00000			−0.0759190
$695$		0			0
$696$		0			0
$697$	24.5000	−	42.4352i	0.928004	−	1.60735i
$698$	14.0000	+	24.2487i	0.529908	+	0.917827i
$699$		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	0.582115	−	0.813107i	$-0.302225\pi$
$709$	−11.0000	−	19.0526i	−0.413114	−	0.715534i	−0.995228	+	0.0975728i	$0.968892\pi$
$710$		0			0
$711$	−16.5000	+	28.5788i	−0.618798	+	1.07179i
$712$	3.50000	+	6.06218i	0.131168	+	0.227190i
$713$	21.0000			0.786456
$714$		0			0
$715$		0			0
$716$	−9.00000	−	15.5885i	−0.336346	−	0.582568i
$717$		0			0
$718$	−2.00000	+	3.46410i	−0.0746393	+	0.129279i
$719$	−10.5000	−	18.1865i	−0.391584	−	0.678243i	0.601075	−	0.799193i	$-0.294739\pi$
$719$	−10.5000	−	18.1865i	−0.391584	−	0.678243i	−0.992659	+	0.120950i	$0.961406\pi$
$720$		0			0
$721$	−17.5000	+	6.06218i	−0.651734	+	0.225767i
$722$	19.0000			0.707107
$723$		0			0
$724$	7.00000	−	12.1244i	0.260153	−	0.450598i
$725$		0			0
$726$		0			0
$727$	−21.0000			−0.778847			−0.389423	−	0.921059i	$-0.627326\pi$
$727$	−21.0000			−0.778847			−0.389423	+	0.921059i	$0.627326\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−28.0000	+	48.4974i	−1.03562	+	1.79374i
$732$		0			0
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	0.707303	−	0.706910i	$-0.249912\pi$
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	−0.965854	+	0.259087i	$0.916578\pi$
$734$	28.0000			1.03350
$735$		0			0
$736$	3.00000			0.110581
$737$	−12.0000	−	20.7846i	−0.442026	−	0.765611i
$738$	10.5000	−	18.1865i	0.386510	−	0.669456i
$739$	22.0000	−	38.1051i	0.809283	−	1.40172i	−0.104078	−	0.994569i	$-0.533189\pi$
$739$	22.0000	−	38.1051i	0.809283	−	1.40172i	0.913361	−	0.407150i	$-0.133477\pi$
$740$		0			0
$741$		0			0
$742$	−2.00000	+	10.3923i	−0.0734223	+	0.381514i
$743$	−9.00000			−0.330178			−0.165089	−	0.986279i	$-0.552791\pi$
$743$	−9.00000			−0.330178			−0.165089	+	0.986279i	$0.552791\pi$
$744$		0			0
$745$		0			0
$746$	2.00000	−	3.46410i	0.0732252	−	0.126830i
$747$	−21.0000	−	36.3731i	−0.768350	−	1.33082i
$748$	−14.0000			−0.511891
$749$	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	$0.879961\pi$
$752$	−3.50000	+	6.06218i	−0.127632	+	0.221065i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	8.00000			0.290765			0.145382	−	0.989376i	$-0.453559\pi$
$757$	8.00000			0.290765			0.145382	+	0.989376i	$0.453559\pi$
$758$	3.00000	+	5.19615i	0.108965	+	0.188733i
$759$		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
$763$	−24.0000	−	20.7846i	−0.868858	−	0.752453i
$764$	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	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$		0			0
$771$		0			0
$772$	2.50000	+	4.33013i	0.0899770	+	0.155845i
$773$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$773$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$774$	−12.0000	+	20.7846i	−0.431331	+	0.747087i
$775$		0			0
$776$	−7.00000			−0.251285
$777$		0			0
$778$	16.0000			0.573628
$779$		0			0
$780$		0			0
$781$	−1.00000	+	1.73205i	−0.0357828	+	0.0619777i
$782$	−10.5000	−	18.1865i	−0.375479	−	0.650349i
$783$		0			0
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$		0			0
$786$		0			0
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	−0.500953	−	0.865474i	$-0.667017\pi$
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	0.999999	+	0.00110111i	$0.000350496\pi$
$788$	10.0000	−	17.3205i	0.356235	−	0.617018i
$789$		0			0
$790$		0			0
$791$	−0.500000	+	2.59808i	−0.0177780	+	0.0923770i
$792$	−6.00000			−0.213201
$793$		0			0
$794$	7.00000	−	12.1244i	0.248421	−	0.430277i
$795$		0			0
$796$	3.50000	+	6.06218i	0.124054	+	0.214868i
$797$	42.0000			1.48772			0.743858	−	0.668338i	$-0.232994\pi$
$797$	42.0000			1.48772			0.743858	+	0.668338i	$0.232994\pi$
$798$		0			0
$799$	49.0000			1.73350
$800$		0			0
$801$	10.5000	−	18.1865i	0.370999	−	0.642590i
$802$	5.00000	−	8.66025i	0.176556	−	0.305804i
$803$	−14.0000	−	24.2487i	−0.494049	−	0.855718i
$804$		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	$-0.656511\pi$
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	0.999491	−	0.0319002i	$-0.0101559\pi$
$810$		0			0
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	−12.0000	−	10.3923i	−0.421117	−	0.364698i
$813$		0			0
$814$	−4.00000	−	6.92820i	−0.140200	−	0.242833i
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−21.0000			−0.734248
$819$		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
$823$	−22.0000	+	38.1051i	−0.766872	+	1.32826i	0.172379	+	0.985031i	$0.444854\pi$
$823$	−22.0000	+	38.1051i	−0.766872	+	1.32826i	−0.939251	+	0.343230i	$0.888479\pi$
$824$	−3.50000	−	6.06218i	−0.121928	−	0.211186i
$825$		0			0
$826$	−7.00000	+	36.3731i	−0.243561	+	1.26558i
$827$	22.0000			0.765015			0.382507	−	0.923952i	$-0.375061\pi$
$827$	22.0000			0.765015			0.382507	+	0.923952i	$0.375061\pi$
$828$	−4.50000	−	7.79423i	−0.156386	−	0.270868i
$829$	−7.00000	+	12.1244i	−0.243120	+	0.421096i	−0.961601	−	0.274450i	$-0.911504\pi$
$829$	−7.00000	+	12.1244i	−0.243120	+	0.421096i	0.718481	+	0.695546i	$0.244838\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	38.5000	−	30.3109i	1.33395	−	1.05021i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−49.0000			−1.69167			−0.845834	−	0.533446i	$-0.820897\pi$
$839$	−49.0000			−1.69167			−0.845834	+	0.533446i	$0.820897\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	10.0000	+	17.3205i	0.344623	+	0.596904i
$843$		0			0
$844$	−8.00000	+	13.8564i	−0.275371	+	0.476957i
$845$		0			0
$846$	21.0000			0.721995
$847$	−17.5000	+	6.06218i	−0.601307	+	0.208299i
$848$	−4.00000			−0.137361
$849$		0			0
$850$		0			0
$851$	6.00000	−	10.3923i	0.205677	−	0.356244i
$852$		0			0
$853$	28.0000			0.958702			0.479351	−	0.877623i	$-0.340872\pi$
$853$	28.0000			0.958702			0.479351	+	0.877623i	$0.340872\pi$
$854$	−28.0000	−	24.2487i	−0.958140	−	0.829774i
$855$		0			0
$856$	3.00000	+	5.19615i	0.102538	+	0.177601i
$857$	−21.0000	+	36.3731i	−0.717346	+	1.24248i	0.244701	+	0.969599i	$0.421310\pi$
$857$	−21.0000	+	36.3731i	−0.717346	+	1.24248i	−0.962048	+	0.272882i	$0.912023\pi$
$858$		0			0
$859$	21.0000	+	36.3731i	0.716511	+	1.24103i	0.962374	+	0.271728i	$0.0875953\pi$
$859$	21.0000	+	36.3731i	0.716511	+	1.24103i	−0.245863	+	0.969305i	$0.579071\pi$
$860$		0			0
$861$		0			0
$862$	3.00000			0.102180
$863$	−5.50000	−	9.52628i	−0.187222	−	0.324278i	0.757101	−	0.653298i	$-0.226615\pi$
$863$	−5.50000	−	9.52628i	−0.187222	−	0.324278i	−0.944323	+	0.329020i	$0.893282\pi$
$864$		0			0
$865$		0			0
$866$	3.50000	+	6.06218i	0.118935	+	0.206001i
$867$		0			0
$868$	−17.5000	+	6.06218i	−0.593989	+	0.205764i
$869$	22.0000			0.746299
$870$		0			0
$871$		0			0
$872$	6.00000	−	10.3923i	0.203186	−	0.351928i
$873$	10.5000	+	18.1865i	0.355371	+	0.615521i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−17.0000	−	29.4449i	−0.574049	−	0.994282i	−0.996144	−	0.0877308i	$-0.972038\pi$
$877$	−17.0000	−	29.4449i	−0.574049	−	0.994282i	0.422095	−	0.906552i	$-0.361295\pi$
$878$	3.50000	−	6.06218i	0.118119	−	0.204589i
$879$		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	$0.299289\pi$
$882$	16.5000	−	12.9904i	0.555584	−	0.437409i
$883$	−6.00000			−0.201916			−0.100958	−	0.994891i	$-0.532191\pi$
$883$	−6.00000			−0.201916			−0.100958	+	0.994891i	$0.532191\pi$
$884$		0			0
$885$		0			0
$886$	10.0000	−	17.3205i	0.335957	−	0.581894i
$887$	28.0000	+	48.4974i	0.940148	+	1.62838i	0.765186	+	0.643809i	$0.222647\pi$
$887$	28.0000	+	48.4974i	0.940148	+	1.62838i	0.174962	+	0.984575i	$0.444020\pi$
$888$		0			0
$889$	−4.00000	+	20.7846i	−0.134156	+	0.697093i
$890$		0			0
$891$	9.00000	+	15.5885i	0.301511	+	0.522233i
$892$	3.50000	−	6.06218i	0.117189	−	0.202977i
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−2.50000	+	0.866025i	−0.0835191	+	0.0289319i
$897$		0			0
$898$	−7.50000	−	12.9904i	−0.250278	−	0.433495i
$899$	21.0000	−	36.3731i	0.700389	−	1.21311i
$900$		0			0
$901$	14.0000	+	24.2487i	0.466408	+	0.807842i
$902$	−14.0000			−0.466149
$903$		0			0
$904$	−1.00000			−0.0332595
$905$		0			0
$906$		0			0
$907$	−5.00000	+	8.66025i	−0.166022	+	0.287559i	−0.937018	−	0.349281i	$-0.886426\pi$
$907$	−5.00000	+	8.66025i	−0.166022	+	0.287559i	0.770996	+	0.636841i	$0.219759\pi$
$908$	7.00000	+	12.1244i	0.232303	+	0.402361i
$909$		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
$913$	−14.0000	+	24.2487i	−0.463332	+	0.802515i
$914$	−5.00000	+	8.66025i	−0.165385	+	0.286456i
$915$		0			0
$916$	−14.0000			−0.462573
$917$	35.0000	−	12.1244i	1.15580	−	0.400381i
$918$		0			0
$919$	12.5000	+	21.6506i	0.412337	+	0.714189i	0.995145	−	0.0984214i	$-0.0313793\pi$
$919$	12.5000	+	21.6506i	0.412337	+	0.714189i	−0.582808	+	0.812610i	$0.698046\pi$
$920$		0			0
$921$		0			0
$922$	14.0000	+	24.2487i	0.461065	+	0.798589i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−11.5000	−	19.9186i	−0.377913	−	0.654565i
$927$	−10.5000	+	18.1865i	−0.344865	+	0.597324i
$928$	3.00000	−	5.19615i	0.0984798	−	0.170572i
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	0.957708	−	0.287742i	$-0.0929044\pi$
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	−0.728046	+	0.685529i	$0.759571\pi$
$930$		0			0
$931$		0			0
$932$	18.0000			0.589610
$933$		0			0
$934$	−7.00000	+	12.1244i	−0.229047	+	0.396721i
$935$		0			0
$936$		0			0
$937$	−14.0000			−0.457360			−0.228680	−	0.973502i	$-0.573441\pi$
$937$	−14.0000			−0.457360			−0.228680	+	0.973502i	$0.573441\pi$
$938$	−6.00000	+	31.1769i	−0.195907	+	1.01796i
$939$		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
$943$	−10.5000	−	18.1865i	−0.341927	−	0.592235i
$944$	−14.0000			−0.455661
$945$		0			0
$946$	16.0000			0.520205
$947$	4.00000	+	6.92820i	0.129983	+	0.225136i	0.923670	−	0.383190i	$-0.125175\pi$
$947$	4.00000	+	6.92820i	0.129983	+	0.225136i	−0.793687	+	0.608326i	$0.791841\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$	14.0000	+	12.1244i	0.453743	+	0.392953i
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$	6.00000	+	10.3923i	0.194257	+	0.336463i
$955$		0			0
$956$	2.50000	−	4.33013i	0.0808558	−	0.140046i
$957$		0			0
$958$	−21.0000			−0.678479
$959$	−6.00000	−	5.19615i	−0.193750	−	0.167793i
$960$		0			0
$961$	−9.00000	−	15.5885i	−0.290323	−	0.502853i
$962$		0			0
$963$	9.00000	−	15.5885i	0.290021	−	0.502331i
$964$	7.00000	+	12.1244i	0.225455	+	0.390499i
$965$		0			0
$966$		0			0
$967$	−37.0000			−1.18984			−0.594920	−	0.803785i	$-0.702816\pi$
$967$	−37.0000			−1.18984			−0.594920	+	0.803785i	$0.702816\pi$
$968$	−3.50000	−	6.06218i	−0.112494	−	0.194846i
$969$		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
$973$	7.00000	−	36.3731i	0.224410	−	1.16607i
$974$	−37.0000			−1.18556
$975$		0			0
$976$	7.00000	−	12.1244i	0.224065	−	0.388091i
$977$	−25.5000	+	44.1673i	−0.815817	+	1.41304i	0.0929223	+	0.995673i	$0.470379\pi$
$977$	−25.5000	+	44.1673i	−0.815817	+	1.41304i	−0.908740	+	0.417364i	$0.862954\pi$
$978$		0			0
$979$	−14.0000			−0.447442
$980$		0			0
$981$	−36.0000			−1.14939
$982$	−18.0000	−	31.1769i	−0.574403	−	0.994895i
$983$	28.0000	−	48.4974i	0.893061	−	1.54683i	0.0568755	−	0.998381i	$-0.481886\pi$
$983$	28.0000	−	48.4974i	0.893061	−	1.54683i	0.836186	−	0.548446i	$-0.184780\pi$
$984$		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	$0.0476298\pi$
$992$	−3.50000	−	6.06218i	−0.111125	−	0.192474i
$993$		0			0
$994$	2.50000	−	0.866025i	0.0792952	−	0.0274687i
$995$		0			0
$996$		0			0
$997$	−14.0000	+	24.2487i	−0.443384	+	0.767964i	−0.997938	−	0.0641836i	$-0.979556\pi$
$997$	−14.0000	+	24.2487i	−0.443384	+	0.767964i	0.554554	+	0.832148i	$0.312889\pi$
$998$	−3.00000	+	5.19615i	−0.0949633	+	0.164481i
$999$		0			0

Twists

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

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

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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.00000 - 1.73205i) q^{11} +(-2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.50000 + 6.06218i) q^{17} +(-1.50000 + 2.59808i) q^{18} +2.00000 q^{22} +(1.50000 + 2.59808i) q^{23} +(-2.00000 - 1.73205i) q^{28} +6.00000 q^{29} +(3.50000 - 6.06218i) q^{31} +(0.500000 - 0.866025i) q^{32} -7.00000 q^{34} -3.00000 q^{36} +(-2.00000 - 3.46410i) q^{37} -7.00000 q^{41} +8.00000 q^{43} +(1.00000 + 1.73205i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(-3.50000 - 6.06218i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(2.00000 - 3.46410i) q^{53} +(0.500000 - 2.59808i) q^{56} +(3.00000 + 5.19615i) q^{58} +(7.00000 - 12.1244i) q^{59} +(7.00000 + 12.1244i) q^{61} +7.00000 q^{62} +(-7.50000 + 2.59808i) q^{63} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{67} +(-3.50000 - 6.06218i) q^{68} -1.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} +(7.00000 - 12.1244i) q^{73} +(2.00000 - 3.46410i) q^{74} +(4.00000 + 3.46410i) q^{77} +(5.50000 + 9.52628i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-3.50000 - 6.06218i) q^{82} -14.0000 q^{83} +(4.00000 + 6.92820i) q^{86} +(-1.00000 + 1.73205i) q^{88} +(-3.50000 - 6.06218i) q^{89} -3.00000 q^{92} +(3.50000 - 6.06218i) q^{94} +7.00000 q^{97} +(-1.00000 - 6.92820i) q^{98} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + q^2 - q^4 - q^7 - 2 * q^8 + 3 * q^9	\( 2 q + q^{2} - q^{4} - q^{7} - 2 q^{8} + 3 q^{9} + 2 q^{11} - 5 q^{14} - q^{16} - 7 q^{17} - 3 q^{18} + 4 q^{22} + 3 q^{23} - 4 q^{28} + 12 q^{29} + 7 q^{31} + q^{32} - 14 q^{34} - 6 q^{36} - 4 q^{37} - 14 q^{41} + 16 q^{43} + 2 q^{44} - 3 q^{46} - 7 q^{47} - 13 q^{49} + 4 q^{53} + q^{56} + 6 q^{58} + 14 q^{59} + 14 q^{61} + 14 q^{62} - 15 q^{63} + 2 q^{64} + 12 q^{67} - 7 q^{68} - 2 q^{71} - 3 q^{72} + 14 q^{73} + 4 q^{74} + 8 q^{77} + 11 q^{79} - 9 q^{81} - 7 q^{82} - 28 q^{83} + 8 q^{86} - 2 q^{88} - 7 q^{89} - 6 q^{92} + 7 q^{94} + 14 q^{97} - 2 q^{98} + 12 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^4 - q^7 - 2 * q^8 + 3 * q^9 + 2 * q^11 - 5 * q^14 - q^16 - 7 * q^17 - 3 * q^18 + 4 * q^22 + 3 * q^23 - 4 * q^28 + 12 * q^29 + 7 * q^31 + q^32 - 14 * q^34 - 6 * q^36 - 4 * q^37 - 14 * q^41 + 16 * q^43 + 2 * q^44 - 3 * q^46 - 7 * q^47 - 13 * q^49 + 4 * q^53 + q^56 + 6 * q^58 + 14 * q^59 + 14 * q^61 + 14 * q^62 - 15 * q^63 + 2 * q^64 + 12 * q^67 - 7 * q^68 - 2 * q^71 - 3 * q^72 + 14 * q^73 + 4 * q^74 + 8 * q^77 + 11 * q^79 - 9 * q^81 - 7 * q^82 - 28 * q^83 + 8 * q^86 - 2 * q^88 - 7 * q^89 - 6 * q^92 + 7 * q^94 + 14 * q^97 - 2 * q^98 + 12 * q^99

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