LMFDB - Embedded newform 450.3.k.a.149.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,3,Mod(149,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("450.149");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	450.k (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:	$12.2616118962$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.2
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	450.149
Dual form			450.3.k.a.299.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(1.73205 - 2.44949i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-4.22474 - 0.389270i) q^{6} +(5.49794 - 3.17423i) q^{7} +2.82843 q^{8} +(-3.00000 - 8.48528i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(1.73205 - 2.44949i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-4.22474 - 0.389270i) q^{6} +(5.49794 - 3.17423i) q^{7} +2.82843 q^{8} +(-3.00000 - 8.48528i) q^{9} +(8.17423 - 4.71940i) q^{11} +(2.51059 + 5.44949i) q^{12} +(17.0580 + 9.84847i) q^{13} +(-7.77526 - 4.48905i) q^{14} +(-2.00000 - 3.46410i) q^{16} -1.90702 q^{17} +(-8.27098 + 9.67423i) q^{18} -4.69694 q^{19} +(1.74745 - 18.9651i) q^{21} +(-11.5601 - 6.67423i) q^{22} +(4.71940 - 8.17423i) q^{23} +(4.89898 - 6.92820i) q^{24} -27.8557i q^{26} +(-25.9808 - 7.34847i) q^{27} +12.6969i q^{28} +(2.84847 - 1.64456i) q^{29} +(20.5227 - 35.5464i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(2.59808 - 28.1969i) q^{33} +(1.34847 + 2.33562i) q^{34} +(17.6969 + 3.28913i) q^{36} +17.3031i q^{37} +(3.32124 + 5.75255i) q^{38} +(53.6691 - 24.7255i) q^{39} +(-53.5454 - 30.9145i) q^{41} +(-24.4630 + 11.2702i) q^{42} +(-0.826701 + 0.477296i) q^{43} +18.8776i q^{44} -13.3485 q^{46} +(-7.05501 - 12.2196i) q^{47} +(-11.9494 - 1.10102i) q^{48} +(-4.34847 + 7.53177i) q^{49} +(-3.30306 + 4.67123i) q^{51} +(-34.1161 + 19.6969i) q^{52} +9.53512 q^{53} +(9.37117 + 37.0160i) q^{54} +(15.5505 - 8.97809i) q^{56} +(-8.13534 + 11.5051i) q^{57} +(-4.02834 - 2.32577i) q^{58} +(-79.2650 - 45.7637i) q^{59} +(37.5454 + 65.0306i) q^{61} -58.0470 q^{62} +(-43.4281 - 37.1288i) q^{63} +8.00000 q^{64} +(-36.3712 + 16.7563i) q^{66} +(-26.8075 - 15.4773i) q^{67} +(1.90702 - 3.30306i) q^{68} +(-11.8485 - 25.7183i) q^{69} -85.9026i q^{71} +(-8.48528 - 24.0000i) q^{72} +96.0908i q^{73} +(21.1918 - 12.2351i) q^{74} +(4.69694 - 8.13534i) q^{76} +(29.9609 - 51.8939i) q^{77} +(-68.2322 - 48.2474i) q^{78} +(14.8712 + 25.7576i) q^{79} +(-63.0000 + 50.9117i) q^{81} +87.4393i q^{82} +(43.9530 + 76.1288i) q^{83} +(31.1010 + 21.9917i) q^{84} +(1.16913 + 0.674999i) q^{86} +(0.905350 - 9.82577i) q^{87} +(23.1202 - 13.3485i) q^{88} -41.3766i q^{89} +125.045 q^{91} +(9.43879 + 16.3485i) q^{92} +(-51.5241 - 111.838i) q^{93} +(-9.97730 + 17.2812i) q^{94} +(7.10102 + 15.4135i) q^{96} +(83.0333 - 47.9393i) q^{97} +12.2993 q^{98} +(-64.5681 - 55.2025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 24 q^{6} - 24 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 24 * q^6 - 24 * q^9	$ 8 q - 8 q^{4} - 24 q^{6} - 24 q^{9} + 36 q^{11} - 72 q^{14} - 16 q^{16} + 80 q^{19} - 84 q^{21} - 36 q^{29} + 76 q^{31} - 48 q^{34} + 24 q^{36} + 204 q^{39} - 252 q^{41} - 48 q^{46} + 24 q^{49} - 144 q^{51} - 72 q^{54} + 144 q^{56} - 252 q^{59} + 124 q^{61} + 64 q^{64} - 144 q^{66} - 36 q^{69} - 144 q^{74} - 80 q^{76} - 28 q^{79} - 504 q^{81} + 288 q^{84} - 216 q^{86} + 824 q^{91} - 168 q^{94} + 96 q^{96} - 252 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 24 * q^6 - 24 * q^9 + 36 * q^11 - 72 * q^14 - 16 * q^16 + 80 * q^19 - 84 * q^21 - 36 * q^29 + 76 * q^31 - 48 * q^34 + 24 * q^36 + 204 * q^39 - 252 * q^41 - 48 * q^46 + 24 * q^49 - 144 * q^51 - 72 * q^54 + 144 * q^56 - 252 * q^59 + 124 * q^61 + 64 * q^64 - 144 * q^66 - 36 * q^69 - 144 * q^74 - 80 * q^76 - 28 * q^79 - 504 * q^81 + 288 * q^84 - 216 * q^86 + 824 * q^91 - 168 * q^94 + 96 * q^96 - 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$3$	1.73205	−	2.44949i	0.577350	−	0.816497i
$3$	1.73205	−	2.44949i	0.577350	−	0.816497i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−4.22474	−	0.389270i	−0.704124	−	0.0648783i
$7$	5.49794	−	3.17423i	0.785419	−	0.453462i	−0.0529281	−	0.998598i	$-0.516855\pi$
$7$	5.49794	−	3.17423i	0.785419	−	0.453462i	0.838347	+	0.545136i	$0.183522\pi$
$8$	2.82843			0.353553
$9$	−3.00000	−	8.48528i	−0.333333	−	0.942809i
$10$		0			0
$11$	8.17423	−	4.71940i	0.743112	−	0.429036i	−0.0800876	−	0.996788i	$-0.525520\pi$
$11$	8.17423	−	4.71940i	0.743112	−	0.429036i	0.823200	+	0.567752i	$0.192187\pi$
$12$	2.51059	+	5.44949i	0.209216	+	0.454124i
$13$	17.0580	+	9.84847i	1.31216	+	0.757575i	0.982453	−	0.186510i	$-0.0597176\pi$
$13$	17.0580	+	9.84847i	1.31216	+	0.757575i	0.329704	+	0.944084i	$0.393051\pi$
$14$	−7.77526	−	4.48905i	−0.555375	−	0.320646i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−1.90702			−0.112178			−0.0560889	−	0.998426i	$-0.517863\pi$
$17$	−1.90702			−0.112178			−0.0560889	+	0.998426i	$0.517863\pi$
$18$	−8.27098	+	9.67423i	−0.459499	+	0.537457i
$19$	−4.69694			−0.247207			−0.123604	−	0.992332i	$-0.539445\pi$
$19$	−4.69694			−0.247207			−0.123604	+	0.992332i	$0.539445\pi$
$20$		0			0
$21$	1.74745	−	18.9651i	0.0832118	−	0.903099i
$22$	−11.5601	−	6.67423i	−0.525460	−	0.303374i
$23$	4.71940	−	8.17423i	0.205191	−	0.355402i	−0.745002	−	0.667062i	$-0.767552\pi$
$23$	4.71940	−	8.17423i	0.205191	−	0.355402i	0.950194	+	0.311660i	$0.100885\pi$
$24$	4.89898	−	6.92820i	0.204124	−	0.288675i
$25$		0			0
$26$		−	27.8557i		−	1.07137i
$27$	−25.9808	−	7.34847i	−0.962250	−	0.272166i
$28$			12.6969i			0.453462i
$29$	2.84847	−	1.64456i	0.0982231	−	0.0567091i	−0.450084	−	0.892986i	$-0.648606\pi$
$29$	2.84847	−	1.64456i	0.0982231	−	0.0567091i	0.548307	+	0.836277i	$0.315273\pi$
$30$		0			0
$31$	20.5227	−	35.5464i	0.662023	−	1.14666i	−0.318061	−	0.948070i	$-0.603032\pi$
$31$	20.5227	−	35.5464i	0.662023	−	1.14666i	0.980083	−	0.198587i	$-0.0636351\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$	2.59808	−	28.1969i	0.0787296	−	0.854453i
$34$	1.34847	+	2.33562i	0.0396609	+	0.0686946i
$35$		0			0
$36$	17.6969	+	3.28913i	0.491582	+	0.0913647i
$37$			17.3031i			0.467650i	0.972279	+	0.233825i	$0.0751243\pi$
$37$			17.3031i			0.467650i	−0.972279	+	0.233825i	$0.924876\pi$
$38$	3.32124	+	5.75255i	0.0874010	+	0.151383i
$39$	53.6691	−	24.7255i	1.37613	−	0.633986i
$40$		0			0
$41$	−53.5454	−	30.9145i	−1.30599	−	0.754011i	−0.324562	−	0.945864i	$-0.605217\pi$
$41$	−53.5454	−	30.9145i	−1.30599	−	0.754011i	−0.981424	+	0.191853i	$0.938550\pi$
$42$	−24.4630	+	11.2702i	−0.582453	+	0.268337i
$43$	−0.826701	+	0.477296i	−0.0192256	+	0.0110999i	−0.509582	−	0.860422i	$-0.670200\pi$
$43$	−0.826701	+	0.477296i	−0.0192256	+	0.0110999i	0.490356	+	0.871522i	$0.336867\pi$
$44$			18.8776i			0.429036i
$45$		0			0
$46$	−13.3485			−0.290184
$47$	−7.05501	−	12.2196i	−0.150107	−	0.259992i	0.781160	−	0.624331i	$-0.214628\pi$
$47$	−7.05501	−	12.2196i	−0.150107	−	0.259992i	−0.931267	+	0.364339i	$0.881295\pi$
$48$	−11.9494	−	1.10102i	−0.248945	−	0.0229379i
$49$	−4.34847	+	7.53177i	−0.0887443	+	0.153710i
$50$		0			0
$51$	−3.30306	+	4.67123i	−0.0647659	+	0.0915928i
$52$	−34.1161	+	19.6969i	−0.656079	+	0.378787i
$53$	9.53512			0.179908			0.0899539	−	0.995946i	$-0.471328\pi$
$53$	9.53512			0.179908			0.0899539	+	0.995946i	$0.471328\pi$
$54$	9.37117	+	37.0160i	0.173540	+	0.685481i
$55$		0			0
$56$	15.5505	−	8.97809i	0.277688	−	0.160323i
$57$	−8.13534	+	11.5051i	−0.142725	+	0.201844i
$58$	−4.02834	−	2.32577i	−0.0694542	−	0.0400994i
$59$	−79.2650	−	45.7637i	−1.34348	−	0.775656i	−0.356160	−	0.934425i	$-0.615914\pi$
$59$	−79.2650	−	45.7637i	−1.34348	−	0.775656i	−0.987316	+	0.158769i	$0.949247\pi$
$60$		0			0
$61$	37.5454	+	65.0306i	0.615498	+	1.06607i	0.990297	+	0.138968i	$0.0443786\pi$
$61$	37.5454	+	65.0306i	0.615498	+	1.06607i	−0.374798	+	0.927106i	$0.622288\pi$
$62$	−58.0470			−0.936241
$63$	−43.4281	−	37.1288i	−0.689335	−	0.589346i
$64$	8.00000			0.125000
$65$		0			0
$66$	−36.3712	+	16.7563i	−0.551078	+	0.253883i
$67$	−26.8075	−	15.4773i	−0.400111	−	0.231004i	0.286421	−	0.958104i	$-0.407535\pi$
$67$	−26.8075	−	15.4773i	−0.400111	−	0.231004i	−0.686532	+	0.727100i	$0.740868\pi$
$68$	1.90702	−	3.30306i	0.0280445	−	0.0485744i
$69$	−11.8485	−	25.7183i	−0.171717	−	0.372729i
$70$		0			0
$71$		−	85.9026i		−	1.20990i	−0.796265	−	0.604948i	$-0.793194\pi$
$71$		−	85.9026i		−	1.20990i	0.796265	−	0.604948i	$-0.206806\pi$
$72$	−8.48528	−	24.0000i	−0.117851	−	0.333333i
$73$			96.0908i			1.31631i	0.752881	+	0.658156i	$0.228663\pi$
$73$			96.0908i			1.31631i	−0.752881	+	0.658156i	$0.771337\pi$
$74$	21.1918	−	12.2351i	0.286376	−	0.165339i
$75$		0			0
$76$	4.69694	−	8.13534i	0.0618018	−	0.107044i
$77$	29.9609	−	51.8939i	0.389103	−	0.673946i
$78$	−68.2322	−	48.2474i	−0.874772	−	0.618557i
$79$	14.8712	+	25.7576i	0.188243	+	0.326046i	0.944664	−	0.328038i	$-0.106388\pi$
$79$	14.8712	+	25.7576i	0.188243	+	0.326046i	−0.756422	+	0.654084i	$0.773054\pi$
$80$		0			0
$81$	−63.0000	+	50.9117i	−0.777778	+	0.628539i
$82$			87.4393i			1.06633i
$83$	43.9530	+	76.1288i	0.529554	+	0.917215i	0.999406	+	0.0344693i	$0.0109741\pi$
$83$	43.9530	+	76.1288i	0.529554	+	0.917215i	−0.469852	+	0.882745i	$0.655693\pi$
$84$	31.1010	+	21.9917i	0.370250	+	0.261806i
$85$		0			0
$86$	1.16913	+	0.674999i	0.0135946	+	0.00784882i
$87$	0.905350	−	9.82577i	0.0104063	−	0.112940i
$88$	23.1202	−	13.3485i	0.262730	−	0.151687i
$89$		−	41.3766i		−	0.464905i	−0.972608	−	0.232453i	$-0.925325\pi$
$89$		−	41.3766i		−	0.464905i	0.972608	−	0.232453i	$-0.0746751\pi$
$90$		0			0
$91$	125.045			1.37413
$92$	9.43879	+	16.3485i	0.102596	+	0.177701i
$93$	−51.5241	−	111.838i	−0.554023	−	1.20256i
$94$	−9.97730	+	17.2812i	−0.106141	+	0.183842i
$95$		0			0
$96$	7.10102	+	15.4135i	0.0739690	+	0.160557i
$97$	83.0333	−	47.9393i	0.856013	−	0.494219i	−0.00666202	−	0.999978i	$-0.502121\pi$
$97$	83.0333	−	47.9393i	0.856013	−	0.494219i	0.862675	+	0.505758i	$0.168787\pi$
$98$	12.2993			0.125503
$99$	−64.5681	−	55.2025i	−0.652203	−	0.557601i
$100$		0			0
$101$	−136.772	+	78.9656i	−1.35418	+	0.781838i	−0.988832	−	0.149032i	$-0.952384\pi$
$101$	−136.772	+	78.9656i	−1.35418	+	0.781838i	−0.365350	+	0.930870i	$0.619051\pi$
$102$	8.05669	+	0.742346i	0.0789871	+	0.00727790i
$103$	25.2327	+	14.5681i	0.244978	+	0.141438i	0.617462	−	0.786600i	$-0.288161\pi$
$103$	25.2327	+	14.5681i	0.244978	+	0.141438i	−0.372485	+	0.928038i	$0.621494\pi$
$104$	48.2474	+	27.8557i	0.463918	+	0.267843i
$105$		0			0
$106$	−6.74235	−	11.6781i	−0.0636070	−	0.110171i
$107$	171.805			1.60566			0.802829	−	0.596210i	$-0.203327\pi$
$107$	171.805			1.60566			0.802829	+	0.596210i	$0.203327\pi$
$108$	38.7087	−	37.6515i	0.358414	−	0.348625i
$109$	−116.272			−1.06672			−0.533360	−	0.845888i	$-0.679071\pi$
$109$	−116.272			−1.06672			−0.533360	+	0.845888i	$0.679071\pi$
$110$		0			0
$111$	42.3837	+	29.9698i	0.381835	+	0.269998i
$112$	−21.9917	−	12.6969i	−0.196355	−	0.113366i
$113$	101.132	−	175.166i	0.894976	−	1.55014i	0.0611424	−	0.998129i	$-0.480526\pi$
$113$	101.132	−	175.166i	0.894976	−	1.55014i	0.833834	−	0.552015i	$-0.186141\pi$
$114$	19.8434	+	1.82838i	0.174065	+	0.0160384i
$115$		0			0
$116$			6.57826i			0.0567091i
$117$	32.3929	−	174.288i	0.276862	−	1.48964i
$118$			129.439i			1.09694i
$119$	−10.4847	+	6.05334i	−0.0881067	+	0.0508684i
$120$		0			0
$121$	−15.9546	+	27.6342i	−0.131856	+	0.228382i
$122$	53.0972	−	91.9671i	0.435223	−	0.753829i
$123$	−168.468	+	77.6135i	−1.36966	+	0.631004i
$124$	41.0454	+	71.0927i	0.331011	+	0.573328i
$125$		0			0
$126$	−14.7650	+	79.4424i	−0.117183	+	0.630495i
$127$			10.0908i			0.0794552i	0.999211	+	0.0397276i	$0.0126490\pi$
$127$			10.0908i			0.0794552i	−0.999211	+	0.0397276i	$0.987351\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$	−0.262756	+	2.85170i	−0.00203687	+	0.0221062i
$130$		0			0
$131$	4.29567	+	2.48010i	0.0327913	+	0.0189321i	0.516306	−	0.856404i	$-0.327307\pi$
$131$	4.29567	+	2.48010i	0.0327913	+	0.0189321i	−0.483515	+	0.875336i	$0.660640\pi$
$132$	46.2405	+	32.6969i	0.350306	+	0.247704i
$133$	−25.8235	+	14.9092i	−0.194161	+	0.112099i
$134$			43.7764i			0.326690i
$135$		0			0
$136$	−5.39388			−0.0396609
$137$	117.342	+	203.242i	0.856511	+	1.48352i	0.875236	+	0.483696i	$0.160706\pi$
$137$	117.342	+	203.242i	0.856511	+	1.48352i	−0.0187249	+	0.999825i	$0.505961\pi$
$138$	−23.1202	+	32.6969i	−0.167538	+	0.236934i
$139$	53.2650	−	92.2578i	0.383202	−	0.663725i	−0.608316	−	0.793695i	$-0.708155\pi$
$139$	53.2650	−	92.2578i	0.383202	−	0.663725i	0.991518	+	0.129970i	$0.0414881\pi$
$140$		0			0
$141$	−42.1515	−	3.88386i	−0.298947	−	0.0275451i
$142$	−105.209	+	60.7423i	−0.740907	+	0.427763i
$143$	185.915			1.30011
$144$	−23.3939	+	27.3629i	−0.162457	+	0.190020i
$145$		0			0
$146$	117.687	−	67.9465i	0.806074	−	0.465387i
$147$	10.9172	+	23.6969i	0.0742668	+	0.161204i
$148$	−29.9698	−	17.3031i	−0.202499	−	0.116913i
$149$	91.0301	+	52.5563i	0.610940	+	0.352727i	0.773333	−	0.634000i	$-0.218588\pi$
$149$	91.0301	+	52.5563i	0.610940	+	0.352727i	−0.162393	+	0.986726i	$0.551921\pi$
$150$		0			0
$151$	142.614	+	247.014i	0.944460	+	1.63585i	0.756828	+	0.653614i	$0.226748\pi$
$151$	142.614	+	247.014i	0.944460	+	1.63585i	0.187632	+	0.982239i	$0.439919\pi$
$152$	−13.2849			−0.0874010
$153$	5.72107	+	16.1816i	0.0373926	+	0.105762i
$154$	−84.7423			−0.550275
$155$		0			0
$156$	−10.8434	+	117.683i	−0.0695088	+	0.754379i
$157$	170.764	+	98.5908i	1.08767	+	0.627967i	0.932955	−	0.359992i	$-0.117221\pi$
$157$	170.764	+	98.5908i	1.08767	+	0.627967i	0.154715	+	0.987959i	$0.450554\pi$
$158$	21.0310	−	36.4268i	0.133108	−	0.230549i
$159$	16.5153	−	23.3562i	0.103870	−	0.146894i
$160$		0			0
$161$		−	59.9219i		−	0.372186i
$162$	106.902	+	41.1589i	0.659886	+	0.254067i
$163$			249.060i			1.52798i	0.645230	+	0.763988i	$0.276762\pi$
$163$			249.060i			1.52798i	−0.645230	+	0.763988i	$0.723238\pi$
$164$	107.091	−	61.8289i	0.652993	−	0.377006i
$165$		0			0
$166$	62.1589	−	107.662i	0.374451	−	0.648569i
$167$	24.2182	−	41.9472i	0.145019	−	0.251181i	−0.784361	−	0.620305i	$-0.787009\pi$
$167$	24.2182	−	41.9472i	0.145019	−	0.251181i	0.929380	+	0.369124i	$0.120342\pi$
$168$	4.94253	−	53.6413i	0.0294198	−	0.319294i
$169$	109.485	+	189.633i	0.647838	+	1.12209i
$170$		0			0
$171$	14.0908	+	39.8548i	0.0824024	+	0.233069i
$172$		−	1.90918i		−	0.0110999i
$173$	−50.2206	−	86.9847i	−0.290293	−	0.502802i	0.683586	−	0.729870i	$-0.260419\pi$
$173$	−50.2206	−	86.9847i	−0.290293	−	0.502802i	−0.973879	+	0.227068i	$0.927086\pi$
$174$	−12.6742	+	5.83904i	−0.0728404	+	0.0335577i
$175$		0			0
$176$	−32.6969	−	18.8776i	−0.185778	−	0.107259i
$177$	−249.389	+	114.894i	−1.40898	+	0.649118i
$178$	−50.6757	+	29.2577i	−0.284695	+	0.164369i
$179$			285.071i			1.59257i	0.604919	+	0.796287i	$0.293206\pi$
$179$			285.071i			1.59257i	−0.604919	+	0.796287i	$0.706794\pi$
$180$		0			0
$181$	37.1214			0.205091			0.102545	−	0.994728i	$-0.467301\pi$
$181$	37.1214			0.205091			0.102545	+	0.994728i	$0.467301\pi$
$182$	−88.4205	−	153.149i	−0.485827	−	0.841476i
$183$	224.322	+	20.6691i	1.22580	+	0.112946i
$184$	13.3485	−	23.1202i	0.0725460	−	0.125653i
$185$		0			0
$186$	−100.540	+	142.185i	−0.540539	+	0.764438i
$187$	−15.5885	+	9.00000i	−0.0833607	+	0.0481283i
$188$	28.2201			0.150107
$189$	−166.166	+	42.0676i	−0.879187	+	0.222580i
$190$		0			0
$191$	−15.5227	+	8.96204i	−0.0812707	+	0.0469217i	−0.540085	−	0.841611i	$-0.681608\pi$
$191$	−15.5227	+	8.96204i	−0.0812707	+	0.0469217i	0.458814	+	0.888532i	$0.348274\pi$
$192$	13.8564	−	19.5959i	0.0721688	−	0.102062i
$193$	−82.6657	−	47.7270i	−0.428319	−	0.247290i	0.270311	−	0.962773i	$-0.412873\pi$
$193$	−82.6657	−	47.7270i	−0.428319	−	0.247290i	−0.698630	+	0.715483i	$0.746207\pi$
$194$	−117.427	−	67.7964i	−0.605293	−	0.349466i
$195$		0			0
$196$	−8.69694	−	15.0635i	−0.0443721	−	0.0768548i
$197$	−160.363			−0.814026			−0.407013	−	0.913422i	$-0.633430\pi$
$197$	−160.363			−0.814026			−0.407013	+	0.913422i	$0.633430\pi$
$198$	−21.9524	+	118.114i	−0.110871	+	0.596533i
$199$	−6.51531			−0.0327402			−0.0163701	−	0.999866i	$-0.505211\pi$
$199$	−6.51531			−0.0327402			−0.0163701	+	0.999866i	$0.505211\pi$
$200$		0			0
$201$	−84.3434	+	38.8571i	−0.419619	+	0.193319i
$202$	193.425	+	111.674i	0.957552	+	0.552843i
$203$	10.4405	−	18.0834i	0.0514309	−	0.0890809i
$204$	−4.78775	−	10.3923i	−0.0234694	−	0.0509427i
$205$		0			0
$206$		−	41.2048i		−	0.200024i
$207$	−83.5189	−	15.5227i	−0.403473	−	0.0749889i
$208$		−	78.7878i		−	0.378787i
$209$	−38.3939	+	22.1667i	−0.183703	+	0.106061i
$210$		0			0
$211$	77.2196	−	133.748i	0.365970	−	0.633878i	−0.622961	−	0.782253i	$-0.714071\pi$
$211$	77.2196	−	133.748i	0.365970	−	0.633878i	0.988931	+	0.148374i	$0.0474040\pi$
$212$	−9.53512	+	16.5153i	−0.0449770	+	0.0779024i
$213$	−210.418	−	148.788i	−0.987876	−	0.698534i
$214$	−121.485	−	210.418i	−0.567685	−	0.983260i
$215$		0			0
$216$	−73.4847	−	20.7846i	−0.340207	−	0.0962250i
$217$		−	260.576i		−	1.20081i
$218$	82.2170	+	142.404i	0.377142	+	0.653230i
$219$	235.373	+	166.434i	1.07476	+	0.759973i
$220$		0			0
$221$	−32.5301	−	18.7813i	−0.147195	−	0.0849831i
$222$	6.73555	−	73.1010i	0.0303403	−	0.329284i
$223$	−80.3437	+	46.3865i	−0.360286	+	0.208011i	−0.669206	−	0.743077i	$-0.733366\pi$
$223$	−80.3437	+	46.3865i	−0.360286	+	0.208011i	0.308920	+	0.951088i	$0.400032\pi$
$224$			35.9124i			0.160323i
$225$		0			0
$226$	−286.045			−1.26569
$227$	84.9010	+	147.053i	0.374013	+	0.647810i	0.990179	−	0.139807i	$-0.0446482\pi$
$227$	84.9010	+	147.053i	0.374013	+	0.647810i	−0.616166	+	0.787617i	$0.711315\pi$
$228$	−11.7921	−	25.5959i	−0.0517197	−	0.112263i
$229$	203.772	−	352.944i	0.889836	−	1.54124i	0.0497675	−	0.998761i	$-0.484152\pi$
$229$	203.772	−	352.944i	0.889836	−	1.54124i	0.840068	−	0.542480i	$-0.182515\pi$
$230$		0			0
$231$	−75.2196	−	163.272i	−0.325626	−	0.706805i
$232$	8.05669	−	4.65153i	0.0347271	−	0.0200497i
$233$	15.2562			0.0654772			0.0327386	−	0.999464i	$-0.489577\pi$
$233$	15.2562			0.0654772			0.0327386	+	0.999464i	$0.489577\pi$
$234$	−236.363	+	83.5670i	−1.01010	+	0.357124i
$235$		0			0
$236$	158.530	−	91.5274i	0.671738	−	0.387828i
$237$	88.8507	+	8.18673i	0.374897	+	0.0345432i
$238$	14.8276	+	8.56072i	0.0623008	+	0.0359694i
$239$	−48.9620	−	28.2682i	−0.204862	−	0.118277i	0.394059	−	0.919085i	$-0.371070\pi$
$239$	−48.9620	−	28.2682i	−0.204862	−	0.118277i	−0.598921	+	0.800808i	$0.704404\pi$
$240$		0			0
$241$	−42.1061	−	72.9299i	−0.174714	−	0.302614i	0.765348	−	0.643617i	$-0.222567\pi$
$241$	−42.1061	−	72.9299i	−0.174714	−	0.302614i	−0.940062	+	0.341003i	$0.889233\pi$
$242$	45.1264			0.186473
$243$	15.5885	+	242.499i	0.0641500	+	0.997940i
$244$	−150.182			−0.615498
$245$		0			0
$246$	214.182	+	151.449i	0.870657	+	0.615647i
$247$	−80.1206	−	46.2577i	−0.324375	−	0.187278i
$248$	58.0470	−	100.540i	0.234060	−	0.405404i
$249$	262.606	+	24.1966i	1.05464	+	0.0971750i
$250$		0			0
$251$			218.903i			0.872123i	0.899917	+	0.436062i	$0.143627\pi$
$251$			218.903i			0.872123i	−0.899917	+	0.436062i	$0.856373\pi$
$252$	107.737	−	38.0908i	0.427528	−	0.151154i
$253$		−	89.0908i		−	0.352138i
$254$	12.3587	−	7.13528i	0.0486562	−	0.0280917i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	6.41212	−	11.1061i	0.0249499	−	0.0432145i	−0.853281	−	0.521452i	$-0.825391\pi$
$257$	6.41212	−	11.1061i	0.0249499	−	0.0432145i	0.878231	+	0.478237i	$0.158724\pi$
$258$	3.67840	−	1.69464i	0.0142574	−	0.00656839i
$259$	54.9240	+	95.1311i	0.212062	+	0.367302i
$260$		0			0
$261$	−22.5000	−	19.2364i	−0.0862069	−	0.0737026i
$262$		−	7.01479i		−	0.0267740i
$263$	−168.232	−	291.386i	−0.639666	−	1.10793i	−0.985506	−	0.169640i	$-0.945739\pi$
$263$	−168.232	−	291.386i	−0.639666	−	1.10793i	0.345840	−	0.938293i	$-0.387594\pi$
$264$	7.34847	−	79.7530i	0.0278351	−	0.302095i
$265$		0			0
$266$	36.5199	+	21.0848i	0.137293	+	0.0792661i
$267$	−101.351	−	71.6663i	−0.379594	−	0.268413i
$268$	53.6149	−	30.9546i	0.200056	−	0.115502i
$269$		−	60.4468i		−	0.224709i	−0.993668	−	0.112355i	$-0.964161\pi$
$269$		−	60.4468i		−	0.224709i	0.993668	−	0.112355i	$-0.0358393\pi$
$270$		0			0
$271$	274.636			1.01342			0.506708	−	0.862118i	$-0.330862\pi$
$271$	274.636			1.01342			0.506708	+	0.862118i	$0.330862\pi$
$272$	3.81405	+	6.60612i	0.0140222	+	0.0242872i
$273$	216.585	−	306.297i	0.793352	−	1.12197i
$274$	165.947	−	287.428i	0.605645	−	1.04901i
$275$		0			0
$276$	56.3939	+	5.19615i	0.204326	+	0.0188266i
$277$	−42.4352	+	24.5000i	−0.153196	+	0.0884477i	−0.574638	−	0.818407i	$-0.694857\pi$
$277$	−42.4352	+	24.5000i	−0.153196	+	0.0884477i	0.421442	+	0.906855i	$0.361524\pi$
$278$	−150.656			−0.541929
$279$	−363.189	−	67.5018i	−1.30175	−	0.241942i
$280$		0			0
$281$	−297.121	+	171.543i	−1.05737	+	0.610473i	−0.924704	−	0.380688i	$-0.875687\pi$
$281$	−297.121	+	171.543i	−1.05737	+	0.610473i	−0.132666	+	0.991161i	$0.542354\pi$
$282$	25.0489	+	54.3712i	0.0888259	+	0.192806i
$283$	−297.401	−	171.704i	−1.05089	−	0.606729i	−0.127988	−	0.991776i	$-0.540852\pi$
$283$	−297.401	−	171.704i	−1.05089	−	0.606729i	−0.922897	+	0.385047i	$0.874185\pi$
$284$	148.788	+	85.9026i	0.523901	+	0.302474i
$285$		0			0
$286$	−131.462	−	227.699i	−0.459657	−	0.796150i
$287$	−392.519			−1.36766
$288$	50.0545	+	9.30306i	0.173800	+	0.0323023i
$289$	−285.363			−0.987416
$290$		0			0
$291$	26.3911	−	286.422i	0.0906910	−	0.984270i
$292$	−166.434	−	96.0908i	−0.569980	−	0.329078i
$293$	−143.226	+	248.076i	−0.488828	+	0.846674i	−0.999917	−	0.0128532i	$-0.995909\pi$
$293$	−143.226	+	248.076i	−0.488828	+	0.846674i	0.511090	+	0.859527i	$0.329242\pi$
$294$	21.3031	−	30.1271i	0.0724594	−	0.102473i
$295$		0			0
$296$			48.9404i			0.165339i
$297$	−247.053	+	62.5454i	−0.831829	+	0.210591i
$298$		−	148.652i		−	0.498831i
$299$	161.007	−	92.9577i	0.538486	−	0.310895i
$300$		0			0
$301$	−3.03010	+	5.24829i	−0.0100668	+	0.0174362i
$302$	201.686	−	349.330i	0.667834	−	1.15672i
$303$	−43.4714	+	471.795i	−0.143470	+	1.55708i
$304$	9.39388	+	16.2707i	0.0309009	+	0.0535219i
$305$		0			0
$306$	15.7730	−	18.4490i	0.0515456	−	0.0602908i
$307$			154.091i			0.501924i	0.967997	+	0.250962i	$0.0807470\pi$
$307$			154.091i			0.501924i	−0.967997	+	0.250962i	$0.919253\pi$
$308$	59.9219	+	103.788i	0.194552	+	0.336973i
$309$	79.3888	−	36.5746i	0.256922	−	0.118364i
$310$		0			0
$311$	−62.3411	−	35.9926i	−0.200454	−	0.115732i	0.396413	−	0.918072i	$-0.370255\pi$
$311$	−62.3411	−	35.9926i	−0.200454	−	0.115732i	−0.596867	+	0.802340i	$0.703588\pi$
$312$	151.799	−	69.9342i	0.486536	−	0.224148i
$313$	318.356	−	183.803i	1.01711	−	0.587230i	0.103846	−	0.994593i	$-0.466885\pi$
$313$	318.356	−	183.803i	1.01711	−	0.587230i	0.913266	+	0.407363i	$0.133552\pi$
$314$		−	278.857i		−	0.888079i
$315$		0			0
$316$	−59.4847			−0.188243
$317$	−53.7987	−	93.1821i	−0.169712	−	0.293950i	0.768607	−	0.639722i	$-0.220950\pi$
$317$	−53.7987	−	93.1821i	−0.169712	−	0.293950i	−0.938319	+	0.345772i	$0.887617\pi$
$318$	−40.2834	−	3.71173i	−0.126677	−	0.0116721i
$319$	15.5227	−	26.8861i	0.0486605	−	0.0842825i
$320$		0			0
$321$	297.576	−	420.835i	0.927027	−	1.31101i
$322$	−73.3890	+	42.3712i	−0.227916	+	0.131587i
$323$	8.95717			0.0277312
$324$	−25.1816	−	160.031i	−0.0777211	−	0.493922i
$325$		0			0
$326$	305.035	−	176.112i	0.935691	−	0.540221i
$327$	−201.390	+	284.808i	−0.615871	+	0.870973i
$328$	−151.449	−	87.4393i	−0.461736	−	0.266583i
$329$	−77.5760	−	44.7885i	−0.235793	−	0.136135i
$330$		0			0
$331$	−8.59873	−	14.8934i	−0.0259780	−	0.0449953i	0.852744	−	0.522329i	$-0.174937\pi$
$331$	−8.59873	−	14.8934i	−0.0259780	−	0.0449953i	−0.878722	+	0.477334i	$0.841603\pi$
$332$	−175.812			−0.529554
$333$	146.821	−	51.9092i	0.440905	−	0.155883i
$334$	−68.4995			−0.205088
$335$		0			0
$336$	−69.1918	+	31.8768i	−0.205928	+	0.0948714i
$337$	−315.574	−	182.197i	−0.936422	−	0.540644i	−0.0475854	−	0.998867i	$-0.515153\pi$
$337$	−315.574	−	182.197i	−0.936422	−	0.540644i	−0.888837	+	0.458223i	$0.848486\pi$
$338$	154.835	−	268.182i	0.458091	−	0.793437i
$339$	−253.902	−	551.120i	−0.748973	−	1.62572i
$340$		0			0
$341$		−	387.419i		−	1.13613i
$342$	38.8483	−	45.4393i	0.113592	−	0.132863i
$343$			366.287i			1.06789i
$344$	−2.33826	+	1.35000i	−0.00679728	+	0.00392441i
$345$		0			0
$346$	−71.0227	+	123.015i	−0.205268	+	0.355534i
$347$	−291.697	+	505.234i	−0.840626	+	1.45601i	0.0487402	+	0.998811i	$0.484479\pi$
$347$	−291.697	+	505.234i	−0.840626	+	1.45601i	−0.889366	+	0.457196i	$0.848854\pi$
$348$	16.1134	+	11.3939i	0.0463028	+	0.0327410i
$349$	156.379	+	270.856i	0.448076	+	0.776091i	0.998261	−	0.0589524i	$-0.0187760\pi$
$349$	156.379	+	270.856i	0.448076	+	0.776091i	−0.550185	+	0.835043i	$0.685443\pi$
$350$		0			0
$351$	−370.810	−	381.221i	−1.05644	−	1.08610i
$352$			53.3939i			0.151687i
$353$	18.8078	+	32.5760i	0.0532798	+	0.0922834i	0.891435	−	0.453148i	$-0.149699\pi$
$353$	18.8078	+	32.5760i	0.0532798	+	0.0922834i	−0.838155	+	0.545431i	$0.816366\pi$
$354$	317.060	+	224.195i	0.895650	+	0.633320i
$355$		0			0
$356$	71.6663	+	41.3766i	0.201310	+	0.116226i
$357$	−3.33243	+	36.1668i	−0.00933453	+	0.101308i
$358$	349.139	−	201.576i	0.975249	−	0.563060i
$359$			294.028i			0.819019i	0.912306	+	0.409510i	$0.134300\pi$
$359$			294.028i			0.819019i	−0.912306	+	0.409510i	$0.865700\pi$
$360$		0			0
$361$	−338.939			−0.938889
$362$	−26.2488	−	45.4643i	−0.0725105	−	0.125592i
$363$	40.0554	+	86.9444i	0.110346	+	0.239516i
$364$	−125.045	+	216.585i	−0.343531	+	0.595014i
$365$		0			0
$366$	−133.305	−	289.353i	−0.364222	−	0.790581i
$367$	−28.7755	+	16.6135i	−0.0784072	+	0.0452684i	−0.538691	−	0.842503i	$-0.681081\pi$
$367$	−28.7755	+	16.6135i	−0.0784072	+	0.0452684i	0.460284	+	0.887772i	$0.347748\pi$
$368$	−37.7552			−0.102596
$369$	−101.682	+	547.091i	−0.275560	+	1.48263i
$370$		0			0
$371$	52.4235	−	30.2667i	0.141303	−	0.0815814i
$372$	245.234	+	22.5959i	0.659230	+	0.0607417i
$373$	−194.881	−	112.515i	−0.522470	−	0.301648i	0.215475	−	0.976509i	$-0.430870\pi$
$373$	−194.881	−	112.515i	−0.522470	−	0.301648i	−0.737945	+	0.674861i	$0.764203\pi$
$374$	22.0454	+	12.7279i	0.0589449	+	0.0340319i
$375$		0			0
$376$	−19.9546	−	34.5624i	−0.0530707	−	0.0919212i
$377$	64.7858			0.171846
$378$	169.019	+	173.765i	0.447141	+	0.459696i
$379$	166.334			0.438875			0.219438	−	0.975627i	$-0.429578\pi$
$379$	166.334			0.438875			0.219438	+	0.975627i	$0.429578\pi$
$380$		0			0
$381$	24.7173	+	17.4778i	0.0648749	+	0.0458735i
$382$	21.9524	+	12.6742i	0.0574671	+	0.0331786i
$383$	−368.493	+	638.249i	−0.962124	+	1.66645i	−0.244972	+	0.969530i	$0.578779\pi$
$383$	−368.493	+	638.249i	−0.962124	+	1.66645i	−0.717152	+	0.696917i	$0.754555\pi$
$384$	−33.7980	−	3.11416i	−0.0880155	−	0.00810978i
$385$		0			0
$386$			134.992i			0.349721i
$387$	6.53010	+	5.58290i	0.0168736	+	0.0144261i
$388$			191.757i			0.494219i
$389$	146.682	−	84.6867i	0.377074	−	0.217704i	−0.299471	−	0.954106i	$-0.596810\pi$
$389$	146.682	−	84.6867i	0.377074	−	0.217704i	0.676544	+	0.736402i	$0.263477\pi$
$390$		0			0
$391$	−9.00000	+	15.5885i	−0.0230179	+	0.0398682i
$392$	−12.2993	+	21.3031i	−0.0313758	+	0.0543445i
$393$	13.5153	−	6.22652i	0.0343901	−	0.0158436i
$394$	113.394	+	196.404i	0.287802	+	0.498487i
$395$		0			0
$396$	160.182	−	56.6328i	0.404499	−	0.143012i
$397$		−	256.272i		−	0.645523i	−0.946480	−	0.322761i	$-0.895389\pi$
$397$		−	256.272i		−	0.645523i	0.946480	−	0.322761i	$-0.104611\pi$
$398$	4.60702	+	7.97959i	0.0115754	+	0.0200492i
$399$	−8.20766	+	89.0778i	−0.0205706	+	0.223253i
$400$		0			0
$401$	226.364	+	130.691i	0.564498	+	0.325913i	0.754949	−	0.655784i	$-0.227662\pi$
$401$	226.364	+	130.691i	0.564498	+	0.325913i	−0.190451	+	0.981697i	$0.560995\pi$
$402$	107.230	+	75.8230i	0.266741	+	0.188614i
$403$	700.155	−	404.234i	1.73736	−	1.00306i
$404$		−	315.862i		−	0.781838i
$405$		0			0
$406$	−29.5301			−0.0727342
$407$	81.6600	+	141.439i	0.200639	+	0.347517i
$408$	−9.34247	+	13.2122i	−0.0228982	+	0.0323830i
$409$	−221.894	+	384.331i	−0.542528	+	0.939686i	0.456230	+	0.889862i	$0.349199\pi$
$409$	−221.894	+	384.331i	−0.542528	+	0.939686i	−0.998758	+	0.0498240i	$0.984134\pi$
$410$		0			0
$411$	701.082	+	64.5980i	1.70580	+	0.157173i
$412$	−50.4654	+	29.1362i	−0.122489	+	0.0707190i
$413$	−581.059			−1.40692
$414$	40.0454	+	113.266i	0.0967280	+	0.273588i
$415$		0			0
$416$	−96.4949	+	55.7114i	−0.231959	+	0.133922i
$417$	−133.727	−	290.267i	−0.320688	−	0.696085i
$418$	54.2971	+	31.3485i	0.129897	+	0.0749963i
$419$	−9.32525	−	5.38394i	−0.0222560	−	0.0128495i	0.488831	−	0.872379i	$-0.337424\pi$
$419$	−9.32525	−	5.38394i	−0.0222560	−	0.0128495i	−0.511087	+	0.859529i	$0.670757\pi$
$420$		0			0
$421$	−127.152	−	220.233i	−0.302023	−	0.523119i	0.674571	−	0.738210i	$-0.264328\pi$
$421$	−127.152	−	220.233i	−0.302023	−	0.523119i	−0.976594	+	0.215091i	$0.930995\pi$
$422$	−218.410			−0.517560
$423$	−82.5221	+	96.5227i	−0.195088	+	0.228186i
$424$	26.9694			0.0636070
$425$		0			0
$426$	−33.4393	+	362.917i	−0.0784960	+	0.851917i
$427$	412.844	+	238.356i	0.966849	+	0.558210i
$428$	−171.805	+	297.576i	−0.401414	+	0.695270i
$429$	322.015	−	455.398i	0.750617	−	1.06153i
$430$		0			0
$431$			698.663i			1.62103i	0.585719	+	0.810514i	$0.300812\pi$
$431$			698.663i			1.62103i	−0.585719	+	0.810514i	$0.699188\pi$
$432$	26.5057	+	104.697i	0.0613557	+	0.242354i
$433$		−	211.728i		−	0.488978i	−0.969652	−	0.244489i	$-0.921380\pi$
$433$		−	211.728i		−	0.488978i	0.969652	−	0.244489i	$-0.0786202\pi$
$434$	−319.139	+	184.255i	−0.735342	+	0.424550i
$435$		0			0
$436$	116.272	−	201.390i	0.266680	−	0.461903i
$437$	−22.1667	+	38.3939i	−0.0507247	+	0.0878578i
$438$	37.4052	−	405.959i	0.0854001	−	0.926847i
$439$	139.931	+	242.368i	0.318750	+	0.552092i	0.980228	−	0.197874i	$-0.0634035\pi$
$439$	139.931	+	242.368i	0.318750	+	0.552092i	−0.661477	+	0.749965i	$0.730070\pi$
$440$		0			0
$441$	76.9546	+	14.3027i	0.174500	+	0.0324324i
$442$			53.1214i			0.120184i
$443$	275.627	+	477.400i	0.622183	+	1.07765i	0.989078	+	0.147391i	$0.0470874\pi$
$443$	275.627	+	477.400i	0.622183	+	1.07765i	−0.366895	+	0.930262i	$0.619579\pi$
$444$	−94.2929	+	43.4409i	−0.212371	+	0.0978398i
$445$		0			0
$446$	113.623	+	65.6004i	0.254761	+	0.147086i
$447$	286.405	−	131.947i	0.640727	−	0.295184i
$448$	43.9835	−	25.3939i	0.0981774	−	0.0566828i
$449$		−	542.865i		−	1.20905i	−0.796585	−	0.604527i	$-0.793362\pi$
$449$		−	542.865i		−	1.20905i	0.796585	−	0.604527i	$-0.206638\pi$
$450$		0			0
$451$	−583.590			−1.29399
$452$	202.265	+	350.333i	0.447488	+	0.775072i
$453$	852.072	+	78.5102i	1.88095	+	0.173312i
$454$	120.068	−	207.964i	0.264467	−	0.458071i
$455$		0			0
$456$	−23.0102	+	32.5413i	−0.0504610	+	0.0713626i
$457$	79.9898	−	46.1821i	0.175032	−	0.101055i	−0.409924	−	0.912120i	$-0.634445\pi$
$457$	79.9898	−	46.1821i	0.175032	−	0.101055i	0.584957	+	0.811065i	$0.301112\pi$
$458$	−576.356			−1.25842
$459$	49.5459	+	14.0137i	0.107943	+	0.0305309i
$460$		0			0
$461$	−199.030	+	114.910i	−0.431736	+	0.249263i	−0.700086	−	0.714059i	$-0.746855\pi$
$461$	−199.030	+	114.910i	−0.431736	+	0.249263i	0.268350	+	0.963321i	$0.413522\pi$
$462$	−146.778	+	207.576i	−0.317701	+	0.449298i
$463$	−442.368	−	255.401i	−0.955438	−	0.551623i	−0.0606723	−	0.998158i	$-0.519324\pi$
$463$	−442.368	−	255.401i	−0.955438	−	0.551623i	−0.894766	+	0.446535i	$0.852658\pi$
$464$	−11.3939	−	6.57826i	−0.0245558	−	0.0141773i
$465$		0			0
$466$	−10.7878	−	18.6849i	−0.0231497	−	0.0400964i
$467$	833.657			1.78513			0.892567	−	0.450915i	$-0.148902\pi$
$467$	833.657			1.78513			0.892567	+	0.450915i	$0.148902\pi$
$468$	269.482	+	230.394i	0.575817	+	0.492295i
$469$	−196.514			−0.419007
$470$		0			0
$471$	537.270	−	247.521i	1.14070	−	0.525523i
$472$	−224.195	−	129.439i	−0.474990	−	0.274236i
$473$	−4.50510	+	7.80306i	−0.00952452	+	0.0164970i
$474$	−52.8003	−	114.608i	−0.111393	−	0.241790i
$475$		0			0
$476$		−	24.2134i		−	0.0508684i
$477$	−28.6054	−	80.9082i	−0.0599693	−	0.169619i
$478$			79.9546i			0.167269i
$479$	−569.144	+	328.595i	−1.18819	+	0.686003i	−0.957895	−	0.287118i	$-0.907303\pi$
$479$	−569.144	+	328.595i	−1.18819	+	0.686003i	−0.230296	+	0.973121i	$0.573969\pi$
$480$		0			0
$481$	−170.409	+	295.156i	−0.354280	+	0.613631i
$482$	−59.5471	+	103.139i	−0.123542	+	0.213980i
$483$	−146.778	−	103.788i	−0.303888	−	0.214881i
$484$	−31.9092	−	55.2683i	−0.0659281	−	0.114191i
$485$		0			0
$486$	285.977	−	190.565i	0.588431	−	0.392109i
$487$		−	351.666i		−	0.722107i	−0.932545	−	0.361054i	$-0.882417\pi$
$487$		−	351.666i		−	0.722107i	0.932545	−	0.361054i	$-0.117583\pi$
$488$	106.194	+	183.934i	0.217612	+	0.376914i
$489$	610.070	+	431.385i	1.24759	+	0.882178i
$490$		0			0
$491$	212.539	+	122.709i	0.432869	+	0.249917i	0.700568	−	0.713586i	$-0.252930\pi$
$491$	212.539	+	122.709i	0.432869	+	0.249917i	−0.267699	+	0.963503i	$0.586263\pi$
$492$	34.0374	−	369.409i	0.0691818	−	0.750831i
$493$	−5.43210	+	3.13622i	−0.0110185	+	0.00636151i
$494$			130.836i			0.264851i
$495$		0			0
$496$	−164.182			−0.331011
$497$	−272.675	−	472.287i	−0.548642	−	0.950276i
$498$	−156.056	−	338.734i	−0.313365	−	0.680190i
$499$	315.113	−	545.792i	0.631489	−	1.09377i	−0.355758	−	0.934578i	$-0.615777\pi$
$499$	315.113	−	545.792i	0.631489	−	1.09377i	0.987247	−	0.159193i	$-0.0508892\pi$
$500$		0			0
$501$	−60.8020	−	131.977i	−0.121361	−	0.263427i
$502$	268.100	−	154.788i	0.534064	−	0.308342i
$503$	286.891			0.570360			0.285180	−	0.958474i	$-0.407947\pi$
$503$	286.891			0.570360			0.285180	+	0.958474i	$0.407947\pi$
$504$	−122.833	−	105.016i	−0.243717	−	0.208365i
$505$		0			0
$506$	−109.114	+	62.9967i	−0.215639	+	0.124499i
$507$	654.137	+	60.2724i	1.29021	+	0.118881i
$508$	−17.4778	−	10.0908i	−0.0344051	−	0.0198638i
$509$	−755.454	−	436.161i	−1.48419	−	0.856898i	−0.484353	−	0.874873i	$-0.660945\pi$
$509$	−755.454	−	436.161i	−1.48419	−	0.856898i	−0.999838	+	0.0179741i	$0.994278\pi$
$510$		0			0
$511$	305.015	+	528.301i	0.596898	+	1.03386i
$512$	22.6274			0.0441942
$513$	122.030	+	34.5153i	0.237875	+	0.0672813i
$514$	−18.1362			−0.0352845
$515$		0			0
$516$	−4.67653	−	3.30680i	−0.00906304	−	0.00640854i
$517$	−115.339	−	66.5908i	−0.223092	−	0.128802i
$518$	77.6742	−	134.536i	0.149950	−	0.259721i
$519$	−300.053	−	27.6470i	−0.578136	−	0.0532697i
$520$		0			0
$521$			206.132i			0.395646i	0.980238	+	0.197823i	$0.0633872\pi$
$521$			206.132i			0.395646i	−0.980238	+	0.197823i	$0.936613\pi$
$522$	−7.64974	+	41.1589i	−0.0146547	+	0.0788485i
$523$		−	884.817i		−	1.69181i	−0.533333	−	0.845906i	$-0.679061\pi$
$523$		−	884.817i		−	1.69181i	0.533333	−	0.845906i	$-0.320939\pi$
$524$	−8.59133	+	4.96021i	−0.0163957	+	0.00946604i
$525$		0			0
$526$	−237.916	+	412.083i	−0.452312	+	0.783427i
$527$	−39.1373	+	67.7878i	−0.0742643	+	0.128630i
$528$	−102.873	+	47.3939i	−0.194836	+	0.0897611i
$529$	219.955	+	380.973i	0.415793	+	0.720175i
$530$		0			0
$531$	−150.523	+	809.877i	−0.283470	+	1.52519i
$532$		−	59.6367i		−	0.112099i
$533$	−608.920	−	1054.68i	−1.14244	−	1.97876i
$534$	−16.1066	+	174.805i	−0.0301622	+	0.327351i
$535$		0			0
$536$	−75.8230	−	43.7764i	−0.141461	−	0.0816724i
$537$	698.278	+	493.757i	1.30033	+	0.919473i
$538$	−74.0319	+	42.7423i	−0.137606	+	0.0794467i
$539$			82.0886i			0.152298i
$540$		0			0
$541$	−509.151			−0.941129			−0.470565	−	0.882365i	$-0.655950\pi$
$541$	−509.151			−0.941129			−0.470565	+	0.882365i	$0.655950\pi$
$542$	−194.197	−	336.359i	−0.358297	−	0.620588i
$543$	64.2962	−	90.9286i	0.118409	−	0.167456i
$544$	5.39388	−	9.34247i	0.00991521	−	0.0171737i
$545$		0			0
$546$	−528.285	−	48.6764i	−0.967555	−	0.0891509i
$547$	474.620	−	274.022i	0.867679	−	0.500955i	0.00110267	−	0.999999i	$-0.499649\pi$
$547$	474.620	−	274.022i	0.867679	−	0.500955i	0.866576	+	0.499045i	$0.166316\pi$
$548$	−469.368			−0.856511
$549$	439.166	−	513.675i	0.799939	−	0.935656i
$550$		0			0
$551$	−13.3791	+	7.72442i	−0.0242815	+	0.0140189i
$552$	−33.5125	−	72.7423i	−0.0607111	−	0.131780i
$553$	163.522	+	94.4092i	0.295699	+	0.170722i
$554$	60.0125	+	34.6482i	0.108326	+	0.0625419i
$555$		0			0
$556$	106.530	+	184.516i	0.191601	+	0.331862i
$557$	406.542			0.729879			0.364939	−	0.931031i	$-0.381090\pi$
$557$	406.542			0.729879			0.364939	+	0.931031i	$0.381090\pi$
$558$	174.141	+	492.545i	0.312080	+	0.882697i
$559$	−18.8025			−0.0336360
$560$		0			0
$561$	−4.95459	+	53.7722i	−0.00883172	+	0.0958507i
$562$	420.192	+	242.598i	0.747673	+	0.431669i
$563$	−303.236	+	525.220i	−0.538607	+	0.932895i	0.460372	+	0.887726i	$0.347716\pi$
$563$	−303.236	+	525.220i	−0.538607	+	0.932895i	−0.998979	+	0.0451687i	$0.985617\pi$
$564$	48.8786	−	69.1247i	0.0866641	−	0.122562i
$565$		0			0
$566$			485.653i			0.858045i
$567$	−184.764	+	479.886i	−0.325863	+	0.846360i
$568$		−	242.969i		−	0.427763i
$569$	224.954	−	129.877i	0.395350	−	0.228255i	−0.289126	−	0.957291i	$-0.593365\pi$
$569$	224.954	−	129.877i	0.395350	−	0.228255i	0.684476	+	0.729036i	$0.260031\pi$
$570$		0			0
$571$	43.9166	−	76.0657i	0.0769117	−	0.133215i	−0.825004	−	0.565126i	$-0.808827\pi$
$571$	43.9166	−	76.0657i	0.0769117	−	0.133215i	0.901916	+	0.431911i	$0.142161\pi$
$572$	−185.915	+	322.015i	−0.325027	+	0.562963i
$573$	−4.93369	+	53.5454i	−0.00861029	+	0.0934475i
$574$	277.553	+	480.736i	0.483541	+	0.837518i
$575$		0			0
$576$	−24.0000	−	67.8823i	−0.0416667	−	0.117851i
$577$		−	132.091i		−	0.228927i	−0.993427	−	0.114463i	$-0.963485\pi$
$577$		−	132.091i		−	0.228927i	0.993427	−	0.114463i	$-0.0365149\pi$
$578$	201.782	+	349.497i	0.349104	+	0.604666i
$579$	−260.088	+	119.823i	−0.449202	+	0.206948i
$580$		0			0
$581$	483.302	+	279.034i	0.831844	+	0.480266i
$582$	−369.456	+	170.209i	−0.634804	+	0.292455i
$583$	77.9423	−	45.0000i	0.133692	−	0.0771870i
$584$			271.786i			0.465387i
$585$		0			0
$586$	405.106			0.691306
$587$	−283.833	−	491.614i	−0.483532	−	0.837502i	0.516289	−	0.856414i	$-0.327313\pi$
$587$	−283.833	−	491.614i	−0.483532	−	0.837502i	−0.999821	+	0.0189125i	$0.993980\pi$
$588$	−51.9615	−	4.78775i	−0.0883699	−	0.00814244i
$589$	−96.3939	+	166.959i	−0.163657	+	0.283462i
$590$		0			0
$591$	−277.757	+	392.808i	−0.469978	+	0.664650i
$592$	59.9396	−	34.6061i	0.101249	−	0.0584563i
$593$	−77.0321			−0.129902			−0.0649512	−	0.997888i	$-0.520689\pi$
$593$	−77.0321			−0.129902			−0.0649512	+	0.997888i	$0.520689\pi$
$594$	251.295	+	258.351i	0.423056	+	0.434934i
$595$		0			0
$596$	−182.060	+	105.113i	−0.305470	+	0.176363i
$597$	−11.2848	+	15.9592i	−0.0189026	+	0.0267323i
$598$	−227.699	−	131.462i	−0.380767	−	0.219836i
$599$	764.917	+	441.625i	1.27699	+	0.737270i	0.976294	−	0.216450i	$-0.0694479\pi$
$599$	764.917	+	441.625i	1.27699	+	0.737270i	0.300696	+	0.953720i	$0.402781\pi$
$600$		0			0
$601$	397.545	+	688.569i	0.661473	+	1.14571i	0.980229	+	0.197868i	$0.0634018\pi$
$601$	397.545	+	688.569i	0.661473	+	1.14571i	−0.318755	+	0.947837i	$0.603265\pi$
$602$	8.57042			0.0142366
$603$	−50.9068	+	273.901i	−0.0844226	+	0.454230i
$604$	−570.454			−0.944460
$605$		0			0
$606$	608.568	−	280.368i	1.00424	−	0.462654i
$607$	256.987	+	148.372i	0.423373	+	0.244434i	0.696519	−	0.717538i	$-0.254731\pi$
$607$	256.987	+	148.372i	0.423373	+	0.244434i	−0.273147	+	0.961972i	$0.588064\pi$
$608$	13.2849	−	23.0102i	0.0218502	−	0.0378457i
$609$	−26.2117	−	56.8952i	−0.0430406	−	0.0934240i
$610$		0			0
$611$		−	277.924i		−	0.454868i
$612$	−33.7485	−	6.27245i	−0.0551446	−	0.0102491i
$613$			517.181i			0.843688i	0.906668	+	0.421844i	$0.138617\pi$
$613$			517.181i			0.843688i	−0.906668	+	0.421844i	$0.861383\pi$
$614$	188.722	−	108.959i	0.307365	−	0.177457i
$615$		0			0
$616$	84.7423	−	146.778i	0.137569	−	0.238276i
$617$	132.738	−	229.909i	0.215134	−	0.372623i	−0.738180	−	0.674604i	$-0.764314\pi$
$617$	132.738	−	229.909i	0.215134	−	0.372623i	0.953314	+	0.301981i	$0.0976478\pi$
$618$	−100.931	−	71.3689i	−0.163319	−	0.115484i
$619$	−98.5227	−	170.646i	−0.159164	−	0.275681i	0.775403	−	0.631466i	$-0.217547\pi$
$619$	−98.5227	−	170.646i	−0.159164	−	0.275681i	−0.934568	+	0.355786i	$0.884213\pi$
$620$		0			0
$621$	−182.682	+	177.693i	−0.294173	+	0.286139i
$622$			101.803i			0.163670i
$623$	−131.339	−	227.486i	−0.210817	−	0.365146i
$624$	−192.990	−	136.464i	−0.309279	−	0.218693i
$625$		0			0
$626$	−450.224	−	259.937i	−0.719207	−	0.415234i
$627$	−12.2030	+	132.439i	−0.0194625	+	0.211227i
$628$	−341.529	+	197.182i	−0.543835	+	0.313983i
$629$		−	32.9973i		−	0.0524600i
$630$		0			0
$631$	−160.879			−0.254958			−0.127479	−	0.991841i	$-0.540689\pi$
$631$	−160.879			−0.254958			−0.127479	+	0.991841i	$0.540689\pi$
$632$	42.0620	+	72.8536i	0.0665538	+	0.115275i
$633$	−193.867	−	420.808i	−0.306267	−	0.664783i
$634$	−76.0829	+	131.779i	−0.120005	+	0.207854i
$635$		0			0
$636$	23.9388	+	51.9615i	0.0376396	+	0.0817005i
$637$	−148.353	+	85.6515i	−0.232893	+	0.134461i
$638$	−43.9048			−0.0688164
$639$	−728.908	+	257.708i	−1.14070	+	0.403299i
$640$		0			0
$641$	−267.894	+	154.669i	−0.417931	+	0.241293i	−0.694192	−	0.719790i	$-0.744238\pi$
$641$	−267.894	+	154.669i	−0.417931	+	0.241293i	0.276261	+	0.961083i	$0.410905\pi$
$642$	−725.834	−	66.8786i	−1.13058	−	0.104172i
$643$	341.726	+	197.296i	0.531456	+	0.306836i	0.741609	−	0.670832i	$-0.234063\pi$
$643$	341.726	+	197.296i	0.531456	+	0.306836i	−0.210153	+	0.977668i	$0.567396\pi$
$644$	103.788	+	59.9219i	0.161161	+	0.0930464i
$645$		0			0
$646$	−6.33368	−	10.9703i	−0.00980445	−	0.0169818i
$647$	−418.736			−0.647196			−0.323598	−	0.946195i	$-0.604892\pi$
$647$	−418.736			−0.647196			−0.323598	+	0.946195i	$0.604892\pi$
$648$	−178.191	+	144.000i	−0.274986	+	0.222222i
$649$	−863.908			−1.33114
$650$		0			0
$651$	−638.277	−	451.330i	−0.980456	−	0.693287i
$652$	−431.385	−	249.060i	−0.661633	−	0.381994i
$653$	−265.363	+	459.621i	−0.406375	+	0.703861i	−0.994480	−	0.104923i	$-0.966540\pi$
$653$	−265.363	+	459.621i	−0.406375	+	0.703861i	0.588106	+	0.808784i	$0.299874\pi$
$654$	491.221	+	45.2613i	0.751103	+	0.0692069i
$655$		0			0
$656$			247.316i			0.377006i
$657$	815.358	−	288.272i	1.24103	−	0.438771i
$658$			126.681i			0.192524i
$659$	−310.204	+	179.096i	−0.470719	+	0.271770i	−0.716541	−	0.697545i	$-0.754276\pi$
$659$	−310.204	+	179.096i	−0.470719	+	0.271770i	0.245822	+	0.969315i	$0.420942\pi$
$660$		0			0
$661$	111.136	−	192.493i	0.168133	−	0.291214i	−0.769631	−	0.638489i	$-0.779560\pi$
$661$	111.136	−	192.493i	0.168133	−	0.291214i	0.937763	+	0.347275i	$0.112893\pi$
$662$	−12.1604	+	21.0625i	−0.0183692	+	0.0318165i
$663$	−102.348	+	47.1520i	−0.154371	+	0.0711192i
$664$	124.318	+	215.325i	0.187226	+	0.324284i
$665$		0			0
$666$	−167.394	−	143.113i	−0.251342	−	0.214885i
$667$		−	31.0454i		−	0.0465448i
$668$	48.4365	+	83.8944i	0.0725097	+	0.125590i
$669$	−25.5362	+	277.145i	−0.0381708	+	0.414267i
$670$		0			0
$671$	613.810	+	354.383i	0.914769	+	0.528142i
$672$	87.9670	+	62.2020i	0.130903	+	0.0925626i
$673$	250.464	−	144.606i	0.372161	−	0.214867i	−0.302241	−	0.953231i	$-0.597735\pi$
$673$	250.464	−	144.606i	0.372161	−	0.214867i	0.674402	+	0.738364i	$0.264401\pi$
$674$			515.331i			0.764586i
$675$		0			0
$676$	−437.939			−0.647838
$677$	232.226	+	402.227i	0.343022	+	0.594131i	0.984992	−	0.172598i	$-0.0552163\pi$
$677$	232.226	+	402.227i	0.343022	+	0.594131i	−0.641971	+	0.766729i	$0.721883\pi$
$678$	−495.445	+	700.665i	−0.730745	+	1.03343i
$679$	304.341	−	527.134i	0.448220	−	0.776339i
$680$		0			0
$681$	507.257	+	46.7389i	0.744871	+	0.0686327i
$682$	−474.490	+	273.947i	−0.695733	+	0.401681i
$683$	1126.36			1.64913			0.824565	−	0.565767i	$-0.191420\pi$
$683$	1126.36			1.64913			0.824565	+	0.565767i	$0.191420\pi$
$684$	−83.1214	−	15.4488i	−0.121523	−	0.0225860i
$685$		0			0
$686$	448.608	−	259.004i	0.653948	−	0.377557i
$687$	−511.589	−	1110.46i	−0.744671	−	1.61638i
$688$	3.30680	+	1.90918i	0.00480640	+	0.00277498i
$689$	162.650	+	93.9063i	0.236067	+	0.136294i
$690$		0			0
$691$	−518.841	−	898.658i	−0.750855	−	1.30052i	−0.947409	−	0.320025i	$-0.896309\pi$
$691$	−518.841	−	898.658i	−0.750855	−	1.30052i	0.196554	−	0.980493i	$-0.437025\pi$
$692$	200.883			0.290293
$693$	−530.217	−	98.5454i	−0.765104	−	0.142201i
$694$	825.044			1.18882
$695$		0			0
$696$	2.56072	−	27.7915i	0.00367919	−	0.0399303i
$697$	102.112	+	58.9546i	0.146503	+	0.0845833i
$698$	221.153	−	383.048i	0.316838	−	0.548779i
$699$	26.4245	−	37.3699i	0.0378033	−	0.0534619i
$700$		0			0
$701$		−	778.180i		−	1.11010i	−0.831817	−	0.555050i	$-0.812699\pi$
$701$		−	778.180i		−	1.11010i	0.831817	−	0.555050i	$-0.187301\pi$
$702$	−204.697	+	723.712i	−0.291591	+	1.03093i
$703$		−	81.2714i		−	0.115607i
$704$	65.3939	−	37.7552i	0.0928890	−	0.0536295i
$705$		0			0
$706$	26.5982	−	46.0695i	0.0376745	−	0.0652542i
$707$	−501.311	+	868.296i	−0.709068	+	1.22814i
$708$	50.3868	−	546.848i	0.0711678	−	0.772384i
$709$	−586.014	−	1015.01i	−0.826536	−	1.43160i	−0.900739	−	0.434360i	$-0.856975\pi$
$709$	−586.014	−	1015.01i	−0.826536	−	1.43160i	0.0742031	−	0.997243i	$-0.476359\pi$
$710$		0			0
$711$	173.947	−	203.459i	0.244651	−	0.286159i
$712$		−	117.031i		−	0.164369i
$713$	−193.710	−	335.515i	−0.271682	−	0.470568i
$714$	46.6515	−	21.4924i	0.0653383	−	0.0301015i
$715$		0			0
$716$	−493.757	−	285.071i	−0.689605	−	0.398144i
$717$	−154.047	+	70.9699i	−0.214850	+	0.0989817i
$718$	360.109	−	207.909i	0.501545	−	0.289567i
$719$		−	515.416i		−	0.716851i	−0.933558	−	0.358426i	$-0.883314\pi$
$719$		−	515.416i		−	0.716851i	0.933558	−	0.358426i	$-0.116686\pi$
$720$		0			0
$721$	184.970			0.256547
$722$	239.666	+	415.114i	0.331947	+	0.574949i
$723$	−251.571	−	23.1799i	−0.347954	−	0.0320607i
$724$	−37.1214	+	64.2962i	−0.0512727	+	0.0888069i
$725$		0			0
$726$	78.1612	−	110.537i	0.107660	−	0.152254i
$727$	−728.681	+	420.704i	−1.00231	+	0.578685i	−0.908932	−	0.416945i	$-0.863101\pi$
$727$	−728.681	+	420.704i	−1.00231	+	0.578685i	−0.0933809	+	0.995630i	$0.529767\pi$
$728$	353.682			0.485827
$729$	621.000	+	381.838i	0.851852	+	0.523783i
$730$		0			0
$731$	1.57654	−	0.910215i	0.00215669	−	0.00124516i
$732$	−260.122	+	367.868i	−0.355358	+	0.502552i
$733$	525.125	+	303.181i	0.716405	+	0.413617i	0.813428	−	0.581665i	$-0.197599\pi$
$733$	525.125	+	303.181i	0.716405	+	0.413617i	−0.0970229	+	0.995282i	$0.530932\pi$
$734$	40.6946	+	23.4951i	0.0554423	+	0.0320096i
$735$		0			0
$736$	26.6969	+	46.2405i	0.0362730	+	0.0628267i
$737$	−292.174			−0.396437
$738$	741.947	−	262.318i	1.00535	−	0.355444i
$739$	389.362			0.526877			0.263439	−	0.964676i	$-0.415143\pi$
$739$	389.362			0.526877			0.263439	+	0.964676i	$0.415143\pi$
$740$		0			0
$741$	−252.081	+	116.134i	−0.340190	+	0.156726i
$742$	−74.1380	−	42.8036i	−0.0999164	−	0.0576868i
$743$	522.375	−	904.779i	0.703061	−	1.21774i	−0.264325	−	0.964434i	$-0.585149\pi$
$743$	522.375	−	904.779i	0.703061	−	1.21774i	0.967387	−	0.253304i	$-0.0815174\pi$
$744$	−145.732	−	316.326i	−0.195877	−	0.425170i
$745$		0			0
$746$			318.240i			0.426595i
$747$	514.116	−	601.340i	0.688240	−	0.805007i
$748$		−	36.0000i		−	0.0481283i
$749$	944.574	−	545.350i	1.26111	−	0.728105i
$750$		0			0
$751$	645.916	−	1118.76i	0.860074	−	1.48969i	−0.0117826	−	0.999931i	$-0.503751\pi$
$751$	645.916	−	1118.76i	0.860074	−	1.48969i	0.871857	−	0.489761i	$-0.162916\pi$
$752$	−28.2201	+	48.8786i	−0.0375267	+	0.0649981i
$753$	536.201	+	379.151i	0.712086	+	0.503521i
$754$	−45.8105	−	79.3460i	−0.0607566	−	0.105233i
$755$		0			0
$756$	93.3031	−	329.876i	0.123417	−	0.436344i
$757$			1042.36i			1.37697i	0.725252	+	0.688483i	$0.241723\pi$
$757$			1042.36i			1.37697i	−0.725252	+	0.688483i	$0.758277\pi$
$758$	−117.616	−	203.716i	−0.155166	−	0.268755i
$759$	−218.227	−	154.310i	−0.287519	−	0.203307i
$760$		0			0
$761$	−281.607	−	162.586i	−0.370048	−	0.213647i	0.303431	−	0.952853i	$-0.401868\pi$
$761$	−281.607	−	162.586i	−0.370048	−	0.213647i	−0.673479	+	0.739206i	$0.735201\pi$
$762$	3.92805	−	42.6311i	0.00515492	−	0.0559464i
$763$	−639.258	+	369.076i	−0.837822	+	0.483717i
$764$		−	35.8481i		−	0.0469217i
$765$		0			0
$766$	1042.26			1.36065
$767$	−901.405	−	1561.28i	−1.17523	−	2.03557i
$768$	20.0847	+	43.5959i	0.0261520	+	0.0567655i
$769$	171.348	−	296.783i	0.222819	−	0.385934i	−0.732844	−	0.680397i	$-0.761807\pi$
$769$	171.348	−	296.783i	0.222819	−	0.385934i	0.955663	+	0.294463i	$0.0951407\pi$
$770$		0			0
$771$	−16.0982	−	34.9428i	−0.0208797	−	0.0453214i
$772$	165.331	−	95.4541i	0.214160	−	0.123645i
$773$	532.579			0.688977			0.344488	−	0.938791i	$-0.388052\pi$
$773$	532.579			0.688977			0.344488	+	0.938791i	$0.388052\pi$
$774$	2.22016	−	11.9454i	0.00286842	−	0.0154333i
$775$		0			0
$776$	234.854	−	135.593i	0.302646	−	0.174733i
$777$	328.154	+	30.2362i	0.422334	+	0.0389140i
$778$	−207.439	−	119.765i	−0.266631	−	0.153940i
$779$	251.499	+	145.203i	0.322849	+	0.186397i
$780$		0			0
$781$	−405.409	−	702.188i	−0.519089	−	0.899089i
$782$	25.4558			0.0325522
$783$	−86.0904	+	21.7951i	−0.109949	+	0.0278354i
$784$	34.7878			0.0443721
$785$		0			0
$786$	−17.1827	−	12.1500i	−0.0218609	−	0.0154580i
$787$	90.0264	+	51.9768i	0.114392	+	0.0660442i	0.556104	−	0.831113i	$-0.312296\pi$
$787$	90.0264	+	51.9768i	0.114392	+	0.0660442i	−0.441712	+	0.897157i	$0.645629\pi$
$788$	160.363	−	277.757i	0.203507	−	0.352484i
$789$	−1005.13	−	92.6135i	−1.27393	−	0.117381i
$790$		0			0
$791$		−	1284.07i		−	1.62335i
$792$	−182.626	−	156.136i	−0.230589	−	0.197142i
$793$			1479.06i			1.86514i
$794$	−313.868	+	181.212i	−0.395300	+	0.228227i
$795$		0			0
$796$	6.51531	−	11.2848i	0.00818506	−	0.0141769i
$797$	552.138	−	956.331i	0.692770	−	1.19991i	−0.278156	−	0.960536i	$-0.589723\pi$
$797$	552.138	−	956.331i	0.692770	−	1.19991i	0.970927	−	0.239378i	$-0.0769434\pi$
$798$	114.901	−	52.9352i	0.143987	−	0.0663349i
$799$	13.4541	+	23.3031i	0.0168386	+	0.0291654i
$800$		0			0
$801$	−351.092	+	124.130i	−0.438317	+	0.154968i
$802$		−	369.650i		−	0.460911i
$803$	453.491	+	785.469i	0.564746	+	0.978168i
$804$	17.0408	−	184.944i	0.0211951	−	0.230030i
$805$		0			0
$806$	−990.168	−	571.674i	−1.22850	−	0.709273i
$807$	−148.064	−	104.697i	−0.183474	−	0.129736i
$808$	−386.851	+	223.348i	−0.478776	+	0.276421i
$809$		−	256.465i		−	0.317015i	−0.987358	−	0.158508i	$-0.949332\pi$
$809$		−	256.465i		−	0.317015i	0.987358	−	0.158508i	$-0.0506683\pi$
$810$		0			0
$811$	735.362			0.906735			0.453368	−	0.891324i	$-0.350222\pi$
$811$	735.362			0.906735			0.453368	+	0.891324i	$0.350222\pi$
$812$	20.8809	+	36.1668i	0.0257154	+	0.0445404i
$813$	475.683	−	672.717i	0.585096	−	0.827451i
$814$	115.485	−	200.025i	0.141873	−	0.245731i
$815$		0			0
$816$	22.7878	+	2.09967i	0.0279262	+	0.00257313i
$817$	3.88296	−	2.24183i	0.00475271	−	0.00274398i
$818$	627.611			0.767250
$819$	−375.136	−	1061.05i	−0.458042	−	1.29554i
$820$		0			0
$821$	1078.45	−	622.645i	1.31358	−	0.758398i	0.330896	−	0.943667i	$-0.392649\pi$
$821$	1078.45	−	622.645i	1.31358	−	0.758398i	0.982688	+	0.185269i	$0.0593157\pi$
$822$	−416.624	−	904.325i	−0.506842	−	1.10015i
$823$	−1335.63	−	771.129i	−1.62288	−	0.936973i	−0.986143	−	0.165896i	$-0.946948\pi$
$823$	−1335.63	−	771.129i	−1.62288	−	0.936973i	−0.636742	−	0.771077i	$-0.719718\pi$
$824$	71.3689	+	41.2048i	0.0866127	+	0.0500059i
$825$		0			0
$826$	410.871	+	711.649i	0.497422	+	0.861560i
$827$	955.707			1.15563			0.577815	−	0.816167i	$-0.303905\pi$
$827$	955.707			1.15563			0.577815	+	0.816167i	$0.303905\pi$
$828$	110.405	−	129.136i	0.133339	−	0.155962i
$829$	−1082.88			−1.30625			−0.653123	−	0.757252i	$-0.726542\pi$
$829$	−1082.88			−1.30625			−0.653123	+	0.757252i	$0.726542\pi$
$830$		0			0
$831$	−13.4875	+	146.380i	−0.0162304	+	0.176149i
$832$	136.464	+	78.7878i	0.164020	+	0.0946968i
$833$	8.29263	−	14.3633i	0.00995514	−	0.0172428i
$834$	−260.944	+	369.031i	−0.312883	+	0.442483i
$835$		0			0
$836$		−	88.6669i		−	0.106061i
$837$	−794.407	+	772.711i	−0.949112	+	0.923191i
$838$			15.2281i			0.0181719i
$839$	−903.778	+	521.797i	−1.07721	+	0.621927i	−0.930142	−	0.367200i	$-0.880317\pi$
$839$	−903.778	+	521.797i	−1.07721	+	0.621927i	−0.147067	+	0.989127i	$0.546983\pi$
$840$		0			0
$841$	−415.091	+	718.958i	−0.493568	+	0.854885i
$842$	−179.819	+	311.456i	−0.213562	+	0.369901i
$843$	−94.4361	+	1024.92i	−0.112024	+	1.21580i
$844$	154.439	+	267.497i	0.182985	+	0.316939i
$845$		0			0
$846$	176.568	+	32.8166i	0.208709	+	0.0387903i
$847$			202.574i			0.239167i
$848$	−19.0702	−	33.0306i	−0.0224885	−	0.0389512i
$849$	−935.701	+	431.079i	−1.10212	+	0.507749i
$850$		0			0
$851$	141.439	+	81.6600i	0.166204	+	0.0959577i
$852$	468.126	−	215.666i	0.549443	−	0.253129i
$853$	−410.338	+	236.909i	−0.481053	+	0.277736i	−0.720855	−	0.693086i	$-0.756251\pi$
$853$	−410.338	+	236.909i	−0.481053	+	0.277736i	0.239802	+	0.970822i	$0.422917\pi$
$854$		−	674.172i		−	0.789429i
$855$		0			0
$856$	485.939			0.567685
$857$	458.381	+	793.939i	0.534867	+	0.926417i	0.999170	+	0.0407403i	$0.0129716\pi$
$857$	458.381	+	793.939i	0.534867	+	0.926417i	−0.464303	+	0.885677i	$0.653695\pi$
$858$	−785.445	−	72.3712i	−0.915437	−	0.0843487i
$859$	478.901	−	829.480i	0.557510	−	0.965635i	−0.440194	−	0.897903i	$-0.645090\pi$
$859$	478.901	−	829.480i	0.557510	−	0.965635i	0.997704	−	0.0677322i	$-0.0215764\pi$
$860$		0			0
$861$	−679.863	+	961.471i	−0.789620	+	1.11669i
$862$	855.684	−	494.030i	0.992673	−	0.573120i
$863$	524.200			0.607416			0.303708	−	0.952765i	$-0.401775\pi$
$863$	524.200			0.607416			0.303708	+	0.952765i	$0.401775\pi$
$864$	109.485	−	106.495i	0.126718	−	0.123258i
$865$		0			0
$866$	−259.312	+	149.714i	−0.299437	+	0.172880i
$867$	−494.264	+	698.994i	−0.570085	+	0.806222i
$868$	451.330	+	260.576i	0.519965	+	0.300202i
$869$	243.121	+	140.366i	0.279771	+	0.161526i
$870$		0			0
$871$	−304.855	−	528.025i	−0.350006	−	0.606228i
$872$	−328.868			−0.377142
$873$	−655.878	−	560.743i	−0.751292	−	0.642317i
$874$	62.6969			0.0717356
$875$		0			0
$876$	−523.646	+	241.245i	−0.597769	+	0.275393i
$877$	−872.742	−	503.878i	−0.995145	−	0.574547i	−0.0883370	−	0.996091i	$-0.528155\pi$
$877$	−872.742	−	503.878i	−0.995145	−	0.574547i	−0.906808	+	0.421543i	$0.861489\pi$
$878$	197.893	−	342.760i	0.225390	−	0.390388i
$879$	359.583	+	780.511i	0.409082	+	0.887954i
$880$		0			0
$881$		−	1536.71i		−	1.74428i	−0.489254	−	0.872141i	$-0.662731\pi$
$881$		−	1536.71i		−	1.74428i	0.489254	−	0.872141i	$-0.337269\pi$
$882$	−36.8980	−	104.363i	−0.0418345	−	0.118326i
$883$			294.213i			0.333197i	0.986025	+	0.166599i	$0.0532784\pi$
$883$			294.213i			0.333197i	−0.986025	+	0.166599i	$0.946722\pi$
$884$	65.0602	−	37.5625i	0.0735975	−	0.0424915i
$885$		0			0
$886$	389.796	−	675.146i	0.439950	−	0.762016i
$887$	287.402	−	497.794i	0.324015	−	0.561211i	−0.657297	−	0.753631i	$-0.728300\pi$
$887$	287.402	−	497.794i	0.324015	−	0.561211i	0.981313	+	0.192420i	$0.0616337\pi$
$888$	119.879	+	84.7673i	0.134999	+	0.0954587i
$889$	32.0306	+	55.4787i	0.0360299	+	0.0624057i
$890$		0			0
$891$	−274.704	+	713.486i	−0.308310	+	0.800770i
$892$		−	185.546i		−	0.208011i
$893$	33.1370	+	57.3949i	0.0371075	+	0.0642720i
$894$	−364.120	−	257.472i	−0.407294	−	0.288000i
$895$		0			0
$896$	−62.2020	−	35.9124i	−0.0694219	−	0.0400808i
$897$	51.1741	−	555.393i	0.0570503	−	0.619168i
$898$	−664.872	+	383.864i	−0.740391	+	0.427465i
$899$		−	135.004i		−	0.150171i
$900$		0			0
$901$	−18.1837			−0.0201817
$902$	412.661	+	714.749i	0.457495	+	0.792405i
$903$	7.60734	+	16.5125i	0.00842452	+	0.0182863i
$904$	286.045	−	495.445i	0.316422	−	0.548059i
$905$		0			0
$906$	−506.351	−	1099.09i	−0.558886	−	1.21312i
$907$	−441.737	+	255.037i	−0.487031	+	0.281187i	−0.723342	−	0.690490i	$-0.757395\pi$
$907$	−441.737	+	255.037i	−0.487031	+	0.281187i	0.236311	+	0.971677i	$0.424062\pi$
$908$	−339.604			−0.374013
$909$	1080.36	+	923.656i	1.18852	+	1.01612i
$910$		0			0
$911$	−803.127	+	463.685i	−0.881588	+	0.508985i	−0.871182	−	0.490961i	$-0.836646\pi$
$911$	−803.127	+	463.685i	−0.881588	+	0.508985i	−0.0104064	+	0.999946i	$0.503313\pi$
$912$	56.1255	+	5.17143i	0.0615411	+	0.00567042i
$913$	718.564	+	414.863i	0.787036	+	0.454396i
$914$	−113.123	−	65.3114i	−0.123767	−	0.0714567i
$915$		0			0
$916$	407.545	+	705.888i	0.444918	+	0.770621i
$917$	31.4897			0.0343399
$918$	−17.8710	−	70.5903i	−0.0194674	−	0.0768958i
$919$	1240.63			1.34998			0.674991	−	0.737826i	$-0.264147\pi$
$919$	1240.63			1.34998			0.674991	+	0.737826i	$0.264147\pi$
$920$		0			0
$921$	377.444	+	266.893i	0.409820	+	0.289786i
$922$	281.471	+	162.507i	0.305283	+	0.176255i
$923$	846.010	−	1465.33i	0.916587	−	1.58757i
$924$	358.015	+	32.9876i	0.387462	+	0.0357009i
$925$		0			0
$926$			722.384i			0.780112i
$927$	47.9164	−	257.811i	0.0516897	−	0.278113i
$928$			18.6061i			0.0200497i
$929$	−293.576	+	169.496i	−0.316013	+	0.182450i	−0.649614	−	0.760264i	$-0.725069\pi$
$929$	−293.576	+	169.496i	−0.316013	+	0.182450i	0.333601	+	0.942714i	$0.391736\pi$
$930$		0			0
$931$	20.4245	−	35.3763i	0.0219382	−	0.0379981i
$932$	−15.2562	+	26.4245i	−0.0163693	+	0.0283525i
$933$	−196.141	+	90.3627i	−0.210227	+	0.0968518i
$934$	−589.485	−	1021.02i	−0.631140	−	1.09317i
$935$		0			0
$936$	91.6209	−	492.960i	0.0978856	−	0.526667i
$937$			1322.21i			1.41111i	0.708655	+	0.705556i	$0.249302\pi$
$937$			1322.21i			1.41111i	−0.708655	+	0.705556i	$0.750698\pi$
$938$	138.957	+	240.680i	0.148141	+	0.256588i
$939$	101.185	−	1098.17i	0.107759	−	1.16951i
$940$		0			0
$941$	−310.984	−	179.547i	−0.330482	−	0.190804i	0.325573	−	0.945517i	$-0.394443\pi$
$941$	−310.984	−	179.547i	−0.330482	−	0.190804i	−0.656055	+	0.754713i	$0.727776\pi$
$942$	−683.057	−	482.994i	−0.725114	−	0.512733i
$943$	−505.404	+	291.795i	−0.535953	+	0.309433i
$944$			366.110i			0.387828i
$945$		0			0
$946$	12.7423			0.0134697
$947$	−387.896	−	671.855i	−0.409605	−	0.709457i	0.585240	−	0.810860i	$-0.301000\pi$
$947$	−387.896	−	671.855i	−0.409605	−	0.709457i	−0.994845	+	0.101403i	$0.967667\pi$
$948$	−103.031	+	145.707i	−0.108682	+	0.153700i
$949$	−946.347	+	1639.12i	−0.997205	+	1.72721i
$950$		0			0
$951$	−321.431	−	29.6168i	−0.337992	−	0.0311428i
$952$	−29.6552	+	17.1214i	−0.0311504	+	0.0179847i
$953$	465.082			0.488019			0.244010	−	0.969773i	$-0.421537\pi$
$953$	465.082			0.488019			0.244010	+	0.969773i	$0.421537\pi$
$954$	−78.8648	+	92.2450i	−0.0826675	+	0.0966928i
$955$		0			0
$956$	97.9240	−	56.5364i	0.102431	−	0.0591385i
$957$	−38.9711	−	84.5908i	−0.0407222	−	0.0883917i
$958$	804.891	+	464.704i	0.840178	+	0.485077i
$959$	1290.28	+	744.942i	1.34544	+	0.776791i
$960$		0			0
$961$	−361.863	−	626.765i	−0.376548	−	0.652200i
$962$	481.989			0.501028
$963$	−515.416	−	1457.82i	−0.535219	−	1.51383i
$964$	168.424			0.174714
$965$		0			0
$966$	−23.3258	+	253.155i	−0.0241468	+	0.262065i
$967$	−1060.21	−	612.113i	−1.09639	−	0.633002i	−0.161121	−	0.986935i	$-0.551511\pi$
$967$	−1060.21	−	612.113i	−1.09639	−	0.633002i	−0.935271	+	0.353933i	$0.884844\pi$
$968$	−45.1264	+	78.1612i	−0.0466182	+	0.0807451i
$969$	15.5143	−	21.9405i	0.0160106	−	0.0226424i
$970$		0			0
$971$			658.702i			0.678375i	0.940719	+	0.339188i	$0.110152\pi$
$971$			658.702i			0.678375i	−0.940719	+	0.339188i	$0.889848\pi$
$972$	−435.610	−	215.499i	−0.448158	−	0.221707i
$973$		−	676.303i		−	0.695070i
$974$	−430.702	+	248.666i	−0.442199	+	0.255304i
$975$		0			0
$976$	150.182	−	260.122i	0.153875	−	0.266519i
$977$	−759.170	+	1314.92i	−0.777042	+	1.34588i	0.156597	+	0.987663i	$0.449948\pi$
$977$	−759.170	+	1314.92i	−0.777042	+	1.34588i	−0.933639	+	0.358214i	$0.883386\pi$
$978$	96.9515	−	1052.22i	0.0991325	−	1.07589i
$979$	−195.272	−	338.222i	−0.199461	−	0.345477i
$980$		0			0
$981$	348.817	+	986.604i	0.355573	+	1.00571i
$982$		−	347.074i		−	0.353436i
$983$	−413.920	−	716.930i	−0.421078	−	0.729329i	0.574967	−	0.818177i	$-0.305015\pi$
$983$	−413.920	−	716.930i	−0.421078	−	0.729329i	−0.996045	+	0.0888477i	$0.971682\pi$
$984$	−476.499	+	219.524i	−0.484247	+	0.223094i
$985$		0			0
$986$	7.68215	+	4.43529i	0.00779122	+	0.00449826i
$987$	−244.075	+	112.446i	−0.247289	+	0.113927i
$988$	160.241	−	92.5153i	0.162187	−	0.0936390i
$989$			9.01020i			0.00911041i
$990$		0			0
$991$	429.546			0.433447			0.216723	−	0.976233i	$-0.430463\pi$
$991$	429.546			0.433447			0.216723	+	0.976233i	$0.430463\pi$
$992$	116.094	+	201.081i	0.117030	+	0.202702i
$993$	−51.3747	−	4.73369i	−0.0517369	−	0.00476706i
$994$	−385.621	+	667.915i	−0.387949	+	0.671947i
$995$		0			0
$996$	−304.515	+	430.650i	−0.305738	+	0.432379i
$997$	−601.886	+	347.499i	−0.603697	+	0.348545i	−0.770495	−	0.637447i	$-0.779991\pi$
$997$	−601.886	+	347.499i	−0.603697	+	0.348545i	0.166798	+	0.985991i	$0.446657\pi$
$998$	−891.274			−0.893060
$999$	127.151	−	449.547i	0.127278	−	0.449997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.3.k.a.149.2		8
3.2	odd	2		1350.3.k.a.449.3		8
5.2	odd	4		450.3.i.b.401.2		4
5.3	odd	4		18.3.d.a.5.1	✓	4
5.4	even	2	inner	450.3.k.a.149.3		8
9.2	odd	6	inner	450.3.k.a.299.3		8
9.7	even	3		1350.3.k.a.899.2		8
15.2	even	4		1350.3.i.b.1151.1		4
15.8	even	4		54.3.d.a.17.2		4
15.14	odd	2		1350.3.k.a.449.2		8
20.3	even	4		144.3.q.c.113.1		4
40.3	even	4		576.3.q.e.257.2		4
40.13	odd	4		576.3.q.f.257.1		4
45.2	even	12		450.3.i.b.101.2		4
45.7	odd	12		1350.3.i.b.251.1		4
45.13	odd	12		162.3.b.a.161.2		4
45.23	even	12		162.3.b.a.161.3		4
45.29	odd	6	inner	450.3.k.a.299.2		8
45.34	even	6		1350.3.k.a.899.3		8
45.38	even	12		18.3.d.a.11.1	yes	4
45.43	odd	12		54.3.d.a.35.2		4
60.23	odd	4		432.3.q.d.17.2		4
120.53	even	4		1728.3.q.d.449.1		4
120.83	odd	4		1728.3.q.c.449.2		4
180.23	odd	12		1296.3.e.g.161.1		4
180.43	even	12		432.3.q.d.305.2		4
180.83	odd	12		144.3.q.c.65.1		4
180.103	even	12		1296.3.e.g.161.3		4
360.43	even	12		1728.3.q.c.1601.2		4
360.83	odd	12		576.3.q.e.65.2		4
360.133	odd	12		1728.3.q.d.1601.1		4
360.173	even	12		576.3.q.f.65.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.3.d.a.5.1	✓	4	5.3	odd	4
18.3.d.a.11.1	yes	4	45.38	even	12
54.3.d.a.17.2		4	15.8	even	4
54.3.d.a.35.2		4	45.43	odd	12
144.3.q.c.65.1		4	180.83	odd	12
144.3.q.c.113.1		4	20.3	even	4
162.3.b.a.161.2		4	45.13	odd	12
162.3.b.a.161.3		4	45.23	even	12
432.3.q.d.17.2		4	60.23	odd	4
432.3.q.d.305.2		4	180.43	even	12
450.3.i.b.101.2		4	45.2	even	12
450.3.i.b.401.2		4	5.2	odd	4
450.3.k.a.149.2		8	1.1	even	1	trivial
450.3.k.a.149.3		8	5.4	even	2	inner
450.3.k.a.299.2		8	45.29	odd	6	inner
450.3.k.a.299.3		8	9.2	odd	6	inner
576.3.q.e.65.2		4	360.83	odd	12
576.3.q.e.257.2		4	40.3	even	4
576.3.q.f.65.1		4	360.173	even	12
576.3.q.f.257.1		4	40.13	odd	4
1296.3.e.g.161.1		4	180.23	odd	12
1296.3.e.g.161.3		4	180.103	even	12
1350.3.i.b.251.1		4	45.7	odd	12
1350.3.i.b.1151.1		4	15.2	even	4
1350.3.k.a.449.2		8	15.14	odd	2
1350.3.k.a.449.3		8	3.2	odd	2
1350.3.k.a.899.2		8	9.7	even	3
1350.3.k.a.899.3		8	45.34	even	6
1728.3.q.c.449.2		4	120.83	odd	4
1728.3.q.c.1601.2		4	360.43	even	12
1728.3.q.d.449.1		4	120.53	even	4
1728.3.q.d.1601.1		4	360.133	odd	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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	450.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(1.73205 - 2.44949i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-4.22474 - 0.389270i) q^{6} +(5.49794 - 3.17423i) q^{7} +2.82843 q^{8} +(-3.00000 - 8.48528i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(1.73205 - 2.44949i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-4.22474 - 0.389270i) q^{6} +(5.49794 - 3.17423i) q^{7} +2.82843 q^{8} +(-3.00000 - 8.48528i) q^{9} +(8.17423 - 4.71940i) q^{11} +(2.51059 + 5.44949i) q^{12} +(17.0580 + 9.84847i) q^{13} +(-7.77526 - 4.48905i) q^{14} +(-2.00000 - 3.46410i) q^{16} -1.90702 q^{17} +(-8.27098 + 9.67423i) q^{18} -4.69694 q^{19} +(1.74745 - 18.9651i) q^{21} +(-11.5601 - 6.67423i) q^{22} +(4.71940 - 8.17423i) q^{23} +(4.89898 - 6.92820i) q^{24} -27.8557i q^{26} +(-25.9808 - 7.34847i) q^{27} +12.6969i q^{28} +(2.84847 - 1.64456i) q^{29} +(20.5227 - 35.5464i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(2.59808 - 28.1969i) q^{33} +(1.34847 + 2.33562i) q^{34} +(17.6969 + 3.28913i) q^{36} +17.3031i q^{37} +(3.32124 + 5.75255i) q^{38} +(53.6691 - 24.7255i) q^{39} +(-53.5454 - 30.9145i) q^{41} +(-24.4630 + 11.2702i) q^{42} +(-0.826701 + 0.477296i) q^{43} +18.8776i q^{44} -13.3485 q^{46} +(-7.05501 - 12.2196i) q^{47} +(-11.9494 - 1.10102i) q^{48} +(-4.34847 + 7.53177i) q^{49} +(-3.30306 + 4.67123i) q^{51} +(-34.1161 + 19.6969i) q^{52} +9.53512 q^{53} +(9.37117 + 37.0160i) q^{54} +(15.5505 - 8.97809i) q^{56} +(-8.13534 + 11.5051i) q^{57} +(-4.02834 - 2.32577i) q^{58} +(-79.2650 - 45.7637i) q^{59} +(37.5454 + 65.0306i) q^{61} -58.0470 q^{62} +(-43.4281 - 37.1288i) q^{63} +8.00000 q^{64} +(-36.3712 + 16.7563i) q^{66} +(-26.8075 - 15.4773i) q^{67} +(1.90702 - 3.30306i) q^{68} +(-11.8485 - 25.7183i) q^{69} -85.9026i q^{71} +(-8.48528 - 24.0000i) q^{72} +96.0908i q^{73} +(21.1918 - 12.2351i) q^{74} +(4.69694 - 8.13534i) q^{76} +(29.9609 - 51.8939i) q^{77} +(-68.2322 - 48.2474i) q^{78} +(14.8712 + 25.7576i) q^{79} +(-63.0000 + 50.9117i) q^{81} +87.4393i q^{82} +(43.9530 + 76.1288i) q^{83} +(31.1010 + 21.9917i) q^{84} +(1.16913 + 0.674999i) q^{86} +(0.905350 - 9.82577i) q^{87} +(23.1202 - 13.3485i) q^{88} -41.3766i q^{89} +125.045 q^{91} +(9.43879 + 16.3485i) q^{92} +(-51.5241 - 111.838i) q^{93} +(-9.97730 + 17.2812i) q^{94} +(7.10102 + 15.4135i) q^{96} +(83.0333 - 47.9393i) q^{97} +12.2993 q^{98} +(-64.5681 - 55.2025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 24 q^{6} - 24 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 24 * q^6 - 24 * q^9	\( 8 q - 8 q^{4} - 24 q^{6} - 24 q^{9} + 36 q^{11} - 72 q^{14} - 16 q^{16} + 80 q^{19} - 84 q^{21} - 36 q^{29} + 76 q^{31} - 48 q^{34} + 24 q^{36} + 204 q^{39} - 252 q^{41} - 48 q^{46} + 24 q^{49} - 144 q^{51} - 72 q^{54} + 144 q^{56} - 252 q^{59} + 124 q^{61} + 64 q^{64} - 144 q^{66} - 36 q^{69} - 144 q^{74} - 80 q^{76} - 28 q^{79} - 504 q^{81} + 288 q^{84} - 216 q^{86} + 824 q^{91} - 168 q^{94} + 96 q^{96} - 252 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 24 * q^6 - 24 * q^9 + 36 * q^11 - 72 * q^14 - 16 * q^16 + 80 * q^19 - 84 * q^21 - 36 * q^29 + 76 * q^31 - 48 * q^34 + 24 * q^36 + 204 * q^39 - 252 * q^41 - 48 * q^46 + 24 * q^49 - 144 * q^51 - 72 * q^54 + 144 * q^56 - 252 * q^59 + 124 * q^61 + 64 * q^64 - 144 * q^66 - 36 * q^69 - 144 * q^74 - 80 * q^76 - 28 * q^79 - 504 * q^81 + 288 * q^84 - 216 * q^86 + 824 * q^91 - 168 * q^94 + 96 * q^96 - 252 * q^99

Introduction

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