LMFDB - Embedded newform 1890.2.bf.f.629.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(629,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3, 3]))

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

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

chi := DirichletCharacter("1890.629");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.bf (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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			629.9
Character	$\chi$	$=$	1890.629
Dual form			1890.2.bf.f.1259.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.150780 - 2.23098i) q^{5} +(-2.28974 + 1.32556i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.150780 - 2.23098i) q^{5} +(-2.28974 + 1.32556i) q^{7} -1.00000 q^{8} +(-1.85669 - 1.24607i) q^{10} +(2.86892 + 1.65637i) q^{11} +(2.91974 + 5.05714i) q^{13} +(0.00309790 + 2.64575i) q^{14} +(-0.500000 + 0.866025i) q^{16} +2.78294i q^{17} -0.0210849i q^{19} +(-2.00747 + 0.984910i) q^{20} +(2.86892 - 1.65637i) q^{22} +(2.80015 + 4.85001i) q^{23} +(-4.95453 - 0.672775i) q^{25} +5.83948 q^{26} +(2.29284 + 1.32019i) q^{28} +(-1.43484 - 0.828404i) q^{29} +(-5.24289 + 3.02698i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.41010 + 1.39147i) q^{34} +(2.61204 + 5.30822i) q^{35} -4.54272i q^{37} +(-0.0182600 - 0.0105424i) q^{38} +(-0.150780 + 2.23098i) q^{40} +(5.58921 + 9.68080i) q^{41} +(2.13226 + 1.23106i) q^{43} -3.31275i q^{44} +5.60031 q^{46} +(3.89705 + 2.24996i) q^{47} +(3.48579 - 6.07036i) q^{49} +(-3.05991 + 3.95436i) q^{50} +(2.91974 - 5.05714i) q^{52} -0.154097 q^{53} +(4.12791 - 6.15076i) q^{55} +(2.28974 - 1.32556i) q^{56} +(-1.43484 + 0.828404i) q^{58} +(3.32508 + 5.75921i) q^{59} +(-7.58810 - 4.38099i) q^{61} +6.05396i q^{62} +1.00000 q^{64} +(11.7226 - 5.75136i) q^{65} +(11.9504 - 6.89958i) q^{67} +(2.41010 - 1.39147i) q^{68} +(5.90308 + 0.392015i) q^{70} -14.4531i q^{71} -0.567999 q^{73} +(-3.93411 - 2.27136i) q^{74} +(-0.0182600 + 0.0105424i) q^{76} +(-8.76470 + 0.0102626i) q^{77} +(2.02885 - 3.51406i) q^{79} +(1.85669 + 1.24607i) q^{80} +11.1784 q^{82} +(11.5525 + 6.66983i) q^{83} +(6.20868 + 0.419612i) q^{85} +(2.13226 - 1.23106i) q^{86} +(-2.86892 - 1.65637i) q^{88} -6.33024 q^{89} +(-13.3890 - 7.70923i) q^{91} +(2.80015 - 4.85001i) q^{92} +(3.89705 - 2.24996i) q^{94} +(-0.0470399 - 0.00317918i) q^{95} +(-4.93235 + 8.54307i) q^{97} +(-3.51419 - 6.05396i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8}+O(q^{10}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 24 q^{11} - 16 q^{16} + 24 q^{22} + 24 q^{23} - 58 q^{25} + 36 q^{29} + 16 q^{32} + 48 q^{35} - 54 q^{43} + 48 q^{46} + 32 q^{49} - 50 q^{50} + 24 q^{53} + 36 q^{58} + 32 q^{64} + 90 q^{65} - 66 q^{67} + 36 q^{70} - 12 q^{74} - 18 q^{77} + 34 q^{79} + 4 q^{85} - 54 q^{86} - 24 q^{88} + 16 q^{91} + 24 q^{92} - 12 q^{95} + 64 q^{98}+O(q^{100}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 24 * q^11 - 16 * q^16 + 24 * q^22 + 24 * q^23 - 58 * q^25 + 36 * q^29 + 16 * q^32 + 48 * q^35 - 54 * q^43 + 48 * q^46 + 32 * q^49 - 50 * q^50 + 24 * q^53 + 36 * q^58 + 32 * q^64 + 90 * q^65 - 66 * q^67 + 36 * q^70 - 12 * q^74 - 18 * q^77 + 34 * q^79 + 4 * q^85 - 54 * q^86 - 24 * q^88 + 16 * q^91 + 24 * q^92 - 12 * q^95 + 64 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.150780	−	2.23098i	0.0674310	−	0.997724i
$5$	0.150780	−	2.23098i	0.0674310	−	0.997724i
$6$		0			0
$7$	−2.28974	+	1.32556i	−0.865439	+	0.501014i
$7$	−2.28974	+	1.32556i	−0.865439	+	0.501014i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.85669	−	1.24607i	−0.587138	−	0.394042i
$11$	2.86892	+	1.65637i	0.865013	+	0.499416i	0.865688	−	0.500584i	$-0.166881\pi$
$11$	2.86892	+	1.65637i	0.865013	+	0.499416i	−0.000674708		1.00000i	$0.500215\pi$
$12$		0			0
$13$	2.91974	+	5.05714i	0.809790	+	1.40260i	0.913009	+	0.407939i	$0.133752\pi$
$13$	2.91974	+	5.05714i	0.809790	+	1.40260i	−0.103219	+	0.994659i	$0.532914\pi$
$14$	0.00309790	+	2.64575i	0.000827948	+	0.707106i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$			2.78294i			0.674962i	0.941332	+	0.337481i	$0.109575\pi$
$17$			2.78294i			0.674962i	−0.941332	+	0.337481i	$0.890425\pi$
$18$		0			0
$19$		−	0.0210849i		−	0.00483720i	−0.999997	−	0.00241860i	$-0.999230\pi$
$19$		−	0.0210849i		−	0.00483720i	0.999997	−	0.00241860i	$-0.000769865\pi$
$20$	−2.00747	+	0.984910i	−0.448885	+	0.220233i
$21$		0			0
$22$	2.86892	−	1.65637i	0.611657	−	0.353140i
$23$	2.80015	+	4.85001i	0.583873	+	1.01130i	0.995015	+	0.0997259i	$0.0317966\pi$
$23$	2.80015	+	4.85001i	0.583873	+	1.01130i	−0.411142	+	0.911571i	$0.634870\pi$
$24$		0			0
$25$	−4.95453	−	0.672775i	−0.990906	−	0.134555i
$26$	5.83948			1.14522
$27$		0			0
$28$	2.29284	+	1.32019i	0.433305	+	0.249493i
$29$	−1.43484	−	0.828404i	−0.266443	−	0.153831i	0.360827	−	0.932633i	$-0.382494\pi$
$29$	−1.43484	−	0.828404i	−0.266443	−	0.153831i	−0.627270	+	0.778802i	$0.715828\pi$
$30$		0			0
$31$	−5.24289	+	3.02698i	−0.941650	+	0.543662i	−0.890477	−	0.455028i	$-0.849629\pi$
$31$	−5.24289	+	3.02698i	−0.941650	+	0.543662i	−0.0511731	+	0.998690i	$0.516296\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	2.41010	+	1.39147i	0.413328	+	0.238635i
$35$	2.61204	+	5.30822i	0.441516	+	0.897253i
$36$		0			0
$37$		−	4.54272i		−	0.746819i	−0.927667	−	0.373410i	$-0.878189\pi$
$37$		−	4.54272i		−	0.746819i	0.927667	−	0.373410i	$-0.121811\pi$
$38$	−0.0182600	−	0.0105424i	−0.00296217	−	0.00171021i
$39$		0			0
$40$	−0.150780	+	2.23098i	−0.0238404	+	0.352749i
$41$	5.58921	+	9.68080i	0.872888	+	1.51189i	0.858995	+	0.511984i	$0.171089\pi$
$41$	5.58921	+	9.68080i	0.872888	+	1.51189i	0.0138932	+	0.999903i	$0.495578\pi$
$42$		0			0
$43$	2.13226	+	1.23106i	0.325166	+	0.187735i	0.653693	−	0.756760i	$-0.273219\pi$
$43$	2.13226	+	1.23106i	0.325166	+	0.187735i	−0.328527	+	0.944495i	$0.606552\pi$
$44$		−	3.31275i		−	0.499416i
$45$		0			0
$46$	5.60031			0.825721
$47$	3.89705	+	2.24996i	0.568443	+	0.328191i	0.756527	−	0.653962i	$-0.226894\pi$
$47$	3.89705	+	2.24996i	0.568443	+	0.328191i	−0.188084	+	0.982153i	$0.560228\pi$
$48$		0			0
$49$	3.48579	−	6.07036i	0.497971	−	0.867194i
$50$	−3.05991	+	3.95436i	−0.432736	+	0.559231i
$51$		0			0
$52$	2.91974	−	5.05714i	0.404895	−	0.701299i
$53$	−0.154097			−0.0211669			−0.0105835	−	0.999944i	$-0.503369\pi$
$53$	−0.154097			−0.0211669			−0.0105835	+	0.999944i	$0.503369\pi$
$54$		0			0
$55$	4.12791	−	6.15076i	0.556608	−	0.829368i
$56$	2.28974	−	1.32556i	0.305979	−	0.177135i
$57$		0			0
$58$	−1.43484	+	0.828404i	−0.188404	+	0.108775i
$59$	3.32508	+	5.75921i	0.432889	+	0.749786i	0.997121	−	0.0758307i	$-0.0241608\pi$
$59$	3.32508	+	5.75921i	0.432889	+	0.749786i	−0.564232	+	0.825617i	$0.690828\pi$
$60$		0			0
$61$	−7.58810	−	4.38099i	−0.971556	−	0.560928i	−0.0718459	−	0.997416i	$-0.522889\pi$
$61$	−7.58810	−	4.38099i	−0.971556	−	0.560928i	−0.899710	+	0.436487i	$0.856222\pi$
$62$			6.05396i			0.768854i
$63$		0			0
$64$	1.00000			0.125000
$65$	11.7226	−	5.75136i	1.45401	−	0.713368i
$66$		0			0
$67$	11.9504	−	6.89958i	1.45998	−	0.842918i	0.460968	−	0.887417i	$-0.347502\pi$
$67$	11.9504	−	6.89958i	1.45998	−	0.842918i	0.999009	+	0.0444983i	$0.0141689\pi$
$68$	2.41010	−	1.39147i	0.292267	−	0.168741i
$69$		0			0
$70$	5.90308	+	0.392015i	0.705553	+	0.0468548i
$71$		−	14.4531i		−	1.71527i	−0.514257	−	0.857636i	$-0.671932\pi$
$71$		−	14.4531i		−	1.71527i	0.514257	−	0.857636i	$-0.328068\pi$
$72$		0			0
$73$	−0.567999			−0.0664793			−0.0332396	−	0.999447i	$-0.510582\pi$
$73$	−0.567999			−0.0664793			−0.0332396	+	0.999447i	$0.510582\pi$
$74$	−3.93411	−	2.27136i	−0.457332	−	0.264040i
$75$		0			0
$76$	−0.0182600	+	0.0105424i	−0.00209457	+	0.00120930i
$77$	−8.76470	+	0.0102626i	−0.998830	+	0.00116953i
$78$		0			0
$79$	2.02885	−	3.51406i	0.228263	−	0.395363i	−0.729030	−	0.684481i	$-0.760029\pi$
$79$	2.02885	−	3.51406i	0.228263	−	0.395363i	0.957293	+	0.289118i	$0.0933621\pi$
$80$	1.85669	+	1.24607i	0.207585	+	0.139315i
$81$		0			0
$82$	11.1784			1.23445
$83$	11.5525	+	6.66983i	1.26805	+	0.732109i	0.974619	−	0.223872i	$-0.0718696\pi$
$83$	11.5525	+	6.66983i	1.26805	+	0.732109i	0.293431	+	0.955980i	$0.405203\pi$
$84$		0			0
$85$	6.20868	+	0.419612i	0.673426	+	0.0455134i
$86$	2.13226	−	1.23106i	0.229927	−	0.132749i
$87$		0			0
$88$	−2.86892	−	1.65637i	−0.305828	−	0.176570i
$89$	−6.33024			−0.671004			−0.335502	−	0.942040i	$-0.608906\pi$
$89$	−6.33024			−0.671004			−0.335502	+	0.942040i	$0.608906\pi$
$90$		0			0
$91$	−13.3890	−	7.70923i	−1.40354	−	0.808147i
$92$	2.80015	−	4.85001i	0.291936	−	0.505649i
$93$		0			0
$94$	3.89705	−	2.24996i	0.401950	−	0.232066i
$95$	−0.0470399	−	0.00317918i	−0.00482619	−	0.000326177i
$96$		0			0
$97$	−4.93235	+	8.54307i	−0.500804	+	0.867418i	0.499196	+	0.866489i	$0.333629\pi$
$97$	−4.93235	+	8.54307i	−0.500804	+	0.867418i	−1.00000		0.000928464i	$0.999704\pi$
$98$	−3.51419	−	6.05396i	−0.354986	−	0.611543i
$99$		0			0
$100$	1.89463	+	4.62714i	0.189463	+	0.462714i
$101$	4.81017	−	8.33145i	0.478630	−	0.829011i	−0.521070	−	0.853514i	$-0.674467\pi$
$101$	4.81017	−	8.33145i	0.478630	−	0.829011i	0.999700	+	0.0245031i	$0.00780036\pi$
$102$		0			0
$103$	9.20075	+	15.9362i	0.906577	+	1.57024i	0.818787	+	0.574098i	$0.194647\pi$
$103$	9.20075	+	15.9362i	0.906577	+	1.57024i	0.0877898	+	0.996139i	$0.472020\pi$
$104$	−2.91974	−	5.05714i	−0.286304	−	0.495893i
$105$		0			0
$106$	−0.0770487	+	0.133452i	−0.00748363	+	0.0129620i
$107$	−8.66665			−0.837837			−0.418918	−	0.908024i	$-0.637591\pi$
$107$	−8.66665			−0.837837			−0.418918	+	0.908024i	$0.637591\pi$
$108$		0			0
$109$	−4.72231			−0.452316			−0.226158	−	0.974091i	$-0.572616\pi$
$109$	−4.72231			−0.452316			−0.226158	+	0.974091i	$0.572616\pi$
$110$	−3.26276	−	6.65026i	−0.311092	−	0.634077i
$111$		0			0
$112$	−0.00309790	−	2.64575i	−0.000292724	−	0.250000i
$113$	8.68986	+	15.0513i	0.817473	+	1.41590i	0.907538	+	0.419969i	$0.137959\pi$
$113$	8.68986	+	15.0513i	0.817473	+	1.41590i	−0.0900654	+	0.995936i	$0.528708\pi$
$114$		0			0
$115$	11.2425	−	5.51580i	1.04837	−	0.514351i
$116$			1.65681i			0.153831i
$117$		0			0
$118$	6.65017			0.612198
$119$	−3.68895	−	6.37220i	−0.338165	−	0.584139i
$120$		0			0
$121$	−0.0128499	−	0.0222567i	−0.00116817	−	0.00202334i
$122$	−7.58810	+	4.38099i	−0.686994	+	0.396636i
$123$		0			0
$124$	5.24289	+	3.02698i	0.470825	+	0.271831i
$125$	−2.24799	+	10.9520i	−0.201067	+	0.979578i
$126$		0			0
$127$			17.1354i			1.52052i	0.649618	+	0.760260i	$0.274929\pi$
$127$			17.1354i			1.52052i	−0.649618	+	0.760260i	$0.725071\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	0.880478	−	13.0278i	0.0772230	−	1.14261i
$131$	−1.23726	−	2.14299i	−0.108100	−	0.187234i	0.806901	−	0.590687i	$-0.201143\pi$
$131$	−1.23726	−	2.14299i	−0.108100	−	0.187234i	−0.915000	+	0.403453i	$0.867810\pi$
$132$		0			0
$133$	0.0279492	+	0.0482788i	0.00242350	+	0.00418630i
$134$		−	13.7992i		−	1.19207i
$135$		0			0
$136$		−	2.78294i		−	0.238635i
$137$	6.68489	−	11.5786i	0.571129	−	0.989224i	−0.425322	−	0.905042i	$-0.639839\pi$
$137$	6.68489	−	11.5786i	0.571129	−	0.989224i	0.996450	−	0.0841815i	$-0.0268276\pi$
$138$		0			0
$139$	−8.17233	+	4.71830i	−0.693168	+	0.400201i	−0.804798	−	0.593549i	$-0.797726\pi$
$139$	−8.17233	+	4.71830i	−0.693168	+	0.400201i	0.111630	+	0.993750i	$0.464393\pi$
$140$	3.29103	−	4.91621i	0.278143	−	0.415495i
$141$		0			0
$142$	−12.5168	−	7.22657i	−1.05039	−	0.606440i
$143$			19.3447i			1.61769i
$144$		0			0
$145$	−2.06450	+	3.07619i	−0.171447	+	0.255463i
$146$	−0.284000	+	0.491902i	−0.0235040	+	0.0407101i
$147$		0			0
$148$	−3.93411	+	2.27136i	−0.323382	+	0.186705i
$149$	−1.96371	+	1.13375i	−0.160873	+	0.0928803i	−0.578275	−	0.815842i	$-0.696274\pi$
$149$	−1.96371	+	1.13375i	−0.160873	+	0.0928803i	0.417402	+	0.908722i	$0.362941\pi$
$150$		0			0
$151$	−5.68081	+	9.83946i	−0.462298	+	0.800724i	−0.999075	−	0.0430005i	$-0.986308\pi$
$151$	−5.68081	+	9.83946i	−0.462298	+	0.800724i	0.536777	+	0.843724i	$0.319642\pi$
$152$			0.0210849i			0.00171021i
$153$		0			0
$154$	−4.37346	+	7.59559i	−0.352424	+	0.612070i
$155$	5.96261	+	12.1532i	0.478928	+	0.976167i
$156$		0			0
$157$	−6.02781	−	10.4405i	−0.481071	−	0.833240i	0.518693	−	0.854961i	$-0.326419\pi$
$157$	−6.02781	−	10.4405i	−0.481071	−	0.833240i	−0.999764	+	0.0217208i	$0.993085\pi$
$158$	−2.02885	−	3.51406i	−0.161406	−	0.279564i
$159$		0			0
$160$	2.00747	−	0.984910i	0.158705	−	0.0778640i
$161$	−12.8406	−	7.39348i	−1.01198	−	0.582688i
$162$		0			0
$163$		−	11.3370i		−	0.887986i	−0.896030	−	0.443993i	$-0.853561\pi$
$163$		−	11.3370i		−	0.887986i	0.896030	−	0.443993i	$-0.146439\pi$
$164$	5.58921	−	9.68080i	0.436444	−	0.755944i
$165$		0			0
$166$	11.5525	−	6.66983i	0.896646	−	0.517679i
$167$	7.97315	−	4.60330i	0.616981	−	0.356214i	−0.158712	−	0.987325i	$-0.550734\pi$
$167$	7.97315	−	4.60330i	0.616981	−	0.356214i	0.775693	+	0.631111i	$0.217401\pi$
$168$		0			0
$169$	−10.5498	+	18.2727i	−0.811520	+	1.40559i
$170$	3.46774	−	5.16707i	0.265963	−	0.396296i
$171$		0			0
$172$		−	2.46212i		−	0.187735i
$173$	−16.9261	−	9.77231i	−1.28687	−	0.742975i	−0.308776	−	0.951135i	$-0.599919\pi$
$173$	−16.9261	−	9.77231i	−1.28687	−	0.742975i	−0.978095	+	0.208160i	$0.933253\pi$
$174$		0			0
$175$	12.2364	−	5.02704i	0.924983	−	0.380008i
$176$	−2.86892	+	1.65637i	−0.216253	+	0.124854i
$177$		0			0
$178$	−3.16512	+	5.48214i	−0.237236	+	0.410904i
$179$			3.69210i			0.275960i	0.990435	+	0.137980i	$0.0440610\pi$
$179$			3.69210i			0.275960i	−0.990435	+	0.137980i	$0.955939\pi$
$180$		0			0
$181$		−	9.83581i		−	0.731090i	−0.930794	−	0.365545i	$-0.880883\pi$
$181$		−	9.83581i		−	0.731090i	0.930794	−	0.365545i	$-0.119117\pi$
$182$	−13.3709	+	7.74056i	−0.991115	+	0.573769i
$183$		0			0
$184$	−2.80015	−	4.85001i	−0.206430	−	0.357547i
$185$	−10.1347	−	0.684953i	−0.745119	−	0.0503588i
$186$		0			0
$187$	−4.60959	+	7.98405i	−0.337087	+	0.583851i
$188$		−	4.49993i		−	0.328191i
$189$		0			0
$190$	−0.0262732	+	0.0391481i	−0.00190606	+	0.00284010i
$191$	21.2231	+	12.2531i	1.53565	+	0.886606i	0.999086	+	0.0427436i	$0.0136098\pi$
$191$	21.2231	+	12.2531i	1.53565	+	0.886606i	0.536560	+	0.843862i	$0.319723\pi$
$192$		0			0
$193$	−17.4708	+	10.0868i	−1.25757	+	0.726061i	−0.972602	−	0.232475i	$-0.925318\pi$
$193$	−17.4708	+	10.0868i	−1.25757	+	0.726061i	−0.284972	+	0.958536i	$0.591984\pi$
$194$	4.93235	+	8.54307i	0.354122	+	0.613357i
$195$		0			0
$196$	−6.99998	+	0.0163925i	−0.499999	+	0.00117089i
$197$	12.2435			0.872314			0.436157	−	0.899871i	$-0.356339\pi$
$197$	12.2435			0.872314			0.436157	+	0.899871i	$0.356339\pi$
$198$		0			0
$199$			4.63305i			0.328428i	0.986425	+	0.164214i	$0.0525087\pi$
$199$			4.63305i			0.328428i	−0.986425	+	0.164214i	$0.947491\pi$
$200$	4.95453	+	0.672775i	0.350338	+	0.0475724i
$201$		0			0
$202$	−4.81017	−	8.33145i	−0.338442	−	0.586199i
$203$	4.38350	−	0.00513262i	0.307661	−	0.000360240i
$204$		0			0
$205$	22.4404	−	11.0097i	1.56731	−	0.768954i
$206$	18.4015			1.28209
$207$		0			0
$208$	−5.83948			−0.404895
$209$	0.0349244	−	0.0604908i	0.00241577	−	0.00418424i
$210$		0			0
$211$	0.00959279	+	0.0166152i	0.000660395	+	0.00114384i	0.866355	−	0.499428i	$-0.166456\pi$
$211$	0.00959279	+	0.0166152i	0.000660395	+	0.00114384i	−0.865695	+	0.500572i	$0.833123\pi$
$212$	0.0770487	+	0.133452i	0.00529173	+	0.00916554i
$213$		0			0
$214$	−4.33332	+	7.50554i	−0.296220	+	0.513068i
$215$	3.06797	−	4.57140i	0.209234	−	0.311767i
$216$		0			0
$217$	7.99240	−	13.8807i	0.542559	−	0.942286i
$218$	−2.36116	+	4.08964i	−0.159918	+	0.276986i
$219$		0			0
$220$	−7.39067	−	0.499497i	−0.498279	−	0.0336761i
$221$	−14.0737	+	8.12546i	−0.946700	+	0.546578i
$222$		0			0
$223$	3.22276	−	5.58199i	0.215812	−	0.373797i	−0.737711	−	0.675116i	$-0.764093\pi$
$223$	3.22276	−	5.58199i	0.215812	−	0.373797i	0.953523	+	0.301319i	$0.0974268\pi$
$224$	−2.29284	−	1.32019i	−0.153196	−	0.0882090i
$225$		0			0
$226$	17.3797			1.15608
$227$	0.186994	+	0.107961i	0.0124113	+	0.00716564i	0.506193	−	0.862420i	$-0.331052\pi$
$227$	0.186994	+	0.107961i	0.0124113	+	0.00716564i	−0.493782	+	0.869586i	$0.664386\pi$
$228$		0			0
$229$	13.7857	−	7.95917i	0.910984	−	0.525957i	0.0302361	−	0.999543i	$-0.490374\pi$
$229$	13.7857	−	7.95917i	0.910984	−	0.525957i	0.880748	+	0.473586i	$0.157041\pi$
$230$	0.844416	−	12.4942i	0.0556791	−	0.823841i
$231$		0			0
$232$	1.43484	+	0.828404i	0.0942018	+	0.0543874i
$233$	6.15993			0.403550			0.201775	−	0.979432i	$-0.435329\pi$
$233$	6.15993			0.403550			0.201775	+	0.979432i	$0.435329\pi$
$234$		0			0
$235$	5.60722	−	8.35499i	0.365775	−	0.545019i
$236$	3.32508	−	5.75921i	0.216445	−	0.374893i
$237$		0			0
$238$	−7.36296	+	0.00862127i	−0.477270	+	0.000558834i
$239$	−11.9037	+	6.87261i	−0.769987	+	0.444552i	−0.832870	−	0.553469i	$-0.813304\pi$
$239$	−11.9037	+	6.87261i	−0.769987	+	0.444552i	0.0628829	+	0.998021i	$0.479971\pi$
$240$		0			0
$241$	−13.5191	−	7.80524i	−0.870840	−	0.502780i	−0.00321270	−	0.999995i	$-0.501023\pi$
$241$	−13.5191	−	7.80524i	−0.870840	−	0.502780i	−0.867627	+	0.497215i	$0.834356\pi$
$242$	−0.0256998			−0.00165205
$243$		0			0
$244$			8.76198i			0.560928i
$245$	−13.0172	−	8.69202i	−0.831641	−	0.555313i
$246$		0			0
$247$	0.106629	−	0.0615623i	0.00678464	−	0.00391711i
$248$	5.24289	−	3.02698i	0.332924	−	0.192214i
$249$		0			0
$250$	8.36072	+	7.42282i	0.528779	+	0.469461i
$251$	15.1753			0.957856			0.478928	−	0.877854i	$-0.341026\pi$
$251$	15.1753			0.957856			0.478928	+	0.877854i	$0.341026\pi$
$252$		0			0
$253$			18.5524i			1.16638i
$254$	14.8397	+	8.56770i	0.931125	+	0.537585i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.303030	+	0.174954i	−0.0189025	+	0.0109134i	−0.509421	−	0.860517i	$-0.670141\pi$
$257$	−0.303030	+	0.174954i	−0.0189025	+	0.0109134i	0.490519	+	0.871431i	$0.336807\pi$
$258$		0			0
$259$	6.02164	+	10.4016i	0.374167	+	0.646327i
$260$	−10.8421	−	7.27639i	−0.672400	−	0.451263i
$261$		0			0
$262$	−2.47452			−0.152876
$263$	−13.4046	+	23.2174i	−0.826561	+	1.43165i	0.0741586	+	0.997246i	$0.476373\pi$
$263$	−13.4046	+	23.2174i	−0.826561	+	1.43165i	−0.900720	+	0.434400i	$0.856960\pi$
$264$		0			0
$265$	−0.0232348	+	0.343788i	−0.00142730	+	0.0211187i
$266$	0.0557852		6.53187e-5i	0.00342041		4.00495e-6i
$267$		0			0
$268$	−11.9504	−	6.89958i	−0.729989	−	0.421459i
$269$	−14.1709			−0.864014			−0.432007	−	0.901870i	$-0.642194\pi$
$269$	−14.1709			−0.864014			−0.432007	+	0.901870i	$0.642194\pi$
$270$		0			0
$271$			19.1244i			1.16172i	0.814002	+	0.580862i	$0.197285\pi$
$271$			19.1244i			1.16172i	−0.814002	+	0.580862i	$0.802715\pi$
$272$	−2.41010	−	1.39147i	−0.146134	−	0.0843703i
$273$		0			0
$274$	−6.68489	−	11.5786i	−0.403849	−	0.699487i
$275$	−13.0998	−	10.1367i	−0.789948	−	0.611266i
$276$		0			0
$277$	16.0289	+	9.25427i	0.963082	+	0.556035i	0.897120	−	0.441787i	$-0.145655\pi$
$277$	16.0289	+	9.25427i	0.963082	+	0.556035i	0.0659615	+	0.997822i	$0.478989\pi$
$278$			9.43660i			0.565969i
$279$		0			0
$280$	−2.61204	−	5.30822i	−0.156099	−	0.317227i
$281$	−12.3152	−	7.11019i	−0.734664	−	0.424159i	0.0854618	−	0.996341i	$-0.472763\pi$
$281$	−12.3152	−	7.11019i	−0.734664	−	0.424159i	−0.820126	+	0.572183i	$0.806097\pi$
$282$		0			0
$283$	−3.87175	−	6.70606i	−0.230152	−	0.398634i	0.727701	−	0.685894i	$-0.240589\pi$
$283$	−3.87175	−	6.70606i	−0.230152	−	0.398634i	−0.957853	+	0.287260i	$0.907256\pi$
$284$	−12.5168	+	7.22657i	−0.742735	+	0.428818i
$285$		0			0
$286$	16.7530	+	9.67236i	0.990627	+	0.571939i
$287$	−25.6303	−	14.7577i	−1.51291	−	0.871118i
$288$		0			0
$289$	9.25524			0.544426
$290$	1.63181	+	3.32600i	0.0958230	+	0.195309i
$291$		0			0
$292$	0.284000	+	0.491902i	0.0166198	+	0.0287864i
$293$	8.56477	−	4.94487i	0.500359	−	0.288882i	−0.228503	−	0.973543i	$-0.573383\pi$
$293$	8.56477	−	4.94487i	0.500359	−	0.288882i	0.728862	+	0.684661i	$0.240050\pi$
$294$		0			0
$295$	13.3500	−	6.54982i	0.777269	−	0.381345i
$296$			4.54272i			0.264040i
$297$		0			0
$298$			2.26750i			0.131353i
$299$	−16.3514	+	28.3215i	−0.945628	+	1.63788i
$300$		0			0
$301$	−6.51415	+	0.00762740i	−0.375470	+	0.000439636i
$302$	5.68081	+	9.83946i	0.326894	+	0.566197i
$303$		0			0
$304$	0.0182600	+	0.0105424i	0.00104728	+	0.000604650i
$305$	−10.9180	+	16.2683i	−0.625165	+	0.931521i
$306$		0			0
$307$	−10.4384			−0.595752			−0.297876	−	0.954605i	$-0.596278\pi$
$307$	−10.4384			−0.595752			−0.297876	+	0.954605i	$0.596278\pi$
$308$	4.39124	+	7.58532i	0.250214	+	0.432214i
$309$		0			0
$310$	13.5063	+	0.912818i	0.767104	+	0.0518446i
$311$	2.84870	+	4.93410i	0.161535	+	0.279787i	0.935419	−	0.353540i	$-0.115022\pi$
$311$	2.84870	+	4.93410i	0.161535	+	0.279787i	−0.773884	+	0.633327i	$0.781689\pi$
$312$		0			0
$313$	−5.43340	+	9.41092i	−0.307114	+	0.531937i	−0.977730	−	0.209868i	$-0.932697\pi$
$313$	−5.43340	+	9.41092i	−0.307114	+	0.531937i	0.670616	+	0.741805i	$0.266030\pi$
$314$	−12.0556			−0.680337
$315$		0			0
$316$	−4.05769			−0.228263
$317$	15.6097	−	27.0368i	0.876729	−	1.51854i	0.0218195	−	0.999762i	$-0.493054\pi$
$317$	15.6097	−	27.0368i	0.876729	−	1.51854i	0.854909	−	0.518777i	$-0.173613\pi$
$318$		0			0
$319$	−2.74429	−	4.75326i	−0.153651	−	0.266131i
$320$	0.150780	−	2.23098i	0.00842887	−	0.124715i
$321$		0			0
$322$	−12.8232	+	7.42353i	−0.714611	+	0.413697i
$323$	0.0586779			0.00326493
$324$		0			0
$325$	−11.0636	−	27.0201i	−0.613699	−	1.49880i
$326$	−9.81817	−	5.66852i	−0.543778	−	0.313951i
$327$		0			0
$328$	−5.58921	−	9.68080i	−0.308613	−	0.534533i
$329$	−11.9057	+	0.0139403i	−0.656381	+	0.000768555i
$330$		0			0
$331$	14.8390	−	25.7018i	0.815623	−	1.41270i	−0.0932572	−	0.995642i	$-0.529728\pi$
$331$	14.8390	−	25.7018i	0.815623	−	1.41270i	0.908880	−	0.417058i	$-0.136939\pi$
$332$		−	13.3397i		−	0.732109i
$333$		0			0
$334$		−	9.20661i		−	0.503763i
$335$	−13.5909	−	27.7015i	−0.742552	−	1.51349i
$336$		0			0
$337$	−22.3741	+	12.9177i	−1.21879	+	0.703670i	−0.964660	−	0.263499i	$-0.915123\pi$
$337$	−22.3741	+	12.9177i	−1.21879	+	0.703670i	−0.254133	+	0.967169i	$0.581790\pi$
$338$	10.5498	+	18.2727i	0.573831	+	0.993904i
$339$		0			0
$340$	−2.74095	−	5.58668i	−0.148649	−	0.302980i
$341$	−20.0553			−1.08605
$342$		0			0
$343$	0.0650557	+	18.5201i	0.00351268	+	0.999994i
$344$	−2.13226	−	1.23106i	−0.114964	−	0.0663743i
$345$		0			0
$346$	−16.9261	+	9.77231i	−0.909955	+	0.525363i
$347$	5.52659	+	9.57234i	0.296683	+	0.513870i	0.975375	−	0.220553i	$-0.0707862\pi$
$347$	5.52659	+	9.57234i	0.296683	+	0.513870i	−0.678692	+	0.734423i	$0.737453\pi$
$348$		0			0
$349$	−27.9803	−	16.1544i	−1.49775	−	0.864727i	−0.497754	−	0.867318i	$-0.665842\pi$
$349$	−27.9803	−	16.1544i	−1.49775	−	0.864727i	−0.999997	+	0.00259132i	$0.999175\pi$
$350$	1.76465	−	13.1105i	0.0943243	−	0.700787i
$351$		0			0
$352$			3.31275i			0.176570i
$353$	13.4192	+	7.74759i	0.714233	+	0.412362i	0.812626	−	0.582785i	$-0.198037\pi$
$353$	13.4192	+	7.74759i	0.714233	+	0.412362i	−0.0983936	+	0.995148i	$0.531370\pi$
$354$		0			0
$355$	−32.2446	−	2.17925i	−1.71137	−	0.115662i
$356$	3.16512	+	5.48214i	0.167751	+	0.290553i
$357$		0			0
$358$	3.19745	+	1.84605i	0.168990	+	0.0975667i
$359$		−	2.94433i		−	0.155396i	−0.996977	−	0.0776980i	$-0.975243\pi$
$359$		−	2.94433i		−	0.155396i	0.996977	−	0.0776980i	$-0.0247570\pi$
$360$		0			0
$361$	18.9996			0.999977
$362$	−8.51806	−	4.91791i	−0.447699	−	0.258479i
$363$		0			0
$364$	0.0180901	+	15.4498i	0.000948179	+	0.809789i
$365$	−0.0856431	+	1.26719i	−0.00448276	+	0.0663280i
$366$		0			0
$367$	5.59040	−	9.68286i	0.291817	−	0.505441i	−0.682423	−	0.730958i	$-0.739074\pi$
$367$	5.59040	−	9.68286i	0.291817	−	0.505441i	0.974239	+	0.225516i	$0.0724070\pi$
$368$	−5.60031			−0.291936
$369$		0			0
$370$	−5.66055	+	8.43445i	−0.294278	+	0.438486i
$371$	0.352842	−	0.204265i	0.0183187	−	0.0106049i
$372$		0			0
$373$	−20.8509	+	12.0383i	−1.07962	+	0.623319i	−0.930794	−	0.365544i	$-0.880883\pi$
$373$	−20.8509	+	12.0383i	−1.07962	+	0.623319i	−0.148827	+	0.988863i	$0.547550\pi$
$374$	4.60959	+	7.98405i	0.238356	+	0.412845i
$375$		0			0
$376$	−3.89705	−	2.24996i	−0.200975	−	0.116033i
$377$		−	9.67490i		−	0.498283i
$378$		0			0
$379$	−1.29955			−0.0667532			−0.0333766	−	0.999443i	$-0.510626\pi$
$379$	−1.29955			−0.0667532			−0.0333766	+	0.999443i	$0.510626\pi$
$380$	0.0207667	+	0.0423273i	0.00106531	+	0.00217134i
$381$		0			0
$382$	21.2231	−	12.2531i	1.08587	−	0.626925i
$383$	22.3017	−	12.8759i	1.13956	−	0.657927i	0.193240	−	0.981152i	$-0.438100\pi$
$383$	22.3017	−	12.8759i	1.13956	−	0.657927i	0.946322	+	0.323225i	$0.104767\pi$
$384$		0			0
$385$	−1.29865	+	19.5554i	−0.0661852	+	0.996636i
$386$			20.1735i			1.02681i
$387$		0			0
$388$	9.86469			0.500804
$389$	19.9368	+	11.5105i	1.01083	+	0.583606i	0.911436	−	0.411442i	$-0.134975\pi$
$389$	19.9368	+	11.5105i	1.01083	+	0.583606i	0.0993987	+	0.995048i	$0.468308\pi$
$390$		0			0
$391$	−13.4973	+	7.79266i	−0.682587	+	0.394092i
$392$	−3.48579	+	6.07036i	−0.176059	+	0.306599i
$393$		0			0
$394$	6.12176	−	10.6032i	0.308410	−	0.534181i
$395$	−7.53389	−	5.05616i	−0.379071	−	0.254403i
$396$		0			0
$397$	−13.8085			−0.693031			−0.346515	−	0.938044i	$-0.612635\pi$
$397$	−13.8085			−0.693031			−0.346515	+	0.938044i	$0.612635\pi$
$398$	4.01234	+	2.31652i	0.201120	+	0.116117i
$399$		0			0
$400$	3.05991	−	3.95436i	0.152995	−	0.197718i
$401$	19.7632	−	11.4103i	0.986929	−	0.569804i	0.0825743	−	0.996585i	$-0.473686\pi$
$401$	19.7632	−	11.4103i	0.986929	−	0.569804i	0.904355	+	0.426781i	$0.140352\pi$
$402$		0			0
$403$	−30.6157	−	17.6760i	−1.52508	−	0.880504i
$404$	−9.62034			−0.478630
$405$		0			0
$406$	2.18731	−	3.79879i	0.108554	−	0.188531i
$407$	7.52445	−	13.0327i	0.372973	−	0.646008i
$408$		0			0
$409$	5.52654	−	3.19075i	0.273270	−	0.157772i	−0.357103	−	0.934065i	$-0.616235\pi$
$409$	5.52654	−	3.19075i	0.273270	−	0.157772i	0.630373	+	0.776293i	$0.282902\pi$
$410$	1.68549	−	24.9388i	0.0832402	−	1.23164i
$411$		0			0
$412$	9.20075	−	15.9362i	0.453288	−	0.785118i
$413$	−15.2477	−	8.77950i	−0.750292	−	0.432011i
$414$		0			0
$415$	16.6221	−	24.7677i	0.815948	−	1.21580i
$416$	−2.91974	+	5.05714i	−0.143152	+	0.247947i
$417$		0			0
$418$	−0.0349244	−	0.0604908i	−0.00170821	−	0.00295870i
$419$	−0.937538	−	1.62386i	−0.0458017	−	0.0793309i	0.842216	−	0.539141i	$-0.181251\pi$
$419$	−0.937538	−	1.62386i	−0.0458017	−	0.0793309i	−0.888017	+	0.459810i	$0.847918\pi$
$420$		0			0
$421$	−5.71561	+	9.89973i	−0.278562	+	0.482483i	−0.971028	−	0.238967i	$-0.923191\pi$
$421$	−5.71561	+	9.89973i	−0.278562	+	0.482483i	0.692466	+	0.721451i	$0.256524\pi$
$422$	0.0191856			0.000933940
$423$		0			0
$424$	0.154097			0.00748363
$425$	1.87229	−	13.7882i	0.0908195	−	0.668824i
$426$		0			0
$427$	23.1820	−	0.0271437i	1.12186	−	0.00131358i
$428$	4.33332	+	7.50554i	0.209459	+	0.362794i
$429$		0			0
$430$	−2.42497	−	4.94264i	−0.116942	−	0.238355i
$431$		−	24.1730i		−	1.16437i	−0.813055	−	0.582186i	$-0.802197\pi$
$431$		−	24.1730i		−	1.16437i	0.813055	−	0.582186i	$-0.197803\pi$
$432$		0			0
$433$	−11.2842			−0.542285			−0.271143	−	0.962539i	$-0.587402\pi$
$433$	−11.2842			−0.542285			−0.271143	+	0.962539i	$0.587402\pi$
$434$	−8.02488	−	13.8620i	−0.385207	−	0.665397i
$435$		0			0
$436$	2.36116	+	4.08964i	0.113079	+	0.195858i
$437$	0.102262	−	0.0590409i	0.00489184	−	0.00282431i
$438$		0			0
$439$	−17.1147	−	9.88117i	−0.816839	−	0.471602i	0.0324860	−	0.999472i	$-0.489658\pi$
$439$	−17.1147	−	9.88117i	−0.816839	−	0.471602i	−0.849325	+	0.527870i	$0.822991\pi$
$440$	−4.12791	+	6.15076i	−0.196790	+	0.293226i
$441$		0			0
$442$			16.2509i			0.772978i
$443$	5.98704	−	10.3699i	0.284453	−	0.492687i	−0.688023	−	0.725689i	$-0.741521\pi$
$443$	5.98704	−	10.3699i	0.284453	−	0.492687i	0.972476	+	0.233001i	$0.0748547\pi$
$444$		0			0
$445$	−0.954474	+	14.1226i	−0.0452464	+	0.669476i
$446$	−3.22276	−	5.58199i	−0.152602	−	0.264315i
$447$		0			0
$448$	−2.28974	+	1.32556i	−0.108180	+	0.0626267i
$449$			3.84633i			0.181520i	0.995873	+	0.0907598i	$0.0289296\pi$
$449$			3.84633i			0.181520i	−0.995873	+	0.0907598i	$0.971070\pi$
$450$		0			0
$451$			37.0313i			1.74374i
$452$	8.68986	−	15.0513i	0.408737	−	0.707952i
$453$		0			0
$454$	0.186994	−	0.107961i	0.00877608	−	0.00506687i
$455$	−19.2179	+	28.7081i	−0.900950	+	1.34586i
$456$		0			0
$457$	−5.42777	−	3.13372i	−0.253900	−	0.146589i	0.367649	−	0.929965i	$-0.380163\pi$
$457$	−5.42777	−	3.13372i	−0.253900	−	0.146589i	−0.621549	+	0.783375i	$0.713496\pi$
$458$		−	15.9183i		−	0.743815i
$459$		0			0
$460$	−10.3981	−	6.97837i	−0.484812	−	0.325368i
$461$	−6.72032	+	11.6399i	−0.312997	+	0.542126i	−0.979010	−	0.203814i	$-0.934666\pi$
$461$	−6.72032	+	11.6399i	−0.312997	+	0.542126i	0.666013	+	0.745940i	$0.268000\pi$
$462$		0			0
$463$	−18.1912	+	10.5027i	−0.845419	+	0.488103i	−0.859102	−	0.511804i	$-0.828978\pi$
$463$	−18.1912	+	10.5027i	−0.845419	+	0.488103i	0.0136838	+	0.999906i	$0.495644\pi$
$464$	1.43484	−	0.828404i	0.0666107	−	0.0384577i
$465$		0			0
$466$	3.07997	−	5.33466i	0.142677	−	0.247123i
$467$		−	10.7461i		−	0.497269i	−0.968597	−	0.248634i	$-0.920018\pi$
$467$		−	10.7461i		−	0.497269i	0.968597	−	0.248634i	$-0.0799818\pi$
$468$		0			0
$469$	−18.2176	+	31.6392i	−0.841208	+	1.46096i
$470$	−4.43202	−	9.03349i	−0.204434	−	0.416684i
$471$		0			0
$472$	−3.32508	−	5.75921i	−0.153049	−	0.265089i
$473$	4.07819	+	7.06364i	0.187515	+	0.324786i
$474$		0			0
$475$	−0.0141854	+	0.104466i	−0.000650869	+	0.00479321i
$476$	−3.67402	+	6.38082i	−0.168398	+	0.292465i
$477$		0			0
$478$			13.7452i			0.628692i
$479$	3.20350	−	5.54862i	0.146372	−	0.253523i	−0.783512	−	0.621376i	$-0.786574\pi$
$479$	3.20350	−	5.54862i	0.146372	−	0.253523i	0.929884	+	0.367853i	$0.119907\pi$
$480$		0			0
$481$	22.9732	−	13.2636i	1.04749	−	0.604767i
$482$	−13.5191	+	7.80524i	−0.615777	+	0.355519i
$483$		0			0
$484$	−0.0128499	+	0.0222567i	−0.000584087	+	0.00101167i
$485$	18.3157	+	12.2921i	0.831674	+	0.558155i
$486$		0			0
$487$		−	14.8054i		−	0.670895i	−0.942059	−	0.335447i	$-0.891113\pi$
$487$		−	14.8054i		−	0.670895i	0.942059	−	0.335447i	$-0.108887\pi$
$488$	7.58810	+	4.38099i	0.343497	+	0.198318i
$489$		0			0
$490$	−14.0361	+	6.92726i	−0.634088	+	0.312942i
$491$	11.3475	−	6.55150i	0.512107	−	0.295665i	−0.221592	−	0.975139i	$-0.571125\pi$
$491$	11.3475	−	6.55150i	0.512107	−	0.295665i	0.733699	+	0.679474i	$0.237792\pi$
$492$		0			0
$493$	2.30540	−	3.99307i	0.103830	−	0.179839i
$494$		−	0.123125i		−	0.00553964i
$495$		0			0
$496$		−	6.05396i		−	0.271831i
$497$	19.1585	+	33.0939i	0.859375	+	1.48446i
$498$		0			0
$499$	21.9780	+	38.0670i	0.983870	+	1.70411i	0.646856	+	0.762612i	$0.276083\pi$
$499$	21.9780	+	38.0670i	0.983870	+	1.70411i	0.337014	+	0.941500i	$0.390583\pi$
$500$	10.6087	−	3.52919i	0.474436	−	0.157830i
$501$		0			0
$502$	7.58764	−	13.1422i	0.338653	−	0.586564i
$503$			1.65037i			0.0735862i	0.999323	+	0.0367931i	$0.0117143\pi$
$503$			1.65037i			0.0735862i	−0.999323	+	0.0367931i	$0.988286\pi$
$504$		0			0
$505$	−17.8620	−	11.9876i	−0.794849	−	0.533441i
$506$	16.0669	+	9.27621i	0.714259	+	0.412378i
$507$		0			0
$508$	14.8397	−	8.56770i	0.658405	−	0.380130i
$509$	−6.52579	−	11.3030i	−0.289250	−	0.500996i	0.684381	−	0.729125i	$-0.260073\pi$
$509$	−6.52579	−	11.3030i	−0.289250	−	0.500996i	−0.973631	+	0.228128i	$0.926739\pi$
$510$		0			0
$511$	1.30057	−	0.752916i	0.0575338	−	0.0333070i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$			0.349909i			0.0154338i
$515$	36.9405	−	18.1238i	1.62779	−	0.798631i
$516$		0			0
$517$	7.45356	+	12.9100i	0.327807	+	0.567779i
$518$	12.0189	−	0.0140729i	0.528081	−	0.000618328i
$519$		0			0
$520$	−11.7226	+	5.75136i	−0.514070	+	0.252214i
$521$	−25.9230			−1.13571			−0.567854	−	0.823129i	$-0.692226\pi$
$521$	−25.9230			−1.13571			−0.567854	+	0.823129i	$0.692226\pi$
$522$		0			0
$523$	11.8695			0.519016			0.259508	−	0.965741i	$-0.416440\pi$
$523$	11.8695			0.519016			0.259508	+	0.965741i	$0.416440\pi$
$524$	−1.23726	+	2.14299i	−0.0540499	+	0.0936171i
$525$		0			0
$526$	13.4046	+	23.2174i	0.584467	+	1.01233i
$527$	−8.42391	−	14.5906i	−0.366951	−	0.635578i
$528$		0			0
$529$	−4.18173	+	7.24297i	−0.181814	+	0.314912i
$530$	0.286112	+	0.192016i	0.0124279	+	0.00834064i
$531$		0			0
$532$	0.0278361	−	0.0483441i	0.00120685	−	0.00209598i
$533$	−32.6381	+	56.5308i	−1.41371	+	2.44862i
$534$		0			0
$535$	−1.30676	+	19.3351i	−0.0564961	+	0.835930i
$536$	−11.9504	+	6.89958i	−0.516180	+	0.298017i
$537$		0			0
$538$	−7.08544	+	12.2723i	−0.305475	+	0.529098i
$539$	20.0553	−	11.6416i	0.863841	−	0.501440i
$540$		0			0
$541$	−26.8705			−1.15525			−0.577626	−	0.816301i	$-0.696021\pi$
$541$	−26.8705			−1.15525			−0.577626	+	0.816301i	$0.696021\pi$
$542$	16.5622	+	9.56220i	0.711408	+	0.410732i
$543$		0			0
$544$	−2.41010	+	1.39147i	−0.103332	+	0.0596588i
$545$	−0.712032	+	10.5354i	−0.0305001	+	0.451286i
$546$		0			0
$547$	29.8651	+	17.2426i	1.27694	+	0.737240i	0.976284	−	0.216493i	$-0.0694620\pi$
$547$	29.8651	+	17.2426i	1.27694	+	0.737240i	0.300653	+	0.953733i	$0.402795\pi$
$548$	−13.3698			−0.571129
$549$		0			0
$550$	−15.3285	+	6.27642i	−0.653611	+	0.267627i
$551$	−0.0174668	+	0.0302534i	−0.000744110	+	0.00128884i
$552$		0			0
$553$	0.0125703	+	10.7356i	0.000534544	+	0.456526i
$554$	16.0289	−	9.25427i	0.681002	−	0.393176i
$555$		0			0
$556$	8.17233	+	4.71830i	0.346584	+	0.200100i
$557$	−40.6266			−1.72140			−0.860702	−	0.509109i	$-0.829975\pi$
$557$	−40.6266			−1.72140			−0.860702	+	0.509109i	$0.829975\pi$
$558$		0			0
$559$			14.3775i			0.608103i
$560$	−5.90308	−	0.392015i	−0.249451	−	0.0165657i
$561$		0			0
$562$	−12.3152	+	7.11019i	−0.519486	+	0.299925i
$563$	9.96779	−	5.75491i	0.420092	−	0.242540i	−0.275025	−	0.961437i	$-0.588686\pi$
$563$	9.96779	−	5.75491i	0.420092	−	0.242540i	0.695117	+	0.718897i	$0.255353\pi$
$564$		0			0
$565$	34.8893	−	17.1175i	1.46781	−	0.720137i
$566$	−7.74350			−0.325483
$567$		0			0
$568$			14.4531i			0.606440i
$569$	8.74906	+	5.05127i	0.366780	+	0.211760i	0.672051	−	0.740505i	$-0.265414\pi$
$569$	8.74906	+	5.05127i	0.366780	+	0.211760i	−0.305271	+	0.952266i	$0.598747\pi$
$570$		0			0
$571$	−0.146826	−	0.254309i	−0.00614446	−	0.0106425i	0.862937	−	0.505312i	$-0.168623\pi$
$571$	−0.146826	−	0.254309i	−0.00614446	−	0.0106425i	−0.869081	+	0.494669i	$0.835289\pi$
$572$	16.7530	−	9.67236i	0.700479	−	0.404422i
$573$		0			0
$574$	−25.5957	+	14.8176i	−1.06834	+	0.618477i
$575$	−10.6105	−	25.9134i	−0.442488	−	1.08066i
$576$		0			0
$577$	−26.4319			−1.10038			−0.550188	−	0.835041i	$-0.685444\pi$
$577$	−26.4319			−1.10038			−0.550188	+	0.835041i	$0.685444\pi$
$578$	4.62762	−	8.01527i	0.192484	−	0.333391i
$579$		0			0
$580$	3.69630	+	0.249814i	0.153481	+	0.0103730i
$581$	−35.2934	+	0.0413249i	−1.46422	+	0.00171445i
$582$		0			0
$583$	−0.442094	−	0.255243i	−0.0183096	−	0.0105711i
$584$	0.567999			0.0235040
$585$		0			0
$586$		−	9.88974i		−	0.408542i
$587$	−29.9856	−	17.3122i	−1.23764	−	0.714552i	−0.269028	−	0.963132i	$-0.586703\pi$
$587$	−29.9856	−	17.3122i	−1.23764	−	0.714552i	−0.968611	+	0.248581i	$0.920036\pi$
$588$		0			0
$589$	0.0638235	+	0.110546i	0.00262980	+	0.00455495i
$590$	1.00271	−	14.8364i	0.0412811	−	0.610804i
$591$		0			0
$592$	3.93411	+	2.27136i	0.161691	+	0.0933524i
$593$			25.3186i			1.03971i	0.854255	+	0.519855i	$0.174014\pi$
$593$			25.3186i			1.03971i	−0.854255	+	0.519855i	$0.825986\pi$
$594$		0			0
$595$	−14.7725	+	7.26916i	−0.605612	+	0.298007i
$596$	1.96371	+	1.13375i	0.0804367	+	0.0464401i
$597$		0			0
$598$	16.3514	+	28.3215i	0.668660	+	1.15815i
$599$	19.5167	−	11.2680i	0.797433	−	0.460398i	−0.0451400	−	0.998981i	$-0.514373\pi$
$599$	19.5167	−	11.2680i	0.797433	−	0.460398i	0.842573	+	0.538583i	$0.181040\pi$
$600$		0			0
$601$	39.4649	+	22.7851i	1.60981	+	0.929422i	0.989413	+	0.145131i	$0.0463602\pi$
$601$	39.4649	+	22.7851i	1.60981	+	0.929422i	0.620393	+	0.784291i	$0.286973\pi$
$602$	−3.25047	+	5.64524i	−0.132479	+	0.230083i
$603$		0			0
$604$	11.3616			0.462298
$605$	−0.0515917	+	0.0253120i	−0.00209750	+	0.00102908i
$606$		0			0
$607$	−19.2637	−	33.3657i	−0.781890	−	1.35427i	−0.930839	−	0.365428i	$-0.880922\pi$
$607$	−19.2637	−	33.3657i	−0.781890	−	1.35427i	0.148949	−	0.988845i	$-0.452411\pi$
$608$	0.0182600	−	0.0105424i	0.000740542	−	0.000427552i
$609$		0			0
$610$	8.62976	+	17.5894i	0.349409	+	0.712176i
$611$			26.2772i			1.06306i
$612$		0			0
$613$			3.39696i			0.137202i	0.997644	+	0.0686011i	$0.0218536\pi$
$613$			3.39696i			0.137202i	−0.997644	+	0.0686011i	$0.978146\pi$
$614$	−5.21921	+	9.03994i	−0.210630	+	0.364822i
$615$		0			0
$616$	8.76470	−	0.0102626i	0.353140	−	0.000413490i
$617$	−1.91706	−	3.32044i	−0.0771778	−	0.133676i	0.824853	−	0.565347i	$-0.191258\pi$
$617$	−1.91706	−	3.32044i	−0.0771778	−	0.133676i	−0.902031	+	0.431671i	$0.857924\pi$
$618$		0			0
$619$	19.9022	+	11.4905i	0.799936	+	0.461843i	0.843449	−	0.537210i	$-0.180522\pi$
$619$	19.9022	+	11.4905i	0.799936	+	0.461843i	−0.0435128	+	0.999053i	$0.513855\pi$
$620$	7.54366	−	11.2404i	0.302961	−	0.451424i
$621$		0			0
$622$	5.69741			0.228445
$623$	14.4946	−	8.39109i	0.580713	−	0.336182i
$624$		0			0
$625$	24.0947	+	6.66657i	0.963790	+	0.266663i
$626$	5.43340	+	9.41092i	0.217162	+	0.376136i
$627$		0			0
$628$	−6.02781	+	10.4405i	−0.240536	+	0.416620i
$629$	12.6421			0.504075
$630$		0			0
$631$	−9.64515			−0.383967			−0.191984	−	0.981398i	$-0.561492\pi$
$631$	−9.64515			−0.383967			−0.191984	+	0.981398i	$0.561492\pi$
$632$	−2.02885	+	3.51406i	−0.0807031	+	0.139782i
$633$		0			0
$634$	−15.6097	−	27.0368i	−0.619941	−	1.07377i
$635$	38.2287	+	2.58368i	1.51706	+	0.102530i
$636$		0			0
$637$	40.8762	−	0.0957238i	1.61958	−	0.00379271i
$638$	−5.48859			−0.217295
$639$		0			0
$640$	−1.85669	−	1.24607i	−0.0733923	−	0.0492552i
$641$	13.0157	+	7.51461i	0.514089	+	0.296809i	0.734513	−	0.678595i	$-0.237411\pi$
$641$	13.0157	+	7.51461i	0.514089	+	0.296809i	−0.220424	+	0.975404i	$0.570744\pi$
$642$		0			0
$643$	−1.01830	−	1.76375i	−0.0401578	−	0.0695554i	0.845248	−	0.534374i	$-0.179453\pi$
$643$	−1.01830	−	1.76375i	−0.0401578	−	0.0695554i	−0.885406	+	0.464819i	$0.846119\pi$
$644$	0.0173492	+	14.8170i	0.000683654	+	0.583872i
$645$		0			0
$646$	0.0293390	−	0.0508166i	0.00115433	−	0.00199935i
$647$		−	27.8332i		−	1.09424i	−0.837055	−	0.547118i	$-0.815725\pi$
$647$		−	27.8332i		−	1.09424i	0.837055	−	0.547118i	$-0.184275\pi$
$648$		0			0
$649$			22.0303i			0.864766i
$650$	−28.9319	−	3.92865i	−1.13480	−	0.154095i
$651$		0			0
$652$	−9.81817	+	5.66852i	−0.384509	+	0.221997i
$653$	−0.152462	−	0.264071i	−0.00596629	−	0.0103339i	0.863027	−	0.505158i	$-0.168566\pi$
$653$	−0.152462	−	0.264071i	−0.00596629	−	0.0103339i	−0.868993	+	0.494824i	$0.835232\pi$
$654$		0			0
$655$	−4.96753	+	2.43718i	−0.194097	+	0.0952283i
$656$	−11.1784			−0.436444
$657$		0			0
$658$	−5.94077	+	10.3176i	−0.231595	+	0.402222i
$659$	−33.8347	−	19.5345i	−1.31801	−	0.760955i	−0.334604	−	0.942359i	$-0.608603\pi$
$659$	−33.8347	−	19.5345i	−1.31801	−	0.760955i	−0.983409	+	0.181404i	$0.941936\pi$
$660$		0			0
$661$	−3.76232	+	2.17218i	−0.146337	+	0.0844879i	−0.571381	−	0.820685i	$-0.693592\pi$
$661$	−3.76232	+	2.17218i	−0.146337	+	0.0844879i	0.425044	+	0.905173i	$0.360259\pi$
$662$	−14.8390	−	25.7018i	−0.576732	−	0.998930i
$663$		0			0
$664$	−11.5525	−	6.66983i	−0.448323	−	0.258840i
$665$	0.111923	−	0.0550746i	0.00434019	−	0.00213570i
$666$		0			0
$667$		−	9.27864i		−	0.359270i
$668$	−7.97315	−	4.60330i	−0.308491	−	0.178107i
$669$		0			0
$670$	−30.7857	−	2.08064i	−1.18935	−	0.0803822i
$671$	−14.5131	−	25.1375i	−0.560273	−	0.970421i
$672$		0			0
$673$	−8.16480	−	4.71395i	−0.314730	−	0.181709i	0.334311	−	0.942463i	$-0.391496\pi$
$673$	−8.16480	−	4.71395i	−0.314730	−	0.181709i	−0.649041	+	0.760753i	$0.724830\pi$
$674$			25.8353i			0.995140i
$675$		0			0
$676$	21.0995			0.811520
$677$	−2.59469	−	1.49804i	−0.0997219	−	0.0575745i	0.449310	−	0.893376i	$-0.351670\pi$
$677$	−2.59469	−	1.49804i	−0.0997219	−	0.0575745i	−0.549032	+	0.835802i	$0.685003\pi$
$678$		0			0
$679$	−0.0305598	−	26.0995i	−0.00117278	−	1.00161i
$680$	−6.20868	−	0.419612i	−0.238092	−	0.0160914i
$681$		0			0
$682$	−10.0276	+	17.3684i	−0.383978	+	0.665069i
$683$	22.0783			0.844802			0.422401	−	0.906409i	$-0.361187\pi$
$683$	22.0783			0.844802			0.422401	+	0.906409i	$0.361187\pi$
$684$		0			0
$685$	−24.8236	−	16.6597i	−0.948460	−	0.636533i
$686$	16.0714	+	9.20373i	0.613611	+	0.351400i
$687$		0			0
$688$	−2.13226	+	1.23106i	−0.0812916	+	0.0469337i
$689$	−0.449924	−	0.779291i	−0.0171407	−	0.0296886i
$690$		0			0
$691$	−26.9763	−	15.5748i	−1.02623	−	0.592492i	−0.110325	−	0.993896i	$-0.535189\pi$
$691$	−26.9763	−	15.5748i	−1.02623	−	0.592492i	−0.915901	+	0.401404i	$0.868522\pi$
$692$			19.5446i			0.742975i
$693$		0			0
$694$	11.0532			0.419573
$695$	9.29420	+	18.9437i	0.352549	+	0.718576i
$696$		0			0
$697$	−26.9411	+	15.5544i	−1.02047	+	0.589167i
$698$	−27.9803	+	16.1544i	−1.05907	+	0.611454i
$699$		0			0
$700$	−10.4717	−	8.08349i	−0.395794	−	0.305527i
$701$		−	11.1523i		−	0.421217i	−0.977570	−	0.210609i	$-0.932455\pi$
$701$		−	11.1523i		−	0.421217i	0.977570	−	0.210609i	$-0.0675446\pi$
$702$		0			0
$703$	−0.0957827			−0.00361251
$704$	2.86892	+	1.65637i	0.108127	+	0.0624269i
$705$		0			0
$706$	13.4192	−	7.74759i	0.505039	−	0.291584i
$707$	0.0298028	+	25.4530i	0.00112085	+	0.957258i
$708$		0			0
$709$	21.9499	−	38.0183i	0.824345	−	1.42781i	−0.0780746	−	0.996948i	$-0.524877\pi$
$709$	21.9499	−	38.0183i	0.824345	−	1.42781i	0.902419	−	0.430859i	$-0.141789\pi$
$710$	−18.0096	+	26.8351i	−0.675889	+	1.00710i
$711$		0			0
$712$	6.33024			0.237236
$713$	−29.3618	−	16.9520i	−1.09961	−	0.634859i
$714$		0			0
$715$	43.1577	+	2.91680i	1.61400	+	0.109082i
$716$	3.19745	−	1.84605i	0.119494	−	0.0689901i
$717$		0			0
$718$	−2.54987	−	1.47217i	−0.0951602	−	0.0549408i
$719$	52.2052			1.94692			0.973462	−	0.228848i	$-0.0734958\pi$
$719$	52.2052			1.94692			0.973462	+	0.228848i	$0.0734958\pi$
$720$		0			0
$721$	−42.1916	−	24.2935i	−1.57130	−	0.904737i
$722$	9.49978	−	16.4541i	0.353545	−	0.612358i
$723$		0			0
$724$	−8.51806	+	4.91791i	−0.316571	+	0.182773i
$725$	6.55162	+	5.06968i	0.243321	+	0.188283i
$726$		0			0
$727$	10.8410	−	18.7771i	0.402069	−	0.696404i	−0.591906	−	0.806007i	$-0.701624\pi$
$727$	10.8410	−	18.7771i	0.402069	−	0.696404i	0.993976	+	0.109602i	$0.0349578\pi$
$728$	13.3890	+	7.70923i	0.496228	+	0.285723i
$729$		0			0
$730$	1.05460	+	0.707766i	0.0390325	+	0.0261956i
$731$	−3.42597	+	5.93395i	−0.126714	+	0.219475i
$732$		0			0
$733$	4.27097	+	7.39754i	0.157752	+	0.273234i	0.934058	−	0.357122i	$-0.116242\pi$
$733$	4.27097	+	7.39754i	0.157752	+	0.273234i	−0.776306	+	0.630357i	$0.782909\pi$
$734$	−5.59040	−	9.68286i	−0.206346	−	0.357401i
$735$		0			0
$736$	−2.80015	+	4.85001i	−0.103215	+	0.178774i
$737$	45.7132			1.68387
$738$		0			0
$739$	46.5168			1.71115			0.855575	−	0.517679i	$-0.173204\pi$
$739$	46.5168			1.71115			0.855575	+	0.517679i	$0.173204\pi$
$740$	4.47417	+	9.11940i	0.164474	+	0.335236i
$741$		0			0
$742$	−0.000477378	−	0.407703i	−1.75251e−5	−	0.0149672i
$743$	−7.44987	−	12.9036i	−0.273309	−	0.473386i	0.696398	−	0.717656i	$-0.254785\pi$
$743$	−7.44987	−	12.9036i	−0.273309	−	0.473386i	−0.969707	+	0.244270i	$0.921452\pi$
$744$		0			0
$745$	2.23328	+	4.55194i	0.0818210	+	0.166770i
$746$			24.0766i			0.881507i
$747$		0			0
$748$	9.21918			0.337087
$749$	19.8443	−	11.4881i	0.725097	−	0.419768i
$750$		0			0
$751$	−18.2600	−	31.6273i	−0.666317	−	1.15410i	−0.978926	−	0.204213i	$-0.934536\pi$
$751$	−18.2600	−	31.6273i	−0.666317	−	1.15410i	0.312609	−	0.949882i	$-0.398797\pi$
$752$	−3.89705	+	2.24996i	−0.142111	+	0.0820477i
$753$		0			0
$754$	−8.37871	−	4.83745i	−0.305135	−	0.176170i
$755$	21.0951	+	14.1574i	0.767728	+	0.515239i
$756$		0			0
$757$		−	2.35490i		−	0.0855903i	−0.999084	−	0.0427951i	$-0.986374\pi$
$757$		−	2.35490i		−	0.0855903i	0.999084	−	0.0427951i	$-0.0136263\pi$
$758$	−0.649773	+	1.12544i	−0.0236008	+	0.0408778i
$759$		0			0
$760$	0.0470399	+	0.00317918i	0.00170632	+	0.000115321i
$761$	−17.6608	−	30.5893i	−0.640202	−	1.10886i	−0.985387	−	0.170328i	$-0.945517\pi$
$761$	−17.6608	−	30.5893i	−0.640202	−	1.10886i	0.345185	−	0.938535i	$-0.387816\pi$
$762$		0			0
$763$	10.8129	−	6.25970i	0.391452	−	0.226616i
$764$		−	24.5063i		−	0.886606i
$765$		0			0
$766$		−	25.7518i		−	0.930449i
$767$	−19.4168	+	33.6308i	−0.701098	+	1.21434i
$768$		0			0
$769$	26.9721	−	15.5724i	0.972640	−	0.561554i	0.0726000	−	0.997361i	$-0.476870\pi$
$769$	26.9721	−	15.5724i	0.972640	−	0.561554i	0.900040	+	0.435807i	$0.143537\pi$
$770$	16.2862	+	10.9024i	0.586912	+	0.392894i
$771$		0			0
$772$	17.4708	+	10.0868i	0.628787	+	0.363030i
$773$		−	12.0111i		−	0.432011i	−0.976392	−	0.216005i	$-0.930697\pi$
$773$		−	12.0111i		−	0.432011i	0.976392	−	0.216005i	$-0.0693028\pi$
$774$		0			0
$775$	28.0125	−	11.4700i	1.00624	−	0.412014i
$776$	4.93235	−	8.54307i	0.177061	−	0.306678i
$777$		0			0
$778$	19.9368	−	11.5105i	0.714768	−	0.412672i
$779$	0.204118	−	0.117848i	0.00731330	−	0.00422233i
$780$		0			0
$781$	23.9398	−	41.4650i	0.856634	−	1.48373i
$782$			15.5853i			0.557330i
$783$		0			0
$784$	3.51419	+	6.05396i	0.125507	+	0.216213i
$785$	−24.2013	+	11.8737i	−0.863782	+	0.423790i
$786$		0			0
$787$	27.0080	+	46.7792i	0.962731	+	1.66750i	0.715590	+	0.698520i	$0.246158\pi$
$787$	27.0080	+	46.7792i	0.962731	+	1.66750i	0.247141	+	0.968980i	$0.420509\pi$
$788$	−6.12176	−	10.6032i	−0.218079	−	0.377723i
$789$		0			0
$790$	−8.14571	+	3.99646i	−0.289811	+	0.142188i
$791$	−39.8488	−	22.9446i	−1.41686	−	0.815815i
$792$		0			0
$793$		−	51.1654i		−	1.81694i
$794$	−6.90427	+	11.9585i	−0.245023	+	0.424393i
$795$		0			0
$796$	4.01234	−	2.31652i	0.142213	−	0.0821070i
$797$	−11.0584	+	6.38454i	−0.391707	+	0.226152i	−0.682899	−	0.730512i	$-0.739281\pi$
$797$	−11.0584	+	6.38454i	−0.391707	+	0.226152i	0.291193	+	0.956664i	$0.405948\pi$
$798$		0			0
$799$	−6.26152	+	10.8453i	−0.221517	+	0.383678i
$800$	−1.89463	−	4.62714i	−0.0669851	−	0.163594i
$801$		0			0
$802$		−	22.8206i		−	0.805824i
$803$	−1.62955	−	0.940819i	−0.0575055	−	0.0332008i
$804$		0			0
$805$	−18.4308	+	27.5323i	−0.649601	+	0.970385i
$806$	−30.6157	+	17.6760i	−1.07839	+	0.622610i
$807$		0			0
$808$	−4.81017	+	8.33145i	−0.169221	+	0.293100i
$809$		−	24.6158i		−	0.865445i	−0.901527	−	0.432723i	$-0.857553\pi$
$809$		−	24.6158i		−	0.865445i	0.901527	−	0.432723i	$-0.142447\pi$
$810$		0			0
$811$			7.06824i			0.248199i	0.992270	+	0.124100i	$0.0396043\pi$
$811$			7.06824i			0.248199i	−0.992270	+	0.124100i	$0.960396\pi$
$812$	−2.19620	−	3.79366i	−0.0770713	−	0.133131i
$813$		0			0
$814$	−7.52445	−	13.0327i	−0.263732	−	0.456797i
$815$	−25.2927	−	1.70940i	−0.885965	−	0.0598778i
$816$		0			0
$817$	0.0259567	−	0.0449584i	0.000908111	−	0.00157289i
$818$		−	6.38150i		−	0.223124i
$819$		0			0
$820$	−20.7549	−	13.9291i	−0.724793	−	0.486425i
$821$	−26.9629	−	15.5670i	−0.941012	−	0.543293i	−0.0507345	−	0.998712i	$-0.516156\pi$
$821$	−26.9629	−	15.5670i	−0.941012	−	0.543293i	−0.890277	+	0.455419i	$0.849490\pi$
$822$		0			0
$823$	−19.9909	+	11.5418i	−0.696840	+	0.402321i	−0.806170	−	0.591685i	$-0.798463\pi$
$823$	−19.9909	+	11.5418i	−0.696840	+	0.402321i	0.109329	+	0.994006i	$0.465130\pi$
$824$	−9.20075	−	15.9362i	−0.320523	−	0.555163i
$825$		0			0
$826$	−15.2271	+	8.81518i	−0.529820	+	0.306719i
$827$	17.5943			0.611814			0.305907	−	0.952061i	$-0.401040\pi$
$827$	17.5943			0.611814			0.305907	+	0.952061i	$0.401040\pi$
$828$		0			0
$829$		−	34.9888i		−	1.21521i	−0.794239	−	0.607605i	$-0.792130\pi$
$829$		−	34.9888i		−	1.21521i	0.794239	−	0.607605i	$-0.207870\pi$
$830$	−13.1384	−	26.7790i	−0.456039	−	0.929513i
$831$		0			0
$832$	2.91974	+	5.05714i	0.101224	+	0.175325i
$833$	16.8934	+	9.70076i	0.585323	+	0.336111i
$834$		0			0
$835$	−9.06768	−	18.4820i	−0.313800	−	0.639597i
$836$	−0.0698488			−0.00241577
$837$		0			0
$838$	−1.87508			−0.0647734
$839$	1.56260	−	2.70651i	0.0539470	−	0.0934390i	−0.837791	−	0.545991i	$-0.816153\pi$
$839$	1.56260	−	2.70651i	0.0539470	−	0.0934390i	0.891738	+	0.452552i	$0.149486\pi$
$840$		0			0
$841$	−13.1275	−	22.7375i	−0.452672	−	0.784051i
$842$	5.71561	+	9.89973i	0.196973	+	0.341167i
$843$		0			0
$844$	0.00959279	−	0.0166152i	0.000330198	−	0.000571919i
$845$	39.1753	+	26.2914i	1.34767	+	0.904453i
$846$		0			0
$847$	0.0589254	+	0.0339287i	0.00202470	+	0.00116580i
$848$	0.0770487	−	0.133452i	0.00264586	−	0.00458277i
$849$		0			0
$850$	−11.0048	−	8.51554i	−0.377460	−	0.292080i
$851$	22.0323	−	12.7203i	0.755256	−	0.436047i
$852$		0			0
$853$	18.8954	−	32.7278i	0.646967	−	1.12058i	−0.336877	−	0.941549i	$-0.609371\pi$
$853$	18.8954	−	32.7278i	0.646967	−	1.12058i	0.983844	−	0.179030i	$-0.0572960\pi$
$854$	11.5675	−	20.0898i	0.395832	−	0.687458i
$855$		0			0
$856$	8.66665			0.296220
$857$	22.7409	+	13.1295i	0.776815	+	0.448495i	0.835300	−	0.549794i	$-0.185294\pi$
$857$	22.7409	+	13.1295i	0.776815	+	0.448495i	−0.0584850	+	0.998288i	$0.518627\pi$
$858$		0			0
$859$	24.1275	−	13.9300i	0.823221	−	0.475287i	−0.0283052	−	0.999599i	$-0.509011\pi$
$859$	24.1275	−	13.9300i	0.823221	−	0.475287i	0.851526	+	0.524313i	$0.175678\pi$
$860$	−5.49294	−	0.371239i	−0.187308	−	0.0126591i
$861$		0			0
$862$	−20.9344	−	12.0865i	−0.713030	−	0.411668i
$863$	1.59730			0.0543727			0.0271864	−	0.999630i	$-0.491345\pi$
$863$	1.59730			0.0543727			0.0271864	+	0.999630i	$0.491345\pi$
$864$		0			0
$865$	−24.3539	+	36.2884i	−0.828059	+	1.23384i
$866$	−5.64211	+	9.77243i	−0.191727	+	0.332081i
$867$		0			0
$868$	−16.0173	+	0.0187546i	−0.543662	+	0.000636571i
$869$	11.6412	−	6.72105i	0.394901	−	0.227996i
$870$		0			0
$871$	69.7843	+	40.2900i	2.36455	+	1.36517i
$872$	4.72231			0.159918
$873$		0			0
$874$		−	0.118082i		−	0.00399417i
$875$	−9.37021	−	28.0571i	−0.316771	−	0.948502i
$876$		0			0
$877$	33.5915	−	19.3941i	1.13431	−	0.654892i	0.189292	−	0.981921i	$-0.439381\pi$
$877$	33.5915	−	19.3941i	1.13431	−	0.654892i	0.945014	+	0.327029i	$0.106048\pi$
$878$	−17.1147	+	9.88117i	−0.577593	+	0.333473i
$879$		0			0
$880$	3.26276	+	6.65026i	0.109988	+	0.224180i
$881$	22.6988			0.764741			0.382370	−	0.924009i	$-0.375108\pi$
$881$	22.6988			0.764741			0.382370	+	0.924009i	$0.375108\pi$
$882$		0			0
$883$		−	2.88769i		−	0.0971784i	−0.998819	−	0.0485892i	$-0.984527\pi$
$883$		−	2.88769i		−	0.0971784i	0.998819	−	0.0485892i	$-0.0154725\pi$
$884$	14.0737	+	8.12546i	0.473350	+	0.273289i
$885$		0			0
$886$	−5.98704	−	10.3699i	−0.201139	−	0.348382i
$887$	−41.2357	+	23.8075i	−1.38456	+	0.799376i	−0.992696	−	0.120647i	$-0.961503\pi$
$887$	−41.2357	+	23.8075i	−1.38456	+	0.799376i	−0.391865	+	0.920023i	$0.628170\pi$
$888$		0			0
$889$	−22.7140	−	39.2356i	−0.761802	−	1.31592i
$890$	11.7533	+	7.88791i	0.393972	+	0.264403i
$891$		0			0
$892$	−6.44552			−0.215812
$893$	0.0474402	−	0.0821688i	0.00158752	−	0.00274967i
$894$		0			0
$895$	8.23699	+	0.556695i	0.275332	+	0.0186083i
$896$	0.00309790	+	2.64575i	0.000103494	+	0.0883883i
$897$		0			0
$898$	3.33102	+	1.92317i	0.111158	+	0.0641769i
$899$	10.0303			0.334528
$900$		0			0
$901$		−	0.428844i		−	0.0142869i
$902$	32.0701	+	18.5157i	1.06782	+	0.616504i
$903$		0			0
$904$	−8.68986	−	15.0513i	−0.289020	−	0.500598i
$905$	−21.9435	−	1.48305i	−0.729426	−	0.0492981i
$906$		0			0
$907$	−32.4514	−	18.7358i	−1.07753	−	0.622113i	−0.147302	−	0.989092i	$-0.547059\pi$
$907$	−32.4514	−	18.7358i	−1.07753	−	0.622113i	−0.930229	+	0.366979i	$0.880392\pi$
$908$		−	0.215922i		−	0.00716564i
$909$		0			0
$910$	15.2530	+	30.9973i	0.505631	+	1.02755i
$911$	−38.1165	−	22.0066i	−1.26286	−	0.729111i	−0.289231	−	0.957259i	$-0.593400\pi$
$911$	−38.1165	−	22.0066i	−1.26286	−	0.729111i	−0.973626	+	0.228148i	$0.926733\pi$
$912$		0			0
$913$	22.0955	+	38.2705i	0.731253	+	1.26657i
$914$	−5.42777	+	3.13372i	−0.179535	+	0.103654i
$915$		0			0
$916$	−13.7857	−	7.95917i	−0.455492	−	0.262978i
$917$	5.67366	+	3.26684i	0.187361	+	0.107880i
$918$		0			0
$919$	32.6919			1.07841			0.539203	−	0.842176i	$-0.318725\pi$
$919$	32.6919			1.07841			0.539203	+	0.842176i	$0.318725\pi$
$920$	−11.2425	+	5.51580i	−0.370653	+	0.181851i
$921$		0			0
$922$	6.72032	+	11.6399i	0.221322	+	0.383341i
$923$	73.0915	−	42.1994i	2.40584	−	1.38901i
$924$		0			0
$925$	−3.05623	+	22.5071i	−0.100488	+	0.740028i
$926$			21.0054i			0.690281i
$927$		0			0
$928$		−	1.65681i		−	0.0543874i
$929$	16.0115	−	27.7328i	0.525321	−	0.909882i	−0.474244	−	0.880393i	$-0.657279\pi$
$929$	16.0115	−	27.7328i	0.525321	−	0.909882i	0.999565	−	0.0294890i	$-0.00938799\pi$
$930$		0			0
$931$	−0.127993	−	0.0734975i	−0.00419479	−	0.00240878i
$932$	−3.07997	−	5.33466i	−0.100888	−	0.174742i
$933$		0			0
$934$	−9.30637	−	5.37304i	−0.304514	−	0.175811i
$935$	17.1172	+	11.4877i	0.559792	+	0.375689i
$936$		0			0
$937$	−1.71222			−0.0559359			−0.0279680	−	0.999609i	$-0.508904\pi$
$937$	−1.71222			−0.0559359			−0.0279680	+	0.999609i	$0.508904\pi$
$938$	18.2916	+	31.5965i	0.597242	+	1.03166i
$939$		0			0
$940$	−10.0392	−	0.678500i	−0.327444	−	0.0221302i
$941$	27.4368	+	47.5220i	0.894415	+	1.54917i	0.834527	+	0.550968i	$0.185741\pi$
$941$	27.4368	+	47.5220i	0.894415	+	1.54917i	0.0598886	+	0.998205i	$0.480925\pi$
$942$		0			0
$943$	−31.3013	+	54.2155i	−1.01931	+	1.76550i
$944$	−6.65017			−0.216445
$945$		0			0
$946$	8.15639			0.265187
$947$	12.9347	−	22.4036i	0.420322	−	0.728019i	−0.575649	−	0.817697i	$-0.695250\pi$
$947$	12.9347	−	22.4036i	0.420322	−	0.728019i	0.995971	+	0.0896780i	$0.0285838\pi$
$948$		0			0
$949$	−1.65841	−	2.87245i	−0.0538343	−	0.0932437i
$950$	0.0833771	+	0.0645177i	0.00270511	+	0.00209323i
$951$		0			0
$952$	3.68895	+	6.37220i	0.119560	+	0.206524i
$953$	−7.01251			−0.227158			−0.113579	−	0.993529i	$-0.536231\pi$
$953$	−7.01251			−0.227158			−0.113579	+	0.993529i	$0.536231\pi$
$954$		0			0
$955$	30.5365	−	45.5006i	0.988138	−	1.47237i
$956$	11.9037	+	6.87261i	0.384994	+	0.222276i
$957$		0			0
$958$	−3.20350	−	5.54862i	−0.103500	−	0.179268i
$959$	0.0414182	+	35.3731i	0.00133746	+	1.14226i
$960$		0			0
$961$	2.82525	−	4.89347i	0.0911370	−	0.157854i
$962$		−	26.5271i		−	0.855269i
$963$		0			0
$964$			15.6105i			0.502780i
$965$	19.8691	+	40.4978i	0.639609	+	1.30367i
$966$		0			0
$967$	−33.0101	+	19.0584i	−1.06153	+	0.612877i	−0.925856	−	0.377876i	$-0.876654\pi$
$967$	−33.0101	+	19.0584i	−1.06153	+	0.612877i	−0.135677	+	0.990753i	$0.543321\pi$
$968$	0.0128499	+	0.0222567i	0.000413012	+	0.000715357i
$969$		0			0
$970$	19.8031	−	9.71583i	0.635840	−	0.311957i
$971$	16.6238			0.533484			0.266742	−	0.963768i	$-0.414053\pi$
$971$	16.6238			0.533484			0.266742	+	0.963768i	$0.414053\pi$
$972$		0			0
$973$	12.4581	−	21.6366i	0.399389	−	0.693636i
$974$	−12.8218	−	7.40268i	−0.410837	−	0.237197i
$975$		0			0
$976$	7.58810	−	4.38099i	0.242889	−	0.140232i
$977$	22.9139	+	39.6880i	0.733080	+	1.26973i	0.955561	+	0.294795i	$0.0952512\pi$
$977$	22.9139	+	39.6880i	0.733080	+	1.26973i	−0.222481	+	0.974937i	$0.571415\pi$
$978$		0			0
$979$	−18.1610	−	10.4852i	−0.580427	−	0.335110i
$980$	−1.01889	+	15.6193i	−0.0325472	+	0.498940i
$981$		0			0
$982$		−	13.1030i		−	0.418134i
$983$	−18.7423	−	10.8209i	−0.597787	−	0.345132i	0.170384	−	0.985378i	$-0.445499\pi$
$983$	−18.7423	−	10.8209i	−0.597787	−	0.345132i	−0.768170	+	0.640246i	$0.778833\pi$
$984$		0			0
$985$	1.84608	−	27.3150i	0.0588210	−	0.870329i
$986$	−2.30540	−	3.99307i	−0.0734189	−	0.127165i
$987$		0			0
$988$	−0.106629	−	0.0615623i	−0.00339232	−	0.00195856i
$989$			13.7886i			0.438453i
$990$		0			0
$991$	−37.0001			−1.17535			−0.587674	−	0.809098i	$-0.699956\pi$
$991$	−37.0001			−1.17535			−0.587674	+	0.809098i	$0.699956\pi$
$992$	−5.24289	−	3.02698i	−0.166462	−	0.0961068i
$993$		0			0
$994$	38.2394	−	0.0447744i	1.21288	−	0.00142016i
$995$	10.3362	+	0.698572i	0.327680	+	0.0221462i
$996$		0			0
$997$	11.4148	−	19.7710i	0.361510	−	0.626153i	−0.626700	−	0.779261i	$-0.715595\pi$
$997$	11.4148	−	19.7710i	0.361510	−	0.626153i	0.988210	+	0.153108i	$0.0489281\pi$
$998$	43.9560			1.39140
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bf.f.629.9		32
3.2	odd	2		630.2.bf.e.209.2	✓	32
5.4	even	2		1890.2.bf.e.629.5		32
7.6	odd	2	inner	1890.2.bf.f.629.8		32
9.4	even	3		630.2.bf.f.419.2	yes	32
9.5	odd	6		1890.2.bf.e.1259.12		32
15.14	odd	2		630.2.bf.f.209.15	yes	32
21.20	even	2		630.2.bf.e.209.15	yes	32
35.34	odd	2		1890.2.bf.e.629.12		32
45.4	even	6		630.2.bf.e.419.15	yes	32
45.14	odd	6	inner	1890.2.bf.f.1259.8		32
63.13	odd	6		630.2.bf.f.419.15	yes	32
63.41	even	6		1890.2.bf.e.1259.5		32
105.104	even	2		630.2.bf.f.209.2	yes	32
315.104	even	6	inner	1890.2.bf.f.1259.9		32
315.139	odd	6		630.2.bf.e.419.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bf.e.209.2	✓	32	3.2	odd	2
630.2.bf.e.209.15	yes	32	21.20	even	2
630.2.bf.e.419.2	yes	32	315.139	odd	6
630.2.bf.e.419.15	yes	32	45.4	even	6
630.2.bf.f.209.2	yes	32	105.104	even	2
630.2.bf.f.209.15	yes	32	15.14	odd	2
630.2.bf.f.419.2	yes	32	9.4	even	3
630.2.bf.f.419.15	yes	32	63.13	odd	6
1890.2.bf.e.629.5		32	5.4	even	2
1890.2.bf.e.629.12		32	35.34	odd	2
1890.2.bf.e.1259.5		32	63.41	even	6
1890.2.bf.e.1259.12		32	9.5	odd	6
1890.2.bf.f.629.8		32	7.6	odd	2	inner
1890.2.bf.f.629.9		32	1.1	even	1	trivial
1890.2.bf.f.1259.8		32	45.14	odd	6	inner
1890.2.bf.f.1259.9		32	315.104	even	6	inner

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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.bf (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.150780 - 2.23098i) q^{5} +(-2.28974 + 1.32556i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.150780 - 2.23098i) q^{5} +(-2.28974 + 1.32556i) q^{7} -1.00000 q^{8} +(-1.85669 - 1.24607i) q^{10} +(2.86892 + 1.65637i) q^{11} +(2.91974 + 5.05714i) q^{13} +(0.00309790 + 2.64575i) q^{14} +(-0.500000 + 0.866025i) q^{16} +2.78294i q^{17} -0.0210849i q^{19} +(-2.00747 + 0.984910i) q^{20} +(2.86892 - 1.65637i) q^{22} +(2.80015 + 4.85001i) q^{23} +(-4.95453 - 0.672775i) q^{25} +5.83948 q^{26} +(2.29284 + 1.32019i) q^{28} +(-1.43484 - 0.828404i) q^{29} +(-5.24289 + 3.02698i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.41010 + 1.39147i) q^{34} +(2.61204 + 5.30822i) q^{35} -4.54272i q^{37} +(-0.0182600 - 0.0105424i) q^{38} +(-0.150780 + 2.23098i) q^{40} +(5.58921 + 9.68080i) q^{41} +(2.13226 + 1.23106i) q^{43} -3.31275i q^{44} +5.60031 q^{46} +(3.89705 + 2.24996i) q^{47} +(3.48579 - 6.07036i) q^{49} +(-3.05991 + 3.95436i) q^{50} +(2.91974 - 5.05714i) q^{52} -0.154097 q^{53} +(4.12791 - 6.15076i) q^{55} +(2.28974 - 1.32556i) q^{56} +(-1.43484 + 0.828404i) q^{58} +(3.32508 + 5.75921i) q^{59} +(-7.58810 - 4.38099i) q^{61} +6.05396i q^{62} +1.00000 q^{64} +(11.7226 - 5.75136i) q^{65} +(11.9504 - 6.89958i) q^{67} +(2.41010 - 1.39147i) q^{68} +(5.90308 + 0.392015i) q^{70} -14.4531i q^{71} -0.567999 q^{73} +(-3.93411 - 2.27136i) q^{74} +(-0.0182600 + 0.0105424i) q^{76} +(-8.76470 + 0.0102626i) q^{77} +(2.02885 - 3.51406i) q^{79} +(1.85669 + 1.24607i) q^{80} +11.1784 q^{82} +(11.5525 + 6.66983i) q^{83} +(6.20868 + 0.419612i) q^{85} +(2.13226 - 1.23106i) q^{86} +(-2.86892 - 1.65637i) q^{88} -6.33024 q^{89} +(-13.3890 - 7.70923i) q^{91} +(2.80015 - 4.85001i) q^{92} +(3.89705 - 2.24996i) q^{94} +(-0.0470399 - 0.00317918i) q^{95} +(-4.93235 + 8.54307i) q^{97} +(-3.51419 - 6.05396i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8}+O(q^{10}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 24 q^{11} - 16 q^{16} + 24 q^{22} + 24 q^{23} - 58 q^{25} + 36 q^{29} + 16 q^{32} + 48 q^{35} - 54 q^{43} + 48 q^{46} + 32 q^{49} - 50 q^{50} + 24 q^{53} + 36 q^{58} + 32 q^{64} + 90 q^{65} - 66 q^{67} + 36 q^{70} - 12 q^{74} - 18 q^{77} + 34 q^{79} + 4 q^{85} - 54 q^{86} - 24 q^{88} + 16 q^{91} + 24 q^{92} - 12 q^{95} + 64 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 24 * q^11 - 16 * q^16 + 24 * q^22 + 24 * q^23 - 58 * q^25 + 36 * q^29 + 16 * q^32 + 48 * q^35 - 54 * q^43 + 48 * q^46 + 32 * q^49 - 50 * q^50 + 24 * q^53 + 36 * q^58 + 32 * q^64 + 90 * q^65 - 66 * q^67 + 36 * q^70 - 12 * q^74 - 18 * q^77 + 34 * q^79 + 4 * q^85 - 54 * q^86 - 24 * q^88 + 16 * q^91 + 24 * q^92 - 12 * q^95 + 64 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more