LMFDB - Embedded newform 108.6.b.b.107.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,6,Mod(107,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("108.107");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	108.b (of order $2$, degree $1$, 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:	$17.3214525398$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 30x^{14} + 619x^{12} + 5604x^{10} + 40971x^{8} - 4866x^{6} + 568069x^{4} - 7909632x^{2} + 20340100 $ x^16 + 30x^14 + 619x^12 + 5604x^10 + 40971x^8 - 4866x^6 + 568069x^4 - 7909632*x^2 + 20340100
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{30}\cdot 3^{32}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			107.12
Root			$1.73205 + 3.22829i$ of defining polynomial
Character	$\chi$	$=$	108.107
Dual form			108.6.b.b.107.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.82945 + 4.16357i) q^{2} +(-2.67058 + 31.8884i) q^{4} -46.0468i q^{5} -134.772i q^{7} +(-142.996 + 110.996i) q^{8} +O(q^{10})$	\(q+(3.82945 + 4.16357i) q^{2} +(-2.67058 + 31.8884i) q^{4} -46.0468i q^{5} -134.772i q^{7} +(-142.996 + 110.996i) q^{8} +(191.719 - 176.334i) q^{10} -471.524 q^{11} -987.091 q^{13} +(561.131 - 516.102i) q^{14} +(-1009.74 - 170.321i) q^{16} -1467.20i q^{17} -308.416i q^{19} +(1468.36 + 122.972i) q^{20} +(-1805.68 - 1963.22i) q^{22} +2118.55 q^{23} +1004.70 q^{25} +(-3780.02 - 4109.82i) q^{26} +(4297.65 + 359.919i) q^{28} -5196.05i q^{29} +6363.26i q^{31} +(-3157.59 - 4856.34i) q^{32} +(6108.79 - 5618.57i) q^{34} -6205.80 q^{35} -8747.55 q^{37} +(1284.11 - 1181.07i) q^{38} +(5111.00 + 6584.51i) q^{40} -1393.48i q^{41} +9414.92i q^{43} +(1259.24 - 15036.1i) q^{44} +(8112.88 + 8820.71i) q^{46} +11122.7 q^{47} -1356.43 q^{49} +(3847.44 + 4183.12i) q^{50} +(2636.11 - 31476.7i) q^{52} -28464.4i q^{53} +21712.2i q^{55} +(14959.1 + 19271.9i) q^{56} +(21634.1 - 19898.0i) q^{58} -15062.9 q^{59} -37841.4 q^{61} +(-26493.9 + 24367.8i) q^{62} +(8127.84 - 31744.0i) q^{64} +45452.3i q^{65} +65223.3i q^{67} +(46786.6 + 3918.28i) q^{68} +(-23764.8 - 25838.3i) q^{70} -9860.03 q^{71} -54858.1 q^{73} +(-33498.3 - 36421.0i) q^{74} +(9834.89 + 823.651i) q^{76} +63548.2i q^{77} -91648.1i q^{79} +(-7842.73 + 46495.1i) q^{80} +(5801.85 - 5336.27i) q^{82} +45138.1 q^{83} -67559.8 q^{85} +(-39199.7 + 36054.0i) q^{86} +(67426.2 - 52337.3i) q^{88} +73149.6i q^{89} +133032. i q^{91} +(-5657.75 + 67557.0i) q^{92} +(42593.8 + 46310.0i) q^{94} -14201.6 q^{95} -11422.1 q^{97} +(-5194.40 - 5647.60i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 94 q^{4}+O(q^{10}) $ 16 * q + 94 * q^4	$ 16 q + 94 q^{4} + 1454 q^{10} + 896 q^{13} + 178 q^{16} + 30 q^{22} + 9888 q^{25} + 11454 q^{28} - 6172 q^{34} - 71008 q^{37} - 16618 q^{40} + 35304 q^{46} - 49376 q^{49} + 14876 q^{52} - 10492 q^{58} + 77888 q^{61} + 89206 q^{64} + 229398 q^{70} - 38032 q^{73} + 48960 q^{76} - 224488 q^{82} - 371264 q^{85} + 249102 q^{88} + 68772 q^{94} - 976 q^{97}+O(q^{100}) $ 16 * q + 94 * q^4 + 1454 * q^10 + 896 * q^13 + 178 * q^16 + 30 * q^22 + 9888 * q^25 + 11454 * q^28 - 6172 * q^34 - 71008 * q^37 - 16618 * q^40 + 35304 * q^46 - 49376 * q^49 + 14876 * q^52 - 10492 * q^58 + 77888 * q^61 + 89206 * q^64 + 229398 * q^70 - 38032 * q^73 + 48960 * q^76 - 224488 * q^82 - 371264 * q^85 + 249102 * q^88 + 68772 * q^94 - 976 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$-1$	$-1$

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 $

$2$	3.82945	+	4.16357i	0.676958	+	0.736022i
$2$	3.82945	+	4.16357i	0.676958	+	0.736022i
$3$		0			0
$3$		0			0
$4$	−2.67058	+	31.8884i	−0.0834557	+	0.996511i
$5$		−	46.0468i		−	0.823709i	−0.911250	−	0.411855i	$-0.864881\pi$
$5$		−	46.0468i		−	0.823709i	0.911250	−	0.411855i	$-0.135119\pi$
$6$		0			0
$7$		−	134.772i		−	1.03957i	−0.854297	−	0.519785i	$-0.826012\pi$
$7$		−	134.772i		−	1.03957i	0.854297	−	0.519785i	$-0.173988\pi$
$8$	−142.996	+	110.996i	−0.789950	+	0.613171i
$9$		0			0
$10$	191.719	−	176.334i	0.606268	−	0.557617i
$11$	−471.524			−1.17496			−0.587479	−	0.809239i	$-0.699880\pi$
$11$	−471.524			−1.17496			−0.587479	+	0.809239i	$0.699880\pi$
$12$		0			0
$13$	−987.091			−1.61994			−0.809970	−	0.586471i	$-0.800517\pi$
$13$	−987.091			−1.61994			−0.809970	+	0.586471i	$0.800517\pi$
$14$	561.131	−	516.102i	0.765146	−	0.703745i
$15$		0			0
$16$	−1009.74	−	170.321i	−0.986070	−	0.166329i
$17$		−	1467.20i		−	1.23131i	−0.788016	−	0.615654i	$-0.788892\pi$
$17$		−	1467.20i		−	1.23131i	0.788016	−	0.615654i	$-0.211108\pi$
$18$		0			0
$19$		−	308.416i		−	0.195999i	−0.995186	−	0.0979994i	$-0.968756\pi$
$19$		−	308.416i		−	0.195999i	0.995186	−	0.0979994i	$-0.0312443\pi$
$20$	1468.36	+	122.972i	0.820836	+	0.0687432i
$21$		0			0
$22$	−1805.68	−	1963.22i	−0.795397	−	0.864795i
$23$	2118.55			0.835062			0.417531	−	0.908663i	$-0.362896\pi$
$23$	2118.55			0.835062			0.417531	+	0.908663i	$0.362896\pi$
$24$		0			0
$25$	1004.70			0.321503
$26$	−3780.02	−	4109.82i	−1.09663	−	1.19231i
$27$		0			0
$28$	4297.65	+	359.919i	1.03594	+	0.0867580i
$29$		−	5196.05i		−	1.14730i	−0.819100	−	0.573651i	$-0.805526\pi$
$29$		−	5196.05i		−	1.14730i	0.819100	−	0.573651i	$-0.194474\pi$
$30$		0			0
$31$			6363.26i			1.18926i	0.804001	+	0.594628i	$0.202701\pi$
$31$			6363.26i			1.18926i	−0.804001	+	0.594628i	$0.797299\pi$
$32$	−3157.59	−	4856.34i	−0.545106	−	0.838367i
$33$		0			0
$34$	6108.79	−	5618.57i	0.906270	−	0.833544i
$35$	−6205.80			−0.856304
$36$		0			0
$37$	−8747.55			−1.05047			−0.525233	−	0.850958i	$-0.676022\pi$
$37$	−8747.55			−1.05047			−0.525233	+	0.850958i	$0.676022\pi$
$38$	1284.11	−	1181.07i	0.144259	−	0.132683i
$39$		0			0
$40$	5111.00	+	6584.51i	0.505075	+	0.650689i
$41$		−	1393.48i		−	0.129462i	−0.997903	−	0.0647308i	$-0.979381\pi$
$41$		−	1393.48i		−	0.129462i	0.997903	−	0.0647308i	$-0.0206189\pi$
$42$		0			0
$43$			9414.92i			0.776508i	0.921552	+	0.388254i	$0.126922\pi$
$43$			9414.92i			0.776508i	−0.921552	+	0.388254i	$0.873078\pi$
$44$	1259.24	−	15036.1i	0.0980569	−	1.17086i
$45$		0			0
$46$	8112.88	+	8820.71i	0.565302	+	0.614623i
$47$	11122.7			0.734454			0.367227	−	0.930131i	$-0.380307\pi$
$47$	11122.7			0.734454			0.367227	+	0.930131i	$0.380307\pi$
$48$		0			0
$49$	−1356.43			−0.0807064
$50$	3847.44	+	4183.12i	0.217644	+	0.236633i
$51$		0			0
$52$	2636.11	−	31476.7i	0.135193	−	1.61429i
$53$		−	28464.4i		−	1.39191i	−0.718084	−	0.695957i	$-0.754981\pi$
$53$		−	28464.4i		−	1.39191i	0.718084	−	0.695957i	$-0.245019\pi$
$54$		0			0
$55$			21712.2i			0.967824i
$56$	14959.1	+	19271.9i	0.637435	+	0.821209i
$57$		0			0
$58$	21634.1	−	19898.0i	0.844439	−	0.776676i
$59$	−15062.9			−0.563351			−0.281676	−	0.959510i	$-0.590890\pi$
$59$	−15062.9			−0.563351			−0.281676	+	0.959510i	$0.590890\pi$
$60$		0			0
$61$	−37841.4			−1.30209			−0.651047	−	0.759037i	$-0.725670\pi$
$61$	−37841.4			−1.30209			−0.651047	+	0.759037i	$0.725670\pi$
$62$	−26493.9	+	24367.8i	−0.875319	+	0.805077i
$63$		0			0
$64$	8127.84	−	31744.0i	0.248042	−	0.968749i
$65$			45452.3i			1.33436i
$66$		0			0
$67$			65223.3i			1.77507i	0.460740	+	0.887535i	$0.347584\pi$
$67$			65223.3i			1.77507i	−0.460740	+	0.887535i	$0.652416\pi$
$68$	46786.6	+	3918.28i	1.22701	+	0.102760i
$69$		0			0
$70$	−23764.8	−	25838.3i	−0.579682	−	0.630258i
$71$	−9860.03			−0.232131			−0.116065	−	0.993242i	$-0.537028\pi$
$71$	−9860.03			−0.232131			−0.116065	+	0.993242i	$0.537028\pi$
$72$		0			0
$73$	−54858.1			−1.20485			−0.602426	−	0.798175i	$-0.705799\pi$
$73$	−54858.1			−1.20485			−0.602426	+	0.798175i	$0.705799\pi$
$74$	−33498.3	−	36421.0i	−0.711122	−	0.773166i
$75$		0			0
$76$	9834.89	+	823.651i	0.195315	+	0.0163572i
$77$			63548.2i			1.22145i
$78$		0			0
$79$		−	91648.1i		−	1.65217i	−0.563543	−	0.826087i	$-0.690562\pi$
$79$		−	91648.1i		−	1.65217i	0.563543	−	0.826087i	$-0.309438\pi$
$80$	−7842.73	+	46495.1i	−0.137007	+	0.812235i
$81$		0			0
$82$	5801.85	−	5336.27i	0.0952866	−	0.0876401i
$83$	45138.1			0.719197			0.359598	−	0.933107i	$-0.382914\pi$
$83$	45138.1			0.719197			0.359598	+	0.933107i	$0.382914\pi$
$84$		0			0
$85$	−67559.8			−1.01424
$86$	−39199.7	+	36054.0i	−0.571526	+	0.525663i
$87$		0			0
$88$	67426.2	−	52337.3i	0.928158	−	0.720451i
$89$			73149.6i			0.978896i	0.872032	+	0.489448i	$0.162802\pi$
$89$			73149.6i			0.978896i	−0.872032	+	0.489448i	$0.837198\pi$
$90$		0			0
$91$			133032.i			1.68404i
$92$	−5657.75	+	67557.0i	−0.0696906	+	0.832148i
$93$		0			0
$94$	42593.8	+	46310.0i	0.497194	+	0.540574i
$95$	−14201.6			−0.161446
$96$		0			0
$97$	−11422.1			−0.123259			−0.0616293	−	0.998099i	$-0.519630\pi$
$97$	−11422.1			−0.123259			−0.0616293	+	0.998099i	$0.519630\pi$
$98$	−5194.40	−	5647.60i	−0.0546349	−	0.0594017i
$99$		0			0
$100$	−2683.12	+	32038.1i	−0.0268312	+	0.320381i
$101$		−	78611.4i		−	0.766800i	−0.923582	−	0.383400i	$-0.874753\pi$
$101$		−	78611.4i		−	0.766800i	0.923582	−	0.383400i	$-0.125247\pi$
$102$		0			0
$103$			101937.i			0.946758i	0.880859	+	0.473379i	$0.156966\pi$
$103$			101937.i			0.946758i	−0.880859	+	0.473379i	$0.843034\pi$
$104$	141150.	−	109563.i	1.27967	−	0.993301i
$105$		0			0
$106$	118513.	−	109003.i	1.02448	−	0.942267i
$107$	135660.			1.14550			0.572748	−	0.819731i	$-0.305877\pi$
$107$	135660.			1.14550			0.572748	+	0.819731i	$0.305877\pi$
$108$		0			0
$109$	225285.			1.81621			0.908106	−	0.418741i	$-0.137529\pi$
$109$	225285.			1.81621			0.908106	+	0.418741i	$0.137529\pi$
$110$	−90400.1	+	83145.7i	−0.712340	+	0.655176i
$111$		0			0
$112$	−22954.5	+	136084.i	−0.172911	+	1.02509i
$113$			59823.0i			0.440730i	0.975418	+	0.220365i	$0.0707248\pi$
$113$			59823.0i			0.440730i	−0.975418	+	0.220365i	$0.929275\pi$
$114$		0			0
$115$		−	97552.2i		−	0.687848i
$116$	165693.	+	13876.5i	1.14330	+	0.0957489i
$117$		0			0
$118$	−57682.8	−	62715.5i	−0.381365	−	0.414639i
$119$	−197737.			−1.28003
$120$		0			0
$121$	61284.2			0.380527
$122$	−144912.	−	157555.i	−0.881463	−	0.958369i
$123$		0			0
$124$	−202914.	−	16993.6i	−1.18511	−	0.0992502i
$125$		−	190159.i		−	1.08853i
$126$		0			0
$127$		−	75992.2i		−	0.418080i	−0.977907	−	0.209040i	$-0.932966\pi$
$127$		−	75992.2i		−	0.418080i	0.977907	−	0.209040i	$-0.0670339\pi$
$128$	163293.	−	87721.3i	0.880934	−	0.473238i
$129$		0			0
$130$	−189244.	+	174058.i	−0.982118	+	0.903306i
$131$	−371533.			−1.89156			−0.945778	−	0.324815i	$-0.894698\pi$
$131$	−371533.			−1.89156			−0.945778	+	0.324815i	$0.894698\pi$
$132$		0			0
$133$	−41565.8			−0.203754
$134$	−271561.	+	249769.i	−1.30649	+	1.20165i
$135$		0			0
$136$	162853.	+	209804.i	0.755003	+	0.972672i
$137$		−	389370.i		−	1.77240i	−0.463304	−	0.886199i	$-0.653336\pi$
$137$		−	389370.i		−	1.77240i	0.463304	−	0.886199i	$-0.346664\pi$
$138$		0			0
$139$		−	104310.i		−	0.457918i	−0.973436	−	0.228959i	$-0.926468\pi$
$139$		−	104310.i		−	0.457918i	0.973436	−	0.228959i	$-0.0735322\pi$
$140$	16573.1	−	197893.i	0.0714634	−	0.853317i
$141$		0			0
$142$	−37758.5	−	41052.9i	−0.157143	−	0.170853i
$143$	465438.			1.90336
$144$		0			0
$145$	−239261.			−0.945044
$146$	−210077.	−	228405.i	−0.815634	−	0.886797i
$147$		0			0
$148$	23361.1	−	278945.i	0.0876674	−	1.04680i
$149$			227251.i			0.838570i	0.907855	+	0.419285i	$0.137719\pi$
$149$			227251.i			0.838570i	−0.907855	+	0.419285i	$0.862281\pi$
$150$		0			0
$151$		−	488350.i		−	1.74296i	−0.490427	−	0.871482i	$-0.663159\pi$
$151$		−	488350.i		−	1.74296i	0.490427	−	0.871482i	$-0.336841\pi$
$152$	34232.9	+	44102.4i	0.120181	+	0.154829i
$153$		0			0
$154$	−264587.	+	243355.i	−0.899015	+	0.826872i
$155$	293008.			0.979602
$156$		0			0
$157$	307615.			0.995998			0.497999	−	0.867178i	$-0.334068\pi$
$157$	307615.			0.995998			0.497999	+	0.867178i	$0.334068\pi$
$158$	381583.	−	350962.i	1.21604	−	1.11845i
$159$		0			0
$160$	−223619.	+	145397.i	−0.690571	+	0.449009i
$161$		−	285520.i		−	0.868105i
$162$		0			0
$163$		−	409730.i		−	1.20789i	−0.797024	−	0.603947i	$-0.793594\pi$
$163$		−	409730.i		−	1.20789i	0.797024	−	0.603947i	$-0.206406\pi$
$164$	44435.8	+	3721.40i	0.129010	+	0.0108043i
$165$		0			0
$166$	172854.	+	187935.i	0.486866	+	0.529344i
$167$	−107694.			−0.298814			−0.149407	−	0.988776i	$-0.547736\pi$
$167$	−107694.			−0.298814			−0.149407	+	0.988776i	$0.547736\pi$
$168$		0			0
$169$	603056.			1.62421
$170$	−258717.	−	281290.i	−0.686598	−	0.746503i
$171$		0			0
$172$	−300227.	−	25143.3i	−0.773799	−	0.0648040i
$173$			299962.i			0.761994i	0.924576	+	0.380997i	$0.124419\pi$
$173$			299962.i			0.761994i	−0.924576	+	0.380997i	$0.875581\pi$
$174$		0			0
$175$		−	135405.i		−	0.334225i
$176$	476115.	+	80310.5i	1.15859	+	0.195430i
$177$		0			0
$178$	−304563.	+	280123.i	−0.720489	+	0.662672i
$179$	−539891.			−1.25943			−0.629714	−	0.776827i	$-0.716828\pi$
$179$	−539891.			−1.25943			−0.629714	+	0.776827i	$0.716828\pi$
$180$		0			0
$181$	25867.6			0.0586894			0.0293447	−	0.999569i	$-0.490658\pi$
$181$	25867.6			0.0586894			0.0293447	+	0.999569i	$0.490658\pi$
$182$	−553888.	+	509440.i	−1.23949	+	1.14003i
$183$		0			0
$184$	−302944.	+	235150.i	−0.659657	+	0.512036i
$185$			402796.i			0.865279i
$186$		0			0
$187$			691821.i			1.44674i
$188$	−29704.0	+	354684.i	−0.0612943	+	0.731892i
$189$		0			0
$190$	−54384.2	−	59129.2i	−0.109292	−	0.118828i
$191$	519499.			1.03039			0.515194	−	0.857073i	$-0.327720\pi$
$191$	519499.			1.03039			0.515194	+	0.857073i	$0.327720\pi$
$192$		0			0
$193$	259328.			0.501137			0.250569	−	0.968099i	$-0.419382\pi$
$193$	259328.			0.501137			0.250569	+	0.968099i	$0.419382\pi$
$194$	−43740.5	−	47556.8i	−0.0834410	−	0.0907211i
$195$		0			0
$196$	3622.46	−	43254.4i	0.00673541	−	0.0804249i
$197$		−	372151.i		−	0.683209i	−0.939844	−	0.341604i	$-0.889030\pi$
$197$		−	372151.i		−	0.683209i	0.939844	−	0.341604i	$-0.110970\pi$
$198$		0			0
$199$		−	2717.29i		−	0.00486412i	−0.999997	−	0.00243206i	$-0.999226\pi$
$199$		−	2717.29i		−	0.00486412i	0.999997	−	0.00243206i	$-0.000774149\pi$
$200$	−143668.	+	111517.i	−0.253971	+	0.197136i
$201$		0			0
$202$	327304.	−	301039.i	0.564382	−	0.519092i
$203$	−700280.			−1.19270
$204$		0			0
$205$	−64165.2			−0.106639
$206$	−424422.	+	390363.i	−0.696835	+	0.640916i
$207$		0			0
$208$	996702.	+	168122.i	1.59737	+	0.269443i
$209$			145426.i			0.230290i
$210$		0			0
$211$		−	693979.i		−	1.07310i	−0.843868	−	0.536550i	$-0.819727\pi$
$211$		−	693979.i		−	1.07310i	0.843868	−	0.536550i	$-0.180273\pi$
$212$	907683.	+	76016.5i	1.38706	+	0.116163i
$213$		0			0
$214$	519505.	+	564832.i	0.775453	+	0.843110i
$215$	433527.			0.639617
$216$		0			0
$217$	857588.			1.23632
$218$	862719.	+	937990.i	1.22950	+	1.33677i
$219$		0			0
$220$	−692366.	−	57984.1i	−0.964448	−	0.0807704i
$221$			1.44826e6i			1.99465i
$222$		0			0
$223$			609819.i			0.821180i	0.911820	+	0.410590i	$0.134677\pi$
$223$			609819.i			0.821180i	−0.911820	+	0.410590i	$0.865323\pi$
$224$	−654498.	+	425555.i	−0.871541	+	0.566676i
$225$		0			0
$226$	−249077.	+	229089.i	−0.324387	+	0.298356i
$227$	165538.			0.213223			0.106611	−	0.994301i	$-0.466000\pi$
$227$	165538.			0.213223			0.106611	+	0.994301i	$0.466000\pi$
$228$		0			0
$229$	−793320.			−0.999677			−0.499839	−	0.866119i	$-0.666607\pi$
$229$	−793320.			−0.999677			−0.499839	+	0.866119i	$0.666607\pi$
$230$	406165.	−	373572.i	0.506271	−	0.465644i
$231$		0			0
$232$	576740.	+	743015.i	0.703493	+	0.906312i
$233$		−	523254.i		−	0.631426i	−0.948855	−	0.315713i	$-0.897756\pi$
$233$		−	523254.i		−	0.631426i	0.948855	−	0.315713i	$-0.102244\pi$
$234$		0			0
$235$		−	512163.i		−	0.604977i
$236$	40226.8	−	480332.i	0.0470149	−	0.561386i
$237$		0			0
$238$	−757225.	−	823292.i	−0.866528	−	0.942131i
$239$	−521703.			−0.590784			−0.295392	−	0.955376i	$-0.595450\pi$
$239$	−521703.			−0.590784			−0.295392	+	0.955376i	$0.595450\pi$
$240$		0			0
$241$	−1.08959e6			−1.20842			−0.604212	−	0.796824i	$-0.706512\pi$
$241$	−1.08959e6			−1.20842			−0.604212	+	0.796824i	$0.706512\pi$
$242$	234685.	+	255161.i	0.257601	+	0.280076i
$243$		0			0
$244$	101058.	−	1.20670e6i	0.108667	−	1.29755i
$245$			62459.3i			0.0664786i
$246$		0			0
$247$			304435.i			0.317506i
$248$	−706296.	−	909923.i	−0.729218	−	0.939453i
$249$		0			0
$250$	791740.	−	728205.i	0.801185	−	0.736892i
$251$	1.15105e6			1.15321			0.576606	−	0.817022i	$-0.304377\pi$
$251$	1.15105e6			1.15321			0.576606	+	0.817022i	$0.304377\pi$
$252$		0			0
$253$	−998947.			−0.981162
$254$	316399.	−	291008.i	0.307716	−	0.283023i
$255$		0			0
$256$	990558.	+	343958.i	0.944669	+	0.328024i
$257$			1.26233e6i			1.19218i	0.802918	+	0.596090i	$0.203280\pi$
$257$			1.26233e6i			1.19218i	−0.802918	+	0.596090i	$0.796720\pi$
$258$		0			0
$259$			1.17892e6i			1.09203i
$260$	−1.44940e6	−	121384.i	−1.32970	−	0.111360i
$261$		0			0
$262$	−1.42277e6	−	1.54690e6i	−1.28050	−	1.39223i
$263$	243029.			0.216655			0.108328	−	0.994115i	$-0.465450\pi$
$263$	243029.			0.216655			0.108328	+	0.994115i	$0.465450\pi$
$264$		0			0
$265$	−1.31069e6			−1.14653
$266$	−159174.	−	173062.i	−0.137933	−	0.149968i
$267$		0			0
$268$	−2.07986e6	−	174184.i	−1.76888	−	0.148140i
$269$		−	813756.i		−	0.685667i	−0.939396	−	0.342834i	$-0.888613\pi$
$269$		−	813756.i		−	0.685667i	0.939396	−	0.342834i	$-0.111387\pi$
$270$		0			0
$271$			1.85687e6i			1.53589i	0.640518	+	0.767943i	$0.278720\pi$
$271$			1.85687e6i			1.53589i	−0.640518	+	0.767943i	$0.721280\pi$
$272$	−249895.	+	1.48148e6i	−0.204802	+	1.21416i
$273$		0			0
$274$	1.62117e6	−	1.49108e6i	1.30452	−	1.19984i
$275$	−473739.			−0.377752
$276$		0			0
$277$	634180.			0.496607			0.248304	−	0.968682i	$-0.420127\pi$
$277$	634180.			0.496607			0.248304	+	0.968682i	$0.420127\pi$
$278$	434301.	−	399449.i	0.337038	−	0.309991i
$279$		0			0
$280$	887406.	−	688818.i	0.676437	−	0.525061i
$281$		−	2.12892e6i		−	1.60840i	−0.594361	−	0.804198i	$-0.702595\pi$
$281$		−	2.12892e6i		−	1.60840i	0.594361	−	0.804198i	$-0.297405\pi$
$282$		0			0
$283$		−	1.03774e6i		−	0.770234i	−0.922868	−	0.385117i	$-0.874161\pi$
$283$		−	1.03774e6i		−	0.770234i	0.922868	−	0.385117i	$-0.125839\pi$
$284$	26332.0	−	314420.i	0.0193726	−	0.231321i
$285$		0			0
$286$	1.78237e6	+	1.93788e6i	1.28850	+	1.40092i
$287$	−187802.			−0.134584
$288$		0			0
$289$	−732819.			−0.516121
$290$	−916239.	−	996179.i	−0.639755	−	0.695573i
$291$		0			0
$292$	146503.	−	1.74934e6i	0.100552	−	1.20065i
$293$		−	2.07720e6i		−	1.41354i	−0.707442	−	0.706771i	$-0.750151\pi$
$293$		−	2.07720e6i		−	1.41354i	0.707442	−	0.706771i	$-0.249849\pi$
$294$		0			0
$295$			693599.i			0.464038i
$296$	1.25087e6	−	970942.i	0.829816	−	0.644116i
$297$		0			0
$298$	−946173.	+	870246.i	−0.617206	+	0.567677i
$299$	−2.09120e6			−1.35275
$300$		0			0
$301$	1.26887e6			0.807234
$302$	2.03328e6	−	1.87011e6i	1.28286	−	1.17991i
$303$		0			0
$304$	−52529.8	+	311419.i	−0.0326003	+	0.193269i
$305$			1.74247e6i			1.07255i
$306$		0			0
$307$			277720.i			0.168175i	0.996458	+	0.0840876i	$0.0267976\pi$
$307$			277720.i			0.168175i	−0.996458	+	0.0840876i	$0.973202\pi$
$308$	−2.02645e6	−	169711.i	−1.21719	−	0.101937i
$309$		0			0
$310$	1.12206e6	+	1.21996e6i	0.663149	+	0.721008i
$311$	752701.			0.441287			0.220644	−	0.975354i	$-0.429184\pi$
$311$	752701.			0.441287			0.220644	+	0.975354i	$0.429184\pi$
$312$		0			0
$313$	−1.71292e6			−0.988274			−0.494137	−	0.869384i	$-0.664516\pi$
$313$	−1.71292e6			−0.988274			−0.494137	+	0.869384i	$0.664516\pi$
$314$	1.17800e6	+	1.28078e6i	0.674249	+	0.733076i
$315$		0			0
$316$	2.92251e6	+	244754.i	1.64641	+	0.137883i
$317$		−	738922.i		−	0.413000i	−0.978447	−	0.206500i	$-0.933793\pi$
$317$		−	738922.i		−	0.413000i	0.978447	−	0.206500i	$-0.0662074\pi$
$318$		0			0
$319$			2.45006e6i			1.34803i
$320$	−1.46171e6	−	374261.i	−0.797968	−	0.204315i
$321$		0			0
$322$	1.18878e6	−	1.09339e6i	0.638944	−	0.587671i
$323$	−452508.			−0.241335
$324$		0			0
$325$	−991727.			−0.520815
$326$	1.70594e6	−	1.56904e6i	0.889036	−	0.817694i
$327$		0			0
$328$	154671.	+	199262.i	0.0793822	+	0.102268i
$329$		−	1.49902e6i		−	0.763517i
$330$		0			0
$331$			1.07446e6i			0.539038i	0.962995	+	0.269519i	$0.0868647\pi$
$331$			1.07446e6i			0.539038i	−0.962995	+	0.269519i	$0.913135\pi$
$332$	−120545.	+	1.43938e6i	−0.0600210	+	0.716688i
$333$		0			0
$334$	−412410.	−	448392.i	−0.202285	−	0.219934i
$335$	3.00332e6			1.46214
$336$		0			0
$337$	125481.			0.0601871			0.0300935	−	0.999547i	$-0.490419\pi$
$337$	125481.			0.0601871			0.0300935	+	0.999547i	$0.490419\pi$
$338$	2.30938e6	+	2.51086e6i	1.09952	+	1.19545i
$339$		0			0
$340$	180424.	−	2.15437e6i	0.0846441	−	1.01070i
$341$		−	3.00043e6i		−	1.39733i
$342$		0			0
$343$		−	2.08230e6i		−	0.955670i
$344$	−1.04502e6	−	1.34630e6i	−0.476132	−	0.613402i
$345$		0			0
$346$	−1.24891e6	+	1.14869e6i	−0.560844	+	0.515838i
$347$	−2.54277e6			−1.13366			−0.566830	−	0.823835i	$-0.691830\pi$
$347$	−2.54277e6			−1.13366			−0.566830	+	0.823835i	$0.691830\pi$
$348$		0			0
$349$	554946.			0.243886			0.121943	−	0.992537i	$-0.461087\pi$
$349$	554946.			0.243886			0.121943	+	0.992537i	$0.461087\pi$
$350$	563767.	−	518526.i	0.245997	−	0.226256i
$351$		0			0
$352$	1.48888e6	+	2.28988e6i	0.640477	+	0.985046i
$353$			2.07681e6i			0.887075i	0.896256	+	0.443538i	$0.146277\pi$
$353$			2.07681e6i			0.887075i	−0.896256	+	0.443538i	$0.853723\pi$
$354$		0			0
$355$			454022.i			0.191208i
$356$	−2.33262e6	−	195352.i	−0.975482	−	0.0816945i
$357$		0			0
$358$	−2.06749e6	−	2.24787e6i	−0.852579	−	0.926966i
$359$	3.54117e6			1.45014			0.725071	−	0.688674i	$-0.241807\pi$
$359$	3.54117e6			1.45014			0.725071	+	0.688674i	$0.241807\pi$
$360$		0			0
$361$	2.38098e6			0.961585
$362$	99058.7	+	107701.i	0.0397302	+	0.0431966i
$363$		0			0
$364$	−4.24217e6	−	355273.i	−1.67817	−	0.140543i
$365$			2.52604e6i			0.992448i
$366$		0			0
$367$		−	1.66740e6i		−	0.646211i	−0.946363	−	0.323105i	$-0.895273\pi$
$367$		−	1.66740e6i		−	0.646211i	0.946363	−	0.323105i	$-0.104727\pi$
$368$	−2.13917e6	−	360833.i	−0.823429	−	0.138895i
$369$		0			0
$370$	−1.67707e6	+	1.54249e6i	−0.636864	+	0.585758i
$371$	−3.83620e6			−1.44699
$372$		0			0
$373$	304727.			0.113407			0.0567034	−	0.998391i	$-0.481941\pi$
$373$	304727.			0.113407			0.0567034	+	0.998391i	$0.481941\pi$
$374$	−2.88044e6	+	2.64929e6i	−1.06483	+	0.979380i
$375$		0			0
$376$	−1.59050e6	+	1.23457e6i	−0.580182	+	0.450346i
$377$			5.12897e6i			1.85856i
$378$		0			0
$379$			805622.i			0.288093i	0.989571	+	0.144047i	$0.0460115\pi$
$379$			805622.i			0.288093i	−0.989571	+	0.144047i	$0.953988\pi$
$380$	37926.4	−	452865.i	0.0134736	−	0.160883i
$381$		0			0
$382$	1.98940e6	+	2.16297e6i	0.697530	+	0.758389i
$383$	1.84820e6			0.643800			0.321900	−	0.946774i	$-0.395679\pi$
$383$	1.84820e6			0.643800			0.321900	+	0.946774i	$0.395679\pi$
$384$		0			0
$385$	2.92619e6			1.00612
$386$	993086.	+	1.07973e6i	0.339249	+	0.368848i
$387$		0			0
$388$	30503.7	−	364233.i	0.0102866	−	0.122829i
$389$			3.65126e6i			1.22340i	0.791090	+	0.611700i	$0.209514\pi$
$389$			3.65126e6i			1.22340i	−0.791090	+	0.611700i	$0.790486\pi$
$390$		0			0
$391$		−	3.10833e6i		−	1.02822i
$392$	193965.	−	150558.i	0.0637540	−	0.0494869i
$393$		0			0
$394$	1.54947e6	−	1.42513e6i	0.502856	−	0.462504i
$395$	−4.22010e6			−1.36091
$396$		0			0
$397$	−1.73747e6			−0.553274			−0.276637	−	0.960974i	$-0.589220\pi$
$397$	−1.73747e6			−0.553274			−0.276637	+	0.960974i	$0.589220\pi$
$398$	11313.6	−	10405.8i	0.00358010	−	0.00329280i
$399$		0			0
$400$	−1.01448e6	−	171121.i	−0.317024	−	0.0534753i
$401$		−	2.93873e6i		−	0.912640i	−0.889816	−	0.456320i	$-0.849167\pi$
$401$		−	2.93873e6i		−	0.912640i	0.889816	−	0.456320i	$-0.150833\pi$
$402$		0			0
$403$		−	6.28112e6i		−	1.92652i
$404$	2.50679e6	+	209938.i	0.764125	+	0.0639938i
$405$		0			0
$406$	−2.68169e6	−	2.91566e6i	−0.807409	−	0.877854i
$407$	4.12469e6			1.23425
$408$		0			0
$409$	−1.82104e6			−0.538285			−0.269142	−	0.963100i	$-0.586740\pi$
$409$	−1.82104e6			−0.538285			−0.269142	+	0.963100i	$0.586740\pi$
$410$	−245718.	−	267156.i	−0.0721900	−	0.0784884i
$411$		0			0
$412$	−3.25061e6	−	272231.i	−0.943456	−	0.0790124i
$413$			2.03006e6i			0.585643i
$414$		0			0
$415$		−	2.07846e6i		−	0.592409i
$416$	3.11683e6	+	4.79365e6i	0.883040	+	1.35810i
$417$		0			0
$418$	−605490.	+	556901.i	−0.169499	+	0.155897i
$419$	5.56903e6			1.54969			0.774845	−	0.632151i	$-0.217828\pi$
$419$	5.56903e6			1.54969			0.774845	+	0.632151i	$0.217828\pi$
$420$		0			0
$421$	220888.			0.0607390			0.0303695	−	0.999539i	$-0.490332\pi$
$421$	220888.			0.0607390			0.0303695	+	0.999539i	$0.490332\pi$
$422$	2.88943e6	−	2.65756e6i	0.789825	−	0.726444i
$423$		0			0
$424$	3.15943e6	+	4.07030e6i	0.853481	+	1.09954i
$425$		−	1.47409e6i		−	0.395869i
$426$		0			0
$427$			5.09995e6i			1.35362i
$428$	−362292.	+	4.32599e6i	−0.0955982	+	1.14150i
$429$		0			0
$430$	1.66017e6	+	1.80502e6i	0.432994	+	0.470772i
$431$	−2.90126e6			−0.752304			−0.376152	−	0.926558i	$-0.622753\pi$
$431$	−2.90126e6			−0.752304			−0.376152	+	0.926558i	$0.622753\pi$
$432$		0			0
$433$	1.33580e6			0.342392			0.171196	−	0.985237i	$-0.445237\pi$
$433$	1.33580e6			0.342392			0.171196	+	0.985237i	$0.445237\pi$
$434$	3.28409e6	+	3.57063e6i	0.836934	+	0.909955i
$435$		0			0
$436$	−601642.	+	7.18398e6i	−0.151573	+	1.80988i
$437$		−	653394.i		−	0.163671i
$438$		0			0
$439$		−	8.00279e6i		−	1.98189i	−0.134262	−	0.990946i	$-0.542866\pi$
$439$		−	8.00279e6i		−	1.98189i	0.134262	−	0.990946i	$-0.457134\pi$
$440$	−2.40996e6	−	3.10476e6i	−0.593442	−	0.764533i
$441$		0			0
$442$	−6.02993e6	+	5.54604e6i	−1.46810	+	1.35029i
$443$	−4.46062e6			−1.07991			−0.539953	−	0.841695i	$-0.681558\pi$
$443$	−4.46062e6			−1.07991			−0.539953	+	0.841695i	$0.681558\pi$
$444$		0			0
$445$	3.36830e6			0.806326
$446$	−2.53902e6	+	2.33527e6i	−0.604407	+	0.555905i
$447$		0			0
$448$	−4.27819e6	−	1.09540e6i	−1.00708	−	0.257857i
$449$		−	394596.i		−	0.0923712i	−0.998933	−	0.0461856i	$-0.985293\pi$
$449$		−	394596.i		−	0.0923712i	0.998933	−	0.0461856i	$-0.0147066\pi$
$450$		0			0
$451$			657060.i			0.152112i
$452$	−1.90766e6	−	159762.i	−0.439192	−	0.0367814i
$453$		0			0
$454$	633920.	+	689229.i	0.144343	+	0.156936i
$455$	6.12569e6			1.38716
$456$		0			0
$457$	3.29879e6			0.738863			0.369431	−	0.929258i	$-0.379552\pi$
$457$	3.29879e6			0.738863			0.369431	+	0.929258i	$0.379552\pi$
$458$	−3.03798e6	−	3.30304e6i	−0.676739	−	0.735784i
$459$		0			0
$460$	3.11078e6	+	260521.i	0.685448	+	0.0574048i
$461$			574515.i			0.125907i	0.998016	+	0.0629534i	$0.0200519\pi$
$461$			574515.i			0.125907i	−0.998016	+	0.0629534i	$0.979948\pi$
$462$		0			0
$463$			362906.i			0.0786760i	0.999226	+	0.0393380i	$0.0125249\pi$
$463$			362906.i			0.0786760i	−0.999226	+	0.0393380i	$0.987475\pi$
$464$	−884995.	+	5.24663e6i	−0.190830	+	1.13132i
$465$		0			0
$466$	2.17860e6	−	2.00378e6i	0.464743	−	0.427449i
$467$	−9.20629e6			−1.95340			−0.976702	−	0.214598i	$-0.931156\pi$
$467$	−9.20629e6			−1.95340			−0.976702	+	0.214598i	$0.931156\pi$
$468$		0			0
$469$	8.79026e6			1.84531
$470$	2.13243e6	−	1.96130e6i	0.445276	−	0.409544i
$471$		0			0
$472$	2.15394e6	−	1.67192e6i	0.445019	−	0.345431i
$473$		−	4.43937e6i		−	0.912364i
$474$		0			0
$475$		−	309865.i		−	0.0630141i
$476$	528073.	−	6.30551e6i	0.106826	−	1.27557i
$477$		0			0
$478$	−1.99784e6	−	2.17215e6i	−0.399936	−	0.434830i
$479$	−2.27095e6			−0.452240			−0.226120	−	0.974099i	$-0.572604\pi$
$479$	−2.27095e6			−0.452240			−0.226120	+	0.974099i	$0.572604\pi$
$480$		0			0
$481$	8.63463e6			1.70169
$482$	−4.17252e6	−	4.53657e6i	−0.818052	−	0.889426i
$483$		0			0
$484$	−163665.	+	1.95425e6i	−0.0317571	+	0.379199i
$485$			525952.i			0.101529i
$486$		0			0
$487$			6.09989e6i			1.16547i	0.812664	+	0.582733i	$0.198016\pi$
$487$			6.09989e6i			1.16547i	−0.812664	+	0.582733i	$0.801984\pi$
$488$	5.41117e6	−	4.20024e6i	1.02859	−	0.798407i
$489$		0			0
$490$	−260054.	+	239185.i	−0.0489297	+	0.0450033i
$491$	−536585.			−0.100446			−0.0502232	−	0.998738i	$-0.515993\pi$
$491$	−536585.			−0.100446			−0.0502232	+	0.998738i	$0.515993\pi$
$492$		0			0
$493$	−7.62364e6			−1.41268
$494$	−1.26754e6	+	1.16582e6i	−0.233691	+	0.214938i
$495$		0			0
$496$	1.08380e6	−	6.42522e6i	0.197808	−	1.17269i
$497$			1.32885e6i			0.241316i
$498$		0			0
$499$		−	3.52841e6i		−	0.634348i	−0.948367	−	0.317174i	$-0.897266\pi$
$499$		−	3.52841e6i		−	0.634348i	0.948367	−	0.317174i	$-0.102734\pi$
$500$	6.06386e6	+	507835.i	1.08474	+	0.0908444i
$501$		0			0
$502$	4.40789e6	+	4.79247e6i	0.780676	+	0.848789i
$503$	3.34461e6			0.589422			0.294711	−	0.955586i	$-0.404777\pi$
$503$	3.34461e6			0.589422			0.294711	+	0.955586i	$0.404777\pi$
$504$		0			0
$505$	−3.61980e6			−0.631621
$506$	−3.82542e6	−	4.15918e6i	−0.664206	−	0.722157i
$507$		0			0
$508$	2.42327e6	+	202943.i	0.416622	+	0.0348912i
$509$		−	5.31062e6i		−	0.908553i	−0.890861	−	0.454277i	$-0.849898\pi$
$509$		−	5.31062e6i		−	0.908553i	0.890861	−	0.454277i	$-0.150102\pi$
$510$		0			0
$511$			7.39332e6i			1.25253i
$512$	2.36120e6	+	5.44143e6i	0.398068	+	0.917356i
$513$		0			0
$514$	−5.25581e6	+	4.83405e6i	−0.877470	+	0.807055i
$515$	4.69387e6			0.779854
$516$		0			0
$517$	−5.24461e6			−0.862953
$518$	−4.90853e6	+	4.51463e6i	−0.803761	+	0.739261i
$519$		0			0
$520$	−5.04502e6	−	6.49951e6i	−0.818191	−	1.05408i
$521$		−	4.42521e6i		−	0.714232i	−0.934060	−	0.357116i	$-0.883760\pi$
$521$		−	4.42521e6i		−	0.714232i	0.934060	−	0.357116i	$-0.116240\pi$
$522$		0			0
$523$		−	88509.2i		−	0.0141493i	−0.999975	−	0.00707463i	$-0.997748\pi$
$523$		−	88509.2i		−	0.0141493i	0.999975	−	0.00707463i	$-0.00225194\pi$
$524$	992209.	−	1.18476e7i	0.157861	−	1.88496i
$525$		0			0
$526$	930669.	+	1.01187e6i	0.146667	+	0.159463i
$527$	9.33618e6			1.46434
$528$		0			0
$529$	−1.94810e6			−0.302672
$530$	−5.01924e6	−	5.45716e6i	−0.776154	−	0.843872i
$531$		0			0
$532$	111005.	−	1.32547e6i	0.0170045	−	0.203044i
$533$			1.37549e6i			0.209720i
$534$		0			0
$535$		−	6.24672e6i		−	0.943557i
$536$	−7.23951e6	−	9.32668e6i	−1.08842	−	1.40222i
$537$		0			0
$538$	3.38813e6	−	3.11624e6i	0.504666	−	0.464168i
$539$	639591.			0.0948267
$540$		0			0
$541$	−3.49057e6			−0.512747			−0.256373	−	0.966578i	$-0.582528\pi$
$541$	−3.49057e6			−0.512747			−0.256373	+	0.966578i	$0.582528\pi$
$542$	−7.73122e6	+	7.11081e6i	−1.13045	+	1.03973i
$543$		0			0
$544$	−7.12522e6	+	4.63282e6i	−1.03229	+	0.671194i
$545$		−	1.03737e7i		−	1.49603i
$546$		0			0
$547$		−	4.73741e6i		−	0.676975i	−0.940971	−	0.338487i	$-0.890085\pi$
$547$		−	4.73741e6i		−	0.676975i	0.940971	−	0.338487i	$-0.109915\pi$
$548$	1.24164e7	+	1.03984e6i	1.76622	+	0.147917i
$549$		0			0
$550$	−1.81416e6	−	1.97244e6i	−0.255723	−	0.278034i
$551$	−1.60254e6			−0.224870
$552$		0			0
$553$	−1.23516e7			−1.71755
$554$	2.42856e6	+	2.64045e6i	0.336182	+	0.365514i
$555$		0			0
$556$	3.32627e6	+	278568.i	0.456321	+	0.0382159i
$557$			6.51222e6i			0.889388i	0.895683	+	0.444694i	$0.146688\pi$
$557$			6.51222e6i			0.889388i	−0.895683	+	0.444694i	$0.853312\pi$
$558$		0			0
$559$		−	9.29339e6i		−	1.25790i
$560$	6.26622e6	+	1.05698e6i	0.844376	+	0.142428i
$561$		0			0
$562$	8.86389e6	−	8.15259e6i	1.18381	−	1.08882i
$563$	−1.30164e7			−1.73069			−0.865343	−	0.501180i	$-0.832900\pi$
$563$	−1.30164e7			−1.73069			−0.865343	+	0.501180i	$0.832900\pi$
$564$		0			0
$565$	2.75466e6			0.363033
$566$	4.32070e6	−	3.97398e6i	0.566909	−	0.521416i
$567$		0			0
$568$	1.40995e6	−	1.09442e6i	0.183372	−	0.142336i
$569$			2.32444e6i			0.300980i	0.988612	+	0.150490i	$0.0480851\pi$
$569$			2.32444e6i			0.300980i	−0.988612	+	0.150490i	$0.951915\pi$
$570$		0			0
$571$			1.30746e7i			1.67818i	0.543992	+	0.839091i	$0.316912\pi$
$571$			1.30746e7i			1.67818i	−0.543992	+	0.839091i	$0.683088\pi$
$572$	−1.24299e6	+	1.48420e7i	−0.158846	+	1.89672i
$573$		0			0
$574$	−719178.	−	781925.i	−0.0911081	−	0.0990571i
$575$	2.12850e6			0.268475
$576$		0			0
$577$	−9.92814e6			−1.24145			−0.620724	−	0.784029i	$-0.713161\pi$
$577$	−9.92814e6			−1.24145			−0.620724	+	0.784029i	$0.713161\pi$
$578$	−2.80629e6	−	3.05114e6i	−0.349393	−	0.379877i
$579$		0			0
$580$	638966.	−	7.62964e6i	0.0788693	−	0.941747i
$581$		−	6.08334e6i		−	0.747656i
$582$		0			0
$583$			1.34217e7i			1.63544i
$584$	7.84450e6	−	6.08902e6i	0.951773	−	0.738780i
$585$		0			0
$586$	8.64855e6	−	7.95453e6i	1.04040	−	0.956909i
$587$	−8.76459e6			−1.04987			−0.524936	−	0.851142i	$-0.675911\pi$
$587$	−8.76459e6			−1.04987			−0.524936	+	0.851142i	$0.675911\pi$
$588$		0			0
$589$	1.96253e6			0.233093
$590$	−2.88785e6	+	2.65610e6i	−0.341542	+	0.314134i
$591$		0			0
$592$	8.83272e6	+	1.48989e6i	1.03583	+	0.174723i
$593$			6.94712e6i			0.811275i	0.914034	+	0.405637i	$0.132950\pi$
$593$			6.94712e6i			0.811275i	−0.914034	+	0.405637i	$0.867050\pi$
$594$		0			0
$595$			9.10515e6i			1.05437i
$596$	−7.24665e6	−	606891.i	−0.835645	−	0.0699834i
$597$		0			0
$598$	−8.00815e6	−	8.70685e6i	−0.915755	−	0.995653i
$599$	7.15594e6			0.814892			0.407446	−	0.913229i	$-0.366420\pi$
$599$	7.15594e6			0.814892			0.407446	+	0.913229i	$0.366420\pi$
$600$		0			0
$601$	2.05362e6			0.231918			0.115959	−	0.993254i	$-0.463006\pi$
$601$	2.05362e6			0.231918			0.115959	+	0.993254i	$0.463006\pi$
$602$	4.85906e6	+	5.28301e6i	0.546464	+	0.594142i
$603$		0			0
$604$	1.55727e7	+	1.30418e6i	1.73688	+	0.145460i
$605$		−	2.82194e6i		−	0.313444i
$606$		0			0
$607$			1.85546e6i			0.204399i	0.994764	+	0.102200i	$0.0325881\pi$
$607$			1.85546e6i			0.204399i	−0.994764	+	0.102200i	$0.967412\pi$
$608$	−1.49777e6	+	973853.i	−0.164319	+	0.106840i
$609$		0			0
$610$	−7.25490e6	+	6.67272e6i	−0.789418	+	0.726069i
$611$	−1.09791e7			−1.18977
$612$		0			0
$613$	527592.			0.0567083			0.0283542	−	0.999598i	$-0.490973\pi$
$613$	527592.			0.0567083			0.0283542	+	0.999598i	$0.490973\pi$
$614$	−1.15631e6	+	1.06352e6i	−0.123781	+	0.113848i
$615$		0			0
$616$	−7.05358e6	−	9.08715e6i	−0.748959	−	0.964886i
$617$			1.33503e7i			1.41182i	0.708301	+	0.705910i	$0.249462\pi$
$617$			1.33503e7i			1.41182i	−0.708301	+	0.705910i	$0.750538\pi$
$618$		0			0
$619$			1.22140e7i			1.28124i	0.767856	+	0.640622i	$0.221324\pi$
$619$			1.22140e7i			1.28124i	−0.767856	+	0.640622i	$0.778676\pi$
$620$	−782501.	+	9.34353e6i	−0.0817533	+	0.976185i
$621$		0			0
$622$	2.88243e6	+	3.13392e6i	0.298733	+	0.324797i
$623$	9.85850e6			1.01763
$624$		0			0
$625$	−5.61653e6			−0.575133
$626$	−6.55956e6	−	7.13187e6i	−0.669020	−	0.727391i
$627$		0			0
$628$	−821511.	+	9.80934e6i	−0.0831217	+	0.992524i
$629$			1.28344e7i			1.29345i
$630$		0			0
$631$			842912.i			0.0842770i	0.999112	+	0.0421385i	$0.0134171\pi$
$631$			842912.i			0.0842770i	−0.999112	+	0.0421385i	$0.986583\pi$
$632$	1.01726e7	+	1.31053e7i	1.01307	+	1.30513i
$633$		0			0
$634$	3.07655e6	−	2.82967e6i	0.303977	−	0.279584i
$635$	−3.49919e6			−0.344377
$636$		0			0
$637$	1.33892e6			0.130740
$638$	−1.02010e7	+	9.38240e6i	−0.992181	+	0.912561i
$639$		0			0
$640$	−4.03928e6	−	7.51913e6i	−0.389811	−	0.725634i
$641$		−	4.62200e6i		−	0.444309i	−0.975011	−	0.222155i	$-0.928691\pi$
$641$		−	4.62200e6i		−	0.444309i	0.975011	−	0.222155i	$-0.0713090\pi$
$642$		0			0
$643$		−	9.28181e6i		−	0.885330i	−0.896687	−	0.442665i	$-0.854033\pi$
$643$		−	9.28181e6i		−	0.885330i	0.896687	−	0.442665i	$-0.145967\pi$
$644$	9.10478e6	+	762505.i	0.865077	+	0.0724483i
$645$		0			0
$646$	−1.73286e6	−	1.88405e6i	−0.163374	−	0.177628i
$647$	1.74226e7			1.63626			0.818129	−	0.575034i	$-0.195011\pi$
$647$	1.74226e7			1.63626			0.818129	+	0.575034i	$0.195011\pi$
$648$		0			0
$649$	7.10254e6			0.661914
$650$	−3.79777e6	−	4.12912e6i	−0.352570	−	0.383331i
$651$		0			0
$652$	1.30656e7	+	1.09422e6i	1.20368	+	0.100806i
$653$		−	3.94341e6i		−	0.361901i	−0.983492	−	0.180950i	$-0.942083\pi$
$653$		−	3.94341e6i		−	0.361901i	0.983492	−	0.180950i	$-0.0579173\pi$
$654$		0			0
$655$			1.71079e7i			1.55809i
$656$	−237339.	+	1.40705e6i	−0.0215332	+	0.127658i
$657$		0			0
$658$	6.24128e6	−	5.74044e6i	0.561965	−	0.516869i
$659$	−1.46127e7			−1.31074			−0.655371	−	0.755307i	$-0.727488\pi$
$659$	−1.46127e7			−1.31074			−0.655371	+	0.755307i	$0.727488\pi$
$660$		0			0
$661$	4.83511e6			0.430430			0.215215	−	0.976567i	$-0.430955\pi$
$661$	4.83511e6			0.430430			0.215215	+	0.976567i	$0.430955\pi$
$662$	−4.47358e6	+	4.11459e6i	−0.396744	+	0.364906i
$663$		0			0
$664$	−6.45457e6	+	5.01014e6i	−0.568129	+	0.440991i
$665$			1.91397e6i			0.167834i
$666$		0			0
$667$		−	1.10081e7i		−	0.958068i
$668$	287606.	−	3.43419e6i	0.0249377	−	0.297772i
$669$		0			0
$670$	1.15011e7	+	1.25045e7i	0.989809	+	1.07617i
$671$	1.78431e7			1.52991
$672$		0			0
$673$	−4.36686e6			−0.371648			−0.185824	−	0.982583i	$-0.559495\pi$
$673$	−4.36686e6			−0.371648			−0.185824	+	0.982583i	$0.559495\pi$
$674$	480524.	+	522448.i	0.0407441	+	0.0442990i
$675$		0			0
$676$	−1.61051e6	+	1.92305e7i	−0.135549	+	1.61854i
$677$			3.80499e6i			0.319067i	0.987193	+	0.159534i	$0.0509990\pi$
$677$			3.80499e6i			0.319067i	−0.987193	+	0.159534i	$0.949001\pi$
$678$		0			0
$679$			1.53938e6i			0.128136i
$680$	9.66080e6	−	7.49886e6i	0.801199	−	0.621903i
$681$		0			0
$682$	1.24925e7	−	1.14900e7i	1.02846	−	0.945932i
$683$	8.23750e6			0.675684			0.337842	−	0.941203i	$-0.390303\pi$
$683$	8.23750e6			0.675684			0.337842	+	0.941203i	$0.390303\pi$
$684$		0			0
$685$	−1.79292e7			−1.45994
$686$	8.66980e6	−	7.97407e6i	0.703394	−	0.646949i
$687$		0			0
$688$	1.60356e6	−	9.50659e6i	0.129156	−	0.765691i
$689$			2.80969e7i			2.25482i
$690$		0			0
$691$			2.65718e6i			0.211703i	0.994382	+	0.105851i	$0.0337568\pi$
$691$			2.65718e6i			0.211703i	−0.994382	+	0.105851i	$0.966243\pi$
$692$	−9.56531e6	−	801074.i	−0.759336	−	0.0635927i
$693$		0			0
$694$	−9.73741e6	−	1.05870e7i	−0.767440	−	0.834398i
$695$	−4.80313e6			−0.377191
$696$		0			0
$697$	−2.04451e6			−0.159407
$698$	2.12514e6	+	2.31055e6i	0.165101	+	0.179505i
$699$		0			0
$700$	4.31784e6	+	361609.i	0.333059	+	0.0278930i
$701$		−	1.26405e7i		−	0.971561i	−0.874081	−	0.485780i	$-0.838535\pi$
$701$		−	1.26405e7i		−	0.971561i	0.874081	−	0.485780i	$-0.161465\pi$
$702$		0			0
$703$			2.69789e6i			0.205890i
$704$	−3.83247e6	+	1.49681e7i	−0.291439	+	1.13824i
$705$		0			0
$706$	−8.64695e6	+	7.95305e6i	−0.652907	+	0.600513i
$707$	−1.05946e7			−0.797143
$708$		0			0
$709$	−1.00735e7			−0.752599			−0.376300	−	0.926498i	$-0.622804\pi$
$709$	−1.00735e7			−0.752599			−0.376300	+	0.926498i	$0.622804\pi$
$710$	−1.89035e6	+	1.73866e6i	−0.140733	+	0.129440i
$711$		0			0
$712$	−8.11930e6	−	1.04601e7i	−0.600231	−	0.773279i
$713$			1.34809e7i			0.993103i
$714$		0			0
$715$		−	2.14319e7i		−	1.56782i
$716$	1.44182e6	−	1.72162e7i	0.105106	−	1.25503i
$717$		0			0
$718$	1.35607e7	+	1.47439e7i	0.981686	+	1.06734i
$719$	−3.82437e6			−0.275891			−0.137946	−	0.990440i	$-0.544050\pi$
$719$	−3.82437e6			−0.275891			−0.137946	+	0.990440i	$0.544050\pi$
$720$		0			0
$721$	1.37382e7			0.984222
$722$	9.11784e6	+	9.91336e6i	0.650952	+	0.707747i
$723$		0			0
$724$	−69081.5	+	824875.i	−0.00489796	+	0.0584846i
$725$		−	5.22045e6i		−	0.368861i
$726$		0			0
$727$		−	1.74022e6i		−	0.122115i	−0.998134	−	0.0610575i	$-0.980553\pi$
$727$		−	1.74022e6i		−	0.122115i	0.998134	−	0.0610575i	$-0.0194473\pi$
$728$	−1.47660e7	−	1.90231e7i	−1.03261	−	1.33031i
$729$		0			0
$730$	−1.05173e7	+	9.67334e6i	−0.730463	+	0.671845i
$731$	1.38136e7			0.956121
$732$		0			0
$733$	2.39703e7			1.64783			0.823917	−	0.566711i	$-0.191784\pi$
$733$	2.39703e7			1.64783			0.823917	+	0.566711i	$0.191784\pi$
$734$	6.94233e6	−	6.38523e6i	0.475625	−	0.437458i
$735$		0			0
$736$	−6.68951e6	−	1.02884e7i	−0.455197	−	0.700088i
$737$		−	3.07544e7i		−	2.08563i
$738$		0			0
$739$		−	6.52306e6i		−	0.439380i	−0.975570	−	0.219690i	$-0.929495\pi$
$739$		−	6.52306e6i		−	0.439380i	0.975570	−	0.219690i	$-0.0705046\pi$
$740$	−1.28445e7	−	1.07570e6i	−0.862261	−	0.0722125i
$741$		0			0
$742$	−1.46905e7	−	1.59723e7i	−0.979553	−	1.06502i
$743$	−2.51966e7			−1.67444			−0.837219	−	0.546868i	$-0.815820\pi$
$743$	−2.51966e7			−1.67444			−0.837219	+	0.546868i	$0.815820\pi$
$744$		0			0
$745$	1.04642e7			0.690738
$746$	1.16694e6	+	1.26875e6i	0.0767716	+	0.0834698i
$747$		0			0
$748$	−2.20610e7	−	1.84756e6i	−1.44169	−	0.120738i
$749$		−	1.82832e7i		−	1.19082i
$750$		0			0
$751$		−	6.46901e6i		−	0.418541i	−0.977858	−	0.209270i	$-0.932891\pi$
$751$		−	6.46901e6i		−	0.418541i	0.977858	−	0.209270i	$-0.0671089\pi$
$752$	−1.12310e7	−	1.89442e6i	−0.724223	−	0.122161i
$753$		0			0
$754$	−2.13548e7	+	1.96412e7i	−1.36794	+	1.25817i
$755$	−2.24869e7			−1.43570
$756$		0			0
$757$	−1.26991e7			−0.805440			−0.402720	−	0.915323i	$-0.631935\pi$
$757$	−1.26991e7			−0.805440			−0.402720	+	0.915323i	$0.631935\pi$
$758$	−3.35426e6	+	3.08509e6i	−0.212043	+	0.195027i
$759$		0			0
$760$	2.03077e6	−	1.57632e6i	0.127534	−	0.0989940i
$761$		−	1.71063e7i		−	1.07076i	−0.844610	−	0.535382i	$-0.820167\pi$
$761$		−	1.71063e7i		−	1.07076i	0.844610	−	0.535382i	$-0.179833\pi$
$762$		0			0
$763$		−	3.03621e7i		−	1.88808i
$764$	−1.38736e6	+	1.65660e7i	−0.0859918	+	1.02679i
$765$		0			0
$766$	7.07758e6	+	7.69509e6i	0.435826	+	0.473851i
$767$	1.48685e7			0.912596
$768$		0			0
$769$	−7.68095e6			−0.468381			−0.234190	−	0.972191i	$-0.575244\pi$
$769$	−7.68095e6			−0.468381			−0.234190	+	0.972191i	$0.575244\pi$
$770$	1.12057e7	+	1.21834e7i	0.681102	+	0.740527i
$771$		0			0
$772$	−692558.	+	8.26956e6i	−0.0418228	+	0.499389i
$773$		−	2.27192e6i		−	0.136755i	−0.997660	−	0.0683776i	$-0.978218\pi$
$773$		−	2.27192e6i		−	0.136755i	0.997660	−	0.0683776i	$-0.0217823\pi$
$774$		0			0
$775$			6.39315e6i			0.382349i
$776$	1.63332e6	−	1.26781e6i	0.0973682	−	0.0755787i
$777$		0			0
$778$	−1.52022e7	+	1.39823e7i	−0.900448	+	0.828190i
$779$	−429772.			−0.0253743
$780$		0			0
$781$	4.64924e6			0.272744
$782$	1.29417e7	−	1.19032e7i	0.756791	−	0.696061i
$783$		0			0
$784$	1.36964e6	+	231029.i	0.0795822	+	0.0134238i
$785$		−	1.41647e7i		−	0.820413i
$786$		0			0
$787$			1.56436e7i			0.900324i	0.892947	+	0.450162i	$0.148634\pi$
$787$			1.56436e7i			0.900324i	−0.892947	+	0.450162i	$0.851366\pi$
$788$	1.18673e7	+	993859.i	0.680825	+	0.0570176i
$789$		0			0
$790$	−1.61607e7	−	1.75707e7i	−0.921280	−	1.00166i
$791$	8.06246e6			0.458170
$792$		0			0
$793$	3.73529e7			2.10931
$794$	−6.65355e6	−	7.23406e6i	−0.374543	−	0.407222i
$795$		0			0
$796$	86650.1	+	7256.76i	0.00484715	+	0.000405938i
$797$			2.26016e7i			1.26036i	0.776451	+	0.630178i	$0.217018\pi$
$797$			2.26016e7i			1.26036i	−0.776451	+	0.630178i	$0.782982\pi$
$798$		0			0
$799$		−	1.63192e7i		−	0.904340i
$800$	−3.17242e6	−	4.87915e6i	−0.175253	−	0.269537i
$801$		0			0
$802$	1.22356e7	−	1.12537e7i	0.671723	−	0.617819i
$803$	2.58669e7			1.41565
$804$		0			0
$805$	−1.31473e7			−0.715066
$806$	2.61519e7	−	2.40533e7i	1.41796	−	1.30418i
$807$		0			0
$808$	8.72554e6	+	1.12411e7i	0.470180	+	0.605734i
$809$		−	2.72883e6i		−	0.146590i	−0.997310	−	0.0732952i	$-0.976648\pi$
$809$		−	2.72883e6i		−	0.146590i	0.997310	−	0.0732952i	$-0.0233515\pi$
$810$		0			0
$811$		−	2.69137e6i		−	0.143688i	−0.997416	−	0.0718442i	$-0.977112\pi$
$811$		−	2.69137e6i		−	0.143688i	0.997416	−	0.0718442i	$-0.0228884\pi$
$812$	1.87016e6	−	2.23308e7i	0.0995377	−	1.18854i
$813$		0			0
$814$	1.57953e7	+	1.71734e7i	0.835539	+	0.908438i
$815$	−1.88667e7			−0.994954
$816$		0			0
$817$	2.90372e6			0.152194
$818$	−6.97360e6	−	7.58204e6i	−0.364396	−	0.396189i
$819$		0			0
$820$	171359.	−	2.04612e6i	0.00889961	−	0.106267i
$821$		−	1.32663e7i		−	0.686895i	−0.939172	−	0.343448i	$-0.888405\pi$
$821$		−	1.32663e7i		−	0.686895i	0.939172	−	0.343448i	$-0.111595\pi$
$822$		0			0
$823$		−	2.55966e6i		−	0.131729i	−0.997829	−	0.0658646i	$-0.979019\pi$
$823$		−	2.55966e6i		−	0.131729i	0.997829	−	0.0658646i	$-0.0209805\pi$
$824$	−1.13146e7	−	1.45766e7i	−0.580525	−	0.747892i
$825$		0			0
$826$	−8.45228e6	+	7.77401e6i	−0.431046	+	0.396456i
$827$	1.61642e7			0.821846			0.410923	−	0.911670i	$-0.365206\pi$
$827$	1.61642e7			0.821846			0.410923	+	0.911670i	$0.365206\pi$
$828$		0			0
$829$	2.06742e7			1.04482			0.522411	−	0.852694i	$-0.325033\pi$
$829$	2.06742e7			1.04482			0.522411	+	0.852694i	$0.325033\pi$
$830$	8.65381e6	−	7.95937e6i	0.436026	−	0.401036i
$831$		0			0
$832$	−8.02292e6	+	3.13342e7i	−0.401813	+	1.56932i
$833$			1.99016e6i			0.0993745i
$834$		0			0
$835$			4.95897e6i			0.246136i
$836$	−4.63739e6	−	388371.i	−0.229487	−	0.0192190i
$837$		0			0
$838$	2.13264e7	+	2.31870e7i	1.04907	+	1.14061i
$839$	6.10993e6			0.299662			0.149831	−	0.988712i	$-0.452127\pi$
$839$	6.10993e6			0.299662			0.149831	+	0.988712i	$0.452127\pi$
$840$		0			0
$841$	−6.48774e6			−0.316303
$842$	845882.	+	919684.i	0.0411178	+	0.0447052i
$843$		0			0
$844$	2.21299e7	+	1.85333e6i	1.06936	+	0.0895563i
$845$		−	2.77688e7i		−	1.33787i
$846$		0			0
$847$		−	8.25939e6i		−	0.395584i
$848$	−4.84808e6	+	2.87415e7i	−0.231516	+	1.37252i
$849$		0			0
$850$	6.13747e6	−	5.64496e6i	0.291368	−	0.267987i
$851$	−1.85321e7			−0.877204
$852$		0			0
$853$	2.52983e7			1.19047			0.595236	−	0.803551i	$-0.297058\pi$
$853$	2.52983e7			1.19047			0.595236	+	0.803551i	$0.297058\pi$
$854$	−2.12340e7	+	1.95300e7i	−0.996292	+	0.916343i
$855$		0			0
$856$	−1.93989e7	+	1.50578e7i	−0.904885	+	0.702386i
$857$			4.03581e7i			1.87706i	0.345197	+	0.938530i	$0.387812\pi$
$857$			4.03581e7i			1.87706i	−0.345197	+	0.938530i	$0.612188\pi$
$858$		0			0
$859$		−	358772.i		−	0.0165896i	−0.999966	−	0.00829479i	$-0.997360\pi$
$859$		−	358772.i		−	0.0165896i	0.999966	−	0.00829479i	$-0.00264034\pi$
$860$	−1.15777e6	+	1.38245e7i	−0.0533796	+	0.637385i
$861$		0			0
$862$	−1.11102e7	−	1.20796e7i	−0.509278	−	0.553712i
$863$	−6.43324e6			−0.294038			−0.147019	−	0.989134i	$-0.546968\pi$
$863$	−6.43324e6			−0.294038			−0.147019	+	0.989134i	$0.546968\pi$
$864$		0			0
$865$	1.38123e7			0.627662
$866$	5.11540e6	+	5.56171e6i	0.231785	+	0.252008i
$867$		0			0
$868$	−2.29026e6	+	2.73471e7i	−0.103178	+	1.23200i
$869$			4.32143e7i			1.94123i
$870$		0			0
$871$		−	6.43813e7i		−	2.87551i
$872$	−3.22149e7	+	2.50057e7i	−1.43472	+	1.11365i
$873$		0			0
$874$	2.72045e6	−	2.50214e6i	0.120465	−	0.110798i
$875$	−2.56281e7			−1.13161
$876$		0			0
$877$	3.17951e7			1.39592			0.697962	−	0.716135i	$-0.254090\pi$
$877$	3.17951e7			1.39592			0.697962	+	0.716135i	$0.254090\pi$
$878$	3.33201e7	−	3.06463e7i	1.45872	−	1.34166i
$879$		0			0
$880$	3.69804e6	−	2.19236e7i	0.160977	−	0.954343i
$881$		−	2.35865e7i		−	1.02382i	−0.859039	−	0.511910i	$-0.828938\pi$
$881$		−	2.35865e7i		−	1.02382i	0.859039	−	0.511910i	$-0.171062\pi$
$882$		0			0
$883$			1.09627e7i			0.473167i	0.971611	+	0.236583i	$0.0760277\pi$
$883$			1.09627e7i			0.473167i	−0.971611	+	0.236583i	$0.923972\pi$
$884$	−4.61827e7	−	3.86770e6i	−1.98769	−	0.166465i
$885$		0			0
$886$	−1.70817e7	−	1.85721e7i	−0.731051	−	0.794834i
$887$	1.34104e7			0.572311			0.286156	−	0.958183i	$-0.407623\pi$
$887$	1.34104e7			0.572311			0.286156	+	0.958183i	$0.407623\pi$
$888$		0			0
$889$	−1.02416e7			−0.434624
$890$	1.28987e7	+	1.40241e7i	0.545849	+	0.593474i
$891$		0			0
$892$	−1.94461e7	−	1.62857e6i	−0.818316	−	0.0685322i
$893$		−	3.43041e6i		−	0.143952i
$894$		0			0
$895$			2.48602e7i			1.03740i
$896$	−1.18223e7	−	2.20073e7i	−0.491965	−	0.915793i
$897$		0			0
$898$	1.64293e6	−	1.51109e6i	0.0679872	−	0.0625314i
$899$	3.30638e7			1.36444
$900$		0			0
$901$	−4.17629e7			−1.71388
$902$	−2.73571e6	+	2.51618e6i	−0.111958	+	0.102973i
$903$		0			0
$904$	−6.64011e6	−	8.55447e6i	−0.270243	−	0.348154i
$905$		−	1.19112e6i		−	0.0483430i
$906$		0			0
$907$			4.79385e7i			1.93493i	0.252996	+	0.967467i	$0.418584\pi$
$907$			4.79385e7i			1.93493i	−0.252996	+	0.967467i	$0.581416\pi$
$908$	−442083.	+	5.27874e6i	−0.0177946	+	0.212479i
$909$		0			0
$910$	2.34581e7	+	2.55047e7i	0.939050	+	1.02098i
$911$	−4.06580e6			−0.162312			−0.0811560	−	0.996701i	$-0.525861\pi$
$911$	−4.06580e6			−0.162312			−0.0811560	+	0.996701i	$0.525861\pi$
$912$		0			0
$913$	−2.12837e7			−0.845026
$914$	1.26326e7	+	1.37347e7i	0.500179	+	0.543819i
$915$		0			0
$916$	2.11863e6	−	2.52977e7i	0.0834287	−	0.996190i
$917$			5.00721e7i			1.96640i
$918$		0			0
$919$			1.78821e7i			0.698441i	0.937041	+	0.349220i	$0.113554\pi$
$919$			1.78821e7i			0.698441i	−0.937041	+	0.349220i	$0.886446\pi$
$920$	1.08279e7	+	1.39496e7i	0.421769	+	0.543366i
$921$		0			0
$922$	−2.39203e6	+	2.20008e6i	−0.0926701	+	0.0852336i
$923$	9.73275e6			0.376038
$924$		0			0
$925$	−8.78864e6			−0.337728
$926$	−1.51098e6	+	1.38973e6i	−0.0579072	+	0.0532603i
$927$		0			0
$928$	−2.52338e7	+	1.64070e7i	−0.961860	+	0.625402i
$929$		−	2.23070e7i		−	0.848012i	−0.905659	−	0.424006i	$-0.860624\pi$
$929$		−	2.23070e7i		−	0.848012i	0.905659	−	0.424006i	$-0.139376\pi$
$930$		0			0
$931$			418346.i			0.0158184i
$932$	1.66857e7	+	1.39739e6i	0.629223	+	0.0526961i
$933$		0			0
$934$	−3.52550e7	−	3.83310e7i	−1.32237	−	1.43775i
$935$	3.18561e7			1.19169
$936$		0			0
$937$	−4.03539e7			−1.50154			−0.750770	−	0.660563i	$-0.770317\pi$
$937$	−4.03539e7			−1.50154			−0.750770	+	0.660563i	$0.770317\pi$
$938$	3.36619e7	+	3.65988e7i	1.24920	+	1.35819i
$939$		0			0
$940$	1.63320e7	+	1.36777e6i	0.602866	+	0.0504887i
$941$			1.30625e7i			0.480898i	0.970662	+	0.240449i	$0.0772946\pi$
$941$			1.30625e7i			0.480898i	−0.970662	+	0.240449i	$0.922705\pi$
$942$		0			0
$943$		−	2.95215e6i		−	0.108108i
$944$	1.52096e7	+	2.56553e6i	0.555504	+	0.0937017i
$945$		0			0
$946$	1.84836e7	−	1.70003e7i	0.671520	−	0.617632i
$947$	−3.87893e7			−1.40552			−0.702760	−	0.711427i	$-0.748049\pi$
$947$	−3.87893e7			−1.40552			−0.702760	+	0.711427i	$0.748049\pi$
$948$		0			0
$949$	5.41500e7			1.95179
$950$	1.29014e6	−	1.18661e6i	0.0463798	−	0.0426579i
$951$		0			0
$952$	2.82757e7	−	2.19480e7i	1.01116	−	0.784879i
$953$			1.45546e7i			0.519120i	0.965727	+	0.259560i	$0.0835775\pi$
$953$			1.45546e7i			0.519120i	−0.965727	+	0.259560i	$0.916423\pi$
$954$		0			0
$955$		−	2.39212e7i		−	0.848741i
$956$	1.39325e6	−	1.66363e7i	0.0493043	−	0.588723i
$957$		0			0
$958$	−8.69649e6	−	9.45525e6i	−0.306147	−	0.332858i
$959$	−5.24761e7			−1.84253
$960$		0			0
$961$	−1.18620e7			−0.414332
$962$	3.30659e7	+	3.59509e7i	1.15197	+	1.25248i
$963$		0			0
$964$	2.90983e6	−	3.47451e7i	0.100850	−	1.20421i
$965$		−	1.19412e7i		−	0.412792i
$966$		0			0
$967$			2.33422e7i			0.802741i	0.915916	+	0.401370i	$0.131466\pi$
$967$			2.33422e7i			0.802741i	−0.915916	+	0.401370i	$0.868534\pi$
$968$	−8.76341e6	+	6.80230e6i	−0.300597	+	0.233328i
$969$		0			0
$970$	−2.18984e6	+	2.01411e6i	−0.0747278	+	0.0687311i
$971$	−5.87811e6			−0.200074			−0.100037	−	0.994984i	$-0.531896\pi$
$971$	−5.87811e6			−0.200074			−0.100037	+	0.994984i	$0.531896\pi$
$972$		0			0
$973$	−1.40580e7			−0.476038
$974$	−2.53973e7	+	2.33592e7i	−0.857808	+	0.788971i
$975$		0			0
$976$	3.82098e7	+	6.44518e6i	1.28396	+	0.216576i
$977$			4.06645e7i			1.36295i	0.731843	+	0.681473i	$0.238660\pi$
$977$			4.06645e7i			1.36295i	−0.731843	+	0.681473i	$0.761340\pi$
$978$		0			0
$979$		−	3.44918e7i		−	1.15016i
$980$	−1.99173e6	−	166803.i	−0.0662467	−	0.00554802i
$981$		0			0
$982$	−2.05483e6	−	2.23411e6i	−0.0679980	−	0.0739308i
$983$	3.43471e7			1.13372			0.566861	−	0.823814i	$-0.308158\pi$
$983$	3.43471e7			1.13372			0.566861	+	0.823814i	$0.308158\pi$
$984$		0			0
$985$	−1.71363e7			−0.562765
$986$	−2.91944e7	−	3.17415e7i	−0.956328	−	1.03977i
$987$		0			0
$988$	−9.70793e6	−	813018.i	−0.316399	−	0.0264977i
$989$			1.99460e7i			0.648432i
$990$		0			0
$991$		−	3.27854e7i		−	1.06046i	−0.847853	−	0.530232i	$-0.822105\pi$
$991$		−	3.27854e7i		−	1.06046i	0.847853	−	0.530232i	$-0.177895\pi$
$992$	3.09022e7	−	2.00926e7i	0.997034	−	0.648272i
$993$		0			0
$994$	−5.53277e6	+	5.08878e6i	−0.177614	+	0.163361i
$995$	−125123.			−0.00400662
$996$		0			0
$997$	−4.68704e7			−1.49335			−0.746673	−	0.665191i	$-0.768350\pi$
$997$	−4.68704e7			−1.49335			−0.746673	+	0.665191i	$0.768350\pi$
$998$	1.46908e7	−	1.35119e7i	0.466894	−	0.429427i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.b.b.107.12	yes	16
3.2	odd	2	inner	108.6.b.b.107.5	✓	16
4.3	odd	2	inner	108.6.b.b.107.6	yes	16
12.11	even	2	inner	108.6.b.b.107.11	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.6.b.b.107.5	✓	16	3.2	odd	2	inner
108.6.b.b.107.6	yes	16	4.3	odd	2	inner
108.6.b.b.107.11	yes	16	12.11	even	2	inner
108.6.b.b.107.12	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	108.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(3.82945 + 4.16357i) q^{2} +(-2.67058 + 31.8884i) q^{4} -46.0468i q^{5} -134.772i q^{7} +(-142.996 + 110.996i) q^{8} +O(q^{10})\)	\(q+(3.82945 + 4.16357i) q^{2} +(-2.67058 + 31.8884i) q^{4} -46.0468i q^{5} -134.772i q^{7} +(-142.996 + 110.996i) q^{8} +(191.719 - 176.334i) q^{10} -471.524 q^{11} -987.091 q^{13} +(561.131 - 516.102i) q^{14} +(-1009.74 - 170.321i) q^{16} -1467.20i q^{17} -308.416i q^{19} +(1468.36 + 122.972i) q^{20} +(-1805.68 - 1963.22i) q^{22} +2118.55 q^{23} +1004.70 q^{25} +(-3780.02 - 4109.82i) q^{26} +(4297.65 + 359.919i) q^{28} -5196.05i q^{29} +6363.26i q^{31} +(-3157.59 - 4856.34i) q^{32} +(6108.79 - 5618.57i) q^{34} -6205.80 q^{35} -8747.55 q^{37} +(1284.11 - 1181.07i) q^{38} +(5111.00 + 6584.51i) q^{40} -1393.48i q^{41} +9414.92i q^{43} +(1259.24 - 15036.1i) q^{44} +(8112.88 + 8820.71i) q^{46} +11122.7 q^{47} -1356.43 q^{49} +(3847.44 + 4183.12i) q^{50} +(2636.11 - 31476.7i) q^{52} -28464.4i q^{53} +21712.2i q^{55} +(14959.1 + 19271.9i) q^{56} +(21634.1 - 19898.0i) q^{58} -15062.9 q^{59} -37841.4 q^{61} +(-26493.9 + 24367.8i) q^{62} +(8127.84 - 31744.0i) q^{64} +45452.3i q^{65} +65223.3i q^{67} +(46786.6 + 3918.28i) q^{68} +(-23764.8 - 25838.3i) q^{70} -9860.03 q^{71} -54858.1 q^{73} +(-33498.3 - 36421.0i) q^{74} +(9834.89 + 823.651i) q^{76} +63548.2i q^{77} -91648.1i q^{79} +(-7842.73 + 46495.1i) q^{80} +(5801.85 - 5336.27i) q^{82} +45138.1 q^{83} -67559.8 q^{85} +(-39199.7 + 36054.0i) q^{86} +(67426.2 - 52337.3i) q^{88} +73149.6i q^{89} +133032. i q^{91} +(-5657.75 + 67557.0i) q^{92} +(42593.8 + 46310.0i) q^{94} -14201.6 q^{95} -11422.1 q^{97} +(-5194.40 - 5647.60i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 94 q^{4}+O(q^{10}) \) 16 * q + 94 * q^4	\( 16 q + 94 q^{4} + 1454 q^{10} + 896 q^{13} + 178 q^{16} + 30 q^{22} + 9888 q^{25} + 11454 q^{28} - 6172 q^{34} - 71008 q^{37} - 16618 q^{40} + 35304 q^{46} - 49376 q^{49} + 14876 q^{52} - 10492 q^{58} + 77888 q^{61} + 89206 q^{64} + 229398 q^{70} - 38032 q^{73} + 48960 q^{76} - 224488 q^{82} - 371264 q^{85} + 249102 q^{88} + 68772 q^{94} - 976 q^{97}+O(q^{100}) \) 16 * q + 94 * q^4 + 1454 * q^10 + 896 * q^13 + 178 * q^16 + 30 * q^22 + 9888 * q^25 + 11454 * q^28 - 6172 * q^34 - 71008 * q^37 - 16618 * q^40 + 35304 * q^46 - 49376 * q^49 + 14876 * q^52 - 10492 * q^58 + 77888 * q^61 + 89206 * q^64 + 229398 * q^70 - 38032 * q^73 + 48960 * q^76 - 224488 * q^82 - 371264 * q^85 + 249102 * q^88 + 68772 * q^94 - 976 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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