LMFDB - Embedded newform 108.6.b.b.107.6

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			107.6
Root			$-1.73205 - 3.22829i$ of defining polynomial
Character	$\chi$	$=$	108.107
Dual form			108.6.b.b.107.5

$q$-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	$0.173988\pi$
$7$			134.772i			1.03957i	−0.854297	+	0.519785i	$0.826012\pi$
$8$	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	$-0.300120\pi$
$11$	471.524			1.17496			0.587479	+	0.809239i	$0.300120\pi$
$12$		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	$0.0312443\pi$
$19$			308.416i			0.195999i	−0.995186	+	0.0979994i	$0.968756\pi$
$20$	−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	$-0.637104\pi$
$23$	−2118.55			−0.835062			−0.417531	+	0.908663i	$0.637104\pi$
$24$		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	$-0.797299\pi$
$31$		−	6363.26i		−	1.18926i	0.804001	−	0.594628i	$-0.202701\pi$
$32$	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	$-0.873078\pi$
$43$		−	9414.92i		−	0.776508i	0.921552	−	0.388254i	$-0.126922\pi$
$44$	−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	$-0.619693\pi$
$47$	−11122.7			−0.734454			−0.367227	+	0.930131i	$0.619693\pi$
$48$		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	$-0.409110\pi$
$59$	15062.9			0.563351			0.281676	+	0.959510i	$0.409110\pi$
$60$		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	$-0.652416\pi$
$67$		−	65223.3i		−	1.77507i	0.460740	−	0.887535i	$-0.347584\pi$
$68$	−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	$-0.462972\pi$
$71$	9860.03			0.232131			0.116065	+	0.993242i	$0.462972\pi$
$72$		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	$0.309438\pi$
$79$			91648.1i			1.65217i	−0.563543	+	0.826087i	$0.690562\pi$
$80$	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	$-0.617086\pi$
$83$	−45138.1			−0.719197			−0.359598	+	0.933107i	$0.617086\pi$
$84$		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	$-0.843034\pi$
$103$		−	101937.i		−	0.946758i	0.880859	−	0.473379i	$-0.156966\pi$
$104$	−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	$-0.694123\pi$
$107$	−135660.			−1.14550			−0.572748	+	0.819731i	$0.694123\pi$
$108$		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	$0.0670339\pi$
$127$			75992.2i			0.418080i	−0.977907	+	0.209040i	$0.932966\pi$
$128$	−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	$-0.105302\pi$
$131$	371533.			1.89156			0.945778	+	0.324815i	$0.105302\pi$
$132$		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	$0.0735322\pi$
$139$			104310.i			0.457918i	−0.973436	+	0.228959i	$0.926468\pi$
$140$	−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	$0.336841\pi$
$151$			488350.i			1.74296i	−0.490427	+	0.871482i	$0.663159\pi$
$152$	−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	$0.206406\pi$
$163$			409730.i			1.20789i	−0.797024	+	0.603947i	$0.793594\pi$
$164$	−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	$-0.452264\pi$
$167$	107694.			0.298814			0.149407	+	0.988776i	$0.452264\pi$
$168$		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	$-0.283172\pi$
$179$	539891.			1.25943			0.629714	+	0.776827i	$0.283172\pi$
$180$		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	$-0.672280\pi$
$191$	−519499.			−1.03039			−0.515194	+	0.857073i	$0.672280\pi$
$192$		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	$0.000774149\pi$
$199$			2717.29i			0.00486412i	−0.999997	+	0.00243206i	$0.999226\pi$
$200$	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	$0.180273\pi$
$211$			693979.i			1.07310i	−0.843868	+	0.536550i	$0.819727\pi$
$212$	−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	$-0.865323\pi$
$223$		−	609819.i		−	0.821180i	0.911820	−	0.410590i	$-0.134677\pi$
$224$	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	$-0.534000\pi$
$227$	−165538.			−0.213223			−0.106611	+	0.994301i	$0.534000\pi$
$228$		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	$-0.404550\pi$
$239$	521703.			0.590784			0.295392	+	0.955376i	$0.404550\pi$
$240$		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	$-0.695623\pi$
$251$	−1.15105e6			−1.15321			−0.576606	+	0.817022i	$0.695623\pi$
$252$		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	$-0.534550\pi$
$263$	−243029.			−0.216655			−0.108328	+	0.994115i	$0.534550\pi$
$264$		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	$-0.721280\pi$
$271$		−	1.85687e6i		−	1.53589i	0.640518	−	0.767943i	$-0.278720\pi$
$272$	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	$0.125839\pi$
$283$			1.03774e6i			0.770234i	−0.922868	+	0.385117i	$0.874161\pi$
$284$	−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	$-0.973202\pi$
$307$		−	277720.i		−	0.168175i	0.996458	−	0.0840876i	$-0.0267976\pi$
$308$	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	$-0.570816\pi$
$311$	−752701.			−0.441287			−0.220644	+	0.975354i	$0.570816\pi$
$312$		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	$-0.913135\pi$
$331$		−	1.07446e6i		−	0.539038i	0.962995	−	0.269519i	$-0.0868647\pi$
$332$	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	$-0.308170\pi$
$347$	2.54277e6			1.13366			0.566830	+	0.823835i	$0.308170\pi$
$348$		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	$-0.758193\pi$
$359$	−3.54117e6			−1.45014			−0.725071	+	0.688674i	$0.758193\pi$
$360$		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	$0.104727\pi$
$367$			1.66740e6i			0.646211i	−0.946363	+	0.323105i	$0.895273\pi$
$368$	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	$-0.953988\pi$
$379$		−	805622.i		−	0.288093i	0.989571	−	0.144047i	$-0.0460115\pi$
$380$	−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	$-0.604321\pi$
$383$	−1.84820e6			−0.643800			−0.321900	+	0.946774i	$0.604321\pi$
$384$		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	$-0.782172\pi$
$419$	−5.56903e6			−1.54969			−0.774845	+	0.632151i	$0.782172\pi$
$420$		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	$-0.377247\pi$
$431$	2.90126e6			0.752304			0.376152	+	0.926558i	$0.377247\pi$
$432$		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	$0.457134\pi$
$439$			8.00279e6i			1.98189i	−0.134262	+	0.990946i	$0.542866\pi$
$440$	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	$-0.318442\pi$
$443$	4.46062e6			1.07991			0.539953	+	0.841695i	$0.318442\pi$
$444$		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	$-0.987475\pi$
$463$		−	362906.i		−	0.0786760i	0.999226	−	0.0393380i	$-0.0125249\pi$
$464$	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	$-0.0688441\pi$
$467$	9.20629e6			1.95340			0.976702	+	0.214598i	$0.0688441\pi$
$468$		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	$-0.427396\pi$
$479$	2.27095e6			0.452240			0.226120	+	0.974099i	$0.427396\pi$
$480$		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	$-0.801984\pi$
$487$		−	6.09989e6i		−	1.16547i	0.812664	−	0.582733i	$-0.198016\pi$
$488$	−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	$-0.484007\pi$
$491$	536585.			0.100446			0.0502232	+	0.998738i	$0.484007\pi$
$492$		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	$0.102734\pi$
$499$			3.52841e6i			0.634348i	−0.948367	+	0.317174i	$0.897266\pi$
$500$	−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	$-0.595223\pi$
$503$	−3.34461e6			−0.589422			−0.294711	+	0.955586i	$0.595223\pi$
$504$		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	$0.00225194\pi$
$523$			88509.2i			0.0141493i	−0.999975	+	0.00707463i	$0.997748\pi$
$524$	−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	$0.109915\pi$
$547$			4.73741e6i			0.676975i	−0.940971	+	0.338487i	$0.890085\pi$
$548$	−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	$-0.167100\pi$
$563$	1.30164e7			1.73069			0.865343	+	0.501180i	$0.167100\pi$
$564$		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	$-0.683088\pi$
$571$		−	1.30746e7i		−	1.67818i	0.543992	−	0.839091i	$-0.316912\pi$
$572$	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	$-0.324089\pi$
$587$	8.76459e6			1.04987			0.524936	+	0.851142i	$0.324089\pi$
$588$		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	$-0.633580\pi$
$599$	−7.15594e6			−0.814892			−0.407446	+	0.913229i	$0.633580\pi$
$600$		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	$-0.967412\pi$
$607$		−	1.85546e6i		−	0.204399i	0.994764	−	0.102200i	$-0.0325881\pi$
$608$	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	$-0.778676\pi$
$619$		−	1.22140e7i		−	1.28124i	0.767856	−	0.640622i	$-0.221324\pi$
$620$	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	$-0.986583\pi$
$631$		−	842912.i		−	0.0842770i	0.999112	−	0.0421385i	$-0.0134171\pi$
$632$	−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	$0.145967\pi$
$643$			9.28181e6i			0.885330i	−0.896687	+	0.442665i	$0.854033\pi$
$644$	−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	$-0.804989\pi$
$647$	−1.74226e7			−1.63626			−0.818129	+	0.575034i	$0.804989\pi$
$648$		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	$-0.272512\pi$
$659$	1.46127e7			1.31074			0.655371	+	0.755307i	$0.272512\pi$
$660$		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	$-0.609697\pi$
$683$	−8.23750e6			−0.675684			−0.337842	+	0.941203i	$0.609697\pi$
$684$		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	$-0.966243\pi$
$691$		−	2.65718e6i		−	0.211703i	0.994382	−	0.105851i	$-0.0337568\pi$
$692$	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	$-0.455950\pi$
$719$	3.82437e6			0.275891			0.137946	+	0.990440i	$0.455950\pi$
$720$		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	$0.0194473\pi$
$727$			1.74022e6i			0.122115i	−0.998134	+	0.0610575i	$0.980553\pi$
$728$	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	$0.0705046\pi$
$739$			6.52306e6i			0.439380i	−0.975570	+	0.219690i	$0.929495\pi$
$740$	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	$-0.184180\pi$
$743$	2.51966e7			1.67444			0.837219	+	0.546868i	$0.184180\pi$
$744$		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	$0.0671089\pi$
$751$			6.46901e6i			0.418541i	−0.977858	+	0.209270i	$0.932891\pi$
$752$	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	$-0.851366\pi$
$787$		−	1.56436e7i		−	0.900324i	0.892947	−	0.450162i	$-0.148634\pi$
$788$	−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	$0.0228884\pi$
$811$			2.69137e6i			0.143688i	−0.997416	+	0.0718442i	$0.977112\pi$
$812$	−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	$0.0209805\pi$
$823$			2.55966e6i			0.131729i	−0.997829	+	0.0658646i	$0.979019\pi$
$824$	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	$-0.634794\pi$
$827$	−1.61642e7			−0.821846			−0.410923	+	0.911670i	$0.634794\pi$
$828$		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	$-0.547873\pi$
$839$	−6.10993e6			−0.299662			−0.149831	+	0.988712i	$0.547873\pi$
$840$		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	$0.00264034\pi$
$859$			358772.i			0.0165896i	−0.999966	+	0.00829479i	$0.997360\pi$
$860$	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	$-0.453032\pi$
$863$	6.43324e6			0.294038			0.147019	+	0.989134i	$0.453032\pi$
$864$		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	$-0.923972\pi$
$883$		−	1.09627e7i		−	0.473167i	0.971611	−	0.236583i	$-0.0760277\pi$
$884$	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	$-0.592377\pi$
$887$	−1.34104e7			−0.572311			−0.286156	+	0.958183i	$0.592377\pi$
$888$		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	$-0.581416\pi$
$907$		−	4.79385e7i		−	1.93493i	0.252996	−	0.967467i	$-0.418584\pi$
$908$	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	$-0.474139\pi$
$911$	4.06580e6			0.162312			0.0811560	+	0.996701i	$0.474139\pi$
$912$		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	$-0.886446\pi$
$919$		−	1.78821e7i		−	0.698441i	0.937041	−	0.349220i	$-0.113554\pi$
$920$	−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	$-0.251951\pi$
$947$	3.87893e7			1.40552			0.702760	+	0.711427i	$0.251951\pi$
$948$		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	$-0.868534\pi$
$967$		−	2.33422e7i		−	0.802741i	0.915916	−	0.401370i	$-0.131466\pi$
$968$	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	$-0.468104\pi$
$971$	5.87811e6			0.200074			0.100037	+	0.994984i	$0.468104\pi$
$972$		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	$-0.691842\pi$
$983$	−3.43471e7			−1.13372			−0.566861	+	0.823814i	$0.691842\pi$
$984$		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	$0.177895\pi$
$991$			3.27854e7i			1.06046i	−0.847853	+	0.530232i	$0.822105\pi$
$992$	−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.107.6	yes	16
3.2	odd	2	inner	108.6.b.b.107.11	yes	16
4.3	odd	2	inner	108.6.b.b.107.12	yes	16
12.11	even	2	inner	108.6.b.b.107.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.6.b.b.107.5	✓	16	12.11	even	2	inner
108.6.b.b.107.6	yes	16	1.1	even	1	trivial
108.6.b.b.107.11	yes	16	3.2	odd	2	inner
108.6.b.b.107.12	yes	16	4.3	odd	2	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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
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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