LMFDB - Embedded newform 108.6.b.b.107.16

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			107.16
Root			$1.73205 + 3.53958i$ of defining polynomial
Character	$\chi$	$=$	108.107
Dual form			108.6.b.b.107.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.65395 + 0.181119i) q^{2} +(31.9344 + 2.04808i) q^{4} -69.1814i q^{5} +238.886i q^{7} +(180.185 + 17.3637i) q^{8} +O(q^{10})$	\(q+(5.65395 + 0.181119i) q^{2} +(31.9344 + 2.04808i) q^{4} -69.1814i q^{5} +238.886i q^{7} +(180.185 + 17.3637i) q^{8} +(12.5301 - 391.148i) q^{10} +350.956 q^{11} +669.928 q^{13} +(-43.2668 + 1350.65i) q^{14} +(1015.61 + 130.808i) q^{16} -1396.15i q^{17} -1789.28i q^{19} +(141.689 - 2209.26i) q^{20} +(1984.29 + 63.5648i) q^{22} +1322.78 q^{23} -1661.06 q^{25} +(3787.74 + 121.337i) q^{26} +(-489.257 + 7628.68i) q^{28} +6894.21i q^{29} +2334.13i q^{31} +(5718.52 + 923.531i) q^{32} +(252.870 - 7893.79i) q^{34} +16526.5 q^{35} -12929.6 q^{37} +(324.073 - 10116.5i) q^{38} +(1201.24 - 12465.4i) q^{40} -8719.02i q^{41} +10647.8i q^{43} +(11207.6 + 718.785i) q^{44} +(7478.94 + 239.581i) q^{46} -3988.75 q^{47} -40259.6 q^{49} +(-9391.56 - 300.850i) q^{50} +(21393.8 + 1372.07i) q^{52} +4057.38i q^{53} -24279.6i q^{55} +(-4147.94 + 43043.6i) q^{56} +(-1248.67 + 38979.5i) q^{58} -25135.6 q^{59} +8968.91 q^{61} +(-422.756 + 13197.1i) q^{62} +(32165.0 + 6257.33i) q^{64} -46346.6i q^{65} +12405.9i q^{67} +(2859.43 - 44585.3i) q^{68} +(93439.9 + 2993.26i) q^{70} +6503.43 q^{71} -45851.0 q^{73} +(-73103.6 - 2341.81i) q^{74} +(3664.59 - 57139.6i) q^{76} +83838.4i q^{77} -37453.2i q^{79} +(9049.50 - 70261.3i) q^{80} +(1579.18 - 49296.9i) q^{82} -48693.7 q^{83} -96587.8 q^{85} +(-1928.52 + 60202.1i) q^{86} +(63236.8 + 6093.88i) q^{88} +7935.52i q^{89} +160037. i q^{91} +(42242.2 + 2709.16i) q^{92} +(-22552.2 - 722.439i) q^{94} -123785. q^{95} +56596.2 q^{97} +(-227626. - 7291.78i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.65395	+	0.181119i	0.999487	+	0.0320176i
$2$	5.65395	+	0.181119i	0.999487	+	0.0320176i
$3$		0			0
$3$		0			0
$4$	31.9344	+	2.04808i	0.997950	+	0.0640025i
$5$		−	69.1814i		−	1.23755i	−0.785567	−	0.618777i	$-0.787628\pi$
$5$		−	69.1814i		−	1.23755i	0.785567	−	0.618777i	$-0.212372\pi$
$6$		0			0
$7$			238.886i			1.84266i	0.388779	+	0.921331i	$0.372897\pi$
$7$			238.886i			1.84266i	−0.388779	+	0.921331i	$0.627103\pi$
$8$	180.185	+	17.3637i	0.995389	+	0.0959216i
$9$		0			0
$10$	12.5301	−	391.148i	0.0396236	−	1.23692i
$11$	350.956			0.874521			0.437261	−	0.899335i	$-0.355949\pi$
$11$	350.956			0.874521			0.437261	+	0.899335i	$0.355949\pi$
$12$		0			0
$13$	669.928			1.09944			0.549718	−	0.835350i	$-0.314735\pi$
$13$	669.928			1.09944			0.549718	+	0.835350i	$0.314735\pi$
$14$	−43.2668	+	1350.65i	−0.0589977	+	1.84172i
$15$		0			0
$16$	1015.61	+	130.808i	0.991807	+	0.127742i
$17$		−	1396.15i		−	1.17168i	−0.810425	−	0.585842i	$-0.800764\pi$
$17$		−	1396.15i		−	1.17168i	0.810425	−	0.585842i	$-0.199236\pi$
$18$		0			0
$19$		−	1789.28i		−	1.13709i	−0.822652	−	0.568545i	$-0.807507\pi$
$19$		−	1789.28i		−	1.13709i	0.822652	−	0.568545i	$-0.192493\pi$
$20$	141.689	−	2209.26i	0.0792065	−	1.23502i
$21$		0			0
$22$	1984.29	+	63.5648i	0.874073	+	0.0280001i
$23$	1322.78			0.521397			0.260698	−	0.965420i	$-0.416047\pi$
$23$	1322.78			0.521397			0.260698	+	0.965420i	$0.416047\pi$
$24$		0			0
$25$	−1661.06			−0.531540
$26$	3787.74	+	121.337i	1.09887	+	0.0352014i
$27$		0			0
$28$	−489.257	+	7628.68i	−0.117935	+	1.83888i
$29$			6894.21i			1.52226i	0.648598	+	0.761131i	$0.275356\pi$
$29$			6894.21i			1.52226i	−0.648598	+	0.761131i	$0.724644\pi$
$30$		0			0
$31$			2334.13i			0.436236i	0.975922	+	0.218118i	$0.0699918\pi$
$31$			2334.13i			0.436236i	−0.975922	+	0.218118i	$0.930008\pi$
$32$	5718.52	+	923.531i	0.987209	+	0.159432i
$33$		0			0
$34$	252.870	−	7893.79i	0.0375146	−	1.17108i
$35$	16526.5			2.28039
$36$		0			0
$37$	−12929.6			−1.55268			−0.776341	−	0.630314i	$-0.782926\pi$
$37$	−12929.6			−1.55268			−0.776341	+	0.630314i	$0.782926\pi$
$38$	324.073	−	10116.5i	0.0364069	−	1.13651i
$39$		0			0
$40$	1201.24	−	12465.4i	0.118708	−	1.23185i
$41$		−	8719.02i		−	0.810043i	−0.914307	−	0.405021i	$-0.867264\pi$
$41$		−	8719.02i		−	0.810043i	0.914307	−	0.405021i	$-0.132736\pi$
$42$		0			0
$43$			10647.8i			0.878189i	0.898441	+	0.439095i	$0.144701\pi$
$43$			10647.8i			0.878189i	−0.898441	+	0.439095i	$0.855299\pi$
$44$	11207.6	+	718.785i	0.872728	+	0.0559715i
$45$		0			0
$46$	7478.94	+	239.581i	0.521130	+	0.0166939i
$47$	−3988.75			−0.263386			−0.131693	−	0.991291i	$-0.542041\pi$
$47$	−3988.75			−0.263386			−0.131693	+	0.991291i	$0.542041\pi$
$48$		0			0
$49$	−40259.6			−2.39540
$50$	−9391.56	−	300.850i	−0.531267	−	0.0170186i
$51$		0			0
$52$	21393.8	+	1372.07i	1.09718	+	0.0703666i
$53$			4057.38i			0.198406i	0.995067	+	0.0992032i	$0.0316294\pi$
$53$			4057.38i			0.198406i	−0.995067	+	0.0992032i	$0.968371\pi$
$54$		0			0
$55$		−	24279.6i		−	1.08227i
$56$	−4147.94	+	43043.6i	−0.176751	+	1.83417i
$57$		0			0
$58$	−1248.67	+	38979.5i	−0.0487393	+	1.52148i
$59$	−25135.6			−0.940068			−0.470034	−	0.882648i	$-0.655758\pi$
$59$	−25135.6			−0.940068			−0.470034	+	0.882648i	$0.655758\pi$
$60$		0			0
$61$	8968.91			0.308614			0.154307	−	0.988023i	$-0.450686\pi$
$61$	8968.91			0.308614			0.154307	+	0.988023i	$0.450686\pi$
$62$	−422.756	+	13197.1i	−0.0139673	+	0.436012i
$63$		0			0
$64$	32165.0	+	6257.33i	0.981598	+	0.190959i
$65$		−	46346.6i		−	1.36061i
$66$		0			0
$67$			12405.9i			0.337631i	0.985648	+	0.168815i	$0.0539942\pi$
$67$			12405.9i			0.337631i	−0.985648	+	0.168815i	$0.946006\pi$
$68$	2859.43	−	44585.3i	0.0749907	−	1.16928i
$69$		0			0
$70$	93439.9	+	2993.26i	2.27922	+	0.0730128i
$71$	6503.43			0.153108			0.0765538	−	0.997065i	$-0.475608\pi$
$71$	6503.43			0.153108			0.0765538	+	0.997065i	$0.475608\pi$
$72$		0			0
$73$	−45851.0			−1.00703			−0.503515	−	0.863987i	$-0.667960\pi$
$73$	−45851.0			−1.00703			−0.503515	+	0.863987i	$0.667960\pi$
$74$	−73103.6	−	2341.81i	−1.55189	−	0.0497132i
$75$		0			0
$76$	3664.59	−	57139.6i	0.0727766	−	1.13476i
$77$			83838.4i			1.61145i
$78$		0			0
$79$		−	37453.2i		−	0.675182i	−0.941293	−	0.337591i	$-0.890388\pi$
$79$		−	37453.2i		−	0.675182i	0.941293	−	0.337591i	$-0.109612\pi$
$80$	9049.50	−	70261.3i	0.158088	−	1.22742i
$81$		0			0
$82$	1579.18	−	49296.9i	0.0259357	−	0.809628i
$83$	−48693.7			−0.775849			−0.387925	−	0.921691i	$-0.626808\pi$
$83$	−48693.7			−0.775849			−0.387925	+	0.921691i	$0.626808\pi$
$84$		0			0
$85$	−96587.8			−1.45002
$86$	−1928.52	+	60202.1i	−0.0281175	+	0.877739i
$87$		0			0
$88$	63236.8	+	6093.88i	0.870489	+	0.0838855i
$89$			7935.52i			0.106194i	0.998589	+	0.0530971i	$0.0169093\pi$
$89$			7935.52i			0.106194i	−0.998589	+	0.0530971i	$0.983091\pi$
$90$		0			0
$91$			160037.i			2.02589i
$92$	42242.2	+	2709.16i	0.520328	+	0.0333707i
$93$		0			0
$94$	−22552.2	−	722.439i	−0.263251	−	0.00843299i
$95$	−123785.			−1.40721
$96$		0			0
$97$	56596.2			0.610742			0.305371	−	0.952233i	$-0.401219\pi$
$97$	56596.2			0.610742			0.305371	+	0.952233i	$0.401219\pi$
$98$	−227626.	−	7291.78i	−2.39418	−	0.0766952i
$99$		0			0
$100$	−53045.0	−	3401.98i	−0.530450	−	0.0340198i
$101$			72884.7i			0.710940i	0.934688	+	0.355470i	$0.115679\pi$
$101$			72884.7i			0.710940i	−0.934688	+	0.355470i	$0.884321\pi$
$102$		0			0
$103$		−	97537.9i		−	0.905900i	−0.891536	−	0.452950i	$-0.850372\pi$
$103$		−	97537.9i		−	0.905900i	0.891536	−	0.452950i	$-0.149628\pi$
$104$	120711.	+	11632.4i	1.09437	+	0.105460i
$105$		0			0
$106$	−734.869	+	22940.2i	−0.00635251	+	0.198305i
$107$	−16437.8			−0.138798			−0.0693990	−	0.997589i	$-0.522108\pi$
$107$	−16437.8			−0.138798			−0.0693990	+	0.997589i	$0.522108\pi$
$108$		0			0
$109$	−173939.			−1.40226			−0.701132	−	0.713032i	$-0.747322\pi$
$109$	−173939.			−1.40226			−0.701132	+	0.713032i	$0.747322\pi$
$110$	4397.50	−	137276.i	0.0346517	−	1.08171i
$111$		0			0
$112$	−31248.3	+	242615.i	−0.235386	+	1.82757i
$113$		−	228039.i		−	1.68002i	−0.542573	−	0.840009i	$-0.682550\pi$
$113$		−	228039.i		−	1.68002i	0.542573	−	0.840009i	$-0.317450\pi$
$114$		0			0
$115$		−	91511.8i		−	0.645257i
$116$	−14119.9	+	220162.i	−0.0974285	+	1.51914i
$117$		0			0
$118$	−142116.	−	4552.54i	−0.939586	−	0.0300988i
$119$	333522.			2.15902
$120$		0			0
$121$	−37881.2			−0.235212
$122$	50709.8	+	1624.44i	0.308455	+	0.00988108i
$123$		0			0
$124$	−4780.49	+	74539.2i	−0.0279202	+	0.435342i
$125$		−	101277.i		−	0.579745i
$126$		0			0
$127$		−	170464.i		−	0.937827i	−0.883244	−	0.468913i	$-0.844646\pi$
$127$		−	170464.i		−	0.937827i	0.883244	−	0.468913i	$-0.155354\pi$
$128$	180726.	+	41204.4i	0.974981	+	0.222289i
$129$		0			0
$130$	8394.25	−	262041.i	0.0435636	−	1.35991i
$131$	−29943.1			−0.152447			−0.0762234	−	0.997091i	$-0.524286\pi$
$131$	−29943.1			−0.152447			−0.0762234	+	0.997091i	$0.524286\pi$
$132$		0			0
$133$	427435.			2.09527
$134$	−2246.95	+	70142.5i	−0.0108101	+	0.337458i
$135$		0			0
$136$	24242.4	−	251565.i	0.112390	−	1.16628i
$137$			171047.i			0.778600i	0.921111	+	0.389300i	$0.127283\pi$
$137$			171047.i			0.778600i	−0.921111	+	0.389300i	$0.872717\pi$
$138$		0			0
$139$			263941.i			1.15870i	0.815080	+	0.579348i	$0.196693\pi$
$139$			263941.i			1.15870i	−0.815080	+	0.579348i	$0.803307\pi$
$140$	527763.	+	33847.5i	2.27572	+	0.145951i
$141$		0			0
$142$	36770.1	+	1177.90i	0.153029	+	0.00490215i
$143$	235115.			0.961480
$144$		0			0
$145$	476951.			1.88388
$146$	−259240.	−	8304.50i	−1.00651	−	0.0322427i
$147$		0			0
$148$	−412900.	−	26480.9i	−1.54950	−	0.0993754i
$149$			47653.0i			0.175843i	0.996127	+	0.0879215i	$0.0280225\pi$
$149$			47653.0i			0.175843i	−0.996127	+	0.0879215i	$0.971978\pi$
$150$		0			0
$151$			351084.i			1.25305i	0.779402	+	0.626525i	$0.215523\pi$
$151$			351084.i			1.25305i	−0.779402	+	0.626525i	$0.784477\pi$
$152$	31068.5	−	322401.i	0.109072	−	1.13185i
$153$		0			0
$154$	−15184.7	+	474018.i	−0.0515948	+	1.61062i
$155$	161479.			0.539866
$156$		0			0
$157$	285818.			0.925424			0.462712	−	0.886509i	$-0.346876\pi$
$157$	285818.			0.925424			0.462712	+	0.886509i	$0.346876\pi$
$158$	6783.49	−	211759.i	0.0216177	−	0.674836i
$159$		0			0
$160$	63891.1	−	395615.i	0.197306	−	1.22172i
$161$			315994.i			0.960758i
$162$		0			0
$163$		−	128969.i		−	0.380203i	−0.981764	−	0.190101i	$-0.939118\pi$
$163$		−	128969.i		−	0.380203i	0.981764	−	0.190101i	$-0.0608816\pi$
$164$	17857.2	−	278437.i	0.0518447	−	0.808382i
$165$		0			0
$166$	−275312.	−	8819.36i	−0.775452	−	0.0248409i
$167$	−559823.			−1.55331			−0.776657	−	0.629924i	$-0.783086\pi$
$167$	−559823.			−1.55331			−0.776657	+	0.629924i	$0.783086\pi$
$168$		0			0
$169$	77511.0			0.208760
$170$	−546103.	−	17493.9i	−1.44928	−	0.0464263i
$171$		0			0
$172$	−21807.5	+	340030.i	−0.0562063	+	0.876389i
$173$		−	523424.i		−	1.32965i	−0.746997	−	0.664827i	$-0.768505\pi$
$173$		−	523424.i		−	1.32965i	0.746997	−	0.664827i	$-0.231495\pi$
$174$		0			0
$175$		−	396804.i		−	0.979448i
$176$	356434.	+	45907.9i	0.867357	+	0.111714i
$177$		0			0
$178$	−1437.28	+	44867.1i	−0.00340009	+	0.106140i
$179$	715299.			1.66861			0.834305	−	0.551303i	$-0.185869\pi$
$179$	715299.			1.66861			0.834305	+	0.551303i	$0.185869\pi$
$180$		0			0
$181$	286861.			0.650841			0.325420	−	0.945569i	$-0.394494\pi$
$181$	286861.			0.650841			0.325420	+	0.945569i	$0.394494\pi$
$182$	−28985.7	+	904839.i	−0.0648642	+	2.02485i
$183$		0			0
$184$	238345.	+	22968.3i	0.518993	+	0.0500132i
$185$			894490.i			1.92153i
$186$		0			0
$187$		−	489988.i		−	1.02466i
$188$	−127378.	−	8169.28i	−0.262846	−	0.0168573i
$189$		0			0
$190$	−699875.	−	22419.8i	−1.40649	−	0.0450556i
$191$	−121929.			−0.241838			−0.120919	−	0.992662i	$-0.538584\pi$
$191$	−121929.			−0.241838			−0.120919	+	0.992662i	$0.538584\pi$
$192$		0			0
$193$	237611.			0.459170			0.229585	−	0.973289i	$-0.426263\pi$
$193$	237611.			0.459170			0.229585	+	0.973289i	$0.426263\pi$
$194$	319992.	+	10250.7i	0.610429	+	0.0195545i
$195$		0			0
$196$	−1.28566e6	−	82454.7i	−2.39049	−	0.153312i
$197$		−	667755.i		−	1.22589i	−0.790126	−	0.612945i	$-0.789985\pi$
$197$		−	667755.i		−	1.22589i	0.790126	−	0.612945i	$-0.210015\pi$
$198$		0			0
$199$		−	230496.i		−	0.412602i	−0.978489	−	0.206301i	$-0.933857\pi$
$199$		−	230496.i		−	0.412602i	0.978489	−	0.206301i	$-0.0661425\pi$
$200$	−299298.	−	28842.1i	−0.529089	−	0.0509862i
$201$		0			0
$202$	−13200.8	+	412087.i	−0.0227626	+	0.710576i
$203$	−1.64693e6			−2.80502
$204$		0			0
$205$	−603194.			−1.00247
$206$	17666.0	−	551475.i	0.0290048	−	0.905436i
$207$		0			0
$208$	680386.	+	87632.2i	1.09043	+	0.140445i
$209$		−	627959.i		−	0.994410i
$210$		0			0
$211$			788636.i			1.21947i	0.792606	+	0.609734i	$0.208724\pi$
$211$			788636.i			1.21947i	−0.792606	+	0.609734i	$0.791276\pi$
$212$	−8309.83	+	129570.i	−0.0126985	+	0.198000i
$213$		0			0
$214$	−92938.3	−	2977.19i	−0.138727	−	0.00444398i
$215$	736628.			1.08681
$216$		0			0
$217$	−557592.			−0.803836
$218$	−983441.	−	31503.6i	−1.40154	−	0.0448972i
$219$		0			0
$220$	49726.5	−	775354.i	0.0692678	−	1.08005i
$221$		−	935323.i		−	1.28819i
$222$		0			0
$223$			1.42387e6i			1.91738i	0.284450	+	0.958691i	$0.408189\pi$
$223$			1.42387e6i			1.91738i	−0.284450	+	0.958691i	$0.591811\pi$
$224$	−220619.	+	1.36608e6i	−0.293780	+	1.81909i
$225$		0			0
$226$	41302.3	−	1.28932e6i	0.0537902	−	1.67916i
$227$	−714849.			−0.920767			−0.460383	−	0.887720i	$-0.652288\pi$
$227$	−714849.			−0.920767			−0.460383	+	0.887720i	$0.652288\pi$
$228$		0			0
$229$	640469.			0.807066			0.403533	−	0.914965i	$-0.367782\pi$
$229$	640469.			0.807066			0.403533	+	0.914965i	$0.367782\pi$
$230$	16574.5	−	517404.i	0.0206596	−	0.644926i
$231$		0			0
$232$	−119709.	+	1.24223e6i	−0.146018	+	1.51524i
$233$			965359.i			1.16493i	0.812857	+	0.582464i	$0.197911\pi$
$233$			965359.i			1.16493i	−0.812857	+	0.582464i	$0.802089\pi$
$234$		0			0
$235$			275947.i			0.325954i
$236$	−802690.	−	51479.7i	−0.938141	−	0.0601667i
$237$		0			0
$238$	1.88572e6	+	60407.2i	2.15791	+	0.0691267i
$239$	−657323.			−0.744361			−0.372181	−	0.928160i	$-0.621390\pi$
$239$	−657323.			−0.744361			−0.372181	+	0.928160i	$0.621390\pi$
$240$		0			0
$241$	−1.08719e6			−1.20577			−0.602885	−	0.797828i	$-0.705982\pi$
$241$	−1.08719e6			−1.20577			−0.602885	+	0.797828i	$0.705982\pi$
$242$	−214178.	−	6861.00i	−0.235092	−	0.00753094i
$243$		0			0
$244$	286417.	+	18369.0i	0.307981	+	0.0197520i
$245$			2.78521e6i			2.96444i
$246$		0			0
$247$		−	1.19869e6i		−	1.25016i
$248$	−40529.1	+	420575.i	−0.0418445	+	0.434225i
$249$		0			0
$250$	18343.3	−	572617.i	0.0185621	−	0.579448i
$251$	−51518.6			−0.0516155			−0.0258077	−	0.999667i	$-0.508216\pi$
$251$	−51518.6			−0.0516155			−0.0258077	+	0.999667i	$0.508216\pi$
$252$		0			0
$253$	464237.			0.455973
$254$	30874.2	−	963794.i	0.0300270	−	0.937346i
$255$		0			0
$256$	1.01435e6	+	265701.i	0.967364	+	0.253392i
$257$		−	1.05873e6i		−	0.999888i	−0.866058	−	0.499944i	$-0.833354\pi$
$257$		−	1.05873e6i		−	0.999888i	0.866058	−	0.499944i	$-0.166646\pi$
$258$		0			0
$259$		−	3.08871e6i		−	2.86107i
$260$	94921.4	−	1.48005e6i	0.0870825	−	1.35782i
$261$		0			0
$262$	−169297.	−	5423.26i	−0.152369	−	0.00488098i
$263$	1.68934e6			1.50601			0.753004	−	0.658016i	$-0.228604\pi$
$263$	1.68934e6			1.50601			0.753004	+	0.658016i	$0.228604\pi$
$264$		0			0
$265$	280695.			0.245539
$266$	2.41670e6	+	77416.6i	2.09420	+	0.0670857i
$267$		0			0
$268$	−25408.3	+	396176.i	−0.0216092	+	0.336939i
$269$		−	930054.i		−	0.783660i	−0.920038	−	0.391830i	$-0.871842\pi$
$269$		−	930054.i		−	0.783660i	0.920038	−	0.391830i	$-0.128158\pi$
$270$		0			0
$271$			2.01579e6i			1.66733i	0.552272	+	0.833664i	$0.313761\pi$
$271$			2.01579e6i			1.66733i	−0.552272	+	0.833664i	$0.686239\pi$
$272$	182628.	−	1.41795e6i	0.149674	−	1.16209i
$273$		0			0
$274$	−30979.9	+	967093.i	−0.0249289	+	0.778201i
$275$	−582959.			−0.464843
$276$		0			0
$277$	−2.46037e6			−1.92664			−0.963320	−	0.268354i	$-0.913520\pi$
$277$	−2.46037e6			−1.92664			−0.963320	+	0.268354i	$0.913520\pi$
$278$	−47804.8	+	1.49231e6i	−0.0370987	+	1.15810i
$279$		0			0
$280$	2.97782e6	+	286960.i	2.26988	+	0.218739i
$281$		−	1.20772e6i		−	0.912433i	−0.889869	−	0.456217i	$-0.849204\pi$
$281$		−	1.20772e6i		−	0.912433i	0.889869	−	0.456217i	$-0.150796\pi$
$282$		0			0
$283$		−	516965.i		−	0.383703i	−0.981424	−	0.191852i	$-0.938551\pi$
$283$		−	516965.i		−	0.383703i	0.981424	−	0.191852i	$-0.0614492\pi$
$284$	207683.	+	13319.5i	0.152794	+	0.00979927i
$285$		0			0
$286$	1.32933e6	+	42583.9i	0.960988	+	0.0307843i
$287$	2.08285e6			1.49264
$288$		0			0
$289$	−529388.			−0.372846
$290$	2.69666e6	+	86384.9i	1.88292	+	0.0603175i
$291$		0			0
$292$	−1.46423e6	−	93906.5i	−1.00496	−	0.0644523i
$293$			2.06534e6i			1.40547i	0.711451	+	0.702736i	$0.248038\pi$
$293$			2.06534e6i			1.40547i	−0.711451	+	0.702736i	$0.751962\pi$
$294$		0			0
$295$			1.73892e6i			1.16338i
$296$	−2.32972e6	−	224506.i	−1.54552	−	0.148936i
$297$		0			0
$298$	−8630.88	+	269428.i	−0.00563008	+	0.175753i
$299$	886169.			0.573243
$300$		0			0
$301$	−2.54361e6			−1.61821
$302$	−63588.0	+	1.98501e6i	−0.0401197	+	1.25241i
$303$		0			0
$304$	234053.	−	1.81721e6i	0.145255	−	1.12777i
$305$		−	620481.i		−	0.381926i
$306$		0			0
$307$		−	443153.i		−	0.268354i	−0.990957	−	0.134177i	$-0.957161\pi$
$307$		−	443153.i		−	0.268354i	0.990957	−	0.134177i	$-0.0428390\pi$
$308$	−171708.	+	2.67733e6i	−0.103137	+	1.60814i
$309$		0			0
$310$	912993.	+	29246.9i	0.539589	+	0.0172852i
$311$	1.59260e6			0.933696			0.466848	−	0.884338i	$-0.345390\pi$
$311$	1.59260e6			0.933696			0.466848	+	0.884338i	$0.345390\pi$
$312$		0			0
$313$	−230766.			−0.133141			−0.0665703	−	0.997782i	$-0.521206\pi$
$313$	−230766.			−0.133141			−0.0665703	+	0.997782i	$0.521206\pi$
$314$	1.61600e6	+	51767.2i	0.924950	+	0.0296299i
$315$		0			0
$316$	76707.0	−	1.19604e6i	0.0432133	−	0.673798i
$317$		−	1.84281e6i		−	1.02999i	−0.857193	−	0.514995i	$-0.827794\pi$
$317$		−	1.84281e6i		−	1.02999i	0.857193	−	0.514995i	$-0.172206\pi$
$318$		0			0
$319$			2.41956e6i			1.33125i
$320$	432891.	−	2.22522e6i	0.236322	−	1.21478i
$321$		0			0
$322$	−57232.6	+	1.78662e6i	−0.0307612	+	0.960266i
$323$	−2.49811e6			−1.33231
$324$		0			0
$325$	−1.11279e6			−0.584394
$326$	23358.7	−	729183.i	0.0121732	−	0.380008i
$327$		0			0
$328$	151394.	−	1.57103e6i	0.0777007	−	0.806308i
$329$		−	952857.i		−	0.485331i
$330$		0			0
$331$			2.00465e6i			1.00570i	0.864374	+	0.502850i	$0.167715\pi$
$331$			2.00465e6i			1.00570i	−0.864374	+	0.502850i	$0.832285\pi$
$332$	−1.55500e6	−	99728.5i	−0.774259	−	0.0496563i
$333$		0			0
$334$	−3.16521e6	−	101395.i	−1.55252	−	0.0497335i
$335$	858259.			0.417836
$336$		0			0
$337$	−1.11878e6			−0.536623			−0.268311	−	0.963332i	$-0.586466\pi$
$337$	−1.11878e6			−0.536623			−0.268311	+	0.963332i	$0.586466\pi$
$338$	438244.	+	14038.7i	0.208653	+	0.00668400i
$339$		0			0
$340$	−3.08447e6	−	197819.i	−1.44705	−	0.0928051i
$341$			819178.i			0.381498i
$342$		0			0
$343$		−	5.60249e6i		−	2.57126i
$344$	−184885.	+	1.91857e6i	−0.0842373	+	0.874140i
$345$		0			0
$346$	94802.2	−	2.95942e6i	0.0425724	−	1.32897i
$347$	351285.			0.156616			0.0783080	−	0.996929i	$-0.475048\pi$
$347$	351285.			0.156616			0.0783080	+	0.996929i	$0.475048\pi$
$348$		0			0
$349$	1.58849e6			0.698105			0.349053	−	0.937103i	$-0.386503\pi$
$349$	1.58849e6			0.698105			0.349053	+	0.937103i	$0.386503\pi$
$350$	71868.9	−	2.24351e6i	0.0313596	−	0.978946i
$351$		0			0
$352$	2.00695e6	+	324118.i	0.863335	+	0.139427i
$353$		−	1.88702e6i		−	0.806010i	−0.915198	−	0.403005i	$-0.867966\pi$
$353$		−	1.88702e6i		−	0.806010i	0.915198	−	0.403005i	$-0.132034\pi$
$354$		0			0
$355$		−	449916.i		−	0.189479i
$356$	−16252.6	+	253416.i	−0.00679669	+	0.105976i
$357$		0			0
$358$	4.04427e6	+	129554.i	1.66775	+	0.0534250i
$359$	−2.13280e6			−0.873400			−0.436700	−	0.899607i	$-0.643853\pi$
$359$	−2.13280e6			−0.873400			−0.436700	+	0.899607i	$0.643853\pi$
$360$		0			0
$361$	−725432.			−0.292974
$362$	1.62190e6	+	51956.0i	0.650507	+	0.0208384i
$363$		0			0
$364$	−327767.	+	5.11067e6i	−0.129662	+	2.02174i
$365$			3.17204e6i			1.24625i
$366$		0			0
$367$		−	1.63065e6i		−	0.631970i	−0.948764	−	0.315985i	$-0.897665\pi$
$367$		−	1.63065e6i		−	0.631970i	0.948764	−	0.315985i	$-0.102335\pi$
$368$	1.34343e6	+	173031.i	0.517125	+	0.0666045i
$369$		0			0
$370$	−162009.	+	5.05741e6i	−0.0615228	+	1.92054i
$371$	−969251.			−0.365596
$372$		0			0
$373$	3.06922e6			1.14224			0.571118	−	0.820868i	$-0.306510\pi$
$373$	3.06922e6			1.14224			0.571118	+	0.820868i	$0.306510\pi$
$374$	88746.2	−	2.77037e6i	0.0328073	−	1.02414i
$375$		0			0
$376$	−718712.	−	69259.4i	−0.262171	−	0.0252644i
$377$			4.61863e6i			1.67363i
$378$		0			0
$379$			2.56651e6i			0.917792i	0.888490	+	0.458896i	$0.151755\pi$
$379$			2.56651e6i			0.917792i	−0.888490	+	0.458896i	$0.848245\pi$
$380$	−3.95300e6	−	253521.i	−1.40433	−	0.0900649i
$381$		0			0
$382$	−689382.	−	22083.7i	−0.241714	−	0.00774307i
$383$	3.73053e6			1.29949			0.649745	−	0.760152i	$-0.274876\pi$
$383$	3.73053e6			1.29949			0.649745	+	0.760152i	$0.274876\pi$
$384$		0			0
$385$	5.80006e6			1.99425
$386$	1.34344e6	+	43035.9i	0.458934	+	0.0147015i
$387$		0			0
$388$	1.80737e6	+	115913.i	0.609490	+	0.0390890i
$389$			3.32039e6i			1.11254i	0.831002	+	0.556270i	$0.187768\pi$
$389$			3.32039e6i			1.11254i	−0.831002	+	0.556270i	$0.812232\pi$
$390$		0			0
$391$		−	1.84681e6i		−	0.610913i
$392$	−7.25415e6	−	699054.i	−2.38436	−	0.229771i
$393$		0			0
$394$	120943.	−	3.77545e6i	0.0392501	−	1.22526i
$395$	−2.59106e6			−0.835574
$396$		0			0
$397$	2.24589e6			0.715173			0.357587	−	0.933880i	$-0.383600\pi$
$397$	2.24589e6			0.715173			0.357587	+	0.933880i	$0.383600\pi$
$398$	41747.3	−	1.30321e6i	0.0132105	−	0.412390i
$399$		0			0
$400$	−1.68699e6	−	217281.i	−0.527185	−	0.0679002i
$401$		−	4.54280e6i		−	1.41079i	−0.708814	−	0.705395i	$-0.750770\pi$
$401$		−	4.54280e6i		−	1.41079i	0.708814	−	0.705395i	$-0.249230\pi$
$402$		0			0
$403$			1.56370e6i			0.479614i
$404$	−149274.	+	2.32753e6i	−0.0455019	+	0.709483i
$405$		0			0
$406$	−9.31167e6	−	298291.i	−2.80358	−	0.0898100i
$407$	−4.53773e6			−1.35785
$408$		0			0
$409$	1.14681e6			0.338986			0.169493	−	0.985531i	$-0.445787\pi$
$409$	1.14681e6			0.338986			0.169493	+	0.985531i	$0.445787\pi$
$410$	−3.41043e6	−	109250.i	−1.00196	−	0.0320968i
$411$		0			0
$412$	199765.	−	3.11481e6i	0.0579798	−	0.904043i
$413$		−	6.00455e6i		−	1.73223i
$414$		0			0
$415$			3.36870e6i			0.960155i
$416$	3.83100e6	+	618699.i	1.08537	+	0.175286i
$417$		0			0
$418$	113735.	−	3.55045e6i	0.0318387	−	0.993900i
$419$	−6.30867e6			−1.75551			−0.877754	−	0.479112i	$-0.840959\pi$
$419$	−6.30867e6			−1.75551			−0.877754	+	0.479112i	$0.840959\pi$
$420$		0			0
$421$	3.98399e6			1.09550			0.547750	−	0.836642i	$-0.315484\pi$
$421$	3.98399e6			1.09550			0.547750	+	0.836642i	$0.315484\pi$
$422$	−142837.	+	4.45891e6i	−0.0390445	+	1.21884i
$423$		0			0
$424$	−70451.0	+	731077.i	−0.0190315	+	0.197492i
$425$			2.31910e6i			0.622797i
$426$		0			0
$427$			2.14255e6i			0.568671i
$428$	−524930.	−	33665.8i	−0.138513	−	0.00888341i
$429$		0			0
$430$	4.16486e6	+	133417.i	1.08625	+	0.0347970i
$431$	2.55041e6			0.661327			0.330663	−	0.943749i	$-0.392728\pi$
$431$	2.55041e6			0.661327			0.330663	+	0.943749i	$0.392728\pi$
$432$		0			0
$433$	2.49831e6			0.640365			0.320182	−	0.947356i	$-0.396256\pi$
$433$	2.49831e6			0.640365			0.320182	+	0.947356i	$0.396256\pi$
$434$	−3.15260e6	−	100991.i	−0.803424	−	0.0257369i
$435$		0			0
$436$	−5.55462e6	−	356240.i	−1.39939	−	0.0897483i
$437$		−	2.36683e6i		−	0.592875i
$438$		0			0
$439$		−	3.48279e6i		−	0.862514i	−0.902229	−	0.431257i	$-0.858070\pi$
$439$		−	3.48279e6i		−	0.862514i	0.902229	−	0.431257i	$-0.141930\pi$
$440$	421583.	−	4.37481e6i	0.103813	−	1.07728i
$441$		0			0
$442$	169405.	−	5.28827e6i	0.0412449	−	1.28753i
$443$	−5.85754e6			−1.41810			−0.709049	−	0.705160i	$-0.750875\pi$
$443$	−5.85754e6			−1.41810			−0.709049	+	0.705160i	$0.750875\pi$
$444$		0			0
$445$	548990.			0.131421
$446$	−257890.	+	8.05050e6i	−0.0613901	+	1.91640i
$447$		0			0
$448$	−1.49479e6	+	7.68377e6i	−0.351872	+	1.80875i
$449$		−	208069.i		−	0.0487071i	−0.999703	−	0.0243535i	$-0.992247\pi$
$449$		−	208069.i		−	0.0487071i	0.999703	−	0.0243535i	$-0.00775274\pi$
$450$		0			0
$451$		−	3.05999e6i		−	0.708400i
$452$	467043.	−	7.28230e6i	0.107525	−	1.67657i
$453$		0			0
$454$	−4.04172e6	−	129473.i	−0.920295	−	0.0294808i
$455$	1.10715e7			2.50715
$456$		0			0
$457$	−15198.4			−0.00340415			−0.00170207	−	0.999999i	$-0.500542\pi$
$457$	−15198.4			−0.00340415			−0.00170207	+	0.999999i	$0.500542\pi$
$458$	3.62118e6	+	116001.i	0.806652	+	0.0258404i
$459$		0			0
$460$	187423.	−	2.92237e6i	0.0412980	−	0.643934i
$461$			344817.i			0.0755678i	0.999286	+	0.0377839i	$0.0120299\pi$
$461$			344817.i			0.0755678i	−0.999286	+	0.0377839i	$0.987970\pi$
$462$		0			0
$463$			60401.9i			0.0130948i	0.999979	+	0.00654739i	$0.00208411\pi$
$463$			60401.9i			0.0130948i	−0.999979	+	0.00654739i	$0.997916\pi$
$464$	−901820.	+	7.00183e6i	−0.194458	+	1.50979i
$465$		0			0
$466$	−174845.	+	5.45810e6i	−0.0372982	+	1.16433i
$467$	−3.80574e6			−0.807509			−0.403754	−	0.914867i	$-0.632295\pi$
$467$	−3.80574e6			−0.807509			−0.403754	+	0.914867i	$0.632295\pi$
$468$		0			0
$469$	−2.96360e6			−0.622140
$470$	−49979.3	+	1.56019e6i	−0.0104363	+	0.325787i
$471$		0			0
$472$	−4.52905e6	−	436446.i	−0.935733	−	0.0901729i
$473$			3.73690e6i			0.767995i
$474$		0			0
$475$			2.97211e6i			0.604408i
$476$	1.06508e7	+	683079.i	2.15459	+	0.138183i
$477$		0			0
$478$	−3.71647e6	−	119054.i	−0.743980	−	0.0238327i
$479$	4.93357e6			0.982476			0.491238	−	0.871025i	$-0.336544\pi$
$479$	4.93357e6			0.982476			0.491238	+	0.871025i	$0.336544\pi$
$480$		0			0
$481$	−8.66194e6			−1.70707
$482$	−6.14694e6	−	196912.i	−1.20515	−	0.0386059i
$483$		0			0
$484$	−1.20971e6	−	77583.6i	−0.234730	−	0.0150542i
$485$		−	3.91540e6i		−	0.755827i
$486$		0			0
$487$			1.40275e6i			0.268013i	0.990980	+	0.134007i	$0.0427844\pi$
$487$			1.40275e6i			0.268013i	−0.990980	+	0.134007i	$0.957216\pi$
$488$	1.61606e6	+	155733.i	0.307191	+	0.0296027i
$489$		0			0
$490$	−504455.	+	1.57475e7i	−0.0949144	+	2.96292i
$491$	9.21228e6			1.72450			0.862250	−	0.506483i	$-0.169055\pi$
$491$	9.21228e6			1.72450			0.862250	+	0.506483i	$0.169055\pi$
$492$		0			0
$493$	9.62537e6			1.78361
$494$	217106.	−	6.77734e6i	0.0400271	−	1.24952i
$495$		0			0
$496$	−305324.	+	2.37057e6i	−0.0557259	+	0.432662i
$497$			1.55358e6i			0.282126i
$498$		0			0
$499$		−	3.76154e6i		−	0.676260i	−0.941099	−	0.338130i	$-0.890206\pi$
$499$		−	3.76154e6i		−	0.676260i	0.941099	−	0.338130i	$-0.109794\pi$
$500$	207424.	−	3.23423e6i	0.0371051	−	0.578556i
$501$		0			0
$502$	−291284.	−	9331.01i	−0.0515890	−	0.00165261i
$503$	5.84609e6			1.03026			0.515128	−	0.857113i	$-0.327744\pi$
$503$	5.84609e6			1.03026			0.515128	+	0.857113i	$0.327744\pi$
$504$		0			0
$505$	5.04227e6			0.879827
$506$	2.62478e6	+	84082.3i	0.455739	+	0.0145992i
$507$		0			0
$508$	349123.	−	5.44366e6i	0.0600232	−	0.935904i
$509$		−	2.06029e6i		−	0.352480i	−0.984347	−	0.176240i	$-0.943607\pi$
$509$		−	2.06029e6i		−	0.352480i	0.984347	−	0.176240i	$-0.0563934\pi$
$510$		0			0
$511$		−	1.09532e7i		−	1.85561i
$512$	5.68699e6	+	1.68598e6i	0.958755	+	0.284235i
$513$		0			0
$514$	191756.	−	5.98599e6i	0.0320140	−	0.999375i
$515$	−6.74780e6			−1.12110
$516$		0			0
$517$	−1.39987e6			−0.230337
$518$	559425.	−	1.74634e7i	0.0916046	−	2.85960i
$519$		0			0
$520$	804746.	−	8.35094e6i	0.130512	−	1.35434i
$521$			9.31147e6i			1.50288i	0.659802	+	0.751439i	$0.270640\pi$
$521$			9.31147e6i			1.50288i	−0.659802	+	0.751439i	$0.729360\pi$
$522$		0			0
$523$			6.91429e6i			1.10533i	0.833402	+	0.552667i	$0.186390\pi$
$523$			6.91429e6i			1.10533i	−0.833402	+	0.552667i	$0.813610\pi$
$524$	−956214.	−	61325.8i	−0.152134	−	0.00975696i
$525$		0			0
$526$	9.55144e6	+	305971.i	1.50524	+	0.0482188i
$527$	3.25881e6			0.511131
$528$		0			0
$529$	−4.68659e6			−0.728145
$530$	1.58704e6	+	50839.2i	0.245413	+	0.00786157i
$531$		0			0
$532$	1.36499e7	+	875420.i	2.09098	+	0.134103i
$533$		−	5.84112e6i		−	0.890591i
$534$		0			0
$535$			1.13719e6i			0.171770i
$536$	−215412.	+	2.23536e6i	−0.0323861	+	0.336074i
$537$		0			0
$538$	168451.	−	5.25848e6i	0.0250909	−	0.783258i
$539$	−1.41293e7			−2.09483
$540$		0			0
$541$	−6.91946e6			−1.01643			−0.508217	−	0.861229i	$-0.669695\pi$
$541$	−6.91946e6			−1.01643			−0.508217	+	0.861229i	$0.669695\pi$
$542$	−365097.	+	1.13972e7i	−0.0533839	+	1.66647i
$543$		0			0
$544$	1.28939e6	−	7.98394e6i	0.186804	−	1.15670i
$545$			1.20333e7i			1.73538i
$546$		0			0
$547$			8.94295e6i			1.27795i	0.769229	+	0.638973i	$0.220640\pi$
$547$			8.94295e6i			1.27795i	−0.769229	+	0.638973i	$0.779360\pi$
$548$	−350318.	+	5.46229e6i	−0.0498323	+	0.777004i
$549$		0			0
$550$	−3.29602e6	−	105585.i	−0.464604	−	0.0148832i
$551$	1.23357e7			1.73095
$552$		0			0
$553$	8.94704e6			1.24413
$554$	−1.39108e7	−	445620.i	−1.92565	−	0.0616865i
$555$		0			0
$556$	−540572.	+	8.42879e6i	−0.0741594	+	1.15632i
$557$			3.85092e6i			0.525928i	0.964806	+	0.262964i	$0.0847000\pi$
$557$			3.85092e6i			0.525928i	−0.964806	+	0.262964i	$0.915300\pi$
$558$		0			0
$559$			7.13325e6i			0.965513i
$560$	1.67845e7	+	2.16180e6i	2.26171	+	0.291303i
$561$		0			0
$562$	218742.	−	6.82841e6i	0.0292140	−	0.911966i
$563$	6.40391e6			0.851480			0.425740	−	0.904846i	$-0.360014\pi$
$563$	6.40391e6			0.851480			0.425740	+	0.904846i	$0.360014\pi$
$564$		0			0
$565$	−1.57761e7			−2.07911
$566$	93632.3	−	2.92290e6i	0.0122853	−	0.383506i
$567$		0			0
$568$	1.17182e6	+	112924.i	0.152402	+	0.0146863i
$569$		−	1.05210e7i		−	1.36231i	−0.732137	−	0.681157i	$-0.761477\pi$
$569$		−	1.05210e7i		−	1.36231i	0.732137	−	0.681157i	$-0.238523\pi$
$570$		0			0
$571$		−	1.25121e6i		−	0.160598i	−0.996771	−	0.0802990i	$-0.974412\pi$
$571$		−	1.25121e6i		−	0.160598i	0.996771	−	0.0802990i	$-0.0255875\pi$
$572$	7.50826e6	+	481534.i	0.959509	+	0.0615371i
$573$		0			0
$574$	1.17764e7	+	377244.i	1.49187	+	0.0477907i
$575$	−2.19722e6			−0.277143
$576$		0			0
$577$	578609.			0.0723511			0.0361756	−	0.999345i	$-0.488482\pi$
$577$	578609.			0.0723511			0.0361756	+	0.999345i	$0.488482\pi$
$578$	−2.99313e6	−	95882.2i	−0.372655	−	0.0119376i
$579$		0			0
$580$	1.52311e7	+	976833.i	1.88002	+	0.120573i
$581$		−	1.16322e7i		−	1.42963i
$582$		0			0
$583$			1.42396e6i			0.173511i
$584$	−8.26165e6	−	796142.i	−1.00239	−	0.0965959i
$585$		0			0
$586$	−374072.	+	1.16773e7i	−0.0449999	+	1.40475i
$587$	−6.35138e6			−0.760804			−0.380402	−	0.924821i	$-0.624214\pi$
$587$	−6.35138e6			−0.760804			−0.380402	+	0.924821i	$0.624214\pi$
$588$		0			0
$589$	4.17643e6			0.496040
$590$	−314951.	+	9.83175e6i	−0.0372488	+	1.16279i
$591$		0			0
$592$	−1.31315e7	−	1.69130e6i	−1.53996	−	0.198343i
$593$		−	1.12494e7i		−	1.31369i	−0.754026	−	0.656845i	$-0.771891\pi$
$593$		−	1.12494e7i		−	1.31369i	0.754026	−	0.656845i	$-0.228109\pi$
$594$		0			0
$595$		−	2.30735e7i		−	2.67190i
$596$	−97597.2	+	1.52177e6i	−0.0112544	+	0.175482i
$597$		0			0
$598$	5.01036e6	+	160502.i	0.572949	+	0.0183539i
$599$	3.98685e6			0.454007			0.227004	−	0.973894i	$-0.427107\pi$
$599$	3.98685e6			0.454007			0.227004	+	0.973894i	$0.427107\pi$
$600$		0			0
$601$	−5.93772e6			−0.670553			−0.335277	−	0.942120i	$-0.608830\pi$
$601$	−5.93772e6			−0.670553			−0.335277	+	0.942120i	$0.608830\pi$
$602$	−1.43814e7	−	460696.i	−1.61738	−	0.0518111i
$603$		0			0
$604$	−719047.	+	1.12116e7i	−0.0801982	+	1.25048i
$605$			2.62067e6i			0.291088i
$606$		0			0
$607$			7.86463e6i			0.866376i	0.901304	+	0.433188i	$0.142611\pi$
$607$			7.86463e6i			0.866376i	−0.901304	+	0.433188i	$0.857389\pi$
$608$	1.65246e6	−	1.02321e7i	0.181289	−	1.12255i
$609$		0			0
$610$	112381.	−	3.50817e6i	0.0122284	−	0.381730i
$611$	−2.67218e6			−0.289576
$612$		0			0
$613$	−6.66739e6			−0.716646			−0.358323	−	0.933598i	$-0.616651\pi$
$613$	−6.66739e6			−0.716646			−0.358323	+	0.933598i	$0.616651\pi$
$614$	80263.4	−	2.50556e6i	0.00859205	−	0.268216i
$615$		0			0
$616$	−1.45574e6	+	1.51064e7i	−0.154573	+	1.60402i
$617$		−	1.13568e7i		−	1.20100i	−0.799627	−	0.600498i	$-0.794969\pi$
$617$		−	1.13568e7i		−	1.20100i	0.799627	−	0.600498i	$-0.205031\pi$
$618$		0			0
$619$			5.72429e6i			0.600475i	0.953864	+	0.300237i	$0.0970659\pi$
$619$			5.72429e6i			0.600475i	−0.953864	+	0.300237i	$0.902934\pi$
$620$	5.15672e6	+	330721.i	0.538759	+	0.0345527i
$621$		0			0
$622$	9.00448e6	+	288450.i	0.933217	+	0.0298947i
$623$	−1.89569e6			−0.195680
$624$		0			0
$625$	−1.21973e7			−1.24901
$626$	−1.30474e6	−	41796.1i	−0.133072	−	0.00426285i
$627$		0			0
$628$	9.12743e6	+	585378.i	0.923527	+	0.0592294i
$629$			1.80518e7i			1.81925i
$630$		0			0
$631$		−	1.24837e7i		−	1.24816i	−0.781360	−	0.624080i	$-0.785474\pi$
$631$		−	1.24837e7i		−	1.24816i	0.781360	−	0.624080i	$-0.214526\pi$
$632$	650325.	−	6.74849e6i	0.0647646	−	0.672069i
$633$		0			0
$634$	333769.	−	1.04192e7i	0.0329779	−	1.02946i
$635$	−1.17929e7			−1.16061
$636$		0			0
$637$	−2.69710e7			−2.63359
$638$	−438229.	+	1.36801e7i	−0.0426235	+	1.33057i
$639$		0			0
$640$	2.85058e6	−	1.25029e7i	0.275095	−	1.20659i
$641$			1.81736e7i			1.74702i	0.486810	+	0.873508i	$0.338160\pi$
$641$			1.81736e7i			1.74702i	−0.486810	+	0.873508i	$0.661840\pi$
$642$		0			0
$643$		−	5.93003e6i		−	0.565626i	−0.959175	−	0.282813i	$-0.908732\pi$
$643$		−	5.93003e6i		−	0.565626i	0.959175	−	0.282813i	$-0.0912676\pi$
$644$	−647181.	+	1.00911e7i	−0.0614909	+	0.958789i
$645$		0			0
$646$	−1.41242e7	−	452456.i	−1.33163	−	0.0426575i
$647$	−1.54374e7			−1.44982			−0.724909	−	0.688844i	$-0.758118\pi$
$647$	−1.54374e7			−1.44982			−0.724909	+	0.688844i	$0.758118\pi$
$648$		0			0
$649$	−8.82148e6			−0.822110
$650$	−6.29168e6	−	201548.i	−0.584094	−	0.0187109i
$651$		0			0
$652$	264138.	−	4.11854e6i	0.0243339	−	0.379423i
$653$			1.88052e7i			1.72582i	0.505357	+	0.862910i	$0.331361\pi$
$653$			1.88052e7i			1.72582i	−0.505357	+	0.862910i	$0.668639\pi$
$654$		0			0
$655$			2.07150e6i			0.188661i
$656$	1.14052e6	−	8.85513e6i	0.103477	−	0.803407i
$657$		0			0
$658$	172581.	−	5.38741e6i	0.0155392	−	0.485082i
$659$	−1.30752e7			−1.17283			−0.586416	−	0.810010i	$-0.699461\pi$
$659$	−1.30752e7			−1.17283			−0.586416	+	0.810010i	$0.699461\pi$
$660$		0			0
$661$	1.29277e7			1.15085			0.575424	−	0.817855i	$-0.304837\pi$
$661$	1.29277e7			1.15085			0.575424	+	0.817855i	$0.304837\pi$
$662$	−363080.	+	1.13342e7i	−0.0322001	+	1.00518i
$663$		0			0
$664$	−8.77385e6	−	845501.i	−0.772272	−	0.0744208i
$665$		−	2.95705e7i		−	2.59301i
$666$		0			0
$667$			9.11953e6i			0.793703i
$668$	−1.78776e7	−	1.14656e6i	−1.55013	−	0.0994159i
$669$		0			0
$670$	4.85256e6	+	155447.i	0.417622	+	0.0133781i
$671$	3.14769e6			0.269889
$672$		0			0
$673$	−2.11203e6			−0.179748			−0.0898738	−	0.995953i	$-0.528646\pi$
$673$	−2.11203e6			−0.179748			−0.0898738	+	0.995953i	$0.528646\pi$
$674$	−6.32552e6	−	202632.i	−0.536348	−	0.0171814i
$675$		0			0
$676$	2.47527e6	+	158749.i	0.208332	+	0.0133611i
$677$			1.57270e6i			0.131878i	0.997824	+	0.0659391i	$0.0210043\pi$
$677$			1.57270e6i			0.131878i	−0.997824	+	0.0659391i	$0.978996\pi$
$678$		0			0
$679$			1.35200e7i			1.12539i
$680$	−1.74036e7	−	1.67712e6i	−1.44334	−	0.139089i
$681$		0			0
$682$	−148369.	+	4.63159e6i	−0.0122147	+	0.381302i
$683$	990320.			0.0812314			0.0406157	−	0.999175i	$-0.487068\pi$
$683$	990320.			0.0812314			0.0406157	+	0.999175i	$0.487068\pi$
$684$		0			0
$685$	1.18333e7			0.963559
$686$	1.01472e6	−	3.16762e7i	0.0823256	−	2.56994i
$687$		0			0
$688$	−1.39282e6	+	1.08140e7i	−0.112182	+	0.870994i
$689$			2.71815e6i			0.218135i
$690$		0			0
$691$			3.19912e6i			0.254880i	0.991846	+	0.127440i	$0.0406760\pi$
$691$			3.19912e6i			0.254880i	−0.991846	+	0.127440i	$0.959324\pi$
$692$	1.07201e6	−	1.67152e7i	0.0851011	−	1.32693i
$693$		0			0
$694$	1.98615e6	+	63624.4i	0.156536	+	0.00501447i
$695$	1.82598e7			1.43395
$696$		0			0
$697$	−1.21731e7			−0.949115
$698$	8.98125e6	+	287706.i	0.697747	+	0.0223517i
$699$		0			0
$700$	812687.	−	1.26717e7i	0.0626871	−	0.977440i
$701$			1.09808e7i			0.843993i	0.906597	+	0.421996i	$0.138671\pi$
$701$			1.09808e7i			0.843993i	−0.906597	+	0.421996i	$0.861329\pi$
$702$		0			0
$703$			2.31348e7i			1.76554i
$704$	1.12885e7	+	2.19605e6i	0.858429	+	0.166997i
$705$		0			0
$706$	341776.	−	1.06691e7i	0.0258066	−	0.805597i
$707$	−1.74111e7			−1.31002
$708$		0			0
$709$	2.37875e7			1.77719			0.888594	−	0.458694i	$-0.151683\pi$
$709$	2.37875e7			1.77719			0.888594	+	0.458694i	$0.151683\pi$
$710$	81488.5	−	2.54381e6i	0.00606667	−	0.189382i
$711$		0			0
$712$	−137790.	+	1.42986e6i	−0.0101863	+	0.105704i
$713$			3.08755e6i			0.227452i
$714$		0			0
$715$		−	1.62656e7i		−	1.18988i
$716$	2.28426e7	+	1.46499e6i	1.66519	+	0.106795i
$717$		0			0
$718$	−1.20587e7	−	386290.i	−0.872952	−	0.0279642i
$719$	1.91638e7			1.38248			0.691239	−	0.722626i	$-0.257065\pi$
$719$	1.91638e7			1.38248			0.691239	+	0.722626i	$0.257065\pi$
$720$		0			0
$721$	2.33004e7			1.66927
$722$	−4.10156e6	−	131390.i	−0.292824	−	0.00938033i
$723$		0			0
$724$	9.16073e6	+	587513.i	0.649506	+	0.0416554i
$725$		−	1.14517e7i		−	0.809143i
$726$		0			0
$727$		−	977419.i		−	0.0685874i	−0.999412	−	0.0342937i	$-0.989082\pi$
$727$		−	977419.i		−	0.0685874i	0.999412	−	0.0342937i	$-0.0109182\pi$
$728$	−2.77882e6	+	2.88361e7i	−0.194327	+	2.01655i
$729$		0			0
$730$	−574517.	+	1.79346e7i	−0.0399021	+	1.24561i
$731$	1.48659e7			1.02896
$732$		0			0
$733$	1.68872e6			0.116091			0.0580455	−	0.998314i	$-0.481513\pi$
$733$	1.68872e6			0.116091			0.0580455	+	0.998314i	$0.481513\pi$
$734$	295343.	−	9.21964e6i	0.0202342	−	0.631646i
$735$		0			0
$736$	7.56436e6	+	1.22163e6i	0.514728	+	0.0831275i
$737$			4.35393e6i			0.295265i
$738$		0			0
$739$		−	5.82227e6i		−	0.392176i	−0.980586	−	0.196088i	$-0.937176\pi$
$739$		−	5.82227e6i		−	0.392176i	0.980586	−	0.196088i	$-0.0628238\pi$
$740$	−1.83199e6	+	2.85650e7i	−0.122982	+	1.91759i
$741$		0			0
$742$	−5.48010e6	−	175550.i	−0.365409	−	0.0117055i
$743$	−4.95294e6			−0.329148			−0.164574	−	0.986365i	$-0.552625\pi$
$743$	−4.95294e6			−0.329148			−0.164574	+	0.986365i	$0.552625\pi$
$744$		0			0
$745$	3.29670e6			0.217615
$746$	1.73532e7	+	555895.i	1.14165	+	0.0365717i
$747$		0			0
$748$	1.00353e6	−	1.56475e7i	0.0655810	−	1.02256i
$749$		−	3.92675e6i		−	0.255758i
$750$		0			0
$751$		−	1.06174e7i		−	0.686940i	−0.939164	−	0.343470i	$-0.888398\pi$
$751$		−	1.06174e7i		−	0.686940i	0.939164	−	0.343470i	$-0.111602\pi$
$752$	−4.05102e6	−	521762.i	−0.261228	−	0.0336456i
$753$		0			0
$754$	−836522.	+	2.61135e7i	−0.0535857	+	1.67277i
$755$	2.42884e7			1.55072
$756$		0			0
$757$	−4.59623e6			−0.291516			−0.145758	−	0.989320i	$-0.546562\pi$
$757$	−4.59623e6			−0.291516			−0.145758	+	0.989320i	$0.546562\pi$
$758$	−464843.	+	1.45109e7i	−0.0293855	+	0.917322i
$759$		0			0
$760$	−2.23042e7	−	2.14936e6i	−1.40072	−	0.134982i
$761$		−	2.15027e7i		−	1.34596i	−0.739661	−	0.672979i	$-0.765014\pi$
$761$		−	2.15027e7i		−	1.34596i	0.739661	−	0.672979i	$-0.234986\pi$
$762$		0			0
$763$		−	4.15515e7i		−	2.58390i
$764$	−3.89373e6	−	249720.i	−0.241342	−	0.0154782i
$765$		0			0
$766$	2.10922e7	+	675670.i	1.29882	+	0.0416066i
$767$	−1.68391e7			−1.03354
$768$		0			0
$769$	2.82987e7			1.72564			0.862821	−	0.505510i	$-0.168696\pi$
$769$	2.82987e7			1.72564			0.862821	+	0.505510i	$0.168696\pi$
$770$	3.27932e7	+	1.05050e6i	1.99323	+	0.0638513i
$771$		0			0
$772$	7.58796e6	+	486646.i	0.458228	+	0.0293880i
$773$			1.93324e6i			0.116369i	0.998306	+	0.0581845i	$0.0185312\pi$
$773$			1.93324e6i			0.116369i	−0.998306	+	0.0581845i	$0.981469\pi$
$774$		0			0
$775$		−	3.87714e6i		−	0.231877i
$776$	1.01978e7	+	982718.i	0.607926	+	0.0585834i
$777$		0			0
$778$	−601387.	+	1.87733e7i	−0.0356209	+	1.11197i
$779$	−1.56008e7			−0.921092
$780$		0			0
$781$	2.28242e6			0.133896
$782$	334492.	−	1.04418e7i	0.0195600	−	0.610600i
$783$		0			0
$784$	−4.08880e7	−	5.26628e6i	−2.37578	−	0.305995i
$785$		−	1.97733e7i		−	1.14526i
$786$		0			0
$787$			7.01512e6i			0.403737i	0.979413	+	0.201868i	$0.0647013\pi$
$787$			7.01512e6i			0.403737i	−0.979413	+	0.201868i	$0.935299\pi$
$788$	1.36761e6	−	2.13243e7i	0.0784600	−	1.22338i
$789$		0			0
$790$	−1.46497e7	−	469291.i	−0.835146	−	0.0267531i
$791$	5.44754e7			3.09570
$792$		0			0
$793$	6.00853e6			0.339301
$794$	1.26981e7	+	406773.i	0.714807	+	0.0228982i
$795$		0			0
$796$	472074.	−	7.36075e6i	0.0264075	−	0.411756i
$797$			1.01331e7i			0.565060i	0.959258	+	0.282530i	$0.0911737\pi$
$797$			1.01331e7i			0.565060i	−0.959258	+	0.282530i	$0.908826\pi$
$798$		0			0
$799$			5.56891e6i			0.308605i
$800$	−9.49882e6	−	1.53404e6i	−0.524741	−	0.0847446i
$801$		0			0
$802$	822787.	−	2.56848e7i	0.0451702	−	1.41007i
$803$	−1.60917e7			−0.880669
$804$		0			0
$805$	2.18609e7			1.18899
$806$	−283217.	+	8.84110e6i	−0.0153561	+	0.479368i
$807$		0			0
$808$	−1.26555e6	+	1.31327e7i	−0.0681946	+	0.707662i
$809$			5.65648e6i			0.303861i	0.988391	+	0.151930i	$0.0485490\pi$
$809$			5.65648e6i			0.303861i	−0.988391	+	0.151930i	$0.951451\pi$
$810$		0			0
$811$			2.13565e7i			1.14019i	0.821579	+	0.570095i	$0.193093\pi$
$811$			2.13565e7i			1.14019i	−0.821579	+	0.570095i	$0.806907\pi$
$812$	−5.25937e7	−	3.37304e6i	−2.79926	−	0.179528i
$813$		0			0
$814$	−2.56561e7	−	821870.i	−1.35716	−	0.0434753i
$815$	−8.92223e6			−0.470521
$816$		0			0
$817$	1.90519e7			0.998580
$818$	6.48400e6	+	207709.i	0.338813	+	0.0108535i
$819$		0			0
$820$	−1.92626e7	−	1.23539e6i	−1.00042	−	0.0641607i
$821$		−	2.63136e7i		−	1.36246i	−0.732071	−	0.681229i	$-0.761446\pi$
$821$		−	2.63136e7i		−	1.36246i	0.732071	−	0.681229i	$-0.238554\pi$
$822$		0			0
$823$			1.75614e7i			0.903772i	0.892076	+	0.451886i	$0.149249\pi$
$823$			1.75614e7i			0.903772i	−0.892076	+	0.451886i	$0.850751\pi$
$824$	1.69362e6	−	1.75748e7i	0.0868954	−	0.901723i
$825$		0			0
$826$	1.08754e6	−	3.39494e7i	0.0554619	−	1.73134i
$827$	−5.50797e6			−0.280045			−0.140022	−	0.990148i	$-0.544717\pi$
$827$	−5.50797e6			−0.280045			−0.140022	+	0.990148i	$0.544717\pi$
$828$		0			0
$829$	7.81244e6			0.394821			0.197411	−	0.980321i	$-0.436747\pi$
$829$	7.81244e6			0.394821			0.197411	+	0.980321i	$0.436747\pi$
$830$	−610135.	+	1.90465e7i	−0.0307419	+	0.959663i
$831$		0			0
$832$	2.15483e7	+	4.19197e6i	1.07920	+	0.209947i
$833$			5.62085e7i			2.80666i
$834$		0			0
$835$			3.87293e7i			1.92231i
$836$	1.28611e6	−	2.00535e7i	0.0636447	−	0.992371i
$837$		0			0
$838$	−3.56689e7	−	1.14262e6i	−1.75461	−	0.0562072i
$839$	3.55868e7			1.74535			0.872677	−	0.488298i	$-0.162382\pi$
$839$	3.55868e7			1.74535			0.872677	+	0.488298i	$0.162382\pi$
$840$		0			0
$841$	−2.70190e7			−1.31728
$842$	2.25253e7	+	721576.i	1.09494	+	0.0350754i
$843$		0			0
$844$	−1.61519e6	+	2.51846e7i	−0.0780489	+	1.21697i
$845$		−	5.36232e6i		−	0.258351i
$846$		0			0
$847$		−	9.04928e6i		−	0.433417i
$848$	−530739.	+	4.12072e6i	−0.0253449	+	0.196781i
$849$		0			0
$850$	−420033.	+	1.31121e7i	−0.0199405	+	0.622478i
$851$	−1.71031e7			−0.809563
$852$		0			0
$853$	−2.84336e6			−0.133801			−0.0669006	−	0.997760i	$-0.521311\pi$
$853$	−2.84336e6			−0.133801			−0.0669006	+	0.997760i	$0.521311\pi$
$854$	−388056.	+	1.21139e7i	−0.0182075	+	0.568379i
$855$		0			0
$856$	−2.96183e6	−	285420.i	−0.138158	−	0.0133137i
$857$			2.74865e7i			1.27840i	0.769039	+	0.639202i	$0.220735\pi$
$857$			2.74865e7i			1.27840i	−0.769039	+	0.639202i	$0.779265\pi$
$858$		0			0
$859$		−	6.08862e6i		−	0.281537i	−0.990043	−	0.140769i	$-0.955043\pi$
$859$		−	6.08862e6i		−	0.281537i	0.990043	−	0.140769i	$-0.0449574\pi$
$860$	2.35238e7	+	1.50867e6i	1.08458	+	0.0695583i
$861$		0			0
$862$	1.44199e7	+	461927.i	0.660988	+	0.0211741i
$863$	−4.93253e6			−0.225446			−0.112723	−	0.993626i	$-0.535957\pi$
$863$	−4.93253e6			−0.225446			−0.112723	+	0.993626i	$0.535957\pi$
$864$		0			0
$865$	−3.62112e7			−1.64552
$866$	1.41254e7	+	452493.i	0.640036	+	0.0205030i
$867$		0			0
$868$	−1.78064e7	−	1.14199e6i	−0.802188	−	0.0514475i
$869$		−	1.31444e7i		−	0.590461i
$870$		0			0
$871$			8.31108e6i			0.371204i
$872$	−3.13411e7	−	3.02021e6i	−1.39580	−	0.134507i
$873$		0			0
$874$	428678.	−	1.33819e7i	0.0189825	−	0.592571i
$875$	2.41937e7			1.06827
$876$		0			0
$877$	−3.46817e6			−0.152266			−0.0761328	−	0.997098i	$-0.524257\pi$
$877$	−3.46817e6			−0.152266			−0.0761328	+	0.997098i	$0.524257\pi$
$878$	630800.	−	1.96915e7i	0.0276157	−	0.862072i
$879$		0			0
$880$	3.17597e6	−	2.46586e7i	0.138252	−	1.07340i
$881$			2.97742e6i			0.129241i	0.997910	+	0.0646204i	$0.0205837\pi$
$881$			2.97742e6i			0.129241i	−0.997910	+	0.0646204i	$0.979416\pi$
$882$		0			0
$883$			1.81106e6i			0.0781682i	0.999236	+	0.0390841i	$0.0124440\pi$
$883$			1.81106e6i			0.0781682i	−0.999236	+	0.0390841i	$0.987556\pi$
$884$	1.91561e6	−	2.98690e7i	0.0824475	−	1.28555i
$885$		0			0
$886$	−3.31183e7	−	1.06091e6i	−1.41737	−	0.0454041i
$887$	−3.34260e7			−1.42651			−0.713256	−	0.700903i	$-0.752780\pi$
$887$	−3.34260e7			−1.42651			−0.713256	+	0.700903i	$0.752780\pi$
$888$		0			0
$889$	4.07214e7			1.72810
$890$	3.10397e6	+	99432.7i	0.131354	+	0.00420779i
$891$		0			0
$892$	−2.91620e6	+	4.54705e7i	−0.122717	+	1.91345i
$893$			7.13700e6i			0.299493i
$894$		0			0
$895$		−	4.94853e7i		−	2.06500i
$896$	−9.84315e6	+	4.31730e7i	−0.409604	+	1.79656i
$897$		0			0
$898$	37685.3	−	1.17641e6i	0.00155949	−	0.0486821i
$899$	−1.60920e7			−0.664066
$900$		0			0
$901$	5.66472e6			0.232470
$902$	554223.	−	1.73010e7i	0.0226813	−	0.708037i
$903$		0			0
$904$	3.95960e6	−	4.10892e7i	0.161150	−	1.67227i
$905$		−	1.98454e7i		−	0.805451i
$906$		0			0
$907$		−	3.39164e7i		−	1.36896i	−0.729031	−	0.684481i	$-0.760029\pi$
$907$		−	3.39164e7i		−	1.36896i	0.729031	−	0.684481i	$-0.239971\pi$
$908$	−2.28283e7	−	1.46407e6i	−0.918879	−	0.0589313i
$909$		0			0
$910$	6.25980e7	+	2.00527e6i	2.50586	+	0.0802730i
$911$	−2.31991e7			−0.926136			−0.463068	−	0.886323i	$-0.653251\pi$
$911$	−2.31991e7			−0.926136			−0.463068	+	0.886323i	$0.653251\pi$
$912$		0			0
$913$	−1.70893e7			−0.678497
$914$	−85931.3	−	2752.73i	−0.00340240	−	0.000108993i
$915$		0			0
$916$	2.04530e7	+	1.31173e6i	0.805411	+	0.0516542i
$917$		−	7.15298e6i		−	0.280908i
$918$		0			0
$919$		−	4.47623e7i		−	1.74833i	−0.485628	−	0.874165i	$-0.661409\pi$
$919$		−	4.47623e7i		−	1.74833i	0.485628	−	0.874165i	$-0.338591\pi$
$920$	1.58898e6	−	1.64890e7i	0.0618941	−	0.642281i
$921$		0			0
$922$	−62453.0	+	1.94958e6i	−0.00241950	+	0.0755290i
$923$	4.35684e6			0.168332
$924$		0			0
$925$	2.14769e7			0.825312
$926$	−10939.9	+	341509.i	−0.000419264	+	0.0130881i
$927$		0			0
$928$	−6.36701e6	+	3.94247e7i	−0.242698	+	1.50279i
$929$			1.75173e7i			0.665927i	0.942940	+	0.332964i	$0.108049\pi$
$929$			1.75173e7i			0.665927i	−0.942940	+	0.332964i	$0.891951\pi$
$930$		0			0
$931$			7.20357e7i			2.72379i
$932$	−1.97713e6	+	3.08282e7i	−0.0745582	+	1.16254i
$933$		0			0
$934$	−2.15175e7	−	689293.i	−0.807095	−	0.0258545i
$935$	−3.38980e7			−1.26808
$936$		0			0
$937$	3.08368e7			1.14742			0.573708	−	0.819060i	$-0.305505\pi$
$937$	3.08368e7			1.14742			0.573708	+	0.819060i	$0.305505\pi$
$938$	−1.67561e7	−	536765.i	−0.621821	−	0.0199194i
$939$		0			0
$940$	−565162.	+	8.81221e6i	−0.0208619	+	0.325286i
$941$		−	1.99825e7i		−	0.735658i	−0.929894	−	0.367829i	$-0.880101\pi$
$941$		−	1.99825e7i		−	0.735658i	0.929894	−	0.367829i	$-0.119899\pi$
$942$		0			0
$943$		−	1.15334e7i		−	0.422354i
$944$	−2.55280e7	−	3.28795e6i	−0.932366	−	0.120087i
$945$		0			0
$946$	−676824.	+	2.11283e7i	−0.0245894	+	0.767601i
$947$	3.21068e7			1.16338			0.581690	−	0.813410i	$-0.302392\pi$
$947$	3.21068e7			1.16338			0.581690	+	0.813410i	$0.302392\pi$
$948$		0			0
$949$	−3.07169e7			−1.10716
$950$	−538306.	+	1.68042e7i	−0.0193517	+	0.604099i
$951$		0			0
$952$	6.00955e7	+	5.79116e6i	2.14906	+	0.207097i
$953$		−	2.79150e7i		−	0.995648i	−0.867278	−	0.497824i	$-0.834133\pi$
$953$		−	2.79150e7i		−	0.995648i	0.867278	−	0.497824i	$-0.165867\pi$
$954$		0			0
$955$			8.43522e6i			0.299287i
$956$	−2.09912e7	−	1.34625e6i	−0.742835	−	0.0476410i
$957$		0			0
$958$	2.78942e7	+	893563.i	0.981973	+	0.0314566i
$959$	−4.08608e7			−1.43470
$960$		0			0
$961$	2.31810e7			0.809698
$962$	−4.89742e7	−	1.56884e6i	−1.70620	−	0.0546565i
$963$		0			0
$964$	−3.47189e7	−	2.22666e6i	−1.20330	−	0.0771722i
$965$		−	1.64382e7i		−	0.568247i
$966$		0			0
$967$		−	1.25000e7i		−	0.429878i	−0.976628	−	0.214939i	$-0.931045\pi$
$967$		−	1.25000e7i		−	0.429878i	0.976628	−	0.214939i	$-0.0689552\pi$
$968$	−6.82560e6	−	657756.i	−0.234128	−	0.0225619i
$969$		0			0
$970$	709154.	−	2.21375e7i	0.0241998	−	0.755439i
$971$	2.43379e7			0.828390			0.414195	−	0.910188i	$-0.364063\pi$
$971$	2.43379e7			0.828390			0.414195	+	0.910188i	$0.364063\pi$
$972$		0			0
$973$	−6.30518e7			−2.13509
$974$	−254064.	+	7.93106e6i	−0.00858116	+	0.267876i
$975$		0			0
$976$	9.10892e6	+	1.17321e6i	0.306085	+	0.0394231i
$977$		−	1.85003e7i		−	0.620073i	−0.950725	−	0.310037i	$-0.899659\pi$
$977$		−	1.85003e7i		−	0.620073i	0.950725	−	0.310037i	$-0.100341\pi$
$978$		0			0
$979$			2.78502e6i			0.0928691i
$980$	−5.70433e6	+	8.89440e7i	−0.189732	+	2.95836i
$981$		0			0
$982$	5.20858e7	+	1.66852e6i	1.72362	+	0.0552144i
$983$	−5.11354e7			−1.68787			−0.843933	−	0.536449i	$-0.819765\pi$
$983$	−5.11354e7			−1.68787			−0.843933	+	0.536449i	$0.819765\pi$
$984$		0			0
$985$	−4.61962e7			−1.51710
$986$	5.44214e7	+	1.74334e6i	1.78270	+	0.0571070i
$987$		0			0
$988$	2.45501e6	−	3.82795e7i	0.0800132	−	1.24759i
$989$			1.40847e7i			0.457885i
$990$		0			0
$991$			9.59641e6i			0.310402i	0.987883	+	0.155201i	$0.0496025\pi$
$991$			9.59641e6i			0.310402i	−0.987883	+	0.155201i	$0.950397\pi$
$992$	−2.15564e6	+	1.33478e7i	−0.0695501	+	0.430656i
$993$		0			0
$994$	−281383.	+	8.78387e6i	−0.00903300	+	0.281981i
$995$	−1.59460e7			−0.510617
$996$		0			0
$997$	−4.14442e7			−1.32046			−0.660232	−	0.751062i	$-0.729542\pi$
$997$	−4.14442e7			−1.32046			−0.660232	+	0.751062i	$0.729542\pi$
$998$	681286.	−	2.12676e7i	0.0216523	−	0.675914i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.b.b.107.16	yes	16
3.2	odd	2	inner	108.6.b.b.107.1	✓	16
4.3	odd	2	inner	108.6.b.b.107.2	yes	16
12.11	even	2	inner	108.6.b.b.107.15	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.6.b.b.107.1	✓	16	3.2	odd	2	inner
108.6.b.b.107.2	yes	16	4.3	odd	2	inner
108.6.b.b.107.15	yes	16	12.11	even	2	inner
108.6.b.b.107.16	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)

\(f(q)\)	\(=\)	\(q+(5.65395 + 0.181119i) q^{2} +(31.9344 + 2.04808i) q^{4} -69.1814i q^{5} +238.886i q^{7} +(180.185 + 17.3637i) q^{8} +O(q^{10})\)	\(q+(5.65395 + 0.181119i) q^{2} +(31.9344 + 2.04808i) q^{4} -69.1814i q^{5} +238.886i q^{7} +(180.185 + 17.3637i) q^{8} +(12.5301 - 391.148i) q^{10} +350.956 q^{11} +669.928 q^{13} +(-43.2668 + 1350.65i) q^{14} +(1015.61 + 130.808i) q^{16} -1396.15i q^{17} -1789.28i q^{19} +(141.689 - 2209.26i) q^{20} +(1984.29 + 63.5648i) q^{22} +1322.78 q^{23} -1661.06 q^{25} +(3787.74 + 121.337i) q^{26} +(-489.257 + 7628.68i) q^{28} +6894.21i q^{29} +2334.13i q^{31} +(5718.52 + 923.531i) q^{32} +(252.870 - 7893.79i) q^{34} +16526.5 q^{35} -12929.6 q^{37} +(324.073 - 10116.5i) q^{38} +(1201.24 - 12465.4i) q^{40} -8719.02i q^{41} +10647.8i q^{43} +(11207.6 + 718.785i) q^{44} +(7478.94 + 239.581i) q^{46} -3988.75 q^{47} -40259.6 q^{49} +(-9391.56 - 300.850i) q^{50} +(21393.8 + 1372.07i) q^{52} +4057.38i q^{53} -24279.6i q^{55} +(-4147.94 + 43043.6i) q^{56} +(-1248.67 + 38979.5i) q^{58} -25135.6 q^{59} +8968.91 q^{61} +(-422.756 + 13197.1i) q^{62} +(32165.0 + 6257.33i) q^{64} -46346.6i q^{65} +12405.9i q^{67} +(2859.43 - 44585.3i) q^{68} +(93439.9 + 2993.26i) q^{70} +6503.43 q^{71} -45851.0 q^{73} +(-73103.6 - 2341.81i) q^{74} +(3664.59 - 57139.6i) q^{76} +83838.4i q^{77} -37453.2i q^{79} +(9049.50 - 70261.3i) q^{80} +(1579.18 - 49296.9i) q^{82} -48693.7 q^{83} -96587.8 q^{85} +(-1928.52 + 60202.1i) q^{86} +(63236.8 + 6093.88i) q^{88} +7935.52i q^{89} +160037. i q^{91} +(42242.2 + 2709.16i) q^{92} +(-22552.2 - 722.439i) q^{94} -123785. q^{95} +56596.2 q^{97} +(-227626. - 7291.78i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 94 q^{4}+O(q^{10}) \) 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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