LMFDB - Embedded newform 108.6.b.c.107.4

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:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 94 x^{18} + 5872 x^{16} - 207192 x^{14} + 5271952 x^{12} - 76648960 x^{10} + 792478720 x^{8} + \cdots + 41943040000 $ x^20 - 94x^18 + 5872x^16 - 207192x^14 + 5271952x^12 - 76648960x^10 + 792478720x^8 - 4371873792x^6 + 17152147456x^4 - 32033996800*x^2 + 41943040000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{50}\cdot 3^{40} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			107.4
Root			$5.24560 + 3.02855i$ of defining polynomial
Character	$\chi$	$=$	108.107
Dual form			108.6.b.c.107.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.45658 + 3.48409i) q^{2} +(7.72226 - 31.0543i) q^{4} -40.4806i q^{5} +148.504i q^{7} +(73.7809 + 165.301i) q^{8} +O(q^{10})$	\(q+(-4.45658 + 3.48409i) q^{2} +(7.72226 - 31.0543i) q^{4} -40.4806i q^{5} +148.504i q^{7} +(73.7809 + 165.301i) q^{8} +(141.038 + 180.405i) q^{10} -608.102 q^{11} +883.839 q^{13} +(-517.402 - 661.822i) q^{14} +(-904.733 - 479.618i) q^{16} -1133.69i q^{17} -1111.90i q^{19} +(-1257.09 - 312.602i) q^{20} +(2710.06 - 2118.68i) q^{22} +1347.14 q^{23} +1486.32 q^{25} +(-3938.90 + 3079.37i) q^{26} +(4611.69 + 1146.79i) q^{28} +1856.29i q^{29} +606.496i q^{31} +(5703.05 - 1014.71i) q^{32} +(3949.86 + 5052.36i) q^{34} +6011.54 q^{35} +13662.1 q^{37} +(3873.96 + 4955.28i) q^{38} +(6691.48 - 2986.69i) q^{40} -21260.5i q^{41} -12478.1i q^{43} +(-4695.92 + 18884.1i) q^{44} +(-6003.66 + 4693.57i) q^{46} +16295.9 q^{47} -5246.55 q^{49} +(-6623.92 + 5178.48i) q^{50} +(6825.24 - 27447.0i) q^{52} -1343.79i q^{53} +24616.3i q^{55} +(-24547.9 + 10956.8i) q^{56} +(-6467.48 - 8272.72i) q^{58} +31250.9 q^{59} +6502.94 q^{61} +(-2113.09 - 2702.90i) q^{62} +(-21880.8 + 24392.1i) q^{64} -35778.3i q^{65} -2355.02i q^{67} +(-35205.7 - 8754.61i) q^{68} +(-26790.9 + 20944.7i) q^{70} -26941.5 q^{71} -52309.9 q^{73} +(-60886.2 + 47599.9i) q^{74} +(-34529.3 - 8586.40i) q^{76} -90305.8i q^{77} -35732.6i q^{79} +(-19415.2 + 36624.1i) q^{80} +(74073.6 + 94749.4i) q^{82} +62926.7 q^{83} -45892.2 q^{85} +(43474.7 + 55609.6i) q^{86} +(-44866.3 - 100520. i) q^{88} -54560.1i q^{89} +131254. i q^{91} +(10403.0 - 41834.5i) q^{92} +(-72624.2 + 56776.5i) q^{94} -45010.4 q^{95} -142704. q^{97} +(23381.7 - 18279.4i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{4}+O(q^{10}) $ 20 * q + 20 * q^4	$ 20 q + 20 q^{4} + 184 q^{10} - 116 q^{13} - 4168 q^{16} + 696 q^{22} - 15228 q^{25} - 4764 q^{28} - 16520 q^{34} - 6452 q^{37} + 1504 q^{40} - 9336 q^{46} - 44464 q^{49} + 8236 q^{52} - 58736 q^{58} + 84604 q^{61} - 6496 q^{64} + 138696 q^{70} + 85420 q^{73} + 89172 q^{76} + 221200 q^{82} + 180320 q^{85} - 85824 q^{88} - 60936 q^{94} - 219908 q^{97}+O(q^{100}) $ 20 * q + 20 * q^4 + 184 * q^10 - 116 * q^13 - 4168 * q^16 + 696 * q^22 - 15228 * q^25 - 4764 * q^28 - 16520 * q^34 - 6452 * q^37 + 1504 * q^40 - 9336 * q^46 - 44464 * q^49 + 8236 * q^52 - 58736 * q^58 + 84604 * q^61 - 6496 * q^64 + 138696 * q^70 + 85420 * q^73 + 89172 * q^76 + 221200 * q^82 + 180320 * q^85 - 85824 * q^88 - 60936 * q^94 - 219908 * 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 $

$2$	−4.45658	+	3.48409i	−0.787820	+	0.615906i
$2$	−4.45658	+	3.48409i	−0.787820	+	0.615906i
$3$		0			0
$3$		0			0
$4$	7.72226	−	31.0543i	0.241321	−	0.970445i
$5$		−	40.4806i		−	0.724139i	−0.932151	−	0.362069i	$-0.882070\pi$
$5$		−	40.4806i		−	0.724139i	0.932151	−	0.362069i	$-0.117930\pi$
$6$		0			0
$7$			148.504i			1.14550i	0.819731	+	0.572749i	$0.194123\pi$
$7$			148.504i			1.14550i	−0.819731	+	0.572749i	$0.805877\pi$
$8$	73.7809	+	165.301i	0.407586	+	0.913167i
$9$		0			0
$10$	141.038	+	180.405i	0.446001	+	0.570491i
$11$	−608.102			−1.51529			−0.757643	−	0.652670i	$-0.773649\pi$
$11$	−608.102			−1.51529			−0.757643	+	0.652670i	$0.773649\pi$
$12$		0			0
$13$	883.839			1.45049			0.725245	−	0.688490i	$-0.241726\pi$
$13$	883.839			1.45049			0.725245	+	0.688490i	$0.241726\pi$
$14$	−517.402	−	661.822i	−0.705518	−	0.902446i
$15$		0			0
$16$	−904.733	−	479.618i	−0.883529	−	0.468377i
$17$		−	1133.69i		−	0.951415i	−0.879603	−	0.475708i	$-0.842192\pi$
$17$		−	1133.69i		−	0.951415i	0.879603	−	0.475708i	$-0.157808\pi$
$18$		0			0
$19$		−	1111.90i		−	0.706614i	−0.935507	−	0.353307i	$-0.885057\pi$
$19$		−	1111.90i		−	0.706614i	0.935507	−	0.353307i	$-0.114943\pi$
$20$	−1257.09	−	312.602i	−0.702737	−	0.174750i
$21$		0			0
$22$	2710.06	−	2118.68i	1.19377	−	0.933273i
$23$	1347.14			0.531000			0.265500	−	0.964111i	$-0.414463\pi$
$23$	1347.14			0.531000			0.265500	+	0.964111i	$0.414463\pi$
$24$		0			0
$25$	1486.32			0.475623
$26$	−3938.90	+	3079.37i	−1.14273	+	0.893365i
$27$		0			0
$28$	4611.69	+	1146.79i	1.11164	+	0.276432i
$29$			1856.29i			0.409875i	0.978775	+	0.204937i	$0.0656991\pi$
$29$			1856.29i			0.409875i	−0.978775	+	0.204937i	$0.934301\pi$
$30$		0			0
$31$			606.496i			0.113351i	0.998393	+	0.0566753i	$0.0180500\pi$
$31$			606.496i			0.113351i	−0.998393	+	0.0566753i	$0.981950\pi$
$32$	5703.05	−	1014.71i	0.984538	−	0.175174i
$33$		0			0
$34$	3949.86	+	5052.36i	0.585982	+	0.749544i
$35$	6011.54			0.829499
$36$		0			0
$37$	13662.1			1.64064			0.820319	−	0.571906i	$-0.193796\pi$
$37$	13662.1			1.64064			0.820319	+	0.571906i	$0.193796\pi$
$38$	3873.96	+	4955.28i	0.435208	+	0.556685i
$39$		0			0
$40$	6691.48	−	2986.69i	0.661260	−	0.295148i
$41$		−	21260.5i		−	1.97522i	−0.156939	−	0.987608i	$-0.550163\pi$
$41$		−	21260.5i		−	1.97522i	0.156939	−	0.987608i	$-0.449837\pi$
$42$		0			0
$43$		−	12478.1i		−	1.02914i	−0.857447	−	0.514572i	$-0.827951\pi$
$43$		−	12478.1i		−	1.02914i	0.857447	−	0.514572i	$-0.172049\pi$
$44$	−4695.92	+	18884.1i	−0.365670	+	1.47050i
$45$		0			0
$46$	−6003.66	+	4693.57i	−0.418332	+	0.327046i
$47$	16295.9			1.07606			0.538028	−	0.842927i	$-0.319170\pi$
$47$	16295.9			1.07606			0.538028	+	0.842927i	$0.319170\pi$
$48$		0			0
$49$	−5246.55			−0.312165
$50$	−6623.92	+	5178.48i	−0.374705	+	0.292939i
$51$		0			0
$52$	6825.24	−	27447.0i	0.350033	−	1.40762i
$53$		−	1343.79i		−	0.0657115i	−0.999460	−	0.0328558i	$-0.989540\pi$
$53$		−	1343.79i		−	0.0657115i	0.999460	−	0.0328558i	$-0.0104602\pi$
$54$		0			0
$55$			24616.3i			1.09728i
$56$	−24547.9	+	10956.8i	−1.04603	+	0.466888i
$57$		0			0
$58$	−6467.48	−	8272.72i	−0.252444	−	0.322907i
$59$	31250.9			1.16878			0.584389	−	0.811474i	$-0.301334\pi$
$59$	31250.9			1.16878			0.584389	+	0.811474i	$0.301334\pi$
$60$		0			0
$61$	6502.94			0.223761			0.111881	−	0.993722i	$-0.464313\pi$
$61$	6502.94			0.223761			0.111881	+	0.993722i	$0.464313\pi$
$62$	−2113.09	−	2702.90i	−0.0698133	−	0.0892999i
$63$		0			0
$64$	−21880.8	+	24392.1i	−0.667748	+	0.744387i
$65$		−	35778.3i		−	1.05036i
$66$		0			0
$67$		−	2355.02i		−	0.0640924i	−0.999486	−	0.0320462i	$-0.989798\pi$
$67$		−	2355.02i		−	0.0640924i	0.999486	−	0.0320462i	$-0.0102024\pi$
$68$	−35205.7	−	8754.61i	−0.923297	−	0.229596i
$69$		0			0
$70$	−26790.9	+	20944.7i	−0.653496	+	0.510893i
$71$	−26941.5			−0.634273			−0.317137	−	0.948380i	$-0.602721\pi$
$71$	−26941.5			−0.634273			−0.317137	+	0.948380i	$0.602721\pi$
$72$		0			0
$73$	−52309.9			−1.14889			−0.574443	−	0.818545i	$-0.694781\pi$
$73$	−52309.9			−1.14889			−0.574443	+	0.818545i	$0.694781\pi$
$74$	−60886.2	+	47599.9i	−1.29253	+	1.01048i
$75$		0			0
$76$	−34529.3	−	8586.40i	−0.685731	−	0.170521i
$77$		−	90305.8i		−	1.73576i
$78$		0			0
$79$		−	35732.6i		−	0.644165i	−0.946712	−	0.322082i	$-0.895617\pi$
$79$		−	35732.6i		−	0.644165i	0.946712	−	0.322082i	$-0.104383\pi$
$80$	−19415.2	+	36624.1i	−0.339170	+	0.639797i
$81$		0			0
$82$	74073.6	+	94749.4i	1.21655	+	1.55612i
$83$	62926.7			1.00263			0.501314	−	0.865266i	$-0.332850\pi$
$83$	62926.7			1.00263			0.501314	+	0.865266i	$0.332850\pi$
$84$		0			0
$85$	−45892.2			−0.688957
$86$	43474.7	+	55609.6i	0.633856	+	0.810781i
$87$		0			0
$88$	−44866.3	−	100520.i	−0.617608	−	1.38371i
$89$		−	54560.1i		−	0.730130i	−0.930982	−	0.365065i	$-0.881047\pi$
$89$		−	54560.1i		−	0.730130i	0.930982	−	0.365065i	$-0.118953\pi$
$90$		0			0
$91$			131254.i			1.66153i
$92$	10403.0	−	41834.5i	0.128141	−	0.515306i
$93$		0			0
$94$	−72624.2	+	56776.5i	−0.847738	+	0.662749i
$95$	−45010.4			−0.511687
$96$		0			0
$97$	−142704.			−1.53995			−0.769973	−	0.638076i	$-0.779730\pi$
$97$	−142704.			−1.53995			−0.769973	+	0.638076i	$0.779730\pi$
$98$	23381.7	−	18279.4i	0.245930	−	0.192264i
$99$		0			0
$100$	11477.8	−	46156.6i	0.114778	−	0.461566i
$101$			81531.3i			0.795282i	0.917541	+	0.397641i	$0.130171\pi$
$101$			81531.3i			0.795282i	−0.917541	+	0.397641i	$0.869829\pi$
$102$		0			0
$103$		−	154038.i		−	1.43065i	−0.698790	−	0.715327i	$-0.746278\pi$
$103$		−	154038.i		−	1.43065i	0.698790	−	0.715327i	$-0.253722\pi$
$104$	65210.4	+	146099.i	0.591199	+	1.32454i
$105$		0			0
$106$	4681.88	+	5988.71i	0.0404721	+	0.0517688i
$107$	164110.			1.38572			0.692859	−	0.721073i	$-0.256351\pi$
$107$	164110.			1.38572			0.692859	+	0.721073i	$0.256351\pi$
$108$		0			0
$109$	136782.			1.10271			0.551355	−	0.834271i	$-0.314111\pi$
$109$	136782.			1.10271			0.551355	+	0.834271i	$0.314111\pi$
$110$	−85765.4	−	109705.i	−0.675819	−	0.864456i
$111$		0			0
$112$	71225.4	−	134357.i	0.536525	−	1.01208i
$113$			172572.i			1.27138i	0.771946	+	0.635688i	$0.219284\pi$
$113$			172572.i			1.27138i	−0.771946	+	0.635688i	$0.780716\pi$
$114$		0			0
$115$		−	54533.2i		−	0.384517i
$116$	57645.7	+	14334.8i	0.397761	+	0.0989112i
$117$		0			0
$118$	−139272.	+	108881.i	−0.920786	+	0.719857i
$119$	168357.			1.08984
$120$		0			0
$121$	208737.			1.29609
$122$	−28980.9	+	22656.8i	−0.176284	+	0.137816i
$123$		0			0
$124$	18834.3	+	4683.52i	0.110001	+	0.0273538i
$125$		−	186669.i		−	1.06856i
$126$		0			0
$127$			247316.i			1.36064i	0.732916	+	0.680319i	$0.238159\pi$
$127$			247316.i			1.36064i	−0.732916	+	0.680319i	$0.761841\pi$
$128$	12529.3	−	184940.i	0.0675929	−	0.997713i
$129$		0			0
$130$	124655.	+	159449.i	0.646920	+	0.827492i
$131$	−356981.			−1.81747			−0.908733	−	0.417377i	$-0.862949\pi$
$131$	−356981.			−1.81747			−0.908733	+	0.417377i	$0.862949\pi$
$132$		0			0
$133$	165122.			0.809425
$134$	8205.08	+	10495.3i	0.0394749	+	0.0504933i
$135$		0			0
$136$	187399.	−	83644.3i	0.868801	−	0.387783i
$137$			256006.i			1.16533i	0.812713	+	0.582664i	$0.197990\pi$
$137$			256006.i			1.16533i	−0.812713	+	0.582664i	$0.802010\pi$
$138$		0			0
$139$			69026.5i			0.303025i	0.988455	+	0.151513i	$0.0484144\pi$
$139$			69026.5i			0.303025i	−0.988455	+	0.151513i	$0.951586\pi$
$140$	46422.7	−	186684.i	0.200175	−	0.804984i
$141$		0			0
$142$	120067.	−	93866.7i	0.499693	−	0.390653i
$143$	−537464.			−2.19791
$144$		0			0
$145$	75143.7			0.296806
$146$	233123.	−	182252.i	0.905115	−	0.707605i
$147$		0			0
$148$	105502.	−	424266.i	0.395920	−	1.59215i
$149$			52137.4i			0.192390i	0.995362	+	0.0961952i	$0.0306673\pi$
$149$			52137.4i			0.192390i	−0.995362	+	0.0961952i	$0.969333\pi$
$150$		0			0
$151$		−	328419.i		−	1.17216i	−0.810254	−	0.586078i	$-0.800671\pi$
$151$		−	328419.i		−	1.17216i	0.810254	−	0.586078i	$-0.199329\pi$
$152$	183798.	−	82037.1i	0.645257	−	0.288006i
$153$		0			0
$154$	314633.	+	402455.i	1.06906	+	1.36746i
$155$	24551.3			0.0820816
$156$		0			0
$157$	−312765.			−1.01267			−0.506336	−	0.862336i	$-0.669001\pi$
$157$	−312765.			−1.01267			−0.506336	+	0.862336i	$0.669001\pi$
$158$	124496.	+	159245.i	0.396745	+	0.507486i
$159$		0			0
$160$	−41076.2	−	230863.i	−0.126850	−	0.712942i
$161$			200057.i			0.608259i
$162$		0			0
$163$		−	517503.i		−	1.52561i	−0.646628	−	0.762806i	$-0.723821\pi$
$163$		−	517503.i		−	1.52561i	0.646628	−	0.762806i	$-0.276179\pi$
$164$	−660230.	−	164179.i	−1.91684	−	0.476661i
$165$		0			0
$166$	−280438.	+	219242.i	−0.789890	+	0.617524i
$167$	−315354.			−0.875000			−0.437500	−	0.899219i	$-0.644136\pi$
$167$	−315354.			−0.875000			−0.437500	+	0.899219i	$0.644136\pi$
$168$		0			0
$169$	409879.			1.10392
$170$	204523.	−	159893.i	0.542774	−	0.424332i
$171$		0			0
$172$	−387497.	−	96359.0i	−0.998729	−	0.248354i
$173$			624427.i			1.58623i	0.609072	+	0.793115i	$0.291542\pi$
$173$			624427.i			1.58623i	−0.609072	+	0.793115i	$0.708458\pi$
$174$		0			0
$175$			220725.i			0.544825i
$176$	550170.	+	291656.i	1.33880	+	0.709725i
$177$		0			0
$178$	190092.	+	243152.i	0.449691	+	0.575211i
$179$	−69186.2			−0.161394			−0.0806969	−	0.996739i	$-0.525715\pi$
$179$	−69186.2			−0.161394			−0.0806969	+	0.996739i	$0.525715\pi$
$180$		0			0
$181$	−193421.			−0.438840			−0.219420	−	0.975630i	$-0.570417\pi$
$181$	−193421.			−0.438840			−0.219420	+	0.975630i	$0.570417\pi$
$182$	−457301.	−	584944.i	−1.02335	−	1.30899i
$183$		0			0
$184$	99393.4	+	222684.i	0.216428	+	0.484891i
$185$		−	553049.i		−	1.18805i
$186$		0			0
$187$			689396.i			1.44167i
$188$	125841.	−	506058.i	0.259674	−	1.04425i
$189$		0			0
$190$	200593.	−	156820.i	0.403117	−	0.315151i
$191$	790470.			1.56784			0.783920	−	0.620861i	$-0.213217\pi$
$191$	790470.			1.56784			0.783920	+	0.620861i	$0.213217\pi$
$192$		0			0
$193$	−62439.3			−0.120660			−0.0603302	−	0.998178i	$-0.519215\pi$
$193$	−62439.3			−0.120660			−0.0603302	+	0.998178i	$0.519215\pi$
$194$	635970.	−	497192.i	1.21320	−	0.948461i
$195$		0			0
$196$	−40515.2	+	162928.i	−0.0753318	+	0.302939i
$197$			965729.i			1.77292i	0.462803	+	0.886461i	$0.346844\pi$
$197$			965729.i			1.77292i	−0.462803	+	0.886461i	$0.653156\pi$
$198$		0			0
$199$			63953.7i			0.114481i	0.998360	+	0.0572405i	$0.0182302\pi$
$199$			63953.7i			0.114481i	−0.998360	+	0.0572405i	$0.981770\pi$
$200$	109662.	+	245690.i	0.193857	+	0.434323i
$201$		0			0
$202$	−284062.	−	363351.i	−0.489818	−	0.626539i
$203$	−275667.			−0.469510
$204$		0			0
$205$	−860639.			−1.43033
$206$	536682.	+	686483.i	0.881148	+	1.12710i
$207$		0			0
$208$	−799639.	−	423905.i	−1.28155	−	0.679377i
$209$			676149.i			1.07072i
$210$		0			0
$211$			351620.i			0.543710i	0.962338	+	0.271855i	$0.0876371\pi$
$211$			351620.i			0.543710i	−0.962338	+	0.271855i	$0.912363\pi$
$212$	−41730.4	−	10377.1i	−0.0637694	−	0.0158575i
$213$		0			0
$214$	−731369.	+	571773.i	−1.09170	+	0.853472i
$215$	−505120.			−0.745244
$216$		0			0
$217$	−90067.4			−0.129843
$218$	−609578.	+	476559.i	−0.868737	+	0.679165i
$219$		0			0
$220$	764441.	+	190094.i	1.06485	+	0.264795i
$221$		−	1.00200e6i		−	1.38002i
$222$		0			0
$223$		−	146682.i		−	0.197521i	−0.995111	−	0.0987605i	$-0.968512\pi$
$223$		−	146682.i		−	0.197521i	0.995111	−	0.0987605i	$-0.0314878\pi$
$224$	150689.	+	846928.i	0.200661	+	1.12779i
$225$		0			0
$226$	−601256.	−	769082.i	−0.783048	−	1.00162i
$227$	647121.			0.833529			0.416764	−	0.909015i	$-0.363164\pi$
$227$	647121.			0.833529			0.416764	+	0.909015i	$0.363164\pi$
$228$		0			0
$229$	290803.			0.366446			0.183223	−	0.983071i	$-0.441347\pi$
$229$	290803.			0.366446			0.183223	+	0.983071i	$0.441347\pi$
$230$	189998.	+	243032.i	0.236826	+	0.302931i
$231$		0			0
$232$	−306847.	+	136959.i	−0.374284	+	0.167059i
$233$		−	1.59729e6i		−	1.92750i	−0.266808	−	0.963750i	$-0.585969\pi$
$233$		−	1.59729e6i		−	1.92750i	0.266808	−	0.963750i	$-0.414031\pi$
$234$		0			0
$235$		−	659669.i		−	0.779213i
$236$	241327.	−	970472.i	0.282050	−	1.13423i
$237$		0			0
$238$	−750298.	+	586571.i	−0.858601	+	0.671241i
$239$	129472.			0.146616			0.0733082	−	0.997309i	$-0.476644\pi$
$239$	129472.			0.146616			0.0733082	+	0.997309i	$0.476644\pi$
$240$		0			0
$241$	−609709.			−0.676208			−0.338104	−	0.941109i	$-0.609786\pi$
$241$	−609709.			−0.676208			−0.338104	+	0.941109i	$0.609786\pi$
$242$	−930252.	+	727256.i	−1.02109	+	0.798269i
$243$		0			0
$244$	50217.4	−	201944.i	0.0539982	−	0.217148i
$245$			212383.i			0.226050i
$246$		0			0
$247$		−	982743.i		−	1.02494i
$248$	−100254.	+	44747.8i	−0.103508	+	0.0462001i
$249$		0			0
$250$	650371.	+	831906.i	0.658129	+	0.841830i
$251$	−529459.			−0.530454			−0.265227	−	0.964186i	$-0.585447\pi$
$251$	−529459.			−0.530454			−0.265227	+	0.964186i	$0.585447\pi$
$252$		0			0
$253$	−819200.			−0.804616
$254$	−861670.	−	1.10218e6i	−0.838025	−	1.07194i
$255$		0			0
$256$	588509.	+	867853.i	0.561246	+	0.827649i
$257$			82551.1i			0.0779633i	0.999240	+	0.0389817i	$0.0124114\pi$
$257$			82551.1i			0.0779633i	−0.999240	+	0.0389817i	$0.987589\pi$
$258$		0			0
$259$			2.02888e6i			1.87935i
$260$	−1.11107e6	−	276290.i	−1.01931	−	0.253473i
$261$		0			0
$262$	1.59091e6	−	1.24375e6i	1.43184	−	1.11939i
$263$	866335.			0.772318			0.386159	−	0.922432i	$-0.373802\pi$
$263$	866335.			0.772318			0.386159	+	0.922432i	$0.373802\pi$
$264$		0			0
$265$	−54397.4			−0.0475842
$266$	−735881.	+	575301.i	−0.637681	+	0.498529i
$267$		0			0
$268$	−73133.3	−	18186.0i	−0.0621982	−	0.0154668i
$269$		−	1.20342e6i		−	1.01400i	−0.861946	−	0.507000i	$-0.830755\pi$
$269$		−	1.20342e6i		−	1.01400i	0.861946	−	0.507000i	$-0.169245\pi$
$270$		0			0
$271$		−	1.46736e6i		−	1.21371i	−0.794814	−	0.606853i	$-0.792432\pi$
$271$		−	1.46736e6i		−	1.21371i	0.794814	−	0.606853i	$-0.207568\pi$
$272$	−543736.	+	1.02568e6i	−0.445621	+	0.840603i
$273$		0			0
$274$	−891946.	−	1.14091e6i	−0.717732	−	0.918068i
$275$	−903835.			−0.720705
$276$		0			0
$277$	2.23950e6			1.75368			0.876841	−	0.480781i	$-0.159647\pi$
$277$	2.23950e6			1.75368			0.876841	+	0.480781i	$0.159647\pi$
$278$	−240494.	−	307622.i	−0.186635	−	0.238729i
$279$		0			0
$280$	443537.	+	993714.i	0.338092	+	0.757471i
$281$		−	153902.i		−	0.116273i	−0.998309	−	0.0581364i	$-0.981484\pi$
$281$		−	153902.i		−	0.116273i	0.998309	−	0.0581364i	$-0.0185158\pi$
$282$		0			0
$283$			1.61247e6i			1.19681i	0.801194	+	0.598405i	$0.204199\pi$
$283$			1.61247e6i			1.19681i	−0.801194	+	0.598405i	$0.795801\pi$
$284$	−208050.	+	836649.i	−0.153063	+	0.615528i
$285$		0			0
$286$	2.39525e6	−	1.87257e6i	1.73156	−	1.35370i
$287$	3.15728e6			2.26261
$288$		0			0
$289$	134615.			0.0948090
$290$	−334884.	+	261807.i	−0.233830	+	0.182805i
$291$		0			0
$292$	−403951.	+	1.62445e6i	−0.277250	+	1.11493i
$293$		−	1.89615e6i		−	1.29034i	−0.764041	−	0.645168i	$-0.776787\pi$
$293$		−	1.89615e6i		−	1.29034i	0.764041	−	0.645168i	$-0.223213\pi$
$294$		0			0
$295$		−	1.26505e6i		−	0.846357i
$296$	1.00800e6	+	2.25835e6i	0.668700	+	1.49818i
$297$		0			0
$298$	−181651.	−	232355.i	−0.118494	−	0.151569i
$299$	1.19066e6			0.770210
$300$		0			0
$301$	1.85305e6			1.17888
$302$	1.14424e6	+	1.46363e6i	0.721938	+	0.923449i
$303$		0			0
$304$	−533288.	+	1.00597e6i	−0.330962	+	0.624314i
$305$		−	263243.i		−	0.162034i
$306$		0			0
$307$		−	92336.2i		−	0.0559147i	−0.999609	−	0.0279573i	$-0.991100\pi$
$307$		−	92336.2i		−	0.0559147i	0.999609	−	0.0279573i	$-0.00890026\pi$
$308$	−2.80438e6	−	697364.i	−1.68446	−	0.418874i
$309$		0			0
$310$	−109415.	+	85539.0i	−0.0646655	+	0.0505545i
$311$	−30371.7			−0.0178060			−0.00890302	−	0.999960i	$-0.502834\pi$
$311$	−30371.7			−0.0178060			−0.00890302	+	0.999960i	$0.502834\pi$
$312$		0			0
$313$	1.36319e6			0.786494			0.393247	−	0.919433i	$-0.371352\pi$
$313$	1.36319e6			0.786494			0.393247	+	0.919433i	$0.371352\pi$
$314$	1.39386e6	−	1.08970e6i	0.797804	−	0.623711i
$315$		0			0
$316$	−1.10965e6	−	275937.i	−0.625127	−	0.155450i
$317$		−	1.16441e6i		−	0.650818i	−0.945573	−	0.325409i	$-0.894498\pi$
$317$		−	1.16441e6i		−	0.650818i	0.945573	−	0.325409i	$-0.105502\pi$
$318$		0			0
$319$		−	1.12881e6i		−	0.621077i
$320$	987406.	+	885746.i	0.539040	+	0.483542i
$321$		0			0
$322$	−697015.	−	891569.i	−0.374630	−	0.479199i
$323$	−1.26055e6			−0.672284
$324$		0			0
$325$	1.31367e6			0.689887
$326$	1.80303e6	+	2.30629e6i	0.939632	+	1.20191i
$327$		0			0
$328$	3.51439e6	−	1.56862e6i	1.80370	−	0.805070i
$329$			2.42002e6i			1.23262i
$330$		0			0
$331$		−	451430.i		−	0.226475i	−0.993568	−	0.113237i	$-0.963878\pi$
$331$		−	451430.i		−	0.226475i	0.993568	−	0.113237i	$-0.0361221\pi$
$332$	485936.	−	1.95414e6i	0.241955	−	0.972995i
$333$		0			0
$334$	1.40540e6	−	1.09872e6i	0.689342	−	0.538917i
$335$	−95332.4			−0.0464118
$336$		0			0
$337$	−2.16248e6			−1.03723			−0.518617	−	0.855007i	$-0.673553\pi$
$337$	−2.16248e6			−1.03723			−0.518617	+	0.855007i	$0.673553\pi$
$338$	−1.82666e6	+	1.42805e6i	−0.869693	+	0.679913i
$339$		0			0
$340$	−354392.	+	1.42515e6i	−0.166259	+	0.668595i
$341$		−	368811.i		−	0.171759i
$342$		0			0
$343$			1.71678e6i			0.787914i
$344$	2.06264e6	−	920643.i	0.939781	−	0.419465i
$345$		0			0
$346$	−2.17556e6	−	2.78281e6i	−0.976968	−	1.24966i
$347$	3.10525e6			1.38444			0.692219	−	0.721688i	$-0.256633\pi$
$347$	3.10525e6			1.38444			0.692219	+	0.721688i	$0.256633\pi$
$348$		0			0
$349$	−2.35425e6			−1.03464			−0.517320	−	0.855792i	$-0.673070\pi$
$349$	−2.35425e6			−1.03464			−0.517320	+	0.855792i	$0.673070\pi$
$350$	−769027.	−	983681.i	−0.335561	−	0.429224i
$351$		0			0
$352$	−3.46803e6	+	617049.i	−1.49186	+	0.265438i
$353$		−	1.94097e6i		−	0.829052i	−0.910037	−	0.414526i	$-0.863947\pi$
$353$		−	1.94097e6i		−	0.829052i	0.910037	−	0.414526i	$-0.136053\pi$
$354$		0			0
$355$			1.09061e6i			0.459302i
$356$	−1.69432e6	−	421327.i	−0.708552	−	0.176195i
$357$		0			0
$358$	308334.	−	241051.i	0.127149	−	0.0994034i
$359$	−1.33715e6			−0.547574			−0.273787	−	0.961790i	$-0.588276\pi$
$359$	−1.33715e6			−0.547574			−0.273787	+	0.961790i	$0.588276\pi$
$360$		0			0
$361$	1.23977e6			0.500696
$362$	861995.	−	673895.i	0.345727	−	0.270284i
$363$		0			0
$364$	4.07600e6	+	1.01358e6i	1.61243	+	0.400962i
$365$			2.11754e6i			0.831953i
$366$		0			0
$367$		−	1.64386e6i		−	0.637087i	−0.947908	−	0.318544i	$-0.896806\pi$
$367$		−	1.64386e6i		−	0.637087i	0.947908	−	0.318544i	$-0.103194\pi$
$368$	−1.21881e6	−	646114.i	−0.469154	−	0.248708i
$369$		0			0
$370$	1.92687e6	+	2.46471e6i	0.731726	+	0.935969i
$371$	199559.			0.0752724
$372$		0			0
$373$	−393084.			−0.146290			−0.0731448	−	0.997321i	$-0.523304\pi$
$373$	−393084.			−0.146290			−0.0731448	+	0.997321i	$0.523304\pi$
$374$	−2.40192e6	−	3.07235e6i	−0.887930	−	1.13577i
$375$		0			0
$376$	1.20233e6	+	2.69373e6i	0.438585	+	0.982618i
$377$			1.64066e6i			0.594519i
$378$		0			0
$379$			2.30537e6i			0.824410i	0.911091	+	0.412205i	$0.135241\pi$
$379$			2.30537e6i			0.824410i	−0.911091	+	0.412205i	$0.864759\pi$
$380$	−347582.	+	1.39777e6i	−0.123481	+	0.496564i
$381$		0			0
$382$	−3.52279e6	+	2.75407e6i	−1.23518	+	0.965642i
$383$	−2.70064e6			−0.940741			−0.470370	−	0.882469i	$-0.655880\pi$
$383$	−2.70064e6			−0.940741			−0.470370	+	0.882469i	$0.655880\pi$
$384$		0			0
$385$	−3.65563e6			−1.25693
$386$	278266.	−	217544.i	0.0950587	−	0.0743154i
$387$		0			0
$388$	−1.10199e6	+	4.43155e6i	−0.371621	+	1.49443i
$389$			1.65579e6i			0.554793i	0.960755	+	0.277397i	$0.0894716\pi$
$389$			1.65579e6i			0.554793i	−0.960755	+	0.277397i	$0.910528\pi$
$390$		0			0
$391$		−	1.52724e6i		−	0.505201i
$392$	−387095.	−	867260.i	−0.127234	−	0.285058i
$393$		0			0
$394$	−3.36469e6	−	4.30385e6i	−1.09195	−	1.39674i
$395$	−1.44648e6			−0.466465
$396$		0			0
$397$	−1.69988e6			−0.541306			−0.270653	−	0.962677i	$-0.587240\pi$
$397$	−1.69988e6			−0.541306			−0.270653	+	0.962677i	$0.587240\pi$
$398$	−222820.	−	285015.i	−0.0705095	−	0.0901904i
$399$		0			0
$400$	−1.34473e6	−	712867.i	−0.420227	−	0.222771i
$401$			535612.i			0.166337i	0.996535	+	0.0831687i	$0.0265040\pi$
$401$			535612.i			0.166337i	−0.996535	+	0.0831687i	$0.973496\pi$
$402$		0			0
$403$			536045.i			0.164414i
$404$	2.53189e6	+	629606.i	0.771778	+	0.191918i
$405$		0			0
$406$	1.22853e6	−	960449.i	0.369890	−	0.289174i
$407$	−8.30794e6			−2.48603
$408$		0			0
$409$	−1.71273e6			−0.506268			−0.253134	−	0.967431i	$-0.581461\pi$
$409$	−1.71273e6			−0.506268			−0.253134	+	0.967431i	$0.581461\pi$
$410$	3.83551e6	−	2.99854e6i	1.12684	−	0.880949i
$411$		0			0
$412$	−4.78353e6	−	1.18952e6i	−1.38837	−	0.345246i
$413$			4.64089e6i			1.33883i
$414$		0			0
$415$		−	2.54731e6i		−	0.726041i
$416$	5.04058e6	−	896844.i	1.42806	−	0.254088i
$417$		0			0
$418$	−2.35576e6	−	3.01332e6i	−0.659464	−	0.843537i
$419$	−1.98989e6			−0.553725			−0.276863	−	0.960909i	$-0.589295\pi$
$419$	−1.98989e6			−0.553725			−0.276863	+	0.960909i	$0.589295\pi$
$420$		0			0
$421$	849032.			0.233463			0.116732	−	0.993163i	$-0.462758\pi$
$421$	849032.			0.233463			0.116732	+	0.993163i	$0.462758\pi$
$422$	−1.22507e6	−	1.56702e6i	−0.334874	−	0.428346i
$423$		0			0
$424$	222130.	−	99145.9i	0.0600056	−	0.0267831i
$425$		−	1.68502e6i		−	0.452515i
$426$		0			0
$427$			965714.i			0.256318i
$428$	1.26730e6	−	5.09631e6i	0.334403	−	1.34476i
$429$		0			0
$430$	2.25111e6	−	1.75988e6i	0.587118	−	0.459000i
$431$	3.02456e6			0.784277			0.392139	−	0.919906i	$-0.371735\pi$
$431$	3.02456e6			0.784277			0.392139	+	0.919906i	$0.371735\pi$
$432$		0			0
$433$	−1.32400e6			−0.339365			−0.169683	−	0.985499i	$-0.554274\pi$
$433$	−1.32400e6			−0.339365			−0.169683	+	0.985499i	$0.554274\pi$
$434$	401393.	−	313803.i	0.102293	−	0.0799709i
$435$		0			0
$436$	1.05626e6	−	4.24765e6i	0.266107	−	1.07012i
$437$		−	1.49789e6i		−	0.375212i
$438$		0			0
$439$		−	1.74480e6i		−	0.432100i	−0.976382	−	0.216050i	$-0.930683\pi$
$439$		−	1.74480e6i		−	0.432100i	0.976382	−	0.216050i	$-0.0693175\pi$
$440$	−4.06910e6	+	1.81621e6i	−1.00200	+	0.447234i
$441$		0			0
$442$	3.49104e6	+	4.46548e6i	0.849961	+	1.08721i
$443$	−4.60857e6			−1.11572			−0.557862	−	0.829934i	$-0.688378\pi$
$443$	−4.60857e6			−1.11572			−0.557862	+	0.829934i	$0.688378\pi$
$444$		0			0
$445$	−2.20863e6			−0.528715
$446$	511051.	+	653698.i	0.121654	+	0.155611i
$447$		0			0
$448$	−3.62233e6	−	3.24939e6i	−0.852694	−	0.764904i
$449$		−	363410.i		−	0.0850709i	−0.999095	−	0.0425355i	$-0.986456\pi$
$449$		−	363410.i		−	0.0850709i	0.999095	−	0.0425355i	$-0.0135435\pi$
$450$		0			0
$451$			1.29286e7i			2.99302i
$452$	5.35910e6	+	1.33265e6i	1.23380	+	0.306809i
$453$		0			0
$454$	−2.88395e6	+	2.25463e6i	−0.656671	+	0.513375i
$455$	5.31324e6			1.20318
$456$		0			0
$457$	2.52447e6			0.565431			0.282716	−	0.959204i	$-0.408765\pi$
$457$	2.52447e6			0.565431			0.282716	+	0.959204i	$0.408765\pi$
$458$	−1.29599e6	+	1.01318e6i	−0.288693	+	0.225696i
$459$		0			0
$460$	−1.69349e6	−	421119.i	−0.373153	−	0.0927920i
$461$			6.13081e6i			1.34359i	0.740739	+	0.671793i	$0.234476\pi$
$461$			6.13081e6i			1.34359i	−0.740739	+	0.671793i	$0.765524\pi$
$462$		0			0
$463$		−	4.72811e6i		−	1.02503i	−0.858679	−	0.512513i	$-0.828715\pi$
$463$		−	4.72811e6i		−	1.02503i	0.858679	−	0.512513i	$-0.171285\pi$
$464$	890311.	−	1.67945e6i	0.191976	−	0.362136i
$465$		0			0
$466$	5.56510e6	+	7.11846e6i	1.18716	+	1.51852i
$467$	3.47705e6			0.737767			0.368884	−	0.929476i	$-0.379740\pi$
$467$	3.47705e6			0.737767			0.368884	+	0.929476i	$0.379740\pi$
$468$		0			0
$469$	349730.			0.0734177
$470$	2.29834e6	+	2.93987e6i	0.479922	+	0.613880i
$471$		0			0
$472$	2.30572e6	+	5.16579e6i	0.476377	+	1.06729i
$473$			7.58794e6i			1.55945i
$474$		0			0
$475$		−	1.65265e6i		−	0.336082i
$476$	1.30010e6	−	5.22821e6i	0.263002	−	1.05763i
$477$		0			0
$478$	−577004.	+	451093.i	−0.115507	+	0.0903018i
$479$	−2.90668e6			−0.578841			−0.289420	−	0.957202i	$-0.593463\pi$
$479$	−2.90668e6			−0.578841			−0.289420	+	0.957202i	$0.593463\pi$
$480$		0			0
$481$	1.20751e7			2.37973
$482$	2.71722e6	−	2.12428e6i	0.532730	−	0.416480i
$483$		0			0
$484$	1.61192e6	−	6.48216e6i	0.312773	−	1.25778i
$485$			5.77672e6i			1.11513i
$486$		0			0
$487$		−	5.40021e6i		−	1.03178i	−0.856654	−	0.515892i	$-0.827461\pi$
$487$		−	5.40021e6i		−	1.03178i	0.856654	−	0.515892i	$-0.172539\pi$
$488$	479792.	+	1.07494e6i	0.0912019	+	0.204331i
$489$		0			0
$490$	−739963.	−	946504.i	−0.139226	−	0.178087i
$491$	9.72452e6			1.82039			0.910195	−	0.414181i	$-0.135932\pi$
$491$	9.72452e6			1.82039			0.910195	+	0.414181i	$0.135932\pi$
$492$		0			0
$493$	2.10445e6			0.389961
$494$	3.42396e6	+	4.37967e6i	0.631265	+	0.807466i
$495$		0			0
$496$	290887.	−	548717.i	0.0530908	−	0.100149i
$497$		−	4.00094e6i		−	0.726559i
$498$		0			0
$499$			1.47884e6i			0.265870i	0.991125	+	0.132935i	$0.0424402\pi$
$499$			1.47884e6i			0.265870i	−0.991125	+	0.132935i	$0.957560\pi$
$500$	−5.79687e6	−	1.44151e6i	−1.03698	−	0.257865i
$501$		0			0
$502$	2.35958e6	−	1.84468e6i	0.417902	−	0.326710i
$503$	−6.19630e6			−1.09198			−0.545988	−	0.837793i	$-0.683845\pi$
$503$	−6.19630e6			−1.09198			−0.545988	+	0.837793i	$0.683845\pi$
$504$		0			0
$505$	3.30043e6			0.575894
$506$	3.65083e6	−	2.85417e6i	0.633893	−	0.495568i
$507$		0			0
$508$	7.68021e6	+	1.90984e6i	1.32042	+	0.328350i
$509$		−	400657.i		−	0.0685454i	−0.999413	−	0.0342727i	$-0.989089\pi$
$509$		−	400657.i		−	0.0685454i	0.999413	−	0.0342727i	$-0.0109115\pi$
$510$		0			0
$511$		−	7.76825e6i		−	1.31605i
$512$	−5.64642e6	−	1.81724e6i	−0.951914	−	0.306364i
$513$		0			0
$514$	−287615.	−	367896.i	−0.0480180	−	0.0614210i
$515$	−6.23554e6			−1.03599
$516$		0			0
$517$	−9.90958e6			−1.63053
$518$	−7.06880e6	−	9.04187e6i	−1.15750	−	1.48059i
$519$		0			0
$520$	5.91419e6	−	2.63976e6i	0.959151	−	0.428110i
$521$			210060.i			0.0339039i	0.999856	+	0.0169520i	$0.00539624\pi$
$521$			210060.i			0.0339039i	−0.999856	+	0.0169520i	$0.994604\pi$
$522$		0			0
$523$			5.32849e6i			0.851824i	0.904765	+	0.425912i	$0.140047\pi$
$523$			5.32849e6i			0.851824i	−0.904765	+	0.425912i	$0.859953\pi$
$524$	−2.75670e6	+	1.10858e7i	−0.438592	+	1.76375i
$525$		0			0
$526$	−3.86089e6	+	3.01839e6i	−0.608448	+	0.475675i
$527$	687576.			0.107844
$528$		0			0
$529$	−4.62155e6			−0.718039
$530$	242426.	−	189525.i	0.0374878	−	0.0293074i
$531$		0			0
$532$	1.27512e6	−	5.12775e6i	0.195331	−	0.785503i
$533$		−	1.87909e7i		−	2.86503i
$534$		0			0
$535$		−	6.64326e6i		−	1.00345i
$536$	389286.	−	173755.i	0.0585271	−	0.0261232i
$537$		0			0
$538$	4.19283e6	+	5.36315e6i	0.624528	+	0.798849i
$539$	3.19044e6			0.473019
$540$		0			0
$541$	4.80721e6			0.706155			0.353077	−	0.935594i	$-0.385135\pi$
$541$	4.80721e6			0.706155			0.353077	+	0.935594i	$0.385135\pi$
$542$	5.11241e6	+	6.53941e6i	0.747529	+	0.956182i
$543$		0			0
$544$	−1.15037e6	−	6.46546e6i	−0.166663	−	0.936704i
$545$		−	5.53700e6i		−	0.798515i
$546$		0			0
$547$			1.22838e7i			1.75535i	0.479254	+	0.877676i	$0.340907\pi$
$547$			1.22838e7i			1.75535i	−0.479254	+	0.877676i	$0.659093\pi$
$548$	7.95006e6	+	1.97694e6i	1.13089	+	0.281218i
$549$		0			0
$550$	4.02802e6	−	3.14904e6i	0.567786	−	0.443886i
$551$	2.06401e6			0.289623
$552$		0			0
$553$	5.30645e6			0.737889
$554$	−9.98050e6	+	7.80260e6i	−1.38159	+	1.08010i
$555$		0			0
$556$	2.14357e6	+	533041.i	0.294070	+	0.0731263i
$557$		−	6.64124e6i		−	0.907008i	−0.891254	−	0.453504i	$-0.850174\pi$
$557$		−	6.64124e6i		−	0.907008i	0.891254	−	0.453504i	$-0.149826\pi$
$558$		0			0
$559$		−	1.10286e7i		−	1.49277i
$560$	−5.43884e6	−	2.88324e6i	−0.732886	−	0.388518i
$561$		0			0
$562$	536207.	+	685876.i	0.0716130	+	0.0916020i
$563$	−9.15547e6			−1.21733			−0.608667	−	0.793426i	$-0.708295\pi$
$563$	−9.15547e6			−1.21733			−0.608667	+	0.793426i	$0.708295\pi$
$564$		0			0
$565$	6.98582e6			0.920653
$566$	−5.61798e6	−	7.18610e6i	−0.737122	−	0.942871i
$567$		0			0
$568$	−1.98777e6	−	4.45346e6i	−0.258521	−	0.579198i
$569$		−	538876.i		−	0.0697763i	−0.999391	−	0.0348882i	$-0.988893\pi$
$569$		−	538876.i		−	0.0697763i	0.999391	−	0.0348882i	$-0.0111075\pi$
$570$		0			0
$571$			4.75530e6i			0.610362i	0.952294	+	0.305181i	$0.0987170\pi$
$571$			4.75530e6i			0.610362i	−0.952294	+	0.305181i	$0.901283\pi$
$572$	−4.15044e6	+	1.66905e7i	−0.530400	+	2.13295i
$573$		0			0
$574$	−1.40707e7	+	1.10003e7i	−1.78253	+	1.39355i
$575$	2.00229e6			0.252556
$576$		0			0
$577$	−573068.			−0.0716583			−0.0358291	−	0.999358i	$-0.511407\pi$
$577$	−573068.			−0.0716583			−0.0358291	+	0.999358i	$0.511407\pi$
$578$	−599924.	+	469011.i	−0.0746924	+	0.0583934i
$579$		0			0
$580$	580280.	−	2.33353e6i	0.0716254	−	0.288034i
$581$			9.34489e6i			1.14851i
$582$		0			0
$583$			817160.i			0.0995717i
$584$	−3.85947e6	−	8.64688e6i	−0.468269	−	1.04912i
$585$		0			0
$586$	6.60634e6	+	8.45033e6i	0.794725	+	1.01655i
$587$	3.58562e6			0.429505			0.214753	−	0.976668i	$-0.431105\pi$
$587$	3.58562e6			0.429505			0.214753	+	0.976668i	$0.431105\pi$
$588$		0			0
$589$	674364.			0.0800952
$590$	4.40756e6	+	5.63781e6i	0.521276	+	0.666777i
$591$		0			0
$592$	−1.23605e7	−	6.55258e6i	−1.44955	−	0.768437i
$593$			3.03733e6i			0.354695i	0.984148	+	0.177348i	$0.0567517\pi$
$593$			3.03733e6i			0.354695i	−0.984148	+	0.177348i	$0.943248\pi$
$594$		0			0
$595$		−	6.81520e6i		−	0.789198i
$596$	1.61909e6	+	402618.i	0.186704	+	0.0464278i
$597$		0			0
$598$	−5.30627e6	+	4.14836e6i	−0.606787	+	0.474377i
$599$	8.69696e6			0.990377			0.495188	−	0.868786i	$-0.335099\pi$
$599$	8.69696e6			0.990377			0.495188	+	0.868786i	$0.335099\pi$
$600$		0			0
$601$	−2.30820e6			−0.260668			−0.130334	−	0.991470i	$-0.541605\pi$
$601$	−2.30820e6			−0.260668			−0.130334	+	0.991470i	$0.541605\pi$
$602$	−8.25827e6	+	6.45619e6i	−0.928748	+	0.726081i
$603$		0			0
$604$	−1.01988e7	−	2.53614e6i	−1.13751	−	0.282866i
$605$		−	8.44978e6i		−	0.938549i
$606$		0			0
$607$			1.78272e7i			1.96387i	0.189229	+	0.981933i	$0.439401\pi$
$607$			1.78272e7i			1.96387i	−0.189229	+	0.981933i	$0.560599\pi$
$608$	−1.12826e6	−	6.34123e6i	−0.123780	−	0.695688i
$609$		0			0
$610$	917160.	+	1.17316e6i	0.0997978	+	0.127654i
$611$	1.44030e7			1.56081
$612$		0			0
$613$	−8.66354e6			−0.931202			−0.465601	−	0.884995i	$-0.654162\pi$
$613$	−8.66354e6			−0.931202			−0.465601	+	0.884995i	$0.654162\pi$
$614$	321707.	+	411504.i	0.0344382	+	0.0440507i
$615$		0			0
$616$	1.49276e7	−	6.66284e6i	1.58503	−	0.707469i
$617$		−	4.06215e6i		−	0.429579i	−0.976660	−	0.214789i	$-0.931093\pi$
$617$		−	4.06215e6i		−	0.429579i	0.976660	−	0.214789i	$-0.0689065\pi$
$618$		0			0
$619$			4.23718e6i			0.444478i	0.974992	+	0.222239i	$0.0713365\pi$
$619$			4.23718e6i			0.444478i	−0.974992	+	0.222239i	$0.928664\pi$
$620$	189592.	−	762423.i	0.0198080	−	0.0796557i
$621$		0			0
$622$	135354.	−	105818.i	0.0140280	−	0.0109668i
$623$	8.10242e6			0.836362
$624$		0			0
$625$	−2.91171e6			−0.298159
$626$	−6.07517e6	+	4.74947e6i	−0.619616	+	0.484406i
$627$		0			0
$628$	−2.41525e6	+	9.71269e6i	−0.244379	+	0.982744i
$629$		−	1.54885e7i		−	1.56093i
$630$		0			0
$631$		−	1.26919e7i		−	1.26898i	−0.772932	−	0.634489i	$-0.781211\pi$
$631$		−	1.26919e7i		−	1.26898i	0.772932	−	0.634489i	$-0.218789\pi$
$632$	5.90663e6	−	2.63638e6i	0.588230	−	0.262552i
$633$		0			0
$634$	4.05692e6	+	5.18931e6i	0.400842	+	0.512727i
$635$	1.00115e7			0.985291
$636$		0			0
$637$	−4.63711e6			−0.452792
$638$	3.93289e6	+	5.03065e6i	0.382525	+	0.489297i
$639$		0			0
$640$	−7.48647e6	−	507192.i	−0.722483	−	0.0489466i
$641$			5.25962e6i			0.505603i	0.967518	+	0.252801i	$0.0813519\pi$
$641$			5.25962e6i			0.505603i	−0.967518	+	0.252801i	$0.918648\pi$
$642$		0			0
$643$			2.43696e6i			0.232446i	0.993223	+	0.116223i	$0.0370787\pi$
$643$			2.43696e6i			0.232446i	−0.993223	+	0.116223i	$0.962921\pi$
$644$	6.21261e6	+	1.54489e6i	0.590282	+	0.146785i
$645$		0			0
$646$	5.61773e6	−	4.39186e6i	0.529639	−	0.414063i
$647$	3.95714e6			0.371639			0.185819	−	0.982584i	$-0.440506\pi$
$647$	3.95714e6			0.371639			0.185819	+	0.982584i	$0.440506\pi$
$648$		0			0
$649$	−1.90037e7			−1.77103
$650$	−5.85448e6	+	4.57694e6i	−0.543507	+	0.424905i
$651$		0			0
$652$	−1.60707e7	−	3.99629e6i	−1.48052	−	0.368161i
$653$			1.87789e6i			0.172340i	0.996280	+	0.0861702i	$0.0274629\pi$
$653$			1.87789e6i			0.172340i	−0.996280	+	0.0861702i	$0.972537\pi$
$654$		0			0
$655$			1.44508e7i			1.31610i
$656$	−1.01969e7	+	1.92351e7i	−0.925146	+	1.74516i
$657$		0			0
$658$	−8.43155e6	−	1.07850e7i	−0.759177	−	0.971082i
$659$	−6.18082e6			−0.554412			−0.277206	−	0.960810i	$-0.589408\pi$
$659$	−6.18082e6			−0.554412			−0.277206	+	0.960810i	$0.589408\pi$
$660$		0			0
$661$	−468167.			−0.0416771			−0.0208385	−	0.999783i	$-0.506634\pi$
$661$	−468167.			−0.0416771			−0.0208385	+	0.999783i	$0.506634\pi$
$662$	1.57282e6	+	2.01183e6i	0.139487	+	0.178421i
$663$		0			0
$664$	4.64278e6	+	1.04018e7i	0.408656	+	0.915566i
$665$		−	6.68425e6i		−	0.586136i
$666$		0			0
$667$			2.50069e6i			0.217643i
$668$	−2.43525e6	+	9.79310e6i	−0.211155	+	0.849139i
$669$		0			0
$670$	424857.	−	332147.i	0.0365642	−	0.0285853i
$671$	−3.95445e6			−0.339062
$672$		0			0
$673$	−7.27492e6			−0.619142			−0.309571	−	0.950876i	$-0.600186\pi$
$673$	−7.27492e6			−0.619142			−0.309571	+	0.950876i	$0.600186\pi$
$674$	9.63726e6	−	7.53426e6i	0.817154	−	0.638838i
$675$		0			0
$676$	3.16519e6	−	1.27285e7i	0.266399	−	1.07130i
$677$			5.70914e6i			0.478739i	0.970929	+	0.239370i	$0.0769407\pi$
$677$			5.70914e6i			0.478739i	−0.970929	+	0.239370i	$0.923059\pi$
$678$		0			0
$679$		−	2.11921e7i		−	1.76400i
$680$	−3.38597e6	−	7.58603e6i	−0.280809	−	0.629132i
$681$		0			0
$682$	1.28497e6	+	1.64364e6i	0.105787	+	0.135315i
$683$	−6.52835e6			−0.535490			−0.267745	−	0.963490i	$-0.586279\pi$
$683$	−6.52835e6			−0.535490			−0.267745	+	0.963490i	$0.586279\pi$
$684$		0			0
$685$	1.03633e7			0.843859
$686$	−5.98140e6	−	7.65096e6i	−0.485280	−	0.620734i
$687$		0			0
$688$	−5.98471e6	+	1.12893e7i	−0.482028	+	0.909279i
$689$		−	1.18769e6i		−	0.0953139i
$690$		0			0
$691$		−	1.14706e7i		−	0.913884i	−0.889496	−	0.456942i	$-0.848945\pi$
$691$		−	1.14706e7i		−	0.913884i	0.889496	−	0.456942i	$-0.151055\pi$
$692$	1.93911e7	+	4.82198e6i	1.53935	+	0.382790i
$693$		0			0
$694$	−1.38388e7	+	1.08190e7i	−1.09069	+	0.852683i
$695$	2.79423e6			0.219432
$696$		0			0
$697$	−2.41028e7			−1.87925
$698$	1.04919e7	−	8.20242e6i	0.815110	−	0.637240i
$699$		0			0
$700$	6.85446e6	+	1.70450e6i	0.528723	+	0.131478i
$701$			1.82344e6i			0.140151i	0.997542	+	0.0700756i	$0.0223240\pi$
$701$			1.82344e6i			0.140151i	−0.997542	+	0.0700756i	$0.977676\pi$
$702$		0			0
$703$		−	1.51909e7i		−	1.15930i
$704$	1.33057e7	−	1.48329e7i	1.01183	−	1.12796i
$705$		0			0
$706$	6.76251e6	+	8.65009e6i	0.510618	+	0.653144i
$707$	−1.21078e7			−0.910993
$708$		0			0
$709$	1.40708e7			1.05124			0.525621	−	0.850719i	$-0.323833\pi$
$709$	1.40708e7			1.05124			0.525621	+	0.850719i	$0.323833\pi$
$710$	−3.79978e6	−	4.86039e6i	−0.282887	−	0.361847i
$711$		0			0
$712$	9.01884e6	−	4.02549e6i	0.666731	−	0.297591i
$713$			817038.i			0.0601892i
$714$		0			0
$715$			2.17569e7i			1.59159i
$716$	−534274.	+	2.14853e6i	−0.0389477	+	0.156624i
$717$		0			0
$718$	5.95910e6	−	4.65874e6i	0.431390	−	0.337254i
$719$	−3.92597e6			−0.283220			−0.141610	−	0.989923i	$-0.545228\pi$
$719$	−3.92597e6			−0.283220			−0.141610	+	0.989923i	$0.545228\pi$
$720$		0			0
$721$	2.28753e7			1.63881
$722$	−5.52515e6	+	4.31948e6i	−0.394458	+	0.308381i
$723$		0			0
$724$	−1.49365e6	+	6.00654e6i	−0.105901	+	0.425871i
$725$			2.75905e6i			0.194946i
$726$		0			0
$727$		−	8.54731e6i		−	0.599782i	−0.953973	−	0.299891i	$-0.903050\pi$
$727$		−	8.54731e6i		−	0.599782i	0.953973	−	0.299891i	$-0.0969503\pi$
$728$	−2.16964e7	+	9.68404e6i	−1.51726	+	0.677217i
$729$		0			0
$730$	−7.37768e6	−	9.43697e6i	−0.512404	−	0.655429i
$731$	−1.41462e7			−0.979144
$732$		0			0
$733$	1.32847e7			0.913256			0.456628	−	0.889658i	$-0.349057\pi$
$733$	1.32847e7			0.913256			0.456628	+	0.889658i	$0.349057\pi$
$734$	5.72734e6	+	7.32598e6i	0.392385	+	0.501910i
$735$		0			0
$736$	7.68283e6	−	1.36696e6i	0.522789	−	0.0930171i
$737$			1.43209e6i			0.0971183i
$738$		0			0
$739$			2.75514e7i			1.85581i	0.372819	+	0.927904i	$0.378391\pi$
$739$			2.75514e7i			1.85581i	−0.372819	+	0.927904i	$0.621609\pi$
$740$	−1.71745e7	−	4.27079e6i	−1.15294	−	0.286701i
$741$		0			0
$742$	−889349.	+	695280.i	−0.0593011	+	0.0463607i
$743$	−357532.			−0.0237598			−0.0118799	−	0.999929i	$-0.503782\pi$
$743$	−357532.			−0.0237598			−0.0118799	+	0.999929i	$0.503782\pi$
$744$		0			0
$745$	2.11055e6			0.139317
$746$	1.75181e6	−	1.36954e6i	0.115250	−	0.0901006i
$747$		0			0
$748$	2.14087e7	+	5.32369e6i	1.39906	+	0.347904i
$749$			2.43710e7i			1.58734i
$750$		0			0
$751$			2.39756e6i			0.155121i	0.996988	+	0.0775603i	$0.0247130\pi$
$751$			2.39756e6i			0.155121i	−0.996988	+	0.0775603i	$0.975287\pi$
$752$	−1.47435e7	−	7.81582e6i	−0.950726	−	0.504000i
$753$		0			0
$754$	−5.71622e6	−	7.31175e6i	−0.366168	−	0.468374i
$755$	−1.32946e7			−0.848804
$756$		0			0
$757$	−1.85832e7			−1.17864			−0.589320	−	0.807900i	$-0.700604\pi$
$757$	−1.85832e7			−1.17864			−0.589320	+	0.807900i	$0.700604\pi$
$758$	−8.03213e6	−	1.02741e7i	−0.507759	−	0.649487i
$759$		0			0
$760$	−3.32091e6	−	7.44027e6i	−0.208556	−	0.467256i
$761$		−	2.59191e7i		−	1.62240i	−0.584769	−	0.811200i	$-0.698815\pi$
$761$		−	2.59191e7i		−	1.62240i	0.584769	−	0.811200i	$-0.301185\pi$
$762$		0			0
$763$			2.03127e7i			1.26315i
$764$	6.10421e6	−	2.45475e7i	0.378352	−	1.52150i
$765$		0			0
$766$	1.20356e7	−	9.40927e6i	0.741134	−	0.579408i
$767$	2.76207e7			1.69530
$768$		0			0
$769$	2.70826e7			1.65148			0.825741	−	0.564050i	$-0.190757\pi$
$769$	2.70826e7			1.65148			0.825741	+	0.564050i	$0.190757\pi$
$770$	1.62916e7	−	1.27365e7i	0.990233	−	0.774149i
$771$		0			0
$772$	−482173.	+	1.93901e6i	−0.0291178	+	0.117094i
$773$			3.16270e7i			1.90375i	0.306492	+	0.951873i	$0.400845\pi$
$773$			3.16270e7i			1.90375i	−0.306492	+	0.951873i	$0.599155\pi$
$774$		0			0
$775$			901449.i			0.0539122i
$776$	−1.05288e7	−	2.35890e7i	−0.627660	−	1.40623i
$777$		0			0
$778$	−5.76892e6	−	7.37917e6i	−0.341700	−	0.437077i
$779$	−2.36396e7			−1.39572
$780$		0			0
$781$	1.63832e7			0.961105
$782$	5.32103e6	+	6.80626e6i	0.311156	+	0.398008i
$783$		0			0
$784$	4.74673e6	+	2.51634e6i	0.275806	+	0.146211i
$785$			1.26609e7i			0.733316i
$786$		0			0
$787$		−	2.34131e7i		−	1.34748i	−0.738969	−	0.673739i	$-0.764687\pi$
$787$		−	2.34131e7i		−	1.34748i	0.738969	−	0.673739i	$-0.235313\pi$
$788$	2.99900e7	+	7.45761e6i	1.72052	+	0.427843i
$789$		0			0
$790$	6.44634e6	−	5.03965e6i	0.367490	−	0.287298i
$791$	−2.56277e7			−1.45636
$792$		0			0
$793$	5.74755e6			0.324564
$794$	7.57567e6	−	5.92255e6i	0.426452	−	0.333394i
$795$		0			0
$796$	1.98604e6	+	493867.i	0.111098	+	0.0276266i
$797$		−	1.66862e7i		−	0.930490i	−0.885182	−	0.465245i	$-0.845966\pi$
$797$		−	1.66862e7i		−	0.930490i	0.885182	−	0.465245i	$-0.154034\pi$
$798$		0			0
$799$		−	1.84745e7i		−	1.02378i
$800$	8.47657e6	−	1.50819e6i	0.468269	−	0.0833166i
$801$		0			0
$802$	−1.86612e6	−	2.38700e6i	−0.102448	−	0.131044i
$803$	3.18097e7			1.74089
$804$		0			0
$805$	8.09841e6			0.440464
$806$	−1.86763e6	−	2.38893e6i	−0.101264	−	0.129529i
$807$		0			0
$808$	−1.34772e7	+	6.01545e6i	−0.726225	+	0.324145i
$809$			2.53067e7i			1.35945i	0.733466	+	0.679726i	$0.237901\pi$
$809$			2.53067e7i			1.35945i	−0.733466	+	0.679726i	$0.762099\pi$
$810$		0			0
$811$		−	2.91246e7i		−	1.55492i	−0.628933	−	0.777460i	$-0.716508\pi$
$811$		−	2.91246e7i		−	1.55492i	0.628933	−	0.777460i	$-0.283492\pi$
$812$	−2.12878e6	+	8.56065e6i	−0.113303	+	0.455634i
$813$		0			0
$814$	3.70250e7	−	2.89456e7i	1.95855	−	1.53116i
$815$	−2.09488e7			−1.10475
$816$		0			0
$817$	−1.38744e7			−0.727209
$818$	7.63291e6	−	5.96729e6i	0.398848	−	0.311813i
$819$		0			0
$820$	−6.64608e6	+	2.67265e7i	−0.345168	+	1.38806i
$821$			2.36944e7i			1.22684i	0.789756	+	0.613421i	$0.210207\pi$
$821$			2.36944e7i			1.22684i	−0.789756	+	0.613421i	$0.789793\pi$
$822$		0			0
$823$		−	2.40085e7i		−	1.23556i	−0.786350	−	0.617782i	$-0.788032\pi$
$823$		−	2.40085e7i		−	1.23556i	0.786350	−	0.617782i	$-0.211968\pi$
$824$	2.54626e7	−	1.13651e7i	1.30643	−	0.583114i
$825$		0			0
$826$	−1.61693e7	−	2.06825e7i	−0.824594	−	1.05476i
$827$	−1.83314e7			−0.932035			−0.466018	−	0.884775i	$-0.654312\pi$
$827$	−1.83314e7			−0.932035			−0.466018	+	0.884775i	$0.654312\pi$
$828$		0			0
$829$	−1.28295e7			−0.648372			−0.324186	−	0.945993i	$-0.605090\pi$
$829$	−1.28295e7			−0.648372			−0.324186	+	0.945993i	$0.605090\pi$
$830$	8.87505e6	+	1.13523e7i	0.447173	+	0.571990i
$831$		0			0
$832$	−1.93391e7	+	2.15587e7i	−0.968562	+	1.07973i
$833$			5.94794e6i			0.296998i
$834$		0			0
$835$			1.27657e7i			0.633621i
$836$	2.09973e7	+	5.22140e6i	1.03908	+	0.258387i
$837$		0			0
$838$	8.86812e6	−	6.93296e6i	0.436236	−	0.341043i
$839$	−1.64336e7			−0.805985			−0.402992	−	0.915203i	$-0.632030\pi$
$839$	−1.64336e7			−0.805985			−0.402992	+	0.915203i	$0.632030\pi$
$840$		0			0
$841$	1.70653e7			0.832003
$842$	−3.78378e6	+	2.95810e6i	−0.183927	+	0.143791i
$843$		0			0
$844$	1.09193e7	+	2.71530e6i	0.527641	+	0.131208i
$845$		−	1.65921e7i		−	0.799394i
$846$		0			0
$847$			3.09983e7i			1.48467i
$848$	−644506.	+	1.21577e6i	−0.0307778	+	0.0580580i
$849$		0			0
$850$	5.87076e6	+	7.50944e6i	0.278707	+	0.356501i
$851$	1.84048e7			0.871178
$852$		0			0
$853$	−9.70416e6			−0.456652			−0.228326	−	0.973585i	$-0.573325\pi$
$853$	−9.70416e6			−0.456652			−0.228326	+	0.973585i	$0.573325\pi$
$854$	−3.36463e6	−	4.30379e6i	−0.157868	−	0.201932i
$855$		0			0
$856$	1.21082e7	+	2.71275e7i	0.564799	+	1.26539i
$857$			8.17649e6i			0.380290i	0.981756	+	0.190145i	$0.0608958\pi$
$857$			8.17649e6i			0.380290i	−0.981756	+	0.190145i	$0.939104\pi$
$858$		0			0
$859$			1.67886e7i			0.776305i	0.921595	+	0.388152i	$0.126887\pi$
$859$			1.67886e7i			0.776305i	−0.921595	+	0.388152i	$0.873113\pi$
$860$	−3.90067e6	+	1.56861e7i	−0.179843	+	0.723218i
$861$		0			0
$862$	−1.34792e7	+	1.05379e7i	−0.617869	+	0.483041i
$863$	1.14812e7			0.524761			0.262381	−	0.964964i	$-0.415492\pi$
$863$	1.14812e7			0.524761			0.262381	+	0.964964i	$0.415492\pi$
$864$		0			0
$865$	2.52772e7			1.14865
$866$	5.90050e6	−	4.61292e6i	0.267359	−	0.209017i
$867$		0			0
$868$	−695524.	+	2.79697e6i	−0.0313338	+	0.126005i
$869$			2.17291e7i			0.976094i
$870$		0			0
$871$		−	2.08146e6i		−	0.0929655i
$872$	1.00919e7	+	2.26101e7i	0.449449	+	1.00696i
$873$		0			0
$874$	5.21879e6	+	6.67548e6i	0.231095	+	0.295600i
$875$	2.77212e7			1.22403
$876$		0			0
$877$	−2.84809e7			−1.25042			−0.625209	−	0.780458i	$-0.714986\pi$
$877$	−2.84809e7			−1.25042			−0.625209	+	0.780458i	$0.714986\pi$
$878$	6.07904e6	+	7.77585e6i	0.266133	+	0.340417i
$879$		0			0
$880$	1.18064e7	−	2.22712e7i	0.513939	−	0.969475i
$881$		−	4.49952e6i		−	0.195311i	−0.995220	−	0.0976555i	$-0.968866\pi$
$881$		−	4.49952e6i		−	0.195311i	0.995220	−	0.0976555i	$-0.0311343\pi$
$882$		0			0
$883$			2.85783e7i			1.23349i	0.787164	+	0.616743i	$0.211548\pi$
$883$			2.85783e7i			1.23349i	−0.787164	+	0.616743i	$0.788452\pi$
$884$	−3.11162e7	−	7.73767e6i	−1.33923	−	0.333027i
$885$		0			0
$886$	2.05385e7	−	1.60567e7i	0.878989	−	0.687180i
$887$	3.38213e6			0.144338			0.0721691	−	0.997392i	$-0.477008\pi$
$887$	3.38213e6			0.144338			0.0721691	+	0.997392i	$0.477008\pi$
$888$		0			0
$889$	−3.67275e7			−1.55861
$890$	9.84292e6	−	7.69505e6i	0.416533	−	0.325639i
$891$		0			0
$892$	−4.55509e6	−	1.13271e6i	−0.191683	−	0.0476659i
$893$		−	1.81195e7i		−	0.760356i
$894$		0			0
$895$			2.80070e6i			0.116872i
$896$	2.74644e7	+	1.86065e6i	1.14288	+	0.0774275i
$897$		0			0
$898$	1.26615e6	+	1.61957e6i	0.0523956	+	0.0670206i
$899$	−1.12583e6			−0.0464596
$900$		0			0
$901$	−1.52343e6			−0.0625189
$902$	−4.50443e7	−	5.76172e7i	−1.84342	−	2.35796i
$903$		0			0
$904$	−2.85263e7	+	1.27325e7i	−1.16098	+	0.518195i
$905$			7.82978e6i			0.317781i
$906$		0			0
$907$		−	4.94792e7i		−	1.99712i	−0.0536189	−	0.998561i	$-0.517076\pi$
$907$		−	4.94792e7i		−	1.99712i	0.0536189	−	0.998561i	$-0.482924\pi$
$908$	4.99723e6	−	2.00958e7i	0.201148	−	0.808894i
$909$		0			0
$910$	−2.36789e7	+	1.85118e7i	−0.947890	+	0.741046i
$911$	−3.42077e7			−1.36561			−0.682807	−	0.730599i	$-0.739241\pi$
$911$	−3.42077e7			−1.36561			−0.682807	+	0.730599i	$0.739241\pi$
$912$		0			0
$913$	−3.82658e7			−1.51927
$914$	−1.12505e7	+	8.79548e6i	−0.445458	+	0.348252i
$915$		0			0
$916$	2.24565e6	−	9.03066e6i	0.0884309	−	0.355616i
$917$		−	5.30132e7i		−	2.08190i
$918$		0			0
$919$			3.51998e7i			1.37484i	0.726262	+	0.687418i	$0.241256\pi$
$919$			3.51998e7i			1.37484i	−0.726262	+	0.687418i	$0.758744\pi$
$920$	9.01438e6	−	4.02350e6i	0.351129	−	0.156724i
$921$		0			0
$922$	−2.13603e7	−	2.73225e7i	−0.827522	−	1.05850i
$923$	−2.38120e7			−0.920008
$924$		0			0
$925$	2.03063e7			0.780325
$926$	1.64731e7	+	2.10712e7i	0.631319	+	0.807536i
$927$		0			0
$928$	1.88360e6	+	1.05865e7i	0.0717992	+	0.403537i
$929$			5.15625e7i			1.96017i	0.198568	+	0.980087i	$0.436371\pi$
$929$			5.15625e7i			1.96017i	−0.198568	+	0.980087i	$0.563629\pi$
$930$		0			0
$931$			5.83365e6i			0.220580i
$932$	−4.96027e7	−	1.23347e7i	−1.87053	−	0.465145i
$933$		0			0
$934$	−1.54958e7	+	1.21144e7i	−0.581228	+	0.454395i
$935$	2.79071e7			1.04397
$936$		0			0
$937$	1.98027e7			0.736844			0.368422	−	0.929659i	$-0.379898\pi$
$937$	1.98027e7			0.736844			0.368422	+	0.929659i	$0.379898\pi$
$938$	−1.55860e6	+	1.21849e6i	−0.0578400	+	0.0452184i
$939$		0			0
$940$	−2.04855e7	−	5.09413e6i	−0.756184	−	0.188040i
$941$		−	1.34418e7i		−	0.494862i	−0.968905	−	0.247431i	$-0.920414\pi$
$941$		−	1.34418e7i		−	0.494862i	0.968905	−	0.247431i	$-0.0795864\pi$
$942$		0			0
$943$		−	2.86410e7i		−	1.04884i
$944$	−2.82737e7	−	1.49885e7i	−1.03265	−	0.547429i
$945$		0			0
$946$	−2.64370e7	−	3.38163e7i	−0.960473	−	1.22856i
$947$	3.05645e7			1.10750			0.553748	−	0.832684i	$-0.313197\pi$
$947$	3.05645e7			1.10750			0.553748	+	0.832684i	$0.313197\pi$
$948$		0			0
$949$	−4.62336e7			−1.66645
$950$	5.75796e6	+	7.36515e6i	0.206995	+	0.264772i
$951$		0			0
$952$	1.24215e7	+	2.78296e7i	0.444205	+	0.995209i
$953$		−	5.63507e6i		−	0.200987i	−0.994938	−	0.100493i	$-0.967958\pi$
$953$		−	5.63507e6i		−	0.200987i	0.994938	−	0.100493i	$-0.0320421\pi$
$954$		0			0
$955$		−	3.19987e7i		−	1.13533i
$956$	999819.	−	4.02067e6i	0.0353815	−	0.142283i
$957$		0			0
$958$	1.29539e7	−	1.01271e7i	0.456022	−	0.356511i
$959$	−3.80180e7			−1.33488
$960$		0			0
$961$	2.82613e7			0.987152
$962$	−5.38136e7	+	4.20707e7i	−1.87480	+	1.46569i
$963$		0			0
$964$	−4.70833e6	+	1.89341e7i	−0.163183	+	0.656223i
$965$			2.52758e6i			0.0873749i
$966$		0			0
$967$			2.26391e7i			0.778560i	0.921119	+	0.389280i	$0.127276\pi$
$967$			2.26391e7i			0.778560i	−0.921119	+	0.389280i	$0.872724\pi$
$968$	1.54008e7	+	3.45043e7i	0.528267	+	1.18355i
$969$		0			0
$970$	−2.01266e7	−	2.57444e7i	−0.686817	−	0.878525i
$971$	2.10762e6			0.0717372			0.0358686	−	0.999357i	$-0.488580\pi$
$971$	2.10762e6			0.0717372			0.0358686	+	0.999357i	$0.488580\pi$
$972$		0			0
$973$	−1.02507e7			−0.347115
$974$	1.88148e7	+	2.40665e7i	0.635481	+	0.812859i
$975$		0			0
$976$	−5.88342e6	−	3.11893e6i	−0.197699	−	0.104805i
$977$		−	2.61881e7i		−	0.877745i	−0.898549	−	0.438873i	$-0.855378\pi$
$977$		−	2.61881e7i		−	0.877745i	0.898549	−	0.438873i	$-0.144622\pi$
$978$		0			0
$979$			3.31781e7i			1.10636i
$980$	6.59541e6	+	1.64008e6i	0.219370	+	0.0545506i
$981$		0			0
$982$	−4.33381e7	+	3.38811e7i	−1.43414	+	1.12119i
$983$	4.01037e7			1.32373			0.661866	−	0.749622i	$-0.269765\pi$
$983$	4.01037e7			1.32373			0.661866	+	0.749622i	$0.269765\pi$
$984$		0			0
$985$	3.90933e7			1.28384
$986$	−9.37865e6	+	7.33209e6i	−0.307219	+	0.240179i
$987$		0			0
$988$	−3.05183e7	−	7.58899e6i	−0.994646	−	0.247339i
$989$		−	1.68098e7i		−	0.546476i
$990$		0			0
$991$			4.06829e7i			1.31592i	0.753055	+	0.657958i	$0.228580\pi$
$991$			4.06829e7i			1.31592i	−0.753055	+	0.657958i	$0.771420\pi$
$992$	615420.	+	3.45888e6i	0.0198560	+	0.111598i
$993$		0			0
$994$	1.39396e7	+	1.78305e7i	0.447492	+	0.572397i
$995$	2.58888e6			0.0829001
$996$		0			0
$997$	−1.33781e7			−0.426242			−0.213121	−	0.977026i	$-0.568363\pi$
$997$	−1.33781e7			−0.426242			−0.213121	+	0.977026i	$0.568363\pi$
$998$	−5.15241e6	−	6.59057e6i	−0.163751	−	0.209458i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.b.c.107.4	yes	20
3.2	odd	2	inner	108.6.b.c.107.17	yes	20
4.3	odd	2	inner	108.6.b.c.107.18	yes	20
12.11	even	2	inner	108.6.b.c.107.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.6.b.c.107.3	✓	20	12.11	even	2	inner
108.6.b.c.107.4	yes	20	1.1	even	1	trivial
108.6.b.c.107.17	yes	20	3.2	odd	2	inner
108.6.b.c.107.18	yes	20	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)

\(f(q)\)	\(=\)	\(q+(-4.45658 + 3.48409i) q^{2} +(7.72226 - 31.0543i) q^{4} -40.4806i q^{5} +148.504i q^{7} +(73.7809 + 165.301i) q^{8} +O(q^{10})\)	\(q+(-4.45658 + 3.48409i) q^{2} +(7.72226 - 31.0543i) q^{4} -40.4806i q^{5} +148.504i q^{7} +(73.7809 + 165.301i) q^{8} +(141.038 + 180.405i) q^{10} -608.102 q^{11} +883.839 q^{13} +(-517.402 - 661.822i) q^{14} +(-904.733 - 479.618i) q^{16} -1133.69i q^{17} -1111.90i q^{19} +(-1257.09 - 312.602i) q^{20} +(2710.06 - 2118.68i) q^{22} +1347.14 q^{23} +1486.32 q^{25} +(-3938.90 + 3079.37i) q^{26} +(4611.69 + 1146.79i) q^{28} +1856.29i q^{29} +606.496i q^{31} +(5703.05 - 1014.71i) q^{32} +(3949.86 + 5052.36i) q^{34} +6011.54 q^{35} +13662.1 q^{37} +(3873.96 + 4955.28i) q^{38} +(6691.48 - 2986.69i) q^{40} -21260.5i q^{41} -12478.1i q^{43} +(-4695.92 + 18884.1i) q^{44} +(-6003.66 + 4693.57i) q^{46} +16295.9 q^{47} -5246.55 q^{49} +(-6623.92 + 5178.48i) q^{50} +(6825.24 - 27447.0i) q^{52} -1343.79i q^{53} +24616.3i q^{55} +(-24547.9 + 10956.8i) q^{56} +(-6467.48 - 8272.72i) q^{58} +31250.9 q^{59} +6502.94 q^{61} +(-2113.09 - 2702.90i) q^{62} +(-21880.8 + 24392.1i) q^{64} -35778.3i q^{65} -2355.02i q^{67} +(-35205.7 - 8754.61i) q^{68} +(-26790.9 + 20944.7i) q^{70} -26941.5 q^{71} -52309.9 q^{73} +(-60886.2 + 47599.9i) q^{74} +(-34529.3 - 8586.40i) q^{76} -90305.8i q^{77} -35732.6i q^{79} +(-19415.2 + 36624.1i) q^{80} +(74073.6 + 94749.4i) q^{82} +62926.7 q^{83} -45892.2 q^{85} +(43474.7 + 55609.6i) q^{86} +(-44866.3 - 100520. i) q^{88} -54560.1i q^{89} +131254. i q^{91} +(10403.0 - 41834.5i) q^{92} +(-72624.2 + 56776.5i) q^{94} -45010.4 q^{95} -142704. q^{97} +(23381.7 - 18279.4i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{4}+O(q^{10}) \) 20 * q + 20 * q^4	\( 20 q + 20 q^{4} + 184 q^{10} - 116 q^{13} - 4168 q^{16} + 696 q^{22} - 15228 q^{25} - 4764 q^{28} - 16520 q^{34} - 6452 q^{37} + 1504 q^{40} - 9336 q^{46} - 44464 q^{49} + 8236 q^{52} - 58736 q^{58} + 84604 q^{61} - 6496 q^{64} + 138696 q^{70} + 85420 q^{73} + 89172 q^{76} + 221200 q^{82} + 180320 q^{85} - 85824 q^{88} - 60936 q^{94} - 219908 q^{97}+O(q^{100}) \) 20 * q + 20 * q^4 + 184 * q^10 - 116 * q^13 - 4168 * q^16 + 696 * q^22 - 15228 * q^25 - 4764 * q^28 - 16520 * q^34 - 6452 * q^37 + 1504 * q^40 - 9336 * q^46 - 44464 * q^49 + 8236 * q^52 - 58736 * q^58 + 84604 * q^61 - 6496 * q^64 + 138696 * q^70 + 85420 * q^73 + 89172 * q^76 + 221200 * q^82 + 180320 * q^85 - 85824 * q^88 - 60936 * q^94 - 219908 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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