LMFDB - Embedded newform 36.7.d.c.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,7,Mod(19,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("36.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	36.d (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:	$8.28194701031$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-15}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 4 $ x^2 - x + 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 4)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.2
Root			$0.500000 - 1.93649i$ of defining polynomial
Character	$\chi$	$=$	36.19
Dual form			36.7.d.c.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 7.74597i) q^{2} +(-56.0000 - 30.9839i) q^{4} -10.0000 q^{5} -309.839i q^{7} +(352.000 - 371.806i) q^{8} +O(q^{10})$	\(q+(-2.00000 + 7.74597i) q^{2} +(-56.0000 - 30.9839i) q^{4} -10.0000 q^{5} -309.839i q^{7} +(352.000 - 371.806i) q^{8} +(20.0000 - 77.4597i) q^{10} -960.500i q^{11} +1466.00 q^{13} +(2400.00 + 619.677i) q^{14} +(2176.00 + 3470.19i) q^{16} +4766.00 q^{17} -7529.08i q^{19} +(560.000 + 309.839i) q^{20} +(7440.00 + 1921.00i) q^{22} -10472.5i q^{23} -15525.0 q^{25} +(-2932.00 + 11355.6i) q^{26} +(-9600.00 + 17351.0i) q^{28} -25498.0 q^{29} -41890.2i q^{31} +(-31232.0 + 9914.84i) q^{32} +(-9532.00 + 36917.3i) q^{34} +3098.39i q^{35} +1994.00 q^{37} +(58320.0 + 15058.2i) q^{38} +(-3520.00 + 3718.06i) q^{40} -29362.0 q^{41} +21533.8i q^{43} +(-29760.0 + 53788.0i) q^{44} +(81120.0 + 20945.1i) q^{46} -7560.06i q^{47} +21649.0 q^{49} +(31050.0 - 120256. i) q^{50} +(-82096.0 - 45422.3i) q^{52} +192854. q^{53} +9605.00i q^{55} +(-115200. - 109063. i) q^{56} +(50996.0 - 197507. i) q^{58} -78420.2i q^{59} -10918.0 q^{61} +(324480. + 83780.4i) q^{62} +(-14336.0 - 261752. i) q^{64} -14660.0 q^{65} +394146. i q^{67} +(-266896. - 147669. i) q^{68} +(-24000.0 - 6196.77i) q^{70} +532241. i q^{71} +288626. q^{73} +(-3988.00 + 15445.5i) q^{74} +(-233280. + 421628. i) q^{76} -297600. q^{77} +310706. i q^{79} +(-21760.0 - 34701.9i) q^{80} +(58724.0 - 227437. i) q^{82} -204153. i q^{83} -47660.0 q^{85} +(-166800. - 43067.6i) q^{86} +(-357120. - 338096. i) q^{88} -310738. q^{89} -454223. i q^{91} +(-324480. + 586463. i) q^{92} +(58560.0 + 15120.1i) q^{94} +75290.8i q^{95} -1.45709e6 q^{97} +(-43298.0 + 167692. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} - 112 q^{4} - 20 q^{5} + 704 q^{8}+O(q^{10}) $ 2 * q - 4 * q^2 - 112 * q^4 - 20 * q^5 + 704 * q^8	$ 2 q - 4 q^{2} - 112 q^{4} - 20 q^{5} + 704 q^{8} + 40 q^{10} + 2932 q^{13} + 4800 q^{14} + 4352 q^{16} + 9532 q^{17} + 1120 q^{20} + 14880 q^{22} - 31050 q^{25} - 5864 q^{26} - 19200 q^{28} - 50996 q^{29} - 62464 q^{32} - 19064 q^{34} + 3988 q^{37} + 116640 q^{38} - 7040 q^{40} - 58724 q^{41} - 59520 q^{44} + 162240 q^{46} + 43298 q^{49} + 62100 q^{50} - 164192 q^{52} + 385708 q^{53} - 230400 q^{56} + 101992 q^{58} - 21836 q^{61} + 648960 q^{62} - 28672 q^{64} - 29320 q^{65} - 533792 q^{68} - 48000 q^{70} + 577252 q^{73} - 7976 q^{74} - 466560 q^{76} - 595200 q^{77} - 43520 q^{80} + 117448 q^{82} - 95320 q^{85} - 333600 q^{86} - 714240 q^{88} - 621476 q^{89} - 648960 q^{92} + 117120 q^{94} - 2914172 q^{97} - 86596 q^{98}+O(q^{100}) $ 2 * q - 4 * q^2 - 112 * q^4 - 20 * q^5 + 704 * q^8 + 40 * q^10 + 2932 * q^13 + 4800 * q^14 + 4352 * q^16 + 9532 * q^17 + 1120 * q^20 + 14880 * q^22 - 31050 * q^25 - 5864 * q^26 - 19200 * q^28 - 50996 * q^29 - 62464 * q^32 - 19064 * q^34 + 3988 * q^37 + 116640 * q^38 - 7040 * q^40 - 58724 * q^41 - 59520 * q^44 + 162240 * q^46 + 43298 * q^49 + 62100 * q^50 - 164192 * q^52 + 385708 * q^53 - 230400 * q^56 + 101992 * q^58 - 21836 * q^61 + 648960 * q^62 - 28672 * q^64 - 29320 * q^65 - 533792 * q^68 - 48000 * q^70 + 577252 * q^73 - 7976 * q^74 - 466560 * q^76 - 595200 * q^77 - 43520 * q^80 + 117448 * q^82 - 95320 * q^85 - 333600 * q^86 - 714240 * q^88 - 621476 * q^89 - 648960 * q^92 + 117120 * q^94 - 2914172 * q^97 - 86596 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$1$

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 $

$2$	−2.00000	+	7.74597i	−0.250000	+	0.968246i
$2$	−2.00000	+	7.74597i	−0.250000	+	0.968246i
$3$		0			0
$3$		0			0
$4$	−56.0000	−	30.9839i	−0.875000	−	0.484123i
$5$	−10.0000			−0.0800000			−0.0400000	−	0.999200i	$-0.512736\pi$
$5$	−10.0000			−0.0800000			−0.0400000	+	0.999200i	$0.512736\pi$
$6$		0			0
$7$		−	309.839i		−	0.903320i	−0.892190	−	0.451660i	$-0.850832\pi$
$7$		−	309.839i		−	0.903320i	0.892190	−	0.451660i	$-0.149168\pi$
$8$	352.000	−	371.806i	0.687500	−	0.726184i
$9$		0			0
$10$	20.0000	−	77.4597i	0.0200000	−	0.0774597i
$11$		−	960.500i		−	0.721638i	−0.932636	−	0.360819i	$-0.882497\pi$
$11$		−	960.500i		−	0.721638i	0.932636	−	0.360819i	$-0.117503\pi$
$12$		0			0
$13$	1466.00			0.667274			0.333637	−	0.942702i	$-0.391724\pi$
$13$	1466.00			0.667274			0.333637	+	0.942702i	$0.391724\pi$
$14$	2400.00	+	619.677i	0.874636	+	0.225830i
$15$		0			0
$16$	2176.00	+	3470.19i	0.531250	+	0.847215i
$17$	4766.00			0.970079			0.485040	−	0.874492i	$-0.338805\pi$
$17$	4766.00			0.970079			0.485040	+	0.874492i	$0.338805\pi$
$18$		0			0
$19$		−	7529.08i		−	1.09769i	−0.835923	−	0.548847i	$-0.815067\pi$
$19$		−	7529.08i		−	1.09769i	0.835923	−	0.548847i	$-0.184933\pi$
$20$	560.000	+	309.839i	0.0700000	+	0.0387298i
$21$		0			0
$22$	7440.00	+	1921.00i	0.698723	+	0.180409i
$23$		−	10472.5i		−	0.860734i	−0.902654	−	0.430367i	$-0.858384\pi$
$23$		−	10472.5i		−	0.860734i	0.902654	−	0.430367i	$-0.141616\pi$
$24$		0			0
$25$	−15525.0			−0.993600
$26$	−2932.00	+	11355.6i	−0.166818	+	0.646085i
$27$		0			0
$28$	−9600.00	+	17351.0i	−0.437318	+	0.790405i
$29$	−25498.0			−1.04547			−0.522736	−	0.852495i	$-0.675089\pi$
$29$	−25498.0			−1.04547			−0.522736	+	0.852495i	$0.675089\pi$
$30$		0			0
$31$		−	41890.2i		−	1.40614i	−0.711123	−	0.703068i	$-0.751813\pi$
$31$		−	41890.2i		−	1.40614i	0.711123	−	0.703068i	$-0.248187\pi$
$32$	−31232.0	+	9914.84i	−0.953125	+	0.302577i
$33$		0			0
$34$	−9532.00	+	36917.3i	−0.242520	+	0.939275i
$35$			3098.39i			0.0722656i
$36$		0			0
$37$	1994.00			0.0393659			0.0196829	−	0.999806i	$-0.493734\pi$
$37$	1994.00			0.0393659			0.0196829	+	0.999806i	$0.493734\pi$
$38$	58320.0	+	15058.2i	1.06284	+	0.274423i
$39$		0			0
$40$	−3520.00	+	3718.06i	−0.0550000	+	0.0580948i
$41$	−29362.0			−0.426024			−0.213012	−	0.977050i	$-0.568327\pi$
$41$	−29362.0			−0.426024			−0.213012	+	0.977050i	$0.568327\pi$
$42$		0			0
$43$			21533.8i			0.270841i	0.990788	+	0.135421i	$0.0432386\pi$
$43$			21533.8i			0.270841i	−0.990788	+	0.135421i	$0.956761\pi$
$44$	−29760.0	+	53788.0i	−0.349361	+	0.631433i
$45$		0			0
$46$	81120.0	+	20945.1i	0.833402	+	0.215183i
$47$		−	7560.06i		−	0.0728168i	−0.999337	−	0.0364084i	$-0.988408\pi$
$47$		−	7560.06i		−	0.0728168i	0.999337	−	0.0364084i	$-0.0115917\pi$
$48$		0			0
$49$	21649.0			0.184013
$50$	31050.0	−	120256.i	0.248400	−	0.962049i
$51$		0			0
$52$	−82096.0	−	45422.3i	−0.583864	−	0.323042i
$53$	192854.			1.29539			0.647696	−	0.761899i	$-0.275733\pi$
$53$	192854.			1.29539			0.647696	+	0.761899i	$0.275733\pi$
$54$		0			0
$55$			9605.00i			0.0577310i
$56$	−115200.	−	109063.i	−0.655977	−	0.621032i
$57$		0			0
$58$	50996.0	−	197507.i	0.261368	−	1.01227i
$59$		−	78420.2i		−	0.381831i	−0.981606	−	0.190916i	$-0.938854\pi$
$59$		−	78420.2i		−	0.381831i	0.981606	−	0.190916i	$-0.0611457\pi$
$60$		0			0
$61$	−10918.0			−0.0481009			−0.0240505	−	0.999711i	$-0.507656\pi$
$61$	−10918.0			−0.0481009			−0.0240505	+	0.999711i	$0.507656\pi$
$62$	324480.	+	83780.4i	1.36149	+	0.351534i
$63$		0			0
$64$	−14336.0	−	261752.i	−0.0546875	−	0.998504i
$65$	−14660.0			−0.0533819
$66$		0			0
$67$			394146.i			1.31049i	0.755418	+	0.655243i	$0.227434\pi$
$67$			394146.i			1.31049i	−0.755418	+	0.655243i	$0.772566\pi$
$68$	−266896.	−	147669.i	−0.848819	−	0.469638i
$69$		0			0
$70$	−24000.0	−	6196.77i	−0.0699708	−	0.0180664i
$71$			532241.i			1.48708i	0.668694	+	0.743538i	$0.266854\pi$
$71$			532241.i			1.48708i	−0.668694	+	0.743538i	$0.733146\pi$
$72$		0			0
$73$	288626.			0.741937			0.370968	−	0.928646i	$-0.379026\pi$
$73$	288626.			0.741937			0.370968	+	0.928646i	$0.379026\pi$
$74$	−3988.00	+	15445.5i	−0.00984147	+	0.0381159i
$75$		0			0
$76$	−233280.	+	421628.i	−0.531419	+	0.960482i
$77$	−297600.			−0.651870
$78$		0			0
$79$			310706.i			0.630186i	0.949061	+	0.315093i	$0.102036\pi$
$79$			310706.i			0.630186i	−0.949061	+	0.315093i	$0.897964\pi$
$80$	−21760.0	−	34701.9i	−0.0425000	−	0.0677772i
$81$		0			0
$82$	58724.0	−	227437.i	0.106506	−	0.412496i
$83$		−	204153.i		−	0.357043i	−0.983936	−	0.178522i	$-0.942869\pi$
$83$		−	204153.i		−	0.357043i	0.983936	−	0.178522i	$-0.0571314\pi$
$84$		0			0
$85$	−47660.0			−0.0776064
$86$	−166800.	−	43067.6i	−0.262241	−	0.0677104i
$87$		0			0
$88$	−357120.	−	338096.i	−0.524042	−	0.496126i
$89$	−310738.			−0.440783			−0.220391	−	0.975412i	$-0.570733\pi$
$89$	−310738.			−0.440783			−0.220391	+	0.975412i	$0.570733\pi$
$90$		0			0
$91$		−	454223.i		−	0.602761i
$92$	−324480.	+	586463.i	−0.416701	+	0.753142i
$93$		0			0
$94$	58560.0	+	15120.1i	0.0705046	+	0.0182042i
$95$			75290.8i			0.0878155i
$96$		0			0
$97$	−1.45709e6			−1.59650			−0.798252	−	0.602324i	$-0.794242\pi$
$97$	−1.45709e6			−1.59650			−0.798252	+	0.602324i	$0.794242\pi$
$98$	−43298.0	+	167692.i	−0.0460034	+	0.178170i
$99$		0			0
$100$	869400.	+	481025.i	0.869400	+	0.481025i
$101$	639158.			0.620360			0.310180	−	0.950678i	$-0.399611\pi$
$101$	639158.			0.620360			0.310180	+	0.950678i	$0.399611\pi$
$102$		0			0
$103$		−	1.38913e6i		−	1.27125i	−0.771997	−	0.635626i	$-0.780742\pi$
$103$		−	1.38913e6i		−	1.27125i	0.771997	−	0.635626i	$-0.219258\pi$
$104$	516032.	−	545068.i	0.458751	−	0.484564i
$105$		0			0
$106$	−385708.	+	1.49384e6i	−0.323848	+	1.25426i
$107$		−	1.14935e6i		−	0.938209i	−0.883143	−	0.469105i	$-0.844577\pi$
$107$		−	1.14935e6i		−	0.938209i	0.883143	−	0.469105i	$-0.155423\pi$
$108$		0			0
$109$	1.53574e6			1.18587			0.592936	−	0.805250i	$-0.297969\pi$
$109$	1.53574e6			1.18587			0.592936	+	0.805250i	$0.297969\pi$
$110$	−74400.0	−	19210.0i	−0.0558978	−	0.0144328i
$111$		0			0
$112$	1.07520e6	−	674209.i	0.765306	−	0.479889i
$113$	601694.			0.417004			0.208502	−	0.978022i	$-0.433141\pi$
$113$	601694.			0.417004			0.208502	+	0.978022i	$0.433141\pi$
$114$		0			0
$115$			104725.i			0.0688587i
$116$	1.42789e6	+	790027.i	0.914787	+	0.506137i
$117$		0			0
$118$	607440.	+	156840.i	0.369707	+	0.0954579i
$119$		−	1.47669e6i		−	0.876292i
$120$		0			0
$121$	849001.			0.479239
$122$	21836.0	−	84570.5i	0.0120252	−	0.0465735i
$123$		0			0
$124$	−1.29792e6	+	2.34585e6i	−0.680743	+	1.23037i
$125$	311500.			0.159488
$126$		0			0
$127$		−	1.67462e6i		−	0.817531i	−0.912640	−	0.408765i	$-0.865959\pi$
$127$		−	1.67462e6i		−	0.817531i	0.912640	−	0.408765i	$-0.134041\pi$
$128$	2.05619e6	+	412457.i	0.980469	+	0.196675i
$129$		0			0
$130$	29320.0	−	113556.i	0.0133455	−	0.0516868i
$131$			2.84454e6i			1.26531i	0.774433	+	0.632656i	$0.218035\pi$
$131$			2.84454e6i			1.26531i	−0.774433	+	0.632656i	$0.781965\pi$
$132$		0			0
$133$	−2.33280e6			−0.991568
$134$	−3.05304e6	−	788292.i	−1.26887	−	0.327622i
$135$		0			0
$136$	1.67763e6	−	1.77203e6i	0.666930	−	0.704456i
$137$	−3.81003e6			−1.48172			−0.740862	−	0.671658i	$-0.765583\pi$
$137$	−3.81003e6			−1.48172			−0.740862	+	0.671658i	$0.765583\pi$
$138$		0			0
$139$		−	138839.i		−	0.0516971i	−0.999666	−	0.0258485i	$-0.991771\pi$
$139$		−	138839.i		−	0.0516971i	0.999666	−	0.0258485i	$-0.00822877\pi$
$140$	96000.0	−	173510.i	0.0349854	−	0.0632324i
$141$		0			0
$142$	−4.12272e6	−	1.06448e6i	−1.43986	−	0.371769i
$143$		−	1.40809e6i		−	0.481530i
$144$		0			0
$145$	254980.			0.0836377
$146$	−577252.	+	2.23569e6i	−0.185484	+	0.718377i
$147$		0			0
$148$	−111664.	−	61781.8i	−0.0344451	−	0.0190579i
$149$	3.27426e6			0.989816			0.494908	−	0.868945i	$-0.335202\pi$
$149$	3.27426e6			0.989816			0.494908	+	0.868945i	$0.335202\pi$
$150$		0			0
$151$			5.59352e6i			1.62463i	0.583220	+	0.812314i	$0.301793\pi$
$151$			5.59352e6i			1.62463i	−0.583220	+	0.812314i	$0.698207\pi$
$152$	−2.79936e6	−	2.65024e6i	−0.797128	−	0.754664i
$153$		0			0
$154$	595200.	−	2.30520e6i	0.162967	−	0.631170i
$155$			418902.i			0.112491i
$156$		0			0
$157$	816794.			0.211064			0.105532	−	0.994416i	$-0.466345\pi$
$157$	816794.			0.211064			0.105532	+	0.994416i	$0.466345\pi$
$158$	−2.40672e6	−	621412.i	−0.610175	−	0.157546i
$159$		0			0
$160$	312320.	−	99148.4i	0.0762500	−	0.0242061i
$161$	−3.24480e6			−0.777518
$162$		0			0
$163$			1.84593e6i			0.426237i	0.977026	+	0.213119i	$0.0683621\pi$
$163$			1.84593e6i			0.426237i	−0.977026	+	0.213119i	$0.931638\pi$
$164$	1.64427e6	+	909748.i	0.372771	+	0.206248i
$165$		0			0
$166$	1.58136e6	+	408305.i	0.345706	+	0.0892608i
$167$			7.96515e6i			1.71019i	0.518471	+	0.855095i	$0.326501\pi$
$167$			7.96515e6i			1.71019i	−0.518471	+	0.855095i	$0.673499\pi$
$168$		0			0
$169$	−2.67765e6			−0.554746
$170$	95320.0	−	369173.i	0.0194016	−	0.0751420i
$171$		0			0
$172$	667200.	−	1.20589e6i	0.131121	−	0.236986i
$173$	5.12653e6			0.990115			0.495057	−	0.868860i	$-0.335147\pi$
$173$	5.12653e6			0.990115			0.495057	+	0.868860i	$0.335147\pi$
$174$		0			0
$175$			4.81025e6i			0.897538i
$176$	3.33312e6	−	2.09005e6i	0.611382	−	0.383370i
$177$		0			0
$178$	621476.	−	2.40697e6i	0.110196	−	0.426786i
$179$		−	2.33411e6i		−	0.406969i	−0.979078	−	0.203485i	$-0.934773\pi$
$179$		−	2.33411e6i		−	0.406969i	0.979078	−	0.203485i	$-0.0652267\pi$
$180$		0			0
$181$	9.69156e6			1.63440			0.817199	−	0.576355i	$-0.195525\pi$
$181$	9.69156e6			1.63440			0.817199	+	0.576355i	$0.195525\pi$
$182$	3.51840e6	+	908447.i	0.583621	+	0.150690i
$183$		0			0
$184$	−3.89376e6	−	3.68634e6i	−0.625051	−	0.591754i
$185$	−19940.0			−0.00314927
$186$		0			0
$187$		−	4.57774e6i		−	0.700046i
$188$	−234240.	+	423364.i	−0.0352523	+	0.0637147i
$189$		0			0
$190$	−583200.	−	150582.i	−0.0850270	−	0.0219539i
$191$		−	1.14164e7i		−	1.63844i	−0.573479	−	0.819220i	$-0.694407\pi$
$191$		−	1.14164e7i		−	1.63844i	0.573479	−	0.819220i	$-0.305593\pi$
$192$		0			0
$193$	−2.43033e6			−0.338060			−0.169030	−	0.985611i	$-0.554064\pi$
$193$	−2.43033e6			−0.338060			−0.169030	+	0.985611i	$0.554064\pi$
$194$	2.91417e6	−	1.12865e7i	0.399126	−	1.54581i
$195$		0			0
$196$	−1.21234e6	−	670770.i	−0.161012	−	0.0890851i
$197$	2.23065e6			0.291764			0.145882	−	0.989302i	$-0.453398\pi$
$197$	2.23065e6			0.291764			0.145882	+	0.989302i	$0.453398\pi$
$198$		0			0
$199$		−	4.89576e6i		−	0.621242i	−0.950534	−	0.310621i	$-0.899463\pi$
$199$		−	4.89576e6i		−	0.621242i	0.950534	−	0.310621i	$-0.100537\pi$
$200$	−5.46480e6	+	5.77229e6i	−0.683100	+	0.721537i
$201$		0			0
$202$	−1.27832e6	+	4.95090e6i	−0.155090	+	0.600661i
$203$			7.90027e6i			0.944395i
$204$		0			0
$205$	293620.			0.0340819
$206$	1.07602e7	+	2.77826e6i	1.23088	+	0.317813i
$207$		0			0
$208$	3.19002e6	+	5.08730e6i	0.354489	+	0.565324i
$209$	−7.23168e6			−0.792137
$210$		0			0
$211$		−	3.90951e6i		−	0.416174i	−0.978110	−	0.208087i	$-0.933276\pi$
$211$		−	3.90951e6i		−	0.416174i	0.978110	−	0.208087i	$-0.0667238\pi$
$212$	−1.07998e7	−	5.97536e6i	−1.13347	−	0.627129i
$213$		0			0
$214$	8.90280e6	+	2.29869e6i	0.908417	+	0.234552i
$215$		−	215338.i		−	0.0216673i
$216$		0			0
$217$	−1.29792e7			−1.27019
$218$	−3.07148e6	+	1.18958e7i	−0.296468	+	1.14822i
$219$		0			0
$220$	297600.	−	537880.i	0.0279489	−	0.0505146i
$221$	6.98696e6			0.647308
$222$		0			0
$223$		−	3.33114e6i		−	0.300385i	−0.988657	−	0.150192i	$-0.952011\pi$
$223$		−	3.33114e6i		−	0.300385i	0.988657	−	0.150192i	$-0.0479893\pi$
$224$	3.07200e6	+	9.67688e6i	0.273324	+	0.860977i
$225$		0			0
$226$	−1.20339e6	+	4.66070e6i	−0.104251	+	0.403763i
$227$		−	1.35033e7i		−	1.15442i	−0.816597	−	0.577208i	$-0.804142\pi$
$227$		−	1.35033e7i		−	1.15442i	0.816597	−	0.577208i	$-0.195858\pi$
$228$		0			0
$229$	1.59598e6			0.132899			0.0664493	−	0.997790i	$-0.478833\pi$
$229$	1.59598e6			0.132899			0.0664493	+	0.997790i	$0.478833\pi$
$230$	−811200.	−	209451.i	−0.0666721	−	0.0172147i
$231$		0			0
$232$	−8.97530e6	+	9.48032e6i	−0.718762	+	0.759205i
$233$	−8.04383e6			−0.635909			−0.317954	−	0.948106i	$-0.602996\pi$
$233$	−8.04383e6			−0.635909			−0.317954	+	0.948106i	$0.602996\pi$
$234$		0			0
$235$			75600.6i			0.00582535i
$236$	−2.42976e6	+	4.39153e6i	−0.184853	+	0.334103i
$237$		0			0
$238$	1.14384e7	+	2.95338e6i	0.848466	+	0.219073i
$239$			1.12532e7i			0.824296i	0.911117	+	0.412148i	$0.135221\pi$
$239$			1.12532e7i			0.824296i	−0.911117	+	0.412148i	$0.864779\pi$
$240$		0			0
$241$	5.05104e6			0.360853			0.180426	−	0.983589i	$-0.442252\pi$
$241$	5.05104e6			0.360853			0.180426	+	0.983589i	$0.442252\pi$
$242$	−1.69800e6	+	6.57633e6i	−0.119810	+	0.464021i
$243$		0			0
$244$	611408.	+	338282.i	0.0420883	+	0.0232868i
$245$	−216490.			−0.0147211
$246$		0			0
$247$		−	1.10376e7i		−	0.732462i
$248$	−1.55750e7	−	1.47453e7i	−1.02111	−	0.966718i
$249$		0			0
$250$	−623000.	+	2.41287e6i	−0.0398720	+	0.154424i
$251$			4.71590e6i			0.298225i	0.988820	+	0.149112i	$0.0476416\pi$
$251$			4.71590e6i			0.298225i	−0.988820	+	0.149112i	$0.952358\pi$
$252$		0			0
$253$	−1.00589e7			−0.621138
$254$	1.29715e7	+	3.34923e6i	0.791571	+	0.204383i
$255$		0			0
$256$	−7.30726e6	+	1.51023e7i	−0.435547	+	0.900166i
$257$	−2.34552e7			−1.38178			−0.690892	−	0.722958i	$-0.742782\pi$
$257$	−2.34552e7			−1.38178			−0.690892	+	0.722958i	$0.742782\pi$
$258$		0			0
$259$		−	617818.i		−	0.0355600i
$260$	820960.	+	454223.i	0.0467091	+	0.0258434i
$261$		0			0
$262$	−2.20337e7	−	5.68907e6i	−1.22513	−	0.316328i
$263$		−	2.16993e7i		−	1.19283i	−0.802676	−	0.596415i	$-0.796591\pi$
$263$		−	2.16993e7i		−	1.19283i	0.802676	−	0.596415i	$-0.203409\pi$
$264$		0			0
$265$	−1.92854e6			−0.103631
$266$	4.66560e6	−	1.80698e7i	0.247892	−	0.960082i
$267$		0			0
$268$	1.22122e7	−	2.20722e7i	0.634436	−	1.14668i
$269$	2.94278e7			1.51182			0.755911	−	0.654674i	$-0.227194\pi$
$269$	2.94278e7			1.51182			0.755911	+	0.654674i	$0.227194\pi$
$270$		0			0
$271$			8.51474e6i			0.427822i	0.976853	+	0.213911i	$0.0686203\pi$
$271$			8.51474e6i			0.427822i	−0.976853	+	0.213911i	$0.931380\pi$
$272$	1.03708e7	+	1.65389e7i	0.515355	+	0.821866i
$273$		0			0
$274$	7.62007e6	−	2.95124e7i	0.370431	−	1.43467i
$275$			1.49118e7i			0.717019i
$276$		0			0
$277$	2.76226e7			1.29965			0.649824	−	0.760085i	$-0.274843\pi$
$277$	2.76226e7			1.29965			0.649824	+	0.760085i	$0.274843\pi$
$278$	1.07544e6	+	277677.i	0.0500555	+	0.0129243i
$279$		0			0
$280$	1.15200e6	+	1.09063e6i	0.0524781	+	0.0496826i
$281$	−8.64008e6			−0.389403			−0.194701	−	0.980863i	$-0.562374\pi$
$281$	−8.64008e6			−0.389403			−0.194701	+	0.980863i	$0.562374\pi$
$282$		0			0
$283$			1.27350e7i			0.561873i	0.959726	+	0.280937i	$0.0906450\pi$
$283$			1.27350e7i			0.561873i	−0.959726	+	0.280937i	$0.909355\pi$
$284$	1.64909e7	−	2.98055e7i	0.719928	−	1.30119i
$285$		0			0
$286$	1.09070e7	+	2.81619e6i	0.466239	+	0.120382i
$287$			9.09748e6i			0.384836i
$288$		0			0
$289$	−1.42281e6			−0.0589460
$290$	−509960.	+	1.97507e6i	−0.0209094	+	0.0809819i
$291$		0			0
$292$	−1.61631e7	−	8.94275e6i	−0.649195	−	0.359189i
$293$	4.45415e7			1.77077			0.885385	−	0.464859i	$-0.153895\pi$
$293$	4.45415e7			1.77077			0.885385	+	0.464859i	$0.153895\pi$
$294$		0			0
$295$			784202.i			0.0305465i
$296$	701888.	−	741382.i	0.0270640	−	0.0285869i
$297$		0			0
$298$	−6.54852e6	+	2.53623e7i	−0.247454	+	0.958386i
$299$		−	1.53528e7i		−	0.574345i
$300$		0			0
$301$	6.67200e6			0.244656
$302$	−4.33272e7	−	1.11870e7i	−1.57304	−	0.406157i
$303$		0			0
$304$	2.61274e7	−	1.63833e7i	0.929983	−	0.583150i
$305$	109180.			0.00384808
$306$		0			0
$307$			4.89051e7i			1.69020i	0.534606	+	0.845102i	$0.320460\pi$
$307$			4.89051e7i			1.69020i	−0.534606	+	0.845102i	$0.679540\pi$
$308$	1.66656e7	+	9.22080e6i	0.570386	+	0.315585i
$309$		0			0
$310$	−3.24480e6	−	837804.i	−0.108919	−	0.0281227i
$311$			5.00220e7i			1.66295i	0.555559	+	0.831477i	$0.312504\pi$
$311$			5.00220e7i			1.66295i	−0.555559	+	0.831477i	$0.687496\pi$
$312$		0			0
$313$	1.12719e6			0.0367589			0.0183795	−	0.999831i	$-0.494149\pi$
$313$	1.12719e6			0.0367589			0.0183795	+	0.999831i	$0.494149\pi$
$314$	−1.63359e6	+	6.32686e6i	−0.0527659	+	0.204362i
$315$		0			0
$316$	9.62688e6	−	1.73995e7i	0.305087	−	0.551413i
$317$	−3.44882e7			−1.08266			−0.541330	−	0.840810i	$-0.682079\pi$
$317$	−3.44882e7			−1.08266			−0.541330	+	0.840810i	$0.682079\pi$
$318$		0			0
$319$			2.44908e7i			0.754452i
$320$	143360.	+	2.61752e6i	0.00437500	+	0.0798803i
$321$		0			0
$322$	6.48960e6	−	2.51341e7i	0.194379	−	0.752828i
$323$		−	3.58836e7i		−	1.06485i
$324$		0			0
$325$	−2.27596e7			−0.663003
$326$	−1.42985e7	−	3.69185e6i	−0.412702	−	0.106559i
$327$		0			0
$328$	−1.03354e7	+	1.09170e7i	−0.292891	+	0.309372i
$329$	−2.34240e6			−0.0657769
$330$		0			0
$331$		−	4.02696e7i		−	1.11044i	−0.831705	−	0.555218i	$-0.812635\pi$
$331$		−	4.02696e7i		−	1.11044i	0.831705	−	0.555218i	$-0.187365\pi$
$332$	−6.32544e6	+	1.14326e7i	−0.172853	+	0.312413i
$333$		0			0
$334$	−6.16978e7	−	1.59303e7i	−1.65588	−	0.427547i
$335$		−	3.94146e6i		−	0.104839i
$336$		0			0
$337$	−3.42531e7			−0.894973			−0.447487	−	0.894291i	$-0.647681\pi$
$337$	−3.42531e7			−0.894973			−0.447487	+	0.894291i	$0.647681\pi$
$338$	5.35531e6	−	2.07410e7i	0.138687	−	0.537131i
$339$		0			0
$340$	2.66896e6	+	1.47669e6i	0.0679056	+	0.0375710i
$341$	−4.02355e7			−1.01472
$342$		0			0
$343$		−	4.31599e7i		−	1.06954i
$344$	8.00640e6	+	7.57989e6i	0.196681	+	0.186203i
$345$		0			0
$346$	−1.02531e7	+	3.97100e7i	−0.247529	+	0.958674i
$347$			5.45496e7i			1.30558i	0.757539	+	0.652790i	$0.226401\pi$
$347$			5.45496e7i			1.30558i	−0.757539	+	0.652790i	$0.773599\pi$
$348$		0			0
$349$	4.70009e7			1.10568			0.552840	−	0.833287i	$-0.313544\pi$
$349$	4.70009e7			1.10568			0.552840	+	0.833287i	$0.313544\pi$
$350$	−3.72600e7	−	9.62049e6i	−0.869038	−	0.224385i
$351$		0			0
$352$	9.52320e6	+	2.99983e7i	0.218351	+	0.687811i
$353$	1.27231e7			0.289248			0.144624	−	0.989487i	$-0.453803\pi$
$353$	1.27231e7			0.289248			0.144624	+	0.989487i	$0.453803\pi$
$354$		0			0
$355$		−	5.32241e6i		−	0.118966i
$356$	1.74013e7	+	9.62786e6i	0.385685	+	0.213393i
$357$		0			0
$358$	1.80799e7	+	4.66822e6i	0.394046	+	0.101742i
$359$		−	2.02153e7i		−	0.436915i	−0.975846	−	0.218457i	$-0.929898\pi$
$359$		−	2.02153e7i		−	0.436915i	0.975846	−	0.218457i	$-0.0701025\pi$
$360$		0			0
$361$	−9.64116e6			−0.204931
$362$	−1.93831e7	+	7.50705e7i	−0.408600	+	1.58250i
$363$		0			0
$364$	−1.40736e7	+	2.54365e7i	−0.291811	+	0.527416i
$365$	−2.88626e6			−0.0593549
$366$		0			0
$367$			1.11057e7i			0.224672i	0.993670	+	0.112336i	$0.0358333\pi$
$367$			1.11057e7i			0.224672i	−0.993670	+	0.112336i	$0.964167\pi$
$368$	3.63418e7	−	2.27883e7i	0.729227	−	0.457265i
$369$		0			0
$370$	39880.0	−	154455.i	0.000787318	−	0.00304927i
$371$		−	5.97536e7i		−	1.17015i
$372$		0			0
$373$	687146.			0.0132411			0.00662053	−	0.999978i	$-0.497893\pi$
$373$	687146.			0.0132411			0.00662053	+	0.999978i	$0.497893\pi$
$374$	3.54590e7	+	9.15548e6i	0.677817	+	0.175011i
$375$		0			0
$376$	−2.81088e6	−	2.66114e6i	−0.0528785	−	0.0500616i
$377$	−3.73801e7			−0.697615
$378$		0			0
$379$		−	1.48499e7i		−	0.272775i	−0.990656	−	0.136388i	$-0.956451\pi$
$379$		−	1.48499e7i		−	0.272775i	0.990656	−	0.136388i	$-0.0435492\pi$
$380$	2.33280e6	−	4.21628e6i	0.0425135	−	0.0768385i
$381$		0			0
$382$	8.84314e7	+	2.28329e7i	1.58641	+	0.409610i
$383$		−	3.35885e7i		−	0.597853i	−0.954276	−	0.298926i	$-0.903372\pi$
$383$		−	3.35885e7i		−	0.597853i	0.954276	−	0.298926i	$-0.0966285\pi$
$384$		0			0
$385$	2.97600e6			0.0521496
$386$	4.86067e6	−	1.88253e7i	0.0845150	−	0.327325i
$387$		0			0
$388$	8.15968e7	+	4.51462e7i	1.39694	+	0.772904i
$389$	1.01122e8			1.71789			0.858946	−	0.512066i	$-0.171120\pi$
$389$	1.01122e8			1.71789			0.858946	+	0.512066i	$0.171120\pi$
$390$		0			0
$391$		−	4.99122e7i		−	0.834980i
$392$	7.62045e6	−	8.04924e6i	0.126509	−	0.133628i
$393$		0			0
$394$	−4.46129e6	+	1.72785e7i	−0.0729410	+	0.282499i
$395$		−	3.10706e6i		−	0.0504149i
$396$		0			0
$397$	−3.48266e7			−0.556595			−0.278297	−	0.960495i	$-0.589770\pi$
$397$	−3.48266e7			−0.556595			−0.278297	+	0.960495i	$0.589770\pi$
$398$	3.79224e7	+	9.79152e6i	0.601515	+	0.155311i
$399$		0			0
$400$	−3.37824e7	−	5.38747e7i	−0.527850	−	0.841793i
$401$	6.88398e7			1.06760			0.533798	−	0.845612i	$-0.320764\pi$
$401$	6.88398e7			1.06760			0.533798	+	0.845612i	$0.320764\pi$
$402$		0			0
$403$		−	6.14110e7i		−	0.938277i
$404$	−3.57928e7	−	1.98036e7i	−0.542815	−	0.300331i
$405$		0			0
$406$	−6.11952e7	−	1.58005e7i	−0.914406	−	0.236099i
$407$		−	1.91524e6i		−	0.0284079i
$408$		0			0
$409$	4.59959e7			0.672278			0.336139	−	0.941812i	$-0.390879\pi$
$409$	4.59959e7			0.672278			0.336139	+	0.941812i	$0.390879\pi$
$410$	−587240.	+	2.27437e6i	−0.00852048	+	0.0329997i
$411$		0			0
$412$	−4.30406e7	+	7.77913e7i	−0.615442	+	1.11234i
$413$	−2.42976e7			−0.344916
$414$		0			0
$415$			2.04153e6i			0.0285635i
$416$	−4.57861e7	+	1.45352e7i	−0.635995	+	0.201902i
$417$		0			0
$418$	1.44634e7	−	5.60164e7i	0.198034	−	0.766983i
$419$			2.71153e7i			0.368615i	0.982869	+	0.184307i	$0.0590042\pi$
$419$			2.71153e7i			0.368615i	−0.982869	+	0.184307i	$0.940996\pi$
$420$		0			0
$421$	−9.42078e7			−1.26253			−0.631263	−	0.775569i	$-0.717463\pi$
$421$	−9.42078e7			−1.26253			−0.631263	+	0.775569i	$0.717463\pi$
$422$	3.02830e7	+	7.81903e6i	0.402959	+	0.104044i
$423$		0			0
$424$	6.78846e7	−	7.17044e7i	0.890582	−	0.940693i
$425$	−7.39922e7			−0.963871
$426$		0			0
$427$			3.38282e6i			0.0434505i
$428$	−3.56112e7	+	6.43634e7i	−0.454209	+	0.820933i
$429$		0			0
$430$	1.66800e6	+	430676.i	0.0209793	+	0.00541683i
$431$		−	5.19187e7i		−	0.648473i	−0.945976	−	0.324236i	$-0.894893\pi$
$431$		−	5.19187e7i		−	0.648473i	0.945976	−	0.324236i	$-0.105107\pi$
$432$		0			0
$433$	8.40210e7			1.03496			0.517481	−	0.855695i	$-0.326870\pi$
$433$	8.40210e7			1.03496			0.517481	+	0.855695i	$0.326870\pi$
$434$	2.59584e7	−	1.00536e8i	0.317548	−	1.22986i
$435$		0			0
$436$	−8.60013e7	−	4.75831e7i	−1.03764	−	0.574108i
$437$	−7.88486e7			−0.944822
$438$		0			0
$439$			1.48115e8i			1.75068i	0.483512	+	0.875338i	$0.339361\pi$
$439$			1.48115e8i			1.75068i	−0.483512	+	0.875338i	$0.660639\pi$
$440$	3.57120e6	+	3.38096e6i	0.0419234	+	0.0396901i
$441$		0			0
$442$	−1.39739e7	+	5.41207e7i	−0.161827	+	0.626754i
$443$			8.03735e7i			0.924489i	0.886752	+	0.462245i	$0.152956\pi$
$443$			8.03735e7i			0.924489i	−0.886752	+	0.462245i	$0.847044\pi$
$444$		0			0
$445$	3.10738e6			0.0352626
$446$	2.58029e7	+	6.66227e6i	0.290846	+	0.0750962i
$447$		0			0
$448$	−8.11008e7	+	4.44185e6i	−0.901968	+	0.0494003i
$449$	8.80925e7			0.973196			0.486598	−	0.873626i	$-0.338238\pi$
$449$	8.80925e7			0.973196			0.486598	+	0.873626i	$0.338238\pi$
$450$		0			0
$451$			2.82022e7i			0.307435i
$452$	−3.36949e7	−	1.86428e7i	−0.364879	−	0.201881i
$453$		0			0
$454$	1.04596e8	+	2.70066e7i	1.11776	+	0.288604i
$455$			4.54223e6i			0.0482209i
$456$		0			0
$457$	−3.75423e7			−0.393344			−0.196672	−	0.980469i	$-0.563013\pi$
$457$	−3.75423e7			−0.393344			−0.196672	+	0.980469i	$0.563013\pi$
$458$	−3.19196e6	+	1.23624e7i	−0.0332247	+	0.128679i
$459$		0			0
$460$	3.24480e6	−	5.86463e6i	0.0333361	−	0.0602514i
$461$	−1.15260e8			−1.17646			−0.588228	−	0.808695i	$-0.700174\pi$
$461$	−1.15260e8			−1.17646			−0.588228	+	0.808695i	$0.700174\pi$
$462$		0			0
$463$			1.03415e7i			0.104194i	0.998642	+	0.0520970i	$0.0165905\pi$
$463$			1.03415e7i			0.104194i	−0.998642	+	0.0520970i	$0.983410\pi$
$464$	−5.54836e7	−	8.84830e7i	−0.555407	−	0.885739i
$465$		0			0
$466$	1.60877e7	−	6.23072e7i	0.158977	−	0.615716i
$467$			1.64223e8i			1.61243i	0.591620	+	0.806217i	$0.298489\pi$
$467$			1.64223e8i			1.61243i	−0.591620	+	0.806217i	$0.701511\pi$
$468$		0			0
$469$	1.22122e8			1.18379
$470$	−585600.	−	151201.i	−0.00564037	−	0.00145634i
$471$		0			0
$472$	−2.91571e7	−	2.76039e7i	−0.277280	−	0.262509i
$473$	2.06832e7			0.195449
$474$		0			0
$475$			1.16889e8i			1.09067i
$476$	−4.57536e7	+	8.26947e7i	−0.424233	+	0.766755i
$477$		0			0
$478$	−8.71670e7	−	2.25064e7i	−0.798121	−	0.206074i
$479$			7.76230e7i			0.706291i	0.935568	+	0.353146i	$0.114888\pi$
$479$			7.76230e7i			0.706291i	−0.935568	+	0.353146i	$0.885112\pi$
$480$		0			0
$481$	2.92320e6			0.0262678
$482$	−1.01021e7	+	3.91252e7i	−0.0902132	+	0.349394i
$483$		0			0
$484$	−4.75441e7	−	2.63053e7i	−0.419334	−	0.232011i
$485$	1.45709e7			0.127720
$486$		0			0
$487$			1.08071e7i			0.0935670i	0.998905	+	0.0467835i	$0.0148971\pi$
$487$			1.08071e7i			0.0935670i	−0.998905	+	0.0467835i	$0.985103\pi$
$488$	−3.84314e6	+	4.05938e6i	−0.0330694	+	0.0349302i
$489$		0			0
$490$	432980.	−	1.67692e6i	0.00368027	−	0.0142536i
$491$		−	1.85067e8i		−	1.56345i	−0.623624	−	0.781724i	$-0.714340\pi$
$491$		−	1.85067e8i		−	1.56345i	0.623624	−	0.781724i	$-0.285660\pi$
$492$		0			0
$493$	−1.21523e8			−1.01419
$494$	8.54971e7	+	2.20753e7i	0.709203	+	0.183115i
$495$		0			0
$496$	1.45367e8	−	9.11530e7i	1.19130	−	0.747010i
$497$	1.64909e8			1.34331
$498$		0			0
$499$			6.83704e7i			0.550258i	0.961407	+	0.275129i	$0.0887206\pi$
$499$			6.83704e7i			0.550258i	−0.961407	+	0.275129i	$0.911279\pi$
$500$	−1.74440e7	−	9.65147e6i	−0.139552	−	0.0772118i
$501$		0			0
$502$	−3.65292e7	−	9.43180e6i	−0.288755	−	0.0745561i
$503$			1.31562e7i			0.103377i	0.998663	+	0.0516887i	$0.0164604\pi$
$503$			1.31562e7i			0.103377i	−0.998663	+	0.0516887i	$0.983540\pi$
$504$		0			0
$505$	−6.39158e6			−0.0496288
$506$	2.01178e7	−	7.79157e7i	0.155284	−	0.601414i
$507$		0			0
$508$	−5.18861e7	+	9.37785e7i	−0.395785	+	0.715339i
$509$	−1.34186e8			−1.01755			−0.508775	−	0.860900i	$-0.669901\pi$
$509$	−1.34186e8			−1.01755			−0.508775	+	0.860900i	$0.669901\pi$
$510$		0			0
$511$		−	8.94275e7i		−	0.670206i
$512$	−1.02367e8	−	8.68064e7i	−0.762695	−	0.646758i
$513$		0			0
$514$	4.69105e7	−	1.81683e8i	0.345446	−	1.33791i
$515$			1.38913e7i			0.101700i
$516$		0			0
$517$	−7.26144e6			−0.0525474
$518$	4.78560e6	+	1.23564e6i	0.0344308	+	0.00888999i
$519$		0			0
$520$	−5.16032e6	+	5.45068e6i	−0.0367000	+	0.0387651i
$521$	1.98565e8			1.40407			0.702036	−	0.712142i	$-0.252275\pi$
$521$	1.98565e8			1.40407			0.702036	+	0.712142i	$0.252275\pi$
$522$		0			0
$523$		−	2.15512e8i		−	1.50649i	−0.657740	−	0.753245i	$-0.728487\pi$
$523$		−	2.15512e8i		−	1.50649i	0.657740	−	0.753245i	$-0.271513\pi$
$524$	8.81347e7	−	1.59294e8i	0.612566	−	1.10715i
$525$		0			0
$526$	1.68082e8	+	4.33986e7i	1.15495	+	0.298207i
$527$		−	1.99649e8i		−	1.36406i
$528$		0			0
$529$	3.83616e7			0.259137
$530$	3.85708e6	−	1.49384e7i	0.0259078	−	0.100341i
$531$		0			0
$532$	1.30637e8	+	7.22792e7i	0.867622	+	0.480041i
$533$	−4.30447e7			−0.284275
$534$		0			0
$535$			1.14935e7i			0.0750567i
$536$	1.46546e8	+	1.38739e8i	0.951655	+	0.900959i
$537$		0			0
$538$	−5.88556e7	+	2.27947e8i	−0.377956	+	1.46382i
$539$		−	2.07939e7i		−	0.132791i
$540$		0			0
$541$	1.44188e7			0.0910623			0.0455311	−	0.998963i	$-0.485502\pi$
$541$	1.44188e7			0.0910623			0.0455311	+	0.998963i	$0.485502\pi$
$542$	−6.59549e7	−	1.70295e7i	−0.414237	−	0.106956i
$543$		0			0
$544$	−1.48852e8	+	4.72541e7i	−0.924607	+	0.293524i
$545$	−1.53574e7			−0.0948697
$546$		0			0
$547$		−	4.24129e7i		−	0.259141i	−0.991570	−	0.129571i	$-0.958640\pi$
$547$		−	4.24129e7i		−	0.259141i	0.991570	−	0.129571i	$-0.0413599\pi$
$548$	2.13362e8	+	1.18050e8i	1.29651	+	0.717336i
$549$		0			0
$550$	−1.15506e8	−	2.98235e7i	−0.694251	−	0.179255i
$551$			1.91976e8i			1.14761i
$552$		0			0
$553$	9.62688e7			0.569259
$554$	−5.52453e7	+	2.13964e8i	−0.324912	+	1.25838i
$555$		0			0
$556$	−4.30176e6	+	7.77497e6i	−0.0250277	+	0.0452350i
$557$	−8.90848e7			−0.515511			−0.257756	−	0.966210i	$-0.582983\pi$
$557$	−8.90848e7			−0.515511			−0.257756	+	0.966210i	$0.582983\pi$
$558$		0			0
$559$			3.15685e7i			0.180725i
$560$	−1.07520e7	+	6.74209e6i	−0.0612245	+	0.0383911i
$561$		0			0
$562$	1.72802e7	−	6.69258e7i	0.0973507	−	0.377037i
$563$		−	2.41576e8i		−	1.35372i	−0.736112	−	0.676860i	$-0.763340\pi$
$563$		−	2.41576e8i		−	1.35372i	0.736112	−	0.676860i	$-0.236660\pi$
$564$		0			0
$565$	−6.01694e6			−0.0333603
$566$	−9.86446e7	−	2.54699e7i	−0.544031	−	0.140468i
$567$		0			0
$568$	1.97891e8	+	1.87349e8i	1.07989	+	1.02236i
$569$	2.56141e7			0.139041			0.0695203	−	0.997581i	$-0.477853\pi$
$569$	2.56141e7			0.139041			0.0695203	+	0.997581i	$0.477853\pi$
$570$		0			0
$571$		−	1.10781e8i		−	0.595057i	−0.954713	−	0.297528i	$-0.903838\pi$
$571$		−	1.10781e8i		−	0.595057i	0.954713	−	0.297528i	$-0.0961623\pi$
$572$	−4.36282e7	+	7.88532e7i	−0.233120	+	0.421339i
$573$		0			0
$574$	−7.04688e7	−	1.81950e7i	−0.372616	−	0.0962090i
$575$			1.62586e8i			0.855225i
$576$		0			0
$577$	1.07272e8			0.558415			0.279208	−	0.960231i	$-0.409928\pi$
$577$	1.07272e8			0.558415			0.279208	+	0.960231i	$0.409928\pi$
$578$	2.84563e6	−	1.10211e7i	0.0147365	−	0.0570742i
$579$		0			0
$580$	−1.42789e7	−	7.90027e6i	−0.0731830	−	0.0404909i
$581$	−6.32544e7			−0.322524
$582$		0			0
$583$		−	1.85236e8i		−	0.934803i
$584$	1.01596e8	−	1.07313e8i	0.510082	−	0.538783i
$585$		0			0
$586$	−8.90830e7	+	3.45017e8i	−0.442692	+	1.71454i
$587$			2.16397e7i			0.106988i	0.998568	+	0.0534941i	$0.0170358\pi$
$587$			2.16397e7i			0.106988i	−0.998568	+	0.0534941i	$0.982964\pi$
$588$		0			0
$589$	−3.15395e8			−1.54351
$590$	−6.07440e6	−	1.56840e6i	−0.0295765	−	0.00763663i
$591$		0			0
$592$	4.33894e6	+	6.91956e6i	0.0209131	+	0.0333514i
$593$	−2.00341e8			−0.960738			−0.480369	−	0.877066i	$-0.659497\pi$
$593$	−2.00341e8			−0.960738			−0.480369	+	0.877066i	$0.659497\pi$
$594$		0			0
$595$			1.47669e7i			0.0701033i
$596$	−1.83359e8	−	1.01449e8i	−0.866089	−	0.479193i
$597$		0			0
$598$	1.18922e8	+	3.07055e7i	0.556107	+	0.143586i
$599$		−	1.37592e8i		−	0.640197i	−0.947384	−	0.320098i	$-0.896284\pi$
$599$		−	1.37592e8i		−	0.640197i	0.947384	−	0.320098i	$-0.103716\pi$
$600$		0			0
$601$	−1.90306e8			−0.876655			−0.438327	−	0.898815i	$-0.644429\pi$
$601$	−1.90306e8			−0.876655			−0.438327	+	0.898815i	$0.644429\pi$
$602$	−1.33440e7	+	5.16811e7i	−0.0611641	+	0.236888i
$603$		0			0
$604$	1.73309e8	−	3.13237e8i	0.786520	−	1.42155i
$605$	−8.49001e6			−0.0383391
$606$		0			0
$607$		−	1.25461e8i		−	0.560974i	−0.959858	−	0.280487i	$-0.909504\pi$
$607$		−	1.25461e8i		−	0.560974i	0.959858	−	0.280487i	$-0.0904960\pi$
$608$	7.46496e7	+	2.35148e8i	0.332137	+	1.04624i
$609$		0			0
$610$	−218360.	+	845705.i	−0.000962019	+	0.00372588i
$611$		−	1.10831e7i		−	0.0485888i
$612$		0			0
$613$	−9.91111e7			−0.430270			−0.215135	−	0.976584i	$-0.569019\pi$
$613$	−9.91111e7			−0.430270			−0.215135	+	0.976584i	$0.569019\pi$
$614$	−3.78817e8	−	9.78102e7i	−1.63653	−	0.422551i
$615$		0			0
$616$	−1.04755e8	+	1.10650e8i	−0.448160	+	0.473378i
$617$	−3.70827e7			−0.157876			−0.0789379	−	0.996880i	$-0.525153\pi$
$617$	−3.70827e7			−0.157876			−0.0789379	+	0.996880i	$0.525153\pi$
$618$		0			0
$619$			4.05274e8i			1.70874i	0.519662	+	0.854372i	$0.326058\pi$
$619$			4.05274e8i			1.70874i	−0.519662	+	0.854372i	$0.673942\pi$
$620$	1.29792e7	−	2.34585e7i	0.0544594	−	0.0984295i
$621$		0			0
$622$	−3.87469e8	−	1.00044e8i	−1.61015	−	0.415738i
$623$			9.62786e7i			0.398168i
$624$		0			0
$625$	2.39463e8			0.980841
$626$	−2.25437e6	+	8.73115e6i	−0.00918973	+	0.0355917i
$627$		0			0
$628$	−4.57405e7	−	2.53074e7i	−0.184681	−	0.102181i
$629$	9.50340e6			0.0381880
$630$		0			0
$631$			2.52648e7i			0.100561i	0.998735	+	0.0502803i	$0.0160115\pi$
$631$			2.52648e7i			0.100561i	−0.998735	+	0.0502803i	$0.983989\pi$
$632$	1.15523e8	+	1.09369e8i	0.457631	+	0.433253i
$633$		0			0
$634$	6.89763e7	−	2.67144e8i	0.270665	−	1.04828i
$635$			1.67462e7i			0.0654025i
$636$		0			0
$637$	3.17374e7			0.122787
$638$	−1.89705e8	−	4.89817e7i	−0.730495	−	0.188613i
$639$		0			0
$640$	−2.05619e7	−	4.12457e6i	−0.0784375	−	0.0157340i
$641$	4.21293e8			1.59959			0.799797	−	0.600270i	$-0.204940\pi$
$641$	4.21293e8			1.59959			0.799797	+	0.600270i	$0.204940\pi$
$642$		0			0
$643$		−	8.17706e7i		−	0.307584i	−0.988103	−	0.153792i	$-0.950851\pi$
$643$		−	8.17706e7i		−	0.307584i	0.988103	−	0.153792i	$-0.0491486\pi$
$644$	1.81709e8	+	1.00536e8i	0.680328	+	0.376414i
$645$		0			0
$646$	2.77953e8	+	7.17672e7i	1.03104	+	0.266212i
$647$		−	1.84284e8i		−	0.680416i	−0.940350	−	0.340208i	$-0.889503\pi$
$647$		−	1.84284e8i		−	0.680416i	0.940350	−	0.340208i	$-0.110497\pi$
$648$		0			0
$649$	−7.53226e7			−0.275544
$650$	4.55193e7	−	1.76295e8i	0.165751	−	0.641950i
$651$		0			0
$652$	5.71939e7	−	1.03372e8i	0.206351	−	0.372958i
$653$	−6.43842e7			−0.231228			−0.115614	−	0.993294i	$-0.536883\pi$
$653$	−6.43842e7			−0.231228			−0.115614	+	0.993294i	$0.536883\pi$
$654$		0			0
$655$		−	2.84454e7i		−	0.101225i
$656$	−6.38917e7	−	1.01892e8i	−0.226325	−	0.360934i
$657$		0			0
$658$	4.68480e6	−	1.81442e7i	0.0164442	−	0.0636882i
$659$			5.38099e8i			1.88021i	0.340889	+	0.940103i	$0.389272\pi$
$659$			5.38099e8i			1.88021i	−0.340889	+	0.940103i	$0.610728\pi$
$660$		0			0
$661$	2.83897e8			0.983008			0.491504	−	0.870875i	$-0.336447\pi$
$661$	2.83897e8			0.983008			0.491504	+	0.870875i	$0.336447\pi$
$662$	3.11927e8	+	8.05393e7i	1.07518	+	0.277609i
$663$		0			0
$664$	−7.59053e7	−	7.18617e7i	−0.259279	−	0.245467i
$665$	2.33280e7			0.0793255
$666$		0			0
$667$			2.67029e8i			0.899872i
$668$	2.46791e8	−	4.46048e8i	0.827942	−	1.49642i
$669$		0			0
$670$	3.05304e7	+	7.88292e6i	0.101510	+	0.0262097i
$671$			1.04867e7i			0.0347115i
$672$		0			0
$673$	2.77693e8			0.911002			0.455501	−	0.890235i	$-0.349460\pi$
$673$	2.77693e8			0.911002			0.455501	+	0.890235i	$0.349460\pi$
$674$	6.85062e7	−	2.65323e8i	0.223743	−	0.866554i
$675$		0			0
$676$	1.49949e8	+	8.29640e7i	0.485403	+	0.268565i
$677$	9.23026e7			0.297473			0.148737	−	0.988877i	$-0.452479\pi$
$677$	9.23026e7			0.297473			0.148737	+	0.988877i	$0.452479\pi$
$678$		0			0
$679$			4.51462e8i			1.44215i
$680$	−1.67763e7	+	1.77203e7i	−0.0533544	+	0.0563565i
$681$		0			0
$682$	8.04710e7	−	3.11663e8i	0.253680	−	0.982499i
$683$		−	2.70862e8i		−	0.850132i	−0.905162	−	0.425066i	$-0.860251\pi$
$683$		−	2.70862e8i		−	0.850132i	0.905162	−	0.425066i	$-0.139749\pi$
$684$		0			0
$685$	3.81003e7			0.118538
$686$	3.34315e8	+	8.63198e7i	1.03558	+	0.267386i
$687$		0			0
$688$	−7.47264e7	+	4.68575e7i	−0.229461	+	0.143884i
$689$	2.82724e8			0.864380
$690$		0			0
$691$			1.92568e7i			0.0583645i	0.999574	+	0.0291823i	$0.00929032\pi$
$691$			1.92568e7i			0.0583645i	−0.999574	+	0.0291823i	$0.990710\pi$
$692$	−2.87086e8	−	1.58840e8i	−0.866350	−	0.479337i
$693$		0			0
$694$	−4.22539e8	−	1.09099e8i	−1.26412	−	0.326395i
$695$			1.38839e6i			0.00413577i
$696$		0			0
$697$	−1.39939e8			−0.413277
$698$	−9.40017e7	+	3.64067e8i	−0.276420	+	1.07057i
$699$		0			0
$700$	1.49040e8	−	2.69374e8i	0.434519	−	0.785346i
$701$	−3.52234e8			−1.02253			−0.511266	−	0.859423i	$-0.670823\pi$
$701$	−3.52234e8			−1.02253			−0.511266	+	0.859423i	$0.670823\pi$
$702$		0			0
$703$		−	1.50130e7i		−	0.0432117i
$704$	−2.51412e8	+	1.37697e7i	−0.720558	+	0.0394646i
$705$		0			0
$706$	−2.54463e7	+	9.85530e7i	−0.0723119	+	0.280063i
$707$		−	1.98036e8i		−	0.560384i
$708$		0			0
$709$	4.62733e8			1.29835			0.649175	−	0.760639i	$-0.275114\pi$
$709$	4.62733e8			1.29835			0.649175	+	0.760639i	$0.275114\pi$
$710$	4.12272e7	+	1.06448e7i	0.115188	+	0.0297415i
$711$		0			0
$712$	−1.09380e8	+	1.15534e8i	−0.303038	+	0.320089i
$713$	−4.38697e8			−1.21031
$714$		0			0
$715$			1.40809e7i			0.0385224i
$716$	−7.23197e7	+	1.30710e8i	−0.197023	+	0.356098i
$717$		0			0
$718$	1.56587e8	+	4.04306e7i	0.423041	+	0.109229i
$719$			4.60385e8i			1.23861i	0.785150	+	0.619305i	$0.212586\pi$
$719$			4.60385e8i			1.23861i	−0.785150	+	0.619305i	$0.787414\pi$
$720$		0			0
$721$	−4.30406e8			−1.14835
$722$	1.92823e7	−	7.46801e7i	0.0512327	−	0.198424i
$723$		0			0
$724$	−5.42727e8	−	3.00282e8i	−1.43010	−	0.791250i
$725$	3.95856e8			1.03878
$726$		0			0
$727$		−	4.82173e8i		−	1.25487i	−0.778668	−	0.627437i	$-0.784104\pi$
$727$		−	4.82173e8i		−	1.25487i	0.778668	−	0.627437i	$-0.215896\pi$
$728$	−1.68883e8	−	1.59887e8i	−0.437716	−	0.414398i
$729$		0			0
$730$	5.77252e6	−	2.23569e7i	0.0148387	−	0.0574702i
$731$			1.02630e8i			0.262738i
$732$		0			0
$733$	−5.08270e8			−1.29057			−0.645287	−	0.763941i	$-0.723262\pi$
$733$	−5.08270e8			−1.29057			−0.645287	+	0.763941i	$0.723262\pi$
$734$	−8.60246e7	−	2.22115e7i	−0.217538	−	0.0561680i
$735$		0			0
$736$	1.03834e8	+	3.27079e8i	0.260438	+	0.820387i
$737$	3.78577e8			0.945696
$738$		0			0
$739$		−	1.27767e8i		−	0.316582i	−0.987392	−	0.158291i	$-0.949402\pi$
$739$		−	1.27767e8i		−	0.316582i	0.987392	−	0.158291i	$-0.0505984\pi$
$740$	1.11664e6	+	617818.i	0.00275561	+	0.00152463i
$741$		0			0
$742$	4.62850e8	+	1.19507e8i	1.13300	+	0.292538i
$743$		−	2.83312e8i		−	0.690716i	−0.938471	−	0.345358i	$-0.887758\pi$
$743$		−	2.83312e8i		−	0.690716i	0.938471	−	0.345358i	$-0.112242\pi$
$744$		0			0
$745$	−3.27426e7			−0.0791853
$746$	−1.37429e6	+	5.32261e6i	−0.00331026	+	0.0128206i
$747$		0			0
$748$	−1.41836e8	+	2.56354e8i	−0.338908	+	0.612540i
$749$	−3.56112e8			−0.847503
$750$		0			0
$751$			2.15309e8i			0.508325i	0.967161	+	0.254163i	$0.0817999\pi$
$751$			2.15309e8i			0.508325i	−0.967161	+	0.254163i	$0.918200\pi$
$752$	2.62349e7	−	1.64507e7i	0.0616915	−	0.0386839i
$753$		0			0
$754$	7.47601e7	−	2.89545e8i	0.174404	−	0.675463i
$755$		−	5.59352e7i		−	0.129970i
$756$		0			0
$757$	−3.03985e8			−0.700753			−0.350377	−	0.936609i	$-0.613946\pi$
$757$	−3.03985e8			−0.700753			−0.350377	+	0.936609i	$0.613946\pi$
$758$	1.15026e8	+	2.96997e7i	0.264113	+	0.0681938i
$759$		0			0
$760$	2.79936e7	+	2.65024e7i	0.0637702	+	0.0603731i
$761$	−8.63611e8			−1.95959			−0.979793	−	0.200014i	$-0.935901\pi$
$761$	−8.63611e8			−1.95959			−0.979793	+	0.200014i	$0.935901\pi$
$762$		0			0
$763$		−	4.75831e8i		−	1.07122i
$764$	−3.53725e8	+	6.39321e8i	−0.793206	+	1.43364i
$765$		0			0
$766$	2.60175e8	+	6.71770e7i	0.578868	+	0.149463i
$767$		−	1.14964e8i		−	0.254786i
$768$		0			0
$769$	−1.97898e7			−0.0435174			−0.0217587	−	0.999763i	$-0.506927\pi$
$769$	−1.97898e7			−0.0435174			−0.0217587	+	0.999763i	$0.506927\pi$
$770$	−5.95200e6	+	2.30520e7i	−0.0130374	+	0.0504936i
$771$		0			0
$772$	1.36099e8	+	7.53011e7i	0.295803	+	0.163663i
$773$	5.64048e8			1.22117			0.610587	−	0.791949i	$-0.290933\pi$
$773$	5.64048e8			1.22117			0.610587	+	0.791949i	$0.290933\pi$
$774$		0			0
$775$			6.50345e8i			1.39714i
$776$	−5.12894e8	+	5.41754e8i	−1.09760	+	1.15936i
$777$		0			0
$778$	−2.02244e8	+	7.83286e8i	−0.429473	+	1.66334i
$779$			2.21069e8i			0.467644i
$780$		0			0
$781$	5.11217e8			1.07313
$782$	3.86618e8	+	9.98243e7i	0.808466	+	0.208745i
$783$		0			0
$784$	4.71082e7	+	7.51262e7i	0.0977572	+	0.155899i
$785$	−8.16794e6			−0.0168851
$786$		0			0
$787$		−	4.04198e8i		−	0.829220i	−0.909999	−	0.414610i	$-0.863918\pi$
$787$		−	4.04198e8i		−	0.829220i	0.909999	−	0.414610i	$-0.136082\pi$
$788$	−1.24916e8	−	6.91140e7i	−0.255294	−	0.141250i
$789$		0			0
$790$	2.40672e7	+	6.21412e6i	0.0488140	+	0.0126037i
$791$		−	1.86428e8i		−	0.376688i
$792$		0			0
$793$	−1.60058e7			−0.0320965
$794$	6.96531e7	−	2.69765e8i	0.139149	−	0.538921i
$795$		0			0
$796$	−1.51690e8	+	2.74163e8i	−0.300758	+	0.543587i
$797$	2.15998e7			0.0426654			0.0213327	−	0.999772i	$-0.493209\pi$
$797$	2.15998e7			0.0426654			0.0213327	+	0.999772i	$0.493209\pi$
$798$		0			0
$799$		−	3.60313e7i		−	0.0706381i
$800$	4.84877e8	−	1.53928e8i	0.947025	−	0.300640i
$801$		0			0
$802$	−1.37680e8	+	5.33231e8i	−0.266899	+	1.03369i
$803$		−	2.77225e8i		−	0.535410i
$804$		0			0
$805$	3.24480e7			0.0622014
$806$	4.75688e8	+	1.22822e8i	0.908483	+	0.234569i
$807$		0			0
$808$	2.24984e8	−	2.37643e8i	0.426498	−	0.450496i
$809$	−6.51310e8			−1.23011			−0.615053	−	0.788486i	$-0.710865\pi$
$809$	−6.51310e8			−1.23011			−0.615053	+	0.788486i	$0.710865\pi$
$810$		0			0
$811$		−	5.52891e8i		−	1.03652i	−0.855223	−	0.518259i	$-0.826580\pi$
$811$		−	5.52891e8i		−	1.03652i	0.855223	−	0.518259i	$-0.173420\pi$
$812$	2.44781e8	−	4.42415e8i	0.457203	−	0.826346i
$813$		0			0
$814$	1.48354e7	+	3.83047e6i	0.0275058	+	0.00710198i
$815$		−	1.84593e7i		−	0.0340990i
$816$		0			0
$817$	1.62130e8			0.297301
$818$	−9.19917e7	+	3.56282e8i	−0.168069	+	0.650930i
$819$		0			0
$820$	−1.64427e7	−	9.09748e6i	−0.0298217	−	0.0164998i
$821$	8.94865e8			1.61707			0.808534	−	0.588450i	$-0.200262\pi$
$821$	8.94865e8			1.61707			0.808534	+	0.588450i	$0.200262\pi$
$822$		0			0
$823$		−	8.44482e8i		−	1.51492i	−0.652879	−	0.757462i	$-0.726439\pi$
$823$		−	8.44482e8i		−	1.51492i	0.652879	−	0.757462i	$-0.273561\pi$
$824$	−5.16488e8	−	4.88974e8i	−0.923163	−	0.873985i
$825$		0			0
$826$	4.85952e7	−	1.88208e8i	0.0862290	−	0.333963i
$827$		−	3.11099e7i		−	0.0550024i	−0.999622	−	0.0275012i	$-0.991245\pi$
$827$		−	3.11099e7i		−	0.0550024i	0.999622	−	0.0275012i	$-0.00875501\pi$
$828$		0			0
$829$	−4.05444e7			−0.0711652			−0.0355826	−	0.999367i	$-0.511329\pi$
$829$	−4.05444e7			−0.0711652			−0.0355826	+	0.999367i	$0.511329\pi$
$830$	−1.58136e7	−	4.08305e6i	−0.0276565	−	0.00714087i
$831$		0			0
$832$	−2.10166e7	−	3.83728e8i	−0.0364915	−	0.666275i
$833$	1.03179e8			0.178508
$834$		0			0
$835$		−	7.96515e7i		−	0.136815i
$836$	4.04974e8	+	2.24065e8i	0.693120	+	0.383492i
$837$		0			0
$838$	−2.10034e8	−	5.42306e7i	−0.356910	−	0.0921537i
$839$		−	4.17820e8i		−	0.707463i	−0.935347	−	0.353731i	$-0.884913\pi$
$839$		−	4.17820e8i		−	0.707463i	0.935347	−	0.353731i	$-0.115087\pi$
$840$		0			0
$841$	5.53247e7			0.0930103
$842$	1.88416e8	−	7.29730e8i	0.315632	−	1.22244i
$843$		0			0
$844$	−1.21132e8	+	2.18933e8i	−0.201480	+	0.364153i
$845$	2.67765e7			0.0443797
$846$		0			0
$847$		−	2.63053e8i		−	0.432906i
$848$	4.19650e8	+	6.69241e8i	0.688177	+	1.09748i
$849$		0			0
$850$	1.47984e8	−	5.73141e8i	0.240968	−	0.933264i
$851$		−	2.08823e7i		−	0.0338835i
$852$		0			0
$853$	−4.28994e8			−0.691201			−0.345601	−	0.938382i	$-0.612325\pi$
$853$	−4.28994e8			−0.691201			−0.345601	+	0.938382i	$0.612325\pi$
$854$	−2.62032e7	−	6.76564e6i	−0.0420708	−	0.0108626i
$855$		0			0
$856$	−4.27334e8	−	4.04570e8i	−0.681313	−	0.645019i
$857$	−2.20598e8			−0.350476			−0.175238	−	0.984526i	$-0.556070\pi$
$857$	−2.20598e8			−0.350476			−0.175238	+	0.984526i	$0.556070\pi$
$858$		0			0
$859$			1.14768e9i			1.81068i	0.424689	+	0.905339i	$0.360383\pi$
$859$			1.14768e9i			1.81068i	−0.424689	+	0.905339i	$0.639617\pi$
$860$	−6.67200e6	+	1.20589e7i	−0.0104896	+	0.0189589i
$861$		0			0
$862$	4.02160e8	+	1.03837e8i	0.627881	+	0.162118i
$863$			6.44987e7i			0.100350i	0.998740	+	0.0501752i	$0.0159780\pi$
$863$			6.44987e7i			0.100350i	−0.998740	+	0.0501752i	$0.984022\pi$
$864$		0			0
$865$	−5.12653e7			−0.0792092
$866$	−1.68042e8	+	6.50824e8i	−0.258740	+	1.00210i
$867$		0			0
$868$	7.26835e8	+	4.02146e8i	1.11142	+	0.614928i
$869$	2.98433e8			0.454766
$870$		0			0
$871$			5.77818e8i			0.874453i
$872$	5.40580e8	−	5.70997e8i	0.815287	−	0.861161i
$873$		0			0
$874$	1.57697e8	−	6.10759e8i	0.236205	−	0.914820i
$875$		−	9.65147e7i		−	0.144069i
$876$		0			0
$877$	5.15252e8			0.763873			0.381937	−	0.924189i	$-0.375257\pi$
$877$	5.15252e8			0.763873			0.381937	+	0.924189i	$0.375257\pi$
$878$	−1.14729e9	−	2.96230e8i	−1.69508	−	0.437669i
$879$		0			0
$880$	−3.33312e7	+	2.09005e7i	−0.0489106	+	0.0306696i
$881$	1.18519e8			0.173324			0.0866622	−	0.996238i	$-0.472380\pi$
$881$	1.18519e8			0.173324			0.0866622	+	0.996238i	$0.472380\pi$
$882$		0			0
$883$			1.28669e8i			0.186893i	0.995624	+	0.0934466i	$0.0297884\pi$
$883$			1.28669e8i			0.186893i	−0.995624	+	0.0934466i	$0.970212\pi$
$884$	−3.91270e8	−	2.16483e8i	−0.566395	−	0.313377i
$885$		0			0
$886$	−6.22571e8	−	1.60747e8i	−0.895133	−	0.231122i
$887$			5.09948e8i			0.730727i	0.930865	+	0.365363i	$0.119055\pi$
$887$			5.09948e8i			0.730727i	−0.930865	+	0.365363i	$0.880945\pi$
$888$		0			0
$889$	−5.18861e8			−0.738492
$890$	−6.21476e6	+	2.40697e7i	−0.00881565	+	0.0341429i
$891$		0			0
$892$	−1.03212e8	+	1.86544e8i	−0.145423	+	0.262837i
$893$	−5.69203e7			−0.0799306
$894$		0			0
$895$			2.33411e7i			0.0325576i
$896$	1.27795e8	−	6.37088e8i	0.177660	−	0.885677i
$897$		0			0
$898$	−1.76185e8	+	6.82362e8i	−0.243299	+	0.942293i
$899$			1.06812e9i			1.47007i
$900$		0			0
$901$	9.19142e8			1.25663
$902$	−2.18453e8	−	5.64044e7i	−0.297673	−	0.0768588i
$903$		0			0
$904$	2.11796e8	−	2.23714e8i	0.286690	−	0.302822i
$905$	−9.69156e7			−0.130752
$906$		0			0
$907$			5.43212e8i			0.728027i	0.931394	+	0.364014i	$0.118594\pi$
$907$			5.43212e8i			0.728027i	−0.931394	+	0.364014i	$0.881406\pi$
$908$	−4.18384e8	+	7.56185e8i	−0.558879	+	1.01011i
$909$		0			0
$910$	−3.51840e7	−	9.08447e6i	−0.0466897	−	0.0120552i
$911$		−	5.99585e8i		−	0.793041i	−0.918026	−	0.396520i	$-0.870218\pi$
$911$		−	5.99585e8i		−	0.793041i	0.918026	−	0.396520i	$-0.129782\pi$
$912$		0			0
$913$	−1.96089e8			−0.257656
$914$	7.50846e7	−	2.90801e8i	0.0983359	−	0.380853i
$915$		0			0
$916$	−8.93748e7	−	4.94496e7i	−0.116286	−	0.0643393i
$917$	8.81347e8			1.14298
$918$		0			0
$919$			9.66486e8i			1.24523i	0.782529	+	0.622614i	$0.213929\pi$
$919$			9.66486e8i			1.24523i	−0.782529	+	0.622614i	$0.786071\pi$
$920$	3.89376e7	+	3.68634e7i	0.0500041	+	0.0473404i
$921$		0			0
$922$	2.30520e8	−	8.92800e8i	0.294114	−	1.13910i
$923$			7.80265e8i			0.992286i
$924$		0			0
$925$	−3.09568e7			−0.0391139
$926$	−8.01053e7	−	2.06831e7i	−0.100885	−	0.0260485i
$927$		0			0
$928$	7.96354e8	−	2.52809e8i	0.996465	−	0.316335i
$929$	−7.22626e8			−0.901295			−0.450647	−	0.892702i	$-0.648807\pi$
$929$	−7.22626e8			−0.901295			−0.450647	+	0.892702i	$0.648807\pi$
$930$		0			0
$931$		−	1.62997e8i		−	0.201990i
$932$	4.50454e8	+	2.49229e8i	0.556420	+	0.307858i
$933$		0			0
$934$	−1.27206e9	−	3.28445e8i	−1.56123	−	0.403109i
$935$			4.57774e7i			0.0560037i
$936$		0			0
$937$	−4.12016e8			−0.500836			−0.250418	−	0.968138i	$-0.580568\pi$
$937$	−4.12016e8			−0.500836			−0.250418	+	0.968138i	$0.580568\pi$
$938$	−2.44243e8	+	9.45950e8i	−0.295947	+	1.14620i
$939$		0			0
$940$	2.34240e6	−	4.23364e6i	0.00282018	−	0.00509718i
$941$	−7.87666e8			−0.945308			−0.472654	−	0.881248i	$-0.656704\pi$
$941$	−7.87666e8			−0.945308			−0.472654	+	0.881248i	$0.656704\pi$
$942$		0			0
$943$			3.07495e8i			0.366693i
$944$	2.72133e8	−	1.70642e8i	0.323493	−	0.202848i
$945$		0			0
$946$	−4.13664e7	+	1.60211e8i	−0.0488623	+	0.189243i
$947$		−	5.29504e8i		−	0.623475i	−0.950168	−	0.311738i	$-0.899089\pi$
$947$		−	5.29504e8i		−	0.623475i	0.950168	−	0.311738i	$-0.100911\pi$
$948$		0			0
$949$	4.23126e8			0.495075
$950$	−9.05418e8	−	2.33778e8i	−1.05603	−	0.272667i
$951$		0			0
$952$	−5.49043e8	−	5.19795e8i	−0.636349	−	0.602451i
$953$	−1.18323e9			−1.36706			−0.683532	−	0.729920i	$-0.739557\pi$
$953$	−1.18323e9			−1.36706			−0.683532	+	0.729920i	$0.739557\pi$
$954$		0			0
$955$			1.14164e8i			0.131075i
$956$	3.48668e8	−	6.30180e8i	0.399060	−	0.721259i
$957$		0			0
$958$	−6.01265e8	−	1.55246e8i	−0.683864	−	0.176573i
$959$			1.18050e9i			1.33847i
$960$		0			0
$961$	−8.67284e8			−0.977218
$962$	−5.84641e6	+	2.26430e7i	−0.00656695	+	0.0254337i
$963$		0			0
$964$	−2.82858e8	−	1.56501e8i	−0.315746	−	0.174697i
$965$	2.43033e7			0.0270448
$966$		0			0
$967$		−	4.78688e8i		−	0.529387i	−0.964333	−	0.264693i	$-0.914729\pi$
$967$		−	4.78688e8i		−	0.529387i	0.964333	−	0.264693i	$-0.0852708\pi$
$968$	2.98848e8	−	3.15664e8i	0.329477	−	0.348016i
$969$		0			0
$970$	−2.91417e7	+	1.12865e8i	−0.0319301	+	0.123665i
$971$		−	7.02914e8i		−	0.767793i	−0.923376	−	0.383897i	$-0.874582\pi$
$971$		−	7.02914e8i		−	0.767793i	0.923376	−	0.383897i	$-0.125418\pi$
$972$		0			0
$973$	−4.30176e7			−0.0466990
$974$	−8.37115e7	−	2.16142e7i	−0.0905959	−	0.0233918i
$975$		0			0
$976$	−2.37576e7	−	3.78876e7i	−0.0255536	−	0.0407518i
$977$	9.21323e8			0.987934			0.493967	−	0.869481i	$-0.335546\pi$
$977$	9.21323e8			0.987934			0.493967	+	0.869481i	$0.335546\pi$
$978$		0			0
$979$			2.98464e8i			0.318085i
$980$	1.21234e7	+	6.70770e6i	0.0128809	+	0.00712681i
$981$		0			0
$982$	1.43352e9	+	3.70133e8i	1.51380	+	0.390862i
$983$			2.44410e8i			0.257311i	0.991689	+	0.128655i	$0.0410661\pi$
$983$			2.44410e8i			0.257311i	−0.991689	+	0.128655i	$0.958934\pi$
$984$		0			0
$985$	−2.23065e7			−0.0233411
$986$	2.43047e8	−	9.41317e8i	0.253548	−	0.981985i
$987$		0			0
$988$	−3.41988e8	+	6.18107e8i	−0.354602	+	0.640904i
$989$	2.25514e8			0.233122
$990$		0			0
$991$		−	1.78184e9i		−	1.83083i	−0.402516	−	0.915413i	$-0.631864\pi$
$991$		−	1.78184e9i		−	1.83083i	0.402516	−	0.915413i	$-0.368136\pi$
$992$	4.15334e8	+	1.30831e9i	0.425464	+	1.34022i
$993$		0			0
$994$	−3.29818e8	+	1.27738e9i	−0.335826	+	1.30065i
$995$			4.89576e7i			0.0496994i
$996$		0			0
$997$	1.36790e9			1.38029			0.690143	−	0.723673i	$-0.257548\pi$
$997$	1.36790e9			1.38029			0.690143	+	0.723673i	$0.257548\pi$
$998$	−5.29595e8	−	1.36741e8i	−0.532785	−	0.137565i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.7.d.c.19.2		2
3.2	odd	2		4.7.b.a.3.1	✓	2
4.3	odd	2	inner	36.7.d.c.19.1		2
8.3	odd	2		576.7.g.h.127.2		2
8.5	even	2		576.7.g.h.127.1		2
12.11	even	2		4.7.b.a.3.2	yes	2
15.2	even	4		100.7.d.a.99.4		4
15.8	even	4		100.7.d.a.99.1		4
15.14	odd	2		100.7.b.c.51.2		2
24.5	odd	2		64.7.c.c.63.1		2
24.11	even	2		64.7.c.c.63.2		2
48.5	odd	4		256.7.d.f.127.4		4
48.11	even	4		256.7.d.f.127.2		4
48.29	odd	4		256.7.d.f.127.1		4
48.35	even	4		256.7.d.f.127.3		4
60.23	odd	4		100.7.d.a.99.3		4
60.47	odd	4		100.7.d.a.99.2		4
60.59	even	2		100.7.b.c.51.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.7.b.a.3.1	✓	2	3.2	odd	2
4.7.b.a.3.2	yes	2	12.11	even	2
36.7.d.c.19.1		2	4.3	odd	2	inner
36.7.d.c.19.2		2	1.1	even	1	trivial
64.7.c.c.63.1		2	24.5	odd	2
64.7.c.c.63.2		2	24.11	even	2
100.7.b.c.51.1		2	60.59	even	2
100.7.b.c.51.2		2	15.14	odd	2
100.7.d.a.99.1		4	15.8	even	4
100.7.d.a.99.2		4	60.47	odd	4
100.7.d.a.99.3		4	60.23	odd	4
100.7.d.a.99.4		4	15.2	even	4
256.7.d.f.127.1		4	48.29	odd	4
256.7.d.f.127.2		4	48.11	even	4
256.7.d.f.127.3		4	48.35	even	4
256.7.d.f.127.4		4	48.5	odd	4
576.7.g.h.127.1		2	8.5	even	2
576.7.g.h.127.2		2	8.3	odd	2

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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	36.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 7.74597i) q^{2} +(-56.0000 - 30.9839i) q^{4} -10.0000 q^{5} -309.839i q^{7} +(352.000 - 371.806i) q^{8} +O(q^{10})\)	\(q+(-2.00000 + 7.74597i) q^{2} +(-56.0000 - 30.9839i) q^{4} -10.0000 q^{5} -309.839i q^{7} +(352.000 - 371.806i) q^{8} +(20.0000 - 77.4597i) q^{10} -960.500i q^{11} +1466.00 q^{13} +(2400.00 + 619.677i) q^{14} +(2176.00 + 3470.19i) q^{16} +4766.00 q^{17} -7529.08i q^{19} +(560.000 + 309.839i) q^{20} +(7440.00 + 1921.00i) q^{22} -10472.5i q^{23} -15525.0 q^{25} +(-2932.00 + 11355.6i) q^{26} +(-9600.00 + 17351.0i) q^{28} -25498.0 q^{29} -41890.2i q^{31} +(-31232.0 + 9914.84i) q^{32} +(-9532.00 + 36917.3i) q^{34} +3098.39i q^{35} +1994.00 q^{37} +(58320.0 + 15058.2i) q^{38} +(-3520.00 + 3718.06i) q^{40} -29362.0 q^{41} +21533.8i q^{43} +(-29760.0 + 53788.0i) q^{44} +(81120.0 + 20945.1i) q^{46} -7560.06i q^{47} +21649.0 q^{49} +(31050.0 - 120256. i) q^{50} +(-82096.0 - 45422.3i) q^{52} +192854. q^{53} +9605.00i q^{55} +(-115200. - 109063. i) q^{56} +(50996.0 - 197507. i) q^{58} -78420.2i q^{59} -10918.0 q^{61} +(324480. + 83780.4i) q^{62} +(-14336.0 - 261752. i) q^{64} -14660.0 q^{65} +394146. i q^{67} +(-266896. - 147669. i) q^{68} +(-24000.0 - 6196.77i) q^{70} +532241. i q^{71} +288626. q^{73} +(-3988.00 + 15445.5i) q^{74} +(-233280. + 421628. i) q^{76} -297600. q^{77} +310706. i q^{79} +(-21760.0 - 34701.9i) q^{80} +(58724.0 - 227437. i) q^{82} -204153. i q^{83} -47660.0 q^{85} +(-166800. - 43067.6i) q^{86} +(-357120. - 338096. i) q^{88} -310738. q^{89} -454223. i q^{91} +(-324480. + 586463. i) q^{92} +(58560.0 + 15120.1i) q^{94} +75290.8i q^{95} -1.45709e6 q^{97} +(-43298.0 + 167692. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} - 112 q^{4} - 20 q^{5} + 704 q^{8}+O(q^{10}) \) 2 * q - 4 * q^2 - 112 * q^4 - 20 * q^5 + 704 * q^8	\( 2 q - 4 q^{2} - 112 q^{4} - 20 q^{5} + 704 q^{8} + 40 q^{10} + 2932 q^{13} + 4800 q^{14} + 4352 q^{16} + 9532 q^{17} + 1120 q^{20} + 14880 q^{22} - 31050 q^{25} - 5864 q^{26} - 19200 q^{28} - 50996 q^{29} - 62464 q^{32} - 19064 q^{34} + 3988 q^{37} + 116640 q^{38} - 7040 q^{40} - 58724 q^{41} - 59520 q^{44} + 162240 q^{46} + 43298 q^{49} + 62100 q^{50} - 164192 q^{52} + 385708 q^{53} - 230400 q^{56} + 101992 q^{58} - 21836 q^{61} + 648960 q^{62} - 28672 q^{64} - 29320 q^{65} - 533792 q^{68} - 48000 q^{70} + 577252 q^{73} - 7976 q^{74} - 466560 q^{76} - 595200 q^{77} - 43520 q^{80} + 117448 q^{82} - 95320 q^{85} - 333600 q^{86} - 714240 q^{88} - 621476 q^{89} - 648960 q^{92} + 117120 q^{94} - 2914172 q^{97} - 86596 q^{98}+O(q^{100}) \) 2 * q - 4 * q^2 - 112 * q^4 - 20 * q^5 + 704 * q^8 + 40 * q^10 + 2932 * q^13 + 4800 * q^14 + 4352 * q^16 + 9532 * q^17 + 1120 * q^20 + 14880 * q^22 - 31050 * q^25 - 5864 * q^26 - 19200 * q^28 - 50996 * q^29 - 62464 * q^32 - 19064 * q^34 + 3988 * q^37 + 116640 * q^38 - 7040 * q^40 - 58724 * q^41 - 59520 * q^44 + 162240 * q^46 + 43298 * q^49 + 62100 * q^50 - 164192 * q^52 + 385708 * q^53 - 230400 * q^56 + 101992 * q^58 - 21836 * q^61 + 648960 * q^62 - 28672 * q^64 - 29320 * q^65 - 533792 * q^68 - 48000 * q^70 + 577252 * q^73 - 7976 * q^74 - 466560 * q^76 - 595200 * q^77 - 43520 * q^80 + 117448 * q^82 - 95320 * q^85 - 333600 * q^86 - 714240 * q^88 - 621476 * q^89 - 648960 * q^92 + 117120 * q^94 - 2914172 * q^97 - 86596 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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