LMFDB - Embedded newform 72.7.b.b.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,7,Mod(19,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("72.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	72.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:	$16.5638940206$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.3803625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 6x^{2} - 16x + 256 $ x^4 - x^3 + 6x^2 - 16x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 8)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.3
Root			$-2.31174 - 3.26433i$ of defining polynomial
Character	$\chi$	$=$	72.19
Dual form			72.7.b.b.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.62348 - 6.52867i) q^{2} +(-21.2470 - 60.3702i) q^{4} -199.084i q^{5} -19.6656i q^{7} +(-492.372 - 140.406i) q^{8} +O(q^{10})$	\(q+(4.62348 - 6.52867i) q^{2} +(-21.2470 - 60.3702i) q^{4} -199.084i q^{5} -19.6656i q^{7} +(-492.372 - 140.406i) q^{8} +(-1299.76 - 920.462i) q^{10} +924.152 q^{11} +1550.92i q^{13} +(-128.390 - 90.9235i) q^{14} +(-3193.13 + 2565.37i) q^{16} -5140.78 q^{17} -1696.10 q^{19} +(-12018.8 + 4229.94i) q^{20} +(4272.80 - 6033.48i) q^{22} -19210.4i q^{23} -24009.6 q^{25} +(10125.4 + 7170.62i) q^{26} +(-1187.22 + 417.835i) q^{28} +16588.1i q^{29} +7550.64i q^{31} +(1985.05 + 32707.8i) q^{32} +(-23768.3 + 33562.4i) q^{34} -3915.12 q^{35} -28960.5i q^{37} +(-7841.89 + 11073.3i) q^{38} +(-27952.7 + 98023.6i) q^{40} +52111.3 q^{41} +5896.43 q^{43} +(-19635.4 - 55791.3i) q^{44} +(-125419. - 88819.0i) q^{46} -64453.4i q^{47} +117262. q^{49} +(-111008. + 156751. i) q^{50} +(93629.2 - 32952.2i) q^{52} -197386. i q^{53} -183984. i q^{55} +(-2761.17 + 9682.80i) q^{56} +(108298. + 76694.7i) q^{58} -142210. q^{59} -96476.4i q^{61} +(49295.6 + 34910.2i) q^{62} +(222716. + 138264. i) q^{64} +308763. q^{65} -75260.9 q^{67} +(109226. + 310350. i) q^{68} +(-18101.5 + 25560.5i) q^{70} -556121. i q^{71} +285914. q^{73} +(-189073. - 133898. i) q^{74} +(36037.0 + 102394. i) q^{76} -18174.0i q^{77} -342014. i q^{79} +(510725. + 635703. i) q^{80} +(240935. - 340217. i) q^{82} +929558. q^{83} +1.02345e6i q^{85} +(27262.0 - 38495.9i) q^{86} +(-455027. - 129757. i) q^{88} -434757. q^{89} +30499.7 q^{91} +(-1.15974e6 + 408163. i) q^{92} +(-420795. - 297999. i) q^{94} +337668. i q^{95} +643314. q^{97} +(542159. - 765566. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 44 q^{4} - 248 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 44 * q^4 - 248 * q^8	$ 4 q - 2 q^{2} - 44 q^{4} - 248 q^{8} - 1920 q^{10} - 976 q^{11} - 5760 q^{14} - 14576 q^{16} - 4168 q^{17} - 1456 q^{19} - 31680 q^{20} + 24428 q^{22} - 23900 q^{25} + 59520 q^{26} + 59520 q^{28} + 48928 q^{32} - 81916 q^{34} + 49920 q^{35} - 26572 q^{38} - 13440 q^{40} + 117944 q^{41} + 197456 q^{43} - 37144 q^{44} - 213120 q^{46} + 2116 q^{49} - 357650 q^{50} - 254400 q^{52} - 349440 q^{56} + 516480 q^{58} - 542032 q^{59} + 407040 q^{62} + 463936 q^{64} + 205440 q^{65} - 790192 q^{67} + 213848 q^{68} - 360960 q^{70} + 443912 q^{73} + 32640 q^{74} + 70616 q^{76} + 1032960 q^{80} + 404708 q^{82} + 3465008 q^{83} - 989548 q^{86} - 1950448 q^{88} - 761224 q^{89} + 3398400 q^{91} - 2743680 q^{92} + 971520 q^{94} - 926776 q^{97} + 2391262 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 44 * q^4 - 248 * q^8 - 1920 * q^10 - 976 * q^11 - 5760 * q^14 - 14576 * q^16 - 4168 * q^17 - 1456 * q^19 - 31680 * q^20 + 24428 * q^22 - 23900 * q^25 + 59520 * q^26 + 59520 * q^28 + 48928 * q^32 - 81916 * q^34 + 49920 * q^35 - 26572 * q^38 - 13440 * q^40 + 117944 * q^41 + 197456 * q^43 - 37144 * q^44 - 213120 * q^46 + 2116 * q^49 - 357650 * q^50 - 254400 * q^52 - 349440 * q^56 + 516480 * q^58 - 542032 * q^59 + 407040 * q^62 + 463936 * q^64 + 205440 * q^65 - 790192 * q^67 + 213848 * q^68 - 360960 * q^70 + 443912 * q^73 + 32640 * q^74 + 70616 * q^76 + 1032960 * q^80 + 404708 * q^82 + 3465008 * q^83 - 989548 * q^86 - 1950448 * q^88 - 761224 * q^89 + 3398400 * q^91 - 2743680 * q^92 + 971520 * q^94 - 926776 * q^97 + 2391262 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	4.62348	−	6.52867i	0.577934	−	0.816083i
$2$	4.62348	−	6.52867i	0.577934	−	0.816083i
$3$		0			0
$3$		0			0
$4$	−21.2470	−	60.3702i	−0.331984	−	0.943285i
$5$		−	199.084i		−	1.59268i	−0.604852	−	0.796338i	$-0.706768\pi$
$5$		−	199.084i		−	1.59268i	0.604852	−	0.796338i	$-0.293232\pi$
$6$		0			0
$7$		−	19.6656i		−	0.0573342i	−0.999589	−	0.0286671i	$-0.990874\pi$
$7$		−	19.6656i		−	0.0573342i	0.999589	−	0.0286671i	$-0.00912627\pi$
$8$	−492.372	−	140.406i	−0.961664	−	0.274231i
$9$		0			0
$10$	−1299.76	−	920.462i	−1.29976	−	0.920462i
$11$	924.152			0.694329			0.347165	−	0.937804i	$-0.387144\pi$
$11$	924.152			0.694329			0.347165	+	0.937804i	$0.387144\pi$
$12$		0			0
$13$			1550.92i			0.705925i	0.935638	+	0.352962i	$0.114826\pi$
$13$			1550.92i			0.705925i	−0.935638	+	0.352962i	$0.885174\pi$
$14$	−128.390	−	90.9235i	−0.0467895	−	0.0331354i
$15$		0			0
$16$	−3193.13	+	2565.37i	−0.779574	+	0.626310i
$17$	−5140.78			−1.04636			−0.523181	−	0.852221i	$-0.675255\pi$
$17$	−5140.78			−1.04636			−0.523181	+	0.852221i	$0.675255\pi$
$18$		0			0
$19$	−1696.10			−0.247281			−0.123641	−	0.992327i	$-0.539457\pi$
$19$	−1696.10			−0.247281			−0.123641	+	0.992327i	$0.539457\pi$
$20$	−12018.8	+	4229.94i	−1.50235	+	0.528742i
$21$		0			0
$22$	4272.80	−	6033.48i	0.401277	−	0.566631i
$23$		−	19210.4i		−	1.57890i	−0.613817	−	0.789448i	$-0.710367\pi$
$23$		−	19210.4i		−	1.57890i	0.613817	−	0.789448i	$-0.289633\pi$
$24$		0			0
$25$	−24009.6			−1.53662
$26$	10125.4	+	7170.62i	0.576093	+	0.407978i
$27$		0			0
$28$	−1187.22	+	417.835i	−0.0540825	+	0.0190340i
$29$			16588.1i			0.680147i	0.940399	+	0.340074i	$0.110452\pi$
$29$			16588.1i			0.680147i	−0.940399	+	0.340074i	$0.889548\pi$
$30$		0			0
$31$			7550.64i			0.253454i	0.991938	+	0.126727i	$0.0404472\pi$
$31$			7550.64i			0.253454i	−0.991938	+	0.126727i	$0.959553\pi$
$32$	1985.05	+	32707.8i	0.0605789	+	0.998163i
$33$		0			0
$34$	−23768.3	+	33562.4i	−0.604729	+	0.853919i
$35$	−3915.12			−0.0913148
$36$		0			0
$37$		−	28960.5i		−	0.571743i	−0.958268	−	0.285871i	$-0.907717\pi$
$37$		−	28960.5i		−	0.571743i	0.958268	−	0.285871i	$-0.0922830\pi$
$38$	−7841.89	+	11073.3i	−0.142912	+	0.201802i
$39$		0			0
$40$	−27952.7	+	98023.6i	−0.436761	+	1.53162i
$41$	52111.3			0.756101			0.378051	−	0.925785i	$-0.376594\pi$
$41$	52111.3			0.756101			0.378051	+	0.925785i	$0.376594\pi$
$42$		0			0
$43$	5896.43			0.0741625			0.0370812	−	0.999312i	$-0.488194\pi$
$43$	5896.43			0.0741625			0.0370812	+	0.999312i	$0.488194\pi$
$44$	−19635.4	−	55791.3i	−0.230506	−	0.654951i
$45$		0			0
$46$	−125419.	−	88819.0i	−1.28851	−	0.912499i
$47$		−	64453.4i		−	0.620801i	−0.950606	−	0.310400i	$-0.899537\pi$
$47$		−	64453.4i		−	0.620801i	0.950606	−	0.310400i	$-0.100463\pi$
$48$		0			0
$49$	117262.			0.996713
$50$	−111008.	+	156751.i	−0.888064	+	1.25401i
$51$		0			0
$52$	93629.2	−	32952.2i	0.665888	−	0.234355i
$53$		−	197386.i		−	1.32583i	−0.748694	−	0.662916i	$-0.769319\pi$
$53$		−	197386.i		−	1.32583i	0.748694	−	0.662916i	$-0.230681\pi$
$54$		0			0
$55$		−	183984.i		−	1.10584i
$56$	−2761.17	+	9682.80i	−0.0157228	+	0.0551362i
$57$		0			0
$58$	108298.	+	76694.7i	0.555057	+	0.393080i
$59$	−142210.			−0.692425			−0.346212	−	0.938156i	$-0.612532\pi$
$59$	−142210.			−0.692425			−0.346212	+	0.938156i	$0.612532\pi$
$60$		0			0
$61$		−	96476.4i		−	0.425042i	−0.977157	−	0.212521i	$-0.931833\pi$
$61$		−	96476.4i		−	0.425042i	0.977157	−	0.212521i	$-0.0681673\pi$
$62$	49295.6	+	34910.2i	0.206839	+	0.146480i
$63$		0			0
$64$	222716.	+	138264.i	0.849595	+	0.527436i
$65$	308763.			1.12431
$66$		0			0
$67$	−75260.9			−0.250233			−0.125117	−	0.992142i	$-0.539930\pi$
$67$	−75260.9			−0.250233			−0.125117	+	0.992142i	$0.539930\pi$
$68$	109226.	+	310350.i	0.347375	+	0.987018i
$69$		0			0
$70$	−18101.5	+	25560.5i	−0.0527740	+	0.0745205i
$71$		−	556121.i		−	1.55380i	−0.629625	−	0.776899i	$-0.716792\pi$
$71$		−	556121.i		−	1.55380i	0.629625	−	0.776899i	$-0.283208\pi$
$72$		0			0
$73$	285914.			0.734965			0.367483	−	0.930030i	$-0.380220\pi$
$73$	285914.			0.734965			0.367483	+	0.930030i	$0.380220\pi$
$74$	−189073.	−	133898.i	−0.466590	−	0.330430i
$75$		0			0
$76$	36037.0	+	102394.i	0.0820934	+	0.233257i
$77$		−	18174.0i		−	0.0398088i
$78$		0			0
$79$		−	342014.i		−	0.693686i	−0.937923	−	0.346843i	$-0.887254\pi$
$79$		−	342014.i		−	0.693686i	0.937923	−	0.346843i	$-0.112746\pi$
$80$	510725.	+	635703.i	0.997510	+	1.24161i
$81$		0			0
$82$	240935.	−	340217.i	0.436977	−	0.617042i
$83$	929558.			1.62571			0.812853	−	0.582469i	$-0.197913\pi$
$83$	929558.			1.62571			0.812853	+	0.582469i	$0.197913\pi$
$84$		0			0
$85$			1.02345e6i			1.66652i
$86$	27262.0	−	38495.9i	0.0428610	−	0.0605227i
$87$		0			0
$88$	−455027.	−	129757.i	−0.667712	−	0.190406i
$89$	−434757.			−0.616704			−0.308352	−	0.951272i	$-0.599777\pi$
$89$	−434757.			−0.616704			−0.308352	+	0.951272i	$0.599777\pi$
$90$		0			0
$91$	30499.7			0.0404736
$92$	−1.15974e6	+	408163.i	−1.48935	+	0.524168i
$93$		0			0
$94$	−420795.	−	297999.i	−0.506625	−	0.358782i
$95$			337668.i			0.393839i
$96$		0			0
$97$	643314.			0.704868			0.352434	−	0.935837i	$-0.385354\pi$
$97$	643314.			0.704868			0.352434	+	0.935837i	$0.385354\pi$
$98$	542159.	−	765566.i	0.576035	−	0.813401i
$99$		0			0
$100$	510131.	+	1.44947e6i	0.510131	+	1.44947i
$101$			858368.i			0.833123i	0.909107	+	0.416562i	$0.136765\pi$
$101$			858368.i			0.833123i	−0.909107	+	0.416562i	$0.863235\pi$
$102$		0			0
$103$		−	2.13382e6i		−	1.95275i	−0.216089	−	0.976374i	$-0.569330\pi$
$103$		−	2.13382e6i		−	1.95275i	0.216089	−	0.976374i	$-0.430670\pi$
$104$	217758.	−	763628.i	0.193586	−	0.678862i
$105$		0			0
$106$	−1.28867e6	−	912609.i	−1.08199	−	0.766244i
$107$	−1.81311e6			−1.48004			−0.740019	−	0.672585i	$-0.765184\pi$
$107$	−1.81311e6			−1.48004			−0.740019	+	0.672585i	$0.765184\pi$
$108$		0			0
$109$			1.43023e6i			1.10440i	0.833711	+	0.552201i	$0.186212\pi$
$109$			1.43023e6i			1.10440i	−0.833711	+	0.552201i	$0.813788\pi$
$110$	−1.20117e6	−	850647.i	−0.902459	−	0.639104i
$111$		0			0
$112$	50449.6	+	62795.0i	0.0359090	+	0.0446962i
$113$	−628373.			−0.435494			−0.217747	−	0.976005i	$-0.569871\pi$
$113$	−628373.			−0.435494			−0.217747	+	0.976005i	$0.569871\pi$
$114$		0			0
$115$	−3.82450e6			−2.51467
$116$	1.00143e6	−	352447.i	0.641573	−	0.225798i
$117$		0			0
$118$	−657502.	+	928438.i	−0.400176	+	0.565076i
$119$			101097.i			0.0599924i
$120$		0			0
$121$	−917503.			−0.517907
$122$	−629862.	−	446056.i	−0.346869	−	0.245646i
$123$		0			0
$124$	455834.	−	160428.i	0.239079	−	0.0841425i
$125$			1.66925e6i			0.854656i
$126$		0			0
$127$			2.43195e6i			1.18725i	0.804741	+	0.593626i	$0.202304\pi$
$127$			2.43195e6i			1.18725i	−0.804741	+	0.593626i	$0.797696\pi$
$128$	1.93240e6	−	814779.i	0.921442	−	0.388517i
$129$		0			0
$130$	1.42756e6	−	2.01581e6i	0.649777	−	0.917530i
$131$	−2.66985e6			−1.18761			−0.593804	−	0.804610i	$-0.702374\pi$
$131$	−2.66985e6			−1.18761			−0.593804	+	0.804610i	$0.702374\pi$
$132$		0			0
$133$			33354.9i			0.0141777i
$134$	−347967.	+	491353.i	−0.144618	+	0.204211i
$135$		0			0
$136$	2.53118e6	+	721797.i	1.00625	+	0.286945i
$137$	4.00205e6			1.55640			0.778199	−	0.628018i	$-0.216133\pi$
$137$	4.00205e6			1.55640			0.778199	+	0.628018i	$0.216133\pi$
$138$		0			0
$139$	1.89422e6			0.705319			0.352660	−	0.935752i	$-0.385277\pi$
$139$	1.89422e6			0.705319			0.352660	+	0.935752i	$0.385277\pi$
$140$	83184.4	+	236357.i	0.0303150	+	0.0861359i
$141$		0			0
$142$	−3.63073e6	−	2.57121e6i	−1.26803	−	0.897993i
$143$			1.43328e6i			0.490144i
$144$		0			0
$145$	3.30243e6			1.08325
$146$	1.32192e6	−	1.86664e6i	0.424762	−	0.599793i
$147$		0			0
$148$	−1.74835e6	+	615322.i	−0.539316	+	0.189809i
$149$			3.06394e6i			0.926235i	0.886297	+	0.463118i	$0.153269\pi$
$149$			3.06394e6i			0.926235i	−0.886297	+	0.463118i	$0.846731\pi$
$150$		0			0
$151$		−	2.24437e6i		−	0.651873i	−0.945392	−	0.325936i	$-0.894320\pi$
$151$		−	2.24437e6i		−	0.651873i	0.945392	−	0.325936i	$-0.105680\pi$
$152$	835114.	+	238143.i	0.237802	+	0.0678122i
$153$		0			0
$154$	−118652.	−	84027.2i	−0.0324873	−	0.0230069i
$155$	1.50322e6			0.403670
$156$		0			0
$157$			4.89064e6i			1.26377i	0.775064	+	0.631883i	$0.217718\pi$
$157$			4.89064e6i			1.26377i	−0.775064	+	0.631883i	$0.782282\pi$
$158$	−2.23290e6	−	1.58129e6i	−0.566105	−	0.400905i
$159$		0			0
$160$	6.51162e6	−	395193.i	1.58975	−	0.0964825i
$161$	−377785.			−0.0905248
$162$		0			0
$163$	1.82987e6			0.422529			0.211265	−	0.977429i	$-0.432242\pi$
$163$	1.82987e6			0.422529			0.211265	+	0.977429i	$0.432242\pi$
$164$	−1.10721e6	−	3.14597e6i	−0.251013	−	0.713219i
$165$		0			0
$166$	4.29779e6	−	6.06877e6i	0.939552	−	1.32671i
$167$		−	3.94279e6i		−	0.846554i	−0.906000	−	0.423277i	$-0.860880\pi$
$167$		−	3.94279e6i		−	0.846554i	0.906000	−	0.423277i	$-0.139120\pi$
$168$		0			0
$169$	2.42147e6			0.501670
$170$	6.68176e6	+	4.73189e6i	1.36002	+	0.963137i
$171$		0			0
$172$	−125281.	−	355969.i	−0.0246207	−	0.0699563i
$173$			205167.i			0.0396249i	0.999804	+	0.0198125i	$0.00630692\pi$
$173$			205167.i			0.0396249i	−0.999804	+	0.0198125i	$0.993693\pi$
$174$		0			0
$175$			472164.i			0.0881007i
$176$	−2.95094e6	+	2.37079e6i	−0.541281	+	0.434866i
$177$		0			0
$178$	−2.01009e6	+	2.83838e6i	−0.356415	+	0.503282i
$179$	3.36007e6			0.585853			0.292927	−	0.956135i	$-0.405371\pi$
$179$	3.36007e6			0.585853			0.292927	+	0.956135i	$0.405371\pi$
$180$		0			0
$181$		−	2.39145e6i		−	0.403298i	−0.979458	−	0.201649i	$-0.935370\pi$
$181$		−	2.39145e6i		−	0.403298i	0.979458	−	0.201649i	$-0.0646300\pi$
$182$	141015.	−	199123.i	0.0233911	−	0.0330298i
$183$		0			0
$184$	−2.69726e6	+	9.45868e6i	−0.432982	+	1.51837i
$185$	−5.76558e6			−0.910601
$186$		0			0
$187$	−4.75086e6			−0.726520
$188$	−3.89107e6	+	1.36944e6i	−0.585592	+	0.206096i
$189$		0			0
$190$	2.20452e6	+	1.56120e6i	0.321406	+	0.227613i
$191$		−	2.02441e6i		−	0.290535i	−0.989392	−	0.145268i	$-0.953596\pi$
$191$		−	2.02441e6i		−	0.290535i	0.989392	−	0.145268i	$-0.0464043\pi$
$192$		0			0
$193$	−7.92510e6			−1.10238			−0.551192	−	0.834378i	$-0.685827\pi$
$193$	−7.92510e6			−1.10238			−0.551192	+	0.834378i	$0.685827\pi$
$194$	2.97434e6	−	4.19998e6i	0.407367	−	0.575231i
$195$		0			0
$196$	−2.49147e6	−	7.07915e6i	−0.330892	−	0.940184i
$197$		−	4.12787e6i		−	0.539917i	−0.962872	−	0.269959i	$-0.912990\pi$
$197$		−	4.12787e6i		−	0.539917i	0.962872	−	0.269959i	$-0.0870100\pi$
$198$		0			0
$199$		−	1.18196e7i		−	1.49983i	−0.661532	−	0.749917i	$-0.730093\pi$
$199$		−	1.18196e7i		−	1.49983i	0.661532	−	0.749917i	$-0.269907\pi$
$200$	1.18217e7	+	3.37110e6i	1.47771	+	0.421387i
$201$		0			0
$202$	5.60400e6	+	3.96864e6i	0.679898	+	0.481491i
$203$	326215.			0.0389957
$204$		0			0
$205$		−	1.03745e7i		−	1.20422i
$206$	−1.39310e7	−	9.86566e6i	−1.59360	−	1.12856i
$207$		0			0
$208$	−3.97867e6	−	4.95228e6i	−0.442128	−	0.550320i
$209$	−1.56746e6			−0.171695
$210$		0			0
$211$	1.19422e7			1.27127			0.635635	−	0.771989i	$-0.280738\pi$
$211$	1.19422e7			1.27127			0.635635	+	0.771989i	$0.280738\pi$
$212$	−1.19162e7	+	4.19385e6i	−1.25064	+	0.440155i
$213$		0			0
$214$	−8.38288e6	+	1.18372e7i	−0.855365	+	1.20783i
$215$		−	1.17389e6i		−	0.118117i
$216$		0			0
$217$	148488.			0.0145316
$218$	9.33752e6	+	6.61265e6i	0.901284	+	0.638272i
$219$		0			0
$220$	−1.11072e7	+	3.90911e6i	−1.04312	+	0.367121i
$221$		−	7.97292e6i		−	0.738653i
$222$		0			0
$223$			2.10926e7i			1.90202i	0.309153	+	0.951012i	$0.399955\pi$
$223$			2.10926e7i			1.90202i	−0.309153	+	0.951012i	$0.600045\pi$
$224$	643220.	−	39037.2i	0.0572289	−	0.00347324i
$225$		0			0
$226$	−2.90526e6	+	4.10243e6i	−0.251687	+	0.355399i
$227$	−2.73658e6			−0.233954			−0.116977	−	0.993135i	$-0.537320\pi$
$227$	−2.73658e6			−0.233954			−0.116977	+	0.993135i	$0.537320\pi$
$228$		0			0
$229$			7.23777e6i			0.602696i	0.953514	+	0.301348i	$0.0974366\pi$
$229$			7.23777e6i			0.602696i	−0.953514	+	0.301348i	$0.902563\pi$
$230$	−1.76825e7	+	2.49689e7i	−1.45331	+	2.05218i
$231$		0			0
$232$	2.32907e6	−	8.16752e6i	0.186517	−	0.654073i
$233$	1.63958e7			1.29618			0.648088	−	0.761565i	$-0.275569\pi$
$233$	1.63958e7			1.29618			0.648088	+	0.761565i	$0.275569\pi$
$234$		0			0
$235$	−1.28317e7			−0.988734
$236$	3.02152e6	+	8.58522e6i	0.229874	+	0.653154i
$237$		0			0
$238$	660026.	+	467418.i	0.0489588	+	0.0346717i
$239$			1.73985e7i			1.27443i	0.770685	+	0.637217i	$0.219914\pi$
$239$			1.73985e7i			1.27443i	−0.770685	+	0.637217i	$0.780086\pi$
$240$		0			0
$241$	1.34047e7			0.957645			0.478822	−	0.877912i	$-0.341064\pi$
$241$	1.34047e7			0.957645			0.478822	+	0.877912i	$0.341064\pi$
$242$	−4.24205e6	+	5.99007e6i	−0.299316	+	0.422655i
$243$		0			0
$244$	−5.82430e6	+	2.04983e6i	−0.400935	+	0.141107i
$245$		−	2.33451e7i		−	1.58744i
$246$		0			0
$247$		−	2.63051e6i		−	0.174562i
$248$	1.06016e6	−	3.71772e6i	0.0695048	−	0.243737i
$249$		0			0
$250$	1.08980e7	+	7.71774e6i	0.697471	+	0.493935i
$251$	1.70047e7			1.07534			0.537672	−	0.843154i	$-0.319304\pi$
$251$	1.70047e7			1.07534			0.537672	+	0.843154i	$0.319304\pi$
$252$		0			0
$253$		−	1.77534e7i		−	1.09627i
$254$	1.58774e7	+	1.12440e7i	0.968896	+	0.686154i
$255$		0			0
$256$	3.61500e6	−	1.63831e7i	0.215471	−	0.976510i
$257$	−1.94325e7			−1.14480			−0.572400	−	0.819974i	$-0.693988\pi$
$257$	−1.94325e7			−1.14480			−0.572400	+	0.819974i	$0.693988\pi$
$258$		0			0
$259$	−569526.			−0.0327804
$260$	−6.56028e6	−	1.86401e7i	−0.373252	−	1.06054i
$261$		0			0
$262$	−1.23440e7	+	1.74305e7i	−0.686359	+	0.969186i
$263$		−	1.33303e7i		−	0.732778i	−0.930462	−	0.366389i	$-0.880594\pi$
$263$		−	1.33303e7i		−	0.732778i	0.930462	−	0.366389i	$-0.119406\pi$
$264$		0			0
$265$	−3.92965e7			−2.11162
$266$	217763.	+	154216.i	0.0115702	+	0.00819377i
$267$		0			0
$268$	1.59906e6	+	4.54352e6i	0.0830733	+	0.236041i
$269$		−	7.13509e6i		−	0.366558i	−0.983061	−	0.183279i	$-0.941329\pi$
$269$		−	7.13509e6i		−	0.366558i	0.983061	−	0.183279i	$-0.0586712\pi$
$270$		0			0
$271$			6.93561e6i			0.348479i	0.984703	+	0.174240i	$0.0557467\pi$
$271$			6.93561e6i			0.348479i	−0.984703	+	0.174240i	$0.944253\pi$
$272$	1.64152e7	−	1.31880e7i	0.815717	−	0.655348i
$273$		0			0
$274$	1.85034e7	−	2.61280e7i	0.899496	−	1.27015i
$275$	−2.21886e7			−1.06692
$276$		0			0
$277$		−	1.79332e7i		−	0.843757i	−0.906652	−	0.421879i	$-0.861371\pi$
$277$		−	1.79332e7i		−	0.843757i	0.906652	−	0.421879i	$-0.138629\pi$
$278$	8.75787e6	−	1.23667e7i	0.407628	−	0.575599i
$279$		0			0
$280$	1.92770e6	+	549707.i	0.0878141	+	0.0250413i
$281$	4.29329e6			0.193496			0.0967479	−	0.995309i	$-0.469156\pi$
$281$	4.29329e6			0.193496			0.0967479	+	0.995309i	$0.469156\pi$
$282$		0			0
$283$	3.39377e7			1.49735			0.748674	−	0.662938i	$-0.230691\pi$
$283$	3.39377e7			1.49735			0.748674	+	0.662938i	$0.230691\pi$
$284$	−3.35732e7	+	1.18159e7i	−1.46567	+	0.515835i
$285$		0			0
$286$	9.35743e6	+	6.62675e6i	0.399998	+	0.283271i
$287$		−	1.02480e6i		−	0.0433505i
$288$		0			0
$289$	2.29005e6			0.0948751
$290$	1.52687e7	−	2.15605e7i	0.626050	−	0.884025i
$291$		0			0
$292$	−6.07480e6	−	1.72607e7i	−0.243996	−	0.693282i
$293$			3.15178e7i			1.25301i	0.779419	+	0.626504i	$0.215515\pi$
$293$			3.15178e7i			1.25301i	−0.779419	+	0.626504i	$0.784485\pi$
$294$		0			0
$295$			2.83117e7i			1.10281i
$296$	−4.06623e6	+	1.42593e7i	−0.156789	+	0.549824i
$297$		0			0
$298$	2.00034e7	+	1.41660e7i	0.755885	+	0.535303i
$299$	2.97938e7			1.11458
$300$		0			0
$301$		−	115957.i		−	0.00425204i
$302$	−1.46527e7	−	1.03768e7i	−0.531983	−	0.376740i
$303$		0			0
$304$	5.41589e6	−	4.35113e6i	0.192774	−	0.154875i
$305$	−1.92069e7			−0.676953
$306$		0			0
$307$	3.45268e7			1.19328			0.596638	−	0.802510i	$-0.296503\pi$
$307$	3.45268e7			1.19328			0.596638	+	0.802510i	$0.296503\pi$
$308$	−1.09717e6	+	386143.i	−0.0375511	+	0.0132159i
$309$		0			0
$310$	6.95008e6	−	9.81399e6i	0.233295	−	0.329428i
$311$			1.55896e7i			0.518268i	0.965841	+	0.259134i	$0.0834371\pi$
$311$			1.55896e7i			0.518268i	−0.965841	+	0.259134i	$0.916563\pi$
$312$		0			0
$313$	2.13473e6			0.0696160			0.0348080	−	0.999394i	$-0.488918\pi$
$313$	2.13473e6			0.0696160			0.0348080	+	0.999394i	$0.488918\pi$
$314$	3.19293e7	+	2.26117e7i	1.03134	+	0.730374i
$315$		0			0
$316$	−2.06475e7	+	7.26676e6i	−0.654343	+	0.230292i
$317$			4.15440e7i			1.30416i	0.758151	+	0.652079i	$0.226103\pi$
$317$			4.15440e7i			1.30416i	−0.758151	+	0.652079i	$0.773897\pi$
$318$		0			0
$319$			1.53299e7i			0.472246i
$320$	2.75262e7	−	4.43393e7i	0.840034	−	1.35313i
$321$		0			0
$322$	−1.74668e6	+	2.46643e6i	−0.0523174	+	0.0738757i
$323$	8.71930e6			0.258746
$324$		0			0
$325$		−	3.72369e7i		−	1.08474i
$326$	8.46034e6	−	1.19466e7i	0.244194	−	0.344819i
$327$		0			0
$328$	−2.56581e7	−	7.31674e6i	−0.727115	−	0.207346i
$329$	−1.26752e6			−0.0355931
$330$		0			0
$331$	1.78997e7			0.493585			0.246793	−	0.969068i	$-0.420623\pi$
$331$	1.78997e7			0.493585			0.246793	+	0.969068i	$0.420623\pi$
$332$	−1.97503e7	−	5.61176e7i	−0.539708	−	1.53350i
$333$		0			0
$334$	−2.57412e7	−	1.82294e7i	−0.690858	−	0.489253i
$335$			1.49833e7i			0.398540i
$336$		0			0
$337$	1.86244e7			0.486624			0.243312	−	0.969948i	$-0.421766\pi$
$337$	1.86244e7			0.486624			0.243312	+	0.969948i	$0.421766\pi$
$338$	1.11956e7	−	1.58089e7i	0.289933	−	0.409405i
$339$		0			0
$340$	6.17859e7	−	2.17452e7i	1.57200	−	0.553256i
$341$			6.97794e6i			0.175980i
$342$		0			0
$343$		−	4.61968e6i		−	0.114480i
$344$	−2.90324e6	−	827896.i	−0.0713194	−	0.0203376i
$345$		0			0
$346$	1.33946e6	+	948583.i	0.0323372	+	0.0229006i
$347$	−3.96438e7			−0.948827			−0.474414	−	0.880302i	$-0.657340\pi$
$347$	−3.96438e7			−0.948827			−0.474414	+	0.880302i	$0.657340\pi$
$348$		0			0
$349$			6.84414e7i			1.61006i	0.593232	+	0.805031i	$0.297852\pi$
$349$			6.84414e7i			1.61006i	−0.593232	+	0.805031i	$0.702148\pi$
$350$	3.08260e6	+	2.18304e6i	0.0718975	+	0.0509164i
$351$		0			0
$352$	1.83449e6	+	3.02270e7i	0.0420617	+	0.693054i
$353$	3.01604e7			0.685666			0.342833	−	0.939396i	$-0.388613\pi$
$353$	3.01604e7			0.685666			0.342833	+	0.939396i	$0.388613\pi$
$354$		0			0
$355$	−1.10715e8			−2.47470
$356$	9.23727e6	+	2.62464e7i	0.204736	+	0.581728i
$357$		0			0
$358$	1.55352e7	−	2.19368e7i	0.338585	−	0.478105i
$359$			6.13950e7i			1.32694i	0.748205	+	0.663468i	$0.230916\pi$
$359$			6.13950e7i			1.32694i	−0.748205	+	0.663468i	$0.769084\pi$
$360$		0			0
$361$	−4.41691e7			−0.938852
$362$	−1.56130e7	−	1.10568e7i	−0.329125	−	0.233080i
$363$		0			0
$364$	−648027.	−	1.84128e6i	−0.0134366	−	0.0381782i
$365$		−	5.69210e7i		−	1.17056i
$366$		0			0
$367$		−	4.17679e7i		−	0.844976i	−0.906368	−	0.422488i	$-0.861157\pi$
$367$		−	4.17679e7i		−	0.844976i	0.906368	−	0.422488i	$-0.138843\pi$
$368$	4.92818e7	+	6.13415e7i	0.988880	+	1.23087i
$369$		0			0
$370$	−2.66570e7	+	3.76416e7i	−0.526268	+	0.743126i
$371$	−3.88172e6			−0.0760155
$372$		0			0
$373$			5.61502e7i			1.08199i	0.841025	+	0.540997i	$0.181953\pi$
$373$			5.61502e7i			1.08199i	−0.841025	+	0.540997i	$0.818047\pi$
$374$	−2.19655e7	+	3.10168e7i	−0.419881	+	0.592901i
$375$		0			0
$376$	−9.04965e6	+	3.17350e7i	−0.170243	+	0.597001i
$377$	−2.57268e7			−0.480133
$378$		0			0
$379$	−1.96484e7			−0.360919			−0.180460	−	0.983582i	$-0.557758\pi$
$379$	−1.96484e7			−0.360919			−0.180460	+	0.983582i	$0.557758\pi$
$380$	2.03851e7	−	7.17441e6i	0.371503	−	0.130748i
$381$		0			0
$382$	−1.32167e7	−	9.35982e6i	−0.237101	−	0.167910i
$383$		−	3.86630e7i		−	0.688176i	−0.938937	−	0.344088i	$-0.888188\pi$
$383$		−	3.86630e7i		−	0.688176i	0.938937	−	0.344088i	$-0.111812\pi$
$384$		0			0
$385$	−3.61817e6			−0.0634025
$386$	−3.66415e7	+	5.17403e7i	−0.637106	+	0.899637i
$387$		0			0
$388$	−1.36685e7	−	3.88370e7i	−0.234004	−	0.664891i
$389$		−	2.94915e6i		−	0.0501012i	−0.999686	−	0.0250506i	$-0.992025\pi$
$389$		−	2.94915e6i		−	0.0501012i	0.999686	−	0.0250506i	$-0.00797470\pi$
$390$		0			0
$391$			9.87566e7i			1.65210i
$392$	−5.77366e7	−	1.64643e7i	−0.958503	−	0.273329i
$393$		0			0
$394$	−2.69495e7	−	1.90851e7i	−0.440617	−	0.312037i
$395$	−6.80897e7			−1.10482
$396$		0			0
$397$		−	6.88167e7i		−	1.09982i	−0.835223	−	0.549911i	$-0.814662\pi$
$397$		−	6.88167e7i		−	1.09982i	0.835223	−	0.549911i	$-0.185338\pi$
$398$	−7.71662e7	−	5.46476e7i	−1.22399	−	0.866806i
$399$		0			0
$400$	7.66660e7	−	6.15935e7i	1.19791	−	0.962399i
$401$	−3.42281e7			−0.530823			−0.265412	−	0.964135i	$-0.585508\pi$
$401$	−3.42281e7			−0.530823			−0.265412	+	0.964135i	$0.585508\pi$
$402$		0			0
$403$	−1.17104e7			−0.178919
$404$	5.18199e7	−	1.82377e7i	0.785873	−	0.276583i
$405$		0			0
$406$	1.50825e6	−	2.12975e6i	0.0225369	−	0.0318237i
$407$		−	2.67639e7i		−	0.396978i
$408$		0			0
$409$	7.43891e7			1.08728			0.543638	−	0.839320i	$-0.317047\pi$
$409$	7.43891e7			1.08728			0.543638	+	0.839320i	$0.317047\pi$
$410$	−6.77319e7	−	4.79665e7i	−0.982747	−	0.695963i
$411$		0			0
$412$	−1.28819e8	+	4.53372e7i	−1.84200	+	0.648280i
$413$			2.79664e6i			0.0396996i
$414$		0			0
$415$		−	1.85061e8i		−	2.58922i
$416$	−5.07271e7	+	3.07865e6i	−0.704628	+	0.0427641i
$417$		0			0
$418$	−7.24710e6	+	1.02334e7i	−0.0992283	+	0.140117i
$419$	3.78200e7			0.514138			0.257069	−	0.966393i	$-0.417243\pi$
$419$	3.78200e7			0.514138			0.257069	+	0.966393i	$0.417243\pi$
$420$		0			0
$421$			6.21731e7i			0.833213i	0.909087	+	0.416607i	$0.136781\pi$
$421$			6.21731e7i			0.833213i	−0.909087	+	0.416607i	$0.863219\pi$
$422$	5.52146e7	−	7.79668e7i	0.734711	−	1.03746i
$423$		0			0
$424$	−2.77142e7	+	9.71873e7i	−0.363584	+	1.27501i
$425$	1.23428e8			1.60786
$426$		0			0
$427$	−1.89727e6			−0.0243694
$428$	3.85231e7	+	1.09458e8i	0.491349	+	1.39610i
$429$		0			0
$430$	−7.66393e6	−	5.42745e6i	−0.0963931	−	0.0682637i
$431$		−	1.00561e8i		−	1.25603i	−0.778202	−	0.628014i	$-0.783868\pi$
$431$		−	1.00561e8i		−	1.25603i	0.778202	−	0.628014i	$-0.216132\pi$
$432$		0			0
$433$	1.07677e8			1.32636			0.663179	−	0.748461i	$-0.269207\pi$
$433$	1.07677e8			1.32636			0.663179	+	0.748461i	$0.269207\pi$
$434$	686531.	−	969429.i	0.00839829	−	0.0118590i
$435$		0			0
$436$	8.63436e7	−	3.03881e7i	1.04177	−	0.366644i
$437$			3.25829e7i			0.390432i
$438$		0			0
$439$		−	6.85796e7i		−	0.810590i	−0.914186	−	0.405295i	$-0.867169\pi$
$439$		−	6.85796e7i		−	0.810590i	0.914186	−	0.405295i	$-0.132831\pi$
$440$	−2.58325e7	+	9.05888e7i	−0.303256	+	1.06345i
$441$		0			0
$442$	−5.20525e7	−	3.68626e7i	−0.602803	−	0.426893i
$443$	8.84819e7			1.01776			0.508878	−	0.860839i	$-0.330061\pi$
$443$	8.84819e7			1.01776			0.508878	+	0.860839i	$0.330061\pi$
$444$		0			0
$445$			8.65534e7i			0.982210i
$446$	1.37707e8	+	9.75213e7i	1.55221	+	1.09925i
$447$		0			0
$448$	2.71905e6	−	4.37985e6i	0.0302401	−	0.0487108i
$449$	−4.28752e7			−0.473661			−0.236830	−	0.971551i	$-0.576109\pi$
$449$	−4.28752e7			−0.473661			−0.236830	+	0.971551i	$0.576109\pi$
$450$		0			0
$451$	4.81588e7			0.524983
$452$	1.33510e7	+	3.79350e7i	0.144577	+	0.410795i
$453$		0			0
$454$	−1.26525e7	+	1.78662e7i	−0.135210	+	0.190926i
$455$		−	6.07203e6i		−	0.0644614i
$456$		0			0
$457$	−7.01681e7			−0.735176			−0.367588	−	0.929989i	$-0.619816\pi$
$457$	−7.01681e7			−0.735176			−0.367588	+	0.929989i	$0.619816\pi$
$458$	4.72530e7	+	3.34637e7i	0.491850	+	0.348319i
$459$		0			0
$460$	8.12590e7	+	2.30886e8i	0.834830	+	2.37205i
$461$			5.37805e7i			0.548937i	0.961596	+	0.274468i	$0.0885018\pi$
$461$			5.37805e7i			0.548937i	−0.961596	+	0.274468i	$0.911498\pi$
$462$		0			0
$463$		−	4.36059e7i		−	0.439342i	−0.975574	−	0.219671i	$-0.929502\pi$
$463$		−	4.36059e7i		−	0.439342i	0.975574	−	0.219671i	$-0.0704984\pi$
$464$	−4.25546e7	−	5.29680e7i	−0.425983	−	0.530225i
$465$		0			0
$466$	7.58055e7	−	1.07043e8i	0.749105	−	1.05779i
$467$	3.09469e7			0.303855			0.151928	−	0.988392i	$-0.451452\pi$
$467$	3.09469e7			0.303855			0.151928	+	0.988392i	$0.451452\pi$
$468$		0			0
$469$			1.48005e6i			0.0143469i
$470$	−5.93269e7	+	8.37737e7i	−0.571423	+	0.806889i
$471$		0			0
$472$	7.00200e7	+	1.99671e7i	0.665880	+	0.189884i
$473$	5.44920e6			0.0514932
$474$		0			0
$475$	4.07228e7			0.379977
$476$	6.10323e6	−	2.14800e6i	0.0565899	−	0.0199165i
$477$		0			0
$478$	1.13589e8	+	8.04414e7i	1.04004	+	0.736539i
$479$		−	9.72219e7i		−	0.884622i	−0.896862	−	0.442311i	$-0.854159\pi$
$479$		−	9.72219e7i		−	0.884622i	0.896862	−	0.442311i	$-0.145841\pi$
$480$		0			0
$481$	4.49153e7			0.403607
$482$	6.19761e7	−	8.75145e7i	0.553456	−	0.781518i
$483$		0			0
$484$	1.94941e7	+	5.53899e7i	0.171937	+	0.488534i
$485$		−	1.28074e8i		−	1.12263i
$486$		0			0
$487$		−	9.02434e7i		−	0.781320i	−0.920535	−	0.390660i	$-0.872247\pi$
$487$		−	9.02434e7i		−	0.781320i	0.920535	−	0.390660i	$-0.127753\pi$
$488$	−1.35459e7	+	4.75022e7i	−0.116559	+	0.408747i
$489$		0			0
$490$	−1.52412e8	−	1.07935e8i	−1.29548	−	0.917436i
$491$	1.00966e8			0.852962			0.426481	−	0.904497i	$-0.359753\pi$
$491$	1.00966e8			0.852962			0.426481	+	0.904497i	$0.359753\pi$
$492$		0			0
$493$		−	8.52758e7i		−	0.711681i
$494$	−1.71738e7	−	1.21621e7i	−0.142457	−	0.100885i
$495$		0			0
$496$	−1.93702e7	−	2.41102e7i	−0.158741	−	0.197586i
$497$	−1.09365e7			−0.0890857
$498$		0			0
$499$	−1.47819e8			−1.18968			−0.594839	−	0.803845i	$-0.702784\pi$
$499$	−1.47819e8			−1.18968			−0.594839	+	0.803845i	$0.702784\pi$
$500$	1.00773e8	−	3.54665e7i	0.806185	−	0.283732i
$501$		0			0
$502$	7.86207e7	−	1.11018e8i	0.621478	−	0.877570i
$503$		−	3.38774e7i		−	0.266199i	−0.991103	−	0.133099i	$-0.957507\pi$
$503$		−	3.38774e7i		−	0.266199i	0.991103	−	0.133099i	$-0.0424929\pi$
$504$		0			0
$505$	1.70888e8			1.32690
$506$	−1.15906e8	−	8.20823e7i	−0.894651	−	0.633575i
$507$		0			0
$508$	1.46817e8	−	5.16714e7i	1.11992	−	0.394148i
$509$			5.16056e7i			0.391331i	0.980671	+	0.195665i	$0.0626866\pi$
$509$			5.16056e7i			0.391331i	−0.980671	+	0.195665i	$0.937313\pi$
$510$		0			0
$511$		−	5.62268e6i		−	0.0421386i
$512$	−9.02461e7	−	9.93481e7i	−0.672386	−	0.740201i
$513$		0			0
$514$	−8.98458e7	+	1.26868e8i	−0.661620	+	0.934253i
$515$	−4.24810e8			−3.11009
$516$		0			0
$517$		−	5.95647e7i		−	0.431040i
$518$	−2.63319e6	+	3.71825e6i	−0.0189449	+	0.0267515i
$519$		0			0
$520$	−1.52026e8	−	4.33523e7i	−1.08121	−	0.308320i
$521$	1.06575e8			0.753602			0.376801	−	0.926294i	$-0.377024\pi$
$521$	1.06575e8			0.753602			0.376801	+	0.926294i	$0.377024\pi$
$522$		0			0
$523$	1.10885e8			0.775117			0.387558	−	0.921845i	$-0.373319\pi$
$523$	1.10885e8			0.775117			0.387558	+	0.921845i	$0.373319\pi$
$524$	5.67261e7	+	1.61179e8i	0.394266	+	1.12025i
$525$		0			0
$526$	−8.70290e7	−	6.16323e7i	−0.598008	−	0.423498i
$527$		−	3.88162e7i		−	0.265205i
$528$		0			0
$529$	−2.21005e8			−1.49292
$530$	−1.81686e8	+	2.56554e8i	−1.22038	+	1.72326i
$531$		0			0
$532$	2.01365e6	−	708691.i	0.0133736	−	0.00470676i
$533$			8.08202e7i			0.533751i
$534$		0			0
$535$			3.60962e8i			2.35722i
$536$	3.70563e7	+	1.05671e7i	0.240640	+	0.0686216i
$537$		0			0
$538$	−4.65826e7	−	3.29889e7i	−0.299142	−	0.211846i
$539$	1.08368e8			0.692047
$540$		0			0
$541$			8.74191e7i			0.552096i	0.961144	+	0.276048i	$0.0890248\pi$
$541$			8.74191e7i			0.552096i	−0.961144	+	0.276048i	$0.910975\pi$
$542$	4.52803e7	+	3.20666e7i	0.284388	+	0.201398i
$543$		0			0
$544$	−1.02047e7	−	1.68144e8i	−0.0633875	−	1.04444i
$545$	2.84737e8			1.75896
$546$		0			0
$547$	−1.11073e7			−0.0678653			−0.0339326	−	0.999424i	$-0.510803\pi$
$547$	−1.11073e7			−0.0678653			−0.0339326	+	0.999424i	$0.510803\pi$
$548$	−8.50313e7	−	2.41605e8i	−0.516699	−	1.46813i
$549$		0			0
$550$	−1.02588e8	+	1.44862e8i	−0.616609	+	0.870694i
$551$		−	2.81351e7i		−	0.168188i
$552$		0			0
$553$	−6.72592e6			−0.0397719
$554$	−1.17080e8	−	8.29135e7i	−0.688576	−	0.487636i
$555$		0			0
$556$	−4.02464e7	−	1.14354e8i	−0.234154	−	0.665317i
$557$		−	4.54249e7i		−	0.262862i	−0.991325	−	0.131431i	$-0.958043\pi$
$557$		−	4.54249e7i		−	0.262862i	0.991325	−	0.131431i	$-0.0419573\pi$
$558$		0			0
$559$			9.14488e6i			0.0523531i
$560$	1.25015e7	−	1.00437e7i	0.0711866	−	0.0571914i
$561$		0			0
$562$	1.98499e7	−	2.80295e7i	0.111828	−	0.157909i
$563$	−5.57201e7			−0.312239			−0.156119	−	0.987738i	$-0.549898\pi$
$563$	−5.57201e7			−0.312239			−0.156119	+	0.987738i	$0.549898\pi$
$564$		0			0
$565$			1.25099e8i			0.693600i
$566$	1.56910e8	−	2.21568e8i	0.865369	−	1.22196i
$567$		0			0
$568$	−7.80828e7	+	2.73819e8i	−0.426099	+	1.49423i
$569$	−3.43539e8			−1.86483			−0.932416	−	0.361387i	$-0.882303\pi$
$569$	−3.43539e8			−1.86483			−0.932416	+	0.361387i	$0.882303\pi$
$570$		0			0
$571$	−2.25486e8			−1.21119			−0.605593	−	0.795775i	$-0.707064\pi$
$571$	−2.25486e8			−1.21119			−0.605593	+	0.795775i	$0.707064\pi$
$572$	8.65277e7	−	3.04529e7i	0.462346	−	0.162720i
$573$		0			0
$574$	−6.69058e6	−	4.73814e6i	−0.0353776	−	0.0250537i
$575$			4.61236e8i			2.42616i
$576$		0			0
$577$	−8.79050e7			−0.457600			−0.228800	−	0.973473i	$-0.573480\pi$
$577$	−8.79050e7			−0.457600			−0.228800	+	0.973473i	$0.573480\pi$
$578$	1.05880e7	−	1.49510e7i	0.0548316	−	0.0774259i
$579$		0			0
$580$	−7.01667e7	−	1.99369e8i	−0.359622	−	1.02182i
$581$		−	1.82803e7i		−	0.0932085i
$582$		0			0
$583$		−	1.82415e8i		−	0.920564i
$584$	−1.40776e8	−	4.01441e7i	−0.706789	−	0.201550i
$585$		0			0
$586$	2.05769e8	+	1.45722e8i	1.02256	+	0.724156i
$587$	3.94523e7			0.195056			0.0975278	−	0.995233i	$-0.468907\pi$
$587$	3.94523e7			0.195056			0.0975278	+	0.995233i	$0.468907\pi$
$588$		0			0
$589$		−	1.28067e7i		−	0.0626744i
$590$	1.84838e8	+	1.30898e8i	0.899983	+	0.637351i
$591$		0			0
$592$	7.42943e7	+	9.24747e7i	0.358088	+	0.445716i
$593$	−2.30474e8			−1.10524			−0.552622	−	0.833432i	$-0.686373\pi$
$593$	−2.30474e8			−1.10524			−0.552622	+	0.833432i	$0.686373\pi$
$594$		0			0
$595$	2.01268e7			0.0955484
$596$	1.84971e8	−	6.50994e7i	0.873704	−	0.307495i
$597$		0			0
$598$	1.37751e8	−	1.94514e8i	0.644155	−	0.909592i
$599$			1.85523e8i			0.863212i	0.902062	+	0.431606i	$0.142053\pi$
$599$			1.85523e8i			0.863212i	−0.902062	+	0.431606i	$0.857947\pi$
$600$		0			0
$601$	−4.38545e7			−0.202018			−0.101009	−	0.994885i	$-0.532207\pi$
$601$	−4.38545e7			−0.202018			−0.101009	+	0.994885i	$0.532207\pi$
$602$	−757045.	−	536125.i	−0.00347002	−	0.00245740i
$603$		0			0
$604$	−1.35493e8	+	4.76859e7i	−0.614902	+	0.216411i
$605$			1.82661e8i			0.824858i
$606$		0			0
$607$			2.43622e8i			1.08931i	0.838661	+	0.544654i	$0.183339\pi$
$607$			2.43622e8i			1.08931i	−0.838661	+	0.544654i	$0.816661\pi$
$608$	−3.36685e6	−	5.54758e7i	−0.0149800	−	0.246827i
$609$		0			0
$610$	−8.88028e7	+	1.25396e8i	−0.391235	+	0.552450i
$611$	9.99618e7			0.438238
$612$		0			0
$613$		−	3.31194e8i		−	1.43781i	−0.695109	−	0.718905i	$-0.744644\pi$
$613$		−	3.31194e8i		−	1.43781i	0.695109	−	0.718905i	$-0.255356\pi$
$614$	1.59634e8	−	2.25414e8i	0.689635	−	0.973813i
$615$		0			0
$616$	−2.55175e6	+	8.94839e6i	−0.0109168	+	0.0382827i
$617$	−1.49869e8			−0.638054			−0.319027	−	0.947746i	$-0.603356\pi$
$617$	−1.49869e8			−0.638054			−0.319027	+	0.947746i	$0.603356\pi$
$618$		0			0
$619$	8.10701e7			0.341813			0.170907	−	0.985287i	$-0.445330\pi$
$619$	8.10701e7			0.341813			0.170907	+	0.985287i	$0.445330\pi$
$620$	−3.19387e7	−	9.07495e7i	−0.134012	−	0.380776i
$621$		0			0
$622$	1.01779e8	+	7.20782e7i	0.422949	+	0.299525i
$623$			8.54977e6i			0.0353582i
$624$		0			0
$625$	−4.28287e7			−0.175426
$626$	9.86985e6	−	1.39369e7i	0.0402335	−	0.0568125i
$627$		0			0
$628$	2.95249e8	−	1.03911e8i	1.19209	−	0.419550i
$629$			1.48879e8i			0.598250i
$630$		0			0
$631$		−	2.70423e8i		−	1.07635i	−0.842832	−	0.538177i	$-0.819113\pi$
$631$		−	2.70423e8i		−	1.07635i	0.842832	−	0.538177i	$-0.180887\pi$
$632$	−4.80209e7	+	1.68398e8i	−0.190230	+	0.667092i
$633$		0			0
$634$	2.71227e8	+	1.92078e8i	1.06430	+	0.753718i
$635$	4.84163e8			1.89091
$636$		0			0
$637$			1.81864e8i			0.703604i
$638$	1.00084e8	+	7.08776e7i	0.385392	+	0.272927i
$639$		0			0
$640$	−1.62210e8	−	3.84711e8i	−0.618782	−	1.46756i
$641$	−7.98693e7			−0.303254			−0.151627	−	0.988438i	$-0.548451\pi$
$641$	−7.98693e7			−0.303254			−0.151627	+	0.988438i	$0.548451\pi$
$642$		0			0
$643$	3.07378e8			1.15622			0.578110	−	0.815959i	$-0.303791\pi$
$643$	3.07378e8			1.15622			0.578110	+	0.815959i	$0.303791\pi$
$644$	8.02679e6	+	2.28070e7i	0.0300527	+	0.0853907i
$645$		0			0
$646$	4.03135e7	−	5.69254e7i	0.149538	−	0.211158i
$647$			3.33867e7i			0.123271i	0.998099	+	0.0616354i	$0.0196316\pi$
$647$			3.33867e7i			0.123271i	−0.998099	+	0.0616354i	$0.980368\pi$
$648$		0			0
$649$	−1.31423e8			−0.480771
$650$	−2.43107e8	−	1.72164e8i	−0.885234	−	0.626906i
$651$		0			0
$652$	−3.88791e7	−	1.10469e8i	−0.140273	−	0.398565i
$653$		−	3.92550e8i		−	1.40979i	−0.709309	−	0.704897i	$-0.750993\pi$
$653$		−	3.92550e8i		−	1.40979i	0.709309	−	0.704897i	$-0.249007\pi$
$654$		0			0
$655$			5.31525e8i			1.89147i
$656$	−1.66398e8	+	1.33685e8i	−0.589437	+	0.473554i
$657$		0			0
$658$	−5.86033e6	+	8.27519e6i	−0.0205705	+	0.0290469i
$659$	−4.88173e8			−1.70576			−0.852879	−	0.522109i	$-0.825145\pi$
$659$	−4.88173e8			−1.70576			−0.852879	+	0.522109i	$0.825145\pi$
$660$		0			0
$661$			2.56127e8i			0.886853i	0.896311	+	0.443427i	$0.146237\pi$
$661$			2.56127e8i			0.886853i	−0.896311	+	0.443427i	$0.853763\pi$
$662$	8.27589e7	−	1.16861e8i	0.285260	−	0.402807i
$663$		0			0
$664$	−4.57688e8	−	1.30516e8i	−1.56338	−	0.445819i
$665$	6.64045e6			0.0225805
$666$		0			0
$667$	3.18665e8			1.07388
$668$	−2.38027e8	+	8.37723e7i	−0.798542	+	0.281042i
$669$		0			0
$670$	9.78208e7	+	6.92748e7i	0.325242	+	0.230330i
$671$		−	8.91589e7i		−	0.295119i
$672$		0			0
$673$	2.16653e8			0.710754			0.355377	−	0.934723i	$-0.384352\pi$
$673$	2.16653e8			0.710754			0.355377	+	0.934723i	$0.384352\pi$
$674$	8.61096e7	−	1.21593e8i	0.281237	−	0.397126i
$675$		0			0
$676$	−5.14488e7	−	1.46185e8i	−0.166546	−	0.473218i
$677$			1.50931e8i			0.486420i	0.969974	+	0.243210i	$0.0782005\pi$
$677$			1.50931e8i			0.486420i	−0.969974	+	0.243210i	$0.921800\pi$
$678$		0			0
$679$		−	1.26512e7i		−	0.0404130i
$680$	1.43699e8	−	5.03918e8i	0.457010	−	1.60263i
$681$		0			0
$682$	4.55567e7	+	3.22623e7i	0.143615	+	0.101705i
$683$	3.69947e8			1.16112			0.580561	−	0.814217i	$-0.302833\pi$
$683$	3.69947e8			1.16112			0.580561	+	0.814217i	$0.302833\pi$
$684$		0			0
$685$		−	7.96746e8i		−	2.47884i
$686$	−3.01603e7	−	2.13590e7i	−0.0934251	−	0.0661619i
$687$		0			0
$688$	−1.88281e7	+	1.51265e7i	−0.0578151	+	0.0464487i
$689$	3.06129e8			0.935938
$690$		0			0
$691$	−2.15167e7			−0.0652141			−0.0326070	−	0.999468i	$-0.510381\pi$
$691$	−2.15167e7			−0.0652141			−0.0326070	+	0.999468i	$0.510381\pi$
$692$	1.23860e7	−	4.35917e6i	0.0373776	−	0.0131548i
$693$		0			0
$694$	−1.83292e8	+	2.58821e8i	−0.548360	+	0.774322i
$695$		−	3.77109e8i		−	1.12334i
$696$		0			0
$697$	−2.67893e8			−0.791156
$698$	4.46831e8	+	3.16437e8i	1.31394	+	0.930511i
$699$		0			0
$700$	2.85047e7	−	1.00321e7i	0.0831040	−	0.0292480i
$701$		−	2.95578e8i		−	0.858060i	−0.903290	−	0.429030i	$-0.858855\pi$
$701$		−	2.95578e8i		−	0.858060i	0.903290	−	0.429030i	$-0.141145\pi$
$702$		0			0
$703$			4.91200e7i			0.141381i
$704$	2.05824e8	+	1.27777e8i	0.589899	+	0.366214i
$705$		0			0
$706$	1.39446e8	−	1.96907e8i	0.396270	−	0.559561i
$707$	1.68803e7			0.0477665
$708$		0			0
$709$		−	3.43066e8i		−	0.962584i	−0.876560	−	0.481292i	$-0.840168\pi$
$709$		−	3.43066e8i		−	0.962584i	0.876560	−	0.481292i	$-0.159832\pi$
$710$	−5.11889e8	+	7.22822e8i	−1.43021	+	2.01956i
$711$		0			0
$712$	2.14062e8	+	6.10426e7i	0.593062	+	0.169119i
$713$	1.45051e8			0.400177
$714$		0			0
$715$	2.85344e8			0.780641
$716$	−7.13912e7	−	2.02848e8i	−0.194494	−	0.552627i
$717$		0			0
$718$	4.00828e8	+	2.83858e8i	1.08289	+	0.766882i
$719$			2.69203e8i			0.724257i	0.932128	+	0.362129i	$0.117950\pi$
$719$			2.69203e8i			0.724257i	−0.932128	+	0.362129i	$0.882050\pi$
$720$		0			0
$721$	−4.19629e7			−0.111959
$722$	−2.04215e8	+	2.88365e8i	−0.542595	+	0.766181i
$723$		0			0
$724$	−1.44373e8	+	5.08111e7i	−0.380425	+	0.133888i
$725$		−	3.98274e8i		−	1.04513i
$726$		0			0
$727$			1.90694e8i			0.496287i	0.968723	+	0.248144i	$0.0798205\pi$
$727$			1.90694e8i			0.496287i	−0.968723	+	0.248144i	$0.920180\pi$
$728$	−1.50172e7	−	4.28235e6i	−0.0389220	−	0.0110991i
$729$		0			0
$730$	−3.71618e8	−	2.63173e8i	−0.955275	−	0.676508i
$731$	−3.03123e7			−0.0776008
$732$		0			0
$733$			4.68798e8i			1.19035i	0.803597	+	0.595174i	$0.202917\pi$
$733$			4.68798e8i			1.19035i	−0.803597	+	0.595174i	$0.797083\pi$
$734$	−2.72689e8	−	1.93113e8i	−0.689571	−	0.488341i
$735$		0			0
$736$	6.28332e8	−	3.81337e7i	1.57600	−	0.0956478i
$737$	−6.95525e7			−0.173744
$738$		0			0
$739$	−6.73855e8			−1.66968			−0.834840	−	0.550493i	$-0.814440\pi$
$739$	−6.73855e8			−1.66968			−0.834840	+	0.550493i	$0.814440\pi$
$740$	1.22501e8	+	3.48070e8i	0.302305	+	0.858956i
$741$		0			0
$742$	−1.79470e7	+	2.53424e7i	−0.0439320	+	0.0620350i
$743$			7.42053e7i			0.180913i	0.995900	+	0.0904563i	$0.0288325\pi$
$743$			7.42053e7i			0.180913i	−0.995900	+	0.0904563i	$0.971167\pi$
$744$		0			0
$745$	6.09983e8			1.47519
$746$	3.66586e8	+	2.59609e8i	0.882997	+	0.625321i
$747$		0			0
$748$	1.00941e8	+	2.86811e8i	0.241193	+	0.685316i
$749$			3.56560e7i			0.0848568i
$750$		0			0
$751$		−	9.05182e7i		−	0.213706i	−0.994275	−	0.106853i	$-0.965923\pi$
$751$		−	9.05182e7i		−	0.213706i	0.994275	−	0.106853i	$-0.0340774\pi$
$752$	1.65347e8	+	2.05808e8i	0.388814	+	0.483960i
$753$		0			0
$754$	−1.18947e8	+	1.67961e8i	−0.277485	+	0.391828i
$755$	−4.46819e8			−1.03822
$756$		0			0
$757$		−	2.19809e8i		−	0.506709i	−0.967374	−	0.253354i	$-0.918466\pi$
$757$		−	2.19809e8i		−	0.506709i	0.967374	−	0.253354i	$-0.0815339\pi$
$758$	−9.08439e7	+	1.28278e8i	−0.208588	+	0.294540i
$759$		0			0
$760$	4.74106e7	−	1.66258e8i	0.108003	−	0.378741i
$761$	−8.05220e7			−0.182709			−0.0913547	−	0.995818i	$-0.529120\pi$
$761$	−8.05220e7			−0.182709			−0.0913547	+	0.995818i	$0.529120\pi$
$762$		0			0
$763$	2.81264e7			0.0633200
$764$	−1.22214e8	+	4.30126e7i	−0.274058	+	0.0964530i
$765$		0			0
$766$	−2.52418e8	−	1.78758e8i	−0.561609	−	0.397721i
$767$		−	2.20555e8i		−	0.488800i
$768$		0			0
$769$	−8.94416e8			−1.96680			−0.983400	−	0.181449i	$-0.941921\pi$
$769$	−8.94416e8			−1.96680			−0.983400	+	0.181449i	$0.941921\pi$
$770$	−1.67285e7	+	2.36218e7i	−0.0366425	+	0.0517417i
$771$		0			0
$772$	1.68384e8	+	4.78440e8i	0.365973	+	1.03986i
$773$		−	7.83108e8i		−	1.69544i	−0.530442	−	0.847721i	$-0.677974\pi$
$773$		−	7.83108e8i		−	1.69544i	0.530442	−	0.847721i	$-0.322026\pi$
$774$		0			0
$775$		−	1.81288e8i		−	0.389461i
$776$	−3.16750e8	−	9.03252e7i	−0.677846	−	0.193296i
$777$		0			0
$778$	−1.92540e7	−	1.36353e7i	−0.0408868	−	0.0289552i
$779$	−8.83861e7			−0.186970
$780$		0			0
$781$		−	5.13941e8i		−	1.07885i
$782$	6.44749e8	+	4.56599e8i	1.34825	+	0.954805i
$783$		0			0
$784$	−3.74434e8	+	3.00821e8i	−0.777011	+	0.624252i
$785$	9.73650e8			2.01277
$786$		0			0
$787$	4.40033e7			0.0902737			0.0451368	−	0.998981i	$-0.485628\pi$
$787$	4.40033e7			0.0902737			0.0451368	+	0.998981i	$0.485628\pi$
$788$	−2.49200e8	+	8.77046e7i	−0.509296	+	0.179244i
$789$		0			0
$790$	−3.14811e8	+	4.44535e8i	−0.638511	+	0.901622i
$791$			1.23573e7i			0.0249687i
$792$		0			0
$793$	1.49627e8			0.300047
$794$	−4.49281e8	−	3.18172e8i	−0.897546	−	0.635625i
$795$		0			0
$796$	−7.13552e8	+	2.51130e8i	−1.41477	+	0.497920i
$797$			9.71867e8i			1.91969i	0.280526	+	0.959846i	$0.409491\pi$
$797$			9.71867e8i			1.91969i	−0.280526	+	0.959846i	$0.590509\pi$
$798$		0			0
$799$			3.31341e8i			0.649583i
$800$	−4.76603e7	−	7.85303e8i	−0.0930865	−	1.53379i
$801$		0			0
$802$	−1.58253e8	+	2.23464e8i	−0.306781	+	0.433196i
$803$	2.64228e8			0.510308
$804$		0			0
$805$			7.52112e7i			0.144177i
$806$	−5.41428e7	+	7.64534e7i	−0.103404	+	0.146013i
$807$		0			0
$808$	1.20520e8	−	4.22636e8i	0.228468	−	0.801185i
$809$	−9.68480e8			−1.82913			−0.914566	−	0.404436i	$-0.867468\pi$
$809$	−9.68480e8			−1.82913			−0.914566	+	0.404436i	$0.867468\pi$
$810$		0			0
$811$	6.66747e8			1.24997			0.624984	−	0.780638i	$-0.285106\pi$
$811$	6.66747e8			1.24997			0.624984	+	0.780638i	$0.285106\pi$
$812$	−6.93108e6	−	1.96937e7i	−0.0129459	−	0.0367840i
$813$		0			0
$814$	−1.74733e8	−	1.23742e8i	−0.323967	−	0.229427i
$815$		−	3.64298e8i		−	0.672952i
$816$		0			0
$817$	−1.00010e7			−0.0183390
$818$	3.43936e8	−	4.85662e8i	0.628374	−	0.887307i
$819$		0			0
$820$	−6.26314e8	+	2.20427e8i	−1.13593	+	0.399783i
$821$			1.01581e9i			1.83563i	0.397009	+	0.917815i	$0.370048\pi$
$821$			1.01581e9i			1.83563i	−0.397009	+	0.917815i	$0.629952\pi$
$822$		0			0
$823$		−	9.24417e8i		−	1.65832i	−0.559011	−	0.829160i	$-0.688819\pi$
$823$		−	9.24417e8i		−	1.65832i	0.559011	−	0.829160i	$-0.311181\pi$
$824$	−2.99601e8	+	1.05063e9i	−0.535503	+	1.87789i
$825$		0			0
$826$	1.82583e7	+	1.29302e7i	0.0323982	+	0.0229438i
$827$	5.14562e8			0.909748			0.454874	−	0.890556i	$-0.349684\pi$
$827$	5.14562e8			0.909748			0.454874	+	0.890556i	$0.349684\pi$
$828$		0			0
$829$			7.43047e8i			1.30423i	0.758122	+	0.652113i	$0.226117\pi$
$829$			7.43047e8i			1.30423i	−0.758122	+	0.652113i	$0.773883\pi$
$830$	−1.20820e9	−	8.55623e8i	−2.11302	−	1.49640i
$831$		0			0
$832$	−2.14436e8	+	3.45414e8i	−0.372330	+	0.599750i
$833$	−6.02820e8			−1.04292
$834$		0			0
$835$	−7.84949e8			−1.34829
$836$	3.33037e7	+	9.46278e7i	0.0569999	+	0.161957i
$837$		0			0
$838$	1.74860e8	−	2.46914e8i	0.297138	−	0.419579i
$839$		−	9.70115e8i		−	1.64262i	−0.570482	−	0.821310i	$-0.693244\pi$
$839$		−	9.70115e8i		−	1.64262i	0.570482	−	0.821310i	$-0.306756\pi$
$840$		0			0
$841$	3.19658e8			0.537400
$842$	4.05907e8	+	2.87456e8i	0.679971	+	0.481543i
$843$		0			0
$844$	−2.53736e8	−	7.20956e8i	−0.422041	−	1.19917i
$845$		−	4.82077e8i		−	0.798998i
$846$		0			0
$847$			1.80433e7i			0.0296938i
$848$	5.06368e8	+	6.30280e8i	0.830383	+	1.03358i
$849$		0			0
$850$	5.70667e8	−	8.05822e8i	0.929237	−	1.31215i
$851$	−5.56344e8			−0.902723
$852$		0			0
$853$			4.99318e8i			0.804507i	0.915528	+	0.402254i	$0.131773\pi$
$853$			4.99318e8i			0.804507i	−0.915528	+	0.402254i	$0.868227\pi$
$854$	−8.77197e6	+	1.23866e7i	−0.0140839	+	0.0198875i
$855$		0			0
$856$	8.92725e8	+	2.54572e8i	1.42330	+	0.405872i
$857$	9.80356e8			1.55755			0.778774	−	0.627305i	$-0.215842\pi$
$857$	9.80356e8			1.55755			0.778774	+	0.627305i	$0.215842\pi$
$858$		0			0
$859$	1.39198e8			0.219610			0.109805	−	0.993953i	$-0.464977\pi$
$859$	1.39198e8			0.219610			0.109805	+	0.993953i	$0.464977\pi$
$860$	−7.08680e7	+	2.49416e7i	−0.111418	+	0.0392128i
$861$		0			0
$862$	−6.56531e8	−	4.64943e8i	−1.02502	−	0.725902i
$863$			4.80087e7i			0.0746943i	0.999302	+	0.0373471i	$0.0118907\pi$
$863$			4.80087e7i			0.0746943i	−0.999302	+	0.0373471i	$0.988109\pi$
$864$		0			0
$865$	4.08455e7			0.0631097
$866$	4.97844e8	−	7.02990e8i	0.766548	−	1.08242i
$867$		0			0
$868$	−3.15492e6	−	8.96426e6i	−0.00482424	−	0.0137074i
$869$		−	3.16073e8i		−	0.481646i
$870$		0			0
$871$		−	1.16723e8i		−	0.176646i
$872$	2.00814e8	−	7.04207e8i	0.302861	−	1.06206i
$873$		0			0
$874$	2.12723e8	+	1.50646e8i	0.318625	+	0.225644i
$875$	3.28269e7			0.0490010
$876$		0			0
$877$		−	1.09245e8i		−	0.161959i	−0.996716	−	0.0809793i	$-0.974195\pi$
$877$		−	1.09245e8i		−	0.161959i	0.996716	−	0.0809793i	$-0.0258048\pi$
$878$	−4.47733e8	−	3.17076e8i	−0.661509	−	0.468468i
$879$		0			0
$880$	4.71988e8	+	5.87487e8i	0.692600	+	0.862085i
$881$	−5.54386e8			−0.810746			−0.405373	−	0.914151i	$-0.632858\pi$
$881$	−5.54386e8			−0.810746			−0.405373	+	0.914151i	$0.632858\pi$
$882$		0			0
$883$	−8.44750e8			−1.22700			−0.613502	−	0.789693i	$-0.710240\pi$
$883$	−8.44750e8			−1.22700			−0.613502	+	0.789693i	$0.710240\pi$
$884$	−4.81327e8	+	1.69400e8i	−0.696761	+	0.245221i
$885$		0			0
$886$	4.09094e8	−	5.77669e8i	0.588196	−	0.830573i
$887$			7.33580e8i			1.05118i	0.850738	+	0.525589i	$0.176155\pi$
$887$			7.33580e8i			1.05118i	−0.850738	+	0.525589i	$0.823845\pi$
$888$		0			0
$889$	4.78257e7			0.0680701
$890$	5.65078e8	+	4.00178e8i	0.801565	+	0.567653i
$891$		0			0
$892$	1.27337e9	−	4.48154e8i	1.79415	−	0.631441i
$893$			1.09320e8i			0.153512i
$894$		0			0
$895$		−	6.68937e8i		−	0.933075i
$896$	−1.60231e7	−	3.80019e7i	−0.0222753	−	0.0528301i
$897$		0			0
$898$	−1.98233e8	+	2.79918e8i	−0.273745	+	0.386547i
$899$	−1.25251e8			−0.172386
$900$		0			0
$901$			1.01472e9i			1.38730i
$902$	2.22661e8	−	3.14412e8i	0.303406	−	0.428430i
$903$		0			0
$904$	3.09393e8	+	8.82274e7i	0.418799	+	0.119426i
$905$	−4.76101e8			−0.642323
$906$		0			0
$907$	1.71358e8			0.229658			0.114829	−	0.993385i	$-0.463368\pi$
$907$	1.71358e8			0.229658			0.114829	+	0.993385i	$0.463368\pi$
$908$	5.81440e7	+	1.65208e8i	0.0776690	+	0.220686i
$909$		0			0
$910$	−3.96422e7	−	2.80739e7i	−0.0526058	−	0.0372544i
$911$			7.97986e8i			1.05546i	0.849413	+	0.527728i	$0.176956\pi$
$911$			7.97986e8i			1.05546i	−0.849413	+	0.527728i	$0.823044\pi$
$912$		0			0
$913$	8.59053e8			1.12878
$914$	−3.24420e8	+	4.58104e8i	−0.424883	+	0.599965i
$915$		0			0
$916$	4.36946e8	−	1.53781e8i	0.568514	−	0.200085i
$917$			5.25042e7i			0.0680905i
$918$		0			0
$919$			7.66471e7i			0.0987527i	0.998780	+	0.0493764i	$0.0157234\pi$
$919$			7.66471e7i			0.0987527i	−0.998780	+	0.0493764i	$0.984277\pi$
$920$	1.88308e9	+	5.36983e8i	2.41827	+	0.689600i
$921$		0			0
$922$	3.51115e8	+	2.48653e8i	0.447978	+	0.317249i
$923$	8.62498e8			1.09686
$924$		0			0
$925$			6.95331e8i			0.878549i
$926$	−2.84689e8	−	2.01611e8i	−0.358539	−	0.253911i
$927$		0			0
$928$	−5.42561e8	+	3.29282e7i	−0.678898	+	0.0412026i
$929$	5.09008e8			0.634860			0.317430	−	0.948282i	$-0.397180\pi$
$929$	5.09008e8			0.634860			0.317430	+	0.948282i	$0.397180\pi$
$930$		0			0
$931$	−1.98889e8			−0.246469
$932$	−3.48360e8	−	9.89817e8i	−0.430310	−	1.22266i
$933$		0			0
$934$	1.43082e8	−	2.02042e8i	0.175608	−	0.247971i
$935$			9.45823e8i			1.15711i
$936$		0			0
$937$	8.59374e8			1.04463			0.522316	−	0.852752i	$-0.325068\pi$
$937$	8.59374e8			1.04463			0.522316	+	0.852752i	$0.325068\pi$
$938$	9.66277e6	+	6.84299e6i	0.0117083	+	0.00829158i
$939$		0			0
$940$	2.72634e8	+	7.74651e8i	0.328243	+	0.932658i
$941$			1.07856e8i			0.129442i	0.997903	+	0.0647208i	$0.0206157\pi$
$941$			1.07856e8i			0.129442i	−0.997903	+	0.0647208i	$0.979384\pi$
$942$		0			0
$943$		−	1.00108e9i		−	1.19381i
$944$	4.54094e8	−	3.64820e8i	0.539796	−	0.433673i
$945$		0			0
$946$	2.51943e7	−	3.55760e7i	0.0297597	−	0.0420227i
$947$	−1.41217e9			−1.66279			−0.831396	−	0.555680i	$-0.812458\pi$
$947$	−1.41217e9			−1.66279			−0.831396	+	0.555680i	$0.812458\pi$
$948$		0			0
$949$			4.43429e8i			0.518830i
$950$	1.88281e8	−	2.65866e8i	0.219602	−	0.310093i
$951$		0			0
$952$	1.41946e7	−	4.97772e7i	0.0164517	−	0.0576925i
$953$	1.38550e9			1.60077			0.800385	−	0.599486i	$-0.204628\pi$
$953$	1.38550e9			1.60077			0.800385	+	0.599486i	$0.204628\pi$
$954$		0			0
$955$	−4.03029e8			−0.462729
$956$	1.05035e9	−	3.69664e8i	1.20215	−	0.423091i
$957$		0			0
$958$	−6.34729e8	−	4.49503e8i	−0.721925	−	0.511253i
$959$		−	7.87028e7i		−	0.0892348i
$960$		0			0
$961$	8.30491e8			0.935761
$962$	2.07665e8	−	2.93237e8i	0.233259	−	0.329377i
$963$		0			0
$964$	−2.84808e8	−	8.09242e8i	−0.317922	−	0.903332i
$965$			1.57777e9i			1.75574i
$966$		0			0
$967$			1.22400e9i			1.35364i	0.736148	+	0.676821i	$0.236643\pi$
$967$			1.22400e9i			1.35364i	−0.736148	+	0.676821i	$0.763357\pi$
$968$	4.51753e8	+	1.28823e8i	0.498052	+	0.142026i
$969$		0			0
$970$	−8.36151e8	−	5.92146e8i	−0.916156	−	0.648804i
$971$	8.21087e8			0.896874			0.448437	−	0.893814i	$-0.351981\pi$
$971$	8.21087e8			0.896874			0.448437	+	0.893814i	$0.351981\pi$
$972$		0			0
$973$		−	3.72510e7i		−	0.0404389i
$974$	−5.89169e8	−	4.17238e8i	−0.637622	−	0.451552i
$975$		0			0
$976$	2.47497e8	+	3.08062e8i	0.266208	+	0.331351i
$977$	3.89473e8			0.417632			0.208816	−	0.977955i	$-0.433039\pi$
$977$	3.89473e8			0.417632			0.208816	+	0.977955i	$0.433039\pi$
$978$		0			0
$979$	−4.01782e8			−0.428196
$980$	−1.40935e9	+	4.96012e8i	−1.49741	+	0.527004i
$981$		0			0
$982$	4.66813e8	−	6.59172e8i	0.492956	−	0.696088i
$983$		−	1.66072e9i		−	1.74838i	−0.485584	−	0.874190i	$-0.661393\pi$
$983$		−	1.66072e9i		−	1.74838i	0.485584	−	0.874190i	$-0.338607\pi$
$984$		0			0
$985$	−8.21794e8			−0.859913
$986$	−5.56737e8	−	3.94271e8i	−0.580791	−	0.411305i
$987$		0			0
$988$	−1.58805e8	+	5.58904e7i	−0.164662	+	0.0579517i
$989$		−	1.13273e8i		−	0.117095i
$990$		0			0
$991$			3.03432e8i			0.311775i	0.987775	+	0.155887i	$0.0498237\pi$
$991$			3.03432e8i			0.311775i	−0.987775	+	0.155887i	$0.950176\pi$
$992$	−2.46965e8	+	1.49884e7i	−0.252988	+	0.0153539i
$993$		0			0
$994$	−5.05645e7	+	7.14006e7i	−0.0514857	+	0.0727014i
$995$	−2.35310e9			−2.38875
$996$		0			0
$997$		−	1.20614e9i		−	1.21706i	−0.793532	−	0.608528i	$-0.791760\pi$
$997$		−	1.20614e9i		−	1.21706i	0.793532	−	0.608528i	$-0.208240\pi$
$998$	−6.83438e8	+	9.65062e8i	−0.687555	+	0.970876i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.b.b.19.3		4
3.2	odd	2		8.7.d.b.3.2	yes	4
4.3	odd	2		288.7.b.b.271.1		4
8.3	odd	2	inner	72.7.b.b.19.4		4
8.5	even	2		288.7.b.b.271.4		4
12.11	even	2		32.7.d.b.15.4		4
24.5	odd	2		32.7.d.b.15.3		4
24.11	even	2		8.7.d.b.3.1	✓	4
48.5	odd	4		256.7.c.l.255.7		8
48.11	even	4		256.7.c.l.255.1		8
48.29	odd	4		256.7.c.l.255.2		8
48.35	even	4		256.7.c.l.255.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.7.d.b.3.1	✓	4	24.11	even	2
8.7.d.b.3.2	yes	4	3.2	odd	2
32.7.d.b.15.3		4	24.5	odd	2
32.7.d.b.15.4		4	12.11	even	2
72.7.b.b.19.3		4	1.1	even	1	trivial
72.7.b.b.19.4		4	8.3	odd	2	inner
256.7.c.l.255.1		8	48.11	even	4
256.7.c.l.255.2		8	48.29	odd	4
256.7.c.l.255.7		8	48.5	odd	4
256.7.c.l.255.8		8	48.35	even	4
288.7.b.b.271.1		4	4.3	odd	2
288.7.b.b.271.4		4	8.5	even	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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	72.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(4.62348 - 6.52867i) q^{2} +(-21.2470 - 60.3702i) q^{4} -199.084i q^{5} -19.6656i q^{7} +(-492.372 - 140.406i) q^{8} +O(q^{10})\)	\(q+(4.62348 - 6.52867i) q^{2} +(-21.2470 - 60.3702i) q^{4} -199.084i q^{5} -19.6656i q^{7} +(-492.372 - 140.406i) q^{8} +(-1299.76 - 920.462i) q^{10} +924.152 q^{11} +1550.92i q^{13} +(-128.390 - 90.9235i) q^{14} +(-3193.13 + 2565.37i) q^{16} -5140.78 q^{17} -1696.10 q^{19} +(-12018.8 + 4229.94i) q^{20} +(4272.80 - 6033.48i) q^{22} -19210.4i q^{23} -24009.6 q^{25} +(10125.4 + 7170.62i) q^{26} +(-1187.22 + 417.835i) q^{28} +16588.1i q^{29} +7550.64i q^{31} +(1985.05 + 32707.8i) q^{32} +(-23768.3 + 33562.4i) q^{34} -3915.12 q^{35} -28960.5i q^{37} +(-7841.89 + 11073.3i) q^{38} +(-27952.7 + 98023.6i) q^{40} +52111.3 q^{41} +5896.43 q^{43} +(-19635.4 - 55791.3i) q^{44} +(-125419. - 88819.0i) q^{46} -64453.4i q^{47} +117262. q^{49} +(-111008. + 156751. i) q^{50} +(93629.2 - 32952.2i) q^{52} -197386. i q^{53} -183984. i q^{55} +(-2761.17 + 9682.80i) q^{56} +(108298. + 76694.7i) q^{58} -142210. q^{59} -96476.4i q^{61} +(49295.6 + 34910.2i) q^{62} +(222716. + 138264. i) q^{64} +308763. q^{65} -75260.9 q^{67} +(109226. + 310350. i) q^{68} +(-18101.5 + 25560.5i) q^{70} -556121. i q^{71} +285914. q^{73} +(-189073. - 133898. i) q^{74} +(36037.0 + 102394. i) q^{76} -18174.0i q^{77} -342014. i q^{79} +(510725. + 635703. i) q^{80} +(240935. - 340217. i) q^{82} +929558. q^{83} +1.02345e6i q^{85} +(27262.0 - 38495.9i) q^{86} +(-455027. - 129757. i) q^{88} -434757. q^{89} +30499.7 q^{91} +(-1.15974e6 + 408163. i) q^{92} +(-420795. - 297999. i) q^{94} +337668. i q^{95} +643314. q^{97} +(542159. - 765566. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 44 q^{4} - 248 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 44 * q^4 - 248 * q^8	\( 4 q - 2 q^{2} - 44 q^{4} - 248 q^{8} - 1920 q^{10} - 976 q^{11} - 5760 q^{14} - 14576 q^{16} - 4168 q^{17} - 1456 q^{19} - 31680 q^{20} + 24428 q^{22} - 23900 q^{25} + 59520 q^{26} + 59520 q^{28} + 48928 q^{32} - 81916 q^{34} + 49920 q^{35} - 26572 q^{38} - 13440 q^{40} + 117944 q^{41} + 197456 q^{43} - 37144 q^{44} - 213120 q^{46} + 2116 q^{49} - 357650 q^{50} - 254400 q^{52} - 349440 q^{56} + 516480 q^{58} - 542032 q^{59} + 407040 q^{62} + 463936 q^{64} + 205440 q^{65} - 790192 q^{67} + 213848 q^{68} - 360960 q^{70} + 443912 q^{73} + 32640 q^{74} + 70616 q^{76} + 1032960 q^{80} + 404708 q^{82} + 3465008 q^{83} - 989548 q^{86} - 1950448 q^{88} - 761224 q^{89} + 3398400 q^{91} - 2743680 q^{92} + 971520 q^{94} - 926776 q^{97} + 2391262 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 44 * q^4 - 248 * q^8 - 1920 * q^10 - 976 * q^11 - 5760 * q^14 - 14576 * q^16 - 4168 * q^17 - 1456 * q^19 - 31680 * q^20 + 24428 * q^22 - 23900 * q^25 + 59520 * q^26 + 59520 * q^28 + 48928 * q^32 - 81916 * q^34 + 49920 * q^35 - 26572 * q^38 - 13440 * q^40 + 117944 * q^41 + 197456 * q^43 - 37144 * q^44 - 213120 * q^46 + 2116 * q^49 - 357650 * q^50 - 254400 * q^52 - 349440 * q^56 + 516480 * q^58 - 542032 * q^59 + 407040 * q^62 + 463936 * q^64 + 205440 * q^65 - 790192 * q^67 + 213848 * q^68 - 360960 * q^70 + 443912 * q^73 + 32640 * q^74 + 70616 * q^76 + 1032960 * q^80 + 404708 * q^82 + 3465008 * q^83 - 989548 * q^86 - 1950448 * q^88 - 761224 * q^89 + 3398400 * q^91 - 2743680 * q^92 + 971520 * q^94 - 926776 * q^97 + 2391262 * q^98

Introduction

L-functions

Modular forms

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Database

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