LMFDB - Embedded newform 72.7.b.b.19.4

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.62348 + 6.52867i) q^{2} +(-21.2470 + 60.3702i) q^{4} +199.084i q^{5} +19.6656i q^{7} +(-492.372 + 140.406i) q^{8} +O(q^{10})$	\(q+(4.62348 + 6.52867i) q^{2} +(-21.2470 + 60.3702i) q^{4} +199.084i q^{5} +19.6656i q^{7} +(-492.372 + 140.406i) q^{8} +(-1299.76 + 920.462i) q^{10} +924.152 q^{11} -1550.92i q^{13} +(-128.390 + 90.9235i) q^{14} +(-3193.13 - 2565.37i) q^{16} -5140.78 q^{17} -1696.10 q^{19} +(-12018.8 - 4229.94i) q^{20} +(4272.80 + 6033.48i) q^{22} +19210.4i q^{23} -24009.6 q^{25} +(10125.4 - 7170.62i) q^{26} +(-1187.22 - 417.835i) q^{28} -16588.1i q^{29} -7550.64i q^{31} +(1985.05 - 32707.8i) q^{32} +(-23768.3 - 33562.4i) q^{34} -3915.12 q^{35} +28960.5i q^{37} +(-7841.89 - 11073.3i) q^{38} +(-27952.7 - 98023.6i) q^{40} +52111.3 q^{41} +5896.43 q^{43} +(-19635.4 + 55791.3i) q^{44} +(-125419. + 88819.0i) q^{46} +64453.4i q^{47} +117262. q^{49} +(-111008. - 156751. i) q^{50} +(93629.2 + 32952.2i) q^{52} +197386. i q^{53} +183984. i q^{55} +(-2761.17 - 9682.80i) q^{56} +(108298. - 76694.7i) q^{58} -142210. q^{59} +96476.4i q^{61} +(49295.6 - 34910.2i) q^{62} +(222716. - 138264. i) q^{64} +308763. q^{65} -75260.9 q^{67} +(109226. - 310350. i) q^{68} +(-18101.5 - 25560.5i) q^{70} +556121. i q^{71} +285914. q^{73} +(-189073. + 133898. i) q^{74} +(36037.0 - 102394. i) q^{76} +18174.0i q^{77} +342014. i q^{79} +(510725. - 635703. i) q^{80} +(240935. + 340217. i) q^{82} +929558. q^{83} -1.02345e6i q^{85} +(27262.0 + 38495.9i) q^{86} +(-455027. + 129757. i) q^{88} -434757. q^{89} +30499.7 q^{91} +(-1.15974e6 - 408163. i) q^{92} +(-420795. + 297999. i) q^{94} -337668. i q^{95} +643314. q^{97} +(542159. + 765566. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.293232\pi$
$5$			199.084i			1.59268i	−0.604852	+	0.796338i	$0.706768\pi$
$6$		0			0
$7$			19.6656i			0.0573342i	0.999589	+	0.0286671i	$0.00912627\pi$
$7$			19.6656i			0.0573342i	−0.999589	+	0.0286671i	$0.990874\pi$
$8$	−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	$-0.885174\pi$
$13$		−	1550.92i		−	0.705925i	0.935638	−	0.352962i	$-0.114826\pi$
$14$	−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	$0.289633\pi$
$23$			19210.4i			1.57890i	−0.613817	+	0.789448i	$0.710367\pi$
$24$		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	$-0.889548\pi$
$29$		−	16588.1i		−	0.680147i	0.940399	−	0.340074i	$-0.110452\pi$
$30$		0			0
$31$		−	7550.64i		−	0.253454i	−0.991938	−	0.126727i	$-0.959553\pi$
$31$		−	7550.64i		−	0.253454i	0.991938	−	0.126727i	$-0.0404472\pi$
$32$	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	$0.0922830\pi$
$37$			28960.5i			0.571743i	−0.958268	+	0.285871i	$0.907717\pi$
$38$	−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	$0.100463\pi$
$47$			64453.4i			0.620801i	−0.950606	+	0.310400i	$0.899537\pi$
$48$		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	$0.230681\pi$
$53$			197386.i			1.32583i	−0.748694	+	0.662916i	$0.769319\pi$
$54$		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	$0.0681673\pi$
$61$			96476.4i			0.425042i	−0.977157	+	0.212521i	$0.931833\pi$
$62$	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	$0.283208\pi$
$71$			556121.i			1.55380i	−0.629625	+	0.776899i	$0.716792\pi$
$72$		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	$0.112746\pi$
$79$			342014.i			0.693686i	−0.937923	+	0.346843i	$0.887254\pi$
$80$	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	$-0.863235\pi$
$101$		−	858368.i		−	0.833123i	0.909107	−	0.416562i	$-0.136765\pi$
$102$		0			0
$103$			2.13382e6i			1.95275i	0.216089	+	0.976374i	$0.430670\pi$
$103$			2.13382e6i			1.95275i	−0.216089	+	0.976374i	$0.569330\pi$
$104$	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	$-0.813788\pi$
$109$		−	1.43023e6i		−	1.10440i	0.833711	−	0.552201i	$-0.186212\pi$
$110$	−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	$-0.797696\pi$
$127$		−	2.43195e6i		−	1.18725i	0.804741	−	0.593626i	$-0.202304\pi$
$128$	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	$-0.846731\pi$
$149$		−	3.06394e6i		−	0.926235i	0.886297	−	0.463118i	$-0.153269\pi$
$150$		0			0
$151$			2.24437e6i			0.651873i	0.945392	+	0.325936i	$0.105680\pi$
$151$			2.24437e6i			0.651873i	−0.945392	+	0.325936i	$0.894320\pi$
$152$	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	$-0.782282\pi$
$157$		−	4.89064e6i		−	1.26377i	0.775064	−	0.631883i	$-0.217718\pi$
$158$	−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	$0.139120\pi$
$167$			3.94279e6i			0.846554i	−0.906000	+	0.423277i	$0.860880\pi$
$168$		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	$-0.993693\pi$
$173$		−	205167.i		−	0.0396249i	0.999804	−	0.0198125i	$-0.00630692\pi$
$174$		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	$0.0646300\pi$
$181$			2.39145e6i			0.403298i	−0.979458	+	0.201649i	$0.935370\pi$
$182$	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	$0.0464043\pi$
$191$			2.02441e6i			0.290535i	−0.989392	+	0.145268i	$0.953596\pi$
$192$		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	$0.0870100\pi$
$197$			4.12787e6i			0.539917i	−0.962872	+	0.269959i	$0.912990\pi$
$198$		0			0
$199$			1.18196e7i			1.49983i	0.661532	+	0.749917i	$0.269907\pi$
$199$			1.18196e7i			1.49983i	−0.661532	+	0.749917i	$0.730093\pi$
$200$	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	$-0.600045\pi$
$223$		−	2.10926e7i		−	1.90202i	0.309153	−	0.951012i	$-0.399955\pi$
$224$	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	$-0.902563\pi$
$229$		−	7.23777e6i		−	0.602696i	0.953514	−	0.301348i	$-0.0974366\pi$
$230$	−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	$-0.780086\pi$
$239$		−	1.73985e7i		−	1.27443i	0.770685	−	0.637217i	$-0.219914\pi$
$240$		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	$0.119406\pi$
$263$			1.33303e7i			0.732778i	−0.930462	+	0.366389i	$0.880594\pi$
$264$		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	$0.0586712\pi$
$269$			7.13509e6i			0.366558i	−0.983061	+	0.183279i	$0.941329\pi$
$270$		0			0
$271$		−	6.93561e6i		−	0.348479i	−0.984703	−	0.174240i	$-0.944253\pi$
$271$		−	6.93561e6i		−	0.348479i	0.984703	−	0.174240i	$-0.0557467\pi$
$272$	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	$0.138629\pi$
$277$			1.79332e7i			0.843757i	−0.906652	+	0.421879i	$0.861371\pi$
$278$	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	$-0.784485\pi$
$293$		−	3.15178e7i		−	1.25301i	0.779419	−	0.626504i	$-0.215515\pi$
$294$		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	$-0.916563\pi$
$311$		−	1.55896e7i		−	0.518268i	0.965841	−	0.259134i	$-0.0834371\pi$
$312$		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	$-0.773897\pi$
$317$		−	4.15440e7i		−	1.30416i	0.758151	−	0.652079i	$-0.226103\pi$
$318$		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	$-0.702148\pi$
$349$		−	6.84414e7i		−	1.61006i	0.593232	−	0.805031i	$-0.297852\pi$
$350$	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	$-0.769084\pi$
$359$		−	6.13950e7i		−	1.32694i	0.748205	−	0.663468i	$-0.230916\pi$
$360$		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	$0.138843\pi$
$367$			4.17679e7i			0.844976i	−0.906368	+	0.422488i	$0.861157\pi$
$368$	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	$-0.818047\pi$
$373$		−	5.61502e7i		−	1.08199i	0.841025	−	0.540997i	$-0.181953\pi$
$374$	−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	$0.111812\pi$
$383$			3.86630e7i			0.688176i	−0.938937	+	0.344088i	$0.888188\pi$
$384$		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	$0.00797470\pi$
$389$			2.94915e6i			0.0501012i	−0.999686	+	0.0250506i	$0.992025\pi$
$390$		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	$0.185338\pi$
$397$			6.88167e7i			1.09982i	−0.835223	+	0.549911i	$0.814662\pi$
$398$	−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	$-0.863219\pi$
$421$		−	6.21731e7i		−	0.833213i	0.909087	−	0.416607i	$-0.136781\pi$
$422$	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	$0.216132\pi$
$431$			1.00561e8i			1.25603i	−0.778202	+	0.628014i	$0.783868\pi$
$432$		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	$0.132831\pi$
$439$			6.85796e7i			0.810590i	−0.914186	+	0.405295i	$0.867169\pi$
$440$	−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	$-0.911498\pi$
$461$		−	5.37805e7i		−	0.548937i	0.961596	−	0.274468i	$-0.0885018\pi$
$462$		0			0
$463$			4.36059e7i			0.439342i	0.975574	+	0.219671i	$0.0704984\pi$
$463$			4.36059e7i			0.439342i	−0.975574	+	0.219671i	$0.929502\pi$
$464$	−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	$0.145841\pi$
$479$			9.72219e7i			0.884622i	−0.896862	+	0.442311i	$0.854159\pi$
$480$		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	$0.127753\pi$
$487$			9.02434e7i			0.781320i	−0.920535	+	0.390660i	$0.872247\pi$
$488$	−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	$0.0424929\pi$
$503$			3.38774e7i			0.266199i	−0.991103	+	0.133099i	$0.957507\pi$
$504$		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	$-0.937313\pi$
$509$		−	5.16056e7i		−	0.391331i	0.980671	−	0.195665i	$-0.0626866\pi$
$510$		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	$-0.910975\pi$
$541$		−	8.74191e7i		−	0.552096i	0.961144	−	0.276048i	$-0.0890248\pi$
$542$	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	$0.0419573\pi$
$557$			4.54249e7i			0.262862i	−0.991325	+	0.131431i	$0.958043\pi$
$558$		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	$-0.857947\pi$
$599$		−	1.85523e8i		−	0.863212i	0.902062	−	0.431606i	$-0.142053\pi$
$600$		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	$-0.816661\pi$
$607$		−	2.43622e8i		−	1.08931i	0.838661	−	0.544654i	$-0.183339\pi$
$608$	−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	$0.255356\pi$
$613$			3.31194e8i			1.43781i	−0.695109	+	0.718905i	$0.744644\pi$
$614$	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	$0.180887\pi$
$631$			2.70423e8i			1.07635i	−0.842832	+	0.538177i	$0.819113\pi$
$632$	−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	$-0.980368\pi$
$647$		−	3.33867e7i		−	0.123271i	0.998099	−	0.0616354i	$-0.0196316\pi$
$648$		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	$0.249007\pi$
$653$			3.92550e8i			1.40979i	−0.709309	+	0.704897i	$0.750993\pi$
$654$		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	$-0.853763\pi$
$661$		−	2.56127e8i		−	0.886853i	0.896311	−	0.443427i	$-0.146237\pi$
$662$	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	$-0.921800\pi$
$677$		−	1.50931e8i		−	0.486420i	0.969974	−	0.243210i	$-0.0782005\pi$
$678$		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	$0.141145\pi$
$701$			2.95578e8i			0.858060i	−0.903290	+	0.429030i	$0.858855\pi$
$702$		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	$0.159832\pi$
$709$			3.43066e8i			0.962584i	−0.876560	+	0.481292i	$0.840168\pi$
$710$	−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	$-0.882050\pi$
$719$		−	2.69203e8i		−	0.724257i	0.932128	−	0.362129i	$-0.117950\pi$
$720$		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	$-0.920180\pi$
$727$		−	1.90694e8i		−	0.496287i	0.968723	−	0.248144i	$-0.0798205\pi$
$728$	−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	$-0.797083\pi$
$733$		−	4.68798e8i		−	1.19035i	0.803597	−	0.595174i	$-0.202917\pi$
$734$	−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	$-0.971167\pi$
$743$		−	7.42053e7i		−	0.180913i	0.995900	−	0.0904563i	$-0.0288325\pi$
$744$		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	$0.0340774\pi$
$751$			9.05182e7i			0.213706i	−0.994275	+	0.106853i	$0.965923\pi$
$752$	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	$0.0815339\pi$
$757$			2.19809e8i			0.506709i	−0.967374	+	0.253354i	$0.918466\pi$
$758$	−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	$0.322026\pi$
$773$			7.83108e8i			1.69544i	−0.530442	+	0.847721i	$0.677974\pi$
$774$		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	$-0.590509\pi$
$797$		−	9.71867e8i		−	1.91969i	0.280526	−	0.959846i	$-0.409491\pi$
$798$		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	$-0.629952\pi$
$821$		−	1.01581e9i		−	1.83563i	0.397009	−	0.917815i	$-0.370048\pi$
$822$		0			0
$823$			9.24417e8i			1.65832i	0.559011	+	0.829160i	$0.311181\pi$
$823$			9.24417e8i			1.65832i	−0.559011	+	0.829160i	$0.688819\pi$
$824$	−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	$-0.773883\pi$
$829$		−	7.43047e8i		−	1.30423i	0.758122	−	0.652113i	$-0.226117\pi$
$830$	−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	$0.306756\pi$
$839$			9.70115e8i			1.64262i	−0.570482	+	0.821310i	$0.693244\pi$
$840$		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	$-0.868227\pi$
$853$		−	4.99318e8i		−	0.804507i	0.915528	−	0.402254i	$-0.131773\pi$
$854$	−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	$-0.988109\pi$
$863$		−	4.80087e7i		−	0.0746943i	0.999302	−	0.0373471i	$-0.0118907\pi$
$864$		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	$0.0258048\pi$
$877$			1.09245e8i			0.161959i	−0.996716	+	0.0809793i	$0.974195\pi$
$878$	−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	$-0.823845\pi$
$887$		−	7.33580e8i		−	1.05118i	0.850738	−	0.525589i	$-0.176155\pi$
$888$		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	$-0.823044\pi$
$911$		−	7.97986e8i		−	1.05546i	0.849413	−	0.527728i	$-0.176956\pi$
$912$		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	$-0.984277\pi$
$919$		−	7.66471e7i		−	0.0987527i	0.998780	−	0.0493764i	$-0.0157234\pi$
$920$	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	$-0.979384\pi$
$941$		−	1.07856e8i		−	0.129442i	0.997903	−	0.0647208i	$-0.0206157\pi$
$942$		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	$-0.763357\pi$
$967$		−	1.22400e9i		−	1.35364i	0.736148	−	0.676821i	$-0.236643\pi$
$968$	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	$0.338607\pi$
$983$			1.66072e9i			1.74838i	−0.485584	+	0.874190i	$0.661393\pi$
$984$		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	$-0.950176\pi$
$991$		−	3.03432e8i		−	0.311775i	0.987775	−	0.155887i	$-0.0498237\pi$
$992$	−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	$0.208240\pi$
$997$			1.20614e9i			1.21706i	−0.793532	+	0.608528i	$0.791760\pi$
$998$	−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.19.4		4
3.2	odd	2		8.7.d.b.3.1	✓	4
4.3	odd	2		288.7.b.b.271.4		4
8.3	odd	2	inner	72.7.b.b.19.3		4
8.5	even	2		288.7.b.b.271.1		4
12.11	even	2		32.7.d.b.15.3		4
24.5	odd	2		32.7.d.b.15.4		4
24.11	even	2		8.7.d.b.3.2	yes	4
48.5	odd	4		256.7.c.l.255.8		8
48.11	even	4		256.7.c.l.255.2		8
48.29	odd	4		256.7.c.l.255.1		8
48.35	even	4		256.7.c.l.255.7		8

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

Varieties

Fields

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Groups

Database

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