LMFDB - Embedded newform 72.7.m.a.41.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,7,Mod(41,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("72.41");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	72.m (of order $6$, degree $2$, 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:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.9
Character	$\chi$	$=$	72.41
Dual form			72.7.m.a.65.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.709327 - 26.9907i) q^{3} +(157.631 + 91.0083i) q^{5} +(199.766 + 346.005i) q^{7} +(-727.994 - 38.2905i) q^{9} +O(q^{10})$	\(q+(0.709327 - 26.9907i) q^{3} +(157.631 + 91.0083i) q^{5} +(199.766 + 346.005i) q^{7} +(-727.994 - 38.2905i) q^{9} +(-742.403 + 428.627i) q^{11} +(-1517.70 + 2628.73i) q^{13} +(2568.19 - 4190.01i) q^{15} +5076.79i q^{17} +11718.7 q^{19} +(9480.61 - 5146.39i) q^{21} +(-881.443 - 508.901i) q^{23} +(8752.52 + 15159.8i) q^{25} +(-1549.87 + 19621.9i) q^{27} +(18759.7 - 10830.9i) q^{29} +(15297.2 - 26495.6i) q^{31} +(11042.3 + 20342.0i) q^{33} +72721.5i q^{35} -91005.2 q^{37} +(69874.7 + 42828.4i) q^{39} +(35642.6 + 20578.3i) q^{41} +(9614.93 + 16653.5i) q^{43} +(-111270. - 72289.2i) q^{45} +(148590. - 85788.7i) q^{47} +(-20988.5 + 36353.1i) q^{49} +(137026. + 3601.10i) q^{51} +78707.1i q^{53} -156034. q^{55} +(8312.40 - 316296. i) q^{57} +(-72111.7 - 41633.7i) q^{59} +(-159567. - 276378. i) q^{61} +(-132180. - 259539. i) q^{63} +(-478473. + 276246. i) q^{65} +(-37184.1 + 64404.8i) q^{67} +(-14360.8 + 23429.8i) q^{69} +514112. i q^{71} -27624.1 q^{73} +(415382. - 225483. i) q^{75} +(-296614. - 171250. i) q^{77} +(-218752. - 378890. i) q^{79} +(528509. + 55750.4i) q^{81} +(537767. - 310480. i) q^{83} +(-462030. + 800259. i) q^{85} +(-279026. - 514019. i) q^{87} +648769. i q^{89} -1.21274e6 q^{91} +(-704282. - 431676. i) q^{93} +(1.84723e6 + 1.06650e6i) q^{95} +(-686929. - 1.18980e6i) q^{97} +(556877. - 283611. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 10 q^{3} + 74 q^{9}+O(q^{10}) $ 36 * q + 10 * q^3 + 74 * q^9	$ 36 q + 10 q^{3} + 74 q^{9} + 1350 q^{11} + 7912 q^{15} + 9540 q^{19} + 3828 q^{21} + 30888 q^{23} + 56250 q^{25} + 11392 q^{27} + 38556 q^{29} + 27720 q^{31} + 33514 q^{33} + 134068 q^{39} + 179226 q^{41} + 15930 q^{43} - 185620 q^{45} + 187596 q^{47} - 198774 q^{49} - 158098 q^{51} - 197064 q^{55} - 244990 q^{57} - 408618 q^{59} + 17136 q^{61} - 417048 q^{63} - 125712 q^{65} + 27090 q^{67} - 848504 q^{69} - 534060 q^{73} - 1405714 q^{75} + 48168 q^{77} + 172620 q^{79} + 349010 q^{81} + 1801980 q^{83} - 791568 q^{85} + 28500 q^{87} + 538560 q^{91} - 1116448 q^{93} + 1832652 q^{95} + 770706 q^{97} - 614260 q^{99}+O(q^{100}) $ 36 * q + 10 * q^3 + 74 * q^9 + 1350 * q^11 + 7912 * q^15 + 9540 * q^19 + 3828 * q^21 + 30888 * q^23 + 56250 * q^25 + 11392 * q^27 + 38556 * q^29 + 27720 * q^31 + 33514 * q^33 + 134068 * q^39 + 179226 * q^41 + 15930 * q^43 - 185620 * q^45 + 187596 * q^47 - 198774 * q^49 - 158098 * q^51 - 197064 * q^55 - 244990 * q^57 - 408618 * q^59 + 17136 * q^61 - 417048 * q^63 - 125712 * q^65 + 27090 * q^67 - 848504 * q^69 - 534060 * q^73 - 1405714 * q^75 + 48168 * q^77 + 172620 * q^79 + 349010 * q^81 + 1801980 * q^83 - 791568 * q^85 + 28500 * q^87 + 538560 * q^91 - 1116448 * q^93 + 1832652 * q^95 + 770706 * q^97 - 614260 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$37$	$55$	$65$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	0.709327	−	26.9907i	0.0262714	−	0.999655i
$3$	0.709327	−	26.9907i	0.0262714	−	0.999655i
$4$		0			0
$5$	157.631	+	91.0083i	1.26105	+	0.728066i	0.973277	−	0.229633i	$-0.0737526\pi$
$5$	157.631	+	91.0083i	1.26105	+	0.728066i	0.287771	+	0.957699i	$0.407086\pi$
$6$		0			0
$7$	199.766	+	346.005i	0.582408	+	1.00876i	0.995193	+	0.0979322i	$0.0312228\pi$
$7$	199.766	+	346.005i	0.582408	+	1.00876i	−0.412785	+	0.910829i	$0.635444\pi$
$8$		0			0
$9$	−727.994	−	38.2905i	−0.998620	−	0.0525246i
$10$		0			0
$11$	−742.403	+	428.627i	−0.557778	+	0.322034i	−0.752253	−	0.658874i	$-0.771033\pi$
$11$	−742.403	+	428.627i	−0.557778	+	0.322034i	0.194475	+	0.980907i	$0.437700\pi$
$12$		0			0
$13$	−1517.70	+	2628.73i	−0.690805	+	1.19651i	0.280769	+	0.959775i	$0.409411\pi$
$13$	−1517.70	+	2628.73i	−0.690805	+	1.19651i	−0.971574	+	0.236735i	$0.923923\pi$
$14$		0			0
$15$	2568.19	−	4190.01i	0.760944	−	1.24149i
$16$		0			0
$17$			5076.79i			1.03334i	0.856185	+	0.516669i	$0.172828\pi$
$17$			5076.79i			1.03334i	−0.856185	+	0.516669i	$0.827172\pi$
$18$		0			0
$19$	11718.7			1.70852			0.854258	−	0.519850i	$-0.174012\pi$
$19$	11718.7			1.70852			0.854258	+	0.519850i	$0.174012\pi$
$20$		0			0
$21$	9480.61	−	5146.39i	1.02371	−	0.555706i
$22$		0			0
$23$	−881.443	−	508.901i	−0.0724454	−	0.0418264i	0.463340	−	0.886181i	$-0.346651\pi$
$23$	−881.443	−	508.901i	−0.0724454	−	0.0418264i	−0.535785	+	0.844354i	$0.679984\pi$
$24$		0			0
$25$	8752.52	+	15159.8i	0.560161	+	0.970228i
$26$		0			0
$27$	−1549.87	+	19621.9i	−0.0787416	+	0.996895i
$28$		0			0
$29$	18759.7	−	10830.9i	0.769185	−	0.444089i	−0.0633987	−	0.997988i	$-0.520194\pi$
$29$	18759.7	−	10830.9i	0.769185	−	0.444089i	0.832584	+	0.553899i	$0.186861\pi$
$30$		0			0
$31$	15297.2	−	26495.6i	0.513485	−	0.889381i	−0.486393	−	0.873740i	$-0.661688\pi$
$31$	15297.2	−	26495.6i	0.513485	−	0.889381i	0.999878	−	0.0156412i	$-0.00497895\pi$
$32$		0			0
$33$	11042.3	+	20342.0i	0.307269	+	0.566046i
$34$		0			0
$35$			72721.5i			1.69613i
$36$		0			0
$37$	−91005.2			−1.79664			−0.898320	−	0.439342i	$-0.855212\pi$
$37$	−91005.2			−1.79664			−0.898320	+	0.439342i	$0.855212\pi$
$38$		0			0
$39$	69874.7	+	42828.4i	1.17795	+	0.722001i
$40$		0			0
$41$	35642.6	+	20578.3i	0.517151	+	0.298578i	0.735768	−	0.677233i	$-0.236821\pi$
$41$	35642.6	+	20578.3i	0.517151	+	0.298578i	−0.218617	+	0.975811i	$0.570155\pi$
$42$		0			0
$43$	9614.93	+	16653.5i	0.120932	+	0.209460i	0.920135	−	0.391600i	$-0.128078\pi$
$43$	9614.93	+	16653.5i	0.120932	+	0.209460i	−0.799204	+	0.601060i	$0.794745\pi$
$44$		0			0
$45$	−111270.	−	72289.2i	−1.22107	−	0.793297i
$46$		0			0
$47$	148590.	−	85788.7i	1.43119	−	0.826298i	0.433978	−	0.900924i	$-0.357110\pi$
$47$	148590.	−	85788.7i	1.43119	−	0.826298i	0.997212	+	0.0746259i	$0.0237763\pi$
$48$		0			0
$49$	−20988.5	+	36353.1i	−0.178399	+	0.308996i
$50$		0			0
$51$	137026.	+	3601.10i	1.03298	+	0.0271472i
$52$		0			0
$53$			78707.1i			0.528672i	0.964431	+	0.264336i	$0.0851528\pi$
$53$			78707.1i			0.528672i	−0.964431	+	0.264336i	$0.914847\pi$
$54$		0			0
$55$	−156034.			−0.937847
$56$		0			0
$57$	8312.40	−	316296.i	0.0448851	−	1.70793i
$58$		0			0
$59$	−72111.7	−	41633.7i	−0.351115	−	0.202717i	0.314061	−	0.949403i	$-0.398310\pi$
$59$	−72111.7	−	41633.7i	−0.351115	−	0.202717i	−0.665176	+	0.746686i	$0.731644\pi$
$60$		0			0
$61$	−159567.	−	276378.i	−0.702996	−	1.21762i	−0.967410	−	0.253215i	$-0.918512\pi$
$61$	−159567.	−	276378.i	−0.702996	−	1.21762i	0.264414	−	0.964409i	$-0.414821\pi$
$62$		0			0
$63$	−132180.	−	259539.i	−0.528620	−	1.03796i
$64$		0			0
$65$	−478473.	+	276246.i	−1.74228	+	1.00590i
$66$		0			0
$67$	−37184.1	+	64404.8i	−0.123633	+	0.214138i	−0.921198	−	0.389095i	$-0.872788\pi$
$67$	−37184.1	+	64404.8i	−0.123633	+	0.214138i	0.797565	+	0.603233i	$0.206121\pi$
$68$		0			0
$69$	−14360.8	+	23429.8i	−0.0437152	+	0.0713215i
$70$		0			0
$71$			514112.i			1.43642i	0.695825	+	0.718212i	$0.255039\pi$
$71$			514112.i			1.43642i	−0.695825	+	0.718212i	$0.744961\pi$
$72$		0			0
$73$	−27624.1			−0.0710100			−0.0355050	−	0.999369i	$-0.511304\pi$
$73$	−27624.1			−0.0710100			−0.0355050	+	0.999369i	$0.511304\pi$
$74$		0			0
$75$	415382.	−	225483.i	0.984609	−	0.534479i
$76$		0			0
$77$	−296614.	−	171250.i	−0.649710	−	0.375110i
$78$		0			0
$79$	−218752.	−	378890.i	−0.443682	−	0.768480i	0.554277	−	0.832332i	$-0.312995\pi$
$79$	−218752.	−	378890.i	−0.443682	−	0.768480i	−0.997959	+	0.0638523i	$0.979661\pi$
$80$		0			0
$81$	528509.	+	55750.4i	0.994482	+	0.104904i
$82$		0			0
$83$	537767.	−	310480.i	0.940502	−	0.542999i	0.0503845	−	0.998730i	$-0.483955\pi$
$83$	537767.	−	310480.i	0.940502	−	0.542999i	0.890118	+	0.455731i	$0.150622\pi$
$84$		0			0
$85$	−462030.	+	800259.i	−0.752338	+	1.30309i
$86$		0			0
$87$	−279026.	−	514019.i	−0.423728	−	0.780586i
$88$		0			0
$89$			648769.i			0.920280i	0.887846	+	0.460140i	$0.152201\pi$
$89$			648769.i			0.920280i	−0.887846	+	0.460140i	$0.847799\pi$
$90$		0			0
$91$	−1.21274e6			−1.60932
$92$		0			0
$93$	−704282.	−	431676.i	−0.875584	−	0.536673i
$94$		0			0
$95$	1.84723e6	+	1.06650e6i	2.15452	+	1.24391i
$96$		0			0
$97$	−686929.	−	1.18980e6i	−0.752656	−	1.30364i	−0.946531	−	0.322612i	$-0.895439\pi$
$97$	−686929.	−	1.18980e6i	−0.752656	−	1.30364i	0.193875	−	0.981026i	$-0.437894\pi$
$98$		0			0
$99$	556877.	−	283611.i	0.573923	−	0.292292i
$100$		0			0
$101$	400560.	−	231264.i	0.388780	−	0.224462i	−0.292852	−	0.956158i	$-0.594604\pi$
$101$	400560.	−	231264.i	0.388780	−	0.224462i	0.681631	+	0.731696i	$0.261271\pi$
$102$		0			0
$103$	−89420.1	+	154880.i	−0.0818321	+	0.141737i	−0.904037	−	0.427454i	$-0.859410\pi$
$103$	−89420.1	+	154880.i	−0.0818321	+	0.141737i	0.822205	+	0.569192i	$0.192744\pi$
$104$		0			0
$105$	1.96280e6	+	51583.3i	1.69554	+	0.0445596i
$106$		0			0
$107$			107165.i			0.0874789i	0.999043	+	0.0437394i	$0.0139271\pi$
$107$			107165.i			0.0874789i	−0.999043	+	0.0437394i	$0.986073\pi$
$108$		0			0
$109$	1.24740e6			0.963223			0.481611	−	0.876385i	$-0.340052\pi$
$109$	1.24740e6			0.963223			0.481611	+	0.876385i	$0.340052\pi$
$110$		0			0
$111$	−64552.5	+	2.45629e6i	−0.0472002	+	1.79602i
$112$		0			0
$113$	2.26245e6	+	1.30623e6i	1.56799	+	0.905280i	0.996403	+	0.0847393i	$0.0270057\pi$
$113$	2.26245e6	+	1.30623e6i	1.56799	+	0.905280i	0.571588	+	0.820541i	$0.306328\pi$
$114$		0			0
$115$	−92628.5	−	160437.i	−0.0609047	−	0.105490i
$116$		0			0
$117$	1.20553e6	−	1.85559e6i	0.752698	−	1.15857i
$118$		0			0
$119$	−1.75659e6	+	1.01417e6i	−1.04239	+	0.601824i
$120$		0			0
$121$	−518339.	+	897789.i	−0.292589	+	0.506779i
$122$		0			0
$123$	580704.	−	947421.i	0.312061	−	0.509129i
$124$		0			0
$125$			342197.i			0.175205i
$126$		0			0
$127$	−2.06704e6			−1.00911			−0.504554	−	0.863380i	$-0.668343\pi$
$127$	−2.06704e6			−1.00911			−0.504554	+	0.863380i	$0.668343\pi$
$128$		0			0
$129$	456311.	−	247701.i	0.212565	−	0.115387i
$130$		0			0
$131$	−1.31488e6	−	759149.i	−0.584889	−	0.337686i	0.178185	−	0.983997i	$-0.442978\pi$
$131$	−1.31488e6	−	759149.i	−0.584889	−	0.337686i	−0.763074	+	0.646311i	$0.776311\pi$
$132$		0			0
$133$	2.34100e6	+	4.05473e6i	0.995054	+	1.72348i
$134$		0			0
$135$	−2.03006e6	+	2.95197e6i	−0.825103	+	1.19980i
$136$		0			0
$137$	−4.21951e6	+	2.43614e6i	−1.64097	+	0.947415i	−0.660481	+	0.750843i	$0.729647\pi$
$137$	−4.21951e6	+	2.43614e6i	−1.64097	+	0.947415i	−0.980489	+	0.196572i	$0.937019\pi$
$138$		0			0
$139$	1.25926e6	−	2.18110e6i	0.468889	−	0.812140i	−0.530478	−	0.847698i	$-0.677988\pi$
$139$	1.25926e6	−	2.18110e6i	0.468889	−	0.812140i	0.999368	+	0.0355585i	$0.0113210\pi$
$140$		0			0
$141$	−2.21010e6	−	4.07141e6i	−0.788413	−	1.45240i
$142$		0			0
$143$		−	2.60211e6i		−	0.889850i
$144$		0			0
$145$	3.94280e6			1.29331
$146$		0			0
$147$	966307.	+	592279.i	0.304203	+	0.186455i
$148$		0			0
$149$	−347068.	−	200380.i	−0.104920	−	0.0605753i	0.446622	−	0.894723i	$-0.352627\pi$
$149$	−347068.	−	200380.i	−0.104920	−	0.0605753i	−0.551542	+	0.834147i	$0.685960\pi$
$150$		0			0
$151$	−2.79583e6	−	4.84251e6i	−0.812044	−	1.40650i	−0.911431	−	0.411452i	$-0.865022\pi$
$151$	−2.79583e6	−	4.84251e6i	−0.812044	−	1.40650i	0.0993879	−	0.995049i	$-0.468312\pi$
$152$		0			0
$153$	194392.	−	3.69587e6i	0.0542757	−	1.03191i
$154$		0			0
$155$	4.82263e6	−	2.78435e6i	1.29506	−	0.747702i
$156$		0			0
$157$	−987228.	+	1.70993e6i	−0.255105	+	0.441855i	−0.964924	−	0.262529i	$-0.915443\pi$
$157$	−987228.	+	1.70993e6i	−0.255105	+	0.441855i	0.709819	+	0.704384i	$0.248777\pi$
$158$		0			0
$159$	2.12436e6	+	55829.1i	0.528490	+	0.0138890i
$160$		0			0
$161$		−	406645.i		−	0.0974401i
$162$		0			0
$163$	−1.57176e6			−0.362931			−0.181466	−	0.983397i	$-0.558084\pi$
$163$	−1.57176e6			−0.362931			−0.181466	+	0.983397i	$0.558084\pi$
$164$		0			0
$165$	−110679.	+	4.21147e6i	−0.0246385	+	0.937523i
$166$		0			0
$167$	−1.80150e6	−	1.04009e6i	−0.386798	−	0.223318i	0.293974	−	0.955813i	$-0.405022\pi$
$167$	−1.80150e6	−	1.04009e6i	−0.386798	−	0.223318i	−0.680772	+	0.732496i	$0.738355\pi$
$168$		0			0
$169$	−2.19342e6	−	3.79911e6i	−0.454424	−	0.787086i
$170$		0			0
$171$	−8.53115e6	−	448715.i	−1.70616	−	0.0897391i
$172$		0			0
$173$	3.45267e6	−	1.99340e6i	0.666832	−	0.384996i	−0.128043	−	0.991769i	$-0.540870\pi$
$173$	3.45267e6	−	1.99340e6i	0.666832	−	0.384996i	0.794875	+	0.606773i	$0.207536\pi$
$174$		0			0
$175$	−3.49691e6	+	6.05683e6i	−0.652485	+	1.13014i
$176$		0			0
$177$	−1.17487e6	+	1.91681e6i	−0.211871	+	0.345669i
$178$		0			0
$179$		−	3.92946e6i		−	0.685131i	−0.939494	−	0.342566i	$-0.888704\pi$
$179$		−	3.92946e6i		−	0.685131i	0.939494	−	0.342566i	$-0.111296\pi$
$180$		0			0
$181$	7.81525e6			1.31798			0.658988	−	0.752154i	$-0.270985\pi$
$181$	7.81525e6			1.31798			0.658988	+	0.752154i	$0.270985\pi$
$182$		0			0
$183$	−7.57280e6	+	4.11077e6i	−1.23567	+	0.670764i
$184$		0			0
$185$	−1.43452e7	−	8.28223e6i	−2.26565	−	1.30807i
$186$		0			0
$187$	−2.17605e6	−	3.76902e6i	−0.332769	−	0.576373i
$188$		0			0
$189$	−7.09888e6	+	3.38352e6i	−1.05149	+	0.501169i
$190$		0			0
$191$	4.12160e6	−	2.37960e6i	0.591514	−	0.341511i	−0.174182	−	0.984714i	$-0.555728\pi$
$191$	4.12160e6	−	2.37960e6i	0.591514	−	0.341511i	0.765696	+	0.643203i	$0.222395\pi$
$192$		0			0
$193$	1.03985e6	−	1.80107e6i	0.144644	−	0.250530i	−0.784596	−	0.620007i	$-0.787130\pi$
$193$	1.03985e6	−	1.80107e6i	0.144644	−	0.250530i	0.929240	+	0.369477i	$0.120463\pi$
$194$		0			0
$195$	7.11669e6	+	1.31103e7i	0.959785	+	1.76810i
$196$		0			0
$197$		−	2.91437e6i		−	0.381193i	−0.981668	−	0.190597i	$-0.938958\pi$
$197$		−	2.91437e6i		−	0.381193i	0.981668	−	0.190597i	$-0.0610423\pi$
$198$		0			0
$199$	1.23012e7			1.56095			0.780474	−	0.625188i	$-0.214978\pi$
$199$	1.23012e7			1.56095			0.780474	+	0.625188i	$0.214978\pi$
$200$		0			0
$201$	1.71195e6	+	1.04931e6i	0.210816	+	0.129216i
$202$		0			0
$203$	7.49509e6	+	4.32729e6i	0.895960	+	0.517283i
$204$		0			0
$205$	3.74558e6	+	6.48754e6i	0.434768	+	0.753041i
$206$		0			0
$207$	622199.	+	404228.i	0.0701485	+	0.0455738i
$208$		0			0
$209$	−8.70001e6	+	5.02295e6i	−0.952973	+	0.550199i
$210$		0			0
$211$	1.71418e6	−	2.96904e6i	0.182477	−	0.316059i	−0.760247	−	0.649635i	$-0.774922\pi$
$211$	1.71418e6	−	2.96904e6i	0.182477	−	0.316059i	0.942723	+	0.333575i	$0.108255\pi$
$212$		0			0
$213$	1.38762e7	+	364673.i	1.43593	+	0.0377368i
$214$		0			0
$215$			3.50015e6i			0.352186i
$216$		0			0
$217$	1.22235e7			1.19623
$218$		0			0
$219$	−19594.5	+	745593.i	−0.00186553	+	0.0709855i
$220$		0			0
$221$	−1.33455e7	−	7.70503e6i	−1.23640	−	0.713835i
$222$		0			0
$223$	434651.	+	752837.i	0.0391945	+	0.0678869i	0.884957	−	0.465672i	$-0.154187\pi$
$223$	434651.	+	752837.i	0.0391945	+	0.0678869i	−0.845763	+	0.533559i	$0.820854\pi$
$224$		0			0
$225$	−5.79130e6	−	1.13714e7i	−0.508427	−	0.998310i
$226$		0			0
$227$	1.73764e7	−	1.00323e7i	1.48553	−	0.857672i	0.485667	−	0.874144i	$-0.338577\pi$
$227$	1.73764e7	−	1.00323e7i	1.48553	−	0.857672i	0.999864	+	0.0164724i	$0.00524355\pi$
$228$		0			0
$229$	−2.00206e6	+	3.46768e6i	−0.166714	+	0.288757i	−0.937263	−	0.348624i	$-0.886649\pi$
$229$	−2.00206e6	+	3.46768e6i	−0.166714	+	0.288757i	0.770549	+	0.637381i	$0.219982\pi$
$230$		0			0
$231$	−4.83255e6	+	7.88434e6i	−0.392049	+	0.639631i
$232$		0			0
$233$			5.50136e6i			0.434913i	0.976070	+	0.217456i	$0.0697760\pi$
$233$			5.50136e6i			0.434913i	−0.976070	+	0.217456i	$0.930224\pi$
$234$		0			0
$235$	3.12299e7			2.40640
$236$		0			0
$237$	−1.03817e7	+	5.63552e6i	−0.779871	+	0.423340i
$238$		0			0
$239$	−1.96836e6	−	1.13643e6i	−0.144182	−	0.0832435i	0.426174	−	0.904641i	$-0.359861\pi$
$239$	−1.96836e6	−	1.13643e6i	−0.144182	−	0.0832435i	−0.570356	+	0.821398i	$0.693195\pi$
$240$		0			0
$241$	7.85641e6	+	1.36077e7i	0.561271	+	0.972151i	0.997386	+	0.0722594i	$0.0230209\pi$
$241$	7.85641e6	+	1.36077e7i	0.561271	+	0.972151i	−0.436115	+	0.899891i	$0.643646\pi$
$242$		0			0
$243$	1.87963e6	−	1.42253e7i	0.130994	−	0.991383i
$244$		0			0
$245$	−6.61686e6	+	3.82025e6i	−0.449939	+	0.259773i
$246$		0			0
$247$	−1.77855e7	+	3.08053e7i	−1.18025	+	2.04426i
$248$		0			0
$249$	−7.99861e6	−	1.47349e7i	−0.518104	−	0.954443i
$250$		0			0
$251$		−	1.36844e7i		−	0.865375i	−0.901544	−	0.432688i	$-0.857565\pi$
$251$		−	1.36844e7i		−	0.865375i	0.901544	−	0.432688i	$-0.142435\pi$
$252$		0			0
$253$	872515.			0.0538780
$254$		0			0
$255$	2.12718e7	+	1.30381e7i	1.28287	+	0.786312i
$256$		0			0
$257$	2.79516e7	+	1.61378e7i	1.64667	+	0.950705i	0.978383	+	0.206802i	$0.0663057\pi$
$257$	2.79516e7	+	1.61378e7i	1.64667	+	0.950705i	0.668287	+	0.743903i	$0.267028\pi$
$258$		0			0
$259$	−1.81797e7	−	3.14882e7i	−1.04638	−	1.81238i
$260$		0			0
$261$	−1.40716e7	+	7.16651e6i	−0.791449	+	0.403075i
$262$		0			0
$263$	−1.05705e7	+	6.10286e6i	−0.581068	+	0.335480i	−0.761558	−	0.648097i	$-0.775565\pi$
$263$	−1.05705e7	+	6.10286e6i	−0.581068	+	0.335480i	0.180490	+	0.983577i	$0.442232\pi$
$264$		0			0
$265$	−7.16300e6	+	1.24067e7i	−0.384909	+	0.666681i
$266$		0			0
$267$	1.75107e7	+	460190.i	0.919963	+	0.0241770i
$268$		0			0
$269$		−	4.21697e6i		−	0.216643i	−0.994116	−	0.108321i	$-0.965452\pi$
$269$		−	4.21697e6i		−	0.216643i	0.994116	−	0.108321i	$-0.0345476\pi$
$270$		0			0
$271$	−1.38368e7			−0.695231			−0.347615	−	0.937637i	$-0.613008\pi$
$271$	−1.38368e7			−0.695231			−0.347615	+	0.937637i	$0.613008\pi$
$272$		0			0
$273$	−860229.	+	3.27327e7i	−0.0422791	+	1.60877i
$274$		0			0
$275$	−1.29958e7	−	7.50312e6i	−0.624892	−	0.360781i
$276$		0			0
$277$	−1.98591e7	−	3.43970e7i	−0.934373	−	1.61838i	−0.775748	−	0.631043i	$-0.782627\pi$
$277$	−1.98591e7	−	3.43970e7i	−0.934373	−	1.61838i	−0.158625	−	0.987339i	$-0.550706\pi$
$278$		0			0
$279$	−1.21508e7	+	1.87029e7i	−0.559490	+	0.861183i
$280$		0			0
$281$	−1.70231e6	+	982828.i	−0.0767219	+	0.0442954i	−0.537870	−	0.843028i	$-0.680771\pi$
$281$	−1.70231e6	+	982828.i	−0.0767219	+	0.0442954i	0.461148	+	0.887323i	$0.347438\pi$
$282$		0			0
$283$	1.56611e7	−	2.71259e7i	0.690978	−	1.19681i	−0.280540	−	0.959842i	$-0.590514\pi$
$283$	1.56611e7	−	2.71259e7i	0.690978	−	1.19681i	0.971518	−	0.236966i	$-0.0761531\pi$
$284$		0			0
$285$	3.00958e7	−	4.91015e7i	1.30009	−	2.12110i
$286$		0			0
$287$			1.64434e7i			0.695576i
$288$		0			0
$289$	−1.63618e6			−0.0677858
$290$		0			0
$291$	−3.26007e7	+	1.76967e7i	−1.32296	+	0.718148i
$292$		0			0
$293$	1.93071e7	+	1.11469e7i	0.767562	+	0.443152i	0.832004	−	0.554769i	$-0.187193\pi$
$293$	1.93071e7	+	1.11469e7i	0.767562	+	0.443152i	−0.0644419	+	0.997921i	$0.520527\pi$
$294$		0			0
$295$	−7.57803e6	−	1.31255e7i	−0.295182	−	0.511271i
$296$		0			0
$297$	−7.25983e6	−	1.52317e7i	−0.277113	−	0.581404i
$298$		0			0
$299$	2.67553e6	−	1.54472e6i	0.100091	−	0.0577877i
$300$		0			0
$301$	−3.84147e6	+	6.65362e6i	−0.140863	+	0.243983i
$302$		0			0
$303$	−5.95783e6	−	1.09754e7i	−0.214171	−	0.394542i
$304$		0			0
$305$		−	5.80876e7i		−	2.04731i
$306$		0			0
$307$	−3.00412e7			−1.03825			−0.519125	−	0.854698i	$-0.673742\pi$
$307$	−3.00412e7			−1.03825			−0.519125	+	0.854698i	$0.673742\pi$
$308$		0			0
$309$	4.11689e6	+	2.52337e6i	0.139539	+	0.0855275i
$310$		0			0
$311$	−1.75309e7	−	1.01215e7i	−0.582805	−	0.336483i	0.179442	−	0.983769i	$-0.442571\pi$
$311$	−1.75309e7	−	1.01215e7i	−0.582805	−	0.336483i	−0.762247	+	0.647286i	$0.775904\pi$
$312$		0			0
$313$	−7.20574e6	−	1.24807e7i	−0.234988	−	0.407011i	0.724281	−	0.689505i	$-0.242172\pi$
$313$	−7.20574e6	−	1.24807e7i	−0.234988	−	0.407011i	−0.959269	+	0.282494i	$0.908838\pi$
$314$		0			0
$315$	2.78454e6	−	5.29408e7i	0.0890885	−	1.69379i
$316$		0			0
$317$	−3.30101e7	+	1.90584e7i	−1.03626	+	0.598285i	−0.918772	−	0.394789i	$-0.870818\pi$
$317$	−3.30101e7	+	1.90584e7i	−1.03626	+	0.598285i	−0.117488	+	0.993074i	$0.537484\pi$
$318$		0			0
$319$	−9.28482e6	+	1.60818e7i	−0.286023	+	0.495407i
$320$		0			0
$321$	2.89247e6	+	76015.4i	0.0874487	+	0.00229819i
$322$		0			0
$323$			5.94934e7i			1.76547i
$324$		0			0
$325$	−5.31348e7			−1.54785
$326$		0			0
$327$	884816.	−	3.36682e7i	0.0253052	−	0.962890i
$328$		0			0
$329$	5.93666e7	+	3.42753e7i	1.66707	+	0.962485i
$330$		0			0
$331$	2.25754e7	+	3.91018e7i	0.622518	+	1.07823i	0.989015	+	0.147813i	$0.0472235\pi$
$331$	2.25754e7	+	3.91018e7i	0.622518	+	1.07823i	−0.366497	+	0.930419i	$0.619443\pi$
$332$		0			0
$333$	6.62512e7	+	3.48463e6i	1.79416	+	0.0943678i
$334$		0			0
$335$	−1.17227e7	+	6.76812e6i	−0.311813	+	0.180025i
$336$		0			0
$337$	−6.28575e6	+	1.08872e7i	−0.164236	+	0.284465i	−0.936384	−	0.350978i	$-0.885849\pi$
$337$	−6.28575e6	+	1.08872e7i	−0.164236	+	0.284465i	0.772148	+	0.635443i	$0.219182\pi$
$338$		0			0
$339$	3.68607e7	−	6.01385e7i	0.946161	−	1.54367i
$340$		0			0
$341$			2.62272e7i			0.661437i
$342$		0			0
$343$	3.02334e7			0.749213
$344$		0			0
$345$	−4.39601e6	+	2.38630e6i	−0.107054	+	0.0581123i
$346$		0			0
$347$	−2.02402e6	−	1.16857e6i	−0.0484426	−	0.0279683i	0.475583	−	0.879671i	$-0.342237\pi$
$347$	−2.02402e6	−	1.16857e6i	−0.0484426	−	0.0279683i	−0.524026	+	0.851702i	$0.675570\pi$
$348$		0			0
$349$	−1.44412e7	−	2.50130e7i	−0.339726	−	0.588422i	0.644655	−	0.764473i	$-0.277001\pi$
$349$	−1.44412e7	−	2.50130e7i	−0.339726	−	0.588422i	−0.984381	+	0.176051i	$0.943668\pi$
$350$		0			0
$351$	−4.92284e7	−	3.38543e7i	−1.13840	−	0.782876i
$352$		0			0
$353$	1.53593e7	−	8.86771e6i	0.349179	−	0.201598i	−0.315145	−	0.949044i	$-0.602053\pi$
$353$	1.53593e7	−	8.86771e6i	0.349179	−	0.201598i	0.664323	+	0.747445i	$0.268720\pi$
$354$		0			0
$355$	−4.67884e7	+	8.10399e7i	−1.04581	+	1.81140i
$356$		0			0
$357$	2.61271e7	+	4.81310e7i	0.574231	+	1.05784i
$358$		0			0
$359$			6.28807e7i			1.35905i	0.733655	+	0.679523i	$0.237813\pi$
$359$			6.28807e7i			1.35905i	−0.733655	+	0.679523i	$0.762187\pi$
$360$		0			0
$361$	9.02822e7			1.91903
$362$		0			0
$363$	2.38643e7	+	1.46271e7i	0.498917	+	0.305802i
$364$		0			0
$365$	−4.35441e6	−	2.51402e6i	−0.0895470	−	0.0517000i
$366$		0			0
$367$	−3.66579e7	−	6.34934e7i	−0.741600	−	1.28449i	−0.951767	−	0.306823i	$-0.900734\pi$
$367$	−3.66579e7	−	6.34934e7i	−0.741600	−	1.28449i	0.210167	−	0.977665i	$-0.432599\pi$
$368$		0			0
$369$	−2.51596e7	−	1.63456e7i	−0.500755	−	0.325329i
$370$		0			0
$371$	−2.72331e7	+	1.57230e7i	−0.533304	+	0.307903i
$372$		0			0
$373$	−3.28846e6	+	5.69578e6i	−0.0633674	+	0.109756i	−0.895969	−	0.444117i	$-0.853517\pi$
$373$	−3.28846e6	+	5.69578e6i	−0.0633674	+	0.109756i	0.832601	+	0.553873i	$0.186851\pi$
$374$		0			0
$375$	9.23614e6	+	242730.i	0.175145	+	0.00460288i
$376$		0			0
$377$			6.57522e7i			1.22712i
$378$		0			0
$379$	−3.03275e7			−0.557081			−0.278541	−	0.960424i	$-0.589851\pi$
$379$	−3.03275e7			−0.557081			−0.278541	+	0.960424i	$0.589851\pi$
$380$		0			0
$381$	−1.46621e6	+	5.57908e7i	−0.0265106	+	1.00876i
$382$		0			0
$383$	1.95104e7	+	1.12643e7i	0.347272	+	0.200497i	0.663483	−	0.748191i	$-0.269078\pi$
$383$	1.95104e7	+	1.12643e7i	0.347272	+	0.200497i	−0.316211	+	0.948689i	$0.602411\pi$
$384$		0			0
$385$	−3.11704e7	−	5.39886e7i	−0.546210	−	0.946063i
$386$		0			0
$387$	−6.36193e6	−	1.24918e7i	−0.109763	−	0.215523i
$388$		0			0
$389$	9.99280e7	−	5.76934e7i	1.69761	−	0.980116i	0.749594	−	0.661898i	$-0.230249\pi$
$389$	9.99280e7	−	5.76934e7i	1.69761	−	0.980116i	0.948018	−	0.318218i	$-0.103084\pi$
$390$		0			0
$391$	2.58358e6	−	4.47490e6i	0.0432207	−	0.0748605i
$392$		0			0
$393$	−2.14226e7	+	3.49511e7i	−0.352935	+	0.575816i
$394$		0			0
$395$		−	7.96332e7i		−	1.29212i
$396$		0			0
$397$	6.85735e6			0.109593			0.0547967	−	0.998498i	$-0.482549\pi$
$397$	6.85735e6			0.109593			0.0547967	+	0.998498i	$0.482549\pi$
$398$		0			0
$399$	1.11100e8	−	6.03091e7i	1.74903	−	0.949432i
$400$		0			0
$401$	1.61123e7	+	9.30243e6i	0.249876	+	0.144266i	0.619707	−	0.784833i	$-0.287251\pi$
$401$	1.61123e7	+	9.30243e6i	0.249876	+	0.144266i	−0.369832	+	0.929099i	$0.620585\pi$
$402$		0			0
$403$	4.64332e7	+	8.04246e7i	0.709436	+	1.22878i
$404$		0			0
$405$	7.82356e7	+	5.68867e7i	1.17771	+	0.856338i
$406$		0			0
$407$	6.75625e7	−	3.90072e7i	1.00213	−	0.578578i
$408$		0			0
$409$	−7.58573e6	+	1.31389e7i	−0.110873	+	0.192038i	−0.916123	−	0.400898i	$-0.868698\pi$
$409$	−7.58573e6	+	1.31389e7i	−0.110873	+	0.192038i	0.805249	+	0.592936i	$0.202031\pi$
$410$		0			0
$411$	6.27600e7	+	1.15616e8i	0.903977	+	1.66529i
$412$		0			0
$413$		−	3.32680e7i		−	0.472255i
$414$		0			0
$415$	1.13025e8			1.58136
$416$		0			0
$417$	−5.79761e7	−	3.55353e7i	−0.799541	−	0.490063i
$418$		0			0
$419$	−1.95238e7	−	1.12721e7i	−0.265413	−	0.153236i	0.361388	−	0.932415i	$-0.382303\pi$
$419$	−1.95238e7	−	1.12721e7i	−0.265413	−	0.153236i	−0.626801	+	0.779179i	$0.715636\pi$
$420$		0			0
$421$	−5.84710e7	−	1.01275e8i	−0.783599	−	1.35723i	−0.929832	−	0.367983i	$-0.880048\pi$
$421$	−5.84710e7	−	1.01275e8i	−0.783599	−	1.35723i	0.146233	−	0.989250i	$-0.453285\pi$
$422$		0			0
$423$	−1.11458e8	+	5.67640e7i	−1.47261	+	0.749984i
$424$		0			0
$425$	−7.69631e7	+	4.44347e7i	−1.00257	+	0.578835i
$426$		0			0
$427$	6.37520e7	−	1.10422e8i	0.818861	−	1.41831i
$428$		0			0
$429$	−7.02326e7	−	1.84574e6i	−0.889543	−	0.0233776i
$430$		0			0
$431$			7.01047e7i			0.875620i	0.899068	+	0.437810i	$0.144246\pi$
$431$			7.01047e7i			0.875620i	−0.899068	+	0.437810i	$0.855754\pi$
$432$		0			0
$433$	−1.39867e8			−1.72287			−0.861434	−	0.507869i	$-0.830433\pi$
$433$	−1.39867e8			−1.72287			−0.861434	+	0.507869i	$0.830433\pi$
$434$		0			0
$435$	2.79674e6	−	1.06419e8i	0.0339769	−	1.29286i
$436$		0			0
$437$	−1.03294e7	−	5.96367e6i	−0.123774	−	0.0714610i
$438$		0			0
$439$	3.26945e7	+	5.66285e7i	0.386439	+	0.669332i	0.991968	−	0.126492i	$-0.0403717\pi$
$439$	3.26945e7	+	5.66285e7i	0.386439	+	0.669332i	−0.605529	+	0.795823i	$0.707038\pi$
$440$		0			0
$441$	1.66714e7	−	2.56612e7i	0.194383	−	0.299199i
$442$		0			0
$443$	−5.72120e7	+	3.30314e7i	−0.658076	+	0.379940i	−0.791543	−	0.611113i	$-0.790722\pi$
$443$	−5.72120e7	+	3.30314e7i	−0.658076	+	0.379940i	0.133468	+	0.991053i	$0.457389\pi$
$444$		0			0
$445$	−5.90434e7	+	1.02266e8i	−0.670025	+	1.16052i
$446$		0			0
$447$	−5.65458e6	+	9.22548e6i	−0.0633108	+	0.103292i
$448$		0			0
$449$		−	8.39435e7i		−	0.927359i	−0.886003	−	0.463679i	$-0.846529\pi$
$449$		−	8.39435e7i		−	0.927359i	0.886003	−	0.463679i	$-0.153471\pi$
$450$		0			0
$451$	−3.52816e7			−0.384608
$452$		0			0
$453$	−1.32686e8	+	7.20263e7i	−1.42735	+	0.774813i
$454$		0			0
$455$	−1.91165e8	−	1.10369e8i	−2.02943	−	1.17169i
$456$		0			0
$457$	5.31949e7	+	9.21362e7i	0.557341	+	0.965343i	0.997717	+	0.0675296i	$0.0215117\pi$
$457$	5.31949e7	+	9.21362e7i	0.557341	+	0.965343i	−0.440376	+	0.897813i	$0.645155\pi$
$458$		0			0
$459$	−9.96161e7	−	7.86836e6i	−1.03013	−	0.0813666i
$460$		0			0
$461$	1.14283e8	−	6.59815e7i	1.16649	−	0.673472i	0.213637	−	0.976913i	$-0.431469\pi$
$461$	1.14283e8	−	6.59815e7i	1.16649	−	0.673472i	0.952850	+	0.303441i	$0.0981355\pi$
$462$		0			0
$463$	−376890.	+	652792.i	−0.00379727	+	0.00657706i	−0.867918	−	0.496708i	$-0.834542\pi$
$463$	−376890.	+	652792.i	−0.00379727	+	0.00657706i	0.864121	+	0.503285i	$0.167875\pi$
$464$		0			0
$465$	−7.17306e7	−	1.32141e8i	−0.713421	−	1.31425i
$466$		0			0
$467$			1.21401e8i			1.19199i	0.802988	+	0.595995i	$0.203242\pi$
$467$			1.21401e8i			1.19199i	−0.802988	+	0.595995i	$0.796758\pi$
$468$		0			0
$469$	−2.97125e7			−0.288019
$470$		0			0
$471$	4.54519e7	+	2.78589e7i	0.435000	+	0.266625i
$472$		0			0
$473$	−1.42763e7	−	8.24243e6i	−0.134906	−	0.0778882i
$474$		0			0
$475$	1.02568e8	+	1.77653e8i	0.957044	+	1.65765i
$476$		0			0
$477$	3.01373e6	−	5.72983e7i	0.0277683	−	0.527943i
$478$		0			0
$479$	3.81018e7	−	2.19981e7i	0.346688	−	0.200161i	−0.316537	−	0.948580i	$-0.602520\pi$
$479$	3.81018e7	−	2.19981e7i	0.346688	−	0.200161i	0.663226	+	0.748419i	$0.269187\pi$
$480$		0			0
$481$	1.38119e8	−	2.39228e8i	1.24113	−	2.14970i
$482$		0			0
$483$	−1.09756e7	−	288444.i	−0.0974064	−	0.00255989i
$484$		0			0
$485$		−	2.50065e8i		−	2.19193i
$486$		0			0
$487$	1.06253e8			0.919931			0.459965	−	0.887937i	$-0.347862\pi$
$487$	1.06253e8			0.919931			0.459965	+	0.887937i	$0.347862\pi$
$488$		0			0
$489$	−1.11490e6	+	4.24230e7i	−0.00953471	+	0.362806i
$490$		0			0
$491$	−1.37564e8	−	7.94224e7i	−1.16214	−	0.670963i	−0.210326	−	0.977631i	$-0.567453\pi$
$491$	−1.37564e8	−	7.94224e7i	−1.16214	−	0.670963i	−0.951817	+	0.306668i	$0.900786\pi$
$492$		0			0
$493$	5.49861e7	+	9.52388e7i	0.458894	+	0.794828i
$494$		0			0
$495$	1.13592e8	+	5.97462e6i	0.936553	+	0.0492601i
$496$		0			0
$497$	−1.77885e8	+	1.02702e8i	−1.44901	+	0.836585i
$498$		0			0
$499$	1.21553e8	−	2.10536e8i	0.978284	−	1.69444i	0.309642	−	0.950853i	$-0.399791\pi$
$499$	1.21553e8	−	2.10536e8i	0.978284	−	1.69444i	0.668642	−	0.743584i	$-0.266876\pi$
$500$		0			0
$501$	−2.93507e7	+	4.78859e7i	−0.233403	+	0.380798i
$502$		0			0
$503$		−	1.62447e8i		−	1.27646i	−0.769846	−	0.638229i	$-0.779667\pi$
$503$		−	1.62447e8i		−	1.27646i	0.769846	−	0.638229i	$-0.220333\pi$
$504$		0			0
$505$	8.41876e7			0.653693
$506$		0			0
$507$	−1.04096e8	+	5.65070e7i	−0.798752	+	0.433589i
$508$		0			0
$509$	−3.36093e7	−	1.94044e7i	−0.254863	−	0.147145i	0.367126	−	0.930171i	$-0.380342\pi$
$509$	−3.36093e7	−	1.94044e7i	−0.254863	−	0.147145i	−0.621989	+	0.783026i	$0.713675\pi$
$510$		0			0
$511$	−5.51836e6	−	9.55807e6i	−0.0413568	−	0.0716321i
$512$		0			0
$513$	−1.81625e7	+	2.29943e8i	−0.134531	+	1.70321i
$514$		0			0
$515$	−2.81908e7	+	1.62759e7i	−0.206388	+	0.119158i
$516$		0			0
$517$	−7.35426e7	+	1.27380e8i	−0.532191	+	0.921782i
$518$		0			0
$519$	−5.13541e7	−	9.46039e7i	−0.367344	−	0.676717i
$520$		0			0
$521$			1.24936e6i			0.00883437i	0.999990	+	0.00441718i	$0.00140604\pi$
$521$			1.24936e6i			0.00883437i	−0.999990	+	0.00441718i	$0.998594\pi$
$522$		0			0
$523$	−2.90613e7			−0.203147			−0.101573	−	0.994828i	$-0.532388\pi$
$523$	−2.90613e7			−0.203147			−0.101573	+	0.994828i	$0.532388\pi$
$524$		0			0
$525$	1.60997e8	+	9.86803e7i	1.11261	+	0.681950i
$526$		0			0
$527$	1.34512e8	+	7.76607e7i	0.919031	+	0.530603i
$528$		0			0
$529$	−7.35000e7	−	1.27306e8i	−0.496501	−	0.859965i
$530$		0			0
$531$	5.09027e7	+	3.30703e7i	0.339983	+	0.220879i
$532$		0			0
$533$	−1.08189e8	+	6.24632e7i	−0.714502	+	0.412518i
$534$		0			0
$535$	−9.75294e6	+	1.68926e7i	−0.0636904	+	0.110315i
$536$		0			0
$537$	−1.06059e8	−	2.78727e6i	−0.684895	−	0.0179993i
$538$		0			0
$539$		−	3.59849e7i		−	0.229802i
$540$		0			0
$541$	−6.31130e7			−0.398591			−0.199295	−	0.979939i	$-0.563865\pi$
$541$	−6.31130e7			−0.398591			−0.199295	+	0.979939i	$0.563865\pi$
$542$		0			0
$543$	5.54357e6	−	2.10939e8i	0.0346250	−	1.31752i
$544$		0			0
$545$	1.96629e8	+	1.13524e8i	1.21467	+	0.701290i
$546$		0			0
$547$	−1.63831e7	−	2.83763e7i	−0.100100	−	0.173378i	0.811626	−	0.584178i	$-0.198583\pi$
$547$	−1.63831e7	−	2.83763e7i	−0.100100	−	0.173378i	−0.911726	+	0.410800i	$0.865250\pi$
$548$		0			0
$549$	1.05581e8	+	2.07311e8i	0.638070	+	1.25287i
$550$		0			0
$551$	2.19839e8	−	1.26924e8i	1.31416	−	0.758733i
$552$		0			0
$553$	8.73987e7	−	1.51379e8i	0.516808	−	0.895138i
$554$		0			0
$555$	−2.33718e8	+	3.81313e8i	−1.36714	+	2.23050i
$556$		0			0
$557$		−	2.68165e8i		−	1.55180i	−0.630855	−	0.775900i	$-0.717296\pi$
$557$		−	2.68165e8i		−	1.55180i	0.630855	−	0.775900i	$-0.282704\pi$
$558$		0			0
$559$	−5.83703e7			−0.334161
$560$		0			0
$561$	−1.03272e8	+	5.60595e7i	−0.584917	+	0.317512i
$562$		0			0
$563$	1.62459e8	+	9.37957e7i	0.910371	+	0.525603i	0.880551	−	0.473952i	$-0.157173\pi$
$563$	1.62459e8	+	9.37957e7i	0.910371	+	0.525603i	0.0298206	+	0.999555i	$0.490506\pi$
$564$		0			0
$565$	2.37755e8	+	4.11803e8i	1.31821	+	2.28320i
$566$		0			0
$567$	8.62882e7	+	1.94004e8i	0.473372	+	1.06429i
$568$		0			0
$569$	−1.00007e8	+	5.77392e7i	−0.542869	+	0.313425i	−0.746241	−	0.665676i	$-0.768143\pi$
$569$	−1.00007e8	+	5.77392e7i	−0.542869	+	0.313425i	0.203372	+	0.979102i	$0.434810\pi$
$570$		0			0
$571$	−1.74327e8	+	3.01944e8i	−0.936392	+	1.62188i	−0.164258	+	0.986417i	$0.552523\pi$
$571$	−1.74327e8	+	3.01944e8i	−0.936392	+	1.62188i	−0.772133	+	0.635460i	$0.780810\pi$
$572$		0			0
$573$	−6.13036e7	−	1.12933e8i	−0.325853	−	0.600282i
$574$		0			0
$575$		−	1.78167e7i		−	0.0937180i
$576$		0			0
$577$	2.44107e8			1.27073			0.635365	−	0.772212i	$-0.280850\pi$
$577$	2.44107e8			1.27073			0.635365	+	0.772212i	$0.280850\pi$
$578$		0			0
$579$	−4.78746e7	−	2.93438e7i	−0.246643	−	0.151175i
$580$		0			0
$581$	2.14855e8	+	1.24047e8i	1.09551	+	0.632495i
$582$		0			0
$583$	−3.37360e7	−	5.84324e7i	−0.170250	−	0.294882i
$584$		0			0
$585$	3.58903e8	−	1.82785e8i	1.79271	−	0.913003i
$586$		0			0
$587$	2.53559e8	−	1.46392e8i	1.25361	−	0.723775i	0.281789	−	0.959476i	$-0.409072\pi$
$587$	2.53559e8	−	1.46392e8i	1.25361	−	0.723775i	0.971825	+	0.235702i	$0.0757388\pi$
$588$		0			0
$589$	1.79264e8	−	3.10494e8i	0.877296	−	1.51952i
$590$		0			0
$591$	−7.86607e7	−	2.06724e6i	−0.381062	−	0.0100145i
$592$		0			0
$593$			3.45463e8i			1.65668i	0.560228	+	0.828339i	$0.310714\pi$
$593$			3.45463e8i			1.65668i	−0.560228	+	0.828339i	$0.689286\pi$
$594$		0			0
$595$	−3.69191e8			−1.75267
$596$		0			0
$597$	8.72558e6	−	3.32018e8i	0.0410083	−	1.56041i
$598$		0			0
$599$	−2.43277e8	−	1.40456e8i	−1.13193	−	0.653522i	−0.187513	−	0.982262i	$-0.560043\pi$
$599$	−2.43277e8	−	1.40456e8i	−1.13193	−	0.653522i	−0.944421	+	0.328740i	$0.893376\pi$
$600$		0			0
$601$	1.41918e8	+	2.45810e8i	0.653755	+	1.13234i	0.982204	+	0.187815i	$0.0601406\pi$
$601$	1.41918e8	+	2.45810e8i	0.653755	+	1.13234i	−0.328450	+	0.944522i	$0.606526\pi$
$602$		0			0
$603$	2.95359e7	−	4.54625e7i	0.134709	−	0.207349i
$604$		0			0
$605$	−1.63413e8	+	9.43463e7i	−0.737937	+	0.426048i
$606$		0			0
$607$	−3.08419e6	+	5.34197e6i	−0.0137903	+	0.0238855i	−0.872838	−	0.488010i	$-0.837723\pi$
$607$	−3.08419e6	+	5.34197e6i	−0.0137903	+	0.0238855i	0.859048	+	0.511895i	$0.171056\pi$
$608$		0			0
$609$	1.22113e8	−	1.99228e8i	0.540642	−	0.882061i
$610$		0			0
$611$			5.20806e8i			2.28324i
$612$		0			0
$613$	−2.83531e8			−1.23089			−0.615446	−	0.788179i	$-0.711024\pi$
$613$	−2.83531e8			−1.23089			−0.615446	+	0.788179i	$0.711024\pi$
$614$		0			0
$615$	1.77760e8	−	9.64941e7i	0.764203	−	0.414835i
$616$		0			0
$617$	−1.83195e6	−	1.05768e6i	−0.00779936	−	0.00450296i	0.496095	−	0.868268i	$-0.334767\pi$
$617$	−1.83195e6	−	1.05768e6i	−0.00779936	−	0.00450296i	−0.503895	+	0.863765i	$0.668100\pi$
$618$		0			0
$619$	−8.27089e7	−	1.43256e8i	−0.348723	−	0.604006i	0.637300	−	0.770616i	$-0.280051\pi$
$619$	−8.27089e7	−	1.43256e8i	−0.348723	−	0.604006i	−0.986023	+	0.166610i	$0.946718\pi$
$620$		0			0
$621$	1.13517e7	−	1.65068e7i	0.0474010	−	0.0689270i
$622$		0			0
$623$	−2.24477e8	+	1.29602e8i	−0.928343	+	0.535979i
$624$		0			0
$625$	1.05615e8	−	1.82931e8i	0.432600	−	0.749285i
$626$		0			0
$627$	1.29402e8	+	2.38382e8i	0.524973	+	0.967099i
$628$		0			0
$629$		−	4.62014e8i		−	1.85653i
$630$		0			0
$631$	9.75259e7			0.388179			0.194090	−	0.980984i	$-0.437825\pi$
$631$	9.75259e7			0.388179			0.194090	+	0.980984i	$0.437825\pi$
$632$		0			0
$633$	−7.89205e7	−	4.83728e7i	−0.311156	−	0.190717i
$634$		0			0
$635$	−3.25829e8	−	1.88118e8i	−1.27253	−	0.734697i
$636$		0			0
$637$	−6.37083e7	−	1.10346e8i	−0.246478	−	0.426912i
$638$		0			0
$639$	1.96856e7	−	3.74270e8i	0.0754476	−	1.43444i
$640$		0			0
$641$	−6.96228e7	+	4.01968e7i	−0.264349	+	0.152622i	−0.626317	−	0.779569i	$-0.715438\pi$
$641$	−6.96228e7	+	4.01968e7i	−0.264349	+	0.152622i	0.361968	+	0.932191i	$0.382105\pi$
$642$		0			0
$643$	−2.39687e7	+	4.15150e7i	−0.0901594	+	0.156161i	−0.907578	−	0.419883i	$-0.862071\pi$
$643$	−2.39687e7	+	4.15150e7i	−0.0901594	+	0.156161i	0.817419	+	0.576044i	$0.195404\pi$
$644$		0			0
$645$	9.44715e7	+	2.48275e6i	0.352064	+	0.00925240i
$646$		0			0
$647$		−	9.94412e7i		−	0.367159i	−0.983005	−	0.183579i	$-0.941232\pi$
$647$		−	9.94412e7i		−	0.367159i	0.983005	−	0.183579i	$-0.0587684\pi$
$648$		0			0
$649$	7.13813e7			0.261126
$650$		0			0
$651$	8.67043e6	−	3.29919e8i	0.0314266	−	1.19582i
$652$		0			0
$653$	−1.05701e8	−	6.10267e7i	−0.379613	−	0.219170i	0.298037	−	0.954554i	$-0.403668\pi$
$653$	−1.05701e8	−	6.10267e7i	−0.379613	−	0.219170i	−0.677650	+	0.735385i	$0.737001\pi$
$654$		0			0
$655$	−1.38178e8	−	2.39331e8i	−0.491715	−	0.851676i
$656$		0			0
$657$	2.01102e7	+	1.05774e6i	0.0709120	+	0.00372977i
$658$		0			0
$659$	2.06024e8	−	1.18948e8i	0.719883	−	0.415625i	−0.0948267	−	0.995494i	$-0.530230\pi$
$659$	2.06024e8	−	1.18948e8i	0.719883	−	0.415625i	0.814710	+	0.579869i	$0.196896\pi$
$660$		0			0
$661$	−2.05664e8	+	3.56221e8i	−0.712121	+	1.23343i	0.251938	+	0.967743i	$0.418932\pi$
$661$	−2.05664e8	+	3.56221e8i	−0.712121	+	1.23343i	−0.964059	+	0.265687i	$0.914401\pi$
$662$		0			0
$663$	−2.17430e8	+	3.54739e8i	−0.746070	+	1.21722i
$664$		0			0
$665$			8.52202e8i			2.89786i
$666$		0			0
$667$	−2.20474e7			−0.0742985
$668$		0			0
$669$	2.06279e7	−	1.11975e7i	0.0688932	−	0.0373975i
$670$		0			0
$671$	2.36926e8	+	1.36789e8i	0.784232	+	0.452776i
$672$		0			0
$673$	1.70745e8	+	2.95740e8i	0.560149	+	0.970207i	0.997483	+	0.0709074i	$0.0225895\pi$
$673$	1.70745e8	+	2.95740e8i	0.560149	+	0.970207i	−0.437334	+	0.899299i	$0.644077\pi$
$674$		0			0
$675$	−3.11029e8	+	1.48245e8i	−1.01132	+	0.482025i
$676$		0			0
$677$	−6.61964e6	+	3.82185e6i	−0.0213338	+	0.0123171i	−0.510629	−	0.859801i	$-0.670587\pi$
$677$	−6.61964e6	+	3.82185e6i	−0.0213338	+	0.0123171i	0.489295	+	0.872118i	$0.337254\pi$
$678$		0			0
$679$	2.74450e8	−	4.75362e8i	0.876706	−	1.51850i
$680$		0			0
$681$	−2.58452e8	−	4.76116e8i	−0.818349	−	1.50755i
$682$		0			0
$683$			3.29207e8i			1.03325i	0.856211	+	0.516626i	$0.172812\pi$
$683$			3.29207e8i			1.03325i	−0.856211	+	0.516626i	$0.827188\pi$
$684$		0			0
$685$	−8.86835e8			−2.75912
$686$		0			0
$687$	9.21748e7	+	5.64968e7i	0.284277	+	0.174242i
$688$		0			0
$689$	−2.06900e8	−	1.19454e8i	−0.632562	−	0.365210i
$690$		0			0
$691$	−1.33318e8	−	2.30914e8i	−0.404068	−	0.699867i	0.590144	−	0.807298i	$-0.299071\pi$
$691$	−1.33318e8	−	2.30914e8i	−0.404068	−	0.699867i	−0.994213	+	0.107431i	$0.965738\pi$
$692$		0			0
$693$	2.09376e8	+	1.36026e8i	0.629110	+	0.408718i
$694$		0			0
$695$	3.96996e8	−	2.29206e8i	1.18258	−	0.682765i
$696$		0			0
$697$	−1.04471e8	+	1.80950e8i	−0.308531	+	0.534392i
$698$		0			0
$699$	1.48485e8	+	3.90226e6i	0.434763	+	0.0114258i
$700$		0			0
$701$		−	2.01424e8i		−	0.584733i	−0.956306	−	0.292366i	$-0.905557\pi$
$701$		−	2.01424e8i		−	0.584733i	0.956306	−	0.292366i	$-0.0944427\pi$
$702$		0			0
$703$	−1.06646e9			−3.06959
$704$		0			0
$705$	2.21522e7	−	8.42917e8i	0.0632194	−	2.40557i
$706$		0			0
$707$	1.60037e8	+	9.23972e7i	0.452857	+	0.261457i
$708$		0			0
$709$	−7.75165e7	−	1.34263e8i	−0.217498	−	0.376718i	0.736544	−	0.676389i	$-0.236456\pi$
$709$	−7.75165e7	−	1.34263e8i	−0.217498	−	0.376718i	−0.954042	+	0.299671i	$0.903123\pi$
$710$		0			0
$711$	1.44743e8	+	2.84206e8i	0.402705	+	0.790723i
$712$		0			0
$713$	−2.69672e7	+	1.55695e7i	−0.0743992	+	0.0429544i
$714$		0			0
$715$	2.36813e8	−	4.10172e8i	0.647870	−	1.12214i
$716$		0			0
$717$	−3.20693e7	+	5.23213e7i	−0.0870027	+	0.141945i
$718$		0			0
$719$			2.01271e8i			0.541495i	0.962650	+	0.270748i	$0.0872709\pi$
$719$			2.01271e8i			0.541495i	−0.962650	+	0.270748i	$0.912729\pi$
$720$		0			0
$721$	−7.14524e7			−0.190639
$722$		0			0
$723$	3.72854e8	−	2.02397e8i	0.986560	−	0.535538i
$724$		0			0
$725$	3.28388e8	+	1.89595e8i	0.861735	+	0.497523i
$726$		0			0
$727$	4.39179e7	+	7.60680e7i	0.114298	+	0.197970i	0.917499	−	0.397738i	$-0.130205\pi$
$727$	4.39179e7	+	7.60680e7i	0.114298	+	0.197970i	−0.803201	+	0.595708i	$0.796872\pi$
$728$		0			0
$729$	−3.82616e8	−	6.08228e7i	−0.987600	−	0.156994i
$730$		0			0
$731$	−8.45465e7	+	4.88129e7i	−0.216443	+	0.124963i
$732$		0			0
$733$	−1.08255e8	+	1.87503e8i	−0.274875	+	0.476097i	−0.970104	−	0.242691i	$-0.921970\pi$
$733$	−1.08255e8	+	1.87503e8i	−0.274875	+	0.476097i	0.695229	+	0.718789i	$0.255303\pi$
$734$		0			0
$735$	9.84176e7	+	1.81303e8i	0.247862	+	0.456609i
$736$		0			0
$737$		−	6.37524e7i		−	0.159255i
$738$		0			0
$739$	−1.17807e8			−0.291902			−0.145951	−	0.989292i	$-0.546624\pi$
$739$	−1.17807e8			−0.291902			−0.145951	+	0.989292i	$0.546624\pi$
$740$		0			0
$741$	8.18842e8	+	5.01893e8i	2.01254	+	1.23355i
$742$		0			0
$743$	2.93172e8	+	1.69263e8i	0.714754	+	0.412663i	0.812819	−	0.582517i	$-0.197932\pi$
$743$	2.93172e8	+	1.69263e8i	0.714754	+	0.412663i	−0.0980650	+	0.995180i	$0.531265\pi$
$744$		0			0
$745$	−3.64725e7	−	6.31722e7i	−0.0882057	−	0.152777i
$746$		0			0
$747$	−4.03379e8	+	2.05436e8i	−0.967725	+	0.492850i
$748$		0			0
$749$	−3.70798e7	+	2.14080e7i	−0.0882453	+	0.0509484i
$750$		0			0
$751$	−1.34900e8	+	2.33654e8i	−0.318488	+	0.551637i	−0.980173	−	0.198145i	$-0.936508\pi$
$751$	−1.34900e8	+	2.33654e8i	−0.318488	+	0.551637i	0.661685	+	0.749782i	$0.269842\pi$
$752$		0			0
$753$	−3.69351e8	−	9.70671e6i	−0.865076	−	0.0227346i
$754$		0			0
$755$		−	1.01777e9i		−	2.36489i
$756$		0			0
$757$	4.99015e8			1.15034			0.575170	−	0.818034i	$-0.304936\pi$
$757$	4.99015e8			1.15034			0.575170	+	0.818034i	$0.304936\pi$
$758$		0			0
$759$	618898.	−	2.35498e7i	0.00141545	−	0.0538594i
$760$		0			0
$761$	6.91750e7	+	3.99382e7i	0.156962	+	0.0906222i	0.576424	−	0.817151i	$-0.304448\pi$
$761$	6.91750e7	+	3.99382e7i	0.156962	+	0.0906222i	−0.419462	+	0.907773i	$0.637781\pi$
$762$		0			0
$763$	2.49188e8	+	4.31607e8i	0.560989	+	0.971661i
$764$		0			0
$765$	3.66997e8	−	5.64892e8i	0.819744	−	1.26177i
$766$		0			0
$767$	2.18888e8	−	1.26375e8i	0.485105	−	0.280075i
$768$		0			0
$769$	2.15306e8	−	3.72921e8i	0.473454	−	0.820046i	−0.526085	−	0.850432i	$-0.676340\pi$
$769$	2.15306e8	−	3.72921e8i	0.473454	−	0.820046i	0.999538	+	0.0303866i	$0.00967383\pi$
$770$		0			0
$771$	4.55398e8	−	7.42984e8i	0.993638	−	1.62113i
$772$		0			0
$773$			6.33287e8i			1.37108i	0.728036	+	0.685539i	$0.240434\pi$
$773$			6.33287e8i			1.37108i	−0.728036	+	0.685539i	$0.759566\pi$
$774$		0			0
$775$	5.35557e8			1.15054
$776$		0			0
$777$	−8.62785e8	+	4.68348e8i	−1.83924	+	0.998403i
$778$		0			0
$779$	4.17685e8	+	2.41151e8i	0.883561	+	0.510124i
$780$		0			0
$781$	−2.20362e8	−	3.81678e8i	−0.462576	−	0.801206i
$782$		0			0
$783$	1.83447e8	+	3.84886e8i	0.382143	+	0.801765i
$784$		0			0
$785$	−3.11236e8	+	1.79692e8i	−0.643399	+	0.371466i
$786$		0			0
$787$	−1.51221e8	+	2.61922e8i	−0.310232	+	0.537338i	−0.978413	−	0.206661i	$-0.933740\pi$
$787$	−1.51221e8	+	2.61922e8i	−0.310232	+	0.537338i	0.668180	+	0.743999i	$0.267073\pi$
$788$		0			0
$789$	1.57222e8	+	2.89633e8i	0.320098	+	0.589681i
$790$		0			0
$791$			1.04376e9i			2.10897i
$792$		0			0
$793$	9.68697e8			1.94253
$794$		0			0
$795$	3.29784e8	+	2.02135e8i	0.656339	+	0.402290i
$796$		0			0
$797$	−6.44383e8	−	3.72035e8i	−1.27283	−	0.734867i	−0.297307	−	0.954782i	$-0.596089\pi$
$797$	−6.44383e8	−	3.72035e8i	−1.27283	−	0.734867i	−0.975519	+	0.219915i	$0.929422\pi$
$798$		0			0
$799$	4.35531e8	+	7.54362e8i	0.853844	+	1.47890i
$800$		0			0
$801$	2.48417e7	−	4.72300e8i	0.0483374	−	0.919010i
$802$		0			0
$803$	2.05082e7	−	1.18404e7i	0.0396078	−	0.0228676i
$804$		0			0
$805$	3.70080e7	−	6.40998e7i	0.0709428	−	0.122877i
$806$		0			0
$807$	−1.13819e8	−	2.99122e6i	−0.216568	−	0.00569150i
$808$		0			0
$809$		−	3.53190e8i		−	0.667058i	−0.942740	−	0.333529i	$-0.891761\pi$
$809$		−	3.53190e8i		−	0.667058i	0.942740	−	0.333529i	$-0.108239\pi$
$810$		0			0
$811$	2.70373e8			0.506875			0.253438	−	0.967352i	$-0.418439\pi$
$811$	2.70373e8			0.506875			0.253438	+	0.967352i	$0.418439\pi$
$812$		0			0
$813$	−9.81484e6	+	3.73466e8i	−0.0182647	+	0.694991i
$814$		0			0
$815$	−2.47759e8	−	1.43044e8i	−0.457674	−	0.264238i
$816$		0			0
$817$	1.12675e8	+	1.95158e8i	0.206614	+	0.357866i
$818$		0			0
$819$	8.82867e8	+	4.64363e7i	1.60710	+	0.0845291i
$820$		0			0
$821$	−7.77575e8	+	4.48933e8i	−1.40512	+	0.811245i	−0.994912	−	0.100748i	$-0.967876\pi$
$821$	−7.77575e8	+	4.48933e8i	−1.40512	+	0.811245i	−0.410206	+	0.911993i	$0.634543\pi$
$822$		0			0
$823$	−5.32686e7	+	9.22639e7i	−0.0955590	+	0.165513i	−0.909842	−	0.414955i	$-0.863797\pi$
$823$	−5.32686e7	+	9.22639e7i	−0.0955590	+	0.165513i	0.814283	+	0.580468i	$0.197131\pi$
$824$		0			0
$825$	−2.11733e8	+	3.45443e8i	−0.377074	+	0.615198i
$826$		0			0
$827$		−	5.52541e8i		−	0.976895i	−0.872593	−	0.488448i	$-0.837563\pi$
$827$		−	5.52541e8i		−	0.976895i	0.872593	−	0.488448i	$-0.162437\pi$
$828$		0			0
$829$	−1.61843e8			−0.284073			−0.142036	−	0.989861i	$-0.545365\pi$
$829$	−1.61843e8			−0.284073			−0.142036	+	0.989861i	$0.545365\pi$
$830$		0			0
$831$	−9.42484e8	+	5.11612e8i	−1.64237	+	0.891534i
$832$		0			0
$833$	−1.84557e8	−	1.06554e8i	−0.319297	−	0.184346i
$834$		0			0
$835$	−1.89314e8	−	3.27902e8i	−0.325180	−	0.563229i
$836$		0			0
$837$	4.96184e8	+	3.41225e8i	0.846187	+	0.581921i
$838$		0			0
$839$	−1.57132e8	+	9.07201e7i	−0.266059	+	0.153609i	−0.627095	−	0.778942i	$-0.715756\pi$
$839$	−1.57132e8	+	9.07201e7i	−0.266059	+	0.153609i	0.361036	+	0.932552i	$0.382423\pi$
$840$		0			0
$841$	−6.27952e7	+	1.08764e8i	−0.105569	+	0.182852i
$842$		0			0
$843$	2.53197e7	+	4.66436e7i	0.0422645	+	0.0778591i
$844$		0			0
$845$		−	7.98477e8i		−	1.32340i
$846$		0			0
$847$	−4.14186e8			−0.681625
$848$		0			0
$849$	−7.21037e8	−	4.41946e8i	−1.17824	−	0.722181i
$850$		0			0
$851$	8.02159e7	+	4.63127e7i	0.130158	+	0.0751469i
$852$		0			0
$853$	2.50718e8	+	4.34256e8i	0.403960	+	0.699680i	0.994200	−	0.107549i	$-0.0343001\pi$
$853$	2.50718e8	+	4.34256e8i	0.403960	+	0.699680i	−0.590240	+	0.807228i	$0.700967\pi$
$854$		0			0
$855$	−1.30394e9	−	8.47136e8i	−2.08621	−	1.35536i
$856$		0			0
$857$	1.22184e8	−	7.05432e7i	0.194121	−	0.112076i	−0.399789	−	0.916607i	$-0.630917\pi$
$857$	1.22184e8	−	7.05432e7i	0.194121	−	0.112076i	0.593910	+	0.804531i	$0.297583\pi$
$858$		0			0
$859$	4.31344e6	−	7.47109e6i	0.00680525	−	0.0117870i	−0.862603	−	0.505882i	$-0.831167\pi$
$859$	4.31344e6	−	7.47109e6i	0.00680525	−	0.0117870i	0.869408	+	0.494095i	$0.164500\pi$
$860$		0			0
$861$	4.43817e8	+	1.16637e7i	0.695336	+	0.0182737i
$862$		0			0
$863$		−	1.89360e8i		−	0.294616i	−0.989091	−	0.147308i	$-0.952939\pi$
$863$		−	1.89360e8i		−	0.294616i	0.989091	−	0.147308i	$-0.0470608\pi$
$864$		0			0
$865$	7.25664e8			1.12121
$866$		0			0
$867$	−1.16059e6	+	4.41617e7i	−0.00178083	+	0.0677624i
$868$		0			0
$869$	3.24805e8	+	1.87526e8i	0.494952	+	0.285761i
$870$		0			0
$871$	−1.12869e8	−	1.95494e8i	−0.170812	−	0.295855i
$872$		0			0
$873$	4.54522e8	+	8.92467e8i	0.683144	+	1.34137i
$874$		0			0
$875$	−1.18402e8	+	6.83594e7i	−0.176740	+	0.102041i
$876$		0			0
$877$	−2.83343e8	+	4.90764e8i	−0.420062	+	0.727569i	−0.995945	−	0.0899631i	$-0.971325\pi$
$877$	−2.83343e8	+	4.90764e8i	−0.420062	+	0.727569i	0.575883	+	0.817532i	$0.304658\pi$
$878$		0			0
$879$	3.14559e8	−	5.13204e8i	0.463164	−	0.755655i
$880$		0			0
$881$		−	9.14863e8i		−	1.33791i	−0.743301	−	0.668957i	$-0.766741\pi$
$881$		−	9.14863e8i		−	1.33791i	0.743301	−	0.668957i	$-0.233259\pi$
$882$		0			0
$883$	1.22232e9			1.77543			0.887716	−	0.460392i	$-0.152291\pi$
$883$	1.22232e9			1.77543			0.887716	+	0.460392i	$0.152291\pi$
$884$		0			0
$885$	−3.59642e8	+	1.95226e8i	−0.518849	+	0.281649i
$886$		0			0
$887$	−2.44500e8	−	1.41162e8i	−0.350354	−	0.202277i	0.314487	−	0.949262i	$-0.398168\pi$
$887$	−2.44500e8	−	1.41162e8i	−0.350354	−	0.202277i	−0.664841	+	0.746985i	$0.731501\pi$
$888$		0			0
$889$	−4.12924e8	−	7.15206e8i	−0.587713	−	1.01795i
$890$		0			0
$891$	−4.16263e8	+	1.85144e8i	−0.588484	+	0.261743i
$892$		0			0
$893$	1.74129e9	−	1.00533e9i	2.44521	−	1.41174i
$894$		0			0
$895$	3.57613e8	−	6.19405e8i	0.498821	−	0.863983i
$896$		0			0
$897$	−3.97952e7	−	7.33101e7i	−0.0551383	−	0.101575i
$898$		0			0
$899$		−	6.62730e8i		−	0.912132i
$900$		0			0
$901$	−3.99579e8			−0.546297
$902$		0			0
$903$	1.76861e8	+	1.08404e8i	0.240198	+	0.147225i
$904$		0			0
$905$	1.23193e9	+	7.11253e8i	1.66203	+	0.959573i
$906$		0			0
$907$	−1.54357e8	−	2.67354e8i	−0.206873	−	0.358315i	0.743855	−	0.668341i	$-0.232995\pi$
$907$	−1.54357e8	−	2.67354e8i	−0.206873	−	0.358315i	−0.950728	+	0.310026i	$0.899662\pi$
$908$		0			0
$909$	−3.00460e8	+	1.53021e8i	−0.400033	+	0.203732i
$910$		0			0
$911$	−4.57054e8	+	2.63881e8i	−0.604523	+	0.349022i	−0.770819	−	0.637054i	$-0.780153\pi$
$911$	−4.57054e8	+	2.63881e8i	−0.604523	+	0.349022i	0.166296	+	0.986076i	$0.446819\pi$
$912$		0			0
$913$	−2.66160e8	+	4.61003e8i	−0.349728	+	0.605747i
$914$		0			0
$915$	−1.56782e9	−	4.12031e7i	−2.04660	−	0.0537857i
$916$		0			0
$917$		−	6.06609e8i		−	0.786684i
$918$		0			0
$919$	3.44911e8			0.444387			0.222193	−	0.975003i	$-0.428678\pi$
$919$	3.44911e8			0.444387			0.222193	+	0.975003i	$0.428678\pi$
$920$		0			0
$921$	−2.13090e7	+	8.10832e8i	−0.0272763	+	1.03789i
$922$		0			0
$923$	−1.35146e9	−	7.80267e8i	−1.71869	−	0.992289i
$924$		0			0
$925$	−7.96524e8	−	1.37962e9i	−1.00641	−	1.74315i
$926$		0			0
$927$	7.10277e7	−	1.09328e8i	0.0891638	−	0.137243i
$928$		0			0
$929$	1.04582e8	−	6.03806e7i	0.130440	−	0.0753096i	−0.433360	−	0.901221i	$-0.642672\pi$
$929$	1.04582e8	−	6.03806e7i	0.130440	−	0.0753096i	0.563800	+	0.825911i	$0.309339\pi$
$930$		0			0
$931$	−2.45958e8	+	4.26011e8i	−0.304797	+	0.527925i
$932$		0			0
$933$	−2.85621e8	+	4.65992e8i	−0.351678	+	0.573764i
$934$		0			0
$935$		−	7.92153e8i		−	0.969112i
$936$		0			0
$937$	1.90750e7			0.0231870			0.0115935	−	0.999933i	$-0.496310\pi$
$937$	1.90750e7			0.0231870			0.0115935	+	0.999933i	$0.496310\pi$
$938$		0			0
$939$	−3.41974e8	+	1.85635e8i	−0.413044	+	0.224214i
$940$		0			0
$941$	−1.13088e9	−	6.52916e8i	−1.35722	−	0.783589i	−0.367968	−	0.929838i	$-0.619946\pi$
$941$	−1.13088e9	−	6.52916e8i	−1.35722	−	0.783589i	−0.989248	+	0.146250i	$0.953280\pi$
$942$		0			0
$943$	−2.09446e7	−	3.62771e7i	−0.0249768	−	0.0432611i
$944$		0			0
$945$	−1.42693e9	−	1.12709e8i	−1.69086	−	0.133556i
$946$		0			0
$947$	−1.23687e9	+	7.14108e8i	−1.45638	+	0.840842i	−0.998831	−	0.0483423i	$-0.984606\pi$
$947$	−1.23687e9	+	7.14108e8i	−1.45638	+	0.840842i	−0.457550	+	0.889184i	$0.651273\pi$
$948$		0			0
$949$	4.19251e7	−	7.26163e7i	0.0490541	−	0.0849642i
$950$		0			0
$951$	4.90984e8	+	9.04483e8i	0.570855	+	1.05162i
$952$		0			0
$953$			1.44061e9i			1.66443i	0.554451	+	0.832216i	$0.312928\pi$
$953$			1.44061e9i			1.66443i	−0.554451	+	0.832216i	$0.687072\pi$
$954$		0			0
$955$	8.66255e8			0.994571
$956$		0			0
$957$	4.27472e8	+	2.62011e8i	0.487722	+	0.298940i
$958$		0			0
$959$	−1.68583e9	−	9.73315e8i	−1.91143	−	1.10356i
$960$		0			0
$961$	−2.42578e7	−	4.20158e7i	−0.0273327	−	0.0473416i
$962$		0			0
$963$	4.10341e6	−	7.80157e7i	0.00459480	−	0.0873581i
$964$		0			0
$965$	3.27825e8	−	1.89270e8i	0.364805	−	0.210620i
$966$		0			0
$967$	−5.31605e8	+	9.20767e8i	−0.587909	+	1.01829i	0.406597	+	0.913607i	$0.366715\pi$
$967$	−5.31605e8	+	9.20767e8i	−0.587909	+	1.01829i	−0.994506	+	0.104680i	$0.966618\pi$
$968$		0			0
$969$	1.60577e9	+	4.22003e7i	1.76486	+	0.0463814i
$970$		0			0
$971$			4.08439e8i			0.446139i	0.974803	+	0.223069i	$0.0716076\pi$
$971$			4.08439e8i			0.446139i	−0.974803	+	0.223069i	$0.928392\pi$
$972$		0			0
$973$	1.00623e9			1.09234
$974$		0			0
$975$	−3.76899e7	+	1.43414e9i	−0.0406641	+	1.54731i
$976$		0			0
$977$	−8.92898e7	−	5.15515e7i	−0.0957454	−	0.0552786i	0.451363	−	0.892341i	$-0.350938\pi$
$977$	−8.92898e7	−	5.15515e7i	−0.0957454	−	0.0552786i	−0.547108	+	0.837062i	$0.684271\pi$
$978$		0			0
$979$	−2.78080e8	−	4.81648e8i	−0.296361	−	0.513313i
$980$		0			0
$981$	−9.08100e8	−	4.77636e7i	−0.961893	−	0.0505929i
$982$		0			0
$983$	−8.17979e8	+	4.72260e8i	−0.861155	+	0.497188i	−0.864399	−	0.502806i	$-0.832301\pi$
$983$	−8.17979e8	+	4.72260e8i	−0.861155	+	0.497188i	0.00324369	+	0.999995i	$0.498967\pi$
$984$		0			0
$985$	2.65231e8	−	4.59394e8i	0.277534	−	0.480703i
$986$		0			0
$987$	9.67225e8	−	1.57803e9i	1.00595	−	1.64121i
$988$		0			0
$989$		−	1.95722e7i		−	0.0202326i
$990$		0			0
$991$	5.79442e8			0.595373			0.297687	−	0.954664i	$-0.403785\pi$
$991$	5.79442e8			0.595373			0.297687	+	0.954664i	$0.403785\pi$
$992$		0			0
$993$	1.07140e9	−	5.81590e8i	1.09421	−	0.593976i
$994$		0			0
$995$	1.93905e9	+	1.11951e9i	1.96843	+	1.13647i
$996$		0			0
$997$	6.25125e8	+	1.08275e9i	0.630786	+	1.09255i	0.987391	+	0.158298i	$0.0506006\pi$
$997$	6.25125e8	+	1.08275e9i	0.630786	+	1.09255i	−0.356606	+	0.934255i	$0.616066\pi$
$998$		0			0
$999$	1.41046e8	−	1.78569e9i	0.141470	−	1.79106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.m.a.41.9	✓	36
3.2	odd	2		216.7.m.a.17.3		36
4.3	odd	2		144.7.q.d.113.10		36
9.2	odd	6	inner	72.7.m.a.65.9	yes	36
9.4	even	3		648.7.e.c.161.5		36
9.5	odd	6		648.7.e.c.161.32		36
9.7	even	3		216.7.m.a.89.3		36
12.11	even	2		432.7.q.d.17.3		36
36.7	odd	6		432.7.q.d.305.3		36
36.11	even	6		144.7.q.d.65.10		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.m.a.41.9	✓	36	1.1	even	1	trivial
72.7.m.a.65.9	yes	36	9.2	odd	6	inner
144.7.q.d.65.10		36	36.11	even	6
144.7.q.d.113.10		36	4.3	odd	2
216.7.m.a.17.3		36	3.2	odd	2
216.7.m.a.89.3		36	9.7	even	3
432.7.q.d.17.3		36	12.11	even	2
432.7.q.d.305.3		36	36.7	odd	6
648.7.e.c.161.5		36	9.4	even	3
648.7.e.c.161.32		36	9.5	odd	6

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.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.709327 - 26.9907i) q^{3} +(157.631 + 91.0083i) q^{5} +(199.766 + 346.005i) q^{7} +(-727.994 - 38.2905i) q^{9} +O(q^{10})\)	\(q+(0.709327 - 26.9907i) q^{3} +(157.631 + 91.0083i) q^{5} +(199.766 + 346.005i) q^{7} +(-727.994 - 38.2905i) q^{9} +(-742.403 + 428.627i) q^{11} +(-1517.70 + 2628.73i) q^{13} +(2568.19 - 4190.01i) q^{15} +5076.79i q^{17} +11718.7 q^{19} +(9480.61 - 5146.39i) q^{21} +(-881.443 - 508.901i) q^{23} +(8752.52 + 15159.8i) q^{25} +(-1549.87 + 19621.9i) q^{27} +(18759.7 - 10830.9i) q^{29} +(15297.2 - 26495.6i) q^{31} +(11042.3 + 20342.0i) q^{33} +72721.5i q^{35} -91005.2 q^{37} +(69874.7 + 42828.4i) q^{39} +(35642.6 + 20578.3i) q^{41} +(9614.93 + 16653.5i) q^{43} +(-111270. - 72289.2i) q^{45} +(148590. - 85788.7i) q^{47} +(-20988.5 + 36353.1i) q^{49} +(137026. + 3601.10i) q^{51} +78707.1i q^{53} -156034. q^{55} +(8312.40 - 316296. i) q^{57} +(-72111.7 - 41633.7i) q^{59} +(-159567. - 276378. i) q^{61} +(-132180. - 259539. i) q^{63} +(-478473. + 276246. i) q^{65} +(-37184.1 + 64404.8i) q^{67} +(-14360.8 + 23429.8i) q^{69} +514112. i q^{71} -27624.1 q^{73} +(415382. - 225483. i) q^{75} +(-296614. - 171250. i) q^{77} +(-218752. - 378890. i) q^{79} +(528509. + 55750.4i) q^{81} +(537767. - 310480. i) q^{83} +(-462030. + 800259. i) q^{85} +(-279026. - 514019. i) q^{87} +648769. i q^{89} -1.21274e6 q^{91} +(-704282. - 431676. i) q^{93} +(1.84723e6 + 1.06650e6i) q^{95} +(-686929. - 1.18980e6i) q^{97} +(556877. - 283611. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{3} + 74 q^{9}+O(q^{10}) \) 36 * q + 10 * q^3 + 74 * q^9	\( 36 q + 10 q^{3} + 74 q^{9} + 1350 q^{11} + 7912 q^{15} + 9540 q^{19} + 3828 q^{21} + 30888 q^{23} + 56250 q^{25} + 11392 q^{27} + 38556 q^{29} + 27720 q^{31} + 33514 q^{33} + 134068 q^{39} + 179226 q^{41} + 15930 q^{43} - 185620 q^{45} + 187596 q^{47} - 198774 q^{49} - 158098 q^{51} - 197064 q^{55} - 244990 q^{57} - 408618 q^{59} + 17136 q^{61} - 417048 q^{63} - 125712 q^{65} + 27090 q^{67} - 848504 q^{69} - 534060 q^{73} - 1405714 q^{75} + 48168 q^{77} + 172620 q^{79} + 349010 q^{81} + 1801980 q^{83} - 791568 q^{85} + 28500 q^{87} + 538560 q^{91} - 1116448 q^{93} + 1832652 q^{95} + 770706 q^{97} - 614260 q^{99}+O(q^{100}) \) 36 * q + 10 * q^3 + 74 * q^9 + 1350 * q^11 + 7912 * q^15 + 9540 * q^19 + 3828 * q^21 + 30888 * q^23 + 56250 * q^25 + 11392 * q^27 + 38556 * q^29 + 27720 * q^31 + 33514 * q^33 + 134068 * q^39 + 179226 * q^41 + 15930 * q^43 - 185620 * q^45 + 187596 * q^47 - 198774 * q^49 - 158098 * q^51 - 197064 * q^55 - 244990 * q^57 - 408618 * q^59 + 17136 * q^61 - 417048 * q^63 - 125712 * q^65 + 27090 * q^67 - 848504 * q^69 - 534060 * q^73 - 1405714 * q^75 + 48168 * q^77 + 172620 * q^79 + 349010 * q^81 + 1801980 * q^83 - 791568 * q^85 + 28500 * q^87 + 538560 * q^91 - 1116448 * q^93 + 1832652 * q^95 + 770706 * q^97 - 614260 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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