LMFDB - Embedded newform 72.8.d.b.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,8,Mod(37,72)]

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([0, 1, 0]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("72.37");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	72.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$22.4917218349$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 10x^{4} - 24x^{3} - 320x^{2} - 3072x + 32768 $ x^6 - 3x^5 - 10x^4 - 24x^3 - 320x^2 - 3072*x + 32768
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 8)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			37.3
Root			$0.776001 - 5.60338i$ of defining polynomial
Character	$\chi$	$=$	72.37
Dual form			72.8.d.b.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.55200 - 11.2068i) q^{2} +(-123.183 + 34.7858i) q^{4} -184.916i q^{5} +1051.96 q^{7} +(581.015 + 1326.49i) q^{8} +O(q^{10})$	\(q+(-1.55200 - 11.2068i) q^{2} +(-123.183 + 34.7858i) q^{4} -184.916i q^{5} +1051.96 q^{7} +(581.015 + 1326.49i) q^{8} +(-2072.30 + 286.989i) q^{10} +4324.35i q^{11} +11253.2i q^{13} +(-1632.64 - 11789.0i) q^{14} +(13963.9 - 8570.01i) q^{16} +21746.4 q^{17} -45466.5i q^{19} +(6432.44 + 22778.4i) q^{20} +(48462.0 - 6711.41i) q^{22} -4414.37 q^{23} +43931.2 q^{25} +(126112. - 17465.1i) q^{26} +(-129583. + 36593.2i) q^{28} +23687.1i q^{29} +72941.9 q^{31} +(-117714. - 143189. i) q^{32} +(-33750.5 - 243707. i) q^{34} -194523. i q^{35} -483338. i q^{37} +(-509532. + 70564.1i) q^{38} +(245289. - 107439. i) q^{40} +411040. q^{41} +96165.3i q^{43} +(-150426. - 532685. i) q^{44} +(6851.11 + 49470.7i) q^{46} +156171. q^{47} +283070. q^{49} +(-68181.3 - 492326. i) q^{50} +(-391453. - 1.38620e6i) q^{52} -686962. i q^{53} +799641. q^{55} +(611203. + 1.39541e6i) q^{56} +(265456. - 36762.4i) q^{58} +1.79961e6i q^{59} +1.36394e6i q^{61} +(-113206. - 817441. i) q^{62} +(-1.42199e6 + 1.54142e6i) q^{64} +2.08090e6 q^{65} +1.08853e6i q^{67} +(-2.67878e6 + 756466. i) q^{68} +(-2.17997e6 + 301900. i) q^{70} +5.60830e6 q^{71} +21698.7 q^{73} +(-5.41665e6 + 750142. i) q^{74} +(1.58159e6 + 5.60068e6i) q^{76} +4.54903e6i q^{77} +2.34010e6 q^{79} +(-1.58473e6 - 2.58214e6i) q^{80} +(-637935. - 4.60643e6i) q^{82} -882169. i q^{83} -4.02125e6i q^{85} +(1.07770e6 - 149249. i) q^{86} +(-5.73621e6 + 2.51252e6i) q^{88} +1.34738e6 q^{89} +1.18379e7i q^{91} +(543773. - 153557. i) q^{92} +(-242378. - 1.75017e6i) q^{94} -8.40746e6 q^{95} +7.32798e6 q^{97} +(-439325. - 3.17229e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 116 q^{4} - 688 q^{7} - 1512 q^{8}+O(q^{10}) $ 6 * q - 6 * q^2 + 116 * q^4 - 688 * q^7 - 1512 * q^8	$ 6 q - 6 q^{2} + 116 q^{4} - 688 q^{7} - 1512 q^{8} - 1656 q^{10} - 12048 q^{14} + 35344 q^{16} - 1452 q^{17} + 114768 q^{20} + 152860 q^{22} + 1296 q^{23} - 39314 q^{25} + 316968 q^{26} - 480800 q^{28} - 89280 q^{31} - 817056 q^{32} - 1009108 q^{34} - 974124 q^{38} + 954464 q^{40} - 521244 q^{41} + 1096344 q^{44} + 929840 q^{46} - 1566432 q^{47} - 511050 q^{49} + 148626 q^{50} + 823952 q^{52} - 3270256 q^{55} + 2468928 q^{56} + 3130744 q^{58} + 7055808 q^{62} - 4792768 q^{64} - 1416480 q^{65} - 6608040 q^{68} - 7406912 q^{70} + 7597104 q^{71} + 2089564 q^{73} - 7744200 q^{74} + 9241288 q^{76} + 16015904 q^{79} + 12600384 q^{80} + 10715932 q^{82} + 5639076 q^{86} + 1541200 q^{88} - 2169084 q^{89} - 669600 q^{92} + 15503712 q^{94} - 48537936 q^{95} - 1088308 q^{97} + 14983242 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 + 116 * q^4 - 688 * q^7 - 1512 * q^8 - 1656 * q^10 - 12048 * q^14 + 35344 * q^16 - 1452 * q^17 + 114768 * q^20 + 152860 * q^22 + 1296 * q^23 - 39314 * q^25 + 316968 * q^26 - 480800 * q^28 - 89280 * q^31 - 817056 * q^32 - 1009108 * q^34 - 974124 * q^38 + 954464 * q^40 - 521244 * q^41 + 1096344 * q^44 + 929840 * q^46 - 1566432 * q^47 - 511050 * q^49 + 148626 * q^50 + 823952 * q^52 - 3270256 * q^55 + 2468928 * q^56 + 3130744 * q^58 + 7055808 * q^62 - 4792768 * q^64 - 1416480 * q^65 - 6608040 * q^68 - 7406912 * q^70 + 7597104 * q^71 + 2089564 * q^73 - 7744200 * q^74 + 9241288 * q^76 + 16015904 * q^79 + 12600384 * q^80 + 10715932 * q^82 + 5639076 * q^86 + 1541200 * q^88 - 2169084 * q^89 - 669600 * q^92 + 15503712 * q^94 - 48537936 * q^95 - 1088308 * q^97 + 14983242 * 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 $

$2$	−1.55200	−	11.2068i	−0.137179	−	0.990546i
$2$	−1.55200	−	11.2068i	−0.137179	−	0.990546i
$3$		0			0
$3$		0			0
$4$	−123.183	+	34.7858i	−0.962364	+	0.271764i
$5$		−	184.916i		−	0.661574i	−0.943705	−	0.330787i	$-0.892686\pi$
$5$		−	184.916i		−	0.661574i	0.943705	−	0.330787i	$-0.107314\pi$
$6$		0			0
$7$	1051.96			1.15919			0.579595	−	0.814905i	$-0.303211\pi$
$7$	1051.96			1.15919			0.579595	+	0.814905i	$0.303211\pi$
$8$	581.015	+	1326.49i	0.401211	+	0.915986i
$9$		0			0
$10$	−2072.30	+	286.989i	−0.655320	+	0.0907540i
$11$			4324.35i			0.979596i	0.871836	+	0.489798i	$0.162929\pi$
$11$			4324.35i			0.979596i	−0.871836	+	0.489798i	$0.837071\pi$
$12$		0			0
$13$			11253.2i			1.42061i	0.703892	+	0.710307i	$0.251444\pi$
$13$			11253.2i			1.42061i	−0.703892	+	0.710307i	$0.748556\pi$
$14$	−1632.64	−	11789.0i	−0.159016	−	1.14823i
$15$		0			0
$16$	13963.9	−	8570.01i	0.852289	−	0.523072i
$17$	21746.4			1.07354			0.536768	−	0.843730i	$-0.319645\pi$
$17$	21746.4			1.07354			0.536768	+	0.843730i	$0.319645\pi$
$18$		0			0
$19$		−	45466.5i		−	1.52074i	−0.649492	−	0.760368i	$-0.725019\pi$
$19$		−	45466.5i		−	1.52074i	0.649492	−	0.760368i	$-0.274981\pi$
$20$	6432.44	+	22778.4i	0.179792	+	0.636675i
$21$		0			0
$22$	48462.0	−	6711.41i	0.970335	−	0.134380i
$23$	−4414.37			−0.0756522			−0.0378261	−	0.999284i	$-0.512043\pi$
$23$	−4414.37			−0.0756522			−0.0378261	+	0.999284i	$0.512043\pi$
$24$		0			0
$25$	43931.2			0.562320
$26$	126112.	−	17465.1i	1.40718	−	0.194878i
$27$		0			0
$28$	−129583.	+	36593.2i	−1.11556	+	0.315026i
$29$			23687.1i			0.180351i	0.995926	+	0.0901756i	$0.0287428\pi$
$29$			23687.1i			0.180351i	−0.995926	+	0.0901756i	$0.971257\pi$
$30$		0			0
$31$	72941.9			0.439755			0.219878	−	0.975527i	$-0.429434\pi$
$31$	72941.9			0.439755			0.219878	+	0.975527i	$0.429434\pi$
$32$	−117714.	−	143189.i	−0.635043	−	0.772477i
$33$		0			0
$34$	−33750.5	−	243707.i	−0.147266	−	1.06339i
$35$		−	194523.i		−	0.766890i
$36$		0			0
$37$		−	483338.i		−	1.56872i	−0.620307	−	0.784359i	$-0.712992\pi$
$37$		−	483338.i		−	1.56872i	0.620307	−	0.784359i	$-0.287008\pi$
$38$	−509532.	+	70564.1i	−1.50636	+	0.208613i
$39$		0			0
$40$	245289.	−	107439.i	0.605992	−	0.265431i
$41$	411040.			0.931410			0.465705	−	0.884940i	$-0.345801\pi$
$41$	411040.			0.931410			0.465705	+	0.884940i	$0.345801\pi$
$42$		0			0
$43$			96165.3i			0.184450i	0.995738	+	0.0922250i	$0.0293979\pi$
$43$			96165.3i			0.184450i	−0.995738	+	0.0922250i	$0.970602\pi$
$44$	−150426.	−	532685.i	−0.266219	−	0.942728i
$45$		0			0
$46$	6851.11	+	49470.7i	0.0103779	+	0.0749370i
$47$	156171.			0.219411			0.109705	−	0.993964i	$-0.465009\pi$
$47$	156171.			0.219411			0.109705	+	0.993964i	$0.465009\pi$
$48$		0			0
$49$	283070.			0.343722
$50$	−68181.3	−	492326.i	−0.0771384	−	0.557004i
$51$		0			0
$52$	−391453.	−	1.38620e6i	−0.386072	−	1.36715i
$53$		−	686962.i		−	0.633822i	−0.948455	−	0.316911i	$-0.897354\pi$
$53$		−	686962.i		−	0.633822i	0.948455	−	0.316911i	$-0.102646\pi$
$54$		0			0
$55$	799641.			0.648075
$56$	611203.	+	1.39541e6i	0.465080	+	1.06180i
$57$		0			0
$58$	265456.	−	36762.4i	0.178646	−	0.0247404i
$59$			1.79961e6i			1.14077i	0.821378	+	0.570384i	$0.193206\pi$
$59$			1.79961e6i			1.14077i	−0.821378	+	0.570384i	$0.806794\pi$
$60$		0			0
$61$			1.36394e6i			0.769379i	0.923046	+	0.384690i	$0.125692\pi$
$61$			1.36394e6i			0.769379i	−0.923046	+	0.384690i	$0.874308\pi$
$62$	−113206.	−	817441.i	−0.0603251	−	0.435598i
$63$		0			0
$64$	−1.42199e6	+	1.54142e6i	−0.678060	+	0.735007i
$65$	2.08090e6			0.939841
$66$		0			0
$67$			1.08853e6i			0.442160i	0.975256	+	0.221080i	$0.0709582\pi$
$67$			1.08853e6i			0.442160i	−0.975256	+	0.221080i	$0.929042\pi$
$68$	−2.67878e6	+	756466.i	−1.03313	+	0.291748i
$69$		0			0
$70$	−2.17997e6	+	301900.i	−0.759640	+	0.105201i
$71$	5.60830e6			1.85963			0.929816	−	0.368025i	$-0.119966\pi$
$71$	5.60830e6			1.85963			0.929816	+	0.368025i	$0.119966\pi$
$72$		0			0
$73$	21698.7			0.00652837			0.00326418	−	0.999995i	$-0.498961\pi$
$73$	21698.7			0.00652837			0.00326418	+	0.999995i	$0.498961\pi$
$74$	−5.41665e6	+	750142.i	−1.55389	+	0.215195i
$75$		0			0
$76$	1.58159e6	+	5.60068e6i	0.413281	+	1.46350i
$77$			4.54903e6i			1.13554i
$78$		0			0
$79$	2.34010e6			0.533998			0.266999	−	0.963697i	$-0.413968\pi$
$79$	2.34010e6			0.533998			0.266999	+	0.963697i	$0.413968\pi$
$80$	−1.58473e6	−	2.58214e6i	−0.346051	−	0.563852i
$81$		0			0
$82$	−637935.	−	4.60643e6i	−0.127770	−	0.922605i
$83$		−	882169.i		−	0.169347i	−0.996409	−	0.0846736i	$-0.973015\pi$
$83$		−	882169.i		−	0.169347i	0.996409	−	0.0846736i	$-0.0269848\pi$
$84$		0			0
$85$		−	4.02125e6i		−	0.710223i
$86$	1.07770e6	−	149249.i	0.182706	−	0.0253026i
$87$		0			0
$88$	−5.73621e6	+	2.51252e6i	−0.897296	+	0.393024i
$89$	1.34738e6			0.202594			0.101297	−	0.994856i	$-0.467701\pi$
$89$	1.34738e6			0.202594			0.101297	+	0.994856i	$0.467701\pi$
$90$		0			0
$91$			1.18379e7i			1.64676i
$92$	543773.	−	153557.i	0.0728049	−	0.0205595i
$93$		0			0
$94$	−242378.	−	1.75017e6i	−0.0300985	−	0.217337i
$95$	−8.40746e6			−1.00608
$96$		0			0
$97$	7.32798e6			0.815236			0.407618	−	0.913153i	$-0.366360\pi$
$97$	7.32798e6			0.815236			0.407618	+	0.913153i	$0.366360\pi$
$98$	−439325.	−	3.17229e6i	−0.0471514	−	0.340473i
$99$		0			0
$100$	−5.41156e6	+	1.52818e6i	−0.541156	+	0.152818i
$101$		−	9.66027e6i		−	0.932963i	−0.884531	−	0.466482i	$-0.845521\pi$
$101$		−	9.66027e6i		−	0.932963i	0.884531	−	0.466482i	$-0.154479\pi$
$102$		0			0
$103$	−1.38659e7			−1.25031			−0.625154	−	0.780501i	$-0.714964\pi$
$103$	−1.38659e7			−1.25031			−0.625154	+	0.780501i	$0.714964\pi$
$104$	−1.49273e7	+	6.53831e6i	−1.30126	+	0.569966i
$105$		0			0
$106$	−7.69862e6	+	1.06617e6i	−0.627830	+	0.0869470i
$107$			1.88354e7i			1.48638i	0.669078	+	0.743192i	$0.266689\pi$
$107$			1.88354e7i			1.48638i	−0.669078	+	0.743192i	$0.733311\pi$
$108$		0			0
$109$		−	8.60619e6i		−	0.636529i	−0.948002	−	0.318265i	$-0.896900\pi$
$109$		−	8.60619e6i		−	0.636529i	0.948002	−	0.318265i	$-0.103100\pi$
$110$	−1.24104e6	−	8.96137e6i	−0.0889022	−	0.641949i
$111$		0			0
$112$	1.46894e7	−	9.01528e6i	0.987965	−	0.606340i
$113$	1.31340e7			0.856292			0.428146	−	0.903709i	$-0.359167\pi$
$113$	1.31340e7			0.856292			0.428146	+	0.903709i	$0.359167\pi$
$114$		0			0
$115$			816286.i			0.0500495i
$116$	−823975.	−	2.91784e6i	−0.0490130	−	0.173564i
$117$		0			0
$118$	2.01678e7	−	2.79301e6i	1.12998	−	0.156489i
$119$	2.28763e7			1.24443
$120$		0			0
$121$	787128.			0.0403921
$122$	1.52853e7	−	2.11684e6i	0.762106	−	0.105543i
$123$		0			0
$124$	−8.98517e6	+	2.53734e6i	−0.423205	+	0.119510i
$125$		−	2.25701e7i		−	1.03359i
$126$		0			0
$127$	3.18768e7			1.38090			0.690449	−	0.723381i	$-0.257413\pi$
$127$	3.18768e7			1.38090			0.690449	+	0.723381i	$0.257413\pi$
$128$	1.94813e7	+	1.35436e7i	0.821074	+	0.570822i
$129$		0			0
$130$	−3.22956e6	−	2.33201e7i	−0.128926	−	0.930956i
$131$		−	1.17050e7i		−	0.454905i	−0.973789	−	0.227453i	$-0.926960\pi$
$131$		−	1.17050e7i		−	0.454905i	0.973789	−	0.227453i	$-0.0730397\pi$
$132$		0			0
$133$		−	4.78288e7i		−	1.76282i
$134$	1.21989e7	−	1.68940e6i	0.437980	−	0.0606551i
$135$		0			0
$136$	1.26350e7	+	2.88464e7i	0.430714	+	0.983343i
$137$	−3.79174e7			−1.25984			−0.629921	−	0.776659i	$-0.716913\pi$
$137$	−3.79174e7			−1.25984			−0.629921	+	0.776659i	$0.716913\pi$
$138$		0			0
$139$			2.80300e7i			0.885260i	0.896704	+	0.442630i	$0.145955\pi$
$139$			2.80300e7i			0.885260i	−0.896704	+	0.442630i	$0.854045\pi$
$140$	6.76665e6	+	2.39619e7i	0.208413	+	0.738028i
$141$		0			0
$142$	−8.70409e6	−	6.28508e7i	−0.255102	−	1.84205i
$143$	−4.86630e7			−1.39163
$144$		0			0
$145$	4.38012e6			0.119316
$146$	−33676.5	−	243173.i	−0.000895554	−	0.00646665i
$147$		0			0
$148$	1.68133e7	+	5.95388e7i	0.426321	+	1.50968i
$149$			6.82083e6i			0.168922i	0.996427	+	0.0844608i	$0.0269168\pi$
$149$			6.82083e6i			0.168922i	−0.996427	+	0.0844608i	$0.973083\pi$
$150$		0			0
$151$	−7.62068e7			−1.80125			−0.900626	−	0.434595i	$-0.856891\pi$
$151$	−7.62068e7			−1.80125			−0.900626	+	0.434595i	$0.856891\pi$
$152$	6.03108e7	−	2.64167e7i	1.39297	−	0.610136i
$153$		0			0
$154$	5.09799e7	−	7.06011e6i	1.12480	−	0.155772i
$155$		−	1.34881e7i		−	0.290931i
$156$		0			0
$157$		−	4.28737e7i		−	0.884183i	−0.896970	−	0.442092i	$-0.854237\pi$
$157$		−	4.28737e7i		−	0.884183i	0.896970	−	0.442092i	$-0.145763\pi$
$158$	−3.63184e6	−	2.62249e7i	−0.0732532	−	0.528950i
$159$		0			0
$160$	−2.64779e7	+	2.17671e7i	−0.511051	+	0.420128i
$161$	−4.64373e6			−0.0876952
$162$		0			0
$163$			4.12127e7i			0.745374i	0.927957	+	0.372687i	$0.121563\pi$
$163$			4.12127e7i			0.745374i	−0.927957	+	0.372687i	$0.878437\pi$
$164$	−5.06330e7	+	1.42984e7i	−0.896356	+	0.253124i
$165$		0			0
$166$	−9.88624e6	+	1.36913e6i	−0.167746	+	0.0232309i
$167$	−2.41703e7			−0.401582			−0.200791	−	0.979634i	$-0.564351\pi$
$167$	−2.41703e7			−0.401582			−0.200791	+	0.979634i	$0.564351\pi$
$168$		0			0
$169$	−6.38869e7			−1.01814
$170$	−4.50652e7	+	6.24099e6i	−0.703509	+	0.0974276i
$171$		0			0
$172$	−3.34519e6	−	1.18459e7i	−0.0501269	−	0.177508i
$173$		−	5.90454e7i		−	0.867011i	−0.901151	−	0.433505i	$-0.857277\pi$
$173$		−	5.90454e7i		−	0.867011i	0.901151	−	0.433505i	$-0.142723\pi$
$174$		0			0
$175$	4.62137e7			0.651835
$176$	3.70598e7	+	6.03848e7i	0.512399	+	0.834898i
$177$		0			0
$178$	−2.09114e6	−	1.50998e7i	−0.0277916	−	0.200679i
$179$			1.20311e8i			1.56791i	0.620819	+	0.783954i	$0.286800\pi$
$179$			1.20311e8i			1.56791i	−0.620819	+	0.783954i	$0.713200\pi$
$180$		0			0
$181$		−	3.21539e6i		−	0.0403049i	−0.999797	−	0.0201525i	$-0.993585\pi$
$181$		−	3.21539e6i		−	0.0403049i	0.999797	−	0.0201525i	$-0.00641517\pi$
$182$	1.32665e8	−	1.83725e7i	1.63119	−	0.225901i
$183$		0			0
$184$	−2.56482e6	−	5.85561e6i	−0.0303525	−	0.0692963i
$185$	−8.93768e7			−1.03782
$186$		0			0
$187$			9.40392e7i			1.05163i
$188$	−1.92376e7	+	5.43254e6i	−0.211153	+	0.0596280i
$189$		0			0
$190$	1.30484e7	+	9.42204e7i	0.138013	+	0.996569i
$191$	−7.04122e7			−0.731191			−0.365596	−	0.930774i	$-0.619135\pi$
$191$	−7.04122e7			−0.731191			−0.365596	+	0.930774i	$0.619135\pi$
$192$		0			0
$193$	1.17861e7			0.118010			0.0590050	−	0.998258i	$-0.481207\pi$
$193$	1.17861e7			0.118010			0.0590050	+	0.998258i	$0.481207\pi$
$194$	−1.13730e7	−	8.21229e7i	−0.111833	−	0.807529i
$195$		0			0
$196$	−3.48693e7	+	9.84682e6i	−0.330786	+	0.0934113i
$197$		−	8.97008e7i		−	0.835920i	−0.908465	−	0.417960i	$-0.862745\pi$
$197$		−	8.97008e7i		−	0.835920i	0.908465	−	0.417960i	$-0.137255\pi$
$198$		0			0
$199$	−3.98955e7			−0.358871			−0.179436	−	0.983770i	$-0.557427\pi$
$199$	−3.98955e7			−0.358871			−0.179436	+	0.983770i	$0.557427\pi$
$200$	2.55247e7	+	5.82743e7i	0.225609	+	0.515077i
$201$		0			0
$202$	−1.08260e8	+	1.49928e7i	−0.924143	+	0.127983i
$203$			2.49178e7i			0.209061i
$204$		0			0
$205$		−	7.60078e7i		−	0.616197i
$206$	2.15199e7	+	1.55392e8i	0.171516	+	1.23849i
$207$		0			0
$208$	9.64404e7	+	1.57139e8i	0.743083	+	1.21077i
$209$	1.96613e8			1.48971
$210$		0			0
$211$			6.63604e7i			0.486318i	0.969986	+	0.243159i	$0.0781837\pi$
$211$			6.63604e7i			0.486318i	−0.969986	+	0.243159i	$0.921816\pi$
$212$	2.38965e7	+	8.46218e7i	0.172250	+	0.609967i
$213$		0			0
$214$	2.11083e8	−	2.92325e7i	1.47233	−	0.203901i
$215$	1.77825e7			0.122027
$216$		0			0
$217$	7.67317e7			0.509760
$218$	−9.64475e7	+	1.33568e7i	−0.630512	+	0.0873184i
$219$		0			0
$220$	−9.85018e7	+	2.78161e7i	−0.623684	+	0.176124i
$221$			2.44718e8i			1.52508i
$222$		0			0
$223$	−1.57269e8			−0.949675			−0.474837	−	0.880074i	$-0.657493\pi$
$223$	−1.57269e8			−0.949675			−0.474837	+	0.880074i	$0.657493\pi$
$224$	−1.23830e8	−	1.50629e8i	−0.736136	−	0.895448i
$225$		0			0
$226$	−2.03840e7	−	1.47189e8i	−0.117465	−	0.848197i
$227$		−	1.95129e8i		−	1.10721i	−0.832778	−	0.553607i	$-0.813251\pi$
$227$		−	1.95129e8i		−	1.10721i	0.832778	−	0.553607i	$-0.186749\pi$
$228$		0			0
$229$			6.95136e7i			0.382512i	0.981540	+	0.191256i	$0.0612561\pi$
$229$			6.95136e7i			0.382512i	−0.981540	+	0.191256i	$0.938744\pi$
$230$	9.14791e6	−	1.26688e6i	0.0495764	−	0.00686574i
$231$		0			0
$232$	−3.14207e7	+	1.37626e7i	−0.165199	+	0.0723589i
$233$	3.81872e7			0.197776			0.0988878	−	0.995099i	$-0.468472\pi$
$233$	3.81872e7			0.197776			0.0988878	+	0.995099i	$0.468472\pi$
$234$		0			0
$235$		−	2.88785e7i		−	0.145157i
$236$	−6.26010e7	−	2.21681e8i	−0.310020	−	1.09783i
$237$		0			0
$238$	−3.55040e7	−	2.56369e8i	−0.170710	−	1.23267i
$239$	2.63549e8			1.24873			0.624366	−	0.781132i	$-0.285357\pi$
$239$	2.63549e8			1.24873			0.624366	+	0.781132i	$0.285357\pi$
$240$		0			0
$241$	1.21337e8			0.558386			0.279193	−	0.960235i	$-0.409933\pi$
$241$	1.21337e8			0.558386			0.279193	+	0.960235i	$0.409933\pi$
$242$	−1.22162e6	−	8.82115e6i	−0.00554094	−	0.0400102i
$243$		0			0
$244$	−4.74457e7	−	1.68014e8i	−0.209090	−	0.740423i
$245$		−	5.23441e7i		−	0.227398i
$246$		0			0
$247$	5.11645e8			2.16038
$248$	4.23803e7	+	9.67566e7i	0.176435	+	0.402809i
$249$		0			0
$250$	−2.52938e8	+	3.50288e7i	−1.02382	+	0.141787i
$251$			3.62042e7i			0.144511i	0.997386	+	0.0722555i	$0.0230197\pi$
$251$			3.62042e7i			0.144511i	−0.997386	+	0.0722555i	$0.976980\pi$
$252$		0			0
$253$		−	1.90893e7i		−	0.0741085i
$254$	−4.94728e7	−	3.57235e8i	−0.189430	−	1.36784i
$255$		0			0
$256$	1.21545e8	−	2.39341e8i	0.452792	−	0.891616i
$257$	−1.75550e8			−0.645111			−0.322555	−	0.946551i	$-0.604542\pi$
$257$	−1.75550e8			−0.645111			−0.322555	+	0.946551i	$0.604542\pi$
$258$		0			0
$259$		−	5.08451e8i		−	1.81844i
$260$	−2.56331e8	+	7.23858e7i	−0.904469	+	0.255415i
$261$		0			0
$262$	−1.31175e8	+	1.81661e7i	−0.450605	+	0.0624034i
$263$	1.10733e8			0.375348			0.187674	−	0.982231i	$-0.439905\pi$
$263$	1.10733e8			0.375348			0.187674	+	0.982231i	$0.439905\pi$
$264$		0			0
$265$	−1.27030e8			−0.419320
$266$	−5.36005e8	+	7.42304e7i	−1.74616	+	0.241822i
$267$		0			0
$268$	−3.78655e7	−	1.34088e8i	−0.120163	−	0.425519i
$269$		−	3.07561e8i		−	0.963382i	−0.876341	−	0.481691i	$-0.840023\pi$
$269$		−	3.07561e8i		−	0.963382i	0.876341	−	0.481691i	$-0.159977\pi$
$270$		0			0
$271$	−2.86036e8			−0.873027			−0.436513	−	0.899698i	$-0.643787\pi$
$271$	−2.86036e8			−0.873027			−0.436513	+	0.899698i	$0.643787\pi$
$272$	3.03665e8	−	1.86367e8i	0.914962	−	0.561536i
$273$		0			0
$274$	5.88478e7	+	4.24930e8i	0.172824	+	1.24793i
$275$			1.89974e8i			0.550846i
$276$		0			0
$277$			3.15642e8i			0.892309i	0.894956	+	0.446155i	$0.147207\pi$
$277$			3.15642e8i			0.892309i	−0.894956	+	0.446155i	$0.852793\pi$
$278$	3.14125e8	−	4.35026e7i	0.876891	−	0.121439i
$279$		0			0
$280$	2.58033e8	−	1.13021e8i	0.702461	−	0.307685i
$281$	2.50451e8			0.673366			0.336683	−	0.941618i	$-0.390695\pi$
$281$	2.50451e8			0.673366			0.336683	+	0.941618i	$0.390695\pi$
$282$		0			0
$283$		−	3.47387e7i		−	0.0911088i	−0.998962	−	0.0455544i	$-0.985495\pi$
$283$		−	3.47387e7i		−	0.0911088i	0.998962	−	0.0455544i	$-0.0145054\pi$
$284$	−6.90845e8	+	1.95089e8i	−1.78964	+	0.505381i
$285$		0			0
$286$	7.55251e7	+	5.45354e8i	0.190902	+	1.37847i
$287$	4.32397e8			1.07968
$288$		0			0
$289$	6.25676e7			0.152478
$290$	−6.79795e6	−	4.90869e7i	−0.0163676	−	0.118188i
$291$		0			0
$292$	−2.67291e6	+	754808.i	−0.00628267	+	0.00177418i
$293$			5.34336e8i			1.24102i	0.784200	+	0.620508i	$0.213074\pi$
$293$			5.34336e8i			1.24102i	−0.784200	+	0.620508i	$0.786926\pi$
$294$		0			0
$295$	3.32777e8			0.754703
$296$	6.41143e8	−	2.80827e8i	1.43692	−	0.629387i
$297$		0			0
$298$	7.64393e7	−	1.05859e7i	0.167325	−	0.0231725i
$299$		−	4.96760e7i		−	0.107472i
$300$		0			0
$301$			1.01162e8i			0.213813i
$302$	1.18273e8	+	8.54031e8i	0.247094	+	1.78422i
$303$		0			0
$304$	−3.89648e8	−	6.34889e8i	−0.795454	−	1.29611i
$305$	2.52214e8			0.509002
$306$		0			0
$307$		−	1.68851e8i		−	0.333057i	−0.986037	−	0.166529i	$-0.946744\pi$
$307$		−	1.68851e8i		−	0.333057i	0.986037	−	0.166529i	$-0.0532558\pi$
$308$	−1.58242e8	−	5.60362e8i	−0.308598	−	1.09280i
$309$		0			0
$310$	−1.51158e8	+	2.09335e7i	−0.288180	+	0.0399095i
$311$	−6.99677e8			−1.31897			−0.659487	−	0.751716i	$-0.729226\pi$
$311$	−6.99677e8			−1.31897			−0.659487	+	0.751716i	$0.729226\pi$
$312$		0			0
$313$	5.06345e8			0.933343			0.466671	−	0.884431i	$-0.345453\pi$
$313$	5.06345e8			0.933343			0.466671	+	0.884431i	$0.345453\pi$
$314$	−4.80475e8	+	6.65401e7i	−0.875825	+	0.121291i
$315$		0			0
$316$	−2.88260e8	+	8.14022e7i	−0.513900	+	0.145121i
$317$			4.78996e8i			0.844548i	0.906468	+	0.422274i	$0.138768\pi$
$317$			4.78996e8i			0.844548i	−0.906468	+	0.422274i	$0.861232\pi$
$318$		0			0
$319$	−1.02431e8			−0.176671
$320$	2.85033e8	+	2.62949e8i	0.486262	+	0.448587i
$321$		0			0
$322$	7.20707e6	+	5.20411e7i	0.0120299	+	0.0868662i
$323$		−	9.88733e8i		−	1.63256i
$324$		0			0
$325$			4.94369e8i			0.798839i
$326$	4.61860e8	−	6.39621e7i	0.738327	−	0.102250i
$327$		0			0
$328$	2.38821e8	+	5.45241e8i	0.373692	+	0.853159i
$329$	1.64285e8			0.254339
$330$		0			0
$331$			4.20825e8i			0.637828i	0.947784	+	0.318914i	$0.103318\pi$
$331$			4.20825e8i			0.637828i	−0.947784	+	0.318914i	$0.896682\pi$
$332$	3.06869e7	+	1.08668e8i	0.0460225	+	0.162974i
$333$		0			0
$334$	3.75123e7	+	2.70871e8i	0.0550886	+	0.397786i
$335$	2.01287e8			0.292522
$336$		0			0
$337$	−1.02987e9			−1.46580			−0.732902	−	0.680334i	$-0.761835\pi$
$337$	−1.02987e9			−1.46580			−0.732902	+	0.680334i	$0.761835\pi$
$338$	9.91526e7	+	7.15965e8i	0.139668	+	1.00852i
$339$		0			0
$340$	1.39882e8	+	4.95348e8i	0.193013	+	0.683493i
$341$			3.15427e8i			0.430782i
$342$		0			0
$343$	−5.68554e8			−0.760751
$344$	−1.27562e8	+	5.58735e7i	−0.168954	+	0.0740033i
$345$		0			0
$346$	−6.61707e8	+	9.16385e7i	−0.858814	+	0.118936i
$347$			5.31496e8i			0.682883i	0.939903	+	0.341442i	$0.110915\pi$
$347$			5.31496e8i			0.682883i	−0.939903	+	0.341442i	$0.889085\pi$
$348$		0			0
$349$			1.31436e9i			1.65511i	0.561385	+	0.827555i	$0.310269\pi$
$349$			1.31436e9i			1.65511i	−0.561385	+	0.827555i	$0.689731\pi$
$350$	−7.17238e7	−	5.17906e8i	−0.0894181	−	0.645673i
$351$		0			0
$352$	6.19201e8	−	5.09037e8i	0.756715	−	0.622085i
$353$	−1.42031e9			−1.71858			−0.859291	−	0.511486i	$-0.829095\pi$
$353$	−1.42031e9			−1.71858			−0.859291	+	0.511486i	$0.829095\pi$
$354$		0			0
$355$		−	1.03706e9i		−	1.23028i
$356$	−1.65974e8	+	4.68698e7i	−0.194969	+	0.0550577i
$357$		0			0
$358$	1.34830e9	−	1.86723e8i	1.55309	−	0.215084i
$359$	−7.59524e8			−0.866385			−0.433193	−	0.901301i	$-0.642613\pi$
$359$	−7.59524e8			−0.866385			−0.433193	+	0.901301i	$0.642613\pi$
$360$		0			0
$361$	−1.17333e9			−1.31264
$362$	−3.60340e7	+	4.99029e6i	−0.0399239	+	0.00552899i
$363$		0			0
$364$	−4.11792e8	−	1.45823e9i	−0.447531	−	1.58478i
$365$		−	4.01244e6i		−	0.00431900i
$366$		0			0
$367$	3.76159e8			0.397228			0.198614	−	0.980078i	$-0.436356\pi$
$367$	3.76159e8			0.397228			0.198614	+	0.980078i	$0.436356\pi$
$368$	−6.16418e7	+	3.78312e7i	−0.0644775	+	0.0395715i
$369$		0			0
$370$	1.38713e8	+	1.00162e9i	0.142368	+	1.02801i
$371$		−	7.22655e8i		−	0.734720i
$372$		0			0
$373$			4.57130e8i			0.456099i	0.973650	+	0.228049i	$0.0732347\pi$
$373$			4.57130e8i			0.456099i	−0.973650	+	0.228049i	$0.926765\pi$
$374$	1.05387e9	−	1.45949e8i	1.04169	−	0.144262i
$375$		0			0
$376$	9.07378e7	+	2.07159e8i	0.0880301	+	0.200977i
$377$	−2.66557e8			−0.256209
$378$		0			0
$379$		−	1.91565e9i		−	1.80750i	−0.428056	−	0.903752i	$-0.640801\pi$
$379$		−	1.91565e9i		−	1.80750i	0.428056	−	0.903752i	$-0.359199\pi$
$380$	1.03565e9	−	2.92460e8i	0.968215	−	0.273416i
$381$		0			0
$382$	1.09280e8	+	7.89092e8i	0.100304	+	0.724279i
$383$	−1.57853e9			−1.43568			−0.717839	−	0.696209i	$-0.754869\pi$
$383$	−1.57853e9			−1.43568			−0.717839	+	0.696209i	$0.754869\pi$
$384$		0			0
$385$	8.41187e8			0.751243
$386$	−1.82920e7	−	1.32084e8i	−0.0161885	−	0.116894i
$387$		0			0
$388$	−9.02680e8	+	2.54910e8i	−0.784554	+	0.221552i
$389$		−	2.21214e9i		−	1.90541i	−0.303890	−	0.952707i	$-0.598285\pi$
$389$		−	2.21214e9i		−	1.90541i	0.303890	−	0.952707i	$-0.401715\pi$
$390$		0			0
$391$	−9.59967e7			−0.0812153
$392$	1.64468e8	+	3.75489e8i	0.137905	+	0.314845i
$393$		0			0
$394$	−1.00526e9	+	1.39216e8i	−0.828017	+	0.114671i
$395$		−	4.32721e8i		−	0.353279i
$396$		0			0
$397$		−	1.30879e9i		−	1.04979i	−0.851167	−	0.524896i	$-0.824104\pi$
$397$		−	1.30879e9i		−	1.04979i	0.851167	−	0.524896i	$-0.175896\pi$
$398$	6.19180e7	+	4.47100e8i	0.0492296	+	0.355479i
$399$		0			0
$400$	6.13451e8	−	3.76491e8i	0.479259	−	0.294134i
$401$	−1.04514e8			−0.0809413			−0.0404706	−	0.999181i	$-0.512886\pi$
$401$	−1.04514e8			−0.0809413			−0.0404706	+	0.999181i	$0.512886\pi$
$402$		0			0
$403$			8.20832e8i			0.624722i
$404$	3.36040e8	+	1.18998e9i	0.253546	+	0.897850i
$405$		0			0
$406$	2.79248e8	−	3.86725e7i	0.207085	−	0.0286788i
$407$	2.09013e9			1.53671
$408$		0			0
$409$	1.94107e9			1.40284			0.701421	−	0.712747i	$-0.252549\pi$
$409$	1.94107e9			1.40284			0.701421	+	0.712747i	$0.252549\pi$
$410$	−8.51800e8	+	1.17964e8i	−0.610372	+	0.0845292i
$411$		0			0
$412$	1.70804e9	−	4.82336e8i	1.20325	−	0.339789i
$413$			1.89312e9i			1.32237i
$414$		0			0
$415$	−1.63127e8			−0.112036
$416$	1.61134e9	−	1.32466e9i	1.09739	−	0.902150i
$417$		0			0
$418$	−3.05144e8	−	2.20340e9i	−0.204356	−	1.47562i
$419$			1.96429e9i			1.30454i	0.757989	+	0.652268i	$0.226182\pi$
$419$			1.96429e9i			1.30454i	−0.757989	+	0.652268i	$0.773818\pi$
$420$		0			0
$421$		−	2.33176e9i		−	1.52299i	−0.648174	−	0.761493i	$-0.724467\pi$
$421$		−	2.33176e9i		−	1.52299i	0.648174	−	0.761493i	$-0.275533\pi$
$422$	7.43685e8	−	1.02992e8i	0.481721	−	0.0667126i
$423$		0			0
$424$	9.11248e8	−	3.99136e8i	0.580572	−	0.254296i
$425$	9.55346e8			0.603670
$426$		0			0
$427$			1.43480e9i			0.891857i
$428$	−6.55204e8	−	2.32019e9i	−0.403946	−	1.43044i
$429$		0			0
$430$	−2.75984e7	−	1.99284e8i	−0.0167396	−	0.120874i
$431$	−1.72745e8			−0.103929			−0.0519643	−	0.998649i	$-0.516548\pi$
$431$	−1.72745e8			−0.103929			−0.0519643	+	0.998649i	$0.516548\pi$
$432$		0			0
$433$	−2.71381e9			−1.60647			−0.803233	−	0.595665i	$-0.796889\pi$
$433$	−2.71381e9			−1.60647			−0.803233	+	0.595665i	$0.796889\pi$
$434$	−1.19088e8	−	8.59913e8i	−0.0699283	−	0.504941i
$435$		0			0
$436$	2.99373e8	+	1.06013e9i	0.172986	+	0.612573i
$437$			2.00706e8i			0.115047i
$438$		0			0
$439$	−2.73808e8			−0.154461			−0.0772307	−	0.997013i	$-0.524608\pi$
$439$	−2.73808e8			−0.154461			−0.0772307	+	0.997013i	$0.524608\pi$
$440$	4.64604e8	+	1.06071e9i	0.260015	+	0.593628i
$441$		0			0
$442$	2.74249e9	−	3.79802e8i	1.51066	−	0.209209i
$443$		−	2.72048e9i		−	1.48673i	−0.668886	−	0.743365i	$-0.733229\pi$
$443$		−	2.72048e9i		−	1.48673i	0.668886	−	0.743365i	$-0.266771\pi$
$444$		0			0
$445$		−	2.49152e8i		−	0.134031i
$446$	2.44081e8	+	1.76247e9i	0.130275	+	0.940697i
$447$		0			0
$448$	−1.49588e9	+	1.62151e9i	−0.786000	+	0.852013i
$449$	−1.69111e9			−0.881675			−0.440837	−	0.897587i	$-0.645318\pi$
$449$	−1.69111e9			−0.881675			−0.440837	+	0.897587i	$0.645318\pi$
$450$		0			0
$451$			1.77748e9i			0.912406i
$452$	−1.61788e9	+	4.56876e8i	−0.824065	+	0.232709i
$453$		0			0
$454$	−2.18676e9	+	3.02841e8i	−1.09675	+	0.151886i
$455$	2.18902e9			1.08945
$456$		0			0
$457$	−1.15773e8			−0.0567413			−0.0283706	−	0.999597i	$-0.509032\pi$
$457$	−1.15773e8			−0.0567413			−0.0283706	+	0.999597i	$0.509032\pi$
$458$	7.79021e8	−	1.07885e8i	0.378896	−	0.0524726i
$459$		0			0
$460$	−2.83952e7	−	1.00552e8i	−0.0136017	−	0.0481658i
$461$		−	9.34713e8i		−	0.444350i	−0.975007	−	0.222175i	$-0.928684\pi$
$461$		−	9.34713e8i		−	0.444350i	0.975007	−	0.222175i	$-0.0713156\pi$
$462$		0			0
$463$	1.91738e9			0.897790			0.448895	−	0.893584i	$-0.351818\pi$
$463$	1.91738e9			0.897790			0.448895	+	0.893584i	$0.351818\pi$
$464$	2.02999e8	+	3.30764e8i	0.0943367	+	0.153711i
$465$		0			0
$466$	−5.92667e7	−	4.27955e8i	−0.0271306	−	0.195906i
$467$			1.65838e9i			0.753485i	0.926318	+	0.376742i	$0.122956\pi$
$467$			1.65838e9i			0.753485i	−0.926318	+	0.376742i	$0.877044\pi$
$468$		0			0
$469$			1.14509e9i			0.512548i
$470$	−3.23634e8	+	4.48195e7i	−0.143784	+	0.0199124i
$471$		0			0
$472$	−2.38717e9	+	1.04560e9i	−1.04493	+	0.457689i
$473$	−4.15853e8			−0.180686
$474$		0			0
$475$		−	1.99740e9i		−	0.855140i
$476$	−2.81796e9	+	7.95770e8i	−1.19760	+	0.338192i
$477$		0			0
$478$	−4.09029e8	−	2.95353e9i	−0.171300	−	1.23693i
$479$	−4.09755e9			−1.70353			−0.851766	−	0.523923i	$-0.824468\pi$
$479$	−4.09755e9			−1.70353			−0.851766	+	0.523923i	$0.824468\pi$
$480$		0			0
$481$	5.43912e9			2.22854
$482$	−1.88316e8	−	1.35980e9i	−0.0765988	−	0.553107i
$483$		0			0
$484$	−9.69604e7	+	2.73809e7i	−0.0388719	+	0.0109771i
$485$		−	1.35506e9i		−	0.539339i
$486$		0			0
$487$	−3.24167e9			−1.27180			−0.635898	−	0.771773i	$-0.719370\pi$
$487$	−3.24167e9			−1.27180			−0.635898	+	0.771773i	$0.719370\pi$
$488$	−1.80925e9	+	7.92470e8i	−0.704741	+	0.308683i
$489$		0			0
$490$	−5.86607e8	+	8.12381e7i	−0.225248	+	0.0311942i
$491$			2.16351e9i			0.824847i	0.910992	+	0.412423i	$0.135318\pi$
$491$			2.16351e9i			0.824847i	−0.910992	+	0.412423i	$0.864682\pi$
$492$		0			0
$493$			5.15110e8i			0.193613i
$494$	−7.94075e8	−	5.73388e9i	−0.296358	−	2.13995i
$495$		0			0
$496$	1.01855e9	−	6.25112e8i	0.374798	−	0.230024i
$497$	5.89969e9			2.15567
$498$		0			0
$499$			2.16713e9i			0.780787i	0.920648	+	0.390394i	$0.127661\pi$
$499$			2.16713e9i			0.780787i	−0.920648	+	0.390394i	$0.872339\pi$
$500$	7.85119e8	+	2.78024e9i	0.280893	+	0.994690i
$501$		0			0
$502$	4.05731e8	−	5.61890e7i	0.143145	−	0.0198238i
$503$	2.58480e9			0.905606			0.452803	−	0.891611i	$-0.350424\pi$
$503$	2.58480e9			0.905606			0.452803	+	0.891611i	$0.350424\pi$
$504$		0			0
$505$	−1.78633e9			−0.617224
$506$	−2.13929e8	+	2.96266e7i	−0.0734079	+	0.0101661i
$507$		0			0
$508$	−3.92666e9	+	1.10886e9i	−1.32893	+	0.375278i
$509$		−	2.11747e9i		−	0.711712i	−0.934541	−	0.355856i	$-0.884189\pi$
$509$		−	2.11747e9i		−	0.711712i	0.934541	−	0.355856i	$-0.115811\pi$
$510$		0			0
$511$	2.28261e7			0.00756762
$512$	−2.87088e9	−	9.90670e8i	−0.945301	−	0.326200i
$513$		0			0
$514$	2.72454e8	+	1.96734e9i	0.0884956	+	0.639012i
$515$			2.56402e9i			0.827172i
$516$		0			0
$517$			6.75339e8i			0.214934i
$518$	−5.69808e9	+	7.89117e8i	−1.80125	+	0.249452i
$519$		0			0
$520$	1.20903e9	+	2.76029e9i	0.377074	+	0.860881i
$521$	2.34354e9			0.726006			0.363003	−	0.931788i	$-0.381751\pi$
$521$	2.34354e9			0.726006			0.363003	+	0.931788i	$0.381751\pi$
$522$		0			0
$523$			3.26155e9i			0.996939i	0.866907	+	0.498470i	$0.166104\pi$
$523$			3.26155e9i			0.996939i	−0.866907	+	0.498470i	$0.833896\pi$
$524$	4.07167e8	+	1.44185e9i	0.123627	+	0.437785i
$525$		0			0
$526$	−1.71859e8	−	1.24096e9i	−0.0514898	−	0.371799i
$527$	1.58622e9			0.472093
$528$		0			0
$529$	−3.38534e9			−0.994277
$530$	1.97151e8	+	1.42359e9i	0.0575219	+	0.415356i
$531$		0			0
$532$	1.66376e9	+	5.89167e9i	0.479072	+	1.69648i
$533$			4.62554e9i			1.32317i
$534$		0			0
$535$	3.48296e9			0.983354
$536$	−1.44393e9	+	6.32454e8i	−0.405013	+	0.177400i
$537$		0			0
$538$	−3.44676e9	+	4.77336e8i	−0.954275	+	0.132156i
$539$			1.22409e9i			0.336709i
$540$		0			0
$541$		−	7.24638e9i		−	1.96757i	−0.179344	−	0.983787i	$-0.557397\pi$
$541$		−	7.24638e9i		−	1.96757i	0.179344	−	0.983787i	$-0.442603\pi$
$542$	4.43928e8	+	3.20553e9i	0.119761	+	0.864773i
$543$		0			0
$544$	−2.55986e9	−	3.11385e9i	−0.681741	−	0.829281i
$545$	−1.59142e9			−0.421111
$546$		0			0
$547$			6.41460e9i			1.67577i	0.545848	+	0.837884i	$0.316207\pi$
$547$			6.41460e9i			1.67577i	−0.545848	+	0.837884i	$0.683793\pi$
$548$	4.67076e9	−	1.31899e9i	1.21243	−	0.342380i
$549$		0			0
$550$	2.12899e9	−	2.94840e8i	0.545638	−	0.0755644i
$551$	1.07697e9			0.274267
$552$		0			0
$553$	2.46168e9			0.619005
$554$	3.53732e9	−	4.89877e8i	0.883873	−	0.122406i
$555$		0			0
$556$	−9.75045e8	−	3.45281e9i	−0.240582	−	0.851943i
$557$		−	1.76223e9i		−	0.432085i	−0.976384	−	0.216042i	$-0.930685\pi$
$557$		−	1.76223e9i		−	0.432085i	0.976384	−	0.216042i	$-0.0693149\pi$
$558$		0			0
$559$	−1.08217e9			−0.262032
$560$	−1.66707e9	−	2.71630e9i	−0.401139	−	0.653612i
$561$		0			0
$562$	−3.88701e8	−	2.80674e9i	−0.0923715	−	0.667000i
$563$		−	2.33270e9i		−	0.550909i	−0.961314	−	0.275454i	$-0.911172\pi$
$563$		−	2.33270e9i		−	0.550909i	0.961314	−	0.275454i	$-0.0888283\pi$
$564$		0			0
$565$		−	2.42868e9i		−	0.566501i
$566$	−3.89307e8	+	5.39144e7i	−0.0902475	+	0.0124982i
$567$		0			0
$568$	3.25851e9	+	7.43935e9i	0.746104	+	1.70340i
$569$	−5.53591e9			−1.25978			−0.629892	−	0.776683i	$-0.716901\pi$
$569$	−5.53591e9			−1.25978			−0.629892	+	0.776683i	$0.716901\pi$
$570$		0			0
$571$			3.70890e9i			0.833717i	0.908971	+	0.416858i	$0.136869\pi$
$571$			3.70890e9i			0.833717i	−0.908971	+	0.416858i	$0.863131\pi$
$572$	5.99444e9	−	1.69278e9i	1.33925	−	0.378194i
$573$		0			0
$574$	−6.71081e8	−	4.84576e9i	−0.148110	−	1.06947i
$575$	−1.93929e8			−0.0425407
$576$		0			0
$577$	3.63713e9			0.788212			0.394106	−	0.919065i	$-0.371054\pi$
$577$	3.63713e9			0.788212			0.394106	+	0.919065i	$0.371054\pi$
$578$	−9.71050e7	−	7.01180e8i	−0.0209168	−	0.151036i
$579$		0			0
$580$	−5.39554e8	+	1.52366e8i	−0.114825	+	0.0324257i
$581$		−	9.28003e8i		−	0.196306i
$582$		0			0
$583$	2.97067e9			0.620889
$584$	1.26073e7	+	2.87832e7i	0.00261925	+	0.00597989i
$585$		0			0
$586$	5.98817e9	−	8.29290e8i	1.22928	−	0.170241i
$587$			2.04311e9i			0.416926i	0.978030	+	0.208463i	$0.0668461\pi$
$587$			2.04311e9i			0.416926i	−0.978030	+	0.208463i	$0.933154\pi$
$588$		0			0
$589$		−	3.31641e9i		−	0.668752i
$590$	−5.16470e8	−	3.72935e9i	−0.103529	−	0.747568i
$591$		0			0
$592$	−4.14221e9	−	6.74928e9i	−0.820553	−	1.33700i
$593$	5.74764e9			1.13187			0.565937	−	0.824448i	$-0.308514\pi$
$593$	5.74764e9			1.13187			0.565937	+	0.824448i	$0.308514\pi$
$594$		0			0
$595$		−	4.23018e9i		−	0.823284i
$596$	−2.37268e8	−	8.40207e8i	−0.0459068	−	0.162564i
$597$		0			0
$598$	−5.56706e8	+	7.70972e7i	−0.106456	+	0.0147430i
$599$	−3.14564e8			−0.0598020			−0.0299010	−	0.999553i	$-0.509519\pi$
$599$	−3.14564e8			−0.0598020			−0.0299010	+	0.999553i	$0.509519\pi$
$600$		0			0
$601$	−2.49586e9			−0.468985			−0.234493	−	0.972118i	$-0.575343\pi$
$601$	−2.49586e9			−0.468985			−0.234493	+	0.972118i	$0.575343\pi$
$602$	1.13369e9	−	1.57003e8i	0.211791	−	0.0293306i
$603$		0			0
$604$	9.38735e9	−	2.65091e9i	1.73346	−	0.489516i
$605$		−	1.45552e8i		−	0.0267224i
$606$		0			0
$607$	−2.81126e9			−0.510200			−0.255100	−	0.966915i	$-0.582108\pi$
$607$	−2.81126e9			−0.510200			−0.255100	+	0.966915i	$0.582108\pi$
$608$	−6.51031e9	+	5.35204e9i	−1.17473	+	0.965733i
$609$		0			0
$610$	−3.91436e8	−	2.82650e9i	−0.0698243	−	0.504190i
$611$			1.75743e9i			0.311698i
$612$		0			0
$613$			2.34343e9i			0.410904i	0.978667	+	0.205452i	$0.0658664\pi$
$613$			2.34343e9i			0.410904i	−0.978667	+	0.205452i	$0.934134\pi$
$614$	−1.89227e9	+	2.62057e8i	−0.329908	+	0.0456884i
$615$		0			0
$616$	−6.03424e9	+	2.64306e9i	−1.04014	+	0.455590i
$617$	6.26737e8			0.107420			0.0537102	−	0.998557i	$-0.482895\pi$
$617$	6.26737e8			0.107420			0.0537102	+	0.998557i	$0.482895\pi$
$618$		0			0
$619$		−	8.90879e9i		−	1.50974i	−0.655876	−	0.754869i	$-0.727700\pi$
$619$		−	8.90879e9i		−	1.50974i	0.655876	−	0.754869i	$-0.272300\pi$
$620$	4.69194e8	+	1.66150e9i	0.0790645	+	0.279981i
$621$		0			0
$622$	1.08590e9	+	7.84110e9i	0.180935	+	1.30650i
$623$	1.41739e9			0.234845
$624$		0			0
$625$	−7.41437e8			−0.121477
$626$	−7.85848e8	−	5.67448e9i	−0.128035	−	0.924519i
$627$		0			0
$628$	1.49140e9	+	5.28130e9i	0.240289	+	0.850906i
$629$		−	1.05109e10i		−	1.68407i
$630$		0			0
$631$	−2.21942e9			−0.351671			−0.175835	−	0.984420i	$-0.556263\pi$
$631$	−2.21942e9			−0.351671			−0.175835	+	0.984420i	$0.556263\pi$
$632$	1.35963e9	+	3.10412e9i	0.214246	+	0.489134i
$633$		0			0
$634$	5.36799e9	−	7.43403e8i	0.836564	−	0.115854i
$635$		−	5.89451e9i		−	0.913566i
$636$		0			0
$637$			3.18545e9i			0.488296i
$638$	1.58974e8	+	1.14792e9i	0.0242356	+	0.175001i
$639$		0			0
$640$	2.50443e9	−	3.60239e9i	0.377641	−	0.543201i
$641$	−8.58104e9			−1.28688			−0.643438	−	0.765498i	$-0.722493\pi$
$641$	−8.58104e9			−1.28688			−0.643438	+	0.765498i	$0.722493\pi$
$642$		0			0
$643$		−	7.71279e9i		−	1.14412i	−0.820210	−	0.572062i	$-0.806144\pi$
$643$		−	7.71279e9i		−	1.14412i	0.820210	−	0.572062i	$-0.193856\pi$
$644$	5.72026e8	−	1.61536e8i	0.0843947	−	0.0238324i
$645$		0			0
$646$	−1.10805e10	+	1.53452e9i	−1.61713	+	0.223953i
$647$	−1.18898e10			−1.72587			−0.862935	−	0.505316i	$-0.831376\pi$
$647$	−1.18898e10			−1.72587			−0.862935	+	0.505316i	$0.831376\pi$
$648$		0			0
$649$	−7.78217e9			−1.11749
$650$	5.54027e9	−	7.67261e8i	0.791287	−	0.109584i
$651$		0			0
$652$	−1.43362e9	−	5.07668e9i	−0.202566	−	0.717321i
$653$			2.00345e9i			0.281567i	0.990040	+	0.140784i	$0.0449622\pi$
$653$			2.00345e9i			0.281567i	−0.990040	+	0.140784i	$0.955038\pi$
$654$		0			0
$655$	−2.16443e9			−0.300954
$656$	5.73973e9	−	3.52262e9i	0.793830	−	0.487194i
$657$		0			0
$658$	−2.54971e8	−	1.84110e9i	−0.0348899	−	0.251935i
$659$		−	7.66944e9i		−	1.04391i	−0.852972	−	0.521957i	$-0.825202\pi$
$659$		−	7.66944e9i		−	1.04391i	0.852972	−	0.521957i	$-0.174798\pi$
$660$		0			0
$661$			4.04041e9i			0.544152i	0.962276	+	0.272076i	$0.0877103\pi$
$661$			4.04041e9i			0.544152i	−0.962276	+	0.272076i	$0.912290\pi$
$662$	4.71608e9	−	6.53121e8i	0.631798	−	0.0874965i
$663$		0			0
$664$	1.17019e9	−	5.12554e8i	0.155120	−	0.0679440i
$665$	−8.84429e9			−1.16624
$666$		0			0
$667$		−	1.04564e8i		−	0.0136440i
$668$	2.97736e9	−	8.40783e8i	0.386468	−	0.109136i
$669$		0			0
$670$	−3.12397e8	−	2.25577e9i	−0.0401278	−	0.289756i
$671$	−5.89816e9			−0.753681
$672$		0			0
$673$	4.11138e9			0.519918			0.259959	−	0.965620i	$-0.416291\pi$
$673$	4.11138e9			0.519918			0.259959	+	0.965620i	$0.416291\pi$
$674$	1.59835e9	+	1.15414e10i	0.201077	+	1.45195i
$675$		0			0
$676$	7.86976e9	−	2.22236e9i	0.979824	−	0.276695i
$677$			1.12671e10i			1.39557i	0.716305	+	0.697787i	$0.245832\pi$
$677$			1.12671e10i			1.39557i	−0.716305	+	0.697787i	$0.754168\pi$
$678$		0			0
$679$	7.70872e9			0.945014
$680$	5.33414e9	−	2.33641e9i	0.650554	−	0.284949i
$681$		0			0
$682$	3.53491e9	−	4.89543e8i	0.426710	−	0.0590942i
$683$			8.00228e9i			0.961039i	0.876984	+	0.480520i	$0.159552\pi$
$683$			8.00228e9i			0.961039i	−0.876984	+	0.480520i	$0.840448\pi$
$684$		0			0
$685$			7.01151e9i			0.833479i
$686$	8.82397e8	+	6.37165e9i	0.104359	+	0.753559i
$687$		0			0
$688$	8.24137e8	+	1.34284e9i	0.0964806	+	0.157205i
$689$	7.73055e9			0.900416
$690$		0			0
$691$			7.24716e9i			0.835593i	0.908541	+	0.417797i	$0.137197\pi$
$691$			7.24716e9i			0.835593i	−0.908541	+	0.417797i	$0.862803\pi$
$692$	2.05394e9	+	7.27336e9i	0.235622	+	0.834380i
$693$		0			0
$694$	5.95634e9	−	8.24882e8i	0.676428	−	0.0936772i
$695$	5.18318e9			0.585665
$696$		0			0
$697$	8.93865e9			0.999902
$698$	1.47298e10	−	2.03990e9i	1.63946	−	0.227046i
$699$		0			0
$700$	−5.69273e9	+	1.60758e9i	−0.627303	+	0.177145i
$701$			4.68293e8i			0.0513458i	0.999670	+	0.0256729i	$0.00817283\pi$
$701$			4.68293e8i			0.0513458i	−0.999670	+	0.0256729i	$0.991827\pi$
$702$		0			0
$703$	−2.19757e10			−2.38561
$704$	−6.66565e9	−	6.14921e9i	−0.720010	−	0.664224i
$705$		0			0
$706$	2.20432e9	+	1.59170e10i	0.235753	+	1.70234i
$707$		−	1.01622e10i		−	1.08148i
$708$		0			0
$709$		−	1.08926e10i		−	1.14781i	−0.818923	−	0.573903i	$-0.805429\pi$
$709$		−	1.08926e10i		−	1.14781i	0.818923	−	0.573903i	$-0.194571\pi$
$710$	−1.16221e10	+	1.60952e9i	−1.21865	+	0.168769i
$711$		0			0
$712$	7.82851e8	+	1.78729e9i	0.0812829	+	0.185573i
$713$	−3.21992e8			−0.0332684
$714$		0			0
$715$			8.99855e9i			0.920664i
$716$	−4.18512e9	−	1.48203e10i	−0.426101	−	1.50890i
$717$		0			0
$718$	1.17878e9	+	8.51180e9i	0.118850	+	0.858195i
$719$	7.40284e9			0.742758			0.371379	−	0.928481i	$-0.378885\pi$
$719$	7.40284e9			0.742758			0.371379	+	0.928481i	$0.378885\pi$
$720$		0			0
$721$	−1.45863e10			−1.44935
$722$	1.82101e9	+	1.31492e10i	0.180066	+	1.30023i
$723$		0			0
$724$	1.11850e8	+	3.96080e8i	0.0109534	+	0.0387880i
$725$			1.04060e9i			0.101415i
$726$		0			0
$727$	1.04295e10			1.00668			0.503342	−	0.864087i	$-0.332103\pi$
$727$	1.04295e10			1.00668			0.503342	+	0.864087i	$0.332103\pi$
$728$	−1.57029e10	+	6.87802e9i	−1.50841	+	0.660699i
$729$		0			0
$730$	−4.49664e7	+	6.22731e6i	−0.00427817	+	0.000592476i
$731$			2.09125e9i			0.198014i
$732$		0			0
$733$			1.55538e10i			1.45873i	0.684127	+	0.729363i	$0.260184\pi$
$733$			1.55538e10i			1.45873i	−0.684127	+	0.729363i	$0.739816\pi$
$734$	−5.83799e8	−	4.21552e9i	−0.0544913	−	0.393473i
$735$		0			0
$736$	5.19633e8	+	6.32090e8i	0.0480424	+	0.0584395i
$737$	−4.70720e9			−0.433138
$738$		0			0
$739$		−	1.07140e10i		−	0.976554i	−0.872689	−	0.488277i	$-0.837626\pi$
$739$		−	1.07140e10i		−	0.976554i	0.872689	−	0.488277i	$-0.162374\pi$
$740$	1.10097e10	−	3.10904e9i	0.998764	−	0.282043i
$741$		0			0
$742$	−8.09861e9	+	1.12156e9i	−0.727775	+	0.100788i
$743$	5.46982e9			0.489229			0.244615	−	0.969620i	$-0.421339\pi$
$743$	5.46982e9			0.489229			0.244615	+	0.969620i	$0.421339\pi$
$744$		0			0
$745$	1.26128e9			0.111754
$746$	5.12294e9	−	7.09467e8i	0.451787	−	0.0625671i
$747$		0			0
$748$	−3.27123e9	−	1.15840e10i	−0.285795	−	1.01205i
$749$			1.98140e10i			1.72300i
$750$		0			0
$751$	5.68185e9			0.489497			0.244749	−	0.969587i	$-0.421295\pi$
$751$	5.68185e9			0.489497			0.244749	+	0.969587i	$0.421295\pi$
$752$	2.18076e9	−	1.33839e9i	0.187001	−	0.114768i
$753$		0			0
$754$	4.13697e8	+	2.98724e9i	0.0351465	+	0.253787i
$755$			1.40918e10i			1.19166i
$756$		0			0
$757$			5.38304e9i			0.451016i	0.974241	+	0.225508i	$0.0724043\pi$
$757$			5.38304e9i			0.451016i	−0.974241	+	0.225508i	$0.927596\pi$
$758$	−2.14682e10	+	2.97310e9i	−1.79042	+	0.247951i
$759$		0			0
$760$	−4.88487e9	−	1.11524e10i	−0.403650	−	0.921555i
$761$	3.28593e9			0.270279			0.135139	−	0.990827i	$-0.456852\pi$
$761$	3.28593e9			0.270279			0.135139	+	0.990827i	$0.456852\pi$
$762$		0			0
$763$		−	9.05334e9i		−	0.737858i
$764$	8.67355e9	−	2.44934e9i	0.703672	−	0.198711i
$765$		0			0
$766$	2.44988e9	+	1.76902e10i	0.196945	+	1.42211i
$767$	−2.02515e10			−1.62059
$768$		0			0
$769$	7.10914e9			0.563735			0.281868	−	0.959453i	$-0.409046\pi$
$769$	7.10914e9			0.563735			0.281868	+	0.959453i	$0.409046\pi$
$770$	−1.30552e9	−	9.42698e9i	−0.103055	−	0.744141i
$771$		0			0
$772$	−1.45184e9	+	4.09988e8i	−0.113569	+	0.0320709i
$773$		−	1.08690e10i		−	0.846370i	−0.906043	−	0.423185i	$-0.860912\pi$
$773$		−	1.08690e10i		−	0.846370i	0.906043	−	0.423185i	$-0.139088\pi$
$774$		0			0
$775$	3.20443e9			0.247283
$776$	4.25767e9	+	9.72049e9i	0.327082	+	0.746745i
$777$		0			0
$778$	−2.47909e10	+	3.43325e9i	−1.88740	+	0.261383i
$779$		−	1.86886e10i		−	1.41643i
$780$		0			0
$781$			2.42523e10i			1.82169i
$782$	1.48987e8	+	1.07581e9i	0.0111410	+	0.0804475i
$783$		0			0
$784$	3.95276e9	−	2.42591e9i	0.292950	−	0.179791i
$785$	−7.92802e9			−0.584953
$786$		0			0
$787$		−	1.94246e10i		−	1.42050i	−0.703951	−	0.710248i	$-0.748583\pi$
$787$		−	1.94246e10i		−	1.42050i	0.703951	−	0.710248i	$-0.251417\pi$
$788$	3.12032e9	+	1.10496e10i	0.227173	+	0.804459i
$789$		0			0
$790$	−4.84940e9	+	6.71584e8i	−0.349939	+	0.0484624i
$791$	1.38164e10			0.992606
$792$		0			0
$793$	−1.53487e10			−1.09299
$794$	−1.46673e10	+	2.03124e9i	−1.03987	+	0.144009i
$795$		0			0
$796$	4.91444e9	−	1.38780e9i	0.345365	−	0.0975283i
$797$		−	2.30309e10i		−	1.61141i	−0.592314	−	0.805707i	$-0.701786\pi$
$797$		−	2.30309e10i		−	1.61141i	0.592314	−	0.805707i	$-0.298214\pi$
$798$		0			0
$799$	3.39616e9			0.235545
$800$	−5.17132e9	−	6.29048e9i	−0.357097	−	0.434379i
$801$		0			0
$802$	1.62206e8	+	1.17126e9i	0.0111034	+	0.0801761i
$803$			9.38331e7i			0.00639516i
$804$		0			0
$805$			8.58697e8i			0.0580169i
$806$	9.19887e9	−	1.27393e9i	0.618816	−	0.0856987i
$807$		0			0
$808$	1.28142e10	−	5.61277e9i	0.854581	−	0.374315i
$809$	1.50546e10			0.999656			0.499828	−	0.866125i	$-0.333397\pi$
$809$	1.50546e10			0.999656			0.499828	+	0.866125i	$0.333397\pi$
$810$		0			0
$811$		−	1.98821e10i		−	1.30885i	−0.756128	−	0.654424i	$-0.772911\pi$
$811$		−	1.98821e10i		−	1.30885i	0.756128	−	0.654424i	$-0.227089\pi$
$812$	−8.66786e8	−	3.06944e9i	−0.0568154	−	0.201193i
$813$		0			0
$814$	−3.24388e9	−	2.34235e10i	−0.210804	−	1.52218i
$815$	7.62086e9			0.493120
$816$		0			0
$817$	4.37230e9			0.280500
$818$	−3.01254e9	−	2.17530e10i	−0.192440	−	1.38958i
$819$		0			0
$820$	2.64399e9	+	9.36284e9i	0.167460	+	0.593006i
$821$			2.29870e10i			1.44971i	0.688901	+	0.724855i	$0.258093\pi$
$821$			2.29870e10i			1.44971i	−0.688901	+	0.724855i	$0.741907\pi$
$822$		0			0
$823$	1.46696e10			0.917316			0.458658	−	0.888613i	$-0.348330\pi$
$823$	1.46696e10			0.917316			0.458658	+	0.888613i	$0.348330\pi$
$824$	−8.05629e9	−	1.83929e10i	−0.501638	−	1.14527i
$825$		0			0
$826$	2.12157e10	−	2.93812e9i	1.30987	−	0.181401i
$827$		−	1.26591e9i		−	0.0778277i	−0.999243	−	0.0389138i	$-0.987610\pi$
$827$		−	1.26591e9i		−	0.0778277i	0.999243	−	0.0389138i	$-0.0123898\pi$
$828$		0			0
$829$		−	2.49778e10i		−	1.52270i	−0.648342	−	0.761349i	$-0.724537\pi$
$829$		−	2.49778e10i		−	1.52270i	0.648342	−	0.761349i	$-0.275463\pi$
$830$	2.53173e8	+	1.82812e9i	0.0153689	+	0.110977i
$831$		0			0
$832$	−1.73460e10	−	1.60020e10i	−1.04416	−	0.963261i
$833$	6.15576e9			0.368998
$834$		0			0
$835$			4.46947e9i			0.265676i
$836$	−2.42193e10	+	6.83935e9i	−1.43364	+	0.404849i
$837$		0			0
$838$	2.20133e10	−	3.04858e9i	1.29220	−	0.178955i
$839$	3.09477e10			1.80909			0.904547	−	0.426373i	$-0.140209\pi$
$839$	3.09477e10			1.80909			0.904547	+	0.426373i	$0.140209\pi$
$840$		0			0
$841$	1.66888e10			0.967473
$842$	−2.61314e10	+	3.61889e9i	−1.50859	+	0.208921i
$843$		0			0
$844$	−2.30840e9	−	8.17445e9i	−0.132164	−	0.468015i
$845$			1.18137e10i			0.673577i
$846$		0			0
$847$	8.28024e8			0.0468221
$848$	−5.88727e9	−	9.59267e9i	−0.331534	−	0.540199i
$849$		0			0
$850$	−1.48270e9	−	1.07063e10i	−0.0828108	−	0.597963i
$851$			2.13363e9i			0.118677i
$852$		0			0
$853$			1.86385e10i			1.02823i	0.857723	+	0.514113i	$0.171879\pi$
$853$			1.86385e10i			1.02823i	−0.857723	+	0.514113i	$0.828121\pi$
$854$	1.60795e10	−	2.22682e9i	0.883426	−	0.122344i
$855$		0			0
$856$	−2.49849e10	+	1.09436e10i	−1.36151	+	0.596354i
$857$	2.37366e10			1.28821			0.644103	−	0.764939i	$-0.277231\pi$
$857$	2.37366e10			1.28821			0.644103	+	0.764939i	$0.277231\pi$
$858$		0			0
$859$			2.46268e10i			1.32566i	0.748770	+	0.662830i	$0.230645\pi$
$859$			2.46268e10i			1.32566i	−0.748770	+	0.662830i	$0.769355\pi$
$860$	−2.19049e9	+	6.18577e8i	−0.117435	+	0.0331626i
$861$		0			0
$862$	2.68100e8	+	1.93591e9i	0.0142568	+	0.102946i
$863$	−2.50051e10			−1.32431			−0.662157	−	0.749365i	$-0.730359\pi$
$863$	−2.50051e10			−1.32431			−0.662157	+	0.749365i	$0.730359\pi$
$864$		0			0
$865$	−1.09184e10			−0.573592
$866$	4.21184e9	+	3.04130e10i	0.220373	+	1.59128i
$867$		0			0
$868$	−9.45201e9	+	2.66917e9i	−0.490575	+	0.138534i
$869$			1.01194e10i			0.523102i
$870$		0			0
$871$	−1.22495e10			−0.628139
$872$	1.14160e10	−	5.00033e9i	0.583052	−	0.255382i
$873$		0			0
$874$	2.24926e9	−	3.11496e8i	0.113959	−	0.0157820i
$875$		−	2.37428e10i		−	1.19813i
$876$		0			0
$877$		−	1.07280e10i		−	0.537057i	−0.963272	−	0.268528i	$-0.913463\pi$
$877$		−	1.07280e10i		−	0.537057i	0.963272	−	0.268528i	$-0.0865373\pi$
$878$	4.24950e8	+	3.06850e9i	0.0211888	+	0.153001i
$879$		0			0
$880$	1.11661e10	−	6.85293e9i	0.552347	−	0.338990i
$881$	−5.94499e9			−0.292911			−0.146455	−	0.989217i	$-0.546786\pi$
$881$	−5.94499e9			−0.292911			−0.146455	+	0.989217i	$0.546786\pi$
$882$		0			0
$883$			1.60870e10i			0.786342i	0.919465	+	0.393171i	$0.128622\pi$
$883$			1.60870e10i			0.786342i	−0.919465	+	0.393171i	$0.871378\pi$
$884$	−8.51270e9	−	3.01449e10i	−0.414462	−	1.46768i
$885$		0			0
$886$	−3.04877e10	+	4.22219e9i	−1.47267	+	0.203948i
$887$	2.61884e10			1.26001			0.630007	−	0.776589i	$-0.283052\pi$
$887$	2.61884e10			1.26001			0.630007	+	0.776589i	$0.283052\pi$
$888$		0			0
$889$	3.35330e10			1.60072
$890$	−2.79219e9	+	3.86685e8i	−0.132764	+	0.0183862i
$891$		0			0
$892$	1.93727e10	−	5.47071e9i	0.913933	−	0.258087i
$893$		−	7.10056e9i		−	0.333666i
$894$		0			0
$895$	2.22474e10			1.03729
$896$	2.04934e10	+	1.42473e10i	0.951781	+	0.661691i
$897$		0			0
$898$	2.62460e9	+	1.89518e10i	0.120947	+	0.873340i
$899$			1.72778e9i			0.0793104i
$900$		0			0
$901$		−	1.49390e10i		−	0.680430i
$902$	1.99198e10	−	2.75866e9i	0.903780	−	0.125163i
$903$		0			0
$904$	7.63105e9	+	1.74221e10i	0.343554	+	0.784352i
$905$	−5.94575e8			−0.0266647
$906$		0			0
$907$		−	1.79753e9i		−	0.0799929i	−0.999200	−	0.0399964i	$-0.987265\pi$
$907$		−	1.79753e9i		−	0.0799929i	0.999200	−	0.0399964i	$-0.0127347\pi$
$908$	6.78772e9	+	2.40365e10i	0.300901	+	1.06554i
$909$		0			0
$910$	−3.39736e9	−	2.45318e10i	−0.149450	−	1.07916i
$911$	−3.70021e10			−1.62148			−0.810740	−	0.585406i	$-0.800935\pi$
$911$	−3.70021e10			−1.62148			−0.810740	+	0.585406i	$0.800935\pi$
$912$		0			0
$913$	3.81481e9			0.165892
$914$	1.79679e8	+	1.29743e9i	0.00778370	+	0.0562048i
$915$		0			0
$916$	−2.41809e9	−	8.56286e9i	−0.103953	−	0.368116i
$917$		−	1.23131e10i		−	0.527322i
$918$		0			0
$919$	−2.44812e10			−1.04047			−0.520234	−	0.854024i	$-0.674155\pi$
$919$	−2.44812e10			−1.04047			−0.520234	+	0.854024i	$0.674155\pi$
$920$	−1.08279e9	+	4.74275e8i	−0.0458446	+	0.0200804i
$921$		0			0
$922$	−1.04751e10	+	1.45068e9i	−0.440149	+	0.0609554i
$923$			6.31115e10i			2.64182i
$924$		0			0
$925$		−	2.12336e10i		−	0.882121i
$926$	−2.97578e9	−	2.14876e10i	−0.123158	−	0.889303i
$927$		0			0
$928$	3.39174e9	−	2.78830e9i	0.139317	−	0.114531i
$929$	6.19981e9			0.253702			0.126851	−	0.991922i	$-0.459513\pi$
$929$	6.19981e9			0.253702			0.126851	+	0.991922i	$0.459513\pi$
$930$		0			0
$931$		−	1.28702e10i		−	0.522711i
$932$	−4.70400e9	+	1.32837e9i	−0.190332	+	0.0537483i
$933$		0			0
$934$	1.85850e10	−	2.57381e9i	0.746361	−	0.103362i
$935$	1.73893e10			0.695732
$936$		0			0
$937$	−2.78747e10			−1.10693			−0.553466	−	0.832871i	$-0.686695\pi$
$937$	−2.78747e10			−1.10693			−0.553466	+	0.832871i	$0.686695\pi$
$938$	1.28327e10	−	1.77718e9i	0.507702	−	0.0703107i
$939$		0			0
$940$	1.00456e9	+	3.55733e9i	0.0394484	+	0.139693i
$941$		−	3.45921e10i		−	1.35336i	−0.736277	−	0.676680i	$-0.763418\pi$
$941$		−	3.45921e10i		−	1.35336i	0.736277	−	0.676680i	$-0.236582\pi$
$942$		0			0
$943$	−1.81448e9			−0.0704632
$944$	1.54227e10	+	2.51296e10i	0.596704	+	0.972264i
$945$		0			0
$946$	6.45404e8	+	4.66036e9i	0.0247864	+	0.178978i
$947$		−	2.20475e10i		−	0.843598i	−0.906689	−	0.421799i	$-0.861399\pi$
$947$		−	2.20475e10i		−	0.843598i	0.906689	−	0.421799i	$-0.138601\pi$
$948$		0			0
$949$			2.44181e8i			0.00927429i
$950$	−2.23844e10	+	3.09997e9i	−0.847056	+	0.117307i
$951$		0			0
$952$	1.32915e10	+	3.03451e10i	0.499280	+	1.13988i
$953$	3.95876e9			0.148161			0.0740805	−	0.997252i	$-0.476398\pi$
$953$	3.95876e9			0.148161			0.0740805	+	0.997252i	$0.476398\pi$
$954$		0			0
$955$			1.30203e10i			0.483737i
$956$	−3.24647e10	+	9.16778e9i	−1.20174	+	0.339361i
$957$		0			0
$958$	6.35941e9	+	4.59203e10i	0.233689	+	1.68743i
$959$	−3.98874e10			−1.46040
$960$		0			0
$961$	−2.21921e10			−0.806615
$962$	−8.44153e9	−	6.09549e10i	−0.305709	−	2.20747i
$963$		0			0
$964$	−1.49466e10	+	4.22082e9i	−0.537371	+	0.151749i
$965$		−	2.17943e9i		−	0.0780724i
$966$		0			0
$967$	−9.76598e9			−0.347315			−0.173657	−	0.984806i	$-0.555559\pi$
$967$	−9.76598e9			−0.347315			−0.173657	+	0.984806i	$0.555559\pi$
$968$	4.57333e8	+	1.04412e9i	0.0162058	+	0.0369986i
$969$		0			0
$970$	−1.51858e10	+	2.10305e9i	−0.534240	+	0.0739859i
$971$			2.15553e10i			0.755589i	0.925889	+	0.377795i	$0.123317\pi$
$971$			2.15553e10i			0.755589i	−0.925889	+	0.377795i	$0.876683\pi$
$972$		0			0
$973$			2.94863e10i			1.02619i
$974$	5.03108e9	+	3.63286e10i	0.174464	+	1.25977i
$975$		0			0
$976$	1.16890e10	+	1.90459e10i	0.402441	+	0.655733i
$977$	−5.24340e10			−1.79880			−0.899398	−	0.437131i	$-0.855995\pi$
$977$	−5.24340e10			−1.79880			−0.899398	+	0.437131i	$0.855995\pi$
$978$		0			0
$979$			5.82657e9i			0.198460i
$980$	1.82083e9	+	6.44788e9i	0.0617985	+	0.218839i
$981$		0			0
$982$	2.42459e10	−	3.35777e9i	0.817049	−	0.113152i
$983$	2.85116e10			0.957380			0.478690	−	0.877984i	$-0.341112\pi$
$983$	2.85116e10			0.957380			0.478690	+	0.877984i	$0.341112\pi$
$984$		0			0
$985$	−1.65871e10			−0.553023
$986$	5.77271e9	−	7.99451e8i	0.191783	−	0.0265597i
$987$		0			0
$988$	−6.30258e10	+	1.77980e10i	−2.07907	+	0.587113i
$989$		−	4.24509e8i		−	0.0139540i
$990$		0			0
$991$	−2.72290e10			−0.888738			−0.444369	−	0.895844i	$-0.646572\pi$
$991$	−2.72290e10			−0.888738			−0.444369	+	0.895844i	$0.646572\pi$
$992$	−8.58628e9	−	1.04445e10i	−0.279263	−	0.339701i
$993$		0			0
$994$	−9.15633e9	−	6.61163e10i	−0.295712	−	2.13529i
$995$			7.37731e9i			0.237420i
$996$		0			0
$997$		−	1.30057e10i		−	0.415624i	−0.978169	−	0.207812i	$-0.933366\pi$
$997$		−	1.30057e10i		−	0.415624i	0.978169	−	0.207812i	$-0.0666343\pi$
$998$	2.42865e10	−	3.36339e9i	0.773406	−	0.107107i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.8.d.b.37.3		6
3.2	odd	2		8.8.b.a.5.4	yes	6
4.3	odd	2		288.8.d.b.145.3		6
8.3	odd	2		288.8.d.b.145.4		6
8.5	even	2	inner	72.8.d.b.37.4		6
12.11	even	2		32.8.b.a.17.3		6
24.5	odd	2		8.8.b.a.5.3	✓	6
24.11	even	2		32.8.b.a.17.4		6
48.5	odd	4		256.8.a.r.1.4		6
48.11	even	4		256.8.a.q.1.3		6
48.29	odd	4		256.8.a.r.1.3		6
48.35	even	4		256.8.a.q.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.8.b.a.5.3	✓	6	24.5	odd	2
8.8.b.a.5.4	yes	6	3.2	odd	2
32.8.b.a.17.3		6	12.11	even	2
32.8.b.a.17.4		6	24.11	even	2
72.8.d.b.37.3		6	1.1	even	1	trivial
72.8.d.b.37.4		6	8.5	even	2	inner
256.8.a.q.1.3		6	48.11	even	4
256.8.a.q.1.4		6	48.35	even	4
256.8.a.r.1.3		6	48.29	odd	4
256.8.a.r.1.4		6	48.5	odd	4
288.8.d.b.145.3		6	4.3	odd	2
288.8.d.b.145.4		6	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	72.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.55200 - 11.2068i) q^{2} +(-123.183 + 34.7858i) q^{4} -184.916i q^{5} +1051.96 q^{7} +(581.015 + 1326.49i) q^{8} +O(q^{10})\)	\(q+(-1.55200 - 11.2068i) q^{2} +(-123.183 + 34.7858i) q^{4} -184.916i q^{5} +1051.96 q^{7} +(581.015 + 1326.49i) q^{8} +(-2072.30 + 286.989i) q^{10} +4324.35i q^{11} +11253.2i q^{13} +(-1632.64 - 11789.0i) q^{14} +(13963.9 - 8570.01i) q^{16} +21746.4 q^{17} -45466.5i q^{19} +(6432.44 + 22778.4i) q^{20} +(48462.0 - 6711.41i) q^{22} -4414.37 q^{23} +43931.2 q^{25} +(126112. - 17465.1i) q^{26} +(-129583. + 36593.2i) q^{28} +23687.1i q^{29} +72941.9 q^{31} +(-117714. - 143189. i) q^{32} +(-33750.5 - 243707. i) q^{34} -194523. i q^{35} -483338. i q^{37} +(-509532. + 70564.1i) q^{38} +(245289. - 107439. i) q^{40} +411040. q^{41} +96165.3i q^{43} +(-150426. - 532685. i) q^{44} +(6851.11 + 49470.7i) q^{46} +156171. q^{47} +283070. q^{49} +(-68181.3 - 492326. i) q^{50} +(-391453. - 1.38620e6i) q^{52} -686962. i q^{53} +799641. q^{55} +(611203. + 1.39541e6i) q^{56} +(265456. - 36762.4i) q^{58} +1.79961e6i q^{59} +1.36394e6i q^{61} +(-113206. - 817441. i) q^{62} +(-1.42199e6 + 1.54142e6i) q^{64} +2.08090e6 q^{65} +1.08853e6i q^{67} +(-2.67878e6 + 756466. i) q^{68} +(-2.17997e6 + 301900. i) q^{70} +5.60830e6 q^{71} +21698.7 q^{73} +(-5.41665e6 + 750142. i) q^{74} +(1.58159e6 + 5.60068e6i) q^{76} +4.54903e6i q^{77} +2.34010e6 q^{79} +(-1.58473e6 - 2.58214e6i) q^{80} +(-637935. - 4.60643e6i) q^{82} -882169. i q^{83} -4.02125e6i q^{85} +(1.07770e6 - 149249. i) q^{86} +(-5.73621e6 + 2.51252e6i) q^{88} +1.34738e6 q^{89} +1.18379e7i q^{91} +(543773. - 153557. i) q^{92} +(-242378. - 1.75017e6i) q^{94} -8.40746e6 q^{95} +7.32798e6 q^{97} +(-439325. - 3.17229e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 116 q^{4} - 688 q^{7} - 1512 q^{8}+O(q^{10}) \) 6 * q - 6 * q^2 + 116 * q^4 - 688 * q^7 - 1512 * q^8	\( 6 q - 6 q^{2} + 116 q^{4} - 688 q^{7} - 1512 q^{8} - 1656 q^{10} - 12048 q^{14} + 35344 q^{16} - 1452 q^{17} + 114768 q^{20} + 152860 q^{22} + 1296 q^{23} - 39314 q^{25} + 316968 q^{26} - 480800 q^{28} - 89280 q^{31} - 817056 q^{32} - 1009108 q^{34} - 974124 q^{38} + 954464 q^{40} - 521244 q^{41} + 1096344 q^{44} + 929840 q^{46} - 1566432 q^{47} - 511050 q^{49} + 148626 q^{50} + 823952 q^{52} - 3270256 q^{55} + 2468928 q^{56} + 3130744 q^{58} + 7055808 q^{62} - 4792768 q^{64} - 1416480 q^{65} - 6608040 q^{68} - 7406912 q^{70} + 7597104 q^{71} + 2089564 q^{73} - 7744200 q^{74} + 9241288 q^{76} + 16015904 q^{79} + 12600384 q^{80} + 10715932 q^{82} + 5639076 q^{86} + 1541200 q^{88} - 2169084 q^{89} - 669600 q^{92} + 15503712 q^{94} - 48537936 q^{95} - 1088308 q^{97} + 14983242 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 + 116 * q^4 - 688 * q^7 - 1512 * q^8 - 1656 * q^10 - 12048 * q^14 + 35344 * q^16 - 1452 * q^17 + 114768 * q^20 + 152860 * q^22 + 1296 * q^23 - 39314 * q^25 + 316968 * q^26 - 480800 * q^28 - 89280 * q^31 - 817056 * q^32 - 1009108 * q^34 - 974124 * q^38 + 954464 * q^40 - 521244 * q^41 + 1096344 * q^44 + 929840 * q^46 - 1566432 * q^47 - 511050 * q^49 + 148626 * q^50 + 823952 * q^52 - 3270256 * q^55 + 2468928 * q^56 + 3130744 * q^58 + 7055808 * q^62 - 4792768 * q^64 - 1416480 * q^65 - 6608040 * q^68 - 7406912 * q^70 + 7597104 * q^71 + 2089564 * q^73 - 7744200 * q^74 + 9241288 * q^76 + 16015904 * q^79 + 12600384 * q^80 + 10715932 * q^82 + 5639076 * q^86 + 1541200 * q^88 - 2169084 * q^89 - 669600 * q^92 + 15503712 * q^94 - 48537936 * q^95 - 1088308 * q^97 + 14983242 * q^98

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