LMFDB - Embedded newform 72.7.b.d.19.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("72.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	72.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.5638940206$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 78x^{10} + 3408x^{8} + 73216x^{6} + 13959168x^{4} + 1308622848x^{2} + 68719476736 $ x^12 + 78x^10 + 3408x^8 + 73216x^6 + 13959168x^4 + 1308622848*x^2 + 68719476736
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{30}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.10
Root			$-4.24448 + 6.78118i$ of defining polynomial
Character	$\chi$	$=$	72.19
Dual form			72.7.b.d.19.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.24448 + 6.78118i) q^{2} +(-27.9688 + 57.5651i) q^{4} -206.098i q^{5} +210.403i q^{7} +(-509.073 + 54.6722i) q^{8} +O(q^{10})$	\(q+(4.24448 + 6.78118i) q^{2} +(-27.9688 + 57.5651i) q^{4} -206.098i q^{5} +210.403i q^{7} +(-509.073 + 54.6722i) q^{8} +(1397.59 - 874.779i) q^{10} +2261.83 q^{11} -3538.83i q^{13} +(-1426.78 + 893.050i) q^{14} +(-2531.49 - 3220.06i) q^{16} +3485.68 q^{17} +9846.20 q^{19} +(11864.1 + 5764.32i) q^{20} +(9600.28 + 15337.9i) q^{22} +2096.31i q^{23} -26851.4 q^{25} +(23997.4 - 15020.5i) q^{26} +(-12111.9 - 5884.72i) q^{28} +10106.1i q^{29} -1373.11i q^{31} +(11091.0 - 30834.0i) q^{32} +(14794.9 + 23637.0i) q^{34} +43363.6 q^{35} -55063.1i q^{37} +(41792.0 + 66768.9i) q^{38} +(11267.8 + 104919. i) q^{40} +58478.9 q^{41} -106639. q^{43} +(-63260.7 + 130203. i) q^{44} +(-14215.4 + 8897.73i) q^{46} -84028.3i q^{47} +73379.7 q^{49} +(-113970. - 182084. i) q^{50} +(203713. + 98976.9i) q^{52} +80372.5i q^{53} -466159. i q^{55} +(-11503.2 - 107110. i) q^{56} +(-68531.0 + 42894.9i) q^{58} -84520.5 q^{59} -160512. i q^{61} +(9311.30 - 5828.13i) q^{62} +(256166. - 55664.2i) q^{64} -729346. q^{65} -229254. q^{67} +(-97490.4 + 200654. i) q^{68} +(184056. + 294057. i) q^{70} -184976. i q^{71} -356258. q^{73} +(373393. - 233714. i) q^{74} +(-275387. + 566798. i) q^{76} +475895. i q^{77} +443857. i q^{79} +(-663648. + 521735. i) q^{80} +(248212. + 396556. i) q^{82} +356957. q^{83} -718392. i q^{85} +(-452628. - 723140. i) q^{86} +(-1.15144e6 + 123659. i) q^{88} +593976. q^{89} +744580. q^{91} +(-120674. - 58631.3i) q^{92} +(569811. - 356656. i) q^{94} -2.02928e6i q^{95} -783783. q^{97} +(311458. + 497601. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 156 q^{4}+O(q^{10}) $ 12 * q - 156 * q^4	$ 12 q - 156 q^{4} + 1416 q^{10} - 1464 q^{16} + 3936 q^{19} + 15888 q^{22} - 47796 q^{25} + 11256 q^{28} + 50016 q^{34} + 70896 q^{40} - 340704 q^{43} + 213696 q^{46} - 304644 q^{49} + 548016 q^{52} - 38616 q^{58} + 206544 q^{64} - 962112 q^{67} + 1074480 q^{70} - 1069560 q^{73} + 1064352 q^{76} - 694944 q^{82} - 3072672 q^{88} + 775008 q^{91} + 3752256 q^{94} - 86952 q^{97}+O(q^{100}) $ 12 * q - 156 * q^4 + 1416 * q^10 - 1464 * q^16 + 3936 * q^19 + 15888 * q^22 - 47796 * q^25 + 11256 * q^28 + 50016 * q^34 + 70896 * q^40 - 340704 * q^43 + 213696 * q^46 - 304644 * q^49 + 548016 * q^52 - 38616 * q^58 + 206544 * q^64 - 962112 * q^67 + 1074480 * q^70 - 1069560 * q^73 + 1064352 * q^76 - 694944 * q^82 - 3072672 * q^88 + 775008 * q^91 + 3752256 * q^94 - 86952 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	4.24448	+	6.78118i	0.530560	+	0.847648i
$2$	4.24448	+	6.78118i	0.530560	+	0.847648i
$3$		0			0
$3$		0			0
$4$	−27.9688	+	57.5651i	−0.437013	+	0.899455i
$5$		−	206.098i		−	1.64878i	−0.566019	−	0.824392i	$-0.691517\pi$
$5$		−	206.098i		−	1.64878i	0.566019	−	0.824392i	$-0.308483\pi$
$6$		0			0
$7$			210.403i			0.613419i	0.951803	+	0.306710i	$0.0992280\pi$
$7$			210.403i			0.613419i	−0.951803	+	0.306710i	$0.900772\pi$
$8$	−509.073	+	54.6722i	−0.994283	+	0.106782i
$9$		0			0
$10$	1397.59	−	874.779i	1.39759	−	0.874779i
$11$	2261.83			1.69935			0.849673	−	0.527310i	$-0.176799\pi$
$11$	2261.83			1.69935			0.849673	+	0.527310i	$0.176799\pi$
$12$		0			0
$13$		−	3538.83i		−	1.61076i	−0.592762	−	0.805378i	$-0.701962\pi$
$13$		−	3538.83i		−	1.61076i	0.592762	−	0.805378i	$-0.298038\pi$
$14$	−1426.78	+	893.050i	−0.519963	+	0.325455i
$15$		0			0
$16$	−2531.49	−	3220.06i	−0.618039	−	0.786147i
$17$	3485.68			0.709481			0.354740	−	0.934965i	$-0.384569\pi$
$17$	3485.68			0.709481			0.354740	+	0.934965i	$0.384569\pi$
$18$		0			0
$19$	9846.20			1.43552			0.717758	−	0.696293i	$-0.245168\pi$
$19$	9846.20			1.43552			0.717758	+	0.696293i	$0.245168\pi$
$20$	11864.1	+	5764.32i	1.48301	+	0.720540i
$21$		0			0
$22$	9600.28	+	15337.9i	0.901605	+	1.44045i
$23$			2096.31i			0.172294i	0.996282	+	0.0861472i	$0.0274556\pi$
$23$			2096.31i			0.172294i	−0.996282	+	0.0861472i	$0.972544\pi$
$24$		0			0
$25$	−26851.4			−1.71849
$26$	23997.4	−	15020.5i	1.36535	−	0.854602i
$27$		0			0
$28$	−12111.9	−	5884.72i	−0.551743	−	0.268072i
$29$			10106.1i			0.414369i	0.978302	+	0.207185i	$0.0664301\pi$
$29$			10106.1i			0.414369i	−0.978302	+	0.207185i	$0.933570\pi$
$30$		0			0
$31$		−	1373.11i		−	0.0460914i	−0.999734	−	0.0230457i	$-0.992664\pi$
$31$		−	1373.11i		−	0.0460914i	0.999734	−	0.0230457i	$-0.00733632\pi$
$32$	11091.0	−	30834.0i	0.338469	−	0.940977i
$33$		0			0
$34$	14794.9	+	23637.0i	0.376422	+	0.601390i
$35$	43363.6			1.01140
$36$		0			0
$37$		−	55063.1i		−	1.08706i	−0.839388	−	0.543532i	$-0.817087\pi$
$37$		−	55063.1i		−	1.08706i	0.839388	−	0.543532i	$-0.182913\pi$
$38$	41792.0	+	66768.9i	0.761627	+	1.21681i
$39$		0			0
$40$	11267.8	+	104919.i	0.176060	+	1.63936i
$41$	58478.9			0.848491			0.424246	−	0.905547i	$-0.360539\pi$
$41$	58478.9			0.848491			0.424246	+	0.905547i	$0.360539\pi$
$42$		0			0
$43$	−106639.			−1.34126			−0.670628	−	0.741794i	$-0.733975\pi$
$43$	−106639.			−1.34126			−0.670628	+	0.741794i	$0.733975\pi$
$44$	−63260.7	+	130203.i	−0.742636	+	1.52849i
$45$		0			0
$46$	−14215.4	+	8897.73i	−0.146045	+	0.0914125i
$47$		−	84028.3i		−	0.809342i	−0.914462	−	0.404671i	$-0.867386\pi$
$47$		−	84028.3i		−	0.809342i	0.914462	−	0.404671i	$-0.132614\pi$
$48$		0			0
$49$	73379.7			0.623717
$50$	−113970.	−	182084.i	−0.911762	−	1.45668i
$51$		0			0
$52$	203713.	+	98976.9i	1.44880	+	0.703921i
$53$			80372.5i			0.539859i	0.962880	+	0.269929i	$0.0870003\pi$
$53$			80372.5i			0.539859i	−0.962880	+	0.269929i	$0.913000\pi$
$54$		0			0
$55$		−	466159.i		−	2.80186i
$56$	−11503.2	−	107110.i	−0.0655019	−	0.609912i
$57$		0			0
$58$	−68531.0	+	42894.9i	−0.351239	+	0.219848i
$59$	−84520.5			−0.411534			−0.205767	−	0.978601i	$-0.565969\pi$
$59$	−84520.5			−0.411534			−0.205767	+	0.978601i	$0.565969\pi$
$60$		0			0
$61$		−	160512.i		−	0.707159i	−0.935405	−	0.353579i	$-0.884964\pi$
$61$		−	160512.i		−	0.707159i	0.935405	−	0.353579i	$-0.115036\pi$
$62$	9311.30	−	5828.13i	0.0390693	−	0.0244542i
$63$		0			0
$64$	256166.	−	55664.2i	0.977195	−	0.212342i
$65$	−729346.			−2.65579
$66$		0			0
$67$	−229254.			−0.762240			−0.381120	−	0.924525i	$-0.624462\pi$
$67$	−229254.			−0.762240			−0.381120	+	0.924525i	$0.624462\pi$
$68$	−97490.4	+	200654.i	−0.310052	+	0.638146i
$69$		0			0
$70$	184056.	+	294057.i	0.536606	+	0.857308i
$71$		−	184976.i		−	0.516821i	−0.966035	−	0.258411i	$-0.916801\pi$
$71$		−	184976.i		−	0.516821i	0.966035	−	0.258411i	$-0.0831987\pi$
$72$		0			0
$73$	−356258.			−0.915791			−0.457895	−	0.889006i	$-0.651397\pi$
$73$	−356258.			−0.915791			−0.457895	+	0.889006i	$0.651397\pi$
$74$	373393.	−	233714.i	0.921448	−	0.576753i
$75$		0			0
$76$	−275387.	+	566798.i	−0.627339	+	1.29118i
$77$			475895.i			1.04241i
$78$		0			0
$79$			443857.i			0.900247i	0.892966	+	0.450124i	$0.148620\pi$
$79$			443857.i			0.900247i	−0.892966	+	0.450124i	$0.851380\pi$
$80$	−663648.	+	521735.i	−1.29619	+	1.01901i
$81$		0			0
$82$	248212.	+	396556.i	0.450175	+	0.719222i
$83$	356957.			0.624284			0.312142	−	0.950035i	$-0.398954\pi$
$83$	356957.			0.624284			0.312142	+	0.950035i	$0.398954\pi$
$84$		0			0
$85$		−	718392.i		−	1.16978i
$86$	−452628.	−	723140.i	−0.711616	−	1.13691i
$87$		0			0
$88$	−1.15144e6	+	123659.i	−1.68963	+	0.181459i
$89$	593976.			0.842556			0.421278	−	0.906932i	$-0.361582\pi$
$89$	593976.			0.842556			0.421278	+	0.906932i	$0.361582\pi$
$90$		0			0
$91$	744580.			0.988068
$92$	−120674.	−	58631.3i	−0.154971	−	0.0752949i
$93$		0			0
$94$	569811.	−	356656.i	0.686037	−	0.429404i
$95$		−	2.02928e6i		−	2.36686i
$96$		0			0
$97$	−783783.			−0.858778			−0.429389	−	0.903120i	$-0.641271\pi$
$97$	−783783.			−0.858778			−0.429389	+	0.903120i	$0.641271\pi$
$98$	311458.	+	497601.i	0.330919	+	0.528692i
$99$		0			0
$100$	751003.	−	1.54571e6i	0.751003	−	1.54571i
$101$			1.57046e6i			1.52428i	0.647415	+	0.762138i	$0.275850\pi$
$101$			1.57046e6i			1.52428i	−0.647415	+	0.762138i	$0.724150\pi$
$102$		0			0
$103$			79752.8i			0.0729851i	0.999334	+	0.0364925i	$0.0116185\pi$
$103$			79752.8i			0.0729851i	−0.999334	+	0.0364925i	$0.988381\pi$
$104$	193475.	+	1.80152e6i	0.171999	+	1.60155i
$105$		0			0
$106$	−545021.	+	341139.i	−0.457610	+	0.286427i
$107$	2.07013e6			1.68984			0.844922	−	0.534890i	$-0.179647\pi$
$107$	2.07013e6			1.68984			0.844922	+	0.534890i	$0.179647\pi$
$108$		0			0
$109$			1.62532e6i			1.25505i	0.778598	+	0.627523i	$0.215931\pi$
$109$			1.62532e6i			1.25505i	−0.778598	+	0.627523i	$0.784069\pi$
$110$	3.16111e6	−	1.97860e6i	2.37499	−	1.48655i
$111$		0			0
$112$	677509.	−	532632.i	0.482238	−	0.379117i
$113$	−1.61000e6			−1.11581			−0.557904	−	0.829905i	$-0.688394\pi$
$113$	−1.61000e6			−1.11581			−0.557904	+	0.829905i	$0.688394\pi$
$114$		0			0
$115$	432045.			0.284077
$116$	−581756.	−	282655.i	−0.372707	−	0.181085i
$117$		0			0
$118$	−358745.	−	573149.i	−0.218344	−	0.348836i
$119$			733397.i			0.435209i
$120$		0			0
$121$	3.34431e6			1.88778
$122$	1.08846e6	−	681288.i	0.599421	−	0.375190i
$123$		0			0
$124$	79043.2	+	38404.3i	0.0414572	+	0.0201425i
$125$			2.31375e6i			1.18464i
$126$		0			0
$127$			499189.i			0.243699i	0.992549	+	0.121849i	$0.0388825\pi$
$127$			499189.i			0.243699i	−0.992549	+	0.121849i	$0.961117\pi$
$128$	1.46476e6	+	1.50084e6i	0.698452	+	0.715657i
$129$		0			0
$130$	−3.09569e6	−	4.94583e6i	−1.40905	−	2.25117i
$131$	1.65837e6			0.737680			0.368840	−	0.929493i	$-0.379755\pi$
$131$	1.65837e6			0.737680			0.368840	+	0.929493i	$0.379755\pi$
$132$		0			0
$133$			2.07167e6i			0.880573i
$134$	−973062.	−	1.55461e6i	−0.404414	−	0.646111i
$135$		0			0
$136$	−1.77446e6	+	190570.i	−0.705424	+	0.0757595i
$137$	−1.62443e6			−0.631742			−0.315871	−	0.948802i	$-0.602297\pi$
$137$	−1.62443e6			−0.631742			−0.315871	+	0.948802i	$0.602297\pi$
$138$		0			0
$139$	−2.94535e6			−1.09671			−0.548355	−	0.836246i	$-0.684746\pi$
$139$	−2.94535e6			−1.09671			−0.548355	+	0.836246i	$0.684746\pi$
$140$	−1.21283e6	+	2.49623e6i	−0.441993	+	0.909706i
$141$		0			0
$142$	1.25436e6	−	785126.i	0.438082	−	0.274204i
$143$		−	8.00423e6i		−	2.73723i
$144$		0			0
$145$	2.08284e6			0.683206
$146$	−1.51213e6	−	2.41585e6i	−0.485882	−	0.776268i
$147$		0			0
$148$	3.16971e6	+	1.54005e6i	0.977766	+	0.475061i
$149$			1.59888e6i			0.483346i	0.970358	+	0.241673i	$0.0776961\pi$
$149$			1.59888e6i			0.483346i	−0.970358	+	0.241673i	$0.922304\pi$
$150$		0			0
$151$			5.58054e6i			1.62086i	0.585836	+	0.810429i	$0.300766\pi$
$151$			5.58054e6i			1.62086i	−0.585836	+	0.810429i	$0.699234\pi$
$152$	−5.01243e6	+	538313.i	−1.42731	+	0.153287i
$153$		0			0
$154$	−3.22713e6	+	2.01993e6i	−0.883598	+	0.553061i
$155$	−282995.			−0.0759948
$156$		0			0
$157$			4.58044e6i			1.18361i	0.806082	+	0.591804i	$0.201584\pi$
$157$			4.58044e6i			1.18361i	−0.806082	+	0.591804i	$0.798416\pi$
$158$	−3.00987e6	+	1.88394e6i	−0.763093	+	0.477635i
$159$		0			0
$160$	−6.35482e6	−	2.28583e6i	−1.55147	−	0.558063i
$161$	−441069.			−0.105689
$162$		0			0
$163$	4.50036e6			1.03917			0.519583	−	0.854420i	$-0.326087\pi$
$163$	4.50036e6			1.03917			0.519583	+	0.854420i	$0.326087\pi$
$164$	−1.63559e6	+	3.36634e6i	−0.370802	+	0.763180i
$165$		0			0
$166$	1.51510e6	+	2.42059e6i	0.331220	+	0.529173i
$167$			6.07108e6i			1.30352i	0.758427	+	0.651758i	$0.225968\pi$
$167$			6.07108e6i			1.30352i	−0.758427	+	0.651758i	$0.774032\pi$
$168$		0			0
$169$	−7.69651e6			−1.59453
$170$	4.87155e6	−	3.04920e6i	0.991562	−	0.620639i
$171$		0			0
$172$	2.98257e6	−	6.13870e6i	0.586146	−	1.20640i
$173$			1.67216e6i			0.322954i	0.986877	+	0.161477i	$0.0516257\pi$
$173$			1.67216e6i			0.322954i	−0.986877	+	0.161477i	$0.948374\pi$
$174$		0			0
$175$		−	5.64962e6i		−	1.05416i
$176$	−5.72580e6	−	7.28323e6i	−1.05026	−	1.33594i
$177$		0			0
$178$	2.52112e6	+	4.02786e6i	0.447026	+	0.714191i
$179$	−4.71439e6			−0.821990			−0.410995	−	0.911638i	$-0.634819\pi$
$179$	−4.71439e6			−0.821990			−0.410995	+	0.911638i	$0.634819\pi$
$180$		0			0
$181$		−	9.41548e6i		−	1.58784i	−0.608022	−	0.793920i	$-0.708037\pi$
$181$		−	9.41548e6i		−	1.58784i	0.608022	−	0.793920i	$-0.291963\pi$
$182$	3.16035e6	+	5.04913e6i	0.524229	+	0.837534i
$183$		0			0
$184$	−114610.	−	1.06717e6i	−0.0183979	−	0.171309i
$185$	−1.13484e7			−1.79234
$186$		0			0
$187$	7.88401e6			1.20565
$188$	4.83710e6	+	2.35017e6i	0.727967	+	0.353693i
$189$		0			0
$190$	1.37609e7	−	8.61325e6i	2.00626	−	1.25576i
$191$		−	9.01454e6i		−	1.29373i	−0.762604	−	0.646865i	$-0.776080\pi$
$191$		−	9.01454e6i		−	1.29373i	0.762604	−	0.646865i	$-0.223920\pi$
$192$		0			0
$193$	803577.			0.111778			0.0558889	−	0.998437i	$-0.482201\pi$
$193$	803577.			0.111778			0.0558889	+	0.998437i	$0.482201\pi$
$194$	−3.32675e6	−	5.31497e6i	−0.455633	−	0.727941i
$195$		0			0
$196$	−2.05234e6	+	4.22411e6i	−0.272572	+	0.561005i
$197$		−	1.11135e6i		−	0.145362i	−0.997355	−	0.0726812i	$-0.976844\pi$
$197$		−	1.11135e6i		−	0.145362i	0.997355	−	0.0726812i	$-0.0231556\pi$
$198$		0			0
$199$			1.01000e6i			0.128163i	0.997945	+	0.0640814i	$0.0204117\pi$
$199$			1.01000e6i			0.128163i	−0.997945	+	0.0640814i	$0.979588\pi$
$200$	1.36693e7	−	1.46803e6i	1.70867	−	0.183503i
$201$		0			0
$202$	−1.06496e7	+	6.66579e6i	−1.29205	+	0.808719i
$203$	−2.12634e6			−0.254182
$204$		0			0
$205$		−	1.20524e7i		−	1.39898i
$206$	−540818.	+	338509.i	−0.0618656	+	0.0387229i
$207$		0			0
$208$	−1.13952e7	+	8.95851e6i	−1.26629	+	0.995510i
$209$	2.22704e7			2.43944
$210$		0			0
$211$	−1.52288e7			−1.62113			−0.810565	−	0.585648i	$-0.800840\pi$
$211$	−1.52288e7			−1.62113			−0.810565	+	0.585648i	$0.800840\pi$
$212$	−4.62665e6	−	2.24793e6i	−0.485579	−	0.235925i
$213$		0			0
$214$	8.78662e6	+	1.40379e7i	0.896563	+	1.43239i
$215$			2.19781e7i			2.21144i
$216$		0			0
$217$	288906.			0.0282734
$218$	−1.10216e7	+	6.89864e6i	−1.06384	+	0.665877i
$219$		0			0
$220$	2.68345e7	+	1.30379e7i	2.52014	+	1.22445i
$221$		−	1.23352e7i		−	1.14280i
$222$		0			0
$223$		−	7.55064e6i		−	0.680877i	−0.940267	−	0.340439i	$-0.889424\pi$
$223$		−	7.55064e6i		−	0.680877i	0.940267	−	0.340439i	$-0.110576\pi$
$224$	6.48755e6	+	2.33357e6i	0.577214	+	0.207623i
$225$		0			0
$226$	−6.83360e6	−	1.09177e7i	−0.592003	−	0.945813i
$227$	1.93352e7			1.65299			0.826497	−	0.562941i	$-0.190330\pi$
$227$	1.93352e7			1.65299			0.826497	+	0.562941i	$0.190330\pi$
$228$		0			0
$229$			1.03537e7i			0.862159i	0.902314	+	0.431079i	$0.141867\pi$
$229$			1.03537e7i			0.862159i	−0.902314	+	0.431079i	$0.858133\pi$
$230$	1.83380e6	+	2.92977e6i	0.150720	+	0.240797i
$231$		0			0
$232$	−552520.	−	5.14472e6i	−0.0442470	−	0.412000i
$233$	1.04567e7			0.826663			0.413331	−	0.910581i	$-0.364365\pi$
$233$	1.04567e7			0.826663			0.413331	+	0.910581i	$0.364365\pi$
$234$		0			0
$235$	−1.73181e7			−1.33443
$236$	2.36394e6	−	4.86544e6i	0.179846	−	0.370157i
$237$		0			0
$238$	−4.97329e6	+	3.11288e6i	−0.368904	+	0.230904i
$239$		−	2.58738e6i		−	0.189525i	−0.995500	−	0.0947626i	$-0.969791\pi$
$239$		−	2.58738e6i		−	0.189525i	0.995500	−	0.0947626i	$-0.0302092\pi$
$240$		0			0
$241$	−4.98127e6			−0.355868			−0.177934	−	0.984042i	$-0.556941\pi$
$241$	−4.98127e6			−0.355868			−0.177934	+	0.984042i	$0.556941\pi$
$242$	1.41949e7	+	2.26784e7i	1.00158	+	1.60017i
$243$		0			0
$244$	9.23987e6	+	4.48932e6i	0.636058	+	0.309038i
$245$		−	1.51234e7i		−	1.02838i
$246$		0			0
$247$		−	3.48440e7i		−	2.31227i
$248$	75070.8	+	699012.i	0.00492171	+	0.0458279i
$249$		0			0
$250$	−1.56899e7	+	9.82064e6i	−1.00416	+	0.628521i
$251$	−1.36281e7			−0.861816			−0.430908	−	0.902396i	$-0.641807\pi$
$251$	−1.36281e7			−0.861816			−0.430908	+	0.902396i	$0.641807\pi$
$252$		0			0
$253$			4.74149e6i			0.292788i
$254$	−3.38509e6	+	2.11879e6i	−0.206571	+	0.129297i
$255$		0			0
$256$	−3.96034e6	+	1.63031e7i	−0.236055	+	0.971740i
$257$	−5.80282e6			−0.341853			−0.170927	−	0.985284i	$-0.554676\pi$
$257$	−5.80282e6			−0.341853			−0.170927	+	0.985284i	$0.554676\pi$
$258$		0			0
$259$	1.15854e7			0.666826
$260$	2.03990e7	−	4.19849e7i	1.16061	−	2.38876i
$261$		0			0
$262$	7.03892e6	+	1.12457e7i	0.391383	+	0.625292i
$263$			2.82908e7i			1.55517i	0.628778	+	0.777585i	$0.283555\pi$
$263$			2.82908e7i			1.55517i	−0.628778	+	0.777585i	$0.716445\pi$
$264$		0			0
$265$	1.65646e7			0.890111
$266$	−1.40484e7	+	8.79315e6i	−0.746416	+	0.467196i
$267$		0			0
$268$	6.41196e6	−	1.31970e7i	0.333109	−	0.685601i
$269$		−	5.02831e6i		−	0.258324i	−0.991624	−	0.129162i	$-0.958771\pi$
$269$		−	5.02831e6i		−	0.258324i	0.991624	−	0.129162i	$-0.0412287\pi$
$270$		0			0
$271$			3.34374e7i			1.68006i	0.542541	+	0.840029i	$0.317462\pi$
$271$			3.34374e7i			1.68006i	−0.542541	+	0.840029i	$0.682538\pi$
$272$	−8.82396e6	−	1.12241e7i	−0.438487	−	0.557756i
$273$		0			0
$274$	−6.89487e6	−	1.10156e7i	−0.335177	−	0.535495i
$275$	−6.07334e7			−2.92031
$276$		0			0
$277$		−	1.94246e7i		−	0.913929i	−0.889485	−	0.456965i	$-0.848937\pi$
$277$		−	1.94246e7i		−	0.913929i	0.889485	−	0.456965i	$-0.151063\pi$
$278$	−1.25014e7	−	1.99729e7i	−0.581870	−	0.929624i
$279$		0			0
$280$	−2.20752e7	+	2.37078e6i	−1.00561	+	0.107998i
$281$	2.59526e7			1.16967			0.584833	−	0.811154i	$-0.301160\pi$
$281$	2.59526e7			1.16967			0.584833	+	0.811154i	$0.301160\pi$
$282$		0			0
$283$	−336420.			−0.0148430			−0.00742152	−	0.999972i	$-0.502362\pi$
$283$	−336420.			−0.0148430			−0.00742152	+	0.999972i	$0.502362\pi$
$284$	1.06482e7	+	5.17356e6i	0.464857	+	0.225858i
$285$		0			0
$286$	5.42781e7	−	3.39738e7i	2.32021	−	1.45226i
$287$			1.23041e7i			0.520481i
$288$		0			0
$289$	−1.19876e7			−0.496637
$290$	8.84056e6	+	1.41241e7i	0.362481	+	0.579118i
$291$		0			0
$292$	9.96413e6	−	2.05081e7i	0.400213	−	0.823713i
$293$		−	1.59063e7i		−	0.632364i	−0.948699	−	0.316182i	$-0.897599\pi$
$293$		−	1.59063e7i		−	0.632364i	0.948699	−	0.316182i	$-0.102401\pi$
$294$		0			0
$295$			1.74195e7i			0.678532i
$296$	3.01042e6	+	2.80311e7i	0.116078	+	1.08085i
$297$		0			0
$298$	−1.08423e7	+	6.78642e6i	−0.409707	+	0.256444i
$299$	7.41847e6			0.277524
$300$		0			0
$301$		−	2.24372e7i		−	0.822752i
$302$	−3.78426e7	+	2.36865e7i	−1.37392	+	0.859962i
$303$		0			0
$304$	−2.49256e7	−	3.17054e7i	−0.887205	−	1.12853i
$305$	−3.30811e7			−1.16595
$306$		0			0
$307$	5.19952e7			1.79700			0.898500	−	0.438974i	$-0.144658\pi$
$307$	5.19952e7			1.79700			0.898500	+	0.438974i	$0.144658\pi$
$308$	−2.73950e7	−	1.33102e7i	−0.937602	−	0.455547i
$309$		0			0
$310$	−1.20117e6	−	1.91904e6i	−0.0403198	−	0.0644168i
$311$		−	6.97946e6i		−	0.232028i	−0.993248	−	0.116014i	$-0.962988\pi$
$311$		−	6.97946e6i		−	0.232028i	0.993248	−	0.116014i	$-0.0370118\pi$
$312$		0			0
$313$	−1.81265e7			−0.591127			−0.295564	−	0.955323i	$-0.595507\pi$
$313$	−1.81265e7			−0.591127			−0.295564	+	0.955323i	$0.595507\pi$
$314$	−3.10608e7	+	1.94416e7i	−1.00328	+	0.627974i
$315$		0			0
$316$	−2.55507e7	−	1.24142e7i	−0.809732	−	0.393420i
$317$		−	3.82943e7i		−	1.20214i	−0.799195	−	0.601072i	$-0.794740\pi$
$317$		−	3.82943e7i		−	1.20214i	0.799195	−	0.601072i	$-0.205260\pi$
$318$		0			0
$319$			2.28582e7i			0.704157i
$320$	−1.14723e7	−	5.27953e7i	−0.350106	−	1.61118i
$321$		0			0
$322$	−1.87211e6	−	2.99097e6i	−0.0560742	−	0.0895868i
$323$	3.43207e7			1.01847
$324$		0			0
$325$			9.50227e7i			2.76807i
$326$	1.91017e7	+	3.05178e7i	0.551339	+	0.880846i
$327$		0			0
$328$	−2.97700e7	+	3.19717e6i	−0.843640	+	0.0906032i
$329$	1.76798e7			0.496466
$330$		0			0
$331$	4.87879e6			0.134533			0.0672664	−	0.997735i	$-0.478572\pi$
$331$	4.87879e6			0.134533			0.0672664	+	0.997735i	$0.478572\pi$
$332$	−9.98368e6	+	2.05483e7i	−0.272820	+	0.561515i
$333$		0			0
$334$	−4.11691e7	+	2.57686e7i	−1.10492	+	0.691593i
$335$			4.72488e7i			1.25677i
$336$		0			0
$337$	5.80289e6			0.151619			0.0758097	−	0.997122i	$-0.475846\pi$
$337$	5.80289e6			0.151619			0.0758097	+	0.997122i	$0.475846\pi$
$338$	−3.26677e7	−	5.21914e7i	−0.845995	−	1.35160i
$339$		0			0
$340$	4.13543e7	+	2.00926e7i	1.05217	+	0.511210i
$341$		−	3.10574e6i		−	0.0783253i
$342$		0			0
$343$			4.01930e7i			0.996019i
$344$	5.42871e7	−	5.83019e6i	1.33359	−	0.143221i
$345$		0			0
$346$	−1.13392e7	+	7.09746e6i	−0.273751	+	0.171346i
$347$	−2.11799e7			−0.506916			−0.253458	−	0.967346i	$-0.581568\pi$
$347$	−2.11799e7			−0.506916			−0.253458	+	0.967346i	$0.581568\pi$
$348$		0			0
$349$			3.02066e7i			0.710600i	0.934752	+	0.355300i	$0.115621\pi$
$349$			3.02066e7i			0.710600i	−0.934752	+	0.355300i	$0.884379\pi$
$350$	3.83111e7	−	2.39797e7i	0.893552	−	0.559292i
$351$		0			0
$352$	2.50859e7	−	6.97412e7i	0.575176	−	1.59905i
$353$	−5.47613e6			−0.124494			−0.0622472	−	0.998061i	$-0.519827\pi$
$353$	−5.47613e6			−0.124494			−0.0622472	+	0.998061i	$0.519827\pi$
$354$		0			0
$355$	−3.81232e7			−0.852127
$356$	−1.66128e7	+	3.41923e7i	−0.368208	+	0.757841i
$357$		0			0
$358$	−2.00101e7	−	3.19692e7i	−0.436115	−	0.696758i
$359$		−	6.76347e7i		−	1.46179i	−0.682487	−	0.730897i	$-0.739102\pi$
$359$		−	6.76347e7i		−	1.46179i	0.682487	−	0.730897i	$-0.260898\pi$
$360$		0			0
$361$	4.99019e7			1.06071
$362$	6.38481e7	−	3.99638e7i	1.34593	−	0.842444i
$363$		0			0
$364$	−2.08250e7	+	4.28618e7i	−0.431799	+	0.888723i
$365$			7.34241e7i			1.50994i
$366$		0			0
$367$		−	4.80835e7i		−	0.972743i	−0.873752	−	0.486371i	$-0.838320\pi$
$367$		−	4.80835e7i		−	0.972743i	0.873752	−	0.486371i	$-0.161680\pi$
$368$	6.75023e6	−	5.30678e6i	0.135449	−	0.106485i
$369$		0			0
$370$	−4.81680e7	−	7.69556e7i	−0.950941	−	1.51927i
$371$	−1.69106e7			−0.331160
$372$		0			0
$373$		−	5.09422e7i		−	0.981637i	−0.871262	−	0.490819i	$-0.836698\pi$
$373$		−	5.09422e7i		−	0.981637i	0.871262	−	0.490819i	$-0.163302\pi$
$374$	3.34635e7	+	5.34629e7i	0.639671	+	1.02197i
$375$		0			0
$376$	4.59401e6	+	4.27765e7i	0.0864228	+	0.804714i
$377$	3.57636e7			0.667448
$378$		0			0
$379$	−4.01401e7			−0.737329			−0.368665	−	0.929563i	$-0.620185\pi$
$379$	−4.01401e7			−0.737329			−0.368665	+	0.929563i	$0.620185\pi$
$380$	1.16816e8	+	5.67567e7i	2.12888	+	1.03435i
$381$		0			0
$382$	6.11293e7	−	3.82620e7i	1.09663	−	0.686401i
$383$			2.67862e7i			0.476777i	0.971170	+	0.238388i	$0.0766191\pi$
$383$			2.67862e7i			0.476777i	−0.971170	+	0.238388i	$0.923381\pi$
$384$		0			0
$385$	9.80811e7			1.71871
$386$	3.41076e6	+	5.44920e6i	0.0593048	+	0.0947482i
$387$		0			0
$388$	2.19215e7	−	4.51186e7i	0.375297	−	0.772432i
$389$			5.82424e7i			0.989442i	0.869052	+	0.494721i	$0.164730\pi$
$389$			5.82424e7i			0.989442i	−0.869052	+	0.494721i	$0.835270\pi$
$390$		0			0
$391$			7.30705e6i			0.122240i
$392$	−3.73556e7	+	4.01183e6i	−0.620151	+	0.0666015i
$393$		0			0
$394$	7.53626e6	−	4.71710e6i	0.123216	−	0.0771234i
$395$	9.14781e7			1.48431
$396$		0			0
$397$			1.92002e7i			0.306856i	0.988160	+	0.153428i	$0.0490312\pi$
$397$			1.92002e7i			0.306856i	−0.988160	+	0.153428i	$0.950969\pi$
$398$	−6.84899e6	+	4.28692e6i	−0.108637	+	0.0679980i
$399$		0			0
$400$	6.79741e7	+	8.64632e7i	1.06210	+	1.35099i
$401$	4.53461e6			0.0703245			0.0351623	−	0.999382i	$-0.488805\pi$
$401$	4.53461e6			0.0703245			0.0351623	+	0.999382i	$0.488805\pi$
$402$		0			0
$403$	−4.85920e6			−0.0742420
$404$	−9.04039e7	−	4.39240e7i	−1.37102	−	0.666128i
$405$		0			0
$406$	−9.02521e6	−	1.44191e7i	−0.134859	−	0.215457i
$407$		−	1.24543e8i		−	1.84730i
$408$		0			0
$409$	−1.02088e8			−1.49213			−0.746063	−	0.665876i	$-0.768058\pi$
$409$	−1.02088e8			−1.49213			−0.746063	+	0.665876i	$0.768058\pi$
$410$	8.17294e7	−	5.11561e7i	1.18584	−	0.742242i
$411$		0			0
$412$	−4.59098e6	−	2.23059e6i	−0.0656468	−	0.0318954i
$413$		−	1.77834e7i		−	0.252443i
$414$		0			0
$415$		−	7.35682e7i		−	1.02931i
$416$	−1.09116e8	−	3.92490e7i	−1.51568	−	0.545191i
$417$		0			0
$418$	9.45264e7	+	1.51020e8i	1.29427	+	2.06778i
$419$	1.36648e8			1.85764			0.928820	−	0.370531i	$-0.120824\pi$
$419$	1.36648e8			1.85764			0.928820	+	0.370531i	$0.120824\pi$
$420$		0			0
$421$		−	3.78060e7i		−	0.506657i	−0.967380	−	0.253329i	$-0.918475\pi$
$421$		−	3.78060e7i		−	0.506657i	0.967380	−	0.253329i	$-0.0815254\pi$
$422$	−6.46383e7	−	1.03269e8i	−0.860107	−	1.37415i
$423$		0			0
$424$	−4.39414e6	−	4.09154e7i	−0.0576469	−	0.536772i
$425$	−9.35955e7			−1.21924
$426$		0			0
$427$	3.37721e7			0.433785
$428$	−5.78991e7	+	1.19167e8i	−0.738484	+	1.51994i
$429$		0			0
$430$	−1.49038e8	+	9.32857e7i	−1.87452	+	1.17330i
$431$			3.82526e6i			0.0477781i	0.999715	+	0.0238891i	$0.00760485\pi$
$431$			3.82526e6i			0.0477781i	−0.999715	+	0.0238891i	$0.992395\pi$
$432$		0			0
$433$	−7.51604e7			−0.925818			−0.462909	−	0.886406i	$-0.653194\pi$
$433$	−7.51604e7			−0.925818			−0.462909	+	0.886406i	$0.653194\pi$
$434$	1.22625e6	+	1.95912e6i	0.0150007	+	0.0239658i
$435$		0			0
$436$	−9.35618e7	−	4.54583e7i	−1.12886	−	0.548472i
$437$			2.06407e7i			0.247332i
$438$		0			0
$439$		−	2.64865e7i		−	0.313063i	−0.987673	−	0.156531i	$-0.949969\pi$
$439$		−	2.64865e7i		−	0.313063i	0.987673	−	0.156531i	$-0.0500312\pi$
$440$	2.54859e7	+	2.37309e8i	0.299187	+	2.78584i
$441$		0			0
$442$	8.36474e7	−	5.23566e7i	0.968692	−	0.606324i
$443$	−8.65074e7			−0.995044			−0.497522	−	0.867451i	$-0.665757\pi$
$443$	−8.65074e7			−0.995044			−0.497522	+	0.867451i	$0.665757\pi$
$444$		0			0
$445$		−	1.22417e8i		−	1.38919i
$446$	5.12022e7	−	3.20485e7i	0.577144	−	0.361246i
$447$		0			0
$448$	1.17119e7	+	5.38980e7i	0.130255	+	0.599430i
$449$	−2.98909e7			−0.330217			−0.165109	−	0.986275i	$-0.552797\pi$
$449$	−2.98909e7			−0.330217			−0.165109	+	0.986275i	$0.552797\pi$
$450$		0			0
$451$	1.32269e8			1.44188
$452$	4.50297e7	−	9.26797e7i	0.487623	−	1.00362i
$453$		0			0
$454$	8.20679e7	+	1.31116e8i	0.877012	+	1.40116i
$455$		−	1.53456e8i		−	1.62911i
$456$		0			0
$457$	−7.17316e7			−0.751557			−0.375779	−	0.926709i	$-0.622625\pi$
$457$	−7.17316e7			−0.751557			−0.375779	+	0.926709i	$0.622625\pi$
$458$	−7.02100e7	+	4.39459e7i	−0.730807	+	0.457427i
$459$		0			0
$460$	−1.20838e7	+	2.48707e7i	−0.124145	+	0.255514i
$461$			1.44580e8i			1.47572i	0.674952	+	0.737861i	$0.264164\pi$
$461$			1.44580e8i			1.47572i	−0.674952	+	0.737861i	$0.735836\pi$
$462$		0			0
$463$		−	8.06977e6i		−	0.0813052i	−0.999173	−	0.0406526i	$-0.987056\pi$
$463$		−	8.06977e6i		−	0.0813052i	0.999173	−	0.0406526i	$-0.0129437\pi$
$464$	3.25421e7	−	2.55834e7i	0.325755	−	0.256097i
$465$		0			0
$466$	4.43834e7	+	7.09090e7i	0.438594	+	0.700719i
$467$	−8.38502e7			−0.823291			−0.411646	−	0.911344i	$-0.635046\pi$
$467$	−8.38502e7			−0.823291			−0.411646	+	0.911344i	$0.635046\pi$
$468$		0			0
$469$		−	4.82356e7i		−	0.467573i
$470$	−7.35062e7	−	1.17437e8i	−0.707995	−	1.13113i
$471$		0			0
$472$	4.30271e7	−	4.62092e6i	0.409181	−	0.0439443i
$473$	−2.41200e8			−2.27926
$474$		0			0
$475$	−2.64385e8			−2.46692
$476$	−4.22181e7	−	2.05122e7i	−0.391451	−	0.190192i
$477$		0			0
$478$	1.75455e7	−	1.09821e7i	0.160651	−	0.100554i
$479$			9.09446e7i			0.827505i	0.910389	+	0.413752i	$0.135782\pi$
$479$			9.09446e7i			0.827505i	−0.910389	+	0.413752i	$0.864218\pi$
$480$		0			0
$481$	−1.94859e8			−1.75100
$482$	−2.11429e7	−	3.37789e7i	−0.188809	−	0.301651i
$483$		0			0
$484$	−9.35365e7	+	1.92516e8i	−0.824983	+	1.69797i
$485$			1.61536e8i			1.41594i
$486$		0			0
$487$			1.12400e8i			0.973151i	0.873639	+	0.486575i	$0.161754\pi$
$487$			1.12400e8i			0.973151i	−0.873639	+	0.486575i	$0.838246\pi$
$488$	8.77551e6	+	8.17121e7i	0.0755115	+	0.703116i
$489$		0			0
$490$	1.02555e8	−	6.41910e7i	0.871700	−	0.545614i
$491$	4.04565e7			0.341777			0.170889	−	0.985290i	$-0.445336\pi$
$491$	4.04565e7			0.341777			0.170889	+	0.985290i	$0.445336\pi$
$492$		0			0
$493$			3.52265e7i			0.293987i
$494$	2.36284e8	−	1.47895e8i	1.95999	−	1.22679i
$495$		0			0
$496$	−4.42149e6	+	3.47601e6i	−0.0362346	+	0.0284863i
$497$	3.89194e7			0.317028
$498$		0			0
$499$	1.36162e8			1.09586			0.547931	−	0.836524i	$-0.315416\pi$
$499$	1.36162e8			1.09586			0.547931	+	0.836524i	$0.315416\pi$
$500$	−1.33191e8	−	6.47128e7i	−1.06553	−	0.517702i
$501$		0			0
$502$	−5.78442e7	−	9.24147e7i	−0.457245	−	0.730516i
$503$		−	1.62786e8i		−	1.27912i	−0.768739	−	0.639562i	$-0.779116\pi$
$503$		−	1.62786e8i		−	1.27912i	0.768739	−	0.639562i	$-0.220884\pi$
$504$		0			0
$505$	3.23669e8			2.51320
$506$	−3.21529e7	+	2.01251e7i	−0.248181	+	0.155341i
$507$		0			0
$508$	−2.87359e7	−	1.39617e7i	−0.219196	−	0.106500i
$509$		−	1.23236e8i		−	0.934511i	−0.884122	−	0.467255i	$-0.845243\pi$
$509$		−	1.23236e8i		−	0.934511i	0.884122	−	0.467255i	$-0.154757\pi$
$510$		0			0
$511$		−	7.49577e7i		−	0.561764i
$512$	−1.27364e8	+	4.23423e7i	−0.948934	+	0.315474i
$513$		0			0
$514$	−2.46299e7	−	3.93500e7i	−0.181374	−	0.289771i
$515$	1.64369e7			0.120337
$516$		0			0
$517$		−	1.90058e8i		−	1.37535i
$518$	4.91741e7	+	7.85629e7i	0.353791	+	0.565234i
$519$		0			0
$520$	3.71290e8	−	3.98749e7i	2.64061	−	0.283589i
$521$	−2.46388e7			−0.174223			−0.0871115	−	0.996199i	$-0.527764\pi$
$521$	−2.46388e7			−0.174223			−0.0871115	+	0.996199i	$0.527764\pi$
$522$		0			0
$523$	−8.82039e7			−0.616571			−0.308285	−	0.951294i	$-0.599755\pi$
$523$	−8.82039e7			−0.616571			−0.308285	+	0.951294i	$0.599755\pi$
$524$	−4.63827e7	+	9.54644e7i	−0.322376	+	0.663510i
$525$		0			0
$526$	−1.91845e8	+	1.20080e8i	−1.31824	+	0.825110i
$527$		−	4.78622e6i		−	0.0327010i
$528$		0			0
$529$	1.43641e8			0.970315
$530$	7.03082e7	+	1.12328e8i	0.472257	+	0.754500i
$531$		0			0
$532$	−1.19256e8	−	5.79422e7i	−0.792036	−	0.384822i
$533$		−	2.06947e8i		−	1.36671i
$534$		0			0
$535$		−	4.26650e8i		−	2.78619i
$536$	1.16707e8	−	1.25338e7i	0.757882	−	0.0813932i
$537$		0			0
$538$	3.40979e7	−	2.13425e7i	0.218968	−	0.137056i
$539$	1.65972e8			1.05991
$540$		0			0
$541$			3.02964e8i			1.91337i	0.291128	+	0.956684i	$0.405969\pi$
$541$			3.02964e8i			1.91337i	−0.291128	+	0.956684i	$0.594031\pi$
$542$	−2.26745e8	+	1.41924e8i	−1.42410	+	0.891371i
$543$		0			0
$544$	3.86595e7	−	1.07477e8i	0.240137	−	0.667605i
$545$	3.34976e8			2.06930
$546$		0			0
$547$	9.88974e6			0.0604258			0.0302129	−	0.999543i	$-0.490381\pi$
$547$	9.88974e6			0.0604258			0.0302129	+	0.999543i	$0.490381\pi$
$548$	4.54335e7	−	9.35107e7i	0.276080	−	0.568224i
$549$		0			0
$550$	−2.57781e8	−	4.11844e8i	−1.54940	−	2.47540i
$551$			9.95063e7i			0.594834i
$552$		0			0
$553$	−9.33887e7			−0.552229
$554$	1.31722e8	−	8.24472e7i	0.774690	−	0.484894i
$555$		0			0
$556$	8.23779e7	−	1.69549e8i	0.479277	−	0.986441i
$557$			3.10741e8i			1.79818i	0.437763	+	0.899090i	$0.355771\pi$
$557$			3.10741e8i			1.79818i	−0.437763	+	0.899090i	$0.644229\pi$
$558$		0			0
$559$			3.77378e8i			2.16043i
$560$	−1.09774e8	−	1.39633e8i	−0.625083	−	0.795106i
$561$		0			0
$562$	1.10155e8	+	1.75989e8i	0.620577	+	0.991464i
$563$	1.02595e8			0.574913			0.287457	−	0.957794i	$-0.407190\pi$
$563$	1.02595e8			0.574913			0.287457	+	0.957794i	$0.407190\pi$
$564$		0			0
$565$			3.31817e8i			1.83973i
$566$	−1.42793e6	−	2.28133e6i	−0.00787512	−	0.0125817i
$567$		0			0
$568$	1.01130e7	+	9.41662e7i	0.0551870	+	0.513866i
$569$	2.40381e8			1.30486			0.652428	−	0.757851i	$-0.273751\pi$
$569$	2.40381e8			1.30486			0.652428	+	0.757851i	$0.273751\pi$
$570$		0			0
$571$	−4.46256e7			−0.239704			−0.119852	−	0.992792i	$-0.538242\pi$
$571$	−4.46256e7			−0.239704			−0.119852	+	0.992792i	$0.538242\pi$
$572$	4.60765e8	+	2.23869e8i	2.46202	+	1.19621i
$573$		0			0
$574$	−8.34364e7	+	5.22245e7i	−0.441184	+	0.276146i
$575$		−	5.62888e7i		−	0.296087i
$576$		0			0
$577$	1.24361e8			0.647377			0.323689	−	0.946164i	$-0.395077\pi$
$577$	1.24361e8			0.647377			0.323689	+	0.946164i	$0.395077\pi$
$578$	−5.08811e7	−	8.12902e7i	−0.263496	−	0.420973i
$579$		0			0
$580$	−5.82546e7	+	1.19899e8i	−0.298570	+	0.614513i
$581$			7.51048e7i			0.382948i
$582$		0			0
$583$			1.81789e8i			0.917407i
$584$	1.81361e8	−	1.94774e7i	0.910555	−	0.0977896i
$585$		0			0
$586$	1.07864e8	−	6.75140e7i	0.536022	−	0.335507i
$587$	−1.65460e8			−0.818046			−0.409023	−	0.912524i	$-0.634130\pi$
$587$	−1.65460e8			−0.818046			−0.409023	+	0.912524i	$0.634130\pi$
$588$		0			0
$589$		−	1.35199e7i		−	0.0661650i
$590$	−1.18125e8	+	7.39368e7i	−0.575156	+	0.360002i
$591$		0			0
$592$	−1.77306e8	+	1.39392e8i	−0.854593	+	0.671849i
$593$	−3.64689e8			−1.74887			−0.874437	−	0.485139i	$-0.838769\pi$
$593$	−3.64689e8			−1.74887			−0.874437	+	0.485139i	$0.838769\pi$
$594$		0			0
$595$	1.51152e8			0.717566
$596$	−9.20399e7	−	4.47189e7i	−0.434748	−	0.211228i
$597$		0			0
$598$	3.14875e7	+	5.03060e7i	0.147243	+	0.235243i
$599$			4.13919e8i			1.92590i	0.269672	+	0.962952i	$0.413085\pi$
$599$			4.13919e8i			1.92590i	−0.269672	+	0.962952i	$0.586915\pi$
$600$		0			0
$601$	−1.49949e8			−0.690747			−0.345373	−	0.938465i	$-0.612248\pi$
$601$	−1.49949e8			−0.690747			−0.345373	+	0.938465i	$0.612248\pi$
$602$	1.52151e8	−	9.52341e7i	0.697404	−	0.436519i
$603$		0			0
$604$	−3.21244e8	−	1.56081e8i	−1.45789	−	0.708336i
$605$		−	6.89257e8i		−	3.11254i
$606$		0			0
$607$			3.28292e8i			1.46789i	0.679207	+	0.733946i	$0.262324\pi$
$607$			3.28292e8i			1.46789i	−0.679207	+	0.733946i	$0.737676\pi$
$608$	1.09204e8	−	3.03597e8i	0.485878	−	1.35079i
$609$		0			0
$610$	−1.40412e8	−	2.24329e8i	−0.618607	−	0.988317i
$611$	−2.97362e8			−1.30365
$612$		0			0
$613$		−	9.28329e7i		−	0.403014i	−0.979487	−	0.201507i	$-0.935416\pi$
$613$		−	9.28329e7i		−	0.403014i	0.979487	−	0.201507i	$-0.0645839\pi$
$614$	2.20692e8	+	3.52589e8i	0.953416	+	1.52322i
$615$		0			0
$616$	−2.60182e7	−	2.42265e8i	−0.111310	−	1.03645i
$617$	1.94762e8			0.829178			0.414589	−	0.910009i	$-0.363925\pi$
$617$	1.94762e8			0.829178			0.414589	+	0.910009i	$0.363925\pi$
$618$		0			0
$619$	5.23439e6			0.0220696			0.0110348	−	0.999939i	$-0.496487\pi$
$619$	5.23439e6			0.0220696			0.0110348	+	0.999939i	$0.496487\pi$
$620$	7.91505e6	−	1.62907e7i	0.0332107	−	0.0683539i
$621$		0			0
$622$	4.73290e7	−	2.96242e7i	0.196678	−	0.123105i
$623$			1.24974e8i			0.516840i
$624$		0			0
$625$	5.73051e7			0.234722
$626$	−7.69375e7	−	1.22919e8i	−0.313628	−	0.501067i
$627$		0			0
$628$	−2.63673e8	−	1.28109e8i	−1.06460	−	0.517252i
$629$		−	1.91932e8i		−	0.771252i
$630$		0			0
$631$			2.99018e8i			1.19017i	0.803662	+	0.595086i	$0.202882\pi$
$631$			2.99018e8i			1.19017i	−0.803662	+	0.595086i	$0.797118\pi$
$632$	−2.42666e7	−	2.25955e8i	−0.0961298	−	0.895100i
$633$		0			0
$634$	2.59681e8	−	1.62539e8i	1.01900	−	0.637810i
$635$	1.02882e8			0.401807
$636$		0			0
$637$		−	2.59678e8i		−	1.00466i
$638$	−1.55005e8	+	9.70210e7i	−0.596877	+	0.373597i
$639$		0			0
$640$	3.09321e8	−	3.01884e8i	1.17996	−	1.15160i
$641$	−2.26180e8			−0.858777			−0.429389	−	0.903120i	$-0.641271\pi$
$641$	−2.26180e8			−0.858777			−0.429389	+	0.903120i	$0.641271\pi$
$642$		0			0
$643$	4.23603e8			1.59341			0.796703	−	0.604371i	$-0.206575\pi$
$643$	4.23603e8			1.59341			0.796703	+	0.604371i	$0.206575\pi$
$644$	1.23362e7	−	2.53902e7i	0.0461874	−	0.0950623i
$645$		0			0
$646$	1.45673e8	+	2.32735e8i	0.540360	+	0.863305i
$647$			2.69306e8i			0.994337i	0.867654	+	0.497168i	$0.165627\pi$
$647$			2.69306e8i			0.994337i	−0.867654	+	0.497168i	$0.834373\pi$
$648$		0			0
$649$	−1.91171e8			−0.699340
$650$	−6.44366e8	+	4.03321e8i	−2.34635	+	1.46863i
$651$		0			0
$652$	−1.25870e8	+	2.59064e8i	−0.454129	+	0.934683i
$653$			2.66960e8i			0.958754i	0.877609	+	0.479377i	$0.159137\pi$
$653$			2.66960e8i			0.958754i	−0.877609	+	0.479377i	$0.840863\pi$
$654$		0			0
$655$		−	3.41787e8i		−	1.21628i
$656$	−1.48039e8	−	1.88305e8i	−0.524401	−	0.667039i
$657$		0			0
$658$	7.50414e7	+	1.19890e8i	0.263405	+	0.420828i
$659$	−7.64400e7			−0.267094			−0.133547	−	0.991042i	$-0.542637\pi$
$659$	−7.64400e7			−0.267094			−0.133547	+	0.991042i	$0.542637\pi$
$660$		0			0
$661$			1.85402e8i			0.641963i	0.947085	+	0.320981i	$0.104013\pi$
$661$			1.85402e8i			0.641963i	−0.947085	+	0.320981i	$0.895987\pi$
$662$	2.07079e7	+	3.30840e7i	0.0713777	+	0.114036i
$663$		0			0
$664$	−1.81717e8	+	1.95156e7i	−0.620714	+	0.0666620i
$665$	4.26967e8			1.45188
$666$		0			0
$667$	−2.11854e7			−0.0713936
$668$	−3.49483e8	−	1.69801e8i	−1.17245	−	0.569654i
$669$		0			0
$670$	−3.20402e8	+	2.00546e8i	−1.06530	+	0.666792i
$671$		−	3.63050e8i		−	1.20171i
$672$		0			0
$673$	−4.60309e7			−0.151009			−0.0755047	−	0.997145i	$-0.524057\pi$
$673$	−4.60309e7			−0.151009			−0.0755047	+	0.997145i	$0.524057\pi$
$674$	2.46302e7	+	3.93504e7i	0.0804431	+	0.128520i
$675$		0			0
$676$	2.15262e8	−	4.43051e8i	0.696832	−	1.43421i
$677$		−	2.19932e8i		−	0.708797i	−0.935095	−	0.354398i	$-0.884686\pi$
$677$		−	2.19932e8i		−	0.708797i	0.935095	−	0.354398i	$-0.115314\pi$
$678$		0			0
$679$		−	1.64910e8i		−	0.526791i
$680$	3.92760e7	+	3.65714e8i	0.124911	+	1.16309i
$681$		0			0
$682$	2.10606e7	−	1.31822e7i	0.0663922	−	0.0415562i
$683$	−5.36350e8			−1.68339			−0.841697	−	0.539950i	$-0.818443\pi$
$683$	−5.36350e8			−1.68339			−0.841697	+	0.539950i	$0.818443\pi$
$684$		0			0
$685$			3.34792e8i			1.04161i
$686$	−2.72556e8	+	1.70598e8i	−0.844273	+	0.528447i
$687$		0			0
$688$	2.69956e8	+	3.43384e8i	0.828949	+	1.05442i
$689$	2.84425e8			0.869580
$690$		0			0
$691$	4.81630e8			1.45975			0.729877	−	0.683579i	$-0.239577\pi$
$691$	4.81630e8			1.45975			0.729877	+	0.683579i	$0.239577\pi$
$692$	−9.62583e7	−	4.67684e7i	−0.290482	−	0.141135i
$693$		0			0
$694$	−8.98978e7	−	1.43625e8i	−0.268949	−	0.429686i
$695$			6.07030e8i			1.80824i
$696$		0			0
$697$	2.03839e8			0.601988
$698$	−2.04836e8	+	1.28211e8i	−0.602338	+	0.377016i
$699$		0			0
$700$	3.25221e8	+	1.58013e8i	0.948166	+	0.460680i
$701$		−	4.69995e8i		−	1.36439i	−0.731169	−	0.682196i	$-0.761025\pi$
$701$		−	4.69995e8i		−	1.36439i	0.731169	−	0.682196i	$-0.238975\pi$
$702$		0			0
$703$		−	5.42162e8i		−	1.56050i
$704$	5.79404e8	−	1.25903e8i	1.66059	−	0.360843i
$705$		0			0
$706$	−2.32433e7	−	3.71347e7i	−0.0660517	−	0.105527i
$707$	−3.30430e8			−0.935020
$708$		0			0
$709$		−	4.05087e8i		−	1.13660i	−0.822820	−	0.568302i	$-0.807600\pi$
$709$		−	4.05087e8i		−	1.13660i	0.822820	−	0.568302i	$-0.192400\pi$
$710$	−1.61813e8	−	2.58520e8i	−0.452104	−	0.722303i
$711$		0			0
$712$	−3.02377e8	+	3.24739e7i	−0.837739	+	0.0899694i
$713$	2.87846e6			0.00794130
$714$		0			0
$715$	−1.64966e9			−4.51311
$716$	1.31856e8	−	2.71385e8i	0.359220	−	0.739343i
$717$		0			0
$718$	4.58643e8	−	2.87074e8i	1.23909	−	0.775569i
$719$		−	3.74151e8i		−	1.00661i	−0.864109	−	0.503304i	$-0.832118\pi$
$719$		−	3.74151e8i		−	1.00661i	0.864109	−	0.503304i	$-0.167882\pi$
$720$		0			0
$721$	−1.67802e7			−0.0447704
$722$	2.11807e8	+	3.38394e8i	0.562768	+	0.899105i
$723$		0			0
$724$	5.42003e8	+	2.63340e8i	1.42819	+	0.693907i
$725$		−	2.71362e8i		−	0.712090i
$726$		0			0
$727$			2.13805e8i			0.556435i	0.960518	+	0.278218i	$0.0897436\pi$
$727$			2.13805e8i			0.556435i	−0.960518	+	0.278218i	$0.910256\pi$
$728$	−3.79045e8	+	4.07078e7i	−0.982419	+	0.105507i
$729$		0			0
$730$	−4.97902e8	+	3.11647e8i	−1.27990	+	0.801114i
$731$	−3.71710e8			−0.951595
$732$		0			0
$733$		−	5.56686e8i		−	1.41351i	−0.707459	−	0.706754i	$-0.750159\pi$
$733$		−	5.56686e8i		−	1.41351i	0.707459	−	0.706754i	$-0.249841\pi$
$734$	3.26063e8	−	2.04089e8i	0.824543	−	0.516098i
$735$		0			0
$736$	6.46374e7	+	2.32501e7i	0.162125	+	0.0583164i
$737$	−5.18533e8			−1.29531
$738$		0			0
$739$	2.10164e8			0.520744			0.260372	−	0.965508i	$-0.416155\pi$
$739$	2.10164e8			0.520744			0.260372	+	0.965508i	$0.416155\pi$
$740$	3.17401e8	−	6.53272e8i	0.783274	−	1.61213i
$741$		0			0
$742$	−7.17766e7	−	1.14674e8i	−0.175700	−	0.280707i
$743$			5.71643e8i			1.39367i	0.717234	+	0.696833i	$0.245408\pi$
$743$			5.71643e8i			1.39367i	−0.717234	+	0.696833i	$0.754592\pi$
$744$		0			0
$745$	3.29527e8			0.796933
$746$	3.45448e8	−	2.16223e8i	0.832082	−	0.520817i
$747$		0			0
$748$	−2.20507e8	+	4.53844e8i	−0.526886	+	1.08443i
$749$			4.35561e8i			1.03658i
$750$		0			0
$751$		−	2.96917e8i		−	0.700996i	−0.936564	−	0.350498i	$-0.886012\pi$
$751$		−	2.96917e8i		−	0.700996i	0.936564	−	0.350498i	$-0.113988\pi$
$752$	−2.70576e8	+	2.12717e8i	−0.636262	+	0.500205i
$753$		0			0
$754$	1.51798e8	+	2.42519e8i	0.354121	+	0.565760i
$755$	1.15014e9			2.67245
$756$		0			0
$757$			5.06152e8i			1.16679i	0.812188	+	0.583396i	$0.198276\pi$
$757$			5.06152e8i			1.16679i	−0.812188	+	0.583396i	$0.801724\pi$
$758$	−1.70374e8	−	2.72198e8i	−0.391197	−	0.624995i
$759$		0			0
$760$	1.10945e8	+	1.03305e9i	0.252737	+	2.35332i
$761$	−3.88935e8			−0.882518			−0.441259	−	0.897380i	$-0.645468\pi$
$761$	−3.88935e8			−0.882518			−0.441259	+	0.897380i	$0.645468\pi$
$762$		0			0
$763$	−3.41972e8			−0.769869
$764$	5.18923e8	+	2.52126e8i	1.16365	+	0.565377i
$765$		0			0
$766$	−1.81642e8	+	1.13693e8i	−0.404138	+	0.252958i
$767$			2.99104e8i			0.662881i
$768$		0			0
$769$	3.96129e7			0.0871079			0.0435540	−	0.999051i	$-0.486132\pi$
$769$	3.96129e7			0.0871079			0.0435540	+	0.999051i	$0.486132\pi$
$770$	4.16303e8	+	6.65106e8i	0.911879	+	1.45686i
$771$		0			0
$772$	−2.24751e7	+	4.62580e7i	−0.0488483	+	0.100539i
$773$			5.41418e8i			1.17218i	0.810246	+	0.586090i	$0.199334\pi$
$773$			5.41418e8i			1.17218i	−0.810246	+	0.586090i	$0.800666\pi$
$774$		0			0
$775$			3.68699e7i			0.0792077i
$776$	3.99003e8	−	4.28511e7i	0.853867	−	0.0917016i
$777$		0			0
$778$	−3.94952e8	+	2.47208e8i	−0.838698	+	0.524958i
$779$	5.75795e8			1.21802
$780$		0			0
$781$		−	4.18384e8i		−	0.878258i
$782$	−4.95505e7	+	3.10146e7i	−0.103616	+	0.0648554i
$783$		0			0
$784$	−1.85760e8	−	2.36287e8i	−0.385482	−	0.490333i
$785$	9.44019e8			1.95151
$786$		0			0
$787$	2.10149e8			0.431126			0.215563	−	0.976490i	$-0.430841\pi$
$787$	2.10149e8			0.431126			0.215563	+	0.976490i	$0.430841\pi$
$788$	6.39750e7	+	3.10832e7i	0.130747	+	0.0635252i
$789$		0			0
$790$	3.88277e8	+	6.20330e8i	0.787517	+	1.25818i
$791$		−	3.38748e8i		−	0.684459i
$792$		0			0
$793$	−5.68023e8			−1.13906
$794$	−1.30200e8	+	8.14948e7i	−0.260105	+	0.162805i
$795$		0			0
$796$	−5.81407e7	−	2.82485e7i	−0.115277	−	0.0560088i
$797$		−	6.44520e8i		−	1.27310i	−0.771237	−	0.636548i	$-0.780362\pi$
$797$		−	6.44520e8i		−	1.27310i	0.771237	−	0.636548i	$-0.219638\pi$
$798$		0			0
$799$		−	2.92896e8i		−	0.574213i
$800$	−2.97808e8	+	8.27936e8i	−0.581656	+	1.61706i
$801$		0			0
$802$	1.92471e7	+	3.07500e7i	0.0373114	+	0.0596104i
$803$	−8.05795e8			−1.55625
$804$		0			0
$805$			9.09034e7i			0.174258i
$806$	−2.06248e7	−	3.29511e7i	−0.0393898	−	0.0629311i
$807$		0			0
$808$	−8.58606e7	−	7.99480e8i	−0.162765	−	1.51556i
$809$	4.12527e8			0.779125			0.389562	−	0.921000i	$-0.372626\pi$
$809$	4.12527e8			0.779125			0.389562	+	0.921000i	$0.372626\pi$
$810$		0			0
$811$	1.60499e8			0.300891			0.150446	−	0.988618i	$-0.451929\pi$
$811$	1.60499e8			0.300891			0.150446	+	0.988618i	$0.451929\pi$
$812$	5.94713e7	−	1.22403e8i	0.111081	−	0.228625i
$813$		0			0
$814$	8.44551e8	−	5.28621e8i	1.56586	−	0.980103i
$815$		−	9.27516e8i		−	1.71336i
$816$		0			0
$817$	−1.04999e9			−1.92539
$818$	−4.33311e8	−	6.92278e8i	−0.791661	−	1.26480i
$819$		0			0
$820$	6.93797e8	+	3.37091e8i	1.25832	+	0.611372i
$821$		−	3.60585e8i		−	0.651596i	−0.945439	−	0.325798i	$-0.894367\pi$
$821$		−	3.60585e8i		−	0.651596i	0.945439	−	0.325798i	$-0.105633\pi$
$822$		0			0
$823$		−	6.90554e8i		−	1.23879i	−0.785079	−	0.619396i	$-0.787378\pi$
$823$		−	6.90554e8i		−	1.23879i	0.785079	−	0.619396i	$-0.212622\pi$
$824$	−4.36026e6	−	4.05999e7i	−0.00779346	−	0.0725678i
$825$		0			0
$826$	1.20592e8	−	7.54810e7i	0.213983	−	0.133936i
$827$	1.02908e9			1.81941			0.909706	−	0.415252i	$-0.136307\pi$
$827$	1.02908e9			1.81941			0.909706	+	0.415252i	$0.136307\pi$
$828$		0			0
$829$		−	3.71431e8i		−	0.651950i	−0.945378	−	0.325975i	$-0.894307\pi$
$829$		−	3.71431e8i		−	0.651950i	0.945378	−	0.325975i	$-0.105693\pi$
$830$	4.98879e8	−	3.12259e8i	0.872492	−	0.546110i
$831$		0			0
$832$	−1.96986e8	−	9.06528e8i	−0.342031	−	1.57402i
$833$	2.55778e8			0.442515
$834$		0			0
$835$	1.25124e9			2.14922
$836$	−6.22878e8	+	1.28200e9i	−1.06607	+	2.19417i
$837$		0			0
$838$	5.80000e8	+	9.26636e8i	0.985589	+	1.57462i
$839$		−	1.45962e7i		−	0.0247145i	−0.999924	−	0.0123573i	$-0.996066\pi$
$839$		−	1.45962e7i		−	0.0247145i	0.999924	−	0.0123573i	$-0.00393354\pi$
$840$		0			0
$841$	4.92691e8			0.828298
$842$	2.56369e8	−	1.60467e8i	0.429467	−	0.268812i
$843$		0			0
$844$	4.25932e8	−	8.76647e8i	0.708455	−	1.45813i
$845$			1.58624e9i			2.62904i
$846$		0			0
$847$			7.03653e8i			1.15800i
$848$	2.58804e8	−	2.03462e8i	0.424408	−	0.333654i
$849$		0			0
$850$	−3.97264e8	−	6.34688e8i	−0.646878	−	1.03348i
$851$	1.15429e8			0.187295
$852$		0			0
$853$		−	7.71644e8i		−	1.24328i	−0.783302	−	0.621641i	$-0.786466\pi$
$853$		−	7.71644e8i		−	1.24328i	0.783302	−	0.621641i	$-0.213534\pi$
$854$	1.43345e8	+	2.29015e8i	0.230149	+	0.367697i
$855$		0			0
$856$	−1.05385e9	+	1.13179e8i	−1.68018	+	0.180444i
$857$	−7.73106e8			−1.22828			−0.614139	−	0.789198i	$-0.710496\pi$
$857$	−7.73106e8			−1.22828			−0.614139	+	0.789198i	$0.710496\pi$
$858$		0			0
$859$	−2.50724e8			−0.395563			−0.197782	−	0.980246i	$-0.563374\pi$
$859$	−2.50724e8			−0.395563			−0.197782	+	0.980246i	$0.563374\pi$
$860$	−1.26517e9	−	6.14703e8i	−1.98909	−	0.966429i
$861$		0			0
$862$	−2.59398e7	+	1.62362e7i	−0.0404990	+	0.0253492i
$863$		−	7.52441e8i		−	1.17068i	−0.810786	−	0.585342i	$-0.800960\pi$
$863$		−	7.52441e8i		−	1.17068i	0.810786	−	0.585342i	$-0.199040\pi$
$864$		0			0
$865$	3.44630e8			0.532481
$866$	−3.19017e8	−	5.09677e8i	−0.491202	−	0.784768i
$867$		0			0
$868$	−8.08036e6	+	1.66309e7i	−0.0123558	+	0.0254306i
$869$			1.00393e9i			1.52983i
$870$		0			0
$871$			8.11290e8i			1.22778i
$872$	−8.88598e7	−	8.27407e8i	−0.134016	−	1.24787i
$873$		0			0
$874$	−1.39968e8	+	8.76088e7i	−0.209650	+	0.131224i
$875$	−4.86819e8			−0.726680
$876$		0			0
$877$			6.37458e8i			0.945046i	0.881318	+	0.472523i	$0.156657\pi$
$877$			6.37458e8i			0.945046i	−0.881318	+	0.472523i	$0.843343\pi$
$878$	1.79610e8	−	1.12421e8i	0.265367	−	0.166098i
$879$		0			0
$880$	−1.50106e9	+	1.18008e9i	−2.20267	+	1.73166i
$881$	−1.02174e9			−1.49421			−0.747107	−	0.664704i	$-0.768558\pi$
$881$	−1.02174e9			−1.49421			−0.747107	+	0.664704i	$0.768558\pi$
$882$		0			0
$883$	2.63930e8			0.383360			0.191680	−	0.981457i	$-0.438606\pi$
$883$	2.63930e8			0.383360			0.191680	+	0.981457i	$0.438606\pi$
$884$	7.10079e8	+	3.45002e8i	1.02790	+	0.499419i
$885$		0			0
$886$	−3.67179e8	−	5.86622e8i	−0.527930	−	0.843446i
$887$		−	3.72432e8i		−	0.533674i	−0.963742	−	0.266837i	$-0.914022\pi$
$887$		−	3.72432e8i		−	0.533674i	0.963742	−	0.266837i	$-0.0859785\pi$
$888$		0			0
$889$	−1.05031e8			−0.149490
$890$	8.30134e8	−	5.19597e8i	1.17755	−	0.737050i
$891$		0			0
$892$	4.34653e8	+	2.11182e8i	0.612419	+	0.297552i
$893$		−	8.27360e8i		−	1.16182i
$894$		0			0
$895$			9.71627e8i			1.35529i
$896$	−3.15781e8	+	3.08189e8i	−0.438998	+	0.428444i
$897$		0			0
$898$	−1.26871e8	−	2.02696e8i	−0.175200	−	0.279908i
$899$	1.38767e7			0.0190989
$900$		0			0
$901$			2.80153e8i			0.383019i
$902$	5.61414e8	+	8.96942e8i	0.765003	+	1.22221i
$903$		0			0
$904$	8.19606e8	−	8.80220e7i	1.10943	−	0.119148i
$905$	−1.94051e9			−2.61801
$906$		0			0
$907$	−9.13146e8			−1.22382			−0.611911	−	0.790927i	$-0.709599\pi$
$907$	−9.13146e8			−1.22382			−0.611911	+	0.790927i	$0.709599\pi$
$908$	−5.40783e8	+	1.11303e9i	−0.722380	+	1.48679i
$909$		0			0
$910$	1.04062e9	−	6.51342e8i	1.38091	−	0.864341i
$911$			9.98295e8i			1.32039i	0.751092	+	0.660197i	$0.229527\pi$
$911$			9.98295e8i			1.32039i	−0.751092	+	0.660197i	$0.770473\pi$
$912$		0			0
$913$	8.07377e8			1.06087
$914$	−3.04463e8	−	4.86425e8i	−0.398746	−	0.637056i
$915$		0			0
$916$	−5.96010e8	−	2.89580e8i	−0.775473	−	0.376775i
$917$			3.48926e8i			0.452507i
$918$		0			0
$919$		−	2.77108e8i		−	0.357029i	−0.983937	−	0.178514i	$-0.942871\pi$
$919$		−	2.77108e8i		−	0.357029i	0.983937	−	0.178514i	$-0.0571291\pi$
$920$	−2.19942e8	+	2.36208e7i	−0.282452	+	0.0303341i
$921$		0			0
$922$	−9.80422e8	+	6.13666e8i	−1.25089	+	0.782959i
$923$	−6.54598e8			−0.832472
$924$		0			0
$925$			1.47852e9i			1.86811i
$926$	5.47226e7	−	3.42519e7i	0.0689181	−	0.0431372i
$927$		0			0
$928$	3.11610e8	+	1.12086e8i	0.389912	+	0.140251i
$929$	8.71196e8			1.08660			0.543299	−	0.839539i	$-0.317175\pi$
$929$	8.71196e8			1.08660			0.543299	+	0.839539i	$0.317175\pi$
$930$		0			0
$931$	7.22511e8			0.895356
$932$	−2.92463e8	+	6.01943e8i	−0.361262	+	0.743546i
$933$		0			0
$934$	−3.55900e8	−	5.68603e8i	−0.436805	−	0.697861i
$935$		−	1.62488e9i		−	1.98786i
$936$		0			0
$937$	1.53726e7			0.0186865			0.00934324	−	0.999956i	$-0.497026\pi$
$937$	1.53726e7			0.0186865			0.00934324	+	0.999956i	$0.497026\pi$
$938$	3.27094e8	−	2.04735e8i	0.396337	−	0.248075i
$939$		0			0
$940$	4.84366e8	−	9.96917e8i	0.583164	−	1.20026i
$941$			1.32198e9i			1.58656i	0.608856	+	0.793281i	$0.291629\pi$
$941$			1.32198e9i			1.58656i	−0.608856	+	0.793281i	$0.708371\pi$
$942$		0			0
$943$			1.22590e8i			0.146190i
$944$	2.13963e8	+	2.72161e8i	0.254344	+	0.323527i
$945$		0			0
$946$	−1.02377e9	−	1.63562e9i	−1.20928	−	1.93201i
$947$	5.85382e8			0.689270			0.344635	−	0.938737i	$-0.388003\pi$
$947$	5.85382e8			0.689270			0.344635	+	0.938737i	$0.388003\pi$
$948$		0			0
$949$			1.26074e9i			1.47512i
$950$	−1.12217e9	−	1.79284e9i	−1.30885	−	2.09108i
$951$		0			0
$952$	−4.00964e7	−	3.73352e8i	−0.0464723	−	0.432721i
$953$	−3.94470e8			−0.455759			−0.227880	−	0.973689i	$-0.573179\pi$
$953$	−3.94470e8			−0.455759			−0.227880	+	0.973689i	$0.573179\pi$
$954$		0			0
$955$	−1.85788e9			−2.13308
$956$	1.48943e8	+	7.23661e7i	0.170469	+	0.0828250i
$957$		0			0
$958$	−6.16712e8	+	3.86012e8i	−0.701432	+	0.439041i
$959$		−	3.41785e8i		−	0.387523i
$960$		0			0
$961$	8.85618e8			0.997876
$962$	−8.27074e8	−	1.32137e9i	−0.929008	−	1.48423i
$963$		0			0
$964$	1.39320e8	−	2.86747e8i	0.155519	−	0.320087i
$965$		−	1.65616e8i		−	0.184297i
$966$		0			0
$967$		−	8.33074e8i		−	0.921306i	−0.887580	−	0.460653i	$-0.847615\pi$
$967$		−	8.33074e8i		−	0.921306i	0.887580	−	0.460653i	$-0.152385\pi$
$968$	−1.70250e9	+	1.82841e8i	−1.87698	+	0.201580i
$969$		0			0
$970$	−1.09541e9	+	6.85637e8i	−1.20022	+	0.751240i
$971$	1.01281e9			1.10630			0.553148	−	0.833083i	$-0.313426\pi$
$971$	1.01281e9			1.10630			0.553148	+	0.833083i	$0.313426\pi$
$972$		0			0
$973$		−	6.19709e8i		−	0.672743i
$974$	−7.62206e8	+	4.77080e8i	−0.824889	+	0.516314i
$975$		0			0
$976$	−5.16857e8	+	4.06333e8i	−0.555931	+	0.437052i
$977$	7.78748e6			0.00835051			0.00417526	−	0.999991i	$-0.498671\pi$
$977$	7.78748e6			0.00835051			0.00417526	+	0.999991i	$0.498671\pi$
$978$		0			0
$979$	1.34347e9			1.43179
$980$	8.70581e8	+	4.22984e8i	0.924977	+	0.449413i
$981$		0			0
$982$	1.71717e8	+	2.74343e8i	0.181333	+	0.289707i
$983$		−	1.06247e9i		−	1.11856i	−0.828980	−	0.559278i	$-0.811079\pi$
$983$		−	1.06247e9i		−	1.11856i	0.828980	−	0.559278i	$-0.188921\pi$
$984$		0			0
$985$	−2.29047e8			−0.239671
$986$	−2.38877e8	+	1.49518e8i	−0.249197	+	0.155978i
$987$		0			0
$988$	2.00580e9	+	9.74547e8i	2.07978	+	1.01049i
$989$		−	2.23549e8i		−	0.231091i
$990$		0			0
$991$			3.44802e8i			0.354281i	0.984186	+	0.177141i	$0.0566848\pi$
$991$			3.44802e8i			0.354281i	−0.984186	+	0.177141i	$0.943315\pi$
$992$	−4.23384e7	−	1.52291e7i	−0.0433710	−	0.0156005i
$993$		0			0
$994$	1.65193e8	+	2.63920e8i	0.168202	+	0.268728i
$995$	2.08159e8			0.211313
$996$		0			0
$997$			1.24019e9i			1.25142i	0.780056	+	0.625709i	$0.215190\pi$
$997$			1.24019e9i			1.25142i	−0.780056	+	0.625709i	$0.784810\pi$
$998$	5.77938e8	+	9.23342e8i	0.581420	+	0.928904i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.b.d.19.10	yes	12
3.2	odd	2	inner	72.7.b.d.19.3	✓	12
4.3	odd	2		288.7.b.c.271.1		12
8.3	odd	2	inner	72.7.b.d.19.9	yes	12
8.5	even	2		288.7.b.c.271.12		12
12.11	even	2		288.7.b.c.271.11		12
24.5	odd	2		288.7.b.c.271.2		12
24.11	even	2	inner	72.7.b.d.19.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.b.d.19.3	✓	12	3.2	odd	2	inner
72.7.b.d.19.4	yes	12	24.11	even	2	inner
72.7.b.d.19.9	yes	12	8.3	odd	2	inner
72.7.b.d.19.10	yes	12	1.1	even	1	trivial
288.7.b.c.271.1		12	4.3	odd	2
288.7.b.c.271.2		12	24.5	odd	2
288.7.b.c.271.11		12	12.11	even	2
288.7.b.c.271.12		12	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	72.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(4.24448 + 6.78118i) q^{2} +(-27.9688 + 57.5651i) q^{4} -206.098i q^{5} +210.403i q^{7} +(-509.073 + 54.6722i) q^{8} +O(q^{10})\)	\(q+(4.24448 + 6.78118i) q^{2} +(-27.9688 + 57.5651i) q^{4} -206.098i q^{5} +210.403i q^{7} +(-509.073 + 54.6722i) q^{8} +(1397.59 - 874.779i) q^{10} +2261.83 q^{11} -3538.83i q^{13} +(-1426.78 + 893.050i) q^{14} +(-2531.49 - 3220.06i) q^{16} +3485.68 q^{17} +9846.20 q^{19} +(11864.1 + 5764.32i) q^{20} +(9600.28 + 15337.9i) q^{22} +2096.31i q^{23} -26851.4 q^{25} +(23997.4 - 15020.5i) q^{26} +(-12111.9 - 5884.72i) q^{28} +10106.1i q^{29} -1373.11i q^{31} +(11091.0 - 30834.0i) q^{32} +(14794.9 + 23637.0i) q^{34} +43363.6 q^{35} -55063.1i q^{37} +(41792.0 + 66768.9i) q^{38} +(11267.8 + 104919. i) q^{40} +58478.9 q^{41} -106639. q^{43} +(-63260.7 + 130203. i) q^{44} +(-14215.4 + 8897.73i) q^{46} -84028.3i q^{47} +73379.7 q^{49} +(-113970. - 182084. i) q^{50} +(203713. + 98976.9i) q^{52} +80372.5i q^{53} -466159. i q^{55} +(-11503.2 - 107110. i) q^{56} +(-68531.0 + 42894.9i) q^{58} -84520.5 q^{59} -160512. i q^{61} +(9311.30 - 5828.13i) q^{62} +(256166. - 55664.2i) q^{64} -729346. q^{65} -229254. q^{67} +(-97490.4 + 200654. i) q^{68} +(184056. + 294057. i) q^{70} -184976. i q^{71} -356258. q^{73} +(373393. - 233714. i) q^{74} +(-275387. + 566798. i) q^{76} +475895. i q^{77} +443857. i q^{79} +(-663648. + 521735. i) q^{80} +(248212. + 396556. i) q^{82} +356957. q^{83} -718392. i q^{85} +(-452628. - 723140. i) q^{86} +(-1.15144e6 + 123659. i) q^{88} +593976. q^{89} +744580. q^{91} +(-120674. - 58631.3i) q^{92} +(569811. - 356656. i) q^{94} -2.02928e6i q^{95} -783783. q^{97} +(311458. + 497601. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 156 q^{4}+O(q^{10}) \) 12 * q - 156 * q^4	\( 12 q - 156 q^{4} + 1416 q^{10} - 1464 q^{16} + 3936 q^{19} + 15888 q^{22} - 47796 q^{25} + 11256 q^{28} + 50016 q^{34} + 70896 q^{40} - 340704 q^{43} + 213696 q^{46} - 304644 q^{49} + 548016 q^{52} - 38616 q^{58} + 206544 q^{64} - 962112 q^{67} + 1074480 q^{70} - 1069560 q^{73} + 1064352 q^{76} - 694944 q^{82} - 3072672 q^{88} + 775008 q^{91} + 3752256 q^{94} - 86952 q^{97}+O(q^{100}) \) 12 * q - 156 * q^4 + 1416 * q^10 - 1464 * q^16 + 3936 * q^19 + 15888 * q^22 - 47796 * q^25 + 11256 * q^28 + 50016 * q^34 + 70896 * q^40 - 340704 * q^43 + 213696 * q^46 - 304644 * q^49 + 548016 * q^52 - 38616 * q^58 + 206544 * q^64 - 962112 * q^67 + 1074480 * q^70 - 1069560 * q^73 + 1064352 * q^76 - 694944 * q^82 - 3072672 * q^88 + 775008 * q^91 + 3752256 * q^94 - 86952 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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