LMFDB - Embedded newform 72.7.m.a.41.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("72.41");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	72.m (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.5638940206$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.10
Character	$\chi$	$=$	72.41
Dual form			72.7.m.a.65.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.83005 - 26.9379i) q^{3} +(86.3751 + 49.8687i) q^{5} +(-207.661 - 359.679i) q^{7} +(-722.302 - 98.5953i) q^{9} +O(q^{10})$	\(q+(1.83005 - 26.9379i) q^{3} +(86.3751 + 49.8687i) q^{5} +(-207.661 - 359.679i) q^{7} +(-722.302 - 98.5953i) q^{9} +(1641.05 - 947.463i) q^{11} +(-335.248 + 580.666i) q^{13} +(1501.43 - 2235.50i) q^{15} -594.749i q^{17} -9514.73 q^{19} +(-10069.0 + 4935.72i) q^{21} +(-13766.9 - 7948.35i) q^{23} +(-2838.72 - 4916.81i) q^{25} +(-3977.80 + 19276.9i) q^{27} +(-14337.7 + 8277.87i) q^{29} +(22971.5 - 39787.8i) q^{31} +(-22519.5 - 45940.5i) q^{33} -41423.1i q^{35} -20749.4 q^{37} +(15028.4 + 10093.5i) q^{39} +(-45300.1 - 26154.0i) q^{41} +(51531.5 + 89255.1i) q^{43} +(-57472.1 - 44536.4i) q^{45} +(-42344.5 + 24447.6i) q^{47} +(-27421.6 + 47495.5i) q^{49} +(-16021.3 - 1088.42i) q^{51} -152594. i q^{53} +188995. q^{55} +(-17412.4 + 256307. i) q^{57} +(297704. + 171879. i) q^{59} +(33078.1 + 57293.0i) q^{61} +(114531. + 280271. i) q^{63} +(-57914.1 + 33436.7i) q^{65} +(173996. - 301369. i) q^{67} +(-239306. + 356307. i) q^{69} -564987. i q^{71} +675795. q^{73} +(-137644. + 67471.3i) q^{75} +(-681565. - 393502. i) q^{77} +(239627. + 415047. i) q^{79} +(511999. + 142431. i) q^{81} +(520059. - 300256. i) q^{83} +(29659.4 - 51371.6i) q^{85} +(196750. + 401376. i) q^{87} +333280. i q^{89} +278471. q^{91} +(-1.02976e6 - 691617. i) q^{93} +(-821836. - 474487. i) q^{95} +(272344. + 471714. i) q^{97} +(-1.27875e6 + 522554. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 10 q^{3} + 74 q^{9}+O(q^{10}) $ 36 * q + 10 * q^3 + 74 * q^9	$ 36 q + 10 q^{3} + 74 q^{9} + 1350 q^{11} + 7912 q^{15} + 9540 q^{19} + 3828 q^{21} + 30888 q^{23} + 56250 q^{25} + 11392 q^{27} + 38556 q^{29} + 27720 q^{31} + 33514 q^{33} + 134068 q^{39} + 179226 q^{41} + 15930 q^{43} - 185620 q^{45} + 187596 q^{47} - 198774 q^{49} - 158098 q^{51} - 197064 q^{55} - 244990 q^{57} - 408618 q^{59} + 17136 q^{61} - 417048 q^{63} - 125712 q^{65} + 27090 q^{67} - 848504 q^{69} - 534060 q^{73} - 1405714 q^{75} + 48168 q^{77} + 172620 q^{79} + 349010 q^{81} + 1801980 q^{83} - 791568 q^{85} + 28500 q^{87} + 538560 q^{91} - 1116448 q^{93} + 1832652 q^{95} + 770706 q^{97} - 614260 q^{99}+O(q^{100}) $ 36 * q + 10 * q^3 + 74 * q^9 + 1350 * q^11 + 7912 * q^15 + 9540 * q^19 + 3828 * q^21 + 30888 * q^23 + 56250 * q^25 + 11392 * q^27 + 38556 * q^29 + 27720 * q^31 + 33514 * q^33 + 134068 * q^39 + 179226 * q^41 + 15930 * q^43 - 185620 * q^45 + 187596 * q^47 - 198774 * q^49 - 158098 * q^51 - 197064 * q^55 - 244990 * q^57 - 408618 * q^59 + 17136 * q^61 - 417048 * q^63 - 125712 * q^65 + 27090 * q^67 - 848504 * q^69 - 534060 * q^73 - 1405714 * q^75 + 48168 * q^77 + 172620 * q^79 + 349010 * q^81 + 1801980 * q^83 - 791568 * q^85 + 28500 * q^87 + 538560 * q^91 - 1116448 * q^93 + 1832652 * q^95 + 770706 * q^97 - 614260 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.83005	−	26.9379i	0.0677795	−	0.997700i
$3$	1.83005	−	26.9379i	0.0677795	−	0.997700i
$4$		0			0
$5$	86.3751	+	49.8687i	0.691001	+	0.398950i	0.803987	−	0.594647i	$-0.202708\pi$
$5$	86.3751	+	49.8687i	0.691001	+	0.398950i	−0.112986	+	0.993597i	$0.536041\pi$
$6$		0			0
$7$	−207.661	−	359.679i	−0.605425	−	1.04863i	−0.991984	−	0.126363i	$-0.959670\pi$
$7$	−207.661	−	359.679i	−0.605425	−	1.04863i	0.386559	−	0.922265i	$-0.373664\pi$
$8$		0			0
$9$	−722.302	−	98.5953i	−0.990812	−	0.135247i
$10$		0			0
$11$	1641.05	−	947.463i	1.23295	−	0.711843i	0.265305	−	0.964165i	$-0.414527\pi$
$11$	1641.05	−	947.463i	1.23295	−	0.711843i	0.967643	+	0.252321i	$0.0811940\pi$
$12$		0			0
$13$	−335.248	+	580.666i	−0.152593	+	0.264300i	−0.932180	−	0.361995i	$-0.882096\pi$
$13$	−335.248	+	580.666i	−0.152593	+	0.264300i	0.779587	+	0.626294i	$0.215429\pi$
$14$		0			0
$15$	1501.43	−	2235.50i	0.444868	−	0.662371i
$16$		0			0
$17$		−	594.749i		−	0.121056i	−0.998166	−	0.0605281i	$-0.980722\pi$
$17$		−	594.749i		−	0.121056i	0.998166	−	0.0605281i	$-0.0192785\pi$
$18$		0			0
$19$	−9514.73			−1.38719			−0.693594	−	0.720366i	$-0.743974\pi$
$19$	−9514.73			−1.38719			−0.693594	+	0.720366i	$0.743974\pi$
$20$		0			0
$21$	−10069.0	+	4935.72i	−1.08725	+	0.532957i
$22$		0			0
$23$	−13766.9	−	7948.35i	−1.13150	−	0.653271i	−0.187187	−	0.982324i	$-0.559937\pi$
$23$	−13766.9	−	7948.35i	−1.13150	−	0.653271i	−0.944311	+	0.329053i	$0.893271\pi$
$24$		0			0
$25$	−2838.72	−	4916.81i	−0.181678	−	0.314676i
$26$		0			0
$27$	−3977.80	+	19276.9i	−0.202093	+	0.979366i
$28$		0			0
$29$	−14337.7	+	8277.87i	−0.587876	+	0.339410i	−0.764257	−	0.644912i	$-0.776894\pi$
$29$	−14337.7	+	8277.87i	−0.587876	+	0.339410i	0.176381	+	0.984322i	$0.443561\pi$
$30$		0			0
$31$	22971.5	−	39787.8i	0.771088	−	1.33556i	−0.165879	−	0.986146i	$-0.553046\pi$
$31$	22971.5	−	39787.8i	0.771088	−	1.33556i	0.936967	−	0.349417i	$-0.113620\pi$
$32$		0			0
$33$	−22519.5	−	45940.5i	−0.626637	−	1.27836i
$34$		0			0
$35$		−	41423.1i		−	0.966137i
$36$		0			0
$37$	−20749.4			−0.409637			−0.204819	−	0.978800i	$-0.565660\pi$
$37$	−20749.4			−0.409637			−0.204819	+	0.978800i	$0.565660\pi$
$38$		0			0
$39$	15028.4	+	10093.5i	0.253349	+	0.170157i
$40$		0			0
$41$	−45300.1	−	26154.0i	−0.657275	−	0.379478i	0.133963	−	0.990986i	$-0.457230\pi$
$41$	−45300.1	−	26154.0i	−0.657275	−	0.379478i	−0.791238	+	0.611508i	$0.790563\pi$
$42$		0			0
$43$	51531.5	+	89255.1i	0.648138	+	1.12261i	0.983567	+	0.180542i	$0.0577851\pi$
$43$	51531.5	+	89255.1i	0.648138	+	1.12261i	−0.335430	+	0.942065i	$0.608882\pi$
$44$		0			0
$45$	−57472.1	−	44536.4i	−0.630695	−	0.488740i
$46$		0			0
$47$	−42344.5	+	24447.6i	−0.407853	+	0.235474i	−0.689867	−	0.723936i	$-0.742331\pi$
$47$	−42344.5	+	24447.6i	−0.407853	+	0.235474i	0.282014	+	0.959410i	$0.408998\pi$
$48$		0			0
$49$	−27421.6	+	47495.5i	−0.233079	+	0.403705i
$50$		0			0
$51$	−16021.3	−	1088.42i	−0.120778	−	0.00820514i
$52$		0			0
$53$		−	152594.i		−	1.02496i	−0.858698	−	0.512482i	$-0.828726\pi$
$53$		−	152594.i		−	1.02496i	0.858698	−	0.512482i	$-0.171274\pi$
$54$		0			0
$55$	188995.			1.13596
$56$		0			0
$57$	−17412.4	+	256307.i	−0.0940230	+	1.38400i
$58$		0			0
$59$	297704.	+	171879.i	1.44953	+	0.836888i	0.998453	−	0.0555960i	$-0.0177059\pi$
$59$	297704.	+	171879.i	1.44953	+	0.836888i	0.451079	+	0.892484i	$0.351039\pi$
$60$		0			0
$61$	33078.1	+	57293.0i	0.145731	+	0.252413i	0.929645	−	0.368456i	$-0.120113\pi$
$61$	33078.1	+	57293.0i	0.145731	+	0.252413i	−0.783915	+	0.620869i	$0.786780\pi$
$62$		0			0
$63$	114531.	+	280271.i	0.458038	+	1.12087i
$64$		0			0
$65$	−57914.1	+	33436.7i	−0.210884	+	0.121754i
$66$		0			0
$67$	173996.	−	301369.i	0.578514	−	1.00202i	−0.417136	−	0.908844i	$-0.636966\pi$
$67$	173996.	−	301369.i	0.578514	−	1.00202i	0.995650	−	0.0931713i	$-0.0297004\pi$
$68$		0			0
$69$	−239306.	+	356307.i	−0.728461	+	1.08462i
$70$		0			0
$71$		−	564987.i		−	1.57857i	−0.614029	−	0.789284i	$-0.710452\pi$
$71$		−	564987.i		−	1.57857i	0.614029	−	0.789284i	$-0.289548\pi$
$72$		0			0
$73$	675795.			1.73719			0.868594	−	0.495525i	$-0.165024\pi$
$73$	675795.			1.73719			0.868594	+	0.495525i	$0.165024\pi$
$74$		0			0
$75$	−137644.	+	67471.3i	−0.326267	+	0.159932i
$76$		0			0
$77$	−681565.	−	393502.i	−1.49292	−	0.861936i
$78$		0			0
$79$	239627.	+	415047.i	0.486021	+	0.841814i	0.999871	−	0.0160667i	$-0.00511442\pi$
$79$	239627.	+	415047.i	0.486021	+	0.841814i	−0.513850	+	0.857880i	$0.671781\pi$
$80$		0			0
$81$	511999.	+	142431.i	0.963416	+	0.268009i
$82$		0			0
$83$	520059.	−	300256.i	0.909534	−	0.525119i	0.0292525	−	0.999572i	$-0.490687\pi$
$83$	520059.	−	300256.i	0.909534	−	0.525119i	0.880281	+	0.474453i	$0.157354\pi$
$84$		0			0
$85$	29659.4	−	51371.6i	0.0482954	−	0.0836500i
$86$		0			0
$87$	196750.	+	401376.i	0.298784	+	0.609529i
$88$		0			0
$89$			333280.i			0.472759i	0.971661	+	0.236379i	$0.0759608\pi$
$89$			333280.i			0.472759i	−0.971661	+	0.236379i	$0.924039\pi$
$90$		0			0
$91$	278471.			0.369536
$92$		0			0
$93$	−1.02976e6	−	691617.i	−1.28023	−	0.859839i
$94$		0			0
$95$	−821836.	−	474487.i	−0.958549	−	0.553418i
$96$		0			0
$97$	272344.	+	471714.i	0.298403	+	0.516848i	0.975771	−	0.218796i	$-0.0702129\pi$
$97$	272344.	+	471714.i	0.298403	+	0.516848i	−0.677368	+	0.735644i	$0.736880\pi$
$98$		0			0
$99$	−1.27875e6	+	522554.i	−1.31789	+	0.538550i
$100$		0			0
$101$	−188900.	+	109062.i	−0.183345	+	0.105854i	−0.588863	−	0.808233i	$-0.700424\pi$
$101$	−188900.	+	109062.i	−0.183345	+	0.105854i	0.405519	+	0.914087i	$0.367091\pi$
$102$		0			0
$103$	−275093.	+	476475.i	−0.251749	+	0.436042i	−0.964007	−	0.265875i	$-0.914339\pi$
$103$	−275093.	+	476475.i	−0.251749	+	0.436042i	0.712259	+	0.701917i	$0.247672\pi$
$104$		0			0
$105$	−1.11585e6	−	75806.3i	−0.963915	−	0.0654843i
$106$		0			0
$107$		−	1.00684e6i		−	0.821879i	−0.911663	−	0.410939i	$-0.865201\pi$
$107$		−	1.00684e6i		−	0.821879i	0.911663	−	0.410939i	$-0.134799\pi$
$108$		0			0
$109$	1.53682e6			1.18670			0.593352	−	0.804943i	$-0.297804\pi$
$109$	1.53682e6			1.18670			0.593352	+	0.804943i	$0.297804\pi$
$110$		0			0
$111$	−37972.3	+	558944.i	−0.0277650	+	0.408695i
$112$		0			0
$113$	−1.47341e6	−	850672.i	−1.02114	−	0.589558i	−0.106709	−	0.994290i	$-0.534031\pi$
$113$	−1.47341e6	−	850672.i	−1.02114	−	0.589558i	−0.914435	+	0.404732i	$0.867365\pi$
$114$		0			0
$115$	−792748.	−	1.37308e6i	−0.521245	−	0.902822i
$116$		0			0
$117$	299401.	−	386362.i	0.186937	−	0.241233i
$118$		0			0
$119$	−213919.	+	123506.i	−0.126943	+	0.0732905i
$120$		0			0
$121$	909592.	−	1.57546e6i	0.513441	−	0.889306i
$122$		0			0
$123$	−787435.	+	1.17243e6i	−0.423155	+	0.630043i
$124$		0			0
$125$		−	2.12465e6i		−	1.08782i
$126$		0			0
$127$	−3.04921e6			−1.48859			−0.744296	−	0.667850i	$-0.767215\pi$
$127$	−3.04921e6			−1.48859			−0.744296	+	0.667850i	$0.767215\pi$
$128$		0			0
$129$	2.49865e6	−	1.22481e6i	1.16396	−	0.570557i
$130$		0			0
$131$	−1.02242e6	−	590292.i	−0.454793	−	0.262575i	0.255059	−	0.966925i	$-0.417905\pi$
$131$	−1.02242e6	−	590292.i	−0.454793	−	0.262575i	−0.709852	+	0.704351i	$0.751238\pi$
$132$		0			0
$133$	1.97584e6	+	3.42225e6i	0.839839	+	1.45464i
$134$		0			0
$135$	−1.30490e6	+	1.46667e6i	−0.530364	+	0.596118i
$136$		0			0
$137$	−252872.	+	145995.i	−0.0983418	+	0.0567777i	−0.548364	−	0.836240i	$-0.684749\pi$
$137$	−252872.	+	145995.i	−0.0983418	+	0.0567777i	0.450022	+	0.893017i	$0.351416\pi$
$138$		0			0
$139$	2.48488e6	−	4.30393e6i	0.925253	−	1.60259i	0.134099	−	0.990968i	$-0.457186\pi$
$139$	2.48488e6	−	4.30393e6i	0.925253	−	1.60259i	0.791154	−	0.611617i	$-0.209481\pi$
$140$		0			0
$141$	581075.	+	1.18541e6i	0.207288	+	0.422875i
$142$		0			0
$143$			1.27054e6i			0.434490i
$144$		0			0
$145$	−1.65123e6			−0.541630
$146$		0			0
$147$	1.22925e6	+	825599.i	0.386979	+	0.259906i
$148$		0			0
$149$	4.22477e6	+	2.43917e6i	1.27716	+	0.737367i	0.976325	−	0.216310i	$-0.0694021\pi$
$149$	4.22477e6	+	2.43917e6i	1.27716	+	0.737367i	0.300833	+	0.953677i	$0.402735\pi$
$150$		0			0
$151$	626266.	+	1.08472e6i	0.181898	+	0.315056i	0.942527	−	0.334131i	$-0.108443\pi$
$151$	626266.	+	1.08472e6i	0.181898	+	0.315056i	−0.760629	+	0.649187i	$0.775109\pi$
$152$		0			0
$153$	−58639.5	+	429589.i	−0.0163725	+	0.119944i
$154$		0			0
$155$	3.96833e6	−	2.29112e6i	1.06565	−	0.615251i
$156$		0			0
$157$	−1.63418e6	+	2.83048e6i	−0.422280	+	0.731410i	−0.996162	−	0.0875279i	$-0.972103\pi$
$157$	−1.63418e6	+	2.83048e6i	−0.422280	+	0.731410i	0.573882	+	0.818938i	$0.305437\pi$
$158$		0			0
$159$	−4.11055e6	−	279254.i	−1.02261	−	0.0694716i
$160$		0			0
$161$			6.60225e6i			1.58203i
$162$		0			0
$163$	−5.96607e6			−1.37761			−0.688803	−	0.724948i	$-0.741864\pi$
$163$	−5.96607e6			−1.37761			−0.688803	+	0.724948i	$0.741864\pi$
$164$		0			0
$165$	345870.	−	5.09113e6i	0.0769947	−	1.13335i
$166$		0			0
$167$	4.47983e6	+	2.58643e6i	0.961860	+	0.555330i	0.896745	−	0.442548i	$-0.145925\pi$
$167$	4.47983e6	+	2.58643e6i	0.961860	+	0.555330i	0.0651149	+	0.997878i	$0.479259\pi$
$168$		0			0
$169$	2.18862e6	+	3.79081e6i	0.453430	+	0.785365i
$170$		0			0
$171$	6.87250e6	+	938107.i	1.37444	+	0.187614i
$172$		0			0
$173$	−5.54989e6	+	3.20423e6i	−1.07188	+	0.618850i	−0.928694	−	0.370846i	$-0.879068\pi$
$173$	−5.54989e6	+	3.20423e6i	−1.07188	+	0.618850i	−0.143185	+	0.989696i	$0.545734\pi$
$174$		0			0
$175$	−1.17898e6	+	2.04206e6i	−0.219985	+	0.381026i
$176$		0			0
$177$	5.17488e6	−	7.70496e6i	0.933212	−	1.38948i
$178$		0			0
$179$			1.83866e6i			0.320585i	0.987070	+	0.160292i	$0.0512437\pi$
$179$			1.83866e6i			0.320585i	−0.987070	+	0.160292i	$0.948756\pi$
$180$		0			0
$181$	5.78967e6			0.976378			0.488189	−	0.872738i	$-0.337658\pi$
$181$	5.78967e6			0.976378			0.488189	+	0.872738i	$0.337658\pi$
$182$		0			0
$183$	1.60389e6	−	786207.i	0.261710	−	0.128287i
$184$		0			0
$185$	−1.79223e6	−	1.03474e6i	−0.283060	−	0.163425i
$186$		0			0
$187$	−563503.	−	976016.i	−0.0861731	−	0.149256i
$188$		0			0
$189$	7.75952e6	−	2.57232e6i	1.14934	−	0.381013i
$190$		0			0
$191$	5.06864e6	−	2.92638e6i	0.727430	−	0.419982i	−0.0900514	−	0.995937i	$-0.528703\pi$
$191$	5.06864e6	−	2.92638e6i	0.727430	−	0.419982i	0.817481	+	0.575955i	$0.195370\pi$
$192$		0			0
$193$	3.91069e6	−	6.77351e6i	0.543977	−	0.942197i	−0.454693	−	0.890648i	$-0.650251\pi$
$193$	3.91069e6	−	6.77351e6i	0.543977	−	0.942197i	0.998670	−	0.0515484i	$-0.0164156\pi$
$194$		0			0
$195$	794730.	+	1.62128e6i	0.107181	+	0.218652i
$196$		0			0
$197$		−	1.13162e6i		−	0.148014i	−0.997258	−	0.0740069i	$-0.976421\pi$
$197$		−	1.13162e6i		−	0.148014i	0.997258	−	0.0740069i	$-0.0235787\pi$
$198$		0			0
$199$	−1.44240e7			−1.83032			−0.915160	−	0.403090i	$-0.867936\pi$
$199$	−1.44240e7			−1.83032			−0.915160	+	0.403090i	$0.867936\pi$
$200$		0			0
$201$	−7.79983e6	−	5.23860e6i	−0.960500	−	0.645100i
$202$		0			0
$203$	5.95476e6	+	3.43798e6i	0.711829	+	0.410975i
$204$		0			0
$205$	−2.60853e6	−	4.51811e6i	−0.302785	−	0.524439i
$206$		0			0
$207$	9.16022e6	+	7.09847e6i	1.03275	+	0.800301i
$208$		0			0
$209$	−1.56142e7	+	9.01485e6i	−1.71033	+	0.987461i
$210$		0			0
$211$	142920.	−	247545.i	0.0152141	−	0.0263516i	−0.858318	−	0.513118i	$-0.828490\pi$
$211$	142920.	−	247545.i	0.0152141	−	0.0263516i	0.873532	+	0.486766i	$0.161824\pi$
$212$		0			0
$213$	−1.52196e7	−	1.03395e6i	−1.57494	−	0.106995i
$214$		0			0
$215$			1.02792e7i			1.03430i
$216$		0			0
$217$	−1.90811e7			−1.86734
$218$		0			0
$219$	1.23674e6	−	1.82045e7i	0.117746	−	1.73319i
$220$		0			0
$221$	345351.	+	199388.i	0.0319951	+	0.0184724i
$222$		0			0
$223$	−6.86168e6	−	1.18848e7i	−0.618751	−	1.07171i	−0.989714	−	0.143060i	$-0.954306\pi$
$223$	−6.86168e6	−	1.18848e7i	−0.618751	−	1.07171i	0.370963	−	0.928648i	$-0.379028\pi$
$224$		0			0
$225$	1.56564e6	+	3.83131e6i	0.137450	+	0.336356i
$226$		0			0
$227$	1.39089e7	−	8.03031e6i	1.18909	−	0.686523i	0.230992	−	0.972956i	$-0.425803\pi$
$227$	1.39089e7	−	8.03031e6i	1.18909	−	0.686523i	0.958100	+	0.286433i	$0.0924696\pi$
$228$		0			0
$229$	−2.67395e6	+	4.63142e6i	−0.222662	+	0.385663i	−0.955616	−	0.294616i	$-0.904808\pi$
$229$	−2.67395e6	+	4.63142e6i	−0.222662	+	0.385663i	0.732953	+	0.680279i	$0.238141\pi$
$230$		0			0
$231$	−1.18474e7	+	1.76398e7i	−0.961143	+	1.43106i
$232$		0			0
$233$		−	1.52125e6i		−	0.120263i	−0.998190	−	0.0601315i	$-0.980848\pi$
$233$		−	1.52125e6i		−	0.120263i	0.998190	−	0.0601315i	$-0.0191520\pi$
$234$		0			0
$235$	−4.87668e6			−0.375769
$236$		0			0
$237$	1.16190e7	−	5.69551e6i	0.872820	−	0.427846i
$238$		0			0
$239$	7.31852e6	+	4.22535e6i	0.536080	+	0.309506i	0.743489	−	0.668749i	$-0.233170\pi$
$239$	7.31852e6	+	4.22535e6i	0.536080	+	0.309506i	−0.207409	+	0.978254i	$0.566503\pi$
$240$		0			0
$241$	8.23037e6	+	1.42554e7i	0.587988	+	1.01842i	0.994496	+	0.104778i	$0.0334131\pi$
$241$	8.23037e6	+	1.42554e7i	0.587988	+	1.01842i	−0.406508	+	0.913647i	$0.633254\pi$
$242$		0			0
$243$	4.77378e6	−	1.35315e7i	0.332693	−	0.943035i
$244$		0			0
$245$	−4.73708e6	+	2.73496e6i	−0.322116	+	0.185974i
$246$		0			0
$247$	3.18979e6	−	5.52488e6i	0.211676	−	0.366633i
$248$		0			0
$249$	−7.13655e6	−	1.45588e7i	−0.462264	−	0.943034i
$250$		0			0
$251$		−	2.09175e7i		−	1.32278i	−0.750040	−	0.661392i	$-0.769966\pi$
$251$		−	2.09175e7i		−	1.32278i	0.750040	−	0.661392i	$-0.230034\pi$
$252$		0			0
$253$	−3.01231e7			−1.86011
$254$		0			0
$255$	−1.32956e6	−	892974.i	−0.0801842	−	0.0538540i
$256$		0			0
$257$	3.28454e6	+	1.89633e6i	0.193497	+	0.111716i	0.593619	−	0.804746i	$-0.297699\pi$
$257$	3.28454e6	+	1.89633e6i	0.193497	+	0.111716i	−0.400122	+	0.916462i	$0.631032\pi$
$258$		0			0
$259$	4.30883e6	+	7.46311e6i	0.248005	+	0.429557i
$260$		0			0
$261$	1.11723e7	−	4.56549e6i	0.628378	−	0.256783i
$262$		0			0
$263$	−2.09725e7	+	1.21085e7i	−1.15288	+	0.665614i	−0.949587	−	0.313505i	$-0.898497\pi$
$263$	−2.09725e7	+	1.21085e7i	−1.15288	+	0.665614i	−0.203290	+	0.979118i	$0.565164\pi$
$264$		0			0
$265$	7.60964e6	−	1.31803e7i	0.408909	−	0.708251i
$266$		0			0
$267$	8.97787e6	+	609919.i	0.471672	+	0.0320434i
$268$		0			0
$269$			6.42268e6i			0.329959i	0.986297	+	0.164979i	$0.0527557\pi$
$269$			6.42268e6i			0.329959i	−0.986297	+	0.164979i	$0.947244\pi$
$270$		0			0
$271$	1.79911e7			0.903960			0.451980	−	0.892028i	$-0.350718\pi$
$271$	1.79911e7			0.903960			0.451980	+	0.892028i	$0.350718\pi$
$272$		0			0
$273$	509616.	−	7.50144e6i	0.0250470	−	0.368686i
$274$		0			0
$275$	−9.31700e6	−	5.37917e6i	−0.448000	−	0.258653i
$276$		0			0
$277$	1.40065e7	+	2.42599e7i	0.659006	+	1.14143i	0.980873	+	0.194646i	$0.0623560\pi$
$277$	1.40065e7	+	2.42599e7i	0.659006	+	1.14143i	−0.321868	+	0.946785i	$0.604311\pi$
$278$		0			0
$279$	−2.05152e7	+	2.64739e7i	−0.944635	+	1.21900i
$280$		0			0
$281$	2.79637e7	−	1.61449e7i	1.26031	−	0.727638i	0.287172	−	0.957879i	$-0.407285\pi$
$281$	2.79637e7	−	1.61449e7i	1.26031	−	0.727638i	0.973134	+	0.230241i	$0.0739516\pi$
$282$		0			0
$283$	1.66288e7	−	2.88019e7i	0.733670	−	1.27075i	−0.221635	−	0.975130i	$-0.571139\pi$
$283$	1.66288e7	−	2.88019e7i	0.733670	−	1.27075i	0.955305	−	0.295623i	$-0.0955273\pi$
$284$		0			0
$285$	−1.42857e7	+	2.12702e7i	−0.617116	+	0.918834i
$286$		0			0
$287$			2.17246e7i			0.918982i
$288$		0			0
$289$	2.37838e7			0.985345
$290$		0			0
$291$	1.32054e7	−	6.47312e6i	0.535885	−	0.262685i
$292$		0			0
$293$	−1.77415e7	−	1.02431e7i	−0.705323	−	0.407218i	0.104004	−	0.994577i	$-0.466835\pi$
$293$	−1.77415e7	−	1.02431e7i	−0.705323	−	0.407218i	−0.809327	+	0.587359i	$0.800168\pi$
$294$		0			0
$295$	1.71428e7	+	2.96922e7i	0.667752	+	1.15658i
$296$		0			0
$297$	1.17363e7	+	3.54032e7i	0.447985	+	1.35137i
$298$		0			0
$299$	9.23068e6	−	5.32933e6i	0.345319	−	0.199370i
$300$		0			0
$301$	2.14021e7	−	3.70696e7i	0.784798	−	1.35931i
$302$		0			0
$303$	2.59219e6	+	5.28816e6i	0.0931836	+	0.190098i
$304$		0			0
$305$			6.59825e6i			0.232557i
$306$		0			0
$307$	−1.62714e7			−0.562353			−0.281176	−	0.959656i	$-0.590725\pi$
$307$	−1.62714e7			−0.562353			−0.281176	+	0.959656i	$0.590725\pi$
$308$		0			0
$309$	1.23318e7	+	8.28240e6i	0.417976	+	0.280725i
$310$		0			0
$311$	−3.16807e7	−	1.82909e7i	−1.05321	−	0.608069i	−0.129661	−	0.991558i	$-0.541389\pi$
$311$	−3.16807e7	−	1.82909e7i	−1.05321	−	0.608069i	−0.923545	+	0.383489i	$0.874722\pi$
$312$		0			0
$313$	2.24297e7	+	3.88493e7i	0.731459	+	1.26692i	0.956260	+	0.292519i	$0.0944935\pi$
$313$	2.24297e7	+	3.88493e7i	0.731459	+	1.26692i	−0.224801	+	0.974405i	$0.572173\pi$
$314$		0			0
$315$	−4.08412e6	+	2.99200e7i	−0.130667	+	0.957260i
$316$		0			0
$317$	4.39103e6	−	2.53516e6i	0.137844	−	0.0795844i	−0.429492	−	0.903071i	$-0.641307\pi$
$317$	4.39103e6	−	2.53516e6i	0.137844	−	0.0795844i	0.567336	+	0.823486i	$0.307974\pi$
$318$		0			0
$319$	−1.56860e7	+	2.71689e7i	−0.483213	+	0.836950i
$320$		0			0
$321$	−2.71221e7	−	1.84256e6i	−0.819989	−	0.0557066i
$322$		0			0
$323$			5.65888e6i			0.167928i
$324$		0			0
$325$	3.80670e6			0.110892
$326$		0			0
$327$	2.81245e6	−	4.13986e7i	0.0804342	−	1.18397i
$328$		0			0
$329$	1.75866e7	+	1.01536e7i	0.493848	+	0.285124i
$330$		0			0
$331$	1.82785e7	+	3.16593e7i	0.504031	+	0.873006i	0.999989	+	0.00466031i	$0.00148343\pi$
$331$	1.82785e7	+	3.16593e7i	0.504031	+	0.873006i	−0.495959	+	0.868346i	$0.665183\pi$
$332$		0			0
$333$	1.49873e7	+	2.04579e6i	0.405873	+	0.0554024i
$334$		0			0
$335$	3.00578e7	−	1.73539e7i	0.799507	−	0.461596i
$336$		0			0
$337$	1.06337e7	−	1.84181e7i	0.277839	−	0.481232i	−0.693008	−	0.720930i	$-0.743715\pi$
$337$	1.06337e7	−	1.84181e7i	0.277839	−	0.481232i	0.970848	+	0.239698i	$0.0770484\pi$
$338$		0			0
$339$	−2.56117e7	+	3.81337e7i	−0.657415	+	0.978836i
$340$		0			0
$341$		−	8.70585e7i		−	2.19557i
$342$		0			0
$343$	−2.60846e7			−0.646402
$344$		0			0
$345$	−3.84387e7	+	1.88422e7i	−0.936076	+	0.458853i
$346$		0			0
$347$	−4.12339e7	−	2.38064e7i	−0.986883	−	0.569777i	−0.0825418	−	0.996588i	$-0.526304\pi$
$347$	−4.12339e7	−	2.38064e7i	−0.986883	−	0.569777i	−0.904341	+	0.426811i	$0.859637\pi$
$348$		0			0
$349$	−2.81464e7	−	4.87510e7i	−0.662135	−	1.14685i	−0.980054	−	0.198733i	$-0.936317\pi$
$349$	−2.81464e7	−	4.87510e7i	−0.662135	−	1.14685i	0.317919	−	0.948118i	$-0.397016\pi$
$350$		0			0
$351$	−9.85988e6	−	8.77230e6i	−0.228008	−	0.202858i
$352$		0			0
$353$	1.59643e7	−	9.21697e6i	0.362932	−	0.209539i	−0.307434	−	0.951569i	$-0.599470\pi$
$353$	1.59643e7	−	9.21697e6i	0.362932	−	0.209539i	0.670366	+	0.742031i	$0.266137\pi$
$354$		0			0
$355$	2.81752e7	−	4.88008e7i	0.629769	−	1.09079i
$356$		0			0
$357$	2.93552e6	+	5.98855e6i	0.0645178	+	0.131619i
$358$		0			0
$359$		−	4.17453e7i		−	0.902245i	−0.892462	−	0.451122i	$-0.851024\pi$
$359$		−	4.17453e7i		−	0.902245i	0.892462	−	0.451122i	$-0.148976\pi$
$360$		0			0
$361$	4.34841e7			0.924292
$362$		0			0
$363$	−4.07750e7	−	2.73857e7i	−0.852460	−	0.572537i
$364$		0			0
$365$	5.83719e7	+	3.37010e7i	1.20040	+	0.693050i
$366$		0			0
$367$	1.25909e7	+	2.18082e7i	0.254718	+	0.441185i	0.964819	−	0.262915i	$-0.0846839\pi$
$367$	1.25909e7	+	2.18082e7i	0.254718	+	0.441185i	−0.710101	+	0.704100i	$0.751351\pi$
$368$		0			0
$369$	3.01417e7	+	2.33575e7i	0.599913	+	0.464886i
$370$		0			0
$371$	−5.48847e7	+	3.16877e7i	−1.07481	+	0.620539i
$372$		0			0
$373$	−1.29804e7	+	2.24827e7i	−0.250128	+	0.433234i	−0.963561	−	0.267489i	$-0.913806\pi$
$373$	−1.29804e7	+	2.24827e7i	−0.250128	+	0.433234i	0.713433	+	0.700723i	$0.247139\pi$
$374$		0			0
$375$	−5.72337e7	−	3.88821e6i	−1.08532	−	0.0737320i
$376$		0			0
$377$		−	1.11006e7i		−	0.207167i
$378$		0			0
$379$	5.80301e7			1.06595			0.532974	−	0.846132i	$-0.321074\pi$
$379$	5.80301e7			1.06595			0.532974	+	0.846132i	$0.321074\pi$
$380$		0			0
$381$	−5.58019e6	+	8.21392e7i	−0.100896	+	1.48517i
$382$		0			0
$383$	−7.29275e7	−	4.21047e7i	−1.29806	−	0.749435i	−0.317991	−	0.948094i	$-0.603008\pi$
$383$	−7.29275e7	−	4.21047e7i	−1.29806	−	0.749435i	−0.980069	+	0.198658i	$0.936342\pi$
$384$		0			0
$385$	−3.92469e7	−	6.79776e7i	−0.687738	−	1.19120i
$386$		0			0
$387$	−2.84211e7	−	6.95499e7i	−0.490353	−	1.19995i
$388$		0			0
$389$	−7.25057e7	+	4.18612e7i	−1.23175	+	0.711153i	−0.967395	−	0.253272i	$-0.918493\pi$
$389$	−7.25057e7	+	4.18612e7i	−1.23175	+	0.711153i	−0.264358	+	0.964425i	$0.585160\pi$
$390$		0			0
$391$	−4.72728e6	+	8.18788e6i	−0.0790826	+	0.136975i
$392$		0			0
$393$	−1.77723e7	+	2.64615e7i	−0.292797	+	0.435950i
$394$		0			0
$395$			4.77996e7i			0.775592i
$396$		0			0
$397$	−8.51334e7			−1.36059			−0.680297	−	0.732937i	$-0.738149\pi$
$397$	−8.51334e7			−1.36059			−0.680297	+	0.732937i	$0.738149\pi$
$398$		0			0
$399$	9.58041e7	−	4.69620e7i	1.50822	−	0.739313i
$400$		0			0
$401$	−5.13758e7	−	2.96618e7i	−0.796756	−	0.460007i	0.0455795	−	0.998961i	$-0.485487\pi$
$401$	−5.13758e7	−	2.96618e7i	−0.796756	−	0.460007i	−0.842336	+	0.538953i	$0.818820\pi$
$402$		0			0
$403$	1.54023e7	+	2.66775e7i	0.235326	+	0.407596i
$404$		0			0
$405$	3.71211e7	+	3.78352e7i	0.558799	+	0.569549i
$406$		0			0
$407$	−3.40508e7	+	1.96593e7i	−0.505062	+	0.291597i
$408$		0			0
$409$	−2.05055e7	+	3.55165e7i	−0.299709	+	0.519111i	−0.976069	−	0.217460i	$-0.930223\pi$
$409$	−2.05055e7	+	3.55165e7i	−0.299709	+	0.519111i	0.676360	+	0.736571i	$0.263556\pi$
$410$		0			0
$411$	3.47005e6	+	7.07901e6i	0.0499816	+	0.101964i
$412$		0			0
$413$		−	1.42770e8i		−	2.02669i
$414$		0			0
$415$	5.98936e7			0.837985
$416$		0			0
$417$	−1.11392e8	−	7.48138e7i	−1.53619	−	1.03175i
$418$		0			0
$419$	3.77563e7	+	2.17986e7i	0.513272	+	0.296338i	0.734178	−	0.678958i	$-0.237568\pi$
$419$	3.77563e7	+	2.17986e7i	0.513272	+	0.296338i	−0.220906	+	0.975295i	$0.570901\pi$
$420$		0			0
$421$	2.33594e7	+	4.04597e7i	0.313051	+	0.542221i	0.979021	−	0.203758i	$-0.0653155\pi$
$421$	2.33594e7	+	4.04597e7i	0.313051	+	0.542221i	−0.665970	+	0.745978i	$0.731982\pi$
$422$		0			0
$423$	3.29959e7	−	1.34836e7i	0.435952	−	0.178149i
$424$		0			0
$425$	−2.92427e6	+	1.68833e6i	−0.0380935	+	0.0219933i
$426$		0			0
$427$	1.37381e7	−	2.37950e7i	0.176458	−	0.305635i
$428$		0			0
$429$	3.42257e7	+	2.32515e6i	0.433491	+	0.0294496i
$430$		0			0
$431$			1.19205e8i			1.48889i	0.667685	+	0.744443i	$0.267285\pi$
$431$			1.19205e8i			1.48889i	−0.667685	+	0.744443i	$0.732715\pi$
$432$		0			0
$433$	1.04949e6			0.0129275			0.00646377	−	0.999979i	$-0.497943\pi$
$433$	1.04949e6			0.0129275			0.00646377	+	0.999979i	$0.497943\pi$
$434$		0			0
$435$	−3.02182e6	+	4.44806e7i	−0.0367114	+	0.540385i
$436$		0			0
$437$	1.30989e8	+	7.56264e7i	1.56960	+	0.906210i
$438$		0			0
$439$	2.53760e7	+	4.39526e7i	0.299937	+	0.519506i	0.976121	−	0.217226i	$-0.0697010\pi$
$439$	2.53760e7	+	4.39526e7i	0.299937	+	0.519506i	−0.676184	+	0.736733i	$0.736368\pi$
$440$		0			0
$441$	2.44895e7	−	3.16025e7i	0.285538	−	0.368473i
$442$		0			0
$443$	8.07260e7	−	4.66072e7i	0.928544	−	0.536095i	0.0421931	−	0.999109i	$-0.486566\pi$
$443$	8.07260e7	−	4.66072e7i	0.928544	−	0.536095i	0.886351	+	0.463014i	$0.153232\pi$
$444$		0			0
$445$	−1.66203e7	+	2.87871e7i	−0.188607	+	0.326677i
$446$		0			0
$447$	7.34378e7	−	1.09343e8i	0.822237	−	1.22424i
$448$		0			0
$449$			5.96004e7i			0.658431i	0.944255	+	0.329216i	$0.106784\pi$
$449$			5.96004e7i			0.658431i	−0.944255	+	0.329216i	$0.893216\pi$
$450$		0			0
$451$	−9.91198e7			−1.08051
$452$		0			0
$453$	3.03663e7	−	1.48852e7i	0.326661	−	0.160125i
$454$		0			0
$455$	2.40530e7	+	1.38870e7i	0.255350	+	0.147426i
$456$		0			0
$457$	−8.79814e7	−	1.52388e8i	−0.921812	−	1.59663i	−0.796610	−	0.604494i	$-0.793375\pi$
$457$	−8.79814e7	−	1.52388e8i	−0.921812	−	1.59663i	−0.125203	−	0.992131i	$-0.539958\pi$
$458$		0			0
$459$	1.14649e7	+	2.36579e6i	0.118558	+	0.0244646i
$460$		0			0
$461$	1.06549e8	−	6.15164e7i	1.08755	−	0.627896i	0.154626	−	0.987973i	$-0.450583\pi$
$461$	1.06549e8	−	6.15164e7i	1.08755	−	0.627896i	0.932923	+	0.360077i	$0.117250\pi$
$462$		0			0
$463$	8.76488e6	−	1.51812e7i	0.0883086	−	0.152955i	−0.818488	−	0.574524i	$-0.805187\pi$
$463$	8.76488e6	−	1.51812e7i	0.0883086	−	0.152955i	0.906796	+	0.421569i	$0.138521\pi$
$464$		0			0
$465$	−5.44556e7	−	1.11091e8i	−0.541607	−	1.10490i
$466$		0			0
$467$			1.37634e8i			1.35137i	0.737189	+	0.675687i	$0.236153\pi$
$467$			1.37634e8i			1.35137i	−0.737189	+	0.675687i	$0.763847\pi$
$468$		0			0
$469$	−1.44528e8			−1.40099
$470$		0			0
$471$	7.32565e7	+	4.92012e7i	0.701106	+	0.470883i
$472$		0			0
$473$	1.69132e8	+	9.76483e7i	1.59824	+	0.922744i
$474$		0			0
$475$	2.70097e7	+	4.67821e7i	0.252022	+	0.436515i
$476$		0			0
$477$	−1.50450e7	+	1.10219e8i	−0.138624	+	1.01555i
$478$		0			0
$479$	9.55663e7	−	5.51752e7i	0.869558	−	0.502039i	0.00235639	−	0.999997i	$-0.499250\pi$
$479$	9.55663e7	−	5.51752e7i	0.869558	−	0.502039i	0.867201	+	0.497958i	$0.165917\pi$
$480$		0			0
$481$	6.95618e6	−	1.20484e7i	0.0625080	−	0.108267i
$482$		0			0
$483$	1.77851e8	+	1.20824e7i	1.57839	+	0.107229i
$484$		0			0
$485$			5.43258e7i			0.476190i
$486$		0			0
$487$	1.64810e8			1.42691			0.713454	−	0.700702i	$-0.247130\pi$
$487$	1.64810e8			1.42691			0.713454	+	0.700702i	$0.247130\pi$
$488$		0			0
$489$	−1.09182e7	+	1.60713e8i	−0.0933736	+	1.37444i
$490$		0			0
$491$	−7.49352e7	−	4.32639e7i	−0.633055	−	0.365494i	0.148879	−	0.988855i	$-0.452433\pi$
$491$	−7.49352e7	−	4.32639e7i	−0.633055	−	0.365494i	−0.781934	+	0.623361i	$0.785767\pi$
$492$		0			0
$493$	4.92326e6	+	8.52734e6i	0.0410877	+	0.0711660i
$494$		0			0
$495$	−1.36511e8	−	1.86340e7i	−1.12552	−	0.153635i
$496$		0			0
$497$	−2.03214e8	+	1.17326e8i	−1.65533	+	0.955705i
$498$		0			0
$499$	−1.21159e8	+	2.09854e8i	−0.975113	+	1.68894i	−0.295550	+	0.955327i	$0.595503\pi$
$499$	−1.21159e8	+	2.09854e8i	−0.975113	+	1.68894i	−0.679563	+	0.733617i	$0.737831\pi$
$500$		0			0
$501$	7.78713e7	−	1.15944e8i	0.619247	−	0.922008i
$502$		0			0
$503$		−	8.54544e6i		−	0.0671476i	−0.999436	−	0.0335738i	$-0.989311\pi$
$503$		−	8.54544e6i		−	0.0671476i	0.999436	−	0.0335738i	$-0.0106889\pi$
$504$		0			0
$505$	−2.17550e7			−0.168922
$506$		0			0
$507$	1.06122e8	−	5.20196e7i	0.814292	−	0.399156i
$508$		0			0
$509$	−8.07522e7	−	4.66223e7i	−0.612352	−	0.353541i	0.161534	−	0.986867i	$-0.448356\pi$
$509$	−8.07522e7	−	4.66223e7i	−0.612352	−	0.353541i	−0.773885	+	0.633326i	$0.781689\pi$
$510$		0			0
$511$	−1.40336e8	−	2.43070e8i	−1.05174	−	1.82166i
$512$		0			0
$513$	3.78477e7	−	1.83414e8i	0.280341	−	1.35857i
$514$		0			0
$515$	−4.75224e7	+	2.74370e7i	−0.347917	+	0.200870i
$516$		0			0
$517$	−4.63264e7	+	8.02397e7i	−0.335241	+	0.580654i
$518$		0			0
$519$	7.61586e7	+	1.55366e8i	0.544775	+	1.11136i
$520$		0			0
$521$			1.51554e8i			1.07165i	0.844328	+	0.535827i	$0.180000\pi$
$521$			1.51554e8i			1.07165i	−0.844328	+	0.535827i	$0.820000\pi$
$522$		0			0
$523$	−6.92213e7			−0.483877			−0.241938	−	0.970292i	$-0.577783\pi$
$523$	−6.92213e7			−0.483877			−0.241938	+	0.970292i	$0.577783\pi$
$524$		0			0
$525$	5.28512e7	+	3.54964e7i	0.365239	+	0.245305i
$526$		0			0
$527$	−2.36638e7	−	1.36623e7i	−0.161678	−	0.0933450i
$528$		0			0
$529$	5.23346e7	+	9.06462e7i	0.353527	+	0.612326i
$530$		0			0
$531$	−1.98085e8	−	1.53501e8i	−1.32303	−	1.02524i
$532$		0			0
$533$	3.03735e7	−	1.75361e7i	0.200592	−	0.115812i
$534$		0			0
$535$	5.02096e7	−	8.69656e7i	0.327888	−	0.567919i
$536$		0			0
$537$	4.95297e7	+	3.36484e6i	0.319847	+	0.0217291i
$538$		0			0
$539$			1.03924e8i			0.663664i
$540$		0			0
$541$	−4.28051e7			−0.270336			−0.135168	−	0.990823i	$-0.543157\pi$
$541$	−4.28051e7			−0.270336			−0.135168	+	0.990823i	$0.543157\pi$
$542$		0			0
$543$	1.05954e7	−	1.55962e8i	0.0661785	−	0.974133i
$544$		0			0
$545$	1.32743e8	+	7.66390e7i	0.820014	+	0.473435i
$546$		0			0
$547$	−2.73793e7	−	4.74223e7i	−0.167286	−	0.289748i	0.770179	−	0.637828i	$-0.220167\pi$
$547$	−2.73793e7	−	4.74223e7i	−0.167286	−	0.289748i	−0.937465	+	0.348080i	$0.886834\pi$
$548$		0			0
$549$	−1.82436e7	−	4.46442e7i	−0.110254	−	0.269804i
$550$		0			0
$551$	1.36419e8	−	7.87617e7i	0.815494	−	0.470826i
$552$		0			0
$553$	9.95225e7	−	1.72378e8i	0.588499	−	1.01931i
$554$		0			0
$555$	−3.11537e7	+	4.63853e7i	−0.182234	+	0.271332i
$556$		0			0
$557$		−	2.76165e8i		−	1.59809i	−0.601268	−	0.799047i	$-0.705338\pi$
$557$		−	2.76165e8i		−	1.59809i	0.601268	−	0.799047i	$-0.294662\pi$
$558$		0			0
$559$	−6.91032e7			−0.395606
$560$		0			0
$561$	−2.73231e7	+	1.33934e7i	−0.154754	+	0.0758584i
$562$		0			0
$563$	1.09201e7	+	6.30471e6i	0.0611929	+	0.0353297i	0.530284	−	0.847820i	$-0.322085\pi$
$563$	1.09201e7	+	6.30471e6i	0.0611929	+	0.0353297i	−0.469091	+	0.883150i	$0.655419\pi$
$564$		0			0
$565$	−8.48438e7	−	1.46954e8i	−0.470408	−	0.814771i
$566$		0			0
$567$	−5.50926e7	−	2.13733e8i	−0.302235	−	1.17252i
$568$		0			0
$569$	−1.91111e8	+	1.10338e8i	−1.03741	+	0.598948i	−0.919098	−	0.394029i	$-0.871081\pi$
$569$	−1.91111e8	+	1.10338e8i	−1.03741	+	0.598948i	−0.118310	+	0.992977i	$0.537748\pi$
$570$		0			0
$571$	−1.14680e8	+	1.98631e8i	−0.615996	+	1.06694i	0.374213	+	0.927343i	$0.377913\pi$
$571$	−1.14680e8	+	1.98631e8i	−0.615996	+	1.06694i	−0.990209	+	0.139593i	$0.955421\pi$
$572$		0			0
$573$	−6.95547e7	−	1.41894e8i	−0.369711	−	0.754223i
$574$		0			0
$575$			9.02527e7i			0.474741i
$576$		0			0
$577$	2.80584e8			1.46061			0.730307	−	0.683119i	$-0.239377\pi$
$577$	2.80584e8			1.46061			0.730307	+	0.683119i	$0.239377\pi$
$578$		0			0
$579$	−1.75307e8	−	1.17742e8i	−0.903159	−	0.606588i
$580$		0			0
$581$	−2.15992e8	−	1.24703e8i	−1.10131	−	0.635841i
$582$		0			0
$583$	−1.44577e8	−	2.50414e8i	−0.729614	−	1.26373i
$584$		0			0
$585$	4.51282e7	−	1.84414e7i	0.225414	−	0.0921139i
$586$		0			0
$587$	−8.27003e7	+	4.77470e7i	−0.408877	+	0.236065i	−0.690307	−	0.723517i	$-0.742525\pi$
$587$	−8.27003e7	+	4.77470e7i	−0.408877	+	0.236065i	0.281430	+	0.959582i	$0.409191\pi$
$588$		0			0
$589$	−2.18567e8	+	3.78570e8i	−1.06964	+	1.85268i
$590$		0			0
$591$	−3.04835e7	−	2.07092e6i	−0.147673	−	0.0100323i
$592$		0			0
$593$		−	1.21878e8i		−	0.584471i	−0.956346	−	0.292235i	$-0.905601\pi$
$593$		−	1.21878e8i		−	0.584471i	0.956346	−	0.292235i	$-0.0943991\pi$
$594$		0			0
$595$	−2.46364e7			−0.116957
$596$		0			0
$597$	−2.63966e7	+	3.88553e8i	−0.124058	+	1.82611i
$598$		0			0
$599$	3.69933e6	+	2.13581e6i	0.0172124	+	0.00993760i	0.508582	−	0.861014i	$-0.330170\pi$
$599$	3.69933e6	+	2.13581e6i	0.0172124	+	0.00993760i	−0.491369	+	0.870951i	$0.663503\pi$
$600$		0			0
$601$	−1.51180e7	−	2.61851e7i	−0.0696418	−	0.120623i	0.829102	−	0.559098i	$-0.188852\pi$
$601$	−1.51180e7	−	2.61851e7i	−0.0696418	−	0.120623i	−0.898744	+	0.438475i	$0.855519\pi$
$602$		0			0
$603$	−1.55391e8	+	2.00524e8i	−0.708718	+	0.914566i
$604$		0			0
$605$	1.57132e8	−	9.07204e7i	0.709577	−	0.409674i
$606$		0			0
$607$	−1.30421e8	+	2.25896e8i	−0.583153	+	1.01005i	0.411950	+	0.911206i	$0.364848\pi$
$607$	−1.30421e8	+	2.25896e8i	−0.583153	+	1.01005i	−0.995103	+	0.0988436i	$0.968486\pi$
$608$		0			0
$609$	1.03509e8	−	1.54117e8i	0.458277	−	0.682337i
$610$		0			0
$611$		−	3.27840e7i		−	0.143727i
$612$		0			0
$613$	2.88624e8			1.25300			0.626500	−	0.779422i	$-0.284487\pi$
$613$	2.88624e8			1.25300			0.626500	+	0.779422i	$0.284487\pi$
$614$		0			0
$615$	−1.26482e8	+	6.20000e7i	−0.543756	+	0.266543i
$616$		0			0
$617$	1.35310e8	+	7.81215e7i	0.576070	+	0.332594i	0.759570	−	0.650425i	$-0.225409\pi$
$617$	1.35310e8	+	7.81215e7i	0.576070	+	0.332594i	−0.183500	+	0.983020i	$0.558743\pi$
$618$		0			0
$619$	−4.48054e6	−	7.76052e6i	−0.0188911	−	0.0327204i	0.856425	−	0.516271i	$-0.172680\pi$
$619$	−4.48054e6	−	7.76052e6i	−0.0188911	−	0.0327204i	−0.875316	+	0.483551i	$0.839347\pi$
$620$		0			0
$621$	2.07981e8	−	2.33767e8i	0.868460	−	0.976130i
$622$		0			0
$623$	1.19874e8	−	6.92093e7i	0.495748	−	0.286220i
$624$		0			0
$625$	6.15985e7	−	1.06692e8i	0.252308	−	0.437010i
$626$		0			0
$627$	2.14267e8	+	4.37111e8i	0.869264	+	1.77333i
$628$		0			0
$629$			1.23407e7i			0.0495892i
$630$		0			0
$631$	1.20098e8			0.478021			0.239010	−	0.971017i	$-0.423177\pi$
$631$	1.20098e8			0.478021			0.239010	+	0.971017i	$0.423177\pi$
$632$		0			0
$633$	−6.40679e6	−	4.30299e6i	−0.0252598	−	0.0169652i
$634$		0			0
$635$	−2.63376e8	−	1.52060e8i	−1.02862	−	0.593873i
$636$		0			0
$637$	−1.83860e7	−	3.18455e7i	−0.0711328	−	0.123206i
$638$		0			0
$639$	−5.57050e7	+	4.08091e8i	−0.213497	+	1.56406i
$640$		0			0
$641$	−1.12042e8	+	6.46875e7i	−0.425409	+	0.245610i	−0.697389	−	0.716693i	$-0.745655\pi$
$641$	−1.12042e8	+	6.46875e7i	−0.425409	+	0.245610i	0.271980	+	0.962303i	$0.412322\pi$
$642$		0			0
$643$	1.17521e8	−	2.03552e8i	0.442060	−	0.765670i	−0.555782	−	0.831328i	$-0.687581\pi$
$643$	1.17521e8	−	2.03552e8i	0.442060	−	0.765670i	0.997842	+	0.0656577i	$0.0209145\pi$
$644$		0			0
$645$	2.76901e8	+	1.88115e7i	1.03192	+	0.0701042i
$646$		0			0
$647$		−	3.71853e8i		−	1.37296i	−0.727148	−	0.686481i	$-0.759154\pi$
$647$		−	3.71853e8i		−	1.37296i	0.727148	−	0.686481i	$-0.240846\pi$
$648$		0			0
$649$	6.51397e8			2.38293
$650$		0			0
$651$	−3.49193e7	+	5.14005e8i	−0.126568	+	1.86305i
$652$		0			0
$653$	−1.70500e8	−	9.84380e7i	−0.612328	−	0.353528i	0.161548	−	0.986865i	$-0.448351\pi$
$653$	−1.70500e8	−	9.84380e7i	−0.612328	−	0.353528i	−0.773876	+	0.633337i	$0.781685\pi$
$654$		0			0
$655$	−5.88742e7	−	1.01973e8i	−0.209508	−	0.362879i
$656$		0			0
$657$	−4.88128e8	−	6.66303e7i	−1.72123	−	0.234950i
$658$		0			0
$659$	1.36750e8	−	7.89529e7i	0.477829	−	0.275875i	−0.241682	−	0.970355i	$-0.577699\pi$
$659$	1.36750e8	−	7.89529e7i	0.477829	−	0.275875i	0.719511	+	0.694481i	$0.244366\pi$
$660$		0			0
$661$	−4.50661e7	+	7.80568e7i	−0.156044	+	0.270275i	−0.933439	−	0.358737i	$-0.883207\pi$
$661$	−4.50661e7	+	7.80568e7i	−0.156044	+	0.270275i	0.777395	+	0.629013i	$0.216541\pi$
$662$		0			0
$663$	6.00311e6	−	8.93814e6i	0.0205985	−	0.0306695i
$664$		0			0
$665$			3.94130e8i			1.34021i
$666$		0			0
$667$	2.63182e8			0.886907
$668$		0			0
$669$	−3.32708e8	+	1.63090e8i	−1.11118	+	0.544688i
$670$		0			0
$671$	1.08566e8	+	6.26806e7i	0.359357	+	0.207475i
$672$		0			0
$673$	1.51945e8	+	2.63177e8i	0.498473	+	0.863381i	0.999998	−	0.00176204i	$-0.000560877\pi$
$673$	1.51945e8	+	2.63177e8i	0.498473	+	0.863381i	−0.501525	+	0.865143i	$0.667228\pi$
$674$		0			0
$675$	1.06073e8	−	3.51636e7i	0.344899	−	0.114336i
$676$		0			0
$677$	−1.56583e7	+	9.04033e6i	−0.0504637	+	0.0291352i	−0.525020	−	0.851090i	$-0.675942\pi$
$677$	−1.56583e7	+	9.04033e6i	−0.0504637	+	0.0291352i	0.474556	+	0.880225i	$0.342609\pi$
$678$		0			0
$679$	1.13110e8	−	1.95913e8i	0.361321	−	0.625826i
$680$		0			0
$681$	−1.90866e8	−	3.89373e8i	−0.604348	−	1.23289i
$682$		0			0
$683$		−	2.51133e8i		−	0.788209i	−0.919066	−	0.394105i	$-0.871055\pi$
$683$		−	2.51133e8i		−	0.788209i	0.919066	−	0.394105i	$-0.128945\pi$
$684$		0			0
$685$	−2.91224e7			−0.0906058
$686$		0			0
$687$	1.19867e8	+	8.05064e7i	0.369684	+	0.248290i
$688$		0			0
$689$	8.86059e7	+	5.11567e7i	0.270898	+	0.156403i
$690$		0			0
$691$	−8.37607e7	−	1.45078e8i	−0.253867	−	0.439710i	0.710720	−	0.703475i	$-0.248369\pi$
$691$	−8.37607e7	−	1.45078e8i	−0.253867	−	0.439710i	−0.964587	+	0.263764i	$0.915036\pi$
$692$		0			0
$693$	4.53499e8	+	3.51426e8i	1.36262	+	1.05593i
$694$		0			0
$695$	4.29263e8	−	2.47835e8i	1.27870	−	0.738259i
$696$		0			0
$697$	−1.55551e7	+	2.69422e7i	−0.0459382	+	0.0795673i
$698$		0			0
$699$	−4.09792e7	−	2.78396e6i	−0.119986	−	0.00815137i
$700$		0			0
$701$		−	4.19959e8i		−	1.21914i	−0.792733	−	0.609569i	$-0.791343\pi$
$701$		−	4.19959e8i		−	1.21914i	0.792733	−	0.609569i	$-0.208657\pi$
$702$		0			0
$703$	1.97424e8			0.568244
$704$		0			0
$705$	−8.92456e6	+	1.31368e8i	−0.0254694	+	0.374905i
$706$		0			0
$707$	7.84543e7	+	4.52956e7i	0.222003	+	0.128173i
$708$		0			0
$709$	2.92143e8	+	5.06006e8i	0.819702	+	1.41977i	0.905902	+	0.423488i	$0.139194\pi$
$709$	2.92143e8	+	5.06006e8i	0.819702	+	1.41977i	−0.0861995	+	0.996278i	$0.527472\pi$
$710$		0			0
$711$	−1.32162e8	−	3.23415e8i	−0.367703	−	0.899812i
$712$		0			0
$713$	−6.32494e8	+	3.65171e8i	−1.74497	+	1.00746i
$714$		0			0
$715$	−6.33602e7	+	1.09743e8i	−0.173340	+	0.300233i
$716$		0			0
$717$	1.27215e8	−	1.89413e8i	0.345129	−	0.513869i
$718$		0			0
$719$			1.23867e8i			0.333249i	0.986020	+	0.166625i	$0.0532868\pi$
$719$			1.23867e8i			0.333249i	−0.986020	+	0.166625i	$0.946713\pi$
$720$		0			0
$721$	2.28504e8			0.609660
$722$		0			0
$723$	3.99073e8	−	1.95621e8i	1.05594	−	0.517607i
$724$		0			0
$725$	8.14015e7	+	4.69972e7i	0.213608	+	0.123327i
$726$		0			0
$727$	2.59463e8	+	4.49403e8i	0.675262	+	1.16959i	0.976392	+	0.216005i	$0.0693028\pi$
$727$	2.59463e8	+	4.49403e8i	0.675262	+	1.16959i	−0.301130	+	0.953583i	$0.597364\pi$
$728$		0			0
$729$	−3.55775e8	−	1.53359e8i	−0.918317	−	0.395846i
$730$		0			0
$731$	5.30844e7	−	3.06483e7i	0.135899	−	0.0784611i
$732$		0			0
$733$	1.52477e7	−	2.64097e7i	0.0387161	−	0.0670582i	−0.846018	−	0.533154i	$-0.821007\pi$
$733$	1.52477e7	−	2.64097e7i	0.0387161	−	0.0670582i	0.884734	+	0.466096i	$0.154340\pi$
$734$		0			0
$735$	6.50049e7	+	1.32612e8i	0.163713	+	0.333981i
$736$		0			0
$737$		−	6.59417e8i		−	1.64724i
$738$		0			0
$739$	−4.95085e7			−0.122672			−0.0613361	−	0.998117i	$-0.519536\pi$
$739$	−4.95085e7			−0.122672			−0.0613361	+	0.998117i	$0.519536\pi$
$740$		0			0
$741$	−1.42991e8	−	9.60371e7i	−0.351443	−	0.236039i
$742$		0			0
$743$	−3.72630e8	−	2.15138e8i	−0.908473	−	0.524507i	−0.0285333	−	0.999593i	$-0.509084\pi$
$743$	−3.72630e8	−	2.15138e8i	−0.908473	−	0.524507i	−0.879939	+	0.475086i	$0.842417\pi$
$744$		0			0
$745$	2.43277e8	+	4.21368e8i	0.588345	+	1.01904i
$746$		0			0
$747$	−4.05244e8	+	1.65600e8i	−0.972198	+	0.397283i
$748$		0			0
$749$	−3.62138e8	+	2.09081e8i	−0.861844	+	0.497586i
$750$		0			0
$751$	−1.53847e8	+	2.66471e8i	−0.363219	+	0.629114i	−0.988489	−	0.151295i	$-0.951656\pi$
$751$	−1.53847e8	+	2.66471e8i	−0.363219	+	0.629114i	0.625269	+	0.780409i	$0.284989\pi$
$752$		0			0
$753$	−5.63474e8	−	3.82800e7i	−1.31974	−	0.0896577i
$754$		0			0
$755$			1.24924e8i			0.290272i
$756$		0			0
$757$	−6.63191e8			−1.52880			−0.764400	−	0.644742i	$-0.776965\pi$
$757$	−6.63191e8			−1.52880			−0.764400	+	0.644742i	$0.776965\pi$
$758$		0			0
$759$	−5.51267e7	+	8.11453e8i	−0.126077	+	1.85583i
$760$		0			0
$761$	3.60784e7	+	2.08299e7i	0.0818641	+	0.0472642i	0.540373	−	0.841425i	$-0.318283\pi$
$761$	3.60784e7	+	2.08299e7i	0.0818641	+	0.0472642i	−0.458509	+	0.888690i	$0.651616\pi$
$762$		0			0
$763$	−3.19137e8	−	5.52761e8i	−0.718461	−	1.24441i
$764$		0			0
$765$	−2.64880e7	+	3.41815e7i	−0.0591650	+	0.0763496i
$766$		0			0
$767$	−1.99609e8	+	1.15244e8i	−0.442378	+	0.255407i
$768$		0			0
$769$	2.66593e8	−	4.61753e8i	0.586232	−	1.01538i	−0.408488	−	0.912764i	$-0.633944\pi$
$769$	2.66593e8	−	4.61753e8i	0.586232	−	1.01538i	0.994721	−	0.102621i	$-0.0327228\pi$
$770$		0			0
$771$	5.70940e7	−	8.50082e7i	0.124574	−	0.185480i
$772$		0			0
$773$		−	3.84433e8i		−	0.832304i	−0.909295	−	0.416152i	$-0.863378\pi$
$773$		−	3.84433e8i		−	0.832304i	0.909295	−	0.416152i	$-0.136622\pi$
$774$		0			0
$775$	−2.60839e8			−0.560360
$776$		0			0
$777$	2.08926e8	−	1.02413e8i	0.445379	−	0.218319i
$778$		0			0
$779$	4.31018e8	+	2.48848e8i	0.911764	+	0.526407i
$780$		0			0
$781$	−5.35304e8	−	9.27174e8i	−1.12369	−	1.94629i
$782$		0			0
$783$	−1.02539e8	−	3.09314e8i	−0.213601	−	0.644338i
$784$		0			0
$785$	−2.82305e8	+	1.62989e8i	−0.583591	+	0.336937i
$786$		0			0
$787$	3.48013e8	−	6.02776e8i	0.713956	−	1.23661i	−0.249405	−	0.968399i	$-0.580235\pi$
$787$	3.48013e8	−	6.02776e8i	0.713956	−	1.23661i	0.963361	−	0.268208i	$-0.0864315\pi$
$788$		0			0
$789$	2.87796e8	+	5.87114e8i	0.585942	+	1.19534i
$790$		0			0
$791$			7.06605e8i			1.42773i
$792$		0			0
$793$	−4.43575e7			−0.0889503
$794$		0			0
$795$	−3.41123e8	−	2.29108e8i	−0.678907	−	0.455974i
$796$		0			0
$797$	−6.61308e8	−	3.81806e8i	−1.30626	−	0.754168i	−0.324788	−	0.945787i	$-0.605293\pi$
$797$	−6.61308e8	−	3.81806e8i	−1.30626	−	0.754168i	−0.981469	+	0.191619i	$0.938626\pi$
$798$		0			0
$799$	1.45402e7	+	2.51844e7i	0.0285056	+	0.0493731i
$800$		0			0
$801$	3.28599e7	−	2.40729e8i	0.0639394	−	0.468415i
$802$		0			0
$803$	1.10902e9	−	6.40291e8i	2.14186	−	1.23660i
$804$		0			0
$805$	−3.29245e8	+	5.70270e8i	−0.631149	+	1.09318i
$806$		0			0
$807$	1.73014e8	+	1.17538e7i	0.329200	+	0.0223644i
$808$		0			0
$809$			4.08074e8i			0.770714i	0.922768	+	0.385357i	$0.125922\pi$
$809$			4.08074e8i			0.770714i	−0.922768	+	0.385357i	$0.874078\pi$
$810$		0			0
$811$	3.33812e8			0.625806			0.312903	−	0.949785i	$-0.398699\pi$
$811$	3.33812e8			0.625806			0.312903	+	0.949785i	$0.398699\pi$
$812$		0			0
$813$	3.29245e7	−	4.84642e8i	0.0612700	−	0.901881i
$814$		0			0
$815$	−5.15320e8	−	2.97520e8i	−0.951928	−	0.549596i
$816$		0			0
$817$	−4.90308e8	−	8.49238e8i	−0.899089	−	1.55727i
$818$		0			0
$819$	−2.01140e8	−	2.74560e7i	−0.366140	−	0.0499787i
$820$		0			0
$821$	4.65460e8	−	2.68733e8i	0.841110	−	0.485615i	−0.0165317	−	0.999863i	$-0.505262\pi$
$821$	4.65460e8	−	2.68733e8i	0.841110	−	0.485615i	0.857641	+	0.514249i	$0.171929\pi$
$822$		0			0
$823$	2.46925e7	−	4.27687e7i	0.0442962	−	0.0767233i	−0.843027	−	0.537871i	$-0.819229\pi$
$823$	2.46925e7	−	4.27687e7i	0.0442962	−	0.0767233i	0.887323	+	0.461148i	$0.152562\pi$
$824$		0			0
$825$	−1.61954e8	+	2.41136e8i	−0.288423	+	0.429438i
$826$		0			0
$827$		−	2.72468e8i		−	0.481726i	−0.970559	−	0.240863i	$-0.922570\pi$
$827$		−	2.72468e8i		−	0.481726i	0.970559	−	0.240863i	$-0.0774304\pi$
$828$		0			0
$829$	1.23939e8			0.217542			0.108771	−	0.994067i	$-0.465308\pi$
$829$	1.23939e8			0.217542			0.108771	+	0.994067i	$0.465308\pi$
$830$		0			0
$831$	6.79143e8	−	3.32908e8i	1.18347	−	0.580124i
$832$		0			0
$833$	2.82479e7	+	1.63090e7i	0.0488711	+	0.0282157i
$834$		0			0
$835$	2.57964e8	+	4.46806e8i	0.443097	+	0.767467i
$836$		0			0
$837$	6.75608e8	+	6.01086e8i	1.15217	+	1.02509i
$838$		0			0
$839$	−4.50756e8	+	2.60244e8i	−0.763231	+	0.440651i	−0.830454	−	0.557087i	$-0.811919\pi$
$839$	−4.50756e8	+	2.60244e8i	−0.763231	+	0.440651i	0.0672238	+	0.997738i	$0.478586\pi$
$840$		0			0
$841$	−1.60365e8	+	2.77761e8i	−0.269602	+	0.466964i
$842$		0			0
$843$	−3.83734e8	−	7.82830e8i	−0.640541	−	1.30673i
$844$		0			0
$845$			4.36575e8i			0.723584i
$846$		0			0
$847$	−7.55547e8			−1.24340
$848$		0			0
$849$	−7.45430e8	−	5.00653e8i	−1.21810	−	0.818113i
$850$		0			0
$851$	2.85655e8	+	1.64923e8i	0.463504	+	0.267604i
$852$		0			0
$853$	1.67400e6	+	2.89945e6i	0.00269716	+	0.00467163i	0.867371	−	0.497662i	$-0.165808\pi$
$853$	1.67400e6	+	2.89945e6i	0.00269716	+	0.00467163i	−0.864674	+	0.502334i	$0.832475\pi$
$854$		0			0
$855$	5.46831e8	+	4.23752e8i	0.874893	+	0.677975i
$856$		0			0
$857$	4.23377e8	−	2.44437e8i	0.672643	−	0.388351i	−0.124434	−	0.992228i	$-0.539712\pi$
$857$	4.23377e8	−	2.44437e8i	0.672643	−	0.388351i	0.797077	+	0.603877i	$0.206378\pi$
$858$		0			0
$859$	−3.06897e8	+	5.31560e8i	−0.484186	+	0.838635i	−0.999835	−	0.0181649i	$-0.994218\pi$
$859$	−3.06897e8	+	5.31560e8i	−0.484186	+	0.838635i	0.515649	+	0.856800i	$0.327551\pi$
$860$		0			0
$861$	5.85217e8	+	3.97571e7i	0.916869	+	0.0622882i
$862$		0			0
$863$			1.53387e8i			0.238647i	0.992855	+	0.119324i	$0.0380726\pi$
$863$			1.53387e8i			0.238647i	−0.992855	+	0.119324i	$0.961927\pi$
$864$		0			0
$865$	−6.39163e8			−0.987559
$866$		0			0
$867$	4.35256e7	−	6.40687e8i	0.0667863	−	0.983079i
$868$		0			0
$869$	7.86483e8	+	4.54076e8i	1.19848	+	0.691942i
$870$		0			0
$871$	1.16663e8	+	2.02067e8i	0.176555	+	0.305802i
$872$		0			0
$873$	−1.50206e8	−	3.67571e8i	−0.225758	−	0.552458i
$874$		0			0
$875$	−7.64193e8	+	4.41207e8i	−1.14072	+	0.658595i
$876$		0			0
$877$	−5.58483e7	+	9.67321e7i	−0.0827963	+	0.143407i	−0.904450	−	0.426580i	$-0.859718\pi$
$877$	−5.58483e7	+	9.67321e7i	−0.0827963	+	0.143407i	0.821654	+	0.569987i	$0.193052\pi$
$878$		0			0
$879$	−3.08395e8	+	4.59174e8i	−0.454088	+	0.676100i
$880$		0			0
$881$			1.19379e9i			1.74583i	0.487873	+	0.872915i	$0.337773\pi$
$881$			1.19379e9i			1.74583i	−0.487873	+	0.872915i	$0.662227\pi$
$882$		0			0
$883$	−6.64444e8			−0.965109			−0.482554	−	0.875866i	$-0.660291\pi$
$883$	−6.64444e8			−0.965109			−0.482554	+	0.875866i	$0.660291\pi$
$884$		0			0
$885$	8.31217e8	−	4.07453e8i	1.19918	−	0.587824i
$886$		0			0
$887$	2.83018e8	+	1.63401e8i	0.405550	+	0.234144i	0.688876	−	0.724879i	$-0.258105\pi$
$887$	2.83018e8	+	1.63401e8i	0.405550	+	0.234144i	−0.283326	+	0.959024i	$0.591438\pi$
$888$		0			0
$889$	6.33201e8	+	1.09674e9i	0.901231	+	1.56098i
$890$		0			0
$891$	9.75166e8	−	2.51363e8i	1.37862	−	0.355360i
$892$		0			0
$893$	4.02896e8	−	2.32612e8i	0.565768	−	0.326647i
$894$		0			0
$895$	−9.16917e7	+	1.58815e8i	−0.127897	+	0.221524i
$896$		0			0
$897$	−1.26669e8	−	2.58408e8i	−0.175506	−	0.358038i
$898$		0			0
$899$			7.60620e8i			1.04686i
$900$		0			0
$901$	−9.07549e7			−0.124078
$902$		0			0
$903$	−9.59410e8	−	6.44368e8i	−1.30299	−	0.875126i
$904$		0			0
$905$	5.00084e8	+	2.88723e8i	0.674679	+	0.389526i
$906$		0			0
$907$	−1.78077e8	−	3.08439e8i	−0.238664	−	0.413377i	0.721667	−	0.692240i	$-0.243376\pi$
$907$	−1.78077e8	−	3.08439e8i	−0.238664	−	0.413377i	−0.960331	+	0.278862i	$0.910043\pi$
$908$		0			0
$909$	1.47196e8	−	6.01507e7i	0.195976	−	0.0800846i
$910$		0			0
$911$	−9.50415e7	+	5.48722e7i	−0.125707	+	0.0725768i	−0.561535	−	0.827453i	$-0.689789\pi$
$911$	−9.50415e7	+	5.48722e7i	−0.125707	+	0.0725768i	0.435828	+	0.900030i	$0.356456\pi$
$912$		0			0
$913$	5.68964e8	−	9.85474e8i	0.747605	−	1.29489i
$914$		0			0
$915$	1.77743e8	+	1.20751e7i	0.232022	+	0.0157626i
$916$		0			0
$917$			4.90322e8i			0.635878i
$918$		0			0
$919$	−6.99498e8			−0.901239			−0.450620	−	0.892716i	$-0.648797\pi$
$919$	−6.99498e8			−0.901239			−0.450620	+	0.892716i	$0.648797\pi$
$920$		0			0
$921$	−2.97774e7	+	4.38316e8i	−0.0381160	+	0.561059i
$922$		0			0
$923$	3.28069e8	+	1.89411e8i	0.417215	+	0.240879i
$924$		0			0
$925$	5.89017e7	+	1.02021e8i	0.0744222	+	0.128903i
$926$		0			0
$927$	2.45678e8	−	3.17036e8i	0.308409	−	0.397987i
$928$		0			0
$929$	5.93754e8	−	3.42804e8i	0.740558	−	0.427561i	−0.0817140	−	0.996656i	$-0.526039\pi$
$929$	5.93754e8	−	3.42804e8i	0.740558	−	0.427561i	0.822272	+	0.569094i	$0.192706\pi$
$930$		0			0
$931$	2.60909e8	−	4.51907e8i	0.323325	−	0.560016i
$932$		0			0
$933$	−5.50695e8	+	8.19939e8i	−0.678057	+	1.00957i
$934$		0			0
$935$		−	1.12405e8i		−	0.137515i
$936$		0			0
$937$	1.04563e9			1.27104			0.635520	−	0.772084i	$-0.280786\pi$
$937$	1.04563e9			1.27104			0.635520	+	0.772084i	$0.280786\pi$
$938$		0			0
$939$	1.08757e9	−	5.33112e8i	1.31359	−	0.643905i
$940$		0			0
$941$	8.81017e7	+	5.08655e7i	0.105734	+	0.0610456i	0.551935	−	0.833887i	$-0.313890\pi$
$941$	8.81017e7	+	5.08655e7i	0.105734	+	0.0610456i	−0.446200	+	0.894933i	$0.647223\pi$
$942$		0			0
$943$	4.15762e8	+	7.20121e8i	0.495804	+	0.858758i
$944$		0			0
$945$	7.98508e8	+	1.64773e8i	0.946202	+	0.195250i
$946$		0			0
$947$	−1.09024e9	+	6.29449e8i	−1.28372	+	0.741158i	−0.977527	−	0.210811i	$-0.932390\pi$
$947$	−1.09024e9	+	6.29449e8i	−1.28372	+	0.741158i	−0.306196	+	0.951968i	$0.599056\pi$
$948$		0			0
$949$	−2.26559e8	+	3.92412e8i	−0.265083	+	0.459138i
$950$		0			0
$951$	−6.02562e7	−	1.22925e8i	−0.0700584	−	0.142921i
$952$		0			0
$953$			2.21916e8i			0.256396i	0.991749	+	0.128198i	$0.0409192\pi$
$953$			2.21916e8i			0.256396i	−0.991749	+	0.128198i	$0.959081\pi$
$954$		0			0
$955$	5.83739e8			0.670206
$956$		0			0
$957$	7.03167e8	+	4.72267e8i	0.802274	+	0.538830i
$958$		0			0
$959$	1.05023e8	+	6.06351e7i	0.119077	+	0.0687493i
$960$		0			0
$961$	−6.11626e8	−	1.05937e9i	−0.689153	−	1.19365i
$962$		0			0
$963$	−9.92694e7	+	7.27240e8i	−0.111157	+	0.814327i
$964$		0			0
$965$	6.75572e8	−	3.90042e8i	0.751778	−	0.434039i
$966$		0			0
$967$	3.89189e8	−	6.74095e8i	0.430409	−	0.745490i	−0.566500	−	0.824062i	$-0.691703\pi$
$967$	3.89189e8	−	6.74095e8i	0.430409	−	0.745490i	0.996908	+	0.0785723i	$0.0250361\pi$
$968$		0			0
$969$	1.52438e8	+	1.03560e7i	0.167542	+	0.0113821i
$970$		0			0
$971$		−	1.29298e9i		−	1.41232i	−0.708053	−	0.706159i	$-0.750426\pi$
$971$		−	1.29298e9i		−	1.41232i	0.708053	−	0.706159i	$-0.249574\pi$
$972$		0			0
$973$	−2.06405e9			−2.24069
$974$		0			0
$975$	6.96645e6	−	1.02545e8i	0.00751619	−	0.110637i
$976$		0			0
$977$	6.37032e8	+	3.67791e8i	0.683090	+	0.394382i	0.801018	−	0.598640i	$-0.204292\pi$
$977$	6.37032e8	+	3.67791e8i	0.683090	+	0.394382i	−0.117928	+	0.993022i	$0.537625\pi$
$978$		0			0
$979$	3.15771e8	+	5.46931e8i	0.336530	+	0.582887i
$980$		0			0
$981$	−1.11005e9	−	1.51523e8i	−1.17580	−	0.160499i
$982$		0			0
$983$	−9.38767e8	+	5.41997e8i	−0.988319	+	0.570606i	−0.904772	−	0.425897i	$-0.859958\pi$
$983$	−9.38767e8	+	5.41997e8i	−0.988319	+	0.570606i	−0.0835479	+	0.996504i	$0.526625\pi$
$984$		0			0
$985$	5.64325e7	−	9.77439e7i	0.0590501	−	0.102278i
$986$		0			0
$987$	3.05701e8	−	4.55164e8i	0.317941	−	0.473387i
$988$		0			0
$989$		−	1.63836e9i		−	1.69364i
$990$		0			0
$991$	−1.15250e7			−0.0118419			−0.00592095	−	0.999982i	$-0.501885\pi$
$991$	−1.15250e7			−0.0118419			−0.00592095	+	0.999982i	$0.501885\pi$
$992$		0			0
$993$	8.86286e8	−	4.34447e8i	0.905162	−	0.443699i
$994$		0			0
$995$	−1.24588e9	−	7.19307e8i	−1.26475	−	0.730206i
$996$		0			0
$997$	−6.25279e7	−	1.08302e8i	−0.0630941	−	0.109282i	0.832753	−	0.553645i	$-0.186763\pi$
$997$	−6.25279e7	−	1.08302e8i	−0.0630941	−	0.109282i	−0.895847	+	0.444363i	$0.853430\pi$
$998$		0			0
$999$	8.25368e7	−	3.99983e8i	0.0827849	−	0.401185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.m.a.41.10	✓	36
3.2	odd	2		216.7.m.a.17.5		36
4.3	odd	2		144.7.q.d.113.9		36
9.2	odd	6	inner	72.7.m.a.65.10	yes	36
9.4	even	3		648.7.e.c.161.12		36
9.5	odd	6		648.7.e.c.161.25		36
9.7	even	3		216.7.m.a.89.5		36
12.11	even	2		432.7.q.d.17.5		36
36.7	odd	6		432.7.q.d.305.5		36
36.11	even	6		144.7.q.d.65.9		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.m.a.41.10	✓	36	1.1	even	1	trivial
72.7.m.a.65.10	yes	36	9.2	odd	6	inner
144.7.q.d.65.9		36	36.11	even	6
144.7.q.d.113.9		36	4.3	odd	2
216.7.m.a.17.5		36	3.2	odd	2
216.7.m.a.89.5		36	9.7	even	3
432.7.q.d.17.5		36	12.11	even	2
432.7.q.d.305.5		36	36.7	odd	6
648.7.e.c.161.12		36	9.4	even	3
648.7.e.c.161.25		36	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	72.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.83005 - 26.9379i) q^{3} +(86.3751 + 49.8687i) q^{5} +(-207.661 - 359.679i) q^{7} +(-722.302 - 98.5953i) q^{9} +O(q^{10})\)	\(q+(1.83005 - 26.9379i) q^{3} +(86.3751 + 49.8687i) q^{5} +(-207.661 - 359.679i) q^{7} +(-722.302 - 98.5953i) q^{9} +(1641.05 - 947.463i) q^{11} +(-335.248 + 580.666i) q^{13} +(1501.43 - 2235.50i) q^{15} -594.749i q^{17} -9514.73 q^{19} +(-10069.0 + 4935.72i) q^{21} +(-13766.9 - 7948.35i) q^{23} +(-2838.72 - 4916.81i) q^{25} +(-3977.80 + 19276.9i) q^{27} +(-14337.7 + 8277.87i) q^{29} +(22971.5 - 39787.8i) q^{31} +(-22519.5 - 45940.5i) q^{33} -41423.1i q^{35} -20749.4 q^{37} +(15028.4 + 10093.5i) q^{39} +(-45300.1 - 26154.0i) q^{41} +(51531.5 + 89255.1i) q^{43} +(-57472.1 - 44536.4i) q^{45} +(-42344.5 + 24447.6i) q^{47} +(-27421.6 + 47495.5i) q^{49} +(-16021.3 - 1088.42i) q^{51} -152594. i q^{53} +188995. q^{55} +(-17412.4 + 256307. i) q^{57} +(297704. + 171879. i) q^{59} +(33078.1 + 57293.0i) q^{61} +(114531. + 280271. i) q^{63} +(-57914.1 + 33436.7i) q^{65} +(173996. - 301369. i) q^{67} +(-239306. + 356307. i) q^{69} -564987. i q^{71} +675795. q^{73} +(-137644. + 67471.3i) q^{75} +(-681565. - 393502. i) q^{77} +(239627. + 415047. i) q^{79} +(511999. + 142431. i) q^{81} +(520059. - 300256. i) q^{83} +(29659.4 - 51371.6i) q^{85} +(196750. + 401376. i) q^{87} +333280. i q^{89} +278471. q^{91} +(-1.02976e6 - 691617. i) q^{93} +(-821836. - 474487. i) q^{95} +(272344. + 471714. i) q^{97} +(-1.27875e6 + 522554. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{3} + 74 q^{9}+O(q^{10}) \) 36 * q + 10 * q^3 + 74 * q^9	\( 36 q + 10 q^{3} + 74 q^{9} + 1350 q^{11} + 7912 q^{15} + 9540 q^{19} + 3828 q^{21} + 30888 q^{23} + 56250 q^{25} + 11392 q^{27} + 38556 q^{29} + 27720 q^{31} + 33514 q^{33} + 134068 q^{39} + 179226 q^{41} + 15930 q^{43} - 185620 q^{45} + 187596 q^{47} - 198774 q^{49} - 158098 q^{51} - 197064 q^{55} - 244990 q^{57} - 408618 q^{59} + 17136 q^{61} - 417048 q^{63} - 125712 q^{65} + 27090 q^{67} - 848504 q^{69} - 534060 q^{73} - 1405714 q^{75} + 48168 q^{77} + 172620 q^{79} + 349010 q^{81} + 1801980 q^{83} - 791568 q^{85} + 28500 q^{87} + 538560 q^{91} - 1116448 q^{93} + 1832652 q^{95} + 770706 q^{97} - 614260 q^{99}+O(q^{100}) \) 36 * q + 10 * q^3 + 74 * q^9 + 1350 * q^11 + 7912 * q^15 + 9540 * q^19 + 3828 * q^21 + 30888 * q^23 + 56250 * q^25 + 11392 * q^27 + 38556 * q^29 + 27720 * q^31 + 33514 * q^33 + 134068 * q^39 + 179226 * q^41 + 15930 * q^43 - 185620 * q^45 + 187596 * q^47 - 198774 * q^49 - 158098 * q^51 - 197064 * q^55 - 244990 * q^57 - 408618 * q^59 + 17136 * q^61 - 417048 * q^63 - 125712 * q^65 + 27090 * q^67 - 848504 * q^69 - 534060 * q^73 - 1405714 * q^75 + 48168 * q^77 + 172620 * q^79 + 349010 * q^81 + 1801980 * q^83 - 791568 * q^85 + 28500 * q^87 + 538560 * q^91 - 1116448 * q^93 + 1832652 * q^95 + 770706 * q^97 - 614260 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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