LMFDB - Embedded newform 180.7.c.b.91.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,7,Mod(91,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("180.91");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	180.c (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:	$41.4097350516$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.19
Character	$\chi$	$=$	180.91
Dual form			180.7.c.b.91.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.53904 - 7.17462i) q^{2} +(-38.9505 - 50.7825i) q^{4} -55.9017 q^{5} -99.9522i q^{7} +(-502.192 + 99.7338i) q^{8} +O(q^{10})$	\(q+(3.53904 - 7.17462i) q^{2} +(-38.9505 - 50.7825i) q^{4} -55.9017 q^{5} -99.9522i q^{7} +(-502.192 + 99.7338i) q^{8} +(-197.838 + 401.074i) q^{10} +2399.27i q^{11} +3619.28 q^{13} +(-717.119 - 353.734i) q^{14} +(-1061.72 + 3956.00i) q^{16} +927.422 q^{17} +773.488i q^{19} +(2177.40 + 2838.83i) q^{20} +(17213.9 + 8491.11i) q^{22} -12221.5i q^{23} +3125.00 q^{25} +(12808.8 - 25967.0i) q^{26} +(-5075.82 + 3893.18i) q^{28} -29029.7 q^{29} +9560.97i q^{31} +(24625.3 + 21617.9i) q^{32} +(3282.18 - 6653.91i) q^{34} +5587.50i q^{35} +88644.4 q^{37} +(5549.49 + 2737.40i) q^{38} +(28073.4 - 5575.29i) q^{40} +53763.7 q^{41} -140348. i q^{43} +(121841. - 93452.8i) q^{44} +(-87684.9 - 43252.5i) q^{46} +105555. i q^{47} +107659. q^{49} +(11059.5 - 22420.7i) q^{50} +(-140973. - 183796. i) q^{52} +80965.8 q^{53} -134123. i q^{55} +(9968.61 + 50195.2i) q^{56} +(-102737. + 208277. i) q^{58} -59057.3i q^{59} +116330. q^{61} +(68596.4 + 33836.6i) q^{62} +(242250. - 100171. i) q^{64} -202324. q^{65} -134450. i q^{67} +(-36123.5 - 47096.8i) q^{68} +(40088.2 + 19774.4i) q^{70} +468387. i q^{71} +79504.8 q^{73} +(313716. - 635990. i) q^{74} +(39279.7 - 30127.7i) q^{76} +239813. q^{77} +670660. i q^{79} +(59352.2 - 221147. i) q^{80} +(190272. - 385734. i) q^{82} -549656. i q^{83} -51844.5 q^{85} +(-1.00694e6 - 496695. i) q^{86} +(-239288. - 1.20490e6i) q^{88} -785334. q^{89} -361755. i q^{91} +(-620640. + 476034. i) q^{92} +(757314. + 373561. i) q^{94} -43239.3i q^{95} +664400. q^{97} +(381007. - 772410. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8}+O(q^{10}) $ 24 * q - 20 * q^2 - 246 * q^4 + 340 * q^8	$ 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8} - 750 q^{10} + 5040 q^{13} + 2596 q^{14} + 4194 q^{16} - 7000 q^{20} + 45780 q^{22} + 75000 q^{25} - 75852 q^{26} + 54300 q^{28} - 132800 q^{29} + 10700 q^{32} - 173484 q^{34} - 69840 q^{37} - 215800 q^{38} - 14250 q^{40} + 70448 q^{41} + 395668 q^{44} - 158760 q^{46} - 642984 q^{49} - 62500 q^{50} - 210240 q^{52} + 644320 q^{53} + 917708 q^{56} - 1345020 q^{58} - 222864 q^{61} - 1948520 q^{62} + 935922 q^{64} - 266000 q^{65} - 572680 q^{68} + 220500 q^{70} + 771120 q^{73} + 589164 q^{74} - 191544 q^{76} - 1383840 q^{77} + 946000 q^{80} + 2672520 q^{82} - 372000 q^{85} - 1781528 q^{86} + 956940 q^{88} + 1566224 q^{89} + 3040560 q^{92} - 3788352 q^{94} - 1666800 q^{97} + 2709660 q^{98}+O(q^{100}) $ 24 * q - 20 * q^2 - 246 * q^4 + 340 * q^8 - 750 * q^10 + 5040 * q^13 + 2596 * q^14 + 4194 * q^16 - 7000 * q^20 + 45780 * q^22 + 75000 * q^25 - 75852 * q^26 + 54300 * q^28 - 132800 * q^29 + 10700 * q^32 - 173484 * q^34 - 69840 * q^37 - 215800 * q^38 - 14250 * q^40 + 70448 * q^41 + 395668 * q^44 - 158760 * q^46 - 642984 * q^49 - 62500 * q^50 - 210240 * q^52 + 644320 * q^53 + 917708 * q^56 - 1345020 * q^58 - 222864 * q^61 - 1948520 * q^62 + 935922 * q^64 - 266000 * q^65 - 572680 * q^68 + 220500 * q^70 + 771120 * q^73 + 589164 * q^74 - 191544 * q^76 - 1383840 * q^77 + 946000 * q^80 + 2672520 * q^82 - 372000 * q^85 - 1781528 * q^86 + 956940 * q^88 + 1566224 * q^89 + 3040560 * q^92 - 3788352 * q^94 - 1666800 * q^97 + 2709660 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	3.53904	−	7.17462i	0.442379	−	0.896828i
$2$	3.53904	−	7.17462i	0.442379	−	0.896828i
$3$		0			0
$3$		0			0
$4$	−38.9505	−	50.7825i	−0.608601	−	0.793477i
$5$	−55.9017			−0.447214
$5$	−55.9017			−0.447214
$6$		0			0
$7$		−	99.9522i		−	0.291406i	−0.989328	−	0.145703i	$-0.953456\pi$
$7$		−	99.9522i		−	0.291406i	0.989328	−	0.145703i	$-0.0465444\pi$
$8$	−502.192	+	99.7338i	−0.980844	+	0.194793i
$9$		0			0
$10$	−197.838	+	401.074i	−0.197838	+	0.401074i
$11$			2399.27i			1.80261i	0.433186	+	0.901304i	$0.357389\pi$
$11$			2399.27i			1.80261i	−0.433186	+	0.901304i	$0.642611\pi$
$12$		0			0
$13$	3619.28			1.64737			0.823687	−	0.567045i	$-0.191913\pi$
$13$	3619.28			1.64737			0.823687	+	0.567045i	$0.191913\pi$
$14$	−717.119	−	353.734i	−0.261341	−	0.128912i
$15$		0			0
$16$	−1061.72	+	3956.00i	−0.259210	+	0.965821i
$17$	927.422			0.188769			0.0943845	−	0.995536i	$-0.469912\pi$
$17$	927.422			0.188769			0.0943845	+	0.995536i	$0.469912\pi$
$18$		0			0
$19$			773.488i			0.112770i	0.998409	+	0.0563849i	$0.0179574\pi$
$19$			773.488i			0.112770i	−0.998409	+	0.0563849i	$0.982043\pi$
$20$	2177.40	+	2838.83i	0.272175	+	0.354854i
$21$		0			0
$22$	17213.9	+	8491.11i	1.61663	+	0.797437i
$23$		−	12221.5i		−	1.00448i	−0.864728	−	0.502241i	$-0.832509\pi$
$23$		−	12221.5i		−	1.00448i	0.864728	−	0.502241i	$-0.167491\pi$
$24$		0			0
$25$	3125.00			0.200000
$26$	12808.8	−	25967.0i	0.728764	−	1.47741i
$27$		0			0
$28$	−5075.82	+	3893.18i	−0.231224	+	0.177350i
$29$	−29029.7			−1.19028			−0.595139	−	0.803623i	$-0.702903\pi$
$29$	−29029.7			−1.19028			−0.595139	+	0.803623i	$0.702903\pi$
$30$		0			0
$31$			9560.97i			0.320935i	0.987041	+	0.160467i	$0.0513002\pi$
$31$			9560.97i			0.320935i	−0.987041	+	0.160467i	$0.948700\pi$
$32$	24625.3	+	21617.9i	0.751506	+	0.659726i
$33$		0			0
$34$	3282.18	−	6653.91i	0.0835076	−	0.169293i
$35$			5587.50i			0.130321i
$36$		0			0
$37$	88644.4			1.75003			0.875016	−	0.484093i	$-0.160851\pi$
$37$	88644.4			1.75003			0.875016	+	0.484093i	$0.160851\pi$
$38$	5549.49	+	2737.40i	0.101135	+	0.0498870i
$39$		0			0
$40$	28073.4	−	5575.29i	0.438647	−	0.0871139i
$41$	53763.7			0.780077			0.390039	−	0.920799i	$-0.372462\pi$
$41$	53763.7			0.780077			0.390039	+	0.920799i	$0.372462\pi$
$42$		0			0
$43$		−	140348.i		−	1.76522i	−0.470103	−	0.882612i	$-0.655783\pi$
$43$		−	140348.i		−	1.76522i	0.470103	−	0.882612i	$-0.344217\pi$
$44$	121841.	−	93452.8i	1.43033	−	1.09707i
$45$		0			0
$46$	−87684.9	−	43252.5i	−0.900848	−	0.444362i
$47$			105555.i			1.01668i	0.861157	+	0.508339i	$0.169740\pi$
$47$			105555.i			1.01668i	−0.861157	+	0.508339i	$0.830260\pi$
$48$		0			0
$49$	107659.			0.915083
$50$	11059.5	−	22420.7i	0.0884759	−	0.179366i
$51$		0			0
$52$	−140973.	−	183796.i	−1.00259	−	1.30715i
$53$	80965.8			0.543844			0.271922	−	0.962319i	$-0.412341\pi$
$53$	80965.8			0.543844			0.271922	+	0.962319i	$0.412341\pi$
$54$		0			0
$55$		−	134123.i		−	0.806151i
$56$	9968.61	+	50195.2i	0.0567637	+	0.285824i
$57$		0			0
$58$	−102737.	+	208277.i	−0.526555	+	1.06747i
$59$		−	59057.3i		−	0.287553i	−0.989610	−	0.143776i	$-0.954075\pi$
$59$		−	59057.3i		−	0.287553i	0.989610	−	0.143776i	$-0.0459246\pi$
$60$		0			0
$61$	116330.			0.512508			0.256254	−	0.966609i	$-0.417512\pi$
$61$	116330.			0.512508			0.256254	+	0.966609i	$0.417512\pi$
$62$	68596.4	+	33836.6i	0.287823	+	0.141975i
$63$		0			0
$64$	242250.	−	100171.i	0.924112	−	0.382122i
$65$	−202324.			−0.736728
$66$		0			0
$67$		−	134450.i		−	0.447029i	−0.974701	−	0.223514i	$-0.928247\pi$
$67$		−	134450.i		−	0.447029i	0.974701	−	0.223514i	$-0.0717529\pi$
$68$	−36123.5	−	47096.8i	−0.114885	−	0.149784i
$69$		0			0
$70$	40088.2	+	19774.4i	0.116875	+	0.0576512i
$71$			468387.i			1.30867i	0.756206	+	0.654334i	$0.227051\pi$
$71$			468387.i			1.30867i	−0.756206	+	0.654334i	$0.772949\pi$
$72$		0			0
$73$	79504.8			0.204373			0.102187	−	0.994765i	$-0.467416\pi$
$73$	79504.8			0.204373			0.102187	+	0.994765i	$0.467416\pi$
$74$	313716.	−	635990.i	0.774178	−	1.56948i
$75$		0			0
$76$	39279.7	−	30127.7i	0.0894802	−	0.0686318i
$77$	239813.			0.525291
$78$		0			0
$79$			670660.i			1.36026i	0.733093	+	0.680129i	$0.238076\pi$
$79$			670660.i			1.36026i	−0.733093	+	0.680129i	$0.761924\pi$
$80$	59352.2	−	221147.i	0.115922	−	0.431928i
$81$		0			0
$82$	190272.	−	385734.i	0.345090	−	0.699595i
$83$		−	549656.i		−	0.961296i	−0.876914	−	0.480648i	$-0.840402\pi$
$83$		−	549656.i		−	0.961296i	0.876914	−	0.480648i	$-0.159598\pi$
$84$		0			0
$85$	−51844.5			−0.0844201
$86$	−1.00694e6	−	496695.i	−1.58310	−	0.780899i
$87$		0			0
$88$	−239288.	−	1.20490e6i	−0.351135	−	1.76808i
$89$	−785334.			−1.11400			−0.556999	−	0.830513i	$-0.688047\pi$
$89$	−785334.			−1.11400			−0.556999	+	0.830513i	$0.688047\pi$
$90$		0			0
$91$		−	361755.i		−	0.480054i
$92$	−620640.	+	476034.i	−0.797033	+	0.611329i
$93$		0			0
$94$	757314.	+	373561.i	0.911785	+	0.449757i
$95$		−	43239.3i		−	0.0504322i
$96$		0			0
$97$	664400.			0.727972			0.363986	−	0.931404i	$-0.381416\pi$
$97$	664400.			0.727972			0.363986	+	0.931404i	$0.381416\pi$
$98$	381007.	−	772410.i	0.404814	−	0.820672i
$99$		0			0
$100$	−121720.	−	158695.i	−0.121720	−	0.158695i
$101$	1.49801e6			1.45396			0.726978	−	0.686661i	$-0.240924\pi$
$101$	1.49801e6			1.45396			0.726978	+	0.686661i	$0.240924\pi$
$102$		0			0
$103$		−	799842.i		−	0.731968i	−0.930621	−	0.365984i	$-0.880732\pi$
$103$		−	799842.i		−	0.731968i	0.930621	−	0.365984i	$-0.119268\pi$
$104$	−1.81758e6	+	360965.i	−1.61582	+	0.320896i
$105$		0			0
$106$	286541.	−	580899.i	0.240585	−	0.487734i
$107$			349292.i			0.285126i	0.989786	+	0.142563i	$0.0455344\pi$
$107$			349292.i			0.285126i	−0.989786	+	0.142563i	$0.954466\pi$
$108$		0			0
$109$	680148.			0.525199			0.262599	−	0.964905i	$-0.415420\pi$
$109$	680148.			0.525199			0.262599	+	0.964905i	$0.415420\pi$
$110$	−962285.	−	474668.i	−0.722979	−	0.356625i
$111$		0			0
$112$	395411.	+	106122.i	0.281446	+	0.0755353i
$113$	1.68229e6			1.16591			0.582955	−	0.812505i	$-0.301896\pi$
$113$	1.68229e6			1.16591			0.582955	+	0.812505i	$0.301896\pi$
$114$		0			0
$115$			683205.i			0.449218i
$116$	1.13072e6	+	1.47420e6i	0.724404	+	0.944458i
$117$		0			0
$118$	−423714.	−	209006.i	−0.257886	−	0.127208i
$119$		−	92697.9i		−	0.0550084i
$120$		0			0
$121$	−3.98495e6			−2.24940
$122$	411695.	−	834621.i	0.226723	−	0.459632i
$123$		0			0
$124$	485530.	−	372404.i	0.254654	−	0.195321i
$125$	−174693.			−0.0894427
$126$		0			0
$127$			2.92911e6i			1.42996i	0.699145	+	0.714980i	$0.253564\pi$
$127$			2.92911e6i			1.42996i	−0.699145	+	0.714980i	$0.746436\pi$
$128$	138643.	−	2.09256e6i	0.0661101	−	0.997812i
$129$		0			0
$130$	−716032.	+	1.45160e6i	−0.325913	+	0.660718i
$131$			1.57652e6i			0.701272i	0.936512	+	0.350636i	$0.114035\pi$
$131$			1.57652e6i			0.701272i	−0.936512	+	0.350636i	$0.885965\pi$
$132$		0			0
$133$	77311.8			0.0328618
$134$	−964626.	−	475822.i	−0.400908	−	0.197756i
$135$		0			0
$136$	−465744.	+	92495.3i	−0.185153	+	0.0367708i
$137$	3.34075e6			1.29922			0.649609	−	0.760269i	$-0.274933\pi$
$137$	3.34075e6			1.29922			0.649609	+	0.760269i	$0.274933\pi$
$138$		0			0
$139$			857823.i			0.319413i	0.987165	+	0.159707i	$0.0510549\pi$
$139$			857823.i			0.319413i	−0.987165	+	0.159707i	$0.948945\pi$
$140$	283747.	−	217636.i	0.103406	−	0.0793132i
$141$		0			0
$142$	3.36050e6	+	1.65764e6i	1.17365	+	0.578928i
$143$			8.68364e6i			2.96957i
$144$		0			0
$145$	1.62281e6			0.532309
$146$	281370.	−	570417.i	0.0904106	−	0.183288i
$147$		0			0
$148$	−3.45274e6	−	4.50158e6i	−1.06507	−	1.38861i
$149$	4.93323e6			1.49133			0.745663	−	0.666323i	$-0.232133\pi$
$149$	4.93323e6			1.49133			0.745663	+	0.666323i	$0.232133\pi$
$150$		0			0
$151$			2.17991e6i			0.633151i	0.948567	+	0.316575i	$0.102533\pi$
$151$			2.17991e6i			0.633151i	−0.948567	+	0.316575i	$0.897467\pi$
$152$	−77142.9	−	388440.i	−0.0219667	−	0.110610i
$153$		0			0
$154$	848705.	−	1.72056e6i	0.232378	−	0.471095i
$155$		−	534475.i		−	0.143526i
$156$		0			0
$157$	−561357.			−0.145058			−0.0725288	−	0.997366i	$-0.523107\pi$
$157$	−561357.			−0.145058			−0.0725288	+	0.997366i	$0.523107\pi$
$158$	4.81173e6	+	2.37349e6i	1.21992	+	0.601750i
$159$		0			0
$160$	−1.37660e6	−	1.20848e6i	−0.336084	−	0.295039i
$161$	−1.22157e6			−0.292712
$162$		0			0
$163$			3.42959e6i			0.791915i	0.918269	+	0.395958i	$0.129587\pi$
$163$			3.42959e6i			0.791915i	−0.918269	+	0.395958i	$0.870413\pi$
$164$	−2.09412e6	−	2.73025e6i	−0.474756	−	0.618973i
$165$		0			0
$166$	−3.94358e6	−	1.94525e6i	−0.862117	−	0.425257i
$167$			4.96116e6i			1.06521i	0.846365	+	0.532603i	$0.178786\pi$
$167$			4.96116e6i			1.06521i	−0.846365	+	0.532603i	$0.821214\pi$
$168$		0			0
$169$	8.27239e6			1.71384
$170$	−183479.	+	371965.i	−0.0373457	+	0.0757103i
$171$		0			0
$172$	−7.12720e6	+	5.46660e6i	−1.40066	+	1.07432i
$173$	−1.02232e7			−1.97447			−0.987235	−	0.159271i	$-0.949086\pi$
$173$	−1.02232e7			−1.97447			−0.987235	+	0.159271i	$0.949086\pi$
$174$		0			0
$175$		−	312351.i		−	0.0582812i
$176$	−9.49153e6	−	2.54737e6i	−1.74100	−	0.467254i
$177$		0			0
$178$	−2.77932e6	+	5.63447e6i	−0.492810	+	0.999064i
$179$			162204.i			0.0282815i	0.999900	+	0.0141407i	$0.00450128\pi$
$179$			162204.i			0.0282815i	−0.999900	+	0.0141407i	$0.995499\pi$
$180$		0			0
$181$	−6.54734e6			−1.10415			−0.552076	−	0.833794i	$-0.686164\pi$
$181$	−6.54734e6			−1.10415			−0.552076	+	0.833794i	$0.686164\pi$
$182$	−2.59546e6	−	1.28026e6i	−0.430526	−	0.212366i
$183$		0			0
$184$	1.21890e6	+	6.13756e6i	0.195666	+	0.985241i
$185$	−4.95537e6			−0.782638
$186$		0			0
$187$			2.22514e6i			0.340277i
$188$	5.36032e6	−	4.11140e6i	0.806710	−	0.618751i
$189$		0			0
$190$	−310226.	−	153025.i	−0.0452290	−	0.0223102i
$191$		−	3.54149e6i		−	0.508260i	−0.967170	−	0.254130i	$-0.918211\pi$
$191$		−	3.54149e6i		−	0.508260i	0.967170	−	0.254130i	$-0.0817891\pi$
$192$		0			0
$193$	8.80294e6			1.22449			0.612246	−	0.790667i	$-0.290266\pi$
$193$	8.80294e6			1.22449			0.612246	+	0.790667i	$0.290266\pi$
$194$	2.35134e6	−	4.76682e6i	0.322040	−	0.652865i
$195$		0			0
$196$	−4.19335e6	−	5.46717e6i	−0.556920	−	0.726097i
$197$	−3.09941e6			−0.405397			−0.202698	−	0.979241i	$-0.564971\pi$
$197$	−3.09941e6			−0.405397			−0.202698	+	0.979241i	$0.564971\pi$
$198$		0			0
$199$		−	852821.i		−	0.108218i	−0.998535	−	0.0541089i	$-0.982768\pi$
$199$		−	852821.i		−	0.108218i	0.998535	−	0.0541089i	$-0.0172318\pi$
$200$	−1.56935e6	+	311668.i	−0.196169	+	0.0389585i
$201$		0			0
$202$	5.30152e6	−	1.07477e7i	0.643200	−	1.30395i
$203$			2.90158e6i			0.346854i
$204$		0			0
$205$	−3.00548e6			−0.348861
$206$	−5.73856e6	−	2.83067e6i	−0.656450	−	0.323808i
$207$		0			0
$208$	−3.84268e6	+	1.43179e7i	−0.427016	+	1.59107i
$209$	−1.85581e6			−0.203280
$210$		0			0
$211$			1.07917e7i			1.14880i	0.818576	+	0.574399i	$0.194764\pi$
$211$			1.07917e7i			1.14880i	−0.818576	+	0.574399i	$0.805236\pi$
$212$	−3.15366e6	−	4.11165e6i	−0.330984	−	0.431527i
$213$		0			0
$214$	2.50604e6	+	1.23616e6i	0.255709	+	0.126134i
$215$			7.84567e6i			0.789432i
$216$		0			0
$217$	955640.			0.0935223
$218$	2.40707e6	−	4.87980e6i	0.232337	−	0.471013i
$219$		0			0
$220$	−6.81112e6	+	5.22417e6i	−0.639662	+	0.490624i
$221$	3.35660e6			0.310973
$222$		0			0
$223$		−	1.42777e7i		−	1.28749i	−0.765240	−	0.643745i	$-0.777380\pi$
$223$		−	1.42777e7i		−	1.28749i	0.765240	−	0.643745i	$-0.222620\pi$
$224$	2.16076e6	−	2.46136e6i	0.192248	−	0.218993i
$225$		0			0
$226$	5.95368e6	−	1.20698e7i	0.515774	−	1.04562i
$227$			1.14371e7i			0.977776i	0.872347	+	0.488888i	$0.162597\pi$
$227$			1.14371e7i			0.977776i	−0.872347	+	0.488888i	$0.837403\pi$
$228$		0			0
$229$	−1.28721e7			−1.07187			−0.535936	−	0.844258i	$-0.680041\pi$
$229$	−1.28721e7			−1.07187			−0.535936	+	0.844258i	$0.680041\pi$
$230$	4.90174e6	+	2.41789e6i	0.402871	+	0.198725i
$231$		0			0
$232$	1.45785e7	−	2.89524e6i	1.16748	−	0.231857i
$233$	9.25991e6			0.732047			0.366023	−	0.930606i	$-0.380719\pi$
$233$	9.25991e6			0.732047			0.366023	+	0.930606i	$0.380719\pi$
$234$		0			0
$235$		−	5.90068e6i		−	0.454672i
$236$	−2.99908e6	+	2.30031e6i	−0.228167	+	0.175005i
$237$		0			0
$238$	−665073.	−	328061.i	−0.0493331	−	0.0243346i
$239$		−	4.26361e6i		−	0.312308i	−0.987733	−	0.156154i	$-0.950090\pi$
$239$		−	4.26361e6i		−	0.312308i	0.987733	−	0.156154i	$-0.0499097\pi$
$240$		0			0
$241$	−1.13558e7			−0.811271			−0.405636	−	0.914035i	$-0.632950\pi$
$241$	−1.13558e7			−0.811271			−0.405636	+	0.914035i	$0.632950\pi$
$242$	−1.41029e7	+	2.85905e7i	−0.995088	+	2.01732i
$243$		0			0
$244$	−4.53109e6	−	5.90751e6i	−0.311913	−	0.406663i
$245$	−6.01830e6			−0.409237
$246$		0			0
$247$			2.79947e6i			0.185774i
$248$	−953552.	−	4.80145e6i	−0.0625157	−	0.314787i
$249$		0			0
$250$	−618244.	+	1.25336e6i	−0.0395676	+	0.0802147i
$251$		−	2.40153e7i		−	1.51868i	−0.650692	−	0.759342i	$-0.725521\pi$
$251$		−	2.40153e7i		−	1.51868i	0.650692	−	0.759342i	$-0.274479\pi$
$252$		0			0
$253$	2.93228e7			1.81069
$254$	2.10152e7	+	1.03662e7i	1.28243	+	0.632585i
$255$		0			0
$256$	−1.45227e7	−	8.40037e6i	−0.865620	−	0.500701i
$257$	7.77314e6			0.457928			0.228964	−	0.973435i	$-0.426466\pi$
$257$	7.77314e6			0.457928			0.228964	+	0.973435i	$0.426466\pi$
$258$		0			0
$259$		−	8.86020e6i		−	0.509970i
$260$	7.88061e6	+	1.02745e7i	0.448373	+	0.584576i
$261$		0			0
$262$	1.13110e7	+	5.57938e6i	0.628921	+	0.310229i
$263$		−	2.33758e7i		−	1.28499i	−0.766292	−	0.642493i	$-0.777900\pi$
$263$		−	2.33758e7i		−	1.28499i	0.766292	−	0.642493i	$-0.222100\pi$
$264$		0			0
$265$	−4.52613e6			−0.243214
$266$	273609.	−	554683.i	0.0145374	−	0.0294714i
$267$		0			0
$268$	−6.82769e6	+	5.23687e6i	−0.354707	+	0.272062i
$269$	2.52755e7			1.29850			0.649252	−	0.760573i	$-0.275082\pi$
$269$	2.52755e7			1.29850			0.649252	+	0.760573i	$0.275082\pi$
$270$		0			0
$271$		−	1.98065e7i		−	0.995175i	−0.867414	−	0.497588i	$-0.834219\pi$
$271$		−	1.98065e7i		−	0.995175i	0.867414	−	0.497588i	$-0.165781\pi$
$272$	−984667.	+	3.66889e6i	−0.0489308	+	0.182317i
$273$		0			0
$274$	1.18230e7	−	2.39686e7i	0.574747	−	1.16517i
$275$			7.49773e6i			0.360522i
$276$		0			0
$277$	−1.96620e6			−0.0925101			−0.0462551	−	0.998930i	$-0.514729\pi$
$277$	−1.96620e6			−0.0925101			−0.0462551	+	0.998930i	$0.514729\pi$
$278$	6.15456e6	+	3.03587e6i	0.286459	+	0.141302i
$279$		0			0
$280$	−557262.	−	2.80600e6i	−0.0253855	−	0.127824i
$281$	3.71366e7			1.67372			0.836862	−	0.547414i	$-0.184388\pi$
$281$	3.71366e7			1.67372			0.836862	+	0.547414i	$0.184388\pi$
$282$		0			0
$283$			1.30641e7i			0.576395i	0.957571	+	0.288197i	$0.0930559\pi$
$283$			1.30641e7i			0.576395i	−0.957571	+	0.288197i	$0.906944\pi$
$284$	2.37858e7	−	1.82439e7i	1.03840	−	0.796456i
$285$		0			0
$286$	6.23019e7	+	3.07317e7i	2.66319	+	1.31368i
$287$		−	5.37380e6i		−	0.227319i
$288$		0			0
$289$	−2.32775e7			−0.964366
$290$	5.74318e6	−	1.16430e7i	0.235482	−	0.477389i
$291$		0			0
$292$	−3.09675e6	−	4.03745e6i	−0.124382	−	0.162166i
$293$	−2.99876e7			−1.19217			−0.596085	−	0.802921i	$-0.703278\pi$
$293$	−2.99876e7			−1.19217			−0.596085	+	0.802921i	$0.703278\pi$
$294$		0			0
$295$			3.30141e6i			0.128598i
$296$	−4.45165e7	+	8.84084e6i	−1.71651	+	0.340893i
$297$		0			0
$298$	1.74589e7	−	3.53941e7i	0.659732	−	1.33746i
$299$		−	4.42332e7i		−	1.65476i
$300$		0			0
$301$	−1.40281e7			−0.514396
$302$	1.56400e7	+	7.71477e6i	0.567827	+	0.280093i
$303$		0			0
$304$	−3.05992e6	−	821231.i	−0.108915	−	0.0292311i
$305$	−6.50302e6			−0.229201
$306$		0			0
$307$			2.02161e7i			0.698688i	0.936995	+	0.349344i	$0.113596\pi$
$307$			2.02161e7i			0.698688i	−0.936995	+	0.349344i	$0.886404\pi$
$308$	−9.34081e6	−	1.21783e7i	−0.319692	−	0.416806i
$309$		0			0
$310$	−3.83465e6	−	1.89152e6i	−0.128719	−	0.0634932i
$311$			2.22851e6i			0.0740856i	0.999314	+	0.0370428i	$0.0117938\pi$
$311$			2.22851e6i			0.0740856i	−0.999314	+	0.0370428i	$0.988206\pi$
$312$		0			0
$313$	5.08300e7			1.65763			0.828814	−	0.559525i	$-0.189016\pi$
$313$	5.08300e7			1.65763			0.828814	+	0.559525i	$0.189016\pi$
$314$	−1.98666e6	+	4.02753e6i	−0.0641705	+	0.130092i
$315$		0			0
$316$	3.40578e7	−	2.61225e7i	1.07933	−	0.827854i
$317$	−2.26114e7			−0.709821			−0.354911	−	0.934900i	$-0.615489\pi$
$317$	−2.26114e7			−0.709821			−0.354911	+	0.934900i	$0.615489\pi$
$318$		0			0
$319$		−	6.96501e7i		−	2.14561i
$320$	−1.35422e7	+	5.59973e6i	−0.413275	+	0.170890i
$321$		0			0
$322$	−4.32318e6	+	8.76430e6i	−0.129490	+	0.262512i
$323$			717350.i			0.0212874i
$324$		0			0
$325$	1.13103e7			0.329475
$326$	2.46060e7	+	1.21374e7i	0.710212	+	0.350327i
$327$		0			0
$328$	−2.69997e7	+	5.36206e6i	−0.765134	+	0.151953i
$329$	1.05504e7			0.296266
$330$		0			0
$331$			2.54747e7i			0.702467i	0.936288	+	0.351233i	$0.114238\pi$
$331$			2.54747e7i			0.702467i	−0.936288	+	0.351233i	$0.885762\pi$
$332$	−2.79129e7	+	2.14094e7i	−0.762766	+	0.585045i
$333$		0			0
$334$	3.55945e7	+	1.75577e7i	0.955307	+	0.471225i
$335$			7.51596e6i			0.199917i
$336$		0			0
$337$	−6.19868e7			−1.61961			−0.809803	−	0.586702i	$-0.800426\pi$
$337$	−6.19868e7			−1.61961			−0.809803	+	0.586702i	$0.800426\pi$
$338$	2.92763e7	−	5.93513e7i	0.758168	−	1.53702i
$339$		0			0
$340$	2.01937e6	+	2.63279e6i	0.0513781	+	0.0669854i
$341$	−2.29394e7			−0.578520
$342$		0			0
$343$		−	2.25200e7i		−	0.558066i
$344$	1.39974e7	+	7.04815e7i	0.343852	+	1.73141i
$345$		0			0
$346$	−3.61804e7	+	7.33479e7i	−0.873465	+	1.77076i
$347$		−	5.60089e7i		−	1.34051i	−0.742133	−	0.670253i	$-0.766186\pi$
$347$		−	5.60089e7i		−	1.34051i	0.742133	−	0.670253i	$-0.233814\pi$
$348$		0			0
$349$	4.87021e7			1.14570			0.572850	−	0.819660i	$-0.305838\pi$
$349$	4.87021e7			1.14570			0.572850	+	0.819660i	$0.305838\pi$
$350$	−2.24100e6	−	1.10542e6i	−0.0522682	−	0.0257824i
$351$		0			0
$352$	−5.18673e7	+	5.90829e7i	−1.18923	+	1.35467i
$353$	−4.35162e7			−0.989297			−0.494649	−	0.869093i	$-0.664703\pi$
$353$	−4.35162e7			−0.989297			−0.494649	+	0.869093i	$0.664703\pi$
$354$		0			0
$355$		−	2.61836e7i		−	0.585254i
$356$	3.05891e7	+	3.98812e7i	0.677980	+	0.883931i
$357$		0			0
$358$	1.16375e6	+	574045.i	0.0253636	+	0.0125111i
$359$		−	1.34201e7i		−	0.290049i	−0.989428	−	0.145025i	$-0.953674\pi$
$359$		−	1.34201e7i		−	0.290049i	0.989428	−	0.145025i	$-0.0463261\pi$
$360$		0			0
$361$	4.64476e7			0.987283
$362$	−2.31713e7	+	4.69747e7i	−0.488454	+	0.990235i
$363$		0			0
$364$	−1.83708e7	+	1.40905e7i	−0.380912	+	0.292161i
$365$	−4.44445e6			−0.0913986
$366$		0			0
$367$			2.34709e7i			0.474823i	0.971409	+	0.237411i	$0.0762989\pi$
$367$			2.34709e7i			0.474823i	−0.971409	+	0.237411i	$0.923701\pi$
$368$	4.83484e7	+	1.29759e7i	0.970150	+	0.260372i
$369$		0			0
$370$	−1.75372e7	+	3.55529e7i	−0.346223	+	0.701892i
$371$		−	8.09271e6i		−	0.158479i
$372$		0			0
$373$	−5.34360e7			−1.02969			−0.514847	−	0.857282i	$-0.672151\pi$
$373$	−5.34360e7			−1.02969			−0.514847	+	0.857282i	$0.672151\pi$
$374$	1.59645e7	+	7.87485e6i	0.305170	+	0.150531i
$375$		0			0
$376$	−1.05274e7	−	5.30087e7i	−0.198041	−	0.997203i
$377$	−1.05067e8			−1.96083
$378$		0			0
$379$		−	2.02671e7i		−	0.372285i	−0.982523	−	0.186142i	$-0.940401\pi$
$379$		−	2.02671e7i		−	0.372285i	0.982523	−	0.186142i	$-0.0595985\pi$
$380$	−2.19580e6	+	1.68419e6i	−0.0400168	+	0.0306931i
$381$		0			0
$382$	−2.54089e7	−	1.25335e7i	−0.455822	−	0.224844i
$383$		−	5.58252e6i		−	0.0993651i	−0.998765	−	0.0496826i	$-0.984179\pi$
$383$		−	5.58252e6i		−	0.0993651i	0.998765	−	0.0496826i	$-0.0158210\pi$
$384$		0			0
$385$	−1.34059e7			−0.234917
$386$	3.11539e7	−	6.31578e7i	0.541690	−	1.09816i
$387$		0			0
$388$	−2.58787e7	−	3.37399e7i	−0.443044	−	0.577629i
$389$	1.05876e7			0.179865			0.0899327	−	0.995948i	$-0.471335\pi$
$389$	1.05876e7			0.179865			0.0899327	+	0.995948i	$0.471335\pi$
$390$		0			0
$391$		−	1.13345e7i		−	0.189615i
$392$	−5.40653e7	+	1.07372e7i	−0.897554	+	0.178251i
$393$		0			0
$394$	−1.09689e7	+	2.22371e7i	−0.179339	+	0.363571i
$395$		−	3.74910e7i		−	0.608326i
$396$		0			0
$397$	−1.89692e7			−0.303164			−0.151582	−	0.988445i	$-0.548437\pi$
$397$	−1.89692e7			−0.303164			−0.151582	+	0.988445i	$0.548437\pi$
$398$	−6.11867e6	−	3.01817e6i	−0.0970528	−	0.0478734i
$399$		0			0
$400$	−3.31789e6	+	1.23625e7i	−0.0518420	+	0.193164i
$401$	−9.20319e6			−0.142727			−0.0713634	−	0.997450i	$-0.522735\pi$
$401$	−9.20319e6			−0.142727			−0.0713634	+	0.997450i	$0.522735\pi$
$402$		0			0
$403$			3.46038e7i			0.528700i
$404$	−5.83482e7	−	7.60728e7i	−0.884879	−	1.15368i
$405$		0			0
$406$	2.08178e7	+	1.02688e7i	0.311068	+	0.153441i
$407$			2.12682e8i			3.15462i
$408$		0			0
$409$	−6.63022e7			−0.969076			−0.484538	−	0.874770i	$-0.661012\pi$
$409$	−6.63022e7			−0.969076			−0.484538	+	0.874770i	$0.661012\pi$
$410$	−1.06365e7	+	2.15632e7i	−0.154329	+	0.312868i
$411$		0			0
$412$	−4.06180e7	+	3.11542e7i	−0.580800	+	0.445477i
$413$	−5.90291e6			−0.0837946
$414$		0			0
$415$			3.07267e7i			0.429904i
$416$	8.91261e7	+	7.82413e7i	1.23801	+	1.08682i
$417$		0			0
$418$	−6.56777e6	+	1.33147e7i	−0.0899268	+	0.182307i
$419$		−	1.06809e8i		−	1.45200i	−0.687696	−	0.725999i	$-0.741378\pi$
$419$		−	1.06809e8i		−	1.45200i	0.687696	−	0.725999i	$-0.258622\pi$
$420$		0			0
$421$	−3.11843e7			−0.417916			−0.208958	−	0.977925i	$-0.567007\pi$
$421$	−3.11843e7			−0.417916			−0.208958	+	0.977925i	$0.567007\pi$
$422$	7.74266e7	+	3.81923e7i	1.03027	+	0.508204i
$423$		0			0
$424$	−4.06604e7	+	8.07503e6i	−0.533426	+	0.105937i
$425$	2.89820e6			0.0377538
$426$		0			0
$427$		−	1.16274e7i		−	0.149348i
$428$	1.77379e7	−	1.36051e7i	0.226241	−	0.173528i
$429$		0			0
$430$	5.62897e7	+	2.77661e7i	0.707985	+	0.349228i
$431$			9.72310e7i			1.21443i	0.794537	+	0.607215i	$0.207714\pi$
$431$			9.72310e7i			1.21443i	−0.794537	+	0.607215i	$0.792286\pi$
$432$		0			0
$433$	−6.52726e7			−0.804021			−0.402010	−	0.915635i	$-0.631688\pi$
$433$	−6.52726e7			−0.804021			−0.402010	+	0.915635i	$0.631688\pi$
$434$	3.38204e6	−	6.85636e6i	0.0413723	−	0.0838734i
$435$		0			0
$436$	−2.64921e7	−	3.45396e7i	−0.319636	−	0.416733i
$437$	9.45321e6			0.113275
$438$		0			0
$439$		−	8.96022e7i		−	1.05907i	−0.848288	−	0.529536i	$-0.822366\pi$
$439$		−	8.96022e7i		−	1.05907i	0.848288	−	0.529536i	$-0.177634\pi$
$440$	1.33766e7	+	6.73558e7i	0.157032	+	0.790709i
$441$		0			0
$442$	1.18791e7	−	2.40824e7i	0.137568	−	0.278890i
$443$		−	5.37278e7i		−	0.617999i	−0.951062	−	0.309000i	$-0.900006\pi$
$443$		−	5.37278e7i		−	0.617999i	0.951062	−	0.309000i	$-0.0999942\pi$
$444$		0			0
$445$	4.39015e7			0.498195
$446$	−1.02437e8	−	5.05293e7i	−1.15466	−	0.569560i
$447$		0			0
$448$	−1.00123e7	−	2.42135e7i	−0.111353	−	0.269292i
$449$	−1.07640e8			−1.18914			−0.594571	−	0.804043i	$-0.702678\pi$
$449$	−1.07640e8			−1.18914			−0.594571	+	0.804043i	$0.702678\pi$
$450$		0			0
$451$			1.28994e8i			1.40617i
$452$	−6.55259e7	−	8.54308e7i	−0.709573	−	0.925122i
$453$		0			0
$454$	8.20571e7	+	4.04764e7i	0.876897	+	0.432548i
$455$			2.02227e7i			0.214687i
$456$		0			0
$457$	5.35694e7			0.561266			0.280633	−	0.959815i	$-0.409456\pi$
$457$	5.35694e7			0.561266			0.280633	+	0.959815i	$0.409456\pi$
$458$	−4.55548e7	+	9.23525e7i	−0.474174	+	0.961285i
$459$		0			0
$460$	3.46948e7	−	2.66111e7i	0.356444	−	0.273395i
$461$	5.79532e7			0.591528			0.295764	−	0.955261i	$-0.404426\pi$
$461$	5.79532e7			0.591528			0.295764	+	0.955261i	$0.404426\pi$
$462$		0			0
$463$		−	5.12513e6i		−	0.0516371i	−0.999667	−	0.0258185i	$-0.991781\pi$
$463$		−	5.12513e6i		−	0.0516371i	0.999667	−	0.0258185i	$-0.00821921\pi$
$464$	3.08215e7	−	1.14842e8i	0.308532	−	1.14960i
$465$		0			0
$466$	3.27711e7	−	6.64364e7i	0.323843	−	0.656520i
$467$			2.52747e7i			0.248162i	0.992272	+	0.124081i	$0.0395983\pi$
$467$			2.52747e7i			0.248162i	−0.992272	+	0.124081i	$0.960402\pi$
$468$		0			0
$469$	−1.34385e7			−0.130267
$470$	−4.23352e7	−	2.08827e7i	−0.407763	−	0.201138i
$471$		0			0
$472$	5.89001e6	+	2.96581e7i	0.0560132	+	0.282045i
$473$	3.36732e8			3.18201
$474$		0			0
$475$			2.41715e6i			0.0225540i
$476$	−4.70743e6	+	3.61062e6i	−0.0436479	+	0.0334782i
$477$		0			0
$478$	−3.05898e7	−	1.50891e7i	−0.280087	−	0.138159i
$479$		−	1.83052e8i		−	1.66559i	−0.553583	−	0.832794i	$-0.686740\pi$
$479$		−	1.83052e8i		−	1.66559i	0.553583	−	0.832794i	$-0.313260\pi$
$480$		0			0
$481$	3.20829e8			2.88296
$482$	−4.01885e7	+	8.14735e7i	−0.358890	+	0.727571i
$483$		0			0
$484$	1.55216e8	+	2.02366e8i	1.36899	+	1.78485i
$485$	−3.71411e7			−0.325559
$486$		0			0
$487$			7.19456e7i			0.622899i	0.950263	+	0.311449i	$0.100814\pi$
$487$			7.19456e7i			0.622899i	−0.950263	+	0.311449i	$0.899186\pi$
$488$	−5.84198e7	+	1.16020e7i	−0.502691	+	0.0998327i
$489$		0			0
$490$	−2.12990e7	+	4.31790e7i	−0.181038	+	0.367016i
$491$		−	5.86205e7i		−	0.495227i	−0.968859	−	0.247614i	$-0.920354\pi$
$491$		−	5.86205e7i		−	0.495227i	0.968859	−	0.247614i	$-0.0796464\pi$
$492$		0			0
$493$	−2.69228e7			−0.224688
$494$	2.00851e7	+	9.90743e6i	0.166607	+	0.0821826i
$495$		0			0
$496$	−3.78232e7	−	1.01511e7i	−0.309966	−	0.0831896i
$497$	4.68163e7			0.381353
$498$		0			0
$499$			2.37768e8i			1.91360i	0.290743	+	0.956801i	$0.406098\pi$
$499$			2.37768e8i			1.91360i	−0.290743	+	0.956801i	$0.593902\pi$
$500$	6.80436e6	+	8.87134e6i	0.0544349	+	0.0709707i
$501$		0			0
$502$	−1.72301e8	−	8.49911e7i	−1.36200	−	0.671834i
$503$			2.08303e8i			1.63678i	0.574660	+	0.818392i	$0.305134\pi$
$503$			2.08303e8i			1.63678i	−0.574660	+	0.818392i	$0.694866\pi$
$504$		0			0
$505$	−8.37414e7			−0.650229
$506$	1.03774e8	−	2.10380e8i	0.801012	−	1.62388i
$507$		0			0
$508$	1.48747e8	−	1.14090e8i	1.13464	−	0.870275i
$509$	6.06760e7			0.460112			0.230056	−	0.973177i	$-0.426109\pi$
$509$	6.06760e7			0.460112			0.230056	+	0.973177i	$0.426109\pi$
$510$		0			0
$511$		−	7.94667e6i		−	0.0595556i
$512$	−1.11666e8	+	7.44657e7i	−0.831975	+	0.554813i
$513$		0			0
$514$	2.75094e7	−	5.57693e7i	0.202578	−	0.410682i
$515$			4.47125e7i			0.327346i
$516$		0			0
$517$	−2.53254e8			−1.83267
$518$	−6.35686e7	−	3.13566e7i	−0.457355	−	0.225600i
$519$		0			0
$520$	1.01606e8	−	2.01785e7i	0.722616	−	0.143509i
$521$	4.23437e7			0.299416			0.149708	−	0.988730i	$-0.452167\pi$
$521$	4.23437e7			0.299416			0.149708	+	0.988730i	$0.452167\pi$
$522$		0			0
$523$			2.64065e8i			1.84589i	0.384928	+	0.922947i	$0.374226\pi$
$523$			2.64065e8i			1.84589i	−0.384928	+	0.922947i	$0.625774\pi$
$524$	8.00598e7	−	6.14063e7i	0.556443	−	0.426795i
$525$		0			0
$526$	−1.67712e8	−	8.27276e7i	−1.15241	−	0.568451i
$527$			8.86706e6i			0.0605826i
$528$		0			0
$529$	−1.33004e6			−0.00898459
$530$	−1.60181e7	+	3.24733e7i	−0.107593	+	0.218121i
$531$		0			0
$532$	−3.01133e6	−	3.92609e6i	−0.0199997	−	0.0260750i
$533$	1.94586e8			1.28508
$534$		0			0
$535$		−	1.95260e7i		−	0.127512i
$536$	1.34092e7	+	6.75196e7i	0.0870778	+	0.438465i
$537$		0			0
$538$	8.94510e7	−	1.81342e8i	0.574432	−	1.16454i
$539$			2.58302e8i			1.64954i
$540$		0			0
$541$	−4.99745e7			−0.315614			−0.157807	−	0.987470i	$-0.550442\pi$
$541$	−4.99745e7			−0.315614			−0.157807	+	0.987470i	$0.550442\pi$
$542$	−1.42104e8	−	7.00958e7i	−0.892501	−	0.440245i
$543$		0			0
$544$	2.28381e7	+	2.00489e7i	0.141861	+	0.124536i
$545$	−3.80214e7			−0.234876
$546$		0			0
$547$		−	2.70311e8i		−	1.65159i	−0.563971	−	0.825795i	$-0.690727\pi$
$547$		−	2.70311e8i		−	1.65159i	0.563971	−	0.825795i	$-0.309273\pi$
$548$	−1.30124e8	−	1.69651e8i	−0.790705	−	1.03090i
$549$		0			0
$550$	5.37934e7	+	2.65347e7i	0.323326	+	0.159487i
$551$		−	2.24541e7i		−	0.134227i
$552$		0			0
$553$	6.70339e7			0.396387
$554$	−6.95846e6	+	1.41068e7i	−0.0409246	+	0.0829656i
$555$		0			0
$556$	4.35624e7	−	3.34126e7i	0.253447	−	0.194395i
$557$	−1.75087e8			−1.01319			−0.506593	−	0.862185i	$-0.669095\pi$
$557$	−1.75087e8			−1.01319			−0.506593	+	0.862185i	$0.669095\pi$
$558$		0			0
$559$		−	5.07957e8i		−	2.90798i
$560$	−2.21042e7	−	5.93238e6i	−0.125866	−	0.0337804i
$561$		0			0
$562$	1.31428e8	−	2.66441e8i	0.740421	−	1.50104i
$563$		−	1.20097e7i		−	0.0672989i	−0.999434	−	0.0336495i	$-0.989287\pi$
$563$		−	1.20097e7i		−	0.0672989i	0.999434	−	0.0336495i	$-0.0107130\pi$
$564$		0			0
$565$	−9.40427e7			−0.521411
$566$	9.37299e7	+	4.62343e7i	0.516927	+	0.254985i
$567$		0			0
$568$	−4.67140e7	−	2.35220e8i	−0.254919	−	1.28360i
$569$	−1.60968e8			−0.873781			−0.436891	−	0.899515i	$-0.643920\pi$
$569$	−1.60968e8			−0.873781			−0.436891	+	0.899515i	$0.643920\pi$
$570$		0			0
$571$		−	3.01355e8i		−	1.61871i	−0.587319	−	0.809356i	$-0.699816\pi$
$571$		−	3.01355e8i		−	1.61871i	0.587319	−	0.809356i	$-0.300184\pi$
$572$	4.40977e8	−	3.38232e8i	2.35629	−	1.80728i
$573$		0			0
$574$	−3.85550e7	−	1.90181e7i	−0.203866	−	0.100561i
$575$		−	3.81923e7i		−	0.200896i
$576$		0			0
$577$	3.49901e8			1.82145			0.910726	−	0.413012i	$-0.135523\pi$
$577$	3.49901e8			1.82145			0.910726	+	0.413012i	$0.135523\pi$
$578$	−8.23798e7	+	1.67007e8i	−0.426616	+	0.864871i
$579$		0			0
$580$	−6.32091e7	−	8.24103e7i	−0.323963	−	0.422374i
$581$	−5.49393e7			−0.280127
$582$		0			0
$583$			1.94259e8i			0.980338i
$584$	−3.99267e7	+	7.92931e6i	−0.200459	+	0.0398104i
$585$		0			0
$586$	−1.06127e8	+	2.15149e8i	−0.527392	+	1.06917i
$587$			3.88340e7i			0.191998i	0.995381	+	0.0959992i	$0.0306046\pi$
$587$			3.88340e7i			0.191998i	−0.995381	+	0.0959992i	$0.969395\pi$
$588$		0			0
$589$	−7.39530e6			−0.0361918
$590$	2.36863e7	+	1.16838e7i	0.115330	+	0.0568889i
$591$		0			0
$592$	−9.41159e7	+	3.50677e8i	−0.453626	+	1.69022i
$593$	1.76851e8			0.848091			0.424046	−	0.905641i	$-0.360610\pi$
$593$	1.76851e8			0.848091			0.424046	+	0.905641i	$0.360610\pi$
$594$		0			0
$595$			5.18197e6i			0.0246005i
$596$	−1.92152e8	−	2.50522e8i	−0.907622	−	1.18333i
$597$		0			0
$598$	−3.17356e8	−	1.56543e8i	−1.48403	−	0.732031i
$599$		−	1.77934e8i		−	0.827900i	−0.910300	−	0.413950i	$-0.864149\pi$
$599$		−	1.77934e8i		−	0.827900i	0.910300	−	0.413950i	$-0.135851\pi$
$600$		0			0
$601$	−1.37416e8			−0.633016			−0.316508	−	0.948590i	$-0.602510\pi$
$601$	−1.37416e8			−0.633016			−0.316508	+	0.948590i	$0.602510\pi$
$602$	−4.96458e7	+	1.00646e8i	−0.227558	+	0.461325i
$603$		0			0
$604$	1.10701e8	−	8.49084e7i	0.502390	−	0.385336i
$605$	2.22765e8			1.00596
$606$		0			0
$607$			3.25760e8i			1.45657i	0.685275	+	0.728284i	$0.259682\pi$
$607$			3.25760e8i			1.45657i	−0.685275	+	0.728284i	$0.740318\pi$
$608$	−1.67212e7	+	1.90474e7i	−0.0743972	+	0.0847472i
$609$		0			0
$610$	−2.30144e7	+	4.66567e7i	−0.101394	+	0.205553i
$611$			3.82032e8i			1.67485i
$612$		0			0
$613$	1.79249e8			0.778173			0.389087	−	0.921201i	$-0.372791\pi$
$613$	1.79249e8			0.778173			0.389087	+	0.921201i	$0.372791\pi$
$614$	1.45043e8	+	7.15457e7i	0.626603	+	0.309085i
$615$		0			0
$616$	−1.20432e8	+	2.39174e7i	−0.515228	+	0.102323i
$617$	4.40621e7			0.187590			0.0937951	−	0.995592i	$-0.470100\pi$
$617$	4.40621e7			0.187590			0.0937951	+	0.995592i	$0.470100\pi$
$618$		0			0
$619$		−	3.99677e8i		−	1.68515i	−0.538582	−	0.842573i	$-0.681040\pi$
$619$		−	3.99677e8i		−	1.68515i	0.538582	−	0.842573i	$-0.318960\pi$
$620$	−2.71420e7	+	2.08180e7i	−0.113885	+	0.0873503i
$621$		0			0
$622$	1.59887e7	+	7.88678e6i	0.0664420	+	0.0327739i
$623$			7.84958e7i			0.324625i
$624$		0			0
$625$	9.76562e6			0.0400000
$626$	1.79889e8	−	3.64686e8i	0.733300	−	1.48661i
$627$		0			0
$628$	2.18651e7	+	2.85071e7i	0.0882821	+	0.115100i
$629$	8.22108e7			0.330352
$630$		0			0
$631$			1.34075e8i			0.533654i	0.963744	+	0.266827i	$0.0859753\pi$
$631$			1.34075e8i			0.533654i	−0.963744	+	0.266827i	$0.914025\pi$
$632$	−6.68875e7	−	3.36800e8i	−0.264968	−	1.33420i
$633$		0			0
$634$	−8.00224e7	+	1.62228e8i	−0.314010	+	0.636587i
$635$		−	1.63742e8i		−	0.639498i
$636$		0			0
$637$	3.89647e8			1.50748
$638$	−4.99714e8	−	2.46494e8i	−1.92424	−	0.949172i
$639$		0			0
$640$	−7.75038e6	+	1.16978e8i	−0.0295653	+	0.446235i
$641$	−4.99004e8			−1.89466			−0.947328	−	0.320266i	$-0.896228\pi$
$641$	−4.99004e8			−1.89466			−0.947328	+	0.320266i	$0.896228\pi$
$642$		0			0
$643$			4.27044e8i			1.60635i	0.595745	+	0.803174i	$0.296857\pi$
$643$			4.27044e8i			1.60635i	−0.595745	+	0.803174i	$0.703143\pi$
$644$	4.75807e7	+	6.20343e7i	0.178145	+	0.232260i
$645$		0			0
$646$	5.14672e6	+	2.53873e6i	0.0190912	+	0.00941713i
$647$		−	2.61812e7i		−	0.0966666i	−0.998831	−	0.0483333i	$-0.984609\pi$
$647$		−	2.61812e7i		−	0.0966666i	0.998831	−	0.0483333i	$-0.0153910\pi$
$648$		0			0
$649$	1.41695e8			0.518346
$650$	4.00274e7	−	8.11468e7i	0.145753	−	0.295482i
$651$		0			0
$652$	1.74163e8	−	1.33584e8i	0.628366	−	0.481960i
$653$	−4.83197e8			−1.73534			−0.867671	−	0.497139i	$-0.834384\pi$
$653$	−4.83197e8			−1.73534			−0.867671	+	0.497139i	$0.834384\pi$
$654$		0			0
$655$		−	8.81304e7i		−	0.313619i
$656$	−5.70822e7	+	2.12689e8i	−0.202204	+	0.753415i
$657$		0			0
$658$	3.73383e7	−	7.56952e7i	0.131062	−	0.265700i
$659$		−	2.51071e6i		−	0.00877283i	−0.999990	−	0.00438642i	$-0.998604\pi$
$659$		−	2.51071e6i		−	0.00877283i	0.999990	−	0.00438642i	$-0.00139624\pi$
$660$		0			0
$661$	4.38678e8			1.51894			0.759472	−	0.650540i	$-0.225458\pi$
$661$	4.38678e8			1.51894			0.759472	+	0.650540i	$0.225458\pi$
$662$	1.82772e8	+	9.01560e7i	0.629992	+	0.310757i
$663$		0			0
$664$	5.48193e7	+	2.76033e8i	0.187253	+	0.942881i
$665$	−4.32186e6			−0.0146962
$666$		0			0
$667$			3.54787e8i			1.19561i
$668$	2.51940e8	−	1.93239e8i	0.845216	−	0.648285i
$669$		0			0
$670$	5.39242e7	+	2.65993e7i	0.179291	+	0.0884393i
$671$			2.79106e8i			0.923852i
$672$		0			0
$673$	−1.98183e8			−0.650160			−0.325080	−	0.945686i	$-0.605391\pi$
$673$	−1.98183e8			−0.650160			−0.325080	+	0.945686i	$0.605391\pi$
$674$	−2.19373e8	+	4.44732e8i	−0.716480	+	1.45251i
$675$		0			0
$676$	−3.22213e8	−	4.20092e8i	−1.04305	−	1.35989i
$677$	1.73607e8			0.559500			0.279750	−	0.960073i	$-0.409748\pi$
$677$	1.73607e8			0.559500			0.279750	+	0.960073i	$0.409748\pi$
$678$		0			0
$679$		−	6.64082e7i		−	0.212135i
$680$	2.60359e7	−	5.17065e6i	0.0828030	−	0.0164444i
$681$		0			0
$682$	−8.11833e7	+	1.64581e8i	−0.255925	+	0.518833i
$683$			1.59479e8i			0.500544i	0.968176	+	0.250272i	$0.0805200\pi$
$683$			1.59479e8i			0.500544i	−0.968176	+	0.250272i	$0.919480\pi$
$684$		0			0
$685$	−1.86753e8			−0.581028
$686$	−1.61572e8	−	7.96990e7i	−0.500489	−	0.246877i
$687$		0			0
$688$	5.55216e8	+	1.49011e8i	1.70489	+	0.457564i
$689$	2.93038e8			0.895914
$690$		0			0
$691$			3.01483e8i			0.913753i	0.889530	+	0.456877i	$0.151032\pi$
$691$			3.01483e8i			0.913753i	−0.889530	+	0.456877i	$0.848968\pi$
$692$	3.98200e8	+	5.19162e8i	1.20166	+	1.56670i
$693$		0			0
$694$	−4.01843e8	−	1.98218e8i	−1.20220	−	0.593012i
$695$		−	4.79538e7i		−	0.142846i
$696$		0			0
$697$	4.98617e7			0.147254
$698$	1.72358e8	−	3.49419e8i	0.506834	−	1.02750i
$699$		0			0
$700$	−1.58619e7	+	1.21662e7i	−0.0462447	+	0.0354700i
$701$	−1.33555e8			−0.387710			−0.193855	−	0.981030i	$-0.562099\pi$
$701$	−1.33555e8			−0.387710			−0.193855	+	0.981030i	$0.562099\pi$
$702$		0			0
$703$			6.85654e7i			0.197351i
$704$	2.40338e8	+	5.81225e8i	0.688817	+	1.66581i
$705$		0			0
$706$	−1.54005e8	+	3.12212e8i	−0.437645	+	0.887229i
$707$		−	1.49730e8i		−	0.423691i
$708$		0			0
$709$	−6.26975e8			−1.75919			−0.879593	−	0.475728i	$-0.842185\pi$
$709$	−6.26975e8			−1.75919			−0.879593	+	0.475728i	$0.842185\pi$
$710$	−1.87858e8	−	9.26647e7i	−0.524872	−	0.258904i
$711$		0			0
$712$	3.94389e8	−	7.83243e7i	1.09266	−	0.216998i
$713$	1.16850e8			0.322373
$714$		0			0
$715$		−	4.85430e8i		−	1.32803i
$716$	8.23711e6	−	6.31791e6i	0.0224407	−	0.0172121i
$717$		0			0
$718$	−9.62840e7	−	4.74941e7i	−0.260124	−	0.128312i
$719$			1.61719e8i			0.435084i	0.976051	+	0.217542i	$0.0698039\pi$
$719$			1.61719e8i			0.435084i	−0.976051	+	0.217542i	$0.930196\pi$
$720$		0			0
$721$	−7.99459e7			−0.213300
$722$	1.64380e8	−	3.33244e8i	0.436754	−	0.885423i
$723$		0			0
$724$	2.55022e8	+	3.32490e8i	0.671988	+	0.876119i
$725$	−9.07178e7			−0.238056
$726$		0			0
$727$		−	2.51088e8i		−	0.653466i	−0.945117	−	0.326733i	$-0.894052\pi$
$727$		−	2.51088e8i		−	0.653466i	0.945117	−	0.326733i	$-0.105948\pi$
$728$	3.60792e7	+	1.81671e8i	0.0935110	+	0.470859i
$729$		0			0
$730$	−1.57291e7	+	3.18873e7i	−0.0404329	+	0.0819688i
$731$		−	1.30162e8i		−	0.333220i
$732$		0			0
$733$	1.62811e8			0.413400			0.206700	−	0.978404i	$-0.433728\pi$
$733$	1.62811e8			0.413400			0.206700	+	0.978404i	$0.433728\pi$
$734$	1.68395e8	+	8.30643e7i	0.425834	+	0.210052i
$735$		0			0
$736$	2.64204e8	−	3.00960e8i	0.662683	−	0.754874i
$737$	3.22581e8			0.805818
$738$		0			0
$739$		−	1.02236e8i		−	0.253320i	−0.991946	−	0.126660i	$-0.959574\pi$
$739$		−	1.02236e8i		−	0.253320i	0.991946	−	0.126660i	$-0.0404257\pi$
$740$	1.93014e8	+	2.51646e8i	0.476314	+	0.621005i
$741$		0			0
$742$	−5.80622e7	−	2.86404e7i	−0.142129	−	0.0701080i
$743$		−	4.84447e8i		−	1.18108i	−0.807008	−	0.590540i	$-0.798915\pi$
$743$		−	4.84447e8i		−	1.18108i	0.807008	−	0.590540i	$-0.201085\pi$
$744$		0			0
$745$	−2.75776e8			−0.666941
$746$	−1.89112e8	+	3.83384e8i	−0.455515	+	0.923458i
$747$		0			0
$748$	1.12998e8	−	8.66702e7i	0.270002	−	0.207093i
$749$	3.49125e7			0.0830874
$750$		0			0
$751$			5.03888e8i			1.18964i	0.803860	+	0.594818i	$0.202776\pi$
$751$			5.03888e8i			1.18964i	−0.803860	+	0.594818i	$0.797224\pi$
$752$	−4.17574e8	−	1.12070e8i	−0.981929	−	0.263533i
$753$		0			0
$754$	−3.71834e8	+	7.53813e8i	−0.867432	+	1.75853i
$755$		−	1.21861e8i		−	0.283154i
$756$		0			0
$757$	−1.36114e8			−0.313772			−0.156886	−	0.987617i	$-0.550145\pi$
$757$	−1.36114e8			−0.313772			−0.156886	+	0.987617i	$0.550145\pi$
$758$	−1.45409e8	−	7.17262e7i	−0.333875	−	0.164691i
$759$		0			0
$760$	4.31242e6	+	2.17144e7i	0.00982381	+	0.0494661i
$761$	6.36763e8			1.44485			0.722426	−	0.691448i	$-0.243027\pi$
$761$	6.36763e8			1.44485			0.722426	+	0.691448i	$0.243027\pi$
$762$		0			0
$763$		−	6.79822e7i		−	0.153046i
$764$	−1.79846e8	+	1.37943e8i	−0.403292	+	0.309328i
$765$		0			0
$766$	−4.00525e7	−	1.97567e7i	−0.0891134	−	0.0439571i
$767$		−	2.13745e8i		−	0.473707i
$768$		0			0
$769$	−3.95443e8			−0.869570			−0.434785	−	0.900534i	$-0.643176\pi$
$769$	−3.95443e8			−0.869570			−0.434785	+	0.900534i	$0.643176\pi$
$770$	−4.74441e7	+	9.61825e7i	−0.103923	+	0.210680i
$771$		0			0
$772$	−3.42879e8	−	4.47035e8i	−0.745227	−	0.971606i
$773$	−4.24812e8			−0.919725			−0.459863	−	0.887990i	$-0.652101\pi$
$773$	−4.24812e8			−0.919725			−0.459863	+	0.887990i	$0.652101\pi$
$774$		0			0
$775$			2.98780e7i			0.0641870i
$776$	−3.33657e8	+	6.62631e7i	−0.714027	+	0.141803i
$777$		0			0
$778$	3.74698e7	−	7.59618e7i	0.0795687	−	0.161308i
$779$			4.15856e7i			0.0879691i
$780$		0			0
$781$	−1.12379e9			−2.35902
$782$	−8.13210e7	−	4.01133e7i	−0.170052	−	0.0838819i
$783$		0			0
$784$	−1.14304e8	+	4.25898e8i	−0.237199	+	0.883806i
$785$	3.13808e7			0.0648717
$786$		0			0
$787$		−	7.13202e8i		−	1.46315i	−0.681762	−	0.731574i	$-0.738786\pi$
$787$		−	7.13202e8i		−	1.46315i	0.681762	−	0.731574i	$-0.261214\pi$
$788$	1.20723e8	+	1.57396e8i	0.246725	+	0.321673i
$789$		0			0
$790$	−2.68984e8	−	1.32682e8i	−0.545564	−	0.269111i
$791$		−	1.68148e8i		−	0.339753i
$792$		0			0
$793$	4.21029e8			0.844293
$794$	−6.71328e7	+	1.36097e8i	−0.134114	+	0.271886i
$795$		0			0
$796$	−4.33084e7	+	3.32178e7i	−0.0858683	+	0.0658615i
$797$	4.19593e8			0.828807			0.414404	−	0.910093i	$-0.363990\pi$
$797$	4.19593e8			0.828807			0.414404	+	0.910093i	$0.363990\pi$
$798$		0			0
$799$			9.78937e7i			0.191917i
$800$	7.69542e7	+	6.75560e7i	0.150301	+	0.131945i
$801$		0			0
$802$	−3.25704e7	+	6.60294e7i	−0.0631394	+	0.128001i
$803$			1.90754e8i			0.368405i
$804$		0			0
$805$	6.82878e7			0.130905
$806$	2.48270e8	+	1.22464e8i	0.474153	+	0.233886i
$807$		0			0
$808$	−7.52290e8	+	1.49402e8i	−1.42610	+	0.283220i
$809$	−8.33070e8			−1.57339			−0.786695	−	0.617342i	$-0.788209\pi$
$809$	−8.33070e8			−1.57339			−0.786695	+	0.617342i	$0.788209\pi$
$810$		0			0
$811$			3.54040e8i			0.663727i	0.943327	+	0.331864i	$0.107677\pi$
$811$			3.54040e8i			0.663727i	−0.943327	+	0.331864i	$0.892323\pi$
$812$	1.47350e8	−	1.13018e8i	0.275220	−	0.211096i
$813$		0			0
$814$	1.52591e9	+	7.52689e8i	2.82916	+	1.39554i
$815$		−	1.91720e8i		−	0.354155i
$816$		0			0
$817$	1.08557e8			0.199064
$818$	−2.34646e8	+	4.75693e8i	−0.428699	+	0.869094i
$819$		0			0
$820$	1.17065e8	+	1.52626e8i	0.212317	+	0.276813i
$821$	−1.14351e8			−0.206638			−0.103319	−	0.994648i	$-0.532946\pi$
$821$	−1.14351e8			−0.206638			−0.103319	+	0.994648i	$0.532946\pi$
$822$		0			0
$823$			8.23571e8i			1.47741i	0.674028	+	0.738706i	$0.264563\pi$
$823$			8.23571e8i			1.47741i	−0.674028	+	0.738706i	$0.735437\pi$
$824$	7.97712e7	+	4.01674e8i	0.142582	+	0.717947i
$825$		0			0
$826$	−2.08906e7	+	4.23512e7i	−0.0370690	+	0.0751493i
$827$		−	1.96296e7i		−	0.0347053i	−0.999849	−	0.0173526i	$-0.994476\pi$
$827$		−	1.96296e7i		−	0.0347053i	0.999849	−	0.0173526i	$-0.00552379\pi$
$828$		0			0
$829$	−8.54284e8			−1.49947			−0.749737	−	0.661736i	$-0.769820\pi$
$829$	−8.54284e8			−1.49947			−0.749737	+	0.661736i	$0.769820\pi$
$830$	2.20453e8	+	1.08743e8i	0.385550	+	0.190181i
$831$		0			0
$832$	8.76772e8	−	3.62547e8i	1.52236	−	0.629498i
$833$	9.98450e7			0.172739
$834$		0			0
$835$		−	2.77337e8i		−	0.476375i
$836$	7.22846e7	+	9.42426e7i	0.123716	+	0.161298i
$837$		0			0
$838$	−7.66314e8	−	3.78001e8i	−1.30219	−	0.642334i
$839$		−	6.38615e8i		−	1.08132i	−0.841242	−	0.540659i	$-0.818175\pi$
$839$		−	6.38615e8i		−	1.08132i	0.841242	−	0.540659i	$-0.181825\pi$
$840$		0			0
$841$	2.47900e8			0.416762
$842$	−1.10362e8	+	2.23735e8i	−0.184877	+	0.374799i
$843$		0			0
$844$	5.48031e8	−	4.20343e8i	0.911544	−	0.699159i
$845$	−4.62440e8			−0.766453
$846$		0			0
$847$			3.98304e8i			0.655488i
$848$	−8.59634e7	+	3.20301e8i	−0.140970	+	0.525256i
$849$		0			0
$850$	1.02568e7	−	2.07935e7i	0.0167015	−	0.0338587i
$851$		−	1.08337e9i		−	1.75788i
$852$		0			0
$853$	−8.91021e7			−0.143562			−0.0717812	−	0.997420i	$-0.522868\pi$
$853$	−8.91021e7			−0.143562			−0.0717812	+	0.997420i	$0.522868\pi$
$854$	−8.34222e7	−	4.11498e7i	−0.133939	−	0.0660684i
$855$		0			0
$856$	−3.48362e7	−	1.75412e8i	−0.0555404	−	0.279664i
$857$	−1.62561e8			−0.258269			−0.129135	−	0.991627i	$-0.541220\pi$
$857$	−1.62561e8			−0.258269			−0.129135	+	0.991627i	$0.541220\pi$
$858$		0			0
$859$		−	8.52772e8i		−	1.34541i	−0.739913	−	0.672703i	$-0.765133\pi$
$859$		−	8.52772e8i		−	1.34541i	0.739913	−	0.672703i	$-0.234867\pi$
$860$	3.98423e8	−	3.05592e8i	0.626396	−	0.480449i
$861$		0			0
$862$	6.97596e8	+	3.44104e8i	1.08914	+	0.537239i
$863$			5.82925e8i			0.906944i	0.891271	+	0.453472i	$0.149815\pi$
$863$			5.82925e8i			0.906944i	−0.891271	+	0.453472i	$0.850185\pi$
$864$		0			0
$865$	5.71497e8			0.883010
$866$	−2.31002e8	+	4.68307e8i	−0.355682	+	0.721069i
$867$		0			0
$868$	−3.72226e7	−	4.85298e7i	−0.0569178	−	0.0742078i
$869$	−1.60910e9			−2.45201
$870$		0			0
$871$		−	4.86611e8i		−	0.736423i
$872$	−3.41565e8	+	6.78337e7i	−0.515138	+	0.102305i
$873$		0			0
$874$	3.34553e7	−	6.78232e7i	0.0501106	−	0.101588i
$875$			1.74609e7i			0.0260641i
$876$		0			0
$877$	−1.43231e8			−0.212343			−0.106172	−	0.994348i	$-0.533859\pi$
$877$	−1.43231e8			−0.212343			−0.106172	+	0.994348i	$0.533859\pi$
$878$	−6.42862e8	−	3.17106e8i	−0.949805	−	0.468511i
$879$		0			0
$880$	5.30593e8	+	1.42402e8i	0.778598	+	0.208963i
$881$	−1.71050e8			−0.250147			−0.125073	−	0.992147i	$-0.539917\pi$
$881$	−1.71050e8			−0.250147			−0.125073	+	0.992147i	$0.539917\pi$
$882$		0			0
$883$			1.32995e8i			0.193177i	0.995324	+	0.0965883i	$0.0307930\pi$
$883$			1.32995e8i			0.193177i	−0.995324	+	0.0965883i	$0.969207\pi$
$884$	−1.30741e8	−	1.70457e8i	−0.189259	−	0.246750i
$885$		0			0
$886$	−3.85477e8	−	1.90145e8i	−0.554239	−	0.273390i
$887$		−	1.22634e9i		−	1.75727i	−0.477492	−	0.878636i	$-0.658454\pi$
$887$		−	1.22634e9i		−	1.75727i	0.477492	−	0.878636i	$-0.341546\pi$
$888$		0			0
$889$	2.92770e8			0.416699
$890$	1.55369e8	−	3.14977e8i	0.220391	−	0.446795i
$891$		0			0
$892$	−7.25058e8	+	5.56124e8i	−1.02159	+	0.783568i
$893$	−8.16452e7			−0.114651
$894$		0			0
$895$		−	9.06746e6i		−	0.0126479i
$896$	−2.09156e8	−	1.38577e7i	−0.290768	−	0.0192649i
$897$		0			0
$898$	−3.80941e8	+	7.72275e8i	−0.526052	+	1.06646i
$899$		−	2.77552e8i		−	0.382002i
$900$		0			0
$901$	7.50895e7			0.102661
$902$	9.25482e8	+	4.56514e8i	1.26110	+	0.622063i
$903$		0			0
$904$	−8.44832e8	+	1.67781e8i	−1.14358	+	0.227110i
$905$	3.66007e8			0.493792
$906$		0			0
$907$		−	8.14503e8i		−	1.09162i	−0.837910	−	0.545809i	$-0.816222\pi$
$907$		−	8.14503e8i		−	1.09162i	0.837910	−	0.545809i	$-0.183778\pi$
$908$	5.80806e8	−	4.45481e8i	0.775842	−	0.595075i
$909$		0			0
$910$	1.45090e8	+	7.15689e7i	0.192537	+	0.0949730i
$911$			1.69872e8i			0.224681i	0.993670	+	0.112341i	$0.0358348\pi$
$911$			1.69872e8i			0.224681i	−0.993670	+	0.112341i	$0.964165\pi$
$912$		0			0
$913$	1.31878e9			1.73284
$914$	1.89584e8	−	3.84341e8i	0.248292	−	0.503359i
$915$		0			0
$916$	5.01374e8	+	6.53678e8i	0.652342	+	0.850506i
$917$	1.57577e8			0.204355
$918$		0			0
$919$			5.97220e7i			0.0769464i	0.999260	+	0.0384732i	$0.0122494\pi$
$919$			5.97220e7i			0.0769464i	−0.999260	+	0.0384732i	$0.987751\pi$
$920$	−6.81386e7	−	3.43100e8i	−0.0875043	−	0.440613i
$921$		0			0
$922$	2.05099e8	−	4.15793e8i	0.261680	−	0.530498i
$923$			1.69522e9i			2.15587i
$924$		0			0
$925$	2.77014e8			0.350007
$926$	−3.67709e7	−	1.81380e7i	−0.0463096	−	0.0228432i
$927$		0			0
$928$	−7.14866e8	−	6.27561e8i	−0.894501	−	0.785258i
$929$	7.77993e8			0.970351			0.485175	−	0.874417i	$-0.338756\pi$
$929$	7.77993e8			0.970351			0.485175	+	0.874417i	$0.338756\pi$
$930$		0			0
$931$			8.32726e7i			0.103194i
$932$	−3.60678e8	−	4.70241e8i	−0.445524	−	0.580862i
$933$		0			0
$934$	1.81337e8	+	8.94482e7i	0.222559	+	0.109782i
$935$		−	1.24389e8i		−	0.152176i
$936$		0			0
$937$	5.16472e8			0.627810			0.313905	−	0.949454i	$-0.398363\pi$
$937$	5.16472e8			0.627810			0.313905	+	0.949454i	$0.398363\pi$
$938$	−4.75595e7	+	9.64164e7i	−0.0576273	+	0.116827i
$939$		0			0
$940$	−2.99651e8	+	2.29834e8i	−0.360772	+	0.276714i
$941$	8.72197e8			1.04676			0.523379	−	0.852100i	$-0.324671\pi$
$941$	8.72197e8			1.04676			0.523379	+	0.852100i	$0.324671\pi$
$942$		0			0
$943$		−	6.57075e8i		−	0.783574i
$944$	2.33631e8	+	6.27026e7i	0.277725	+	0.0745366i
$945$		0			0
$946$	1.19171e9	−	2.41593e9i	1.40765	−	2.85371i
$947$		−	9.56619e8i		−	1.12639i	−0.826324	−	0.563195i	$-0.809572\pi$
$947$		−	9.56619e8i		−	1.12639i	0.826324	−	0.563195i	$-0.190428\pi$
$948$		0			0
$949$	2.87750e8			0.336680
$950$	1.73421e7	+	8.55438e6i	0.0202270	+	0.00997741i
$951$		0			0
$952$	9.24511e6	+	4.65522e7i	0.0107152	+	0.0539547i
$953$	−2.31699e8			−0.267699			−0.133849	−	0.991002i	$-0.542734\pi$
$953$	−2.31699e8			−0.267699			−0.133849	+	0.991002i	$0.542734\pi$
$954$		0			0
$955$			1.97975e8i			0.227301i
$956$	−2.16517e8	+	1.66070e8i	−0.247809	+	0.190071i
$957$		0			0
$958$	−1.31333e9	−	6.47827e8i	−1.49375	−	0.736822i
$959$		−	3.33915e8i		−	0.378599i
$960$		0			0
$961$	7.96091e8			0.897001
$962$	1.13543e9	−	2.30183e9i	1.27536	−	2.58552i
$963$		0			0
$964$	4.42313e8	+	5.76675e8i	0.493740	+	0.643725i
$965$	−4.92099e8			−0.547609
$966$		0			0
$967$		−	6.25565e8i		−	0.691820i	−0.938268	−	0.345910i	$-0.887570\pi$
$967$		−	6.25565e8i		−	0.691820i	0.938268	−	0.345910i	$-0.112430\pi$
$968$	2.00121e9	−	3.97434e8i	2.20631	−	0.438166i
$969$		0			0
$970$	−1.31444e8	+	2.66473e8i	−0.144021	+	0.291970i
$971$			5.82254e8i			0.635997i	0.948091	+	0.317999i	$0.103011\pi$
$971$			5.82254e8i			0.635997i	−0.948091	+	0.317999i	$0.896989\pi$
$972$		0			0
$973$	8.57413e7			0.0930789
$974$	5.16183e8	+	2.54618e8i	0.558633	+	0.275558i
$975$		0			0
$976$	−1.23510e8	+	4.60200e8i	−0.132847	+	0.494991i
$977$	9.44037e8			1.01229			0.506145	−	0.862448i	$-0.331070\pi$
$977$	9.44037e8			1.01229			0.506145	+	0.862448i	$0.331070\pi$
$978$		0			0
$979$		−	1.88423e9i		−	2.00810i
$980$	2.34415e8	+	3.05624e8i	0.249062	+	0.324720i
$981$		0			0
$982$	−4.20580e8	−	2.07460e8i	−0.444134	−	0.219078i
$983$			7.66179e8i			0.806621i	0.915063	+	0.403311i	$0.132141\pi$
$983$			7.66179e8i			0.806621i	−0.915063	+	0.403311i	$0.867859\pi$
$984$		0			0
$985$	1.73262e8			0.181299
$986$	−9.52807e7	+	1.93161e8i	−0.0993972	+	0.201506i
$987$		0			0
$988$	1.42164e8	−	1.09041e8i	0.147407	−	0.113062i
$989$	−1.71526e9			−1.77314
$990$		0			0
$991$		−	3.33236e8i		−	0.342398i	−0.985236	−	0.171199i	$-0.945236\pi$
$991$		−	3.33236e8i		−	0.342398i	0.985236	−	0.171199i	$-0.0547641\pi$
$992$	−2.06688e8	+	2.35442e8i	−0.211729	+	0.241185i
$993$		0			0
$994$	1.65684e8	−	3.35889e8i	0.168703	−	0.342008i
$995$			4.76742e7i			0.0483965i
$996$		0			0
$997$	−1.69413e9			−1.70947			−0.854737	−	0.519062i	$-0.826281\pi$
$997$	−1.69413e9			−1.70947			−0.854737	+	0.519062i	$0.826281\pi$
$998$	1.70590e9	+	8.41469e8i	1.71617	+	0.846538i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.7.c.b.91.19		24
3.2	odd	2		60.7.c.a.31.6	yes	24
4.3	odd	2	inner	180.7.c.b.91.20		24
12.11	even	2		60.7.c.a.31.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.c.a.31.5	✓	24	12.11	even	2
60.7.c.a.31.6	yes	24	3.2	odd	2
180.7.c.b.91.19		24	1.1	even	1	trivial
180.7.c.b.91.20		24	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	180.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(3.53904 - 7.17462i) q^{2} +(-38.9505 - 50.7825i) q^{4} -55.9017 q^{5} -99.9522i q^{7} +(-502.192 + 99.7338i) q^{8} +O(q^{10})\)	\(q+(3.53904 - 7.17462i) q^{2} +(-38.9505 - 50.7825i) q^{4} -55.9017 q^{5} -99.9522i q^{7} +(-502.192 + 99.7338i) q^{8} +(-197.838 + 401.074i) q^{10} +2399.27i q^{11} +3619.28 q^{13} +(-717.119 - 353.734i) q^{14} +(-1061.72 + 3956.00i) q^{16} +927.422 q^{17} +773.488i q^{19} +(2177.40 + 2838.83i) q^{20} +(17213.9 + 8491.11i) q^{22} -12221.5i q^{23} +3125.00 q^{25} +(12808.8 - 25967.0i) q^{26} +(-5075.82 + 3893.18i) q^{28} -29029.7 q^{29} +9560.97i q^{31} +(24625.3 + 21617.9i) q^{32} +(3282.18 - 6653.91i) q^{34} +5587.50i q^{35} +88644.4 q^{37} +(5549.49 + 2737.40i) q^{38} +(28073.4 - 5575.29i) q^{40} +53763.7 q^{41} -140348. i q^{43} +(121841. - 93452.8i) q^{44} +(-87684.9 - 43252.5i) q^{46} +105555. i q^{47} +107659. q^{49} +(11059.5 - 22420.7i) q^{50} +(-140973. - 183796. i) q^{52} +80965.8 q^{53} -134123. i q^{55} +(9968.61 + 50195.2i) q^{56} +(-102737. + 208277. i) q^{58} -59057.3i q^{59} +116330. q^{61} +(68596.4 + 33836.6i) q^{62} +(242250. - 100171. i) q^{64} -202324. q^{65} -134450. i q^{67} +(-36123.5 - 47096.8i) q^{68} +(40088.2 + 19774.4i) q^{70} +468387. i q^{71} +79504.8 q^{73} +(313716. - 635990. i) q^{74} +(39279.7 - 30127.7i) q^{76} +239813. q^{77} +670660. i q^{79} +(59352.2 - 221147. i) q^{80} +(190272. - 385734. i) q^{82} -549656. i q^{83} -51844.5 q^{85} +(-1.00694e6 - 496695. i) q^{86} +(-239288. - 1.20490e6i) q^{88} -785334. q^{89} -361755. i q^{91} +(-620640. + 476034. i) q^{92} +(757314. + 373561. i) q^{94} -43239.3i q^{95} +664400. q^{97} +(381007. - 772410. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8}+O(q^{10}) \) 24 * q - 20 * q^2 - 246 * q^4 + 340 * q^8	\( 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8} - 750 q^{10} + 5040 q^{13} + 2596 q^{14} + 4194 q^{16} - 7000 q^{20} + 45780 q^{22} + 75000 q^{25} - 75852 q^{26} + 54300 q^{28} - 132800 q^{29} + 10700 q^{32} - 173484 q^{34} - 69840 q^{37} - 215800 q^{38} - 14250 q^{40} + 70448 q^{41} + 395668 q^{44} - 158760 q^{46} - 642984 q^{49} - 62500 q^{50} - 210240 q^{52} + 644320 q^{53} + 917708 q^{56} - 1345020 q^{58} - 222864 q^{61} - 1948520 q^{62} + 935922 q^{64} - 266000 q^{65} - 572680 q^{68} + 220500 q^{70} + 771120 q^{73} + 589164 q^{74} - 191544 q^{76} - 1383840 q^{77} + 946000 q^{80} + 2672520 q^{82} - 372000 q^{85} - 1781528 q^{86} + 956940 q^{88} + 1566224 q^{89} + 3040560 q^{92} - 3788352 q^{94} - 1666800 q^{97} + 2709660 q^{98}+O(q^{100}) \) 24 * q - 20 * q^2 - 246 * q^4 + 340 * q^8 - 750 * q^10 + 5040 * q^13 + 2596 * q^14 + 4194 * q^16 - 7000 * q^20 + 45780 * q^22 + 75000 * q^25 - 75852 * q^26 + 54300 * q^28 - 132800 * q^29 + 10700 * q^32 - 173484 * q^34 - 69840 * q^37 - 215800 * q^38 - 14250 * q^40 + 70448 * q^41 + 395668 * q^44 - 158760 * q^46 - 642984 * q^49 - 62500 * q^50 - 210240 * q^52 + 644320 * q^53 + 917708 * q^56 - 1345020 * q^58 - 222864 * q^61 - 1948520 * q^62 + 935922 * q^64 - 266000 * q^65 - 572680 * q^68 + 220500 * q^70 + 771120 * q^73 + 589164 * q^74 - 191544 * q^76 - 1383840 * q^77 + 946000 * q^80 + 2672520 * q^82 - 372000 * q^85 - 1781528 * q^86 + 956940 * q^88 + 1566224 * q^89 + 3040560 * q^92 - 3788352 * q^94 - 1666800 * q^97 + 2709660 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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