LMFDB - Embedded newform 300.3.c.f.151.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,3,Mod(151,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("300.151");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	300.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:	$8.17440793081$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.6080256576.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 7x^{6} - 12x^{5} + 12x^{4} - 48x^{3} + 112x^{2} - 192x + 256 $ x^8 - 3x^7 + 7x^6 - 12x^5 + 12x^4 - 48x^3 + 112x^2 - 192*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.6
Root			$1.96705 + 0.361553i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.3.c.f.151.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29664 + 1.52274i) q^{2} +1.73205i q^{3} +(-0.637459 + 3.94888i) q^{4} +(-2.63746 + 2.24584i) q^{6} -0.837253i q^{7} +(-6.83966 + 4.14959i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(1.29664 + 1.52274i) q^{2} +1.73205i q^{3} +(-0.637459 + 3.94888i) q^{4} +(-2.63746 + 2.24584i) q^{6} -0.837253i q^{7} +(-6.83966 + 4.14959i) q^{8} -3.00000 q^{9} +15.7955i q^{11} +(-6.83966 - 1.10411i) q^{12} +5.18655 q^{13} +(1.27492 - 1.08561i) q^{14} +(-15.1873 - 5.03449i) q^{16} -27.3586 q^{17} +(-3.88991 - 4.56821i) q^{18} +17.9667i q^{19} +1.45017 q^{21} +(-24.0524 + 20.4811i) q^{22} -19.1101i q^{23} +(-7.18729 - 11.8466i) q^{24} +(6.72508 + 7.89776i) q^{26} -5.19615i q^{27} +(3.30621 + 0.533714i) q^{28} +45.6495 q^{29} -13.6243i q^{31} +(-12.0262 - 29.6542i) q^{32} -27.3586 q^{33} +(-35.4743 - 41.6600i) q^{34} +(1.91238 - 11.8466i) q^{36} +15.5597 q^{37} +(-27.3586 + 23.2964i) q^{38} +8.98337i q^{39} +13.2990 q^{41} +(1.88034 + 2.20822i) q^{42} +27.9430i q^{43} +(-62.3746 - 10.0690i) q^{44} +(29.0997 - 24.7789i) q^{46} +55.6558i q^{47} +(8.72000 - 26.3052i) q^{48} +48.2990 q^{49} -47.3865i q^{51} +(-3.30621 + 20.4811i) q^{52} -15.5597 q^{53} +(7.91238 - 6.73753i) q^{54} +(3.47425 + 5.72653i) q^{56} -31.1193 q^{57} +(59.1909 + 69.5122i) q^{58} +87.6625i q^{59} +38.0000 q^{61} +(20.7462 - 17.6658i) q^{62} +2.51176i q^{63} +(29.5619 - 56.7635i) q^{64} +(-35.4743 - 41.6600i) q^{66} -92.2015i q^{67} +(17.4400 - 108.036i) q^{68} +33.0997 q^{69} +130.707i q^{71} +(20.5190 - 12.4488i) q^{72} +54.7173 q^{73} +(20.1752 + 23.6933i) q^{74} +(-70.9485 - 11.4531i) q^{76} +13.2249 q^{77} +(-13.6793 + 11.6482i) q^{78} -13.6243i q^{79} +9.00000 q^{81} +(17.2440 + 20.2509i) q^{82} +59.0048i q^{83} +(-0.924421 + 5.72653i) q^{84} +(-42.5498 + 36.2319i) q^{86} +79.0673i q^{87} +(-65.5448 - 108.036i) q^{88} -39.8007 q^{89} -4.34246i q^{91} +(75.4635 + 12.1819i) q^{92} +23.5980 q^{93} +(-84.7492 + 72.1654i) q^{94} +(51.3625 - 20.8300i) q^{96} +168.821 q^{97} +(62.6263 + 73.5467i) q^{98} -47.3865i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{4} - 6 q^{6} - 24 q^{9}+O(q^{10}) $ 8 * q + 10 * q^4 - 6 * q^6 - 24 * q^9	$ 8 q + 10 q^{4} - 6 q^{6} - 24 q^{9} - 20 q^{14} - 46 q^{16} + 72 q^{21} + 18 q^{24} + 84 q^{26} + 184 q^{29} - 12 q^{34} - 30 q^{36} - 256 q^{41} - 348 q^{44} + 112 q^{46} + 24 q^{49} + 18 q^{54} - 244 q^{56} + 304 q^{61} + 10 q^{64} - 12 q^{66} + 144 q^{69} + 252 q^{74} - 24 q^{76} + 72 q^{81} + 204 q^{84} - 280 q^{86} - 560 q^{89} - 376 q^{94} + 426 q^{96}+O(q^{100}) $ 8 * q + 10 * q^4 - 6 * q^6 - 24 * q^9 - 20 * q^14 - 46 * q^16 + 72 * q^21 + 18 * q^24 + 84 * q^26 + 184 * q^29 - 12 * q^34 - 30 * q^36 - 256 * q^41 - 348 * q^44 + 112 * q^46 + 24 * q^49 + 18 * q^54 - 244 * q^56 + 304 * q^61 + 10 * q^64 - 12 * q^66 + 144 * q^69 + 252 * q^74 - 24 * q^76 + 72 * q^81 + 204 * q^84 - 280 * q^86 - 560 * q^89 - 376 * q^94 + 426 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.29664	+	1.52274i	0.648319	+	0.761369i
$2$	1.29664	+	1.52274i	0.648319	+	0.761369i
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−0.637459	+	3.94888i	−0.159365	+	0.987220i
$5$		0			0
$5$		0			0
$6$	−2.63746	+	2.24584i	−0.439576	+	0.374307i
$7$		−	0.837253i		−	0.119608i	−0.998210	−	0.0598038i	$-0.980952\pi$
$7$		−	0.837253i		−	0.119608i	0.998210	−	0.0598038i	$-0.0190475\pi$
$8$	−6.83966	+	4.14959i	−0.854957	+	0.518698i
$9$	−3.00000			−0.333333
$10$		0			0
$11$			15.7955i			1.43596i	0.696066	+	0.717978i	$0.254932\pi$
$11$			15.7955i			1.43596i	−0.696066	+	0.717978i	$0.745068\pi$
$12$	−6.83966	−	1.10411i	−0.569972	−	0.0920092i
$13$	5.18655			0.398966			0.199483	−	0.979901i	$-0.436074\pi$
$13$	5.18655			0.398966			0.199483	+	0.979901i	$0.436074\pi$
$14$	1.27492	−	1.08561i	0.0910655	−	0.0775439i
$15$		0			0
$16$	−15.1873	−	5.03449i	−0.949206	−	0.314656i
$17$	−27.3586			−1.60933			−0.804666	−	0.593728i	$-0.797656\pi$
$17$	−27.3586			−1.60933			−0.804666	+	0.593728i	$0.797656\pi$
$18$	−3.88991	−	4.56821i	−0.216106	−	0.253790i
$19$			17.9667i			0.945618i	0.881165	+	0.472809i	$0.156760\pi$
$19$			17.9667i			0.945618i	−0.881165	+	0.472809i	$0.843240\pi$
$20$		0			0
$21$	1.45017			0.0690555
$22$	−24.0524	+	20.4811i	−1.09329	+	0.930958i
$23$		−	19.1101i		−	0.830874i	−0.909622	−	0.415437i	$-0.863629\pi$
$23$		−	19.1101i		−	0.830874i	0.909622	−	0.415437i	$-0.136371\pi$
$24$	−7.18729	−	11.8466i	−0.299471	−	0.493610i
$25$		0			0
$26$	6.72508	+	7.89776i	0.258657	+	0.303760i
$27$		−	5.19615i		−	0.192450i
$28$	3.30621	+	0.533714i	0.118079	+	0.0190612i
$29$	45.6495			1.57412			0.787060	−	0.616876i	$-0.211602\pi$
$29$	45.6495			1.57412			0.787060	+	0.616876i	$0.211602\pi$
$30$		0			0
$31$		−	13.6243i		−	0.439493i	−0.975557	−	0.219747i	$-0.929477\pi$
$31$		−	13.6243i		−	0.439493i	0.975557	−	0.219747i	$-0.0705230\pi$
$32$	−12.0262	−	29.6542i	−0.375819	−	0.926693i
$33$	−27.3586			−0.829050
$34$	−35.4743	−	41.6600i	−1.04336	−	1.22529i
$35$		0			0
$36$	1.91238	−	11.8466i	0.0531216	−	0.329073i
$37$	15.5597			0.420531			0.210266	−	0.977644i	$-0.432567\pi$
$37$	15.5597			0.420531			0.210266	+	0.977644i	$0.432567\pi$
$38$	−27.3586	+	23.2964i	−0.719964	+	0.613062i
$39$			8.98337i			0.230343i
$40$		0			0
$41$	13.2990			0.324366			0.162183	−	0.986761i	$-0.448147\pi$
$41$	13.2990			0.324366			0.162183	+	0.986761i	$0.448147\pi$
$42$	1.88034	+	2.20822i	0.0447700	+	0.0525767i
$43$			27.9430i			0.649837i	0.945742	+	0.324918i	$0.105337\pi$
$43$			27.9430i			0.649837i	−0.945742	+	0.324918i	$0.894663\pi$
$44$	−62.3746	−	10.0690i	−1.41760	−	0.228841i
$45$		0			0
$46$	29.0997	−	24.7789i	0.632601	−	0.538672i
$47$			55.6558i			1.18417i	0.805877	+	0.592083i	$0.201694\pi$
$47$			55.6558i			1.18417i	−0.805877	+	0.592083i	$0.798306\pi$
$48$	8.72000	−	26.3052i	0.181667	−	0.548024i
$49$	48.2990			0.985694
$50$		0			0
$51$		−	47.3865i		−	0.929148i
$52$	−3.30621	+	20.4811i	−0.0635810	+	0.393867i
$53$	−15.5597			−0.293578			−0.146789	−	0.989168i	$-0.546894\pi$
$53$	−15.5597			−0.293578			−0.146789	+	0.989168i	$0.546894\pi$
$54$	7.91238	−	6.73753i	0.146525	−	0.124769i
$55$		0			0
$56$	3.47425	+	5.72653i	0.0620403	+	0.102259i
$57$	−31.1193			−0.545953
$58$	59.1909	+	69.5122i	1.02053	+	1.19849i
$59$			87.6625i			1.48581i	0.669400	+	0.742903i	$0.266551\pi$
$59$			87.6625i			1.48581i	−0.669400	+	0.742903i	$0.733449\pi$
$60$		0			0
$61$	38.0000			0.622951			0.311475	−	0.950254i	$-0.399177\pi$
$61$	38.0000			0.622951			0.311475	+	0.950254i	$0.399177\pi$
$62$	20.7462	−	17.6658i	0.334616	−	0.284932i
$63$			2.51176i			0.0398692i
$64$	29.5619	−	56.7635i	0.461904	−	0.886930i
$65$		0			0
$66$	−35.4743	−	41.6600i	−0.537489	−	0.631212i
$67$		−	92.2015i		−	1.37614i	−0.725643	−	0.688071i	$-0.758458\pi$
$67$		−	92.2015i		−	1.37614i	0.725643	−	0.688071i	$-0.241542\pi$
$68$	17.4400	−	108.036i	0.256471	−	1.58876i
$69$	33.0997			0.479705
$70$		0			0
$71$			130.707i			1.84094i	0.390816	+	0.920469i	$0.372193\pi$
$71$			130.707i			1.84094i	−0.390816	+	0.920469i	$0.627807\pi$
$72$	20.5190	−	12.4488i	0.284986	−	0.172899i
$73$	54.7173			0.749552			0.374776	−	0.927115i	$-0.377720\pi$
$73$	54.7173			0.749552			0.374776	+	0.927115i	$0.377720\pi$
$74$	20.1752	+	23.6933i	0.272638	+	0.320179i
$75$		0			0
$76$	−70.9485	−	11.4531i	−0.933533	−	0.150698i
$77$	13.2249			0.171751
$78$	−13.6793	+	11.6482i	−0.175376	+	0.149336i
$79$		−	13.6243i		−	0.172459i	−0.996275	−	0.0862297i	$-0.972518\pi$
$79$		−	13.6243i		−	0.172459i	0.996275	−	0.0862297i	$-0.0274819\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	17.2440	+	20.2509i	0.210293	+	0.246962i
$83$			59.0048i			0.710901i	0.934695	+	0.355451i	$0.115673\pi$
$83$			59.0048i			0.710901i	−0.934695	+	0.355451i	$0.884327\pi$
$84$	−0.924421	+	5.72653i	−0.0110050	+	0.0681730i
$85$		0			0
$86$	−42.5498	+	36.2319i	−0.494766	+	0.421302i
$87$			79.0673i			0.908819i
$88$	−65.5448	−	108.036i	−0.744828	−	1.22768i
$89$	−39.8007			−0.447198			−0.223599	−	0.974681i	$-0.571781\pi$
$89$	−39.8007			−0.447198			−0.223599	+	0.974681i	$0.571781\pi$
$90$		0			0
$91$		−	4.34246i		−	0.0477193i
$92$	75.4635	+	12.1819i	0.820255	+	0.132412i
$93$	23.5980			0.253741
$94$	−84.7492	+	72.1654i	−0.901587	+	0.767717i
$95$		0			0
$96$	51.3625	−	20.8300i	0.535026	−	0.216979i
$97$	168.821			1.74043			0.870214	−	0.492675i	$-0.163981\pi$
$97$	168.821			1.74043			0.870214	+	0.492675i	$0.163981\pi$
$98$	62.6263	+	73.5467i	0.639044	+	0.750477i
$99$		−	47.3865i		−	0.478652i
$100$		0			0
$101$	44.5498			0.441087			0.220544	−	0.975377i	$-0.429217\pi$
$101$	44.5498			0.441087			0.220544	+	0.975377i	$0.429217\pi$
$102$	72.1573	−	61.4432i	0.707424	−	0.602384i
$103$		−	126.466i		−	1.22782i	−0.789375	−	0.613911i	$-0.789595\pi$
$103$		−	126.466i		−	1.22782i	0.789375	−	0.613911i	$-0.210405\pi$
$104$	−35.4743	+	21.5220i	−0.341099	+	0.206943i
$105$		0			0
$106$	−20.1752	−	23.6933i	−0.190333	−	0.223521i
$107$		−	104.383i		−	0.975546i	−0.872971	−	0.487773i	$-0.837809\pi$
$107$		−	104.383i		−	0.975546i	0.872971	−	0.487773i	$-0.162191\pi$
$108$	20.5190	+	3.31233i	0.189991	+	0.0306697i
$109$	0.501656			0.00460235			0.00230117	−	0.999997i	$-0.499268\pi$
$109$	0.501656			0.00460235			0.00230117	+	0.999997i	$0.499268\pi$
$110$		0			0
$111$			26.9501i			0.242794i
$112$	−4.21515	+	12.7156i	−0.0376352	+	0.113532i
$113$	−16.9855			−0.150314			−0.0751572	−	0.997172i	$-0.523946\pi$
$113$	−16.9855			−0.150314			−0.0751572	+	0.997172i	$0.523946\pi$
$114$	−40.3505	−	47.3865i	−0.353952	−	0.415671i
$115$		0			0
$116$	−29.0997	+	180.264i	−0.250859	+	1.55400i
$117$	−15.5597			−0.132989
$118$	−133.487	+	113.667i	−1.13125	+	0.963276i
$119$			22.9061i			0.192488i
$120$		0			0
$121$	−128.498			−1.06197
$122$	49.2723	+	57.8640i	0.403871	+	0.474295i
$123$			23.0346i			0.187273i
$124$	53.8007	+	8.68492i	0.433876	+	0.0700397i
$125$		0			0
$126$	−3.82475	+	3.25684i	−0.0303552	+	0.0258480i
$127$		−	8.45598i		−	0.0665825i	−0.999446	−	0.0332913i	$-0.989401\pi$
$127$		−	8.45598i		−	0.0665825i	0.999446	−	0.0332913i	$-0.0105989\pi$
$128$	124.767	−	28.5867i	0.974742	−	0.223334i
$129$	−48.3987			−0.375184
$130$		0			0
$131$		−	51.7290i		−	0.394878i	−0.980315	−	0.197439i	$-0.936738\pi$
$131$		−	51.7290i		−	0.394878i	0.980315	−	0.197439i	$-0.0632624\pi$
$132$	17.4400	−	108.036i	0.132121	−	0.818454i
$133$	15.0427			0.113103
$134$	140.399	−	119.552i	1.04775	−	0.892179i
$135$		0			0
$136$	187.124	−	113.527i	1.37591	−	0.834757i
$137$	53.8083			0.392762			0.196381	−	0.980528i	$-0.437081\pi$
$137$	53.8083			0.392762			0.196381	+	0.980528i	$0.437081\pi$
$138$	42.9183	+	50.4021i	0.311002	+	0.365233i
$139$			13.6243i			0.0980165i	0.998798	+	0.0490082i	$0.0156061\pi$
$139$			13.6243i			0.0980165i	−0.998798	+	0.0490082i	$0.984394\pi$
$140$		0			0
$141$	−96.3987			−0.683679
$142$	−199.032	+	169.479i	−1.40163	+	1.19352i
$143$			81.9243i			0.572897i
$144$	45.5619	+	15.1035i	0.316402	+	0.104885i
$145$		0			0
$146$	70.9485	+	83.3200i	0.485949	+	0.570685i
$147$			83.6563i			0.569091i
$148$	−9.91864	+	61.4432i	−0.0670178	+	0.415157i
$149$	33.6495			0.225836			0.112918	−	0.993604i	$-0.463980\pi$
$149$	33.6495			0.225836			0.112918	+	0.993604i	$0.463980\pi$
$150$		0			0
$151$		−	139.988i		−	0.927076i	−0.886077	−	0.463538i	$-0.846580\pi$
$151$		−	139.988i		−	0.927076i	0.886077	−	0.463538i	$-0.153420\pi$
$152$	−74.5546	−	122.886i	−0.490490	−	0.808463i
$153$	82.0759			0.536444
$154$	17.1478	+	20.1380i	0.111350	+	0.130766i
$155$		0			0
$156$	−35.4743	−	5.72653i	−0.227399	−	0.0367085i
$157$	−21.2631			−0.135434			−0.0677170	−	0.997705i	$-0.521572\pi$
$157$	−21.2631			−0.135434			−0.0677170	+	0.997705i	$0.521572\pi$
$158$	20.7462	−	17.6658i	0.131305	−	0.111809i
$159$		−	26.9501i		−	0.169498i
$160$		0			0
$161$	−16.0000			−0.0993789
$162$	11.6697	+	13.7046i	0.0720355	+	0.0845965i
$163$		−	210.211i		−	1.28964i	−0.764335	−	0.644819i	$-0.776933\pi$
$163$		−	210.211i		−	1.28964i	0.764335	−	0.644819i	$-0.223067\pi$
$164$	−8.47757	+	52.5162i	−0.0516925	+	0.320221i
$165$		0			0
$166$	−89.8488	+	76.5079i	−0.541258	+	0.460891i
$167$			238.384i			1.42745i	0.700426	+	0.713725i	$0.252994\pi$
$167$			238.384i			1.42745i	−0.700426	+	0.713725i	$0.747006\pi$
$168$	−9.91864	+	6.01759i	−0.0590395	+	0.0358190i
$169$	−142.100			−0.840826
$170$		0			0
$171$		−	53.9002i		−	0.315206i
$172$	−110.343	−	17.8125i	−0.641532	−	0.103561i
$173$	−2.33481			−0.0134960			−0.00674800	−	0.999977i	$-0.502148\pi$
$173$	−2.33481			−0.0134960			−0.00674800	+	0.999977i	$0.502148\pi$
$174$	−120.399	+	102.522i	−0.691946	+	0.589205i
$175$		0			0
$176$	79.5224	−	239.891i	0.451832	−	1.36302i
$177$	−151.836			−0.857830
$178$	−51.6071	−	60.6060i	−0.289927	−	0.340483i
$179$		−	227.054i		−	1.26846i	−0.773145	−	0.634229i	$-0.781318\pi$
$179$		−	227.054i		−	1.26846i	0.773145	−	0.634229i	$-0.218682\pi$
$180$		0			0
$181$	114.096			0.630367			0.315183	−	0.949031i	$-0.397934\pi$
$181$	114.096			0.630367			0.315183	+	0.949031i	$0.397934\pi$
$182$	6.61243	−	5.63060i	0.0363320	−	0.0309374i
$183$			65.8179i			0.359661i
$184$	79.2990	+	130.707i	0.430973	+	0.710362i
$185$		0			0
$186$	30.5980	+	35.9335i	0.164505	+	0.193191i
$187$		−	432.144i		−	2.31093i
$188$	−219.778	−	35.4783i	−1.16903	−	0.188714i
$189$	−4.35050			−0.0230185
$190$		0			0
$191$		−	139.392i		−	0.729798i	−0.931047	−	0.364899i	$-0.881103\pi$
$191$		−	139.392i		−	0.729798i	0.931047	−	0.364899i	$-0.118897\pi$
$192$	98.3173	+	51.2027i	0.512069	+	0.266681i
$193$	−182.046			−0.943245			−0.471623	−	0.881801i	$-0.656331\pi$
$193$	−182.046			−0.943245			−0.471623	+	0.881801i	$0.656331\pi$
$194$	218.900	+	257.071i	1.12835	+	1.32511i
$195$		0			0
$196$	−30.7886	+	190.727i	−0.157085	+	0.973097i
$197$	−258.027			−1.30978			−0.654890	−	0.755724i	$-0.727285\pi$
$197$	−258.027			−1.30978			−0.654890	+	0.755724i	$0.727285\pi$
$198$	72.1573	−	61.4432i	0.364431	−	0.310319i
$199$		−	256.474i		−	1.28881i	−0.764683	−	0.644407i	$-0.777104\pi$
$199$		−	256.474i		−	1.28881i	0.764683	−	0.644407i	$-0.222896\pi$
$200$		0			0
$201$	159.698			0.794516
$202$	57.7650	+	67.8377i	0.285965	+	0.335830i
$203$		−	38.2202i		−	0.188277i
$204$	187.124	+	30.2070i	0.917273	+	0.148073i
$205$		0			0
$206$	192.574	−	163.980i	0.934825	−	0.796020i
$207$			57.3303i			0.276958i
$208$	−78.7697	−	26.1117i	−0.378700	−	0.125537i
$209$	−283.794			−1.35787
$210$		0			0
$211$			211.855i			1.00405i	0.864852	+	0.502027i	$0.167412\pi$
$211$			211.855i			1.00405i	−0.864852	+	0.502027i	$0.832588\pi$
$212$	9.91864	−	61.4432i	0.0467860	−	0.289826i
$213$	−226.390			−1.06287
$214$	158.949	−	135.348i	0.742750	−	0.632465i
$215$		0			0
$216$	21.5619	+	35.5399i	0.0998235	+	0.164537i
$217$	−11.4070			−0.0525667
$218$	0.650466	+	0.763890i	0.00298379	+	0.00350408i
$219$			94.7731i			0.432754i
$220$		0			0
$221$	−141.897			−0.642068
$222$	−41.0380	+	34.9446i	−0.184856	+	0.157408i
$223$			349.843i			1.56880i	0.620255	+	0.784401i	$0.287029\pi$
$223$			349.843i			1.56880i	−0.620255	+	0.784401i	$0.712971\pi$
$224$	−24.8281	+	10.0690i	−0.110840	+	0.0449508i
$225$		0			0
$226$	−22.0241	−	25.8645i	−0.0974517	−	0.114445i
$227$			185.554i			0.817418i	0.912665	+	0.408709i	$0.134021\pi$
$227$			185.554i			0.817418i	−0.912665	+	0.408709i	$0.865979\pi$
$228$	19.8373	−	122.886i	0.0870056	−	0.538976i
$229$	−263.897			−1.15239			−0.576194	−	0.817313i	$-0.695463\pi$
$229$	−263.897			−1.15239			−0.576194	+	0.817313i	$0.695463\pi$
$230$		0			0
$231$			22.9061i			0.0991607i
$232$	−312.227	+	189.427i	−1.34581	+	0.816494i
$233$	58.4780			0.250978			0.125489	−	0.992095i	$-0.459950\pi$
$233$	58.4780			0.250978			0.125489	+	0.992095i	$0.459950\pi$
$234$	−20.1752	−	23.6933i	−0.0862190	−	0.101253i
$235$		0			0
$236$	−346.169	−	55.8812i	−1.46682	−	0.236785i
$237$	23.5980			0.0995694
$238$	−34.8800	+	29.7009i	−0.146555	+	0.124794i
$239$		−	113.337i		−	0.474212i	−0.971484	−	0.237106i	$-0.923801\pi$
$239$		−	113.337i		−	0.474212i	0.971484	−	0.237106i	$-0.0761989\pi$
$240$		0			0
$241$	−77.7940			−0.322797			−0.161398	−	0.986889i	$-0.551600\pi$
$241$	−77.7940			−0.322797			−0.161398	+	0.986889i	$0.551600\pi$
$242$	−166.616	−	195.669i	−0.688495	−	0.808551i
$243$			15.5885i			0.0641500i
$244$	−24.2234	+	150.057i	−0.0992763	+	0.614989i
$245$		0			0
$246$	−35.0756	+	29.8675i	−0.142584	+	0.121413i
$247$			93.1855i			0.377269i
$248$	56.5351	+	93.1855i	0.227964	+	0.375748i
$249$	−102.199			−0.410439
$250$		0			0
$251$		−	106.226i		−	0.423212i	−0.977355	−	0.211606i	$-0.932131\pi$
$251$		−	106.226i		−	0.423212i	0.977355	−	0.211606i	$-0.0678693\pi$
$252$	−9.91864	−	1.60114i	−0.0393597	−	0.00635374i
$253$	301.854			1.19310
$254$	12.8762	−	10.9644i	0.0506939	−	0.0431667i
$255$		0			0
$256$	205.308	+	152.921i	0.801983	+	0.597346i
$257$	−381.078			−1.48279			−0.741397	−	0.671067i	$-0.765836\pi$
$257$	−381.078			−1.48279			−0.741397	+	0.671067i	$0.765836\pi$
$258$	−62.7556	−	73.6985i	−0.243239	−	0.285653i
$259$		−	13.0274i		−	0.0502988i
$260$		0			0
$261$	−136.949			−0.524707
$262$	78.7697	−	67.0738i	0.300648	−	0.256007i
$263$		−	11.4914i		−	0.0436934i	−0.999761	−	0.0218467i	$-0.993045\pi$
$263$		−	11.4914i		−	0.0436934i	0.999761	−	0.0218467i	$-0.00695458\pi$
$264$	187.124	−	113.527i	0.708802	−	0.430027i
$265$		0			0
$266$	19.5050	+	22.9061i	0.0733269	+	0.0861132i
$267$		−	68.9368i		−	0.258190i
$268$	364.093	+	58.7746i	1.35855	+	0.219308i
$269$	77.9518			0.289784			0.144892	−	0.989447i	$-0.453717\pi$
$269$	77.9518			0.289784			0.144892	+	0.989447i	$0.453717\pi$
$270$		0			0
$271$			86.6851i			0.319871i	0.987127	+	0.159936i	$0.0511287\pi$
$271$			86.6851i			0.319871i	−0.987127	+	0.159936i	$0.948871\pi$
$272$	415.504	+	137.737i	1.52759	+	0.506386i
$273$	7.52136			0.0275508
$274$	69.7700	+	81.9360i	0.254635	+	0.299036i
$275$		0			0
$276$	−21.0997	+	130.707i	−0.0764481	+	0.473575i
$277$	287.328			1.03729			0.518643	−	0.854991i	$-0.326437\pi$
$277$	287.328			1.03729			0.518643	+	0.854991i	$0.326437\pi$
$278$	−20.7462	+	17.6658i	−0.0746267	+	0.0635459i
$279$			40.8729i			0.146498i
$280$		0			0
$281$	−224.598			−0.799281			−0.399641	−	0.916672i	$-0.630865\pi$
$281$	−224.598			−0.799281			−0.399641	+	0.916672i	$0.630865\pi$
$282$	−124.994	−	146.790i	−0.443242	−	0.520531i
$283$		−	84.1224i		−	0.297252i	−0.988893	−	0.148626i	$-0.952515\pi$
$283$		−	84.1224i		−	0.297252i	0.988893	−	0.148626i	$-0.0474851\pi$
$284$	−516.145	−	83.3200i	−1.81741	−	0.293380i
$285$		0			0
$286$	−124.749	+	106.226i	−0.436186	+	0.371420i
$287$		−	11.1346i		−	0.0387967i
$288$	36.0786	+	88.9625i	0.125273	+	0.308898i
$289$	459.495			1.58995
$290$		0			0
$291$			292.407i			1.00484i
$292$	−34.8800	+	216.072i	−0.119452	+	0.739972i
$293$	−246.620			−0.841706			−0.420853	−	0.907129i	$-0.638269\pi$
$293$	−246.620			−0.841706			−0.420853	+	0.907129i	$0.638269\pi$
$294$	−127.387	+	108.472i	−0.433288	+	0.368952i
$295$		0			0
$296$	−106.423	+	64.5661i	−0.359536	+	0.218129i
$297$	82.0759			0.276350
$298$	43.6312	+	51.2394i	0.146414	+	0.171944i
$299$		−	99.1156i		−	0.331490i
$300$		0			0
$301$	23.3954			0.0777255
$302$	213.166	−	181.514i	0.705846	−	0.601041i
$303$			77.1626i			0.254662i
$304$	90.4535	−	272.866i	0.297544	−	0.897586i
$305$		0			0
$306$	106.423	+	124.980i	0.347787	+	0.408432i
$307$			115.811i			0.377236i	0.982051	+	0.188618i	$0.0604008\pi$
$307$			115.811i			0.377236i	−0.982051	+	0.188618i	$0.939599\pi$
$308$	−8.43030	+	52.2233i	−0.0273711	+	0.169556i
$309$	219.045			0.708883
$310$		0			0
$311$		−	203.767i		−	0.655201i	−0.944816	−	0.327600i	$-0.893760\pi$
$311$		−	203.767i		−	0.655201i	0.944816	−	0.327600i	$-0.106240\pi$
$312$	−37.2773	−	61.4432i	−0.119478	−	0.196933i
$313$	−99.0614			−0.316490			−0.158245	−	0.987400i	$-0.550584\pi$
$313$	−99.0614			−0.316490			−0.158245	+	0.987400i	$0.550584\pi$
$314$	−27.5706	−	32.3782i	−0.0878045	−	0.103115i
$315$		0			0
$316$	53.8007	+	8.68492i	0.170255	+	0.0274839i
$317$	471.192			1.48641			0.743206	−	0.669063i	$-0.233304\pi$
$317$	471.192			1.48641			0.743206	+	0.669063i	$0.233304\pi$
$318$	41.0380	−	34.9446i	0.129050	−	0.109889i
$319$			721.057i			2.26037i
$320$		0			0
$321$	180.797			0.563232
$322$	−20.7462	−	24.3638i	−0.0644292	−	0.0756640i
$323$		−	491.546i		−	1.52181i
$324$	−5.73713	+	35.5399i	−0.0177072	+	0.109691i
$325$		0			0
$326$	320.096	−	272.568i	0.981891	−	0.836098i
$327$			0.868893i			0.00265717i
$328$	−90.9607	+	55.1854i	−0.277319	+	0.168248i
$329$	46.5980			0.141635
$330$		0			0
$331$		−	270.695i		−	0.817810i	−0.912577	−	0.408905i	$-0.865911\pi$
$331$		−	270.695i		−	0.817810i	0.912577	−	0.408905i	$-0.134089\pi$
$332$	−233.003	−	37.6131i	−0.701816	−	0.113293i
$333$	−46.6790			−0.140177
$334$	−362.997	+	309.098i	−1.08682	+	0.925444i
$335$		0			0
$336$	−22.0241	−	7.30085i	−0.0655479	−	0.0217287i
$337$	377.317			1.11964			0.559818	−	0.828615i	$-0.310871\pi$
$337$	377.317			1.11964			0.559818	+	0.828615i	$0.310871\pi$
$338$	−184.252	−	216.380i	−0.545124	−	0.640179i
$339$		−	29.4198i		−	0.0867841i
$340$		0			0
$341$	215.203			0.631093
$342$	82.0759	−	69.8891i	0.239988	−	0.204354i
$343$		−	81.4639i		−	0.237504i
$344$	−115.952	−	191.121i	−0.337069	−	0.555583i
$345$		0			0
$346$	−3.02740	−	3.55530i	−0.00874971	−	0.0102754i
$347$		−	462.222i		−	1.33205i	−0.745929	−	0.666025i	$-0.767994\pi$
$347$		−	462.222i		−	1.33205i	0.745929	−	0.666025i	$-0.232006\pi$
$348$	−312.227	−	50.4021i	−0.897204	−	0.144834i
$349$	−200.598			−0.574779			−0.287390	−	0.957814i	$-0.592787\pi$
$349$	−200.598			−0.574779			−0.287390	+	0.957814i	$0.592787\pi$
$350$		0			0
$351$		−	26.9501i		−	0.0767810i
$352$	468.403	−	189.960i	1.33069	−	0.539660i
$353$	250.897			0.710757			0.355379	−	0.934722i	$-0.384352\pi$
$353$	250.897			0.710757			0.355379	+	0.934722i	$0.384352\pi$
$354$	−196.876	−	231.206i	−0.556148	−	0.653125i
$355$		0			0
$356$	25.3713	−	157.168i	0.0712676	−	0.441483i
$357$	−39.6746			−0.111133
$358$	345.744	−	294.407i	0.965764	−	0.822366i
$359$			215.601i			0.600560i	0.953851	+	0.300280i	$0.0970801\pi$
$359$			215.601i			0.600560i	−0.953851	+	0.300280i	$0.902920\pi$
$360$		0			0
$361$	38.1960			0.105806
$362$	147.942	+	173.739i	0.408679	+	0.479941i
$363$		−	222.566i		−	0.613129i
$364$	17.1478	+	2.76814i	0.0471095	+	0.00760478i
$365$		0			0
$366$	−100.223	+	85.3420i	−0.273835	+	0.233175i
$367$			67.0637i			0.182735i	0.995817	+	0.0913675i	$0.0291238\pi$
$367$			67.0637i			0.182735i	−0.995817	+	0.0913675i	$0.970876\pi$
$368$	−96.2097	+	290.231i	−0.261439	+	0.788670i
$369$	−39.8970			−0.108122
$370$		0			0
$371$			13.0274i			0.0351142i
$372$	−15.0427	+	93.1855i	−0.0404374	+	0.250499i
$373$	567.402			1.52119			0.760593	−	0.649230i	$-0.224909\pi$
$373$	567.402			1.52119			0.760593	+	0.649230i	$0.224909\pi$
$374$	658.042	−	560.334i	1.75947	−	1.49822i
$375$		0			0
$376$	−230.949	−	380.667i	−0.614225	−	1.01241i
$377$	236.764			0.628020
$378$	−5.64102	−	6.62466i	−0.0149233	−	0.0175256i
$379$		−	240.298i		−	0.634031i	−0.948420	−	0.317016i	$-0.897319\pi$
$379$		−	240.298i		−	0.634031i	0.948420	−	0.317016i	$-0.102681\pi$
$380$		0			0
$381$	14.6462			0.0384414
$382$	212.257	−	180.740i	0.555646	−	0.473142i
$383$			670.068i			1.74952i	0.484553	+	0.874762i	$0.338982\pi$
$383$			670.068i			1.74952i	−0.484553	+	0.874762i	$0.661018\pi$
$384$	49.5137	+	216.103i	0.128942	+	0.562768i
$385$		0			0
$386$	−236.048	−	277.209i	−0.611524	−	0.718157i
$387$		−	83.8290i		−	0.216612i
$388$	−107.617	+	666.655i	−0.277363	+	1.71818i
$389$	474.640			1.22015			0.610077	−	0.792342i	$-0.291139\pi$
$389$	474.640			1.22015			0.610077	+	0.792342i	$0.291139\pi$
$390$		0			0
$391$			522.826i			1.33715i
$392$	−330.349	+	200.421i	−0.842726	+	0.511278i
$393$	89.5973			0.227983
$394$	−334.567	−	392.907i	−0.849156	−	0.997226i
$395$		0			0
$396$	187.124	+	30.2070i	0.472535	+	0.0762802i
$397$	−499.460			−1.25809			−0.629043	−	0.777371i	$-0.716553\pi$
$397$	−499.460			−1.25809			−0.629043	+	0.777371i	$0.716553\pi$
$398$	390.542	−	332.554i	0.981262	−	0.835562i
$399$			26.0548i			0.0653001i
$400$		0			0
$401$	344.694			0.859587			0.429793	−	0.902927i	$-0.358586\pi$
$401$	344.694			0.859587			0.429793	+	0.902927i	$0.358586\pi$
$402$	207.070	+	243.178i	0.515100	+	0.604920i
$403$		−	70.6631i		−	0.175343i
$404$	−28.3987	+	175.922i	−0.0702938	+	0.435450i
$405$		0			0
$406$	58.1993	−	49.5578i	0.143348	−	0.122063i
$407$			245.773i			0.603864i
$408$	196.635	+	324.108i	0.481947	+	0.794382i
$409$	501.890			1.22712			0.613558	−	0.789650i	$-0.289738\pi$
$409$	501.890			1.22712			0.613558	+	0.789650i	$0.289738\pi$
$410$		0			0
$411$			93.1988i			0.226761i
$412$	499.397	+	80.6166i	1.21213	+	0.195671i
$413$	73.3957			0.177714
$414$	−87.2990	+	74.3367i	−0.210867	+	0.179557i
$415$		0			0
$416$	−62.3746	−	153.803i	−0.149939	−	0.369719i
$417$	−23.5980			−0.0565898
$418$	−367.978	−	432.144i	−0.880331	−	1.03384i
$419$			218.369i			0.521167i	0.965451	+	0.260584i	$0.0839150\pi$
$419$			218.369i			0.521167i	−0.965451	+	0.260584i	$0.916085\pi$
$420$		0			0
$421$	281.698			0.669116			0.334558	−	0.942375i	$-0.391413\pi$
$421$	281.698			0.669116			0.334558	+	0.942375i	$0.391413\pi$
$422$	−322.600	+	274.700i	−0.764455	+	0.650947i
$423$		−	166.967i		−	0.394722i
$424$	106.423	−	64.5661i	0.250997	−	0.152279i
$425$		0			0
$426$	−293.547	−	344.733i	−0.689076	−	0.809233i
$427$		−	31.8156i		−	0.0745097i
$428$	412.197	+	66.5401i	0.963078	+	0.155468i
$429$	−141.897			−0.330762
$430$		0			0
$431$		−	441.081i		−	1.02339i	−0.859167	−	0.511694i	$-0.829018\pi$
$431$		−	441.081i		−	1.02339i	0.859167	−	0.511694i	$-0.170982\pi$
$432$	−26.1600	+	78.9155i	−0.0605556	+	0.182675i
$433$	−123.443			−0.285089			−0.142544	−	0.989788i	$-0.545528\pi$
$433$	−123.443			−0.285089			−0.142544	+	0.989788i	$0.545528\pi$
$434$	−14.7907	−	17.3698i	−0.0340800	−	0.0400227i
$435$		0			0
$436$	−0.319785	+	1.98098i	−0.000733451	+	0.00454353i
$437$	343.346			0.785690
$438$	−144.315	+	122.886i	−0.329485	+	0.280563i
$439$		−	330.728i		−	0.753368i	−0.926342	−	0.376684i	$-0.877064\pi$
$439$		−	330.728i		−	0.753368i	0.926342	−	0.376684i	$-0.122936\pi$
$440$		0			0
$441$	−144.897			−0.328565
$442$	−183.989	−	216.072i	−0.416265	−	0.488850i
$443$			154.952i			0.349780i	0.984588	+	0.174890i	$0.0559569\pi$
$443$			154.952i			0.349780i	−0.984588	+	0.174890i	$0.944043\pi$
$444$	−106.423	−	17.1796i	−0.239691	−	0.0386928i
$445$		0			0
$446$	−532.718	+	453.619i	−1.19444	+	1.01708i
$447$			58.2826i			0.130386i
$448$	−47.5254	−	24.7508i	−0.106084	−	0.0552473i
$449$	95.8970			0.213579			0.106790	−	0.994282i	$-0.465943\pi$
$449$	95.8970			0.213579			0.106790	+	0.994282i	$0.465943\pi$
$450$		0			0
$451$			210.065i			0.465775i
$452$	10.8276	−	67.0738i	0.0239548	−	0.148393i
$453$	242.467			0.535247
$454$	−282.550	+	240.596i	−0.622356	+	0.529948i
$455$		0			0
$456$	212.846	−	129.132i	0.466767	−	0.283185i
$457$	−485.718			−1.06284			−0.531420	−	0.847108i	$-0.678341\pi$
$457$	−485.718			−1.06284			−0.531420	+	0.847108i	$0.678341\pi$
$458$	−342.179	−	401.846i	−0.747116	−	0.877393i
$459$			142.160i			0.309716i
$460$		0			0
$461$	353.650			0.767136			0.383568	−	0.923513i	$-0.374695\pi$
$461$	353.650			0.767136			0.383568	+	0.923513i	$0.374695\pi$
$462$	−34.8800	+	29.7009i	−0.0754978	+	0.0642878i
$463$			421.720i			0.910842i	0.890276	+	0.455421i	$0.150511\pi$
$463$			421.720i			0.910842i	−0.890276	+	0.455421i	$0.849489\pi$
$464$	−693.292	−	229.822i	−1.49416	−	0.495306i
$465$		0			0
$466$	75.8248	+	89.0466i	0.162714	+	0.191087i
$467$		−	640.974i		−	1.37254i	−0.727349	−	0.686268i	$-0.759248\pi$
$467$		−	640.974i		−	1.37254i	0.727349	−	0.686268i	$-0.240752\pi$
$468$	9.91864	−	61.4432i	0.0211937	−	0.131289i
$469$	−77.1960			−0.164597
$470$		0			0
$471$		−	36.8289i		−	0.0781929i
$472$	−363.763	−	599.582i	−0.770684	−	1.27030i
$473$	−441.374			−0.933137
$474$	30.5980	+	35.9335i	0.0645528	+	0.0758091i
$475$		0			0
$476$	−90.4535	−	14.6017i	−0.190028	−	0.0306758i
$477$	46.6790			0.0978595
$478$	172.582	−	146.957i	0.361050	−	0.307441i
$479$			221.137i			0.461664i	0.972994	+	0.230832i	$0.0741448\pi$
$479$			221.137i			0.461664i	−0.972994	+	0.230832i	$0.925855\pi$
$480$		0			0
$481$	80.7010			0.167778
$482$	−100.871	−	118.460i	−0.209275	−	0.245767i
$483$		−	27.7128i		−	0.0573764i
$484$	81.9124	−	507.424i	0.169240	−	1.04840i
$485$		0			0
$486$	−23.7371	+	20.2126i	−0.0488418	+	0.0415897i
$487$			889.949i			1.82741i	0.406377	+	0.913705i	$0.366792\pi$
$487$			889.949i			1.82741i	−0.406377	+	0.913705i	$0.633208\pi$
$488$	−259.907	+	157.684i	−0.532596	+	0.323123i
$489$	364.096			0.744573
$490$		0			0
$491$			552.843i			1.12595i	0.826473	+	0.562977i	$0.190344\pi$
$491$			552.843i			1.12595i	−0.826473	+	0.562977i	$0.809656\pi$
$492$	−90.9607	−	14.6836i	−0.184879	−	0.0298447i
$493$	−1248.91			−2.53328
$494$	−141.897	+	120.828i	−0.287241	+	0.244591i
$495$		0			0
$496$	−68.5914	+	206.916i	−0.138289	+	0.417169i
$497$	109.435			0.220190
$498$	−132.516	−	155.623i	−0.266096	−	0.312495i
$499$			533.302i			1.06874i	0.845250	+	0.534371i	$0.179451\pi$
$499$			533.302i			1.06874i	−0.845250	+	0.534371i	$0.820549\pi$
$500$		0			0
$501$	−412.894			−0.824139
$502$	161.755	−	137.737i	0.322220	−	0.274376i
$503$		−	574.914i		−	1.14297i	−0.820612	−	0.571485i	$-0.806367\pi$
$503$		−	574.914i		−	1.14297i	0.820612	−	0.571485i	$-0.193633\pi$
$504$	−10.4228	−	17.1796i	−0.0206801	−	0.0340865i
$505$		0			0
$506$	391.395	+	459.644i	0.773509	+	0.908388i
$507$		−	246.124i		−	0.485451i
$508$	33.3917	+	5.39034i	0.0657316	+	0.0106109i
$509$	−207.547			−0.407753			−0.203877	−	0.978997i	$-0.565354\pi$
$509$	−207.547			−0.407753			−0.203877	+	0.978997i	$0.565354\pi$
$510$		0			0
$511$		−	45.8122i		−	0.0896521i
$512$	33.3518	+	510.913i	0.0651403	+	0.997876i
$513$	93.3580			0.181984
$514$	−494.120	−	580.282i	−0.961324	−	1.12895i
$515$		0			0
$516$	30.8522	−	191.121i	0.0597910	−	0.370389i
$517$	−879.112			−1.70041
$518$	19.8373	−	16.8918i	0.0382959	−	0.0326096i
$519$		−	4.04401i		−	0.00779192i
$520$		0			0
$521$	−712.900			−1.36833			−0.684165	−	0.729327i	$-0.739833\pi$
$521$	−712.900			−1.36833			−0.684165	+	0.729327i	$0.739833\pi$
$522$	−177.573	−	208.537i	−0.340178	−	0.399495i
$523$		−	139.548i		−	0.266822i	−0.991061	−	0.133411i	$-0.957407\pi$
$523$		−	139.548i		−	0.266822i	0.991061	−	0.133411i	$-0.0425931\pi$
$524$	204.272	+	32.9751i	0.389831	+	0.0629296i
$525$		0			0
$526$	17.4983	−	14.9002i	0.0332668	−	0.0283273i
$527$			372.742i			0.707290i
$528$	415.504	+	137.737i	0.786939	+	0.260865i
$529$	163.804			0.309648
$530$		0			0
$531$		−	262.988i		−	0.495268i
$532$	−9.58911	+	59.4019i	−0.0180246	+	0.111658i
$533$	68.9760			0.129411
$534$	104.973	−	89.3861i	0.196578	−	0.167390i
$535$		0			0
$536$	382.598	+	630.627i	0.713802	+	1.17654i
$537$	393.269			0.732345
$538$	101.075	+	118.700i	0.187872	+	0.220632i
$539$			762.908i			1.41541i
$540$		0			0
$541$	−946.688			−1.74988			−0.874942	−	0.484227i	$-0.839101\pi$
$541$	−946.688			−1.74988			−0.874942	+	0.484227i	$0.839101\pi$
$542$	−131.999	+	112.399i	−0.243540	+	0.207379i
$543$			197.621i			0.363942i
$544$	329.021	+	811.298i	0.604818	+	1.49136i
$545$		0			0
$546$	9.75248	+	11.4531i	0.0178617	+	0.0209763i
$547$			50.3388i			0.0920271i	0.998941	+	0.0460136i	$0.0146517\pi$
$547$			50.3388i			0.0920271i	−0.998941	+	0.0460136i	$0.985348\pi$
$548$	−34.3006	+	212.483i	−0.0625923	+	0.387742i
$549$	−114.000			−0.207650
$550$		0			0
$551$			820.173i			1.48852i
$552$	−226.390	+	137.350i	−0.410128	+	0.248822i
$553$	−11.4070			−0.0206275
$554$	372.561	+	437.525i	0.672492	+	0.789757i
$555$		0			0
$556$	−53.8007	−	8.68492i	−0.0967638	−	0.0156204i
$557$	−790.157			−1.41859			−0.709297	−	0.704910i	$-0.750987\pi$
$557$	−790.157			−1.41859			−0.709297	+	0.704910i	$0.750987\pi$
$558$	−62.2386	+	52.9973i	−0.111539	+	0.0949773i
$559$			144.928i			0.259263i
$560$		0			0
$561$	748.495			1.33422
$562$	−291.222	−	342.004i	−0.518189	−	0.608548i
$563$			354.133i			0.629010i	0.949256	+	0.314505i	$0.101838\pi$
$563$			354.133i			0.629010i	−0.949256	+	0.314505i	$0.898162\pi$
$564$	61.4502	−	380.667i	0.108954	−	0.674941i
$565$		0			0
$566$	128.096	−	109.076i	0.226319	−	0.192714i
$567$		−	7.53528i		−	0.0132897i
$568$	−542.378	−	893.989i	−0.954891	−	1.57392i
$569$	−55.4983			−0.0975366			−0.0487683	−	0.998810i	$-0.515530\pi$
$569$	−55.4983			−0.0975366			−0.0487683	+	0.998810i	$0.515530\pi$
$570$		0			0
$571$		−	791.134i		−	1.38552i	−0.721167	−	0.692762i	$-0.756394\pi$
$571$		−	791.134i		−	1.38552i	0.721167	−	0.692762i	$-0.243606\pi$
$572$	−323.509	−	52.2233i	−0.565575	−	0.0912995i
$573$	241.433			0.421349
$574$	16.9551	−	14.4376i	0.0295386	−	0.0251526i
$575$		0			0
$576$	−88.6856	+	170.291i	−0.153968	+	0.295643i
$577$	−201.759			−0.349668			−0.174834	−	0.984598i	$-0.555939\pi$
$577$	−201.759			−0.349668			−0.174834	+	0.984598i	$0.555939\pi$
$578$	595.799	+	699.690i	1.03079	+	1.21054i
$579$		−	315.313i		−	0.544583i
$580$		0			0
$581$	49.4020			0.0850292
$582$	−445.260	+	379.146i	−0.765051	+	0.651454i
$583$		−	245.773i		−	0.421566i
$584$	−374.248	+	227.054i	−0.640835	+	0.388791i
$585$		0			0
$586$	−319.777	−	375.537i	−0.545694	−	0.640848i
$587$		−	444.556i		−	0.757335i	−0.925533	−	0.378668i	$-0.876382\pi$
$587$		−	444.556i		−	0.757335i	0.925533	−	0.378668i	$-0.123618\pi$
$588$	−330.349	−	53.3274i	−0.561818	−	0.0906929i
$589$	244.784			0.415593
$590$		0			0
$591$		−	446.915i		−	0.756202i
$592$	−236.309	−	78.3350i	−0.399171	−	0.132323i
$593$	563.908			0.950942			0.475471	−	0.879731i	$-0.342278\pi$
$593$	563.908			0.950942			0.475471	+	0.879731i	$0.342278\pi$
$594$	106.423	+	124.980i	0.179163	+	0.210404i
$595$		0			0
$596$	−21.4502	+	132.878i	−0.0359902	+	0.222949i
$597$	444.226			0.744097
$598$	150.927	−	128.517i	0.252386	−	0.214911i
$599$		−	845.034i		−	1.41074i	−0.708839	−	0.705371i	$-0.750781\pi$
$599$		−	845.034i		−	1.41074i	0.708839	−	0.705371i	$-0.249219\pi$
$600$		0			0
$601$	672.296			1.11863			0.559314	−	0.828956i	$-0.311065\pi$
$601$	672.296			1.11863			0.559314	+	0.828956i	$0.311065\pi$
$602$	30.3353	+	35.6250i	0.0503909	+	0.0591777i
$603$			276.604i			0.458714i
$604$	552.797	+	89.2368i	0.915227	+	0.147743i
$605$		0			0
$606$	−117.498	+	100.052i	−0.193892	+	0.165102i
$607$			882.664i			1.45414i	0.686562	+	0.727071i	$0.259119\pi$
$607$			882.664i			1.45414i	−0.686562	+	0.727071i	$0.740881\pi$
$608$	532.789	−	216.072i	0.876298	−	0.355381i
$609$	66.1993			0.108702
$610$		0			0
$611$			288.662i			0.472442i
$612$	−52.3200	+	324.108i	−0.0854902	+	0.529588i
$613$	−469.374			−0.765701			−0.382850	−	0.923810i	$-0.625057\pi$
$613$	−469.374			−0.765701			−0.382850	+	0.923810i	$0.625057\pi$
$614$	−176.350	+	150.166i	−0.287216	+	0.244569i
$615$		0			0
$616$	−90.4535	+	54.8777i	−0.146840	+	0.0890871i
$617$	−218.994			−0.354934			−0.177467	−	0.984127i	$-0.556790\pi$
$617$	−218.994			−0.354934			−0.177467	+	0.984127i	$0.556790\pi$
$618$	284.022	+	333.548i	0.459582	+	0.539721i
$619$		−	879.610i		−	1.42102i	−0.703689	−	0.710509i	$-0.748465\pi$
$619$		−	879.610i		−	1.42102i	0.703689	−	0.710509i	$-0.251535\pi$
$620$		0			0
$621$	−99.2990			−0.159902
$622$	310.284	−	264.213i	0.498849	−	0.424779i
$623$			33.3232i			0.0534884i
$624$	45.2267	−	136.433i	0.0724787	−	0.218643i
$625$		0			0
$626$	−128.447	−	150.845i	−0.205187	−	0.240966i
$627$		−	491.546i		−	0.783964i
$628$	13.5544	−	83.9656i	0.0215834	−	0.133703i
$629$	−425.691			−0.676774
$630$		0			0
$631$		−	635.566i		−	1.00724i	−0.863926	−	0.503618i	$-0.832002\pi$
$631$		−	635.566i		−	1.00724i	0.863926	−	0.503618i	$-0.167998\pi$
$632$	56.5351	+	93.1855i	0.0894543	+	0.147445i
$633$	−366.944			−0.579691
$634$	610.966	+	717.502i	0.963669	+	1.13171i
$635$		0			0
$636$	106.423	+	17.1796i	0.167331	+	0.0270119i
$637$	250.505			0.393258
$638$	−1097.98	+	934.951i	−1.72097	+	1.46544i
$639$		−	392.120i		−	0.613646i
$640$		0			0
$641$	−296.309			−0.462260			−0.231130	−	0.972923i	$-0.574242\pi$
$641$	−296.309			−0.462260			−0.231130	+	0.972923i	$0.574242\pi$
$642$	234.429	+	275.307i	0.365154	+	0.428827i
$643$			591.032i			0.919179i	0.888131	+	0.459590i	$0.152003\pi$
$643$			591.032i			0.919179i	−0.888131	+	0.459590i	$0.847997\pi$
$644$	10.1993	−	63.1821i	0.0158375	−	0.0981088i
$645$		0			0
$646$	748.495	−	637.357i	1.15866	−	0.986621i
$647$			166.507i			0.257352i	0.991687	+	0.128676i	$0.0410728\pi$
$647$			166.507i			0.257352i	−0.991687	+	0.128676i	$0.958927\pi$
$648$	−61.5569	+	37.3463i	−0.0949953	+	0.0576331i
$649$	−1384.67			−2.13355
$650$		0			0
$651$		−	19.7575i		−	0.0303494i
$652$	830.098	+	134.001i	1.27316	+	0.205523i
$653$	621.335			0.951509			0.475754	−	0.879578i	$-0.342175\pi$
$653$	621.335			0.951509			0.475754	+	0.879578i	$0.342175\pi$
$654$	−1.32310	+	1.12664i	−0.00202308	+	0.00172269i
$655$		0			0
$656$	−201.976	−	66.9538i	−0.307890	−	0.102064i
$657$	−164.152			−0.249851
$658$	60.4208	+	70.9565i	0.0918249	+	0.107837i
$659$		−	702.113i		−	1.06542i	−0.846297	−	0.532711i	$-0.821173\pi$
$659$		−	702.113i		−	1.06542i	0.846297	−	0.532711i	$-0.178827\pi$
$660$		0			0
$661$	358.193			0.541895			0.270948	−	0.962594i	$-0.412663\pi$
$661$	358.193			0.541895			0.270948	+	0.962594i	$0.412663\pi$
$662$	412.197	−	350.994i	0.622655	−	0.530202i
$663$		−	245.773i		−	0.370698i
$664$	−244.846	−	403.573i	−0.368743	−	0.607790i
$665$		0			0
$666$	−60.5257	−	71.0798i	−0.0908795	−	0.106726i
$667$		−	872.367i		−	1.30790i
$668$	−941.351	−	151.960i	−1.40921	−	0.227485i
$669$	−605.945			−0.905748
$670$		0			0
$671$			600.230i			0.894530i
$672$	−17.4400	−	43.0035i	−0.0259524	−	0.0639933i
$673$	714.176			1.06118			0.530592	−	0.847628i	$-0.321970\pi$
$673$	714.176			1.06118			0.530592	+	0.847628i	$0.321970\pi$
$674$	489.244	+	574.555i	0.725882	+	0.852456i
$675$		0			0
$676$	90.5827	−	561.134i	0.133998	−	0.830081i
$677$	509.833			0.753077			0.376538	−	0.926401i	$-0.377114\pi$
$677$	509.833			0.753077			0.376538	+	0.926401i	$0.377114\pi$
$678$	44.7986	−	38.1468i	0.0660747	−	0.0562638i
$679$		−	141.346i		−	0.208168i
$680$		0			0
$681$	−321.389			−0.471936
$682$	279.040	+	327.697i	0.409150	+	0.480494i
$683$		−	1263.93i		−	1.85055i	−0.379298	−	0.925275i	$-0.623834\pi$
$683$		−	1263.93i		−	1.85055i	0.379298	−	0.925275i	$-0.376166\pi$
$684$	212.846	+	34.3592i	0.311178	+	0.0502327i
$685$		0			0
$686$	124.048	−	105.629i	0.180828	−	0.153978i
$687$		−	457.083i		−	0.665332i
$688$	140.679	−	424.378i	0.204475	−	0.616829i
$689$	−80.7010			−0.117128
$690$		0			0
$691$		−	512.351i		−	0.741463i	−0.928740	−	0.370731i	$-0.879107\pi$
$691$		−	512.351i		−	0.741463i	0.928740	−	0.370731i	$-0.120893\pi$
$692$	1.48834	−	9.21987i	0.00215078	−	0.0133235i
$693$	−39.6746			−0.0572504
$694$	703.842	−	599.334i	1.01418	−	0.863594i
$695$		0			0
$696$	−328.096	−	540.793i	−0.471403	−	0.777002i
$697$	−363.843			−0.522012
$698$	−260.103	−	305.458i	−0.372640	−	0.437619i
$699$			101.287i			0.144902i
$700$		0			0
$701$	1092.03			1.55781			0.778907	−	0.627139i	$-0.215774\pi$
$701$	1092.03			1.55781			0.778907	+	0.627139i	$0.215774\pi$
$702$	41.0380	−	34.9446i	0.0584586	−	0.0497786i
$703$			279.556i			0.397662i
$704$	896.609	+	466.945i	1.27359	+	0.663274i
$705$		0			0
$706$	325.323	+	382.051i	0.460798	+	0.541148i
$707$		−	37.2995i		−	0.0527574i
$708$	96.7891	−	599.582i	0.136708	−	0.846867i
$709$	−416.887			−0.587993			−0.293997	−	0.955806i	$-0.594985\pi$
$709$	−416.887			−0.587993			−0.293997	+	0.955806i	$0.594985\pi$
$710$		0			0
$711$			40.8729i			0.0574864i
$712$	272.223	−	165.156i	0.382336	−	0.231961i
$713$	−260.362			−0.365163
$714$	−51.4435	−	60.4139i	−0.0720498	−	0.0846133i
$715$		0			0
$716$	896.609	+	144.738i	1.25225	+	0.202147i
$717$	196.305			0.273787
$718$	−328.304	+	279.556i	−0.457247	+	0.389354i
$719$		−	395.268i		−	0.549747i	−0.961480	−	0.274874i	$-0.911364\pi$
$719$		−	395.268i		−	0.549747i	0.961480	−	0.274874i	$-0.0886361\pi$
$720$		0			0
$721$	−105.884			−0.146857
$722$	49.5264	+	58.1625i	0.0685962	+	0.0805575i
$723$		−	134.743i		−	0.186367i
$724$	−72.7317	+	450.553i	−0.100458	+	0.622310i
$725$		0			0
$726$	338.909	−	288.587i	0.466817	−	0.397503i
$727$			597.583i			0.821985i	0.911639	+	0.410993i	$0.134818\pi$
$727$			597.583i			0.821985i	−0.911639	+	0.410993i	$0.865182\pi$
$728$	18.0194	+	29.7009i	0.0247519	+	0.0407980i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$		−	764.482i		−	1.04580i
$732$	−259.907	−	41.9562i	−0.355064	−	0.0573172i
$733$	−23.8650			−0.0325580			−0.0162790	−	0.999867i	$-0.505182\pi$
$733$	−23.8650			−0.0325580			−0.0162790	+	0.999867i	$0.505182\pi$
$734$	−102.120	+	86.9574i	−0.139129	+	0.118471i
$735$		0			0
$736$	−566.694	+	229.822i	−0.769965	+	0.312258i
$737$	1456.37			1.97608
$738$	−51.7320	−	60.7527i	−0.0700976	−	0.0823207i
$739$			125.767i			0.170186i	0.996373	+	0.0850928i	$0.0271187\pi$
$739$			125.767i			0.170186i	−0.996373	+	0.0850928i	$0.972881\pi$
$740$		0			0
$741$	−161.402			−0.217816
$742$	−19.8373	+	16.8918i	−0.0267349	+	0.0227652i
$743$		−	148.841i		−	0.200325i	−0.994971	−	0.100162i	$-0.968064\pi$
$743$		−	148.841i		−	0.200325i	0.994971	−	0.100162i	$-0.0319362\pi$
$744$	−161.402	+	97.9217i	−0.216938	+	0.131615i
$745$		0			0
$746$	735.715	+	864.004i	0.986213	+	1.15818i
$747$		−	177.014i		−	0.236967i
$748$	1706.48	+	275.474i	2.28140	+	0.368280i
$749$	−87.3954			−0.116683
$750$		0			0
$751$			463.390i			0.617030i	0.951219	+	0.308515i	$0.0998321\pi$
$751$			463.390i			0.617030i	−0.951219	+	0.308515i	$0.900168\pi$
$752$	280.199	−	845.261i	0.372605	−	1.12402i
$753$	183.989			0.244341
$754$	306.997	+	360.529i	0.407157	+	0.478155i
$755$		0			0
$756$	2.77326	−	17.1796i	0.00366834	−	0.0227243i
$757$	719.363			0.950281			0.475141	−	0.879910i	$-0.342397\pi$
$757$	719.363			0.950281			0.475141	+	0.879910i	$0.342397\pi$
$758$	365.910	−	311.579i	0.482731	−	0.411054i
$759$			522.826i			0.688836i
$760$		0			0
$761$	−1107.49			−1.45530			−0.727651	−	0.685947i	$-0.759388\pi$
$761$	−1107.49			−1.45530			−0.727651	+	0.685947i	$0.759388\pi$
$762$	18.9908	+	22.3023i	0.0249223	+	0.0292681i
$763$		−	0.420013i		−	0.000550476i
$764$	550.440	+	88.8563i	0.720472	+	0.116304i
$765$		0			0
$766$	−1020.34	+	868.835i	−1.33203	+	1.13425i
$767$			454.666i			0.592785i
$768$	−264.866	+	355.603i	−0.344878	+	0.463025i
$769$	231.691			0.301289			0.150644	−	0.988588i	$-0.451865\pi$
$769$	231.691			0.301289			0.150644	+	0.988588i	$0.451865\pi$
$770$		0			0
$771$		−	660.047i		−	0.856092i
$772$	116.047	−	718.879i	0.150320	−	0.931190i
$773$	519.956			0.672647			0.336324	−	0.941746i	$-0.390816\pi$
$773$	519.956			0.672647			0.336324	+	0.941746i	$0.390816\pi$
$774$	127.650	−	108.696i	0.164922	−	0.140434i
$775$		0			0
$776$	−1154.68	+	700.539i	−1.48799	+	0.902756i
$777$	22.5641			0.0290400
$778$	615.436	+	722.751i	0.791049	+	0.928986i
$779$			238.940i			0.306726i
$780$		0			0
$781$	−2064.58			−2.64351
$782$	−796.127	+	677.917i	−1.01807	+	0.866901i
$783$		−	237.202i		−	0.302940i
$784$	−733.531	−	243.161i	−0.935626	−	0.310154i
$785$		0			0
$786$	116.175	+	136.433i	0.147806	+	0.173579i
$787$			46.0288i			0.0584864i	0.999572	+	0.0292432i	$0.00930972\pi$
$787$			46.0288i			0.0584864i	−0.999572	+	0.0292432i	$0.990690\pi$
$788$	164.481	−	1018.92i	0.208733	−	1.29304i
$789$	19.9036			0.0252264
$790$		0			0
$791$			14.2212i			0.0179788i
$792$	196.635	+	324.108i	0.248276	+	0.409227i
$793$	197.089			0.248536
$794$	−647.619	−	760.546i	−0.815641	−	0.957867i
$795$		0			0
$796$	1012.78	+	163.491i	1.27234	+	0.205391i
$797$	−15.3098			−0.0192093			−0.00960463	−	0.999954i	$-0.503057\pi$
$797$	−15.3098			−0.0192093			−0.00960463	+	0.999954i	$0.503057\pi$
$798$	−39.6746	+	33.7836i	−0.0497175	+	0.0423353i
$799$		−	1522.67i		−	1.90572i
$800$		0			0
$801$	119.402			0.149066
$802$	446.944	+	524.879i	0.557287	+	0.654463i
$803$			864.288i			1.07632i
$804$	−101.801	+	630.627i	−0.126618	+	0.784362i
$805$		0			0
$806$	107.601	−	91.6245i	0.133500	−	0.113678i
$807$			135.017i			0.167307i
$808$	−304.706	+	184.863i	−0.377111	+	0.228791i
$809$	313.093			0.387012			0.193506	−	0.981099i	$-0.438014\pi$
$809$	313.093			0.387012			0.193506	+	0.981099i	$0.438014\pi$
$810$		0			0
$811$			1056.89i			1.30319i	0.758566	+	0.651596i	$0.225900\pi$
$811$			1056.89i			1.30319i	−0.758566	+	0.651596i	$0.774100\pi$
$812$	150.927	+	24.3638i	0.185871	+	0.0300047i
$813$	−150.143			−0.184678
$814$	−374.248	+	318.678i	−0.459764	+	0.391497i
$815$		0			0
$816$	−238.567	+	719.673i	−0.292362	+	0.881953i
$817$	−502.045			−0.614498
$818$	650.770	+	764.247i	0.795563	+	0.934288i
$819$			13.0274i			0.0159064i
$820$		0			0
$821$	308.659			0.375955			0.187978	−	0.982173i	$-0.439807\pi$
$821$	308.659			0.375955			0.187978	+	0.982173i	$0.439807\pi$
$822$	−141.917	+	120.845i	−0.172649	+	0.147014i
$823$		−	109.680i		−	0.133269i	−0.997777	−	0.0666344i	$-0.978774\pi$
$823$		−	109.680i		−	0.133269i	0.997777	−	0.0666344i	$-0.0212261\pi$
$824$	524.780	+	864.982i	0.636869	+	1.04974i
$825$		0			0
$826$	95.1677	+	111.762i	0.115215	+	0.135306i
$827$		−	711.971i		−	0.860908i	−0.902613	−	0.430454i	$-0.858354\pi$
$827$		−	711.971i		−	0.860908i	0.902613	−	0.430454i	$-0.141646\pi$
$828$	−226.390	−	36.5457i	−0.273418	−	0.0441373i
$829$	118.688			0.143170			0.0715849	−	0.997435i	$-0.477194\pi$
$829$	118.688			0.143170			0.0715849	+	0.997435i	$0.477194\pi$
$830$		0			0
$831$			497.667i			0.598877i
$832$	153.324	−	294.407i	0.184284	−	0.353854i
$833$	−1321.40			−1.58631
$834$	−30.5980	−	35.9335i	−0.0366883	−	0.0430857i
$835$		0			0
$836$	180.907	−	1120.67i	0.216396	−	1.34051i
$837$	−70.7939			−0.0845805
$838$	−332.519	+	283.146i	−0.396800	+	0.337883i
$839$			1413.67i			1.68495i	0.538736	+	0.842475i	$0.318902\pi$
$839$			1413.67i			1.68495i	−0.538736	+	0.842475i	$0.681098\pi$
$840$		0			0
$841$	1242.88			1.47786
$842$	365.260	+	428.952i	0.433800	+	0.509444i
$843$		−	389.015i		−	0.461465i
$844$	−836.591	−	135.049i	−0.991222	−	0.160011i
$845$		0			0
$846$	254.248	−	216.496i	0.300529	−	0.255906i
$847$			107.586i			0.127020i
$848$	236.309	+	78.3350i	0.278666	+	0.0923762i
$849$	145.704			0.171619
$850$		0			0
$851$		−	297.347i		−	0.349409i
$852$	144.315	−	893.989i	0.169383	−	1.04928i
$853$	1308.03			1.53344			0.766722	−	0.641979i	$-0.221886\pi$
$853$	1308.03			1.53344			0.766722	+	0.641979i	$0.221886\pi$
$854$	48.4469	−	41.2534i	0.0567293	−	0.0483060i
$855$		0			0
$856$	433.148	+	713.947i	0.506014	+	0.834050i
$857$	−719.755			−0.839854			−0.419927	−	0.907558i	$-0.637944\pi$
$857$	−719.755			−0.839854			−0.419927	+	0.907558i	$0.637944\pi$
$858$	−183.989	−	216.072i	−0.214440	−	0.251832i
$859$			1402.44i			1.63264i	0.577601	+	0.816319i	$0.303989\pi$
$859$			1402.44i			1.63264i	−0.577601	+	0.816319i	$0.696011\pi$
$860$		0			0
$861$	19.2858			0.0223993
$862$	671.650	−	571.922i	0.779176	−	0.663483i
$863$		−	72.4412i		−	0.0839411i	−0.999119	−	0.0419706i	$-0.986636\pi$
$863$		−	72.4412i		−	0.0839411i	0.999119	−	0.0419706i	$-0.0133636\pi$
$864$	−154.088	+	62.4900i	−0.178342	+	0.0723264i
$865$		0			0
$866$	−160.061	−	187.972i	−0.184828	−	0.217058i
$867$			795.869i			0.917957i
$868$	7.27148	−	45.0448i	0.00837728	−	0.0518949i
$869$	215.203			0.247644
$870$		0			0
$871$		−	478.208i		−	0.549033i
$872$	−3.43115	+	2.08166i	−0.00393481	+	0.00238723i
$873$	−506.464			−0.580142
$874$	445.196	+	522.826i	0.509378	+	0.598200i
$875$		0			0
$876$	−374.248	−	60.4139i	−0.427223	−	0.0689657i
$877$	1382.21			1.57606			0.788032	−	0.615635i	$-0.211100\pi$
$877$	1382.21			1.57606			0.788032	+	0.615635i	$0.211100\pi$
$878$	503.613	−	428.835i	0.573591	−	0.488423i
$879$		−	427.158i		−	0.485959i
$880$		0			0
$881$	−1131.38			−1.28419			−0.642097	−	0.766623i	$-0.721936\pi$
$881$	−1131.38			−1.28419			−0.642097	+	0.766623i	$0.721936\pi$
$882$	−187.879	−	220.640i	−0.213015	−	0.250159i
$883$			1077.39i			1.22014i	0.792346	+	0.610072i	$0.208860\pi$
$883$			1077.39i			1.22014i	−0.792346	+	0.610072i	$0.791140\pi$
$884$	90.4535	−	560.334i	0.102323	−	0.633862i
$885$		0			0
$886$	−235.952	+	200.917i	−0.266311	+	0.226769i
$887$		−	766.896i		−	0.864595i	−0.901731	−	0.432297i	$-0.857703\pi$
$887$		−	766.896i		−	0.864595i	0.901731	−	0.432297i	$-0.142297\pi$
$888$	−111.832	−	184.330i	−0.125937	−	0.207578i
$889$	−7.07980			−0.00796378
$890$		0			0
$891$			142.160i			0.159551i
$892$	−1381.49	−	223.010i	−1.54875	−	0.250011i
$893$	−999.954			−1.11977
$894$	−88.7492	+	75.5715i	−0.0992720	+	0.0845319i
$895$		0			0
$896$	−23.9344	−	104.462i	−0.0267124	−	0.116587i
$897$	171.673			0.191386
$898$	124.344	+	146.026i	0.138467	+	0.162612i
$899$		−	621.942i		−	0.691815i
$900$		0			0
$901$	425.691			0.472465
$902$	−319.873	+	272.378i	−0.354627	+	0.301971i
$903$			40.5220i			0.0448748i
$904$	116.175	−	70.4829i	0.128512	−	0.0779678i
$905$		0			0
$906$	314.392	+	369.214i	0.347011	+	0.407521i
$907$			1086.43i			1.19783i	0.800814	+	0.598913i	$0.204400\pi$
$907$			1086.43i			1.19783i	−0.800814	+	0.598913i	$0.795600\pi$
$908$	−732.730	−	118.283i	−0.806971	−	0.130268i
$909$	−133.650			−0.147029
$910$		0			0
$911$		−	237.746i		−	0.260973i	−0.991450	−	0.130486i	$-0.958346\pi$
$911$		−	237.746i		−	0.260973i	0.991450	−	0.130486i	$-0.0416539\pi$
$912$	472.618	+	156.670i	0.518222	+	0.171787i
$913$	−932.012			−1.02082
$914$	−629.801	−	739.621i	−0.689060	−	0.809214i
$915$		0			0
$916$	168.223	−	1042.10i	0.183650	−	1.13766i
$917$	−43.3103			−0.0472304
$918$	−216.472	+	184.330i	−0.235808	+	0.200795i
$919$			344.517i			0.374882i	0.982276	+	0.187441i	$0.0600194\pi$
$919$			344.517i			0.374882i	−0.982276	+	0.187441i	$0.939981\pi$
$920$		0			0
$921$	−200.591			−0.217797
$922$	458.555	+	538.515i	0.497349	+	0.584073i
$923$			677.917i			0.734471i
$924$	−90.4535	−	14.6017i	−0.0978934	−	0.0158027i
$925$		0			0
$926$	−642.169	+	546.818i	−0.693487	+	0.590516i
$927$			379.397i			0.409274i
$928$	−548.991	−	1353.70i	−0.591585	−	1.45873i
$929$	−1478.10			−1.59106			−0.795531	−	0.605913i	$-0.792808\pi$
$929$	−1478.10			−1.59106			−0.795531	+	0.605913i	$0.792808\pi$
$930$		0			0
$931$			867.776i			0.932090i
$932$	−37.2773	+	230.922i	−0.0399971	+	0.247771i
$933$	352.935			0.378280
$934$	976.035	−	831.111i	1.04501	−	0.889841i
$935$		0			0
$936$	106.423	−	64.5661i	0.113700	−	0.0689809i
$937$	−246.887			−0.263486			−0.131743	−	0.991284i	$-0.542057\pi$
$937$	−246.887			−0.263486			−0.131743	+	0.991284i	$0.542057\pi$
$938$	−100.095	−	117.549i	−0.106711	−	0.125319i
$939$		−	171.579i		−	0.182726i
$940$		0			0
$941$	1658.64			1.76264			0.881318	−	0.472525i	$-0.156657\pi$
$941$	1658.64			1.76264			0.881318	+	0.472525i	$0.156657\pi$
$942$	56.0807	−	47.7537i	0.0595336	−	0.0506940i
$943$		−	254.145i		−	0.269507i
$944$	441.336	−	1331.36i	0.467517	−	1.41033i
$945$		0			0
$946$	−572.302	−	672.097i	−0.604971	−	0.710462i
$947$		−	6.00750i		−	0.00634372i	−0.999995	−	0.00317186i	$-0.998990\pi$
$947$		−	6.00750i		−	0.00634372i	0.999995	−	0.00317186i	$-0.00100964\pi$
$948$	−15.0427	+	93.1855i	−0.0158678	+	0.0982969i
$949$	283.794			0.299045
$950$		0			0
$951$			816.129i			0.858180i
$952$	−95.0509	−	156.670i	−0.0998434	−	0.164569i
$953$	1089.55			1.14329			0.571643	−	0.820503i	$-0.306306\pi$
$953$	1089.55			1.14329			0.571643	+	0.820503i	$0.306306\pi$
$954$	60.5257	+	71.0798i	0.0634442	+	0.0745072i
$955$		0			0
$956$	447.553	+	72.2475i	0.468152	+	0.0755727i
$957$	−1248.91			−1.30502
$958$	−336.734	+	286.735i	−0.351497	+	0.299306i
$959$		−	45.0512i		−	0.0469773i
$960$		0			0
$961$	775.379			0.806846
$962$	104.640	+	122.886i	0.108773	+	0.127741i
$963$			313.150i			0.325182i
$964$	49.5905	−	307.199i	0.0514424	−	0.318671i
$965$		0			0
$966$	42.1993	−	35.9335i	0.0436846	−	0.0371982i
$967$		−	1699.27i		−	1.75726i	−0.477502	−	0.878630i	$-0.658458\pi$
$967$		−	1699.27i		−	1.75726i	0.477502	−	0.878630i	$-0.341542\pi$
$968$	878.885	−	533.215i	0.907939	−	0.550842i
$969$	851.382			0.878619
$970$		0			0
$971$		−	197.851i		−	0.203760i	−0.994797	−	0.101880i	$-0.967514\pi$
$971$		−	197.851i		−	0.203760i	0.994797	−	0.101880i	$-0.0324857\pi$
$972$	−61.5569	−	9.93700i	−0.0633302	−	0.0102232i
$973$	11.4070			0.0117235
$974$	−1355.16	+	1153.94i	−1.39133	+	1.18475i
$975$		0			0
$976$	−577.117	−	191.311i	−0.591309	−	0.196015i
$977$	−847.868			−0.867828			−0.433914	−	0.900954i	$-0.642868\pi$
$977$	−847.868			−0.867828			−0.433914	+	0.900954i	$0.642868\pi$
$978$	472.101	+	554.423i	0.482721	+	0.566895i
$979$		−	628.672i		−	0.642157i
$980$		0			0
$981$	−1.50497			−0.00153412
$982$	−841.835	+	716.837i	−0.857266	+	0.729977i
$983$			96.0512i			0.0977123i	0.998806	+	0.0488562i	$0.0155576\pi$
$983$			96.0512i			0.0977123i	−0.998806	+	0.0488562i	$0.984442\pi$
$984$	−95.5839	−	157.549i	−0.0971381	−	0.160110i
$985$		0			0
$986$	−1619.38	−	1901.76i	−1.64238	−	1.92876i
$987$			80.7101i			0.0817732i
$988$	−367.978	−	59.4019i	−0.372448	−	0.0601234i
$989$	533.993			0.539933
$990$		0			0
$991$		−	1184.45i		−	1.19520i	−0.801793	−	0.597602i	$-0.796120\pi$
$991$		−	1184.45i		−	1.19520i	0.801793	−	0.597602i	$-0.203880\pi$
$992$	−404.017	+	163.849i	−0.407275	+	0.165170i
$993$	468.858			0.472163
$994$	141.897	+	166.640i	0.142754	+	0.167646i
$995$		0			0
$996$	65.1478	−	403.573i	0.0654095	−	0.405194i
$997$	−1887.35			−1.89303			−0.946517	−	0.322655i	$-0.895425\pi$
$997$	−1887.35			−1.89303			−0.946517	+	0.322655i	$0.895425\pi$
$998$	−812.079	+	691.500i	−0.813706	+	0.692886i
$999$		−	80.8504i		−	0.0809313i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.3.c.f.151.6		8
3.2	odd	2		900.3.c.r.451.3		8
4.3	odd	2	inner	300.3.c.f.151.5		8
5.2	odd	4		60.3.f.b.19.2	yes	8
5.3	odd	4		60.3.f.b.19.7	yes	8
5.4	even	2	inner	300.3.c.f.151.3		8
12.11	even	2		900.3.c.r.451.4		8
15.2	even	4		180.3.f.h.19.7		8
15.8	even	4		180.3.f.h.19.2		8
15.14	odd	2		900.3.c.r.451.6		8
20.3	even	4		60.3.f.b.19.1	✓	8
20.7	even	4		60.3.f.b.19.8	yes	8
20.19	odd	2	inner	300.3.c.f.151.4		8
40.3	even	4		960.3.j.e.319.2		8
40.13	odd	4		960.3.j.e.319.6		8
40.27	even	4		960.3.j.e.319.5		8
40.37	odd	4		960.3.j.e.319.1		8
60.23	odd	4		180.3.f.h.19.8		8
60.47	odd	4		180.3.f.h.19.1		8
60.59	even	2		900.3.c.r.451.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.f.b.19.1	✓	8	20.3	even	4
60.3.f.b.19.2	yes	8	5.2	odd	4
60.3.f.b.19.7	yes	8	5.3	odd	4
60.3.f.b.19.8	yes	8	20.7	even	4
180.3.f.h.19.1		8	60.47	odd	4
180.3.f.h.19.2		8	15.8	even	4
180.3.f.h.19.7		8	15.2	even	4
180.3.f.h.19.8		8	60.23	odd	4
300.3.c.f.151.3		8	5.4	even	2	inner
300.3.c.f.151.4		8	20.19	odd	2	inner
300.3.c.f.151.5		8	4.3	odd	2	inner
300.3.c.f.151.6		8	1.1	even	1	trivial
900.3.c.r.451.3		8	3.2	odd	2
900.3.c.r.451.4		8	12.11	even	2
900.3.c.r.451.5		8	60.59	even	2
900.3.c.r.451.6		8	15.14	odd	2
960.3.j.e.319.1		8	40.37	odd	4
960.3.j.e.319.2		8	40.3	even	4
960.3.j.e.319.5		8	40.27	even	4
960.3.j.e.319.6		8	40.13	odd	4

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	300.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29664 + 1.52274i) q^{2} +1.73205i q^{3} +(-0.637459 + 3.94888i) q^{4} +(-2.63746 + 2.24584i) q^{6} -0.837253i q^{7} +(-6.83966 + 4.14959i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(1.29664 + 1.52274i) q^{2} +1.73205i q^{3} +(-0.637459 + 3.94888i) q^{4} +(-2.63746 + 2.24584i) q^{6} -0.837253i q^{7} +(-6.83966 + 4.14959i) q^{8} -3.00000 q^{9} +15.7955i q^{11} +(-6.83966 - 1.10411i) q^{12} +5.18655 q^{13} +(1.27492 - 1.08561i) q^{14} +(-15.1873 - 5.03449i) q^{16} -27.3586 q^{17} +(-3.88991 - 4.56821i) q^{18} +17.9667i q^{19} +1.45017 q^{21} +(-24.0524 + 20.4811i) q^{22} -19.1101i q^{23} +(-7.18729 - 11.8466i) q^{24} +(6.72508 + 7.89776i) q^{26} -5.19615i q^{27} +(3.30621 + 0.533714i) q^{28} +45.6495 q^{29} -13.6243i q^{31} +(-12.0262 - 29.6542i) q^{32} -27.3586 q^{33} +(-35.4743 - 41.6600i) q^{34} +(1.91238 - 11.8466i) q^{36} +15.5597 q^{37} +(-27.3586 + 23.2964i) q^{38} +8.98337i q^{39} +13.2990 q^{41} +(1.88034 + 2.20822i) q^{42} +27.9430i q^{43} +(-62.3746 - 10.0690i) q^{44} +(29.0997 - 24.7789i) q^{46} +55.6558i q^{47} +(8.72000 - 26.3052i) q^{48} +48.2990 q^{49} -47.3865i q^{51} +(-3.30621 + 20.4811i) q^{52} -15.5597 q^{53} +(7.91238 - 6.73753i) q^{54} +(3.47425 + 5.72653i) q^{56} -31.1193 q^{57} +(59.1909 + 69.5122i) q^{58} +87.6625i q^{59} +38.0000 q^{61} +(20.7462 - 17.6658i) q^{62} +2.51176i q^{63} +(29.5619 - 56.7635i) q^{64} +(-35.4743 - 41.6600i) q^{66} -92.2015i q^{67} +(17.4400 - 108.036i) q^{68} +33.0997 q^{69} +130.707i q^{71} +(20.5190 - 12.4488i) q^{72} +54.7173 q^{73} +(20.1752 + 23.6933i) q^{74} +(-70.9485 - 11.4531i) q^{76} +13.2249 q^{77} +(-13.6793 + 11.6482i) q^{78} -13.6243i q^{79} +9.00000 q^{81} +(17.2440 + 20.2509i) q^{82} +59.0048i q^{83} +(-0.924421 + 5.72653i) q^{84} +(-42.5498 + 36.2319i) q^{86} +79.0673i q^{87} +(-65.5448 - 108.036i) q^{88} -39.8007 q^{89} -4.34246i q^{91} +(75.4635 + 12.1819i) q^{92} +23.5980 q^{93} +(-84.7492 + 72.1654i) q^{94} +(51.3625 - 20.8300i) q^{96} +168.821 q^{97} +(62.6263 + 73.5467i) q^{98} -47.3865i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{4} - 6 q^{6} - 24 q^{9}+O(q^{10}) \) 8 * q + 10 * q^4 - 6 * q^6 - 24 * q^9	\( 8 q + 10 q^{4} - 6 q^{6} - 24 q^{9} - 20 q^{14} - 46 q^{16} + 72 q^{21} + 18 q^{24} + 84 q^{26} + 184 q^{29} - 12 q^{34} - 30 q^{36} - 256 q^{41} - 348 q^{44} + 112 q^{46} + 24 q^{49} + 18 q^{54} - 244 q^{56} + 304 q^{61} + 10 q^{64} - 12 q^{66} + 144 q^{69} + 252 q^{74} - 24 q^{76} + 72 q^{81} + 204 q^{84} - 280 q^{86} - 560 q^{89} - 376 q^{94} + 426 q^{96}+O(q^{100}) \) 8 * q + 10 * q^4 - 6 * q^6 - 24 * q^9 - 20 * q^14 - 46 * q^16 + 72 * q^21 + 18 * q^24 + 84 * q^26 + 184 * q^29 - 12 * q^34 - 30 * q^36 - 256 * q^41 - 348 * q^44 + 112 * q^46 + 24 * q^49 + 18 * q^54 - 244 * q^56 + 304 * q^61 + 10 * q^64 - 12 * q^66 + 144 * q^69 + 252 * q^74 - 24 * q^76 + 72 * q^81 + 204 * q^84 - 280 * q^86 - 560 * q^89 - 376 * q^94 + 426 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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