LMFDB - Embedded newform 300.3.c.f.151.3

Newspace parameters

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

Self dual:	no
Analytic conductor:	$8.17440793081$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.6080256576.2
Defining polynomial:	$x^{8} - 3 x^{7} + 7 x^{6} - 12 x^{5} + 12 x^{4} - 48 x^{3} + 112 x^{2} - 192 x + 256$
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			151.3
Root			$0.670410 + 1.88429i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.3.c.f.151.4

$q$-expansion

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

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	$0.0190475\pi$
$7$			0.837253i			0.119608i	−0.998210	+	0.0598038i	$0.980952\pi$
$8$	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	$-0.563926\pi$
$13$	−5.18655			−0.398966			−0.199483	+	0.979901i	$0.563926\pi$
$14$	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	$-0.202344\pi$
$17$	27.3586			1.60933			0.804666	+	0.593728i	$0.202344\pi$
$18$	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	$0.136371\pi$
$23$			19.1101i			0.830874i	−0.909622	+	0.415437i	$0.863629\pi$
$24$	−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	$-0.567433\pi$
$37$	−15.5597			−0.420531			−0.210266	+	0.977644i	$0.567433\pi$
$38$	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	$-0.894663\pi$
$43$		−	27.9430i		−	0.649837i	0.945742	−	0.324918i	$-0.105337\pi$
$44$	−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	$-0.798306\pi$
$47$		−	55.6558i		−	1.18417i	0.805877	−	0.592083i	$-0.201694\pi$
$48$	−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	$-0.453106\pi$
$53$	15.5597			0.293578			0.146789	+	0.989168i	$0.453106\pi$
$54$	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	$0.241542\pi$
$67$			92.2015i			1.37614i	−0.725643	+	0.688071i	$0.758458\pi$
$68$	−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	$-0.622280\pi$
$73$	−54.7173			−0.749552			−0.374776	+	0.927115i	$0.622280\pi$
$74$	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	$-0.884327\pi$
$83$		−	59.0048i		−	0.710901i	0.934695	−	0.355451i	$-0.115673\pi$
$84$	−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	$-0.836019\pi$
$97$	−168.821			−1.74043			−0.870214	+	0.492675i	$0.836019\pi$
$98$	−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	$0.210405\pi$
$103$			126.466i			1.22782i	−0.789375	+	0.613911i	$0.789595\pi$
$104$	−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	$0.162191\pi$
$107$			104.383i			0.975546i	−0.872971	+	0.487773i	$0.837809\pi$
$108$	−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	$-0.476054\pi$
$113$	16.9855			0.150314			0.0751572	+	0.997172i	$0.476054\pi$
$114$	−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	$0.0105989\pi$
$127$			8.45598i			0.0665825i	−0.999446	+	0.0332913i	$0.989401\pi$
$128$	−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	$-0.562919\pi$
$137$	−53.8083			−0.392762			−0.196381	+	0.980528i	$0.562919\pi$
$138$	−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	$-0.478428\pi$
$157$	21.2631			0.135434			0.0677170	+	0.997705i	$0.478428\pi$
$158$	−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	$0.223067\pi$
$163$			210.211i			1.28964i	−0.764335	+	0.644819i	$0.776933\pi$
$164$	−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	$-0.747006\pi$
$167$		−	238.384i		−	1.42745i	0.700426	−	0.713725i	$-0.252994\pi$
$168$	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	$-0.497852\pi$
$173$	2.33481			0.0134960			0.00674800	+	0.999977i	$0.497852\pi$
$174$	−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	$-0.343669\pi$
$193$	182.046			0.943245			0.471623	+	0.881801i	$0.343669\pi$
$194$	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	$-0.272715\pi$
$197$	258.027			1.30978			0.654890	+	0.755724i	$0.272715\pi$
$198$	−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	$-0.712971\pi$
$223$		−	349.843i		−	1.56880i	0.620255	−	0.784401i	$-0.287029\pi$
$224$	−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	$-0.865979\pi$
$227$		−	185.554i		−	0.817418i	0.912665	−	0.408709i	$-0.134021\pi$
$228$	−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	$-0.540050\pi$
$233$	−58.4780			−0.250978			−0.125489	+	0.992095i	$0.540050\pi$
$234$	−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	$-0.234164\pi$
$257$	381.078			1.48279			0.741397	+	0.671067i	$0.234164\pi$
$258$	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	$0.00695458\pi$
$263$			11.4914i			0.0436934i	−0.999761	+	0.0218467i	$0.993045\pi$
$264$	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	$-0.673563\pi$
$277$	−287.328			−1.03729			−0.518643	+	0.854991i	$0.673563\pi$
$278$	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	$0.0474851\pi$
$283$			84.1224i			0.297252i	−0.988893	+	0.148626i	$0.952515\pi$
$284$	−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	$-0.361731\pi$
$293$	246.620			0.841706			0.420853	+	0.907129i	$0.361731\pi$
$294$	−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	$-0.939599\pi$
$307$		−	115.811i		−	0.377236i	0.982051	−	0.188618i	$-0.0604008\pi$
$308$	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	$-0.449416\pi$
$313$	99.0614			0.316490			0.158245	+	0.987400i	$0.449416\pi$
$314$	−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	$-0.766696\pi$
$317$	−471.192			−1.48641			−0.743206	+	0.669063i	$0.766696\pi$
$318$	−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	$-0.689129\pi$
$337$	−377.317			−1.11964			−0.559818	+	0.828615i	$0.689129\pi$
$338$	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	$0.232006\pi$
$347$			462.222i			1.33205i	−0.745929	+	0.666025i	$0.767994\pi$
$348$	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	$-0.615648\pi$
$353$	−250.897			−0.710757			−0.355379	+	0.934722i	$0.615648\pi$
$354$	−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	$-0.970876\pi$
$367$		−	67.0637i		−	0.182735i	0.995817	−	0.0913675i	$-0.0291238\pi$
$368$	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	$-0.775091\pi$
$373$	−567.402			−1.52119			−0.760593	+	0.649230i	$0.775091\pi$
$374$	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	$-0.661018\pi$
$383$		−	670.068i		−	1.74952i	0.484553	−	0.874762i	$-0.338982\pi$
$384$	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	$-0.283447\pi$
$397$	499.460			1.25809			0.629043	+	0.777371i	$0.283447\pi$
$398$	−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	$-0.454472\pi$
$433$	123.443			0.285089			0.142544	+	0.989788i	$0.454472\pi$
$434$	−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	$-0.944043\pi$
$443$		−	154.952i		−	0.349780i	0.984588	−	0.174890i	$-0.0559569\pi$
$444$	−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	$-0.321659\pi$
$457$	485.718			1.06284			0.531420	+	0.847108i	$0.321659\pi$
$458$	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	$-0.849489\pi$
$463$		−	421.720i		−	0.910842i	0.890276	−	0.455421i	$-0.150511\pi$
$464$	−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	$0.240752\pi$
$467$			640.974i			1.37254i	−0.727349	+	0.686268i	$0.759248\pi$
$468$	−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	$-0.633208\pi$
$487$		−	889.949i		−	1.82741i	0.406377	−	0.913705i	$-0.366792\pi$
$488$	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	$0.193633\pi$
$503$			574.914i			1.14297i	−0.820612	+	0.571485i	$0.806367\pi$
$504$	−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	$0.0425931\pi$
$523$			139.548i			0.266822i	−0.991061	+	0.133411i	$0.957407\pi$
$524$	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	$-0.985348\pi$
$547$		−	50.3388i		−	0.0920271i	0.998941	−	0.0460136i	$-0.0146517\pi$
$548$	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	$-0.249013\pi$
$557$	790.157			1.41859			0.709297	+	0.704910i	$0.249013\pi$
$558$	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	$-0.898162\pi$
$563$		−	354.133i		−	0.629010i	0.949256	−	0.314505i	$-0.101838\pi$
$564$	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	$-0.444061\pi$
$577$	201.759			0.349668			0.174834	+	0.984598i	$0.444061\pi$
$578$	−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	$0.123618\pi$
$587$			444.556i			0.757335i	−0.925533	+	0.378668i	$0.876382\pi$
$588$	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	$-0.657722\pi$
$593$	−563.908			−0.950942			−0.475471	+	0.879731i	$0.657722\pi$
$594$	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	$-0.740881\pi$
$607$		−	882.664i		−	1.45414i	0.686562	−	0.727071i	$-0.259119\pi$
$608$	−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	$-0.374943\pi$
$613$	469.374			0.765701			0.382850	+	0.923810i	$0.374943\pi$
$614$	−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	$-0.443210\pi$
$617$	218.994			0.354934			0.177467	+	0.984127i	$0.443210\pi$
$618$	−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	$-0.847997\pi$
$643$		−	591.032i		−	0.919179i	0.888131	−	0.459590i	$-0.152003\pi$
$644$	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	$-0.958927\pi$
$647$		−	166.507i		−	0.257352i	0.991687	−	0.128676i	$-0.0410728\pi$
$648$	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	$-0.657825\pi$
$653$	−621.335			−0.951509			−0.475754	+	0.879578i	$0.657825\pi$
$654$	−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	$-0.678030\pi$
$673$	−714.176			−1.06118			−0.530592	+	0.847628i	$0.678030\pi$
$674$	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	$-0.622886\pi$
$677$	−509.833			−0.753077			−0.376538	+	0.926401i	$0.622886\pi$
$678$	−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	$0.376166\pi$
$683$			1263.93i			1.85055i	−0.379298	+	0.925275i	$0.623834\pi$
$684$	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	$-0.865182\pi$
$727$		−	597.583i		−	0.821985i	0.911639	−	0.410993i	$-0.134818\pi$
$728$	−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	$-0.494818\pi$
$733$	23.8650			0.0325580			0.0162790	+	0.999867i	$0.494818\pi$
$734$	−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	$0.0319362\pi$
$743$			148.841i			0.200325i	−0.994971	+	0.100162i	$0.968064\pi$
$744$	−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	$-0.657603\pi$
$757$	−719.363			−0.950281			−0.475141	+	0.879910i	$0.657603\pi$
$758$	−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	$-0.609184\pi$
$773$	−519.956			−0.672647			−0.336324	+	0.941746i	$0.609184\pi$
$774$	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

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)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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