LMFDB - Embedded newform 300.3.f.b.199.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,3,Mod(199,300)]

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, 1]))

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

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

chi := DirichletCharacter("300.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	300.f (of order $2$, degree $1$, not 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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 5x^{14} + 12x^{12} + 25x^{10} + 53x^{8} + 100x^{6} + 192x^{4} + 320x^{2} + 256 $ x^16 + 5x^14 + 12x^12 + 25x^10 + 53x^8 + 100x^6 + 192x^4 + 320*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{24} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.9
Root			$0.957636 - 1.04064i$ of defining polynomial
Character	$\chi$	$=$	300.199
Dual form			300.3.f.b.199.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.169449 - 1.99281i) q^{2} -1.73205 q^{3} +(-3.94257 - 0.675358i) q^{4} +(-0.293494 + 3.45165i) q^{6} +12.3959 q^{7} +(-2.01392 + 7.74236i) q^{8} +3.00000 q^{9} -11.0403i q^{11} +(6.82874 + 1.16975i) q^{12} -2.82009i q^{13} +(2.10047 - 24.7027i) q^{14} +(15.0878 + 5.32529i) q^{16} +6.52606i q^{17} +(0.508346 - 5.97843i) q^{18} -27.9928i q^{19} -21.4703 q^{21} +(-22.0012 - 1.87077i) q^{22} +7.90421 q^{23} +(3.48822 - 13.4102i) q^{24} +(-5.61989 - 0.477860i) q^{26} -5.19615 q^{27} +(-48.8718 - 8.37167i) q^{28} -50.7169 q^{29} -36.3467i q^{31} +(13.1689 - 29.1647i) q^{32} +19.1224i q^{33} +(13.0052 + 1.10583i) q^{34} +(-11.8277 - 2.02607i) q^{36} -18.9279i q^{37} +(-55.7842 - 4.74333i) q^{38} +4.88453i q^{39} +5.30410 q^{41} +(-3.63812 + 42.7863i) q^{42} +45.5870 q^{43} +(-7.45616 + 43.5273i) q^{44} +(1.33936 - 15.7516i) q^{46} +11.7246 q^{47} +(-26.1328 - 9.22368i) q^{48} +104.658 q^{49} -11.3035i q^{51} +(-1.90457 + 11.1184i) q^{52} -41.1680i q^{53} +(-0.880481 + 10.3549i) q^{54} +(-24.9644 + 95.9735i) q^{56} +48.4849i q^{57} +(-8.59391 + 101.069i) q^{58} +10.7008i q^{59} +56.1297 q^{61} +(-72.4319 - 6.15889i) q^{62} +37.1877 q^{63} +(-55.8882 - 31.1850i) q^{64} +(38.1073 + 3.24026i) q^{66} -16.1709 q^{67} +(4.40743 - 25.7295i) q^{68} -13.6905 q^{69} -66.1617i q^{71} +(-6.04177 + 23.2271i) q^{72} -15.6330i q^{73} +(-37.7198 - 3.20731i) q^{74} +(-18.9051 + 110.363i) q^{76} -136.855i q^{77} +(9.73394 + 0.827677i) q^{78} +123.057i q^{79} +9.00000 q^{81} +(0.898773 - 10.5701i) q^{82} +99.6700 q^{83} +(84.6484 + 14.5002i) q^{84} +(7.72465 - 90.8461i) q^{86} +87.8443 q^{87} +(85.4781 + 22.2343i) q^{88} -101.083 q^{89} -34.9575i q^{91} +(-31.1629 - 5.33817i) q^{92} +62.9543i q^{93} +(1.98672 - 23.3649i) q^{94} +(-22.8092 + 50.5148i) q^{96} +127.293i q^{97} +(17.7342 - 208.564i) q^{98} -33.1209i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 20 q^{4} - 12 q^{6} + 48 q^{9} + 40 q^{14} + 68 q^{16} - 96 q^{21} - 36 q^{24} - 72 q^{26} - 128 q^{29} + 184 q^{34} - 60 q^{36} - 32 q^{41} - 344 q^{44} + 304 q^{46} + 112 q^{49} - 36 q^{54} + 232 q^{56}+ \cdots - 348 q^{96}+O(q^{100}) $ 16 * q - 20 * q^4 - 12 * q^6 + 48 * q^9 + 40 * q^14 + 68 * q^16 - 96 * q^21 - 36 * q^24 - 72 * q^26 - 128 * q^29 + 184 * q^34 - 60 * q^36 - 32 * q^41 - 344 * q^44 + 304 * q^46 + 112 * q^49 - 36 * q^54 + 232 * q^56 - 352 * q^61 + 220 * q^64 + 216 * q^66 + 192 * q^69 - 264 * q^74 - 48 * q^76 + 144 * q^81 + 72 * q^84 - 400 * q^86 - 160 * q^89 + 192 * q^94 - 348 * q^96

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 $

$2$	0.169449	−	1.99281i	0.0847243	−	0.996404i
$2$	0.169449	−	1.99281i	0.0847243	−	0.996404i
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−3.94257	−	0.675358i	−0.985644	−	0.168839i
$5$		0			0
$5$		0			0
$6$	−0.293494	+	3.45165i	−0.0489156	+	0.575274i
$7$	12.3959			1.77084			0.885422	−	0.464789i	$-0.153870\pi$
$7$	12.3959			1.77084			0.885422	+	0.464789i	$0.153870\pi$
$8$	−2.01392	+	7.74236i	−0.251740	+	0.967795i
$9$	3.00000			0.333333
$10$		0			0
$11$		−	11.0403i		−	1.00366i	−0.864965	−	0.501832i	$-0.832659\pi$
$11$		−	11.0403i		−	1.00366i	0.864965	−	0.501832i	$-0.167341\pi$
$12$	6.82874	+	1.16975i	0.569062	+	0.0974795i
$13$		−	2.82009i		−	0.216930i	−0.994100	−	0.108465i	$-0.965407\pi$
$13$		−	2.82009i		−	0.216930i	0.994100	−	0.108465i	$-0.0345935\pi$
$14$	2.10047	−	24.7027i	0.150034	−	1.76448i
$15$		0			0
$16$	15.0878	+	5.32529i	0.942987	+	0.332831i
$17$			6.52606i			0.383886i	0.981406	+	0.191943i	$0.0614789\pi$
$17$			6.52606i			0.383886i	−0.981406	+	0.191943i	$0.938521\pi$
$18$	0.508346	−	5.97843i	0.0282414	−	0.332135i
$19$		−	27.9928i		−	1.47330i	−0.676273	−	0.736651i	$-0.736406\pi$
$19$		−	27.9928i		−	1.47330i	0.676273	−	0.736651i	$-0.263594\pi$
$20$		0			0
$21$	−21.4703			−1.02240
$22$	−22.0012	−	1.87077i	−1.00006	−	0.0850348i
$23$	7.90421			0.343661			0.171831	−	0.985126i	$-0.445032\pi$
$23$	7.90421			0.343661			0.171831	+	0.985126i	$0.445032\pi$
$24$	3.48822	−	13.4102i	0.145342	−	0.558757i
$25$		0			0
$26$	−5.61989	−	0.477860i	−0.216150	−	0.0183792i
$27$	−5.19615			−0.192450
$28$	−48.8718	−	8.37167i	−1.74542	−	0.298988i
$29$	−50.7169			−1.74886			−0.874429	−	0.485153i	$-0.838764\pi$
$29$	−50.7169			−1.74886			−0.874429	+	0.485153i	$0.838764\pi$
$30$		0			0
$31$		−	36.3467i		−	1.17247i	−0.810140	−	0.586236i	$-0.800609\pi$
$31$		−	36.3467i		−	1.17247i	0.810140	−	0.586236i	$-0.199391\pi$
$32$	13.1689	−	29.1647i	0.411528	−	0.911397i
$33$			19.1224i			0.579466i
$34$	13.0052	+	1.10583i	0.382506	+	0.0325245i
$35$		0			0
$36$	−11.8277	−	2.02607i	−0.328548	−	0.0562798i
$37$		−	18.9279i		−	0.511566i	−0.966734	−	0.255783i	$-0.917667\pi$
$37$		−	18.9279i		−	0.511566i	0.966734	−	0.255783i	$-0.0823332\pi$
$38$	−55.7842	−	4.74333i	−1.46801	−	0.124825i
$39$			4.88453i			0.125244i
$40$		0			0
$41$	5.30410			0.129368			0.0646842	−	0.997906i	$-0.479396\pi$
$41$	5.30410			0.129368			0.0646842	+	0.997906i	$0.479396\pi$
$42$	−3.63812	+	42.7863i	−0.0866219	+	1.01872i
$43$	45.5870			1.06016			0.530081	−	0.847947i	$-0.322162\pi$
$43$	45.5870			1.06016			0.530081	+	0.847947i	$0.322162\pi$
$44$	−7.45616	+	43.5273i	−0.169458	+	0.989256i
$45$		0			0
$46$	1.33936	−	15.7516i	0.0291165	−	0.342426i
$47$	11.7246			0.249460			0.124730	−	0.992191i	$-0.460194\pi$
$47$	11.7246			0.249460			0.124730	+	0.992191i	$0.460194\pi$
$48$	−26.1328	−	9.22368i	−0.544434	−	0.192160i
$49$	104.658			2.13589
$50$		0			0
$51$		−	11.3035i		−	0.221637i
$52$	−1.90457	+	11.1184i	−0.0366263	+	0.213815i
$53$		−	41.1680i		−	0.776755i	−0.921500	−	0.388378i	$-0.873036\pi$
$53$		−	41.1680i		−	0.776755i	0.921500	−	0.388378i	$-0.126964\pi$
$54$	−0.880481	+	10.3549i	−0.0163052	+	0.191758i
$55$		0			0
$56$	−24.9644	+	95.9735i	−0.445793	+	1.71381i
$57$			48.4849i			0.850612i
$58$	−8.59391	+	101.069i	−0.148171	+	1.74257i
$59$			10.7008i			0.181370i	0.995880	+	0.0906848i	$0.0289056\pi$
$59$			10.7008i			0.181370i	−0.995880	+	0.0906848i	$0.971094\pi$
$60$		0			0
$61$	56.1297			0.920159			0.460080	−	0.887878i	$-0.347821\pi$
$61$	56.1297			0.920159			0.460080	+	0.887878i	$0.347821\pi$
$62$	−72.4319	−	6.15889i	−1.16826	−	0.0993370i
$63$	37.1877			0.590281
$64$	−55.8882	−	31.1850i	−0.873254	−	0.487266i
$65$		0			0
$66$	38.1073	+	3.24026i	0.577383	+	0.0490949i
$67$	−16.1709			−0.241357			−0.120679	−	0.992692i	$-0.538507\pi$
$67$	−16.1709			−0.241357			−0.120679	+	0.992692i	$0.538507\pi$
$68$	4.40743	−	25.7295i	0.0648151	−	0.378375i
$69$	−13.6905			−0.198413
$70$		0			0
$71$		−	66.1617i		−	0.931855i	−0.884823	−	0.465928i	$-0.845721\pi$
$71$		−	66.1617i		−	0.931855i	0.884823	−	0.465928i	$-0.154279\pi$
$72$	−6.04177	+	23.2271i	−0.0839134	+	0.322598i
$73$		−	15.6330i		−	0.214150i	−0.994251	−	0.107075i	$-0.965851\pi$
$73$		−	15.6330i		−	0.214150i	0.994251	−	0.107075i	$-0.0341485\pi$
$74$	−37.7198	−	3.20731i	−0.509727	−	0.0433421i
$75$		0			0
$76$	−18.9051	+	110.363i	−0.248752	+	1.45215i
$77$		−	136.855i		−	1.77733i
$78$	9.73394	+	0.827677i	0.124794	+	0.0106112i
$79$			123.057i			1.55768i	0.627223	+	0.778840i	$0.284191\pi$
$79$			123.057i			1.55768i	−0.627223	+	0.778840i	$0.715809\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	0.898773	−	10.5701i	0.0109606	−	0.128903i
$83$	99.6700			1.20084			0.600422	−	0.799684i	$-0.294999\pi$
$83$	99.6700			1.20084			0.600422	+	0.799684i	$0.294999\pi$
$84$	84.6484	+	14.5002i	1.00772	+	0.172621i
$85$		0			0
$86$	7.72465	−	90.8461i	0.0898215	−	1.05635i
$87$	87.8443			1.00970
$88$	85.4781	+	22.2343i	0.971342	+	0.252663i
$89$	−101.083			−1.13576			−0.567881	−	0.823110i	$-0.692237\pi$
$89$	−101.083			−1.13576			−0.567881	+	0.823110i	$0.692237\pi$
$90$		0			0
$91$		−	34.9575i		−	0.384148i
$92$	−31.1629	−	5.33817i	−0.338728	−	0.0580236i
$93$			62.9543i			0.676927i
$94$	1.98672	−	23.3649i	0.0211353	−	0.248563i
$95$		0			0
$96$	−22.8092	+	50.5148i	−0.237596	+	0.526195i
$97$			127.293i			1.31230i	0.754630	+	0.656151i	$0.227817\pi$
$97$			127.293i			1.31230i	−0.754630	+	0.656151i	$0.772183\pi$
$98$	17.7342	−	208.564i	0.180962	−	2.12821i
$99$		−	33.1209i		−	0.334555i
$100$		0			0
$101$	−94.3535			−0.934193			−0.467096	−	0.884206i	$-0.654700\pi$
$101$	−94.3535			−0.934193			−0.467096	+	0.884206i	$0.654700\pi$
$102$	−22.5257	−	1.91536i	−0.220840	−	0.0187780i
$103$	31.8455			0.309180			0.154590	−	0.987979i	$-0.450594\pi$
$103$	31.8455			0.309180			0.154590	+	0.987979i	$0.450594\pi$
$104$	21.8341	+	5.67943i	0.209943	+	0.0546099i
$105$		0			0
$106$	−82.0400	−	6.97587i	−0.773962	−	0.0658101i
$107$	33.7912			0.315805			0.157903	−	0.987455i	$-0.449527\pi$
$107$	33.7912			0.315805			0.157903	+	0.987455i	$0.449527\pi$
$108$	20.4862	+	3.50926i	0.189687	+	0.0324932i
$109$	83.4266			0.765382			0.382691	−	0.923876i	$-0.374997\pi$
$109$	83.4266			0.765382			0.382691	+	0.923876i	$0.374997\pi$
$110$		0			0
$111$			32.7842i			0.295353i
$112$	187.027	+	66.0118i	1.66988	+	0.589391i
$113$			111.796i			0.989342i	0.869080	+	0.494671i	$0.164711\pi$
$113$			111.796i			0.989342i	−0.869080	+	0.494671i	$0.835289\pi$
$114$	96.6211	+	8.21569i	0.847553	+	0.0720675i
$115$		0			0
$116$	199.955	+	34.2520i	1.72375	+	0.295276i
$117$		−	8.46026i		−	0.0723099i
$118$	21.3247	+	1.81324i	0.180717	+	0.0153664i
$119$			80.8964i			0.679802i
$120$		0			0
$121$	−0.888544			−0.00734334
$122$	9.51110	−	111.856i	0.0779599	−	0.916851i
$123$	−9.18697			−0.0746908
$124$	−24.5470	+	143.299i	−0.197960	+	1.15564i
$125$		0			0
$126$	6.30141	−	74.1080i	0.0500112	−	0.588159i
$127$	16.6855			0.131382			0.0656909	−	0.997840i	$-0.479075\pi$
$127$	16.6855			0.131382			0.0656909	+	0.997840i	$0.479075\pi$
$128$	−71.6160	+	106.090i	−0.559500	+	0.828831i
$129$	−78.9589			−0.612085
$130$		0			0
$131$			196.418i			1.49937i	0.661794	+	0.749686i	$0.269796\pi$
$131$			196.418i			1.49937i	−0.661794	+	0.749686i	$0.730204\pi$
$132$	12.9144	−	75.3914i	0.0978367	−	0.571147i
$133$		−	346.995i		−	2.60899i
$134$	−2.74015	+	32.2256i	−0.0204488	+	0.240490i
$135$		0			0
$136$	−50.5271	−	13.1430i	−0.371523	−	0.0966396i
$137$		−	117.127i		−	0.854942i	−0.904029	−	0.427471i	$-0.859405\pi$
$137$		−	117.127i		−	0.854942i	0.904029	−	0.427471i	$-0.140595\pi$
$138$	−2.31984	+	27.2825i	−0.0168104	+	0.197700i
$139$		−	187.238i		−	1.34704i	−0.739170	−	0.673519i	$-0.764782\pi$
$139$		−	187.238i		−	1.34704i	0.739170	−	0.673519i	$-0.235218\pi$
$140$		0			0
$141$	−20.3076			−0.144026
$142$	−131.848	−	11.2110i	−0.928505	−	0.0789508i
$143$	−31.1346			−0.217725
$144$	45.2634	+	15.9759i	0.314329	+	0.110944i
$145$		0			0
$146$	−31.1535	−	2.64899i	−0.213380	−	0.0181437i
$147$	−181.274			−1.23315
$148$	−12.7831	+	74.6248i	−0.0863725	+	0.504222i
$149$	50.2274			0.337096			0.168548	−	0.985693i	$-0.446092\pi$
$149$	50.2274			0.337096			0.168548	+	0.985693i	$0.446092\pi$
$150$		0			0
$151$			213.160i			1.41166i	0.708382	+	0.705829i	$0.249425\pi$
$151$			213.160i			1.41166i	−0.708382	+	0.705829i	$0.750575\pi$
$152$	216.730	+	56.3752i	1.42585	+	0.370890i
$153$			19.5782i			0.127962i
$154$	−272.725	−	23.1898i	−1.77094	−	0.150583i
$155$		0			0
$156$	3.29880	−	19.2576i	0.0211462	−	0.123446i
$157$			203.918i			1.29884i	0.760431	+	0.649419i	$0.224988\pi$
$157$			203.918i			1.29884i	−0.760431	+	0.649419i	$0.775012\pi$
$158$	245.228	+	20.8518i	1.55208	+	0.131973i
$159$			71.3051i			0.448460i
$160$		0			0
$161$	97.9798			0.608570
$162$	1.52504	−	17.9353i	0.00941381	−	0.110712i
$163$	−215.898			−1.32452			−0.662262	−	0.749272i	$-0.730404\pi$
$163$	−215.898			−1.32452			−0.662262	+	0.749272i	$0.730404\pi$
$164$	−20.9118	−	3.58216i	−0.127511	−	0.0218425i
$165$		0			0
$166$	16.8889	−	198.623i	0.101741	−	1.19653i
$167$	−255.029			−1.52712			−0.763560	−	0.645737i	$-0.776550\pi$
$167$	−255.029			−1.52712			−0.763560	+	0.645737i	$0.776550\pi$
$168$	43.2396	−	166.231i	0.257378	−	0.989470i
$169$	161.047			0.952942
$170$		0			0
$171$		−	83.9783i		−	0.491101i
$172$	−179.730	−	30.7875i	−1.04494	−	0.178997i
$173$			235.426i			1.36084i	0.732822	+	0.680421i	$0.238203\pi$
$173$			235.426i			1.36084i	−0.732822	+	0.680421i	$0.761797\pi$
$174$	14.8851	−	175.057i	0.0855465	−	1.00607i
$175$		0			0
$176$	58.7929	−	166.574i	0.334051	−	0.946443i
$177$		−	18.5343i		−	0.104714i
$178$	−17.1284	+	201.439i	−0.0962267	+	1.13168i
$179$		−	102.669i		−	0.573572i	−0.957995	−	0.286786i	$-0.907413\pi$
$179$		−	102.669i		−	0.573572i	0.957995	−	0.286786i	$-0.0925869\pi$
$180$		0			0
$181$	−56.8222			−0.313935			−0.156967	−	0.987604i	$-0.550172\pi$
$181$	−56.8222			−0.313935			−0.156967	+	0.987604i	$0.550172\pi$
$182$	−69.6636	−	5.92350i	−0.382767	−	0.0325467i
$183$	−97.2195			−0.531254
$184$	−15.9185	+	61.1972i	−0.0865134	+	0.332594i
$185$		0			0
$186$	125.456	+	10.6675i	0.674493	+	0.0573522i
$187$	72.0498			0.385293
$188$	−46.2251	−	7.91830i	−0.245878	−	0.0421186i
$189$	−64.4110			−0.340799
$190$		0			0
$191$		−	158.493i		−	0.829808i	−0.909865	−	0.414904i	$-0.863815\pi$
$191$		−	158.493i		−	0.829808i	0.909865	−	0.414904i	$-0.136185\pi$
$192$	96.8013	+	54.0140i	0.504173	+	0.281323i
$193$			156.732i			0.812084i	0.913854	+	0.406042i	$0.133091\pi$
$193$			156.732i			0.812084i	−0.913854	+	0.406042i	$0.866909\pi$
$194$	253.671	+	21.5697i	1.30758	+	0.111184i
$195$		0			0
$196$	−412.624	−	70.6819i	−2.10522	−	0.360622i
$197$			260.127i			1.32044i	0.751072	+	0.660221i	$0.229537\pi$
$197$			260.127i			1.32044i	−0.751072	+	0.660221i	$0.770463\pi$
$198$	−66.0037	−	5.61230i	−0.333352	−	0.0283449i
$199$		−	14.0326i		−	0.0705157i	−0.999378	−	0.0352579i	$-0.988775\pi$
$199$		−	14.0326i		−	0.0705157i	0.999378	−	0.0352579i	$-0.0112253\pi$
$200$		0			0
$201$	28.0089			0.139348
$202$	−15.9881	+	188.028i	−0.0791489	+	0.930834i
$203$	−628.682			−3.09696
$204$	−7.63389	+	44.5648i	−0.0374210	+	0.218455i
$205$		0			0
$206$	5.39618	−	63.4620i	0.0261950	−	0.308068i
$207$	23.7126			0.114554
$208$	15.0178	−	42.5488i	0.0722009	−	0.204562i
$209$	−309.049			−1.47870
$210$		0			0
$211$		−	74.4941i		−	0.353052i	−0.984296	−	0.176526i	$-0.943514\pi$
$211$		−	74.4941i		−	0.353052i	0.984296	−	0.176526i	$-0.0564860\pi$
$212$	−27.8031	+	162.308i	−0.131147	+	0.765604i
$213$			114.595i			0.538007i
$214$	5.72587	−	67.3393i	0.0267564	−	0.314670i
$215$		0			0
$216$	10.4646	−	40.2305i	0.0484474	−	0.186252i
$217$		−	450.550i		−	2.07627i
$218$	14.1365	−	166.253i	0.0648465	−	0.762630i
$219$			27.0771i			0.123640i
$220$		0			0
$221$	18.4041			0.0832763
$222$	65.3326	+	5.55523i	0.294291	+	0.0250236i
$223$	−159.996			−0.717471			−0.358736	−	0.933439i	$-0.616792\pi$
$223$	−159.996			−0.717471			−0.358736	+	0.933439i	$0.616792\pi$
$224$	163.240	−	361.523i	0.728752	−	1.61394i
$225$		0			0
$226$	222.787	+	18.9436i	0.985784	+	0.0838213i
$227$	175.978			0.775236			0.387618	−	0.921820i	$-0.373298\pi$
$227$	175.978			0.775236			0.387618	+	0.921820i	$0.373298\pi$
$228$	32.7446	−	191.155i	0.143617	−	0.838400i
$229$	114.170			0.498560			0.249280	−	0.968431i	$-0.419806\pi$
$229$	114.170			0.498560			0.249280	+	0.968431i	$0.419806\pi$
$230$		0			0
$231$			237.039i			1.02614i
$232$	102.140	−	392.668i	0.440258	−	1.69254i
$233$		−	260.062i		−	1.11615i	−0.829792	−	0.558073i	$-0.811541\pi$
$233$		−	260.062i		−	1.11615i	0.829792	−	0.558073i	$-0.188459\pi$
$234$	−16.8597	−	1.43358i	−0.0720499	−	0.00612641i
$235$		0			0
$236$	7.22687	−	42.1887i	0.0306223	−	0.178766i
$237$		−	213.140i		−	0.899327i
$238$	161.211	+	13.7078i	0.677358	+	0.0575958i
$239$		−	140.089i		−	0.586147i	−0.956090	−	0.293073i	$-0.905322\pi$
$239$		−	140.089i		−	0.586147i	0.956090	−	0.293073i	$-0.0946780\pi$
$240$		0			0
$241$	105.920			0.439503			0.219752	−	0.975556i	$-0.429475\pi$
$241$	105.920			0.439503			0.219752	+	0.975556i	$0.429475\pi$
$242$	−0.150563	+	1.77070i	−0.000622159	+	0.00731693i
$243$	−15.5885			−0.0641500
$244$	−221.296	−	37.9076i	−0.906949	−	0.155359i
$245$		0			0
$246$	−1.55672	+	18.3079i	−0.00632813	+	0.0744223i
$247$	−78.9419			−0.319603
$248$	281.409	+	73.1993i	1.13471	+	0.295159i
$249$	−172.633			−0.693307
$250$		0			0
$251$			167.879i			0.668839i	0.942424	+	0.334420i	$0.108540\pi$
$251$			167.879i			0.668839i	−0.942424	+	0.334420i	$0.891460\pi$
$252$	−146.615	−	25.1150i	−0.581807	−	0.0996627i
$253$		−	87.2650i		−	0.344921i
$254$	2.82733	−	33.2510i	0.0111312	−	0.130909i
$255$		0			0
$256$	199.282	+	160.694i	0.778447	+	0.627710i
$257$			198.849i			0.773732i	0.922136	+	0.386866i	$0.126442\pi$
$257$			198.849i			0.773732i	−0.922136	+	0.386866i	$0.873558\pi$
$258$	−13.3795	+	157.350i	−0.0518585	+	0.609884i
$259$		−	234.629i		−	0.905903i
$260$		0			0
$261$	−152.151			−0.582953
$262$	391.423	+	33.2827i	1.49398	+	0.127033i
$263$	480.528			1.82710			0.913552	−	0.406722i	$-0.133328\pi$
$263$	480.528			1.82710			0.913552	+	0.406722i	$0.133328\pi$
$264$	−148.052	−	38.5110i	−0.560804	−	0.145875i
$265$		0			0
$266$	−691.496	−	58.7979i	−2.59961	−	0.221045i
$267$	175.081			0.655733
$268$	63.7552	+	10.9212i	0.237892	+	0.0407506i
$269$	291.496			1.08363			0.541815	−	0.840498i	$-0.317737\pi$
$269$	291.496			1.08363			0.541815	+	0.840498i	$0.317737\pi$
$270$		0			0
$271$			174.063i			0.642299i	0.947029	+	0.321150i	$0.104069\pi$
$271$			174.063i			0.642299i	−0.947029	+	0.321150i	$0.895931\pi$
$272$	−34.7532	+	98.4638i	−0.127769	+	0.361999i
$273$			60.5482i			0.221788i
$274$	−233.412	−	19.8470i	−0.851868	−	0.0724344i
$275$		0			0
$276$	53.9758	+	9.24598i	0.195564	+	0.0334999i
$277$		−	50.5203i		−	0.182384i	−0.995833	−	0.0911918i	$-0.970932\pi$
$277$		−	50.5203i		−	0.182384i	0.995833	−	0.0911918i	$-0.0290676\pi$
$278$	−373.130	−	31.7273i	−1.34219	−	0.114127i
$279$		−	109.040i		−	0.390824i
$280$		0			0
$281$	−66.0514			−0.235058			−0.117529	−	0.993069i	$-0.537497\pi$
$281$	−66.0514			−0.235058			−0.117529	+	0.993069i	$0.537497\pi$
$282$	−3.44110	+	40.4692i	−0.0122025	+	0.143508i
$283$	−116.934			−0.413196			−0.206598	−	0.978426i	$-0.566239\pi$
$283$	−116.934			−0.413196			−0.206598	+	0.978426i	$0.566239\pi$
$284$	−44.6828	+	260.848i	−0.157334	+	0.918477i
$285$		0			0
$286$	−5.27572	+	62.0454i	−0.0184466	+	0.216942i
$287$	65.7491			0.229091
$288$	39.5067	−	87.4941i	0.137176	−	0.303799i
$289$	246.411			0.852631
$290$		0			0
$291$		−	220.478i		−	0.757658i
$292$	−10.5578	+	61.6341i	−0.0361570	+	0.211076i
$293$			68.3732i			0.233356i	0.993170	+	0.116678i	$0.0372245\pi$
$293$			68.3732i			0.233356i	−0.993170	+	0.116678i	$0.962776\pi$
$294$	−30.7166	+	361.244i	−0.104478	+	1.22872i
$295$		0			0
$296$	146.547	+	38.1194i	0.495091	+	0.128782i
$297$			57.3672i			0.193155i
$298$	8.51096	−	100.094i	0.0285603	−	0.335884i
$299$		−	22.2905i		−	0.0745503i
$300$		0			0
$301$	565.092			1.87738
$302$	424.788	+	36.1197i	1.40658	+	0.119602i
$303$	163.425			0.539356
$304$	149.070	−	422.349i	0.490361	−	1.38930i
$305$		0			0
$306$	39.0156	+	3.31750i	0.127502	+	0.0108415i
$307$	−369.497			−1.20357			−0.601786	−	0.798657i	$-0.705544\pi$
$307$	−369.497			−1.20357			−0.601786	+	0.798657i	$0.705544\pi$
$308$	−92.4258	+	539.560i	−0.300084	+	1.75182i
$309$	−55.1580			−0.178505
$310$		0			0
$311$			303.446i			0.975712i	0.872924	+	0.487856i	$0.162221\pi$
$311$			303.446i			0.975712i	−0.872924	+	0.487856i	$0.837779\pi$
$312$	−37.8178	−	9.83707i	−0.121211	−	0.0315291i
$313$		−	297.693i		−	0.951097i	−0.879689	−	0.475549i	$-0.842250\pi$
$313$		−	297.693i		−	0.951097i	0.879689	−	0.475549i	$-0.157750\pi$
$314$	406.369	+	34.5536i	1.29417	+	0.110043i
$315$		0			0
$316$	83.1072	−	485.160i	0.262998	−	1.53532i
$317$			264.678i			0.834948i	0.908689	+	0.417474i	$0.137084\pi$
$317$			264.678i			0.834948i	−0.908689	+	0.417474i	$0.862916\pi$
$318$	142.097	+	12.0826i	0.446847	+	0.0379955i
$319$			559.931i			1.75527i
$320$		0			0
$321$	−58.5280			−0.182330
$322$	16.6026	−	195.255i	0.0515607	−	0.606382i
$323$	182.682			0.565580
$324$	−35.4832	−	6.07822i	−0.109516	−	0.0187599i
$325$		0			0
$326$	−36.5835	+	430.243i	−0.112219	+	1.31976i
$327$	−144.499			−0.441893
$328$	−10.6820	+	41.0663i	−0.0325672	+	0.125202i
$329$	145.337			0.441754
$330$		0			0
$331$		−	473.426i		−	1.43029i	−0.698976	−	0.715145i	$-0.746361\pi$
$331$		−	473.426i		−	1.43029i	0.698976	−	0.715145i	$-0.253639\pi$
$332$	−392.956	−	67.3129i	−1.18360	−	0.202750i
$333$		−	56.7838i		−	0.170522i
$334$	−43.2143	+	508.224i	−0.129384	+	1.52163i
$335$		0			0
$336$	−323.940	−	114.336i	−0.964107	−	0.340285i
$337$			29.7588i			0.0883051i	0.999025	+	0.0441526i	$0.0140588\pi$
$337$			29.7588i			0.0883051i	−0.999025	+	0.0441526i	$0.985941\pi$
$338$	27.2892	−	320.936i	0.0807373	−	0.949515i
$339$		−	193.636i		−	0.571197i
$340$		0			0
$341$	−401.278			−1.17677
$342$	−167.353	−	14.2300i	−0.489335	−	0.0416082i
$343$	689.937			2.01148
$344$	−91.8086	+	352.951i	−0.266885	+	1.02602i
$345$		0			0
$346$	469.158	+	39.8925i	1.35595	+	0.115296i
$347$	306.190			0.882391			0.441195	−	0.897411i	$-0.354555\pi$
$347$	306.190			0.882391			0.441195	+	0.897411i	$0.354555\pi$
$348$	−346.333	−	59.3263i	−0.995208	−	0.170478i
$349$	−649.149			−1.86002			−0.930012	−	0.367528i	$-0.880204\pi$
$349$	−649.149			−1.86002			−0.930012	+	0.367528i	$0.880204\pi$
$350$		0			0
$351$			14.6536i			0.0417481i
$352$	−321.988	−	145.389i	−0.914737	−	0.413036i
$353$			275.547i			0.780587i	0.920691	+	0.390293i	$0.127626\pi$
$353$			275.547i			0.780587i	−0.920691	+	0.390293i	$0.872374\pi$
$354$	−36.9354	−	3.14062i	−0.104337	−	0.00887181i
$355$		0			0
$356$	398.527	+	68.2671i	1.11946	+	0.191761i
$357$		−	140.117i		−	0.392484i
$358$	−204.600	−	17.3972i	−0.571510	−	0.0485955i
$359$			507.672i			1.41413i	0.707149	+	0.707065i	$0.249981\pi$
$359$			507.672i			1.41413i	−0.707149	+	0.707065i	$0.750019\pi$
$360$		0			0
$361$	−422.594			−1.17062
$362$	−9.62845	+	113.236i	−0.0265979	+	0.312806i
$363$	1.53900			0.00423968
$364$	−23.6088	+	137.823i	−0.0648594	+	0.378633i
$365$		0			0
$366$	−16.4737	+	193.740i	−0.0450102	+	0.529344i
$367$	−62.7671			−0.171028			−0.0855138	−	0.996337i	$-0.527253\pi$
$367$	−62.7671			−0.171028			−0.0855138	+	0.996337i	$0.527253\pi$
$368$	119.257	+	42.0923i	0.324068	+	0.114381i
$369$	15.9123			0.0431228
$370$		0			0
$371$		−	510.315i		−	1.37551i
$372$	42.5166	−	248.202i	0.114292	−	0.667209i
$373$			272.776i			0.731302i	0.930752	+	0.365651i	$0.119154\pi$
$373$			272.776i			0.731302i	−0.930752	+	0.365651i	$0.880846\pi$
$374$	12.2087	−	143.581i	0.0326437	−	0.383908i
$375$		0			0
$376$	−23.6124	+	90.7761i	−0.0627990	+	0.241426i
$377$			143.026i			0.379379i
$378$	−10.9144	+	128.359i	−0.0288740	+	0.339574i
$379$			376.828i			0.994270i	0.867673	+	0.497135i	$0.165615\pi$
$379$			376.828i			0.994270i	−0.867673	+	0.497135i	$0.834385\pi$
$380$		0			0
$381$	−28.9001			−0.0758533
$382$	−315.847	−	26.8565i	−0.826825	−	0.0703049i
$383$	412.206			1.07625			0.538127	−	0.842864i	$-0.319132\pi$
$383$	412.206			1.07625			0.538127	+	0.842864i	$0.319132\pi$
$384$	124.042	−	183.754i	0.323027	−	0.478526i
$385$		0			0
$386$	312.337	+	26.5581i	0.809164	+	0.0688032i
$387$	136.761			0.353387
$388$	85.9685	−	501.863i	0.221568	−	1.29346i
$389$	161.289			0.414623			0.207312	−	0.978275i	$-0.433529\pi$
$389$	161.289			0.414623			0.207312	+	0.978275i	$0.433529\pi$
$390$		0			0
$391$			51.5834i			0.131927i
$392$	−210.774	+	810.303i	−0.537689	+	2.06710i
$393$		−	340.206i		−	0.865663i
$394$	518.383	+	44.0782i	1.31569	+	0.111874i
$395$		0			0
$396$	−22.3685	+	130.582i	−0.0564861	+	0.329752i
$397$		−	186.505i		−	0.469785i	−0.972021	−	0.234893i	$-0.924526\pi$
$397$		−	186.505i		−	0.469785i	0.972021	−	0.234893i	$-0.0754738\pi$
$398$	−27.9643	−	2.37781i	−0.0702622	−	0.00597440i
$399$			601.014i			1.50630i
$400$		0			0
$401$	239.061			0.596162			0.298081	−	0.954541i	$-0.403653\pi$
$401$	239.061			0.596162			0.298081	+	0.954541i	$0.403653\pi$
$402$	4.74607	−	55.8164i	0.0118061	−	0.138847i
$403$	−102.501			−0.254344
$404$	371.996	+	63.7223i	0.920781	+	0.157729i
$405$		0			0
$406$	−106.529	+	1252.84i	−0.262387	+	3.08582i
$407$	−208.970			−0.513441
$408$	87.5155	+	22.7643i	0.214499	+	0.0557949i
$409$	−47.8016			−0.116874			−0.0584372	−	0.998291i	$-0.518612\pi$
$409$	−47.8016			−0.116874			−0.0584372	+	0.998291i	$0.518612\pi$
$410$		0			0
$411$			202.870i			0.493601i
$412$	−125.553	−	21.5071i	−0.304741	−	0.0522017i
$413$			132.646i			0.321177i
$414$	4.01807	−	47.2547i	0.00970549	−	0.114142i
$415$		0			0
$416$	−82.2470	−	37.1374i	−0.197709	−	0.0892726i
$417$			324.306i			0.777713i
$418$	−52.3679	+	615.875i	−0.125282	+	1.47339i
$419$		−	239.009i		−	0.570428i	−0.958464	−	0.285214i	$-0.907935\pi$
$419$		−	239.009i		−	0.570428i	0.958464	−	0.285214i	$-0.0920647\pi$
$420$		0			0
$421$	−257.592			−0.611857			−0.305929	−	0.952054i	$-0.598967\pi$
$421$	−257.592			−0.611857			−0.305929	+	0.952054i	$0.598967\pi$
$422$	−148.452	−	12.6229i	−0.351783	−	0.0299121i
$423$	35.1738			0.0831532
$424$	318.738	+	82.9092i	0.751740	+	0.195541i
$425$		0			0
$426$	228.367	+	19.4181i	0.536073	+	0.0455823i
$427$	695.779			1.62946
$428$	−133.224	−	22.8211i	−0.311271	−	0.0533204i
$429$	53.9268			0.125703
$430$		0			0
$431$		−	343.164i		−	0.796205i	−0.917341	−	0.398103i	$-0.869669\pi$
$431$		−	343.164i		−	0.796205i	0.917341	−	0.398103i	$-0.130331\pi$
$432$	−78.3984	−	27.6710i	−0.181478	−	0.0640533i
$433$			234.760i			0.542171i	0.962555	+	0.271085i	$0.0873826\pi$
$433$			234.760i			0.542171i	−0.962555	+	0.271085i	$0.912617\pi$
$434$	−897.859	−	76.3450i	−2.06880	−	0.175910i
$435$		0			0
$436$	−328.916	−	56.3428i	−0.754394	−	0.129227i
$437$		−	221.261i		−	0.506317i
$438$	53.9595	+	4.58818i	0.123195	+	0.0104753i
$439$		−	374.473i		−	0.853013i	−0.904484	−	0.426507i	$-0.859744\pi$
$439$		−	374.473i		−	0.853013i	0.904484	−	0.426507i	$-0.140256\pi$
$440$		0			0
$441$	313.975			0.711962
$442$	3.11854	−	36.6758i	0.00705553	−	0.0829768i
$443$	−108.557			−0.245050			−0.122525	−	0.992465i	$-0.539099\pi$
$443$	−108.557			−0.245050			−0.122525	+	0.992465i	$0.539099\pi$
$444$	22.1410	−	129.254i	0.0498672	−	0.291113i
$445$		0			0
$446$	−27.1111	+	318.842i	−0.0607873	+	0.714891i
$447$	−86.9963			−0.194623
$448$	−692.785	−	386.566i	−1.54640	−	0.862872i
$449$	431.511			0.961050			0.480525	−	0.876981i	$-0.340446\pi$
$449$	431.511			0.961050			0.480525	+	0.876981i	$0.340446\pi$
$450$		0			0
$451$		−	58.5589i		−	0.129842i
$452$	75.5020	−	440.762i	0.167040	−	0.975138i
$453$		−	369.205i		−	0.815021i
$454$	29.8193	−	350.692i	0.0656813	−	0.772448i
$455$		0			0
$456$	−375.387	−	97.6448i	−0.823218	−	0.214133i
$457$			219.747i			0.480847i	0.970668	+	0.240424i	$0.0772864\pi$
$457$			219.747i			0.480847i	−0.970668	+	0.240424i	$0.922714\pi$
$458$	19.3460	−	227.520i	0.0422402	−	0.496768i
$459$		−	33.9104i		−	0.0738789i
$460$		0			0
$461$	223.434			0.484673			0.242337	−	0.970192i	$-0.422086\pi$
$461$	223.434			0.484673			0.242337	+	0.970192i	$0.422086\pi$
$462$	472.374	+	40.1660i	1.02245	+	0.0869394i
$463$	740.855			1.60012			0.800059	−	0.599921i	$-0.204802\pi$
$463$	740.855			1.60012			0.800059	+	0.599921i	$0.204802\pi$
$464$	−765.206	−	270.082i	−1.64915	−	0.582074i
$465$		0			0
$466$	−518.254	−	44.0672i	−1.11213	−	0.0945648i
$467$	−249.381			−0.534007			−0.267004	−	0.963696i	$-0.586034\pi$
$467$	−249.381			−0.534007			−0.267004	+	0.963696i	$0.586034\pi$
$468$	−5.71370	+	33.3552i	−0.0122088	+	0.0712718i
$469$	−200.454			−0.427406
$470$		0			0
$471$		−	353.196i		−	0.749885i
$472$	−82.8495	−	21.5506i	−0.175529	−	0.0456580i
$473$		−	503.294i		−	1.06405i
$474$	−424.748	−	36.1164i	−0.896093	−	0.0761948i
$475$		0			0
$476$	54.6340	−	318.940i	0.114777	−	0.670043i
$477$		−	123.504i		−	0.258918i
$478$	−279.171	−	23.7379i	−0.584039	−	0.0496609i
$479$			210.915i			0.440324i	0.975463	+	0.220162i	$0.0706587\pi$
$479$			210.915i			0.440324i	−0.975463	+	0.220162i	$0.929341\pi$
$480$		0			0
$481$	−53.3784			−0.110974
$482$	17.9480	−	211.079i	0.0372366	−	0.437923i
$483$	−169.706			−0.351358
$484$	3.50315	+	0.600085i	0.00723791	+	0.00123984i
$485$		0			0
$486$	−2.64144	+	31.0648i	−0.00543507	+	0.0639194i
$487$	710.541			1.45902			0.729508	−	0.683972i	$-0.239749\pi$
$487$	710.541			1.45902			0.729508	+	0.683972i	$0.239749\pi$
$488$	−113.041	+	434.576i	−0.231641	+	0.890525i
$489$	373.946			0.764715
$490$		0			0
$491$		−	697.876i		−	1.42134i	−0.703528	−	0.710668i	$-0.748393\pi$
$491$		−	697.876i		−	1.42134i	0.703528	−	0.710668i	$-0.251607\pi$
$492$	36.2203	+	6.20449i	0.0736185	+	0.0126108i
$493$		−	330.982i		−	0.671363i
$494$	−13.3766	+	157.316i	−0.0270781	+	0.318454i
$495$		0			0
$496$	193.557	−	548.390i	0.390235	−	1.10563i
$497$		−	820.135i		−	1.65017i
$498$	−29.2525	+	344.025i	−0.0587400	+	0.690814i
$499$		−	875.602i		−	1.75471i	−0.479838	−	0.877357i	$-0.659305\pi$
$499$		−	875.602i		−	1.75471i	0.479838	−	0.877357i	$-0.340695\pi$
$500$		0			0
$501$	441.723			0.881683
$502$	334.550	+	28.4468i	0.666434	+	0.0566670i
$503$	−142.849			−0.283995			−0.141997	−	0.989867i	$-0.545352\pi$
$503$	−142.849			−0.283995			−0.141997	+	0.989867i	$0.545352\pi$
$504$	−74.8932	+	287.921i	−0.148598	+	0.571271i
$505$		0			0
$506$	−173.902	−	14.7869i	−0.343681	−	0.0292232i
$507$	−278.942			−0.550181
$508$	−65.7837	−	11.2687i	−0.129496	−	0.0221824i
$509$	147.662			0.290102			0.145051	−	0.989424i	$-0.453665\pi$
$509$	147.662			0.290102			0.145051	+	0.989424i	$0.453665\pi$
$510$		0			0
$511$		−	193.785i		−	0.379227i
$512$	354.000	−	369.903i	0.691407	−	0.722466i
$513$			145.455i			0.283537i
$514$	396.268	+	33.6947i	0.770950	+	0.0655539i
$515$		0			0
$516$	311.301	+	53.3255i	0.603297	+	0.103344i
$517$		−	129.443i		−	0.250374i
$518$	−467.571	−	39.7576i	−0.902646	−	0.0767520i
$519$		−	407.769i		−	0.785682i
$520$		0			0
$521$	−348.592			−0.669082			−0.334541	−	0.942381i	$-0.608581\pi$
$521$	−348.592			−0.669082			−0.334541	+	0.942381i	$0.608581\pi$
$522$	−25.7817	+	303.207i	−0.0493903	+	0.580857i
$523$	−370.317			−0.708063			−0.354032	−	0.935233i	$-0.615189\pi$
$523$	−370.317			−0.708063			−0.354032	+	0.935233i	$0.615189\pi$
$524$	132.652	−	774.392i	0.253153	−	1.47785i
$525$		0			0
$526$	81.4249	−	957.601i	0.154800	−	1.82053i
$527$	237.201			0.450096
$528$	−101.832	+	288.514i	−0.192864	+	0.546429i
$529$	−466.523			−0.881897
$530$		0			0
$531$			32.1024i			0.0604565i
$532$	−234.346	+	1368.06i	−0.440500	+	2.57153i
$533$		−	14.9580i		−	0.0280638i
$534$	29.6672	−	348.902i	0.0555565	−	0.653375i
$535$		0			0
$536$	32.5670	−	125.201i	0.0607594	−	0.233584i
$537$			177.829i			0.331152i
$538$	49.3937	−	580.897i	0.0918098	−	1.07973i
$539$		−	1155.46i		−	2.14371i
$540$		0			0
$541$	−279.719			−0.517041			−0.258520	−	0.966006i	$-0.583235\pi$
$541$	−279.719			−0.517041			−0.258520	+	0.966006i	$0.583235\pi$
$542$	346.874	+	29.4947i	0.639990	+	0.0544183i
$543$	98.4190			0.181250
$544$	190.331	+	85.9411i	0.349873	+	0.157980i
$545$		0			0
$546$	120.661	+	10.2598i	0.220991	+	0.0187909i
$547$	−387.716			−0.708804			−0.354402	−	0.935093i	$-0.615315\pi$
$547$	−387.716			−0.708804			−0.354402	+	0.935093i	$0.615315\pi$
$548$	−79.1026	+	461.782i	−0.144348	+	0.842668i
$549$	168.389			0.306720
$550$		0			0
$551$			1419.71i			2.57660i
$552$	27.5716	−	105.997i	0.0499485	−	0.192023i
$553$			1525.40i			2.75841i
$554$	−100.677	−	8.56059i	−0.181728	−	0.0154523i
$555$		0			0
$556$	−126.453	+	738.201i	−0.227433	+	1.32770i
$557$			43.5564i			0.0781983i	0.999235	+	0.0390991i	$0.0124488\pi$
$557$			43.5564i			0.0781983i	−0.999235	+	0.0390991i	$0.987551\pi$
$558$	−217.296	−	18.4767i	−0.389419	−	0.0331123i
$559$		−	128.559i		−	0.229981i
$560$		0			0
$561$	−124.794			−0.222449
$562$	−11.1923	+	131.628i	−0.0199152	+	0.234213i
$563$	361.646			0.642355			0.321178	−	0.947019i	$-0.395921\pi$
$563$	361.646			0.642355			0.321178	+	0.947019i	$0.395921\pi$
$564$	80.0642	+	13.7149i	0.141958	+	0.0243172i
$565$		0			0
$566$	−19.8144	+	233.028i	−0.0350078	+	0.411710i
$567$	111.563			0.196760
$568$	512.248	+	133.245i	0.901845	+	0.234586i
$569$	−888.559			−1.56161			−0.780807	−	0.624772i	$-0.785192\pi$
$569$	−888.559			−1.56161			−0.780807	+	0.624772i	$0.785192\pi$
$570$		0			0
$571$			447.745i			0.784142i	0.919935	+	0.392071i	$0.128241\pi$
$571$			447.745i			0.784142i	−0.919935	+	0.392071i	$0.871759\pi$
$572$	122.751	+	21.0270i	0.214599	+	0.0367605i
$573$			274.519i			0.479090i
$574$	11.1411	−	131.025i	0.0194096	−	0.228267i
$575$		0			0
$576$	−167.665	−	93.5551i	−0.291085	−	0.162422i
$577$			1069.90i			1.85425i	0.374756	+	0.927124i	$0.377727\pi$
$577$			1069.90i			1.85425i	−0.374756	+	0.927124i	$0.622273\pi$
$578$	41.7539	−	491.049i	0.0722386	−	0.849566i
$579$		−	271.468i		−	0.468857i
$580$		0			0
$581$	1235.50			2.12651
$582$	−439.371	−	37.3598i	−0.754934	−	0.0641921i
$583$	−454.508			−0.779602
$584$	121.036	+	31.4836i	0.207253	+	0.0539102i
$585$		0			0
$586$	136.255	+	11.5857i	0.232517	+	0.0197709i
$587$	−129.637			−0.220847			−0.110424	−	0.993885i	$-0.535221\pi$
$587$	−129.637			−0.220847			−0.110424	+	0.993885i	$0.535221\pi$
$588$	714.685	+	122.425i	1.21545	+	0.208205i
$589$	−1017.44			−1.72741
$590$		0			0
$591$		−	450.553i		−	0.762357i
$592$	100.797	−	285.581i	0.170265	−	0.482400i
$593$		−	892.757i		−	1.50549i	−0.658311	−	0.752746i	$-0.728729\pi$
$593$		−	892.757i		−	1.50549i	0.658311	−	0.752746i	$-0.271271\pi$
$594$	114.322	+	9.72079i	0.192461	+	0.0163650i
$595$		0			0
$596$	−198.025	−	33.9214i	−0.332257	−	0.0569151i
$597$			24.3052i			0.0407123i
$598$	−44.4208	−	3.77710i	−0.0742823	−	0.00631623i
$599$			1030.62i			1.72057i	0.509816	+	0.860284i	$0.329714\pi$
$599$			1030.62i			1.72057i	−0.509816	+	0.860284i	$0.670286\pi$
$600$		0			0
$601$	−815.961			−1.35767			−0.678836	−	0.734289i	$-0.737515\pi$
$601$	−815.961			−1.35767			−0.678836	+	0.734289i	$0.737515\pi$
$602$	95.7540	−	1126.12i	0.159060	−	1.87063i
$603$	−48.5128			−0.0804525
$604$	143.959	−	840.401i	0.238343	−	1.39139i
$605$		0			0
$606$	27.6921	−	325.675i	0.0456966	−	0.537417i
$607$	−842.678			−1.38827			−0.694133	−	0.719847i	$-0.744212\pi$
$607$	−842.678			−1.38827			−0.694133	+	0.719847i	$0.744212\pi$
$608$	−816.400	−	368.634i	−1.34276	−	0.606305i
$609$	1088.91			1.78803
$610$		0			0
$611$		−	33.0644i		−	0.0541152i
$612$	13.2223	−	77.1885i	0.0216050	−	0.126125i
$613$			731.088i			1.19264i	0.802747	+	0.596320i	$0.203371\pi$
$613$			731.088i			1.19264i	−0.802747	+	0.596320i	$0.796629\pi$
$614$	−62.6107	+	736.336i	−0.101972	+	1.19924i
$615$		0			0
$616$	1059.58	+	275.615i	1.72009	+	0.447426i
$617$		−	919.609i		−	1.49045i	−0.666812	−	0.745226i	$-0.732342\pi$
$617$		−	919.609i		−	1.49045i	0.666812	−	0.745226i	$-0.267658\pi$
$618$	−9.34645	+	109.919i	−0.0151237	+	0.177863i
$619$			688.974i			1.11304i	0.830833	+	0.556522i	$0.187865\pi$
$619$			688.974i			1.11304i	−0.830833	+	0.556522i	$0.812135\pi$
$620$		0			0
$621$	−41.0715			−0.0661377
$622$	604.711	+	51.4186i	0.972203	+	0.0826665i
$623$	−1253.01			−2.01126
$624$	−26.0116	+	73.6968i	−0.0416852	+	0.118104i
$625$		0			0
$626$	−593.246	−	50.4438i	−0.947678	−	0.0805811i
$627$	535.288			0.853729
$628$	137.717	−	803.960i	0.219295	−	1.28019i
$629$	123.525			0.196383
$630$		0			0
$631$		−	418.968i		−	0.663975i	−0.943284	−	0.331987i	$-0.892281\pi$
$631$		−	418.968i		−	0.663975i	0.943284	−	0.331987i	$-0.107719\pi$
$632$	−952.749	−	247.827i	−1.50751	−	0.392131i
$633$			129.027i			0.203835i
$634$	527.454	+	44.8494i	0.831946	+	0.0707404i
$635$		0			0
$636$	48.1565	−	281.126i	0.0757177	−	0.442022i
$637$		−	295.146i		−	0.463337i
$638$	1115.83	+	94.8795i	1.74896	+	0.148714i
$639$		−	198.485i		−	0.310618i
$640$		0			0
$641$	−47.2426			−0.0737014			−0.0368507	−	0.999321i	$-0.511733\pi$
$641$	−47.2426			−0.0737014			−0.0368507	+	0.999321i	$0.511733\pi$
$642$	−9.91749	+	116.635i	−0.0154478	+	0.181675i
$643$	−710.880			−1.10557			−0.552784	−	0.833325i	$-0.686435\pi$
$643$	−710.880			−1.10557			−0.552784	+	0.833325i	$0.686435\pi$
$644$	−386.293	−	66.1714i	−0.599834	−	0.102751i
$645$		0			0
$646$	30.9553	−	364.051i	0.0479184	−	0.563547i
$647$	468.195			0.723641			0.361820	−	0.932248i	$-0.382155\pi$
$647$	468.195			0.723641			0.361820	+	0.932248i	$0.382155\pi$
$648$	−18.1253	+	69.6812i	−0.0279711	+	0.107533i
$649$	118.140			0.182034
$650$		0			0
$651$			780.375i			1.19873i
$652$	851.192	+	145.808i	1.30551	+	0.223632i
$653$		−	551.066i		−	0.843900i	−0.906619	−	0.421950i	$-0.861346\pi$
$653$		−	551.066i		−	0.843900i	0.906619	−	0.421950i	$-0.138654\pi$
$654$	−24.4852	+	287.959i	−0.0374391	+	0.440304i
$655$		0			0
$656$	80.0271	+	28.2459i	0.121993	+	0.0430578i
$657$		−	46.8989i		−	0.0713834i
$658$	24.6272	−	289.629i	0.0374273	−	0.440165i
$659$		−	158.259i		−	0.240151i	−0.992765	−	0.120075i	$-0.961686\pi$
$659$		−	158.259i		−	0.240151i	0.992765	−	0.120075i	$-0.0383136\pi$
$660$		0			0
$661$	92.4953			0.139932			0.0699662	−	0.997549i	$-0.477711\pi$
$661$	92.4953			0.139932			0.0699662	+	0.997549i	$0.477711\pi$
$662$	−943.447	−	80.2214i	−1.42515	−	0.121180i
$663$	−31.8768			−0.0480796
$664$	−200.728	+	771.681i	−0.302301	+	1.16217i
$665$		0			0
$666$	−113.159	−	9.62194i	−0.169909	−	0.0144474i
$667$	−400.877			−0.601015
$668$	1005.47	+	172.236i	1.50520	+	0.257838i
$669$	277.121			0.414232
$670$		0			0
$671$		−	619.690i		−	0.923532i
$672$	−282.741	+	626.176i	−0.420745	+	0.931810i
$673$		−	956.062i		−	1.42060i	−0.703900	−	0.710299i	$-0.748560\pi$
$673$		−	956.062i		−	1.42060i	0.703900	−	0.710299i	$-0.251440\pi$
$674$	59.3037	+	5.04259i	0.0879876	+	0.00748159i
$675$		0			0
$676$	−634.940	−	108.764i	−0.939261	−	0.160894i
$677$			1116.67i			1.64944i	0.565543	+	0.824719i	$0.308667\pi$
$677$			1116.67i			1.64944i	−0.565543	+	0.824719i	$0.691333\pi$
$678$	−385.879	−	32.8113i	−0.569143	−	0.0483942i
$679$			1577.92i			2.32388i
$680$		0			0
$681$	−304.804			−0.447583
$682$	−67.9961	+	799.671i	−0.0997010	+	1.17254i
$683$	−826.776			−1.21051			−0.605254	−	0.796033i	$-0.706928\pi$
$683$	−826.776			−1.21051			−0.605254	+	0.796033i	$0.706928\pi$
$684$	−56.7153	+	331.090i	−0.0829172	+	0.484050i
$685$		0			0
$686$	116.909	−	1374.91i	0.170421	−	2.00424i
$687$	−197.749			−0.287844
$688$	687.806	+	242.764i	0.999718	+	0.352855i
$689$	−116.097			−0.168501
$690$		0			0
$691$			965.432i			1.39715i	0.715536	+	0.698576i	$0.246182\pi$
$691$			965.432i			1.39715i	−0.715536	+	0.698576i	$0.753818\pi$
$692$	158.996	−	928.183i	0.229764	−	1.34130i
$693$		−	410.564i		−	0.592444i
$694$	51.8834	−	610.177i	0.0747600	−	0.879218i
$695$		0			0
$696$	−176.912	+	680.122i	−0.254183	+	0.977186i
$697$			34.6149i			0.0496627i
$698$	−109.997	+	1293.63i	−0.157589	+	1.85334i
$699$			450.441i			0.644408i
$700$		0			0
$701$	−1109.94			−1.58337			−0.791686	−	0.610928i	$-0.790797\pi$
$701$	−1109.94			−1.58337			−0.791686	+	0.610928i	$0.790797\pi$
$702$	29.2018	+	2.48303i	0.0415980	+	0.00353708i
$703$	−529.845			−0.753691
$704$	−344.292	+	617.024i	−0.489052	+	0.876454i
$705$		0			0
$706$	549.113	+	46.6911i	0.777780	+	0.0661347i
$707$	−1169.60			−1.65431
$708$	−12.5173	+	73.0730i	−0.0176798	+	0.103210i
$709$	964.244			1.36001			0.680003	−	0.733210i	$-0.261979\pi$
$709$	964.244			1.36001			0.680003	+	0.733210i	$0.261979\pi$
$710$		0			0
$711$			369.170i			0.519226i
$712$	203.573	−	782.620i	0.285917	−	1.09919i
$713$		−	287.292i		−	0.402934i
$714$	−279.226	−	23.7426i	−0.391073	−	0.0332529i
$715$		0			0
$716$	−69.3385	+	404.782i	−0.0968415	+	0.565338i
$717$			242.641i			0.338412i
$718$	1011.69	+	86.0244i	1.40904	+	0.119811i
$719$		−	190.820i		−	0.265396i	−0.991157	−	0.132698i	$-0.957636\pi$
$719$		−	190.820i		−	0.265396i	0.991157	−	0.132698i	$-0.0423641\pi$
$720$		0			0
$721$	394.754			0.547509
$722$	−71.6080	+	842.149i	−0.0991801	+	1.16641i
$723$	−183.459			−0.253747
$724$	224.026	+	38.3753i	0.309428	+	0.0530046i
$725$		0			0
$726$	0.260782	−	3.06694i	0.000359204	−	0.00422443i
$727$	−202.134			−0.278039			−0.139019	−	0.990290i	$-0.544395\pi$
$727$	−202.134			−0.278039			−0.139019	+	0.990290i	$0.544395\pi$
$728$	270.654	+	70.4017i	0.371777	+	0.0967056i
$729$	27.0000			0.0370370
$730$		0			0
$731$			297.503i			0.406981i
$732$	383.295	+	65.6579i	0.523627	+	0.0896966i
$733$			962.435i			1.31301i	0.754322	+	0.656504i	$0.227966\pi$
$733$			962.435i			1.31301i	−0.754322	+	0.656504i	$0.772034\pi$
$734$	−10.6358	+	125.083i	−0.0144902	+	0.170413i
$735$		0			0
$736$	104.090	−	230.524i	0.141426	−	0.313212i
$737$			178.532i			0.242242i
$738$	2.69632	−	31.7102i	0.00365355	−	0.0429677i
$739$		−	932.112i		−	1.26132i	−0.776061	−	0.630658i	$-0.782785\pi$
$739$		−	932.112i		−	1.26132i	0.776061	−	0.630658i	$-0.217215\pi$
$740$		0			0
$741$	136.731			0.184523
$742$	−1016.96	−	86.4722i	−1.37057	−	0.116539i
$743$	1153.70			1.55276			0.776379	−	0.630266i	$-0.217054\pi$
$743$	1153.70			1.55276			0.776379	+	0.630266i	$0.217054\pi$
$744$	−487.414	−	126.785i	−0.655127	−	0.170410i
$745$		0			0
$746$	543.590	+	46.2215i	0.728672	+	0.0619591i
$747$	299.010			0.400281
$748$	−284.062	−	48.6594i	−0.379762	−	0.0650526i
$749$	418.872			0.559242
$750$		0			0
$751$			204.359i			0.272116i	0.990701	+	0.136058i	$0.0434434\pi$
$751$			204.359i			0.272116i	−0.990701	+	0.136058i	$0.956557\pi$
$752$	176.898	+	62.4369i	0.235237	+	0.0830279i
$753$		−	290.774i		−	0.386155i
$754$	285.023	+	24.2356i	0.378015	+	0.0321427i
$755$		0			0
$756$	253.945	+	43.5005i	0.335906	+	0.0575403i
$757$		−	216.739i		−	0.286314i	−0.989700	−	0.143157i	$-0.954275\pi$
$757$		−	216.739i		−	0.286314i	0.989700	−	0.143157i	$-0.0457253\pi$
$758$	750.947	+	63.8530i	0.990695	+	0.0842388i
$759$			151.147i			0.199140i
$760$		0			0
$761$	1324.78			1.74085			0.870424	−	0.492303i	$-0.163845\pi$
$761$	1324.78			1.74085			0.870424	+	0.492303i	$0.163845\pi$
$762$	−4.89708	+	57.5924i	−0.00642662	+	0.0755805i
$763$	1034.15			1.35537
$764$	−107.040	+	624.872i	−0.140104	+	0.817895i
$765$		0			0
$766$	69.8477	−	821.447i	0.0911849	−	1.07238i
$767$	30.1772			0.0393444
$768$	−345.167	−	278.330i	−0.449437	−	0.362409i
$769$	−444.088			−0.577488			−0.288744	−	0.957406i	$-0.593238\pi$
$769$	−444.088			−0.577488			−0.288744	+	0.957406i	$0.593238\pi$
$770$		0			0
$771$		−	344.417i		−	0.446714i
$772$	105.850	−	617.928i	0.137112	−	0.800425i
$773$			751.987i			0.972817i	0.873732	+	0.486408i	$0.161693\pi$
$773$			751.987i			0.972817i	−0.873732	+	0.486408i	$0.838307\pi$
$774$	23.1739	−	272.538i	0.0299405	−	0.352117i
$775$		0			0
$776$	−985.550	−	256.359i	−1.27004	−	0.330359i
$777$			406.389i			0.523023i
$778$	27.3301	−	321.417i	0.0351287	−	0.413133i
$779$		−	148.476i		−	0.190599i
$780$		0			0
$781$	−730.446			−0.935271
$782$	102.796	+	8.74073i	0.131452	+	0.0111774i
$783$	263.533			0.336568
$784$	1579.06	+	557.337i	2.01411	+	0.710889i
$785$		0			0
$786$	−677.965	−	57.6474i	−0.862550	−	0.0733427i
$787$	442.296			0.562002			0.281001	−	0.959707i	$-0.409334\pi$
$787$	442.296			0.562002			0.281001	+	0.959707i	$0.409334\pi$
$788$	175.679	−	1025.57i	0.222943	−	1.30148i
$789$	−832.299			−1.05488
$790$		0			0
$791$			1385.81i			1.75197i
$792$	256.434	+	66.7030i	0.323781	+	0.0842210i
$793$		−	158.291i		−	0.199610i
$794$	−371.668	−	31.6030i	−0.468096	−	0.0398022i
$795$		0			0
$796$	−9.47704	+	55.3247i	−0.0119058	+	0.0695034i
$797$		−	56.2072i		−	0.0705235i	−0.999378	−	0.0352618i	$-0.988774\pi$
$797$		−	56.2072i		−	0.0705235i	0.999378	−	0.0352618i	$-0.0112265\pi$
$798$	1197.71	+	101.841i	1.50088	+	0.127620i
$799$			76.5155i			0.0957641i
$800$		0			0
$801$	−303.249			−0.378588
$802$	40.5086	−	476.403i	0.0505094	−	0.594019i
$803$	−172.593			−0.214935
$804$	−110.427	−	18.9160i	−0.137347	−	0.0235274i
$805$		0			0
$806$	−17.3686	+	204.264i	−0.0215491	+	0.253430i
$807$	−504.887			−0.625634
$808$	190.021	−	730.518i	0.235174	−	0.904107i
$809$	−1522.16			−1.88153			−0.940765	−	0.339060i	$-0.889891\pi$
$809$	−1522.16			−1.88153			−0.940765	+	0.339060i	$0.889891\pi$
$810$		0			0
$811$			930.734i			1.14764i	0.818982	+	0.573819i	$0.194539\pi$
$811$			930.734i			1.14764i	−0.818982	+	0.573819i	$0.805461\pi$
$812$	2478.63	+	424.585i	3.05249	+	0.522888i
$813$		−	301.486i		−	0.370832i
$814$	−35.4098	+	416.438i	−0.0435009	+	0.511595i
$815$		0			0
$816$	60.1943	−	170.544i	0.0737676	−	0.209000i
$817$		−	1276.10i		−	1.56194i
$818$	−8.09992	+	95.2595i	−0.00990210	+	0.116454i
$819$		−	104.873i		−	0.128049i
$820$		0			0
$821$	349.814			0.426083			0.213041	−	0.977043i	$-0.431663\pi$
$821$	349.814			0.426083			0.213041	+	0.977043i	$0.431663\pi$
$822$	404.281	+	34.3761i	0.491826	+	0.0418200i
$823$	61.2187			0.0743849			0.0371924	−	0.999308i	$-0.488159\pi$
$823$	61.2187			0.0743849			0.0371924	+	0.999308i	$0.488159\pi$
$824$	−64.1344	+	246.559i	−0.0778330	+	0.299222i
$825$		0			0
$826$	264.338	+	22.4767i	0.320022	+	0.0272115i
$827$	−46.2063			−0.0558721			−0.0279361	−	0.999610i	$-0.508893\pi$
$827$	−46.2063			−0.0558721			−0.0279361	+	0.999610i	$0.508893\pi$
$828$	−93.4888	−	16.0145i	−0.112909	−	0.0193412i
$829$	−223.832			−0.270002			−0.135001	−	0.990845i	$-0.543104\pi$
$829$	−223.832			−0.270002			−0.135001	+	0.990845i	$0.543104\pi$
$830$		0			0
$831$			87.5037i			0.105299i
$832$	−87.9444	+	157.610i	−0.105702	+	0.189435i
$833$			683.007i			0.819937i
$834$	646.280	+	54.9532i	0.774916	+	0.0658912i
$835$		0			0
$836$	1218.45	+	208.718i	1.45747	+	0.249663i
$837$			188.863i			0.225642i
$838$	−476.300	−	40.4998i	−0.568377	−	0.0483291i
$839$			361.794i			0.431220i	0.976480	+	0.215610i	$0.0691740\pi$
$839$			361.794i			0.431220i	−0.976480	+	0.215610i	$0.930826\pi$
$840$		0			0
$841$	1731.20			2.05851
$842$	−43.6486	+	513.332i	−0.0518392	+	0.609657i
$843$	114.404			0.135711
$844$	−50.3101	+	293.698i	−0.0596092	+	0.347984i
$845$		0			0
$846$	5.96015	−	70.0947i	0.00704510	−	0.0828542i
$847$	−11.0143			−0.0130039
$848$	219.232	−	621.134i	0.258528	−	0.732470i
$849$	202.536			0.238559
$850$		0			0
$851$		−	149.610i		−	0.175805i
$852$	77.3929	−	451.801i	0.0908368	−	0.530283i
$853$			844.503i			0.990039i	0.868882	+	0.495019i	$0.164839\pi$
$853$			844.503i			0.990039i	−0.868882	+	0.495019i	$0.835161\pi$
$854$	117.899	−	1386.55i	0.138055	−	1.62360i
$855$		0			0
$856$	−68.0528	+	261.623i	−0.0795009	+	0.305635i
$857$		−	1389.51i		−	1.62137i	−0.585482	−	0.810685i	$-0.699095\pi$
$857$		−	1389.51i		−	1.62137i	0.585482	−	0.810685i	$-0.300905\pi$
$858$	9.13782	−	107.466i	0.0106501	−	0.125251i
$859$		−	1205.45i		−	1.40332i	−0.712512	−	0.701660i	$-0.752442\pi$
$859$		−	1205.45i		−	1.40332i	0.712512	−	0.701660i	$-0.247558\pi$
$860$		0			0
$861$	−113.881			−0.132266
$862$	−683.861	−	58.1487i	−0.793342	−	0.0674579i
$863$	258.868			0.299963			0.149981	−	0.988689i	$-0.452079\pi$
$863$	258.868			0.299963			0.149981	+	0.988689i	$0.452079\pi$
$864$	−68.4276	+	151.544i	−0.0791986	+	0.175398i
$865$		0			0
$866$	467.832	+	39.7798i	0.540222	+	0.0459351i
$867$	−426.796			−0.492267
$868$	−304.282	+	1776.33i	−0.350555	+	2.04646i
$869$	1358.58			1.56339
$870$		0			0
$871$			45.6035i			0.0523576i
$872$	−168.015	+	645.919i	−0.192677	+	0.740732i
$873$			381.880i			0.437434i
$874$	−440.930	−	37.4923i	−0.504497	−	0.0428974i
$875$		0			0
$876$	18.2867	−	106.753i	0.0208752	−	0.121865i
$877$		−	156.268i		−	0.178185i	−0.996023	−	0.0890926i	$-0.971603\pi$
$877$		−	156.268i		−	0.178185i	0.996023	−	0.0890926i	$-0.0283967\pi$
$878$	−746.253	−	63.4539i	−0.849946	−	0.0722710i
$879$		−	118.426i		−	0.134728i
$880$		0			0
$881$	−1343.58			−1.52507			−0.762533	−	0.646950i	$-0.776044\pi$
$881$	−1343.58			−1.52507			−0.762533	+	0.646950i	$0.776044\pi$
$882$	53.2027	−	625.693i	0.0603205	−	0.709402i
$883$	149.478			0.169284			0.0846420	−	0.996411i	$-0.473025\pi$
$883$	149.478			0.169284			0.0846420	+	0.996411i	$0.473025\pi$
$884$	−72.5594	−	12.4293i	−0.0820807	−	0.0140603i
$885$		0			0
$886$	−18.3949	+	216.334i	−0.0207617	+	0.244169i
$887$	1532.07			1.72725			0.863626	−	0.504134i	$-0.168188\pi$
$887$	1532.07			1.72725			0.863626	+	0.504134i	$0.168188\pi$
$888$	−253.827	−	66.0247i	−0.285841	−	0.0743522i
$889$	206.832			0.232656
$890$		0			0
$891$		−	99.3628i		−	0.111518i
$892$	630.796	+	108.055i	0.707171	+	0.121137i
$893$		−	328.204i		−	0.367529i
$894$	−14.7414	+	173.367i	−0.0164893	+	0.193923i
$895$		0			0
$896$	−887.745	+	1315.09i	−0.990786	+	1.46773i
$897$			38.6084i			0.0430417i
$898$	73.1190	−	859.919i	0.0814243	−	0.957594i
$899$			1843.39i			2.05049i
$900$		0			0
$901$	268.665			0.298186
$902$	−116.697	−	9.92273i	−0.129376	−	0.0110008i
$903$	−978.767			−1.08391
$904$	−865.562	−	225.148i	−0.957480	−	0.249057i
$905$		0			0
$906$	−735.754	−	62.5612i	−0.812091	−	0.0690521i
$907$	1245.02			1.37268			0.686341	−	0.727280i	$-0.259216\pi$
$907$	1245.02			1.37268			0.686341	+	0.727280i	$0.259216\pi$
$908$	−693.808	−	118.848i	−0.764106	−	0.130890i
$909$	−283.060			−0.311398
$910$		0			0
$911$		−	173.681i		−	0.190649i	−0.995446	−	0.0953245i	$-0.969611\pi$
$911$		−	173.681i		−	0.190649i	0.995446	−	0.0953245i	$-0.0303889\pi$
$912$	−258.196	+	731.529i	−0.283110	+	0.802115i
$913$		−	1100.39i		−	1.20524i
$914$	437.914	+	37.2359i	0.479118	+	0.0407395i
$915$		0			0
$916$	−450.125	−	77.1058i	−0.491403	−	0.0841766i
$917$			2434.78i			2.65515i
$918$	−67.5770	−	5.74607i	−0.0736133	−	0.00625934i
$919$		−	874.426i		−	0.951498i	−0.879581	−	0.475749i	$-0.842177\pi$
$919$		−	874.426i		−	0.951498i	0.879581	−	0.475749i	$-0.157823\pi$
$920$		0			0
$921$	639.987			0.694882
$922$	37.8607	−	445.262i	0.0410636	−	0.482931i
$923$	−186.582			−0.202147
$924$	160.086	−	934.545i	0.173254	−	1.01141i
$925$		0			0
$926$	125.537	−	1476.38i	0.135569	−	1.59436i
$927$	95.5365			0.103060
$928$	−667.886	+	1479.14i	−0.719705	+	1.59390i
$929$	1564.05			1.68358			0.841792	−	0.539803i	$-0.181501\pi$
$929$	1564.05			1.68358			0.841792	+	0.539803i	$0.181501\pi$
$930$		0			0
$931$		−	2929.68i		−	3.14681i
$932$	−175.635	+	1025.31i	−0.188450	+	1.10012i
$933$		−	525.584i		−	0.563327i
$934$	−42.2573	+	496.970i	−0.0452434	+	0.532087i
$935$		0			0
$936$	65.5023	+	17.0383i	0.0699811	+	0.0182033i
$937$			958.621i			1.02308i	0.859261	+	0.511538i	$0.170924\pi$
$937$			958.621i			1.02308i	−0.859261	+	0.511538i	$0.829076\pi$
$938$	−33.9666	+	399.466i	−0.0362117	+	0.425869i
$939$			515.620i			0.549116i
$940$		0			0
$941$	−752.357			−0.799529			−0.399765	−	0.916618i	$-0.630908\pi$
$941$	−752.357			−0.799529			−0.399765	+	0.916618i	$0.630908\pi$
$942$	−703.852	−	59.8485i	−0.747188	−	0.0635335i
$943$	41.9247			0.0444589
$944$	−56.9849	+	161.451i	−0.0603654	+	0.171029i
$945$		0			0
$946$	−1002.97	−	85.2825i	−1.06022	−	0.0901507i
$947$	−1013.16			−1.06986			−0.534932	−	0.844895i	$-0.679663\pi$
$947$	−1013.16			−1.06986			−0.534932	+	0.844895i	$0.679663\pi$
$948$	−143.946	+	840.322i	−0.151842	+	0.886415i
$949$	−44.0863			−0.0464555
$950$		0			0
$951$		−	458.436i		−	0.482057i
$952$	−626.329	−	162.919i	−0.657909	−	0.171134i
$953$			21.5482i			0.0226109i	0.999936	+	0.0113054i	$0.00359871\pi$
$953$			21.5482i			0.0226109i	−0.999936	+	0.0113054i	$0.996401\pi$
$954$	−246.120	−	20.9276i	−0.257987	−	0.0219367i
$955$		0			0
$956$	−94.6102	+	552.312i	−0.0989646	+	0.577732i
$957$		−	969.828i		−	1.01340i
$958$	420.314	+	35.7393i	0.438741	+	0.0373062i
$959$		−	1451.90i		−	1.51397i
$960$		0			0
$961$	−360.079			−0.374692
$962$	−9.04490	+	106.373i	−0.00940218	+	0.110575i
$963$	101.373			0.105268
$964$	−417.599	−	71.5340i	−0.433193	−	0.0742054i
$965$		0			0
$966$	−28.7565	+	338.192i	−0.0297686	+	0.350095i
$967$	−303.965			−0.314338			−0.157169	−	0.987572i	$-0.550237\pi$
$967$	−303.965			−0.314338			−0.157169	+	0.987572i	$0.550237\pi$
$968$	1.78946	−	6.87942i	0.00184861	−	0.00710684i
$969$	−316.415			−0.326538
$970$		0			0
$971$		−	356.162i		−	0.366799i	−0.983038	−	0.183399i	$-0.941290\pi$
$971$		−	356.162i		−	0.366799i	0.983038	−	0.183399i	$-0.0587101\pi$
$972$	61.4587	+	10.5278i	0.0632291	+	0.0108311i
$973$		−	2320.99i		−	2.38539i
$974$	120.400	−	1415.97i	0.123614	−	1.45377i
$975$		0			0
$976$	846.873	+	298.907i	0.867698	+	0.306257i
$977$		−	1845.09i		−	1.88852i	−0.329194	−	0.944262i	$-0.606777\pi$
$977$		−	1845.09i		−	1.88852i	0.329194	−	0.944262i	$-0.393223\pi$
$978$	63.3646	−	745.202i	0.0647899	−	0.761965i
$979$			1115.99i			1.13993i
$980$		0			0
$981$	250.280			0.255127
$982$	−1390.73	−	118.254i	−1.41623	−	0.120422i
$983$	−289.444			−0.294449			−0.147225	−	0.989103i	$-0.547034\pi$
$983$	−289.444			−0.294449			−0.147225	+	0.989103i	$0.547034\pi$
$984$	18.5019	−	71.1288i	0.0188027	−	0.0722854i
$985$		0			0
$986$	−659.583	−	56.0844i	−0.668949	−	0.0568807i
$987$	−251.731			−0.255047
$988$	311.234	+	53.3140i	0.315015	+	0.0539616i
$989$	360.329			0.364337
$990$		0			0
$991$		−	441.980i		−	0.445994i	−0.974819	−	0.222997i	$-0.928416\pi$
$991$		−	441.980i		−	0.445994i	0.974819	−	0.222997i	$-0.0715840\pi$
$992$	−1060.04	−	478.645i	−1.06859	−	0.482505i
$993$			819.998i			0.825778i
$994$	−1634.37	−	138.971i	−1.64424	−	0.139810i
$995$		0			0
$996$	680.620	+	116.589i	0.683354	+	0.117058i
$997$		−	1045.42i		−	1.04856i	−0.851545	−	0.524282i	$-0.824334\pi$
$997$		−	1045.42i		−	1.04856i	0.851545	−	0.524282i	$-0.175666\pi$
$998$	−1744.91	−	148.370i	−1.74841	−	0.148667i
$999$			98.3525i			0.0984509i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.3.f.b.199.9		16
3.2	odd	2		900.3.f.f.199.8		16
4.3	odd	2	inner	300.3.f.b.199.7		16
5.2	odd	4		300.3.c.d.151.8		8
5.3	odd	4		60.3.c.a.31.1	✓	8
5.4	even	2	inner	300.3.f.b.199.8		16
12.11	even	2		900.3.f.f.199.10		16
15.2	even	4		900.3.c.u.451.1		8
15.8	even	4		180.3.c.b.91.8		8
15.14	odd	2		900.3.f.f.199.9		16
20.3	even	4		60.3.c.a.31.2	yes	8
20.7	even	4		300.3.c.d.151.7		8
20.19	odd	2	inner	300.3.f.b.199.10		16
40.3	even	4		960.3.e.c.511.4		8
40.13	odd	4		960.3.e.c.511.7		8
60.23	odd	4		180.3.c.b.91.7		8
60.47	odd	4		900.3.c.u.451.2		8
60.59	even	2		900.3.f.f.199.7		16
120.53	even	4		2880.3.e.j.2431.1		8
120.83	odd	4		2880.3.e.j.2431.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.c.a.31.1	✓	8	5.3	odd	4
60.3.c.a.31.2	yes	8	20.3	even	4
180.3.c.b.91.7		8	60.23	odd	4
180.3.c.b.91.8		8	15.8	even	4
300.3.c.d.151.7		8	20.7	even	4
300.3.c.d.151.8		8	5.2	odd	4
300.3.f.b.199.7		16	4.3	odd	2	inner
300.3.f.b.199.8		16	5.4	even	2	inner
300.3.f.b.199.9		16	1.1	even	1	trivial
300.3.f.b.199.10		16	20.19	odd	2	inner
900.3.c.u.451.1		8	15.2	even	4
900.3.c.u.451.2		8	60.47	odd	4
900.3.f.f.199.7		16	60.59	even	2
900.3.f.f.199.8		16	3.2	odd	2
900.3.f.f.199.9		16	15.14	odd	2
900.3.f.f.199.10		16	12.11	even	2
960.3.e.c.511.4		8	40.3	even	4
960.3.e.c.511.7		8	40.13	odd	4
2880.3.e.j.2431.1		8	120.53	even	4
2880.3.e.j.2431.4		8	120.83	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.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.169449 - 1.99281i) q^{2} -1.73205 q^{3} +(-3.94257 - 0.675358i) q^{4} +(-0.293494 + 3.45165i) q^{6} +12.3959 q^{7} +(-2.01392 + 7.74236i) q^{8} +3.00000 q^{9} -11.0403i q^{11} +(6.82874 + 1.16975i) q^{12} -2.82009i q^{13} +(2.10047 - 24.7027i) q^{14} +(15.0878 + 5.32529i) q^{16} +6.52606i q^{17} +(0.508346 - 5.97843i) q^{18} -27.9928i q^{19} -21.4703 q^{21} +(-22.0012 - 1.87077i) q^{22} +7.90421 q^{23} +(3.48822 - 13.4102i) q^{24} +(-5.61989 - 0.477860i) q^{26} -5.19615 q^{27} +(-48.8718 - 8.37167i) q^{28} -50.7169 q^{29} -36.3467i q^{31} +(13.1689 - 29.1647i) q^{32} +19.1224i q^{33} +(13.0052 + 1.10583i) q^{34} +(-11.8277 - 2.02607i) q^{36} -18.9279i q^{37} +(-55.7842 - 4.74333i) q^{38} +4.88453i q^{39} +5.30410 q^{41} +(-3.63812 + 42.7863i) q^{42} +45.5870 q^{43} +(-7.45616 + 43.5273i) q^{44} +(1.33936 - 15.7516i) q^{46} +11.7246 q^{47} +(-26.1328 - 9.22368i) q^{48} +104.658 q^{49} -11.3035i q^{51} +(-1.90457 + 11.1184i) q^{52} -41.1680i q^{53} +(-0.880481 + 10.3549i) q^{54} +(-24.9644 + 95.9735i) q^{56} +48.4849i q^{57} +(-8.59391 + 101.069i) q^{58} +10.7008i q^{59} +56.1297 q^{61} +(-72.4319 - 6.15889i) q^{62} +37.1877 q^{63} +(-55.8882 - 31.1850i) q^{64} +(38.1073 + 3.24026i) q^{66} -16.1709 q^{67} +(4.40743 - 25.7295i) q^{68} -13.6905 q^{69} -66.1617i q^{71} +(-6.04177 + 23.2271i) q^{72} -15.6330i q^{73} +(-37.7198 - 3.20731i) q^{74} +(-18.9051 + 110.363i) q^{76} -136.855i q^{77} +(9.73394 + 0.827677i) q^{78} +123.057i q^{79} +9.00000 q^{81} +(0.898773 - 10.5701i) q^{82} +99.6700 q^{83} +(84.6484 + 14.5002i) q^{84} +(7.72465 - 90.8461i) q^{86} +87.8443 q^{87} +(85.4781 + 22.2343i) q^{88} -101.083 q^{89} -34.9575i q^{91} +(-31.1629 - 5.33817i) q^{92} +62.9543i q^{93} +(1.98672 - 23.3649i) q^{94} +(-22.8092 + 50.5148i) q^{96} +127.293i q^{97} +(17.7342 - 208.564i) q^{98} -33.1209i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 20 q^{4} - 12 q^{6} + 48 q^{9} + 40 q^{14} + 68 q^{16} - 96 q^{21} - 36 q^{24} - 72 q^{26} - 128 q^{29} + 184 q^{34} - 60 q^{36} - 32 q^{41} - 344 q^{44} + 304 q^{46} + 112 q^{49} - 36 q^{54} + 232 q^{56}+ \cdots - 348 q^{96}+O(q^{100}) \) 16 * q - 20 * q^4 - 12 * q^6 + 48 * q^9 + 40 * q^14 + 68 * q^16 - 96 * q^21 - 36 * q^24 - 72 * q^26 - 128 * q^29 + 184 * q^34 - 60 * q^36 - 32 * q^41 - 344 * q^44 + 304 * q^46 + 112 * q^49 - 36 * q^54 + 232 * q^56 - 352 * q^61 + 220 * q^64 + 216 * q^66 + 192 * q^69 - 264 * q^74 - 48 * q^76 + 144 * q^81 + 72 * q^84 - 400 * q^86 - 160 * q^89 + 192 * q^94 - 348 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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