LMFDB - Embedded newform 84.4.e.a.71.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,4,Mod(71,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("84.71");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	84.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.95616044048$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.17
Character	$\chi$	$=$	84.71
Dual form			84.4.e.a.71.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0878767 - 2.82706i) q^{2} +(-0.849945 + 5.12617i) q^{3} +(-7.98456 + 0.496866i) q^{4} -11.8826i q^{5} +(14.5667 + 1.95238i) q^{6} -7.00000i q^{7} +(2.10633 + 22.5292i) q^{8} +(-25.5552 - 8.71392i) q^{9} +(-33.5929 + 1.04421i) q^{10} -57.5490 q^{11} +(4.23942 - 41.3525i) q^{12} -59.9367 q^{13} +(-19.7894 + 0.615137i) q^{14} +(60.9123 + 10.0996i) q^{15} +(63.5062 - 7.93450i) q^{16} -51.9634i q^{17} +(-22.3891 + 73.0118i) q^{18} -20.5454i q^{19} +(5.90407 + 94.8774i) q^{20} +(35.8832 + 5.94962i) q^{21} +(5.05721 + 162.694i) q^{22} +53.7192 q^{23} +(-117.279 - 8.35118i) q^{24} -16.1967 q^{25} +(5.26704 + 169.445i) q^{26} +(66.3895 - 123.594i) q^{27} +(3.47806 + 55.8919i) q^{28} -158.741i q^{29} +(23.1994 - 173.090i) q^{30} +302.431i q^{31} +(-28.0120 - 178.839i) q^{32} +(48.9135 - 295.006i) q^{33} +(-146.904 + 4.56637i) q^{34} -83.1783 q^{35} +(208.376 + 56.8793i) q^{36} +284.534 q^{37} +(-58.0830 + 1.80546i) q^{38} +(50.9429 - 307.245i) q^{39} +(267.706 - 25.0287i) q^{40} -157.215i q^{41} +(13.6666 - 101.967i) q^{42} -83.6549i q^{43} +(459.503 - 28.5941i) q^{44} +(-103.544 + 303.663i) q^{45} +(-4.72067 - 151.868i) q^{46} -479.631 q^{47} +(-13.3032 + 332.288i) q^{48} -49.0000 q^{49} +(1.42331 + 45.7890i) q^{50} +(266.373 + 44.1660i) q^{51} +(478.568 - 29.7805i) q^{52} +265.944i q^{53} +(-355.241 - 176.826i) q^{54} +683.832i q^{55} +(157.704 - 14.7443i) q^{56} +(105.319 + 17.4624i) q^{57} +(-448.770 + 13.9496i) q^{58} -148.259 q^{59} +(-491.376 - 50.3754i) q^{60} -476.710 q^{61} +(854.991 - 26.5766i) q^{62} +(-60.9975 + 178.886i) q^{63} +(-503.127 + 94.9075i) q^{64} +712.205i q^{65} +(-838.297 - 112.357i) q^{66} -779.619i q^{67} +(25.8188 + 414.905i) q^{68} +(-45.6584 + 275.374i) q^{69} +(7.30944 + 235.150i) q^{70} +615.023 q^{71} +(142.490 - 594.091i) q^{72} +327.327 q^{73} +(-25.0039 - 804.395i) q^{74} +(13.7663 - 83.0269i) q^{75} +(10.2083 + 164.046i) q^{76} +402.843i q^{77} +(-873.079 - 117.019i) q^{78} -448.606i q^{79} +(-94.2827 - 754.621i) q^{80} +(577.135 + 445.372i) q^{81} +(-444.456 + 13.8155i) q^{82} -680.159 q^{83} +(-289.467 - 29.6759i) q^{84} -617.461 q^{85} +(-236.498 + 7.35132i) q^{86} +(813.732 + 134.921i) q^{87} +(-121.217 - 1296.53i) q^{88} -413.171i q^{89} +(867.572 + 266.041i) q^{90} +419.557i q^{91} +(-428.924 + 26.6912i) q^{92} +(-1550.31 - 257.050i) q^{93} +(42.1483 + 1355.95i) q^{94} -244.133 q^{95} +(940.566 + 8.40876i) q^{96} +552.922 q^{97} +(4.30596 + 138.526i) q^{98} +(1470.67 + 501.477i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 12 q^{4} + 30 q^{6} + 20 q^{9} - 132 q^{10} - 78 q^{12} + 324 q^{16} + 424 q^{18} - 240 q^{22} - 382 q^{24} - 900 q^{25} + 168 q^{28} + 476 q^{30} + 848 q^{33} - 576 q^{34} + 412 q^{36} + 528 q^{37}+ \cdots - 72 q^{97}+O(q^{100}) $ 36 * q + 12 * q^4 + 30 * q^6 + 20 * q^9 - 132 * q^10 - 78 * q^12 + 324 * q^16 + 424 * q^18 - 240 * q^22 - 382 * q^24 - 900 * q^25 + 168 * q^28 + 476 * q^30 + 848 * q^33 - 576 * q^34 + 412 * q^36 + 528 * q^37 - 1068 * q^40 + 70 * q^42 - 984 * q^45 + 288 * q^46 + 526 * q^48 - 1764 * q^49 + 468 * q^52 - 1826 * q^54 + 1840 * q^57 + 1536 * q^58 + 652 * q^60 + 2448 * q^61 - 2604 * q^64 - 1188 * q^66 - 744 * q^69 + 252 * q^70 + 1888 * q^72 - 1656 * q^73 - 972 * q^76 - 1348 * q^78 + 2452 * q^81 + 888 * q^82 + 490 * q^84 + 2904 * q^85 + 4008 * q^88 + 3184 * q^90 - 6744 * q^93 + 3264 * q^94 - 1330 * q^96 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−0.0878767	−	2.82706i	−0.0310691	−	0.999517i
$2$	−0.0878767	−	2.82706i	−0.0310691	−	0.999517i
$3$	−0.849945	+	5.12617i	−0.163572	+	0.986531i
$3$	−0.849945	+	5.12617i	−0.163572	+	0.986531i
$4$	−7.98456	+	0.496866i	−0.998069	+	0.0621082i
$5$		−	11.8826i		−	1.06281i	−0.847117	−	0.531407i	$-0.821664\pi$
$5$		−	11.8826i		−	1.06281i	0.847117	−	0.531407i	$-0.178336\pi$
$6$	14.5667	+	1.95238i	0.991137	+	0.132842i
$7$		−	7.00000i		−	0.377964i
$7$		−	7.00000i		−	0.377964i
$8$	2.10633	+	22.5292i	0.0930873	+	0.995658i
$9$	−25.5552	−	8.71392i	−0.946488	−	0.322738i
$10$	−33.5929	+	1.04421i	−1.06230	+	0.0330207i
$11$	−57.5490			−1.57742			−0.788712	−	0.614763i	$-0.789252\pi$
$11$	−57.5490			−1.57742			−0.788712	+	0.614763i	$0.789252\pi$
$12$	4.23942	−	41.3525i	0.101985	−	0.994786i
$13$	−59.9367			−1.27873			−0.639363	−	0.768905i	$-0.720802\pi$
$13$	−59.9367			−1.27873			−0.639363	+	0.768905i	$0.720802\pi$
$14$	−19.7894	+	0.615137i	−0.377782	+	0.0117430i
$15$	60.9123	+	10.0996i	1.04850	+	0.173847i
$16$	63.5062	−	7.93450i	0.992285	−	0.123977i
$17$		−	51.9634i		−	0.741351i	−0.928762	−	0.370676i	$-0.879126\pi$
$17$		−	51.9634i		−	0.741351i	0.928762	−	0.370676i	$-0.120874\pi$
$18$	−22.3891	+	73.0118i	−0.293175	+	0.956059i
$19$		−	20.5454i		−	0.248075i	−0.992278	−	0.124038i	$-0.960416\pi$
$19$		−	20.5454i		−	0.248075i	0.992278	−	0.124038i	$-0.0395843\pi$
$20$	5.90407	+	94.8774i	0.0660095	+	1.06076i
$21$	35.8832	+	5.94962i	0.372874	+	0.0618244i
$22$	5.05721	+	162.694i	0.0490091	+	1.57666i
$23$	53.7192			0.487010			0.243505	−	0.969900i	$-0.421703\pi$
$23$	53.7192			0.487010			0.243505	+	0.969900i	$0.421703\pi$
$24$	−117.279	−	8.35118i	−0.997474	−	0.0710282i
$25$	−16.1967			−0.129573
$26$	5.26704	+	169.445i	0.0397289	+	1.27811i
$27$	66.3895	−	123.594i	0.473210	−	0.880950i
$28$	3.47806	+	55.8919i	0.0234747	+	0.377235i
$29$		−	158.741i		−	1.01646i	−0.861220	−	0.508232i	$-0.830299\pi$
$29$		−	158.741i		−	1.01646i	0.861220	−	0.508232i	$-0.169701\pi$
$30$	23.1994	−	173.090i	0.141187	−	1.05339i
$31$			302.431i			1.75220i	0.482129	+	0.876100i	$0.339864\pi$
$31$			302.431i			1.75220i	−0.482129	+	0.876100i	$0.660136\pi$
$32$	−28.0120	−	178.839i	−0.154746	−	0.987954i
$33$	48.9135	−	295.006i	0.258022	−	1.55618i
$34$	−146.904	+	4.56637i	−0.740993	+	0.0230331i
$35$	−83.1783			−0.401706
$36$	208.376	+	56.8793i	0.964706	+	0.263330i
$37$	284.534			1.26425			0.632123	−	0.774868i	$-0.282184\pi$
$37$	284.534			1.26425			0.632123	+	0.774868i	$0.282184\pi$
$38$	−58.0830	+	1.80546i	−0.247955	+	0.00770747i
$39$	50.9429	−	307.245i	0.209164	−	1.26150i
$40$	267.706	−	25.0287i	1.05820	−	0.0989345i
$41$		−	157.215i		−	0.598849i	−0.954120	−	0.299425i	$-0.903205\pi$
$41$		−	157.215i		−	0.598849i	0.954120	−	0.299425i	$-0.0967947\pi$
$42$	13.6666	−	101.967i	0.0502097	−	0.374615i
$43$		−	83.6549i		−	0.296680i	−0.988936	−	0.148340i	$-0.952607\pi$
$43$		−	83.6549i		−	0.296680i	0.988936	−	0.148340i	$-0.0473931\pi$
$44$	459.503	−	28.5941i	1.57438	−	0.0979710i
$45$	−103.544	+	303.663i	−0.343010	+	1.00594i
$46$	−4.72067	−	151.868i	−0.0151310	−	0.486775i
$47$	−479.631			−1.48854			−0.744269	−	0.667880i	$-0.767202\pi$
$47$	−479.631			−1.48854			−0.744269	+	0.667880i	$0.767202\pi$
$48$	−13.3032	+	332.288i	−0.0400033	+	0.999200i
$49$	−49.0000			−0.142857
$50$	1.42331	+	45.7890i	0.00402573	+	0.129511i
$51$	266.373	+	44.1660i	0.731366	+	0.121264i
$52$	478.568	−	29.7805i	1.27626	−	0.0794194i
$53$			265.944i			0.689251i	0.938740	+	0.344625i	$0.111994\pi$
$53$			265.944i			0.689251i	−0.938740	+	0.344625i	$0.888006\pi$
$54$	−355.241	−	176.826i	−0.895227	−	0.445611i
$55$			683.832i			1.67651i
$56$	157.704	−	14.7443i	0.376323	−	0.0351837i
$57$	105.319	+	17.4624i	0.244734	+	0.0405782i
$58$	−448.770	+	13.9496i	−1.01597	+	0.0315806i
$59$	−148.259			−0.327148			−0.163574	−	0.986531i	$-0.552302\pi$
$59$	−148.259			−0.327148			−0.163574	+	0.986531i	$0.552302\pi$
$60$	−491.376	−	50.3754i	−1.05727	−	0.108391i
$61$	−476.710			−1.00060			−0.500299	−	0.865853i	$-0.666776\pi$
$61$	−476.710			−1.00060			−0.500299	+	0.865853i	$0.666776\pi$
$62$	854.991	−	26.5766i	1.75136	−	0.0544393i
$63$	−60.9975	+	178.886i	−0.121983	+	0.357739i
$64$	−503.127	+	94.9075i	−0.982670	+	0.185366i
$65$			712.205i			1.35905i
$66$	−838.297	−	112.357i	−1.56344	−	0.209549i
$67$		−	779.619i		−	1.42158i	−0.703406	−	0.710788i	$-0.748338\pi$
$67$		−	779.619i		−	1.42158i	0.703406	−	0.710788i	$-0.251662\pi$
$68$	25.8188	+	414.905i	0.0460440	+	0.739920i
$69$	−45.6584	+	275.374i	−0.0796613	+	0.480451i
$70$	7.30944	+	235.150i	0.0124806	+	0.401512i
$71$	615.023			1.02803			0.514013	−	0.857782i	$-0.328158\pi$
$71$	615.023			1.02803			0.514013	+	0.857782i	$0.328158\pi$
$72$	142.490	−	594.091i	0.233230	−	0.972421i
$73$	327.327			0.524805			0.262403	−	0.964958i	$-0.415485\pi$
$73$	327.327			0.524805			0.262403	+	0.964958i	$0.415485\pi$
$74$	−25.0039	−	804.395i	−0.0392790	−	1.26364i
$75$	13.7663	−	83.0269i	0.0211946	−	0.127828i
$76$	10.2083	+	164.046i	0.0154075	+	0.247596i
$77$			402.843i			0.596210i
$78$	−873.079	−	117.019i	−1.26739	−	0.169869i
$79$		−	448.606i		−	0.638887i	−0.947605	−	0.319444i	$-0.896504\pi$
$79$		−	448.606i		−	0.638887i	0.947605	−	0.319444i	$-0.103496\pi$
$80$	−94.2827	−	754.621i	−0.131764	−	1.05461i
$81$	577.135	+	445.372i	0.791681	+	0.610935i
$82$	−444.456	+	13.8155i	−0.598560	+	0.0186057i
$83$	−680.159			−0.899484			−0.449742	−	0.893159i	$-0.648484\pi$
$83$	−680.159			−0.899484			−0.449742	+	0.893159i	$0.648484\pi$
$84$	−289.467	−	29.6759i	−0.375994	−	0.0385465i
$85$	−617.461			−0.787919
$86$	−236.498	+	7.35132i	−0.296537	+	0.00921759i
$87$	813.732	+	134.921i	1.00277	+	0.166265i
$88$	−121.217	−	1296.53i	−0.146838	−	1.57057i
$89$		−	413.171i		−	0.492090i	−0.969258	−	0.246045i	$-0.920869\pi$
$89$		−	413.171i		−	0.492090i	0.969258	−	0.246045i	$-0.0791312\pi$
$90$	867.572	+	266.041i	1.01611	+	0.311591i
$91$			419.557i			0.483313i
$92$	−428.924	+	26.6912i	−0.486070	+	0.0302473i
$93$	−1550.31	−	257.050i	−1.72860	−	0.286611i
$94$	42.1483	+	1355.95i	0.0462476	+	1.48782i
$95$	−244.133			−0.263658
$96$	940.566	+	8.40876i	0.999960	+	0.00893975i
$97$	552.922			0.578771			0.289385	−	0.957213i	$-0.406549\pi$
$97$	552.922			0.578771			0.289385	+	0.957213i	$0.406549\pi$
$98$	4.30596	+	138.526i	0.00443844	+	0.142788i
$99$	1470.67	+	501.477i	1.49301	+	0.509094i
$100$	129.323	−	8.04757i	0.129323	−	0.00804757i
$101$		−	81.5446i		−	0.0803366i	−0.999193	−	0.0401683i	$-0.987211\pi$
$101$		−	81.5446i		−	0.0803366i	0.999193	−	0.0401683i	$-0.0127894\pi$
$102$	101.452	−	756.934i	0.0984829	−	0.734781i
$103$		−	1015.94i		−	0.971881i	−0.873992	−	0.485940i	$-0.838477\pi$
$103$		−	1015.94i		−	0.971881i	0.873992	−	0.485940i	$-0.161523\pi$
$104$	−126.246	−	1350.32i	−0.119033	−	1.27317i
$105$	70.6970	−	426.386i	0.0657078	−	0.396295i
$106$	751.841	−	23.3703i	0.688918	−	0.0214144i
$107$	−2141.69			−1.93500			−0.967499	−	0.252874i	$-0.918624\pi$
$107$	−2141.69			−1.93500			−0.967499	+	0.252874i	$0.918624\pi$
$108$	−468.681	+	1019.83i	−0.417582	+	0.908639i
$109$	67.7332			0.0595199			0.0297599	−	0.999557i	$-0.490526\pi$
$109$	67.7332			0.0595199			0.0297599	+	0.999557i	$0.490526\pi$
$110$	1933.24	−	60.0929i	1.67570	−	0.0520876i
$111$	−241.838	+	1458.57i	−0.206795	+	1.24722i
$112$	−55.5415	−	444.544i	−0.0468587	−	0.375049i
$113$			1228.08i			1.02237i	0.859471	+	0.511185i	$0.170793\pi$
$113$			1228.08i			1.02237i	−0.859471	+	0.511185i	$0.829207\pi$
$114$	40.1123	−	299.278i	0.0329549	−	0.245877i
$115$		−	638.325i		−	0.517601i
$116$	78.8729	+	1267.48i	0.0631307	+	1.01450i
$117$	1531.69	+	522.284i	1.21030	+	0.412693i
$118$	13.0285	+	419.138i	0.0101642	+	0.326990i
$119$	−363.744			−0.280204
$120$	−99.2339	+	1393.58i	−0.0754898	+	1.06013i
$121$	1980.88			1.48827
$122$	41.8917	+	1347.69i	0.0310877	+	1.00011i
$123$	805.909	+	133.624i	0.590784	+	0.0979550i
$124$	−150.268	−	2414.78i	−0.108826	−	1.74882i
$125$		−	1292.87i		−	0.925101i
$126$	511.083	+	156.724i	0.361356	+	0.110810i
$127$			1138.85i			0.795724i	0.917445	+	0.397862i	$0.130248\pi$
$127$			1138.85i			0.795724i	−0.917445	+	0.397862i	$0.869752\pi$
$128$	312.523	+	1414.03i	0.215807	+	0.976436i
$129$	428.829	+	71.1021i	0.292684	+	0.0485286i
$130$	2013.45	−	62.5862i	1.35839	−	0.0422244i
$131$	−1538.22			−1.02591			−0.512956	−	0.858415i	$-0.671450\pi$
$131$	−1538.22			−1.02591			−0.512956	+	0.858415i	$0.671450\pi$
$132$	−243.974	+	2379.79i	−0.160873	+	1.56920i
$133$	−143.817			−0.0937636
$134$	−2204.03	+	68.5103i	−1.42089	+	0.0441671i
$135$	−1468.62	−	788.882i	−0.936286	−	0.502934i
$136$	1170.69	−	109.452i	0.738132	−	0.0690104i
$137$		−	1885.75i		−	1.17599i	−0.808866	−	0.587993i	$-0.799918\pi$
$137$		−	1885.75i		−	1.17599i	0.808866	−	0.587993i	$-0.200082\pi$
$138$	782.511	+	104.880i	0.482694	+	0.0646956i
$139$		−	704.823i		−	0.430089i	−0.976604	−	0.215044i	$-0.931010\pi$
$139$		−	704.823i		−	0.430089i	0.976604	−	0.215044i	$-0.0689896\pi$
$140$	664.142	−	41.3285i	0.400930	−	0.0249492i
$141$	407.660	−	2458.67i	0.243483	−	1.46849i
$142$	−54.0462	−	1738.71i	−0.0319398	−	1.02753i
$143$	3449.29			2.01709
$144$	−1692.05	−	350.621i	−0.979198	−	0.202906i
$145$	−1886.26			−1.08031
$146$	−28.7644	−	925.375i	−0.0163052	−	0.524552i
$147$	41.6473	−	251.182i	0.0233674	−	0.140933i
$148$	−2271.88	+	141.375i	−1.26181	+	0.0785201i
$149$		−	2025.45i		−	1.11363i	−0.830636	−	0.556816i	$-0.812023\pi$
$149$		−	2025.45i		−	1.11363i	0.830636	−	0.556816i	$-0.187977\pi$
$150$	−235.932	−	31.6220i	−0.128425	−	0.0172129i
$151$		−	1333.21i		−	0.718513i	−0.933239	−	0.359256i	$-0.883030\pi$
$151$		−	1333.21i		−	0.718513i	0.933239	−	0.359256i	$-0.116970\pi$
$152$	462.870	−	43.2752i	0.246998	−	0.0230927i
$153$	−452.805	+	1327.93i	−0.239262	+	0.701680i
$154$	1138.86	−	35.4005i	0.595922	−	0.0185237i
$155$	3593.67			1.86226
$156$	−254.097	+	2478.53i	−0.130410	+	1.27206i
$157$	−1977.17			−1.00506			−0.502532	−	0.864558i	$-0.667598\pi$
$157$	−1977.17			−1.00506			−0.502532	+	0.864558i	$0.667598\pi$
$158$	−1268.24	+	39.4220i	−0.638579	+	0.0198497i
$159$	−1363.28	−	226.038i	−0.679967	−	0.112742i
$160$	−2125.07	+	332.856i	−1.05001	+	0.164466i
$161$		−	376.035i		−	0.184073i
$162$	1208.38	−	1670.73i	0.586044	−	0.810280i
$163$			1678.40i			0.806516i	0.915086	+	0.403258i	$0.132122\pi$
$163$			1678.40i			0.806516i	−0.915086	+	0.403258i	$0.867878\pi$
$164$	78.1146	+	1255.29i	0.0371935	+	0.597693i
$165$	−3505.44	−	581.220i	−1.65393	−	0.274230i
$166$	59.7701	+	1922.85i	0.0279462	+	0.899050i
$167$	−2933.39			−1.35924			−0.679619	−	0.733565i	$-0.737855\pi$
$167$	−2933.39			−1.35924			−0.679619	+	0.733565i	$0.737855\pi$
$168$	−58.4582	+	820.950i	−0.0268461	+	0.377010i
$169$	1395.41			0.635141
$170$	54.2604	+	1745.60i	0.0244799	+	0.787538i
$171$	−179.031	+	525.040i	−0.0800632	+	0.234800i
$172$	41.5652	+	667.947i	0.0184263	+	0.296108i
$173$			2035.22i			0.894420i	0.894429	+	0.447210i	$0.147582\pi$
$173$			2035.22i			0.894420i	−0.894429	+	0.447210i	$0.852418\pi$
$174$	309.922	−	2312.33i	0.135029	−	1.00745i
$175$			113.377i			0.0489742i
$176$	−3654.72	+	456.622i	−1.56525	+	0.195564i
$177$	126.012	−	760.002i	0.0535122	−	0.322742i
$178$	−1168.06	+	36.3081i	−0.491853	+	0.0152888i
$179$	3632.86			1.51694			0.758472	−	0.651706i	$-0.225946\pi$
$179$	3632.86			1.51694			0.758472	+	0.651706i	$0.225946\pi$
$180$	675.875	−	2476.06i	0.279871	−	1.02530i
$181$	−2086.31			−0.856762			−0.428381	−	0.903598i	$-0.640916\pi$
$181$	−2086.31			−0.856762			−0.428381	+	0.903598i	$0.640916\pi$
$182$	1186.11	−	36.8693i	0.483080	−	0.0150161i
$183$	405.177	−	2443.69i	0.163670	−	0.987121i
$184$	113.150	+	1210.25i	0.0453345	+	0.484896i
$185$		−	3381.01i		−	1.34366i
$186$	−590.459	+	4405.42i	−0.232767	+	1.73667i
$187$			2990.44i			1.16943i
$188$	3829.64	−	238.312i	1.48567	−	0.0924505i
$189$	−865.157	−	464.727i	−0.332968	−	0.178857i
$190$	21.4536	+	690.178i	0.00819161	+	0.263530i
$191$	1170.52			0.443433			0.221716	−	0.975111i	$-0.428834\pi$
$191$	1170.52			0.443433			0.221716	+	0.975111i	$0.428834\pi$
$192$	−58.8818	−	2659.78i	−0.0221324	−	0.999755i
$193$	2386.62			0.890116			0.445058	−	0.895502i	$-0.353183\pi$
$193$	2386.62			0.890116			0.445058	+	0.895502i	$0.353183\pi$
$194$	−48.5890	−	1563.15i	−0.0179819	−	0.578491i
$195$	−3650.88	−	605.335i	−1.34074	−	0.222302i
$196$	391.243	−	24.3464i	0.142581	−	0.00887260i
$197$			4598.82i			1.66321i	0.555369	+	0.831604i	$0.312577\pi$
$197$			4598.82i			1.66321i	−0.555369	+	0.831604i	$0.687423\pi$
$198$	1288.47	−	4201.76i	0.462462	−	1.50811i
$199$			1007.78i			0.358992i	0.983759	+	0.179496i	$0.0574467\pi$
$199$			1007.78i			0.358992i	−0.983759	+	0.179496i	$0.942553\pi$
$200$	−34.1155	−	364.898i	−0.0120616	−	0.129011i
$201$	3996.46	+	662.633i	1.40243	+	0.232530i
$202$	−230.532	+	7.16587i	−0.0802978	+	0.00249598i
$203$	−1111.19			−0.384187
$204$	−2148.81	−	220.294i	−0.737486	−	0.0756064i
$205$	−1868.12			−0.636466
$206$	−2872.13	+	89.2776i	−0.971411	+	0.0301955i
$207$	−1372.81	−	468.105i	−0.460950	−	0.157177i
$208$	−3806.35	+	475.568i	−1.26886	+	0.158532i
$209$			1182.36i			0.391320i
$210$	−1211.63	−	162.395i	−0.398146	−	0.0533636i
$211$		−	4982.89i		−	1.62576i	−0.582429	−	0.812881i	$-0.697898\pi$
$211$		−	4982.89i		−	1.62576i	0.582429	−	0.812881i	$-0.302102\pi$
$212$	−132.139	−	2123.45i	−0.0428081	−	0.687920i
$213$	−522.736	+	3152.71i	−0.168156	+	1.01418i
$214$	188.204	+	6054.69i	0.0601187	+	1.93406i
$215$	−994.040			−0.315316
$216$	2924.30	+	1235.37i	0.921174	+	0.389150i
$217$	2117.02			0.662270
$218$	−5.95217	−	191.486i	−0.00184923	−	0.0594911i
$219$	−278.210	+	1677.94i	−0.0858434	+	0.517737i
$220$	−339.773	−	5460.10i	−0.104125	−	1.67327i
$221$			3114.51i			0.947986i
$222$	4144.72	+	555.518i	1.25304	+	0.167946i
$223$		−	341.997i		−	0.102699i	−0.998681	−	0.0513493i	$-0.983648\pi$
$223$		−	341.997i		−	0.102699i	0.998681	−	0.0513493i	$-0.0163522\pi$
$224$	−1251.87	+	196.084i	−0.373412	+	0.0584885i
$225$	413.909	+	141.137i	0.122640	+	0.0418183i
$226$	3471.85	−	107.919i	1.02188	−	0.0317641i
$227$	−1179.18			−0.344779			−0.172389	−	0.985029i	$-0.555149\pi$
$227$	−1179.18			−0.344779			−0.172389	+	0.985029i	$0.555149\pi$
$228$	−849.601	−	87.1003i	−0.246782	−	0.0252998i
$229$	−1424.43			−0.411043			−0.205522	−	0.978653i	$-0.565889\pi$
$229$	−1424.43			−0.411043			−0.205522	+	0.978653i	$0.565889\pi$
$230$	−1804.59	+	56.0939i	−0.517351	+	0.0160814i
$231$	−2065.04	−	342.394i	−0.588180	−	0.0975233i
$232$	3576.30	−	334.360i	1.01205	−	0.0946199i
$233$			573.154i			0.161153i	0.996748	+	0.0805763i	$0.0256761\pi$
$233$			573.154i			0.161153i	−0.996748	+	0.0805763i	$0.974324\pi$
$234$	1341.93	−	4376.09i	0.374891	−	1.22254i
$235$			5699.27i			1.58204i
$236$	1183.78	−	73.6650i	0.326516	−	0.0203186i
$237$	2299.63	+	381.290i	0.630283	+	0.104504i
$238$	31.9646	+	1028.33i	0.00870570	+	0.280069i
$239$	5563.85			1.50584			0.752920	−	0.658112i	$-0.228645\pi$
$239$	5563.85			1.50584			0.752920	+	0.658112i	$0.228645\pi$
$240$	3948.45	+	158.077i	1.06196	+	0.0425161i
$241$	4691.92			1.25408			0.627039	−	0.778988i	$-0.284267\pi$
$241$	4691.92			1.25408			0.627039	+	0.778988i	$0.284267\pi$
$242$	−174.073	−	5600.08i	−0.0462391	−	1.48755i
$243$	−2773.58	+	2579.95i	−0.732204	+	0.681086i
$244$	3806.32	−	236.861i	0.998666	−	0.0621453i
$245$			582.248i			0.151831i
$246$	306.943	−	2290.10i	0.0795526	−	0.593542i
$247$			1231.42i			0.317220i
$248$	−6813.52	+	637.018i	−1.74459	+	0.163108i
$249$	578.098	−	3486.61i	0.147130	−	0.887369i
$250$	−3655.02	+	113.613i	−0.924655	+	0.0287421i
$251$	4505.81			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$251$	4505.81			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$252$	398.155	−	1458.64i	0.0995294	−	0.364625i
$253$	−3091.49			−0.768222
$254$	3219.61	−	100.079i	0.795339	−	0.0247224i
$255$	524.808	−	3165.21i	0.128881	−	0.777306i
$256$	3970.09	−	1007.78i	0.969260	−	0.246040i
$257$			1625.67i			0.394578i	0.980345	+	0.197289i	$0.0632137\pi$
$257$			1625.67i			0.394578i	−0.980345	+	0.197289i	$0.936786\pi$
$258$	163.326	−	1218.57i	0.0394117	−	0.294051i
$259$		−	1991.74i		−	0.477840i
$260$	−353.870	−	5686.64i	−0.0844080	−	1.35642i
$261$	−1383.26	+	4056.65i	−0.328051	+	0.962071i
$262$	135.173	+	4348.63i	0.0318742	+	1.02542i
$263$	−2356.53			−0.552509			−0.276254	−	0.961085i	$-0.589093\pi$
$263$	−2356.53			−0.552509			−0.276254	+	0.961085i	$0.589093\pi$
$264$	6749.26	+	480.602i	1.57344	+	0.112042i
$265$	3160.12			0.732545
$266$	12.6382	+	406.581i	0.00291315	+	0.0937183i
$267$	2117.98	+	351.173i	0.485463	+	0.0804922i
$268$	387.366	+	6224.91i	0.0882916	+	1.41883i
$269$		−	2337.79i		−	0.529880i	−0.964265	−	0.264940i	$-0.914648\pi$
$269$		−	2337.79i		−	0.529880i	0.964265	−	0.264940i	$-0.0853521\pi$
$270$	−2101.16	+	4221.20i	−0.473602	+	0.951459i
$271$			1373.37i			0.307846i	0.988083	+	0.153923i	$0.0491908\pi$
$271$			1373.37i			0.307846i	−0.988083	+	0.153923i	$0.950809\pi$
$272$	−412.304	−	3300.00i	−0.0919102	−	0.735632i
$273$	−2150.72	−	356.600i	−0.476804	−	0.0790565i
$274$	−5331.12	+	165.713i	−1.17542	+	0.0365368i
$275$	932.102			0.204392
$276$	227.738	−	2221.42i	0.0496675	−	0.484471i
$277$	1893.14			0.410642			0.205321	−	0.978695i	$-0.434176\pi$
$277$	1893.14			0.410642			0.205321	+	0.978695i	$0.434176\pi$
$278$	−1992.58	+	61.9375i	−0.429881	+	0.0133625i
$279$	2635.36	−	7728.68i	0.565502	−	1.65844i
$280$	−175.201	−	1873.94i	−0.0373937	−	0.399962i
$281$		−	3960.77i		−	0.840852i	−0.907327	−	0.420426i	$-0.861881\pi$
$281$		−	3960.77i		−	0.840852i	0.907327	−	0.420426i	$-0.138119\pi$
$282$	−6986.63	−	936.420i	−1.47535	−	0.197741i
$283$		−	3479.48i		−	0.730860i	−0.930839	−	0.365430i	$-0.880922\pi$
$283$		−	3479.48i		−	0.730860i	0.930839	−	0.365430i	$-0.119078\pi$
$284$	−4910.69	+	305.584i	−1.02604	+	0.0638488i
$285$	207.499	−	1251.47i	0.0431270	−	0.260107i
$286$	−303.112	−	9751.37i	−0.0626693	−	2.01612i
$287$	−1100.50			−0.226344
$288$	−842.535	+	4814.35i	−0.172385	+	0.985030i
$289$	2212.81			0.450398
$290$	165.758	+	5332.57i	0.0335643	+	1.07979i
$291$	−469.954	+	2834.37i	−0.0946707	+	0.570975i
$292$	−2613.56	+	162.638i	−0.523792	+	0.0325947i
$293$			1778.78i			0.354667i	0.984151	+	0.177334i	$0.0567471\pi$
$293$			1778.78i			0.354667i	−0.984151	+	0.177334i	$0.943253\pi$
$294$	−713.767	−	95.6665i	−0.141591	−	0.0189775i
$295$			1761.71i			0.347697i
$296$	599.322	+	6410.32i	0.117685	+	1.25876i
$297$	−3820.65	+	7112.69i	−0.746453	+	1.38963i
$298$	−5726.07	+	177.990i	−1.11309	+	0.0345995i
$299$	−3219.75			−0.622753
$300$	−68.6645	+	669.773i	−0.0132145	+	0.128898i
$301$	−585.584			−0.112135
$302$	−3769.08	+	117.158i	−0.718166	+	0.0223235i
$303$	418.011	+	69.3084i	0.0792545	+	0.0131408i
$304$	−163.017	−	1304.76i	−0.0307555	−	0.246161i
$305$			5664.56i			1.06345i
$306$	3793.94	+	1163.41i	0.708775	+	0.217346i
$307$		−	25.4001i		−	0.00472203i	−0.999997	−	0.00236101i	$-0.999248\pi$
$307$		−	25.4001i		−	0.00472203i	0.999997	−	0.00236101i	$-0.000751534\pi$
$308$	−200.159	−	3216.52i	−0.0370295	−	0.595059i
$309$	5207.89	+	863.495i	0.958791	+	0.158972i
$310$	−315.800	−	10159.5i	−0.0578588	−	1.86136i
$311$	3038.33			0.553981			0.276991	−	0.960873i	$-0.410663\pi$
$311$	3038.33			0.553981			0.276991	+	0.960873i	$0.410663\pi$
$312$	7029.29	+	500.542i	1.27550	+	0.0908256i
$313$	−8947.92			−1.61587			−0.807934	−	0.589274i	$-0.799414\pi$
$313$	−8947.92			−1.61587			−0.807934	+	0.589274i	$0.799414\pi$
$314$	173.747	+	5589.58i	0.0312265	+	1.00458i
$315$	2125.64	+	724.810i	0.380210	+	0.129646i
$316$	222.897	+	3581.92i	0.0396801	+	0.637654i
$317$			10.5693i			0.00187266i	1.00000		0.000936328i	$0.000298043\pi$
$317$			10.5693i			0.00187266i	−1.00000		0.000936328i	$0.999702\pi$
$318$	−519.224	+	3873.93i	−0.0915617	+	0.683142i
$319$			9135.37i			1.60339i
$320$	1127.75	+	5978.46i	0.197010	+	1.04439i
$321$	1820.32	−	10978.7i	0.316512	−	1.90894i
$322$	−1063.07	+	33.0447i	−0.183984	+	0.00571897i
$323$	−1067.61			−0.183911
$324$	−4829.46	−	3269.34i	−0.828096	−	0.560586i
$325$	970.775			0.165689
$326$	4744.93	−	147.492i	0.806127	−	0.0250577i
$327$	−57.5695	+	347.212i	−0.00973579	+	0.0587182i
$328$	3541.92	−	331.146i	0.596249	−	0.0557453i
$329$			3357.41i			0.562615i
$330$	−1335.10	+	9961.17i	−0.222711	+	1.66165i
$331$		−	7153.70i		−	1.18792i	−0.804493	−	0.593962i	$-0.797563\pi$
$331$		−	7153.70i		−	1.18792i	0.804493	−	0.593962i	$-0.202437\pi$
$332$	5430.77	−	337.948i	0.897747	−	0.0558653i
$333$	−7271.32	−	2479.41i	−1.19659	−	0.408020i
$334$	257.777	+	8292.89i	0.0422303	+	1.35858i
$335$	−9263.92			−1.51087
$336$	2326.01	+	93.1227i	0.377662	+	0.0151198i
$337$	−8329.05			−1.34633			−0.673163	−	0.739494i	$-0.735065\pi$
$337$	−8329.05			−1.34633			−0.673163	+	0.739494i	$0.735065\pi$
$338$	−122.624	−	3944.90i	−0.0197333	−	0.634835i
$339$	−6295.33	−	1043.80i	−1.00860	−	0.167231i
$340$	4930.15	−	306.795i	0.786397	−	0.0489362i
$341$		−	17404.6i		−	2.76396i
$342$	1500.05	+	459.992i	0.237174	+	0.0727296i
$343$			343.000i			0.0539949i
$344$	1884.68	−	176.205i	0.295392	−	0.0276172i
$345$	3272.16	+	542.542i	0.510630	+	0.0846651i
$346$	5753.68	−	178.848i	0.893988	−	0.0277888i
$347$	4245.62			0.656821			0.328411	−	0.944535i	$-0.393487\pi$
$347$	4245.62			0.656821			0.328411	+	0.944535i	$0.393487\pi$
$348$	−6564.33	−	672.969i	−1.01116	−	0.103664i
$349$	−6998.42			−1.07340			−0.536700	−	0.843773i	$-0.680329\pi$
$349$	−6998.42			−1.07340			−0.536700	+	0.843773i	$0.680329\pi$
$350$	320.523	−	9.96317i	0.0489505	−	0.00152158i
$351$	−3979.17	+	7407.80i	−0.605106	+	1.12649i
$352$	1612.06	+	10292.0i	0.244100	+	1.55842i
$353$		−	6706.36i		−	1.01117i	−0.862776	−	0.505586i	$-0.831276\pi$
$353$		−	6706.36i		−	1.01117i	0.862776	−	0.505586i	$-0.168724\pi$
$354$	−2159.65	−	289.458i	−0.324248	−	0.0434591i
$355$		−	7308.09i		−	1.09260i
$356$	205.290	+	3298.99i	0.0305628	+	0.491140i
$357$	309.162	−	1864.61i	0.0458336	−	0.276431i
$358$	−319.244	−	10270.3i	−0.0471301	−	1.51621i
$359$	2823.78			0.415135			0.207567	−	0.978221i	$-0.433445\pi$
$359$	2823.78			0.415135			0.207567	+	0.978221i	$0.433445\pi$
$360$	−7059.36	−	1693.15i	−1.03350	−	0.247881i
$361$	6436.89			0.938459
$362$	183.338	+	5898.12i	0.0266188	+	0.856348i
$363$	−1683.64	+	10154.3i	−0.243439	+	1.46822i
$364$	−208.463	−	3349.97i	−0.0300177	−	0.482380i
$365$		−	3889.51i		−	0.557770i
$366$	−6944.08	−	930.717i	−0.991729	−	0.132922i
$367$		−	4911.38i		−	0.698561i	−0.937018	−	0.349280i	$-0.886426\pi$
$367$		−	4911.38i		−	0.698561i	0.937018	−	0.349280i	$-0.113574\pi$
$368$	3411.51	−	426.235i	0.483253	−	0.0603779i
$369$	−1369.96	+	4017.65i	−0.193271	+	0.566804i
$370$	−9558.33	+	297.112i	−1.34301	+	0.0417463i
$371$	1861.61			0.260512
$372$	12506.3	+	1282.13i	1.74306	+	0.178697i
$373$	−1837.65			−0.255094			−0.127547	−	0.991833i	$-0.540710\pi$
$373$	−1837.65			−0.255094			−0.127547	+	0.991833i	$0.540710\pi$
$374$	8454.15	−	262.790i	1.16886	−	0.0363330i
$375$	6627.46	+	1098.87i	0.912642	+	0.151321i
$376$	−1010.26	−	10805.7i	−0.138564	−	1.48208i
$377$			9514.40i			1.29978i
$378$	−1237.78	+	2486.69i	−0.168425	+	0.338364i
$379$		−	2325.05i		−	0.315118i	−0.987510	−	0.157559i	$-0.949638\pi$
$379$		−	2325.05i		−	0.315118i	0.987510	−	0.157559i	$-0.0503624\pi$
$380$	1949.29	−	121.301i	0.263149	−	0.0163753i
$381$	−5837.95	−	967.963i	−0.785006	−	0.130158i
$382$	−102.861	−	3309.12i	−0.0137770	−	0.443218i
$383$	9467.13			1.26305			0.631525	−	0.775356i	$-0.282429\pi$
$383$	9467.13			1.26305			0.631525	+	0.775356i	$0.282429\pi$
$384$	−7514.18	+	400.195i	−0.998585	+	0.0531832i
$385$	4786.83			0.633661
$386$	−209.728	−	6747.11i	−0.0276551	−	0.889686i
$387$	−728.962	+	2137.82i	−0.0957500	+	0.280805i
$388$	−4414.84	+	274.728i	−0.577653	+	0.0359464i
$389$			3593.30i			0.468348i	0.972195	+	0.234174i	$0.0752386\pi$
$389$			3593.30i			0.468348i	−0.972195	+	0.234174i	$0.924761\pi$
$390$	−1390.49	+	10374.5i	−0.180539	+	1.34700i
$391$		−	2791.43i		−	0.361046i
$392$	−103.210	−	1103.93i	−0.0132982	−	0.142237i
$393$	1307.40	−	7885.15i	0.167811	−	1.01210i
$394$	13001.1	−	404.129i	1.66241	−	0.0516744i
$395$	−5330.61			−0.679019
$396$	−11991.8	−	3273.34i	−1.52175	−	0.415383i
$397$	12570.5			1.58916			0.794578	−	0.607163i	$-0.207692\pi$
$397$	12570.5			1.58916			0.794578	+	0.607163i	$0.207692\pi$
$398$	2849.05	−	88.5600i	0.358819	−	0.0111536i
$399$	122.237	−	737.233i	0.0153371	−	0.0925007i
$400$	−1028.59	+	128.513i	−0.128574	+	0.0160641i
$401$		−	12634.4i		−	1.57340i	−0.617338	−	0.786698i	$-0.711789\pi$
$401$		−	12634.4i		−	1.57340i	0.617338	−	0.786698i	$-0.288211\pi$
$402$	1522.11	−	11356.5i	0.188846	−	1.40898i
$403$		−	18126.7i		−	2.24059i
$404$	40.5167	+	651.097i	0.00498956	+	0.0801815i
$405$	5292.18	−	6857.88i	0.649310	−	0.841409i
$406$	97.6474	+	3141.39i	0.0119363	+	0.384002i
$407$	−16374.6			−1.99425
$408$	−433.955	+	6094.19i	−0.0526569	+	0.739479i
$409$	12338.3			1.49167			0.745834	−	0.666132i	$-0.232051\pi$
$409$	12338.3			1.49167			0.745834	+	0.666132i	$0.232051\pi$
$410$	164.165	+	5281.30i	0.0197744	+	0.636158i
$411$	9666.65	+	1602.78i	1.16015	+	0.192359i
$412$	504.786	+	8111.84i	0.0603618	+	0.970004i
$413$			1037.82i			0.123650i
$414$	−1202.73	+	3922.14i	−0.142779	+	0.465610i
$415$			8082.07i			0.955984i
$416$	1678.95	+	10719.0i	0.197878	+	1.26332i
$417$	3613.04	+	599.061i	0.424296	+	0.0703505i
$418$	3342.62	−	103.902i	0.391131	−	0.0121579i
$419$	10572.5			1.23270			0.616348	−	0.787474i	$-0.288611\pi$
$419$	10572.5			1.23270			0.616348	+	0.787474i	$0.288611\pi$
$420$	−352.628	+	3439.63i	−0.0409678	+	0.399611i
$421$	6245.67			0.723030			0.361515	−	0.932366i	$-0.382260\pi$
$421$	6245.67			0.723030			0.361515	+	0.932366i	$0.382260\pi$
$422$	−14086.9	+	437.879i	−1.62498	+	0.0505110i
$423$	12257.1	+	4179.46i	1.40888	+	0.480408i
$424$	−5991.51	+	560.166i	−0.686258	+	0.0641605i
$425$			841.635i			0.0960595i
$426$	8958.85	+	1200.76i	1.01891	+	0.136565i
$427$			3336.97i			0.378190i
$428$	17100.4	−	1064.13i	1.93126	−	0.120179i
$429$	−2931.71	+	17681.7i	−0.329940	+	1.98993i
$430$	87.3529	+	2810.21i	0.00979658	+	0.315164i
$431$	−9318.09			−1.04138			−0.520692	−	0.853745i	$-0.674326\pi$
$431$	−9318.09			−1.04138			−0.520692	+	0.853745i	$0.674326\pi$
$432$	3235.49	−	8375.75i	0.360342	−	0.932820i
$433$	−13699.1			−1.52041			−0.760204	−	0.649685i	$-0.774901\pi$
$433$	−13699.1			−1.52041			−0.760204	+	0.649685i	$0.774901\pi$
$434$	−186.036	−	5984.94i	−0.0205761	−	0.661950i
$435$	1603.22	−	9669.27i	0.176709	−	1.06576i
$436$	−540.820	+	33.6543i	−0.0594050	+	0.00369667i
$437$		−	1103.68i		−	0.120815i
$438$	4768.07	+	639.066i	0.520154	+	0.0697164i
$439$			7199.35i			0.782702i	0.920242	+	0.391351i	$0.127992\pi$
$439$			7199.35i			0.782702i	−0.920242	+	0.391351i	$0.872008\pi$
$440$	−15406.2	+	1440.37i	−1.66923	+	0.156062i
$441$	1252.20	+	426.982i	0.135213	+	0.0461054i
$442$	8804.92	−	273.693i	0.947528	−	0.0294531i
$443$	−15697.3			−1.68353			−0.841763	−	0.539847i	$-0.818482\pi$
$443$	−15697.3			−1.68353			−0.841763	+	0.539847i	$0.818482\pi$
$444$	1206.26	−	11766.2i	0.128934	−	1.25765i
$445$	−4909.55			−0.523000
$446$	−966.846	+	30.0535i	−0.102649	+	0.00319075i
$447$	10382.8	+	1721.52i	1.09863	+	0.182159i
$448$	664.353	+	3521.89i	0.0700619	+	0.371414i
$449$			16461.7i			1.73024i	0.501567	+	0.865119i	$0.332757\pi$
$449$			16461.7i			1.73024i	−0.501567	+	0.865119i	$0.667243\pi$
$450$	362.629	−	1182.55i	0.0379878	−	0.123880i
$451$			9047.55i			0.944639i
$452$	−610.189	−	9805.65i	−0.0634975	−	1.02040i
$453$	6834.28	+	1133.16i	0.708836	+	0.117529i
$454$	103.622	+	3333.61i	0.0107120	+	0.344612i
$455$	4985.43			0.513672
$456$	−171.578	+	2409.53i	−0.0176203	+	0.247449i
$457$	4880.98			0.499612			0.249806	−	0.968296i	$-0.419633\pi$
$457$	4880.98			0.499612			0.249806	+	0.968296i	$0.419633\pi$
$458$	125.174	+	4026.95i	0.0127707	+	0.410845i
$459$	−6422.35	−	3449.82i	−0.653093	−	0.350815i
$460$	317.162	+	5096.75i	0.0321473	+	0.516602i
$461$			10228.4i			1.03337i	0.856176	+	0.516685i	$0.172834\pi$
$461$			10228.4i			1.03337i	−0.856176	+	0.516685i	$0.827166\pi$
$462$	−786.501	+	5868.08i	−0.0792020	+	0.590926i
$463$			10248.4i			1.02869i	0.857584	+	0.514345i	$0.171965\pi$
$463$			10248.4i			1.02869i	−0.857584	+	0.514345i	$0.828035\pi$
$464$	−1259.53	−	10081.0i	−0.126018	−	1.00862i
$465$	−3054.43	+	18421.8i	−0.304614	+	1.83718i
$466$	1620.34	−	50.3669i	0.161075	−	0.00500687i
$467$	4813.88			0.477002			0.238501	−	0.971142i	$-0.423344\pi$
$467$	4813.88			0.477002			0.238501	+	0.971142i	$0.423344\pi$
$468$	−12489.4	−	3409.16i	−1.23359	−	0.336727i
$469$	−5457.33			−0.537305
$470$	16112.2	−	500.833i	1.58128	−	0.0491525i
$471$	1680.48	−	10135.3i	0.164400	−	0.991528i
$472$	−312.282	−	3340.16i	−0.0304533	−	0.325727i
$473$			4814.25i			0.467991i
$474$	875.848	−	6534.70i	0.0848714	−	0.633225i
$475$			332.767i			0.0321440i
$476$	2904.33	−	180.732i	0.279664	−	0.0174030i
$477$	2317.42	−	6796.26i	0.222447	−	0.652368i
$478$	−488.933	−	15729.4i	−0.0467851	−	1.50511i
$479$	−11369.2			−1.08450			−0.542249	−	0.840218i	$-0.682427\pi$
$479$	−11369.2			−1.08450			−0.542249	+	0.840218i	$0.682427\pi$
$480$	99.9182	−	11176.4i	0.00950129	−	1.06277i
$481$	−17054.0			−1.61663
$482$	−412.310	−	13264.3i	−0.0389631	−	1.25347i
$483$	1927.62	+	319.609i	0.181593	+	0.0301091i
$484$	−15816.5	+	984.232i	−1.48539	+	0.0924335i
$485$		−	6570.17i		−	0.615125i
$486$	7537.41	+	7614.37i	0.703506	+	0.710689i
$487$		−	4160.42i		−	0.387118i	−0.981089	−	0.193559i	$-0.937997\pi$
$487$		−	4160.42i		−	0.387118i	0.981089	−	0.193559i	$-0.0620031\pi$
$488$	−1004.11	−	10739.9i	−0.0931429	−	0.996253i
$489$	−8603.74	−	1426.54i	−0.795653	−	0.131923i
$490$	1646.05	−	51.1661i	0.151757	−	0.00471724i
$491$	−15620.4			−1.43572			−0.717862	−	0.696185i	$-0.754879\pi$
$491$	−15620.4			−1.43572			−0.717862	+	0.696185i	$0.754879\pi$
$492$	−6501.22	−	666.499i	−0.595727	−	0.0610734i
$493$	−8248.72			−0.753557
$494$	3481.30	−	108.213i	0.317067	−	0.00985575i
$495$	5958.86	−	17475.5i	0.541073	−	1.58680i
$496$	2399.64	+	19206.3i	0.217232	+	1.73868i
$497$		−	4305.16i		−	0.388557i
$498$	−9907.66	−	1327.93i	−0.891512	−	0.119490i
$499$			4722.33i			0.423648i	0.977308	+	0.211824i	$0.0679404\pi$
$499$			4722.33i			0.423648i	−0.977308	+	0.211824i	$0.932060\pi$
$500$	642.382	+	10323.0i	0.0574564	+	0.923315i
$501$	2493.22	−	15037.1i	0.222333	−	1.34093i
$502$	−395.956	−	12738.2i	−0.0352039	−	1.13254i
$503$	−647.849			−0.0574278			−0.0287139	−	0.999588i	$-0.509141\pi$
$503$	−647.849			−0.0574278			−0.0287139	+	0.999588i	$0.509141\pi$
$504$	−4158.64	−	997.429i	−0.367541	−	0.0881528i
$505$	−968.964			−0.0853828
$506$	271.670	+	8739.82i	0.0238680	+	0.767851i
$507$	−1186.02	+	7153.08i	−0.103891	+	0.626587i
$508$	−565.857	−	9093.24i	−0.0494210	−	0.794187i
$509$			17395.7i			1.51483i	0.652932	+	0.757417i	$0.273539\pi$
$509$			17395.7i			1.51483i	−0.652932	+	0.757417i	$0.726461\pi$
$510$	−8994.36	−	1205.52i	−0.780935	−	0.104669i
$511$		−	2291.29i		−	0.198358i
$512$	−3197.94	−	11135.1i	−0.276035	−	0.961147i
$513$	−2539.28	−	1364.00i	−0.218542	−	0.117392i
$514$	4595.87	−	142.858i	0.394387	−	0.0122592i
$515$	−12072.1			−1.03293
$516$	−3459.34	−	354.648i	−0.295133	−	0.0302568i
$517$	27602.2			2.34806
$518$	−5630.77	+	175.027i	−0.477610	+	0.0148461i
$519$	−10432.9	−	1729.82i	−0.882373	−	0.146302i
$520$	−16045.4	+	1500.14i	−1.35315	+	0.126510i
$521$		−	15959.1i		−	1.34200i	−0.741458	−	0.670999i	$-0.765866\pi$
$521$		−	15959.1i		−	1.34200i	0.741458	−	0.670999i	$-0.234134\pi$
$522$	11590.0	+	3554.06i	0.971799	+	0.298002i
$523$		−	5571.06i		−	0.465784i	−0.972503	−	0.232892i	$-0.925181\pi$
$523$		−	5571.06i		−	0.465784i	0.972503	−	0.232892i	$-0.0748189\pi$
$524$	12282.0	−	764.287i	1.02393	−	0.0637176i
$525$	−581.188	−	96.3640i	−0.0483146	−	0.00801080i
$526$	207.084	+	6662.05i	0.0171659	+	0.552242i
$527$	15715.3			1.29900
$528$	765.588	−	19122.8i	0.0631021	−	1.57616i
$529$	−9281.24			−0.762821
$530$	−277.701	−	8933.85i	−0.0227595	−	0.732192i
$531$	3788.80	+	1291.92i	0.309642	+	0.105583i
$532$	1148.32	−	71.4580i	0.0935826	−	0.00582349i
$533$			9422.93i			0.765765i
$534$	806.665	−	6018.53i	0.0653705	−	0.487729i
$535$			25448.9i			2.05654i
$536$	17564.2	−	1642.13i	1.41540	−	0.132331i
$537$	−3087.73	+	18622.7i	−0.248130	+	1.49651i
$538$	−6609.08	+	205.437i	−0.529624	+	0.0164629i
$539$	2819.90			0.225346
$540$	12118.2	+	5569.16i	0.965714	+	0.443812i
$541$	4627.15			0.367721			0.183860	−	0.982952i	$-0.441141\pi$
$541$	4627.15			0.367721			0.183860	+	0.982952i	$0.441141\pi$
$542$	3882.60	−	120.687i	0.307698	−	0.00956450i
$543$	1773.25	−	10694.8i	0.140142	−	0.845223i
$544$	−9293.07	+	1455.60i	−0.732421	+	0.114721i
$545$		−	804.848i		−	0.0632586i
$546$	−819.133	+	6111.55i	−0.0642045	+	0.479030i
$547$			4288.22i			0.335194i	0.985856	+	0.167597i	$0.0536007\pi$
$547$			4288.22i			0.335194i	−0.985856	+	0.167597i	$0.946399\pi$
$548$	936.962	+	15056.8i	0.0730384	+	1.17372i
$549$	12182.4	+	4154.01i	0.947054	+	0.322931i
$550$	−81.9100	−	2635.11i	−0.00635028	−	0.204294i
$551$	−3261.39			−0.252159
$552$	−6300.12	−	448.619i	−0.485780	−	0.0345915i
$553$	−3140.24			−0.241477
$554$	−166.363	−	5352.02i	−0.0127583	−	0.410443i
$555$	17331.6	+	2873.67i	1.32556	+	0.219785i
$556$	350.202	+	5627.70i	0.0267120	+	0.429258i
$557$			13183.7i			1.00289i	0.865189	+	0.501446i	$0.167199\pi$
$557$			13183.7i			1.00289i	−0.865189	+	0.501446i	$0.832801\pi$
$558$	−22081.1	−	6771.16i	−1.67521	−	0.513702i
$559$			5014.00i			0.379373i
$560$	−5282.34	+	659.979i	−0.398607	+	0.0498021i
$561$	−15329.5	−	2541.71i	−1.15367	−	0.191285i
$562$	−11197.3	+	348.059i	−0.840446	+	0.0261245i
$563$	5054.25			0.378350			0.189175	−	0.981943i	$-0.439419\pi$
$563$	5054.25			0.378350			0.189175	+	0.981943i	$0.439419\pi$
$564$	−2033.35	+	19833.9i	−0.151808	+	1.48078i
$565$	14592.8			1.08659
$566$	−9836.70	+	305.765i	−0.730508	+	0.0227072i
$567$	3117.60	−	4039.95i	0.230912	−	0.299227i
$568$	1295.44	+	13856.0i	0.0956962	+	1.02356i
$569$		−	1790.71i		−	0.131934i	−0.997822	−	0.0659671i	$-0.978987\pi$
$569$		−	1790.71i		−	0.131934i	0.997822	−	0.0659671i	$-0.0210132\pi$
$570$	−3556.20	−	476.639i	−0.261321	−	0.0350249i
$571$		−	10998.7i		−	0.806099i	−0.915178	−	0.403049i	$-0.867950\pi$
$571$		−	10998.7i		−	0.806099i	0.915178	−	0.403049i	$-0.132050\pi$
$572$	−27541.1	+	1713.84i	−2.01320	+	0.125278i
$573$	−994.875	+	6000.26i	−0.0725332	+	0.437460i
$574$	96.7086	+	3111.19i	0.00703230	+	0.226235i
$575$	−870.074			−0.0631036
$576$	13684.5	+	1958.83i	0.989910	+	0.141698i
$577$	−25965.2			−1.87339			−0.936695	−	0.350147i	$-0.886132\pi$
$577$	−25965.2			−1.87339			−0.936695	+	0.350147i	$0.886132\pi$
$578$	−194.454	−	6255.74i	−0.0139935	−	0.450181i
$579$	−2028.49	+	12234.2i	−0.145598	+	0.878127i
$580$	15060.9	−	937.217i	1.07823	−	0.0670962i
$581$			4761.11i			0.339973i
$582$	8054.24	+	1079.51i	0.573641	+	0.0768853i
$583$		−	15304.8i		−	1.08724i
$584$	689.458	+	7374.41i	0.0488527	+	0.522526i
$585$	6206.10	−	18200.5i	0.438616	−	1.28632i
$586$	5028.72	−	156.313i	0.354496	−	0.0110192i
$587$	11193.8			0.787084			0.393542	−	0.919307i	$-0.371250\pi$
$587$	11193.8			0.787084			0.393542	+	0.919307i	$0.371250\pi$
$588$	−207.731	+	2026.27i	−0.0145692	+	0.142112i
$589$	6213.55			0.434678
$590$	4980.46	−	154.813i	0.347529	−	0.0108026i
$591$	−23574.3	−	3908.74i	−1.64081	−	0.272054i
$592$	18069.7	−	2257.64i	1.25449	−	0.156737i
$593$		−	14750.7i		−	1.02148i	−0.859735	−	0.510740i	$-0.829371\pi$
$593$		−	14750.7i		−	1.02148i	0.859735	−	0.510740i	$-0.170629\pi$
$594$	20443.8	+	10176.2i	1.41215	+	0.702918i
$595$			4322.23i			0.297805i
$596$	1006.38	+	16172.3i	0.0691657	+	1.11148i
$597$	−5166.03	−	856.555i	−0.354157	−	0.0587210i
$598$	282.941	+	9102.44i	0.0193484	+	0.622452i
$599$	5736.96			0.391329			0.195664	−	0.980671i	$-0.437314\pi$
$599$	5736.96			0.391329			0.195664	+	0.980671i	$0.437314\pi$
$600$	1899.52	+	135.261i	0.129246	+	0.00920337i
$601$	11522.6			0.782054			0.391027	−	0.920379i	$-0.372120\pi$
$601$	11522.6			0.782054			0.391027	+	0.920379i	$0.372120\pi$
$602$	51.4592	+	1655.48i	0.00348392	+	0.112081i
$603$	−6793.54	+	19923.3i	−0.458797	+	1.34551i
$604$	662.428	+	10645.1i	0.0446255	+	0.717126i
$605$		−	23538.1i		−	1.58175i
$606$	159.206	−	1187.83i	0.0106721	−	0.0796245i
$607$		−	18497.3i		−	1.23687i	−0.785835	−	0.618436i	$-0.787766\pi$
$607$		−	18497.3i		−	1.23687i	0.785835	−	0.618436i	$-0.212234\pi$
$608$	−3674.31	+	575.517i	−0.245087	+	0.0383887i
$609$	944.447	−	5696.13i	0.0628423	−	0.379013i
$610$	16014.1	−	497.783i	1.06294	−	0.0330404i
$611$	28747.5			1.90343
$612$	2955.64	−	10827.9i	0.195220	−	0.715186i
$613$	8751.26			0.576607			0.288304	−	0.957539i	$-0.406909\pi$
$613$	8751.26			0.576607			0.288304	+	0.957539i	$0.406909\pi$
$614$	−71.8077	+	2.23208i	−0.00471975	+	0.000146709i
$615$	1587.80	−	9576.32i	0.104108	−	0.627893i
$616$	−9075.71	+	848.518i	−0.593621	+	0.0554996i
$617$			14023.7i			0.915030i	0.889202	+	0.457515i	$0.151260\pi$
$617$			14023.7i			0.915030i	−0.889202	+	0.457515i	$0.848740\pi$
$618$	1983.50	−	14798.9i	0.129107	−	0.963267i
$619$		−	20122.5i		−	1.30661i	−0.757096	−	0.653304i	$-0.773382\pi$
$619$		−	20122.5i		−	1.30661i	0.757096	−	0.653304i	$-0.226618\pi$
$620$	−28693.9	+	1785.57i	−1.85867	+	0.115662i
$621$	3566.40	−	6639.37i	0.230458	−	0.429032i
$622$	−266.999	−	8589.56i	−0.0172117	−	0.553714i
$623$	−2892.20			−0.185993
$624$	797.352	−	19916.2i	0.0511533	−	1.27770i
$625$	−17387.3			−1.11278
$626$	786.314	+	25296.3i	0.0502035	+	1.61509i
$627$	−6060.99	−	1004.94i	−0.386049	−	0.0640089i
$628$	15786.8	−	982.387i	1.00312	−	0.0624228i
$629$		−	14785.4i		−	0.937251i
$630$	1862.29	−	6073.00i	0.117770	−	0.384054i
$631$			15050.4i			0.949523i	0.880115	+	0.474761i	$0.157466\pi$
$631$			15050.4i			0.949523i	−0.880115	+	0.474761i	$0.842534\pi$
$632$	10106.7	−	944.910i	0.636113	−	0.0594723i
$633$	25543.1	+	4235.18i	1.60387	+	0.265929i
$634$	29.8801	−	0.928797i	0.00187175	−	5.81817e-5i
$635$	13532.6			0.845706
$636$	10997.5	+	1127.45i	0.685657	+	0.0702929i
$637$	2936.90			0.182675
$638$	25826.3	−	802.786i	1.60262	−	0.0498160i
$639$	−15717.0	−	5359.27i	−0.973015	−	0.331783i
$640$	16802.4	−	3713.59i	1.03777	−	0.229363i
$641$		−	12990.3i		−	0.800444i	−0.916418	−	0.400222i	$-0.868933\pi$
$641$		−	12990.3i		−	0.800444i	0.916418	−	0.400222i	$-0.131067\pi$
$642$	−31197.3	−	4181.38i	−1.91785	−	0.257050i
$643$			13304.0i			0.815956i	0.912992	+	0.407978i	$0.133766\pi$
$643$			13304.0i			0.815956i	−0.912992	+	0.407978i	$0.866234\pi$
$644$	186.839	+	3002.47i	0.0114324	+	0.183717i
$645$	844.879	−	5095.61i	0.0515769	−	0.311069i
$646$	93.8177	+	3018.19i	0.00571394	+	0.183822i
$647$	−11304.7			−0.686912			−0.343456	−	0.939169i	$-0.611598\pi$
$647$	−11304.7			−0.686912			−0.343456	+	0.939169i	$0.611598\pi$
$648$	−8818.22	+	13940.5i	−0.534587	+	0.845113i
$649$	8532.17			0.516051
$650$	−85.3085	−	2744.44i	−0.00514781	−	0.165609i
$651$	−1799.35	+	10852.2i	−0.108329	+	0.653350i
$652$	−833.937	−	13401.2i	−0.0500912	−	0.804959i
$653$		−	19130.0i		−	1.14643i	−0.819407	−	0.573213i	$-0.805697\pi$
$653$		−	19130.0i		−	1.14643i	0.819407	−	0.573213i	$-0.194303\pi$
$654$	986.648	+	132.241i	0.0589924	+	0.00790676i
$655$			18278.0i			1.09035i
$656$	−1247.42	−	9984.12i	−0.0742433	−	0.594229i
$657$	−8364.91	−	2852.31i	−0.496722	−	0.169374i
$658$	9491.62	−	295.038i	0.562343	−	0.0174799i
$659$	−23752.1			−1.40402			−0.702011	−	0.712166i	$-0.747714\pi$
$659$	−23752.1			−1.40402			−0.702011	+	0.712166i	$0.747714\pi$
$660$	28278.2	+	2899.05i	1.66777	+	0.170978i
$661$	7980.69			0.469611			0.234805	−	0.972042i	$-0.424555\pi$
$661$	7980.69			0.469611			0.234805	+	0.972042i	$0.424555\pi$
$662$	−20224.0	+	628.643i	−1.18735	+	0.0369077i
$663$	−15965.5	−	2647.16i	−0.935218	−	0.155064i
$664$	−1432.64	−	15323.4i	−0.0837306	−	0.895578i
$665$			1708.93i			0.0996533i
$666$	−6370.46	+	20774.4i	−0.370646	+	1.20869i
$667$		−	8527.44i		−	0.495028i
$668$	23421.8	−	1457.50i	1.35661	−	0.0844199i
$669$	1753.13	+	290.678i	0.101315	+	0.0167986i
$670$	814.082	+	26189.7i	0.0469414	+	1.51014i
$671$	27434.2			1.57837
$672$	58.8614	−	6583.97i	0.00337891	−	0.377949i
$673$	8141.43			0.466313			0.233157	−	0.972439i	$-0.425094\pi$
$673$	8141.43			0.466313			0.233157	+	0.972439i	$0.425094\pi$
$674$	731.929	+	23546.7i	0.0418292	+	1.34568i
$675$	−1075.29	+	2001.81i	−0.0613155	+	0.114148i
$676$	−11141.7	+	693.329i	−0.633915	+	0.0394475i
$677$			8089.20i			0.459222i	0.973283	+	0.229611i	$0.0737454\pi$
$677$			8089.20i			0.459222i	−0.973283	+	0.229611i	$0.926255\pi$
$678$	−2397.67	+	17889.0i	−0.135814	+	1.01331i
$679$		−	3870.46i		−	0.218755i
$680$	−1300.57	−	13910.9i	−0.0733452	−	0.784497i
$681$	1002.24	−	6044.66i	0.0563961	−	0.340135i
$682$	−49203.9	+	1529.46i	−2.76263	+	0.0858739i
$683$	−1228.57			−0.0688287			−0.0344143	−	0.999408i	$-0.510957\pi$
$683$	−1228.57			−0.0688287			−0.0344143	+	0.999408i	$0.510957\pi$
$684$	1168.61	−	4281.17i	0.0653257	−	0.239320i
$685$	−22407.6			−1.24986
$686$	969.682	−	30.1417i	0.0539689	−	0.00167757i
$687$	1210.69	−	7301.86i	0.0672351	−	0.405507i
$688$	−663.760	−	5312.61i	−0.0367814	−	0.294392i
$689$		−	15939.8i		−	0.881363i
$690$	1246.25	−	9298.28i	0.0687594	−	0.513014i
$691$			16599.3i			0.913844i	0.889507	+	0.456922i	$0.151048\pi$
$691$			16599.3i			0.913844i	−0.889507	+	0.456922i	$0.848952\pi$
$692$	−1011.23	−	16250.3i	−0.0555508	−	0.892693i
$693$	3510.34	−	10294.7i	0.192420	−	0.564306i
$694$	−373.091	−	12002.6i	−0.0204068	−	0.656504i
$695$	−8375.15			−0.457104
$696$	−1325.67	+	18616.9i	−0.0721976	+	1.01390i
$697$	−8169.41			−0.443958
$698$	614.998	+	19785.0i	0.0333496	+	1.07288i
$699$	−2938.08	−	487.150i	−0.158982	−	0.0263601i
$700$	−56.3330	−	905.263i	−0.00304170	−	0.0488796i
$701$		−	23398.3i		−	1.26069i	−0.776316	−	0.630344i	$-0.782914\pi$
$701$		−	23398.3i		−	1.26069i	0.776316	−	0.630344i	$-0.217086\pi$
$702$	21292.0	+	10598.4i	1.14475	+	0.569815i
$703$		−	5845.85i		−	0.313628i
$704$	28954.4	−	5461.83i	1.55009	−	0.292401i
$705$	−29215.4	−	4844.07i	−1.56073	−	0.258777i
$706$	−18959.3	+	589.333i	−1.01068	+	0.0314162i
$707$	−570.812			−0.0303644
$708$	−628.533	+	6130.89i	−0.0333640	+	0.325442i
$709$	4729.80			0.250538			0.125269	−	0.992123i	$-0.460021\pi$
$709$	4729.80			0.250538			0.125269	+	0.992123i	$0.460021\pi$
$710$	−20660.4	+	642.211i	−1.09207	+	0.0339461i
$711$	−3909.12	+	11464.2i	−0.206193	+	0.604700i
$712$	9308.40	−	870.273i	0.489954	−	0.0458074i
$713$			16246.4i			0.853340i
$714$	−5298.54	−	710.165i	−0.277721	−	0.0372230i
$715$		−	40986.6i		−	2.14380i
$716$	−29006.8	+	1805.04i	−1.51402	+	0.0942147i
$717$	−4728.97	+	28521.2i	−0.246313	+	1.48556i
$718$	−248.144	−	7983.00i	−0.0128979	−	0.414934i
$719$	17392.3			0.902120			0.451060	−	0.892494i	$-0.351046\pi$
$719$	17392.3			0.902120			0.451060	+	0.892494i	$0.351046\pi$
$720$	−4166.29	+	20106.0i	−0.215651	+	1.04071i
$721$	−7111.59			−0.367336
$722$	−565.652	−	18197.5i	−0.0291571	−	0.938006i
$723$	−3987.87	+	24051.5i	−0.205132	+	1.23719i
$724$	16658.2	−	1036.61i	0.855108	−	0.0532119i
$725$			2571.08i			0.131707i
$726$	28854.9	+	3867.43i	1.47508	+	0.197705i
$727$			2259.30i			0.115258i	0.998338	+	0.0576292i	$0.0183541\pi$
$727$			2259.30i			0.115258i	−0.998338	+	0.0576292i	$0.981646\pi$
$728$	−9452.26	+	883.723i	−0.481215	+	0.0449903i
$729$	−10867.9	−	16410.7i	−0.552145	−	0.833748i
$730$	−10995.9	+	341.797i	−0.557501	+	0.0173294i
$731$	−4346.99			−0.219944
$732$	−2020.97	+	19713.1i	−0.102045	+	0.995380i
$733$	9477.23			0.477557			0.238779	−	0.971074i	$-0.423253\pi$
$733$	9477.23			0.477557			0.238779	+	0.971074i	$0.423253\pi$
$734$	−13884.8	+	431.595i	−0.698223	+	0.0217036i
$735$	−2984.70	−	494.879i	−0.149786	−	0.0248352i
$736$	−1504.79	−	9607.09i	−0.0753630	−	0.481144i
$737$			44866.3i			2.24243i
$738$	11478.5	+	3519.90i	0.572535	+	0.175568i
$739$			11228.4i			0.558922i	0.960157	+	0.279461i	$0.0901558\pi$
$739$			11228.4i			0.558922i	−0.960157	+	0.279461i	$0.909844\pi$
$740$	1679.91	+	26995.9i	0.0834522	+	1.34106i
$741$	−6312.47	−	1046.64i	−0.312948	−	0.0518884i
$742$	−163.592	−	5262.89i	−0.00809388	−	0.260386i
$743$	32368.4			1.59822			0.799112	−	0.601182i	$-0.205303\pi$
$743$	32368.4			1.59822			0.799112	+	0.601182i	$0.205303\pi$
$744$	2525.66	−	35468.7i	0.124456	−	1.74778i
$745$	−24067.6			−1.18358
$746$	161.487	+	5195.16i	0.00792554	+	0.254971i
$747$	17381.6	+	5926.85i	0.851351	+	0.290298i
$748$	−1485.85	−	23877.3i	−0.0726309	−	1.16717i
$749$			14991.8i			0.731361i
$750$	2524.17	−	18832.8i	0.122893	−	0.916902i
$751$		−	6776.22i		−	0.329251i	−0.986356	−	0.164626i	$-0.947358\pi$
$751$		−	6776.22i		−	0.329251i	0.986356	−	0.164626i	$-0.0526416\pi$
$752$	−30459.5	+	3805.63i	−1.47705	+	0.184544i
$753$	−3829.69	+	23097.5i	−0.185341	+	1.11782i
$754$	26897.8	−	836.094i	1.29915	−	0.0403830i
$755$	−15842.1			−0.763646
$756$	7138.80	+	3280.77i	0.343433	+	0.157831i
$757$	16374.4			0.786180			0.393090	−	0.919500i	$-0.371406\pi$
$757$	16374.4			0.786180			0.393090	+	0.919500i	$0.371406\pi$
$758$	−6573.05	+	204.317i	−0.314966	+	0.00979042i
$759$	2627.59	−	15847.5i	0.125660	−	0.757875i
$760$	−514.223	−	5500.11i	−0.0245432	−	0.262513i
$761$		−	6365.36i		−	0.303212i	−0.988441	−	0.151606i	$-0.951556\pi$
$761$		−	6365.36i		−	0.303212i	0.988441	−	0.151606i	$-0.0484445\pi$
$762$	−2223.47	+	16589.3i	−0.105706	+	0.788671i
$763$		−	474.133i		−	0.0224964i
$764$	−9346.06	+	581.589i	−0.442576	+	0.0275408i
$765$	15779.3	+	5380.51i	0.745756	+	0.254291i
$766$	−831.940	−	26764.2i	−0.0392418	−	1.26244i
$767$	8886.17			0.418333
$768$	1791.70	+	21207.9i	0.0841827	+	0.996450i
$769$	−540.012			−0.0253229			−0.0126615	−	0.999920i	$-0.504030\pi$
$769$	−540.012			−0.0253229			−0.0126615	+	0.999920i	$0.504030\pi$
$770$	−420.650	−	13532.7i	−0.0196873	−	0.633355i
$771$	−8333.45	−	1381.73i	−0.389263	−	0.0645418i
$772$	−19056.1	+	1185.83i	−0.888398	+	0.0552835i
$773$			20167.6i			0.938394i	0.883094	+	0.469197i	$0.155457\pi$
$773$			20167.6i			0.938394i	−0.883094	+	0.469197i	$0.844543\pi$
$774$	6107.80	+	1872.96i	0.283644	+	0.0869794i
$775$		−	4898.38i		−	0.227039i
$776$	1164.63	+	12456.9i	0.0538762	+	0.576258i
$777$	10210.0	+	1692.87i	0.471404	+	0.0781613i
$778$	10158.5	−	315.767i	0.468122	−	0.0145512i
$779$	−3230.03			−0.148560
$780$	29451.4	+	3019.33i	1.35196	+	0.138602i
$781$	−35394.0			−1.62163
$782$	−7891.56	+	245.302i	−0.360871	+	0.0112174i
$783$	−19619.4	−	10538.7i	−0.895453	−	0.481001i
$784$	−3111.81	+	388.791i	−0.141755	+	0.0177109i
$785$			23493.9i			1.06820i
$786$	−22406.7	−	3003.18i	−1.01682	−	0.136285i
$787$		−	39007.0i		−	1.76677i	−0.468646	−	0.883386i	$-0.655258\pi$
$787$		−	39007.0i		−	1.76677i	0.468646	−	0.883386i	$-0.344742\pi$
$788$	−2284.99	−	36719.5i	−0.103299	−	1.66000i
$789$	2002.92	−	12080.0i	0.0903750	−	0.545067i
$790$	468.437	+	15070.0i	0.0210965	+	0.678691i
$791$	8596.54			0.386419
$792$	−8200.14	+	34189.3i	−0.367903	+	1.53392i
$793$	28572.4			1.27949
$794$	−1104.65	−	35537.5i	−0.0493736	−	1.58839i
$795$	−2685.93	+	16199.3i	−0.119824	+	0.722679i
$796$	−500.729	−	8046.65i	−0.0222963	−	0.358299i
$797$		−	9334.99i		−	0.414884i	−0.978247	−	0.207442i	$-0.933486\pi$
$797$		−	9334.99i		−	0.414884i	0.978247	−	0.207442i	$-0.0665138\pi$
$798$	−2094.94	−	280.786i	−0.0929326	−	0.0124558i
$799$			24923.2i			1.10353i
$800$	453.702	+	2896.60i	0.0200510	+	0.128013i
$801$	−3600.34	+	10558.7i	−0.158816	+	0.465758i
$802$	−35718.2	+	1110.27i	−1.57264	+	0.0488840i
$803$	−18837.3			−0.827840
$804$	−32239.2	−	3305.13i	−1.41416	−	0.144979i
$805$	−4468.28			−0.195635
$806$	−51245.3	+	1592.92i	−2.23950	+	0.0696130i
$807$	11983.9	+	1986.99i	0.522743	+	0.0866735i
$808$	1837.13	−	171.760i	0.0799877	−	0.00747831i
$809$			11699.2i			0.508433i	0.967147	+	0.254217i	$0.0818176\pi$
$809$			11699.2i			0.508433i	−0.967147	+	0.254217i	$0.918182\pi$
$810$	−19852.7	−	14358.7i	−0.861176	−	0.622855i
$811$		−	27172.5i		−	1.17652i	−0.808673	−	0.588258i	$-0.799814\pi$
$811$		−	27172.5i		−	1.17652i	0.808673	−	0.588258i	$-0.200186\pi$
$812$	8872.33	−	552.110i	0.383445	−	0.0238612i
$813$	−7040.13	−	1167.29i	−0.303700	−	0.0503550i
$814$	1438.95	+	46292.1i	0.0619596	+	1.99329i
$815$	19943.7			0.857176
$816$	17266.8	+	691.282i	0.740758	+	0.0296565i
$817$	−1718.72			−0.0735990
$818$	−1084.25	−	34881.3i	−0.0463448	−	1.49095i
$819$	3655.98	−	10721.9i	0.155983	−	0.457450i
$820$	14916.1	−	928.206i	0.635237	−	0.0395297i
$821$		−	25582.6i		−	1.08750i	−0.839247	−	0.543751i	$-0.817004\pi$
$821$		−	25582.6i		−	1.08750i	0.839247	−	0.543751i	$-0.182996\pi$
$822$	3681.69	−	27469.1i	0.156221	−	1.16556i
$823$			14407.8i			0.610237i	0.952314	+	0.305119i	$0.0986961\pi$
$823$			14407.8i			0.610237i	−0.952314	+	0.305119i	$0.901304\pi$
$824$	22888.3	−	2139.90i	0.967661	−	0.0904698i
$825$	−792.236	+	4778.11i	−0.0334329	+	0.201639i
$826$	2933.97	−	91.1998i	0.123591	−	0.00384170i
$827$	15273.7			0.642225			0.321113	−	0.947041i	$-0.395943\pi$
$827$	15273.7			0.642225			0.321113	+	0.947041i	$0.395943\pi$
$828$	11193.8	+	3055.51i	0.469822	+	0.128244i
$829$	13333.4			0.558610			0.279305	−	0.960202i	$-0.409896\pi$
$829$	13333.4			0.558610			0.279305	+	0.960202i	$0.409896\pi$
$830$	22848.5	−	710.226i	0.955523	−	0.0297016i
$831$	−1609.06	+	9704.55i	−0.0671695	+	0.405111i
$832$	30155.7	−	5688.44i	1.25657	−	0.237033i
$833$			2546.21i			0.105907i
$834$	1376.08	−	10266.9i	0.0571340	−	0.426277i
$835$			34856.4i			1.44462i
$836$	−587.476	−	9440.65i	−0.0243042	−	0.390564i
$837$	37378.6	+	20078.3i	1.54360	+	0.829159i
$838$	−929.075	−	29889.1i	−0.0382988	−	1.23210i
$839$	−18346.1			−0.754919			−0.377460	−	0.926026i	$-0.623202\pi$
$839$	−18346.1			−0.754919			−0.377460	+	0.926026i	$0.623202\pi$
$840$	9755.04	+	694.637i	0.400691	+	0.0285324i
$841$	−809.675			−0.0331984
$842$	−548.849	−	17656.9i	−0.0224639	−	0.722681i
$843$	20303.6	+	3366.43i	0.829527	+	0.137540i
$844$	2475.82	+	39786.1i	0.100973	+	1.62262i
$845$		−	16581.1i		−	0.675037i
$846$	10738.5	−	35018.7i	0.436403	−	1.42313i
$847$		−	13866.2i		−	0.562512i
$848$	2110.14	+	16889.1i	0.0854509	+	0.683933i
$849$	17836.4	+	2957.37i	0.721017	+	0.119548i
$850$	2379.35	−	73.9600i	0.0960131	−	0.00298448i
$851$	15285.0			0.615701
$852$	2607.34	−	25432.7i	0.104843	−	1.02267i
$853$	35153.2			1.41105			0.705524	−	0.708686i	$-0.250712\pi$
$853$	35153.2			1.41105			0.705524	+	0.708686i	$0.250712\pi$
$854$	9433.82	−	293.242i	0.378008	−	0.0117500i
$855$	6238.86	+	2127.35i	0.249549	+	0.0850923i
$856$	−4511.09	−	48250.5i	−0.180124	−	1.92660i
$857$		−	15229.6i		−	0.607041i	−0.952825	−	0.303521i	$-0.901838\pi$
$857$		−	15229.6i		−	0.607041i	0.952825	−	0.303521i	$-0.0981621\pi$
$858$	50244.8	+	6734.32i	1.99922	+	0.267956i
$859$			33945.5i			1.34832i	0.738585	+	0.674160i	$0.235494\pi$
$859$			33945.5i			1.34832i	−0.738585	+	0.674160i	$0.764506\pi$
$860$	7936.97	−	493.904i	0.314707	−	0.0195837i
$861$	935.368	−	5641.37i	0.0370235	−	0.223295i
$862$	818.842	+	26342.8i	0.0323549	+	1.04088i
$863$	−43822.0			−1.72853			−0.864264	−	0.503039i	$-0.832215\pi$
$863$	−43822.0			−1.72853			−0.864264	+	0.503039i	$0.832215\pi$
$864$	−23963.1	−	8410.91i	−0.943565	−	0.331186i
$865$	24183.7			0.950602
$866$	1203.83	+	38728.2i	0.0472377	+	1.51967i
$867$	−1880.76	+	11343.2i	−0.0736725	+	0.444332i
$868$	−16903.4	+	1051.87i	−0.660991	+	0.0411324i
$869$			25816.8i			1.00780i
$870$	−27476.5	−	3682.69i	−1.07074	−	0.143511i
$871$			46727.8i			1.81781i
$872$	142.668	+	1525.97i	0.00554055	+	0.0592614i
$873$	−14130.0	−	4818.12i	−0.547800	−	0.186791i
$874$	−3120.17	+	96.9878i	−0.120757	+	0.00375362i
$875$	−9050.08			−0.349655
$876$	1387.68	−	13535.8i	0.0535220	−	0.522069i
$877$	−37852.1			−1.45744			−0.728719	−	0.684813i	$-0.759884\pi$
$877$	−37852.1			−1.45744			−0.728719	+	0.684813i	$0.759884\pi$
$878$	20353.0	−	632.655i	0.782324	−	0.0243178i
$879$	−9118.33	−	1511.87i	−0.349890	−	0.0580136i
$880$	5425.87	+	43427.6i	0.207848	+	1.66357i
$881$			3600.18i			0.137677i	0.997628	+	0.0688384i	$0.0219293\pi$
$881$			3600.18i			0.137677i	−0.997628	+	0.0688384i	$0.978071\pi$
$882$	1097.07	−	3577.58i	0.0418822	−	0.136580i
$883$		−	43272.5i		−	1.64919i	−0.565722	−	0.824596i	$-0.691403\pi$
$883$		−	43272.5i		−	1.64919i	0.565722	−	0.824596i	$-0.308597\pi$
$884$	−1547.49	−	24868.0i	−0.0588777	−	0.946155i
$885$	−9030.82	−	1497.36i	−0.343014	−	0.0568735i
$886$	1379.43	+	44377.3i	0.0523057	+	1.68271i
$887$	−24028.0			−0.909562			−0.454781	−	0.890603i	$-0.650283\pi$
$887$	−24028.0			−0.909562			−0.454781	+	0.890603i	$0.650283\pi$
$888$	−33369.7	−	2376.19i	−1.26105	−	0.0897972i
$889$	7971.97			0.300755
$890$	431.435	+	13879.6i	0.0162492	+	0.522748i
$891$	−33213.5	−	25630.7i	−1.24882	−	0.963704i
$892$	169.926	+	2730.69i	0.00637843	+	0.102500i
$893$			9854.18i			0.369269i
$894$	3954.44	−	29504.1i	0.147938	−	1.10376i
$895$		−	43167.9i		−	1.61223i
$896$	9898.21	−	2187.66i	0.369058	−	0.0815675i
$897$	2736.61	−	16505.0i	0.101865	−	0.614365i
$898$	46538.3	−	1446.60i	1.72940	−	0.0537569i
$899$	48008.2			1.78105
$900$	−3375.01	−	921.256i	−0.125000	−	0.0341206i
$901$	13819.4			0.510977
$902$	25578.0	−	795.068i	0.944183	−	0.0293491i
$903$	497.715	−	3001.80i	0.0183421	−	0.110624i
$904$	−27667.5	+	2586.73i	−1.01793	+	0.0951696i
$905$			24790.8i			0.910579i
$906$	2602.94	−	19420.5i	0.0954490	−	0.712145i
$907$			3259.12i			0.119313i	0.998219	+	0.0596567i	$0.0190006\pi$
$907$			3259.12i			0.119313i	−0.998219	+	0.0596567i	$0.980999\pi$
$908$	9415.21	−	585.893i	0.344113	−	0.0214136i
$909$	−710.573	+	2083.89i	−0.0259276	+	0.0760376i
$910$	−438.103	−	14094.1i	−0.0159593	−	0.513424i
$911$	4957.30			0.180288			0.0901441	−	0.995929i	$-0.471267\pi$
$911$	4957.30			0.180288			0.0901441	+	0.995929i	$0.471267\pi$
$912$	6826.97	+	273.320i	0.247877	+	0.00992382i
$913$	39142.5			1.41887
$914$	−428.924	−	13798.8i	−0.0155225	−	0.499371i
$915$	−29037.5	−	4814.57i	−1.04913	−	0.173950i
$916$	11373.4	−	707.749i	0.410250	−	0.0255291i
$917$			10767.5i			0.387759i
$918$	−9188.49	+	18459.5i	−0.330355	+	0.663677i
$919$			14412.7i			0.517334i	0.965967	+	0.258667i	$0.0832832\pi$
$919$			14412.7i			0.517334i	−0.965967	+	0.258667i	$0.916717\pi$
$920$	14380.9	−	1344.52i	0.515354	−	0.0481821i
$921$	130.205	+	21.5887i	0.00465843	+	0.000772391i
$922$	28916.3	−	898.837i	1.03287	−	0.0321059i
$923$	−36862.5			−1.31456
$924$	16658.5	+	1707.82i	0.593102	+	0.0608042i
$925$	−4608.51			−0.163813
$926$	28972.8	−	900.595i	1.02819	−	0.0319604i
$927$	−8852.84	+	25962.6i	−0.313663	+	0.919874i
$928$	−28389.0	+	4446.66i	−1.00422	+	0.157294i
$929$			3928.90i			0.138755i	0.997590	+	0.0693774i	$0.0221013\pi$
$929$			3928.90i			0.138755i	−0.997590	+	0.0693774i	$0.977899\pi$
$930$	52347.9	+	7016.21i	1.84576	+	0.247388i
$931$			1006.72i			0.0354393i
$932$	−284.781	−	4576.38i	−0.0100089	−	0.160842i
$933$	−2582.42	+	15575.0i	−0.0906158	+	0.546520i
$934$	−423.028	−	13609.1i	−0.0148200	−	0.476771i
$935$	35534.2			1.24288
$936$	−8540.37	+	35607.9i	−0.298238	+	1.24346i
$937$	−22929.1			−0.799426			−0.399713	−	0.916640i	$-0.630890\pi$
$937$	−22929.1			−0.799426			−0.399713	+	0.916640i	$0.630890\pi$
$938$	479.572	+	15428.2i	0.0166936	+	0.537046i
$939$	7605.24	−	45868.5i	0.264311	−	1.59410i
$940$	−2831.77	−	45506.1i	−0.0982576	−	1.57899i
$941$			5458.91i			0.189113i	0.995519	+	0.0945565i	$0.0301433\pi$
$941$			5458.91i			0.189113i	−0.995519	+	0.0945565i	$0.969857\pi$
$942$	−28800.8	−	3860.18i	−0.996157	−	0.133515i
$943$		−	8445.46i		−	0.291646i
$944$	−9415.39	+	1176.36i	−0.324624	+	0.0405587i
$945$	−5522.17	+	10280.3i	−0.190091	+	0.353883i
$946$	13610.2	−	423.061i	0.467765	−	0.0145400i
$947$	9864.40			0.338490			0.169245	−	0.985574i	$-0.445867\pi$
$947$	9864.40			0.338490			0.169245	+	0.985574i	$0.445867\pi$
$948$	−18551.0	−	1901.83i	−0.635556	−	0.0651566i
$949$	−19618.9			−0.671082
$950$	940.752	−	29.2424i	0.0321284	−	0.000998684i
$951$	−54.1801	−	8.98334i	−0.00184743	−	0.000306314i
$952$	−766.163	−	8194.84i	−0.0260835	−	0.278988i
$953$		−	39622.9i		−	1.34681i	−0.739273	−	0.673406i	$-0.764831\pi$
$953$		−	39622.9i		−	1.34681i	0.739273	−	0.673406i	$-0.235169\pi$
$954$	−19417.1	−	5954.25i	−0.658964	−	0.202071i
$955$		−	13908.8i		−	0.471286i
$956$	−44424.9	+	2764.49i	−1.50293	+	0.0935250i
$957$	−46829.5	−	7764.57i	−1.58180	−	0.262270i
$958$	999.092	+	32141.6i	0.0336943	+	1.08397i
$959$	−13200.2			−0.444481
$960$	−31605.1	+	699.670i	−1.06255	+	0.0235226i
$961$	−61673.6			−2.07021
$962$	1498.65	+	48212.8i	0.0502271	+	1.61585i
$963$	54731.2	+	18662.5i	1.83145	+	0.624497i
$964$	−37462.9	+	2331.25i	−1.25166	+	0.0778885i
$965$		−	28359.3i		−	0.946028i
$966$	734.161	−	5477.58i	0.0244526	−	0.182441i
$967$			58502.3i			1.94551i	0.231838	+	0.972754i	$0.425526\pi$
$967$			58502.3i			1.94551i	−0.231838	+	0.972754i	$0.574474\pi$
$968$	4172.38	+	44627.6i	0.138539	+	1.48180i
$969$	907.407	−	5472.73i	0.0300827	−	0.181434i
$970$	−18574.3	+	577.364i	−0.614828	+	0.0191114i
$971$	23211.9			0.767154			0.383577	−	0.923509i	$-0.374692\pi$
$971$	23211.9			0.767154			0.383577	+	0.923509i	$0.374692\pi$
$972$	20863.9	−	21977.9i	0.688489	−	0.725247i
$973$	−4933.76			−0.162558
$974$	−11761.8	+	365.604i	−0.386931	+	0.0120274i
$975$	−825.106	+	4976.36i	−0.0271021	+	0.163457i
$976$	−30274.1	+	3782.46i	−0.992878	+	0.124051i
$977$		−	29085.1i		−	0.952421i	−0.879331	−	0.476210i	$-0.842010\pi$
$977$		−	29085.1i		−	0.952421i	0.879331	−	0.476210i	$-0.157990\pi$
$978$	−3276.86	+	24448.7i	−0.107140	+	0.799368i
$979$			23777.6i			0.776235i
$980$	−289.299	−	4648.99i	−0.00942992	−	0.151537i
$981$	−1730.94	−	590.222i	−0.0563349	−	0.0192093i
$982$	1372.67	+	44160.0i	0.0446067	+	1.43503i
$983$	−13441.3			−0.436125			−0.218063	−	0.975935i	$-0.569974\pi$
$983$	−13441.3			−0.436125			−0.218063	+	0.975935i	$0.569974\pi$
$984$	−1312.93	+	18437.9i	−0.0425352	+	0.597337i
$985$	54646.0			1.76768
$986$	724.870	+	23319.6i	0.0234123	+	0.753193i
$987$	−17210.7	−	2853.62i	−0.555037	−	0.0920280i
$988$	−611.850	−	9832.34i	−0.0197020	−	0.316608i
$989$		−	4493.88i		−	0.144486i
$990$	−49927.9	−	15310.4i	−1.60284	−	0.491511i
$991$		−	18843.6i		−	0.604022i	−0.953304	−	0.302011i	$-0.902342\pi$
$991$		−	18843.6i		−	0.604022i	0.953304	−	0.302011i	$-0.0976580\pi$
$992$	54086.4	−	8471.71i	1.73109	−	0.271146i
$993$	36671.1	+	6080.25i	1.17192	+	0.194311i
$994$	−12171.0	+	378.324i	−0.388370	+	0.0120721i
$995$	11975.0			0.381542
$996$	−2883.48	+	28126.3i	−0.0917335	+	0.894794i
$997$	3446.16			0.109469			0.0547346	−	0.998501i	$-0.482569\pi$
$997$	3446.16			0.109469			0.0547346	+	0.998501i	$0.482569\pi$
$998$	13350.3	−	414.982i	0.423443	−	0.0131624i
$999$	18890.1	−	35166.7i	0.598254	−	1.11374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.4.e.a.71.17	✓	36
3.2	odd	2	inner	84.4.e.a.71.20	yes	36
4.3	odd	2	inner	84.4.e.a.71.19	yes	36
12.11	even	2	inner	84.4.e.a.71.18	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.e.a.71.17	✓	36	1.1	even	1	trivial
84.4.e.a.71.18	yes	36	12.11	even	2	inner
84.4.e.a.71.19	yes	36	4.3	odd	2	inner
84.4.e.a.71.20	yes	36	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	84.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0878767 - 2.82706i) q^{2} +(-0.849945 + 5.12617i) q^{3} +(-7.98456 + 0.496866i) q^{4} -11.8826i q^{5} +(14.5667 + 1.95238i) q^{6} -7.00000i q^{7} +(2.10633 + 22.5292i) q^{8} +(-25.5552 - 8.71392i) q^{9} +(-33.5929 + 1.04421i) q^{10} -57.5490 q^{11} +(4.23942 - 41.3525i) q^{12} -59.9367 q^{13} +(-19.7894 + 0.615137i) q^{14} +(60.9123 + 10.0996i) q^{15} +(63.5062 - 7.93450i) q^{16} -51.9634i q^{17} +(-22.3891 + 73.0118i) q^{18} -20.5454i q^{19} +(5.90407 + 94.8774i) q^{20} +(35.8832 + 5.94962i) q^{21} +(5.05721 + 162.694i) q^{22} +53.7192 q^{23} +(-117.279 - 8.35118i) q^{24} -16.1967 q^{25} +(5.26704 + 169.445i) q^{26} +(66.3895 - 123.594i) q^{27} +(3.47806 + 55.8919i) q^{28} -158.741i q^{29} +(23.1994 - 173.090i) q^{30} +302.431i q^{31} +(-28.0120 - 178.839i) q^{32} +(48.9135 - 295.006i) q^{33} +(-146.904 + 4.56637i) q^{34} -83.1783 q^{35} +(208.376 + 56.8793i) q^{36} +284.534 q^{37} +(-58.0830 + 1.80546i) q^{38} +(50.9429 - 307.245i) q^{39} +(267.706 - 25.0287i) q^{40} -157.215i q^{41} +(13.6666 - 101.967i) q^{42} -83.6549i q^{43} +(459.503 - 28.5941i) q^{44} +(-103.544 + 303.663i) q^{45} +(-4.72067 - 151.868i) q^{46} -479.631 q^{47} +(-13.3032 + 332.288i) q^{48} -49.0000 q^{49} +(1.42331 + 45.7890i) q^{50} +(266.373 + 44.1660i) q^{51} +(478.568 - 29.7805i) q^{52} +265.944i q^{53} +(-355.241 - 176.826i) q^{54} +683.832i q^{55} +(157.704 - 14.7443i) q^{56} +(105.319 + 17.4624i) q^{57} +(-448.770 + 13.9496i) q^{58} -148.259 q^{59} +(-491.376 - 50.3754i) q^{60} -476.710 q^{61} +(854.991 - 26.5766i) q^{62} +(-60.9975 + 178.886i) q^{63} +(-503.127 + 94.9075i) q^{64} +712.205i q^{65} +(-838.297 - 112.357i) q^{66} -779.619i q^{67} +(25.8188 + 414.905i) q^{68} +(-45.6584 + 275.374i) q^{69} +(7.30944 + 235.150i) q^{70} +615.023 q^{71} +(142.490 - 594.091i) q^{72} +327.327 q^{73} +(-25.0039 - 804.395i) q^{74} +(13.7663 - 83.0269i) q^{75} +(10.2083 + 164.046i) q^{76} +402.843i q^{77} +(-873.079 - 117.019i) q^{78} -448.606i q^{79} +(-94.2827 - 754.621i) q^{80} +(577.135 + 445.372i) q^{81} +(-444.456 + 13.8155i) q^{82} -680.159 q^{83} +(-289.467 - 29.6759i) q^{84} -617.461 q^{85} +(-236.498 + 7.35132i) q^{86} +(813.732 + 134.921i) q^{87} +(-121.217 - 1296.53i) q^{88} -413.171i q^{89} +(867.572 + 266.041i) q^{90} +419.557i q^{91} +(-428.924 + 26.6912i) q^{92} +(-1550.31 - 257.050i) q^{93} +(42.1483 + 1355.95i) q^{94} -244.133 q^{95} +(940.566 + 8.40876i) q^{96} +552.922 q^{97} +(4.30596 + 138.526i) q^{98} +(1470.67 + 501.477i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 12 q^{4} + 30 q^{6} + 20 q^{9} - 132 q^{10} - 78 q^{12} + 324 q^{16} + 424 q^{18} - 240 q^{22} - 382 q^{24} - 900 q^{25} + 168 q^{28} + 476 q^{30} + 848 q^{33} - 576 q^{34} + 412 q^{36} + 528 q^{37}+ \cdots - 72 q^{97}+O(q^{100}) \) 36 * q + 12 * q^4 + 30 * q^6 + 20 * q^9 - 132 * q^10 - 78 * q^12 + 324 * q^16 + 424 * q^18 - 240 * q^22 - 382 * q^24 - 900 * q^25 + 168 * q^28 + 476 * q^30 + 848 * q^33 - 576 * q^34 + 412 * q^36 + 528 * q^37 - 1068 * q^40 + 70 * q^42 - 984 * q^45 + 288 * q^46 + 526 * q^48 - 1764 * q^49 + 468 * q^52 - 1826 * q^54 + 1840 * q^57 + 1536 * q^58 + 652 * q^60 + 2448 * q^61 - 2604 * q^64 - 1188 * q^66 - 744 * q^69 + 252 * q^70 + 1888 * q^72 - 1656 * q^73 - 972 * q^76 - 1348 * q^78 + 2452 * q^81 + 888 * q^82 + 490 * q^84 + 2904 * q^85 + 4008 * q^88 + 3184 * q^90 - 6744 * q^93 + 3264 * q^94 - 1330 * q^96 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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