LMFDB - Embedded newform 225.4.k.d.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(49,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("225.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.k (of order $6$, degree $2$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Character	$\chi$	$=$	225.49
Dual form			225.4.k.d.124.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.60336 + 2.65775i) q^{2} +(-0.153351 + 5.19389i) q^{3} +(10.1273 - 17.5410i) q^{4} +(-13.0981 - 24.3169i) q^{6} +(-11.6339 + 6.71686i) q^{7} +65.1396i q^{8} +(-26.9530 - 1.59298i) q^{9} +O(q^{10})$	\(q+(-4.60336 + 2.65775i) q^{2} +(-0.153351 + 5.19389i) q^{3} +(10.1273 - 17.5410i) q^{4} +(-13.0981 - 24.3169i) q^{6} +(-11.6339 + 6.71686i) q^{7} +65.1396i q^{8} +(-26.9530 - 1.59298i) q^{9} +(23.4628 + 40.6388i) q^{11} +(89.5531 + 55.2901i) q^{12} +(-31.2935 - 18.0673i) q^{13} +(35.7035 - 61.8403i) q^{14} +(-92.1064 - 159.533i) q^{16} -54.6071i q^{17} +(128.308 - 64.3013i) q^{18} -111.339 q^{19} +(-33.1026 - 61.4555i) q^{21} +(-216.016 - 124.717i) q^{22} +(-31.1544 - 17.9870i) q^{23} +(-338.328 - 9.98925i) q^{24} +192.074 q^{26} +(12.4070 - 139.746i) q^{27} +272.095i q^{28} +(29.0588 + 50.3312i) q^{29} +(147.833 - 256.055i) q^{31} +(396.699 + 229.034i) q^{32} +(-214.671 + 115.631i) q^{33} +(145.132 + 251.377i) q^{34} +(-300.904 + 456.650i) q^{36} -53.0417i q^{37} +(512.533 - 295.911i) q^{38} +(98.6386 - 159.765i) q^{39} +(-64.1795 + 111.162i) q^{41} +(315.717 + 194.924i) q^{42} +(142.177 - 82.0858i) q^{43} +950.461 q^{44} +191.220 q^{46} +(76.0646 - 43.9159i) q^{47} +(842.721 - 453.926i) q^{48} +(-81.2675 + 140.759i) q^{49} +(283.623 + 8.37409i) q^{51} +(-633.839 + 365.947i) q^{52} +479.247i q^{53} +(314.297 + 676.279i) q^{54} +(-437.533 - 757.830i) q^{56} +(17.0739 - 578.281i) q^{57} +(-267.536 - 154.462i) q^{58} +(317.807 - 550.458i) q^{59} +(-24.0128 - 41.5915i) q^{61} +1571.62i q^{62} +(324.269 - 162.507i) q^{63} -961.163 q^{64} +(680.892 - 1102.84i) q^{66} +(25.0440 + 14.4592i) q^{67} +(-957.865 - 553.024i) q^{68} +(98.2001 - 159.054i) q^{69} +576.183 q^{71} +(103.766 - 1755.70i) q^{72} -835.057i q^{73} +(140.972 + 244.170i) q^{74} +(-1127.56 + 1952.99i) q^{76} +(-545.930 - 315.193i) q^{77} +(-29.4548 + 997.612i) q^{78} +(-101.869 - 176.442i) q^{79} +(723.925 + 85.8711i) q^{81} -682.294i q^{82} +(-402.249 + 232.239i) q^{83} +(-1413.23 - 41.7262i) q^{84} +(-436.328 + 755.742i) q^{86} +(-265.871 + 143.210i) q^{87} +(-2647.19 + 1528.36i) q^{88} -993.782 q^{89} +485.423 q^{91} +(-631.021 + 364.320i) q^{92} +(1307.25 + 807.097i) q^{93} +(-233.435 + 404.322i) q^{94} +(-1250.41 + 2025.29i) q^{96} +(763.328 - 440.708i) q^{97} -863.956i q^{98} +(-567.656 - 1132.71i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9}+O(q^{10}) $ 28 * q + 72 * q^4 - 62 * q^6 - 34 * q^9	$ 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9} + 46 q^{11} + 42 q^{14} - 648 q^{16} - 1116 q^{19} + 360 q^{21} - 96 q^{24} + 1432 q^{26} + 592 q^{29} - 488 q^{31} + 250 q^{34} - 4798 q^{36} - 1268 q^{39} - 94 q^{41} + 220 q^{44} + 2868 q^{46} + 2450 q^{49} + 3034 q^{51} + 8132 q^{54} - 1962 q^{56} + 170 q^{59} - 1656 q^{61} - 8944 q^{64} + 9860 q^{66} + 1644 q^{69} - 1312 q^{71} + 2632 q^{74} - 5578 q^{76} + 4220 q^{79} - 4334 q^{81} - 11550 q^{84} - 5138 q^{86} - 12192 q^{89} + 13352 q^{91} - 1034 q^{94} - 1186 q^{96} - 4640 q^{99}+O(q^{100}) $ 28 * q + 72 * q^4 - 62 * q^6 - 34 * q^9 + 46 * q^11 + 42 * q^14 - 648 * q^16 - 1116 * q^19 + 360 * q^21 - 96 * q^24 + 1432 * q^26 + 592 * q^29 - 488 * q^31 + 250 * q^34 - 4798 * q^36 - 1268 * q^39 - 94 * q^41 + 220 * q^44 + 2868 * q^46 + 2450 * q^49 + 3034 * q^51 + 8132 * q^54 - 1962 * q^56 + 170 * q^59 - 1656 * q^61 - 8944 * q^64 + 9860 * q^66 + 1644 * q^69 - 1312 * q^71 + 2632 * q^74 - 5578 * q^76 + 4220 * q^79 - 4334 * q^81 - 11550 * q^84 - 5138 * q^86 - 12192 * q^89 + 13352 * q^91 - 1034 * q^94 - 1186 * q^96 - 4640 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−4.60336	+	2.65775i	−1.62754	+	0.939658i	−0.642710	+	0.766110i	$0.722190\pi$
$2$	−4.60336	+	2.65775i	−1.62754	+	0.939658i	−0.984825	+	0.173548i	$0.944477\pi$
$3$	−0.153351	+	5.19389i	−0.0295125	+	0.999564i
$3$	−0.153351	+	5.19389i	−0.0295125	+	0.999564i
$4$	10.1273	−	17.5410i	1.26591	−	2.19263i
$5$		0			0
$5$		0			0
$6$	−13.0981	−	24.3169i	−0.891216	−	1.65456i
$7$	−11.6339	+	6.71686i	−0.628174	+	0.362676i	−0.780045	−	0.625724i	$-0.784804\pi$
$7$	−11.6339	+	6.71686i	−0.628174	+	0.362676i	0.151871	+	0.988400i	$0.451470\pi$
$8$			65.1396i			2.87879i
$9$	−26.9530	−	1.59298i	−0.998258	−	0.0589993i
$10$		0			0
$11$	23.4628	+	40.6388i	0.643119	+	1.11391i	0.984733	+	0.174074i	$0.0556932\pi$
$11$	23.4628	+	40.6388i	0.643119	+	1.11391i	−0.341614	+	0.939840i	$0.610974\pi$
$12$	89.5531	+	55.2901i	2.15431	+	1.33007i
$13$	−31.2935	−	18.0673i	−0.667636	−	0.385460i	0.127544	−	0.991833i	$-0.459290\pi$
$13$	−31.2935	−	18.0673i	−0.667636	−	0.385460i	−0.795180	+	0.606373i	$0.792624\pi$
$14$	35.7035	−	61.8403i	0.681584	−	1.18054i
$15$		0			0
$16$	−92.1064	−	159.533i	−1.43916	−	2.49270i
$17$		−	54.6071i		−	0.779069i	−0.921012	−	0.389535i	$-0.872636\pi$
$17$		−	54.6071i		−	0.779069i	0.921012	−	0.389535i	$-0.127364\pi$
$18$	128.308	−	64.3013i	1.68014	−	0.841998i
$19$	−111.339			−1.34436			−0.672180	−	0.740388i	$-0.734642\pi$
$19$	−111.339			−1.34436			−0.672180	+	0.740388i	$0.734642\pi$
$20$		0			0
$21$	−33.1026	−	61.4555i	−0.343980	−	0.638604i
$22$	−216.016	−	124.717i	−2.09340	−	1.20862i
$23$	−31.1544	−	17.9870i	−0.282441	−	0.163067i	0.352087	−	0.935967i	$-0.385472\pi$
$23$	−31.1544	−	17.9870i	−0.282441	−	0.163067i	−0.634528	+	0.772900i	$0.718805\pi$
$24$	−338.328	−	9.98925i	−2.87754	−	0.0849603i
$25$		0			0
$26$	192.074			1.44880
$27$	12.4070	−	139.746i	0.0884347	−	0.996082i
$28$			272.095i			1.83647i
$29$	29.0588	+	50.3312i	0.186072	+	0.322285i	0.943937	−	0.330125i	$-0.107091\pi$
$29$	29.0588	+	50.3312i	0.186072	+	0.322285i	−0.757866	+	0.652411i	$0.773758\pi$
$30$		0			0
$31$	147.833	−	256.055i	0.856506	−	1.48351i	−0.0187353	−	0.999824i	$-0.505964\pi$
$31$	147.833	−	256.055i	0.856506	−	1.48351i	0.875241	−	0.483687i	$-0.160703\pi$
$32$	396.699	+	229.034i	2.19147	+	1.26525i
$33$	−214.671	+	115.631i	−1.13241	+	0.609964i
$34$	145.132	+	251.377i	0.732059	+	1.26796i
$35$		0			0
$36$	−300.904	+	456.650i	−1.39307	+	2.11412i
$37$		−	53.0417i		−	0.235676i	−0.993033	−	0.117838i	$-0.962404\pi$
$37$		−	53.0417i		−	0.235676i	0.993033	−	0.117838i	$-0.0375963\pi$
$38$	512.533	−	295.911i	2.18799	−	1.26324i
$39$	98.6386	−	159.765i	0.404995	−	0.655969i
$40$		0			0
$41$	−64.1795	+	111.162i	−0.244467	+	0.423430i	−0.961982	−	0.273114i	$-0.911946\pi$
$41$	−64.1795	+	111.162i	−0.244467	+	0.423430i	0.717514	+	0.696544i	$0.245280\pi$
$42$	315.717	+	194.924i	1.15991	+	0.716127i
$43$	142.177	−	82.0858i	0.504227	−	0.291116i	−0.226230	−	0.974074i	$-0.572640\pi$
$43$	142.177	−	82.0858i	0.504227	−	0.291116i	0.730457	+	0.682958i	$0.239307\pi$
$44$	950.461			3.25653
$45$		0			0
$46$	191.220			0.612910
$47$	76.0646	−	43.9159i	0.236067	−	0.136294i	−0.377301	−	0.926091i	$-0.623148\pi$
$47$	76.0646	−	43.9159i	0.236067	−	0.136294i	0.613368	+	0.789797i	$0.289814\pi$
$48$	842.721	−	453.926i	2.53409	−	1.36497i
$49$	−81.2675	+	140.759i	−0.236932	+	0.410378i
$50$		0			0
$51$	283.623	+	8.37409i	0.778730	+	0.0229923i
$52$	−633.839	+	365.947i	−1.69034	+	0.975918i
$53$			479.247i			1.24207i	0.783783	+	0.621035i	$0.213287\pi$
$53$			479.247i			1.24207i	−0.783783	+	0.621035i	$0.786713\pi$
$54$	314.297	+	676.279i	0.792046	+	1.70426i
$55$		0			0
$56$	−437.533	−	757.830i	−1.04407	−	1.80838i
$57$	17.0739	−	578.281i	0.0396754	−	1.34377i
$58$	−267.536	−	154.462i	−0.605676	−	0.349687i
$59$	317.807	−	550.458i	0.701271	−	1.21464i	−0.266750	−	0.963766i	$-0.585950\pi$
$59$	317.807	−	550.458i	0.701271	−	1.21464i	0.968021	−	0.250871i	$-0.0807169\pi$
$60$		0			0
$61$	−24.0128	−	41.5915i	−0.0504021	−	0.0872990i	0.839724	−	0.543014i	$-0.182717\pi$
$61$	−24.0128	−	41.5915i	−0.0504021	−	0.0872990i	−0.890126	+	0.455715i	$0.849384\pi$
$62$			1571.62i			3.21929i
$63$	324.269	−	162.507i	0.648477	−	0.324983i
$64$	−961.163			−1.87727
$65$		0			0
$66$	680.892	−	1102.84i	1.26988	−	2.05682i
$67$	25.0440	+	14.4592i	0.0456658	+	0.0263652i	0.522659	−	0.852542i	$-0.324940\pi$
$67$	25.0440	+	14.4592i	0.0456658	+	0.0263652i	−0.476993	+	0.878907i	$0.658273\pi$
$68$	−957.865	−	553.024i	−1.70821	−	0.986235i
$69$	98.2001	−	159.054i	0.171332	−	0.277505i
$70$		0			0
$71$	576.183			0.963103			0.481552	−	0.876418i	$-0.340073\pi$
$71$	576.183			0.963103			0.481552	+	0.876418i	$0.340073\pi$
$72$	103.766	−	1755.70i	0.169847	−	2.87377i
$73$		−	835.057i		−	1.33885i	−0.742880	−	0.669425i	$-0.766541\pi$
$73$		−	835.057i		−	1.33885i	0.742880	−	0.669425i	$-0.233459\pi$
$74$	140.972	+	244.170i	0.221455	+	0.383571i
$75$		0			0
$76$	−1127.56	+	1952.99i	−1.70184	+	2.94768i
$77$	−545.930	−	315.193i	−0.807981	−	0.466488i
$78$	−29.4548	+	997.612i	−0.0427577	+	1.44817i
$79$	−101.869	−	176.442i	−0.145078	−	0.251282i	0.784324	−	0.620351i	$-0.213010\pi$
$79$	−101.869	−	176.442i	−0.145078	−	0.251282i	−0.929402	+	0.369069i	$0.879676\pi$
$80$		0			0
$81$	723.925	+	85.8711i	0.993038	+	0.117793i
$82$		−	682.294i		−	0.918863i
$83$	−402.249	+	232.239i	−0.531959	+	0.307127i	−0.741814	−	0.670606i	$-0.766034\pi$
$83$	−402.249	+	232.239i	−0.531959	+	0.307127i	0.209855	+	0.977733i	$0.432701\pi$
$84$	−1413.23	−	41.7262i	−1.83567	−	0.0541988i
$85$		0			0
$86$	−436.328	+	755.742i	−0.547098	+	0.947602i
$87$	−265.871	+	143.210i	−0.327636	+	0.176479i
$88$	−2647.19	+	1528.36i	−3.20672	+	1.85140i
$89$	−993.782			−1.18360			−0.591801	−	0.806084i	$-0.701583\pi$
$89$	−993.782			−1.18360			−0.591801	+	0.806084i	$0.701583\pi$
$90$		0			0
$91$	485.423			0.559189
$92$	−631.021	+	364.320i	−0.715092	+	0.412859i
$93$	1307.25	+	807.097i	1.45759	+	0.899915i
$94$	−233.435	+	404.322i	−0.256139	+	0.443645i
$95$		0			0
$96$	−1250.41	+	2025.29i	−1.32937	+	2.15318i
$97$	763.328	−	440.708i	0.799012	−	0.461310i	−0.0441134	−	0.999027i	$-0.514046\pi$
$97$	763.328	−	440.708i	0.799012	−	0.461310i	0.843126	+	0.537717i	$0.180713\pi$
$98$		−	863.956i		−	0.890538i
$99$	−567.656	−	1132.71i	−0.576278	−	1.14992i
$100$		0			0
$101$	−604.869	−	1047.66i	−0.595909	−	1.03214i	−0.993418	−	0.114546i	$-0.963459\pi$
$101$	−604.869	−	1047.66i	−0.595909	−	1.03214i	0.397509	−	0.917598i	$-0.369875\pi$
$102$	−1327.88	+	715.252i	−1.28902	+	0.694319i
$103$	645.053	+	372.421i	0.617077	+	0.356270i	0.775730	−	0.631065i	$-0.217382\pi$
$103$	645.053	+	372.421i	0.617077	+	0.356270i	−0.158653	+	0.987334i	$0.550715\pi$
$104$	1176.90	−	2038.45i	1.10966	−	1.92198i
$105$		0			0
$106$	−1273.72	−	2206.15i	−1.16712	−	2.02151i
$107$		−	1000.14i		−	0.903622i	−0.892114	−	0.451811i	$-0.850778\pi$
$107$		−	1000.14i		−	0.903622i	0.892114	−	0.451811i	$-0.149222\pi$
$108$	−2325.65	−	1632.89i	−2.07209	−	1.45486i
$109$	915.517			0.804502			0.402251	−	0.915530i	$-0.368228\pi$
$109$	915.517			0.804502			0.402251	+	0.915530i	$0.368228\pi$
$110$		0			0
$111$	275.493	+	8.13403i	0.235573	+	0.00695538i
$112$	2143.12	+	1237.33i	1.80809	+	1.04390i
$113$	−1147.40	−	662.451i	−0.955206	−	0.551488i	−0.0605114	−	0.998168i	$-0.519273\pi$
$113$	−1147.40	−	662.451i	−0.955206	−	0.551488i	−0.894694	+	0.446679i	$0.852606\pi$
$114$	1458.33	+	2707.42i	1.19812	+	2.22432i
$115$		0			0
$116$	1177.15			0.942202
$117$	814.673	+	536.818i	0.643731	+	0.424178i
$118$			3378.61i			2.63582i
$119$	366.789	+	635.297i	0.282550	+	0.489391i
$120$		0			0
$121$	−435.508	+	754.321i	−0.327203	+	0.566733i
$122$	221.080	+	127.640i	0.164062	+	0.0947215i
$123$	−567.522	−	350.388i	−0.416030	−	0.256857i
$124$	−2994.31	−	5186.30i	−2.16853	−	3.75600i
$125$		0			0
$126$	−1060.83	+	1609.91i	−0.750047	+	1.13827i
$127$		−	993.635i		−	0.694259i	−0.937817	−	0.347129i	$-0.887157\pi$
$127$		−	993.635i		−	0.694259i	0.937817	−	0.347129i	$-0.112843\pi$
$128$	1251.00	−	722.262i	0.863855	−	0.498747i
$129$	404.542	+	751.039i	0.276108	+	0.512599i
$130$		0			0
$131$	−691.995	+	1198.57i	−0.461526	+	0.799386i	−0.999037	−	0.0438704i	$-0.986031\pi$
$131$	−691.995	+	1198.57i	−0.461526	+	0.799386i	0.537512	+	0.843256i	$0.319364\pi$
$132$	−145.755	+	4936.59i	−0.0961084	+	3.25511i
$133$	1295.31	−	747.847i	0.844492	−	0.487568i
$134$	−153.715			−0.0990970
$135$		0			0
$136$	3557.09			2.24278
$137$	1339.86	−	773.568i	0.835561	−	0.482411i	−0.0201918	−	0.999796i	$-0.506428\pi$
$137$	1339.86	−	773.568i	0.835561	−	0.482411i	0.855753	+	0.517385i	$0.173094\pi$
$138$	−29.3239	+	993.176i	−0.0180885	+	0.612643i
$139$	−269.752	+	467.225i	−0.164605	+	0.285104i	−0.936515	−	0.350628i	$-0.885968\pi$
$139$	−269.752	+	467.225i	−0.164605	+	0.285104i	0.771910	+	0.635732i	$0.219302\pi$
$140$		0			0
$141$	216.430	+	401.806i	0.129267	+	0.239987i
$142$	−2652.38	+	1531.35i	−1.56748	+	0.904988i
$143$		−	1695.64i		−	0.991586i
$144$	2228.41	+	4446.61i	1.28959	+	2.57327i
$145$		0			0
$146$	2219.38	+	3844.07i	1.25806	+	2.17902i
$147$	−718.627	−	443.680i	−0.403206	−	0.248940i
$148$	−930.406	−	537.170i	−0.516749	−	0.298345i
$149$	−602.335	+	1043.27i	−0.331176	+	0.573613i	−0.982743	−	0.184978i	$-0.940779\pi$
$149$	−602.335	+	1043.27i	−0.331176	+	0.573613i	0.651567	+	0.758591i	$0.274112\pi$
$150$		0			0
$151$	−1486.46	−	2574.62i	−0.801100	−	1.38755i	−0.918893	−	0.394508i	$-0.870915\pi$
$151$	−1486.46	−	2574.62i	−0.801100	−	1.38755i	0.117793	−	0.993038i	$-0.462418\pi$
$152$		−	7252.55i		−	3.87013i
$153$	−86.9881	+	1471.82i	−0.0459645	+	0.777712i
$154$	3350.82			1.75336
$155$		0			0
$156$	−1803.49	−	3348.21i	−0.925607	−	1.71840i
$157$	342.739	+	197.880i	0.174226	+	0.100590i	0.584577	−	0.811338i	$-0.301260\pi$
$157$	342.739	+	197.880i	0.174226	+	0.100590i	−0.410351	+	0.911928i	$0.634594\pi$
$158$	937.877	+	541.484i	0.472238	+	0.272646i
$159$	−2489.16	−	73.4932i	−1.24153	−	0.0366566i
$160$		0			0
$161$	483.265			0.236563
$162$	−3560.71	+	1528.72i	−1.72689	+	0.741404i
$163$		−	3861.43i		−	1.85553i	−0.373169	−	0.927764i	$-0.621729\pi$
$163$		−	3861.43i		−	1.85553i	0.373169	−	0.927764i	$-0.378271\pi$
$164$	1299.93	+	2251.55i	0.618949	+	1.07205i
$165$		0			0
$166$	1234.47	−	2138.16i	0.577188	−	0.999719i
$167$	−1762.34	−	1017.49i	−0.816609	−	0.471470i	0.0326366	−	0.999467i	$-0.489610\pi$
$167$	−1762.34	−	1017.49i	−0.816609	−	0.471470i	−0.849246	+	0.527998i	$0.822943\pi$
$168$	4003.18	−	2156.29i	1.83841	−	0.990244i
$169$	−445.643	−	771.876i	−0.202842	−	0.351332i
$170$		0			0
$171$	3000.91	+	177.360i	1.34202	+	0.0793163i
$172$		−	3325.24i		−	1.47411i
$173$	−1339.67	+	773.458i	−0.588746	+	0.339913i	−0.764602	−	0.644503i	$-0.777064\pi$
$173$	−1339.67	+	773.458i	−0.588746	+	0.339913i	0.175855	+	0.984416i	$0.443731\pi$
$174$	843.286	−	1365.87i	0.367410	−	0.595092i
$175$		0			0
$176$	4322.15	−	7486.19i	1.85111	−	3.20621i
$177$	2810.28	+	1735.07i	1.19341	+	0.736812i
$178$	4574.74	−	2641.23i	1.92636	−	1.11218i
$179$	823.973			0.344059			0.172030	−	0.985092i	$-0.444967\pi$
$179$	823.973			0.344059			0.172030	+	0.985092i	$0.444967\pi$
$180$		0			0
$181$	−4403.55			−1.80836			−0.904180	−	0.427152i	$-0.859517\pi$
$181$	−4403.55			−1.80836			−0.904180	+	0.427152i	$0.859517\pi$
$182$	−2234.58	+	1290.14i	−0.910099	+	0.525446i
$183$	219.704	−	118.342i	0.0887485	−	0.0478037i
$184$	1171.67	−	2029.38i	0.469437	−	0.813088i
$185$		0			0
$186$	−8162.82	−	241.010i	−3.21789	−	0.0950093i
$187$	2219.17	−	1281.24i	0.867816	−	0.501034i
$188$		−	1779.00i		−	0.690144i
$189$	794.315	+	1709.14i	0.305703	+	0.657786i
$190$		0			0
$191$	1523.46	+	2638.72i	0.577141	+	0.999637i	0.995805	+	0.0914964i	$0.0291650\pi$
$191$	1523.46	+	2638.72i	0.577141	+	0.999637i	−0.418664	+	0.908141i	$0.637502\pi$
$192$	147.396	−	4992.18i	0.0554030	−	1.87645i
$193$	1637.57	+	945.452i	0.610751	+	0.352617i	0.773259	−	0.634090i	$-0.218625\pi$
$193$	1637.57	+	945.452i	0.610751	+	0.352617i	−0.162508	+	0.986707i	$0.551958\pi$
$194$	−2342.58	+	4057.48i	−0.866947	+	1.50160i
$195$		0			0
$196$	1646.04	+	2851.03i	0.599870	+	1.03901i
$197$			3652.00i			1.32078i	0.750921	+	0.660392i	$0.229610\pi$
$197$			3652.00i			1.32078i	−0.750921	+	0.660392i	$0.770390\pi$
$198$	5623.60	+	3705.60i	2.01844	+	1.33003i
$199$	−3217.26			−1.14606			−0.573029	−	0.819535i	$-0.694232\pi$
$199$	−3217.26			−1.14606			−0.573029	+	0.819535i	$0.694232\pi$
$200$		0			0
$201$	−78.9398	+	127.858i	−0.0277014	+	0.0448678i
$202$	5568.87	+	3215.19i	1.93972	+	1.11990i
$203$	−676.136	−	390.367i	−0.233771	−	0.134968i
$204$	3019.23	−	4890.24i	1.03622	−	1.67836i
$205$		0			0
$206$	−3959.22			−1.33909
$207$	811.051	+	534.432i	0.272328	+	0.179447i
$208$			6656.47i			2.21896i
$209$	−2612.32	−	4524.67i	−0.864583	−	1.49750i
$210$		0			0
$211$	−2473.90	+	4284.92i	−0.807159	+	1.39804i	0.107666	+	0.994187i	$0.465662\pi$
$211$	−2473.90	+	4284.92i	−0.807159	+	1.39804i	−0.914824	+	0.403853i	$0.867671\pi$
$212$	8406.48	+	4853.49i	2.72339	+	1.57235i
$213$	−88.3585	+	2992.63i	−0.0284236	+	0.962684i
$214$	2658.14	+	4604.03i	0.849096	+	1.47068i
$215$		0			0
$216$	9103.02	+	808.189i	2.86751	+	0.254585i
$217$			3971.91i			1.24254i
$218$	−4214.46	+	2433.22i	−1.30935	+	0.755956i
$219$	4337.19	+	128.057i	1.33827	+	0.0395128i
$220$		0			0
$221$	−986.606	+	1708.85i	−0.300300	+	0.520135i
$222$	−1289.81	+	694.748i	−0.389939	+	0.210038i
$223$	−956.189	+	552.056i	−0.287135	+	0.165778i	−0.636649	−	0.771154i	$-0.719680\pi$
$223$	−956.189	+	552.056i	−0.287135	+	0.165778i	0.349514	+	0.936931i	$0.386347\pi$
$224$	−6153.56			−1.83550
$225$		0			0
$226$	7042.53			2.07284
$227$	−3308.43	+	1910.12i	−0.967348	+	0.558498i	−0.898427	−	0.439124i	$-0.855289\pi$
$227$	−3308.43	+	1910.12i	−0.967348	+	0.558498i	−0.0689210	+	0.997622i	$0.521956\pi$
$228$	−9970.72	−	6155.92i	−2.89617	−	1.78810i
$229$	72.3848	−	125.374i	0.0208879	−	0.0361788i	−0.855393	−	0.517980i	$-0.826684\pi$
$229$	72.3848	−	125.374i	0.0208879	−	0.0361788i	0.876280	+	0.481801i	$0.160017\pi$
$230$		0			0
$231$	1720.80	−	2787.17i	0.490130	−	0.793862i
$232$	−3278.55	+	1892.87i	−0.927792	+	0.535661i
$233$		−	1286.31i		−	0.361670i	−0.983513	−	0.180835i	$-0.942120\pi$
$233$		−	1286.31i		−	0.361670i	0.983513	−	0.180835i	$-0.0578800\pi$
$234$	−5176.97	−	305.970i	−1.44628	−	0.0854782i
$235$		0			0
$236$	−6437.07	−	11149.3i	−1.77550	−	3.07525i
$237$	932.041	−	502.037i	0.255454	−	0.137598i
$238$	−3376.92	−	1949.67i	−0.919721	−	0.531001i
$239$	2109.73	−	3654.15i	0.570991	−	0.988986i	−0.425473	−	0.904971i	$-0.639892\pi$
$239$	2109.73	−	3654.15i	0.570991	−	0.988986i	0.996465	−	0.0840147i	$-0.0267743\pi$
$240$		0			0
$241$	−1141.57	−	1977.25i	−0.305124	−	0.528490i	0.672165	−	0.740401i	$-0.265364\pi$
$241$	−1141.57	−	1977.25i	−0.305124	−	0.528490i	−0.977289	+	0.211912i	$0.932031\pi$
$242$		−	4629.89i		−	1.22984i
$243$	−557.020	+	3746.82i	−0.147049	+	0.989129i
$244$	−972.742			−0.255219
$245$		0			0
$246$	3543.76	+	104.631i	0.918462	+	0.0271179i
$247$	3484.18	+	2011.59i	0.897543	+	0.518197i
$248$	16679.3	+	9629.81i	4.27072	+	2.46570i
$249$	−1144.54	−	2124.85i	−0.291293	−	0.540791i
$250$		0			0
$251$	−7922.23			−1.99222			−0.996109	−	0.0881290i	$-0.971911\pi$
$251$	−7922.23			−1.99222			−0.996109	+	0.0881290i	$0.971911\pi$
$252$	433.442	−	7333.77i	0.108350	−	1.83327i
$253$		−	1688.10i		−	0.419487i
$254$	2640.84	+	4574.06i	0.652366	+	1.12993i
$255$		0			0
$256$	5.46197	−	9.46041i	0.00133349	−	0.00230967i
$257$	−1959.10	−	1131.09i	−0.475508	−	0.274535i	0.243035	−	0.970018i	$-0.421857\pi$
$257$	−1959.10	−	1131.09i	−0.475508	−	0.274535i	−0.718542	+	0.695483i	$0.755190\pi$
$258$	−3858.33	−	2382.13i	−0.931043	−	0.574826i
$259$	356.274	+	617.085i	0.0854741	+	0.148045i
$260$		0			0
$261$	−703.043	−	1402.87i	−0.166733	−	0.332702i
$262$		−	7356.61i		−	1.73471i
$263$	−141.569	+	81.7349i	−0.0331921	+	0.0191635i	−0.516504	−	0.856285i	$-0.672767\pi$
$263$	−141.569	+	81.7349i	−0.0331921	+	0.0191635i	0.483312	+	0.875448i	$0.339434\pi$
$264$	−7532.17	−	13983.6i	−1.75596	−	3.25997i
$265$		0			0
$266$	−3975.18	+	6885.22i	−0.916294	+	1.58707i
$267$	152.398	−	5161.59i	0.0349311	−	1.18309i
$268$	507.257	−	292.865i	0.115618	−	0.0667521i
$269$	−3304.13			−0.748908			−0.374454	−	0.927246i	$-0.622170\pi$
$269$	−3304.13			−0.748908			−0.374454	+	0.927246i	$0.622170\pi$
$270$		0			0
$271$	−1954.96			−0.438212			−0.219106	−	0.975701i	$-0.570314\pi$
$271$	−1954.96			−0.438212			−0.219106	+	0.975701i	$0.570314\pi$
$272$	−8711.64	+	5029.67i	−1.94199	+	1.12121i
$273$	−74.4403	+	2521.23i	−0.0165031	+	0.558945i
$274$	−4111.91	+	7122.03i	−0.906603	+	1.57028i
$275$		0			0
$276$	−1795.47	−	3333.32i	−0.391575	−	0.726965i
$277$	−3674.85	+	2121.67i	−0.797112	+	0.460213i	−0.842460	−	0.538758i	$-0.818894\pi$
$277$	−3674.85	+	2121.67i	−0.797112	+	0.460213i	0.0453482	+	0.998971i	$0.485560\pi$
$278$		−	2867.74i		−	0.618689i
$279$	−4392.44	+	6665.95i	−0.942540	+	1.43039i
$280$		0			0
$281$	1311.15	+	2270.97i	0.278350	+	0.482117i	0.970975	−	0.239181i	$-0.0768791\pi$
$281$	1311.15	+	2270.97i	0.278350	+	0.482117i	−0.692625	+	0.721298i	$0.743546\pi$
$282$	−2064.21	−	1274.44i	−0.435893	−	0.269120i
$283$	−6.12688	−	3.53735i	−0.00128694	−	0.000743017i	0.499356	−	0.866397i	$-0.333570\pi$
$283$	−6.12688	−	3.53735i	−0.00128694	−	0.000743017i	−0.500643	+	0.865654i	$0.666903\pi$
$284$	5835.18	−	10106.8i	1.21921	−	2.11173i
$285$		0			0
$286$	4506.60	+	7805.66i	0.931751	+	1.61384i
$287$		−	1724.34i		−	0.354650i
$288$	−10327.4	−	6805.08i	−2.11301	−	1.39234i
$289$	1931.06			0.393051
$290$		0			0
$291$	2171.93	+	4032.22i	0.437528	+	0.812279i
$292$	−14647.7	−	8456.88i	−2.93560	−	1.69487i
$293$	−3877.62	−	2238.75i	−0.773150	−	0.446378i	0.0608470	−	0.998147i	$-0.480620\pi$
$293$	−3877.62	−	2238.75i	−0.773150	−	0.446378i	−0.833997	+	0.551769i	$0.813953\pi$
$294$	4487.29	+	132.489i	0.890151	+	0.0262820i
$295$		0			0
$296$	3455.12			0.678461
$297$	5970.23	−	2774.64i	1.16642	−	0.542090i
$298$		−	6403.43i		−	1.24477i
$299$	649.955	+	1125.75i	0.125712	+	0.217739i
$300$		0			0
$301$	−1102.72	+	1909.96i	−0.211162	+	0.365743i
$302$	13685.4	+	7901.27i	2.60764	+	1.50552i
$303$	5534.21	−	2980.96i	1.04928	−	0.565188i
$304$	10255.0	+	17762.2i	1.93475	+	3.35109i
$305$		0			0
$306$	−3511.31	−	7006.54i	−0.655975	−	1.30895i
$307$		−	3889.78i		−	0.723132i	−0.932347	−	0.361566i	$-0.882242\pi$
$307$		−	3889.78i		−	0.723132i	0.932347	−	0.361566i	$-0.117758\pi$
$308$	−11057.6	+	6384.12i	−2.04567	+	1.18107i
$309$	−2033.24	+	3293.22i	−0.374326	+	0.606294i
$310$		0			0
$311$	3647.83	−	6318.23i	0.665111	−	1.15201i	−0.314145	−	0.949375i	$-0.601718\pi$
$311$	3647.83	−	6318.23i	0.665111	−	1.15201i	0.979255	−	0.202630i	$-0.0649490\pi$
$312$	10407.0	+	6425.28i	1.88840	+	1.16590i
$313$	550.854	−	318.036i	0.0994765	−	0.0574328i	−0.449436	−	0.893312i	$-0.648375\pi$
$313$	550.854	−	318.036i	0.0994765	−	0.0574328i	0.548913	+	0.835880i	$0.315042\pi$
$314$	−2103.67			−0.378080
$315$		0			0
$316$	−4126.62			−0.734623
$317$	−5322.90	+	3073.18i	−0.943104	+	0.544501i	−0.890932	−	0.454137i	$-0.849948\pi$
$317$	−5322.90	+	3073.18i	−0.943104	+	0.544501i	−0.0521721	+	0.998638i	$0.516614\pi$
$318$	11653.8	−	6277.25i	2.05508	−	1.10695i
$319$	−1363.60	+	2361.83i	−0.239332	+	0.414536i
$320$		0			0
$321$	5194.64	+	153.374i	0.903229	+	0.0266682i
$322$	−2224.65	+	1284.40i	−0.385014	+	0.222288i
$323$			6079.89i			1.04735i
$324$	8837.68	−	11828.7i	1.51538	−	2.02825i
$325$		0			0
$326$	10262.7	+	17775.6i	1.74356	+	3.01994i
$327$	−140.396	+	4755.10i	−0.0237429	+	0.804151i
$328$	−7241.06	−	4180.63i	−1.21897	−	0.703770i
$329$	−589.954	+	1021.83i	−0.0988609	+	0.171232i
$330$		0			0
$331$	−5867.20	−	10162.3i	−0.974291	−	1.68752i	−0.682255	−	0.731114i	$-0.739001\pi$
$331$	−5867.20	−	10162.3i	−0.974291	−	1.68752i	−0.292036	−	0.956407i	$-0.594333\pi$
$332$			9407.82i			1.55518i
$333$	−84.4945	+	1429.63i	−0.0139047	+	0.235265i
$334$	10816.9			1.77208
$335$		0			0
$336$	−6755.22	+	10941.4i	−1.09681	+	1.77649i
$337$	−5441.49	−	3141.65i	−0.879575	−	0.507823i	−0.00905696	−	0.999959i	$-0.502883\pi$
$337$	−5441.49	−	3141.65i	−0.879575	−	0.507823i	−0.870518	+	0.492136i	$0.836216\pi$
$338$	4102.91	+	2368.82i	0.660264	+	0.381203i
$339$	3616.65	−	5857.88i	0.579438	−	0.938514i
$340$		0			0
$341$	13874.4			2.20334
$342$	−14285.7	+	7159.22i	−2.25871	+	1.13195i
$343$		−	6791.22i		−	1.06907i
$344$	5347.04	+	9261.34i	0.838061	+	1.45156i
$345$		0			0
$346$	4111.32	−	7121.02i	0.638803	−	1.10644i
$347$	−4157.63	−	2400.41i	−0.643209	−	0.371357i	0.142641	−	0.989775i	$-0.454441\pi$
$347$	−4157.63	−	2400.41i	−0.643209	−	0.371357i	−0.785849	+	0.618418i	$0.787774\pi$
$348$	−180.517	+	6113.98i	−0.0278068	+	0.941792i
$349$	−1946.23	−	3370.97i	−0.298508	−	0.517031i	0.677287	−	0.735719i	$-0.263156\pi$
$349$	−1946.23	−	3370.97i	−0.298508	−	0.517031i	−0.975795	+	0.218688i	$0.929822\pi$
$350$		0			0
$351$	−2913.11	+	4149.00i	−0.442992	+	0.630932i
$352$			21495.2i			3.25482i
$353$	2568.87	−	1483.14i	0.387329	−	0.223624i	−0.293673	−	0.955906i	$-0.594878\pi$
$353$	2568.87	−	1483.14i	0.387329	−	0.223624i	0.681002	+	0.732281i	$0.261544\pi$
$354$	−17548.1	−	518.115i	−2.63467	−	0.0777896i
$355$		0			0
$356$	−10064.3	+	17431.9i	−1.49834	+	2.59520i
$357$	−3355.91	+	1807.64i	−0.497517	+	0.267984i
$358$	−3793.05	+	2189.92i	−0.559969	+	0.323298i
$359$	9584.91			1.40911			0.704557	−	0.709647i	$-0.251146\pi$
$359$	9584.91			1.40911			0.704557	+	0.709647i	$0.251146\pi$
$360$		0			0
$361$	5537.30			0.807304
$362$	20271.1	−	11703.5i	2.94317	−	1.69924i
$363$	−3851.08	−	2377.65i	−0.556829	−	0.343787i
$364$	4916.03	−	8514.82i	0.707885	−	1.22609i
$365$		0			0
$366$	−696.853	+	1128.69i	−0.0995221	+	0.161195i
$367$	3929.31	−	2268.59i	0.558879	−	0.322669i	−0.193817	−	0.981038i	$-0.562087\pi$
$367$	3929.31	−	2268.59i	0.558879	−	0.322669i	0.752695	+	0.658369i	$0.228753\pi$
$368$			6626.88i			0.938722i
$369$	1906.91	−	2893.91i	0.269023	−	0.408269i
$370$		0			0
$371$	−3219.04	−	5575.54i	−0.450469	−	0.780236i
$372$	27396.3	−	14756.8i	3.81836	−	2.05673i
$373$	11372.0	+	6565.65i	1.57861	+	0.911411i	0.995054	+	0.0993385i	$0.0316727\pi$
$373$	11372.0	+	6565.65i	1.57861	+	0.911411i	0.583557	+	0.812073i	$0.301661\pi$
$374$	−6810.43	+	11796.0i	−0.941601	+	1.63090i
$375$		0			0
$376$	2860.66	+	4954.82i	0.392360	+	0.679588i
$377$		−	2100.06i		−	0.286892i
$378$	−8198.99	−	5756.70i	−1.11564	−	0.783314i
$379$	9451.10			1.28092			0.640462	−	0.767990i	$-0.278743\pi$
$379$	9451.10			1.28092			0.640462	+	0.767990i	$0.278743\pi$
$380$		0			0
$381$	5160.83	+	152.375i	0.693956	+	0.0204893i
$382$	−14026.1	−	8097.98i	−1.87863	−	1.08463i
$383$	−7445.25	−	4298.52i	−0.993301	−	0.573483i	−0.0870420	−	0.996205i	$-0.527741\pi$
$383$	−7445.25	−	4298.52i	−0.993301	−	0.573483i	−0.906260	+	0.422722i	$0.861075\pi$
$384$	3559.51	+	6608.29i	0.473035	+	0.878198i
$385$		0			0
$386$	−10051.1			−1.32536
$387$	−3962.85	+	1985.97i	−0.520524	+	0.260860i
$388$		−	17852.7i		−	2.33592i
$389$	2221.04	+	3846.95i	0.289489	+	0.501410i	0.973688	−	0.227886i	$-0.0731813\pi$
$389$	2221.04	+	3846.95i	0.289489	+	0.501410i	−0.684199	+	0.729295i	$0.739848\pi$
$390$		0			0
$391$	−982.219	+	1701.25i	−0.127041	+	0.220041i
$392$	−9169.01	−	5293.73i	−1.18139	−	0.682076i
$393$	−6119.12	−	3777.95i	−0.785417	−	0.484917i
$394$	−9706.13	−	16811.5i	−1.24109	−	2.14962i
$395$		0			0
$396$	−25617.7	−	1514.07i	−3.25086	−	0.192133i
$397$			10445.6i			1.32053i	0.751033	+	0.660265i	$0.229556\pi$
$397$			10445.6i			1.32053i	−0.751033	+	0.660265i	$0.770444\pi$
$398$	14810.2	−	8550.68i	1.86525	−	1.07690i
$399$	3685.59	+	6842.37i	0.462432	+	0.858514i
$400$		0			0
$401$	6341.72	−	10984.2i	0.789751	−	1.36789i	−0.136368	−	0.990658i	$-0.543543\pi$
$401$	6341.72	−	10984.2i	0.789751	−	1.36789i	0.926119	−	0.377231i	$-0.123124\pi$
$402$	23.5725	−	798.381i	0.00292460	−	0.0990538i
$403$	−9252.47	+	5341.91i	−1.14367	+	0.660297i
$404$	−24502.8			−3.01748
$405$		0			0
$406$	4150.00			0.507293
$407$	2155.55	−	1244.51i	0.262523	−	0.151568i
$408$	−545.484	+	18475.1i	−0.0661899	+	2.24180i
$409$	−5556.30	+	9623.79i	−0.671739	+	1.16349i	0.305671	+	0.952137i	$0.401119\pi$
$409$	−5556.30	+	9623.79i	−0.671739	+	1.16349i	−0.977411	+	0.211349i	$0.932214\pi$
$410$		0			0
$411$	3812.36	+	7077.71i	0.457542	+	0.849434i
$412$	13065.3	−	7543.26i	1.56233	−	0.902014i
$413$			8538.67i			1.01734i
$414$	−5153.95	−	304.610i	−0.611843	−	0.0361613i
$415$		0			0
$416$	−8276.08	−	14334.6i	−0.975404	−	1.68945i
$417$	−2385.35	−	1472.71i	−0.280122	−	0.172947i
$418$	24050.9	+	13885.8i	2.81428	+	1.62482i
$419$	1009.26	−	1748.09i	0.117675	−	0.203818i	−0.801171	−	0.598435i	$-0.795789\pi$
$419$	1009.26	−	1748.09i	0.117675	−	0.203818i	0.918846	+	0.394617i	$0.129123\pi$
$420$		0			0
$421$	5478.85	+	9489.65i	0.634259	+	1.09857i	0.986672	+	0.162724i	$0.0520280\pi$
$421$	5478.85	+	9489.65i	0.634259	+	1.09857i	−0.352413	+	0.935845i	$0.614639\pi$
$422$		−	26300.1i		−	3.03381i
$423$	−2120.12	+	1062.49i	−0.243697	+	0.122128i
$424$	−31218.0			−3.57565
$425$		0			0
$426$	−7546.93	−	14011.0i	−0.858333	−	1.59351i
$427$	558.728	+	322.582i	0.0633226	+	0.0365593i
$428$	−17543.5	−	10128.8i	−1.98131	−	1.14391i
$429$	8806.98	+	260.029i	0.991154	+	0.0292642i
$430$		0			0
$431$	−2124.75			−0.237460			−0.118730	−	0.992927i	$-0.537882\pi$
$431$	−2124.75			−0.237460			−0.118730	+	0.992927i	$0.537882\pi$
$432$	−23436.9	+	10892.2i	−2.61021	+	1.21308i
$433$			16169.2i			1.79456i	0.441463	+	0.897279i	$0.354460\pi$
$433$			16169.2i			1.79456i	−0.441463	+	0.897279i	$0.645540\pi$
$434$	−10556.4	−	18284.1i	−1.16756	−	2.02227i
$435$		0			0
$436$	9271.73	−	16059.1i	1.01843	−	1.76397i
$437$	3468.69	+	2002.65i	0.379702	+	0.219221i
$438$	−20306.0	+	10937.7i	−2.21520	+	1.19320i
$439$	346.098	+	599.460i	0.0376273	+	0.0651724i	0.884226	−	0.467060i	$-0.154687\pi$
$439$	346.098	+	599.460i	0.0376273	+	0.0651724i	−0.846598	+	0.532232i	$0.821353\pi$
$440$		0			0
$441$	2414.63	−	3664.43i	0.260731	−	0.395684i
$442$		−	10488.6i		−	1.12872i
$443$	5776.83	−	3335.26i	0.619561	−	0.357704i	−0.157137	−	0.987577i	$-0.550226\pi$
$443$	5776.83	−	3335.26i	0.619561	−	0.357704i	0.776698	+	0.629873i	$0.216893\pi$
$444$	2932.68	−	4750.05i	0.313466	−	0.507719i
$445$		0			0
$446$	2934.46	−	5082.63i	0.311549	−	0.539618i
$447$	−5326.28	−	3288.45i	−0.563589	−	0.347960i
$448$	11182.1	−	6456.00i	1.17925	−	0.680843i
$449$	9743.18			1.02407			0.512037	−	0.858964i	$-0.328891\pi$
$449$	9743.18			1.02407			0.512037	+	0.858964i	$0.328891\pi$
$450$		0			0
$451$	−6023.33			−0.628886
$452$	−23240.1	+	13417.7i	−2.41842	+	1.39627i
$453$	13600.2	−	7325.67i	1.41058	−	0.759801i
$454$	10153.3	−	17586.0i	1.04959	−	1.81795i
$455$		0			0
$456$	37669.0	+	1112.19i	3.86844	+	0.114217i
$457$	3847.51	−	2221.36i	0.393827	−	0.227376i	−0.289990	−	0.957030i	$-0.593652\pi$
$457$	3847.51	−	2221.36i	0.393827	−	0.227376i	0.683817	+	0.729654i	$0.260319\pi$
$458$			769.524i			0.0785098i
$459$	−7631.15	−	677.513i	−0.776017	−	0.0688967i
$460$		0			0
$461$	−9469.70	−	16402.0i	−0.956720	−	1.65709i	−0.730383	−	0.683038i	$-0.760658\pi$
$461$	−9469.70	−	16402.0i	−0.956720	−	1.65709i	−0.226337	−	0.974049i	$-0.572675\pi$
$462$	−513.853	+	17403.8i	−0.0517459	+	1.75259i
$463$	−14542.5	−	8396.10i	−1.45971	−	0.842764i	−0.460714	−	0.887549i	$-0.652407\pi$
$463$	−14542.5	−	8396.10i	−1.45971	−	0.842764i	−0.998997	+	0.0447846i	$0.985740\pi$
$464$	5353.00	−	9271.66i	0.535575	−	0.927642i
$465$		0			0
$466$	3418.70	+	5921.36i	0.339846	+	0.588630i
$467$			1367.93i			0.135547i	0.997701	+	0.0677735i	$0.0215895\pi$
$467$			1367.93i			0.135547i	−0.997701	+	0.0677735i	$0.978410\pi$
$468$	17666.8	−	8853.67i	1.74497	−	0.874489i
$469$	−388.480			−0.0382481
$470$		0			0
$471$	−1080.33	+	1749.80i	−0.105688	+	0.171182i
$472$	35856.6	+	20701.8i	3.49668	+	2.01881i
$473$	6671.74	+	3851.93i	0.648556	+	0.374444i
$474$	−2956.23	+	4788.19i	−0.286465	+	0.463985i
$475$		0			0
$476$	14858.3			1.43074
$477$	763.432	−	12917.1i	0.0732812	−	1.23991i
$478$			22428.5i			2.14615i
$479$	101.371	+	175.579i	0.00966960	+	0.0167482i	0.870820	−	0.491603i	$-0.163589\pi$
$479$	101.371	+	175.579i	0.00966960	+	0.0167482i	−0.861150	+	0.508351i	$0.830255\pi$
$480$		0			0
$481$	−958.323	+	1659.86i	−0.0908436	+	0.157346i
$482$	10510.1	+	6068.01i	0.993199	+	0.573424i
$483$	−74.1094	+	2510.02i	−0.00698156	+	0.236460i
$484$	8821.04	+	15278.5i	0.828423	+	1.43487i
$485$		0			0
$486$	−7393.95	−	18728.4i	−0.690116	−	1.74802i
$487$			18961.3i			1.76431i	0.470964	+	0.882153i	$0.343906\pi$
$487$			18961.3i			1.76431i	−0.470964	+	0.882153i	$0.656094\pi$
$488$	2709.25	−	1564.19i	0.251315	−	0.145097i
$489$	20055.9	+	592.157i	1.85472	+	0.0547612i
$490$		0			0
$491$	−5856.15	+	10143.1i	−0.538257	+	0.932289i	0.460741	+	0.887535i	$0.347584\pi$
$491$	−5856.15	+	10143.1i	−0.538257	+	0.932289i	−0.998998	+	0.0447541i	$0.985750\pi$
$492$	−11893.6	+	6406.43i	−1.08985	+	0.587041i
$493$	2748.45	−	1586.82i	0.251083	−	0.144963i
$494$	−21385.3			−1.94771
$495$		0			0
$496$	−54465.7			−4.93061
$497$	−6703.28	+	3870.14i	−0.604996	+	0.349295i
$498$	10916.1	+	6739.57i	0.982249	+	0.606441i
$499$	4312.44	−	7469.36i	0.386876	−	0.670089i	−0.605151	−	0.796110i	$-0.706887\pi$
$499$	4312.44	−	7469.36i	0.386876	−	0.670089i	0.992028	+	0.126021i	$0.0402208\pi$
$500$		0			0
$501$	5554.97	−	8997.35i	0.495364	−	0.802339i
$502$	36468.9	−	21055.3i	3.24241	−	1.87200i
$503$		−	4856.12i		−	0.430465i	−0.976563	−	0.215232i	$-0.930949\pi$
$503$		−	4856.12i		−	0.430465i	0.976563	−	0.215232i	$-0.0690509\pi$
$504$	10585.6	+	21122.8i	0.935557	+	1.86683i
$505$		0			0
$506$	4486.56	+	7770.96i	0.394174	+	0.682730i
$507$	4077.38	−	2196.25i	0.357165	−	0.192384i
$508$	−17429.4	−	10062.9i	−1.52225	−	0.878872i
$509$	−5425.17	+	9396.67i	−0.472429	+	0.818271i	−0.999502	−	0.0315486i	$-0.989956\pi$
$509$	−5425.17	+	9396.67i	−0.472429	+	0.818271i	0.527073	+	0.849820i	$0.323289\pi$
$510$		0			0
$511$	5608.96	+	9715.01i	0.485569	+	0.841030i
$512$			11614.3i			1.00251i
$513$	−1381.38	+	15559.2i	−0.118888	+	1.33909i
$514$	12024.6			1.03187
$515$		0			0
$516$	17270.9	+	509.930i	1.47347	+	0.0435047i
$517$	3569.38	+	2060.78i	0.303639	+	0.175306i
$518$	−3280.12	−	1893.78i	−0.278224	−	0.160633i
$519$	−3811.81	−	7076.70i	−0.322389	−	0.598521i
$520$		0			0
$521$	3559.30			0.299301			0.149651	−	0.988739i	$-0.452185\pi$
$521$	3559.30			0.299301			0.149651	+	0.988739i	$0.452185\pi$
$522$	6964.84	+	4589.39i	0.583990	+	0.384813i
$523$		−	22191.7i		−	1.85540i	−0.373321	−	0.927702i	$-0.621781\pi$
$523$		−	22191.7i		−	1.85540i	0.373321	−	0.927702i	$-0.378219\pi$
$524$	14016.1	+	24276.6i	1.16850	+	2.02391i
$525$		0			0
$526$	434.463	−	752.511i	0.0360142	−	0.0623784i
$527$	−13982.4	−	8072.77i	−1.15576	−	0.667277i
$528$	38219.6	+	23596.8i	3.15018	+	1.94492i
$529$	−5436.44	−	9416.18i	−0.446818	−	0.773912i
$530$		0			0
$531$	−9442.72	+	14330.2i	−0.771712	+	1.17115i
$532$		−	30294.7i		−	2.46888i
$533$	4016.81	−	2319.11i	0.326430	−	0.188465i
$534$	13016.7	+	24165.7i	1.05485	+	1.95834i
$535$		0			0
$536$	−941.863	+	1631.35i	−0.0758998	+	0.131462i
$537$	−126.357	+	4279.63i	−0.0101541	+	0.343910i
$538$	15210.1	−	8781.56i	1.21887	−	0.703717i
$539$	−7627.06			−0.609500
$540$		0			0
$541$	4257.08			0.338311			0.169155	−	0.985589i	$-0.445896\pi$
$541$	4257.08			0.338311			0.169155	+	0.985589i	$0.445896\pi$
$542$	8999.40	−	5195.81i	0.713206	−	0.411770i
$543$	675.290	−	22871.5i	0.0533692	−	1.80757i
$544$	12506.9	−	21662.6i	0.985715	−	1.70731i
$545$		0			0
$546$	−6358.14	−	11804.0i	−0.498358	−	0.925210i
$547$	−18375.5	+	10609.1i	−1.43634	+	0.829272i	−0.997593	−	0.0693385i	$-0.977911\pi$
$547$	−18375.5	+	10609.1i	−1.43634	+	0.829272i	−0.438748	+	0.898610i	$0.644578\pi$
$548$		−	31336.7i		−	2.44277i
$549$	580.963	+	1159.27i	0.0451637	+	0.0901206i
$550$		0			0
$551$	−3235.36	−	5603.81i	−0.250147	−	0.433268i
$552$	10360.7	+	6396.71i	0.798880	+	0.493228i
$553$	2370.27	+	1368.48i	0.182268	+	0.105232i
$554$	11277.8	−	19533.7i	0.864885	−	1.49803i
$555$		0			0
$556$	5463.73	+	9463.46i	0.416752	+	0.721835i
$557$			2506.42i			0.190665i	0.995445	+	0.0953324i	$0.0303914\pi$
$557$			2506.42i			0.190665i	−0.995445	+	0.0953324i	$0.969609\pi$
$558$	2503.56	−	42359.8i	0.189936	−	3.21368i
$559$	−5932.29			−0.448854
$560$		0			0
$561$	6314.29	+	11722.6i	0.475204	+	0.882225i
$562$	−12071.4	−	6969.41i	−0.906050	−	0.523108i
$563$	14964.6	+	8639.80i	1.12022	+	0.646757i	0.941456	−	0.337136i	$-0.109458\pi$
$563$	14964.6	+	8639.80i	1.12022	+	0.646757i	0.178759	+	0.983893i	$0.442792\pi$
$564$	9239.93	+	272.812i	0.689843	+	0.0203679i
$565$		0			0
$566$	37.6057			0.00279273
$567$	−8998.89	+	3863.48i	−0.666522	+	0.286157i
$568$			37532.3i			2.77257i
$569$	−10254.1	−	17760.5i	−0.755487	−	1.30854i	−0.945132	−	0.326689i	$-0.894067\pi$
$569$	−10254.1	−	17760.5i	−0.755487	−	1.30854i	0.189645	−	0.981853i	$-0.439266\pi$
$570$		0			0
$571$	−3412.53	+	5910.68i	−0.250105	+	0.433195i	−0.963555	−	0.267512i	$-0.913799\pi$
$571$	−3412.53	+	5910.68i	−0.250105	+	0.433195i	0.713449	+	0.700707i	$0.247132\pi$
$572$	−29743.3	−	17172.3i	−2.17418	−	1.25526i
$573$	−13938.8	+	7508.05i	−1.01623	+	0.547388i
$574$	4582.87	+	7937.77i	0.333250	+	0.577206i
$575$		0			0
$576$	25906.2	+	1531.11i	1.87400	+	0.110758i
$577$			4249.00i			0.306565i	0.988182	+	0.153283i	$0.0489845\pi$
$577$			4249.00i			0.306565i	−0.988182	+	0.153283i	$0.951016\pi$
$578$	−8889.37	+	5132.28i	−0.639704	+	0.369333i
$579$	−5161.70	+	8360.38i	−0.370489	+	0.600079i
$580$		0			0
$581$	3119.83	−	5403.71i	0.222775	−	0.385858i
$582$	−20714.8	−	12789.3i	−1.47536	−	0.910885i
$583$	−19476.0	+	11244.5i	−1.38356	+	0.798798i
$584$	54395.2			3.85426
$585$		0			0
$586$	23800.1			1.67777
$587$	16184.3	−	9344.04i	1.13799	−	0.657018i	0.192057	−	0.981384i	$-0.438484\pi$
$587$	16184.3	−	9344.04i	1.13799	−	0.657018i	0.945932	+	0.324365i	$0.105151\pi$
$588$	−15060.4	+	8112.16i	−1.05626	+	0.568945i
$589$	−16459.6	+	28508.8i	−1.15145	+	1.99437i
$590$		0			0
$591$	−18968.1	−	560.040i	−1.32021	−	0.0389797i
$592$	−8461.91	+	4885.48i	−0.587470	+	0.339176i
$593$			12434.5i			0.861084i	0.902570	+	0.430542i	$0.141678\pi$
$593$			12434.5i			0.861084i	−0.902570	+	0.430542i	$0.858322\pi$
$594$	−20108.8	+	28640.1i	−1.38902	+	1.97831i
$595$		0			0
$596$	12200.1	+	21131.1i	0.838480	+	1.45229i
$597$	493.371	−	16710.1i	0.0338230	−	1.14556i
$598$	−5983.96	−	3454.84i	−0.409201	−	0.236252i
$599$	−3021.52	+	5233.42i	−0.206103	+	0.356981i	−0.950484	−	0.310774i	$-0.899412\pi$
$599$	−3021.52	+	5233.42i	−0.206103	+	0.356981i	0.744380	+	0.667756i	$0.232745\pi$
$600$		0			0
$601$	315.654	+	546.729i	0.0214239	+	0.0371074i	0.876539	−	0.481332i	$-0.159847\pi$
$601$	315.654	+	546.729i	0.0214239	+	0.0371074i	−0.855115	+	0.518439i	$0.826513\pi$
$602$		−	11723.0i		−	0.793679i
$603$	−651.977	−	429.612i	−0.0440307	−	0.0290135i
$604$	−60215.2			−4.05649
$605$		0			0
$606$	−17553.3	+	28431.0i	−1.17666	+	1.90583i
$607$	8188.16	+	4727.43i	0.547524	+	0.316113i	0.748123	−	0.663560i	$-0.230955\pi$
$607$	8188.16	+	4727.43i	0.547524	+	0.316113i	−0.200599	+	0.979673i	$0.564289\pi$
$608$	−44167.9	−	25500.4i	−2.94613	−	1.70095i
$609$	2131.21	−	3451.91i	0.141808	−	0.229686i
$610$		0			0
$611$	−3173.77			−0.210143
$612$	24936.3	+	16431.5i	1.64705	+	1.08530i
$613$			2682.66i			0.176757i	0.996087	+	0.0883783i	$0.0281684\pi$
$613$			2682.66i			0.176757i	−0.996087	+	0.0883783i	$0.971832\pi$
$614$	10338.1	+	17906.1i	0.679497	+	1.17692i
$615$		0			0
$616$	20531.5	−	35561.7i	1.34292	−	2.32601i
$617$	2025.22	+	1169.26i	0.132143	+	0.0762930i	0.564614	−	0.825355i	$-0.309025\pi$
$617$	2025.22	+	1169.26i	0.132143	+	0.0762930i	−0.432471	+	0.901648i	$0.642358\pi$
$618$	607.152	−	20563.7i	0.0395198	−	1.33850i
$619$	−5965.11	−	10331.9i	−0.387331	−	0.670878i	0.604758	−	0.796409i	$-0.293270\pi$
$619$	−5965.11	−	10331.9i	−0.387331	−	0.670878i	−0.992090	+	0.125531i	$0.959936\pi$
$620$		0			0
$621$	−2900.15	+	4130.55i	−0.187406	+	0.266914i
$622$			38780.1i			2.49991i
$623$	11561.6	−	6675.09i	0.743509	−	0.429265i
$624$	−34573.0	−	1020.78i	−2.21799	−	0.0654870i
$625$		0			0
$626$	−1690.52	+	2928.07i	−0.107934	+	0.186948i
$627$	23901.2	−	12874.2i	1.52237	−	0.820012i
$628$	6942.05	−	4008.00i	0.441111	−	0.254676i
$629$	−2896.46			−0.183608
$630$		0			0
$631$	4106.81			0.259096			0.129548	−	0.991573i	$-0.458647\pi$
$631$	4106.81			0.259096			0.129548	+	0.991573i	$0.458647\pi$
$632$	11493.3	−	6635.68i	0.723387	−	0.417648i
$633$	−21876.0	−	13506.3i	−1.37361	−	0.848067i
$634$	16335.5	−	28293.9i	1.02329	−	1.77239i
$635$		0			0
$636$	−26497.6	+	42918.1i	−1.65204	+	2.67580i
$637$	5086.30	−	2936.58i	0.316368	−	0.182655i
$638$		−	14496.5i		−	0.899562i
$639$	−15529.8	−	917.848i	−0.961425	−	0.0568224i
$640$		0			0
$641$	−7462.65	−	12925.7i	−0.459839	−	0.796465i	0.539113	−	0.842234i	$-0.318760\pi$
$641$	−7462.65	−	12925.7i	−0.459839	−	0.796465i	−0.998952	+	0.0457684i	$0.985426\pi$
$642$	−24320.4	+	13100.0i	−1.49510	+	0.805323i
$643$	16459.4	+	9502.84i	1.00948	+	0.582823i	0.911039	−	0.412319i	$-0.135281\pi$
$643$	16459.4	+	9502.84i	1.00948	+	0.582823i	0.0984406	+	0.995143i	$0.468615\pi$
$644$	4894.18	−	8476.96i	0.299468	−	0.518694i
$645$		0			0
$646$	−16158.8	−	27987.9i	−0.984151	−	1.70460i
$647$			9252.81i			0.562234i	0.959673	+	0.281117i	$0.0907050\pi$
$647$			9252.81i			0.562234i	−0.959673	+	0.281117i	$0.909295\pi$
$648$	−5593.61	+	47156.1i	−0.339101	+	2.85875i
$649$	29826.6			1.80400
$650$		0			0
$651$	−20629.7	−	609.098i	−1.24200	−	0.0366704i
$652$	−67733.5	−	39106.0i	−4.06848	−	2.34894i
$653$	19875.9	+	11475.3i	1.19112	+	0.687695i	0.958561	−	0.284887i	$-0.0919562\pi$
$653$	19875.9	+	11475.3i	1.19112	+	0.687695i	0.232561	+	0.972582i	$0.425289\pi$
$654$	−11991.6	−	22262.6i	−0.716985	−	1.33109i
$655$		0			0
$656$	23645.4			1.40731
$657$	−1330.23	+	22507.3i	−0.0789912	+	1.33652i
$658$		−	6271.81i		−	0.371582i
$659$	3258.54	+	5643.96i	0.192617	+	0.333623i	0.946117	−	0.323826i	$-0.104969\pi$
$659$	3258.54	+	5643.96i	0.192617	+	0.333623i	−0.753500	+	0.657448i	$0.771636\pi$
$660$		0			0
$661$	2598.16	−	4500.15i	0.152885	−	0.264804i	−0.779402	−	0.626524i	$-0.784477\pi$
$661$	2598.16	−	4500.15i	0.152885	−	0.264804i	0.932287	+	0.361720i	$0.117810\pi$
$662$	54017.7	+	31187.1i	3.17139	+	1.83100i
$663$	−8724.29	−	5386.37i	−0.511045	−	0.315520i
$664$	−15127.9	−	26202.3i	−0.884153	−	1.53140i
$665$		0			0
$666$	−3410.65	−	6805.68i	−0.198439	−	0.395968i
$667$		−	2090.72i		−	0.121369i
$668$	−35695.5	+	20608.8i	−2.06751	+	1.19368i
$669$	−2720.69	−	5051.00i	−0.157231	−	0.291903i
$670$		0			0
$671$	1126.82	−	1951.71i	0.0648291	−	0.112287i
$672$	943.658	−	31960.9i	0.0541702	−	1.83470i
$673$	−24413.2	+	14095.0i	−1.39831	+	0.807313i	−0.994215	−	0.107405i	$-0.965746\pi$
$673$	−24413.2	+	14095.0i	−1.39831	+	0.807313i	−0.404093	+	0.914718i	$0.632413\pi$
$674$	33398.9			1.90872
$675$		0			0
$676$	−18052.7			−1.02712
$677$	7514.40	−	4338.44i	0.426590	−	0.246292i	−0.271303	−	0.962494i	$-0.587454\pi$
$677$	7514.40	−	4338.44i	0.426590	−	0.246292i	0.697893	+	0.716202i	$0.254121\pi$
$678$	−1079.98	+	36578.1i	−0.0611747	+	2.07194i
$679$	−5920.34	+	10254.3i	−0.334613	+	0.579566i
$680$		0			0
$681$	−9413.60	−	17476.5i	−0.529706	−	0.983409i
$682$	−63868.7	+	36874.6i	−3.58601	+	2.07039i
$683$		−	20624.1i		−	1.15543i	−0.816239	−	0.577714i	$-0.803945\pi$
$683$		−	20624.1i		−	1.15543i	0.816239	−	0.577714i	$-0.196055\pi$
$684$	33502.2	−	50842.8i	1.87279	−	2.84214i
$685$		0			0
$686$	18049.4	+	31262.5i	1.00456	+	1.73995i
$687$	640.079	+	395.185i	0.0355466	+	0.0219465i
$688$	−26190.8	−	15121.3i	−1.45133	−	0.837926i
$689$	8658.72	−	14997.3i	0.478768	−	0.829250i
$690$		0			0
$691$	−3493.03	−	6050.10i	−0.192303	−	0.333078i	0.753710	−	0.657207i	$-0.228262\pi$
$691$	−3493.03	−	6050.10i	−0.192303	−	0.333078i	−0.946013	+	0.324129i	$0.894929\pi$
$692$			31332.2i			1.72120i
$693$	14212.3	+	9365.04i	0.779051	+	0.513346i
$694$	25518.8			1.39579
$695$		0			0
$696$	−9328.61	−	17318.7i	−0.508046	−	0.943196i
$697$	6070.25	+	3504.66i	0.329881	+	0.190457i
$698$	17918.4	+	10345.2i	0.971664	+	0.560991i
$699$	6680.96	+	197.258i	0.361512	+	0.0106738i
$700$		0			0
$701$	7848.55			0.422875			0.211438	−	0.977391i	$-0.432185\pi$
$701$	7848.55			0.422875			0.211438	+	0.977391i	$0.432185\pi$
$702$	2383.07	−	26841.7i	0.128124	−	1.44312i
$703$			5905.60i			0.316833i
$704$	−22551.6	−	39060.5i	−1.20731	−	2.09112i
$705$		0			0
$706$	−7883.63	+	13654.8i	−0.420261	+	0.727913i
$707$	14074.0	+	8125.65i	0.748669	+	0.432244i
$708$	58895.5	−	31723.6i	3.12631	−	1.68397i
$709$	−12712.3	−	22018.3i	−0.673371	−	1.16631i	−0.976942	−	0.213504i	$-0.931512\pi$
$709$	−12712.3	−	22018.3i	−0.673371	−	1.16631i	0.303571	−	0.952809i	$-0.401821\pi$
$710$		0			0
$711$	2464.60	+	4917.90i	0.129999	+	0.259403i
$712$		−	64734.5i		−	3.40734i
$713$	−9211.33	+	5318.16i	−0.483825	+	0.279336i
$714$	10644.2	−	17240.4i	0.557913	−	0.903649i
$715$		0			0
$716$	8344.63	−	14453.3i	0.435550	−	0.754394i
$717$	18655.7	+	11518.1i	0.971703	+	0.599930i
$718$	−44122.8	+	25474.3i	−2.29338	+	1.32409i
$719$	−16707.2			−0.866584			−0.433292	−	0.901254i	$-0.642648\pi$
$719$	−16707.2			−0.866584			−0.433292	+	0.901254i	$0.642648\pi$
$720$		0			0
$721$	−10006.0			−0.516843
$722$	−25490.2	+	14716.8i	−1.31392	+	0.758590i
$723$	10444.7	−	5625.96i	0.537264	−	0.289394i
$724$	−44596.1	+	77242.7i	−2.28923	+	3.96506i
$725$		0			0
$726$	24047.1	+	710.000i	1.22930	+	0.0362956i
$727$	1244.03	−	718.240i	0.0634642	−	0.0366410i	−0.467932	−	0.883764i	$-0.655001\pi$
$727$	1244.03	−	718.240i	0.0634642	−	0.0366410i	0.531396	+	0.847123i	$0.321668\pi$
$728$			31620.3i			1.60979i
$729$	−19375.1	−	3467.68i	−0.984359	−	0.176176i
$730$		0			0
$731$	−4482.47	−	7763.87i	−0.226799	−	0.392828i
$732$	149.171	−	5052.31i	0.00753215	−	0.255108i
$733$	9994.70	+	5770.44i	0.503633	+	0.290772i	0.730212	−	0.683220i	$-0.239421\pi$
$733$	9994.70	+	5770.44i	0.503633	+	0.290772i	−0.226580	+	0.973993i	$0.572754\pi$
$734$	−12058.7	+	20886.3i	−0.606397	+	1.05031i
$735$		0			0
$736$	−8239.28	−	14270.9i	−0.412641	−	0.714715i
$737$			1357.01i			0.0678237i
$738$	−1086.88	+	18389.8i	−0.0542122	+	0.917262i
$739$	−4127.87			−0.205475			−0.102737	−	0.994709i	$-0.532760\pi$
$739$	−4127.87			−0.205475			−0.102737	+	0.994709i	$0.532760\pi$
$740$		0			0
$741$	−10982.3	+	17788.0i	−0.544460	+	0.881859i
$742$	29636.8	+	17110.8i	1.46631	+	0.846574i
$743$	−23813.1	−	13748.5i	−1.17580	−	0.678846i	−0.220758	−	0.975329i	$-0.570853\pi$
$743$	−23813.1	−	13748.5i	−1.17580	−	0.678846i	−0.955038	+	0.296482i	$0.904186\pi$
$744$	−52574.0	+	85153.8i	−2.59066	+	4.19609i
$745$		0			0
$746$	−69799.5			−3.42566
$747$	11211.8	−	5618.75i	0.549153	−	0.275207i
$748$		−	51902.0i		−	2.53706i
$749$	6717.83	+	11635.6i	0.327723	+	0.567632i
$750$		0			0
$751$	−17197.1	+	29786.2i	−0.835592	+	1.44729i	0.0579559	+	0.998319i	$0.481542\pi$
$751$	−17197.1	+	29786.2i	−0.835592	+	1.44729i	−0.893548	+	0.448968i	$0.851792\pi$
$752$	−14012.1	−	8089.88i	−0.679479	−	0.392297i
$753$	1214.89	−	41147.2i	0.0587953	−	1.99135i
$754$	5581.44	+	9667.33i	0.269581	+	0.466928i
$755$		0			0
$756$	38024.3	+	3375.89i	1.82927	+	0.162408i
$757$		−	30459.8i		−	1.46246i	−0.682132	−	0.731229i	$-0.738947\pi$
$757$		−	30459.8i		−	1.46246i	0.682132	−	0.731229i	$-0.261053\pi$
$758$	−43506.8	+	25118.7i	−2.08475	+	1.20363i
$759$	8767.82	+	258.873i	0.419304	+	0.0123801i
$760$		0			0
$761$	−223.584	+	387.259i	−0.0106504	+	0.0184469i	−0.871301	−	0.490748i	$-0.836724\pi$
$761$	−223.584	+	387.259i	−0.0106504	+	0.0184469i	0.860651	+	0.509195i	$0.170057\pi$
$762$	−24162.2	+	13014.8i	−1.14869	+	0.618734i
$763$	−10651.1	+	6149.40i	−0.505367	+	0.291774i
$764$	61714.3			2.92244
$765$		0			0
$766$	45697.6			2.15551
$767$	−19890.6	+	11483.9i	−0.936387	+	0.540623i
$768$	48.2987	+	29.8196i	0.00226931	+	0.00140107i
$769$	−4028.59	+	6977.71i	−0.188914	+	0.327208i	−0.944888	−	0.327393i	$-0.893830\pi$
$769$	−4028.59	+	6977.71i	−0.188914	+	0.327208i	0.755975	+	0.654601i	$0.227163\pi$
$770$		0			0
$771$	6175.18	−	10001.9i	0.288448	−	0.467198i
$772$	33168.4	−	19149.8i	1.54632	−	0.892767i
$773$			19600.4i			0.912001i	0.889980	+	0.456000i	$0.150718\pi$
$773$			19600.4i			0.912001i	−0.889980	+	0.456000i	$0.849282\pi$
$774$	12964.2	−	19674.4i	0.602053	−	0.913673i
$775$		0			0
$776$	28707.5	+	49722.8i	1.32801	+	2.30019i
$777$	−3259.70	+	1755.82i	−0.150504	+	0.0810677i
$778$	−20448.5	−	11806.0i	−0.942307	−	0.544041i
$779$	7145.66	−	12376.7i	0.328652	−	0.569242i
$780$		0			0
$781$	13518.9	+	23415.4i	0.619390	+	1.07281i
$782$		−	10442.0i		−	0.477500i
$783$	7394.14	−	3436.40i	0.337478	−	0.156841i
$784$	29941.0			1.36393
$785$		0			0
$786$	38209.4	+	1128.15i	1.73395	+	0.0511955i
$787$	−15533.3	−	8968.18i	−0.703563	−	0.406202i	0.105110	−	0.994461i	$-0.466480\pi$
$787$	−15533.3	−	8968.18i	−0.703563	−	0.406202i	−0.808673	+	0.588258i	$0.799814\pi$
$788$	64059.9	+	36985.0i	2.89599	+	1.67200i
$789$	−402.812	−	747.828i	−0.0181755	−	0.0337432i
$790$		0			0
$791$	17798.4			0.800047
$792$	73784.4	−	36976.8i	3.31037	−	1.65898i
$793$			1735.39i			0.0777119i
$794$	−27761.9	−	48085.0i	−1.24085	−	2.14921i
$795$		0			0
$796$	−32582.2	+	56434.0i	−1.45081	+	2.51288i
$797$	15538.8	+	8971.31i	0.690604	+	0.398720i	0.803838	−	0.594848i	$-0.202788\pi$
$797$	15538.8	+	8971.31i	0.690604	+	0.398720i	−0.113235	+	0.993568i	$0.536121\pi$
$798$	−35151.5	−	21702.5i	−1.55933	−	0.962733i
$799$	−2398.12	−	4153.67i	−0.106182	−	0.183913i
$800$		0			0
$801$	26785.4	+	1583.08i	1.18154	+	0.0698317i
$802$			67418.9i			2.96838i
$803$	33935.7	−	19592.8i	1.49136	−	0.861039i
$804$	1443.32	+	2679.55i	0.0633108	+	0.117538i
$805$		0			0
$806$	28395.0	−	49181.6i	1.24091	−	2.14931i
$807$	506.693	−	17161.3i	0.0221021	−	0.748582i
$808$	68244.4	−	39400.9i	2.97132	−	1.71549i
$809$	−29094.2			−1.26440			−0.632200	−	0.774806i	$-0.717848\pi$
$809$	−29094.2			−1.26440			−0.632200	+	0.774806i	$0.717848\pi$
$810$		0			0
$811$	1438.31			0.0622760			0.0311380	−	0.999515i	$-0.490087\pi$
$811$	1438.31			0.0622760			0.0311380	+	0.999515i	$0.490087\pi$
$812$	−13694.9	+	7906.74i	−0.591867	+	0.341715i
$813$	299.796	−	10153.9i	0.0129327	−	0.438021i
$814$	−6615.19	+	11457.9i	−0.284843	+	0.493363i
$815$		0			0
$816$	−24787.6	−	46018.6i	−1.06341	−	1.97423i
$817$	−15829.8	+	9139.33i	−0.677863	+	0.391364i
$818$		−	59069.1i		−	2.52482i
$819$	−13083.6	−	773.270i	−0.558215	−	0.0329917i
$820$		0			0
$821$	121.415	+	210.297i	0.00516128	+	0.00893959i	0.868595	−	0.495524i	$-0.165024\pi$
$821$	121.415	+	210.297i	0.00516128	+	0.00893959i	−0.863433	+	0.504463i	$0.831690\pi$
$822$	−36360.5	−	22449.0i	−1.54284	−	0.952552i
$823$	15736.5	+	9085.50i	0.666515	+	0.384812i	0.794755	−	0.606931i	$-0.207599\pi$
$823$	15736.5	+	9085.50i	0.666515	+	0.384812i	−0.128240	+	0.991743i	$0.540933\pi$
$824$	−24259.4	+	42018.5i	−1.02563	+	1.77644i
$825$		0			0
$826$	−22693.7	−	39306.6i	−0.955949	−	1.65575i
$827$			12181.7i			0.512213i	0.966649	+	0.256107i	$0.0824398\pi$
$827$			12181.7i			0.512213i	−0.966649	+	0.256107i	$0.917560\pi$
$828$	17588.2	−	8814.30i	0.738205	−	0.369950i
$829$	17370.0			0.727724			0.363862	−	0.931453i	$-0.381458\pi$
$829$	17370.0			0.727724			0.363862	+	0.931453i	$0.381458\pi$
$830$		0			0
$831$	−10456.2	−	19412.1i	−0.436488	−	0.810347i
$832$	30078.2	+	17365.7i	1.25333	+	0.723613i
$833$	7686.47	+	4437.79i	0.319713	+	0.184586i
$834$	14894.7	+	439.772i	0.618420	+	0.0182591i
$835$		0			0
$836$	−105823.			−4.37795
$837$	−33948.6	−	23836.1i	−1.40195	−	0.984344i
$838$			10729.5i			0.442296i
$839$	15681.5	+	27161.2i	0.645275	+	1.11765i	0.984238	+	0.176849i	$0.0565906\pi$
$839$	15681.5	+	27161.2i	0.645275	+	1.11765i	−0.338963	+	0.940800i	$0.610076\pi$
$840$		0			0
$841$	10505.7	−	18196.4i	0.430755	−	0.746089i
$842$	−50442.3	−	29122.9i	−2.06456	−	1.19197i
$843$	−11996.2	+	6461.69i	−0.490122	+	0.264001i
$844$	50108.0	+	86789.5i	2.04359	+	3.53960i
$845$		0			0
$846$	6935.85	−	10525.8i	0.281867	−	0.427760i
$847$		−	11701.0i		−	0.474676i
$848$	76455.7	−	44141.7i	3.09611	−	1.78754i
$849$	19.3122	−	31.2799i	0.000780674	−	0.00126445i
$850$		0			0
$851$	−954.062	+	1652.48i	−0.0384311	+	0.0665645i
$852$	51598.9	+	31857.2i	2.07482	+	1.28100i
$853$	34361.8	−	19838.8i	1.37928	−	0.796326i	0.387205	−	0.921993i	$-0.373440\pi$
$853$	34361.8	−	19838.8i	1.37928	−	0.796326i	0.992072	+	0.125667i	$0.0401071\pi$
$854$	−3429.37			−0.137413
$855$		0			0
$856$	65149.0			2.60134
$857$	28760.1	−	16604.7i	1.14636	−	0.661849i	0.198360	−	0.980129i	$-0.436439\pi$
$857$	28760.1	−	16604.7i	1.14636	−	0.661849i	0.947997	+	0.318280i	$0.103105\pi$
$858$	−41232.8	+	22209.8i	−1.64064	+	0.883717i
$859$	17202.4	−	29795.5i	0.683282	−	1.18348i	−0.290691	−	0.956817i	$-0.593885\pi$
$859$	17202.4	−	29795.5i	0.683282	−	1.18348i	0.973973	−	0.226663i	$-0.0727815\pi$
$860$		0			0
$861$	8956.03	+	264.430i	0.354496	+	0.0104666i
$862$	9780.98	−	5647.05i	0.386475	−	0.223131i
$863$		−	12999.7i		−	0.512765i	−0.966575	−	0.256382i	$-0.917469\pi$
$863$		−	12999.7i		−	0.512765i	0.966575	−	0.256382i	$-0.0825306\pi$
$864$	36928.6	−	52595.6i	1.45409	−	2.07099i
$865$		0			0
$866$	−42973.9	−	74432.9i	−1.68627	−	2.92071i
$867$	−296.131	+	10029.7i	−0.0115999	+	0.392880i
$868$	69671.3	+	40224.8i	2.72442	+	1.57295i
$869$	4780.25	−	8279.64i	0.186604	−	0.323208i
$870$		0			0
$871$	−522.477	−	904.956i	−0.0203254	−	0.0352047i
$872$			59636.4i			2.31599i
$873$	−21276.0	+	10662.4i	−0.824837	+	0.413365i
$874$	−21290.2			−0.823972
$875$		0			0
$876$	46170.4	−	74781.9i	1.78077	−	2.88430i
$877$	19772.6	+	11415.7i	0.761317	+	0.439546i	0.829768	−	0.558108i	$-0.188473\pi$
$877$	19772.6	+	11415.7i	0.761317	+	0.439546i	−0.0684517	+	0.997654i	$0.521806\pi$
$878$	−3186.43	−	1839.69i	−0.122479	−	0.0707135i
$879$	12222.4	−	19796.6i	0.469002	−	0.759640i
$880$		0			0
$881$	−1889.31			−0.0722502			−0.0361251	−	0.999347i	$-0.511501\pi$
$881$	−1889.31			−0.0722502			−0.0361251	+	0.999347i	$0.511501\pi$
$882$	−1376.27	+	23286.2i	−0.0525411	+	0.888987i
$883$			1778.37i			0.0677768i	0.999426	+	0.0338884i	$0.0107891\pi$
$883$			1778.37i			0.0677768i	−0.999426	+	0.0338884i	$0.989211\pi$
$884$	19983.3	+	34612.1i	0.760308	+	1.31689i
$885$		0			0
$886$	−17728.6	+	30706.8i	−0.672239	+	1.16435i
$887$	−19904.8	−	11492.1i	−0.753482	−	0.435023i	0.0734685	−	0.997298i	$-0.476593\pi$
$887$	−19904.8	−	11492.1i	−0.753482	−	0.435023i	−0.826951	+	0.562274i	$0.809927\pi$
$888$	−529.847	+	17945.5i	−0.0200231	+	0.678166i
$889$	6674.11	+	11559.9i	0.251791	+	0.436115i
$890$		0			0
$891$	13495.6	+	31434.2i	0.507430	+	1.18191i
$892$			22363.4i			0.839441i
$893$	−8468.93	+	4889.54i	−0.317359	+	0.183228i
$894$	33258.7	+	981.975i	1.24423	+	0.0367362i
$895$		0			0
$896$	−9702.67	+	16805.5i	−0.361767	+	0.626600i
$897$	−5946.71	+	3203.16i	−0.221355	+	0.119231i
$898$	−44851.4	+	25895.0i	−1.66672	+	0.962279i
$899$	17183.4			0.637485
$900$		0			0
$901$	26170.3			0.967658
$902$	27727.6	−	16008.5i	1.02353	−	0.590938i
$903$	−9751.04	−	6020.29i	−0.359351	−	0.221864i
$904$	43151.8	−	74741.1i	1.58762	−	2.74984i
$905$		0			0
$906$	−43137.0	+	69868.8i	−1.58182	+	2.56207i
$907$	39326.3	−	22705.0i	1.43970	−	0.831211i	0.441872	−	0.897078i	$-0.354315\pi$
$907$	39326.3	−	22705.0i	1.43970	−	0.831211i	0.997828	+	0.0658671i	$0.0209813\pi$
$908$			77377.5i			2.82804i
$909$	14634.1	+	29201.2i	0.533975	+	1.06550i
$910$		0			0
$911$	15390.9	+	26657.8i	0.559740	+	0.969497i	0.997518	+	0.0704143i	$0.0224321\pi$
$911$	15390.9	+	26657.8i	0.559740	+	0.969497i	−0.437778	+	0.899083i	$0.644235\pi$
$912$	−93827.5	+	50539.5i	−3.40673	+	1.83501i
$913$	−18875.8	−	10898.0i	−0.684226	−	0.395038i
$914$	−11807.7	+	20451.5i	−0.427311	+	0.740125i
$915$		0			0
$916$	−1466.13	−	2539.41i	−0.0528845	−	0.0915986i
$917$		−	18592.1i		−	0.669538i
$918$	36929.7	−	17162.9i	1.32773	−	0.617059i
$919$	22457.3			0.806093			0.403046	−	0.915180i	$-0.367951\pi$
$919$	22457.3			0.806093			0.403046	+	0.915180i	$0.367951\pi$
$920$		0			0
$921$	20203.1	+	596.503i	0.722817	+	0.0213414i
$922$	87185.0	+	50336.3i	3.11419	+	1.79798i
$923$	−18030.8	−	10410.1i	−0.643002	−	0.371238i
$924$	−31462.7	−	58411.0i	−1.12018	−	2.07963i
$925$		0			0
$926$	89259.1			3.16764
$927$	−16792.8	−	11065.4i	−0.594983	−	0.392056i
$928$			26621.8i			0.941706i
$929$	−21827.1	−	37805.7i	−0.770855	−	1.33516i	−0.937095	−	0.349075i	$-0.886496\pi$
$929$	−21827.1	−	37805.7i	−0.770855	−	1.33516i	0.166240	−	0.986085i	$-0.446837\pi$
$930$		0			0
$931$	9048.22	−	15672.0i	0.318521	−	0.551695i
$932$	−22563.2	−	13026.9i	−0.793007	−	0.457843i
$933$	32256.8	+	19915.3i	1.13187	+	0.698819i
$934$	−3635.63	−	6297.10i	−0.127368	−	0.220607i
$935$		0			0
$936$	−34968.1	+	53067.4i	−1.22112	+	1.85317i
$937$		−	41123.3i		−	1.43377i	−0.697193	−	0.716884i	$-0.745568\pi$
$937$		−	41123.3i		−	1.43377i	0.697193	−	0.716884i	$-0.254432\pi$
$938$	1788.32	−	1032.49i	0.0622501	−	0.0359401i
$939$	1567.37	+	2909.85i	0.0544720	+	0.101128i
$940$		0			0
$941$	−11038.9	+	19119.9i	−0.382419	+	0.662370i	−0.991408	−	0.130810i	$-0.958242\pi$
$941$	−11038.9	+	19119.9i	−0.382419	+	0.662370i	0.608988	+	0.793179i	$0.291576\pi$
$942$	322.601	−	10926.2i	0.0111581	−	0.377915i
$943$	3998.95	−	2308.80i	0.138095	−	0.0797293i
$944$	−117088.			−4.03697
$945$		0			0
$946$	−40949.9			−1.40740
$947$	7462.03	−	4308.20i	0.256054	−	0.147833i	−0.366479	−	0.930426i	$-0.619437\pi$
$947$	7462.03	−	4308.20i	0.256054	−	0.147833i	0.622533	+	0.782593i	$0.286104\pi$
$948$	632.824	−	21433.2i	0.0216805	−	0.734303i
$949$	−15087.3	+	26131.9i	−0.516073	+	0.893864i
$950$		0			0
$951$	−15145.5	−	28117.8i	−0.516431	−	0.958763i
$952$	−41382.9	+	23892.5i	−1.40885	+	0.813402i
$953$			29558.0i			1.00470i	0.864664	+	0.502350i	$0.167531\pi$
$953$			29558.0i			1.00470i	−0.864664	+	0.502350i	$0.832469\pi$
$954$	30816.2	+	61491.3i	1.04582	+	2.08685i
$955$		0			0
$956$	−42731.7	−	74013.5i	−1.44565	−	2.50394i
$957$	−12057.9	−	7444.58i	−0.407292	−	0.251462i
$958$	−933.291	−	538.836i	−0.0314752	−	0.0181722i
$959$	−10391.9	+	17999.3i	−0.349919	+	0.606077i
$960$		0			0
$961$	−28814.0	−	49907.3i	−0.967204	−	1.67525i
$962$		−	10187.9i		−	0.341448i
$963$	−1593.21	+	26956.9i	−0.0533131	+	0.902048i
$964$	−46244.0			−1.54504
$965$		0			0
$966$	−6329.88	−	11751.5i	−0.210829	−	0.391407i
$967$	−38603.9	−	22288.0i	−1.28378	−	0.741192i	−0.306244	−	0.951953i	$-0.599072\pi$
$967$	−38603.9	−	22288.0i	−1.28378	−	0.741192i	−0.977538	+	0.210761i	$0.932406\pi$
$968$	−49136.2	−	28368.8i	−1.63150	−	0.941949i
$969$	−31578.3	−	932.360i	−1.04689	−	0.0309099i
$970$		0			0
$971$	43702.8			1.44438			0.722188	−	0.691696i	$-0.243136\pi$
$971$	43702.8			1.44438			0.722188	+	0.691696i	$0.243136\pi$
$972$	60081.9	+	47715.9i	1.98264	+	1.57458i
$973$		−	7247.56i		−	0.238793i
$974$	−50394.4	−	87285.6i	−1.65784	−	2.87147i
$975$		0			0
$976$	−4423.47	+	7661.68i	−0.145074	+	0.251275i
$977$	−39267.1	−	22670.9i	−1.28584	−	0.742381i	−0.307932	−	0.951408i	$-0.599637\pi$
$977$	−39267.1	−	22670.9i	−1.28584	−	0.742381i	−0.977910	+	0.209027i	$0.932970\pi$
$978$	−93898.3	+	50577.6i	−3.07008	+	1.65368i
$979$	−23316.9	−	40386.1i	−0.761197	−	1.31843i
$980$		0			0
$981$	−24675.9	−	1458.40i	−0.803100	−	0.0474650i
$982$		−	62256.8i		−	2.02311i
$983$	−6374.40	+	3680.26i	−0.206828	+	0.119412i	−0.599836	−	0.800123i	$-0.704768\pi$
$983$	−6374.40	+	3680.26i	−0.206828	+	0.119412i	0.393009	+	0.919535i	$0.371434\pi$
$984$	22824.1	−	36968.1i	0.739438	−	1.19766i
$985$		0			0
$986$	−8434.73	+	14609.4i	−0.272431	+	0.471864i
$987$	−5216.81	−	3220.86i	−0.168240	−	0.103871i
$988$	70570.8	−	40744.1i	2.27242	−	1.31199i
$989$	−5905.91			−0.189886
$990$		0			0
$991$	33328.4			1.06833			0.534164	−	0.845381i	$-0.320627\pi$
$991$	33328.4			1.06833			0.534164	+	0.845381i	$0.320627\pi$
$992$	117291.	−	67717.8i	3.75402	−	2.16738i
$993$	53681.5	−	28915.2i	1.71554	−	0.924064i
$994$	20571.8	−	35631.3i	0.656435	−	1.13698i
$995$		0			0
$996$	−48863.2	−	1442.70i	−1.55451	−	0.0458974i
$997$	−30598.1	+	17665.8i	−0.971968	+	0.561166i	−0.899836	−	0.436229i	$-0.856314\pi$
$997$	−30598.1	+	17665.8i	−0.971968	+	0.561166i	−0.0721326	+	0.997395i	$0.522980\pi$
$998$			45845.6i			1.45412i
$999$	−7412.39	−	658.091i	−0.234752	−	0.0208419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.k.d.49.2		28
5.2	odd	4		225.4.e.d.76.1		14
5.3	odd	4		45.4.e.c.31.7	yes	14
5.4	even	2	inner	225.4.k.d.49.13		28
9.7	even	3	inner	225.4.k.d.124.13		28
15.8	even	4		135.4.e.c.91.1		14
45.7	odd	12		225.4.e.d.151.1		14
45.13	odd	12		405.4.a.m.1.1		7
45.22	odd	12		2025.4.a.bb.1.7		7
45.23	even	12		405.4.a.n.1.7		7
45.32	even	12		2025.4.a.ba.1.1		7
45.34	even	6	inner	225.4.k.d.124.2		28
45.38	even	12		135.4.e.c.46.1		14
45.43	odd	12		45.4.e.c.16.7	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.7	✓	14	45.43	odd	12
45.4.e.c.31.7	yes	14	5.3	odd	4
135.4.e.c.46.1		14	45.38	even	12
135.4.e.c.91.1		14	15.8	even	4
225.4.e.d.76.1		14	5.2	odd	4
225.4.e.d.151.1		14	45.7	odd	12
225.4.k.d.49.2		28	1.1	even	1	trivial
225.4.k.d.49.13		28	5.4	even	2	inner
225.4.k.d.124.2		28	45.34	even	6	inner
225.4.k.d.124.13		28	9.7	even	3	inner
405.4.a.m.1.1		7	45.13	odd	12
405.4.a.n.1.7		7	45.23	even	12
2025.4.a.ba.1.1		7	45.32	even	12
2025.4.a.bb.1.7		7	45.22	odd	12

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.60336 + 2.65775i) q^{2} +(-0.153351 + 5.19389i) q^{3} +(10.1273 - 17.5410i) q^{4} +(-13.0981 - 24.3169i) q^{6} +(-11.6339 + 6.71686i) q^{7} +65.1396i q^{8} +(-26.9530 - 1.59298i) q^{9} +O(q^{10})\)	\(q+(-4.60336 + 2.65775i) q^{2} +(-0.153351 + 5.19389i) q^{3} +(10.1273 - 17.5410i) q^{4} +(-13.0981 - 24.3169i) q^{6} +(-11.6339 + 6.71686i) q^{7} +65.1396i q^{8} +(-26.9530 - 1.59298i) q^{9} +(23.4628 + 40.6388i) q^{11} +(89.5531 + 55.2901i) q^{12} +(-31.2935 - 18.0673i) q^{13} +(35.7035 - 61.8403i) q^{14} +(-92.1064 - 159.533i) q^{16} -54.6071i q^{17} +(128.308 - 64.3013i) q^{18} -111.339 q^{19} +(-33.1026 - 61.4555i) q^{21} +(-216.016 - 124.717i) q^{22} +(-31.1544 - 17.9870i) q^{23} +(-338.328 - 9.98925i) q^{24} +192.074 q^{26} +(12.4070 - 139.746i) q^{27} +272.095i q^{28} +(29.0588 + 50.3312i) q^{29} +(147.833 - 256.055i) q^{31} +(396.699 + 229.034i) q^{32} +(-214.671 + 115.631i) q^{33} +(145.132 + 251.377i) q^{34} +(-300.904 + 456.650i) q^{36} -53.0417i q^{37} +(512.533 - 295.911i) q^{38} +(98.6386 - 159.765i) q^{39} +(-64.1795 + 111.162i) q^{41} +(315.717 + 194.924i) q^{42} +(142.177 - 82.0858i) q^{43} +950.461 q^{44} +191.220 q^{46} +(76.0646 - 43.9159i) q^{47} +(842.721 - 453.926i) q^{48} +(-81.2675 + 140.759i) q^{49} +(283.623 + 8.37409i) q^{51} +(-633.839 + 365.947i) q^{52} +479.247i q^{53} +(314.297 + 676.279i) q^{54} +(-437.533 - 757.830i) q^{56} +(17.0739 - 578.281i) q^{57} +(-267.536 - 154.462i) q^{58} +(317.807 - 550.458i) q^{59} +(-24.0128 - 41.5915i) q^{61} +1571.62i q^{62} +(324.269 - 162.507i) q^{63} -961.163 q^{64} +(680.892 - 1102.84i) q^{66} +(25.0440 + 14.4592i) q^{67} +(-957.865 - 553.024i) q^{68} +(98.2001 - 159.054i) q^{69} +576.183 q^{71} +(103.766 - 1755.70i) q^{72} -835.057i q^{73} +(140.972 + 244.170i) q^{74} +(-1127.56 + 1952.99i) q^{76} +(-545.930 - 315.193i) q^{77} +(-29.4548 + 997.612i) q^{78} +(-101.869 - 176.442i) q^{79} +(723.925 + 85.8711i) q^{81} -682.294i q^{82} +(-402.249 + 232.239i) q^{83} +(-1413.23 - 41.7262i) q^{84} +(-436.328 + 755.742i) q^{86} +(-265.871 + 143.210i) q^{87} +(-2647.19 + 1528.36i) q^{88} -993.782 q^{89} +485.423 q^{91} +(-631.021 + 364.320i) q^{92} +(1307.25 + 807.097i) q^{93} +(-233.435 + 404.322i) q^{94} +(-1250.41 + 2025.29i) q^{96} +(763.328 - 440.708i) q^{97} -863.956i q^{98} +(-567.656 - 1132.71i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9}+O(q^{10}) \) 28 * q + 72 * q^4 - 62 * q^6 - 34 * q^9	\( 28 q + 72 q^{4} - 62 q^{6} - 34 q^{9} + 46 q^{11} + 42 q^{14} - 648 q^{16} - 1116 q^{19} + 360 q^{21} - 96 q^{24} + 1432 q^{26} + 592 q^{29} - 488 q^{31} + 250 q^{34} - 4798 q^{36} - 1268 q^{39} - 94 q^{41} + 220 q^{44} + 2868 q^{46} + 2450 q^{49} + 3034 q^{51} + 8132 q^{54} - 1962 q^{56} + 170 q^{59} - 1656 q^{61} - 8944 q^{64} + 9860 q^{66} + 1644 q^{69} - 1312 q^{71} + 2632 q^{74} - 5578 q^{76} + 4220 q^{79} - 4334 q^{81} - 11550 q^{84} - 5138 q^{86} - 12192 q^{89} + 13352 q^{91} - 1034 q^{94} - 1186 q^{96} - 4640 q^{99}+O(q^{100}) \) 28 * q + 72 * q^4 - 62 * q^6 - 34 * q^9 + 46 * q^11 + 42 * q^14 - 648 * q^16 - 1116 * q^19 + 360 * q^21 - 96 * q^24 + 1432 * q^26 + 592 * q^29 - 488 * q^31 + 250 * q^34 - 4798 * q^36 - 1268 * q^39 - 94 * q^41 + 220 * q^44 + 2868 * q^46 + 2450 * q^49 + 3034 * q^51 + 8132 * q^54 - 1962 * q^56 + 170 * q^59 - 1656 * q^61 - 8944 * q^64 + 9860 * q^66 + 1644 * q^69 - 1312 * q^71 + 2632 * q^74 - 5578 * q^76 + 4220 * q^79 - 4334 * q^81 - 11550 * q^84 - 5138 * q^86 - 12192 * q^89 + 13352 * q^91 - 1034 * q^94 - 1186 * q^96 - 4640 * q^99

Introduction

L-functions

Modular forms

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Database

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