LMFDB - Embedded newform 380.3.h.a.39.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,3,Mod(39,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("380.39");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	380.h (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:	$10.3542500457$
Analytic rank:	$0$
Dimension:	$108$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.13
Character	$\chi$	$=$	380.39
Dual form			380.3.h.a.39.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.85933 - 0.736815i) q^{2} -2.04408 q^{3} +(2.91421 + 2.73996i) q^{4} +(-4.55181 - 2.06907i) q^{5} +(3.80062 + 1.50611i) q^{6} -11.4458 q^{7} +(-3.39962 - 7.24172i) q^{8} -4.82174 q^{9} +O(q^{10})$	\(q+(-1.85933 - 0.736815i) q^{2} -2.04408 q^{3} +(2.91421 + 2.73996i) q^{4} +(-4.55181 - 2.06907i) q^{5} +(3.80062 + 1.50611i) q^{6} -11.4458 q^{7} +(-3.39962 - 7.24172i) q^{8} -4.82174 q^{9} +(6.93879 + 7.20092i) q^{10} -2.74195i q^{11} +(-5.95687 - 5.60070i) q^{12} -23.9054i q^{13} +(21.2815 + 8.43345i) q^{14} +(9.30426 + 4.22934i) q^{15} +(0.985208 + 15.9696i) q^{16} +18.6947i q^{17} +(8.96520 + 3.55273i) q^{18} -4.35890i q^{19} +(-7.59575 - 18.5015i) q^{20} +23.3962 q^{21} +(-2.02031 + 5.09819i) q^{22} -33.3470 q^{23} +(6.94910 + 14.8027i) q^{24} +(16.4379 + 18.8360i) q^{25} +(-17.6139 + 44.4480i) q^{26} +28.2527 q^{27} +(-33.3555 - 31.3611i) q^{28} -14.3317 q^{29} +(-14.1834 - 14.7192i) q^{30} +6.39501i q^{31} +(9.93485 - 30.4187i) q^{32} +5.60477i q^{33} +(13.7745 - 34.7596i) q^{34} +(52.0992 + 23.6822i) q^{35} +(-14.0515 - 13.2114i) q^{36} +9.68409i q^{37} +(-3.21170 + 8.10463i) q^{38} +48.8645i q^{39} +(0.490825 + 39.9970i) q^{40} +8.81555 q^{41} +(-43.5012 - 17.2386i) q^{42} +32.1849 q^{43} +(7.51285 - 7.99062i) q^{44} +(21.9476 + 9.97650i) q^{45} +(62.0030 + 24.5705i) q^{46} -11.9702 q^{47} +(-2.01384 - 32.6432i) q^{48} +82.0068 q^{49} +(-16.6849 - 47.1340i) q^{50} -38.2135i q^{51} +(65.4999 - 69.6653i) q^{52} +101.668i q^{53} +(-52.5311 - 20.8170i) q^{54} +(-5.67328 + 12.4808i) q^{55} +(38.9115 + 82.8875i) q^{56} +8.90994i q^{57} +(26.6473 + 10.5598i) q^{58} -51.3607i q^{59} +(15.5263 + 37.8185i) q^{60} +41.5193 q^{61} +(4.71194 - 11.8904i) q^{62} +55.1887 q^{63} +(-40.8851 + 49.2383i) q^{64} +(-49.4619 + 108.813i) q^{65} +(4.12968 - 10.4211i) q^{66} +91.4221 q^{67} +(-51.2228 + 54.4802i) q^{68} +68.1638 q^{69} +(-79.4201 - 82.4204i) q^{70} -93.7587i q^{71} +(16.3921 + 34.9177i) q^{72} -77.6994i q^{73} +(7.13539 - 18.0059i) q^{74} +(-33.6004 - 38.5023i) q^{75} +(11.9432 - 12.7027i) q^{76} +31.3839i q^{77} +(36.0041 - 90.8552i) q^{78} -59.7780i q^{79} +(28.5578 - 74.7292i) q^{80} -14.3552 q^{81} +(-16.3910 - 6.49543i) q^{82} -53.7068 q^{83} +(68.1813 + 64.1046i) q^{84} +(38.6806 - 85.0947i) q^{85} +(-59.8423 - 23.7143i) q^{86} +29.2951 q^{87} +(-19.8565 + 9.32161i) q^{88} +16.6798 q^{89} +(-33.4570 - 34.7209i) q^{90} +273.617i q^{91} +(-97.1800 - 91.3694i) q^{92} -13.0719i q^{93} +(22.2566 + 8.81983i) q^{94} +(-9.01885 + 19.8409i) q^{95} +(-20.3076 + 62.1783i) q^{96} +94.6828i q^{97} +(-152.478 - 60.4238i) q^{98} +13.2210i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 4 q^{5} + 324 q^{9}+O(q^{10}) $ 108 * q + 4 * q^5 + 324 * q^9	$ 108 q + 4 q^{5} + 324 q^{9} - 8 q^{10} + 8 q^{14} - 104 q^{16} - 16 q^{21} - 8 q^{24} - 76 q^{25} + 80 q^{26} - 88 q^{29} - 140 q^{30} - 88 q^{34} - 256 q^{36} + 44 q^{40} - 200 q^{41} - 8 q^{44} + 108 q^{45} + 272 q^{46} + 916 q^{49} - 276 q^{50} - 320 q^{54} - 328 q^{56} + 172 q^{60} + 200 q^{61} - 216 q^{64} - 192 q^{65} + 152 q^{66} - 592 q^{69} + 200 q^{70} - 232 q^{74} + 340 q^{80} + 1052 q^{81} + 208 q^{84} + 248 q^{85} - 1048 q^{86} + 760 q^{89} + 268 q^{90} - 320 q^{94} + 720 q^{96}+O(q^{100}) $ 108 * q + 4 * q^5 + 324 * q^9 - 8 * q^10 + 8 * q^14 - 104 * q^16 - 16 * q^21 - 8 * q^24 - 76 * q^25 + 80 * q^26 - 88 * q^29 - 140 * q^30 - 88 * q^34 - 256 * q^36 + 44 * q^40 - 200 * q^41 - 8 * q^44 + 108 * q^45 + 272 * q^46 + 916 * q^49 - 276 * q^50 - 320 * q^54 - 328 * q^56 + 172 * q^60 + 200 * q^61 - 216 * q^64 - 192 * q^65 + 152 * q^66 - 592 * q^69 + 200 * q^70 - 232 * q^74 + 340 * q^80 + 1052 * q^81 + 208 * q^84 + 248 * q^85 - 1048 * q^86 + 760 * q^89 + 268 * q^90 - 320 * q^94 + 720 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.85933	−	0.736815i	−0.929664	−	0.368408i
$2$	−1.85933	−	0.736815i	−0.929664	−	0.368408i
$3$	−2.04408			−0.681360			−0.340680	−	0.940179i	$-0.610657\pi$
$3$	−2.04408			−0.681360			−0.340680	+	0.940179i	$0.610657\pi$
$4$	2.91421	+	2.73996i	0.728552	+	0.684991i
$5$	−4.55181	−	2.06907i	−0.910362	−	0.413813i
$5$	−4.55181	−	2.06907i	−0.910362	−	0.413813i
$6$	3.80062	+	1.50611i	0.633436	+	0.251018i
$7$	−11.4458			−1.63512			−0.817558	−	0.575846i	$-0.804673\pi$
$7$	−11.4458			−1.63512			−0.817558	+	0.575846i	$0.804673\pi$
$8$	−3.39962	−	7.24172i	−0.424953	−	0.905215i
$9$	−4.82174			−0.535749
$10$	6.93879	+	7.20092i	0.693879	+	0.720092i
$11$		−	2.74195i		−	0.249268i	−0.992203	−	0.124634i	$-0.960224\pi$
$11$		−	2.74195i		−	0.249268i	0.992203	−	0.124634i	$-0.0397757\pi$
$12$	−5.95687	−	5.60070i	−0.496406	−	0.466725i
$13$		−	23.9054i		−	1.83888i	−0.393235	−	0.919438i	$-0.628644\pi$
$13$		−	23.9054i		−	1.83888i	0.393235	−	0.919438i	$-0.371356\pi$
$14$	21.2815	+	8.43345i	1.52011	+	0.602389i
$15$	9.30426	+	4.22934i	0.620284	+	0.281956i
$16$	0.985208	+	15.9696i	0.0615755	+	0.998102i
$17$			18.6947i			1.09969i	0.835267	+	0.549844i	$0.185313\pi$
$17$			18.6947i			1.09969i	−0.835267	+	0.549844i	$0.814687\pi$
$18$	8.96520	+	3.55273i	0.498067	+	0.197374i
$19$		−	4.35890i		−	0.229416i
$19$		−	4.35890i		−	0.229416i
$20$	−7.59575	−	18.5015i	−0.379787	−	0.925074i
$21$	23.3962			1.11410
$22$	−2.02031	+	5.09819i	−0.0918324	+	0.231736i
$23$	−33.3470			−1.44987			−0.724934	−	0.688818i	$-0.758130\pi$
$23$	−33.3470			−1.44987			−0.724934	+	0.688818i	$0.758130\pi$
$24$	6.94910	+	14.8027i	0.289546	+	0.616777i
$25$	16.4379	+	18.8360i	0.657517	+	0.753440i
$26$	−17.6139	+	44.4480i	−0.677456	+	1.70954i
$27$	28.2527			1.04640
$28$	−33.3555	−	31.3611i	−1.19127	−	1.12004i
$29$	−14.3317			−0.494196			−0.247098	−	0.968991i	$-0.579477\pi$
$29$	−14.3317			−0.494196			−0.247098	+	0.968991i	$0.579477\pi$
$30$	−14.1834	−	14.7192i	−0.472781	−	0.490642i
$31$			6.39501i			0.206291i	0.994666	+	0.103145i	$0.0328907\pi$
$31$			6.39501i			0.206291i	−0.994666	+	0.103145i	$0.967109\pi$
$32$	9.93485	−	30.4187i	0.310464	−	0.950585i
$33$			5.60477i			0.169841i
$34$	13.7745	−	34.7596i	0.405133	−	1.02234i
$35$	52.0992	+	23.6822i	1.48855	+	0.676633i
$36$	−14.0515	−	13.2114i	−0.390321	−	0.366983i
$37$			9.68409i			0.261732i	0.991400	+	0.130866i	$0.0417758\pi$
$37$			9.68409i			0.261732i	−0.991400	+	0.130866i	$0.958224\pi$
$38$	−3.21170	+	8.10463i	−0.0845185	+	0.213280i
$39$			48.8645i			1.25294i
$40$	0.490825	+	39.9970i	0.0122706	+	0.999925i
$41$	8.81555			0.215014			0.107507	−	0.994204i	$-0.465713\pi$
$41$	8.81555			0.215014			0.107507	+	0.994204i	$0.465713\pi$
$42$	−43.5012	−	17.2386i	−1.03574	−	0.410444i
$43$	32.1849			0.748486			0.374243	−	0.927331i	$-0.377903\pi$
$43$	32.1849			0.748486			0.374243	+	0.927331i	$0.377903\pi$
$44$	7.51285	−	7.99062i	0.170747	−	0.181605i
$45$	21.9476	+	9.97650i	0.487725	+	0.221700i
$46$	62.0030	+	24.5705i	1.34789	+	0.534142i
$47$	−11.9702			−0.254685			−0.127343	−	0.991859i	$-0.540645\pi$
$47$	−11.9702			−0.254685			−0.127343	+	0.991859i	$0.540645\pi$
$48$	−2.01384	−	32.6432i	−0.0419551	−	0.680067i
$49$	82.0068			1.67361
$50$	−16.6849	−	47.1340i	−0.333697	−	0.942680i
$51$		−	38.2135i		−	0.749283i
$52$	65.4999	−	69.6653i	1.25961	−	1.33972i
$53$			101.668i			1.91826i	0.282958	+	0.959132i	$0.408684\pi$
$53$			101.668i			1.91826i	−0.282958	+	0.959132i	$0.591316\pi$
$54$	−52.5311	−	20.8170i	−0.972799	−	0.385501i
$55$	−5.67328	+	12.4808i	−0.103151	+	0.226924i
$56$	38.9115	+	82.8875i	0.694848	+	1.48013i
$57$			8.90994i			0.156315i
$58$	26.6473	+	10.5598i	0.459436	+	0.182065i
$59$		−	51.3607i		−	0.870520i	−0.900305	−	0.435260i	$-0.856657\pi$
$59$		−	51.3607i		−	0.870520i	0.900305	−	0.435260i	$-0.143343\pi$
$60$	15.5263	+	37.8185i	0.258772	+	0.630308i
$61$	41.5193			0.680644			0.340322	−	0.940309i	$-0.389464\pi$
$61$	41.5193			0.680644			0.340322	+	0.940309i	$0.389464\pi$
$62$	4.71194	−	11.8904i	0.0759990	−	0.191781i
$63$	55.1887			0.876012
$64$	−40.8851	+	49.2383i	−0.638830	+	0.769348i
$65$	−49.4619	+	108.813i	−0.760952	+	1.67404i
$66$	4.12968	−	10.4211i	0.0625709	−	0.157896i
$67$	91.4221			1.36451			0.682254	−	0.731115i	$-0.261000\pi$
$67$	91.4221			1.36451			0.682254	+	0.731115i	$0.261000\pi$
$68$	−51.2228	+	54.4802i	−0.753276	+	0.801180i
$69$	68.1638			0.987882
$70$	−79.4201	−	82.4204i	−1.13457	−	1.17743i
$71$		−	93.7587i		−	1.32054i	−0.751026	−	0.660272i	$-0.770441\pi$
$71$		−	93.7587i		−	1.32054i	0.751026	−	0.660272i	$-0.229559\pi$
$72$	16.3921	+	34.9177i	0.227668	+	0.484968i
$73$		−	77.6994i		−	1.06438i	−0.846626	−	0.532188i	$-0.821370\pi$
$73$		−	77.6994i		−	1.06438i	0.846626	−	0.532188i	$-0.178630\pi$
$74$	7.13539	−	18.0059i	0.0964241	−	0.243323i
$75$	−33.6004	−	38.5023i	−0.448006	−	0.513364i
$76$	11.9432	−	12.7027i	0.157148	−	0.167141i
$77$			31.3839i			0.407583i
$78$	36.0041	−	90.8552i	0.461591	−	1.16481i
$79$		−	59.7780i		−	0.756684i	−0.925666	−	0.378342i	$-0.876494\pi$
$79$		−	59.7780i		−	0.756684i	0.925666	−	0.378342i	$-0.123506\pi$
$80$	28.5578	−	74.7292i	0.356972	−	0.934115i
$81$	−14.3552			−0.177224
$82$	−16.3910	−	6.49543i	−0.199890	−	0.0792126i
$83$	−53.7068			−0.647070			−0.323535	−	0.946216i	$-0.604871\pi$
$83$	−53.7068			−0.647070			−0.323535	+	0.946216i	$0.604871\pi$
$84$	68.1813	+	64.1046i	0.811682	+	0.763150i
$85$	38.6806	−	85.0947i	0.455066	−	1.00111i
$86$	−59.8423	−	23.7143i	−0.695841	−	0.275748i
$87$	29.2951			0.336725
$88$	−19.8565	+	9.32161i	−0.225642	+	0.105927i
$89$	16.6798			0.187413			0.0937067	−	0.995600i	$-0.470128\pi$
$89$	16.6798			0.187413			0.0937067	+	0.995600i	$0.470128\pi$
$90$	−33.4570	−	34.7209i	−0.371745	−	0.385788i
$91$			273.617i			3.00678i
$92$	−97.1800	−	91.3694i	−1.05630	−	0.993146i
$93$		−	13.0719i		−	0.140558i
$94$	22.2566	+	8.81983i	0.236772	+	0.0938280i
$95$	−9.01885	+	19.8409i	−0.0949353	+	0.208851i
$96$	−20.3076	+	62.1783i	−0.211538	+	0.647691i
$97$			94.6828i			0.976112i	0.872812	+	0.488056i	$0.162294\pi$
$97$			94.6828i			0.976112i	−0.872812	+	0.488056i	$0.837706\pi$
$98$	−152.478	−	60.4238i	−1.55589	−	0.616569i
$99$			13.2210i			0.133545i
$100$	−3.70641	+	99.9313i	−0.0370641	+	0.999313i
$101$	−124.174			−1.22945			−0.614723	−	0.788743i	$-0.710732\pi$
$101$	−124.174			−1.22945			−0.614723	+	0.788743i	$0.710732\pi$
$102$	−28.1562	+	71.0514i	−0.276042	+	0.696582i
$103$	−97.7643			−0.949168			−0.474584	−	0.880210i	$-0.657401\pi$
$103$	−97.7643			−0.949168			−0.474584	+	0.880210i	$0.657401\pi$
$104$	−173.116	+	81.2693i	−1.66458	+	0.781436i
$105$	−106.495	−	48.4082i	−1.01424	−	0.461031i
$106$	74.9105	−	189.034i	0.706703	−	1.78334i
$107$	−102.168			−0.954843			−0.477421	−	0.878674i	$-0.658429\pi$
$107$	−102.168			−0.954843			−0.477421	+	0.878674i	$0.658429\pi$
$108$	82.3343	+	77.4114i	0.762355	+	0.716773i
$109$	−160.969			−1.47678			−0.738388	−	0.674376i	$-0.764413\pi$
$109$	−160.969			−1.47678			−0.738388	+	0.674376i	$0.764413\pi$
$110$	19.7446	−	19.0258i	0.179496	−	0.172962i
$111$		−	19.7951i		−	0.178334i
$112$	−11.2765	−	182.786i	−0.100683	−	1.63201i
$113$			100.754i			0.891631i	0.895125	+	0.445815i	$0.147086\pi$
$113$			100.754i			0.891631i	−0.895125	+	0.445815i	$0.852914\pi$
$114$	6.56497	−	16.5665i	0.0575875	−	0.145320i
$115$	151.789	+	68.9971i	1.31990	+	0.599975i
$116$	−41.7655	−	39.2682i	−0.360047	−	0.338519i
$117$			115.266i			0.985176i
$118$	−37.8433	+	95.4963i	−0.320706	+	0.809291i
$119$		−	213.976i		−	1.79812i
$120$	−1.00329	−	81.7570i	−0.00836071	−	0.681309i
$121$	113.482			0.937865
$122$	−77.1980	−	30.5920i	−0.632771	−	0.250754i
$123$	−18.0197			−0.146502
$124$	−17.5221	+	18.6364i	−0.141307	+	0.150293i
$125$	−35.8493	−	119.749i	−0.286795	−	0.957992i
$126$	−102.614	−	40.6639i	−0.814397	−	0.322729i
$127$	145.043			1.14207			0.571036	−	0.820925i	$-0.306542\pi$
$127$	145.043			1.14207			0.571036	+	0.820925i	$0.306542\pi$
$128$	112.298	−	61.4254i	0.877331	−	0.479886i
$129$	−65.7885			−0.509988
$130$	172.141	−	165.874i	1.32416	−	1.27596i
$131$			34.7566i			0.265318i	0.991162	+	0.132659i	$0.0423515\pi$
$131$			34.7566i			0.265318i	−0.991162	+	0.132659i	$0.957649\pi$
$132$	−15.3569	+	16.3335i	−0.116340	+	0.123738i
$133$			49.8912i			0.375122i
$134$	−169.984	−	67.3612i	−1.26854	−	0.502695i
$135$	−128.601	−	58.4568i	−0.952600	−	0.433013i
$136$	135.382	−	63.5549i	0.995455	−	0.467316i
$137$		−	21.1188i		−	0.154152i	−0.997025	−	0.0770760i	$-0.975442\pi$
$137$		−	21.1188i		−	0.154152i	0.997025	−	0.0770760i	$-0.0245584\pi$
$138$	−126.739	−	50.2241i	−0.918399	−	0.363943i
$139$		−	83.4567i		−	0.600408i	−0.953875	−	0.300204i	$-0.902945\pi$
$139$		−	83.4567i		−	0.600408i	0.953875	−	0.300204i	$-0.0970548\pi$
$140$	86.9395	+	211.765i	0.620997	+	1.51260i
$141$	24.4681			0.173532
$142$	−69.0828	+	174.328i	−0.486499	+	1.22766i
$143$	−65.5474			−0.458374
$144$	−4.75041	−	77.0014i	−0.0329890	−	0.534732i
$145$	65.2350	+	29.6532i	0.449897	+	0.204505i
$146$	−57.2501	+	144.469i	−0.392124	+	0.989512i
$147$	−167.628			−1.14033
$148$	−26.5341	+	28.2215i	−0.179284	+	0.190686i
$149$	22.5107			0.151079			0.0755393	−	0.997143i	$-0.475932\pi$
$149$	22.5107			0.151079			0.0755393	+	0.997143i	$0.475932\pi$
$150$	34.1052	+	96.3457i	0.227368	+	0.642305i
$151$			199.079i			1.31840i	0.751967	+	0.659200i	$0.229105\pi$
$151$			199.079i			1.31840i	−0.751967	+	0.659200i	$0.770895\pi$
$152$	−31.5659	+	14.8186i	−0.207671	+	0.0974909i
$153$		−	90.1410i		−	0.589157i
$154$	23.1241	−	58.3530i	0.150157	−	0.378915i
$155$	13.2317	−	29.1089i	0.0853658	−	0.187799i
$156$	−133.887	+	142.401i	−0.858250	+	0.912829i
$157$			79.7919i			0.508229i	0.967174	+	0.254114i	$0.0817840\pi$
$157$			79.7919i			0.508229i	−0.967174	+	0.254114i	$0.918216\pi$
$158$	−44.0454	+	111.147i	−0.278768	+	0.703462i
$159$		−	207.818i		−	1.30703i
$160$	−108.160	+	117.904i	−0.675999	+	0.736902i
$161$	381.683			2.37070
$162$	26.6910	+	10.5771i	0.164759	+	0.0652908i
$163$	−74.4218			−0.456576			−0.228288	−	0.973594i	$-0.573313\pi$
$163$	−74.4218			−0.456576			−0.228288	+	0.973594i	$0.573313\pi$
$164$	25.6904	+	24.1543i	0.156648	+	0.147282i
$165$	11.5966	−	25.5118i	0.0702827	−	0.154617i
$166$	99.8586	+	39.5720i	0.601558	+	0.238385i
$167$	131.561			0.787788			0.393894	−	0.919156i	$-0.371128\pi$
$167$	131.561			0.787788			0.393894	+	0.919156i	$0.371128\pi$
$168$	−79.5381	−	169.429i	−0.473441	−	1.00850i
$169$	−402.468			−2.38147
$170$	−134.619	+	129.719i	−0.791876	+	0.763051i
$171$			21.0175i			0.122909i
$172$	93.7935	+	88.1855i	0.545311	+	0.512706i
$173$		−	210.203i		−	1.21505i	−0.794301	−	0.607524i	$-0.792163\pi$
$173$		−	210.203i		−	1.21505i	0.794301	−	0.607524i	$-0.207837\pi$
$174$	−54.4692	−	21.5851i	−0.313041	−	0.124052i
$175$	−188.145	−	215.593i	−1.07512	−	1.23196i
$176$	43.7880	−	2.70139i	0.248795	−	0.0153488i
$177$			104.985i			0.593137i
$178$	−31.0132	−	12.2899i	−0.174232	−	0.0690445i
$179$			149.767i			0.836689i	0.908288	+	0.418344i	$0.137390\pi$
$179$			149.767i			0.836689i	−0.908288	+	0.418344i	$0.862610\pi$
$180$	36.6247	+	89.2093i	0.203471	+	0.495607i
$181$	160.111			0.884590			0.442295	−	0.896870i	$-0.354164\pi$
$181$	160.111			0.884590			0.442295	+	0.896870i	$0.354164\pi$
$182$	201.605	−	508.744i	1.10772	−	2.79529i
$183$	−84.8687			−0.463764
$184$	113.367	+	241.489i	0.616126	+	1.31244i
$185$	20.0370	−	44.0801i	0.108308	−	0.238271i
$186$	−9.63158	+	24.3050i	−0.0517827	+	0.130672i
$187$	51.2600			0.274118
$188$	−34.8837	−	32.7979i	−0.185551	−	0.174457i
$189$	−323.376			−1.71098
$190$	31.3881	−	30.2455i	0.165200	−	0.159187i
$191$		−	31.9042i		−	0.167038i	−0.996506	−	0.0835189i	$-0.973384\pi$
$191$		−	31.9042i		−	0.167038i	0.996506	−	0.0835189i	$-0.0266159\pi$
$192$	83.5724	−	100.647i	0.435273	−	0.524203i
$193$		−	230.383i		−	1.19369i	−0.802356	−	0.596846i	$-0.796420\pi$
$193$		−	230.383i		−	1.19369i	0.802356	−	0.596846i	$-0.203580\pi$
$194$	69.7637	−	176.047i	0.359607	−	0.907456i
$195$	101.104	−	222.422i	0.518482	−	1.14063i
$196$	238.985	+	224.695i	1.21931	+	1.14641i
$197$			142.787i			0.724808i	0.932021	+	0.362404i	$0.118044\pi$
$197$			142.787i			0.724808i	−0.932021	+	0.362404i	$0.881956\pi$
$198$	9.74142	−	24.5821i	0.0491991	−	0.124152i
$199$		−	82.3959i		−	0.414050i	−0.978336	−	0.207025i	$-0.933622\pi$
$199$		−	82.3959i		−	0.414050i	0.978336	−	0.207025i	$-0.0663781\pi$
$200$	80.5223	−	183.074i	0.402612	−	0.915371i
$201$	−186.874			−0.929721
$202$	230.880	+	91.4933i	1.14297	+	0.452937i
$203$	164.038			0.808068
$204$	104.703	−	111.362i	0.513252	−	0.545892i
$205$	−40.1267	−	18.2400i	−0.195740	−	0.0889755i
$206$	181.776	+	72.0342i	0.882408	+	0.349681i
$207$	160.790			0.776765
$208$	381.760	−	23.5518i	1.83539	−	0.113230i
$209$	−11.9519			−0.0571861
$210$	162.341	+	168.474i	0.773053	+	0.802256i
$211$			196.430i			0.930948i	0.885062	+	0.465474i	$0.154116\pi$
$211$			196.430i			0.930948i	−0.885062	+	0.465474i	$0.845884\pi$
$212$	−278.567	+	296.282i	−1.31399	+	1.39756i
$213$			191.650i			0.899766i
$214$	189.964	+	75.2791i	0.887684	+	0.351771i
$215$	−146.500	−	66.5927i	−0.681393	−	0.309734i
$216$	−96.0487	−	204.598i	−0.444670	−	0.947215i
$217$		−	73.1961i		−	0.337309i
$218$	299.294	+	118.604i	1.37291	+	0.544056i
$219$			158.824i			0.725223i
$220$	−50.7302	+	20.8272i	−0.230592	+	0.0946690i
$221$	446.904			2.02219
$222$	−14.5853	+	36.8055i	−0.0656995	+	0.165791i
$223$	120.260			0.539283			0.269642	−	0.962961i	$-0.413095\pi$
$223$	120.260			0.539283			0.269642	+	0.962961i	$0.413095\pi$
$224$	−113.712	+	348.167i	−0.507645	+	1.55432i
$225$	−79.2594	−	90.8222i	−0.352264	−	0.403654i
$226$	74.2373	−	187.335i	0.328483	−	0.828917i
$227$	36.2600			0.159736			0.0798679	−	0.996805i	$-0.474550\pi$
$227$	36.2600			0.159736			0.0798679	+	0.996805i	$0.474550\pi$
$228$	−24.4129	+	25.9654i	−0.107074	+	0.113883i
$229$	271.674			1.18635			0.593175	−	0.805073i	$-0.297874\pi$
$229$	271.674			1.18635			0.593175	+	0.805073i	$0.297874\pi$
$230$	−231.388	−	240.129i	−1.00603	−	1.04404i
$231$		−	64.1512i		−	0.277711i
$232$	48.7223	+	103.786i	0.210010	+	0.447353i
$233$		−	400.370i		−	1.71833i	−0.511701	−	0.859164i	$-0.670984\pi$
$233$		−	400.370i		−	1.71833i	0.511701	−	0.859164i	$-0.329016\pi$
$234$	84.9294	−	214.317i	0.362946	−	0.915883i
$235$	54.4861	+	24.7672i	0.231856	+	0.105392i
$236$	140.726	−	149.676i	0.596298	−	0.634219i
$237$			122.191i			0.515574i
$238$	−157.661	+	397.852i	−0.662441	+	1.67165i
$239$			87.9110i			0.367828i	0.982942	+	0.183914i	$0.0588769\pi$
$239$			87.9110i			0.367828i	−0.982942	+	0.183914i	$0.941123\pi$
$240$	−58.3744	+	152.752i	−0.243227	+	0.636468i
$241$	−254.143			−1.05453			−0.527267	−	0.849700i	$-0.676783\pi$
$241$	−254.143			−1.05453			−0.527267	+	0.849700i	$0.676783\pi$
$242$	−211.000	−	83.6150i	−0.871900	−	0.345517i
$243$	−224.931			−0.925644
$244$	120.996	+	113.761i	0.495884	+	0.466235i
$245$	−373.279	−	169.677i	−1.52359	−	0.692561i
$246$	33.5045	+	13.2772i	0.136197	+	0.0539723i
$247$	−104.201			−0.421867
$248$	46.3109	−	21.7406i	0.186737	−	0.0876638i
$249$	109.781			0.440887
$250$	−21.5771	+	249.067i	−0.0863086	+	0.996268i
$251$			430.927i			1.71684i	0.512947	+	0.858420i	$0.328554\pi$
$251$			430.927i			1.71684i	−0.512947	+	0.858420i	$0.671446\pi$
$252$	160.831	+	151.215i	0.638220	+	0.600060i
$253$			91.4358i			0.361406i
$254$	−269.683	−	106.870i	−1.06174	−	0.420748i
$255$	−79.0662	+	173.940i	−0.310064	+	0.682119i
$256$	−254.059	+	31.4668i	−0.992417	+	0.122917i
$257$			174.440i			0.678755i	0.940650	+	0.339378i	$0.110216\pi$
$257$			174.440i			0.678755i	−0.940650	+	0.339378i	$0.889784\pi$
$258$	122.322	+	48.4740i	0.474118	+	0.187884i
$259$		−	110.842i		−	0.427963i
$260$	−442.285	+	181.579i	−1.70110	+	0.698382i
$261$	69.1036			0.264765
$262$	25.6092	−	64.6240i	0.0977450	−	0.246656i
$263$	−182.849			−0.695245			−0.347622	−	0.937635i	$-0.613011\pi$
$263$	−182.849			−0.695245			−0.347622	+	0.937635i	$0.613011\pi$
$264$	40.5882	−	19.0541i	0.153743	−	0.0721746i
$265$	210.358	−	462.773i	0.793804	−	1.74631i
$266$	36.7606	−	92.7641i	0.138198	−	0.348737i
$267$	−34.0948			−0.127696
$268$	266.423	+	250.493i	0.994115	+	0.934676i
$269$	189.187			0.703296			0.351648	−	0.936132i	$-0.385621\pi$
$269$	189.187			0.703296			0.351648	+	0.936132i	$0.385621\pi$
$270$	196.040	+	203.446i	0.726073	+	0.753502i
$271$			185.885i			0.685921i	0.939350	+	0.342960i	$0.111430\pi$
$271$			185.885i			0.685921i	−0.939350	+	0.342960i	$0.888570\pi$
$272$	−298.548	+	18.4182i	−1.09760	+	0.0677138i
$273$		−	559.294i		−	2.04870i
$274$	−15.5607	+	39.2668i	−0.0567907	+	0.143310i
$275$	51.6474	−	45.0720i	0.187809	−	0.163898i
$276$	198.644	+	186.766i	0.719723	+	0.676690i
$277$		−	281.462i		−	1.01611i	−0.861325	−	0.508055i	$-0.830365\pi$
$277$		−	281.462i		−	1.01611i	0.861325	−	0.508055i	$-0.169635\pi$
$278$	−61.4922	+	155.174i	−0.221195	+	0.558178i
$279$		−	30.8351i		−	0.110520i
$280$	−5.61789	−	457.798i	−0.0200639	−	1.63499i
$281$	−284.766			−1.01340			−0.506702	−	0.862121i	$-0.669136\pi$
$281$	−284.766			−1.01340			−0.506702	+	0.862121i	$0.669136\pi$
$282$	−45.4942	−	18.0284i	−0.161327	−	0.0639306i
$283$	500.619			1.76897			0.884486	−	0.466568i	$-0.154510\pi$
$283$	500.619			1.76897			0.884486	+	0.466568i	$0.154510\pi$
$284$	256.895	−	273.232i	0.904561	−	0.962085i
$285$	18.4353	−	40.5563i	0.0646851	−	0.142303i
$286$	121.874	+	48.2963i	0.426134	+	0.168868i
$287$	−100.901			−0.351572
$288$	−47.9032	+	146.671i	−0.166331	+	0.509275i
$289$	−60.4918			−0.209314
$290$	−99.4444	−	103.201i	−0.342912	−	0.355866i
$291$		−	193.539i		−	0.665083i
$292$	212.893	−	226.432i	0.729087	−	0.775453i
$293$			510.917i			1.74375i	0.489732	+	0.871873i	$0.337094\pi$
$293$			510.917i			1.74375i	−0.489732	+	0.871873i	$0.662906\pi$
$294$	311.676	+	123.511i	1.06012	+	0.420106i
$295$	−106.269	+	233.784i	−0.360233	+	0.792488i
$296$	70.1295	−	32.9223i	0.236924	−	0.111224i
$297$		−	77.4677i		−	0.260834i
$298$	−41.8548	−	16.5862i	−0.140452	−	0.0556585i
$299$			797.172i			2.66613i
$300$	7.57620	−	204.268i	0.0252540	−	0.680892i
$301$	−368.383			−1.22386
$302$	146.684	−	370.152i	0.485709	−	1.22567i
$303$	253.822			0.837695
$304$	69.6100	−	4.29442i	0.228980	−	0.0141264i
$305$	−188.988	−	85.9062i	−0.619632	−	0.281660i
$306$	−66.4172	+	167.602i	−0.217050	+	0.547718i
$307$	113.220			0.368796			0.184398	−	0.982852i	$-0.440967\pi$
$307$	113.220			0.368796			0.184398	+	0.982852i	$0.440967\pi$
$308$	−85.9907	+	91.4592i	−0.279191	+	0.296945i
$309$	199.838			0.646725
$310$	−46.0499	+	44.3736i	−0.148548	+	0.143141i
$311$			608.707i			1.95726i	0.205638	+	0.978628i	$0.434073\pi$
$311$			608.707i			1.95726i	−0.205638	+	0.978628i	$0.565927\pi$
$312$	353.863	−	166.121i	1.13418	−	0.532439i
$313$		−	356.316i		−	1.13839i	−0.822202	−	0.569196i	$-0.807255\pi$
$313$		−	356.316i		−	1.13839i	0.822202	−	0.569196i	$-0.192745\pi$
$314$	58.7919	−	148.359i	0.187235	−	0.472482i
$315$	−251.209	−	114.189i	−0.797488	−	0.362505i
$316$	163.790	−	174.206i	0.518322	−	0.551284i
$317$		−	64.3114i		−	0.202875i	−0.994842	−	0.101438i	$-0.967656\pi$
$317$		−	64.3114i		−	0.202875i	0.994842	−	0.101438i	$-0.0323442\pi$
$318$	−153.123	+	386.401i	−0.481519	+	1.21510i
$319$			39.2968i			0.123187i
$320$	287.979	−	139.529i	0.899933	−	0.436029i
$321$	208.840			0.650592
$322$	−709.675	−	281.230i	−2.20396	−	0.873385i
$323$	81.4883			0.252286
$324$	−41.8340	−	39.3327i	−0.129117	−	0.121397i
$325$	450.282	−	392.955i	1.38548	−	1.20909i
$326$	138.375	+	54.8351i	0.424462	+	0.168206i
$327$	329.033			1.00622
$328$	−29.9696	−	63.8398i	−0.0913706	−	0.194634i
$329$	137.009			0.416440
$330$	−40.3595	+	38.8903i	−0.122301	+	0.117849i
$331$			91.5907i			0.276709i	0.990383	+	0.138355i	$0.0441813\pi$
$331$			91.5907i			0.276709i	−0.990383	+	0.138355i	$0.955819\pi$
$332$	−156.513	−	147.155i	−0.471424	−	0.443237i
$333$		−	46.6942i		−	0.140223i
$334$	−244.614	−	96.9358i	−0.732378	−	0.290227i
$335$	−416.136	−	189.158i	−1.24220	−	0.564652i
$336$	23.0501	+	373.628i	0.0686014	+	1.11199i
$337$			407.188i			1.20827i	0.796881	+	0.604136i	$0.206482\pi$
$337$			407.188i			1.20827i	−0.796881	+	0.604136i	$0.793518\pi$
$338$	748.320	+	296.544i	2.21396	+	0.877350i
$339$		−	205.950i		−	0.607521i
$340$	345.880	−	142.000i	1.01729	−	0.417648i
$341$	17.5348			0.0514217
$342$	15.4860	−	39.0784i	0.0452807	−	0.114264i
$343$	−377.789			−1.10143
$344$	−109.417	−	233.074i	−0.318071	−	0.677541i
$345$	−310.269	−	141.036i	−0.899330	−	0.408799i
$346$	−154.881	+	390.837i	−0.447633	+	1.12959i
$347$	496.653			1.43128			0.715639	−	0.698471i	$-0.246136\pi$
$347$	496.653			1.43128			0.715639	+	0.698471i	$0.246136\pi$
$348$	85.3719	+	80.2674i	0.245322	+	0.230654i
$349$	349.147			1.00042			0.500210	−	0.865904i	$-0.333256\pi$
$349$	349.147			1.00042			0.500210	+	0.865904i	$0.333256\pi$
$350$	190.972	+	539.487i	0.545634	+	1.54139i
$351$		−	675.393i		−	1.92420i
$352$	−83.4067	−	27.2409i	−0.236951	−	0.0773888i
$353$			23.3474i			0.0661399i	0.999453	+	0.0330699i	$0.0105284\pi$
$353$			23.3474i			0.0661399i	−0.999453	+	0.0330699i	$0.989472\pi$
$354$	77.3547	−	195.202i	0.218516	−	0.551418i
$355$	−193.993	+	426.772i	−0.546459	+	1.20217i
$356$	48.6084	+	45.7020i	0.136540	+	0.128376i
$357$			437.384i			1.22517i
$358$	110.351	−	278.467i	0.308242	−	0.777840i
$359$		−	443.056i		−	1.23414i	−0.786909	−	0.617069i	$-0.788320\pi$
$359$		−	443.056i		−	1.23414i	0.786909	−	0.617069i	$-0.211680\pi$
$360$	−2.36663	−	192.855i	−0.00657397	−	0.535708i
$361$	−19.0000			−0.0526316
$362$	−297.699	−	117.972i	−0.822372	−	0.325890i
$363$	−231.966			−0.639024
$364$	−749.700	+	797.376i	−2.05961	+	2.19059i
$365$	−160.765	+	353.673i	−0.440453	+	0.968967i
$366$	157.799	+	62.5326i	0.431144	+	0.170854i
$367$	−655.820			−1.78698			−0.893488	−	0.449087i	$-0.851749\pi$
$367$	−655.820			−1.78698			−0.893488	+	0.449087i	$0.851749\pi$
$368$	−32.8537	−	532.539i	−0.0892763	−	1.44712i
$369$	−42.5063			−0.115193
$370$	−69.7344	+	67.1959i	−0.188471	+	0.181611i
$371$		−	1163.67i		−	3.13659i
$372$	35.8165	−	38.0943i	0.0962810	−	0.102404i
$373$			226.395i			0.606958i	0.952838	+	0.303479i	$0.0981483\pi$
$373$			226.395i			0.606958i	−0.952838	+	0.303479i	$0.901852\pi$
$374$	−95.3092	−	37.7691i	−0.254837	−	0.100987i
$375$	73.2789	+	244.776i	0.195410	+	0.652737i
$376$	40.6942	+	86.6849i	0.108229	+	0.230545i
$377$			342.604i			0.908764i
$378$	601.262	+	238.268i	1.59064	+	0.630339i
$379$			256.082i			0.675679i	0.941204	+	0.337839i	$0.109696\pi$
$379$			256.082i			0.675679i	−0.941204	+	0.337839i	$0.890304\pi$
$380$	−80.6461	+	33.1091i	−0.212226	+	0.0871292i
$381$	−296.479			−0.778161
$382$	−23.5075	+	59.3204i	−0.0615380	+	0.155289i
$383$	407.580			1.06418			0.532089	−	0.846688i	$-0.321407\pi$
$383$	407.580			1.06418			0.532089	+	0.846688i	$0.321407\pi$
$384$	−229.547	+	125.558i	−0.597778	+	0.326975i
$385$	64.9354	−	142.853i	0.168663	−	0.371048i
$386$	−169.749	+	428.357i	−0.439765	+	1.10973i
$387$	−155.187			−0.401001
$388$	−259.427	+	275.925i	−0.668627	+	0.711148i
$389$	−9.07468			−0.0233282			−0.0116641	−	0.999932i	$-0.503713\pi$
$389$	−9.07468			−0.0233282			−0.0116641	+	0.999932i	$0.503713\pi$
$390$	−351.869	+	339.061i	−0.902229	+	0.869386i
$391$		−	623.411i		−	1.59440i
$392$	−278.792	−	593.870i	−0.711204	−	1.51498i
$393$		−	71.0453i		−	0.180777i
$394$	105.208	−	265.488i	0.267025	−	0.673828i
$395$	−123.685	+	272.098i	−0.313126	+	0.688856i
$396$	−36.2250	+	38.5287i	−0.0914773	+	0.0972946i
$397$		−	496.049i		−	1.24949i	−0.780827	−	0.624747i	$-0.785202\pi$
$397$		−	496.049i		−	1.24949i	0.780827	−	0.624747i	$-0.214798\pi$
$398$	−60.7106	+	153.201i	−0.152539	+	0.384927i
$399$		−	101.982i		−	0.255593i
$400$	−284.609	+	281.065i	−0.711523	+	0.702663i
$401$	107.217			0.267373			0.133687	−	0.991024i	$-0.457318\pi$
$401$	107.217			0.267373			0.133687	+	0.991024i	$0.457318\pi$
$402$	347.460	+	137.692i	0.864329	+	0.342516i
$403$	152.875			0.379343
$404$	−361.869	−	340.232i	−0.895715	−	0.842159i
$405$	65.3420	+	29.7018i	0.161338	+	0.0733379i
$406$	−305.000	−	120.865i	−0.751232	−	0.297698i
$407$	26.5533			0.0652416
$408$	−276.731	+	129.911i	−0.678263	+	0.318410i
$409$	716.625			1.75214			0.876070	−	0.482184i	$-0.160156\pi$
$409$	716.625			1.75214			0.876070	+	0.482184i	$0.160156\pi$
$410$	61.1693	+	63.4801i	0.149193	+	0.154829i
$411$			43.1685i			0.105033i
$412$	−284.905	−	267.871i	−0.691518	−	0.650171i
$413$			587.865i			1.42340i
$414$	−298.962	−	118.473i	−0.722131	−	0.286166i
$415$	244.463	+	111.123i	0.589067	+	0.267766i
$416$	−727.171	−	237.496i	−1.74801	−	0.570905i
$417$			170.592i			0.409094i
$418$	22.2225	+	8.80634i	0.0531639	+	0.0210678i
$419$			322.453i			0.769577i	0.923005	+	0.384789i	$0.125726\pi$
$419$			322.453i			0.769577i	−0.923005	+	0.384789i	$0.874274\pi$
$420$	−177.711	−	432.864i	−0.423122	−	1.03063i
$421$	−701.943			−1.66732			−0.833662	−	0.552275i	$-0.813760\pi$
$421$	−701.943			−1.66732			−0.833662	+	0.552275i	$0.813760\pi$
$422$	144.733	−	365.228i	0.342968	−	0.865469i
$423$	57.7172			0.136447
$424$	736.252	−	345.633i	1.73644	−	0.815172i
$425$	−352.133	+	307.302i	−0.828549	+	0.723064i
$426$	141.211	−	356.341i	0.331481	−	0.836481i
$427$	−475.222			−1.11293
$428$	−297.739	−	279.937i	−0.695653	−	0.654059i
$429$	133.984			0.312317
$430$	223.324	+	231.761i	0.519359	+	0.538979i
$431$		−	459.176i		−	1.06537i	−0.846313	−	0.532686i	$-0.821183\pi$
$431$		−	459.176i		−	1.06537i	0.846313	−	0.532686i	$-0.178817\pi$
$432$	27.8348	+	451.186i	0.0644324	+	1.04441i
$433$			493.392i			1.13947i	0.821827	+	0.569737i	$0.192955\pi$
$433$			493.392i			1.13947i	−0.821827	+	0.569737i	$0.807045\pi$
$434$	−53.9320	+	136.096i	−0.124267	+	0.313585i
$435$	−133.346	−	60.6135i	−0.306542	−	0.139341i
$436$	−469.096	−	441.048i	−1.07591	−	1.01158i
$437$			145.356i			0.332623i
$438$	117.024	−	295.306i	0.267177	−	0.674214i
$439$			22.4502i			0.0511394i	0.999673	+	0.0255697i	$0.00813998\pi$
$439$			22.4502i			0.0511394i	−0.999673	+	0.0255697i	$0.991860\pi$
$440$	109.670	−	1.34582i	0.249250	−	0.00305868i
$441$	−395.415			−0.896633
$442$	−830.942	−	329.286i	−1.87996	−	0.744990i
$443$	393.229			0.887649			0.443825	−	0.896114i	$-0.353621\pi$
$443$	393.229			0.887649			0.443825	+	0.896114i	$0.353621\pi$
$444$	54.2377	−	57.6869i	0.122157	−	0.129925i
$445$	−75.9232	−	34.5116i	−0.170614	−	0.0775542i
$446$	−223.603	−	88.6095i	−0.501353	−	0.198676i
$447$	−46.0137			−0.102939
$448$	467.964	−	563.572i	1.04456	−	1.25797i
$449$	−580.271			−1.29236			−0.646182	−	0.763184i	$-0.723635\pi$
$449$	−580.271			−1.29236			−0.646182	+	0.763184i	$0.723635\pi$
$450$	80.4500	+	227.268i	0.178778	+	0.505040i
$451$		−	24.1718i		−	0.0535961i
$452$	−276.063	+	293.619i	−0.610759	+	0.649599i
$453$		−	406.932i		−	0.898305i
$454$	−67.4193	−	26.7169i	−0.148501	−	0.0588479i
$455$	566.131	−	1245.45i	1.24424	−	2.73726i
$456$	64.5233	−	30.2904i	0.141498	−	0.0664264i
$457$			687.158i			1.50363i	0.659375	+	0.751814i	$0.270821\pi$
$457$			687.158i			1.50363i	−0.659375	+	0.751814i	$0.729179\pi$
$458$	−505.132	−	200.174i	−1.10291	−	0.437060i
$459$			528.176i			1.15071i
$460$	253.295	+	616.968i	0.550641	+	1.34123i
$461$	370.328			0.803314			0.401657	−	0.915790i	$-0.368434\pi$
$461$	370.328			0.803314			0.401657	+	0.915790i	$0.368434\pi$
$462$	−47.2675	+	119.278i	−0.102311	+	0.258178i
$463$	−592.806			−1.28036			−0.640179	−	0.768225i	$-0.721140\pi$
$463$	−592.806			−1.28036			−0.640179	+	0.768225i	$0.721140\pi$
$464$	−14.1197	−	228.872i	−0.0304303	−	0.493258i
$465$	−27.0467	+	59.5008i	−0.0581649	+	0.127959i
$466$	−294.999	+	744.420i	−0.633045	+	1.59747i
$467$	−175.365			−0.375513			−0.187757	−	0.982216i	$-0.560122\pi$
$467$	−175.365			−0.375513			−0.187757	+	0.982216i	$0.560122\pi$
$468$	−315.823	+	335.908i	−0.674836	+	0.717751i
$469$	−1046.40			−2.23113
$470$	−83.0587	−	86.1965i	−0.176721	−	0.183397i
$471$		−	163.101i		−	0.346287i
$472$	−371.940	+	174.607i	−0.788008	+	0.369930i
$473$		−	88.2495i		−	0.186574i
$474$	90.0322	−	227.193i	0.189941	−	0.479311i
$475$	82.1042	−	71.6512i	0.172851	−	0.150845i
$476$	586.287	−	623.571i	1.23169	−	1.31002i
$477$		−	490.217i		−	1.02771i
$478$	64.7741	−	163.455i	0.135511	−	0.341957i
$479$			644.273i			1.34504i	0.740080	+	0.672519i	$0.234787\pi$
$479$			644.273i			1.34504i	−0.740080	+	0.672519i	$0.765213\pi$
$480$	221.087	−	241.006i	0.460599	−	0.502096i
$481$	231.502			0.481293
$482$	472.535	+	187.256i	0.980362	+	0.388498i
$483$	−780.191			−1.61530
$484$	330.709	+	310.936i	0.683283	+	0.642429i
$485$	195.905	−	430.978i	0.403928	−	0.888615i
$486$	418.222	+	165.733i	0.860538	+	0.341014i
$487$	839.297			1.72340			0.861702	−	0.507415i	$-0.169399\pi$
$487$	839.297			1.72340			0.861702	+	0.507415i	$0.169399\pi$
$488$	−141.150	−	300.671i	−0.289242	−	0.616130i
$489$	152.124			0.311092
$490$	569.028	+	590.524i	1.16128	+	1.20515i
$491$		−	292.665i		−	0.596060i	−0.954557	−	0.298030i	$-0.903671\pi$
$491$		−	292.665i		−	0.596060i	0.954557	−	0.298030i	$-0.0963295\pi$
$492$	−52.5131	−	49.3733i	−0.106734	−	0.100352i
$493$		−	267.926i		−	0.543461i
$494$	193.744	+	76.7770i	0.392195	+	0.155419i
$495$	27.3551	−	60.1794i	0.0552628	−	0.121574i
$496$	−102.126	+	6.30041i	−0.205899	+	0.0127024i
$497$			1073.14i			2.15925i
$498$	−204.119	−	80.8882i	−0.409877	−	0.162426i
$499$		−	949.957i		−	1.90372i	−0.306531	−	0.951861i	$-0.599168\pi$
$499$		−	949.957i		−	1.90372i	0.306531	−	0.951861i	$-0.400832\pi$
$500$	223.635	−	447.199i	0.447271	−	0.894399i
$501$	−268.920			−0.536767
$502$	317.513	−	801.235i	0.632497	−	1.59609i
$503$	369.688			0.734967			0.367484	−	0.930030i	$-0.380219\pi$
$503$	369.688			0.734967			0.367484	+	0.930030i	$0.380219\pi$
$504$	−187.621	−	399.662i	−0.372264	−	0.792979i
$505$	565.216	+	256.924i	1.11924	+	0.508761i
$506$	67.3713	−	170.009i	0.133145	−	0.335987i
$507$	822.676			1.62263
$508$	422.685	+	397.412i	0.832058	+	0.782308i
$509$	260.958			0.512688			0.256344	−	0.966586i	$-0.417482\pi$
$509$	260.958			0.512688			0.256344	+	0.966586i	$0.417482\pi$
$510$	275.172	−	265.155i	0.539553	−	0.519912i
$511$			889.333i			1.74038i
$512$	495.564	+	128.687i	0.967898	+	0.251342i
$513$		−	123.151i		−	0.240060i
$514$	128.530	−	324.342i	0.250059	−	0.631015i
$515$	445.004	+	202.281i	0.864086	+	0.392778i
$516$	−191.721	−	180.258i	−0.371553	−	0.349337i
$517$			32.8217i			0.0634850i
$518$	−81.6703	+	206.092i	−0.157665	+	0.397862i
$519$			429.672i			0.827885i
$520$	956.144	−	11.7334i	1.83874	−	0.0225642i
$521$	505.966			0.971145			0.485572	−	0.874196i	$-0.338611\pi$
$521$	505.966			0.971145			0.485572	+	0.874196i	$0.338611\pi$
$522$	−128.486	−	50.9166i	−0.246142	−	0.0975413i
$523$	573.948			1.09741			0.548707	−	0.836015i	$-0.315120\pi$
$523$	573.948			1.09741			0.548707	+	0.836015i	$0.315120\pi$
$524$	−95.2318	+	101.288i	−0.181740	+	0.193298i
$525$	384.584	+	440.690i	0.732542	+	0.839410i
$526$	339.977	+	134.726i	0.646344	+	0.256133i
$527$	−119.553			−0.226855
$528$	−89.5061	+	5.52186i	−0.169519	+	0.0104581i
$529$	583.020			1.10212
$530$	−732.103	+	705.453i	−1.38133	+	1.33104i
$531$			247.648i			0.466380i
$532$	−136.700	+	145.393i	−0.256955	+	0.273295i
$533$		−	210.739i		−	0.395383i
$534$	63.3935	+	25.1216i	0.118714	+	0.0470441i
$535$	465.050	+	211.393i	0.869253	+	0.395127i
$536$	−310.801	−	662.053i	−0.579852	−	1.23517i
$537$		−	306.136i		−	0.570086i
$538$	−351.760	−	139.396i	−0.653829	−	0.259099i
$539$		−	224.859i		−	0.417177i
$540$	−214.601	−	522.717i	−0.397409	−	0.967995i
$541$	20.2184			0.0373723			0.0186861	−	0.999825i	$-0.494052\pi$
$541$	20.2184			0.0373723			0.0186861	+	0.999825i	$0.494052\pi$
$542$	136.963	−	345.620i	0.252698	−	0.637676i
$543$	−327.279			−0.602724
$544$	568.669	+	185.729i	1.04535	+	0.341414i
$545$	732.699	+	333.055i	1.34440	+	0.611110i
$546$	−412.097	+	1039.91i	−0.754756	+	1.90460i
$547$	−602.082			−1.10070			−0.550349	−	0.834935i	$-0.685505\pi$
$547$	−602.082			−1.10070			−0.550349	+	0.834935i	$0.685505\pi$
$548$	57.8648	−	61.5446i	0.105593	−	0.112308i
$549$	−200.195			−0.364654
$550$	−129.239	+	45.7491i	−0.234980	+	0.0831802i
$551$			62.4703i			0.113376i
$552$	−231.731	−	493.624i	−0.419803	−	0.894246i
$553$			684.209i			1.23727i
$554$	−207.386	+	523.331i	−0.374342	+	0.944641i
$555$	−40.9573	+	90.1033i	−0.0737969	+	0.162348i
$556$	228.668	−	243.210i	0.411274	−	0.437429i
$557$			881.797i			1.58312i	0.611093	+	0.791559i	$0.290730\pi$
$557$			881.797i			1.58312i	−0.611093	+	0.791559i	$0.709270\pi$
$558$	−22.7197	+	57.3325i	−0.0407164	+	0.102746i
$559$		−	769.393i		−	1.37637i
$560$	−326.867	+	855.337i	−0.583691	+	1.52739i
$561$	−104.779			−0.186773
$562$	529.474	+	209.820i	0.942125	+	0.373346i
$563$	−237.455			−0.421767			−0.210884	−	0.977511i	$-0.567634\pi$
$563$	−237.455			−0.421767			−0.210884	+	0.977511i	$0.567634\pi$
$564$	71.3050	+	67.0416i	0.126427	+	0.118868i
$565$	208.467	−	458.614i	0.368969	−	0.811706i
$566$	−930.815	−	368.863i	−1.64455	−	0.651702i
$567$	164.307			0.289783
$568$	−678.974	+	318.744i	−1.19538	+	0.561169i
$569$	−783.361			−1.37673			−0.688366	−	0.725363i	$-0.741672\pi$
$569$	−783.361			−1.37673			−0.688366	+	0.725363i	$0.741672\pi$
$570$	−64.1597	+	61.8242i	−0.112561	+	0.108463i
$571$		−	731.368i		−	1.28086i	−0.768018	−	0.640428i	$-0.778757\pi$
$571$		−	731.368i		−	1.28086i	0.768018	−	0.640428i	$-0.221243\pi$
$572$	−191.019	−	179.598i	−0.333949	−	0.313982i
$573$			65.2148i			0.113813i
$574$	187.609	+	74.3455i	0.326844	+	0.129522i
$575$	−548.155	−	628.123i	−0.953313	−	1.09239i
$576$	197.137	−	237.414i	0.342252	−	0.412177i
$577$			561.878i			0.973793i	0.873460	+	0.486896i	$0.161871\pi$
$577$			561.878i			0.973793i	−0.873460	+	0.486896i	$0.838129\pi$
$578$	112.474	+	44.5713i	0.194592	+	0.0771130i
$579$			470.921i			0.813334i
$580$	108.860	+	265.157i	0.187689	+	0.457167i
$581$	614.718			1.05803
$582$	−142.603	+	359.853i	−0.245022	+	0.618304i
$583$	278.769			0.478163
$584$	−562.678	+	264.149i	−0.963489	+	0.452309i
$585$	238.492	−	524.667i	0.407679	−	0.896866i
$586$	376.452	−	949.964i	0.642409	−	1.62110i
$587$	478.025			0.814352			0.407176	−	0.913350i	$-0.366514\pi$
$587$	478.025			0.814352			0.407176	+	0.913350i	$0.366514\pi$
$588$	−488.504	−	459.295i	−0.830789	−	0.781115i
$589$	27.8752			0.0473263
$590$	369.844	−	356.381i	0.626854	−	0.604035i
$591$		−	291.868i		−	0.493855i
$592$	−154.651	+	9.54084i	−0.261236	+	0.0161163i
$593$		−	29.6903i		−	0.0500679i	−0.999687	−	0.0250340i	$-0.992031\pi$
$593$		−	29.6903i		−	0.0500679i	0.999687	−	0.0250340i	$-0.00796939\pi$
$594$	−57.0793	+	144.038i	−0.0960932	+	0.242488i
$595$	−442.731	+	973.978i	−0.744086	+	1.63694i
$596$	65.6009	+	61.6785i	0.110069	+	0.103487i
$597$			168.424i			0.282117i
$598$	587.368	−	1482.21i	0.982221	−	2.47860i
$599$		−	1048.76i		−	1.75085i	−0.483352	−	0.875426i	$-0.660581\pi$
$599$		−	1048.76i		−	1.75085i	0.483352	−	0.875426i	$-0.339419\pi$
$600$	−164.594	+	374.218i	−0.274323	+	0.623697i
$601$	178.402			0.296842			0.148421	−	0.988924i	$-0.452581\pi$
$601$	178.402			0.296842			0.148421	+	0.988924i	$0.452581\pi$
$602$	684.944	+	271.430i	1.13778	+	0.450880i
$603$	−440.813			−0.731034
$604$	−545.468	+	580.156i	−0.903092	+	0.960523i
$605$	−516.547	−	234.801i	−0.853797	−	0.388101i
$606$	−471.938	−	187.020i	−0.778775	−	0.308613i
$607$	81.1634			0.133712			0.0668562	−	0.997763i	$-0.478703\pi$
$607$	81.1634			0.133712			0.0668562	+	0.997763i	$0.478703\pi$
$608$	−132.592	−	43.3050i	−0.218079	−	0.0712253i
$609$	−335.306			−0.550585
$610$	288.094	+	298.977i	0.472285	+	0.490126i
$611$			286.152i			0.468335i
$612$	246.983	−	262.689i	0.403567	−	0.429231i
$613$		−	80.4976i		−	0.131317i	−0.997842	−	0.0656587i	$-0.979085\pi$
$613$		−	80.4976i		−	0.131317i	0.997842	−	0.0656587i	$-0.0209149\pi$
$614$	−210.514	−	83.4224i	−0.342856	−	0.135867i
$615$	82.0222	+	37.2840i	0.133369	+	0.0606243i
$616$	227.273	−	106.693i	0.368950	−	0.173204i
$617$			372.812i			0.604234i	0.953271	+	0.302117i	$0.0976933\pi$
$617$			372.812i			0.604234i	−0.953271	+	0.302117i	$0.902307\pi$
$618$	−371.565	−	147.244i	−0.601237	−	0.238258i
$619$			805.616i			1.30148i	0.759301	+	0.650740i	$0.225541\pi$
$619$			805.616i			1.30148i	−0.759301	+	0.650740i	$0.774459\pi$
$620$	118.317	−	48.5749i	0.190834	−	0.0783466i
$621$	−942.143			−1.51714
$622$	448.504	−	1131.79i	0.721068	−	1.81959i
$623$	−190.914			−0.306443
$624$	−780.349	+	48.1417i	−1.25056	+	0.0771502i
$625$	−84.5894	+	619.249i	−0.135343	+	0.990799i
$626$	−262.539	+	662.509i	−0.419392	+	1.05832i
$627$	24.4306			0.0389643
$628$	−218.627	+	232.530i	−0.348132	+	0.370271i
$629$	−181.041			−0.287824
$630$	382.943	+	397.410i	0.607846	+	0.630809i
$631$			451.728i			0.715892i	0.933742	+	0.357946i	$0.116523\pi$
$631$			451.728i			0.715892i	−0.933742	+	0.357946i	$0.883477\pi$
$632$	−432.896	+	203.223i	−0.684962	+	0.321555i
$633$		−	401.519i		−	0.634311i
$634$	−47.3856	+	119.576i	−0.0747407	+	0.188606i
$635$	−660.208	−	300.104i	−1.03970	−	0.472604i
$636$	569.412	−	605.623i	0.895302	−	0.952238i
$637$		−	1960.40i		−	3.07756i
$638$	28.9544	−	73.0656i	0.0453831	−	0.114523i
$639$			452.080i			0.707480i
$640$	−638.254	+	47.2436i	−0.997272	+	0.0738182i
$641$	−783.962			−1.22303			−0.611515	−	0.791233i	$-0.709440\pi$
$641$	−783.962			−1.22303			−0.611515	+	0.791233i	$0.709440\pi$
$642$	−388.302	−	153.876i	−0.604832	−	0.239683i
$643$	353.224			0.549338			0.274669	−	0.961539i	$-0.411432\pi$
$643$	353.224			0.549338			0.274669	+	0.961539i	$0.411432\pi$
$644$	1112.30	+	1045.80i	1.72718	+	1.62391i
$645$	299.457	+	136.121i	0.464274	+	0.211040i
$646$	−151.514	−	60.0418i	−0.234541	−	0.0929440i
$647$	619.032			0.956772			0.478386	−	0.878150i	$-0.341222\pi$
$647$	619.032			0.956772			0.478386	+	0.878150i	$0.341222\pi$
$648$	48.8022	+	103.956i	0.0753121	+	0.160426i
$649$	−140.828			−0.216993
$650$	−1126.76	+	398.858i	−1.73347	+	0.613628i
$651$			149.619i			0.229829i
$652$	−216.881	−	203.913i	−0.332639	−	0.312750i
$653$			1030.56i			1.57819i	0.614273	+	0.789093i	$0.289449\pi$
$653$			1030.56i			1.57819i	−0.614273	+	0.789093i	$0.710551\pi$
$654$	−611.780	−	242.436i	−0.935444	−	0.370698i
$655$	71.9138	−	158.205i	0.109792	−	0.241535i
$656$	8.68515	+	140.781i	0.0132396	+	0.214606i
$657$			374.646i			0.570238i
$658$	−254.744	−	100.950i	−0.387150	−	0.153420i
$659$			524.462i			0.795845i	0.917419	+	0.397922i	$0.130269\pi$
$659$			524.462i			0.795845i	−0.917419	+	0.397922i	$0.869731\pi$
$660$	103.697	−	42.5724i	0.157116	−	0.0645036i
$661$	1272.23			1.92470			0.962352	−	0.271806i	$-0.0876208\pi$
$661$	1272.23			1.92470			0.962352	+	0.271806i	$0.0876208\pi$
$662$	67.4854	−	170.297i	0.101942	−	0.257247i
$663$	−913.508			−1.37784
$664$	182.583	+	388.930i	0.274974	+	0.585737i
$665$	103.228	−	227.095i	0.155230	−	0.341496i
$666$	−34.4050	+	86.8198i	−0.0516591	+	0.130360i
$667$	477.918			0.716518
$668$	383.395	+	360.471i	0.573944	+	0.539627i
$669$	−245.821			−0.367446
$670$	634.359	+	658.323i	0.946804	+	0.982571i
$671$		−	113.844i		−	0.169663i
$672$	232.437	−	711.681i	0.345889	−	1.05905i
$673$		−	234.326i		−	0.348181i	−0.984730	−	0.174090i	$-0.944301\pi$
$673$		−	234.326i		−	0.348181i	0.984730	−	0.174090i	$-0.0556985\pi$
$674$	300.022	−	757.096i	0.445136	−	1.12329i
$675$	464.416	+	532.168i	0.688024	+	0.788398i
$676$	−1172.87	−	1102.75i	−1.73502	−	1.63128i
$677$			389.637i			0.575535i	0.957700	+	0.287767i	$0.0929130\pi$
$677$			389.637i			0.575535i	−0.957700	+	0.287767i	$0.907087\pi$
$678$	−151.747	+	382.928i	−0.223815	+	0.564791i
$679$		−	1083.72i		−	1.59606i
$680$	−747.732	+	9.17582i	−1.09961	+	0.0134939i
$681$	−74.1184			−0.108838
$682$	−32.6030	−	12.9199i	−0.0478050	−	0.0189442i
$683$	−391.558			−0.573292			−0.286646	−	0.958037i	$-0.592540\pi$
$683$	−391.558			−0.573292			−0.286646	+	0.958037i	$0.592540\pi$
$684$	−57.5871	+	61.2493i	−0.0841917	+	0.0895457i
$685$	−43.6962	+	96.1288i	−0.0637901	+	0.140334i
$686$	702.435	+	278.361i	1.02396	+	0.405774i
$687$	−555.324			−0.808331
$688$	31.7088	+	513.981i	0.0460884	+	0.747066i
$689$	2430.41			3.52745
$690$	472.975	+	490.842i	0.685470	+	0.711365i
$691$			1154.29i			1.67047i	0.549895	+	0.835233i	$0.314668\pi$
$691$			1154.29i			1.67047i	−0.549895	+	0.835233i	$0.685332\pi$
$692$	575.949	−	612.576i	0.832297	−	0.885226i
$693$		−	151.325i		−	0.218362i
$694$	−923.442	−	365.942i	−1.33061	−	0.527293i
$695$	−172.678	+	379.879i	−0.248457	+	0.546589i
$696$	−99.5922	−	212.147i	−0.143092	−	0.304809i
$697$			164.804i			0.236448i
$698$	−649.179	−	257.257i	−0.930056	−	0.368563i
$699$			818.389i			1.17080i
$700$	42.4229	−	1143.80i	0.0606041	−	1.63399i
$701$	−350.121			−0.499459			−0.249730	−	0.968316i	$-0.580342\pi$
$701$	−350.121			−0.499459			−0.249730	+	0.968316i	$0.580342\pi$
$702$	−497.639	+	1255.78i	−0.708888	+	1.78886i
$703$	42.2120			0.0600455
$704$	135.009	+	112.105i	0.191774	+	0.159240i
$705$	−111.374	−	50.6260i	−0.157977	−	0.0718100i
$706$	17.2027	−	43.4104i	0.0243664	−	0.0614879i
$707$	1421.27			2.01029
$708$	−287.656	+	305.949i	−0.406293	+	0.432131i
$709$	199.134			0.280866			0.140433	−	0.990090i	$-0.455151\pi$
$709$	199.134			0.280866			0.140433	+	0.990090i	$0.455151\pi$
$710$	675.148	−	650.572i	0.950913	−	0.916298i
$711$			288.234i			0.405393i
$712$	−56.7050	−	120.790i	−0.0796419	−	0.169649i
$713$		−	213.254i		−	0.299094i
$714$	322.271	−	813.241i	0.451360	−	1.13899i
$715$	298.359	+	135.622i	0.417286	+	0.189681i
$716$	−410.357	+	436.453i	−0.573124	+	0.609571i
$717$		−	179.697i		−	0.250623i
$718$	−326.450	+	823.786i	−0.454666	+	1.14733i
$719$			59.8196i			0.0831983i	0.999134	+	0.0415991i	$0.0132452\pi$
$719$			59.8196i			0.0831983i	−0.999134	+	0.0415991i	$0.986755\pi$
$720$	−137.698	+	360.325i	−0.191247	+	0.500451i
$721$	1118.99			1.55200
$722$	35.3272	+	13.9995i	0.0489297	+	0.0193899i
$723$	519.488			0.718517
$724$	466.596	+	438.698i	0.644470	+	0.605936i
$725$	−235.583	−	269.951i	−0.324942	−	0.372347i
$726$	431.300	+	170.916i	0.594078	+	0.235421i
$727$	−924.398			−1.27152			−0.635762	−	0.771885i	$-0.719314\pi$
$727$	−924.398			−1.27152			−0.635762	+	0.771885i	$0.719314\pi$
$728$	1981.46	−	930.194i	2.72178	−	1.27774i
$729$	588.974			0.807921
$730$	559.507	−	539.140i	0.766448	−	0.738548i
$731$			601.687i			0.823102i
$732$	−247.325	−	232.537i	−0.337876	−	0.317674i
$733$		−	509.601i		−	0.695226i	−0.937638	−	0.347613i	$-0.886992\pi$
$733$		−	509.601i		−	0.695226i	0.937638	−	0.347613i	$-0.113008\pi$
$734$	1219.39	+	483.218i	1.66129	+	0.658335i
$735$	763.012	+	346.834i	1.03811	+	0.471883i
$736$	−331.297	+	1014.37i	−0.450132	+	1.37822i
$737$		−	250.675i		−	0.340129i
$738$	79.0332	+	31.3193i	0.107091	+	0.0424380i
$739$			918.755i			1.24324i	0.783319	+	0.621621i	$0.213525\pi$
$739$			918.755i			1.24324i	−0.783319	+	0.621621i	$0.786475\pi$
$740$	179.170	−	73.5579i	0.242122	−	0.0994026i
$741$	212.995			0.287443
$742$	−857.412	+	2163.65i	−1.15554	+	2.91597i
$743$	−505.977			−0.680992			−0.340496	−	0.940246i	$-0.610595\pi$
$743$	−505.977			−0.680992			−0.340496	+	0.940246i	$0.610595\pi$
$744$	−94.6632	+	44.4396i	−0.127235	+	0.0597306i
$745$	−102.465	−	46.5762i	−0.137536	−	0.0625184i
$746$	166.812	−	420.944i	0.223608	−	0.564267i
$747$	258.960			0.346667
$748$	149.382	+	140.450i	0.199709	+	0.187768i
$749$	1169.40			1.56128
$750$	44.1054	−	509.113i	0.0588072	−	0.678817i
$751$			25.3490i			0.0337537i	0.999858	+	0.0168768i	$0.00537232\pi$
$751$			25.3490i			0.0337537i	−0.999858	+	0.0168768i	$0.994628\pi$
$752$	−11.7931	−	191.160i	−0.0156824	−	0.254202i
$753$		−	880.849i		−	1.16979i
$754$	252.436	−	637.014i	0.334796	−	0.844846i
$755$	411.907	−	906.167i	0.545572	−	1.20022i
$756$	−942.384	−	886.037i	−1.24654	−	1.17201i
$757$		−	1209.37i		−	1.59759i	−0.601606	−	0.798793i	$-0.705472\pi$
$757$		−	1209.37i		−	1.59759i	0.601606	−	0.798793i	$-0.294528\pi$
$758$	188.685	−	476.141i	0.248925	−	0.628154i
$759$		−	186.902i		−	0.246248i
$760$	174.343	−	2.13946i	0.229398	−	0.00281507i
$761$	−725.650			−0.953548			−0.476774	−	0.879026i	$-0.658194\pi$
$761$	−725.650			−0.953548			−0.476774	+	0.879026i	$0.658194\pi$
$762$	551.253	+	218.451i	0.723429	+	0.286680i
$763$	1842.42			2.41470
$764$	87.4164	−	92.9755i	0.114419	−	0.121696i
$765$	−186.508	+	410.304i	−0.243801	+	0.536346i
$766$	−757.826	−	300.311i	−0.989329	−	0.392051i
$767$	−1227.80			−1.60078
$768$	519.316	−	64.3207i	0.676193	−	0.0837509i
$769$	−1011.56			−1.31542			−0.657709	−	0.753272i	$-0.728474\pi$
$769$	−1011.56			−1.31542			−0.657709	+	0.753272i	$0.728474\pi$
$770$	−225.993	+	217.766i	−0.293497	+	0.282813i
$771$		−	356.569i		−	0.462477i
$772$	631.240	−	671.383i	0.817668	−	0.869667i
$773$		−	493.834i		−	0.638854i	−0.947611	−	0.319427i	$-0.896510\pi$
$773$		−	493.834i		−	0.638854i	0.947611	−	0.319427i	$-0.103490\pi$
$774$	288.544	+	114.344i	0.372796	+	0.147732i
$775$	−120.456	+	105.121i	−0.155428	+	0.135640i
$776$	685.667	−	321.886i	0.883591	−	0.414802i
$777$			226.571i			0.291597i
$778$	16.8728	+	6.68636i	0.0216874	+	0.00859429i
$779$		−	38.4261i		−	0.0493275i
$780$	904.066	−	371.163i	1.15906	−	0.475849i
$781$	−257.082			−0.329170
$782$	−459.339	+	1159.13i	−0.587390	+	1.48226i
$783$	−404.909			−0.517125
$784$	80.7937	+	1309.62i	0.103053	+	1.67043i
$785$	165.095	−	363.198i	0.210312	−	0.462672i
$786$	−52.3472	+	132.097i	−0.0665995	+	0.168062i
$787$	−741.489			−0.942171			−0.471085	−	0.882088i	$-0.656138\pi$
$787$	−741.489			−0.942171			−0.471085	+	0.882088i	$0.656138\pi$
$788$	−391.232	+	416.111i	−0.496487	+	0.528060i
$789$	373.759			0.473712
$790$	430.457	−	414.787i	0.544882	−	0.525047i
$791$		−	1153.22i		−	1.45792i
$792$	95.7427	−	44.9464i	0.120887	−	0.0567504i
$793$		−	992.535i		−	1.25162i
$794$	−365.496	+	922.318i	−0.460323	+	1.16161i
$795$	−429.988	+	945.946i	−0.540866	+	1.18987i
$796$	225.762	−	240.119i	0.283620	−	0.301657i
$797$			298.886i			0.375013i	0.982263	+	0.187507i	$0.0600406\pi$
$797$			298.886i			0.375013i	−0.982263	+	0.187507i	$0.939959\pi$
$798$	−75.1415	+	189.617i	−0.0941623	+	0.237615i
$799$		−	223.779i		−	0.280074i
$800$	736.275	−	312.888i	0.920344	−	0.391110i
$801$	−80.4256			−0.100406
$802$	−199.351	−	78.9988i	−0.248567	−	0.0985023i
$803$	−213.048			−0.265315
$804$	−544.590	−	512.028i	−0.677350	−	0.636851i
$805$	−1737.35	−	789.728i	−2.15820	−	0.981029i
$806$	−284.245	−	112.641i	−0.352662	−	0.139753i
$807$	−386.712			−0.479198
$808$	422.145	+	899.234i	0.522457	+	1.11291i
$809$	300.965			0.372021			0.186010	−	0.982548i	$-0.440444\pi$
$809$	300.965			0.372021			0.186010	+	0.982548i	$0.440444\pi$
$810$	−99.6076	−	103.370i	−0.122972	−	0.127618i
$811$		−	204.774i		−	0.252495i	−0.991999	−	0.126248i	$-0.959707\pi$
$811$		−	204.774i		−	0.252495i	0.991999	−	0.126248i	$-0.0402934\pi$
$812$	478.040	+	449.457i	0.588719	+	0.553519i
$813$		−	379.963i		−	0.467359i
$814$	−49.3714	−	19.5649i	−0.0606528	−	0.0240355i
$815$	338.754	+	153.984i	0.415649	+	0.188937i
$816$	610.255	−	37.6482i	0.747862	−	0.0461375i
$817$		−	140.291i		−	0.171715i
$818$	−1332.44	−	528.020i	−1.62890	−	0.645501i
$819$		−	1319.31i		−	1.61088i
$820$	−66.9607	−	163.101i	−0.0816594	−	0.198903i
$821$	−1147.53			−1.39772			−0.698860	−	0.715258i	$-0.746309\pi$
$821$	−1147.53			−1.39772			−0.698860	+	0.715258i	$0.746309\pi$
$822$	31.8072	−	80.2645i	0.0386949	−	0.0976454i
$823$	−1448.47			−1.75999			−0.879996	−	0.474980i	$-0.842455\pi$
$823$	−1448.47			−1.75999			−0.879996	+	0.474980i	$0.842455\pi$
$824$	332.362	+	707.982i	0.403352	+	0.859202i
$825$	−105.571	+	92.1308i	−0.127965	+	0.111674i
$826$	433.148	−	1093.03i	0.524392	−	1.32329i
$827$	1583.37			1.91460			0.957300	−	0.289097i	$-0.0933551\pi$
$827$	1583.37			1.91460			0.957300	+	0.289097i	$0.0933551\pi$
$828$	468.576	+	440.560i	0.565913	+	0.532077i
$829$	−349.395			−0.421466			−0.210733	−	0.977544i	$-0.567585\pi$
$829$	−349.395			−0.421466			−0.210733	+	0.977544i	$0.567585\pi$
$830$	−372.660	−	386.738i	−0.448988	−	0.465949i
$831$			575.331i			0.692336i
$832$	1177.06	+	977.375i	1.41474	+	1.17473i
$833$			1533.09i			1.84045i
$834$	125.695	−	317.187i	0.150713	−	0.380320i
$835$	−598.839	−	272.208i	−0.717172	−	0.325997i
$836$	−34.8303	−	32.7477i	−0.0416630	−	0.0391719i
$837$			180.677i			0.215862i
$838$	237.588	−	599.546i	0.283518	−	0.715449i
$839$		−	21.6515i		−	0.0258064i	−0.999917	−	0.0129032i	$-0.995893\pi$
$839$		−	21.6515i		−	0.0258064i	0.999917	−	0.0129032i	$-0.00410732\pi$
$840$	11.4834	+	935.776i	0.0136707	+	1.11402i
$841$	−635.603			−0.755771
$842$	1305.14	+	517.202i	1.55005	+	0.614255i
$843$	582.085			0.690493
$844$	−538.211	+	572.438i	−0.637691	+	0.678244i
$845$	1831.96	+	832.733i	2.16800	+	0.985482i
$846$	−107.315	−	42.5269i	−0.126850	−	0.0502682i
$847$	−1298.89			−1.53352
$848$	−1623.60	+	100.164i	−1.91462	+	0.118118i
$849$	−1023.30			−1.20531
$850$	881.156	−	311.918i	1.03665	−	0.366963i
$851$		−	322.935i		−	0.379477i
$852$	−525.114	+	558.508i	−0.616331	+	0.655526i
$853$			1105.08i			1.29552i	0.761844	+	0.647760i	$0.224294\pi$
$853$			1105.08i			1.29552i	−0.761844	+	0.647760i	$0.775706\pi$
$854$	883.594	+	350.151i	1.03465	+	0.410013i
$855$	43.4866	−	95.6675i	0.0508615	−	0.111892i
$856$	347.333	+	739.874i	0.405763	+	0.864339i
$857$			705.460i			0.823174i	0.911370	+	0.411587i	$0.135025\pi$
$857$			705.460i			0.823174i	−0.911370	+	0.411587i	$0.864975\pi$
$858$	−249.121	−	98.7216i	−0.290350	−	0.115060i
$859$		−	908.583i		−	1.05772i	−0.848708	−	0.528861i	$-0.822619\pi$
$859$		−	908.583i		−	1.05772i	0.848708	−	0.528861i	$-0.177381\pi$
$860$	−244.468	−	595.468i	−0.284266	−	0.692405i
$861$	206.250			0.239547
$862$	−338.328	+	853.759i	−0.392491	+	0.990439i
$863$	934.917			1.08333			0.541667	−	0.840593i	$-0.317794\pi$
$863$	934.917			1.08333			0.541667	+	0.840593i	$0.317794\pi$
$864$	280.687	−	859.412i	0.324869	−	0.994690i
$865$	−434.925	+	956.805i	−0.502803	+	1.10613i
$866$	363.539	−	917.378i	0.419791	−	1.05933i
$867$	123.650			0.142618
$868$	200.555	−	213.309i	0.231054	−	0.245747i
$869$	−163.909			−0.188617
$870$	203.272	+	210.951i	0.233646	+	0.242473i
$871$		−	2185.48i		−	2.50916i
$872$	547.233	+	1165.69i	0.627561	+	1.33680i
$873$		−	456.536i		−	0.522951i
$874$	107.101	−	270.265i	0.122541	−	0.309227i
$875$	410.325	+	1370.63i	0.468943	+	1.56643i
$876$	−435.171	+	462.845i	−0.496771	+	0.528362i
$877$		−	362.510i		−	0.413352i	−0.978409	−	0.206676i	$-0.933735\pi$
$877$		−	362.510i		−	0.413352i	0.978409	−	0.206676i	$-0.0662646\pi$
$878$	16.5416	−	41.7423i	0.0188401	−	0.0475425i
$879$		−	1044.36i		−	1.18812i
$880$	−204.904	−	78.3041i	−0.232845	−	0.0889819i
$881$	−1085.75			−1.23241			−0.616205	−	0.787586i	$-0.711331\pi$
$881$	−1085.75			−1.23241			−0.616205	+	0.787586i	$0.711331\pi$
$882$	735.207	+	291.348i	0.833568	+	0.330326i
$883$	−1275.77			−1.44481			−0.722405	−	0.691470i	$-0.756963\pi$
$883$	−1275.77			−1.44481			−0.722405	+	0.691470i	$0.756963\pi$
$884$	1302.37	+	1224.50i	1.47327	+	1.38518i
$885$	217.222	−	477.873i	0.245448	−	0.539969i
$886$	−731.141	−	289.737i	−0.825216	−	0.327017i
$887$	−67.8817			−0.0765296			−0.0382648	−	0.999268i	$-0.512183\pi$
$887$	−67.8817			−0.0765296			−0.0382648	+	0.999268i	$0.512183\pi$
$888$	−143.350	+	67.2957i	−0.161431	+	0.0757835i
$889$	−1660.14			−1.86742
$890$	115.738	+	120.110i	0.130042	+	0.134955i
$891$			39.3612i			0.0441765i
$892$	350.463	+	329.509i	0.392896	+	0.369404i
$893$			52.1769i			0.0584288i
$894$	85.5546	+	33.9036i	0.0956987	+	0.0379235i
$895$	309.879	−	681.712i	0.346233	−	0.761690i
$896$	−1285.35	+	703.064i	−1.43454	+	0.784669i
$897$		−	1629.48i		−	1.81659i
$898$	1078.91	+	427.552i	1.20146	+	0.476116i
$899$		−	91.6512i		−	0.101948i
$900$	17.8713	−	481.843i	0.0198570	−	0.535381i
$901$	−1900.65			−2.10949
$902$	−17.8102	+	44.9434i	−0.0197452	+	0.0498264i
$903$	753.003			0.833891
$904$	729.635	−	342.527i	0.807118	−	0.378901i
$905$	−728.794	−	331.280i	−0.805297	−	0.366055i
$906$	−299.834	+	756.621i	−0.330942	+	0.835122i
$907$	−755.868			−0.833372			−0.416686	−	0.909050i	$-0.636809\pi$
$907$	−755.868			−0.833372			−0.416686	+	0.909050i	$0.636809\pi$
$908$	105.669	+	99.3512i	0.116376	+	0.109418i
$909$	598.735			0.658674
$910$	−1970.29	+	1898.57i	−2.16516	+	2.08634i
$911$		−	721.241i		−	0.791702i	−0.918315	−	0.395851i	$-0.870450\pi$
$911$		−	721.241i		−	0.791702i	0.918315	−	0.395851i	$-0.129550\pi$
$912$	−142.288	+	8.77814i	−0.156018	+	0.00962515i
$913$			147.261i			0.161294i
$914$	506.308	−	1277.65i	0.553948	−	1.39787i
$915$	386.306	+	175.599i	0.422193	+	0.191912i
$916$	791.715	+	744.377i	0.864318	+	0.812639i
$917$		−	397.818i		−	0.433825i
$918$	389.168	−	982.054i	0.423931	−	1.06978i
$919$		−	224.888i		−	0.244710i	−0.992486	−	0.122355i	$-0.960955\pi$
$919$		−	224.888i		−	0.244710i	0.992486	−	0.122355i	$-0.0390446\pi$
$920$	−16.3675	−	1333.78i	−0.0177908	−	1.44976i
$921$	−231.431			−0.251283
$922$	−688.561	−	272.863i	−0.746812	−	0.295947i
$923$	−2241.34			−2.42832
$924$	175.772	−	186.950i	0.190229	−	0.202327i
$925$	−182.410	+	159.186i	−0.197200	+	0.172093i
$926$	1102.22	+	436.788i	1.19030	+	0.471694i
$927$	471.394			0.508516
$928$	−142.383	+	435.951i	−0.153430	+	0.469775i
$929$	742.525			0.799273			0.399637	−	0.916674i	$-0.369136\pi$
$929$	742.525			0.799273			0.399637	+	0.916674i	$0.369136\pi$
$930$	94.1297	−	90.7032i	0.101215	−	0.0975304i
$931$		−	357.459i		−	0.383952i
$932$	1097.00	−	1166.76i	1.17704	−	1.25189i
$933$		−	1244.24i		−	1.33360i
$934$	326.060	+	129.211i	0.349101	+	0.138342i
$935$	−233.326	−	106.060i	−0.249546	−	0.113434i
$936$	834.721	−	391.859i	0.891796	−	0.418653i
$937$			258.624i			0.276012i	0.990431	+	0.138006i	$0.0440694\pi$
$937$			258.624i			0.276012i	−0.990431	+	0.138006i	$0.955931\pi$
$938$	1945.60	+	771.004i	2.07420	+	0.821966i
$939$			728.339i			0.775654i
$940$	90.9227	+	221.467i	0.0967262	+	0.235603i
$941$	410.419			0.436152			0.218076	−	0.975932i	$-0.430022\pi$
$941$	410.419			0.436152			0.218076	+	0.975932i	$0.430022\pi$
$942$	−120.175	+	303.258i	−0.127575	+	0.321930i
$943$	−293.972			−0.311741
$944$	820.211	−	50.6009i	0.868868	−	0.0536027i
$945$	1471.94	+	669.086i	1.55761	+	0.708027i
$946$	−65.0236	+	164.085i	−0.0687353	+	0.173451i
$947$	814.171			0.859737			0.429868	−	0.902892i	$-0.358560\pi$
$947$	814.171			0.859737			0.429868	+	0.902892i	$0.358560\pi$
$948$	−334.799	+	356.090i	−0.353164	+	0.375622i
$949$	−1857.43			−1.95725
$950$	−205.452	+	72.7276i	−0.216266	+	0.0765554i
$951$			131.458i			0.138231i
$952$	−1549.56	+	727.438i	−1.62768	+	0.764116i
$953$		−	1074.25i		−	1.12723i	−0.826039	−	0.563614i	$-0.809411\pi$
$953$		−	1074.25i		−	1.12723i	0.826039	−	0.563614i	$-0.190589\pi$
$954$	−361.199	+	911.474i	−0.378615	+	0.955423i
$955$	−66.0120	+	145.222i	−0.0691225	+	0.152065i
$956$	−240.873	+	256.191i	−0.251959	+	0.267982i
$957$		−	80.3257i		−	0.0839349i
$958$	474.710	−	1197.91i	0.495522	−	1.25043i
$959$			241.722i			0.252056i
$960$	−588.651	+	285.209i	−0.613178	+	0.297092i
$961$	920.104			0.957444
$962$	−430.438	−	170.574i	−0.447441	−	0.177312i
$963$	492.628			0.511556
$964$	−740.624	−	696.341i	−0.768282	−	0.722346i
$965$	−476.677	+	1048.66i	−0.493966	+	1.08669i
$966$	1450.63	+	574.856i	1.50169	+	0.595089i
$967$	−428.625			−0.443252			−0.221626	−	0.975132i	$-0.571136\pi$
$967$	−428.625			−0.443252			−0.221626	+	0.975132i	$0.571136\pi$
$968$	−385.795	−	821.803i	−0.398549	−	0.848970i
$969$	−166.569			−0.171897
$970$	−681.803	+	656.984i	−0.702890	+	0.677303i
$971$			208.313i			0.214534i	0.994230	+	0.107267i	$0.0342100\pi$
$971$			208.313i			0.214534i	−0.994230	+	0.107267i	$0.965790\pi$
$972$	−655.497	−	616.304i	−0.674380	−	0.634057i
$973$			955.231i			0.981738i
$974$	−1560.53	−	618.407i	−1.60219	−	0.634915i
$975$	−920.412	+	803.231i	−0.944012	+	0.823827i
$976$	40.9051	+	663.048i	0.0419110	+	0.679353i
$977$		−	1379.97i		−	1.41246i	−0.707982	−	0.706231i	$-0.750394\pi$
$977$		−	1379.97i		−	1.41246i	0.707982	−	0.706231i	$-0.249606\pi$
$978$	−282.849	−	112.087i	−0.289211	−	0.114609i
$979$		−	45.7352i		−	0.0467162i
$980$	−622.903	−	1517.25i	−0.635615	−	1.54821i
$981$	776.149			0.791181
$982$	−215.640	+	544.161i	−0.219593	+	0.554135i
$983$	−33.6274			−0.0342090			−0.0171045	−	0.999854i	$-0.505445\pi$
$983$	−33.6274			−0.0342090			−0.0171045	+	0.999854i	$0.505445\pi$
$984$	61.2602	+	130.494i	0.0622563	+	0.132615i
$985$	295.436	−	649.940i	0.299935	−	0.659837i
$986$	−197.412	+	498.163i	−0.200215	+	0.505236i
$987$	−280.057			−0.283746
$988$	−303.664	−	285.507i	−0.307352	−	0.288975i
$989$	−1073.27			−1.08521
$990$	−95.2032	+	91.7376i	−0.0961648	+	0.0926642i
$991$			816.440i			0.823855i	0.911217	+	0.411928i	$0.135144\pi$
$991$			816.440i			0.823855i	−0.911217	+	0.411928i	$0.864856\pi$
$992$	194.528	+	63.5334i	0.196097	+	0.0640458i
$993$		−	187.219i		−	0.188538i
$994$	790.709	−	1995.33i	0.795482	−	2.00737i
$995$	−170.483	+	375.050i	−0.171339	+	0.376935i
$996$	319.924	+	300.796i	0.321209	+	0.302004i
$997$		−	1785.20i		−	1.79058i	−0.445488	−	0.895288i	$-0.646970\pi$
$997$		−	1785.20i		−	1.79058i	0.445488	−	0.895288i	$-0.353030\pi$
$998$	−699.943	+	1766.28i	−0.701345	+	1.76982i
$999$			273.602i			0.273876i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.3.h.a.39.13	✓	108
4.3	odd	2	inner	380.3.h.a.39.95	yes	108
5.4	even	2	inner	380.3.h.a.39.96	yes	108
20.19	odd	2	inner	380.3.h.a.39.14	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.3.h.a.39.13	✓	108	1.1	even	1	trivial
380.3.h.a.39.14	yes	108	20.19	odd	2	inner
380.3.h.a.39.95	yes	108	4.3	odd	2	inner
380.3.h.a.39.96	yes	108	5.4	even	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.85933 - 0.736815i) q^{2} -2.04408 q^{3} +(2.91421 + 2.73996i) q^{4} +(-4.55181 - 2.06907i) q^{5} +(3.80062 + 1.50611i) q^{6} -11.4458 q^{7} +(-3.39962 - 7.24172i) q^{8} -4.82174 q^{9} +O(q^{10})\)	\(q+(-1.85933 - 0.736815i) q^{2} -2.04408 q^{3} +(2.91421 + 2.73996i) q^{4} +(-4.55181 - 2.06907i) q^{5} +(3.80062 + 1.50611i) q^{6} -11.4458 q^{7} +(-3.39962 - 7.24172i) q^{8} -4.82174 q^{9} +(6.93879 + 7.20092i) q^{10} -2.74195i q^{11} +(-5.95687 - 5.60070i) q^{12} -23.9054i q^{13} +(21.2815 + 8.43345i) q^{14} +(9.30426 + 4.22934i) q^{15} +(0.985208 + 15.9696i) q^{16} +18.6947i q^{17} +(8.96520 + 3.55273i) q^{18} -4.35890i q^{19} +(-7.59575 - 18.5015i) q^{20} +23.3962 q^{21} +(-2.02031 + 5.09819i) q^{22} -33.3470 q^{23} +(6.94910 + 14.8027i) q^{24} +(16.4379 + 18.8360i) q^{25} +(-17.6139 + 44.4480i) q^{26} +28.2527 q^{27} +(-33.3555 - 31.3611i) q^{28} -14.3317 q^{29} +(-14.1834 - 14.7192i) q^{30} +6.39501i q^{31} +(9.93485 - 30.4187i) q^{32} +5.60477i q^{33} +(13.7745 - 34.7596i) q^{34} +(52.0992 + 23.6822i) q^{35} +(-14.0515 - 13.2114i) q^{36} +9.68409i q^{37} +(-3.21170 + 8.10463i) q^{38} +48.8645i q^{39} +(0.490825 + 39.9970i) q^{40} +8.81555 q^{41} +(-43.5012 - 17.2386i) q^{42} +32.1849 q^{43} +(7.51285 - 7.99062i) q^{44} +(21.9476 + 9.97650i) q^{45} +(62.0030 + 24.5705i) q^{46} -11.9702 q^{47} +(-2.01384 - 32.6432i) q^{48} +82.0068 q^{49} +(-16.6849 - 47.1340i) q^{50} -38.2135i q^{51} +(65.4999 - 69.6653i) q^{52} +101.668i q^{53} +(-52.5311 - 20.8170i) q^{54} +(-5.67328 + 12.4808i) q^{55} +(38.9115 + 82.8875i) q^{56} +8.90994i q^{57} +(26.6473 + 10.5598i) q^{58} -51.3607i q^{59} +(15.5263 + 37.8185i) q^{60} +41.5193 q^{61} +(4.71194 - 11.8904i) q^{62} +55.1887 q^{63} +(-40.8851 + 49.2383i) q^{64} +(-49.4619 + 108.813i) q^{65} +(4.12968 - 10.4211i) q^{66} +91.4221 q^{67} +(-51.2228 + 54.4802i) q^{68} +68.1638 q^{69} +(-79.4201 - 82.4204i) q^{70} -93.7587i q^{71} +(16.3921 + 34.9177i) q^{72} -77.6994i q^{73} +(7.13539 - 18.0059i) q^{74} +(-33.6004 - 38.5023i) q^{75} +(11.9432 - 12.7027i) q^{76} +31.3839i q^{77} +(36.0041 - 90.8552i) q^{78} -59.7780i q^{79} +(28.5578 - 74.7292i) q^{80} -14.3552 q^{81} +(-16.3910 - 6.49543i) q^{82} -53.7068 q^{83} +(68.1813 + 64.1046i) q^{84} +(38.6806 - 85.0947i) q^{85} +(-59.8423 - 23.7143i) q^{86} +29.2951 q^{87} +(-19.8565 + 9.32161i) q^{88} +16.6798 q^{89} +(-33.4570 - 34.7209i) q^{90} +273.617i q^{91} +(-97.1800 - 91.3694i) q^{92} -13.0719i q^{93} +(22.2566 + 8.81983i) q^{94} +(-9.01885 + 19.8409i) q^{95} +(-20.3076 + 62.1783i) q^{96} +94.6828i q^{97} +(-152.478 - 60.4238i) q^{98} +13.2210i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 4 q^{5} + 324 q^{9}+O(q^{10}) \) 108 * q + 4 * q^5 + 324 * q^9	\( 108 q + 4 q^{5} + 324 q^{9} - 8 q^{10} + 8 q^{14} - 104 q^{16} - 16 q^{21} - 8 q^{24} - 76 q^{25} + 80 q^{26} - 88 q^{29} - 140 q^{30} - 88 q^{34} - 256 q^{36} + 44 q^{40} - 200 q^{41} - 8 q^{44} + 108 q^{45} + 272 q^{46} + 916 q^{49} - 276 q^{50} - 320 q^{54} - 328 q^{56} + 172 q^{60} + 200 q^{61} - 216 q^{64} - 192 q^{65} + 152 q^{66} - 592 q^{69} + 200 q^{70} - 232 q^{74} + 340 q^{80} + 1052 q^{81} + 208 q^{84} + 248 q^{85} - 1048 q^{86} + 760 q^{89} + 268 q^{90} - 320 q^{94} + 720 q^{96}+O(q^{100}) \) 108 * q + 4 * q^5 + 324 * q^9 - 8 * q^10 + 8 * q^14 - 104 * q^16 - 16 * q^21 - 8 * q^24 - 76 * q^25 + 80 * q^26 - 88 * q^29 - 140 * q^30 - 88 * q^34 - 256 * q^36 + 44 * q^40 - 200 * q^41 - 8 * q^44 + 108 * q^45 + 272 * q^46 + 916 * q^49 - 276 * q^50 - 320 * q^54 - 328 * q^56 + 172 * q^60 + 200 * q^61 - 216 * q^64 - 192 * q^65 + 152 * q^66 - 592 * q^69 + 200 * q^70 - 232 * q^74 + 340 * q^80 + 1052 * q^81 + 208 * q^84 + 248 * q^85 - 1048 * q^86 + 760 * q^89 + 268 * q^90 - 320 * q^94 + 720 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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