LMFDB - Embedded newform 576.2.bd.b.37.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(37,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 9, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("576.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bd (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 192)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			37.12
Character	$\chi$	$=$	576.37
Dual form			576.2.bd.b.109.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.899186 + 1.09154i) q^{2} +(-0.382930 + 1.96300i) q^{4} +(-0.713613 + 3.58757i) q^{5} +(-0.499893 + 1.20685i) q^{7} +(-2.48702 + 1.34712i) q^{8} +(-4.55766 + 2.44696i) q^{10} +(-0.165075 + 0.110300i) q^{11} +(-0.763008 - 3.83590i) q^{13} +(-1.76682 + 0.539527i) q^{14} +(-3.70673 - 1.50338i) q^{16} +(3.40067 - 3.40067i) q^{17} +(1.60520 - 0.319294i) q^{19} +(-6.76914 - 2.77461i) q^{20} +(-0.268830 - 0.0810065i) q^{22} +(-5.45175 + 2.25819i) q^{23} +(-7.74204 - 3.20686i) q^{25} +(3.50096 - 4.28204i) q^{26} +(-2.17762 - 1.44343i) q^{28} +(4.85792 + 3.24596i) q^{29} +7.27965i q^{31} +(-1.69203 - 5.39787i) q^{32} +(6.76981 + 0.654141i) q^{34} +(-3.97293 - 2.65462i) q^{35} +(10.9804 + 2.18414i) q^{37} +(1.79190 + 1.46504i) q^{38} +(-3.05811 - 9.88369i) q^{40} +(-4.05331 + 1.67894i) q^{41} +(4.87955 + 7.30276i) q^{43} +(-0.153306 - 0.366279i) q^{44} +(-7.36704 - 3.92028i) q^{46} +(-7.45854 + 7.45854i) q^{47} +(3.74316 + 3.74316i) q^{49} +(-3.46111 - 11.3343i) q^{50} +(7.82205 - 0.0289041i) q^{52} +(-6.21917 + 4.15552i) q^{53} +(-0.277908 - 0.670930i) q^{55} +(-0.382521 - 3.67487i) q^{56} +(0.825071 + 8.22134i) q^{58} +(1.52940 - 7.68882i) q^{59} +(-0.775973 + 1.16133i) q^{61} +(-7.94605 + 6.54576i) q^{62} +(4.37055 - 6.70062i) q^{64} +14.3061 q^{65} +(-2.61387 + 3.91193i) q^{67} +(5.37330 + 7.97773i) q^{68} +(-0.674764 - 6.72362i) q^{70} +(3.70757 - 8.95087i) q^{71} +(-0.717326 - 1.73178i) q^{73} +(7.48937 + 13.9496i) q^{74} +(0.0120954 + 3.27328i) q^{76} +(-0.0505950 - 0.254358i) q^{77} +(-7.84113 - 7.84113i) q^{79} +(8.03866 - 12.2253i) q^{80} +(-5.47731 - 2.91469i) q^{82} +(8.03366 - 1.59800i) q^{83} +(9.77339 + 14.6269i) q^{85} +(-3.58365 + 11.8928i) q^{86} +(0.261959 - 0.496693i) q^{88} +(9.80970 + 4.06331i) q^{89} +(5.01077 + 0.996705i) q^{91} +(-2.34518 - 11.5665i) q^{92} +(-14.8479 - 1.43470i) q^{94} +5.98663i q^{95} -6.53575i q^{97} +(-0.720021 + 7.45161i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 16 q^{22} + 80 q^{26} - 80 q^{28} + 80 q^{32} - 80 q^{34} + 80 q^{38} - 80 q^{40} + 16 q^{44} - 48 q^{50} + 48 q^{52} - 64 q^{55} - 112 q^{56} + 128 q^{59} - 96 q^{62} + 96 q^{64} - 32 q^{67} - 96 q^{68}+ \cdots - 96 q^{94}+O(q^{100}) $ 128 * q - 16 * q^22 + 80 * q^26 - 80 * q^28 + 80 * q^32 - 80 * q^34 + 80 * q^38 - 80 * q^40 + 16 * q^44 - 48 * q^50 + 48 * q^52 - 64 * q^55 - 112 * q^56 + 128 * q^59 - 96 * q^62 + 96 * q^64 - 32 * q^67 - 96 * q^68 + 96 * q^70 + 128 * q^71 - 112 * q^74 + 16 * q^76 - 32 * q^79 - 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{16}\right)$

Coefficient data

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

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

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

$2$	0.899186	+	1.09154i	0.635820	+	0.771837i
$2$	0.899186	+	1.09154i	0.635820	+	0.771837i
$3$		0			0
$3$		0			0
$4$	−0.382930	+	1.96300i	−0.191465	+	0.981499i
$5$	−0.713613	+	3.58757i	−0.319137	+	1.60441i	0.404706	+	0.914447i	$0.367374\pi$
$5$	−0.713613	+	3.58757i	−0.319137	+	1.60441i	−0.723843	+	0.689965i	$0.757626\pi$
$6$		0			0
$7$	−0.499893	+	1.20685i	−0.188942	+	0.456146i	−0.989756	−	0.142767i	$-0.954400\pi$
$7$	−0.499893	+	1.20685i	−0.188942	+	0.456146i	0.800815	+	0.598912i	$0.204400\pi$
$8$	−2.48702	+	1.34712i	−0.879295	+	0.476278i
$9$		0			0
$10$	−4.55766	+	2.44696i	−1.44126	+	0.773796i
$11$	−0.165075	+	0.110300i	−0.0497720	+	0.0332566i	−0.580207	−	0.814469i	$-0.697028\pi$
$11$	−0.165075	+	0.110300i	−0.0497720	+	0.0332566i	0.530435	+	0.847725i	$0.322028\pi$
$12$		0			0
$13$	−0.763008	−	3.83590i	−0.211620	−	1.06389i	−0.929810	−	0.368040i	$-0.880029\pi$
$13$	−0.763008	−	3.83590i	−0.211620	−	1.06389i	0.718190	−	0.695848i	$-0.244971\pi$
$14$	−1.76682	+	0.539527i	−0.472203	+	0.144195i
$15$		0			0
$16$	−3.70673	−	1.50338i	−0.926682	−	0.375845i
$17$	3.40067	−	3.40067i	0.824784	−	0.824784i	−0.162006	−	0.986790i	$-0.551796\pi$
$17$	3.40067	−	3.40067i	0.824784	−	0.824784i	0.986790	+	0.162006i	$0.0517964\pi$
$18$		0			0
$19$	1.60520	−	0.319294i	0.368258	−	0.0732512i	−0.00749226	−	0.999972i	$-0.502385\pi$
$19$	1.60520	−	0.319294i	0.368258	−	0.0732512i	0.375751	+	0.926721i	$0.377385\pi$
$20$	−6.76914	−	2.77461i	−1.51363	−	0.620421i
$21$		0			0
$22$	−0.268830	−	0.0810065i	−0.0573147	−	0.0172706i
$23$	−5.45175	+	2.25819i	−1.13677	+	0.470865i	−0.870076	−	0.492917i	$-0.835930\pi$
$23$	−5.45175	+	2.25819i	−1.13677	+	0.470865i	−0.266691	+	0.963782i	$0.585930\pi$
$24$		0			0
$25$	−7.74204	−	3.20686i	−1.54841	−	0.641372i
$26$	3.50096	−	4.28204i	0.686595	−	0.839778i
$27$		0			0
$28$	−2.17762	−	1.44343i	−0.411531	−	0.272782i
$29$	4.85792	+	3.24596i	0.902092	+	0.602759i	0.917767	−	0.397118i	$-0.129990\pi$
$29$	4.85792	+	3.24596i	0.902092	+	0.602759i	−0.0156751	+	0.999877i	$0.504990\pi$
$30$		0			0
$31$			7.27965i			1.30746i	0.756726	+	0.653732i	$0.226798\pi$
$31$			7.27965i			1.30746i	−0.756726	+	0.653732i	$0.773202\pi$
$32$	−1.69203	−	5.39787i	−0.299112	−	0.954218i
$33$		0			0
$34$	6.76981	+	0.654141i	1.16101	+	0.112184i
$35$	−3.97293	−	2.65462i	−0.671547	−	0.448714i
$36$		0			0
$37$	10.9804	+	2.18414i	1.80517	+	0.359071i	0.978922	−	0.204233i	$-0.0654699\pi$
$37$	10.9804	+	2.18414i	1.80517	+	0.359071i	0.826250	+	0.563304i	$0.190470\pi$
$38$	1.79190	+	1.46504i	0.290684	+	0.237661i
$39$		0			0
$40$	−3.05811	−	9.88369i	−0.483530	−	1.56275i
$41$	−4.05331	+	1.67894i	−0.633021	+	0.262206i	−0.676036	−	0.736868i	$-0.736304\pi$
$41$	−4.05331	+	1.67894i	−0.633021	+	0.262206i	0.0430149	+	0.999074i	$0.486304\pi$
$42$		0			0
$43$	4.87955	+	7.30276i	0.744124	+	1.11366i	0.989542	+	0.144244i	$0.0460749\pi$
$43$	4.87955	+	7.30276i	0.744124	+	1.11366i	−0.245418	+	0.969417i	$0.578925\pi$
$44$	−0.153306	−	0.366279i	−0.0231117	−	0.0552186i
$45$		0			0
$46$	−7.36704	−	3.92028i	−1.08621	−	0.578014i
$47$	−7.45854	+	7.45854i	−1.08794	+	1.08794i	−0.0921995	+	0.995741i	$0.529390\pi$
$47$	−7.45854	+	7.45854i	−1.08794	+	1.08794i	−0.995741	+	0.0921995i	$0.970610\pi$
$48$		0			0
$49$	3.74316	+	3.74316i	0.534737	+	0.534737i
$50$	−3.46111	−	11.3343i	−0.489475	−	1.60292i
$51$		0			0
$52$	7.82205	−	0.0289041i	1.08472	−	0.00400827i
$53$	−6.21917	+	4.15552i	−0.854269	+	0.570804i	−0.903794	−	0.427968i	$-0.859229\pi$
$53$	−6.21917	+	4.15552i	−0.854269	+	0.570804i	0.0495244	+	0.998773i	$0.484229\pi$
$54$		0			0
$55$	−0.277908	−	0.670930i	−0.0374731	−	0.0904681i
$56$	−0.382521	−	3.67487i	−0.0511166	−	0.491075i
$57$		0			0
$58$	0.825071	+	8.22134i	0.108337	+	1.07951i
$59$	1.52940	−	7.68882i	0.199111	−	1.00100i	−0.743913	−	0.668276i	$-0.767032\pi$
$59$	1.52940	−	7.68882i	0.199111	−	1.00100i	0.943024	−	0.332723i	$-0.107968\pi$
$60$		0			0
$61$	−0.775973	+	1.16133i	−0.0993531	+	0.148692i	−0.877816	−	0.478999i	$-0.841000\pi$
$61$	−0.775973	+	1.16133i	−0.0993531	+	0.148692i	0.778463	+	0.627691i	$0.216000\pi$
$62$	−7.94605	+	6.54576i	−1.00915	+	0.831312i
$63$		0			0
$64$	4.37055	−	6.70062i	0.546319	−	0.837577i
$65$	14.3061			1.77445
$66$		0			0
$67$	−2.61387	+	3.91193i	−0.319335	+	0.477919i	−0.956059	−	0.293173i	$-0.905289\pi$
$67$	−2.61387	+	3.91193i	−0.319335	+	0.477919i	0.636724	+	0.771091i	$0.280289\pi$
$68$	5.37330	+	7.97773i	0.651608	+	0.967442i
$69$		0			0
$70$	−0.674764	−	6.72362i	−0.0806497	−	0.803626i
$71$	3.70757	−	8.95087i	0.440008	−	1.06227i	−0.535938	−	0.844257i	$-0.680042\pi$
$71$	3.70757	−	8.95087i	0.440008	−	1.06227i	0.975945	−	0.218015i	$-0.0699582\pi$
$72$		0			0
$73$	−0.717326	−	1.73178i	−0.0839566	−	0.202689i	0.876326	−	0.481719i	$-0.159987\pi$
$73$	−0.717326	−	1.73178i	−0.0839566	−	0.202689i	−0.960283	+	0.279029i	$0.909987\pi$
$74$	7.48937	+	13.9496i	0.870621	+	1.62160i
$75$		0			0
$76$	0.0120954	+	3.27328i	0.00138744	+	0.375471i
$77$	−0.0505950	−	0.254358i	−0.00576584	−	0.0289868i
$78$		0			0
$79$	−7.84113	−	7.84113i	−0.882196	−	0.882196i	0.111561	−	0.993758i	$-0.464415\pi$
$79$	−7.84113	−	7.84113i	−0.882196	−	0.882196i	−0.993758	+	0.111561i	$0.964415\pi$
$80$	8.03866	−	12.2253i	0.898749	−	1.36683i
$81$		0			0
$82$	−5.47731	−	2.91469i	−0.604868	−	0.321873i
$83$	8.03366	−	1.59800i	0.881809	−	0.175403i	0.266638	−	0.963797i	$-0.414087\pi$
$83$	8.03366	−	1.59800i	0.881809	−	0.175403i	0.615171	+	0.788394i	$0.289087\pi$
$84$		0			0
$85$	9.77339	+	14.6269i	1.06007	+	1.58651i
$86$	−3.58365	+	11.8928i	−0.386435	+	1.28243i
$87$		0			0
$88$	0.261959	−	0.496693i	0.0279249	−	0.0529476i
$89$	9.80970	+	4.06331i	1.03983	+	0.430710i	0.836250	−	0.548349i	$-0.184743\pi$
$89$	9.80970	+	4.06331i	1.03983	+	0.430710i	0.203576	+	0.979059i	$0.434743\pi$
$90$		0			0
$91$	5.01077	+	0.996705i	0.525272	+	0.104483i
$92$	−2.34518	−	11.5665i	−0.244502	−	1.20589i
$93$		0			0
$94$	−14.8479	−	1.43470i	−1.53145	−	0.147978i
$95$			5.98663i			0.614215i
$96$		0			0
$97$		−	6.53575i		−	0.663605i	−0.943349	−	0.331802i	$-0.892343\pi$
$97$		−	6.53575i		−	0.663605i	0.943349	−	0.331802i	$-0.107657\pi$
$98$	−0.720021	+	7.45161i	−0.0727331	+	0.752726i
$99$		0			0
$100$	9.25972	−	13.9696i	0.925972	−	1.39696i
$101$	12.0391	+	2.39472i	1.19793	+	0.238284i	0.753452	−	0.657503i	$-0.228387\pi$
$101$	12.0391	+	2.39472i	1.19793	+	0.238284i	0.444483	+	0.895787i	$0.353387\pi$
$102$		0			0
$103$	−3.02423	−	1.25268i	−0.297986	−	0.123430i	0.228681	−	0.973501i	$-0.426559\pi$
$103$	−3.02423	−	1.25268i	−0.297986	−	0.123430i	−0.526667	+	0.850072i	$0.676559\pi$
$104$	7.06503	+	8.51211i	0.692783	+	0.834681i
$105$		0			0
$106$	−10.1281	−	3.05191i	−0.983730	−	0.296428i
$107$	−5.92917	−	8.87362i	−0.573194	−	0.857846i	0.425700	−	0.904864i	$-0.360028\pi$
$107$	−5.92917	−	8.87362i	−0.573194	−	0.857846i	−0.998894	+	0.0470188i	$0.985028\pi$
$108$		0			0
$109$	9.42819	−	1.87538i	0.903056	−	0.179629i	0.278342	−	0.960482i	$-0.410215\pi$
$109$	9.42819	−	1.87538i	0.903056	−	0.179629i	0.624715	+	0.780853i	$0.285215\pi$
$110$	0.482457	−	0.906639i	0.0460005	−	0.0864446i
$111$		0			0
$112$	3.66732	−	3.72193i	0.346529	−	0.351689i
$113$	−3.00161	−	3.00161i	−0.282368	−	0.282368i	0.551685	−	0.834053i	$-0.313985\pi$
$113$	−3.00161	−	3.00161i	−0.282368	−	0.282368i	−0.834053	+	0.551685i	$0.813985\pi$
$114$		0			0
$115$	−4.21098	−	21.1700i	−0.392676	−	1.97411i
$116$	−8.23205	+	8.29311i	−0.764326	+	0.769996i
$117$		0			0
$118$	9.76790	−	5.24427i	0.899208	−	0.482775i
$119$	2.40412	+	5.80407i	0.220386	+	0.532058i
$120$		0			0
$121$	−4.19443	+	10.1263i	−0.381312	+	0.920569i
$122$	−1.96538	+	0.197240i	−0.177937	+	0.0178573i
$123$		0			0
$124$	−14.2899	−	2.78759i	−1.28328	−	0.250333i
$125$	6.86868	−	10.2797i	0.614353	−	0.919445i
$126$		0			0
$127$	8.30918			0.737321			0.368660	−	0.929564i	$-0.379817\pi$
$127$	8.30918			0.737321			0.368660	+	0.929564i	$0.379817\pi$
$128$	11.2439	−	1.25446i	0.993834	−	0.110879i
$129$		0			0
$130$	12.8638	+	15.6157i	1.12823	+	1.36959i
$131$	0.0841669	−	0.125965i	0.00735370	−	0.0110056i	−0.827775	−	0.561061i	$-0.810393\pi$
$131$	0.0841669	−	0.125965i	0.00735370	−	0.0110056i	0.835128	+	0.550055i	$0.185393\pi$
$132$		0			0
$133$	−0.417089	+	2.09685i	−0.0361662	+	0.181820i
$134$	−6.62039	+	0.664405i	−0.571915	+	0.0573958i
$135$		0			0
$136$	−3.87644	+	13.0386i	−0.332402	+	1.11805i
$137$	−7.53903	−	18.2008i	−0.644103	−	1.55500i	−0.821096	−	0.570790i	$-0.806637\pi$
$137$	−7.53903	−	18.2008i	−0.644103	−	1.55500i	0.176993	−	0.984212i	$-0.443363\pi$
$138$		0			0
$139$	5.12863	−	3.42684i	0.435005	−	0.290661i	−0.318723	−	0.947848i	$-0.603254\pi$
$139$	5.12863	−	3.42684i	0.435005	−	0.290661i	0.753728	+	0.657187i	$0.228254\pi$
$140$	6.73238	−	6.78232i	0.568990	−	0.573210i
$141$		0			0
$142$	13.1040	−	4.00152i	1.09967	−	0.335800i
$143$	0.549052	+	0.549052i	0.0459140	+	0.0459140i
$144$		0			0
$145$	−15.1118	+	15.1118i	−1.25496	+	1.25496i
$146$	1.24530	−	2.34018i	0.103062	−	0.193675i
$147$		0			0
$148$	−8.49221	+	20.7182i	−0.698055	+	1.70303i
$149$	3.31602	+	4.96278i	0.271659	+	0.406567i	0.942066	−	0.335427i	$-0.108881\pi$
$149$	3.31602	+	4.96278i	0.271659	+	0.406567i	−0.670407	+	0.741993i	$0.733881\pi$
$150$		0			0
$151$	−15.2579	+	6.32003i	−1.24167	+	0.514317i	−0.904236	−	0.427033i	$-0.859559\pi$
$151$	−15.2579	+	6.32003i	−1.24167	+	0.514317i	−0.337434	+	0.941349i	$0.609559\pi$
$152$	−3.56204	+	2.95649i	−0.288920	+	0.239803i
$153$		0			0
$154$	0.232149	−	0.283942i	0.0187071	−	0.0228807i
$155$	−26.1163	−	5.19485i	−2.09771	−	0.417261i
$156$		0			0
$157$	2.68759	+	1.79579i	0.214493	+	0.143320i	0.658176	−	0.752864i	$-0.271328\pi$
$157$	2.68759	+	1.79579i	0.214493	+	0.143320i	−0.443683	+	0.896184i	$0.646328\pi$
$158$	1.50829	−	15.6096i	0.119993	−	1.24183i
$159$		0			0
$160$	20.5727	−	2.21831i	1.62642	−	0.175373i
$161$		−	7.70828i		−	0.607498i
$162$		0			0
$163$	−9.67619	−	6.46543i	−0.757898	−	0.506411i	0.115566	−	0.993300i	$-0.463132\pi$
$163$	−9.67619	−	6.46543i	−0.757898	−	0.506411i	−0.873464	+	0.486888i	$0.838132\pi$
$164$	−1.74362	−	8.59957i	−0.136154	−	0.671513i
$165$		0			0
$166$	8.96804	+	7.33219i	0.696055	+	0.569088i
$167$	18.0933	+	7.49447i	1.40010	+	0.579940i	0.949777	−	0.312927i	$-0.101310\pi$
$167$	18.0933	+	7.49447i	1.40010	+	0.579940i	0.450321	+	0.892867i	$0.351310\pi$
$168$		0			0
$169$	−2.12152	+	0.878764i	−0.163194	+	0.0675972i
$170$	−7.17780	+	23.8204i	−0.550512	+	1.82694i
$171$		0			0
$172$	−16.2038	+	6.78211i	−1.23553	+	0.517131i
$173$	13.6336	−	2.71189i	1.03654	−	0.206181i	0.352645	−	0.935757i	$-0.385282\pi$
$173$	13.6336	−	2.71189i	1.03654	−	0.206181i	0.683900	+	0.729576i	$0.260282\pi$
$174$		0			0
$175$	7.74038	−	7.74038i	0.585118	−	0.585118i
$176$	0.777710	−	0.160680i	0.0586221	−	0.0121117i
$177$		0			0
$178$	4.38547	+	14.3614i	0.328705	+	1.07643i
$179$	4.72336	+	23.7459i	0.353040	+	1.77485i	0.594148	+	0.804356i	$0.297489\pi$
$179$	4.72336	+	23.7459i	0.353040	+	1.77485i	−0.241107	+	0.970498i	$0.577511\pi$
$180$		0			0
$181$	17.1020	−	11.4272i	1.27118	−	0.849374i	0.277401	−	0.960754i	$-0.410527\pi$
$181$	17.1020	−	11.4272i	1.27118	−	0.849374i	0.993778	+	0.111380i	$0.0355271\pi$
$182$	3.41767	+	6.36569i	0.253335	+	0.471857i
$183$		0			0
$184$	10.5166	−	12.9603i	0.775292	−	0.955446i
$185$	−15.6716	+	37.8345i	−1.15220	+	2.78165i
$186$		0			0
$187$	−0.186273	+	0.936458i	−0.0136216	+	0.0684806i
$188$	−11.7850	−	17.4972i	−0.859510	−	1.27611i
$189$		0			0
$190$	−6.53466	+	5.38309i	−0.474074	+	0.390531i
$191$	−2.23266			−0.161550			−0.0807749	−	0.996732i	$-0.525739\pi$
$191$	−2.23266			−0.161550			−0.0807749	+	0.996732i	$0.525739\pi$
$192$		0			0
$193$	19.2570			1.38615			0.693074	−	0.720867i	$-0.256256\pi$
$193$	19.2570			1.38615			0.693074	+	0.720867i	$0.256256\pi$
$194$	7.13405	−	5.87685i	0.512195	−	0.421933i
$195$		0			0
$196$	−8.78118	+	5.91445i	−0.627227	+	0.422461i
$197$	2.96931	−	14.9277i	0.211554	−	1.06356i	−0.718329	−	0.695703i	$-0.755093\pi$
$197$	2.96931	−	14.9277i	0.211554	−	1.06356i	0.929884	−	0.367853i	$-0.119907\pi$
$198$		0			0
$199$	−7.09511	+	17.1291i	−0.502959	+	1.21425i	0.444906	+	0.895577i	$0.353237\pi$
$199$	−7.09511	+	17.1291i	−0.502959	+	1.21425i	−0.947865	+	0.318673i	$0.896763\pi$
$200$	23.5746	−	2.45391i	1.66698	−	0.173518i
$201$		0			0
$202$	8.21144	+	15.2945i	0.577755	+	1.07612i
$203$	−6.34581	+	4.24014i	−0.445389	+	0.297599i
$204$		0			0
$205$	−3.13082	−	15.7397i	−0.218666	−	1.09931i
$206$	−1.35199	−	4.42746i	−0.0941978	−	0.308476i
$207$		0			0
$208$	−2.93856	+	15.3657i	−0.203752	+	1.06542i
$209$	−0.229761	+	0.229761i	−0.0158929	+	0.0158929i
$210$		0			0
$211$	4.58044	−	0.911106i	0.315330	−	0.0627231i	−0.0348879	−	0.999391i	$-0.511107\pi$
$211$	4.58044	−	0.911106i	0.315330	−	0.0627231i	0.350218	+	0.936668i	$0.386107\pi$
$212$	−5.77577	−	13.7995i	−0.396682	−	0.947754i
$213$		0			0
$214$	4.35452	−	14.4510i	0.297669	−	0.987848i
$215$	−29.6813	+	12.2944i	−2.02425	+	0.838471i
$216$		0			0
$217$	−8.78544	−	3.63905i	−0.596394	−	0.247035i
$218$	10.5248	+	8.60495i	0.712826	+	0.582801i
$219$		0			0
$220$	1.42345	−	0.288615i	0.0959692	−	0.0194584i
$221$	−15.6394	−	10.4499i	−1.05202	−	0.702936i
$222$		0			0
$223$			10.0197i			0.670969i	0.942046	+	0.335485i	$0.108900\pi$
$223$			10.0197i			0.670969i	−0.942046	+	0.335485i	$0.891100\pi$
$224$	7.36025	+	0.656328i	0.491777	+	0.0438528i
$225$		0			0
$226$	0.577380	−	5.97540i	0.0384067	−	0.397477i
$227$	4.13349	+	2.76191i	0.274349	+	0.183314i	0.685132	−	0.728419i	$-0.259745\pi$
$227$	4.13349	+	2.76191i	0.274349	+	0.183314i	−0.410783	+	0.911733i	$0.634745\pi$
$228$		0			0
$229$	−6.49438	−	1.29181i	−0.429161	−	0.0853654i	−0.0242164	−	0.999707i	$-0.507709\pi$
$229$	−6.49438	−	1.29181i	−0.429161	−	0.0853654i	−0.404944	+	0.914341i	$0.632709\pi$
$230$	19.3215	−	23.6322i	1.27402	−	1.55826i
$231$		0			0
$232$	−16.4544	−	1.52858i	−1.08029	−	0.100356i
$233$	−10.0645	+	4.16886i	−0.659349	+	0.273111i	−0.687165	−	0.726502i	$-0.741145\pi$
$233$	−10.0645	+	4.16886i	−0.659349	+	0.273111i	0.0278157	+	0.999613i	$0.491145\pi$
$234$		0			0
$235$	−21.4356	−	32.0806i	−1.39830	−	2.09271i
$236$	14.5075	+	5.94649i	0.944358	+	0.387084i
$237$		0			0
$238$	−4.17363	+	7.84314i	−0.270536	+	0.508395i
$239$	18.9787	−	18.9787i	1.22763	−	1.22763i	0.262772	−	0.964858i	$-0.415363\pi$
$239$	18.9787	−	18.9787i	1.22763	−	1.22763i	0.964858	−	0.262772i	$-0.0846366\pi$
$240$		0			0
$241$	−7.41861	−	7.41861i	−0.477875	−	0.477875i	0.426577	−	0.904451i	$-0.359719\pi$
$241$	−7.41861	−	7.41861i	−0.477875	−	0.477875i	−0.904451	+	0.426577i	$0.859719\pi$
$242$	−14.8248	+	4.52699i	−0.952975	+	0.291006i
$243$		0			0
$244$	−1.98254	−	1.96794i	−0.126919	−	0.125984i
$245$	−16.1000	+	10.7577i	−1.02859	+	0.687283i
$246$		0			0
$247$	−2.44956	−	5.91377i	−0.155862	−	0.376284i
$248$	−9.80654	−	18.1047i	−0.622716	−	1.14965i
$249$		0			0
$250$	17.3969	−	1.74591i	1.10028	−	0.110421i
$251$	3.96207	−	19.9187i	0.250084	−	1.25725i	−0.627798	−	0.778377i	$-0.716044\pi$
$251$	3.96207	−	19.9187i	0.250084	−	1.25725i	0.877881	−	0.478878i	$-0.158956\pi$
$252$		0			0
$253$	0.650870	−	0.974095i	0.0409198	−	0.0612408i
$254$	7.47150	+	9.06983i	0.468804	+	0.569091i
$255$		0			0
$256$	11.4797	+	11.1453i	0.717481	+	0.696578i
$257$	1.37931			0.0860393			0.0430196	−	0.999074i	$-0.486302\pi$
$257$	1.37931			0.0860393			0.0430196	+	0.999074i	$0.486302\pi$
$258$		0			0
$259$	−8.12497	+	12.1599i	−0.504861	+	0.755578i
$260$	−5.47822	+	28.0828i	−0.339745	+	1.74162i
$261$		0			0
$262$	0.213178	−	0.0213939i	0.0131702	−	0.00132172i
$263$	−1.86485	+	4.50216i	−0.114992	+	0.277615i	−0.970888	−	0.239532i	$-0.923006\pi$
$263$	−1.86485	+	4.50216i	−0.114992	+	0.277615i	0.855897	+	0.517147i	$0.173006\pi$
$264$		0			0
$265$	−10.4701	−	25.2772i	−0.643176	−	1.55276i
$266$	−2.66384	+	1.43019i	−0.163330	+	0.0876903i
$267$		0			0
$268$	−6.67819	−	6.62902i	−0.407935	−	0.404932i
$269$	−0.807880	−	4.06149i	−0.0492573	−	0.247633i	0.948310	−	0.317346i	$-0.102792\pi$
$269$	−0.807880	−	4.06149i	−0.0492573	−	0.247633i	−0.997567	+	0.0697128i	$0.977792\pi$
$270$		0			0
$271$	4.86041	+	4.86041i	0.295249	+	0.295249i	0.839150	−	0.543901i	$-0.183053\pi$
$271$	4.86041	+	4.86041i	0.295249	+	0.295249i	−0.543901	+	0.839150i	$0.683053\pi$
$272$	−17.7179	+	7.49286i	−1.07430	+	0.454322i
$273$		0			0
$274$	13.0880	−	24.5951i	0.790675	−	1.48584i
$275$	1.63173	−	0.324572i	0.0983972	−	0.0195724i
$276$		0			0
$277$	−9.49029	−	14.2032i	−0.570216	−	0.853389i	0.428526	−	0.903529i	$-0.359033\pi$
$277$	−9.49029	−	14.2032i	−0.570216	−	0.853389i	−0.998742	+	0.0501407i	$0.984033\pi$
$278$	8.35214	+	2.51675i	0.500928	+	0.150945i
$279$		0			0
$280$	13.4568	+	1.25011i	0.804200	+	0.0747085i
$281$	−4.37830	−	1.81355i	−0.261187	−	0.108187i	0.248247	−	0.968697i	$-0.420145\pi$
$281$	−4.37830	−	1.81355i	−0.261187	−	0.108187i	−0.509435	+	0.860509i	$0.670145\pi$
$282$		0			0
$283$	−4.66157	−	0.927244i	−0.277102	−	0.0551189i	0.0545831	−	0.998509i	$-0.482617\pi$
$283$	−4.66157	−	0.927244i	−0.277102	−	0.0551189i	−0.331685	+	0.943390i	$0.607617\pi$
$284$	16.1508	+	10.7055i	0.958374	+	0.635255i
$285$		0			0
$286$	−0.105614	+	1.09301i	−0.00624507	+	0.0646312i
$287$		−	5.73102i		−	0.338292i
$288$		0			0
$289$		−	6.12913i		−	0.360537i
$290$	−30.0834	−	2.90685i	−1.76656	−	0.170696i
$291$		0			0
$292$	3.67416	−	0.744961i	0.215014	−	0.0435955i
$293$	6.99926	+	1.39224i	0.408901	+	0.0813355i	0.395255	−	0.918571i	$-0.370656\pi$
$293$	6.99926	+	1.39224i	0.408901	+	0.0813355i	0.0136460	+	0.999907i	$0.495656\pi$
$294$		0			0
$295$	26.4928	+	10.9737i	1.54247	+	0.638913i
$296$	−30.2509	+	9.35992i	−1.75830	+	0.544034i
$297$		0			0
$298$	−2.43536	+	8.08204i	−0.141077	+	0.468180i
$299$	12.8219	+	19.1893i	0.741510	+	1.10975i
$300$		0			0
$301$	−11.2526	+	2.23828i	−0.648588	+	0.129012i
$302$	−20.6183	−	10.9718i	−1.18645	−	0.631354i
$303$		0			0
$304$	−6.43007	−	1.22969i	−0.368790	−	0.0705276i
$305$	−3.61259	−	3.61259i	−0.206857	−	0.206857i
$306$		0			0
$307$	−3.43935	−	17.2908i	−0.196294	−	0.986838i	−0.945778	−	0.324815i	$-0.894698\pi$
$307$	−3.43935	−	17.2908i	−0.196294	−	0.986838i	0.749484	−	0.662023i	$-0.230302\pi$
$308$	0.518680	−	0.00191663i	0.0295545	−	0.000109210i
$309$		0			0
$310$	−17.8130	−	33.1782i	−1.01171	−	1.88439i
$311$	−0.364148	−	0.879131i	−0.0206489	−	0.0498509i	0.913219	−	0.407470i	$-0.133589\pi$
$311$	−0.364148	−	0.879131i	−0.0206489	−	0.0498509i	−0.933868	+	0.357619i	$0.883589\pi$
$312$		0			0
$313$	11.4921	−	27.7444i	0.649571	−	1.56820i	−0.163822	−	0.986490i	$-0.552382\pi$
$313$	11.4921	−	27.7444i	0.649571	−	1.56820i	0.813394	−	0.581714i	$-0.197618\pi$
$314$	0.456462	+	4.54837i	0.0257597	+	0.256680i
$315$		0			0
$316$	18.3947	−	12.3895i	1.03478	−	0.696966i
$317$	12.2103	−	18.2741i	0.685801	−	1.02637i	−0.311302	−	0.950311i	$-0.600765\pi$
$317$	12.2103	−	18.2741i	0.685801	−	1.02637i	0.997103	−	0.0760631i	$-0.0242351\pi$
$318$		0			0
$319$	−1.15995			−0.0649446
$320$	20.9201	+	20.4613i	1.16947	+	1.14382i
$321$		0			0
$322$	8.41392	−	6.93118i	0.468889	−	0.386259i
$323$	4.37295	−	6.54458i	0.243317	−	0.364150i
$324$		0			0
$325$	−6.39395	+	32.1446i	−0.354673	+	1.78306i
$326$	−1.64341	−	16.3756i	−0.0910201	−	0.906960i
$327$		0			0
$328$	7.81895	−	9.63584i	0.431729	−	0.532050i
$329$	−5.27286	−	12.7298i	−0.290702	−	0.701817i
$330$		0			0
$331$	−9.80351	+	6.55049i	−0.538849	+	0.360048i	−0.795019	−	0.606584i	$-0.792539\pi$
$331$	−9.80351	+	6.55049i	−0.538849	+	0.360048i	0.256170	+	0.966632i	$0.417539\pi$
$332$	0.0605348	+	16.3820i	0.00332228	+	0.899079i
$333$		0			0
$334$	8.08867	+	26.4885i	0.442592	+	1.44939i
$335$	−12.1691	−	12.1691i	−0.664866	−	0.664866i
$336$		0			0
$337$	−20.0178	+	20.0178i	−1.09044	+	1.09044i	−0.0949600	+	0.995481i	$0.530272\pi$
$337$	−20.0178	+	20.0178i	−1.09044	+	1.09044i	−0.995481	+	0.0949600i	$0.969728\pi$
$338$	−2.86685	−	1.52556i	−0.155936	−	0.0829795i
$339$		0			0
$340$	−32.4551	+	13.5841i	−1.76013	+	0.736700i
$341$	−0.802942	−	1.20169i	−0.0434818	−	0.0650751i
$342$		0			0
$343$	−14.8365	+	6.14550i	−0.801098	+	0.331826i
$344$	−21.9732	−	11.5888i	−1.18472	−	0.624826i
$345$		0			0
$346$	15.2193	+	12.4432i	0.818195	+	0.668949i
$347$	−20.6727	−	4.11207i	−1.10977	−	0.220747i	−0.394020	−	0.919102i	$-0.628916\pi$
$347$	−20.6727	−	4.11207i	−1.10977	−	0.220747i	−0.715752	+	0.698355i	$0.753916\pi$
$348$		0			0
$349$	2.15070	+	1.43705i	0.115125	+	0.0769238i	0.611800	−	0.791013i	$-0.290446\pi$
$349$	2.15070	+	1.43705i	0.115125	+	0.0769238i	−0.496675	+	0.867937i	$0.665446\pi$
$350$	15.4090	+	1.48891i	0.823646	+	0.0795858i
$351$		0			0
$352$	0.874695	+	0.704423i	0.0466214	+	0.0375459i
$353$		−	2.31496i		−	0.123213i	−0.998101	−	0.0616065i	$-0.980378\pi$
$353$		−	2.31496i		−	0.123213i	0.998101	−	0.0616065i	$-0.0196224\pi$
$354$		0			0
$355$	29.4661	+	19.6886i	1.56390	+	1.04496i
$356$	−11.7327	+	17.7005i	−0.621832	+	0.938123i
$357$		0			0
$358$	−21.6725	+	26.5078i	−1.14543	+	1.40098i
$359$	−7.38180	−	3.05764i	−0.389596	−	0.161376i	0.179282	−	0.983798i	$-0.442622\pi$
$359$	−7.38180	−	3.05764i	−0.389596	−	0.161376i	−0.568878	+	0.822422i	$0.692622\pi$
$360$		0			0
$361$	−15.0790	+	6.24592i	−0.793631	+	0.328733i
$362$	27.8511	+	8.39237i	1.46382	+	0.441093i
$363$		0			0
$364$	−3.87530	+	9.45447i	−0.203121	+	0.495549i
$365$	6.72477	−	1.33764i	0.351991	−	0.0700153i
$366$		0			0
$367$	9.81262	−	9.81262i	0.512214	−	0.512214i	−0.402990	−	0.915204i	$-0.632029\pi$
$367$	9.81262	−	9.81262i	0.512214	−	0.512214i	0.915204	+	0.402990i	$0.132029\pi$
$368$	23.6031	−	0.174439i	1.23039	−	0.00909325i
$369$		0			0
$370$	−55.3896	+	16.9141i	−2.87957	+	0.879320i
$371$	−1.90616	−	9.58291i	−0.0989629	−	0.497520i
$372$		0			0
$373$	−0.177392	+	0.118530i	−0.00918504	+	0.00613724i	−0.560154	−	0.828388i	$-0.689258\pi$
$373$	−0.177392	+	0.118530i	−0.00918504	+	0.00613724i	0.550969	+	0.834526i	$0.314258\pi$
$374$	−1.18968	+	0.638725i	−0.0615168	+	0.0330277i
$375$		0			0
$376$	8.50203	−	28.5971i	0.438458	−	1.47478i
$377$	8.74454	−	21.1112i	0.450366	−	1.08728i
$378$		0			0
$379$	5.76906	−	29.0030i	0.296337	−	1.48979i	−0.489855	−	0.871804i	$-0.662950\pi$
$379$	5.76906	−	29.0030i	0.296337	−	1.48979i	0.786192	−	0.617982i	$-0.212050\pi$
$380$	−11.7518	−	2.29246i	−0.602852	−	0.117601i
$381$		0			0
$382$	−2.00758	−	2.43705i	−0.102717	−	0.124690i
$383$	−12.8505			−0.656630			−0.328315	−	0.944568i	$-0.606481\pi$
$383$	−12.8505			−0.656630			−0.328315	+	0.944568i	$0.606481\pi$
$384$		0			0
$385$	0.948635			0.0483469
$386$	17.3156	+	21.0198i	0.881341	+	1.06988i
$387$		0			0
$388$	12.8297	+	2.50273i	0.651328	+	0.127057i
$389$	−5.91554	+	29.7394i	−0.299930	+	1.50785i	0.477362	+	0.878707i	$0.341593\pi$
$389$	−5.91554	+	29.7394i	−0.299930	+	1.50785i	−0.777291	+	0.629141i	$0.783407\pi$
$390$		0			0
$391$	−10.8602	+	26.2189i	−0.549226	+	1.32595i
$392$	−14.3518	−	4.26684i	−0.724875	−	0.215508i
$393$		0			0
$394$	18.9642	−	10.1817i	0.955403	−	0.512945i
$395$	33.7262	−	22.5351i	1.69695	−	1.13386i
$396$		0			0
$397$	0.547363	+	2.75178i	0.0274713	+	0.138108i	0.992087	−	0.125552i	$-0.0400703\pi$
$397$	0.547363	+	2.75178i	0.0274713	+	0.138108i	−0.964616	+	0.263660i	$0.915070\pi$
$398$	−25.0770	+	7.65764i	−1.25700	+	0.383843i
$399$		0			0
$400$	23.8765	+	23.5262i	1.19383	+	1.17631i
$401$	−5.30890	+	5.30890i	−0.265114	+	0.265114i	−0.827128	−	0.562014i	$-0.810027\pi$
$401$	−5.30890	+	5.30890i	−0.265114	+	0.265114i	0.562014	+	0.827128i	$0.310027\pi$
$402$		0			0
$403$	27.9240	−	5.55443i	1.39099	−	0.276686i
$404$	−9.31097	+	22.7157i	−0.463238	+	1.13015i
$405$		0			0
$406$	−10.3344	−	3.11405i	−0.512885	−	0.154548i
$407$	−2.05350	+	0.850589i	−0.101788	+	0.0421622i
$408$		0			0
$409$	31.4593	+	13.0309i	1.55556	+	0.644336i	0.984312	−	0.176438i	$-0.0564576\pi$
$409$	31.4593	+	13.0309i	1.55556	+	0.644336i	0.571253	+	0.820774i	$0.306458\pi$
$410$	14.3653	−	17.5703i	0.709453	−	0.867736i
$411$		0			0
$412$	3.61707	−	5.45687i	0.178200	−	0.268840i
$413$	8.51471	+	5.68935i	0.418981	+	0.279954i
$414$		0			0
$415$			29.9617i			1.47076i
$416$	−19.4147	+	10.6091i	−0.951882	+	0.520154i
$417$		0			0
$418$	−0.457391	−	0.0441959i	−0.0223717	−	0.00216169i
$419$	20.2970	+	13.5620i	0.991575	+	0.662549i	0.941787	−	0.336211i	$-0.109145\pi$
$419$	20.2970	+	13.5620i	0.991575	+	0.662549i	0.0497881	+	0.998760i	$0.484145\pi$
$420$		0			0
$421$	−13.5127	−	2.68784i	−0.658567	−	0.130997i	−0.145517	−	0.989356i	$-0.546484\pi$
$421$	−13.5127	−	2.68784i	−0.658567	−	0.130997i	−0.513050	+	0.858359i	$0.671484\pi$
$422$	5.11318	+	4.18049i	0.248906	+	0.203503i
$423$		0			0
$424$	9.86925	−	18.7128i	0.479293	−	0.908775i
$425$	−37.2336	+	15.4227i	−1.80610	+	0.748109i
$426$		0			0
$427$	−1.01364	−	1.51702i	−0.0490535	−	0.0734137i
$428$	19.6894	−	8.24097i	0.951722	−	0.398343i
$429$		0			0
$430$	−40.1089	−	21.3435i	−1.93422	−	1.02927i
$431$	20.9078	−	20.9078i	1.00709	−	1.00709i	0.00711650	−	0.999975i	$-0.497735\pi$
$431$	20.9078	−	20.9078i	1.00709	−	1.00709i	0.999975	−	0.00711650i	$-0.00226527\pi$
$432$		0			0
$433$	−0.457834	−	0.457834i	−0.0220021	−	0.0220021i	0.696020	−	0.718022i	$-0.254952\pi$
$433$	−0.457834	−	0.457834i	−0.0220021	−	0.0220021i	−0.718022	+	0.696020i	$0.754952\pi$
$434$	−3.92757	−	12.8619i	−0.188529	−	0.617389i
$435$		0			0
$436$	0.0710428	+	19.2257i	0.00340233	+	0.920742i
$437$	−8.03012	+	5.36556i	−0.384133	+	0.256669i
$438$		0			0
$439$	6.59677	+	15.9260i	0.314847	+	0.760107i	0.999512	+	0.0312490i	$0.00994849\pi$
$439$	6.59677	+	15.9260i	0.314847	+	0.760107i	−0.684665	+	0.728858i	$0.740052\pi$
$440$	1.59498	+	1.29424i	0.0760379	+	0.0617005i
$441$		0			0
$442$	−2.65620	−	26.4674i	−0.126343	−	1.25893i
$443$	−2.90152	+	14.5869i	−0.137856	+	0.693047i	0.848602	+	0.529031i	$0.177445\pi$
$443$	−2.90152	+	14.5869i	−0.137856	+	0.693047i	−0.986458	+	0.164015i	$0.947555\pi$
$444$		0			0
$445$	−21.5777	+	32.2934i	−1.02288	+	1.53085i
$446$	−10.9369	+	9.00958i	−0.517879	+	0.426616i
$447$		0			0
$448$	5.90182	+	8.62418i	0.278835	+	0.407454i
$449$	−15.4273			−0.728058			−0.364029	−	0.931388i	$-0.618599\pi$
$449$	−15.4273			−0.728058			−0.364029	+	0.931388i	$0.618599\pi$
$450$		0			0
$451$	0.483915	−	0.724229i	0.0227866	−	0.0341026i
$452$	7.04157	−	4.74276i	0.331208	−	0.223081i
$453$		0			0
$454$	0.702034	+	6.99535i	0.0329481	+	0.328308i
$455$	−7.15150	+	17.2653i	−0.335268	+	0.809408i
$456$		0			0
$457$	4.44301	+	10.7264i	0.207835	+	0.501758i	0.993082	−	0.117425i	$-0.0374639\pi$
$457$	4.44301	+	10.7264i	0.207835	+	0.501758i	−0.785247	+	0.619183i	$0.787464\pi$
$458$	−4.42959	−	8.25047i	−0.206981	−	0.385519i
$459$		0			0
$460$	43.1692	−	0.159519i	2.01277	−	0.00743762i
$461$	1.96662	+	9.88687i	0.0915946	+	0.460477i	0.999175	+	0.0405999i	$0.0129269\pi$
$461$	1.96662	+	9.88687i	0.0915946	+	0.460477i	−0.907581	+	0.419877i	$0.862073\pi$
$462$		0			0
$463$	−20.2792	−	20.2792i	−0.942453	−	0.942453i	0.0559787	−	0.998432i	$-0.482172\pi$
$463$	−20.2792	−	20.2792i	−0.942453	−	0.942453i	−0.998432	+	0.0559787i	$0.982172\pi$
$464$	−13.1271	−	19.3352i	−0.609409	−	0.897613i
$465$		0			0
$466$	−13.6004	−	7.23727i	−0.630025	−	0.335260i
$467$	6.72549	−	1.33778i	0.311219	−	0.0619053i	−0.0370098	−	0.999315i	$-0.511783\pi$
$467$	6.72549	−	1.33778i	0.311219	−	0.0619053i	0.348229	+	0.937410i	$0.386783\pi$
$468$		0			0
$469$	−3.41445	−	5.11009i	−0.157665	−	0.235962i
$470$	15.7428	−	52.2442i	0.726159	−	2.40985i
$471$		0			0
$472$	6.55409	+	21.1826i	0.301676	+	0.975006i
$473$	−1.61098	−	0.667291i	−0.0740731	−	0.0306821i
$474$		0			0
$475$	−13.4515	−	2.67566i	−0.617196	−	0.122768i
$476$	−12.3140	+	2.49674i	−0.564411	+	0.114438i
$477$		0			0
$478$	37.7814	+	3.65068i	1.72808	+	0.166978i
$479$		−	23.5713i		−	1.07700i	−0.842626	−	0.538500i	$-0.818991\pi$
$479$		−	23.5713i		−	1.07700i	0.842626	−	0.538500i	$-0.181009\pi$
$480$		0			0
$481$		−	43.7864i		−	1.99649i
$482$	1.42702	−	14.7684i	0.0649989	−	0.672684i
$483$		0			0
$484$	−18.2717	−	12.1113i	−0.830530	−	0.550514i
$485$	23.4475	+	4.66399i	1.06470	+	0.211781i
$486$		0			0
$487$	−16.3288	−	6.76359i	−0.739927	−	0.306488i	−0.0193027	−	0.999814i	$-0.506145\pi$
$487$	−16.3288	−	6.76359i	−0.739927	−	0.306488i	−0.720624	+	0.693326i	$0.756145\pi$
$488$	0.365420	−	3.93357i	0.0165418	−	0.178064i
$489$		0			0
$490$	−26.2194	−	7.90069i	−1.18447	−	0.356917i
$491$	−4.13695	−	6.19138i	−0.186698	−	0.279413i	0.726300	−	0.687378i	$-0.241238\pi$
$491$	−4.13695	−	6.19138i	−0.186698	−	0.279413i	−0.912997	+	0.407965i	$0.866238\pi$
$492$		0			0
$493$	27.5586	−	5.48175i	1.24118	−	0.246885i
$494$	4.25252	−	7.99138i	0.191330	−	0.359549i
$495$		0			0
$496$	10.9441	−	26.9837i	0.491404	−	1.21160i
$497$	8.94895	+	8.94895i	0.401415	+	0.401415i
$498$		0			0
$499$	2.64752	+	13.3100i	0.118519	+	0.595836i	0.993703	+	0.112045i	$0.0357402\pi$
$499$	2.64752	+	13.3100i	0.118519	+	0.595836i	−0.875184	+	0.483790i	$0.839260\pi$
$500$	17.5488	+	17.4196i	0.784807	+	0.779029i
$501$		0			0
$502$	25.3047	−	13.5858i	1.12940	−	0.606365i
$503$	−2.32837	−	5.62119i	−0.103817	−	0.250636i	0.863432	−	0.504465i	$-0.168310\pi$
$503$	−2.32837	−	5.62119i	−0.103817	−	0.250636i	−0.967249	+	0.253828i	$0.918310\pi$
$504$		0			0
$505$	−17.1825	+	41.4822i	−0.764611	+	1.84593i
$506$	1.64852	−	0.165441i	0.0732856	−	0.00735474i
$507$		0			0
$508$	−3.18183	+	16.3109i	−0.141171	+	0.723680i
$509$	−11.8294	+	17.7040i	−0.524330	+	0.784716i	−0.995239	−	0.0974662i	$-0.968926\pi$
$509$	−11.8294	+	17.7040i	−0.524330	+	0.784716i	0.470908	+	0.882182i	$0.343926\pi$
$510$		0			0
$511$	2.44858			0.108319
$512$	−1.84314	+	22.5522i	−0.0814561	+	0.996677i
$513$		0			0
$514$	1.24026	+	1.50558i	0.0547055	+	0.0664083i
$515$	6.65219	−	9.95571i	0.293131	−	0.438701i
$516$		0			0
$517$	0.408545	−	2.05389i	0.0179678	−	0.0903301i
$518$	−20.5789	+	2.06524i	−0.904184	+	0.0907415i
$519$		0			0
$520$	−35.5795	+	19.2719i	−1.56026	+	0.845131i
$521$	1.46823	+	3.54461i	0.0643242	+	0.155292i	0.952773	−	0.303683i	$-0.0982165\pi$
$521$	1.46823	+	3.54461i	0.0643242	+	0.155292i	−0.888449	+	0.458976i	$0.848217\pi$
$522$		0			0
$523$	23.2525	−	15.5368i	1.01676	−	0.679378i	0.0687557	−	0.997634i	$-0.478097\pi$
$523$	23.2525	−	15.5368i	1.01676	−	0.679378i	0.948005	+	0.318256i	$0.103097\pi$
$524$	0.215039	+	0.213455i	0.00939400	+	0.00932483i
$525$		0			0
$526$	−6.59115	+	2.01271i	−0.287388	+	0.0877583i
$527$	24.7557	+	24.7557i	1.07838	+	1.07838i
$528$		0			0
$529$	8.35867	−	8.35867i	0.363420	−	0.363420i
$530$	18.1765	−	34.1575i	0.789537	−	1.48371i
$531$		0			0
$532$	−3.95639	−	1.62169i	−0.171531	−	0.0703092i
$533$	9.53295	+	14.2671i	0.412918	+	0.617975i
$534$		0			0
$535$	36.0659	−	14.9390i	1.55927	−	0.645869i
$536$	1.23092	−	13.2502i	0.0531676	−	0.572324i
$537$		0			0
$538$	3.70685	−	4.53387i	0.159814	−	0.195469i
$539$	−1.03077	−	0.205033i	−0.0443984	−	0.00883139i
$540$		0			0
$541$	−10.5737	−	7.06514i	−0.454600	−	0.303754i	0.307108	−	0.951675i	$-0.400639\pi$
$541$	−10.5737	−	7.06514i	−0.454600	−	0.303754i	−0.761708	+	0.647921i	$0.775639\pi$
$542$	−0.934932	+	9.67576i	−0.0401588	+	0.415610i
$543$		0			0
$544$	−24.1104	−	12.6023i	−1.03373	−	0.540320i
$545$			35.1626i			1.50620i
$546$		0			0
$547$	33.6594	+	22.4905i	1.43917	+	0.961623i	0.997935	+	0.0642313i	$0.0204595\pi$
$547$	33.6594	+	22.4905i	1.43917	+	0.961623i	0.441235	+	0.897391i	$0.354540\pi$
$548$	38.6151	−	7.82947i	1.64956	−	0.334459i
$549$		0			0
$550$	1.82151	+	1.48925i	0.0776696	+	0.0635020i
$551$	8.83435	+	3.65931i	0.376356	+	0.155892i
$552$		0			0
$553$	13.3828	−	5.54333i	0.569094	−	0.235726i
$554$	6.96988	−	23.1304i	0.296122	−	0.982716i
$555$		0			0
$556$	4.76299	+	11.3797i	0.201996	+	0.482609i
$557$	−32.9955	+	6.56322i	−1.39807	+	0.278092i	−0.835877	−	0.548917i	$-0.815040\pi$
$557$	−32.9955	+	6.56322i	−1.39807	+	0.278092i	−0.562188	+	0.827009i	$0.690040\pi$
$558$		0			0
$559$	24.2895	−	24.2895i	1.02734	−	1.02734i
$560$	10.7357	+	15.8128i	0.453664	+	0.668213i
$561$		0			0
$562$	−1.95734	−	6.40981i	−0.0825652	−	0.270382i
$563$	4.55918	+	22.9206i	0.192147	+	0.965986i	0.949688	+	0.313199i	$0.101401\pi$
$563$	4.55918	+	22.9206i	0.192147	+	0.965986i	−0.757541	+	0.652788i	$0.773599\pi$
$564$		0			0
$565$	12.9105	−	8.62652i	0.543149	−	0.362920i
$566$	−3.17949	−	5.92207i	−0.133644	−	0.248923i
$567$		0			0
$568$	2.83706	+	27.2555i	0.119040	+	1.14362i
$569$	8.28246	−	19.9956i	0.347219	−	0.838261i	−0.649727	−	0.760168i	$-0.725117\pi$
$569$	8.28246	−	19.9956i	0.347219	−	0.838261i	0.996946	−	0.0780932i	$-0.0248832\pi$
$570$		0			0
$571$	−8.18055	+	41.1264i	−0.342345	+	1.72109i	0.299364	+	0.954139i	$0.403225\pi$
$571$	−8.18055	+	41.1264i	−0.342345	+	1.72109i	−0.641710	+	0.766948i	$0.721775\pi$
$572$	−1.28804	+	0.867540i	−0.0538555	+	0.0362737i
$573$		0			0
$574$	6.25566	−	5.15326i	0.261106	−	0.215093i
$575$	49.4493			2.06218
$576$		0			0
$577$	12.5421			0.522135			0.261068	−	0.965321i	$-0.415925\pi$
$577$	12.5421			0.522135			0.261068	+	0.965321i	$0.415925\pi$
$578$	6.69020	−	5.51122i	0.278276	−	0.229237i
$579$		0			0
$580$	−23.8777	−	35.4511i	−0.991466	−	1.47203i
$581$	−2.08743	+	10.4942i	−0.0866014	+	0.435374i
$582$		0			0
$583$	0.568278	−	1.37194i	0.0235357	−	0.0568201i
$584$	4.11691	+	3.34065i	0.170359	+	0.138237i
$585$		0			0
$586$	4.77395	+	8.89187i	0.197210	+	0.367320i
$587$	2.09167	−	1.39761i	0.0863325	−	0.0576855i	−0.511655	−	0.859191i	$-0.670967\pi$
$587$	2.09167	−	1.39761i	0.0863325	−	0.0576855i	0.597987	+	0.801506i	$0.295967\pi$
$588$		0			0
$589$	2.32435	+	11.6853i	0.0957733	+	0.481485i
$590$	11.8437	+	38.7854i	0.487599	+	1.59677i
$591$		0			0
$592$	−37.4179	−	24.6038i	−1.53787	−	1.01121i
$593$	23.0604	−	23.0604i	0.946976	−	0.946976i	−0.0516877	−	0.998663i	$-0.516460\pi$
$593$	23.0604	−	23.0604i	0.946976	−	0.946976i	0.998663	+	0.0516877i	$0.0164600\pi$
$594$		0			0
$595$	−22.5381	+	4.48311i	−0.923973	+	0.183790i
$596$	−11.0117	+	4.60895i	−0.451058	+	0.188790i
$597$		0			0
$598$	−9.41670	+	31.2504i	−0.385078	+	1.27793i
$599$	−19.8116	+	8.20624i	−0.809480	+	0.335298i	−0.748747	−	0.662856i	$-0.769344\pi$
$599$	−19.8116	+	8.20624i	−0.809480	+	0.335298i	−0.0607337	+	0.998154i	$0.519344\pi$
$600$		0			0
$601$	−16.8700	−	6.98779i	−0.688142	−	0.285038i	0.0110839	−	0.999939i	$-0.496472\pi$
$601$	−16.8700	−	6.98779i	−0.688142	−	0.285038i	−0.699226	+	0.714901i	$0.746472\pi$
$602$	−12.5613	−	10.2700i	−0.511962	−	0.418576i
$603$		0			0
$604$	−6.56351	−	32.3714i	−0.267065	−	1.31717i
$605$	−33.3355	−	22.2741i	−1.35528	−	0.905570i
$606$		0			0
$607$		−	26.2051i		−	1.06363i	−0.846860	−	0.531815i	$-0.821510\pi$
$607$		−	26.2051i		−	1.06363i	0.846860	−	0.531815i	$-0.178490\pi$
$608$	−4.43957	−	8.12441i	−0.180048	−	0.329489i
$609$		0			0
$610$	0.694906	−	7.19169i	0.0281359	−	0.291183i
$611$	34.3012	+	22.9193i	1.38768	+	0.927216i
$612$		0			0
$613$	−15.9508	−	3.17282i	−0.644248	−	0.128149i	−0.137856	−	0.990452i	$-0.544021\pi$
$613$	−15.9508	−	3.17282i	−0.644248	−	0.128149i	−0.506392	+	0.862303i	$0.669021\pi$
$614$	15.7810	−	19.3018i	0.636870	−	0.778959i
$615$		0			0
$616$	0.468481	+	0.564437i	0.0188757	+	0.0227418i
$617$	12.3333	−	5.10860i	0.496518	−	0.205665i	−0.120349	−	0.992732i	$-0.538401\pi$
$617$	12.3333	−	5.10860i	0.496518	−	0.205665i	0.616868	+	0.787067i	$0.288401\pi$
$618$		0			0
$619$	8.00890	+	11.9862i	0.321905	+	0.481765i	0.956765	−	0.290862i	$-0.0939422\pi$
$619$	8.00890	+	11.9862i	0.321905	+	0.481765i	−0.634860	+	0.772627i	$0.718942\pi$
$620$	20.1982	−	49.2770i	0.811179	−	1.97901i
$621$		0			0
$622$	0.632172	−	1.18799i	0.0253478	−	0.0476339i
$623$	−9.80760	+	9.80760i	−0.392933	+	0.392933i
$624$		0			0
$625$	2.35010	+	2.35010i	0.0940039	+	0.0940039i
$626$	40.6177	−	12.4032i	1.62341	−	0.495733i
$627$		0			0
$628$	−4.55430	+	4.58808i	−0.181736	+	0.183084i
$629$	44.7684	−	29.9133i	1.78503	−	1.19272i
$630$		0			0
$631$	−1.25822	−	3.03762i	−0.0500891	−	0.120926i	0.896854	−	0.442326i	$-0.145847\pi$
$631$	−1.25822	−	3.03762i	−0.0500891	−	0.120926i	−0.946943	+	0.321400i	$0.895847\pi$
$632$	30.0640	+	8.93814i	1.19588	+	0.355540i
$633$		0			0
$634$	30.9263	−	3.10368i	1.22824	−	0.123263i
$635$	−5.92954	+	29.8098i	−0.235307	+	1.18297i
$636$		0			0
$637$	11.5023	−	17.2144i	0.455739	−	0.682061i
$638$	−1.04301	−	1.26613i	−0.0412931	−	0.0501266i
$639$		0			0
$640$	−3.52336	+	41.2337i	−0.139273	+	1.62990i
$641$	4.48078			0.176980			0.0884902	−	0.996077i	$-0.471796\pi$
$641$	4.48078			0.176980			0.0884902	+	0.996077i	$0.471796\pi$
$642$		0			0
$643$	16.9882	−	25.4247i	0.669950	−	1.00265i	−0.328361	−	0.944552i	$-0.606496\pi$
$643$	16.9882	−	25.4247i	0.669950	−	1.00265i	0.998311	−	0.0580984i	$-0.0185037\pi$
$644$	15.1313	+	2.95173i	0.596259	+	0.116314i
$645$		0			0
$646$	11.0758	−	1.11153i	0.435771	−	0.0437327i
$647$	−4.54775	+	10.9792i	−0.178791	+	0.431639i	−0.987713	−	0.156276i	$-0.950051\pi$
$647$	−4.54775	+	10.9792i	−0.178791	+	0.431639i	0.808923	+	0.587915i	$0.200051\pi$
$648$		0			0
$649$	0.595608	+	1.43792i	0.0233797	+	0.0564435i
$650$	−40.8365	+	21.9247i	−1.60174	+	0.859956i
$651$		0			0
$652$	16.3969	−	16.5186i	0.642153	−	0.646917i
$653$	−3.94799	−	19.8479i	−0.154497	−	0.776707i	−0.977871	−	0.209208i	$-0.932911\pi$
$653$	−3.94799	−	19.8479i	−0.154497	−	0.776707i	0.823374	−	0.567498i	$-0.192089\pi$
$654$		0			0
$655$	0.391845	+	0.391845i	0.0153107	+	0.0153107i
$656$	17.5486	−	0.129693i	0.685159	−	0.00506367i
$657$		0			0
$658$	9.15384	−	17.2020i	0.356854	−	0.670604i
$659$	12.1097	−	2.40876i	0.471725	−	0.0938320i	0.0464977	−	0.998918i	$-0.485194\pi$
$659$	12.1097	−	2.40876i	0.471725	−	0.0938320i	0.425228	+	0.905086i	$0.360194\pi$
$660$		0			0
$661$	−7.87981	−	11.7930i	−0.306489	−	0.458693i	0.645969	−	0.763364i	$-0.276454\pi$
$661$	−7.87981	−	11.7930i	−0.306489	−	0.458693i	−0.952458	+	0.304671i	$0.901454\pi$
$662$	−15.9653	−	4.81083i	−0.620510	−	0.186978i
$663$		0			0
$664$	−17.8272	+	14.7965i	−0.691830	+	0.574217i
$665$	−7.22496	−	2.99267i	−0.280172	−	0.116051i
$666$		0			0
$667$	−33.8141	−	6.72604i	−1.30929	−	0.260433i
$668$	−21.6401	+	32.6472i	−0.837280	+	1.26316i
$669$		0			0
$670$	2.34080	−	24.2253i	0.0904329	−	0.935904i
$671$		−	0.277295i		−	0.0107049i
$672$		0			0
$673$		−	4.98171i		−	0.192031i	−0.995380	−	0.0960155i	$-0.969390\pi$
$673$		−	4.98171i		−	0.192031i	0.995380	−	0.0960155i	$-0.0306098\pi$
$674$	−39.8501	−	3.85056i	−1.53497	−	0.148318i
$675$		0			0
$676$	−0.912618	−	4.50105i	−0.0351007	−	0.173117i
$677$	−34.8922	−	6.94050i	−1.34102	−	0.266745i	−0.528129	−	0.849164i	$-0.677106\pi$
$677$	−34.8922	−	6.94050i	−1.34102	−	0.266745i	−0.812889	+	0.582419i	$0.802106\pi$
$678$		0			0
$679$	7.88766	+	3.26717i	0.302700	+	0.125383i
$680$	−44.0108	−	23.2116i	−1.68774	−	0.890123i
$681$		0			0
$682$	0.589699	−	1.95699i	0.0225807	−	0.0749369i
$683$	−20.6276	−	30.8714i	−0.789294	−	1.18126i	−0.979879	−	0.199592i	$-0.936038\pi$
$683$	−20.6276	−	30.8714i	−0.789294	−	1.18126i	0.190585	−	0.981671i	$-0.438962\pi$
$684$		0			0
$685$	70.6768	−	14.0585i	2.70042	−	0.537147i
$686$	−20.0489	−	10.6688i	−0.765470	−	0.407335i
$687$		0			0
$688$	−7.10834	−	34.4052i	−0.271003	−	1.31169i
$689$	20.6854	+	20.6854i	0.788053	+	0.788053i
$690$		0			0
$691$	3.38609	+	17.0230i	0.128813	+	0.647587i	0.990202	+	0.139641i	$0.0445949\pi$
$691$	3.38609	+	17.0230i	0.128813	+	0.647587i	−0.861389	+	0.507946i	$0.830405\pi$
$692$	0.102731	+	27.8012i	0.00390526	+	1.05684i
$693$		0			0
$694$	−14.1001	−	26.2627i	−0.535234	−	0.996918i
$695$	8.63420	+	20.8448i	0.327514	+	0.790688i
$696$		0			0
$697$	−8.07447	+	19.4935i	−0.305842	+	0.738369i
$698$	0.365277	+	3.63976i	0.0138259	+	0.137767i
$699$		0			0
$700$	12.2303	+	18.1584i	0.462264	+	0.686323i
$701$	−7.68353	+	11.4992i	−0.290203	+	0.434319i	−0.947712	−	0.319127i	$-0.896610\pi$
$701$	−7.68353	+	11.4992i	−0.290203	+	0.434319i	0.657509	+	0.753447i	$0.271610\pi$
$702$		0			0
$703$	18.3232			0.691072
$704$	0.0176065	+	1.58817i	0.000663571	+	0.0598566i
$705$		0			0
$706$	2.52688	−	2.08158i	0.0951003	−	0.0783413i
$707$	−8.90833	+	13.3323i	−0.335032	+	0.501411i
$708$		0			0
$709$	−7.70005	+	38.7108i	−0.289182	+	1.45381i	0.513851	+	0.857879i	$0.328218\pi$
$709$	−7.70005	+	38.7108i	−0.289182	+	1.45381i	−0.803033	+	0.595935i	$0.796782\pi$
$710$	5.00454	+	49.8673i	0.187817	+	1.87149i
$711$		0			0
$712$	−29.8707	+	3.10927i	−1.11945	+	0.116525i
$713$	−16.4388	−	39.6868i	−0.615638	−	1.48628i
$714$		0			0
$715$	−2.36157	+	1.57795i	−0.0883178	+	0.0590121i
$716$	−48.4220	+	0.178929i	−1.80961	+	0.00668689i
$717$		0			0
$718$	−3.30006	−	10.8069i	−0.123157	−	0.403311i
$719$	18.6339	+	18.6339i	0.694926	+	0.694926i	0.963312	−	0.268385i	$-0.0864900\pi$
$719$	18.6339	+	18.6339i	0.694926	+	0.694926i	−0.268385	+	0.963312i	$0.586490\pi$
$720$		0			0
$721$	3.02358	−	3.02358i	0.112604	−	0.112604i
$722$	−20.3765	−	10.8431i	−0.758335	−	0.403539i
$723$		0			0
$724$	15.8827	+	37.9469i	0.590274	+	1.41029i
$725$	−27.2009	−	40.7090i	−1.01021	−	1.51189i
$726$		0			0
$727$	−13.3918	+	5.54705i	−0.496673	+	0.205729i	−0.616936	−	0.787013i	$-0.711626\pi$
$727$	−13.3918	+	5.54705i	−0.496673	+	0.205729i	0.120263	+	0.992742i	$0.461626\pi$
$728$	−13.8046	+	4.27127i	−0.511632	+	0.158304i
$729$		0			0
$730$	7.50691	+	6.13758i	0.277843	+	0.227162i
$731$	41.4280	+	8.24055i	1.53227	+	0.304788i
$732$		0			0
$733$	−14.4510	−	9.65582i	−0.533758	−	0.356646i	0.259295	−	0.965798i	$-0.416510\pi$
$733$	−14.4510	−	9.65582i	−0.533758	−	0.356646i	−0.793053	+	0.609152i	$0.791510\pi$
$734$	19.5343	+	1.88752i	0.721022	+	0.0696697i
$735$		0			0
$736$	21.4139	+	25.6069i	0.789329	+	0.943883i
$737$		−	0.934071i		−	0.0344069i
$738$		0			0
$739$	27.1683	+	18.1533i	0.999401	+	0.667779i	0.943746	−	0.330671i	$-0.107275\pi$
$739$	27.1683	+	18.1533i	0.999401	+	0.667779i	0.0556553	+	0.998450i	$0.482275\pi$
$740$	−68.2679	−	45.2512i	−2.50958	−	1.66347i
$741$		0			0
$742$	8.74616	−	10.6975i	0.321082	−	0.392717i
$743$	1.39715	+	0.578718i	0.0512564	+	0.0212311i	0.408164	−	0.912908i	$-0.366169\pi$
$743$	1.39715	+	0.578718i	0.0512564	+	0.0212311i	−0.356908	+	0.934140i	$0.616169\pi$
$744$		0			0
$745$	−20.1707	+	8.35497i	−0.738997	+	0.306102i
$746$	−0.288889	−	0.0870510i	−0.0105770	−	0.00318717i
$747$		0			0
$748$	−1.76694	−	0.724251i	−0.0646056	−	0.0264813i
$749$	13.6731	−	2.71974i	0.499603	−	0.0993772i
$750$		0			0
$751$	−14.2852	+	14.2852i	−0.521274	+	0.521274i	−0.917956	−	0.396682i	$-0.870162\pi$
$751$	−14.2852	+	14.2852i	−0.521274	+	0.521274i	0.396682	+	0.917956i	$0.370162\pi$
$752$	38.8598	−	16.4338i	1.41707	−	0.599278i
$753$		0			0
$754$	30.9067	−	9.43784i	1.12556	−	0.343706i
$755$	−11.7853	−	59.2489i	−0.428912	−	2.15629i
$756$		0			0
$757$	−7.91280	+	5.28717i	−0.287596	+	0.192165i	−0.690997	−	0.722858i	$-0.742828\pi$
$757$	−7.91280	+	5.28717i	−0.287596	+	0.192165i	0.403401	+	0.915023i	$0.367828\pi$
$758$	36.8455	−	19.7820i	1.33829	−	0.718513i
$759$		0			0
$760$	−8.06469	−	14.8889i	−0.292537	−	0.540076i
$761$	8.41830	−	20.3236i	0.305163	−	0.736729i	−0.694685	−	0.719314i	$-0.744456\pi$
$761$	8.41830	−	20.3236i	0.305163	−	0.736729i	0.999848	−	0.0174150i	$-0.00554366\pi$
$762$		0			0
$763$	−2.44978	+	12.3159i	−0.0886880	+	0.445865i
$764$	0.854952	−	4.38271i	0.0309311	−	0.158561i
$765$		0			0
$766$	−11.5550	−	14.0269i	−0.417498	−	0.506811i
$767$	−30.6605			−1.10709
$768$		0			0
$769$	23.8552			0.860241			0.430120	−	0.902772i	$-0.358471\pi$
$769$	23.8552			0.860241			0.430120	+	0.902772i	$0.358471\pi$
$770$	0.852999	+	1.03547i	0.0307399	+	0.0373159i
$771$		0			0
$772$	−7.37407	+	37.8014i	−0.265398	+	1.36050i
$773$	−5.32227	+	26.7568i	−0.191429	+	0.962377i	0.758919	+	0.651186i	$0.225728\pi$
$773$	−5.32227	+	26.7568i	−0.191429	+	0.962377i	−0.950347	+	0.311191i	$0.899272\pi$
$774$		0			0
$775$	23.3448	−	56.3594i	0.838571	−	2.02449i
$776$	8.80442	+	16.2545i	0.316060	+	0.583504i
$777$		0			0
$778$	−37.7810	+	20.2842i	−1.35451	+	0.727224i
$779$	−5.97031	+	3.98923i	−0.213909	+	0.142929i
$780$		0			0
$781$	0.375250	+	1.88651i	0.0134275	+	0.0675045i
$782$	−38.3845	+	11.7213i	−1.37263	+	0.419152i
$783$		0			0
$784$	−8.24748	−	19.5023i	−0.294553	−	0.696509i
$785$	−8.36044	+	8.36044i	−0.298397	+	0.298397i
$786$		0			0
$787$	−34.0492	+	6.77280i	−1.21372	+	0.241424i	−0.760122	−	0.649781i	$-0.774861\pi$
$787$	−34.0492	+	6.77280i	−1.21372	+	0.241424i	−0.453601	+	0.891205i	$0.649861\pi$
$788$	28.1661	+	11.5450i	1.00337	+	0.411274i
$789$		0			0
$790$	54.9241	+	16.5503i	1.95411	+	0.588833i
$791$	5.12298	−	2.12201i	0.182152	−	0.0754499i
$792$		0			0
$793$	5.04680	+	2.09045i	0.179217	+	0.0742342i
$794$	−2.51150	+	3.07183i	−0.0891298	+	0.109015i
$795$		0			0
$796$	−30.9075	−	20.4869i	−1.09549	−	0.726140i
$797$	−31.6098	−	21.1210i	−1.11968	−	0.748143i	−0.149072	−	0.988826i	$-0.547629\pi$
$797$	−31.6098	−	21.1210i	−1.11968	−	0.748143i	−0.970604	+	0.240683i	$0.922629\pi$
$798$		0			0
$799$			50.7281i			1.79463i
$800$	−4.21041	+	47.2167i	−0.148860	+	1.66936i
$801$		0			0
$802$	−10.5686	−	1.02120i	−0.373190	−	0.0360599i
$803$	0.309427	+	0.206752i	0.0109194	+	0.00729613i
$804$		0			0
$805$	27.6540	+	5.50073i	0.974676	+	0.193875i
$806$	31.1718	+	25.4858i	1.09798	+	0.897699i
$807$		0			0
$808$	−33.1675	+	10.2623i	−1.16683	+	0.361028i
$809$	9.19116	−	3.80710i	0.323144	−	0.133851i	−0.215214	−	0.976567i	$-0.569045\pi$
$809$	9.19116	−	3.80710i	0.323144	−	0.133851i	0.538358	+	0.842716i	$0.319045\pi$
$810$		0			0
$811$	14.2202	+	21.2820i	0.499339	+	0.747314i	0.992450	−	0.122653i	$-0.0391402\pi$
$811$	14.2202	+	21.2820i	0.499339	+	0.747314i	−0.493110	+	0.869967i	$0.664140\pi$
$812$	−5.89338	−	14.0805i	−0.206817	−	0.494129i
$813$		0			0
$814$	−2.77494	−	1.47665i	−0.0972615	−	0.0517565i
$815$	30.1002	−	30.1002i	1.05437	−	1.05437i
$816$		0			0
$817$	10.1644	+	10.1644i	0.355607	+	0.355607i
$818$	14.0640	+	46.0564i	0.491737	+	1.61032i
$819$		0			0
$820$	32.0958	−	0.118601i	1.12084	−	0.00414172i
$821$	−7.65208	+	5.11296i	−0.267059	+	0.178443i	−0.681889	−	0.731456i	$-0.738841\pi$
$821$	−7.65208	+	5.11296i	−0.267059	+	0.178443i	0.414829	+	0.909899i	$0.363841\pi$
$822$		0			0
$823$	−21.4961	−	51.8962i	−0.749307	−	1.80899i	−0.562922	−	0.826510i	$-0.690323\pi$
$823$	−21.4961	−	51.8962i	−0.749307	−	1.80899i	−0.186385	−	0.982477i	$-0.559677\pi$
$824$	9.20882	−	0.958555i	0.320804	−	0.0333929i
$825$		0			0
$826$	1.44614	+	14.4099i	0.0503177	+	0.501386i
$827$	−5.27266	+	26.5075i	−0.183348	+	0.921755i	0.774081	+	0.633087i	$0.218212\pi$
$827$	−5.27266	+	26.5075i	−0.183348	+	0.921755i	−0.957429	+	0.288668i	$0.906788\pi$
$828$		0			0
$829$	−5.97593	+	8.94362i	−0.207553	+	0.310625i	−0.920612	−	0.390480i	$-0.872309\pi$
$829$	−5.97593	+	8.94362i	−0.207553	+	0.310625i	0.713059	+	0.701104i	$0.247309\pi$
$830$	−32.7045	+	26.9411i	−1.13519	+	0.935141i
$831$		0			0
$832$	−29.0377	−	11.6524i	−1.00670	−	0.403974i
$833$	25.4585			0.882085
$834$		0			0
$835$	−39.7986	+	59.5627i	−1.37729	+	2.06125i
$836$	−0.363038	−	0.539002i	−0.0125559	−	0.0186418i
$837$		0			0
$838$	3.44726	+	34.3499i	0.119084	+	1.18660i
$839$	−5.86620	+	14.1623i	−0.202524	+	0.488936i	−0.992210	−	0.124575i	$-0.960243\pi$
$839$	−5.86620	+	14.1623i	−0.202524	+	0.488936i	0.789686	+	0.613511i	$0.210243\pi$
$840$		0			0
$841$	1.96530	+	4.74465i	0.0677689	+	0.163609i
$842$	−9.21651	−	17.1665i	−0.317622	−	0.591597i
$843$		0			0
$844$	0.0345143	+	9.34029i	0.00118803	+	0.321506i
$845$	−1.63868	−	8.23822i	−0.0563724	−	0.283403i
$846$		0			0
$847$	−10.1241	−	10.1241i	−0.347868	−	0.347868i
$848$	29.3001	−	6.05360i	1.00617	−	0.207881i
$849$		0			0
$850$	−50.3144	−	26.7742i	−1.72577	−	0.918348i
$851$	−64.7947	+	12.8885i	−2.22114	+	0.441811i
$852$		0			0
$853$	−22.9937	−	34.4126i	−0.787290	−	1.17826i	−0.980387	−	0.197084i	$-0.936853\pi$
$853$	−22.9937	−	34.4126i	−0.787290	−	1.17826i	0.193096	−	0.981180i	$-0.438147\pi$
$854$	0.744440	−	2.47051i	0.0254742	−	0.0845392i
$855$		0			0
$856$	26.6998	+	14.0816i	0.912580	+	0.481300i
$857$	−11.8164	−	4.89452i	−0.403641	−	0.167193i	0.171621	−	0.985163i	$-0.445100\pi$
$857$	−11.8164	−	4.89452i	−0.403641	−	0.167193i	−0.575261	+	0.817970i	$0.695100\pi$
$858$		0			0
$859$	−15.5583	−	3.09474i	−0.530843	−	0.105591i	−0.0776110	−	0.996984i	$-0.524729\pi$
$859$	−15.5583	−	3.09474i	−0.530843	−	0.105591i	−0.453232	+	0.891392i	$0.649729\pi$
$860$	−12.7680	−	62.9723i	−0.435387	−	2.14734i
$861$		0			0
$862$	41.6217	+	4.02174i	1.41764	+	0.136981i
$863$		−	11.5978i		−	0.394793i	−0.980324	−	0.197396i	$-0.936751\pi$
$863$		−	11.5978i		−	0.394793i	0.980324	−	0.197396i	$-0.0632486\pi$
$864$		0			0
$865$			50.8468i			1.72884i
$866$	0.0880674	−	0.911424i	0.00299265	−	0.0309714i
$867$		0			0
$868$	10.5076	−	15.8523i	0.356653	−	0.538062i
$869$	2.15925	+	0.429501i	0.0732475	+	0.0145698i
$870$		0			0
$871$	17.0002	+	7.04171i	0.576029	+	0.238599i
$872$	−20.9217	+	17.3650i	−0.708500	+	0.588053i
$873$		0			0
$874$	−13.0773	−	3.94059i	−0.442346	−	0.133292i
$875$	8.97244	+	13.4282i	0.303324	+	0.453956i
$876$		0			0
$877$	−29.2277	+	5.81375i	−0.986949	+	0.196316i	−0.662072	−	0.749440i	$-0.730323\pi$
$877$	−29.2277	+	5.81375i	−0.986949	+	0.196316i	−0.324876	+	0.945756i	$0.605323\pi$
$878$	−11.4522	+	21.5211i	−0.386493	+	0.726302i
$879$		0			0
$880$	0.0214676	+	2.90476i	0.000723674	+	0.0979193i
$881$	−14.4448	−	14.4448i	−0.486658	−	0.486658i	0.420592	−	0.907250i	$-0.361823\pi$
$881$	−14.4448	−	14.4448i	−0.486658	−	0.486658i	−0.907250	+	0.420592i	$0.861823\pi$
$882$		0			0
$883$	−1.31696	−	6.62080i	−0.0443192	−	0.222808i	0.952278	−	0.305232i	$-0.0987339\pi$
$883$	−1.31696	−	6.62080i	−0.0443192	−	0.222808i	−0.996597	+	0.0824239i	$0.973734\pi$
$884$	26.5019	−	26.6985i	0.891356	−	0.897968i
$885$		0			0
$886$	−18.5313	+	9.94924i	−0.622570	+	0.334251i
$887$	−6.51843	−	15.7369i	−0.218867	−	0.528392i	0.775865	−	0.630899i	$-0.217314\pi$
$887$	−6.51843	−	15.7369i	−0.218867	−	0.528392i	−0.994732	+	0.102506i	$0.967314\pi$
$888$		0			0
$889$	−4.15370	+	10.0279i	−0.139311	+	0.336326i
$890$	−54.6520	+	5.48473i	−1.83194	+	0.183848i
$891$		0			0
$892$	−19.6687	−	3.83684i	−0.658556	−	0.128467i
$893$	−9.59099	+	14.3539i	−0.320950	+	0.480336i
$894$		0			0
$895$	−88.5609			−2.96027
$896$	−4.10683	+	14.1968i	−0.137200	+	0.474283i
$897$		0			0
$898$	−13.8720	−	16.8395i	−0.462914	−	0.561942i
$899$	−23.6294	+	35.3639i	−0.788086	+	1.17945i
$900$		0			0
$901$	−7.01781	+	35.2809i	−0.233797	+	1.17538i
$902$	1.22566	−	0.123003i	0.0408099	−	0.00409557i
$903$		0			0
$904$	11.5086	+	3.42155i	0.382770	+	0.113799i
$905$	28.7916	+	69.5091i	0.957065	+	2.31056i
$906$		0			0
$907$	40.1409	−	26.8213i	1.33286	−	0.890586i	0.334204	−	0.942501i	$-0.391532\pi$
$907$	40.1409	−	26.8213i	1.33286	−	0.890586i	0.998652	+	0.0519149i	$0.0165325\pi$
$908$	−7.00446	+	7.05642i	−0.232451	+	0.234175i
$909$		0			0
$910$	−25.2763	+	7.71850i	−0.837901	+	0.255866i
$911$	−5.78484	−	5.78484i	−0.191660	−	0.191660i	0.604753	−	0.796413i	$-0.293272\pi$
$911$	−5.78484	−	5.78484i	−0.191660	−	0.191660i	−0.796413	+	0.604753i	$0.793272\pi$
$912$		0			0
$913$	−1.14990	+	1.14990i	−0.0380561	+	0.0380561i
$914$	−7.71320	+	14.4947i	−0.255130	+	0.479443i
$915$		0			0
$916$	5.02272	−	12.2538i	0.165955	−	0.404877i
$917$	0.109946	+	0.164546i	0.00363073	+	0.00543377i
$918$		0			0
$919$	0.487110	−	0.201768i	0.0160683	−	0.00665570i	−0.374635	−	0.927172i	$-0.622232\pi$
$919$	0.487110	−	0.201768i	0.0160683	−	0.00665570i	0.390703	+	0.920517i	$0.372232\pi$
$920$	38.9913	+	46.9776i	1.28550	+	1.54881i
$921$		0			0
$922$	−9.02358	+	11.0368i	−0.297176	+	0.363477i
$923$	−37.1635	−	7.39229i	−1.22325	−	0.243320i
$924$		0			0
$925$	−78.0067	−	52.1224i	−2.56485	−	1.71378i
$926$	3.90083	−	40.3703i	0.128189	−	1.32665i
$927$		0			0
$928$	9.30149	−	31.7147i	0.305336	−	1.04109i
$929$		−	33.3160i		−	1.09306i	−0.837439	−	0.546531i	$-0.815948\pi$
$929$		−	33.3160i		−	1.09306i	0.837439	−	0.546531i	$-0.184052\pi$
$930$		0			0
$931$	7.20369	+	4.81335i	0.236091	+	0.157751i
$932$	−4.32947	−	21.3530i	−0.141816	−	0.699442i
$933$		0			0
$934$	7.50772	+	6.13825i	0.245660	+	0.200850i
$935$	−3.22669	−	1.33654i	−0.105524	−	0.0437094i
$936$		0			0
$937$	−21.7371	+	9.00381i	−0.710121	+	0.294142i	−0.708355	−	0.705857i	$-0.750562\pi$
$937$	−21.7371	+	9.00381i	−0.710121	+	0.294142i	−0.00176640	+	0.999998i	$0.500562\pi$
$938$	2.50765	−	8.32194i	0.0818778	−	0.271721i
$939$		0			0
$940$	71.1824	−	29.7934i	2.32172	−	0.971753i
$941$	38.3485	−	7.62799i	1.25013	−	0.248665i	0.474724	−	0.880134i	$-0.342548\pi$
$941$	38.3485	−	7.62799i	1.25013	−	0.248665i	0.775401	+	0.631469i	$0.217548\pi$
$942$		0			0
$943$	18.3063	−	18.3063i	0.596135	−	0.596135i
$944$	−17.2283	+	26.2011i	−0.560734	+	0.852774i
$945$		0			0
$946$	−0.720197	−	2.35847i	−0.0234156	−	0.0766806i
$947$	−8.47316	−	42.5975i	−0.275341	−	1.38423i	−0.832592	−	0.553887i	$-0.813144\pi$
$947$	−8.47316	−	42.5975i	−0.275341	−	1.38423i	0.557251	−	0.830344i	$-0.311856\pi$
$948$		0			0
$949$	−6.09560	+	4.07295i	−0.197872	+	0.132214i
$950$	−9.17477	−	17.0888i	−0.297669	−	0.554433i
$951$		0			0
$952$	−13.7979	−	11.1962i	−0.447191	−	0.362871i
$953$	−19.4752	+	47.0173i	−0.630863	+	1.52304i	0.207676	+	0.978198i	$0.433410\pi$
$953$	−19.4752	+	47.0173i	−0.630863	+	1.52304i	−0.838539	+	0.544841i	$0.816590\pi$
$954$		0			0
$955$	1.59326	−	8.00984i	0.0515566	−	0.259192i
$956$	29.9877	+	44.5227i	0.969870	+	1.43997i
$957$		0			0
$958$	25.7290	−	21.1950i	0.831268	−	0.684778i
$959$	25.7344			0.831006
$960$		0			0
$961$	−21.9933			−0.709462
$962$	47.7947	−	39.3721i	1.54096	−	1.26941i
$963$		0			0
$964$	17.4035	−	11.7219i	0.560530	−	0.377538i
$965$	−13.7420	+	69.0858i	−0.442371	+	2.22395i
$966$		0			0
$967$	12.0763	−	29.1548i	0.388348	−	0.937556i	−0.601942	−	0.798540i	$-0.705606\pi$
$967$	12.0763	−	29.1548i	0.388348	−	0.937556i	0.990290	−	0.139016i	$-0.0443939\pi$
$968$	−3.20961	−	30.8346i	−0.103161	−	0.991062i
$969$		0			0
$970$	15.9927	+	29.7877i	0.513494	+	0.956426i
$971$	−4.79328	+	3.20277i	−0.153824	+	0.102782i	−0.630100	−	0.776514i	$-0.716986\pi$
$971$	−4.79328	+	3.20277i	−0.153824	+	0.102782i	0.476276	+	0.879296i	$0.341986\pi$
$972$		0			0
$973$	1.57191	+	7.90254i	0.0503932	+	0.253344i
$974$	−7.29984	−	23.9053i	−0.233902	−	0.765974i
$975$		0			0
$976$	4.62223	−	3.13814i	0.147954	−	0.100449i
$977$	1.57017	−	1.57017i	0.0502341	−	0.0502341i	−0.681543	−	0.731778i	$-0.738691\pi$
$977$	1.57017	−	1.57017i	0.0502341	−	0.0502341i	0.731778	+	0.681543i	$0.238691\pi$
$978$		0			0
$979$	−2.06752	+	0.411255i	−0.0660781	+	0.0131438i
$980$	−14.9522	−	35.7238i	−0.477629	−	1.14115i
$981$		0			0
$982$	3.03827	−	10.0829i	0.0969550	−	0.321757i
$983$	26.6882	−	11.0546i	0.851221	−	0.352587i	0.0859528	−	0.996299i	$-0.472607\pi$
$983$	26.6882	−	11.0546i	0.851221	−	0.352587i	0.765268	+	0.643712i	$0.222607\pi$
$984$		0			0
$985$	51.4354	+	21.3052i	1.63887	+	0.678841i
$986$	30.7639	+	25.1523i	0.979721	+	0.801011i
$987$		0			0
$988$	12.5467	−	2.54393i	0.399165	−	0.0809333i
$989$	−43.0931	−	28.7939i	−1.37028	−	0.915592i
$990$		0			0
$991$		−	52.5768i		−	1.67016i	−0.550132	−	0.835078i	$-0.685423\pi$
$991$		−	52.5768i		−	1.67016i	0.550132	−	0.835078i	$-0.314577\pi$
$992$	39.2946	−	12.3174i	1.24761	−	0.391079i
$993$		0			0
$994$	−1.72139	+	17.8149i	−0.0545992	+	0.565055i
$995$	−56.3888	−	37.6778i	−1.78764	−	1.19447i
$996$		0			0
$997$	2.31625	+	0.460731i	0.0733564	+	0.0145915i	0.231632	−	0.972803i	$-0.425593\pi$
$997$	2.31625	+	0.460731i	0.0733564	+	0.0145915i	−0.158276	+	0.987395i	$0.550593\pi$
$998$	−12.1478	+	14.8580i	−0.384531	+	0.470322i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bd.b.37.12		128
3.2	odd	2		192.2.r.a.37.5	✓	128
12.11	even	2		768.2.r.a.241.8		128
64.45	even	16	inner	576.2.bd.b.109.12		128
192.83	even	16		768.2.r.a.529.8		128
192.173	odd	16		192.2.r.a.109.5	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.37.5	✓	128	3.2	odd	2
192.2.r.a.109.5	yes	128	192.173	odd	16
576.2.bd.b.37.12		128	1.1	even	1	trivial
576.2.bd.b.109.12		128	64.45	even	16	inner
768.2.r.a.241.8		128	12.11	even	2
768.2.r.a.529.8		128	192.83	even	16

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bd (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.899186 + 1.09154i) q^{2} +(-0.382930 + 1.96300i) q^{4} +(-0.713613 + 3.58757i) q^{5} +(-0.499893 + 1.20685i) q^{7} +(-2.48702 + 1.34712i) q^{8} +(-4.55766 + 2.44696i) q^{10} +(-0.165075 + 0.110300i) q^{11} +(-0.763008 - 3.83590i) q^{13} +(-1.76682 + 0.539527i) q^{14} +(-3.70673 - 1.50338i) q^{16} +(3.40067 - 3.40067i) q^{17} +(1.60520 - 0.319294i) q^{19} +(-6.76914 - 2.77461i) q^{20} +(-0.268830 - 0.0810065i) q^{22} +(-5.45175 + 2.25819i) q^{23} +(-7.74204 - 3.20686i) q^{25} +(3.50096 - 4.28204i) q^{26} +(-2.17762 - 1.44343i) q^{28} +(4.85792 + 3.24596i) q^{29} +7.27965i q^{31} +(-1.69203 - 5.39787i) q^{32} +(6.76981 + 0.654141i) q^{34} +(-3.97293 - 2.65462i) q^{35} +(10.9804 + 2.18414i) q^{37} +(1.79190 + 1.46504i) q^{38} +(-3.05811 - 9.88369i) q^{40} +(-4.05331 + 1.67894i) q^{41} +(4.87955 + 7.30276i) q^{43} +(-0.153306 - 0.366279i) q^{44} +(-7.36704 - 3.92028i) q^{46} +(-7.45854 + 7.45854i) q^{47} +(3.74316 + 3.74316i) q^{49} +(-3.46111 - 11.3343i) q^{50} +(7.82205 - 0.0289041i) q^{52} +(-6.21917 + 4.15552i) q^{53} +(-0.277908 - 0.670930i) q^{55} +(-0.382521 - 3.67487i) q^{56} +(0.825071 + 8.22134i) q^{58} +(1.52940 - 7.68882i) q^{59} +(-0.775973 + 1.16133i) q^{61} +(-7.94605 + 6.54576i) q^{62} +(4.37055 - 6.70062i) q^{64} +14.3061 q^{65} +(-2.61387 + 3.91193i) q^{67} +(5.37330 + 7.97773i) q^{68} +(-0.674764 - 6.72362i) q^{70} +(3.70757 - 8.95087i) q^{71} +(-0.717326 - 1.73178i) q^{73} +(7.48937 + 13.9496i) q^{74} +(0.0120954 + 3.27328i) q^{76} +(-0.0505950 - 0.254358i) q^{77} +(-7.84113 - 7.84113i) q^{79} +(8.03866 - 12.2253i) q^{80} +(-5.47731 - 2.91469i) q^{82} +(8.03366 - 1.59800i) q^{83} +(9.77339 + 14.6269i) q^{85} +(-3.58365 + 11.8928i) q^{86} +(0.261959 - 0.496693i) q^{88} +(9.80970 + 4.06331i) q^{89} +(5.01077 + 0.996705i) q^{91} +(-2.34518 - 11.5665i) q^{92} +(-14.8479 - 1.43470i) q^{94} +5.98663i q^{95} -6.53575i q^{97} +(-0.720021 + 7.45161i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{22} + 80 q^{26} - 80 q^{28} + 80 q^{32} - 80 q^{34} + 80 q^{38} - 80 q^{40} + 16 q^{44} - 48 q^{50} + 48 q^{52} - 64 q^{55} - 112 q^{56} + 128 q^{59} - 96 q^{62} + 96 q^{64} - 32 q^{67} - 96 q^{68}+ \cdots - 96 q^{94}+O(q^{100}) \) 128 * q - 16 * q^22 + 80 * q^26 - 80 * q^28 + 80 * q^32 - 80 * q^34 + 80 * q^38 - 80 * q^40 + 16 * q^44 - 48 * q^50 + 48 * q^52 - 64 * q^55 - 112 * q^56 + 128 * q^59 - 96 * q^62 + 96 * q^64 - 32 * q^67 - 96 * q^68 + 96 * q^70 + 128 * q^71 - 112 * q^74 + 16 * q^76 - 32 * q^79 - 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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