LMFDB - Embedded newform 738.2.u.f.289.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [738,2,Mod(289,738)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(738, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("738.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.u (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,8,0,0,4,0,0,-4,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 246)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			289.4
Character	$\chi$	$=$	738.289
Dual form			738.2.u.f.595.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.951057 - 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(1.36852 + 1.88361i) q^{5} +(0.450716 + 0.884580i) q^{7} +(0.587785 - 0.809017i) q^{8} +(1.88361 + 1.36852i) q^{10} +(4.25890 - 0.674543i) q^{11} +(-4.47477 - 2.28001i) q^{13} +(0.702007 + 0.702007i) q^{14} +(0.309017 - 0.951057i) q^{16} +(0.916094 + 5.78399i) q^{17} +(2.19158 - 1.11666i) q^{19} +(2.21431 + 0.719473i) q^{20} +(3.84201 - 1.95760i) q^{22} +(1.44482 + 4.44671i) q^{23} +(-0.130038 + 0.400217i) q^{25} +(-4.96033 - 0.785638i) q^{26} +(0.884580 + 0.450716i) q^{28} +(0.443776 - 2.80189i) q^{29} +(0.852603 + 0.619452i) q^{31} -1.00000i q^{32} +(2.65861 + 5.21781i) q^{34} +(-1.04939 + 2.05954i) q^{35} +(-6.22236 + 4.52081i) q^{37} +(1.73925 - 1.73925i) q^{38} +2.32826 q^{40} +(6.23226 - 1.46935i) q^{41} +(-3.34734 + 1.08762i) q^{43} +(3.04904 - 3.04904i) q^{44} +(2.74822 + 3.78260i) q^{46} +(-0.455717 + 0.894395i) q^{47} +(3.53516 - 4.86573i) q^{49} +0.420813i q^{50} +(-4.96033 + 0.785638i) q^{52} +(1.03993 - 6.56584i) q^{53} +(7.09896 + 7.09896i) q^{55} +(0.980565 + 0.155306i) q^{56} +(-0.443776 - 2.80189i) q^{58} +(-3.12046 - 9.60379i) q^{59} +(9.07026 + 2.94711i) q^{61} +(1.00229 + 0.325665i) q^{62} +(-0.309017 - 0.951057i) q^{64} +(-1.82917 - 11.5489i) q^{65} +(-8.47486 - 1.34229i) q^{67} +(4.14088 + 4.14088i) q^{68} +(-0.361594 + 2.28301i) q^{70} +(-13.7194 + 2.17295i) q^{71} -13.5640i q^{73} +(-4.52081 + 6.22236i) q^{74} +(1.11666 - 2.19158i) q^{76} +(2.51624 + 3.46331i) q^{77} +(-1.80575 + 1.80575i) q^{79} +(2.21431 - 0.719473i) q^{80} +(5.47317 - 3.32331i) q^{82} -11.3789 q^{83} +(-9.64106 + 9.64106i) q^{85} +(-2.84742 + 2.06877i) q^{86} +(1.95760 - 3.84201i) q^{88} +(0.955171 + 1.87463i) q^{89} -4.98594i q^{91} +(3.78260 + 2.74822i) q^{92} +(-0.157029 + 0.991444i) q^{94} +(5.10257 + 2.59989i) q^{95} +(-8.01558 - 1.26954i) q^{97} +(1.85854 - 5.72001i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{11} - 12 q^{13} - 4 q^{14} - 8 q^{16} + 4 q^{17} - 4 q^{19} - 4 q^{22} - 40 q^{23} + 12 q^{25} - 8 q^{26} - 4 q^{28} - 16 q^{29} - 4 q^{31} - 16 q^{34} + 8 q^{35}+ \cdots + 56 q^{98}+O(q^{100}) $ 32 * q + 8 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^11 - 12 * q^13 - 4 * q^14 - 8 * q^16 + 4 * q^17 - 4 * q^19 - 4 * q^22 - 40 * q^23 + 12 * q^25 - 8 * q^26 - 4 * q^28 - 16 * q^29 - 4 * q^31 - 16 * q^34 + 8 * q^35 - 44 * q^37 + 16 * q^38 - 16 * q^40 + 28 * q^41 - 40 * q^43 + 16 * q^44 - 20 * q^46 + 48 * q^47 - 40 * q^49 - 8 * q^52 + 8 * q^53 + 72 * q^55 + 4 * q^56 + 16 * q^58 - 32 * q^59 + 100 * q^61 + 8 * q^64 - 56 * q^67 - 4 * q^68 + 48 * q^70 + 80 * q^71 + 4 * q^76 + 48 * q^79 + 12 * q^82 - 72 * q^83 - 52 * q^85 - 4 * q^86 + 4 * q^88 - 44 * q^89 - 20 * q^92 + 28 * q^94 + 40 * q^95 + 92 * q^97 + 56 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$1$	$e\left(\frac{13}{20}\right)$

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 $

$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$3$		0			0
$3$		0			0
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	1.36852	+	1.88361i	0.612020	+	0.842374i	0.996742	−	0.0806590i	$-0.0257025\pi$
$5$	1.36852	+	1.88361i	0.612020	+	0.842374i	−0.384721	+	0.923033i	$0.625702\pi$
$6$		0			0
$7$	0.450716	+	0.884580i	0.170355	+	0.334340i	0.960361	−	0.278759i	$-0.0899229\pi$
$7$	0.450716	+	0.884580i	0.170355	+	0.334340i	−0.790007	+	0.613098i	$0.789923\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$		0			0
$10$	1.88361	+	1.36852i	0.595648	+	0.432764i
$11$	4.25890	−	0.674543i	1.28411	−	0.203382i	0.523181	−	0.852222i	$-0.324745\pi$
$11$	4.25890	−	0.674543i	1.28411	−	0.203382i	0.760926	+	0.648839i	$0.224745\pi$
$12$		0			0
$13$	−4.47477	−	2.28001i	−1.24108	−	0.632361i	−0.294753	−	0.955574i	$-0.595237\pi$
$13$	−4.47477	−	2.28001i	−1.24108	−	0.632361i	−0.946327	+	0.323212i	$0.895237\pi$
$14$	0.702007	+	0.702007i	0.187619	+	0.187619i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	0.916094	+	5.78399i	0.222186	+	1.40282i	0.806470	+	0.591275i	$0.201375\pi$
$17$	0.916094	+	5.78399i	0.222186	+	1.40282i	−0.584284	+	0.811549i	$0.698625\pi$
$18$		0			0
$19$	2.19158	−	1.11666i	0.502782	−	0.256180i	−0.184155	−	0.982897i	$-0.558955\pi$
$19$	2.19158	−	1.11666i	0.502782	−	0.256180i	0.686937	+	0.726717i	$0.258955\pi$
$20$	2.21431	+	0.719473i	0.495135	+	0.160879i
$21$		0			0
$22$	3.84201	−	1.95760i	0.819119	−	0.417362i
$23$	1.44482	+	4.44671i	0.301267	+	0.927203i	0.981044	+	0.193785i	$0.0620764\pi$
$23$	1.44482	+	4.44671i	0.301267	+	0.927203i	−0.679777	+	0.733418i	$0.737924\pi$
$24$		0			0
$25$	−0.130038	+	0.400217i	−0.0260076	+	0.0800433i
$26$	−4.96033	−	0.785638i	−0.972800	−	0.154076i
$27$		0			0
$28$	0.884580	+	0.450716i	0.167170	+	0.0851773i
$29$	0.443776	−	2.80189i	0.0824070	−	0.520298i	−0.911609	−	0.411059i	$-0.865159\pi$
$29$	0.443776	−	2.80189i	0.0824070	−	0.520298i	0.994016	−	0.109238i	$-0.0348411\pi$
$30$		0			0
$31$	0.852603	+	0.619452i	0.153132	+	0.111257i	0.661713	−	0.749757i	$-0.269830\pi$
$31$	0.852603	+	0.619452i	0.153132	+	0.111257i	−0.508581	+	0.861014i	$0.669830\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	2.65861	+	5.21781i	0.455948	+	0.894848i
$35$	−1.04939	+	2.05954i	−0.177379	+	0.348125i
$36$		0			0
$37$	−6.22236	+	4.52081i	−1.02295	+	0.743216i	−0.966885	−	0.255211i	$-0.917855\pi$
$37$	−6.22236	+	4.52081i	−1.02295	+	0.743216i	−0.0560636	+	0.998427i	$0.517855\pi$
$38$	1.73925	−	1.73925i	0.282143	−	0.282143i
$39$		0			0
$40$	2.32826			0.368131
$41$	6.23226	−	1.46935i	0.973315	−	0.229474i
$41$	6.23226	−	1.46935i	0.973315	−	0.229474i
$42$		0			0
$43$	−3.34734	+	1.08762i	−0.510464	+	0.165860i	−0.552913	−	0.833239i	$-0.686484\pi$
$43$	−3.34734	+	1.08762i	−0.510464	+	0.165860i	0.0424490	+	0.999099i	$0.486484\pi$
$44$	3.04904	−	3.04904i	0.459659	−	0.459659i
$45$		0			0
$46$	2.74822	+	3.78260i	0.405203	+	0.557714i
$47$	−0.455717	+	0.894395i	−0.0664731	+	0.130461i	−0.921852	−	0.387542i	$-0.873324\pi$
$47$	−0.455717	+	0.894395i	−0.0664731	+	0.130461i	0.855379	+	0.518003i	$0.173324\pi$
$48$		0			0
$49$	3.53516	−	4.86573i	0.505023	−	0.695104i
$50$			0.420813i			0.0595119i
$51$		0			0
$52$	−4.96033	+	0.785638i	−0.687873	+	0.108948i
$53$	1.03993	−	6.56584i	0.142845	−	0.901887i	−0.807314	−	0.590122i	$-0.799080\pi$
$53$	1.03993	−	6.56584i	0.142845	−	0.901887i	0.950159	−	0.311765i	$-0.100920\pi$
$54$		0			0
$55$	7.09896	+	7.09896i	0.957223	+	0.957223i
$56$	0.980565	+	0.155306i	0.131033	+	0.0207537i
$57$		0			0
$58$	−0.443776	−	2.80189i	−0.0582706	−	0.367906i
$59$	−3.12046	−	9.60379i	−0.406249	−	1.25031i	−0.919848	−	0.392276i	$-0.871688\pi$
$59$	−3.12046	−	9.60379i	−0.406249	−	1.25031i	0.513598	−	0.858031i	$-0.328312\pi$
$60$		0			0
$61$	9.07026	+	2.94711i	1.16133	+	0.377338i	0.825399	−	0.564549i	$-0.190950\pi$
$61$	9.07026	+	2.94711i	1.16133	+	0.377338i	0.335928	+	0.941888i	$0.390950\pi$
$62$	1.00229	+	0.325665i	0.127292	+	0.0413595i
$63$		0			0
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−1.82917	−	11.5489i	−0.226881	−	1.43247i
$66$		0			0
$67$	−8.47486	−	1.34229i	−1.03537	−	0.163986i	−0.384459	−	0.923142i	$-0.625612\pi$
$67$	−8.47486	−	1.34229i	−1.03537	−	0.163986i	−0.650909	+	0.759156i	$0.725612\pi$
$68$	4.14088	+	4.14088i	0.502156	+	0.502156i
$69$		0			0
$70$	−0.361594	+	2.28301i	−0.0432187	+	0.272872i
$71$	−13.7194	+	2.17295i	−1.62820	+	0.257881i	−0.902677	−	0.430319i	$-0.858401\pi$
$71$	−13.7194	+	2.17295i	−1.62820	+	0.257881i	−0.725521	+	0.688200i	$0.758401\pi$
$72$		0			0
$73$		−	13.5640i		−	1.58755i	−0.608210	−	0.793776i	$-0.708112\pi$
$73$		−	13.5640i		−	1.58755i	0.608210	−	0.793776i	$-0.291888\pi$
$74$	−4.52081	+	6.22236i	−0.525533	+	0.723334i
$75$		0			0
$76$	1.11666	−	2.19158i	0.128090	−	0.251391i
$77$	2.51624	+	3.46331i	0.286752	+	0.394681i
$78$		0			0
$79$	−1.80575	+	1.80575i	−0.203163	+	0.203163i	−0.801354	−	0.598191i	$-0.795886\pi$
$79$	−1.80575	+	1.80575i	−0.203163	+	0.203163i	0.598191	+	0.801354i	$0.295886\pi$
$80$	2.21431	−	0.719473i	0.247567	−	0.0804395i
$81$		0			0
$82$	5.47317	−	3.32331i	0.604411	−	0.366998i
$83$	−11.3789			−1.24900			−0.624501	−	0.781024i	$-0.714698\pi$
$83$	−11.3789			−1.24900			−0.624501	+	0.781024i	$0.714698\pi$
$84$		0			0
$85$	−9.64106	+	9.64106i	−1.04572	+	1.04572i
$86$	−2.84742	+	2.06877i	−0.307045	+	0.223081i
$87$		0			0
$88$	1.95760	−	3.84201i	0.208681	−	0.409559i
$89$	0.955171	+	1.87463i	0.101248	+	0.198710i	0.936074	−	0.351804i	$-0.114432\pi$
$89$	0.955171	+	1.87463i	0.101248	+	0.198710i	−0.834826	+	0.550514i	$0.814432\pi$
$90$		0			0
$91$		−	4.98594i		−	0.522668i
$92$	3.78260	+	2.74822i	0.394363	+	0.286522i
$93$		0			0
$94$	−0.157029	+	0.991444i	−0.0161963	+	0.102260i
$95$	5.10257	+	2.59989i	0.523513	+	0.266743i
$96$		0			0
$97$	−8.01558	−	1.26954i	−0.813859	−	0.128903i	−0.264389	−	0.964416i	$-0.585170\pi$
$97$	−8.01558	−	1.26954i	−0.813859	−	0.128903i	−0.549470	+	0.835513i	$0.685170\pi$
$98$	1.85854	−	5.72001i	0.187741	−	0.577808i
$99$		0			0
$100$	0.130038	+	0.400217i	0.0130038	+	0.0400217i
$101$	8.17612	−	4.16594i	0.813554	−	0.414527i	0.00285973	−	0.999996i	$-0.499090\pi$
$101$	8.17612	−	4.16594i	0.813554	−	0.414527i	0.810695	+	0.585469i	$0.199090\pi$
$102$		0			0
$103$	9.57271	+	3.11036i	0.943227	+	0.306473i	0.739960	−	0.672651i	$-0.234844\pi$
$103$	9.57271	+	3.11036i	0.943227	+	0.306473i	0.203266	+	0.979123i	$0.434844\pi$
$104$	−4.47477	+	2.28001i	−0.438788	+	0.223574i
$105$		0			0
$106$	−1.03993	−	6.56584i	−0.101007	−	0.637731i
$107$	−3.25632	+	10.0219i	−0.314800	+	0.968856i	0.661036	+	0.750354i	$0.270117\pi$
$107$	−3.25632	+	10.0219i	−0.314800	+	0.968856i	−0.975837	+	0.218502i	$0.929883\pi$
$108$		0			0
$109$	−8.82994	−	8.82994i	−0.845755	−	0.845755i	0.143845	−	0.989600i	$-0.454053\pi$
$109$	−8.82994	−	8.82994i	−0.845755	−	0.845755i	−0.989600	+	0.143845i	$0.954053\pi$
$110$	8.94521	+	4.55781i	0.852892	+	0.434570i
$111$		0			0
$112$	0.980565	−	0.155306i	0.0926547	−	0.0146751i
$113$	2.19349	+	1.59366i	0.206346	+	0.149919i	0.686159	−	0.727452i	$-0.259295\pi$
$113$	2.19349	+	1.59366i	0.206346	+	0.149919i	−0.479813	+	0.877371i	$0.659295\pi$
$114$		0			0
$115$	−6.39858	+	8.80689i	−0.596670	+	0.821246i
$116$	−1.28789	−	2.52762i	−0.119577	−	0.234684i
$117$		0			0
$118$	−5.93547	−	8.16947i	−0.546404	−	0.752061i
$119$	−4.70351	+	3.41730i	−0.431170	+	0.313263i
$120$		0			0
$121$	7.22159	−	2.34644i	0.656508	−	0.213313i
$122$	9.53703			0.863443
$123$		0			0
$124$	1.05388			0.0946408
$125$	10.1397	−	3.29460i	0.906926	−	0.294678i
$126$		0			0
$127$	−15.4232	+	11.2056i	−1.36858	+	0.994334i	−0.370737	+	0.928738i	$0.620895\pi$
$127$	−15.4232	+	11.2056i	−1.36858	+	0.994334i	−0.997846	+	0.0655963i	$0.979105\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$		0			0
$130$	−5.30847	−	10.4185i	−0.465583	−	0.913759i
$131$	−9.92289	+	13.6577i	−0.866967	+	1.19328i	0.112896	+	0.993607i	$0.463987\pi$
$131$	−9.92289	+	13.6577i	−0.866967	+	1.19328i	−0.979863	+	0.199671i	$0.936013\pi$
$132$		0			0
$133$	1.97556	+	1.43533i	0.171303	+	0.124459i
$134$	−8.47486	+	1.34229i	−0.732116	+	0.115956i
$135$		0			0
$136$	5.21781	+	2.65861i	0.447424	+	0.227974i
$137$	0.678124	+	0.678124i	0.0579361	+	0.0579361i	0.735481	−	0.677545i	$-0.236956\pi$
$137$	0.678124	+	0.678124i	0.0579361	+	0.0579361i	−0.677545	+	0.735481i	$0.736956\pi$
$138$		0			0
$139$	3.32957	−	10.2474i	0.282411	−	0.869171i	−0.704752	−	0.709454i	$-0.748942\pi$
$139$	3.32957	−	10.2474i	0.282411	−	0.869171i	0.987163	−	0.159717i	$-0.0510582\pi$
$140$	0.361594	+	2.28301i	0.0305603	+	0.192950i
$141$		0			0
$142$	−12.3765	+	6.30613i	−1.03861	+	0.529199i
$143$	−20.5956	−	6.69191i	−1.72229	−	0.559606i
$144$		0			0
$145$	5.88497	−	2.99854i	0.488720	−	0.249015i
$146$	−4.19152	−	12.9002i	−0.346893	−	1.06763i
$147$		0			0
$148$	−2.37673	+	7.31482i	−0.195366	+	0.601274i
$149$	−22.5985	−	3.57925i	−1.85134	−	0.293223i	−0.871110	−	0.491087i	$-0.836600\pi$
$149$	−22.5985	−	3.57925i	−1.85134	−	0.293223i	−0.980230	+	0.197864i	$0.936600\pi$
$150$		0			0
$151$	−13.5715	−	6.91504i	−1.10444	−	0.562738i	−0.195933	−	0.980617i	$-0.562773\pi$
$151$	−13.5715	−	6.91504i	−1.10444	−	0.562738i	−0.908502	+	0.417879i	$0.862773\pi$
$152$	0.384776	−	2.42938i	0.0312095	−	0.197049i
$153$		0			0
$154$	3.46331	+	2.51624i	0.279082	+	0.202765i
$155$			2.45370i			0.197086i
$156$		0			0
$157$	−0.857457	−	1.68285i	−0.0684325	−	0.134306i	0.854256	−	0.519852i	$-0.174013\pi$
$157$	−0.857457	−	1.68285i	−0.0684325	−	0.134306i	−0.922689	+	0.385546i	$0.874013\pi$
$158$	−1.15936	+	2.27538i	−0.0922339	+	0.181019i
$159$		0			0
$160$	1.88361	−	1.36852i	0.148912	−	0.108191i
$161$	−3.28227	+	3.28227i	−0.258679	+	0.258679i
$162$		0			0
$163$	−0.0414919			−0.00324990			−0.00162495	−	0.999999i	$-0.500517\pi$
$163$	−0.0414919			−0.00324990			−0.00162495	+	0.999999i	$0.500517\pi$
$164$	4.17834	−	4.85196i	0.326273	−	0.378874i
$165$		0			0
$166$	−10.8220	+	3.51629i	−0.839952	+	0.272917i
$167$	9.78990	−	9.78990i	0.757565	−	0.757565i	−0.218314	−	0.975879i	$-0.570056\pi$
$167$	9.78990	−	9.78990i	0.757565	−	0.757565i	0.975879	+	0.218314i	$0.0700556\pi$
$168$		0			0
$169$	7.18395	+	9.88786i	0.552611	+	0.760604i
$170$	−6.18994	+	12.1484i	−0.474747	+	0.931744i
$171$		0			0
$172$	−2.06877	+	2.84742i	−0.157742	+	0.217113i
$173$			10.3524i			0.787077i	0.919308	+	0.393539i	$0.128749\pi$
$173$			10.3524i			0.787077i	−0.919308	+	0.393539i	$0.871251\pi$
$174$		0			0
$175$	−0.412634	+	0.0653548i	−0.0311922	+	0.00494036i
$176$	0.674543	−	4.25890i	0.0508456	−	0.321027i
$177$		0			0
$178$	1.48771	+	1.48771i	0.111509	+	0.111509i
$179$	19.9976	+	3.16732i	1.49469	+	0.236736i	0.849625	−	0.527388i	$-0.176828\pi$
$179$	19.9976	+	3.16732i	1.49469	+	0.236736i	0.645069	+	0.764124i	$0.276828\pi$
$180$		0			0
$181$	−1.62559	−	10.2636i	−0.120829	−	0.762886i	−0.971474	−	0.237146i	$-0.923788\pi$
$181$	−1.62559	−	10.2636i	−0.120829	−	0.762886i	0.850645	−	0.525741i	$-0.176212\pi$
$182$	−1.54074	−	4.74191i	−0.114207	−	0.351493i
$183$		0			0
$184$	4.44671	+	1.44482i	0.327816	+	0.106514i
$185$	−17.0308	−	5.53365i	−1.25213	−	0.406842i
$186$		0			0
$187$	7.80311	+	24.0155i	0.570620	+	1.75619i
$188$	0.157029	+	0.991444i	0.0114525	+	0.0723085i
$189$		0			0
$190$	5.65624	+	0.895861i	0.410347	+	0.0649926i
$191$	−6.75572	−	6.75572i	−0.488827	−	0.488827i	0.419109	−	0.907936i	$-0.362342\pi$
$191$	−6.75572	−	6.75572i	−0.488827	−	0.488827i	−0.907936	+	0.419109i	$0.862342\pi$
$192$		0			0
$193$	2.84547	−	17.9656i	0.204821	−	1.29319i	−0.644210	−	0.764849i	$-0.722814\pi$
$193$	2.84547	−	17.9656i	0.204821	−	1.29319i	0.849031	−	0.528342i	$-0.177186\pi$
$194$	−8.01558	+	1.26954i	−0.575485	+	0.0911479i
$195$		0			0
$196$		−	6.01437i		−	0.429598i
$197$	−6.31935	+	8.69785i	−0.450235	+	0.619696i	−0.972448	−	0.233119i	$-0.925107\pi$
$197$	−6.31935	+	8.69785i	−0.450235	+	0.619696i	0.522213	+	0.852815i	$0.325107\pi$
$198$		0			0
$199$	−3.26081	+	6.39969i	−0.231152	+	0.453662i	−0.977226	−	0.212201i	$-0.931937\pi$
$199$	−3.26081	+	6.39969i	−0.231152	+	0.453662i	0.746073	+	0.665864i	$0.231937\pi$
$200$	0.247347	+	0.340444i	0.0174901	+	0.0240731i
$201$		0			0
$202$	6.48861	−	6.48861i	0.456537	−	0.456537i
$203$	2.67851	−	0.870301i	0.187995	−	0.0610832i
$204$		0			0
$205$	11.2966	+	9.72827i	0.788991	+	0.679452i
$206$	10.0653			0.701285
$207$		0			0
$208$	−3.55120	+	3.55120i	−0.246232	+	0.246232i
$209$	8.58047	−	6.23408i	0.593523	−	0.431220i
$210$		0			0
$211$	9.63714	−	18.9139i	0.663448	−	1.30209i	−0.276579	−	0.960991i	$-0.589201\pi$
$211$	9.63714	−	18.9139i	0.663448	−	1.30209i	0.940027	−	0.341099i	$-0.110799\pi$
$212$	−3.01798	−	5.92313i	−0.207276	−	0.406802i
$213$		0			0
$214$			10.5377i			0.720341i
$215$	−6.62954	−	4.81664i	−0.452131	−	0.328492i
$216$		0			0
$217$	−0.163673	+	1.03339i	−0.0111109	+	0.0701513i
$218$	−11.1264	−	5.66917i	−0.753573	−	0.383965i
$219$		0			0
$220$	9.91584	+	1.57051i	0.668526	+	0.105884i
$221$	9.08825	−	27.9708i	0.611342	−	1.88152i
$222$		0			0
$223$	2.54840	+	7.84318i	0.170654	+	0.525218i	0.999408	−	0.0343941i	$-0.0109502\pi$
$223$	2.54840	+	7.84318i	0.170654	+	0.525218i	−0.828755	+	0.559612i	$0.810950\pi$
$224$	0.884580	−	0.450716i	0.0591035	−	0.0301147i
$225$		0			0
$226$	2.57860	+	0.837838i	0.171526	+	0.0557322i
$227$	13.7591	−	7.01060i	0.913222	−	0.465310i	0.0667662	−	0.997769i	$-0.478732\pi$
$227$	13.7591	−	7.01060i	0.913222	−	0.465310i	0.846456	+	0.532459i	$0.178732\pi$
$228$		0			0
$229$	−1.78572	−	11.2746i	−0.118004	−	0.745045i	−0.973745	−	0.227641i	$-0.926899\pi$
$229$	−1.78572	−	11.2746i	−0.118004	−	0.745045i	0.855741	−	0.517404i	$-0.173101\pi$
$230$	−3.36393	+	10.3531i	−0.221811	+	0.682664i
$231$		0			0
$232$	−2.00593	−	2.00593i	−0.131696	−	0.131696i
$233$	2.09832	+	1.06915i	0.137466	+	0.0700423i	0.521371	−	0.853330i	$-0.325421\pi$
$233$	2.09832	+	1.06915i	0.137466	+	0.0700423i	−0.383905	+	0.923373i	$0.625421\pi$
$234$		0			0
$235$	−2.30834	+	0.365606i	−0.150580	+	0.0238495i
$236$	−8.16947	−	5.93547i	−0.531787	−	0.386366i
$237$		0			0
$238$	−3.41730	+	4.70351i	−0.221511	+	0.304883i
$239$	−1.59102	−	3.12254i	−0.102914	−	0.201981i	0.833808	−	0.552055i	$-0.186156\pi$
$239$	−1.59102	−	3.12254i	−0.102914	−	0.201981i	−0.936722	+	0.350075i	$0.886156\pi$
$240$		0			0
$241$	13.5141	+	18.6006i	0.870519	+	1.19817i	0.978958	+	0.204064i	$0.0654150\pi$
$241$	13.5141	+	18.6006i	0.870519	+	1.19817i	−0.108438	+	0.994103i	$0.534585\pi$
$242$	6.14305	−	4.46319i	0.394890	−	0.286905i
$243$		0			0
$244$	9.07026	−	2.94711i	0.580664	−	0.188669i
$245$	14.0030			0.894622
$246$		0			0
$247$	−12.3528			−0.785991
$248$	1.00229	−	0.325665i	0.0636458	−	0.0206798i
$249$		0			0
$250$	8.62538	−	6.26671i	0.545517	−	0.396341i
$251$	1.76548	+	2.42998i	0.111436	+	0.153379i	0.861092	−	0.508449i	$-0.169781\pi$
$251$	1.76548	+	2.42998i	0.111436	+	0.153379i	−0.749656	+	0.661828i	$0.769781\pi$
$252$		0			0
$253$	9.15286	+	17.9635i	0.575435	+	1.12936i
$254$	−11.2056	+	15.4232i	−0.703100	+	0.967735i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−17.1367	+	2.71419i	−1.06896	+	0.169306i	−0.666030	−	0.745925i	$-0.732008\pi$
$257$	−17.1367	+	2.71419i	−1.06896	+	0.169306i	−0.402928	+	0.915232i	$0.632008\pi$
$258$		0			0
$259$	−6.80353	−	3.46657i	−0.422751	−	0.215402i
$260$	−8.26813	−	8.26813i	−0.512768	−	0.512768i
$261$		0			0
$262$	−5.21677	+	16.0556i	−0.322293	+	0.991917i
$263$	0.433028	+	2.73403i	0.0267016	+	0.168587i	0.997436	−	0.0715700i	$-0.0228009\pi$
$263$	0.433028	+	2.73403i	0.0267016	+	0.168587i	−0.970734	+	0.240157i	$0.922801\pi$
$264$		0			0
$265$	13.7906	−	7.02666i	0.847150	−	0.431645i
$266$	2.32241	+	0.754596i	0.142396	+	0.0462673i
$267$		0			0
$268$	−7.64528	+	3.89546i	−0.467010	+	0.237953i
$269$	9.26317	+	28.5091i	0.564785	+	1.73823i	0.668589	+	0.743633i	$0.266899\pi$
$269$	9.26317	+	28.5091i	0.564785	+	1.73823i	−0.103803	+	0.994598i	$0.533101\pi$
$270$		0			0
$271$	−3.66697	+	11.2858i	−0.222753	+	0.685562i	0.775759	+	0.631029i	$0.217367\pi$
$271$	−3.66697	+	11.2858i	−0.222753	+	0.685562i	−0.998512	+	0.0545333i	$0.982633\pi$
$272$	5.78399	+	0.916094i	0.350706	+	0.0555464i
$273$		0			0
$274$	0.854486	+	0.435382i	0.0516214	+	0.0263024i
$275$	−0.283856	+	1.79220i	−0.0171172	+	0.108074i
$276$		0			0
$277$	−22.8922	−	16.6321i	−1.37546	−	0.999329i	−0.997288	−	0.0735928i	$-0.976553\pi$
$277$	−22.8922	−	16.6321i	−1.37546	−	0.999329i	−0.378170	−	0.925736i	$-0.623447\pi$
$278$		−	10.7747i		−	0.646225i
$279$		0			0
$280$	1.04939	+	2.05954i	0.0627128	+	0.123081i
$281$	−4.40260	+	8.64059i	−0.262637	+	0.515455i	−0.984237	−	0.176856i	$-0.943407\pi$
$281$	−4.40260	+	8.64059i	−0.262637	+	0.515455i	0.721599	+	0.692311i	$0.243407\pi$
$282$		0			0
$283$	11.7063	−	8.50511i	0.695866	−	0.505577i	−0.182717	−	0.983166i	$-0.558489\pi$
$283$	11.7063	−	8.50511i	0.695866	−	0.505577i	0.878583	+	0.477589i	$0.158489\pi$
$284$	−9.82204	+	9.82204i	−0.582831	+	0.582831i
$285$		0			0
$286$	−21.6555			−1.28052
$287$	4.10874	+	4.85067i	0.242531	+	0.286326i
$288$		0			0
$289$	−16.4474	+	5.34408i	−0.967493	+	0.314357i
$290$	4.67034	−	4.67034i	0.274252	−	0.274252i
$291$		0			0
$292$	−7.97275	−	10.9735i	−0.466570	−	0.642178i
$293$	1.00370	−	1.96987i	0.0586367	−	0.115081i	−0.859828	−	0.510583i	$-0.829429\pi$
$293$	1.00370	−	1.96987i	0.0586367	−	0.115081i	0.918465	+	0.395502i	$0.129429\pi$
$294$		0			0
$295$	13.8193	−	19.0207i	0.804593	−	1.10743i
$296$			7.69125i			0.447045i
$297$		0			0
$298$	−22.5985	+	3.57925i	−1.30909	+	0.207340i
$299$	3.67329	−	23.1922i	0.212432	−	1.34124i
$300$		0			0
$301$	−2.47078	−	2.47078i	−0.142414	−	0.142414i
$302$	−15.0442	−	2.38276i	−0.865694	−	0.137112i
$303$		0			0
$304$	−0.384776	−	2.42938i	−0.0220684	−	0.139335i
$305$	6.86164	+	21.1180i	0.392896	+	1.20921i
$306$		0			0
$307$	9.75421	+	3.16933i	0.556702	+	0.180883i	0.573837	−	0.818970i	$-0.305454\pi$
$307$	9.75421	+	3.16933i	0.556702	+	0.180883i	−0.0171347	+	0.999853i	$0.505454\pi$
$308$	4.07137	+	1.32287i	0.231988	+	0.0753773i
$309$		0			0
$310$	0.758235	+	2.33361i	0.0430649	+	0.132540i
$311$	2.10285	+	13.2769i	0.119242	+	0.752862i	0.972763	+	0.231804i	$0.0744627\pi$
$311$	2.10285	+	13.2769i	0.119242	+	0.752862i	−0.853521	+	0.521059i	$0.825537\pi$
$312$		0			0
$313$	31.7580	+	5.02997i	1.79507	+	0.284311i	0.962830	−	0.270107i	$-0.0870592\pi$
$313$	31.7580	+	5.02997i	1.79507	+	0.284311i	0.832238	+	0.554418i	$0.187059\pi$
$314$	−1.33552	−	1.33552i	−0.0753678	−	0.0753678i
$315$		0			0
$316$	−0.399489	+	2.52227i	−0.0224730	+	0.141889i
$317$	33.7377	−	5.34352i	1.89490	−	0.300122i	0.903251	−	0.429112i	$-0.141173\pi$
$317$	33.7377	−	5.34352i	1.89490	−	0.300122i	0.991646	+	0.128989i	$0.0411734\pi$
$318$		0			0
$319$		−	12.2323i		−	0.684878i
$320$	1.36852	−	1.88361i	0.0765025	−	0.105297i
$321$		0			0
$322$	−2.10735	+	4.13590i	−0.117438	+	0.230485i
$323$	8.46647	+	11.6531i	0.471087	+	0.648396i
$324$		0			0
$325$	1.49439	−	1.49439i	0.0828938	−	0.0828938i
$326$	−0.0394612	+	0.0128217i	−0.00218555	+	0.000710129i
$327$		0			0
$328$	2.47450	−	5.90566i	0.136631	−	0.326086i
$329$	−0.996563			−0.0549423
$330$		0			0
$331$	−18.9893	+	18.9893i	−1.04374	+	1.04374i	−0.0447463	+	0.998998i	$0.514248\pi$
$331$	−18.9893	+	18.9893i	−1.04374	+	1.04374i	−0.998998	+	0.0447463i	$0.985752\pi$
$332$	−9.20576	+	6.68838i	−0.505232	+	0.367072i
$333$		0			0
$334$	6.28550	−	12.3360i	0.343927	−	0.674995i
$335$	−9.06967	−	17.8002i	−0.495529	−	0.972530i
$336$		0			0
$337$		−	26.6494i		−	1.45169i	−0.687859	−	0.725844i	$-0.741449\pi$
$337$		−	26.6494i		−	1.45169i	0.687859	−	0.725844i	$-0.258551\pi$
$338$	9.88786	+	7.18395i	0.537828	+	0.390755i
$339$		0			0
$340$	−2.13291	+	13.4667i	−0.115673	+	0.730332i
$341$	4.04900	+	2.06307i	0.219266	+	0.111721i
$342$		0			0
$343$	12.7614	+	2.02121i	0.689053	+	0.109135i
$344$	−1.08762	+	3.34734i	−0.0586403	+	0.180476i
$345$		0			0
$346$	3.19906	+	9.84570i	0.171983	+	0.529308i
$347$	26.8294	−	13.6702i	1.44028	−	0.733857i	0.452797	−	0.891613i	$-0.350426\pi$
$347$	26.8294	−	13.6702i	1.44028	−	0.733857i	0.987478	+	0.157756i	$0.0504261\pi$
$348$		0			0
$349$	11.9046	+	3.86803i	0.637238	+	0.207051i	0.609779	−	0.792572i	$-0.291258\pi$
$349$	11.9046	+	3.86803i	0.637238	+	0.207051i	0.0274592	+	0.999623i	$0.491258\pi$
$350$	−0.372242	+	0.189667i	−0.0198972	+	0.0101381i
$351$		0			0
$352$	−0.674543	−	4.25890i	−0.0359533	−	0.227000i
$353$	−4.72931	+	14.5553i	−0.251716	+	0.774702i	0.742743	+	0.669576i	$0.233524\pi$
$353$	−4.72931	+	14.5553i	−0.251716	+	0.774702i	−0.994459	+	0.105125i	$0.966476\pi$
$354$		0			0
$355$	−22.8683	−	22.8683i	−1.21372	−	1.21372i
$356$	1.87463	+	0.955171i	0.0993551	+	0.0506239i
$357$		0			0
$358$	19.9976	−	3.16732i	1.05691	−	0.167398i
$359$	12.8914	+	9.36611i	0.680379	+	0.494325i	0.873484	−	0.486854i	$-0.161855\pi$
$359$	12.8914	+	9.36611i	0.680379	+	0.494325i	−0.193104	+	0.981178i	$0.561855\pi$
$360$		0			0
$361$	−7.61185	+	10.4768i	−0.400624	+	0.551411i
$362$	−4.71765	−	9.25892i	−0.247954	−	0.486638i
$363$		0			0
$364$	−2.93066	−	4.03371i	−0.153608	−	0.211424i
$365$	25.5493	−	18.5627i	1.33731	−	0.971614i
$366$		0			0
$367$	−20.2592	+	6.58260i	−1.05752	+	0.343609i	−0.785615	−	0.618715i	$-0.787653\pi$
$367$	−20.2592	+	6.58260i	−1.05752	+	0.343609i	−0.271904	+	0.962324i	$0.587653\pi$
$368$	4.67555			0.243730
$369$		0			0
$370$	−17.9073			−0.930955
$371$	6.27672	−	2.03943i	0.325871	−	0.105882i
$372$		0			0
$373$	28.0860	−	20.4057i	1.45424	−	1.05657i	0.469420	−	0.882975i	$-0.344463\pi$
$373$	28.0860	−	20.4057i	1.45424	−	1.05657i	0.984818	−	0.173591i	$-0.0555370\pi$
$374$	14.8424	+	20.4288i	0.767482	+	1.05635i
$375$		0			0
$376$	0.455717	+	0.894395i	0.0235018	+	0.0461249i
$377$	−8.37413	+	11.5260i	−0.431290	+	0.593620i
$378$		0			0
$379$	9.84247	+	7.15098i	0.505574	+	0.367321i	0.811142	−	0.584849i	$-0.198846\pi$
$379$	9.84247	+	7.15098i	0.505574	+	0.367321i	−0.305568	+	0.952170i	$0.598846\pi$
$380$	5.65624	−	0.895861i	0.290159	−	0.0459567i
$381$		0			0
$382$	−8.51271	−	4.33744i	−0.435548	−	0.221923i
$383$	−10.2831	−	10.2831i	−0.525444	−	0.525444i	0.393767	−	0.919210i	$-0.371172\pi$
$383$	−10.2831	−	10.2831i	−0.525444	−	0.525444i	−0.919210	+	0.393767i	$0.871172\pi$
$384$		0			0
$385$	−3.07998	+	9.47921i	−0.156970	+	0.483105i
$386$	−2.84547	−	17.9656i	−0.144831	−	0.914424i
$387$		0			0
$388$	−7.23096	+	3.68436i	−0.367096	+	0.187045i
$389$	−25.9162	−	8.42068i	−1.31400	−	0.426945i	−0.433571	−	0.901119i	$-0.642747\pi$
$389$	−25.9162	−	8.42068i	−1.31400	−	0.426945i	−0.880431	+	0.474174i	$0.842747\pi$
$390$		0			0
$391$	−24.3961	+	12.4305i	−1.23377	+	0.628635i
$392$	−1.85854	−	5.72001i	−0.0938706	−	0.288904i
$393$		0			0
$394$	−3.32228	+	10.2249i	−0.167374	+	0.515125i
$395$	−5.87252	−	0.930116i	−0.295479	−	0.0467992i
$396$		0			0
$397$	18.1916	+	9.26906i	0.913008	+	0.465201i	0.846381	−	0.532577i	$-0.178776\pi$
$397$	18.1916	+	9.26906i	0.913008	+	0.465201i	0.0666266	+	0.997778i	$0.478776\pi$
$398$	−1.12360	+	7.09412i	−0.0563209	+	0.355596i
$399$		0			0
$400$	0.340444	+	0.247347i	0.0170222	+	0.0123674i
$401$		−	17.8463i		−	0.891203i	−0.895231	−	0.445602i	$-0.852990\pi$
$401$		−	17.8463i		−	0.891203i	0.895231	−	0.445602i	$-0.147010\pi$
$402$		0			0
$403$	−2.40285	−	4.71585i	−0.119694	−	0.234913i
$404$	4.16594	−	8.17612i	0.207263	−	0.406777i
$405$		0			0
$406$	2.27848	−	1.65541i	0.113079	−	0.0821567i
$407$	−23.4509	+	23.4509i	−1.16242	+	1.16242i
$408$		0			0
$409$	32.3127			1.59776			0.798881	−	0.601490i	$-0.205426\pi$
$409$	32.3127			1.59776			0.798881	+	0.601490i	$0.205426\pi$
$410$	13.7499	+	5.76129i	0.679061	+	0.284530i
$411$		0			0
$412$	9.57271	−	3.11036i	0.471613	−	0.153236i
$413$	7.08888	−	7.08888i	0.348821	−	0.348821i
$414$		0			0
$415$	−15.5723	−	21.4334i	−0.764415	−	1.05213i
$416$	−2.28001	+	4.47477i	−0.111787	+	0.219394i
$417$		0			0
$418$	6.23408	−	8.58047i	0.304919	−	0.419684i
$419$			24.6623i			1.20483i	0.798182	+	0.602416i	$0.205795\pi$
$419$			24.6623i			1.20483i	−0.798182	+	0.602416i	$0.794205\pi$
$420$		0			0
$421$	−18.4368	+	2.92010i	−0.898554	+	0.142317i	−0.588590	−	0.808432i	$-0.700317\pi$
$421$	−18.4368	+	2.92010i	−0.898554	+	0.142317i	−0.309963	+	0.950748i	$0.600317\pi$
$422$	3.32073	−	20.9663i	0.161651	−	1.02062i
$423$		0			0
$424$	−4.70062	−	4.70062i	−0.228282	−	0.228282i
$425$	−2.43398	−	0.385504i	−0.118065	−	0.0186997i
$426$		0			0
$427$	1.48116	+	9.35168i	0.0716784	+	0.452560i
$428$	3.25632	+	10.0219i	0.157400	+	0.484428i
$429$		0			0
$430$	−7.79349	−	2.53226i	−0.375835	−	0.122116i
$431$	9.99971	+	3.24910i	0.481669	+	0.156504i	0.539779	−	0.841806i	$-0.318508\pi$
$431$	9.99971	+	3.24910i	0.481669	+	0.156504i	−0.0581106	+	0.998310i	$0.518508\pi$
$432$		0			0
$433$	−8.08586	−	24.8857i	−0.388582	−	1.19593i	−0.933849	−	0.357669i	$-0.883572\pi$
$433$	−8.08586	−	24.8857i	−0.388582	−	1.19593i	0.545267	−	0.838262i	$-0.316428\pi$
$434$	0.163673	+	1.03339i	0.00785657	+	0.0496045i
$435$		0			0
$436$	−12.3337	−	1.95346i	−0.590676	−	0.0935539i
$437$	8.13193	+	8.13193i	0.389003	+	0.389003i
$438$		0			0
$439$	−4.21100	+	26.5872i	−0.200980	+	1.26894i	0.656462	+	0.754359i	$0.272052\pi$
$439$	−4.21100	+	26.5872i	−0.200980	+	1.26894i	−0.857442	+	0.514580i	$0.827948\pi$
$440$	9.91584	−	1.57051i	0.472719	−	0.0748714i
$441$		0			0
$442$		−	29.4102i		−	1.39890i
$443$	6.68819	−	9.20551i	0.317766	−	0.437367i	−0.620018	−	0.784588i	$-0.712875\pi$
$443$	6.68819	−	9.20551i	0.317766	−	0.437367i	0.937783	+	0.347221i	$0.112875\pi$
$444$		0			0
$445$	−2.22389	+	4.36463i	−0.105422	+	0.206903i
$446$	4.84735	+	6.67180i	0.229529	+	0.315919i
$447$		0			0
$448$	0.702007	−	0.702007i	0.0331667	−	0.0331667i
$449$	1.61770	−	0.525624i	0.0763442	−	0.0248057i	−0.270596	−	0.962693i	$-0.587221\pi$
$449$	1.61770	−	0.525624i	0.0763442	−	0.0248057i	0.346940	+	0.937887i	$0.387221\pi$
$450$		0			0
$451$	25.5514	−	10.4617i	1.20317	−	0.492624i
$452$	2.71130			0.127529
$453$		0			0
$454$	10.9193	−	10.9193i	0.512467	−	0.512467i
$455$	9.39153	−	6.82335i	0.440282	−	0.319883i
$456$		0			0
$457$	0.344881	−	0.676866i	0.0161328	−	0.0316625i	−0.882799	−	0.469750i	$-0.844344\pi$
$457$	0.344881	−	0.676866i	0.0161328	−	0.0316625i	0.898932	+	0.438088i	$0.144344\pi$
$458$	−5.18235	−	10.1709i	−0.242156	−	0.475257i
$459$		0			0
$460$			10.8859i			0.507558i
$461$	1.11433	+	0.809608i	0.0518995	+	0.0377072i	0.613433	−	0.789747i	$-0.289788\pi$
$461$	1.11433	+	0.809608i	0.0518995	+	0.0377072i	−0.561533	+	0.827454i	$0.689788\pi$
$462$		0			0
$463$	−0.805040	+	5.08282i	−0.0374134	+	0.236219i	−0.999308	−	0.0372026i	$-0.988155\pi$
$463$	−0.805040	+	5.08282i	−0.0374134	+	0.236219i	0.961894	+	0.273421i	$0.0881553\pi$
$464$	−2.52762	−	1.28789i	−0.117342	−	0.0597886i
$465$		0			0
$466$	2.32601	+	0.368404i	0.107750	+	0.0170660i
$467$	−7.70328	+	23.7083i	−0.356465	+	1.09709i	0.598689	+	0.800981i	$0.295688\pi$
$467$	−7.70328	+	23.7083i	−0.356465	+	1.09709i	−0.955155	+	0.296107i	$0.904312\pi$
$468$		0			0
$469$	−2.63240	−	8.10168i	−0.121553	−	0.374101i
$470$	−2.08239	+	1.06103i	−0.0960534	+	0.0489416i
$471$		0			0
$472$	−9.60379	−	3.12046i	−0.442050	−	0.143631i
$473$	−13.5223	+	6.88997i	−0.621758	+	0.316801i
$474$		0			0
$475$	0.161919	+	1.02231i	0.00742934	+	0.0469070i
$476$	−1.79658	+	5.52930i	−0.0823461	+	0.253435i
$477$		0			0
$478$	−2.47806	−	2.47806i	−0.113344	−	0.113344i
$479$	22.4926	+	11.4606i	1.02771	+	0.523646i	0.884742	−	0.466081i	$-0.154334\pi$
$479$	22.4926	+	11.4606i	1.02771	+	0.523646i	0.142971	+	0.989727i	$0.454334\pi$
$480$		0			0
$481$	38.1511	−	6.04255i	1.73954	−	0.275516i
$482$	18.6006	+	13.5141i	0.847232	+	0.615550i
$483$		0			0
$484$	4.46319	−	6.14305i	0.202872	−	0.279230i
$485$	−8.57816	−	16.8356i	−0.389514	−	0.764465i
$486$		0			0
$487$	18.3828	+	25.3018i	0.833005	+	1.14653i	0.987356	+	0.158517i	$0.0506713\pi$
$487$	18.3828	+	25.3018i	0.833005	+	1.14653i	−0.154351	+	0.988016i	$0.549329\pi$
$488$	7.71562	−	5.60573i	0.349270	−	0.253759i
$489$		0			0
$490$	13.3177	−	4.32718i	0.601632	−	0.195482i
$491$	−11.8927			−0.536710			−0.268355	−	0.963320i	$-0.586480\pi$
$491$	−11.8927			−0.536710			−0.268355	+	0.963320i	$0.586480\pi$
$492$		0			0
$493$	16.6126			0.748196
$494$	−11.7482	+	3.81723i	−0.528578	+	0.171745i
$495$		0			0
$496$	0.852603	−	0.619452i	0.0382830	−	0.0278142i
$497$	−8.10572	−	11.1566i	−0.363591	−	0.500440i
$498$		0			0
$499$	17.6777	+	34.6945i	0.791364	+	1.55314i	0.832526	+	0.553986i	$0.186894\pi$
$499$	17.6777	+	34.6945i	0.791364	+	1.55314i	−0.0411623	+	0.999152i	$0.513106\pi$
$500$	6.26671	−	8.62538i	0.280256	−	0.385739i
$501$		0			0
$502$	2.42998	+	1.76548i	0.108455	+	0.0787973i
$503$	7.68202	−	1.21671i	0.342524	−	0.0542505i	0.0171974	−	0.999852i	$-0.494526\pi$
$503$	7.68202	−	1.21671i	0.342524	−	0.0542505i	0.325327	+	0.945602i	$0.394526\pi$
$504$		0			0
$505$	19.0362	+	9.69941i	0.847098	+	0.431618i
$506$	14.2559	+	14.2559i	0.633753	+	0.633753i
$507$		0			0
$508$	−5.89112	+	18.1310i	−0.261376	+	0.804433i
$509$	−3.38057	−	21.3441i	−0.149841	−	0.946059i	−0.941968	−	0.335703i	$-0.891026\pi$
$509$	−3.38057	−	21.3441i	−0.149841	−	0.946059i	0.792127	−	0.610356i	$-0.208974\pi$
$510$		0			0
$511$	11.9985	−	6.11354i	0.530782	−	0.270447i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$		0			0
$514$	−15.4592	+	7.87688i	−0.681878	+	0.347434i
$515$	7.24174	+	22.2878i	0.319109	+	0.982117i
$516$		0			0
$517$	−1.33754	+	4.11654i	−0.0588251	+	0.181045i
$518$	−7.54177	−	1.19450i	−0.331366	−	0.0524833i
$519$		0			0
$520$	−10.4185	−	5.30847i	−0.456880	−	0.232792i
$521$	3.25864	−	20.5743i	0.142764	−	0.901375i	−0.807486	−	0.589886i	$-0.799173\pi$
$521$	3.25864	−	20.5743i	0.142764	−	0.901375i	0.950250	−	0.311488i	$-0.100827\pi$
$522$		0			0
$523$	5.26281	+	3.82365i	0.230126	+	0.167197i	0.696873	−	0.717194i	$-0.254574\pi$
$523$	5.26281	+	3.82365i	0.230126	+	0.167197i	−0.466747	+	0.884391i	$0.654574\pi$
$524$			16.8818i			0.737486i
$525$		0			0
$526$	1.25670	+	2.46640i	0.0547945	+	0.107540i
$527$	−2.80184	+	5.49893i	−0.122050	+	0.239537i
$528$		0			0
$529$	0.921668	−	0.669631i	0.0400725	−	0.0291144i
$530$	10.9443	−	10.9443i	0.475389	−	0.475389i
$531$		0			0
$532$	2.44192			0.105871
$533$	−31.2381	−	7.63460i	−1.35307	−	0.330691i
$534$		0			0
$535$	−23.3337	+	7.58157i	−1.00880	+	0.327780i
$536$	−6.06733	+	6.06733i	−0.262069	+	0.262069i
$537$		0			0
$538$	17.6196	+	24.2513i	0.759635	+	1.04555i
$539$	11.7737	−	23.1073i	0.507131	−	0.995301i
$540$		0			0
$541$	−4.79036	+	6.59337i	−0.205954	+	0.283471i	−0.899481	−	0.436959i	$-0.856055\pi$
$541$	−4.79036	+	6.59337i	−0.205954	+	0.283471i	0.693528	+	0.720430i	$0.256055\pi$
$542$			11.8666i			0.509713i
$543$		0			0
$544$	5.78399	−	0.916094i	0.247987	−	0.0392772i
$545$	4.54818	−	28.7161i	0.194823	−	1.23006i
$546$		0			0
$547$	−12.7377	−	12.7377i	−0.544627	−	0.544627i	0.380255	−	0.924882i	$-0.375836\pi$
$547$	−12.7377	−	12.7377i	−0.544627	−	0.544627i	−0.924882	+	0.380255i	$0.875836\pi$
$548$	0.947205	+	0.150023i	0.0404626	+	0.00640865i
$549$		0			0
$550$	0.283856	+	1.79220i	0.0121037	+	0.0764196i
$551$	−2.15620	−	6.63610i	−0.0918572	−	0.282708i
$552$		0			0
$553$	−2.41121	−	0.783450i	−0.102535	−	0.0333157i
$554$	−26.9114	−	8.74404i	−1.14336	−	0.371499i
$555$		0			0
$556$	−3.32957	−	10.2474i	−0.141205	−	0.434585i
$557$	1.96184	+	12.3866i	0.0831260	+	0.524837i	0.993752	+	0.111606i	$0.0355996\pi$
$557$	1.96184	+	12.3866i	0.0831260	+	0.524837i	−0.910626	+	0.413230i	$0.864400\pi$
$558$		0			0
$559$	17.4584	+	2.76513i	0.738410	+	0.116953i
$560$	1.63446	+	1.63446i	0.0690684	+	0.0690684i
$561$		0			0
$562$	−1.51703	+	9.57817i	−0.0639922	+	0.404031i
$563$	3.43915	−	0.544707i	0.144943	−	0.0229567i	−0.0835414	−	0.996504i	$-0.526623\pi$
$563$	3.43915	−	0.544707i	0.144943	−	0.0229567i	0.228484	+	0.973548i	$0.426623\pi$
$564$		0			0
$565$			6.31263i			0.265574i
$566$	8.50511	−	11.7063i	0.357497	−	0.492052i
$567$		0			0
$568$	−6.30613	+	12.3765i	−0.264600	+	0.519306i
$569$	24.2202	+	33.3362i	1.01536	+	1.39753i	0.915404	+	0.402536i	$0.131871\pi$
$569$	24.2202	+	33.3362i	1.01536	+	1.39753i	0.0999592	+	0.994992i	$0.468129\pi$
$570$		0			0
$571$	0.620108	−	0.620108i	0.0259507	−	0.0259507i	−0.694012	−	0.719963i	$-0.744159\pi$
$571$	0.620108	−	0.620108i	0.0259507	−	0.0259507i	0.719963	+	0.694012i	$0.244159\pi$
$572$	−20.5956	+	6.69191i	−0.861145	+	0.279803i
$573$		0			0
$574$	5.40658	+	3.34359i	0.225666	+	0.139559i
$575$	−1.96753			−0.0820517
$576$		0			0
$577$	−26.1016	+	26.1016i	−1.08662	+	1.08662i	−0.0907510	+	0.995874i	$0.528927\pi$
$577$	−26.1016	+	26.1016i	−1.08662	+	1.08662i	−0.995874	+	0.0907510i	$0.971073\pi$
$578$	−13.9910	+	10.1650i	−0.581948	+	0.422810i
$579$		0			0
$580$	2.99854	−	5.88497i	0.124508	−	0.244360i
$581$	−5.12868	−	10.0656i	−0.212773	−	0.417591i
$582$		0			0
$583$		−	28.6647i		−	1.18717i
$584$	−10.9735	−	7.97275i	−0.454089	−	0.329915i
$585$		0			0
$586$	0.345851	−	2.18362i	0.0142870	−	0.0902044i
$587$	−32.6183	−	16.6199i	−1.34630	−	0.685975i	−0.375718	−	0.926734i	$-0.622604\pi$
$587$	−32.6183	−	16.6199i	−1.34630	−	0.685975i	−0.970585	+	0.240759i	$0.922604\pi$
$588$		0			0
$589$	2.56027	+	0.405506i	0.105494	+	0.0167086i
$590$	7.26526	−	22.3602i	0.299106	−	0.920553i
$591$		0			0
$592$	2.37673	+	7.31482i	0.0976829	+	0.300637i
$593$	8.19770	−	4.17694i	0.336639	−	0.171526i	−0.277497	−	0.960727i	$-0.589505\pi$
$593$	8.19770	−	4.17694i	0.336639	−	0.171526i	0.614136	+	0.789200i	$0.289505\pi$
$594$		0			0
$595$	−12.8737	−	4.18291i	−0.527769	−	0.171483i
$596$	−20.3864	+	10.3874i	−0.835059	+	0.425484i
$597$		0			0
$598$	−3.67329	−	23.1922i	−0.150212	−	0.948401i
$599$	2.75987	−	8.49400i	0.112765	−	0.347055i	−0.878709	−	0.477357i	$-0.841595\pi$
$599$	2.75987	−	8.49400i	0.112765	−	0.347055i	0.991474	+	0.130302i	$0.0415947\pi$
$600$		0			0
$601$	−12.1900	−	12.1900i	−0.497241	−	0.497241i	0.413337	−	0.910578i	$-0.364363\pi$
$601$	−12.1900	−	12.1900i	−0.497241	−	0.497241i	−0.910578	+	0.413337i	$0.864363\pi$
$602$	−3.11337	−	1.58634i	−0.126891	−	0.0646544i
$603$		0			0
$604$	−15.0442	+	2.38276i	−0.612138	+	0.0969531i
$605$	14.3027	+	10.3915i	0.581485	+	0.422474i
$606$		0			0
$607$	−25.3541	+	34.8969i	−1.02909	+	1.41642i	−0.123462	+	0.992349i	$0.539400\pi$
$607$	−25.3541	+	34.8969i	−1.02909	+	1.41642i	−0.905629	+	0.424072i	$0.860600\pi$
$608$	−1.11666	−	2.19158i	−0.0452867	−	0.0888802i
$609$		0			0
$610$	13.0516	+	17.9640i	0.528444	+	0.727341i
$611$	4.07846	−	2.96318i	0.164997	−	0.119877i
$612$		0			0
$613$	9.22259	−	2.99660i	0.372497	−	0.121032i	−0.116785	−	0.993157i	$-0.537259\pi$
$613$	9.22259	−	2.99660i	0.372497	−	0.121032i	0.489282	+	0.872126i	$0.337259\pi$
$614$	10.2562			0.413906
$615$		0			0
$616$	4.28089			0.172482
$617$	−11.2369	+	3.65109i	−0.452381	+	0.146988i	−0.526341	−	0.850274i	$-0.676436\pi$
$617$	−11.2369	+	3.65109i	−0.452381	+	0.146988i	0.0739597	+	0.997261i	$0.476436\pi$
$618$		0			0
$619$	−23.3929	+	16.9959i	−0.940240	+	0.683124i	−0.948478	−	0.316842i	$-0.897378\pi$
$619$	−23.3929	+	16.9959i	−0.940240	+	0.683124i	0.00823843	+	0.999966i	$0.497378\pi$
$620$	1.44225	+	1.98508i	0.0579221	+	0.0797229i
$621$		0			0
$622$	6.10271	+	11.9772i	0.244696	+	0.480244i
$623$	−1.22775	+	1.68985i	−0.0491887	+	0.0677024i
$624$		0			0
$625$	21.7844	+	15.8273i	0.871375	+	0.633091i
$626$	31.7580	−	5.02997i	1.26931	−	0.201038i
$627$		0			0
$628$	−1.68285	−	0.857457i	−0.0671532	−	0.0342163i
$629$	−31.8486	−	31.8486i	−1.26989	−	1.26989i
$630$		0			0
$631$	0.151484	−	0.466219i	0.00603047	−	0.0185599i	−0.947996	−	0.318282i	$-0.896894\pi$
$631$	0.151484	−	0.466219i	0.00603047	−	0.0185599i	0.954026	+	0.299722i	$0.0968940\pi$
$632$	0.399489	+	2.52227i	0.0158908	+	0.100331i
$633$		0			0
$634$	30.4352	−	15.5075i	1.20874	−	0.615882i
$635$	−42.2138	−	13.7161i	−1.67520	−	0.544306i
$636$		0			0
$637$	−26.9130	+	13.7128i	−1.06633	+	0.543322i
$638$	−3.77999	−	11.6336i	−0.149651	−	0.460579i
$639$		0			0
$640$	0.719473	−	2.21431i	0.0284397	−	0.0875283i
$641$	−28.0664	−	4.44528i	−1.10855	−	0.175578i	−0.424798	−	0.905288i	$-0.639655\pi$
$641$	−28.0664	−	4.44528i	−1.10855	−	0.175578i	−0.683757	+	0.729710i	$0.739655\pi$
$642$		0			0
$643$	−18.4171	−	9.38396i	−0.726298	−	0.370067i	0.0514230	−	0.998677i	$-0.483624\pi$
$643$	−18.4171	−	9.38396i	−0.726298	−	0.370067i	−0.777721	+	0.628610i	$0.783624\pi$
$644$	−0.726142	+	4.58468i	−0.0286140	+	0.180662i
$645$		0			0
$646$	11.6531	+	8.46647i	0.458485	+	0.333109i
$647$			36.2825i			1.42641i	0.700955	+	0.713206i	$0.252758\pi$
$647$			36.2825i			1.42641i	−0.700955	+	0.713206i	$0.747242\pi$
$648$		0			0
$649$	−19.7679	−	38.7967i	−0.775958	−	1.52290i
$650$	0.959457	−	1.88304i	0.0376330	−	0.0738590i
$651$		0			0
$652$	−0.0335677	+	0.0243884i	−0.00131461	+	0.000955122i
$653$	−14.6608	+	14.6608i	−0.573723	+	0.573723i	−0.933167	−	0.359444i	$-0.882966\pi$
$653$	−14.6608	+	14.6608i	−0.573723	+	0.573723i	0.359444	+	0.933167i	$0.382966\pi$
$654$		0			0
$655$	−39.3054			−1.53579
$656$	0.528438	−	6.38128i	0.0206320	−	0.249147i
$657$		0			0
$658$	−0.947788	+	0.307955i	−0.0369486	+	0.0120053i
$659$	−33.0322	+	33.0322i	−1.28675	+	1.28675i	−0.350005	+	0.936748i	$0.613820\pi$
$659$	−33.0322	+	33.0322i	−1.28675	+	1.28675i	−0.936748	+	0.350005i	$0.886180\pi$
$660$		0			0
$661$	−11.0162	−	15.1624i	−0.428479	−	0.589751i	0.539124	−	0.842226i	$-0.318755\pi$
$661$	−11.0162	−	15.1624i	−0.428479	−	0.589751i	−0.967603	+	0.252476i	$0.918755\pi$
$662$	−12.1919	+	23.9279i	−0.473850	+	0.929983i
$663$		0			0
$664$	−6.68838	+	9.20576i	−0.259559	+	0.357253i
$665$			5.68544i			0.220472i
$666$		0			0
$667$	13.1004	−	2.07489i	0.507248	−	0.0803402i
$668$	2.16584	−	13.6745i	0.0837987	−	0.529084i
$669$		0			0
$670$	−14.1263	−	14.1263i	−0.545748	−	0.545748i
$671$	40.6173	+	6.43314i	1.56801	+	0.248349i
$672$		0			0
$673$	1.86340	+	11.7650i	0.0718287	+	0.453509i	0.997221	+	0.0744983i	$0.0237355\pi$
$673$	1.86340	+	11.7650i	0.0718287	+	0.453509i	−0.925392	+	0.379010i	$0.876264\pi$
$674$	−8.23513	−	25.3451i	−0.317205	−	0.976258i
$675$		0			0
$676$	11.6239	+	3.77682i	0.447072	+	0.145262i
$677$	18.5183	+	6.01695i	0.711715	+	0.231250i	0.642427	−	0.766347i	$-0.277927\pi$
$677$	18.5183	+	6.01695i	0.711715	+	0.231250i	0.0692875	+	0.997597i	$0.477927\pi$
$678$		0			0
$679$	−2.48974	−	7.66263i	−0.0955474	−	0.294065i
$680$	2.13291	+	13.4667i	0.0817933	+	0.516423i
$681$		0			0
$682$	4.48835	+	0.710885i	0.171868	+	0.0272212i
$683$	−6.05998	−	6.05998i	−0.231879	−	0.231879i	0.581598	−	0.813476i	$-0.302428\pi$
$683$	−6.05998	−	6.05998i	−0.231879	−	0.231879i	−0.813476	+	0.581598i	$0.802428\pi$
$684$		0			0
$685$	−0.349292	+	2.20534i	−0.0133458	+	0.0842619i
$686$	12.7614	−	2.02121i	0.487234	−	0.0771703i
$687$		0			0
$688$			3.51960i			0.134184i
$689$	−19.6236	+	27.0096i	−0.747601	+	1.02898i
$690$		0			0
$691$	19.7427	−	38.7473i	0.751049	−	1.47402i	−0.125187	−	0.992133i	$-0.539953\pi$
$691$	19.7427	−	38.7473i	0.751049	−	1.47402i	0.876236	−	0.481883i	$-0.160047\pi$
$692$	6.08498	+	8.37525i	0.231316	+	0.318379i
$693$		0			0
$694$	21.2919	−	21.2919i	0.808229	−	0.808229i
$695$	23.8586	−	7.75212i	0.905008	−	0.294055i
$696$		0			0
$697$	14.2080	+	34.7013i	0.538168	+	1.31440i
$698$	12.5172			0.473784
$699$		0			0
$700$	−0.295413	+	0.295413i	−0.0111656	+	0.0111656i
$701$	18.2574	−	13.2648i	0.689571	−	0.501003i	−0.186948	−	0.982370i	$-0.559860\pi$
$701$	18.2574	−	13.2648i	0.689571	−	0.501003i	0.876519	+	0.481367i	$0.159860\pi$
$702$		0			0
$703$	−8.58855	+	16.8560i	−0.323923	+	0.635735i
$704$	−1.95760	−	3.84201i	−0.0737799	−	0.144801i
$705$		0			0
$706$			15.3044i			0.575988i
$707$	7.37022	+	5.35478i	0.277186	+	0.201387i
$708$		0			0
$709$	6.23855	−	39.3886i	0.234294	−	1.47927i	−0.537427	−	0.843310i	$-0.680604\pi$
$709$	6.23855	−	39.3886i	0.234294	−	1.47927i	0.771721	−	0.635961i	$-0.219396\pi$
$710$	−28.8157	−	14.6823i	−1.08143	−	0.551019i
$711$		0			0
$712$	2.07804	+	0.329129i	0.0778779	+	0.0123346i
$713$	−1.52266	+	4.68628i	−0.0570242	+	0.175503i
$714$		0			0
$715$	−15.5805	−	47.9519i	−0.582679	−	1.79330i
$716$	18.0401	−	9.19191i	0.674192	−	0.343518i
$717$		0			0
$718$	15.1547	+	4.92406i	0.565568	+	0.183764i
$719$	10.6628	−	5.43295i	0.397654	−	0.202615i	−0.243716	−	0.969847i	$-0.578366\pi$
$719$	10.6628	−	5.43295i	0.397654	−	0.202615i	0.641370	+	0.767232i	$0.278366\pi$
$720$		0			0
$721$	1.56321	+	9.86972i	0.0582170	+	0.367567i
$722$	−4.00179	+	12.3162i	−0.148931	+	0.458363i
$723$		0			0
$724$	−7.34792	−	7.34792i	−0.273083	−	0.273083i
$725$	1.06365	+	0.541959i	0.0395031	+	0.0201278i
$726$		0			0
$727$	41.7216	−	6.60805i	1.54737	−	0.245079i	0.676443	−	0.736495i	$-0.263521\pi$
$727$	41.7216	−	6.60805i	1.54737	−	0.245079i	0.870925	+	0.491416i	$0.163521\pi$
$728$	−4.03371	−	2.93066i	−0.149499	−	0.108617i
$729$		0			0
$730$	18.5627	−	25.5493i	0.687035	−	0.945622i
$731$	−9.35724	−	18.3646i	−0.346090	−	0.679240i
$732$		0			0
$733$	−8.99317	−	12.3780i	−0.332170	−	0.457193i	0.609964	−	0.792429i	$-0.291184\pi$
$733$	−8.99317	−	12.3780i	−0.332170	−	0.457193i	−0.942134	+	0.335236i	$0.891184\pi$
$734$	−17.2335	+	12.5208i	−0.636099	+	0.462153i
$735$		0			0
$736$	4.44671	−	1.44482i	0.163908	−	0.0532569i
$737$	−36.9990			−1.36288
$738$		0			0
$739$	−40.6144			−1.49402			−0.747012	−	0.664810i	$-0.768512\pi$
$739$	−40.6144			−1.49402			−0.747012	+	0.664810i	$0.768512\pi$
$740$	−17.0308	+	5.53365i	−0.626066	+	0.203421i
$741$		0			0
$742$	5.33930	−	3.87923i	0.196012	−	0.142411i
$743$	17.1056	+	23.5438i	0.627542	+	0.863738i	0.997875	−	0.0651612i	$-0.0207562\pi$
$743$	17.1056	+	23.5438i	0.627542	+	0.863738i	−0.370332	+	0.928899i	$0.620756\pi$
$744$		0			0
$745$	−24.1846	−	47.4649i	−0.886054	−	1.73898i
$746$	20.4057	−	28.0860i	0.747105	−	1.02830i
$747$		0			0
$748$	20.4288	+	14.8424i	0.746951	+	0.542692i
$749$	−10.3329	+	1.63657i	−0.377555	+	0.0597988i
$750$		0			0
$751$	−12.5463	−	6.39264i	−0.457820	−	0.233271i	0.209842	−	0.977735i	$-0.432705\pi$
$751$	−12.5463	−	6.39264i	−0.457820	−	0.233271i	−0.667662	+	0.744464i	$0.732705\pi$
$752$	0.709796	+	0.709796i	0.0258836	+	0.0258836i
$753$		0			0
$754$	−4.40254	+	13.5496i	−0.160331	+	0.493449i
$755$	−5.54769	−	35.0268i	−0.201901	−	1.27475i
$756$		0			0
$757$	−21.7550	+	11.0847i	−0.790698	+	0.402881i	−0.802202	−	0.597053i	$-0.796338\pi$
$757$	−21.7550	+	11.0847i	−0.790698	+	0.402881i	0.0115038	+	0.999934i	$0.496338\pi$
$758$	11.5705	+	3.75949i	0.420260	+	0.136551i
$759$		0			0
$760$	5.10257	−	2.59989i	0.185090	−	0.0943079i
$761$	−1.66740	−	5.13173i	−0.0604433	−	0.186025i	0.916276	−	0.400548i	$-0.131180\pi$
$761$	−1.66740	−	5.13173i	−0.0604433	−	0.186025i	−0.976719	+	0.214523i	$0.931180\pi$
$762$		0			0
$763$	3.83100	−	11.7906i	0.138691	−	0.426848i
$764$	−9.43641	−	1.49458i	−0.341397	−	0.0540720i
$765$		0			0
$766$	−12.9575	−	6.60218i	−0.468174	−	0.238547i
$767$	−7.93339	+	50.0895i	−0.286458	+	1.80863i
$768$		0			0
$769$	−20.3755	−	14.8037i	−0.734760	−	0.533835i	0.156306	−	0.987709i	$-0.450042\pi$
$769$	−20.3755	−	14.8037i	−0.734760	−	0.533835i	−0.891066	+	0.453874i	$0.850042\pi$
$770$			9.96704i			0.359187i
$771$		0			0
$772$	−8.25787	−	16.2070i	−0.297207	−	0.583302i
$773$	−10.8086	+	21.2130i	−0.388757	+	0.762979i	−0.999586	−	0.0287842i	$-0.990836\pi$
$773$	−10.8086	+	21.2130i	−0.388757	+	0.762979i	0.610829	+	0.791763i	$0.290836\pi$
$774$		0			0
$775$	−0.358786	+	0.260673i	−0.0128880	+	0.00936366i
$776$	−5.73852	+	5.73852i	−0.206001	+	0.206001i
$777$		0			0
$778$	−27.2499			−0.976956
$779$	12.0177	−	10.1795i	0.430579	−	0.364720i
$780$		0			0
$781$	−56.9640	+	18.5087i	−2.03833	+	0.662294i
$782$	−19.3609	+	19.3609i	−0.692344	+	0.692344i
$783$		0			0
$784$	−3.53516	−	4.86573i	−0.126256	−	0.173776i
$785$	1.99639	−	3.91813i	0.0712541	−	0.139844i
$786$		0			0
$787$	23.6487	−	32.5496i	0.842984	−	1.16027i	−0.142381	−	0.989812i	$-0.545476\pi$
$787$	23.6487	−	32.5496i	0.842984	−	1.16027i	0.985365	−	0.170456i	$-0.0545242\pi$
$788$			10.7511i			0.382993i
$789$		0			0
$790$	−5.87252	+	0.930116i	−0.208935	+	0.0330920i
$791$	−0.421082	+	2.65861i	−0.0149720	+	0.0945292i
$792$		0			0
$793$	−33.8679	−	33.8679i	−1.20269	−	1.20269i
$794$	20.1655	+	3.19390i	0.715647	+	0.113347i
$795$		0			0
$796$	1.12360	+	7.09412i	0.0398249	+	0.251444i
$797$	−5.29684	−	16.3020i	−0.187624	−	0.577446i	0.812360	−	0.583156i	$-0.198182\pi$
$797$	−5.29684	−	16.3020i	−0.187624	−	0.577446i	−0.999984	+	0.00570996i	$0.998182\pi$
$798$		0			0
$799$	−5.59065	−	1.81651i	−0.197783	−	0.0642636i
$800$	0.400217	+	0.130038i	0.0141498	+	0.00459755i
$801$		0			0
$802$	−5.51482	−	16.9729i	−0.194735	−	0.599333i
$803$	−9.14954	−	57.7679i	−0.322880	−	2.03859i
$804$		0			0
$805$	−10.6743	−	1.69065i	−0.376221	−	0.0595876i
$806$	−3.74252	−	3.74252i	−0.131825	−	0.131825i
$807$		0			0
$808$	1.43549	−	9.06330i	0.0505002	−	0.318846i
$809$	5.34383	−	0.846380i	0.187879	−	0.0297571i	−0.0617857	−	0.998089i	$-0.519680\pi$
$809$	5.34383	−	0.846380i	0.187879	−	0.0297571i	0.249665	+	0.968332i	$0.419680\pi$
$810$		0			0
$811$		−	52.4209i		−	1.84075i	−0.391041	−	0.920373i	$-0.627885\pi$
$811$		−	52.4209i		−	1.84075i	0.391041	−	0.920373i	$-0.372115\pi$
$812$	1.65541	−	2.27848i	0.0580936	−	0.0799589i
$813$		0			0
$814$	−15.0564	+	29.5499i	−0.527727	+	1.03572i
$815$	−0.0567825	−	0.0781544i	−0.00198900	−	0.00273763i
$816$		0			0
$817$	−6.12145	+	6.12145i	−0.214162	+	0.214162i
$818$	30.7312	−	9.98518i	1.07449	−	0.349124i
$819$		0			0
$820$	14.8573	+	1.23034i	0.518840	+	0.0429654i
$821$	47.0851			1.64328			0.821641	−	0.570006i	$-0.193059\pi$
$821$	47.0851			1.64328			0.821641	+	0.570006i	$0.193059\pi$
$822$		0			0
$823$	−24.0442	+	24.0442i	−0.838128	+	0.838128i	−0.988612	−	0.150484i	$-0.951917\pi$
$823$	−24.0442	+	24.0442i	−0.838128	+	0.838128i	0.150484	+	0.988612i	$0.451917\pi$
$824$	8.14303	−	5.91626i	0.283676	−	0.206103i
$825$		0			0
$826$	4.55134	−	8.93251i	0.158361	−	0.310802i
$827$	−13.6854	−	26.8592i	−0.475889	−	0.933984i	−0.996766	−	0.0803531i	$-0.974395\pi$
$827$	−13.6854	−	26.8592i	−0.475889	−	0.933984i	0.520878	−	0.853631i	$-0.325605\pi$
$828$		0			0
$829$			55.6284i			1.93205i	0.258442	+	0.966027i	$0.416791\pi$
$829$			55.6284i			1.93205i	−0.258442	+	0.966027i	$0.583209\pi$
$830$	−21.4334	−	15.5723i	−0.743966	−	0.540523i
$831$		0			0
$832$	−0.785638	+	4.96033i	−0.0272371	+	0.171968i
$833$	31.3819	+	15.9899i	1.08732	+	0.554016i
$834$		0			0
$835$	31.8380	+	5.04264i	1.10180	+	0.174508i
$836$	3.27745	−	10.0869i	0.113353	−	0.348864i
$837$		0			0
$838$	7.62107	+	23.4553i	0.263266	+	0.810248i
$839$	−39.8212	+	20.2899i	−1.37478	+	0.700486i	−0.976246	−	0.216667i	$-0.930482\pi$
$839$	−39.8212	+	20.2899i	−1.37478	+	0.700486i	−0.398536	+	0.917153i	$0.630482\pi$
$840$		0			0
$841$	19.9270	+	6.47467i	0.687138	+	0.223265i
$842$	−16.6321	+	8.47446i	−0.573179	+	0.292049i
$843$		0			0
$844$	−3.32073	−	20.9663i	−0.114304	−	0.721689i
$845$	−8.79344	+	27.0634i	−0.302504	+	0.931011i
$846$		0			0
$847$	5.33050	+	5.33050i	0.183158	+	0.183158i
$848$	−5.92313	−	3.01798i	−0.203401	−	0.103638i
$849$		0			0
$850$	−2.43398	+	0.385504i	−0.0834847	+	0.0132227i
$851$	−29.0929	−	21.1372i	−0.997293	−	0.724576i
$852$		0			0
$853$	−11.9830	+	16.4932i	−0.410289	+	0.564715i	−0.963289	−	0.268467i	$-0.913483\pi$
$853$	−11.9830	+	16.4932i	−0.410289	+	0.564715i	0.553000	+	0.833182i	$0.313483\pi$
$854$	4.29850	+	8.43627i	0.147091	+	0.288683i
$855$		0			0
$856$	6.19389	+	8.52516i	0.211703	+	0.291384i
$857$	−24.9965	+	18.1610i	−0.853864	+	0.620369i	−0.926209	−	0.377011i	$-0.876952\pi$
$857$	−24.9965	+	18.1610i	−0.853864	+	0.620369i	0.0723445	+	0.997380i	$0.476952\pi$
$858$		0			0
$859$	−23.3962	+	7.60188i	−0.798267	+	0.259373i	−0.679621	−	0.733564i	$-0.737856\pi$
$859$	−23.3962	+	7.60188i	−0.798267	+	0.259373i	−0.118647	+	0.992937i	$0.537856\pi$
$860$	−8.19456			−0.279432
$861$		0			0
$862$	10.5143			0.358119
$863$	−7.01793	+	2.28026i	−0.238893	+	0.0776211i	−0.426017	−	0.904715i	$-0.640084\pi$
$863$	−7.01793	+	2.28026i	−0.238893	+	0.0776211i	0.187124	+	0.982336i	$0.440084\pi$
$864$		0			0
$865$	−19.4998	+	14.1674i	−0.663013	+	0.481707i
$866$	−15.3802	−	21.1691i	−0.522641	−	0.719354i
$867$		0			0
$868$	0.474999	+	0.932237i	0.0161225	+	0.0316422i
$869$	−6.47245	+	8.90856i	−0.219563	+	0.302202i
$870$		0			0
$871$	34.8626	+	25.3292i	1.18128	+	0.858247i
$872$	−12.3337	+	1.95346i	−0.417671	+	0.0661526i
$873$		0			0
$874$	10.2468	+	5.22102i	0.346604	+	0.176604i
$875$	7.48449	+	7.48449i	0.253022	+	0.253022i
$876$		0			0
$877$	−8.46788	+	26.0615i	−0.285940	+	0.880033i	0.700175	+	0.713971i	$0.253105\pi$
$877$	−8.46788	+	26.0615i	−0.285940	+	0.880033i	−0.986115	+	0.166062i	$0.946895\pi$
$878$	4.21100	+	26.5872i	0.142114	+	0.897275i
$879$		0			0
$880$	8.94521	−	4.55781i	0.301543	−	0.153644i
$881$	13.7302	+	4.46121i	0.462582	+	0.150302i	0.531031	−	0.847353i	$-0.321805\pi$
$881$	13.7302	+	4.46121i	0.462582	+	0.150302i	−0.0684486	+	0.997655i	$0.521805\pi$
$882$		0			0
$883$	23.7953	−	12.1243i	0.800775	−	0.408015i	−0.00518410	−	0.999987i	$-0.501650\pi$
$883$	23.7953	−	12.1243i	0.800775	−	0.408015i	0.805959	+	0.591971i	$0.201650\pi$
$884$	−9.08825	−	27.9708i	−0.305671	−	0.940759i
$885$		0			0
$886$	3.51619	−	10.8217i	0.118129	−	0.363563i
$887$	−14.7387	−	2.33439i	−0.494879	−	0.0783811i	−0.0959934	−	0.995382i	$-0.530603\pi$
$887$	−14.7387	−	2.33439i	−0.494879	−	0.0783811i	−0.398885	+	0.917001i	$0.630603\pi$
$888$		0			0
$889$	−16.8637	−	8.59248i	−0.565590	−	0.288183i
$890$	−0.766300	+	4.83823i	−0.0256864	+	0.162178i
$891$		0			0
$892$	6.67180	+	4.84735i	0.223389	+	0.162301i
$893$			2.46902i			0.0826225i
$894$		0			0
$895$	21.4012	+	42.0022i	0.715363	+	1.40398i
$896$	0.450716	−	0.884580i	0.0150574	−	0.0295518i
$897$		0			0
$898$	1.37610	−	0.999797i	0.0459211	−	0.0333636i
$899$	2.11400	−	2.11400i	0.0705059	−	0.0705059i
$900$		0			0
$901$	38.9294			1.29693
$902$	21.0680	−	17.8455i	0.701487	−	0.594191i
$903$		0			0
$904$	2.57860	−	0.837838i	0.0857630	−	0.0278661i
$905$	17.1079	−	17.1079i	0.568686	−	0.568686i
$906$		0			0
$907$	22.8226	+	31.4126i	0.757812	+	1.04304i	0.997393	+	0.0721623i	$0.0229900\pi$
$907$	22.8226	+	31.4126i	0.757812	+	1.04304i	−0.239581	+	0.970876i	$0.577010\pi$
$908$	7.01060	−	13.7591i	0.232655	−	0.456611i
$909$		0			0
$910$	6.82335	−	9.39153i	0.226192	−	0.311326i
$911$		−	50.4026i		−	1.66991i	−0.550317	−	0.834956i	$-0.685493\pi$
$911$		−	50.4026i		−	1.66991i	0.550317	−	0.834956i	$-0.314507\pi$
$912$		0			0
$913$	−48.4618	+	7.67559i	−1.60385	+	0.254025i
$914$	0.118838	−	0.750312i	0.00393080	−	0.0248181i
$915$		0			0
$916$	−8.07171	−	8.07171i	−0.266697	−	0.266697i
$917$	−16.5537	−	2.62185i	−0.546652	−	0.0865812i
$918$		0			0
$919$	−0.431257	−	2.72285i	−0.0142258	−	0.0898185i	0.979554	−	0.201182i	$-0.0644782\pi$
$919$	−0.431257	−	2.72285i	−0.0142258	−	0.0898185i	−0.993780	+	0.111363i	$0.964478\pi$
$920$	3.36393	+	10.3531i	0.110906	+	0.341332i
$921$		0			0
$922$	1.30997	+	0.425636i	0.0431417	+	0.0140176i
$923$	66.3457	+	21.5570i	2.18380	+	0.709559i
$924$		0			0
$925$	−1.00016	−	3.07817i	−0.0328850	−	0.101210i
$926$	0.805040	+	5.08282i	0.0264552	+	0.167032i
$927$		0			0
$928$	−2.80189	−	0.443776i	−0.0919765	−	0.0145676i
$929$	18.2088	+	18.2088i	0.597411	+	0.597411i	0.939623	−	0.342212i	$-0.111176\pi$
$929$	18.2088	+	18.2088i	0.597411	+	0.597411i	−0.342212	+	0.939623i	$0.611176\pi$
$930$		0			0
$931$	2.31419	−	14.6112i	0.0758445	−	0.478863i
$932$	2.32601	−	0.368404i	0.0761909	−	0.0120675i
$933$		0			0
$934$			24.9284i			0.815681i
$935$	−34.5570	+	47.5636i	−1.13013	+	1.55550i
$936$		0			0
$937$	15.3353	−	30.0972i	0.500982	−	0.983233i	−0.492614	−	0.870248i	$-0.663959\pi$
$937$	15.3353	−	30.0972i	0.500982	−	0.983233i	0.993597	−	0.112985i	$-0.0360413\pi$
$938$	−5.00711	−	6.89170i	−0.163488	−	0.225022i
$939$		0			0
$940$	−1.65259	+	1.65259i	−0.0539016	+	0.0539016i
$941$	−1.68682	+	0.548082i	−0.0549889	+	0.0178670i	−0.336382	−	0.941726i	$-0.609203\pi$
$941$	−1.68682	+	0.548082i	−0.0549889	+	0.0178670i	0.281393	+	0.959592i	$0.409203\pi$
$942$		0			0
$943$	15.5383	+	25.5901i	0.505996	+	0.833328i
$944$	−10.0980			−0.328663
$945$		0			0
$946$	−10.7314	+	10.7314i	−0.348907	+	0.348907i
$947$	−29.8170	+	21.6633i	−0.968921	+	0.703962i	−0.955205	−	0.295944i	$-0.904366\pi$
$947$	−29.8170	+	21.6633i	−0.968921	+	0.703962i	−0.0137156	+	0.999906i	$0.504366\pi$
$948$		0			0
$949$	−30.9262	+	60.6961i	−1.00391	+	1.97028i
$950$	0.469906	+	0.922243i	0.0152458	+	0.0299215i
$951$		0			0
$952$			5.81385i			0.188428i
$953$	0.429810	+	0.312276i	0.0139229	+	0.0101156i	0.594725	−	0.803929i	$-0.297261\pi$
$953$	0.429810	+	0.312276i	0.0139229	+	0.0101156i	−0.580802	+	0.814045i	$0.697261\pi$
$954$		0			0
$955$	3.47978	−	21.9704i	0.112603	−	0.710947i
$956$	−3.12254	−	1.59102i	−0.100990	−	0.0514571i
$957$		0			0
$958$	24.9332	+	3.94904i	0.805556	+	0.127588i
$959$	−0.294214	+	0.905497i	−0.00950066	+	0.0292400i
$960$		0			0
$961$	−9.23632	−	28.4265i	−0.297946	−	0.916983i
$962$	34.4166	−	17.5361i	1.10964	−	0.565388i
$963$		0			0
$964$	21.8663	+	7.10478i	0.704265	+	0.228830i
$965$	37.7341	−	19.2265i	1.21470	−	0.618923i
$966$		0			0
$967$	7.83852	+	49.4904i	0.252070	+	1.59151i	0.711104	+	0.703087i	$0.248195\pi$
$967$	7.83852	+	49.4904i	0.252070	+	1.59151i	−0.459034	+	0.888418i	$0.651805\pi$
$968$	2.34644	−	7.22159i	0.0754174	−	0.232111i
$969$		0			0
$970$	−13.3608	−	13.3608i	−0.428989	−	0.428989i
$971$	33.3263	+	16.9806i	1.06949	+	0.544933i	0.897884	−	0.440233i	$-0.145104\pi$
$971$	33.3263	+	16.9806i	1.06949	+	0.544933i	0.171607	+	0.985165i	$0.445104\pi$
$972$		0			0
$973$	10.5653	−	1.67338i	0.338708	−	0.0536461i
$974$	25.3018	+	18.3828i	0.810721	+	0.589024i
$975$		0			0
$976$	5.60573	−	7.71562i	0.179435	−	0.246971i
$977$	−17.7787	−	34.8926i	−0.568789	−	1.11631i	−0.978912	−	0.204282i	$-0.934514\pi$
$977$	−17.7787	−	34.8926i	−0.568789	−	1.11631i	0.410123	−	0.912030i	$-0.365486\pi$
$978$		0			0
$979$	5.33249	+	7.33955i	0.170427	+	0.234573i
$980$	11.3287	−	8.23078i	0.361882	−	0.262923i
$981$		0			0
$982$	−11.3106	+	3.67505i	−0.360937	+	0.117275i
$983$	−58.7461			−1.87371			−0.936854	−	0.349721i	$-0.886276\pi$
$983$	−58.7461			−1.87371			−0.936854	+	0.349721i	$0.886276\pi$
$984$		0			0
$985$	−25.0315			−0.797569
$986$	15.7996	−	5.13359i	0.503161	−	0.163487i
$987$		0			0
$988$	−9.99364	+	7.26081i	−0.317940	+	0.230997i
$989$	−9.67263	−	13.3132i	−0.307572	−	0.423336i
$990$		0			0
$991$	1.59055	+	3.12163i	0.0505254	+	0.0991618i	0.914889	−	0.403706i	$-0.132278\pi$
$991$	1.59055	+	3.12163i	0.0505254	+	0.0991618i	−0.864363	+	0.502868i	$0.832278\pi$
$992$	0.619452	−	0.852603i	0.0196676	−	0.0270702i
$993$		0			0
$994$	−11.1566	−	8.10572i	−0.353865	−	0.257098i
$995$	−16.5170	+	2.61603i	−0.523623	+	0.0829338i
$996$		0			0
$997$	39.2812	+	20.0148i	1.24405	+	0.633875i	0.947075	−	0.321011i	$-0.104023\pi$
$997$	39.2812	+	20.0148i	1.24405	+	0.633875i	0.296974	+	0.954886i	$0.404023\pi$
$998$	27.5337	+	27.5337i	0.871564	+	0.871564i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.u.f.289.4		32
3.2	odd	2		246.2.n.b.43.1	✓	32
41.21	even	20	inner	738.2.u.f.595.4		32
123.62	odd	20		246.2.n.b.103.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
246.2.n.b.43.1	✓	32	3.2	odd	2
246.2.n.b.103.1	yes	32	123.62	odd	20
738.2.u.f.289.4		32	1.1	even	1	trivial
738.2.u.f.595.4		32	41.21	even	20	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(1.36852 + 1.88361i) q^{5} +(0.450716 + 0.884580i) q^{7} +(0.587785 - 0.809017i) q^{8} +(1.88361 + 1.36852i) q^{10} +(4.25890 - 0.674543i) q^{11} +(-4.47477 - 2.28001i) q^{13} +(0.702007 + 0.702007i) q^{14} +(0.309017 - 0.951057i) q^{16} +(0.916094 + 5.78399i) q^{17} +(2.19158 - 1.11666i) q^{19} +(2.21431 + 0.719473i) q^{20} +(3.84201 - 1.95760i) q^{22} +(1.44482 + 4.44671i) q^{23} +(-0.130038 + 0.400217i) q^{25} +(-4.96033 - 0.785638i) q^{26} +(0.884580 + 0.450716i) q^{28} +(0.443776 - 2.80189i) q^{29} +(0.852603 + 0.619452i) q^{31} -1.00000i q^{32} +(2.65861 + 5.21781i) q^{34} +(-1.04939 + 2.05954i) q^{35} +(-6.22236 + 4.52081i) q^{37} +(1.73925 - 1.73925i) q^{38} +2.32826 q^{40} +(6.23226 - 1.46935i) q^{41} +(-3.34734 + 1.08762i) q^{43} +(3.04904 - 3.04904i) q^{44} +(2.74822 + 3.78260i) q^{46} +(-0.455717 + 0.894395i) q^{47} +(3.53516 - 4.86573i) q^{49} +0.420813i q^{50} +(-4.96033 + 0.785638i) q^{52} +(1.03993 - 6.56584i) q^{53} +(7.09896 + 7.09896i) q^{55} +(0.980565 + 0.155306i) q^{56} +(-0.443776 - 2.80189i) q^{58} +(-3.12046 - 9.60379i) q^{59} +(9.07026 + 2.94711i) q^{61} +(1.00229 + 0.325665i) q^{62} +(-0.309017 - 0.951057i) q^{64} +(-1.82917 - 11.5489i) q^{65} +(-8.47486 - 1.34229i) q^{67} +(4.14088 + 4.14088i) q^{68} +(-0.361594 + 2.28301i) q^{70} +(-13.7194 + 2.17295i) q^{71} -13.5640i q^{73} +(-4.52081 + 6.22236i) q^{74} +(1.11666 - 2.19158i) q^{76} +(2.51624 + 3.46331i) q^{77} +(-1.80575 + 1.80575i) q^{79} +(2.21431 - 0.719473i) q^{80} +(5.47317 - 3.32331i) q^{82} -11.3789 q^{83} +(-9.64106 + 9.64106i) q^{85} +(-2.84742 + 2.06877i) q^{86} +(1.95760 - 3.84201i) q^{88} +(0.955171 + 1.87463i) q^{89} -4.98594i q^{91} +(3.78260 + 2.74822i) q^{92} +(-0.157029 + 0.991444i) q^{94} +(5.10257 + 2.59989i) q^{95} +(-8.01558 - 1.26954i) q^{97} +(1.85854 - 5.72001i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{11} - 12 q^{13} - 4 q^{14} - 8 q^{16} + 4 q^{17} - 4 q^{19} - 4 q^{22} - 40 q^{23} + 12 q^{25} - 8 q^{26} - 4 q^{28} - 16 q^{29} - 4 q^{31} - 16 q^{34} + 8 q^{35}+ \cdots + 56 q^{98}+O(q^{100}) \) 32 * q + 8 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^11 - 12 * q^13 - 4 * q^14 - 8 * q^16 + 4 * q^17 - 4 * q^19 - 4 * q^22 - 40 * q^23 + 12 * q^25 - 8 * q^26 - 4 * q^28 - 16 * q^29 - 4 * q^31 - 16 * q^34 + 8 * q^35 - 44 * q^37 + 16 * q^38 - 16 * q^40 + 28 * q^41 - 40 * q^43 + 16 * q^44 - 20 * q^46 + 48 * q^47 - 40 * q^49 - 8 * q^52 + 8 * q^53 + 72 * q^55 + 4 * q^56 + 16 * q^58 - 32 * q^59 + 100 * q^61 + 8 * q^64 - 56 * q^67 - 4 * q^68 + 48 * q^70 + 80 * q^71 + 4 * q^76 + 48 * q^79 + 12 * q^82 - 72 * q^83 - 52 * q^85 - 4 * q^86 + 4 * q^88 - 44 * q^89 - 20 * q^92 + 28 * q^94 + 40 * q^95 + 92 * q^97 + 56 * q^98

Introduction

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