LMFDB - Embedded newform 738.2.u.f.595.4

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)

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);

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")

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			595.4
Character	$\chi$	$=$	738.595
Dual form			738.2.u.f.289.4

$q$-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 $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{20}\right)$

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	−0.384721	−	0.923033i	$-0.625702\pi$
$5$	1.36852	−	1.88361i	0.612020	−	0.842374i	0.996742	+	0.0806590i	$0.0257025\pi$
$6$		0			0
$7$	0.450716	−	0.884580i	0.170355	−	0.334340i	−0.790007	−	0.613098i	$-0.789923\pi$
$7$	0.450716	−	0.884580i	0.170355	−	0.334340i	0.960361	+	0.278759i	$0.0899229\pi$
$8$	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	0.760926	−	0.648839i	$-0.224745\pi$
$11$	4.25890	+	0.674543i	1.28411	+	0.203382i	0.523181	+	0.852222i	$0.324745\pi$
$12$		0			0
$13$	−4.47477	+	2.28001i	−1.24108	+	0.632361i	−0.946327	−	0.323212i	$-0.895237\pi$
$13$	−4.47477	+	2.28001i	−1.24108	+	0.632361i	−0.294753	+	0.955574i	$0.595237\pi$
$14$	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	−0.584284	−	0.811549i	$-0.698625\pi$
$17$	0.916094	−	5.78399i	0.222186	−	1.40282i	0.806470	−	0.591275i	$-0.201375\pi$
$18$		0			0
$19$	2.19158	+	1.11666i	0.502782	+	0.256180i	0.686937	−	0.726717i	$-0.258955\pi$
$19$	2.19158	+	1.11666i	0.502782	+	0.256180i	−0.184155	+	0.982897i	$0.558955\pi$
$20$	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	−0.679777	−	0.733418i	$-0.737924\pi$
$23$	1.44482	−	4.44671i	0.301267	−	0.927203i	0.981044	−	0.193785i	$-0.0620764\pi$
$24$		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	0.994016	+	0.109238i	$0.0348411\pi$
$29$	0.443776	+	2.80189i	0.0824070	+	0.520298i	−0.911609	+	0.411059i	$0.865159\pi$
$30$		0			0
$31$	0.852603	−	0.619452i	0.153132	−	0.111257i	−0.508581	−	0.861014i	$-0.669830\pi$
$31$	0.852603	−	0.619452i	0.153132	−	0.111257i	0.661713	+	0.749757i	$0.269830\pi$
$32$			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	−0.0560636	−	0.998427i	$-0.517855\pi$
$37$	−6.22236	−	4.52081i	−1.02295	−	0.743216i	−0.966885	+	0.255211i	$0.917855\pi$
$38$	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	0.0424490	−	0.999099i	$-0.486484\pi$
$43$	−3.34734	−	1.08762i	−0.510464	−	0.165860i	−0.552913	+	0.833239i	$0.686484\pi$
$44$	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	0.855379	−	0.518003i	$-0.173324\pi$
$47$	−0.455717	−	0.894395i	−0.0664731	−	0.130461i	−0.921852	+	0.387542i	$0.873324\pi$
$48$		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	0.950159	+	0.311765i	$0.100920\pi$
$53$	1.03993	+	6.56584i	0.142845	+	0.901887i	−0.807314	+	0.590122i	$0.799080\pi$
$54$		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	0.513598	+	0.858031i	$0.328312\pi$
$59$	−3.12046	+	9.60379i	−0.406249	+	1.25031i	−0.919848	+	0.392276i	$0.871688\pi$
$60$		0			0
$61$	9.07026	−	2.94711i	1.16133	−	0.377338i	0.335928	−	0.941888i	$-0.390950\pi$
$61$	9.07026	−	2.94711i	1.16133	−	0.377338i	0.825399	+	0.564549i	$0.190950\pi$
$62$	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	−0.650909	−	0.759156i	$-0.725612\pi$
$67$	−8.47486	+	1.34229i	−1.03537	+	0.163986i	−0.384459	+	0.923142i	$0.625612\pi$
$68$	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	−0.725521	−	0.688200i	$-0.758401\pi$
$71$	−13.7194	−	2.17295i	−1.62820	−	0.257881i	−0.902677	+	0.430319i	$0.858401\pi$
$72$		0			0
$73$			13.5640i			1.58755i	0.608210	+	0.793776i	$0.291888\pi$
$73$			13.5640i			1.58755i	−0.608210	+	0.793776i	$0.708112\pi$
$74$	−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	0.598191	−	0.801354i	$-0.295886\pi$
$79$	−1.80575	−	1.80575i	−0.203163	−	0.203163i	−0.801354	+	0.598191i	$0.795886\pi$
$80$	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	−0.834826	−	0.550514i	$-0.814432\pi$
$89$	0.955171	−	1.87463i	0.101248	−	0.198710i	0.936074	+	0.351804i	$0.114432\pi$
$90$		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	−0.549470	−	0.835513i	$-0.685170\pi$
$97$	−8.01558	+	1.26954i	−0.813859	+	0.128903i	−0.264389	+	0.964416i	$0.585170\pi$
$98$	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	0.810695	−	0.585469i	$-0.199090\pi$
$101$	8.17612	+	4.16594i	0.813554	+	0.414527i	0.00285973	+	0.999996i	$0.499090\pi$
$102$		0			0
$103$	9.57271	−	3.11036i	0.943227	−	0.306473i	0.203266	−	0.979123i	$-0.434844\pi$
$103$	9.57271	−	3.11036i	0.943227	−	0.306473i	0.739960	+	0.672651i	$0.234844\pi$
$104$	−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	−0.975837	−	0.218502i	$-0.929883\pi$
$107$	−3.25632	−	10.0219i	−0.314800	−	0.968856i	0.661036	−	0.750354i	$-0.270117\pi$
$108$		0			0
$109$	−8.82994	+	8.82994i	−0.845755	+	0.845755i	−0.989600	−	0.143845i	$-0.954053\pi$
$109$	−8.82994	+	8.82994i	−0.845755	+	0.845755i	0.143845	+	0.989600i	$0.454053\pi$
$110$	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	−0.479813	−	0.877371i	$-0.659295\pi$
$113$	2.19349	−	1.59366i	0.206346	−	0.149919i	0.686159	+	0.727452i	$0.259295\pi$
$114$		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	−0.997846	−	0.0655963i	$-0.979105\pi$
$127$	−15.4232	−	11.2056i	−1.36858	−	0.994334i	−0.370737	−	0.928738i	$-0.620895\pi$
$128$	−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	−0.979863	−	0.199671i	$-0.936013\pi$
$131$	−9.92289	−	13.6577i	−0.866967	−	1.19328i	0.112896	−	0.993607i	$-0.463987\pi$
$132$		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	−0.677545	−	0.735481i	$-0.736956\pi$
$137$	0.678124	−	0.678124i	0.0579361	−	0.0579361i	0.735481	+	0.677545i	$0.236956\pi$
$138$		0			0
$139$	3.32957	+	10.2474i	0.282411	+	0.869171i	0.987163	+	0.159717i	$0.0510582\pi$
$139$	3.32957	+	10.2474i	0.282411	+	0.869171i	−0.704752	+	0.709454i	$0.748942\pi$
$140$	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	−0.980230	−	0.197864i	$-0.936600\pi$
$149$	−22.5985	+	3.57925i	−1.85134	+	0.293223i	−0.871110	+	0.491087i	$0.836600\pi$
$150$		0			0
$151$	−13.5715	+	6.91504i	−1.10444	+	0.562738i	−0.908502	−	0.417879i	$-0.862773\pi$
$151$	−13.5715	+	6.91504i	−1.10444	+	0.562738i	−0.195933	+	0.980617i	$0.562773\pi$
$152$	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	−0.922689	−	0.385546i	$-0.874013\pi$
$157$	−0.857457	+	1.68285i	−0.0684325	+	0.134306i	0.854256	+	0.519852i	$0.174013\pi$
$158$	−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	0.975879	−	0.218314i	$-0.0700556\pi$
$167$	9.78990	+	9.78990i	0.757565	+	0.757565i	−0.218314	+	0.975879i	$0.570056\pi$
$168$		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	$-0.871251\pi$
$173$		−	10.3524i		−	0.787077i	0.919308	−	0.393539i	$-0.128749\pi$
$174$		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	0.645069	−	0.764124i	$-0.276828\pi$
$179$	19.9976	−	3.16732i	1.49469	−	0.236736i	0.849625	+	0.527388i	$0.176828\pi$
$180$		0			0
$181$	−1.62559	+	10.2636i	−0.120829	+	0.762886i	0.850645	+	0.525741i	$0.176212\pi$
$181$	−1.62559	+	10.2636i	−0.120829	+	0.762886i	−0.971474	+	0.237146i	$0.923788\pi$
$182$	−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	−0.907936	−	0.419109i	$-0.862342\pi$
$191$	−6.75572	+	6.75572i	−0.488827	+	0.488827i	0.419109	+	0.907936i	$0.362342\pi$
$192$		0			0
$193$	2.84547	+	17.9656i	0.204821	+	1.29319i	0.849031	+	0.528342i	$0.177186\pi$
$193$	2.84547	+	17.9656i	0.204821	+	1.29319i	−0.644210	+	0.764849i	$0.722814\pi$
$194$	−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	0.522213	−	0.852815i	$-0.325107\pi$
$197$	−6.31935	−	8.69785i	−0.450235	−	0.619696i	−0.972448	+	0.233119i	$0.925107\pi$
$198$		0			0
$199$	−3.26081	−	6.39969i	−0.231152	−	0.453662i	0.746073	−	0.665864i	$-0.231937\pi$
$199$	−3.26081	−	6.39969i	−0.231152	−	0.453662i	−0.977226	+	0.212201i	$0.931937\pi$
$200$	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	0.940027	+	0.341099i	$0.110799\pi$
$211$	9.63714	+	18.9139i	0.663448	+	1.30209i	−0.276579	+	0.960991i	$0.589201\pi$
$212$	−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	−0.828755	−	0.559612i	$-0.810950\pi$
$223$	2.54840	−	7.84318i	0.170654	−	0.525218i	0.999408	+	0.0343941i	$0.0109502\pi$
$224$	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	0.846456	−	0.532459i	$-0.178732\pi$
$227$	13.7591	+	7.01060i	0.913222	+	0.465310i	0.0667662	+	0.997769i	$0.478732\pi$
$228$		0			0
$229$	−1.78572	+	11.2746i	−0.118004	+	0.745045i	0.855741	+	0.517404i	$0.173101\pi$
$229$	−1.78572	+	11.2746i	−0.118004	+	0.745045i	−0.973745	+	0.227641i	$0.926899\pi$
$230$	−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	−0.383905	−	0.923373i	$-0.625421\pi$
$233$	2.09832	−	1.06915i	0.137466	−	0.0700423i	0.521371	+	0.853330i	$0.325421\pi$
$234$		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	−0.936722	−	0.350075i	$-0.886156\pi$
$239$	−1.59102	+	3.12254i	−0.102914	+	0.201981i	0.833808	+	0.552055i	$0.186156\pi$
$240$		0			0
$241$	13.5141	−	18.6006i	0.870519	−	1.19817i	−0.108438	−	0.994103i	$-0.534585\pi$
$241$	13.5141	−	18.6006i	0.870519	−	1.19817i	0.978958	−	0.204064i	$-0.0654150\pi$
$242$	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	−0.749656	−	0.661828i	$-0.769781\pi$
$251$	1.76548	−	2.42998i	0.111436	−	0.153379i	0.861092	+	0.508449i	$0.169781\pi$
$252$		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	−0.402928	−	0.915232i	$-0.632008\pi$
$257$	−17.1367	−	2.71419i	−1.06896	−	0.169306i	−0.666030	+	0.745925i	$0.732008\pi$
$258$		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	−0.970734	−	0.240157i	$-0.922801\pi$
$263$	0.433028	−	2.73403i	0.0267016	−	0.168587i	0.997436	+	0.0715700i	$0.0228009\pi$
$264$		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	−0.103803	−	0.994598i	$-0.533101\pi$
$269$	9.26317	−	28.5091i	0.564785	−	1.73823i	0.668589	−	0.743633i	$-0.266899\pi$
$270$		0			0
$271$	−3.66697	−	11.2858i	−0.222753	−	0.685562i	−0.998512	−	0.0545333i	$-0.982633\pi$
$271$	−3.66697	−	11.2858i	−0.222753	−	0.685562i	0.775759	−	0.631029i	$-0.217367\pi$
$272$	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	−0.378170	+	0.925736i	$0.623447\pi$
$277$	−22.8922	+	16.6321i	−1.37546	+	0.999329i	−0.997288	+	0.0735928i	$0.976553\pi$
$278$			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	0.721599	−	0.692311i	$-0.243407\pi$
$281$	−4.40260	−	8.64059i	−0.262637	−	0.515455i	−0.984237	+	0.176856i	$0.943407\pi$
$282$		0			0
$283$	11.7063	+	8.50511i	0.695866	+	0.505577i	0.878583	−	0.477589i	$-0.158489\pi$
$283$	11.7063	+	8.50511i	0.695866	+	0.505577i	−0.182717	+	0.983166i	$0.558489\pi$
$284$	−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	0.918465	−	0.395502i	$-0.129429\pi$
$293$	1.00370	+	1.96987i	0.0586367	+	0.115081i	−0.859828	+	0.510583i	$0.829429\pi$
$294$		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	−0.0171347	−	0.999853i	$-0.505454\pi$
$307$	9.75421	−	3.16933i	0.556702	−	0.180883i	0.573837	+	0.818970i	$0.305454\pi$
$308$	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	−0.853521	−	0.521059i	$-0.825537\pi$
$311$	2.10285	−	13.2769i	0.119242	−	0.752862i	0.972763	−	0.231804i	$-0.0744627\pi$
$312$		0			0
$313$	31.7580	−	5.02997i	1.79507	−	0.284311i	0.832238	−	0.554418i	$-0.187059\pi$
$313$	31.7580	−	5.02997i	1.79507	−	0.284311i	0.962830	+	0.270107i	$0.0870592\pi$
$314$	−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	0.991646	−	0.128989i	$-0.0411734\pi$
$317$	33.7377	+	5.34352i	1.89490	+	0.300122i	0.903251	+	0.429112i	$0.141173\pi$
$318$		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	−0.998998	−	0.0447463i	$-0.985752\pi$
$331$	−18.9893	−	18.9893i	−1.04374	−	1.04374i	−0.0447463	−	0.998998i	$-0.514248\pi$
$332$	−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	$0.258551\pi$
$337$			26.6494i			1.45169i	−0.687859	+	0.725844i	$0.741449\pi$
$338$	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	0.987478	−	0.157756i	$-0.0504261\pi$
$347$	26.8294	+	13.6702i	1.44028	+	0.733857i	0.452797	+	0.891613i	$0.350426\pi$
$348$		0			0
$349$	11.9046	−	3.86803i	0.637238	−	0.207051i	0.0274592	−	0.999623i	$-0.491258\pi$
$349$	11.9046	−	3.86803i	0.637238	−	0.207051i	0.609779	+	0.792572i	$0.291258\pi$
$350$	−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	−0.994459	−	0.105125i	$-0.966476\pi$
$353$	−4.72931	−	14.5553i	−0.251716	−	0.774702i	0.742743	−	0.669576i	$-0.233524\pi$
$354$		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	−0.193104	−	0.981178i	$-0.561855\pi$
$359$	12.8914	−	9.36611i	0.680379	−	0.494325i	0.873484	+	0.486854i	$0.161855\pi$
$360$		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	−0.271904	−	0.962324i	$-0.587653\pi$
$367$	−20.2592	−	6.58260i	−1.05752	−	0.343609i	−0.785615	+	0.618715i	$0.787653\pi$
$368$	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	0.984818	+	0.173591i	$0.0555370\pi$
$373$	28.0860	+	20.4057i	1.45424	+	1.05657i	0.469420	+	0.882975i	$0.344463\pi$
$374$	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	−0.305568	−	0.952170i	$-0.598846\pi$
$379$	9.84247	−	7.15098i	0.505574	−	0.367321i	0.811142	+	0.584849i	$0.198846\pi$
$380$	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	−0.919210	−	0.393767i	$-0.871172\pi$
$383$	−10.2831	+	10.2831i	−0.525444	+	0.525444i	0.393767	+	0.919210i	$0.371172\pi$
$384$		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	−0.880431	−	0.474174i	$-0.842747\pi$
$389$	−25.9162	+	8.42068i	−1.31400	+	0.426945i	−0.433571	+	0.901119i	$0.642747\pi$
$390$		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	0.0666266	−	0.997778i	$-0.478776\pi$
$397$	18.1916	−	9.26906i	0.913008	−	0.465201i	0.846381	+	0.532577i	$0.178776\pi$
$398$	−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	$0.147010\pi$
$401$			17.8463i			0.891203i	−0.895231	+	0.445602i	$0.852990\pi$
$402$		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	$-0.794205\pi$
$419$		−	24.6623i		−	1.20483i	0.798182	−	0.602416i	$-0.205795\pi$
$420$		0			0
$421$	−18.4368	−	2.92010i	−0.898554	−	0.142317i	−0.309963	−	0.950748i	$-0.600317\pi$
$421$	−18.4368	−	2.92010i	−0.898554	−	0.142317i	−0.588590	+	0.808432i	$0.700317\pi$
$422$	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	−0.0581106	−	0.998310i	$-0.518508\pi$
$431$	9.99971	−	3.24910i	0.481669	−	0.156504i	0.539779	+	0.841806i	$0.318508\pi$
$432$		0			0
$433$	−8.08586	+	24.8857i	−0.388582	+	1.19593i	0.545267	+	0.838262i	$0.316428\pi$
$433$	−8.08586	+	24.8857i	−0.388582	+	1.19593i	−0.933849	+	0.357669i	$0.883572\pi$
$434$	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	−0.857442	−	0.514580i	$-0.827948\pi$
$439$	−4.21100	−	26.5872i	−0.200980	−	1.26894i	0.656462	−	0.754359i	$-0.272052\pi$
$440$	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	0.937783	−	0.347221i	$-0.112875\pi$
$443$	6.68819	+	9.20551i	0.317766	+	0.437367i	−0.620018	+	0.784588i	$0.712875\pi$
$444$		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	0.346940	−	0.937887i	$-0.387221\pi$
$449$	1.61770	+	0.525624i	0.0763442	+	0.0248057i	−0.270596	+	0.962693i	$0.587221\pi$
$450$		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	0.898932	−	0.438088i	$-0.144344\pi$
$457$	0.344881	+	0.676866i	0.0161328	+	0.0316625i	−0.882799	+	0.469750i	$0.844344\pi$
$458$	−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	−0.561533	−	0.827454i	$-0.689788\pi$
$461$	1.11433	−	0.809608i	0.0518995	−	0.0377072i	0.613433	+	0.789747i	$0.289788\pi$
$462$		0			0
$463$	−0.805040	−	5.08282i	−0.0374134	−	0.236219i	0.961894	−	0.273421i	$-0.0881553\pi$
$463$	−0.805040	−	5.08282i	−0.0374134	−	0.236219i	−0.999308	+	0.0372026i	$0.988155\pi$
$464$	−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	−0.955155	−	0.296107i	$-0.904312\pi$
$467$	−7.70328	−	23.7083i	−0.356465	−	1.09709i	0.598689	−	0.800981i	$-0.295688\pi$
$468$		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	0.142971	−	0.989727i	$-0.454334\pi$
$479$	22.4926	−	11.4606i	1.02771	−	0.523646i	0.884742	+	0.466081i	$0.154334\pi$
$480$		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	−0.154351	−	0.988016i	$-0.549329\pi$
$487$	18.3828	−	25.3018i	0.833005	−	1.14653i	0.987356	−	0.158517i	$-0.0506713\pi$
$488$	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	−0.0411623	−	0.999152i	$-0.513106\pi$
$499$	17.6777	−	34.6945i	0.791364	−	1.55314i	0.832526	−	0.553986i	$-0.186894\pi$
$500$	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	0.325327	−	0.945602i	$-0.394526\pi$
$503$	7.68202	+	1.21671i	0.342524	+	0.0542505i	0.0171974	+	0.999852i	$0.494526\pi$
$504$		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	0.792127	+	0.610356i	$0.208974\pi$
$509$	−3.38057	+	21.3441i	−0.149841	+	0.946059i	−0.941968	+	0.335703i	$0.891026\pi$
$510$		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	0.950250	+	0.311488i	$0.100827\pi$
$521$	3.25864	+	20.5743i	0.142764	+	0.901375i	−0.807486	+	0.589886i	$0.799173\pi$
$522$		0			0
$523$	5.26281	−	3.82365i	0.230126	−	0.167197i	−0.466747	−	0.884391i	$-0.654574\pi$
$523$	5.26281	−	3.82365i	0.230126	−	0.167197i	0.696873	+	0.717194i	$0.254574\pi$
$524$		−	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	0.693528	−	0.720430i	$-0.256055\pi$
$541$	−4.79036	−	6.59337i	−0.205954	−	0.283471i	−0.899481	+	0.436959i	$0.856055\pi$
$542$		−	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	−0.924882	−	0.380255i	$-0.875836\pi$
$547$	−12.7377	+	12.7377i	−0.544627	+	0.544627i	0.380255	+	0.924882i	$0.375836\pi$
$548$	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	−0.910626	−	0.413230i	$-0.864400\pi$
$557$	1.96184	−	12.3866i	0.0831260	−	0.524837i	0.993752	−	0.111606i	$-0.0355996\pi$
$558$		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	0.228484	−	0.973548i	$-0.426623\pi$
$563$	3.43915	+	0.544707i	0.144943	+	0.0229567i	−0.0835414	+	0.996504i	$0.526623\pi$
$564$		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	0.0999592	−	0.994992i	$-0.468129\pi$
$569$	24.2202	−	33.3362i	1.01536	−	1.39753i	0.915404	−	0.402536i	$-0.131871\pi$
$570$		0			0
$571$	0.620108	+	0.620108i	0.0259507	+	0.0259507i	0.719963	−	0.694012i	$-0.244159\pi$
$571$	0.620108	+	0.620108i	0.0259507	+	0.0259507i	−0.694012	+	0.719963i	$0.744159\pi$
$572$	−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	−0.995874	−	0.0907510i	$-0.971073\pi$
$577$	−26.1016	−	26.1016i	−1.08662	−	1.08662i	−0.0907510	−	0.995874i	$-0.528927\pi$
$578$	−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	−0.970585	−	0.240759i	$-0.922604\pi$
$587$	−32.6183	+	16.6199i	−1.34630	+	0.685975i	−0.375718	+	0.926734i	$0.622604\pi$
$588$		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	0.614136	−	0.789200i	$-0.289505\pi$
$593$	8.19770	+	4.17694i	0.336639	+	0.171526i	−0.277497	+	0.960727i	$0.589505\pi$
$594$		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	0.991474	−	0.130302i	$-0.0415947\pi$
$599$	2.75987	+	8.49400i	0.112765	+	0.347055i	−0.878709	+	0.477357i	$0.841595\pi$
$600$		0			0
$601$	−12.1900	+	12.1900i	−0.497241	+	0.497241i	−0.910578	−	0.413337i	$-0.864363\pi$
$601$	−12.1900	+	12.1900i	−0.497241	+	0.497241i	0.413337	+	0.910578i	$0.364363\pi$
$602$	−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	−0.905629	−	0.424072i	$-0.860600\pi$
$607$	−25.3541	−	34.8969i	−1.02909	−	1.41642i	−0.123462	−	0.992349i	$-0.539400\pi$
$608$	−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	0.489282	−	0.872126i	$-0.337259\pi$
$613$	9.22259	+	2.99660i	0.372497	+	0.121032i	−0.116785	+	0.993157i	$0.537259\pi$
$614$	10.2562			0.413906
$615$		0			0
$616$	4.28089			0.172482
$617$	−11.2369	−	3.65109i	−0.452381	−	0.146988i	0.0739597	−	0.997261i	$-0.476436\pi$
$617$	−11.2369	−	3.65109i	−0.452381	−	0.146988i	−0.526341	+	0.850274i	$0.676436\pi$
$618$		0			0
$619$	−23.3929	−	16.9959i	−0.940240	−	0.683124i	0.00823843	−	0.999966i	$-0.497378\pi$
$619$	−23.3929	−	16.9959i	−0.940240	−	0.683124i	−0.948478	+	0.316842i	$0.897378\pi$
$620$	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	0.954026	−	0.299722i	$-0.0968940\pi$
$631$	0.151484	+	0.466219i	0.00603047	+	0.0185599i	−0.947996	+	0.318282i	$0.896894\pi$
$632$	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	−0.683757	−	0.729710i	$-0.739655\pi$
$641$	−28.0664	+	4.44528i	−1.10855	+	0.175578i	−0.424798	+	0.905288i	$0.639655\pi$
$642$		0			0
$643$	−18.4171	+	9.38396i	−0.726298	+	0.370067i	−0.777721	−	0.628610i	$-0.783624\pi$
$643$	−18.4171	+	9.38396i	−0.726298	+	0.370067i	0.0514230	+	0.998677i	$0.483624\pi$
$644$	−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	$-0.747242\pi$
$647$		−	36.2825i		−	1.42641i	0.700955	−	0.713206i	$-0.252758\pi$
$648$		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	0.359444	−	0.933167i	$-0.382966\pi$
$653$	−14.6608	−	14.6608i	−0.573723	−	0.573723i	−0.933167	+	0.359444i	$0.882966\pi$
$654$		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	−0.936748	−	0.350005i	$-0.886180\pi$
$659$	−33.0322	−	33.0322i	−1.28675	−	1.28675i	−0.350005	−	0.936748i	$-0.613820\pi$
$660$		0			0
$661$	−11.0162	+	15.1624i	−0.428479	+	0.589751i	−0.967603	−	0.252476i	$-0.918755\pi$
$661$	−11.0162	+	15.1624i	−0.428479	+	0.589751i	0.539124	+	0.842226i	$0.318755\pi$
$662$	−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	−0.925392	−	0.379010i	$-0.876264\pi$
$673$	1.86340	−	11.7650i	0.0718287	−	0.453509i	0.997221	−	0.0744983i	$-0.0237355\pi$
$674$	−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	0.0692875	−	0.997597i	$-0.477927\pi$
$677$	18.5183	−	6.01695i	0.711715	−	0.231250i	0.642427	+	0.766347i	$0.277927\pi$
$678$		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	−0.813476	−	0.581598i	$-0.802428\pi$
$683$	−6.05998	+	6.05998i	−0.231879	+	0.231879i	0.581598	+	0.813476i	$0.302428\pi$
$684$		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	0.876236	+	0.481883i	$0.160047\pi$
$691$	19.7427	+	38.7473i	0.751049	+	1.47402i	−0.125187	+	0.992133i	$0.539953\pi$
$692$	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	0.876519	−	0.481367i	$-0.159860\pi$
$701$	18.2574	+	13.2648i	0.689571	+	0.501003i	−0.186948	+	0.982370i	$0.559860\pi$
$702$		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	0.771721	+	0.635961i	$0.219396\pi$
$709$	6.23855	+	39.3886i	0.234294	+	1.47927i	−0.537427	+	0.843310i	$0.680604\pi$
$710$	−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	0.641370	−	0.767232i	$-0.278366\pi$
$719$	10.6628	+	5.43295i	0.397654	+	0.202615i	−0.243716	+	0.969847i	$0.578366\pi$
$720$		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	0.870925	−	0.491416i	$-0.163521\pi$
$727$	41.7216	+	6.60805i	1.54737	+	0.245079i	0.676443	+	0.736495i	$0.263521\pi$
$728$	−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	−0.942134	−	0.335236i	$-0.891184\pi$
$733$	−8.99317	+	12.3780i	−0.332170	+	0.457193i	0.609964	+	0.792429i	$0.291184\pi$
$734$	−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	−0.370332	−	0.928899i	$-0.620756\pi$
$743$	17.1056	−	23.5438i	0.627542	−	0.863738i	0.997875	+	0.0651612i	$0.0207562\pi$
$744$		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	−0.667662	−	0.744464i	$-0.732705\pi$
$751$	−12.5463	+	6.39264i	−0.457820	+	0.233271i	0.209842	+	0.977735i	$0.432705\pi$
$752$	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	0.0115038	−	0.999934i	$-0.496338\pi$
$757$	−21.7550	−	11.0847i	−0.790698	−	0.402881i	−0.802202	+	0.597053i	$0.796338\pi$
$758$	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	−0.976719	−	0.214523i	$-0.931180\pi$
$761$	−1.66740	+	5.13173i	−0.0604433	+	0.186025i	0.916276	+	0.400548i	$0.131180\pi$
$762$		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	−0.891066	−	0.453874i	$-0.850042\pi$
$769$	−20.3755	+	14.8037i	−0.734760	+	0.533835i	0.156306	+	0.987709i	$0.450042\pi$
$770$		−	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	0.610829	−	0.791763i	$-0.290836\pi$
$773$	−10.8086	−	21.2130i	−0.388757	−	0.762979i	−0.999586	+	0.0287842i	$0.990836\pi$
$774$		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	0.985365	+	0.170456i	$0.0545242\pi$
$787$	23.6487	+	32.5496i	0.842984	+	1.16027i	−0.142381	+	0.989812i	$0.545476\pi$
$788$		−	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	−0.999984	−	0.00570996i	$-0.998182\pi$
$797$	−5.29684	+	16.3020i	−0.187624	+	0.577446i	0.812360	+	0.583156i	$0.198182\pi$
$798$		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	0.249665	−	0.968332i	$-0.419680\pi$
$809$	5.34383	+	0.846380i	0.187879	+	0.0297571i	−0.0617857	+	0.998089i	$0.519680\pi$
$810$		0			0
$811$			52.4209i			1.84075i	0.391041	+	0.920373i	$0.372115\pi$
$811$			52.4209i			1.84075i	−0.391041	+	0.920373i	$0.627885\pi$
$812$	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	0.150484	−	0.988612i	$-0.451917\pi$
$823$	−24.0442	−	24.0442i	−0.838128	−	0.838128i	−0.988612	+	0.150484i	$0.951917\pi$
$824$	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	0.520878	+	0.853631i	$0.325605\pi$
$827$	−13.6854	+	26.8592i	−0.475889	+	0.933984i	−0.996766	+	0.0803531i	$0.974395\pi$
$828$		0			0
$829$		−	55.6284i		−	1.93205i	−0.258442	−	0.966027i	$-0.583209\pi$
$829$		−	55.6284i		−	1.93205i	0.258442	−	0.966027i	$-0.416791\pi$
$830$	−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	−0.398536	−	0.917153i	$-0.630482\pi$
$839$	−39.8212	−	20.2899i	−1.37478	−	0.700486i	−0.976246	+	0.216667i	$0.930482\pi$
$840$		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	0.553000	−	0.833182i	$-0.313483\pi$
$853$	−11.9830	−	16.4932i	−0.410289	−	0.564715i	−0.963289	+	0.268467i	$0.913483\pi$
$854$	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	0.0723445	−	0.997380i	$-0.476952\pi$
$857$	−24.9965	−	18.1610i	−0.853864	−	0.620369i	−0.926209	+	0.377011i	$0.876952\pi$
$858$		0			0
$859$	−23.3962	−	7.60188i	−0.798267	−	0.259373i	−0.118647	−	0.992937i	$-0.537856\pi$
$859$	−23.3962	−	7.60188i	−0.798267	−	0.259373i	−0.679621	+	0.733564i	$0.737856\pi$
$860$	−8.19456			−0.279432
$861$		0			0
$862$	10.5143			0.358119
$863$	−7.01793	−	2.28026i	−0.238893	−	0.0776211i	0.187124	−	0.982336i	$-0.440084\pi$
$863$	−7.01793	−	2.28026i	−0.238893	−	0.0776211i	−0.426017	+	0.904715i	$0.640084\pi$
$864$		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	−0.986115	−	0.166062i	$-0.946895\pi$
$877$	−8.46788	−	26.0615i	−0.285940	−	0.880033i	0.700175	−	0.713971i	$-0.253105\pi$
$878$	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	−0.0684486	−	0.997655i	$-0.521805\pi$
$881$	13.7302	−	4.46121i	0.462582	−	0.150302i	0.531031	+	0.847353i	$0.321805\pi$
$882$		0			0
$883$	23.7953	+	12.1243i	0.800775	+	0.408015i	0.805959	−	0.591971i	$-0.201650\pi$
$883$	23.7953	+	12.1243i	0.800775	+	0.408015i	−0.00518410	+	0.999987i	$0.501650\pi$
$884$	−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	−0.398885	−	0.917001i	$-0.630603\pi$
$887$	−14.7387	+	2.33439i	−0.494879	+	0.0783811i	−0.0959934	+	0.995382i	$0.530603\pi$
$888$		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	−0.239581	−	0.970876i	$-0.577010\pi$
$907$	22.8226	−	31.4126i	0.757812	−	1.04304i	0.997393	−	0.0721623i	$-0.0229900\pi$
$908$	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	$0.314507\pi$
$911$			50.4026i			1.66991i	−0.550317	+	0.834956i	$0.685493\pi$
$912$		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	−0.993780	−	0.111363i	$-0.964478\pi$
$919$	−0.431257	+	2.72285i	−0.0142258	+	0.0898185i	0.979554	+	0.201182i	$0.0644782\pi$
$920$	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	−0.342212	−	0.939623i	$-0.611176\pi$
$929$	18.2088	−	18.2088i	0.597411	−	0.597411i	0.939623	+	0.342212i	$0.111176\pi$
$930$		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	0.993597	+	0.112985i	$0.0360413\pi$
$937$	15.3353	+	30.0972i	0.500982	+	0.983233i	−0.492614	+	0.870248i	$0.663959\pi$
$938$	−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	0.281393	−	0.959592i	$-0.409203\pi$
$941$	−1.68682	−	0.548082i	−0.0549889	−	0.0178670i	−0.336382	+	0.941726i	$0.609203\pi$
$942$		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	−0.0137156	−	0.999906i	$-0.504366\pi$
$947$	−29.8170	−	21.6633i	−0.968921	−	0.703962i	−0.955205	+	0.295944i	$0.904366\pi$
$948$		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	−0.580802	−	0.814045i	$-0.697261\pi$
$953$	0.429810	−	0.312276i	0.0139229	−	0.0101156i	0.594725	+	0.803929i	$0.297261\pi$
$954$		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	−0.459034	−	0.888418i	$-0.651805\pi$
$967$	7.83852	−	49.4904i	0.252070	−	1.59151i	0.711104	−	0.703087i	$-0.248195\pi$
$968$	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	0.171607	−	0.985165i	$-0.445104\pi$
$971$	33.3263	−	16.9806i	1.06949	−	0.544933i	0.897884	+	0.440233i	$0.145104\pi$
$972$		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	0.410123	+	0.912030i	$0.365486\pi$
$977$	−17.7787	+	34.8926i	−0.568789	+	1.11631i	−0.978912	+	0.204282i	$0.934514\pi$
$978$		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	−0.864363	−	0.502868i	$-0.832278\pi$
$991$	1.59055	−	3.12163i	0.0505254	−	0.0991618i	0.914889	+	0.403706i	$0.132278\pi$
$992$	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	0.296974	−	0.954886i	$-0.404023\pi$
$997$	39.2812	−	20.0148i	1.24405	−	0.633875i	0.947075	+	0.321011i	$0.104023\pi$
$998$	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.595.4		32
3.2	odd	2		246.2.n.b.103.1	yes	32
41.2	even	20	inner	738.2.u.f.289.4		32
123.2	odd	20		246.2.n.b.43.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
246.2.n.b.43.1	✓	32	123.2	odd	20
246.2.n.b.103.1	yes	32	3.2	odd	2
738.2.u.f.289.4		32	41.2	even	20	inner
738.2.u.f.595.4		32	1.1	even	1	trivial

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

L-functions

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