LMFDB - Embedded newform 945.2.bl.j.881.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(251,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 3]))

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

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

chi := DirichletCharacter("945.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.bl (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.3
Character	$\chi$	$=$	945.881
Dual form			945.2.bl.j.251.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.94805 + 1.12471i) q^{2} +(1.52994 - 2.64993i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.315547 - 2.62687i) q^{7} +2.38412i q^{8} +O(q^{10})$	\(q+(-1.94805 + 1.12471i) q^{2} +(1.52994 - 2.64993i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.315547 - 2.62687i) q^{7} +2.38412i q^{8} +2.24942i q^{10} +(-2.13353 + 1.23180i) q^{11} +(-0.336443 - 0.194245i) q^{13} +(2.33976 + 5.47217i) q^{14} +(0.378445 + 0.655486i) q^{16} +4.81075 q^{17} +1.11761i q^{19} +(-1.52994 - 2.64993i) q^{20} +(2.77082 - 4.79920i) q^{22} +(1.85078 + 1.06855i) q^{23} +(-0.500000 - 0.866025i) q^{25} +0.873878 q^{26} +(-6.47826 - 4.85513i) q^{28} +(4.02738 - 2.32521i) q^{29} +(-5.61553 - 3.24213i) q^{31} +(-5.60387 - 3.23540i) q^{32} +(-9.37160 + 5.41070i) q^{34} +(-2.11716 - 1.58671i) q^{35} +4.29543 q^{37} +(-1.25698 - 2.17716i) q^{38} +(2.06470 + 1.19206i) q^{40} +(-0.476591 + 0.825479i) q^{41} +(-5.21348 - 9.03002i) q^{43} +7.53829i q^{44} -4.80723 q^{46} +(-2.81296 - 4.87220i) q^{47} +(-6.80086 - 1.65780i) q^{49} +(1.94805 + 1.12471i) q^{50} +(-1.02947 + 0.594368i) q^{52} -9.72792i q^{53} +2.46359i q^{55} +(6.26275 + 0.752301i) q^{56} +(-5.23036 + 9.05925i) q^{58} +(-6.18688 + 10.7160i) q^{59} +(-0.631916 + 0.364837i) q^{61} +14.5858 q^{62} +13.0417 q^{64} +(-0.336443 + 0.194245i) q^{65} +(5.73742 - 9.93750i) q^{67} +(7.36016 - 12.7482i) q^{68} +(5.90892 + 0.709797i) q^{70} -15.1436i q^{71} -10.5746i q^{73} +(-8.36772 + 4.83111i) q^{74} +(2.96158 + 1.70987i) q^{76} +(2.56253 + 5.99319i) q^{77} +(7.35947 + 12.7470i) q^{79} +0.756890 q^{80} -2.14410i q^{82} +(-5.97335 - 10.3461i) q^{83} +(2.40538 - 4.16623i) q^{85} +(20.3123 + 11.7273i) q^{86} +(-2.93674 - 5.08659i) q^{88} -14.2521 q^{89} +(-0.616420 + 0.822497i) q^{91} +(5.66317 - 3.26963i) q^{92} +(10.9596 + 6.32753i) q^{94} +(0.967875 + 0.558803i) q^{95} +(3.46717 - 2.00177i) q^{97} +(15.1130 - 4.41951i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{2} + 18 q^{4} + 12 q^{5} + 9 q^{7}+O(q^{10}) $ 24 * q - 6 * q^2 + 18 * q^4 + 12 * q^5 + 9 * q^7	$ 24 q - 6 q^{2} + 18 q^{4} + 12 q^{5} + 9 q^{7} - 9 q^{11} + 3 q^{13} - 18 q^{14} - 18 q^{16} - 18 q^{17} - 18 q^{20} - 9 q^{22} - 9 q^{23} - 12 q^{25} + 18 q^{26} - 9 q^{28} - 9 q^{29} - 42 q^{31} - 18 q^{32} - 39 q^{34} + 9 q^{35} + 12 q^{38} - 6 q^{40} + 33 q^{41} + 18 q^{43} - 30 q^{46} + 9 q^{49} + 6 q^{50} + 129 q^{52} + 9 q^{56} - 15 q^{58} - 12 q^{59} - 15 q^{61} - 12 q^{62} - 60 q^{64} + 3 q^{65} - 15 q^{67} - 9 q^{68} - 9 q^{70} + 18 q^{74} + 54 q^{76} + 45 q^{77} + 21 q^{79} - 36 q^{80} + 30 q^{83} - 9 q^{85} + 102 q^{86} - 9 q^{88} - 102 q^{89} + 42 q^{91} + 3 q^{92} - 156 q^{94} + 18 q^{95} - 45 q^{97} - 3 q^{98}+O(q^{100}) $ 24 * q - 6 * q^2 + 18 * q^4 + 12 * q^5 + 9 * q^7 - 9 * q^11 + 3 * q^13 - 18 * q^14 - 18 * q^16 - 18 * q^17 - 18 * q^20 - 9 * q^22 - 9 * q^23 - 12 * q^25 + 18 * q^26 - 9 * q^28 - 9 * q^29 - 42 * q^31 - 18 * q^32 - 39 * q^34 + 9 * q^35 + 12 * q^38 - 6 * q^40 + 33 * q^41 + 18 * q^43 - 30 * q^46 + 9 * q^49 + 6 * q^50 + 129 * q^52 + 9 * q^56 - 15 * q^58 - 12 * q^59 - 15 * q^61 - 12 * q^62 - 60 * q^64 + 3 * q^65 - 15 * q^67 - 9 * q^68 - 9 * q^70 + 18 * q^74 + 54 * q^76 + 45 * q^77 + 21 * q^79 - 36 * q^80 + 30 * q^83 - 9 * q^85 + 102 * q^86 - 9 * q^88 - 102 * q^89 + 42 * q^91 + 3 * q^92 - 156 * q^94 + 18 * q^95 - 45 * q^97 - 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.94805	+	1.12471i	−1.37748	+	0.795289i	−0.991856	−	0.127366i	$-0.959348\pi$
$2$	−1.94805	+	1.12471i	−1.37748	+	0.795289i	−0.385626	+	0.922655i	$0.626014\pi$
$3$		0			0
$3$		0			0
$4$	1.52994	−	2.64993i	0.764970	−	1.32497i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	0.315547	−	2.62687i	0.119266	−	0.992862i
$7$	0.315547	−	2.62687i	0.119266	−	0.992862i
$8$			2.38412i			0.842912i
$9$		0			0
$10$			2.24942i			0.711328i
$11$	−2.13353	+	1.23180i	−0.643284	+	0.371400i	−0.785878	−	0.618381i	$-0.787789\pi$
$11$	−2.13353	+	1.23180i	−0.643284	+	0.371400i	0.142594	+	0.989781i	$0.454456\pi$
$12$		0			0
$13$	−0.336443	−	0.194245i	−0.0933124	−	0.0538740i	0.452618	−	0.891705i	$-0.350490\pi$
$13$	−0.336443	−	0.194245i	−0.0933124	−	0.0538740i	−0.545930	+	0.837831i	$0.683824\pi$
$14$	2.33976	+	5.47217i	0.625327	+	1.46250i
$15$		0			0
$16$	0.378445	+	0.655486i	0.0946113	+	0.163872i
$17$	4.81075			1.16678			0.583389	−	0.812193i	$-0.301726\pi$
$17$	4.81075			1.16678			0.583389	+	0.812193i	$0.301726\pi$
$18$		0			0
$19$			1.11761i			0.256396i	0.991749	+	0.128198i	$0.0409194\pi$
$19$			1.11761i			0.256396i	−0.991749	+	0.128198i	$0.959081\pi$
$20$	−1.52994	−	2.64993i	−0.342105	−	0.592543i
$21$		0			0
$22$	2.77082	−	4.79920i	0.590741	−	1.02319i
$23$	1.85078	+	1.06855i	0.385915	+	0.222808i	0.680388	−	0.732852i	$-0.261811\pi$
$23$	1.85078	+	1.06855i	0.385915	+	0.222808i	−0.294474	+	0.955660i	$0.595144\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.873878			0.171382
$27$		0			0
$28$	−6.47826	−	4.85513i	−1.22428	−	0.917533i
$29$	4.02738	−	2.32521i	0.747865	−	0.431780i	−0.0770570	−	0.997027i	$-0.524552\pi$
$29$	4.02738	−	2.32521i	0.747865	−	0.431780i	0.824922	+	0.565247i	$0.191219\pi$
$30$		0			0
$31$	−5.61553	−	3.24213i	−1.00858	−	0.582303i	−0.0978037	−	0.995206i	$-0.531182\pi$
$31$	−5.61553	−	3.24213i	−1.00858	−	0.582303i	−0.910775	+	0.412902i	$0.864515\pi$
$32$	−5.60387	−	3.23540i	−0.990634	−	0.571943i
$33$		0			0
$34$	−9.37160	+	5.41070i	−1.60722	+	0.927927i
$35$	−2.11716	−	1.58671i	−0.357865	−	0.268202i
$36$		0			0
$37$	4.29543			0.706164			0.353082	−	0.935592i	$-0.385134\pi$
$37$	4.29543			0.706164			0.353082	+	0.935592i	$0.385134\pi$
$38$	−1.25698	−	2.17716i	−0.203909	−	0.353181i
$39$		0			0
$40$	2.06470	+	1.19206i	0.326458	+	0.188481i
$41$	−0.476591	+	0.825479i	−0.0744310	+	0.128918i	−0.900839	−	0.434154i	$-0.857047\pi$
$41$	−0.476591	+	0.825479i	−0.0744310	+	0.128918i	0.826408	+	0.563072i	$0.190381\pi$
$42$		0			0
$43$	−5.21348	−	9.03002i	−0.795049	−	1.37706i	−0.922808	−	0.385259i	$-0.874112\pi$
$43$	−5.21348	−	9.03002i	−0.795049	−	1.37706i	0.127760	−	0.991805i	$-0.459221\pi$
$44$			7.53829i			1.13644i
$45$		0			0
$46$	−4.80723			−0.708787
$47$	−2.81296	−	4.87220i	−0.410313	−	0.710683i	0.584611	−	0.811314i	$-0.301247\pi$
$47$	−2.81296	−	4.87220i	−0.410313	−	0.710683i	−0.994924	+	0.100631i	$0.967914\pi$
$48$		0			0
$49$	−6.80086	−	1.65780i	−0.971551	−	0.236829i
$50$	1.94805	+	1.12471i	0.275496	+	0.159058i
$51$		0			0
$52$	−1.02947	+	0.594368i	−0.142762	+	0.0824239i
$53$		−	9.72792i		−	1.33623i	−0.744057	−	0.668117i	$-0.767101\pi$
$53$		−	9.72792i		−	1.33623i	0.744057	−	0.668117i	$-0.232899\pi$
$54$		0			0
$55$			2.46359i			0.332190i
$56$	6.26275	+	0.752301i	0.836896	+	0.100530i
$57$		0			0
$58$	−5.23036	+	9.05925i	−0.686780	+	1.18954i
$59$	−6.18688	+	10.7160i	−0.805463	+	1.39510i	0.110515	+	0.993875i	$0.464750\pi$
$59$	−6.18688	+	10.7160i	−0.805463	+	1.39510i	−0.915978	+	0.401229i	$0.868583\pi$
$60$		0			0
$61$	−0.631916	+	0.364837i	−0.0809085	+	0.0467125i	−0.539908	−	0.841724i	$-0.681541\pi$
$61$	−0.631916	+	0.364837i	−0.0809085	+	0.0467125i	0.459000	+	0.888436i	$0.348208\pi$
$62$	14.5858			1.85240
$63$		0			0
$64$	13.0417			1.63022
$65$	−0.336443	+	0.194245i	−0.0417306	+	0.0240932i
$66$		0			0
$67$	5.73742	−	9.93750i	0.700937	−	1.21406i	−0.267201	−	0.963641i	$-0.586099\pi$
$67$	5.73742	−	9.93750i	0.700937	−	1.21406i	0.968138	−	0.250418i	$-0.0805679\pi$
$68$	7.36016	−	12.7482i	0.892551	−	1.54594i
$69$		0			0
$70$	5.90892	+	0.709797i	0.706251	+	0.0848370i
$71$		−	15.1436i		−	1.79721i	−0.438754	−	0.898607i	$-0.644580\pi$
$71$		−	15.1436i		−	1.79721i	0.438754	−	0.898607i	$-0.355420\pi$
$72$		0			0
$73$		−	10.5746i		−	1.23766i	−0.785524	−	0.618831i	$-0.787607\pi$
$73$		−	10.5746i		−	1.23766i	0.785524	−	0.618831i	$-0.212393\pi$
$74$	−8.36772	+	4.83111i	−0.972728	+	0.561605i
$75$		0			0
$76$	2.96158	+	1.70987i	0.339717	+	0.196136i
$77$	2.56253	+	5.99319i	0.292028	+	0.682988i
$78$		0			0
$79$	7.35947	+	12.7470i	0.828005	+	1.43415i	0.899601	+	0.436713i	$0.143857\pi$
$79$	7.35947	+	12.7470i	0.828005	+	1.43415i	−0.0715959	+	0.997434i	$0.522809\pi$
$80$	0.756890			0.0846229
$81$		0			0
$82$		−	2.14410i		−	0.236777i
$83$	−5.97335	−	10.3461i	−0.655660	−	1.13564i	−0.981728	−	0.190291i	$-0.939057\pi$
$83$	−5.97335	−	10.3461i	−0.655660	−	1.13564i	0.326067	−	0.945347i	$-0.394276\pi$
$84$		0			0
$85$	2.40538	−	4.16623i	0.260900	−	0.451891i
$86$	20.3123	+	11.7273i	2.19033	+	1.26459i
$87$		0			0
$88$	−2.93674	−	5.08659i	−0.313058	−	0.542232i
$89$	−14.2521			−1.51072			−0.755362	−	0.655308i	$-0.772539\pi$
$89$	−14.2521			−1.51072			−0.755362	+	0.655308i	$0.772539\pi$
$90$		0			0
$91$	−0.616420	+	0.822497i	−0.0646184	+	0.0862211i
$92$	5.66317	−	3.26963i	0.590426	−	0.340883i
$93$		0			0
$94$	10.9596	+	6.32753i	1.13040	+	0.652635i
$95$	0.967875	+	0.558803i	0.0993019	+	0.0573320i
$96$		0			0
$97$	3.46717	−	2.00177i	0.352038	−	0.203249i	−0.313545	−	0.949573i	$-0.601517\pi$
$97$	3.46717	−	2.00177i	0.352038	−	0.203249i	0.665582	+	0.746324i	$0.268183\pi$
$98$	15.1130	−	4.41951i	1.52664	−	0.446437i
$99$		0			0
$100$	−3.05988			−0.305988
$101$	−3.71469	−	6.43403i	−0.369625	−	0.640210i	0.619882	−	0.784695i	$-0.287181\pi$
$101$	−3.71469	−	6.43403i	−0.369625	−	0.640210i	−0.989507	+	0.144485i	$0.953847\pi$
$102$		0			0
$103$	7.59032	+	4.38227i	0.747896	+	0.431798i	0.824933	−	0.565230i	$-0.191213\pi$
$103$	7.59032	+	4.38227i	0.747896	+	0.431798i	−0.0770370	+	0.997028i	$0.524546\pi$
$104$	0.463103	−	0.802118i	0.0454110	−	0.0786542i
$105$		0			0
$106$	10.9411	+	18.9505i	1.06269	+	1.84064i
$107$			4.06484i			0.392963i	0.980508	+	0.196482i	$0.0629516\pi$
$107$			4.06484i			0.392963i	−0.980508	+	0.196482i	$0.937048\pi$
$108$		0			0
$109$	11.3809			1.09009			0.545046	−	0.838406i	$-0.316512\pi$
$109$	11.3809			1.09009			0.545046	+	0.838406i	$0.316512\pi$
$110$	−2.77082	−	4.79920i	−0.264188	−	0.457586i
$111$		0			0
$112$	1.84129	−	0.787288i	0.173986	−	0.0743917i
$113$	7.59510	+	4.38503i	0.714487	+	0.412509i	0.812720	−	0.582654i	$-0.197986\pi$
$113$	7.59510	+	4.38503i	0.714487	+	0.412509i	−0.0982332	+	0.995163i	$0.531319\pi$
$114$		0			0
$115$	1.85078	−	1.06855i	0.172586	−	0.0996427i
$116$		−	14.2297i		−	1.32120i
$117$		0			0
$118$		−	27.8338i		−	2.56231i
$119$	1.51802	−	12.6372i	0.139157	−	1.15845i
$120$		0			0
$121$	−2.46536	+	4.27013i	−0.224124	+	0.388194i
$122$	0.820670	−	1.42144i	0.0743000	−	0.128691i
$123$		0			0
$124$	−17.1829	+	9.92053i	−1.54307	+	0.890889i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−5.13475			−0.455635			−0.227818	−	0.973704i	$-0.573159\pi$
$127$	−5.13475			−0.455635			−0.227818	+	0.973704i	$0.573159\pi$
$128$	−14.1983	+	8.19737i	−1.25496	+	0.724552i
$129$		0			0
$130$	0.436939	−	0.756800i	0.0383221	−	0.0663758i
$131$	6.25464	−	10.8334i	0.546470	−	0.946514i	−0.452042	−	0.891996i	$-0.649304\pi$
$131$	6.25464	−	10.8334i	0.546470	−	0.946514i	0.998513	−	0.0545179i	$-0.0173622\pi$
$132$		0			0
$133$	2.93580	+	0.352657i	0.254566	+	0.0305793i
$134$			25.8117i			2.22979i
$135$		0			0
$136$			11.4694i			0.983492i
$137$	6.12680	−	3.53731i	0.523448	−	0.302213i	−0.214896	−	0.976637i	$-0.568941\pi$
$137$	6.12680	−	3.53731i	0.523448	−	0.302213i	0.738344	+	0.674424i	$0.235608\pi$
$138$		0			0
$139$	9.58572	+	5.53432i	0.813050	+	0.469415i	0.848014	−	0.529974i	$-0.177798\pi$
$139$	9.58572	+	5.53432i	0.813050	+	0.469415i	−0.0349638	+	0.999389i	$0.511132\pi$
$140$	−7.44379	+	3.18277i	−0.629115	+	0.268993i
$141$		0			0
$142$	17.0321	+	29.5005i	1.42931	+	2.47563i
$143$	0.957082			0.0800352
$144$		0			0
$145$		−	4.65041i		−	0.386196i
$146$	11.8933	+	20.5999i	0.984299	+	1.70486i
$147$		0			0
$148$	6.57175	−	11.3826i	0.540194	−	0.935644i
$149$	7.40128	+	4.27313i	0.606336	+	0.350068i	0.771530	−	0.636193i	$-0.219492\pi$
$149$	7.40128	+	4.27313i	0.606336	+	0.350068i	−0.165194	+	0.986261i	$0.552825\pi$
$150$		0			0
$151$	−7.86677	−	13.6256i	−0.640188	−	1.10884i	−0.985390	−	0.170311i	$-0.945523\pi$
$151$	−7.86677	−	13.6256i	−0.640188	−	1.10884i	0.345202	−	0.938528i	$-0.387810\pi$
$152$	−2.66450			−0.216120
$153$		0			0
$154$	−11.7325	−	8.79296i	−0.945436	−	0.708557i
$155$	−5.61553	+	3.24213i	−0.451050	+	0.260414i
$156$		0			0
$157$	−17.2311	−	9.94836i	−1.37519	−	0.793966i	−0.383613	−	0.923494i	$-0.625320\pi$
$157$	−17.2311	−	9.94836i	−1.37519	−	0.793966i	−0.991576	+	0.129528i	$0.958654\pi$
$158$	−28.6733	−	16.5545i	−2.28112	−	1.31701i
$159$		0			0
$160$	−5.60387	+	3.23540i	−0.443025	+	0.255781i
$161$	3.39094	−	4.52458i	0.267244	−	0.356587i
$162$		0			0
$163$	0.220738			0.0172895			0.00864477	−	0.999963i	$-0.497248\pi$
$163$	0.220738			0.0172895			0.00864477	+	0.999963i	$0.497248\pi$
$164$	1.45831	+	2.52587i	0.113875	+	0.197237i
$165$		0			0
$166$	23.2728	+	13.4366i	1.80632	+	1.04288i
$167$	−12.6948	+	21.9881i	−0.982356	+	1.70149i	−0.329215	+	0.944255i	$0.606784\pi$
$167$	−12.6948	+	21.9881i	−0.982356	+	1.70149i	−0.653141	+	0.757236i	$0.726549\pi$
$168$		0			0
$169$	−6.42454	−	11.1276i	−0.494195	−	0.855971i
$170$			10.8214i			0.829963i
$171$		0			0
$172$	−31.9053			−2.43275
$173$	7.26041	+	12.5754i	0.551999	+	0.956090i	0.998130	+	0.0611226i	$0.0194681\pi$
$173$	7.26041	+	12.5754i	0.551999	+	0.956090i	−0.446131	+	0.894967i	$0.647199\pi$
$174$		0			0
$175$	−2.43271	+	1.04016i	−0.183895	+	0.0786288i
$176$	−1.61485	−	0.932334i	−0.121724	−	0.0702773i
$177$		0			0
$178$	27.7639	−	16.0295i	2.08099	−	1.20146i
$179$		−	15.0447i		−	1.12449i	−0.826971	−	0.562245i	$-0.809938\pi$
$179$		−	15.0447i		−	1.12449i	0.826971	−	0.562245i	$-0.190062\pi$
$180$		0			0
$181$		−	18.1625i		−	1.35001i	−0.737813	−	0.675006i	$-0.764141\pi$
$181$		−	18.1625i		−	1.35001i	0.737813	−	0.675006i	$-0.235859\pi$
$182$	0.275750	−	2.29556i	0.0204399	−	0.170158i
$183$		0			0
$184$	−2.54754	+	4.41248i	−0.187807	+	0.325292i
$185$	2.14771	−	3.71995i	0.157903	−	0.273496i
$186$		0			0
$187$	−10.2639	+	5.92586i	−0.750570	+	0.433342i
$188$	−17.2147			−1.25551
$189$		0			0
$190$	−2.51396			−0.182382
$191$	1.71849	−	0.992168i	0.124345	−	0.0717908i	−0.436537	−	0.899686i	$-0.643795\pi$
$191$	1.71849	−	0.992168i	0.124345	−	0.0717908i	0.560882	+	0.827895i	$0.310462\pi$
$192$		0			0
$193$	6.61042	−	11.4496i	0.475829	−	0.824159i	−0.523788	−	0.851849i	$-0.675482\pi$
$193$	6.61042	−	11.4496i	0.475829	−	0.824159i	0.999617	+	0.0276894i	$0.00881495\pi$
$194$	−4.50282	+	7.79911i	−0.323284	+	0.559943i
$195$		0			0
$196$	−14.7980	+	15.4855i	−1.05700	+	1.10611i
$197$			16.1651i			1.15172i	0.817550	+	0.575858i	$0.195332\pi$
$197$			16.1651i			1.15172i	−0.817550	+	0.575858i	$0.804668\pi$
$198$		0			0
$199$			27.3385i			1.93798i	0.247107	+	0.968988i	$0.420520\pi$
$199$			27.3385i			1.93798i	−0.247107	+	0.968988i	$0.579480\pi$
$200$	2.06470	−	1.19206i	0.145997	−	0.0842912i
$201$		0			0
$202$	14.4728	+	8.35589i	1.01830	+	0.587918i
$203$	−4.83718	−	11.3131i	−0.339504	−	0.794023i
$204$		0			0
$205$	0.476591	+	0.825479i	0.0332865	+	0.0576540i
$206$	−19.7151			−1.37362
$207$		0			0
$208$		−	0.294045i		−	0.0203883i
$209$	−1.37666	−	2.38445i	−0.0952257	−	0.164936i
$210$		0			0
$211$	−0.788116	+	1.36506i	−0.0542561	+	0.0939744i	−0.891878	−	0.452276i	$-0.850612\pi$
$211$	−0.788116	+	1.36506i	−0.0542561	+	0.0939744i	0.837622	+	0.546251i	$0.183945\pi$
$212$	−25.7784	−	14.8831i	−1.77047	−	1.02218i
$213$		0			0
$214$	−4.57176	−	7.91853i	−0.312519	−	0.541299i
$215$	−10.4270			−0.711113
$216$		0			0
$217$	−10.2886	+	13.7282i	−0.698436	+	0.931931i
$218$	−22.1706	+	12.8002i	−1.50158	+	0.866939i
$219$		0			0
$220$	6.52835	+	3.76915i	0.440141	+	0.254116i
$221$	−1.61854	−	0.934466i	−0.108875	−	0.0628590i
$222$		0			0
$223$	−12.6487	+	7.30272i	−0.847019	+	0.489026i	−0.859644	−	0.510894i	$-0.829314\pi$
$223$	−12.6487	+	7.30272i	−0.847019	+	0.489026i	0.0126252	+	0.999920i	$0.495981\pi$
$224$	−10.2672	+	13.6997i	−0.686009	+	0.915350i
$225$		0			0
$226$	−19.7275			−1.31226
$227$	1.45581	+	2.52154i	0.0966257	+	0.167361i	0.910286	−	0.413980i	$-0.135862\pi$
$227$	1.45581	+	2.52154i	0.0966257	+	0.167361i	−0.813660	+	0.581341i	$0.802528\pi$
$228$		0			0
$229$	16.2387	+	9.37541i	1.07308	+	0.619545i	0.929022	−	0.370024i	$-0.120651\pi$
$229$	16.2387	+	9.37541i	1.07308	+	0.619545i	0.144061	+	0.989569i	$0.453984\pi$
$230$	−2.40361	+	4.16318i	−0.158490	+	0.274512i
$231$		0			0
$232$	5.54356	+	9.60173i	0.363953	+	0.630384i
$233$		−	5.14191i		−	0.336858i	−0.985714	−	0.168429i	$-0.946131\pi$
$233$		−	5.14191i		−	0.336858i	0.985714	−	0.168429i	$-0.0538693\pi$
$234$		0			0
$235$	−5.62593			−0.366995
$236$	18.9311	+	32.7897i	1.23231	+	2.13443i
$237$		0			0
$238$	11.2560	+	26.3253i	0.729618	+	1.70641i
$239$	−14.7909	−	8.53953i	−0.956743	−	0.552376i	−0.0615742	−	0.998103i	$-0.519612\pi$
$239$	−14.7909	−	8.53953i	−0.956743	−	0.552376i	−0.895169	+	0.445726i	$0.852945\pi$
$240$		0			0
$241$	−18.1230	+	10.4633i	−1.16740	+	0.674000i	−0.953067	−	0.302760i	$-0.902092\pi$
$241$	−18.1230	+	10.4633i	−1.16740	+	0.674000i	−0.214335	+	0.976760i	$0.568759\pi$
$242$		−	11.0913i		−	0.712973i
$243$		0			0
$244$			2.23271i			0.142935i
$245$	−4.83613	+	5.06082i	−0.308969	+	0.323324i
$246$		0			0
$247$	0.217090	−	0.376010i	0.0138131	−	0.0239250i
$248$	7.72961	−	13.3881i	0.490831	−	0.850143i
$249$		0			0
$250$	1.94805	−	1.12471i	0.123206	−	0.0711328i
$251$	3.52350			0.222401			0.111201	−	0.993798i	$-0.464530\pi$
$251$	3.52350			0.222401			0.111201	+	0.993798i	$0.464530\pi$
$252$		0			0
$253$	−5.26493			−0.331004
$254$	10.0028	−	5.77510i	0.627629	−	0.362362i
$255$		0			0
$256$	5.39757	−	9.34886i	0.337348	−	0.584304i
$257$	−0.354048	+	0.613230i	−0.0220849	+	0.0382522i	−0.876857	−	0.480752i	$-0.840364\pi$
$257$	−0.354048	+	0.613230i	−0.0220849	+	0.0382522i	0.854772	+	0.519004i	$0.173697\pi$
$258$		0			0
$259$	1.35541	−	11.2835i	0.0842210	−	0.701124i
$260$			1.18874i			0.0737222i
$261$		0			0
$262$			28.1386i			1.73841i
$263$	−8.83427	+	5.10047i	−0.544744	+	0.314508i	−0.747000	−	0.664825i	$-0.768506\pi$
$263$	−8.83427	+	5.10047i	−0.544744	+	0.314508i	0.202255	+	0.979333i	$0.435173\pi$
$264$		0			0
$265$	−8.42463	−	4.86396i	−0.517521	−	0.298791i
$266$	−6.11574	+	2.61493i	−0.374980	+	0.160332i
$267$		0			0
$268$	−17.5558	−	30.4076i	−1.07239	−	1.85744i
$269$	30.0939			1.83486			0.917429	−	0.397900i	$-0.130261\pi$
$269$	30.0939			1.83486			0.917429	+	0.397900i	$0.130261\pi$
$270$		0			0
$271$			6.23015i			0.378455i	0.981933	+	0.189227i	$0.0605983\pi$
$271$			6.23015i			0.378455i	−0.981933	+	0.189227i	$0.939402\pi$
$272$	1.82061	+	3.15338i	0.110390	+	0.191202i
$273$		0			0
$274$	−7.95689	+	13.7817i	−0.480693	+	0.832585i
$275$	2.13353	+	1.23180i	0.128657	+	0.0742800i
$276$		0			0
$277$	−0.132848	−	0.230100i	−0.00798208	−	0.0138254i	0.862007	−	0.506897i	$-0.169207\pi$
$277$	−0.132848	−	0.230100i	−0.00798208	−	0.0138254i	−0.869989	+	0.493071i	$0.835874\pi$
$278$	−24.8980			−1.49328
$279$		0			0
$280$	3.78289	−	5.04755i	0.226071	−	0.301649i
$281$	−12.0611	+	6.96348i	−0.719505	+	0.415406i	−0.814570	−	0.580065i	$-0.803027\pi$
$281$	−12.0611	+	6.96348i	−0.719505	+	0.415406i	0.0950655	+	0.995471i	$0.469694\pi$
$282$		0			0
$283$	−13.7248	−	7.92403i	−0.815856	−	0.471035i	0.0331293	−	0.999451i	$-0.489453\pi$
$283$	−13.7248	−	7.92403i	−0.815856	−	0.471035i	−0.848985	+	0.528416i	$0.822786\pi$
$284$	−40.1295	−	23.1688i	−2.38125	−	1.37482i
$285$		0			0
$286$	−1.86445	+	1.07644i	−0.110247	+	0.0636511i
$287$	2.01804	+	1.51242i	0.119121	+	0.0892752i
$288$		0			0
$289$	6.14333			0.361372
$290$	5.23036	+	9.05925i	0.307137	+	0.531978i
$291$		0			0
$292$	−28.0220	−	16.1785i	−1.63986	−	0.946775i
$293$	3.37071	−	5.83823i	0.196919	−	0.341073i	−0.750609	−	0.660747i	$-0.770240\pi$
$293$	3.37071	−	5.83823i	0.196919	−	0.341073i	0.947528	+	0.319673i	$0.103573\pi$
$294$		0			0
$295$	6.18688	+	10.7160i	0.360214	+	0.623909i
$296$			10.2408i			0.595234i
$297$		0			0
$298$	−19.2241			−1.11362
$299$	−0.415121	−	0.719011i	−0.0240071	−	0.0415815i
$300$		0			0
$301$	−25.3658	+	10.8457i	−1.46206	+	0.625137i
$302$	30.6498	+	17.6956i	1.76370	+	1.01827i
$303$		0			0
$304$	−0.732575	+	0.422953i	−0.0420161	+	0.0242580i
$305$			0.729673i			0.0417810i
$306$		0			0
$307$		−	1.61431i		−	0.0921335i	−0.998938	−	0.0460668i	$-0.985331\pi$
$307$		−	1.61431i		−	0.0921335i	0.998938	−	0.0460668i	$-0.0146687\pi$
$308$	19.8021	+	2.37869i	1.12833	+	0.135538i
$309$		0			0
$310$	7.29290	−	12.6317i	0.414209	−	0.717431i
$311$	7.87129	−	13.6335i	0.446340	−	0.773083i	−0.551805	−	0.833973i	$-0.686061\pi$
$311$	7.87129	−	13.6335i	0.446340	−	0.773083i	0.998144	+	0.0608901i	$0.0193939\pi$
$312$		0			0
$313$	3.38500	−	1.95433i	0.191332	−	0.110465i	−0.401274	−	0.915958i	$-0.631433\pi$
$313$	3.38500	−	1.95433i	0.191332	−	0.110465i	0.592606	+	0.805493i	$0.298099\pi$
$314$	44.7560			2.52573
$315$		0			0
$316$	45.0382			2.53360
$317$	21.3367	−	12.3187i	1.19839	−	0.691889i	0.238191	−	0.971218i	$-0.423446\pi$
$317$	21.3367	−	12.3187i	1.19839	−	0.691889i	0.960195	+	0.279330i	$0.0901123\pi$
$318$		0			0
$319$	−5.72836	+	9.92180i	−0.320726	+	0.555514i
$320$	6.52087	−	11.2945i	0.364528	−	0.631380i
$321$		0			0
$322$	−1.51691	+	12.6279i	−0.0845339	+	0.703728i
$323$			5.37653i			0.299158i
$324$		0			0
$325$			0.388491i			0.0215496i
$326$	−0.430010	+	0.248266i	−0.0238160	+	0.0137502i
$327$		0			0
$328$	−1.96804	−	1.13625i	−0.108667	−	0.0627388i
$329$	−13.6862	+	5.85187i	−0.754546	+	0.322624i
$330$		0			0
$331$	−4.61821	−	7.99898i	−0.253840	−	0.439664i	0.710740	−	0.703455i	$-0.248360\pi$
$331$	−4.61821	−	7.99898i	−0.253840	−	0.439664i	−0.964580	+	0.263791i	$0.915027\pi$
$332$	−36.5555			−2.00624
$333$		0			0
$334$		−	57.1120i		−	3.12503i
$335$	−5.73742	−	9.93750i	−0.313469	−	0.542943i
$336$		0			0
$337$	1.28651	−	2.22831i	0.0700809	−	0.121384i	−0.828856	−	0.559462i	$-0.811008\pi$
$337$	1.28651	−	2.22831i	0.0700809	−	0.121384i	0.898937	+	0.438079i	$0.144341\pi$
$338$	25.0307	+	14.4515i	1.36149	+	0.786056i
$339$		0			0
$340$	−7.36016	−	12.7482i	−0.399161	−	0.691367i
$341$	15.9745			0.865070
$342$		0			0
$343$	−6.50081	+	17.3418i	−0.351011	+	0.936371i
$344$	21.5286	−	12.4295i	1.16074	−	0.670156i
$345$		0			0
$346$	−28.2873	−	16.3317i	−1.52074	−	0.877998i
$347$	16.4541	+	9.49979i	0.883303	+	0.509975i	0.871746	−	0.489958i	$-0.162988\pi$
$347$	16.4541	+	9.49979i	0.883303	+	0.509975i	0.0115570	+	0.999933i	$0.496321\pi$
$348$		0			0
$349$	9.19557	−	5.30906i	0.492227	−	0.284188i	−0.233271	−	0.972412i	$-0.574943\pi$
$349$	9.19557	−	5.30906i	0.492227	−	0.284188i	0.725498	+	0.688224i	$0.241609\pi$
$350$	3.56916	−	4.76238i	0.190780	−	0.254560i
$351$		0			0
$352$	15.9414			0.849679
$353$	0.838153	+	1.45172i	0.0446104	+	0.0772674i	0.887468	−	0.460869i	$-0.152462\pi$
$353$	0.838153	+	1.45172i	0.0446104	+	0.0772674i	−0.842858	+	0.538136i	$0.819129\pi$
$354$		0			0
$355$	−13.1147	−	7.57180i	−0.696058	−	0.401869i
$356$	−21.8049	+	37.7672i	−1.15566	+	2.00166i
$357$		0			0
$358$	16.9209	+	29.3078i	0.894295	+	1.54896i
$359$		−	20.7692i		−	1.09616i	−0.836428	−	0.548078i	$-0.815360\pi$
$359$		−	20.7692i		−	1.09616i	0.836428	−	0.548078i	$-0.184640\pi$
$360$		0			0
$361$	17.7510			0.934261
$362$	20.4276	+	35.3816i	1.07365	+	1.85962i
$363$		0			0
$364$	1.23648	+	2.89184i	0.0648090	+	0.151574i
$365$	−9.15786	−	5.28729i	−0.479344	−	0.276750i
$366$		0			0
$367$	25.5963	−	14.7780i	1.33612	−	0.771407i	0.349886	−	0.936792i	$-0.386220\pi$
$367$	25.5963	−	14.7780i	1.33612	−	0.771407i	0.986229	+	0.165385i	$0.0528868\pi$
$368$			1.61755i			0.0843205i
$369$		0			0
$370$			9.66221i			0.502314i
$371$	−25.5540	−	3.06962i	−1.32670	−	0.159367i
$372$		0			0
$373$	−5.41206	+	9.37397i	−0.280226	+	0.485366i	−0.971440	−	0.237284i	$-0.923743\pi$
$373$	−5.41206	+	9.37397i	−0.280226	+	0.485366i	0.691214	+	0.722650i	$0.257076\pi$
$374$	13.3297	−	23.0878i	0.689264	−	1.19384i
$375$		0			0
$376$	11.6159	−	6.70643i	0.599043	−	0.345858i
$377$	−1.80664			−0.0930468
$378$		0			0
$379$	30.6805			1.57595			0.787976	−	0.615706i	$-0.211129\pi$
$379$	30.6805			1.57595			0.787976	+	0.615706i	$0.211129\pi$
$380$	2.96158	−	1.70987i	0.151926	−	0.0877145i
$381$		0			0
$382$	−2.23180	+	3.86559i	−0.114189	+	0.197781i
$383$	7.24288	−	12.5450i	0.370094	−	0.641022i	−0.619486	−	0.785008i	$-0.712659\pi$
$383$	7.24288	−	12.5450i	0.370094	−	0.641022i	0.989580	+	0.143986i	$0.0459921\pi$
$384$		0			0
$385$	6.47152	+	0.777379i	0.329819	+	0.0396189i
$386$			29.7392i			1.51369i
$387$		0			0
$388$		−	12.2504i		−	0.621918i
$389$	16.0958	−	9.29294i	0.816092	−	0.471171i	−0.0329752	−	0.999456i	$-0.510498\pi$
$389$	16.0958	−	9.29294i	0.816092	−	0.471171i	0.849067	+	0.528285i	$0.177165\pi$
$390$		0			0
$391$	8.90365	+	5.14052i	0.450277	+	0.259967i
$392$	3.95239	−	16.2140i	0.199626	−	0.818932i
$393$		0			0
$394$	−18.1810	−	31.4905i	−0.915947	−	1.58647i
$395$	14.7189			0.740590
$396$		0			0
$397$			10.0525i			0.504521i	0.967659	+	0.252261i	$0.0811740\pi$
$397$			10.0525i			0.504521i	−0.967659	+	0.252261i	$0.918826\pi$
$398$	−30.7479	−	53.2569i	−1.54125	−	2.66953i
$399$		0			0
$400$	0.378445	−	0.655486i	0.0189223	−	0.0327743i
$401$	16.3738	+	9.45340i	0.817667	+	0.472080i	0.849611	−	0.527410i	$-0.176837\pi$
$401$	16.3738	+	9.45340i	0.817667	+	0.472080i	−0.0319444	+	0.999490i	$0.510170\pi$
$402$		0			0
$403$	1.25954	+	2.18158i	0.0627420	+	0.108672i
$404$	−22.7330			−1.13101
$405$		0			0
$406$	22.1470	+	16.5981i	1.09914	+	0.823749i
$407$	−9.16443	+	5.29109i	−0.454264	+	0.262269i
$408$		0			0
$409$	4.97809	+	2.87410i	0.246151	+	0.142115i	0.618000	−	0.786178i	$-0.287943\pi$
$409$	4.97809	+	2.87410i	0.246151	+	0.142115i	−0.371850	+	0.928293i	$0.621276\pi$
$410$	−1.85685	−	1.07205i	−0.0917032	−	0.0529449i
$411$		0			0
$412$	23.2255	−	13.4092i	1.14424	−	0.660625i
$413$	26.1972	+	19.6335i	1.28908	+	0.966102i
$414$		0			0
$415$	−11.9467			−0.586440
$416$	1.25692	+	2.17705i	0.0616256	+	0.106739i
$417$		0			0
$418$	5.36362	+	3.09669i	0.262343	+	0.151464i
$419$	3.76615	−	6.52317i	0.183989	−	0.318678i	−0.759247	−	0.650803i	$-0.774432\pi$
$419$	3.76615	−	6.52317i	0.183989	−	0.318678i	0.943235	+	0.332125i	$0.107766\pi$
$420$		0			0
$421$	4.57617	+	7.92615i	0.223029	+	0.386297i	0.955726	−	0.294257i	$-0.0950723\pi$
$421$	4.57617	+	7.92615i	0.223029	+	0.386297i	−0.732697	+	0.680554i	$0.761739\pi$
$422$		−	3.54560i		−	0.172597i
$423$		0			0
$424$	23.1925			1.12633
$425$	−2.40538	−	4.16623i	−0.116678	−	0.202092i
$426$		0			0
$427$	0.758978	+	1.77508i	0.0367295	+	0.0859022i
$428$	10.7716	+	6.21897i	0.520663	+	0.300605i
$429$		0			0
$430$	20.3123	−	11.7273i	0.979545	−	0.565541i
$431$			5.09485i			0.245410i	0.992443	+	0.122705i	$0.0391570\pi$
$431$			5.09485i			0.245410i	−0.992443	+	0.122705i	$0.960843\pi$
$432$		0			0
$433$			35.8805i			1.72430i	0.506649	+	0.862152i	$0.330884\pi$
$433$			35.8805i			1.72430i	−0.506649	+	0.862152i	$0.669116\pi$
$434$	4.60251	−	38.3150i	0.220927	−	1.83918i
$435$		0			0
$436$	17.4121	−	30.1586i	0.833888	−	1.44434i
$437$	−1.19422	+	2.06844i	−0.0571271	+	0.0989471i
$438$		0			0
$439$	0.641214	−	0.370205i	0.0306035	−	0.0176689i	−0.484620	−	0.874725i	$-0.661042\pi$
$439$	0.641214	−	0.370205i	0.0306035	−	0.0176689i	0.515224	+	0.857056i	$0.327709\pi$
$440$	−5.87348			−0.280007
$441$		0			0
$442$	4.20401			0.199964
$443$	14.9440	−	8.62790i	0.710009	−	0.409924i	−0.101056	−	0.994881i	$-0.532222\pi$
$443$	14.9440	−	8.62790i	0.710009	−	0.409924i	0.811064	+	0.584957i	$0.198889\pi$
$444$		0			0
$445$	−7.12607	+	12.3427i	−0.337808	+	0.585101i
$446$	16.4269	−	28.4522i	0.777835	−	1.34725i
$447$		0			0
$448$	4.11528	−	34.2589i	0.194429	−	1.61858i
$449$			20.5062i			0.967747i	0.875138	+	0.483874i	$0.160771\pi$
$449$			20.5062i			0.967747i	−0.875138	+	0.483874i	$0.839229\pi$
$450$		0			0
$451$		−	2.34825i		−	0.110575i
$452$	23.2401	−	13.4177i	1.09312	−	0.631115i
$453$		0			0
$454$	−5.67200	−	3.27473i	−0.266200	−	0.153691i
$455$	0.404093	+	0.945084i	0.0189442	+	0.0443062i
$456$		0			0
$457$	4.57715	+	7.92786i	0.214110	+	0.370849i	0.952997	−	0.302980i	$-0.0979816\pi$
$457$	4.57715	+	7.92786i	0.214110	+	0.370849i	−0.738887	+	0.673829i	$0.764648\pi$
$458$	−42.1785			−1.97087
$459$		0			0
$460$		−	6.53927i		−	0.304895i
$461$	5.07463	+	8.78951i	0.236349	+	0.409368i	0.959664	−	0.281150i	$-0.0907158\pi$
$461$	5.07463	+	8.78951i	0.236349	+	0.409368i	−0.723315	+	0.690518i	$0.757382\pi$
$462$		0			0
$463$	−0.613755	+	1.06305i	−0.0285236	+	0.0494043i	−0.879935	−	0.475094i	$-0.842414\pi$
$463$	−0.613755	+	1.06305i	−0.0285236	+	0.0494043i	0.851411	+	0.524499i	$0.175747\pi$
$464$	3.04828	+	1.75993i	0.141513	+	0.0817025i
$465$		0			0
$466$	5.78315	+	10.0167i	0.267899	+	0.464015i
$467$	−23.2327			−1.07508			−0.537540	−	0.843238i	$-0.680646\pi$
$467$	−23.2327			−1.07508			−0.537540	+	0.843238i	$0.680646\pi$
$468$		0			0
$469$	−24.2941	−	18.2072i	−1.12180	−	0.840729i
$470$	10.9596	−	6.32753i	0.505529	−	0.291867i
$471$		0			0
$472$	−25.5482	−	14.7502i	−1.17595	−	0.678935i
$473$	22.2463	+	12.8439i	1.02288	+	0.590562i
$474$		0			0
$475$	0.967875	−	0.558803i	0.0444092	−	0.0256396i
$476$	−31.1653	−	23.3568i	−1.42846	−	1.07056i
$477$		0			0
$478$	38.4179			1.75720
$479$	15.6175	+	27.0504i	0.713583	+	1.23596i	0.963503	+	0.267696i	$0.0862623\pi$
$479$	15.6175	+	27.0504i	0.713583	+	1.23596i	−0.249920	+	0.968266i	$0.580404\pi$
$480$		0			0
$481$	−1.44517	−	0.834367i	−0.0658939	−	0.0380438i
$482$	23.5363	−	40.7661i	1.07205	−	1.85684i
$483$		0			0
$484$	7.54371	+	13.0661i	0.342896	+	0.593913i
$485$		−	4.00354i		−	0.181791i
$486$		0			0
$487$	−10.7164			−0.485605			−0.242802	−	0.970076i	$-0.578067\pi$
$487$	−10.7164			−0.485605			−0.242802	+	0.970076i	$0.578067\pi$
$488$	−0.869813	−	1.50656i	−0.0393746	−	0.0681988i
$489$		0			0
$490$	3.72909	−	15.2980i	0.168463	−	0.691092i
$491$	0.912341	+	0.526740i	0.0411734	+	0.0237715i	0.520445	−	0.853895i	$-0.325766\pi$
$491$	0.912341	+	0.526740i	0.0411734	+	0.0237715i	−0.479272	+	0.877666i	$0.659099\pi$
$492$		0			0
$493$	19.3747	−	11.1860i	0.872593	−	0.503792i
$494$			0.976651i			0.0439416i
$495$		0			0
$496$		−	4.90787i		−	0.220370i
$497$	−39.7802	−	4.77852i	−1.78439	−	0.214346i
$498$		0			0
$499$	−2.52065	+	4.36589i	−0.112840	+	0.195444i	−0.916914	−	0.399085i	$-0.869328\pi$
$499$	−2.52065	+	4.36589i	−0.112840	+	0.195444i	0.804074	+	0.594529i	$0.202661\pi$
$500$	−1.52994	+	2.64993i	−0.0684210	+	0.118509i
$501$		0			0
$502$	−6.86396	+	3.96291i	−0.306354	+	0.176873i
$503$	−34.8769			−1.55508			−0.777542	−	0.628831i	$-0.783534\pi$
$503$	−34.8769			−1.55508			−0.777542	+	0.628831i	$0.783534\pi$
$504$		0			0
$505$	−7.42938			−0.330603
$506$	10.2564	−	5.92152i	0.455951	−	0.263244i
$507$		0			0
$508$	−7.85586	+	13.6067i	−0.348547	+	0.603702i
$509$	−3.07394	+	5.32422i	−0.136250	+	0.235992i	−0.926074	−	0.377341i	$-0.876838\pi$
$509$	−3.07394	+	5.32422i	−0.136250	+	0.235992i	0.789824	+	0.613333i	$0.210172\pi$
$510$		0			0
$511$	−27.7780	−	3.33678i	−1.22883	−	0.147610i
$512$		−	8.50671i		−	0.375947i
$513$		0			0
$514$		−	1.59280i		−	0.0702556i
$515$	7.59032	−	4.38227i	0.334469	−	0.193106i
$516$		0			0
$517$	12.0031	+	6.92999i	0.527896	+	0.304781i
$518$	10.0503	+	23.5053i	0.441583	+	1.03276i
$519$		0			0
$520$	−0.463103	−	0.802118i	−0.0203084	−	0.0351752i
$521$	−20.2902			−0.888932			−0.444466	−	0.895796i	$-0.646606\pi$
$521$	−20.2902			−0.888932			−0.444466	+	0.895796i	$0.646606\pi$
$522$		0			0
$523$			15.6812i			0.685690i	0.939392	+	0.342845i	$0.111391\pi$
$523$			15.6812i			0.685690i	−0.939392	+	0.342845i	$0.888609\pi$
$524$	−19.1385	−	33.1488i	−0.836067	−	1.44811i
$525$		0			0
$526$	11.4731	−	19.8720i	0.500250	−	0.866459i
$527$	−27.0149	−	15.5971i	−1.17679	−	0.679419i
$528$		0			0
$529$	−9.21641	−	15.9633i	−0.400713	−	0.694056i
$530$	21.8822			0.950501
$531$		0			0
$532$	5.42612	−	7.24014i	0.235252	−	0.313900i
$533$	0.320691	−	0.185151i	0.0138907	−	0.00801978i
$534$		0			0
$535$	3.52026	+	2.03242i	0.152194	+	0.0878692i
$536$	23.6921	+	13.6787i	1.02334	+	0.590828i
$537$		0			0
$538$	−58.6245	+	33.8469i	−2.52748	+	1.45924i
$539$	16.5519	−	4.84030i	0.712942	−	0.208486i
$540$		0			0
$541$	19.2258			0.826583			0.413291	−	0.910599i	$-0.364379\pi$
$541$	19.2258			0.826583			0.413291	+	0.910599i	$0.364379\pi$
$542$	−7.00711	−	12.1367i	−0.300981	−	0.521314i
$543$		0			0
$544$	−26.9588	−	15.5647i	−1.15585	−	0.667331i
$545$	5.69045	−	9.85615i	0.243752	−	0.422191i
$546$		0			0
$547$	−12.9816	−	22.4848i	−0.555053	−	0.961379i	−0.997899	−	0.0647821i	$-0.979365\pi$
$547$	−12.9816	−	22.4848i	−0.555053	−	0.961379i	0.442847	−	0.896597i	$-0.353969\pi$
$548$		−	21.6475i		−	0.924735i
$549$		0			0
$550$	−5.54164			−0.236296
$551$	2.59866	+	4.50102i	0.110707	+	0.191750i
$552$		0			0
$553$	35.8069	−	15.3101i	1.52266	−	0.651051i
$554$	0.517591	+	0.298831i	0.0219903	+	0.0126961i
$555$		0			0
$556$	29.3312	−	16.9344i	1.24392	−	0.718177i
$557$			5.78189i			0.244987i	0.992469	+	0.122493i	$0.0390890\pi$
$557$			5.78189i			0.244987i	−0.992469	+	0.122493i	$0.960911\pi$
$558$		0			0
$559$			4.05078i			0.171330i
$560$	0.238834	−	1.98825i	0.0100926	−	0.0840189i
$561$		0			0
$562$	15.6638	−	27.1305i	0.660737	−	1.14443i
$563$	−18.8450	+	32.6404i	−0.794220	+	1.37563i	0.129113	+	0.991630i	$0.458787\pi$
$563$	−18.8450	+	32.6404i	−0.794220	+	1.37563i	−0.923333	+	0.384000i	$0.874546\pi$
$564$		0			0
$565$	7.59510	−	4.38503i	0.319528	−	0.184480i
$566$	35.6489			1.49844
$567$		0			0
$568$	36.1041			1.51489
$569$	−11.9150	+	6.87915i	−0.499504	+	0.288389i	−0.728509	−	0.685037i	$-0.759786\pi$
$569$	−11.9150	+	6.87915i	−0.499504	+	0.288389i	0.229005	+	0.973425i	$0.426453\pi$
$570$		0			0
$571$	−10.5199	+	18.2211i	−0.440246	+	0.762528i	−0.997707	−	0.0676747i	$-0.978442\pi$
$571$	−10.5199	+	18.2211i	−0.440246	+	0.762528i	0.557462	+	0.830203i	$0.311775\pi$
$572$	1.46428	−	2.53620i	0.0612245	−	0.106044i
$573$		0			0
$574$	−5.63228	−	0.676566i	−0.235087	−	0.0282393i
$575$		−	2.13710i		−	0.0891231i
$576$		0			0
$577$		−	12.0259i		−	0.500643i	−0.968163	−	0.250321i	$-0.919464\pi$
$577$		−	12.0259i		−	0.500643i	0.968163	−	0.250321i	$-0.0805363\pi$
$578$	−11.9675	+	6.90946i	−0.497784	+	0.287396i
$579$		0			0
$580$	−12.3233	−	7.11485i	−0.511697	−	0.295428i
$581$	−29.0628	+	12.4265i	−1.20573	+	0.515538i
$582$		0			0
$583$	11.9828	+	20.7548i	0.496277	+	0.859577i
$584$	25.2110			1.04324
$585$		0			0
$586$			15.1643i			0.626429i
$587$	0.136440	+	0.236321i	0.00563148	+	0.00975402i	0.868827	−	0.495115i	$-0.164874\pi$
$587$	0.136440	+	0.236321i	0.00563148	+	0.00975402i	−0.863196	+	0.504869i	$0.831541\pi$
$588$		0			0
$589$	3.62342	−	6.27595i	0.149300	−	0.258596i
$590$	−24.1047	−	13.9169i	−0.992377	−	0.572949i
$591$		0			0
$592$	1.62558	+	2.81559i	0.0668111	+	0.115720i
$593$	3.61889			0.148610			0.0743050	−	0.997236i	$-0.476326\pi$
$593$	3.61889			0.148610			0.0743050	+	0.997236i	$0.476326\pi$
$594$		0			0
$595$	−10.1851	−	7.63324i	−0.417550	−	0.312933i
$596$	22.6470	−	13.0753i	0.927658	−	0.535584i
$597$		0			0
$598$	1.61736	+	0.933781i	0.0661386	+	0.0381852i
$599$	21.6954	+	12.5258i	0.886448	+	0.511791i	0.872779	−	0.488115i	$-0.162315\pi$
$599$	21.6954	+	12.5258i	0.886448	+	0.511791i	0.0136692	+	0.999907i	$0.495649\pi$
$600$		0			0
$601$	17.6859	−	10.2110i	0.721424	−	0.416515i	−0.0938524	−	0.995586i	$-0.529918\pi$
$601$	17.6859	−	10.2110i	0.721424	−	0.416515i	0.815277	+	0.579072i	$0.196585\pi$
$602$	37.2155	−	49.6571i	1.51679	−	2.02387i
$603$		0			0
$604$	−48.1427			−1.95890
$605$	2.46536	+	4.27013i	0.100231	+	0.173606i
$606$		0			0
$607$	20.8266	+	12.0243i	0.845327	+	0.488050i	0.859071	−	0.511856i	$-0.171042\pi$
$607$	20.8266	+	12.0243i	0.845327	+	0.488050i	−0.0137445	+	0.999906i	$0.504375\pi$
$608$	3.61590	−	6.26292i	0.146644	−	0.253995i
$609$		0			0
$610$	−0.820670	−	1.42144i	−0.0332280	−	0.0575525i
$611$			2.18562i			0.0884207i
$612$		0			0
$613$	19.0207			0.768239			0.384120	−	0.923283i	$-0.374505\pi$
$613$	19.0207			0.768239			0.384120	+	0.923283i	$0.374505\pi$
$614$	1.81563	+	3.14476i	0.0732728	+	0.126912i
$615$		0			0
$616$	−14.2885	+	6.10937i	−0.575699	+	0.246154i
$617$	28.5311	+	16.4725i	1.14862	+	0.663157i	0.948551	−	0.316625i	$-0.102550\pi$
$617$	28.5311	+	16.4725i	1.14862	+	0.663157i	0.200070	+	0.979782i	$0.435883\pi$
$618$		0			0
$619$	−17.7455	+	10.2454i	−0.713253	+	0.411797i	−0.812264	−	0.583290i	$-0.801765\pi$
$619$	−17.7455	+	10.2454i	−0.713253	+	0.411797i	0.0990114	+	0.995086i	$0.468432\pi$
$620$			19.8411i			0.796836i
$621$		0			0
$622$			35.4116i			1.41988i
$623$	−4.49722	+	37.4385i	−0.180177	+	1.49994i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−4.39611	+	7.61429i	−0.175704	+	0.304328i
$627$		0			0
$628$	−52.7250	+	30.4408i	−2.10396	+	1.21472i
$629$	20.6642			0.823937
$630$		0			0
$631$	−47.0272			−1.87212			−0.936061	−	0.351838i	$-0.885557\pi$
$631$	−47.0272			−1.87212			−0.936061	+	0.351838i	$0.885557\pi$
$632$	−30.3903	+	17.5458i	−1.20886	+	0.697935i
$633$		0			0
$634$	−27.7100	+	47.9951i	−1.10050	+	1.90613i
$635$	−2.56737	+	4.44682i	−0.101883	+	0.176467i
$636$		0			0
$637$	1.96608	+	1.87879i	0.0778989	+	0.0744404i
$638$		−	25.7709i		−	1.02028i
$639$		0			0
$640$			16.3947i			0.648059i
$641$	1.78047	−	1.02796i	0.0703244	−	0.0406018i	−0.464426	−	0.885612i	$-0.653739\pi$
$641$	1.78047	−	1.02796i	0.0703244	−	0.0406018i	0.534750	+	0.845010i	$0.320406\pi$
$642$		0			0
$643$	−38.6058	−	22.2891i	−1.52246	−	0.878995i	−0.999647	−	0.0265505i	$-0.991548\pi$
$643$	−38.6058	−	22.2891i	−1.52246	−	0.878995i	−0.522817	−	0.852445i	$-0.675119\pi$
$644$	−6.80189	−	15.9081i	−0.268032	−	0.626868i
$645$		0			0
$646$	−6.04703	−	10.4738i	−0.237917	−	0.412084i
$647$	−8.06386			−0.317023			−0.158512	−	0.987357i	$-0.550670\pi$
$647$	−8.06386			−0.317023			−0.158512	+	0.987357i	$0.550670\pi$
$648$		0			0
$649$		−	30.4839i		−	1.19660i
$650$	−0.436939	−	0.756800i	−0.0171382	−	0.0296842i
$651$		0			0
$652$	0.337716	−	0.584942i	0.0132260	−	0.0229081i
$653$	10.8478	+	6.26301i	0.424509	+	0.245090i	0.697005	−	0.717067i	$-0.254516\pi$
$653$	10.8478	+	6.26301i	0.424509	+	0.245090i	−0.272496	+	0.962157i	$0.587849\pi$
$654$		0			0
$655$	−6.25464	−	10.8334i	−0.244389	−	0.423294i
$656$	−0.721454			−0.0281680
$657$		0			0
$658$	20.0799	−	26.7928i	0.782794	−	1.04449i
$659$	−5.31567	+	3.06900i	−0.207069	+	0.119551i	−0.599949	−	0.800039i	$-0.704812\pi$
$659$	−5.31567	+	3.06900i	−0.207069	+	0.119551i	0.392880	+	0.919590i	$0.371479\pi$
$660$		0			0
$661$	−5.75735	−	3.32400i	−0.223935	−	0.129289i	0.383836	−	0.923401i	$-0.374603\pi$
$661$	−5.75735	−	3.32400i	−0.223935	−	0.129289i	−0.607771	+	0.794112i	$0.707936\pi$
$662$	17.9930	+	10.3883i	0.699319	+	0.403752i
$663$		0			0
$664$	24.6664	−	14.2412i	0.957242	−	0.552664i
$665$	1.77331	−	2.36615i	0.0687661	−	0.0917554i
$666$		0			0
$667$	9.93839			0.384816
$668$	38.8447	+	67.2810i	1.50295	+	2.60318i
$669$		0			0
$670$	22.3536	+	12.9058i	0.863594	+	0.498596i
$671$	0.898808	−	1.55678i	0.0346981	−	0.0600989i
$672$		0			0
$673$	0.875991	+	1.51726i	0.0337670	+	0.0584861i	0.882415	−	0.470472i	$-0.155916\pi$
$673$	0.875991	+	1.51726i	0.0337670	+	0.0584861i	−0.848648	+	0.528958i	$0.822583\pi$
$674$			5.78781i			0.222938i
$675$		0			0
$676$	−39.3166			−1.51218
$677$	7.49127	+	12.9753i	0.287913	+	0.498680i	0.973311	−	0.229488i	$-0.0737053\pi$
$677$	7.49127	+	12.9753i	0.287913	+	0.498680i	−0.685398	+	0.728168i	$0.740372\pi$
$678$		0			0
$679$	−4.16433	−	9.73944i	−0.159812	−	0.373765i
$680$	9.93278	+	5.73469i	0.380905	+	0.219915i
$681$		0			0
$682$	−31.1193	+	17.9667i	−1.19162	+	0.687981i
$683$			11.6024i			0.443954i	0.975052	+	0.221977i	$0.0712509\pi$
$683$			11.6024i			0.443954i	−0.975052	+	0.221977i	$0.928749\pi$
$684$		0			0
$685$		−	7.07462i		−	0.270307i
$686$	−6.84060	−	41.0943i	−0.261175	−	1.56899i
$687$		0			0
$688$	3.94603	−	6.83473i	0.150441	−	0.260572i
$689$	−1.88960	+	3.27289i	−0.0719882	+	0.124687i
$690$		0			0
$691$	7.00564	−	4.04471i	0.266507	−	0.153868i	−0.360792	−	0.932646i	$-0.617494\pi$
$691$	7.00564	−	4.04471i	0.266507	−	0.153868i	0.627299	+	0.778778i	$0.284160\pi$
$692$	44.4320			1.68905
$693$		0			0
$694$	−42.7380			−1.62231
$695$	9.58572	−	5.53432i	0.363607	−	0.209929i
$696$		0			0
$697$	−2.29276	+	3.97118i	−0.0868445	+	0.150419i
$698$	−11.9423	+	20.6847i	−0.452023	+	0.782926i
$699$		0			0
$700$	−0.965536	+	8.03790i	−0.0364938	+	0.303804i
$701$			39.1808i			1.47984i	0.672696	+	0.739919i	$0.265136\pi$
$701$			39.1808i			1.47984i	−0.672696	+	0.739919i	$0.734864\pi$
$702$		0			0
$703$			4.80060i			0.181058i
$704$	−27.8250	+	16.0647i	−1.04869	+	0.605463i
$705$		0			0
$706$	−3.26553	−	1.88536i	−0.122900	−	0.0709563i
$707$	−18.0735	+	7.72775i	−0.679724	+	0.290632i
$708$		0			0
$709$	7.25588	+	12.5676i	0.272500	+	0.471984i	0.969501	−	0.245086i	$-0.0788161\pi$
$709$	7.25588	+	12.5676i	0.272500	+	0.471984i	−0.697001	+	0.717070i	$0.745483\pi$
$710$	34.0643			1.27841
$711$		0			0
$712$		−	33.9787i		−	1.27341i
$713$	−6.92874	−	12.0009i	−0.259484	−	0.449439i
$714$		0			0
$715$	0.478541	−	0.828857i	0.0178964	−	0.0309975i
$716$	−39.8674	−	23.0174i	−1.48991	−	0.860202i
$717$		0			0
$718$	23.3593	+	40.4595i	0.871760	+	1.50993i
$719$	19.8590			0.740618			0.370309	−	0.928909i	$-0.379252\pi$
$719$	19.8590			0.740618			0.370309	+	0.928909i	$0.379252\pi$
$720$		0			0
$721$	13.9067	−	18.5559i	0.517914	−	0.691059i
$722$	−34.5798	+	19.9647i	−1.28693	+	0.743008i
$723$		0			0
$724$	−48.1295	−	27.7876i	−1.78872	−	1.03272i
$725$	−4.02738	−	2.32521i	−0.149573	−	0.0863560i
$726$		0			0
$727$	35.4470	−	20.4653i	1.31466	−	0.759017i	0.331793	−	0.943352i	$-0.392346\pi$
$727$	35.4470	−	20.4653i	1.31466	−	0.759017i	0.982864	+	0.184335i	$0.0590131\pi$
$728$	−1.96093	−	1.46962i	−0.0726768	−	0.0544676i
$729$		0			0
$730$	23.7867			0.880384
$731$	−25.0808	−	43.4412i	−0.927646	−	1.60673i
$732$		0			0
$733$	−22.0712	−	12.7428i	−0.815217	−	0.470666i	0.0335476	−	0.999437i	$-0.489319\pi$
$733$	−22.0712	−	12.7428i	−0.815217	−	0.470666i	−0.848764	+	0.528772i	$0.822653\pi$
$734$	−33.2420	+	57.5768i	−1.22698	+	2.12520i
$735$		0			0
$736$	−6.91436	−	11.9760i	−0.254867	−	0.441442i
$737$			28.2693i			1.04131i
$738$		0			0
$739$	22.6712			0.833973			0.416986	−	0.908913i	$-0.363086\pi$
$739$	22.6712			0.833973			0.416986	+	0.908913i	$0.363086\pi$
$740$	−6.57175	−	11.3826i	−0.241582	−	0.418433i
$741$		0			0
$742$	53.2329	−	22.7610i	1.95424	−	0.835582i
$743$	−1.37485	−	0.793772i	−0.0504385	−	0.0291207i	0.474569	−	0.880218i	$-0.342604\pi$
$743$	−1.37485	−	0.793772i	−0.0504385	−	0.0291207i	−0.525007	+	0.851098i	$0.675937\pi$
$744$		0			0
$745$	7.40128	−	4.27313i	0.271162	−	0.156555i
$746$		−	24.3480i		−	0.891443i
$747$		0			0
$748$			36.2649i			1.32597i
$749$	10.6778	+	1.28265i	0.390158	+	0.0468670i
$750$		0			0
$751$	−18.8024	+	32.5667i	−0.686109	+	1.18838i	0.286978	+	0.957937i	$0.407349\pi$
$751$	−18.8024	+	32.5667i	−0.686109	+	1.18838i	−0.973087	+	0.230439i	$0.925984\pi$
$752$	2.12910	−	3.68772i	0.0776404	−	0.134477i
$753$		0			0
$754$	3.51943	−	2.03195i	0.128170	−	0.0739991i
$755$	−15.7335			−0.572602
$756$		0			0
$757$	10.5426			0.383178			0.191589	−	0.981475i	$-0.438636\pi$
$757$	10.5426			0.383178			0.191589	+	0.981475i	$0.438636\pi$
$758$	−59.7672	+	34.5066i	−2.17084	+	1.25334i
$759$		0			0
$760$	−1.33225	+	2.30753i	−0.0483258	+	0.0837028i
$761$	9.26305	−	16.0441i	0.335785	−	0.581597i	−0.647850	−	0.761768i	$-0.724332\pi$
$761$	9.26305	−	16.0441i	0.335785	−	0.581597i	0.983635	+	0.180171i	$0.0576650\pi$
$762$		0			0
$763$	3.59121	−	29.8961i	0.130010	−	1.08231i
$764$		−	6.07183i		−	0.219671i
$765$		0			0
$766$			32.5845i			1.17733i
$767$	4.16306	−	2.40355i	0.150319	−	0.0867870i
$768$		0			0
$769$	28.4505	+	16.4259i	1.02595	+	0.592333i	0.915822	−	0.401584i	$-0.131540\pi$
$769$	28.4505	+	16.4259i	1.02595	+	0.592333i	0.110129	+	0.993917i	$0.464874\pi$
$770$	−13.4812	+	5.76421i	−0.485829	+	0.207728i
$771$		0			0
$772$	−20.2271	−	35.0344i	−0.727989	−	1.26091i
$773$	27.5217			0.989887			0.494944	−	0.868925i	$-0.335189\pi$
$773$	27.5217			0.989887			0.494944	+	0.868925i	$0.335189\pi$
$774$		0			0
$775$			6.48426i			0.232921i
$776$	4.77245	+	8.26613i	0.171321	+	0.296737i
$777$		0			0
$778$	−20.9037	+	36.2063i	−0.749434	+	1.29806i
$779$	−0.922561	−	0.532641i	−0.0330542	−	0.0190838i
$780$		0			0
$781$	18.6538	+	32.3093i	0.667486	+	1.15612i
$782$	−23.1264			−0.826997
$783$		0			0
$784$	−1.48709	−	5.08526i	−0.0531102	−	0.181616i
$785$	−17.2311	+	9.94836i	−0.615003	+	0.355072i
$786$		0			0
$787$	−8.80451	−	5.08329i	−0.313847	−	0.181200i	0.334800	−	0.942289i	$-0.391331\pi$
$787$	−8.80451	−	5.08329i	−0.313847	−	0.181200i	−0.648647	+	0.761090i	$0.724665\pi$
$788$	42.8365	+	24.7316i	1.52599	+	0.881028i
$789$		0			0
$790$	−28.6733	+	16.5545i	−1.02015	+	0.588983i
$791$	13.9155	−	18.5676i	0.494779	−	0.660189i
$792$		0			0
$793$	0.283471			0.0100664
$794$	−11.3061	−	19.5828i	−0.401240	−	0.694968i
$795$		0			0
$796$	72.4453	+	41.8263i	2.56776	+	1.48249i
$797$	11.2524	−	19.4897i	0.398580	−	0.690362i	−0.594971	−	0.803747i	$-0.702836\pi$
$797$	11.2524	−	19.4897i	0.398580	−	0.690362i	0.993551	+	0.113386i	$0.0361696\pi$
$798$		0			0
$799$	−13.5325	−	23.4389i	−0.478744	−	0.829210i
$800$			6.47079i			0.228777i
$801$		0			0
$802$	−42.5293			−1.50176
$803$	13.0257	+	22.5612i	0.459668	+	0.796168i
$804$		0			0
$805$	−2.22293	−	5.19893i	−0.0783479	−	0.183238i
$806$	−4.90729	−	2.83322i	−0.172852	−	0.0997960i
$807$		0			0
$808$	15.3395	−	8.85625i	0.539641	−	0.311562i
$809$			24.8607i			0.874056i	0.899448	+	0.437028i	$0.143969\pi$
$809$			24.8607i			0.874056i	−0.899448	+	0.437028i	$0.856031\pi$
$810$		0			0
$811$			40.0552i			1.40653i	0.710928	+	0.703264i	$0.248275\pi$
$811$			40.0552i			1.40653i	−0.710928	+	0.703264i	$0.751725\pi$
$812$	−37.3796	−	4.49014i	−1.31177	−	0.157573i
$813$		0			0
$814$	11.9019	−	20.6146i	0.417160	−	0.722543i
$815$	0.110369	−	0.191165i	0.00386606	−	0.00669621i
$816$		0			0
$817$	10.0920	−	5.82662i	0.353074	−	0.203848i
$818$	−12.9301			−0.452091
$819$		0			0
$820$	2.91662			0.101853
$821$	−29.4435	+	16.9992i	−1.02759	+	0.593277i	−0.916292	−	0.400511i	$-0.868833\pi$
$821$	−29.4435	+	16.9992i	−1.02759	+	0.593277i	−0.111294	+	0.993788i	$0.535499\pi$
$822$		0			0
$823$	15.2864	−	26.4768i	0.532850	−	0.922923i	−0.466414	−	0.884566i	$-0.654454\pi$
$823$	15.2864	−	26.4768i	0.532850	−	0.922923i	0.999264	−	0.0383565i	$-0.0122122\pi$
$824$	−10.4478	+	18.0962i	−0.363968	+	0.630411i
$825$		0			0
$826$	−73.1156	−	8.78286i	−2.54402	−	0.305595i
$827$		−	36.8463i		−	1.28127i	−0.767845	−	0.640635i	$-0.778671\pi$
$827$		−	36.8463i		−	1.28127i	0.767845	−	0.640635i	$-0.221329\pi$
$828$		0			0
$829$			41.5579i			1.44337i	0.692224	+	0.721683i	$0.256631\pi$
$829$			41.5579i			1.44337i	−0.692224	+	0.721683i	$0.743369\pi$
$830$	23.2728	−	13.4366i	0.807811	−	0.466390i
$831$		0			0
$832$	−4.38780	−	2.53330i	−0.152120	−	0.0878262i
$833$	−32.7172	−	7.97527i	−1.13359	−	0.276327i
$834$		0			0
$835$	12.6948	+	21.9881i	0.439323	+	0.760930i
$836$	−8.42484			−0.291379
$837$		0			0
$838$			16.9433i			0.585297i
$839$	13.2465	+	22.9437i	0.457321	+	0.792103i	0.998818	−	0.0485991i	$-0.0154757\pi$
$839$	13.2465	+	22.9437i	0.457321	+	0.792103i	−0.541497	+	0.840703i	$0.682142\pi$
$840$		0			0
$841$	−3.68683	+	6.38578i	−0.127132	+	0.220199i
$842$	−17.8292	−	10.2937i	−0.614436	−	0.354745i
$843$		0			0
$844$	2.41154	+	4.17691i	0.0830086	+	0.143775i
$845$	−12.8491			−0.442022
$846$		0			0
$847$	10.4391	+	7.82360i	0.358693	+	0.268822i
$848$	6.37652	−	3.68148i	0.218971	−	0.126423i
$849$		0			0
$850$	9.37160	+	5.41070i	0.321443	+	0.185585i
$851$	7.94990	+	4.58987i	0.272519	+	0.157339i
$852$		0			0
$853$	−2.66454	+	1.53837i	−0.0912321	+	0.0526729i	−0.544922	−	0.838487i	$-0.683441\pi$
$853$	−2.66454	+	1.53837i	−0.0912321	+	0.0526729i	0.453690	+	0.891160i	$0.350107\pi$
$854$	−3.47498	−	2.60432i	−0.118911	−	0.0891181i
$855$		0			0
$856$	−9.69105			−0.331233
$857$	−0.835486	−	1.44710i	−0.0285397	−	0.0494321i	0.851403	−	0.524512i	$-0.175752\pi$
$857$	−0.835486	−	1.44710i	−0.0285397	−	0.0494321i	−0.879942	+	0.475080i	$0.842419\pi$
$858$		0			0
$859$	−30.7586	−	17.7585i	−1.04947	−	0.605911i	−0.126968	−	0.991907i	$-0.540525\pi$
$859$	−30.7586	−	17.7585i	−1.04947	−	0.605911i	−0.922501	+	0.385996i	$0.873858\pi$
$860$	−15.9526	+	27.6308i	−0.543980	+	0.942202i
$861$		0			0
$862$	−5.73023	−	9.92504i	−0.195172	−	0.338048i
$863$		−	29.1514i		−	0.992325i	−0.868230	−	0.496162i	$-0.834742\pi$
$863$		−	29.1514i		−	0.992325i	0.868230	−	0.496162i	$-0.165258\pi$
$864$		0			0
$865$	14.5208			0.493723
$866$	−40.3551	−	69.8970i	−1.37132	−	2.37520i
$867$		0			0
$868$	20.6379	+	48.2675i	0.700496	+	1.63830i
$869$	−31.4033	−	18.1307i	−1.06528	−	0.615042i
$870$		0			0
$871$	−3.86062	+	2.22893i	−0.130812	+	0.0755245i
$872$			27.1334i			0.918852i
$873$		0			0
$874$		−	5.37259i		−	0.181730i
$875$	−0.315547	+	2.62687i	−0.0106674	+	0.0888043i
$876$		0			0
$877$	−3.35894	+	5.81786i	−0.113423	+	0.196455i	−0.917148	−	0.398546i	$-0.869515\pi$
$877$	−3.35894	+	5.81786i	−0.113423	+	0.196455i	0.803725	+	0.595001i	$0.202848\pi$
$878$	−0.832745	+	1.44236i	−0.0281038	+	0.0486772i
$879$		0			0
$880$	−1.61485	+	0.932334i	−0.0544366	+	0.0314290i
$881$	−1.09027			−0.0367322			−0.0183661	−	0.999831i	$-0.505846\pi$
$881$	−1.09027			−0.0367322			−0.0183661	+	0.999831i	$0.505846\pi$
$882$		0			0
$883$	−6.11832			−0.205898			−0.102949	−	0.994687i	$-0.532828\pi$
$883$	−6.11832			−0.205898			−0.102949	+	0.994687i	$0.532828\pi$
$884$	−4.95255	+	2.85935i	−0.166572	+	0.0961705i
$885$		0			0
$886$	−19.4077	+	33.6152i	−0.652016	+	1.12932i
$887$	−22.6970	+	39.3124i	−0.762091	+	1.31998i	0.179679	+	0.983725i	$0.442494\pi$
$887$	−22.6970	+	39.3124i	−0.762091	+	1.31998i	−0.941771	+	0.336256i	$0.890839\pi$
$888$		0			0
$889$	−1.62025	+	13.4883i	−0.0543416	+	0.452383i
$890$		−	32.0590i		−	1.07462i
$891$		0			0
$892$			44.6909i			1.49636i
$893$	5.44520	−	3.14379i	0.182217	−	0.105203i
$894$		0			0
$895$	−13.0291	−	7.52233i	−0.435513	−	0.251444i
$896$	17.0532	+	39.8836i	0.569707	+	1.33242i
$897$		0			0
$898$	−23.0635	−	39.9472i	−0.769639	−	1.33305i
$899$	−30.1545			−1.00571
$900$		0			0
$901$		−	46.7986i		−	1.55909i
$902$	2.64110	+	4.57451i	0.0879389	+	0.152315i
$903$		0			0
$904$	−10.4544	+	18.1076i	−0.347709	+	0.602250i
$905$	−15.7292	−	9.08127i	−0.522857	−	0.301872i
$906$		0			0
$907$	4.94352	+	8.56242i	0.164147	+	0.284311i	0.936352	−	0.351063i	$-0.114180\pi$
$907$	4.94352	+	8.56242i	0.164147	+	0.284311i	−0.772205	+	0.635373i	$0.780846\pi$
$908$	8.90923			0.295663
$909$		0			0
$910$	−1.85014	−	1.38659i	−0.0613315	−	0.0459649i
$911$	34.9512	−	20.1791i	1.15798	−	0.668563i	0.207165	−	0.978306i	$-0.433576\pi$
$911$	34.9512	−	20.1791i	1.15798	−	0.668563i	0.950820	+	0.309743i	$0.100243\pi$
$912$		0			0
$913$	25.4887	+	14.7159i	0.843552	+	0.487025i
$914$	−17.8331	−	10.2959i	−0.589865	−	0.340559i
$915$		0			0
$916$	49.6885	−	28.6877i	1.64175	−	0.947867i
$917$	−26.4841	−	19.8485i	−0.874583	−	0.655456i
$918$		0			0
$919$	20.1949			0.666167			0.333084	−	0.942897i	$-0.391911\pi$
$919$	20.1949			0.666167			0.333084	+	0.942897i	$0.391911\pi$
$920$	2.54754	+	4.41248i	0.0839900	+	0.145475i
$921$		0			0
$922$	−19.7713	−	11.4150i	−0.651133	−	0.375932i
$923$	−2.94157	+	5.09495i	−0.0968230	+	0.167702i
$924$		0			0
$925$	−2.14771	−	3.71995i	−0.0706164	−	0.122311i
$926$		−	2.76118i		−	0.0907381i
$927$		0			0
$928$	−30.0919			−0.987814
$929$	2.47705	+	4.29038i	0.0812694	+	0.140763i	0.903795	−	0.427965i	$-0.140769\pi$
$929$	2.47705	+	4.29038i	0.0812694	+	0.140763i	−0.822526	+	0.568727i	$0.807436\pi$
$930$		0			0
$931$	1.85277	−	7.60068i	0.0607220	−	0.249102i
$932$	−13.6257	−	7.86681i	−0.446325	−	0.257686i
$933$		0			0
$934$	45.2585	−	26.1300i	1.48090	−	0.854999i
$935$			11.8517i			0.387593i
$936$		0			0
$937$		−	32.1771i		−	1.05118i	−0.850738	−	0.525590i	$-0.823845\pi$
$937$		−	32.1771i		−	1.05118i	0.850738	−	0.525590i	$-0.176155\pi$
$938$	67.8039	+	8.14480i	2.21388	+	0.265937i
$939$		0			0
$940$	−8.60733	+	14.9083i	−0.280740	+	0.486256i
$941$	9.92726	−	17.1945i	0.323619	−	0.560525i	−0.657613	−	0.753356i	$-0.728434\pi$
$941$	9.92726	−	17.1945i	0.323619	−	0.560525i	0.981232	+	0.192831i	$0.0617669\pi$
$942$		0			0
$943$	−1.76413	+	1.01852i	−0.0574480	+	0.0331676i
$944$	−9.36558			−0.304824
$945$		0			0
$946$	−57.7825			−1.87867
$947$	9.34865	−	5.39744i	0.303790	−	0.175393i	−0.340354	−	0.940297i	$-0.610547\pi$
$947$	9.34865	−	5.39744i	0.303790	−	0.175393i	0.644144	+	0.764904i	$0.277214\pi$
$948$		0			0
$949$	−2.05406	+	3.55774i	−0.0666777	+	0.115489i
$950$	−1.25698	+	2.17716i	−0.0407819	+	0.0706363i
$951$		0			0
$952$	30.1286	+	3.61913i	0.976472	+	0.117297i
$953$		−	16.7368i		−	0.542157i	−0.962557	−	0.271079i	$-0.912620\pi$
$953$		−	16.7368i		−	0.542157i	0.962557	−	0.271079i	$-0.0873804\pi$
$954$		0			0
$955$		−	1.98434i		−	0.0642116i
$956$	−45.2584	+	26.1299i	−1.46376	+	0.845103i
$957$		0			0
$958$	−60.8476	−	35.1304i	−1.96590	−	1.13501i
$959$	−7.35875	−	17.2105i	−0.237626	−	0.555755i
$960$		0			0
$961$	5.52279	+	9.56574i	0.178154	+	0.308572i
$962$	3.75368			0.121023
$963$		0			0
$964$			64.0329i			2.06236i
$965$	−6.61042	−	11.4496i	−0.212797	−	0.368575i
$966$		0			0
$967$	−25.6781	+	44.4758i	−0.825752	+	1.43024i	0.0755915	+	0.997139i	$0.475915\pi$
$967$	−25.6781	+	44.4758i	−0.825752	+	1.43024i	−0.901343	+	0.433105i	$0.857418\pi$
$968$	−10.1805	−	5.87771i	−0.327213	−	0.188917i
$969$		0			0
$970$	4.50282	+	7.79911i	0.144577	+	0.250414i
$971$	5.95642			0.191151			0.0955753	−	0.995422i	$-0.469531\pi$
$971$	5.95642			0.191151			0.0955753	+	0.995422i	$0.469531\pi$
$972$		0			0
$973$	17.5627	−	23.4341i	0.563033	−	0.751262i
$974$	20.8760	−	12.0528i	0.668911	−	0.386196i
$975$		0			0
$976$	−0.478291	−	0.276141i	−0.0153097	−	0.00883907i
$977$	18.8015	+	10.8550i	0.601512	+	0.347283i	0.769636	−	0.638483i	$-0.220438\pi$
$977$	18.8015	+	10.8550i	0.601512	+	0.347283i	−0.168124	+	0.985766i	$0.553771\pi$
$978$		0			0
$979$	30.4074	−	17.5557i	0.971824	−	0.561083i
$980$	6.01185	+	20.5582i	0.192041	+	0.656707i
$981$		0			0
$982$	−2.36972			−0.0756207
$983$	−6.84543	−	11.8566i	−0.218335	−	0.378168i	0.735964	−	0.677021i	$-0.236729\pi$
$983$	−6.84543	−	11.8566i	−0.218335	−	0.378168i	−0.954299	+	0.298853i	$0.903396\pi$
$984$		0			0
$985$	13.9994	+	8.08255i	0.446058	+	0.257531i
$986$	−25.1620	+	43.5818i	−0.801320	+	1.38793i
$987$		0			0
$988$	−0.664269	−	1.15055i	−0.0211332	−	0.0366038i
$989$		−	22.2834i		−	0.708572i
$990$		0			0
$991$	25.1854			0.800040			0.400020	−	0.916506i	$-0.369003\pi$
$991$	25.1854			0.800040			0.400020	+	0.916506i	$0.369003\pi$
$992$	20.9791	+	36.3369i	0.666088	+	1.15370i
$993$		0			0
$994$	82.8684	−	35.4324i	2.62843	−	1.12385i
$995$	23.6759	+	13.6693i	0.750575	+	0.433345i
$996$		0			0
$997$	−24.4950	+	14.1422i	−0.775766	+	0.447888i	−0.834927	−	0.550360i	$-0.814490\pi$
$997$	−24.4950	+	14.1422i	−0.775766	+	0.447888i	0.0591620	+	0.998248i	$0.481157\pi$
$998$		−	11.3400i		−	0.358961i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.bl.j.881.3		24
3.2	odd	2		315.2.bl.j.41.10	yes	24
7.6	odd	2		945.2.bl.i.881.3		24
9.2	odd	6		945.2.bl.i.251.3		24
9.7	even	3		315.2.bl.i.146.10	yes	24
21.20	even	2		315.2.bl.i.41.10	✓	24
63.20	even	6	inner	945.2.bl.j.251.3		24
63.34	odd	6		315.2.bl.j.146.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bl.i.41.10	✓	24	21.20	even	2
315.2.bl.i.146.10	yes	24	9.7	even	3
315.2.bl.j.41.10	yes	24	3.2	odd	2
315.2.bl.j.146.10	yes	24	63.34	odd	6
945.2.bl.i.251.3		24	9.2	odd	6
945.2.bl.i.881.3		24	7.6	odd	2
945.2.bl.j.251.3		24	63.20	even	6	inner
945.2.bl.j.881.3		24	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bl (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.94805 + 1.12471i) q^{2} +(1.52994 - 2.64993i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.315547 - 2.62687i) q^{7} +2.38412i q^{8} +O(q^{10})\)	\(q+(-1.94805 + 1.12471i) q^{2} +(1.52994 - 2.64993i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.315547 - 2.62687i) q^{7} +2.38412i q^{8} +2.24942i q^{10} +(-2.13353 + 1.23180i) q^{11} +(-0.336443 - 0.194245i) q^{13} +(2.33976 + 5.47217i) q^{14} +(0.378445 + 0.655486i) q^{16} +4.81075 q^{17} +1.11761i q^{19} +(-1.52994 - 2.64993i) q^{20} +(2.77082 - 4.79920i) q^{22} +(1.85078 + 1.06855i) q^{23} +(-0.500000 - 0.866025i) q^{25} +0.873878 q^{26} +(-6.47826 - 4.85513i) q^{28} +(4.02738 - 2.32521i) q^{29} +(-5.61553 - 3.24213i) q^{31} +(-5.60387 - 3.23540i) q^{32} +(-9.37160 + 5.41070i) q^{34} +(-2.11716 - 1.58671i) q^{35} +4.29543 q^{37} +(-1.25698 - 2.17716i) q^{38} +(2.06470 + 1.19206i) q^{40} +(-0.476591 + 0.825479i) q^{41} +(-5.21348 - 9.03002i) q^{43} +7.53829i q^{44} -4.80723 q^{46} +(-2.81296 - 4.87220i) q^{47} +(-6.80086 - 1.65780i) q^{49} +(1.94805 + 1.12471i) q^{50} +(-1.02947 + 0.594368i) q^{52} -9.72792i q^{53} +2.46359i q^{55} +(6.26275 + 0.752301i) q^{56} +(-5.23036 + 9.05925i) q^{58} +(-6.18688 + 10.7160i) q^{59} +(-0.631916 + 0.364837i) q^{61} +14.5858 q^{62} +13.0417 q^{64} +(-0.336443 + 0.194245i) q^{65} +(5.73742 - 9.93750i) q^{67} +(7.36016 - 12.7482i) q^{68} +(5.90892 + 0.709797i) q^{70} -15.1436i q^{71} -10.5746i q^{73} +(-8.36772 + 4.83111i) q^{74} +(2.96158 + 1.70987i) q^{76} +(2.56253 + 5.99319i) q^{77} +(7.35947 + 12.7470i) q^{79} +0.756890 q^{80} -2.14410i q^{82} +(-5.97335 - 10.3461i) q^{83} +(2.40538 - 4.16623i) q^{85} +(20.3123 + 11.7273i) q^{86} +(-2.93674 - 5.08659i) q^{88} -14.2521 q^{89} +(-0.616420 + 0.822497i) q^{91} +(5.66317 - 3.26963i) q^{92} +(10.9596 + 6.32753i) q^{94} +(0.967875 + 0.558803i) q^{95} +(3.46717 - 2.00177i) q^{97} +(15.1130 - 4.41951i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{2} + 18 q^{4} + 12 q^{5} + 9 q^{7}+O(q^{10}) \) 24 * q - 6 * q^2 + 18 * q^4 + 12 * q^5 + 9 * q^7	\( 24 q - 6 q^{2} + 18 q^{4} + 12 q^{5} + 9 q^{7} - 9 q^{11} + 3 q^{13} - 18 q^{14} - 18 q^{16} - 18 q^{17} - 18 q^{20} - 9 q^{22} - 9 q^{23} - 12 q^{25} + 18 q^{26} - 9 q^{28} - 9 q^{29} - 42 q^{31} - 18 q^{32} - 39 q^{34} + 9 q^{35} + 12 q^{38} - 6 q^{40} + 33 q^{41} + 18 q^{43} - 30 q^{46} + 9 q^{49} + 6 q^{50} + 129 q^{52} + 9 q^{56} - 15 q^{58} - 12 q^{59} - 15 q^{61} - 12 q^{62} - 60 q^{64} + 3 q^{65} - 15 q^{67} - 9 q^{68} - 9 q^{70} + 18 q^{74} + 54 q^{76} + 45 q^{77} + 21 q^{79} - 36 q^{80} + 30 q^{83} - 9 q^{85} + 102 q^{86} - 9 q^{88} - 102 q^{89} + 42 q^{91} + 3 q^{92} - 156 q^{94} + 18 q^{95} - 45 q^{97} - 3 q^{98}+O(q^{100}) \) 24 * q - 6 * q^2 + 18 * q^4 + 12 * q^5 + 9 * q^7 - 9 * q^11 + 3 * q^13 - 18 * q^14 - 18 * q^16 - 18 * q^17 - 18 * q^20 - 9 * q^22 - 9 * q^23 - 12 * q^25 + 18 * q^26 - 9 * q^28 - 9 * q^29 - 42 * q^31 - 18 * q^32 - 39 * q^34 + 9 * q^35 + 12 * q^38 - 6 * q^40 + 33 * q^41 + 18 * q^43 - 30 * q^46 + 9 * q^49 + 6 * q^50 + 129 * q^52 + 9 * q^56 - 15 * q^58 - 12 * q^59 - 15 * q^61 - 12 * q^62 - 60 * q^64 + 3 * q^65 - 15 * q^67 - 9 * q^68 - 9 * q^70 + 18 * q^74 + 54 * q^76 + 45 * q^77 + 21 * q^79 - 36 * q^80 + 30 * q^83 - 9 * q^85 + 102 * q^86 - 9 * q^88 - 102 * q^89 + 42 * q^91 + 3 * q^92 - 156 * q^94 + 18 * q^95 - 45 * q^97 - 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more