LMFDB - Embedded newform 225.3.j.e.101.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,3,Mod(101,225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(225, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("225.101"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	225.j (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.13080594811$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 3 x^{18} - 19 x^{16} - 66 x^{14} + 109 x^{12} + 813 x^{10} + 981 x^{8} - 5346 x^{6} + \cdots + 59049 $ x^20 + 3x^18 - 19x^16 - 66x^14 + 109x^12 + 813x^10 + 981x^8 - 5346x^6 - 13851x^4 + 19683*x^2 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{10} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.2
Root			$1.69702 - 0.346576i$ of defining polynomial
Character	$\chi$	$=$	225.101
Dual form			225.3.j.e.176.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.46092 - 1.42081i) q^{2} +(0.600288 - 2.93933i) q^{3} +(2.03740 + 3.52889i) q^{4} +(-5.65349 + 6.38055i) q^{6} +(4.86464 - 8.42581i) q^{7} -0.212574i q^{8} +(-8.27931 - 3.52889i) q^{9} +(0.370966 + 0.214177i) q^{11} +(11.5956 - 3.87025i) q^{12} +(-9.37595 - 16.2396i) q^{13} +(-23.9429 + 13.8235i) q^{14} +(7.84759 - 13.5924i) q^{16} -2.85718i q^{17} +(15.3608 + 20.4476i) q^{18} -0.530568 q^{19} +(-21.8460 - 19.3567i) q^{21} +(-0.608611 - 1.05414i) q^{22} +(-18.8557 + 10.8863i) q^{23} +(-0.624825 - 0.127606i) q^{24} +53.2858i q^{26} +(-15.3425 + 22.2173i) q^{27} +39.6450 q^{28} +(21.0633 + 12.1609i) q^{29} +(6.33163 + 10.9667i) q^{31} +(-39.3609 + 22.7250i) q^{32} +(0.852224 - 0.961823i) q^{33} +(-4.05951 + 7.03128i) q^{34} +(-4.41525 - 36.4065i) q^{36} +14.5875 q^{37} +(1.30568 + 0.753837i) q^{38} +(-53.3619 + 17.8106i) q^{39} +(-33.1200 + 19.1218i) q^{41} +(26.2591 + 78.6743i) q^{42} +(-28.8831 + 50.0269i) q^{43} +1.74546i q^{44} +61.8697 q^{46} +(-42.9289 - 24.7850i) q^{47} +(-35.2418 - 31.2260i) q^{48} +(-22.8295 - 39.5418i) q^{49} +(-8.39819 - 1.71513i) q^{51} +(38.2052 - 66.1734i) q^{52} -44.5876i q^{53} +(69.3232 - 32.8760i) q^{54} +(-1.79111 - 1.03410i) q^{56} +(-0.318494 + 1.55951i) q^{57} +(-34.5566 - 59.8538i) q^{58} +(54.6329 - 31.5423i) q^{59} +(11.0823 - 19.1951i) q^{61} -35.9842i q^{62} +(-70.0096 + 52.5931i) q^{63} +66.3710 q^{64} +(-3.46382 + 1.15612i) q^{66} +(-16.2720 - 28.1839i) q^{67} +(10.0827 - 5.82123i) q^{68} +(20.6797 + 61.9581i) q^{69} -89.8896i q^{71} +(-0.750149 + 1.75996i) q^{72} +144.328 q^{73} +(-35.8987 - 20.7261i) q^{74} +(-1.08098 - 1.87232i) q^{76} +(3.60923 - 2.08379i) q^{77} +(156.625 + 31.9868i) q^{78} +(25.1240 - 43.5160i) q^{79} +(56.0939 + 58.4335i) q^{81} +108.674 q^{82} +(-66.2606 - 38.2556i) q^{83} +(23.7984 - 116.530i) q^{84} +(142.158 - 82.0747i) q^{86} +(48.3889 - 54.6118i) q^{87} +(0.0455285 - 0.0788577i) q^{88} -28.9588i q^{89} -182.443 q^{91} +(-76.8334 - 44.3598i) q^{92} +(36.0355 - 12.0276i) q^{93} +(70.4296 + 121.988i) q^{94} +(43.1684 + 129.336i) q^{96} +(-11.4950 + 19.9099i) q^{97} +129.746i q^{98} +(-2.31554 - 3.08234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 18 q^{4} + 12 q^{6} + 18 q^{9} - 24 q^{11} - 30 q^{14} - 26 q^{16} + 8 q^{19} - 96 q^{21} + 102 q^{24} + 114 q^{29} + 28 q^{31} + 4 q^{34} + 432 q^{36} - 240 q^{39} + 102 q^{41} + 116 q^{46} + 40 q^{49}+ \cdots + 468 q^{99}+O(q^{100}) $ 20 * q + 18 * q^4 + 12 * q^6 + 18 * q^9 - 24 * q^11 - 30 * q^14 - 26 * q^16 + 8 * q^19 - 96 * q^21 + 102 * q^24 + 114 * q^29 + 28 * q^31 + 4 * q^34 + 432 * q^36 - 240 * q^39 + 102 * q^41 + 116 * q^46 + 40 * q^49 - 156 * q^51 + 270 * q^54 - 618 * q^56 - 120 * q^59 - 50 * q^61 - 140 * q^64 - 768 * q^66 - 162 * q^69 - 504 * q^74 - 96 * q^76 + 128 * q^79 + 846 * q^81 - 450 * q^84 + 1488 * q^86 - 288 * q^91 - 218 * q^94 - 474 * q^96 + 468 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−2.46092	−	1.42081i	−1.23046	−	0.710405i	−0.263332	−	0.964705i	$-0.584822\pi$
$2$	−2.46092	−	1.42081i	−1.23046	−	0.710405i	−0.967125	+	0.254300i	$0.918155\pi$
$3$	0.600288	−	2.93933i	0.200096	−	0.979776i
$3$	0.600288	−	2.93933i	0.200096	−	0.979776i
$4$	2.03740	+	3.52889i	0.509351	+	0.882222i
$5$		0			0
$5$		0			0
$6$	−5.65349	+	6.38055i	−0.942248	+	1.06342i
$7$	4.86464	−	8.42581i	0.694949	−	1.20369i	−0.275249	−	0.961373i	$-0.588760\pi$
$7$	4.86464	−	8.42581i	0.694949	−	1.20369i	0.970198	−	0.242314i	$-0.0779064\pi$
$8$		−	0.212574i		−	0.0265717i
$9$	−8.27931	−	3.52889i	−0.919923	−	0.392099i
$10$		0			0
$11$	0.370966	+	0.214177i	0.0337242	+	0.0194707i	0.516767	−	0.856126i	$-0.327135\pi$
$11$	0.370966	+	0.214177i	0.0337242	+	0.0194707i	−0.483043	+	0.875597i	$0.660469\pi$
$12$	11.5956	−	3.87025i	0.966299	−	0.322521i
$13$	−9.37595	−	16.2396i	−0.721227	−	1.24920i	−0.960508	−	0.278252i	$-0.910245\pi$
$13$	−9.37595	−	16.2396i	−0.721227	−	1.24920i	0.239281	−	0.970950i	$-0.423088\pi$
$14$	−23.9429	+	13.8235i	−1.71021	+	0.987391i
$15$		0			0
$16$	7.84759	−	13.5924i	0.490474	−	0.849526i
$17$		−	2.85718i		−	0.168069i	−0.996463	−	0.0840347i	$-0.973219\pi$
$17$		−	2.85718i		−	0.168069i	0.996463	−	0.0840347i	$-0.0267807\pi$
$18$	15.3608	+	20.4476i	0.853378	+	1.13598i
$19$	−0.530568			−0.0279246			−0.0139623	−	0.999903i	$-0.504444\pi$
$19$	−0.530568			−0.0279246			−0.0139623	+	0.999903i	$0.504444\pi$
$20$		0			0
$21$	−21.8460	−	19.3567i	−1.04029	−	0.921747i
$22$	−0.608611	−	1.05414i	−0.0276641	−	0.0479157i
$23$	−18.8557	+	10.8863i	−0.819813	+	0.473319i	−0.850352	−	0.526214i	$-0.823611\pi$
$23$	−18.8557	+	10.8863i	−0.819813	+	0.473319i	0.0305388	+	0.999534i	$0.490278\pi$
$24$	−0.624825	−	0.127606i	−0.0260344	−	0.00531690i
$25$		0			0
$26$			53.2858i			2.04945i
$27$	−15.3425	+	22.2173i	−0.568242	+	0.822862i
$28$	39.6450			1.41589
$29$	21.0633	+	12.1609i	0.726320	+	0.419341i	0.817074	−	0.576532i	$-0.195595\pi$
$29$	21.0633	+	12.1609i	0.726320	+	0.419341i	−0.0907547	+	0.995873i	$0.528928\pi$
$30$		0			0
$31$	6.33163	+	10.9667i	0.204246	+	0.353765i	0.949892	−	0.312577i	$-0.101192\pi$
$31$	6.33163	+	10.9667i	0.204246	+	0.353765i	−0.745646	+	0.666342i	$0.767859\pi$
$32$	−39.3609	+	22.7250i	−1.23003	+	0.710157i
$33$	0.852224	−	0.961823i	0.0258250	−	0.0291462i
$34$	−4.05951	+	7.03128i	−0.119397	+	0.206802i
$35$		0			0
$36$	−4.41525	−	36.4065i	−0.122646	−	1.01129i
$37$	14.5875			0.394257			0.197129	−	0.980378i	$-0.436838\pi$
$37$	14.5875			0.394257			0.197129	+	0.980378i	$0.436838\pi$
$38$	1.30568	+	0.753837i	0.0343601	+	0.0198378i
$39$	−53.3619	+	17.8106i	−1.36825	+	0.456681i
$40$		0			0
$41$	−33.1200	+	19.1218i	−0.807804	+	0.466386i	−0.846193	−	0.532877i	$-0.821111\pi$
$41$	−33.1200	+	19.1218i	−0.807804	+	0.466386i	0.0383889	+	0.999263i	$0.487777\pi$
$42$	26.2591	+	78.6743i	0.625216	+	1.87320i
$43$	−28.8831	+	50.0269i	−0.671699	+	1.16342i	0.305723	+	0.952121i	$0.401102\pi$
$43$	−28.8831	+	50.0269i	−0.671699	+	1.16342i	−0.977422	+	0.211297i	$0.932231\pi$
$44$			1.74546i			0.0396696i
$45$		0			0
$46$	61.8697			1.34499
$47$	−42.9289	−	24.7850i	−0.913381	−	0.527341i	−0.0318635	−	0.999492i	$-0.510144\pi$
$47$	−42.9289	−	24.7850i	−0.913381	−	0.527341i	−0.881517	+	0.472152i	$0.843478\pi$
$48$	−35.2418	−	31.2260i	−0.734204	−	0.650542i
$49$	−22.8295	−	39.5418i	−0.465908	−	0.806976i
$50$		0			0
$51$	−8.39819	−	1.71513i	−0.164670	−	0.0336300i
$52$	38.2052	−	66.1734i	0.734716	−	1.27256i
$53$		−	44.5876i		−	0.841275i	−0.907229	−	0.420637i	$-0.861807\pi$
$53$		−	44.5876i		−	0.841275i	0.907229	−	0.420637i	$-0.138193\pi$
$54$	69.3232	−	32.8760i	1.28376	−	0.608815i
$55$		0			0
$56$	−1.79111	−	1.03410i	−0.0319840	−	0.0184660i
$57$	−0.318494	+	1.55951i	−0.00558761	+	0.0273599i
$58$	−34.5566	−	59.8538i	−0.595804	−	1.03196i
$59$	54.6329	−	31.5423i	0.925981	−	0.534615i	0.0404426	−	0.999182i	$-0.487123\pi$
$59$	54.6329	−	31.5423i	0.925981	−	0.534615i	0.885538	+	0.464567i	$0.153790\pi$
$60$		0			0
$61$	11.0823	−	19.1951i	0.181677	−	0.314673i	−0.760775	−	0.649016i	$-0.775181\pi$
$61$	11.0823	−	19.1951i	0.181677	−	0.314673i	0.942452	+	0.334343i	$0.108514\pi$
$62$		−	35.9842i		−	0.580390i
$63$	−70.0096	+	52.5931i	−1.11126	+	0.834811i
$64$	66.3710			1.03705
$65$		0			0
$66$	−3.46382	+	1.15612i	−0.0524821	+	0.0175169i
$67$	−16.2720	−	28.1839i	−0.242866	−	0.420655i	0.718664	−	0.695358i	$-0.244754\pi$
$67$	−16.2720	−	28.1839i	−0.242866	−	0.420655i	−0.961529	+	0.274702i	$0.911421\pi$
$68$	10.0827	−	5.82123i	0.148274	−	0.0856063i
$69$	20.6797	+	61.9581i	0.299706	+	0.897943i
$70$		0			0
$71$		−	89.8896i		−	1.26605i	−0.774131	−	0.633025i	$-0.781813\pi$
$71$		−	89.8896i		−	1.26605i	0.774131	−	0.633025i	$-0.218187\pi$
$72$	−0.750149	+	1.75996i	−0.0104187	+	0.0244440i
$73$	144.328			1.97709			0.988545	−	0.150926i	$-0.0482254\pi$
$73$	144.328			1.97709			0.988545	+	0.150926i	$0.0482254\pi$
$74$	−35.8987	−	20.7261i	−0.485117	−	0.280082i
$75$		0			0
$76$	−1.08098	−	1.87232i	−0.0142234	−	0.0246357i
$77$	3.60923	−	2.08379i	0.0468732	−	0.0270622i
$78$	156.625	+	31.9868i	2.00801	+	0.410087i
$79$	25.1240	−	43.5160i	0.318025	−	0.550836i	−0.662051	−	0.749459i	$-0.730314\pi$
$79$	25.1240	−	43.5160i	0.318025	−	0.550836i	0.980076	+	0.198623i	$0.0636470\pi$
$80$		0			0
$81$	56.0939	+	58.4335i	0.692518	+	0.721401i
$82$	108.674			1.32529
$83$	−66.2606	−	38.2556i	−0.798321	−	0.460911i	0.0445628	−	0.999007i	$-0.485811\pi$
$83$	−66.2606	−	38.2556i	−0.798321	−	0.460911i	−0.842884	+	0.538096i	$0.819144\pi$
$84$	23.7984	−	116.530i	0.283314	−	1.38726i
$85$		0			0
$86$	142.158	−	82.0747i	1.65300	−	0.954357i
$87$	48.3889	−	54.6118i	0.556194	−	0.627722i
$88$	0.0455285	−	0.0788577i	0.000517369	−	0.000896110i
$89$		−	28.9588i		−	0.325379i	−0.986677	−	0.162690i	$-0.947983\pi$
$89$		−	28.9588i		−	0.325379i	0.986677	−	0.162690i	$-0.0520169\pi$
$90$		0			0
$91$	−182.443			−2.00486
$92$	−76.8334	−	44.3598i	−0.835145	−	0.482171i
$93$	36.0355	−	12.0276i	0.387479	−	0.129329i
$94$	70.4296	+	121.988i	0.749251	+	1.29774i
$95$		0			0
$96$	43.1684	+	129.336i	0.449671	+	1.34725i
$97$	−11.4950	+	19.9099i	−0.118505	+	0.205257i	−0.919175	−	0.393848i	$-0.871143\pi$
$97$	−11.4950	+	19.9099i	−0.118505	+	0.205257i	0.800670	+	0.599105i	$0.204477\pi$
$98$			129.746i			1.32393i
$99$	−2.31554	−	3.08234i	−0.0233892	−	0.0311347i
$100$		0			0
$101$	−49.7337	−	28.7138i	−0.492413	−	0.284295i	0.233162	−	0.972438i	$-0.425093\pi$
$101$	−49.7337	−	28.7138i	−0.492413	−	0.284295i	−0.725575	+	0.688143i	$0.758426\pi$
$102$	18.2304	+	16.1530i	0.178729	+	0.158363i
$103$	−43.0952	−	74.6430i	−0.418400	−	0.724689i	0.577379	−	0.816476i	$-0.304076\pi$
$103$	−43.0952	−	74.6430i	−0.418400	−	0.724689i	−0.995779	+	0.0917868i	$0.970742\pi$
$104$	−3.45212	+	1.99308i	−0.0331935	+	0.0191643i
$105$		0			0
$106$	−63.3504	+	109.726i	−0.597646	+	1.03515i
$107$			97.0919i			0.907401i	0.891154	+	0.453701i	$0.149896\pi$
$107$			97.0919i			0.907401i	−0.891154	+	0.453701i	$0.850104\pi$
$108$	−109.661	−	8.87650i	−1.01538	−	0.0821898i
$109$	−164.495			−1.50913			−0.754565	−	0.656225i	$-0.772152\pi$
$109$	−164.495			−1.50913			−0.754565	+	0.656225i	$0.772152\pi$
$110$		0			0
$111$	8.75671	−	42.8775i	0.0788893	−	0.386284i
$112$	−76.3514	−	132.245i	−0.681709	−	1.18075i
$113$	37.0700	−	21.4024i	0.328053	−	0.189401i	−0.326924	−	0.945051i	$-0.606012\pi$
$113$	37.0700	−	21.4024i	0.328053	−	0.189401i	0.654976	+	0.755649i	$0.272679\pi$
$114$	2.99956	−	3.38532i	0.0263119	−	0.0296957i
$115$		0			0
$116$			99.1065i			0.854366i
$117$	20.3186	+	167.540i	0.173663	+	1.43196i
$118$	−179.262			−1.51917
$119$	−24.0740	−	13.8992i	−0.202303	−	0.116800i
$120$		0			0
$121$	−60.4083	−	104.630i	−0.499242	−	0.864712i
$122$	−54.5451	+	31.4916i	−0.447091	+	0.258128i
$123$	36.3238	+	108.829i	0.295315	+	0.884789i
$124$	−25.8002	+	44.6872i	−0.208066	+	0.360381i
$125$		0			0
$126$	247.013	−	29.9568i	1.96042	−	0.237752i
$127$	78.7223			0.619861			0.309931	−	0.950759i	$-0.399694\pi$
$127$	78.7223			0.619861			0.309931	+	0.950759i	$0.399694\pi$
$128$	−5.88999	−	3.40059i	−0.0460155	−	0.0265671i
$129$	129.707	+	114.927i	1.00548	+	0.890910i
$130$		0			0
$131$	158.295	−	91.3914i	1.20836	−	0.697644i	0.245956	−	0.969281i	$-0.420898\pi$
$131$	158.295	−	91.3914i	1.20836	−	0.697644i	0.962400	+	0.271637i	$0.0875649\pi$
$132$	5.13049	+	1.04778i	0.0388673	+	0.00793773i
$133$	−2.58103	+	4.47047i	−0.0194062	+	0.0336125i
$134$			92.4776i			0.690132i
$135$		0			0
$136$	−0.607362			−0.00446589
$137$	4.81850	+	2.78196i	0.0351715	+	0.0203063i	0.517483	−	0.855694i	$-0.326869\pi$
$137$	4.81850	+	2.78196i	0.0351715	+	0.0203063i	−0.482311	+	0.876000i	$0.660203\pi$
$138$	37.1396	−	181.856i	0.269128	−	1.31779i
$139$	−84.9601	−	147.155i	−0.611224	−	1.05867i	−0.991034	−	0.133607i	$-0.957344\pi$
$139$	−84.9601	−	147.155i	−0.611224	−	1.05867i	0.379810	−	0.925064i	$-0.375989\pi$
$140$		0			0
$141$	−98.6210	+	111.304i	−0.699440	+	0.789390i
$142$	−127.716	+	221.211i	−0.899409	+	1.55782i
$143$		−	8.03247i		−	0.0561711i
$144$	−112.939	+	84.8426i	−0.784297	+	0.589185i
$145$		0			0
$146$	−355.178	−	205.062i	−2.43273	−	1.40454i
$147$	−129.931	+	43.3669i	−0.883883	+	0.295013i
$148$	29.7207	+	51.4777i	0.200815	+	0.347822i
$149$	69.9180	−	40.3672i	0.469249	−	0.270921i	−0.246677	−	0.969098i	$-0.579339\pi$
$149$	69.9180	−	40.3672i	0.469249	−	0.270921i	0.715925	+	0.698177i	$0.246005\pi$
$150$		0			0
$151$	−44.1372	+	76.4478i	−0.292299	+	0.506277i	−0.974353	−	0.225025i	$-0.927754\pi$
$151$	−44.1372	+	76.4478i	−0.292299	+	0.506277i	0.682054	+	0.731302i	$0.261087\pi$
$152$			0.112785i			0.000742006i
$153$	−10.0827	+	23.6555i	−0.0658998	+	0.154611i
$154$	−11.8427			−0.0769006
$155$		0			0
$156$	−171.571	−	152.021i	−1.09982	−	0.974492i
$157$	31.3732	+	54.3401i	0.199830	+	0.346115i	0.948473	−	0.316858i	$-0.102628\pi$
$157$	31.3732	+	54.3401i	0.199830	+	0.346115i	−0.748643	+	0.662973i	$0.769294\pi$
$158$	−123.656	+	71.3929i	−0.782633	+	0.451854i
$159$	−131.057	−	26.7654i	−0.824261	−	0.168336i
$160$		0			0
$161$			211.833i			1.31573i
$162$	−55.0195	−	223.499i	−0.339627	−	1.37962i
$163$	241.437			1.48121			0.740605	−	0.671941i	$-0.234539\pi$
$163$	241.437			1.48121			0.740605	+	0.671941i	$0.234539\pi$
$164$	−134.957	−	77.9177i	−0.822911	−	0.475108i
$165$		0			0
$166$	108.708	+	188.288i	0.654867	+	1.13426i
$167$	115.332	−	66.5872i	0.690613	−	0.398726i	−0.113229	−	0.993569i	$-0.536119\pi$
$167$	115.332	−	66.5872i	0.690613	−	0.398726i	0.803842	+	0.594843i	$0.202786\pi$
$168$	−4.11473	+	4.64390i	−0.0244924	+	0.0276422i
$169$	−91.3170	+	158.166i	−0.540338	+	0.935892i
$170$		0			0
$171$	4.39274	+	1.87232i	0.0256885	+	0.0109492i
$172$	−235.386			−1.36852
$173$	58.0603	+	33.5211i	0.335609	+	0.193764i	0.658328	−	0.752731i	$-0.271264\pi$
$173$	58.0603	+	33.5211i	0.335609	+	0.193764i	−0.322720	+	0.946495i	$0.604597\pi$
$174$	−196.674	+	65.6437i	−1.13031	+	0.377263i
$175$		0			0
$176$	5.82238	−	3.36155i	0.0330817	−	0.0190997i
$177$	−59.9177	−	179.518i	−0.338518	−	1.01423i
$178$	−41.1449	+	71.2651i	−0.231151	+	0.400366i
$179$			37.9613i			0.212074i	0.994362	+	0.106037i	$0.0338162\pi$
$179$			37.9613i			0.212074i	−0.994362	+	0.106037i	$0.966184\pi$
$180$		0			0
$181$	278.012			1.53598			0.767990	−	0.640462i	$-0.221257\pi$
$181$	278.012			1.53598			0.767990	+	0.640462i	$0.221257\pi$
$182$	448.976	+	259.216i	2.46690	+	1.42427i
$183$	−49.7681	−	44.0970i	−0.271957	−	0.240967i
$184$	2.31415	+	4.00823i	0.0125769	+	0.0217839i
$185$		0			0
$186$	−105.769	−	21.6009i	−0.568652	−	0.116134i
$187$	0.611943	−	1.05992i	0.00327242	−	0.00566800i
$188$		−	201.988i		−	1.07441i
$189$	112.563	+	237.352i	0.595569	+	1.25583i
$190$		0			0
$191$	50.4943	+	29.1529i	0.264368	+	0.152633i	0.626326	−	0.779562i	$-0.284558\pi$
$191$	50.4943	+	29.1529i	0.264368	+	0.152633i	−0.361957	+	0.932195i	$0.617891\pi$
$192$	39.8417	−	195.086i	0.207509	−	1.01607i
$193$	63.2837	+	109.611i	0.327895	+	0.567930i	0.982094	−	0.188392i	$-0.0603276\pi$
$193$	63.2837	+	109.611i	0.327895	+	0.567930i	−0.654199	+	0.756322i	$0.726994\pi$
$194$	56.5764	−	32.6644i	0.291631	−	0.168373i
$195$		0			0
$196$	93.0258	−	161.125i	0.474621	−	0.822068i
$197$		−	335.557i		−	1.70333i	−0.524083	−	0.851667i	$-0.675592\pi$
$197$		−	335.557i		−	1.70333i	0.524083	−	0.851667i	$-0.324408\pi$
$198$	1.31892	+	10.8753i	0.00666121	+	0.0549258i
$199$	127.161			0.638998			0.319499	−	0.947587i	$-0.396485\pi$
$199$	127.161			0.638998			0.319499	+	0.947587i	$0.396485\pi$
$200$		0			0
$201$	−92.6097	+	30.9103i	−0.460745	+	0.153782i
$202$	81.5937	+	141.324i	0.403929	+	0.699626i
$203$	204.931	−	118.317i	1.00951	−	0.582841i
$204$	−11.0580	−	33.1307i	−0.0542059	−	0.162405i
$205$		0			0
$206$			244.920i			1.18893i
$207$	194.529	−	23.5918i	0.939753	−	0.113970i
$208$	−294.314			−1.41497
$209$	−0.196823	−	0.113636i	−0.000941736	−	0.000543712i
$210$		0			0
$211$	−48.8580	−	84.6246i	−0.231555	−	0.401064i	0.726711	−	0.686943i	$-0.241048\pi$
$211$	−48.8580	−	84.6246i	−0.231555	−	0.401064i	−0.958266	+	0.285879i	$0.907715\pi$
$212$	157.344	−	90.8428i	0.742191	−	0.428504i
$213$	−264.215	−	53.9596i	−1.24045	−	0.253332i
$214$	137.949	−	238.935i	0.644623	−	1.11652i
$215$		0			0
$216$	4.72281	+	3.26142i	0.0218649	+	0.0150992i
$217$	123.204			0.567762
$218$	404.809	+	233.716i	1.85692	+	1.07209i
$219$	86.6381	−	424.226i	0.395608	−	1.93711i
$220$		0			0
$221$	−46.3995	+	26.7888i	−0.209953	+	0.121216i
$222$	−82.4704	+	93.0763i	−0.371488	+	0.419263i
$223$	−46.7130	+	80.9094i	−0.209476	+	0.362822i	−0.951549	−	0.307496i	$-0.900509\pi$
$223$	−46.7130	+	80.9094i	−0.209476	+	0.362822i	0.742074	+	0.670318i	$0.233842\pi$
$224$			442.196i			1.97409i
$225$		0			0
$226$	−121.635			−0.538207
$227$	−171.464	−	98.9949i	−0.755349	−	0.436101i	0.0722743	−	0.997385i	$-0.476974\pi$
$227$	−171.464	−	98.9949i	−0.755349	−	0.436101i	−0.827623	+	0.561284i	$0.810308\pi$
$228$	−6.15225	+	2.05343i	−0.0269836	+	0.00900629i
$229$	90.6197	+	156.958i	0.395719	+	0.685406i	0.993193	−	0.116483i	$-0.0371620\pi$
$229$	90.6197	+	156.958i	0.395719	+	0.685406i	−0.597473	+	0.801889i	$0.703829\pi$
$230$		0			0
$231$	−3.95837	−	11.8596i	−0.0171358	−	0.0513403i
$232$	2.58509	−	4.47750i	0.0111426	−	0.0192996i
$233$		−	178.525i		−	0.766202i	−0.923706	−	0.383101i	$-0.874856\pi$
$233$		−	178.525i		−	0.766202i	0.923706	−	0.383101i	$-0.125144\pi$
$234$	188.040	−	441.170i	0.803588	−	1.88534i
$235$		0			0
$236$	222.618	+	128.529i	0.943298	+	0.544613i
$237$	−112.826	−	99.9698i	−0.476060	−	0.421814i
$238$	39.4961	+	68.4093i	0.165950	+	0.287434i
$239$	−13.2157	+	7.63006i	−0.0552956	+	0.0319250i	−0.527393	−	0.849621i	$-0.676830\pi$
$239$	−13.2157	+	7.63006i	−0.0552956	+	0.0319250i	0.472097	+	0.881546i	$0.343497\pi$
$240$		0			0
$241$	159.583	−	276.406i	0.662170	−	1.14691i	−0.317874	−	0.948133i	$-0.602969\pi$
$241$	159.583	−	276.406i	0.662170	−	1.14691i	0.980044	−	0.198779i	$-0.0636976\pi$
$242$			343.315i			1.41866i
$243$	205.428	−	129.802i	0.845382	−	0.534163i
$244$	90.3163			0.370149
$245$		0			0
$246$	65.2356	−	319.428i	0.265185	−	1.29849i
$247$	4.97458	+	8.61623i	0.0201400	+	0.0348835i
$248$	2.33123	−	1.34594i	0.00940014	−	0.00542717i
$249$	−152.221	+	171.797i	−0.611330	+	0.689950i
$250$		0			0
$251$			95.3404i			0.379842i	0.981799	+	0.189921i	$0.0608232\pi$
$251$			95.3404i			0.379842i	−0.981799	+	0.189921i	$0.939177\pi$
$252$	−328.233	−	139.903i	−1.30251	−	0.555169i
$253$	−9.32644			−0.0368634
$254$	−193.729	−	111.850i	−0.762713	−	0.440352i
$255$		0			0
$256$	−123.079	−	213.179i	−0.480777	−	0.832730i
$257$	6.86996	−	3.96637i	0.0267313	−	0.0154334i	−0.486575	−	0.873639i	$-0.661754\pi$
$257$	6.86996	−	3.96637i	0.0267313	−	0.0154334i	0.513306	+	0.858206i	$0.328421\pi$
$258$	−155.909	−	467.116i	−0.604299	−	1.81053i
$259$	70.9631	−	122.912i	0.273989	−	0.474562i
$260$		0			0
$261$	−131.475	−	175.014i	−0.503735	−	0.670550i
$262$	−519.399			−1.98244
$263$	−355.399	−	205.189i	−1.35133	−	0.780188i	−0.362890	−	0.931832i	$-0.618210\pi$
$263$	−355.399	−	205.189i	−1.35133	−	0.780188i	−0.988435	+	0.151644i	$0.951543\pi$
$264$	−0.204459	−	0.181161i	−0.000774464	−	0.000686214i
$265$		0			0
$266$	12.7034	−	7.33429i	0.0477570	−	0.0275725i
$267$	−85.1193	−	17.3836i	−0.318799	−	0.0651071i
$268$	66.3052	−	114.844i	0.247408	−	0.428522i
$269$		−	201.081i		−	0.747513i	−0.927527	−	0.373757i	$-0.878070\pi$
$269$		−	201.081i		−	0.747513i	0.927527	−	0.373757i	$-0.121930\pi$
$270$		0			0
$271$	121.070			0.446751			0.223376	−	0.974732i	$-0.428292\pi$
$271$	121.070			0.446751			0.223376	+	0.974732i	$0.428292\pi$
$272$	−38.8360	−	22.4220i	−0.142779	−	0.0824337i
$273$	−109.518	+	536.259i	−0.401165	+	1.96432i
$274$	−7.90527	−	13.6923i	−0.0288514	−	0.0499720i
$275$		0			0
$276$	−176.510	+	199.210i	−0.639529	+	0.721775i
$277$	−167.504	+	290.125i	−0.604707	+	1.04738i	0.387391	+	0.921916i	$0.373376\pi$
$277$	−167.504	+	290.125i	−0.604707	+	1.04738i	−0.992098	+	0.125468i	$0.959957\pi$
$278$			482.849i			1.73687i
$279$	−13.7213	−	113.140i	−0.0491802	−	0.405521i
$280$		0			0
$281$	120.265	+	69.4349i	0.427989	+	0.247099i	0.698489	−	0.715620i	$-0.253856\pi$
$281$	120.265	+	69.4349i	0.427989	+	0.247099i	−0.270501	+	0.962720i	$0.587189\pi$
$282$	400.840	−	133.788i	1.42142	−	0.474426i
$283$	−48.4023	−	83.8352i	−0.171033	−	0.296237i	0.767748	−	0.640751i	$-0.221377\pi$
$283$	−48.4023	−	83.8352i	−0.171033	−	0.296237i	−0.938781	+	0.344514i	$0.888044\pi$
$284$	317.210	−	183.141i	1.11694	−	0.644864i
$285$		0			0
$286$	−11.4126	+	19.7672i	−0.0399042	+	0.0691162i
$287$			372.083i			1.29646i
$288$	406.075	−	49.2473i	1.40998	−	0.170998i
$289$	280.837			0.971753
$290$		0			0
$291$	51.6214	+	45.7392i	0.177393	+	0.157179i
$292$	294.054	+	509.316i	1.00703	+	1.74423i
$293$	−333.488	+	192.539i	−1.13818	+	0.657131i	−0.945980	−	0.324224i	$-0.894897\pi$
$293$	−333.488	+	192.539i	−1.13818	+	0.657131i	−0.192204	+	0.981355i	$0.561563\pi$
$294$	381.365	+	77.8846i	1.29716	+	0.264914i
$295$		0			0
$296$		−	3.10093i		−	0.0104761i
$297$	−10.4500	+	4.95583i	−0.0351852	+	0.0166863i
$298$	−229.417			−0.769854
$299$	353.580	+	204.140i	1.18254	+	0.682742i
$300$		0			0
$301$	281.012	+	486.726i	0.933593	+	1.61703i
$302$	217.236	−	125.421i	0.719324	−	0.415302i
$303$	−114.254	+	128.947i	−0.377075	+	0.425569i
$304$	−4.16368	+	7.21171i	−0.0136963	+	0.0237227i
$305$		0			0
$306$	58.4225	−	43.8886i	0.190923	−	0.143427i
$307$	−207.311			−0.675281			−0.337641	−	0.941275i	$-0.609629\pi$
$307$	−207.311			−0.675281			−0.337641	+	0.941275i	$0.609629\pi$
$308$	14.7069	+	8.49105i	0.0477498	+	0.0275684i
$309$	−245.270	+	81.8636i	−0.793754	+	0.264931i
$310$		0			0
$311$	140.437	−	81.0816i	0.451567	−	0.260712i	−0.256925	−	0.966431i	$-0.582709\pi$
$311$	140.437	−	81.0816i	0.451567	−	0.260712i	0.708492	+	0.705719i	$0.249376\pi$
$312$	3.78606	+	11.3433i	0.0121348	+	0.0363569i
$313$	113.407	−	196.427i	0.362322	−	0.627561i	−0.626020	−	0.779807i	$-0.715317\pi$
$313$	113.407	−	196.427i	0.362322	−	0.627561i	0.988343	+	0.152246i	$0.0486506\pi$
$314$		−	178.302i		−	0.567840i
$315$		0			0
$316$	204.751			0.647946
$317$	423.293	+	244.388i	1.33531	+	0.770941i	0.986108	−	0.166108i	$-0.0531199\pi$
$317$	423.293	+	244.388i	1.33531	+	0.770941i	0.349200	+	0.937048i	$0.386453\pi$
$318$	284.493	+	252.075i	0.894632	+	0.792689i
$319$	5.20917	+	9.02255i	0.0163297	+	0.0282839i
$320$		0			0
$321$	285.385	+	58.2831i	0.889050	+	0.181567i
$322$	300.974	−	521.302i	0.934702	−	1.61895i
$323$			1.51593i			0.00469328i
$324$	−91.9192	+	317.002i	−0.283701	+	0.978400i
$325$		0			0
$326$	−594.157	−	343.036i	−1.82257	−	1.05226i
$327$	−98.7444	+	483.505i	−0.301971	+	1.47861i
$328$	4.06480	+	7.04044i	0.0123927	+	0.0214647i
$329$	−417.667	+	241.140i	−1.26951	+	0.732950i
$330$		0			0
$331$	−118.823	+	205.808i	−0.358982	+	0.621775i	−0.987791	−	0.155785i	$-0.950209\pi$
$331$	−118.823	+	205.808i	−0.358982	+	0.621775i	0.628809	+	0.777560i	$0.283543\pi$
$332$		−	311.768i		−	0.939061i
$333$	−120.775	−	51.4777i	−0.362687	−	0.154588i
$334$	−378.431			−1.13303
$335$		0			0
$336$	−434.543	+	145.037i	−1.29328	+	0.431658i
$337$	−141.018	−	244.250i	−0.418450	−	0.724777i	0.577334	−	0.816508i	$-0.304093\pi$
$337$	−141.018	−	244.250i	−0.418450	−	0.724777i	−0.995784	+	0.0917314i	$0.970760\pi$
$338$	449.447	−	259.488i	1.32973	−	0.767717i
$339$	−40.6559	−	121.808i	−0.119929	−	0.359317i
$340$		0			0
$341$			5.42437i			0.0159072i
$342$	−8.14996	−	10.8489i	−0.0238303	−	0.0317218i
$343$	32.5057			0.0947688
$344$	10.6344	+	6.13979i	0.0309140	+	0.0178482i
$345$		0			0
$346$	−95.2543	−	164.985i	−0.275302	−	0.476836i
$347$	−381.026	+	219.985i	−1.09806	+	0.633963i	−0.935710	−	0.352771i	$-0.885240\pi$
$347$	−381.026	+	219.985i	−1.09806	+	0.633963i	−0.162347	+	0.986734i	$0.551906\pi$
$348$	291.307	+	59.4924i	0.837088	+	0.170955i
$349$	−48.6291	+	84.2280i	−0.139338	+	0.241341i	−0.927246	−	0.374452i	$-0.877831\pi$
$349$	−48.6291	+	84.2280i	−0.139338	+	0.241341i	0.787908	+	0.615793i	$0.211164\pi$
$350$		0			0
$351$	504.651	+	40.8489i	1.43775	+	0.116379i
$352$	−19.4687			−0.0553089
$353$	−85.0399	−	49.0978i	−0.240906	−	0.139087i	0.374687	−	0.927151i	$-0.377750\pi$
$353$	−85.0399	−	49.0978i	−0.240906	−	0.139087i	−0.615593	+	0.788064i	$0.711084\pi$
$354$	−107.609	+	526.911i	−0.303980	+	1.48845i
$355$		0			0
$356$	102.192	−	59.0007i	0.287057	−	0.165732i
$357$	−55.3055	+	62.4180i	−0.154917	+	0.174840i
$358$	53.9358	−	93.4195i	0.150659	−	0.260948i
$359$		−	500.068i		−	1.39295i	−0.717582	−	0.696474i	$-0.754751\pi$
$359$		−	500.068i		−	1.39295i	0.717582	−	0.696474i	$-0.245249\pi$
$360$		0			0
$361$	−360.718			−0.999220
$362$	−684.165	−	395.003i	−1.88996	−	1.09117i
$363$	−343.805	+	114.752i	−0.947121	+	0.316120i
$364$	−371.709	−	643.819i	−1.02118	−	1.76873i
$365$		0			0
$366$	59.8215	+	179.230i	0.163447	+	0.489699i
$367$	170.909	−	296.023i	0.465692	−	0.806603i	−0.533540	−	0.845775i	$-0.679139\pi$
$367$	170.909	−	296.023i	0.465692	−	0.806603i	0.999232	+	0.0391718i	$0.0124720\pi$
$368$			341.726i			0.928604i
$369$	341.689	−	41.4388i	0.925987	−	0.112300i
$370$		0			0
$371$	−375.686	−	216.902i	−1.01263	−	0.584643i
$372$	115.863	+	102.660i	0.311459	+	0.275969i
$373$	305.522	+	529.179i	0.819093	+	1.41871i	0.906351	+	0.422525i	$0.138856\pi$
$373$	305.522	+	529.179i	0.819093	+	1.41871i	−0.0872584	+	0.996186i	$0.527811\pi$
$374$	−3.01188	+	1.73891i	−0.00805316	+	0.00464949i
$375$		0			0
$376$	−5.26865	+	9.12556i	−0.0140124	+	0.0242701i
$377$		−	456.080i		−	1.20976i
$378$	60.2257	−	744.034i	0.159327	−	1.96834i
$379$	−187.436			−0.494555			−0.247277	−	0.968945i	$-0.579536\pi$
$379$	−187.436			−0.494555			−0.247277	+	0.968945i	$0.579536\pi$
$380$		0			0
$381$	47.2561	−	231.391i	0.124032	−	0.607325i
$382$	−82.8415	−	143.486i	−0.216863	−	0.375617i
$383$	128.014	−	73.9088i	0.334240	−	0.192973i	−0.323482	−	0.946234i	$-0.604854\pi$
$383$	128.014	−	73.9088i	0.334240	−	0.192973i	0.657722	+	0.753261i	$0.271520\pi$
$384$	−13.5311	+	15.2713i	−0.0352373	+	0.0397690i
$385$		0			0
$386$		−	359.656i		−	0.931752i
$387$	415.671	−	312.263i	1.07409	−	0.806882i
$388$	−93.6797			−0.241442
$389$	397.890	+	229.722i	1.02285	+	0.590545i	0.914929	−	0.403615i	$-0.132246\pi$
$389$	397.890	+	229.722i	1.02285	+	0.590545i	0.107924	+	0.994159i	$0.465580\pi$
$390$		0			0
$391$	31.1042	+	53.8741i	0.0795505	+	0.137786i
$392$	−8.40556	+	4.85295i	−0.0214428	+	0.0123800i
$393$	−173.607	−	520.141i	−0.441748	−	1.32351i
$394$	−476.763	+	825.777i	−1.21006	+	2.09588i
$395$		0			0
$396$	6.15954	−	14.4512i	0.0155544	−	0.0364930i
$397$	718.905			1.81084			0.905422	−	0.424512i	$-0.139554\pi$
$397$	718.905			1.81084			0.905422	+	0.424512i	$0.139554\pi$
$398$	−312.932	−	180.671i	−0.786260	−	0.453948i
$399$	11.5908	+	10.2700i	0.0290497	+	0.0257395i
$400$		0			0
$401$	−65.5957	+	37.8717i	−0.163580	+	0.0944431i	−0.579555	−	0.814933i	$-0.696774\pi$
$401$	−65.5957	+	37.8717i	−0.163580	+	0.0944431i	0.415975	+	0.909376i	$0.363440\pi$
$402$	271.822	+	55.5132i	0.676175	+	0.138093i
$403$	118.730	−	205.647i	0.294616	−	0.510289i
$404$		−	234.006i		−	0.579223i
$405$		0			0
$406$	−672.422			−1.65621
$407$	5.41148	+	3.12432i	0.0132960	+	0.00767646i
$408$	−0.364592	+	1.78524i	−0.000893607	+	0.00437558i
$409$	255.035	+	441.733i	0.623556	+	1.08003i	0.988818	+	0.149126i	$0.0476461\pi$
$409$	255.035	+	441.733i	0.623556	+	1.08003i	−0.365262	+	0.930905i	$0.619021\pi$
$410$		0			0
$411$	11.0696	−	12.4932i	0.0269333	−	0.0303970i
$412$	175.604	−	304.156i	0.426224	−	0.738242i
$413$		−	613.768i		−	1.48612i
$414$	−512.239	−	218.331i	−1.23729	−	0.527370i
$415$		0			0
$416$	738.092	+	426.137i	1.77426	+	1.02437i
$417$	−483.538	+	161.390i	−1.15956	+	0.387027i
$418$	0.322910	+	0.559296i	0.000772511	+	0.00133803i
$419$	−603.768	+	348.586i	−1.44097	+	0.831947i	−0.997915	−	0.0645450i	$-0.979440\pi$
$419$	−603.768	+	348.586i	−1.44097	+	0.831947i	−0.443060	+	0.896492i	$0.646107\pi$
$420$		0			0
$421$	−378.410	+	655.425i	−0.898836	+	1.55683i	−0.0698516	+	0.997557i	$0.522253\pi$
$421$	−378.410	+	655.425i	−0.898836	+	1.55683i	−0.828984	+	0.559272i	$0.811081\pi$
$422$			277.672i			0.657990i
$423$	267.958	+	356.694i	0.633471	+	0.843248i
$424$	−9.47815			−0.0223541
$425$		0			0
$426$	573.545	+	508.190i	1.34635	+	1.19293i
$427$	−107.823	−	186.754i	−0.252512	−	0.437364i
$428$	−342.626	+	197.815i	−0.800529	+	0.462186i
$429$	−23.6101	−	4.82179i	−0.0550351	−	0.0112396i
$430$		0			0
$431$		−	497.875i		−	1.15516i	−0.816333	−	0.577581i	$-0.803997\pi$
$431$		−	497.875i		−	1.15516i	0.816333	−	0.577581i	$-0.196003\pi$
$432$	181.585	+	382.894i	0.420335	+	0.886329i
$433$	−421.645			−0.973775			−0.486888	−	0.873465i	$-0.661868\pi$
$433$	−421.645			−0.973775			−0.486888	+	0.873465i	$0.661868\pi$
$434$	−303.196	−	175.050i	−0.698608	−	0.403341i
$435$		0			0
$436$	−335.143	−	580.485i	−0.768677	−	1.33139i
$437$	10.0042	−	5.77595i	0.0228930	−	0.0132173i
$438$	−815.954	+	920.889i	−1.86291	+	2.10249i
$439$	228.743	−	396.195i	0.521055	−	0.902494i	−0.478645	−	0.878009i	$-0.658872\pi$
$439$	228.743	−	396.195i	0.521055	−	0.902494i	0.999700	−	0.0244857i	$-0.00779481\pi$
$440$		0			0
$441$	49.4738	+	407.942i	0.112185	+	0.925038i
$442$	152.247			0.344450
$443$	201.153	+	116.136i	0.454069	+	0.262157i	0.709547	−	0.704658i	$-0.248899\pi$
$443$	201.153	+	116.136i	0.454069	+	0.262157i	−0.255478	+	0.966815i	$0.582233\pi$
$444$	169.151	−	56.4574i	0.380970	−	0.127156i
$445$		0			0
$446$	229.914	−	132.741i	0.515502	−	0.297625i
$447$	−76.6815	−	229.744i	−0.171547	−	0.513969i
$448$	322.871	−	559.230i	0.720695	−	1.24828i
$449$			678.345i			1.51079i	0.655269	+	0.755395i	$0.272555\pi$
$449$			678.345i			1.51079i	−0.655269	+	0.755395i	$0.727445\pi$
$450$		0			0
$451$	−16.3818			−0.0363234
$452$	151.053	+	87.2105i	0.334188	+	0.192943i
$453$	198.210	+	175.624i	0.437550	+	0.387692i
$454$	281.306	+	487.236i	0.619617	+	1.07321i
$455$		0			0
$456$	0.331512	+	0.0677034i	0.000727000	+	0.000148472i
$457$	−367.777	+	637.008i	−0.804763	+	1.39389i	0.111688	+	0.993743i	$0.464374\pi$
$457$	−367.777	+	637.008i	−0.804763	+	1.39389i	−0.916451	+	0.400147i	$0.868959\pi$
$458$		−	515.014i		−	1.12448i
$459$	63.4787	+	43.8364i	0.138298	+	0.0955040i
$460$		0			0
$461$	344.752	+	199.043i	0.747835	+	0.431763i	0.824911	−	0.565263i	$-0.191225\pi$
$461$	344.752	+	199.043i	0.747835	+	0.431763i	−0.0770763	+	0.997025i	$0.524559\pi$
$462$	−7.10903	+	34.8096i	−0.0153875	+	0.0753454i
$463$	80.2955	+	139.076i	0.173424	+	0.300380i	0.939615	−	0.342234i	$-0.111183\pi$
$463$	80.2955	+	139.076i	0.173424	+	0.300380i	−0.766191	+	0.642613i	$0.777850\pi$
$464$	330.592	−	190.867i	0.712482	−	0.411352i
$465$		0			0
$466$	−253.650	+	439.335i	−0.544314	+	0.942780i
$467$		−	406.660i		−	0.870792i	−0.900239	−	0.435396i	$-0.856608\pi$
$467$		−	406.660i		−	0.870792i	0.900239	−	0.435396i	$-0.143392\pi$
$468$	−549.831	+	413.048i	−1.17485	+	0.882581i
$469$	−316.630			−0.675117
$470$		0			0
$471$	178.556	−	59.5966i	0.379100	−	0.126532i
$472$	−6.70507	−	11.6135i	−0.0142057	−	0.0246049i
$473$	−21.4293	+	12.3722i	−0.0453050	+	0.0261569i
$474$	135.618	+	406.322i	0.286114	+	0.857220i
$475$		0			0
$476$		−	113.273i		−	0.237968i
$477$	−157.344	+	369.154i	−0.329862	+	0.773908i
$478$	43.3635			0.0907186
$479$	−731.450	−	422.303i	−1.52704	−	0.881635i	−0.999484	−	0.0321123i	$-0.989777\pi$
$479$	−731.450	−	422.303i	−1.52704	−	0.881635i	−0.527552	−	0.849523i	$-0.676890\pi$
$480$		0			0
$481$	−136.772	−	236.896i	−0.284349	−	0.492507i
$482$	−785.440	+	453.474i	−1.62954	+	0.940818i
$483$	622.646	+	127.161i	1.28912	+	0.263272i
$484$	246.152	−	426.348i	0.508579	−	0.880884i
$485$		0			0
$486$	−689.964	+	27.5569i	−1.41968	+	0.0567014i
$487$	225.518			0.463075			0.231538	−	0.972826i	$-0.425624\pi$
$487$	225.518			0.463075			0.231538	+	0.972826i	$0.425624\pi$
$488$	−4.08037	−	2.35580i	−0.00836141	−	0.00482746i
$489$	144.932	−	709.663i	0.296384	−	1.45125i
$490$		0			0
$491$	−662.639	+	382.575i	−1.34957	+	0.779175i	−0.988189	−	0.153243i	$-0.951028\pi$
$491$	−662.639	+	382.575i	−1.34957	+	0.779175i	−0.361382	+	0.932418i	$0.617695\pi$
$492$	−310.039	+	349.911i	−0.630161	+	0.711202i
$493$	34.7458	−	60.1815i	0.0704783	−	0.122072i
$494$		−	28.2718i		−	0.0572303i
$495$		0			0
$496$	198.752			0.400710
$497$	−757.392	−	437.281i	−1.52393	−	0.879841i
$498$	618.695	−	206.501i	1.24236	−	0.414662i
$499$	−102.024	−	176.711i	−0.204458	−	0.354131i	0.745502	−	0.666503i	$-0.232210\pi$
$499$	−102.024	−	176.711i	−0.204458	−	0.354131i	−0.949960	+	0.312372i	$0.898876\pi$
$500$		0			0
$501$	−126.489	−	378.971i	−0.252473	−	0.756429i
$502$	135.461	−	234.625i	0.269842	−	0.467380i
$503$			585.545i			1.16411i	0.813151	+	0.582053i	$0.197750\pi$
$503$			585.545i			1.16411i	−0.813151	+	0.582053i	$0.802250\pi$
$504$	11.1799	+	14.8822i	0.0221824	+	0.0295282i
$505$		0			0
$506$	22.9516	+	13.2511i	0.0453588	+	0.0261879i
$507$	410.085	+	363.356i	0.808846	+	0.716678i
$508$	160.389	+	277.802i	0.315727	+	0.546855i
$509$	−10.3361	+	5.96756i	−0.0203067	+	0.0117241i	−0.510119	−	0.860104i	$-0.670399\pi$
$509$	−10.3361	+	5.96756i	−0.0203067	+	0.0117241i	0.489812	+	0.871828i	$0.337065\pi$
$510$		0			0
$511$	702.102	−	1216.08i	1.37398	−	2.37980i
$512$			726.692i			1.41932i
$513$	8.14026	−	11.7878i	0.0158680	−	0.0229781i
$514$	−22.5418			−0.0438557
$515$		0			0
$516$	−141.299	+	691.877i	−0.273836	+	1.34085i
$517$	−10.6168	−	18.3888i	−0.0205354	−	0.0355683i
$518$	−349.268	+	201.650i	−0.674263	+	0.389286i
$519$	133.383	−	150.536i	0.256999	−	0.290050i
$520$		0			0
$521$		−	541.869i		−	1.04006i	−0.854149	−	0.520028i	$-0.825922\pi$
$521$		−	541.869i		−	1.04006i	0.854149	−	0.520028i	$-0.174078\pi$
$522$	74.8876	+	617.495i	0.143463	+	1.18294i
$523$	356.100			0.680880			0.340440	−	0.940266i	$-0.389424\pi$
$523$	356.100			0.680880			0.340440	+	0.940266i	$0.389424\pi$
$524$	645.020	+	372.402i	1.23095	+	0.710692i
$525$		0			0
$526$	583.071	+	1009.91i	1.10850	+	1.91998i
$527$	31.3338	−	18.0906i	0.0594570	−	0.0343275i
$528$	−6.38560	−	19.1318i	−0.0120939	−	0.0362344i
$529$	−27.4749	+	47.5879i	−0.0519374	+	0.0899582i
$530$		0			0
$531$	−563.632	+	68.3553i	−1.06145	+	0.128729i
$532$	−21.0344			−0.0395383
$533$	621.062	+	358.571i	1.16522	+	0.672740i
$534$	184.773	+	163.718i	0.346016	+	0.306588i
$535$		0			0
$536$	−5.99116	+	3.45900i	−0.0111775	+	0.00645336i
$537$	111.581	+	22.7877i	0.207785	+	0.0424352i
$538$	−285.698	+	494.843i	−0.531037	+	0.919783i
$539$		−	19.5582i		−	0.0362862i
$540$		0			0
$541$	378.892			0.700355			0.350178	−	0.936683i	$-0.386121\pi$
$541$	378.892			0.700355			0.350178	+	0.936683i	$0.386121\pi$
$542$	−297.942	−	172.017i	−0.549709	−	0.317375i
$543$	166.887	−	817.170i	0.307343	−	1.50492i
$544$	64.9294	+	112.461i	0.119356	+	0.206730i
$545$		0			0
$546$	1031.44	−	1164.08i	1.88908	−	2.13202i
$547$	279.673	−	484.407i	0.511285	−	0.885571i	−0.488630	−	0.872491i	$-0.662503\pi$
$547$	279.673	−	484.407i	0.511285	−	0.885571i	0.999914	−	0.0130799i	$-0.00416359\pi$
$548$			22.6719i			0.0413721i
$549$	−159.491	+	119.814i	−0.290511	+	0.218240i
$550$		0			0
$551$	−11.1755	−	6.45218i	−0.0202822	−	0.0117099i
$552$	13.1707	−	4.39596i	0.0238599	−	0.00796370i
$553$	−244.439	−	423.380i	−0.442023	−	0.765606i
$554$	824.426	−	475.982i	1.48813	−	0.859174i
$555$		0			0
$556$	346.196	−	599.629i	0.622655	−	1.07847i
$557$			471.971i			0.847345i	0.905815	+	0.423673i	$0.139259\pi$
$557$			471.971i			0.847345i	−0.905815	+	0.423673i	$0.860741\pi$
$558$	−126.984	+	297.924i	−0.227570	+	0.533914i
$559$	1083.23			1.93779
$560$		0			0
$561$	−2.74810	−	2.43496i	−0.00489858	−	0.00434039i
$562$	−197.308	−	341.747i	−0.351081	−	0.608090i
$563$	−428.316	+	247.289i	−0.760775	+	0.439234i	−0.829574	−	0.558397i	$-0.811417\pi$
$563$	−428.316	+	247.289i	−0.760775	+	0.439234i	0.0687990	+	0.997631i	$0.478083\pi$
$564$	−593.710	−	121.251i	−1.05268	−	0.214984i
$565$		0			0
$566$			275.082i			0.486010i
$567$	765.226	−	188.379i	1.34961	−	0.332237i
$568$	−19.1082			−0.0336412
$569$	−143.305	−	82.7370i	−0.251853	−	0.145408i	0.368759	−	0.929525i	$-0.379783\pi$
$569$	−143.305	−	82.7370i	−0.251853	−	0.145408i	−0.620613	+	0.784117i	$0.713116\pi$
$570$		0			0
$571$	−25.5302	−	44.2195i	−0.0447113	−	0.0774423i	0.842804	−	0.538221i	$-0.180903\pi$
$571$	−25.5302	−	44.2195i	−0.0447113	−	0.0774423i	−0.887515	+	0.460779i	$0.847570\pi$
$572$	28.3457	−	16.3654i	0.0495554	−	0.0286108i
$573$	116.001	−	130.919i	0.202445	−	0.228480i
$574$	528.660	−	915.665i	0.921010	−	1.59524i
$575$		0			0
$576$	−549.506	−	234.216i	−0.954004	−	0.406625i
$577$	707.833			1.22675			0.613373	−	0.789793i	$-0.289812\pi$
$577$	707.833			1.22675			0.613373	+	0.789793i	$0.289812\pi$
$578$	−691.115	−	399.015i	−1.19570	−	0.690338i
$579$	360.170	−	120.214i	0.622055	−	0.207623i
$580$		0			0
$581$	−644.669	+	372.200i	−1.10958	+	0.640619i
$582$	−62.0492	−	185.905i	−0.106614	−	0.319424i
$583$	9.54964	−	16.5405i	0.0163802	−	0.0283713i
$584$		−	30.6803i		−	0.0525347i
$585$		0			0
$586$	1094.25			1.86732
$587$	391.878	+	226.251i	0.667594	+	0.385436i	0.795164	−	0.606394i	$-0.207385\pi$
$587$	391.878	+	226.251i	0.667594	+	0.385436i	−0.127570	+	0.991830i	$0.540718\pi$
$588$	−417.758	−	370.155i	−0.710473	−	0.629515i
$589$	−3.35936	−	5.81859i	−0.00570350	−	0.00987875i
$590$		0			0
$591$	−986.312	−	201.431i	−1.66889	−	0.340830i
$592$	114.477	−	198.280i	0.193373	−	0.334932i
$593$		−	227.811i		−	0.384168i	−0.981379	−	0.192084i	$-0.938475\pi$
$593$		−	227.811i		−	0.384168i	0.981379	−	0.192084i	$-0.0615245\pi$
$594$	32.7578	+	2.65158i	0.0551479	+	0.00446394i
$595$		0			0
$596$	284.903	+	164.489i	0.478024	+	0.275988i
$597$	76.3330	−	373.767i	0.127861	−	0.626075i
$598$	−580.088	−	1004.74i	−0.970047	−	1.68017i
$599$	484.611	−	279.790i	0.809033	−	0.467096i	−0.0375869	−	0.999293i	$-0.511967\pi$
$599$	484.611	−	279.790i	0.809033	−	0.467096i	0.846620	+	0.532198i	$0.178634\pi$
$600$		0			0
$601$	−335.271	+	580.707i	−0.557856	+	0.966235i	0.439819	+	0.898086i	$0.355043\pi$
$601$	−335.271	+	580.707i	−0.557856	+	0.966235i	−0.997675	+	0.0681485i	$0.978291\pi$
$602$		−	1597.06i		−	2.65292i
$603$	35.2630	+	290.765i	0.0584793	+	0.482198i
$604$	−359.701			−0.595532
$605$		0			0
$606$	464.379	−	154.995i	0.766301	−	0.255768i
$607$	−499.009	−	864.308i	−0.822090	−	1.42390i	−0.904123	−	0.427272i	$-0.859475\pi$
$607$	−499.009	−	864.308i	−0.822090	−	1.42390i	0.0820329	−	0.996630i	$-0.473859\pi$
$608$	20.8836	−	12.0572i	0.0343481	−	0.0198309i
$609$	−224.754	−	673.382i	−0.369055	−	1.10572i
$610$		0			0
$611$			929.533i			1.52133i
$612$	−104.020	+	12.6152i	−0.169967	+	0.0206130i
$613$	229.314			0.374086			0.187043	−	0.982352i	$-0.440110\pi$
$613$	229.314			0.374086			0.187043	+	0.982352i	$0.440110\pi$
$614$	510.176	+	294.550i	0.830905	+	0.479723i
$615$		0			0
$616$	−0.442960	−	0.767229i	−0.000719091	−	0.00124550i
$617$	430.791	−	248.717i	0.698203	−	0.403108i	−0.108475	−	0.994099i	$-0.534597\pi$
$617$	430.791	−	248.717i	0.698203	−	0.403108i	0.806678	+	0.590992i	$0.201263\pi$
$618$	719.901	+	147.023i	1.16489	+	0.237901i
$619$	−528.867	+	916.025i	−0.854390	+	1.47985i	0.0228204	+	0.999740i	$0.492735\pi$
$619$	−528.867	+	916.025i	−0.854390	+	1.47985i	−0.877210	+	0.480107i	$0.840598\pi$
$620$		0			0
$621$	47.4293	−	585.946i	0.0763757	−	0.943553i
$622$	−460.806			−0.740846
$623$	−244.001	−	140.874i	−0.391655	−	0.226122i
$624$	−176.673	+	865.087i	−0.283130	+	1.38636i
$625$		0			0
$626$	−558.170	+	322.259i	−0.891645	+	0.514792i
$627$	−0.452163	+	0.510313i	−0.000721153	+	0.000813896i
$628$	−127.840	+	221.425i	−0.203567	+	0.352588i
$629$		−	41.6792i		−	0.0662626i
$630$		0			0
$631$	638.591			1.01203			0.506015	−	0.862524i	$-0.331118\pi$
$631$	638.591			1.01203			0.506015	+	0.862524i	$0.331118\pi$
$632$	−9.25037	−	5.34071i	−0.0146367	−	0.00845048i
$633$	−278.068	+	92.8107i	−0.439286	+	0.146620i
$634$	−694.458	−	1202.84i	−1.09536	−	1.89722i
$635$		0			0
$636$	−172.565	−	517.019i	−0.271329	−	0.812923i
$637$	−428.097	+	741.485i	−0.672051	+	1.16403i
$638$		−	29.6050i		−	0.0464028i
$639$	−317.210	+	744.224i	−0.496417	+	1.16467i
$640$		0			0
$641$	765.794	+	442.131i	1.19469	+	0.689753i	0.959366	−	0.282165i	$-0.0910526\pi$
$641$	765.794	+	442.131i	1.19469	+	0.689753i	0.235321	+	0.971918i	$0.424386\pi$
$642$	−619.500	−	548.908i	−0.964953	−	0.854997i
$643$	−510.613	−	884.408i	−0.794111	−	1.37544i	−0.923402	−	0.383834i	$-0.874604\pi$
$643$	−510.613	−	884.408i	−0.794111	−	1.37544i	0.129291	−	0.991607i	$-0.458730\pi$
$644$	−747.534	+	431.589i	−1.16077	+	0.670169i
$645$		0			0
$646$	2.15385	−	3.73057i	0.00333413	−	0.00577488i
$647$			488.043i			0.754317i	0.926149	+	0.377159i	$0.123099\pi$
$647$			488.043i			0.754317i	−0.926149	+	0.377159i	$0.876901\pi$
$648$	12.4214	−	11.9241i	0.0191689	−	0.0184014i
$649$	27.0226			0.0416373
$650$		0			0
$651$	73.9581	−	362.138i	0.113607	−	0.556280i
$652$	491.905	+	852.005i	0.754456	+	1.30676i
$653$	529.397	−	305.648i	0.810716	−	0.468067i	−0.0364887	−	0.999334i	$-0.511617\pi$
$653$	529.397	−	305.648i	0.810716	−	0.468067i	0.847204	+	0.531267i	$0.178284\pi$
$654$	929.971	−	1049.57i	1.42197	−	1.60485i
$655$		0			0
$656$			600.240i			0.915001i
$657$	−1194.93	−	509.316i	−1.81877	−	0.775214i
$658$	1370.46			2.08276
$659$	−125.687	−	72.5657i	−0.190724	−	0.110115i	0.401597	−	0.915816i	$-0.368455\pi$
$659$	−125.687	−	72.5657i	−0.190724	−	0.110115i	−0.592322	+	0.805702i	$0.701789\pi$
$660$		0			0
$661$	−415.128	−	719.023i	−0.628030	−	1.08778i	−0.987947	−	0.154796i	$-0.950528\pi$
$661$	−415.128	−	719.023i	−0.628030	−	1.08778i	0.359916	−	0.932985i	$-0.382805\pi$
$662$	584.827	−	337.650i	0.883424	−	0.510045i
$663$	50.8880	+	152.464i	0.0767541	+	0.229961i
$664$	−8.13214	+	14.0853i	−0.0122472	+	0.0212128i
$665$		0			0
$666$	224.076	+	298.280i	0.336451	+	0.447868i
$667$	−529.550			−0.793929
$668$	469.957	+	271.330i	0.703529	+	0.406182i
$669$	209.778	+	185.874i	0.313569	+	0.277838i
$670$		0			0
$671$	8.22230	−	4.74715i	0.0122538	−	0.00707473i
$672$	1299.76	+	265.445i	1.93417	+	0.395007i
$673$	−135.708	+	235.054i	−0.201647	+	0.349262i	−0.949059	−	0.315098i	$-0.897963\pi$
$673$	−135.708	+	235.054i	−0.201647	+	0.349262i	0.747412	+	0.664360i	$0.231296\pi$
$674$			801.438i			1.18908i
$675$		0			0
$676$	−744.199			−1.10089
$677$	775.906	+	447.970i	1.14609	+	0.661698i	0.947933	−	0.318471i	$-0.103169\pi$
$677$	775.906	+	447.970i	1.14609	+	0.661698i	0.198162	+	0.980169i	$0.436503\pi$
$678$	−73.0158	+	357.524i	−0.107693	+	0.527322i
$679$	111.838	+	193.709i	0.164710	+	0.285286i
$680$		0			0
$681$	−393.907	+	444.564i	−0.578424	+	0.652811i
$682$	7.70700	−	13.3489i	0.0113006	−	0.0195732i
$683$			255.548i			0.374155i	0.982345	+	0.187078i	$0.0599016\pi$
$683$			255.548i			0.374155i	−0.982345	+	0.187078i	$0.940098\pi$
$684$	2.34259	+	19.3161i	0.00342484	+	0.0282400i
$685$		0			0
$686$	−79.9938	−	46.1844i	−0.116609	−	0.0673242i
$687$	515.749	−	172.141i	0.750726	−	0.250569i
$688$	453.325	+	785.182i	0.658902	+	1.14125i
$689$	−724.085	+	418.051i	−1.05092	+	0.606750i
$690$		0			0
$691$	−61.2973	+	106.170i	−0.0887081	+	0.153647i	−0.906965	−	0.421205i	$-0.861607\pi$
$691$	−61.2973	+	106.170i	−0.0887081	+	0.153647i	0.818257	+	0.574852i	$0.194940\pi$
$692$			273.184i			0.394775i
$693$	−37.2354	+	4.51578i	−0.0537308	+	0.00651628i
$694$	1250.23			1.80148
$695$		0			0
$696$	−11.6091	−	10.2862i	−0.0166797	−	0.0147790i
$697$	54.6344	+	94.6296i	0.0783852	+	0.135767i
$698$	239.344	−	138.185i	0.342900	−	0.197973i
$699$	−524.744	−	107.166i	−0.750707	−	0.153314i
$700$		0			0
$701$		−	595.027i		−	0.848826i	−0.905469	−	0.424413i	$-0.860480\pi$
$701$		−	595.027i		−	0.848826i	0.905469	−	0.424413i	$-0.139520\pi$
$702$	−1183.86	−	817.539i	−1.68642	−	1.16459i
$703$	−7.73968			−0.0110095
$704$	24.6214	+	14.2152i	0.0349736	+	0.0201920i
$705$		0			0
$706$	139.517	+	241.651i	0.197617	+	0.342282i
$707$	−483.874	+	279.365i	−0.684404	+	0.395141i
$708$	511.423	−	577.194i	0.722350	−	0.815246i
$709$	280.492	−	485.826i	0.395616	−	0.685227i	−0.597564	−	0.801822i	$-0.703864\pi$
$709$	280.492	−	485.826i	0.395616	−	0.685227i	0.993180	+	0.116594i	$0.0371978\pi$
$710$		0			0
$711$	−361.572	+	271.623i	−0.508541	+	0.382030i
$712$	−6.15588			−0.00864589
$713$	−238.775	−	137.857i	−0.334887	−	0.193347i
$714$	224.786	−	75.0268i	0.314827	−	0.105080i
$715$		0			0
$716$	−133.961	+	77.3424i	−0.187096	+	0.108020i
$717$	14.4941	+	43.4254i	0.0202149	+	0.0605654i
$718$	−710.502	+	1230.63i	−0.989557	+	1.71396i
$719$		−	1218.37i		−	1.69453i	−0.531168	−	0.847266i	$-0.678247\pi$
$719$		−	1218.37i		−	1.69453i	0.531168	−	0.847266i	$-0.321753\pi$
$720$		0			0
$721$	−838.570			−1.16307
$722$	887.698	+	512.513i	1.22950	+	0.709851i
$723$	−716.652	−	634.990i	−0.991220	−	0.878271i
$724$	566.423	+	981.074i	0.782353	+	1.35507i
$725$		0			0
$726$	1009.11	+	206.088i	1.38997	+	0.283867i
$727$	−397.172	+	687.921i	−0.546316	+	0.946247i	0.452207	+	0.891913i	$0.350637\pi$
$727$	−397.172	+	687.921i	−0.546316	+	0.946247i	−0.998523	+	0.0543338i	$0.982696\pi$
$728$			38.7825i			0.0532727i
$729$	−258.214	−	681.738i	−0.354203	−	0.935169i
$730$		0			0
$731$	142.936	+	82.5241i	0.195535	+	0.112892i
$732$	54.2158	−	265.469i	0.0740652	−	0.362663i
$733$	393.411	+	681.408i	0.536714	+	0.929615i	0.999078	+	0.0429255i	$0.0136678\pi$
$733$	393.411	+	681.408i	0.536714	+	0.929615i	−0.462365	+	0.886690i	$0.652999\pi$
$734$	−841.186	+	485.659i	−1.14603	+	0.661661i
$735$		0			0
$736$	494.785	−	856.992i	0.672262	−	1.16439i
$737$		−	13.9404i		−	0.0189150i
$738$	−899.745	−	383.498i	−1.21917	−	0.519645i
$739$	−1398.66			−1.89264			−0.946320	−	0.323231i	$-0.895231\pi$
$739$	−1398.66			−1.89264			−0.946320	+	0.323231i	$0.895231\pi$
$740$		0			0
$741$	28.3121	−	9.44972i	0.0382080	−	0.0127527i
$742$	616.355	+	1067.56i	0.830667	+	1.43876i
$743$	475.127	−	274.315i	0.639471	−	0.369199i	−0.144940	−	0.989440i	$-0.546299\pi$
$743$	475.127	−	274.315i	0.639471	−	0.369199i	0.784411	+	0.620242i	$0.212965\pi$
$744$	−2.55675	−	7.66022i	−0.00343649	−	0.0102960i
$745$		0			0
$746$		−	1736.35i		−	2.32755i
$747$	413.593	+	550.556i	0.553672	+	0.737023i
$748$	4.98710			0.00666725
$749$	818.078	+	472.318i	1.09223	+	0.630598i
$750$		0			0
$751$	133.681	+	231.542i	0.178003	+	0.308311i	0.941197	−	0.337859i	$-0.109703\pi$
$751$	133.681	+	231.542i	0.178003	+	0.308311i	−0.763193	+	0.646170i	$0.776370\pi$
$752$	−673.777	+	389.005i	−0.895980	+	0.517294i
$753$	280.237	+	57.2317i	0.372160	+	0.0760049i
$754$	−648.003	+	1122.37i	−0.859420	+	1.48856i
$755$		0			0
$756$	−608.254	+	880.803i	−0.804569	+	1.16508i
$757$	−471.386			−0.622703			−0.311351	−	0.950295i	$-0.600782\pi$
$757$	−471.386			−0.622703			−0.311351	+	0.950295i	$0.600782\pi$
$758$	461.265	+	266.311i	0.608529	+	0.351334i
$759$	−5.59855	+	27.4135i	−0.00737621	+	0.0361179i
$760$		0			0
$761$	917.999	−	530.007i	1.20631	−	0.696461i	0.244356	−	0.969686i	$-0.421424\pi$
$761$	917.999	−	530.007i	1.20631	−	0.696461i	0.961950	+	0.273225i	$0.0880902\pi$
$762$	−445.056	+	502.292i	−0.584063	+	0.659175i
$763$	−800.210	+	1386.00i	−1.04877	+	1.81652i
$764$			237.585i			0.310975i
$765$		0			0
$766$	−420.042			−0.548357
$767$	−1024.47	−	591.478i	−1.33569	−	0.771158i
$768$	−700.486	+	233.801i	−0.912091	+	0.304428i
$769$	216.513	+	375.012i	0.281551	+	0.487661i	0.971767	−	0.235942i	$-0.0758176\pi$
$769$	216.513	+	375.012i	0.281551	+	0.487661i	−0.690216	+	0.723604i	$0.742484\pi$
$770$		0			0
$771$	−7.53452	−	22.5740i	−0.00977240	−	0.0292789i
$772$	−257.869	+	446.642i	−0.334027	+	0.578552i
$773$			1088.28i			1.40787i	0.710264	+	0.703936i	$0.248576\pi$
$773$			1088.28i			1.40787i	−0.710264	+	0.703936i	$0.751424\pi$
$774$	−1466.60	+	177.864i	−1.89483	+	0.229798i
$775$		0			0
$776$	4.23232	+	2.44353i	0.00545402	+	0.00314888i
$777$	−318.680	−	282.366i	−0.410141	−	0.363406i
$778$	−652.782	−	1130.65i	−0.839052	−	1.45328i
$779$	17.5724	−	10.1454i	0.0225576	−	0.0130237i
$780$		0			0
$781$	19.2523	−	33.3460i	0.0246509	−	0.0426965i
$782$		−	176.773i		−	0.226052i
$783$	−593.345	+	281.390i	−0.757785	+	0.359374i
$784$	−716.626			−0.914063
$785$		0			0
$786$	−311.789	+	1526.69i	−0.396678	+	1.94235i
$787$	161.467	+	279.669i	0.205168	+	0.355361i	0.950186	−	0.311683i	$-0.100893\pi$
$787$	161.467	+	279.669i	0.205168	+	0.355361i	−0.745018	+	0.667044i	$0.767559\pi$
$788$	1184.14	−	683.665i	1.50272	−	0.867595i
$789$	−816.461	+	921.461i	−1.03480	+	1.16788i
$790$		0			0
$791$		−	416.459i		−	0.526497i
$792$	−0.655225	+	0.492222i	−0.000827304	+	0.000621493i
$793$	−415.628			−0.524121
$794$	−1769.17	−	1021.43i	−2.22817	−	1.28643i
$795$		0			0
$796$	259.078	+	448.736i	0.325474	+	0.563738i
$797$	1251.78	−	722.713i	1.57061	−	0.906792i	0.574516	−	0.818494i	$-0.305190\pi$
$797$	1251.78	−	722.713i	1.57061	−	0.906792i	0.996094	−	0.0882984i	$-0.0281429\pi$
$798$	−13.9322	−	41.7421i	−0.0174589	−	0.0523084i
$799$	−70.8152	+	122.656i	−0.0886298	+	0.153511i
$800$		0			0
$801$	−102.192	+	239.759i	−0.127581	+	0.299324i
$802$	215.234			0.268372
$803$	53.5406	+	30.9117i	0.0666758	+	0.0384953i
$804$	−297.762	−	263.832i	−0.370351	−	0.328150i
$805$		0			0
$806$	−584.370	+	337.386i	−0.725024	+	0.418593i
$807$	−591.043	−	120.706i	−0.732396	−	0.149574i
$808$	−6.10380	+	10.5721i	−0.00755421	+	0.0130843i
$809$		−	981.839i		−	1.21365i	−0.794837	−	0.606823i	$-0.792444\pi$
$809$		−	981.839i		−	1.21365i	0.794837	−	0.606823i	$-0.207556\pi$
$810$		0			0
$811$	−600.049			−0.739888			−0.369944	−	0.929054i	$-0.620623\pi$
$811$	−600.049			−0.739888			−0.369944	+	0.929054i	$0.620623\pi$
$812$	835.052	+	482.118i	1.02839	+	0.593741i
$813$	72.6766	−	355.864i	0.0893932	−	0.437717i
$814$	−8.87812	−	15.3774i	−0.0109068	−	0.0188911i
$815$		0			0
$816$	−89.2183	+	100.692i	−0.109336	+	0.123397i
$817$	15.3244	−	26.5427i	0.0187570	−	0.0324880i
$818$		−	1449.42i		−	1.77191i
$819$	1510.50	+	643.819i	1.84432	+	0.786104i
$820$		0			0
$821$	−896.354	−	517.510i	−1.09178	−	0.630342i	−0.157733	−	0.987482i	$-0.550418\pi$
$821$	−896.354	−	517.510i	−1.09178	−	0.630342i	−0.934051	+	0.357140i	$0.883752\pi$
$822$	−44.9917	+	15.0169i	−0.0547344	+	0.0182687i
$823$	−704.012	−	1219.38i	−0.855421	−	1.48163i	−0.876254	−	0.481850i	$-0.839965\pi$
$823$	−704.012	−	1219.38i	−0.855421	−	1.48163i	0.0208322	−	0.999783i	$-0.493368\pi$
$824$	−15.8672	+	9.16091i	−0.0192563	+	0.0111176i
$825$		0			0
$826$	−872.048	+	1510.43i	−1.05575	+	1.82861i
$827$			1535.05i			1.85617i	0.372367	+	0.928086i	$0.378546\pi$
$827$			1535.05i			1.85617i	−0.372367	+	0.928086i	$0.621454\pi$
$828$	479.587	+	638.404i	0.579211	+	0.771020i
$829$	185.325			0.223552			0.111776	−	0.993733i	$-0.464346\pi$
$829$	185.325			0.223552			0.111776	+	0.993733i	$0.464346\pi$
$830$		0			0
$831$	752.223	+	666.507i	0.905202	+	0.802055i
$832$	−622.292	−	1077.84i	−0.747947	−	1.29548i
$833$	−112.978	+	65.2280i	−0.135628	+	0.0783049i
$834$	1419.25	+	289.848i	1.70174	+	0.347540i
$835$		0			0
$836$		−	0.926087i		−	0.00110776i
$837$	−340.793	−	27.5855i	−0.407161	−	0.0329575i
$838$	1981.10			2.36408
$839$	1120.53	+	646.937i	1.33555	+	0.771081i	0.986144	−	0.165889i	$-0.0530494\pi$
$839$	1120.53	+	646.937i	1.33555	+	0.771081i	0.349408	+	0.936971i	$0.386383\pi$
$840$		0			0
$841$	−124.726	−	216.032i	−0.148307	−	0.256875i
$842$	1862.47	−	1075.30i	2.21196	−	1.27708i
$843$	276.285	−	311.817i	0.327741	−	0.369889i
$844$	199.087	−	344.829i	0.235885	−	0.408565i
$845$		0			0
$846$	−152.628	−	1258.51i	−0.180411	−	1.48760i
$847$	−1175.46			−1.38779
$848$	−606.053	−	349.905i	−0.714685	−	0.412623i
$849$	−275.474	+	91.9449i	−0.324469	+	0.108298i
$850$		0			0
$851$	−275.058	+	158.805i	−0.323217	+	0.186610i
$852$	−347.895	−	1042.32i	−0.408328	−	1.22338i
$853$	−193.832	+	335.726i	−0.227235	+	0.393583i	−0.956988	−	0.290128i	$-0.906302\pi$
$853$	−193.832	+	335.726i	−0.227235	+	0.393583i	0.729752	+	0.683711i	$0.239635\pi$
$854$			612.782i			0.717543i
$855$		0			0
$856$	20.6392			0.0241112
$857$	−68.5365	−	39.5696i	−0.0799726	−	0.0461722i	0.459480	−	0.888188i	$-0.348036\pi$
$857$	−68.5365	−	39.5696i	−0.0799726	−	0.0461722i	−0.539453	+	0.842016i	$0.681369\pi$
$858$	51.2515	+	45.4115i	0.0597337	+	0.0529271i
$859$	−329.529	−	570.761i	−0.383620	−	0.664448i	0.607957	−	0.793970i	$-0.291989\pi$
$859$	−329.529	−	570.761i	−0.383620	−	0.664448i	−0.991577	+	0.129521i	$0.958656\pi$
$860$		0			0
$861$	1093.67	+	223.357i	1.27024	+	0.259416i
$862$	−707.386	+	1225.23i	−0.820633	+	1.42138i
$863$			1070.61i			1.24057i	0.784375	+	0.620286i	$0.212984\pi$
$863$			1070.61i			1.24057i	−0.784375	+	0.620286i	$0.787016\pi$
$864$	99.0077	−	1223.15i	0.114592	−	1.41568i
$865$		0			0
$866$	1037.63	+	599.077i	1.19819	+	0.691775i
$867$	168.583	−	825.471i	0.194444	−	0.952100i
$868$	251.017	+	434.775i	0.289190	+	0.500892i
$869$	18.6403	−	10.7620i	0.0214503	−	0.0123843i
$870$		0			0
$871$	−305.131	+	528.502i	−0.350322	+	0.606776i
$872$			34.9674i			0.0401002i
$873$	165.430	−	124.276i	0.189496	−	0.142355i
$874$	−32.8261			−0.0375585
$875$		0			0
$876$	1673.56	−	558.584i	1.91046	−	0.637653i
$877$	536.244	+	928.802i	0.611452	+	1.05907i	0.990996	+	0.133893i	$0.0427478\pi$
$877$	536.244	+	928.802i	0.611452	+	1.05907i	−0.379543	+	0.925174i	$0.623919\pi$
$878$	−1125.84	+	650.002i	−1.28227	+	0.740321i
$879$	365.748	+	1095.81i	0.416095	+	1.24666i
$880$		0			0
$881$		−	1433.62i		−	1.62726i	−0.581381	−	0.813632i	$-0.697487\pi$
$881$		−	1433.62i		−	1.62726i	0.581381	−	0.813632i	$-0.302513\pi$
$882$	457.857	−	1074.20i	0.519112	−	1.21792i
$883$	−731.816			−0.828784			−0.414392	−	0.910099i	$-0.636006\pi$
$883$	−731.816			−0.828784			−0.414392	+	0.910099i	$0.636006\pi$
$884$	−189.069	−	109.159i	−0.213879	−	0.123483i
$885$		0			0
$886$	−330.013	−	571.600i	−0.372475	−	0.645146i
$887$	−1112.81	+	642.482i	−1.25458	+	0.724331i	−0.972015	−	0.234918i	$-0.924518\pi$
$887$	−1112.81	+	642.482i	−1.25458	+	0.724331i	−0.282563	+	0.959249i	$0.591185\pi$
$888$	−9.11464	−	1.86145i	−0.0102642	−	0.00209623i
$889$	382.956	−	663.299i	0.430772	−	0.746119i
$890$		0			0
$891$	8.29381	+	33.6909i	0.00930843	+	0.0378124i
$892$	−380.693			−0.426786
$893$	22.7767	+	13.1501i	0.0255058	+	0.0147258i
$894$	−137.716	+	674.331i	−0.154045	+	0.754285i
$895$		0			0
$896$	−57.3054	+	33.0853i	−0.0639569	+	0.0369255i
$897$	812.284	−	916.747i	0.905556	−	1.02201i
$898$	963.800	−	1669.35i	1.07327	−	1.85896i
$899$			307.993i			0.342595i
$900$		0			0
$901$	−127.395			−0.141392
$902$	40.3143	+	23.2755i	0.0446944	+	0.0258043i
$903$	1599.34	−	533.810i	1.77114	−	0.591151i
$904$	−4.54958	−	7.88010i	−0.00503272	−	0.00871693i
$905$		0			0
$906$	−238.250	−	713.816i	−0.262969	−	0.787877i
$907$	506.427	−	877.157i	0.558353	−	0.967097i	−0.439281	−	0.898350i	$-0.644767\pi$
$907$	506.427	−	877.157i	0.558353	−	0.967097i	0.997634	−	0.0687467i	$-0.0219000\pi$
$908$		−	806.770i		−	0.888514i
$909$	310.433	+	413.235i	0.341511	+	0.454604i
$910$		0			0
$911$	551.233	+	318.255i	0.605086	+	0.349347i	0.771040	−	0.636787i	$-0.219737\pi$
$911$	551.233	+	318.255i	0.605086	+	0.349347i	−0.165954	+	0.986134i	$0.553070\pi$
$912$	18.6982	+	16.5675i	0.0205024	+	0.0181662i
$913$	−16.3870	−	28.3831i	−0.0179485	−	0.0310877i
$914$	1810.13	−	1045.08i	1.98045	−	1.14342i
$915$		0			0
$916$	−369.258	+	639.573i	−0.403120	+	0.698224i
$917$		−	1778.35i		−	1.93931i
$918$	−93.9326	−	198.069i	−0.102323	−	0.215761i
$919$	−1142.09			−1.24275			−0.621377	−	0.783511i	$-0.713427\pi$
$919$	−1142.09			−1.24275			−0.621377	+	0.783511i	$0.713427\pi$
$920$		0			0
$921$	−124.446	+	609.356i	−0.135121	+	0.661625i
$922$	−565.603	−	979.654i	−0.613453	−	1.06253i
$923$	−1459.77	+	842.801i	−1.58155	+	0.913110i
$924$	33.7864	−	38.1314i	0.0365654	−	0.0412678i
$925$		0			0
$926$		−	456.338i		−	0.492806i
$927$	93.3915	+	770.071i	0.100746	+	0.830713i
$928$	−1105.42			−1.19119
$929$	681.162	+	393.269i	0.733221	+	0.423325i	0.819599	−	0.572937i	$-0.194196\pi$
$929$	681.162	+	393.269i	0.733221	+	0.423325i	−0.0863784	+	0.996262i	$0.527529\pi$
$930$		0			0
$931$	12.1126	+	20.9796i	0.0130103	+	0.0225345i
$932$	629.995	−	363.728i	0.675960	−	0.390266i
$933$	−154.023	−	461.464i	−0.165083	−	0.494602i
$934$	−577.787	+	1000.76i	−0.618615	+	1.07147i
$935$		0			0
$936$	35.6145	−	4.31921i	0.0380497	−	0.00461454i
$937$	811.089			0.865623			0.432812	−	0.901484i	$-0.357522\pi$
$937$	811.089			0.865623			0.432812	+	0.901484i	$0.357522\pi$
$938$	779.199	+	449.871i	0.830702	+	0.479606i
$939$	−509.286	−	451.253i	−0.542370	−	0.480567i
$940$		0			0
$941$	−715.505	+	413.097i	−0.760367	+	0.438998i	−0.829428	−	0.558614i	$-0.811333\pi$
$941$	−715.505	+	413.097i	−0.760367	+	0.438998i	0.0690604	+	0.997612i	$0.478000\pi$
$942$	−524.087	−	107.032i	−0.556356	−	0.113622i
$943$	416.333	−	721.111i	0.441499	−	0.764698i
$944$		−	990.124i		−	1.04886i
$945$		0			0
$946$	70.3142			0.0743279
$947$	794.535	+	458.725i	0.839002	+	0.484398i	0.856925	−	0.515441i	$-0.172372\pi$
$947$	794.535	+	458.725i	0.839002	+	0.484398i	−0.0179227	+	0.999839i	$0.505705\pi$
$948$	122.909	−	601.830i	0.129651	−	0.634842i
$949$	−1353.21	−	2343.83i	−1.42593	−	2.46979i
$950$		0			0
$951$	972.435	−	1097.49i	1.02254	−	1.15404i
$952$	−2.95460	+	5.11751i	−0.00310357	+	0.00537554i
$953$		−	192.772i		−	0.202279i	−0.994872	−	0.101140i	$-0.967751\pi$
$953$		−	192.772i		−	0.202279i	0.994872	−	0.101140i	$-0.0322489\pi$
$954$	911.709	−	684.901i	0.955670	−	0.717925i
$955$		0			0
$956$	−53.8513	−	31.0910i	−0.0563298	−	0.0325220i
$957$	29.6472	−	9.89534i	0.0309794	−	0.0103400i
$958$	1200.03	+	2078.50i	1.25264	+	2.16963i
$959$	46.8805	−	27.0665i	0.0488848	−	0.0282236i
$960$		0			0
$961$	400.321	−	693.376i	0.416567	−	0.721515i
$962$			777.308i			0.808012i
$963$	342.626	−	803.854i	0.355791	−	0.834740i
$964$	1300.54			1.34911
$965$		0			0
$966$	−1351.61	−	1197.59i	−1.39918	−	1.23974i
$967$	−428.848	−	742.787i	−0.443483	−	0.768136i	0.554462	−	0.832209i	$-0.312924\pi$
$967$	−428.848	−	742.787i	−0.443483	−	0.768136i	−0.997945	+	0.0640734i	$0.979591\pi$
$968$	−22.2416	+	12.8412i	−0.0229769	+	0.0132657i
$969$	4.45581	+	0.909994i	0.00459836	+	0.000939106i
$970$		0			0
$971$			546.278i			0.562594i	0.959621	+	0.281297i	$0.0907645\pi$
$971$			546.278i			0.562594i	−0.959621	+	0.281297i	$0.909235\pi$
$972$	876.594	+	460.473i	0.901846	+	0.473738i
$973$	−1653.20			−1.69908
$974$	−554.980	−	320.418i	−0.569795	−	0.328971i
$975$		0			0
$976$	−173.938	−	301.270i	−0.178215	−	0.308678i
$977$	688.774	−	397.664i	0.704988	−	0.407025i	−0.104214	−	0.994555i	$-0.533233\pi$
$977$	688.774	−	397.664i	0.704988	−	0.407025i	0.809203	+	0.587530i	$0.199899\pi$
$978$	−1364.96	+	1540.50i	−1.39567	+	1.57515i
$979$	6.20231	−	10.7427i	0.00633535	−	0.0109732i
$980$		0			0
$981$	1361.91	+	580.485i	1.38828	+	0.591728i
$982$	2174.27			2.21412
$983$	934.805	+	539.710i	0.950972	+	0.549044i	0.893383	−	0.449297i	$-0.148325\pi$
$983$	934.805	+	539.710i	0.950972	+	0.549044i	0.0575890	+	0.998340i	$0.481659\pi$
$984$	23.1342	−	7.72149i	0.0235104	−	0.00784704i
$985$		0			0
$986$	−171.013	+	98.7344i	−0.173441	+	0.100136i
$987$	458.070	+	1372.42i	0.464104	+	1.39049i
$988$	−20.2705	+	35.1095i	−0.0205167	+	0.0355359i
$989$		−	1257.72i		−	1.27171i
$990$		0			0
$991$	168.017			0.169543			0.0847716	−	0.996400i	$-0.472984\pi$
$991$	168.017			0.169543			0.0847716	+	0.996400i	$0.472984\pi$
$992$	−498.437	−	287.773i	−0.502457	−	0.290093i
$993$	533.608	+	472.804i	0.537370	+	0.476137i
$994$	1242.59	+	2152.22i	1.25009	+	2.16521i
$995$		0			0
$996$	−916.390	−	187.151i	−0.920070	−	0.187902i
$997$	437.117	−	757.109i	0.438432	−	0.759387i	−0.559137	−	0.829076i	$-0.688867\pi$
$997$	437.117	−	757.109i	0.438432	−	0.759387i	0.997569	+	0.0696887i	$0.0222006\pi$
$998$			579.829i			0.580991i
$999$	−223.809	+	324.095i	−0.224033	+	0.324419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.3.j.e.101.2		20
3.2	odd	2		675.3.j.e.251.9		20
5.2	odd	4		45.3.h.a.29.9	yes	20
5.3	odd	4		45.3.h.a.29.2	yes	20
5.4	even	2	inner	225.3.j.e.101.9		20
9.4	even	3		675.3.j.e.476.9		20
9.5	odd	6	inner	225.3.j.e.176.2		20
15.2	even	4		135.3.h.a.89.2		20
15.8	even	4		135.3.h.a.89.9		20
15.14	odd	2		675.3.j.e.251.2		20
45.2	even	12		405.3.d.a.404.17		20
45.4	even	6		675.3.j.e.476.2		20
45.7	odd	12		405.3.d.a.404.4		20
45.13	odd	12		135.3.h.a.44.2		20
45.14	odd	6	inner	225.3.j.e.176.9		20
45.22	odd	12		135.3.h.a.44.9		20
45.23	even	12		45.3.h.a.14.9	yes	20
45.32	even	12		45.3.h.a.14.2	✓	20
45.38	even	12		405.3.d.a.404.3		20
45.43	odd	12		405.3.d.a.404.18		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.h.a.14.2	✓	20	45.32	even	12
45.3.h.a.14.9	yes	20	45.23	even	12
45.3.h.a.29.2	yes	20	5.3	odd	4
45.3.h.a.29.9	yes	20	5.2	odd	4
135.3.h.a.44.2		20	45.13	odd	12
135.3.h.a.44.9		20	45.22	odd	12
135.3.h.a.89.2		20	15.2	even	4
135.3.h.a.89.9		20	15.8	even	4
225.3.j.e.101.2		20	1.1	even	1	trivial
225.3.j.e.101.9		20	5.4	even	2	inner
225.3.j.e.176.2		20	9.5	odd	6	inner
225.3.j.e.176.9		20	45.14	odd	6	inner
405.3.d.a.404.3		20	45.38	even	12
405.3.d.a.404.4		20	45.7	odd	12
405.3.d.a.404.17		20	45.2	even	12
405.3.d.a.404.18		20	45.43	odd	12
675.3.j.e.251.2		20	15.14	odd	2
675.3.j.e.251.9		20	3.2	odd	2
675.3.j.e.476.2		20	45.4	even	6
675.3.j.e.476.9		20	9.4	even	3

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	225.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.46092 - 1.42081i) q^{2} +(0.600288 - 2.93933i) q^{3} +(2.03740 + 3.52889i) q^{4} +(-5.65349 + 6.38055i) q^{6} +(4.86464 - 8.42581i) q^{7} -0.212574i q^{8} +(-8.27931 - 3.52889i) q^{9} +(0.370966 + 0.214177i) q^{11} +(11.5956 - 3.87025i) q^{12} +(-9.37595 - 16.2396i) q^{13} +(-23.9429 + 13.8235i) q^{14} +(7.84759 - 13.5924i) q^{16} -2.85718i q^{17} +(15.3608 + 20.4476i) q^{18} -0.530568 q^{19} +(-21.8460 - 19.3567i) q^{21} +(-0.608611 - 1.05414i) q^{22} +(-18.8557 + 10.8863i) q^{23} +(-0.624825 - 0.127606i) q^{24} +53.2858i q^{26} +(-15.3425 + 22.2173i) q^{27} +39.6450 q^{28} +(21.0633 + 12.1609i) q^{29} +(6.33163 + 10.9667i) q^{31} +(-39.3609 + 22.7250i) q^{32} +(0.852224 - 0.961823i) q^{33} +(-4.05951 + 7.03128i) q^{34} +(-4.41525 - 36.4065i) q^{36} +14.5875 q^{37} +(1.30568 + 0.753837i) q^{38} +(-53.3619 + 17.8106i) q^{39} +(-33.1200 + 19.1218i) q^{41} +(26.2591 + 78.6743i) q^{42} +(-28.8831 + 50.0269i) q^{43} +1.74546i q^{44} +61.8697 q^{46} +(-42.9289 - 24.7850i) q^{47} +(-35.2418 - 31.2260i) q^{48} +(-22.8295 - 39.5418i) q^{49} +(-8.39819 - 1.71513i) q^{51} +(38.2052 - 66.1734i) q^{52} -44.5876i q^{53} +(69.3232 - 32.8760i) q^{54} +(-1.79111 - 1.03410i) q^{56} +(-0.318494 + 1.55951i) q^{57} +(-34.5566 - 59.8538i) q^{58} +(54.6329 - 31.5423i) q^{59} +(11.0823 - 19.1951i) q^{61} -35.9842i q^{62} +(-70.0096 + 52.5931i) q^{63} +66.3710 q^{64} +(-3.46382 + 1.15612i) q^{66} +(-16.2720 - 28.1839i) q^{67} +(10.0827 - 5.82123i) q^{68} +(20.6797 + 61.9581i) q^{69} -89.8896i q^{71} +(-0.750149 + 1.75996i) q^{72} +144.328 q^{73} +(-35.8987 - 20.7261i) q^{74} +(-1.08098 - 1.87232i) q^{76} +(3.60923 - 2.08379i) q^{77} +(156.625 + 31.9868i) q^{78} +(25.1240 - 43.5160i) q^{79} +(56.0939 + 58.4335i) q^{81} +108.674 q^{82} +(-66.2606 - 38.2556i) q^{83} +(23.7984 - 116.530i) q^{84} +(142.158 - 82.0747i) q^{86} +(48.3889 - 54.6118i) q^{87} +(0.0455285 - 0.0788577i) q^{88} -28.9588i q^{89} -182.443 q^{91} +(-76.8334 - 44.3598i) q^{92} +(36.0355 - 12.0276i) q^{93} +(70.4296 + 121.988i) q^{94} +(43.1684 + 129.336i) q^{96} +(-11.4950 + 19.9099i) q^{97} +129.746i q^{98} +(-2.31554 - 3.08234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 18 q^{4} + 12 q^{6} + 18 q^{9} - 24 q^{11} - 30 q^{14} - 26 q^{16} + 8 q^{19} - 96 q^{21} + 102 q^{24} + 114 q^{29} + 28 q^{31} + 4 q^{34} + 432 q^{36} - 240 q^{39} + 102 q^{41} + 116 q^{46} + 40 q^{49}+ \cdots + 468 q^{99}+O(q^{100}) \) 20 * q + 18 * q^4 + 12 * q^6 + 18 * q^9 - 24 * q^11 - 30 * q^14 - 26 * q^16 + 8 * q^19 - 96 * q^21 + 102 * q^24 + 114 * q^29 + 28 * q^31 + 4 * q^34 + 432 * q^36 - 240 * q^39 + 102 * q^41 + 116 * q^46 + 40 * q^49 - 156 * q^51 + 270 * q^54 - 618 * q^56 - 120 * q^59 - 50 * q^61 - 140 * q^64 - 768 * q^66 - 162 * q^69 - 504 * q^74 - 96 * q^76 + 128 * q^79 + 846 * q^81 - 450 * q^84 + 1488 * q^86 - 288 * q^91 - 218 * q^94 - 474 * q^96 + 468 * q^99

Introduction

L-functions

Modular forms

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Database

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