LMFDB - Embedded newform 162.4.e.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,4,Mod(19,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("162.19");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	162.e (of order $9$, degree $6$, 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:	$9.55830942093$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	162.19
Dual form			162.4.e.a.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.87939 - 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(-1.31542 - 7.46011i) q^{5} +(-2.90083 - 2.43409i) q^{7} +(4.00000 - 6.92820i) q^{8} +O(q^{10})$	\(q+(1.87939 - 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(-1.31542 - 7.46011i) q^{5} +(-2.90083 - 2.43409i) q^{7} +(4.00000 - 6.92820i) q^{8} +(-7.57519 - 13.1206i) q^{10} +(8.73232 - 49.5234i) q^{11} +(-7.25902 - 2.64207i) q^{13} +(-7.11679 - 2.59030i) q^{14} +(2.77837 - 15.7569i) q^{16} +(-17.4793 - 30.2751i) q^{17} +(36.2933 - 62.8618i) q^{19} +(-23.2117 - 19.4770i) q^{20} +(-17.4646 - 99.0469i) q^{22} +(-116.403 + 97.6734i) q^{23} +(63.5387 - 23.1262i) q^{25} -15.4498 q^{26} -15.1471 q^{28} +(60.4031 - 21.9849i) q^{29} +(175.978 - 147.663i) q^{31} +(-5.55674 - 31.5138i) q^{32} +(-53.5597 - 44.9420i) q^{34} +(-14.3427 + 24.8423i) q^{35} +(121.156 + 209.848i) q^{37} +(25.2091 - 142.968i) q^{38} +(-56.9468 - 20.7269i) q^{40} +(-382.412 - 139.187i) q^{41} +(-62.2961 + 353.299i) q^{43} +(-100.575 - 174.201i) q^{44} +(-151.953 + 263.190i) q^{46} +(385.943 + 323.845i) q^{47} +(-57.0713 - 323.667i) q^{49} +(103.594 - 86.9261i) q^{50} +(-29.0361 + 10.5683i) q^{52} +70.4742 q^{53} -380.937 q^{55} +(-28.4672 + 10.3612i) q^{56} +(98.4821 - 82.6363i) q^{58} +(144.376 + 818.796i) q^{59} +(540.763 + 453.754i) q^{61} +(229.723 - 397.892i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(-10.1615 + 57.6285i) q^{65} +(-372.347 - 135.523i) q^{67} +(-131.401 - 47.8262i) q^{68} +(-9.96236 + 56.4994i) q^{70} +(78.6838 + 136.284i) q^{71} +(-152.544 + 264.214i) q^{73} +(371.244 + 311.510i) q^{74} +(-50.4181 - 285.935i) q^{76} +(-145.875 + 122.404i) q^{77} +(747.630 - 272.115i) q^{79} -121.203 q^{80} -813.909 q^{82} +(1036.39 - 377.216i) q^{83} +(-202.863 + 170.222i) q^{85} +(124.592 + 706.597i) q^{86} +(-308.179 - 258.593i) q^{88} +(109.125 - 189.010i) q^{89} +(14.6262 + 25.3333i) q^{91} +(-105.545 + 598.577i) q^{92} +(946.858 + 344.628i) q^{94} +(-516.697 - 188.062i) q^{95} +(-113.659 + 644.593i) q^{97} +(-328.660 - 569.257i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8}+O(q^{10}) $ 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8	$ 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8} + 30 q^{10} + 12 q^{11} + 60 q^{13} + 66 q^{14} - 102 q^{17} + 171 q^{19} - 96 q^{20} - 24 q^{22} + 708 q^{23} + 864 q^{25} + 468 q^{26} - 336 q^{28} + 381 q^{29} + 909 q^{31} - 48 q^{34} - 624 q^{35} + 555 q^{37} - 66 q^{38} - 96 q^{40} - 618 q^{41} - 1161 q^{43} - 132 q^{44} + 348 q^{46} + 378 q^{47} + 579 q^{49} - 36 q^{50} + 240 q^{52} + 1794 q^{53} - 3906 q^{55} + 264 q^{56} + 444 q^{58} - 1038 q^{59} + 324 q^{61} - 744 q^{62} - 768 q^{64} - 5718 q^{65} - 576 q^{67} - 1056 q^{68} - 1038 q^{70} - 120 q^{71} + 3036 q^{73} + 1110 q^{74} + 132 q^{76} + 3804 q^{77} - 2991 q^{79} + 480 q^{80} - 3408 q^{82} - 513 q^{83} - 2925 q^{85} + 2322 q^{86} + 480 q^{88} - 1065 q^{89} + 2859 q^{91} - 1884 q^{92} - 828 q^{94} - 6357 q^{95} - 2055 q^{97} - 1356 q^{98}+O(q^{100}) $ 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8 + 30 * q^10 + 12 * q^11 + 60 * q^13 + 66 * q^14 - 102 * q^17 + 171 * q^19 - 96 * q^20 - 24 * q^22 + 708 * q^23 + 864 * q^25 + 468 * q^26 - 336 * q^28 + 381 * q^29 + 909 * q^31 - 48 * q^34 - 624 * q^35 + 555 * q^37 - 66 * q^38 - 96 * q^40 - 618 * q^41 - 1161 * q^43 - 132 * q^44 + 348 * q^46 + 378 * q^47 + 579 * q^49 - 36 * q^50 + 240 * q^52 + 1794 * q^53 - 3906 * q^55 + 264 * q^56 + 444 * q^58 - 1038 * q^59 + 324 * q^61 - 744 * q^62 - 768 * q^64 - 5718 * q^65 - 576 * q^67 - 1056 * q^68 - 1038 * q^70 - 120 * q^71 + 3036 * q^73 + 1110 * q^74 + 132 * q^76 + 3804 * q^77 - 2991 * q^79 + 480 * q^80 - 3408 * q^82 - 513 * q^83 - 2925 * q^85 + 2322 * q^86 + 480 * q^88 - 1065 * q^89 + 2859 * q^91 - 1884 * q^92 - 828 * q^94 - 6357 * q^95 - 2055 * q^97 - 1356 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	1.87939	−	0.684040i	0.664463	−	0.241845i
$2$	1.87939	−	0.684040i	0.664463	−	0.241845i
$3$		0			0
$3$		0			0
$4$	3.06418	−	2.57115i	0.383022	−	0.321394i
$5$	−1.31542	−	7.46011i	−0.117655	−	0.667252i	−0.985402	−	0.170246i	$-0.945544\pi$
$5$	−1.31542	−	7.46011i	−0.117655	−	0.667252i	0.867747	−	0.497006i	$-0.165567\pi$
$6$		0			0
$7$	−2.90083	−	2.43409i	−0.156630	−	0.131428i	0.561105	−	0.827745i	$-0.310377\pi$
$7$	−2.90083	−	2.43409i	−0.156630	−	0.131428i	−0.717735	+	0.696317i	$0.754821\pi$
$8$	4.00000	−	6.92820i	0.176777	−	0.306186i
$9$		0			0
$10$	−7.57519	−	13.1206i	−0.239549	−	0.414910i
$11$	8.73232	−	49.5234i	0.239354	−	1.35744i	−0.593894	−	0.804544i	$-0.702410\pi$
$11$	8.73232	−	49.5234i	0.239354	−	1.35744i	0.833248	−	0.552900i	$-0.186479\pi$
$12$		0			0
$13$	−7.25902	−	2.64207i	−0.154869	−	0.0563675i	0.263423	−	0.964681i	$-0.415149\pi$
$13$	−7.25902	−	2.64207i	−0.154869	−	0.0563675i	−0.418291	+	0.908313i	$0.637371\pi$
$14$	−7.11679	−	2.59030i	−0.135860	−	0.0494491i
$15$		0			0
$16$	2.77837	−	15.7569i	0.0434120	−	0.246202i
$17$	−17.4793	−	30.2751i	−0.249374	−	0.431928i	0.713978	−	0.700168i	$-0.246892\pi$
$17$	−17.4793	−	30.2751i	−0.249374	−	0.431928i	−0.963352	+	0.268239i	$0.913558\pi$
$18$		0			0
$19$	36.2933	−	62.8618i	0.438224	−	0.759026i	−0.559329	−	0.828946i	$-0.688941\pi$
$19$	36.2933	−	62.8618i	0.438224	−	0.759026i	0.997553	+	0.0699200i	$0.0222744\pi$
$20$	−23.2117	−	19.4770i	−0.259515	−	0.217759i
$21$		0			0
$22$	−17.4646	−	99.0469i	−0.169249	−	0.959858i
$23$	−116.403	+	97.6734i	−1.05529	+	0.885492i	−0.993640	−	0.112606i	$-0.964080\pi$
$23$	−116.403	+	97.6734i	−1.05529	+	0.885492i	−0.0616481	+	0.998098i	$0.519636\pi$
$24$		0			0
$25$	63.5387	−	23.1262i	0.508310	−	0.185010i
$26$	−15.4498			−0.116537
$27$		0			0
$28$	−15.1471			−0.102233
$29$	60.4031	−	21.9849i	0.386778	−	0.140776i	−0.141310	−	0.989965i	$-0.545131\pi$
$29$	60.4031	−	21.9849i	0.386778	−	0.140776i	0.528088	+	0.849190i	$0.322909\pi$
$30$		0			0
$31$	175.978	−	147.663i	1.01957	−	0.855518i	0.0299941	−	0.999550i	$-0.490451\pi$
$31$	175.978	−	147.663i	1.01957	−	0.855518i	0.989573	+	0.144032i	$0.0460067\pi$
$32$	−5.55674	−	31.5138i	−0.0306970	−	0.174091i
$33$		0			0
$34$	−53.5597	−	44.9420i	−0.270159	−	0.226691i
$35$	−14.3427	+	24.8423i	−0.0692676	+	0.119975i
$36$		0			0
$37$	121.156	+	209.848i	0.538322	+	0.932402i	0.998995	+	0.0448313i	$0.0142750\pi$
$37$	121.156	+	209.848i	0.538322	+	0.932402i	−0.460672	+	0.887570i	$0.652392\pi$
$38$	25.2091	−	142.968i	0.107617	−	0.610327i
$39$		0			0
$40$	−56.9468	−	20.7269i	−0.225102	−	0.0819304i
$41$	−382.412	−	139.187i	−1.45665	−	0.530178i	−0.512212	−	0.858859i	$-0.671174\pi$
$41$	−382.412	−	139.187i	−1.45665	−	0.530178i	−0.944441	+	0.328681i	$0.893396\pi$
$42$		0			0
$43$	−62.2961	+	353.299i	−0.220932	+	1.25297i	0.649380	+	0.760464i	$0.275029\pi$
$43$	−62.2961	+	353.299i	−0.220932	+	1.25297i	−0.870311	+	0.492502i	$0.836082\pi$
$44$	−100.575	−	174.201i	−0.344596	−	0.596858i
$45$		0			0
$46$	−151.953	+	263.190i	−0.487048	+	0.843592i
$47$	385.943	+	323.845i	1.19778	+	1.00506i	0.999691	+	0.0248708i	$0.00791744\pi$
$47$	385.943	+	323.845i	1.19778	+	1.00506i	0.198087	+	0.980184i	$0.436527\pi$
$48$		0			0
$49$	−57.0713	−	323.667i	−0.166389	−	0.943636i
$50$	103.594	−	86.9261i	0.293009	−	0.245864i
$51$		0			0
$52$	−29.0361	+	10.5683i	−0.0774343	+	0.0281838i
$53$	70.4742			0.182649			0.0913243	−	0.995821i	$-0.470890\pi$
$53$	70.4742			0.182649			0.0913243	+	0.995821i	$0.470890\pi$
$54$		0			0
$55$	−380.937			−0.933918
$56$	−28.4672	+	10.3612i	−0.0679301	+	0.0247245i
$57$		0			0
$58$	98.4821	−	82.6363i	0.222954	−	0.187081i
$59$	144.376	+	818.796i	0.318579	+	1.80675i	0.551412	+	0.834233i	$0.314089\pi$
$59$	144.376	+	818.796i	0.318579	+	1.80675i	−0.232834	+	0.972517i	$0.574800\pi$
$60$		0			0
$61$	540.763	+	453.754i	1.13504	+	0.952415i	0.999265	−	0.0383245i	$-0.0122020\pi$
$61$	540.763	+	453.754i	1.13504	+	0.952415i	0.135778	+	0.990739i	$0.456646\pi$
$62$	229.723	−	397.892i	0.470562	−	0.815037i
$63$		0			0
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	−10.1615	+	57.6285i	−0.0193904	+	0.109968i
$66$		0			0
$67$	−372.347	−	135.523i	−0.678946	−	0.247116i	−0.0205511	−	0.999789i	$-0.506542\pi$
$67$	−372.347	−	135.523i	−0.678946	−	0.247116i	−0.658395	+	0.752673i	$0.728764\pi$
$68$	−131.401	−	47.8262i	−0.234335	−	0.0852909i
$69$		0			0
$70$	−9.96236	+	56.4994i	−0.0170104	+	0.0964709i
$71$	78.6838	+	136.284i	0.131522	+	0.227802i	0.924263	−	0.381755i	$-0.124680\pi$
$71$	78.6838	+	136.284i	0.131522	+	0.227802i	−0.792742	+	0.609558i	$0.791347\pi$
$72$		0			0
$73$	−152.544	+	264.214i	−0.244574	+	0.423615i	−0.962012	−	0.273008i	$-0.911982\pi$
$73$	−152.544	+	264.214i	−0.244574	+	0.423615i	0.717437	+	0.696623i	$0.245315\pi$
$74$	371.244	+	311.510i	0.583192	+	0.489356i
$75$		0			0
$76$	−50.4181	−	285.935i	−0.0760968	−	0.431566i
$77$	−145.875	+	122.404i	−0.215897	+	0.181159i
$78$		0			0
$79$	747.630	−	272.115i	1.06475	−	0.387536i	0.250537	−	0.968107i	$-0.419393\pi$
$79$	747.630	−	272.115i	1.06475	−	0.387536i	0.814210	+	0.580571i	$0.197171\pi$
$80$	−121.203			−0.169386
$81$		0			0
$82$	−813.909			−1.09611
$83$	1036.39	−	377.216i	1.37059	−	0.498853i	0.451276	−	0.892384i	$-0.350969\pi$
$83$	1036.39	−	377.216i	1.37059	−	0.498853i	0.919311	+	0.393531i	$0.128747\pi$
$84$		0			0
$85$	−202.863	+	170.222i	−0.258865	+	0.217214i
$86$	124.592	+	706.597i	0.156222	+	0.885981i
$87$		0			0
$88$	−308.179	−	258.593i	−0.373318	−	0.313251i
$89$	109.125	−	189.010i	0.129968	−	0.225112i	−0.793696	−	0.608315i	$-0.791846\pi$
$89$	109.125	−	189.010i	0.129968	−	0.225112i	0.923664	+	0.383203i	$0.125179\pi$
$90$		0			0
$91$	14.6262	+	25.3333i	0.0168488	+	0.0291830i
$92$	−105.545	+	598.577i	−0.119607	+	0.678326i
$93$		0			0
$94$	946.858	+	344.628i	1.03895	+	0.378146i
$95$	−516.697	−	188.062i	−0.558021	−	0.203103i
$96$		0			0
$97$	−113.659	+	644.593i	−0.118972	+	0.674726i	0.865734	+	0.500505i	$0.166852\pi$
$97$	−113.659	+	644.593i	−0.118972	+	0.674726i	−0.984706	+	0.174222i	$0.944259\pi$
$98$	−328.660	−	569.257i	−0.338773	−	0.586771i
$99$		0			0
$100$	135.233	−	234.230i	0.135233	−	0.234230i
$101$	−145.500	−	122.089i	−0.143344	−	0.120280i	0.568296	−	0.822824i	$-0.307603\pi$
$101$	−145.500	−	122.089i	−0.143344	−	0.120280i	−0.711640	+	0.702544i	$0.752047\pi$
$102$		0			0
$103$	102.136	+	579.242i	0.0977064	+	0.554121i	0.993884	+	0.110426i	$0.0352215\pi$
$103$	102.136	+	579.242i	0.0977064	+	0.554121i	−0.896178	+	0.443695i	$0.853667\pi$
$104$	−47.3409	+	39.7237i	−0.0446361	+	0.0374541i
$105$		0			0
$106$	132.448	−	48.2072i	0.121363	−	0.0441726i
$107$	−463.844			−0.419080			−0.209540	−	0.977800i	$-0.567197\pi$
$107$	−463.844			−0.419080			−0.209540	+	0.977800i	$0.567197\pi$
$108$		0			0
$109$	−1592.94			−1.39978			−0.699890	−	0.714251i	$-0.746768\pi$
$109$	−1592.94			−1.39978			−0.699890	+	0.714251i	$0.746768\pi$
$110$	−715.927	+	260.576i	−0.620554	+	0.225863i
$111$		0			0
$112$	−46.4133	+	38.9454i	−0.0391575	+	0.0328571i
$113$	−41.0404	−	232.752i	−0.0341660	−	0.193765i	0.962948	−	0.269688i	$-0.0869207\pi$
$113$	−41.0404	−	232.752i	−0.0341660	−	0.193765i	−0.997114	+	0.0759234i	$0.975810\pi$
$114$		0			0
$115$	881.772	+	739.894i	0.715006	+	0.599961i
$116$	128.559	−	222.671i	0.102900	−	0.178228i
$117$		0			0
$118$	831.428	+	1440.07i	0.648637	+	1.12347i
$119$	−22.9876	+	130.369i	−0.0177081	+	0.100428i
$120$		0			0
$121$	−1125.59	−	409.680i	−0.845670	−	0.307799i
$122$	1326.69	+	482.875i	0.984531	+	0.358340i
$123$		0			0
$124$	159.564	−	904.932i	0.115559	−	0.655365i
$125$	−729.553	−	1263.62i	−0.522026	−	0.904175i
$126$		0			0
$127$	1383.14	−	2395.67i	0.966409	−	1.67387i	0.260627	−	0.965440i	$-0.416071\pi$
$127$	1383.14	−	2395.67i	0.966409	−	1.67387i	0.705782	−	0.708429i	$-0.250596\pi$
$128$	−98.0537	−	82.2768i	−0.0677094	−	0.0568149i
$129$		0			0
$130$	20.3229	+	115.257i	0.0137111	+	0.0777593i
$131$	528.579	−	443.531i	0.352536	−	0.295813i	−0.449272	−	0.893395i	$-0.648316\pi$
$131$	528.579	−	443.531i	0.352536	−	0.295813i	0.801807	+	0.597583i	$0.203872\pi$
$132$		0			0
$133$	−258.292	+	94.0105i	−0.168397	+	0.0612913i
$134$	−792.486			−0.510898
$135$		0			0
$136$	−279.669			−0.176334
$137$	546.073	−	198.754i	0.340541	−	0.123947i	−0.166088	−	0.986111i	$-0.553114\pi$
$137$	546.073	−	198.754i	0.340541	−	0.123947i	0.506629	+	0.862164i	$0.330891\pi$
$138$		0			0
$139$	295.475	−	247.933i	0.180301	−	0.151291i	−0.548170	−	0.836367i	$-0.684675\pi$
$139$	295.475	−	247.933i	0.180301	−	0.151291i	0.728472	+	0.685076i	$0.240231\pi$
$140$	19.9247	+	112.999i	0.0120282	+	0.0682152i
$141$		0			0
$142$	241.101	+	202.308i	0.142484	+	0.119558i
$143$	−194.232	+	336.420i	−0.113584	+	0.196733i
$144$		0			0
$145$	−243.465	−	421.694i	−0.139439	−	0.241516i
$146$	−105.956	+	600.906i	−0.0600615	+	0.340626i
$147$		0			0
$148$	910.795	+	331.502i	0.505857	+	0.184117i
$149$	−2327.68	−	847.208i	−1.27981	−	0.465812i	−0.389439	−	0.921052i	$-0.627331\pi$
$149$	−2327.68	−	847.208i	−1.27981	−	0.465812i	−0.890369	+	0.455240i	$0.849553\pi$
$150$		0			0
$151$	378.388	−	2145.94i	0.203926	−	1.15652i	−0.695196	−	0.718820i	$-0.744682\pi$
$151$	378.388	−	2145.94i	0.203926	−	1.15652i	0.899122	−	0.437699i	$-0.144206\pi$
$152$	−290.346	−	502.895i	−0.154936	−	0.268356i
$153$		0			0
$154$	−190.427	+	329.829i	−0.0996430	+	0.172587i
$155$	−1333.07	−	1118.58i	−0.690803	−	0.579653i
$156$		0			0
$157$	−344.673	−	1954.74i	−0.175210	−	0.993663i	−0.937902	−	0.346901i	$-0.887234\pi$
$157$	−344.673	−	1954.74i	−0.175210	−	0.993663i	0.762692	−	0.646762i	$-0.223877\pi$
$158$	1218.95	−	1022.82i	0.613761	−	0.515007i
$159$		0			0
$160$	−227.787	+	82.9078i	−0.112551	+	0.0409652i
$161$	575.410			0.281669
$162$		0			0
$163$	95.9235			0.0460939			0.0230470	−	0.999734i	$-0.492663\pi$
$163$	95.9235			0.0460939			0.0230470	+	0.999734i	$0.492663\pi$
$164$	−1529.65	+	556.747i	−0.728326	+	0.265089i
$165$		0			0
$166$	1689.75	−	1417.87i	0.790060	−	0.662939i
$167$	−205.011	−	1162.68i	−0.0949954	−	0.538746i	−0.994749	−	0.102347i	$-0.967365\pi$
$167$	−205.011	−	1162.68i	−0.0949954	−	0.538746i	0.899753	−	0.436399i	$-0.143746\pi$
$168$		0			0
$169$	−1637.29	−	1373.85i	−0.745237	−	0.625329i
$170$	−264.818	+	458.679i	−0.119474	+	0.206936i
$171$		0			0
$172$	717.498	+	1242.74i	0.318074	+	0.550920i
$173$	189.246	−	1073.27i	0.0831681	−	0.471670i	−0.914569	−	0.404430i	$-0.867470\pi$
$173$	189.246	−	1073.27i	0.0831681	−	0.471670i	0.997737	−	0.0672394i	$-0.0214191\pi$
$174$		0			0
$175$	−240.606	−	87.5735i	−0.103932	−	0.0378282i
$176$	−756.075	−	275.189i	−0.323814	−	0.117859i
$177$		0			0
$178$	75.7972	−	429.867i	0.0319171	−	0.181011i
$179$	2166.11	+	3751.81i	0.904485	+	1.56661i	0.821608	+	0.570054i	$0.193078\pi$
$179$	2166.11	+	3751.81i	0.904485	+	1.56661i	0.0828771	+	0.996560i	$0.473589\pi$
$180$		0			0
$181$	2207.36	−	3823.27i	0.906475	−	1.57006i	0.0875506	−	0.996160i	$-0.472096\pi$
$181$	2207.36	−	3823.27i	0.906475	−	1.57006i	0.818925	−	0.573901i	$-0.194571\pi$
$182$	44.8172	+	37.6061i	0.0182531	+	0.0153162i
$183$		0			0
$184$	211.091	+	1197.15i	0.0845750	+	0.479649i
$185$	1406.12	−	1179.88i	0.558811	−	0.468898i
$186$		0			0
$187$	−1651.96	+	601.264i	−0.646007	+	0.235127i
$188$	2015.25			0.781794
$189$		0			0
$190$	−1099.71			−0.419904
$191$	2001.12	−	728.349i	0.758095	−	0.275924i	0.0660868	−	0.997814i	$-0.478949\pi$
$191$	2001.12	−	728.349i	0.758095	−	0.275924i	0.692008	+	0.721890i	$0.256726\pi$
$192$		0			0
$193$	−3145.22	+	2639.15i	−1.17304	+	0.984301i	−1.00000		0.000612502i	$-0.999805\pi$
$193$	−3145.22	+	2639.15i	−1.17304	+	0.984301i	−0.173045	+	0.984914i	$0.555361\pi$
$194$	227.318	+	1289.19i	0.0841262	+	0.477104i
$195$		0			0
$196$	−1007.07	−	845.035i	−0.367009	−	0.307957i
$197$	−436.204	+	755.528i	−0.157758	+	0.273244i	−0.934060	−	0.357117i	$-0.883760\pi$
$197$	−436.204	+	755.528i	−0.157758	+	0.273244i	0.776302	+	0.630361i	$0.217093\pi$
$198$		0			0
$199$	2284.01	+	3956.02i	0.813614	+	1.40922i	0.910319	+	0.413907i	$0.135836\pi$
$199$	2284.01	+	3956.02i	0.813614	+	1.40922i	−0.0967057	+	0.995313i	$0.530831\pi$
$200$	93.9318	−	532.714i	0.0332099	−	0.188343i
$201$		0			0
$202$	−356.963	−	129.924i	−0.124336	−	0.0452546i
$203$	−228.732	−	83.2518i	−0.0790831	−	0.0287839i
$204$		0			0
$205$	−535.316	+	3035.93i	−0.182381	+	1.03433i
$206$	588.178	+	1018.75i	0.198933	+	0.344563i
$207$		0			0
$208$	−61.7991	+	107.039i	−0.0206010	+	0.0356819i
$209$	−2796.21	−	2346.30i	−0.925444	−	0.776540i
$210$		0			0
$211$	845.116	+	4792.89i	0.275736	+	1.56377i	0.736615	+	0.676312i	$0.236423\pi$
$211$	845.116	+	4792.89i	0.275736	+	1.56377i	−0.460880	+	0.887463i	$0.652466\pi$
$212$	215.946	−	181.200i	0.0699585	−	0.0587021i
$213$		0			0
$214$	−871.742	+	317.288i	−0.278463	+	0.101352i
$215$	2717.59			0.862038
$216$		0			0
$217$	−869.907			−0.272134
$218$	−2993.75	+	1089.63i	−0.930102	+	0.338529i
$219$		0			0
$220$	−1167.26	+	979.446i	−0.357711	+	0.300156i
$221$	46.8940	+	265.949i	0.0142734	+	0.0809487i
$222$		0			0
$223$	1412.91	+	1185.57i	0.424283	+	0.356016i	0.829790	−	0.558076i	$-0.188460\pi$
$223$	1412.91	+	1185.57i	0.424283	+	0.356016i	−0.405506	+	0.914092i	$0.632905\pi$
$224$	−60.5882	+	104.942i	−0.0180724	+	0.0313024i
$225$		0			0
$226$	−236.342	−	409.357i	−0.0695630	−	0.120487i
$227$	−97.7394	+	554.308i	−0.0285779	+	0.162074i	−0.995757	−	0.0920225i	$-0.970667\pi$
$227$	−97.7394	+	554.308i	−0.0285779	+	0.162074i	0.967179	+	0.254096i	$0.0817779\pi$
$228$		0			0
$229$	322.169	+	117.260i	0.0929673	+	0.0338373i	0.388085	−	0.921624i	$-0.373137\pi$
$229$	322.169	+	117.260i	0.0929673	+	0.0338373i	−0.295118	+	0.955461i	$0.595359\pi$
$230$	2163.31	+	787.379i	0.620192	+	0.225732i
$231$		0			0
$232$	89.2963	−	506.425i	0.0252698	−	0.143312i
$233$	1923.63	+	3331.82i	0.540863	+	0.936803i	0.998855	+	0.0478463i	$0.0152358\pi$
$233$	1923.63	+	3331.82i	0.540863	+	0.936803i	−0.457991	+	0.888957i	$0.651431\pi$
$234$		0			0
$235$	1908.24	−	3305.17i	0.529701	−	0.917469i
$236$	2547.64	+	2137.73i	0.702701	+	0.589636i
$237$		0			0
$238$	45.9751	+	260.738i	0.0125215	+	0.0710132i
$239$	−1926.63	+	1616.64i	−0.521438	+	0.437538i	−0.865133	−	0.501543i	$-0.832766\pi$
$239$	−1926.63	+	1616.64i	−0.521438	+	0.437538i	0.343695	+	0.939081i	$0.388321\pi$
$240$		0			0
$241$	−3937.97	+	1433.30i	−1.05256	+	0.383100i	−0.809628	−	0.586943i	$-0.800331\pi$
$241$	−3937.97	+	1433.30i	−1.05256	+	0.383100i	−0.242931	+	0.970043i	$0.578109\pi$
$242$	−2395.65			−0.636356
$243$		0			0
$244$	2823.67			0.740847
$245$	−2339.52	+	851.516i	−0.610067	+	0.222046i
$246$		0			0
$247$	−429.539	+	360.426i	−0.110651	+	0.0928476i
$248$	−319.128	−	1809.86i	−0.0817122	−	0.463413i
$249$		0			0
$250$	−2235.48	−	1875.79i	−0.565537	−	0.474542i
$251$	−3211.53	+	5562.54i	−0.807610	+	1.39882i	0.106905	+	0.994269i	$0.465906\pi$
$251$	−3211.53	+	5562.54i	−0.807610	+	1.39882i	−0.914515	+	0.404552i	$0.867427\pi$
$252$		0			0
$253$	3820.66	+	6617.57i	0.949418	+	1.64444i
$254$	960.720	−	5448.51i	0.237326	−	1.34594i
$255$		0			0
$256$	−240.561	−	87.5572i	−0.0587308	−	0.0213763i
$257$	5127.24	+	1866.16i	1.24447	+	0.452950i	0.878529	−	0.477689i	$-0.158525\pi$
$257$	5127.24	+	1866.16i	1.24447	+	0.452950i	0.365940	+	0.930638i	$0.380748\pi$
$258$		0			0
$259$	159.336	−	903.639i	0.0382264	−	0.216793i
$260$	117.035	+	202.711i	0.0279162	+	0.0483522i
$261$		0			0
$262$	690.012	−	1195.14i	0.162706	−	0.281816i
$263$	1870.44	+	1569.49i	0.438542	+	0.367980i	0.835163	−	0.550002i	$-0.185373\pi$
$263$	1870.44	+	1569.49i	0.438542	+	0.367980i	−0.396622	+	0.917982i	$0.629818\pi$
$264$		0			0
$265$	−92.7031	−	525.745i	−0.0214894	−	0.121873i
$266$	−421.123	+	353.364i	−0.0970703	+	0.0814516i
$267$		0			0
$268$	−1489.39	+	542.092i	−0.339473	+	0.123558i
$269$	−1924.48			−0.436200			−0.218100	−	0.975926i	$-0.569986\pi$
$269$	−1924.48			−0.436200			−0.218100	+	0.975926i	$0.569986\pi$
$270$		0			0
$271$	−2678.00			−0.600284			−0.300142	−	0.953895i	$-0.597034\pi$
$271$	−2678.00			−0.600284			−0.300142	+	0.953895i	$0.597034\pi$
$272$	−525.606	+	191.305i	−0.117167	+	0.0426455i
$273$		0			0
$274$	890.326	−	747.072i	0.196301	−	0.164716i
$275$	−590.449	−	3348.60i	−0.129474	−	0.734284i
$276$		0			0
$277$	−3478.87	−	2919.12i	−0.754603	−	0.633187i	0.182113	−	0.983278i	$-0.441706\pi$
$277$	−3478.87	−	2919.12i	−0.754603	−	0.633187i	−0.936716	+	0.350090i	$0.886151\pi$
$278$	385.715	−	668.078i	0.0832146	−	0.144132i
$279$		0			0
$280$	114.742	+	198.739i	0.0244898	+	0.0424176i
$281$	−609.316	+	3455.60i	−0.129355	+	0.733608i	0.849271	+	0.527958i	$0.177042\pi$
$281$	−609.316	+	3455.60i	−0.129355	+	0.733608i	−0.978626	+	0.205650i	$0.934069\pi$
$282$		0			0
$283$	4695.64	+	1709.07i	0.986313	+	0.358989i	0.784291	−	0.620393i	$-0.213027\pi$
$283$	4695.64	+	1709.07i	0.986313	+	0.358989i	0.202021	+	0.979381i	$0.435249\pi$
$284$	591.509	+	215.292i	0.123590	+	0.0449831i
$285$		0			0
$286$	−134.912	+	765.126i	−0.0278935	+	0.158192i
$287$	770.521	+	1334.58i	0.158475	+	0.274487i
$288$		0			0
$289$	1845.45	−	3196.41i	0.375625	−	0.650602i
$290$	−746.021	−	625.986i	−0.151062	−	0.126756i
$291$		0			0
$292$	211.912	+	1201.81i	0.0424699	+	0.240859i
$293$	202.559	−	169.967i	0.0403879	−	0.0338894i	−0.622370	−	0.782723i	$-0.713830\pi$
$293$	202.559	−	169.967i	0.0403879	−	0.0338894i	0.662758	+	0.748834i	$0.269386\pi$
$294$		0			0
$295$	5918.39	−	2154.12i	1.16808	−	0.425145i
$296$	1938.50			0.380651
$297$		0			0
$298$	−4954.14			−0.963039
$299$	1103.03	−	401.470i	0.213344	−	0.0776508i
$300$		0			0
$301$	1040.67	−	873.226i	0.199280	−	0.167216i
$302$	−756.775	−	4291.89i	−0.144197	−	0.817782i
$303$		0			0
$304$	−889.673	−	746.524i	−0.167849	−	0.140842i
$305$	2673.73	−	4631.03i	0.501958	−	0.869416i
$306$		0			0
$307$	−1499.70	−	2597.56i	−0.278803	−	0.482901i	0.692285	−	0.721624i	$-0.256604\pi$
$307$	−1499.70	−	2597.56i	−0.278803	−	0.482901i	−0.971087	+	0.238724i	$0.923271\pi$
$308$	−132.269	+	750.135i	−0.0244699	+	0.138776i
$309$		0			0
$310$	−3270.50	−	1190.36i	−0.599199	−	0.218091i
$311$	3529.90	+	1284.78i	0.643609	+	0.234254i	0.643144	−	0.765745i	$-0.277630\pi$
$311$	3529.90	+	1284.78i	0.643609	+	0.234254i	0.000465010		1.00000i	$0.499852\pi$
$312$		0			0
$313$	8.46837	−	48.0265i	0.00152927	−	0.00867291i	−0.984034	−	0.177983i	$-0.943043\pi$
$313$	8.46837	−	48.0265i	0.00152927	−	0.00867291i	0.985563	+	0.169310i	$0.0541539\pi$
$314$	−1984.89	−	3437.94i	−0.356733	−	0.617879i
$315$		0			0
$316$	1591.22	−	2756.08i	0.283270	−	0.490638i
$317$	−4348.86	−	3649.13i	−0.770525	−	0.646548i	0.170318	−	0.985389i	$-0.445520\pi$
$317$	−4348.86	−	3649.13i	−0.770525	−	0.646548i	−0.940843	+	0.338842i	$0.889965\pi$
$318$		0			0
$319$	−561.310	−	3183.35i	−0.0985183	−	0.558725i
$320$	−371.388	+	311.631i	−0.0648788	+	0.0544397i
$321$		0			0
$322$	1081.42	−	393.603i	0.187158	−	0.0681201i
$323$	−2537.53			−0.437126
$324$		0			0
$325$	−522.330			−0.0891497
$326$	180.277	−	65.6155i	0.0306277	−	0.0111476i
$327$		0			0
$328$	−2493.96	+	2092.68i	−0.419836	+	0.352284i
$329$	−331.290	−	1878.84i	−0.0555155	−	0.314844i
$330$		0			0
$331$	1412.73	+	1185.42i	0.234594	+	0.196848i	0.752505	−	0.658587i	$-0.228845\pi$
$331$	1412.73	+	1185.42i	0.234594	+	0.196848i	−0.517910	+	0.855435i	$0.673290\pi$
$332$	2205.81	−	3820.57i	0.364637	−	0.631570i
$333$		0			0
$334$	−1180.61	−	2044.88i	−0.193414	−	0.335003i
$335$	−521.225	+	2956.02i	−0.0850077	+	0.482103i
$336$		0			0
$337$	−2095.39	−	762.659i	−0.338703	−	0.123278i	0.167068	−	0.985945i	$-0.446570\pi$
$337$	−2095.39	−	762.659i	−0.338703	−	0.123278i	−0.505772	+	0.862667i	$0.668792\pi$
$338$	−4016.86	−	1462.02i	−0.646415	−	0.235276i
$339$		0			0
$340$	−183.941	+	1043.18i	−0.0293400	+	0.166395i
$341$	−5776.09	−	10004.5i	−0.917281	−	1.58878i
$342$		0			0
$343$	−1271.71	+	2202.67i	−0.200192	+	0.346743i
$344$	2198.54	+	1844.79i	0.344585	+	0.289141i
$345$		0			0
$346$	−378.491	−	2146.53i	−0.0588087	−	0.333521i
$347$	−1534.58	+	1287.66i	−0.237407	+	0.199208i	−0.753727	−	0.657187i	$-0.771746\pi$
$347$	−1534.58	+	1287.66i	−0.237407	+	0.199208i	0.516320	+	0.856396i	$0.327302\pi$
$348$		0			0
$349$	7756.20	−	2823.03i	1.18963	−	0.432989i	0.330035	−	0.943969i	$-0.392940\pi$
$349$	7756.20	−	2823.03i	1.18963	−	0.432989i	0.859593	+	0.510980i	$0.170717\pi$
$350$	−512.096			−0.0782076
$351$		0			0
$352$	−1609.20			−0.243666
$353$	−1140.70	+	415.179i	−0.171992	+	0.0625999i	−0.426581	−	0.904449i	$-0.640282\pi$
$353$	−1140.70	+	415.179i	−0.171992	+	0.0625999i	0.254589	+	0.967049i	$0.418060\pi$
$354$		0			0
$355$	913.194	−	766.260i	0.136528	−	0.114560i
$356$	−151.594	−	859.735i	−0.0225688	−	0.127994i
$357$		0			0
$358$	6637.35	+	5569.40i	0.979874	+	0.822212i
$359$	2128.68	−	3686.98i	0.312945	−	0.542037i	−0.666053	−	0.745904i	$-0.732018\pi$
$359$	2128.68	−	3686.98i	0.312945	−	0.542037i	0.978999	+	0.203867i	$0.0653510\pi$
$360$		0			0
$361$	795.094	+	1377.14i	0.115920	+	0.200779i
$362$	1533.22	−	8695.31i	0.222608	−	1.26247i
$363$		0			0
$364$	109.953	+	40.0196i	0.0158327	+	0.00576262i
$365$	2171.72	+	790.443i	0.311434	+	0.113353i
$366$		0			0
$367$	1322.52	−	7500.37i	0.188106	−	1.06680i	−0.733794	−	0.679372i	$-0.762252\pi$
$367$	1322.52	−	7500.37i	0.188106	−	1.06680i	0.921900	−	0.387429i	$-0.126637\pi$
$368$	1215.62	+	2105.52i	0.172198	+	0.298255i
$369$		0			0
$370$	1835.56	−	3179.28i	0.257909	−	0.446711i
$371$	−204.434	−	171.540i	−0.0286083	−	0.0240052i
$372$		0			0
$373$	−128.604	−	729.349i	−0.0178522	−	0.101245i	0.974580	−	0.224041i	$-0.0719249\pi$
$373$	−128.604	−	729.349i	−0.0178522	−	0.101245i	−0.992432	+	0.122796i	$0.960814\pi$
$374$	−2693.38	+	2260.02i	−0.372383	+	0.312467i
$375$		0			0
$376$	3787.43	−	1378.51i	0.519473	−	0.189073i
$377$	−496.553			−0.0678350
$378$		0			0
$379$	−11672.7			−1.58202			−0.791009	−	0.611804i	$-0.790444\pi$
$379$	−11672.7			−1.58202			−0.791009	+	0.611804i	$0.790444\pi$
$380$	−2066.79	+	752.249i	−0.279010	+	0.101551i
$381$		0			0
$382$	3262.66	−	2737.70i	0.436995	−	0.366682i
$383$	409.142	+	2320.36i	0.0545854	+	0.309569i	0.999860	−	0.0167054i	$-0.00531773\pi$
$383$	409.142	+	2320.36i	0.0545854	+	0.309569i	−0.945275	+	0.326275i	$0.894207\pi$
$384$		0			0
$385$	1105.03	+	927.233i	0.146280	+	0.122743i
$386$	−4105.79	+	7111.43i	−0.541397	+	0.937727i
$387$		0			0
$388$	1309.07	+	2267.38i	0.171284	+	0.296672i
$389$	−2228.62	+	12639.1i	−0.290477	+	1.64738i	0.394561	+	0.918870i	$0.370897\pi$
$389$	−2228.62	+	12639.1i	−0.290477	+	1.64738i	−0.685038	+	0.728508i	$0.740214\pi$
$390$		0			0
$391$	4991.71	+	1816.83i	0.645630	+	0.234990i
$392$	−2470.72	−	899.268i	−0.318342	−	0.115867i
$393$		0			0
$394$	−302.984	+	1718.31i	−0.0387414	+	0.219714i
$395$	−3013.45	−	5219.46i	−0.383857	−	0.664859i
$396$		0			0
$397$	−3961.44	+	6861.42i	−0.500804	+	0.867418i	0.499195	+	0.866489i	$0.333629\pi$
$397$	−3961.44	+	6861.42i	−0.500804	+	0.867418i	−1.00000		0.000928721i	$0.999704\pi$
$398$	6998.61	+	5872.53i	0.881429	+	0.739606i
$399$		0			0
$400$	−187.864	−	1065.43i	−0.0234830	−	0.133178i
$401$	−4405.63	+	3696.76i	−0.548645	+	0.460368i	−0.874482	−	0.485058i	$-0.838798\pi$
$401$	−4405.63	+	3696.76i	−0.548645	+	0.460368i	0.325837	+	0.945426i	$0.394354\pi$
$402$		0			0
$403$	−1667.56	+	606.944i	−0.206122	+	0.0750224i
$404$	−759.745			−0.0935612
$405$		0			0
$406$	−486.824			−0.0595090
$407$	11450.4	−	4167.60i	1.39453	−	0.507568i
$408$		0			0
$409$	6471.68	−	5430.39i	0.782406	−	0.656517i	−0.161447	−	0.986881i	$-0.551616\pi$
$409$	6471.68	−	5430.39i	0.782406	−	0.656517i	0.943853	+	0.330365i	$0.107172\pi$
$410$	1070.63	+	6071.85i	0.128963	+	0.731384i
$411$		0			0
$412$	1802.28	+	1512.29i	0.215515	+	0.180838i
$413$	1574.21	−	2726.61i	0.187559	−	0.324862i
$414$		0			0
$415$	−4177.36	−	7235.39i	−0.494117	−	0.855835i
$416$	−42.9252	+	243.441i	−0.00505909	+	0.0286915i
$417$		0			0
$418$	−6860.12	−	2496.88i	−0.802726	−	0.292168i
$419$	−8713.65	−	3171.51i	−1.01597	−	0.369781i	−0.220245	−	0.975445i	$-0.570686\pi$
$419$	−8713.65	−	3171.51i	−1.01597	−	0.369781i	−0.795721	+	0.605663i	$0.792908\pi$
$420$		0			0
$421$	−2315.95	+	13134.4i	−0.268106	+	1.52050i	0.491937	+	0.870631i	$0.336289\pi$
$421$	−2315.95	+	13134.4i	−0.268106	+	1.52050i	−0.760043	+	0.649873i	$0.774822\pi$
$422$	4866.83	+	8429.60i	0.561407	+	0.972385i
$423$		0			0
$424$	281.897	−	488.260i	0.0322880	−	0.0559245i
$425$	−1810.76	−	1519.41i	−0.206670	−	0.173417i
$426$		0			0
$427$	−464.186	−	2632.53i	−0.0526078	−	0.298354i
$428$	−1421.30	+	1192.61i	−0.160517	+	0.134690i
$429$		0			0
$430$	5107.40	−	1858.94i	0.572792	−	0.208479i
$431$	57.3080			0.00640471			0.00320236	−	0.999995i	$-0.498981\pi$
$431$	57.3080			0.00640471			0.00320236	+	0.999995i	$0.498981\pi$
$432$		0			0
$433$	7382.71			0.819378			0.409689	−	0.912225i	$-0.365637\pi$
$433$	7382.71			0.819378			0.409689	+	0.912225i	$0.365637\pi$
$434$	−1634.89	+	595.051i	−0.180823	+	0.0658142i
$435$		0			0
$436$	−4881.05	+	4095.69i	−0.536147	+	0.449880i
$437$	1915.29	+	10862.2i	0.209659	+	1.18903i
$438$		0			0
$439$	270.542	+	227.012i	0.0294129	+	0.0246803i	0.657376	−	0.753563i	$-0.271667\pi$
$439$	270.542	+	227.012i	0.0294129	+	0.0246803i	−0.627963	+	0.778243i	$0.716111\pi$
$440$	−1523.75	+	2639.21i	−0.165095	+	0.285953i
$441$		0			0
$442$	270.052	+	467.743i	0.0290612	+	0.0503355i
$443$	−1042.80	+	5914.04i	−0.111840	+	0.634277i	0.876426	+	0.481536i	$0.159921\pi$
$443$	−1042.80	+	5914.04i	−0.111840	+	0.634277i	−0.988266	+	0.152741i	$0.951190\pi$
$444$		0			0
$445$	−1553.58	−	565.455i	−0.165498	−	0.0602363i
$446$	3466.37	+	1261.66i	0.368021	+	0.133949i
$447$		0			0
$448$	−42.0842	+	238.671i	−0.00443815	+	0.0251700i
$449$	−8448.21	−	14632.7i	−0.887964	−	1.53800i	−0.842279	−	0.539042i	$-0.818786\pi$
$449$	−8448.21	−	14632.7i	−0.887964	−	1.53800i	−0.0456852	−	0.998956i	$-0.514547\pi$
$450$		0			0
$451$	−10232.4	+	17723.0i	−1.06834	+	1.85042i
$452$	−724.194	−	607.671i	−0.0753612	−	0.0632355i
$453$		0			0
$454$	195.479	+	1108.62i	0.0202077	+	0.114603i
$455$	169.749	−	142.437i	0.0174901	−	0.0146759i
$456$		0			0
$457$	−14386.9	+	5236.41i	−1.47263	+	0.535993i	−0.948813	−	0.315838i	$-0.897715\pi$
$457$	−14386.9	+	5236.41i	−1.47263	+	0.535993i	−0.523817	+	0.851831i	$0.675492\pi$
$458$	685.689			0.0699567
$459$		0			0
$460$	4604.29			0.466687
$461$	13012.5	−	4736.17i	1.31465	−	0.478493i	0.412909	−	0.910772i	$-0.364513\pi$
$461$	13012.5	−	4736.17i	1.31465	−	0.478493i	0.901740	+	0.432279i	$0.142290\pi$
$462$		0			0
$463$	−609.748	+	511.640i	−0.0612039	+	0.0513562i	−0.672876	−	0.739755i	$-0.734941\pi$
$463$	−609.748	+	511.640i	−0.0612039	+	0.0513562i	0.611673	+	0.791111i	$0.290497\pi$
$464$	−178.593	−	1012.85i	−0.0178684	−	0.101337i
$465$		0			0
$466$	5894.34	+	4945.94i	0.585945	+	0.491666i
$467$	5786.59	−	10022.7i	0.573386	−	0.993134i	−0.422829	−	0.906210i	$-0.638963\pi$
$467$	5786.59	−	10022.7i	0.573386	−	0.993134i	0.996215	−	0.0869242i	$-0.0277038\pi$
$468$		0			0
$469$	750.240	+	1299.45i	0.0738654	+	0.127939i
$470$	1325.45	−	7516.99i	0.130082	−	0.737730i
$471$		0			0
$472$	6250.29	+	2274.92i	0.609519	+	0.221847i
$473$	16952.6	+	6170.23i	1.64795	+	0.599805i
$474$		0			0
$475$	852.274	−	4833.49i	0.0823263	−	0.466896i
$476$	264.760	+	458.578i	0.0254943	+	0.0441574i
$477$		0			0
$478$	−2515.04	+	4356.18i	−0.240660	+	0.416835i
$479$	−1001.99	−	840.767i	−0.0955782	−	0.0801996i	0.593747	−	0.804652i	$-0.297648\pi$
$479$	−1001.99	−	840.767i	−0.0955782	−	0.0801996i	−0.689325	+	0.724453i	$0.742093\pi$
$480$		0			0
$481$	−325.041	−	1843.40i	−0.0308120	−	0.174744i
$482$	−6420.52	+	5387.46i	−0.606736	+	0.509112i
$483$		0			0
$484$	−4502.35	+	1638.72i	−0.422835	+	0.153899i
$485$	4958.24			0.464210
$486$		0			0
$487$	−5396.18			−0.502103			−0.251052	−	0.967974i	$-0.580776\pi$
$487$	−5396.18			−0.502103			−0.251052	+	0.967974i	$0.580776\pi$
$488$	5306.76	−	1931.50i	0.492266	−	0.179170i
$489$		0			0
$490$	−3814.39	+	3200.65i	−0.351666	+	0.295083i
$491$	−1999.71	−	11340.9i	−0.183800	−	1.04238i	−0.927488	−	0.373854i	$-0.878036\pi$
$491$	−1999.71	−	11340.9i	−0.183800	−	1.04238i	0.743688	−	0.668527i	$-0.233075\pi$
$492$		0			0
$493$	−1721.40	−	1444.43i	−0.157258	−	0.131955i
$494$	−560.723	+	971.201i	−0.0510691	+	0.0884543i
$495$		0			0
$496$	−1837.78	−	3183.13i	−0.166369	−	0.288159i
$497$	103.479	−	586.861i	0.00933941	−	0.0529664i
$498$		0			0
$499$	−11532.2	−	4197.38i	−1.03457	−	0.376554i	−0.231753	−	0.972775i	$-0.574446\pi$
$499$	−11532.2	−	4197.38i	−1.03457	−	0.376554i	−0.802821	+	0.596220i	$0.796668\pi$
$500$	−5484.45	−	1996.18i	−0.490544	−	0.178543i
$501$		0			0
$502$	−2230.71	+	12651.0i	−0.198329	+	1.12478i
$503$	8642.67	+	14969.5i	0.766119	+	1.32696i	0.939653	+	0.342129i	$0.111148\pi$
$503$	8642.67	+	14969.5i	0.766119	+	1.32696i	−0.173534	+	0.984828i	$0.555519\pi$
$504$		0			0
$505$	−719.402	+	1246.04i	−0.0633920	+	0.109798i
$506$	11707.2	+	9823.48i	1.02855	+	0.863058i
$507$		0			0
$508$	−1921.44	−	10897.0i	−0.167815	−	0.951727i
$509$	1601.96	−	1344.20i	0.139500	−	0.117054i	−0.570368	−	0.821390i	$-0.693199\pi$
$509$	1601.96	−	1344.20i	0.139500	−	0.117054i	0.709867	+	0.704335i	$0.248755\pi$
$510$		0			0
$511$	1085.62	−	395.135i	0.0939827	−	0.0342069i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	10912.6			0.936447
$515$	4186.86	−	1523.89i	0.358243	−	0.130390i
$516$		0			0
$517$	19408.1	−	16285.3i	1.65100	−	1.38535i
$518$	−318.672	−	1807.28i	−0.0270302	−	0.153296i
$519$		0			0
$520$	358.616	+	300.915i	0.0302430	+	0.0253769i
$521$	−1773.39	+	3071.60i	−0.149124	+	0.258290i	−0.930904	−	0.365264i	$-0.880979\pi$
$521$	−1773.39	+	3071.60i	−0.149124	+	0.258290i	0.781780	+	0.623554i	$0.214312\pi$
$522$		0			0
$523$	3047.50	+	5278.43i	0.254795	+	0.441318i	0.964840	−	0.262838i	$-0.0846586\pi$
$523$	3047.50	+	5278.43i	0.254795	+	0.441318i	−0.710045	+	0.704157i	$0.751325\pi$
$524$	479.277	−	2718.11i	0.0399567	−	0.226606i
$525$		0			0
$526$	4588.88	+	1670.21i	0.380389	+	0.138450i
$527$	−7546.49	−	2746.70i	−0.623776	−	0.227036i
$528$		0			0
$529$	1896.70	−	10756.7i	0.155889	−	0.884089i
$530$	−533.856	−	924.665i	−0.0437532	−	0.0757828i
$531$		0			0
$532$	−549.737	+	952.172i	−0.0448010	+	0.0775975i
$533$	2408.20	+	2020.72i	0.195705	+	0.164216i
$534$		0			0
$535$	610.149	+	3460.33i	0.0493066	+	0.279632i
$536$	−2428.32	+	2037.60i	−0.195685	+	0.164200i
$537$		0			0
$538$	−3616.84	+	1316.42i	−0.289839	+	0.105493i
$539$	−16527.5			−1.32076
$540$		0			0
$541$	7761.32			0.616793			0.308397	−	0.951258i	$-0.400208\pi$
$541$	7761.32			0.616793			0.308397	+	0.951258i	$0.400208\pi$
$542$	−5032.99	+	1831.86i	−0.398866	+	0.145175i
$543$		0			0
$544$	−856.956	+	719.071i	−0.0675399	+	0.0566727i
$545$	2095.38	+	11883.5i	0.164690	+	0.934006i
$546$		0			0
$547$	−5095.85	−	4275.93i	−0.398324	−	0.334233i	0.421522	−	0.906818i	$-0.361496\pi$
$547$	−5095.85	−	4275.93i	−0.398324	−	0.334233i	−0.819845	+	0.572585i	$0.805941\pi$
$548$	1162.24	−	2013.05i	0.0905992	−	0.156922i
$549$		0			0
$550$	−3400.26	−	5889.42i	−0.263614	−	0.456592i
$551$	810.215	−	4594.96i	0.0626430	−	0.355266i
$552$		0			0
$553$	−2831.10	−	1030.44i	−0.217705	−	0.0792380i
$554$	−8534.93	−	3106.46i	−0.654539	−	0.238233i
$555$		0			0
$556$	267.915	−	1519.42i	0.0204355	−	0.115895i
$557$	2884.06	+	4995.34i	0.219392	+	0.379999i	0.954622	−	0.297819i	$-0.0962591\pi$
$557$	2884.06	+	4995.34i	0.219392	+	0.379999i	−0.735230	+	0.677818i	$0.762926\pi$
$558$		0			0
$559$	1385.65	−	2400.01i	0.104842	−	0.181592i
$560$	351.590	+	295.019i	0.0265310	+	0.0222622i
$561$		0			0
$562$	1218.63	+	6911.20i	0.0914677	+	0.518739i
$563$	−4927.18	+	4134.39i	−0.368838	+	0.309492i	−0.808302	−	0.588769i	$-0.799613\pi$
$563$	−4927.18	+	4134.39i	−0.368838	+	0.309492i	0.439464	+	0.898260i	$0.355168\pi$
$564$		0			0
$565$	−1682.37	+	612.331i	−0.125270	+	0.0455946i
$566$	9993.98			0.742188
$567$		0			0
$568$	1258.94			0.0930000
$569$	−20176.1	+	7343.51i	−1.48652	+	0.541048i	−0.952530	−	0.304446i	$-0.901529\pi$
$569$	−20176.1	+	7343.51i	−1.48652	+	0.541048i	−0.533986	+	0.845493i	$0.679307\pi$
$570$		0			0
$571$	−17303.3	+	14519.2i	−1.26816	+	1.06412i	−0.273402	+	0.961900i	$0.588149\pi$
$571$	−17303.3	+	14519.2i	−1.26816	+	1.06412i	−0.994762	+	0.102216i	$0.967407\pi$
$572$	269.825	+	1530.25i	0.0197237	+	0.111859i
$573$		0			0
$574$	2361.01	+	1981.13i	0.171684	+	0.144060i
$575$	−5137.26	+	8897.99i	−0.372589	+	0.645342i
$576$		0			0
$577$	−1749.08	−	3029.50i	−0.126196	−	0.218578i	0.796004	−	0.605292i	$-0.206944\pi$
$577$	−1749.08	−	3029.50i	−0.126196	−	0.218578i	−0.922200	+	0.386714i	$0.873610\pi$
$578$	1281.83	−	7269.64i	0.0922444	−	0.523144i
$579$		0			0
$580$	−1830.26	−	666.160i	−0.131030	−	0.0476910i
$581$	−3924.57	−	1428.43i	−0.280239	−	0.101999i
$582$		0			0
$583$	615.403	−	3490.13i	0.0437177	−	0.247935i
$584$	1220.35	+	2113.71i	0.0864701	+	0.149771i
$585$		0			0
$586$	264.422	−	457.993i	0.0186403	−	0.0322859i
$587$	−15566.0	−	13061.4i	−1.09451	−	0.918402i	−0.0974652	−	0.995239i	$-0.531073\pi$
$587$	−15566.0	−	13061.4i	−1.09451	−	0.918402i	−0.997044	+	0.0768370i	$0.975518\pi$
$588$		0			0
$589$	−2895.55	−	16421.5i	−0.202562	−	1.14879i
$590$	9649.44	−	8096.84i	0.673324	−	0.564986i
$591$		0			0
$592$	3643.18	−	1326.01i	0.252929	−	0.0920585i
$593$	16453.0			1.13937			0.569684	−	0.821864i	$-0.307066\pi$
$593$	16453.0			1.13937			0.569684	+	0.821864i	$0.307066\pi$
$594$		0			0
$595$	1002.81			0.0690941
$596$	−9310.74	+	3388.83i	−0.639904	+	0.232906i
$597$		0			0
$598$	1798.39	−	1509.03i	0.122980	−	0.103192i
$599$	−784.985	−	4451.87i	−0.0535453	−	0.303670i	0.946260	−	0.323407i	$-0.104828\pi$
$599$	−784.985	−	4451.87i	−0.0535453	−	0.303670i	−0.999805	+	0.0197368i	$0.993717\pi$
$600$		0			0
$601$	11380.4	+	9549.28i	0.772405	+	0.648125i	0.941324	−	0.337505i	$-0.109583\pi$
$601$	11380.4	+	9549.28i	0.772405	+	0.648125i	−0.168918	+	0.985630i	$0.554027\pi$
$602$	1358.50	−	2352.99i	0.0919738	−	0.159303i
$603$		0			0
$604$	−4358.10	−	7548.44i	−0.293590	−	0.508513i
$605$	−1575.64	+	8935.90i	−0.105882	+	0.600489i
$606$		0			0
$607$	23778.0	+	8654.47i	1.58998	+	0.578705i	0.977343	−	0.211660i	$-0.0678869\pi$
$607$	23778.0	+	8654.47i	1.58998	+	0.578705i	0.612636	+	0.790365i	$0.290109\pi$
$608$	−2182.69	−	794.434i	−0.145592	−	0.0529911i
$609$		0			0
$610$	1857.15	−	10532.4i	0.123269	−	0.699091i
$611$	−1945.95	−	3370.48i	−0.128846	−	0.223167i
$612$		0			0
$613$	−1715.29	+	2970.96i	−0.113018	+	0.195752i	−0.916986	−	0.398920i	$-0.869385\pi$
$613$	−1715.29	+	2970.96i	−0.113018	+	0.195752i	0.803968	+	0.594673i	$0.202718\pi$
$614$	−4595.35	−	3855.96i	−0.302041	−	0.253443i
$615$		0			0
$616$	264.538	+	1500.27i	0.0173028	+	0.0981292i
$617$	16657.5	−	13977.3i	1.08688	−	0.911999i	0.0904044	−	0.995905i	$-0.471184\pi$
$617$	16657.5	−	13977.3i	1.08688	−	0.911999i	0.996474	+	0.0839061i	$0.0267396\pi$
$618$		0			0
$619$	6857.09	−	2495.78i	0.445250	−	0.162058i	−0.109658	−	0.993969i	$-0.534976\pi$
$619$	6857.09	−	2495.78i	0.445250	−	0.162058i	0.554908	+	0.831912i	$0.312753\pi$
$620$	−6960.78			−0.450890
$621$		0			0
$622$	7512.88			0.484307
$623$	−776.618	+	282.666i	−0.0499431	+	0.0181778i
$624$		0			0
$625$	−1992.44	+	1671.86i	−0.127516	+	0.106999i
$626$	−16.9367	−	96.0531i	−0.00108136	−	0.00613267i
$627$		0			0
$628$	−6082.07	−	5103.46i	−0.386466	−	0.324284i
$629$	4235.45	−	7336.01i	0.268487	−	0.465033i
$630$		0			0
$631$	−12910.8	−	22362.1i	−0.814532	−	1.41081i	−0.909663	−	0.415346i	$-0.863660\pi$
$631$	−12910.8	−	22362.1i	−0.814532	−	1.41081i	0.0951313	−	0.995465i	$-0.469673\pi$
$632$	1105.25	−	6268.19i	0.0695642	−	0.394518i
$633$		0			0
$634$	−10669.3	−	3883.32i	−0.668350	−	0.243259i
$635$	−19691.4	−	7167.07i	−1.23060	−	0.447900i
$636$		0			0
$637$	−440.869	+	2500.29i	−0.0274221	+	0.155518i
$638$	−3232.46	−	5598.78i	−0.200587	−	0.347426i
$639$		0			0
$640$	−484.812	+	839.719i	−0.0299436	+	0.0518638i
$641$	−1749.08	−	1467.66i	−0.107776	−	0.0904351i	0.587307	−	0.809364i	$-0.300188\pi$
$641$	−1749.08	−	1467.66i	−0.107776	−	0.0904351i	−0.695083	+	0.718929i	$0.744633\pi$
$642$		0			0
$643$	4403.81	+	24975.3i	0.270093	+	1.53177i	0.754131	+	0.656724i	$0.228058\pi$
$643$	4403.81	+	24975.3i	0.270093	+	1.53177i	−0.484038	+	0.875047i	$0.660831\pi$
$644$	1763.16	−	1479.46i	0.107885	−	0.0905265i
$645$		0			0
$646$	−4768.99	+	1735.77i	−0.290454	+	0.105717i
$647$	−4679.12			−0.284320			−0.142160	−	0.989844i	$-0.545405\pi$
$647$	−4679.12			−0.284320			−0.142160	+	0.989844i	$0.545405\pi$
$648$		0			0
$649$	41810.4			2.52881
$650$	−981.659	+	357.295i	−0.0592367	+	0.0215604i
$651$		0			0
$652$	293.927	−	246.634i	0.0176550	−	0.0148143i
$653$	1438.84	+	8160.08i	0.0862270	+	0.489018i	0.997085	+	0.0762978i	$0.0243100\pi$
$653$	1438.84	+	8160.08i	0.0862270	+	0.489018i	−0.910858	+	0.412720i	$0.864579\pi$
$654$		0			0
$655$	−4004.09	−	3359.83i	−0.238859	−	0.200427i
$656$	−3255.64	+	5638.93i	−0.193767	+	0.335615i
$657$		0			0
$658$	−1907.82	−	3304.44i	−0.113031	−	0.195776i
$659$	3090.71	−	17528.3i	0.182696	−	1.03612i	−0.746184	−	0.665740i	$-0.768116\pi$
$659$	3090.71	−	17528.3i	0.182696	−	1.03612i	0.928880	−	0.370381i	$-0.120773\pi$
$660$		0			0
$661$	−5592.66	−	2035.56i	−0.329091	−	0.119779i	0.172190	−	0.985064i	$-0.444916\pi$
$661$	−5592.66	−	2035.56i	−0.329091	−	0.119779i	−0.501281	+	0.865284i	$0.667138\pi$
$662$	3465.94	+	1261.50i	0.203486	+	0.0740628i
$663$		0			0
$664$	1532.14	−	8689.19i	0.0895460	−	0.507841i
$665$	1041.09	+	1803.22i	0.0607094	+	0.105152i
$666$		0			0
$667$	−4883.74	+	8458.88i	−0.283507	+	0.491048i
$668$	−3617.61	−	3035.53i	−0.209535	−	0.175821i
$669$		0			0
$670$	1042.45	+	5912.03i	0.0601095	+	0.340898i
$671$	27193.6	−	22818.1i	1.56453	−	1.31279i
$672$		0			0
$673$	7821.08	−	2846.64i	0.447965	−	0.163046i	−0.108180	−	0.994131i	$-0.534502\pi$
$673$	7821.08	−	2846.64i	0.447965	−	0.163046i	0.556145	+	0.831085i	$0.312280\pi$
$674$	−4459.73			−0.254870
$675$		0			0
$676$	−8549.30			−0.486419
$677$	−8388.92	+	3053.32i	−0.476237	+	0.173336i	−0.568975	−	0.822355i	$-0.692660\pi$
$677$	−8388.92	+	3053.32i	−0.476237	+	0.173336i	0.0927388	+	0.995690i	$0.470438\pi$
$678$		0			0
$679$	1898.70	−	1593.20i	0.107313	−	0.0900462i
$680$	367.882	+	2086.36i	0.0207465	+	0.117659i
$681$		0			0
$682$	−17699.0	−	14851.2i	−0.993736	−	0.833844i
$683$	−6680.31	+	11570.6i	−0.374253	+	0.648225i	−0.990215	−	0.139551i	$-0.955434\pi$
$683$	−6680.31	+	11570.6i	−0.374253	+	0.648225i	0.615962	+	0.787776i	$0.288768\pi$
$684$		0			0
$685$	−2201.04	−	3812.32i	−0.122770	−	0.212644i
$686$	−883.321	+	5009.56i	−0.0491623	+	0.278813i
$687$		0			0
$688$	5393.82	+	1963.19i	0.298892	+	0.108788i
$689$	−511.574	−	186.198i	−0.0282865	−	0.0102955i
$690$		0			0
$691$	55.3491	−	313.900i	0.00304715	−	0.0172812i	−0.983246	−	0.182282i	$-0.941652\pi$
$691$	55.3491	−	313.900i	0.00304715	−	0.0172812i	0.986293	+	0.165001i	$0.0527627\pi$
$692$	−2179.65	−	3775.26i	−0.119737	−	0.207390i
$693$		0			0
$694$	−2003.25	+	3469.73i	−0.109571	+	0.189782i
$695$	−2238.28	−	1878.14i	−0.122162	−	0.102506i
$696$		0			0
$697$	2470.42	+	14010.4i	0.134252	+	0.761382i
$698$	12645.8	−	10611.1i	0.685747	−	0.575410i
$699$		0			0
$700$	−962.425	+	350.294i	−0.0519661	+	0.0189141i
$701$	5490.46			0.295823			0.147911	−	0.989001i	$-0.452745\pi$
$701$	5490.46			0.295823			0.147911	+	0.989001i	$0.452745\pi$
$702$		0			0
$703$	17588.6			0.943623
$704$	−3024.30	+	1100.76i	−0.161907	+	0.0589294i
$705$		0			0
$706$	−1859.81	+	1560.56i	−0.0991427	+	0.0831906i
$707$	124.895	+	708.317i	0.00664381	+	0.0376789i
$708$		0			0
$709$	−24791.2	−	20802.3i	−1.31319	−	1.10190i	−0.987702	−	0.156351i	$-0.950027\pi$
$709$	−24791.2	−	20802.3i	−1.31319	−	1.10190i	−0.325488	−	0.945546i	$-0.605529\pi$
$710$	1192.09	−	2064.76i	0.0630117	−	0.109140i
$711$		0			0
$712$	−872.998	−	1512.08i	−0.0459508	−	0.0795891i
$713$	−6061.55	+	34376.7i	−0.318382	+	1.80564i
$714$		0			0
$715$	2765.23	+	1006.46i	0.144635	+	0.0526427i
$716$	16283.8	+	5926.83i	0.849938	+	0.309352i
$717$		0			0
$718$	1478.56	−	8385.36i	0.0768517	−	0.435848i
$719$	4974.59	+	8616.24i	0.258026	+	0.446914i	0.965713	−	0.259612i	$-0.0835946\pi$
$719$	4974.59	+	8616.24i	0.258026	+	0.446914i	−0.707687	+	0.706526i	$0.750261\pi$
$720$		0			0
$721$	1113.65	−	1928.89i	0.0575234	−	0.0996334i
$722$	2436.31	+	2044.31i	0.125582	+	0.105376i
$723$		0			0
$724$	−3066.44	−	17390.6i	−0.157408	−	0.892704i
$725$	3329.51	−	2793.79i	0.170558	−	0.143115i
$726$		0			0
$727$	−11536.1	+	4198.81i	−0.588517	+	0.214203i	−0.619077	−	0.785330i	$-0.712493\pi$
$727$	−11536.1	+	4198.81i	−0.588517	+	0.214203i	0.0305599	+	0.999533i	$0.490271\pi$
$728$	234.019			0.0119139
$729$		0			0
$730$	4622.20			0.234350
$731$	11785.0	−	4289.40i	0.596286	−	0.217030i
$732$		0			0
$733$	−14236.2	+	11945.6i	−0.717362	+	0.601939i	−0.926654	−	0.375915i	$-0.877329\pi$
$733$	−14236.2	+	11945.6i	−0.717362	+	0.601939i	0.209292	+	0.977853i	$0.432884\pi$
$734$	−2645.03	−	15000.7i	−0.133011	−	0.754342i
$735$		0			0
$736$	3724.88	+	3125.55i	0.186550	+	0.156534i
$737$	−9963.02	+	17256.5i	−0.497955	+	0.862483i
$738$		0			0
$739$	−13567.3	−	23499.3i	−0.675348	−	1.16974i	−0.976367	−	0.216119i	$-0.930660\pi$
$739$	−13567.3	−	23499.3i	−0.675348	−	1.16974i	0.301019	−	0.953618i	$-0.402673\pi$
$740$	1274.97	−	7230.69i	0.0633361	−	0.359197i
$741$		0			0
$742$	−501.550	−	182.549i	−0.0248147	−	0.00903180i
$743$	14327.9	+	5214.91i	0.707454	+	0.257492i	0.670590	−	0.741828i	$-0.266041\pi$
$743$	14327.9	+	5214.91i	0.707454	+	0.257492i	0.0368637	+	0.999320i	$0.488263\pi$
$744$		0			0
$745$	−3258.38	+	18479.2i	−0.160239	+	0.908759i
$746$	−740.600	−	1282.76i	−0.0363476	−	0.0629558i
$747$		0			0
$748$	−3515.96	+	6089.82i	−0.171867	+	0.297682i
$749$	1345.53	+	1129.04i	0.0656405	+	0.0550789i
$750$		0			0
$751$	3393.71	+	19246.7i	0.164898	+	0.935181i	0.949170	+	0.314764i	$0.101925\pi$
$751$	3393.71	+	19246.7i	0.164898	+	0.935181i	−0.784272	+	0.620417i	$0.786963\pi$
$752$	6175.09	−	5181.51i	0.299445	−	0.251264i
$753$		0			0
$754$	−933.215	+	339.662i	−0.0450738	+	0.0164055i
$755$	−16506.7			−0.795683
$756$		0			0
$757$	16436.1			0.789140			0.394570	−	0.918866i	$-0.370894\pi$
$757$	16436.1			0.789140			0.394570	+	0.918866i	$0.370894\pi$
$758$	−21937.5	+	7984.58i	−1.05119	+	0.382603i
$759$		0			0
$760$	−3369.72	+	2827.53i	−0.160832	+	0.134954i
$761$	917.678	+	5204.41i	0.0437133	+	0.247910i	0.998832	−	0.0483121i	$-0.0153842\pi$
$761$	917.678	+	5204.41i	0.0437133	+	0.247910i	−0.955119	+	0.296222i	$0.904273\pi$
$762$		0			0
$763$	4620.85	+	3877.35i	0.219248	+	0.183971i
$764$	4259.10	−	7376.97i	0.201687	−	0.349332i
$765$		0			0
$766$	2356.16	+	4080.98i	0.111138	+	0.192496i
$767$	1115.29	−	6325.11i	0.0525042	−	0.297766i
$768$		0			0
$769$	−1379.47	−	502.087i	−0.0646879	−	0.0235445i	0.309474	−	0.950908i	$-0.399847\pi$
$769$	−1379.47	−	502.087i	−0.0646879	−	0.0235445i	−0.374161	+	0.927364i	$0.622069\pi$
$770$	2711.05	+	986.741i	0.126882	+	0.0461814i
$771$		0			0
$772$	−2851.85	+	16173.6i	−0.132954	+	0.754019i
$773$	6559.09	+	11360.7i	0.305193	+	0.528609i	0.977304	−	0.211841i	$-0.0679458\pi$
$773$	6559.09	+	11360.7i	0.305193	+	0.528609i	−0.672112	+	0.740450i	$0.734612\pi$
$774$		0			0
$775$	7766.53	−	13452.0i	0.359977	−	0.623498i
$776$	4011.23	+	3365.82i	0.185560	+	0.155704i
$777$		0			0
$778$	4457.24	+	25278.3i	0.205398	+	1.16487i
$779$	−22628.5	+	18987.6i	−1.04076	+	0.873301i
$780$		0			0
$781$	7436.36	−	2706.61i	0.340709	−	0.124008i
$782$	10624.1			0.485829
$783$		0			0
$784$	−5258.57			−0.239548
$785$	−14129.2	+	5142.60i	−0.642410	+	0.233818i
$786$		0			0
$787$	−17839.9	+	14969.5i	−0.808036	+	0.678022i	−0.950138	−	0.311830i	$-0.899058\pi$
$787$	−17839.9	+	14969.5i	−0.808036	+	0.678022i	0.142102	+	0.989852i	$0.454614\pi$
$788$	605.969	+	3436.62i	0.0273943	+	0.155361i
$789$		0			0
$790$	−9233.76	−	7748.04i	−0.415851	−	0.348941i
$791$	−447.486	+	775.069i	−0.0201148	+	0.0348398i
$792$		0			0
$793$	−2726.56	−	4722.55i	−0.122097	−	0.211479i
$794$	−2751.59	+	15605.0i	−0.122985	+	0.697484i
$795$		0			0
$796$	17170.1	+	6249.42i	0.764547	+	0.278272i
$797$	29762.9	+	10832.8i	1.32278	+	0.481453i	0.904349	−	0.426795i	$-0.140357\pi$
$797$	29762.9	+	10832.8i	1.32278	+	0.481453i	0.418433	+	0.908248i	$0.362580\pi$
$798$		0			0
$799$	3058.40	−	17345.0i	0.135417	−	0.767989i
$800$	−1081.86	−	1873.84i	−0.0478121	−	0.0828129i
$801$		0			0
$802$	−5751.14	+	9961.27i	−0.253217	+	0.438585i
$803$	11752.7	+	9861.71i	0.516494	+	0.433390i
$804$		0			0
$805$	−756.904	−	4292.62i	−0.0331396	−	0.187944i
$806$	−2718.82	+	2281.36i	−0.118817	+	0.0996992i
$807$		0			0
$808$	−1427.85	+	519.696i	−0.0621680	+	0.0226273i
$809$	23422.3			1.01790			0.508952	−	0.860795i	$-0.330033\pi$
$809$	23422.3			1.01790			0.508952	+	0.860795i	$0.330033\pi$
$810$		0			0
$811$	10950.1			0.474119			0.237060	−	0.971495i	$-0.423816\pi$
$811$	10950.1			0.474119			0.237060	+	0.971495i	$0.423816\pi$
$812$	−914.930	+	333.007i	−0.0395415	+	0.0143919i
$813$		0			0
$814$	18668.9	−	15665.1i	0.803862	−	0.674521i
$815$	−126.179	−	715.599i	−0.00542316	−	0.0307563i
$816$		0			0
$817$	19948.1	+	16738.4i	0.854216	+	0.716773i
$818$	8448.18	−	14632.7i	0.361105	−	0.625452i
$819$		0			0
$820$	6165.52	+	10679.0i	0.262572	+	0.454789i
$821$	1812.48	−	10279.1i	0.0770477	−	0.436959i	−0.921743	−	0.387801i	$-0.873235\pi$
$821$	1812.48	−	10279.1i	0.0770477	−	0.436959i	0.998791	−	0.0491585i	$-0.0156540\pi$
$822$		0			0
$823$	−10203.4	−	3713.73i	−0.432160	−	0.157293i	0.116775	−	0.993158i	$-0.462744\pi$
$823$	−10203.4	−	3713.73i	−0.432160	−	0.157293i	−0.548935	+	0.835865i	$0.684967\pi$
$824$	4421.65	+	1609.35i	0.186936	+	0.0680393i
$825$		0			0
$826$	1093.44	−	6201.18i	0.0460599	−	0.261219i
$827$	18559.5	+	32146.0i	0.780383	+	1.35166i	0.931719	+	0.363181i	$0.118309\pi$
$827$	18559.5	+	32146.0i	0.780383	+	1.35166i	−0.151336	+	0.988482i	$0.548357\pi$
$828$		0			0
$829$	−8581.65	+	14863.8i	−0.359533	+	0.622729i	−0.987883	−	0.155201i	$-0.950397\pi$
$829$	−8581.65	+	14863.8i	−0.359533	+	0.622729i	0.628350	+	0.777931i	$0.283731\pi$
$830$	−12800.2	−	10740.6i	−0.535301	−	0.449171i
$831$		0			0
$832$	85.8504	+	486.882i	0.00357732	+	0.0202880i
$833$	−8801.48	+	7385.32i	−0.366090	+	0.307186i
$834$		0			0
$835$	−8404.01	+	3058.81i	−0.348303	+	0.126772i
$836$	−14600.8			−0.604041
$837$		0			0
$838$	−18545.8			−0.764502
$839$	34585.7	−	12588.2i	1.42316	−	0.517987i	0.488196	−	0.872734i	$-0.337655\pi$
$839$	34585.7	−	12588.2i	1.42316	−	0.517987i	0.934962	+	0.354747i	$0.115433\pi$
$840$		0			0
$841$	−15517.9	+	13021.0i	−0.636265	+	0.533890i
$842$	4631.90	+	26268.8i	0.189579	+	1.07516i
$843$		0			0
$844$	14912.8	+	12513.4i	0.608200	+	0.510341i
$845$	−8095.33	+	14021.5i	−0.329571	+	0.570834i
$846$		0			0
$847$	2267.94	+	3928.19i	0.0920040	+	0.159356i
$848$	195.803	−	1110.46i	0.00792915	−	0.0449684i
$849$		0			0
$850$	−4442.45	−	1616.92i	−0.179265	−	0.0652470i
$851$	−34599.5	−	12593.2i	−1.39372	−	0.507272i
$852$		0			0
$853$	−3956.56	+	22438.8i	−0.158816	+	0.900691i	0.796397	+	0.604774i	$0.206736\pi$
$853$	−3956.56	+	22438.8i	−0.158816	+	0.900691i	−0.955214	+	0.295917i	$0.904375\pi$
$854$	−2673.14	−	4630.02i	−0.107111	−	0.185522i
$855$		0			0
$856$	−1855.38	+	3213.61i	−0.0740835	+	0.128316i
$857$	−31842.5	−	26719.0i	−1.26922	−	1.06500i	−0.994636	−	0.103434i	$-0.967017\pi$
$857$	−31842.5	−	26719.0i	−1.26922	−	1.06500i	−0.274579	−	0.961564i	$-0.588539\pi$
$858$		0			0
$859$	−547.358	−	3104.22i	−0.0217411	−	0.123300i	0.972006	−	0.234958i	$-0.0754951\pi$
$859$	−547.358	−	3104.22i	−0.0217411	−	0.123300i	−0.993747	+	0.111658i	$0.964384\pi$
$860$	8327.18	−	6987.34i	0.330180	−	0.277054i
$861$		0			0
$862$	107.704	−	39.2010i	0.00425569	−	0.00154895i
$863$	10366.1			0.408882			0.204441	−	0.978879i	$-0.434462\pi$
$863$	10366.1			0.408882			0.204441	+	0.978879i	$0.434462\pi$
$864$		0			0
$865$	−8255.61			−0.324508
$866$	13875.0	−	5050.07i	0.544446	−	0.198162i
$867$		0			0
$868$	−2665.55	+	2236.66i	−0.104233	+	0.0874623i
$869$	−6947.53	−	39401.4i	−0.271207	−	1.53809i
$870$		0			0
$871$	2344.81	+	1967.53i	0.0912180	+	0.0765410i
$872$	−6371.76	+	11036.2i	−0.247448	+	0.428593i
$873$		0			0
$874$	11029.7	+	19104.1i	0.426872	+	0.739364i
$875$	−959.457	+	5441.35i	−0.0370692	+	0.210230i
$876$		0			0
$877$	−936.400	−	340.822i	−0.0360547	−	0.0131228i	0.323930	−	0.946081i	$-0.394996\pi$
$877$	−936.400	−	340.822i	−0.0360547	−	0.0131228i	−0.359985	+	0.932958i	$0.617218\pi$
$878$	663.737	+	241.581i	0.0255126	+	0.00928582i
$879$		0			0
$880$	−1058.38	+	6002.39i	−0.0405433	+	0.229933i
$881$	−13730.2	−	23781.4i	−0.525066	−	0.909440i	−0.999574	−	0.0291893i	$-0.990707\pi$
$881$	−13730.2	−	23781.4i	−0.525066	−	0.909440i	0.474508	−	0.880251i	$-0.342626\pi$
$882$		0			0
$883$	−17615.1	+	30510.3i	−0.671344	+	1.16280i	0.306180	+	0.951974i	$0.400949\pi$
$883$	−17615.1	+	30510.3i	−0.671344	+	1.16280i	−0.977523	+	0.210827i	$0.932384\pi$
$884$	827.486	+	694.343i	0.0314835	+	0.0264178i
$885$		0			0
$886$	2085.61	+	11828.1i	0.0790829	+	0.448501i
$887$	−15772.9	+	13235.1i	−0.597073	+	0.501004i	−0.890503	−	0.454977i	$-0.849648\pi$
$887$	−15772.9	+	13235.1i	−0.597073	+	0.501004i	0.293430	+	0.955980i	$0.405203\pi$
$888$		0			0
$889$	−9843.52	+	3582.75i	−0.371362	+	0.135165i
$890$	−3306.56			−0.124535
$891$		0			0
$892$	7377.67			0.276931
$893$	34364.6	−	12507.7i	1.28776	−	0.468706i
$894$		0			0
$895$	25139.6	−	21094.6i	0.938910	−	0.787839i
$896$	84.1683	+	477.342i	0.00313824	+	0.0177979i
$897$		0			0
$898$	−25886.8	−	21721.6i	−0.961976	−	0.807194i
$899$	7383.25	−	12788.2i	0.273910	−	0.474426i
$900$		0			0
$901$	−1231.84	−	2133.61i	−0.0455478	−	0.0788911i
$902$	−7107.32	+	40307.6i	−0.262359	+	1.48791i
$903$		0			0
$904$	−1776.71	−	646.670i	−0.0653679	−	0.0237920i
$905$	−31425.6	−	11438.0i	−1.15428	−	0.420123i
$906$		0			0
$907$	−4828.36	+	27383.0i	−0.176762	+	1.00247i	0.759329	+	0.650707i	$0.225528\pi$
$907$	−4828.36	+	27383.0i	−0.176762	+	1.00247i	−0.936091	+	0.351759i	$0.885584\pi$
$908$	1125.72	+	1949.80i	0.0411435	+	0.0712626i
$909$		0			0
$910$	221.592	−	383.809i	0.00807221	−	0.0139815i
$911$	15716.9	+	13188.1i	0.571597	+	0.479627i	0.882175	−	0.470921i	$-0.156078\pi$
$911$	15716.9	+	13188.1i	0.571597	+	0.479627i	−0.310579	+	0.950548i	$0.600523\pi$
$912$		0			0
$913$	−9630.92	−	54619.6i	−0.349109	−	1.97990i
$914$	−23456.7	+	19682.5i	−0.848881	+	0.712296i
$915$		0			0
$916$	1288.67	−	469.039i	0.0464836	−	0.0169187i
$917$	−2612.91			−0.0940959
$918$		0			0
$919$	−33795.3			−1.21306			−0.606531	−	0.795060i	$-0.707440\pi$
$919$	−33795.3			−1.21306			−0.606531	+	0.795060i	$0.707440\pi$
$920$	8653.23	−	3149.52i	0.310096	−	0.112866i
$921$		0			0
$922$	21215.8	−	17802.2i	0.757815	−	0.635882i
$923$	−211.095	−	1197.18i	−0.00752793	−	0.0426930i
$924$		0			0
$925$	12551.1	+	10531.6i	0.446138	+	0.374354i
$926$	−795.970	+	1378.66i	−0.0282475	+	0.0489261i
$927$		0			0
$928$	−1028.47	−	1781.37i	−0.0363807	−	0.0630133i
$929$	8515.16	−	48291.9i	0.300725	−	1.70550i	−0.342251	−	0.939609i	$-0.611189\pi$
$929$	8515.16	−	48291.9i	0.300725	−	1.70550i	0.642976	−	0.765886i	$-0.277700\pi$
$930$		0			0
$931$	−22417.6	−	8159.35i	−0.789160	−	0.287231i
$932$	14461.0	+	5263.36i	0.508245	+	0.184986i
$933$		0			0
$934$	4019.32	−	22794.7i	0.140810	−	0.798571i
$935$	6658.52	+	11532.9i	0.232895	+	0.403386i
$936$		0			0
$937$	20548.4	−	35591.0i	0.716423	−	1.24088i	−0.245985	−	0.969274i	$-0.579111\pi$
$937$	20548.4	−	35591.0i	0.716423	−	1.24088i	0.962408	−	0.271608i	$-0.0875553\pi$
$938$	2298.87	+	1928.98i	0.0800221	+	0.0671465i
$939$		0			0
$940$	−2650.90	−	15034.0i	−0.0919817	−	0.521654i
$941$	−13382.4	+	11229.2i	−0.463606	+	0.389012i	−0.844456	−	0.535625i	$-0.820076\pi$
$941$	−13382.4	+	11229.2i	−0.463606	+	0.389012i	0.380849	+	0.924637i	$0.375632\pi$
$942$		0			0
$943$	58108.6	−	21149.8i	2.00666	−	0.730363i
$944$	13302.8			0.458655
$945$		0			0
$946$	36081.1			1.24006
$947$	−35549.5	+	12939.0i	−1.21986	+	0.443992i	−0.870112	−	0.492853i	$-0.835954\pi$
$947$	−35549.5	+	12939.0i	−1.21986	+	0.443992i	−0.349745	+	0.936845i	$0.613732\pi$
$948$		0			0
$949$	1805.39	−	1514.90i	0.0617550	−	0.0518186i
$950$	−1704.55	−	9666.97i	−0.0582135	−	0.330145i
$951$		0			0
$952$	811.273	+	680.739i	0.0276192	+	0.0231753i
$953$	21074.2	−	36501.6i	0.716328	−	1.24072i	−0.246117	−	0.969240i	$-0.579155\pi$
$953$	21074.2	−	36501.6i	0.716328	−	1.24072i	0.962445	−	0.271477i	$-0.0875120\pi$
$954$		0			0
$955$	−8065.87	−	13970.5i	−0.273304	−	0.473377i
$956$	−1746.93	+	9907.33i	−0.0591002	+	0.335174i
$957$		0			0
$958$	−2458.24	−	894.725i	−0.0829040	−	0.0301746i
$959$	−2067.85	−	752.636i	−0.0696292	−	0.0253429i
$960$		0			0
$961$	3990.72	−	22632.5i	0.133957	−	0.759709i
$962$	−1871.83	−	3242.11i	−0.0627342	−	0.108659i
$963$		0			0
$964$	−8381.40	+	14517.0i	−0.280028	+	0.485022i
$965$	23825.6	+	19992.1i	0.794791	+	0.666909i
$966$		0			0
$967$	−6778.95	−	38445.3i	−0.225436	−	1.27851i	−0.861850	−	0.507162i	$-0.830694\pi$
$967$	−6778.95	−	38445.3i	−0.225436	−	1.27851i	0.636415	−	0.771347i	$-0.280417\pi$
$968$	−7340.70	+	6159.58i	−0.243739	+	0.204521i
$969$		0			0
$970$	9318.44	−	3391.64i	0.308451	−	0.112267i
$971$	−4597.07			−0.151933			−0.0759666	−	0.997110i	$-0.524204\pi$
$971$	−4597.07			−0.151933			−0.0759666	+	0.997110i	$0.524204\pi$
$972$		0			0
$973$	−1460.61			−0.0481245
$974$	−10141.5	+	3691.20i	−0.333629	+	0.121431i
$975$		0			0
$976$	8652.22	−	7260.07i	0.283761	−	0.238104i
$977$	1437.55	+	8152.77i	0.0470741	+	0.266971i	0.999256	−	0.0385604i	$-0.0122772\pi$
$977$	1437.55	+	8152.77i	0.0470741	+	0.266971i	−0.952182	+	0.305531i	$0.901166\pi$
$978$		0			0
$979$	−8407.49	−	7054.72i	−0.274468	−	0.230306i
$980$	−4979.33	+	8624.45i	−0.162305	+	0.281120i
$981$		0			0
$982$	−11515.9	−	19946.1i	−0.374223	−	0.648173i
$983$	4467.93	−	25338.9i	0.144969	−	0.822161i	−0.822423	−	0.568877i	$-0.807378\pi$
$983$	4467.93	−	25338.9i	0.144969	−	0.822161i	0.967392	−	0.253284i	$-0.0815108\pi$
$984$		0			0
$985$	6210.11	+	2260.30i	0.200884	+	0.0731157i
$986$	−4223.22	−	1537.13i	−0.136404	−	0.0496471i
$987$		0			0
$988$	−389.474	+	2208.82i	−0.0125413	+	0.0711254i
$989$	−27256.4	−	47209.6i	−0.876344	−	1.51787i
$990$		0			0
$991$	21735.8	−	37647.5i	0.696730	−	1.20677i	−0.272864	−	0.962053i	$-0.587971\pi$
$991$	21735.8	−	37647.5i	0.696730	−	1.20677i	0.969594	−	0.244720i	$-0.0786959\pi$
$992$	−5631.30	−	4725.22i	−0.180236	−	0.151236i
$993$		0			0
$994$	−206.959	−	1173.72i	−0.00660396	−	0.0374529i
$995$	26507.9	−	22242.8i	0.844580	−	0.708687i
$996$		0			0
$997$	−54000.3	+	19654.5i	−1.71535	+	0.624337i	−0.997421	−	0.0717779i	$-0.977133\pi$
$997$	−54000.3	+	19654.5i	−1.71535	+	0.624337i	−0.717931	+	0.696115i	$0.754910\pi$
$998$	−24544.6			−0.778504
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.a.19.1		24
3.2	odd	2		54.4.e.a.7.3	✓	24
27.2	odd	18		1458.4.a.h.1.11		12
27.4	even	9	inner	162.4.e.a.145.1		24
27.23	odd	18		54.4.e.a.31.3	yes	24
27.25	even	9		1458.4.a.e.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.a.7.3	✓	24	3.2	odd	2
54.4.e.a.31.3	yes	24	27.23	odd	18
162.4.e.a.19.1		24	1.1	even	1	trivial
162.4.e.a.145.1		24	27.4	even	9	inner
1458.4.a.e.1.2		12	27.25	even	9
1458.4.a.h.1.11		12	27.2	odd	18

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	162.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.87939 - 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(-1.31542 - 7.46011i) q^{5} +(-2.90083 - 2.43409i) q^{7} +(4.00000 - 6.92820i) q^{8} +O(q^{10})\)	\(q+(1.87939 - 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(-1.31542 - 7.46011i) q^{5} +(-2.90083 - 2.43409i) q^{7} +(4.00000 - 6.92820i) q^{8} +(-7.57519 - 13.1206i) q^{10} +(8.73232 - 49.5234i) q^{11} +(-7.25902 - 2.64207i) q^{13} +(-7.11679 - 2.59030i) q^{14} +(2.77837 - 15.7569i) q^{16} +(-17.4793 - 30.2751i) q^{17} +(36.2933 - 62.8618i) q^{19} +(-23.2117 - 19.4770i) q^{20} +(-17.4646 - 99.0469i) q^{22} +(-116.403 + 97.6734i) q^{23} +(63.5387 - 23.1262i) q^{25} -15.4498 q^{26} -15.1471 q^{28} +(60.4031 - 21.9849i) q^{29} +(175.978 - 147.663i) q^{31} +(-5.55674 - 31.5138i) q^{32} +(-53.5597 - 44.9420i) q^{34} +(-14.3427 + 24.8423i) q^{35} +(121.156 + 209.848i) q^{37} +(25.2091 - 142.968i) q^{38} +(-56.9468 - 20.7269i) q^{40} +(-382.412 - 139.187i) q^{41} +(-62.2961 + 353.299i) q^{43} +(-100.575 - 174.201i) q^{44} +(-151.953 + 263.190i) q^{46} +(385.943 + 323.845i) q^{47} +(-57.0713 - 323.667i) q^{49} +(103.594 - 86.9261i) q^{50} +(-29.0361 + 10.5683i) q^{52} +70.4742 q^{53} -380.937 q^{55} +(-28.4672 + 10.3612i) q^{56} +(98.4821 - 82.6363i) q^{58} +(144.376 + 818.796i) q^{59} +(540.763 + 453.754i) q^{61} +(229.723 - 397.892i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(-10.1615 + 57.6285i) q^{65} +(-372.347 - 135.523i) q^{67} +(-131.401 - 47.8262i) q^{68} +(-9.96236 + 56.4994i) q^{70} +(78.6838 + 136.284i) q^{71} +(-152.544 + 264.214i) q^{73} +(371.244 + 311.510i) q^{74} +(-50.4181 - 285.935i) q^{76} +(-145.875 + 122.404i) q^{77} +(747.630 - 272.115i) q^{79} -121.203 q^{80} -813.909 q^{82} +(1036.39 - 377.216i) q^{83} +(-202.863 + 170.222i) q^{85} +(124.592 + 706.597i) q^{86} +(-308.179 - 258.593i) q^{88} +(109.125 - 189.010i) q^{89} +(14.6262 + 25.3333i) q^{91} +(-105.545 + 598.577i) q^{92} +(946.858 + 344.628i) q^{94} +(-516.697 - 188.062i) q^{95} +(-113.659 + 644.593i) q^{97} +(-328.660 - 569.257i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8}+O(q^{10}) \) 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8	\( 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8} + 30 q^{10} + 12 q^{11} + 60 q^{13} + 66 q^{14} - 102 q^{17} + 171 q^{19} - 96 q^{20} - 24 q^{22} + 708 q^{23} + 864 q^{25} + 468 q^{26} - 336 q^{28} + 381 q^{29} + 909 q^{31} - 48 q^{34} - 624 q^{35} + 555 q^{37} - 66 q^{38} - 96 q^{40} - 618 q^{41} - 1161 q^{43} - 132 q^{44} + 348 q^{46} + 378 q^{47} + 579 q^{49} - 36 q^{50} + 240 q^{52} + 1794 q^{53} - 3906 q^{55} + 264 q^{56} + 444 q^{58} - 1038 q^{59} + 324 q^{61} - 744 q^{62} - 768 q^{64} - 5718 q^{65} - 576 q^{67} - 1056 q^{68} - 1038 q^{70} - 120 q^{71} + 3036 q^{73} + 1110 q^{74} + 132 q^{76} + 3804 q^{77} - 2991 q^{79} + 480 q^{80} - 3408 q^{82} - 513 q^{83} - 2925 q^{85} + 2322 q^{86} + 480 q^{88} - 1065 q^{89} + 2859 q^{91} - 1884 q^{92} - 828 q^{94} - 6357 q^{95} - 2055 q^{97} - 1356 q^{98}+O(q^{100}) \) 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8 + 30 * q^10 + 12 * q^11 + 60 * q^13 + 66 * q^14 - 102 * q^17 + 171 * q^19 - 96 * q^20 - 24 * q^22 + 708 * q^23 + 864 * q^25 + 468 * q^26 - 336 * q^28 + 381 * q^29 + 909 * q^31 - 48 * q^34 - 624 * q^35 + 555 * q^37 - 66 * q^38 - 96 * q^40 - 618 * q^41 - 1161 * q^43 - 132 * q^44 + 348 * q^46 + 378 * q^47 + 579 * q^49 - 36 * q^50 + 240 * q^52 + 1794 * q^53 - 3906 * q^55 + 264 * q^56 + 444 * q^58 - 1038 * q^59 + 324 * q^61 - 744 * q^62 - 768 * q^64 - 5718 * q^65 - 576 * q^67 - 1056 * q^68 - 1038 * q^70 - 120 * q^71 + 3036 * q^73 + 1110 * q^74 + 132 * q^76 + 3804 * q^77 - 2991 * q^79 + 480 * q^80 - 3408 * q^82 - 513 * q^83 - 2925 * q^85 + 2322 * q^86 + 480 * q^88 - 1065 * q^89 + 2859 * q^91 - 1884 * q^92 - 828 * q^94 - 6357 * q^95 - 2055 * q^97 - 1356 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more