LMFDB - Embedded newform 243.4.e.b.136.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,4,Mod(28,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("243.28");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	243.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:	$14.3374641314$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			136.7
Character	$\chi$	$=$	243.136
Dual form			243.4.e.b.109.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.61428 + 2.19364i) q^{2} +(0.633205 + 3.59108i) q^{4} +(-10.3200 - 3.75618i) q^{5} +(-0.765086 + 4.33902i) q^{7} +(7.42861 - 12.8667i) q^{8} +O(q^{10})$	\(q+(2.61428 + 2.19364i) q^{2} +(0.633205 + 3.59108i) q^{4} +(-10.3200 - 3.75618i) q^{5} +(-0.765086 + 4.33902i) q^{7} +(7.42861 - 12.8667i) q^{8} +(-18.7397 - 32.4581i) q^{10} +(54.1997 - 19.7271i) q^{11} +(30.0290 - 25.1973i) q^{13} +(-11.5184 + 9.66507i) q^{14} +(75.0580 - 27.3189i) q^{16} +(44.7356 + 77.4844i) q^{17} +(29.6770 - 51.4022i) q^{19} +(6.95407 - 39.4385i) q^{20} +(184.967 + 67.3225i) q^{22} +(3.97027 + 22.5165i) q^{23} +(-3.36157 - 2.82069i) q^{25} +133.778 q^{26} -16.0662 q^{28} +(45.1257 + 37.8649i) q^{29} +(-57.9966 - 328.915i) q^{31} +(144.460 + 52.5792i) q^{32} +(-53.0214 + 300.699i) q^{34} +(24.1938 - 41.9050i) q^{35} +(-47.4944 - 82.2627i) q^{37} +(190.342 - 69.2787i) q^{38} +(-124.993 + 104.882i) q^{40} +(277.092 - 232.508i) q^{41} +(-443.174 + 161.302i) q^{43} +(105.161 + 182.144i) q^{44} +(-39.0137 + 67.5738i) q^{46} +(-41.1310 + 233.266i) q^{47} +(304.073 + 110.673i) q^{49} +(-2.60049 - 14.7481i) q^{50} +(109.500 + 91.8815i) q^{52} -391.866 q^{53} -633.441 q^{55} +(50.1455 + 42.0770i) q^{56} +(34.9090 + 197.979i) q^{58} +(526.804 + 191.741i) q^{59} +(29.3061 - 166.203i) q^{61} +(569.902 - 987.099i) q^{62} +(-57.1812 - 99.0407i) q^{64} +(-404.545 + 147.242i) q^{65} +(-416.993 + 349.898i) q^{67} +(-249.926 + 209.713i) q^{68} +(155.174 - 56.4786i) q^{70} +(97.0579 + 168.109i) q^{71} +(-80.6653 + 139.716i) q^{73} +(56.2911 - 319.243i) q^{74} +(203.381 + 74.0247i) q^{76} +(44.1287 + 250.266i) q^{77} +(278.476 + 233.669i) q^{79} -877.215 q^{80} +1234.43 q^{82} +(432.830 + 363.187i) q^{83} +(-170.627 - 967.676i) q^{85} +(-1512.42 - 550.475i) q^{86} +(148.805 - 843.918i) q^{88} +(-187.611 + 324.952i) q^{89} +(86.3568 + 149.574i) q^{91} +(-78.3448 + 28.5152i) q^{92} +(-619.228 + 519.594i) q^{94} +(-499.344 + 418.999i) q^{95} +(548.136 - 199.505i) q^{97} +(552.153 + 956.357i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 3 q^{2} + 3 q^{4} + 21 q^{5} + 3 q^{7} + 75 q^{8}+O(q^{10}) $ 48 * q - 3 * q^2 + 3 * q^4 + 21 * q^5 + 3 * q^7 + 75 * q^8	$ 48 q - 3 q^{2} + 3 q^{4} + 21 q^{5} + 3 q^{7} + 75 q^{8} - 3 q^{10} + 159 q^{11} + 3 q^{13} + 336 q^{14} - 45 q^{16} + 207 q^{17} - 3 q^{19} - 681 q^{20} + 111 q^{22} - 33 q^{23} + 435 q^{25} - 1914 q^{26} - 12 q^{28} + 51 q^{29} + 111 q^{31} - 1647 q^{32} - 513 q^{34} + 1257 q^{35} - 3 q^{37} + 525 q^{38} - 6 q^{40} - 447 q^{41} + 516 q^{43} + 2211 q^{44} - 3 q^{46} - 2109 q^{47} - 591 q^{49} + 4938 q^{50} - 1350 q^{52} - 2736 q^{53} - 12 q^{55} + 7773 q^{56} - 888 q^{58} - 3048 q^{59} + 57 q^{61} + 2118 q^{62} - 195 q^{64} - 3297 q^{65} + 2082 q^{67} - 3573 q^{68} + 1524 q^{70} + 3105 q^{71} - 219 q^{73} - 9006 q^{74} - 1425 q^{76} + 8985 q^{77} - 1401 q^{79} - 9870 q^{80} - 12 q^{82} + 8511 q^{83} - 1827 q^{85} - 12507 q^{86} - 3693 q^{88} + 5202 q^{89} + 267 q^{91} - 5118 q^{92} - 2211 q^{94} - 5178 q^{95} + 1569 q^{97} + 4392 q^{98}+O(q^{100}) $ 48 * q - 3 * q^2 + 3 * q^4 + 21 * q^5 + 3 * q^7 + 75 * q^8 - 3 * q^10 + 159 * q^11 + 3 * q^13 + 336 * q^14 - 45 * q^16 + 207 * q^17 - 3 * q^19 - 681 * q^20 + 111 * q^22 - 33 * q^23 + 435 * q^25 - 1914 * q^26 - 12 * q^28 + 51 * q^29 + 111 * q^31 - 1647 * q^32 - 513 * q^34 + 1257 * q^35 - 3 * q^37 + 525 * q^38 - 6 * q^40 - 447 * q^41 + 516 * q^43 + 2211 * q^44 - 3 * q^46 - 2109 * q^47 - 591 * q^49 + 4938 * q^50 - 1350 * q^52 - 2736 * q^53 - 12 * q^55 + 7773 * q^56 - 888 * q^58 - 3048 * q^59 + 57 * q^61 + 2118 * q^62 - 195 * q^64 - 3297 * q^65 + 2082 * q^67 - 3573 * q^68 + 1524 * q^70 + 3105 * q^71 - 219 * q^73 - 9006 * q^74 - 1425 * q^76 + 8985 * q^77 - 1401 * q^79 - 9870 * q^80 - 12 * q^82 + 8511 * q^83 - 1827 * q^85 - 12507 * q^86 - 3693 * q^88 + 5202 * q^89 + 267 * q^91 - 5118 * q^92 - 2211 * q^94 - 5178 * q^95 + 1569 * q^97 + 4392 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	2.61428	+	2.19364i	0.924286	+	0.775568i	0.974783	−	0.223156i	$-0.0716360\pi$
$2$	2.61428	+	2.19364i	0.924286	+	0.775568i	−0.0504967	+	0.998724i	$0.516080\pi$
$3$		0			0
$3$		0			0
$4$	0.633205	+	3.59108i	0.0791506	+	0.448886i
$5$	−10.3200	−	3.75618i	−0.923051	−	0.335963i	−0.163599	−	0.986527i	$-0.552310\pi$
$5$	−10.3200	−	3.75618i	−0.923051	−	0.335963i	−0.759452	+	0.650564i	$0.774533\pi$
$6$		0			0
$7$	−0.765086	+	4.33902i	−0.0413108	+	0.234285i	−0.998471	−	0.0552729i	$-0.982397\pi$
$7$	−0.765086	+	4.33902i	−0.0413108	+	0.234285i	0.957161	+	0.289558i	$0.0935082\pi$
$8$	7.42861	−	12.8667i	0.328301	−	0.568635i
$9$		0			0
$10$	−18.7397	−	32.4581i	−0.592601	−	1.02641i
$11$	54.1997	−	19.7271i	1.48562	−	0.540722i	0.533328	−	0.845909i	$-0.320941\pi$
$11$	54.1997	−	19.7271i	1.48562	−	0.540722i	0.952292	+	0.305187i	$0.0987190\pi$
$12$		0			0
$13$	30.0290	−	25.1973i	0.640657	−	0.537575i	−0.263563	−	0.964642i	$-0.584898\pi$
$13$	30.0290	−	25.1973i	0.640657	−	0.537575i	0.904220	+	0.427067i	$0.140453\pi$
$14$	−11.5184	+	9.66507i	−0.219887	+	0.184507i
$15$		0			0
$16$	75.0580	−	27.3189i	1.17278	−	0.426857i
$17$	44.7356	+	77.4844i	0.638235	+	1.10545i	0.985820	+	0.167806i	$0.0536683\pi$
$17$	44.7356	+	77.4844i	0.638235	+	1.10545i	−0.347585	+	0.937648i	$0.612998\pi$
$18$		0			0
$19$	29.6770	−	51.4022i	0.358336	−	0.620656i	−0.629347	−	0.777124i	$-0.716678\pi$
$19$	29.6770	−	51.4022i	0.358336	−	0.620656i	0.987683	+	0.156468i	$0.0500109\pi$
$20$	6.95407	−	39.4385i	0.0777489	−	0.440936i
$21$		0			0
$22$	184.967	+	67.3225i	1.79250	+	0.652418i
$23$	3.97027	+	22.5165i	0.0359939	+	0.204131i	0.997501	−	0.0706474i	$-0.0225065\pi$
$23$	3.97027	+	22.5165i	0.0359939	+	0.204131i	−0.961507	+	0.274779i	$0.911395\pi$
$24$		0			0
$25$	−3.36157	−	2.82069i	−0.0268925	−	0.0225655i
$26$	133.778			1.00908
$27$		0			0
$28$	−16.0662			−0.108437
$29$	45.1257	+	37.8649i	0.288953	+	0.242460i	0.775728	−	0.631067i	$-0.217383\pi$
$29$	45.1257	+	37.8649i	0.288953	+	0.242460i	−0.486776	+	0.873527i	$0.661827\pi$
$30$		0			0
$31$	−57.9966	−	328.915i	−0.336016	−	1.90564i	−0.416962	−	0.908924i	$-0.636905\pi$
$31$	−57.9966	−	328.915i	−0.336016	−	1.90564i	0.0809453	−	0.996719i	$-0.474206\pi$
$32$	144.460	+	52.5792i	0.798037	+	0.290462i
$33$		0			0
$34$	−53.0214	+	300.699i	−0.267444	+	1.51675i
$35$	24.1938	−	41.9050i	0.116843	−	0.202378i
$36$		0			0
$37$	−47.4944	−	82.2627i	−0.211028	−	0.365511i	0.741009	−	0.671495i	$-0.234348\pi$
$37$	−47.4944	−	82.2627i	−0.211028	−	0.365511i	−0.952036	+	0.305985i	$0.901014\pi$
$38$	190.342	−	69.2787i	0.812566	−	0.295750i
$39$		0			0
$40$	−124.993	+	104.882i	−0.494079	+	0.414582i
$41$	277.092	−	232.508i	1.05547	−	0.885649i	0.0618163	−	0.998088i	$-0.480311\pi$
$41$	277.092	−	232.508i	1.05547	−	0.885649i	0.993659	+	0.112439i	$0.0358663\pi$
$42$		0			0
$43$	−443.174	+	161.302i	−1.57171	+	0.572054i	−0.973380	−	0.229198i	$-0.926390\pi$
$43$	−443.174	+	161.302i	−1.57171	+	0.572054i	−0.598326	+	0.801252i	$0.704167\pi$
$44$	105.161	+	182.144i	0.360310	+	0.624075i
$45$		0			0
$46$	−39.0137	+	67.5738i	−0.125049	+	0.216591i
$47$	−41.1310	+	233.266i	−0.127651	+	0.723943i	0.852048	+	0.523464i	$0.175361\pi$
$47$	−41.1310	+	233.266i	−0.127651	+	0.723943i	−0.979698	+	0.200478i	$0.935750\pi$
$48$		0			0
$49$	304.073	+	110.673i	0.886510	+	0.322663i
$50$	−2.60049	−	14.7481i	−0.00735530	−	0.0417140i
$51$		0			0
$52$	109.500	+	91.8815i	0.292018	+	0.245032i
$53$	−391.866			−1.01560			−0.507802	−	0.861474i	$-0.669542\pi$
$53$	−391.866			−1.01560			−0.507802	+	0.861474i	$0.669542\pi$
$54$		0			0
$55$	−633.441			−1.55297
$56$	50.1455	+	42.0770i	0.119660	+	0.100407i
$57$		0			0
$58$	34.9090	+	197.979i	0.0790306	+	0.448205i
$59$	526.804	+	191.741i	1.16244	+	0.423094i	0.849969	−	0.526833i	$-0.176621\pi$
$59$	526.804	+	191.741i	1.16244	+	0.423094i	0.312473	+	0.949927i	$0.398843\pi$
$60$		0			0
$61$	29.3061	−	166.203i	0.0615126	−	0.348855i	−0.938481	−	0.345330i	$-0.887767\pi$
$61$	29.3061	−	166.203i	0.0615126	−	0.348855i	0.999994	−	0.00352488i	$-0.00112200\pi$
$62$	569.902	−	987.099i	1.16738	−	2.02196i
$63$		0			0
$64$	−57.1812	−	99.0407i	−0.111682	−	0.193439i
$65$	−404.545	+	147.242i	−0.771964	+	0.280972i
$66$		0			0
$67$	−416.993	+	349.898i	−0.760354	+	0.638013i	−0.938219	−	0.346042i	$-0.887526\pi$
$67$	−416.993	+	349.898i	−0.760354	+	0.638013i	0.177865	+	0.984055i	$0.443081\pi$
$68$	−249.926	+	209.713i	−0.445706	+	0.373992i
$69$		0			0
$70$	155.174	−	56.4786i	0.264954	−	0.0964355i
$71$	97.0579	+	168.109i	0.162235	+	0.280998i	0.935670	−	0.352877i	$-0.114797\pi$
$71$	97.0579	+	168.109i	0.162235	+	0.280998i	−0.773435	+	0.633875i	$0.781463\pi$
$72$		0			0
$73$	−80.6653	+	139.716i	−0.129331	+	0.224008i	−0.923418	−	0.383797i	$-0.874616\pi$
$73$	−80.6653	+	139.716i	−0.129331	+	0.224008i	0.794087	+	0.607805i	$0.207950\pi$
$74$	56.2911	−	319.243i	0.0884285	−	0.501503i
$75$		0			0
$76$	203.381	+	74.0247i	0.306966	+	0.111726i
$77$	44.1287	+	250.266i	0.0653108	+	0.370396i
$78$		0			0
$79$	278.476	+	233.669i	0.396595	+	0.332783i	0.819176	−	0.573542i	$-0.194431\pi$
$79$	278.476	+	233.669i	0.396595	+	0.332783i	−0.422581	+	0.906325i	$0.638876\pi$
$80$	−877.215			−1.22594
$81$		0			0
$82$	1234.43			1.66244
$83$	432.830	+	363.187i	0.572400	+	0.480301i	0.882441	−	0.470422i	$-0.155898\pi$
$83$	432.830	+	363.187i	0.572400	+	0.480301i	−0.310041	+	0.950723i	$0.600343\pi$
$84$		0			0
$85$	−170.627	−	967.676i	−0.217731	−	1.23481i
$86$	−1512.42	−	550.475i	−1.89637	−	0.690223i
$87$		0			0
$88$	148.805	−	843.918i	0.180258	−	1.02229i
$89$	−187.611	+	324.952i	−0.223446	+	0.387021i	−0.955852	−	0.293848i	$-0.905064\pi$
$89$	−187.611	+	324.952i	−0.223446	+	0.387021i	0.732406	+	0.680868i	$0.238397\pi$
$90$		0			0
$91$	86.3568	+	149.574i	0.0994797	+	0.172304i
$92$	−78.3448	+	28.5152i	−0.0887827	+	0.0323143i
$93$		0			0
$94$	−619.228	+	519.594i	−0.679452	+	0.570128i
$95$	−499.344	+	418.999i	−0.539280	+	0.452509i
$96$		0			0
$97$	548.136	−	199.505i	0.573760	−	0.208832i	−0.0388115	−	0.999247i	$-0.512357\pi$
$97$	548.136	−	199.505i	0.573760	−	0.208832i	0.612572	+	0.790415i	$0.290135\pi$
$98$	552.153	+	956.357i	0.569141	+	0.985782i
$99$		0			0
$100$	8.00078	−	13.8578i	0.00800078	−	0.0138578i
$101$	−8.55984	+	48.5453i	−0.00843303	+	0.0478261i	−0.988734	−	0.149684i	$-0.952174\pi$
$101$	−8.55984	+	48.5453i	−0.00843303	+	0.0478261i	0.980301	+	0.197510i	$0.0632855\pi$
$102$		0			0
$103$	−339.056	−	123.406i	−0.324352	−	0.118054i	0.174712	−	0.984620i	$-0.444100\pi$
$103$	−339.056	−	123.406i	−0.324352	−	0.118054i	−0.499064	+	0.866565i	$0.666323\pi$
$104$	−101.133	−	573.556i	−0.0953552	−	0.540786i
$105$		0			0
$106$	−1024.45	−	859.613i	−0.938708	−	0.787670i
$107$	−1057.66			−0.955583			−0.477792	−	0.878473i	$-0.658563\pi$
$107$	−1057.66			−0.955583			−0.477792	+	0.878473i	$0.658563\pi$
$108$		0			0
$109$	9.04341			0.00794680			0.00397340	−	0.999992i	$-0.498735\pi$
$109$	9.04341			0.00794680			0.00397340	+	0.999992i	$0.498735\pi$
$110$	−1655.99	−	1389.54i	−1.43538	−	1.20443i
$111$		0			0
$112$	61.1113	+	346.579i	0.0515578	+	0.292399i
$113$	−189.066	−	68.8143i	−0.157397	−	0.0572877i	0.262120	−	0.965035i	$-0.415578\pi$
$113$	−189.066	−	68.8143i	−0.157397	−	0.0572877i	−0.419517	+	0.907748i	$0.637801\pi$
$114$		0			0
$115$	43.6029	−	247.284i	0.0353564	−	0.200516i
$116$	−107.402	+	186.026i	−0.0859660	+	0.148898i
$117$		0			0
$118$	956.601	+	1656.88i	0.746290	+	1.29261i
$119$	−370.433	+	134.827i	−0.285357	+	0.103862i
$120$		0			0
$121$	1528.84	−	1282.85i	1.14864	−	0.963826i
$122$	441.204	−	370.214i	0.327416	−	0.274735i
$123$		0			0
$124$	1144.44	−	416.542i	0.828820	−	0.301666i
$125$	710.493	+	1230.61i	0.508387	+	0.880552i
$126$		0			0
$127$	619.475	−	1072.96i	0.432831	−	0.749685i	−0.564285	−	0.825580i	$-0.690848\pi$
$127$	619.475	−	1072.96i	0.432831	−	0.749685i	0.997116	+	0.0758949i	$0.0241813\pi$
$128$	281.333	−	1595.52i	0.194270	−	1.10176i
$129$		0			0
$130$	−1380.59	−	502.494i	−0.931429	−	0.339012i
$131$	−113.960	−	646.297i	−0.0760053	−	0.431048i	−0.998938	−	0.0460851i	$-0.985325\pi$
$131$	−113.960	−	646.297i	−0.0760053	−	0.431048i	0.922932	−	0.384963i	$-0.125786\pi$
$132$		0			0
$133$	200.329	+	168.096i	0.130607	+	0.109592i
$134$	−1857.68			−1.19761
$135$		0			0
$136$	1329.29			0.838133
$137$	37.9244	+	31.8223i	0.0236504	+	0.0198450i	0.654536	−	0.756031i	$-0.272864\pi$
$137$	37.9244	+	31.8223i	0.0236504	+	0.0198450i	−0.630886	+	0.775876i	$0.717308\pi$
$138$		0			0
$139$	347.687	+	1971.83i	0.212161	+	1.20323i	0.885765	+	0.464134i	$0.153634\pi$
$139$	347.687	+	1971.83i	0.212161	+	1.20323i	−0.673604	+	0.739093i	$0.735254\pi$
$140$	165.804	+	60.3477i	0.100093	+	0.0364308i
$141$		0			0
$142$	−115.035	+	652.393i	−0.0679823	+	0.385547i
$143$	1130.49	−	1958.07i	0.661094	−	1.14505i
$144$		0			0
$145$	−323.470	−	560.267i	−0.185260	−	0.320880i
$146$	−517.368	+	188.307i	−0.293272	+	0.106742i
$147$		0			0
$148$	265.339	−	222.645i	0.147370	−	0.123658i
$149$	−2032.19	+	1705.21i	−1.11734	+	0.937559i	−0.998467	−	0.0553509i	$-0.982372\pi$
$149$	−2032.19	+	1705.21i	−1.11734	+	0.937559i	−0.118872	+	0.992910i	$0.537928\pi$
$150$		0			0
$151$	−394.116	+	143.447i	−0.212402	+	0.0773080i	−0.446030	−	0.895018i	$-0.647162\pi$
$151$	−394.116	+	143.447i	−0.212402	+	0.0773080i	0.233628	+	0.972326i	$0.424940\pi$
$152$	−440.919	−	763.693i	−0.235284	−	0.407524i
$153$		0			0
$154$	−433.629	+	751.068i	−0.226901	+	0.393005i
$155$	−636.939	+	3612.26i	−0.330065	+	1.87189i
$156$		0			0
$157$	−2326.88	−	846.913i	−1.18283	−	0.430516i	−0.325632	−	0.945497i	$-0.605577\pi$
$157$	−2326.88	−	846.913i	−1.18283	−	0.430516i	−0.857202	+	0.514980i	$0.827799\pi$
$158$	215.428	+	1221.75i	0.108472	+	0.615173i
$159$		0			0
$160$	−1293.34	−	1085.24i	−0.639044	−	0.536222i
$161$	−100.737			−0.0493118
$162$		0			0
$163$	−2583.99			−1.24168			−0.620840	−	0.783938i	$-0.713208\pi$
$163$	−2583.99			−1.24168			−0.620840	+	0.783938i	$0.713208\pi$
$164$	1010.41	+	847.835i	0.481096	+	0.403688i
$165$		0			0
$166$	334.835	+	1898.94i	0.156556	+	0.887871i
$167$	596.104	+	216.964i	0.276215	+	0.100534i	0.476414	−	0.879221i	$-0.341936\pi$
$167$	596.104	+	216.964i	0.276215	+	0.100534i	−0.200198	+	0.979755i	$0.564159\pi$
$168$		0			0
$169$	−114.670	+	650.324i	−0.0521938	+	0.296006i
$170$	1676.66	−	2904.07i	0.756437	−	1.31019i
$171$		0			0
$172$	−859.869	−	1489.34i	−0.381188	−	0.660238i
$173$	1596.36	−	581.026i	0.701553	−	0.255345i	0.0334794	−	0.999439i	$-0.489341\pi$
$173$	1596.36	−	581.026i	0.701553	−	0.255345i	0.668074	+	0.744095i	$0.267119\pi$
$174$		0			0
$175$	14.8109	−	12.4278i	0.00639771	−	0.00536832i
$176$	3529.20	−	2961.35i	1.51150	−	1.26830i
$177$		0			0
$178$	−1203.29	+	437.963i	−0.506689	+	0.184420i
$179$	324.339	+	561.772i	0.135432	+	0.234574i	0.925762	−	0.378106i	$-0.123425\pi$
$179$	324.339	+	561.772i	0.135432	+	0.234574i	−0.790331	+	0.612681i	$0.790091\pi$
$180$		0			0
$181$	−1836.50	+	3180.92i	−0.754178	+	1.30627i	0.191605	+	0.981472i	$0.438631\pi$
$181$	−1836.50	+	3180.92i	−0.754178	+	1.30627i	−0.945782	+	0.324802i	$0.894702\pi$
$182$	−102.351	+	580.464i	−0.0416857	+	0.236411i
$183$		0			0
$184$	319.208	+	116.182i	0.127893	+	0.0465493i
$185$	181.150	+	1027.35i	0.0719912	+	0.408283i
$186$		0			0
$187$	3953.20	+	3317.13i	1.54592	+	1.29718i
$188$	−863.721			−0.335071
$189$		0			0
$190$	−2224.55			−0.849401
$191$	1323.99	+	1110.96i	0.501575	+	0.420871i	0.858153	−	0.513394i	$-0.171612\pi$
$191$	1323.99	+	1110.96i	0.501575	+	0.420871i	−0.356578	+	0.934266i	$0.616057\pi$
$192$		0			0
$193$	188.684	+	1070.08i	0.0703718	+	0.399099i	0.999565	+	0.0295033i	$0.00939254\pi$
$193$	188.684	+	1070.08i	0.0703718	+	0.399099i	−0.929193	+	0.369595i	$0.879496\pi$
$194$	1870.62	+	680.850i	0.692282	+	0.251970i
$195$		0			0
$196$	−204.897	+	1162.03i	−0.0746710	+	0.423480i
$197$	−1804.76	+	3125.94i	−0.652711	+	1.13053i	0.329751	+	0.944068i	$0.393035\pi$
$197$	−1804.76	+	3125.94i	−0.652711	+	1.13053i	−0.982462	+	0.186461i	$0.940298\pi$
$198$		0			0
$199$	−726.376	−	1258.12i	−0.258751	−	0.448169i	0.707157	−	0.707057i	$-0.249977\pi$
$199$	−726.376	−	1258.12i	−0.258751	−	0.448169i	−0.965908	+	0.258887i	$0.916644\pi$
$200$	−61.2648	+	22.2986i	−0.0216604	+	0.00788374i
$201$		0			0
$202$	−128.869	+	108.134i	−0.0448869	+	0.0376646i
$203$	−198.822	+	166.831i	−0.0687416	+	0.0576810i
$204$		0			0
$205$	−3732.94	+	1358.68i	−1.27180	+	0.462898i
$206$	−615.678	−	1066.39i	−0.208235	−	0.360673i
$207$		0			0
$208$	1565.55	−	2711.62i	0.521882	−	0.903927i
$209$	594.473	−	3371.42i	0.196749	−	1.11582i
$210$		0			0
$211$	3037.97	+	1105.73i	0.991197	+	0.360766i	0.786184	−	0.617993i	$-0.212054\pi$
$211$	3037.97	+	1105.73i	0.991197	+	0.360766i	0.205013	+	0.978759i	$0.434276\pi$
$212$	−248.132	−	1407.23i	−0.0803857	−	0.455890i
$213$		0			0
$214$	−2765.00	−	2320.11i	−0.883232	−	0.741120i
$215$	5179.44			1.64295
$216$		0			0
$217$	1471.54			0.460344
$218$	23.6420	+	19.8380i	0.00734512	+	0.00616329i
$219$		0			0
$220$	−401.098	−	2274.74i	−0.122918	−	0.697104i
$221$	3295.76	+	1199.56i	1.00315	+	0.365118i
$222$		0			0
$223$	342.826	−	1944.26i	0.102948	−	0.583845i	−0.889073	−	0.457766i	$-0.848650\pi$
$223$	342.826	−	1944.26i	0.102948	−	0.583845i	0.992020	−	0.126079i	$-0.0402392\pi$
$224$	−338.666	+	586.587i	−0.101018	+	0.174969i
$225$		0			0
$226$	−343.317	−	594.642i	−0.101049	−	0.175022i
$227$	1481.41	−	539.188i	0.433147	−	0.157653i	−0.116239	−	0.993221i	$-0.537084\pi$
$227$	1481.41	−	539.188i	0.433147	−	0.157653i	0.549386	+	0.835569i	$0.314862\pi$
$228$		0			0
$229$	4956.09	−	4158.65i	1.43016	−	1.20005i	0.484548	−	0.874765i	$-0.338984\pi$
$229$	4956.09	−	4158.65i	1.43016	−	1.20005i	0.945616	−	0.325285i	$-0.105460\pi$
$230$	656.442	−	550.820i	0.188193	−	0.157913i
$231$		0			0
$232$	822.419	−	299.336i	0.232735	−	0.0847085i
$233$	1287.98	+	2230.85i	0.362139	+	0.627244i	0.988313	−	0.152440i	$-0.0487131\pi$
$233$	1287.98	+	2230.85i	0.362139	+	0.627244i	−0.626173	+	0.779684i	$0.715380\pi$
$234$		0			0
$235$	1300.66	−	2252.81i	0.361046	−	0.625350i
$236$	−354.983	+	2013.21i	−0.0979129	+	0.555291i
$237$		0			0
$238$	−1264.17	−	460.122i	−0.344303	−	0.125316i
$239$	26.3109	+	149.216i	0.00712096	+	0.0403850i	0.988161	−	0.153419i	$-0.0490285\pi$
$239$	26.3109	+	149.216i	0.00712096	+	0.0403850i	−0.981040	+	0.193804i	$0.937917\pi$
$240$		0			0
$241$	4391.96	+	3685.29i	1.17390	+	0.985023i	1.00000		0.000260554i	$8.29368e-5\pi$
$241$	4391.96	+	3685.29i	1.17390	+	0.985023i	0.173905	+	0.984762i	$0.444362\pi$
$242$	6810.93			1.80919
$243$		0			0
$244$	615.407			0.161465
$245$	−2722.33	−	2284.31i	−0.709891	−	0.595669i
$246$		0			0
$247$	−404.024	−	2291.34i	−0.104079	−	0.590260i
$248$	−4662.90	−	1697.16i	−1.19393	−	0.434555i
$249$		0			0
$250$	−842.088	+	4775.72i	−0.213033	+	1.20817i
$251$	352.490	−	610.530i	0.0886413	−	0.153531i	−0.818296	−	0.574797i	$-0.805081\pi$
$251$	352.490	−	610.530i	0.0886413	−	0.153531i	0.906937	+	0.421266i	$0.138414\pi$
$252$		0			0
$253$	659.373	+	1142.07i	0.163851	+	0.283799i
$254$	3973.17	−	1446.12i	0.981492	−	0.357234i
$255$		0			0
$256$	3534.62	−	2965.90i	0.862945	−	0.724097i
$257$	−576.896	+	484.074i	−0.140023	+	0.117493i	−0.710109	−	0.704092i	$-0.751354\pi$
$257$	−576.896	+	484.074i	−0.140023	+	0.117493i	0.570086	+	0.821585i	$0.306910\pi$
$258$		0			0
$259$	393.276	−	143.141i	0.0943514	−	0.0343411i
$260$	−784.920	−	1359.52i	−0.187226	−	0.324285i
$261$		0			0
$262$	1119.82	−	1939.58i	0.264056	−	0.457359i
$263$	1078.57	−	6116.85i	0.252879	−	1.43415i	−0.548580	−	0.836098i	$-0.684831\pi$
$263$	1078.57	−	6116.85i	0.252879	−	1.43415i	0.801459	−	0.598050i	$-0.204058\pi$
$264$		0			0
$265$	4044.07	+	1471.92i	0.937454	+	0.341205i
$266$	154.974	+	878.900i	0.0357220	+	0.202590i
$267$		0			0
$268$	−1520.56	−	1275.90i	−0.346577	−	0.290813i
$269$	−3724.81			−0.844259			−0.422130	−	0.906535i	$-0.638717\pi$
$269$	−3724.81			−0.844259			−0.422130	+	0.906535i	$0.638717\pi$
$270$		0			0
$271$	5353.13			1.19992			0.599962	−	0.800028i	$-0.295182\pi$
$271$	5353.13			1.19992			0.599962	+	0.800028i	$0.295182\pi$
$272$	5474.55	+	4593.70i	1.22038	+	1.02402i
$273$		0			0
$274$	29.3381	+	166.385i	0.00646854	+	0.0366849i
$275$	−237.840	−	86.5667i	−0.0521538	−	0.0189824i
$276$		0			0
$277$	520.822	−	2953.73i	0.112972	−	0.640694i	−0.874763	−	0.484551i	$-0.838983\pi$
$277$	520.822	−	2953.73i	0.112972	−	0.640694i	0.987735	−	0.156143i	$-0.0499060\pi$
$278$	−3416.53	+	5917.61i	−0.737086	+	1.27667i
$279$		0			0
$280$	−359.453	−	622.591i	−0.0767194	−	0.132882i
$281$	−6936.81	+	2524.79i	−1.47265	+	0.536002i	−0.948819	−	0.315819i	$-0.897721\pi$
$281$	−6936.81	+	2524.79i	−1.47265	+	0.536002i	−0.523833	+	0.851821i	$0.675499\pi$
$282$		0			0
$283$	−6736.75	+	5652.80i	−1.41505	+	1.18736i	−0.461114	+	0.887341i	$0.652550\pi$
$283$	−6736.75	+	5652.80i	−1.41505	+	1.18736i	−0.953932	+	0.300024i	$0.903005\pi$
$284$	−542.237	+	454.991i	−0.113295	+	0.0950659i
$285$		0			0
$286$	7250.71	−	2639.04i	1.49910	−	0.545629i
$287$	796.856	+	1380.19i	0.163892	+	0.283869i
$288$		0			0
$289$	−1546.06	+	2677.85i	−0.314687	+	0.545053i
$290$	383.382	−	2174.27i	0.0776310	−	0.440267i
$291$		0			0
$292$	−552.811	−	201.207i	−0.110790	−	0.0403244i
$293$	−171.495	−	972.594i	−0.0341939	−	0.193923i	0.962926	−	0.269766i	$-0.0869464\pi$
$293$	−171.495	−	972.594i	−0.0341939	−	0.193923i	−0.997120	+	0.0758428i	$0.975835\pi$
$294$		0			0
$295$	−4716.42	−	3957.54i	−0.930849	−	0.781075i
$296$	−1411.27			−0.277123
$297$		0			0
$298$	−9053.32			−1.75988
$299$	686.579	+	576.108i	0.132796	+	0.111429i
$300$		0			0
$301$	−360.826	−	2046.35i	−0.0690953	−	0.391859i
$302$	−1345.00	−	489.539i	−0.256278	−	0.0932775i
$303$		0			0
$304$	823.250	−	4668.88i	0.155318	−	0.880852i
$305$	−926.730	+	1605.14i	−0.173982	+	0.301345i
$306$		0			0
$307$	833.402	+	1443.49i	0.154934	+	0.268354i	0.933035	−	0.359786i	$-0.117150\pi$
$307$	833.402	+	1443.49i	0.154934	+	0.268354i	−0.778101	+	0.628139i	$0.783817\pi$
$308$	−870.785	+	316.940i	−0.161096	+	0.0586342i
$309$		0			0
$310$	−9589.12	+	8046.23i	−1.75686	+	1.47418i
$311$	−3266.44	+	2740.87i	−0.595572	+	0.499744i	−0.890019	−	0.455924i	$-0.849309\pi$
$311$	−3266.44	+	2740.87i	−0.595572	+	0.499744i	0.294447	+	0.955668i	$0.404865\pi$
$312$		0			0
$313$	−1440.39	+	524.260i	−0.260114	+	0.0946739i	−0.468786	−	0.883312i	$-0.655308\pi$
$313$	−1440.39	+	524.260i	−0.260114	+	0.0946739i	0.208671	+	0.977986i	$0.433086\pi$
$314$	−4225.27	−	7318.39i	−0.759382	−	1.31529i
$315$		0			0
$316$	−662.794	+	1147.99i	−0.117991	+	0.204366i
$317$	−1413.56	+	8016.68i	−0.250452	+	1.42038i	0.557030	+	0.830492i	$0.311941\pi$
$317$	−1413.56	+	8016.68i	−0.250452	+	1.42038i	−0.807482	+	0.589892i	$0.799170\pi$
$318$		0			0
$319$	3192.76	+	1162.07i	0.560377	+	0.203961i
$320$	218.096	+	1236.89i	0.0380999	+	0.216075i
$321$		0			0
$322$	−263.355	−	220.981i	−0.0455782	−	0.0382447i
$323$	5310.49			0.914809
$324$		0			0
$325$	−172.018			−0.0293596
$326$	−6755.26	−	5668.34i	−1.14767	−	0.963007i
$327$		0			0
$328$	−933.206	−	5292.48i	−0.157097	−	0.890939i
$329$	−980.675	−	356.937i	−0.164336	−	0.0598132i
$330$		0			0
$331$	−472.291	+	2678.49i	−0.0784273	+	0.444783i	0.920155	+	0.391554i	$0.128062\pi$
$331$	−472.291	+	2678.49i	−0.0784273	+	0.444783i	−0.998582	+	0.0532291i	$0.983049\pi$
$332$	−1030.17	+	1784.30i	−0.170294	+	0.294958i
$333$		0			0
$334$	1082.44	+	1874.84i	0.177331	+	0.307146i
$335$	5617.65	−	2044.66i	0.916195	−	0.333468i
$336$		0			0
$337$	−5243.78	+	4400.06i	−0.847617	+	0.711235i	−0.959264	−	0.282513i	$-0.908832\pi$
$337$	−5243.78	+	4400.06i	−0.847617	+	0.711235i	0.111646	+	0.993748i	$0.464388\pi$
$338$	−1726.35	+	1448.58i	−0.277814	+	0.233114i
$339$		0			0
$340$	3366.96	−	1225.48i	0.537057	−	0.195473i
$341$	−9631.94	−	16683.0i	−1.52961	−	2.64937i
$342$		0			0
$343$	−1468.48	+	2543.48i	−0.231167	+	0.400393i
$344$	−1216.74	+	6900.45i	−0.190703	+	1.08153i
$345$		0			0
$346$	5447.88	+	1982.86i	0.846473	+	0.308091i
$347$	−1684.95	−	9555.81i	−0.260671	−	1.47834i	−0.781086	−	0.624423i	$-0.785334\pi$
$347$	−1684.95	−	9555.81i	−0.260671	−	1.47834i	0.520416	−	0.853913i	$-0.325777\pi$
$348$		0			0
$349$	−210.474	−	176.609i	−0.0322820	−	0.0270878i	0.626504	−	0.779418i	$-0.284485\pi$
$349$	−210.474	−	176.609i	−0.0322820	−	0.0270878i	−0.658786	+	0.752330i	$0.728930\pi$
$350$	65.9820			0.0100768
$351$		0			0
$352$	8866.93			1.34264
$353$	−1328.64	−	1114.86i	−0.200330	−	0.168097i	0.537104	−	0.843516i	$-0.319518\pi$
$353$	−1328.64	−	1114.86i	−0.200330	−	0.168097i	−0.737434	+	0.675419i	$0.763963\pi$
$354$		0			0
$355$	−370.191	−	2099.46i	−0.0553456	−	0.313881i
$356$	−1285.73	−	467.966i	−0.191414	−	0.0696690i
$357$		0			0
$358$	−384.412	+	2180.11i	−0.0567509	+	0.321850i
$359$	−2140.65	+	3707.72i	−0.314706	+	0.545087i	−0.979375	−	0.202051i	$-0.935239\pi$
$359$	−2140.65	+	3707.72i	−0.314706	+	0.545087i	0.664669	+	0.747138i	$0.268573\pi$
$360$		0			0
$361$	1668.05	+	2889.14i	0.243191	+	0.421219i
$362$	−11778.9	+	4287.17i	−1.71018	+	0.622455i
$363$		0			0
$364$	−482.453	+	404.826i	−0.0694708	+	0.0582930i
$365$	1357.27	−	1138.88i	0.194637	−	0.163320i
$366$		0			0
$367$	−3806.51	+	1385.46i	−0.541412	+	0.197058i	−0.598227	−	0.801327i	$-0.704128\pi$
$367$	−3806.51	+	1385.46i	−0.541412	+	0.197058i	0.0568146	+	0.998385i	$0.481906\pi$
$368$	913.127	+	1581.58i	0.129348	+	0.224037i
$369$		0			0
$370$	−1780.06	+	3083.15i	−0.250110	+	0.433204i
$371$	299.811	−	1700.32i	0.0419554	−	0.237941i
$372$		0			0
$373$	−13066.7	−	4755.90i	−1.81386	−	0.660191i	−0.996455	−	0.0841290i	$-0.973189\pi$
$373$	−13066.7	−	4755.90i	−1.81386	−	0.660191i	−0.817406	−	0.576062i	$-0.804589\pi$
$374$	3058.18	+	17343.8i	0.422819	+	2.39793i
$375$		0			0
$376$	2695.82	+	2262.06i	0.369751	+	0.310258i
$377$	2309.17			0.315460
$378$		0			0
$379$	5487.05			0.743669			0.371835	−	0.928299i	$-0.378729\pi$
$379$	5487.05			0.743669			0.371835	+	0.928299i	$0.378729\pi$
$380$	−1820.85	−	1527.87i	−0.245809	−	0.206259i
$381$		0			0
$382$	1024.23	+	5808.72i	0.137184	+	0.778011i
$383$	8422.82	+	3065.66i	1.12372	+	0.409002i	0.836010	−	0.548714i	$-0.184883\pi$
$383$	8422.82	+	3065.66i	1.12372	+	0.409002i	0.287714	+	0.957716i	$0.407105\pi$
$384$		0			0
$385$	484.636	−	2748.51i	0.0641542	−	0.363836i
$386$	−1854.10	+	3211.39i	−0.244484	+	0.423459i
$387$		0			0
$388$	1063.52	+	1842.07i	0.139155	+	0.241024i
$389$	−5415.31	+	1971.01i	−0.705828	+	0.256900i	−0.669897	−	0.742454i	$-0.733662\pi$
$389$	−5415.31	+	1971.01i	−0.705828	+	0.256900i	−0.0359310	+	0.999354i	$0.511440\pi$
$390$		0			0
$391$	−1567.07	+	1314.93i	−0.202685	+	0.170073i
$392$	3682.84	−	3090.27i	0.474520	−	0.398169i
$393$		0			0
$394$	−11575.3	+	4213.08i	−1.48009	+	0.538710i
$395$	−1996.18	−	3457.48i	−0.254275	−	0.440417i
$396$		0			0
$397$	849.799	−	1471.89i	0.107431	−	0.186076i	−0.807298	−	0.590144i	$-0.799071\pi$
$397$	849.799	−	1471.89i	0.107431	−	0.186076i	0.914729	+	0.404068i	$0.132404\pi$
$398$	860.912	−	4882.48i	0.108426	−	0.614916i
$399$		0			0
$400$	−329.371	−	119.881i	−0.0411713	−	0.0149851i
$401$	−1819.64	−	10319.7i	−0.226605	−	1.28514i	−0.859592	−	0.510980i	$-0.829283\pi$
$401$	−1819.64	−	10319.7i	−0.226605	−	1.28514i	0.632987	−	0.774162i	$-0.281829\pi$
$402$		0			0
$403$	−10029.4	−	8415.63i	−1.23970	−	1.04023i
$404$	−179.750			−0.0221359
$405$		0			0
$406$	−885.741			−0.108272
$407$	−4196.98	−	3521.69i	−0.511147	−	0.428903i
$408$		0			0
$409$	−357.046	−	2024.91i	−0.0431657	−	0.244805i	0.955589	−	0.294704i	$-0.0952211\pi$
$409$	−357.046	−	2024.91i	−0.0431657	−	0.244805i	−0.998754	+	0.0498993i	$0.984110\pi$
$410$	−12739.4	−	4636.75i	−1.53452	−	0.558519i
$411$		0			0
$412$	228.471	−	1295.72i	0.0273203	−	0.154941i
$413$	−1235.02	+	2139.11i	−0.147146	+	0.254864i
$414$		0			0
$415$	−3102.61	−	5373.89i	−0.366991	−	0.635647i
$416$	5662.84	−	2061.11i	0.667413	−	0.242918i
$417$		0			0
$418$	8949.80	−	7509.77i	1.04725	−	0.878744i
$419$	2008.19	−	1685.07i	0.234145	−	0.196471i	−0.518164	−	0.855281i	$-0.673384\pi$
$419$	2008.19	−	1685.07i	0.234145	−	0.196471i	0.752309	+	0.658810i	$0.228940\pi$
$420$		0			0
$421$	7645.13	−	2782.60i	0.885038	−	0.322128i	0.140797	−	0.990038i	$-0.455034\pi$
$421$	7645.13	−	2782.60i	0.885038	−	0.322128i	0.744241	+	0.667911i	$0.232811\pi$
$422$	5516.52	+	9554.90i	0.636351	+	1.10219i
$423$		0			0
$424$	−2911.02	+	5042.04i	−0.333424	+	0.577507i
$425$	68.1776	−	386.655i	0.00778141	−	0.0441306i
$426$		0			0
$427$	698.738	+	254.320i	0.0791904	+	0.0288229i
$428$	−669.713	−	3798.13i	−0.0756350	−	0.428948i
$429$		0			0
$430$	13540.5	+	11361.8i	1.51856	+	1.27422i
$431$	−10524.6			−1.17622			−0.588112	−	0.808780i	$-0.700128\pi$
$431$	−10524.6			−1.17622			−0.588112	+	0.808780i	$0.700128\pi$
$432$		0			0
$433$	−15556.7			−1.72658			−0.863290	−	0.504708i	$-0.831600\pi$
$433$	−15556.7			−1.72658			−0.863290	+	0.504708i	$0.831600\pi$
$434$	3847.01	+	3228.03i	0.425490	+	0.357028i
$435$		0			0
$436$	5.72633	+	32.4756i	0.000628995	+	0.00356721i
$437$	1275.22	+	464.144i	0.139593	+	0.0508078i
$438$		0			0
$439$	2473.12	−	14025.8i	0.268874	−	1.52486i	−0.488900	−	0.872340i	$-0.662602\pi$
$439$	2473.12	−	14025.8i	0.268874	−	1.52486i	0.757773	−	0.652518i	$-0.226287\pi$
$440$	−4705.58	+	8150.31i	−0.509841	+	0.883070i
$441$		0			0
$442$	5984.63	+	10365.7i	0.644027	+	1.11549i
$443$	9858.79	−	3588.31i	1.05735	−	0.384843i	0.245917	−	0.969291i	$-0.420911\pi$
$443$	9858.79	−	3588.31i	1.05735	−	0.384843i	0.811431	+	0.584448i	$0.198689\pi$
$444$		0			0
$445$	3156.73	−	2648.81i	0.336277	−	0.282170i
$446$	5161.25	−	4330.80i	0.547964	−	0.459797i
$447$		0			0
$448$	473.488	−	172.336i	0.0499335	−	0.0181743i
$449$	5192.42	+	8993.54i	0.545759	+	0.945282i	0.998559	+	0.0536697i	$0.0170918\pi$
$449$	5192.42	+	8993.54i	0.545759	+	0.945282i	−0.452800	+	0.891612i	$0.649575\pi$
$450$		0			0
$451$	10431.6	−	18068.1i	1.08915	−	1.88646i
$452$	127.401	−	722.525i	0.0132576	−	0.0751874i
$453$		0			0
$454$	5055.59	+	1840.08i	0.522622	+	0.190219i
$455$	−329.376	−	1867.98i	−0.0339371	−	0.192467i
$456$		0			0
$457$	419.782	+	352.239i	0.0429685	+	0.0360548i	0.664019	−	0.747716i	$-0.268849\pi$
$457$	419.782	+	352.239i	0.0429685	+	0.0360548i	−0.621051	+	0.783771i	$0.713294\pi$
$458$	22079.2			2.25260
$459$		0			0
$460$	915.628			0.0928074
$461$	8411.57	+	7058.15i	0.849818	+	0.713082i	0.959750	−	0.280857i	$-0.0906188\pi$
$461$	8411.57	+	7058.15i	0.849818	+	0.713082i	−0.109932	+	0.993939i	$0.535063\pi$
$462$		0			0
$463$	1692.97	+	9601.33i	0.169933	+	0.963740i	0.943831	+	0.330429i	$0.107193\pi$
$463$	1692.97	+	9601.33i	0.169933	+	0.963740i	−0.773898	+	0.633311i	$0.781695\pi$
$464$	4421.47	+	1609.28i	0.442374	+	0.161011i
$465$		0			0
$466$	−1526.54	+	8657.42i	−0.151750	+	0.860617i
$467$	7561.18	−	13096.3i	0.749228	−	1.29770i	−0.198965	−	0.980007i	$-0.563758\pi$
$467$	7561.18	−	13096.3i	0.749228	−	1.29770i	0.948193	−	0.317695i	$-0.102909\pi$
$468$		0			0
$469$	−1199.18	−	2077.04i	−0.118066	−	0.204496i
$470$	8342.14	−	3036.29i	0.818711	−	0.297987i
$471$		0			0
$472$	6380.50	−	5353.88i	0.622217	−	0.522102i
$473$	−20837.9	+	17485.0i	−2.02564	+	1.69971i
$474$		0			0
$475$	−244.751	+	89.0821i	−0.0236420	+	0.00860498i
$476$	−718.733	−	1244.88i	−0.0692082	−	0.119872i
$477$		0			0
$478$	−258.543	+	447.809i	−0.0247395	+	0.0428500i
$479$	501.655	−	2845.03i	0.0478522	−	0.271383i	−0.951489	−	0.307684i	$-0.900446\pi$
$479$	501.655	−	2845.03i	0.0478522	−	0.271383i	0.999341	+	0.0363002i	$0.0115573\pi$
$480$		0			0
$481$	−3499.00	−	1273.53i	−0.331686	−	0.120724i
$482$	3397.60	+	19268.7i	0.321071	+	1.82089i
$483$		0			0
$484$	5574.91	+	4677.90i	0.523564	+	0.439322i
$485$	−6406.15			−0.599770
$486$		0			0
$487$	15221.1			1.41629			0.708146	−	0.706066i	$-0.249532\pi$
$487$	15221.1			1.41629			0.708146	+	0.706066i	$0.249532\pi$
$488$	−1920.79	−	1611.73i	−0.178176	−	0.149508i
$489$		0			0
$490$	−2105.98	−	11943.6i	−0.194160	−	1.10114i
$491$	2636.65	+	959.662i	0.242343	+	0.0882056i	0.460336	−	0.887745i	$-0.347729\pi$
$491$	2636.65	+	959.662i	0.242343	+	0.0882056i	−0.217993	+	0.975950i	$0.569951\pi$
$492$		0			0
$493$	−915.216	+	5190.45i	−0.0836090	+	0.474170i
$494$	3970.13	−	6876.47i	0.361588	−	0.626289i
$495$		0			0
$496$	−13338.7	−	23103.3i	−1.20751	−	2.09147i
$497$	−803.686	+	292.518i	−0.0725357	+	0.0264008i
$498$		0			0
$499$	3778.64	−	3170.66i	0.338989	−	0.284445i	−0.457362	−	0.889281i	$-0.651206\pi$
$499$	3778.64	−	3170.66i	0.338989	−	0.284445i	0.796350	+	0.604835i	$0.206761\pi$
$500$	−3969.34	+	3330.67i	−0.355028	+	0.297904i
$501$		0			0
$502$	2260.79	−	822.859i	0.201004	−	0.0731594i
$503$	−2185.55	−	3785.49i	−0.193735	−	0.335560i	0.752750	−	0.658307i	$-0.228727\pi$
$503$	−2185.55	−	3785.49i	−0.193735	−	0.335560i	−0.946485	+	0.322747i	$0.895394\pi$
$504$		0			0
$505$	270.683	−	468.836i	0.0238519	−	0.0413127i
$506$	−781.500	+	4432.10i	−0.0686599	+	0.389389i
$507$		0			0
$508$	4245.35	+	1545.18i	0.370782	+	0.134954i
$509$	−3169.78	−	17976.7i	−0.276027	−	1.56543i	−0.735679	−	0.677330i	$-0.763137\pi$
$509$	−3169.78	−	17976.7i	−0.276027	−	1.56543i	0.459652	−	0.888099i	$-0.347974\pi$
$510$		0			0
$511$	−544.516	−	456.903i	−0.0471389	−	0.0395542i
$512$	2785.52			0.240437
$513$		0			0
$514$	−2570.05			−0.220545
$515$	3035.53	+	2547.12i	0.259731	+	0.217940i
$516$		0			0
$517$	2372.36	+	13454.3i	0.201811	+	1.14453i
$518$	1342.13	+	488.496i	0.113842	+	0.0414349i
$519$		0			0
$520$	−1110.68	+	6298.98i	−0.0936665	+	0.531209i
$521$	4209.97	−	7291.88i	0.354016	−	0.613173i	−0.632933	−	0.774206i	$-0.718149\pi$
$521$	4209.97	−	7291.88i	0.354016	−	0.613173i	0.986949	+	0.161033i	$0.0514827\pi$
$522$		0			0
$523$	−1221.04	−	2114.91i	−0.102089	−	0.176823i	0.810456	−	0.585799i	$-0.199219\pi$
$523$	−1221.04	−	2114.91i	−0.102089	−	0.176823i	−0.912545	+	0.408976i	$0.865886\pi$
$524$	2248.75	−	818.477i	0.187475	−	0.0682354i
$525$		0			0
$526$	16237.8	−	13625.1i	1.34601	−	1.12944i
$527$	22891.3	−	19208.1i	1.89214	−	1.58770i
$528$		0			0
$529$	10942.0	−	3982.57i	0.899319	−	0.327325i
$530$	7343.45	+	12719.2i	0.601848	+	1.04243i
$531$		0			0
$532$	−476.798	+	825.839i	−0.0388568	+	0.0673020i
$533$	2462.22	−	13963.9i	0.200095	−	1.13479i
$534$		0			0
$535$	10915.0	+	3972.75i	0.882052	+	0.321041i
$536$	1404.37	+	7964.59i	0.113171	+	0.641824i
$537$		0			0
$538$	−9737.69	−	8170.89i	−0.780337	−	0.654781i
$539$	18663.9			1.49149
$540$		0			0
$541$	−22321.4			−1.77389			−0.886943	−	0.461879i	$-0.847176\pi$
$541$	−22321.4			−1.77389			−0.886943	+	0.461879i	$0.847176\pi$
$542$	13994.6	+	11742.8i	1.10907	+	0.930623i
$543$		0			0
$544$	2388.45	+	13545.6i	0.188243	+	1.06758i
$545$	−93.3282	−	33.9687i	−0.00733530	−	0.00266983i
$546$		0			0
$547$	−1549.26	+	8786.27i	−0.121100	+	0.686789i	0.862449	+	0.506144i	$0.168930\pi$
$547$	−1549.26	+	8786.27i	−0.121100	+	0.686789i	−0.983548	+	0.180645i	$0.942181\pi$
$548$	−90.2628	+	156.340i	−0.00703619	+	0.0121870i
$549$		0			0
$550$	−431.883	−	748.044i	−0.0334828	−	0.0579940i
$551$	3285.53	−	1195.84i	0.254026	−	0.0924580i
$552$		0			0
$553$	−1226.95	+	1029.54i	−0.0943497	+	0.0791688i
$554$	7840.98	−	6579.36i	0.601320	−	0.504567i
$555$		0			0
$556$	−6860.86	+	2497.15i	−0.523318	+	0.190472i
$557$	−268.972	−	465.874i	−0.0204609	−	0.0354393i	0.855614	−	0.517615i	$-0.173180\pi$
$557$	−268.972	−	465.874i	−0.0204609	−	0.0354393i	−0.876075	+	0.482176i	$0.839847\pi$
$558$		0			0
$559$	−9243.68	+	16010.5i	−0.699402	+	1.21140i
$560$	671.145	−	3806.25i	0.0506447	−	0.287220i
$561$		0			0
$562$	−23673.2	−	8616.35i	−1.77686	−	0.646724i
$563$	1343.84	+	7621.32i	0.100597	+	0.570516i	0.992888	+	0.119054i	$0.0379862\pi$
$563$	1343.84	+	7621.32i	0.100597	+	0.570516i	−0.892290	+	0.451462i	$0.850903\pi$
$564$		0			0
$565$	1692.69	+	1420.33i	0.126039	+	0.105759i
$566$	−30011.9			−2.22879
$567$		0			0
$568$	2884.02			0.213047
$569$	−6106.18	−	5123.70i	−0.449885	−	0.377498i	0.389508	−	0.921023i	$-0.372645\pi$
$569$	−6106.18	−	5123.70i	−0.449885	−	0.377498i	−0.839393	+	0.543525i	$0.817089\pi$
$570$		0			0
$571$	1403.64	+	7960.43i	0.102873	+	0.583421i	0.992049	+	0.125855i	$0.0401675\pi$
$571$	1403.64	+	7960.43i	0.102873	+	0.583421i	−0.889176	+	0.457566i	$0.848721\pi$
$572$	7747.43	+	2819.83i	0.566322	+	0.206124i
$573$		0			0
$574$	−944.446	+	5356.22i	−0.0686767	+	0.389485i
$575$	50.1658	−	86.8898i	0.00363836	−	0.00630183i
$576$		0			0
$577$	4242.14	+	7347.60i	0.306070	+	0.530130i	0.977499	−	0.210940i	$-0.0676524\pi$
$577$	4242.14	+	7347.60i	0.306070	+	0.530130i	−0.671429	+	0.741069i	$0.734319\pi$
$578$	−9916.04	+	3609.15i	−0.713587	+	0.259724i
$579$		0			0
$580$	1807.14	−	1516.37i	0.129375	−	0.108559i
$581$	−1907.03	+	1600.19i	−0.136174	+	0.114263i
$582$		0			0
$583$	−21239.0	+	7730.38i	−1.50880	+	0.549159i
$584$	1198.46	+	2075.80i	0.0849190	+	0.147084i
$585$		0			0
$586$	1685.18	−	2918.82i	0.118796	−	0.205760i
$587$	−2873.45	+	16296.2i	−0.202044	+	1.14585i	0.699979	+	0.714163i	$0.253193\pi$
$587$	−2873.45	+	16296.2i	−0.202044	+	1.14585i	−0.902023	+	0.431687i	$0.857918\pi$
$588$		0			0
$589$	−18628.1	−	6780.08i	−1.30316	−	0.474310i
$590$	−3648.60	−	20692.2i	−0.254594	−	1.44387i
$591$		0			0
$592$	−5812.15	−	4876.98i	−0.403510	−	0.338585i
$593$	−12748.0			−0.882796			−0.441398	−	0.897311i	$-0.645517\pi$
$593$	−12748.0			−0.882796			−0.441398	+	0.897311i	$0.645517\pi$
$594$		0			0
$595$	4329.31			0.298293
$596$	−7410.35	−	6218.02i	−0.509295	−	0.427349i
$597$		0			0
$598$	531.134	+	3012.21i	0.0363206	+	0.205984i
$599$	23393.1	+	8514.39i	1.59569	+	0.580783i	0.978538	−	0.206064i	$-0.0660656\pi$
$599$	23393.1	+	8514.39i	1.59569	+	0.580783i	0.617148	+	0.786847i	$0.288288\pi$
$600$		0			0
$601$	−2949.21	+	16725.8i	−0.200167	+	1.13521i	0.704698	+	0.709508i	$0.251083\pi$
$601$	−2949.21	+	16725.8i	−0.200167	+	1.13521i	−0.904865	+	0.425698i	$0.860028\pi$
$602$	3545.65	−	6141.24i	0.240050	−	0.415778i
$603$		0			0
$604$	−764.685	−	1324.47i	−0.0515142	−	0.0892253i
$605$	−20596.3	+	7496.45i	−1.38407	+	0.503759i
$606$		0			0
$607$	−2424.14	+	2034.09i	−0.162097	+	0.136015i	−0.720228	−	0.693737i	$-0.755963\pi$
$607$	−2424.14	+	2034.09i	−0.162097	+	0.136015i	0.558131	+	0.829753i	$0.311518\pi$
$608$	6989.83	−	5865.17i	0.466242	−	0.391224i
$609$		0			0
$610$	−5943.83	+	2163.38i	−0.394523	+	0.143594i
$611$	4642.54	+	8041.12i	0.307393	+	0.532421i
$612$		0			0
$613$	3473.88	−	6016.94i	0.228889	−	0.396447i	−0.728590	−	0.684950i	$-0.759824\pi$
$613$	3473.88	−	6016.94i	0.228889	−	0.396447i	0.957479	+	0.288503i	$0.0931575\pi$
$614$	−987.761	+	5601.87i	−0.0649231	+	0.368197i
$615$		0			0
$616$	3547.93	+	1291.34i	0.232062	+	0.0844635i
$617$	3318.80	+	18821.9i	0.216548	+	1.22810i	0.878201	+	0.478293i	$0.158744\pi$
$617$	3318.80	+	18821.9i	0.216548	+	1.22810i	−0.661653	+	0.749810i	$0.730145\pi$
$618$		0			0
$619$	−9966.32	−	8362.73i	−0.647141	−	0.543016i	0.259061	−	0.965861i	$-0.416587\pi$
$619$	−9966.32	−	8362.73i	−0.647141	−	0.543016i	−0.906202	+	0.422845i	$0.861031\pi$
$620$	−13375.2			−0.866391
$621$		0			0
$622$	−14551.8			−0.938064
$623$	−1266.43	−	1062.66i	−0.0814424	−	0.0683382i
$624$		0			0
$625$	−2614.66	−	14828.5i	−0.167338	−	0.949022i
$626$	−4915.62	−	1789.14i	−0.313846	−	0.114231i
$627$		0			0
$628$	1567.95	−	8892.28i	0.0996305	−	0.565033i
$629$	4249.38	−	7360.15i	0.269370	−	0.466563i
$630$		0			0
$631$	12528.8	+	21700.5i	0.790432	+	1.36907i	0.925700	+	0.378259i	$0.123477\pi$
$631$	12528.8	+	21700.5i	0.790432	+	1.36907i	−0.135268	+	0.990809i	$0.543189\pi$
$632$	5075.25	−	1847.24i	0.319435	−	0.116265i
$633$		0			0
$634$	−21281.1	+	17857.0i	−1.33309	+	1.11860i
$635$	−10423.2	+	8746.14i	−0.651392	+	0.546583i
$636$		0			0
$637$	11919.7	−	4338.40i	0.741404	−	0.269849i
$638$	5797.60	+	10041.7i	0.359763	+	0.623129i
$639$		0			0
$640$	−8896.43	+	15409.1i	−0.549472	+	0.951714i
$641$	−1384.86	+	7853.93i	−0.0853334	+	0.483950i	0.911951	+	0.410300i	$0.134576\pi$
$641$	−1384.86	+	7853.93i	−0.0853334	+	0.483950i	−0.997284	+	0.0736500i	$0.976535\pi$
$642$		0			0
$643$	−11197.1	−	4075.43i	−0.686737	−	0.249952i	−0.0249998	−	0.999687i	$-0.507959\pi$
$643$	−11197.1	−	4075.43i	−0.686737	−	0.249952i	−0.661738	+	0.749735i	$0.730181\pi$
$644$	−63.7873	−	361.756i	−0.00390306	−	0.0221354i
$645$		0			0
$646$	13883.1	+	11649.3i	0.845546	+	0.709497i
$647$	−3355.80			−0.203911			−0.101955	−	0.994789i	$-0.532510\pi$
$647$	−3355.80			−0.203911			−0.101955	+	0.994789i	$0.532510\pi$
$648$		0			0
$649$	32335.1			1.95572
$650$	−449.703	−	377.346i	−0.0271366	−	0.0227703i
$651$		0			0
$652$	−1636.20	−	9279.33i	−0.0982797	−	0.557372i
$653$	−26473.9	−	9635.72i	−1.58653	−	0.577450i	−0.609920	−	0.792463i	$-0.708799\pi$
$653$	−26473.9	−	9635.72i	−1.58653	−	0.577450i	−0.976611	+	0.215012i	$0.931021\pi$
$654$		0			0
$655$	−1251.54	+	7097.85i	−0.0746593	+	0.423414i
$656$	14446.1	−	25021.4i	0.859795	−	1.48921i
$657$		0			0
$658$	−1780.77	−	3084.38i	−0.105504	−	0.182738i
$659$	10183.6	−	3706.54i	0.601970	−	0.219099i	−0.0230158	−	0.999735i	$-0.507327\pi$
$659$	10183.6	−	3706.54i	0.601970	−	0.219099i	0.624986	+	0.780636i	$0.285105\pi$
$660$		0			0
$661$	19264.9	−	16165.2i	1.13361	−	0.951214i	0.134401	−	0.990927i	$-0.457089\pi$
$661$	19264.9	−	16165.2i	1.13361	−	0.951214i	0.999211	+	0.0397130i	$0.0126444\pi$
$662$	−7110.34	+	5966.28i	−0.417449	+	0.350281i
$663$		0			0
$664$	7888.35	−	2871.13i	0.461035	−	0.167803i
$665$	−1436.00	−	2487.23i	−0.0837381	−	0.145039i
$666$		0			0
$667$	−673.426	+	1166.41i	−0.0390932	+	0.0677114i
$668$	−401.681	+	2278.04i	−0.0232657	+	0.131946i
$669$		0			0
$670$	19171.3	+	6977.80i	1.10545	+	0.402352i
$671$	−1690.32	−	9586.30i	−0.0972492	−	0.551528i
$672$		0			0
$673$	7274.92	+	6104.39i	0.416683	+	0.349639i	0.826900	−	0.562350i	$-0.190102\pi$
$673$	7274.92	+	6104.39i	0.416683	+	0.349639i	−0.410217	+	0.911988i	$0.634547\pi$
$674$	−23360.8			−1.33505
$675$		0			0
$676$	−2407.98			−0.137004
$677$	−2770.73	−	2324.92i	−0.157294	−	0.131985i	0.560744	−	0.827989i	$-0.310515\pi$
$677$	−2770.73	−	2324.92i	−0.157294	−	0.131985i	−0.718038	+	0.696004i	$0.754960\pi$
$678$		0			0
$679$	446.285	+	2531.01i	0.0252236	+	0.143050i
$680$	−13718.4	−	4993.07i	−0.773640	−	0.281582i
$681$		0			0
$682$	11415.9	−	64742.9i	0.640966	−	3.63510i
$683$	−1790.30	+	3100.89i	−0.100298	+	0.173722i	−0.911808	−	0.410618i	$-0.865313\pi$
$683$	−1790.30	+	3100.89i	−0.100298	+	0.173722i	0.811509	+	0.584340i	$0.198646\pi$
$684$		0			0
$685$	−271.850	−	470.858i	−0.0151633	−	0.0262636i
$686$	−9418.47	+	3428.04i	−0.524197	+	0.190792i
$687$		0			0
$688$	−28857.1	+	24214.0i	−1.59908	+	1.34179i
$689$	−11767.3	+	9873.98i	−0.650653	+	0.545963i
$690$		0			0
$691$	15363.7	−	5591.94i	0.845822	−	0.307854i	0.117487	−	0.993074i	$-0.462516\pi$
$691$	15363.7	−	5591.94i	0.845822	−	0.307854i	0.728336	+	0.685220i	$0.240294\pi$
$692$	3097.34	+	5364.74i	0.170149	+	0.294706i
$693$		0			0
$694$	16557.1	−	28677.7i	0.905616	−	1.56857i
$695$	3818.42	−	21655.3i	0.208404	−	1.18192i
$696$		0			0
$697$	30411.6	+	11068.9i	1.65269	+	0.601528i
$698$	−162.822	−	923.407i	−0.00882935	−	0.0500737i
$699$		0			0
$700$	54.0077	+	45.3179i	0.00291614	+	0.00244694i
$701$	−11210.5			−0.604015			−0.302007	−	0.953306i	$-0.597657\pi$
$701$	−11210.5			−0.604015			−0.302007	+	0.953306i	$0.597657\pi$
$702$		0			0
$703$	−5637.97			−0.302475
$704$	−5052.99	−	4239.96i	−0.270514	−	0.226988i
$705$		0			0
$706$	−1027.83	−	5829.11i	−0.0547916	−	0.310739i
$707$	−204.090	−	74.2826i	−0.0108566	−	0.00395147i
$708$		0			0
$709$	1416.45	−	8033.11i	0.0750297	−	0.425514i	−0.924036	−	0.382305i	$-0.875131\pi$
$709$	1416.45	−	8033.11i	0.0750297	−	0.425514i	0.999066	−	0.0432098i	$-0.0137584\pi$
$710$	3637.67	−	6300.63i	0.192281	−	0.333040i
$711$		0			0
$712$	2787.38	+	4827.88i	0.146716	+	0.254119i
$713$	7175.77	−	2611.77i	0.376907	−	0.137183i
$714$		0			0
$715$	−19021.6	+	15961.0i	−0.994918	+	0.834835i
$716$	−1812.00	+	1520.45i	−0.0945776	+	0.0793600i
$717$		0			0
$718$	−13729.7	+	4997.19i	−0.713630	+	0.259740i
$719$	12784.1	+	22142.8i	0.663099	+	1.14852i	0.979797	+	0.199994i	$0.0640924\pi$
$719$	12784.1	+	22142.8i	0.663099	+	1.14852i	−0.316698	+	0.948526i	$0.602574\pi$
$720$		0			0
$721$	794.870	−	1376.76i	0.0410576	−	0.0711138i
$722$	−1976.99	+	11212.1i	−0.101906	+	0.577938i
$723$		0			0
$724$	−12585.8	−	4580.86i	−0.646061	−	0.235147i
$725$	−44.8877	−	254.571i	−0.00229943	−	0.0130407i
$726$		0			0
$727$	−12418.2	−	10420.1i	−0.633515	−	0.531582i	0.268504	−	0.963279i	$-0.413471\pi$
$727$	−12418.2	−	10420.1i	−0.633515	−	0.531582i	−0.902019	+	0.431696i	$0.857915\pi$
$728$	2566.04			0.130637
$729$		0			0
$730$	6046.57			0.306566
$731$	−32324.1	−	27123.1i	−1.63550	−	1.37235i
$732$		0			0
$733$	−4003.77	−	22706.5i	−0.201750	−	1.14418i	−0.902473	−	0.430747i	$-0.858250\pi$
$733$	−4003.77	−	22706.5i	−0.201750	−	1.14418i	0.700723	−	0.713434i	$-0.252861\pi$
$734$	−12990.5	−	4728.14i	−0.653252	−	0.237764i
$735$		0			0
$736$	−610.355	+	3461.50i	−0.0305679	+	0.173359i
$737$	−15698.4	+	27190.4i	−0.784611	+	1.35899i
$738$		0			0
$739$	−9222.49	−	15973.8i	−0.459073	−	0.795137i	0.539840	−	0.841768i	$-0.318485\pi$
$739$	−9222.49	−	15973.8i	−0.459073	−	0.795137i	−0.998912	+	0.0466309i	$0.985152\pi$
$740$	−3574.60	+	1301.05i	−0.177574	+	0.0646317i
$741$		0			0
$742$	4513.67	−	3787.42i	0.223318	−	0.187386i
$743$	−8601.48	+	7217.49i	−0.424707	+	0.356372i	−0.829950	−	0.557837i	$-0.811631\pi$
$743$	−8601.48	+	7217.49i	−0.424707	+	0.356372i	0.405243	+	0.914209i	$0.367187\pi$
$744$		0			0
$745$	27377.3	−	9964.53i	1.34635	−	0.490030i
$746$	−23727.3	−	41096.9i	−1.16450	−	2.01698i
$747$		0			0
$748$	−9408.90	+	16296.7i	−0.459925	+	0.796613i
$749$	809.197	−	4589.19i	0.0394759	−	0.223879i
$750$		0			0
$751$	25956.7	+	9447.48i	1.26122	+	0.459046i	0.884178	−	0.467151i	$-0.154719\pi$
$751$	25956.7	+	9447.48i	1.26122	+	0.459046i	0.377041	+	0.926197i	$0.376942\pi$
$752$	3285.34	+	18632.1i	0.159314	+	0.903515i
$753$		0			0
$754$	6036.81	+	5065.48i	0.291575	+	0.244661i
$755$	4606.10			0.222031
$756$		0			0
$757$	−1558.81			−0.0748425			−0.0374213	−	0.999300i	$-0.511914\pi$
$757$	−1558.81			−0.0748425			−0.0374213	+	0.999300i	$0.511914\pi$
$758$	14344.7	+	12036.6i	0.687363	+	0.576766i
$759$		0			0
$760$	1681.72	+	9537.50i	0.0802663	+	0.455213i
$761$	−13156.0	−	4788.39i	−0.626681	−	0.228093i	0.00910498	−	0.999959i	$-0.497102\pi$
$761$	−13156.0	−	4788.39i	−0.626681	−	0.228093i	−0.635786	+	0.771865i	$0.719324\pi$
$762$		0			0
$763$	−6.91898	+	39.2395i	−0.000328288	+	0.00186182i
$764$	−3151.20	+	5458.04i	−0.149223	+	0.258462i
$765$		0			0
$766$	15294.6	+	26491.1i	0.721433	+	1.24956i
$767$	20650.7	−	7516.26i	0.972171	−	0.353841i
$768$		0			0
$769$	−6398.15	+	5368.68i	−0.300030	+	0.251755i	−0.780357	−	0.625335i	$-0.784963\pi$
$769$	−6398.15	+	5368.68i	−0.300030	+	0.251755i	0.480327	+	0.877090i	$0.340518\pi$
$770$	7296.21	−	6122.25i	0.341477	−	0.286533i
$771$		0			0
$772$	−3723.27	+	1355.16i	−0.173580	+	0.0631778i
$773$	13400.6	+	23210.5i	0.623527	+	1.07998i	0.988824	+	0.149089i	$0.0476341\pi$
$773$	13400.6	+	23210.5i	0.623527	+	1.07998i	−0.365297	+	0.930891i	$0.619033\pi$
$774$		0			0
$775$	−732.808	+	1269.26i	−0.0339655	+	0.0588300i
$776$	1504.91	−	8534.76i	0.0696174	−	0.394820i
$777$		0			0
$778$	−18480.8	−	6726.46i	−0.851631	−	0.309968i
$779$	−3728.13	−	21143.3i	−0.171469	−	0.972446i
$780$		0			0
$781$	8576.81	+	7196.80i	0.392961	+	0.329733i
$782$	−6981.22			−0.319243
$783$		0			0
$784$	25846.6			1.17741
$785$	20832.3	+	17480.3i	0.947178	+	0.794777i
$786$		0			0
$787$	−183.323	−	1039.67i	−0.00830336	−	0.0470907i	0.980375	−	0.197144i	$-0.0631666\pi$
$787$	−183.323	−	1039.67i	−0.00830336	−	0.0470907i	−0.988678	+	0.150053i	$0.952056\pi$
$788$	−12368.3	−	4501.70i	−0.559141	−	0.203511i
$789$		0			0
$790$	2365.90	−	13417.7i	0.106551	−	0.604279i
$791$	443.238	−	767.711i	0.0199238	−	0.0345091i
$792$		0			0
$793$	−3307.84	−	5729.35i	−0.148127	−	0.256564i
$794$	5450.41	−	1983.79i	0.243612	−	0.0886675i
$795$		0			0
$796$	4058.07	−	3405.12i	0.180697	−	0.151622i
$797$	−7844.59	+	6582.39i	−0.348644	+	0.292547i	−0.800245	−	0.599673i	$-0.795297\pi$
$797$	−7844.59	+	6582.39i	−0.348644	+	0.292547i	0.451601	+	0.892220i	$0.350853\pi$
$798$		0			0
$799$	−19914.5	+	7248.28i	−0.881757	+	0.320933i
$800$	−337.303	−	584.226i	−0.0149068	−	0.0258194i
$801$		0			0
$802$	17880.7	−	30970.2i	0.787267	−	1.36359i
$803$	−1615.84	+	9163.87i	−0.0710108	+	0.402722i
$804$		0			0
$805$	1039.61	+	378.387i	0.0455173	+	0.0165670i
$806$	−7758.66	−	44001.5i	−0.339066	−	1.92294i
$807$		0			0
$808$	561.032	+	470.761i	0.0244270	+	0.0204967i
$809$	11391.9			0.495077			0.247538	−	0.968878i	$-0.420378\pi$
$809$	11391.9			0.495077			0.247538	+	0.968878i	$0.420378\pi$
$810$		0			0
$811$	−8743.55			−0.378579			−0.189289	−	0.981921i	$-0.560618\pi$
$811$	−8743.55			−0.378579			−0.189289	+	0.981921i	$0.560618\pi$
$812$	−724.999	−	608.347i	−0.0313331	−	0.0262916i
$813$		0			0
$814$	−3246.77	−	18413.3i	−0.139802	−	0.792858i
$815$	26666.8	+	9705.93i	1.14613	+	0.417158i
$816$		0			0
$817$	−4860.82	+	27567.1i	−0.208150	+	1.18048i
$818$	3508.50	−	6076.89i	0.149965	−	0.259748i
$819$		0			0
$820$	−7242.84	−	12545.0i	−0.308452	−	0.534255i
$821$	−32343.5	+	11772.1i	−1.37490	+	0.500424i	−0.920629	−	0.390438i	$-0.872323\pi$
$821$	−32343.5	+	11772.1i	−1.37490	+	0.500424i	−0.454274	+	0.890862i	$0.650101\pi$
$822$		0			0
$823$	14548.9	−	12208.0i	0.616212	−	0.517063i	−0.280399	−	0.959884i	$-0.590467\pi$
$823$	14548.9	−	12208.0i	0.616212	−	0.517063i	0.896610	+	0.442821i	$0.146022\pi$
$824$	−4106.56	+	3445.81i	−0.173615	+	0.145680i
$825$		0			0
$826$	−7921.12	+	2883.05i	−0.333669	+	0.121446i
$827$	2770.81	+	4799.19i	0.116506	+	0.201795i	0.918381	−	0.395698i	$-0.129497\pi$
$827$	2770.81	+	4799.19i	0.116506	+	0.201795i	−0.801875	+	0.597492i	$0.796164\pi$
$828$		0			0
$829$	−21645.5	+	37491.1i	−0.906850	+	1.57071i	−0.0884355	+	0.996082i	$0.528187\pi$
$829$	−21645.5	+	37491.1i	−0.906850	+	1.57071i	−0.818414	+	0.574628i	$0.805147\pi$
$830$	3677.27	−	20854.8i	0.153783	−	0.872147i
$831$		0			0
$832$	−4212.65	−	1533.28i	−0.175538	−	0.0638905i
$833$	5027.43	+	28512.0i	0.209112	+	1.18593i
$834$		0			0
$835$	−5336.85	−	4478.15i	−0.221185	−	0.185596i
$836$	12483.5			0.516448
$837$		0			0
$838$	8946.41			0.368793
$839$	18955.6	+	15905.7i	0.780002	+	0.654499i	0.943249	−	0.332086i	$-0.107752\pi$
$839$	18955.6	+	15905.7i	0.780002	+	0.654499i	−0.163247	+	0.986585i	$0.552197\pi$
$840$		0			0
$841$	−3632.53	−	20601.1i	−0.148941	−	0.844689i
$842$	26090.5	+	9496.17i	1.06786	+	0.388669i
$843$		0			0
$844$	−2047.12	+	11609.8i	−0.0834889	+	0.473489i
$845$	3626.13	−	6280.64i	0.147624	−	0.255693i
$846$		0			0
$847$	4396.62	+	7615.18i	0.178359	+	0.308926i
$848$	−29412.7	+	10705.3i	−1.19108	+	0.433518i
$849$		0			0
$850$	1026.41	−	861.264i	0.0414185	−	0.0347543i
$851$	1663.70	−	1396.01i	0.0670165	−	0.0562335i
$852$		0			0
$853$	24373.5	−	8871.21i	0.978349	−	0.356090i	0.197151	−	0.980373i	$-0.436831\pi$
$853$	24373.5	−	8871.21i	0.978349	−	0.356090i	0.781198	+	0.624283i	$0.214609\pi$
$854$	1268.81	+	2197.64i	0.0508404	+	0.0880582i
$855$		0			0
$856$	−7856.91	+	13608.6i	−0.313719	+	0.543378i
$857$	−1686.17	+	9562.75i	−0.0672094	+	0.381164i	0.932586	+	0.360947i	$0.117547\pi$
$857$	−1686.17	+	9562.75i	−0.0672094	+	0.381164i	−0.999796	+	0.0202163i	$0.993565\pi$
$858$		0			0
$859$	−8650.88	−	3148.66i	−0.343614	−	0.125065i	0.164448	−	0.986386i	$-0.447416\pi$
$859$	−8650.88	−	3148.66i	−0.343614	−	0.125065i	−0.508062	+	0.861321i	$0.669638\pi$
$860$	3279.65	+	18599.8i	0.130041	+	0.737498i
$861$		0			0
$862$	−27514.2	−	23087.2i	−1.08717	−	0.912241i
$863$	−13248.8			−0.522590			−0.261295	−	0.965259i	$-0.584150\pi$
$863$	−13248.8			−0.522590			−0.261295	+	0.965259i	$0.584150\pi$
$864$		0			0
$865$	−18656.9			−0.733356
$866$	−40669.6	−	34125.9i	−1.59585	−	1.33908i
$867$		0			0
$868$	931.788	+	5284.43i	0.0364366	+	0.206642i
$869$	19702.9	+	7171.28i	0.769133	+	0.279941i
$870$		0			0
$871$	−3705.37	+	21014.2i	−0.144146	+	0.817495i
$872$	67.1800	−	116.359i	0.00260895	−	0.00451883i
$873$		0			0
$874$	2315.62	+	4010.78i	0.0896192	+	0.155225i
$875$	−5883.22	+	2141.32i	−0.227302	+	0.0827312i
$876$		0			0
$877$	−28936.2	+	24280.3i	−1.11415	+	0.934879i	−0.998294	−	0.0583879i	$-0.981404\pi$
$877$	−28936.2	+	24280.3i	−1.11415	+	0.934879i	−0.115851	+	0.993267i	$0.536960\pi$
$878$	37232.8	−	31242.1i	1.43115	−	1.20088i
$879$		0			0
$880$	−47544.8	+	17304.9i	−1.82129	+	0.662895i
$881$	−2464.91	−	4269.35i	−0.0942622	−	0.163267i	0.815038	−	0.579407i	$-0.196716\pi$
$881$	−2464.91	−	4269.35i	−0.0942622	−	0.163267i	−0.909300	+	0.416140i	$0.863383\pi$
$882$		0			0
$883$	10096.6	−	17487.8i	0.384799	−	0.666492i	−0.606942	−	0.794746i	$-0.707604\pi$
$883$	10096.6	−	17487.8i	0.384799	−	0.666492i	0.991741	+	0.128254i	$0.0409374\pi$
$884$	−2220.83	+	12594.9i	−0.0844960	+	0.479201i
$885$		0			0
$886$	33645.0	+	12245.8i	1.27576	+	0.464340i
$887$	6549.95	+	37146.6i	0.247943	+	1.40616i	0.813557	+	0.581486i	$0.197528\pi$
$887$	6549.95	+	37146.6i	0.247943	+	1.40616i	−0.565614	+	0.824670i	$0.691361\pi$
$888$		0			0
$889$	4181.65	+	3508.82i	0.157759	+	0.132376i
$890$	14063.1			0.529658
$891$		0			0
$892$	7199.09			0.270228
$893$	10769.7	+	9036.86i	0.403578	+	0.338642i
$894$		0			0
$895$	−1237.07	−	7015.78i	−0.0462019	−	0.262024i
$896$	6707.75	+	2441.42i	0.250101	+	0.0910292i
$897$		0			0
$898$	−6154.15	+	34901.9i	−0.228693	+	1.29698i
$899$	9837.21	−	17038.6i	0.364949	−	0.632111i
$900$		0			0
$901$	−17530.4	−	30363.5i	−0.648193	−	1.12270i
$902$	66905.8	−	24351.7i	2.46976	−	0.898918i
$903$		0			0
$904$	−2289.91	+	1921.46i	−0.0842493	+	0.0706936i
$905$	30900.8	−	25928.9i	1.13500	−	0.952382i
$906$		0			0
$907$	17188.1	−	6255.97i	0.629242	−	0.229025i	−0.00765914	−	0.999971i	$-0.502438\pi$
$907$	17188.1	−	6255.97i	0.629242	−	0.229025i	0.636902	+	0.770945i	$0.280216\pi$
$908$	2874.30	+	4978.44i	0.105052	+	0.181955i
$909$		0			0
$910$	3236.60	−	5605.95i	0.117903	−	0.204215i
$911$	−4666.46	+	26464.8i	−0.169711	+	0.962478i	0.774362	+	0.632742i	$0.218071\pi$
$911$	−4666.46	+	26464.8i	−0.169711	+	0.962478i	−0.944073	+	0.329736i	$0.893040\pi$
$912$		0			0
$913$	30623.9	+	11146.2i	1.11008	+	0.404036i
$914$	324.741	+	1841.70i	0.0117522	+	0.0666499i
$915$		0			0
$916$	18072.3	+	15164.5i	0.651883	+	0.546995i
$917$	2891.48			0.104128
$918$		0			0
$919$	−12622.5			−0.453078			−0.226539	−	0.974002i	$-0.572741\pi$
$919$	−12622.5			−0.453078			−0.226539	+	0.974002i	$0.572741\pi$
$920$	−2857.83	−	2398.01i	−0.102413	−	0.0859347i
$921$		0			0
$922$	6507.15	+	36903.9i	0.232431	+	1.31818i
$923$	7150.45	+	2602.55i	0.254994	+	0.0928104i
$924$		0			0
$925$	−72.3820	+	410.498i	−0.00257287	+	0.0145915i
$926$	−16635.9	+	28814.3i	−0.590379	+	1.02257i
$927$		0			0
$928$	4527.95	+	7842.64i	0.160170	+	0.277422i
$929$	−10067.6	+	3664.31i	−0.355552	+	0.129410i	−0.513620	−	0.858018i	$-0.671696\pi$
$929$	−10067.6	+	3664.31i	−0.355552	+	0.129410i	0.158068	+	0.987428i	$0.449474\pi$
$930$		0			0
$931$	14712.8	−	12345.5i	0.517931	−	0.434596i
$932$	−7195.61	+	6037.84i	−0.252897	+	0.212206i
$933$		0			0
$934$	48495.6	−	17651.0i	1.69896	−	0.618370i
$935$	−28337.4	−	49081.8i	−0.991156	−	1.71673i
$936$		0			0
$937$	−8051.62	+	13945.8i	−0.280720	+	0.486222i	−0.971562	−	0.236784i	$-0.923907\pi$
$937$	−8051.62	+	13945.8i	−0.280720	+	0.486222i	0.690842	+	0.723006i	$0.257240\pi$
$938$	1421.29	−	8060.52i	0.0494741	−	0.280581i
$939$		0			0
$940$	8913.63	+	3244.29i	0.309288	+	0.112572i
$941$	−3865.23	−	21920.8i	−0.133903	−	0.759402i	−0.975617	−	0.219479i	$-0.929564\pi$
$941$	−3865.23	−	21920.8i	−0.133903	−	0.759402i	0.841714	−	0.539923i	$-0.181547\pi$
$942$		0			0
$943$	6335.40	+	5316.03i	0.218779	+	0.183578i
$944$	44779.0			1.54389
$945$		0			0
$946$	−92831.8			−3.19051
$947$	35997.5	+	30205.5i	1.23523	+	1.03648i	0.997882	+	0.0650540i	$0.0207220\pi$
$947$	35997.5	+	30205.5i	1.23523	+	1.03648i	0.237346	+	0.971425i	$0.423722\pi$
$948$		0			0
$949$	1098.18	+	6228.08i	0.0375642	+	0.213037i
$950$	−835.260	−	304.010i	−0.0285257	−	0.0103825i
$951$		0			0
$952$	−1017.02	+	5767.83i	−0.0346239	+	0.196362i
$953$	−562.035	+	973.474i	−0.0191040	+	0.0330891i	−0.875419	−	0.483364i	$-0.839415\pi$
$953$	−562.035	+	973.474i	−0.0191040	+	0.0330891i	0.856315	+	0.516453i	$0.172748\pi$
$954$		0			0
$955$	−9490.67	−	16438.3i	−0.321582	−	0.556996i
$956$	−519.188	+	188.969i	−0.0175646	+	0.00639299i
$957$		0			0
$958$	7552.43	−	6337.24i	0.254705	−	0.213723i
$959$	−167.093	+	140.208i	−0.00562640	+	0.00472111i
$960$		0			0
$961$	−76827.3	+	27962.8i	−2.57887	+	0.938634i
$962$	−6353.69	−	11004.9i	−0.212943	−	0.368828i
$963$		0			0
$964$	−10453.2	+	18105.4i	−0.349247	+	0.604914i
$965$	2072.19	−	11752.0i	0.0691256	−	0.392031i
$966$		0			0
$967$	−43890.4	−	15974.8i	−1.45959	−	0.531246i	−0.514335	−	0.857590i	$-0.671961\pi$
$967$	−43890.4	−	15974.8i	−1.45959	−	0.531246i	−0.945251	+	0.326344i	$0.894183\pi$
$968$	−5148.93	−	29201.0i	−0.170964	−	0.969584i
$969$		0			0
$970$	−16747.4	−	14052.8i	−0.554359	−	0.465162i
$971$	43151.1			1.42614			0.713071	−	0.701091i	$-0.247304\pi$
$971$	43151.1			1.42614			0.713071	+	0.701091i	$0.247304\pi$
$972$		0			0
$973$	−8821.82			−0.290662
$974$	39792.2	+	33389.6i	1.30906	+	1.09843i
$975$		0			0
$976$	−2340.83	−	13275.5i	−0.0767706	−	0.435388i
$977$	−494.587	−	180.015i	−0.0161957	−	0.00589476i	0.333910	−	0.942605i	$-0.391632\pi$
$977$	−494.587	−	180.015i	−0.0161957	−	0.00589476i	−0.350105	+	0.936710i	$0.613854\pi$
$978$		0			0
$979$	−3758.11	+	21313.3i	−0.122686	+	0.695788i
$980$	6479.34	−	11222.5i	0.211199	−	0.365807i
$981$		0			0
$982$	4787.78	+	8292.67i	0.155585	+	0.269480i
$983$	1361.23	−	495.447i	0.0441674	−	0.0160756i	−0.319842	−	0.947471i	$-0.603630\pi$
$983$	1361.23	−	495.447i	0.0441674	−	0.0160756i	0.364009	+	0.931395i	$0.381408\pi$
$984$		0			0
$985$	30366.8	−	25480.8i	0.982302	−	0.824249i
$986$	−13778.6	+	11561.6i	−0.445030	+	0.373425i
$987$		0			0
$988$	7972.55	−	2901.77i	0.256721	−	0.0934389i
$989$	−5391.48	−	9338.32i	−0.173346	−	0.300244i
$990$		0			0
$991$	22811.2	−	39510.2i	0.731203	−	1.26648i	−0.225166	−	0.974320i	$-0.572292\pi$
$991$	22811.2	−	39510.2i	0.731203	−	1.26648i	0.956369	−	0.292161i	$-0.0943743\pi$
$992$	8915.90	−	50564.6i	0.285363	−	1.61837i
$993$		0			0
$994$	−2742.74	−	998.274i	−0.0875194	−	0.0318545i
$995$	2770.49	+	15712.2i	0.0882717	+	0.500614i
$996$		0			0
$997$	17564.5	+	14738.4i	0.557948	+	0.468174i	0.877622	−	0.479353i	$-0.159129\pi$
$997$	17564.5	+	14738.4i	0.557948	+	0.468174i	−0.319673	+	0.947528i	$0.603573\pi$
$998$	16833.7			0.533929
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.4.e.b.136.7		48
3.2	odd	2		243.4.e.c.136.2		48
9.2	odd	6		27.4.e.a.25.2	yes	48
9.4	even	3		243.4.e.a.55.2		48
9.5	odd	6		243.4.e.d.55.7		48
9.7	even	3		81.4.e.a.73.7		48
27.4	even	9		81.4.e.a.10.7		48
27.5	odd	18		243.4.e.c.109.2		48
27.7	even	9		729.4.a.c.1.19		24
27.13	even	9		243.4.e.a.190.2		48
27.14	odd	18		243.4.e.d.190.7		48
27.20	odd	18		729.4.a.d.1.6		24
27.22	even	9	inner	243.4.e.b.109.7		48
27.23	odd	18		27.4.e.a.13.2	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.13.2	✓	48	27.23	odd	18
27.4.e.a.25.2	yes	48	9.2	odd	6
81.4.e.a.10.7		48	27.4	even	9
81.4.e.a.73.7		48	9.7	even	3
243.4.e.a.55.2		48	9.4	even	3
243.4.e.a.190.2		48	27.13	even	9
243.4.e.b.109.7		48	27.22	even	9	inner
243.4.e.b.136.7		48	1.1	even	1	trivial
243.4.e.c.109.2		48	27.5	odd	18
243.4.e.c.136.2		48	3.2	odd	2
243.4.e.d.55.7		48	9.5	odd	6
243.4.e.d.190.7		48	27.14	odd	18
729.4.a.c.1.19		24	27.7	even	9
729.4.a.d.1.6		24	27.20	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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	243.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.61428 + 2.19364i) q^{2} +(0.633205 + 3.59108i) q^{4} +(-10.3200 - 3.75618i) q^{5} +(-0.765086 + 4.33902i) q^{7} +(7.42861 - 12.8667i) q^{8} +O(q^{10})\)	\(q+(2.61428 + 2.19364i) q^{2} +(0.633205 + 3.59108i) q^{4} +(-10.3200 - 3.75618i) q^{5} +(-0.765086 + 4.33902i) q^{7} +(7.42861 - 12.8667i) q^{8} +(-18.7397 - 32.4581i) q^{10} +(54.1997 - 19.7271i) q^{11} +(30.0290 - 25.1973i) q^{13} +(-11.5184 + 9.66507i) q^{14} +(75.0580 - 27.3189i) q^{16} +(44.7356 + 77.4844i) q^{17} +(29.6770 - 51.4022i) q^{19} +(6.95407 - 39.4385i) q^{20} +(184.967 + 67.3225i) q^{22} +(3.97027 + 22.5165i) q^{23} +(-3.36157 - 2.82069i) q^{25} +133.778 q^{26} -16.0662 q^{28} +(45.1257 + 37.8649i) q^{29} +(-57.9966 - 328.915i) q^{31} +(144.460 + 52.5792i) q^{32} +(-53.0214 + 300.699i) q^{34} +(24.1938 - 41.9050i) q^{35} +(-47.4944 - 82.2627i) q^{37} +(190.342 - 69.2787i) q^{38} +(-124.993 + 104.882i) q^{40} +(277.092 - 232.508i) q^{41} +(-443.174 + 161.302i) q^{43} +(105.161 + 182.144i) q^{44} +(-39.0137 + 67.5738i) q^{46} +(-41.1310 + 233.266i) q^{47} +(304.073 + 110.673i) q^{49} +(-2.60049 - 14.7481i) q^{50} +(109.500 + 91.8815i) q^{52} -391.866 q^{53} -633.441 q^{55} +(50.1455 + 42.0770i) q^{56} +(34.9090 + 197.979i) q^{58} +(526.804 + 191.741i) q^{59} +(29.3061 - 166.203i) q^{61} +(569.902 - 987.099i) q^{62} +(-57.1812 - 99.0407i) q^{64} +(-404.545 + 147.242i) q^{65} +(-416.993 + 349.898i) q^{67} +(-249.926 + 209.713i) q^{68} +(155.174 - 56.4786i) q^{70} +(97.0579 + 168.109i) q^{71} +(-80.6653 + 139.716i) q^{73} +(56.2911 - 319.243i) q^{74} +(203.381 + 74.0247i) q^{76} +(44.1287 + 250.266i) q^{77} +(278.476 + 233.669i) q^{79} -877.215 q^{80} +1234.43 q^{82} +(432.830 + 363.187i) q^{83} +(-170.627 - 967.676i) q^{85} +(-1512.42 - 550.475i) q^{86} +(148.805 - 843.918i) q^{88} +(-187.611 + 324.952i) q^{89} +(86.3568 + 149.574i) q^{91} +(-78.3448 + 28.5152i) q^{92} +(-619.228 + 519.594i) q^{94} +(-499.344 + 418.999i) q^{95} +(548.136 - 199.505i) q^{97} +(552.153 + 956.357i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 3 q^{2} + 3 q^{4} + 21 q^{5} + 3 q^{7} + 75 q^{8}+O(q^{10}) \) 48 * q - 3 * q^2 + 3 * q^4 + 21 * q^5 + 3 * q^7 + 75 * q^8	\( 48 q - 3 q^{2} + 3 q^{4} + 21 q^{5} + 3 q^{7} + 75 q^{8} - 3 q^{10} + 159 q^{11} + 3 q^{13} + 336 q^{14} - 45 q^{16} + 207 q^{17} - 3 q^{19} - 681 q^{20} + 111 q^{22} - 33 q^{23} + 435 q^{25} - 1914 q^{26} - 12 q^{28} + 51 q^{29} + 111 q^{31} - 1647 q^{32} - 513 q^{34} + 1257 q^{35} - 3 q^{37} + 525 q^{38} - 6 q^{40} - 447 q^{41} + 516 q^{43} + 2211 q^{44} - 3 q^{46} - 2109 q^{47} - 591 q^{49} + 4938 q^{50} - 1350 q^{52} - 2736 q^{53} - 12 q^{55} + 7773 q^{56} - 888 q^{58} - 3048 q^{59} + 57 q^{61} + 2118 q^{62} - 195 q^{64} - 3297 q^{65} + 2082 q^{67} - 3573 q^{68} + 1524 q^{70} + 3105 q^{71} - 219 q^{73} - 9006 q^{74} - 1425 q^{76} + 8985 q^{77} - 1401 q^{79} - 9870 q^{80} - 12 q^{82} + 8511 q^{83} - 1827 q^{85} - 12507 q^{86} - 3693 q^{88} + 5202 q^{89} + 267 q^{91} - 5118 q^{92} - 2211 q^{94} - 5178 q^{95} + 1569 q^{97} + 4392 q^{98}+O(q^{100}) \) 48 * q - 3 * q^2 + 3 * q^4 + 21 * q^5 + 3 * q^7 + 75 * q^8 - 3 * q^10 + 159 * q^11 + 3 * q^13 + 336 * q^14 - 45 * q^16 + 207 * q^17 - 3 * q^19 - 681 * q^20 + 111 * q^22 - 33 * q^23 + 435 * q^25 - 1914 * q^26 - 12 * q^28 + 51 * q^29 + 111 * q^31 - 1647 * q^32 - 513 * q^34 + 1257 * q^35 - 3 * q^37 + 525 * q^38 - 6 * q^40 - 447 * q^41 + 516 * q^43 + 2211 * q^44 - 3 * q^46 - 2109 * q^47 - 591 * q^49 + 4938 * q^50 - 1350 * q^52 - 2736 * q^53 - 12 * q^55 + 7773 * q^56 - 888 * q^58 - 3048 * q^59 + 57 * q^61 + 2118 * q^62 - 195 * q^64 - 3297 * q^65 + 2082 * q^67 - 3573 * q^68 + 1524 * q^70 + 3105 * q^71 - 219 * q^73 - 9006 * q^74 - 1425 * q^76 + 8985 * q^77 - 1401 * q^79 - 9870 * q^80 - 12 * q^82 + 8511 * q^83 - 1827 * q^85 - 12507 * q^86 - 3693 * q^88 + 5202 * q^89 + 267 * q^91 - 5118 * q^92 - 2211 * q^94 - 5178 * q^95 + 1569 * q^97 + 4392 * q^98

Introduction

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