LMFDB - Embedded newform 162.4.e.a.19.4

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			19.4
Character	$\chi$	$=$	162.19
Dual form			162.4.e.a.145.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.87939 - 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(2.50669 + 14.2161i) q^{5} +(0.855575 + 0.717913i) q^{7} +(4.00000 - 6.92820i) q^{8} +O(q^{10})$	\(q+(1.87939 - 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(2.50669 + 14.2161i) q^{5} +(0.855575 + 0.717913i) q^{7} +(4.00000 - 6.92820i) q^{8} +(14.4354 + 25.0029i) q^{10} +(-7.01766 + 39.7991i) q^{11} +(54.5985 + 19.8722i) q^{13} +(2.09904 + 0.763987i) q^{14} +(2.77837 - 15.7569i) q^{16} +(-4.91345 - 8.51035i) q^{17} +(-52.1806 + 90.3795i) q^{19} +(44.2328 + 37.1157i) q^{20} +(14.0353 + 79.5982i) q^{22} +(72.7227 - 61.0216i) q^{23} +(-78.3534 + 28.5183i) q^{25} +116.205 q^{26} +4.46750 q^{28} +(254.197 - 92.5203i) q^{29} +(70.1181 - 58.8361i) q^{31} +(-5.55674 - 31.5138i) q^{32} +(-15.0557 - 12.6332i) q^{34} +(-8.06128 + 13.9626i) q^{35} +(-59.5071 - 103.069i) q^{37} +(-36.2443 + 205.552i) q^{38} +(108.519 + 39.4977i) q^{40} +(-483.315 - 175.912i) q^{41} +(-93.2087 + 528.613i) q^{43} +(80.8261 + 139.995i) q^{44} +(94.9328 - 164.428i) q^{46} +(-32.1596 - 26.9851i) q^{47} +(-59.3447 - 336.561i) q^{49} +(-127.748 + 107.194i) q^{50} +(218.394 - 79.4888i) q^{52} +25.9337 q^{53} -583.380 q^{55} +(8.39615 - 3.05595i) q^{56} +(414.447 - 347.762i) q^{58} +(-103.921 - 589.363i) q^{59} +(-220.481 - 185.006i) q^{61} +(91.5327 - 158.539i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(-145.645 + 825.992i) q^{65} +(413.370 + 150.454i) q^{67} +(-36.9371 - 13.4440i) q^{68} +(-5.59931 + 31.7553i) q^{70} +(-114.284 - 197.945i) q^{71} +(472.425 - 818.264i) q^{73} +(-182.340 - 153.002i) q^{74} +(72.4886 + 411.103i) q^{76} +(-34.5764 + 29.0131i) q^{77} +(-583.884 + 212.516i) q^{79} +230.967 q^{80} -1028.67 q^{82} +(-734.263 + 267.250i) q^{83} +(108.668 - 91.1831i) q^{85} +(186.417 + 1057.23i) q^{86} +(247.666 + 207.816i) q^{88} +(507.530 - 879.069i) q^{89} +(32.4466 + 56.1991i) q^{91} +(65.9396 - 373.962i) q^{92} +(-78.8992 - 28.7169i) q^{94} +(-1415.65 - 515.254i) q^{95} +(-28.9437 + 164.148i) q^{97} +(-341.753 - 591.933i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.50669	+	14.2161i	0.224205	+	1.27153i	0.864199	+	0.503150i	$0.167826\pi$
$5$	2.50669	+	14.2161i	0.224205	+	1.27153i	−0.639994	+	0.768380i	$0.721063\pi$
$6$		0			0
$7$	0.855575	+	0.717913i	0.0461967	+	0.0387636i	0.665594	−	0.746314i	$-0.268178\pi$
$7$	0.855575	+	0.717913i	0.0461967	+	0.0387636i	−0.619397	+	0.785078i	$0.712623\pi$
$8$	4.00000	−	6.92820i	0.176777	−	0.306186i
$9$		0			0
$10$	14.4354	+	25.0029i	0.456489	+	0.790662i
$11$	−7.01766	+	39.7991i	−0.192355	+	1.09090i	0.723781	+	0.690030i	$0.242403\pi$
$11$	−7.01766	+	39.7991i	−0.192355	+	1.09090i	−0.916136	+	0.400868i	$0.868708\pi$
$12$		0			0
$13$	54.5985	+	19.8722i	1.16484	+	0.423966i	0.850823	−	0.525452i	$-0.176104\pi$
$13$	54.5985	+	19.8722i	1.16484	+	0.423966i	0.314014	+	0.949418i	$0.398326\pi$
$14$	2.09904	+	0.763987i	0.0400708	+	0.0145846i
$15$		0			0
$16$	2.77837	−	15.7569i	0.0434120	−	0.246202i
$17$	−4.91345	−	8.51035i	−0.0700993	−	0.121415i	0.828845	−	0.559478i	$-0.188998\pi$
$17$	−4.91345	−	8.51035i	−0.0700993	−	0.121415i	−0.898945	+	0.438062i	$0.855665\pi$
$18$		0			0
$19$	−52.1806	+	90.3795i	−0.630056	+	1.09129i	0.357484	+	0.933919i	$0.383635\pi$
$19$	−52.1806	+	90.3795i	−0.630056	+	1.09129i	−0.987540	+	0.157369i	$0.949699\pi$
$20$	44.2328	+	37.1157i	0.494537	+	0.414966i
$21$		0			0
$22$	14.0353	+	79.5982i	0.136015	+	0.771382i
$23$	72.7227	−	61.0216i	0.659293	−	0.553213i	−0.250582	−	0.968095i	$-0.580622\pi$
$23$	72.7227	−	61.0216i	0.659293	−	0.553213i	0.909875	+	0.414883i	$0.136177\pi$
$24$		0			0
$25$	−78.3534	+	28.5183i	−0.626827	+	0.228146i
$26$	116.205			0.876525
$27$		0			0
$28$	4.46750			0.0301528
$29$	254.197	−	92.5203i	1.62770	−	0.592434i	0.642872	−	0.765974i	$-0.277743\pi$
$29$	254.197	−	92.5203i	1.62770	−	0.592434i	0.984827	+	0.173540i	$0.0555205\pi$
$30$		0			0
$31$	70.1181	−	58.8361i	0.406245	−	0.340880i	−0.416657	−	0.909064i	$-0.636798\pi$
$31$	70.1181	−	58.8361i	0.406245	−	0.340880i	0.822901	+	0.568184i	$0.192354\pi$
$32$	−5.55674	−	31.5138i	−0.0306970	−	0.174091i
$33$		0			0
$34$	−15.0557	−	12.6332i	−0.0759421	−	0.0637230i
$35$	−8.06128	+	13.9626i	−0.0389316	+	0.0674315i
$36$		0			0
$37$	−59.5071	−	103.069i	−0.264403	−	0.457959i	0.703004	−	0.711186i	$-0.251842\pi$
$37$	−59.5071	−	103.069i	−0.264403	−	0.457959i	−0.967407	+	0.253227i	$0.918508\pi$
$38$	−36.2443	+	205.552i	−0.154726	+	0.877497i
$39$		0			0
$40$	108.519	+	39.4977i	0.428959	+	0.156128i
$41$	−483.315	−	175.912i	−1.84100	−	0.670070i	−0.989271	−	0.146091i	$-0.953331\pi$
$41$	−483.315	−	175.912i	−1.84100	−	0.670070i	−0.851731	−	0.523979i	$-0.824447\pi$
$42$		0			0
$43$	−93.2087	+	528.613i	−0.330563	+	1.87471i	0.136726	+	0.990609i	$0.456342\pi$
$43$	−93.2087	+	528.613i	−0.330563	+	1.87471i	−0.467288	+	0.884105i	$0.654769\pi$
$44$	80.8261	+	139.995i	0.276932	+	0.479660i
$45$		0			0
$46$	94.9328	−	164.428i	0.304284	−	0.527036i
$47$	−32.1596	−	26.9851i	−0.0998076	−	0.0837486i	0.591518	−	0.806292i	$-0.298529\pi$
$47$	−32.1596	−	26.9851i	−0.0998076	−	0.0837486i	−0.691326	+	0.722543i	$0.742973\pi$
$48$		0			0
$49$	−59.3447	−	336.561i	−0.173017	−	0.981226i
$50$	−127.748	+	107.194i	−0.361327	+	0.303190i
$51$		0			0
$52$	218.394	−	79.4888i	0.582419	−	0.211983i
$53$	25.9337			0.0672125			0.0336063	−	0.999435i	$-0.489301\pi$
$53$	25.9337			0.0672125			0.0336063	+	0.999435i	$0.489301\pi$
$54$		0			0
$55$	−583.380			−1.43024
$56$	8.39615	−	3.05595i	0.0200354	−	0.00729229i
$57$		0			0
$58$	414.447	−	347.762i	0.938269	−	0.787301i
$59$	−103.921	−	589.363i	−0.229310	−	1.30048i	−0.854271	−	0.519827i	$-0.825996\pi$
$59$	−103.921	−	589.363i	−0.229310	−	1.30048i	0.624961	−	0.780656i	$-0.285115\pi$
$60$		0			0
$61$	−220.481	−	185.006i	−0.462783	−	0.388321i	0.381371	−	0.924422i	$-0.375452\pi$
$61$	−220.481	−	185.006i	−0.462783	−	0.388321i	−0.844154	+	0.536101i	$0.819897\pi$
$62$	91.5327	−	158.539i	0.187495	−	0.324750i
$63$		0			0
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	−145.645	+	825.992i	−0.277923	+	1.57618i
$66$		0			0
$67$	413.370	+	150.454i	0.753748	+	0.274342i	0.690182	−	0.723636i	$-0.257530\pi$
$67$	413.370	+	150.454i	0.753748	+	0.274342i	0.0635662	+	0.997978i	$0.479753\pi$
$68$	−36.9371	−	13.4440i	−0.0658718	−	0.0239754i
$69$		0			0
$70$	−5.59931	+	31.7553i	−0.00956065	+	0.0542211i
$71$	−114.284	−	197.945i	−0.191028	−	0.330871i	0.754563	−	0.656228i	$-0.227849\pi$
$71$	−114.284	−	197.945i	−0.191028	−	0.330871i	−0.945591	+	0.325357i	$0.894516\pi$
$72$		0			0
$73$	472.425	−	818.264i	0.757441	−	1.31193i	−0.186711	−	0.982415i	$-0.559783\pi$
$73$	472.425	−	818.264i	0.757441	−	1.31193i	0.944152	−	0.329511i	$-0.106884\pi$
$74$	−182.340	−	153.002i	−0.286441	−	0.240353i
$75$		0			0
$76$	72.4886	+	411.103i	0.109408	+	0.620484i
$77$	−34.5764	+	29.0131i	−0.0511734	+	0.0429396i
$78$		0			0
$79$	−583.884	+	212.516i	−0.831545	+	0.302658i	−0.722493	−	0.691378i	$-0.757004\pi$
$79$	−583.884	+	212.516i	−0.831545	+	0.302658i	−0.109052	+	0.994036i	$0.534782\pi$
$80$	230.967			0.322786
$81$		0			0
$82$	−1028.67			−1.38533
$83$	−734.263	+	267.250i	−0.971034	+	0.353427i	−0.778348	−	0.627833i	$-0.783942\pi$
$83$	−734.263	+	267.250i	−0.971034	+	0.353427i	−0.192686	+	0.981261i	$0.561720\pi$
$84$		0			0
$85$	108.668	−	91.1831i	0.138667	−	0.116355i
$86$	186.417	+	1057.23i	0.233743	+	1.32562i
$87$		0			0
$88$	247.666	+	207.816i	0.300014	+	0.251742i
$89$	507.530	−	879.069i	0.604473	−	1.04698i	−0.387661	−	0.921802i	$-0.626717\pi$
$89$	507.530	−	879.069i	0.604473	−	1.04698i	0.992134	−	0.125177i	$-0.0399497\pi$
$90$		0			0
$91$	32.4466	+	56.1991i	0.0373772	+	0.0647392i
$92$	65.9396	−	373.962i	0.0747248	−	0.423785i
$93$		0			0
$94$	−78.8992	−	28.7169i	−0.0865726	−	0.0315099i
$95$	−1415.65	−	515.254i	−1.52887	−	0.556462i
$96$		0			0
$97$	−28.9437	+	164.148i	−0.0302968	+	0.171822i	−0.996202	−	0.0870754i	$-0.972248\pi$
$97$	−28.9437	+	164.148i	−0.0302968	+	0.171822i	0.965905	+	0.258897i	$0.0833590\pi$
$98$	−341.753	−	591.933i	−0.352268	−	0.610145i
$99$		0			0
$100$	−166.764	+	288.843i	−0.166764	+	0.288843i
$101$	926.967	+	777.818i	0.913234	+	0.766295i	0.972732	−	0.231934i	$-0.0745053\pi$
$101$	926.967	+	777.818i	0.913234	+	0.766295i	−0.0594972	+	0.998228i	$0.518950\pi$
$102$		0			0
$103$	−178.887	−	1014.52i	−0.171129	−	0.970521i	−0.942518	−	0.334157i	$-0.891549\pi$
$103$	−178.887	−	1014.52i	−0.171129	−	0.970521i	0.771388	−	0.636365i	$-0.219563\pi$
$104$	356.073	−	298.780i	0.335729	−	0.281710i
$105$		0			0
$106$	48.7394	−	17.7397i	0.0446603	−	0.0162550i
$107$	243.322			0.219839			0.109920	−	0.993940i	$-0.464941\pi$
$107$	243.322			0.219839			0.109920	+	0.993940i	$0.464941\pi$
$108$		0			0
$109$	313.673			0.275637			0.137818	−	0.990458i	$-0.455991\pi$
$109$	313.673			0.275637			0.137818	+	0.990458i	$0.455991\pi$
$110$	−1096.40	+	399.056i	−0.950339	+	0.345895i
$111$		0			0
$112$	13.6892	−	11.4866i	0.0115492	−	0.00969091i
$113$	189.236	+	1073.21i	0.157538	+	0.893445i	0.956428	+	0.291968i	$0.0943100\pi$
$113$	189.236	+	1073.21i	0.157538	+	0.893445i	−0.798890	+	0.601478i	$0.794579\pi$
$114$		0			0
$115$	1049.78	+	880.874i	0.851243	+	0.714278i
$116$	541.022	−	937.078i	0.433040	−	0.750048i
$117$		0			0
$118$	−598.455	−	1036.55i	−0.466883	−	0.808665i
$119$	1.90586	−	10.8087i	0.00146815	−	0.00832630i
$120$		0			0
$121$	−283.991	−	103.364i	−0.213366	−	0.0776590i
$122$	−540.921	−	196.879i	−0.401416	−	0.146103i
$123$		0			0
$124$	63.5780	−	360.568i	0.0460441	−	0.261129i
$125$	300.388	+	520.287i	0.214940	+	0.372287i
$126$		0			0
$127$	1068.81	−	1851.23i	0.746784	−	1.29347i	−0.202572	−	0.979267i	$-0.564930\pi$
$127$	1068.81	−	1851.23i	0.746784	−	1.29347i	0.949356	−	0.314201i	$-0.101737\pi$
$128$	−98.0537	−	82.2768i	−0.0677094	−	0.0568149i
$129$		0			0
$130$	291.289	+	1651.98i	0.196521	+	1.11453i
$131$	1293.07	−	1085.01i	0.862413	−	0.723650i	−0.100074	−	0.994980i	$-0.531908\pi$
$131$	1293.07	−	1085.01i	0.862413	−	0.723650i	0.962486	+	0.271330i	$0.0874634\pi$
$132$		0			0
$133$	−109.529	+	39.8653i	−0.0714088	+	0.0259907i
$134$	879.798			0.567186
$135$		0			0
$136$	−78.6152			−0.0495677
$137$	1907.94	−	694.432i	1.18983	−	0.433061i	0.330163	−	0.943924i	$-0.392896\pi$
$137$	1907.94	−	694.432i	1.18983	−	0.433061i	0.859662	+	0.510863i	$0.170674\pi$
$138$		0			0
$139$	−1043.96	+	875.986i	−0.637032	+	0.534534i	−0.903105	−	0.429419i	$-0.858718\pi$
$139$	−1043.96	+	875.986i	−0.637032	+	0.534534i	0.266073	+	0.963953i	$0.414274\pi$
$140$	11.1986	+	63.5105i	0.00676040	+	0.0383401i
$141$		0			0
$142$	−350.186	−	293.841i	−0.206950	−	0.173652i
$143$	−1174.05	+	2033.51i	−0.686566	+	1.18917i
$144$		0			0
$145$	1952.47	+	3381.78i	1.11824	+	1.93684i
$146$	328.143	−	1860.99i	0.186009	−	1.05491i
$147$		0			0
$148$	−447.347	−	162.821i	−0.248457	−	0.0904311i
$149$	1687.63	+	614.247i	0.927892	+	0.337725i	0.761374	−	0.648313i	$-0.224525\pi$
$149$	1687.63	+	614.247i	0.927892	+	0.337725i	0.166519	+	0.986038i	$0.446747\pi$
$150$		0			0
$151$	−485.297	+	2752.25i	−0.261542	+	1.48328i	0.517162	+	0.855888i	$0.326989\pi$
$151$	−485.297	+	2752.25i	−0.261542	+	1.48328i	−0.778704	+	0.627392i	$0.784123\pi$
$152$	417.445	+	723.036i	0.222758	+	0.385829i
$153$		0			0
$154$	−45.1363	+	78.1784i	−0.0236181	+	0.0409078i
$155$	1012.19	+	849.325i	0.524521	+	0.440125i
$156$		0			0
$157$	33.7892	+	191.628i	0.0171763	+	0.0974115i	0.992191	−	0.124730i	$-0.0398064\pi$
$157$	33.7892	+	191.628i	0.0171763	+	0.0974115i	−0.975014	+	0.222141i	$0.928695\pi$
$158$	−951.973	+	798.800i	−0.479335	+	0.402210i
$159$		0			0
$160$	434.076	−	157.991i	0.214480	−	0.0780642i
$161$	106.028			0.0519017
$162$		0			0
$163$	−1675.93			−0.805331			−0.402666	−	0.915347i	$-0.631916\pi$
$163$	−1675.93			−0.805331			−0.402666	+	0.915347i	$0.631916\pi$
$164$	−1933.26	+	703.649i	−0.920501	+	0.335035i
$165$		0			0
$166$	−1197.15	+	1004.53i	−0.559741	+	0.469679i
$167$	−2.47417	−	14.0317i	−0.00114645	−	0.00650185i	0.984229	−	0.176898i	$-0.0566063\pi$
$167$	−2.47417	−	14.0317i	−0.00114645	−	0.00650185i	−0.985376	+	0.170396i	$0.945495\pi$
$168$		0			0
$169$	903.087	+	757.780i	0.411054	+	0.344916i
$170$	141.856	−	245.701i	0.0639990	−	0.110850i
$171$		0			0
$172$	1073.54	+	1859.42i	0.475909	+	0.824298i
$173$	191.383	−	1085.39i	0.0841074	−	0.476996i	−0.913438	−	0.406977i	$-0.866583\pi$
$173$	191.383	−	1085.39i	0.0841074	−	0.476996i	0.997546	−	0.0700192i	$-0.0223061\pi$
$174$		0			0
$175$	−87.5108	−	31.8513i	−0.0378011	−	0.0137585i
$176$	607.614	+	221.153i	0.260231	+	0.0947163i
$177$		0			0
$178$	352.527	−	1999.28i	0.148444	−	0.841867i
$179$	349.627	+	605.572i	0.145991	+	0.252864i	0.929742	−	0.368211i	$-0.120030\pi$
$179$	349.627	+	605.572i	0.145991	+	0.252864i	−0.783751	+	0.621075i	$0.786696\pi$
$180$		0			0
$181$	689.175	−	1193.69i	0.283016	−	0.490199i	−0.689110	−	0.724657i	$-0.741998\pi$
$181$	689.175	−	1193.69i	0.283016	−	0.490199i	0.972126	+	0.234458i	$0.0753316\pi$
$182$	99.4220	+	83.4250i	0.0404926	+	0.0339773i
$183$		0			0
$184$	−131.879	−	747.924i	−0.0528384	−	0.299662i
$185$	1316.08	−	1104.32i	0.523028	−	0.438873i
$186$		0			0
$187$	373.185	−	135.828i	0.145936	−	0.0531163i
$188$	−167.925			−0.0651448
$189$		0			0
$190$	−3013.00			−1.15045
$191$	686.511	−	249.869i	0.260074	−	0.0946592i	−0.208692	−	0.977981i	$-0.566921\pi$
$191$	686.511	−	249.869i	0.260074	−	0.0946592i	0.468767	+	0.883322i	$0.344699\pi$
$192$		0			0
$193$	3449.69	−	2894.63i	1.28660	−	1.07959i	0.294303	−	0.955712i	$-0.404913\pi$
$193$	3449.69	−	2894.63i	1.28660	−	1.07959i	0.992298	−	0.123874i	$-0.0395318\pi$
$194$	57.8874	+	328.296i	0.0214231	+	0.121496i
$195$		0			0
$196$	−1047.19	−	878.697i	−0.381629	−	0.320225i
$197$	−1660.03	+	2875.26i	−0.600366	+	1.03987i	0.392399	+	0.919795i	$0.371645\pi$
$197$	−1660.03	+	2875.26i	−0.600366	+	1.03987i	−0.992765	+	0.120070i	$0.961688\pi$
$198$		0			0
$199$	1873.08	+	3244.27i	0.667231	+	1.15568i	0.978675	+	0.205414i	$0.0658540\pi$
$199$	1873.08	+	3244.27i	0.667231	+	1.15568i	−0.311444	+	0.950265i	$0.600813\pi$
$200$	−115.833	+	656.921i	−0.0409531	+	0.232257i
$201$		0			0
$202$	2274.19	+	827.736i	0.792135	+	0.288313i
$203$	283.906	+	103.333i	0.0981592	+	0.0357270i
$204$		0			0
$205$	1289.27	−	7311.83i	0.439252	−	2.49112i
$206$	−1030.17	−	1784.31i	−0.348424	−	0.603489i
$207$		0			0
$208$	464.820	−	805.091i	0.154949	−	0.268380i
$209$	−3230.84	−	2711.00i	−1.06929	−	0.897241i
$210$		0			0
$211$	−193.037	−	1094.77i	−0.0629820	−	0.357189i	−0.999969	−	0.00782555i	$-0.997509\pi$
$211$	−193.037	−	1094.77i	−0.0629820	−	0.357189i	0.936987	−	0.349363i	$-0.113602\pi$
$212$	79.4654	−	66.6794i	0.0257439	−	0.0216017i
$213$		0			0
$214$	457.295	−	166.442i	0.146075	−	0.0531670i
$215$	−7748.48			−2.45787
$216$		0			0
$217$	102.231			0.0319809
$218$	589.512	−	214.565i	0.183150	−	0.0666613i
$219$		0			0
$220$	−1787.58	+	1499.96i	−0.547812	+	0.459669i
$221$	−99.1475	−	562.293i	−0.0301782	−	0.171149i
$222$		0			0
$223$	−4613.43	−	3871.13i	−1.38537	−	1.16247i	−0.967175	−	0.254111i	$-0.918217\pi$
$223$	−4613.43	−	3871.13i	−1.38537	−	1.16247i	−0.418199	−	0.908355i	$-0.637338\pi$
$224$	17.8700	−	30.9517i	0.00533031	−	0.00923236i
$225$		0			0
$226$	1089.77	+	1887.53i	0.320754	+	0.555561i
$227$	−270.708	+	1535.26i	−0.0791521	+	0.448894i	0.919314	+	0.393525i	$0.128745\pi$
$227$	−270.708	+	1535.26i	−0.0791521	+	0.448894i	−0.998466	+	0.0553687i	$0.982367\pi$
$228$		0			0
$229$	−4207.42	−	1531.37i	−1.21412	−	0.441904i	−0.345990	−	0.938238i	$-0.612457\pi$
$229$	−4207.42	−	1531.37i	−1.21412	−	0.441904i	−0.868132	+	0.496334i	$0.834679\pi$
$230$	2575.50	+	937.407i	0.738364	+	0.268742i
$231$		0			0
$232$	375.790	−	2131.21i	0.106344	−	0.603107i
$233$	−699.083	−	1210.85i	−0.196560	−	0.340452i	0.750851	−	0.660472i	$-0.229644\pi$
$233$	−699.083	−	1210.85i	−0.196560	−	0.340452i	−0.947411	+	0.320020i	$0.896310\pi$
$234$		0			0
$235$	303.010	−	524.828i	0.0841114	−	0.145685i
$236$	−1833.77	−	1538.72i	−0.505798	−	0.424415i
$237$		0			0
$238$	−3.81172	−	21.6173i	−0.00103814	−	0.00588758i
$239$	−880.905	+	739.167i	−0.238414	+	0.200053i	−0.754164	−	0.656686i	$-0.771958\pi$
$239$	−880.905	+	739.167i	−0.238414	+	0.200053i	0.515750	+	0.856739i	$0.327513\pi$
$240$		0			0
$241$	−3147.60	+	1145.63i	−0.841305	+	0.306210i	−0.726490	−	0.687177i	$-0.758850\pi$
$241$	−3147.60	+	1145.63i	−0.841305	+	0.306210i	−0.114815	+	0.993387i	$0.536628\pi$
$242$	−604.433			−0.160555
$243$		0			0
$244$	−1151.27			−0.302060
$245$	4635.83	−	1687.30i	1.20887	−	0.439992i
$246$		0			0
$247$	−4645.02	+	3897.64i	−1.19658	+	1.00405i
$248$	−127.156	−	721.137i	−0.0325581	−	0.184646i
$249$		0			0
$250$	920.442	+	772.342i	0.232855	+	0.195389i
$251$	−531.035	+	919.780i	−0.133540	+	0.231299i	−0.925039	−	0.379872i	$-0.875968\pi$
$251$	−531.035	+	919.780i	−0.133540	+	0.231299i	0.791498	+	0.611171i	$0.209301\pi$
$252$		0			0
$253$	1918.26	+	3322.53i	0.476681	+	0.825635i
$254$	742.388	−	4210.29i	0.183392	−	1.04007i
$255$		0			0
$256$	−240.561	−	87.5572i	−0.0587308	−	0.0213763i
$257$	−1003.65	−	365.297i	−0.243602	−	0.0886638i	0.217334	−	0.976097i	$-0.430264\pi$
$257$	−1003.65	−	365.297i	−0.243602	−	0.0886638i	−0.460936	+	0.887433i	$0.652486\pi$
$258$		0			0
$259$	23.0820	−	130.904i	0.00553762	−	0.0314054i
$260$	1677.47	+	2905.46i	0.400124	+	0.693035i
$261$		0			0
$262$	1687.98	−	2923.67i	0.398030	−	0.689409i
$263$	−4064.50	−	3410.52i	−0.952959	−	0.799627i	0.0268348	−	0.999640i	$-0.491457\pi$
$263$	−4064.50	−	3410.52i	−0.952959	−	0.799627i	−0.979793	+	0.200013i	$0.935902\pi$
$264$		0			0
$265$	65.0076	+	368.677i	0.0150694	+	0.0854627i
$266$	−178.578	+	149.845i	−0.0411628	+	0.0345397i
$267$		0			0
$268$	1653.48	−	601.817i	0.376874	−	0.137171i
$269$	3416.76			0.774437			0.387218	−	0.921988i	$-0.373436\pi$
$269$	3416.76			0.774437			0.387218	+	0.921988i	$0.373436\pi$
$270$		0			0
$271$	−1903.98			−0.426784			−0.213392	−	0.976967i	$-0.568451\pi$
$271$	−1903.98			−0.426784			−0.213392	+	0.976967i	$0.568451\pi$
$272$	−147.748	+	53.7760i	−0.0329359	+	0.0119877i
$273$		0			0
$274$	3110.73	−	2610.21i	0.685861	−	0.575506i
$275$	−585.146	−	3318.53i	−0.128311	−	0.727689i
$276$		0			0
$277$	707.314	+	593.507i	0.153424	+	0.128738i	0.716268	−	0.697825i	$-0.245849\pi$
$277$	707.314	+	593.507i	0.153424	+	0.128738i	−0.562845	+	0.826563i	$0.690293\pi$
$278$	−1362.79	+	2360.43i	−0.294010	+	0.509241i
$279$		0			0
$280$	64.4903	+	111.700i	0.0137644	+	0.0238406i
$281$	−379.919	+	2154.63i	−0.0806550	+	0.457417i	0.917555	+	0.397609i	$0.130160\pi$
$281$	−379.919	+	2154.63i	−0.0806550	+	0.457417i	−0.998210	+	0.0598082i	$0.980951\pi$
$282$		0			0
$283$	−6581.17	−	2395.35i	−1.38237	−	0.503140i	−0.459472	−	0.888192i	$-0.651961\pi$
$283$	−6581.17	−	2395.35i	−1.38237	−	0.503140i	−0.922895	+	0.385052i	$0.874184\pi$
$284$	−859.134	−	312.699i	−0.179508	−	0.0653355i
$285$		0			0
$286$	−815.486	+	4624.85i	−0.168604	+	0.956200i
$287$	−287.223	−	497.484i	−0.0590739	−	0.102319i
$288$		0			0
$289$	2408.22	−	4171.15i	0.490172	−	0.849003i
$290$	5982.73	+	5020.10i	1.21144	+	1.01652i
$291$		0			0
$292$	−656.286	−	3721.98i	−0.131528	−	0.745934i
$293$	−2406.75	+	2019.51i	−0.479877	+	0.402665i	−0.850382	−	0.526166i	$-0.823629\pi$
$293$	−2406.75	+	2019.51i	−0.479877	+	0.402665i	0.370505	+	0.928831i	$0.379185\pi$
$294$		0			0
$295$	8117.96	−	2954.70i	1.60219	−	0.583149i
$296$	−952.114			−0.186961
$297$		0			0
$298$	3591.88			0.698227
$299$	5183.18	−	1886.52i	1.00251	−	0.364885i
$300$		0			0
$301$	−459.245	+	385.352i	−0.0879417	+	0.0737918i
$302$	970.593	+	5504.51i	0.184938	+	1.04884i
$303$		0			0
$304$	1279.13	+	1073.31i	0.241325	+	0.202496i
$305$	2077.39	−	3598.15i	0.390003	−	0.675506i
$306$		0			0
$307$	838.413	+	1452.17i	0.155866	+	0.269967i	0.933374	−	0.358905i	$-0.116850\pi$
$307$	838.413	+	1452.17i	0.155866	+	0.269967i	−0.777508	+	0.628873i	$0.783517\pi$
$308$	−31.3514	+	177.802i	−0.00580003	+	0.0328936i
$309$		0			0
$310$	2483.26	+	903.833i	0.454967	+	0.165594i
$311$	2656.43	+	966.863i	0.484349	+	0.176289i	0.572641	−	0.819806i	$-0.305919\pi$
$311$	2656.43	+	966.863i	0.484349	+	0.176289i	−0.0882924	+	0.996095i	$0.528141\pi$
$312$		0			0
$313$	−947.076	+	5371.14i	−0.171028	+	0.969951i	0.771600	+	0.636108i	$0.219457\pi$
$313$	−947.076	+	5371.14i	−0.171028	+	0.969951i	−0.942629	+	0.333843i	$0.891654\pi$
$314$	194.585	+	337.030i	0.0349715	+	0.0605723i
$315$		0			0
$316$	−1242.71	+	2152.44i	−0.221228	+	0.383178i
$317$	−3847.11	−	3228.11i	−0.681625	−	0.571951i	0.234856	−	0.972030i	$-0.424538\pi$
$317$	−3847.11	−	3228.11i	−0.681625	−	0.571951i	−0.916481	+	0.400079i	$0.868983\pi$
$318$		0			0
$319$	1898.35	+	10766.1i	0.333190	+	1.88961i
$320$	707.724	−	593.851i	0.123634	−	0.103741i
$321$		0			0
$322$	199.267	−	72.5274i	0.0344868	−	0.0125522i
$323$	1025.55			0.176666
$324$		0			0
$325$	−4844.69			−0.826878
$326$	−3149.72	+	1146.40i	−0.535113	+	0.194765i
$327$		0			0
$328$	−3152.02	+	2644.85i	−0.530613	+	0.445237i
$329$	−8.14200	−	46.1756i	−0.00136439	−	0.00773782i
$330$		0			0
$331$	1289.64	+	1082.13i	0.214153	+	0.179696i	0.743554	−	0.668676i	$-0.233139\pi$
$331$	1289.64	+	1082.13i	0.214153	+	0.179696i	−0.529400	+	0.848372i	$0.677583\pi$
$332$	−1562.77	+	2706.80i	−0.258338	+	0.447455i
$333$		0			0
$334$	−14.2482	−	24.6786i	−0.00233421	−	0.00404297i
$335$	−1102.69	+	6253.66i	−0.179840	+	1.01992i
$336$		0			0
$337$	10491.3	+	3818.52i	1.69584	+	0.617234i	0.995341	−	0.0964224i	$-0.0307400\pi$
$337$	10491.3	+	3818.52i	1.69584	+	0.617234i	0.700496	+	0.713656i	$0.252962\pi$
$338$	2215.60	+	806.412i	0.356547	+	0.129772i
$339$		0			0
$340$	98.5319	−	558.802i	0.0157166	−	0.0891333i
$341$	1849.56	+	3203.53i	0.293722	+	0.508742i
$342$		0			0
$343$	382.391	−	662.321i	0.0601959	−	0.104262i
$344$	3289.50	+	2760.22i	0.515576	+	0.432619i
$345$		0			0
$346$	−382.766	−	2170.77i	−0.0594729	−	0.337287i
$347$	−1369.30	+	1148.98i	−0.211839	+	0.177754i	−0.742533	−	0.669810i	$-0.766376\pi$
$347$	−1369.30	+	1148.98i	−0.211839	+	0.177754i	0.530694	+	0.847563i	$0.321931\pi$
$348$		0			0
$349$	−5799.72	+	2110.92i	−0.889547	+	0.323769i	−0.746056	−	0.665883i	$-0.768055\pi$
$349$	−5799.72	+	2110.92i	−0.889547	+	0.323769i	−0.143491	+	0.989652i	$0.545833\pi$
$350$	−186.254			−0.0284449
$351$		0			0
$352$	1293.22			0.195820
$353$	−9872.20	+	3593.19i	−1.48851	+	0.541773i	−0.953057	−	0.302791i	$-0.902081\pi$
$353$	−9872.20	+	3593.19i	−1.48851	+	0.541773i	−0.535453	+	0.844565i	$0.679859\pi$
$354$		0			0
$355$	2527.55	−	2120.86i	0.377882	−	0.317081i
$356$	−705.054	−	3998.56i	−0.104966	−	0.595290i
$357$		0			0
$358$	1071.32	+	898.944i	0.158159	+	0.132711i
$359$	4423.23	−	7661.26i	0.650276	−	1.12631i	−0.332780	−	0.943005i	$-0.607987\pi$
$359$	4423.23	−	7661.26i	0.650276	−	1.12631i	0.983056	−	0.183307i	$-0.0586802\pi$
$360$		0			0
$361$	−2016.14	−	3492.05i	−0.293941	−	0.509120i
$362$	478.696	−	2714.82i	0.0695019	−	0.394165i
$363$		0			0
$364$	243.918	+	88.7790i	0.0351231	+	0.0127838i
$365$	12816.8	+	4664.93i	1.83797	+	0.668968i
$366$		0			0
$367$	−1476.06	+	8371.15i	−0.209945	+	1.19066i	0.679522	+	0.733655i	$0.262187\pi$
$367$	−1476.06	+	8371.15i	−0.209945	+	1.19066i	−0.889467	+	0.457000i	$0.848924\pi$
$368$	−759.462	−	1315.43i	−0.107581	−	0.186335i
$369$		0			0
$370$	1718.02	−	2975.70i	0.241394	−	0.418106i
$371$	22.1882	+	18.6181i	0.00310500	+	0.00260540i
$372$		0			0
$373$	−957.026	−	5427.56i	−0.132850	−	0.753428i	−0.976333	−	0.216272i	$-0.930610\pi$
$373$	−957.026	−	5427.56i	−0.132850	−	0.753428i	0.843483	−	0.537155i	$-0.180501\pi$
$374$	608.447	−	510.548i	0.0841231	−	0.0705877i
$375$		0			0
$376$	−315.597	+	114.868i	−0.0432863	+	0.0157549i
$377$	15717.4			2.14718
$378$		0			0
$379$	−5059.38			−0.685706			−0.342853	−	0.939389i	$-0.611393\pi$
$379$	−5059.38			−0.685706			−0.342853	+	0.939389i	$0.611393\pi$
$380$	−5662.59	+	2061.01i	−0.764434	+	0.278231i
$381$		0			0
$382$	1119.30	−	939.202i	0.149917	−	0.125795i
$383$	−549.506	−	3116.40i	−0.0733118	−	0.415772i	−0.999272	−	0.0381509i	$-0.987853\pi$
$383$	−549.506	−	3116.40i	−0.0733118	−	0.415772i	0.925960	−	0.377621i	$-0.123258\pi$
$384$		0			0
$385$	−499.126	−	418.816i	−0.0660722	−	0.0554412i
$386$	4503.25	−	7799.85i	0.593806	−	1.02850i
$387$		0			0
$388$	333.360	+	577.397i	0.0436181	+	0.0755487i
$389$	−1.98599	+	11.2631i	−0.000258853	+	0.00146803i	−0.984937	−	0.172914i	$-0.944682\pi$
$389$	−1.98599	+	11.2631i	−0.000258853	+	0.00146803i	0.984678	+	0.174382i	$0.0557928\pi$
$390$		0			0
$391$	−876.635	−	319.069i	−0.113385	−	0.0412686i
$392$	−2569.14	−	935.090i	−0.331023	−	0.120483i
$393$		0			0
$394$	−1153.04	+	6539.24i	−0.147435	+	0.836147i
$395$	−4484.78	−	7767.86i	−0.571275	−	0.989477i
$396$		0			0
$397$	−4129.97	+	7153.32i	−0.522109	+	0.904320i	0.477560	+	0.878599i	$0.341521\pi$
$397$	−4129.97	+	7153.32i	−0.522109	+	0.904320i	−0.999669	+	0.0257208i	$0.991812\pi$
$398$	5739.45	+	4815.97i	0.722845	+	0.606539i
$399$		0			0
$400$	231.666	+	1313.84i	0.0289582	+	0.164230i
$401$	−8697.20	+	7297.82i	−1.08309	+	0.908817i	−0.996173	−	0.0873986i	$-0.972145\pi$
$401$	−8697.20	+	7297.82i	−1.08309	+	0.908817i	−0.0869129	+	0.996216i	$0.527700\pi$
$402$		0			0
$403$	4997.54	−	1818.96i	0.617731	−	0.224836i
$404$	4840.28			0.596071
$405$		0			0
$406$	604.254			0.0738636
$407$	4519.67	−	1645.02i	0.550446	−	0.200346i
$408$		0			0
$409$	6651.68	−	5581.42i	0.804167	−	0.674776i	−0.145041	−	0.989426i	$-0.546331\pi$
$409$	6651.68	−	5581.42i	0.804167	−	0.674776i	0.949208	+	0.314649i	$0.101887\pi$
$410$	−2578.54	−	14623.7i	−0.310598	−	1.76149i
$411$		0			0
$412$	−3156.63	−	2648.73i	−0.377466	−	0.316731i
$413$	334.199	−	578.850i	0.0398181	−	0.0689669i
$414$		0			0
$415$	−5639.82	−	9768.46i	−0.667104	−	1.15546i
$416$	322.860	−	1831.03i	0.0380518	−	0.215802i
$417$		0			0
$418$	−7926.42	−	2884.98i	−0.927497	−	0.337581i
$419$	−5614.47	−	2043.50i	−0.654618	−	0.238261i	−0.00670689	−	0.999978i	$-0.502135\pi$
$419$	−5614.47	−	2043.50i	−0.654618	−	0.238261i	−0.647911	+	0.761716i	$0.724357\pi$
$420$		0			0
$421$	1494.83	−	8477.59i	0.173049	−	0.981407i	−0.767324	−	0.641260i	$-0.778412\pi$
$421$	1494.83	−	8477.59i	0.173049	−	0.981407i	0.940372	−	0.340147i	$-0.110477\pi$
$422$	−1111.66	−	1925.44i	−0.128233	−	0.222107i
$423$		0			0
$424$	103.735	−	179.674i	0.0118816	−	0.0205796i
$425$	627.686	+	526.691i	0.0716406	+	0.0601136i
$426$		0			0
$427$	−55.8204	−	316.573i	−0.00632631	−	0.0358783i
$428$	745.581	−	625.617i	0.0842034	−	0.0706550i
$429$		0			0
$430$	−14562.4	+	5300.27i	−1.63316	+	0.594423i
$431$	−6638.77			−0.741945			−0.370972	−	0.928644i	$-0.620976\pi$
$431$	−6638.77			−0.741945			−0.370972	+	0.928644i	$0.620976\pi$
$432$		0			0
$433$	−15093.1			−1.67512			−0.837560	−	0.546345i	$-0.816019\pi$
$433$	−15093.1			−1.67512			−0.837560	+	0.546345i	$0.816019\pi$
$434$	192.131	−	69.9298i	0.0212501	−	0.00773442i
$435$		0			0
$436$	961.149	−	806.500i	0.105575	−	0.0885879i
$437$	1720.39	+	9756.79i	0.188323	+	1.06803i
$438$		0			0
$439$	10152.7	+	8519.17i	1.10379	+	0.926191i	0.997674	−	0.0681631i	$-0.0217138\pi$
$439$	10152.7	+	8519.17i	1.10379	+	0.926191i	0.106117	+	0.994354i	$0.466158\pi$
$440$	−2333.52	+	4041.78i	−0.252832	+	0.437919i
$441$		0			0
$442$	−570.967	−	988.945i	−0.0614438	−	0.106424i
$443$	−511.547	+	2901.13i	−0.0548630	+	0.311144i	−0.999874	−	0.0158960i	$-0.994940\pi$
$443$	−511.547	+	2901.13i	−0.0548630	+	0.311144i	0.945011	+	0.327040i	$0.106051\pi$
$444$		0			0
$445$	13769.2	+	5011.57i	1.46679	+	0.533868i
$446$	−11318.4	−	4119.57i	−1.20167	−	0.437371i
$447$		0			0
$448$	12.4124	−	70.3940i	0.00130899	−	0.00742367i
$449$	785.690	+	1360.85i	0.0825813	+	0.143035i	0.904358	−	0.426775i	$-0.140350\pi$
$449$	785.690	+	1360.85i	0.0825813	+	0.143035i	−0.821777	+	0.569810i	$0.807017\pi$
$450$		0			0
$451$	10392.9	−	18001.0i	1.08510	−	1.87946i
$452$	3339.24	+	2801.96i	0.347489	+	0.291577i
$453$		0			0
$454$	541.416	+	3070.52i	0.0559690	+	0.317416i
$455$	−717.600	+	602.138i	−0.0739376	+	0.0620410i
$456$		0			0
$457$	−731.707	+	266.320i	−0.0748967	+	0.0272602i	−0.379197	−	0.925316i	$-0.623800\pi$
$457$	−731.707	+	266.320i	−0.0748967	+	0.0272602i	0.304300	+	0.952576i	$0.401577\pi$
$458$	−8954.88			−0.913611
$459$		0			0
$460$	5481.59			0.555609
$461$	−9512.80	+	3462.38i	−0.961075	+	0.349803i	−0.774455	−	0.632630i	$-0.781976\pi$
$461$	−9512.80	+	3462.38i	−0.961075	+	0.349803i	−0.186620	+	0.982432i	$0.559753\pi$
$462$		0			0
$463$	−3201.08	+	2686.02i	−0.321311	+	0.269612i	−0.789148	−	0.614203i	$-0.789478\pi$
$463$	−3201.08	+	2686.02i	−0.321311	+	0.269612i	0.467838	+	0.883814i	$0.345033\pi$
$464$	−751.580	−	4262.42i	−0.0751967	−	0.426461i
$465$		0			0
$466$	−2142.12	−	1797.45i	−0.212943	−	0.178681i
$467$	−618.325	+	1070.97i	−0.0612691	+	0.106121i	−0.895033	−	0.446000i	$-0.852848\pi$
$467$	−618.325	+	1070.97i	−0.0612691	+	0.106121i	0.833764	+	0.552121i	$0.186181\pi$
$468$		0			0
$469$	245.656	+	425.488i	0.0241862	+	0.0418917i
$470$	210.468	−	1193.63i	0.0206557	−	0.117144i
$471$		0			0
$472$	−4498.91	−	1637.47i	−0.438727	−	0.159683i
$473$	−20384.2	−	7419.25i	−1.98154	−	0.721221i
$474$		0			0
$475$	1511.06	−	8569.64i	0.145962	−	0.827794i
$476$	−21.9508	−	38.0200i	−0.00211369	−	0.00366101i
$477$		0			0
$478$	−1149.94	+	1991.75i	−0.110036	+	0.190587i
$479$	11084.9	+	9301.33i	1.05737	+	0.887241i	0.993849	−	0.110739i	$-0.0353219\pi$
$479$	11084.9	+	9301.33i	1.05737	+	0.887241i	0.0635231	+	0.997980i	$0.479766\pi$
$480$		0			0
$481$	−1200.78	−	6809.96i	−0.113827	−	0.645546i
$482$	−5131.89	+	4306.17i	−0.484961	+	0.406931i
$483$		0			0
$484$	−1135.96	+	413.457i	−0.106683	+	0.0388295i
$485$	−2406.10			−0.225269
$486$		0			0
$487$	12301.5			1.14463			0.572313	−	0.820036i	$-0.306046\pi$
$487$	12301.5			1.14463			0.572313	+	0.820036i	$0.306046\pi$
$488$	−2163.68	+	787.517i	−0.200708	+	0.0730517i
$489$		0			0
$490$	7558.33	−	6342.19i	0.696838	−	0.584716i
$491$	−325.193	−	1844.26i	−0.0298895	−	0.169512i	0.966209	−	0.257760i	$-0.0829843\pi$
$491$	−325.193	−	1844.26i	−0.0298895	−	0.169512i	−0.996099	+	0.0882480i	$0.971873\pi$
$492$		0			0
$493$	−2036.37	−	1708.71i	−0.186031	−	0.156099i
$494$	−6063.65	+	10502.5i	−0.552260	+	0.956542i
$495$		0			0
$496$	−732.262	−	1268.31i	−0.0662894	−	0.114817i
$497$	44.3291	−	251.403i	0.00400087	−	0.0226901i
$498$		0			0
$499$	9088.75	+	3308.03i	0.815367	+	0.296769i	0.715839	−	0.698265i	$-0.246044\pi$
$499$	9088.75	+	3308.03i	0.815367	+	0.296769i	0.0995283	+	0.995035i	$0.468267\pi$
$500$	2258.18	+	821.909i	0.201978	+	0.0735138i
$501$		0			0
$502$	−368.853	+	2091.87i	−0.0327943	+	0.185986i
$503$	8143.67	+	14105.3i	0.721886	+	1.25034i	0.960243	+	0.279165i	$0.0900577\pi$
$503$	8143.67	+	14105.3i	0.721886	+	1.25034i	−0.238357	+	0.971177i	$0.576609\pi$
$504$		0			0
$505$	−8733.94	+	15127.6i	−0.769615	+	1.33301i
$506$	5877.90	+	4932.14i	0.516412	+	0.433321i
$507$		0			0
$508$	−1484.78	−	8420.58i	−0.129678	−	0.735439i
$509$	3254.28	−	2730.67i	0.283386	−	0.237789i	−0.490003	−	0.871721i	$-0.663004\pi$
$509$	3254.28	−	2730.67i	0.283386	−	0.237789i	0.773389	+	0.633932i	$0.218560\pi$
$510$		0			0
$511$	991.638	−	360.927i	0.0858463	−	0.0312455i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	−2136.11			−0.183307
$515$	13974.1	−	5086.17i	1.19568	−	0.435191i
$516$		0			0
$517$	1299.67	−	1090.55i	0.110560	−	0.0927706i
$518$	−46.1640	−	261.809i	−0.00391569	−	0.0222070i
$519$		0			0
$520$	5140.06	+	4313.03i	0.433474	+	0.363728i
$521$	5399.52	−	9352.25i	0.454045	−	0.786429i	−0.544588	−	0.838704i	$-0.683314\pi$
$521$	5399.52	−	9352.25i	0.454045	−	0.786429i	0.998633	+	0.0522750i	$0.0166472\pi$
$522$		0			0
$523$	−8078.14	−	13991.7i	−0.675396	−	1.16982i	−0.976353	−	0.216183i	$-0.930639\pi$
$523$	−8078.14	−	13991.7i	−0.675396	−	1.16982i	0.300956	−	0.953638i	$-0.402694\pi$
$524$	1172.46	−	6649.36i	0.0977466	−	0.554348i
$525$		0			0
$526$	−9971.71	−	3629.40i	−0.826591	−	0.300855i
$527$	−845.238	−	307.641i	−0.0698655	−	0.0254290i
$528$		0			0
$529$	−547.819	+	3106.84i	−0.0450250	+	0.255349i
$530$	374.364	+	648.418i	0.0306818	+	0.0531424i
$531$		0			0
$532$	−233.117	+	403.770i	−0.0189979	+	0.0329054i
$533$	−22892.5	−	19209.1i	−1.86038	−	1.56105i
$534$		0			0
$535$	609.932	+	3459.10i	0.0492891	+	0.279532i
$536$	2695.86	−	2262.09i	0.217245	−	0.182290i
$537$		0			0
$538$	6421.41	−	2337.20i	0.514585	−	0.187293i
$539$	13811.3			1.10370
$540$		0			0
$541$	21721.4			1.72621			0.863103	−	0.505028i	$-0.168518\pi$
$541$	21721.4			1.72621			0.863103	+	0.505028i	$0.168518\pi$
$542$	−3578.31	+	1302.40i	−0.283582	+	0.103215i
$543$		0			0
$544$	−240.891	+	202.132i	−0.0189855	+	0.0159307i
$545$	786.279	+	4459.21i	0.0617991	+	0.350480i
$546$		0			0
$547$	−13101.7	−	10993.7i	−1.02411	−	0.859334i	−0.0339749	−	0.999423i	$-0.510817\pi$
$547$	−13101.7	−	10993.7i	−1.02411	−	0.859334i	−0.990139	+	0.140089i	$0.955261\pi$
$548$	4060.77	−	7033.46i	0.316546	−	0.548274i
$549$		0			0
$550$	−3369.72	−	5836.52i	−0.261246	−	0.452491i
$551$	−4902.24	+	27802.0i	−0.379025	+	2.14956i
$552$		0			0
$553$	−652.125	−	237.354i	−0.0501468	−	0.0182519i
$554$	1735.30	+	631.597i	0.133079	+	0.0484368i
$555$		0			0
$556$	−946.586	+	5368.35i	−0.0722017	+	0.409476i
$557$	−5438.47	−	9419.70i	−0.413708	−	0.716563i	0.581584	−	0.813486i	$-0.302433\pi$
$557$	−5438.47	−	9419.70i	−0.413708	−	0.716563i	−0.995292	+	0.0969236i	$0.969100\pi$
$558$		0			0
$559$	−15593.8	+	27009.2i	−1.17987	+	2.04359i
$560$	197.610	+	165.814i	0.0149117	+	0.0125124i
$561$		0			0
$562$	759.838	+	4309.26i	0.0570317	+	0.323443i
$563$	13697.2	−	11493.3i	1.02534	−	0.860364i	0.0350528	−	0.999385i	$-0.488840\pi$
$563$	13697.2	−	11493.3i	1.02534	−	0.860364i	0.990289	+	0.139021i	$0.0443956\pi$
$564$		0			0
$565$	−14782.6	+	5380.42i	−1.10072	+	0.400630i
$566$	−14007.1			−1.04021
$567$		0			0
$568$	−1828.54			−0.135077
$569$	13029.0	−	4742.16i	0.959936	−	0.349388i	0.185927	−	0.982563i	$-0.440471\pi$
$569$	13029.0	−	4742.16i	0.959936	−	0.349388i	0.774008	+	0.633175i	$0.218249\pi$
$570$		0			0
$571$	−3425.78	+	2874.57i	−0.251076	+	0.210678i	−0.759635	−	0.650349i	$-0.774623\pi$
$571$	−3425.78	+	2874.57i	−0.251076	+	0.210678i	0.508560	+	0.861027i	$0.330178\pi$
$572$	1630.97	+	9249.70i	0.119221	+	0.676136i
$573$		0			0
$574$	−880.101	−	738.492i	−0.0639977	−	0.0537005i
$575$	−3957.84	+	6855.18i	−0.287049	+	0.497184i
$576$		0			0
$577$	−919.141	−	1592.00i	−0.0663160	−	0.114863i	0.830961	−	0.556331i	$-0.187791\pi$
$577$	−919.141	−	1592.00i	−0.0663160	−	0.114863i	−0.897277	+	0.441468i	$0.854458\pi$
$578$	1672.73	−	9486.52i	0.120374	−	0.682677i
$579$		0			0
$580$	14677.8	+	5342.28i	1.05080	+	0.382459i
$581$	−820.079	−	298.484i	−0.0585587	−	0.0213136i
$582$		0			0
$583$	−181.994	+	1032.14i	−0.0129287	+	0.0733221i
$584$	−3779.40	−	6546.12i	−0.267796	−	0.463836i
$585$		0			0
$586$	−3141.79	+	5441.74i	−0.221478	+	0.383612i
$587$	−2748.43	−	2306.21i	−0.193254	−	0.162159i	0.541027	−	0.841006i	$-0.318036\pi$
$587$	−2748.43	−	2306.21i	−0.193254	−	0.162159i	−0.734280	+	0.678846i	$0.762480\pi$
$588$		0			0
$589$	1658.77	+	9407.35i	0.116041	+	0.658104i
$590$	13235.6	−	11106.0i	0.923564	−	0.774963i
$591$		0			0
$592$	−1789.39	+	651.284i	−0.124229	+	0.0452156i
$593$	1664.70			0.115280			0.0576399	−	0.998337i	$-0.481642\pi$
$593$	1664.70			0.115280			0.0576399	+	0.998337i	$0.481642\pi$
$594$		0			0
$595$	158.435			0.0109163
$596$	6750.52	−	2456.99i	0.463946	−	0.168863i
$597$		0			0
$598$	8450.74	−	7091.01i	0.577887	−	0.484905i
$599$	519.066	+	2943.77i	0.0354064	+	0.200800i	0.997380	−	0.0723435i	$-0.0230478\pi$
$599$	519.066	+	2943.77i	0.0354064	+	0.200800i	−0.961973	+	0.273143i	$0.911937\pi$
$600$		0			0
$601$	−2450.84	−	2056.50i	−0.166342	−	0.139578i	0.555817	−	0.831305i	$-0.312406\pi$
$601$	−2450.84	−	2056.50i	−0.166342	−	0.139578i	−0.722159	+	0.691727i	$0.756850\pi$
$602$	−599.502	+	1038.37i	−0.0405878	+	0.0703002i
$603$		0			0
$604$	5589.42	+	9681.16i	0.376540	+	0.652187i
$605$	757.562	−	4296.35i	0.0509079	−	0.288713i
$606$		0			0
$607$	3722.39	+	1354.84i	0.248908	+	0.0905952i	0.463461	−	0.886117i	$-0.346607\pi$
$607$	3722.39	+	1354.84i	0.248908	+	0.0905952i	−0.214553	+	0.976712i	$0.568830\pi$
$608$	3138.16	+	1142.20i	0.209324	+	0.0761878i
$609$		0			0
$610$	1442.94	−	8183.32i	0.0957753	−	0.543169i
$611$	−1219.61	−	2112.43i	−0.0807531	−	0.139869i
$612$		0			0
$613$	−12207.1	+	21143.4i	−0.804309	+	1.39310i	0.112447	+	0.993658i	$0.464131\pi$
$613$	−12207.1	+	21143.4i	−0.804309	+	1.39310i	−0.916756	+	0.399447i	$0.869202\pi$
$614$	2569.05	+	2155.69i	0.168857	+	0.141688i
$615$		0			0
$616$	62.7027	+	355.605i	0.00410124	+	0.0232593i
$617$	−4051.09	+	3399.26i	−0.264328	+	0.221798i	−0.765313	−	0.643658i	$-0.777416\pi$
$617$	−4051.09	+	3399.26i	−0.264328	+	0.221798i	0.500985	+	0.865456i	$0.332971\pi$
$618$		0			0
$619$	24666.9	−	8978.01i	1.60169	−	0.582967i	0.621917	−	0.783083i	$-0.286354\pi$
$619$	24666.9	−	8978.01i	1.60169	−	0.582967i	0.979772	+	0.200116i	$0.0641320\pi$
$620$	5285.26			0.342357
$621$		0			0
$622$	5653.83			0.364466
$623$	1065.33	−	387.747i	0.0685094	−	0.0249354i
$624$		0			0
$625$	−14627.8	+	12274.2i	−0.936177	+	0.785546i
$626$	1894.15	+	10742.3i	0.120935	+	0.685859i
$627$		0			0
$628$	596.242	+	500.306i	0.0378863	+	0.0317904i
$629$	−584.771	+	1012.85i	−0.0370689	+	0.0642052i
$630$		0			0
$631$	−8267.35	−	14319.5i	−0.521581	−	0.903406i	−0.999685	−	0.0251021i	$-0.992009\pi$
$631$	−8267.35	−	14319.5i	−0.521581	−	0.903406i	0.478103	−	0.878304i	$-0.341324\pi$
$632$	−863.179	+	4895.33i	−0.0543282	+	0.308111i
$633$		0			0
$634$	−9438.36	−	3435.28i	−0.591238	−	0.215193i
$635$	28996.6	+	10553.9i	1.81212	+	0.659556i
$636$		0			0
$637$	3448.07	−	19555.0i	0.214470	−	1.21632i
$638$	10932.2	+	18935.1i	0.678385	+	1.17500i
$639$		0			0
$640$	923.868	−	1600.19i	0.0570611	−	0.0988327i
$641$	−9574.38	−	8033.86i	−0.589961	−	0.495036i	0.298240	−	0.954491i	$-0.403600\pi$
$641$	−9574.38	−	8033.86i	−0.589961	−	0.495036i	−0.888201	+	0.459455i	$0.848045\pi$
$642$		0			0
$643$	−888.699	−	5040.06i	−0.0545052	−	0.309114i	0.945351	−	0.326054i	$-0.105719\pi$
$643$	−888.699	−	5040.06i	−0.0545052	−	0.309114i	−0.999857	+	0.0169391i	$0.994608\pi$
$644$	324.889	−	272.614i	0.0198795	−	0.0166809i
$645$		0			0
$646$	1927.40	−	701.516i	0.117388	−	0.0427257i
$647$	−14662.7			−0.890959			−0.445479	−	0.895292i	$-0.646967\pi$
$647$	−14662.7			−0.890959			−0.445479	+	0.895292i	$0.646967\pi$
$648$		0			0
$649$	24185.4			1.46280
$650$	−9105.05	+	3313.97i	−0.549430	+	0.199976i
$651$		0			0
$652$	−5135.35	+	4309.07i	−0.308460	+	0.258829i
$653$	715.178	+	4055.98i	0.0428592	+	0.243067i	0.998709	−	0.0507874i	$-0.0161731\pi$
$653$	715.178	+	4055.98i	0.0428592	+	0.243067i	−0.955850	+	0.293854i	$0.905062\pi$
$654$		0			0
$655$	18666.0	+	15662.7i	1.11350	+	0.934337i
$656$	−4114.66	+	7126.81i	−0.244894	+	0.424169i
$657$		0			0
$658$	−46.8879	−	81.2122i	−0.00277793	−	0.00481152i
$659$	1072.18	−	6080.65i	0.0633784	−	0.359436i	−0.936581	−	0.350450i	$-0.886029\pi$
$659$	1072.18	−	6080.65i	0.0633784	−	0.359436i	0.999960	−	0.00898604i	$-0.00286038\pi$
$660$		0			0
$661$	−22433.8	−	8165.23i	−1.32008	−	0.480470i	−0.416596	−	0.909092i	$-0.636777\pi$
$661$	−22433.8	−	8165.23i	−1.32008	−	0.480470i	−0.903484	+	0.428622i	$0.858999\pi$
$662$	3163.94	+	1151.58i	0.185756	+	0.0676095i
$663$		0			0
$664$	−1085.49	+	6156.12i	−0.0634415	+	0.359795i
$665$	−841.286	−	1457.15i	−0.0490581	−	0.0849712i
$666$		0			0
$667$	12840.2	−	22239.9i	0.745389	−	1.29105i
$668$	−43.6590	−	36.6343i	−0.00252877	−	0.00212189i
$669$		0			0
$670$	2205.38	+	12507.3i	0.127166	+	0.721194i
$671$	8910.33	−	7476.66i	0.512637	−	0.430154i
$672$		0			0
$673$	−9064.37	+	3299.16i	−0.519177	+	0.188965i	−0.588299	−	0.808643i	$-0.700202\pi$
$673$	−9064.37	+	3299.16i	−0.519177	+	0.188965i	0.0691226	+	0.997608i	$0.477980\pi$
$674$	22329.2			1.27610
$675$		0			0
$676$	4715.58			0.268297
$677$	9992.89	−	3637.11i	0.567294	−	0.206478i	−0.0424198	−	0.999100i	$-0.513507\pi$
$677$	9992.89	−	3637.11i	0.567294	−	0.206478i	0.609714	+	0.792622i	$0.291284\pi$
$678$		0			0
$679$	−142.607	+	119.662i	−0.00806004	+	0.00676318i
$680$	−197.064	−	1117.60i	−0.0111133	−	0.0630267i
$681$		0			0
$682$	5667.38	+	4755.49i	0.318204	+	0.267005i
$683$	−4796.16	+	8307.19i	−0.268697	+	0.465396i	−0.968526	−	0.248914i	$-0.919926\pi$
$683$	−4796.16	+	8307.19i	−0.268697	+	0.465396i	0.699829	+	0.714311i	$0.253260\pi$
$684$		0			0
$685$	14654.7	+	25382.8i	0.817415	+	1.41580i
$686$	265.606	−	1506.33i	0.0147826	−	0.0838365i
$687$		0			0
$688$	8070.34	+	2937.37i	0.447208	+	0.162770i
$689$	1415.94	+	515.360i	0.0782917	+	0.0284958i
$690$		0			0
$691$	−693.958	+	3935.63i	−0.0382046	+	0.216669i	−0.997933	−	0.0642597i	$-0.979531\pi$
$691$	−693.958	+	3935.63i	−0.0382046	+	0.216669i	0.959729	+	0.280929i	$0.0906425\pi$
$692$	−2204.26	−	3817.89i	−0.121089	−	0.209732i
$693$		0			0
$694$	−1787.50	+	3096.04i	−0.0977701	+	0.169343i
$695$	−15070.0	−	12645.2i	−0.822501	−	0.690160i
$696$		0			0
$697$	877.670	+	4977.52i	0.0476960	+	0.270498i
$698$	−9455.95	+	7934.48i	−0.512769	+	0.430264i
$699$		0			0
$700$	−350.043	+	127.405i	−0.0189006	+	0.00687924i
$701$	−9451.41			−0.509236			−0.254618	−	0.967042i	$-0.581950\pi$
$701$	−9451.41			−0.509236			−0.254618	+	0.967042i	$0.581950\pi$
$702$		0			0
$703$	12420.5			0.666354
$704$	2430.46	−	884.613i	0.130115	−	0.0473581i
$705$		0			0
$706$	−16095.8	+	13506.0i	−0.858035	+	0.719977i
$707$	234.685	+	1330.96i	0.0124841	+	0.0708006i
$708$		0			0
$709$	−4913.32	−	4122.77i	−0.260259	−	0.218383i	0.503316	−	0.864103i	$-0.332113\pi$
$709$	−4913.32	−	4122.77i	−0.260259	−	0.218383i	−0.763575	+	0.645719i	$0.776558\pi$
$710$	3299.48	−	5714.86i	0.174404	−	0.302077i
$711$		0			0
$712$	−4060.24	−	7032.55i	−0.213714	−	0.370163i
$713$	1508.91	−	8557.44i	0.0792553	−	0.449479i
$714$		0			0
$715$	−31851.7	−	11593.1i	−1.66599	−	0.606372i
$716$	2628.34	+	956.636i	0.137187	+	0.0499318i
$717$		0			0
$718$	3072.34	−	17424.1i	0.159692	−	0.905658i
$719$	7391.16	+	12801.9i	0.383371	+	0.664018i	0.991542	−	0.129788i	$-0.0414297\pi$
$719$	7391.16	+	12801.9i	0.383371	+	0.664018i	−0.608171	+	0.793806i	$0.708096\pi$
$720$		0			0
$721$	575.286	−	996.424i	0.0297153	−	0.0514685i
$722$	−6177.81	−	5183.79i	−0.318441	−	0.267203i
$723$		0			0
$724$	−957.392	−	5429.64i	−0.0491453	−	0.278717i
$725$	−17278.7	+	14498.5i	−0.885124	+	0.742707i
$726$		0			0
$727$	−3112.78	+	1132.96i	−0.158799	+	0.0577981i	−0.420196	−	0.907433i	$-0.638039\pi$
$727$	−3112.78	+	1132.96i	−0.158799	+	0.0577981i	0.261398	+	0.965231i	$0.415817\pi$
$728$	519.145			0.0264297
$729$		0			0
$730$	27278.7			1.38305
$731$	4956.66	−	1804.08i	0.250791	−	0.0912806i
$732$		0			0
$733$	−13479.0	+	11310.2i	−0.679206	+	0.569921i	−0.915774	−	0.401694i	$-0.868422\pi$
$733$	−13479.0	+	11310.2i	−0.679206	+	0.569921i	0.236568	+	0.971615i	$0.423977\pi$
$734$	2952.12	+	16742.3i	0.148453	+	0.841921i
$735$		0			0
$736$	−2327.13	−	1952.69i	−0.116548	−	0.0977951i
$737$	−8888.83	+	15395.9i	−0.444266	+	0.769492i
$738$		0			0
$739$	−5293.89	−	9169.29i	−0.263517	−	0.456425i	0.703657	−	0.710540i	$-0.251549\pi$
$739$	−5293.89	−	9169.29i	−0.263517	−	0.456425i	−0.967174	+	0.254115i	$0.918216\pi$
$740$	1193.33	−	6767.69i	0.0592804	−	0.336196i
$741$		0			0
$742$	54.4357	+	19.8130i	0.00269326	+	0.000980266i
$743$	−22222.3	−	8088.27i	−1.09725	−	0.399367i	−0.270949	−	0.962594i	$-0.587338\pi$
$743$	−22222.3	−	8088.27i	−1.09725	−	0.399367i	−0.826302	+	0.563227i	$0.809560\pi$
$744$		0			0
$745$	−4501.85	+	25531.3i	−0.221390	+	1.25556i
$746$	−5511.29	−	9545.84i	−0.270486	−	0.468496i
$747$		0			0
$748$	794.271	−	1375.72i	0.0388254	−	0.0672476i
$749$	208.180	+	174.684i	0.0101559	+	0.00852177i
$750$		0			0
$751$	−3469.14	−	19674.5i	−0.168563	−	0.955968i	−0.945314	−	0.326160i	$-0.894245\pi$
$751$	−3469.14	−	19674.5i	−0.168563	−	0.955968i	0.776752	−	0.629807i	$-0.216866\pi$
$752$	−514.554	+	431.762i	−0.0249519	+	0.0209371i
$753$		0			0
$754$	29539.0	−	10751.3i	1.42672	−	0.519283i
$755$	−40342.9			−1.94467
$756$		0			0
$757$	−3951.21			−0.189708			−0.0948540	−	0.995491i	$-0.530238\pi$
$757$	−3951.21			−0.189708			−0.0948540	+	0.995491i	$0.530238\pi$
$758$	−9508.52	+	3460.82i	−0.455626	+	0.165834i
$759$		0			0
$760$	−9232.37	+	7746.88i	−0.440649	+	0.369749i
$761$	5486.47	+	31115.3i	0.261346	+	1.48217i	0.779241	+	0.626724i	$0.215605\pi$
$761$	5486.47	+	31115.3i	0.261346	+	1.48217i	−0.517895	+	0.855444i	$0.673284\pi$
$762$		0			0
$763$	268.371	+	225.190i	0.0127335	+	0.0106847i
$764$	1461.14	−	2530.77i	0.0691913	−	0.119843i
$765$		0			0
$766$	−3164.48	−	5481.04i	−0.149265	−	0.258535i
$767$	6038.04	−	34243.4i	0.284252	−	1.61207i
$768$		0			0
$769$	−3746.39	−	1363.57i	−0.175680	−	0.0639424i	0.252682	−	0.967549i	$-0.418687\pi$
$769$	−3746.39	−	1363.57i	−0.175680	−	0.0639424i	−0.428363	+	0.903607i	$0.640909\pi$
$770$	−1224.54	−	445.695i	−0.0573107	−	0.0208594i
$771$		0			0
$772$	3127.92	−	17739.3i	0.145824	−	0.827011i
$773$	−20859.1	−	36129.1i	−0.970570	−	1.68108i	−0.693840	−	0.720129i	$-0.744083\pi$
$773$	−20859.1	−	36129.1i	−0.970570	−	1.68108i	−0.276730	−	0.960948i	$-0.589251\pi$
$774$		0			0
$775$	−3816.09	+	6609.65i	−0.176875	+	0.306356i
$776$	1021.48	+	857.120i	0.0472536	+	0.0396505i
$777$		0			0
$778$	3.97198	+	22.5262i	0.000183036	+	0.00103805i
$779$	41118.5	−	34502.6i	1.89117	−	1.58688i
$780$		0			0
$781$	8680.06	−	3159.28i	0.397691	−	0.144748i
$782$	−1865.79			−0.0853204
$783$		0			0
$784$	−5468.04			−0.249091
$785$	−2639.51	+	960.705i	−0.120011	+	0.0436803i
$786$		0			0
$787$	3105.64	−	2605.95i	0.140666	−	0.118033i	−0.569740	−	0.821825i	$-0.692956\pi$
$787$	3105.64	−	2605.95i	0.140666	−	0.118033i	0.710406	+	0.703792i	$0.248511\pi$
$788$	2306.09	+	13078.5i	0.104253	+	0.591246i
$789$		0			0
$790$	−13742.1	−	11531.0i	−0.618891	−	0.519311i
$791$	−608.567	+	1054.07i	−0.0273554	+	0.0473810i
$792$		0			0
$793$	−8361.47	−	14482.5i	−0.374432	−	0.648535i
$794$	−2868.65	+	16268.9i	−0.128217	+	0.727157i
$795$		0			0
$796$	14080.9	+	5125.04i	0.626992	+	0.228207i
$797$	−3801.97	−	1383.80i	−0.168975	−	0.0615017i	0.256148	−	0.966638i	$-0.417547\pi$
$797$	−3801.97	−	1383.80i	−0.168975	−	0.0615017i	−0.425122	+	0.905136i	$0.639769\pi$
$798$		0			0
$799$	−71.6380	+	406.279i	−0.00317193	+	0.0179889i
$800$	1334.11	+	2310.75i	0.0589599	+	0.102122i
$801$		0			0
$802$	−11353.4	+	19664.7i	−0.499878	+	0.865814i
$803$	29250.9	+	24544.4i	1.28548	+	1.07865i
$804$		0			0
$805$	265.779	+	1507.31i	0.0116366	+	0.0659946i
$806$	8148.07	−	6837.04i	0.356084	−	0.298790i
$807$		0			0
$808$	9096.75	−	3310.95i	0.396067	−	0.144157i
$809$	40058.3			1.74088			0.870442	−	0.492271i	$-0.163833\pi$
$809$	40058.3			1.74088			0.870442	+	0.492271i	$0.163833\pi$
$810$		0			0
$811$	11099.0			0.480565			0.240283	−	0.970703i	$-0.422760\pi$
$811$	11099.0			0.480565			0.240283	+	0.970703i	$0.422760\pi$
$812$	1135.63	−	413.334i	0.0490796	−	0.0178635i
$813$		0			0
$814$	7368.93	−	6183.27i	0.317298	−	0.266245i
$815$	−4201.04	−	23825.3i	−0.180559	−	1.02400i
$816$		0			0
$817$	−42912.1	−	36007.5i	−1.83758	−	1.54191i
$818$	8683.15	−	15039.7i	0.371148	−	0.642848i
$819$		0			0
$820$	−14849.2	−	25719.6i	−0.632388	−	1.09533i
$821$	−253.082	+	1435.30i	−0.0107584	+	0.0610137i	−0.989714	−	0.143058i	$-0.954306\pi$
$821$	−253.082	+	1435.30i	−0.0107584	+	0.0610137i	0.978956	+	0.204072i	$0.0654176\pi$
$822$		0			0
$823$	−18529.5	−	6744.18i	−0.784808	−	0.285647i	−0.0816318	−	0.996663i	$-0.526013\pi$
$823$	−18529.5	−	6744.18i	−0.784808	−	0.285647i	−0.703176	+	0.711016i	$0.748235\pi$
$824$	−7744.36	−	2818.71i	−0.327412	−	0.119168i
$825$		0			0
$826$	232.132	−	1316.49i	0.00977835	−	0.0554558i
$827$	11358.2	+	19672.9i	0.477585	+	0.827201i	0.999670	−	0.0256923i	$-0.00817902\pi$
$827$	11358.2	+	19672.9i	0.477585	+	0.827201i	−0.522085	+	0.852893i	$0.674846\pi$
$828$		0			0
$829$	−8215.40	+	14229.5i	−0.344189	+	0.596153i	−0.985206	−	0.171374i	$-0.945179\pi$
$829$	−8215.40	+	14229.5i	−0.344189	+	0.596153i	0.641017	+	0.767527i	$0.278513\pi$
$830$	−17281.4	−	14500.8i	−0.722707	−	0.606423i
$831$		0			0
$832$	−645.721	−	3662.06i	−0.0269067	−	0.152595i
$833$	−2572.66	+	2158.72i	−0.107008	+	0.0897901i
$834$		0			0
$835$	193.275	−	70.3464i	0.00801025	−	0.00291549i
$836$	−16870.2			−0.697930
$837$		0			0
$838$	−11949.6			−0.492592
$839$	−44031.6	+	16026.2i	−1.81185	+	0.659458i	−0.815059	+	0.579378i	$0.803295\pi$
$839$	−44031.6	+	16026.2i	−1.81185	+	0.659458i	−0.996788	+	0.0800802i	$0.974482\pi$
$840$		0			0
$841$	37373.2	−	31359.9i	1.53238	−	1.28582i
$842$	−2989.65	−	16955.2i	−0.122364	−	0.693960i
$843$		0			0
$844$	−3406.31	−	2858.23i	−0.138922	−	0.116569i
$845$	−8508.94	+	14737.9i	−0.346410	+	0.600000i
$846$		0			0
$847$	−168.769	−	292.316i	−0.00684648	−	0.0118585i
$848$	72.0534	−	408.635i	0.00291783	−	0.0165479i
$849$		0			0
$850$	1539.94	+	560.493i	0.0621407	+	0.0226174i
$851$	−10617.0	−	3864.26i	−0.427668	−	0.155658i
$852$		0			0
$853$	1804.08	−	10231.5i	0.0724157	−	0.410690i	−0.926953	−	0.375176i	$-0.877582\pi$
$853$	1804.08	−	10231.5i	0.0724157	−	0.410690i	0.999369	−	0.0355136i	$-0.0113067\pi$
$854$	−321.457	−	556.779i	−0.0128806	−	0.0223098i
$855$		0			0
$856$	973.287	−	1685.78i	0.0388625	−	0.0673118i
$857$	−3942.49	−	3308.14i	−0.157145	−	0.131860i	0.560825	−	0.827934i	$-0.310484\pi$
$857$	−3942.49	−	3308.14i	−0.157145	−	0.131860i	−0.717970	+	0.696074i	$0.754928\pi$
$858$		0			0
$859$	1412.84	+	8012.63i	0.0561182	+	0.318262i	0.999925	−	0.0122350i	$-0.00389463\pi$
$859$	1412.84	+	8012.63i	0.0561182	+	0.318262i	−0.943807	+	0.330497i	$0.892784\pi$
$860$	−23742.7	+	19922.5i	−0.941418	+	0.789944i
$861$		0			0
$862$	−12476.8	+	4541.18i	−0.492995	+	0.179435i
$863$	−39280.9			−1.54941			−0.774703	−	0.632325i	$-0.782101\pi$
$863$	−39280.9			−1.54941			−0.774703	+	0.632325i	$0.782101\pi$
$864$		0			0
$865$	15909.7			0.625372
$866$	−28365.7	+	10324.3i	−1.11306	+	0.405119i
$867$		0			0
$868$	313.252	−	262.850i	0.0122494	−	0.0102785i
$869$	−4360.46	−	24729.4i	−0.170217	−	0.965349i
$870$		0			0
$871$	19579.5	+	16429.1i	0.761683	+	0.639128i
$872$	1254.69	−	2173.19i	0.0487261	−	0.0843961i
$873$		0			0
$874$	9907.31	+	17160.0i	0.383432	+	0.664124i
$875$	−116.516	+	660.797i	−0.00450168	+	0.0255303i
$876$		0			0
$877$	28919.7	+	10525.9i	1.11351	+	0.405285i	0.832280	−	0.554356i	$-0.187035\pi$
$877$	28919.7	+	10525.9i	1.11351	+	0.405285i	0.281230	+	0.959640i	$0.409258\pi$
$878$	24908.4	+	9065.91i	0.957423	+	0.348473i
$879$		0			0
$880$	−1620.85	+	9192.28i	−0.0620895	+	0.352127i
$881$	2299.26	+	3982.43i	0.0879273	+	0.152295i	0.906635	−	0.421916i	$-0.138642\pi$
$881$	2299.26	+	3982.43i	0.0879273	+	0.152295i	−0.818708	+	0.574211i	$0.805309\pi$
$882$		0			0
$883$	−32.0452	+	55.5040i	−0.00122130	+	0.00211535i	−0.866635	−	0.498942i	$-0.833722\pi$
$883$	−32.0452	+	55.5040i	−0.00122130	+	0.00211535i	0.865414	+	0.501057i	$0.167055\pi$
$884$	−1749.55	−	1468.04i	−0.0665651	−	0.0558548i
$885$		0			0
$886$	1023.09	+	5802.25i	0.0387940	+	0.220012i
$887$	−25184.9	+	21132.6i	−0.953356	+	0.799960i	−0.979859	−	0.199688i	$-0.936007\pi$
$887$	−25184.9	+	21132.6i	−0.953356	+	0.799960i	0.0265038	+	0.999649i	$0.491563\pi$
$888$		0			0
$889$	2243.47	−	816.557i	0.0846385	−	0.0308059i
$890$	29305.7			1.10374
$891$		0			0
$892$	−24089.6			−0.904239
$893$	4117.01	−	1498.47i	0.154278	−	0.0561527i
$894$		0			0
$895$	−7732.49	+	6488.33i	−0.288792	+	0.242325i
$896$	−24.8247	−	140.788i	−0.000925598	−	0.00524933i
$897$		0			0
$898$	2407.49	+	2020.13i	0.0894645	+	0.0750696i
$899$	12380.3	−	21443.3i	0.459295	−	0.795523i
$900$		0			0
$901$	−127.424	−	220.705i	−0.00471155	−	0.00816064i
$902$	7218.82	−	40940.0i	0.266475	−	1.51126i
$903$		0			0
$904$	8192.38	+	2981.78i	0.301410	+	0.109704i
$905$	18697.1	+	6805.20i	0.686756	+	0.249959i
$906$		0			0
$907$	−1099.62	+	6236.28i	−0.0402563	+	0.228305i	−0.998298	−	0.0583254i	$-0.981424\pi$
$907$	−1099.62	+	6236.28i	−0.0402563	+	0.228305i	0.958041	+	0.286630i	$0.0925350\pi$
$908$	3117.89	+	5400.34i	0.113955	+	0.197375i
$909$		0			0
$910$	−936.761	+	1622.52i	−0.0341245	+	0.0591054i
$911$	30990.5	+	26004.1i	1.12707	+	0.945725i	0.998940	−	0.0460320i	$-0.0146576\pi$
$911$	30990.5	+	26004.1i	1.12707	+	0.945725i	0.128131	+	0.991757i	$0.459102\pi$
$912$		0			0
$913$	−5483.50	−	31098.5i	−0.198770	−	1.12728i
$914$	−1192.99	+	1001.03i	−0.0431734	+	0.0362268i
$915$		0			0
$916$	−16829.7	+	6125.50i	−0.607061	+	0.220952i
$917$	1885.26			0.0678920
$918$		0			0
$919$	18959.1			0.680525			0.340263	−	0.940330i	$-0.389484\pi$
$919$	18959.1			0.680525			0.340263	+	0.940330i	$0.389484\pi$
$920$	10302.0	−	3749.63i	0.369182	−	0.134371i
$921$		0			0
$922$	−15509.8	+	13014.3i	−0.554001	+	0.464862i
$923$	−2306.11	−	13078.6i	−0.0822389	−	0.466400i
$924$		0			0
$925$	7601.94	+	6378.79i	0.270217	+	0.226739i
$926$	−4178.71	+	7237.74i	−0.148295	+	0.256854i
$927$		0			0
$928$	−4328.18	−	7496.63i	−0.153103	−	0.265182i
$929$	−5627.64	+	31915.9i	−0.198748	+	1.12716i	0.708231	+	0.705981i	$0.249493\pi$
$929$	−5627.64	+	31915.9i	−0.198748	+	1.12716i	−0.906979	+	0.421176i	$0.861618\pi$
$930$		0			0
$931$	33514.8	+	12198.4i	1.17981	+	0.429416i
$932$	−5255.39	−	1912.80i	−0.184706	−	0.0672275i
$933$		0			0
$934$	−429.484	+	2435.72i	−0.0150462	+	0.0853312i
$935$	2866.41	+	4964.77i	0.100259	+	0.173653i
$936$		0			0
$937$	689.399	−	1194.07i	0.0240360	−	0.0416315i	−0.853757	−	0.520671i	$-0.825682\pi$
$937$	689.399	−	1194.07i	0.0240360	−	0.0416315i	0.877793	+	0.479040i	$0.159015\pi$
$938$	752.733	+	631.618i	0.0262021	+	0.0219862i
$939$		0			0
$940$	−420.937	−	2387.25i	−0.0146058	−	0.0828336i
$941$	29711.5	−	24930.9i	1.02930	−	0.863682i	0.0385294	−	0.999257i	$-0.487733\pi$
$941$	29711.5	−	24930.9i	1.02930	−	0.863682i	0.990767	+	0.135575i	$0.0432882\pi$
$942$		0			0
$943$	−45882.4	+	16699.8i	−1.58445	+	0.576693i
$944$	−9575.27			−0.330136
$945$		0			0
$946$	−43384.9			−1.49108
$947$	40868.7	−	14875.0i	1.40238	−	0.510425i	0.473496	−	0.880796i	$-0.342992\pi$
$947$	40868.7	−	14875.0i	1.40238	−	0.510425i	0.928884	+	0.370371i	$0.120770\pi$
$948$		0			0
$949$	42054.4	−	35287.8i	1.43851	−	1.20705i
$950$	−3022.12	−	17139.3i	−0.103211	−	0.585339i
$951$		0			0
$952$	−67.2613	−	56.4389i	−0.00228986	−	0.00192142i
$953$	−2326.72	+	4030.00i	−0.0790869	+	0.136983i	−0.902856	−	0.429943i	$-0.858534\pi$
$953$	−2326.72	+	4030.00i	−0.0790869	+	0.136983i	0.823769	+	0.566925i	$0.191867\pi$
$954$		0			0
$955$	5273.04	+	9133.18i	0.178672	+	0.309469i
$956$	−798.740	+	4529.88i	−0.0270221	+	0.153250i
$957$		0			0
$958$	27195.3	+	9898.26i	0.917160	+	0.333819i
$959$	2130.93	+	775.593i	0.0717530	+	0.0261160i
$960$		0			0
$961$	−3718.29	+	21087.5i	−0.124812	+	0.707846i
$962$	−6915.02	−	11977.2i	−0.231756	−	0.401413i
$963$		0			0
$964$	−6699.21	+	11603.4i	−0.223825	+	0.387676i
$965$	49797.8	+	41785.3i	1.66119	+	1.39390i
$966$		0			0
$967$	8331.51	+	47250.4i	0.277067	+	1.57132i	0.732320	+	0.680961i	$0.238438\pi$
$967$	8331.51	+	47250.4i	0.277067	+	1.57132i	−0.455253	+	0.890362i	$0.650451\pi$
$968$	−1852.09	+	1554.09i	−0.0614963	+	0.0516015i
$969$		0			0
$970$	−4521.99	+	1645.87i	−0.149683	+	0.0544801i
$971$	46142.0			1.52499			0.762496	−	0.646993i	$-0.223974\pi$
$971$	46142.0			1.52499			0.762496	+	0.646993i	$0.223974\pi$
$972$		0			0
$973$	−1522.07			−0.0501493
$974$	23119.2	−	8414.70i	0.760561	−	0.276822i
$975$		0			0
$976$	−3527.70	+	2960.10i	−0.115696	+	0.0970803i
$977$	−3244.80	−	18402.2i	−0.106254	−	0.602598i	−0.990712	−	0.135978i	$-0.956583\pi$
$977$	−3244.80	−	18402.2i	−0.106254	−	0.602598i	0.884458	−	0.466621i	$-0.154529\pi$
$978$		0			0
$979$	31424.5	+	26368.3i	1.02587	+	0.860810i
$980$	9866.70	−	17089.6i	0.321612	−	0.557049i
$981$		0			0
$982$	−1872.71	−	3243.63i	−0.0608560	−	0.105406i
$983$	−4561.77	+	25871.1i	−0.148014	+	0.839430i	0.816883	+	0.576803i	$0.195700\pi$
$983$	−4561.77	+	25871.1i	−0.148014	+	0.839430i	−0.964897	+	0.262627i	$0.915411\pi$
$984$		0			0
$985$	−45036.2	−	16391.8i	−1.45682	−	0.530241i
$986$	−4995.95	−	1818.38i	−0.161362	−	0.0587311i
$987$		0			0
$988$	−4211.77	+	23886.1i	−0.135622	+	0.769148i
$989$	25478.4	+	44129.9i	0.819178	+	1.41886i
$990$		0			0
$991$	1426.66	−	2471.05i	0.0457309	−	0.0792082i	−0.842254	−	0.539081i	$-0.818772\pi$
$991$	1426.66	−	2471.05i	0.0457309	−	0.0792082i	0.887985	+	0.459873i	$0.152105\pi$
$992$	−2243.78	−	1882.75i	−0.0718146	−	0.0602596i
$993$		0			0
$994$	−88.6583	−	502.806i	−0.00282904	−	0.0160443i
$995$	−41425.7	+	34760.3i	−1.31988	+	1.10751i
$996$		0			0
$997$	22541.1	−	8204.29i	0.716032	−	0.260614i	0.0417916	−	0.999126i	$-0.486693\pi$
$997$	22541.1	−	8204.29i	0.716032	−	0.260614i	0.674240	+	0.738512i	$0.264471\pi$
$998$	19344.1			0.613554
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.a.19.4		24
3.2	odd	2		54.4.e.a.7.4	✓	24
27.2	odd	18		1458.4.a.h.1.3		12
27.4	even	9	inner	162.4.e.a.145.4		24
27.23	odd	18		54.4.e.a.31.4	yes	24
27.25	even	9		1458.4.a.e.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.a.7.4	✓	24	3.2	odd	2
54.4.e.a.31.4	yes	24	27.23	odd	18
162.4.e.a.19.4		24	1.1	even	1	trivial
162.4.e.a.145.4		24	27.4	even	9	inner
1458.4.a.e.1.10		12	27.25	even	9
1458.4.a.h.1.3		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)

\(f(q)\)	\(=\)	\(q+(1.87939 - 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(2.50669 + 14.2161i) q^{5} +(0.855575 + 0.717913i) q^{7} +(4.00000 - 6.92820i) q^{8} +O(q^{10})\)	\(q+(1.87939 - 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(2.50669 + 14.2161i) q^{5} +(0.855575 + 0.717913i) q^{7} +(4.00000 - 6.92820i) q^{8} +(14.4354 + 25.0029i) q^{10} +(-7.01766 + 39.7991i) q^{11} +(54.5985 + 19.8722i) q^{13} +(2.09904 + 0.763987i) q^{14} +(2.77837 - 15.7569i) q^{16} +(-4.91345 - 8.51035i) q^{17} +(-52.1806 + 90.3795i) q^{19} +(44.2328 + 37.1157i) q^{20} +(14.0353 + 79.5982i) q^{22} +(72.7227 - 61.0216i) q^{23} +(-78.3534 + 28.5183i) q^{25} +116.205 q^{26} +4.46750 q^{28} +(254.197 - 92.5203i) q^{29} +(70.1181 - 58.8361i) q^{31} +(-5.55674 - 31.5138i) q^{32} +(-15.0557 - 12.6332i) q^{34} +(-8.06128 + 13.9626i) q^{35} +(-59.5071 - 103.069i) q^{37} +(-36.2443 + 205.552i) q^{38} +(108.519 + 39.4977i) q^{40} +(-483.315 - 175.912i) q^{41} +(-93.2087 + 528.613i) q^{43} +(80.8261 + 139.995i) q^{44} +(94.9328 - 164.428i) q^{46} +(-32.1596 - 26.9851i) q^{47} +(-59.3447 - 336.561i) q^{49} +(-127.748 + 107.194i) q^{50} +(218.394 - 79.4888i) q^{52} +25.9337 q^{53} -583.380 q^{55} +(8.39615 - 3.05595i) q^{56} +(414.447 - 347.762i) q^{58} +(-103.921 - 589.363i) q^{59} +(-220.481 - 185.006i) q^{61} +(91.5327 - 158.539i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(-145.645 + 825.992i) q^{65} +(413.370 + 150.454i) q^{67} +(-36.9371 - 13.4440i) q^{68} +(-5.59931 + 31.7553i) q^{70} +(-114.284 - 197.945i) q^{71} +(472.425 - 818.264i) q^{73} +(-182.340 - 153.002i) q^{74} +(72.4886 + 411.103i) q^{76} +(-34.5764 + 29.0131i) q^{77} +(-583.884 + 212.516i) q^{79} +230.967 q^{80} -1028.67 q^{82} +(-734.263 + 267.250i) q^{83} +(108.668 - 91.1831i) q^{85} +(186.417 + 1057.23i) q^{86} +(247.666 + 207.816i) q^{88} +(507.530 - 879.069i) q^{89} +(32.4466 + 56.1991i) q^{91} +(65.9396 - 373.962i) q^{92} +(-78.8992 - 28.7169i) q^{94} +(-1415.65 - 515.254i) q^{95} +(-28.9437 + 164.148i) q^{97} +(-341.753 - 591.933i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8}+O(q^{10}) \) 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

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