LMFDB - Embedded newform 936.2.ed.d.739.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(19,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.ed (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			739.3
Character	$\chi$	$=$	936.739
Dual form			936.2.ed.d.19.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.977524 - 1.02198i) q^{2} +(-0.0888919 + 1.99802i) q^{4} +(-2.13831 + 2.13831i) q^{5} +(1.43298 - 0.383965i) q^{7} +(2.12884 - 1.86227i) q^{8} +(4.27556 + 0.0950627i) q^{10} +(1.14540 + 0.306909i) q^{11} +(1.50651 + 3.27573i) q^{13} +(-1.79317 - 1.08914i) q^{14} +(-3.98420 - 0.355216i) q^{16} +(0.917474 + 0.529704i) q^{17} +(-3.01087 + 0.806761i) q^{19} +(-4.08231 - 4.46247i) q^{20} +(-0.806001 - 1.47059i) q^{22} +(-2.44668 - 4.23777i) q^{23} -4.14473i q^{25} +(1.87509 - 4.74173i) q^{26} +(0.639791 + 2.89725i) q^{28} +(-0.430121 + 0.248330i) q^{29} +(-0.180109 + 0.180109i) q^{31} +(3.53162 + 4.41901i) q^{32} +(-0.355506 - 1.45544i) q^{34} +(-2.24311 + 3.88518i) q^{35} +(-0.869322 + 3.24435i) q^{37} +(3.76770 + 2.28843i) q^{38} +(-0.570000 + 8.53422i) q^{40} +(-1.95534 + 7.29743i) q^{41} +(-0.979452 - 0.565487i) q^{43} +(-0.715028 + 2.26125i) q^{44} +(-1.93923 + 6.64298i) q^{46} +(-5.29277 - 5.29277i) q^{47} +(-4.15619 + 2.39957i) q^{49} +(-4.23584 + 4.05158i) q^{50} +(-6.67891 + 2.71886i) q^{52} +13.2050i q^{53} +(-3.10549 + 1.79295i) q^{55} +(2.33553 - 3.48599i) q^{56} +(0.674242 + 0.196826i) q^{58} +(1.58626 + 5.92000i) q^{59} +(-9.32964 - 5.38647i) q^{61} +(0.360130 + 0.00800711i) q^{62} +(1.06389 - 7.92894i) q^{64} +(-10.2259 - 3.78314i) q^{65} +(-3.22308 + 12.0287i) q^{67} +(-1.13992 + 1.78605i) q^{68} +(6.16328 - 1.50544i) q^{70} +(1.99632 + 7.45038i) q^{71} +(4.04472 - 4.04472i) q^{73} +(4.16545 - 2.28300i) q^{74} +(-1.34429 - 6.08751i) q^{76} +1.75917 q^{77} +0.933621i q^{79} +(9.27901 - 7.75988i) q^{80} +(9.36923 - 5.13509i) q^{82} +(6.19701 + 6.19701i) q^{83} +(-3.09451 + 0.829172i) q^{85} +(0.379521 + 1.55376i) q^{86} +(3.00992 - 1.47969i) q^{88} +(-2.06105 - 0.552258i) q^{89} +(3.41656 + 4.11560i) q^{91} +(8.68465 - 4.51181i) q^{92} +(-0.235301 + 10.5829i) q^{94} +(4.71307 - 8.16328i) q^{95} +(-3.94895 + 1.05812i) q^{97} +(6.51509 + 1.90190i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{2} - 6 q^{4} + 10 q^{8} - 6 q^{10} + 8 q^{11} - 8 q^{14} - 10 q^{16} + 12 q^{17} - 8 q^{19} - 10 q^{20} - 20 q^{22} + 2 q^{26} + 12 q^{28} - 16 q^{32} - 46 q^{34} + 4 q^{35} - 32 q^{40} - 12 q^{43}+ \cdots + 16 q^{98}+O(q^{100}) $ 48 * q + 4 * q^2 - 6 * q^4 + 10 * q^8 - 6 * q^10 + 8 * q^11 - 8 * q^14 - 10 * q^16 + 12 * q^17 - 8 * q^19 - 10 * q^20 - 20 * q^22 + 2 * q^26 + 12 * q^28 - 16 * q^32 - 46 * q^34 + 4 * q^35 - 32 * q^40 - 12 * q^43 + 16 * q^44 + 34 * q^46 - 60 * q^49 - 86 * q^50 + 12 * q^52 - 48 * q^56 + 30 * q^58 + 64 * q^59 - 42 * q^62 + 16 * q^65 - 8 * q^67 + 32 * q^68 + 36 * q^70 - 12 * q^73 - 38 * q^74 - 94 * q^76 + 108 * q^80 + 54 * q^82 + 48 * q^83 - 80 * q^86 - 108 * q^88 - 12 * q^89 + 104 * q^91 + 20 * q^92 + 26 * q^94 + 4 * q^97 + 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.977524	−	1.02198i	−0.691214	−	0.722650i
$2$	−0.977524	−	1.02198i	−0.691214	−	0.722650i
$3$		0			0
$3$		0			0
$4$	−0.0888919	+	1.99802i	−0.0444460	+	0.999012i
$5$	−2.13831	+	2.13831i	−0.956281	+	0.956281i	−0.999084	−	0.0428025i	$-0.986371\pi$
$5$	−2.13831	+	2.13831i	−0.956281	+	0.956281i	0.0428025	+	0.999084i	$0.486371\pi$
$6$		0			0
$7$	1.43298	−	0.383965i	0.541614	−	0.145125i	0.0223680	−	0.999750i	$-0.492879\pi$
$7$	1.43298	−	0.383965i	0.541614	−	0.145125i	0.519246	+	0.854625i	$0.326213\pi$
$8$	2.12884	−	1.86227i	0.752658	−	0.658412i
$9$		0			0
$10$	4.27556	+	0.0950627i	1.35205	+	0.0300615i
$11$	1.14540	+	0.306909i	0.345351	+	0.0925365i	0.427325	−	0.904098i	$-0.359456\pi$
$11$	1.14540	+	0.306909i	0.345351	+	0.0925365i	−0.0819743	+	0.996634i	$0.526123\pi$
$12$		0			0
$13$	1.50651	+	3.27573i	0.417831	+	0.908525i
$13$	1.50651	+	3.27573i	0.417831	+	0.908525i
$14$	−1.79317	−	1.08914i	−0.479246	−	0.291085i
$15$		0			0
$16$	−3.98420	−	0.355216i	−0.996049	−	0.0888041i
$17$	0.917474	+	0.529704i	0.222520	+	0.128472i	0.607117	−	0.794613i	$-0.292326\pi$
$17$	0.917474	+	0.529704i	0.222520	+	0.128472i	−0.384597	+	0.923085i	$0.625659\pi$
$18$		0			0
$19$	−3.01087	+	0.806761i	−0.690742	+	0.185084i	−0.587080	−	0.809529i	$-0.699723\pi$
$19$	−3.01087	+	0.806761i	−0.690742	+	0.185084i	−0.103662	+	0.994613i	$0.533056\pi$
$20$	−4.08231	−	4.46247i	−0.912833	−	0.997839i
$21$		0			0
$22$	−0.806001	−	1.47059i	−0.171840	−	0.313530i
$23$	−2.44668	−	4.23777i	−0.510167	−	0.883635i	−0.999931	−	0.0117799i	$-0.996250\pi$
$23$	−2.44668	−	4.23777i	−0.510167	−	0.883635i	0.489764	−	0.871855i	$-0.337083\pi$
$24$		0			0
$25$		−	4.14473i		−	0.828947i
$26$	1.87509	−	4.74173i	0.367735	−	0.929931i
$27$		0			0
$28$	0.639791	+	2.89725i	0.120909	+	0.547529i
$29$	−0.430121	+	0.248330i	−0.0798714	+	0.0461138i	−0.539404	−	0.842047i	$-0.681350\pi$
$29$	−0.430121	+	0.248330i	−0.0798714	+	0.0461138i	0.459532	+	0.888161i	$0.348017\pi$
$30$		0			0
$31$	−0.180109	+	0.180109i	−0.0323486	+	0.0323486i	−0.723096	−	0.690747i	$-0.757282\pi$
$31$	−0.180109	+	0.180109i	−0.0323486	+	0.0323486i	0.690747	+	0.723096i	$0.257282\pi$
$32$	3.53162	+	4.41901i	0.624309	+	0.781177i
$33$		0			0
$34$	−0.355506	−	1.45544i	−0.0609687	−	0.249606i
$35$	−2.24311	+	3.88518i	−0.379155	+	0.656716i
$36$		0			0
$37$	−0.869322	+	3.24435i	−0.142916	+	0.533368i	0.856924	+	0.515443i	$0.172373\pi$
$37$	−0.869322	+	3.24435i	−0.142916	+	0.533368i	−0.999839	+	0.0179251i	$0.994294\pi$
$38$	3.76770	+	2.28843i	0.611201	+	0.371232i
$39$		0			0
$40$	−0.570000	+	8.53422i	−0.0901250	+	1.34938i
$41$	−1.95534	+	7.29743i	−0.305373	+	1.13967i	0.627251	+	0.778817i	$0.284180\pi$
$41$	−1.95534	+	7.29743i	−0.305373	+	1.13967i	−0.932624	+	0.360850i	$0.882487\pi$
$42$		0			0
$43$	−0.979452	−	0.565487i	−0.149365	−	0.0862359i	0.423455	−	0.905917i	$-0.360817\pi$
$43$	−0.979452	−	0.565487i	−0.149365	−	0.0862359i	−0.572820	+	0.819681i	$0.694151\pi$
$44$	−0.715028	+	2.26125i	−0.107795	+	0.340897i
$45$		0			0
$46$	−1.93923	+	6.64298i	−0.285924	+	0.979453i
$47$	−5.29277	−	5.29277i	−0.772030	−	0.772030i	0.206431	−	0.978461i	$-0.433815\pi$
$47$	−5.29277	−	5.29277i	−0.772030	−	0.772030i	−0.978461	+	0.206431i	$0.933815\pi$
$48$		0			0
$49$	−4.15619	+	2.39957i	−0.593741	+	0.342796i
$50$	−4.23584	+	4.05158i	−0.599038	+	0.572980i
$51$		0			0
$52$	−6.67891	+	2.71886i	−0.926198	+	0.377038i
$53$			13.2050i			1.81385i	0.421292	+	0.906925i	$0.361577\pi$
$53$			13.2050i			1.81385i	−0.421292	+	0.906925i	$0.638423\pi$
$54$		0			0
$55$	−3.10549	+	1.79295i	−0.418744	+	0.241762i
$56$	2.33553	−	3.48599i	0.312098	−	0.465835i
$57$		0			0
$58$	0.674242	+	0.196826i	0.0885324	+	0.0258446i
$59$	1.58626	+	5.92000i	0.206513	+	0.770718i	0.988983	+	0.148029i	$0.0472930\pi$
$59$	1.58626	+	5.92000i	0.206513	+	0.770718i	−0.782470	+	0.622689i	$0.786040\pi$
$60$		0			0
$61$	−9.32964	−	5.38647i	−1.19454	−	0.689667i	−0.235206	−	0.971946i	$-0.575576\pi$
$61$	−9.32964	−	5.38647i	−1.19454	−	0.689667i	−0.959332	+	0.282279i	$0.908910\pi$
$62$	0.360130	+	0.00800711i	0.0457365	+	0.00101690i
$63$		0			0
$64$	1.06389	−	7.92894i	0.132987	−	0.991118i
$65$	−10.2259	−	3.78314i	−1.26837	−	0.469241i
$66$		0			0
$67$	−3.22308	+	12.0287i	−0.393762	+	1.46954i	0.430118	+	0.902773i	$0.358472\pi$
$67$	−3.22308	+	12.0287i	−0.393762	+	1.46954i	−0.823879	+	0.566765i	$0.808195\pi$
$68$	−1.13992	+	1.78605i	−0.138235	+	0.216590i
$69$		0			0
$70$	6.16328	−	1.50544i	0.736653	−	0.179935i
$71$	1.99632	+	7.45038i	0.236920	+	0.884197i	0.977274	+	0.211980i	$0.0679912\pi$
$71$	1.99632	+	7.45038i	0.236920	+	0.884197i	−0.740354	+	0.672217i	$0.765342\pi$
$72$		0			0
$73$	4.04472	−	4.04472i	0.473399	−	0.473399i	−0.429614	−	0.903013i	$-0.641350\pi$
$73$	4.04472	−	4.04472i	0.473399	−	0.473399i	0.903013	+	0.429614i	$0.141350\pi$
$74$	4.16545	−	2.28300i	0.484224	−	0.265394i
$75$		0			0
$76$	−1.34429	−	6.08751i	−0.154200	−	0.698285i
$77$	1.75917			0.200476
$78$		0			0
$79$			0.933621i			0.105041i	0.998620	+	0.0525203i	$0.0167254\pi$
$79$			0.933621i			0.105041i	−0.998620	+	0.0525203i	$0.983275\pi$
$80$	9.27901	−	7.75988i	1.03742	−	0.867581i
$81$		0			0
$82$	9.36923	−	5.13509i	1.03466	−	0.567076i
$83$	6.19701	+	6.19701i	0.680210	+	0.680210i	0.960047	−	0.279837i	$-0.0902805\pi$
$83$	6.19701	+	6.19701i	0.680210	+	0.680210i	−0.279837	+	0.960047i	$0.590281\pi$
$84$		0			0
$85$	−3.09451	+	0.829172i	−0.335647	+	0.0899363i
$86$	0.379521	+	1.55376i	0.0409248	+	0.167546i
$87$		0			0
$88$	3.00992	−	1.47969i	0.320858	−	0.157735i
$89$	−2.06105	−	0.552258i	−0.218471	−	0.0585392i	0.147923	−	0.988999i	$-0.452741\pi$
$89$	−2.06105	−	0.552258i	−0.218471	−	0.0585392i	−0.366394	+	0.930460i	$0.619408\pi$
$90$		0			0
$91$	3.41656	+	4.11560i	0.358153	+	0.431432i
$92$	8.68465	−	4.51181i	0.905437	−	0.470389i
$93$		0			0
$94$	−0.235301	+	10.5829i	−0.0242694	+	1.09155i
$95$	4.71307	−	8.16328i	0.483551	−	0.837535i
$96$		0			0
$97$	−3.94895	+	1.05812i	−0.400955	+	0.107436i	−0.453661	−	0.891174i	$-0.649882\pi$
$97$	−3.94895	+	1.05812i	−0.400955	+	0.107436i	0.0527054	+	0.998610i	$0.483216\pi$
$98$	6.51509	+	1.90190i	0.658124	+	0.192121i
$99$		0			0
$100$	8.28128	+	0.368433i	0.828128	+	0.0368433i
$101$	−5.45375	−	9.44617i	−0.542668	−	0.939929i	−0.998750	−	0.0499909i	$-0.984081\pi$
$101$	−5.45375	−	9.44617i	−0.542668	−	0.939929i	0.456081	−	0.889938i	$-0.349253\pi$
$102$		0			0
$103$	5.93866			0.585154			0.292577	−	0.956242i	$-0.405487\pi$
$103$	5.93866			0.585154			0.292577	+	0.956242i	$0.405487\pi$
$104$	9.30742	+	4.16797i	0.912667	+	0.408703i
$105$		0			0
$106$	13.4953	−	12.9082i	1.31078	−	1.25376i
$107$	−3.86681	−	6.69752i	−0.373819	−	0.647474i	0.616330	−	0.787488i	$-0.288619\pi$
$107$	−3.86681	−	6.69752i	−0.373819	−	0.647474i	−0.990150	+	0.140014i	$0.955285\pi$
$108$		0			0
$109$	−4.46618	+	4.46618i	−0.427782	+	0.427782i	−0.887872	−	0.460090i	$-0.847817\pi$
$109$	−4.46618	+	4.46618i	−0.427782	+	0.427782i	0.460090	+	0.887872i	$0.347817\pi$
$110$	4.86805	+	1.42109i	0.464151	+	0.135496i
$111$		0			0
$112$	−5.84565	+	1.02077i	−0.552362	+	0.0964542i
$113$	−5.74089	+	9.94352i	−0.540058	+	0.935408i	0.458842	+	0.888518i	$0.348264\pi$
$113$	−5.74089	+	9.94352i	−0.540058	+	0.935408i	−0.998900	+	0.0468899i	$0.985069\pi$
$114$		0			0
$115$	14.2934	+	3.82991i	1.33287	+	0.357141i
$116$	−0.457936	−	0.881466i	−0.0425182	−	0.0818420i
$117$		0			0
$118$	4.49952	−	7.40807i	0.414214	−	0.681968i
$119$	1.51811	+	0.406775i	0.139165	+	0.0372890i
$120$		0			0
$121$	−8.30853	−	4.79693i	−0.755321	−	0.436085i
$122$	3.61508	+	14.8001i	0.327294	+	1.33994i
$123$		0			0
$124$	−0.343853	−	0.375873i	−0.0308789	−	0.0337544i
$125$	−1.82882	−	1.82882i	−0.163575	−	0.163575i
$126$		0			0
$127$	−4.40510	−	7.62986i	−0.390890	−	0.677041i	0.601678	−	0.798739i	$-0.294499\pi$
$127$	−4.40510	−	7.62986i	−0.390890	−	0.677041i	−0.992567	+	0.121698i	$0.961166\pi$
$128$	−9.14321	+	6.66346i	−0.808154	+	0.588972i
$129$		0			0
$130$	6.12978	+	14.1488i	0.537617	+	1.24093i
$131$	14.7822			1.29153			0.645765	−	0.763536i	$-0.276539\pi$
$131$	14.7822			1.29153			0.645765	+	0.763536i	$0.276539\pi$
$132$		0			0
$133$	−4.00474	+	2.31214i	−0.347255	+	0.200488i
$134$	15.4437	−	8.46441i	1.33414	−	0.731214i
$135$		0			0
$136$	2.93960	−	0.580932i	0.252069	−	0.0498145i
$137$	−0.0261039	−	0.0974210i	−0.00223021	−	0.00832324i	0.964802	−	0.262978i	$-0.0847048\pi$
$137$	−0.0261039	−	0.0974210i	−0.00223021	−	0.00832324i	−0.967032	+	0.254655i	$0.918038\pi$
$138$		0			0
$139$	3.39564	−	5.88143i	0.288015	−	0.498856i	−0.685321	−	0.728241i	$-0.740338\pi$
$139$	3.39564	−	5.88143i	0.288015	−	0.498856i	0.973336	+	0.229385i	$0.0736715\pi$
$140$	−7.56329	−	4.82715i	−0.639215	−	0.407969i
$141$		0			0
$142$	5.66269	−	9.32313i	0.475203	−	0.782380i
$143$	0.720205	+	4.21439i	0.0602266	+	0.352425i
$144$		0			0
$145$	0.388724	−	1.45074i	0.0322818	−	0.120477i
$146$	−8.08744	−	0.179816i	−0.669322	−	0.0148817i
$147$		0			0
$148$	−6.40502	−	2.02532i	−0.526489	−	0.166480i
$149$	−3.37169	−	12.5833i	−0.276220	−	1.03087i	−0.955020	−	0.296543i	$-0.904166\pi$
$149$	−3.37169	−	12.5833i	−0.276220	−	1.03087i	0.678800	−	0.734323i	$-0.262500\pi$
$150$		0			0
$151$	8.53114	+	8.53114i	0.694254	+	0.694254i	0.963165	−	0.268911i	$-0.0866638\pi$
$151$	8.53114	+	8.53114i	0.694254	+	0.694254i	−0.268911	+	0.963165i	$0.586664\pi$
$152$	−4.90725	+	7.32452i	−0.398030	+	0.594097i
$153$		0			0
$154$	−1.71963	−	1.79784i	−0.138572	−	0.144874i
$155$		−	0.770259i		−	0.0618687i
$156$		0			0
$157$		−	0.522164i		−	0.0416732i	−0.999783	−	0.0208366i	$-0.993367\pi$
$157$		−	0.522164i		−	0.0416732i	0.999783	−	0.0208366i	$-0.00663298\pi$
$158$	0.954143	−	0.912637i	0.0759076	−	0.0726055i
$159$		0			0
$160$	−17.0009	−	1.89750i	−1.34404	−	0.150010i
$161$	−5.13318	−	5.13318i	−0.404551	−	0.404551i
$162$		0			0
$163$	6.43789	+	24.0265i	0.504255	+	1.88190i	0.470353	+	0.882479i	$0.344127\pi$
$163$	6.43789	+	24.0265i	0.504255	+	1.88190i	0.0339021	+	0.999425i	$0.489207\pi$
$164$	−14.4066	−	4.55550i	−1.12497	−	0.355725i
$165$		0			0
$166$	0.275500	−	12.3910i	0.0213830	−	0.961725i
$167$	−0.809102	+	3.01961i	−0.0626102	+	0.233665i	−0.990139	−	0.140087i	$-0.955262\pi$
$167$	−0.809102	+	3.01961i	−0.0626102	+	0.233665i	0.927529	+	0.373751i	$0.121929\pi$
$168$		0			0
$169$	−8.46085	+	9.86985i	−0.650835	+	0.759220i
$170$	3.87236	+	2.35200i	0.296996	+	0.180390i
$171$		0			0
$172$	1.21692	−	1.90670i	0.0927894	−	0.145385i
$173$	3.28703	−	5.69330i	0.249908	−	0.432853i	−0.713592	−	0.700561i	$-0.752933\pi$
$173$	3.28703	−	5.69330i	0.249908	−	0.432853i	0.963500	+	0.267708i	$0.0862663\pi$
$174$		0			0
$175$	−1.59143	−	5.93931i	−0.120301	−	0.448969i
$176$	−4.45448	−	1.62965i	−0.335769	−	0.122840i
$177$		0			0
$178$	1.45033	+	2.64621i	0.108707	+	0.198341i
$179$	−19.1587	+	11.0613i	−1.43199	+	0.826760i	−0.997273	−	0.0738069i	$-0.976485\pi$
$179$	−19.1587	+	11.0613i	−1.43199	+	0.826760i	−0.434718	+	0.900567i	$0.643152\pi$
$180$		0			0
$181$	21.7718			1.61828			0.809141	−	0.587614i	$-0.199933\pi$
$181$	21.7718			1.61828			0.809141	+	0.587614i	$0.199933\pi$
$182$	0.866296	−	7.51476i	0.0642141	−	0.557031i
$183$		0			0
$184$	−13.1004	−	4.46514i	−0.965777	−	0.329174i
$185$	−5.07855	−	8.79631i	−0.373383	−	0.646718i
$186$		0			0
$187$	0.888303	+	0.888303i	0.0649592	+	0.0649592i
$188$	11.0456	−	10.1046i	0.805581	−	0.736954i
$189$		0			0
$190$	−12.9499	+	3.16313i	−0.939482	+	0.229478i
$191$	1.44924	+	0.836719i	0.104863	+	0.0605429i	0.551514	−	0.834165i	$-0.314050\pi$
$191$	1.44924	+	0.836719i	0.104863	+	0.0605429i	−0.446651	+	0.894708i	$0.647383\pi$
$192$		0			0
$193$	−5.90121	−	1.58123i	−0.424779	−	0.113819i	0.0400956	−	0.999196i	$-0.487234\pi$
$193$	−5.90121	−	1.58123i	−0.424779	−	0.113819i	−0.464874	+	0.885377i	$0.653900\pi$
$194$	4.94158	+	3.00142i	0.354784	+	0.215489i
$195$		0			0
$196$	−4.42496	−	8.51746i	−0.316068	−	0.608390i
$197$	−8.91936	−	2.38994i	−0.635478	−	0.170276i	−0.0733239	−	0.997308i	$-0.523361\pi$
$197$	−8.91936	−	2.38994i	−0.635478	−	0.170276i	−0.562154	+	0.827032i	$0.690027\pi$
$198$		0			0
$199$	10.3397	−	17.9089i	0.732961	−	1.26953i	−0.222651	−	0.974898i	$-0.571471\pi$
$199$	10.3397	−	17.9089i	0.732961	−	1.26953i	0.955612	−	0.294628i	$-0.0951957\pi$
$200$	−7.71862	−	8.82346i	−0.545789	−	0.623913i
$201$		0			0
$202$	−4.32264	+	14.8075i	−0.304140	+	1.04185i
$203$	−0.521003	+	0.521003i	−0.0365672	+	0.0365672i
$204$		0			0
$205$	−11.4230	−	19.7853i	−0.797820	−	1.38186i
$206$	−5.80519	−	6.06920i	−0.404467	−	0.422861i
$207$		0			0
$208$	−4.83864	−	13.5863i	−0.335499	−	0.942040i
$209$	−3.69625			−0.255675
$210$		0			0
$211$	−10.7064	−	18.5440i	−0.737059	−	1.27662i	−0.953814	−	0.300398i	$-0.902881\pi$
$211$	−10.7064	−	18.5440i	−0.737059	−	1.27662i	0.216755	−	0.976226i	$-0.430453\pi$
$212$	−26.3840	−	1.17382i	−1.81206	−	0.0806183i
$213$		0			0
$214$	−3.06483	+	10.4988i	−0.209508	+	0.717683i
$215$	3.30356	−	0.885185i	0.225301	−	0.0603691i
$216$		0			0
$217$	−0.188937	+	0.327248i	−0.0128259	+	0.0222151i
$218$	8.93015	+	0.198553i	0.604826	+	0.0134477i
$219$		0			0
$220$	−3.30631	−	6.36421i	−0.222911	−	0.429075i
$221$	−0.352984	+	3.80340i	−0.0237442	+	0.255845i
$222$		0			0
$223$	9.84578	+	2.63817i	0.659323	+	0.176665i	0.572940	−	0.819597i	$-0.305803\pi$
$223$	9.84578	+	2.63817i	0.659323	+	0.176665i	0.0863822	+	0.996262i	$0.472469\pi$
$224$	6.75748	+	4.97631i	0.451503	+	0.332494i
$225$		0			0
$226$	15.7740	−	3.85295i	1.04927	−	0.256294i
$227$	−3.62620	+	0.971637i	−0.240679	+	0.0644898i	−0.377142	−	0.926155i	$-0.623093\pi$
$227$	−3.62620	+	0.971637i	−0.240679	+	0.0644898i	0.136463	+	0.990645i	$0.456427\pi$
$228$		0			0
$229$	5.43768	+	5.43768i	0.359332	+	0.359332i	0.863567	−	0.504235i	$-0.168225\pi$
$229$	5.43768	+	5.43768i	0.359332	+	0.359332i	−0.504235	+	0.863567i	$0.668225\pi$
$230$	−10.0581	−	18.3514i	−0.663209	−	1.21006i
$231$		0			0
$232$	−0.453198	+	1.32966i	−0.0297539	+	0.0872962i
$233$		−	2.92911i		−	0.191892i	−0.995387	−	0.0959461i	$-0.969412\pi$
$233$		−	2.92911i		−	0.191892i	0.995387	−	0.0959461i	$-0.0305876\pi$
$234$		0			0
$235$	22.6352			1.47656
$236$	−11.9693	+	2.64314i	−0.779135	+	0.172054i
$237$		0			0
$238$	−1.06827	−	1.94911i	−0.0692456	−	0.126342i
$239$	14.3258	−	14.3258i	0.926659	−	0.926659i	−0.0708299	−	0.997488i	$-0.522565\pi$
$239$	14.3258	−	14.3258i	0.926659	−	0.926659i	0.997488	+	0.0708299i	$0.0225647\pi$
$240$		0			0
$241$	3.51676	+	13.1247i	0.226534	+	0.845437i	0.981784	+	0.190000i	$0.0608488\pi$
$241$	3.51676	+	13.1247i	0.226534	+	0.845437i	−0.755250	+	0.655437i	$0.772484\pi$
$242$	3.21942	+	13.1803i	0.206952	+	0.847261i
$243$		0			0
$244$	11.5916	−	18.1620i	0.742078	−	1.16270i
$245$	3.75618	−	14.0182i	0.239973	−	0.895593i
$246$		0			0
$247$	−7.17865	−	8.64742i	−0.456766	−	0.550222i
$248$	−0.0480110	+	0.718836i	−0.00304870	+	0.0456461i
$249$		0			0
$250$	−0.0813039	+	3.65674i	−0.00514211	+	0.231273i
$251$	9.51992	+	5.49633i	0.600892	+	0.346925i	0.769392	−	0.638777i	$-0.220559\pi$
$251$	9.51992	+	5.49633i	0.600892	+	0.346925i	−0.168501	+	0.985702i	$0.553893\pi$
$252$		0			0
$253$	−1.50181	−	5.60484i	−0.0944182	−	0.352373i
$254$	−3.49148	+	11.9603i	−0.219075	+	0.750456i
$255$		0			0
$256$	15.7476	+	2.83050i	0.984228	+	0.176906i
$257$	11.6764	−	6.74138i	0.728355	−	0.420516i	−0.0894651	−	0.995990i	$-0.528516\pi$
$257$	11.6764	−	6.74138i	0.728355	−	0.420516i	0.817820	+	0.575474i	$0.195182\pi$
$258$		0			0
$259$			4.98287i			0.309621i
$260$	8.46781	−	20.0953i	0.525151	−	1.24626i
$261$		0			0
$262$	−14.4500	−	15.1072i	−0.892724	−	0.933324i
$263$	−18.3764	+	10.6096i	−1.13313	+	0.654216i	−0.944721	−	0.327874i	$-0.893668\pi$
$263$	−18.3764	+	10.6096i	−1.13313	+	0.654216i	−0.188413	+	0.982090i	$0.560334\pi$
$264$		0			0
$265$	−28.2364	−	28.2364i	−1.73455	−	1.73455i
$266$	6.27770	+	1.83260i	0.384910	+	0.112364i
$267$		0			0
$268$	−23.7471	−	7.50904i	−1.45058	−	0.458688i
$269$	25.1549	+	14.5232i	1.53372	+	0.885495i	0.999186	+	0.0403505i	$0.0128475\pi$
$269$	25.1549	+	14.5232i	1.53372	+	0.885495i	0.534537	+	0.845145i	$0.320486\pi$
$270$		0			0
$271$	3.45071	−	12.8782i	0.209616	−	0.782296i	−0.778377	−	0.627797i	$-0.783957\pi$
$271$	3.45071	−	12.8782i	0.209616	−	0.782296i	0.987993	−	0.154500i	$-0.0493765\pi$
$272$	−3.46724	−	2.43634i	−0.210232	−	0.147725i
$273$		0			0
$274$	−0.0740453	+	0.121909i	−0.00447324	+	0.00736480i
$275$	1.27206	−	4.74738i	0.0767079	−	0.286278i
$276$		0			0
$277$	−12.3608	+	21.4095i	−0.742686	+	1.28637i	0.208583	+	0.978005i	$0.433115\pi$
$277$	−12.3608	+	21.4095i	−0.742686	+	1.28637i	−0.951268	+	0.308364i	$0.900218\pi$
$278$	−9.33003	+	2.27895i	−0.559578	+	0.136683i
$279$		0			0
$280$	2.46005	+	12.4482i	0.147016	+	0.743922i
$281$	19.1640	−	19.1640i	1.14323	−	1.14323i	0.155371	−	0.987856i	$-0.450343\pi$
$281$	19.1640	−	19.1640i	1.14323	−	1.14323i	0.987856	−	0.155371i	$-0.0496572\pi$
$282$		0			0
$283$	16.9756	−	9.80085i	1.00909	−	0.582600i	0.0981670	−	0.995170i	$-0.468702\pi$
$283$	16.9756	−	9.80085i	1.00909	−	0.582600i	0.910926	+	0.412570i	$0.135369\pi$
$284$	−15.0635	+	3.32642i	−0.893854	+	0.197387i
$285$		0			0
$286$	3.60300	−	4.85570i	0.213050	−	0.287124i
$287$			11.2078i			0.661577i
$288$		0			0
$289$	−7.93883	−	13.7505i	−0.466990	−	0.808850i
$290$	−1.86261	+	1.02086i	−0.109376	+	0.0599471i
$291$		0			0
$292$	7.72191	+	8.44099i	0.451890	+	0.493972i
$293$	−10.7632	+	2.88398i	−0.628792	+	0.168484i	−0.559121	−	0.829086i	$-0.688861\pi$
$293$	−10.7632	+	2.88398i	−0.628792	+	0.168484i	−0.0696703	+	0.997570i	$0.522195\pi$
$294$		0			0
$295$	−16.0507	−	9.26687i	−0.934507	−	0.539538i
$296$	4.19122	+	8.52561i	0.243610	+	0.495541i
$297$		0			0
$298$	−9.56401	+	15.7463i	−0.554028	+	0.912159i
$299$	10.1958	−	14.3989i	0.589641	−	0.832710i
$300$		0			0
$301$	−1.62066	−	0.434254i	−0.0934132	−	0.0250300i
$302$	0.379268	−	17.0581i	0.0218244	−	0.981581i
$303$		0			0
$304$	12.2825	−	2.14478i	0.704449	−	0.123012i
$305$	31.4676	−	8.43172i	1.80183	−	0.482799i
$306$		0			0
$307$	−8.52938	+	8.52938i	−0.486797	+	0.486797i	−0.907294	−	0.420497i	$-0.861856\pi$
$307$	−8.52938	+	8.52938i	−0.486797	+	0.486797i	0.420497	+	0.907294i	$0.361856\pi$
$308$	−0.156376	+	3.51487i	−0.00891037	+	0.200278i
$309$		0			0
$310$	−0.787191	+	0.752947i	−0.0447094	+	0.0427645i
$311$	8.81350			0.499768			0.249884	−	0.968276i	$-0.419608\pi$
$311$	8.81350			0.499768			0.249884	+	0.968276i	$0.419608\pi$
$312$		0			0
$313$	13.8328			0.781877			0.390938	−	0.920417i	$-0.372151\pi$
$313$	13.8328			0.781877			0.390938	+	0.920417i	$0.372151\pi$
$314$	−0.533642	+	0.510428i	−0.0301151	+	0.0288051i
$315$		0			0
$316$	−1.86540	−	0.0829914i	−0.104937	−	0.00466863i
$317$	−11.7109	+	11.7109i	−0.657749	+	0.657749i	−0.954847	−	0.297098i	$-0.903981\pi$
$317$	−11.7109	+	11.7109i	−0.657749	+	0.657749i	0.297098	+	0.954847i	$0.403981\pi$
$318$		0			0
$319$	−0.568875	+	0.152430i	−0.0318509	+	0.00853442i
$320$	14.6796	+	19.2295i	0.820615	+	1.07496i
$321$		0			0
$322$	−0.228206	+	10.2638i	−0.0127174	+	0.571981i
$323$	−3.18974	−	0.854688i	−0.177482	−	0.0475561i
$324$		0			0
$325$	13.5770	−	6.24409i	0.753119	−	0.346360i
$326$	18.2615	−	30.0659i	1.01141	−	1.66520i
$327$		0			0
$328$	9.42719	+	19.1764i	0.520530	+	1.05884i
$329$	−9.61666	−	5.55218i	−0.530184	−	0.306102i
$330$		0			0
$331$	13.8576	−	3.71314i	0.761683	−	0.204092i	0.142989	−	0.989724i	$-0.454329\pi$
$331$	13.8576	−	3.71314i	0.761683	−	0.204092i	0.618694	+	0.785632i	$0.287662\pi$
$332$	−12.9326	+	11.8309i	−0.709770	+	0.649305i
$333$		0			0
$334$	3.87690	−	2.12486i	0.212135	−	0.116267i
$335$	−18.8291	−	32.6130i	−1.02874	−	1.78184i
$336$		0			0
$337$		−	26.5479i		−	1.44616i	−0.690765	−	0.723079i	$-0.742726\pi$
$337$		−	26.5479i		−	1.44616i	0.690765	−	0.723079i	$-0.257274\pi$
$338$	18.3575	−	1.00119i	0.998516	−	0.0544576i
$339$		0			0
$340$	−1.38163	−	6.25662i	−0.0749293	−	0.339313i
$341$	−0.261574	+	0.151020i	−0.0141650	+	0.00817819i
$342$		0			0
$343$	−12.3774	+	12.3774i	−0.668319	+	0.668319i
$344$	−3.13818	+	0.620176i	−0.169200	+	0.0334376i
$345$		0			0
$346$	−9.03159	+	2.20606i	−0.485541	+	0.118598i
$347$	0.588542	−	1.01939i	0.0315946	−	0.0547235i	−0.849796	−	0.527112i	$-0.823275\pi$
$347$	0.588542	−	1.01939i	0.0315946	−	0.0547235i	0.881390	+	0.472389i	$0.156608\pi$
$348$		0			0
$349$	−7.72090	+	28.8148i	−0.413291	+	1.54242i	0.374945	+	0.927047i	$0.377662\pi$
$349$	−7.72090	+	28.8148i	−0.413291	+	1.54242i	−0.788235	+	0.615374i	$0.789005\pi$
$350$	−4.51420	+	7.43223i	−0.241294	+	0.397269i
$351$		0			0
$352$	2.68889	+	6.14542i	0.143318	+	0.327552i
$353$	−6.75802	+	25.2213i	−0.359693	+	1.34239i	0.514781	+	0.857322i	$0.327873\pi$
$353$	−6.75802	+	25.2213i	−0.359693	+	1.34239i	−0.874474	+	0.485072i	$0.838793\pi$
$354$		0			0
$355$	−20.2000	−	11.6625i	−1.07210	−	0.618979i
$356$	1.28664	−	4.06895i	0.0681916	−	0.215654i
$357$		0			0
$358$	30.0326	+	8.76717i	1.58727	+	0.463359i
$359$	21.1519	+	21.1519i	1.11636	+	1.11636i	0.992272	+	0.124086i	$0.0395998\pi$
$359$	21.1519	+	21.1519i	1.11636	+	1.11636i	0.124086	+	0.992272i	$0.460400\pi$
$360$		0			0
$361$	−8.03999	+	4.64189i	−0.423157	+	0.244310i
$362$	−21.2824	−	22.2503i	−1.11858	−	1.16945i
$363$		0			0
$364$	−8.52677	+	6.46053i	−0.446924	+	0.338624i
$365$			17.2977i			0.905405i
$366$		0			0
$367$	17.9908	−	10.3870i	0.939114	−	0.542198i	0.0494315	−	0.998778i	$-0.484259\pi$
$367$	17.9908	−	10.3870i	0.939114	−	0.542198i	0.889682	+	0.456580i	$0.150926\pi$
$368$	8.24271	+	17.7532i	0.429681	+	0.925449i
$369$		0			0
$370$	−4.02526	+	13.7888i	−0.209263	+	0.716845i
$371$	5.07027	+	18.9225i	0.263235	+	0.982407i
$372$		0			0
$373$	12.6271	+	7.29024i	0.653804	+	0.377474i	0.789912	−	0.613220i	$-0.210126\pi$
$373$	12.6271	+	7.29024i	0.653804	+	0.377474i	−0.136108	+	0.990694i	$0.543459\pi$
$374$	0.0394912	−	1.77617i	0.00204204	−	0.0918434i
$375$		0			0
$376$	−21.1240	−	1.41087i	−1.08939	−	0.0727602i
$377$	−1.46145	−	1.03485i	−0.0752683	−	0.0532974i
$378$		0			0
$379$	3.47679	−	12.9756i	0.178591	−	0.666509i	−0.817321	−	0.576182i	$-0.804542\pi$
$379$	3.47679	−	12.9756i	0.178591	−	0.666509i	0.995912	−	0.0903274i	$-0.0287914\pi$
$380$	15.8915	+	10.1425i	0.815215	+	0.520298i
$381$		0			0
$382$	−0.561556	−	2.29901i	−0.0287317	−	0.117628i
$383$	3.31127	+	12.3578i	0.169198	+	0.631456i	0.997467	+	0.0711259i	$0.0226592\pi$
$383$	3.31127	+	12.3578i	0.169198	+	0.631456i	−0.828269	+	0.560331i	$0.810674\pi$
$384$		0			0
$385$	−3.76166	+	3.76166i	−0.191712	+	0.191712i
$386$	4.15260	+	7.57662i	0.211362	+	0.385640i
$387$		0			0
$388$	−1.76312	−	7.98416i	−0.0895087	−	0.405334i
$389$	−9.99223			−0.506626			−0.253313	−	0.967384i	$-0.581520\pi$
$389$	−9.99223			−0.506626			−0.253313	+	0.967384i	$0.581520\pi$
$390$		0			0
$391$		−	5.18405i		−	0.262169i
$392$	−4.37918	+	12.8482i	−0.221182	+	0.648934i
$393$		0			0
$394$	6.27643	+	11.4516i	0.316202	+	0.576926i
$395$	−1.99637	−	1.99637i	−0.100448	−	0.100448i
$396$		0			0
$397$	−4.54273	+	1.21722i	−0.227993	+	0.0610906i	−0.371007	−	0.928630i	$-0.620987\pi$
$397$	−4.54273	+	1.21722i	−0.227993	+	0.0610906i	0.143014	+	0.989721i	$0.454321\pi$
$398$	−28.4098	+	6.93939i	−1.42406	+	0.347840i
$399$		0			0
$400$	−1.47228	+	16.5134i	−0.0736139	+	0.825672i
$401$	2.57682	+	0.690456i	0.128680	+	0.0344797i	0.322584	−	0.946541i	$-0.395448\pi$
$401$	2.57682	+	0.690456i	0.128680	+	0.0344797i	−0.193904	+	0.981020i	$0.562115\pi$
$402$		0			0
$403$	−0.861327	−	0.318653i	−0.0429058	−	0.0158733i
$404$	19.3585	−	10.0570i	0.963120	−	0.500356i
$405$		0			0
$406$	1.04175	+	0.0231622i	0.0517011	+	0.00114952i
$407$	−1.99144	+	3.44928i	−0.0987121	+	0.170974i
$408$		0			0
$409$	25.4794	−	6.82718i	1.25987	−	0.337582i	0.433731	−	0.901042i	$-0.357197\pi$
$409$	25.4794	−	6.82718i	1.25987	−	0.337582i	0.826143	+	0.563460i	$0.190530\pi$
$410$	−9.05389	+	31.0147i	−0.447140	+	1.53171i
$411$		0			0
$412$	−0.527899	+	11.8656i	−0.0260077	+	0.584575i
$413$	4.54614	+	7.87415i	0.223701	+	0.387461i
$414$		0			0
$415$	−26.5022			−1.30094
$416$	−9.15506	+	18.2259i	−0.448864	+	0.893600i
$417$		0			0
$418$	3.61318	+	3.77750i	0.176726	+	0.184764i
$419$	−14.0047	−	24.2568i	−0.684174	−	1.18502i	−0.973696	−	0.227853i	$-0.926830\pi$
$419$	−14.0047	−	24.2568i	−0.684174	−	1.18502i	0.289522	−	0.957171i	$-0.406504\pi$
$420$		0			0
$421$	−0.583969	+	0.583969i	−0.0284609	+	0.0284609i	−0.721194	−	0.692733i	$-0.756406\pi$
$421$	−0.583969	+	0.583969i	−0.0284609	+	0.0284609i	0.692733	+	0.721194i	$0.256406\pi$
$422$	−8.48589	+	29.0690i	−0.413086	+	1.41506i
$423$		0			0
$424$	24.5913	+	28.1114i	1.19426	+	1.36521i
$425$	2.19548	−	3.80268i	0.106496	−	0.184457i
$426$		0			0
$427$	−15.4374	−	4.13643i	−0.747067	−	0.200176i
$428$	13.7255	−	7.13063i	0.663448	−	0.344672i
$429$		0			0
$430$	−4.13395	−	2.51088i	−0.199357	−	0.121086i
$431$	16.3546	+	4.38219i	0.787772	+	0.211083i	0.630208	−	0.776426i	$-0.282969\pi$
$431$	16.3546	+	4.38219i	0.787772	+	0.211083i	0.157563	+	0.987509i	$0.449636\pi$
$432$		0			0
$433$	19.1457	+	11.0538i	0.920082	+	0.531209i	0.883661	−	0.468127i	$-0.155071\pi$
$433$	19.1457	+	11.0538i	0.920082	+	0.531209i	0.0364205	+	0.999337i	$0.488404\pi$
$434$	0.519132	−	0.126803i	0.0249191	−	0.00608675i
$435$		0			0
$436$	−8.52652	−	9.32054i	−0.408346	−	0.446373i
$437$	10.7855	+	10.7855i	0.515940	+	0.515940i
$438$		0			0
$439$	18.7931	+	32.5507i	0.896947	+	1.55356i	0.831376	+	0.555710i	$0.187553\pi$
$439$	18.7931	+	32.5507i	0.896947	+	1.55356i	0.0655708	+	0.997848i	$0.479113\pi$
$440$	−3.27211	+	9.60016i	−0.155992	+	0.457670i
$441$		0			0
$442$	4.23206	−	3.35718i	0.201298	−	0.159685i
$443$	−16.9312			−0.804428			−0.402214	−	0.915546i	$-0.631759\pi$
$443$	−16.9312			−0.804428			−0.402214	+	0.915546i	$0.631759\pi$
$444$		0			0
$445$	5.58807	−	3.22627i	0.264900	−	0.152940i
$446$	−6.92833	−	12.6411i	−0.328066	−	0.598573i
$447$		0			0
$448$	−1.51990	−	11.7705i	−0.0718086	−	0.556103i
$449$	0.0228713	+	0.0853569i	0.00107936	+	0.00402824i	0.966463	−	0.256804i	$-0.0826696\pi$
$449$	0.0228713	+	0.0853569i	0.00107936	+	0.00402824i	−0.965384	+	0.260833i	$0.916003\pi$
$450$		0			0
$451$	−4.47929	+	7.75836i	−0.210922	+	0.365327i
$452$	−19.3571	−	12.3543i	−0.910480	−	0.581099i
$453$		0			0
$454$	4.53769	+	2.75611i	0.212964	+	0.129351i
$455$	−16.1061	−	1.49476i	−0.755065	−	0.0700756i
$456$		0			0
$457$	−6.35265	+	23.7084i	−0.297164	+	1.10903i	0.642319	+	0.766438i	$0.277973\pi$
$457$	−6.35265	+	23.7084i	−0.297164	+	1.10903i	−0.939483	+	0.342595i	$0.888694\pi$
$458$	0.241742	−	10.8727i	0.0112959	−	0.508046i
$459$		0			0
$460$	−8.92281	+	28.2181i	−0.416028	+	1.31568i
$461$	1.14969	+	4.29072i	0.0535466	+	0.199839i	0.987517	−	0.157511i	$-0.0503470\pi$
$461$	1.14969	+	4.29072i	0.0535466	+	0.199839i	−0.933971	+	0.357350i	$0.883680\pi$
$462$		0			0
$463$	15.6374	+	15.6374i	0.726731	+	0.726731i	0.969967	−	0.243236i	$-0.0782089\pi$
$463$	15.6374	+	15.6374i	0.726731	+	0.726731i	−0.243236	+	0.969967i	$0.578209\pi$
$464$	1.80190	−	0.836611i	0.0836509	−	0.0388387i
$465$		0			0
$466$	−2.99349	+	2.86327i	−0.138671	+	0.132639i
$467$		−	8.82470i		−	0.408358i	−0.978934	−	0.204179i	$-0.934547\pi$
$467$		−	8.82470i		−	0.408358i	0.978934	−	0.204179i	$-0.0654525\pi$
$468$		0			0
$469$			18.4744i			0.853067i
$470$	−22.1264	−	23.1327i	−1.02062	−	1.06703i
$471$		0			0
$472$	14.4015	+	9.64866i	0.662884	+	0.444116i
$473$	−0.948311	−	0.948311i	−0.0436034	−	0.0436034i
$474$		0			0
$475$	3.34381	+	12.4793i	0.153424	+	0.572588i
$476$	−0.947694	+	2.99705i	−0.0434375	+	0.137370i
$477$		0			0
$478$	−28.6445	−	0.636881i	−1.31017	−	0.0291303i
$479$	8.93153	−	33.3329i	0.408092	−	1.52302i	−0.390189	−	0.920735i	$-0.627591\pi$
$479$	8.93153	−	33.3329i	0.408092	−	1.52302i	0.798281	−	0.602285i	$-0.205743\pi$
$480$		0			0
$481$	−11.9373	+	2.03999i	−0.544293	+	0.0930154i
$482$	9.97550	−	16.4238i	0.454371	−	0.748083i
$483$		0			0
$484$	10.3229	−	16.1742i	0.469225	−	0.735192i
$485$	6.18150	−	10.7067i	0.280687	−	0.486165i
$486$		0			0
$487$	6.09032	+	22.7294i	0.275979	+	1.02997i	0.955183	+	0.296017i	$0.0956586\pi$
$487$	6.09032	+	22.7294i	0.275979	+	1.02997i	−0.679204	+	0.733950i	$0.737675\pi$
$488$	−29.8924	+	5.90740i	−1.35316	+	0.267416i
$489$		0			0
$490$	−17.9981	+	9.86443i	−0.813073	+	0.445630i
$491$	28.1779	−	16.2685i	1.27165	−	0.734187i	0.296351	−	0.955079i	$-0.404230\pi$
$491$	28.1779	−	16.2685i	1.27165	−	0.734187i	0.975298	+	0.220892i	$0.0708967\pi$
$492$		0			0
$493$	−0.526166			−0.0236973
$494$	−1.82020	+	15.7895i	−0.0818947	+	0.710403i
$495$		0			0
$496$	0.781569	−	0.653613i	0.0350935	−	0.0293481i
$497$	5.72137	+	9.90970i	0.256638	+	0.444511i
$498$		0			0
$499$	0.938780	+	0.938780i	0.0420256	+	0.0420256i	0.727807	−	0.685782i	$-0.240540\pi$
$499$	0.938780	+	0.938780i	0.0420256	+	0.0420256i	−0.685782	+	0.727807i	$0.740540\pi$
$500$	3.81660	−	3.49146i	0.170684	−	0.156143i
$501$		0			0
$502$	−3.68881	−	15.1020i	−0.164640	−	0.674034i
$503$	3.62331	+	2.09192i	0.161555	+	0.0932739i	0.578598	−	0.815613i	$-0.303600\pi$
$503$	3.62331	+	2.09192i	0.161555	+	0.0932739i	−0.417043	+	0.908887i	$0.636933\pi$
$504$		0			0
$505$	31.8606	+	8.53703i	1.41778	+	0.379893i
$506$	−4.25999	+	7.01370i	−0.189379	+	0.311797i
$507$		0			0
$508$	15.6362	−	8.12327i	0.693745	−	0.360412i
$509$	23.6241	+	6.33007i	1.04712	+	0.280575i	0.741062	−	0.671437i	$-0.234323\pi$
$509$	23.6241	+	6.33007i	1.04712	+	0.280575i	0.306060	+	0.952012i	$0.400989\pi$
$510$		0			0
$511$	4.24296	−	7.34902i	0.187697	−	0.325102i
$512$	−12.5010	−	18.8607i	−0.552471	−	0.833532i
$513$		0			0
$514$	−18.3036	−	5.34322i	−0.807335	−	0.235679i
$515$	−12.6987	+	12.6987i	−0.559571	+	0.559571i
$516$		0			0
$517$	−4.43794	−	7.68674i	−0.195180	−	0.338062i
$518$	5.09240	−	4.87088i	0.223747	−	0.214014i
$519$		0			0
$520$	−28.8145	+	10.9897i	−1.26360	+	0.481932i
$521$	10.9083			0.477900			0.238950	−	0.971032i	$-0.423197\pi$
$521$	10.9083			0.477900			0.238950	+	0.971032i	$0.423197\pi$
$522$		0			0
$523$	−9.42167	−	16.3188i	−0.411981	−	0.713572i	0.583126	−	0.812382i	$-0.301830\pi$
$523$	−9.42167	−	16.3188i	−0.411981	−	0.713572i	−0.995106	+	0.0988105i	$0.968496\pi$
$524$	−1.31402	+	29.5353i	−0.0574033	+	1.29025i
$525$		0			0
$526$	28.8061	+	8.40916i	1.25601	+	0.366657i
$527$	−0.260650	+	0.0698410i	−0.0113541	+	0.00304232i
$528$		0			0
$529$	−0.472439	+	0.818288i	−0.0205408	+	0.0355777i
$530$	−1.25531	+	56.4589i	−0.0545270	+	2.45242i
$531$		0			0
$532$	−4.26372	−	8.20710i	−0.184856	−	0.355823i
$533$	−26.8502	+	4.58848i	−1.16301	+	0.198749i
$534$		0			0
$535$	22.5898	+	6.05292i	0.976643	+	0.261691i
$536$	15.5393	+	31.6094i	0.671194	+	1.36532i
$537$		0			0
$538$	−9.74711	−	39.9047i	−0.420228	−	1.72041i
$539$	−5.49694	+	1.47290i	−0.236770	+	0.0634424i
$540$		0			0
$541$	1.32217	+	1.32217i	0.0568444	+	0.0568444i	0.734958	−	0.678113i	$-0.237202\pi$
$541$	1.32217	+	1.32217i	0.0568444	+	0.0568444i	−0.678113	+	0.734958i	$0.737202\pi$
$542$	−16.5345	+	9.06222i	−0.710216	+	0.389256i
$543$		0			0
$544$	0.899408	+	5.92504i	0.0385618	+	0.254034i
$545$		−	19.1001i		−	0.818160i
$546$		0			0
$547$	17.9127			0.765894			0.382947	−	0.923770i	$-0.374909\pi$
$547$	17.9127			0.765894			0.382947	+	0.923770i	$0.374909\pi$
$548$	0.196970	−	0.0434962i	0.00841414	−	0.00185807i
$549$		0			0
$550$	−6.09520	+	3.34066i	−0.259900	+	0.142446i
$551$	1.09470	−	1.09470i	0.0466356	−	0.0466356i
$552$		0			0
$553$	0.358478	+	1.33786i	0.0152440	+	0.0568915i
$554$	33.9630	−	8.29580i	1.44295	−	0.352455i
$555$		0			0
$556$	11.4494	+	7.30739i	0.485562	+	0.309902i
$557$	10.4145	−	38.8674i	0.441276	−	1.64686i	−0.284309	−	0.958733i	$-0.591764\pi$
$557$	10.4145	−	38.8674i	0.441276	−	1.64686i	0.725585	−	0.688132i	$-0.241569\pi$
$558$		0			0
$559$	0.376829	−	4.06033i	0.0159382	−	0.171734i
$560$	10.3171	−	14.6825i	0.435976	−	0.620451i
$561$		0			0
$562$	−38.3185	−	0.851972i	−1.61637	−	0.0359383i
$563$	9.19054	+	5.30616i	0.387335	+	0.223628i	0.681005	−	0.732279i	$-0.261543\pi$
$563$	9.19054	+	5.30616i	0.387335	+	0.223628i	−0.293670	+	0.955907i	$0.594877\pi$
$564$		0			0
$565$	−8.98651	−	33.5381i	−0.378066	−	1.41096i
$566$	−26.6103	−	7.76815i	−1.11852	−	0.326520i
$567$		0			0
$568$	18.1245	+	12.1429i	0.760486	+	0.509507i
$569$	−5.37353	+	3.10241i	−0.225270	+	0.130060i	−0.608388	−	0.793640i	$-0.708184\pi$
$569$	−5.37353	+	3.10241i	−0.225270	+	0.130060i	0.383118	+	0.923699i	$0.374850\pi$
$570$		0			0
$571$		−	10.5785i		−	0.442697i	−0.975195	−	0.221348i	$-0.928954\pi$
$571$		−	10.5785i		−	0.442697i	0.975195	−	0.221348i	$-0.0710458\pi$
$572$	−8.48446	+	1.06436i	−0.354753	+	0.0445032i
$573$		0			0
$574$	11.4542	−	10.9559i	0.478089	−	0.457291i
$575$	−17.5644	+	10.1408i	−0.732487	+	0.422901i
$576$		0			0
$577$	−8.26875	−	8.26875i	−0.344233	−	0.344233i	0.513723	−	0.857956i	$-0.328266\pi$
$577$	−8.26875	−	8.26875i	−0.344233	−	0.344233i	−0.857956	+	0.513723i	$0.828266\pi$
$578$	−6.29231	+	21.5547i	−0.261726	+	0.896559i
$579$		0			0
$580$	2.86405	+	0.905639i	0.118923	+	0.0376046i
$581$	11.2596	+	6.50073i	0.467127	+	0.269696i
$582$		0			0
$583$	−4.05274	+	15.1250i	−0.167847	+	0.626415i
$584$	1.07818	−	16.1429i	0.0446156	−	0.667999i
$585$		0			0
$586$	13.4686	+	8.18060i	0.556385	+	0.337938i
$587$	4.88481	−	18.2304i	0.201618	−	0.752447i	−0.788836	−	0.614603i	$-0.789316\pi$
$587$	4.88481	−	18.2304i	0.201618	−	0.752447i	0.990454	−	0.137844i	$-0.0440172\pi$
$588$		0			0
$589$	0.396981	−	0.687592i	0.0163573	−	0.0283317i
$590$	6.21937	+	25.4621i	0.256048	+	1.04826i
$591$		0			0
$592$	4.61600	−	12.6173i	0.189716	−	0.518570i
$593$	8.56694	−	8.56694i	0.351802	−	0.351802i	−0.508978	−	0.860780i	$-0.669976\pi$
$593$	8.56694	−	8.56694i	0.351802	−	0.351802i	0.860780	+	0.508978i	$0.169976\pi$
$594$		0			0
$595$	−4.11599	+	2.37637i	−0.168739	+	0.0974216i
$596$	25.4415	−	5.61816i	1.04212	−	0.230129i
$597$		0			0
$598$	−24.6821	+	3.65531i	−1.00933	+	0.149477i
$599$			22.4062i			0.915491i	0.889083	+	0.457745i	$0.151343\pi$
$599$			22.4062i			0.915491i	−0.889083	+	0.457745i	$0.848657\pi$
$600$		0			0
$601$	11.5194	+	19.9522i	0.469887	+	0.813867i	0.999407	−	0.0344297i	$-0.0109615\pi$
$601$	11.5194	+	19.9522i	0.469887	+	0.813867i	−0.529521	+	0.848297i	$0.677628\pi$
$602$	1.14043	+	2.08078i	0.0464806	+	0.0848061i
$603$		0			0
$604$	−17.8038	+	16.2871i	−0.724425	+	0.662711i
$605$	28.0235	−	7.50888i	1.13932	−	0.305280i
$606$		0			0
$607$	−15.0714	−	8.70147i	−0.611729	−	0.353182i	0.161913	−	0.986805i	$-0.448234\pi$
$607$	−15.0714	−	8.70147i	−0.611729	−	0.353182i	−0.773642	+	0.633623i	$0.781567\pi$
$608$	−14.1984	−	10.4559i	−0.575819	−	0.424042i
$609$		0			0
$610$	−39.3774	−	23.9171i	−1.59434	−	0.968375i
$611$	9.36409	−	25.3113i	0.378831	−	1.02399i
$612$		0			0
$613$	23.9979	+	6.43022i	0.969266	+	0.259714i	0.708518	−	0.705693i	$-0.249364\pi$
$613$	23.9979	+	6.43022i	0.969266	+	0.259714i	0.260748	+	0.965407i	$0.416031\pi$
$614$	17.0545	+	0.379190i	0.688265	+	0.0153029i
$615$		0			0
$616$	3.74499	−	3.27606i	0.150890	−	0.131996i
$617$	−16.8453	+	4.51370i	−0.678168	+	0.181715i	−0.581431	−	0.813595i	$-0.697507\pi$
$617$	−16.8453	+	4.51370i	−0.678168	+	0.181715i	−0.0967368	+	0.995310i	$0.530840\pi$
$618$		0			0
$619$	−22.2153	+	22.2153i	−0.892907	+	0.892907i	−0.994796	−	0.101889i	$-0.967511\pi$
$619$	−22.2153	+	22.2153i	−0.892907	+	0.892907i	0.101889	+	0.994796i	$0.467511\pi$
$620$	1.53900	+	0.0684698i	0.0618076	+	0.00274981i
$621$		0			0
$622$	−8.61541	−	9.00723i	−0.345447	−	0.361157i
$623$	−3.16549			−0.126823
$624$		0			0
$625$	28.5448			1.14179
$626$	−13.5219	−	14.1369i	−0.540444	−	0.565023i
$627$		0			0
$628$	1.04330	+	0.0464161i	0.0416320	+	0.00185221i
$629$	−2.51613	+	2.51613i	−0.100324	+	0.100324i
$630$		0			0
$631$	−23.0172	+	6.16745i	−0.916302	+	0.245522i	−0.686004	−	0.727598i	$-0.740637\pi$
$631$	−23.0172	+	6.16745i	−0.916302	+	0.245522i	−0.230298	+	0.973120i	$0.573970\pi$
$632$	1.73866	+	1.98753i	0.0691600	+	0.0790596i
$633$		0			0
$634$	23.4160	+	0.520630i	0.929968	+	0.0206769i
$635$	25.7345	+	6.89553i	1.02124	+	0.273641i
$636$		0			0
$637$	−14.1217	−	9.99957i	−0.559522	−	0.396197i
$638$	0.711869	+	0.432376i	0.0281832	+	0.0171179i
$639$		0			0
$640$	5.30249	−	33.7995i	0.209599	−	1.33604i
$641$	−19.3494	−	11.1714i	−0.764257	−	0.441244i	0.0665652	−	0.997782i	$-0.478796\pi$
$641$	−19.3494	−	11.1714i	−0.764257	−	0.441244i	−0.830822	+	0.556538i	$0.812129\pi$
$642$		0			0
$643$	−4.36483	+	1.16955i	−0.172132	+	0.0461227i	−0.343856	−	0.939023i	$-0.611733\pi$
$643$	−4.36483	+	1.16955i	−0.172132	+	0.0461227i	0.171724	+	0.985145i	$0.445066\pi$
$644$	10.7125	−	9.79992i	0.422132	−	0.386171i
$645$		0			0
$646$	2.24457	+	4.09533i	0.0883116	+	0.161129i
$647$	4.37758	+	7.58218i	0.172100	+	0.298086i	0.939154	−	0.343497i	$-0.111611\pi$
$647$	4.37758	+	7.58218i	0.172100	+	0.298086i	−0.767054	+	0.641583i	$0.778278\pi$
$648$		0			0
$649$			7.26760i			0.285278i
$650$	−19.6532	−	7.77174i	−0.770863	−	0.304833i
$651$		0			0
$652$	−48.5779	+	10.7273i	−1.90246	+	0.420113i
$653$	5.94625	−	3.43307i	0.232695	−	0.134346i	−0.379120	−	0.925348i	$-0.623773\pi$
$653$	5.94625	−	3.43307i	0.232695	−	0.134346i	0.611815	+	0.791001i	$0.290440\pi$
$654$		0			0
$655$	−31.6090	+	31.6090i	−1.23507	+	1.23507i
$656$	10.3826	−	28.3798i	0.405373	−	1.10805i
$657$		0			0
$658$	3.72629	+	15.2554i	0.145266	+	0.594719i
$659$	7.77012	−	13.4582i	0.302681	−	0.524259i	−0.674061	−	0.738675i	$-0.735452\pi$
$659$	7.77012	−	13.4582i	0.302681	−	0.524259i	0.976742	+	0.214417i	$0.0687850\pi$
$660$		0			0
$661$	10.9023	−	40.6880i	0.424051	−	1.58258i	−0.341936	−	0.939723i	$-0.611082\pi$
$661$	10.9023	−	40.6880i	0.424051	−	1.58258i	0.765987	−	0.642856i	$-0.222251\pi$
$662$	−17.3409	−	10.5325i	−0.673974	−	0.409359i
$663$		0			0
$664$	24.7329	+	1.65191i	0.959824	+	0.0641066i
$665$	3.61931	−	13.5074i	0.140351	−	0.523796i
$666$		0			0
$667$	2.10473	+	1.21517i	0.0814955	+	0.0470515i
$668$	−5.96133	−	1.88502i	−0.230651	−	0.0729338i
$669$		0			0
$670$	−14.9239	+	51.1230i	−0.576562	+	1.97505i
$671$	−9.03301	−	9.03301i	−0.348716	−	0.348716i
$672$		0			0
$673$	5.42846	−	3.13412i	0.209252	−	0.120812i	−0.391712	−	0.920088i	$-0.628117\pi$
$673$	5.42846	−	3.13412i	0.209252	−	0.120812i	0.600964	+	0.799276i	$0.294784\pi$
$674$	−27.1315	+	25.9512i	−1.04507	+	0.999605i
$675$		0			0
$676$	−18.9681	−	17.7823i	−0.729542	−	0.683936i
$677$			21.1245i			0.811881i	0.913900	+	0.405940i	$0.133056\pi$
$677$			21.1245i			0.811881i	−0.913900	+	0.405940i	$0.866944\pi$
$678$		0			0
$679$	−5.25248	+	3.03252i	−0.201572	+	0.116377i
$680$	−5.04357	+	7.52799i	−0.193412	+	0.288685i
$681$		0			0
$682$	0.410035	+	0.119698i	0.0157011	+	0.00458349i
$683$	7.19116	+	26.8378i	0.275162	+	1.02692i	0.955733	+	0.294236i	$0.0950653\pi$
$683$	7.19116	+	26.8378i	0.275162	+	1.02692i	−0.680571	+	0.732683i	$0.738268\pi$
$684$		0			0
$685$	0.264135	+	0.152498i	0.0100921	+	0.00582665i
$686$	24.7488	+	0.550263i	0.944913	+	0.0210092i
$687$		0			0
$688$	3.70146	+	2.60093i	0.141117	+	0.0991594i
$689$	−43.2561	+	19.8935i	−1.64793	+	0.757883i
$690$		0			0
$691$	4.73219	−	17.6608i	0.180021	−	0.671848i	−0.815621	−	0.578587i	$-0.803604\pi$
$691$	4.73219	−	17.6608i	0.180021	−	0.671848i	0.995642	−	0.0932606i	$-0.0297290\pi$
$692$	11.0831	+	7.07364i	0.421318	+	0.268900i
$693$		0			0
$694$	−1.61711	+	0.394995i	−0.0613846	+	0.0149938i
$695$	5.31537	+	19.8372i	0.201624	+	0.752470i
$696$		0			0
$697$	−5.65945	+	5.65945i	−0.214367	+	0.214367i
$698$	36.9956	−	20.2766i	1.40030	−	0.767479i
$699$		0			0
$700$	12.0083	−	2.65176i	0.453873	−	0.100227i
$701$	−17.2336			−0.650904			−0.325452	−	0.945559i	$-0.605516\pi$
$701$	−17.2336			−0.650904			−0.325452	+	0.945559i	$0.605516\pi$
$702$		0			0
$703$		−	10.4697i		−	0.394871i
$704$	3.65205	−	8.75529i	0.137642	−	0.329977i
$705$		0			0
$706$	32.3818	−	17.7479i	1.21871	−	0.667949i
$707$	−11.4421	−	11.4421i	−0.430324	−	0.430324i
$708$		0			0
$709$	32.3352	−	8.66420i	1.21437	−	0.325391i	0.405898	−	0.913919i	$-0.366959\pi$
$709$	32.3352	−	8.66420i	1.21437	−	0.325391i	0.808477	+	0.588528i	$0.200292\pi$
$710$	7.82715	+	32.0443i	0.293748	+	1.20260i
$711$		0			0
$712$	−5.41610	+	2.66258i	−0.202977	+	0.0997842i
$713$	1.20393	+	0.322592i	0.0450876	+	0.0120812i
$714$		0			0
$715$	−10.5517	−	7.47164i	−0.394611	−	0.279423i
$716$	−20.3977	−	39.2628i	−0.762297	−	1.46732i
$717$		0			0
$718$	0.940351	−	42.2934i	0.0350936	−	1.57838i
$719$	8.93537	−	15.4765i	0.333233	−	0.577177i	−0.649911	−	0.760011i	$-0.725194\pi$
$719$	8.93537	−	15.4765i	0.333233	−	0.577177i	0.983144	+	0.182834i	$0.0585270\pi$
$720$		0			0
$721$	8.50996	−	2.28024i	0.316928	−	0.0849205i
$722$	12.6032	+	3.67916i	0.469043	+	0.136924i
$723$		0			0
$724$	−1.93533	+	43.5005i	−0.0719261	+	1.61668i
$725$	1.02926	+	1.78274i	0.0382259	+	0.0662091i
$726$		0			0
$727$	−21.2697			−0.788848			−0.394424	−	0.918928i	$-0.629056\pi$
$727$	−21.2697			−0.788848			−0.394424	+	0.918928i	$0.629056\pi$
$728$	14.9377	+	2.39888i	0.553627	+	0.0889084i
$729$		0			0
$730$	17.6780	−	16.9090i	0.654291	−	0.625829i
$731$	−0.599081	−	1.03764i	−0.0221578	−	0.0383784i
$732$		0			0
$733$	4.74608	−	4.74608i	0.175300	−	0.175300i	−0.614003	−	0.789304i	$-0.710442\pi$
$733$	4.74608	−	4.74608i	0.175300	−	0.175300i	0.789304	+	0.614003i	$0.210442\pi$
$734$	−28.2018	−	8.23274i	−1.04095	−	0.303876i
$735$		0			0
$736$	10.0860	−	25.7781i	0.371774	−	0.950192i
$737$	−7.38342	+	12.7885i	−0.271972	+	0.471069i
$738$		0			0
$739$	−39.5252	−	10.5907i	−1.45396	−	0.389587i	−0.556559	−	0.830808i	$-0.687879\pi$
$739$	−39.5252	−	10.5907i	−1.45396	−	0.389587i	−0.897398	+	0.441221i	$0.854545\pi$
$740$	18.0267	−	9.36515i	0.662674	−	0.344270i
$741$		0			0
$742$	14.3821	−	23.6789i	0.527985	−	0.869281i
$743$	38.1054	+	10.2103i	1.39795	+	0.374580i	0.877609	−	0.479377i	$-0.159137\pi$
$743$	38.1054	+	10.2103i	1.39795	+	0.374580i	0.520343	+	0.853957i	$0.325804\pi$
$744$		0			0
$745$	34.1167	+	19.6973i	1.24994	+	0.721654i
$746$	−4.89277	−	20.0310i	−0.179137	−	0.733387i
$747$		0			0
$748$	−1.85381	+	1.69589i	−0.0677821	+	0.0620078i
$749$	−8.11267	−	8.11267i	−0.296430	−	0.296430i
$750$		0			0
$751$	11.2537	+	19.4920i	0.410655	+	0.711275i	0.994961	−	0.100258i	$-0.0319668\pi$
$751$	11.2537	+	19.4920i	0.410655	+	0.711275i	−0.584307	+	0.811533i	$0.698633\pi$
$752$	19.2074	+	22.9675i	0.700421	+	0.837540i
$753$		0			0
$754$	0.371003	+	2.50516i	0.0135111	+	0.0912325i
$755$	−36.4844			−1.32780
$756$		0			0
$757$	−40.5049	+	23.3855i	−1.47217	+	0.849960i	−0.999511	−	0.0312829i	$-0.990041\pi$
$757$	−40.5049	+	23.3855i	−1.47217	+	0.849960i	−0.472664	+	0.881243i	$0.656707\pi$
$758$	−16.6594	+	9.13071i	−0.605097	+	0.331642i
$759$		0			0
$760$	−5.16888	−	26.1553i	−0.187495	−	0.948753i
$761$	5.99174	+	22.3615i	0.217200	+	0.810603i	0.985380	+	0.170369i	$0.0544960\pi$
$761$	5.99174	+	22.3615i	0.217200	+	0.810603i	−0.768180	+	0.640234i	$0.778837\pi$
$762$		0			0
$763$	−4.68507	+	8.11478i	−0.169611	+	0.293775i
$764$	−1.80061	+	2.82124i	−0.0651438	+	0.102069i
$765$		0			0
$766$	9.39264	−	15.4642i	0.339370	−	0.558743i
$767$	−17.0026	+	14.1147i	−0.613929	+	0.509652i
$768$		0			0
$769$	1.46149	−	5.45437i	0.0527028	−	0.196689i	−0.934555	−	0.355819i	$-0.884202\pi$
$769$	1.46149	−	5.45437i	0.0527028	−	0.196689i	0.987258	+	0.159129i	$0.0508687\pi$
$770$	7.52145	+	0.167232i	0.271054	+	0.00602661i
$771$		0			0
$772$	3.68390	−	11.6502i	0.132586	−	0.419300i
$773$	−13.1234	−	48.9774i	−0.472018	−	1.76159i	−0.632506	−	0.774556i	$-0.717973\pi$
$773$	−13.1234	−	48.9774i	−0.472018	−	1.76159i	0.160488	−	0.987038i	$-0.448693\pi$
$774$		0			0
$775$	0.746506	+	0.746506i	0.0268153	+	0.0268153i
$776$	−6.43617	+	9.60658i	−0.231045	+	0.344856i
$777$		0			0
$778$	9.76765	+	10.2119i	0.350187	+	0.366113i
$779$		−	23.5491i		−	0.843735i
$780$		0			0
$781$			9.14635i			0.327282i
$782$	−5.29800	+	5.06754i	−0.189456	+	0.181215i
$783$		0			0
$784$	17.4114	−	8.08403i	0.621837	−	0.288715i
$785$	1.11655	+	1.11655i	0.0398513	+	0.0398513i
$786$		0			0
$787$	−1.63955	−	6.11890i	−0.0584438	−	0.218115i	0.930528	−	0.366222i	$-0.119349\pi$
$787$	−1.63955	−	6.11890i	−0.0584438	−	0.218115i	−0.988971	+	0.148107i	$0.952682\pi$
$788$	5.56801	−	17.6087i	0.198352	−	0.627282i
$789$		0			0
$790$	−0.0887525	+	3.99175i	−0.00315767	+	0.142020i
$791$	−4.40860	+	16.4531i	−0.156752	+	0.585006i
$792$		0			0
$793$	3.58943	−	38.6762i	0.127465	−	1.37343i
$794$	5.68461	+	3.45272i	0.201739	+	0.122533i
$795$		0			0
$796$	34.8632	+	22.2509i	1.23569	+	0.788662i
$797$	−15.6429	+	27.0944i	−0.554101	+	0.959732i	0.443871	+	0.896090i	$0.353605\pi$
$797$	−15.6429	+	27.0944i	−0.554101	+	0.959732i	−0.997973	+	0.0636413i	$0.979729\pi$
$798$		0			0
$799$	−2.05238	−	7.65958i	−0.0726079	−	0.270976i
$800$	18.3156	−	14.6376i	0.647555	−	0.517519i
$801$		0			0
$802$	−1.81327	−	3.30840i	−0.0640287	−	0.116824i
$803$	5.87418	−	3.39146i	0.207295	−	0.119682i
$804$		0			0
$805$	21.9527			0.773730
$806$	0.516310	+	1.19175i	0.0181863	+	0.0419777i
$807$		0			0
$808$	−29.2015	−	9.95300i	−1.02730	−	0.350145i
$809$	7.70970	+	13.3536i	0.271059	+	0.469487i	0.969133	−	0.246538i	$-0.0792930\pi$
$809$	7.70970	+	13.3536i	0.271059	+	0.469487i	−0.698075	+	0.716025i	$0.745960\pi$
$810$		0			0
$811$	−5.80801	−	5.80801i	−0.203947	−	0.203947i	0.597742	−	0.801689i	$-0.296065\pi$
$811$	−5.80801	−	5.80801i	−0.203947	−	0.203947i	−0.801689	+	0.597742i	$0.796065\pi$
$812$	−0.994663	−	1.08729i	−0.0349058	−	0.0381564i
$813$		0			0
$814$	5.47178	−	1.33654i	0.191786	−	0.0468456i
$815$	−65.1424	−	37.6100i	−2.28184	−	1.31742i
$816$		0			0
$817$	3.40522	+	0.912425i	0.119133	+	0.0319217i
$818$	−31.8840	−	19.3657i	−1.11480	−	0.677106i
$819$		0			0
$820$	40.5469	−	21.0648i	1.41596	−	0.735613i
$821$	−32.4496	−	8.69486i	−1.13250	−	0.303453i	−0.356568	−	0.934269i	$-0.616053\pi$
$821$	−32.4496	−	8.69486i	−1.13250	−	0.303453i	−0.775932	+	0.630817i	$0.782720\pi$
$822$		0			0
$823$	12.8798	−	22.3085i	0.448962	−	0.777625i	−0.549357	−	0.835588i	$-0.685127\pi$
$823$	12.8798	−	22.3085i	0.448962	−	0.777625i	0.998319	+	0.0579627i	$0.0184605\pi$
$824$	12.6424	−	11.0594i	0.440420	−	0.385272i
$825$		0			0
$826$	3.60327	−	12.3432i	0.125374	−	0.429476i
$827$	−22.6971	+	22.6971i	−0.789255	+	0.789255i	−0.981372	−	0.192117i	$-0.938465\pi$
$827$	−22.6971	+	22.6971i	−0.789255	+	0.789255i	0.192117	+	0.981372i	$0.438465\pi$
$828$		0			0
$829$	−28.4583	−	49.2912i	−0.988397	−	1.71195i	−0.625743	−	0.780029i	$-0.715204\pi$
$829$	−28.4583	−	49.2912i	−0.988397	−	1.71195i	−0.362654	−	0.931924i	$-0.618129\pi$
$830$	25.9066	+	27.0848i	0.899231	+	0.940127i
$831$		0			0
$832$	27.5759	−	8.46001i	0.956021	−	0.293298i
$833$	−5.08425			−0.176159
$834$		0			0
$835$	−4.72675	−	8.18697i	−0.163576	−	0.283322i
$836$	0.328567	−	7.38520i	0.0113637	−	0.255423i
$837$		0			0
$838$	−11.1001	+	38.0242i	−0.383447	+	1.31352i
$839$	−0.535224	+	0.143413i	−0.0184780	+	0.00495116i	−0.268046	−	0.963406i	$-0.586378\pi$
$839$	−0.535224	+	0.143413i	−0.0184780	+	0.00495116i	0.249568	+	0.968357i	$0.419711\pi$
$840$		0			0
$841$	−14.3767	+	24.9011i	−0.495747	+	0.858659i
$842$	1.16765	+	0.0259615i	0.0402399	+	0.000894692i
$843$		0			0
$844$	38.0031	−	19.7432i	1.30812	−	0.679590i
$845$	−3.01288	−	39.1967i	−0.103646	−	1.34841i
$846$		0			0
$847$	−13.7478	−	3.68371i	−0.472379	−	0.126574i
$848$	4.69064	−	52.6114i	0.161077	−	1.80668i
$849$		0			0
$850$	−6.03241	+	1.47348i	−0.206910	+	0.0505398i
$851$	15.8758	−	4.25390i	0.544214	−	0.145822i
$852$		0			0
$853$	−6.92158	−	6.92158i	−0.236990	−	0.236990i	0.578612	−	0.815603i	$-0.303594\pi$
$853$	−6.92158	−	6.92158i	−0.236990	−	0.236990i	−0.815603	+	0.578612i	$0.803594\pi$
$854$	10.8631	+	19.8202i	0.371726	+	0.678232i
$855$		0			0
$856$	−20.7044	−	7.05687i	−0.707662	−	0.241199i
$857$			23.8544i			0.814849i	0.913239	+	0.407425i	$0.133573\pi$
$857$			23.8544i			0.814849i	−0.913239	+	0.407425i	$0.866427\pi$
$858$		0			0
$859$	−47.4998			−1.62067			−0.810336	−	0.585966i	$-0.800715\pi$
$859$	−47.4998			−1.62067			−0.810336	+	0.585966i	$0.800715\pi$
$860$	1.47496	+	6.67927i	0.0502958	+	0.227761i
$861$		0			0
$862$	−11.5085	−	20.9978i	−0.391980	−	0.715187i
$863$	6.61684	−	6.61684i	0.225240	−	0.225240i	−0.585461	−	0.810701i	$-0.699086\pi$
$863$	6.61684	−	6.61684i	0.225240	−	0.225240i	0.810701	+	0.585461i	$0.199086\pi$
$864$		0			0
$865$	5.14535	+	19.2027i	0.174947	+	0.652912i
$866$	−7.41862	−	30.3718i	−0.252095	−	1.03208i
$867$		0			0
$868$	−0.637055	−	0.406590i	−0.0216230	−	0.0138006i
$869$	−0.286537	+	1.06937i	−0.00972009	+	0.0362759i
$870$		0			0
$871$	−44.2584	+	7.56341i	−1.49964	+	0.256276i
$872$	−1.19053	+	17.8250i	−0.0403165	+	0.603631i
$873$		0			0
$874$	0.479490	−	21.5657i	0.0162190	−	0.729469i
$875$	−3.32286	−	1.91846i	−0.112333	−	0.0648557i
$876$		0			0
$877$	−5.43918	−	20.2993i	−0.183668	−	0.685458i	−0.994912	−	0.100750i	$-0.967876\pi$
$877$	−5.43918	−	20.2993i	−0.183668	−	0.685458i	0.811244	−	0.584708i	$-0.198791\pi$
$878$	14.8954	−	51.0253i	0.502696	−	1.72202i
$879$		0			0
$880$	13.0097	−	6.04036i	0.438559	−	0.203620i
$881$	43.8036	−	25.2900i	1.47578	−	0.852043i	0.476155	−	0.879361i	$-0.342030\pi$
$881$	43.8036	−	25.2900i	1.47578	−	0.852043i	0.999627	+	0.0273185i	$0.00869683\pi$
$882$		0			0
$883$		−	8.15325i		−	0.274379i	−0.990545	−	0.137189i	$-0.956193\pi$
$883$		−	8.15325i		−	0.274379i	0.990545	−	0.137189i	$-0.0438069\pi$
$884$	−7.56791	−	1.04336i	−0.254536	−	0.0350920i
$885$		0			0
$886$	16.5507	+	17.3034i	0.556032	+	0.581320i
$887$	−35.3131	+	20.3880i	−1.18570	+	0.684563i	−0.957326	−	0.289010i	$-0.906674\pi$
$887$	−35.3131	+	20.3880i	−1.18570	+	0.684563i	−0.228373	+	0.973574i	$0.573340\pi$
$888$		0			0
$889$	−9.24201	−	9.24201i	−0.309967	−	0.309967i
$890$	−8.75967	−	2.55714i	−0.293625	−	0.0857156i
$891$		0			0
$892$	−6.14634	+	19.4376i	−0.205795	+	0.650819i
$893$	20.2059	+	11.6659i	0.676164	+	0.390383i
$894$		0			0
$895$	17.3148	−	64.6197i	0.578770	−	2.16000i
$896$	−10.5435	+	13.0592i	−0.352233	+	0.436279i
$897$		0			0
$898$	0.0648759	−	0.106812i	0.00216494	−	0.00356438i
$899$	0.0327422	−	0.122195i	0.00109201	−	0.00407544i
$900$		0			0
$901$	−6.99475	+	12.1153i	−0.233029	+	0.403618i
$902$	12.3075	−	3.00624i	0.409796	−	0.100097i
$903$		0			0
$904$	6.29610	+	31.8592i	0.209405	+	1.05962i
$905$	−46.5548	+	46.5548i	−1.54753	+	1.54753i
$906$		0			0
$907$	16.2086	−	9.35804i	0.538198	−	0.310729i	−0.206151	−	0.978520i	$-0.566094\pi$
$907$	16.2086	−	9.35804i	0.538198	−	0.310729i	0.744348	+	0.667792i	$0.232760\pi$
$908$	−1.61901	−	7.33160i	−0.0537289	−	0.243308i
$909$		0			0
$910$	14.2165	+	17.9213i	0.471272	+	0.594085i
$911$		−	18.7926i		−	0.622627i	−0.950307	−	0.311313i	$-0.899231\pi$
$911$		−	18.7926i		−	0.622627i	0.950307	−	0.311313i	$-0.100769\pi$
$912$		0			0
$913$	5.19613	+	8.99997i	0.171967	+	0.297856i
$914$	30.4394	−	16.6833i	1.00685	−	0.551833i
$915$		0			0
$916$	−11.3480	+	10.3812i	−0.374947	+	0.343006i
$917$	21.1826	−	5.67586i	0.699511	−	0.187433i
$918$		0			0
$919$	41.2891	+	23.8383i	1.36200	+	0.786352i	0.989890	−	0.141836i	$-0.0453005\pi$
$919$	41.2891	+	23.8383i	1.36200	+	0.786352i	0.372112	+	0.928188i	$0.378634\pi$
$920$	37.5606	−	18.4649i	1.23834	−	0.608771i
$921$		0			0
$922$	3.26118	−	5.36925i	0.107401	−	0.176827i
$923$	−21.3980	+	17.7635i	−0.704323	+	0.584693i
$924$		0			0
$925$	13.4470	+	3.60311i	0.442134	+	0.118469i
$926$	0.695191	−	31.2671i	0.0228454	−	1.02750i
$927$		0			0
$928$	−2.61640	−	1.02370i	−0.0858875	−	0.0336045i
$929$	8.04178	−	2.15479i	0.263842	−	0.0706963i	−0.124473	−	0.992223i	$-0.539724\pi$
$929$	8.04178	−	2.15479i	0.263842	−	0.0706963i	0.388315	+	0.921527i	$0.373057\pi$
$930$		0			0
$931$	10.5779	−	10.5779i	0.346675	−	0.346675i
$932$	5.85242	+	0.260374i	0.191703	+	0.00852883i
$933$		0			0
$934$	−9.01868	+	8.62636i	−0.295100	+	0.282263i
$935$	−3.79893			−0.124238
$936$		0			0
$937$	−46.0216			−1.50346			−0.751730	−	0.659471i	$-0.770780\pi$
$937$	−46.0216			−1.50346			−0.751730	+	0.659471i	$0.770780\pi$
$938$	18.8805	−	18.0592i	0.616469	−	0.589652i
$939$		0			0
$940$	−2.01208	+	45.2256i	−0.0656269	+	1.47510i
$941$	−16.6053	+	16.6053i	−0.541316	+	0.541316i	−0.923915	−	0.382599i	$-0.875029\pi$
$941$	−16.6053	+	16.6053i	−0.541316	+	0.541316i	0.382599	+	0.923915i	$0.375029\pi$
$942$		0			0
$943$	35.7089	−	9.56817i	1.16284	−	0.311582i
$944$	−4.21708	−	24.1499i	−0.137254	−	0.786012i
$945$		0			0
$946$	−0.0421590	+	1.89615i	−0.00137071	+	0.0616493i
$947$	16.2699	+	4.35951i	0.528701	+	0.141665i	0.513289	−	0.858216i	$-0.328427\pi$
$947$	16.2699	+	4.35951i	0.528701	+	0.141665i	0.0154129	+	0.999881i	$0.495094\pi$
$948$		0			0
$949$	19.3428	+	7.15601i	0.627895	+	0.232294i
$950$	9.48492	−	15.6161i	0.307732	−	0.506653i
$951$		0			0
$952$	3.98932	−	1.96117i	0.129295	−	0.0635618i
$953$	45.2296	+	26.1133i	1.46513	+	0.845893i	0.999241	−	0.0389507i	$-0.0124015\pi$
$953$	45.2296	+	26.1133i	1.46513	+	0.845893i	0.465888	+	0.884844i	$0.345735\pi$
$954$		0			0
$955$	−4.88809	+	1.30976i	−0.158175	+	0.0423828i
$956$	27.3498	+	29.8967i	0.884557	+	0.966929i
$957$		0			0
$958$	−42.7964	+	23.4559i	−1.38269	+	0.757825i
$959$	−0.0748125	−	0.129579i	−0.00241582	−	0.00418433i
$960$		0			0
$961$			30.9351i			0.997907i
$962$	13.7538	+	10.2055i	0.443441	+	0.329040i
$963$		0			0
$964$	−26.5361	+	5.85988i	−0.854670	+	0.188734i
$965$	15.9998	−	9.23747i	0.515051	−	0.297365i
$966$		0			0
$967$	−18.5489	+	18.5489i	−0.596493	+	0.596493i	−0.939377	−	0.342885i	$-0.888596\pi$
$967$	−18.5489	+	18.5489i	−0.596493	+	0.596493i	0.342885	+	0.939377i	$0.388596\pi$
$968$	−26.6207	+	5.26085i	−0.855622	+	0.169090i
$969$		0			0
$970$	−16.9846	+	4.14865i	−0.545342	+	0.133205i
$971$	−25.3476	+	43.9034i	−0.813444	+	1.40893i	0.0969959	+	0.995285i	$0.469077\pi$
$971$	−25.3476	+	43.9034i	−0.813444	+	1.40893i	−0.910440	+	0.413642i	$0.864257\pi$
$972$		0			0
$973$	2.60762	−	9.73176i	0.0835963	−	0.311986i
$974$	17.2756	−	28.4427i	0.553545	−	0.911364i
$975$		0			0
$976$	35.2578	+	24.7748i	1.12857	+	0.793022i
$977$	−5.21978	+	19.4805i	−0.166996	+	0.623236i	0.830782	+	0.556598i	$0.187894\pi$
$977$	−5.21978	+	19.4805i	−0.166996	+	0.623236i	−0.997777	+	0.0666376i	$0.978773\pi$
$978$		0			0
$979$	−2.19124	−	1.26511i	−0.0700323	−	0.0404332i
$980$	27.6749	+	8.75104i	0.884042	+	0.279542i
$981$		0			0
$982$	−44.1707	−	12.8944i	−1.40954	−	0.411477i
$983$	−21.7716	−	21.7716i	−0.694405	−	0.694405i	0.268793	−	0.963198i	$-0.413375\pi$
$983$	−21.7716	−	21.7716i	−0.694405	−	0.694405i	−0.963198	+	0.268793i	$0.913375\pi$
$984$		0			0
$985$	24.1828	−	13.9619i	0.770528	−	0.444864i
$986$	0.514340	+	0.537732i	0.0163799	+	0.0171249i
$987$		0			0
$988$	17.9159	−	13.5744i	0.569980	−	0.431860i
$989$			5.53425i			0.175979i
$990$		0			0
$991$	−12.8654	+	7.42785i	−0.408683	+	0.235954i	−0.690224	−	0.723596i	$-0.742488\pi$
$991$	−12.8654	+	7.42785i	−0.408683	+	0.235954i	0.281540	+	0.959549i	$0.409155\pi$
$992$	−1.43198	−	0.159826i	−0.0454655	−	0.00507448i
$993$		0			0
$994$	4.53475	−	15.5341i	0.143834	−	0.492712i
$995$	16.1852	+	60.4042i	0.513107	+	1.91494i
$996$		0			0
$997$	1.48602	+	0.857953i	0.0470627	+	0.0271717i	0.523347	−	0.852120i	$-0.324683\pi$
$997$	1.48602	+	0.857953i	0.0470627	+	0.0271717i	−0.476284	+	0.879291i	$0.658017\pi$
$998$	0.0417353	−	1.87710i	0.00132111	−	0.0594184i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.ed.d.739.3		48
3.2	odd	2		104.2.u.a.11.10	yes	48
8.3	odd	2	inner	936.2.ed.d.739.12		48
12.11	even	2		416.2.bk.a.271.12		48
13.6	odd	12	inner	936.2.ed.d.19.12		48
24.5	odd	2		416.2.bk.a.271.11		48
24.11	even	2		104.2.u.a.11.1	✓	48
39.32	even	12		104.2.u.a.19.1	yes	48
104.19	even	12	inner	936.2.ed.d.19.3		48
156.71	odd	12		416.2.bk.a.175.11		48
312.149	even	12		416.2.bk.a.175.12		48
312.227	odd	12		104.2.u.a.19.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.u.a.11.1	✓	48	24.11	even	2
104.2.u.a.11.10	yes	48	3.2	odd	2
104.2.u.a.19.1	yes	48	39.32	even	12
104.2.u.a.19.10	yes	48	312.227	odd	12
416.2.bk.a.175.11		48	156.71	odd	12
416.2.bk.a.175.12		48	312.149	even	12
416.2.bk.a.271.11		48	24.5	odd	2
416.2.bk.a.271.12		48	12.11	even	2
936.2.ed.d.19.3		48	104.19	even	12	inner
936.2.ed.d.19.12		48	13.6	odd	12	inner
936.2.ed.d.739.3		48	1.1	even	1	trivial
936.2.ed.d.739.12		48	8.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.ed (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.977524 - 1.02198i) q^{2} +(-0.0888919 + 1.99802i) q^{4} +(-2.13831 + 2.13831i) q^{5} +(1.43298 - 0.383965i) q^{7} +(2.12884 - 1.86227i) q^{8} +(4.27556 + 0.0950627i) q^{10} +(1.14540 + 0.306909i) q^{11} +(1.50651 + 3.27573i) q^{13} +(-1.79317 - 1.08914i) q^{14} +(-3.98420 - 0.355216i) q^{16} +(0.917474 + 0.529704i) q^{17} +(-3.01087 + 0.806761i) q^{19} +(-4.08231 - 4.46247i) q^{20} +(-0.806001 - 1.47059i) q^{22} +(-2.44668 - 4.23777i) q^{23} -4.14473i q^{25} +(1.87509 - 4.74173i) q^{26} +(0.639791 + 2.89725i) q^{28} +(-0.430121 + 0.248330i) q^{29} +(-0.180109 + 0.180109i) q^{31} +(3.53162 + 4.41901i) q^{32} +(-0.355506 - 1.45544i) q^{34} +(-2.24311 + 3.88518i) q^{35} +(-0.869322 + 3.24435i) q^{37} +(3.76770 + 2.28843i) q^{38} +(-0.570000 + 8.53422i) q^{40} +(-1.95534 + 7.29743i) q^{41} +(-0.979452 - 0.565487i) q^{43} +(-0.715028 + 2.26125i) q^{44} +(-1.93923 + 6.64298i) q^{46} +(-5.29277 - 5.29277i) q^{47} +(-4.15619 + 2.39957i) q^{49} +(-4.23584 + 4.05158i) q^{50} +(-6.67891 + 2.71886i) q^{52} +13.2050i q^{53} +(-3.10549 + 1.79295i) q^{55} +(2.33553 - 3.48599i) q^{56} +(0.674242 + 0.196826i) q^{58} +(1.58626 + 5.92000i) q^{59} +(-9.32964 - 5.38647i) q^{61} +(0.360130 + 0.00800711i) q^{62} +(1.06389 - 7.92894i) q^{64} +(-10.2259 - 3.78314i) q^{65} +(-3.22308 + 12.0287i) q^{67} +(-1.13992 + 1.78605i) q^{68} +(6.16328 - 1.50544i) q^{70} +(1.99632 + 7.45038i) q^{71} +(4.04472 - 4.04472i) q^{73} +(4.16545 - 2.28300i) q^{74} +(-1.34429 - 6.08751i) q^{76} +1.75917 q^{77} +0.933621i q^{79} +(9.27901 - 7.75988i) q^{80} +(9.36923 - 5.13509i) q^{82} +(6.19701 + 6.19701i) q^{83} +(-3.09451 + 0.829172i) q^{85} +(0.379521 + 1.55376i) q^{86} +(3.00992 - 1.47969i) q^{88} +(-2.06105 - 0.552258i) q^{89} +(3.41656 + 4.11560i) q^{91} +(8.68465 - 4.51181i) q^{92} +(-0.235301 + 10.5829i) q^{94} +(4.71307 - 8.16328i) q^{95} +(-3.94895 + 1.05812i) q^{97} +(6.51509 + 1.90190i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} - 6 q^{4} + 10 q^{8} - 6 q^{10} + 8 q^{11} - 8 q^{14} - 10 q^{16} + 12 q^{17} - 8 q^{19} - 10 q^{20} - 20 q^{22} + 2 q^{26} + 12 q^{28} - 16 q^{32} - 46 q^{34} + 4 q^{35} - 32 q^{40} - 12 q^{43}+ \cdots + 16 q^{98}+O(q^{100}) \) 48 * q + 4 * q^2 - 6 * q^4 + 10 * q^8 - 6 * q^10 + 8 * q^11 - 8 * q^14 - 10 * q^16 + 12 * q^17 - 8 * q^19 - 10 * q^20 - 20 * q^22 + 2 * q^26 + 12 * q^28 - 16 * q^32 - 46 * q^34 + 4 * q^35 - 32 * q^40 - 12 * q^43 + 16 * q^44 + 34 * q^46 - 60 * q^49 - 86 * q^50 + 12 * q^52 - 48 * q^56 + 30 * q^58 + 64 * q^59 - 42 * q^62 + 16 * q^65 - 8 * q^67 + 32 * q^68 + 36 * q^70 - 12 * q^73 - 38 * q^74 - 94 * q^76 + 108 * q^80 + 54 * q^82 + 48 * q^83 - 80 * q^86 - 108 * q^88 - 12 * q^89 + 104 * q^91 + 20 * q^92 + 26 * q^94 + 4 * q^97 + 16 * q^98

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