LMFDB - Embedded newform 936.2.ed.d.19.3

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			19.3
Character	$\chi$	$=$	936.19
Dual form			936.2.ed.d.739.3

$q$-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 $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$1$	$-1$	$-1$

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	0.0428025	−	0.999084i	$-0.486371\pi$
$5$	−2.13831	−	2.13831i	−0.956281	−	0.956281i	−0.999084	+	0.0428025i	$0.986371\pi$
$6$		0			0
$7$	1.43298	+	0.383965i	0.541614	+	0.145125i	0.519246	−	0.854625i	$-0.326213\pi$
$7$	1.43298	+	0.383965i	0.541614	+	0.145125i	0.0223680	+	0.999750i	$0.492879\pi$
$8$	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	−0.0819743	−	0.996634i	$-0.526123\pi$
$11$	1.14540	−	0.306909i	0.345351	−	0.0925365i	0.427325	+	0.904098i	$0.359456\pi$
$12$		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	−0.384597	−	0.923085i	$-0.625659\pi$
$17$	0.917474	−	0.529704i	0.222520	−	0.128472i	0.607117	+	0.794613i	$0.292326\pi$
$18$		0			0
$19$	−3.01087	−	0.806761i	−0.690742	−	0.185084i	−0.103662	−	0.994613i	$-0.533056\pi$
$19$	−3.01087	−	0.806761i	−0.690742	−	0.185084i	−0.587080	+	0.809529i	$0.699723\pi$
$20$	−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	0.489764	+	0.871855i	$0.337083\pi$
$23$	−2.44668	+	4.23777i	−0.510167	+	0.883635i	−0.999931	+	0.0117799i	$0.996250\pi$
$24$		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	0.459532	−	0.888161i	$-0.348017\pi$
$29$	−0.430121	−	0.248330i	−0.0798714	−	0.0461138i	−0.539404	+	0.842047i	$0.681350\pi$
$30$		0			0
$31$	−0.180109	−	0.180109i	−0.0323486	−	0.0323486i	0.690747	−	0.723096i	$-0.257282\pi$
$31$	−0.180109	−	0.180109i	−0.0323486	−	0.0323486i	−0.723096	+	0.690747i	$0.757282\pi$
$32$	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	−0.999839	−	0.0179251i	$-0.994294\pi$
$37$	−0.869322	−	3.24435i	−0.142916	−	0.533368i	0.856924	−	0.515443i	$-0.172373\pi$
$38$	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	−0.932624	−	0.360850i	$-0.882487\pi$
$41$	−1.95534	−	7.29743i	−0.305373	−	1.13967i	0.627251	−	0.778817i	$-0.284180\pi$
$42$		0			0
$43$	−0.979452	+	0.565487i	−0.149365	+	0.0862359i	−0.572820	−	0.819681i	$-0.694151\pi$
$43$	−0.979452	+	0.565487i	−0.149365	+	0.0862359i	0.423455	+	0.905917i	$0.360817\pi$
$44$	−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	−0.978461	−	0.206431i	$-0.933815\pi$
$47$	−5.29277	+	5.29277i	−0.772030	+	0.772030i	0.206431	+	0.978461i	$0.433815\pi$
$48$		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	$-0.638423\pi$
$53$		−	13.2050i		−	1.81385i	0.421292	−	0.906925i	$-0.361577\pi$
$54$		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	−0.782470	−	0.622689i	$-0.786040\pi$
$59$	1.58626	−	5.92000i	0.206513	−	0.770718i	0.988983	−	0.148029i	$-0.0472930\pi$
$60$		0			0
$61$	−9.32964	+	5.38647i	−1.19454	+	0.689667i	−0.959332	−	0.282279i	$-0.908910\pi$
$61$	−9.32964	+	5.38647i	−1.19454	+	0.689667i	−0.235206	+	0.971946i	$0.575576\pi$
$62$	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	−0.823879	−	0.566765i	$-0.808195\pi$
$67$	−3.22308	−	12.0287i	−0.393762	−	1.46954i	0.430118	−	0.902773i	$-0.358472\pi$
$68$	−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	−0.740354	−	0.672217i	$-0.765342\pi$
$71$	1.99632	−	7.45038i	0.236920	−	0.884197i	0.977274	−	0.211980i	$-0.0679912\pi$
$72$		0			0
$73$	4.04472	+	4.04472i	0.473399	+	0.473399i	0.903013	−	0.429614i	$-0.141350\pi$
$73$	4.04472	+	4.04472i	0.473399	+	0.473399i	−0.429614	+	0.903013i	$0.641350\pi$
$74$	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	$-0.983275\pi$
$79$		−	0.933621i		−	0.105041i	0.998620	−	0.0525203i	$-0.0167254\pi$
$80$	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	−0.279837	−	0.960047i	$-0.590281\pi$
$83$	6.19701	−	6.19701i	0.680210	−	0.680210i	0.960047	+	0.279837i	$0.0902805\pi$
$84$		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	−0.366394	−	0.930460i	$-0.619408\pi$
$89$	−2.06105	+	0.552258i	−0.218471	+	0.0585392i	0.147923	+	0.988999i	$0.452741\pi$
$90$		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	0.0527054	−	0.998610i	$-0.483216\pi$
$97$	−3.94895	−	1.05812i	−0.400955	−	0.107436i	−0.453661	+	0.891174i	$0.649882\pi$
$98$	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	0.456081	+	0.889938i	$0.349253\pi$
$101$	−5.45375	+	9.44617i	−0.542668	+	0.939929i	−0.998750	+	0.0499909i	$0.984081\pi$
$102$		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	−0.990150	−	0.140014i	$-0.955285\pi$
$107$	−3.86681	+	6.69752i	−0.373819	+	0.647474i	0.616330	+	0.787488i	$0.288619\pi$
$108$		0			0
$109$	−4.46618	−	4.46618i	−0.427782	−	0.427782i	0.460090	−	0.887872i	$-0.347817\pi$
$109$	−4.46618	−	4.46618i	−0.427782	−	0.427782i	−0.887872	+	0.460090i	$0.847817\pi$
$110$	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	−0.998900	−	0.0468899i	$-0.985069\pi$
$113$	−5.74089	−	9.94352i	−0.540058	−	0.935408i	0.458842	−	0.888518i	$-0.348264\pi$
$114$		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	−0.992567	−	0.121698i	$-0.961166\pi$
$127$	−4.40510	+	7.62986i	−0.390890	+	0.677041i	0.601678	+	0.798739i	$0.294499\pi$
$128$	−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	−0.967032	−	0.254655i	$-0.918038\pi$
$137$	−0.0261039	+	0.0974210i	−0.00223021	+	0.00832324i	0.964802	+	0.262978i	$0.0847048\pi$
$138$		0			0
$139$	3.39564	+	5.88143i	0.288015	+	0.498856i	0.973336	−	0.229385i	$-0.0736715\pi$
$139$	3.39564	+	5.88143i	0.288015	+	0.498856i	−0.685321	+	0.728241i	$0.740338\pi$
$140$	−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	0.678800	+	0.734323i	$0.262500\pi$
$149$	−3.37169	+	12.5833i	−0.276220	+	1.03087i	−0.955020	+	0.296543i	$0.904166\pi$
$150$		0			0
$151$	8.53114	−	8.53114i	0.694254	−	0.694254i	−0.268911	−	0.963165i	$-0.586664\pi$
$151$	8.53114	−	8.53114i	0.694254	−	0.694254i	0.963165	+	0.268911i	$0.0866638\pi$
$152$	−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	$0.00663298\pi$
$157$			0.522164i			0.0416732i	−0.999783	+	0.0208366i	$0.993367\pi$
$158$	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	0.0339021	−	0.999425i	$-0.489207\pi$
$163$	6.43789	−	24.0265i	0.504255	−	1.88190i	0.470353	−	0.882479i	$-0.344127\pi$
$164$	−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	0.927529	−	0.373751i	$-0.121929\pi$
$167$	−0.809102	−	3.01961i	−0.0626102	−	0.233665i	−0.990139	+	0.140087i	$0.955262\pi$
$168$		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	0.963500	−	0.267708i	$-0.0862663\pi$
$173$	3.28703	+	5.69330i	0.249908	+	0.432853i	−0.713592	+	0.700561i	$0.752933\pi$
$174$		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	−0.434718	−	0.900567i	$-0.643152\pi$
$179$	−19.1587	−	11.0613i	−1.43199	−	0.826760i	−0.997273	+	0.0738069i	$0.976485\pi$
$180$		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	−0.446651	−	0.894708i	$-0.647383\pi$
$191$	1.44924	−	0.836719i	0.104863	−	0.0605429i	0.551514	+	0.834165i	$0.314050\pi$
$192$		0			0
$193$	−5.90121	+	1.58123i	−0.424779	+	0.113819i	−0.464874	−	0.885377i	$-0.653900\pi$
$193$	−5.90121	+	1.58123i	−0.424779	+	0.113819i	0.0400956	+	0.999196i	$0.487234\pi$
$194$	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	−0.562154	−	0.827032i	$-0.690027\pi$
$197$	−8.91936	+	2.38994i	−0.635478	+	0.170276i	−0.0733239	+	0.997308i	$0.523361\pi$
$198$		0			0
$199$	10.3397	+	17.9089i	0.732961	+	1.26953i	0.955612	+	0.294628i	$0.0951957\pi$
$199$	10.3397	+	17.9089i	0.732961	+	1.26953i	−0.222651	+	0.974898i	$0.571471\pi$
$200$	−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	0.216755	+	0.976226i	$0.430453\pi$
$211$	−10.7064	+	18.5440i	−0.737059	+	1.27662i	−0.953814	+	0.300398i	$0.902881\pi$
$212$	−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	0.0863822	−	0.996262i	$-0.472469\pi$
$223$	9.84578	−	2.63817i	0.659323	−	0.176665i	0.572940	+	0.819597i	$0.305803\pi$
$224$	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	0.136463	−	0.990645i	$-0.456427\pi$
$227$	−3.62620	−	0.971637i	−0.240679	−	0.0644898i	−0.377142	+	0.926155i	$0.623093\pi$
$228$		0			0
$229$	5.43768	−	5.43768i	0.359332	−	0.359332i	−0.504235	−	0.863567i	$-0.668225\pi$
$229$	5.43768	−	5.43768i	0.359332	−	0.359332i	0.863567	+	0.504235i	$0.168225\pi$
$230$	−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	$0.0305876\pi$
$233$			2.92911i			0.191892i	−0.995387	+	0.0959461i	$0.969412\pi$
$234$		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	0.997488	−	0.0708299i	$-0.0225647\pi$
$239$	14.3258	+	14.3258i	0.926659	+	0.926659i	−0.0708299	+	0.997488i	$0.522565\pi$
$240$		0			0
$241$	3.51676	−	13.1247i	0.226534	−	0.845437i	−0.755250	−	0.655437i	$-0.772484\pi$
$241$	3.51676	−	13.1247i	0.226534	−	0.845437i	0.981784	−	0.190000i	$-0.0608488\pi$
$242$	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	−0.168501	−	0.985702i	$-0.553893\pi$
$251$	9.51992	−	5.49633i	0.600892	−	0.346925i	0.769392	+	0.638777i	$0.220559\pi$
$252$		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	0.817820	−	0.575474i	$-0.195182\pi$
$257$	11.6764	+	6.74138i	0.728355	+	0.420516i	−0.0894651	+	0.995990i	$0.528516\pi$
$258$		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	−0.188413	−	0.982090i	$-0.560334\pi$
$263$	−18.3764	−	10.6096i	−1.13313	−	0.654216i	−0.944721	+	0.327874i	$0.893668\pi$
$264$		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	0.534537	−	0.845145i	$-0.320486\pi$
$269$	25.1549	−	14.5232i	1.53372	−	0.885495i	0.999186	−	0.0403505i	$-0.0128475\pi$
$270$		0			0
$271$	3.45071	+	12.8782i	0.209616	+	0.782296i	0.987993	+	0.154500i	$0.0493765\pi$
$271$	3.45071	+	12.8782i	0.209616	+	0.782296i	−0.778377	+	0.627797i	$0.783957\pi$
$272$	−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	−0.951268	−	0.308364i	$-0.900218\pi$
$277$	−12.3608	−	21.4095i	−0.742686	−	1.28637i	0.208583	−	0.978005i	$-0.433115\pi$
$278$	−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	0.987856	+	0.155371i	$0.0496572\pi$
$281$	19.1640	+	19.1640i	1.14323	+	1.14323i	0.155371	+	0.987856i	$0.450343\pi$
$282$		0			0
$283$	16.9756	+	9.80085i	1.00909	+	0.582600i	0.910926	−	0.412570i	$-0.135369\pi$
$283$	16.9756	+	9.80085i	1.00909	+	0.582600i	0.0981670	+	0.995170i	$0.468702\pi$
$284$	−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	−0.0696703	−	0.997570i	$-0.522195\pi$
$293$	−10.7632	−	2.88398i	−0.628792	−	0.168484i	−0.559121	+	0.829086i	$0.688861\pi$
$294$		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	0.420497	−	0.907294i	$-0.361856\pi$
$307$	−8.52938	−	8.52938i	−0.486797	−	0.486797i	−0.907294	+	0.420497i	$0.861856\pi$
$308$	−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	0.297098	−	0.954847i	$-0.403981\pi$
$317$	−11.7109	−	11.7109i	−0.657749	−	0.657749i	−0.954847	+	0.297098i	$0.903981\pi$
$318$		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	0.618694	−	0.785632i	$-0.287662\pi$
$331$	13.8576	+	3.71314i	0.761683	+	0.204092i	0.142989	+	0.989724i	$0.454329\pi$
$332$	−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	$0.257274\pi$
$337$			26.5479i			1.44616i	−0.690765	+	0.723079i	$0.742726\pi$
$338$	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	0.881390	−	0.472389i	$-0.156608\pi$
$347$	0.588542	+	1.01939i	0.0315946	+	0.0547235i	−0.849796	+	0.527112i	$0.823275\pi$
$348$		0			0
$349$	−7.72090	−	28.8148i	−0.413291	−	1.54242i	−0.788235	−	0.615374i	$-0.789005\pi$
$349$	−7.72090	−	28.8148i	−0.413291	−	1.54242i	0.374945	−	0.927047i	$-0.377662\pi$
$350$	−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	−0.874474	−	0.485072i	$-0.838793\pi$
$353$	−6.75802	−	25.2213i	−0.359693	−	1.34239i	0.514781	−	0.857322i	$-0.327873\pi$
$354$		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	0.124086	−	0.992272i	$-0.460400\pi$
$359$	21.1519	−	21.1519i	1.11636	−	1.11636i	0.992272	−	0.124086i	$-0.0395998\pi$
$360$		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	0.889682	−	0.456580i	$-0.150926\pi$
$367$	17.9908	+	10.3870i	0.939114	+	0.542198i	0.0494315	+	0.998778i	$0.484259\pi$
$368$	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	−0.136108	−	0.990694i	$-0.543459\pi$
$373$	12.6271	−	7.29024i	0.653804	−	0.377474i	0.789912	+	0.613220i	$0.210126\pi$
$374$	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	0.995912	+	0.0903274i	$0.0287914\pi$
$379$	3.47679	+	12.9756i	0.178591	+	0.666509i	−0.817321	+	0.576182i	$0.804542\pi$
$380$	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	−0.828269	−	0.560331i	$-0.810674\pi$
$383$	3.31127	−	12.3578i	0.169198	−	0.631456i	0.997467	−	0.0711259i	$-0.0226592\pi$
$384$		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	0.143014	−	0.989721i	$-0.454321\pi$
$397$	−4.54273	−	1.21722i	−0.227993	−	0.0610906i	−0.371007	+	0.928630i	$0.620987\pi$
$398$	−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	−0.193904	−	0.981020i	$-0.562115\pi$
$401$	2.57682	−	0.690456i	0.128680	−	0.0344797i	0.322584	+	0.946541i	$0.395448\pi$
$402$		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	0.826143	−	0.563460i	$-0.190530\pi$
$409$	25.4794	+	6.82718i	1.25987	+	0.337582i	0.433731	+	0.901042i	$0.357197\pi$
$410$	−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	0.289522	+	0.957171i	$0.406504\pi$
$419$	−14.0047	+	24.2568i	−0.684174	+	1.18502i	−0.973696	+	0.227853i	$0.926830\pi$
$420$		0			0
$421$	−0.583969	−	0.583969i	−0.0284609	−	0.0284609i	0.692733	−	0.721194i	$-0.256406\pi$
$421$	−0.583969	−	0.583969i	−0.0284609	−	0.0284609i	−0.721194	+	0.692733i	$0.756406\pi$
$422$	−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	0.157563	−	0.987509i	$-0.449636\pi$
$431$	16.3546	−	4.38219i	0.787772	−	0.211083i	0.630208	+	0.776426i	$0.282969\pi$
$432$		0			0
$433$	19.1457	−	11.0538i	0.920082	−	0.531209i	0.0364205	−	0.999337i	$-0.488404\pi$
$433$	19.1457	−	11.0538i	0.920082	−	0.531209i	0.883661	+	0.468127i	$0.155071\pi$
$434$	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	0.0655708	−	0.997848i	$-0.479113\pi$
$439$	18.7931	−	32.5507i	0.896947	−	1.55356i	0.831376	−	0.555710i	$-0.187553\pi$
$440$	−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	−0.965384	−	0.260833i	$-0.916003\pi$
$449$	0.0228713	−	0.0853569i	0.00107936	−	0.00402824i	0.966463	+	0.256804i	$0.0826696\pi$
$450$		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	−0.939483	−	0.342595i	$-0.888694\pi$
$457$	−6.35265	−	23.7084i	−0.297164	−	1.10903i	0.642319	−	0.766438i	$-0.277973\pi$
$458$	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	−0.933971	−	0.357350i	$-0.883680\pi$
$461$	1.14969	−	4.29072i	0.0535466	−	0.199839i	0.987517	+	0.157511i	$0.0503470\pi$
$462$		0			0
$463$	15.6374	−	15.6374i	0.726731	−	0.726731i	−0.243236	−	0.969967i	$-0.578209\pi$
$463$	15.6374	−	15.6374i	0.726731	−	0.726731i	0.969967	+	0.243236i	$0.0782089\pi$
$464$	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	$0.0654525\pi$
$467$			8.82470i			0.408358i	−0.978934	+	0.204179i	$0.934547\pi$
$468$		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	0.798281	+	0.602285i	$0.205743\pi$
$479$	8.93153	+	33.3329i	0.408092	+	1.52302i	−0.390189	+	0.920735i	$0.627591\pi$
$480$		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	−0.679204	−	0.733950i	$-0.737675\pi$
$487$	6.09032	−	22.7294i	0.275979	−	1.02997i	0.955183	−	0.296017i	$-0.0956586\pi$
$488$	−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	0.975298	−	0.220892i	$-0.0708967\pi$
$491$	28.1779	+	16.2685i	1.27165	+	0.734187i	0.296351	+	0.955079i	$0.404230\pi$
$492$		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	−0.685782	−	0.727807i	$-0.740540\pi$
$499$	0.938780	−	0.938780i	0.0420256	−	0.0420256i	0.727807	+	0.685782i	$0.240540\pi$
$500$	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	−0.417043	−	0.908887i	$-0.636933\pi$
$503$	3.62331	−	2.09192i	0.161555	−	0.0932739i	0.578598	+	0.815613i	$0.303600\pi$
$504$		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	0.306060	−	0.952012i	$-0.400989\pi$
$509$	23.6241	−	6.33007i	1.04712	−	0.280575i	0.741062	+	0.671437i	$0.234323\pi$
$510$		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	−0.995106	−	0.0988105i	$-0.968496\pi$
$523$	−9.42167	+	16.3188i	−0.411981	+	0.713572i	0.583126	+	0.812382i	$0.301830\pi$
$524$	−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	−0.678113	−	0.734958i	$-0.737202\pi$
$541$	1.32217	−	1.32217i	0.0568444	−	0.0568444i	0.734958	+	0.678113i	$0.237202\pi$
$542$	−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	0.725585	+	0.688132i	$0.241569\pi$
$557$	10.4145	+	38.8674i	0.441276	+	1.64686i	−0.284309	+	0.958733i	$0.591764\pi$
$558$		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	−0.293670	−	0.955907i	$-0.594877\pi$
$563$	9.19054	−	5.30616i	0.387335	−	0.223628i	0.681005	+	0.732279i	$0.261543\pi$
$564$		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	0.383118	−	0.923699i	$-0.374850\pi$
$569$	−5.37353	−	3.10241i	−0.225270	−	0.130060i	−0.608388	+	0.793640i	$0.708184\pi$
$570$		0			0
$571$			10.5785i			0.442697i	0.975195	+	0.221348i	$0.0710458\pi$
$571$			10.5785i			0.442697i	−0.975195	+	0.221348i	$0.928954\pi$
$572$	−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	−0.857956	−	0.513723i	$-0.828266\pi$
$577$	−8.26875	+	8.26875i	−0.344233	+	0.344233i	0.513723	+	0.857956i	$0.328266\pi$
$578$	−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	0.990454	+	0.137844i	$0.0440172\pi$
$587$	4.88481	+	18.2304i	0.201618	+	0.752447i	−0.788836	+	0.614603i	$0.789316\pi$
$588$		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	0.860780	−	0.508978i	$-0.169976\pi$
$593$	8.56694	+	8.56694i	0.351802	+	0.351802i	−0.508978	+	0.860780i	$0.669976\pi$
$594$		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	$-0.848657\pi$
$599$		−	22.4062i		−	0.915491i	0.889083	−	0.457745i	$-0.151343\pi$
$600$		0			0
$601$	11.5194	−	19.9522i	0.469887	−	0.813867i	−0.529521	−	0.848297i	$-0.677628\pi$
$601$	11.5194	−	19.9522i	0.469887	−	0.813867i	0.999407	+	0.0344297i	$0.0109615\pi$
$602$	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	−0.773642	−	0.633623i	$-0.781567\pi$
$607$	−15.0714	+	8.70147i	−0.611729	+	0.353182i	0.161913	+	0.986805i	$0.448234\pi$
$608$	−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	0.260748	−	0.965407i	$-0.416031\pi$
$613$	23.9979	−	6.43022i	0.969266	−	0.259714i	0.708518	+	0.705693i	$0.249364\pi$
$614$	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	−0.0967368	−	0.995310i	$-0.530840\pi$
$617$	−16.8453	−	4.51370i	−0.678168	−	0.181715i	−0.581431	+	0.813595i	$0.697507\pi$
$618$		0			0
$619$	−22.2153	−	22.2153i	−0.892907	−	0.892907i	0.101889	−	0.994796i	$-0.467511\pi$
$619$	−22.2153	−	22.2153i	−0.892907	−	0.892907i	−0.994796	+	0.101889i	$0.967511\pi$
$620$	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	−0.230298	−	0.973120i	$-0.573970\pi$
$631$	−23.0172	−	6.16745i	−0.916302	−	0.245522i	−0.686004	+	0.727598i	$0.740637\pi$
$632$	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	−0.830822	−	0.556538i	$-0.812129\pi$
$641$	−19.3494	+	11.1714i	−0.764257	+	0.441244i	0.0665652	+	0.997782i	$0.478796\pi$
$642$		0			0
$643$	−4.36483	−	1.16955i	−0.172132	−	0.0461227i	0.171724	−	0.985145i	$-0.445066\pi$
$643$	−4.36483	−	1.16955i	−0.172132	−	0.0461227i	−0.343856	+	0.939023i	$0.611733\pi$
$644$	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	−0.767054	−	0.641583i	$-0.778278\pi$
$647$	4.37758	−	7.58218i	0.172100	−	0.298086i	0.939154	+	0.343497i	$0.111611\pi$
$648$		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	0.611815	−	0.791001i	$-0.290440\pi$
$653$	5.94625	+	3.43307i	0.232695	+	0.134346i	−0.379120	+	0.925348i	$0.623773\pi$
$654$		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	0.976742	−	0.214417i	$-0.0687850\pi$
$659$	7.77012	+	13.4582i	0.302681	+	0.524259i	−0.674061	+	0.738675i	$0.735452\pi$
$660$		0			0
$661$	10.9023	+	40.6880i	0.424051	+	1.58258i	0.765987	+	0.642856i	$0.222251\pi$
$661$	10.9023	+	40.6880i	0.424051	+	1.58258i	−0.341936	+	0.939723i	$0.611082\pi$
$662$	−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	0.600964	−	0.799276i	$-0.294784\pi$
$673$	5.42846	+	3.13412i	0.209252	+	0.120812i	−0.391712	+	0.920088i	$0.628117\pi$
$674$	−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	$-0.866944\pi$
$677$		−	21.1245i		−	0.811881i	0.913900	−	0.405940i	$-0.133056\pi$
$678$		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	−0.680571	−	0.732683i	$-0.738268\pi$
$683$	7.19116	−	26.8378i	0.275162	−	1.02692i	0.955733	−	0.294236i	$-0.0950653\pi$
$684$		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	0.995642	+	0.0932606i	$0.0297290\pi$
$691$	4.73219	+	17.6608i	0.180021	+	0.671848i	−0.815621	+	0.578587i	$0.803604\pi$
$692$	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	0.808477	−	0.588528i	$-0.200292\pi$
$709$	32.3352	+	8.66420i	1.21437	+	0.325391i	0.405898	+	0.913919i	$0.366959\pi$
$710$	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	0.983144	−	0.182834i	$-0.0585270\pi$
$719$	8.93537	+	15.4765i	0.333233	+	0.577177i	−0.649911	+	0.760011i	$0.725194\pi$
$720$		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	0.789304	−	0.614003i	$-0.210442\pi$
$733$	4.74608	+	4.74608i	0.175300	+	0.175300i	−0.614003	+	0.789304i	$0.710442\pi$
$734$	−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	−0.897398	−	0.441221i	$-0.854545\pi$
$739$	−39.5252	+	10.5907i	−1.45396	+	0.389587i	−0.556559	+	0.830808i	$0.687879\pi$
$740$	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	0.520343	−	0.853957i	$-0.325804\pi$
$743$	38.1054	−	10.2103i	1.39795	−	0.374580i	0.877609	+	0.479377i	$0.159137\pi$
$744$		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	−0.584307	−	0.811533i	$-0.698633\pi$
$751$	11.2537	−	19.4920i	0.410655	−	0.711275i	0.994961	+	0.100258i	$0.0319668\pi$
$752$	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	−0.472664	−	0.881243i	$-0.656707\pi$
$757$	−40.5049	−	23.3855i	−1.47217	−	0.849960i	−0.999511	+	0.0312829i	$0.990041\pi$
$758$	−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	−0.768180	−	0.640234i	$-0.778837\pi$
$761$	5.99174	−	22.3615i	0.217200	−	0.810603i	0.985380	−	0.170369i	$-0.0544960\pi$
$762$		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	0.987258	−	0.159129i	$-0.0508687\pi$
$769$	1.46149	+	5.45437i	0.0527028	+	0.196689i	−0.934555	+	0.355819i	$0.884202\pi$
$770$	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	0.160488	+	0.987038i	$0.448693\pi$
$773$	−13.1234	+	48.9774i	−0.472018	+	1.76159i	−0.632506	+	0.774556i	$0.717973\pi$
$774$		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	−0.988971	−	0.148107i	$-0.952682\pi$
$787$	−1.63955	+	6.11890i	−0.0584438	+	0.218115i	0.930528	+	0.366222i	$0.119349\pi$
$788$	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	−0.997973	−	0.0636413i	$-0.979729\pi$
$797$	−15.6429	−	27.0944i	−0.554101	−	0.959732i	0.443871	−	0.896090i	$-0.353605\pi$
$798$		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	−0.698075	−	0.716025i	$-0.745960\pi$
$809$	7.70970	−	13.3536i	0.271059	−	0.469487i	0.969133	+	0.246538i	$0.0792930\pi$
$810$		0			0
$811$	−5.80801	+	5.80801i	−0.203947	+	0.203947i	−0.801689	−	0.597742i	$-0.796065\pi$
$811$	−5.80801	+	5.80801i	−0.203947	+	0.203947i	0.597742	+	0.801689i	$0.296065\pi$
$812$	−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	−0.775932	−	0.630817i	$-0.782720\pi$
$821$	−32.4496	+	8.69486i	−1.13250	+	0.303453i	−0.356568	+	0.934269i	$0.616053\pi$
$822$		0			0
$823$	12.8798	+	22.3085i	0.448962	+	0.777625i	0.998319	−	0.0579627i	$-0.0184605\pi$
$823$	12.8798	+	22.3085i	0.448962	+	0.777625i	−0.549357	+	0.835588i	$0.685127\pi$
$824$	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	0.192117	−	0.981372i	$-0.438465\pi$
$827$	−22.6971	−	22.6971i	−0.789255	−	0.789255i	−0.981372	+	0.192117i	$0.938465\pi$
$828$		0			0
$829$	−28.4583	+	49.2912i	−0.988397	+	1.71195i	−0.362654	+	0.931924i	$0.618129\pi$
$829$	−28.4583	+	49.2912i	−0.988397	+	1.71195i	−0.625743	+	0.780029i	$0.715204\pi$
$830$	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	0.249568	−	0.968357i	$-0.419711\pi$
$839$	−0.535224	−	0.143413i	−0.0184780	−	0.00495116i	−0.268046	+	0.963406i	$0.586378\pi$
$840$		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	−0.815603	−	0.578612i	$-0.803594\pi$
$853$	−6.92158	+	6.92158i	−0.236990	+	0.236990i	0.578612	+	0.815603i	$0.303594\pi$
$854$	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	$-0.866427\pi$
$857$		−	23.8544i		−	0.814849i	0.913239	−	0.407425i	$-0.133573\pi$
$858$		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	0.810701	−	0.585461i	$-0.199086\pi$
$863$	6.61684	+	6.61684i	0.225240	+	0.225240i	−0.585461	+	0.810701i	$0.699086\pi$
$864$		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	0.811244	+	0.584708i	$0.198791\pi$
$877$	−5.43918	+	20.2993i	−0.183668	+	0.685458i	−0.994912	+	0.100750i	$0.967876\pi$
$878$	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	0.999627	−	0.0273185i	$-0.00869683\pi$
$881$	43.8036	+	25.2900i	1.47578	+	0.852043i	0.476155	+	0.879361i	$0.342030\pi$
$882$		0			0
$883$			8.15325i			0.274379i	0.990545	+	0.137189i	$0.0438069\pi$
$883$			8.15325i			0.274379i	−0.990545	+	0.137189i	$0.956193\pi$
$884$	−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	−0.228373	−	0.973574i	$-0.573340\pi$
$887$	−35.3131	−	20.3880i	−1.18570	−	0.684563i	−0.957326	+	0.289010i	$0.906674\pi$
$888$		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	0.744348	−	0.667792i	$-0.232760\pi$
$907$	16.2086	+	9.35804i	0.538198	+	0.310729i	−0.206151	+	0.978520i	$0.566094\pi$
$908$	−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	$0.100769\pi$
$911$			18.7926i			0.622627i	−0.950307	+	0.311313i	$0.899231\pi$
$912$		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	0.372112	−	0.928188i	$-0.378634\pi$
$919$	41.2891	−	23.8383i	1.36200	−	0.786352i	0.989890	+	0.141836i	$0.0453005\pi$
$920$	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	0.388315	−	0.921527i	$-0.373057\pi$
$929$	8.04178	+	2.15479i	0.263842	+	0.0706963i	−0.124473	+	0.992223i	$0.539724\pi$
$930$		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	0.382599	−	0.923915i	$-0.375029\pi$
$941$	−16.6053	−	16.6053i	−0.541316	−	0.541316i	−0.923915	+	0.382599i	$0.875029\pi$
$942$		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	0.0154129	−	0.999881i	$-0.495094\pi$
$947$	16.2699	−	4.35951i	0.528701	−	0.141665i	0.513289	+	0.858216i	$0.328427\pi$
$948$		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	0.465888	−	0.884844i	$-0.345735\pi$
$953$	45.2296	−	26.1133i	1.46513	−	0.845893i	0.999241	+	0.0389507i	$0.0124015\pi$
$954$		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	0.342885	−	0.939377i	$-0.388596\pi$
$967$	−18.5489	−	18.5489i	−0.596493	−	0.596493i	−0.939377	+	0.342885i	$0.888596\pi$
$968$	−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	−0.910440	−	0.413642i	$-0.864257\pi$
$971$	−25.3476	−	43.9034i	−0.813444	−	1.40893i	0.0969959	−	0.995285i	$-0.469077\pi$
$972$		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	−0.997777	−	0.0666376i	$-0.978773\pi$
$977$	−5.21978	−	19.4805i	−0.166996	−	0.623236i	0.830782	−	0.556598i	$-0.187894\pi$
$978$		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	−0.963198	−	0.268793i	$-0.913375\pi$
$983$	−21.7716	+	21.7716i	−0.694405	+	0.694405i	0.268793	+	0.963198i	$0.413375\pi$
$984$		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	0.281540	−	0.959549i	$-0.409155\pi$
$991$	−12.8654	−	7.42785i	−0.408683	−	0.235954i	−0.690224	+	0.723596i	$0.742488\pi$
$992$	−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	−0.476284	−	0.879291i	$-0.658017\pi$
$997$	1.48602	−	0.857953i	0.0470627	−	0.0271717i	0.523347	+	0.852120i	$0.324683\pi$
$998$	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.19.3		48
3.2	odd	2		104.2.u.a.19.10	yes	48
8.3	odd	2	inner	936.2.ed.d.19.12		48
12.11	even	2		416.2.bk.a.175.12		48
13.11	odd	12	inner	936.2.ed.d.739.12		48
24.5	odd	2		416.2.bk.a.175.11		48
24.11	even	2		104.2.u.a.19.1	yes	48
39.11	even	12		104.2.u.a.11.1	✓	48
104.11	even	12	inner	936.2.ed.d.739.3		48
156.11	odd	12		416.2.bk.a.271.11		48
312.11	odd	12		104.2.u.a.11.10	yes	48
312.245	even	12		416.2.bk.a.271.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.u.a.11.1	✓	48	39.11	even	12
104.2.u.a.11.10	yes	48	312.11	odd	12
104.2.u.a.19.1	yes	48	24.11	even	2
104.2.u.a.19.10	yes	48	3.2	odd	2
416.2.bk.a.175.11		48	24.5	odd	2
416.2.bk.a.175.12		48	12.11	even	2
416.2.bk.a.271.11		48	156.11	odd	12
416.2.bk.a.271.12		48	312.245	even	12
936.2.ed.d.19.3		48	1.1	even	1	trivial
936.2.ed.d.19.12		48	8.3	odd	2	inner
936.2.ed.d.739.3		48	104.11	even	12	inner
936.2.ed.d.739.12		48	13.11	odd	12	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

Introduction

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