LMFDB - Embedded newform 936.2.ed.d.739.12

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			739.12
Character	$\chi$	$=$	936.739
Dual form			936.2.ed.d.19.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.35755 - 0.396300i) q^{2} +(1.68589 - 1.07599i) q^{4} +(2.13831 - 2.13831i) q^{5} +(-1.43298 + 0.383965i) q^{7} +(1.86227 - 2.12884i) q^{8} +(2.05545 - 3.75028i) q^{10} +(1.14540 + 0.306909i) q^{11} +(-1.50651 - 3.27573i) q^{13} +(-1.79317 + 1.08914i) q^{14} +(1.68447 - 3.62802i) q^{16} +(0.917474 + 0.529704i) q^{17} +(-3.01087 + 0.806761i) q^{19} +(1.30415 - 5.90577i) q^{20} +(1.67657 - 0.0372767i) q^{22} +(2.44668 + 4.23777i) q^{23} -4.14473i q^{25} +(-3.34334 - 3.84995i) q^{26} +(-2.00270 + 2.18920i) q^{28} +(0.430121 - 0.248330i) q^{29} +(0.180109 - 0.180109i) q^{31} +(0.848973 - 5.59279i) q^{32} +(1.45544 + 0.355506i) q^{34} +(-2.24311 + 3.88518i) q^{35} +(0.869322 - 3.24435i) q^{37} +(-3.76770 + 2.28843i) q^{38} +(-0.570000 - 8.53422i) q^{40} +(-1.95534 + 7.29743i) q^{41} +(-0.979452 - 0.565487i) q^{43} +(2.26125 - 0.715028i) q^{44} +(5.00091 + 4.78337i) q^{46} +(5.29277 + 5.29277i) q^{47} +(-4.15619 + 2.39957i) q^{49} +(-1.64256 - 5.62669i) q^{50} +(-6.06449 - 3.90154i) q^{52} -13.2050i q^{53} +(3.10549 - 1.79295i) q^{55} +(-1.85119 + 3.76562i) q^{56} +(0.485498 - 0.507578i) q^{58} +(1.58626 + 5.92000i) q^{59} +(9.32964 + 5.38647i) q^{61} +(0.173131 - 0.315885i) q^{62} +(-1.06389 - 7.92894i) q^{64} +(-10.2259 - 3.78314i) q^{65} +(-3.22308 + 12.0287i) q^{67} +(2.11672 - 0.0941727i) q^{68} +(-1.50544 + 6.16328i) q^{70} +(-1.99632 - 7.45038i) q^{71} +(4.04472 - 4.04472i) q^{73} +(-0.105587 - 4.74889i) q^{74} +(-4.20794 + 4.59979i) q^{76} -1.75917 q^{77} -0.933621i q^{79} +(-4.15591 - 11.3598i) q^{80} +(0.237493 + 10.6815i) q^{82} +(6.19701 + 6.19701i) q^{83} +(3.09451 - 0.829172i) q^{85} +(-1.55376 - 0.379521i) q^{86} +(2.78640 - 1.86682i) q^{88} +(-2.06105 - 0.552258i) q^{89} +(3.41656 + 4.11560i) q^{91} +(8.68465 + 4.51181i) q^{92} +(9.28274 + 5.08769i) q^{94} +(-4.71307 + 8.16328i) q^{95} +(-3.94895 + 1.05812i) q^{97} +(-4.69129 + 4.90464i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.35755	−	0.396300i	0.959934	−	0.280226i
$2$	1.35755	−	0.396300i	0.959934	−	0.280226i
$3$		0			0
$3$		0			0
$4$	1.68589	−	1.07599i	0.842947	−	0.537997i
$5$	2.13831	−	2.13831i	0.956281	−	0.956281i	−0.0428025	−	0.999084i	$-0.513629\pi$
$5$	2.13831	−	2.13831i	0.956281	−	0.956281i	0.999084	+	0.0428025i	$0.0136286\pi$
$6$		0			0
$7$	−1.43298	+	0.383965i	−0.541614	+	0.145125i	−0.519246	−	0.854625i	$-0.673787\pi$
$7$	−1.43298	+	0.383965i	−0.541614	+	0.145125i	−0.0223680	+	0.999750i	$0.507121\pi$
$8$	1.86227	−	2.12884i	0.658412	−	0.752658i
$9$		0			0
$10$	2.05545	−	3.75028i	0.649992	−	1.18594i
$11$	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
$16$	1.68447	−	3.62802i	0.421118	−	0.907006i
$17$	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	$0.533056\pi$
$20$	1.30415	−	5.90577i	0.291617	−	1.32057i
$21$		0			0
$22$	1.67657	−	0.0372767i	0.357445	−	0.00794743i
$23$	2.44668	+	4.23777i	0.510167	+	0.883635i	0.999931	+	0.0117799i	$0.00374976\pi$
$23$	2.44668	+	4.23777i	0.510167	+	0.883635i	−0.489764	+	0.871855i	$0.662917\pi$
$24$		0			0
$25$		−	4.14473i		−	0.828947i
$26$	−3.34334	−	3.84995i	−0.655683	−	0.755037i
$27$		0			0
$28$	−2.00270	+	2.18920i	−0.378475	+	0.413720i
$29$	0.430121	−	0.248330i	0.0798714	−	0.0461138i	−0.459532	−	0.888161i	$-0.651983\pi$
$29$	0.430121	−	0.248330i	0.0798714	−	0.0461138i	0.539404	+	0.842047i	$0.318650\pi$
$30$		0			0
$31$	0.180109	−	0.180109i	0.0323486	−	0.0323486i	−0.690747	−	0.723096i	$-0.742718\pi$
$31$	0.180109	−	0.180109i	0.0323486	−	0.0323486i	0.723096	+	0.690747i	$0.242718\pi$
$32$	0.848973	−	5.59279i	0.150079	−	0.988674i
$33$		0			0
$34$	1.45544	+	0.355506i	0.249606	+	0.0609687i
$35$	−2.24311	+	3.88518i	−0.379155	+	0.656716i
$36$		0			0
$37$	0.869322	−	3.24435i	0.142916	−	0.533368i	−0.856924	−	0.515443i	$-0.827627\pi$
$37$	0.869322	−	3.24435i	0.142916	−	0.533368i	0.999839	−	0.0179251i	$-0.00570604\pi$
$38$	−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	$0.694151\pi$
$44$	2.26125	−	0.715028i	0.340897	−	0.107795i
$45$		0			0
$46$	5.00091	+	4.78337i	0.737344	+	0.705269i
$47$	5.29277	+	5.29277i	0.772030	+	0.772030i	0.978461	−	0.206431i	$-0.0661849\pi$
$47$	5.29277	+	5.29277i	0.772030	+	0.772030i	−0.206431	+	0.978461i	$0.566185\pi$
$48$		0			0
$49$	−4.15619	+	2.39957i	−0.593741	+	0.342796i
$50$	−1.64256	−	5.62669i	−0.232293	−	0.795734i
$51$		0			0
$52$	−6.06449	−	3.90154i	−0.840993	−	0.541046i
$53$		−	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
$56$	−1.85119	+	3.76562i	−0.247376	+	0.503202i
$57$		0			0
$58$	0.485498	−	0.507578i	0.0637490	−	0.0666482i
$59$	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	0.959332	−	0.282279i	$-0.0910903\pi$
$61$	9.32964	+	5.38647i	1.19454	+	0.689667i	0.235206	+	0.971946i	$0.424424\pi$
$62$	0.173131	−	0.315885i	0.0219876	−	0.0401174i
$63$		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	$0.808195\pi$
$68$	2.11672	−	0.0941727i	0.256690	−	0.0114201i
$69$		0			0
$70$	−1.50544	+	6.16328i	−0.179935	+	0.736653i
$71$	−1.99632	−	7.45038i	−0.236920	−	0.884197i	−0.977274	−	0.211980i	$-0.932009\pi$
$71$	−1.99632	−	7.45038i	−0.236920	−	0.884197i	0.740354	−	0.672217i	$-0.234658\pi$
$72$		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	$0.141350\pi$
$74$	−0.105587	−	4.74889i	−0.0122742	−	0.552047i
$75$		0			0
$76$	−4.20794	+	4.59979i	−0.482684	+	0.527633i
$77$	−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	$-0.0167254\pi$
$80$	−4.15591	−	11.3598i	−0.464645	−	1.27006i
$81$		0			0
$82$	0.237493	+	10.6815i	0.0262267	+	1.17958i
$83$	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
$86$	−1.55376	−	0.379521i	−0.167546	−	0.0409248i
$87$		0			0
$88$	2.78640	−	1.86682i	0.297032	−	0.199004i
$89$	−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
$94$	9.28274	+	5.08769i	0.957441	+	0.524755i
$95$	−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	$0.483216\pi$
$98$	−4.69129	+	4.90464i	−0.473891	+	0.495444i
$99$		0			0
$100$	−4.45971	−	6.98758i	−0.445971	−	0.698758i
$101$	5.45375	+	9.44617i	0.542668	+	0.939929i	0.998750	+	0.0499909i	$0.0159192\pi$
$101$	5.45375	+	9.44617i	0.542668	+	0.939929i	−0.456081	+	0.889938i	$0.650747\pi$
$102$		0			0
$103$	−5.93866			−0.585154			−0.292577	−	0.956242i	$-0.594513\pi$
$103$	−5.93866			−0.585154			−0.292577	+	0.956242i	$0.594513\pi$
$104$	−9.77903	−	2.89319i	−0.958913	−	0.283700i
$105$		0			0
$106$	−5.23315	−	17.9265i	−0.508288	−	1.74118i
$107$	−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	−0.460090	−	0.887872i	$-0.652183\pi$
$109$	4.46618	−	4.46618i	0.427782	−	0.427782i	0.887872	+	0.460090i	$0.152183\pi$
$110$	3.50531	−	3.66473i	0.334218	−	0.349418i
$111$		0			0
$112$	−1.02077	+	5.84565i	−0.0964542	+	0.552362i
$113$	−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
$122$	14.8001	+	3.61508i	1.33994	+	0.327294i
$123$		0			0
$124$	0.109848	−	0.497442i	0.00986469	−	0.0446716i
$125$	1.82882	+	1.82882i	0.163575	+	0.163575i
$126$		0			0
$127$	4.40510	+	7.62986i	0.390890	+	0.677041i	0.992567	−	0.121698i	$-0.0388341\pi$
$127$	4.40510	+	7.62986i	0.390890	+	0.677041i	−0.601678	+	0.798739i	$0.705501\pi$
$128$	−4.58653	−	10.3423i	−0.405396	−	0.914141i
$129$		0			0
$130$	−15.3815	−	1.08329i	−1.34904	−	0.0950105i
$131$	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
$134$	0.391471	+	17.6069i	0.0338179	+	1.52100i
$135$		0			0
$136$	2.83624	−	0.966700i	0.243205	−	0.0828938i
$137$	−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	$0.0736715\pi$
$140$	0.398789	+	8.96358i	0.0337038	+	0.757561i
$141$		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
$146$	3.88800	−	7.09384i	0.321773	−	0.587090i
$147$		0			0
$148$	−2.02532	−	6.40502i	−0.166480	−	0.526489i
$149$	3.37169	+	12.5833i	0.276220	+	1.03087i	0.955020	+	0.296543i	$0.0958336\pi$
$149$	3.37169	+	12.5833i	0.276220	+	1.03087i	−0.678800	+	0.734323i	$0.737500\pi$
$150$		0			0
$151$	−8.53114	−	8.53114i	−0.694254	−	0.694254i	0.268911	−	0.963165i	$-0.413336\pi$
$151$	−8.53114	−	8.53114i	−0.694254	−	0.694254i	−0.963165	+	0.268911i	$0.913336\pi$
$152$	−3.88960	+	7.91206i	−0.315488	+	0.641753i
$153$		0			0
$154$	−2.38817	+	0.697160i	−0.192444	+	0.0561787i
$155$		−	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	$0.993367\pi$
$158$	−0.369994	−	1.26744i	−0.0294351	−	0.100832i
$159$		0			0
$160$	−10.1437	−	13.7745i	−0.801933	−	1.08897i
$161$	−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	$0.489207\pi$
$164$	4.55550	+	14.4066i	0.355725	+	1.12497i
$165$		0			0
$166$	10.8686	+	5.95689i	0.843569	+	0.462344i
$167$	0.809102	−	3.01961i	0.0626102	−	0.233665i	−0.927529	−	0.373751i	$-0.878071\pi$
$167$	0.809102	−	3.01961i	0.0626102	−	0.233665i	0.990139	+	0.140087i	$0.0447381\pi$
$168$		0			0
$169$	−8.46085	+	9.86985i	−0.650835	+	0.759220i
$170$	3.87236	−	2.35200i	0.296996	−	0.180390i
$171$		0			0
$172$	−2.25971	+	0.100534i	−0.172301	+	0.00766568i
$173$	−3.28703	+	5.69330i	−0.249908	+	0.432853i	−0.963500	−	0.267708i	$-0.913734\pi$
$173$	−3.28703	+	5.69330i	−0.249908	+	0.432853i	0.713592	+	0.700561i	$0.247067\pi$
$174$		0			0
$175$	1.59143	+	5.93931i	0.120301	+	0.448969i
$176$	3.04287	−	3.63856i	0.229365	−	0.274267i
$177$		0			0
$178$	−3.01685	+	0.0670765i	−0.226122	+	0.00502760i
$179$	−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	$-0.800067\pi$
$181$	−21.7718			−1.61828			−0.809141	+	0.587614i	$0.800067\pi$
$182$	6.26917	+	4.23316i	0.464702	+	0.313783i
$183$		0			0
$184$	13.5779	+	2.68330i	1.00097	+	0.197815i
$185$	−5.07855	−	8.79631i	−0.373383	−	0.646718i
$186$		0			0
$187$	0.888303	+	0.888303i	0.0649592	+	0.0649592i
$188$	14.6180	+	3.22806i	1.06613	+	0.235430i
$189$		0			0
$190$	−3.16313	+	12.9499i	−0.229478	+	0.939482i
$191$	−1.44924	−	0.836719i	−0.104863	−	0.0605429i	0.446651	−	0.894708i	$-0.352617\pi$
$191$	−1.44924	−	0.836719i	−0.104863	−	0.0605429i	−0.551514	+	0.834165i	$0.685950\pi$
$192$		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	0.562154	−	0.827032i	$-0.309973\pi$
$197$	8.91936	+	2.38994i	0.635478	+	0.170276i	0.0733239	+	0.997308i	$0.476639\pi$
$198$		0			0
$199$	−10.3397	+	17.9089i	−0.732961	+	1.26953i	0.222651	+	0.974898i	$0.428529\pi$
$199$	−10.3397	+	17.9089i	−0.732961	+	1.26953i	−0.955612	+	0.294628i	$0.904804\pi$
$200$	−8.82346	−	7.71862i	−0.623913	−	0.545789i
$201$		0			0
$202$	11.1473	+	10.6623i	0.784318	+	0.750200i
$203$	−0.521003	+	0.521003i	−0.0365672	+	0.0365672i
$204$		0			0
$205$	11.4230	+	19.7853i	0.797820	+	1.38186i
$206$	−8.06204	+	2.35349i	−0.561709	+	0.163975i
$207$		0			0
$208$	−14.4221	−	0.0522232i	−0.999993	−	0.00362103i
$209$	−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	$-0.430453\pi$
$212$	−14.2085	−	22.2623i	−0.975846	−	1.52898i
$213$		0			0
$214$	−7.90362	−	7.55981i	−0.540281	−	0.516778i
$215$	−3.30356	+	0.885185i	−0.225301	+	0.0603691i
$216$		0			0
$217$	−0.188937	+	0.327248i	−0.0128259	+	0.0222151i
$218$	4.29312	−	7.83301i	0.290767	−	0.530519i
$219$		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	$-0.527531\pi$
$223$	−9.84578	−	2.63817i	−0.659323	−	0.176665i	−0.572940	+	0.819597i	$0.694197\pi$
$224$	0.930874	+	8.34031i	0.0621967	+	0.557260i
$225$		0			0
$226$	−3.85295	+	15.7740i	−0.256294	+	1.04927i
$227$	−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	0.504235	−	0.863567i	$-0.331775\pi$
$229$	−5.43768	−	5.43768i	−0.359332	−	0.359332i	−0.863567	+	0.504235i	$0.831775\pi$
$230$	20.9218	−	0.465175i	1.37954	−	0.0306727i
$231$		0			0
$232$	0.272347	−	1.37812i	0.0178804	−	0.0904777i
$233$		−	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
$236$	9.04414	+	8.27368i	0.588724	+	0.538570i
$237$		0			0
$238$	−2.22211	+	0.0494064i	−0.144038	+	0.00320254i
$239$	−14.3258	+	14.3258i	−0.926659	+	0.926659i	−0.997488	−	0.0708299i	$-0.977435\pi$
$239$	−14.3258	+	14.3258i	−0.926659	+	0.926659i	0.0708299	+	0.997488i	$0.477435\pi$
$240$		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	$0.772484\pi$
$242$	−13.1803	−	3.21942i	−0.847261	−	0.206952i
$243$		0			0
$244$	21.5246	−	0.957627i	1.37797	−	0.0613058i
$245$	−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
$250$	3.20748	+	1.75796i	0.202859	+	0.111183i
$251$	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
$254$	9.00387	+	8.61219i	0.564953	+	0.540377i
$255$		0			0
$256$	−10.3251	−	12.2226i	−0.645319	−	0.763913i
$257$	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
$260$	−21.3104	+	4.62505i	−1.32162	+	0.286834i
$261$		0			0
$262$	20.0677	−	5.85820i	1.23978	−	0.361921i
$263$	18.3764	−	10.6096i	1.13313	−	0.654216i	0.188413	−	0.982090i	$-0.439666\pi$
$263$	18.3764	−	10.6096i	1.13313	−	0.654216i	0.944721	+	0.327874i	$0.106332\pi$
$264$		0			0
$265$	−28.2364	−	28.2364i	−1.73455	−	1.73455i
$266$	4.52034	−	4.72593i	0.277160	−	0.289765i
$267$		0			0
$268$	7.50904	+	23.7471i	0.458688	+	1.45058i
$269$	−25.1549	−	14.5232i	−1.53372	−	0.885495i	−0.999186	−	0.0403505i	$-0.987153\pi$
$269$	−25.1549	−	14.5232i	−1.53372	−	0.885495i	−0.534537	−	0.845145i	$-0.679514\pi$
$270$		0			0
$271$	−3.45071	+	12.8782i	−0.209616	+	0.782296i	0.778377	+	0.627797i	$0.216043\pi$
$271$	−3.45071	+	12.8782i	−0.209616	+	0.782296i	−0.987993	+	0.154500i	$0.950623\pi$
$272$	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	$-0.566885\pi$
$277$	12.3608	−	21.4095i	0.742686	−	1.28637i	0.951268	−	0.308364i	$-0.0997816\pi$
$278$	2.27895	−	9.33003i	0.136683	−	0.559578i
$279$		0			0
$280$	4.09364	+	12.0105i	0.244642	+	0.717764i
$281$	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	$0.135369\pi$
$284$	−11.3822	−	10.4125i	−0.675407	−	0.617869i
$285$		0			0
$286$	−2.64788	−	5.43583i	−0.156572	−	0.321427i
$287$		−	11.2078i		−	0.661577i
$288$		0			0
$289$	−7.93883	−	13.7505i	−0.466990	−	0.808850i
$290$	−0.0472139	−	2.12350i	−0.00277250	−	0.124696i
$291$		0			0
$292$	2.46687	−	11.1711i	0.144363	−	0.653737i
$293$	10.7632	−	2.88398i	0.628792	−	0.168484i	0.0696703	−	0.997570i	$-0.477805\pi$
$293$	10.7632	−	2.88398i	0.628792	−	0.168484i	0.559121	+	0.829086i	$0.311139\pi$
$294$		0			0
$295$	16.0507	+	9.26687i	0.934507	+	0.539538i
$296$	−5.28779	−	7.89251i	−0.307346	−	0.458743i
$297$		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
$302$	−14.9623	−	8.20057i	−0.860986	−	0.471890i
$303$		0			0
$304$	−2.14478	+	12.2825i	−0.123012	+	0.704449i
$305$	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	$0.361856\pi$
$308$	−2.96578	+	1.89286i	−0.168991	+	0.107856i
$309$		0			0
$310$	−0.305253	−	1.04567i	−0.0173372	−	0.0593899i
$311$	−8.81350			−0.499768			−0.249884	−	0.968276i	$-0.580392\pi$
$311$	−8.81350			−0.499768			−0.249884	+	0.968276i	$0.580392\pi$
$312$		0			0
$313$	13.8328			0.781877			0.390938	−	0.920417i	$-0.372151\pi$
$313$	13.8328			0.781877			0.390938	+	0.920417i	$0.372151\pi$
$314$	0.206933	+	0.708864i	0.0116779	+	0.0400035i
$315$		0			0
$316$	−1.00457	−	1.57399i	−0.0565115	−	0.0885436i
$317$	11.7109	−	11.7109i	0.657749	−	0.657749i	−0.297098	−	0.954847i	$-0.596019\pi$
$317$	11.7109	−	11.7109i	0.657749	−	0.657749i	0.954847	+	0.297098i	$0.0960188\pi$
$318$		0			0
$319$	0.568875	−	0.152430i	0.0318509	−	0.00853442i
$320$	−19.2295	−	14.6796i	−1.07496	−	0.820615i
$321$		0			0
$322$	−9.00284	−	4.93428i	−0.501708	−	0.274977i
$323$	−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
$328$	11.8937	+	17.7524i	0.656718	+	0.980212i
$329$	−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	$0.287662\pi$
$332$	17.1154	+	3.77955i	0.939332	+	0.207430i
$333$		0			0
$334$	−0.0982725	−	4.41992i	−0.00537723	−	0.241848i
$335$	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	$-0.257274\pi$
$338$	−7.57462	+	16.7519i	−0.412005	+	0.911182i
$339$		0			0
$340$	4.32483	−	4.72757i	0.234547	−	0.256389i
$341$	0.261574	−	0.151020i	0.0141650	−	0.00817819i
$342$		0			0
$343$	12.3774	−	12.3774i	0.668319	−	0.668319i
$344$	−3.02783	+	1.03200i	−0.163250	+	0.0556419i
$345$		0			0
$346$	−2.20606	+	9.03159i	−0.118598	+	0.485541i
$347$	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	$-0.622338\pi$
$349$	7.72090	−	28.8148i	0.413291	−	1.54242i	0.788235	−	0.615374i	$-0.210995\pi$
$350$	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
$356$	−4.06895	+	1.28664i	−0.215654	+	0.0681916i
$357$		0			0
$358$	−21.6254	+	22.6089i	−1.14294	+	1.19492i
$359$	−21.1519	−	21.1519i	−1.11636	−	1.11636i	−0.992272	−	0.124086i	$-0.960400\pi$
$359$	−21.1519	−	21.1519i	−1.11636	−	1.11636i	−0.124086	−	0.992272i	$-0.539600\pi$
$360$		0			0
$361$	−8.03999	+	4.64189i	−0.423157	+	0.244310i
$362$	−29.5563	+	8.62814i	−1.55344	+	0.453485i
$363$		0			0
$364$	10.1883	+	3.26226i	0.534013	+	0.170989i
$365$		−	17.2977i		−	0.905405i
$366$		0			0
$367$	−17.9908	+	10.3870i	−0.939114	+	0.542198i	−0.889682	−	0.456580i	$-0.849074\pi$
$367$	−17.9908	+	10.3870i	−0.939114	+	0.542198i	−0.0494315	+	0.998778i	$0.515741\pi$
$368$	19.4961	−	1.73820i	1.01630	−	0.0906098i
$369$		0			0
$370$	−10.3804	−	9.92882i	−0.539650	−	0.516175i
$371$	5.07027	+	18.9225i	0.263235	+	0.982407i
$372$		0			0
$373$	−12.6271	−	7.29024i	−0.653804	−	0.377474i	0.136108	−	0.990694i	$-0.456541\pi$
$373$	−12.6271	−	7.29024i	−0.653804	−	0.377474i	−0.789912	+	0.613220i	$0.789874\pi$
$374$	1.55795	+	0.853883i	0.0805598	+	0.0441533i
$375$		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	$-0.0287914\pi$
$380$	0.837908	+	18.8337i	0.0429838	+	0.966146i
$381$		0			0
$382$	−2.29901	−	0.561556i	−0.117628	−	0.0287317i
$383$	−3.31127	−	12.3578i	−0.169198	−	0.631456i	−0.997467	−	0.0711259i	$-0.977341\pi$
$383$	−3.31127	−	12.3578i	−0.169198	−	0.631456i	0.828269	−	0.560331i	$-0.189326\pi$
$384$		0			0
$385$	−3.76166	+	3.76166i	−0.191712	+	0.191712i
$386$	−8.63784	+	0.192053i	−0.439655	+	0.00977526i
$387$		0			0
$388$	−5.51898	+	6.03293i	−0.280184	+	0.306275i
$389$	9.99223			0.506626			0.253313	−	0.967384i	$-0.418480\pi$
$389$	9.99223			0.506626			0.253313	+	0.967384i	$0.418480\pi$
$390$		0			0
$391$			5.18405i			0.262169i
$392$	−2.63164	+	13.3165i	−0.132918	+	0.672585i
$393$		0			0
$394$	13.0556	−	0.290278i	0.657733	−	0.0146240i
$395$	−1.99637	−	1.99637i	−0.100448	−	0.100448i
$396$		0			0
$397$	4.54273	−	1.21722i	0.227993	−	0.0610906i	−0.143014	−	0.989721i	$-0.545679\pi$
$397$	4.54273	−	1.21722i	0.227993	−	0.0610906i	0.371007	+	0.928630i	$0.379013\pi$
$398$	−6.93939	+	28.4098i	−0.347840	+	1.42406i
$399$		0			0
$400$	−15.0372	−	6.98169i	−0.751860	−	0.349084i
$401$	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
$406$	−0.500815	+	0.913761i	−0.0248550	+	0.0453492i
$407$	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	$0.190530\pi$
$410$	23.3483	+	22.3326i	1.15309	+	1.10293i
$411$		0			0
$412$	−10.0119	+	6.38997i	−0.493253	+	0.314811i
$413$	−4.54614	−	7.87415i	−0.223701	−	0.387461i
$414$		0			0
$415$	26.5022			1.30094
$416$	−19.5995	+	5.64458i	−0.960942	+	0.276748i
$417$		0			0
$418$	−5.01786	+	1.46482i	−0.245431	+	0.0716469i
$419$	−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	−0.692733	−	0.721194i	$-0.743594\pi$
$421$	0.583969	−	0.583969i	0.0284609	−	0.0284609i	0.721194	+	0.692733i	$0.243594\pi$
$422$	−21.8835	−	20.9315i	−1.06527	−	1.01893i
$423$		0			0
$424$	−28.1114	−	24.5913i	−1.36521	−	1.19426i
$425$	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	$-0.550364\pi$
$431$	−16.3546	−	4.38219i	−0.787772	−	0.211083i	−0.630208	+	0.776426i	$0.717031\pi$
$432$		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	$0.488404\pi$
$434$	−0.126803	+	0.519132i	−0.00608675	+	0.0249191i
$435$		0			0
$436$	2.72392	−	12.3351i	0.130452	−	0.590743i
$437$	−10.7855	−	10.7855i	−0.515940	−	0.515940i
$438$		0			0
$439$	−18.7931	−	32.5507i	−0.896947	−	1.55356i	−0.831376	−	0.555710i	$-0.812447\pi$
$439$	−18.7931	−	32.5507i	−0.896947	−	1.55356i	−0.0655708	−	0.997848i	$-0.520887\pi$
$440$	1.96635	−	9.95004i	0.0937421	−	0.474349i
$441$		0			0
$442$	−1.02809	−	5.30320i	−0.0489014	−	0.252248i
$443$	−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
$446$	−14.4117	+	0.320429i	−0.682412	+	0.0151727i
$447$		0			0
$448$	4.56897	+	10.9535i	0.215864	+	0.517504i
$449$	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
$452$	1.02064	+	22.9409i	0.0480068	+	1.07905i
$453$		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	$0.888694\pi$
$458$	−9.53687	−	5.22698i	−0.445629	−	0.244241i
$459$		0			0
$460$	28.2181	−	8.92281i	1.31568	−	0.416028i
$461$	−1.14969	−	4.29072i	−0.0535466	−	0.199839i	0.933971	−	0.357350i	$-0.116320\pi$
$461$	−1.14969	−	4.29072i	−0.0535466	−	0.199839i	−0.987517	+	0.157511i	$0.949653\pi$
$462$		0			0
$463$	−15.6374	−	15.6374i	−0.726731	−	0.726731i	0.243236	−	0.969967i	$-0.421791\pi$
$463$	−15.6374	−	15.6374i	−0.726731	−	0.726731i	−0.969967	+	0.243236i	$0.921791\pi$
$464$	−0.176422	−	1.97879i	−0.00819018	−	0.0918632i
$465$		0			0
$466$	−1.16080	−	3.97641i	−0.0537732	−	0.184204i
$467$		−	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
$470$	30.7284	−	8.97031i	1.41740	−	0.413770i
$471$		0			0
$472$	15.5567	+	7.64775i	0.716057	+	0.352016i
$473$	−0.948311	−	0.948311i	−0.0436034	−	0.0436034i
$474$		0			0
$475$	3.34381	+	12.4793i	0.153424	+	0.572588i
$476$	−2.99705	+	0.947694i	−0.137370	+	0.0434375i
$477$		0			0
$478$	−13.7707	+	25.1253i	−0.629857	+	1.14921i
$479$	−8.93153	+	33.3329i	−0.408092	+	1.52302i	0.390189	+	0.920735i	$0.372409\pi$
$479$	−8.93153	+	33.3329i	−0.408092	+	1.52302i	−0.798281	+	0.602285i	$0.794257\pi$
$480$		0			0
$481$	−11.9373	+	2.03999i	−0.544293	+	0.0930154i
$482$	9.97550	+	16.4238i	0.454371	+	0.748083i
$483$		0			0
$484$	−19.1688	+	0.852817i	−0.871308	+	0.0387644i
$485$	−6.18150	+	10.7067i	−0.280687	+	0.486165i
$486$		0			0
$487$	−6.09032	−	22.7294i	−0.275979	−	1.02997i	−0.955183	−	0.296017i	$-0.904341\pi$
$487$	−6.09032	−	22.7294i	−0.275979	−	1.02997i	0.679204	−	0.733950i	$-0.262325\pi$
$488$	28.8412	−	9.83022i	1.30558	−	0.444993i
$489$		0			0
$490$	0.456220	+	20.5191i	0.0206099	+	0.926957i
$491$	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
$494$	13.1724	+	8.89443i	0.592652	+	0.400179i
$495$		0			0
$496$	−0.350052	−	0.956830i	−0.0157178	−	0.0429629i
$497$	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	$0.740540\pi$
$500$	5.05100	+	1.11540i	0.225888	+	0.0498821i
$501$		0			0
$502$	15.1020	+	3.68881i	0.674034	+	0.164640i
$503$	−3.62331	−	2.09192i	−0.161555	−	0.0932739i	0.417043	−	0.908887i	$-0.363067\pi$
$503$	−3.62331	−	2.09192i	−0.161555	−	0.0932739i	−0.578598	+	0.815613i	$0.696400\pi$
$504$		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	$-0.599011\pi$
$509$	−23.6241	−	6.33007i	−1.04712	−	0.280575i	−0.741062	+	0.671437i	$0.765677\pi$
$510$		0			0
$511$	−4.24296	+	7.34902i	−0.187697	+	0.325102i
$512$	−18.8607	−	12.5010i	−0.833532	−	0.552471i
$513$		0			0
$514$	13.1797	−	13.7791i	0.581333	−	0.607772i
$515$	−12.6987	+	12.6987i	−0.559571	+	0.559571i
$516$		0			0
$517$	4.43794	+	7.68674i	0.195180	+	0.338062i
$518$	1.97471	+	6.76450i	0.0867638	+	0.297215i
$519$		0			0
$520$	−27.0971	+	14.7241i	−1.18829	+	0.645693i
$521$	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	$0.968496\pi$
$524$	24.9213	−	15.9056i	1.08869	−	0.694840i
$525$		0			0
$526$	20.7423	−	21.6856i	0.904406	−	0.945538i
$527$	0.260650	−	0.0698410i	0.0113541	−	0.00304232i
$528$		0			0
$529$	−0.472439	+	0.818288i	−0.0205408	+	0.0355777i
$530$	−49.5225	−	27.1423i	−2.15112	−	1.17899i
$531$		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
$536$	19.6049	+	29.2621i	0.846802	+	1.26393i
$537$		0			0
$538$	−39.9047	−	9.74711i	−1.72041	−	0.420228i
$539$	−5.49694	+	1.47290i	−0.236770	+	0.0634424i
$540$		0			0
$541$	−1.32217	−	1.32217i	−0.0568444	−	0.0568444i	0.678113	−	0.734958i	$-0.262798\pi$
$541$	−1.32217	−	1.32217i	−0.0568444	−	0.0568444i	−0.734958	+	0.678113i	$0.762798\pi$
$542$	0.419119	+	18.8504i	0.0180027	+	0.809693i
$543$		0			0
$544$	3.74143	−	4.68153i	0.160412	−	0.200719i
$545$		−	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	$0.374909\pi$
$548$	−0.148833	−	0.136154i	−0.00635782	−	0.00581620i
$549$		0			0
$550$	−0.154502	−	6.94893i	−0.00658799	−	0.296303i
$551$	−1.09470	+	1.09470i	−0.0466356	+	0.0466356i
$552$		0			0
$553$	0.358478	+	1.33786i	0.0152440	+	0.0568915i
$554$	8.29580	−	33.9630i	0.352455	−	1.44295i
$555$		0			0
$556$	−0.603691	−	13.5692i	−0.0256022	−	0.575460i
$557$	−10.4145	+	38.8674i	−0.441276	+	1.64686i	0.284309	+	0.958733i	$0.408236\pi$
$557$	−10.4145	+	38.8674i	−0.441276	+	1.64686i	−0.725585	+	0.688132i	$0.758431\pi$
$558$		0			0
$559$	−0.376829	+	4.06033i	−0.0159382	+	0.171734i
$560$	10.3171	+	14.6825i	0.435976	+	0.620451i
$561$		0			0
$562$	18.4214	−	33.6108i	0.777060	−	1.41778i
$563$	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
$566$	19.1611	−	20.0326i	0.805403	−	0.842032i
$567$		0			0
$568$	−19.5783	−	9.62478i	−0.821489	−	0.403847i
$569$	−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	$-0.0710458\pi$
$572$	−5.74884	−	6.33007i	−0.240371	−	0.264673i
$573$		0			0
$574$	−4.44166	−	15.2152i	−0.185391	−	0.635070i
$575$	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	$0.828266\pi$
$578$	−16.2267	−	15.5208i	−0.674940	−	0.645580i
$579$		0			0
$580$	−0.905639	−	2.86405i	−0.0376046	−	0.118923i
$581$	−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
$590$	25.4621	+	6.21937i	1.04826	+	0.256048i
$591$		0			0
$592$	−10.3062	−	8.61894i	−0.423584	−	0.354236i
$593$	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
$596$	19.2239	+	17.5862i	0.787441	+	0.720359i
$597$		0			0
$598$	8.13511	−	23.5879i	0.332669	−	0.964579i
$599$		−	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	0.999407	−	0.0344297i	$-0.0109615\pi$
$601$	11.5194	+	19.9522i	0.469887	+	0.813867i	−0.529521	+	0.848297i	$0.677628\pi$
$602$	2.37222	−	0.0527439i	0.0966846	−	0.00214968i
$603$		0			0
$604$	−23.5620	−	5.20313i	−0.958726	−	0.211712i
$605$	−28.0235	+	7.50888i	−1.13932	+	0.305280i
$606$		0			0
$607$	15.0714	+	8.70147i	0.611729	+	0.353182i	0.773642	−	0.633623i	$-0.218433\pi$
$607$	15.0714	+	8.70147i	0.611729	+	0.353182i	−0.161913	+	0.986805i	$0.551766\pi$
$608$	1.95589	+	17.5241i	0.0793218	+	0.710695i
$609$		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	$-0.583969\pi$
$613$	−23.9979	−	6.43022i	−0.969266	−	0.259714i	−0.708518	+	0.705693i	$0.750636\pi$
$614$	−8.19888	+	14.9593i	−0.330880	+	0.603706i
$615$		0			0
$616$	−3.27606	+	3.74499i	−0.131996	+	0.150890i
$617$	−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	$0.467511\pi$
$620$	−0.828795	−	1.29857i	−0.0332852	−	0.0521520i
$621$		0			0
$622$	−11.9648	+	3.49279i	−0.479744	+	0.140048i
$623$	3.16549			0.126823
$624$		0			0
$625$	28.5448			1.14179
$626$	18.7788	−	5.48194i	0.750550	−	0.219102i
$627$		0			0
$628$	0.561845	+	0.880312i	0.0224201	+	0.0351283i
$629$	2.51613	−	2.51613i	0.100324	−	0.100324i
$630$		0			0
$631$	23.0172	−	6.16745i	0.916302	−	0.245522i	0.230298	−	0.973120i	$-0.426030\pi$
$631$	23.0172	−	6.16745i	0.916302	−	0.245522i	0.686004	+	0.727598i	$0.259363\pi$
$632$	−1.98753	−	1.73866i	−0.0790596	−	0.0691600i
$633$		0			0
$634$	11.2571	−	20.5392i	0.447077	−	0.815714i
$635$	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
$640$	−31.9225	−	12.3077i	−1.26185	−	0.486504i
$641$	−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	$0.445066\pi$
$644$	−14.1773	−	3.13072i	−0.558663	−	0.123368i
$645$		0			0
$646$	−4.66895	+	0.103809i	−0.183697	+	0.00408432i
$647$	−4.37758	−	7.58218i	−0.172100	−	0.298086i	0.767054	−	0.641583i	$-0.221722\pi$
$647$	−4.37758	−	7.58218i	−0.172100	−	0.298086i	−0.939154	+	0.343497i	$0.888389\pi$
$648$		0			0
$649$			7.26760i			0.285278i
$650$	−15.9570	+	13.8572i	−0.625885	+	0.543526i
$651$		0			0
$652$	36.7060	+	33.5790i	1.43752	+	1.31506i
$653$	−5.94625	+	3.43307i	−0.232695	+	0.134346i	−0.611815	−	0.791001i	$-0.709560\pi$
$653$	−5.94625	+	3.43307i	−0.232695	+	0.134346i	0.379120	+	0.925348i	$0.376227\pi$
$654$		0			0
$655$	31.6090	−	31.6090i	1.23507	−	1.23507i
$656$	23.1815	+	19.3863i	0.905087	+	0.756909i
$657$		0			0
$658$	−15.2554	−	3.72629i	−0.594719	−	0.145266i
$659$	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	$0.388918\pi$
$661$	−10.9023	+	40.6880i	−0.424051	+	1.58258i	−0.765987	+	0.642856i	$0.777749\pi$
$662$	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
$668$	−1.88502	−	5.96133i	−0.0729338	−	0.230651i
$669$		0			0
$670$	38.4860	+	36.8119i	1.48684	+	1.42217i
$671$	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	$0.294784\pi$
$674$	−10.5209	−	36.0402i	−0.405251	−	1.38822i
$675$		0			0
$676$	−3.64418	+	25.7433i	−0.140161	+	0.990129i
$677$		−	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
$680$	3.99765	−	8.13186i	0.153303	−	0.311842i
$681$		0			0
$682$	0.295252	−	0.308679i	0.0113058	−	0.0118199i
$683$	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
$686$	11.8978	−	21.7082i	0.454262	−	0.828823i
$687$		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	$-0.0297290\pi$
$692$	0.584380	+	13.1351i	0.0222148	+	0.499322i
$693$		0			0
$694$	0.394995	−	1.61711i	0.0149938	−	0.0613846i
$695$	−5.31537	−	19.8372i	−0.201624	−	0.752470i
$696$		0			0
$697$	−5.65945	+	5.65945i	−0.214367	+	0.214367i
$698$	−0.937770	−	42.1774i	−0.0354951	−	1.59644i
$699$		0			0
$700$	9.07365	+	8.30066i	0.342952	+	0.313736i
$701$	17.2336			0.650904			0.325452	−	0.945559i	$-0.394484\pi$
$701$	17.2336			0.650904			0.325452	+	0.945559i	$0.394484\pi$
$702$		0			0
$703$			10.4697i			0.394871i
$704$	1.21488	−	9.40833i	0.0457875	−	0.354590i
$705$		0			0
$706$	0.820820	+	36.9174i	0.0308920	+	1.38940i
$707$	−11.4421	−	11.4421i	−0.430324	−	0.430324i
$708$		0			0
$709$	−32.3352	+	8.66420i	−1.21437	+	0.325391i	−0.808477	−	0.588528i	$-0.799708\pi$
$709$	−32.3352	+	8.66420i	−1.21437	+	0.325391i	−0.405898	+	0.913919i	$0.633041\pi$
$710$	−32.0443	−	7.82715i	−1.20260	−	0.293748i
$711$		0			0
$712$	−5.01391	+	3.35920i	−0.187904	+	0.125891i
$713$	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
$718$	−37.0974	−	20.3324i	−1.38446	−	0.758797i
$719$	−8.93537	+	15.4765i	−0.333233	+	0.577177i	−0.983144	−	0.182834i	$-0.941473\pi$
$719$	−8.93537	+	15.4765i	−0.333233	+	0.577177i	0.649911	+	0.760011i	$0.274806\pi$
$720$		0			0
$721$	8.50996	−	2.28024i	0.316928	−	0.0849205i
$722$	−9.07512	+	9.48785i	−0.337741	+	0.353101i
$723$		0			0
$724$	−36.7049	+	23.4263i	−1.36413	+	0.870632i
$725$	−1.02926	−	1.78274i	−0.0382259	−	0.0662091i
$726$		0			0
$727$	21.2697			0.788848			0.394424	−	0.918928i	$-0.370944\pi$
$727$	21.2697			0.788848			0.394424	+	0.918928i	$0.370944\pi$
$728$	15.1240	+	0.391063i	0.560533	+	0.0144938i
$729$		0			0
$730$	−6.85508	−	23.4826i	−0.253718	−	0.869129i
$731$	−0.599081	−	1.03764i	−0.0221578	−	0.0383784i
$732$		0			0
$733$	−4.74608	+	4.74608i	−0.175300	+	0.175300i	−0.789304	−	0.614003i	$-0.789558\pi$
$733$	−4.74608	+	4.74608i	−0.175300	+	0.175300i	0.614003	+	0.789304i	$0.289558\pi$
$734$	−20.3071	+	21.2307i	−0.749549	+	0.783638i
$735$		0			0
$736$	25.7781	−	10.0860i	0.950192	−	0.371774i
$737$	−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	−0.520343	−	0.853957i	$-0.674196\pi$
$743$	−38.1054	−	10.2103i	−1.39795	−	0.374580i	−0.877609	+	0.479377i	$0.840863\pi$
$744$		0			0
$745$	34.1167	+	19.6973i	1.24994	+	0.721654i
$746$	−20.0310	−	4.89277i	−0.733387	−	0.179137i
$747$		0			0
$748$	2.45339	+	0.541775i	0.0897050	+	0.0198093i
$749$	8.11267	+	8.11267i	0.296430	+	0.296430i
$750$		0			0
$751$	−11.2537	−	19.4920i	−0.410655	−	0.711275i	0.584307	−	0.811533i	$-0.301367\pi$
$751$	−11.2537	−	19.4920i	−0.410655	−	0.711275i	−0.994961	+	0.100258i	$0.968033\pi$
$752$	28.1178	−	10.2868i	1.02535	−	0.375120i
$753$		0			0
$754$	−2.39410	−	0.825690i	−0.0871879	−	0.0300698i
$755$	−36.4844			−1.32780
$756$		0			0
$757$	40.5049	−	23.3855i	1.47217	−	0.849960i	0.472664	−	0.881243i	$-0.343293\pi$
$757$	40.5049	−	23.3855i	1.47217	−	0.849960i	0.999511	+	0.0312829i	$0.00995927\pi$
$758$	−0.422286	−	18.9928i	−0.0153381	−	0.689851i
$759$		0			0
$760$	8.60128	+	25.2356i	0.312001	+	0.915392i
$761$	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
$764$	−3.34357	+	0.148755i	−0.120966	+	0.00538177i
$765$		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	$0.0508687\pi$
$770$	−3.61590	+	6.59739i	−0.130308	+	0.237753i
$771$		0			0
$772$	−11.6502	+	3.68390i	−0.419300	+	0.132586i
$773$	13.1234	+	48.9774i	0.472018	+	1.76159i	0.632506	+	0.774556i	$0.282027\pi$
$773$	13.1234	+	48.9774i	0.472018	+	1.76159i	−0.160488	+	0.987038i	$0.551307\pi$
$774$		0			0
$775$	−0.746506	−	0.746506i	−0.0268153	−	0.0268153i
$776$	−5.10146	+	10.3772i	−0.183132	+	0.372519i
$777$		0			0
$778$	13.5650	−	3.95992i	0.486328	−	0.141970i
$779$		−	23.5491i		−	0.843735i
$780$		0			0
$781$		−	9.14635i		−	0.327282i
$782$	2.05444	+	7.03762i	0.0734665	+	0.251665i
$783$		0			0
$784$	1.70474	+	19.1208i	0.0608834	+	0.682884i
$785$	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	$0.952682\pi$
$788$	17.6087	−	5.56801i	0.627282	−	0.198352i
$789$		0			0
$790$	−3.50134	−	1.91902i	−0.124572	−	0.0682755i
$791$	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
$796$	1.83823	+	41.3179i	0.0651543	+	1.46447i
$797$	15.6429	−	27.0944i	0.554101	−	0.959732i	−0.443871	−	0.896090i	$-0.646395\pi$
$797$	15.6429	−	27.0944i	0.554101	−	0.959732i	0.997973	−	0.0636413i	$-0.0202713\pi$
$798$		0			0
$799$	2.05238	+	7.65958i	0.0726079	+	0.270976i
$800$	−23.1806	−	3.51877i	−0.819558	−	0.124407i
$801$		0			0
$802$	3.77179	−	0.0838618i	0.133187	−	0.00296126i
$803$	5.87418	−	3.39146i	0.207295	−	0.119682i
$804$		0			0
$805$	−21.9527			−0.773730
$806$	−1.29558	−	0.0912450i	−0.0456348	−	0.00321397i
$807$		0			0
$808$	30.2657	+	5.98119i	1.06474	+	0.210417i
$809$	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	$0.796065\pi$
$812$	−0.317759	+	1.43895i	−0.0111512	+	0.0504973i
$813$		0			0
$814$	1.33654	−	5.47178i	0.0468456	−	0.191786i
$815$	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	$-0.217280\pi$
$821$	32.4496	+	8.69486i	1.13250	+	0.303453i	0.356568	+	0.934269i	$0.383947\pi$
$822$		0			0
$823$	−12.8798	+	22.3085i	−0.448962	+	0.777625i	−0.998319	−	0.0579627i	$-0.981540\pi$
$823$	−12.8798	+	22.3085i	−0.448962	+	0.777625i	0.549357	+	0.835588i	$0.314873\pi$
$824$	−11.0594	+	12.6424i	−0.385272	+	0.440420i
$825$		0			0
$826$	−9.29214	−	8.88793i	−0.323315	−	0.309251i
$827$	−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	$0.284796\pi$
$829$	28.4583	+	49.2912i	0.988397	+	1.71195i	0.362654	+	0.931924i	$0.381871\pi$
$830$	35.9782	−	10.5028i	1.24882	−	0.364559i
$831$		0			0
$832$	−24.3703	+	15.4301i	−0.844889	+	0.534941i
$833$	−5.08425			−0.176159
$834$		0			0
$835$	−4.72675	−	8.18697i	−0.163576	−	0.283322i
$836$	−6.23149	+	3.97715i	−0.215521	+	0.137553i
$837$		0			0
$838$	−28.6251	−	27.3799i	−0.988837	−	0.945822i
$839$	0.535224	−	0.143413i	0.0184780	−	0.00495116i	−0.249568	−	0.968357i	$-0.580289\pi$
$839$	0.535224	−	0.143413i	0.0184780	−	0.00495116i	0.268046	+	0.963406i	$0.413622\pi$
$840$		0			0
$841$	−14.3767	+	24.9011i	−0.495747	+	0.858659i
$842$	0.561341	−	1.02419i	0.0193451	−	0.0352961i
$843$		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
$848$	−47.9082	−	22.2435i	−1.64517	−	0.763845i
$849$		0			0
$850$	1.47348	−	6.03241i	0.0505398	−	0.206910i
$851$	15.8758	−	4.25390i	0.544214	−	0.145822i
$852$		0			0
$853$	6.92158	+	6.92158i	0.236990	+	0.236990i	0.815603	−	0.578612i	$-0.196406\pi$
$853$	6.92158	+	6.92158i	0.236990	+	0.236990i	−0.578612	+	0.815603i	$0.696406\pi$
$854$	−22.5963	+	0.502405i	−0.773229	+	0.0171920i
$855$		0			0
$856$	−21.4590	−	4.24078i	−0.733453	−	0.144947i
$857$			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	$0.800715\pi$
$860$	−4.61699	+	5.04694i	−0.157438	+	0.172099i
$861$		0			0
$862$	−23.9388	+	0.532255i	−0.815360	+	0.0181287i
$863$	−6.61684	+	6.61684i	−0.225240	+	0.225240i	−0.810701	−	0.585461i	$-0.800914\pi$
$863$	−6.61684	+	6.61684i	−0.225240	+	0.225240i	0.585461	+	0.810701i	$0.300914\pi$
$864$		0			0
$865$	5.14535	+	19.2027i	0.174947	+	0.652912i
$866$	30.3718	+	7.41862i	1.03208	+	0.252095i
$867$		0			0
$868$	0.0335899	+	0.755001i	0.00114012	+	0.0256264i
$869$	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
$874$	−18.9161	−	10.3676i	−0.639848	−	0.350688i
$875$	−3.32286	−	1.91846i	−0.112333	−	0.0648557i
$876$		0			0
$877$	5.43918	+	20.2993i	0.183668	+	0.685458i	0.994912	+	0.100750i	$0.0321243\pi$
$877$	5.43918	+	20.2993i	0.183668	+	0.685458i	−0.811244	+	0.584708i	$0.801209\pi$
$878$	−38.4125	−	36.7415i	−1.29636	−	1.23997i
$879$		0			0
$880$	−1.27377	−	14.2870i	−0.0429388	−	0.481613i
$881$	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	$-0.0438069\pi$
$884$	−3.49735	−	6.79194i	−0.117629	−	0.228438i
$885$		0			0
$886$	−22.9850	+	6.70984i	−0.772197	+	0.225422i
$887$	35.3131	−	20.3880i	1.18570	−	0.684563i	0.228373	−	0.973574i	$-0.426660\pi$
$887$	35.3131	−	20.3880i	1.18570	−	0.684563i	0.957326	+	0.289010i	$0.0933262\pi$
$888$		0			0
$889$	−9.24201	−	9.24201i	−0.309967	−	0.309967i
$890$	−6.30752	+	6.59439i	−0.211429	+	0.221044i
$891$		0			0
$892$	−19.4376	+	6.14634i	−0.650819	+	0.205795i
$893$	−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
$902$	−3.00624	+	12.3075i	−0.100097	+	0.409796i
$903$		0			0
$904$	10.4770	+	30.7390i	0.348461	+	1.02236i
$905$	−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	$0.232760\pi$
$908$	−5.06791	+	5.53984i	−0.168184	+	0.183846i
$909$		0			0
$910$	22.4572	−	4.35362i	0.744450	−	0.144321i
$911$			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
$914$	0.771584	+	34.7030i	0.0255217	+	1.14787i
$915$		0			0
$916$	−15.0182	−	3.31643i	−0.496217	−	0.109578i
$917$	−21.1826	+	5.67586i	−0.699511	+	0.187433i
$918$		0			0
$919$	−41.2891	−	23.8383i	−1.36200	−	0.786352i	−0.372112	−	0.928188i	$-0.621366\pi$
$919$	−41.2891	−	23.8383i	−1.36200	−	0.786352i	−0.989890	+	0.141836i	$0.954699\pi$
$920$	34.7714	−	23.2960i	1.14638	−	0.768046i
$921$		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
$926$	−27.4257	−	15.0315i	−0.901263	−	0.493965i
$927$		0			0
$928$	−1.02370	−	2.61640i	−0.0336045	−	0.0858875i
$929$	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
$932$	−3.15170	−	4.93816i	−0.103237	−	0.161755i
$933$		0			0
$934$	−3.49723	−	11.9800i	−0.114433	−	0.391997i
$935$	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	$0.770780\pi$
$938$	−7.32139	−	25.0799i	−0.239052	−	0.818888i
$939$		0			0
$940$	38.1605	−	24.3553i	1.24466	−	0.794383i
$941$	16.6053	−	16.6053i	0.541316	−	0.541316i	−0.382599	−	0.923915i	$-0.624971\pi$
$941$	16.6053	−	16.6053i	0.541316	−	0.541316i	0.923915	+	0.382599i	$0.124971\pi$
$942$		0			0
$943$	−35.7089	+	9.56817i	−1.16284	+	0.311582i
$944$	24.1499	+	4.21708i	0.786012	+	0.137254i
$945$		0			0
$946$	−1.66320	−	0.911566i	−0.0540752	−	0.0296376i
$947$	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
$952$	−3.69308	+	2.47427i	−0.119693	+	0.0801917i
$953$	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
$956$	−8.73728	+	39.5662i	−0.282584	+	1.27966i
$957$		0			0
$958$	1.08481	+	48.7907i	0.0350486	+	1.57636i
$959$	0.0748125	+	0.129579i	0.00241582	+	0.00418433i
$960$		0			0
$961$			30.9351i			0.997907i
$962$	−15.3970	+	7.50013i	−0.496420	+	0.241814i
$963$		0			0
$964$	20.0510	+	18.3429i	0.645799	+	0.590784i
$965$	−15.9998	+	9.23747i	−0.515051	+	0.297365i
$966$		0			0
$967$	18.5489	−	18.5489i	0.596493	−	0.596493i	−0.342885	−	0.939377i	$-0.611404\pi$
$967$	18.5489	−	18.5489i	0.596493	−	0.596493i	0.939377	+	0.342885i	$0.111404\pi$
$968$	−25.6846	+	8.75432i	−0.825535	+	0.281375i
$969$		0			0
$970$	−4.14865	+	16.9846i	−0.133205	+	0.545342i
$971$	−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
$980$	8.75104	+	27.6749i	0.279542	+	0.884042i
$981$		0			0
$982$	31.8057	−	33.2522i	1.01496	−	1.06112i
$983$	21.7716	+	21.7716i	0.694405	+	0.694405i	0.963198	−	0.268793i	$-0.0866248\pi$
$983$	21.7716	+	21.7716i	0.694405	+	0.694405i	−0.268793	+	0.963198i	$0.586625\pi$
$984$		0			0
$985$	24.1828	−	13.9619i	0.770528	−	0.444864i
$986$	0.714297	−	0.208519i	0.0227479	−	0.00664061i
$987$		0			0
$988$	21.4070	+	6.85444i	0.681048	+	0.218069i
$989$		−	5.53425i		−	0.175979i
$990$		0			0
$991$	12.8654	−	7.42785i	0.408683	−	0.235954i	−0.281540	−	0.959549i	$-0.590845\pi$
$991$	12.8654	−	7.42785i	0.408683	−	0.235954i	0.690224	+	0.723596i	$0.257512\pi$
$992$	−0.854405	−	1.16022i	−0.0271274	−	0.0368371i
$993$		0			0
$994$	11.6943	+	11.1856i	0.370920	+	0.354784i
$995$	16.1852	+	60.4042i	0.513107	+	1.91494i
$996$		0			0
$997$	−1.48602	−	0.857953i	−0.0470627	−	0.0271717i	0.476284	−	0.879291i	$-0.341983\pi$
$997$	−1.48602	−	0.857953i	−0.0470627	−	0.0271717i	−0.523347	+	0.852120i	$0.675317\pi$
$998$	1.64648	+	0.902404i	0.0521184	+	0.0285651i
$999$		0			0

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(1.35755 - 0.396300i) q^{2} +(1.68589 - 1.07599i) q^{4} +(2.13831 - 2.13831i) q^{5} +(-1.43298 + 0.383965i) q^{7} +(1.86227 - 2.12884i) q^{8} +(2.05545 - 3.75028i) q^{10} +(1.14540 + 0.306909i) q^{11} +(-1.50651 - 3.27573i) q^{13} +(-1.79317 + 1.08914i) q^{14} +(1.68447 - 3.62802i) q^{16} +(0.917474 + 0.529704i) q^{17} +(-3.01087 + 0.806761i) q^{19} +(1.30415 - 5.90577i) q^{20} +(1.67657 - 0.0372767i) q^{22} +(2.44668 + 4.23777i) q^{23} -4.14473i q^{25} +(-3.34334 - 3.84995i) q^{26} +(-2.00270 + 2.18920i) q^{28} +(0.430121 - 0.248330i) q^{29} +(0.180109 - 0.180109i) q^{31} +(0.848973 - 5.59279i) q^{32} +(1.45544 + 0.355506i) q^{34} +(-2.24311 + 3.88518i) q^{35} +(0.869322 - 3.24435i) q^{37} +(-3.76770 + 2.28843i) q^{38} +(-0.570000 - 8.53422i) q^{40} +(-1.95534 + 7.29743i) q^{41} +(-0.979452 - 0.565487i) q^{43} +(2.26125 - 0.715028i) q^{44} +(5.00091 + 4.78337i) q^{46} +(5.29277 + 5.29277i) q^{47} +(-4.15619 + 2.39957i) q^{49} +(-1.64256 - 5.62669i) q^{50} +(-6.06449 - 3.90154i) q^{52} -13.2050i q^{53} +(3.10549 - 1.79295i) q^{55} +(-1.85119 + 3.76562i) q^{56} +(0.485498 - 0.507578i) q^{58} +(1.58626 + 5.92000i) q^{59} +(9.32964 + 5.38647i) q^{61} +(0.173131 - 0.315885i) q^{62} +(-1.06389 - 7.92894i) q^{64} +(-10.2259 - 3.78314i) q^{65} +(-3.22308 + 12.0287i) q^{67} +(2.11672 - 0.0941727i) q^{68} +(-1.50544 + 6.16328i) q^{70} +(-1.99632 - 7.45038i) q^{71} +(4.04472 - 4.04472i) q^{73} +(-0.105587 - 4.74889i) q^{74} +(-4.20794 + 4.59979i) q^{76} -1.75917 q^{77} -0.933621i q^{79} +(-4.15591 - 11.3598i) q^{80} +(0.237493 + 10.6815i) q^{82} +(6.19701 + 6.19701i) q^{83} +(3.09451 - 0.829172i) q^{85} +(-1.55376 - 0.379521i) q^{86} +(2.78640 - 1.86682i) q^{88} +(-2.06105 - 0.552258i) q^{89} +(3.41656 + 4.11560i) q^{91} +(8.68465 + 4.51181i) q^{92} +(9.28274 + 5.08769i) q^{94} +(-4.71307 + 8.16328i) q^{95} +(-3.94895 + 1.05812i) q^{97} +(-4.69129 + 4.90464i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} - 6 q^{4} + 10 q^{8} - 6 q^{10} + 8 q^{11} - 8 q^{14} - 10 q^{16} + 12 q^{17} - 8 q^{19} - 10 q^{20} - 20 q^{22} + 2 q^{26} + 12 q^{28} - 16 q^{32} - 46 q^{34} + 4 q^{35} - 32 q^{40} - 12 q^{43}+ \cdots + 16 q^{98}+O(q^{100}) \) 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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