LMFDB - Embedded newform 936.2.ed.d.19.12

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			19.12
Character	$\chi$	$=$	936.19
Dual form			936.2.ed.d.739.12

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

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

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 $

$2$	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	0.999084	−	0.0428025i	$-0.0136286\pi$
$5$	2.13831	+	2.13831i	0.956281	+	0.956281i	−0.0428025	+	0.999084i	$0.513629\pi$
$6$		0			0
$7$	−1.43298	−	0.383965i	−0.541614	−	0.145125i	−0.0223680	−	0.999750i	$-0.507121\pi$
$7$	−1.43298	−	0.383965i	−0.541614	−	0.145125i	−0.519246	+	0.854625i	$0.673787\pi$
$8$	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	−0.0819743	−	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
$16$	1.68447	+	3.62802i	0.421118	+	0.907006i
$17$	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	$0.699723\pi$
$20$	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	−0.489764	−	0.871855i	$-0.662917\pi$
$23$	2.44668	−	4.23777i	0.510167	−	0.883635i	0.999931	−	0.0117799i	$-0.00374976\pi$
$24$		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	0.539404	−	0.842047i	$-0.318650\pi$
$29$	0.430121	+	0.248330i	0.0798714	+	0.0461138i	−0.459532	+	0.888161i	$0.651983\pi$
$30$		0			0
$31$	0.180109	+	0.180109i	0.0323486	+	0.0323486i	0.723096	−	0.690747i	$-0.242718\pi$
$31$	0.180109	+	0.180109i	0.0323486	+	0.0323486i	−0.690747	+	0.723096i	$0.742718\pi$
$32$	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	0.999839	+	0.0179251i	$0.00570604\pi$
$37$	0.869322	+	3.24435i	0.142916	+	0.533368i	−0.856924	+	0.515443i	$0.827627\pi$
$38$	−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	$0.360817\pi$
$44$	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	−0.206431	−	0.978461i	$-0.566185\pi$
$47$	5.29277	−	5.29277i	0.772030	−	0.772030i	0.978461	+	0.206431i	$0.0661849\pi$
$48$		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	$0.361577\pi$
$53$			13.2050i			1.81385i	−0.421292	+	0.906925i	$0.638423\pi$
$54$		0			0
$55$	3.10549	+	1.79295i	0.418744	+	0.241762i
$56$	−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	−0.782470	−	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	0.235206	−	0.971946i	$-0.424424\pi$
$61$	9.32964	−	5.38647i	1.19454	−	0.689667i	0.959332	+	0.282279i	$0.0910903\pi$
$62$	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	−0.823879	−	0.566765i	$-0.808195\pi$
$67$	−3.22308	−	12.0287i	−0.393762	−	1.46954i	0.430118	−	0.902773i	$-0.358472\pi$
$68$	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	0.740354	+	0.672217i	$0.234658\pi$
$71$	−1.99632	+	7.45038i	−0.236920	+	0.884197i	−0.977274	+	0.211980i	$0.932009\pi$
$72$		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	$0.641350\pi$
$74$	−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	$0.0167254\pi$
$79$			0.933621i			0.105041i	−0.998620	+	0.0525203i	$0.983275\pi$
$80$	−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	−0.279837	−	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
$86$	−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	−0.366394	−	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
$94$	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	0.0527054	−	0.998610i	$-0.483216\pi$
$97$	−3.94895	−	1.05812i	−0.400955	−	0.107436i	−0.453661	+	0.891174i	$0.649882\pi$
$98$	−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	−0.456081	−	0.889938i	$-0.650747\pi$
$101$	5.45375	−	9.44617i	0.542668	−	0.939929i	0.998750	−	0.0499909i	$-0.0159192\pi$
$102$		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	−0.990150	−	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	0.887872	−	0.460090i	$-0.152183\pi$
$109$	4.46618	+	4.46618i	0.427782	+	0.427782i	−0.460090	+	0.887872i	$0.652183\pi$
$110$	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	−0.998900	−	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
$122$	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	−0.601678	−	0.798739i	$-0.705501\pi$
$127$	4.40510	−	7.62986i	0.390890	−	0.677041i	0.992567	+	0.121698i	$0.0388341\pi$
$128$	−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	−0.967032	−	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	$0.740338\pi$
$140$	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	−0.678800	−	0.734323i	$-0.737500\pi$
$149$	3.37169	−	12.5833i	0.276220	−	1.03087i	0.955020	−	0.296543i	$-0.0958336\pi$
$150$		0			0
$151$	−8.53114	+	8.53114i	−0.694254	+	0.694254i	−0.963165	−	0.268911i	$-0.913336\pi$
$151$	−8.53114	+	8.53114i	−0.694254	+	0.694254i	0.268911	+	0.963165i	$0.413336\pi$
$152$	−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	$-0.993367\pi$
$157$		−	0.522164i		−	0.0416732i	0.999783	−	0.0208366i	$-0.00663298\pi$
$158$	−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	0.0339021	−	0.999425i	$-0.489207\pi$
$163$	6.43789	−	24.0265i	0.504255	−	1.88190i	0.470353	−	0.882479i	$-0.344127\pi$
$164$	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	0.990139	−	0.140087i	$-0.0447381\pi$
$167$	0.809102	+	3.01961i	0.0626102	+	0.233665i	−0.927529	+	0.373751i	$0.878071\pi$
$168$		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	0.713592	−	0.700561i	$-0.247067\pi$
$173$	−3.28703	−	5.69330i	−0.249908	−	0.432853i	−0.963500	+	0.267708i	$0.913734\pi$
$174$		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	−0.434718	−	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	$-0.800067\pi$
$181$	−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	−0.551514	−	0.834165i	$-0.685950\pi$
$191$	−1.44924	+	0.836719i	−0.104863	+	0.0605429i	0.446651	+	0.894708i	$0.352617\pi$
$192$		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	0.0733239	−	0.997308i	$-0.476639\pi$
$197$	8.91936	−	2.38994i	0.635478	−	0.170276i	0.562154	+	0.827032i	$0.309973\pi$
$198$		0			0
$199$	−10.3397	−	17.9089i	−0.732961	−	1.26953i	−0.955612	−	0.294628i	$-0.904804\pi$
$199$	−10.3397	−	17.9089i	−0.732961	−	1.26953i	0.222651	−	0.974898i	$-0.428529\pi$
$200$	−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	0.216755	+	0.976226i	$0.430453\pi$
$211$	−10.7064	+	18.5440i	−0.737059	+	1.27662i	−0.953814	+	0.300398i	$0.902881\pi$
$212$	−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	−0.572940	−	0.819597i	$-0.694197\pi$
$223$	−9.84578	+	2.63817i	−0.659323	+	0.176665i	−0.0863822	+	0.996262i	$0.527531\pi$
$224$	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	0.136463	−	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	−0.863567	−	0.504235i	$-0.831775\pi$
$229$	−5.43768	+	5.43768i	−0.359332	+	0.359332i	0.504235	+	0.863567i	$0.331775\pi$
$230$	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	$0.0305876\pi$
$233$			2.92911i			0.191892i	−0.995387	+	0.0959461i	$0.969412\pi$
$234$		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	0.0708299	−	0.997488i	$-0.477435\pi$
$239$	−14.3258	−	14.3258i	−0.926659	−	0.926659i	−0.997488	+	0.0708299i	$0.977435\pi$
$240$		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	$-0.0608488\pi$
$242$	−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	−0.168501	−	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
$254$	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	0.817820	−	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
$260$	−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	0.944721	−	0.327874i	$-0.106332\pi$
$263$	18.3764	+	10.6096i	1.13313	+	0.654216i	0.188413	+	0.982090i	$0.439666\pi$
$264$		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	−0.534537	+	0.845145i	$0.679514\pi$
$269$	−25.1549	+	14.5232i	−1.53372	+	0.885495i	−0.999186	+	0.0403505i	$0.987153\pi$
$270$		0			0
$271$	−3.45071	−	12.8782i	−0.209616	−	0.782296i	−0.987993	−	0.154500i	$-0.950623\pi$
$271$	−3.45071	−	12.8782i	−0.209616	−	0.782296i	0.778377	−	0.627797i	$-0.216043\pi$
$272$	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	$0.0997816\pi$
$277$	12.3608	+	21.4095i	0.742686	+	1.28637i	−0.208583	+	0.978005i	$0.566885\pi$
$278$	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	0.987856	+	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	$0.468702\pi$
$284$	−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	0.559121	−	0.829086i	$-0.311139\pi$
$293$	10.7632	+	2.88398i	0.628792	+	0.168484i	0.0696703	+	0.997570i	$0.477805\pi$
$294$		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	0.420497	−	0.907294i	$-0.361856\pi$
$307$	−8.52938	−	8.52938i	−0.486797	−	0.486797i	−0.907294	+	0.420497i	$0.861856\pi$
$308$	−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	0.954847	−	0.297098i	$-0.0960188\pi$
$317$	11.7109	+	11.7109i	0.657749	+	0.657749i	−0.297098	+	0.954847i	$0.596019\pi$
$318$		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	0.618694	−	0.785632i	$-0.287662\pi$
$331$	13.8576	+	3.71314i	0.761683	+	0.204092i	0.142989	+	0.989724i	$0.454329\pi$
$332$	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	$0.257274\pi$
$337$			26.5479i			1.44616i	−0.690765	+	0.723079i	$0.742726\pi$
$338$	−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	0.881390	−	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	$0.210995\pi$
$349$	7.72090	+	28.8148i	0.413291	+	1.54242i	−0.374945	+	0.927047i	$0.622338\pi$
$350$	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
$356$	−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	−0.124086	+	0.992272i	$0.539600\pi$
$359$	−21.1519	+	21.1519i	−1.11636	+	1.11636i	−0.992272	+	0.124086i	$0.960400\pi$
$360$		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	−0.0494315	−	0.998778i	$-0.515741\pi$
$367$	−17.9908	−	10.3870i	−0.939114	−	0.542198i	−0.889682	+	0.456580i	$0.849074\pi$
$368$	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	−0.789912	−	0.613220i	$-0.789874\pi$
$373$	−12.6271	+	7.29024i	−0.653804	+	0.377474i	0.136108	+	0.990694i	$0.456541\pi$
$374$	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	0.995912	+	0.0903274i	$0.0287914\pi$
$379$	3.47679	+	12.9756i	0.178591	+	0.666509i	−0.817321	+	0.576182i	$0.804542\pi$
$380$	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	0.828269	+	0.560331i	$0.189326\pi$
$383$	−3.31127	+	12.3578i	−0.169198	+	0.631456i	−0.997467	+	0.0711259i	$0.977341\pi$
$384$		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	0.371007	−	0.928630i	$-0.379013\pi$
$397$	4.54273	+	1.21722i	0.227993	+	0.0610906i	−0.143014	+	0.989721i	$0.545679\pi$
$398$	−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	−0.193904	−	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
$406$	−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	0.826143	−	0.563460i	$-0.190530\pi$
$409$	25.4794	+	6.82718i	1.25987	+	0.337582i	0.433731	+	0.901042i	$0.357197\pi$
$410$	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	0.289522	+	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	0.721194	−	0.692733i	$-0.243594\pi$
$421$	0.583969	+	0.583969i	0.0284609	+	0.0284609i	−0.692733	+	0.721194i	$0.743594\pi$
$422$	−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	−0.630208	−	0.776426i	$-0.717031\pi$
$431$	−16.3546	+	4.38219i	−0.787772	+	0.211083i	−0.157563	+	0.987509i	$0.550364\pi$
$432$		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	$0.155071\pi$
$434$	−0.126803	−	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	−0.0655708	+	0.997848i	$0.520887\pi$
$439$	−18.7931	+	32.5507i	−0.896947	+	1.55356i	−0.831376	+	0.555710i	$0.812447\pi$
$440$	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	−0.965384	−	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
$452$	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	−0.939483	−	0.342595i	$-0.888694\pi$
$457$	−6.35265	−	23.7084i	−0.297164	−	1.10903i	0.642319	−	0.766438i	$-0.277973\pi$
$458$	−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	−0.987517	−	0.157511i	$-0.949653\pi$
$461$	−1.14969	+	4.29072i	−0.0535466	+	0.199839i	0.933971	+	0.357350i	$0.116320\pi$
$462$		0			0
$463$	−15.6374	+	15.6374i	−0.726731	+	0.726731i	−0.969967	−	0.243236i	$-0.921791\pi$
$463$	−15.6374	+	15.6374i	−0.726731	+	0.726731i	0.243236	+	0.969967i	$0.421791\pi$
$464$	−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	$0.0654525\pi$
$467$			8.82470i			0.408358i	−0.978934	+	0.204179i	$0.934547\pi$
$468$		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	−0.798281	−	0.602285i	$-0.794257\pi$
$479$	−8.93153	−	33.3329i	−0.408092	−	1.52302i	0.390189	−	0.920735i	$-0.372409\pi$
$480$		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	0.679204	+	0.733950i	$0.262325\pi$
$487$	−6.09032	+	22.7294i	−0.275979	+	1.02997i	−0.955183	+	0.296017i	$0.904341\pi$
$488$	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	0.975298	−	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
$494$	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	−0.685782	−	0.727807i	$-0.740540\pi$
$499$	0.938780	−	0.938780i	0.0420256	−	0.0420256i	0.727807	+	0.685782i	$0.240540\pi$
$500$	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	−0.578598	−	0.815613i	$-0.696400\pi$
$503$	−3.62331	+	2.09192i	−0.161555	+	0.0932739i	0.417043	+	0.908887i	$0.363067\pi$
$504$		0			0
$505$	31.8606	−	8.53703i	1.41778	−	0.379893i
$506$	4.25999	−	7.01370i	0.189379	−	0.311797i
$507$		0			0
$508$	15.6362	−	8.12327i	0.693745	−	0.360412i
$509$	−23.6241	+	6.33007i	−1.04712	+	0.280575i	−0.741062	−	0.671437i	$-0.765677\pi$
$509$	−23.6241	+	6.33007i	−1.04712	+	0.280575i	−0.306060	+	0.952012i	$0.599011\pi$
$510$		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	−0.995106	−	0.0988105i	$-0.968496\pi$
$523$	−9.42167	+	16.3188i	−0.411981	+	0.713572i	0.583126	+	0.812382i	$0.301830\pi$
$524$	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	−0.734958	−	0.678113i	$-0.762798\pi$
$541$	−1.32217	+	1.32217i	−0.0568444	+	0.0568444i	0.678113	+	0.734958i	$0.262798\pi$
$542$	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	−0.725585	−	0.688132i	$-0.758431\pi$
$557$	−10.4145	−	38.8674i	−0.441276	−	1.64686i	0.284309	−	0.958733i	$-0.408236\pi$
$558$		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	−0.293670	−	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
$566$	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	0.383118	−	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	$0.928954\pi$
$572$	−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	−0.857956	−	0.513723i	$-0.828266\pi$
$577$	−8.26875	+	8.26875i	−0.344233	+	0.344233i	0.513723	+	0.857956i	$0.328266\pi$
$578$	−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	0.990454	+	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
$590$	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	0.860780	−	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
$596$	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	$0.151343\pi$
$599$			22.4062i			0.915491i	−0.889083	+	0.457745i	$0.848657\pi$
$600$		0			0
$601$	11.5194	−	19.9522i	0.469887	−	0.813867i	−0.529521	−	0.848297i	$-0.677628\pi$
$601$	11.5194	−	19.9522i	0.469887	−	0.813867i	0.999407	+	0.0344297i	$0.0109615\pi$
$602$	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	−0.161913	−	0.986805i	$-0.551766\pi$
$607$	15.0714	−	8.70147i	0.611729	−	0.353182i	0.773642	+	0.633623i	$0.218433\pi$
$608$	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	−0.708518	−	0.705693i	$-0.750636\pi$
$613$	−23.9979	+	6.43022i	−0.969266	+	0.259714i	−0.260748	+	0.965407i	$0.583969\pi$
$614$	−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	−0.0967368	−	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	$0.967511\pi$
$620$	−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	0.686004	−	0.727598i	$-0.259363\pi$
$631$	23.0172	+	6.16745i	0.916302	+	0.245522i	0.230298	+	0.973120i	$0.426030\pi$
$632$	−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	−0.830822	−	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	$0.611733\pi$
$644$	−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	−0.939154	−	0.343497i	$-0.888389\pi$
$647$	−4.37758	+	7.58218i	−0.172100	+	0.298086i	0.767054	+	0.641583i	$0.221722\pi$
$648$		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	0.379120	−	0.925348i	$-0.376227\pi$
$653$	−5.94625	−	3.43307i	−0.232695	−	0.134346i	−0.611815	+	0.791001i	$0.709560\pi$
$654$		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	0.976742	−	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	$-0.777749\pi$
$661$	−10.9023	−	40.6880i	−0.424051	−	1.58258i	0.341936	−	0.939723i	$-0.388918\pi$
$662$	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	0.600964	−	0.799276i	$-0.294784\pi$
$673$	5.42846	+	3.13412i	0.209252	+	0.120812i	−0.391712	+	0.920088i	$0.628117\pi$
$674$	−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	$0.133056\pi$
$677$			21.1245i			0.811881i	−0.913900	+	0.405940i	$0.866944\pi$
$678$		0			0
$679$	5.25248	+	3.03252i	0.201572	+	0.116377i
$680$	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	−0.680571	−	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
$686$	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	0.995642	+	0.0932606i	$0.0297290\pi$
$691$	4.73219	+	17.6608i	0.180021	+	0.671848i	−0.815621	+	0.578587i	$0.803604\pi$
$692$	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	−0.405898	−	0.913919i	$-0.633041\pi$
$709$	−32.3352	−	8.66420i	−1.21437	−	0.325391i	−0.808477	+	0.588528i	$0.799708\pi$
$710$	−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	0.649911	−	0.760011i	$-0.274806\pi$
$719$	−8.93537	−	15.4765i	−0.333233	−	0.577177i	−0.983144	+	0.182834i	$0.941473\pi$
$720$		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	0.614003	−	0.789304i	$-0.289558\pi$
$733$	−4.74608	−	4.74608i	−0.175300	−	0.175300i	−0.789304	+	0.614003i	$0.789558\pi$
$734$	−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	−0.897398	−	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	−0.877609	−	0.479377i	$-0.840863\pi$
$743$	−38.1054	+	10.2103i	−1.39795	+	0.374580i	−0.520343	+	0.853957i	$0.674196\pi$
$744$		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	−0.994961	−	0.100258i	$-0.968033\pi$
$751$	−11.2537	+	19.4920i	−0.410655	+	0.711275i	0.584307	+	0.811533i	$0.301367\pi$
$752$	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	0.999511	−	0.0312829i	$-0.00995927\pi$
$757$	40.5049	+	23.3855i	1.47217	+	0.849960i	0.472664	+	0.881243i	$0.343293\pi$
$758$	−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	−0.768180	−	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
$764$	−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	0.987258	−	0.159129i	$-0.0508687\pi$
$769$	1.46149	+	5.45437i	0.0527028	+	0.196689i	−0.934555	+	0.355819i	$0.884202\pi$
$770$	−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	−0.160488	−	0.987038i	$-0.551307\pi$
$773$	13.1234	−	48.9774i	0.472018	−	1.76159i	0.632506	−	0.774556i	$-0.282027\pi$
$774$		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	−0.988971	−	0.148107i	$-0.952682\pi$
$787$	−1.63955	+	6.11890i	−0.0584438	+	0.218115i	0.930528	+	0.366222i	$0.119349\pi$
$788$	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	0.997973	+	0.0636413i	$0.0202713\pi$
$797$	15.6429	+	27.0944i	0.554101	+	0.959732i	−0.443871	+	0.896090i	$0.646395\pi$
$798$		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	−0.698075	−	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	$0.296065\pi$
$812$	−0.317759	−	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	0.356568	−	0.934269i	$-0.383947\pi$
$821$	32.4496	−	8.69486i	1.13250	−	0.303453i	0.775932	+	0.630817i	$0.217280\pi$
$822$		0			0
$823$	−12.8798	−	22.3085i	−0.448962	−	0.777625i	0.549357	−	0.835588i	$-0.314873\pi$
$823$	−12.8798	−	22.3085i	−0.448962	−	0.777625i	−0.998319	+	0.0579627i	$0.981540\pi$
$824$	−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	0.192117	−	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	$-0.381871\pi$
$829$	28.4583	−	49.2912i	0.988397	−	1.71195i	0.625743	−	0.780029i	$-0.284796\pi$
$830$	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	0.268046	−	0.963406i	$-0.413622\pi$
$839$	0.535224	+	0.143413i	0.0184780	+	0.00495116i	−0.249568	+	0.968357i	$0.580289\pi$
$840$		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	−0.578612	−	0.815603i	$-0.696406\pi$
$853$	6.92158	−	6.92158i	0.236990	−	0.236990i	0.815603	+	0.578612i	$0.196406\pi$
$854$	−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	$-0.866427\pi$
$857$		−	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	$0.800715\pi$
$860$	−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	0.585461	−	0.810701i	$-0.300914\pi$
$863$	−6.61684	−	6.61684i	−0.225240	−	0.225240i	−0.810701	+	0.585461i	$0.800914\pi$
$864$		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	−0.811244	−	0.584708i	$-0.801209\pi$
$877$	5.43918	−	20.2993i	0.183668	−	0.685458i	0.994912	−	0.100750i	$-0.0321243\pi$
$878$	−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	0.999627	−	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	$0.956193\pi$
$884$	−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	0.957326	−	0.289010i	$-0.0933262\pi$
$887$	35.3131	+	20.3880i	1.18570	+	0.684563i	0.228373	+	0.973574i	$0.426660\pi$
$888$		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	0.744348	−	0.667792i	$-0.232760\pi$
$907$	16.2086	+	9.35804i	0.538198	+	0.310729i	−0.206151	+	0.978520i	$0.566094\pi$
$908$	−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	$-0.899231\pi$
$911$		−	18.7926i		−	0.622627i	0.950307	−	0.311313i	$-0.100769\pi$
$912$		0			0
$913$	5.19613	−	8.99997i	0.171967	−	0.297856i
$914$	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	−0.989890	−	0.141836i	$-0.954699\pi$
$919$	−41.2891	+	23.8383i	−1.36200	+	0.786352i	−0.372112	+	0.928188i	$0.621366\pi$
$920$	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	0.388315	−	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
$932$	−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	0.923915	−	0.382599i	$-0.124971\pi$
$941$	16.6053	+	16.6053i	0.541316	+	0.541316i	−0.382599	+	0.923915i	$0.624971\pi$
$942$		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	0.0154129	−	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
$952$	−3.69308	−	2.47427i	−0.119693	−	0.0801917i
$953$	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
$956$	−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	0.939377	−	0.342885i	$-0.111404\pi$
$967$	18.5489	+	18.5489i	0.596493	+	0.596493i	−0.342885	+	0.939377i	$0.611404\pi$
$968$	−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	−0.910440	−	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
$980$	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	−0.268793	−	0.963198i	$-0.586625\pi$
$983$	21.7716	−	21.7716i	0.694405	−	0.694405i	0.963198	+	0.268793i	$0.0866248\pi$
$984$		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	0.690224	−	0.723596i	$-0.257512\pi$
$991$	12.8654	+	7.42785i	0.408683	+	0.235954i	−0.281540	+	0.959549i	$0.590845\pi$
$992$	−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	−0.523347	−	0.852120i	$-0.675317\pi$
$997$	−1.48602	+	0.857953i	−0.0470627	+	0.0271717i	0.476284	+	0.879291i	$0.341983\pi$
$998$	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.19.12		48
3.2	odd	2		104.2.u.a.19.1	yes	48
8.3	odd	2	inner	936.2.ed.d.19.3		48
12.11	even	2		416.2.bk.a.175.11		48
13.11	odd	12	inner	936.2.ed.d.739.3		48
24.5	odd	2		416.2.bk.a.175.12		48
24.11	even	2		104.2.u.a.19.10	yes	48
39.11	even	12		104.2.u.a.11.10	yes	48
104.11	even	12	inner	936.2.ed.d.739.12		48
156.11	odd	12		416.2.bk.a.271.12		48
312.11	odd	12		104.2.u.a.11.1	✓	48
312.245	even	12		416.2.bk.a.271.11		48

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

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

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