LMFDB - Embedded newform 400.3.i.b.357.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,3,Mod(93,400)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 3]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("400.93");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	400.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			357.7
Character	$\chi$	$=$	400.357
Dual form			400.3.i.b.93.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25977 + 1.55338i) q^{2} -0.119786i q^{3} +(-0.825960 - 3.91379i) q^{4} +(0.186072 + 0.150902i) q^{6} +(-4.73972 + 4.73972i) q^{7} +(7.12012 + 3.64745i) q^{8} +8.98565 q^{9} +O(q^{10})$	\(q+(-1.25977 + 1.55338i) q^{2} -0.119786i q^{3} +(-0.825960 - 3.91379i) q^{4} +(0.186072 + 0.150902i) q^{6} +(-4.73972 + 4.73972i) q^{7} +(7.12012 + 3.64745i) q^{8} +8.98565 q^{9} +(2.49487 + 2.49487i) q^{11} +(-0.468816 + 0.0989381i) q^{12} -18.4567i q^{13} +(-1.39162 - 13.3335i) q^{14} +(-14.6356 + 6.46528i) q^{16} +(-10.7165 - 10.7165i) q^{17} +(-11.3199 + 13.9581i) q^{18} +(0.469722 + 0.469722i) q^{19} +(0.567750 + 0.567750i) q^{21} +(-7.01842 + 0.732510i) q^{22} +(27.9445 + 27.9445i) q^{23} +(0.436912 - 0.852887i) q^{24} +(28.6701 + 23.2511i) q^{26} -2.15442i q^{27} +(22.4651 + 14.6355i) q^{28} +(15.6079 + 15.6079i) q^{29} +49.2667 q^{31} +(8.39445 - 30.8793i) q^{32} +(0.298849 - 0.298849i) q^{33} +(30.1472 - 3.14645i) q^{34} +(-7.42179 - 35.1680i) q^{36} +29.1310i q^{37} +(-1.32140 + 0.137914i) q^{38} -2.21084 q^{39} +16.4684i q^{41} +(-1.59716 + 0.166695i) q^{42} +4.48974 q^{43} +(7.70373 - 11.8251i) q^{44} +(-78.6119 + 8.20470i) q^{46} +(40.6666 + 40.6666i) q^{47} +(0.774447 + 1.75313i) q^{48} +4.07009i q^{49} +(-1.28369 + 1.28369i) q^{51} +(-72.2356 + 15.2445i) q^{52} +78.7038 q^{53} +(3.34663 + 2.71407i) q^{54} +(-51.0353 + 16.4595i) q^{56} +(0.0562658 - 0.0562658i) q^{57} +(-43.9073 + 4.58259i) q^{58} +(3.26583 - 3.26583i) q^{59} +(-23.0393 + 23.0393i) q^{61} +(-62.0647 + 76.5297i) q^{62} +(-42.5895 + 42.5895i) q^{63} +(37.3922 + 51.9406i) q^{64} +(0.0877441 + 0.840705i) q^{66} +58.9247 q^{67} +(-33.0909 + 50.7938i) q^{68} +(3.34734 - 3.34734i) q^{69} -76.8059i q^{71} +(63.9789 + 32.7747i) q^{72} +(-18.7472 - 18.7472i) q^{73} +(-45.2514 - 36.6984i) q^{74} +(1.45042 - 2.22637i) q^{76} -23.6499 q^{77} +(2.78515 - 3.43427i) q^{78} +141.697i q^{79} +80.6128 q^{81} +(-25.5817 - 20.7464i) q^{82} -120.053i q^{83} +(1.75312 - 2.69100i) q^{84} +(-5.65604 + 6.97426i) q^{86} +(1.86960 - 1.86960i) q^{87} +(8.66383 + 26.8636i) q^{88} -87.7260 q^{89} +(87.4794 + 87.4794i) q^{91} +(86.2879 - 132.450i) q^{92} -5.90143i q^{93} +(-114.401 + 11.9400i) q^{94} +(-3.69890 - 1.00553i) q^{96} +(-34.6438 - 34.6438i) q^{97} +(-6.32239 - 5.12738i) q^{98} +(22.4180 + 22.4180i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} + 4 q^{4} - 4 q^{6} + 8 q^{8} - 108 q^{9}+O(q^{10}) $ 44 * q + 2 * q^2 + 4 * q^4 - 4 * q^6 + 8 * q^8 - 108 * q^9	$ 44 q + 2 q^{2} + 4 q^{4} - 4 q^{6} + 8 q^{8} - 108 q^{9} - 4 q^{11} + 8 q^{12} + 24 q^{16} + 4 q^{17} - 22 q^{18} + 32 q^{19} - 4 q^{21} - 92 q^{22} + 36 q^{24} - 52 q^{26} - 36 q^{28} - 8 q^{31} + 132 q^{32} + 4 q^{33} - 88 q^{34} - 116 q^{36} + 216 q^{38} + 72 q^{39} - 16 q^{42} - 124 q^{43} - 168 q^{44} + 108 q^{46} + 4 q^{47} - 340 q^{48} - 100 q^{51} - 48 q^{52} + 4 q^{53} + 228 q^{54} - 172 q^{56} - 36 q^{57} - 16 q^{58} + 64 q^{59} - 36 q^{61} + 356 q^{62} + 200 q^{63} - 176 q^{64} + 276 q^{66} + 292 q^{67} + 72 q^{68} - 60 q^{69} - 448 q^{72} - 48 q^{73} + 284 q^{74} + 252 q^{76} - 192 q^{77} - 620 q^{78} + 100 q^{81} + 240 q^{82} + 288 q^{84} + 20 q^{86} - 36 q^{87} + 624 q^{88} + 188 q^{91} + 412 q^{92} - 340 q^{94} - 24 q^{96} + 4 q^{97} + 78 q^{98} - 92 q^{99}+O(q^{100}) $ 44 * q + 2 * q^2 + 4 * q^4 - 4 * q^6 + 8 * q^8 - 108 * q^9 - 4 * q^11 + 8 * q^12 + 24 * q^16 + 4 * q^17 - 22 * q^18 + 32 * q^19 - 4 * q^21 - 92 * q^22 + 36 * q^24 - 52 * q^26 - 36 * q^28 - 8 * q^31 + 132 * q^32 + 4 * q^33 - 88 * q^34 - 116 * q^36 + 216 * q^38 + 72 * q^39 - 16 * q^42 - 124 * q^43 - 168 * q^44 + 108 * q^46 + 4 * q^47 - 340 * q^48 - 100 * q^51 - 48 * q^52 + 4 * q^53 + 228 * q^54 - 172 * q^56 - 36 * q^57 - 16 * q^58 + 64 * q^59 - 36 * q^61 + 356 * q^62 + 200 * q^63 - 176 * q^64 + 276 * q^66 + 292 * q^67 + 72 * q^68 - 60 * q^69 - 448 * q^72 - 48 * q^73 + 284 * q^74 + 252 * q^76 - 192 * q^77 - 620 * q^78 + 100 * q^81 + 240 * q^82 + 288 * q^84 + 20 * q^86 - 36 * q^87 + 624 * q^88 + 188 * q^91 + 412 * q^92 - 340 * q^94 - 24 * q^96 + 4 * q^97 + 78 * q^98 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−1.25977	+	1.55338i	−0.629885	+	0.776688i
$2$	−1.25977	+	1.55338i	−0.629885	+	0.776688i
$3$		−	0.119786i		−	0.0399285i	−0.999801	−	0.0199643i	$-0.993645\pi$
$3$		−	0.119786i		−	0.0399285i	0.999801	−	0.0199643i	$-0.00635524\pi$
$4$	−0.825960	−	3.91379i	−0.206490	−	0.978449i
$5$		0			0
$5$		0			0
$6$	0.186072	+	0.150902i	0.0310120	+	0.0251504i
$7$	−4.73972	+	4.73972i	−0.677103	+	0.677103i	−0.959344	−	0.282241i	$-0.908922\pi$
$7$	−4.73972	+	4.73972i	−0.677103	+	0.677103i	0.282241	+	0.959344i	$0.408922\pi$
$8$	7.12012	+	3.64745i	0.890015	+	0.455932i
$9$	8.98565			0.998406
$10$		0			0
$11$	2.49487	+	2.49487i	0.226806	+	0.226806i	0.811357	−	0.584551i	$-0.198729\pi$
$11$	2.49487	+	2.49487i	0.226806	+	0.226806i	−0.584551	+	0.811357i	$0.698729\pi$
$12$	−0.468816	+	0.0989381i	−0.0390680	+	0.00824484i
$13$		−	18.4567i		−	1.41974i	−0.704331	−	0.709871i	$-0.748753\pi$
$13$		−	18.4567i		−	1.41974i	0.704331	−	0.709871i	$-0.251247\pi$
$14$	−1.39162	−	13.3335i	−0.0994012	−	0.952395i
$15$		0			0
$16$	−14.6356	+	6.46528i	−0.914724	+	0.404080i
$17$	−10.7165	−	10.7165i	−0.630385	−	0.630385i	0.317780	−	0.948165i	$-0.397063\pi$
$17$	−10.7165	−	10.7165i	−0.630385	−	0.630385i	−0.948165	+	0.317780i	$0.897063\pi$
$18$	−11.3199	+	13.9581i	−0.628881	+	0.775450i
$19$	0.469722	+	0.469722i	0.0247222	+	0.0247222i	0.719360	−	0.694638i	$-0.244435\pi$
$19$	0.469722	+	0.469722i	0.0247222	+	0.0247222i	−0.694638	+	0.719360i	$0.744435\pi$
$20$		0			0
$21$	0.567750	+	0.567750i	0.0270357	+	0.0270357i
$22$	−7.01842	+	0.732510i	−0.319019	+	0.0332959i
$23$	27.9445	+	27.9445i	1.21498	+	1.21498i	0.969369	+	0.245608i	$0.0789876\pi$
$23$	27.9445	+	27.9445i	1.21498	+	1.21498i	0.245608	+	0.969369i	$0.421012\pi$
$24$	0.436912	−	0.852887i	0.0182047	−	0.0355370i
$25$		0			0
$26$	28.6701	+	23.2511i	1.10270	+	0.894275i
$27$		−	2.15442i		−	0.0797934i
$28$	22.4651	+	14.6355i	0.802326	+	0.522695i
$29$	15.6079	+	15.6079i	0.538203	+	0.538203i	0.923001	−	0.384798i	$-0.125729\pi$
$29$	15.6079	+	15.6079i	0.538203	+	0.538203i	−0.384798	+	0.923001i	$0.625729\pi$
$30$		0			0
$31$	49.2667			1.58925			0.794624	−	0.607102i	$-0.207668\pi$
$31$	49.2667			1.58925			0.794624	+	0.607102i	$0.207668\pi$
$32$	8.39445	−	30.8793i	0.262327	−	0.964979i
$33$	0.298849	−	0.298849i	0.00905602	−	0.00905602i
$34$	30.1472	−	3.14645i	0.886682	−	0.0925427i
$35$		0			0
$36$	−7.42179	−	35.1680i	−0.206161	−	0.976889i
$37$			29.1310i			0.787325i	0.919255	+	0.393662i	$0.128792\pi$
$37$			29.1310i			0.787325i	−0.919255	+	0.393662i	$0.871208\pi$
$38$	−1.32140	+	0.137914i	−0.0347736	+	0.00362931i
$39$	−2.21084			−0.0566882
$40$		0			0
$41$			16.4684i			0.401669i	0.979625	+	0.200834i	$0.0643653\pi$
$41$			16.4684i			0.401669i	−0.979625	+	0.200834i	$0.935635\pi$
$42$	−1.59716	+	0.166695i	−0.0380277	+	0.00396894i
$43$	4.48974			0.104413			0.0522063	−	0.998636i	$-0.483375\pi$
$43$	4.48974			0.104413			0.0522063	+	0.998636i	$0.483375\pi$
$44$	7.70373	−	11.8251i	0.175085	−	0.268751i
$45$		0			0
$46$	−78.6119	+	8.20470i	−1.70895	+	0.178363i
$47$	40.6666	+	40.6666i	0.865246	+	0.865246i	0.991942	−	0.126695i	$-0.0404370\pi$
$47$	40.6666	+	40.6666i	0.865246	+	0.865246i	−0.126695	+	0.991942i	$0.540437\pi$
$48$	0.774447	+	1.75313i	0.0161343	+	0.0365236i
$49$			4.07009i			0.0830632i
$50$		0			0
$51$	−1.28369	+	1.28369i	−0.0251703	+	0.0251703i
$52$	−72.2356	+	15.2445i	−1.38915	+	0.293163i
$53$	78.7038			1.48498			0.742488	−	0.669859i	$-0.233646\pi$
$53$	78.7038			1.48498			0.742488	+	0.669859i	$0.233646\pi$
$54$	3.34663	+	2.71407i	0.0619746	+	0.0502606i
$55$		0			0
$56$	−51.0353	+	16.4595i	−0.911344	+	0.293919i
$57$	0.0562658	−	0.0562658i	0.000987120	−	0.000987120i
$58$	−43.9073	+	4.58259i	−0.757022	+	0.0790102i
$59$	3.26583	−	3.26583i	0.0553530	−	0.0553530i	−0.678888	−	0.734241i	$-0.737538\pi$
$59$	3.26583	−	3.26583i	0.0553530	−	0.0553530i	0.734241	+	0.678888i	$0.237538\pi$
$60$		0			0
$61$	−23.0393	+	23.0393i	−0.377694	+	0.377694i	−0.870269	−	0.492576i	$-0.836055\pi$
$61$	−23.0393	+	23.0393i	−0.377694	+	0.377694i	0.492576	+	0.870269i	$0.336055\pi$
$62$	−62.0647	+	76.5297i	−1.00104	+	1.23435i
$63$	−42.5895	+	42.5895i	−0.676023	+	0.676023i
$64$	37.3922	+	51.9406i	0.584253	+	0.811572i
$65$		0			0
$66$	0.0877441	+	0.840705i	0.00132946	+	0.0127380i
$67$	58.9247			0.879474			0.439737	−	0.898127i	$-0.355072\pi$
$67$	58.9247			0.879474			0.439737	+	0.898127i	$0.355072\pi$
$68$	−33.0909	+	50.7938i	−0.486631	+	0.746967i
$69$	3.34734	−	3.34734i	0.0485122	−	0.0485122i
$70$		0			0
$71$		−	76.8059i		−	1.08177i	−0.841096	−	0.540886i	$-0.818089\pi$
$71$		−	76.8059i		−	1.08177i	0.841096	−	0.540886i	$-0.181911\pi$
$72$	63.9789	+	32.7747i	0.888596	+	0.455205i
$73$	−18.7472	−	18.7472i	−0.256811	−	0.256811i	0.566945	−	0.823756i	$-0.308125\pi$
$73$	−18.7472	−	18.7472i	−0.256811	−	0.256811i	−0.823756	+	0.566945i	$0.808125\pi$
$74$	−45.2514	−	36.6984i	−0.611506	−	0.495924i
$75$		0			0
$76$	1.45042	−	2.22637i	0.0190845	−	0.0292943i
$77$	−23.6499			−0.307142
$78$	2.78515	−	3.43427i	0.0357070	−	0.0440291i
$79$			141.697i			1.79363i	0.442407	+	0.896815i	$0.354125\pi$
$79$			141.697i			1.79363i	−0.442407	+	0.896815i	$0.645875\pi$
$80$		0			0
$81$	80.6128			0.995220
$82$	−25.5817	−	20.7464i	−0.311972	−	0.253005i
$83$		−	120.053i		−	1.44642i	−0.690628	−	0.723210i	$-0.742666\pi$
$83$		−	120.053i		−	1.44642i	0.690628	−	0.723210i	$-0.257334\pi$
$84$	1.75312	−	2.69100i	0.0208705	−	0.0320357i
$85$		0			0
$86$	−5.65604	+	6.97426i	−0.0657679	+	0.0810961i
$87$	1.86960	−	1.86960i	0.0214897	−	0.0214897i
$88$	8.66383	+	26.8636i	0.0984526	+	0.305269i
$89$	−87.7260			−0.985686			−0.492843	−	0.870118i	$-0.664042\pi$
$89$	−87.7260			−0.985686			−0.492843	+	0.870118i	$0.664042\pi$
$90$		0			0
$91$	87.4794	+	87.4794i	0.961312	+	0.961312i
$92$	86.2879	−	132.450i	0.937912	−	1.43967i
$93$		−	5.90143i		−	0.0634563i
$94$	−114.401	+	11.9400i	−1.21703	+	0.127021i
$95$		0			0
$96$	−3.69890	−	1.00553i	−0.0385302	−	0.0104743i
$97$	−34.6438	−	34.6438i	−0.357153	−	0.357153i	0.505609	−	0.862762i	$-0.331268\pi$
$97$	−34.6438	−	34.6438i	−0.357153	−	0.357153i	−0.862762	+	0.505609i	$0.831268\pi$
$98$	−6.32239	−	5.12738i	−0.0645142	−	0.0523202i
$99$	22.4180	+	22.4180i	0.226444	+	0.226444i
$100$		0			0
$101$	−29.5707	−	29.5707i	−0.292780	−	0.292780i	0.545398	−	0.838177i	$-0.316379\pi$
$101$	−29.5707	−	29.5707i	−0.292780	−	0.292780i	−0.838177	+	0.545398i	$0.816379\pi$
$102$	−0.376900	−	3.61120i	−0.00369509	−	0.0354039i
$103$	−48.5504	−	48.5504i	−0.471363	−	0.471363i	0.430992	−	0.902356i	$-0.358164\pi$
$103$	−48.5504	−	48.5504i	−0.471363	−	0.471363i	−0.902356	+	0.430992i	$0.858164\pi$
$104$	67.3198	−	131.414i	0.647306	−	1.26359i
$105$		0			0
$106$	−99.1486	+	122.257i	−0.935364	+	1.15336i
$107$			62.1016i			0.580389i	0.956968	+	0.290194i	$0.0937200\pi$
$107$			62.1016i			0.580389i	−0.956968	+	0.290194i	$0.906280\pi$
$108$	−8.43196	+	1.77947i	−0.0780737	+	0.0164765i
$109$	−31.6457	−	31.6457i	−0.290327	−	0.290327i	0.546882	−	0.837209i	$-0.315814\pi$
$109$	−31.6457	−	31.6457i	−0.290327	−	0.290327i	−0.837209	+	0.546882i	$0.815814\pi$
$110$		0			0
$111$	3.48947			0.0314367
$112$	38.7250	−	100.012i	0.345758	−	0.892966i
$113$	56.1211	−	56.1211i	0.496647	−	0.496647i	−0.413745	−	0.910393i	$-0.635780\pi$
$113$	56.1211	−	56.1211i	0.496647	−	0.496647i	0.910393	+	0.413745i	$0.135780\pi$
$114$	0.0165201	+	0.158284i	0.000144913	+	0.00138846i
$115$		0			0
$116$	48.1946	−	73.9776i	0.415471	−	0.637738i
$117$		−	165.845i		−	1.41748i
$118$	0.958871	+	9.18725i	0.00812602	+	0.0778581i
$119$	101.587			0.853671
$120$		0			0
$121$		−	108.551i		−	0.897118i
$122$	−6.76451	−	64.8130i	−0.0554468	−	0.531254i
$123$	1.97268			0.0160380
$124$	−40.6923	−	192.820i	−0.328164	−	1.55500i
$125$		0			0
$126$	−12.5046	−	119.810i	−0.0992427	−	0.950877i
$127$	60.1440	+	60.1440i	0.473575	+	0.473575i	0.903069	−	0.429495i	$-0.141308\pi$
$127$	60.1440	+	60.1440i	0.473575	+	0.473575i	−0.429495	+	0.903069i	$0.641308\pi$
$128$	−127.789	−	7.34905i	−0.998350	−	0.0574144i
$129$		−	0.537806i		−	0.00416904i
$130$		0			0
$131$	129.876	−	129.876i	0.991422	−	0.991422i	−0.00854147	−	0.999964i	$-0.502719\pi$
$131$	129.876	−	129.876i	0.991422	−	0.991422i	0.999964	+	0.00854147i	$0.00271887\pi$
$132$	−1.41647	−	0.922796i	−0.0107308	−	0.00699088i
$133$	−4.45270			−0.0334789
$134$	−74.2316	+	91.5323i	−0.553967	+	0.683077i
$135$		0			0
$136$	−37.2150	−	115.391i	−0.273639	−	0.848464i
$137$	−69.8267	+	69.8267i	−0.509684	+	0.509684i	−0.914429	−	0.404745i	$-0.867360\pi$
$137$	−69.8267	+	69.8267i	−0.509684	+	0.509684i	0.404745	+	0.914429i	$0.367360\pi$
$138$	0.982804	+	9.41657i	0.00712177	+	0.0682360i
$139$	−16.8371	+	16.8371i	−0.121130	+	0.121130i	−0.765073	−	0.643943i	$-0.777297\pi$
$139$	−16.8371	+	16.8371i	−0.121130	+	0.121130i	0.643943	+	0.765073i	$0.277297\pi$
$140$		0			0
$141$	4.87127	−	4.87127i	0.0345480	−	0.0345480i
$142$	119.308	+	96.7577i	0.840201	+	0.681392i
$143$	46.0469	−	46.0469i	0.322006	−	0.322006i
$144$	−131.510	+	58.0947i	−0.913265	+	0.403436i
$145$		0			0
$146$	52.7386	−	5.50431i	0.361223	−	0.0377008i
$147$	0.487538			0.00331659
$148$	114.013	−	24.0611i	0.770357	−	0.162575i
$149$	126.048	−	126.048i	0.845963	−	0.845963i	−0.143664	−	0.989627i	$-0.545888\pi$
$149$	126.048	−	126.048i	0.845963	−	0.845963i	0.989627	+	0.143664i	$0.0458883\pi$
$150$		0			0
$151$			170.000i			1.12583i	0.826516	+	0.562914i	$0.190320\pi$
$151$			170.000i			1.12583i	−0.826516	+	0.562914i	$0.809680\pi$
$152$	1.63119	+	5.05776i	0.0107315	+	0.0332747i
$153$	−96.2951	−	96.2951i	−0.629380	−	0.629380i
$154$	29.7935	−	36.7373i	0.193464	−	0.238554i
$155$		0			0
$156$	1.82607	+	8.65278i	0.0117056	+	0.0554665i
$157$	−12.1854			−0.0776137			−0.0388069	−	0.999247i	$-0.512356\pi$
$157$	−12.1854			−0.0776137			−0.0388069	+	0.999247i	$0.512356\pi$
$158$	−220.108	−	178.505i	−1.39309	−	1.12978i
$159$		−	9.42757i		−	0.0592929i
$160$		0			0
$161$	−264.898			−1.64533
$162$	−101.554	+	125.222i	−0.626874	+	0.772976i
$163$			285.780i			1.75325i	0.481170	+	0.876627i	$0.340212\pi$
$163$			285.780i			1.75325i	−0.481170	+	0.876627i	$0.659788\pi$
$164$	64.4540	−	13.6023i	0.393012	−	0.0829406i
$165$		0			0
$166$	186.487	+	151.239i	1.12342	+	0.911078i
$167$	102.579	−	102.579i	0.614248	−	0.614248i	−0.329802	−	0.944050i	$-0.606982\pi$
$167$	102.579	−	102.579i	0.614248	−	0.614248i	0.944050	+	0.329802i	$0.106982\pi$
$168$	1.97161	+	6.11329i	0.0117357	+	0.0363886i
$169$	−171.648			−1.01567
$170$		0			0
$171$	4.22075	+	4.22075i	0.0246828	+	0.0246828i
$172$	−3.70835	−	17.5719i	−0.0215602	−	0.102162i
$173$		−	68.3056i		−	0.394830i	−0.980320	−	0.197415i	$-0.936745\pi$
$173$		−	68.3056i		−	0.394830i	0.980320	−	0.197415i	$-0.0632546\pi$
$174$	0.548928	+	5.25946i	0.00315476	+	0.0302268i
$175$		0			0
$176$	−52.6438	−	20.3838i	−0.299112	−	0.115817i
$177$	−0.391199	−	0.391199i	−0.00221016	−	0.00221016i
$178$	110.515	−	136.272i	0.620869	−	0.765571i
$179$	−165.892	−	165.892i	−0.926773	−	0.926773i	0.0707227	−	0.997496i	$-0.477469\pi$
$179$	−165.892	−	165.892i	−0.926773	−	0.926773i	−0.997496	+	0.0707227i	$0.977469\pi$
$180$		0			0
$181$	101.633	+	101.633i	0.561506	+	0.561506i	0.929735	−	0.368229i	$-0.120036\pi$
$181$	101.633	+	101.633i	0.561506	+	0.561506i	−0.368229	+	0.929735i	$0.620036\pi$
$182$	−246.092	+	25.6846i	−1.35216	+	0.141124i
$183$	2.75978	+	2.75978i	0.0150807	+	0.0150807i
$184$	97.0418	+	300.894i	0.527401	+	1.63529i
$185$		0			0
$186$	9.16715	+	7.43445i	0.0492858	+	0.0399701i
$187$		−	53.4726i		−	0.285950i
$188$	125.572	−	192.750i	0.667934	−	1.02526i
$189$	10.2114	+	10.2114i	0.0540283	+	0.0540283i
$190$		0			0
$191$	−144.454			−0.756301			−0.378151	−	0.925744i	$-0.623440\pi$
$191$	−144.454			−0.756301			−0.378151	+	0.925744i	$0.623440\pi$
$192$	6.22173	−	4.47904i	0.0324049	−	0.0233283i
$193$	32.7772	−	32.7772i	0.169830	−	0.169830i	−0.617075	−	0.786905i	$-0.711682\pi$
$193$	32.7772	−	32.7772i	0.169830	−	0.169830i	0.786905	+	0.617075i	$0.211682\pi$
$194$	97.4582	−	10.1717i	0.502362	−	0.0524313i
$195$		0			0
$196$	15.9295	−	3.36174i	0.0812730	−	0.0171517i
$197$		−	335.205i		−	1.70155i	−0.525530	−	0.850775i	$-0.676133\pi$
$197$		−	335.205i		−	1.70155i	0.525530	−	0.850775i	$-0.323867\pi$
$198$	−63.0651	+	6.58208i	−0.318511	+	0.0332428i
$199$	−184.734			−0.928313			−0.464156	−	0.885753i	$-0.653642\pi$
$199$	−184.734			−0.928313			−0.464156	+	0.885753i	$0.653642\pi$
$200$		0			0
$201$		−	7.05833i		−	0.0351161i
$202$	83.1869	−	8.68218i	0.411816	−	0.0429811i
$203$	−147.954			−0.728838
$204$	6.08436	+	3.96381i	0.0298253	+	0.0194304i
$205$		0			0
$206$	136.579	−	14.2548i	0.663007	−	0.0691978i
$207$	251.099	+	251.099i	1.21304	+	1.21304i
$208$	119.327	+	270.124i	0.573689	+	1.29867i
$209$			2.34378i			0.0112143i
$210$		0			0
$211$	187.999	−	187.999i	0.890989	−	0.890989i	−0.103627	−	0.994616i	$-0.533045\pi$
$211$	187.999	−	187.999i	0.890989	−	0.890989i	0.994616	+	0.103627i	$0.0330448\pi$
$212$	−65.0062	−	308.030i	−0.306633	−	1.45297i
$213$	−9.20023			−0.0431936
$214$	−96.4672	−	78.2337i	−0.450781	−	0.365578i
$215$		0			0
$216$	7.85815	−	15.3397i	0.0363803	−	0.0710173i
$217$	−233.510	+	233.510i	−1.07608	+	1.07608i
$218$	89.0239	−	9.29139i	0.408366	−	0.0426211i
$219$	−2.24564	+	2.24564i	−0.0102541	+	0.0102541i
$220$		0			0
$221$	−197.791	+	197.791i	−0.894984	+	0.894984i
$222$	−4.39593	+	5.42047i	−0.0198015	+	0.0244165i
$223$	−282.322	+	282.322i	−1.26602	+	1.26602i	−0.317889	+	0.948128i	$0.602974\pi$
$223$	−282.322	+	282.322i	−1.26602	+	1.26602i	−0.948128	+	0.317889i	$0.897026\pi$
$224$	106.572	+	186.147i	0.475768	+	0.831012i
$225$		0			0
$226$	16.4776	+	157.877i	0.0729096	+	0.698571i
$227$	−146.872			−0.647015			−0.323507	−	0.946226i	$-0.604862\pi$
$227$	−146.872			−0.647015			−0.323507	+	0.946226i	$0.604862\pi$
$228$	−0.266686	−	0.173740i	−0.00116968	−	0.000762016i
$229$	194.697	−	194.697i	0.850205	−	0.850205i	−0.139953	−	0.990158i	$-0.544695\pi$
$229$	194.697	−	194.697i	0.850205	−	0.850205i	0.990158	+	0.139953i	$0.0446953\pi$
$230$		0			0
$231$			2.83292i			0.0122637i
$232$	54.2010	+	168.059i	0.233625	+	0.724393i
$233$	87.0218	+	87.0218i	0.373484	+	0.373484i	0.868745	−	0.495260i	$-0.164927\pi$
$233$	87.0218	+	87.0218i	0.373484	+	0.373484i	−0.495260	+	0.868745i	$0.664927\pi$
$234$	257.620	+	208.927i	1.10094	+	0.892849i
$235$		0			0
$236$	−15.4792	−	10.0843i	−0.0655899	−	0.0427302i
$237$	16.9732			0.0716169
$238$	−127.976	+	157.803i	−0.537714	+	0.663036i
$239$			334.837i			1.40099i	0.713657	+	0.700495i	$0.247037\pi$
$239$			334.837i			1.40099i	−0.713657	+	0.700495i	$0.752963\pi$
$240$		0			0
$241$	−378.876			−1.57210			−0.786049	−	0.618164i	$-0.787877\pi$
$241$	−378.876			−1.57210			−0.786049	+	0.618164i	$0.787877\pi$
$242$	168.621	+	136.750i	0.696781	+	0.565081i
$243$		−	29.0460i		−	0.119531i
$244$	109.201	+	71.1416i	0.447544	+	0.291564i
$245$		0			0
$246$	−2.48512	+	3.06431i	−0.0101021	+	0.0124566i
$247$	8.66949	−	8.66949i	0.0350991	−	0.0350991i
$248$	350.784	+	179.698i	1.41445	+	0.724588i
$249$	−14.3806			−0.0577534
$250$		0			0
$251$	−181.937	−	181.937i	−0.724849	−	0.724849i	0.244740	−	0.969589i	$-0.421297\pi$
$251$	−181.937	−	181.937i	−0.724849	−	0.724849i	−0.969589	+	0.244740i	$0.921297\pi$
$252$	201.864	+	131.509i	0.801046	+	0.521862i
$253$			139.435i			0.551128i
$254$	−169.194	+	17.6587i	−0.666118	+	0.0695225i
$255$		0			0
$256$	172.400	−	189.246i	0.673439	−	0.739243i
$257$	−38.2528	−	38.2528i	−0.148843	−	0.148843i	0.628758	−	0.777601i	$-0.283564\pi$
$257$	−38.2528	−	38.2528i	−0.148843	−	0.148843i	−0.777601	+	0.628758i	$0.783564\pi$
$258$	0.835416	+	0.677512i	0.00323804	+	0.00262601i
$259$	−138.073	−	138.073i	−0.533100	−	0.533100i
$260$		0			0
$261$	140.247	+	140.247i	0.537345	+	0.537345i
$262$	38.1326	+	365.361i	0.145544	+	1.39451i
$263$	165.962	+	165.962i	0.631034	+	0.631034i	0.948327	−	0.317294i	$-0.102774\pi$
$263$	165.962	+	165.962i	0.631034	+	0.631034i	−0.317294	+	0.948327i	$0.602774\pi$
$264$	3.21788	−	1.03780i	0.0121889	−	0.00393107i
$265$		0			0
$266$	5.60937	−	6.91672i	0.0210879	−	0.0260027i
$267$			10.5083i			0.0393570i
$268$	−48.6695	−	230.619i	−0.181603	−	0.860520i
$269$	310.294	+	310.294i	1.15351	+	1.15351i	0.985844	+	0.167665i	$0.0536228\pi$
$269$	310.294	+	310.294i	1.15351	+	1.15351i	0.167665	+	0.985844i	$0.446377\pi$
$270$		0			0
$271$	−272.486			−1.00548			−0.502741	−	0.864437i	$-0.667675\pi$
$271$	−272.486			−1.00548			−0.502741	+	0.864437i	$0.667675\pi$
$272$	226.128	+	87.5574i	0.831354	+	0.321902i
$273$	10.4788	−	10.4788i	0.0383838	−	0.0383838i
$274$	−20.5016	−	196.433i	−0.0748235	−	0.716908i
$275$		0			0
$276$	−15.8656	−	10.3360i	−0.0574840	−	0.0374494i
$277$			143.172i			0.516868i	0.966029	+	0.258434i	$0.0832064\pi$
$277$			143.172i			0.516868i	−0.966029	+	0.258434i	$0.916794\pi$
$278$	−4.94350	−	47.3653i	−0.0177824	−	0.170379i
$279$	442.693			1.58671
$280$		0			0
$281$		−	139.408i		−	0.496115i	−0.968745	−	0.248057i	$-0.920208\pi$
$281$		−	139.408i		−	0.496115i	0.968745	−	0.248057i	$-0.0797921\pi$
$282$	1.43024	+	13.7036i	0.00507177	+	0.0485943i
$283$	336.283			1.18828			0.594140	−	0.804362i	$-0.297493\pi$
$283$	336.283			1.18828			0.594140	+	0.804362i	$0.297493\pi$
$284$	−300.602	+	63.4386i	−1.05846	+	0.223375i
$285$		0			0
$286$	13.5197	+	129.537i	0.0472717	+	0.452925i
$287$	−78.0557	−	78.0557i	−0.271971	−	0.271971i
$288$	75.4296	−	277.471i	0.261908	−	0.963441i
$289$		−	59.3116i		−	0.205230i
$290$		0			0
$291$	−4.14983	+	4.14983i	−0.0142606	+	0.0142606i
$292$	−57.8883	+	88.8571i	−0.198247	+	0.304305i
$293$	33.1195			0.113036			0.0565179	−	0.998402i	$-0.482000\pi$
$293$	33.1195			0.113036			0.0565179	+	0.998402i	$0.482000\pi$
$294$	−0.614186	+	0.757331i	−0.00208907	+	0.00257596i
$295$		0			0
$296$	−106.254	+	207.416i	−0.358966	+	0.700731i
$297$	5.37499	−	5.37499i	0.0180976	−	0.0180976i
$298$	37.0087	+	354.593i	0.124190	+	1.18991i
$299$	515.762	−	515.762i	1.72496	−	1.72496i
$300$		0			0
$301$	−21.2801	+	21.2801i	−0.0706981	+	0.0706981i
$302$	−264.074	−	214.161i	−0.874417	−	0.709142i
$303$	−3.54215	+	3.54215i	−0.0116903	+	0.0116903i
$304$	−9.91153	−	3.83777i	−0.0326037	−	0.0126242i
$305$		0			0
$306$	270.892	−	28.2729i	0.885269	−	0.0923952i
$307$	−479.642			−1.56235			−0.781176	−	0.624310i	$-0.785380\pi$
$307$	−479.642			−1.56235			−0.781176	+	0.624310i	$0.785380\pi$
$308$	19.5339	+	92.5610i	0.0634218	+	0.300523i
$309$	−5.81564	+	5.81564i	−0.0188208	+	0.0188208i
$310$		0			0
$311$			328.043i			1.05480i	0.849617	+	0.527401i	$0.176833\pi$
$311$			328.043i			1.05480i	−0.849617	+	0.527401i	$0.823167\pi$
$312$	−15.7414	−	8.06394i	−0.0504533	−	0.0258459i
$313$	−90.2171	−	90.2171i	−0.288233	−	0.288233i	0.548148	−	0.836381i	$-0.315333\pi$
$313$	−90.2171	−	90.2171i	−0.288233	−	0.288233i	−0.836381	+	0.548148i	$0.815333\pi$
$314$	15.3507	−	18.9284i	0.0488877	−	0.0602817i
$315$		0			0
$316$	554.572	−	117.036i	1.75497	−	0.370367i
$317$	−324.328			−1.02312			−0.511558	−	0.859249i	$-0.670932\pi$
$317$	−324.328			−1.02312			−0.511558	+	0.859249i	$0.670932\pi$
$318$	14.6446	+	11.8766i	0.0460521	+	0.0373477i
$319$			77.8792i			0.244135i
$320$		0			0
$321$	7.43887			0.0231741
$322$	333.711	−	411.487i	1.03637	−	1.27791i
$323$		−	10.0676i		−	0.0311690i
$324$	−66.5830	−	315.502i	−0.205503	−	0.973771i
$325$		0			0
$326$	−443.925	−	360.018i	−1.36173	−	1.10435i
$327$	−3.79069	+	3.79069i	−0.0115923	+	0.0115923i
$328$	−60.0678	+	117.257i	−0.183134	+	0.357491i
$329$	−385.496			−1.17172
$330$		0			0
$331$	248.635	+	248.635i	0.751162	+	0.751162i	0.974696	−	0.223534i	$-0.0717594\pi$
$331$	248.635	+	248.635i	0.751162	+	0.751162i	−0.223534	+	0.974696i	$0.571759\pi$
$332$	−469.862	+	99.1589i	−1.41525	+	0.298671i
$333$			261.761i			0.786069i
$334$	30.1181	+	288.571i	0.0901739	+	0.863985i
$335$		0			0
$336$	−11.9800	−	4.63869i	−0.0356548	−	0.0138056i
$337$	82.9415	+	82.9415i	0.246117	+	0.246117i	0.819375	−	0.573258i	$-0.194321\pi$
$337$	82.9415	+	82.9415i	0.246117	+	0.246117i	−0.573258	+	0.819375i	$0.694321\pi$
$338$	216.237	−	266.634i	0.639755	−	0.788859i
$339$	−6.72250	−	6.72250i	−0.0198304	−	0.0198304i
$340$		0			0
$341$	122.914	+	122.914i	0.360451	+	0.360451i
$342$	−11.8736	+	1.23924i	−0.0347181	+	0.00362352i
$343$	−251.537	−	251.537i	−0.733345	−	0.733345i
$344$	31.9675	+	16.3761i	0.0929288	+	0.0476050i
$345$		0			0
$346$	106.104	+	86.0493i	0.306660	+	0.248697i
$347$		−	288.892i		−	0.832540i	−0.909241	−	0.416270i	$-0.863337\pi$
$347$		−	288.892i		−	0.832540i	0.909241	−	0.416270i	$-0.136663\pi$
$348$	−8.86144	−	5.77301i	−0.0254639	−	0.0165891i
$349$	−345.135	−	345.135i	−0.988927	−	0.988927i	0.0110128	−	0.999939i	$-0.496494\pi$
$349$	−345.135	−	345.135i	−0.988927	−	0.988927i	−0.999939	+	0.0110128i	$0.996494\pi$
$350$		0			0
$351$	−39.7634			−0.113286
$352$	97.9828	−	56.0968i	0.278360	−	0.159366i
$353$	−242.242	+	242.242i	−0.686239	+	0.686239i	−0.961399	−	0.275159i	$-0.911269\pi$
$353$	−242.242	+	242.242i	−0.686239	+	0.686239i	0.275159	+	0.961399i	$0.411269\pi$
$354$	1.10050	−	0.114859i	0.00310876	−	0.000324460i
$355$		0			0
$356$	72.4582	+	343.342i	0.203534	+	0.964443i
$357$		−	12.1686i		−	0.0340858i
$358$	466.680	−	48.7072i	1.30357	−	0.136054i
$359$	−221.083			−0.615831			−0.307916	−	0.951414i	$-0.599631\pi$
$359$	−221.083			−0.615831			−0.307916	+	0.951414i	$0.599631\pi$
$360$		0			0
$361$		−	360.559i		−	0.998778i
$362$	−285.907	+	29.8401i	−0.789799	+	0.0824311i
$363$	−13.0029			−0.0358206
$364$	270.122	−	414.631i	0.742093	−	1.13910i
$365$		0			0
$366$	−7.76365	+	0.810290i	−0.0212122	+	0.00221391i
$367$	71.5971	+	71.5971i	0.195087	+	0.195087i	0.797890	−	0.602803i	$-0.205949\pi$
$367$	71.5971	+	71.5971i	0.195087	+	0.195087i	−0.602803	+	0.797890i	$0.705949\pi$
$368$	−589.652	−	228.315i	−1.60232	−	0.620421i
$369$			147.980i			0.401028i
$370$		0			0
$371$	−373.034	+	373.034i	−1.00548	+	1.00548i
$372$	−23.0970	+	4.87435i	−0.0620887	+	0.0131031i
$373$	174.847			0.468758			0.234379	−	0.972145i	$-0.424694\pi$
$373$	174.847			0.468758			0.234379	+	0.972145i	$0.424694\pi$
$374$	83.0632	+	67.3632i	0.222094	+	0.180116i
$375$		0			0
$376$	141.221	+	437.880i	0.375589	+	1.16458i
$377$	288.070	−	288.070i	0.764110	−	0.764110i
$378$	−28.7260	+	2.99813i	−0.0759948	+	0.00793155i
$379$	−329.561	+	329.561i	−0.869553	+	0.869553i	−0.992423	−	0.122870i	$-0.960790\pi$
$379$	−329.561	+	329.561i	−0.869553	+	0.869553i	0.122870	+	0.992423i	$0.460790\pi$
$380$		0			0
$381$	7.20438	−	7.20438i	0.0189091	−	0.0189091i
$382$	181.978	−	224.391i	0.476383	−	0.587411i
$383$	1.40406	−	1.40406i	0.00366594	−	0.00366594i	−0.705271	−	0.708937i	$-0.749175\pi$
$383$	1.40406	−	1.40406i	0.00366594	−	0.00366594i	0.708937	+	0.705271i	$0.249175\pi$
$384$	−0.880310	+	15.3073i	−0.00229247	+	0.0398626i
$385$		0			0
$386$	9.62363	+	92.2072i	0.0249317	+	0.238879i
$387$	40.3433			0.104246
$388$	−106.974	+	164.203i	−0.275707	+	0.423204i
$389$	276.184	−	276.184i	0.709984	−	0.709984i	−0.256548	−	0.966532i	$-0.582585\pi$
$389$	276.184	−	276.184i	0.709984	−	0.709984i	0.966532	+	0.256548i	$0.0825851\pi$
$390$		0			0
$391$		−	598.936i		−	1.53181i
$392$	−14.8455	+	28.9796i	−0.0378711	+	0.0739274i
$393$	−15.5573	−	15.5573i	−0.0395860	−	0.0395860i
$394$	520.701	+	422.282i	1.32157	+	1.07178i
$395$		0			0
$396$	69.2230	−	106.256i	0.174806	−	0.268323i
$397$	692.870			1.74526			0.872632	−	0.488378i	$-0.162411\pi$
$397$	692.870			1.74526			0.872632	+	0.488378i	$0.162411\pi$
$398$	232.723	−	286.962i	0.584730	−	0.721010i
$399$			0.533369i			0.00133676i
$400$		0			0
$401$	755.828			1.88486			0.942429	−	0.334407i	$-0.108536\pi$
$401$	755.828			1.88486			0.942429	+	0.334407i	$0.108536\pi$
$402$	10.9642	+	8.89187i	0.0272742	+	0.0221191i
$403$		−	909.298i		−	2.25632i
$404$	−91.3096	+	140.158i	−0.226014	+	0.346926i
$405$		0			0
$406$	186.388	−	229.829i	0.459084	−	0.566080i
$407$	−72.6780	+	72.6780i	−0.178570	+	0.178570i
$408$	−13.8222	+	4.45781i	−0.0338779	+	0.0109260i
$409$	−43.3293			−0.105940			−0.0529698	−	0.998596i	$-0.516869\pi$
$409$	−43.3293			−0.105940			−0.0529698	+	0.998596i	$0.516869\pi$
$410$		0			0
$411$	8.36423	+	8.36423i	0.0203509	+	0.0203509i
$412$	−149.916	+	230.117i	−0.363873	+	0.558537i
$413$			30.9582i			0.0749594i
$414$	−706.379	+	73.7246i	−1.70623	+	0.178079i
$415$		0			0
$416$	−569.929	−	154.933i	−1.37002	−	0.372436i
$417$	2.01684	+	2.01684i	0.00483655	+	0.00483655i
$418$	−3.64078	−	2.95263i	−0.00871000	−	0.00706370i
$419$	−345.453	−	345.453i	−0.824471	−	0.824471i	0.162274	−	0.986746i	$-0.448117\pi$
$419$	−345.453	−	345.453i	−0.824471	−	0.824471i	−0.986746	+	0.162274i	$0.948117\pi$
$420$		0			0
$421$	−371.173	−	371.173i	−0.881645	−	0.881645i	0.112056	−	0.993702i	$-0.464256\pi$
$421$	−371.173	−	371.173i	−0.881645	−	0.881645i	−0.993702	+	0.112056i	$0.964256\pi$
$422$	55.1978	+	528.868i	0.130800	+	1.25324i
$423$	365.416	+	365.416i	0.863867	+	0.863867i
$424$	560.380	+	287.068i	1.32165	+	0.677048i
$425$		0			0
$426$	11.5902	−	14.2914i	0.0272070	−	0.0335480i
$427$		−	218.400i		−	0.511475i
$428$	243.053	−	51.2935i	0.567881	−	0.119845i
$429$	−5.51575	−	5.51575i	−0.0128572	−	0.0128572i
$430$		0			0
$431$	−150.726			−0.349712			−0.174856	−	0.984594i	$-0.555946\pi$
$431$	−150.726			−0.349712			−0.174856	+	0.984594i	$0.555946\pi$
$432$	13.9289	+	31.5312i	0.0322429	+	0.0729889i
$433$	−249.306	+	249.306i	−0.575765	+	0.575765i	−0.933734	−	0.357969i	$-0.883469\pi$
$433$	−249.306	+	249.306i	−0.575765	+	0.575765i	0.357969	+	0.933734i	$0.383469\pi$
$434$	−68.5603	−	656.899i	−0.157973	−	1.51359i
$435$		0			0
$436$	−97.7165	+	149.993i	−0.224121	+	0.344020i
$437$			26.2522i			0.0600738i
$438$	−0.659337	−	6.31732i	−0.00150534	−	0.0144231i
$439$	106.380			0.242324			0.121162	−	0.992633i	$-0.461338\pi$
$439$	106.380			0.242324			0.121162	+	0.992633i	$0.461338\pi$
$440$		0			0
$441$			36.5725i			0.0829307i
$442$	−58.0730	−	556.416i	−0.131387	−	1.25886i
$443$	−235.281			−0.531108			−0.265554	−	0.964096i	$-0.585555\pi$
$443$	−235.281			−0.531108			−0.265554	+	0.964096i	$0.585555\pi$
$444$	−2.88217	−	13.6571i	−0.00649137	−	0.0307592i
$445$		0			0
$446$	−82.8917	−	794.213i	−0.185856	−	1.78075i
$447$	−15.0988	−	15.0988i	−0.0337780	−	0.0337780i
$448$	−423.412	−	68.9554i	−0.945117	−	0.153918i
$449$		−	78.1899i		−	0.174142i	−0.996202	−	0.0870712i	$-0.972249\pi$
$449$		−	78.1899i		−	0.174142i	0.996202	−	0.0870712i	$-0.0277508\pi$
$450$		0			0
$451$	−41.0865	+	41.0865i	−0.0911009	+	0.0911009i
$452$	−266.000	−	173.293i	−0.588496	−	0.383391i
$453$	20.3635			0.0449526
$454$	185.025	−	228.148i	0.407545	−	0.502529i
$455$		0			0
$456$	0.605847	−	0.195392i	0.00132861	−	0.000428492i
$457$	−401.924	+	401.924i	−0.879483	+	0.879483i	−0.993481	−	0.113998i	$-0.963634\pi$
$457$	−401.924	+	401.924i	−0.879483	+	0.879483i	0.113998	+	0.993481i	$0.463634\pi$
$458$	57.1644	+	547.711i	0.124813	+	1.19588i
$459$	−23.0879	+	23.0879i	−0.0503005	+	0.0503005i
$460$		0			0
$461$	158.945	−	158.945i	0.344783	−	0.344783i	−0.513379	−	0.858162i	$-0.671606\pi$
$461$	158.945	−	158.945i	0.344783	−	0.344783i	0.858162	+	0.513379i	$0.171606\pi$
$462$	−4.40059	−	3.56883i	−0.00952509	−	0.00772473i
$463$	200.675	−	200.675i	0.433422	−	0.433422i	−0.456369	−	0.889791i	$-0.650850\pi$
$463$	200.675	−	200.675i	0.433422	−	0.433422i	0.889791	+	0.456369i	$0.150850\pi$
$464$	−329.340	−	127.521i	−0.709784	−	0.274830i
$465$		0			0
$466$	−244.805	+	25.5502i	−0.525333	+	0.0548288i
$467$	188.298			0.403208			0.201604	−	0.979467i	$-0.435385\pi$
$467$	188.298			0.403208			0.201604	+	0.979467i	$0.435385\pi$
$468$	−649.084	+	136.981i	−1.38693	+	0.292695i
$469$	−279.287	+	279.287i	−0.595494	+	0.595494i
$470$		0			0
$471$			1.45963i			0.00309900i
$472$	35.1650	−	11.3411i	0.0745022	−	0.0240278i
$473$	11.2013	+	11.2013i	0.0236814	+	0.0236814i
$474$	−21.3823	+	26.3658i	−0.0451104	+	0.0556241i
$475$		0			0
$476$	−83.9067	−	397.590i	−0.176274	−	0.835273i
$477$	707.204			1.48261
$478$	−520.127	−	421.817i	−1.08813	−	0.882462i
$479$			175.422i			0.366225i	0.983092	+	0.183112i	$0.0586172\pi$
$479$			175.422i			0.366225i	−0.983092	+	0.183112i	$0.941383\pi$
$480$		0			0
$481$	537.661			1.11780
$482$	477.296	−	588.537i	0.990241	−	1.22103i
$483$			31.7309i			0.0656955i
$484$	−424.847	+	89.6590i	−0.877784	+	0.185246i
$485$		0			0
$486$	45.1194	+	36.5913i	0.0928383	+	0.0752908i
$487$	53.3922	−	53.3922i	0.109635	−	0.109635i	−0.650161	−	0.759796i	$-0.725299\pi$
$487$	53.3922	−	53.3922i	0.109635	−	0.109635i	0.759796	+	0.650161i	$0.225299\pi$
$488$	−248.077	+	80.0078i	−0.508355	+	0.163950i
$489$	34.2324			0.0700048
$490$		0			0
$491$	96.7903	+	96.7903i	0.197129	+	0.197129i	0.798768	−	0.601639i	$-0.205485\pi$
$491$	96.7903	+	96.7903i	0.197129	+	0.197129i	−0.601639	+	0.798768i	$0.705485\pi$
$492$	−1.62935	−	7.72066i	−0.00331170	−	0.0156924i
$493$		−	334.525i		−	0.678550i
$494$	2.54542	+	24.3885i	0.00515268	+	0.0493695i
$495$		0			0
$496$	−721.046	+	318.523i	−1.45372	+	0.642183i
$497$	364.038	+	364.038i	0.732472	+	0.732472i
$498$	18.1162	−	22.3385i	0.0363780	−	0.0448564i
$499$	139.686	+	139.686i	0.279931	+	0.279931i	0.833081	−	0.553150i	$-0.186574\pi$
$499$	139.686	+	139.686i	0.279931	+	0.279931i	−0.553150	+	0.833081i	$0.686574\pi$
$500$		0			0
$501$	−12.2875	−	12.2875i	−0.0245260	−	0.0245260i
$502$	511.815	−	53.4180i	1.01955	−	0.106410i
$503$	−319.688	−	319.688i	−0.635562	−	0.635562i	0.313895	−	0.949458i	$-0.398366\pi$
$503$	−319.688	−	319.688i	−0.635562	−	0.635562i	−0.949458	+	0.313895i	$0.898366\pi$
$504$	−458.585	+	147.899i	−0.909891	+	0.293450i
$505$		0			0
$506$	−216.596	−	175.657i	−0.428055	−	0.347147i
$507$			20.5610i			0.0405542i
$508$	185.715	−	285.068i	0.365580	−	0.561157i
$509$	702.440	+	702.440i	1.38004	+	1.38004i	0.844529	+	0.535510i	$0.179881\pi$
$509$	702.440	+	702.440i	1.38004	+	1.38004i	0.535510	+	0.844529i	$0.320119\pi$
$510$		0			0
$511$	177.713			0.347775
$512$	76.7858	+	506.209i	0.149972	+	0.988690i
$513$	1.01198	−	1.01198i	0.00197267	−	0.00197267i
$514$	107.611	−	11.2313i	0.209359	−	0.0218508i
$515$		0			0
$516$	−2.10486	+	0.444206i	−0.00407919	+	0.000860865i
$517$			202.915i			0.392486i
$518$	388.419	−	40.5392i	0.749844	−	0.0782610i
$519$	−8.18202			−0.0157650
$520$		0			0
$521$			614.419i			1.17931i	0.807656	+	0.589654i	$0.200736\pi$
$521$			614.419i			1.17931i	−0.807656	+	0.589654i	$0.799264\pi$
$522$	−394.536	+	41.1776i	−0.755815	+	0.0788842i
$523$	178.970			0.342199			0.171100	−	0.985254i	$-0.445268\pi$
$523$	178.970			0.342199			0.171100	+	0.985254i	$0.445268\pi$
$524$	−615.582	−	401.037i	−1.17477	−	0.765337i
$525$		0			0
$526$	−466.875	+	48.7276i	−0.887595	+	0.0926380i
$527$	−527.968	−	527.968i	−1.00184	−	1.00184i
$528$	−2.44168	+	6.30596i	−0.00462440	+	0.0119431i
$529$			1032.79i			1.95234i
$530$		0			0
$531$	29.3456	−	29.3456i	0.0552648	−	0.0552648i
$532$	3.67775	+	17.4269i	0.00691307	+	0.0327574i
$533$	303.952			0.570266
$534$	−16.3234	−	13.2381i	−0.0305681	−	0.0247904i
$535$		0			0
$536$	419.551	+	214.925i	0.782745	+	0.400980i
$537$	−19.8715	+	19.8715i	−0.0370047	+	0.0370047i
$538$	−872.903	+	91.1046i	−1.62250	+	0.169339i
$539$	−10.1543	+	10.1543i	−0.0188392	+	0.0188392i
$540$		0			0
$541$	216.557	−	216.557i	0.400291	−	0.400291i	−0.478045	−	0.878336i	$-0.658654\pi$
$541$	216.557	−	216.557i	0.400291	−	0.400291i	0.878336	+	0.478045i	$0.158654\pi$
$542$	343.269	−	423.273i	0.633338	−	0.780947i
$543$	12.1741	−	12.1741i	0.0224201	−	0.0224201i
$544$	−420.879	+	240.960i	−0.773675	+	0.442941i
$545$		0			0
$546$	3.07664	+	29.4783i	0.00563487	+	0.0539896i
$547$	−204.888			−0.374567			−0.187284	−	0.982306i	$-0.559968\pi$
$547$	−204.888			−0.374567			−0.187284	+	0.982306i	$0.559968\pi$
$548$	330.962	+	215.613i	0.603945	+	0.393455i
$549$	−207.023	+	207.023i	−0.377091	+	0.377091i
$550$		0			0
$551$			14.6627i			0.0266111i
$552$	36.0428	−	11.6242i	0.0652949	−	0.0210583i
$553$	−671.603	−	671.603i	−1.21447	−	1.21447i
$554$	−222.401	−	180.364i	−0.401445	−	0.325567i
$555$		0			0
$556$	79.8038	+	51.9902i	0.143532	+	0.0935076i
$557$	−345.777			−0.620784			−0.310392	−	0.950609i	$-0.600460\pi$
$557$	−345.777			−0.620784			−0.310392	+	0.950609i	$0.600460\pi$
$558$	−557.691	+	687.669i	−0.999447	+	1.23238i
$559$		−	82.8656i		−	0.148239i
$560$		0			0
$561$	−6.40525			−0.0114176
$562$	216.553	+	175.622i	0.385326	+	0.312495i
$563$		−	319.750i		−	0.567940i	−0.958833	−	0.283970i	$-0.908348\pi$
$563$		−	319.750i		−	0.567940i	0.958833	−	0.283970i	$-0.0916516\pi$
$564$	−23.0886	−	15.0417i	−0.0409373	−	0.0266696i
$565$		0			0
$566$	−423.639	+	522.374i	−0.748479	+	0.922923i
$567$	−382.082	+	382.082i	−0.673866	+	0.673866i
$568$	280.146	−	546.867i	0.493214	−	0.962794i
$569$	−146.472			−0.257420			−0.128710	−	0.991682i	$-0.541084\pi$
$569$	−146.472			−0.257420			−0.128710	+	0.991682i	$0.541084\pi$
$570$		0			0
$571$	−221.670	−	221.670i	−0.388214	−	0.388214i	0.485836	−	0.874050i	$-0.338515\pi$
$571$	−221.670	−	221.670i	−0.388214	−	0.388214i	−0.874050	+	0.485836i	$0.838515\pi$
$572$	−218.251	−	142.185i	−0.381558	−	0.248575i
$573$			17.3034i			0.0301980i
$574$	219.582	−	22.9177i	0.382547	−	0.0399263i
$575$		0			0
$576$	335.993	+	466.720i	0.583321	+	0.810278i
$577$	293.131	+	293.131i	0.508026	+	0.508026i	0.913920	−	0.405894i	$-0.133040\pi$
$577$	293.131	+	293.131i	0.508026	+	0.508026i	−0.405894	+	0.913920i	$0.633040\pi$
$578$	92.1332	+	74.7189i	0.159400	+	0.129272i
$579$	−3.92624	−	3.92624i	−0.00678107	−	0.00678107i
$580$		0			0
$581$	569.017	+	569.017i	0.979375	+	0.979375i
$582$	−1.21842	−	11.6741i	−0.00209351	−	0.0200586i
$583$	196.355	+	196.355i	0.336801	+	0.336801i
$584$	−65.1028	−	201.862i	−0.111477	−	0.345654i
$585$		0			0
$586$	−41.7229	+	51.4470i	−0.0711995	+	0.0877936i
$587$		−	176.460i		−	0.300614i	−0.988639	−	0.150307i	$-0.951974\pi$
$587$		−	176.460i		−	0.300614i	0.988639	−	0.150307i	$-0.0480262\pi$
$588$	−0.402687	−	1.90813i	−0.000684842	−	0.00324511i
$589$	23.1416	+	23.1416i	0.0392897	+	0.0392897i
$590$		0			0
$591$	−40.1528			−0.0679404
$592$	−188.340	−	426.349i	−0.318142	−	0.720185i
$593$	311.192	−	311.192i	0.524776	−	0.524776i	−0.394234	−	0.919010i	$-0.628990\pi$
$593$	311.192	−	311.192i	0.524776	−	0.524776i	0.919010	+	0.394234i	$0.128990\pi$
$594$	1.57814	+	15.1206i	0.00265679	+	0.0254556i
$595$		0			0
$596$	−597.439	−	389.217i	−1.00241	−	0.653048i
$597$			22.1285i			0.0370661i
$598$	151.431	+	1450.91i	0.253230	+	2.42628i
$599$	−550.344			−0.918771			−0.459386	−	0.888237i	$-0.651930\pi$
$599$	−550.344			−0.918771			−0.459386	+	0.888237i	$0.651930\pi$
$600$		0			0
$601$		−	440.349i		−	0.732693i	−0.930478	−	0.366347i	$-0.880608\pi$
$601$		−	440.349i		−	0.732693i	0.930478	−	0.366347i	$-0.119392\pi$
$602$	−6.24800	−	59.8641i	−0.0103787	−	0.0994420i
$603$	529.477			0.878071
$604$	665.345	−	140.413i	1.10156	−	0.232472i
$605$		0			0
$606$	−1.04000	−	9.96458i	−0.00171617	−	0.0164432i
$607$	12.8864	+	12.8864i	0.0212296	+	0.0212296i	0.717642	−	0.696412i	$-0.245221\pi$
$607$	12.8864	+	12.8864i	0.0212296	+	0.0212296i	−0.696412	+	0.717642i	$0.745221\pi$
$608$	18.4477	−	10.5616i	0.0303417	−	0.0173711i
$609$			17.7228i			0.0291014i
$610$		0			0
$611$	750.569	−	750.569i	1.22843	−	1.22843i
$612$	−297.343	+	456.415i	−0.485855	+	0.745776i
$613$	−228.861			−0.373346			−0.186673	−	0.982422i	$-0.559771\pi$
$613$	−228.861			−0.373346			−0.186673	+	0.982422i	$0.559771\pi$
$614$	604.239	−	745.065i	0.984102	−	1.21346i
$615$		0			0
$616$	−168.390	−	86.2620i	−0.273361	−	0.140036i
$617$	236.901	−	236.901i	0.383957	−	0.383957i	−0.488569	−	0.872525i	$-0.662481\pi$
$617$	236.901	−	236.901i	0.383957	−	0.383957i	0.872525	+	0.488569i	$0.162481\pi$
$618$	−1.70751	−	16.3602i	−0.00276297	−	0.0264729i
$619$	204.389	−	204.389i	0.330192	−	0.330192i	−0.522468	−	0.852659i	$-0.674988\pi$
$619$	204.389	−	204.389i	0.330192	−	0.330192i	0.852659	+	0.522468i	$0.174988\pi$
$620$		0			0
$621$	60.2042	−	60.2042i	0.0969471	−	0.0969471i
$622$	−509.575	−	413.259i	−0.819252	−	0.664403i
$623$	415.797	−	415.797i	0.667411	−	0.667411i
$624$	32.3569	−	14.2937i	0.0518541	−	0.0229066i
$625$		0			0
$626$	253.794	−	26.4884i	0.405421	−	0.0423137i
$627$	0.280751			0.000447769
$628$	10.0646	+	47.6910i	0.0160265	+	0.0759410i
$629$	312.184	−	312.184i	0.496317	−	0.496317i
$630$		0			0
$631$		−	219.606i		−	0.348029i	−0.984743	−	0.174014i	$-0.944326\pi$
$631$		−	219.606i		−	0.348029i	0.984743	−	0.174014i	$-0.0556739\pi$
$632$	−516.832	+	1008.90i	−0.817772	+	1.59636i
$633$	−22.5195	−	22.5195i	−0.0355759	−	0.0355759i
$634$	408.579	−	503.804i	0.644446	−	0.794643i
$635$		0			0
$636$	−36.8976	+	7.78680i	−0.0580151	+	0.0122434i
$637$	75.1203			0.117928
$638$	−120.976	−	98.1098i	−0.189617	−	0.153777i
$639$		−	690.151i		−	1.08005i
$640$		0			0
$641$	−399.195			−0.622770			−0.311385	−	0.950284i	$-0.600793\pi$
$641$	−399.195			−0.622770			−0.311385	+	0.950284i	$0.600793\pi$
$642$	−9.37127	+	11.5554i	−0.0145970	+	0.0179990i
$643$			864.637i			1.34469i	0.740237	+	0.672346i	$0.234713\pi$
$643$			864.637i			1.34469i	−0.740237	+	0.672346i	$0.765287\pi$
$644$	218.795	+	1036.76i	0.339744	+	1.60987i
$645$		0			0
$646$	15.6387	+	12.6828i	0.0242086	+	0.0196329i
$647$	569.775	−	569.775i	0.880641	−	0.880641i	−0.112959	−	0.993600i	$-0.536033\pi$
$647$	569.775	−	569.775i	0.880641	−	0.880641i	0.993600	+	0.112959i	$0.0360329\pi$
$648$	573.973	+	294.031i	0.885760	+	0.453752i
$649$	16.2956			0.0251088
$650$		0			0
$651$	27.9711	+	27.9711i	0.0429664	+	0.0429664i
$652$	1118.49	−	236.043i	1.71547	−	0.362030i
$653$			139.259i			0.213261i	0.994299	+	0.106630i	$0.0340062\pi$
$653$			139.259i			0.213261i	−0.994299	+	0.106630i	$0.965994\pi$
$654$	−1.11297	−	10.6638i	−0.00170180	−	0.0163055i
$655$		0			0
$656$	−106.473	−	241.025i	−0.162306	−	0.367416i
$657$	−168.456	−	168.456i	−0.256402	−	0.256402i
$658$	485.637	−	598.821i	0.738050	−	0.910063i
$659$	348.410	+	348.410i	0.528695	+	0.528695i	0.920183	−	0.391488i	$-0.128040\pi$
$659$	348.410	+	348.410i	0.528695	+	0.528695i	−0.391488	+	0.920183i	$0.628040\pi$
$660$		0			0
$661$	270.659	+	270.659i	0.409469	+	0.409469i	0.881553	−	0.472084i	$-0.156498\pi$
$661$	270.659	+	270.659i	0.409469	+	0.409469i	−0.472084	+	0.881553i	$0.656498\pi$
$662$	−699.446	+	73.0009i	−1.05656	+	0.110273i
$663$	23.6926	+	23.6926i	0.0357354	+	0.0357354i
$664$	437.887	−	854.791i	0.659469	−	1.28734i
$665$		0			0
$666$	−406.614	−	329.759i	−0.610531	−	0.495133i
$667$			872.309i			1.30781i
$668$	−486.202	−	316.748i	−0.727847	−	0.474174i
$669$	33.8181	+	33.8181i	0.0505502	+	0.0505502i
$670$		0			0
$671$	−114.960			−0.171326
$672$	22.2977	−	12.7658i	0.0331811	−	0.0189967i
$673$	29.4792	−	29.4792i	0.0438027	−	0.0438027i	−0.684866	−	0.728669i	$-0.740139\pi$
$673$	29.4792	−	29.4792i	0.0438027	−	0.0438027i	0.728669	+	0.684866i	$0.240139\pi$
$674$	−233.327	+	24.3522i	−0.346182	+	0.0361309i
$675$		0			0
$676$	141.775	+	671.796i	0.209726	+	0.993781i
$677$			519.409i			0.767221i	0.923495	+	0.383611i	$0.125319\pi$
$677$			519.409i			0.767221i	−0.923495	+	0.383611i	$0.874681\pi$
$678$	18.9114	−	1.97377i	0.0278929	−	0.00291117i
$679$	328.404			0.483659
$680$		0			0
$681$			17.5932i			0.0258343i
$682$	−345.774	+	36.0883i	−0.507000	+	0.0529155i
$683$	−254.873			−0.373167			−0.186583	−	0.982439i	$-0.559741\pi$
$683$	−254.873			−0.373167			−0.186583	+	0.982439i	$0.559741\pi$
$684$	13.0330	−	20.0053i	0.0190541	−	0.0292476i
$685$		0			0
$686$	707.612	−	73.8532i	1.03150	−	0.107658i
$687$	−23.3219	−	23.3219i	−0.0339474	−	0.0339474i
$688$	−65.7100	+	29.0274i	−0.0955087	+	0.0421910i
$689$		−	1452.61i		−	2.10828i
$690$		0			0
$691$	−422.293	+	422.293i	−0.611133	+	0.611133i	−0.943241	−	0.332108i	$-0.892240\pi$
$691$	−422.293	+	422.293i	−0.611133	+	0.611133i	0.332108	+	0.943241i	$0.392240\pi$
$692$	−267.334	+	56.4177i	−0.386321	+	0.0815285i
$693$	−212.510			−0.306652
$694$	448.757	+	363.937i	0.646625	+	0.524405i
$695$		0			0
$696$	20.1310	−	6.49249i	0.0289239	−	0.00932830i
$697$	176.484	−	176.484i	0.253206	−	0.253206i
$698$	970.916	−	101.334i	1.39100	−	0.145178i
$699$	10.4240	−	10.4240i	0.0149127	−	0.0149127i
$700$		0			0
$701$	203.994	−	203.994i	0.291004	−	0.291004i	−0.546473	−	0.837477i	$-0.684030\pi$
$701$	203.994	−	203.994i	0.291004	−	0.291004i	0.837477	+	0.546473i	$0.184030\pi$
$702$	50.0927	−	61.7676i	0.0713572	−	0.0879880i
$703$	−13.6835	+	13.6835i	−0.0194644	+	0.0194644i
$704$	−36.2963	+	222.873i	−0.0515573	+	0.316581i
$705$		0			0
$706$	−71.1241	−	681.464i	−0.100742	−	0.965246i
$707$	280.314			0.396484
$708$	−1.20796	+	1.85419i	−0.00170615	+	0.00261891i
$709$	−407.106	+	407.106i	−0.574197	+	0.574197i	−0.933299	−	0.359101i	$-0.883083\pi$
$709$	−407.106	+	407.106i	−0.574197	+	0.574197i	0.359101	+	0.933299i	$0.383083\pi$
$710$		0			0
$711$			1273.24i			1.79077i
$712$	−624.620	−	319.977i	−0.877275	−	0.449405i
$713$	1376.73	+	1376.73i	1.93090	+	1.93090i
$714$	18.9025	+	15.3297i	0.0264740	+	0.0214701i
$715$		0			0
$716$	−512.248	+	786.289i	−0.715431	+	1.09817i
$717$	40.1086			0.0559394
$718$	278.514	−	343.426i	0.387903	−	0.478309i
$719$			725.464i			1.00899i	0.863415	+	0.504495i	$0.168321\pi$
$719$			725.464i			1.00899i	−0.863415	+	0.504495i	$0.831679\pi$
$720$		0			0
$721$	460.231			0.638323
$722$	560.084	+	454.221i	0.775739	+	0.629115i
$723$			45.3838i			0.0627716i
$724$	313.825	−	481.714i	0.433459	−	0.665350i
$725$		0			0
$726$	16.3806	−	20.1984i	0.0225628	−	0.0278214i
$727$	−442.782	+	442.782i	−0.609054	+	0.609054i	−0.942699	−	0.333645i	$-0.891721\pi$
$727$	−442.782	+	442.782i	−0.609054	+	0.609054i	0.333645	+	0.942699i	$0.391721\pi$
$728$	303.787	+	941.941i	0.417289	+	1.29387i
$729$	722.036			0.990447
$730$		0			0
$731$	−48.1145	−	48.1145i	−0.0658201	−	0.0658201i
$732$	8.52173	−	13.0807i	0.0116417	−	0.0178698i
$733$			358.600i			0.489222i	0.969621	+	0.244611i	$0.0786603\pi$
$733$			358.600i			0.489222i	−0.969621	+	0.244611i	$0.921340\pi$
$734$	−201.413	+	21.0214i	−0.274405	+	0.0286395i
$735$		0			0
$736$	1097.49	−	628.328i	1.49115	−	0.853707i
$737$	147.009	+	147.009i	0.199470	+	0.199470i
$738$	−229.868	−	186.420i	−0.311474	−	0.252602i
$739$	−575.294	−	575.294i	−0.778477	−	0.778477i	0.201095	−	0.979572i	$-0.435550\pi$
$739$	−575.294	−	575.294i	−0.778477	−	0.778477i	−0.979572	+	0.201095i	$0.935550\pi$
$740$		0			0
$741$	−1.03848	−	1.03848i	−0.00140146	−	0.00140146i
$742$	−109.525	−	1049.40i	−0.147608	−	1.41428i
$743$	55.8927	+	55.8927i	0.0752258	+	0.0752258i	0.743719	−	0.668493i	$-0.233060\pi$
$743$	55.8927	+	55.8927i	0.0752258	+	0.0752258i	−0.668493	+	0.743719i	$0.733060\pi$
$744$	21.5252	−	42.0189i	0.0289317	−	0.0564770i
$745$		0			0
$746$	−220.266	+	271.603i	−0.295263	+	0.364079i
$747$		−	1078.75i		−	1.44411i
$748$	−209.281	+	44.1663i	−0.279787	+	0.0590458i
$749$	−294.344	−	294.344i	−0.392983	−	0.392983i
$750$		0			0
$751$	−63.5053			−0.0845610			−0.0422805	−	0.999106i	$-0.513462\pi$
$751$	−63.5053			−0.0845610			−0.0422805	+	0.999106i	$0.513462\pi$
$752$	−858.100	−	332.258i	−1.14109	−	0.441833i
$753$	−21.7934	+	21.7934i	−0.0289421	+	0.0289421i
$754$	84.5793	+	810.382i	0.112174	+	1.07478i
$755$		0			0
$756$	31.5310	−	48.3993i	0.0417076	−	0.0640202i
$757$		−	495.675i		−	0.654789i	−0.944888	−	0.327395i	$-0.893829\pi$
$757$		−	495.675i		−	0.654789i	0.944888	−	0.327395i	$-0.106171\pi$
$758$	−96.7614	−	927.102i	−0.127653	−	1.22309i
$759$	16.7023			0.0220057
$760$		0			0
$761$			228.669i			0.300485i	0.988649	+	0.150243i	$0.0480055\pi$
$761$			228.669i			0.300485i	−0.988649	+	0.150243i	$0.951995\pi$
$762$	2.11526	+	20.2670i	0.00277593	+	0.0265971i
$763$	299.983			0.393163
$764$	119.313	+	565.362i	0.156169	+	0.740002i
$765$		0			0
$766$	0.412241	+	3.94982i	0.000538174	+	0.00515642i
$767$	−60.2763	−	60.2763i	−0.0785871	−	0.0785871i
$768$	−22.6690	−	20.6511i	−0.0295169	−	0.0268894i
$769$			804.229i			1.04581i	0.852391	+	0.522906i	$0.175152\pi$
$769$			804.229i			1.04581i	−0.852391	+	0.522906i	$0.824848\pi$
$770$		0			0
$771$	−4.58213	+	4.58213i	−0.00594310	+	0.00594310i
$772$	−155.356	−	101.211i	−0.201238	−	0.131102i
$773$	−186.546			−0.241328			−0.120664	−	0.992693i	$-0.538502\pi$
$773$	−186.546			−0.241328			−0.120664	+	0.992693i	$0.538502\pi$
$774$	−50.8232	+	62.6683i	−0.0656631	+	0.0809668i
$775$		0			0
$776$	−120.306	−	373.030i	−0.155034	−	0.480709i
$777$	−16.5391	+	16.5391i	−0.0212859	+	0.0212859i
$778$	81.0895	+	776.945i	0.104228	+	0.998644i
$779$	−7.73557	+	7.73557i	−0.00993013	+	0.00993013i
$780$		0			0
$781$	191.620	−	191.620i	0.245353	−	0.245353i
$782$	930.374	+	754.522i	1.18974	+	0.964861i
$783$	33.6260	−	33.6260i	0.0429450	−	0.0429450i
$784$	−26.3143	−	59.5682i	−0.0335641	−	0.0759798i
$785$		0			0
$786$	43.7650	−	4.56774i	0.0556806	−	0.00581137i
$787$	−1134.28			−1.44127			−0.720635	−	0.693315i	$-0.756150\pi$
$787$	−1134.28			−1.44127			−0.720635	+	0.693315i	$0.756150\pi$
$788$	−1311.93	+	276.866i	−1.66488	+	0.351353i
$789$	19.8798	−	19.8798i	0.0251962	−	0.0251962i
$790$		0			0
$791$			531.997i			0.672563i
$792$	77.8502	+	241.387i	0.0982957	+	0.304782i
$793$	425.229	+	425.229i	0.536228	+	0.536228i
$794$	−872.856	+	1076.29i	−1.09932	+	1.35553i
$795$		0			0
$796$	152.583	+	723.012i	0.191687	+	0.908306i
$797$	−250.905			−0.314812			−0.157406	−	0.987534i	$-0.550313\pi$
$797$	−250.905			−0.314812			−0.157406	+	0.987534i	$0.550313\pi$
$798$	−0.828523	−	0.671922i	−0.00103825	−	0.000842007i
$799$		−	871.610i		−	1.09088i
$800$		0			0
$801$	−788.276			−0.984114
$802$	−952.169	+	1174.09i	−1.18724	+	1.46395i
$803$		−	93.5435i		−	0.116493i
$804$	−27.6249	+	5.82990i	−0.0343593	+	0.00725112i
$805$		0			0
$806$	1412.48	+	1145.51i	1.75246	+	1.42122i
$807$	37.1687	−	37.1687i	0.0460579	−	0.0460579i
$808$	−102.689	−	318.405i	−0.127091	−	0.394066i
$809$	1099.77			1.35942			0.679712	−	0.733479i	$-0.262105\pi$
$809$	1099.77			1.35942			0.679712	+	0.733479i	$0.262105\pi$
$810$		0			0
$811$	−376.722	−	376.722i	−0.464515	−	0.464515i	0.435617	−	0.900132i	$-0.356530\pi$
$811$	−376.722	−	376.722i	−0.464515	−	0.464515i	−0.900132	+	0.435617i	$0.856530\pi$
$812$	122.204	+	579.062i	0.150498	+	0.713131i
$813$			32.6399i			0.0401474i
$814$	−21.3388	−	204.454i	−0.0262147	−	0.251172i
$815$		0			0
$816$	10.4881	−	27.0869i	0.0128531	−	0.0331947i
$817$	2.10893	+	2.10893i	0.00258131	+	0.00258131i
$818$	54.5849	−	67.3067i	0.0667298	−	0.0822821i
$819$	786.059	+	786.059i	0.959779	+	0.959779i
$820$		0			0
$821$	−164.380	−	164.380i	−0.200220	−	0.200220i	0.599874	−	0.800094i	$-0.295217\pi$
$821$	−164.380	−	164.380i	−0.200220	−	0.200220i	−0.800094	+	0.599874i	$0.795217\pi$
$822$	−23.5298	+	2.45580i	−0.0286251	+	0.00298759i
$823$	−794.892	−	794.892i	−0.965847	−	0.965847i	0.0335887	−	0.999436i	$-0.489306\pi$
$823$	−794.892	−	794.892i	−0.965847	−	0.965847i	−0.999436	+	0.0335887i	$0.989306\pi$
$824$	−168.599	−	522.770i	−0.204611	−	0.634430i
$825$		0			0
$826$	−48.0898	−	39.0002i	−0.0582201	−	0.0472158i
$827$			696.994i			0.842798i	0.906875	+	0.421399i	$0.138461\pi$
$827$			696.994i			0.842798i	−0.906875	+	0.421399i	$0.861539\pi$
$828$	775.353	−	1190.15i	0.936417	−	1.43738i
$829$	−857.248	−	857.248i	−1.03407	−	1.03407i	−0.999399	−	0.0346759i	$-0.988960\pi$
$829$	−857.248	−	857.248i	−1.03407	−	1.03407i	−0.0346759	−	0.999399i	$-0.511040\pi$
$830$		0			0
$831$	17.1500			0.0206378
$832$	958.650	−	690.134i	1.15222	−	0.829489i
$833$	43.6173	−	43.6173i	0.0523617	−	0.0523617i
$834$	−5.67368	+	0.592160i	−0.00680297	+	0.000710024i
$835$		0			0
$836$	9.17309	−	1.93587i	0.0109726	−	0.00231564i
$837$		−	106.141i		−	0.126811i
$838$	971.811	−	101.428i	1.15968	−	0.121035i
$839$	428.122			0.510277			0.255139	−	0.966905i	$-0.417879\pi$
$839$	428.122			0.510277			0.255139	+	0.966905i	$0.417879\pi$
$840$		0			0
$841$		−	353.787i		−	0.420675i
$842$	1044.16	−	108.979i	1.24010	−	0.129429i
$843$	−16.6991			−0.0198091
$844$	−891.068	−	580.509i	−1.05577	−	0.687807i
$845$		0			0
$846$	−1027.97	+	107.289i	−1.21509	+	0.126819i
$847$	514.503	+	514.503i	0.607441	+	0.607441i
$848$	−1151.88	+	508.842i	−1.35834	+	0.600049i
$849$		−	40.2818i		−	0.0474462i
$850$		0			0
$851$	−814.051	+	814.051i	−0.956582	+	0.956582i
$852$	7.59903	+	36.0078i	0.00891904	+	0.0422627i
$853$	−1569.13			−1.83955			−0.919773	−	0.392451i	$-0.871627\pi$
$853$	−1569.13			−1.83955			−0.919773	+	0.392451i	$0.871627\pi$
$854$	339.257	+	275.133i	0.397257	+	0.322170i
$855$		0			0
$856$	−226.513	+	442.171i	−0.264618	+	0.516555i
$857$	−454.985	+	454.985i	−0.530904	+	0.530904i	−0.920841	−	0.389937i	$-0.872497\pi$
$857$	−454.985	+	454.985i	−0.530904	+	0.530904i	0.389937	+	0.920841i	$0.372497\pi$
$858$	15.5166	−	1.61946i	0.0180846	−	0.00188749i
$859$	−620.538	+	620.538i	−0.722396	+	0.722396i	−0.969093	−	0.246697i	$-0.920655\pi$
$859$	−620.538	+	620.538i	−0.722396	+	0.722396i	0.246697	+	0.969093i	$0.420655\pi$
$860$		0			0
$861$	−9.34995	+	9.34995i	−0.0108594	+	0.0108594i
$862$	189.880	−	234.134i	0.220278	−	0.271617i
$863$	234.305	−	234.305i	0.271500	−	0.271500i	−0.558204	−	0.829704i	$-0.688509\pi$
$863$	234.305	−	234.305i	0.271500	−	0.271500i	0.829704	+	0.558204i	$0.188509\pi$
$864$	−66.5271	−	18.0852i	−0.0769989	−	0.0209319i
$865$		0			0
$866$	−73.1981	−	701.335i	−0.0845243	−	0.809855i
$867$	−7.10467			−0.00819454
$868$	1106.78	+	721.041i	1.27509	+	0.830692i
$869$	−353.514	+	353.514i	−0.406806	+	0.406806i
$870$		0			0
$871$		−	1087.55i		−	1.24863i
$872$	−109.895	−	340.747i	−0.126026	−	0.390765i
$873$	−311.297	−	311.297i	−0.356584	−	0.356584i
$874$	−40.7796	−	33.0718i	−0.0466586	−	0.0378396i
$875$		0			0
$876$	10.6438	+	6.93417i	0.0121505	+	0.00791572i
$877$	−1505.10			−1.71620			−0.858098	−	0.513485i	$-0.828354\pi$
$877$	−1505.10			−1.71620			−0.858098	+	0.513485i	$0.828354\pi$
$878$	−134.015	+	165.249i	−0.152637	+	0.188211i
$879$		−	3.96723i		−	0.00451335i
$880$		0			0
$881$	−1589.76			−1.80450			−0.902250	−	0.431213i	$-0.858086\pi$
$881$	−1589.76			−1.80450			−0.902250	+	0.431213i	$0.858086\pi$
$882$	−56.8108	−	46.0729i	−0.0644113	−	0.0522368i
$883$			512.240i			0.580114i	0.957009	+	0.290057i	$0.0936742\pi$
$883$			512.240i			0.580114i	−0.957009	+	0.290057i	$0.906326\pi$
$884$	937.483	+	610.747i	1.06050	+	0.690891i
$885$		0			0
$886$	296.400	−	365.480i	0.334537	−	0.412505i
$887$	495.921	−	495.921i	0.559099	−	0.559099i	−0.369952	−	0.929051i	$-0.620626\pi$
$887$	495.921	−	495.921i	0.559099	−	0.559099i	0.929051	+	0.369952i	$0.120626\pi$
$888$	24.8455	+	12.7277i	0.0279791	+	0.0143330i
$889$	−570.132			−0.641318
$890$		0			0
$891$	201.118	+	201.118i	0.225722	+	0.225722i
$892$	1338.14	+	871.763i	1.50015	+	0.977313i
$893$			38.2039i			0.0427816i
$894$	42.4751	−	4.43311i	0.0475113	−	0.00495874i
$895$		0			0
$896$	640.516	−	570.851i	0.714862	−	0.637111i
$897$	−61.7808	−	61.7808i	−0.0688749	−	0.0688749i
$898$	121.458	+	98.5013i	0.135254	+	0.109690i
$899$	768.949	+	768.949i	0.855338	+	0.855338i
$900$		0			0
$901$	−843.432	−	843.432i	−0.936106	−	0.936106i
$902$	−12.0633	−	115.582i	−0.0133739	−	0.128140i
$903$	2.54905	+	2.54905i	0.00282287	+	0.00282287i
$904$	604.288	−	194.890i	0.668460	−	0.215586i
$905$		0			0
$906$	−25.6534	+	31.6322i	−0.0283150	+	0.0349142i
$907$			530.597i			0.585002i	0.956265	+	0.292501i	$0.0944875\pi$
$907$			530.597i			0.585002i	−0.956265	+	0.292501i	$0.905512\pi$
$908$	121.311	+	574.828i	0.133602	+	0.633071i
$909$	−265.712	−	265.712i	−0.292313	−	0.292313i
$910$		0			0
$911$	964.958			1.05923			0.529615	−	0.848238i	$-0.322337\pi$
$911$	964.958			1.05923			0.529615	+	0.848238i	$0.322337\pi$
$912$	−0.459709	+	1.18726i	−0.000504067	+	0.00130182i
$913$	299.516	−	299.516i	0.328057	−	0.328057i
$914$	−118.008	−	1130.67i	−0.129111	−	1.23706i
$915$		0			0
$916$	−922.815	−	601.192i	−1.00744	−	0.656323i
$917$			1231.15i			1.34259i
$918$	−6.77878	−	64.9497i	−0.00738430	−	0.0707514i
$919$	0.377866			0.000411171			0.000205586	−	1.00000i	$-0.499935\pi$
$919$	0.377866			0.000411171			0.000205586		1.00000i	$0.499935\pi$
$920$		0			0
$921$			57.4542i			0.0623824i
$922$	46.6674	+	447.136i	0.0506154	+	0.484963i
$923$	−1417.58			−1.53584
$924$	11.0875	−	2.33988i	0.0119994	−	0.00253234i
$925$		0			0
$926$	58.9195	+	564.527i	0.0636280	+	0.609640i
$927$	−436.257	−	436.257i	−0.470612	−	0.470612i
$928$	612.981	−	350.942i	0.660540	−	0.378170i
$929$		−	170.314i		−	0.183330i	−0.995790	−	0.0916650i	$-0.970781\pi$
$929$		−	170.314i		−	0.183330i	0.995790	−	0.0916650i	$-0.0292189\pi$
$930$		0			0
$931$	−1.91181	+	1.91181i	−0.00205350	+	0.00205350i
$932$	268.709	−	412.462i	0.288314	−	0.442556i
$933$	39.2948			0.0421166
$934$	−237.212	+	292.498i	−0.253974	+	0.313167i
$935$		0			0
$936$	604.912	−	1180.84i	0.646274	−	1.26158i
$937$	1277.81	−	1277.81i	1.36372	−	1.36372i	0.494603	−	0.869119i	$-0.335314\pi$
$937$	1277.81	−	1277.81i	1.36372	−	1.36372i	0.869119	−	0.494603i	$-0.164686\pi$
$938$	−82.0006	−	785.675i	−0.0874207	−	0.837606i
$939$	−10.8067	+	10.8067i	−0.0115087	+	0.0115087i
$940$		0			0
$941$	−557.710	+	557.710i	−0.592678	+	0.592678i	−0.938354	−	0.345676i	$-0.887650\pi$
$941$	−557.710	+	557.710i	−0.592678	+	0.592678i	0.345676	+	0.938354i	$0.387650\pi$
$942$	−2.26735	−	1.83880i	−0.00240696	−	0.00195201i
$943$	−460.201	+	460.201i	−0.488018	+	0.488018i
$944$	−26.6828	+	68.9118i	−0.0282657	+	0.0729998i
$945$		0			0
$946$	−31.5109	+	3.28878i	−0.0333096	+	0.00347651i
$947$	978.575			1.03334			0.516671	−	0.856184i	$-0.327171\pi$
$947$	978.575			1.03334			0.516671	+	0.856184i	$0.327171\pi$
$948$	−14.0192	−	66.4297i	−0.0147882	−	0.0700735i
$949$	−346.011	+	346.011i	−0.364606	+	0.364606i
$950$		0			0
$951$			38.8498i			0.0408515i
$952$	723.310	+	370.533i	0.759779	+	0.389215i
$953$	−82.0352	−	82.0352i	−0.0860810	−	0.0860810i	0.662755	−	0.748836i	$-0.269387\pi$
$953$	−82.0352	−	82.0352i	−0.0860810	−	0.0860810i	−0.748836	+	0.662755i	$0.769387\pi$
$954$	−890.915	+	1098.56i	−0.933873	+	1.15153i
$955$		0			0
$956$	1310.48	−	276.562i	1.37080	−	0.289290i
$957$	9.32880			0.00974796
$958$	−272.496	−	220.991i	−0.284443	−	0.230679i
$959$		−	661.919i		−	0.690217i
$960$		0			0
$961$	1466.20			1.52571
$962$	−677.329	+	835.190i	−0.704084	+	0.868181i
$963$			558.024i			0.579464i
$964$	312.936	+	1482.84i	0.324623	+	1.53822i
$965$		0			0
$966$	−49.2901	−	39.9737i	−0.0510250	−	0.0413806i
$967$	−241.731	+	241.731i	−0.249980	+	0.249980i	−0.820962	−	0.570982i	$-0.806562\pi$
$967$	−241.731	+	241.731i	−0.249980	+	0.249980i	0.570982	+	0.820962i	$0.306562\pi$
$968$	395.936	−	772.898i	0.409025	−	0.798448i
$969$	−1.20595			−0.00124453
$970$		0			0
$971$	−970.962	−	970.962i	−0.999961	−	0.999961i	3.91262e−5	−	1.00000i	$-0.499988\pi$
$971$	−970.962	−	970.962i	−0.999961	−	0.999961i	−1.00000		3.91262e-5i	$0.999988\pi$
$972$	−113.680	+	23.9909i	−0.116955	+	0.0246820i
$973$		−	159.606i		−	0.164035i
$974$	15.6763	+	150.200i	0.0160948	+	0.154210i
$975$		0			0
$976$	188.238	−	486.149i	0.192867	−	0.498104i
$977$	−1199.24	−	1199.24i	−1.22747	−	1.22747i	−0.964916	−	0.262558i	$-0.915434\pi$
$977$	−1199.24	−	1199.24i	−1.22747	−	1.22747i	−0.262558	−	0.964916i	$-0.584566\pi$
$978$	−43.1249	+	53.1758i	−0.0440950	+	0.0543720i
$979$	−218.865	−	218.865i	−0.223559	−	0.223559i
$980$		0			0
$981$	−284.357	−	284.357i	−0.289864	−	0.289864i
$982$	−272.285	+	28.4183i	−0.277276	+	0.0289392i
$983$	−269.570	−	269.570i	−0.274232	−	0.274232i	0.556569	−	0.830801i	$-0.312117\pi$
$983$	−269.570	−	269.570i	−0.274232	−	0.274232i	−0.830801	+	0.556569i	$0.812117\pi$
$984$	14.0457	+	7.19525i	0.0142741	+	0.00731225i
$985$		0			0
$986$	519.644	+	421.425i	0.527022	+	0.427408i
$987$			46.1769i			0.0467851i
$988$	−41.0913	−	26.7700i	−0.0415903	−	0.0270951i
$989$	125.463	+	125.463i	0.126859	+	0.126859i
$990$		0			0
$991$	−514.885			−0.519561			−0.259781	−	0.965668i	$-0.583650\pi$
$991$	−514.885			−0.519561			−0.259781	+	0.965668i	$0.583650\pi$
$992$	413.566	−	1521.32i	0.416902	−	1.53359i
$993$	29.7828	−	29.7828i	0.0299928	−	0.0299928i
$994$	−1024.09	+	106.884i	−1.03028	+	0.107529i
$995$		0			0
$996$	11.8778	+	56.2827i	0.0119255	+	0.0565087i
$997$		−	1154.22i		−	1.15769i	−0.815437	−	0.578845i	$-0.803504\pi$
$997$		−	1154.22i		−	1.15769i	0.815437	−	0.578845i	$-0.196496\pi$
$998$	−392.956	+	41.0127i	−0.393744	+	0.0410949i
$999$	62.7605			0.0628233

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.i.b.357.7		44
5.2	odd	4		80.3.t.a.53.5	yes	44
5.3	odd	4		400.3.t.b.293.18		44
5.4	even	2		80.3.i.a.37.16	yes	44
16.13	even	4		400.3.t.b.157.18		44
20.7	even	4		320.3.t.a.113.11		44
20.19	odd	2		320.3.i.a.177.12		44
40.19	odd	2		640.3.i.a.97.11		44
40.27	even	4		640.3.t.a.353.12		44
40.29	even	2		640.3.i.b.97.12		44
40.37	odd	4		640.3.t.b.353.11		44
80.13	odd	4	inner	400.3.i.b.93.7		44
80.19	odd	4		320.3.t.a.17.11		44
80.27	even	4		640.3.i.a.33.12		44
80.29	even	4		80.3.t.a.77.5	yes	44
80.37	odd	4		640.3.i.b.33.11		44
80.59	odd	4		640.3.t.a.417.12		44
80.67	even	4		320.3.i.a.273.11		44
80.69	even	4		640.3.t.b.417.11		44
80.77	odd	4		80.3.i.a.13.16	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.16	✓	44	80.77	odd	4
80.3.i.a.37.16	yes	44	5.4	even	2
80.3.t.a.53.5	yes	44	5.2	odd	4
80.3.t.a.77.5	yes	44	80.29	even	4
320.3.i.a.177.12		44	20.19	odd	2
320.3.i.a.273.11		44	80.67	even	4
320.3.t.a.17.11		44	80.19	odd	4
320.3.t.a.113.11		44	20.7	even	4
400.3.i.b.93.7		44	80.13	odd	4	inner
400.3.i.b.357.7		44	1.1	even	1	trivial
400.3.t.b.157.18		44	16.13	even	4
400.3.t.b.293.18		44	5.3	odd	4
640.3.i.a.33.12		44	80.27	even	4
640.3.i.a.97.11		44	40.19	odd	2
640.3.i.b.33.11		44	80.37	odd	4
640.3.i.b.97.12		44	40.29	even	2
640.3.t.a.353.12		44	40.27	even	4
640.3.t.a.417.12		44	80.59	odd	4
640.3.t.b.353.11		44	40.37	odd	4
640.3.t.b.417.11		44	80.69	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25977 + 1.55338i) q^{2} -0.119786i q^{3} +(-0.825960 - 3.91379i) q^{4} +(0.186072 + 0.150902i) q^{6} +(-4.73972 + 4.73972i) q^{7} +(7.12012 + 3.64745i) q^{8} +8.98565 q^{9} +O(q^{10})\)	\(q+(-1.25977 + 1.55338i) q^{2} -0.119786i q^{3} +(-0.825960 - 3.91379i) q^{4} +(0.186072 + 0.150902i) q^{6} +(-4.73972 + 4.73972i) q^{7} +(7.12012 + 3.64745i) q^{8} +8.98565 q^{9} +(2.49487 + 2.49487i) q^{11} +(-0.468816 + 0.0989381i) q^{12} -18.4567i q^{13} +(-1.39162 - 13.3335i) q^{14} +(-14.6356 + 6.46528i) q^{16} +(-10.7165 - 10.7165i) q^{17} +(-11.3199 + 13.9581i) q^{18} +(0.469722 + 0.469722i) q^{19} +(0.567750 + 0.567750i) q^{21} +(-7.01842 + 0.732510i) q^{22} +(27.9445 + 27.9445i) q^{23} +(0.436912 - 0.852887i) q^{24} +(28.6701 + 23.2511i) q^{26} -2.15442i q^{27} +(22.4651 + 14.6355i) q^{28} +(15.6079 + 15.6079i) q^{29} +49.2667 q^{31} +(8.39445 - 30.8793i) q^{32} +(0.298849 - 0.298849i) q^{33} +(30.1472 - 3.14645i) q^{34} +(-7.42179 - 35.1680i) q^{36} +29.1310i q^{37} +(-1.32140 + 0.137914i) q^{38} -2.21084 q^{39} +16.4684i q^{41} +(-1.59716 + 0.166695i) q^{42} +4.48974 q^{43} +(7.70373 - 11.8251i) q^{44} +(-78.6119 + 8.20470i) q^{46} +(40.6666 + 40.6666i) q^{47} +(0.774447 + 1.75313i) q^{48} +4.07009i q^{49} +(-1.28369 + 1.28369i) q^{51} +(-72.2356 + 15.2445i) q^{52} +78.7038 q^{53} +(3.34663 + 2.71407i) q^{54} +(-51.0353 + 16.4595i) q^{56} +(0.0562658 - 0.0562658i) q^{57} +(-43.9073 + 4.58259i) q^{58} +(3.26583 - 3.26583i) q^{59} +(-23.0393 + 23.0393i) q^{61} +(-62.0647 + 76.5297i) q^{62} +(-42.5895 + 42.5895i) q^{63} +(37.3922 + 51.9406i) q^{64} +(0.0877441 + 0.840705i) q^{66} +58.9247 q^{67} +(-33.0909 + 50.7938i) q^{68} +(3.34734 - 3.34734i) q^{69} -76.8059i q^{71} +(63.9789 + 32.7747i) q^{72} +(-18.7472 - 18.7472i) q^{73} +(-45.2514 - 36.6984i) q^{74} +(1.45042 - 2.22637i) q^{76} -23.6499 q^{77} +(2.78515 - 3.43427i) q^{78} +141.697i q^{79} +80.6128 q^{81} +(-25.5817 - 20.7464i) q^{82} -120.053i q^{83} +(1.75312 - 2.69100i) q^{84} +(-5.65604 + 6.97426i) q^{86} +(1.86960 - 1.86960i) q^{87} +(8.66383 + 26.8636i) q^{88} -87.7260 q^{89} +(87.4794 + 87.4794i) q^{91} +(86.2879 - 132.450i) q^{92} -5.90143i q^{93} +(-114.401 + 11.9400i) q^{94} +(-3.69890 - 1.00553i) q^{96} +(-34.6438 - 34.6438i) q^{97} +(-6.32239 - 5.12738i) q^{98} +(22.4180 + 22.4180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} + 4 q^{4} - 4 q^{6} + 8 q^{8} - 108 q^{9}+O(q^{10}) \) 44 * q + 2 * q^2 + 4 * q^4 - 4 * q^6 + 8 * q^8 - 108 * q^9	\( 44 q + 2 q^{2} + 4 q^{4} - 4 q^{6} + 8 q^{8} - 108 q^{9} - 4 q^{11} + 8 q^{12} + 24 q^{16} + 4 q^{17} - 22 q^{18} + 32 q^{19} - 4 q^{21} - 92 q^{22} + 36 q^{24} - 52 q^{26} - 36 q^{28} - 8 q^{31} + 132 q^{32} + 4 q^{33} - 88 q^{34} - 116 q^{36} + 216 q^{38} + 72 q^{39} - 16 q^{42} - 124 q^{43} - 168 q^{44} + 108 q^{46} + 4 q^{47} - 340 q^{48} - 100 q^{51} - 48 q^{52} + 4 q^{53} + 228 q^{54} - 172 q^{56} - 36 q^{57} - 16 q^{58} + 64 q^{59} - 36 q^{61} + 356 q^{62} + 200 q^{63} - 176 q^{64} + 276 q^{66} + 292 q^{67} + 72 q^{68} - 60 q^{69} - 448 q^{72} - 48 q^{73} + 284 q^{74} + 252 q^{76} - 192 q^{77} - 620 q^{78} + 100 q^{81} + 240 q^{82} + 288 q^{84} + 20 q^{86} - 36 q^{87} + 624 q^{88} + 188 q^{91} + 412 q^{92} - 340 q^{94} - 24 q^{96} + 4 q^{97} + 78 q^{98} - 92 q^{99}+O(q^{100}) \) 44 * q + 2 * q^2 + 4 * q^4 - 4 * q^6 + 8 * q^8 - 108 * q^9 - 4 * q^11 + 8 * q^12 + 24 * q^16 + 4 * q^17 - 22 * q^18 + 32 * q^19 - 4 * q^21 - 92 * q^22 + 36 * q^24 - 52 * q^26 - 36 * q^28 - 8 * q^31 + 132 * q^32 + 4 * q^33 - 88 * q^34 - 116 * q^36 + 216 * q^38 + 72 * q^39 - 16 * q^42 - 124 * q^43 - 168 * q^44 + 108 * q^46 + 4 * q^47 - 340 * q^48 - 100 * q^51 - 48 * q^52 + 4 * q^53 + 228 * q^54 - 172 * q^56 - 36 * q^57 - 16 * q^58 + 64 * q^59 - 36 * q^61 + 356 * q^62 + 200 * q^63 - 176 * q^64 + 276 * q^66 + 292 * q^67 + 72 * q^68 - 60 * q^69 - 448 * q^72 - 48 * q^73 + 284 * q^74 + 252 * q^76 - 192 * q^77 - 620 * q^78 + 100 * q^81 + 240 * q^82 + 288 * q^84 + 20 * q^86 - 36 * q^87 + 624 * q^88 + 188 * q^91 + 412 * q^92 - 340 * q^94 - 24 * q^96 + 4 * q^97 + 78 * q^98 - 92 * q^99

Introduction

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