LMFDB - Embedded newform 525.3.s.h.124.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(124,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("525.124");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.s (of order $6$, degree $2$, not 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:	$14.3052138789$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 22x^{14} + 343x^{12} - 2542x^{10} + 13621x^{8} - 35080x^{6} + 64300x^{4} - 28000x^{2} + 10000 $ x^16 - 22x^14 + 343x^12 - 2542x^10 + 13621x^8 - 35080x^6 + 64300x^4 - 28000*x^2 + 10000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			124.4
Root			$-0.583237 + 0.336732i$ of defining polynomial
Character	$\chi$	$=$	525.124
Dual form			525.3.s.h.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.583237 - 0.336732i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-1.77322 - 3.07131i) q^{4} -1.16647i q^{6} +(-1.55742 - 6.82455i) q^{7} +5.08226i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.583237 - 0.336732i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-1.77322 - 3.07131i) q^{4} -1.16647i q^{6} +(-1.55742 - 6.82455i) q^{7} +5.08226i q^{8} +(-1.50000 + 2.59808i) q^{9} +(0.0223800 + 0.0387632i) q^{11} +(3.07131 - 5.31967i) q^{12} +23.0010 q^{13} +(-1.38970 + 4.50476i) q^{14} +(-5.38154 + 9.32109i) q^{16} +(-4.71286 - 8.16292i) q^{17} +(1.74971 - 1.01020i) q^{18} +(-0.991050 - 0.572183i) q^{19} +(8.88806 - 8.24636i) q^{21} -0.0301442i q^{22} +(-38.3133 - 22.1202i) q^{23} +(-7.62339 + 4.40136i) q^{24} +(-13.4150 - 7.74518i) q^{26} -5.19615 q^{27} +(-18.1987 + 16.8848i) q^{28} -53.0004 q^{29} +(19.5690 - 11.2982i) q^{31} +(23.8829 - 13.7888i) q^{32} +(-0.0387632 + 0.0671399i) q^{33} +6.34788i q^{34} +10.6393 q^{36} +(-36.6186 - 21.1418i) q^{37} +(0.385344 + 0.667436i) q^{38} +(19.9195 + 34.5015i) q^{39} +38.2787i q^{41} +(-7.96065 + 1.81669i) q^{42} -76.5222i q^{43} +(0.0793693 - 0.137472i) q^{44} +(14.8971 + 25.8026i) q^{46} +(13.5718 - 23.5070i) q^{47} -18.6422 q^{48} +(-44.1489 + 21.2574i) q^{49} +(8.16292 - 14.1386i) q^{51} +(-40.7860 - 70.6434i) q^{52} +(-16.4439 + 9.49388i) q^{53} +(3.03059 + 1.74971i) q^{54} +(34.6841 - 7.91521i) q^{56} -1.98210i q^{57} +(30.9118 + 17.8469i) q^{58} +(4.21731 - 2.43486i) q^{59} +(-33.6432 - 19.4239i) q^{61} -15.2178 q^{62} +(20.0668 + 6.19052i) q^{63} +24.4798 q^{64} +(0.0452163 - 0.0261056i) q^{66} +(-6.06978 + 3.50439i) q^{67} +(-16.7139 + 28.9494i) q^{68} -76.6266i q^{69} -46.8735 q^{71} +(-13.2041 - 7.62339i) q^{72} +(-41.7976 - 72.3956i) q^{73} +(14.2382 + 24.6613i) q^{74} +4.05843i q^{76} +(0.229686 - 0.213104i) q^{77} -26.8301i q^{78} +(10.2397 - 17.7357i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(12.8897 - 22.3256i) q^{82} +125.683 q^{83} +(-41.0877 - 12.6754i) q^{84} +(-25.7674 + 44.6305i) q^{86} +(-45.8997 - 79.5006i) q^{87} +(-0.197005 + 0.113741i) q^{88} +(-40.4455 - 23.3512i) q^{89} +(-35.8223 - 156.972i) q^{91} +156.896i q^{92} +(33.8945 + 19.5690i) q^{93} +(-15.8311 + 9.14010i) q^{94} +(41.3663 + 23.8829i) q^{96} -3.11494 q^{97} +(32.9073 + 2.46826i) q^{98} -0.134280 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} - 24 q^{9}+O(q^{10}) $ 16 * q + 12 * q^4 - 24 * q^9	$ 16 q + 12 q^{4} - 24 q^{9} + 40 q^{11} + 32 q^{14} - 4 q^{16} + 96 q^{21} - 96 q^{24} + 240 q^{26} + 200 q^{29} - 252 q^{31} - 72 q^{36} + 24 q^{39} + 36 q^{44} - 164 q^{46} - 76 q^{49} + 36 q^{51} - 36 q^{54} + 392 q^{56} + 108 q^{59} - 792 q^{61} + 8 q^{64} + 48 q^{66} + 328 q^{71} + 280 q^{74} + 412 q^{79} - 72 q^{81} - 264 q^{84} + 356 q^{86} - 564 q^{89} - 228 q^{91} - 60 q^{94} - 216 q^{96} - 240 q^{99}+O(q^{100}) $ 16 * q + 12 * q^4 - 24 * q^9 + 40 * q^11 + 32 * q^14 - 4 * q^16 + 96 * q^21 - 96 * q^24 + 240 * q^26 + 200 * q^29 - 252 * q^31 - 72 * q^36 + 24 * q^39 + 36 * q^44 - 164 * q^46 - 76 * q^49 + 36 * q^51 - 36 * q^54 + 392 * q^56 + 108 * q^59 - 792 * q^61 + 8 * q^64 + 48 * q^66 + 328 * q^71 + 280 * q^74 + 412 * q^79 - 72 * q^81 - 264 * q^84 + 356 * q^86 - 564 * q^89 - 228 * q^91 - 60 * q^94 - 216 * q^96 - 240 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.583237	−	0.336732i	−0.291618	−	0.168366i	0.347053	−	0.937845i	$-0.387182\pi$
$2$	−0.583237	−	0.336732i	−0.291618	−	0.168366i	−0.638671	+	0.769480i	$0.720516\pi$
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$4$	−1.77322	−	3.07131i	−0.443306	−	0.767828i
$5$		0			0
$5$		0			0
$6$		−	1.16647i		−	0.194412i
$7$	−1.55742	−	6.82455i	−0.222489	−	0.974935i
$7$	−1.55742	−	6.82455i	−0.222489	−	0.974935i
$8$			5.08226i			0.635282i
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$		0			0
$11$	0.0223800	+	0.0387632i	0.00203454	+	0.00352393i	0.867041	−	0.498237i	$-0.166019\pi$
$11$	0.0223800	+	0.0387632i	0.00203454	+	0.00352393i	−0.865006	+	0.501761i	$0.832686\pi$
$12$	3.07131	−	5.31967i	0.255943	−	0.443306i
$13$	23.0010			1.76931			0.884655	−	0.466246i	$-0.154394\pi$
$13$	23.0010			1.76931			0.884655	+	0.466246i	$0.154394\pi$
$14$	−1.38970	+	4.50476i	−0.0992641	+	0.321768i
$15$		0			0
$16$	−5.38154	+	9.32109i	−0.336346	+	0.582568i
$17$	−4.71286	−	8.16292i	−0.277227	−	0.480172i	0.693467	−	0.720488i	$-0.256082\pi$
$17$	−4.71286	−	8.16292i	−0.277227	−	0.480172i	−0.970695	+	0.240316i	$0.922749\pi$
$18$	1.74971	−	1.01020i	0.0972061	−	0.0561220i
$19$	−0.991050	−	0.572183i	−0.0521605	−	0.0301149i	0.473693	−	0.880690i	$-0.342921\pi$
$19$	−0.991050	−	0.572183i	−0.0521605	−	0.0301149i	−0.525853	+	0.850575i	$0.676254\pi$
$20$		0			0
$21$	8.88806	−	8.24636i	0.423241	−	0.392684i
$22$		−	0.0301442i		−	0.00137019i
$23$	−38.3133	−	22.1202i	−1.66580	−	0.961748i	−0.969866	−	0.243637i	$-0.921659\pi$
$23$	−38.3133	−	22.1202i	−1.66580	−	0.961748i	−0.695929	−	0.718110i	$-0.745007\pi$
$24$	−7.62339	+	4.40136i	−0.317641	+	0.183390i
$25$		0			0
$26$	−13.4150	−	7.74518i	−0.515963	−	0.297891i
$27$	−5.19615			−0.192450
$28$	−18.1987	+	16.8848i	−0.649952	+	0.603028i
$29$	−53.0004			−1.82760			−0.913799	−	0.406166i	$-0.866866\pi$
$29$	−53.0004			−1.82760			−0.913799	+	0.406166i	$0.866866\pi$
$30$		0			0
$31$	19.5690	−	11.2982i	0.631258	−	0.364457i	−0.149981	−	0.988689i	$-0.547921\pi$
$31$	19.5690	−	11.2982i	0.631258	−	0.364457i	0.781239	+	0.624232i	$0.214588\pi$
$32$	23.8829	−	13.7888i	0.746340	−	0.430899i
$33$	−0.0387632	+	0.0671399i	−0.00117464	+	0.00203454i
$34$			6.34788i			0.186702i
$35$		0			0
$36$	10.6393			0.295537
$37$	−36.6186	−	21.1418i	−0.989693	−	0.571400i	−0.0845106	−	0.996423i	$-0.526933\pi$
$37$	−36.6186	−	21.1418i	−0.989693	−	0.571400i	−0.905183	+	0.425023i	$0.860266\pi$
$38$	0.385344	+	0.667436i	0.0101406	+	0.0175641i
$39$	19.9195	+	34.5015i	0.510756	+	0.884655i
$40$		0			0
$41$			38.2787i			0.933628i	0.884356	+	0.466814i	$0.154598\pi$
$41$			38.2787i			0.933628i	−0.884356	+	0.466814i	$0.845402\pi$
$42$	−7.96065	+	1.81669i	−0.189539	+	0.0432545i
$43$		−	76.5222i		−	1.77959i	−0.456365	−	0.889793i	$-0.650849\pi$
$43$		−	76.5222i		−	1.77959i	0.456365	−	0.889793i	$-0.349151\pi$
$44$	0.0793693	−	0.137472i	0.00180385	−	0.00312436i
$45$		0			0
$46$	14.8971	+	25.8026i	0.323851	+	0.560926i
$47$	13.5718	−	23.5070i	0.288761	−	0.500149i	−0.684753	−	0.728775i	$-0.740090\pi$
$47$	13.5718	−	23.5070i	0.288761	−	0.500149i	0.973514	+	0.228626i	$0.0734233\pi$
$48$	−18.6422			−0.388379
$49$	−44.1489	+	21.2574i	−0.900998	+	0.433824i
$50$		0			0
$51$	8.16292	−	14.1386i	0.160057	−	0.277227i
$52$	−40.7860	−	70.6434i	−0.784345	−	1.35853i
$53$	−16.4439	+	9.49388i	−0.310262	+	0.179130i	−0.647044	−	0.762453i	$-0.723995\pi$
$53$	−16.4439	+	9.49388i	−0.310262	+	0.179130i	0.336782	+	0.941583i	$0.390662\pi$
$54$	3.03059	+	1.74971i	0.0561220	+	0.0324020i
$55$		0			0
$56$	34.6841	−	7.91521i	0.619359	−	0.141343i
$57$		−	1.98210i		−	0.0347737i
$58$	30.9118	+	17.8469i	0.532961	+	0.307705i
$59$	4.21731	−	2.43486i	0.0714798	−	0.0412689i	−0.463834	−	0.885922i	$-0.653527\pi$
$59$	4.21731	−	2.43486i	0.0714798	−	0.0412689i	0.535314	+	0.844653i	$0.320193\pi$
$60$		0			0
$61$	−33.6432	−	19.4239i	−0.551528	−	0.318425i	0.198210	−	0.980160i	$-0.436487\pi$
$61$	−33.6432	−	19.4239i	−0.551528	−	0.318425i	−0.749738	+	0.661735i	$0.769821\pi$
$62$	−15.2178			−0.245449
$63$	20.0668	+	6.19052i	0.318521	+	0.0982623i
$64$	24.4798			0.382497
$65$		0			0
$66$	0.0452163	−	0.0261056i	0.000685095	−	0.000395540i
$67$	−6.06978	+	3.50439i	−0.0905938	+	0.0523043i	−0.544612	−	0.838688i	$-0.683323\pi$
$67$	−6.06978	+	3.50439i	−0.0905938	+	0.0523043i	0.454019	+	0.890992i	$0.349990\pi$
$68$	−16.7139	+	28.9494i	−0.245793	+	0.425726i
$69$		−	76.6266i		−	1.11053i
$70$		0			0
$71$	−46.8735			−0.660190			−0.330095	−	0.943948i	$-0.607081\pi$
$71$	−46.8735			−0.660190			−0.330095	+	0.943948i	$0.607081\pi$
$72$	−13.2041	−	7.62339i	−0.183390	−	0.105880i
$73$	−41.7976	−	72.3956i	−0.572570	−	0.991720i	−0.996301	−	0.0859319i	$-0.972613\pi$
$73$	−41.7976	−	72.3956i	−0.572570	−	0.991720i	0.423731	−	0.905788i	$-0.360720\pi$
$74$	14.2382	+	24.6613i	0.192408	+	0.333261i
$75$		0			0
$76$			4.05843i			0.0534004i
$77$	0.229686	−	0.213104i	0.00298294	−	0.00276758i
$78$		−	26.8301i		−	0.343975i
$79$	10.2397	−	17.7357i	0.129617	−	0.224502i	−0.793912	−	0.608033i	$-0.791959\pi$
$79$	10.2397	−	17.7357i	0.129617	−	0.224502i	0.923528	+	0.383531i	$0.125292\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	12.8897	−	22.3256i	0.157191	−	0.272263i
$83$	125.683			1.51425			0.757124	−	0.653271i	$-0.226604\pi$
$83$	125.683			1.51425			0.757124	+	0.653271i	$0.226604\pi$
$84$	−41.0877	−	12.6754i	−0.489139	−	0.150897i
$85$		0			0
$86$	−25.7674	+	44.6305i	−0.299621	+	0.518960i
$87$	−45.8997	−	79.5006i	−0.527582	−	0.913799i
$88$	−0.197005	+	0.113741i	−0.00223869	+	0.00129251i
$89$	−40.4455	−	23.3512i	−0.454444	−	0.262373i	0.255261	−	0.966872i	$-0.417838\pi$
$89$	−40.4455	−	23.3512i	−0.454444	−	0.262373i	−0.709705	+	0.704499i	$0.751172\pi$
$90$		0			0
$91$	−35.8223	−	156.972i	−0.393651	−	1.72496i
$92$			156.896i			1.70539i
$93$	33.8945	+	19.5690i	0.364457	+	0.210419i
$94$	−15.8311	+	9.14010i	−0.168416	+	0.0972351i
$95$		0			0
$96$	41.3663	+	23.8829i	0.430899	+	0.248780i
$97$	−3.11494			−0.0321128			−0.0160564	−	0.999871i	$-0.505111\pi$
$97$	−3.11494			−0.0321128			−0.0160564	+	0.999871i	$0.505111\pi$
$98$	32.9073	+	2.46826i	0.335789	+	0.0251863i
$99$	−0.134280			−0.00135636
$100$		0			0
$101$	−77.4555	+	44.7189i	−0.766886	+	0.442762i	−0.831763	−	0.555132i	$-0.812668\pi$
$101$	−77.4555	+	44.7189i	−0.766886	+	0.442762i	0.0648768	+	0.997893i	$0.479335\pi$
$102$	−9.52183	+	5.49743i	−0.0933512	+	0.0538964i
$103$	−45.6906	+	79.1385i	−0.443598	+	0.768335i	−0.997953	−	0.0639453i	$-0.979632\pi$
$103$	−45.6906	+	79.1385i	−0.443598	+	0.768335i	0.554355	+	0.832280i	$0.312965\pi$
$104$			116.897i			1.12401i
$105$		0			0
$106$	12.7876			0.120637
$107$	91.0219	+	52.5515i	0.850672	+	0.491136i	0.860877	−	0.508812i	$-0.169915\pi$
$107$	91.0219	+	52.5515i	0.850672	+	0.491136i	−0.0102057	+	0.999948i	$0.503249\pi$
$108$	9.21394	+	15.9590i	0.0853143	+	0.147769i
$109$	27.8507	+	48.2388i	0.255511	+	0.442558i	0.965034	−	0.262124i	$-0.0844230\pi$
$109$	27.8507	+	48.2388i	0.255511	+	0.442558i	−0.709523	+	0.704682i	$0.751090\pi$
$110$		0			0
$111$		−	73.2373i		−	0.659795i
$112$	71.9936	+	22.2097i	0.642800	+	0.198301i
$113$			5.25425i			0.0464978i	0.999730	+	0.0232489i	$0.00740102\pi$
$113$			5.25425i			0.0464978i	−0.999730	+	0.0232489i	$0.992599\pi$
$114$	−0.667436	+	1.15603i	−0.00585470	+	0.0101406i
$115$		0			0
$116$	93.9815	+	162.781i	0.810185	+	1.40328i
$117$	−34.5015	+	59.7584i	−0.294885	+	0.510756i
$118$	−3.27958			−0.0277931
$119$	−48.3683	+	44.8763i	−0.406457	+	0.377111i
$120$		0			0
$121$	60.4990	−	104.787i	0.499992	−	0.866011i
$122$	13.0813	+	22.6575i	0.107224	+	0.185717i
$123$	−57.4181	+	33.1504i	−0.466814	+	0.269515i
$124$	−69.4005	−	40.0684i	−0.559681	−	0.323132i
$125$		0			0
$126$	−9.61916	−	10.3677i	−0.0763425	−	0.0822832i
$127$		−	5.54989i		−	0.0436999i	−0.999761	−	0.0218500i	$-0.993044\pi$
$127$		−	5.54989i		−	0.0436999i	0.999761	−	0.0218500i	$-0.00695561\pi$
$128$	−109.809	−	63.3983i	−0.857883	−	0.495299i
$129$	114.783	−	66.2701i	0.889793	−	0.513722i
$130$		0			0
$131$	−144.212	−	83.2606i	−1.10085	−	0.635577i	−0.164407	−	0.986393i	$-0.552571\pi$
$131$	−144.212	−	83.2606i	−1.10085	−	0.635577i	−0.936445	+	0.350815i	$0.885904\pi$
$132$	0.274943			0.00208290
$133$	−2.36141	+	7.65460i	−0.0177550	+	0.0575534i
$134$	4.72016			0.0352251
$135$		0			0
$136$	41.4861	−	23.9520i	0.305045	−	0.176118i
$137$	63.1733	−	36.4731i	0.461119	−	0.266227i	−0.251395	−	0.967884i	$-0.580889\pi$
$137$	63.1733	−	36.4731i	0.461119	−	0.266227i	0.712515	+	0.701657i	$0.247556\pi$
$138$	−25.8026	+	44.6914i	−0.186975	+	0.323851i
$139$		−	114.994i		−	0.827292i	−0.910438	−	0.413646i	$-0.864255\pi$
$139$		−	114.994i		−	0.827292i	0.910438	−	0.413646i	$-0.135745\pi$
$140$		0			0
$141$	47.0140			0.333433
$142$	27.3383	+	15.7838i	0.192523	+	0.111153i
$143$	0.514762	+	0.891594i	0.00359973	+	0.00623492i
$144$	−16.1446	−	27.9633i	−0.112115	−	0.194189i
$145$		0			0
$146$			56.2983i			0.385605i
$147$	−70.1201	−	47.8139i	−0.477008	−	0.325265i
$148$			149.956i			1.01322i
$149$	36.3729	−	62.9997i	0.244113	−	0.422817i	−0.717769	−	0.696282i	$-0.754836\pi$
$149$	36.3729	−	62.9997i	0.244113	−	0.422817i	0.961882	+	0.273465i	$0.0881698\pi$
$150$		0			0
$151$	63.5643	+	110.097i	0.420956	+	0.729117i	0.996033	−	0.0889823i	$-0.0283615\pi$
$151$	63.5643	+	110.097i	0.420956	+	0.729117i	−0.575078	+	0.818099i	$0.695028\pi$
$152$	2.90798	−	5.03677i	0.0191315	−	0.0331366i
$153$	28.2772			0.184818
$154$	−0.205720	+	0.0469471i	−0.00133585	+	0.000304851i
$155$		0			0
$156$	70.6434	−	122.358i	0.452842	−	0.784345i
$157$	75.5327	+	130.826i	0.481100	+	0.833290i	0.999765	−	0.0216880i	$-0.00690404\pi$
$157$	75.5327	+	130.826i	0.481100	+	0.833290i	−0.518665	+	0.854978i	$0.673571\pi$
$158$	−11.9443	+	6.89607i	−0.0755971	+	0.0436460i
$159$	−28.4816	−	16.4439i	−0.179130	−	0.103421i
$160$		0			0
$161$	−91.2904	+	295.921i	−0.567021	+	1.83802i
$162$			6.06117i			0.0374146i
$163$	−51.8990	−	29.9639i	−0.318399	−	0.183828i	0.332280	−	0.943181i	$-0.392182\pi$
$163$	−51.8990	−	29.9639i	−0.318399	−	0.183828i	−0.650679	+	0.759353i	$0.725515\pi$
$164$	117.566	−	67.8768i	0.716866	−	0.413883i
$165$		0			0
$166$	−73.3027	−	42.3213i	−0.441582	−	0.254948i
$167$	224.089			1.34185			0.670924	−	0.741526i	$-0.265898\pi$
$167$	224.089			1.34185			0.670924	+	0.741526i	$0.265898\pi$
$168$	41.9101	+	45.1714i	0.249465	+	0.268877i
$169$	360.047			2.13046
$170$		0			0
$171$	2.97315	−	1.71655i	0.0173868	−	0.0100383i
$172$	−235.024	+	135.691i	−1.36642	+	0.788901i
$173$	95.3092	−	165.080i	0.550920	−	0.954221i	−0.447288	−	0.894390i	$-0.647610\pi$
$173$	95.3092	−	165.080i	0.550920	−	0.954221i	0.998208	−	0.0598317i	$-0.0190564\pi$
$174$			61.8235i			0.355307i
$175$		0			0
$176$	−0.481754			−0.00273724
$177$	7.30459	+	4.21731i	0.0412689	+	0.0238266i
$178$	15.7262	+	27.2386i	0.0883494	+	0.153026i
$179$	108.931	+	188.674i	0.608553	+	1.05404i	0.991479	+	0.130265i	$0.0415829\pi$
$179$	108.931	+	188.674i	0.608553	+	1.05404i	−0.382926	+	0.923779i	$0.625084\pi$
$180$		0			0
$181$			39.0804i			0.215914i	0.994156	+	0.107957i	$0.0344309\pi$
$181$			39.0804i			0.215914i	−0.994156	+	0.107957i	$0.965569\pi$
$182$	−31.9645	+	103.614i	−0.175629	+	0.569308i
$183$		−	67.2865i		−	0.367686i
$184$	112.421	−	194.718i	0.610981	−	1.05825i
$185$		0			0
$186$	−13.1790	−	22.8267i	−0.0708549	−	0.122724i
$187$	0.210947	−	0.365372i	0.00112806	−	0.00195386i
$188$	−96.2632			−0.512038
$189$	8.09259	+	35.4614i	0.0428179	+	0.187626i
$190$		0			0
$191$	−94.7586	+	164.127i	−0.496118	+	0.859302i	−0.999990	−	0.00447651i	$-0.998575\pi$
$191$	−94.7586	+	164.127i	−0.496118	+	0.859302i	0.503872	+	0.863778i	$0.331908\pi$
$192$	21.2001	+	36.7197i	0.110417	+	0.191249i
$193$	236.547	−	136.570i	1.22563	−	0.707619i	0.259519	−	0.965738i	$-0.416436\pi$
$193$	236.547	−	136.570i	1.22563	−	0.707619i	0.966113	+	0.258119i	$0.0831027\pi$
$194$	1.81675	+	1.04890i	0.00936467	+	0.00540669i
$195$		0			0
$196$	143.574	+	97.9010i	0.732520	+	0.499495i
$197$			198.898i			1.00963i	0.863226	+	0.504817i	$0.168440\pi$
$197$			198.898i			1.00963i	−0.863226	+	0.504817i	$0.831560\pi$
$198$	0.0783168	+	0.0452163i	0.000395540	+	0.000228365i
$199$	−33.2334	+	19.1873i	−0.167002	+	0.0964185i	−0.581171	−	0.813781i	$-0.697405\pi$
$199$	−33.2334	+	19.1873i	−0.167002	+	0.0964185i	0.414170	+	0.910200i	$0.364072\pi$
$200$		0			0
$201$	−10.5132	−	6.06978i	−0.0523043	−	0.0301979i
$202$	60.2331			0.298184
$203$	82.5438	+	361.704i	0.406620	+	1.78179i
$204$	−57.8987			−0.283817
$205$		0			0
$206$	53.2969	−	30.7710i	0.258723	−	0.149374i
$207$	114.940	−	66.3606i	0.555265	−	0.320583i
$208$	−123.781	+	214.395i	−0.595100	+	1.03074i
$209$		−	0.0512217i		−	0.000245080i
$210$		0			0
$211$	−127.283			−0.603238			−0.301619	−	0.953429i	$-0.597527\pi$
$211$	−127.283			−0.603238			−0.301619	+	0.953429i	$0.597527\pi$
$212$	58.3173	+	33.6695i	0.275082	+	0.158819i
$213$	−40.5936	−	70.3102i	−0.190580	−	0.330095i
$214$	−35.3915	−	61.2999i	−0.165381	−	0.286448i
$215$		0			0
$216$		−	26.4082i		−	0.122260i
$217$	−107.582	−	115.954i	−0.495770	−	0.534349i
$218$		−	37.5129i		−	0.172077i
$219$	72.3956	−	125.393i	0.330573	−	0.572570i
$220$		0			0
$221$	−108.401	−	187.756i	−0.490501	−	0.849573i
$222$	−24.6613	+	42.7147i	−0.111087	+	0.192408i
$223$	293.558			1.31641			0.658203	−	0.752841i	$-0.271317\pi$
$223$	293.558			1.31641			0.658203	+	0.752841i	$0.271317\pi$
$224$	−131.298	−	141.515i	−0.586151	−	0.631763i
$225$		0			0
$226$	1.76927	−	3.06447i	0.00782864	−	0.0135596i
$227$	107.740	+	186.611i	0.474626	+	0.822077i	0.999578	−	0.0290554i	$-0.00924994\pi$
$227$	107.740	+	186.611i	0.474626	+	0.822077i	−0.524952	+	0.851132i	$0.675917\pi$
$228$	−6.08765	+	3.51471i	−0.0267002	+	0.0154154i
$229$	−124.938	−	72.1332i	−0.545582	−	0.314992i	0.201756	−	0.979436i	$-0.435335\pi$
$229$	−124.938	−	72.1332i	−0.545582	−	0.314992i	−0.747338	+	0.664444i	$0.768668\pi$
$230$		0			0
$231$	0.518570	+	0.159976i	0.00224489	+	0.000692539i
$232$		−	269.361i		−	1.16104i
$233$	−248.058	−	143.216i	−1.06463	−	0.614662i	−0.137918	−	0.990444i	$-0.544041\pi$
$233$	−248.058	−	143.216i	−1.06463	−	0.614662i	−0.926708	+	0.375781i	$0.877374\pi$
$234$	40.2451	−	23.2355i	0.171988	−	0.0992971i
$235$		0			0
$236$	−14.9565	−	8.63511i	−0.0633748	−	0.0365895i
$237$	35.4714			0.149668
$238$	43.3214	−	9.88632i	0.182023	−	0.0415392i
$239$	413.420			1.72979			0.864895	−	0.501954i	$-0.167385\pi$
$239$	413.420			1.72979			0.864895	+	0.501954i	$0.167385\pi$
$240$		0			0
$241$	256.252	−	147.947i	1.06329	−	0.613890i	0.136948	−	0.990578i	$-0.456271\pi$
$241$	256.252	−	147.947i	1.06329	−	0.613890i	0.926340	+	0.376689i	$0.122937\pi$
$242$	−70.5705	+	40.7439i	−0.291613	+	0.168363i
$243$	7.79423	−	13.5000i	0.0320750	−	0.0555556i
$244$			137.772i			0.564639i
$245$		0			0
$246$	44.6511			0.181509
$247$	−22.7952	−	13.1608i	−0.0922881	−	0.0532826i
$248$	57.4202	+	99.4547i	0.231533	+	0.401027i
$249$	108.844	+	188.524i	0.437126	+	0.757124i
$250$		0			0
$251$		−	311.712i		−	1.24188i	−0.783858	−	0.620940i	$-0.786751\pi$
$251$		−	311.712i		−	1.24188i	0.783858	−	0.620940i	$-0.213249\pi$
$252$	−16.5699	−	72.6087i	−0.0657537	−	0.288130i
$253$		−	1.98020i		−	0.00782686i
$254$	−1.86882	+	3.23690i	−0.00735758	+	0.0127437i
$255$		0			0
$256$	−6.26320	−	10.8482i	−0.0244656	−	0.0423757i
$257$	72.3619	−	125.335i	0.281564	−	0.487683i	−0.690206	−	0.723613i	$-0.742480\pi$
$257$	72.3619	−	125.335i	0.281564	−	0.487683i	0.971770	+	0.235930i	$0.0758135\pi$
$258$	−89.2610			−0.345973
$259$	−87.2525	+	282.832i	−0.336882	+	1.09202i
$260$		0			0
$261$	79.5006	−	137.699i	0.304600	−	0.527582i
$262$	56.0730	+	97.1213i	0.214019	+	0.370692i
$263$	198.896	−	114.833i	0.756258	−	0.436626i	−0.0716928	−	0.997427i	$-0.522840\pi$
$263$	198.896	−	114.833i	0.756258	−	0.436626i	0.827950	+	0.560801i	$0.189507\pi$
$264$	−0.341222	−	0.197005i	−0.00129251	−	0.000746230i
$265$		0			0
$266$	3.95481	−	3.66928i	0.0148677	−	0.0137943i
$267$		−	80.8910i		−	0.302962i
$268$	21.5262	+	12.4281i	0.0803215	+	0.0463736i
$269$	−367.508	+	212.181i	−1.36620	+	0.788776i	−0.990440	−	0.137941i	$-0.955952\pi$
$269$	−367.508	+	212.181i	−1.36620	+	0.788776i	−0.375760	+	0.926717i	$0.622618\pi$
$270$		0			0
$271$	252.710	+	145.902i	0.932509	+	0.538385i	0.887604	−	0.460607i	$-0.152368\pi$
$271$	252.710	+	145.902i	0.932509	+	0.538385i	0.0449051	+	0.998991i	$0.485701\pi$
$272$	101.450			0.372977
$273$	204.434	−	189.675i	0.748844	−	0.694779i
$274$	−49.1267			−0.179294
$275$		0			0
$276$	−235.344	+	135.876i	−0.852697	+	0.492305i
$277$	−175.717	+	101.450i	−0.634358	+	0.366247i	−0.782438	−	0.622729i	$-0.786024\pi$
$277$	−175.717	+	101.450i	−0.634358	+	0.366247i	0.148080	+	0.988975i	$0.452691\pi$
$278$	−38.7220	+	67.0684i	−0.139288	+	0.241253i
$279$			67.7890i			0.242971i
$280$		0			0
$281$	254.325			0.905071			0.452536	−	0.891746i	$-0.350520\pi$
$281$	254.325			0.905071			0.452536	+	0.891746i	$0.350520\pi$
$282$	−27.4203	−	15.8311i	−0.0972351	−	0.0561387i
$283$	−221.852	−	384.259i	−0.783930	−	1.35781i	−0.929636	−	0.368478i	$-0.879879\pi$
$283$	−221.852	−	384.259i	−0.783930	−	1.35781i	0.145706	−	0.989328i	$-0.453454\pi$
$284$	83.1172	+	143.963i	0.292666	+	0.506912i
$285$		0			0
$286$		−	0.693347i		−	0.00242429i
$287$	261.235	−	59.6161i	0.910227	−	0.207722i
$288$			82.7327i			0.287266i
$289$	100.078	−	173.340i	0.346290	−	0.599792i
$290$		0			0
$291$	−2.69761	−	4.67241i	−0.00927015	−	0.0160564i
$292$	−148.233	+	256.747i	−0.507647	+	0.879270i
$293$	−223.513			−0.762845			−0.381422	−	0.924401i	$-0.624566\pi$
$293$	−223.513			−0.762845			−0.381422	+	0.924401i	$0.624566\pi$
$294$	24.7962	+	51.4985i	0.0843406	+	0.175165i
$295$		0			0
$296$	107.448	−	186.105i	0.363000	−	0.628734i
$297$	−0.116290	−	0.201420i	−0.000391548	−	0.000678180i
$298$	−42.4280	+	24.4958i	−0.142376	+	0.0822007i
$299$	−881.245	−	508.787i	−2.94731	−	1.70163i
$300$		0			0
$301$	−522.229	+	119.177i	−1.73498	+	0.395937i
$302$		−	85.6165i		−	0.283498i
$303$	−134.157	−	77.4555i	−0.442762	−	0.255629i
$304$	10.6667	−	6.15845i	0.0350880	−	0.0202580i
$305$		0			0
$306$	−16.4923	−	9.52183i	−0.0538964	−	0.0311171i
$307$	47.3887			0.154361			0.0771803	−	0.997017i	$-0.475408\pi$
$307$	47.3887			0.154361			0.0771803	+	0.997017i	$0.475408\pi$
$308$	−1.06179	−	0.327559i	−0.00344738	−	0.00106350i
$309$	−158.277			−0.512223
$310$		0			0
$311$	−313.595	+	181.054i	−1.00834	+	0.582167i	−0.910706	−	0.413055i	$-0.864462\pi$
$311$	−313.595	+	181.054i	−1.00834	+	0.582167i	−0.0976367	+	0.995222i	$0.531128\pi$
$312$	−175.346	+	101.236i	−0.562005	+	0.324474i
$313$	−196.807	+	340.880i	−0.628777	+	1.08907i	0.359020	+	0.933330i	$0.383111\pi$
$313$	−196.807	+	340.880i	−0.628777	+	1.08907i	−0.987797	+	0.155744i	$0.950222\pi$
$314$		−	101.737i		−	0.324003i
$315$		0			0
$316$	−72.6291			−0.229839
$317$	−500.196	−	288.788i	−1.57791	−	0.911004i	−0.995151	−	0.0983557i	$-0.968642\pi$
$317$	−500.196	−	288.788i	−1.57791	−	0.911004i	−0.582754	−	0.812648i	$-0.698025\pi$
$318$	11.0744	+	19.1813i	0.0348250	+	0.0603187i
$319$	−1.18615	−	2.05446i	−0.00371833	−	0.00644033i
$320$		0			0
$321$			182.044i			0.567114i
$322$	152.890	−	141.852i	0.474814	−	0.440533i
$323$			10.7865i			0.0333947i
$324$	−15.9590	+	27.6418i	−0.0492562	+	0.0853143i
$325$		0			0
$326$	20.1796	+	34.9521i	0.0619006	+	0.107215i
$327$	−48.2388	+	83.5521i	−0.147519	+	0.255511i
$328$	−194.542			−0.593117
$329$	−181.562	−	56.0109i	−0.551859	−	0.170246i
$330$		0			0
$331$	91.7974	−	158.998i	0.277333	−	0.480356i	−0.693388	−	0.720565i	$-0.743883\pi$
$331$	91.7974	−	158.998i	0.277333	−	0.480356i	0.970721	+	0.240209i	$0.0772160\pi$
$332$	−222.863	−	386.011i	−0.671275	−	1.16268i
$333$	109.856	−	63.4254i	0.329898	−	0.190467i
$334$	−130.697	−	75.4578i	−0.391307	−	0.225921i
$335$		0			0
$336$	29.0337	+	127.224i	0.0864099	+	0.378644i
$337$		−	205.885i		−	0.610934i	−0.952203	−	0.305467i	$-0.901187\pi$
$337$		−	205.885i		−	0.610934i	0.952203	−	0.305467i	$-0.0988126\pi$
$338$	−209.993	−	121.239i	−0.621280	−	0.358696i
$339$	−7.88138	+	4.55032i	−0.0232489	+	0.0134228i
$340$		0			0
$341$	0.875907	+	0.505705i	0.00256864	+	0.00148301i
$342$	−2.31207			−0.00676043
$343$	213.830	+	268.190i	0.623412	+	0.781894i
$344$	388.905			1.13054
$345$		0			0
$346$	−111.176	+	64.1872i	−0.321317	+	0.185512i
$347$	172.730	−	99.7256i	0.497780	−	0.287394i	−0.230016	−	0.973187i	$-0.573878\pi$
$347$	172.730	−	99.7256i	0.497780	−	0.287394i	0.727796	+	0.685793i	$0.240545\pi$
$348$	−162.781	+	281.944i	−0.467761	+	0.810185i
$349$			391.231i			1.12101i	0.828152	+	0.560503i	$0.189392\pi$
$349$			391.231i			1.12101i	−0.828152	+	0.560503i	$0.810608\pi$
$350$		0			0
$351$	−119.517			−0.340504
$352$	1.06900	+	0.617185i	0.00303692	+	0.00175337i
$353$	46.8243	+	81.1020i	0.132647	+	0.229751i	0.924696	−	0.380706i	$-0.124319\pi$
$353$	46.8243	+	81.1020i	0.132647	+	0.229751i	−0.792049	+	0.610457i	$0.790986\pi$
$354$	−2.84020	−	4.91937i	−0.00802317	−	0.0138965i
$355$		0			0
$356$			165.628i			0.465246i
$357$	−109.203	−	33.6885i	−0.305890	−	0.0943656i
$358$		−	146.722i		−	0.409838i
$359$	73.8759	−	127.957i	0.205782	−	0.356426i	−0.744599	−	0.667512i	$-0.767359\pi$
$359$	73.8759	−	127.957i	0.205782	−	0.356426i	0.950382	+	0.311086i	$0.100693\pi$
$360$		0			0
$361$	−179.845	−	311.501i	−0.498186	−	0.862884i
$362$	13.1596	−	22.7931i	0.0363525	−	0.0629644i
$363$	209.575			0.577341
$364$	−418.588	+	388.367i	−1.14997	+	1.06694i
$365$		0			0
$366$	−22.6575	+	39.2439i	−0.0619057	+	0.107224i
$367$	−41.3085	−	71.5485i	−0.112557	−	0.194955i	0.804243	−	0.594300i	$-0.202571\pi$
$367$	−41.3085	−	71.5485i	−0.112557	−	0.194955i	−0.916801	+	0.399345i	$0.869238\pi$
$368$	412.369	−	238.081i	1.12057	−	0.646960i
$369$	−99.4511	−	57.4181i	−0.269515	−	0.155605i
$370$		0			0
$371$	90.4014	+	97.4361i	0.243670	+	0.262631i
$372$		−	138.801i		−	0.373121i
$373$	−296.744	−	171.325i	−0.795561	−	0.459318i	0.0463554	−	0.998925i	$-0.485239\pi$
$373$	−296.744	−	171.325i	−0.795561	−	0.459318i	−0.841917	+	0.539607i	$0.818573\pi$
$374$	−0.246064	+	0.142065i	−0.000657926	+	0.000379854i
$375$		0			0
$376$	119.469	+	68.9752i	0.317736	+	0.183445i
$377$	−1219.06			−3.23359
$378$	7.22108	−	23.4074i	0.0191034	−	0.0619244i
$379$	−355.679			−0.938467			−0.469233	−	0.883074i	$-0.655470\pi$
$379$	−355.679			−0.938467			−0.469233	+	0.883074i	$0.655470\pi$
$380$		0			0
$381$	8.32483	−	4.80635i	0.0218500	−	0.0126151i
$382$	110.533	−	63.8164i	0.289354	−	0.167059i
$383$	−83.4939	+	144.616i	−0.218000	+	0.377586i	−0.954196	−	0.299181i	$-0.903286\pi$
$383$	−83.4939	+	144.616i	−0.218000	+	0.377586i	0.736197	+	0.676768i	$0.236620\pi$
$384$		−	219.618i		−	0.571922i
$385$		0			0
$386$	−183.950			−0.476556
$387$	198.810	+	114.783i	0.513722	+	0.296598i
$388$	5.52348	+	9.56695i	0.0142358	+	0.0246571i
$389$	79.6452	+	137.950i	0.204744	+	0.354626i	0.950051	−	0.312095i	$-0.101031\pi$
$389$	79.6452	+	137.950i	0.204744	+	0.354626i	−0.745307	+	0.666721i	$0.767697\pi$
$390$		0			0
$391$			416.998i			1.06649i
$392$	−108.035	−	224.376i	−0.275601	−	0.572388i
$393$		−	288.423i		−	0.733901i
$394$	66.9753	−	116.005i	0.169988	−	0.294428i
$395$		0			0
$396$	0.238108	+	0.412415i	0.000601283	+	0.00104145i
$397$	294.652	−	510.352i	0.742196	−	1.28552i	−0.209298	−	0.977852i	$-0.567118\pi$
$397$	294.652	−	510.352i	0.742196	−	1.28552i	0.951494	−	0.307669i	$-0.0995489\pi$
$398$	25.8439			0.0649344
$399$	−13.5269	+	3.08696i	−0.0339021	+	0.00773675i
$400$		0			0
$401$	83.1535	−	144.026i	0.207365	−	0.359167i	−0.743518	−	0.668716i	$-0.766844\pi$
$401$	83.1535	−	144.026i	0.207365	−	0.359167i	0.950884	+	0.309548i	$0.100178\pi$
$402$	4.08778	+	7.08024i	0.0101686	+	0.0176125i
$403$	450.107	−	259.870i	1.11689	−	0.644838i
$404$	274.692	+	158.593i	0.679930	+	0.392558i
$405$		0			0
$406$	73.6545	−	238.754i	0.181415	−	0.588064i
$407$		−	1.89261i		−	0.00465014i
$408$	71.8560	+	41.4861i	0.176118	+	0.101682i
$409$	189.742	−	109.548i	0.463917	−	0.267843i	−0.249773	−	0.968304i	$-0.580356\pi$
$409$	189.742	−	109.548i	0.463917	−	0.267843i	0.713690	+	0.700462i	$0.247023\pi$
$410$		0			0
$411$	109.419	+	63.1733i	0.266227	+	0.153706i
$412$	324.079			0.786599
$413$	−23.1850	−	24.9891i	−0.0561379	−	0.0605063i
$414$	−89.3829			−0.215901
$415$		0			0
$416$	549.331	−	317.156i	1.32051	−	0.762395i
$417$	172.490	−	99.5873i	0.413646	−	0.238819i
$418$	−0.0172480	+	0.0298744i	−4.12631e−5	+	7.14698e-5i
$419$			554.704i			1.32388i	0.749558	+	0.661938i	$0.230266\pi$
$419$			554.704i			1.32388i	−0.749558	+	0.661938i	$0.769734\pi$
$420$		0			0
$421$	642.342			1.52575			0.762876	−	0.646545i	$-0.223787\pi$
$421$	642.342			1.52575			0.762876	+	0.646545i	$0.223787\pi$
$422$	74.2362	+	42.8603i	0.175915	+	0.101565i
$423$	40.7153	+	70.5210i	0.0962537	+	0.166716i
$424$	−48.2503	−	83.5720i	−0.113798	−	0.197104i
$425$		0			0
$426$			54.6767i			0.128349i
$427$	−80.1629	+	259.851i	−0.187735	+	0.608550i
$428$		−	372.742i		−	0.870893i
$429$	−0.891594	+	1.54429i	−0.00207831	+	0.00359973i
$430$		0			0
$431$	−37.6661	−	65.2395i	−0.0873923	−	0.151368i	0.819016	−	0.573771i	$-0.194520\pi$
$431$	−37.6661	−	65.2395i	−0.0873923	−	0.151368i	−0.906408	+	0.422403i	$0.861187\pi$
$432$	27.9633	−	48.4338i	0.0647298	−	0.112115i
$433$	−353.064			−0.815391			−0.407695	−	0.913118i	$-0.633667\pi$
$433$	−353.064			−0.815391			−0.407695	+	0.913118i	$0.633667\pi$
$434$	23.7005	+	103.855i	0.0546095	+	0.239297i
$435$		0			0
$436$	98.7710	−	171.076i	0.226539	−	0.392377i
$437$	25.3136	+	43.8444i	0.0579259	+	0.100331i
$438$	−84.4475	+	48.7558i	−0.192802	+	0.111315i
$439$	235.512	+	135.973i	0.536473	+	0.309733i	0.743648	−	0.668571i	$-0.233094\pi$
$439$	235.512	+	135.973i	0.536473	+	0.309733i	−0.207175	+	0.978304i	$0.566427\pi$
$440$		0			0
$441$	10.9951	−	146.588i	0.0249321	−	0.332400i
$442$			146.008i			0.330335i
$443$	−95.4714	−	55.1204i	−0.215511	−	0.124425i	0.388359	−	0.921508i	$-0.373042\pi$
$443$	−95.4714	−	55.1204i	−0.215511	−	0.124425i	−0.603870	+	0.797083i	$0.706375\pi$
$444$	−224.935	+	129.866i	−0.506610	+	0.292491i
$445$		0			0
$446$	−171.214	−	98.8504i	−0.383888	−	0.221638i
$447$	125.999			0.281878
$448$	−38.1253	−	167.064i	−0.0851012	−	0.372910i
$449$	−59.1007			−0.131627			−0.0658137	−	0.997832i	$-0.520964\pi$
$449$	−59.1007			−0.131627			−0.0658137	+	0.997832i	$0.520964\pi$
$450$		0			0
$451$	−1.48381	+	0.856677i	−0.00329004	+	0.00189950i
$452$	16.1375	−	9.31696i	0.0357023	−	0.0206127i
$453$	−110.097	+	190.693i	−0.243039	+	0.420956i
$454$		−	145.118i		−	0.319643i
$455$		0			0
$456$	10.0735			0.0220911
$457$	177.775	+	102.638i	0.389004	+	0.224592i	0.681729	−	0.731605i	$-0.261228\pi$
$457$	177.775	+	102.638i	0.389004	+	0.224592i	−0.292724	+	0.956197i	$0.594562\pi$
$458$	48.5791	+	84.1414i	0.106068	+	0.183715i
$459$	24.4888	+	42.4158i	0.0533524	+	0.0924091i
$460$		0			0
$461$		−	466.172i		−	1.01122i	−0.862762	−	0.505610i	$-0.831268\pi$
$461$		−	466.172i		−	1.01122i	0.862762	−	0.505610i	$-0.168732\pi$
$462$	−0.248580	−	0.267923i	−0.000538051	−	0.000579920i
$463$		−	191.705i		−	0.414051i	−0.978336	−	0.207025i	$-0.933622\pi$
$463$		−	191.705i		−	0.414051i	0.978336	−	0.207025i	$-0.0663782\pi$
$464$	285.223	−	494.021i	0.614706	−	1.06470i
$465$		0			0
$466$	96.4510	+	167.058i	0.206976	+	0.358493i
$467$	421.617	−	730.261i	0.902819	−	1.56373i	0.0790015	−	0.996874i	$-0.474827\pi$
$467$	421.617	−	730.261i	0.902819	−	1.56373i	0.823818	−	0.566855i	$-0.191840\pi$
$468$	244.716			0.522897
$469$	33.3691	+	35.9657i	0.0711494	+	0.0766859i
$470$		0			0
$471$	−130.826	+	226.598i	−0.277763	+	0.481100i
$472$	12.3746	+	21.4334i	0.0262174	+	0.0454098i
$473$	2.96625	−	1.71256i	0.00627113	−	0.00362064i
$474$	−20.6882	−	11.9443i	−0.0436460	−	0.0251990i
$475$		0			0
$476$	223.597	+	68.9786i	0.469741	+	0.144913i
$477$		−	56.9633i		−	0.119420i
$478$	−241.121	−	139.212i	−0.504438	−	0.291237i
$479$	246.540	−	142.340i	0.514698	−	0.297161i	−0.220065	−	0.975485i	$-0.570627\pi$
$479$	246.540	−	142.340i	0.514698	−	0.297161i	0.734763	+	0.678324i	$0.237293\pi$
$480$		0			0
$481$	−842.267	−	486.283i	−1.75107	−	1.01098i
$482$	−199.274			−0.413432
$483$	−522.942	+	119.340i	−1.08270	+	0.247080i
$484$	−429.113			−0.886597
$485$		0			0
$486$	−9.09176	+	5.24913i	−0.0187073	+	0.0108007i
$487$	−169.434	+	97.8228i	−0.347914	+	0.200868i	−0.663766	−	0.747940i	$-0.731043\pi$
$487$	−169.434	+	97.8228i	−0.347914	+	0.200868i	0.315852	+	0.948808i	$0.397710\pi$
$488$	98.7174	−	170.984i	0.202290	−	0.350376i
$489$		−	103.798i		−	0.212266i
$490$		0			0
$491$	745.464			1.51826			0.759128	−	0.650941i	$-0.225625\pi$
$491$	745.464			1.51826			0.759128	+	0.650941i	$0.225625\pi$
$492$	203.630	+	117.566i	0.413883	+	0.238955i
$493$	249.784	+	432.638i	0.506660	+	0.877562i
$494$	8.86332	+	15.3517i	0.0179419	+	0.0310763i
$495$		0			0
$496$			243.206i			0.490335i
$497$	73.0017	+	319.890i	0.146885	+	0.643642i
$498$		−	146.605i		−	0.294388i
$499$	45.9747	−	79.6306i	0.0921337	−	0.159580i	−0.816275	−	0.577663i	$-0.803965\pi$
$499$	45.9747	−	79.6306i	0.0921337	−	0.159580i	0.908409	+	0.418083i	$0.137298\pi$
$500$		0			0
$501$	194.066	+	336.133i	0.387358	+	0.670924i
$502$	−104.963	+	181.802i	−0.209090	+	0.362155i
$503$	672.220			1.33642			0.668211	−	0.743972i	$-0.267060\pi$
$503$	672.220			1.33642			0.668211	+	0.743972i	$0.267060\pi$
$504$	−31.4618	+	101.985i	−0.0624243	+	0.202351i
$505$		0			0
$506$	−0.666795	+	1.15492i	−0.00131778	+	0.00228246i
$507$	311.810	+	540.071i	0.615010	+	1.06523i
$508$	−17.0454	+	9.84119i	−0.0335540	+	0.0193724i
$509$	−282.238	−	162.950i	−0.554495	−	0.320138i	0.196438	−	0.980516i	$-0.437063\pi$
$509$	−282.238	−	162.950i	−0.554495	−	0.320138i	−0.750933	+	0.660378i	$0.770396\pi$
$510$		0			0
$511$	−428.970	+	398.000i	−0.839473	+	0.778865i
$512$			515.622i			1.00707i
$513$	5.14965	+	2.97315i	0.0100383	+	0.00579561i
$514$	−84.4082	+	48.7331i	−0.164218	+	0.0948115i
$515$		0			0
$516$	−407.073	−	235.024i	−0.788901	−	0.455472i
$517$	1.21494			0.00234999
$518$	146.127	−	135.577i	0.282099	−	0.261733i
$519$	330.161			0.636148
$520$		0			0
$521$	515.449	−	297.595i	0.989346	−	0.571199i	0.0842672	−	0.996443i	$-0.473145\pi$
$521$	515.449	−	297.595i	0.989346	−	0.571199i	0.905079	+	0.425244i	$0.139812\pi$
$522$	−92.7353	+	53.5407i	−0.177654	+	0.102568i
$523$	−25.2007	+	43.6490i	−0.0481850	+	0.0834588i	−0.889112	−	0.457690i	$-0.848677\pi$
$523$	−25.2007	+	43.6490i	−0.0481850	+	0.0834588i	0.840927	+	0.541149i	$0.182010\pi$
$524$			590.559i			1.12702i
$525$		0			0
$526$	−154.671			−0.294051
$527$	−184.452	−	106.494i	−0.350004	−	0.202075i
$528$	−0.417211	−	0.722631i	−0.000790173	−	0.00136862i
$529$	714.106	+	1236.87i	1.34992	+	2.33812i
$530$		0			0
$531$			14.6092i			0.0275126i
$532$	27.6970	−	6.32068i	0.0520620	−	0.0118810i
$533$			880.451i			1.65188i
$534$	−27.2386	+	47.1786i	−0.0510085	+	0.0883494i
$535$		0			0
$536$	−17.8102	−	30.8482i	−0.0332280	−	0.0575526i
$537$	−188.674	+	326.793i	−0.351348	+	0.608553i
$538$	285.792			0.531212
$539$	−1.81205	−	1.23561i	−0.00336188	−	0.00229242i
$540$		0			0
$541$	−468.381	+	811.260i	−0.865769	+	1.49956i	0.000512769		1.00000i	$0.499837\pi$
$541$	−468.381	+	811.260i	−0.865769	+	1.49956i	−0.866282	+	0.499556i	$0.833497\pi$
$542$	−98.2598	−	170.191i	−0.181291	−	0.314006i
$543$	−58.6206	+	33.8446i	−0.107957	+	0.0623290i
$544$	−225.113	−	129.969i	−0.413812	−	0.238914i
$545$		0			0
$546$	−183.103	+	41.7857i	−0.335354	+	0.0765306i
$547$		−	3.89041i		−	0.00711227i	−0.999994	−	0.00355613i	$-0.998868\pi$
$547$		−	3.89041i		−	0.00711227i	0.999994	−	0.00355613i	$-0.00113195\pi$
$548$	−224.041	−	129.350i	−0.408834	−	0.236040i
$549$	100.930	−	58.2718i	0.183843	−	0.106142i
$550$		0			0
$551$	52.5260	+	30.3259i	0.0953285	+	0.0550379i
$552$	389.436			0.705500
$553$	−136.986	−	42.2594i	−0.247714	−	0.0764185i
$554$	136.646			0.246654
$555$		0			0
$556$	−353.181	+	203.909i	−0.635218	+	0.366743i
$557$	334.945	−	193.381i	0.601338	−	0.347183i	−0.168230	−	0.985748i	$-0.553805\pi$
$557$	334.945	−	193.381i	0.601338	−	0.347183i	0.769568	+	0.638565i	$0.220472\pi$
$558$	22.8267	−	39.5370i	0.0409081	−	0.0708549i
$559$		−	1760.09i		−	3.14864i
$560$		0			0
$561$	0.730743			0.00130257
$562$	−148.332	−	85.6393i	−0.263935	−	0.152383i
$563$	60.6226	+	105.001i	0.107678	+	0.186503i	0.914829	−	0.403841i	$-0.132325\pi$
$563$	60.6226	+	105.001i	0.107678	+	0.186503i	−0.807151	+	0.590345i	$0.798992\pi$
$564$	−83.3663	−	144.395i	−0.147813	−	0.256019i
$565$		0			0
$566$			298.819i			0.527948i
$567$	−46.1837	+	42.8493i	−0.0814527	+	0.0755720i
$568$		−	238.223i		−	0.419407i
$569$	204.955	−	354.993i	0.360202	−	0.623889i	−0.627792	−	0.778381i	$-0.716041\pi$
$569$	204.955	−	354.993i	0.360202	−	0.623889i	0.987994	+	0.154493i	$0.0493743\pi$
$570$		0			0
$571$	287.861	+	498.591i	0.504136	+	0.873188i	0.999989	+	0.00478199i	$0.00152216\pi$
$571$	287.861	+	498.591i	0.504136	+	0.873188i	−0.495853	+	0.868406i	$0.665145\pi$
$572$	1.82558	−	3.16199i	0.00319157	−	0.00552796i
$573$	−328.253			−0.572868
$574$	−172.436	−	53.1959i	−0.300412	−	0.0926758i
$575$		0			0
$576$	−36.7197	+	63.6004i	−0.0637495	+	0.110417i
$577$	−116.772	−	202.254i	−0.202377	−	0.350527i	0.746917	−	0.664917i	$-0.231533\pi$
$577$	−116.772	−	202.254i	−0.202377	−	0.350527i	−0.949294	+	0.314390i	$0.898200\pi$
$578$	−116.738	+	67.3988i	−0.201969	+	0.116607i
$579$	409.711	+	236.547i	0.707619	+	0.408544i
$580$		0			0
$581$	−195.741	−	857.727i	−0.336903	−	1.47629i
$582$			3.63349i			0.00624311i
$583$	−0.736027	−	0.424945i	−0.00126248	−	0.000728894i
$584$	367.933	−	212.426i	0.630022	−	0.363743i
$585$		0			0
$586$	130.361	+	75.2641i	0.222459	+	0.128437i
$587$	−606.882			−1.03387			−0.516935	−	0.856024i	$-0.672927\pi$
$587$	−606.882			−1.03387			−0.516935	+	0.856024i	$0.672927\pi$
$588$	−22.5128	+	300.146i	−0.0382872	+	0.510452i
$589$	−25.8585			−0.0439024
$590$		0			0
$591$	−298.347	+	172.251i	−0.504817	+	0.291456i
$592$	394.129	−	227.551i	0.665759	−	0.384376i
$593$	−405.299	+	701.998i	−0.683472	+	1.18381i	0.290443	+	0.956892i	$0.406197\pi$
$593$	−405.299	+	701.998i	−0.683472	+	1.18381i	−0.973914	+	0.226915i	$0.927136\pi$
$594$			0.156634i			0.000263693i
$595$		0			0
$596$	−257.989			−0.432867
$597$	−57.5619	−	33.2334i	−0.0964185	−	0.0556673i
$598$	342.650	+	593.487i	0.572993	+	0.992453i
$599$	−511.389	−	885.752i	−0.853738	−	1.47872i	−0.877811	−	0.479007i	$-0.840997\pi$
$599$	−511.389	−	885.752i	−0.853738	−	1.47872i	0.0240732	−	0.999710i	$-0.492337\pi$
$600$		0			0
$601$			147.884i			0.246063i	0.992403	+	0.123032i	$0.0392617\pi$
$601$			147.884i			0.246063i	−0.992403	+	0.123032i	$0.960738\pi$
$602$	344.714	+	106.343i	0.572614	+	0.176649i
$603$		−	21.0263i		−	0.0348696i
$604$	225.427	−	390.452i	0.373224	−	0.646443i
$605$		0			0
$606$	52.1634	+	90.3497i	0.0860783	+	0.149092i
$607$	−470.823	+	815.490i	−0.775656	+	1.34348i	0.158769	+	0.987316i	$0.449248\pi$
$607$	−470.823	+	815.490i	−0.775656	+	1.34348i	−0.934425	+	0.356160i	$0.884086\pi$
$608$	−31.5588			−0.0519060
$609$	−471.070	+	437.060i	−0.773514	+	0.717669i
$610$		0			0
$611$	312.165	−	540.685i	0.510908	−	0.884919i
$612$	−50.1418	−	86.8481i	−0.0819310	−	0.141909i
$613$	−311.886	+	180.068i	−0.508786	+	0.293748i	−0.732335	−	0.680945i	$-0.761569\pi$
$613$	−311.886	+	180.068i	−0.508786	+	0.293748i	0.223548	+	0.974693i	$0.428236\pi$
$614$	−27.6388	−	15.9573i	−0.0450144	−	0.0259891i
$615$		0			0
$616$	1.08305	+	1.16733i	0.00175819	+	0.00189501i
$617$			769.687i			1.24747i	0.781637	+	0.623734i	$0.214385\pi$
$617$			769.687i			1.24747i	−0.781637	+	0.623734i	$0.785615\pi$
$618$	92.3129	+	53.2969i	0.149374	+	0.0862409i
$619$	853.542	−	492.793i	1.37890	−	0.796111i	0.386877	−	0.922131i	$-0.373554\pi$
$619$	853.542	−	492.793i	1.37890	−	0.796111i	0.992028	+	0.126020i	$0.0402204\pi$
$620$		0			0
$621$	199.082	+	114.940i	0.320583	+	0.185088i
$622$	243.866			0.392068
$623$	−96.3709	+	312.390i	−0.154688	+	0.501428i
$624$	−428.790			−0.687163
$625$		0			0
$626$	229.570	−	132.542i	0.366726	−	0.211729i
$627$	0.0768326	−	0.0443593i	0.000122540	−	7.07485e-5i
$628$	267.873	−	463.969i	0.426549	−	0.738804i
$629$			398.554i			0.633630i
$630$		0			0
$631$	−89.7688			−0.142264			−0.0711322	−	0.997467i	$-0.522661\pi$
$631$	−89.7688			−0.142264			−0.0711322	+	0.997467i	$0.522661\pi$
$632$	90.1373	+	52.0408i	0.142622	+	0.0823431i
$633$	−110.230	−	190.925i	−0.174140	−	0.301619i
$634$	194.488	+	336.864i	0.306764	+	0.531331i
$635$		0			0
$636$			116.635i			0.183388i
$637$	−1015.47	+	488.941i	−1.59414	+	0.767569i
$638$			1.59765i			0.00250416i
$639$	70.3102	−	121.781i	0.110032	−	0.190580i
$640$		0			0
$641$	214.166	+	370.947i	0.334113	+	0.578701i	0.983314	−	0.181916i	$-0.0582300\pi$
$641$	214.166	+	370.947i	0.334113	+	0.578701i	−0.649201	+	0.760617i	$0.724897\pi$
$642$	61.2999	−	106.175i	0.0954827	−	0.165381i
$643$	111.498			0.173403			0.0867015	−	0.996234i	$-0.472367\pi$
$643$	111.498			0.173403			0.0867015	+	0.996234i	$0.472367\pi$
$644$	1070.75	−	244.353i	1.66265	−	0.379431i
$645$		0			0
$646$	3.63215	−	6.29107i	0.00562253	−	0.00973850i
$647$	−144.357	−	250.033i	−0.223117	−	0.386450i	0.732636	−	0.680621i	$-0.238290\pi$
$647$	−144.357	−	250.033i	−0.223117	−	0.386450i	−0.955753	+	0.294171i	$0.904957\pi$
$648$	39.6123	−	22.8702i	0.0611300	−	0.0352934i
$649$	0.188766	+	0.108984i	0.000290857	+	0.000167926i
$650$		0			0
$651$	80.7616	−	261.792i	0.124058	−	0.402138i
$652$			212.531i			0.325967i
$653$	739.322	+	426.848i	1.13219	+	0.653672i	0.944485	−	0.328553i	$-0.106561\pi$
$653$	739.322	+	426.848i	1.13219	+	0.653672i	0.187707	+	0.982225i	$0.439894\pi$
$654$	56.2693	−	32.4871i	0.0860387	−	0.0496744i
$655$		0			0
$656$	−356.800	−	205.998i	−0.543902	−	0.314022i
$657$	250.786			0.381713
$658$	87.0327	+	93.8052i	0.132269	+	0.142561i
$659$	288.693			0.438077			0.219039	−	0.975716i	$-0.429708\pi$
$659$	288.693			0.438077			0.219039	+	0.975716i	$0.429708\pi$
$660$		0			0
$661$	182.367	−	105.289i	0.275895	−	0.159288i	−0.355668	−	0.934612i	$-0.615747\pi$
$661$	182.367	−	105.289i	0.275895	−	0.159288i	0.631564	+	0.775324i	$0.282413\pi$
$662$	−107.079	+	61.8222i	−0.161751	+	0.0933870i
$663$	187.756	−	325.202i	0.283191	−	0.490501i
$664$			638.751i			0.961974i
$665$		0			0
$666$	−85.4293			−0.128272
$667$	2030.62	+	1172.38i	3.04441	+	1.75769i
$668$	−397.359	−	688.246i	−0.594849	−	1.03031i
$669$	254.229	+	440.338i	0.380013	+	0.658203i
$670$		0			0
$671$		−	1.73883i		−	0.00259140i
$672$	98.5650	−	319.502i	0.146674	−	0.475450i
$673$		−	760.139i		−	1.12948i	−0.825269	−	0.564739i	$-0.808977\pi$
$673$		−	760.139i		−	1.12948i	0.825269	−	0.564739i	$-0.191023\pi$
$674$	−69.3279	+	120.080i	−0.102860	+	0.178160i
$675$		0			0
$676$	−638.444	−	1105.82i	−0.944444	−	1.63583i
$677$	−94.2600	+	163.263i	−0.139232	+	0.241157i	−0.927206	−	0.374552i	$-0.877797\pi$
$677$	−94.2600	+	163.263i	−0.139232	+	0.241157i	0.787974	+	0.615708i	$0.211130\pi$
$678$	6.12894			0.00903974
$679$	4.85126	+	21.2580i	0.00714472	+	0.0313079i
$680$		0			0
$681$	−186.611	+	323.220i	−0.274026	+	0.474626i
$682$	−0.340574	−	0.589892i	−0.000499375	−	0.000864944i
$683$	−450.754	+	260.243i	−0.659962	+	0.381029i	−0.792262	−	0.610181i	$-0.791097\pi$
$683$	−450.754	+	260.243i	−0.659962	+	0.381029i	0.132301	+	0.991210i	$0.457764\pi$
$684$	−10.5441	−	6.08765i	−0.0154154	−	0.00890007i
$685$		0			0
$686$	−34.4057	−	228.421i	−0.0501541	−	0.332976i
$687$		−	249.877i		−	0.363721i
$688$	713.270	+	411.807i	1.03673	+	0.598556i
$689$	−378.226	+	218.369i	−0.548949	+	0.316936i
$690$		0			0
$691$	590.615	+	340.991i	0.854724	+	0.493475i	0.862242	−	0.506496i	$-0.169060\pi$
$691$	590.615	+	340.991i	0.854724	+	0.493475i	−0.00751772	+	0.999972i	$0.502393\pi$
$692$	−676.018			−0.976904
$693$	0.209130	+	0.916398i	0.000301775	+	0.00132236i
$694$	−134.323			−0.193549
$695$		0			0
$696$	404.042	−	233.274i	0.580520	−	0.335164i
$697$	312.466	−	180.403i	0.448302	−	0.258827i
$698$	131.740	−	228.180i	0.188739	−	0.326906i
$699$		−	496.116i		−	0.709751i
$700$		0			0
$701$	−946.473			−1.35018			−0.675088	−	0.737737i	$-0.735894\pi$
$701$	−946.473			−1.35018			−0.675088	+	0.737737i	$0.735894\pi$
$702$	69.7066	+	40.2451i	0.0992971	+	0.0573292i
$703$	24.1939	+	41.9051i	0.0344153	+	0.0596090i
$704$	0.547857	+	0.948916i	0.000778206	+	0.00134789i
$705$		0			0
$706$		−	63.0689i		−	0.0893327i
$707$	425.817	+	458.952i	0.602287	+	0.649155i
$708$		−	29.9129i		−	0.0422499i
$709$	−504.785	+	874.313i	−0.711967	+	1.23316i	0.252150	+	0.967688i	$0.418862\pi$
$709$	−504.785	+	874.313i	−0.711967	+	1.23316i	−0.964118	+	0.265475i	$0.914471\pi$
$710$		0			0
$711$	30.7191	+	53.2071i	0.0432055	+	0.0748341i
$712$	118.677	−	205.554i	0.166681	−	0.288700i
$713$	−999.671			−1.40206
$714$	52.3470	+	56.4204i	0.0733151	+	0.0790201i
$715$		0			0
$716$	386.318	−	669.122i	0.539550	−	0.934528i
$717$	358.032	+	620.129i	0.499347	+	0.864895i
$718$	−86.1742	+	49.7527i	−0.120020	+	0.0692935i
$719$	−783.382	−	452.286i	−1.08954	−	0.629049i	−0.156089	−	0.987743i	$-0.549889\pi$
$719$	−783.382	−	452.286i	−1.08954	−	0.629049i	−0.933455	+	0.358694i	$0.883222\pi$
$720$		0			0
$721$	611.244	+	188.566i	0.847773	+	0.261534i
$722$			242.238i			0.335510i
$723$	443.842	+	256.252i	0.613890	+	0.354429i
$724$	120.028	−	69.2983i	0.165785	−	0.0957159i
$725$		0			0
$726$	−122.232	−	70.5705i	−0.168363	−	0.0972045i
$727$	535.515			0.736609			0.368304	−	0.929705i	$-0.379938\pi$
$727$	535.515			0.736609			0.368304	+	0.929705i	$0.379938\pi$
$728$	797.770	−	182.058i	1.09584	−	0.250080i
$729$	27.0000			0.0370370
$730$		0			0
$731$	−624.644	+	360.639i	−0.854507	+	0.493350i
$732$	−206.658	+	119.314i	−0.282319	+	0.162997i
$733$	−376.769	+	652.583i	−0.514009	+	0.890290i	0.485859	+	0.874037i	$0.338507\pi$
$733$	−376.769	+	652.583i	−0.514009	+	0.890290i	−0.999868	+	0.0162527i	$0.994826\pi$
$734$			55.6396i			0.0758033i
$735$		0			0
$736$	−1220.04			−1.65767
$737$	−0.271683	−	0.156856i	−0.000368634	−	0.000212831i
$738$	38.6690	+	66.9767i	0.0523970	+	0.0907543i
$739$	−546.157	−	945.972i	−0.739049	−	1.28007i	−0.952924	−	0.303209i	$-0.901942\pi$
$739$	−546.157	−	945.972i	−0.739049	−	1.28007i	0.213875	−	0.976861i	$-0.431391\pi$
$740$		0			0
$741$		−	45.5903i		−	0.0615254i
$742$	−19.9156	−	87.2693i	−0.0268404	−	0.117614i
$743$			362.303i			0.487622i	0.969823	+	0.243811i	$0.0783976\pi$
$743$			362.303i			0.487622i	−0.969823	+	0.243811i	$0.921602\pi$
$744$	−99.4547	+	172.261i	−0.133676	+	0.231533i
$745$		0			0
$746$	115.381	+	199.847i	0.154667	+	0.267891i
$747$	−188.524	+	326.533i	−0.252375	+	0.437126i
$748$	−1.49623			−0.00200030
$749$	216.881	−	703.028i	0.289561	−	0.938622i
$750$		0			0
$751$	336.270	−	582.437i	0.447763	−	0.775548i	−0.550477	−	0.834850i	$-0.685554\pi$
$751$	336.270	−	582.437i	0.447763	−	0.775548i	0.998240	+	0.0593020i	$0.0188875\pi$
$752$	146.074	+	253.008i	0.194247	+	0.336446i
$753$	467.568	−	269.950i	0.620940	−	0.358500i
$754$	711.002	+	410.497i	0.942974	+	0.544426i
$755$		0			0
$756$	94.5630	−	87.7358i	0.125083	−	0.116053i
$757$		−	368.166i		−	0.486349i	−0.969983	−	0.243174i	$-0.921811\pi$
$757$		−	368.166i		−	0.486349i	0.969983	−	0.243174i	$-0.0781887\pi$
$758$	207.445	+	119.768i	0.273674	+	0.158006i
$759$	2.97029	−	1.71490i	0.00391343	−	0.00225942i
$760$		0			0
$761$	565.660	+	326.584i	0.743312	+	0.429151i	0.823272	−	0.567647i	$-0.192146\pi$
$761$	565.660	+	326.584i	0.743312	+	0.429151i	−0.0799606	+	0.996798i	$0.525479\pi$
$762$	−6.47380			−0.00849580
$763$	285.833	−	265.197i	0.374617	−	0.347571i
$764$	672.113			0.879728
$765$		0			0
$766$	97.3933	−	56.2301i	0.127145	−	0.0734074i
$767$	97.0024	−	56.0043i	0.126470	−	0.0730174i
$768$	10.8482	−	18.7896i	0.0141252	−	0.0244656i
$769$			1393.19i			1.81170i	0.423602	+	0.905848i	$0.360765\pi$
$769$			1393.19i			1.81170i	−0.423602	+	0.905848i	$0.639235\pi$
$770$		0			0
$771$	250.669			0.325122
$772$	−838.901	−	484.340i	−1.08666	−	0.627383i
$773$	−652.302	−	1129.82i	−0.843858	−	1.46160i	−0.886609	−	0.462519i	$-0.846946\pi$
$773$	−652.302	−	1129.82i	−0.843858	−	1.46160i	0.0427514	−	0.999086i	$-0.486388\pi$
$774$	−77.3023	−	133.892i	−0.0998738	−	0.172987i
$775$		0			0
$776$		−	15.8309i		−	0.0204007i
$777$	−499.811	+	114.061i	−0.643258	+	0.146797i
$778$		−	107.276i		−	0.137887i
$779$	21.9024	−	37.9362i	0.0281161	−	0.0486985i
$780$		0			0
$781$	−1.04903	−	1.81697i	−0.00134318	−	0.00232646i
$782$	140.416	−	243.208i	0.179561	−	0.311008i
$783$	275.398			0.351722
$784$	39.4469	−	525.913i	0.0503149	−	0.670808i
$785$		0			0
$786$	−97.1213	+	168.219i	−0.123564	+	0.214019i
$787$	105.237	+	182.275i	0.133719	+	0.231607i	0.925107	−	0.379706i	$-0.123975\pi$
$787$	105.237	+	182.275i	0.133719	+	0.231607i	−0.791389	+	0.611313i	$0.790642\pi$
$788$	610.878	−	352.691i	0.775226	−	0.447577i
$789$	344.498	+	198.896i	0.436626	+	0.252086i
$790$		0			0
$791$	35.8579	−	8.18308i	0.0453323	−	0.0103452i
$792$		−	0.682444i		−	0.000861672i
$793$	−773.829	−	446.770i	−0.975825	−	0.563393i
$794$	−343.703	+	198.437i	−0.432876	+	0.249921i
$795$		0			0
$796$	117.860	+	68.0467i	0.148066	+	0.0854858i
$797$	−254.794			−0.319691			−0.159845	−	0.987142i	$-0.551100\pi$
$797$	−254.794			−0.319691			−0.159845	+	0.987142i	$0.551100\pi$
$798$	8.92888	+	2.75452i	0.0111891	+	0.00345178i
$799$	−255.848			−0.320210
$800$		0			0
$801$	121.336	−	70.0536i	0.151481	−	0.0874577i
$802$	−96.9964	+	56.0009i	−0.120943	+	0.0698265i
$803$	1.87086	−	3.24042i	0.00232983	−	0.00403539i
$804$			43.0523i			0.0535477i
$805$		0			0
$806$	−350.025			−0.434275
$807$	−636.542	−	367.508i	−0.788776	−	0.455400i
$808$	−227.273	−	393.649i	−0.281279	−	0.487189i
$809$	−114.683	−	198.637i	−0.141759	−	0.245533i	0.786400	−	0.617717i	$-0.211942\pi$
$809$	−114.683	−	198.637i	−0.141759	−	0.245533i	−0.928159	+	0.372184i	$0.878609\pi$
$810$		0			0
$811$		−	1108.59i		−	1.36694i	−0.729978	−	0.683470i	$-0.760470\pi$
$811$		−	1108.59i		−	1.36694i	0.729978	−	0.683470i	$-0.239530\pi$
$812$	964.536	−	894.899i	1.18785	−	1.10209i
$813$			505.420i			0.621673i
$814$	−0.637302	+	1.10384i	−0.000782926	+	0.00135607i
$815$		0			0
$816$	87.8581	+	152.175i	0.107669	+	0.186489i
$817$	−43.7847	+	75.8373i	−0.0535920	+	0.0928241i
$818$	−147.553			−0.180382
$819$	461.558	+	142.388i	0.563562	+	0.173856i
$820$		0			0
$821$	−433.762	+	751.297i	−0.528333	+	0.915100i	0.471121	+	0.882069i	$0.343850\pi$
$821$	−433.762	+	751.297i	−0.528333	+	0.915100i	−0.999454	+	0.0330318i	$0.989484\pi$
$822$	−42.5449	−	73.6900i	−0.0517578	−	0.0896472i
$823$	−852.931	+	492.440i	−1.03637	+	0.598348i	−0.918802	−	0.394718i	$-0.870842\pi$
$823$	−852.931	+	492.440i	−1.03637	+	0.598348i	−0.117566	+	0.993065i	$0.537509\pi$
$824$	−402.202	−	232.212i	−0.488110	−	0.281810i
$825$		0			0
$826$	5.10769	+	22.3817i	0.00618364	+	0.0270964i
$827$		−	767.641i		−	0.928224i	−0.885777	−	0.464112i	$-0.846374\pi$
$827$		−	767.641i		−	0.928224i	0.885777	−	0.464112i	$-0.153626\pi$
$828$	−407.628	−	235.344i	−0.492305	−	0.284232i
$829$	153.578	−	88.6684i	0.185257	−	0.106958i	−0.404503	−	0.914537i	$-0.632556\pi$
$829$	153.578	−	88.6684i	0.185257	−	0.106958i	0.589760	+	0.807578i	$0.299222\pi$
$830$		0			0
$831$	−304.351	−	175.717i	−0.366247	−	0.211453i
$832$	563.061			0.676756
$833$	381.590	+	260.201i	0.458091	+	0.312366i
$834$	−134.137			−0.160836
$835$		0			0
$836$	−0.157318	+	0.0908275i	−0.000188179	+	0.000108645i
$837$	−101.684	+	58.7070i	−0.121486	+	0.0701398i
$838$	186.787	−	323.524i	0.222896	−	0.386067i
$839$			15.9176i			0.0189721i	0.999955	+	0.00948606i	$0.00301955\pi$
$839$			15.9176i			0.0189721i	−0.999955	+	0.00948606i	$0.996980\pi$
$840$		0			0
$841$	1968.04			2.34012
$842$	−374.637	−	216.297i	−0.444937	−	0.256885i
$843$	220.252	+	381.488i	0.261272	+	0.452536i
$844$	225.701	+	390.926i	0.267419	+	0.463183i
$845$		0			0
$846$		−	54.8406i		−	0.0648234i
$847$	−809.348	−	249.680i	−0.955547	−	0.294782i
$848$		−	204.367i		−	0.240998i
$849$	384.259	−	665.556i	0.452602	−	0.783930i
$850$		0			0
$851$	935.321	+	1620.02i	1.09908	+	1.90367i
$852$	−143.963	+	249.351i	−0.168971	+	0.292666i
$853$	694.629			0.814336			0.407168	−	0.913353i	$-0.366516\pi$
$853$	694.629			0.814336			0.407168	+	0.913353i	$0.366516\pi$
$854$	134.254	−	124.561i	0.157206	−	0.145856i
$855$		0			0
$856$	−267.080	+	462.597i	−0.312010	+	0.540417i
$857$	−751.232	−	1301.17i	−0.876583	−	1.51829i	−0.855067	−	0.518518i	$-0.826484\pi$
$857$	−751.232	−	1301.17i	−0.876583	−	1.51829i	−0.0215161	−	0.999769i	$-0.506849\pi$
$858$	1.04002	−	0.600456i	0.00121214	−	0.000699832i
$859$	254.436	+	146.898i	0.296200	+	0.171011i	0.640734	−	0.767763i	$-0.278630\pi$
$859$	254.436	+	146.898i	0.296200	+	0.171011i	−0.344535	+	0.938774i	$0.611963\pi$
$860$		0			0
$861$	315.660	+	340.224i	0.366621	+	0.395149i
$862$			50.7334i			0.0588555i
$863$	−223.537	−	129.059i	−0.259023	−	0.149547i	0.364866	−	0.931060i	$-0.381115\pi$
$863$	−223.537	−	129.059i	−0.259023	−	0.149547i	−0.623889	+	0.781513i	$0.714448\pi$
$864$	−124.099	+	71.6486i	−0.143633	+	0.0829266i
$865$		0			0
$866$	205.920	+	118.888i	0.237783	+	0.137284i
$867$	346.680			0.399861
$868$	−165.363	+	536.030i	−0.190510	+	0.617546i
$869$	0.916657			0.00105484
$870$		0			0
$871$	−139.611	+	80.6046i	−0.160288	+	0.0925426i
$872$	−245.162	+	141.544i	−0.281149	+	0.162322i
$873$	4.67241	−	8.09284i	0.00535213	−	0.00927015i
$874$		−	34.0956i		−	0.0390109i
$875$		0			0
$876$	−513.494			−0.586180
$877$	−1158.30	−	668.747i	−1.32076	−	0.762539i	−0.336907	−	0.941538i	$-0.609381\pi$
$877$	−1158.30	−	668.747i	−1.32076	−	0.762539i	−0.983849	+	0.178999i	$0.942714\pi$
$878$	−91.5727	−	158.609i	−0.104297	−	0.180648i
$879$	−193.568	−	335.270i	−0.220214	−	0.381422i
$880$		0			0
$881$		−	606.188i		−	0.688069i	−0.938957	−	0.344034i	$-0.888206\pi$
$881$		−	606.188i		−	0.688069i	0.938957	−	0.344034i	$-0.111794\pi$
$882$	−55.7736	+	81.7932i	−0.0632354	+	0.0927361i
$883$			862.650i			0.976953i	0.872577	+	0.488477i	$0.162447\pi$
$883$			862.650i			0.976953i	−0.872577	+	0.488477i	$0.837553\pi$
$884$	−384.437	+	665.865i	−0.434884	+	0.753241i
$885$		0			0
$886$	37.1216	+	64.2965i	0.0418980	+	0.0725694i
$887$	461.685	−	799.662i	0.520502	−	0.901536i	−0.479214	−	0.877698i	$-0.659078\pi$
$887$	461.685	−	799.662i	0.520502	−	0.901536i	0.999716	−	0.0238378i	$-0.00758852\pi$
$888$	372.211			0.419156
$889$	−37.8755	+	8.64351i	−0.0426046	+	0.00972273i
$890$		0			0
$891$	0.201420	−	0.348869i	0.000226060	−	0.000391548i
$892$	−520.545	−	901.610i	−0.583570	−	1.01077i
$893$	−26.9006	+	15.5311i	−0.0301239	+	0.0173920i
$894$	−73.4874	−	42.4280i	−0.0822007	−	0.0474586i
$895$		0			0
$896$	−261.646	+	848.134i	−0.292015	+	0.946579i
$897$		−	1762.49i		−	1.96487i
$898$	34.4697	+	19.9011i	0.0383850	+	0.0221616i
$899$	−1037.16	+	598.807i	−1.15369	+	0.666082i
$900$		0			0
$901$	154.996	+	89.4867i	0.172026	+	0.0993193i
$902$	1.15388			0.00127925
$903$	−631.029	−	680.133i	−0.698814	−	0.753193i
$904$	−26.7035			−0.0295392
$905$		0			0
$906$	128.425	−	74.1461i	0.141749	−	0.0818389i
$907$	−82.0242	+	47.3567i	−0.0904346	+	0.0522125i	−0.544535	−	0.838738i	$-0.683294\pi$
$907$	−82.0242	+	47.3567i	−0.0904346	+	0.0522125i	0.454101	+	0.890950i	$0.349961\pi$
$908$	382.095	−	661.807i	0.420809	−	0.728863i
$909$		−	268.314i		−	0.295174i
$910$		0			0
$911$	−556.948			−0.611359			−0.305679	−	0.952134i	$-0.598884\pi$
$911$	−556.948			−0.611359			−0.305679	+	0.952134i	$0.598884\pi$
$912$	18.4753	+	10.6667i	0.0202580	+	0.0116960i
$913$	2.81277	+	4.87186i	0.00308080	+	0.00533610i
$914$	−69.1233	−	119.725i	−0.0756272	−	0.130990i
$915$		0			0
$916$			511.633i			0.558551i
$917$	−343.618	+	1113.85i	−0.374720	+	1.21467i
$918$		−	32.9846i		−	0.0359309i
$919$	−478.581	+	828.926i	−0.520762	+	0.901987i	0.478946	+	0.877844i	$0.341019\pi$
$919$	−478.581	+	828.926i	−0.520762	+	0.901987i	−0.999709	+	0.0241428i	$0.992314\pi$
$920$		0			0
$921$	41.0398	+	71.0831i	0.0445601	+	0.0771803i
$922$	−156.975	+	271.889i	−0.170255	+	0.294890i
$923$	−1078.14			−1.16808
$924$	−0.428202	−	1.87636i	−0.000463422	−	0.00203070i
$925$		0			0
$926$	−64.5533	+	111.810i	−0.0697120	+	0.120745i
$927$	−137.072	−	237.416i	−0.147866	−	0.256112i
$928$	−1265.80	+	730.811i	−1.36401	+	0.787511i
$929$	990.414	+	571.816i	1.06611	+	0.615517i	0.927115	−	0.374776i	$-0.122280\pi$
$929$	990.414	+	571.816i	1.06611	+	0.615517i	0.138992	+	0.990294i	$0.455614\pi$
$930$		0			0
$931$	55.9169	+	4.19412i	0.0600611	+	0.00450497i
$932$			1015.82i			1.08993i
$933$	−543.162	−	313.595i	−0.582167	−	0.336114i
$934$	−491.804	+	283.943i	−0.526557	+	0.304008i
$935$		0			0
$936$	−303.708	−	175.346i	−0.324474	−	0.187335i
$937$	578.660			0.617567			0.308783	−	0.951132i	$-0.400078\pi$
$937$	578.660			0.617567			0.308783	+	0.951132i	$0.400078\pi$
$938$	−7.35127	−	32.2129i	−0.00783717	−	0.0343422i
$939$	−681.760			−0.726049
$940$		0			0
$941$	−1086.18	+	627.108i	−1.15428	+	0.666427i	−0.949928	−	0.312470i	$-0.898844\pi$
$941$	−1086.18	+	627.108i	−1.15428	+	0.666427i	−0.204357	+	0.978896i	$0.565510\pi$
$942$	152.606	−	88.1069i	0.162002	−	0.0935317i
$943$	846.733	−	1466.59i	0.897915	−	1.55523i
$944$			52.4132i			0.0555225i
$945$		0			0
$946$	−2.30670			−0.00243837
$947$	1520.76	+	878.012i	1.60587	+	0.927151i	0.990280	+	0.139086i	$0.0444166\pi$
$947$	1520.76	+	878.012i	1.60587	+	0.927151i	0.615592	+	0.788065i	$0.288917\pi$
$948$	−62.8987	−	108.944i	−0.0663488	−	0.114920i
$949$	−961.388	−	1665.17i	−1.01305	−	1.75466i
$950$		0			0
$951$		−	1000.39i		−	1.05194i
$952$	−228.073	−	245.820i	−0.239572	−	0.258215i
$953$			1048.32i			1.10002i	0.835157	+	0.550011i	$0.185376\pi$
$953$			1048.32i			1.10002i	−0.835157	+	0.550011i	$0.814624\pi$
$954$	−19.1813	+	33.2231i	−0.0201062	+	0.0348250i
$955$		0			0
$956$	−733.085	−	1269.74i	−0.766826	−	1.32818i
$957$	2.05446	−	3.55844i	0.00214678	−	0.00371833i
$958$	−191.722			−0.200127
$959$	−347.300	−	374.325i	−0.362148	−	0.390329i
$960$		0			0
$961$	−225.203	+	390.062i	−0.234342	+	0.405892i
$962$	327.494	+	567.236i	0.340430	+	0.589642i
$963$	−273.066	+	157.655i	−0.283557	+	0.163712i
$964$	−908.785	−	524.688i	−0.942723	−	0.544282i
$965$		0			0
$966$	345.184	+	106.488i	0.357334	+	0.110236i
$967$		−	1770.86i		−	1.83130i	−0.401982	−	0.915648i	$-0.631679\pi$
$967$		−	1770.86i		−	1.83130i	0.401982	−	0.915648i	$-0.368321\pi$
$968$	532.556	+	307.471i	0.550161	+	0.317636i
$969$	−16.1797	+	9.34137i	−0.0166973	+	0.00964022i
$970$		0			0
$971$	834.000	+	481.510i	0.858908	+	0.495891i	0.863646	−	0.504098i	$-0.168175\pi$
$971$	834.000	+	481.510i	0.858908	+	0.495891i	−0.00473848	+	0.999989i	$0.501508\pi$
$972$	−55.2836			−0.0568762
$973$	−784.779	+	179.093i	−0.806556	+	0.184063i
$974$	131.760			0.135277
$975$		0			0
$976$	362.105	−	209.061i	0.371009	−	0.214202i
$977$	−466.182	+	269.150i	−0.477157	+	0.275487i	−0.719231	−	0.694771i	$-0.755506\pi$
$977$	−466.182	+	269.150i	−0.477157	+	0.275487i	0.242074	+	0.970258i	$0.422172\pi$
$978$	−34.9521	+	60.5388i	−0.0357383	+	0.0619006i
$979$		−	2.09040i		−	0.00213524i
$980$		0			0
$981$	−167.104			−0.170341
$982$	−434.782	−	251.021i	−0.442751	−	0.255623i
$983$	338.462	+	586.233i	0.344315	+	0.596371i	0.985229	−	0.171241i	$-0.0547778\pi$
$983$	338.462	+	586.233i	0.344315	+	0.596371i	−0.640914	+	0.767613i	$0.721444\pi$
$984$	−168.479	−	291.814i	−0.171218	−	0.296559i
$985$		0			0
$986$		−	336.440i		−	0.341217i
$987$	−73.2206	−	320.849i	−0.0741850	−	0.325075i
$988$			93.3481i			0.0944819i
$989$	−1692.69	+	2931.82i	−1.71151	+	2.96443i
$990$		0			0
$991$	−584.900	−	1013.08i	−0.590212	−	1.02228i	−0.994204	−	0.107514i	$-0.965711\pi$
$991$	−584.900	−	1013.08i	−0.590212	−	1.02228i	0.403992	−	0.914763i	$-0.367622\pi$
$992$	311.576	−	539.666i	0.314089	−	0.544018i
$993$	317.995			0.320237
$994$	65.1400	−	211.154i	0.0655332	−	0.212428i
$995$		0			0
$996$	386.011	−	668.590i	0.387561	−	0.671275i
$997$	301.963	+	523.016i	0.302872	+	0.524590i	0.976785	−	0.214221i	$-0.0687212\pi$
$997$	301.963	+	523.016i	0.302872	+	0.524590i	−0.673913	+	0.738810i	$0.735388\pi$
$998$	−53.6283	+	30.9623i	−0.0537358	+	0.0310244i
$999$	190.276	+	109.856i	0.190467	+	0.109966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.s.h.124.4		16
5.2	odd	4		525.3.o.l.376.3		8
5.3	odd	4		105.3.n.a.61.2	yes	8
5.4	even	2	inner	525.3.s.h.124.5		16
7.3	odd	6	inner	525.3.s.h.199.5		16
15.8	even	4		315.3.w.a.271.3		8
35.3	even	12		105.3.n.a.31.2	✓	8
35.17	even	12		525.3.o.l.451.3		8
35.23	odd	12		735.3.h.a.391.5		8
35.24	odd	6	inner	525.3.s.h.199.4		16
35.33	even	12		735.3.h.a.391.6		8
105.38	odd	12		315.3.w.a.136.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.n.a.31.2	✓	8	35.3	even	12
105.3.n.a.61.2	yes	8	5.3	odd	4
315.3.w.a.136.3		8	105.38	odd	12
315.3.w.a.271.3		8	15.8	even	4
525.3.o.l.376.3		8	5.2	odd	4
525.3.o.l.451.3		8	35.17	even	12
525.3.s.h.124.4		16	1.1	even	1	trivial
525.3.s.h.124.5		16	5.4	even	2	inner
525.3.s.h.199.4		16	35.24	odd	6	inner
525.3.s.h.199.5		16	7.3	odd	6	inner
735.3.h.a.391.5		8	35.23	odd	12
735.3.h.a.391.6		8	35.33	even	12

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.583237 - 0.336732i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-1.77322 - 3.07131i) q^{4} -1.16647i q^{6} +(-1.55742 - 6.82455i) q^{7} +5.08226i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.583237 - 0.336732i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-1.77322 - 3.07131i) q^{4} -1.16647i q^{6} +(-1.55742 - 6.82455i) q^{7} +5.08226i q^{8} +(-1.50000 + 2.59808i) q^{9} +(0.0223800 + 0.0387632i) q^{11} +(3.07131 - 5.31967i) q^{12} +23.0010 q^{13} +(-1.38970 + 4.50476i) q^{14} +(-5.38154 + 9.32109i) q^{16} +(-4.71286 - 8.16292i) q^{17} +(1.74971 - 1.01020i) q^{18} +(-0.991050 - 0.572183i) q^{19} +(8.88806 - 8.24636i) q^{21} -0.0301442i q^{22} +(-38.3133 - 22.1202i) q^{23} +(-7.62339 + 4.40136i) q^{24} +(-13.4150 - 7.74518i) q^{26} -5.19615 q^{27} +(-18.1987 + 16.8848i) q^{28} -53.0004 q^{29} +(19.5690 - 11.2982i) q^{31} +(23.8829 - 13.7888i) q^{32} +(-0.0387632 + 0.0671399i) q^{33} +6.34788i q^{34} +10.6393 q^{36} +(-36.6186 - 21.1418i) q^{37} +(0.385344 + 0.667436i) q^{38} +(19.9195 + 34.5015i) q^{39} +38.2787i q^{41} +(-7.96065 + 1.81669i) q^{42} -76.5222i q^{43} +(0.0793693 - 0.137472i) q^{44} +(14.8971 + 25.8026i) q^{46} +(13.5718 - 23.5070i) q^{47} -18.6422 q^{48} +(-44.1489 + 21.2574i) q^{49} +(8.16292 - 14.1386i) q^{51} +(-40.7860 - 70.6434i) q^{52} +(-16.4439 + 9.49388i) q^{53} +(3.03059 + 1.74971i) q^{54} +(34.6841 - 7.91521i) q^{56} -1.98210i q^{57} +(30.9118 + 17.8469i) q^{58} +(4.21731 - 2.43486i) q^{59} +(-33.6432 - 19.4239i) q^{61} -15.2178 q^{62} +(20.0668 + 6.19052i) q^{63} +24.4798 q^{64} +(0.0452163 - 0.0261056i) q^{66} +(-6.06978 + 3.50439i) q^{67} +(-16.7139 + 28.9494i) q^{68} -76.6266i q^{69} -46.8735 q^{71} +(-13.2041 - 7.62339i) q^{72} +(-41.7976 - 72.3956i) q^{73} +(14.2382 + 24.6613i) q^{74} +4.05843i q^{76} +(0.229686 - 0.213104i) q^{77} -26.8301i q^{78} +(10.2397 - 17.7357i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(12.8897 - 22.3256i) q^{82} +125.683 q^{83} +(-41.0877 - 12.6754i) q^{84} +(-25.7674 + 44.6305i) q^{86} +(-45.8997 - 79.5006i) q^{87} +(-0.197005 + 0.113741i) q^{88} +(-40.4455 - 23.3512i) q^{89} +(-35.8223 - 156.972i) q^{91} +156.896i q^{92} +(33.8945 + 19.5690i) q^{93} +(-15.8311 + 9.14010i) q^{94} +(41.3663 + 23.8829i) q^{96} -3.11494 q^{97} +(32.9073 + 2.46826i) q^{98} -0.134280 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} - 24 q^{9}+O(q^{10}) \) 16 * q + 12 * q^4 - 24 * q^9	\( 16 q + 12 q^{4} - 24 q^{9} + 40 q^{11} + 32 q^{14} - 4 q^{16} + 96 q^{21} - 96 q^{24} + 240 q^{26} + 200 q^{29} - 252 q^{31} - 72 q^{36} + 24 q^{39} + 36 q^{44} - 164 q^{46} - 76 q^{49} + 36 q^{51} - 36 q^{54} + 392 q^{56} + 108 q^{59} - 792 q^{61} + 8 q^{64} + 48 q^{66} + 328 q^{71} + 280 q^{74} + 412 q^{79} - 72 q^{81} - 264 q^{84} + 356 q^{86} - 564 q^{89} - 228 q^{91} - 60 q^{94} - 216 q^{96} - 240 q^{99}+O(q^{100}) \) 16 * q + 12 * q^4 - 24 * q^9 + 40 * q^11 + 32 * q^14 - 4 * q^16 + 96 * q^21 - 96 * q^24 + 240 * q^26 + 200 * q^29 - 252 * q^31 - 72 * q^36 + 24 * q^39 + 36 * q^44 - 164 * q^46 - 76 * q^49 + 36 * q^51 - 36 * q^54 + 392 * q^56 + 108 * q^59 - 792 * q^61 + 8 * q^64 + 48 * q^66 + 328 * q^71 + 280 * q^74 + 412 * q^79 - 72 * q^81 - 264 * q^84 + 356 * q^86 - 564 * q^89 - 228 * q^91 - 60 * q^94 - 216 * q^96 - 240 * q^99

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