LMFDB - Embedded newform 525.3.o.q.451.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(376,525)]

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, 0, 5]))

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

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

chi := DirichletCharacter("525.376");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.o (of order $6$, 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:	$14.3052138789$
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} + 24 x^{14} + 405 x^{12} - 30 x^{11} + 3324 x^{10} - 1302 x^{9} + 19731 x^{8} - 8442 x^{7} + \cdots + 22500 $ x^16 + 24x^14 + 405x^12 - 30x^11 + 3324x^10 - 1302x^9 + 19731x^8 - 8442x^7 + 60390x^6 - 35496x^5 + 130590x^4 - 44820x^3 + 77544x^2 + 20700*x + 22500
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.1
Root			$-1.70407 + 2.95153i$ of defining polynomial
Character	$\chi$	$=$	525.451
Dual form			525.3.o.q.376.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70407 - 2.95153i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-3.80769 + 6.59511i) q^{4} -5.90306i q^{6} +(4.74314 - 5.14807i) q^{7} +12.3217 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.70407 - 2.95153i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-3.80769 + 6.59511i) q^{4} -5.90306i q^{6} +(4.74314 - 5.14807i) q^{7} +12.3217 q^{8} +(1.50000 + 2.59808i) q^{9} +(0.694658 - 1.20318i) q^{11} +(-11.4231 + 6.59511i) q^{12} -3.78639i q^{13} +(-23.2773 - 5.22688i) q^{14} +(-5.76621 - 9.98737i) q^{16} +(27.4592 + 15.8536i) q^{17} +(5.11220 - 8.85459i) q^{18} +(-12.8335 + 7.40942i) q^{19} +(11.5731 - 3.61442i) q^{21} -4.73498 q^{22} +(11.3088 + 19.5874i) q^{23} +(18.4825 + 10.6709i) q^{24} +(-11.1756 + 6.45226i) q^{26} +5.19615i q^{27} +(15.8916 + 50.8838i) q^{28} +42.9485 q^{29} +(-28.0131 - 16.1734i) q^{31} +(4.99133 - 8.64524i) q^{32} +(2.08398 - 1.20318i) q^{33} -108.062i q^{34} -22.8461 q^{36} +(-4.21074 - 7.29321i) q^{37} +(43.7383 + 25.2523i) q^{38} +(3.27911 - 5.67959i) q^{39} -46.3613i q^{41} +(-30.3893 - 27.9991i) q^{42} -9.92743 q^{43} +(5.29008 + 9.16269i) q^{44} +(38.5418 - 66.7564i) q^{46} +(47.2522 - 27.2811i) q^{47} -19.9747i q^{48} +(-4.00517 - 48.8360i) q^{49} +(27.4592 + 47.5607i) q^{51} +(24.9717 + 14.4174i) q^{52} +(42.9734 - 74.4321i) q^{53} +(15.3366 - 8.85459i) q^{54} +(58.4435 - 63.4328i) q^{56} -25.6670 q^{57} +(-73.1872 - 126.764i) q^{58} +(80.4509 + 46.4483i) q^{59} +(1.41863 - 0.819048i) q^{61} +110.242i q^{62} +(20.4898 + 4.60095i) q^{63} -80.1519 q^{64} +(-7.10247 - 4.10061i) q^{66} +(21.8835 - 37.9034i) q^{67} +(-209.112 + 120.731i) q^{68} +39.1748i q^{69} -60.9268 q^{71} +(18.4825 + 32.0127i) q^{72} +(55.9872 + 32.3243i) q^{73} +(-14.3508 + 24.8563i) q^{74} -112.851i q^{76} +(-2.89920 - 9.28302i) q^{77} -22.3513 q^{78} +(-0.744936 - 1.29027i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-136.837 + 79.0028i) q^{82} -13.6731i q^{83} +(-20.2292 + 90.0882i) q^{84} +(16.9170 + 29.3011i) q^{86} +(64.4228 + 37.1945i) q^{87} +(8.55936 - 14.8252i) q^{88} +(-110.062 + 63.5444i) q^{89} +(-19.4926 - 17.9594i) q^{91} -172.241 q^{92} +(-28.0131 - 48.5201i) q^{93} +(-161.042 - 92.9775i) q^{94} +(14.9740 - 8.64524i) q^{96} -119.276i q^{97} +(-137.316 + 95.0412i) q^{98} +4.16795 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 24 q^{3} - 16 q^{4} + 6 q^{7} + 24 q^{9}+O(q^{10}) $ 16 * q + 24 * q^3 - 16 * q^4 + 6 * q^7 + 24 * q^9	$ 16 q + 24 q^{3} - 16 q^{4} + 6 q^{7} + 24 q^{9} - 14 q^{11} - 48 q^{12} - 30 q^{14} - 20 q^{16} + 6 q^{17} + 30 q^{19} + 6 q^{21} - 36 q^{22} - 18 q^{23} - 48 q^{26} - 168 q^{28} + 44 q^{29} + 42 q^{31} + 150 q^{32} - 42 q^{33} - 96 q^{36} + 96 q^{37} + 204 q^{38} - 18 q^{39} - 78 q^{42} - 160 q^{44} - 30 q^{46} - 138 q^{47} - 178 q^{49} + 6 q^{51} + 126 q^{52} + 150 q^{53} - 234 q^{56} + 60 q^{57} - 90 q^{58} + 402 q^{59} + 168 q^{61} + 200 q^{64} - 54 q^{66} + 174 q^{67} - 234 q^{68} + 172 q^{71} + 336 q^{73} - 450 q^{74} - 372 q^{77} - 96 q^{78} + 10 q^{79} - 72 q^{81} - 690 q^{82} - 390 q^{84} + 72 q^{86} + 66 q^{87} + 492 q^{88} - 12 q^{89} - 112 q^{91} + 204 q^{92} + 42 q^{93} + 462 q^{94} + 450 q^{96} - 198 q^{98} - 84 q^{99}+O(q^{100}) $ 16 * q + 24 * q^3 - 16 * q^4 + 6 * q^7 + 24 * q^9 - 14 * q^11 - 48 * q^12 - 30 * q^14 - 20 * q^16 + 6 * q^17 + 30 * q^19 + 6 * q^21 - 36 * q^22 - 18 * q^23 - 48 * q^26 - 168 * q^28 + 44 * q^29 + 42 * q^31 + 150 * q^32 - 42 * q^33 - 96 * q^36 + 96 * q^37 + 204 * q^38 - 18 * q^39 - 78 * q^42 - 160 * q^44 - 30 * q^46 - 138 * q^47 - 178 * q^49 + 6 * q^51 + 126 * q^52 + 150 * q^53 - 234 * q^56 + 60 * q^57 - 90 * q^58 + 402 * q^59 + 168 * q^61 + 200 * q^64 - 54 * q^66 + 174 * q^67 - 234 * q^68 + 172 * q^71 + 336 * q^73 - 450 * q^74 - 372 * q^77 - 96 * q^78 + 10 * q^79 - 72 * q^81 - 690 * q^82 - 390 * q^84 + 72 * q^86 + 66 * q^87 + 492 * q^88 - 12 * q^89 - 112 * q^91 + 204 * q^92 + 42 * q^93 + 462 * q^94 + 450 * q^96 - 198 * q^98 - 84 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.70407	−	2.95153i	−0.852033	−	1.47577i	−0.879370	−	0.476139i	$-0.842036\pi$
$2$	−1.70407	−	2.95153i	−0.852033	−	1.47577i	0.0273367	−	0.999626i	$-0.491297\pi$
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$4$	−3.80769	+	6.59511i	−0.951922	+	1.64878i
$5$		0			0
$5$		0			0
$6$		−	5.90306i		−	0.983843i
$7$	4.74314	−	5.14807i	0.677592	−	0.735438i
$7$	4.74314	−	5.14807i	0.677592	−	0.735438i
$8$	12.3217			1.54021
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	0.694658	−	1.20318i	0.0631508	−	0.109380i	−0.832721	−	0.553692i	$-0.813218\pi$
$11$	0.694658	−	1.20318i	0.0631508	−	0.109380i	0.895872	+	0.444312i	$0.146552\pi$
$12$	−11.4231	+	6.59511i	−0.951922	+	0.549592i
$13$		−	3.78639i		−	0.291261i	−0.989339	−	0.145630i	$-0.953479\pi$
$13$		−	3.78639i		−	0.291261i	0.989339	−	0.145630i	$-0.0465210\pi$
$14$	−23.2773	−	5.22688i	−1.66266	−	0.373349i
$15$		0			0
$16$	−5.76621	−	9.98737i	−0.360388	−	0.624211i
$17$	27.4592	+	15.8536i	1.61525	+	0.932563i	0.988127	+	0.153641i	$0.0491000\pi$
$17$	27.4592	+	15.8536i	1.61525	+	0.932563i	0.627121	+	0.778922i	$0.284233\pi$
$18$	5.11220	−	8.85459i	0.284011	−	0.491922i
$19$	−12.8335	+	7.40942i	−0.675447	+	0.389970i	−0.798137	−	0.602475i	$-0.794181\pi$
$19$	−12.8335	+	7.40942i	−0.675447	+	0.389970i	0.122690	+	0.992445i	$0.460848\pi$
$20$		0			0
$21$	11.5731	−	3.61442i	0.551099	−	0.172115i
$22$	−4.73498			−0.215226
$23$	11.3088	+	19.5874i	0.491686	+	0.851625i	0.999954	−	0.00957359i	$-0.00304741\pi$
$23$	11.3088	+	19.5874i	0.491686	+	0.851625i	−0.508268	+	0.861199i	$0.669714\pi$
$24$	18.4825	+	10.6709i	0.770105	+	0.444620i
$25$		0			0
$26$	−11.1756	+	6.45226i	−0.429833	+	0.248164i
$27$			5.19615i			0.192450i
$28$	15.8916	+	50.8838i	0.567559	+	1.81728i
$29$	42.9485			1.48098			0.740492	−	0.672065i	$-0.234593\pi$
$29$	42.9485			1.48098			0.740492	+	0.672065i	$0.234593\pi$
$30$		0			0
$31$	−28.0131	−	16.1734i	−0.903649	−	0.521722i	−0.0252666	−	0.999681i	$-0.508043\pi$
$31$	−28.0131	−	16.1734i	−0.903649	−	0.521722i	−0.878382	+	0.477959i	$0.841377\pi$
$32$	4.99133	−	8.64524i	0.155979	−	0.270164i
$33$	2.08398	−	1.20318i	0.0631508	−	0.0364601i
$34$		−	108.062i		−	3.17830i
$35$		0			0
$36$	−22.8461			−0.634615
$37$	−4.21074	−	7.29321i	−0.113804	−	0.197114i	0.803497	−	0.595309i	$-0.202970\pi$
$37$	−4.21074	−	7.29321i	−0.113804	−	0.197114i	−0.917301	+	0.398195i	$0.869637\pi$
$38$	43.7383	+	25.2523i	1.15101	+	0.664534i
$39$	3.27911	−	5.67959i	0.0840798	−	0.145630i
$40$		0			0
$41$		−	46.3613i		−	1.13076i	−0.824829	−	0.565382i	$-0.808729\pi$
$41$		−	46.3613i		−	1.13076i	0.824829	−	0.565382i	$-0.191271\pi$
$42$	−30.3893	−	27.9991i	−0.723556	−	0.666644i
$43$	−9.92743			−0.230871			−0.115435	−	0.993315i	$-0.536826\pi$
$43$	−9.92743			−0.230871			−0.115435	+	0.993315i	$0.536826\pi$
$44$	5.29008	+	9.16269i	0.120229	+	0.208243i
$45$		0			0
$46$	38.5418	−	66.7564i	0.837866	−	1.45123i
$47$	47.2522	−	27.2811i	1.00537	−	0.580448i	0.0955345	−	0.995426i	$-0.469544\pi$
$47$	47.2522	−	27.2811i	1.00537	−	0.580448i	0.909832	+	0.414978i	$0.136211\pi$
$48$		−	19.9747i		−	0.416141i
$49$	−4.00517	−	48.8360i	−0.0817381	−	0.996654i
$50$		0			0
$51$	27.4592	+	47.5607i	0.538416	+	0.932563i
$52$	24.9717	+	14.4174i	0.480224	+	0.277258i
$53$	42.9734	−	74.4321i	0.810819	−	1.40438i	−0.101472	−	0.994838i	$-0.532355\pi$
$53$	42.9734	−	74.4321i	0.810819	−	1.40438i	0.912291	−	0.409542i	$-0.134311\pi$
$54$	15.3366	−	8.85459i	0.284011	−	0.163974i
$55$		0			0
$56$	58.4435	−	63.4328i	1.04363	−	1.13273i
$57$	−25.6670			−0.450298
$58$	−73.1872	−	126.764i	−1.26185	−	2.18558i
$59$	80.4509	+	46.4483i	1.36357	+	0.787260i	0.990098	−	0.140380i	$-0.0448323\pi$
$59$	80.4509	+	46.4483i	1.36357	+	0.787260i	0.373477	+	0.927640i	$0.378166\pi$
$60$		0			0
$61$	1.41863	−	0.819048i	0.0232563	−	0.0134270i	−0.488327	−	0.872661i	$-0.662393\pi$
$61$	1.41863	−	0.819048i	0.0232563	−	0.0134270i	0.511583	+	0.859234i	$0.329059\pi$
$62$			110.242i			1.77810i
$63$	20.4898	+	4.60095i	0.325235	+	0.0730310i
$64$	−80.1519			−1.25237
$65$		0			0
$66$	−7.10247	−	4.10061i	−0.107613	−	0.0621305i
$67$	21.8835	−	37.9034i	0.326620	−	0.565722i	−0.655219	−	0.755439i	$-0.727424\pi$
$67$	21.8835	−	37.9034i	0.326620	−	0.565722i	0.981839	+	0.189717i	$0.0607570\pi$
$68$	−209.112	+	120.731i	−3.07518	+	1.77545i
$69$			39.1748i			0.567750i
$70$		0			0
$71$	−60.9268			−0.858124			−0.429062	−	0.903275i	$-0.641156\pi$
$71$	−60.9268			−0.858124			−0.429062	+	0.903275i	$0.641156\pi$
$72$	18.4825	+	32.0127i	0.256702	+	0.444620i
$73$	55.9872	+	32.3243i	0.766949	+	0.442798i	0.831785	−	0.555098i	$-0.187319\pi$
$73$	55.9872	+	32.3243i	0.766949	+	0.442798i	−0.0648364	+	0.997896i	$0.520653\pi$
$74$	−14.3508	+	24.8563i	−0.193929	+	0.335895i
$75$		0			0
$76$		−	112.851i		−	1.48488i
$77$	−2.89920	−	9.28302i	−0.0376520	−	0.120559i
$78$	−22.3513			−0.286555
$79$	−0.744936	−	1.29027i	−0.00942957	−	0.0163325i	0.861272	−	0.508144i	$-0.169668\pi$
$79$	−0.744936	−	1.29027i	−0.00942957	−	0.0163325i	−0.870702	+	0.491812i	$0.836335\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−136.837	+	79.0028i	−1.66874	+	0.963449i
$83$		−	13.6731i		−	0.164736i	−0.996602	−	0.0823681i	$-0.973752\pi$
$83$		−	13.6731i		−	0.164736i	0.996602	−	0.0823681i	$-0.0262483\pi$
$84$	−20.2292	+	90.0882i	−0.240824	+	1.07248i
$85$		0			0
$86$	16.9170	+	29.3011i	0.196709	+	0.340711i
$87$	64.4228	+	37.1945i	0.740492	+	0.427523i
$88$	8.55936	−	14.8252i	0.0972654	−	0.168469i
$89$	−110.062	+	63.5444i	−1.23665	+	0.713982i	−0.968409	−	0.249369i	$-0.919777\pi$
$89$	−110.062	+	63.5444i	−1.23665	+	0.713982i	−0.268244	+	0.963351i	$0.586443\pi$
$90$		0			0
$91$	−19.4926	−	17.9594i	−0.214204	−	0.197356i
$92$	−172.241			−1.87219
$93$	−28.0131	−	48.5201i	−0.301216	−	0.521722i
$94$	−161.042	−	92.9775i	−1.71321	−	0.989123i
$95$		0			0
$96$	14.9740	−	8.64524i	0.155979	−	0.0900546i
$97$		−	119.276i		−	1.22965i	−0.788664	−	0.614824i	$-0.789227\pi$
$97$		−	119.276i		−	1.22965i	0.788664	−	0.614824i	$-0.210773\pi$
$98$	−137.316	+	95.0412i	−1.40118	+	0.969809i
$99$	4.16795			0.0421005
$100$		0			0
$101$	103.691	+	59.8659i	1.02664	+	0.592732i	0.916021	−	0.401131i	$-0.131383\pi$
$101$	103.691	+	59.8659i	1.02664	+	0.592732i	0.110621	+	0.993863i	$0.464716\pi$
$102$	93.5846	−	162.093i	0.917496	−	1.58915i
$103$	54.0203	−	31.1886i	0.524469	−	0.302802i	−0.214292	−	0.976770i	$-0.568744\pi$
$103$	54.0203	−	31.1886i	0.524469	−	0.302802i	0.738761	+	0.673967i	$0.235411\pi$
$104$		−	46.6547i		−	0.448603i
$105$		0			0
$106$	−292.918			−2.76338
$107$	−60.1634	−	104.206i	−0.562275	−	0.973888i	−0.997298	−	0.0734689i	$-0.976593\pi$
$107$	−60.1634	−	104.206i	−0.562275	−	0.973888i	0.435023	−	0.900419i	$-0.356740\pi$
$108$	−34.2692	−	19.7853i	−0.317307	−	0.183197i
$109$	−32.5298	+	56.3433i	−0.298439	+	0.516911i	−0.975779	−	0.218759i	$-0.929799\pi$
$109$	−32.5298	+	56.3433i	−0.298439	+	0.516911i	0.677340	+	0.735670i	$0.263132\pi$
$110$		0			0
$111$		−	14.5864i		−	0.131409i
$112$	−78.7656	−	17.6867i	−0.703265	−	0.157917i
$113$	−133.463			−1.18109			−0.590545	−	0.807005i	$-0.701087\pi$
$113$	−133.463			−1.18109			−0.590545	+	0.807005i	$0.701087\pi$
$114$	43.7383	+	75.7569i	0.383669	+	0.664534i
$115$		0			0
$116$	−163.535	+	283.250i	−1.40978	+	2.44181i
$117$	9.83733	−	5.67959i	0.0840798	−	0.0485435i
$118$		−	316.604i		−	2.68309i
$119$	211.858	−	66.1660i	1.78032	−	0.556017i
$120$		0			0
$121$	59.5349	+	103.117i	0.492024	+	0.852211i
$122$	−4.83489	−	2.79143i	−0.0396303	−	0.0228805i
$123$	40.1501	−	69.5420i	0.326424	−	0.565382i
$124$	213.330	−	123.166i	1.72041	−	0.993277i
$125$		0			0
$126$	−21.3361	−	68.3165i	−0.169334	−	0.542195i
$127$	187.969			1.48007			0.740034	−	0.672570i	$-0.234809\pi$
$127$	187.969			1.48007			0.740034	+	0.672570i	$0.234809\pi$
$128$	116.619	+	201.990i	0.911086	+	1.57805i
$129$	−14.8912	−	8.59741i	−0.115435	−	0.0666466i
$130$		0			0
$131$	61.6992	−	35.6220i	0.470986	−	0.271924i	−0.245666	−	0.969354i	$-0.579007\pi$
$131$	61.6992	−	35.6220i	0.470986	−	0.271924i	0.716652	+	0.697431i	$0.245673\pi$
$132$			18.3254i			0.138829i
$133$	−22.7269	+	101.212i	−0.170879	+	0.760990i
$134$	−149.164			−1.11316
$135$		0			0
$136$	338.343	+	195.343i	2.48782	+	1.43634i
$137$	−18.9907	+	32.8928i	−0.138618	+	0.240093i	−0.926974	−	0.375126i	$-0.877599\pi$
$137$	−18.9907	+	32.8928i	−0.138618	+	0.240093i	0.788356	+	0.615220i	$0.210933\pi$
$138$	115.626	−	66.7564i	0.837866	−	0.483742i
$139$			98.4179i			0.708042i	0.935237	+	0.354021i	$0.115186\pi$
$139$			98.4179i			0.708042i	−0.935237	+	0.354021i	$0.884814\pi$
$140$		0			0
$141$	94.5044			0.670244
$142$	103.823	+	179.827i	0.731150	+	1.26639i
$143$	−4.55572	−	2.63025i	−0.0318582	−	0.0183933i
$144$	17.2986	−	29.9621i	0.120129	−	0.208070i
$145$		0			0
$146$		−	220.331i		−	1.50911i
$147$	36.2855	−	76.7226i	0.246840	−	0.521923i
$148$	64.1327			0.433329
$149$	−89.3441	−	154.748i	−0.599625	−	1.03858i	−0.992876	−	0.119149i	$-0.961983\pi$
$149$	−89.3441	−	154.748i	−0.599625	−	1.03858i	0.393252	−	0.919431i	$-0.371350\pi$
$150$		0			0
$151$	−120.777	+	209.191i	−0.799846	+	1.38537i	0.119870	+	0.992790i	$0.461752\pi$
$151$	−120.777	+	209.191i	−0.799846	+	1.38537i	−0.919716	+	0.392584i	$0.871581\pi$
$152$	−158.130	+	91.2965i	−1.04033	+	0.600635i
$153$			95.1215i			0.621709i
$154$	−22.4587	+	24.3760i	−0.145836	+	0.158286i
$155$		0			0
$156$	24.9717	+	43.2522i	0.160075	+	0.277258i
$157$	35.7883	+	20.6624i	0.227951	+	0.131607i	0.609626	−	0.792689i	$-0.291320\pi$
$157$	35.7883	+	20.6624i	0.227951	+	0.131607i	−0.381676	+	0.924296i	$0.624653\pi$
$158$	−2.53884	+	4.39740i	−0.0160686	+	0.0278317i
$159$	128.920	−	74.4321i	0.810819	−	0.468127i
$160$		0			0
$161$	154.476	+	34.6874i	0.959480	+	0.215450i
$162$	30.6732			0.189341
$163$	34.9366	+	60.5120i	0.214335	+	0.371239i	0.953067	−	0.302760i	$-0.0979082\pi$
$163$	34.9366	+	60.5120i	0.214335	+	0.371239i	−0.738732	+	0.674000i	$0.764575\pi$
$164$	305.758	+	176.529i	1.86438	+	1.07640i
$165$		0			0
$166$	−40.3566	+	23.2999i	−0.243112	+	0.140361i
$167$			32.7058i			0.195843i	0.995194	+	0.0979217i	$0.0312195\pi$
$167$			32.7058i			0.195843i	−0.995194	+	0.0979217i	$0.968781\pi$
$168$	142.600	−	44.5357i	0.848808	−	0.265093i
$169$	154.663			0.915167
$170$		0			0
$171$	−38.5005	−	22.2283i	−0.225149	−	0.129990i
$172$	37.8006	−	65.4725i	0.219771	−	0.380654i
$173$	−21.5197	+	12.4244i	−0.124391	+	0.0718173i	−0.560904	−	0.827881i	$-0.689547\pi$
$173$	−21.5197	+	12.4244i	−0.124391	+	0.0718173i	0.436513	+	0.899698i	$0.356213\pi$
$174$		−	253.528i		−	1.45706i
$175$		0			0
$176$	−16.0222			−0.0910352
$177$	80.4509	+	139.345i	0.454525	+	0.787260i
$178$	375.106	+	216.568i	2.10734	+	1.21667i
$179$	−70.0625	+	121.352i	−0.391411	+	0.677943i	−0.992636	−	0.121136i	$-0.961346\pi$
$179$	−70.0625	+	121.352i	−0.391411	+	0.677943i	0.601225	+	0.799080i	$0.294679\pi$
$180$		0			0
$181$		−	281.086i		−	1.55296i	−0.630142	−	0.776480i	$-0.717003\pi$
$181$		−	281.086i		−	1.55296i	0.630142	−	0.776480i	$-0.282997\pi$
$182$	−19.7910	+	88.1370i	−0.108742	+	0.484269i
$183$	2.83727			0.0155042
$184$	139.343	+	241.349i	0.757300	+	1.31168i
$185$		0			0
$186$	−95.4724	+	165.363i	−0.513293	+	0.889049i
$187$	38.1495	−	22.0256i	0.204008	−	0.117784i
$188$			415.511i			2.21017i
$189$	26.7501	+	24.6461i	0.141535	+	0.130403i
$190$		0			0
$191$	51.1878	+	88.6599i	0.267999	+	0.464188i	0.968345	−	0.249616i	$-0.0803043\pi$
$191$	51.1878	+	88.6599i	0.267999	+	0.464188i	−0.700346	+	0.713804i	$0.746971\pi$
$192$	−120.228	−	69.4136i	−0.626187	−	0.361529i
$193$	−1.34101	+	2.32270i	−0.00694825	+	0.0120347i	−0.869479	−	0.493971i	$-0.835545\pi$
$193$	−1.34101	+	2.32270i	−0.00694825	+	0.0120347i	0.862530	+	0.506005i	$0.168878\pi$
$194$	−352.047	+	203.254i	−1.81467	+	1.04770i
$195$		0			0
$196$	337.329	+	159.538i	1.72107	+	0.813969i
$197$	32.0387			0.162633			0.0813164	−	0.996688i	$-0.474088\pi$
$197$	32.0387			0.162633			0.0813164	+	0.996688i	$0.474088\pi$
$198$	−7.10247	−	12.3018i	−0.0358710	−	0.0621305i
$199$	−14.1309	−	8.15845i	−0.0710093	−	0.0409973i	0.464075	−	0.885796i	$-0.346387\pi$
$199$	−14.1309	−	8.15845i	−0.0710093	−	0.0409973i	−0.535084	+	0.844799i	$0.679720\pi$
$200$		0			0
$201$	65.6506	−	37.9034i	0.326620	−	0.188574i
$202$		−	408.062i		−	2.02011i
$203$	203.711	−	221.102i	1.00350	−	1.08917i
$204$	−418.224			−2.05012
$205$		0			0
$206$	−184.108	−	106.295i	−0.893730	−	0.515995i
$207$	−33.9263	+	58.7621i	−0.163895	+	0.283875i
$208$	−37.8161	+	21.8331i	−0.181808	+	0.104967i
$209$			20.5881i			0.0985075i
$210$		0			0
$211$	−311.474			−1.47618			−0.738091	−	0.674701i	$-0.764272\pi$
$211$	−311.474			−1.47618			−0.738091	+	0.674701i	$0.764272\pi$
$212$	327.259	+	566.829i	1.54367	+	2.67372i
$213$	−91.3902	−	52.7642i	−0.429062	−	0.247719i
$214$	−205.045	+	355.148i	−0.958154	+	1.65957i
$215$		0			0
$216$			64.0253i			0.296414i
$217$	−216.132	+	67.5007i	−0.995999	+	0.311063i
$218$	221.732			1.01712
$219$	55.9872	+	96.9728i	0.255650	+	0.442798i
$220$		0			0
$221$	60.0278	−	103.971i	0.271619	−	0.470458i
$222$	−43.0523	+	24.8563i	−0.193929	+	0.111965i
$223$			111.515i			0.500068i	0.968237	+	0.250034i	$0.0804418\pi$
$223$			111.515i			0.500068i	−0.968237	+	0.250034i	$0.919558\pi$
$224$	−20.8317	−	66.7013i	−0.0929985	−	0.297774i
$225$		0			0
$226$	227.430	+	393.920i	1.00633	+	1.74301i
$227$	−73.8486	−	42.6365i	−0.325324	−	0.187826i	0.328439	−	0.944525i	$-0.393477\pi$
$227$	−73.8486	−	42.6365i	−0.325324	−	0.187826i	−0.653763	+	0.756699i	$0.726811\pi$
$228$	97.7319	−	169.277i	0.428649	−	0.742441i
$229$	60.4219	−	34.8846i	0.263851	−	0.152334i	−0.362239	−	0.932085i	$-0.617988\pi$
$229$	60.4219	−	34.8846i	0.263851	−	0.152334i	0.626090	+	0.779751i	$0.284654\pi$
$230$		0			0
$231$	3.69053	−	16.4353i	0.0159763	−	0.0711485i
$232$	529.198			2.28103
$233$	86.7866	+	150.319i	0.372475	+	0.645145i	0.989946	−	0.141449i	$-0.0451761\pi$
$233$	86.7866	+	150.319i	0.372475	+	0.645145i	−0.617471	+	0.786594i	$0.711843\pi$
$234$	−33.5269	−	19.3568i	−0.143278	−	0.0827213i
$235$		0			0
$236$	−612.664	+	353.722i	−2.59603	+	1.49882i
$237$		−	2.58053i		−	0.0108883i
$238$	−556.311	−	512.555i	−2.33744	−	2.15359i
$239$	108.916			0.455717			0.227858	−	0.973694i	$-0.426828\pi$
$239$	108.916			0.455717			0.227858	+	0.973694i	$0.426828\pi$
$240$		0			0
$241$	−89.8157	−	51.8551i	−0.372679	−	0.215167i	0.301949	−	0.953324i	$-0.402363\pi$
$241$	−89.8157	−	51.8551i	−0.372679	−	0.215167i	−0.674628	+	0.738158i	$0.735696\pi$
$242$	202.903	−	351.438i	0.838442	−	1.45222i
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$			12.4747i			0.0511259i
$245$		0			0
$246$	−273.674			−1.11249
$247$	28.0550	+	48.5926i	0.113583	+	0.196731i
$248$	−345.169	−	199.283i	−1.39181	−	0.803561i
$249$	11.8413	−	20.5097i	0.0475553	−	0.0823681i
$250$		0			0
$251$			231.368i			0.921787i	0.887456	+	0.460893i	$0.152471\pi$
$251$			231.368i			0.921787i	−0.887456	+	0.460893i	$0.847529\pi$
$252$	−108.362	+	117.613i	−0.430010	+	0.466720i
$253$	31.4230			0.124201
$254$	−320.311	−	554.795i	−1.26107	−	2.18423i
$255$		0			0
$256$	237.149	−	410.754i	0.926364	−	1.60451i
$257$	−79.9380	+	46.1522i	−0.311043	+	0.179581i	−0.647393	−	0.762156i	$-0.724141\pi$
$257$	−79.9380	+	46.1522i	−0.311043	+	0.179581i	0.336350	+	0.941737i	$0.390807\pi$
$258$			58.6022i			0.227140i
$259$	−57.5181	−	12.9156i	−0.222078	−	0.0498672i
$260$		0			0
$261$	64.4228	+	111.584i	0.246831	+	0.427523i
$262$	−210.279	−	121.405i	−0.802592	−	0.463377i
$263$	−75.3906	+	130.580i	−0.286656	+	0.496503i	−0.973009	−	0.230765i	$-0.925877\pi$
$263$	−75.3906	+	130.580i	−0.286656	+	0.496503i	0.686353	+	0.727268i	$0.259210\pi$
$264$	25.6781	−	14.8252i	0.0972654	−	0.0561562i
$265$		0			0
$266$	337.457	−	105.392i	1.26864	−	0.396211i
$267$	−220.124			−0.824435
$268$	166.651	+	288.649i	0.621833	+	1.07705i
$269$	95.5538	+	55.1680i	0.355219	+	0.205086i	0.666981	−	0.745074i	$-0.267586\pi$
$269$	95.5538	+	55.1680i	0.355219	+	0.205086i	−0.311763	+	0.950160i	$0.600919\pi$
$270$		0			0
$271$	−85.9659	+	49.6324i	−0.317217	+	0.183145i	−0.650152	−	0.759805i	$-0.725295\pi$
$271$	−85.9659	+	49.6324i	−0.317217	+	0.183145i	0.332934	+	0.942950i	$0.391961\pi$
$272$		−	365.660i		−	1.34434i
$273$	−13.6856	−	43.8202i	−0.0501304	−	0.160513i
$274$	129.445			0.472428
$275$		0			0
$276$	−258.362	−	149.165i	−0.936093	−	0.540454i
$277$	−194.648	+	337.139i	−0.702699	+	1.21711i	0.264817	+	0.964299i	$0.414688\pi$
$277$	−194.648	+	337.139i	−0.702699	+	1.21711i	−0.967516	+	0.252811i	$0.918645\pi$
$278$	290.483	−	167.711i	1.04490	−	0.603276i
$279$		−	97.0403i		−	0.347815i
$280$		0			0
$281$	307.374			1.09386			0.546928	−	0.837180i	$-0.315797\pi$
$281$	307.374			1.09386			0.546928	+	0.837180i	$0.315797\pi$
$282$	−161.042	−	278.933i	−0.571070	−	0.989123i
$283$	−388.915	−	224.540i	−1.37426	−	0.793428i	−0.382796	−	0.923833i	$-0.625039\pi$
$283$	−388.915	−	224.540i	−1.37426	−	0.793428i	−0.991461	+	0.130405i	$0.958372\pi$
$284$	231.990	−	401.819i	0.816867	−	1.41486i
$285$		0			0
$286$			17.9285i			0.0626870i
$287$	−238.671	−	219.898i	−0.831607	−	0.766197i
$288$	29.9480			0.103986
$289$	358.172	+	620.372i	1.23935	+	2.14662i
$290$		0			0
$291$	103.296	−	178.914i	0.354969	−	0.614824i
$292$	−426.364	+	246.161i	−1.46015	+	0.843018i
$293$			73.8439i			0.252027i	0.992029	+	0.126013i	$0.0402182\pi$
$293$			73.8439i			0.252027i	−0.992029	+	0.126013i	$0.959782\pi$
$294$	−288.282	+	23.6427i	−0.980551	+	0.0804175i
$295$		0			0
$296$	−51.8834	−	89.8646i	−0.175282	−	0.303597i
$297$	6.25193	+	3.60955i	0.0210503	+	0.0121534i
$298$	−304.496	+	527.403i	−1.02180	+	1.76981i
$299$	74.1655	−	42.8195i	0.248045	−	0.143209i
$300$		0			0
$301$	−47.0873	+	51.1071i	−0.156436	+	0.169791i
$302$	823.246			2.72598
$303$	103.691	+	179.598i	0.342214	+	0.592732i
$304$	148.001	+	85.4486i	0.486847	+	0.281081i
$305$		0			0
$306$	280.754	−	162.093i	0.917496	−	0.529717i
$307$			162.912i			0.530659i	0.964158	+	0.265330i	$0.0854808\pi$
$307$			162.912i			0.530659i	−0.964158	+	0.265330i	$0.914519\pi$
$308$	72.2618	+	16.2263i	0.234616	+	0.0526827i
$309$	108.041			0.349646
$310$		0			0
$311$	34.3514	+	19.8328i	0.110455	+	0.0637711i	0.554210	−	0.832377i	$-0.313021\pi$
$311$	34.3514	+	19.8328i	0.110455	+	0.0637711i	−0.443755	+	0.896148i	$0.646354\pi$
$312$	40.4041	−	69.9820i	0.129500	−	0.224301i
$313$	128.400	−	74.1316i	0.410222	−	0.236842i	−0.280663	−	0.959806i	$-0.590554\pi$
$313$	128.400	−	74.1316i	0.410222	−	0.236842i	0.690885	+	0.722964i	$0.257221\pi$
$314$		−	140.840i		−	0.448536i
$315$		0			0
$316$	11.3459			0.0359049
$317$	−25.9670	−	44.9762i	−0.0819149	−	0.141881i	0.822158	−	0.569260i	$-0.192770\pi$
$317$	−25.9670	−	44.9762i	−0.0819149	−	0.141881i	−0.904072	+	0.427379i	$0.859437\pi$
$318$	−439.377	−	253.675i	−1.38169	−	0.797719i
$319$	29.8346	−	51.6750i	0.0935253	−	0.161991i
$320$		0			0
$321$		−	208.412i		−	0.649259i
$322$	−160.857	−	515.051i	−0.499556	−	1.59954i
$323$	−469.863			−1.45469
$324$	−34.2692	−	59.3560i	−0.105769	−	0.183197i
$325$		0			0
$326$	119.069	−	206.233i	0.365241	−	0.632617i
$327$	−97.5894	+	56.3433i	−0.298439	+	0.172304i
$328$		−	571.249i		−	1.74161i
$329$	83.6792	−	372.656i	0.254344	−	1.13269i
$330$		0			0
$331$	−193.516	−	335.179i	−0.584639	−	1.01262i	−0.994920	−	0.100666i	$-0.967903\pi$
$331$	−193.516	−	335.179i	−0.584639	−	1.01262i	0.410281	−	0.911959i	$-0.365431\pi$
$332$	90.1756	+	52.0629i	0.271613	+	0.156816i
$333$	12.6322	−	21.8796i	0.0379346	−	0.0657046i
$334$	96.5323	−	55.7329i	0.289019	−	0.166865i
$335$		0			0
$336$	−102.831	−	94.7431i	−0.306046	−	0.281974i
$337$	−574.984			−1.70618			−0.853092	−	0.521761i	$-0.825275\pi$
$337$	−574.984			−1.70618			−0.853092	+	0.521761i	$0.825275\pi$
$338$	−263.556	−	456.493i	−0.779753	−	1.35057i
$339$	−200.195	−	115.582i	−0.590545	−	0.340951i
$340$		0			0
$341$	−38.9191	+	22.4699i	−0.114132	+	0.0658943i
$342$			151.514i			0.443023i
$343$	−270.408	−	211.017i	−0.788362	−	0.615211i
$344$	−122.323			−0.355589
$345$		0			0
$346$	73.3419	+	42.3440i	0.211971	+	0.122381i
$347$	12.2286	−	21.1805i	0.0352408	−	0.0610389i	−0.847867	−	0.530209i	$-0.822114\pi$
$347$	12.2286	−	21.1805i	0.0352408	−	0.0610389i	0.883108	+	0.469170i	$0.155447\pi$
$348$	−490.604	+	283.250i	−1.40978	+	0.813937i
$349$		−	162.352i		−	0.465193i	−0.972573	−	0.232597i	$-0.925278\pi$
$349$		−	162.352i		−	0.465193i	0.972573	−	0.232597i	$-0.0747222\pi$
$350$		0			0
$351$	19.6747			0.0560532
$352$	−6.93454	−	12.0110i	−0.0197004	−	0.0341221i
$353$	−338.314	−	195.326i	−0.958397	−	0.553331i	−0.0627175	−	0.998031i	$-0.519977\pi$
$353$	−338.314	−	195.326i	−0.958397	−	0.553331i	−0.895679	+	0.444701i	$0.853310\pi$
$354$	274.187	−	474.906i	0.774541	−	1.34154i
$355$		0			0
$356$		−	967.828i		−	2.71862i
$357$	375.089	+	84.2256i	1.05067	+	0.235926i
$358$	477.565			1.33398
$359$	168.035	+	291.044i	0.468063	+	0.810709i	0.999334	−	0.0364931i	$-0.0116187\pi$
$359$	168.035	+	291.044i	0.468063	+	0.810709i	−0.531271	+	0.847202i	$0.678285\pi$
$360$		0			0
$361$	−70.7009	+	122.458i	−0.195847	+	0.339218i
$362$	−829.633	+	478.989i	−2.29180	+	1.32317i
$363$			206.235i			0.568140i
$364$	192.666	−	60.1720i	0.529302	−	0.165308i
$365$		0			0
$366$	−4.83489	−	8.37428i	−0.0132101	−	0.0228805i
$367$	302.258	+	174.508i	0.823590	+	0.475500i	0.851653	−	0.524106i	$-0.175601\pi$
$367$	302.258	+	174.508i	0.823590	+	0.475500i	−0.0280628	+	0.999606i	$0.508934\pi$
$368$	130.418	−	225.890i	0.354396	−	0.613832i
$369$	120.450	−	69.5420i	0.326424	−	0.188461i
$370$		0			0
$371$	−179.352	−	574.272i	−0.483430	−	1.54790i
$372$	426.661			1.14694
$373$	−82.1924	−	142.361i	−0.220355	−	0.381666i	0.734561	−	0.678543i	$-0.237388\pi$
$373$	−82.1924	−	142.361i	−0.220355	−	0.381666i	−0.954916	+	0.296877i	$0.904055\pi$
$374$	−130.019	−	75.0663i	−0.347644	−	0.200712i
$375$		0			0
$376$	582.226	−	336.149i	1.54847	−	0.894012i
$377$		−	162.620i		−	0.431353i
$378$	27.1597	−	120.952i	0.0718510	−	0.319980i
$379$	−172.731			−0.455755			−0.227878	−	0.973690i	$-0.573179\pi$
$379$	−172.731			−0.455755			−0.227878	+	0.973690i	$0.573179\pi$
$380$		0			0
$381$	281.953	+	162.786i	0.740034	+	0.427259i
$382$	174.455	−	302.165i	0.456688	−	0.791007i
$383$	−192.569	+	111.180i	−0.502791	+	0.290287i	−0.729866	−	0.683591i	$-0.760417\pi$
$383$	−192.569	+	111.180i	−0.502791	+	0.290287i	0.227074	+	0.973877i	$0.427084\pi$
$384$			403.980i			1.05203i
$385$		0			0
$386$	9.14070			0.0236806
$387$	−14.8912	−	25.7922i	−0.0384784	−	0.0666466i
$388$	786.638	+	454.165i	2.02742	+	1.17053i
$389$	−242.996	+	420.881i	−0.624668	+	1.08196i	0.363937	+	0.931424i	$0.381432\pi$
$389$	−242.996	+	420.881i	−0.624668	+	1.08196i	−0.988605	+	0.150533i	$0.951901\pi$
$390$		0			0
$391$			717.139i			1.83411i
$392$	−49.3504	−	601.742i	−0.125894	−	1.53506i
$393$	123.398			0.313991
$394$	−54.5960	−	94.5631i	−0.138569	−	0.240008i
$395$		0			0
$396$	−15.8702	+	27.4881i	−0.0400764	+	0.0694143i
$397$	342.591	−	197.795i	0.862949	−	0.498224i	−0.00204967	−	0.999998i	$-0.500652\pi$
$397$	342.591	−	197.795i	0.862949	−	0.498224i	0.864999	+	0.501774i	$0.167319\pi$
$398$			55.6102i			0.139724i
$399$	−121.742	+	132.135i	−0.305118	+	0.331166i
$400$		0			0
$401$	−189.425	−	328.093i	−0.472380	−	0.818187i	0.527120	−	0.849791i	$-0.323272\pi$
$401$	−189.425	−	328.093i	−0.472380	−	0.818187i	−0.999500	+	0.0316039i	$0.989939\pi$
$402$	−223.746	−	129.180i	−0.556582	−	0.321343i
$403$	−61.2387	+	106.069i	−0.151957	+	0.263198i
$404$	−789.644	+	455.901i	−1.95456	+	1.12847i
$405$		0			0
$406$	−999.726	−	224.487i	−2.46238	−	0.552924i
$407$	−11.7001			−0.0287472
$408$	338.343	+	586.028i	0.829273	+	1.43634i
$409$	−674.493	−	389.419i	−1.64913	−	0.952124i	−0.977420	−	0.211306i	$-0.932228\pi$
$409$	−674.493	−	389.419i	−1.64913	−	0.952124i	−0.671707	−	0.740817i	$-0.734438\pi$
$410$		0			0
$411$	−56.9720	+	32.8928i	−0.138618	+	0.0800311i
$412$			475.026i			1.15298i
$413$	620.709	−	193.855i	1.50293	−	0.469383i
$414$	231.251			0.558577
$415$		0			0
$416$	−32.7342	−	18.8991i	−0.0786881	−	0.0454306i
$417$	−85.2324	+	147.627i	−0.204394	+	0.354021i
$418$	60.7663	−	35.0834i	0.145374	−	0.0839317i
$419$			350.942i			0.837571i	0.908085	+	0.418785i	$0.137544\pi$
$419$			350.942i			0.837571i	−0.908085	+	0.418785i	$0.862456\pi$
$420$		0			0
$421$	175.760			0.417482			0.208741	−	0.977971i	$-0.433063\pi$
$421$	175.760			0.417482			0.208741	+	0.977971i	$0.433063\pi$
$422$	530.773	+	919.326i	1.25776	+	2.17850i
$423$	141.757	+	81.8432i	0.335122	+	0.193483i
$424$	529.505	−	917.129i	1.24883	−	2.16304i
$425$		0			0
$426$			359.655i			0.844260i
$427$	2.51227	−	11.1881i	0.00588353	−	0.0262016i
$428$	916.334			2.14097
$429$	−4.55572	−	7.89074i	−0.0106194	−	0.0183933i
$430$		0			0
$431$	−427.661	+	740.730i	−0.992252	+	1.71863i	−0.388532	+	0.921435i	$0.627018\pi$
$431$	−427.661	+	740.730i	−0.992252	+	1.71863i	−0.603720	+	0.797196i	$0.706316\pi$
$432$	51.8959	−	29.9621i	0.120129	−	0.0693568i
$433$			67.4511i			0.155776i	0.996962	+	0.0778881i	$0.0248177\pi$
$433$			67.4511i			0.155776i	−0.996962	+	0.0778881i	$0.975182\pi$
$434$	567.533	+	522.894i	1.30768	+	1.20482i
$435$		0			0
$436$	−247.727	−	429.075i	−0.568180	−	0.984117i
$437$	−290.262	−	167.583i	−0.664216	−	0.383485i
$438$	190.812	−	330.496i	0.435644	−	0.754557i
$439$	−242.742	+	140.147i	−0.552944	+	0.319242i	−0.750308	−	0.661088i	$-0.770095\pi$
$439$	−242.742	+	140.147i	−0.552944	+	0.319242i	0.197365	+	0.980330i	$0.436762\pi$
$440$		0			0
$441$	120.872	−	83.6598i	0.274086	−	0.189705i
$442$	−409.166			−0.925715
$443$	231.278	+	400.585i	0.522072	+	0.904256i	0.999670	+	0.0256772i	$0.00817419\pi$
$443$	231.278	+	400.585i	0.522072	+	0.904256i	−0.477598	+	0.878578i	$0.658492\pi$
$444$	96.1991	+	55.5406i	0.216665	+	0.125091i
$445$		0			0
$446$	329.140	−	190.029i	0.737983	−	0.426074i
$447$		−	309.497i		−	0.692387i
$448$	−380.172	+	412.628i	−0.848599	+	0.921044i
$449$	502.561			1.11929			0.559644	−	0.828733i	$-0.310938\pi$
$449$	502.561			1.11929			0.559644	+	0.828733i	$0.310938\pi$
$450$		0			0
$451$	−55.7812	−	32.2053i	−0.123683	−	0.0714086i
$452$	508.186	−	880.203i	1.12430	−	1.94735i
$453$	−362.330	+	209.191i	−0.799846	+	0.461791i
$454$			290.622i			0.640136i
$455$		0			0
$456$	−316.260			−0.693553
$457$	312.299	+	540.918i	0.683368	+	1.18363i	0.973947	+	0.226777i	$0.0728188\pi$
$457$	312.299	+	540.918i	0.683368	+	1.18363i	−0.290579	+	0.956851i	$0.593848\pi$
$458$	−205.926	−	118.891i	−0.449620	−	0.259588i
$459$	−82.3776	+	142.682i	−0.179472	+	0.310854i
$460$		0			0
$461$		−	68.1722i		−	0.147879i	−0.997263	−	0.0739395i	$-0.976443\pi$
$461$		−	68.1722i		−	0.147879i	0.997263	−	0.0739395i	$-0.0235572\pi$
$462$	−54.7982	+	17.1142i	−0.118611	+	0.0370437i
$463$	231.353			0.499682			0.249841	−	0.968287i	$-0.419622\pi$
$463$	231.353			0.499682			0.249841	+	0.968287i	$0.419622\pi$
$464$	−247.650	−	428.943i	−0.533729	−	0.924446i
$465$		0			0
$466$	295.780	−	512.306i	0.634721	−	1.09937i
$467$	−426.312	+	246.131i	−0.912873	+	0.527048i	−0.881355	−	0.472456i	$-0.843368\pi$
$467$	−426.312	+	246.131i	−0.912873	+	0.527048i	−0.0315188	+	0.999503i	$0.510034\pi$
$468$			86.5044i			0.184838i
$469$	−91.3324	−	292.439i	−0.194739	−	0.623538i
$470$		0			0
$471$	35.7883	+	61.9871i	0.0759836	+	0.131607i
$472$	991.290	+	572.322i	2.10019	+	1.21255i
$473$	−6.89618	+	11.9445i	−0.0145797	+	0.0252527i
$474$	−7.61653	+	4.39740i	−0.0160686	+	0.00927722i
$475$		0			0
$476$	−370.318	+	1649.17i	−0.777979	+	3.46464i
$477$	257.841			0.540546
$478$	−185.601	−	321.470i	−0.388286	−	0.672531i
$479$	−621.354	−	358.739i	−1.29719	−	0.748933i	−0.317272	−	0.948335i	$-0.602767\pi$
$479$	−621.354	−	358.739i	−1.29719	−	0.748933i	−0.979918	+	0.199401i	$0.936100\pi$
$480$		0			0
$481$	−27.6150	+	15.9435i	−0.0574116	+	0.0331466i
$482$			353.458i			0.733316i
$483$	201.674	+	185.812i	0.417545	+	0.384703i
$484$	−906.761			−1.87347
$485$		0			0
$486$	46.0098	+	26.5638i	0.0946704	+	0.0546580i
$487$	−200.471	+	347.225i	−0.411644	+	0.712988i	−0.995070	−	0.0991784i	$-0.968379\pi$
$487$	−200.471	+	347.225i	−0.411644	+	0.712988i	0.583426	+	0.812166i	$0.301712\pi$
$488$	17.4799	−	10.0921i	0.0358196	−	0.0206804i
$489$			121.024i			0.247493i
$490$		0			0
$491$	894.115			1.82101			0.910505	−	0.413499i	$-0.135693\pi$
$491$	894.115			1.82101			0.910505	+	0.413499i	$0.135693\pi$
$492$	305.758	+	529.588i	0.621459	+	1.07640i
$493$	1179.33	+	680.888i	2.39216	+	1.38111i
$494$	95.6151	−	165.610i	0.193553	−	0.335243i
$495$		0			0
$496$			373.037i			0.752090i
$497$	−288.985	+	313.655i	−0.581458	+	0.631097i
$498$	−80.7132			−0.162075
$499$	−261.273	−	452.538i	−0.523593	−	0.906890i	−0.999623	−	0.0274608i	$-0.991258\pi$
$499$	−261.273	−	452.538i	−0.523593	−	0.906890i	0.476030	−	0.879429i	$-0.342075\pi$
$500$		0			0
$501$	−28.3241	+	49.0588i	−0.0565351	+	0.0979217i
$502$	682.891	−	394.267i	1.36034	−	0.785393i
$503$		−	849.283i		−	1.68844i	−0.536000	−	0.844218i	$-0.680065\pi$
$503$		−	849.283i		−	1.68844i	0.536000	−	0.844218i	$-0.319935\pi$
$504$	252.469	+	56.6914i	0.500930	+	0.112483i
$505$		0			0
$506$	−53.5468	−	92.7458i	−0.105824	−	0.183292i
$507$	231.995	+	133.942i	0.457584	+	0.264186i
$508$	−715.726	+	1239.67i	−1.40891	+	2.44030i
$509$	589.645	−	340.432i	1.15844	−	0.668824i	0.207509	−	0.978233i	$-0.433464\pi$
$509$	589.645	−	340.432i	1.15844	−	0.668824i	0.950929	+	0.309409i	$0.100131\pi$
$510$		0			0
$511$	431.963	−	134.907i	0.845329	−	0.264007i
$512$	−683.520			−1.33500
$513$	−38.5005	−	66.6848i	−0.0750497	−	0.129990i
$514$	272.439	+	157.293i	0.530037	+	0.306017i
$515$		0			0
$516$	113.402	−	65.4725i	0.219771	−	0.126885i
$517$		−	75.8041i		−	0.146623i
$518$	59.8939	+	191.775i	0.115625	+	0.370223i
$519$	−43.0393			−0.0829274
$520$		0			0
$521$	−65.5525	−	37.8468i	−0.125821	−	0.0726425i	0.435769	−	0.900059i	$-0.356477\pi$
$521$	−65.5525	−	37.8468i	−0.125821	−	0.0726425i	−0.561589	+	0.827416i	$0.689810\pi$
$522$	219.562	−	380.292i	0.420616	−	0.728528i
$523$	154.906	−	89.4351i	0.296188	−	0.171004i	−0.344541	−	0.938771i	$-0.611966\pi$
$523$	154.906	−	89.4351i	0.296188	−	0.171004i	0.640729	+	0.767767i	$0.278632\pi$
$524$			542.550i			1.03540i
$525$		0			0
$526$	513.882			0.976963
$527$	−512.812	−	888.216i	−0.973078	−	1.68542i
$528$	−24.0333	−	13.8756i	−0.0455176	−	0.0262796i
$529$	8.72296	−	15.1086i	0.0164895	−	0.0285607i
$530$		0			0
$531$			278.690i			0.524840i
$532$	−580.965	−	535.269i	−1.09204	−	1.00614i
$533$	−175.542			−0.329347
$534$	375.106	+	649.703i	0.702446	+	1.21667i
$535$		0			0
$536$	269.642	−	467.033i	0.503063	−	0.871331i
$537$	−210.188	+	121.352i	−0.391411	+	0.225981i
$538$		−	376.040i		−	0.698959i
$539$	−61.5409	−	29.1054i	−0.114176	−	0.0539989i
$540$		0			0
$541$	−357.392	−	619.020i	−0.660613	−	1.14422i	−0.980455	−	0.196744i	$-0.936963\pi$
$541$	−357.392	−	619.020i	−0.660613	−	1.14422i	0.319842	−	0.947471i	$-0.396370\pi$
$542$	292.983	+	169.154i	0.540559	+	0.312092i
$543$	243.427	−	421.629i	0.448301	−	0.776480i
$544$	274.116	−	158.261i	0.503890	−	0.290921i
$545$		0			0
$546$	−106.015	+	115.066i	−0.194167	+	0.210743i
$547$	422.685			0.772734			0.386367	−	0.922345i	$-0.373730\pi$
$547$	422.685			0.772734			0.386367	+	0.922345i	$0.373730\pi$
$548$	−144.621	−	250.491i	−0.263907	−	0.457100i
$549$	4.25590	+	2.45715i	0.00775210	+	0.00447567i
$550$		0			0
$551$	−551.180	+	318.224i	−1.00033	+	0.577539i
$552$			482.699i			0.874454i
$553$	−10.1757	−	2.28494i	−0.0184009	−	0.00413190i
$554$	1326.77			2.39489
$555$		0			0
$556$	−649.077	−	374.745i	−1.16740	−	0.674001i
$557$	247.026	−	427.861i	0.443493	−	0.768152i	−0.554453	−	0.832215i	$-0.687072\pi$
$557$	247.026	−	427.861i	0.443493	−	0.768152i	0.997946	+	0.0640629i	$0.0204058\pi$
$558$	−286.417	+	165.363i	−0.513293	+	0.296350i
$559$			37.5891i			0.0672436i
$560$		0			0
$561$	76.2991			0.136005
$562$	−523.785	−	907.222i	−0.932002	−	1.61427i
$563$	210.272	+	121.401i	0.373485	+	0.215632i	0.674980	−	0.737836i	$-0.264152\pi$
$563$	210.272	+	121.401i	0.373485	+	0.215632i	−0.301495	+	0.953468i	$0.597486\pi$
$564$	−359.843	+	623.267i	−0.638020	+	1.10508i
$565$		0			0
$566$			1530.52i			2.70411i
$567$	18.7811	+	60.1354i	0.0331236	+	0.106059i
$568$	−750.721			−1.32169
$569$	−239.174	−	414.262i	−0.420342	−	0.728053i	0.575631	−	0.817710i	$-0.304756\pi$
$569$	−239.174	−	414.262i	−0.420342	−	0.728053i	−0.995973	+	0.0896563i	$0.971423\pi$
$570$		0			0
$571$	−54.1383	+	93.7703i	−0.0948131	+	0.164221i	−0.909531	−	0.415637i	$-0.863559\pi$
$571$	−54.1383	+	93.7703i	−0.0948131	+	0.164221i	0.814717	+	0.579858i	$0.196892\pi$
$572$	34.6935	−	20.0303i	0.0606530	−	0.0350180i
$573$			177.320i			0.309459i
$574$	−242.325	+	1079.17i	−0.422170	+	1.88008i
$575$		0			0
$576$	−120.228	−	208.241i	−0.208729	−	0.361529i
$577$	86.0482	+	49.6800i	0.149130	+	0.0861004i	0.572708	−	0.819759i	$-0.305893\pi$
$577$	86.0482	+	49.6800i	0.149130	+	0.0861004i	−0.423578	+	0.905860i	$0.639226\pi$
$578$	1220.70	−	2114.31i	2.11193	−	3.65798i
$579$	−4.02304	+	2.32270i	−0.00694825	+	0.00401157i
$580$		0			0
$581$	−70.3901	−	64.8535i	−0.121153	−	0.111624i
$582$	−704.093			−1.20978
$583$	−59.7037	−	103.410i	−0.102408	−	0.177375i
$584$	689.857	+	398.289i	1.18126	+	0.682002i
$585$		0			0
$586$	217.952	−	125.835i	0.371932	−	0.214735i
$587$			3.32500i			0.00566440i	0.999996	+	0.00283220i	$0.000901518\pi$
$587$			3.32500i			0.00566440i	−0.999996	+	0.00283220i	$0.999098\pi$
$588$	367.830	+	531.443i	0.625562	+	0.903814i
$589$	479.342			0.813823
$590$		0			0
$591$	48.0580	+	27.7463i	0.0813164	+	0.0469481i
$592$	−48.5600	+	84.1085i	−0.0820271	+	0.142075i
$593$	−405.112	+	233.891i	−0.683157	+	0.394421i	−0.801043	−	0.598606i	$-0.795721\pi$
$593$	−405.112	+	233.891i	−0.683157	+	0.394421i	0.117887	+	0.993027i	$0.462388\pi$
$594$		−	24.6037i		−	0.0414203i
$595$		0			0
$596$	1360.78			2.28318
$597$	−14.1309	−	24.4754i	−0.0236698	−	0.0409973i
$598$	−252.766	−	145.934i	−0.422685	−	0.244038i
$599$	−264.452	+	458.045i	−0.441490	+	0.764683i	−0.997800	−	0.0662916i	$-0.978883\pi$
$599$	−264.452	+	458.045i	−0.441490	+	0.764683i	0.556310	+	0.830975i	$0.312217\pi$
$600$		0			0
$601$			490.357i			0.815901i	0.913004	+	0.407951i	$0.133756\pi$
$601$			490.357i			0.815901i	−0.913004	+	0.407951i	$0.866244\pi$
$602$	231.084	+	51.8896i	0.383860	+	0.0861953i
$603$	131.301			0.217747
$604$	−919.760	−	1593.07i	−1.52278	−	2.63753i
$605$		0			0
$606$	353.392	−	612.093i	0.583155	−	1.01005i
$607$	−86.0283	+	49.6685i	−0.141727	+	0.0818261i	−0.569187	−	0.822208i	$-0.692742\pi$
$607$	−86.0283	+	49.6685i	−0.141727	+	0.0818261i	0.427460	+	0.904034i	$0.359409\pi$
$608$			147.931i			0.243308i
$609$	497.047	−	155.234i	0.816168	−	0.254900i
$610$		0			0
$611$	−103.297	−	178.915i	−0.169062	−	0.292824i
$612$	−627.336	−	362.193i	−1.02506	−	0.591818i
$613$	−143.185	+	248.004i	−0.233581	+	0.404573i	−0.958859	−	0.283882i	$-0.908378\pi$
$613$	−143.185	+	248.004i	−0.233581	+	0.404573i	0.725279	+	0.688455i	$0.241711\pi$
$614$	480.841	−	277.614i	0.783128	−	0.452139i
$615$		0			0
$616$	−35.7231	−	114.382i	−0.0579920	−	0.185686i
$617$	335.855			0.544336			0.272168	−	0.962250i	$-0.412259\pi$
$617$	335.855			0.544336			0.272168	+	0.962250i	$0.412259\pi$
$618$	−184.108	−	318.885i	−0.297910	−	0.515995i
$619$	−539.249	−	311.336i	−0.871162	−	0.502966i	−0.00342798	−	0.999994i	$-0.501091\pi$
$619$	−539.249	−	311.336i	−0.871162	−	0.502966i	−0.867734	+	0.497028i	$0.834424\pi$
$620$		0			0
$621$	−101.779	+	58.7621i	−0.163895	+	0.0946250i
$622$		−	135.186i		−	0.217340i
$623$	−194.910	+	868.007i	−0.312857	+	1.39327i
$624$	−75.6322			−0.121205
$625$		0			0
$626$	−437.603	−	252.650i	−0.699046	−	0.403595i
$627$	−17.8298	+	30.8821i	−0.0284367	+	0.0492537i
$628$	−272.541	+	157.352i	−0.433983	+	0.250560i
$629$		−	267.021i		−	0.424517i
$630$		0			0
$631$	−342.555			−0.542876			−0.271438	−	0.962456i	$-0.587499\pi$
$631$	−342.555			−0.542876			−0.271438	+	0.962456i	$0.587499\pi$
$632$	−9.17886	−	15.8983i	−0.0145235	−	0.0251555i
$633$	−467.212	−	269.745i	−0.738091	−	0.426137i
$634$	−88.4991	+	153.285i	−0.139588	+	0.241774i
$635$		0			0
$636$			1133.66i			1.78248i
$637$	−184.912	+	15.1651i	−0.290286	+	0.0238071i
$638$	−203.360			−0.318747
$639$	−91.3902	−	158.293i	−0.143021	−	0.247719i
$640$		0			0
$641$	486.307	−	842.309i	0.758670	−	1.31405i	−0.184859	−	0.982765i	$-0.559183\pi$
$641$	486.307	−	842.309i	0.758670	−	1.31405i	0.943529	−	0.331289i	$-0.107484\pi$
$642$	−615.135	+	355.148i	−0.958154	+	0.553190i
$643$		−	986.446i		−	1.53413i	−0.641569	−	0.767065i	$-0.721716\pi$
$643$		−	986.446i		−	1.53413i	0.641569	−	0.767065i	$-0.278284\pi$
$644$	−816.965	+	886.709i	−1.26858	+	1.37688i
$645$		0			0
$646$	800.679	+	1386.82i	1.23944	+	2.14677i
$647$	−70.1440	−	40.4977i	−0.108414	−	0.0625930i	0.444812	−	0.895624i	$-0.353270\pi$
$647$	−70.1440	−	40.4977i	−0.108414	−	0.0625930i	−0.553227	+	0.833031i	$0.686604\pi$
$648$	−55.4476	+	96.0380i	−0.0855672	+	0.148207i
$649$	111.772	−	64.5315i	0.172222	−	0.0994321i
$650$		0			0
$651$	−382.655	−	85.9246i	−0.587796	−	0.131989i
$652$	−532.111			−0.816121
$653$	−189.983	−	329.060i	−0.290938	−	0.503920i	0.683093	−	0.730331i	$-0.260634\pi$
$653$	−189.983	−	329.060i	−0.290938	−	0.503920i	−0.974032	+	0.226411i	$0.927301\pi$
$654$	332.598	+	192.025i	0.508559	+	0.293617i
$655$		0			0
$656$	−463.028	+	267.329i	−0.705835	+	0.407514i
$657$			193.946i			0.295199i
$658$	−1242.50	+	388.048i	−1.88830	+	0.589739i
$659$	−409.417			−0.621269			−0.310635	−	0.950529i	$-0.600542\pi$
$659$	−409.417			−0.621269			−0.310635	+	0.950529i	$0.600542\pi$
$660$		0			0
$661$	−392.365	−	226.532i	−0.593592	−	0.342711i	0.172924	−	0.984935i	$-0.444678\pi$
$661$	−392.365	−	226.532i	−0.593592	−	0.342711i	−0.766517	+	0.642224i	$0.778012\pi$
$662$	−659.527	+	1142.33i	−0.996264	+	1.72558i
$663$	180.084	−	103.971i	0.271619	−	0.156819i
$664$		−	168.476i		−	0.253728i
$665$		0			0
$666$	−86.1046			−0.129286
$667$	485.696	+	841.249i	0.728179	+	1.26124i
$668$	−215.699	−	124.534i	−0.322902	−	0.186428i
$669$	−96.5749	+	167.273i	−0.144357	+	0.250034i
$670$		0			0
$671$		−	2.27584i		−	0.00339171i
$672$	26.5175	−	118.093i	0.0394606	−	0.175733i
$673$	−1044.13			−1.55145			−0.775725	−	0.631071i	$-0.782616\pi$
$673$	−1044.13			−1.55145			−0.775725	+	0.631071i	$0.782616\pi$
$674$	979.811	+	1697.08i	1.45372	+	2.51793i
$675$		0			0
$676$	−588.909	+	1020.02i	−0.871168	+	1.50891i
$677$	1144.91	−	661.013i	1.69115	−	0.976386i	0.737558	−	0.675284i	$-0.235979\pi$
$677$	1144.91	−	661.013i	1.69115	−	0.976386i	0.953592	−	0.301102i	$-0.0973543\pi$
$678$			787.841i			1.16201i
$679$	−614.040	−	565.743i	−0.904330	−	0.833200i
$680$		0			0
$681$	−73.8486	−	127.909i	−0.108441	−	0.187826i
$682$	132.641	+	76.5806i	0.194489	+	0.112288i
$683$	412.831	−	715.045i	0.604438	−	1.04692i	−0.387702	−	0.921785i	$-0.626731\pi$
$683$	412.831	−	715.045i	0.604438	−	1.04692i	0.992140	−	0.125133i	$-0.0399358\pi$
$684$	293.196	−	169.277i	0.428649	−	0.247480i
$685$		0			0
$686$	−162.031	+	1157.71i	−0.236197	+	1.68762i
$687$	120.844			0.175901
$688$	57.2437	+	99.1490i	0.0832031	+	0.144112i
$689$	−281.829	−	162.714i	−0.409041	−	0.236160i
$690$		0			0
$691$	−219.857	+	126.935i	−0.318173	+	0.183697i	−0.650578	−	0.759440i	$-0.725473\pi$
$691$	−219.857	+	126.935i	−0.318173	+	0.183697i	0.332405	+	0.943137i	$0.392140\pi$
$692$		−	189.233i		−	0.273458i
$693$	19.7692	−	21.4569i	0.0285270	−	0.0309623i
$694$	−83.3531			−0.120105
$695$		0			0
$696$	793.797	+	458.299i	1.14051	+	0.658476i
$697$	734.993	−	1273.05i	1.05451	−	1.82646i
$698$	−479.188	+	276.659i	−0.686516	+	0.396360i
$699$			300.637i			0.430097i
$700$		0			0
$701$	304.585			0.434500			0.217250	−	0.976116i	$-0.430291\pi$
$701$	304.585			0.434500			0.217250	+	0.976116i	$0.430291\pi$
$702$	−33.5269	−	58.0704i	−0.0477592	−	0.0827213i
$703$	108.077	+	62.3983i	0.153737	+	0.0887600i
$704$	−55.6782	+	96.4375i	−0.0790884	+	0.136985i
$705$		0			0
$706$			1331.39i			1.88582i
$707$	800.014	−	249.854i	1.13156	−	0.353401i
$708$	−1225.33			−1.73069
$709$	23.4875	+	40.6815i	0.0331276	+	0.0573787i	0.882114	−	0.471036i	$-0.156120\pi$
$709$	23.4875	+	40.6815i	0.0331276	+	0.0573787i	−0.848986	+	0.528415i	$0.822787\pi$
$710$		0			0
$711$	2.23481	−	3.87080i	0.00314319	−	0.00544417i
$712$	−1356.15	+	782.973i	−1.90470	+	1.09968i
$713$		−	731.605i		−	1.02609i
$714$	−390.582	−	1250.61i	−0.547033	−	1.75156i
$715$		0			0
$716$	−533.552	−	924.140i	−0.745185	−	1.29070i
$717$	163.374	+	94.3243i	0.227858	+	0.131554i
$718$	572.684	−	991.918i	0.797611	−	1.38150i
$719$	−276.768	+	159.792i	−0.384934	+	0.222242i	−0.679963	−	0.733247i	$-0.738004\pi$
$719$	−276.768	+	159.792i	−0.384934	+	0.222242i	0.295029	+	0.955488i	$0.404671\pi$
$720$		0			0
$721$	95.6649	−	426.032i	0.132684	−	0.590891i
$722$	481.916			0.667474
$723$	−89.8157	−	155.565i	−0.124226	−	0.215167i
$724$	1853.79	+	1070.29i	2.56048	+	1.47830i
$725$		0			0
$726$	608.709	−	351.438i	0.838442	−	0.484075i
$727$		−	1192.80i		−	1.64071i	−0.571855	−	0.820354i	$-0.693776\pi$
$727$		−	1192.80i		−	1.64071i	0.571855	−	0.820354i	$-0.306224\pi$
$728$	−240.181	−	221.290i	−0.329920	−	0.303970i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−272.599	−	157.385i	−0.372913	−	0.215301i
$732$	−10.8034	+	18.7121i	−0.0147588	+	0.0255630i
$733$	−30.5956	+	17.6644i	−0.0417403	+	0.0240988i	−0.520725	−	0.853725i	$-0.674338\pi$
$733$	−30.5956	+	17.6644i	−0.0417403	+	0.0240988i	0.478985	+	0.877823i	$0.341005\pi$
$734$		−	1189.50i		−	1.62057i
$735$		0			0
$736$	225.783			0.306771
$737$	−30.4032	−	52.6598i	−0.0412526	−	0.0714516i
$738$	−410.511	−	237.008i	−0.556247	−	0.321150i
$739$	−392.667	+	680.119i	−0.531349	+	0.920324i	0.467981	+	0.883738i	$0.344981\pi$
$739$	−392.667	+	680.119i	−0.531349	+	0.920324i	−0.999331	+	0.0365854i	$0.988352\pi$
$740$		0			0
$741$			97.1853i			0.131154i
$742$	−1389.35	+	1507.96i	−1.87244	+	2.03229i
$743$	−419.098			−0.564062			−0.282031	−	0.959405i	$-0.591008\pi$
$743$	−419.098			−0.564062			−0.282031	+	0.959405i	$0.591008\pi$
$744$	−345.169	−	597.849i	−0.463936	−	0.803561i
$745$		0			0
$746$	−280.123	+	485.187i	−0.375500	+	0.650384i
$747$	35.5238	−	20.5097i	0.0475553	−	0.0274560i
$748$			335.467i			0.448485i
$749$	−821.823	−	184.539i	−1.09723	−	0.246381i
$750$		0			0
$751$	59.8519	+	103.667i	0.0796963	+	0.138038i	0.903119	−	0.429391i	$-0.141272\pi$
$751$	59.8519	+	103.667i	0.0796963	+	0.138038i	−0.823423	+	0.567429i	$0.807938\pi$
$752$	−544.933	−	314.617i	−0.724644	−	0.418374i
$753$	−200.371	+	347.053i	−0.266097	+	0.460893i
$754$	−479.978	+	277.115i	−0.636575	+	0.367527i
$755$		0			0
$756$	−264.400	+	82.5754i	−0.349735	+	0.109227i
$757$	−995.970			−1.31568			−0.657840	−	0.753157i	$-0.728530\pi$
$757$	−995.970			−1.31568			−0.657840	+	0.753157i	$0.728530\pi$
$758$	294.346	+	509.821i	0.388319	+	0.672588i
$759$	47.1344	+	27.2131i	0.0621007	+	0.0358539i
$760$		0			0
$761$	237.050	−	136.861i	0.311498	−	0.179843i	−0.336099	−	0.941827i	$-0.609108\pi$
$761$	237.050	−	136.861i	0.311498	−	0.179843i	0.647596	+	0.761983i	$0.275774\pi$
$762$		−	1109.59i		−	1.45615i
$763$	135.765	+	434.710i	0.177936	+	0.569738i
$764$	−779.629			−1.02046
$765$		0			0
$766$	656.301	+	378.916i	0.856790	+	0.494668i
$767$	175.872	−	304.619i	0.229298	−	0.397156i
$768$	711.447	−	410.754i	0.926364	−	0.534836i
$769$			694.742i			0.903435i	0.892161	+	0.451718i	$0.149189\pi$
$769$			694.742i			0.903435i	−0.892161	+	0.451718i	$0.850811\pi$
$770$		0			0
$771$	−159.876			−0.207362
$772$	−10.2123	−	17.6882i	−0.0132284	−	0.0229122i
$773$	538.402	+	310.846i	0.696510	+	0.402130i	0.806046	−	0.591853i	$-0.201603\pi$
$773$	538.402	+	310.846i	0.696510	+	0.402130i	−0.109537	+	0.993983i	$0.534937\pi$
$774$	−50.7510	+	87.9034i	−0.0655698	+	0.113570i
$775$		0			0
$776$		−	1469.68i		−	1.89392i
$777$	−75.0919	−	69.1855i	−0.0966434	−	0.0890419i
$778$	1656.32			2.12895
$779$	343.511	+	594.978i	0.440964	+	0.763771i
$780$		0			0
$781$	−42.3233	+	73.3061i	−0.0541912	+	0.0938619i
$782$	2116.66	−	1222.05i	2.70672	−	1.56273i
$783$			223.167i			0.285016i
$784$	−464.649	+	321.600i	−0.592665	+	0.410204i
$785$		0			0
$786$	−210.279	−	364.214i	−0.267531	−	0.463377i
$787$	−20.1986	−	11.6617i	−0.0256653	−	0.0148179i	0.487112	−	0.873339i	$-0.338050\pi$
$787$	−20.1986	−	11.6617i	−0.0256653	−	0.0148179i	−0.512778	+	0.858521i	$0.671384\pi$
$788$	−121.993	+	211.299i	−0.154814	+	0.268145i
$789$	−226.172	+	130.580i	−0.286656	+	0.165501i
$790$		0			0
$791$	−633.035	+	687.077i	−0.800297	+	0.868618i
$792$	51.3561			0.0648436
$793$	−3.10124	−	5.37150i	−0.00391077	−	0.00677365i
$794$	−1167.60	−	674.111i	−1.47052	−	0.849007i
$795$		0			0
$796$	107.612	−	62.1297i	0.135191	−	0.0780524i
$797$			140.581i			0.176388i	0.996103	+	0.0881941i	$0.0281096\pi$
$797$			140.581i			0.176388i	−0.996103	+	0.0881941i	$0.971890\pi$
$798$	597.458	+	134.158i	0.748695	+	0.168118i
$799$	1730.01			2.16522
$800$		0			0
$801$	−330.186	−	190.633i	−0.412218	−	0.237994i
$802$	−645.584	+	1118.18i	−0.804968	+	1.39425i
$803$	77.7840	−	44.9086i	0.0968668	−	0.0559261i
$804$			577.297i			0.718031i
$805$		0			0
$806$	417.420			0.517890
$807$	95.5538	+	165.504i	0.118406	+	0.205086i
$808$	1277.64	+	737.648i	1.58124	+	0.912931i
$809$	−92.8993	+	160.906i	−0.114832	+	0.198895i	−0.917713	−	0.397245i	$-0.869966\pi$
$809$	−92.8993	+	160.906i	−0.114832	+	0.198895i	0.802880	+	0.596140i	$0.203300\pi$
$810$		0			0
$811$		−	683.280i		−	0.842516i	−0.906941	−	0.421258i	$-0.861589\pi$
$811$		−	683.280i		−	0.842516i	0.906941	−	0.421258i	$-0.138411\pi$
$812$	682.523	+	2185.38i	0.840545	+	2.69136i
$813$	−171.932			−0.211478
$814$	19.9378	+	34.5332i	0.0244936	+	0.0424241i
$815$		0			0
$816$	316.671	−	548.491i	0.388078	−	0.672170i
$817$	127.404	−	73.5566i	0.155941	−	0.0900325i
$818$			2654.38i			3.24496i
$819$	17.4210	−	77.5823i	0.0212711	−	0.0947281i
$820$		0			0
$821$	382.762	+	662.963i	0.466214	+	0.807507i	0.999255	−	0.0385823i	$-0.0122842\pi$
$821$	382.762	+	662.963i	0.466214	+	0.807507i	−0.533041	+	0.846089i	$0.678951\pi$
$822$	194.168	+	112.103i	0.236214	+	0.136378i
$823$	−771.839	+	1336.87i	−0.937836	+	1.62438i	−0.168340	+	0.985729i	$0.553841\pi$
$823$	−771.839	+	1336.87i	−0.937836	+	1.62438i	−0.769496	+	0.638651i	$0.779493\pi$
$824$	665.621	−	384.296i	0.807792	−	0.466379i
$825$		0			0
$826$	−1629.90	−	1501.70i	−1.97324	−	1.81804i
$827$	−794.814			−0.961081			−0.480540	−	0.876973i	$-0.659559\pi$
$827$	−794.814			−0.961081			−0.480540	+	0.876973i	$0.659559\pi$
$828$	−258.362	−	447.496i	−0.312031	−	0.540454i
$829$	686.072	+	396.104i	0.827590	+	0.477809i	0.853027	−	0.521867i	$-0.174764\pi$
$829$	686.072	+	396.104i	0.827590	+	0.477809i	−0.0254368	+	0.999676i	$0.508098\pi$
$830$		0			0
$831$	−583.943	+	337.139i	−0.702699	+	0.405703i
$832$			303.487i			0.364768i
$833$	664.247	−	1404.49i	0.797416	−	1.68607i
$834$	580.967			0.696603
$835$		0			0
$836$	−135.781	−	78.3929i	−0.162417	−	0.0937714i
$837$	84.0393	−	145.560i	0.100405	−	0.173907i
$838$	1035.82	−	598.029i	1.23606	−	0.713638i
$839$		−	1167.54i		−	1.39159i	−0.718241	−	0.695795i	$-0.755052\pi$
$839$		−	1167.54i		−	1.39159i	0.718241	−	0.695795i	$-0.244948\pi$
$840$		0			0
$841$	1003.58			1.19331
$842$	−299.507	−	518.761i	−0.355709	−	0.616105i
$843$	461.060	+	266.193i	0.546928	+	0.315769i
$844$	1186.00	−	2054.21i	1.40521	−	2.43389i
$845$		0			0
$846$		−	557.865i		−	0.659415i
$847$	813.238	+	182.611i	0.960140	+	0.215598i
$848$	−991.176			−1.16884
$849$	−388.915	−	673.620i	−0.458086	−	0.793428i
$850$		0			0
$851$	95.2367	−	164.955i	0.111911	−	0.193836i
$852$	695.971	−	401.819i	0.816867	−	0.471618i
$853$		−	1146.86i		−	1.34450i	−0.740324	−	0.672251i	$-0.765328\pi$
$853$		−	1146.86i		−	1.34450i	0.740324	−	0.672251i	$-0.234672\pi$
$854$	−37.3030	+	11.6502i	−0.0436804	+	0.0136419i
$855$		0			0
$856$	−741.314	−	1283.99i	−0.866021	−	1.49999i
$857$	−186.121	−	107.457i	−0.217177	−	0.125387i	0.387465	−	0.921884i	$-0.373351\pi$
$857$	−186.121	−	107.457i	−0.217177	−	0.125387i	−0.604643	+	0.796497i	$0.706684\pi$
$858$	−15.5265	+	26.8927i	−0.0180962	+	0.0313435i
$859$	−986.635	+	569.634i	−1.14859	+	0.663136i	−0.948542	−	0.316651i	$-0.897442\pi$
$859$	−986.635	+	569.634i	−1.14859	+	0.663136i	−0.200044	+	0.979787i	$0.564108\pi$
$860$		0			0
$861$	−167.569	−	536.543i	−0.194622	−	0.623163i
$862$	2915.05			3.38173
$863$	272.020	+	471.152i	0.315203	+	0.545947i	0.979481	−	0.201539i	$-0.0645942\pi$
$863$	272.020	+	471.152i	0.315203	+	0.545947i	−0.664278	+	0.747486i	$0.731261\pi$
$864$	44.9220	+	25.9357i	0.0519930	+	0.0300182i
$865$		0			0
$866$	199.084	−	114.941i	0.229889	−	0.132726i
$867$			1240.74i			1.43108i
$868$	377.788	−	1682.43i	0.435240	−	1.93829i
$869$	−2.06990			−0.00238194
$870$		0			0
$871$	−143.517	−	82.8596i	−0.164773	−	0.0951316i
$872$	−400.822	+	694.244i	−0.459658	+	0.796151i
$873$	309.888	−	178.914i	0.354969	−	0.204941i
$874$			1142.29i			1.30697i
$875$		0			0
$876$	−852.728			−0.973433
$877$	263.311	+	456.068i	0.300241	+	0.520032i	0.976190	−	0.216916i	$-0.0695997\pi$
$877$	263.311	+	456.068i	0.300241	+	0.520032i	−0.675950	+	0.736948i	$0.736266\pi$
$878$	827.298	+	477.641i	0.942253	+	0.544010i
$879$	−63.9507	+	110.766i	−0.0727539	+	0.126013i
$880$		0			0
$881$		−	121.399i		−	0.137797i	−0.997624	−	0.0688983i	$-0.978052\pi$
$881$		−	121.399i		−	0.137797i	0.997624	−	0.0688983i	$-0.0219484\pi$
$882$	−452.898	−	214.195i	−0.513490	−	0.242852i
$883$	243.586			0.275862			0.137931	−	0.990442i	$-0.455955\pi$
$883$	243.586			0.275862			0.137931	+	0.990442i	$0.455955\pi$
$884$	457.135	+	791.780i	0.517120	+	0.895679i
$885$		0			0
$886$	788.226	−	1365.25i	0.889646	−	1.54091i
$887$	−1103.23	+	636.947i	−1.24377	+	0.718092i	−0.969860	−	0.243663i	$-0.921651\pi$
$887$	−1103.23	+	636.947i	−1.24377	+	0.718092i	−0.273911	+	0.961755i	$0.588318\pi$
$888$		−	179.729i		−	0.202398i
$889$	891.562	−	967.675i	1.00288	−	1.08850i
$890$		0			0
$891$	6.25193	+	10.8287i	0.00701675	+	0.0121534i
$892$	−735.454	−	424.615i	−0.824500	−	0.476025i
$893$	−404.274	+	700.223i	−0.452714	+	0.784124i
$894$	−913.489	+	527.403i	−1.02180	+	0.589937i
$895$		0			0
$896$	1593.00	+	357.705i	1.77790	+	0.399225i
$897$	148.331			0.165363
$898$	−856.397	−	1483.32i	−0.953671	−	1.65181i
$899$	−1203.12	−	694.623i	−1.33829	−	0.772662i
$900$		0			0
$901$	2360.03	−	1362.57i	2.61935	−	1.51228i
$902$			219.520i			0.243370i
$903$	−114.891	+	35.8819i	−0.127232	+	0.0397363i
$904$	−1644.49			−1.81913
$905$		0			0
$906$	1234.87	+	712.952i	1.36299	+	0.786923i
$907$	−283.222	+	490.555i	−0.312262	+	0.540854i	−0.978852	−	0.204571i	$-0.934420\pi$
$907$	−283.222	+	490.555i	−0.312262	+	0.540854i	0.666589	+	0.745425i	$0.267753\pi$
$908$	562.384	−	324.693i	0.619366	−	0.357591i
$909$			359.195i			0.395154i
$910$		0			0
$911$	−1468.26			−1.61170			−0.805850	−	0.592120i	$-0.798291\pi$
$911$	−1468.26			−1.61170			−0.805850	+	0.592120i	$0.798291\pi$
$912$	148.001	+	256.346i	0.162282	+	0.281081i
$913$	−16.4513	−	9.49814i	−0.0180189	−	0.0104032i
$914$	1064.36	−	1843.52i	1.16450	−	2.01698i
$915$		0			0
$916$			531.318i			0.580042i
$917$	109.263	−	486.592i	0.119153	−	0.530635i
$918$	561.508			0.611664
$919$	514.213	+	890.643i	0.559535	+	0.969143i	0.997535	+	0.0701683i	$0.0223536\pi$
$919$	514.213	+	890.643i	0.559535	+	0.969143i	−0.438000	+	0.898975i	$0.644313\pi$
$920$		0			0
$921$	−141.086	+	244.369i	−0.153188	+	0.265330i
$922$	−201.212	+	116.170i	−0.218235	+	0.125998i
$923$			230.693i			0.249938i
$924$	94.3403	+	86.9199i	0.102100	+	0.0940692i
$925$		0			0
$926$	−394.241	−	682.845i	−0.425746	−	0.737414i
$927$	162.061	+	93.5659i	0.174823	+	0.100934i
$928$	214.370	−	371.300i	0.231003	−	0.400108i
$929$	551.039	−	318.143i	0.593153	−	0.342457i	−0.173190	−	0.984888i	$-0.555407\pi$
$929$	551.039	−	318.143i	0.593153	−	0.342457i	0.766343	+	0.642431i	$0.222074\pi$
$930$		0			0
$931$	413.247	+	597.061i	0.443874	+	0.641312i
$932$	−1321.82			−1.41827
$933$	34.3514	+	59.4984i	0.0368183	+	0.0637711i
$934$	1452.93	+	838.848i	1.55560	+	0.898124i
$935$		0			0
$936$	121.212	−	69.9820i	0.129500	−	0.0747671i
$937$		−	1396.05i		−	1.48991i	−0.667113	−	0.744956i	$-0.732470\pi$
$937$		−	1396.05i		−	1.48991i	0.667113	−	0.744956i	$-0.267530\pi$
$938$	−707.506	+	767.906i	−0.754271	+	0.818663i
$939$	256.799			0.273482
$940$		0			0
$941$	−334.880	−	193.343i	−0.355877	−	0.205466i	0.311394	−	0.950281i	$-0.399204\pi$
$941$	−334.880	−	193.343i	−0.355877	−	0.205466i	−0.667271	+	0.744815i	$0.732538\pi$
$942$	121.971	−	211.260i	0.129481	−	0.224268i
$943$	908.097	−	524.290i	0.962987	−	0.555981i
$944$		−	1071.32i		−	1.13488i
$945$		0			0
$946$	47.0062			0.0496894
$947$	−288.202	−	499.180i	−0.304331	−	0.527117i	0.672781	−	0.739842i	$-0.265100\pi$
$947$	−288.202	−	499.180i	−0.304331	−	0.527117i	−0.977112	+	0.212725i	$0.931766\pi$
$948$	17.0189	+	9.82587i	0.0179524	+	0.0103648i
$949$	122.392	−	211.990i	0.128970	−	0.223382i
$950$		0			0
$951$		−	89.9524i		−	0.0945872i
$952$	2610.45	−	815.276i	2.74207	−	0.856382i
$953$	1080.91			1.13421			0.567107	−	0.823644i	$-0.308063\pi$
$953$	1080.91			1.13421			0.567107	+	0.823644i	$0.308063\pi$
$954$	−439.377	−	761.024i	−0.460563	−	0.797719i
$955$		0			0
$956$	−414.719	+	718.315i	−0.433807	+	0.751375i
$957$	89.5037	−	51.6750i	0.0935253	−	0.0539968i
$958$			2445.26i			2.55246i
$959$	79.2588	+	253.780i	0.0826473	+	0.264630i
$960$		0			0
$961$	42.6564	+	73.8830i	0.0443875	+	0.0768814i
$962$	94.1155	+	54.3376i	0.0978331	+	0.0564840i
$963$	180.490	−	312.618i	0.187425	−	0.324629i
$964$	683.980	−	394.896i	0.709523	−	0.409643i
$965$		0			0
$966$	204.762	−	911.883i	0.211969	−	0.943978i
$967$	785.695			0.812508			0.406254	−	0.913760i	$-0.366835\pi$
$967$	785.695			0.812508			0.406254	+	0.913760i	$0.366835\pi$
$968$	733.570	+	1270.58i	0.757820	+	1.31258i
$969$	−704.795	−	406.914i	−0.727343	−	0.419932i
$970$		0			0
$971$	−801.304	+	462.633i	−0.825236	+	0.476450i	−0.852219	−	0.523186i	$-0.824743\pi$
$971$	−801.304	+	462.633i	−0.825236	+	0.476450i	0.0269825	+	0.999636i	$0.491410\pi$
$972$		−	118.712i		−	0.122132i
$973$	506.662	+	466.810i	0.520721	+	0.479764i
$974$	1366.46			1.40294
$975$		0			0
$976$	−16.3603	−	9.44562i	−0.0167626	−	0.00967789i
$977$	−160.834	+	278.572i	−0.164620	+	0.285130i	−0.936520	−	0.350614i	$-0.885973\pi$
$977$	−160.834	+	278.572i	−0.164620	+	0.285130i	0.771900	+	0.635743i	$0.219306\pi$
$978$	357.206	−	206.233i	0.365241	−	0.210872i
$979$			176.567i			0.180354i
$980$		0			0
$981$	−195.179			−0.198959
$982$	−1523.63	−	2639.01i	−1.55156	−	2.68738i
$983$	−1235.03	−	713.047i	−1.25639	−	0.725379i	−0.284021	−	0.958818i	$-0.591669\pi$
$983$	−1235.03	−	713.047i	−1.25639	−	0.725379i	−0.972371	+	0.233439i	$0.925002\pi$
$984$	494.716	−	856.874i	0.502761	−	0.870807i
$985$		0			0
$986$		−	4641.11i		−	4.70701i
$987$	448.248	−	486.515i	0.454152	−	0.492923i
$988$	−427.298			−0.432488
$989$	−112.267	−	194.452i	−0.113516	−	0.196615i
$990$		0			0
$991$	−854.919	+	1480.76i	−0.862683	+	1.49421i	0.00664562	+	0.999978i	$0.497885\pi$
$991$	−854.919	+	1480.76i	−0.862683	+	1.49421i	−0.869329	+	0.494234i	$0.835449\pi$
$992$	−279.645	+	161.453i	−0.281901	+	0.162755i
$993$		−	670.358i		−	0.675083i
$994$	1418.21	+	318.457i	1.42677	+	0.320380i
$995$		0			0
$996$	90.1756	+	156.189i	0.0905378	+	0.156816i
$997$	−1190.01	−	687.055i	−1.19359	−	0.689122i	−0.234475	−	0.972122i	$-0.575337\pi$
$997$	−1190.01	−	687.055i	−1.19359	−	0.689122i	−0.959120	+	0.283000i	$0.908670\pi$
$998$	−890.453	+	1542.31i	−0.892238	+	1.54540i
$999$	37.8967	−	21.8796i	0.0379346	−	0.0219015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.o.q.451.1		16
5.2	odd	4		105.3.r.a.94.15	yes	32
5.3	odd	4		105.3.r.a.94.2	yes	32
5.4	even	2		525.3.o.p.451.8		16
7.5	odd	6	inner	525.3.o.q.376.1		16
15.2	even	4		315.3.bi.e.199.2		32
15.8	even	4		315.3.bi.e.199.15		32
35.3	even	12		735.3.e.a.244.13		32
35.12	even	12		105.3.r.a.19.2	✓	32
35.17	even	12		735.3.e.a.244.6		32
35.18	odd	12		735.3.e.a.244.5		32
35.19	odd	6		525.3.o.p.376.8		16
35.32	odd	12		735.3.e.a.244.14		32
35.33	even	12		105.3.r.a.19.15	yes	32
105.47	odd	12		315.3.bi.e.19.15		32
105.68	odd	12		315.3.bi.e.19.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.r.a.19.2	✓	32	35.12	even	12
105.3.r.a.19.15	yes	32	35.33	even	12
105.3.r.a.94.2	yes	32	5.3	odd	4
105.3.r.a.94.15	yes	32	5.2	odd	4
315.3.bi.e.19.2		32	105.68	odd	12
315.3.bi.e.19.15		32	105.47	odd	12
315.3.bi.e.199.2		32	15.2	even	4
315.3.bi.e.199.15		32	15.8	even	4
525.3.o.p.376.8		16	35.19	odd	6
525.3.o.p.451.8		16	5.4	even	2
525.3.o.q.376.1		16	7.5	odd	6	inner
525.3.o.q.451.1		16	1.1	even	1	trivial
735.3.e.a.244.5		32	35.18	odd	12
735.3.e.a.244.6		32	35.17	even	12
735.3.e.a.244.13		32	35.3	even	12
735.3.e.a.244.14		32	35.32	odd	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.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70407 - 2.95153i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-3.80769 + 6.59511i) q^{4} -5.90306i q^{6} +(4.74314 - 5.14807i) q^{7} +12.3217 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.70407 - 2.95153i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-3.80769 + 6.59511i) q^{4} -5.90306i q^{6} +(4.74314 - 5.14807i) q^{7} +12.3217 q^{8} +(1.50000 + 2.59808i) q^{9} +(0.694658 - 1.20318i) q^{11} +(-11.4231 + 6.59511i) q^{12} -3.78639i q^{13} +(-23.2773 - 5.22688i) q^{14} +(-5.76621 - 9.98737i) q^{16} +(27.4592 + 15.8536i) q^{17} +(5.11220 - 8.85459i) q^{18} +(-12.8335 + 7.40942i) q^{19} +(11.5731 - 3.61442i) q^{21} -4.73498 q^{22} +(11.3088 + 19.5874i) q^{23} +(18.4825 + 10.6709i) q^{24} +(-11.1756 + 6.45226i) q^{26} +5.19615i q^{27} +(15.8916 + 50.8838i) q^{28} +42.9485 q^{29} +(-28.0131 - 16.1734i) q^{31} +(4.99133 - 8.64524i) q^{32} +(2.08398 - 1.20318i) q^{33} -108.062i q^{34} -22.8461 q^{36} +(-4.21074 - 7.29321i) q^{37} +(43.7383 + 25.2523i) q^{38} +(3.27911 - 5.67959i) q^{39} -46.3613i q^{41} +(-30.3893 - 27.9991i) q^{42} -9.92743 q^{43} +(5.29008 + 9.16269i) q^{44} +(38.5418 - 66.7564i) q^{46} +(47.2522 - 27.2811i) q^{47} -19.9747i q^{48} +(-4.00517 - 48.8360i) q^{49} +(27.4592 + 47.5607i) q^{51} +(24.9717 + 14.4174i) q^{52} +(42.9734 - 74.4321i) q^{53} +(15.3366 - 8.85459i) q^{54} +(58.4435 - 63.4328i) q^{56} -25.6670 q^{57} +(-73.1872 - 126.764i) q^{58} +(80.4509 + 46.4483i) q^{59} +(1.41863 - 0.819048i) q^{61} +110.242i q^{62} +(20.4898 + 4.60095i) q^{63} -80.1519 q^{64} +(-7.10247 - 4.10061i) q^{66} +(21.8835 - 37.9034i) q^{67} +(-209.112 + 120.731i) q^{68} +39.1748i q^{69} -60.9268 q^{71} +(18.4825 + 32.0127i) q^{72} +(55.9872 + 32.3243i) q^{73} +(-14.3508 + 24.8563i) q^{74} -112.851i q^{76} +(-2.89920 - 9.28302i) q^{77} -22.3513 q^{78} +(-0.744936 - 1.29027i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-136.837 + 79.0028i) q^{82} -13.6731i q^{83} +(-20.2292 + 90.0882i) q^{84} +(16.9170 + 29.3011i) q^{86} +(64.4228 + 37.1945i) q^{87} +(8.55936 - 14.8252i) q^{88} +(-110.062 + 63.5444i) q^{89} +(-19.4926 - 17.9594i) q^{91} -172.241 q^{92} +(-28.0131 - 48.5201i) q^{93} +(-161.042 - 92.9775i) q^{94} +(14.9740 - 8.64524i) q^{96} -119.276i q^{97} +(-137.316 + 95.0412i) q^{98} +4.16795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 24 q^{3} - 16 q^{4} + 6 q^{7} + 24 q^{9}+O(q^{10}) \) 16 * q + 24 * q^3 - 16 * q^4 + 6 * q^7 + 24 * q^9	\( 16 q + 24 q^{3} - 16 q^{4} + 6 q^{7} + 24 q^{9} - 14 q^{11} - 48 q^{12} - 30 q^{14} - 20 q^{16} + 6 q^{17} + 30 q^{19} + 6 q^{21} - 36 q^{22} - 18 q^{23} - 48 q^{26} - 168 q^{28} + 44 q^{29} + 42 q^{31} + 150 q^{32} - 42 q^{33} - 96 q^{36} + 96 q^{37} + 204 q^{38} - 18 q^{39} - 78 q^{42} - 160 q^{44} - 30 q^{46} - 138 q^{47} - 178 q^{49} + 6 q^{51} + 126 q^{52} + 150 q^{53} - 234 q^{56} + 60 q^{57} - 90 q^{58} + 402 q^{59} + 168 q^{61} + 200 q^{64} - 54 q^{66} + 174 q^{67} - 234 q^{68} + 172 q^{71} + 336 q^{73} - 450 q^{74} - 372 q^{77} - 96 q^{78} + 10 q^{79} - 72 q^{81} - 690 q^{82} - 390 q^{84} + 72 q^{86} + 66 q^{87} + 492 q^{88} - 12 q^{89} - 112 q^{91} + 204 q^{92} + 42 q^{93} + 462 q^{94} + 450 q^{96} - 198 q^{98} - 84 q^{99}+O(q^{100}) \) 16 * q + 24 * q^3 - 16 * q^4 + 6 * q^7 + 24 * q^9 - 14 * q^11 - 48 * q^12 - 30 * q^14 - 20 * q^16 + 6 * q^17 + 30 * q^19 + 6 * q^21 - 36 * q^22 - 18 * q^23 - 48 * q^26 - 168 * q^28 + 44 * q^29 + 42 * q^31 + 150 * q^32 - 42 * q^33 - 96 * q^36 + 96 * q^37 + 204 * q^38 - 18 * q^39 - 78 * q^42 - 160 * q^44 - 30 * q^46 - 138 * q^47 - 178 * q^49 + 6 * q^51 + 126 * q^52 + 150 * q^53 - 234 * q^56 + 60 * q^57 - 90 * q^58 + 402 * q^59 + 168 * q^61 + 200 * q^64 - 54 * q^66 + 174 * q^67 - 234 * q^68 + 172 * q^71 + 336 * q^73 - 450 * q^74 - 372 * q^77 - 96 * q^78 + 10 * q^79 - 72 * q^81 - 690 * q^82 - 390 * q^84 + 72 * q^86 + 66 * q^87 + 492 * q^88 - 12 * q^89 - 112 * q^91 + 204 * q^92 + 42 * q^93 + 462 * q^94 + 450 * q^96 - 198 * q^98 - 84 * q^99

Introduction

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