LMFDB - Embedded newform 225.3.i.a.74.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,3,Mod(74,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("225.74");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	225.i (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:	$6.13080594811$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			74.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	225.74
Dual form			225.3.i.a.149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 1.50000i) q^{2} +(2.59808 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(4.50000 - 2.59808i) q^{6} +(-1.73205 - 1.00000i) q^{7} +8.66025 q^{8} +(4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(0.866025 - 1.50000i) q^{2} +(2.59808 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(4.50000 - 2.59808i) q^{6} +(-1.73205 - 1.00000i) q^{7} +8.66025 q^{8} +(4.50000 + 7.79423i) q^{9} +(-1.50000 - 0.866025i) q^{11} +3.00000i q^{12} +(3.46410 - 2.00000i) q^{13} +(-3.00000 + 1.73205i) q^{14} +(5.50000 - 9.52628i) q^{16} +15.5885 q^{17} +15.5885 q^{18} -11.0000 q^{19} +(-3.00000 - 5.19615i) q^{21} +(-2.59808 + 1.50000i) q^{22} +(13.8564 + 24.0000i) q^{23} +(22.5000 + 12.9904i) q^{24} -6.92820i q^{26} +27.0000i q^{27} -2.00000i q^{28} +(-39.0000 - 22.5167i) q^{29} +(-16.0000 - 27.7128i) q^{31} +(7.79423 + 13.5000i) q^{32} +(-2.59808 - 4.50000i) q^{33} +(13.5000 - 23.3827i) q^{34} +(-4.50000 + 7.79423i) q^{36} -34.0000i q^{37} +(-9.52628 + 16.5000i) q^{38} +12.0000 q^{39} +(-10.5000 + 6.06218i) q^{41} -10.3923 q^{42} +(-52.8275 - 30.5000i) q^{43} -1.73205i q^{44} +48.0000 q^{46} +(24.2487 - 42.0000i) q^{47} +(28.5788 - 16.5000i) q^{48} +(-22.5000 - 38.9711i) q^{49} +(40.5000 + 23.3827i) q^{51} +(3.46410 + 2.00000i) q^{52} +(40.5000 + 23.3827i) q^{54} +(-15.0000 - 8.66025i) q^{56} +(-28.5788 - 16.5000i) q^{57} +(-67.5500 + 39.0000i) q^{58} +(-43.5000 + 25.1147i) q^{59} +(-28.0000 + 48.4974i) q^{61} -55.4256 q^{62} -18.0000i q^{63} +71.0000 q^{64} -9.00000 q^{66} +(-26.8468 + 15.5000i) q^{67} +(7.79423 + 13.5000i) q^{68} +83.1384i q^{69} +31.1769i q^{71} +(38.9711 + 67.5000i) q^{72} -65.0000i q^{73} +(-51.0000 - 29.4449i) q^{74} +(-5.50000 - 9.52628i) q^{76} +(1.73205 + 3.00000i) q^{77} +(10.3923 - 18.0000i) q^{78} +(19.0000 - 32.9090i) q^{79} +(-40.5000 + 70.1481i) q^{81} +21.0000i q^{82} +(-24.2487 + 42.0000i) q^{83} +(3.00000 - 5.19615i) q^{84} +(-91.5000 + 52.8275i) q^{86} +(-67.5500 - 117.000i) q^{87} +(-12.9904 - 7.50000i) q^{88} +124.708i q^{89} -8.00000 q^{91} +(-13.8564 + 24.0000i) q^{92} -96.0000i q^{93} +(-42.0000 - 72.7461i) q^{94} +46.7654i q^{96} +(99.5929 + 57.5000i) q^{97} -77.9423 q^{98} -15.5885i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 18 q^{6} + 18 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 18 * q^6 + 18 * q^9	$ 4 q + 2 q^{4} + 18 q^{6} + 18 q^{9} - 6 q^{11} - 12 q^{14} + 22 q^{16} - 44 q^{19} - 12 q^{21} + 90 q^{24} - 156 q^{29} - 64 q^{31} + 54 q^{34} - 18 q^{36} + 48 q^{39} - 42 q^{41} + 192 q^{46} - 90 q^{49} + 162 q^{51} + 162 q^{54} - 60 q^{56} - 174 q^{59} - 112 q^{61} + 284 q^{64} - 36 q^{66} - 204 q^{74} - 22 q^{76} + 76 q^{79} - 162 q^{81} + 12 q^{84} - 366 q^{86} - 32 q^{91} - 168 q^{94}+O(q^{100}) $ 4 * q + 2 * q^4 + 18 * q^6 + 18 * q^9 - 6 * q^11 - 12 * q^14 + 22 * q^16 - 44 * q^19 - 12 * q^21 + 90 * q^24 - 156 * q^29 - 64 * q^31 + 54 * q^34 - 18 * q^36 + 48 * q^39 - 42 * q^41 + 192 * q^46 - 90 * q^49 + 162 * q^51 + 162 * q^54 - 60 * q^56 - 174 * q^59 - 112 * q^61 + 284 * q^64 - 36 * q^66 - 204 * q^74 - 22 * q^76 + 76 * q^79 - 162 * q^81 + 12 * q^84 - 366 * q^86 - 32 * q^91 - 168 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	−	1.50000i	0.433013	−	0.750000i	−0.564118	−	0.825694i	$-0.690784\pi$
$2$	0.866025	−	1.50000i	0.433013	−	0.750000i	0.997131	+	0.0756939i	$0.0241172\pi$
$3$	2.59808	+	1.50000i	0.866025	+	0.500000i
$3$	2.59808	+	1.50000i	0.866025	+	0.500000i
$4$	0.500000	+	0.866025i	0.125000	+	0.216506i
$5$		0			0
$5$		0			0
$6$	4.50000	−	2.59808i	0.750000	−	0.433013i
$7$	−1.73205	−	1.00000i	−0.247436	−	0.142857i	0.371154	−	0.928571i	$-0.378962\pi$
$7$	−1.73205	−	1.00000i	−0.247436	−	0.142857i	−0.618590	+	0.785714i	$0.712296\pi$
$8$	8.66025			1.08253
$9$	4.50000	+	7.79423i	0.500000	+	0.866025i
$10$		0			0
$11$	−1.50000	−	0.866025i	−0.136364	−	0.0787296i	0.430266	−	0.902702i	$-0.358420\pi$
$11$	−1.50000	−	0.866025i	−0.136364	−	0.0787296i	−0.566630	+	0.823972i	$0.691753\pi$
$12$			3.00000i			0.250000i
$13$	3.46410	−	2.00000i	0.266469	−	0.153846i	−0.360813	−	0.932638i	$-0.617501\pi$
$13$	3.46410	−	2.00000i	0.266469	−	0.153846i	0.627282	+	0.778792i	$0.284167\pi$
$14$	−3.00000	+	1.73205i	−0.214286	+	0.123718i
$15$		0			0
$16$	5.50000	−	9.52628i	0.343750	−	0.595392i
$17$	15.5885			0.916968			0.458484	−	0.888703i	$-0.348393\pi$
$17$	15.5885			0.916968			0.458484	+	0.888703i	$0.348393\pi$
$18$	15.5885			0.866025
$19$	−11.0000			−0.578947			−0.289474	−	0.957186i	$-0.593480\pi$
$19$	−11.0000			−0.578947			−0.289474	+	0.957186i	$0.593480\pi$
$20$		0			0
$21$	−3.00000	−	5.19615i	−0.142857	−	0.247436i
$22$	−2.59808	+	1.50000i	−0.118094	+	0.0681818i
$23$	13.8564	+	24.0000i	0.602452	+	1.04348i	0.992449	+	0.122662i	$0.0391430\pi$
$23$	13.8564	+	24.0000i	0.602452	+	1.04348i	−0.389996	+	0.920817i	$0.627524\pi$
$24$	22.5000	+	12.9904i	0.937500	+	0.541266i
$25$		0			0
$26$		−	6.92820i		−	0.266469i
$27$			27.0000i			1.00000i
$28$		−	2.00000i		−	0.0714286i
$29$	−39.0000	−	22.5167i	−1.34483	−	0.776437i	−0.357316	−	0.933984i	$-0.616308\pi$
$29$	−39.0000	−	22.5167i	−1.34483	−	0.776437i	−0.987511	+	0.157547i	$0.949641\pi$
$30$		0			0
$31$	−16.0000	−	27.7128i	−0.516129	−	0.893962i	−0.999825	−	0.0187254i	$-0.994039\pi$
$31$	−16.0000	−	27.7128i	−0.516129	−	0.893962i	0.483696	−	0.875236i	$-0.339294\pi$
$32$	7.79423	+	13.5000i	0.243570	+	0.421875i
$33$	−2.59808	−	4.50000i	−0.0787296	−	0.136364i
$34$	13.5000	−	23.3827i	0.397059	−	0.687726i
$35$		0			0
$36$	−4.50000	+	7.79423i	−0.125000	+	0.216506i
$37$		−	34.0000i		−	0.918919i	−0.888199	−	0.459459i	$-0.848043\pi$
$37$		−	34.0000i		−	0.918919i	0.888199	−	0.459459i	$-0.151957\pi$
$38$	−9.52628	+	16.5000i	−0.250692	+	0.434211i
$39$	12.0000			0.307692
$40$		0			0
$41$	−10.5000	+	6.06218i	−0.256098	+	0.147858i	−0.622553	−	0.782578i	$-0.713905\pi$
$41$	−10.5000	+	6.06218i	−0.256098	+	0.147858i	0.366456	+	0.930436i	$0.380571\pi$
$42$	−10.3923			−0.247436
$43$	−52.8275	−	30.5000i	−1.22855	−	0.709302i	−0.261822	−	0.965116i	$-0.584323\pi$
$43$	−52.8275	−	30.5000i	−1.22855	−	0.709302i	−0.966726	+	0.255814i	$0.917657\pi$
$44$		−	1.73205i		−	0.0393648i
$45$		0			0
$46$	48.0000			1.04348
$47$	24.2487	−	42.0000i	0.515930	−	0.893617i	−0.483899	−	0.875124i	$-0.660780\pi$
$47$	24.2487	−	42.0000i	0.515930	−	0.893617i	0.999829	−	0.0184931i	$-0.00588689\pi$
$48$	28.5788	−	16.5000i	0.595392	−	0.343750i
$49$	−22.5000	−	38.9711i	−0.459184	−	0.795329i
$50$		0			0
$51$	40.5000	+	23.3827i	0.794118	+	0.458484i
$52$	3.46410	+	2.00000i	0.0666173	+	0.0384615i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	40.5000	+	23.3827i	0.750000	+	0.433013i
$55$		0			0
$56$	−15.0000	−	8.66025i	−0.267857	−	0.154647i
$57$	−28.5788	−	16.5000i	−0.501383	−	0.289474i
$58$	−67.5500	+	39.0000i	−1.16465	+	0.672414i
$59$	−43.5000	+	25.1147i	−0.737288	+	0.425674i	−0.821082	−	0.570810i	$-0.806629\pi$
$59$	−43.5000	+	25.1147i	−0.737288	+	0.425674i	0.0837943	+	0.996483i	$0.473296\pi$
$60$		0			0
$61$	−28.0000	+	48.4974i	−0.459016	+	0.795040i	−0.998909	−	0.0466940i	$-0.985131\pi$
$61$	−28.0000	+	48.4974i	−0.459016	+	0.795040i	0.539893	+	0.841734i	$0.318465\pi$
$62$	−55.4256			−0.893962
$63$		−	18.0000i		−	0.285714i
$64$	71.0000			1.10938
$65$		0			0
$66$	−9.00000			−0.136364
$67$	−26.8468	+	15.5000i	−0.400698	+	0.231343i	−0.686785	−	0.726860i	$-0.740979\pi$
$67$	−26.8468	+	15.5000i	−0.400698	+	0.231343i	0.286087	+	0.958204i	$0.407645\pi$
$68$	7.79423	+	13.5000i	0.114621	+	0.198529i
$69$			83.1384i			1.20490i
$70$		0			0
$71$			31.1769i			0.439111i	0.975600	+	0.219556i	$0.0704608\pi$
$71$			31.1769i			0.439111i	−0.975600	+	0.219556i	$0.929539\pi$
$72$	38.9711	+	67.5000i	0.541266	+	0.937500i
$73$		−	65.0000i		−	0.890411i	−0.895428	−	0.445205i	$-0.853131\pi$
$73$		−	65.0000i		−	0.890411i	0.895428	−	0.445205i	$-0.146869\pi$
$74$	−51.0000	−	29.4449i	−0.689189	−	0.397904i
$75$		0			0
$76$	−5.50000	−	9.52628i	−0.0723684	−	0.125346i
$77$	1.73205	+	3.00000i	0.0224942	+	0.0389610i
$78$	10.3923	−	18.0000i	0.133235	−	0.230769i
$79$	19.0000	−	32.9090i	0.240506	−	0.416569i	−0.720352	−	0.693608i	$-0.756020\pi$
$79$	19.0000	−	32.9090i	0.240506	−	0.416569i	0.960859	+	0.277039i	$0.0893532\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.500000	+	0.866025i
$82$			21.0000i			0.256098i
$83$	−24.2487	+	42.0000i	−0.292153	+	0.506024i	−0.974319	−	0.225174i	$-0.927705\pi$
$83$	−24.2487	+	42.0000i	−0.292153	+	0.506024i	0.682165	+	0.731198i	$0.261038\pi$
$84$	3.00000	−	5.19615i	0.0357143	−	0.0618590i
$85$		0			0
$86$	−91.5000	+	52.8275i	−1.06395	+	0.614274i
$87$	−67.5500	−	117.000i	−0.776437	−	1.34483i
$88$	−12.9904	−	7.50000i	−0.147618	−	0.0852273i
$89$			124.708i			1.40121i	0.713549	+	0.700605i	$0.247086\pi$
$89$			124.708i			1.40121i	−0.713549	+	0.700605i	$0.752914\pi$
$90$		0			0
$91$	−8.00000			−0.0879121
$92$	−13.8564	+	24.0000i	−0.150613	+	0.260870i
$93$		−	96.0000i		−	1.03226i
$94$	−42.0000	−	72.7461i	−0.446809	−	0.773895i
$95$		0			0
$96$			46.7654i			0.487139i
$97$	99.5929	+	57.5000i	1.02673	+	0.592784i	0.916047	−	0.401072i	$-0.131362\pi$
$97$	99.5929	+	57.5000i	1.02673	+	0.592784i	0.110685	+	0.993856i	$0.464696\pi$
$98$	−77.9423			−0.795329
$99$		−	15.5885i		−	0.157459i
$100$		0			0
$101$	39.0000	+	22.5167i	0.386139	+	0.222937i	0.680486	−	0.732761i	$-0.261769\pi$
$101$	39.0000	+	22.5167i	0.386139	+	0.222937i	−0.294347	+	0.955699i	$0.595102\pi$
$102$	70.1481	−	40.5000i	0.687726	−	0.397059i
$103$	34.6410	−	20.0000i	0.336321	−	0.194175i	−0.322323	−	0.946630i	$-0.604464\pi$
$103$	34.6410	−	20.0000i	0.336321	−	0.194175i	0.658644	+	0.752455i	$0.271130\pi$
$104$	30.0000	−	17.3205i	0.288462	−	0.166543i
$105$		0			0
$106$		0			0
$107$	−140.296			−1.31118			−0.655589	−	0.755118i	$-0.727580\pi$
$107$	−140.296			−1.31118			−0.655589	+	0.755118i	$0.727580\pi$
$108$	−23.3827	+	13.5000i	−0.216506	+	0.125000i
$109$	52.0000			0.477064			0.238532	−	0.971135i	$-0.423334\pi$
$109$	52.0000			0.477064			0.238532	+	0.971135i	$0.423334\pi$
$110$		0			0
$111$	51.0000	−	88.3346i	0.459459	−	0.795807i
$112$	−19.0526	+	11.0000i	−0.170112	+	0.0982143i
$113$	45.0333	+	78.0000i	0.398525	+	0.690265i	0.993544	−	0.113446i	$-0.0361889\pi$
$113$	45.0333	+	78.0000i	0.398525	+	0.690265i	−0.595019	+	0.803711i	$0.702856\pi$
$114$	−49.5000	+	28.5788i	−0.434211	+	0.250692i
$115$		0			0
$116$		−	45.0333i		−	0.388218i
$117$	31.1769	+	18.0000i	0.266469	+	0.153846i
$118$			87.0000i			0.737288i
$119$	−27.0000	−	15.5885i	−0.226891	−	0.130995i
$120$		0			0
$121$	−59.0000	−	102.191i	−0.487603	−	0.844554i
$122$	48.4974	+	84.0000i	0.397520	+	0.688525i
$123$	−36.3731			−0.295716
$124$	16.0000	−	27.7128i	0.129032	−	0.223490i
$125$		0			0
$126$	−27.0000	−	15.5885i	−0.214286	−	0.123718i
$127$		−	16.0000i		−	0.125984i	−0.998014	−	0.0629921i	$-0.979936\pi$
$127$		−	16.0000i		−	0.125984i	0.998014	−	0.0629921i	$-0.0200643\pi$
$128$	30.3109	−	52.5000i	0.236804	−	0.410156i
$129$	−91.5000	−	158.483i	−0.709302	−	1.22855i
$130$		0			0
$131$	138.000	−	79.6743i	1.05344	−	0.608201i	0.129826	−	0.991537i	$-0.458558\pi$
$131$	138.000	−	79.6743i	1.05344	−	0.608201i	0.923609	+	0.383336i	$0.125225\pi$
$132$	2.59808	−	4.50000i	0.0196824	−	0.0340909i
$133$	19.0526	+	11.0000i	0.143252	+	0.0827068i
$134$			53.6936i			0.400698i
$135$		0			0
$136$	135.000			0.992647
$137$	94.3968	−	163.500i	0.689028	−	1.19343i	−0.283125	−	0.959083i	$-0.591371\pi$
$137$	94.3968	−	163.500i	0.689028	−	1.19343i	0.972153	−	0.234348i	$-0.0752954\pi$
$138$	124.708	+	72.0000i	0.903679	+	0.521739i
$139$	2.50000	+	4.33013i	0.0179856	+	0.0311520i	0.874878	−	0.484343i	$-0.160941\pi$
$139$	2.50000	+	4.33013i	0.0179856	+	0.0311520i	−0.856893	+	0.515495i	$0.827608\pi$
$140$		0			0
$141$	126.000	−	72.7461i	0.893617	−	0.515930i
$142$	46.7654	+	27.0000i	0.329334	+	0.190141i
$143$	−6.92820			−0.0484490
$144$	99.0000			0.687500
$145$		0			0
$146$	−97.5000	−	56.2917i	−0.667808	−	0.385559i
$147$		−	135.000i		−	0.918367i
$148$	29.4449	−	17.0000i	0.198952	−	0.114865i
$149$	132.000	−	76.2102i	0.885906	−	0.511478i	0.0133049	−	0.999911i	$-0.495765\pi$
$149$	132.000	−	76.2102i	0.885906	−	0.511478i	0.872601	+	0.488433i	$0.162431\pi$
$150$		0			0
$151$	−10.0000	+	17.3205i	−0.0662252	+	0.114705i	−0.897237	−	0.441550i	$-0.854429\pi$
$151$	−10.0000	+	17.3205i	−0.0662252	+	0.114705i	0.831012	+	0.556255i	$0.187762\pi$
$152$	−95.2628			−0.626729
$153$	70.1481	+	121.500i	0.458484	+	0.794118i
$154$	6.00000			0.0389610
$155$		0			0
$156$	6.00000	+	10.3923i	0.0384615	+	0.0666173i
$157$	−34.6410	+	20.0000i	−0.220643	+	0.127389i	−0.606248	−	0.795276i	$-0.707326\pi$
$157$	−34.6410	+	20.0000i	−0.220643	+	0.127389i	0.385605	+	0.922664i	$0.373993\pi$
$158$	−32.9090	−	57.0000i	−0.208285	−	0.360759i
$159$		0			0
$160$		0			0
$161$		−	55.4256i		−	0.344259i
$162$	70.1481	+	121.500i	0.433013	+	0.750000i
$163$			106.000i			0.650307i	0.945661	+	0.325153i	$0.105416\pi$
$163$			106.000i			0.650307i	−0.945661	+	0.325153i	$0.894584\pi$
$164$	−10.5000	−	6.06218i	−0.0640244	−	0.0369645i
$165$		0			0
$166$	42.0000	+	72.7461i	0.253012	+	0.438230i
$167$	95.2628	+	165.000i	0.570436	+	0.988024i	0.996521	+	0.0833409i	$0.0265590\pi$
$167$	95.2628	+	165.000i	0.570436	+	0.988024i	−0.426085	+	0.904683i	$0.640108\pi$
$168$	−25.9808	−	45.0000i	−0.154647	−	0.267857i
$169$	−76.5000	+	132.502i	−0.452663	+	0.784035i
$170$		0			0
$171$	−49.5000	−	85.7365i	−0.289474	−	0.501383i
$172$		−	61.0000i		−	0.354651i
$173$	116.047	−	201.000i	0.670794	−	1.16185i	−0.306885	−	0.951747i	$-0.599287\pi$
$173$	116.047	−	201.000i	0.670794	−	1.16185i	0.977679	−	0.210103i	$-0.0673800\pi$
$174$	−234.000			−1.34483
$175$		0			0
$176$	−16.5000	+	9.52628i	−0.0937500	+	0.0541266i
$177$	−150.688			−0.851347
$178$	187.061	+	108.000i	1.05091	+	0.606742i
$179$			62.3538i			0.348345i	0.984715	+	0.174173i	$0.0557251\pi$
$179$			62.3538i			0.348345i	−0.984715	+	0.174173i	$0.944275\pi$
$180$		0			0
$181$	−232.000			−1.28177			−0.640884	−	0.767638i	$-0.721432\pi$
$181$	−232.000			−1.28177			−0.640884	+	0.767638i	$0.721432\pi$
$182$	−6.92820	+	12.0000i	−0.0380671	+	0.0659341i
$183$	−145.492	+	84.0000i	−0.795040	+	0.459016i
$184$	120.000	+	207.846i	0.652174	+	1.12960i
$185$		0			0
$186$	−144.000	−	83.1384i	−0.774194	−	0.446981i
$187$	−23.3827	−	13.5000i	−0.125041	−	0.0721925i
$188$	48.4974			0.257965
$189$	27.0000	−	46.7654i	0.142857	−	0.247436i
$190$		0			0
$191$	201.000	+	116.047i	1.05236	+	0.607578i	0.923308	−	0.384060i	$-0.125475\pi$
$191$	201.000	+	116.047i	1.05236	+	0.607578i	0.129048	+	0.991638i	$0.458808\pi$
$192$	184.463	+	106.500i	0.960747	+	0.554688i
$193$	229.497	−	132.500i	1.18910	−	0.686528i	0.231000	−	0.972954i	$-0.425800\pi$
$193$	229.497	−	132.500i	1.18910	−	0.686528i	0.958103	+	0.286425i	$0.0924670\pi$
$194$	172.500	−	99.5929i	0.889175	−	0.513366i
$195$		0			0
$196$	22.5000	−	38.9711i	0.114796	−	0.198832i
$197$	124.708			0.633034			0.316517	−	0.948587i	$-0.397487\pi$
$197$	124.708			0.633034			0.316517	+	0.948587i	$0.397487\pi$
$198$	−23.3827	−	13.5000i	−0.118094	−	0.0681818i
$199$	−290.000			−1.45729			−0.728643	−	0.684893i	$-0.759849\pi$
$199$	−290.000			−1.45729			−0.728643	+	0.684893i	$0.759849\pi$
$200$		0			0
$201$	−93.0000			−0.462687
$202$	67.5500	−	39.0000i	0.334406	−	0.193069i
$203$	45.0333	+	78.0000i	0.221839	+	0.384236i
$204$			46.7654i			0.229242i
$205$		0			0
$206$		−	69.2820i		−	0.336321i
$207$	−124.708	+	216.000i	−0.602452	+	1.04348i
$208$		−	44.0000i		−	0.211538i
$209$	16.5000	+	9.52628i	0.0789474	+	0.0455803i
$210$		0			0
$211$	47.0000	+	81.4064i	0.222749	+	0.385812i	0.955642	−	0.294532i	$-0.0951637\pi$
$211$	47.0000	+	81.4064i	0.222749	+	0.385812i	−0.732893	+	0.680344i	$0.761830\pi$
$212$		0			0
$213$	−46.7654	+	81.0000i	−0.219556	+	0.380282i
$214$	−121.500	+	210.444i	−0.567757	+	0.983384i
$215$		0			0
$216$			233.827i			1.08253i
$217$			64.0000i			0.294931i
$218$	45.0333	−	78.0000i	0.206575	−	0.357798i
$219$	97.5000	−	168.875i	0.445205	−	0.771119i
$220$		0			0
$221$	54.0000	−	31.1769i	0.244344	−	0.141072i
$222$	−88.3346	−	153.000i	−0.397904	−	0.689189i
$223$	−45.0333	−	26.0000i	−0.201943	−	0.116592i	0.395618	−	0.918415i	$-0.370530\pi$
$223$	−45.0333	−	26.0000i	−0.201943	−	0.116592i	−0.597562	+	0.801823i	$0.703864\pi$
$224$		−	31.1769i		−	0.139183i
$225$		0			0
$226$	156.000			0.690265
$227$	94.3968	−	163.500i	0.415845	−	0.720264i	−0.579672	−	0.814850i	$-0.696819\pi$
$227$	94.3968	−	163.500i	0.415845	−	0.720264i	0.995517	+	0.0945856i	$0.0301526\pi$
$228$		−	33.0000i		−	0.144737i
$229$	133.000	+	230.363i	0.580786	+	1.00595i	0.995386	+	0.0959473i	$0.0305880\pi$
$229$	133.000	+	230.363i	0.580786	+	1.00595i	−0.414600	+	0.910004i	$0.636079\pi$
$230$		0			0
$231$			10.3923i			0.0449883i
$232$	−337.750	−	195.000i	−1.45582	−	0.840517i
$233$	−202.650			−0.869742			−0.434871	−	0.900493i	$-0.643206\pi$
$233$	−202.650			−0.869742			−0.434871	+	0.900493i	$0.643206\pi$
$234$	54.0000	−	31.1769i	0.230769	−	0.133235i
$235$		0			0
$236$	−43.5000	−	25.1147i	−0.184322	−	0.106418i
$237$	98.7269	−	57.0000i	0.416569	−	0.240506i
$238$	−46.7654	+	27.0000i	−0.196493	+	0.113445i
$239$	348.000	−	200.918i	1.45607	−	0.840661i	0.457252	−	0.889337i	$-0.348834\pi$
$239$	348.000	−	200.918i	1.45607	−	0.840661i	0.998815	+	0.0486764i	$0.0155003\pi$
$240$		0			0
$241$	−59.5000	+	103.057i	−0.246888	+	0.427623i	−0.962661	−	0.270711i	$-0.912741\pi$
$241$	−59.5000	+	103.057i	−0.246888	+	0.427623i	0.715773	+	0.698333i	$0.246075\pi$
$242$	−204.382			−0.844554
$243$	−210.444	+	121.500i	−0.866025	+	0.500000i
$244$	−56.0000			−0.229508
$245$		0			0
$246$	−31.5000	+	54.5596i	−0.128049	+	0.221787i
$247$	−38.1051	+	22.0000i	−0.154272	+	0.0890688i
$248$	−138.564	−	240.000i	−0.558726	−	0.967742i
$249$	−126.000	+	72.7461i	−0.506024	+	0.292153i
$250$		0			0
$251$			389.711i			1.55264i	0.630342	+	0.776318i	$0.282915\pi$
$251$			389.711i			1.55264i	−0.630342	+	0.776318i	$0.717085\pi$
$252$	15.5885	−	9.00000i	0.0618590	−	0.0357143i
$253$		−	48.0000i		−	0.189723i
$254$	−24.0000	−	13.8564i	−0.0944882	−	0.0545528i
$255$		0			0
$256$	89.5000	+	155.019i	0.349609	+	0.605541i
$257$	87.4686	+	151.500i	0.340345	+	0.589494i	0.984497	−	0.175403i	$-0.0561229\pi$
$257$	87.4686	+	151.500i	0.340345	+	0.589494i	−0.644152	+	0.764897i	$0.722790\pi$
$258$	−316.965			−1.22855
$259$	−34.0000	+	58.8897i	−0.131274	+	0.227373i
$260$		0			0
$261$		−	405.300i		−	1.55287i
$262$		−	276.000i		−	1.05344i
$263$	22.5167	−	39.0000i	0.0856147	−	0.148289i	−0.820038	−	0.572309i	$-0.806048\pi$
$263$	22.5167	−	39.0000i	0.0856147	−	0.148289i	0.905653	+	0.424020i	$0.139381\pi$
$264$	−22.5000	−	38.9711i	−0.0852273	−	0.147618i
$265$		0			0
$266$	33.0000	−	19.0526i	0.124060	−	0.0716262i
$267$	−187.061	+	324.000i	−0.700605	+	1.21348i
$268$	−26.8468	−	15.5000i	−0.100175	−	0.0578358i
$269$		−	187.061i		−	0.695396i	−0.937607	−	0.347698i	$-0.886963\pi$
$269$		−	187.061i		−	0.695396i	0.937607	−	0.347698i	$-0.113037\pi$
$270$		0			0
$271$	−268.000			−0.988930			−0.494465	−	0.869198i	$-0.664636\pi$
$271$	−268.000			−0.988930			−0.494465	+	0.869198i	$0.664636\pi$
$272$	85.7365	−	148.500i	0.315208	−	0.545956i
$273$	−20.7846	−	12.0000i	−0.0761341	−	0.0439560i
$274$	−163.500	−	283.190i	−0.596715	−	1.03354i
$275$		0			0
$276$	−72.0000	+	41.5692i	−0.260870	+	0.150613i
$277$	−48.4974	−	28.0000i	−0.175081	−	0.101083i	0.409899	−	0.912131i	$-0.365564\pi$
$277$	−48.4974	−	28.0000i	−0.175081	−	0.101083i	−0.584979	+	0.811048i	$0.698897\pi$
$278$	8.66025			0.0311520
$279$	144.000	−	249.415i	0.516129	−	0.893962i
$280$		0			0
$281$	−42.0000	−	24.2487i	−0.149466	−	0.0862943i	0.423402	−	0.905942i	$-0.360836\pi$
$281$	−42.0000	−	24.2487i	−0.149466	−	0.0862943i	−0.572868	+	0.819648i	$0.694169\pi$
$282$		−	252.000i		−	0.893617i
$283$	−323.894	+	187.000i	−1.14450	+	0.660777i	−0.947541	−	0.319634i	$-0.896440\pi$
$283$	−323.894	+	187.000i	−1.14450	+	0.660777i	−0.196959	+	0.980412i	$0.563107\pi$
$284$	−27.0000	+	15.5885i	−0.0950704	+	0.0548889i
$285$		0			0
$286$	−6.00000	+	10.3923i	−0.0209790	+	0.0363367i
$287$	24.2487			0.0844903
$288$	−70.1481	+	121.500i	−0.243570	+	0.421875i
$289$	−46.0000			−0.159170
$290$		0			0
$291$	172.500	+	298.779i	0.592784	+	1.02673i
$292$	56.2917	−	32.5000i	0.192780	−	0.111301i
$293$	−126.440	−	219.000i	−0.431535	−	0.747440i	0.565471	−	0.824768i	$-0.308694\pi$
$293$	−126.440	−	219.000i	−0.431535	−	0.747440i	−0.997006	+	0.0773280i	$0.975361\pi$
$294$	−202.500	−	116.913i	−0.688776	−	0.397665i
$295$		0			0
$296$		−	294.449i		−	0.994759i
$297$	23.3827	−	40.5000i	0.0787296	−	0.136364i
$298$		−	264.000i		−	0.885906i
$299$	96.0000	+	55.4256i	0.321070	+	0.185370i
$300$		0			0
$301$	61.0000	+	105.655i	0.202658	+	0.351014i
$302$	17.3205	+	30.0000i	0.0573527	+	0.0993377i
$303$	67.5500	+	117.000i	0.222937	+	0.386139i
$304$	−60.5000	+	104.789i	−0.199013	+	0.344701i
$305$		0			0
$306$	243.000			0.794118
$307$			533.000i			1.73616i	0.496428	+	0.868078i	$0.334645\pi$
$307$			533.000i			1.73616i	−0.496428	+	0.868078i	$0.665355\pi$
$308$	−1.73205	+	3.00000i	−0.00562354	+	0.00974026i
$309$	120.000			0.388350
$310$		0			0
$311$	−213.000	+	122.976i	−0.684887	+	0.395420i	−0.801694	−	0.597735i	$-0.796068\pi$
$311$	−213.000	+	122.976i	−0.684887	+	0.395420i	0.116806	+	0.993155i	$0.462734\pi$
$312$	103.923			0.333087
$313$	134.234	+	77.5000i	0.428862	+	0.247604i	0.698862	−	0.715257i	$-0.253690\pi$
$313$	134.234	+	77.5000i	0.428862	+	0.247604i	−0.269999	+	0.962860i	$0.587024\pi$
$314$			69.2820i			0.220643i
$315$		0			0
$316$	38.0000			0.120253
$317$	24.2487	−	42.0000i	0.0764944	−	0.132492i	−0.825241	−	0.564781i	$-0.808961\pi$
$317$	24.2487	−	42.0000i	0.0764944	−	0.132492i	0.901735	+	0.432289i	$0.142294\pi$
$318$		0			0
$319$	39.0000	+	67.5500i	0.122257	+	0.211755i
$320$		0			0
$321$	−364.500	−	210.444i	−1.13551	−	0.655589i
$322$	−83.1384	−	48.0000i	−0.258194	−	0.149068i
$323$	−171.473			−0.530876
$324$	−81.0000			−0.250000
$325$		0			0
$326$	159.000	+	91.7987i	0.487730	+	0.281591i
$327$	135.100	+	78.0000i	0.413150	+	0.238532i
$328$	−90.9327	+	52.5000i	−0.277234	+	0.160061i
$329$	−84.0000	+	48.4974i	−0.255319	+	0.147409i
$330$		0			0
$331$	−1.00000	+	1.73205i	−0.00302115	+	0.00523278i	−0.867532	−	0.497381i	$-0.834295\pi$
$331$	−1.00000	+	1.73205i	−0.00302115	+	0.00523278i	0.864511	+	0.502614i	$0.167628\pi$
$332$	−48.4974			−0.146077
$333$	265.004	−	153.000i	0.795807	−	0.459459i
$334$	330.000			0.988024
$335$		0			0
$336$	−66.0000			−0.196429
$337$	66.6840	−	38.5000i	0.197875	−	0.114243i	−0.397789	−	0.917477i	$-0.630222\pi$
$337$	66.6840	−	38.5000i	0.197875	−	0.114243i	0.595664	+	0.803234i	$0.296889\pi$
$338$	132.502	+	229.500i	0.392017	+	0.678994i
$339$			270.200i			0.797050i
$340$		0			0
$341$			55.4256i			0.162538i
$342$	−171.473			−0.501383
$343$			188.000i			0.548105i
$344$	−457.500	−	264.138i	−1.32994	−	0.767842i
$345$		0			0
$346$	−201.000	−	348.142i	−0.580925	−	1.00619i
$347$	56.2917	+	97.5000i	0.162224	+	0.280980i	0.935666	−	0.352887i	$-0.114800\pi$
$347$	56.2917	+	97.5000i	0.162224	+	0.280980i	−0.773442	+	0.633867i	$0.781467\pi$
$348$	67.5500	−	117.000i	0.194109	−	0.336207i
$349$	208.000	−	360.267i	0.595989	−	1.03228i	−0.397418	−	0.917638i	$-0.630094\pi$
$349$	208.000	−	360.267i	0.595989	−	1.03228i	0.993407	−	0.114645i	$-0.0365730\pi$
$350$		0			0
$351$	54.0000	+	93.5307i	0.153846	+	0.266469i
$352$		−	27.0000i		−	0.0767045i
$353$	−0.866025	+	1.50000i	−0.00245333	+	0.00424929i	−0.867249	−	0.497874i	$-0.834114\pi$
$353$	−0.866025	+	1.50000i	−0.00245333	+	0.00424929i	0.864796	+	0.502123i	$0.167448\pi$
$354$	−130.500	+	226.033i	−0.368644	+	0.638510i
$355$		0			0
$356$	−108.000	+	62.3538i	−0.303371	+	0.175151i
$357$	−46.7654	−	81.0000i	−0.130995	−	0.226891i
$358$	93.5307	+	54.0000i	0.261259	+	0.150838i
$359$			592.361i			1.65003i	0.565110	+	0.825016i	$0.308834\pi$
$359$			592.361i			1.65003i	−0.565110	+	0.825016i	$0.691166\pi$
$360$		0			0
$361$	−240.000			−0.664820
$362$	−200.918	+	348.000i	−0.555022	+	0.961326i
$363$		−	354.000i		−	0.975207i
$364$	−4.00000	−	6.92820i	−0.0109890	−	0.0190335i
$365$		0			0
$366$			290.985i			0.795040i
$367$	310.037	+	179.000i	0.844788	+	0.487738i	0.858889	−	0.512162i	$-0.171155\pi$
$367$	310.037	+	179.000i	0.844788	+	0.487738i	−0.0141011	+	0.999901i	$0.504489\pi$
$368$	304.841			0.828372
$369$	−94.5000	−	54.5596i	−0.256098	−	0.147858i
$370$		0			0
$371$		0			0
$372$	83.1384	−	48.0000i	0.223490	−	0.129032i
$373$	502.295	−	290.000i	1.34663	−	0.777480i	0.358863	−	0.933390i	$-0.383164\pi$
$373$	502.295	−	290.000i	1.34663	−	0.777480i	0.987771	+	0.155910i	$0.0498310\pi$
$374$	−40.5000	+	23.3827i	−0.108289	+	0.0625206i
$375$		0			0
$376$	210.000	−	363.731i	0.558511	−	0.967369i
$377$	−180.133			−0.477807
$378$	−46.7654	−	81.0000i	−0.123718	−	0.214286i
$379$	−83.0000			−0.218997			−0.109499	−	0.993987i	$-0.534925\pi$
$379$	−83.0000			−0.218997			−0.109499	+	0.993987i	$0.534925\pi$
$380$		0			0
$381$	24.0000	−	41.5692i	0.0629921	−	0.109106i
$382$	348.142	−	201.000i	0.911367	−	0.526178i
$383$	278.860	+	483.000i	0.728094	+	1.26110i	0.957688	+	0.287810i	$0.0929271\pi$
$383$	278.860	+	483.000i	0.728094	+	1.26110i	−0.229593	+	0.973287i	$0.573740\pi$
$384$	157.500	−	90.9327i	0.410156	−	0.236804i
$385$		0			0
$386$		−	458.993i		−	1.18910i
$387$		−	549.000i		−	1.41860i
$388$			115.000i			0.296392i
$389$	447.000	+	258.076i	1.14910	+	0.663433i	0.948668	−	0.316274i	$-0.102432\pi$
$389$	447.000	+	258.076i	1.14910	+	0.663433i	0.200432	+	0.979708i	$0.435765\pi$
$390$		0			0
$391$	216.000	+	374.123i	0.552430	+	0.956836i
$392$	−194.856	−	337.500i	−0.497081	−	0.860969i
$393$	478.046			1.21640
$394$	108.000	−	187.061i	0.274112	−	0.474775i
$395$		0			0
$396$	13.5000	−	7.79423i	0.0340909	−	0.0196824i
$397$			362.000i			0.911839i	0.890021	+	0.455919i	$0.150689\pi$
$397$			362.000i			0.911839i	−0.890021	+	0.455919i	$0.849311\pi$
$398$	−251.147	+	435.000i	−0.631024	+	1.09296i
$399$	33.0000	+	57.1577i	0.0827068	+	0.143252i
$400$		0			0
$401$	340.500	−	196.588i	0.849127	−	0.490244i	−0.0112291	−	0.999937i	$-0.503574\pi$
$401$	340.500	−	196.588i	0.849127	−	0.490244i	0.860356	+	0.509693i	$0.170241\pi$
$402$	−80.5404	+	139.500i	−0.200349	+	0.347015i
$403$	−110.851	−	64.0000i	−0.275065	−	0.158809i
$404$			45.0333i			0.111469i
$405$		0			0
$406$	156.000			0.384236
$407$	−29.4449	+	51.0000i	−0.0723461	+	0.125307i
$408$	350.740	+	202.500i	0.859658	+	0.496324i
$409$	110.500	+	191.392i	0.270171	+	0.467950i	0.968905	−	0.247431i	$-0.0795864\pi$
$409$	110.500	+	191.392i	0.270171	+	0.467950i	−0.698734	+	0.715381i	$0.746253\pi$
$410$		0			0
$411$	490.500	−	283.190i	1.19343	−	0.689028i
$412$	34.6410	+	20.0000i	0.0840801	+	0.0485437i
$413$	100.459			0.243242
$414$	216.000	+	374.123i	0.521739	+	0.903679i
$415$		0			0
$416$	54.0000	+	31.1769i	0.129808	+	0.0749445i
$417$			15.0000i			0.0359712i
$418$	28.5788	−	16.5000i	0.0683704	−	0.0394737i
$419$	−678.000	+	391.443i	−1.61814	+	0.934233i	−0.630737	+	0.775997i	$0.717247\pi$
$419$	−678.000	+	391.443i	−1.61814	+	0.934233i	−0.987401	+	0.158236i	$0.949419\pi$
$420$		0			0
$421$	341.000	−	590.629i	0.809976	−	1.40292i	−0.102903	−	0.994691i	$-0.532813\pi$
$421$	341.000	−	590.629i	0.809976	−	1.40292i	0.912880	−	0.408229i	$-0.133853\pi$
$422$	162.813			0.385812
$423$	436.477			1.03186
$424$		0			0
$425$		0			0
$426$	81.0000	+	140.296i	0.190141	+	0.329334i
$427$	96.9948	−	56.0000i	0.227154	−	0.131148i
$428$	−70.1481	−	121.500i	−0.163897	−	0.283879i
$429$	−18.0000	−	10.3923i	−0.0419580	−	0.0242245i
$430$		0			0
$431$			280.592i			0.651026i	0.945538	+	0.325513i	$0.105537\pi$
$431$			280.592i			0.651026i	−0.945538	+	0.325513i	$0.894463\pi$
$432$	257.210	+	148.500i	0.595392	+	0.343750i
$433$			295.000i			0.681293i	0.940191	+	0.340647i	$0.110646\pi$
$433$			295.000i			0.681293i	−0.940191	+	0.340647i	$0.889354\pi$
$434$	96.0000	+	55.4256i	0.221198	+	0.127709i
$435$		0			0
$436$	26.0000	+	45.0333i	0.0596330	+	0.103287i
$437$	−152.420	−	264.000i	−0.348788	−	0.604119i
$438$	−168.875	−	292.500i	−0.385559	−	0.667808i
$439$	406.000	−	703.213i	0.924829	−	1.60185i	0.132993	−	0.991117i	$-0.457541\pi$
$439$	406.000	−	703.213i	0.924829	−	1.60185i	0.791836	−	0.610734i	$-0.209126\pi$
$440$		0			0
$441$	202.500	−	350.740i	0.459184	−	0.795329i
$442$		−	108.000i		−	0.244344i
$443$	45.8993	−	79.5000i	0.103610	−	0.179458i	−0.809559	−	0.587038i	$-0.800294\pi$
$443$	45.8993	−	79.5000i	0.103610	−	0.179458i	0.913170	+	0.407580i	$0.133627\pi$
$444$	102.000			0.229730
$445$		0			0
$446$	−78.0000	+	45.0333i	−0.174888	+	0.100972i
$447$	457.261			1.02296
$448$	−122.976	−	71.0000i	−0.274499	−	0.158482i
$449$		−	639.127i		−	1.42344i	−0.702461	−	0.711722i	$-0.747915\pi$
$449$		−	639.127i		−	1.42344i	0.702461	−	0.711722i	$-0.252085\pi$
$450$		0			0
$451$	21.0000			0.0465632
$452$	−45.0333	+	78.0000i	−0.0996312	+	0.172566i
$453$	−51.9615	+	30.0000i	−0.114705	+	0.0662252i
$454$	−163.500	−	283.190i	−0.360132	−	0.623767i
$455$		0			0
$456$	−247.500	−	142.894i	−0.542763	−	0.313364i
$457$	−56.2917	−	32.5000i	−0.123176	−	0.0711160i	0.437146	−	0.899391i	$-0.355989\pi$
$457$	−56.2917	−	32.5000i	−0.123176	−	0.0711160i	−0.560322	+	0.828275i	$0.689323\pi$
$458$	460.726			1.00595
$459$			420.888i			0.916968i
$460$		0			0
$461$	−690.000	−	398.372i	−1.49675	−	0.864147i	−0.496753	−	0.867892i	$-0.665475\pi$
$461$	−690.000	−	398.372i	−1.49675	−	0.864147i	−0.999993	+	0.00374501i	$0.998808\pi$
$462$	15.5885	+	9.00000i	0.0337412	+	0.0194805i
$463$	−635.663	+	367.000i	−1.37292	+	0.792657i	−0.991295	−	0.131660i	$-0.957969\pi$
$463$	−635.663	+	367.000i	−1.37292	+	0.792657i	−0.381627	+	0.924317i	$0.624636\pi$
$464$	−429.000	+	247.683i	−0.924569	+	0.533800i
$465$		0			0
$466$	−175.500	+	303.975i	−0.376609	+	0.652307i
$467$	−202.650			−0.433940			−0.216970	−	0.976178i	$-0.569617\pi$
$467$	−202.650			−0.433940			−0.216970	+	0.976178i	$0.569617\pi$
$468$			36.0000i			0.0769231i
$469$	62.0000			0.132196
$470$		0			0
$471$	−120.000			−0.254777
$472$	−376.721	+	217.500i	−0.798138	+	0.460805i
$473$	52.8275	+	91.5000i	0.111686	+	0.193446i
$474$		−	197.454i		−	0.416569i
$475$		0			0
$476$		−	31.1769i		−	0.0654977i
$477$		0			0
$478$		−	696.000i		−	1.45607i
$479$	−525.000	−	303.109i	−1.09603	−	0.632795i	−0.160857	−	0.986978i	$-0.551426\pi$
$479$	−525.000	−	303.109i	−1.09603	−	0.632795i	−0.935176	+	0.354183i	$0.884759\pi$
$480$		0			0
$481$	−68.0000	−	117.779i	−0.141372	−	0.244864i
$482$	103.057	+	178.500i	0.213811	+	0.370332i
$483$	83.1384	−	144.000i	0.172129	−	0.298137i
$484$	59.0000	−	102.191i	0.121901	−	0.211138i
$485$		0			0
$486$			420.888i			0.866025i
$487$		−	106.000i		−	0.217659i	−0.994060	−	0.108830i	$-0.965290\pi$
$487$		−	106.000i		−	0.217659i	0.994060	−	0.108830i	$-0.0347103\pi$
$488$	−242.487	+	420.000i	−0.496900	+	0.860656i
$489$	−159.000	+	275.396i	−0.325153	+	0.563182i
$490$		0			0
$491$	−199.500	+	115.181i	−0.406314	+	0.234585i	−0.689205	−	0.724567i	$-0.742040\pi$
$491$	−199.500	+	115.181i	−0.406314	+	0.234585i	0.282891	+	0.959152i	$0.408707\pi$
$492$	−18.1865	−	31.5000i	−0.0369645	−	0.0640244i
$493$	−607.950	−	351.000i	−1.23316	−	0.711968i
$494$			76.2102i			0.154272i
$495$		0			0
$496$	−352.000			−0.709677
$497$	31.1769	−	54.0000i	0.0627302	−	0.108652i
$498$			252.000i			0.506024i
$499$	−393.500	−	681.562i	−0.788577	−	1.36586i	−0.926839	−	0.375460i	$-0.877485\pi$
$499$	−393.500	−	681.562i	−0.788577	−	1.36586i	0.138261	−	0.990396i	$-0.455849\pi$
$500$		0			0
$501$			571.577i			1.14087i
$502$	584.567	+	337.500i	1.16448	+	0.672311i
$503$	−623.538			−1.23964			−0.619819	−	0.784745i	$-0.712794\pi$
$503$	−623.538			−1.23964			−0.619819	+	0.784745i	$0.712794\pi$
$504$		−	155.885i		−	0.309295i
$505$		0			0
$506$	−72.0000	−	41.5692i	−0.142292	−	0.0821526i
$507$	−397.506	+	229.500i	−0.784035	+	0.452663i
$508$	13.8564	−	8.00000i	0.0272764	−	0.0157480i
$509$	186.000	−	107.387i	0.365422	−	0.210977i	−0.306034	−	0.952020i	$-0.599002\pi$
$509$	186.000	−	107.387i	0.365422	−	0.210977i	0.671457	+	0.741044i	$0.265669\pi$
$510$		0			0
$511$	−65.0000	+	112.583i	−0.127202	+	0.220320i
$512$	552.524			1.07915
$513$		−	297.000i		−	0.578947i
$514$	303.000			0.589494
$515$		0			0
$516$	91.5000	−	158.483i	0.177326	−	0.307137i
$517$	−72.7461	+	42.0000i	−0.140708	+	0.0812379i
$518$	58.8897	+	102.000i	0.113687	+	0.196911i
$519$	603.000	−	348.142i	1.16185	−	0.670794i
$520$		0			0
$521$			202.650i			0.388963i	0.980906	+	0.194482i	$0.0623025\pi$
$521$			202.650i			0.388963i	−0.980906	+	0.194482i	$0.937698\pi$
$522$	−607.950	−	351.000i	−1.16465	−	0.672414i
$523$			250.000i			0.478011i	0.971018	+	0.239006i	$0.0768215\pi$
$523$			250.000i			0.478011i	−0.971018	+	0.239006i	$0.923179\pi$
$524$	138.000	+	79.6743i	0.263359	+	0.152050i
$525$		0			0
$526$	−39.0000	−	67.5500i	−0.0741445	−	0.128422i
$527$	−249.415	−	432.000i	−0.473274	−	0.819734i
$528$	−57.1577			−0.108253
$529$	−119.500	+	206.980i	−0.225898	+	0.391267i
$530$		0			0
$531$	−391.500	−	226.033i	−0.737288	−	0.425674i
$532$			22.0000i			0.0413534i
$533$	−24.2487	+	42.0000i	−0.0454948	+	0.0787992i
$534$	324.000	+	561.184i	0.606742	+	1.05091i
$535$		0			0
$536$	−232.500	+	134.234i	−0.433769	+	0.250436i
$537$	−93.5307	+	162.000i	−0.174173	+	0.301676i
$538$	−280.592	−	162.000i	−0.521547	−	0.301115i
$539$			77.9423i			0.144605i
$540$		0			0
$541$	650.000			1.20148			0.600739	−	0.799445i	$-0.294873\pi$
$541$	650.000			1.20148			0.600739	+	0.799445i	$0.294873\pi$
$542$	−232.095	+	402.000i	−0.428219	+	0.741697i
$543$	−602.754	−	348.000i	−1.11004	−	0.640884i
$544$	121.500	+	210.444i	0.223346	+	0.386846i
$545$		0			0
$546$	−36.0000	+	20.7846i	−0.0659341	+	0.0380671i
$547$	−539.534	−	311.500i	−0.986351	−	0.569470i	−0.0821692	−	0.996618i	$-0.526185\pi$
$547$	−539.534	−	311.500i	−0.986351	−	0.569470i	−0.904181	+	0.427149i	$0.859518\pi$
$548$	188.794			0.344514
$549$	−504.000			−0.918033
$550$		0			0
$551$	429.000	+	247.683i	0.778584	+	0.449516i
$552$			720.000i			1.30435i
$553$	−65.8179	+	38.0000i	−0.119020	+	0.0687161i
$554$	−84.0000	+	48.4974i	−0.151625	+	0.0875405i
$555$		0			0
$556$	−2.50000	+	4.33013i	−0.00449640	+	0.00778800i
$557$	530.008			0.951540			0.475770	−	0.879570i	$-0.342170\pi$
$557$	530.008			0.951540			0.475770	+	0.879570i	$0.342170\pi$
$558$	−249.415	−	432.000i	−0.446981	−	0.774194i
$559$	−244.000			−0.436494
$560$		0			0
$561$	−40.5000	−	70.1481i	−0.0721925	−	0.125041i
$562$	−72.7461	+	42.0000i	−0.129442	+	0.0747331i
$563$	−56.2917	−	97.5000i	−0.0999852	−	0.173179i	0.811693	−	0.584084i	$-0.198546\pi$
$563$	−56.2917	−	97.5000i	−0.0999852	−	0.173179i	−0.911678	+	0.410905i	$0.865213\pi$
$564$	126.000	+	72.7461i	0.223404	+	0.128983i
$565$		0			0
$566$			647.787i			1.14450i
$567$	140.296	−	81.0000i	0.247436	−	0.142857i
$568$			270.000i			0.475352i
$569$	−565.500	−	326.492i	−0.993849	−	0.573799i	−0.0874263	−	0.996171i	$-0.527864\pi$
$569$	−565.500	−	326.492i	−0.993849	−	0.573799i	−0.906423	+	0.422372i	$0.861198\pi$
$570$		0			0
$571$	−272.500	−	471.984i	−0.477233	−	0.826592i	0.522427	−	0.852684i	$-0.325027\pi$
$571$	−272.500	−	471.984i	−0.477233	−	0.826592i	−0.999660	+	0.0260926i	$0.991694\pi$
$572$	−3.46410	−	6.00000i	−0.00605612	−	0.0104895i
$573$	348.142	+	603.000i	0.607578	+	1.05236i
$574$	21.0000	−	36.3731i	0.0365854	−	0.0633677i
$575$		0			0
$576$	319.500	+	553.390i	0.554688	+	0.960747i
$577$		−	871.000i		−	1.50953i	−0.655994	−	0.754766i	$-0.727750\pi$
$577$		−	871.000i		−	1.50953i	0.655994	−	0.754766i	$-0.272250\pi$
$578$	−39.8372	+	69.0000i	−0.0689224	+	0.119377i
$579$	795.000			1.37306
$580$		0			0
$581$	84.0000	−	48.4974i	0.144578	−	0.0834723i
$582$	597.558			1.02673
$583$		0			0
$584$		−	562.917i		−	0.963898i
$585$		0			0
$586$	−438.000			−0.747440
$587$	0.866025	−	1.50000i	0.00147534	−	0.00255537i	−0.865287	−	0.501277i	$-0.832864\pi$
$587$	0.866025	−	1.50000i	0.00147534	−	0.00255537i	0.866762	+	0.498722i	$0.166197\pi$
$588$	116.913	−	67.5000i	0.198832	−	0.114796i
$589$	176.000	+	304.841i	0.298812	+	0.517557i
$590$		0			0
$591$	324.000	+	187.061i	0.548223	+	0.316517i
$592$	−323.894	−	187.000i	−0.547117	−	0.315878i
$593$	−187.061			−0.315449			−0.157725	−	0.987483i	$-0.550416\pi$
$593$	−187.061			−0.315449			−0.157725	+	0.987483i	$0.550416\pi$
$594$	−40.5000	−	70.1481i	−0.0681818	−	0.118094i
$595$		0			0
$596$	132.000	+	76.2102i	0.221477	+	0.127870i
$597$	−753.442	−	435.000i	−1.26205	−	0.728643i
$598$	166.277	−	96.0000i	0.278055	−	0.160535i
$599$	−489.000	+	282.324i	−0.816361	+	0.471326i	−0.849160	−	0.528136i	$-0.822891\pi$
$599$	−489.000	+	282.324i	−0.816361	+	0.471326i	0.0327992	+	0.999462i	$0.489558\pi$
$600$		0			0
$601$	−230.500	+	399.238i	−0.383527	+	0.664289i	−0.991564	−	0.129620i	$-0.958624\pi$
$601$	−230.500	+	399.238i	−0.383527	+	0.664289i	0.608036	+	0.793909i	$0.291958\pi$
$602$	211.310			0.351014
$603$	−241.621	−	139.500i	−0.400698	−	0.231343i
$604$	−20.0000			−0.0331126
$605$		0			0
$606$	234.000			0.386139
$607$	−96.9948	+	56.0000i	−0.159794	+	0.0922570i	−0.577765	−	0.816204i	$-0.696075\pi$
$607$	−96.9948	+	56.0000i	−0.159794	+	0.0922570i	0.417971	+	0.908461i	$0.362741\pi$
$608$	−85.7365	−	148.500i	−0.141014	−	0.244243i
$609$			270.200i			0.443678i
$610$		0			0
$611$		−	193.990i		−	0.317495i
$612$	−70.1481	+	121.500i	−0.114621	+	0.198529i
$613$		−	902.000i		−	1.47145i	−0.677279	−	0.735726i	$-0.736841\pi$
$613$		−	902.000i		−	1.47145i	0.677279	−	0.735726i	$-0.263159\pi$
$614$	799.500	+	461.592i	1.30212	+	0.751778i
$615$		0			0
$616$	15.0000	+	25.9808i	0.0243506	+	0.0421766i
$617$	−177.535	−	307.500i	−0.287739	−	0.498379i	0.685530	−	0.728044i	$-0.259570\pi$
$617$	−177.535	−	307.500i	−0.287739	−	0.498379i	−0.973270	+	0.229665i	$0.926237\pi$
$618$	103.923	−	180.000i	0.168160	−	0.291262i
$619$	−399.500	+	691.954i	−0.645396	+	1.11786i	0.338814	+	0.940853i	$0.389974\pi$
$619$	−399.500	+	691.954i	−0.645396	+	1.11786i	−0.984210	+	0.177005i	$0.943359\pi$
$620$		0			0
$621$	−648.000	+	374.123i	−1.04348	+	0.602452i
$622$			426.000i			0.684887i
$623$	124.708	−	216.000i	0.200173	−	0.346709i
$624$	66.0000	−	114.315i	0.105769	−	0.183198i
$625$		0			0
$626$	232.500	−	134.234i	0.371406	−	0.214431i
$627$	28.5788	+	49.5000i	0.0455803	+	0.0789474i
$628$	−34.6410	−	20.0000i	−0.0551609	−	0.0318471i
$629$		−	530.008i		−	0.842619i
$630$		0			0
$631$	830.000			1.31537			0.657686	−	0.753292i	$-0.271535\pi$
$631$	830.000			1.31537			0.657686	+	0.753292i	$0.271535\pi$
$632$	164.545	−	285.000i	0.260356	−	0.450949i
$633$			282.000i			0.445498i
$634$	−42.0000	−	72.7461i	−0.0662461	−	0.114742i
$635$		0			0
$636$		0			0
$637$	−155.885	−	90.0000i	−0.244717	−	0.141287i
$638$	135.100			0.211755
$639$	−243.000	+	140.296i	−0.380282	+	0.219556i
$640$		0			0
$641$	−325.500	−	187.928i	−0.507800	−	0.293179i	0.224129	−	0.974560i	$-0.428046\pi$
$641$	−325.500	−	187.928i	−0.507800	−	0.293179i	−0.731929	+	0.681381i	$0.761380\pi$
$642$	−631.333	+	364.500i	−0.983384	+	0.567757i
$643$	11.2583	−	6.50000i	0.0175091	−	0.0101089i	−0.491220	−	0.871036i	$-0.663449\pi$
$643$	11.2583	−	6.50000i	0.0175091	−	0.0101089i	0.508729	+	0.860927i	$0.330116\pi$
$644$	48.0000	−	27.7128i	0.0745342	−	0.0430323i
$645$		0			0
$646$	−148.500	+	257.210i	−0.229876	+	0.398157i
$647$	467.654			0.722803			0.361402	−	0.932410i	$-0.382298\pi$
$647$	467.654			0.722803			0.361402	+	0.932410i	$0.382298\pi$
$648$	−350.740	+	607.500i	−0.541266	+	0.937500i
$649$	87.0000			0.134052
$650$		0			0
$651$	−96.0000	+	166.277i	−0.147465	+	0.255418i
$652$	−91.7987	+	53.0000i	−0.140796	+	0.0812883i
$653$	−188.794	−	327.000i	−0.289117	−	0.500766i	0.684482	−	0.729030i	$-0.260028\pi$
$653$	−188.794	−	327.000i	−0.289117	−	0.500766i	−0.973599	+	0.228264i	$0.926695\pi$
$654$	234.000	−	135.100i	0.357798	−	0.206575i
$655$		0			0
$656$			133.368i			0.203305i
$657$	506.625	−	292.500i	0.771119	−	0.445205i
$658$			168.000i			0.255319i
$659$	852.000	+	491.902i	1.29287	+	0.746438i	0.979162	−	0.203082i	$-0.0650959\pi$
$659$	852.000	+	491.902i	1.29287	+	0.746438i	0.313706	+	0.949520i	$0.398429\pi$
$660$		0			0
$661$	191.000	+	330.822i	0.288956	+	0.500487i	0.973561	−	0.228428i	$-0.0733585\pi$
$661$	191.000	+	330.822i	0.288956	+	0.500487i	−0.684605	+	0.728915i	$0.740025\pi$
$662$	1.73205	+	3.00000i	0.00261639	+	0.00453172i
$663$	187.061			0.282144
$664$	−210.000	+	363.731i	−0.316265	+	0.547787i
$665$		0			0
$666$		−	530.008i		−	0.795807i
$667$		−	1248.00i		−	1.87106i
$668$	−95.2628	+	165.000i	−0.142609	+	0.247006i
$669$	−78.0000	−	135.100i	−0.116592	−	0.201943i
$670$		0			0
$671$	84.0000	−	48.4974i	0.125186	−	0.0722763i
$672$	46.7654	−	81.0000i	0.0695913	−	0.120536i
$673$	500.563	+	289.000i	0.743778	+	0.429421i	0.823441	−	0.567401i	$-0.192051\pi$
$673$	500.563	+	289.000i	0.743778	+	0.429421i	−0.0796633	+	0.996822i	$0.525385\pi$
$674$		−	133.368i		−	0.197875i
$675$		0			0
$676$	−153.000			−0.226331
$677$	−349.874	+	606.000i	−0.516801	+	0.895126i	0.483009	+	0.875616i	$0.339544\pi$
$677$	−349.874	+	606.000i	−0.516801	+	0.895126i	−0.999810	+	0.0195100i	$0.993789\pi$
$678$	405.300	+	234.000i	0.597787	+	0.345133i
$679$	−115.000	−	199.186i	−0.169367	−	0.293352i
$680$		0			0
$681$	490.500	−	283.190i	0.720264	−	0.415845i
$682$	83.1384	+	48.0000i	0.121904	+	0.0703812i
$683$	1044.43			1.52918			0.764588	−	0.644520i	$-0.222943\pi$
$683$	1044.43			1.52918			0.764588	+	0.644520i	$0.222943\pi$
$684$	49.5000	−	85.7365i	0.0723684	−	0.125346i
$685$		0			0
$686$	282.000	+	162.813i	0.411079	+	0.237336i
$687$			798.000i			1.16157i
$688$	−581.103	+	335.500i	−0.844627	+	0.487645i
$689$		0			0
$690$		0			0
$691$	−91.0000	+	157.617i	−0.131693	+	0.228099i	−0.924329	−	0.381596i	$-0.875375\pi$
$691$	−91.0000	+	157.617i	−0.131693	+	0.228099i	0.792636	+	0.609695i	$0.208708\pi$
$692$	232.095			0.335397
$693$	−15.5885	+	27.0000i	−0.0224942	+	0.0389610i
$694$	195.000			0.280980
$695$		0			0
$696$	−585.000	−	1013.25i	−0.840517	−	1.45582i
$697$	−163.679	+	94.5000i	−0.234833	+	0.135581i
$698$	−360.267	−	624.000i	−0.516141	−	0.893983i
$699$	−526.500	−	303.975i	−0.753219	−	0.434871i
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	187.061			0.266469
$703$			374.000i			0.532006i
$704$	−106.500	−	61.4878i	−0.151278	−	0.0873406i
$705$		0			0
$706$	1.50000	+	2.59808i	0.00212465	+	0.00367999i
$707$	−45.0333	−	78.0000i	−0.0636964	−	0.110325i
$708$	−75.3442	−	130.500i	−0.106418	−	0.184322i
$709$	−350.000	+	606.218i	−0.493653	+	0.855032i	−0.999973	−	0.00731341i	$-0.997672\pi$
$709$	−350.000	+	606.218i	−0.493653	+	0.855032i	0.506320	+	0.862346i	$0.331005\pi$
$710$		0			0
$711$	342.000			0.481013
$712$			1080.00i			1.51685i
$713$	443.405	−	768.000i	0.621886	−	1.07714i
$714$	−162.000			−0.226891
$715$		0			0
$716$	−54.0000	+	31.1769i	−0.0754190	+	0.0435432i
$717$	1205.51			1.68132
$718$	888.542	+	513.000i	1.23752	+	0.714485i
$719$		−	592.361i		−	0.823868i	−0.911214	−	0.411934i	$-0.864853\pi$
$719$		−	592.361i		−	0.823868i	0.911214	−	0.411934i	$-0.135147\pi$
$720$		0			0
$721$	−80.0000			−0.110957
$722$	−207.846	+	360.000i	−0.287875	+	0.498615i
$723$	−309.171	+	178.500i	−0.427623	+	0.246888i
$724$	−116.000	−	200.918i	−0.160221	−	0.277511i
$725$		0			0
$726$	−531.000	−	306.573i	−0.731405	−	0.422277i
$727$	575.041	+	332.000i	0.790978	+	0.456671i	0.840307	−	0.542111i	$-0.182375\pi$
$727$	575.041	+	332.000i	0.790978	+	0.456671i	−0.0493289	+	0.998783i	$0.515708\pi$
$728$	−69.2820			−0.0951676
$729$	−729.000			−1.00000
$730$		0			0
$731$	−823.500	−	475.448i	−1.12654	−	0.650408i
$732$	−145.492	−	84.0000i	−0.198760	−	0.114754i
$733$	580.237	−	335.000i	0.791592	−	0.457026i	−0.0489306	−	0.998802i	$-0.515581\pi$
$733$	580.237	−	335.000i	0.791592	−	0.457026i	0.840523	+	0.541776i	$0.182248\pi$
$734$	537.000	−	310.037i	0.731608	−	0.422394i
$735$		0			0
$736$	−216.000	+	374.123i	−0.293478	+	0.508319i
$737$	53.6936			0.0728542
$738$	−163.679	+	94.5000i	−0.221787	+	0.128049i
$739$	−317.000			−0.428958			−0.214479	−	0.976729i	$-0.568805\pi$
$739$	−317.000			−0.428958			−0.214479	+	0.976729i	$0.568805\pi$
$740$		0			0
$741$	−132.000			−0.178138
$742$		0			0
$743$	310.037	+	537.000i	0.417277	+	0.722746i	0.995665	−	0.0930168i	$-0.0296510\pi$
$743$	310.037	+	537.000i	0.417277	+	0.722746i	−0.578387	+	0.815762i	$0.696318\pi$
$744$		−	831.384i		−	1.11745i
$745$		0			0
$746$		−	1004.59i		−	1.34663i
$747$	−436.477			−0.584306
$748$		−	27.0000i		−	0.0360963i
$749$	243.000	+	140.296i	0.324433	+	0.187311i
$750$		0			0
$751$	−655.000	−	1134.49i	−0.872170	−	1.51064i	−0.859747	−	0.510721i	$-0.829379\pi$
$751$	−655.000	−	1134.49i	−0.872170	−	1.51064i	−0.0124237	−	0.999923i	$-0.503955\pi$
$752$	−266.736	−	462.000i	−0.354702	−	0.614362i
$753$	−584.567	+	1012.50i	−0.776318	+	1.34462i
$754$	−156.000	+	270.200i	−0.206897	+	0.358355i
$755$		0			0
$756$	54.0000			0.0714286
$757$			218.000i			0.287979i	0.989579	+	0.143989i	$0.0459931\pi$
$757$			218.000i			0.287979i	−0.989579	+	0.143989i	$0.954007\pi$
$758$	−71.8801	+	124.500i	−0.0948286	+	0.164248i
$759$	72.0000	−	124.708i	0.0948617	−	0.164305i
$760$		0			0
$761$	570.000	−	329.090i	0.749014	−	0.432444i	−0.0763232	−	0.997083i	$-0.524318\pi$
$761$	570.000	−	329.090i	0.749014	−	0.432444i	0.825338	+	0.564639i	$0.190985\pi$
$762$	−41.5692	−	72.0000i	−0.0545528	−	0.0944882i
$763$	−90.0666	−	52.0000i	−0.118043	−	0.0681520i
$764$			232.095i			0.303789i
$765$		0			0
$766$	966.000			1.26110
$767$	−100.459	+	174.000i	−0.130976	+	0.226858i
$768$			537.000i			0.699219i
$769$	511.000	+	885.078i	0.664499	+	1.15095i	0.979421	+	0.201829i	$0.0646885\pi$
$769$	511.000	+	885.078i	0.664499	+	1.15095i	−0.314921	+	0.949118i	$0.601978\pi$
$770$		0			0
$771$			524.811i			0.680689i
$772$	229.497	+	132.500i	0.297276	+	0.171632i
$773$	−1184.72			−1.53263			−0.766315	−	0.642465i	$-0.777912\pi$
$773$	−1184.72			−1.53263			−0.766315	+	0.642465i	$0.777912\pi$
$774$	−823.500	−	475.448i	−1.06395	−	0.614274i
$775$		0			0
$776$	862.500	+	497.965i	1.11147	+	0.641707i
$777$	−176.669	+	102.000i	−0.227373	+	0.131274i
$778$	774.227	−	447.000i	0.995150	−	0.574550i
$779$	115.500	−	66.6840i	0.148267	−	0.0856020i
$780$		0			0
$781$	27.0000	−	46.7654i	0.0345711	−	0.0598788i
$782$	748.246			0.956836
$783$	607.950	−	1053.00i	0.776437	−	1.34483i
$784$	−495.000			−0.631378
$785$		0			0
$786$	414.000	−	717.069i	0.526718	−	0.912302i
$787$	−112.583	+	65.0000i	−0.143054	+	0.0825921i	−0.569819	−	0.821771i	$-0.692987\pi$
$787$	−112.583	+	65.0000i	−0.143054	+	0.0825921i	0.426765	+	0.904363i	$0.359653\pi$
$788$	62.3538	+	108.000i	0.0791292	+	0.137056i
$789$	117.000	−	67.5500i	0.148289	−	0.0856147i
$790$		0			0
$791$		−	180.133i		−	0.227729i
$792$		−	135.000i		−	0.170455i
$793$			224.000i			0.282472i
$794$	543.000	+	313.501i	0.683879	+	0.394838i
$795$		0			0
$796$	−145.000	−	251.147i	−0.182161	−	0.315512i
$797$	157.617	+	273.000i	0.197762	+	0.342535i	0.947803	−	0.318858i	$-0.103299\pi$
$797$	157.617	+	273.000i	0.197762	+	0.342535i	−0.750040	+	0.661392i	$0.769966\pi$
$798$	114.315			0.143252
$799$	378.000	−	654.715i	0.473091	−	0.819418i
$800$		0			0
$801$	−972.000	+	561.184i	−1.21348	+	0.700605i
$802$		−	681.000i		−	0.849127i
$803$	−56.2917	+	97.5000i	−0.0701017	+	0.121420i
$804$	−46.5000	−	80.5404i	−0.0578358	−	0.100175i
$805$		0			0
$806$	−192.000	+	110.851i	−0.238213	+	0.137533i
$807$	280.592	−	486.000i	0.347698	−	0.602230i
$808$	337.750	+	195.000i	0.418007	+	0.241337i
$809$		−	140.296i		−	0.173419i	−0.996234	−	0.0867096i	$-0.972365\pi$
$809$		−	140.296i		−	0.173419i	0.996234	−	0.0867096i	$-0.0276352\pi$
$810$		0			0
$811$	299.000			0.368681			0.184340	−	0.982862i	$-0.440985\pi$
$811$	299.000			0.368681			0.184340	+	0.982862i	$0.440985\pi$
$812$	−45.0333	+	78.0000i	−0.0554598	+	0.0960591i
$813$	−696.284	−	402.000i	−0.856438	−	0.494465i
$814$	51.0000	+	88.3346i	0.0626536	+	0.108519i
$815$		0			0
$816$	445.500	−	257.210i	0.545956	−	0.315208i
$817$	581.103	+	335.500i	0.711264	+	0.410649i
$818$	382.783			0.467950
$819$	−36.0000	−	62.3538i	−0.0439560	−	0.0761341i
$820$		0			0
$821$	525.000	+	303.109i	0.639464	+	0.369195i	0.784408	−	0.620245i	$-0.212967\pi$
$821$	525.000	+	303.109i	0.639464	+	0.369195i	−0.144944	+	0.989440i	$0.546300\pi$
$822$		−	981.000i		−	1.19343i
$823$	704.945	−	407.000i	0.856555	−	0.494532i	−0.00630221	−	0.999980i	$-0.502006\pi$
$823$	704.945	−	407.000i	0.856555	−	0.494532i	0.862857	+	0.505448i	$0.168673\pi$
$824$	300.000	−	173.205i	0.364078	−	0.210200i
$825$		0			0
$826$	87.0000	−	150.688i	0.105327	−	0.182432i
$827$	−1434.14			−1.73415			−0.867073	−	0.498182i	$-0.834001\pi$
$827$	−1434.14			−1.73415			−0.867073	+	0.498182i	$0.834001\pi$
$828$	−249.415			−0.301226
$829$	718.000			0.866104			0.433052	−	0.901369i	$-0.357437\pi$
$829$	718.000			0.866104			0.433052	+	0.901369i	$0.357437\pi$
$830$		0			0
$831$	−84.0000	−	145.492i	−0.101083	−	0.175081i
$832$	245.951	−	142.000i	0.295614	−	0.170673i
$833$	−350.740	−	607.500i	−0.421057	−	0.729292i
$834$	22.5000	+	12.9904i	0.0269784	+	0.0155760i
$835$		0			0
$836$			19.0526i			0.0227901i
$837$	748.246	−	432.000i	0.893962	−	0.516129i
$838$			1356.00i			1.61814i
$839$	690.000	+	398.372i	0.822408	+	0.474817i	0.851246	−	0.524767i	$-0.175847\pi$
$839$	690.000	+	398.372i	0.822408	+	0.474817i	−0.0288384	+	0.999584i	$0.509181\pi$
$840$		0			0
$841$	593.500	+	1027.97i	0.705707	+	1.22232i
$842$	−590.629	−	1023.00i	−0.701460	−	1.21496i
$843$	−72.7461	−	126.000i	−0.0862943	−	0.149466i
$844$	−47.0000	+	81.4064i	−0.0556872	+	0.0964531i
$845$		0			0
$846$	378.000	−	654.715i	0.446809	−	0.773895i
$847$			236.000i			0.278630i
$848$		0			0
$849$	−1122.00			−1.32155
$850$		0			0
$851$	816.000	−	471.118i	0.958872	−	0.553605i
$852$	−93.5307			−0.109778
$853$	1233.22	+	712.000i	1.44574	+	0.834701i	0.998224	−	0.0595725i	$-0.0189738\pi$
$853$	1233.22	+	712.000i	1.44574	+	0.834701i	0.447521	+	0.894274i	$0.352307\pi$
$854$		−	193.990i		−	0.227154i
$855$		0			0
$856$	−1215.00			−1.41939
$857$	−349.874	+	606.000i	−0.408255	+	0.707118i	−0.994694	−	0.102875i	$-0.967196\pi$
$857$	−349.874	+	606.000i	−0.408255	+	0.707118i	0.586440	+	0.809993i	$0.300529\pi$
$858$	−31.1769	+	18.0000i	−0.0363367	+	0.0209790i
$859$	155.500	+	269.334i	0.181024	+	0.313544i	0.942230	−	0.334968i	$-0.108725\pi$
$859$	155.500	+	269.334i	0.181024	+	0.313544i	−0.761205	+	0.648511i	$0.775392\pi$
$860$		0			0
$861$	63.0000	+	36.3731i	0.0731707	+	0.0422451i
$862$	420.888	+	243.000i	0.488270	+	0.281903i
$863$	1028.84			1.19216			0.596082	−	0.802923i	$-0.296723\pi$
$863$	1028.84			1.19216			0.596082	+	0.802923i	$0.296723\pi$
$864$	−364.500	+	210.444i	−0.421875	+	0.243570i
$865$		0			0
$866$	442.500	+	255.477i	0.510970	+	0.295009i
$867$	−119.512	−	69.0000i	−0.137845	−	0.0795848i
$868$	−55.4256	+	32.0000i	−0.0638544	+	0.0368664i
$869$	−57.0000	+	32.9090i	−0.0655926	+	0.0378699i
$870$		0			0
$871$	−62.0000	+	107.387i	−0.0711825	+	0.123292i
$872$	450.333			0.516437
$873$			1035.00i			1.18557i
$874$	−528.000			−0.604119
$875$		0			0
$876$	195.000			0.222603
$877$	90.0666	−	52.0000i	0.102699	−	0.0592930i	−0.447771	−	0.894148i	$-0.647782\pi$
$877$	90.0666	−	52.0000i	0.102699	−	0.0592930i	0.550470	+	0.834855i	$0.314449\pi$
$878$	−703.213	−	1218.00i	−0.800926	−	1.38724i
$879$		−	758.638i		−	0.863070i
$880$		0			0
$881$		−	62.3538i		−	0.0707762i	−0.999374	−	0.0353881i	$-0.988733\pi$
$881$		−	62.3538i		−	0.0707762i	0.999374	−	0.0353881i	$-0.0112667\pi$
$882$	−350.740	−	607.500i	−0.397665	−	0.688776i
$883$		−	119.000i		−	0.134768i	−0.997727	−	0.0673839i	$-0.978535\pi$
$883$		−	119.000i		−	0.134768i	0.997727	−	0.0673839i	$-0.0214652\pi$
$884$	54.0000	+	31.1769i	0.0610860	+	0.0352680i
$885$		0			0
$886$	−79.5000	−	137.698i	−0.0897291	−	0.155415i
$887$	594.093	+	1029.00i	0.669778	+	1.16009i	0.977966	+	0.208765i	$0.0669442\pi$
$887$	594.093	+	1029.00i	0.669778	+	1.16009i	−0.308188	+	0.951326i	$0.599722\pi$
$888$	441.673	−	765.000i	0.497379	−	0.861486i
$889$	−16.0000	+	27.7128i	−0.0179978	+	0.0311730i
$890$		0			0
$891$	121.500	−	70.1481i	0.136364	−	0.0787296i
$892$		−	52.0000i		−	0.0582960i
$893$	−266.736	+	462.000i	−0.298696	+	0.517357i
$894$	396.000	−	685.892i	0.442953	−	0.767217i
$895$		0			0
$896$	−105.000	+	60.6218i	−0.117188	+	0.0676582i
$897$	166.277	+	288.000i	0.185370	+	0.321070i
$898$	−958.690	−	553.500i	−1.06758	−	0.616370i
$899$			1441.07i			1.60297i
$900$		0			0
$901$		0			0
$902$	18.1865	−	31.5000i	0.0201625	−	0.0349224i
$903$			366.000i			0.405316i
$904$	390.000	+	675.500i	0.431416	+	0.747234i
$905$		0			0
$906$			103.923i			0.114705i
$907$	−601.888	−	347.500i	−0.663603	−	0.383131i	0.130046	−	0.991508i	$-0.458488\pi$
$907$	−601.888	−	347.500i	−0.663603	−	0.383131i	−0.793648	+	0.608377i	$0.791821\pi$
$908$	188.794			0.207922
$909$			405.300i			0.445874i
$910$		0			0
$911$	−1500.00	−	866.025i	−1.64654	−	0.950632i	−0.978432	−	0.206569i	$-0.933770\pi$
$911$	−1500.00	−	866.025i	−1.64654	−	0.950632i	−0.668110	−	0.744062i	$-0.732897\pi$
$912$	−314.367	+	181.500i	−0.344701	+	0.199013i
$913$	72.7461	−	42.0000i	0.0796781	−	0.0460022i
$914$	−97.5000	+	56.2917i	−0.106674	+	0.0615882i
$915$		0			0
$916$	−133.000	+	230.363i	−0.145197	+	0.251488i
$917$	−318.697			−0.347543
$918$	631.333	+	364.500i	0.687726	+	0.397059i
$919$	−56.0000			−0.0609358			−0.0304679	−	0.999536i	$-0.509700\pi$
$919$	−56.0000			−0.0609358			−0.0304679	+	0.999536i	$0.509700\pi$
$920$		0			0
$921$	−799.500	+	1384.77i	−0.868078	+	1.50356i
$922$	−1195.12	+	690.000i	−1.29622	+	0.748373i
$923$	62.3538	+	108.000i	0.0675556	+	0.117010i
$924$	−9.00000	+	5.19615i	−0.00974026	+	0.00562354i
$925$		0			0
$926$			1271.33i			1.37292i
$927$	311.769	+	180.000i	0.336321	+	0.194175i
$928$		−	702.000i		−	0.756466i
$929$	690.000	+	398.372i	0.742734	+	0.428818i	0.823063	−	0.567951i	$-0.192264\pi$
$929$	690.000	+	398.372i	0.742734	+	0.428818i	−0.0803285	+	0.996768i	$0.525597\pi$
$930$		0			0
$931$	247.500	+	428.683i	0.265843	+	0.460454i
$932$	−101.325	−	175.500i	−0.108718	−	0.188305i
$933$	−737.854			−0.790840
$934$	−175.500	+	303.975i	−0.187901	+	0.325455i
$935$		0			0
$936$	270.000	+	155.885i	0.288462	+	0.166543i
$937$			470.000i			0.501601i	0.968039	+	0.250800i	$0.0806938\pi$
$937$			470.000i			0.501601i	−0.968039	+	0.250800i	$0.919306\pi$
$938$	53.6936	−	93.0000i	0.0572426	−	0.0991471i
$939$	232.500	+	402.702i	0.247604	+	0.428862i
$940$		0			0
$941$	−348.000	+	200.918i	−0.369819	+	0.213515i	−0.673380	−	0.739297i	$-0.735158\pi$
$941$	−348.000	+	200.918i	−0.369819	+	0.213515i	0.303560	+	0.952812i	$0.401825\pi$
$942$	−103.923	+	180.000i	−0.110322	+	0.191083i
$943$	−290.985	−	168.000i	−0.308573	−	0.178155i
$944$			552.524i			0.585301i
$945$		0			0
$946$	183.000			0.193446
$947$	0.866025	−	1.50000i	0.000914494	−	0.00158395i	−0.865568	−	0.500792i	$-0.833042\pi$
$947$	0.866025	−	1.50000i	0.000914494	−	0.00158395i	0.866482	+	0.499208i	$0.166376\pi$
$948$	98.7269	+	57.0000i	0.104142	+	0.0601266i
$949$	−130.000	−	225.167i	−0.136986	−	0.237267i
$950$		0			0
$951$	126.000	−	72.7461i	0.132492	−	0.0764944i
$952$	−233.827	−	135.000i	−0.245616	−	0.141807i
$953$	−826.188			−0.866934			−0.433467	−	0.901169i	$-0.642710\pi$
$953$	−826.188			−0.866934			−0.433467	+	0.901169i	$0.642710\pi$
$954$		0			0
$955$		0			0
$956$	348.000	+	200.918i	0.364017	+	0.210165i
$957$			234.000i			0.244514i
$958$	−909.327	+	525.000i	−0.949193	+	0.548017i
$959$	−327.000	+	188.794i	−0.340980	+	0.196865i
$960$		0			0
$961$	−31.5000	+	54.5596i	−0.0327784	+	0.0567738i
$962$	−235.559			−0.244864
$963$	−631.333	−	1093.50i	−0.655589	−	1.13551i
$964$	−119.000			−0.123444
$965$		0			0
$966$	−144.000	−	249.415i	−0.149068	−	0.258194i
$967$	1040.96	−	601.000i	1.07649	−	0.621510i	0.146540	−	0.989205i	$-0.453186\pi$
$967$	1040.96	−	601.000i	1.07649	−	0.621510i	0.929946	+	0.367695i	$0.119853\pi$
$968$	−510.955	−	885.000i	−0.527846	−	0.914256i
$969$	−445.500	−	257.210i	−0.459752	−	0.265438i
$970$		0			0
$971$			187.061i			0.192648i	0.995350	+	0.0963241i	$0.0307085\pi$
$971$			187.061i			0.192648i	−0.995350	+	0.0963241i	$0.969291\pi$
$972$	−210.444	−	121.500i	−0.216506	−	0.125000i
$973$		−	10.0000i		−	0.0102775i
$974$	−159.000	−	91.7987i	−0.163244	−	0.0942492i
$975$		0			0
$976$	308.000	+	533.472i	0.315574	+	0.546590i
$977$	−208.712	−	361.500i	−0.213626	−	0.370010i	0.739221	−	0.673463i	$-0.235194\pi$
$977$	−208.712	−	361.500i	−0.213626	−	0.370010i	−0.952847	+	0.303453i	$0.901861\pi$
$978$	275.396	+	477.000i	0.281591	+	0.487730i
$979$	108.000	−	187.061i	0.110317	−	0.191074i
$980$		0			0
$981$	234.000	+	405.300i	0.238532	+	0.413150i
$982$			399.000i			0.406314i
$983$	583.701	−	1011.00i	0.593796	−	1.02848i	−0.399920	−	0.916550i	$-0.630962\pi$
$983$	583.701	−	1011.00i	0.593796	−	1.02848i	0.993716	−	0.111934i	$-0.0357046\pi$
$984$	−315.000			−0.320122
$985$		0			0
$986$	−1053.00	+	607.950i	−1.06795	+	0.616582i
$987$	−290.985			−0.294817
$988$	−38.1051	−	22.0000i	−0.0385679	−	0.0222672i
$989$		−	1690.48i		−	1.70928i
$990$		0			0
$991$	−1420.00			−1.43290			−0.716448	−	0.697640i	$-0.754233\pi$
$991$	−1420.00			−1.43290			−0.716448	+	0.697640i	$0.754233\pi$
$992$	249.415	−	432.000i	0.251427	−	0.435484i
$993$	−5.19615	+	3.00000i	−0.00523278	+	0.00302115i
$994$	−54.0000	−	93.5307i	−0.0543260	−	0.0940953i
$995$		0			0
$996$	−126.000	−	72.7461i	−0.126506	−	0.0730383i
$997$	−453.797	−	262.000i	−0.455163	−	0.262788i	0.254845	−	0.966982i	$-0.417975\pi$
$997$	−453.797	−	262.000i	−0.455163	−	0.262788i	−0.710008	+	0.704193i	$0.751309\pi$
$998$	−1363.12			−1.36586
$999$	918.000			0.918919

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.3.i.a.74.2		4
3.2	odd	2		675.3.i.a.224.1		4
5.2	odd	4		225.3.j.a.101.1		2
5.3	odd	4		9.3.d.a.2.1	✓	2
5.4	even	2	inner	225.3.i.a.74.1		4
9.4	even	3		675.3.i.a.449.2		4
9.5	odd	6	inner	225.3.i.a.149.1		4
15.2	even	4		675.3.j.a.251.1		2
15.8	even	4		27.3.d.a.8.1		2
15.14	odd	2		675.3.i.a.224.2		4
20.3	even	4		144.3.q.a.65.1		2
35.3	even	12		441.3.n.a.128.1		2
35.13	even	4		441.3.r.a.344.1		2
35.18	odd	12		441.3.n.b.128.1		2
35.23	odd	12		441.3.j.a.263.1		2
35.33	even	12		441.3.j.b.263.1		2
40.3	even	4		576.3.q.a.65.1		2
40.13	odd	4		576.3.q.b.65.1		2
45.4	even	6		675.3.i.a.449.1		4
45.13	odd	12		27.3.d.a.17.1		2
45.14	odd	6	inner	225.3.i.a.149.2		4
45.22	odd	12		675.3.j.a.476.1		2
45.23	even	12		9.3.d.a.5.1	yes	2
45.32	even	12		225.3.j.a.176.1		2
45.38	even	12		81.3.b.a.80.1		2
45.43	odd	12		81.3.b.a.80.2		2
60.23	odd	4		432.3.q.a.305.1		2
120.53	even	4		1728.3.q.a.1601.1		2
120.83	odd	4		1728.3.q.b.1601.1		2
180.23	odd	12		144.3.q.a.113.1		2
180.43	even	12		1296.3.e.a.161.2		2
180.83	odd	12		1296.3.e.a.161.1		2
180.103	even	12		432.3.q.a.17.1		2
315.23	even	12		441.3.n.b.410.1		2
315.68	odd	12		441.3.n.a.410.1		2
315.158	even	12		441.3.j.a.275.1		2
315.248	odd	12		441.3.j.b.275.1		2
315.293	odd	12		441.3.r.a.50.1		2
360.13	odd	12		1728.3.q.a.449.1		2
360.203	odd	12		576.3.q.a.257.1		2
360.283	even	12		1728.3.q.b.449.1		2
360.293	even	12		576.3.q.b.257.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.3.d.a.2.1	✓	2	5.3	odd	4
9.3.d.a.5.1	yes	2	45.23	even	12
27.3.d.a.8.1		2	15.8	even	4
27.3.d.a.17.1		2	45.13	odd	12
81.3.b.a.80.1		2	45.38	even	12
81.3.b.a.80.2		2	45.43	odd	12
144.3.q.a.65.1		2	20.3	even	4
144.3.q.a.113.1		2	180.23	odd	12
225.3.i.a.74.1		4	5.4	even	2	inner
225.3.i.a.74.2		4	1.1	even	1	trivial
225.3.i.a.149.1		4	9.5	odd	6	inner
225.3.i.a.149.2		4	45.14	odd	6	inner
225.3.j.a.101.1		2	5.2	odd	4
225.3.j.a.176.1		2	45.32	even	12
432.3.q.a.17.1		2	180.103	even	12
432.3.q.a.305.1		2	60.23	odd	4
441.3.j.a.263.1		2	35.23	odd	12
441.3.j.a.275.1		2	315.158	even	12
441.3.j.b.263.1		2	35.33	even	12
441.3.j.b.275.1		2	315.248	odd	12
441.3.n.a.128.1		2	35.3	even	12
441.3.n.a.410.1		2	315.68	odd	12
441.3.n.b.128.1		2	35.18	odd	12
441.3.n.b.410.1		2	315.23	even	12
441.3.r.a.50.1		2	315.293	odd	12
441.3.r.a.344.1		2	35.13	even	4
576.3.q.a.65.1		2	40.3	even	4
576.3.q.a.257.1		2	360.203	odd	12
576.3.q.b.65.1		2	40.13	odd	4
576.3.q.b.257.1		2	360.293	even	12
675.3.i.a.224.1		4	3.2	odd	2
675.3.i.a.224.2		4	15.14	odd	2
675.3.i.a.449.1		4	45.4	even	6
675.3.i.a.449.2		4	9.4	even	3
675.3.j.a.251.1		2	15.2	even	4
675.3.j.a.476.1		2	45.22	odd	12
1296.3.e.a.161.1		2	180.83	odd	12
1296.3.e.a.161.2		2	180.43	even	12
1728.3.q.a.449.1		2	360.13	odd	12
1728.3.q.a.1601.1		2	120.53	even	4
1728.3.q.b.449.1		2	360.283	even	12
1728.3.q.b.1601.1		2	120.83	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	225.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 1.50000i) q^{2} +(2.59808 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(4.50000 - 2.59808i) q^{6} +(-1.73205 - 1.00000i) q^{7} +8.66025 q^{8} +(4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 1.50000i) q^{2} +(2.59808 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(4.50000 - 2.59808i) q^{6} +(-1.73205 - 1.00000i) q^{7} +8.66025 q^{8} +(4.50000 + 7.79423i) q^{9} +(-1.50000 - 0.866025i) q^{11} +3.00000i q^{12} +(3.46410 - 2.00000i) q^{13} +(-3.00000 + 1.73205i) q^{14} +(5.50000 - 9.52628i) q^{16} +15.5885 q^{17} +15.5885 q^{18} -11.0000 q^{19} +(-3.00000 - 5.19615i) q^{21} +(-2.59808 + 1.50000i) q^{22} +(13.8564 + 24.0000i) q^{23} +(22.5000 + 12.9904i) q^{24} -6.92820i q^{26} +27.0000i q^{27} -2.00000i q^{28} +(-39.0000 - 22.5167i) q^{29} +(-16.0000 - 27.7128i) q^{31} +(7.79423 + 13.5000i) q^{32} +(-2.59808 - 4.50000i) q^{33} +(13.5000 - 23.3827i) q^{34} +(-4.50000 + 7.79423i) q^{36} -34.0000i q^{37} +(-9.52628 + 16.5000i) q^{38} +12.0000 q^{39} +(-10.5000 + 6.06218i) q^{41} -10.3923 q^{42} +(-52.8275 - 30.5000i) q^{43} -1.73205i q^{44} +48.0000 q^{46} +(24.2487 - 42.0000i) q^{47} +(28.5788 - 16.5000i) q^{48} +(-22.5000 - 38.9711i) q^{49} +(40.5000 + 23.3827i) q^{51} +(3.46410 + 2.00000i) q^{52} +(40.5000 + 23.3827i) q^{54} +(-15.0000 - 8.66025i) q^{56} +(-28.5788 - 16.5000i) q^{57} +(-67.5500 + 39.0000i) q^{58} +(-43.5000 + 25.1147i) q^{59} +(-28.0000 + 48.4974i) q^{61} -55.4256 q^{62} -18.0000i q^{63} +71.0000 q^{64} -9.00000 q^{66} +(-26.8468 + 15.5000i) q^{67} +(7.79423 + 13.5000i) q^{68} +83.1384i q^{69} +31.1769i q^{71} +(38.9711 + 67.5000i) q^{72} -65.0000i q^{73} +(-51.0000 - 29.4449i) q^{74} +(-5.50000 - 9.52628i) q^{76} +(1.73205 + 3.00000i) q^{77} +(10.3923 - 18.0000i) q^{78} +(19.0000 - 32.9090i) q^{79} +(-40.5000 + 70.1481i) q^{81} +21.0000i q^{82} +(-24.2487 + 42.0000i) q^{83} +(3.00000 - 5.19615i) q^{84} +(-91.5000 + 52.8275i) q^{86} +(-67.5500 - 117.000i) q^{87} +(-12.9904 - 7.50000i) q^{88} +124.708i q^{89} -8.00000 q^{91} +(-13.8564 + 24.0000i) q^{92} -96.0000i q^{93} +(-42.0000 - 72.7461i) q^{94} +46.7654i q^{96} +(99.5929 + 57.5000i) q^{97} -77.9423 q^{98} -15.5885i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 18 q^{6} + 18 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 18 * q^6 + 18 * q^9	\( 4 q + 2 q^{4} + 18 q^{6} + 18 q^{9} - 6 q^{11} - 12 q^{14} + 22 q^{16} - 44 q^{19} - 12 q^{21} + 90 q^{24} - 156 q^{29} - 64 q^{31} + 54 q^{34} - 18 q^{36} + 48 q^{39} - 42 q^{41} + 192 q^{46} - 90 q^{49} + 162 q^{51} + 162 q^{54} - 60 q^{56} - 174 q^{59} - 112 q^{61} + 284 q^{64} - 36 q^{66} - 204 q^{74} - 22 q^{76} + 76 q^{79} - 162 q^{81} + 12 q^{84} - 366 q^{86} - 32 q^{91} - 168 q^{94}+O(q^{100}) \) 4 * q + 2 * q^4 + 18 * q^6 + 18 * q^9 - 6 * q^11 - 12 * q^14 + 22 * q^16 - 44 * q^19 - 12 * q^21 + 90 * q^24 - 156 * q^29 - 64 * q^31 + 54 * q^34 - 18 * q^36 + 48 * q^39 - 42 * q^41 + 192 * q^46 - 90 * q^49 + 162 * q^51 + 162 * q^54 - 60 * q^56 - 174 * q^59 - 112 * q^61 + 284 * q^64 - 36 * q^66 - 204 * q^74 - 22 * q^76 + 76 * q^79 - 162 * q^81 + 12 * q^84 - 366 * q^86 - 32 * q^91 - 168 * q^94

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