LMFDB - Embedded newform 1050.3.q.e.199.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(199,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1050.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.q (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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.6
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.e.649.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(6.46925 + 2.67372i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(6.46925 + 2.67372i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-0.578394 + 1.00181i) q^{11} +(-1.73205 - 3.00000i) q^{12} -14.8176 q^{13} +(-9.81379 + 1.29982i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(6.30878 - 10.9271i) q^{17} +(3.67423 + 2.12132i) q^{18} +(-16.7162 + 9.65108i) q^{19} +(9.61312 - 7.38837i) q^{21} -1.63595i q^{22} +(-21.0450 + 12.1504i) q^{23} +(4.24264 + 2.44949i) q^{24} +(18.1477 - 10.4776i) q^{26} -5.19615 q^{27} +(11.1003 - 8.53135i) q^{28} -49.0382 q^{29} +(-24.9581 - 14.4096i) q^{31} +(4.89898 + 2.82843i) q^{32} +(1.00181 + 1.73518i) q^{33} +17.8439i q^{34} -6.00000 q^{36} +(46.1728 - 26.6579i) q^{37} +(13.6487 - 23.6402i) q^{38} +(-12.8324 + 22.2264i) q^{39} +38.0398i q^{41} +(-6.54925 + 15.8464i) q^{42} -63.5774i q^{43} +(1.15679 + 2.00362i) q^{44} +(17.1832 - 29.7622i) q^{46} +(-12.5964 - 21.8175i) q^{47} -6.92820 q^{48} +(34.7024 + 34.5940i) q^{49} +(-10.9271 - 18.9263i) q^{51} +(-14.8176 + 25.6648i) q^{52} +(-18.0411 - 10.4160i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-7.56243 + 18.2978i) q^{56} +33.4323i q^{57} +(60.0593 - 34.6752i) q^{58} +(-21.1419 - 12.2063i) q^{59} +(5.53376 - 3.19492i) q^{61} +40.7564 q^{62} +(-2.75734 - 20.8182i) q^{63} -8.00000 q^{64} +(-2.45392 - 1.41677i) q^{66} +(107.812 + 62.2451i) q^{67} +(-12.6176 - 21.8543i) q^{68} +42.0901i q^{69} -118.973 q^{71} +(7.34847 - 4.24264i) q^{72} +(19.7648 - 34.2336i) q^{73} +(-37.7000 + 65.2983i) q^{74} +38.6043i q^{76} +(-6.42033 + 4.93448i) q^{77} -36.2955i q^{78} +(-46.4356 - 80.4288i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-26.8982 - 46.5891i) q^{82} -5.79665 q^{83} +(-3.18391 - 24.0388i) q^{84} +(44.9560 + 77.8661i) q^{86} +(-42.4683 + 73.5573i) q^{87} +(-2.83354 - 1.63595i) q^{88} +(-131.622 + 75.9919i) q^{89} +(-95.8586 - 39.6181i) q^{91} +48.6014i q^{92} +(-43.2287 + 24.9581i) q^{93} +(30.8546 + 17.8139i) q^{94} +(8.48528 - 4.89898i) q^{96} -144.310 q^{97} +(-66.9632 - 17.8305i) q^{98} +3.47036 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} - 48 q^{9}+O(q^{10}) $ 32 * q + 32 * q^4 - 48 * q^9	$ 32 q + 32 q^{4} - 48 q^{9} - 8 q^{11} - 16 q^{14} - 64 q^{16} + 144 q^{19} - 48 q^{21} - 144 q^{29} + 240 q^{31} - 192 q^{36} - 72 q^{39} + 16 q^{44} + 16 q^{46} + 80 q^{49} - 24 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 256 q^{64} + 144 q^{66} - 272 q^{71} + 224 q^{74} - 560 q^{79} - 144 q^{81} + 48 q^{84} - 176 q^{86} + 600 q^{89} - 544 q^{91} + 48 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 - 48 * q^9 - 8 * q^11 - 16 * q^14 - 64 * q^16 + 144 * q^19 - 48 * q^21 - 144 * q^29 + 240 * q^31 - 192 * q^36 - 72 * q^39 + 16 * q^44 + 16 * q^46 + 80 * q^49 - 24 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 256 * q^64 + 144 * q^66 - 272 * q^71 + 224 * q^74 - 560 * q^79 - 144 * q^81 + 48 * q^84 - 176 * q^86 + 600 * q^89 - 544 * q^91 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	6.46925	+	2.67372i	0.924179	+	0.381960i
$7$	6.46925	+	2.67372i	0.924179	+	0.381960i
$8$			2.82843i			0.353553i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	−0.578394	+	1.00181i	−0.0525813	+	0.0910735i	−0.891118	−	0.453772i	$-0.850078\pi$
$11$	−0.578394	+	1.00181i	−0.0525813	+	0.0910735i	0.838537	+	0.544845i	$0.183412\pi$
$12$	−1.73205	−	3.00000i	−0.144338	−	0.250000i
$13$	−14.8176			−1.13981			−0.569906	−	0.821710i	$-0.693021\pi$
$13$	−14.8176			−1.13981			−0.569906	+	0.821710i	$0.693021\pi$
$14$	−9.81379	+	1.29982i	−0.700985	+	0.0928446i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	6.30878	−	10.9271i	0.371105	−	0.642772i	−0.618631	−	0.785682i	$-0.712312\pi$
$17$	6.30878	−	10.9271i	0.371105	−	0.642772i	0.989736	+	0.142909i	$0.0456457\pi$
$18$	3.67423	+	2.12132i	0.204124	+	0.117851i
$19$	−16.7162	+	9.65108i	−0.879798	+	0.507951i	−0.870592	−	0.492006i	$-0.836264\pi$
$19$	−16.7162	+	9.65108i	−0.879798	+	0.507951i	−0.00920603	+	0.999958i	$0.502930\pi$
$20$		0			0
$21$	9.61312	−	7.38837i	0.457768	−	0.351827i
$22$		−	1.63595i		−	0.0743612i
$23$	−21.0450	+	12.1504i	−0.915002	+	0.528277i	−0.882037	−	0.471180i	$-0.843828\pi$
$23$	−21.0450	+	12.1504i	−0.915002	+	0.528277i	−0.0329648	+	0.999457i	$0.510495\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$		0			0
$26$	18.1477	−	10.4776i	0.697990	−	0.402985i
$27$	−5.19615			−0.192450
$28$	11.1003	−	8.53135i	0.396438	−	0.304691i
$29$	−49.0382			−1.69097			−0.845486	−	0.533998i	$-0.820689\pi$
$29$	−49.0382			−1.69097			−0.845486	+	0.533998i	$0.820689\pi$
$30$		0			0
$31$	−24.9581	−	14.4096i	−0.805100	−	0.464825i	0.0401515	−	0.999194i	$-0.487216\pi$
$31$	−24.9581	−	14.4096i	−0.805100	−	0.464825i	−0.845251	+	0.534369i	$0.820549\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$	1.00181	+	1.73518i	0.0303578	+	0.0525813i
$34$			17.8439i			0.524822i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	46.1728	−	26.6579i	1.24791	−	0.720484i	0.277221	−	0.960806i	$-0.410586\pi$
$37$	46.1728	−	26.6579i	1.24791	−	0.720484i	0.970693	+	0.240322i	$0.0772531\pi$
$38$	13.6487	−	23.6402i	0.359176	−	0.622111i
$39$	−12.8324	+	22.2264i	−0.329036	+	0.569906i
$40$		0			0
$41$			38.0398i			0.927800i	0.885888	+	0.463900i	$0.153550\pi$
$41$			38.0398i			0.927800i	−0.885888	+	0.463900i	$0.846450\pi$
$42$	−6.54925	+	15.8464i	−0.155935	+	0.377294i
$43$		−	63.5774i		−	1.47854i	−0.673407	−	0.739272i	$-0.735170\pi$
$43$		−	63.5774i		−	1.47854i	0.673407	−	0.739272i	$-0.264830\pi$
$44$	1.15679	+	2.00362i	0.0262906	+	0.0455367i
$45$		0			0
$46$	17.1832	−	29.7622i	0.373548	−	0.647004i
$47$	−12.5964	−	21.8175i	−0.268008	−	0.464203i	0.700340	−	0.713810i	$-0.253032\pi$
$47$	−12.5964	−	21.8175i	−0.268008	−	0.464203i	−0.968347	+	0.249607i	$0.919699\pi$
$48$	−6.92820			−0.144338
$49$	34.7024	+	34.5940i	0.708213	+	0.705999i
$50$		0			0
$51$	−10.9271	−	18.9263i	−0.214257	−	0.371105i
$52$	−14.8176	+	25.6648i	−0.284953	+	0.493553i
$53$	−18.0411	−	10.4160i	−0.340397	−	0.196529i	0.320050	−	0.947401i	$-0.396300\pi$
$53$	−18.0411	−	10.4160i	−0.340397	−	0.196529i	−0.660448	+	0.750872i	$0.729634\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$		0			0
$56$	−7.56243	+	18.2978i	−0.135043	+	0.326747i
$57$			33.4323i			0.586532i
$58$	60.0593	−	34.6752i	1.03550	−	0.597849i
$59$	−21.1419	−	12.2063i	−0.358337	−	0.206886i	0.310014	−	0.950732i	$-0.399666\pi$
$59$	−21.1419	−	12.2063i	−0.358337	−	0.206886i	−0.668351	+	0.743846i	$0.733000\pi$
$60$		0			0
$61$	5.53376	−	3.19492i	0.0907174	−	0.0523757i	−0.453955	−	0.891025i	$-0.649987\pi$
$61$	5.53376	−	3.19492i	0.0907174	−	0.0523757i	0.544672	+	0.838649i	$0.316654\pi$
$62$	40.7564			0.657361
$63$	−2.75734	−	20.8182i	−0.0437674	−	0.330447i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−2.45392	−	1.41677i	−0.0371806	−	0.0214662i
$67$	107.812	+	62.2451i	1.60913	+	0.929031i	0.989565	+	0.144085i	$0.0460238\pi$
$67$	107.812	+	62.2451i	1.60913	+	0.929031i	0.619564	+	0.784946i	$0.287310\pi$
$68$	−12.6176	−	21.8543i	−0.185552	−	0.321386i
$69$			42.0901i			0.610001i
$70$		0			0
$71$	−118.973			−1.67567			−0.837835	−	0.545924i	$-0.816179\pi$
$71$	−118.973			−1.67567			−0.837835	+	0.545924i	$0.816179\pi$
$72$	7.34847	−	4.24264i	0.102062	−	0.0589256i
$73$	19.7648	−	34.2336i	0.270750	−	0.468953i	−0.698304	−	0.715801i	$-0.746062\pi$
$73$	19.7648	−	34.2336i	0.270750	−	0.468953i	0.969054	+	0.246848i	$0.0793950\pi$
$74$	−37.7000	+	65.2983i	−0.509459	+	0.882409i
$75$		0			0
$76$			38.6043i			0.507951i
$77$	−6.42033	+	4.93448i	−0.0833809	+	0.0640842i
$78$		−	36.2955i		−	0.465327i
$79$	−46.4356	−	80.4288i	−0.587792	−	1.01809i	−0.994521	−	0.104537i	$-0.966664\pi$
$79$	−46.4356	−	80.4288i	−0.587792	−	1.01809i	0.406729	−	0.913549i	$-0.366669\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−26.8982	−	46.5891i	−0.328027	−	0.568159i
$83$	−5.79665			−0.0698392			−0.0349196	−	0.999390i	$-0.511118\pi$
$83$	−5.79665			−0.0698392			−0.0349196	+	0.999390i	$0.511118\pi$
$84$	−3.18391	−	24.0388i	−0.0379037	−	0.286176i
$85$		0			0
$86$	44.9560	+	77.8661i	0.522744	+	0.905420i
$87$	−42.4683	+	73.5573i	−0.488142	+	0.845486i
$88$	−2.83354	−	1.63595i	−0.0321993	−	0.0185903i
$89$	−131.622	+	75.9919i	−1.47890	+	0.853842i	−0.999715	−	0.0238738i	$-0.992400\pi$
$89$	−131.622	+	75.9919i	−1.47890	+	0.853842i	−0.479182	+	0.877715i	$0.659067\pi$
$90$		0			0
$91$	−95.8586	−	39.6181i	−1.05339	−	0.435363i
$92$			48.6014i			0.528277i
$93$	−43.2287	+	24.9581i	−0.464825	+	0.268367i
$94$	30.8546	+	17.8139i	0.328241	+	0.189510i
$95$		0			0
$96$	8.48528	−	4.89898i	0.0883883	−	0.0510310i
$97$	−144.310			−1.48773			−0.743864	−	0.668331i	$-0.767009\pi$
$97$	−144.310			−1.48773			−0.743864	+	0.668331i	$0.767009\pi$
$98$	−66.9632	−	17.8305i	−0.683298	−	0.181943i
$99$	3.47036			0.0350542
$100$		0			0
$101$	−33.8480	−	19.5422i	−0.335129	−	0.193487i	0.322987	−	0.946403i	$-0.395313\pi$
$101$	−33.8480	−	19.5422i	−0.335129	−	0.193487i	−0.658116	+	0.752917i	$0.728646\pi$
$102$	26.7659	+	15.4533i	0.262411	+	0.151503i
$103$	18.9215	+	32.7730i	0.183704	+	0.318185i	0.943139	−	0.332398i	$-0.107858\pi$
$103$	18.9215	+	32.7730i	0.183704	+	0.318185i	−0.759435	+	0.650583i	$0.774525\pi$
$104$		−	41.9104i		−	0.402985i
$105$		0			0
$106$	29.4609			0.277933
$107$	−71.9079	+	41.5160i	−0.672036	+	0.388000i	−0.796848	−	0.604180i	$-0.793501\pi$
$107$	−71.9079	+	41.5160i	−0.672036	+	0.388000i	0.124811	+	0.992180i	$0.460167\pi$
$108$	−5.19615	+	9.00000i	−0.0481125	+	0.0833333i
$109$	−23.8962	+	41.3894i	−0.219231	+	0.379719i	−0.954573	−	0.297977i	$-0.903688\pi$
$109$	−23.8962	+	41.3894i	−0.219231	+	0.379719i	0.735342	+	0.677696i	$0.237022\pi$
$110$		0			0
$111$		−	92.3457i		−	0.831943i
$112$	−3.67646	−	27.7576i	−0.0328255	−	0.247836i
$113$		−	16.2283i		−	0.143613i	−0.997419	−	0.0718064i	$-0.977124\pi$
$113$		−	16.2283i		−	0.143613i	0.997419	−	0.0718064i	$-0.0228764\pi$
$114$	−23.6402	−	40.9461i	−0.207370	−	0.359176i
$115$		0			0
$116$	−49.0382	+	84.9366i	−0.422743	+	0.732212i
$117$	22.2264	+	38.4972i	0.189969	+	0.329036i
$118$	34.5246			0.292581
$119$	70.0292	−	53.8224i	0.588481	−	0.452289i
$120$		0			0
$121$	59.8309	+	103.630i	0.494470	+	0.856448i
$122$	−4.51830	+	7.82592i	−0.0370352	+	0.0641469i
$123$	57.0597	+	32.9434i	0.463900	+	0.267833i
$124$	−49.9162	+	28.8191i	−0.402550	+	0.232412i
$125$		0			0
$126$	18.0977	+	23.5472i	0.143633	+	0.186883i
$127$		−	80.5643i		−	0.634365i	−0.948365	−	0.317182i	$-0.897263\pi$
$127$		−	80.5643i		−	0.634365i	0.948365	−	0.317182i	$-0.102737\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$	−95.3661	−	55.0597i	−0.739272	−	0.426819i
$130$		0			0
$131$	107.981	−	62.3429i	0.824283	−	0.475900i	−0.0276082	−	0.999619i	$-0.508789\pi$
$131$	107.981	−	62.3429i	0.824283	−	0.475900i	0.851891	+	0.523719i	$0.175456\pi$
$132$	4.00723			0.0303578
$133$	−133.945	+	17.7409i	−1.00711	+	0.133390i
$134$	−176.056			−1.31385
$135$		0			0
$136$	30.9066	+	17.8439i	0.227254	+	0.131205i
$137$	−65.8750	−	38.0330i	−0.480840	−	0.277613i	0.239927	−	0.970791i	$-0.422877\pi$
$137$	−65.8750	−	38.0330i	−0.480840	−	0.277613i	−0.720766	+	0.693178i	$0.756210\pi$
$138$	−29.7622	−	51.5496i	−0.215668	−	0.373548i
$139$			91.7680i			0.660201i	0.943946	+	0.330101i	$0.107083\pi$
$139$			91.7680i			0.660201i	−0.943946	+	0.330101i	$0.892917\pi$
$140$		0			0
$141$	−43.6350			−0.309468
$142$	145.711	−	84.1263i	1.02613	−	0.592439i
$143$	8.57039	−	14.8444i	0.0599328	−	0.103807i
$144$	−6.00000	+	10.3923i	−0.0416667	+	0.0721688i
$145$		0			0
$146$			55.9032i			0.382898i
$147$	81.9441	−	22.0944i	0.557443	−	0.150302i
$148$		−	106.632i		−	0.720484i
$149$	−49.4579	−	85.6637i	−0.331933	−	0.574924i	0.650958	−	0.759114i	$-0.274367\pi$
$149$	−49.4579	−	85.6637i	−0.331933	−	0.574924i	−0.982891	+	0.184190i	$0.941034\pi$
$150$		0			0
$151$	−48.8950	+	84.6886i	−0.323808	+	0.560852i	−0.981270	−	0.192635i	$-0.938297\pi$
$151$	−48.8950	+	84.6886i	−0.323808	+	0.560852i	0.657462	+	0.753487i	$0.271630\pi$
$152$	−27.2974	−	47.2804i	−0.179588	−	0.311055i
$153$	−37.8527			−0.247403
$154$	4.37406	−	10.5833i	0.0284030	−	0.0687230i
$155$		0			0
$156$	25.6648	+	44.4527i	0.164518	+	0.284953i
$157$	66.7013	−	115.530i	0.424849	−	0.735860i	−0.571557	−	0.820562i	$-0.693661\pi$
$157$	66.7013	−	115.530i	0.424849	−	0.735860i	0.996406	+	0.0847022i	$0.0269939\pi$
$158$	113.743	+	65.6698i	0.719895	+	0.415632i
$159$	−31.2480	+	18.0411i	−0.196529	+	0.113466i
$160$		0			0
$161$	−168.632	+	22.3352i	−1.04741	+	0.138728i
$162$		−	12.7279i		−	0.0785674i
$163$	−28.3616	+	16.3746i	−0.173998	+	0.100458i	−0.584469	−	0.811416i	$-0.698697\pi$
$163$	−28.3616	+	16.3746i	−0.173998	+	0.100458i	0.410472	+	0.911873i	$0.365364\pi$
$164$	65.8869	+	38.0398i	0.401749	+	0.231950i
$165$		0			0
$166$	7.09942	−	4.09885i	0.0427676	−	0.0246919i
$167$	−171.659			−1.02790			−0.513948	−	0.857821i	$-0.671818\pi$
$167$	−171.659			−1.02790			−0.513948	+	0.857821i	$0.671818\pi$
$168$	20.8975	+	27.1900i	0.124390	+	0.161845i
$169$	50.5603			0.299173
$170$		0			0
$171$	50.1485	+	28.9532i	0.293266	+	0.169317i
$172$	−110.119	−	63.5774i	−0.640229	−	0.369636i
$173$	101.230	+	175.336i	0.585145	+	1.01350i	0.994857	+	0.101287i	$0.0322959\pi$
$173$	101.230	+	175.336i	0.585145	+	1.01350i	−0.409712	+	0.912215i	$0.634371\pi$
$174$		−	120.119i		−	0.690336i
$175$		0			0
$176$	4.62715			0.0262906
$177$	−36.6188	+	21.1419i	−0.206886	+	0.119446i
$178$	107.469	−	186.141i	0.603757	−	1.04574i
$179$	−39.3459	+	68.1491i	−0.219810	+	0.380721i	−0.954750	−	0.297411i	$-0.903877\pi$
$179$	−39.3459	+	68.1491i	−0.219810	+	0.380721i	0.734940	+	0.678132i	$0.237210\pi$
$180$		0			0
$181$		−	58.1509i		−	0.321276i	−0.987013	−	0.160638i	$-0.948645\pi$
$181$		−	58.1509i		−	0.321276i	0.987013	−	0.160638i	$-0.0513551\pi$
$182$	145.416	−	19.2602i	0.798992	−	0.105825i
$183$		−	11.0675i		−	0.0604783i
$184$	−34.3664	−	59.5244i	−0.186774	−	0.323502i
$185$		0			0
$186$	35.2961	−	61.1346i	0.189764	−	0.328681i
$187$	7.29793	+	12.6404i	0.0390263	+	0.0675956i
$188$	−50.3854			−0.268008
$189$	−33.6152	−	13.8931i	−0.177858	−	0.0735083i
$190$		0			0
$191$	−184.204	−	319.051i	−0.964419	−	1.67042i	−0.711168	−	0.703022i	$-0.751834\pi$
$191$	−184.204	−	319.051i	−0.964419	−	1.67042i	−0.253251	−	0.967401i	$-0.581500\pi$
$192$	−6.92820	+	12.0000i	−0.0360844	+	0.0625000i
$193$	−243.196	−	140.409i	−1.26008	−	0.727510i	−0.286994	−	0.957932i	$-0.592656\pi$
$193$	−243.196	−	140.409i	−1.26008	−	0.727510i	−0.973091	+	0.230422i	$0.925989\pi$
$194$	176.742	−	102.042i	0.911044	−	0.525991i
$195$		0			0
$196$	94.6209	−	25.5124i	0.482760	−	0.130165i
$197$		−	7.61779i		−	0.0386690i	−0.999813	−	0.0193345i	$-0.993845\pi$
$197$		−	7.61779i		−	0.0386690i	0.999813	−	0.0193345i	$-0.00615475\pi$
$198$	−4.25031	+	2.45392i	−0.0214662	+	0.0123935i
$199$	174.795	+	100.918i	0.878366	+	0.507125i	0.870119	−	0.492841i	$-0.164042\pi$
$199$	174.795	+	100.918i	0.878366	+	0.507125i	0.00824641	+	0.999966i	$0.497375\pi$
$200$		0			0
$201$	186.735	−	107.812i	0.929031	−	0.536376i
$202$	55.2736			0.273632
$203$	−317.240	−	131.114i	−1.56276	−	0.645884i
$204$	−43.7085			−0.214257
$205$		0			0
$206$	−46.3481	−	26.7591i	−0.224991	−	0.129898i
$207$	63.1351	+	36.4511i	0.305001	+	0.176092i
$208$	29.6351	+	51.3296i	0.142477	+	0.246777i
$209$		−	22.3285i		−	0.106835i
$210$		0			0
$211$	30.3818			0.143989			0.0719947	−	0.997405i	$-0.477064\pi$
$211$	30.3818			0.143989			0.0719947	+	0.997405i	$0.477064\pi$
$212$	−36.0821	+	20.8320i	−0.170199	+	0.0982643i
$213$	−103.033	+	178.459i	−0.483724	+	0.837835i
$214$	58.7126	−	101.693i	0.274358	−	0.475202i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	−122.933	−	159.950i	−0.566512	−	0.737097i
$218$		−	67.5886i		−	0.310039i
$219$	−34.2336	−	59.2943i	−0.156318	−	0.270750i
$220$		0			0
$221$	−93.4808	+	161.914i	−0.422990	+	0.732640i
$222$	65.2983	+	113.100i	0.294136	+	0.509459i
$223$	−16.7377			−0.0750569			−0.0375284	−	0.999296i	$-0.511948\pi$
$223$	−16.7377			−0.0750569			−0.0375284	+	0.999296i	$0.511948\pi$
$224$	24.1303	+	31.3963i	0.107725	+	0.140162i
$225$		0			0
$226$	11.4751	+	19.8755i	0.0507748	+	0.0879446i
$227$	−211.736	+	366.738i	−0.932758	+	1.61558i	−0.154175	+	0.988044i	$0.549272\pi$
$227$	−211.736	+	366.738i	−0.932758	+	1.61558i	−0.778583	+	0.627541i	$0.784061\pi$
$228$	57.9065	+	33.4323i	0.253976	+	0.146633i
$229$	350.596	−	202.417i	1.53099	−	0.883916i	0.531672	−	0.846951i	$-0.321564\pi$
$229$	350.596	−	202.417i	1.53099	−	0.883916i	0.999317	−	0.0369660i	$-0.0117693\pi$
$230$		0			0
$231$	1.84155	+	13.9039i	0.00797209	+	0.0601900i
$232$		−	138.701i		−	0.597849i
$233$	240.147	−	138.649i	1.03068	−	0.595061i	0.113497	−	0.993538i	$-0.463795\pi$
$233$	240.147	−	138.649i	1.03068	−	0.595061i	0.917178	+	0.398478i	$0.130461\pi$
$234$	−54.4432	−	31.4328i	−0.232663	−	0.134328i
$235$		0			0
$236$	−42.2838	+	24.4125i	−0.179169	+	0.103443i
$237$	−160.858			−0.678724
$238$	−47.7097	+	115.437i	−0.200461	+	0.485029i
$239$	−290.247			−1.21442			−0.607211	−	0.794541i	$-0.707712\pi$
$239$	−290.247			−1.21442			−0.607211	+	0.794541i	$0.707712\pi$
$240$		0			0
$241$	−350.574	−	202.404i	−1.45466	−	0.839850i	−0.455922	−	0.890020i	$-0.650690\pi$
$241$	−350.574	−	202.404i	−1.45466	−	0.839850i	−0.998741	+	0.0501703i	$0.984024\pi$
$242$	−146.555	−	84.6137i	−0.605600	−	0.349643i
$243$	7.79423	+	13.5000i	0.0320750	+	0.0555556i
$244$		−	12.7797i		−	0.0523757i
$245$		0			0
$246$	−93.1781			−0.378773
$247$	247.693	−	143.005i	1.00280	−	0.578970i
$248$	40.7564	−	70.5922i	0.164340	−	0.284646i
$249$	−5.02005	+	8.69498i	−0.0201608	+	0.0349196i
$250$		0			0
$251$			155.805i			0.620739i	0.950616	+	0.310369i	$0.100453\pi$
$251$			155.805i			0.620739i	−0.950616	+	0.310369i	$0.899547\pi$
$252$	−38.8155	−	16.0423i	−0.154030	−	0.0636600i
$253$		−	28.1108i		−	0.111110i
$254$	56.9676	+	98.6707i	0.224282	+	0.388467i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	12.9508	+	22.4315i	0.0503923	+	0.0872821i	0.890121	−	0.455724i	$-0.150619\pi$
$257$	12.9508	+	22.4315i	0.0503923	+	0.0872821i	−0.839729	+	0.543006i	$0.817286\pi$
$258$	155.732			0.603613
$259$	369.980	−	49.0033i	1.42849	−	0.189202i
$260$		0			0
$261$	73.5573	+	127.405i	0.281829	+	0.488142i
$262$	−88.1662	+	152.708i	−0.336512	+	0.582856i
$263$	273.495	+	157.902i	1.03990	+	0.600389i	0.919806	−	0.392373i	$-0.128346\pi$
$263$	273.495	+	157.902i	1.03990	+	0.600389i	0.120098	+	0.992762i	$0.461679\pi$
$264$	−4.90784	+	2.83354i	−0.0185903	+	0.0107331i
$265$		0			0
$266$	151.504	−	116.442i	0.569564	−	0.437751i
$267$			263.244i			0.985931i
$268$	215.623	−	124.490i	0.804565	−	0.464516i
$269$	41.4157	+	23.9114i	0.153962	+	0.0888899i	0.575002	−	0.818152i	$-0.305001\pi$
$269$	41.4157	+	23.9114i	0.153962	+	0.0888899i	−0.421040	+	0.907042i	$0.638335\pi$
$270$		0			0
$271$	294.580	−	170.076i	1.08701	−	0.627587i	0.154233	−	0.988035i	$-0.450709\pi$
$271$	294.580	−	170.076i	1.08701	−	0.627587i	0.932779	+	0.360448i	$0.117376\pi$
$272$	−50.4703			−0.185552
$273$	−142.443	+	109.478i	−0.521769	+	0.401017i
$274$	107.573			0.392604
$275$		0			0
$276$	72.9022	+	42.0901i	0.264138	+	0.152500i
$277$	182.374	+	105.293i	0.658388	+	0.380121i	0.791663	−	0.610959i	$-0.209216\pi$
$277$	182.374	+	105.293i	0.658388	+	0.380121i	−0.133274	+	0.991079i	$0.542549\pi$
$278$	−64.8898	−	112.392i	−0.233416	−	0.404289i
$279$			86.4574i			0.309883i
$280$		0			0
$281$	471.785			1.67895			0.839476	−	0.543397i	$-0.182862\pi$
$281$	471.785			1.67895			0.839476	+	0.543397i	$0.182862\pi$
$282$	53.4418	−	30.8546i	0.189510	−	0.109414i
$283$	−234.135	+	405.534i	−0.827333	+	1.43298i	0.0727901	+	0.997347i	$0.476810\pi$
$283$	−234.135	+	405.534i	−0.827333	+	1.43298i	−0.900123	+	0.435636i	$0.856524\pi$
$284$	−118.973	+	206.067i	−0.418917	+	0.725586i
$285$		0			0
$286$			24.2407i			0.0847578i
$287$	−101.708	+	246.089i	−0.354383	+	0.857453i
$288$		−	16.9706i		−	0.0589256i
$289$	64.8985	+	112.408i	0.224562	+	0.388953i
$290$		0			0
$291$	−124.976	+	216.464i	−0.429470	+	0.743864i
$292$	−39.5295	−	68.4671i	−0.135375	−	0.234476i
$293$	63.5067			0.216746			0.108373	−	0.994110i	$-0.465436\pi$
$293$	63.5067			0.216746			0.108373	+	0.994110i	$0.465436\pi$
$294$	−84.7375	+	85.0032i	−0.288223	+	0.289127i
$295$		0			0
$296$	75.3999	+	130.597i	0.254730	+	0.441204i
$297$	3.00542	−	5.20555i	0.0101193	−	0.0175271i
$298$	121.147	+	69.9441i	0.406533	+	0.234712i
$299$	311.836	−	180.039i	1.04293	−	0.602136i
$300$		0			0
$301$	169.988	−	411.298i	0.564745	−	1.36644i
$302$		−	138.296i		−	0.457934i
$303$	−58.6265	+	33.8480i	−0.193487	+	0.111710i
$304$	66.8646	+	38.6043i	0.219949	+	0.126988i
$305$		0			0
$306$	46.3599	−	26.7659i	0.151503	−	0.0874703i
$307$	−211.610			−0.689283			−0.344642	−	0.938734i	$-0.612000\pi$
$307$	−211.610			−0.689283			−0.344642	+	0.938734i	$0.612000\pi$
$308$	2.12644	+	16.0548i	0.00690403	+	0.0521261i
$309$	65.5460			0.212123
$310$		0			0
$311$	58.3090	+	33.6647i	0.187489	+	0.108247i	0.590806	−	0.806813i	$-0.298810\pi$
$311$	58.3090	+	33.6647i	0.187489	+	0.108247i	−0.403318	+	0.915060i	$0.632143\pi$
$312$	−62.8656	−	36.2955i	−0.201492	−	0.116332i
$313$	−69.1168	−	119.714i	−0.220821	−	0.382472i	0.734237	−	0.678893i	$-0.237540\pi$
$313$	−69.1168	−	119.714i	−0.220821	−	0.382472i	−0.955057	+	0.296421i	$0.904207\pi$
$314$			188.660i			0.600827i
$315$		0			0
$316$	−185.742			−0.587792
$317$	−17.1684	+	9.91216i	−0.0541589	+	0.0312686i	−0.526835	−	0.849968i	$-0.676621\pi$
$317$	−17.1684	+	9.91216i	−0.0541589	+	0.0312686i	0.472676	+	0.881236i	$0.343288\pi$
$318$	25.5139	−	44.1914i	0.0802325	−	0.138967i
$319$	28.3634	−	49.1268i	0.0889135	−	0.154003i
$320$		0			0
$321$			143.816i			0.448024i
$322$	190.738	−	146.596i	0.592355	−	0.455267i
$323$			243.546i			0.754013i
$324$	9.00000	+	15.5885i	0.0277778	+	0.0481125i
$325$		0			0
$326$	23.1572	−	40.1094i	0.0710342	−	0.123035i
$327$	41.3894	+	71.6885i	0.126573	+	0.219231i
$328$	−107.593			−0.328027
$329$	−23.1550	−	174.822i	−0.0703799	−	0.531374i
$330$		0			0
$331$	131.139	+	227.139i	0.396189	+	0.686220i	0.993252	−	0.115974i	$-0.0369991\pi$
$331$	131.139	+	227.139i	0.396189	+	0.686220i	−0.597063	+	0.802194i	$0.703666\pi$
$332$	−5.79665	+	10.0401i	−0.0174598	+	0.0302412i
$333$	−138.519	−	79.9737i	−0.415972	−	0.240161i
$334$	210.238	−	121.381i	0.629455	−	0.363416i
$335$		0			0
$336$	−44.8203	−	18.5241i	−0.133394	−	0.0551312i
$337$		−	578.125i		−	1.71550i	−0.514063	−	0.857752i	$-0.671860\pi$
$337$		−	578.125i		−	1.71550i	0.514063	−	0.857752i	$-0.328140\pi$
$338$	−61.9235	+	35.7515i	−0.183206	+	0.105774i
$339$	−24.3424	−	14.0541i	−0.0718064	−	0.0414575i
$340$		0			0
$341$	28.8712	−	16.6688i	0.0846664	−	0.0488822i
$342$	−81.8921			−0.239451
$343$	132.004	+	316.582i	0.384852	+	0.922978i
$344$	179.824			0.522744
$345$		0			0
$346$	−247.962	−	143.161i	−0.716654	−	0.413760i
$347$	398.131	+	229.861i	1.14735	+	0.662423i	0.948240	−	0.317554i	$-0.102861\pi$
$347$	398.131	+	229.861i	1.14735	+	0.662423i	0.199110	+	0.979977i	$0.436195\pi$
$348$	84.9366	+	147.115i	0.244071	+	0.422743i
$349$			389.147i			1.11504i	0.830165	+	0.557518i	$0.188246\pi$
$349$			389.147i			1.11504i	−0.830165	+	0.557518i	$0.811754\pi$
$350$		0			0
$351$	76.9943			0.219357
$352$	−5.66708	+	3.27189i	−0.0160997	+	0.00929515i
$353$	−322.978	+	559.415i	−0.914953	+	1.58475i	−0.107983	+	0.994153i	$0.534439\pi$
$353$	−322.978	+	559.415i	−0.914953	+	1.58475i	−0.806970	+	0.590593i	$0.798894\pi$
$354$	29.8991	−	51.7868i	0.0844608	−	0.146290i
$355$		0			0
$356$			303.968i			0.853842i
$357$	−20.0866	−	151.655i	−0.0562649	−	0.424805i
$358$		−	111.287i		−	0.310858i
$359$	−33.0206	−	57.1934i	−0.0919794	−	0.159313i	0.816365	−	0.577537i	$-0.195986\pi$
$359$	−33.0206	−	57.1934i	−0.0919794	−	0.159313i	−0.908344	+	0.418224i	$0.862653\pi$
$360$		0			0
$361$	5.78661	−	10.0227i	0.0160294	−	0.0277637i
$362$	41.1189	+	71.2200i	0.113588	+	0.196740i
$363$	207.260			0.570965
$364$	−164.479	+	126.414i	−0.451866	+	0.347291i
$365$		0			0
$366$	7.82592	+	13.5549i	0.0213823	+	0.0370352i
$367$	299.966	−	519.556i	0.817346	−	1.41568i	−0.0902858	−	0.995916i	$-0.528778\pi$
$367$	299.966	−	519.556i	0.817346	−	1.41568i	0.907631	−	0.419768i	$-0.137889\pi$
$368$	84.1802	+	48.6014i	0.228750	+	0.132069i
$369$	98.8303	−	57.0597i	0.267833	−	0.154633i
$370$		0			0
$371$	−88.8627	−	115.621i	−0.239522	−	0.311646i
$372$			99.8324i			0.268367i
$373$	350.526	−	202.376i	0.939748	−	0.542564i	0.0498667	−	0.998756i	$-0.484120\pi$
$373$	350.526	−	202.376i	0.939748	−	0.542564i	0.889881	+	0.456192i	$0.150787\pi$
$374$	−17.8762	−	10.3208i	−0.0477973	−	0.0275958i
$375$		0			0
$376$	61.7093	−	35.6279i	0.164120	−	0.0947550i
$377$	726.627			1.92739
$378$	50.9939	−	6.75409i	0.134905	−	0.0178680i
$379$	239.675			0.632388			0.316194	−	0.948695i	$-0.397595\pi$
$379$	239.675			0.632388			0.316194	+	0.948695i	$0.397595\pi$
$380$		0			0
$381$	−120.846	−	69.7707i	−0.317182	−	0.183125i
$382$	451.206	+	260.504i	1.18117	+	0.681947i
$383$	319.555	+	553.486i	0.834347	+	1.44513i	0.894561	+	0.446947i	$0.147489\pi$
$383$	319.555	+	553.486i	0.834347	+	1.44513i	−0.0602133	+	0.998186i	$0.519178\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	397.138			1.02885
$387$	−165.179	+	95.3661i	−0.426819	+	0.246424i
$388$	−144.310	+	249.952i	−0.371932	+	0.644205i
$389$	260.797	−	451.714i	0.670429	−	1.16122i	−0.307353	−	0.951596i	$-0.599443\pi$
$389$	260.797	−	451.714i	0.670429	−	1.16122i	0.977782	−	0.209622i	$-0.0672234\pi$
$390$		0			0
$391$			306.616i			0.784184i
$392$	−97.8465	+	98.1533i	−0.249608	+	0.250391i
$393$		−	215.962i		−	0.549522i
$394$	5.38659	+	9.32985i	0.0136716	+	0.0236798i
$395$		0			0
$396$	3.47036	−	6.01085i	0.00876355	−	0.0151789i
$397$	−72.5800	−	125.712i	−0.182821	−	0.316656i	0.760019	−	0.649901i	$-0.225190\pi$
$397$	−72.5800	−	125.712i	−0.182821	−	0.316656i	−0.942840	+	0.333245i	$0.891856\pi$
$398$	−285.439			−0.717182
$399$	−89.3887	+	216.282i	−0.224032	+	0.542060i
$400$		0			0
$401$	−107.021	−	185.366i	−0.266886	−	0.462260i	0.701170	−	0.712994i	$-0.252661\pi$
$401$	−107.021	−	185.366i	−0.266886	−	0.462260i	−0.968056	+	0.250734i	$0.919328\pi$
$402$	−152.469	+	264.084i	−0.379275	+	0.656924i
$403$	369.818	+	213.515i	0.917663	+	0.529813i
$404$	−67.6960	+	39.0843i	−0.167564	+	0.0967434i
$405$		0			0
$406$	481.250	−	63.7410i	1.18535	−	0.156998i
$407$			61.6751i			0.151536i
$408$	53.5318	−	30.9066i	0.131205	−	0.0757515i
$409$	479.754	+	276.986i	1.17299	+	0.677228i	0.954383	−	0.298585i	$-0.0965145\pi$
$409$	479.754	+	276.986i	1.17299	+	0.677228i	0.218610	+	0.975812i	$0.429848\pi$
$410$		0			0
$411$	−114.099	+	65.8750i	−0.277613	+	0.160280i
$412$	75.6861			0.183704
$413$	−104.136	−	135.493i	−0.252145	−	0.328070i
$414$	−103.099			−0.249032
$415$		0			0
$416$	−72.5910	−	41.9104i	−0.174497	−	0.100746i
$417$	137.652	+	79.4734i	0.330101	+	0.190584i
$418$	15.7886	+	27.3467i	0.0377719	+	0.0654228i
$419$		−	268.003i		−	0.639626i	−0.947481	−	0.319813i	$-0.896380\pi$
$419$		−	268.003i		−	0.639626i	0.947481	−	0.319813i	$-0.103620\pi$
$420$		0			0
$421$	−9.12915			−0.0216844			−0.0108422	−	0.999941i	$-0.503451\pi$
$421$	−9.12915			−0.0216844			−0.0108422	+	0.999941i	$0.503451\pi$
$422$	−37.2099	+	21.4831i	−0.0881751	+	0.0509079i
$423$	−37.7891	+	65.4526i	−0.0893358	+	0.154734i
$424$	29.4609	−	51.0278i	0.0694833	−	0.120349i
$425$		0			0
$426$		−	291.422i		−	0.684089i
$427$	44.3416	−	5.87299i	0.103845	−	0.0137541i
$428$			166.064i			0.388000i
$429$	−14.8444	−	25.7112i	−0.0346022	−	0.0599328i
$430$		0			0
$431$	134.221	−	232.478i	0.311419	−	0.539393i	−0.667251	−	0.744833i	$-0.732529\pi$
$431$	134.221	−	232.478i	0.311419	−	0.539393i	0.978670	+	0.205440i	$0.0658626\pi$
$432$	10.3923	+	18.0000i	0.0240563	+	0.0416667i
$433$	472.254			1.09066			0.545328	−	0.838223i	$-0.316405\pi$
$433$	472.254			1.09066			0.545328	+	0.838223i	$0.316405\pi$
$434$	263.663	+	108.971i	0.607519	+	0.251086i
$435$		0			0
$436$	47.7924	+	82.7788i	0.109616	+	0.189860i
$437$	234.528	−	406.215i	0.536678	−	0.929553i
$438$	83.8548	+	48.4136i	0.191449	+	0.110533i
$439$	−475.788	+	274.696i	−1.08380	+	0.625731i	−0.931919	−	0.362667i	$-0.881866\pi$
$439$	−475.788	+	274.696i	−1.08380	+	0.625731i	−0.151880	+	0.988399i	$0.548533\pi$
$440$		0			0
$441$	37.8241	−	142.050i	0.0857689	−	0.322110i
$442$		−	264.404i		−	0.598198i
$443$	407.734	−	235.405i	0.920392	−	0.531388i	0.0366317	−	0.999329i	$-0.488337\pi$
$443$	407.734	−	235.405i	0.920392	−	0.531388i	0.883760	+	0.467940i	$0.155004\pi$
$444$	−159.947	−	92.3457i	−0.360242	−	0.207986i
$445$		0			0
$446$	20.4994	−	11.8353i	0.0459628	−	0.0265366i
$447$	−171.327			−0.383283
$448$	−51.7540	−	21.3898i	−0.115522	−	0.0477450i
$449$	−559.525			−1.24616			−0.623079	−	0.782159i	$-0.714118\pi$
$449$	−559.525			−1.24616			−0.623079	+	0.782159i	$0.714118\pi$
$450$		0			0
$451$	−38.1086	−	22.0020i	−0.0844980	−	0.0487849i
$452$	−28.1082	−	16.2283i	−0.0621862	−	0.0359032i
$453$	84.6886	+	146.685i	0.186951	+	0.323808i
$454$		−	598.880i		−	1.31912i
$455$		0			0
$456$	−94.5609			−0.207370
$457$	−543.325	+	313.689i	−1.18890	+	0.686409i	−0.958055	−	0.286583i	$-0.907481\pi$
$457$	−543.325	+	313.689i	−1.18890	+	0.686409i	−0.230840	+	0.972992i	$0.574147\pi$
$458$	−286.261	+	495.818i	−0.625023	+	1.08257i
$459$	−32.7814	+	56.7790i	−0.0714192	+	0.123702i
$460$		0			0
$461$			223.659i			0.485160i	0.970131	+	0.242580i	$0.0779936\pi$
$461$			223.659i			0.485160i	−0.970131	+	0.242580i	$0.922006\pi$
$462$	−12.0870	−	15.7265i	−0.0261623	−	0.0340401i
$463$		−	397.204i		−	0.857893i	−0.903330	−	0.428946i	$-0.858885\pi$
$463$		−	397.204i		−	0.857893i	0.903330	−	0.428946i	$-0.141115\pi$
$464$	98.0764	+	169.873i	0.211371	+	0.366106i
$465$		0			0
$466$	−196.079	+	339.620i	−0.420771	+	0.728797i
$467$	166.862	+	289.014i	0.357307	+	0.618874i	0.987510	−	0.157557i	$-0.0503617\pi$
$467$	166.862	+	289.014i	0.357307	+	0.618874i	−0.630203	+	0.776430i	$0.717028\pi$
$468$	88.9054			0.189969
$469$	531.035	+	690.937i	1.13227	+	1.47321i
$470$		0			0
$471$	−115.530	−	200.104i	−0.245287	−	0.424849i
$472$	34.5246	−	59.7983i	0.0731452	−	0.126691i
$473$	63.6924	+	36.7728i	0.134656	+	0.0777438i
$474$	197.009	−	113.743i	0.415632	−	0.239965i
$475$		0			0
$476$	−23.1940	−	175.117i	−0.0487268	−	0.367892i
$477$			62.4961i			0.131019i
$478$	355.478	−	205.235i	0.743678	−	0.429363i
$479$	−527.265	−	304.417i	−1.10076	−	0.635526i	−0.164341	−	0.986404i	$-0.552550\pi$
$479$	−527.265	−	304.417i	−1.10076	−	0.635526i	−0.936421	+	0.350878i	$0.885883\pi$
$480$		0			0
$481$	−684.169	+	395.005i	−1.42239	+	0.821217i
$482$	572.484			1.18773
$483$	−112.537	+	272.291i	−0.232996	+	0.563750i
$484$	239.324			0.494470
$485$		0			0
$486$	−19.0919	−	11.0227i	−0.0392837	−	0.0226805i
$487$	−275.809	−	159.238i	−0.566343	−	0.326978i	0.189344	−	0.981911i	$-0.439364\pi$
$487$	−275.809	−	159.238i	−0.566343	−	0.326978i	−0.755687	+	0.654932i	$0.772697\pi$
$488$	9.03659	+	15.6518i	0.0185176	+	0.0320734i
$489$			56.7232i			0.115998i
$490$		0			0
$491$	523.303			1.06579			0.532895	−	0.846181i	$-0.321104\pi$
$491$	523.303			1.06579			0.532895	+	0.846181i	$0.321104\pi$
$492$	114.119	−	65.8869i	0.231950	−	0.133916i
$493$	−309.371	+	535.847i	−0.627528	+	1.08691i
$494$	−202.240	+	350.290i	−0.409393	+	0.709090i
$495$		0			0
$496$			115.277i			0.232412i
$497$	−769.663	−	318.100i	−1.54862	−	0.640039i
$498$		−	14.1988i		−	0.0285117i
$499$	−391.909	−	678.806i	−0.785388	−	1.36033i	−0.928767	−	0.370664i	$-0.879130\pi$
$499$	−391.909	−	678.806i	−0.785388	−	1.36033i	0.143379	−	0.989668i	$-0.454203\pi$
$500$		0			0
$501$	−148.661	+	257.488i	−0.296728	+	0.513948i
$502$	−110.171	−	190.822i	−0.219464	−	0.380123i
$503$	58.0772			0.115462			0.0577308	−	0.998332i	$-0.481613\pi$
$503$	58.0772			0.115462			0.0577308	+	0.998332i	$0.481613\pi$
$504$	58.8827	−	7.79895i	0.116831	−	0.0154741i
$505$		0			0
$506$	19.8773	+	34.4286i	0.0392833	+	0.0680406i
$507$	43.7865	−	75.8404i	0.0863639	−	0.149587i
$508$	−139.541	−	80.5643i	−0.274688	−	0.158591i
$509$	811.110	−	468.295i	1.59354	−	0.920029i	0.600843	−	0.799367i	$-0.294832\pi$
$509$	811.110	−	468.295i	1.59354	−	0.920029i	0.992694	−	0.120662i	$-0.0385017\pi$
$510$		0			0
$511$	219.394	−	168.620i	0.429343	−	0.329981i
$512$		−	22.6274i		−	0.0441942i
$513$	86.8597	−	50.1485i	0.169317	−	0.0977553i
$514$	−31.7229	−	18.3152i	−0.0617178	−	0.0356328i
$515$		0			0
$516$	−190.732	+	110.119i	−0.369636	+	0.213410i
$517$	29.1426			0.0563687
$518$	−418.480	+	321.632i	−0.807876	+	0.620910i
$519$	350.672			0.675668
$520$		0			0
$521$	−607.133	−	350.528i	−1.16532	−	0.672799i	−0.212749	−	0.977107i	$-0.568242\pi$
$521$	−607.133	−	350.528i	−1.16532	−	0.672799i	−0.952574	+	0.304308i	$0.901575\pi$
$522$	−180.178	−	104.026i	−0.345168	−	0.199283i
$523$	−343.214	−	594.464i	−0.656241	−	1.13664i	−0.981581	−	0.191046i	$-0.938812\pi$
$523$	−343.214	−	594.464i	−0.656241	−	1.13664i	0.325340	−	0.945597i	$-0.394521\pi$
$524$		−	249.372i		−	0.475900i
$525$		0			0
$526$	−446.615			−0.849078
$527$	−314.910	+	181.814i	−0.597553	+	0.344997i
$528$	4.00723	−	6.94073i	0.00758945	−	0.0131453i
$529$	30.7626	−	53.2824i	0.0581524	−	0.100723i
$530$		0			0
$531$			73.2376i			0.137924i
$532$	−103.217	+	249.741i	−0.194017	+	0.469438i
$533$		−	563.657i		−	1.05752i
$534$	−186.141	−	322.406i	−0.348579	−	0.603757i
$535$		0			0
$536$	−176.056	+	304.937i	−0.328462	+	0.568913i
$537$	68.1491	+	118.038i	0.126907	+	0.219810i
$538$	−67.6316			−0.125709
$539$	−54.7282	+	14.7562i	−0.101537	+	0.0273770i
$540$		0			0
$541$	−398.250	−	689.789i	−0.736136	−	1.27503i	−0.954223	−	0.299096i	$-0.903315\pi$
$541$	−398.250	−	689.789i	−0.736136	−	1.27503i	0.218087	−	0.975929i	$-0.430018\pi$
$542$	−240.524	+	416.599i	−0.443771	+	0.768634i
$543$	−87.2263	−	50.3602i	−0.160638	−	0.0927443i
$544$	61.8132	−	35.6879i	0.113627	−	0.0656027i
$545$		0			0
$546$	97.0440	−	234.805i	0.177736	−	0.430045i
$547$			395.055i			0.722221i	0.932523	+	0.361111i	$0.117602\pi$
$547$			395.055i			0.722221i	−0.932523	+	0.361111i	$0.882398\pi$
$548$	−131.750	+	76.0659i	−0.240420	+	0.138806i
$549$	−16.6013	−	9.58476i	−0.0302391	−	0.0174586i
$550$		0			0
$551$	819.730	−	473.271i	1.48771	−	0.858932i
$552$	−119.049			−0.215668
$553$	−85.3592	−	644.470i	−0.154357	−	1.16541i
$554$	−297.815			−0.537572
$555$		0			0
$556$	158.947	+	91.7680i	0.285876	+	0.165050i
$557$	−36.1034	−	20.8443i	−0.0648175	−	0.0374224i	0.467241	−	0.884130i	$-0.345248\pi$
$557$	−36.1034	−	20.8443i	−0.0648175	−	0.0374224i	−0.532059	+	0.846708i	$0.678581\pi$
$558$	−61.1346	−	105.888i	−0.109560	−	0.189764i
$559$			942.063i			1.68526i
$560$		0			0
$561$	25.2808			0.0450637
$562$	−577.817	+	333.603i	−1.02814	+	0.593599i
$563$	369.875	−	640.642i	0.656972	−	1.13791i	−0.324424	−	0.945912i	$-0.605170\pi$
$563$	369.875	−	640.642i	0.656972	−	1.13791i	0.981396	−	0.191996i	$-0.0614962\pi$
$564$	−43.6350	+	75.5781i	−0.0773671	+	0.134004i
$565$		0			0
$566$		−	662.234i		−	1.17003i
$567$	−49.9512	+	38.3911i	−0.0880974	+	0.0677091i
$568$		−	336.505i		−	0.592439i
$569$	2.38030	+	4.12281i	0.00418331	+	0.00724570i	0.868109	−	0.496373i	$-0.165335\pi$
$569$	2.38030	+	4.12281i	0.00418331	+	0.00724570i	−0.863926	+	0.503618i	$0.832002\pi$
$570$		0			0
$571$	−399.848	+	692.557i	−0.700260	+	1.21289i	0.268116	+	0.963387i	$0.413599\pi$
$571$	−399.848	+	692.557i	−0.700260	+	1.21289i	−0.968375	+	0.249498i	$0.919734\pi$
$572$	−17.1408	−	29.6887i	−0.0299664	−	0.0519033i
$573$	−638.101			−1.11362
$574$	−49.4451	−	373.315i	−0.0861412	−	0.650374i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−85.9510	+	148.871i	−0.148962	+	0.258009i	−0.930844	−	0.365417i	$-0.880926\pi$
$577$	−85.9510	+	148.871i	−0.148962	+	0.258009i	0.781882	+	0.623426i	$0.214260\pi$
$578$	−158.968	−	91.7804i	−0.275032	−	0.158790i
$579$	−421.228	+	243.196i	−0.727510	+	0.420028i
$580$		0			0
$581$	−37.5000	−	15.4986i	−0.0645439	−	0.0266758i
$582$		−	353.485i		−	0.607362i
$583$	20.8697	−	12.0491i	0.0357971	−	0.0206675i
$584$	96.8271	+	55.9032i	0.165800	+	0.0957246i
$585$		0			0
$586$	−77.7795	+	44.9060i	−0.132730	+	0.0766314i
$587$	724.352			1.23399			0.616994	−	0.786967i	$-0.288350\pi$
$587$	724.352			1.23399			0.616994	+	0.786967i	$0.288350\pi$
$588$	43.6755	−	164.026i	0.0742781	−	0.278955i
$589$	556.271			0.944433
$590$		0			0
$591$	−11.4267	−	6.59720i	−0.0193345	−	0.0111628i
$592$	−184.691	−	106.632i	−0.311979	−	0.180121i
$593$	−516.320	−	894.293i	−0.870692	−	1.50808i	−0.861282	−	0.508127i	$-0.830338\pi$
$593$	−516.320	−	894.293i	−0.870692	−	1.50808i	−0.00940925	−	0.999956i	$-0.502995\pi$
$594$			8.50062i			0.0143108i
$595$		0			0
$596$	−197.832			−0.331933
$597$	302.753	−	174.795i	0.507125	−	0.292789i
$598$	−254.613	+	441.003i	−0.425775	+	0.737464i
$599$	−212.436	+	367.949i	−0.354650	+	0.614272i	−0.987058	−	0.160363i	$-0.948733\pi$
$599$	−212.436	+	367.949i	−0.354650	+	0.614272i	0.632408	+	0.774636i	$0.282067\pi$
$600$		0			0
$601$			749.418i			1.24695i	0.781843	+	0.623476i	$0.214280\pi$
$601$			749.418i			1.24695i	−0.781843	+	0.623476i	$0.785720\pi$
$602$	82.6395	+	623.935i	0.137275	+	1.03644i
$603$		−	373.471i		−	0.619354i
$604$	97.7900	+	169.377i	0.161904	+	0.280426i
$605$		0			0
$606$	47.8683	−	82.9104i	0.0789906	−	0.136816i
$607$	118.434	+	205.133i	0.195113	+	0.337945i	0.946938	−	0.321418i	$-0.104159\pi$
$607$	118.434	+	205.133i	0.195113	+	0.337945i	−0.751825	+	0.659363i	$0.770826\pi$
$608$	−109.189			−0.179588
$609$	−471.410	+	362.312i	−0.774072	+	0.594929i
$610$		0			0
$611$	186.647	+	323.283i	0.305478	+	0.529104i
$612$	−37.8527	+	65.5628i	−0.0618508	+	0.107129i
$613$	812.659	+	469.189i	1.32571	+	0.765398i	0.984633	−	0.174638i	$-0.0558755\pi$
$613$	812.659	+	469.189i	1.32571	+	0.765398i	0.341075	+	0.940036i	$0.389209\pi$
$614$	259.168	−	149.631i	0.422098	−	0.243698i
$615$		0			0
$616$	−13.9568	−	18.1594i	−0.0226572	−	0.0294796i
$617$		−	225.176i		−	0.364952i	−0.983210	−	0.182476i	$-0.941589\pi$
$617$		−	225.176i		−	0.364952i	0.983210	−	0.182476i	$-0.0584112\pi$
$618$	−80.2772	+	46.3481i	−0.129898	+	0.0749969i
$619$	−916.115	−	528.919i	−1.47999	−	0.854473i	−0.480248	−	0.877133i	$-0.659453\pi$
$619$	−916.115	−	528.919i	−1.47999	−	0.854473i	−0.999743	+	0.0226591i	$0.992787\pi$
$620$		0			0
$621$	109.353	−	63.1351i	0.176092	−	0.101667i
$622$	−95.2182			−0.153084
$623$	−1054.68	+	139.691i	−1.69290	+	0.224222i
$624$	102.659			0.164518
$625$		0			0
$626$	169.301	+	97.7460i	0.270449	+	0.156144i
$627$	−33.4928	−	19.3371i	−0.0534175	−	0.0308406i
$628$	−133.403	−	231.060i	−0.212424	−	0.367930i
$629$		−	672.716i		−	1.06950i
$630$		0			0
$631$	877.283			1.39031			0.695153	−	0.718862i	$-0.255336\pi$
$631$	877.283			1.39031			0.695153	+	0.718862i	$0.255336\pi$
$632$	227.487	−	131.340i	0.359948	−	0.207816i
$633$	26.3114	−	45.5726i	0.0415662	−	0.0719947i
$634$	14.0179	−	24.2797i	0.0221103	−	0.0382961i
$635$		0			0
$636$			72.1643i			0.113466i
$637$	−514.205	−	512.598i	−0.807230	−	0.804707i
$638$			80.2238i			0.125743i
$639$	178.459	+	309.100i	0.279278	+	0.483724i
$640$		0			0
$641$	−26.8684	+	46.5374i	−0.0419163	+	0.0726012i	−0.886222	−	0.463260i	$-0.846680\pi$
$641$	−26.8684	+	46.5374i	−0.0419163	+	0.0726012i	0.844306	+	0.535861i	$0.180013\pi$
$642$	−101.693	−	176.138i	−0.158401	−	0.274358i
$643$	−99.7799			−0.155179			−0.0775893	−	0.996985i	$-0.524722\pi$
$643$	−99.7799			−0.155179			−0.0775893	+	0.996985i	$0.524722\pi$
$644$	−129.947	+	314.415i	−0.201781	+	0.488222i
$645$		0			0
$646$	−172.213	−	298.282i	−0.266584	−	0.461737i
$647$	−379.842	+	657.905i	−0.587081	+	1.01685i	0.407531	+	0.913191i	$0.366390\pi$
$647$	−379.842	+	657.905i	−0.587081	+	1.01685i	−0.994612	+	0.103663i	$0.966944\pi$
$648$	−22.0454	−	12.7279i	−0.0340207	−	0.0196419i
$649$	24.4567	−	14.1201i	0.0376836	−	0.0217567i
$650$		0			0
$651$	−346.388	+	45.8787i	−0.532086	+	0.0704742i
$652$			65.4983i			0.100458i
$653$	995.749	−	574.896i	1.52488	−	0.880392i	0.525318	−	0.850906i	$-0.323946\pi$
$653$	995.749	−	574.896i	1.52488	−	0.880392i	0.999565	−	0.0294854i	$-0.00938687\pi$
$654$	−101.383	−	58.5334i	−0.155020	−	0.0895007i
$655$		0			0
$656$	131.774	−	76.0796i	0.200875	−	0.115975i
$657$	−118.589			−0.180500
$658$	151.977	+	197.740i	0.230968	+	0.300516i
$659$	−213.700			−0.324280			−0.162140	−	0.986768i	$-0.551840\pi$
$659$	−213.700			−0.324280			−0.162140	+	0.986768i	$0.551840\pi$
$660$		0			0
$661$	665.936	+	384.479i	1.00747	+	0.581662i	0.910449	−	0.413621i	$-0.135736\pi$
$661$	665.936	+	384.479i	1.00747	+	0.581662i	0.0970187	+	0.995283i	$0.469069\pi$
$662$	−321.223	−	185.458i	−0.485231	−	0.280148i
$663$	161.914	+	280.442i	0.244213	+	0.422990i
$664$		−	16.3954i		−	0.0246919i
$665$		0			0
$666$	226.200			0.339639
$667$	1032.01	−	595.832i	1.54724	−	0.893301i
$668$	−171.659	+	297.322i	−0.256974	+	0.445092i
$669$	−14.4953	+	25.1065i	−0.0216671	+	0.0375284i
$670$		0			0
$671$			7.39169i			0.0110159i
$672$	67.9919	−	9.00545i	0.101178	−	0.0134010i
$673$		−	1299.78i		−	1.93133i	−0.259796	−	0.965664i	$-0.583655\pi$
$673$		−	1299.78i		−	1.93133i	0.259796	−	0.965664i	$-0.416345\pi$
$674$	408.796	+	708.056i	0.606523	+	1.05053i
$675$		0			0
$676$	50.5603	−	87.5730i	0.0747933	−	0.129546i
$677$	−619.840	−	1073.60i	−0.915569	−	1.58581i	−0.806066	−	0.591826i	$-0.798407\pi$
$677$	−619.840	−	1073.60i	−0.915569	−	1.58581i	−0.109504	−	0.993986i	$-0.534926\pi$
$678$	39.7509			0.0586297
$679$	−933.575	−	385.844i	−1.37493	−	0.568253i
$680$		0			0
$681$	366.738	+	635.208i	0.538528	+	0.932758i
$682$	−23.5733	+	40.8301i	−0.0345649	+	0.0598682i
$683$	403.643	+	233.043i	0.590985	+	0.341205i	0.765487	−	0.643452i	$-0.222498\pi$
$683$	403.643	+	233.043i	0.590985	+	0.341205i	−0.174502	+	0.984657i	$0.555832\pi$
$684$	100.297	−	57.9065i	0.146633	−	0.0846586i
$685$		0			0
$686$	−385.528	−	294.391i	−0.561995	−	0.429141i
$687$		−	701.193i		−	1.02066i
$688$	−220.239	+	127.155i	−0.320114	+	0.184818i
$689$	267.325	+	154.340i	0.387989	+	0.224006i
$690$		0			0
$691$	−93.9272	+	54.2289i	−0.135929	+	0.0784788i	−0.566423	−	0.824115i	$-0.691673\pi$
$691$	−93.9272	+	54.2289i	−0.135929	+	0.0784788i	0.430493	+	0.902594i	$0.358340\pi$
$692$	404.921			0.585145
$693$	22.4507	+	9.27879i	0.0323963	+	0.0133893i
$694$	−650.145			−0.936808
$695$		0			0
$696$	−208.051	−	120.119i	−0.298924	−	0.172584i
$697$	415.666	+	239.985i	0.596364	+	0.344311i
$698$	−275.169	−	476.606i	−0.394224	−	0.682817i
$699$		−	480.295i		−	0.687117i
$700$		0			0
$701$	528.400			0.753780			0.376890	−	0.926258i	$-0.376993\pi$
$701$	528.400			0.753780			0.376890	+	0.926258i	$0.376993\pi$
$702$	−94.2984	+	54.4432i	−0.134328	+	0.0775544i
$703$	−514.555	+	891.235i	−0.731942	+	1.26776i
$704$	4.62715	−	8.01446i	0.00657266	−	0.0113842i
$705$		0			0
$706$		−	913.521i		−	1.29394i
$707$	−166.721	−	216.923i	−0.235815	−	0.306822i
$708$			84.5675i			0.119446i
$709$	−466.779	−	808.484i	−0.658362	−	1.14032i	−0.981040	−	0.193808i	$-0.937916\pi$
$709$	−466.779	−	808.484i	−0.658362	−	1.14032i	0.322678	−	0.946509i	$-0.395417\pi$
$710$		0			0
$711$	−139.307	+	241.286i	−0.195931	+	0.339362i
$712$	−214.938	−	372.283i	−0.301879	−	0.522869i
$713$	700.326			0.982224
$714$	131.837	+	171.536i	0.184646	+	0.240246i
$715$		0			0
$716$	78.6918	+	136.298i	0.109905	+	0.190361i
$717$	−251.361	+	435.370i	−0.350573	+	0.607211i
$718$	80.8836	+	46.6982i	0.112651	+	0.0650392i
$719$	−557.452	+	321.845i	−0.775316	+	0.447629i	−0.834768	−	0.550602i	$-0.814398\pi$
$719$	−557.452	+	321.845i	−0.775316	+	0.447629i	0.0594517	+	0.998231i	$0.481065\pi$
$720$		0			0
$721$	34.7821	+	262.608i	0.0482414	+	0.364227i
$722$			16.3670i			0.0226690i
$723$	−607.211	+	350.574i	−0.839850	+	0.484887i
$724$	−100.720	−	58.1509i	−0.139116	−	0.0803189i
$725$		0			0
$726$	−253.841	+	146.555i	−0.349643	+	0.201867i
$727$	−317.353			−0.436524			−0.218262	−	0.975890i	$-0.570039\pi$
$727$	−317.353			−0.436524			−0.218262	+	0.975890i	$0.570039\pi$
$728$	112.057	−	271.129i	0.153924	−	0.372430i
$729$	27.0000			0.0370370
$730$		0			0
$731$	−694.719	−	401.096i	−0.950368	−	0.548695i
$732$	−19.1695	−	11.0675i	−0.0261879	−	0.0151196i
$733$	−419.747	−	727.023i	−0.572643	−	0.991846i	−0.996293	−	0.0860205i	$-0.972585\pi$
$733$	−419.747	−	727.023i	−0.572643	−	0.991846i	0.423651	−	0.905826i	$-0.360748\pi$
$734$			848.431i			1.15590i
$735$		0			0
$736$	−137.466			−0.186774
$737$	−124.715	+	72.0044i	−0.169220	+	0.0976993i
$738$	−80.6946	+	139.767i	−0.109342	+	0.189386i
$739$	−459.403	+	795.709i	−0.621654	+	1.07674i	0.367523	+	0.930014i	$0.380206\pi$
$739$	−459.403	+	795.709i	−0.621654	+	1.07674i	−0.989178	+	0.146723i	$0.953128\pi$
$740$		0			0
$741$		−	495.386i		−	0.668537i
$742$	190.590	+	78.7703i	0.256860	+	0.106160i
$743$		−	1034.18i		−	1.39190i	−0.718088	−	0.695952i	$-0.754983\pi$
$743$		−	1034.18i		−	1.39190i	0.718088	−	0.695952i	$-0.245017\pi$
$744$	−70.5922	−	122.269i	−0.0948819	−	0.164340i
$745$		0			0
$746$	−286.203	+	495.719i	−0.383651	+	0.664502i
$747$	8.69498	+	15.0601i	0.0116399	+	0.0201608i
$748$	29.1917			0.0390263
$749$	−576.193	+	76.3160i	−0.769283	+	0.101891i
$750$		0			0
$751$	340.948	+	590.540i	0.453992	+	0.786338i	0.998630	−	0.0523339i	$-0.0166660\pi$
$751$	340.948	+	590.540i	0.453992	+	0.786338i	−0.544637	+	0.838672i	$0.683333\pi$
$752$	−50.3854	+	87.2701i	−0.0670019	+	0.116051i
$753$	233.708	+	134.931i	0.310369	+	0.179192i
$754$	−889.932	+	513.803i	−1.18028	+	0.681436i
$755$		0			0
$756$	−57.6787	+	44.3302i	−0.0762946	+	0.0586378i
$757$		−	183.172i		−	0.241971i	−0.992654	−	0.120985i	$-0.961395\pi$
$757$		−	183.172i		−	0.241971i	0.992654	−	0.120985i	$-0.0386054\pi$
$758$	−293.541	+	169.476i	−0.387257	+	0.223583i
$759$	−42.1662	−	24.3447i	−0.0555549	−	0.0320747i
$760$		0			0
$761$	−673.743	+	388.985i	−0.885338	+	0.511150i	−0.872415	−	0.488766i	$-0.837447\pi$
$761$	−673.743	+	388.985i	−0.885338	+	0.511150i	−0.0129235	+	0.999916i	$0.504114\pi$
$762$	197.341			0.258978
$763$	−265.254	+	203.867i	−0.347646	+	0.267191i
$764$	−736.816			−0.964419
$765$		0			0
$766$	−782.747	−	451.919i	−1.02186	−	0.589973i
$767$	313.271	+	180.867i	0.408437	+	0.235811i
$768$	13.8564	+	24.0000i	0.0180422	+	0.0312500i
$769$		−	302.546i		−	0.393428i	−0.980461	−	0.196714i	$-0.936973\pi$
$769$		−	302.546i		−	0.393428i	0.980461	−	0.196714i	$-0.0630271\pi$
$770$		0			0
$771$	44.8630			0.0581881
$772$	−486.393	+	280.819i	−0.630042	+	0.363755i
$773$	64.0833	−	110.995i	0.0829020	−	0.143591i	−0.821593	−	0.570074i	$-0.806914\pi$
$773$	64.0833	−	110.995i	0.0829020	−	0.143591i	0.904495	+	0.426484i	$0.140248\pi$
$774$	134.868	−	233.598i	0.174248	−	0.301807i
$775$		0			0
$776$		−	408.169i		−	0.525991i
$777$	246.907	−	597.407i	0.317769	−	0.768864i
$778$			737.645i			0.948130i
$779$	−367.125	−	635.879i	−0.471277	−	0.816277i
$780$		0			0
$781$	68.8130	−	119.188i	0.0881089	−	0.152609i
$782$	−216.810	−	375.526i	−0.277251	−	0.480213i
$783$	254.810			0.325428
$784$	50.4321	−	189.401i	0.0643267	−	0.241582i
$785$		0			0
$786$	152.708	+	264.499i	0.194285	+	0.336512i
$787$	−269.225	+	466.311i	−0.342090	+	0.592518i	−0.984821	−	0.173575i	$-0.944468\pi$
$787$	−269.225	+	466.311i	−0.342090	+	0.592518i	0.642731	+	0.766092i	$0.277801\pi$
$788$	−13.1944	−	7.61779i	−0.0167442	−	0.00966725i
$789$	473.707	−	273.495i	0.600389	−	0.346635i
$790$		0			0
$791$	43.3898	−	104.985i	0.0548544	−	0.132724i
$792$			9.81567i			0.0123935i
$793$	−81.9969	+	47.3409i	−0.103401	+	0.0596985i
$794$	177.784	+	102.644i	0.223909	+	0.129274i
$795$		0			0
$796$	349.589	−	201.836i	0.439183	−	0.253562i
$797$	−207.481			−0.260328			−0.130164	−	0.991492i	$-0.541550\pi$
$797$	−207.481			−0.260328			−0.130164	+	0.991492i	$0.541550\pi$
$798$	−43.4561	−	328.098i	−0.0544563	−	0.411150i
$799$	−317.871			−0.397836
$800$		0			0
$801$	394.866	+	227.976i	0.492966	+	0.284614i
$802$	262.148	+	151.351i	0.326867	+	0.188717i
$803$	22.8636	+	39.6010i	0.0284728	+	0.0493163i
$804$		−	431.247i		−	0.536376i
$805$		0			0
$806$	−603.911			−0.749269
$807$	71.7341	−	41.4157i	0.0888899	−	0.0513206i
$808$	55.2736	−	95.7366i	0.0684079	−	0.118486i
$809$	722.858	−	1252.03i	0.893520	−	1.54762i	0.0578954	−	0.998323i	$-0.481561\pi$
$809$	722.858	−	1252.03i	0.893520	−	1.54762i	0.835625	−	0.549300i	$-0.185106\pi$
$810$		0			0
$811$			207.868i			0.256310i	0.991754	+	0.128155i	$0.0409055\pi$
$811$			207.868i			0.256310i	−0.991754	+	0.128155i	$0.959094\pi$
$812$	−544.337	+	418.362i	−0.670366	+	0.515224i
$813$		−	589.161i		−	0.724675i
$814$	−43.6109	−	75.5363i	−0.0535760	−	0.0927964i
$815$		0			0
$816$	−43.7085	+	75.7054i	−0.0535644	+	0.0927762i
$817$	613.591	+	1062.77i	0.751029	+	1.30082i
$818$	−783.435			−0.957745
$819$	40.8571	+	308.475i	0.0498866	+	0.376648i
$820$		0			0
$821$	−307.642	−	532.851i	−0.374716	−	0.649027i	0.615568	−	0.788083i	$-0.288926\pi$
$821$	−307.642	−	532.851i	−0.374716	−	0.649027i	−0.990285	+	0.139056i	$0.955593\pi$
$822$	93.1613	−	161.360i	0.113335	−	0.196302i
$823$	290.645	+	167.804i	0.353153	+	0.203893i	0.666073	−	0.745886i	$-0.267974\pi$
$823$	290.645	+	167.804i	0.353153	+	0.203893i	−0.312920	+	0.949779i	$0.601307\pi$
$824$	−92.6961	+	53.5181i	−0.112495	+	0.0649492i
$825$		0			0
$826$	223.348	+	92.3091i	0.270397	+	0.111754i
$827$			1453.38i			1.75741i	0.477362	+	0.878707i	$0.341593\pi$
$827$			1453.38i			1.75741i	−0.477362	+	0.878707i	$0.658407\pi$
$828$	126.270	−	72.9022i	0.152500	−	0.0880461i
$829$	11.2468	+	6.49333i	0.0135667	+	0.00783273i	0.506768	−	0.862082i	$-0.330840\pi$
$829$	11.2468	+	6.49333i	0.0135667	+	0.00783273i	−0.493201	+	0.869915i	$0.664173\pi$
$830$		0			0
$831$	315.880	−	182.374i	0.380121	−	0.219463i
$832$	118.541			0.142477
$833$	596.943	−	160.952i	0.716618	−	0.193220i
$834$	−224.785			−0.269526
$835$		0			0
$836$	−38.6741	−	22.3285i	−0.0462609	−	0.0267087i
$837$	129.686	+	74.8743i	0.154942	+	0.0894555i
$838$	189.507	+	328.236i	0.226142	+	0.391689i
$839$			940.714i			1.12123i	0.828076	+	0.560616i	$0.189436\pi$
$839$			940.714i			1.12123i	−0.828076	+	0.560616i	$0.810564\pi$
$840$		0			0
$841$	1563.74			1.85939
$842$	11.1809	−	6.45529i	0.0132790	−	0.00766661i
$843$	408.578	−	707.678i	0.484671	−	0.839476i
$844$	30.3818	−	52.6228i	0.0359973	−	0.0623492i
$845$		0			0
$846$		−	106.884i		−	0.126340i
$847$	109.983	+	830.381i	0.129850	+	0.980379i
$848$			83.3281i			0.0982643i
$849$	405.534	+	702.406i	0.477661	+	0.827333i
$850$		0			0
$851$	−647.806	+	1122.03i	−0.761230	+	1.31849i
$852$	206.067	+	356.918i	0.241862	+	0.418917i
$853$	−1176.97			−1.37980			−0.689902	−	0.723903i	$-0.742346\pi$
$853$	−1176.97			−1.37980			−0.689902	+	0.723903i	$0.742346\pi$
$854$	−50.1543	+	38.5472i	−0.0587287	+	0.0451372i
$855$		0			0
$856$	−117.425	−	203.386i	−0.137179	−	0.237601i
$857$	239.902	−	415.523i	0.279933	−	0.484858i	−0.691435	−	0.722439i	$-0.743021\pi$
$857$	239.902	−	415.523i	0.279933	−	0.484858i	0.971368	+	0.237581i	$0.0763545\pi$
$858$	36.3611	+	20.9931i	0.0423789	+	0.0244675i
$859$	−1185.54	+	684.470i	−1.38014	+	0.796821i	−0.992175	−	0.124855i	$-0.960154\pi$
$859$	−1185.54	+	684.470i	−1.38014	+	0.796821i	−0.387960	+	0.921676i	$0.626820\pi$
$860$		0			0
$861$	281.052	+	365.681i	0.326425	+	0.424717i
$862$			379.635i			0.440412i
$863$	74.0758	−	42.7677i	0.0858352	−	0.0495570i	−0.456468	−	0.889740i	$-0.650886\pi$
$863$	74.0758	−	42.7677i	0.0858352	−	0.0495570i	0.542303	+	0.840183i	$0.317552\pi$
$864$	−25.4558	−	14.6969i	−0.0294628	−	0.0170103i
$865$		0			0
$866$	−578.391	+	333.934i	−0.667888	+	0.385605i
$867$	224.815			0.259302
$868$	−399.975	+	52.9762i	−0.460800	+	0.0610324i
$869$	107.432			0.123627
$870$		0			0
$871$	−1597.51	−	922.321i	−1.83411	−	1.05892i
$872$	−117.067	−	67.5886i	−0.134251	−	0.0775099i
$873$	216.464	+	374.927i	0.247955	+	0.429470i
$874$			663.346i			0.758977i
$875$		0			0
$876$	−136.934			−0.156318
$877$	409.863	−	236.635i	0.467347	−	0.269823i	−0.247781	−	0.968816i	$-0.579701\pi$
$877$	409.863	−	236.635i	0.467347	−	0.269823i	0.715128	+	0.698993i	$0.246368\pi$
$878$	388.479	−	672.865i	0.442459	−	0.766361i
$879$	54.9984	−	95.2601i	0.0625693	−	0.108373i
$880$		0			0
$881$			442.658i			0.502449i	0.967929	+	0.251225i	$0.0808333\pi$
$881$			442.658i			0.502449i	−0.967929	+	0.251225i	$0.919167\pi$
$882$	54.1200	+	200.721i	0.0613605	+	0.227575i
$883$			432.227i			0.489498i	0.969586	+	0.244749i	$0.0787056\pi$
$883$			432.227i			0.489498i	−0.969586	+	0.244749i	$0.921294\pi$
$884$	186.962	+	323.827i	0.211495	+	0.366320i
$885$		0			0
$886$	−332.913	+	576.622i	−0.375748	+	0.650815i
$887$	−260.739	−	451.613i	−0.293956	−	0.509146i	0.680786	−	0.732483i	$-0.261638\pi$
$887$	−260.739	−	451.613i	−0.293956	−	0.509146i	−0.974741	+	0.223337i	$0.928305\pi$
$888$	261.193			0.294136
$889$	215.407	−	521.191i	0.242302	−	0.586266i
$890$		0			0
$891$	−5.20555	−	9.01627i	−0.00584237	−	0.0101193i
$892$	−16.7377	+	28.9905i	−0.0187642	+	0.0325006i
$893$	421.125	+	243.137i	0.471585	+	0.272270i
$894$	209.832	−	121.147i	0.234712	−	0.135511i
$895$		0			0
$896$	78.5103	−	10.3986i	0.0876231	−	0.0116056i
$897$		−	623.673i		−	0.695287i
$898$	685.275	−	395.644i	0.763113	−	0.440583i
$899$	1223.90	+	706.619i	1.36140	+	0.786005i
$900$		0			0
$901$	−227.634	+	131.425i	−0.252646	+	0.145865i
$902$	62.2311			0.0689923
$903$	−469.733	−	611.177i	−0.520192	−	0.676830i
$904$	45.9004			0.0507748
$905$		0			0
$906$	−207.444	−	119.768i	−0.228967	−	0.132194i
$907$	1097.90	+	633.871i	1.21047	+	0.698865i	0.962862	−	0.269995i	$-0.0870220\pi$
$907$	1097.90	+	633.871i	1.21047	+	0.698865i	0.247608	+	0.968860i	$0.420355\pi$
$908$	423.472	+	733.475i	0.466379	+	0.807792i
$909$			117.253i			0.128991i
$910$		0			0
$911$	789.834			0.866997			0.433498	−	0.901154i	$-0.357279\pi$
$911$	789.834			0.866997			0.433498	+	0.901154i	$0.357279\pi$
$912$	115.813	−	66.8646i	0.126988	−	0.0733165i
$913$	3.35275	−	5.80713i	0.00367223	−	0.00636049i
$914$	443.623	−	768.378i	0.485364	−	0.840676i
$915$		0			0
$916$		−	809.668i		−	0.883916i
$917$	865.244	−	114.601i	0.943560	−	0.124973i
$918$		−	92.7198i		−	0.101002i
$919$	−506.816	−	877.831i	−0.551486	−	0.955202i	−0.998168	−	0.0605090i	$-0.980728\pi$
$919$	−506.816	−	877.831i	−0.551486	−	0.955202i	0.446681	−	0.894693i	$-0.352606\pi$
$920$		0			0
$921$	−183.260	+	317.415i	−0.198979	+	0.344642i
$922$	−158.151	−	273.925i	−0.171530	−	0.297098i
$923$	1762.88			1.90995
$924$	25.9238	+	10.7142i	0.0280561	+	0.0115955i
$925$		0			0
$926$	280.866	+	486.474i	0.303311	+	0.525350i
$927$	56.7645	−	98.3191i	0.0612347	−	0.106062i
$928$	−240.237	−	138.701i	−0.258876	−	0.149462i
$929$	−546.568	+	315.561i	−0.588340	+	0.339678i	−0.764441	−	0.644694i	$-0.776985\pi$
$929$	−546.568	+	315.561i	−0.588340	+	0.339678i	0.176101	+	0.984372i	$0.443652\pi$
$930$		0			0
$931$	−913.960	−	243.362i	−0.981697	−	0.261399i
$932$		−	554.596i		−	0.595061i
$933$	100.994	−	58.3090i	0.108247	−	0.0624963i
$934$	−408.727	−	235.979i	−0.437610	−	0.252654i
$935$		0			0
$936$	−108.886	+	62.8656i	−0.116332	+	0.0671641i
$937$	−867.113			−0.925414			−0.462707	−	0.886511i	$-0.653122\pi$
$937$	−867.113			−0.925414			−0.462707	+	0.886511i	$0.653122\pi$
$938$	−1138.95	−	470.724i	−1.21423	−	0.501838i
$939$	−239.428			−0.254982
$940$		0			0
$941$	−1151.28	−	664.692i	−1.22346	−	0.706367i	−0.257809	−	0.966196i	$-0.583001\pi$
$941$	−1151.28	−	664.692i	−1.22346	−	0.706367i	−0.965655	+	0.259829i	$0.916334\pi$
$942$	282.990	+	163.384i	0.300414	+	0.173444i
$943$	−462.197	−	800.550i	−0.490135	−	0.848939i
$944$			97.6502i			0.103443i
$945$		0			0
$946$	−104.009			−0.109946
$947$	1334.96	−	770.741i	1.40968	−	0.813877i	0.414319	−	0.910132i	$-0.364020\pi$
$947$	1334.96	−	770.741i	1.40968	−	0.813877i	0.995357	+	0.0962547i	$0.0306863\pi$
$948$	−160.858	+	278.613i	−0.169681	+	0.293896i
$949$	−292.866	+	507.258i	−0.308604	+	0.534519i
$950$		0			0
$951$			34.3367i			0.0361059i
$952$	152.233	+	198.073i	0.159908	+	0.208059i
$953$		−	114.779i		−	0.120439i	−0.998185	−	0.0602196i	$-0.980820\pi$
$953$		−	114.779i		−	0.120439i	0.998185	−	0.0602196i	$-0.0191801\pi$
$954$	−44.1914	−	76.5418i	−0.0463222	−	0.0802325i
$955$		0			0
$956$	−290.247	+	502.722i	−0.303605	+	0.525860i
$957$	−49.1268	−	85.0902i	−0.0513342	−	0.0889135i
$958$	861.020			0.898769
$959$	−324.472	−	422.176i	−0.338345	−	0.440225i
$960$		0			0
$961$	−65.2290	−	112.980i	−0.0678761	−	0.117565i
$962$	558.622	−	967.561i	0.580688	−	1.00578i
$963$	215.724	+	124.548i	0.224012	+	0.129333i
$964$	−701.147	+	404.808i	−0.727331	+	0.419925i
$965$		0			0
$966$	−54.7097	−	413.063i	−0.0566353	−	0.427602i
$967$			881.904i			0.912000i	0.889980	+	0.456000i	$0.150718\pi$
$967$			881.904i			0.912000i	−0.889980	+	0.456000i	$0.849282\pi$
$968$	−293.110	+	169.227i	−0.302800	+	0.174822i
$969$	365.319	+	210.917i	0.377007	+	0.217665i
$970$		0			0
$971$	407.102	−	235.041i	0.419261	−	0.242060i	−0.275500	−	0.961301i	$-0.588843\pi$
$971$	407.102	−	235.041i	0.419261	−	0.242060i	0.694761	+	0.719241i	$0.255510\pi$
$972$	31.1769			0.0320750
$973$	−245.362	+	593.670i	−0.252171	+	0.610144i
$974$	450.394			0.462417
$975$		0			0
$976$	−22.1350	−	12.7797i	−0.0226794	−	0.0130939i
$977$	−914.472	−	527.971i	−0.936000	−	0.540400i	−0.0472957	−	0.998881i	$-0.515060\pi$
$977$	−914.472	−	527.971i	−0.936000	−	0.540400i	−0.888704	+	0.458481i	$0.848394\pi$
$978$	−40.1094	−	69.4715i	−0.0410116	−	0.0710342i
$979$		−	175.813i		−	0.179584i
$980$		0			0
$981$	143.377			0.146154
$982$	−640.913	+	370.031i	−0.652661	+	0.376814i
$983$	73.9799	−	128.137i	0.0752593	−	0.130353i	−0.825940	−	0.563758i	$-0.809355\pi$
$983$	73.9799	−	128.137i	0.0752593	−	0.130353i	0.901199	+	0.433406i	$0.142688\pi$
$984$	−93.1781	+	161.389i	−0.0946932	+	0.164013i
$985$		0			0
$986$		−	875.034i		−	0.887458i
$987$	−282.286	−	116.668i	−0.286004	−	0.118205i
$988$		−	572.022i		−	0.578970i
$989$	772.489	+	1337.99i	0.781081	+	1.35287i
$990$		0			0
$991$	653.220	−	1131.41i	0.659153	−	1.14169i	−0.321682	−	0.946848i	$-0.604248\pi$
$991$	653.220	−	1131.41i	0.659153	−	1.14169i	0.980835	−	0.194839i	$-0.0624183\pi$
$992$	−81.5128	−	141.184i	−0.0821702	−	0.142323i
$993$	454.278			0.457480
$994$	1167.57	−	154.643i	1.17462	−	0.155577i
$995$		0			0
$996$	10.0401	+	17.3900i	0.0100804	+	0.0174598i
$997$	−176.798	+	306.223i	−0.177330	+	0.307145i	−0.940965	−	0.338503i	$-0.890079\pi$
$997$	−176.798	+	306.223i	−0.177330	+	0.307145i	0.763635	+	0.645648i	$0.223413\pi$
$998$	959.976	+	554.242i	0.961900	+	0.555353i
$999$	−239.921	+	138.519i	−0.240161	+	0.138657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.q.e.199.6		32
5.2	odd	4		210.3.o.b.31.3	✓	16
5.3	odd	4		1050.3.p.i.451.8		16
5.4	even	2	inner	1050.3.q.e.199.13		32
7.5	odd	6	inner	1050.3.q.e.649.14		32
15.2	even	4		630.3.v.c.451.5		16
35.12	even	12		210.3.o.b.61.3	yes	16
35.17	even	12		1470.3.f.d.391.10		16
35.19	odd	6	inner	1050.3.q.e.649.6		32
35.32	odd	12		1470.3.f.d.391.16		16
35.33	even	12		1050.3.p.i.901.8		16
105.47	odd	12		630.3.v.c.271.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.3	✓	16	5.2	odd	4
210.3.o.b.61.3	yes	16	35.12	even	12
630.3.v.c.271.5		16	105.47	odd	12
630.3.v.c.451.5		16	15.2	even	4
1050.3.p.i.451.8		16	5.3	odd	4
1050.3.p.i.901.8		16	35.33	even	12
1050.3.q.e.199.6		32	1.1	even	1	trivial
1050.3.q.e.199.13		32	5.4	even	2	inner
1050.3.q.e.649.6		32	35.19	odd	6	inner
1050.3.q.e.649.14		32	7.5	odd	6	inner
1470.3.f.d.391.10		16	35.17	even	12
1470.3.f.d.391.16		16	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(6.46925 + 2.67372i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(6.46925 + 2.67372i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-0.578394 + 1.00181i) q^{11} +(-1.73205 - 3.00000i) q^{12} -14.8176 q^{13} +(-9.81379 + 1.29982i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(6.30878 - 10.9271i) q^{17} +(3.67423 + 2.12132i) q^{18} +(-16.7162 + 9.65108i) q^{19} +(9.61312 - 7.38837i) q^{21} -1.63595i q^{22} +(-21.0450 + 12.1504i) q^{23} +(4.24264 + 2.44949i) q^{24} +(18.1477 - 10.4776i) q^{26} -5.19615 q^{27} +(11.1003 - 8.53135i) q^{28} -49.0382 q^{29} +(-24.9581 - 14.4096i) q^{31} +(4.89898 + 2.82843i) q^{32} +(1.00181 + 1.73518i) q^{33} +17.8439i q^{34} -6.00000 q^{36} +(46.1728 - 26.6579i) q^{37} +(13.6487 - 23.6402i) q^{38} +(-12.8324 + 22.2264i) q^{39} +38.0398i q^{41} +(-6.54925 + 15.8464i) q^{42} -63.5774i q^{43} +(1.15679 + 2.00362i) q^{44} +(17.1832 - 29.7622i) q^{46} +(-12.5964 - 21.8175i) q^{47} -6.92820 q^{48} +(34.7024 + 34.5940i) q^{49} +(-10.9271 - 18.9263i) q^{51} +(-14.8176 + 25.6648i) q^{52} +(-18.0411 - 10.4160i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-7.56243 + 18.2978i) q^{56} +33.4323i q^{57} +(60.0593 - 34.6752i) q^{58} +(-21.1419 - 12.2063i) q^{59} +(5.53376 - 3.19492i) q^{61} +40.7564 q^{62} +(-2.75734 - 20.8182i) q^{63} -8.00000 q^{64} +(-2.45392 - 1.41677i) q^{66} +(107.812 + 62.2451i) q^{67} +(-12.6176 - 21.8543i) q^{68} +42.0901i q^{69} -118.973 q^{71} +(7.34847 - 4.24264i) q^{72} +(19.7648 - 34.2336i) q^{73} +(-37.7000 + 65.2983i) q^{74} +38.6043i q^{76} +(-6.42033 + 4.93448i) q^{77} -36.2955i q^{78} +(-46.4356 - 80.4288i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-26.8982 - 46.5891i) q^{82} -5.79665 q^{83} +(-3.18391 - 24.0388i) q^{84} +(44.9560 + 77.8661i) q^{86} +(-42.4683 + 73.5573i) q^{87} +(-2.83354 - 1.63595i) q^{88} +(-131.622 + 75.9919i) q^{89} +(-95.8586 - 39.6181i) q^{91} +48.6014i q^{92} +(-43.2287 + 24.9581i) q^{93} +(30.8546 + 17.8139i) q^{94} +(8.48528 - 4.89898i) q^{96} -144.310 q^{97} +(-66.9632 - 17.8305i) q^{98} +3.47036 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} - 48 q^{9}+O(q^{10}) \) 32 * q + 32 * q^4 - 48 * q^9	\( 32 q + 32 q^{4} - 48 q^{9} - 8 q^{11} - 16 q^{14} - 64 q^{16} + 144 q^{19} - 48 q^{21} - 144 q^{29} + 240 q^{31} - 192 q^{36} - 72 q^{39} + 16 q^{44} + 16 q^{46} + 80 q^{49} - 24 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 256 q^{64} + 144 q^{66} - 272 q^{71} + 224 q^{74} - 560 q^{79} - 144 q^{81} + 48 q^{84} - 176 q^{86} + 600 q^{89} - 544 q^{91} + 48 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 - 48 * q^9 - 8 * q^11 - 16 * q^14 - 64 * q^16 + 144 * q^19 - 48 * q^21 - 144 * q^29 + 240 * q^31 - 192 * q^36 - 72 * q^39 + 16 * q^44 + 16 * q^46 + 80 * q^49 - 24 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 256 * q^64 + 144 * q^66 - 272 * q^71 + 224 * q^74 - 560 * q^79 - 144 * q^81 + 48 * q^84 - 176 * q^86 + 600 * q^89 - 544 * q^91 + 48 * q^99

Introduction

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