LMFDB - Embedded newform 1050.3.q.d.649.8

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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			649.8
Character	$\chi$	$=$	1050.649
Dual form			1050.3.q.d.199.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 + 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(1.64177 - 6.80475i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.22474 + 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(1.64177 - 6.80475i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(8.87741 + 15.3761i) q^{11} +(1.73205 - 3.00000i) q^{12} -2.00882 q^{13} +(6.82244 - 7.17317i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-10.6048 - 18.3681i) q^{17} +(-3.67423 + 2.12132i) q^{18} +(5.70198 + 3.29204i) q^{19} +(-11.6289 + 3.43042i) q^{21} +25.1091i q^{22} +(34.1271 + 19.7033i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-2.46029 - 1.42045i) q^{26} +5.19615 q^{27} +(13.4279 - 3.96111i) q^{28} +25.1091 q^{29} +(4.76798 - 2.75280i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(15.3761 - 26.6322i) q^{33} -29.9950i q^{34} -6.00000 q^{36} +(-10.1772 - 5.87580i) q^{37} +(4.65565 + 8.06382i) q^{38} +(1.73969 + 3.01323i) q^{39} -16.8812i q^{41} +(-16.6682 - 4.02151i) q^{42} +27.7474i q^{43} +(-17.7548 + 30.7523i) q^{44} +(27.8647 + 48.2631i) q^{46} +(22.8388 - 39.5579i) q^{47} +6.92820 q^{48} +(-43.6092 - 22.3437i) q^{49} +(-18.3681 + 31.8145i) q^{51} +(-2.00882 - 3.47938i) q^{52} +(85.2621 - 49.2261i) q^{53} +(6.36396 + 3.67423i) q^{54} +(19.2467 + 4.64364i) q^{56} -11.4040i q^{57} +(30.7523 + 17.7548i) q^{58} +(-10.9872 + 6.34348i) q^{59} +(82.0429 + 47.3675i) q^{61} +7.78609 q^{62} +(15.2166 + 14.4726i) q^{63} -8.00000 q^{64} +(37.6637 - 21.7451i) q^{66} +(-7.23310 + 4.17603i) q^{67} +(21.2096 - 36.7362i) q^{68} -68.2543i q^{69} +71.8225 q^{71} +(-7.34847 - 4.24264i) q^{72} +(-0.402972 - 0.697968i) q^{73} +(-8.30963 - 14.3927i) q^{74} +13.1682i q^{76} +(119.205 - 35.1644i) q^{77} +4.92058i q^{78} +(58.1846 - 100.779i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(11.9368 - 20.6752i) q^{82} +50.1243 q^{83} +(-17.5706 - 16.7115i) q^{84} +(-19.6204 + 33.9835i) q^{86} +(-21.7451 - 37.6637i) q^{87} +(-43.4903 + 25.1091i) q^{88} +(-74.9322 - 43.2621i) q^{89} +(-3.29803 + 13.6695i) q^{91} +78.8133i q^{92} +(-8.25839 - 4.76798i) q^{93} +(55.9433 - 32.2989i) q^{94} +(8.48528 + 4.89898i) q^{96} +165.642 q^{97} +(-37.6107 - 58.2017i) q^{98} -53.2645 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} - 36 q^{9}+O(q^{10}) $ 24 * q + 24 * q^4 - 36 * q^9	$ 24 q + 24 q^{4} - 36 q^{9} - 8 q^{11} - 16 q^{14} - 48 q^{16} - 24 q^{19} + 36 q^{21} - 48 q^{26} + 48 q^{29} - 396 q^{31} - 144 q^{36} + 72 q^{39} + 16 q^{44} + 64 q^{46} - 56 q^{49} - 48 q^{51} + 80 q^{56} + 96 q^{59} + 372 q^{61} - 192 q^{64} + 72 q^{66} - 272 q^{71} + 128 q^{74} + 140 q^{79} - 108 q^{81} + 24 q^{84} - 416 q^{86} - 336 q^{89} + 584 q^{91} + 408 q^{94} + 48 q^{99}+O(q^{100}) $ 24 * q + 24 * q^4 - 36 * q^9 - 8 * q^11 - 16 * q^14 - 48 * q^16 - 24 * q^19 + 36 * q^21 - 48 * q^26 + 48 * q^29 - 396 * q^31 - 144 * q^36 + 72 * q^39 + 16 * q^44 + 64 * q^46 - 56 * q^49 - 48 * q^51 + 80 * q^56 + 96 * q^59 + 372 * q^61 - 192 * q^64 + 72 * q^66 - 272 * q^71 + 128 * q^74 + 140 * q^79 - 108 * q^81 + 24 * q^84 - 416 * q^86 - 336 * q^89 + 584 * q^91 + 408 * q^94 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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
$7$	1.64177	−	6.80475i	0.234539	−	0.972107i
$7$	1.64177	−	6.80475i	0.234539	−	0.972107i
$8$			2.82843i			0.353553i
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$		0			0
$11$	8.87741	+	15.3761i	0.807038	+	1.39783i	0.914907	+	0.403665i	$0.132264\pi$
$11$	8.87741	+	15.3761i	0.807038	+	1.39783i	−0.107869	+	0.994165i	$0.534403\pi$
$12$	1.73205	−	3.00000i	0.144338	−	0.250000i
$13$	−2.00882			−0.154525			−0.0772623	−	0.997011i	$-0.524618\pi$
$13$	−2.00882			−0.154525			−0.0772623	+	0.997011i	$0.524618\pi$
$14$	6.82244	−	7.17317i	0.487317	−	0.512369i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−10.6048	−	18.3681i	−0.623813	−	1.08048i	−0.988769	−	0.149451i	$-0.952249\pi$
$17$	−10.6048	−	18.3681i	−0.623813	−	1.08048i	0.364956	−	0.931025i	$-0.381084\pi$
$18$	−3.67423	+	2.12132i	−0.204124	+	0.117851i
$19$	5.70198	+	3.29204i	0.300104	+	0.173265i	0.642490	−	0.766294i	$-0.277902\pi$
$19$	5.70198	+	3.29204i	0.300104	+	0.173265i	−0.342386	+	0.939560i	$0.611235\pi$
$20$		0			0
$21$	−11.6289	+	3.43042i	−0.553759	+	0.163353i
$22$			25.1091i			1.14132i
$23$	34.1271	+	19.7033i	1.48379	+	0.856666i	0.999830	−	0.0184250i	$-0.00586519\pi$
$23$	34.1271	+	19.7033i	1.48379	+	0.856666i	0.483959	+	0.875091i	$0.339199\pi$
$24$	4.24264	−	2.44949i	0.176777	−	0.102062i
$25$		0			0
$26$	−2.46029	−	1.42045i	−0.0946266	−	0.0546327i
$27$	5.19615			0.192450
$28$	13.4279	−	3.96111i	0.479569	−	0.141468i
$29$	25.1091			0.865832			0.432916	−	0.901434i	$-0.357485\pi$
$29$	25.1091			0.865832			0.432916	+	0.901434i	$0.357485\pi$
$30$		0			0
$31$	4.76798	−	2.75280i	0.153806	−	0.0887999i	−0.421122	−	0.907004i	$-0.638363\pi$
$31$	4.76798	−	2.75280i	0.153806	−	0.0887999i	0.574928	+	0.818204i	$0.305030\pi$
$32$	−4.89898	+	2.82843i	−0.153093	+	0.0883883i
$33$	15.3761	−	26.6322i	0.465943	−	0.807038i
$34$		−	29.9950i		−	0.882205i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	−10.1772	−	5.87580i	−0.275059	−	0.158805i	0.356125	−	0.934438i	$-0.384098\pi$
$37$	−10.1772	−	5.87580i	−0.275059	−	0.158805i	−0.631184	+	0.775633i	$0.717431\pi$
$38$	4.65565	+	8.06382i	0.122517	+	0.212206i
$39$	1.73969	+	3.01323i	0.0446074	+	0.0772623i
$40$		0			0
$41$		−	16.8812i		−	0.411737i	−0.978580	−	0.205868i	$-0.933998\pi$
$41$		−	16.8812i		−	0.411737i	0.978580	−	0.205868i	$-0.0660019\pi$
$42$	−16.6682	−	4.02151i	−0.396861	−	0.0957502i
$43$			27.7474i			0.645290i	0.946520	+	0.322645i	$0.104572\pi$
$43$			27.7474i			0.645290i	−0.946520	+	0.322645i	$0.895428\pi$
$44$	−17.7548	+	30.7523i	−0.403519	+	0.698915i
$45$		0			0
$46$	27.8647	+	48.2631i	0.605754	+	1.04920i
$47$	22.8388	−	39.5579i	0.485931	−	0.841657i	−0.513938	−	0.857827i	$-0.671814\pi$
$47$	22.8388	−	39.5579i	0.485931	−	0.841657i	0.999869	+	0.0161700i	$0.00514730\pi$
$48$	6.92820			0.144338
$49$	−43.6092	−	22.3437i	−0.889983	−	0.455994i
$50$		0			0
$51$	−18.3681	+	31.8145i	−0.360159	+	0.623813i
$52$	−2.00882	−	3.47938i	−0.0386311	−	0.0669111i
$53$	85.2621	−	49.2261i	1.60872	−	0.928794i	0.619061	−	0.785343i	$-0.287513\pi$
$53$	85.2621	−	49.2261i	1.60872	−	0.928794i	0.989657	−	0.143451i	$-0.0458199\pi$
$54$	6.36396	+	3.67423i	0.117851	+	0.0680414i
$55$		0			0
$56$	19.2467	+	4.64364i	0.343692	+	0.0829221i
$57$		−	11.4040i		−	0.200069i
$58$	30.7523	+	17.7548i	0.530211	+	0.306118i
$59$	−10.9872	+	6.34348i	−0.186224	+	0.107517i	−0.590214	−	0.807247i	$-0.700957\pi$
$59$	−10.9872	+	6.34348i	−0.186224	+	0.107517i	0.403990	+	0.914764i	$0.367623\pi$
$60$		0			0
$61$	82.0429	+	47.3675i	1.34497	+	0.776517i	0.987531	−	0.157422i	$-0.0503182\pi$
$61$	82.0429	+	47.3675i	1.34497	+	0.776517i	0.357435	+	0.933938i	$0.383652\pi$
$62$	7.78609			0.125582
$63$	15.2166	+	14.4726i	0.241533	+	0.229723i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	37.6637	−	21.7451i	0.570662	−	0.329472i
$67$	−7.23310	+	4.17603i	−0.107957	+	0.0623289i	−0.553006	−	0.833177i	$-0.686519\pi$
$67$	−7.23310	+	4.17603i	−0.107957	+	0.0623289i	0.445049	+	0.895506i	$0.353186\pi$
$68$	21.2096	−	36.7362i	0.311907	−	0.540238i
$69$		−	68.2543i		−	0.989193i
$70$		0			0
$71$	71.8225			1.01158			0.505792	−	0.862655i	$-0.331200\pi$
$71$	71.8225			1.01158			0.505792	+	0.862655i	$0.331200\pi$
$72$	−7.34847	−	4.24264i	−0.102062	−	0.0589256i
$73$	−0.402972	−	0.697968i	−0.00552017	−	0.00956121i	0.863252	−	0.504773i	$-0.168424\pi$
$73$	−0.402972	−	0.697968i	−0.00552017	−	0.00956121i	−0.868772	+	0.495212i	$0.835090\pi$
$74$	−8.30963	−	14.3927i	−0.112292	−	0.194496i
$75$		0			0
$76$			13.1682i			0.173265i
$77$	119.205	−	35.1644i	1.54812	−	0.456681i
$78$			4.92058i			0.0630844i
$79$	58.1846	−	100.779i	0.736514	−	1.27568i	−0.217542	−	0.976051i	$-0.569804\pi$
$79$	58.1846	−	100.779i	0.736514	−	1.27568i	0.954056	−	0.299628i	$-0.0968627\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	11.9368	−	20.6752i	0.145571	−	0.252136i
$83$	50.1243			0.603907			0.301953	−	0.953323i	$-0.402361\pi$
$83$	50.1243			0.603907			0.301953	+	0.953323i	$0.402361\pi$
$84$	−17.5706	−	16.7115i	−0.209174	−	0.198946i
$85$		0			0
$86$	−19.6204	+	33.9835i	−0.228144	+	0.395158i
$87$	−21.7451	−	37.6637i	−0.249944	−	0.432916i
$88$	−43.4903	+	25.1091i	−0.494208	+	0.285331i
$89$	−74.9322	−	43.2621i	−0.841935	−	0.486091i	0.0159868	−	0.999872i	$-0.494911\pi$
$89$	−74.9322	−	43.2621i	−0.841935	−	0.486091i	−0.857921	+	0.513781i	$0.828244\pi$
$90$		0			0
$91$	−3.29803	+	13.6695i	−0.0362420	+	0.150214i
$92$			78.8133i			0.856666i
$93$	−8.25839	−	4.76798i	−0.0887999	−	0.0512687i
$94$	55.9433	−	32.2989i	0.595141	−	0.343605i
$95$		0			0
$96$	8.48528	+	4.89898i	0.0883883	+	0.0510310i
$97$	165.642			1.70765			0.853823	−	0.520563i	$-0.174278\pi$
$97$	165.642			1.70765			0.853823	+	0.520563i	$0.174278\pi$
$98$	−37.6107	−	58.2017i	−0.383783	−	0.593895i
$99$	−53.2645			−0.538025
$100$		0			0
$101$	−170.953	+	98.7000i	−1.69261	+	0.977227i	−0.740206	+	0.672380i	$0.765272\pi$
$101$	−170.953	+	98.7000i	−1.69261	+	0.977227i	−0.952401	+	0.304847i	$0.901395\pi$
$102$	−44.9925	+	25.9764i	−0.441103	+	0.254671i
$103$	−35.3612	+	61.2474i	−0.343313	+	0.594635i	−0.985046	−	0.172293i	$-0.944882\pi$
$103$	−35.3612	+	61.2474i	−0.343313	+	0.594635i	0.641733	+	0.766928i	$0.278216\pi$
$104$		−	5.68180i		−	0.0546327i
$105$		0			0
$106$	139.232			1.31351
$107$	27.6788	+	15.9804i	0.258680	+	0.149349i	0.623732	−	0.781638i	$-0.285615\pi$
$107$	27.6788	+	15.9804i	0.258680	+	0.149349i	−0.365052	+	0.930987i	$0.618949\pi$
$108$	5.19615	+	9.00000i	0.0481125	+	0.0833333i
$109$	106.026	+	183.643i	0.972717	+	1.68479i	0.687273	+	0.726399i	$0.258808\pi$
$109$	106.026	+	183.643i	0.972717	+	1.68479i	0.285444	+	0.958396i	$0.407859\pi$
$110$		0			0
$111$			20.3544i			0.183373i
$112$	20.2888	+	19.2968i	0.181150	+	0.172293i
$113$			91.0393i			0.805657i	0.915275	+	0.402829i	$0.131973\pi$
$113$			91.0393i			0.805657i	−0.915275	+	0.402829i	$0.868027\pi$
$114$	8.06382	−	13.9669i	0.0707352	−	0.122517i
$115$		0			0
$116$	25.1091	+	43.4903i	0.216458	+	0.374916i
$117$	3.01323	−	5.21906i	0.0257541	−	0.0446074i
$118$	−17.9421			−0.152051
$119$	−142.401	+	42.0069i	−1.19665	+	0.352999i
$120$		0			0
$121$	−97.1170	+	168.212i	−0.802620	+	1.39018i
$122$	66.9878	+	116.026i	0.549080	+	0.951035i
$123$	−25.3218	+	14.6195i	−0.205868	+	0.118858i
$124$	9.53597	+	5.50559i	0.0769030	+	0.0444000i
$125$		0			0
$126$	8.40279	+	28.4850i	0.0666888	+	0.226071i
$127$		−	160.943i		−	1.26727i	−0.773632	−	0.633635i	$-0.781562\pi$
$127$		−	160.943i		−	1.26727i	0.773632	−	0.633635i	$-0.218438\pi$
$128$	−9.79796	−	5.65685i	−0.0765466	−	0.0441942i
$129$	41.6212	−	24.0300i	0.322645	−	0.186279i
$130$		0			0
$131$	−14.4620	−	8.34962i	−0.110397	−	0.0637375i	0.443785	−	0.896133i	$-0.353635\pi$
$131$	−14.4620	−	8.34962i	−0.110397	−	0.0637375i	−0.554182	+	0.832396i	$0.686969\pi$
$132$	61.5045			0.465943
$133$	31.7629	−	33.3957i	0.238818	−	0.251096i
$134$	−11.8116			−0.0881463
$135$		0			0
$136$	51.9528	−	29.9950i	0.382006	−	0.220551i
$137$	109.602	−	63.2788i	0.800015	−	0.461889i	−0.0434613	−	0.999055i	$-0.513839\pi$
$137$	109.602	−	63.2788i	0.800015	−	0.461889i	0.843476	+	0.537166i	$0.180505\pi$
$138$	48.2631	−	83.5941i	0.349732	−	0.605754i
$139$		−	135.361i		−	0.973820i	−0.873452	−	0.486910i	$-0.838124\pi$
$139$		−	135.361i		−	0.973820i	0.873452	−	0.486910i	$-0.161876\pi$
$140$		0			0
$141$	−79.1158			−0.561105
$142$	87.9643	+	50.7862i	0.619467	+	0.357649i
$143$	−17.8331	−	30.8879i	−0.124707	−	0.215999i
$144$	−6.00000	−	10.3923i	−0.0416667	−	0.0721688i
$145$		0			0
$146$		−	1.13978i		−	0.00780669i
$147$	4.25108	+	84.7640i	0.0289189	+	0.576626i
$148$		−	23.5032i		−	0.158805i
$149$	−40.3068	+	69.8135i	−0.270516	+	0.468547i	−0.968994	−	0.247084i	$-0.920527\pi$
$149$	−40.3068	+	69.8135i	−0.270516	+	0.468547i	0.698478	+	0.715631i	$0.253861\pi$
$150$		0			0
$151$	6.96796	+	12.0689i	0.0461454	+	0.0799262i	0.888176	−	0.459504i	$-0.151973\pi$
$151$	6.96796	+	12.0689i	0.0461454	+	0.0799262i	−0.842030	+	0.539430i	$0.818640\pi$
$152$	−9.31129	+	16.1276i	−0.0612585	+	0.106103i
$153$	63.6289			0.415875
$154$	170.861	+	41.2235i	1.10949	+	0.267685i
$155$		0			0
$156$	−3.47938	+	6.02646i	−0.0223037	+	0.0386311i
$157$	12.6333	+	21.8815i	0.0804669	+	0.139373i	0.903451	−	0.428692i	$-0.141026\pi$
$157$	12.6333	+	21.8815i	0.0804669	+	0.139373i	−0.822984	+	0.568065i	$0.807692\pi$
$158$	142.523	−	82.2854i	0.902041	−	0.520794i
$159$	−147.678	−	85.2621i	−0.928794	−	0.536239i
$160$		0			0
$161$	190.105	−	199.878i	1.18078	−	1.24148i
$162$		−	12.7279i		−	0.0785674i
$163$	−48.2658	−	27.8663i	−0.296109	−	0.170959i	0.344585	−	0.938755i	$-0.388020\pi$
$163$	−48.2658	−	27.8663i	−0.296109	−	0.170959i	−0.640694	+	0.767797i	$0.721353\pi$
$164$	29.2391	−	16.8812i	0.178287	−	0.102934i
$165$		0			0
$166$	61.3895	+	35.4432i	0.369816	+	0.213513i
$167$	−262.461			−1.57163			−0.785813	−	0.618464i	$-0.787755\pi$
$167$	−262.461			−1.57163			−0.785813	+	0.618464i	$0.787755\pi$
$168$	−9.70270	−	32.8916i	−0.0577542	−	0.195783i
$169$	−164.965			−0.976122
$170$		0			0
$171$	−17.1059	+	9.87612i	−0.100035	+	0.0577551i
$172$	−48.0600	+	27.7474i	−0.279419	+	0.161322i
$173$	79.1694	−	137.125i	0.457627	−	0.792632i	−0.541208	−	0.840888i	$-0.682033\pi$
$173$	79.1694	−	137.125i	0.457627	−	0.792632i	0.998835	+	0.0482560i	$0.0153663\pi$
$174$		−	61.5045i		−	0.353474i
$175$		0			0
$176$	−71.0193			−0.403519
$177$	19.0304	+	10.9872i	0.107517	+	0.0620747i
$178$	−61.1819	−	105.970i	−0.343718	−	0.595338i
$179$	−5.01415	−	8.68475i	−0.0280120	−	0.0485182i	0.851680	−	0.524063i	$-0.175584\pi$
$179$	−5.01415	−	8.68475i	−0.0280120	−	0.0485182i	−0.879692	+	0.475545i	$0.842251\pi$
$180$		0			0
$181$			318.143i			1.75770i	0.477101	+	0.878848i	$0.341688\pi$
$181$			318.143i			1.75770i	−0.477101	+	0.878848i	$0.658312\pi$
$182$	−13.7050	+	14.4096i	−0.0753024	+	0.0791736i
$183$		−	164.086i		−	0.896644i
$184$	−55.7294	+	96.5261i	−0.302877	+	0.524599i
$185$		0			0
$186$	−6.74295	−	11.6791i	−0.0362524	−	0.0627910i
$187$	188.287	−	326.122i	1.00688	−	1.74397i
$188$	91.3550			0.485931
$189$	8.53091	−	35.3585i	0.0451371	−	0.187082i
$190$		0			0
$191$	1.85642	−	3.21541i	0.00971946	−	0.0168346i	−0.861125	−	0.508394i	$-0.830239\pi$
$191$	1.85642	−	3.21541i	0.00971946	−	0.0168346i	0.870844	+	0.491559i	$0.163573\pi$
$192$	6.92820	+	12.0000i	0.0360844	+	0.0625000i
$193$	−255.946	+	147.770i	−1.32614	+	0.765649i	−0.984701	−	0.174253i	$-0.944249\pi$
$193$	−255.946	+	147.770i	−1.32614	+	0.765649i	−0.341443	+	0.939903i	$0.610916\pi$
$194$	202.869	+	117.126i	1.04572	+	0.603744i
$195$		0			0
$196$	−4.90872	−	97.8770i	−0.0250445	−	0.499372i
$197$		−	231.134i		−	1.17327i	−0.809852	−	0.586635i	$-0.800452\pi$
$197$		−	231.134i		−	1.17327i	0.809852	−	0.586635i	$-0.199548\pi$
$198$	−65.2354	−	37.6637i	−0.329472	−	0.190221i
$199$	25.3639	−	14.6438i	0.127457	−	0.0735871i	−0.434916	−	0.900471i	$-0.643222\pi$
$199$	25.3639	−	14.6438i	0.127457	−	0.0735871i	0.562373	+	0.826884i	$0.309889\pi$
$200$		0			0
$201$	12.5281	+	7.23310i	0.0623289	+	0.0359856i
$202$	−279.166			−1.38201
$203$	41.2235	−	170.861i	0.203071	−	0.841681i
$204$	−73.4724			−0.360159
$205$		0			0
$206$	−86.6169	+	50.0083i	−0.420470	+	0.242759i
$207$	−102.381	+	59.1099i	−0.494596	+	0.285555i
$208$	4.01764	−	6.95875i	0.0193156	−	0.0334555i
$209$			116.899i			0.559326i
$210$		0			0
$211$	−254.413			−1.20575			−0.602874	−	0.797836i	$-0.705978\pi$
$211$	−254.413			−1.20575			−0.602874	+	0.797836i	$0.705978\pi$
$212$	170.524	+	98.4522i	0.804359	+	0.464397i
$213$	−62.2001	−	107.734i	−0.292019	−	0.505792i
$214$	22.5996	+	39.1437i	0.105606	+	0.182915i
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	−10.9041	−	36.9644i	−0.0502495	−	0.170343i
$218$			299.887i			1.37563i
$219$	−0.697968	+	1.20892i	−0.00318707	+	0.00552017i
$220$		0			0
$221$	21.3032	+	36.8982i	0.0963944	+	0.166960i
$222$	−14.3927	+	24.9289i	−0.0648320	+	0.112292i
$223$	−197.116			−0.883927			−0.441964	−	0.897033i	$-0.645718\pi$
$223$	−197.116			−0.883927			−0.441964	+	0.897033i	$0.645718\pi$
$224$	11.2037	+	37.9800i	0.0500166	+	0.169553i
$225$		0			0
$226$	−64.3745	+	111.500i	−0.284843	+	0.493362i
$227$	143.214	+	248.054i	0.630900	+	1.09275i	0.987368	+	0.158443i	$0.0506476\pi$
$227$	143.214	+	248.054i	0.630900	+	1.09275i	−0.356468	+	0.934308i	$0.616019\pi$
$228$	19.7522	−	11.4040i	0.0866326	−	0.0500174i
$229$	178.628	+	103.131i	0.780034	+	0.450353i	0.836442	−	0.548055i	$-0.184632\pi$
$229$	178.628	+	103.131i	0.780034	+	0.450353i	−0.0564084	+	0.998408i	$0.517965\pi$
$230$		0			0
$231$	−155.982	−	148.355i	−0.675245	−	0.642229i
$232$			71.0193i			0.306118i
$233$	−5.96951	−	3.44650i	−0.0256202	−	0.0147918i	0.487135	−	0.873327i	$-0.338042\pi$
$233$	−5.96951	−	3.44650i	−0.0256202	−	0.0147918i	−0.512755	+	0.858535i	$0.671375\pi$
$234$	7.38087	−	4.26135i	0.0315422	−	0.0182109i
$235$		0			0
$236$	−21.9744	−	12.6870i	−0.0931121	−	0.0537583i
$237$	−201.557			−0.850453
$238$	−204.108	−	49.2450i	−0.857598	−	0.206912i
$239$	−289.962			−1.21323			−0.606615	−	0.794995i	$-0.707473\pi$
$239$	−289.962			−1.21323			−0.606615	+	0.794995i	$0.707473\pi$
$240$		0			0
$241$	282.791	−	163.270i	1.17341	−	0.677467i	0.218927	−	0.975741i	$-0.429744\pi$
$241$	282.791	−	163.270i	1.17341	−	0.677467i	0.954480	+	0.298274i	$0.0964110\pi$
$242$	−237.887	+	137.344i	−0.983004	+	0.567538i
$243$	−7.79423	+	13.5000i	−0.0320750	+	0.0555556i
$244$			189.470i			0.776517i
$245$		0			0
$246$	−41.3503			−0.168091
$247$	−11.4542	−	6.61311i	−0.0463735	−	0.0267737i
$248$	7.78609	+	13.4859i	0.0313955	+	0.0543786i
$249$	−43.4089	−	75.1864i	−0.174333	−	0.301953i
$250$		0			0
$251$		−	341.759i		−	1.36159i	−0.732474	−	0.680795i	$-0.761634\pi$
$251$		−	341.759i		−	1.36159i	0.732474	−	0.680795i	$-0.238366\pi$
$252$	−9.85064	+	40.8285i	−0.0390898	+	0.162018i
$253$			699.658i			2.76545i
$254$	113.804	−	197.115i	0.448048	−	0.776042i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	97.4226	−	168.741i	0.379076	−	0.656579i	−0.611852	−	0.790972i	$-0.709575\pi$
$257$	97.4226	−	168.741i	0.379076	−	0.656579i	0.990928	+	0.134393i	$0.0429085\pi$
$258$	67.9671			0.263438
$259$	−56.6920	+	59.6064i	−0.218888	+	0.230141i
$260$		0			0
$261$	−37.6637	+	65.2354i	−0.144305	+	0.249944i
$262$	−11.8081	−	20.4523i	−0.0450692	−	0.0780622i
$263$	119.568	−	69.0324i	0.454630	−	0.262481i	−0.255154	−	0.966900i	$-0.582126\pi$
$263$	119.568	−	69.0324i	0.454630	−	0.262481i	0.709783	+	0.704420i	$0.248793\pi$
$264$	75.3274	+	43.4903i	0.285331	+	0.164736i
$265$		0			0
$266$	62.5157	−	18.4415i	0.235022	−	0.0693291i
$267$			149.864i			0.561290i
$268$	−14.4662	−	8.35207i	−0.0539784	−	0.0311644i
$269$	−8.57284	+	4.94953i	−0.0318693	+	0.0183998i	−0.515850	−	0.856679i	$-0.672524\pi$
$269$	−8.57284	+	4.94953i	−0.0318693	+	0.0183998i	0.483981	+	0.875079i	$0.339190\pi$
$270$		0			0
$271$	−16.4712	−	9.50963i	−0.0607792	−	0.0350909i	0.469302	−	0.883037i	$-0.344505\pi$
$271$	−16.4712	−	9.50963i	−0.0607792	−	0.0350909i	−0.530082	+	0.847947i	$0.677839\pi$
$272$	84.8386			0.311907
$273$	23.3604	−	6.89110i	0.0855693	−	0.0252421i
$274$	178.979			0.653210
$275$		0			0
$276$	118.220	−	68.2543i	0.428333	−	0.247298i
$277$	−177.936	+	102.731i	−0.642367	+	0.370871i	−0.785526	−	0.618829i	$-0.787607\pi$
$277$	−177.936	+	102.731i	−0.642367	+	0.370871i	0.143159	+	0.989700i	$0.454274\pi$
$278$	95.7147	−	165.783i	0.344297	−	0.596340i
$279$			16.5168i			0.0591999i
$280$		0			0
$281$	−449.661			−1.60022			−0.800109	−	0.599854i	$-0.795225\pi$
$281$	−449.661			−1.60022			−0.800109	+	0.599854i	$0.795225\pi$
$282$	−96.8966	−	55.9433i	−0.343605	−	0.198380i
$283$	79.5371	+	137.762i	0.281050	+	0.486792i	0.971644	−	0.236450i	$-0.0759841\pi$
$283$	79.5371	+	137.762i	0.281050	+	0.486792i	−0.690594	+	0.723243i	$0.742651\pi$
$284$	71.8225	+	124.400i	0.252896	+	0.438029i
$285$		0			0
$286$		−	50.4397i		−	0.176363i
$287$	−114.872	−	27.7151i	−0.400252	−	0.0965683i
$288$		−	16.9706i		−	0.0589256i
$289$	−80.4246	+	139.300i	−0.278286	+	0.482005i
$290$		0			0
$291$	−143.450	−	248.463i	−0.492955	−	0.853823i
$292$	0.805944	−	1.39594i	0.00276008	−	0.00478060i
$293$	−451.939			−1.54245			−0.771227	−	0.636560i	$-0.780357\pi$
$293$	−451.939			−1.54245			−0.771227	+	0.636560i	$0.780357\pi$
$294$	−54.7307	+	106.820i	−0.186159	+	0.363334i
$295$		0			0
$296$	16.6193	−	28.7854i	0.0561462	−	0.0972480i
$297$	46.1284	+	79.8967i	0.155314	+	0.269013i
$298$	−98.7311	+	57.0024i	−0.331313	+	0.191283i
$299$	−68.5553	−	39.5804i	−0.229282	−	0.132376i
$300$		0			0
$301$	188.814	+	45.5550i	0.627290	+	0.151346i
$302$			19.7084i			0.0652595i
$303$	296.100	+	170.953i	0.977227	+	0.564202i
$304$	−22.8079	+	13.1682i	−0.0750260	+	0.0433163i
$305$		0			0
$306$	77.9292	+	44.9925i	0.254671	+	0.147034i
$307$	−555.454			−1.80930			−0.904649	−	0.426158i	$-0.859867\pi$
$307$	−555.454			−1.80930			−0.904649	+	0.426158i	$0.859867\pi$
$308$	180.112	+	171.305i	0.584779	+	0.556186i
$309$	122.495			0.396423
$310$		0			0
$311$	146.444	−	84.5493i	0.470880	−	0.271863i	−0.245728	−	0.969339i	$-0.579027\pi$
$311$	146.444	−	84.5493i	0.470880	−	0.271863i	0.716608	+	0.697476i	$0.245694\pi$
$312$	−8.52270	+	4.92058i	−0.0273163	+	0.0157711i
$313$	−292.828	+	507.192i	−0.935552	+	1.62042i	−0.161905	+	0.986806i	$0.551764\pi$
$313$	−292.828	+	507.192i	−0.935552	+	1.62042i	−0.773647	+	0.633617i	$0.781570\pi$
$314$			35.7324i			0.113797i
$315$		0			0
$316$	232.738			0.736514
$317$	−226.230	−	130.614i	−0.713660	−	0.412032i	0.0987546	−	0.995112i	$-0.468514\pi$
$317$	−226.230	−	130.614i	−0.713660	−	0.412032i	−0.812415	+	0.583080i	$0.801847\pi$
$318$	−120.579	−	208.849i	−0.379179	−	0.656756i
$319$	222.904	+	386.081i	0.698759	+	1.21029i
$320$		0			0
$321$		−	55.3576i		−	0.172454i
$322$	374.165	−	110.375i	1.16200	−	0.342780i
$323$		−	139.646i		−	0.432341i
$324$	9.00000	−	15.5885i	0.0277778	−	0.0481125i
$325$		0			0
$326$	−39.4088	−	68.2581i	−0.120886	−	0.209381i
$327$	183.643	−	318.078i	0.561598	−	0.972717i
$328$	47.7472			0.145571
$329$	−231.685	−	220.357i	−0.704211	−	0.669778i
$330$		0			0
$331$	−95.4984	+	165.408i	−0.288515	+	0.499722i	−0.973455	−	0.228877i	$-0.926495\pi$
$331$	−95.4984	+	165.408i	−0.288515	+	0.499722i	0.684941	+	0.728599i	$0.259828\pi$
$332$	50.1243	+	86.8178i	0.150977	+	0.261499i
$333$	30.5315	−	17.6274i	0.0916863	−	0.0529351i
$334$	−321.448	−	185.588i	−0.962420	−	0.555654i
$335$		0			0
$336$	11.3745	−	47.1447i	0.0338528	−	0.140312i
$337$		−	226.109i		−	0.670947i	−0.942050	−	0.335474i	$-0.891104\pi$
$337$		−	226.109i		−	0.670947i	0.942050	−	0.335474i	$-0.108896\pi$
$338$	−202.040	−	116.648i	−0.597750	−	0.345111i
$339$	136.559	−	78.8423i	0.402829	−	0.232573i
$340$		0			0
$341$	84.6548	+	48.8754i	0.248254	+	0.143330i
$342$	−27.9339			−0.0816780
$343$	−223.640	+	260.066i	−0.652011	+	0.758210i
$344$	−78.4816			−0.228144
$345$		0			0
$346$	193.925	−	111.962i	0.560476	−	0.323591i
$347$	−574.410	+	331.636i	−1.65536	+	0.955723i	−0.680548	+	0.732704i	$0.738258\pi$
$347$	−574.410	+	331.636i	−1.65536	+	0.955723i	−0.974814	+	0.223020i	$0.928409\pi$
$348$	43.4903	−	75.3274i	0.124972	−	0.216458i
$349$		−	293.777i		−	0.841769i	−0.907114	−	0.420884i	$-0.861720\pi$
$349$		−	293.777i		−	0.841769i	0.907114	−	0.420884i	$-0.138280\pi$
$350$		0			0
$351$	−10.4381			−0.0297383
$352$	−86.9805	−	50.2182i	−0.247104	−	0.142665i
$353$	−179.030	−	310.089i	−0.507167	−	0.878439i	−0.999966	−	0.00829580i	$-0.997359\pi$
$353$	−179.030	−	310.089i	−0.507167	−	0.878439i	0.492798	−	0.870144i	$-0.335974\pi$
$354$	15.5383	+	26.9131i	0.0438934	+	0.0760257i
$355$		0			0
$356$		−	173.048i		−	0.486091i
$357$	186.333	+	177.222i	0.521942	+	0.496421i
$358$		−	14.1821i		−	0.0396149i
$359$	−28.2996	+	49.0164i	−0.0788291	+	0.136536i	−0.902745	−	0.430176i	$-0.858451\pi$
$359$	−28.2996	+	49.0164i	−0.0788291	+	0.136536i	0.823916	+	0.566712i	$0.191785\pi$
$360$		0			0
$361$	−158.825	−	275.093i	−0.439958	−	0.762030i
$362$	−224.961	+	389.644i	−0.621440	+	1.07637i
$363$	336.423			0.926785
$364$	−26.9743	+	7.95716i	−0.0741052	+	0.0218603i
$365$		0			0
$366$	116.026	−	200.963i	0.317012	−	0.549080i
$367$	242.183	+	419.473i	0.659898	+	1.14298i	0.980642	+	0.195811i	$0.0627340\pi$
$367$	242.183	+	419.473i	0.659898	+	1.14298i	−0.320743	+	0.947166i	$0.603933\pi$
$368$	−136.509	+	78.8133i	−0.370947	+	0.214166i
$369$	43.8586	+	25.3218i	0.118858	+	0.0686228i
$370$		0			0
$371$	−194.990	−	661.005i	−0.525579	−	1.78168i
$372$		−	19.0719i		−	0.0512687i
$373$	305.623	+	176.452i	0.819365	+	0.473061i	0.850198	−	0.526464i	$-0.176482\pi$
$373$	305.623	+	176.452i	0.819365	+	0.473061i	−0.0308322	+	0.999525i	$0.509816\pi$
$374$	461.207	−	266.278i	1.23317	−	0.711973i
$375$		0			0
$376$	111.887	+	64.5978i	0.297571	+	0.171803i
$377$	−50.4397			−0.133792
$378$	35.4504	−	37.2729i	0.0937842	−	0.0986055i
$379$	129.666			0.342126			0.171063	−	0.985260i	$-0.445280\pi$
$379$	129.666			0.342126			0.171063	+	0.985260i	$0.445280\pi$
$380$		0			0
$381$	−241.415	+	139.381i	−0.633635	+	0.365830i
$382$	4.54727	−	2.62537i	0.0119039	−	0.00687269i
$383$	209.819	−	363.416i	0.547829	−	0.948868i	−0.450594	−	0.892729i	$-0.648788\pi$
$383$	209.819	−	363.416i	0.547829	−	0.948868i	0.998423	−	0.0561389i	$-0.0178790\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−417.958			−1.08279
$387$	−72.0900	−	41.6212i	−0.186279	−	0.107548i
$388$	165.642	+	286.900i	0.426912	+	0.739433i
$389$	49.2202	+	85.2518i	0.126530	+	0.219156i	0.922330	−	0.386403i	$-0.126283\pi$
$389$	49.2202	+	85.2518i	0.126530	+	0.219156i	−0.795800	+	0.605560i	$0.792949\pi$
$390$		0			0
$391$		−	835.801i		−	2.13760i
$392$	63.1975	−	123.345i	0.161218	−	0.314656i
$393$			28.9239i			0.0735978i
$394$	163.437	−	283.080i	0.414814	−	0.718478i
$395$		0			0
$396$	−53.2645	−	92.2568i	−0.134506	−	0.232972i
$397$	−92.7842	+	160.707i	−0.233713	+	0.404804i	−0.958898	−	0.283751i	$-0.908421\pi$
$397$	−92.7842	+	160.707i	−0.233713	+	0.404804i	0.725185	+	0.688555i	$0.241754\pi$
$398$	41.4190			0.104068
$399$	−77.6010	−	18.7227i	−0.194489	−	0.0469241i
$400$		0			0
$401$	93.6753	−	162.250i	0.233604	−	0.404614i	−0.725262	−	0.688473i	$-0.758281\pi$
$401$	93.6753	−	162.250i	0.233604	−	0.404614i	0.958866	+	0.283859i	$0.0916147\pi$
$402$	10.2292	+	17.7174i	0.0254457	+	0.0440732i
$403$	−9.57802	+	5.52987i	−0.0237668	+	0.0137218i
$404$	−341.907	−	197.400i	−0.846304	−	0.488614i
$405$		0			0
$406$	171.305	−	180.112i	0.421934	−	0.443626i
$407$		−	208.648i		−	0.512648i
$408$	−89.9849	−	51.9528i	−0.220551	−	0.127335i
$409$	182.953	−	105.628i	0.447319	−	0.258260i	−0.259378	−	0.965776i	$-0.583518\pi$
$409$	182.953	−	105.628i	0.447319	−	0.258260i	0.706697	+	0.707516i	$0.250184\pi$
$410$		0			0
$411$	−189.836	−	109.602i	−0.461889	−	0.266672i
$412$	−141.445			−0.343313
$413$	25.1272	+	85.1798i	0.0608407	+	0.206247i
$414$	−167.188			−0.403836
$415$		0			0
$416$	9.84116	−	5.68180i	0.0236566	−	0.0136582i
$417$	−203.041	+	117.226i	−0.486910	+	0.281118i
$418$	−82.6602	+	143.172i	−0.197752	+	0.342516i
$419$		−	48.9505i		−	0.116827i	−0.998292	−	0.0584134i	$-0.981396\pi$
$419$		−	48.9505i		−	0.116827i	0.998292	−	0.0584134i	$-0.0186042\pi$
$420$		0			0
$421$	−166.539			−0.395581			−0.197790	−	0.980244i	$-0.563376\pi$
$421$	−166.539			−0.395581			−0.197790	+	0.980244i	$0.563376\pi$
$422$	−311.591	−	179.897i	−0.738367	−	0.426297i
$423$	68.5163	+	118.674i	0.161977	+	0.280552i
$424$	139.232	+	241.158i	0.328378	+	0.568768i
$425$		0			0
$426$		−	175.929i		−	0.412978i
$427$	457.020	−	480.515i	1.07030	−	1.12533i
$428$			63.9214i			0.149349i
$429$	−30.8879	+	53.4994i	−0.0719997	+	0.124707i
$430$		0			0
$431$	−95.9137	−	166.127i	−0.222538	−	0.385446i	0.733040	−	0.680185i	$-0.238101\pi$
$431$	−95.9137	−	166.127i	−0.222538	−	0.385446i	−0.955578	+	0.294739i	$0.904767\pi$
$432$	−10.3923	+	18.0000i	−0.0240563	+	0.0416667i
$433$	−509.172			−1.17592			−0.587958	−	0.808891i	$-0.700068\pi$
$433$	−509.172			−1.17592			−0.587958	+	0.808891i	$0.700068\pi$
$434$	12.7830	−	52.9823i	0.0294539	−	0.122079i
$435$		0			0
$436$	−212.052	+	367.285i	−0.486358	+	0.842397i
$437$	129.728	+	224.696i	0.296861	+	0.514178i
$438$	−1.70967	+	0.987076i	−0.00390335	+	0.00225360i
$439$	459.149	+	265.090i	1.04590	+	0.603849i	0.921498	−	0.388383i	$-0.126966\pi$
$439$	459.149	+	265.090i	1.04590	+	0.603849i	0.124400	+	0.992232i	$0.460299\pi$
$440$		0			0
$441$	123.464	−	79.7844i	0.279965	−	0.180917i
$442$			60.2545i			0.136322i
$443$	368.834	+	212.946i	0.832583	+	0.480692i	0.854736	−	0.519063i	$-0.173719\pi$
$443$	368.834	+	212.946i	0.832583	+	0.480692i	−0.0221535	+	0.999755i	$0.507052\pi$
$444$	−35.2548	+	20.3544i	−0.0794027	+	0.0458432i
$445$		0			0
$446$	−241.417	−	139.382i	−0.541293	−	0.312516i
$447$	139.627			0.312364
$448$	−13.1342	+	54.4380i	−0.0293174	+	0.121513i
$449$	294.520			0.655946			0.327973	−	0.944687i	$-0.393635\pi$
$449$	294.520			0.655946			0.327973	+	0.944687i	$0.393635\pi$
$450$		0			0
$451$	259.568	−	149.861i	0.575538	−	0.332287i
$452$	−157.685	+	91.0393i	−0.348860	+	0.201414i
$453$	12.0689	−	20.9039i	0.0266421	−	0.0461454i
$454$			405.071i			0.892227i
$455$		0			0
$456$	32.2553			0.0707352
$457$	70.8765	+	40.9206i	0.155091	+	0.0895418i	0.575537	−	0.817776i	$-0.304793\pi$
$457$	70.8765	+	40.9206i	0.155091	+	0.0895418i	−0.420446	+	0.907318i	$0.638126\pi$
$458$	145.849	+	252.618i	0.318448	+	0.551567i
$459$	−55.1043	−	95.4434i	−0.120053	−	0.207938i
$460$		0			0
$461$			759.149i			1.64674i	0.567502	+	0.823372i	$0.307910\pi$
$461$			759.149i			1.64674i	−0.567502	+	0.823372i	$0.692090\pi$
$462$	−86.1349	−	291.992i	−0.186439	−	0.632018i
$463$		−	394.988i		−	0.853105i	−0.904463	−	0.426552i	$-0.859728\pi$
$463$		−	394.988i		−	0.853105i	0.904463	−	0.426552i	$-0.140272\pi$
$464$	−50.2182	+	86.9805i	−0.108229	+	0.187458i
$465$		0			0
$466$	−4.87409	−	8.44217i	−0.0104594	−	0.0181162i
$467$	134.156	−	232.364i	0.287271	−	0.497568i	−0.685886	−	0.727709i	$-0.740585\pi$
$467$	134.156	−	232.364i	0.287271	−	0.497568i	0.973157	+	0.230140i	$0.0739185\pi$
$468$	12.0529			0.0257541
$469$	16.5417	+	56.0755i	0.0352702	+	0.119564i
$470$		0			0
$471$	21.8815	−	37.8999i	0.0464576	−	0.0804669i
$472$	−17.9421	−	31.0766i	−0.0380128	−	0.0658402i
$473$	−426.648	+	246.326i	−0.902005	+	0.520773i
$474$	−246.856	−	142.523i	−0.520794	−	0.300680i
$475$		0			0
$476$	−215.159	−	204.639i	−0.452015	−	0.429913i
$477$			295.356i			0.619196i
$478$	−355.130	−	205.034i	−0.742949	−	0.428942i
$479$	470.659	−	271.735i	0.982586	−	0.567296i	0.0795360	−	0.996832i	$-0.474656\pi$
$479$	470.659	−	271.735i	0.982586	−	0.567296i	0.903050	+	0.429536i	$0.141323\pi$
$480$		0			0
$481$	20.4441	+	11.8034i	0.0425034	+	0.0245393i
$482$	461.796			0.958083
$483$	−464.453	−	112.058i	−0.961601	−	0.232004i
$484$	−388.468			−0.802620
$485$		0			0
$486$	−19.0919	+	11.0227i	−0.0392837	+	0.0226805i
$487$	−343.398	+	198.261i	−0.705130	+	0.407107i	−0.809255	−	0.587457i	$-0.800129\pi$
$487$	−343.398	+	198.261i	−0.705130	+	0.407107i	0.104125	+	0.994564i	$0.466796\pi$
$488$	−133.976	+	232.052i	−0.274540	+	0.475517i
$489$			96.5315i			0.197406i
$490$		0			0
$491$	750.658			1.52883			0.764417	−	0.644722i	$-0.223027\pi$
$491$	750.658			1.52883			0.764417	+	0.644722i	$0.223027\pi$
$492$	−50.6436	−	29.2391i	−0.102934	−	0.0594291i
$493$	−266.278	−	461.207i	−0.540117	−	0.935511i
$494$	−9.35235	−	16.1987i	−0.0189319	−	0.0327910i
$495$		0			0
$496$			22.0224i			0.0444000i
$497$	117.916	−	488.734i	0.237256	−	0.983368i
$498$		−	122.779i		−	0.246544i
$499$	−66.6787	+	115.491i	−0.133625	+	0.231445i	−0.925071	−	0.379794i	$-0.875995\pi$
$499$	−66.6787	+	115.491i	−0.133625	+	0.231445i	0.791447	+	0.611238i	$0.209328\pi$
$500$		0			0
$501$	227.298	+	393.692i	0.453689	+	0.785813i
$502$	241.660	−	418.568i	0.481395	−	0.833800i
$503$	−226.683			−0.450661			−0.225331	−	0.974282i	$-0.572346\pi$
$503$	−226.683			−0.450661			−0.225331	+	0.974282i	$0.572346\pi$
$504$	−40.9346	+	43.0390i	−0.0812195	+	0.0853949i
$505$		0			0
$506$	−494.733	+	856.903i	−0.977733	+	1.69348i
$507$	142.864	+	247.447i	0.281782	+	0.488061i
$508$	278.762	−	160.943i	0.548744	−	0.316818i
$509$	−17.6930	−	10.2151i	−0.0347603	−	0.0200689i	0.482519	−	0.875885i	$-0.339722\pi$
$509$	−17.6930	−	10.2151i	−0.0347603	−	0.0200689i	−0.517279	+	0.855817i	$0.673055\pi$
$510$		0			0
$511$	−5.41109	+	1.59622i	−0.0105892	+	0.00312371i
$512$		−	22.6274i		−	0.0441942i
$513$	29.6284	+	17.1059i	0.0577551	+	0.0333449i
$514$	238.636	−	137.776i	0.464272	−	0.268047i
$515$		0			0
$516$	83.2423	+	48.0600i	0.161322	+	0.0931395i
$517$	810.996			1.56866
$518$	−111.581	+	32.9154i	−0.215408	+	0.0635432i
$519$	−274.251			−0.528422
$520$		0			0
$521$	775.322	−	447.632i	1.48814	−	0.859179i	0.488233	−	0.872713i	$-0.337642\pi$
$521$	775.322	−	447.632i	1.48814	−	0.859179i	0.999908	+	0.0135342i	$0.00430819\pi$
$522$	−92.2568	+	53.2645i	−0.176737	+	0.102039i
$523$	141.313	−	244.761i	0.270197	−	0.467995i	−0.698715	−	0.715400i	$-0.746244\pi$
$523$	141.313	−	244.761i	0.270197	−	0.467995i	0.968912	+	0.247405i	$0.0795778\pi$
$524$		−	33.3985i		−	0.0637375i
$525$		0			0
$526$	195.253			0.371204
$527$	−101.127	−	58.3859i	−0.191892	−	0.110789i
$528$	61.5045	+	106.529i	0.116486	+	0.201759i
$529$	511.941	+	886.708i	0.967753	+	1.67620i
$530$		0			0
$531$		−	38.0609i		−	0.0716777i
$532$	89.6060	+	21.6191i	0.168432	+	0.0406375i
$533$			33.9113i			0.0636234i
$534$	−105.970	+	183.546i	−0.198446	+	0.343718i
$535$		0			0
$536$	−11.8116	−	20.4583i	−0.0220366	−	0.0381685i
$537$	−8.68475	+	15.0424i	−0.0161727	+	0.0280120i
$538$	−13.9994			−0.0260212
$539$	−43.5768	−	868.895i	−0.0808474	−	1.61205i
$540$		0			0
$541$	−178.897	+	309.858i	−0.330678	+	0.572751i	−0.982645	−	0.185496i	$-0.940611\pi$
$541$	−178.897	+	309.858i	−0.330678	+	0.572751i	0.651967	+	0.758247i	$0.273944\pi$
$542$	−13.4486	−	23.2937i	−0.0248130	−	0.0429774i
$543$	477.215	−	275.520i	0.878848	−	0.507403i
$544$	103.906	+	59.9899i	0.191003	+	0.110276i
$545$		0			0
$546$	33.4833	+	8.07848i	0.0613247	+	0.0147958i
$547$		−	251.048i		−	0.458954i	−0.973314	−	0.229477i	$-0.926298\pi$
$547$		−	251.048i		−	0.458954i	0.973314	−	0.229477i	$-0.0737015\pi$
$548$	219.204	+	126.558i	0.400008	+	0.230944i
$549$	−246.129	+	142.103i	−0.448322	+	0.258839i
$550$		0			0
$551$	143.172	+	82.6602i	0.259840	+	0.150019i
$552$	193.052			0.349732
$553$	−590.247	−	561.387i	−1.06736	−	1.01517i
$554$	−290.568			−0.524490
$555$		0			0
$556$	234.452	−	135.361i	0.421676	−	0.243455i
$557$	−601.496	+	347.274i	−1.07989	+	0.623472i	−0.930866	−	0.365362i	$-0.880945\pi$
$557$	−601.496	+	347.274i	−1.07989	+	0.623472i	−0.149020	+	0.988834i	$0.547612\pi$
$558$	−11.6791	+	20.2288i	−0.0209303	+	0.0362524i
$559$		−	55.7396i		−	0.0997131i
$560$		0			0
$561$	−652.245			−1.16265
$562$	−550.721	−	317.959i	−0.979930	−	0.565763i
$563$	−279.337	−	483.826i	−0.496158	−	0.859371i	0.503832	−	0.863802i	$-0.331923\pi$
$563$	−279.337	−	483.826i	−0.496158	−	0.859371i	−0.999990	+	0.00443074i	$0.998590\pi$
$564$	−79.1158	−	137.033i	−0.140276	−	0.242965i
$565$		0			0
$566$			224.965i			0.397464i
$567$	−60.4257	+	17.8250i	−0.106571	+	0.0314374i
$568$			203.145i			0.357649i
$569$	−270.266	+	468.114i	−0.474983	+	0.822696i	−0.999590	−	0.0286496i	$-0.990879\pi$
$569$	−270.266	+	468.114i	−0.474983	+	0.822696i	0.524606	+	0.851345i	$0.324213\pi$
$570$		0			0
$571$	462.071	+	800.331i	0.809232	+	1.40163i	0.913397	+	0.407071i	$0.133450\pi$
$571$	462.071	+	800.331i	0.809232	+	1.40163i	−0.104164	+	0.994560i	$0.533217\pi$
$572$	35.6662	−	61.7757i	0.0623536	−	0.108000i
$573$	−6.43081			−0.0112231
$574$	−121.092	−	115.171i	−0.210961	−	0.200646i
$575$		0			0
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	484.302	+	838.835i	0.839344	+	1.45379i	0.890444	+	0.455093i	$0.150394\pi$
$577$	484.302	+	838.835i	0.839344	+	1.45379i	−0.0510997	+	0.998694i	$0.516273\pi$
$578$	−196.999	+	113.738i	−0.340829	+	0.196778i
$579$	443.311	+	255.946i	0.765649	+	0.442048i
$580$		0			0
$581$	82.2927	−	341.083i	0.141640	−	0.587062i
$582$		−	405.738i		−	0.697144i
$583$	1513.81	+	874.001i	2.59659	+	1.49914i
$584$	1.97415	−	1.13978i	0.00338040	−	0.00195167i
$585$		0			0
$586$	−553.510	−	319.569i	−0.944556	−	0.545340i
$587$	−698.278			−1.18957			−0.594785	−	0.803885i	$-0.702763\pi$
$587$	−698.278			−1.18957			−0.594785	+	0.803885i	$0.702763\pi$
$588$	−142.564	+	92.1270i	−0.242456	+	0.156679i
$589$	36.2493			0.0615437
$590$		0			0
$591$	−346.701	+	200.168i	−0.586635	+	0.338694i
$592$	40.7087	−	23.5032i	0.0687647	−	0.0397013i
$593$	351.007	−	607.963i	0.591918	−	1.02523i	−0.402056	−	0.915615i	$-0.631704\pi$
$593$	351.007	−	607.963i	0.591918	−	1.02523i	0.993974	−	0.109617i	$-0.0349625\pi$
$594$			130.471i			0.219648i
$595$		0			0
$596$	−161.227			−0.270516
$597$	−43.9315	−	25.3639i	−0.0735871	−	0.0424855i
$598$	−55.9751	−	96.9518i	−0.0936039	−	0.162127i
$599$	−83.1873	−	144.085i	−0.138877	−	0.240542i	0.788195	−	0.615426i	$-0.211016\pi$
$599$	−83.1873	−	144.085i	−0.138877	−	0.240542i	−0.927072	+	0.374884i	$0.877683\pi$
$600$		0			0
$601$			952.482i			1.58483i	0.609983	+	0.792415i	$0.291176\pi$
$601$			952.482i			1.58483i	−0.609983	+	0.792415i	$0.708824\pi$
$602$	199.037	+	189.305i	0.330627	+	0.314460i
$603$		−	25.0562i		−	0.0415526i
$604$	−13.9359	+	24.1377i	−0.0230727	+	0.0399631i
$605$		0			0
$606$	241.765	+	418.748i	0.398951	+	0.691004i
$607$	−400.790	+	694.188i	−0.660279	+	1.14364i	0.320263	+	0.947329i	$0.396229\pi$
$607$	−400.790	+	694.188i	−0.660279	+	1.14364i	−0.980542	+	0.196309i	$0.937105\pi$
$608$	−37.2452			−0.0612585
$609$	−291.992	+	86.1349i	−0.479462	+	0.141437i
$610$		0			0
$611$	−45.8789	+	79.4646i	−0.0750883	+	0.130057i
$612$	63.6289	+	110.209i	0.103969	+	0.180079i
$613$	638.737	−	368.775i	1.04199	−	0.601591i	0.121590	−	0.992580i	$-0.461201\pi$
$613$	638.737	−	368.775i	1.04199	−	0.601591i	0.920395	+	0.390990i	$0.127867\pi$
$614$	−680.290	−	392.766i	−1.10796	−	0.639683i
$615$		0			0
$616$	99.4600	+	337.164i	0.161461	+	0.547344i
$617$		−	244.329i		−	0.395995i	−0.980203	−	0.197997i	$-0.936556\pi$
$617$		−	244.329i		−	0.395995i	0.980203	−	0.197997i	$-0.0634437\pi$
$618$	150.025	+	86.6169i	0.242759	+	0.140157i
$619$	−409.586	+	236.475i	−0.661690	+	0.382027i	−0.792920	−	0.609325i	$-0.791440\pi$
$619$	−409.586	+	236.475i	−0.661690	+	0.382027i	0.131231	+	0.991352i	$0.458107\pi$
$620$		0			0
$621$	177.330	+	102.381i	0.285555	+	0.164865i
$622$	239.142			0.384472
$623$	−417.409	+	438.868i	−0.669999	+	0.704443i
$624$	−13.9175			−0.0223037
$625$		0			0
$626$	−717.278	+	414.121i	−1.14581	+	0.661535i
$627$	175.349	−	101.238i	0.279663	−	0.161464i
$628$	−25.2666	+	43.7630i	−0.0402334	+	0.0696863i
$629$			249.247i			0.396260i
$630$		0			0
$631$	−1204.19			−1.90839			−0.954193	−	0.299191i	$-0.903283\pi$
$631$	−1204.19			−1.90839			−0.954193	+	0.299191i	$0.903283\pi$
$632$	285.045	+	164.571i	0.451021	+	0.260397i
$633$	220.328	+	381.620i	0.348070	+	0.602874i
$634$	−184.716	−	319.938i	−0.291351	−	0.504634i
$635$		0			0
$636$		−	341.048i		−	0.536239i
$637$	87.6029	+	44.8845i	0.137524	+	0.0704623i
$638$			630.468i			0.988194i
$639$	−107.734	+	186.600i	−0.168597	+	0.292019i
$640$		0			0
$641$	273.033	+	472.908i	0.425949	+	0.737766i	0.996509	−	0.0834907i	$-0.0266069\pi$
$641$	273.033	+	472.908i	0.425949	+	0.737766i	−0.570559	+	0.821256i	$0.693274\pi$
$642$	39.1437	−	67.7989i	0.0609715	−	0.105606i
$643$	193.418			0.300805			0.150403	−	0.988625i	$-0.451943\pi$
$643$	193.418			0.300805			0.150403	+	0.988625i	$0.451943\pi$
$644$	536.304	+	129.394i	0.832771	+	0.200922i
$645$		0			0
$646$	98.7446	−	171.031i	0.152855	−	0.264753i
$647$	−59.5245	−	103.099i	−0.0920007	−	0.159350i	0.816352	−	0.577554i	$-0.195993\pi$
$647$	−59.5245	−	103.099i	−0.0920007	−	0.159350i	−0.908353	+	0.418205i	$0.862660\pi$
$648$	22.0454	−	12.7279i	0.0340207	−	0.0196419i
$649$	−195.076	−	112.627i	−0.300580	−	0.173540i
$650$		0			0
$651$	−46.0033	+	48.3683i	−0.0706657	+	0.0742985i
$652$		−	111.465i		−	0.170959i
$653$	−508.970	−	293.854i	−0.779433	−	0.450006i	0.0567963	−	0.998386i	$-0.481911\pi$
$653$	−508.970	−	293.854i	−0.779433	−	0.450006i	−0.836229	+	0.548380i	$0.815245\pi$
$654$	449.831	−	259.710i	0.687815	−	0.397110i
$655$		0			0
$656$	58.4782	+	33.7624i	0.0891436	+	0.0514671i
$657$	2.41783			0.00368011
$658$	−127.939	−	433.707i	−0.194437	−	0.659130i
$659$	36.3580			0.0551714			0.0275857	−	0.999619i	$-0.491218\pi$
$659$	36.3580			0.0551714			0.0275857	+	0.999619i	$0.491218\pi$
$660$		0			0
$661$	279.780	−	161.531i	0.423268	−	0.244374i	−0.273207	−	0.961955i	$-0.588084\pi$
$661$	279.780	−	161.531i	0.423268	−	0.244374i	0.696475	+	0.717582i	$0.254751\pi$
$662$	−233.922	+	135.055i	−0.353357	+	0.204011i
$663$	36.8982	−	63.9095i	0.0556534	−	0.0963944i
$664$			141.773i			0.213513i
$665$		0			0
$666$	49.8578			0.0748616
$667$	856.903	+	494.733i	1.28471	+	0.741729i
$668$	−262.461	−	454.597i	−0.392906	−	0.680534i
$669$	170.707	+	295.674i	0.255168	+	0.441964i
$670$		0			0
$671$			1682.00i			2.50671i
$672$	47.2672	−	49.6972i	0.0703381	−	0.0739541i
$673$		−	705.426i		−	1.04818i	−0.851663	−	0.524091i	$-0.824405\pi$
$673$		−	705.426i		−	1.04818i	0.851663	−	0.524091i	$-0.175595\pi$
$674$	159.883	−	276.926i	0.237216	−	0.410870i
$675$		0			0
$676$	−164.965	−	285.727i	−0.244031	−	0.422673i
$677$	415.780	−	720.152i	0.614151	−	1.06374i	−0.376382	−	0.926465i	$-0.622832\pi$
$677$	415.780	−	720.152i	0.614151	−	1.06374i	0.990533	−	0.137276i	$-0.0438347\pi$
$678$	223.000			0.328908
$679$	271.946	−	1127.15i	0.400510	−	1.66001i
$680$		0			0
$681$	248.054	−	429.643i	0.364250	−	0.630900i
$682$	69.1203	+	119.720i	0.101349	+	0.175542i
$683$	842.246	−	486.271i	1.23316	−	0.711964i	0.265470	−	0.964119i	$-0.414473\pi$
$683$	842.246	−	486.271i	1.23316	−	0.711964i	0.967687	+	0.252155i	$0.0811394\pi$
$684$	−34.2119	−	19.7522i	−0.0500174	−	0.0288775i
$685$		0			0
$686$	−457.796	+	160.377i	−0.667341	+	0.233786i
$687$		−	357.256i		−	0.520023i
$688$	−96.1200	−	55.4949i	−0.139709	−	0.0806612i
$689$	−171.276	+	98.8863i	−0.248586	+	0.143521i
$690$		0			0
$691$	443.849	+	256.256i	0.642328	+	0.370848i	0.785511	−	0.618848i	$-0.212400\pi$
$691$	443.849	+	256.256i	0.642328	+	0.370848i	−0.143183	+	0.989696i	$0.545734\pi$
$692$	316.678			0.457627
$693$	−87.4482	+	362.451i	−0.126188	+	0.523018i
$694$	−938.008			−1.35160
$695$		0			0
$696$	106.529	−	61.5045i	0.153059	−	0.0883686i
$697$	−310.076	+	179.022i	−0.444872	+	0.256847i
$698$	207.732	−	359.802i	0.297610	−	0.515476i
$699$			11.9390i			0.0170802i
$700$		0			0
$701$	−259.526			−0.370223			−0.185111	−	0.982718i	$-0.559265\pi$
$701$	−259.526			−0.370223			−0.185111	+	0.982718i	$0.559265\pi$
$702$	−12.7840	−	7.38087i	−0.0182109	−	0.0105141i
$703$	−38.6867	−	67.0074i	−0.0550309	−	0.0953163i
$704$	−71.0193	−	123.009i	−0.100880	−	0.174729i
$705$		0			0
$706$		−	506.373i		−	0.717243i
$707$	390.962	+	1325.34i	0.552987	+	1.87459i
$708$			43.9489i			0.0620747i
$709$	138.685	−	240.210i	0.195607	−	0.338801i	−0.751492	−	0.659742i	$-0.770666\pi$
$709$	138.685	−	240.210i	0.195607	−	0.338801i	0.947099	+	0.320941i	$0.103999\pi$
$710$		0			0
$711$	174.554	+	302.336i	0.245505	+	0.425226i
$712$	122.364	−	211.940i	0.171859	−	0.297669i
$713$	216.957			0.304287
$714$	102.895	+	348.810i	0.144111	+	0.488529i
$715$		0			0
$716$	10.0283	−	17.3695i	0.0140060	−	0.0242591i
$717$	251.115	+	434.943i	0.350230	+	0.606615i
$718$	−69.3197	+	40.0217i	−0.0965455	+	0.0557406i
$719$	−1165.19	−	672.723i	−1.62057	−	0.935638i	−0.986767	−	0.162144i	$-0.948159\pi$
$719$	−1165.19	−	672.723i	−1.62057	−	0.935638i	−0.633805	−	0.773493i	$-0.718508\pi$
$720$		0			0
$721$	358.718	+	341.178i	0.497528	+	0.473202i
$722$		−	449.225i		−	0.622195i
$723$	−489.809	−	282.791i	−0.677467	−	0.391136i
$724$	−551.040	+	318.143i	−0.761105	+	0.439424i
$725$		0			0
$726$	412.032	+	237.887i	0.567538	+	0.327668i
$727$	−1143.24			−1.57255			−0.786275	−	0.617876i	$-0.787993\pi$
$727$	−1143.24			−1.57255			−0.786275	+	0.617876i	$0.787993\pi$
$728$	−38.6632	−	9.32823i	−0.0531088	−	0.0128135i
$729$	27.0000			0.0370370
$730$		0			0
$731$	509.668	−	294.257i	0.697220	−	0.402540i
$732$	284.205	−	164.086i	0.388258	−	0.224161i
$733$	−682.037	+	1181.32i	−0.930474	+	1.61163i	−0.147961	+	0.988993i	$0.547271\pi$
$733$	−682.037	+	1181.32i	−0.930474	+	1.61163i	−0.782513	+	0.622634i	$0.786062\pi$
$734$			684.996i			0.933237i
$735$		0			0
$736$	−222.918			−0.302877
$737$	−128.423	−	74.1448i	−0.174250	−	0.100603i
$738$	35.8104	+	62.0255i	0.0485236	+	0.0840454i
$739$	−101.096	−	175.103i	−0.136801	−	0.236946i	0.789483	−	0.613772i	$-0.210349\pi$
$739$	−101.096	−	175.103i	−0.136801	−	0.236946i	−0.926284	+	0.376827i	$0.877015\pi$
$740$		0			0
$741$			22.9085i			0.0309156i
$742$	228.588	−	947.441i	0.308070	−	1.27687i
$743$		−	344.793i		−	0.464055i	−0.972709	−	0.232028i	$-0.925464\pi$
$743$		−	344.793i		−	0.464055i	0.972709	−	0.232028i	$-0.0745360\pi$
$744$	13.4859	−	23.3583i	0.0181262	−	0.0313955i
$745$		0			0
$746$	249.540	+	432.217i	0.334505	+	0.579379i
$747$	−75.1864	+	130.227i	−0.100651	+	0.174333i
$748$	753.147			1.00688
$749$	154.185	−	162.111i	0.205854	−	0.216437i
$750$		0			0
$751$	−110.795	+	191.903i	−0.147530	+	0.255530i	−0.930314	−	0.366764i	$-0.880466\pi$
$751$	−110.795	+	191.903i	−0.147530	+	0.255530i	0.782784	+	0.622294i	$0.213799\pi$
$752$	91.3550	+	158.232i	0.121483	+	0.210414i
$753$	−512.639	+	295.972i	−0.680795	+	0.393057i
$754$	−61.7757	−	35.6662i	−0.0819307	−	0.0473027i
$755$		0			0
$756$	69.7736	−	20.5825i	0.0922932	−	0.0272256i
$757$		−	1006.02i		−	1.32895i	−0.747310	−	0.664476i	$-0.768655\pi$
$757$		−	1006.02i		−	1.32895i	0.747310	−	0.664476i	$-0.231345\pi$
$758$	158.807	+	91.6875i	0.209508	+	0.120960i
$759$	1049.49	−	605.922i	1.38272	−	0.798316i
$760$		0			0
$761$	981.832	+	566.861i	1.29019	+	0.744889i	0.978687	−	0.205357i	$-0.0658355\pi$
$761$	981.832	+	566.861i	1.29019	+	0.744889i	0.311499	+	0.950246i	$0.399169\pi$
$762$	−394.229			−0.517361
$763$	1423.71	−	419.981i	1.86594	−	0.550434i
$764$	7.42566			0.00971946
$765$		0			0
$766$	513.948	−	296.728i	0.670951	−	0.387374i
$767$	22.0713	−	12.7429i	0.0287762	−	0.0166139i
$768$	−13.8564	+	24.0000i	−0.0180422	+	0.0312500i
$769$			206.796i			0.268915i	0.990919	+	0.134458i	$0.0429292\pi$
$769$			206.796i			0.268915i	−0.990919	+	0.134458i	$0.957071\pi$
$770$		0			0
$771$	−337.482			−0.437719
$772$	−511.891	−	295.541i	−0.663072	−	0.382825i
$773$	−383.151	−	663.637i	−0.495668	−	0.858521i	0.504320	−	0.863517i	$-0.331743\pi$
$773$	−383.151	−	663.637i	−0.495668	−	0.858521i	−0.999988	+	0.00499551i	$0.998410\pi$
$774$	−58.8612	−	101.951i	−0.0760481	−	0.131719i
$775$		0			0
$776$			468.506i			0.603744i
$777$	138.506	+	33.4173i	0.178258	+	0.0430081i
$778$			139.216i			0.178940i
$779$	55.5736	−	96.2563i	0.0713396	−	0.123564i
$780$		0			0
$781$	637.598	+	1104.35i	0.816387	+	1.41402i
$782$	591.000	−	1023.64i	0.755755	−	1.30901i
$783$	130.471			0.166629
$784$	164.619	−	106.379i	0.209973	−	0.135688i
$785$		0			0
$786$	−20.4523	+	35.4244i	−0.0260207	+	0.0450692i
$787$	441.058	+	763.935i	0.560430	+	0.970693i	0.997459	+	0.0712454i	$0.0226974\pi$
$787$	441.058	+	763.935i	0.560430	+	0.970693i	−0.437029	+	0.899447i	$0.643969\pi$
$788$	400.336	−	231.134i	0.508041	−	0.293317i
$789$	−207.097	−	119.568i	−0.262481	−	0.151543i
$790$		0			0
$791$	619.499	+	149.466i	0.783185	+	0.188958i
$792$		−	150.655i		−	0.190221i
$793$	−164.809	−	95.1527i	−0.207830	−	0.119991i
$794$	−227.274	+	131.217i	−0.286239	+	0.165260i
$795$		0			0
$796$	50.7277	+	29.2877i	0.0637283	+	0.0367936i
$797$	1202.53			1.50882			0.754408	−	0.656406i	$-0.227924\pi$
$797$	1202.53			1.50882			0.754408	+	0.656406i	$0.227924\pi$
$798$	−81.8025	−	77.8028i	−0.102509	−	0.0974972i
$799$	−968.804			−1.21252
$800$		0			0
$801$	224.797	−	129.786i	0.280645	−	0.162030i
$802$	229.457	−	132.477i	0.286106	−	0.165183i
$803$	7.15470	−	12.3923i	0.00890997	−	0.0154325i
$804$			28.9324i			0.0359856i
$805$		0			0
$806$	−15.6408			−0.0194055
$807$	14.8486	+	8.57284i	0.0183998	+	0.0106231i
$808$	−279.166	−	483.529i	−0.345502	−	0.598427i
$809$	693.426	+	1201.05i	0.857140	+	1.48461i	0.874646	+	0.484763i	$0.161094\pi$
$809$	693.426	+	1201.05i	0.857140	+	1.48461i	−0.0175061	+	0.999847i	$0.505573\pi$
$810$		0			0
$811$		−	987.281i		−	1.21736i	−0.793415	−	0.608681i	$-0.791699\pi$
$811$		−	987.281i		−	1.21736i	0.793415	−	0.608681i	$-0.208301\pi$
$812$	337.164	−	99.4600i	0.415226	−	0.122488i
$813$			32.9423i			0.0405195i
$814$	147.536	−	255.540i	0.181248	−	0.313931i
$815$		0			0
$816$	−73.4724	−	127.258i	−0.0900397	−	0.155953i
$817$	−91.3457	+	158.215i	−0.111806	+	0.193654i
$818$	298.762			0.365234
$819$	−30.5674	−	29.0728i	−0.0373228	−	0.0354979i
$820$		0			0
$821$	223.132	−	386.477i	0.271781	−	0.470739i	−0.697537	−	0.716549i	$-0.745721\pi$
$821$	223.132	−	386.477i	0.271781	−	0.470739i	0.969318	+	0.245810i	$0.0790539\pi$
$822$	−155.001	−	268.469i	−0.188565	−	0.326605i
$823$	716.949	−	413.931i	0.871141	−	0.502954i	0.00341406	−	0.999994i	$-0.498913\pi$
$823$	716.949	−	413.931i	0.871141	−	0.502954i	0.867727	+	0.497040i	$0.165580\pi$
$824$	−173.234	−	100.017i	−0.210235	−	0.121379i
$825$		0			0
$826$	−29.4568	+	122.091i	−0.0356620	+	0.147810i
$827$		−	1333.16i		−	1.61204i	−0.591885	−	0.806022i	$-0.701616\pi$
$827$		−	1333.16i		−	1.61204i	0.591885	−	0.806022i	$-0.298384\pi$
$828$	−204.763	−	118.220i	−0.247298	−	0.142778i
$829$	1257.72	−	726.147i	1.51716	−	0.875931i	0.517360	−	0.855768i	$-0.326915\pi$
$829$	1257.72	−	726.147i	1.51716	−	0.875931i	0.999797	−	0.0201631i	$-0.00641856\pi$
$830$		0			0
$831$	308.194	+	177.936i	0.370871	+	0.214122i
$832$	16.0706			0.0193156
$833$	52.0561	+	1037.97i	0.0624924	+	1.24606i
$834$	−331.565			−0.397560
$835$		0			0
$836$	−202.475	+	116.899i	−0.242195	+	0.139832i
$837$	24.7752	−	14.3040i	0.0296000	−	0.0170896i
$838$	34.6132	−	59.9518i	0.0413045	−	0.0715416i
$839$			602.259i			0.717830i	0.933370	+	0.358915i	$0.116853\pi$
$839$			602.259i			0.717830i	−0.933370	+	0.358915i	$0.883147\pi$
$840$		0			0
$841$	−210.532			−0.250335
$842$	−203.968	−	117.761i	−0.242243	−	0.139859i
$843$	389.418	+	674.492i	0.461943	+	0.800109i
$844$	−254.413	−	440.656i	−0.301437	−	0.522105i
$845$		0			0
$846$			193.793i			0.229070i
$847$	985.193	+	937.022i	1.16316	+	1.10628i
$848$			393.809i			0.464397i
$849$	137.762	−	238.611i	0.162264	−	0.281050i
$850$		0			0
$851$	−231.545	−	401.048i	−0.272086	−	0.471267i
$852$	124.400	−	215.468i	0.146010	−	0.252896i
$853$	−487.049			−0.570983			−0.285492	−	0.958381i	$-0.592157\pi$
$853$	−487.049			−0.570983			−0.285492	+	0.958381i	$0.592157\pi$
$854$	899.508	−	265.346i	1.05329	−	0.310710i
$855$		0			0
$856$	−45.1993	+	78.2875i	−0.0528029	+	0.0914573i
$857$	692.754	+	1199.88i	0.808347	+	1.40010i	0.914008	+	0.405696i	$0.132971\pi$
$857$	692.754	+	1199.88i	0.808347	+	1.40010i	−0.105661	+	0.994402i	$0.533696\pi$
$858$	−75.6595	+	43.6820i	−0.0881813	+	0.0509115i
$859$	−1165.46	−	672.881i	−1.35677	−	0.783331i	−0.367582	−	0.929991i	$-0.619814\pi$
$859$	−1165.46	−	672.881i	−1.35677	−	0.783331i	−0.989187	+	0.146660i	$0.953148\pi$
$860$		0			0
$861$	57.9097	+	196.310i	0.0672586	+	0.228003i
$862$		−	271.285i		−	0.314716i
$863$	216.341	+	124.905i	0.250685	+	0.144733i	0.620078	−	0.784540i	$-0.287101\pi$
$863$	216.341	+	124.905i	0.250685	+	0.144733i	−0.369393	+	0.929273i	$0.620434\pi$
$864$	−25.4558	+	14.6969i	−0.0294628	+	0.0170103i
$865$		0			0
$866$	−623.605	−	360.039i	−0.720099	−	0.415749i
$867$	278.599			0.321337
$868$	53.1201	−	55.8509i	0.0611983	−	0.0643444i
$869$	2066.11			2.37758
$870$		0			0
$871$	14.5300	−	8.38890i	0.0166820	−	0.00963134i
$872$	−519.420	+	299.887i	−0.595665	+	0.343907i
$873$	−248.463	+	430.350i	−0.284608	+	0.492955i
$874$			366.927i			0.419825i
$875$		0			0
$876$	−2.79187			−0.00318707
$877$	613.327	+	354.104i	0.699346	+	0.403768i	0.807104	−	0.590409i	$-0.201034\pi$
$877$	613.327	+	354.104i	0.699346	+	0.403768i	−0.107757	+	0.994177i	$0.534367\pi$
$878$	374.894	+	649.335i	0.426986	+	0.739562i
$879$	391.391	+	677.908i	0.445268	+	0.771227i
$880$		0			0
$881$		−	83.7844i		−	0.0951014i	−0.998869	−	0.0475507i	$-0.984858\pi$
$881$		−	83.7844i		−	0.0951014i	0.998869	−	0.0475507i	$-0.0151416\pi$
$882$	207.628	−	10.4130i	0.235406	−	0.0118061i
$883$		−	1155.05i		−	1.30810i	−0.756450	−	0.654051i	$-0.773068\pi$
$883$		−	1155.05i		−	1.30810i	0.756450	−	0.654051i	$-0.226932\pi$
$884$	−42.6063	+	73.7964i	−0.0481972	+	0.0834800i
$885$		0			0
$886$	301.152	+	521.610i	0.339900	+	0.588725i
$887$	−160.634	+	278.227i	−0.181098	+	0.313672i	−0.942255	−	0.334897i	$-0.891299\pi$
$887$	−160.634	+	278.227i	−0.181098	+	0.313672i	0.761157	+	0.648568i	$0.224632\pi$
$888$	−57.5708			−0.0648320
$889$	−1095.18	−	264.233i	−1.23192	−	0.297225i
$890$		0			0
$891$	79.8967	−	138.385i	0.0896709	−	0.155314i
$892$	−197.116	−	341.415i	−0.220982	−	0.382752i
$893$	260.452	−	150.372i	0.291660	−	0.168390i
$894$	171.007	+	98.7311i	0.191283	+	0.110438i
$895$		0			0
$896$	−54.5795	+	57.3854i	−0.0609146	+	0.0640462i
$897$			137.111i			0.152855i
$898$	360.711	+	208.257i	0.401683	+	0.231912i
$899$	119.720	−	69.1203i	0.133170	−	0.0768858i
$900$		0			0
$901$	−1808.38	−	1044.07i	−2.00708	−	1.15879i
$902$	423.872			0.469925
$903$	−95.1855	−	322.673i	−0.105410	−	0.357335i
$904$	−257.498			−0.284843
$905$		0			0
$906$	29.5625	−	17.0679i	0.0326297	−	0.0188388i
$907$	−333.996	+	192.833i	−0.368243	+	0.212605i	−0.672690	−	0.739924i	$-0.734861\pi$
$907$	−333.996	+	192.833i	−0.368243	+	0.212605i	0.304448	+	0.952529i	$0.401528\pi$
$908$	−286.429	+	496.109i	−0.315450	+	0.546376i
$909$		−	592.200i		−	0.651485i
$910$		0			0
$911$	544.040			0.597190			0.298595	−	0.954380i	$-0.403482\pi$
$911$	544.040			0.597190			0.298595	+	0.954380i	$0.403482\pi$
$912$	39.5045	+	22.8079i	0.0433163	+	0.0250087i
$913$	444.974	+	770.718i	0.487376	+	0.844159i
$914$	57.8704	+	100.235i	0.0633156	+	0.109666i
$915$		0			0
$916$			412.523i			0.450353i
$917$	−80.5603	+	84.7018i	−0.0878520	+	0.0923684i
$918$		−	155.858i		−	0.169780i
$919$	305.574	−	529.269i	0.332507	−	0.575919i	−0.650496	−	0.759510i	$-0.725439\pi$
$919$	305.574	−	529.269i	0.332507	−	0.575919i	0.983003	+	0.183591i	$0.0587722\pi$
$920$		0			0
$921$	481.038	+	833.182i	0.522299	+	0.904649i
$922$	−536.799	+	929.764i	−0.582212	+	1.00842i
$923$	−144.278			−0.156315
$924$	100.977	−	418.523i	0.109282	−	0.452947i
$925$		0			0
$926$	279.298	−	483.759i	0.301618	−	0.522418i
$927$	−106.084	−	183.742i	−0.114438	−	0.198212i
$928$	−123.009	+	71.0193i	−0.132553	+	0.0765294i
$929$	744.000	+	429.549i	0.800862	+	0.462378i	0.843772	−	0.536701i	$-0.180330\pi$
$929$	744.000	+	429.549i	0.800862	+	0.462378i	−0.0429108	+	0.999079i	$0.513663\pi$
$930$		0			0
$931$	−175.102	−	270.966i	−0.188080	−	0.291049i
$932$		−	13.7860i		−	0.0147918i
$933$	−253.648	−	146.444i	−0.271863	−	0.156960i
$934$	328.613	−	189.725i	0.351834	−	0.203131i
$935$		0			0
$936$	14.7617	+	8.52270i	0.0157711	+	0.00910545i
$937$	−1665.22			−1.77718			−0.888591	−	0.458700i	$-0.848315\pi$
$937$	−1665.22			−1.77718			−0.888591	+	0.458700i	$0.848315\pi$
$938$	−19.3920	+	80.3750i	−0.0206738	+	0.0856876i
$939$	1014.38			1.08028
$940$		0			0
$941$	946.705	−	546.581i	1.00606	−	0.580851i	0.0960266	−	0.995379i	$-0.469387\pi$
$941$	946.705	−	546.581i	1.00606	−	0.580851i	0.910037	+	0.414528i	$0.136053\pi$
$942$	53.5985	−	30.9451i	0.0568987	−	0.0328505i
$943$	332.616	−	576.107i	0.352721	−	0.610930i
$944$		−	50.7478i		−	0.0537583i
$945$		0			0
$946$	−696.714			−0.736484
$947$	−1216.29	−	702.226i	−1.28436	−	0.741527i	−0.306720	−	0.951800i	$-0.599231\pi$
$947$	−1216.29	−	702.226i	−1.28436	−	0.741527i	−0.977643	+	0.210273i	$0.932565\pi$
$948$	−201.557	−	349.108i	−0.212613	−	0.368257i
$949$	0.809498	+	1.40209i	0.000853001	+	0.00147744i
$950$		0			0
$951$			452.461i			0.475773i
$952$	−118.813	−	402.771i	−0.124804	−	0.423079i
$953$			1284.11i			1.34744i	0.738985	+	0.673722i	$0.235305\pi$
$953$			1284.11i			1.34744i	−0.738985	+	0.673722i	$0.764695\pi$
$954$	−208.849	+	361.736i	−0.218919	+	0.379179i
$955$		0			0
$956$	−289.962	−	502.229i	−0.303308	−	0.525344i
$957$	386.081	−	668.712i	0.403429	−	0.698759i
$958$	768.582			0.802278
$959$	−250.654	−	849.704i	−0.261371	−	0.886031i
$960$		0			0
$961$	−465.344	+	806.000i	−0.484229	+	0.838709i
$962$	16.6926	+	28.9123i	0.0173519	+	0.0300544i
$963$	−83.0364	+	47.9411i	−0.0862268	+	0.0497831i
$964$	565.582	+	326.539i	0.586704	+	0.338733i
$965$		0			0
$966$	−489.600	−	465.661i	−0.506832	−	0.482050i
$967$		−	437.417i		−	0.452344i	−0.974087	−	0.226172i	$-0.927379\pi$
$967$		−	437.417i		−	0.452344i	0.974087	−	0.226172i	$-0.0726212\pi$
$968$	−475.774	−	274.688i	−0.491502	−	0.283769i
$969$	−209.469	+	120.937i	−0.216170	+	0.124806i
$970$		0			0
$971$	−277.241	−	160.065i	−0.285521	−	0.164846i	0.350399	−	0.936601i	$-0.386046\pi$
$971$	−277.241	−	160.065i	−0.285521	−	0.164846i	−0.635920	+	0.771755i	$0.719379\pi$
$972$	−31.1769			−0.0320750
$973$	−921.097	−	222.232i	−0.946657	−	0.228399i
$974$	−560.767			−0.575736
$975$		0			0
$976$	−328.172	+	189.470i	−0.336242	+	0.194129i
$977$	189.720	−	109.535i	0.194187	−	0.112114i	−0.399754	−	0.916622i	$-0.630905\pi$
$977$	189.720	−	109.535i	0.194187	−	0.112114i	0.593941	+	0.804509i	$0.297571\pi$
$978$	−68.2581	+	118.227i	−0.0697936	+	0.120886i
$979$		−	1536.22i		−	1.56918i
$980$		0			0
$981$	−636.157			−0.648478
$982$	919.364	+	530.795i	0.936216	+	0.540525i
$983$	108.847	+	188.528i	0.110729	+	0.191789i	0.916064	−	0.401031i	$-0.131348\pi$
$983$	108.847	+	188.528i	0.110729	+	0.191789i	−0.805335	+	0.592820i	$0.798015\pi$
$984$	−41.3503	−	71.6209i	−0.0420227	−	0.0727854i
$985$		0			0
$986$		−	753.147i		−	0.763841i
$987$	−129.890	+	538.363i	−0.131601	+	0.545454i
$988$		−	26.4524i		−	0.0267737i
$989$	−546.717	+	946.941i	−0.552798	+	0.957473i
$990$		0			0
$991$	−566.322	−	980.899i	−0.571466	−	0.989808i	−0.996416	−	0.0845907i	$-0.973042\pi$
$991$	−566.322	−	980.899i	−0.571466	−	0.989808i	0.424950	−	0.905217i	$-0.360292\pi$
$992$	−15.5722	+	26.9718i	−0.0156978	+	0.0271893i
$993$	330.816			0.333148
$994$	490.005	−	515.195i	0.492962	−	0.518305i
$995$		0			0
$996$	86.8178	−	150.373i	0.0871665	−	0.150977i
$997$	−779.718	−	1350.51i	−0.782065	−	1.35458i	−0.930737	−	0.365689i	$-0.880833\pi$
$997$	−779.718	−	1350.51i	−0.782065	−	1.35458i	0.148672	−	0.988887i	$-0.452500\pi$
$998$	−163.329	+	94.2980i	−0.163656	+	0.0944869i
$999$	−52.8822	−	30.5315i	−0.0529351	−	0.0305621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.q.d.649.8		24
5.2	odd	4		1050.3.p.e.901.3	yes	12
5.3	odd	4		1050.3.p.f.901.4	yes	12
5.4	even	2	inner	1050.3.q.d.649.2		24
7.3	odd	6	inner	1050.3.q.d.199.2		24
35.3	even	12		1050.3.p.f.451.4	yes	12
35.17	even	12		1050.3.p.e.451.3	✓	12
35.24	odd	6	inner	1050.3.q.d.199.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.p.e.451.3	✓	12	35.17	even	12
1050.3.p.e.901.3	yes	12	5.2	odd	4
1050.3.p.f.451.4	yes	12	35.3	even	12
1050.3.p.f.901.4	yes	12	5.3	odd	4
1050.3.q.d.199.2		24	7.3	odd	6	inner
1050.3.q.d.199.8		24	35.24	odd	6	inner
1050.3.q.d.649.2		24	5.4	even	2	inner
1050.3.q.d.649.8		24	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(1.64177 - 6.80475i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.22474 + 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(1.64177 - 6.80475i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(8.87741 + 15.3761i) q^{11} +(1.73205 - 3.00000i) q^{12} -2.00882 q^{13} +(6.82244 - 7.17317i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-10.6048 - 18.3681i) q^{17} +(-3.67423 + 2.12132i) q^{18} +(5.70198 + 3.29204i) q^{19} +(-11.6289 + 3.43042i) q^{21} +25.1091i q^{22} +(34.1271 + 19.7033i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-2.46029 - 1.42045i) q^{26} +5.19615 q^{27} +(13.4279 - 3.96111i) q^{28} +25.1091 q^{29} +(4.76798 - 2.75280i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(15.3761 - 26.6322i) q^{33} -29.9950i q^{34} -6.00000 q^{36} +(-10.1772 - 5.87580i) q^{37} +(4.65565 + 8.06382i) q^{38} +(1.73969 + 3.01323i) q^{39} -16.8812i q^{41} +(-16.6682 - 4.02151i) q^{42} +27.7474i q^{43} +(-17.7548 + 30.7523i) q^{44} +(27.8647 + 48.2631i) q^{46} +(22.8388 - 39.5579i) q^{47} +6.92820 q^{48} +(-43.6092 - 22.3437i) q^{49} +(-18.3681 + 31.8145i) q^{51} +(-2.00882 - 3.47938i) q^{52} +(85.2621 - 49.2261i) q^{53} +(6.36396 + 3.67423i) q^{54} +(19.2467 + 4.64364i) q^{56} -11.4040i q^{57} +(30.7523 + 17.7548i) q^{58} +(-10.9872 + 6.34348i) q^{59} +(82.0429 + 47.3675i) q^{61} +7.78609 q^{62} +(15.2166 + 14.4726i) q^{63} -8.00000 q^{64} +(37.6637 - 21.7451i) q^{66} +(-7.23310 + 4.17603i) q^{67} +(21.2096 - 36.7362i) q^{68} -68.2543i q^{69} +71.8225 q^{71} +(-7.34847 - 4.24264i) q^{72} +(-0.402972 - 0.697968i) q^{73} +(-8.30963 - 14.3927i) q^{74} +13.1682i q^{76} +(119.205 - 35.1644i) q^{77} +4.92058i q^{78} +(58.1846 - 100.779i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(11.9368 - 20.6752i) q^{82} +50.1243 q^{83} +(-17.5706 - 16.7115i) q^{84} +(-19.6204 + 33.9835i) q^{86} +(-21.7451 - 37.6637i) q^{87} +(-43.4903 + 25.1091i) q^{88} +(-74.9322 - 43.2621i) q^{89} +(-3.29803 + 13.6695i) q^{91} +78.8133i q^{92} +(-8.25839 - 4.76798i) q^{93} +(55.9433 - 32.2989i) q^{94} +(8.48528 + 4.89898i) q^{96} +165.642 q^{97} +(-37.6107 - 58.2017i) q^{98} -53.2645 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} - 36 q^{9}+O(q^{10}) \) 24 * q + 24 * q^4 - 36 * q^9	\( 24 q + 24 q^{4} - 36 q^{9} - 8 q^{11} - 16 q^{14} - 48 q^{16} - 24 q^{19} + 36 q^{21} - 48 q^{26} + 48 q^{29} - 396 q^{31} - 144 q^{36} + 72 q^{39} + 16 q^{44} + 64 q^{46} - 56 q^{49} - 48 q^{51} + 80 q^{56} + 96 q^{59} + 372 q^{61} - 192 q^{64} + 72 q^{66} - 272 q^{71} + 128 q^{74} + 140 q^{79} - 108 q^{81} + 24 q^{84} - 416 q^{86} - 336 q^{89} + 584 q^{91} + 408 q^{94} + 48 q^{99}+O(q^{100}) \) 24 * q + 24 * q^4 - 36 * q^9 - 8 * q^11 - 16 * q^14 - 48 * q^16 - 24 * q^19 + 36 * q^21 - 48 * q^26 + 48 * q^29 - 396 * q^31 - 144 * q^36 + 72 * q^39 + 16 * q^44 + 64 * q^46 - 56 * q^49 - 48 * q^51 + 80 * q^56 + 96 * q^59 + 372 * q^61 - 192 * q^64 + 72 * q^66 - 272 * q^71 + 128 * q^74 + 140 * q^79 - 108 * q^81 + 24 * q^84 - 416 * q^86 - 336 * q^89 + 584 * q^91 + 408 * q^94 + 48 * q^99

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