LMFDB - Embedded newform 1050.3.q.d.199.3

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			199.3
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.d.649.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-6.74171 - 1.88399i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-6.74171 - 1.88399i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(1.65702 - 2.87005i) q^{11} +(1.73205 + 3.00000i) q^{12} -19.5077 q^{13} +(9.58905 - 2.45970i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(4.21467 - 7.30003i) q^{17} +(3.67423 + 2.12132i) q^{18} +(-0.704670 + 0.406841i) q^{19} +(8.66447 - 8.48098i) q^{21} +4.68677i q^{22} +(-10.3673 + 5.98556i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(23.8919 - 13.7940i) q^{26} +5.19615 q^{27} +(-10.0049 + 9.79299i) q^{28} -4.68677 q^{29} +(27.9363 + 16.1291i) q^{31} +(4.89898 + 2.82843i) q^{32} +(2.87005 + 4.97107i) q^{33} +11.9209i q^{34} -6.00000 q^{36} +(-5.21854 + 3.01293i) q^{37} +(0.575361 - 0.996554i) q^{38} +(16.8942 - 29.2615i) q^{39} -19.6861i q^{41} +(-4.61481 + 16.5137i) q^{42} -2.53339i q^{43} +(-3.31404 - 5.74009i) q^{44} +(8.46486 - 14.6616i) q^{46} +(9.14110 + 15.8328i) q^{47} +6.92820 q^{48} +(41.9012 + 25.4026i) q^{49} +(7.30003 + 12.6440i) q^{51} +(-19.5077 + 33.7883i) q^{52} +(27.6846 + 15.9837i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(5.32872 - 19.0684i) q^{56} -1.40934i q^{57} +(5.74009 - 3.31404i) q^{58} +(-64.3758 - 37.1674i) q^{59} +(95.1577 - 54.9393i) q^{61} -45.6199 q^{62} +(5.21781 + 20.3414i) q^{63} -8.00000 q^{64} +(-7.03015 - 4.05886i) q^{66} +(81.9962 + 47.3405i) q^{67} +(-8.42935 - 14.6001i) q^{68} -20.7346i q^{69} +98.0047 q^{71} +(7.34847 - 4.24264i) q^{72} +(5.55809 - 9.62690i) q^{73} +(4.26092 - 7.38013i) q^{74} +1.62737i q^{76} +(-16.5783 + 16.2272i) q^{77} +47.7839i q^{78} +(0.500763 + 0.867346i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(13.9202 + 24.1105i) q^{82} -66.8044 q^{83} +(-6.02501 - 23.4883i) q^{84} +(1.79138 + 3.10276i) q^{86} +(4.05886 - 7.03015i) q^{87} +(8.11772 + 4.68677i) q^{88} +(-133.528 + 77.0927i) q^{89} +(131.515 + 36.7523i) q^{91} +23.9422i q^{92} +(-48.3872 + 27.9363i) q^{93} +(-22.3910 - 12.9275i) q^{94} +(-8.48528 + 4.89898i) q^{96} +132.023 q^{97} +(-69.2806 - 1.48309i) q^{98} -9.94213 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 $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

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

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
$7$	−6.74171	−	1.88399i	−0.963101	−	0.269141i
$7$	−6.74171	−	1.88399i	−0.963101	−	0.269141i
$8$			2.82843i			0.353553i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.65702	−	2.87005i	0.150638	−	0.260913i	−0.780824	−	0.624751i	$-0.785200\pi$
$11$	1.65702	−	2.87005i	0.150638	−	0.260913i	0.931462	+	0.363838i	$0.118534\pi$
$12$	1.73205	+	3.00000i	0.144338	+	0.250000i
$13$	−19.5077			−1.50059			−0.750296	−	0.661103i	$-0.770089\pi$
$13$	−19.5077			−1.50059			−0.750296	+	0.661103i	$0.770089\pi$
$14$	9.58905	−	2.45970i	0.684932	−	0.175693i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	4.21467	−	7.30003i	0.247922	−	0.429414i	−0.715027	−	0.699097i	$-0.753586\pi$
$17$	4.21467	−	7.30003i	0.247922	−	0.429414i	0.962949	+	0.269683i	$0.0869190\pi$
$18$	3.67423	+	2.12132i	0.204124	+	0.117851i
$19$	−0.704670	+	0.406841i	−0.0370879	+	0.0214127i	−0.518429	−	0.855120i	$-0.673483\pi$
$19$	−0.704670	+	0.406841i	−0.0370879	+	0.0214127i	0.481341	+	0.876533i	$0.340150\pi$
$20$		0			0
$21$	8.66447	−	8.48098i	0.412594	−	0.403856i
$22$			4.68677i			0.213035i
$23$	−10.3673	+	5.98556i	−0.450752	+	0.260242i	−0.708148	−	0.706064i	$-0.750469\pi$
$23$	−10.3673	+	5.98556i	−0.450752	+	0.260242i	0.257396	+	0.966306i	$0.417136\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$		0			0
$26$	23.8919	−	13.7940i	0.918921	−	0.530539i
$27$	5.19615			0.192450
$28$	−10.0049	+	9.79299i	−0.357317	+	0.349750i
$29$	−4.68677			−0.161613			−0.0808063	−	0.996730i	$-0.525750\pi$
$29$	−4.68677			−0.161613			−0.0808063	+	0.996730i	$0.525750\pi$
$30$		0			0
$31$	27.9363	+	16.1291i	0.901172	+	0.520292i	0.877580	−	0.479430i	$-0.159156\pi$
$31$	27.9363	+	16.1291i	0.901172	+	0.520292i	0.0235920	+	0.999722i	$0.492490\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$	2.87005	+	4.97107i	0.0869711	+	0.150638i
$34$			11.9209i			0.350615i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	−5.21854	+	3.01293i	−0.141042	+	0.0814304i	−0.568860	−	0.822434i	$-0.692616\pi$
$37$	−5.21854	+	3.01293i	−0.141042	+	0.0814304i	0.427819	+	0.903865i	$0.359282\pi$
$38$	0.575361	−	0.996554i	0.0151411	−	0.0262251i
$39$	16.8942	−	29.2615i	0.433183	−	0.750296i
$40$		0			0
$41$		−	19.6861i		−	0.480150i	−0.970754	−	0.240075i	$-0.922828\pi$
$41$		−	19.6861i		−	0.480150i	0.970754	−	0.240075i	$-0.0771720\pi$
$42$	−4.61481	+	16.5137i	−0.109876	+	0.393184i
$43$		−	2.53339i		−	0.0589160i	−0.999566	−	0.0294580i	$-0.990622\pi$
$43$		−	2.53339i		−	0.0589160i	0.999566	−	0.0294580i	$-0.00937814\pi$
$44$	−3.31404	−	5.74009i	−0.0753192	−	0.130457i
$45$		0			0
$46$	8.46486	−	14.6616i	0.184019	−	0.318730i
$47$	9.14110	+	15.8328i	0.194491	+	0.336869i	0.946734	−	0.322018i	$-0.104361\pi$
$47$	9.14110	+	15.8328i	0.194491	+	0.336869i	−0.752242	+	0.658887i	$0.771028\pi$
$48$	6.92820			0.144338
$49$	41.9012	+	25.4026i	0.855126	+	0.518420i
$50$		0			0
$51$	7.30003	+	12.6440i	0.143138	+	0.247922i
$52$	−19.5077	+	33.7883i	−0.375148	+	0.649775i
$53$	27.6846	+	15.9837i	0.522351	+	0.301580i	0.737896	−	0.674914i	$-0.235819\pi$
$53$	27.6846	+	15.9837i	0.522351	+	0.301580i	−0.215545	+	0.976494i	$0.569153\pi$
$54$	−6.36396	+	3.67423i	−0.117851	+	0.0680414i
$55$		0			0
$56$	5.32872	−	19.0684i	0.0951558	−	0.340508i
$57$		−	1.40934i		−	0.0247253i
$58$	5.74009	−	3.31404i	0.0989671	−	0.0571387i
$59$	−64.3758	−	37.1674i	−1.09111	−	0.629956i	−0.157242	−	0.987560i	$-0.550260\pi$
$59$	−64.3758	−	37.1674i	−1.09111	−	0.629956i	−0.933873	+	0.357605i	$0.883594\pi$
$60$		0			0
$61$	95.1577	−	54.9393i	1.55996	−	0.900645i	0.562704	−	0.826659i	$-0.309761\pi$
$61$	95.1577	−	54.9393i	1.55996	−	0.900645i	0.997259	−	0.0739862i	$-0.0235721\pi$
$62$	−45.6199			−0.735804
$63$	5.21781	+	20.3414i	0.0828224	+	0.322880i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−7.03015	−	4.05886i	−0.106517	−	0.0614979i
$67$	81.9962	+	47.3405i	1.22382	+	0.706575i	0.965731	−	0.259545i	$-0.0835725\pi$
$67$	81.9962	+	47.3405i	1.22382	+	0.706575i	0.258093	+	0.966120i	$0.416906\pi$
$68$	−8.42935	−	14.6001i	−0.123961	−	0.214707i
$69$		−	20.7346i		−	0.300501i
$70$		0			0
$71$	98.0047			1.38035			0.690174	−	0.723643i	$-0.257534\pi$
$71$	98.0047			1.38035			0.690174	+	0.723643i	$0.257534\pi$
$72$	7.34847	−	4.24264i	0.102062	−	0.0589256i
$73$	5.55809	−	9.62690i	0.0761383	−	0.131875i	−0.825442	−	0.564486i	$-0.809074\pi$
$73$	5.55809	−	9.62690i	0.0761383	−	0.131875i	0.901581	+	0.432611i	$0.142408\pi$
$74$	4.26092	−	7.38013i	0.0575800	−	0.0997315i
$75$		0			0
$76$			1.62737i			0.0214127i
$77$	−16.5783	+	16.2272i	−0.215302	+	0.210743i
$78$			47.7839i			0.612614i
$79$	0.500763	+	0.867346i	0.00633877	+	0.0109791i	0.869177	−	0.494500i	$-0.164649\pi$
$79$	0.500763	+	0.867346i	0.00633877	+	0.0109791i	−0.862839	+	0.505479i	$0.831316\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	13.9202	+	24.1105i	0.169759	+	0.294031i
$83$	−66.8044			−0.804872			−0.402436	−	0.915448i	$-0.631836\pi$
$83$	−66.8044			−0.804872			−0.402436	+	0.915448i	$0.631836\pi$
$84$	−6.02501	−	23.4883i	−0.0717263	−	0.279622i
$85$		0			0
$86$	1.79138	+	3.10276i	0.0208300	+	0.0360786i
$87$	4.05886	−	7.03015i	0.0466536	−	0.0808063i
$88$	8.11772	+	4.68677i	0.0922468	+	0.0532587i
$89$	−133.528	+	77.0927i	−1.50032	+	0.866210i	−0.500319	+	0.865841i	$0.666784\pi$
$89$	−133.528	+	77.0927i	−1.50032	+	0.866210i	−1.00000		0.000368641i	$0.999883\pi$
$90$		0			0
$91$	131.515	+	36.7523i	1.44522	+	0.403871i
$92$			23.9422i			0.260242i
$93$	−48.3872	+	27.9363i	−0.520292	+	0.300391i
$94$	−22.3910	−	12.9275i	−0.238202	−	0.137526i
$95$		0			0
$96$	−8.48528	+	4.89898i	−0.0883883	+	0.0510310i
$97$	132.023			1.36107			0.680533	−	0.732717i	$-0.261748\pi$
$97$	132.023			1.36107			0.680533	+	0.732717i	$0.261748\pi$
$98$	−69.2806	−	1.48309i	−0.706945	−	0.0151336i
$99$	−9.94213			−0.100426
$100$		0			0
$101$	−15.3107	−	8.83965i	−0.151591	−	0.0875213i	0.422286	−	0.906463i	$-0.361228\pi$
$101$	−15.3107	−	8.83965i	−0.151591	−	0.0875213i	−0.573877	+	0.818942i	$0.694561\pi$
$102$	−17.8813	−	10.3238i	−0.175307	−	0.101214i
$103$	19.5981	+	33.9450i	0.190273	+	0.329563i	0.945341	−	0.326084i	$-0.105729\pi$
$103$	19.5981	+	33.9450i	0.190273	+	0.329563i	−0.755067	+	0.655647i	$0.772396\pi$
$104$		−	55.1761i		−	0.530539i
$105$		0			0
$106$	−45.2088			−0.426498
$107$	115.181	−	66.5000i	1.07646	−	0.621495i	0.146522	−	0.989207i	$-0.453192\pi$
$107$	115.181	−	66.5000i	1.07646	−	0.621495i	0.929940	+	0.367712i	$0.119859\pi$
$108$	5.19615	−	9.00000i	0.0481125	−	0.0833333i
$109$	−24.5640	+	42.5461i	−0.225358	+	0.390332i	−0.956427	−	0.291972i	$-0.905689\pi$
$109$	−24.5640	+	42.5461i	−0.225358	+	0.390332i	0.731069	+	0.682304i	$0.239022\pi$
$110$		0			0
$111$		−	10.4371i		−	0.0940278i
$112$	6.95708	+	27.1219i	0.0621168	+	0.242160i
$113$			141.909i			1.25583i	0.778282	+	0.627915i	$0.216092\pi$
$113$			141.909i			1.25583i	−0.778282	+	0.627915i	$0.783908\pi$
$114$	0.996554	+	1.72608i	0.00874170	+	0.0151411i
$115$		0			0
$116$	−4.68677	+	8.11772i	−0.0404032	+	0.0699803i
$117$	29.2615	+	50.6825i	0.250099	+	0.433183i
$118$	105.125			0.890892
$119$	−42.1673	+	41.2742i	−0.354347	+	0.346842i
$120$		0			0
$121$	55.0086	+	95.2776i	0.454616	+	0.787418i
$122$	−77.6960	+	134.573i	−0.636852	+	1.10306i
$123$	29.5292	+	17.0487i	0.240075	+	0.138607i
$124$	55.8727	−	32.2581i	0.450586	−	0.260146i
$125$		0			0
$126$	−20.7741	−	21.2235i	−0.164874	−	0.168441i
$127$			87.2663i			0.687137i	0.939128	+	0.343568i	$0.111636\pi$
$127$			87.2663i			0.687137i	−0.939128	+	0.343568i	$0.888364\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$	3.80008	+	2.19398i	0.0294580	+	0.0170076i
$130$		0			0
$131$	95.2814	−	55.0107i	0.727339	−	0.419929i	−0.0901091	−	0.995932i	$-0.528722\pi$
$131$	95.2814	−	55.0107i	0.727339	−	0.419929i	0.817448	+	0.576003i	$0.195388\pi$
$132$	11.4802			0.0869711
$133$	5.51716	−	1.41521i	0.0414824	−	0.0106407i
$134$	−133.899			−0.999248
$135$		0			0
$136$	20.6476	+	11.9209i	0.151821	+	0.0876537i
$137$	−119.222	−	68.8331i	−0.870237	−	0.502431i	−0.00280972	−	0.999996i	$-0.500894\pi$
$137$	−119.222	−	68.8331i	−0.870237	−	0.502431i	−0.867427	+	0.497565i	$0.834228\pi$
$138$	14.6616	+	25.3946i	0.106243	+	0.184019i
$139$		−	68.6829i		−	0.494122i	−0.969000	−	0.247061i	$-0.920535\pi$
$139$		−	68.6829i		−	0.494122i	0.969000	−	0.247061i	$-0.0794648\pi$
$140$		0			0
$141$	−31.6657			−0.224579
$142$	−120.031	+	69.2998i	−0.845287	+	0.488027i
$143$	−32.3247	+	55.9880i	−0.226047	+	0.391524i
$144$	−6.00000	+	10.3923i	−0.0416667	+	0.0721688i
$145$		0			0
$146$			15.7207i			0.107676i
$147$	−74.3914	+	40.8525i	−0.506064	+	0.277908i
$148$			12.0517i			0.0814304i
$149$	91.7993	+	159.001i	0.616102	+	1.06712i	0.990190	+	0.139727i	$0.0446226\pi$
$149$	91.7993	+	159.001i	0.616102	+	1.06712i	−0.374088	+	0.927393i	$0.622044\pi$
$150$		0			0
$151$	−70.7469	+	122.537i	−0.468523	+	0.811505i	−0.999353	−	0.0359734i	$-0.988547\pi$
$151$	−70.7469	+	122.537i	−0.468523	+	0.811505i	0.530830	+	0.847478i	$0.321880\pi$
$152$	−1.15072	−	1.99311i	−0.00757054	−	0.0131126i
$153$	−25.2880			−0.165281
$154$	8.82982	−	31.5968i	0.0573365	−	0.205174i
$155$		0			0
$156$	−33.7883	−	58.5231i	−0.216592	−	0.375148i
$157$	−85.8044	+	148.618i	−0.546525	+	0.946609i	0.451984	+	0.892026i	$0.350716\pi$
$157$	−85.8044	+	148.618i	−0.546525	+	0.946609i	−0.998509	+	0.0545830i	$0.982617\pi$
$158$	−1.22661	−	0.708185i	−0.00776337	−	0.00448219i
$159$	−47.9511	+	27.6846i	−0.301580	+	0.174117i
$160$		0			0
$161$	81.1699	−	20.8210i	0.504161	−	0.129323i
$162$		−	12.7279i		−	0.0785674i
$163$	255.872	−	147.728i	1.56977	−	0.906306i	0.573573	−	0.819154i	$-0.305557\pi$
$163$	255.872	−	147.728i	1.56977	−	0.906306i	0.996195	−	0.0871517i	$-0.0277765\pi$
$164$	−34.0974	−	19.6861i	−0.207911	−	0.120037i
$165$		0			0
$166$	81.8183	−	47.2378i	0.492882	−	0.284565i
$167$	168.538			1.00921			0.504604	−	0.863351i	$-0.331639\pi$
$167$	168.538			1.00921			0.504604	+	0.863351i	$0.331639\pi$
$168$	23.9878	+	24.5068i	0.142785	+	0.145874i
$169$	211.550			1.25177
$170$		0			0
$171$	2.11401	+	1.22052i	0.0123626	+	0.00713757i
$172$	−4.38796	−	2.53339i	−0.0255114	−	0.0147290i
$173$	74.5349	+	129.098i	0.430838	+	0.746232i	0.996946	−	0.0780985i	$-0.0248849\pi$
$173$	74.5349	+	129.098i	0.430838	+	0.746232i	−0.566108	+	0.824331i	$0.691552\pi$
$174$			11.4802i			0.0659781i
$175$		0			0
$176$	−13.2562			−0.0753192
$177$	111.502	−	64.3758i	0.629956	−	0.363705i
$178$	109.025	−	188.838i	0.612503	−	1.06089i
$179$	−141.413	+	244.935i	−0.790018	+	1.36835i	0.135937	+	0.990718i	$0.456596\pi$
$179$	−141.413	+	244.935i	−0.790018	+	1.36835i	−0.925955	+	0.377634i	$0.876738\pi$
$180$		0			0
$181$			305.418i			1.68739i	0.536820	+	0.843697i	$0.319625\pi$
$181$			305.418i			1.68739i	−0.536820	+	0.843697i	$0.680375\pi$
$182$	−187.060	+	47.9831i	−1.02780	+	0.263643i
$183$			190.315i			1.03998i
$184$	−16.9297	−	29.3231i	−0.0920093	−	0.159365i
$185$		0			0
$186$	39.5080	−	68.4298i	0.212408	−	0.367902i
$187$	−13.9676	−	24.1926i	−0.0746931	−	0.129372i
$188$	36.5644			0.194491
$189$	−35.0309	−	9.78949i	−0.185349	−	0.0517963i
$190$		0			0
$191$	−24.3372	−	42.1533i	−0.127420	−	0.220698i	0.795256	−	0.606273i	$-0.207336\pi$
$191$	−24.3372	−	42.1533i	−0.127420	−	0.220698i	−0.922676	+	0.385576i	$0.874003\pi$
$192$	6.92820	−	12.0000i	0.0360844	−	0.0625000i
$193$	−129.500	−	74.7666i	−0.670982	−	0.387392i	0.125467	−	0.992098i	$-0.459957\pi$
$193$	−129.500	−	74.7666i	−0.670982	−	0.387392i	−0.796449	+	0.604706i	$0.793291\pi$
$194$	−161.695	+	93.3547i	−0.833479	+	0.481210i
$195$		0			0
$196$	85.8998	−	47.1724i	0.438264	−	0.240675i
$197$		−	219.479i		−	1.11411i	−0.830477	−	0.557053i	$-0.811932\pi$
$197$		−	219.479i		−	1.11411i	0.830477	−	0.557053i	$-0.188068\pi$
$198$	12.1766	−	7.03015i	0.0614979	−	0.0355058i
$199$	254.396	+	146.875i	1.27837	+	0.738067i	0.976548	−	0.215298i	$-0.0690721\pi$
$199$	254.396	+	146.875i	1.27837	+	0.738067i	0.301821	+	0.953365i	$0.402405\pi$
$200$		0			0
$201$	−142.022	+	81.9962i	−0.706575	+	0.407941i
$202$	25.0023			0.123774
$203$	31.5968	+	8.82982i	0.155649	+	0.0434966i
$204$	29.2001			0.143138
$205$		0			0
$206$	−48.0055	−	27.7160i	−0.233036	−	0.134544i
$207$	31.1019	+	17.9567i	0.150251	+	0.0867472i
$208$	39.0154	+	67.5766i	0.187574	+	0.324888i
$209$			2.69658i			0.0129023i
$210$		0			0
$211$	122.768			0.581841			0.290920	−	0.956747i	$-0.406039\pi$
$211$	122.768			0.581841			0.290920	+	0.956747i	$0.406039\pi$
$212$	55.3692	−	31.9674i	0.261176	−	0.150790i
$213$	−84.8746	+	147.007i	−0.398472	+	0.690174i
$214$	−94.0452	+	162.891i	−0.439463	+	0.761173i
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	−157.952	−	161.369i	−0.727888	−	0.743636i
$218$		−	69.4776i		−	0.318704i
$219$	9.62690	+	16.6743i	0.0439585	+	0.0761383i
$220$		0			0
$221$	−82.2185	+	142.407i	−0.372030	+	0.644374i
$222$	7.38013	+	12.7828i	0.0332438	+	0.0575800i
$223$	3.70845			0.0166298			0.00831491	−	0.999965i	$-0.497353\pi$
$223$	3.70845			0.0166298			0.00831491	+	0.999965i	$0.497353\pi$
$224$	−27.6988	−	28.2980i	−0.123655	−	0.126331i
$225$		0			0
$226$	−100.345	−	173.802i	−0.444003	−	0.769036i
$227$	76.1393	−	131.877i	0.335416	−	0.580957i	−0.648149	−	0.761514i	$-0.724457\pi$
$227$	76.1393	−	131.877i	0.335416	−	0.580957i	0.983565	+	0.180557i	$0.0577899\pi$
$228$	−2.44105	−	1.40934i	−0.0107064	−	0.00618132i
$229$	123.917	−	71.5435i	0.541123	−	0.312417i	−0.204411	−	0.978885i	$-0.565528\pi$
$229$	123.917	−	71.5435i	0.541123	−	0.312417i	0.745534	+	0.666468i	$0.232195\pi$
$230$		0			0
$231$	−9.98358	−	38.9206i	−0.0432189	−	0.168487i
$232$		−	13.2562i		−	0.0571387i
$233$	62.3109	−	35.9752i	0.267429	−	0.154400i	−0.360290	−	0.932840i	$-0.617322\pi$
$233$	62.3109	−	35.9752i	0.267429	−	0.154400i	0.627719	+	0.778440i	$0.283989\pi$
$234$	−71.6758	−	41.3820i	−0.306307	−	0.176846i
$235$		0			0
$236$	−128.752	+	74.3347i	−0.545557	+	0.314978i
$237$	−1.73469			−0.00731938
$238$	22.4588	−	80.3672i	0.0943649	−	0.337677i
$239$	453.719			1.89840			0.949202	−	0.314667i	$-0.101893\pi$
$239$	453.719			1.89840			0.949202	+	0.314667i	$0.101893\pi$
$240$		0			0
$241$	−163.281	−	94.2706i	−0.677516	−	0.391164i	0.121402	−	0.992603i	$-0.461261\pi$
$241$	−163.281	−	94.2706i	−0.677516	−	0.391164i	−0.798919	+	0.601439i	$0.794594\pi$
$242$	−134.743	−	77.7938i	−0.556789	−	0.321462i
$243$	−7.79423	−	13.5000i	−0.0320750	−	0.0555556i
$244$		−	219.757i		−	0.900645i
$245$		0			0
$246$	−48.2210			−0.196020
$247$	13.7465	−	7.93653i	0.0556538	−	0.0321317i
$248$	−45.6199	+	79.0159i	−0.183951	+	0.318613i
$249$	57.8543	−	100.207i	0.232347	−	0.402436i
$250$		0			0
$251$		−	233.911i		−	0.931917i	−0.884807	−	0.465958i	$-0.845710\pi$
$251$		−	233.911i		−	0.931917i	0.884807	−	0.465958i	$-0.154290\pi$
$252$	40.4502	+	11.3039i	0.160517	+	0.0448569i
$253$			39.6728i			0.156810i
$254$	−61.7066	−	106.879i	−0.242939	−	0.420783i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−94.0516	−	162.902i	−0.365960	−	0.633861i	0.622970	−	0.782246i	$-0.285926\pi$
$257$	−94.0516	−	162.902i	−0.365960	−	0.633861i	−0.988930	+	0.148385i	$0.952592\pi$
$258$	−6.20551			−0.0240524
$259$	40.8582	−	10.4806i	0.157754	−	0.0404656i
$260$		0			0
$261$	7.03015	+	12.1766i	0.0269354	+	0.0466536i
$262$	−77.7969	+	134.748i	−0.296935	+	0.514306i
$263$	−293.219	−	169.290i	−1.11490	−	0.643688i	−0.174806	−	0.984603i	$-0.555930\pi$
$263$	−293.219	−	169.290i	−1.11490	−	0.643688i	−0.940094	+	0.340915i	$0.889263\pi$
$264$	−14.0603	+	8.11772i	−0.0532587	+	0.0307489i
$265$		0			0
$266$	−5.75641	+	5.63450i	−0.0216406	+	0.0211823i
$267$		−	267.057i		−	1.00021i
$268$	163.992	−	94.6811i	0.611912	−	0.353288i
$269$	−453.034	−	261.559i	−1.68414	−	0.972340i	−0.958856	−	0.283893i	$-0.908374\pi$
$269$	−453.034	−	261.559i	−1.68414	−	0.972340i	−0.725286	−	0.688448i	$-0.758293\pi$
$270$		0			0
$271$	385.799	−	222.741i	1.42361	−	0.821923i	0.427006	−	0.904249i	$-0.359568\pi$
$271$	385.799	−	222.741i	1.42361	−	0.821923i	0.996605	+	0.0823259i	$0.0262348\pi$
$272$	−33.7174			−0.123961
$273$	−169.024	+	165.444i	−0.619135	+	0.606023i
$274$	194.689			0.710545
$275$		0			0
$276$	−35.9133	−	20.7346i	−0.130121	−	0.0751253i
$277$	12.5865	+	7.26684i	0.0454388	+	0.0262341i	0.522547	−	0.852610i	$-0.324982\pi$
$277$	12.5865	+	7.26684i	0.0454388	+	0.0262341i	−0.477109	+	0.878844i	$0.658315\pi$
$278$	48.5662	+	84.1191i	0.174698	+	0.302587i
$279$		−	96.7743i		−	0.346861i
$280$		0			0
$281$	−526.257			−1.87280			−0.936400	−	0.350933i	$-0.885864\pi$
$281$	−526.257			−1.87280			−0.936400	+	0.350933i	$0.885864\pi$
$282$	38.7824	−	22.3910i	0.137526	−	0.0794008i
$283$	252.081	−	436.617i	0.890746	−	1.54282i	0.0517626	−	0.998659i	$-0.483516\pi$
$283$	252.081	−	436.617i	0.890746	−	1.54282i	0.838983	−	0.544157i	$-0.183151\pi$
$284$	98.0047	−	169.749i	0.345087	−	0.597708i
$285$		0			0
$286$		−	91.4280i		−	0.319678i
$287$	−37.0885	+	132.718i	−0.129228	+	0.462433i
$288$		−	16.9706i		−	0.0589256i
$289$	108.973	+	188.747i	0.377069	+	0.653103i
$290$		0			0
$291$	−114.336	+	198.035i	−0.392906	+	0.680533i
$292$	−11.1162	−	19.2538i	−0.0380691	−	0.0659377i
$293$	−220.145			−0.751348			−0.375674	−	0.926752i	$-0.622589\pi$
$293$	−220.145			−0.751348			−0.375674	+	0.926752i	$0.622589\pi$
$294$	62.2234	−	102.636i	0.211644	−	0.349104i
$295$		0			0
$296$	−8.52184	−	14.7603i	−0.0287900	−	0.0498657i
$297$	8.61014	−	14.9132i	0.0289904	−	0.0502128i
$298$	−224.861	−	129.824i	−0.754568	−	0.435650i
$299$	202.242	−	116.764i	0.676394	−	0.390516i
$300$		0			0
$301$	−4.77288	+	17.0794i	−0.0158567	+	0.0567421i
$302$		−	200.102i		−	0.662591i
$303$	26.5190	−	15.3107i	0.0875213	−	0.0505305i
$304$	2.81868	+	1.62737i	0.00927197	+	0.00535318i
$305$		0			0
$306$	30.9714	−	17.8813i	0.101214	−	0.0584358i
$307$	−183.623			−0.598120			−0.299060	−	0.954234i	$-0.596673\pi$
$307$	−183.623			−0.598120			−0.299060	+	0.954234i	$0.596673\pi$
$308$	11.5280	+	44.9416i	0.0374287	+	0.145914i
$309$	−67.8900			−0.219709
$310$		0			0
$311$	−195.658	−	112.963i	−0.629126	−	0.363226i	0.151288	−	0.988490i	$-0.451658\pi$
$311$	−195.658	−	112.963i	−0.629126	−	0.363226i	−0.780414	+	0.625264i	$0.784991\pi$
$312$	82.7641	+	47.7839i	0.265270	+	0.153153i
$313$	−133.773	−	231.701i	−0.427388	−	0.740258i	0.569252	−	0.822163i	$-0.307233\pi$
$313$	−133.773	−	231.701i	−0.427388	−	0.740258i	−0.996640	+	0.0819050i	$0.973900\pi$
$314$		−	242.692i		−	0.772903i
$315$		0			0
$316$	2.00305			0.00633877
$317$	458.814	−	264.896i	1.44736	−	0.835635i	0.449038	−	0.893513i	$-0.351767\pi$
$317$	458.814	−	264.896i	1.44736	−	0.835635i	0.998324	+	0.0578777i	$0.0184333\pi$
$318$	39.1519	−	67.8132i	0.123119	−	0.213249i
$319$	−7.76608	+	13.4512i	−0.0243451	+	0.0421669i
$320$		0			0
$321$			230.363i			0.717641i
$322$	−84.6898	+	82.8962i	−0.263012	+	0.257442i
$323$			6.85882i			0.0212347i
$324$	9.00000	+	15.5885i	0.0277778	+	0.0481125i
$325$		0			0
$326$	−208.919	+	361.858i	−0.640855	+	1.10999i
$327$	−42.5461	−	73.6921i	−0.130111	−	0.225358i
$328$	55.6808			0.169759
$329$	−31.7977	−	123.962i	−0.0966495	−	0.376784i
$330$		0			0
$331$	102.815	+	178.081i	0.310619	+	0.538008i	0.978497	−	0.206263i	$-0.0661302\pi$
$331$	102.815	+	178.081i	0.310619	+	0.538008i	−0.667877	+	0.744271i	$0.732797\pi$
$332$	−66.8044	+	115.709i	−0.201218	+	0.348520i
$333$	15.6556	+	9.03878i	0.0470139	+	0.0271435i
$334$	−206.416	+	119.174i	−0.618011	+	0.356809i
$335$		0			0
$336$	−46.7079	−	13.0527i	−0.139012	−	0.0388472i
$337$		−	333.809i		−	0.990530i	−0.868742	−	0.495265i	$-0.835071\pi$
$337$		−	333.809i		−	0.990530i	0.868742	−	0.495265i	$-0.164929\pi$
$338$	−259.094	+	149.588i	−0.766552	+	0.442569i
$339$	−212.863	−	122.897i	−0.627915	−	0.362527i
$340$		0			0
$341$	92.5823	−	53.4524i	0.271502	−	0.156752i
$342$	−3.45216			−0.0100940
$343$	−234.627	−	250.198i	−0.684044	−	0.729441i
$344$	7.16551			0.0208300
$345$		0			0
$346$	−182.572	−	105.408i	−0.527666	−	0.304648i
$347$	565.569	+	326.532i	1.62988	+	0.941013i	0.984126	+	0.177470i	$0.0567913\pi$
$347$	565.569	+	326.532i	1.62988	+	0.941013i	0.645757	+	0.763543i	$0.276542\pi$
$348$	−8.11772	−	14.0603i	−0.0233268	−	0.0404032i
$349$			244.056i			0.699301i	0.936880	+	0.349651i	$0.113700\pi$
$349$			244.056i			0.699301i	−0.936880	+	0.349651i	$0.886300\pi$
$350$		0			0
$351$	−101.365			−0.288789
$352$	16.2354	−	9.37353i	0.0461234	−	0.0266294i
$353$	208.759	−	361.582i	0.591387	−	1.02431i	−0.402659	−	0.915350i	$-0.631914\pi$
$353$	208.759	−	361.582i	0.591387	−	1.02431i	0.994046	−	0.108962i	$-0.0347526\pi$
$354$	−91.0411	+	157.688i	−0.257178	+	0.445446i
$355$		0			0
$356$			308.371i			0.866210i
$357$	−25.3935	−	98.9954i	−0.0711301	−	0.277298i
$358$		−	399.977i		−	1.11725i
$359$	147.477	+	255.438i	0.410800	+	0.711527i	0.994977	−	0.100099i	$-0.0319161\pi$
$359$	147.477	+	255.438i	0.410800	+	0.711527i	−0.584177	+	0.811626i	$0.698583\pi$
$360$		0			0
$361$	−180.169	+	312.062i	−0.499083	+	0.864437i
$362$	−215.963	−	374.059i	−0.596584	−	1.03331i
$363$	−190.555			−0.524946
$364$	195.172	−	191.039i	0.536186	−	0.524831i
$365$		0			0
$366$	−134.573	−	233.088i	−0.367687	−	0.636852i
$367$	−11.8146	+	20.4635i	−0.0321924	+	0.0557589i	−0.881673	−	0.471861i	$-0.843582\pi$
$367$	−11.8146	+	20.4635i	−0.0321924	+	0.0557589i	0.849480	+	0.527620i	$0.176916\pi$
$368$	41.4692	+	23.9422i	0.112688	+	0.0650604i
$369$	−51.1461	+	29.5292i	−0.138607	+	0.0800250i
$370$		0			0
$371$	−156.528	−	159.915i	−0.421909	−	0.431038i
$372$			111.745i			0.300391i
$373$	143.727	−	82.9807i	0.385326	−	0.222468i	−0.294807	−	0.955557i	$-0.595255\pi$
$373$	143.727	−	82.9807i	0.385326	−	0.222468i	0.680133	+	0.733089i	$0.261922\pi$
$374$	34.2135	+	19.7532i	0.0914800	+	0.0528160i
$375$		0			0
$376$	−44.7820	+	25.8549i	−0.119101	+	0.0687631i
$377$	91.4280			0.242515
$378$	49.8262	−	12.7810i	0.131815	−	0.0338121i
$379$	456.876			1.20548			0.602739	−	0.797938i	$-0.294076\pi$
$379$	456.876			1.20548			0.602739	+	0.797938i	$0.294076\pi$
$380$		0			0
$381$	−130.900	−	75.5749i	−0.343568	−	0.198359i
$382$	59.6137	+	34.4180i	0.156057	+	0.0900995i
$383$	3.33737	+	5.78050i	0.00871377	+	0.0150927i	0.870349	−	0.492435i	$-0.163893\pi$
$383$	3.33737	+	5.78050i	0.00871377	+	0.0150927i	−0.861636	+	0.507527i	$0.830560\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	211.472			0.547855
$387$	−6.58194	+	3.80008i	−0.0170076	+	0.00981934i
$388$	132.023	−	228.671i	0.340267	−	0.589359i
$389$	106.375	−	184.246i	0.273456	−	0.473640i	−0.696288	−	0.717762i	$-0.745166\pi$
$389$	106.375	−	184.246i	0.273456	−	0.473640i	0.969745	+	0.244122i	$0.0784997\pi$
$390$		0			0
$391$			100.909i			0.258079i
$392$	−71.8494	+	118.514i	−0.183289	+	0.302333i
$393$			190.563i			0.484892i
$394$	155.195	+	268.806i	0.393896	+	0.682248i
$395$		0			0
$396$	−9.94213	+	17.2203i	−0.0251064	+	0.0434856i
$397$	126.909	+	219.812i	0.319669	+	0.553684i	0.980419	−	0.196923i	$-0.0630948\pi$
$397$	126.909	+	219.812i	0.319669	+	0.553684i	−0.660750	+	0.750606i	$0.729762\pi$
$398$	−415.426			−1.04378
$399$	−2.65518	+	9.50135i	−0.00665459	+	0.0238129i
$400$		0			0
$401$	−275.993	−	478.033i	−0.688261	−	1.19210i	−0.972400	−	0.233319i	$-0.925041\pi$
$401$	−275.993	−	478.033i	−0.688261	−	1.19210i	0.284140	−	0.958783i	$-0.408292\pi$
$402$	115.960	−	200.849i	0.288458	−	0.499624i
$403$	−544.973	−	314.641i	−1.35229	−	0.780746i
$404$	−30.6215	+	17.6793i	−0.0757957	+	0.0437607i
$405$		0			0
$406$	−44.9416	+	11.5280i	−0.110694	+	0.0283942i
$407$			19.9699i			0.0490662i
$408$	−35.7627	+	20.6476i	−0.0876537	+	0.0506069i
$409$	−135.412	−	78.1800i	−0.331080	−	0.191149i	0.325241	−	0.945631i	$-0.394555\pi$
$409$	−135.412	−	78.1800i	−0.331080	−	0.191149i	−0.656320	+	0.754482i	$0.727888\pi$
$410$		0			0
$411$	206.499	−	119.222i	0.502431	−	0.290079i
$412$	78.3926			0.190273
$413$	363.980	+	371.855i	0.881307	+	0.900375i
$414$	−50.7891			−0.122679
$415$		0			0
$416$	−95.5677	−	55.1761i	−0.229730	−	0.132635i
$417$	103.024	+	59.4812i	0.247061	+	0.142641i
$418$	−1.90677	−	3.30262i	−0.00456165	−	0.00790101i
$419$			57.3609i			0.136899i	0.997655	+	0.0684497i	$0.0218053\pi$
$419$			57.3609i			0.136899i	−0.997655	+	0.0684497i	$0.978195\pi$
$420$		0			0
$421$	−334.545			−0.794644			−0.397322	−	0.917679i	$-0.630060\pi$
$421$	−334.545			−0.794644			−0.397322	+	0.917679i	$0.630060\pi$
$422$	−150.360	+	86.8104i	−0.356303	+	0.205712i
$423$	27.4233	−	47.4985i	0.0648305	−	0.112290i
$424$	−45.2088	+	78.3039i	−0.106624	+	0.184679i
$425$		0			0
$426$		−	240.062i		−	0.563525i
$427$	−745.030	+	191.109i	−1.74480	+	0.447562i
$428$		−	266.000i		−	0.621495i
$429$	−55.9880	−	96.9740i	−0.130508	−	0.226047i
$430$		0			0
$431$	−223.891	+	387.791i	−0.519469	+	0.899746i	0.480275	+	0.877118i	$0.340537\pi$
$431$	−223.891	+	387.791i	−0.519469	+	0.899746i	−0.999744	+	0.0226285i	$0.992797\pi$
$432$	−10.3923	−	18.0000i	−0.0240563	−	0.0416667i
$433$	236.914			0.547146			0.273573	−	0.961851i	$-0.411795\pi$
$433$	236.914			0.547146			0.273573	+	0.961851i	$0.411795\pi$
$434$	307.556	+	85.9473i	0.708654	+	0.198035i
$435$		0			0
$436$	49.1281	+	85.0923i	0.112679	+	0.195166i
$437$	4.87035	−	8.43569i	0.0111450	−	0.0193036i
$438$	−23.5810	−	13.6145i	−0.0538379	−	0.0310833i
$439$	176.852	−	102.105i	0.402852	−	0.232586i	−0.284862	−	0.958569i	$-0.591948\pi$
$439$	176.852	−	102.105i	0.402852	−	0.232586i	0.687714	+	0.725982i	$0.258614\pi$
$440$		0			0
$441$	3.14611	−	146.966i	0.00713403	−	0.333257i
$442$		−	232.549i		−	0.526129i
$443$	133.031	−	76.8057i	0.300297	−	0.173376i	−0.342279	−	0.939598i	$-0.611199\pi$
$443$	133.031	−	76.8057i	0.300297	−	0.173376i	0.642576	+	0.766222i	$0.277866\pi$
$444$	−18.0776	−	10.4371i	−0.0407152	−	0.0235069i
$445$		0			0
$446$	−4.54191	+	2.62227i	−0.0101836	+	0.00587953i
$447$	−318.002			−0.711414
$448$	53.9336	+	15.0719i	0.120388	+	0.0336427i
$449$	200.642			0.446864			0.223432	−	0.974720i	$-0.428274\pi$
$449$	200.642			0.446864			0.223432	+	0.974720i	$0.428274\pi$
$450$		0			0
$451$	−56.5002	−	32.6204i	−0.125278	−	0.0723290i
$452$	245.793	+	141.909i	0.543791	+	0.313958i
$453$	−122.537	−	212.241i	−0.270502	−	0.468523i
$454$			215.355i			0.474349i
$455$		0			0
$456$	3.98622			0.00874170
$457$	343.720	−	198.447i	0.752122	−	0.434238i	−0.0743379	−	0.997233i	$-0.523684\pi$
$457$	343.720	−	198.447i	0.752122	−	0.434238i	0.826460	+	0.562995i	$0.190351\pi$
$458$	−101.178	+	175.245i	−0.220912	+	0.382631i
$459$	21.9001	−	37.9321i	0.0477126	−	0.0826407i
$460$		0			0
$461$		−	337.389i		−	0.731864i	−0.930642	−	0.365932i	$-0.880750\pi$
$461$		−	337.389i		−	0.731864i	0.930642	−	0.365932i	$-0.119250\pi$
$462$	39.7484	+	40.6084i	0.0860354	+	0.0878969i
$463$		−	270.743i		−	0.584759i	−0.956302	−	0.292379i	$-0.905553\pi$
$463$		−	270.743i		−	0.584759i	0.956302	−	0.292379i	$-0.0944470\pi$
$464$	9.37353	+	16.2354i	0.0202016	+	0.0349902i
$465$		0			0
$466$	−50.8766	+	88.1209i	−0.109177	+	0.189101i
$467$	12.8689	+	22.2896i	0.0275565	+	0.0477292i	0.879475	−	0.475946i	$-0.157894\pi$
$467$	12.8689	+	22.2896i	0.0275565	+	0.0477292i	−0.851918	+	0.523675i	$0.824561\pi$
$468$	117.046			0.250099
$469$	−463.605	−	473.636i	−0.988498	−	1.00988i
$470$		0			0
$471$	−148.618	−	257.413i	−0.315536	−	0.546525i
$472$	105.125	−	182.082i	0.222723	−	0.385767i
$473$	−7.27095	−	4.19788i	−0.0153720	−	0.00887502i
$474$	2.12456	−	1.22661i	0.00448219	−	0.00258779i
$475$		0			0
$476$	29.3218	+	114.310i	0.0616005	+	0.240147i
$477$		−	95.9023i		−	0.201053i
$478$	−555.690	+	320.828i	−1.16253	+	0.671187i
$479$	−162.828	−	94.0089i	−0.339934	−	0.196261i	0.320309	−	0.947313i	$-0.396213\pi$
$479$	−162.828	−	94.0089i	−0.339934	−	0.196261i	−0.660243	+	0.751052i	$0.729547\pi$
$480$		0			0
$481$	101.802	−	58.7752i	0.211646	−	0.122194i
$482$	266.637			0.553190
$483$	−39.0637	+	139.786i	−0.0808773	+	0.289413i
$484$	220.034			0.454616
$485$		0			0
$486$	19.0919	+	11.0227i	0.0392837	+	0.0226805i
$487$	259.615	+	149.889i	0.533091	+	0.307780i	0.742274	−	0.670096i	$-0.233747\pi$
$487$	259.615	+	149.889i	0.533091	+	0.307780i	−0.209183	+	0.977876i	$0.567081\pi$
$488$	155.392	+	269.147i	0.318426	+	0.551530i
$489$			511.744i			1.04651i
$490$		0			0
$491$	461.533			0.939985			0.469993	−	0.882670i	$-0.344257\pi$
$491$	461.533			0.939985			0.469993	+	0.882670i	$0.344257\pi$
$492$	59.0584	−	34.0974i	0.120037	−	0.0693037i
$493$	−19.7532	+	34.2135i	−0.0400673	+	0.0693987i
$494$	−11.2240	+	19.4405i	−0.0227206	+	0.0393532i
$495$		0			0
$496$		−	129.032i		−	0.260146i
$497$	−660.719	−	184.640i	−1.32941	−	0.371509i
$498$			163.637i			0.328588i
$499$	−86.9948	−	150.679i	−0.174338	−	0.301963i	0.765594	−	0.643324i	$-0.222445\pi$
$499$	−86.9948	−	150.679i	−0.174338	−	0.301963i	−0.939932	+	0.341362i	$0.889112\pi$
$500$		0			0
$501$	−145.958	+	252.807i	−0.291333	+	0.504604i
$502$	165.400	+	286.481i	0.329482	+	0.570680i
$503$	−26.5806			−0.0528442			−0.0264221	−	0.999651i	$-0.508411\pi$
$503$	−26.5806			−0.0528442			−0.0264221	+	0.999651i	$0.508411\pi$
$504$	−57.5343	+	14.7582i	−0.114155	+	0.0292821i
$505$		0			0
$506$	−28.0529	−	48.5891i	−0.0554405	−	0.0960258i
$507$	−183.207	+	317.325i	−0.361356	+	0.625887i
$508$	151.150	+	87.2663i	0.297539	+	0.171784i
$509$	−74.1139	+	42.7897i	−0.145607	+	0.0840662i	−0.571034	−	0.820927i	$-0.693457\pi$
$509$	−74.1139	+	42.7897i	−0.145607	+	0.0840662i	0.425427	+	0.904993i	$0.360124\pi$
$510$		0			0
$511$	−55.6080	+	54.4304i	−0.108822	+	0.106517i
$512$		−	22.6274i		−	0.0441942i
$513$	−3.66157	+	2.11401i	−0.00713757	+	0.00412088i
$514$	230.378	+	133.009i	0.448207	+	0.258772i
$515$		0			0
$516$	7.60017	−	4.38796i	0.0147290	−	0.00850380i
$517$	60.5880			0.117192
$518$	−42.6300	+	41.7271i	−0.0822972	+	0.0805543i
$519$	−258.196			−0.497488
$520$		0			0
$521$	−698.846	−	403.479i	−1.34136	−	0.774432i	−0.354349	−	0.935113i	$-0.615297\pi$
$521$	−698.846	−	403.479i	−1.34136	−	0.774432i	−0.987006	+	0.160682i	$0.948631\pi$
$522$	−17.2203	−	9.94213i	−0.0329890	−	0.0190462i
$523$	−125.193	−	216.841i	−0.239375	−	0.414610i	0.721160	−	0.692768i	$-0.243609\pi$
$523$	−125.193	−	216.841i	−0.239375	−	0.414610i	−0.960535	+	0.278159i	$0.910276\pi$
$524$		−	220.043i		−	0.419929i
$525$		0			0
$526$	478.824			0.910312
$527$	235.485	−	135.957i	0.446841	−	0.257984i
$528$	11.4802	−	19.8843i	0.0217428	−	0.0376596i
$529$	−192.846	+	334.019i	−0.364549	+	0.631417i
$530$		0			0
$531$			223.004i			0.419970i
$532$	3.06594	−	10.9712i	0.00576304	−	0.0206226i
$533$			384.031i			0.720509i
$534$	188.838	+	327.076i	0.353629	+	0.612503i
$535$		0			0
$536$	−133.899	+	231.920i	−0.249812	+	0.432687i
$537$	−244.935	−	424.240i	−0.456117	−	0.790018i
$538$	739.802			1.37510
$539$	142.338	−	78.1657i	0.264078	−	0.145020i
$540$		0			0
$541$	421.926	+	730.798i	0.779901	+	1.35083i	0.931998	+	0.362462i	$0.118064\pi$
$541$	421.926	+	730.798i	0.779901	+	1.35083i	−0.152098	+	0.988365i	$0.548603\pi$
$542$	−315.003	+	545.602i	−0.581187	+	1.00665i
$543$	−458.127	−	264.500i	−0.843697	−	0.487109i
$544$	41.2952	−	23.8418i	0.0759103	−	0.0438268i
$545$		0			0
$546$	90.0243	−	322.145i	0.164880	−	0.590009i
$547$		−	674.572i		−	1.23322i	−0.787268	−	0.616611i	$-0.788505\pi$
$547$		−	674.572i		−	1.23322i	0.787268	−	0.616611i	$-0.211495\pi$
$548$	−238.445	+	137.666i	−0.435118	+	0.251216i
$549$	−285.473	−	164.818i	−0.519988	−	0.300215i
$550$		0			0
$551$	3.30262	−	1.90677i	0.00599387	−	0.00346056i
$552$	58.6463			0.106243
$553$	−1.74192	−	6.79083i	−0.00314995	−	0.0122800i
$554$	−20.5537			−0.0371006
$555$		0			0
$556$	−118.962	−	68.6829i	−0.213961	−	0.123530i
$557$	507.418	+	292.958i	0.910984	+	0.525957i	0.880748	−	0.473586i	$-0.157041\pi$
$557$	507.418	+	292.958i	0.910984	+	0.525957i	0.0302363	+	0.999543i	$0.490374\pi$
$558$	68.4298	+	118.524i	0.122634	+	0.212408i
$559$			49.4206i			0.0884089i
$560$		0			0
$561$	48.3852			0.0862482
$562$	644.531	−	372.120i	1.14685	−	0.662135i
$563$	−68.2288	+	118.176i	−0.121188	+	0.209904i	−0.920236	−	0.391363i	$-0.872004\pi$
$563$	−68.2288	+	118.176i	−0.121188	+	0.209904i	0.799048	+	0.601267i	$0.205337\pi$
$564$	−31.6657	+	54.8466i	−0.0561448	+	0.0972457i
$565$		0			0
$566$			712.993i			1.25970i
$567$	45.0219	−	44.0684i	0.0794037	−	0.0777221i
$568$			277.199i			0.488027i
$569$	−284.763	−	493.225i	−0.500463	−	0.866827i	−1.00000		0.000534692i	$-0.999830\pi$
$569$	−284.763	−	493.225i	−0.500463	−	0.866827i	0.499537	−	0.866293i	$-0.333504\pi$
$570$		0			0
$571$	38.9272	−	67.4238i	0.0681737	−	0.118080i	−0.829924	−	0.557877i	$-0.811616\pi$
$571$	38.9272	−	67.4238i	0.0681737	−	0.118080i	0.898097	+	0.439797i	$0.144949\pi$
$572$	64.6493	+	111.976i	0.113023	+	0.195762i
$573$	84.3065			0.147132
$574$	−48.4220	−	188.771i	−0.0843589	−	0.328870i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−490.492	+	849.557i	−0.850073	+	1.47237i	0.0310685	+	0.999517i	$0.490109\pi$
$577$	−490.492	+	849.557i	−0.850073	+	1.47237i	−0.881142	+	0.472853i	$0.843224\pi$
$578$	−266.928	−	154.111i	−0.461814	−	0.266628i
$579$	224.300	−	129.500i	0.387392	−	0.223661i
$580$		0			0
$581$	450.376	+	125.859i	0.775173	+	0.216624i
$582$		−	323.390i		−	0.555653i
$583$	91.7480	−	52.9707i	0.157372	−	0.0908589i
$584$	27.2290	+	15.7207i	0.0466250	+	0.0269189i
$585$		0			0
$586$	269.621	−	155.666i	0.460105	−	0.265642i
$587$	−894.491			−1.52384			−0.761918	−	0.647674i	$-0.775742\pi$
$587$	−894.491			−1.52384			−0.761918	+	0.647674i	$0.775742\pi$
$588$	−3.63281	+	169.702i	−0.00617825	+	0.288609i
$589$	−26.2479			−0.0445635
$590$		0			0
$591$	329.218	+	190.074i	0.557053	+	0.321615i
$592$	20.8742	+	12.0517i	0.0352604	+	0.0203576i
$593$	506.901	+	877.978i	0.854808	+	1.48057i	0.876823	+	0.480813i	$0.159658\pi$
$593$	506.901	+	877.978i	0.854808	+	1.48057i	−0.0220156	+	0.999758i	$0.507008\pi$
$594$			24.3532i			0.0409986i
$595$		0			0
$596$	367.197			0.616102
$597$	−440.626	+	254.396i	−0.738067	+	0.426123i
$598$	−165.130	+	286.013i	−0.276137	+	0.478283i
$599$	−339.723	+	588.418i	−0.567151	+	0.982334i	0.429695	+	0.902974i	$0.358621\pi$
$599$	−339.723	+	588.418i	−0.567151	+	0.982334i	−0.996846	+	0.0793601i	$0.974712\pi$
$600$		0			0
$601$		−	13.9775i		−	0.0232571i	−0.999932	−	0.0116285i	$-0.996298\pi$
$601$		−	13.9775i		−	0.0232571i	0.999932	−	0.0116285i	$-0.00370156\pi$
$602$	−6.23138	−	24.2928i	−0.0103511	−	0.0403535i
$603$		−	284.043i		−	0.471050i
$604$	141.494	+	245.074i	0.234261	+	0.405752i
$605$		0			0
$606$	−21.6526	+	37.5035i	−0.0357304	+	0.0618869i
$607$	459.058	+	795.111i	0.756273	+	1.30990i	0.944739	+	0.327823i	$0.106315\pi$
$607$	459.058	+	795.111i	0.756273	+	1.30990i	−0.188466	+	0.982080i	$0.560352\pi$
$608$	−4.60289			−0.00757054
$609$	−40.6084	+	39.7484i	−0.0666804	+	0.0652682i
$610$		0			0
$611$	−178.322	−	308.862i	−0.291852	−	0.505503i
$612$	−25.2880	+	43.8002i	−0.0413203	+	0.0715689i
$613$	541.192	+	312.457i	0.882858	+	0.509718i	0.871600	−	0.490219i	$-0.163083\pi$
$613$	541.192	+	312.457i	0.882858	+	0.509718i	0.0112580	+	0.999937i	$0.496416\pi$
$614$	224.891	−	129.841i	0.366272	−	0.211467i
$615$		0			0
$616$	−45.8974	−	46.8905i	−0.0745088	−	0.0761209i
$617$			11.2800i			0.0182821i	0.999958	+	0.00914103i	$0.00290972\pi$
$617$			11.2800i			0.0182821i	−0.999958	+	0.00914103i	$0.997090\pi$
$618$	83.1479	−	48.0055i	0.134544	−	0.0776787i
$619$	−130.107	−	75.1176i	−0.210190	−	0.121353i	0.391210	−	0.920302i	$-0.372057\pi$
$619$	−130.107	−	75.1176i	−0.210190	−	0.121353i	−0.601400	+	0.798948i	$0.705390\pi$
$620$		0			0
$621$	−53.8700	+	31.1019i	−0.0867472	+	0.0500835i
$622$	319.508			0.513679
$623$	1045.45	−	268.170i	1.67809	−	0.430449i
$624$	−135.153			−0.216592
$625$		0			0
$626$	327.674	+	189.183i	0.523442	+	0.302209i
$627$	−4.04487	−	2.33531i	−0.00645115	−	0.00372457i
$628$	171.609	+	297.235i	0.273262	+	0.473304i
$629$			50.7940i			0.0807536i
$630$		0			0
$631$	768.570			1.21802			0.609009	−	0.793163i	$-0.291567\pi$
$631$	768.570			1.21802			0.609009	+	0.793163i	$0.291567\pi$
$632$	−2.45323	+	1.41637i	−0.00388169	+	0.00224109i
$633$	−106.321	+	184.153i	−0.167963	+	0.290920i
$634$	−374.620	+	648.861i	−0.590883	+	1.02344i
$635$		0			0
$636$			110.738i			0.174117i
$637$	−817.395	−	495.546i	−1.28319	−	0.777937i
$638$		−	21.9658i		−	0.0344291i
$639$	−147.007	−	254.624i	−0.230058	−	0.398472i
$640$		0			0
$641$	23.1711	−	40.1335i	0.0361484	−	0.0626108i	−0.847385	−	0.530979i	$-0.821824\pi$
$641$	23.1711	−	40.1335i	0.0361484	−	0.0626108i	0.883534	+	0.468368i	$0.155158\pi$
$642$	−162.891	−	282.136i	−0.253724	−	0.439463i
$643$	122.504			0.190519			0.0952597	−	0.995452i	$-0.469632\pi$
$643$	122.504			0.190519			0.0952597	+	0.995452i	$0.469632\pi$
$644$	45.1069	−	161.411i	0.0700418	−	0.250639i
$645$		0			0
$646$	−4.84992	−	8.40030i	−0.00750761	−	0.0130036i
$647$	−431.101	+	746.689i	−0.666308	+	1.15408i	0.312621	+	0.949878i	$0.398793\pi$
$647$	−431.101	+	746.689i	−0.666308	+	1.15408i	−0.978929	+	0.204201i	$0.934540\pi$
$648$	−22.0454	−	12.7279i	−0.0340207	−	0.0196419i
$649$	−213.344	+	123.174i	−0.328728	+	0.189791i
$650$		0			0
$651$	378.844	−	97.1777i	0.581941	−	0.149275i
$652$		−	590.912i		−	0.906306i
$653$	574.205	−	331.517i	0.879333	−	0.507683i	0.00889466	−	0.999960i	$-0.497169\pi$
$653$	574.205	−	331.517i	0.879333	−	0.507683i	0.870438	+	0.492277i	$0.163835\pi$
$654$	104.216	+	60.1693i	0.159352	+	0.0920021i
$655$		0			0
$656$	−68.1948	+	39.3723i	−0.103956	+	0.0600187i
$657$	−33.3486			−0.0507589
$658$	126.598	+	129.338i	0.192399	+	0.196562i
$659$	999.565			1.51679			0.758395	−	0.651795i	$-0.225984\pi$
$659$	999.565			1.51679			0.758395	+	0.651795i	$0.225984\pi$
$660$		0			0
$661$	−653.320	−	377.195i	−0.988382	−	0.570642i	−0.0835916	−	0.996500i	$-0.526639\pi$
$661$	−653.320	−	377.195i	−0.988382	−	0.570642i	−0.904790	+	0.425858i	$0.859972\pi$
$662$	−251.844	−	145.402i	−0.380429	−	0.219641i
$663$	−142.407	−	246.656i	−0.214791	−	0.372030i
$664$		−	188.951i		−	0.284565i
$665$		0			0
$666$	−25.5655			−0.0383867
$667$	48.5891	−	28.0529i	0.0728472	−	0.0420583i
$668$	168.538	−	291.916i	0.252302	−	0.437000i
$669$	−3.21161	+	5.56268i	−0.00480062	+	0.00831491i
$670$		0			0
$671$		−	364.143i		−	0.542687i
$672$	66.4349	−	17.0413i	0.0988614	−	0.0253591i
$673$			838.745i			1.24628i	0.782111	+	0.623139i	$0.214143\pi$
$673$			838.745i			1.24628i	−0.782111	+	0.623139i	$0.785857\pi$
$674$	236.038	+	408.830i	0.350205	+	0.606573i
$675$		0			0
$676$	211.550	−	366.415i	0.312943	−	0.542034i
$677$	−69.5041	−	120.385i	−0.102665	−	0.177821i	0.810117	−	0.586268i	$-0.199404\pi$
$677$	−69.5041	−	120.385i	−0.102665	−	0.177821i	−0.912782	+	0.408448i	$0.866070\pi$
$678$	347.604			0.512691
$679$	−890.063	−	248.731i	−1.31084	−	0.366319i
$680$		0			0
$681$	131.877	+	228.418i	0.193652	+	0.335416i
$682$	−75.5931	+	130.931i	−0.110840	+	0.191981i
$683$	895.672	+	517.117i	1.31138	+	0.757125i	0.982325	−	0.187186i	$-0.0599366\pi$
$683$	895.672	+	517.117i	1.31138	+	0.757125i	0.329055	+	0.944311i	$0.393270\pi$
$684$	4.22802	−	2.44105i	0.00618132	−	0.00356878i
$685$		0			0
$686$	464.275	+	140.522i	0.676786	+	0.204843i
$687$			247.834i			0.360748i
$688$	−8.77592	+	5.06678i	−0.0127557	+	0.00736450i
$689$	−540.063	−	311.805i	−0.783835	−	0.452548i
$690$		0			0
$691$	602.952	−	348.115i	0.872579	−	0.503784i	0.00437465	−	0.999990i	$-0.498608\pi$
$691$	602.952	−	348.115i	0.872579	−	0.503784i	0.868204	+	0.496207i	$0.165274\pi$
$692$	298.140			0.430838
$693$	67.0269	+	18.7309i	0.0967200	+	0.0270287i
$694$	−923.571			−1.33079
$695$		0			0
$696$	19.8843	+	11.4802i	0.0285694	+	0.0164945i
$697$	−143.709	−	82.9707i	−0.206183	−	0.119040i
$698$	−172.574	−	298.907i	−0.247240	−	0.428233i
$699$			124.622i			0.178286i
$700$		0			0
$701$	1001.00			1.42796			0.713979	−	0.700167i	$-0.246891\pi$
$701$	1001.00			1.42796			0.713979	+	0.700167i	$0.246891\pi$
$702$	124.146	−	71.6758i	0.176846	−	0.102102i
$703$	2.45157	−	4.24624i	0.00348729	−	0.00604017i
$704$	−13.2562	+	22.9604i	−0.0188298	+	0.0326142i
$705$		0			0
$706$			590.461i			0.836347i
$707$	86.5666	+	88.4396i	0.122442	+	0.125091i
$708$		−	257.503i		−	0.363705i
$709$	−131.927	−	228.505i	−0.186075	−	0.322291i	0.757863	−	0.652414i	$-0.226243\pi$
$709$	−131.927	−	228.505i	−0.186075	−	0.322291i	−0.943938	+	0.330122i	$0.892910\pi$
$710$		0			0
$711$	1.50229	−	2.60204i	0.00211292	−	0.00365969i
$712$	−218.051	−	377.675i	−0.306251	−	0.530443i
$713$	−386.166			−0.541607
$714$	101.101	+	103.288i	0.141598	+	0.144661i
$715$		0			0
$716$	282.827	+	489.870i	0.395009	+	0.684176i
$717$	−392.932	+	680.578i	−0.548022	+	0.949202i
$718$	−361.244	−	208.564i	−0.503125	−	0.290479i
$719$	574.059	−	331.433i	0.798413	−	0.460964i	−0.0445027	−	0.999009i	$-0.514170\pi$
$719$	574.059	−	331.433i	0.798413	−	0.460964i	0.842916	+	0.538045i	$0.180837\pi$
$720$		0			0
$721$	−68.1730	−	265.770i	−0.0945533	−	0.368613i
$722$		−	509.595i		−	0.705810i
$723$	282.812	−	163.281i	0.391164	−	0.225839i
$724$	529.000	+	305.418i	0.730663	+	0.421848i
$725$		0			0
$726$	233.382	−	134.743i	0.321462	−	0.185596i
$727$	−73.2857			−0.100806			−0.0504028	−	0.998729i	$-0.516051\pi$
$727$	−73.2857			−0.100806			−0.0504028	+	0.998729i	$0.516051\pi$
$728$	−103.951	+	371.981i	−0.142790	+	0.510963i
$729$	27.0000			0.0370370
$730$		0			0
$731$	−18.4938	−	10.6774i	−0.0252993	−	0.0146066i
$732$	329.636	+	190.315i	0.450322	+	0.259994i
$733$	665.709	+	1153.04i	0.908198	+	1.57304i	0.816567	+	0.577251i	$0.195875\pi$
$733$	665.709	+	1153.04i	0.908198	+	1.57304i	0.0916311	+	0.995793i	$0.470792\pi$
$734$		−	33.4168i		−	0.0455269i
$735$		0			0
$736$	−67.7189			−0.0920093
$737$	271.739	−	156.889i	0.368710	−	0.212875i
$738$	41.7606	−	72.3315i	0.0565862	−	0.0980102i
$739$	148.610	−	257.400i	0.201096	−	0.348309i	−0.747786	−	0.663940i	$-0.768883\pi$
$739$	148.610	−	257.400i	0.201096	−	0.348309i	0.948882	+	0.315631i	$0.102216\pi$
$740$		0			0
$741$			27.4930i			0.0371025i
$742$	304.784	+	85.1728i	0.410760	+	0.114788i
$743$		−	774.964i		−	1.04302i	−0.853245	−	0.521510i	$-0.825369\pi$
$743$		−	774.964i		−	1.04302i	0.853245	−	0.521510i	$-0.174631\pi$
$744$	−79.0159	−	136.860i	−0.106204	−	0.183951i
$745$		0			0
$746$	−117.352	+	203.260i	−0.157309	+	0.272467i
$747$	100.207	+	173.563i	0.134145	+	0.232347i
$748$	−55.8705			−0.0746931
$749$	−901.804	+	231.323i	−1.20401	+	0.308842i
$750$		0			0
$751$	516.034	+	893.796i	0.687129	+	1.19014i	0.972763	+	0.231803i	$0.0744624\pi$
$751$	516.034	+	893.796i	0.687129	+	1.19014i	−0.285634	+	0.958339i	$0.592204\pi$
$752$	36.5644	−	63.3314i	0.0486229	−	0.0842173i
$753$	350.867	+	202.573i	0.465958	+	0.269021i
$754$	−111.976	+	64.6493i	−0.148509	+	0.0857418i
$755$		0			0
$756$	−51.9868	+	50.8859i	−0.0687656	+	0.0673093i
$757$			450.128i			0.594621i	0.954781	+	0.297310i	$0.0960896\pi$
$757$			450.128i			0.594621i	−0.954781	+	0.297310i	$0.903910\pi$
$758$	−559.557	+	323.060i	−0.738202	+	0.426201i
$759$	−59.5092	−	34.3577i	−0.0784048	−	0.0452670i
$760$		0			0
$761$	−74.2627	+	42.8756i	−0.0975856	+	0.0563411i	−0.547999	−	0.836479i	$-0.684610\pi$
$761$	−74.2627	+	42.8756i	−0.0975856	+	0.0563411i	0.450413	+	0.892820i	$0.351277\pi$
$762$	213.758			0.280522
$763$	245.760	−	240.555i	0.322097	−	0.315276i
$764$	−97.3488			−0.127420
$765$		0			0
$766$	−8.17487	−	4.71976i	−0.0106721	−	0.00616157i
$767$	1255.82	+	725.049i	1.63732	+	0.945306i
$768$	−13.8564	−	24.0000i	−0.0180422	−	0.0312500i
$769$			959.716i			1.24800i	0.781422	+	0.624002i	$0.214494\pi$
$769$			959.716i			1.24800i	−0.781422	+	0.624002i	$0.785506\pi$
$770$		0			0
$771$	325.804			0.422574
$772$	−258.999	+	149.533i	−0.335491	+	0.193696i
$773$	−507.799	+	879.534i	−0.656920	+	1.13782i	0.324488	+	0.945890i	$0.394808\pi$
$773$	−507.799	+	879.534i	−0.656920	+	1.13782i	−0.981409	+	0.191930i	$0.938525\pi$
$774$	5.37413	−	9.30827i	0.00694332	−	0.0120262i
$775$		0			0
$776$			373.419i			0.481210i
$777$	−19.6633	+	70.3637i	−0.0253067	+	0.0905582i
$778$			300.873i			0.386726i
$779$	8.00914	+	13.8722i	0.0102813	+	0.0178077i
$780$		0			0
$781$	162.396	−	281.278i	0.207933	−	0.360151i
$782$	−71.3532	−	123.587i	−0.0912445	−	0.158040i
$783$	−24.3532			−0.0311024
$784$	4.19481	−	195.955i	0.00535052	−	0.249943i
$785$		0			0
$786$	−134.748	−	233.391i	−0.171435	−	0.296935i
$787$	−559.126	+	968.434i	−0.710452	+	1.23054i	0.254236	+	0.967142i	$0.418176\pi$
$787$	−559.126	+	968.434i	−0.710452	+	1.23054i	−0.964688	+	0.263396i	$0.915157\pi$
$788$	−380.148	−	219.479i	−0.482422	−	0.278526i
$789$	507.870	−	293.219i	0.643688	−	0.371633i
$790$		0			0
$791$	267.355	−	956.707i	0.337996	−	1.20949i
$792$		−	28.1206i		−	0.0355058i
$793$	−1856.31	+	1071.74i	−2.34087	+	1.35150i
$794$	−310.862	−	179.476i	−0.391513	−	0.226040i
$795$		0			0
$796$	508.791	−	293.751i	0.639185	−	0.369034i
$797$	803.162			1.00773			0.503866	−	0.863782i	$-0.331911\pi$
$797$	803.162			1.00773			0.503866	+	0.863782i	$0.331911\pi$
$798$	−3.46655	−	13.5142i	−0.00434405	−	0.0169351i
$799$	154.107			0.192875
$800$		0			0
$801$	400.585	+	231.278i	0.500106	+	0.288737i
$802$	676.041	+	390.312i	0.842944	+	0.486674i
$803$	−18.4198	−	31.9040i	−0.0229387	−	0.0397310i
$804$			327.985i			0.407941i
$805$		0			0
$806$	889.938			1.10414
$807$	784.678	−	453.034i	0.972340	−	0.561381i
$808$	25.0023	−	43.3053i	0.0309435	−	0.0535956i
$809$	−255.382	+	442.334i	−0.315676	+	0.546767i	−0.979581	−	0.201050i	$-0.935565\pi$
$809$	−255.382	+	442.334i	−0.315676	+	0.546767i	0.663905	+	0.747817i	$0.268898\pi$
$810$		0			0
$811$		−	572.874i		−	0.706380i	−0.935552	−	0.353190i	$-0.885097\pi$
$811$		−	572.874i		−	0.706380i	0.935552	−	0.353190i	$-0.114903\pi$
$812$	46.8905	−	45.8974i	0.0577469	−	0.0565240i
$813$			771.598i			0.949075i
$814$	−14.1209	−	24.4581i	−0.0173475	−	0.0300468i
$815$		0			0
$816$	29.2001	−	50.5761i	0.0357845	−	0.0619805i
$817$	1.03069	+	1.78520i	0.00126155	+	0.00218507i
$818$	221.126			0.270326
$819$	−101.787	−	396.815i	−0.124283	−	0.484511i
$820$		0			0
$821$	−443.437	−	768.056i	−0.540119	−	0.935513i	−0.998897	−	0.0469621i	$-0.985046\pi$
$821$	−443.437	−	768.056i	−0.540119	−	0.935513i	0.458778	−	0.888551i	$-0.348287\pi$
$822$	−168.606	+	292.034i	−0.205117	+	0.355273i
$823$	−949.506	−	548.198i	−1.15371	−	0.666097i	−0.203924	−	0.978987i	$-0.565370\pi$
$823$	−949.506	−	548.198i	−1.15371	−	0.666097i	−0.949789	+	0.312890i	$0.898703\pi$
$824$	−96.0109	+	55.4319i	−0.116518	+	0.0672718i
$825$		0			0
$826$	−708.723	−	198.055i	−0.858018	−	0.239776i
$827$			556.105i			0.672437i	0.941784	+	0.336218i	$0.109148\pi$
$827$			556.105i			0.672437i	−0.941784	+	0.336218i	$0.890852\pi$
$828$	62.2037	−	35.9133i	0.0751253	−	0.0433736i
$829$	−1002.59	−	578.843i	−1.20939	−	0.698243i	−0.246765	−	0.969075i	$-0.579368\pi$
$829$	−1002.59	−	578.843i	−1.20939	−	0.698243i	−0.962626	+	0.270833i	$0.912701\pi$
$830$		0			0
$831$	−21.8005	+	12.5865i	−0.0262341	+	0.0151463i
$832$	156.061			0.187574
$833$	362.039	−	198.816i	0.434621	−	0.238675i
$834$	−168.238			−0.201724
$835$		0			0
$836$	4.67062	+	2.69658i	0.00558686	+	0.00322558i
$837$	145.162	+	83.8090i	0.173431	+	0.100130i
$838$	−40.5603	−	70.2524i	−0.0484013	−	0.0838334i
$839$			313.727i			0.373930i	0.982367	+	0.186965i	$0.0598651\pi$
$839$			313.727i			0.373930i	−0.982367	+	0.186965i	$0.940135\pi$
$840$		0			0
$841$	−819.034			−0.973881
$842$	409.733	−	236.559i	0.486618	−	0.280949i
$843$	455.752	−	789.386i	0.540631	−	0.936400i
$844$	122.768	−	212.641i	0.145460	−	0.251944i
$845$		0			0
$846$			77.5648i			0.0916841i
$847$	−191.350	−	745.969i	−0.225914	−	0.880719i
$848$		−	127.870i		−	0.150790i
$849$	436.617	+	756.243i	0.514272	+	0.890746i
$850$		0			0
$851$	36.0681	−	62.4718i	0.0423832	−	0.0734098i
$852$	169.749	+	294.014i	0.199236	+	0.345087i
$853$	−638.107			−0.748074			−0.374037	−	0.927414i	$-0.622027\pi$
$853$	−638.107			−0.748074			−0.374037	+	0.927414i	$0.622027\pi$
$854$	777.338	−	760.876i	0.910232	−	0.890955i
$855$		0			0
$856$	188.090	+	325.782i	0.219732	+	0.380586i
$857$	−506.989	+	878.130i	−0.591585	+	1.02466i	0.402434	+	0.915449i	$0.368164\pi$
$857$	−506.989	+	878.130i	−0.591585	+	1.02466i	−0.994019	+	0.109207i	$0.965169\pi$
$858$	137.142	+	79.1789i	0.159839	+	0.0922832i
$859$	211.106	−	121.882i	0.245758	−	0.141888i	−0.372062	−	0.928208i	$-0.621349\pi$
$859$	211.106	−	121.882i	0.245758	−	0.141888i	0.617820	+	0.786319i	$0.288016\pi$
$860$		0			0
$861$	−166.958	−	170.570i	−0.193911	−	0.198107i
$862$		−	633.260i		−	0.734640i
$863$	474.868	−	274.165i	0.550253	−	0.317688i	−0.198971	−	0.980005i	$-0.563760\pi$
$863$	474.868	−	274.165i	0.550253	−	0.317688i	0.749224	+	0.662317i	$0.230427\pi$
$864$	25.4558	+	14.6969i	0.0294628	+	0.0170103i
$865$		0			0
$866$	−290.159	+	167.524i	−0.335057	+	0.193445i
$867$	−377.494			−0.435402
$868$	−437.451	+	112.211i	−0.503976	+	0.129276i
$869$	3.31910			0.00381945
$870$		0			0
$871$	−1599.56	−	923.504i	−1.83646	−	1.06028i
$872$	−120.339	−	69.4776i	−0.138003	−	0.0796761i
$873$	−198.035	−	343.007i	−0.226844	−	0.392906i
$874$			13.7754i			0.0157613i
$875$		0			0
$876$	38.5076			0.0439585
$877$	−929.775	+	536.806i	−1.06018	+	0.612094i	−0.925481	−	0.378793i	$-0.876339\pi$
$877$	−929.775	+	536.806i	−1.06018	+	0.612094i	−0.134696	+	0.990887i	$0.543006\pi$
$878$	−144.399	+	250.106i	−0.164463	+	0.284859i
$879$	190.651	−	330.217i	0.216896	−	0.375674i
$880$		0			0
$881$		−	341.661i		−	0.387811i	−0.981020	−	0.193905i	$-0.937884\pi$
$881$		−	341.661i		−	0.387811i	0.981020	−	0.193905i	$-0.0621155\pi$
$882$	100.068	+	182.221i	0.113455	+	0.206600i
$883$			884.344i			1.00152i	0.865585	+	0.500761i	$0.166947\pi$
$883$			884.344i			1.00152i	−0.865585	+	0.500761i	$0.833053\pi$
$884$	164.437	+	284.813i	0.186015	+	0.322187i
$885$		0			0
$886$	−108.620	+	188.135i	−0.122596	+	0.212342i
$887$	−83.8009	−	145.147i	−0.0944768	−	0.163639i	0.814913	−	0.579583i	$-0.196784\pi$
$887$	−83.8009	−	145.147i	−0.0944768	−	0.163639i	−0.909390	+	0.415944i	$0.863451\pi$
$888$	29.5205			0.0332438
$889$	164.409	−	588.324i	0.184937	−	0.661782i
$890$		0			0
$891$	14.9132	+	25.8304i	0.0167376	+	0.0289904i
$892$	3.70845	−	6.42323i	0.00415746	−	0.00720093i
$893$	−12.8829	−	7.43795i	−0.0144266	−	0.00832918i
$894$	389.471	−	224.861i	0.435650	−	0.251523i
$895$		0			0
$896$	−76.7124	+	19.6776i	−0.0856165	+	0.0219616i
$897$			404.484i			0.450929i
$898$	−245.735	+	141.875i	−0.273647	+	0.157990i
$899$	−130.931	−	75.5931i	−0.145641	−	0.0840858i
$900$		0			0
$901$	233.363	−	134.732i	0.259005	−	0.149536i
$902$	92.2644			0.102289
$903$	−21.4856	−	21.9505i	−0.0237936	−	0.0243084i
$904$	−401.379			−0.444003
$905$		0			0
$906$	300.154	+	173.294i	0.331295	+	0.191274i
$907$	517.124	+	298.562i	0.570148	+	0.329175i	0.757209	−	0.653173i	$-0.226563\pi$
$907$	517.124	+	298.562i	0.570148	+	0.329175i	−0.187060	+	0.982348i	$0.559896\pi$
$908$	−152.279	−	263.754i	−0.167708	−	0.290478i
$909$			53.0379i			0.0583475i
$910$		0			0
$911$	1340.36			1.47131			0.735655	−	0.677357i	$-0.236875\pi$
$911$	1340.36			1.47131			0.735655	+	0.677357i	$0.236875\pi$
$912$	−4.88210	+	2.81868i	−0.00535318	+	0.00309066i
$913$	−110.696	+	191.732i	−0.121245	+	0.210002i
$914$	−280.646	+	486.093i	−0.307053	+	0.531831i
$915$		0			0
$916$		−	286.174i		−	0.312417i
$917$	−745.998	+	191.357i	−0.813521	+	0.208677i
$918$			61.9428i			0.0674758i
$919$	−480.400	−	832.078i	−0.522743	−	0.905417i	−0.999650	−	0.0264631i	$-0.991576\pi$
$919$	−480.400	−	832.078i	−0.522743	−	0.905417i	0.476907	−	0.878954i	$-0.341758\pi$
$920$		0			0
$921$	159.022	−	275.434i	0.172662	−	0.299060i
$922$	238.570	+	413.216i	0.258753	+	0.448173i
$923$	−1911.85			−2.07134
$924$	−77.3960	−	21.6285i	−0.0837619	−	0.0234075i
$925$		0			0
$926$	191.444	+	331.592i	0.206744	+	0.358090i
$927$	58.7944	−	101.835i	0.0634244	−	0.109854i
$928$	−22.9604	−	13.2562i	−0.0247418	−	0.0142847i
$929$	−823.312	+	475.340i	−0.886235	+	0.511668i	−0.872709	−	0.488240i	$-0.837639\pi$
$929$	−823.312	+	475.340i	−0.886235	+	0.511668i	−0.0135260	+	0.999909i	$0.504306\pi$
$930$		0			0
$931$	−39.8613	−	0.853311i	−0.0428156	−	0.000916553i
$932$		−	143.901i		−	0.154400i
$933$	338.890	−	195.658i	0.363226	−	0.209709i
$934$	−31.5222	−	18.1993i	−0.0337497	−	0.0194854i
$935$		0			0
$936$	−143.352	+	82.7641i	−0.153153	+	0.0884232i
$937$	−236.656			−0.252568			−0.126284	−	0.991994i	$-0.540305\pi$
$937$	−236.656			−0.252568			−0.126284	+	0.991994i	$0.540305\pi$
$938$	902.709	+	252.265i	0.962377	+	0.268939i
$939$	463.402			0.493505
$940$		0			0
$941$	454.869	+	262.619i	0.483389	+	0.279085i	0.721828	−	0.692073i	$-0.243302\pi$
$941$	454.869	+	262.619i	0.483389	+	0.279085i	−0.238439	+	0.971158i	$0.576636\pi$
$942$	364.037	+	210.177i	0.386451	+	0.223118i
$943$	117.833	+	204.092i	0.124955	+	0.216428i
$944$			297.339i			0.314978i
$945$		0			0
$946$	11.8734			0.0125512
$947$	−1154.09	+	666.313i	−1.21868	+	0.703604i	−0.964635	−	0.263589i	$-0.915094\pi$
$947$	−1154.09	+	666.313i	−1.21868	+	0.703604i	−0.254042	+	0.967193i	$0.581760\pi$
$948$	−1.73469	+	3.00458i	−0.00182984	+	0.00316938i
$949$	−108.426	+	187.799i	−0.114252	+	0.197891i
$950$		0			0
$951$			917.627i			0.964908i
$952$	−116.741	−	119.267i	−0.122627	−	0.125280i
$953$		−	1748.81i		−	1.83506i	−0.397665	−	0.917531i	$-0.630179\pi$
$953$		−	1748.81i		−	1.83506i	0.397665	−	0.917531i	$-0.369821\pi$
$954$	67.8132	+	117.456i	0.0710830	+	0.123119i
$955$		0			0
$956$	453.719	−	785.864i	0.474601	−	0.822033i
$957$	−13.4512	−	23.2982i	−0.0140556	−	0.0243451i
$958$	265.897			0.277555
$959$	674.082	+	688.666i	0.702900	+	0.718108i
$960$		0			0
$961$	39.7929	+	68.9233i	0.0414078	+	0.0717204i
$962$	−83.1207	+	143.969i	−0.0864040	+	0.149656i
$963$	−345.544	−	199.500i	−0.358820	−	0.207165i
$964$	−326.563	+	188.541i	−0.338758	+	0.195582i
$965$		0			0
$966$	−51.0008	−	198.825i	−0.0527959	−	0.205823i
$967$		−	638.367i		−	0.660152i	−0.943954	−	0.330076i	$-0.892926\pi$
$967$		−	638.367i		−	0.660152i	0.943954	−	0.330076i	$-0.107074\pi$
$968$	−269.486	+	155.588i	−0.278394	+	0.160731i
$969$	−10.2882	−	5.93991i	−0.0106174	−	0.00612994i
$970$		0			0
$971$	−1222.24	+	705.662i	−1.25875	+	0.726737i	−0.972831	−	0.231518i	$-0.925631\pi$
$971$	−1222.24	+	705.662i	−1.25875	+	0.726737i	−0.285915	+	0.958255i	$0.592298\pi$
$972$	−31.1769			−0.0320750
$973$	−129.398	+	463.040i	−0.132989	+	0.475889i
$974$	−423.950			−0.435267
$975$		0			0
$976$	−380.631	−	219.757i	−0.389991	−	0.225161i
$977$	953.192	+	550.326i	0.975632	+	0.563281i	0.900949	−	0.433926i	$-0.142872\pi$
$977$	953.192	+	550.326i	0.975632	+	0.563281i	0.0746833	+	0.997207i	$0.476205\pi$
$978$	−361.858	−	626.756i	−0.369998	−	0.640855i
$979$			510.977i			0.521938i
$980$		0			0
$981$	147.384			0.150239
$982$	−565.260	+	326.353i	−0.575621	+	0.332335i
$983$	698.409	−	1209.68i	0.710488	−	1.23060i	−0.254187	−	0.967155i	$-0.581808\pi$
$983$	698.409	−	1209.68i	0.710488	−	1.23060i	0.964674	−	0.263446i	$-0.0848590\pi$
$984$	−48.2210	+	83.5212i	−0.0490051	+	0.0848793i
$985$		0			0
$986$		−	55.8705i		−	0.0566638i
$987$	213.481	+	59.6578i	0.216293	+	0.0604436i
$988$		−	31.7461i		−	0.0321317i
$989$	15.1638	+	26.2644i	0.0153324	+	0.0265565i
$990$		0			0
$991$	−464.607	+	804.723i	−0.468826	+	0.812031i	−0.999365	−	0.0356298i	$-0.988656\pi$
$991$	−464.607	+	804.723i	−0.468826	+	0.812031i	0.530539	+	0.847661i	$0.321990\pi$
$992$	91.2397	+	158.032i	0.0919755	+	0.159306i
$993$	−356.162			−0.358672
$994$	939.772	−	241.062i	0.945445	−	0.242517i
$995$		0			0
$996$	−115.709	−	200.413i	−0.116173	−	0.201218i
$997$	575.315	−	996.474i	0.577046	−	0.999473i	−0.418770	−	0.908092i	$-0.637539\pi$
$997$	575.315	−	996.474i	0.577046	−	0.999473i	0.995816	−	0.0913804i	$-0.0291279\pi$
$998$	213.093	+	123.029i	0.213520	+	0.123276i
$999$	−27.1163	+	15.6556i	−0.0271435	+	0.0156713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.q.d.199.3		24
5.2	odd	4		1050.3.p.f.451.2	yes	12
5.3	odd	4		1050.3.p.e.451.5	✓	12
5.4	even	2	inner	1050.3.q.d.199.11		24
7.5	odd	6	inner	1050.3.q.d.649.11		24
35.12	even	12		1050.3.p.f.901.2	yes	12
35.19	odd	6	inner	1050.3.q.d.649.3		24
35.33	even	12		1050.3.p.e.901.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.p.e.451.5	✓	12	5.3	odd	4
1050.3.p.e.901.5	yes	12	35.33	even	12
1050.3.p.f.451.2	yes	12	5.2	odd	4
1050.3.p.f.901.2	yes	12	35.12	even	12
1050.3.q.d.199.3		24	1.1	even	1	trivial
1050.3.q.d.199.11		24	5.4	even	2	inner
1050.3.q.d.649.3		24	35.19	odd	6	inner
1050.3.q.d.649.11		24	7.5	odd	6	inner

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)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-6.74171 - 1.88399i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-6.74171 - 1.88399i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(1.65702 - 2.87005i) q^{11} +(1.73205 + 3.00000i) q^{12} -19.5077 q^{13} +(9.58905 - 2.45970i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(4.21467 - 7.30003i) q^{17} +(3.67423 + 2.12132i) q^{18} +(-0.704670 + 0.406841i) q^{19} +(8.66447 - 8.48098i) q^{21} +4.68677i q^{22} +(-10.3673 + 5.98556i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(23.8919 - 13.7940i) q^{26} +5.19615 q^{27} +(-10.0049 + 9.79299i) q^{28} -4.68677 q^{29} +(27.9363 + 16.1291i) q^{31} +(4.89898 + 2.82843i) q^{32} +(2.87005 + 4.97107i) q^{33} +11.9209i q^{34} -6.00000 q^{36} +(-5.21854 + 3.01293i) q^{37} +(0.575361 - 0.996554i) q^{38} +(16.8942 - 29.2615i) q^{39} -19.6861i q^{41} +(-4.61481 + 16.5137i) q^{42} -2.53339i q^{43} +(-3.31404 - 5.74009i) q^{44} +(8.46486 - 14.6616i) q^{46} +(9.14110 + 15.8328i) q^{47} +6.92820 q^{48} +(41.9012 + 25.4026i) q^{49} +(7.30003 + 12.6440i) q^{51} +(-19.5077 + 33.7883i) q^{52} +(27.6846 + 15.9837i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(5.32872 - 19.0684i) q^{56} -1.40934i q^{57} +(5.74009 - 3.31404i) q^{58} +(-64.3758 - 37.1674i) q^{59} +(95.1577 - 54.9393i) q^{61} -45.6199 q^{62} +(5.21781 + 20.3414i) q^{63} -8.00000 q^{64} +(-7.03015 - 4.05886i) q^{66} +(81.9962 + 47.3405i) q^{67} +(-8.42935 - 14.6001i) q^{68} -20.7346i q^{69} +98.0047 q^{71} +(7.34847 - 4.24264i) q^{72} +(5.55809 - 9.62690i) q^{73} +(4.26092 - 7.38013i) q^{74} +1.62737i q^{76} +(-16.5783 + 16.2272i) q^{77} +47.7839i q^{78} +(0.500763 + 0.867346i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(13.9202 + 24.1105i) q^{82} -66.8044 q^{83} +(-6.02501 - 23.4883i) q^{84} +(1.79138 + 3.10276i) q^{86} +(4.05886 - 7.03015i) q^{87} +(8.11772 + 4.68677i) q^{88} +(-133.528 + 77.0927i) q^{89} +(131.515 + 36.7523i) q^{91} +23.9422i q^{92} +(-48.3872 + 27.9363i) q^{93} +(-22.3910 - 12.9275i) q^{94} +(-8.48528 + 4.89898i) q^{96} +132.023 q^{97} +(-69.2806 - 1.48309i) q^{98} -9.94213 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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