LMFDB - Embedded newform 1050.3.q.e.649.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1050.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			649.10
Character	$\chi$	$=$	1050.649
Dual form			1050.3.q.e.199.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 + 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(2.86123 - 6.38854i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.22474 + 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(2.86123 - 6.38854i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-9.98749 - 17.2988i) q^{11} +(-1.73205 + 3.00000i) q^{12} -3.49788 q^{13} +(8.02165 - 5.80113i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(9.12112 + 15.7982i) q^{17} +(-3.67423 + 2.12132i) q^{18} +(21.3143 + 12.3058i) q^{19} +(12.0607 - 1.24079i) q^{21} -28.2489i q^{22} +(21.8155 + 12.5952i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(-4.28401 - 2.47338i) q^{26} -5.19615 q^{27} +(13.9265 - 1.43274i) q^{28} +53.1223 q^{29} +(26.0944 - 15.0656i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(17.2988 - 29.9625i) q^{33} +25.7984i q^{34} -6.00000 q^{36} +(40.5034 + 23.3846i) q^{37} +(17.4030 + 30.1429i) q^{38} +(-3.02925 - 5.24682i) q^{39} +31.5250i q^{41} +(15.6487 + 7.00855i) q^{42} -64.4116i q^{43} +(19.9750 - 34.5977i) q^{44} +(17.8123 + 30.8518i) q^{46} +(14.0313 - 24.3029i) q^{47} -6.92820 q^{48} +(-32.6268 - 36.5581i) q^{49} +(-15.7982 + 27.3634i) q^{51} +(-3.49788 - 6.05851i) q^{52} +(56.1833 - 32.4374i) q^{53} +(-6.36396 - 3.67423i) q^{54} +(18.0695 + 8.09277i) q^{56} +42.6285i q^{57} +(65.0613 + 37.5631i) q^{58} +(-86.7684 + 50.0958i) q^{59} +(6.94896 + 4.01198i) q^{61} +42.6119 q^{62} +(12.3061 + 17.0165i) q^{63} -8.00000 q^{64} +(42.3733 - 24.4642i) q^{66} +(14.0844 - 8.13165i) q^{67} +(-18.2422 + 31.5965i) q^{68} +43.6310i q^{69} -107.725 q^{71} +(-7.34847 - 4.24264i) q^{72} +(-25.8303 - 44.7395i) q^{73} +(33.0709 + 57.2804i) q^{74} +49.2232i q^{76} +(-139.091 + 14.3095i) q^{77} -8.56803i q^{78} +(-10.9877 + 19.0313i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-22.2916 + 38.6101i) q^{82} -0.417479 q^{83} +(14.2098 + 19.6489i) q^{84} +(45.5459 - 78.8878i) q^{86} +(46.0053 + 79.6835i) q^{87} +(48.9285 - 28.2489i) q^{88} +(96.3110 + 55.6052i) q^{89} +(-10.0082 + 22.3463i) q^{91} +50.3807i q^{92} +(45.1968 + 26.0944i) q^{93} +(34.3695 - 19.8432i) q^{94} +(-8.48528 - 4.89898i) q^{96} +74.2244 q^{97} +(-14.1090 - 67.8449i) q^{98} +59.9249 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} - 48 q^{9}+O(q^{10}) $ 32 * q + 32 * q^4 - 48 * q^9	$ 32 q + 32 q^{4} - 48 q^{9} - 8 q^{11} - 16 q^{14} - 64 q^{16} + 144 q^{19} - 48 q^{21} - 144 q^{29} + 240 q^{31} - 192 q^{36} - 72 q^{39} + 16 q^{44} + 16 q^{46} + 80 q^{49} - 24 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 256 q^{64} + 144 q^{66} - 272 q^{71} + 224 q^{74} - 560 q^{79} - 144 q^{81} + 48 q^{84} - 176 q^{86} + 600 q^{89} - 544 q^{91} + 48 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 - 48 * q^9 - 8 * q^11 - 16 * q^14 - 64 * q^16 + 144 * q^19 - 48 * q^21 - 144 * q^29 + 240 * q^31 - 192 * q^36 - 72 * q^39 + 16 * q^44 + 16 * q^46 + 80 * q^49 - 24 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 256 * q^64 + 144 * q^66 - 272 * q^71 + 224 * q^74 - 560 * q^79 - 144 * q^81 + 48 * q^84 - 176 * q^86 + 600 * q^89 - 544 * q^91 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$7$	2.86123	−	6.38854i	0.408747	−	0.912648i
$7$	2.86123	−	6.38854i	0.408747	−	0.912648i
$8$			2.82843i			0.353553i
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$		0			0
$11$	−9.98749	−	17.2988i	−0.907953	−	1.57262i	−0.816903	−	0.576775i	$-0.804311\pi$
$11$	−9.98749	−	17.2988i	−0.907953	−	1.57262i	−0.0910503	−	0.995846i	$-0.529022\pi$
$12$	−1.73205	+	3.00000i	−0.144338	+	0.250000i
$13$	−3.49788			−0.269068			−0.134534	−	0.990909i	$-0.542954\pi$
$13$	−3.49788			−0.269068			−0.134534	+	0.990909i	$0.542954\pi$
$14$	8.02165	−	5.80113i	0.572975	−	0.414367i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	9.12112	+	15.7982i	0.536536	+	0.929308i	0.999087	+	0.0427155i	$0.0136009\pi$
$17$	9.12112	+	15.7982i	0.536536	+	0.929308i	−0.462551	+	0.886593i	$0.653066\pi$
$18$	−3.67423	+	2.12132i	−0.204124	+	0.117851i
$19$	21.3143	+	12.3058i	1.12180	+	0.647673i	0.941861	−	0.336004i	$-0.109076\pi$
$19$	21.3143	+	12.3058i	1.12180	+	0.647673i	0.179942	+	0.983677i	$0.442409\pi$
$20$		0			0
$21$	12.0607	−	1.24079i	0.574319	−	0.0590854i
$22$		−	28.2489i		−	1.28404i
$23$	21.8155	+	12.5952i	0.948500	+	0.547617i	0.892615	−	0.450820i	$-0.148869\pi$
$23$	21.8155	+	12.5952i	0.948500	+	0.547617i	0.0558853	+	0.998437i	$0.482202\pi$
$24$	−4.24264	+	2.44949i	−0.176777	+	0.102062i
$25$		0			0
$26$	−4.28401	−	2.47338i	−0.164770	−	0.0951299i
$27$	−5.19615			−0.192450
$28$	13.9265	−	1.43274i	0.497375	−	0.0511694i
$29$	53.1223			1.83180			0.915902	−	0.401402i	$-0.131477\pi$
$29$	53.1223			1.83180			0.915902	+	0.401402i	$0.131477\pi$
$30$		0			0
$31$	26.0944	−	15.0656i	0.841754	−	0.485987i	−0.0161061	−	0.999870i	$-0.505127\pi$
$31$	26.0944	−	15.0656i	0.841754	−	0.485987i	0.857860	+	0.513883i	$0.171794\pi$
$32$	−4.89898	+	2.82843i	−0.153093	+	0.0883883i
$33$	17.2988	−	29.9625i	0.524207	−	0.907953i
$34$			25.7984i			0.758777i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	40.5034	+	23.3846i	1.09469	+	0.632017i	0.934820	−	0.355122i	$-0.115561\pi$
$37$	40.5034	+	23.3846i	1.09469	+	0.632017i	0.159866	+	0.987139i	$0.448894\pi$
$38$	17.4030	+	30.1429i	0.457974	+	0.793234i
$39$	−3.02925	−	5.24682i	−0.0776732	−	0.134534i
$40$		0			0
$41$			31.5250i			0.768903i	0.923145	+	0.384452i	$0.125609\pi$
$41$			31.5250i			0.768903i	−0.923145	+	0.384452i	$0.874391\pi$
$42$	15.6487	+	7.00855i	0.372587	+	0.166870i
$43$		−	64.4116i		−	1.49794i	−0.662602	−	0.748972i	$-0.730548\pi$
$43$		−	64.4116i		−	1.49794i	0.662602	−	0.748972i	$-0.269452\pi$
$44$	19.9750	−	34.5977i	0.453977	−	0.786311i
$45$		0			0
$46$	17.8123	+	30.8518i	0.387223	+	0.670691i
$47$	14.0313	−	24.3029i	0.298538	−	0.517083i	−0.677264	−	0.735740i	$-0.736834\pi$
$47$	14.0313	−	24.3029i	0.298538	−	0.517083i	0.975802	+	0.218657i	$0.0701677\pi$
$48$	−6.92820			−0.144338
$49$	−32.6268	−	36.5581i	−0.665852	−	0.746084i
$50$		0			0
$51$	−15.7982	+	27.3634i	−0.309769	+	0.536536i
$52$	−3.49788	−	6.05851i	−0.0672670	−	0.116510i
$53$	56.1833	−	32.4374i	1.06006	−	0.612027i	0.134612	−	0.990898i	$-0.457021\pi$
$53$	56.1833	−	32.4374i	1.06006	−	0.612027i	0.925449	+	0.378872i	$0.123688\pi$
$54$	−6.36396	−	3.67423i	−0.117851	−	0.0680414i
$55$		0			0
$56$	18.0695	+	8.09277i	0.322670	+	0.144514i
$57$			42.6285i			0.747869i
$58$	65.0613	+	37.5631i	1.12175	+	0.647640i
$59$	−86.7684	+	50.0958i	−1.47065	+	0.849081i	−0.999457	−	0.0329486i	$-0.989510\pi$
$59$	−86.7684	+	50.0958i	−1.47065	+	0.849081i	−0.471194	+	0.882029i	$0.656177\pi$
$60$		0			0
$61$	6.94896	+	4.01198i	0.113917	+	0.0657702i	0.555876	−	0.831265i	$-0.312383\pi$
$61$	6.94896	+	4.01198i	0.113917	+	0.0657702i	−0.441959	+	0.897035i	$0.645716\pi$
$62$	42.6119			0.687289
$63$	12.3061	+	17.0165i	0.195334	+	0.270103i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	42.3733	−	24.4642i	0.642020	−	0.370670i
$67$	14.0844	−	8.13165i	0.210215	−	0.121368i	−0.391196	−	0.920307i	$-0.627939\pi$
$67$	14.0844	−	8.13165i	0.210215	−	0.121368i	0.601411	+	0.798939i	$0.294605\pi$
$68$	−18.2422	+	31.5965i	−0.268268	+	0.464654i
$69$			43.6310i			0.632333i
$70$		0			0
$71$	−107.725			−1.51725			−0.758625	−	0.651528i	$-0.774128\pi$
$71$	−107.725			−1.51725			−0.758625	+	0.651528i	$0.774128\pi$
$72$	−7.34847	−	4.24264i	−0.102062	−	0.0589256i
$73$	−25.8303	−	44.7395i	−0.353840	−	0.612870i	0.633078	−	0.774088i	$-0.281791\pi$
$73$	−25.8303	−	44.7395i	−0.353840	−	0.612870i	−0.986919	+	0.161218i	$0.948458\pi$
$74$	33.0709	+	57.2804i	0.446904	+	0.774060i
$75$		0			0
$76$			49.2232i			0.647673i
$77$	−139.091	+	14.3095i	−1.80637	+	0.185838i
$78$		−	8.56803i		−	0.109846i
$79$	−10.9877	+	19.0313i	−0.139085	+	0.240903i	−0.927151	−	0.374689i	$-0.877750\pi$
$79$	−10.9877	+	19.0313i	−0.139085	+	0.240903i	0.788065	+	0.615592i	$0.211083\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−22.2916	+	38.6101i	−0.271848	+	0.470855i
$83$	−0.417479			−0.00502987			−0.00251494	−	0.999997i	$-0.500801\pi$
$83$	−0.417479			−0.00502987			−0.00251494	+	0.999997i	$0.500801\pi$
$84$	14.2098	+	19.6489i	0.169164	+	0.233916i
$85$		0			0
$86$	45.5459	−	78.8878i	0.529603	−	0.917300i
$87$	46.0053	+	79.6835i	0.528796	+	0.915902i
$88$	48.9285	−	28.2489i	0.556006	−	0.321010i
$89$	96.3110	+	55.6052i	1.08215	+	0.624778i	0.931475	−	0.363806i	$-0.118523\pi$
$89$	96.3110	+	55.6052i	1.08215	+	0.624778i	0.150672	+	0.988584i	$0.451856\pi$
$90$		0			0
$91$	−10.0082	+	22.3463i	−0.109981	+	0.245564i
$92$			50.3807i			0.547617i
$93$	45.1968	+	26.0944i	0.485987	+	0.280585i
$94$	34.3695	−	19.8432i	0.365633	−	0.211098i
$95$		0			0
$96$	−8.48528	−	4.89898i	−0.0883883	−	0.0510310i
$97$	74.2244			0.765200			0.382600	−	0.923914i	$-0.375029\pi$
$97$	74.2244			0.765200			0.382600	+	0.923914i	$0.375029\pi$
$98$	−14.1090	−	67.8449i	−0.143969	−	0.692295i
$99$	59.9249			0.605302
$100$		0			0
$101$	75.8587	−	43.7970i	0.751076	−	0.433634i	−0.0750065	−	0.997183i	$-0.523898\pi$
$101$	75.8587	−	43.7970i	0.751076	−	0.433634i	0.826083	+	0.563549i	$0.190564\pi$
$102$	−38.6976	+	22.3421i	−0.379388	+	0.219040i
$103$	69.5206	−	120.413i	0.674957	−	1.16906i	−0.301525	−	0.953458i	$-0.597496\pi$
$103$	69.5206	−	120.413i	0.674957	−	1.16906i	0.976482	−	0.215601i	$-0.0691711\pi$
$104$		−	9.89350i		−	0.0951299i
$105$		0			0
$106$	91.7469			0.865537
$107$	−131.800	−	76.0949i	−1.23178	−	0.711168i	−0.264378	−	0.964419i	$-0.585167\pi$
$107$	−131.800	−	76.0949i	−1.23178	−	0.711168i	−0.967400	+	0.253252i	$0.918500\pi$
$108$	−5.19615	−	9.00000i	−0.0481125	−	0.0833333i
$109$	32.3777	+	56.0798i	0.297043	+	0.514494i	0.975458	−	0.220185i	$-0.0706662\pi$
$109$	32.3777	+	56.0798i	0.297043	+	0.514494i	−0.678415	+	0.734679i	$0.737333\pi$
$110$		0			0
$111$			81.0068i			0.729791i
$112$	16.4081	+	22.6887i	0.146501	+	0.202577i
$113$		−	3.25860i		−	0.0288372i	−0.999896	−	0.0144186i	$-0.995410\pi$
$113$		−	3.25860i		−	0.0288372i	0.999896	−	0.0144186i	$-0.00458974\pi$
$114$	−30.1429	+	52.2090i	−0.264411	+	0.457974i
$115$		0			0
$116$	53.1223	+	92.0105i	0.457951	+	0.793194i
$117$	5.24682	−	9.08776i	0.0448446	−	0.0776732i
$118$	−141.692			−1.20078
$119$	127.025	−	13.0682i	1.06744	−	0.109817i
$120$		0			0
$121$	−139.000	+	240.755i	−1.14876	+	1.98971i
$122$	5.67380	+	9.82731i	0.0465066	+	0.0805517i
$123$	−47.2875	+	27.3015i	−0.384452	+	0.221963i
$124$	52.1887	+	30.1312i	0.420877	+	0.242993i
$125$		0			0
$126$	3.03931	+	29.5426i	0.0241215	+	0.234465i
$127$		−	88.5772i		−	0.697458i	−0.937224	−	0.348729i	$-0.886613\pi$
$127$		−	88.5772i		−	0.697458i	0.937224	−	0.348729i	$-0.113387\pi$
$128$	−9.79796	−	5.65685i	−0.0765466	−	0.0441942i
$129$	96.6174	−	55.7821i	0.748972	−	0.432419i
$130$		0			0
$131$	−108.361	−	62.5621i	−0.827181	−	0.477573i	0.0257055	−	0.999670i	$-0.491817\pi$
$131$	−108.361	−	62.5621i	−0.827181	−	0.477573i	−0.852887	+	0.522096i	$0.825150\pi$
$132$	69.1953			0.524207
$133$	139.601	−	100.957i	1.04963	−	0.759077i
$134$	22.9998			0.171640
$135$		0			0
$136$	−44.6842	+	25.7984i	−0.328560	+	0.189694i
$137$	−33.7349	+	19.4769i	−0.246240	+	0.142167i	−0.618042	−	0.786145i	$-0.712074\pi$
$137$	−33.7349	+	19.4769i	−0.246240	+	0.142167i	0.371801	+	0.928312i	$0.378740\pi$
$138$	−30.8518	+	53.4368i	−0.223564	+	0.387223i
$139$			98.9454i			0.711837i	0.934517	+	0.355919i	$0.115832\pi$
$139$			98.9454i			0.711837i	−0.934517	+	0.355919i	$0.884168\pi$
$140$		0			0
$141$	48.6058			0.344722
$142$	−131.935	−	76.1729i	−0.929122	−	0.536429i
$143$	34.9351	+	60.5093i	0.244301	+	0.423142i
$144$	−6.00000	−	10.3923i	−0.0416667	−	0.0721688i
$145$		0			0
$146$		−	73.0593i		−	0.500406i
$147$	26.5815	−	80.6004i	0.180827	−	0.548302i
$148$			93.5385i			0.632017i
$149$	−93.2324	+	161.483i	−0.625721	+	1.08378i	0.362680	+	0.931914i	$0.381862\pi$
$149$	−93.2324	+	161.483i	−0.625721	+	1.08378i	−0.988401	+	0.151867i	$0.951472\pi$
$150$		0			0
$151$	−77.4202	−	134.096i	−0.512716	−	0.888051i	−0.999891	−	0.0147462i	$-0.995306\pi$
$151$	−77.4202	−	134.096i	−0.512716	−	0.888051i	0.487175	−	0.873304i	$-0.338027\pi$
$152$	−34.8060	+	60.2858i	−0.228987	+	0.396617i
$153$	−54.7267			−0.357691
$154$	−180.469	−	80.8265i	−1.17188	−	0.524847i
$155$		0			0
$156$	6.05851	−	10.4936i	0.0388366	−	0.0672670i
$157$	−25.1019	−	43.4777i	−0.159885	−	0.276928i	0.774942	−	0.632032i	$-0.217779\pi$
$157$	−25.1019	−	43.4777i	−0.159885	−	0.276928i	−0.934827	+	0.355104i	$0.884446\pi$
$158$	−26.9143	+	15.5390i	−0.170344	+	0.0983481i
$159$	97.3123	+	56.1833i	0.612027	+	0.353354i
$160$		0			0
$161$	142.884	−	103.331i	0.887477	−	0.641810i
$162$		−	12.7279i		−	0.0785674i
$163$	−100.295	−	57.9054i	−0.615308	−	0.355248i	0.159732	−	0.987160i	$-0.448937\pi$
$163$	−100.295	−	57.9054i	−0.615308	−	0.355248i	−0.775040	+	0.631912i	$0.782270\pi$
$164$	−54.6029	+	31.5250i	−0.332945	+	0.192226i
$165$		0			0
$166$	−0.511306	−	0.295202i	−0.00308015	−	0.00177833i
$167$	−61.3210			−0.367191			−0.183596	−	0.983002i	$-0.558774\pi$
$167$	−61.3210			−0.367191			−0.183596	+	0.983002i	$0.558774\pi$
$168$	3.50949	+	34.1128i	0.0208898	+	0.203052i
$169$	−156.765			−0.927602
$170$		0			0
$171$	−63.9428	+	36.9174i	−0.373934	+	0.215891i
$172$	111.564	−	64.4116i	0.648629	−	0.374486i
$173$	15.8508	−	27.4544i	0.0916232	−	0.158696i	−0.816571	−	0.577245i	$-0.804128\pi$
$173$	15.8508	−	27.4544i	0.0916232	−	0.158696i	0.908194	+	0.418549i	$0.137461\pi$
$174$			130.123i			0.747831i
$175$		0			0
$176$	79.8999			0.453977
$177$	−150.287	−	86.7684i	−0.849081	−	0.490217i
$178$	78.6376	+	136.204i	0.441784	+	0.765193i
$179$	65.9472	+	114.224i	0.368420	+	0.638122i	0.989319	−	0.145768i	$-0.0465655\pi$
$179$	65.9472	+	114.224i	0.368420	+	0.638122i	−0.620899	+	0.783891i	$0.713232\pi$
$180$		0			0
$181$		−	55.1431i		−	0.304658i	−0.988330	−	0.152329i	$-0.951323\pi$
$181$		−	55.1431i		−	0.304658i	0.988330	−	0.152329i	$-0.0486773\pi$
$182$	−28.0588	+	20.2917i	−0.154169	+	0.111493i
$183$			13.8979i			0.0759449i
$184$	−35.6246	+	61.7035i	−0.193612	+	0.335345i
$185$		0			0
$186$	36.9030	+	63.9179i	0.198403	+	0.343645i
$187$	182.194	−	315.569i	0.974300	−	1.68754i
$188$	56.1252			0.298538
$189$	−14.8674	+	33.1958i	−0.0786633	+	0.175639i
$190$		0			0
$191$	−97.5822	+	169.017i	−0.510901	+	0.884907i	0.489019	+	0.872273i	$0.337355\pi$
$191$	−97.5822	+	169.017i	−0.510901	+	0.884907i	−0.999920	+	0.0126340i	$0.995978\pi$
$192$	−6.92820	−	12.0000i	−0.0360844	−	0.0625000i
$193$	−302.035	+	174.380i	−1.56495	+	0.903523i	−0.568204	+	0.822888i	$0.692361\pi$
$193$	−302.035	+	174.380i	−1.56495	+	0.903523i	−0.996744	+	0.0806348i	$0.974305\pi$
$194$	90.9060	+	52.4846i	0.468588	+	0.270539i
$195$		0			0
$196$	30.6937	−	93.0693i	0.156601	−	0.474843i
$197$		−	56.3808i		−	0.286197i	−0.989708	−	0.143098i	$-0.954293\pi$
$197$		−	56.3808i		−	0.286197i	0.989708	−	0.143098i	$-0.0457066\pi$
$198$	73.3927	+	42.3733i	0.370670	+	0.214007i
$199$	−148.357	+	85.6540i	−0.745513	+	0.430422i	−0.824070	−	0.566487i	$-0.808302\pi$
$199$	−148.357	+	85.6540i	−0.745513	+	0.430422i	0.0785571	+	0.996910i	$0.474969\pi$
$200$		0			0
$201$	24.3950	+	14.0844i	0.121368	+	0.0700718i
$202$	123.877			0.613251
$203$	151.995	−	339.374i	0.748744	−	1.67179i
$204$	−63.1930			−0.309769
$205$		0			0
$206$	170.290	−	98.3169i	0.826650	−	0.477267i
$207$	−65.4465	+	37.7856i	−0.316167	+	0.182539i
$208$	6.99576	−	12.1170i	0.0336335	−	0.0582549i
$209$		−	491.616i		−	2.35223i
$210$		0			0
$211$	162.038			0.767954			0.383977	−	0.923343i	$-0.374554\pi$
$211$	162.038			0.767954			0.383977	+	0.923343i	$0.374554\pi$
$212$	112.367	+	64.8748i	0.530031	+	0.306013i
$213$	−93.2923	−	161.587i	−0.437992	−	0.758625i
$214$	−107.614	−	186.394i	−0.502871	−	0.870999i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	−21.5851	−	209.811i	−0.0994707	−	0.966870i
$218$			91.5779i			0.420082i
$219$	44.7395	−	77.4910i	0.204290	−	0.353840i
$220$		0			0
$221$	−31.9046	−	55.2604i	−0.144365	−	0.250047i
$222$	−57.2804	+	99.2126i	−0.258020	+	0.446904i
$223$	365.329			1.63825			0.819123	−	0.573618i	$-0.194461\pi$
$223$	365.329			1.63825			0.819123	+	0.573618i	$0.194461\pi$
$224$	4.05241	+	39.3901i	0.0180911	+	0.175849i
$225$		0			0
$226$	2.30418	−	3.99096i	0.0101955	−	0.0176591i
$227$	128.937	+	223.325i	0.568004	+	0.983811i	0.996763	+	0.0803928i	$0.0256175\pi$
$227$	128.937	+	223.325i	0.568004	+	0.983811i	−0.428759	+	0.903419i	$0.641049\pi$
$228$	−73.8347	+	42.6285i	−0.323837	+	0.186967i
$229$	13.3634	+	7.71538i	0.0583556	+	0.0336916i	0.528894	−	0.848688i	$-0.322607\pi$
$229$	13.3634	+	7.71538i	0.0583556	+	0.0336916i	−0.470538	+	0.882380i	$0.655940\pi$
$230$		0			0
$231$	−141.920	−	196.244i	−0.614374	−	0.849539i
$232$			150.253i			0.647640i
$233$	−108.553	−	62.6734i	−0.465895	−	0.268984i	0.248625	−	0.968600i	$-0.420021\pi$
$233$	−108.553	−	62.6734i	−0.465895	−	0.268984i	−0.714520	+	0.699615i	$0.753355\pi$
$234$	12.8520	−	7.42013i	0.0549232	−	0.0317100i
$235$		0			0
$236$	−173.537	−	100.192i	−0.735326	−	0.424540i
$237$	−38.0626			−0.160602
$238$	164.814	+	73.8151i	0.692496	+	0.310148i
$239$	3.62565			0.0151701			0.00758503	−	0.999971i	$-0.497586\pi$
$239$	3.62565			0.0151701			0.00758503	+	0.999971i	$0.497586\pi$
$240$		0			0
$241$	83.6915	−	48.3193i	0.347268	−	0.200495i	−0.316213	−	0.948688i	$-0.602412\pi$
$241$	83.6915	−	48.3193i	0.347268	−	0.200495i	0.663481	+	0.748193i	$0.269078\pi$
$242$	−340.479	+	196.575i	−1.40694	+	0.812295i
$243$	7.79423	−	13.5000i	0.0320750	−	0.0555556i
$244$			16.0479i			0.0657702i
$245$		0			0
$246$	−77.2202			−0.313903
$247$	−74.5548	−	43.0442i	−0.301841	−	0.174268i
$248$	42.6119	+	73.8060i	0.171822	+	0.297605i
$249$	−0.361548	−	0.626219i	−0.00145200	−	0.00251494i
$250$		0			0
$251$			29.7311i			0.118450i	0.998245	+	0.0592252i	$0.0188630\pi$
$251$			29.7311i			0.118450i	−0.998245	+	0.0592252i	$0.981137\pi$
$252$	−17.1674	+	38.3312i	−0.0681245	+	0.152108i
$253$		−	503.177i		−	1.98884i
$254$	62.6336	−	108.484i	0.246589	−	0.427104i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−220.811	+	382.457i	−0.859189	+	1.48816i	0.0135154	+	0.999909i	$0.495698\pi$
$257$	−220.811	+	382.457i	−0.859189	+	1.48816i	−0.872704	+	0.488250i	$0.837636\pi$
$258$	157.776			0.611533
$259$	265.283	−	191.848i	1.02426	−	0.740728i
$260$		0			0
$261$	−79.6835	+	138.016i	−0.305301	+	0.528796i
$262$	−88.4762	−	153.245i	−0.337695	−	0.584905i
$263$	−297.087	+	171.523i	−1.12961	+	0.652180i	−0.943836	−	0.330413i	$-0.892812\pi$
$263$	−297.087	+	171.523i	−1.12961	+	0.652180i	−0.185772	+	0.982593i	$0.559479\pi$
$264$	84.7466	+	48.9285i	0.321010	+	0.185335i
$265$		0			0
$266$	242.363	−	24.9341i	0.911139	−	0.0937371i
$267$			192.622i			0.721431i
$268$	28.1689	+	16.2633i	0.105108	+	0.0606840i
$269$	−401.274	+	231.676i	−1.49172	+	0.861247i	−0.999955	−	0.00947852i	$-0.996983\pi$
$269$	−401.274	+	231.676i	−1.49172	+	0.861247i	−0.491769	+	0.870726i	$0.663650\pi$
$270$		0			0
$271$	211.814	+	122.291i	0.781600	+	0.451257i	0.836997	−	0.547207i	$-0.184309\pi$
$271$	211.814	+	122.291i	0.781600	+	0.451257i	−0.0553967	+	0.998464i	$0.517642\pi$
$272$	−72.9689			−0.268268
$273$	−42.1869	+	4.34015i	−0.154531	+	0.0158980i
$274$	−55.0889			−0.201054
$275$		0			0
$276$	−75.5711	+	43.6310i	−0.273808	+	0.158083i
$277$	122.126	−	70.5092i	0.440887	−	0.254546i	−0.263087	−	0.964772i	$-0.584741\pi$
$277$	122.126	−	70.5092i	0.440887	−	0.254546i	0.703974	+	0.710226i	$0.251407\pi$
$278$	−69.9650	+	121.183i	−0.251673	+	0.435910i
$279$			90.3935i			0.323991i
$280$		0			0
$281$	84.9953			0.302475			0.151237	−	0.988497i	$-0.451674\pi$
$281$	84.9953			0.302475			0.151237	+	0.988497i	$0.451674\pi$
$282$	59.5297	+	34.3695i	0.211098	+	0.121878i
$283$	58.3392	+	101.047i	0.206146	+	0.357055i	0.950497	−	0.310733i	$-0.100575\pi$
$283$	58.3392	+	101.047i	0.206146	+	0.357055i	−0.744351	+	0.667788i	$0.767241\pi$
$284$	−107.725	−	186.585i	−0.379312	−	0.656988i
$285$		0			0
$286$			98.8112i			0.345494i
$287$	201.399	+	90.2003i	0.701738	+	0.314287i
$288$		−	16.9706i		−	0.0589256i
$289$	−21.8896	+	37.9138i	−0.0757424	+	0.131190i
$290$		0			0
$291$	64.2802	+	111.337i	0.220894	+	0.382600i
$292$	51.6607	−	89.4789i	0.176920	−	0.306435i
$293$	−131.882			−0.450110			−0.225055	−	0.974346i	$-0.572256\pi$
$293$	−131.882			−0.450110			−0.225055	+	0.974346i	$0.572256\pi$
$294$	89.5487	−	79.9189i	0.304587	−	0.271833i
$295$		0			0
$296$	−66.1417	+	114.561i	−0.223452	+	0.387030i
$297$	51.8965	+	89.8874i	0.174736	+	0.302651i
$298$	−228.372	+	131.851i	−0.766348	+	0.442451i
$299$	−76.3080	−	44.0565i	−0.255211	−	0.147346i
$300$		0			0
$301$	−411.496	−	184.296i	−1.36710	−	0.612280i
$302$		−	218.977i		−	0.725090i
$303$	131.391	+	75.8587i	0.433634	+	0.250359i
$304$	−85.2570	+	49.2232i	−0.280451	+	0.161918i
$305$		0			0
$306$	−67.0263	−	38.6976i	−0.219040	−	0.126463i
$307$	429.871			1.40023			0.700115	−	0.714030i	$-0.253132\pi$
$307$	429.871			1.40023			0.700115	+	0.714030i	$0.253132\pi$
$308$	−163.875	−	226.603i	−0.532063	−	0.735723i
$309$	240.826			0.779373
$310$		0			0
$311$	−217.786	+	125.739i	−0.700277	+	0.404305i	−0.807451	−	0.589935i	$-0.799153\pi$
$311$	−217.786	+	125.739i	−0.700277	+	0.404305i	0.107174	+	0.994240i	$0.465820\pi$
$312$	14.8403	−	8.56803i	0.0475649	−	0.0274616i
$313$	6.85166	−	11.8674i	0.0218903	−	0.0379151i	−0.854873	−	0.518838i	$-0.826365\pi$
$313$	6.85166	−	11.8674i	0.0218903	−	0.0379151i	0.876763	+	0.480923i	$0.159698\pi$
$314$		−	70.9988i		−	0.226111i
$315$		0			0
$316$	−43.9509			−0.139085
$317$	28.5183	+	16.4651i	0.0899632	+	0.0519403i	0.544307	−	0.838886i	$-0.316793\pi$
$317$	28.5183	+	16.4651i	0.0899632	+	0.0519403i	−0.454343	+	0.890827i	$0.650126\pi$
$318$	79.4551	+	137.620i	0.249859	+	0.432768i
$319$	−530.558	−	918.954i	−1.66319	−	2.88073i
$320$		0			0
$321$		−	263.601i		−	0.821186i
$322$	248.063	−	25.5204i	0.770381	−	0.0792560i
$323$			448.970i			1.39000i
$324$	9.00000	−	15.5885i	0.0277778	−	0.0481125i
$325$		0			0
$326$	−81.8906	−	141.839i	−0.251198	−	0.435088i
$327$	−56.0798	+	97.1331i	−0.171498	+	0.297043i
$328$	−89.1662			−0.271848
$329$	−115.113	−	159.176i	−0.349888	−	0.483816i
$330$		0			0
$331$	208.940	−	361.895i	0.631240	−	1.09334i	−0.356059	−	0.934464i	$-0.615880\pi$
$331$	208.940	−	361.895i	0.631240	−	1.09334i	0.987299	−	0.158876i	$-0.0507869\pi$
$332$	−0.417479	−	0.723095i	−0.00125747	−	0.00217800i
$333$	−121.510	+	70.1539i	−0.364895	+	0.210672i
$334$	−75.1025	−	43.3605i	−0.224858	−	0.129822i
$335$		0			0
$336$	−19.8232	+	44.2611i	−0.0589975	+	0.131729i
$337$		−	286.688i		−	0.850705i	−0.905028	−	0.425353i	$-0.860150\pi$
$337$		−	286.688i		−	0.850705i	0.905028	−	0.425353i	$-0.139850\pi$
$338$	−191.997	−	110.849i	−0.568038	−	0.327957i
$339$	4.88790	−	2.82203i	0.0144186	−	0.00832458i
$340$		0			0
$341$	−521.234	−	300.935i	−1.52855	−	0.882507i
$342$	−104.418			−0.305316
$343$	−326.905	+	103.836i	−0.953077	+	0.302729i
$344$	182.184			0.529603
$345$		0			0
$346$	38.8264	−	22.4164i	0.112215	−	0.0647874i
$347$	265.693	−	153.398i	0.765685	−	0.442069i	−0.0656479	−	0.997843i	$-0.520911\pi$
$347$	265.693	−	153.398i	0.765685	−	0.442069i	0.831333	+	0.555774i	$0.187578\pi$
$348$	−92.0105	+	159.367i	−0.264398	+	0.457951i
$349$		−	340.162i		−	0.974676i	−0.873214	−	0.487338i	$-0.837968\pi$
$349$		−	340.162i		−	0.974676i	0.873214	−	0.487338i	$-0.162032\pi$
$350$		0			0
$351$	18.1755			0.0517821
$352$	97.8570	+	56.4978i	0.278003	+	0.160505i
$353$	187.501	+	324.761i	0.531165	+	0.920004i	0.999338	+	0.0363676i	$0.0115787\pi$
$353$	187.501	+	324.761i	0.531165	+	0.920004i	−0.468174	+	0.883636i	$0.655088\pi$
$354$	−122.709	−	212.538i	−0.346636	−	0.600391i
$355$		0			0
$356$			222.421i			0.624778i
$357$	129.609	+	179.220i	0.363051	+	0.502018i
$358$			186.527i			0.521025i
$359$	−164.750	+	285.356i	−0.458915	+	0.794863i	−0.998904	−	0.0468084i	$-0.985095\pi$
$359$	−164.750	+	285.356i	−0.458915	+	0.794863i	0.539989	+	0.841672i	$0.318428\pi$
$360$		0			0
$361$	122.365	+	211.942i	0.338961	+	0.587098i
$362$	38.9920	−	67.5362i	0.107713	−	0.186564i
$363$	−481.509			−1.32647
$364$	−48.7132	+	5.01157i	−0.133828	+	0.0137681i
$365$		0			0
$366$	−9.82731	+	17.0214i	−0.0268506	+	0.0465066i
$367$	13.5772	+	23.5163i	0.0369950	+	0.0640772i	0.883930	−	0.467619i	$-0.154888\pi$
$367$	13.5772	+	23.5163i	0.0369950	+	0.0640772i	−0.846935	+	0.531696i	$0.821555\pi$
$368$	−87.2620	+	50.3807i	−0.237125	+	0.136904i
$369$	−81.9044	−	47.2875i	−0.221963	−	0.128151i
$370$		0			0
$371$	−46.4745	−	451.740i	−0.125268	−	1.21763i
$372$			104.377i			0.280585i
$373$	110.416	+	63.7488i	0.296022	+	0.170908i	0.640654	−	0.767829i	$-0.278663\pi$
$373$	110.416	+	63.7488i	0.296022	+	0.170908i	−0.344633	+	0.938738i	$0.611996\pi$
$374$	446.283	−	257.661i	1.19327	−	0.688934i
$375$		0			0
$376$	68.7390	+	39.6865i	0.182817	+	0.105549i
$377$	−185.816			−0.492880
$378$	−41.6817	+	30.1436i	−0.110269	+	0.0797449i
$379$	−319.795			−0.843785			−0.421893	−	0.906646i	$-0.638634\pi$
$379$	−319.795			−0.843785			−0.421893	+	0.906646i	$0.638634\pi$
$380$		0			0
$381$	132.866	−	76.7101i	0.348729	−	0.201339i
$382$	−239.027	+	138.002i	−0.625724	+	0.361262i
$383$	204.471	−	354.155i	0.533867	−	0.924686i	−0.465350	−	0.885127i	$-0.654071\pi$
$383$	204.471	−	354.155i	0.533867	−	0.924686i	0.999217	−	0.0395587i	$-0.0125952\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	−493.221			−1.27777
$387$	167.346	+	96.6174i	0.432419	+	0.249657i
$388$	74.2244	+	128.560i	0.191300	+	0.331341i
$389$	193.576	+	335.284i	0.497626	+	0.861913i	0.999996	−	0.00273932i	$-0.000871952\pi$
$389$	193.576	+	335.284i	0.497626	+	0.861913i	−0.502370	+	0.864652i	$0.667539\pi$
$390$		0			0
$391$			459.529i			1.17526i
$392$	103.402	−	92.2824i	0.263780	−	0.235414i
$393$		−	216.721i		−	0.551454i
$394$	39.8672	−	69.0521i	0.101186	−	0.175259i
$395$		0			0
$396$	59.9249	+	103.793i	0.151326	+	0.262104i
$397$	−15.0556	+	26.0771i	−0.0379234	+	0.0656853i	−0.884364	−	0.466798i	$-0.845408\pi$
$397$	−15.0556	+	26.0771i	−0.0379234	+	0.0656853i	0.846441	+	0.532483i	$0.178741\pi$
$398$	−242.266			−0.608709
$399$	272.334	+	121.970i	0.682541	+	0.305689i
$400$		0			0
$401$	−68.3852	+	118.447i	−0.170537	+	0.295378i	−0.938608	−	0.344987i	$-0.887883\pi$
$401$	−68.3852	+	118.447i	−0.170537	+	0.295378i	0.768071	+	0.640365i	$0.221217\pi$
$402$	19.9184	+	34.4997i	0.0495482	+	0.0858201i
$403$	−91.2750	+	52.6977i	−0.226489	+	0.130763i
$404$	151.717	+	87.5941i	0.375538	+	0.216817i
$405$		0			0
$406$	426.129	−	308.170i	1.04958	−	0.759038i
$407$		−	934.215i		−	2.29537i
$408$	−77.3952	−	44.6842i	−0.189694	−	0.109520i
$409$	426.838	−	246.435i	1.04361	−	0.602531i	0.122759	−	0.992437i	$-0.460826\pi$
$409$	426.838	−	246.435i	1.04361	−	0.602531i	0.920855	+	0.389906i	$0.127493\pi$
$410$		0			0
$411$	−58.4306	−	33.7349i	−0.142167	−	0.0820801i
$412$	278.082			0.674957
$413$	71.7744	+	697.659i	0.173788	+	1.68925i
$414$	−106.874			−0.258149
$415$		0			0
$416$	17.1361	−	9.89350i	0.0411924	−	0.0237825i
$417$	−148.418	+	85.6892i	−0.355919	+	0.205490i
$418$	347.625	−	602.104i	0.831638	−	1.44044i
$419$		−	311.640i		−	0.743771i	−0.928279	−	0.371885i	$-0.878711\pi$
$419$		−	311.640i		−	0.743771i	0.928279	−	0.371885i	$-0.121289\pi$
$420$		0			0
$421$	−539.935			−1.28250			−0.641252	−	0.767330i	$-0.721585\pi$
$421$	−539.935			−1.28250			−0.641252	+	0.767330i	$0.721585\pi$
$422$	198.456	+	114.578i	0.470274	+	0.271513i
$423$	42.0939	+	72.9087i	0.0995127	+	0.172361i
$424$	91.7469	+	158.910i	0.216384	+	0.374788i
$425$		0			0
$426$		−	263.871i		−	0.619414i
$427$	45.5132	−	32.9145i	0.106588	−	0.0770831i
$428$		−	304.380i		−	0.711168i
$429$	−60.5093	+	104.805i	−0.141047	+	0.244301i
$430$		0			0
$431$	314.021	+	543.900i	0.728586	+	1.26195i	0.957481	+	0.288497i	$0.0931555\pi$
$431$	314.021	+	543.900i	0.728586	+	1.26195i	−0.228895	+	0.973451i	$0.573511\pi$
$432$	10.3923	−	18.0000i	0.0240563	−	0.0416667i
$433$	−706.789			−1.63231			−0.816153	−	0.577836i	$-0.803897\pi$
$433$	−706.789			−1.63231			−0.816153	+	0.577836i	$0.803897\pi$
$434$	121.922	−	272.228i	0.280927	−	0.627253i
$435$		0			0
$436$	−64.7554	+	112.160i	−0.148522	+	0.257247i
$437$	309.987	+	536.914i	0.709353	+	1.22864i
$438$	109.589	−	63.2712i	0.250203	−	0.144455i
$439$	−564.452	−	325.886i	−1.28577	−	0.742338i	−0.307871	−	0.951428i	$-0.599617\pi$
$439$	−564.452	−	325.886i	−1.28577	−	0.742338i	−0.977896	+	0.209090i	$0.932950\pi$
$440$		0			0
$441$	143.921	−	29.9297i	0.326351	−	0.0678677i
$442$		−	90.2398i		−	0.204162i
$443$	−20.4605	−	11.8129i	−0.0461863	−	0.0266657i	0.476729	−	0.879050i	$-0.341822\pi$
$443$	−20.4605	−	11.8129i	−0.0461863	−	0.0266657i	−0.522915	+	0.852385i	$0.675156\pi$
$444$	−140.308	+	81.0068i	−0.316009	+	0.182448i
$445$		0			0
$446$	447.435	+	258.326i	1.00322	+	0.579207i
$447$	−322.967			−0.722520
$448$	−22.8898	+	51.1083i	−0.0510933	+	0.114081i
$449$	55.1499			0.122828			0.0614141	−	0.998112i	$-0.480439\pi$
$449$	55.1499			0.122828			0.0614141	+	0.998112i	$0.480439\pi$
$450$		0			0
$451$	545.346	−	314.856i	1.20919	−	0.698128i
$452$	5.64407	−	3.25860i	0.0124869	−	0.00720930i
$453$	134.096	−	232.260i	0.296017	−	0.512716i
$454$			364.689i			0.803279i
$455$		0			0
$456$	−120.572			−0.264411
$457$	−303.778	−	175.386i	−0.664723	−	0.383778i	0.129351	−	0.991599i	$-0.458710\pi$
$457$	−303.778	−	175.386i	−0.664723	−	0.383778i	−0.794074	+	0.607821i	$0.792044\pi$
$458$	10.9112	+	18.8987i	0.0238236	+	0.0412636i
$459$	−47.3947	−	82.0901i	−0.103256	−	0.178845i
$460$		0			0
$461$			471.598i			1.02299i	0.859287	+	0.511494i	$0.170908\pi$
$461$			471.598i			1.02299i	−0.859287	+	0.511494i	$0.829092\pi$
$462$	−35.0510	−	340.701i	−0.0758680	−	0.737448i
$463$		−	387.112i		−	0.836094i	−0.908425	−	0.418047i	$-0.862715\pi$
$463$		−	387.112i		−	0.836094i	0.908425	−	0.418047i	$-0.137285\pi$
$464$	−106.245	+	184.021i	−0.228975	+	0.396597i
$465$		0			0
$466$	−88.6336	−	153.518i	−0.190201	−	0.329437i
$467$	146.673	−	254.045i	0.314075	−	0.543994i	−0.665166	−	0.746696i	$-0.731639\pi$
$467$	146.673	−	254.045i	0.314075	−	0.543994i	0.979240	+	0.202702i	$0.0649724\pi$
$468$	20.9873			0.0448446
$469$	−11.6506	−	113.245i	−0.0248413	−	0.241461i
$470$		0			0
$471$	43.4777	−	75.3056i	0.0923094	−	0.159885i
$472$	−141.692	−	245.418i	−0.300195	−	0.519954i
$473$	−1114.25	+	643.310i	−2.35570	+	1.36006i
$474$	−46.6170	−	26.9143i	−0.0983481	−	0.0567813i
$475$		0			0
$476$	149.660	+	206.946i	0.314412	+	0.434760i
$477$			194.625i			0.408018i
$478$	4.44049	+	2.56372i	0.00928973	+	0.00536343i
$479$	660.805	−	381.516i	1.37955	−	0.796484i	0.387445	−	0.921893i	$-0.373358\pi$
$479$	660.805	−	381.516i	1.37955	−	0.796484i	0.992105	+	0.125409i	$0.0400242\pi$
$480$		0			0
$481$	−141.676	−	81.7967i	−0.294545	−	0.170056i
$482$	136.668			0.283543
$483$	278.738	+	124.838i	0.577098	+	0.258464i
$484$	−555.999			−1.14876
$485$		0			0
$486$	19.0919	−	11.0227i	0.0392837	−	0.0226805i
$487$	−193.893	+	111.944i	−0.398138	+	0.229865i	−0.685680	−	0.727903i	$-0.740495\pi$
$487$	−193.893	+	111.944i	−0.398138	+	0.229865i	0.287542	+	0.957768i	$0.407162\pi$
$488$	−11.3476	+	19.6546i	−0.0232533	+	0.0402759i
$489$		−	200.590i		−	0.410205i
$490$		0			0
$491$	−837.694			−1.70610			−0.853049	−	0.521830i	$-0.825249\pi$
$491$	−837.694			−1.70610			−0.853049	+	0.521830i	$0.825249\pi$
$492$	−94.5751	−	54.6029i	−0.192226	−	0.110982i
$493$	484.535	+	839.239i	0.982829	+	1.70231i
$494$	−60.8737	−	105.436i	−0.123226	−	0.213434i
$495$		0			0
$496$			120.525i			0.242993i
$497$	−308.225	+	688.203i	−0.620171	+	1.38471i
$498$		−	1.02261i		−	0.00205344i
$499$	87.3234	−	151.249i	0.174997	−	0.303103i	−0.765163	−	0.643836i	$-0.777342\pi$
$499$	87.3234	−	151.249i	0.174997	−	0.303103i	0.940160	+	0.340733i	$0.110675\pi$
$500$		0			0
$501$	−53.1055	−	91.9814i	−0.105999	−	0.183596i
$502$	−21.0230	+	36.4130i	−0.0418786	+	0.0725358i
$503$	747.962			1.48700			0.743501	−	0.668734i	$-0.233164\pi$
$503$	747.962			1.48700			0.743501	+	0.668734i	$0.233164\pi$
$504$	−48.1299	+	34.8068i	−0.0954958	+	0.0690611i
$505$		0			0
$506$	355.800	−	616.263i	0.703162	−	1.21791i
$507$	−135.762	−	235.147i	−0.267776	−	0.463801i
$508$	153.420	−	88.5772i	0.302008	−	0.174365i
$509$	203.021	+	117.214i	0.398863	+	0.230284i	0.685993	−	0.727608i	$-0.259368\pi$
$509$	203.021	+	117.214i	0.398863	+	0.230284i	−0.287130	+	0.957892i	$0.592701\pi$
$510$		0			0
$511$	−359.726	+	37.0083i	−0.703965	+	0.0724233i
$512$		−	22.6274i		−	0.0441942i
$513$	−110.752	−	63.9428i	−0.215891	−	0.124645i
$514$	−540.875	+	312.275i	−1.05229	+	0.607538i
$515$		0			0
$516$	193.235	+	111.564i	0.374486	+	0.216210i
$517$	−560.549			−1.08423
$518$	460.561	−	47.3821i	0.889114	−	0.0914712i
$519$	54.9088			0.105797
$520$		0			0
$521$	186.068	−	107.427i	0.357137	−	0.206193i	−0.310687	−	0.950512i	$-0.600559\pi$
$521$	186.068	−	107.427i	0.357137	−	0.206193i	0.667824	+	0.744319i	$0.267226\pi$
$522$	−195.184	+	112.689i	−0.373915	+	0.215880i
$523$	462.520	−	801.108i	0.884360	−	1.53176i	0.0379137	−	0.999281i	$-0.487929\pi$
$523$	462.520	−	801.108i	0.884360	−	1.53176i	0.846446	−	0.532475i	$-0.178738\pi$
$524$		−	250.248i		−	0.477573i
$525$		0			0
$526$	−485.141			−0.922321
$527$	476.020	+	274.830i	0.903263	+	0.521499i
$528$	69.1953	+	119.850i	0.131052	+	0.226988i
$529$	52.7773	+	91.4130i	0.0997681	+	0.172803i
$530$		0			0
$531$		−	300.575i		−	0.566054i
$532$	314.464	+	140.839i	0.591098	+	0.264734i
$533$		−	110.271i		−	0.206887i
$534$	−136.204	+	235.913i	−0.255064	+	0.441784i
$535$		0			0
$536$	22.9998	+	39.8368i	0.0429100	+	0.0743224i
$537$	−114.224	+	197.842i	−0.212707	+	0.368420i
$538$	−655.277			−1.21799
$539$	−306.553	+	929.528i	−0.568744	+	1.72454i
$540$		0			0
$541$	57.1560	−	98.9971i	0.105649	−	0.182989i	−0.808354	−	0.588696i	$-0.799641\pi$
$541$	57.1560	−	98.9971i	0.105649	−	0.182989i	0.914003	+	0.405707i	$0.132975\pi$
$542$	172.945	+	299.550i	0.319087	+	0.552675i
$543$	82.7146	−	47.7553i	0.152329	−	0.0879472i
$544$	−89.3683	−	51.5968i	−0.164280	−	0.0948471i
$545$		0			0
$546$	−54.7371	−	24.5151i	−0.100251	−	0.0448994i
$547$		−	57.7698i		−	0.105612i	−0.998605	−	0.0528060i	$-0.983183\pi$
$547$		−	57.7698i		−	0.105612i	0.998605	−	0.0528060i	$-0.0168165\pi$
$548$	−67.4699	−	38.9538i	−0.123120	−	0.0710835i
$549$	−20.8469	+	12.0359i	−0.0379725	+	0.0219234i
$550$		0			0
$551$	1132.26	+	653.712i	2.05492	+	1.18641i
$552$	−123.407			−0.223564
$553$	90.1438	+	124.648i	0.163009	+	0.225404i
$554$	199.430			0.359982
$555$		0			0
$556$	−171.378	+	98.9454i	−0.308235	+	0.177959i
$557$	−351.738	+	203.076i	−0.631487	+	0.364589i	−0.781328	−	0.624121i	$-0.785457\pi$
$557$	−351.738	+	203.076i	−0.631487	+	0.364589i	0.149841	+	0.988710i	$0.452124\pi$
$558$	−63.9179	+	110.709i	−0.114548	+	0.198403i
$559$			225.304i			0.403049i
$560$		0			0
$561$	631.139			1.12502
$562$	104.098	+	60.1008i	0.185227	+	0.106941i
$563$	214.146	+	370.911i	0.380366	+	0.658813i	0.991114	−	0.133012i	$-0.0424648\pi$
$563$	214.146	+	370.911i	0.380366	+	0.658813i	−0.610749	+	0.791824i	$0.709131\pi$
$564$	48.6058	+	84.1878i	0.0861805	+	0.149269i
$565$		0			0
$566$			165.008i			0.291534i
$567$	−62.6692	+	6.44735i	−0.110528	+	0.0113710i
$568$		−	304.691i		−	0.536429i
$569$	−457.897	+	793.100i	−0.804739	+	1.39385i	0.111728	+	0.993739i	$0.464362\pi$
$569$	−457.897	+	793.100i	−0.804739	+	1.39385i	−0.916467	+	0.400110i	$0.868972\pi$
$570$		0			0
$571$	356.947	+	618.250i	0.625125	+	1.08275i	0.988517	+	0.151112i	$0.0482855\pi$
$571$	356.947	+	618.250i	0.625125	+	1.08275i	−0.363391	+	0.931637i	$0.618381\pi$
$572$	−69.8701	+	121.019i	−0.122151	+	0.211571i
$573$	−338.035			−0.589938
$574$	182.881	+	252.883i	0.318608	+	0.440562i
$575$		0			0
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	−43.7973	−	75.8591i	−0.0759052	−	0.131472i	0.825574	−	0.564293i	$-0.190851\pi$
$577$	−43.7973	−	75.8591i	−0.0759052	−	0.131472i	−0.901480	+	0.432822i	$0.857518\pi$
$578$	−53.6183	+	30.9565i	−0.0927652	+	0.0535580i
$579$	−523.140	−	302.035i	−0.903523	−	0.521649i
$580$		0			0
$581$	−1.19450	+	2.66708i	−0.00205594	+	0.00459050i
$582$			181.812i			0.312392i
$583$	−1122.26	−	647.937i	−1.92497	−	1.11138i
$584$	126.542	−	73.0593i	0.216682	−	0.125101i
$585$		0			0
$586$	−161.522	−	93.2548i	−0.275635	−	0.159138i
$587$	−169.908			−0.289452			−0.144726	−	0.989472i	$-0.546230\pi$
$587$	−169.908			−0.289452			−0.144726	+	0.989472i	$0.546230\pi$
$588$	166.186	−	34.5598i	0.282628	−	0.0587752i
$589$	741.576			1.25904
$590$		0			0
$591$	84.5712	−	48.8272i	0.143098	−	0.0826179i
$592$	−162.014	+	93.5385i	−0.273671	+	0.158004i
$593$	100.126	−	173.424i	0.168847	−	0.292452i	−0.769168	−	0.639047i	$-0.779329\pi$
$593$	100.126	−	173.424i	0.168847	−	0.292452i	0.938015	+	0.346595i	$0.112662\pi$
$594$			146.785i			0.247114i
$595$		0			0
$596$	−372.930			−0.625721
$597$	−256.962	−	148.357i	−0.430422	−	0.248504i
$598$	−62.3053	−	107.916i	−0.104189	−	0.180461i
$599$	−350.201	−	606.566i	−0.584643	−	1.01263i	−0.994920	−	0.100671i	$-0.967901\pi$
$599$	−350.201	−	606.566i	−0.584643	−	1.01263i	0.410277	−	0.911961i	$-0.365432\pi$
$600$		0			0
$601$		−	1039.21i		−	1.72914i	−0.502515	−	0.864569i	$-0.667592\pi$
$601$		−	1039.21i		−	1.72914i	0.502515	−	0.864569i	$-0.332408\pi$
$602$	−373.660	−	516.687i	−0.620698	−	0.858285i
$603$			48.7899i			0.0809119i
$604$	154.840	−	268.191i	0.256358	−	0.444025i
$605$		0			0
$606$	107.280	+	185.815i	0.177030	+	0.306626i
$607$	−30.5796	+	52.9655i	−0.0503783	+	0.0872578i	−0.890115	−	0.455736i	$-0.849376\pi$
$607$	−30.5796	+	52.9655i	−0.0503783	+	0.0872578i	0.839737	+	0.542994i	$0.182709\pi$
$608$	−139.224			−0.228987
$609$	640.692	−	65.9138i	1.05204	−	0.108233i
$610$		0			0
$611$	−49.0798	+	85.0087i	−0.0803270	+	0.139130i
$612$	−54.7267	−	94.7894i	−0.0894227	−	0.154885i
$613$	452.688	−	261.359i	0.738479	−	0.426361i	−0.0830371	−	0.996546i	$-0.526462\pi$
$613$	452.688	−	261.359i	0.738479	−	0.426361i	0.821516	+	0.570185i	$0.193129\pi$
$614$	526.482	+	303.965i	0.857462	+	0.495056i
$615$		0			0
$616$	−40.4734	−	393.408i	−0.0657036	−	0.638649i
$617$		−	608.200i		−	0.985738i	−0.870104	−	0.492869i	$-0.835948\pi$
$617$		−	608.200i		−	0.985738i	0.870104	−	0.492869i	$-0.164052\pi$
$618$	294.951	+	170.290i	0.477267	+	0.275550i
$619$	−902.671	+	521.157i	−1.45827	+	0.841934i	−0.998927	−	0.0463229i	$-0.985250\pi$
$619$	−902.671	+	521.157i	−1.45827	+	0.841934i	−0.459346	+	0.888257i	$0.651916\pi$
$620$		0			0
$621$	−113.357	−	65.4465i	−0.182539	−	0.105389i
$622$	−355.643			−0.571774
$623$	630.804	−	456.187i	1.01253	−	0.732243i
$624$	24.2340			0.0388366
$625$		0			0
$626$	16.7831	−	9.68972i	0.0268100	−	0.0154788i
$627$	737.424	−	425.752i	1.17611	−	0.679030i
$628$	50.2037	−	86.9554i	0.0799423	−	0.138464i
$629$			853.176i			1.35640i
$630$		0			0
$631$	−235.274			−0.372859			−0.186430	−	0.982468i	$-0.559692\pi$
$631$	−235.274			−0.372859			−0.186430	+	0.982468i	$0.559692\pi$
$632$	−53.8287	−	31.0780i	−0.0851720	−	0.0491741i
$633$	140.329	+	243.057i	0.221689	+	0.383977i
$634$	23.2851	+	40.3310i	0.0367273	+	0.0636136i
$635$		0			0
$636$			224.733i			0.353354i
$637$	114.125	+	127.876i	0.179159	+	0.200747i
$638$		−	1500.65i		−	2.35211i
$639$	161.587	−	279.877i	0.252875	−	0.437992i
$640$		0			0
$641$	58.4900	+	101.308i	0.0912481	+	0.158046i	0.908037	−	0.418891i	$-0.137581\pi$
$641$	58.4900	+	101.308i	0.0912481	+	0.158046i	−0.816788	+	0.576937i	$0.804248\pi$
$642$	186.394	−	322.843i	0.290333	−	0.502871i
$643$	874.209			1.35958			0.679789	−	0.733408i	$-0.262071\pi$
$643$	874.209			1.35958			0.679789	+	0.733408i	$0.262071\pi$
$644$	321.859	+	144.151i	0.499781	+	0.223837i
$645$		0			0
$646$	−317.470	+	549.874i	−0.491439	+	0.851198i
$647$	−5.84189	−	10.1185i	−0.00902920	−	0.0156390i	0.861476	−	0.507799i	$-0.169541\pi$
$647$	−5.84189	−	10.1185i	−0.00902920	−	0.0156390i	−0.870505	+	0.492160i	$0.836207\pi$
$648$	22.0454	−	12.7279i	0.0340207	−	0.0196419i
$649$	1733.20	+	1000.66i	2.67057	+	1.54185i
$650$		0			0
$651$	296.023	−	214.079i	0.454720	−	0.328847i
$652$		−	231.622i		−	0.355248i
$653$	552.641	+	319.067i	0.846311	+	0.488618i	0.859404	−	0.511296i	$-0.170835\pi$
$653$	552.641	+	319.067i	0.846311	+	0.488618i	−0.0130935	+	0.999914i	$0.504168\pi$
$654$	−137.367	+	79.3088i	−0.210041	+	0.121267i
$655$		0			0
$656$	−109.206	−	63.0500i	−0.166472	−	0.0961129i
$657$	154.982			0.235894
$658$	−28.4303	−	276.347i	−0.0432071	−	0.419980i
$659$	−870.363			−1.32073			−0.660367	−	0.750943i	$-0.729599\pi$
$659$	−870.363			−1.32073			−0.660367	+	0.750943i	$0.729599\pi$
$660$		0			0
$661$	417.571	−	241.085i	0.631727	−	0.364728i	−0.149694	−	0.988732i	$-0.547829\pi$
$661$	417.571	−	241.085i	0.631727	−	0.364728i	0.781420	+	0.624005i	$0.214495\pi$
$662$	511.797	−	295.486i	0.773108	−	0.446354i
$663$	55.2604	−	95.7138i	0.0833490	−	0.144365i
$664$		−	1.18081i		−	0.00177833i
$665$		0			0
$666$	−198.425			−0.297936
$667$	1158.89	+	669.085i	1.73747	+	1.00313i
$668$	−61.3210	−	106.211i	−0.0917978	−	0.158999i
$669$	316.384	+	547.993i	0.472921	+	0.819123i
$670$		0			0
$671$		−	160.279i		−	0.238865i
$672$	−55.5756	+	40.1914i	−0.0827018	+	0.0598087i
$673$			399.323i			0.593347i	0.954979	+	0.296674i	$0.0958773\pi$
$673$			399.323i			0.593347i	−0.954979	+	0.296674i	$0.904123\pi$
$674$	202.719	−	351.119i	0.300770	−	0.520948i
$675$		0			0
$676$	−156.765	−	271.525i	−0.231901	−	0.401664i
$677$	−70.6707	+	122.405i	−0.104388	+	0.180805i	−0.913488	−	0.406866i	$-0.866622\pi$
$677$	−70.6707	+	122.405i	−0.104388	+	0.180805i	0.809100	+	0.587671i	$0.199955\pi$
$678$	7.98191			0.0117727
$679$	212.373	−	474.185i	0.312773	−	0.698358i
$680$		0			0
$681$	−223.325	+	386.811i	−0.327937	+	0.568004i
$682$	−425.586	−	737.137i	−0.624026	−	1.08085i
$683$	−855.785	+	494.088i	−1.25298	+	0.723408i	−0.971700	−	0.236218i	$-0.924092\pi$
$683$	−855.785	+	494.088i	−1.25298	+	0.723408i	−0.281279	+	0.959626i	$0.590759\pi$
$684$	−127.886	−	73.8347i	−0.186967	−	0.107946i
$685$		0			0
$686$	−473.799	−	103.984i	−0.690669	−	0.151580i
$687$			26.7268i			0.0389037i
$688$	223.128	+	128.823i	0.324314	+	0.187243i
$689$	−196.522	+	113.462i	−0.285228	+	0.164677i
$690$		0			0
$691$	303.829	+	175.415i	0.439694	+	0.253857i	0.703468	−	0.710727i	$-0.251634\pi$
$691$	303.829	+	175.415i	0.439694	+	0.253857i	−0.263774	+	0.964585i	$0.584967\pi$
$692$	63.4033			0.0916232
$693$	171.459	−	382.832i	0.247415	−	0.552428i
$694$	433.875			0.625180
$695$		0			0
$696$	−225.379	+	130.123i	−0.323820	+	0.186958i
$697$	−498.040	+	287.543i	−0.714548	+	0.412544i
$698$	240.531	−	416.611i	0.344600	−	0.596864i
$699$		−	217.107i		−	0.310597i
$700$		0			0
$701$	307.500			0.438659			0.219330	−	0.975651i	$-0.429613\pi$
$701$	307.500			0.438659			0.219330	+	0.975651i	$0.429613\pi$
$702$	22.2604	+	12.8520i	0.0317100	+	0.0183077i
$703$	575.533	+	996.852i	0.818681	+	1.41800i
$704$	79.8999	+	138.391i	0.113494	+	0.196578i
$705$		0			0
$706$			530.333i			0.751180i
$707$	−62.7500	−	609.939i	−0.0887552	−	0.862715i
$708$		−	347.074i		−	0.490217i
$709$	−49.0712	+	84.9938i	−0.0692118	+	0.119878i	−0.898555	−	0.438862i	$-0.855382\pi$
$709$	−49.0712	+	84.9938i	−0.0692118	+	0.119878i	0.829343	+	0.558740i	$0.188715\pi$
$710$		0			0
$711$	−32.9632	−	57.0939i	−0.0463617	−	0.0803009i
$712$	−157.275	+	272.409i	−0.220892	+	0.382597i
$713$	759.016			1.06454
$714$	32.0105	+	311.147i	0.0448326	+	0.435780i
$715$		0			0
$716$	−131.894	+	228.448i	−0.184210	+	0.319061i
$717$	3.13990	+	5.43847i	0.00437922	+	0.00758503i
$718$	−403.554	+	232.992i	−0.562053	+	0.324502i
$719$	−612.340	−	353.535i	−0.851655	−	0.491703i	0.00955403	−	0.999954i	$-0.496959\pi$
$719$	−612.340	−	353.535i	−0.851655	−	0.491703i	−0.861209	+	0.508251i	$0.830292\pi$
$720$		0			0
$721$	−570.349	−	788.664i	−0.791053	−	1.09385i
$722$			346.100i			0.479363i
$723$	144.958	+	83.6915i	0.200495	+	0.115756i
$724$	95.5106	−	55.1431i	0.131921	−	0.0761645i
$725$		0			0
$726$	−589.726	−	340.479i	−0.812295	−	0.468979i
$727$	−1353.85			−1.86225			−0.931123	−	0.364705i	$-0.881170\pi$
$727$	−1353.85			−1.86225			−0.931123	+	0.364705i	$0.881170\pi$
$728$	−63.2050	−	28.3076i	−0.0868201	−	0.0388840i
$729$	27.0000			0.0370370
$730$		0			0
$731$	1017.59	−	587.506i	1.39205	−	0.803701i
$732$	−24.0719	+	13.8979i	−0.0328851	+	0.0189862i
$733$	−276.517	+	478.941i	−0.377240	+	0.653398i	−0.990660	−	0.136359i	$-0.956460\pi$
$733$	−276.517	+	478.941i	−0.377240	+	0.653398i	0.613420	+	0.789757i	$0.289793\pi$
$734$			38.4020i			0.0523188i
$735$		0			0
$736$	−142.498			−0.193612
$737$	−281.336	−	162.429i	−0.381732	−	0.220393i
$738$	−66.8747	−	115.830i	−0.0906161	−	0.156952i
$739$	466.739	+	808.416i	0.631582	+	1.09393i	0.987228	+	0.159312i	$0.0509276\pi$
$739$	466.739	+	808.416i	0.631582	+	1.09393i	−0.355646	+	0.934621i	$0.615739\pi$
$740$		0			0
$741$		−	149.110i		−	0.201227i
$742$	262.509	−	586.128i	0.353785	−	0.789930i
$743$		−	554.921i		−	0.746865i	−0.927657	−	0.373432i	$-0.878181\pi$
$743$		−	554.921i		−	0.746865i	0.927657	−	0.373432i	$-0.121819\pi$
$744$	−73.8060	+	127.836i	−0.0992016	+	0.171822i
$745$		0			0
$746$	90.1544	+	156.152i	0.120850	+	0.209319i
$747$	0.626219	−	1.08464i	0.000838312	−	0.00145200i
$748$	728.776			0.974300
$749$	−863.246	+	624.286i	−1.15253	+	0.833492i
$750$		0			0
$751$	−363.974	+	630.421i	−0.484652	+	0.839442i	−0.999845	−	0.0176322i	$-0.994387\pi$
$751$	−363.974	+	630.421i	−0.484652	+	0.839442i	0.515192	+	0.857075i	$0.327721\pi$
$752$	56.1252	+	97.2117i	0.0746345	+	0.129271i
$753$	−44.5966	+	25.7479i	−0.0592252	+	0.0341937i
$754$	−227.577	−	131.391i	−0.301826	−	0.174259i
$755$		0			0
$756$	−72.3642	+	7.44476i	−0.0957198	+	0.00984756i
$757$			667.167i			0.881330i	0.897672	+	0.440665i	$0.145257\pi$
$757$			667.167i			0.881330i	−0.897672	+	0.440665i	$0.854743\pi$
$758$	−391.667	−	226.129i	−0.516711	−	0.298323i
$759$	754.765	−	435.764i	0.994421	−	0.574129i
$760$		0			0
$761$	−630.061	−	363.766i	−0.827938	−	0.478010i	0.0252080	−	0.999682i	$-0.491975\pi$
$761$	−630.061	−	363.766i	−0.827938	−	0.478010i	−0.853146	+	0.521672i	$0.825309\pi$
$762$	216.969			0.284736
$763$	450.908	−	46.3890i	0.590967	−	0.0607981i
$764$	−390.329			−0.510901
$765$		0			0
$766$	500.850	−	289.166i	0.653851	−	0.377501i
$767$	303.506	−	175.229i	0.395705	−	0.228460i
$768$	13.8564	−	24.0000i	0.0180422	−	0.0312500i
$769$			1374.28i			1.78709i	0.448969	+	0.893547i	$0.351791\pi$
$769$			1374.28i			1.78709i	−0.448969	+	0.893547i	$0.648209\pi$
$770$		0			0
$771$	−764.913			−0.992106
$772$	−604.070	−	348.760i	−0.782474	−	0.451761i
$773$	−46.3356	−	80.2556i	−0.0599425	−	0.103824i	0.834497	−	0.551013i	$-0.185758\pi$
$773$	−46.3356	−	80.2556i	−0.0599425	−	0.103824i	−0.894439	+	0.447189i	$0.852425\pi$
$774$	136.638	+	236.663i	0.176534	+	0.305767i
$775$		0			0
$776$			209.938i			0.270539i
$777$	517.514	+	231.779i	0.666042	+	0.298300i
$778$			547.517i			0.703749i
$779$	−387.940	+	671.932i	−0.497998	+	0.862558i
$780$		0			0
$781$	1075.90	+	1863.51i	1.37759	+	2.38606i
$782$	−324.936	+	562.805i	−0.415519	+	0.719700i
$783$	−276.032			−0.352531
$784$	191.894	−	39.9062i	0.244763	−	0.0509008i
$785$		0			0
$786$	153.245	−	265.428i	0.194968	−	0.337695i
$787$	418.113	+	724.193i	0.531275	+	0.920195i	0.999334	+	0.0364974i	$0.0116201\pi$
$787$	418.113	+	724.193i	0.531275	+	0.920195i	−0.468059	+	0.883697i	$0.655047\pi$
$788$	97.6544	−	56.3808i	0.123927	−	0.0715492i
$789$	−514.570	−	297.087i	−0.652180	−	0.376536i
$790$		0			0
$791$	−20.8177	−	9.32360i	−0.0263182	−	0.0117871i
$792$			169.493i			0.214007i
$793$	−24.3066	−	14.0334i	−0.0306515	−	0.0176967i
$794$	−36.8785	+	21.2918i	−0.0464465	+	0.0268159i
$795$		0			0
$796$	−296.714	−	171.308i	−0.372757	−	0.215211i
$797$	−130.279			−0.163462			−0.0817310	−	0.996654i	$-0.526045\pi$
$797$	−130.279			−0.163462			−0.0817310	+	0.996654i	$0.526045\pi$
$798$	247.294	+	341.951i	0.309892	+	0.428510i
$799$	511.924			0.640706
$800$		0			0
$801$	−288.933	+	166.816i	−0.360716	+	0.208259i
$802$	−167.509	+	96.7113i	−0.208864	+	0.120588i
$803$	−515.960	+	893.670i	−0.642541	+	1.11291i
$804$			56.3377i			0.0700718i
$805$		0			0
$806$	−149.052			−0.184927
$807$	−695.027	−	401.274i	−0.861247	−	0.497241i
$808$	123.877	+	214.561i	0.153313	+	0.265546i
$809$	310.782	+	538.290i	0.384156	+	0.665377i	0.991652	−	0.128946i	$-0.0411592\pi$
$809$	310.782	+	538.290i	0.384156	+	0.665377i	−0.607496	+	0.794323i	$0.707826\pi$
$810$		0			0
$811$		−	445.846i		−	0.549748i	−0.961480	−	0.274874i	$-0.911364\pi$
$811$		−	445.846i		−	0.549748i	0.961480	−	0.274874i	$-0.0886361\pi$
$812$	739.808	−	76.1107i	0.911093	−	0.0937324i
$813$			423.627i			0.521067i
$814$	660.590	−	1144.17i	0.811535	−	1.40562i
$815$		0			0
$816$	−63.1930	−	109.453i	−0.0774423	−	0.134134i
$817$	792.636	−	1372.89i	0.970178	−	1.68040i
$818$	697.023			0.852107
$819$	−43.0451	−	59.5217i	−0.0525582	−	0.0726760i
$820$		0			0
$821$	−628.622	+	1088.81i	−0.765678	+	1.32619i	0.174209	+	0.984709i	$0.444263\pi$
$821$	−628.622	+	1088.81i	−0.765678	+	1.32619i	−0.939887	+	0.341485i	$0.889070\pi$
$822$	−47.7084	−	82.6334i	−0.0580394	−	0.100527i
$823$	−104.219	+	60.1709i	−0.126633	+	0.0731117i	−0.561978	−	0.827152i	$-0.689960\pi$
$823$	−104.219	+	60.1709i	−0.126633	+	0.0731117i	0.435345	+	0.900264i	$0.356626\pi$
$824$	340.580	+	196.634i	0.413325	+	0.238633i
$825$		0			0
$826$	−405.414	+	905.206i	−0.490816	+	1.09589i
$827$			151.053i			0.182652i	0.995821	+	0.0913258i	$0.0291105\pi$
$827$			151.053i			0.182652i	−0.995821	+	0.0913258i	$0.970890\pi$
$828$	−130.893	−	75.5711i	−0.158083	−	0.0912695i
$829$	−217.640	+	125.654i	−0.262533	+	0.151573i	−0.625489	−	0.780233i	$-0.715101\pi$
$829$	−217.640	+	125.654i	−0.262533	+	0.151573i	0.362957	+	0.931806i	$0.381767\pi$
$830$		0			0
$831$	211.528	+	122.126i	0.254546	+	0.146962i
$832$	27.9831			0.0336335
$833$	279.961	−	848.896i	0.336088	−	1.01908i
$834$	−242.366			−0.290606
$835$		0			0
$836$	851.503	−	491.616i	1.01854	−	0.588057i
$837$	−135.590	+	78.2831i	−0.161996	+	0.0935282i
$838$	220.363	−	381.679i	0.262963	−	0.455465i
$839$		−	499.592i		−	0.595461i	−0.954650	−	0.297730i	$-0.903770\pi$
$839$		−	499.592i		−	0.595461i	0.954650	−	0.297730i	$-0.0962297\pi$
$840$		0			0
$841$	1980.98			2.35550
$842$	−661.282	−	381.791i	−0.785371	−	0.453434i
$843$	73.6081	+	127.493i	0.0873169	+	0.151237i
$844$	162.038	+	280.658i	0.191988	+	0.332534i
$845$		0			0
$846$			119.059i			0.140732i
$847$	1140.36	+	1576.86i	1.34635	+	1.86170i
$848$			259.499i			0.306013i
$849$	−101.047	+	175.018i	−0.119018	+	0.206146i
$850$		0			0
$851$	589.068	+	1020.30i	0.692206	+	1.19894i
$852$	186.585	−	323.174i	0.218996	−	0.379312i
$853$	−1265.99			−1.48416			−0.742082	−	0.670310i	$-0.766161\pi$
$853$	−1265.99			−1.48416			−0.742082	+	0.670310i	$0.766161\pi$
$854$	79.0162	−	8.12911i	0.0925248	−	0.00951886i
$855$		0			0
$856$	215.229	−	372.788i	0.251436	−	0.435499i
$857$	184.810	+	320.100i	0.215648	+	0.373513i	0.953473	−	0.301479i	$-0.0974804\pi$
$857$	184.810	+	320.100i	0.215648	+	0.373513i	−0.737825	+	0.674992i	$0.764147\pi$
$858$	−148.217	+	85.5731i	−0.172747	+	0.0997355i
$859$	1089.49	+	629.015i	1.26832	+	0.732264i	0.974670	−	0.223649i	$-0.0717971\pi$
$859$	1089.49	+	629.015i	1.26832	+	0.732264i	0.293649	+	0.955913i	$0.405130\pi$
$860$		0			0
$861$	39.1160	+	380.214i	0.0454309	+	0.441596i
$862$			888.184i			1.03038i
$863$	−204.959	−	118.333i	−0.237496	−	0.137118i	0.376530	−	0.926405i	$-0.377117\pi$
$863$	−204.959	−	118.333i	−0.237496	−	0.137118i	−0.614025	+	0.789286i	$0.710451\pi$
$864$	25.4558	−	14.6969i	0.0294628	−	0.0170103i
$865$		0			0
$866$	−865.636	−	499.775i	−0.999579	−	0.577107i
$867$	−75.8277			−0.0874598
$868$	341.818	−	247.197i	0.393799	−	0.284790i
$869$	438.959			0.505132
$870$		0			0
$871$	−49.2657	+	28.4436i	−0.0565622	+	0.0326562i
$872$	−158.618	+	91.5779i	−0.181901	+	0.105021i
$873$	−111.337	+	192.841i	−0.127533	+	0.220894i
$874$			876.777i			1.00318i
$875$		0			0
$876$	178.958			0.204290
$877$	−697.611	−	402.766i	−0.795451	−	0.459254i	0.0464269	−	0.998922i	$-0.485217\pi$
$877$	−697.611	−	402.766i	−0.795451	−	0.459254i	−0.841878	+	0.539668i	$0.818550\pi$
$878$	−460.873	−	798.256i	−0.524912	−	0.909175i
$879$	−114.213	−	197.823i	−0.129936	−	0.225055i
$880$		0			0
$881$		−	763.260i		−	0.866356i	−0.901308	−	0.433178i	$-0.857392\pi$
$881$		−	763.260i		−	0.866356i	0.901308	−	0.433178i	$-0.142608\pi$
$882$	197.430	+	65.1112i	0.223843	+	0.0738222i
$883$		−	574.986i		−	0.651173i	−0.945512	−	0.325587i	$-0.894438\pi$
$883$		−	574.986i		−	0.651173i	0.945512	−	0.325587i	$-0.105562\pi$
$884$	63.8092	−	110.521i	0.0721823	−	0.125023i
$885$		0			0
$886$	−16.7060	−	28.9356i	−0.0188555	−	0.0326587i
$887$	191.751	−	332.122i	0.216179	−	0.374433i	−0.737458	−	0.675393i	$-0.763974\pi$
$887$	191.751	−	332.122i	0.216179	−	0.374433i	0.953637	+	0.300960i	$0.0973072\pi$
$888$	−229.122			−0.258020
$889$	−565.879	−	253.440i	−0.636534	−	0.285084i
$890$		0			0
$891$	−89.8874	+	155.690i	−0.100884	+	0.174736i
$892$	365.329	+	632.768i	0.409561	+	0.709381i
$893$	598.133	−	345.332i	0.669802	−	0.386710i
$894$	−395.552	−	228.372i	−0.442451	−	0.255449i
$895$		0			0
$896$	−64.1732	+	46.4091i	−0.0716219	+	0.0517958i
$897$		−	152.616i		−	0.170141i
$898$	67.5445	+	38.9968i	0.0752166	+	0.0434263i
$899$	1386.19	−	800.319i	1.54193	−	0.890232i
$900$		0			0
$901$	1024.91	+	591.731i	1.13752	+	0.656749i
$902$	890.547			0.987302
$903$	−79.9215	−	776.849i	−0.0885066	−	0.860298i
$904$	9.21672			0.0101955
$905$		0			0
$906$	328.466	−	189.640i	0.362545	−	0.209316i
$907$	−1006.70	+	581.220i	−1.10993	+	0.640816i	−0.938810	−	0.344435i	$-0.888070\pi$
$907$	−1006.70	+	581.220i	−1.10993	+	0.640816i	−0.171115	+	0.985251i	$0.554737\pi$
$908$	−257.874	+	446.650i	−0.284002	+	0.491906i
$909$			262.782i			0.289089i
$910$		0			0
$911$	1070.03			1.17457			0.587284	−	0.809381i	$-0.300197\pi$
$911$	1070.03			1.17457			0.587284	+	0.809381i	$0.300197\pi$
$912$	−147.669	−	85.2570i	−0.161918	−	0.0934836i
$913$	4.16957	+	7.22190i	0.00456689	+	0.00791008i
$914$	−248.034	−	429.607i	−0.271372	−	0.470030i
$915$		0			0
$916$			30.8615i			0.0336916i
$917$	−709.725	+	513.262i	−0.773964	+	0.559719i
$918$		−	134.053i		−	0.146027i
$919$	583.360	−	1010.41i	0.634777	−	1.09947i	−0.351785	−	0.936081i	$-0.614425\pi$
$919$	583.360	−	1010.41i	0.634777	−	1.09947i	0.986562	−	0.163386i	$-0.0522415\pi$
$920$		0			0
$921$	372.279	+	644.806i	0.404212	+	0.700115i
$922$	−333.470	+	577.587i	−0.361681	+	0.626450i
$923$	376.808			0.408243
$924$	197.984	−	442.057i	0.214268	−	0.478416i
$925$		0			0
$926$	273.729	−	474.113i	0.295604	−	0.512001i
$927$	208.562	+	361.239i	0.224986	+	0.389686i
$928$	−260.245	+	150.253i	−0.280437	+	0.161910i
$929$	−194.325	−	112.194i	−0.209177	−	0.120768i	0.391752	−	0.920071i	$-0.371869\pi$
$929$	−194.325	−	112.194i	−0.209177	−	0.120768i	−0.600929	+	0.799303i	$0.705202\pi$
$930$		0			0
$931$	−245.539	−	1180.71i	−0.263737	−	1.26821i
$932$		−	250.694i		−	0.268984i
$933$	−377.217	−	217.786i	−0.404305	−	0.233426i
$934$	359.274	−	207.427i	0.384662	−	0.222084i
$935$		0			0
$936$	25.7041	+	14.8403i	0.0274616	+	0.0158550i
$937$	−644.185			−0.687497			−0.343749	−	0.939062i	$-0.611697\pi$
$937$	−644.185			−0.687497			−0.343749	+	0.939062i	$0.611697\pi$
$938$	65.8076	−	146.935i	0.0701573	−	0.156647i
$939$	23.7349			0.0252767
$940$		0			0
$941$	−266.097	+	153.631i	−0.282781	+	0.163264i	−0.634682	−	0.772774i	$-0.718869\pi$
$941$	−266.097	+	153.631i	−0.282781	+	0.163264i	0.351901	+	0.936037i	$0.385535\pi$
$942$	106.498	−	61.4868i	0.113055	−	0.0652726i
$943$	−397.063	+	687.734i	−0.421064	+	0.729305i
$944$		−	400.766i		−	0.424540i
$945$		0			0
$946$	−1819.56			−1.92342
$947$	850.013	+	490.755i	0.897585	+	0.518221i	0.876416	−	0.481555i	$-0.159928\pi$
$947$	850.013	+	490.755i	0.897585	+	0.518221i	0.0211694	+	0.999776i	$0.493261\pi$
$948$	−38.0626	−	65.9264i	−0.0401504	−	0.0695426i
$949$	90.3515	+	156.493i	0.0952071	+	0.164903i
$950$		0			0
$951$			57.0367i			0.0599755i
$952$	36.9625	+	359.281i	0.0388262	+	0.377397i
$953$		−	1258.67i		−	1.32075i	−0.750936	−	0.660375i	$-0.770397\pi$
$953$		−	1258.67i		−	1.32075i	0.750936	−	0.660375i	$-0.229603\pi$
$954$	−137.620	+	238.365i	−0.144256	+	0.249859i
$955$		0			0
$956$	3.62565	+	6.27980i	0.00379252	+	0.00656883i
$957$	918.954	−	1591.68i	0.960245	−	1.66319i
$958$	1079.09			1.12640
$959$	27.9054	+	271.245i	0.0290984	+	0.282841i
$960$		0			0
$961$	−26.5559	+	45.9962i	−0.0276336	+	0.0478628i
$962$	−115.678	−	200.360i	−0.120247	−	0.208275i
$963$	395.401	−	228.285i	0.410593	−	0.237056i
$964$	167.383	+	96.6387i	0.173634	+	0.100248i
$965$		0			0
$966$	253.109	+	349.993i	0.262018	+	0.362311i
$967$		−	992.744i		−	1.02662i	−0.858202	−	0.513311i	$-0.828419\pi$
$967$		−	992.744i		−	1.02662i	0.858202	−	0.513311i	$-0.171581\pi$
$968$	−680.957	−	393.151i	−0.703468	−	0.406147i
$969$	−673.455	+	388.820i	−0.695000	+	0.401259i
$970$		0			0
$971$	−309.667	−	178.787i	−0.318916	−	0.184126i	0.331993	−	0.943282i	$-0.392279\pi$
$971$	−309.667	−	178.787i	−0.318916	−	0.184126i	−0.650909	+	0.759155i	$0.725612\pi$
$972$	31.1769			0.0320750
$973$	632.116	+	283.105i	0.649657	+	0.290961i
$974$	−316.626			−0.325078
$975$		0			0
$976$	−27.7958	+	16.0479i	−0.0284793	+	0.0164426i
$977$	−759.804	+	438.673i	−0.777691	+	0.449000i	−0.835611	−	0.549321i	$-0.814886\pi$
$977$	−759.804	+	438.673i	−0.777691	+	0.449000i	0.0579204	+	0.998321i	$0.481553\pi$
$978$	141.839	−	245.672i	0.145029	−	0.251198i
$979$		−	2221.43i		−	2.26908i
$980$		0			0
$981$	−194.266			−0.198029
$982$	−1025.96	−	592.339i	−1.04477	−	0.603197i
$983$	720.104	+	1247.26i	0.732557	+	1.26883i	0.955787	+	0.294061i	$0.0950068\pi$
$983$	720.104	+	1247.26i	0.732557	+	1.26883i	−0.223229	+	0.974766i	$0.571660\pi$
$984$	−77.2202	−	133.749i	−0.0784758	−	0.135924i
$985$		0			0
$986$			1370.47i			1.38993i
$987$	139.072	−	310.520i	0.140904	−	0.314610i
$988$		−	172.177i		−	0.174268i
$989$	811.276	−	1405.17i	0.820299	−	1.42080i
$990$		0			0
$991$	−577.181	−	999.706i	−0.582423	−	1.00879i	−0.995191	−	0.0979496i	$-0.968772\pi$
$991$	−577.181	−	999.706i	−0.582423	−	1.00879i	0.412769	−	0.910836i	$-0.364562\pi$
$992$	−85.2239	+	147.612i	−0.0859111	+	0.148802i
$993$	723.791			0.728893
$994$	−864.130	+	624.925i	−0.869346	+	0.628697i
$995$		0			0
$996$	0.723095	−	1.25244i	0.000725999	−	0.00125747i
$997$	812.451	+	1407.21i	0.814896	+	1.41144i	0.909403	+	0.415916i	$0.136539\pi$
$997$	812.451	+	1407.21i	0.814896	+	1.41144i	−0.0945072	+	0.995524i	$0.530128\pi$
$998$	213.898	−	123.494i	0.214326	−	0.123741i
$999$	−210.462	−	121.510i	−0.210672	−	0.121632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.q.e.649.10		32
5.2	odd	4		1050.3.p.i.901.4		16
5.3	odd	4		210.3.o.b.61.7	yes	16
5.4	even	2	inner	1050.3.q.e.649.1		32
7.3	odd	6	inner	1050.3.q.e.199.1		32
15.8	even	4		630.3.v.c.271.1		16
35.3	even	12		210.3.o.b.31.7	✓	16
35.17	even	12		1050.3.p.i.451.4		16
35.23	odd	12		1470.3.f.d.391.2		16
35.24	odd	6	inner	1050.3.q.e.199.10		32
35.33	even	12		1470.3.f.d.391.8		16
105.38	odd	12		630.3.v.c.451.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.7	✓	16	35.3	even	12
210.3.o.b.61.7	yes	16	5.3	odd	4
630.3.v.c.271.1		16	15.8	even	4
630.3.v.c.451.1		16	105.38	odd	12
1050.3.p.i.451.4		16	35.17	even	12
1050.3.p.i.901.4		16	5.2	odd	4
1050.3.q.e.199.1		32	7.3	odd	6	inner
1050.3.q.e.199.10		32	35.24	odd	6	inner
1050.3.q.e.649.1		32	5.4	even	2	inner
1050.3.q.e.649.10		32	1.1	even	1	trivial
1470.3.f.d.391.2		16	35.23	odd	12
1470.3.f.d.391.8		16	35.33	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(2.86123 - 6.38854i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.22474 + 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(2.86123 - 6.38854i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-9.98749 - 17.2988i) q^{11} +(-1.73205 + 3.00000i) q^{12} -3.49788 q^{13} +(8.02165 - 5.80113i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(9.12112 + 15.7982i) q^{17} +(-3.67423 + 2.12132i) q^{18} +(21.3143 + 12.3058i) q^{19} +(12.0607 - 1.24079i) q^{21} -28.2489i q^{22} +(21.8155 + 12.5952i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(-4.28401 - 2.47338i) q^{26} -5.19615 q^{27} +(13.9265 - 1.43274i) q^{28} +53.1223 q^{29} +(26.0944 - 15.0656i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(17.2988 - 29.9625i) q^{33} +25.7984i q^{34} -6.00000 q^{36} +(40.5034 + 23.3846i) q^{37} +(17.4030 + 30.1429i) q^{38} +(-3.02925 - 5.24682i) q^{39} +31.5250i q^{41} +(15.6487 + 7.00855i) q^{42} -64.4116i q^{43} +(19.9750 - 34.5977i) q^{44} +(17.8123 + 30.8518i) q^{46} +(14.0313 - 24.3029i) q^{47} -6.92820 q^{48} +(-32.6268 - 36.5581i) q^{49} +(-15.7982 + 27.3634i) q^{51} +(-3.49788 - 6.05851i) q^{52} +(56.1833 - 32.4374i) q^{53} +(-6.36396 - 3.67423i) q^{54} +(18.0695 + 8.09277i) q^{56} +42.6285i q^{57} +(65.0613 + 37.5631i) q^{58} +(-86.7684 + 50.0958i) q^{59} +(6.94896 + 4.01198i) q^{61} +42.6119 q^{62} +(12.3061 + 17.0165i) q^{63} -8.00000 q^{64} +(42.3733 - 24.4642i) q^{66} +(14.0844 - 8.13165i) q^{67} +(-18.2422 + 31.5965i) q^{68} +43.6310i q^{69} -107.725 q^{71} +(-7.34847 - 4.24264i) q^{72} +(-25.8303 - 44.7395i) q^{73} +(33.0709 + 57.2804i) q^{74} +49.2232i q^{76} +(-139.091 + 14.3095i) q^{77} -8.56803i q^{78} +(-10.9877 + 19.0313i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-22.2916 + 38.6101i) q^{82} -0.417479 q^{83} +(14.2098 + 19.6489i) q^{84} +(45.5459 - 78.8878i) q^{86} +(46.0053 + 79.6835i) q^{87} +(48.9285 - 28.2489i) q^{88} +(96.3110 + 55.6052i) q^{89} +(-10.0082 + 22.3463i) q^{91} +50.3807i q^{92} +(45.1968 + 26.0944i) q^{93} +(34.3695 - 19.8432i) q^{94} +(-8.48528 - 4.89898i) q^{96} +74.2244 q^{97} +(-14.1090 - 67.8449i) q^{98} +59.9249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} - 48 q^{9}+O(q^{10}) \) 32 * q + 32 * q^4 - 48 * q^9	\( 32 q + 32 q^{4} - 48 q^{9} - 8 q^{11} - 16 q^{14} - 64 q^{16} + 144 q^{19} - 48 q^{21} - 144 q^{29} + 240 q^{31} - 192 q^{36} - 72 q^{39} + 16 q^{44} + 16 q^{46} + 80 q^{49} - 24 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 256 q^{64} + 144 q^{66} - 272 q^{71} + 224 q^{74} - 560 q^{79} - 144 q^{81} + 48 q^{84} - 176 q^{86} + 600 q^{89} - 544 q^{91} + 48 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 - 48 * q^9 - 8 * q^11 - 16 * q^14 - 64 * q^16 + 144 * q^19 - 48 * q^21 - 144 * q^29 + 240 * q^31 - 192 * q^36 - 72 * q^39 + 16 * q^44 + 16 * q^46 + 80 * q^49 - 24 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 256 * q^64 + 144 * q^66 - 272 * q^71 + 224 * q^74 - 560 * q^79 - 144 * q^81 + 48 * q^84 - 176 * q^86 + 600 * q^89 - 544 * q^91 + 48 * q^99

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