LMFDB - Embedded newform 38.4.e.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,4,Mod(5,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, degree $6$, 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:	$2.24207258022$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 135 x^{10} + 730 x^{9} + 7953 x^{8} - 36258 x^{7} - 262940 x^{6} + 918855 x^{5} + \cdots + 272110107 $ x^12 - 6x^11 - 135x^10 + 730x^9 + 7953x^8 - 36258x^7 - 262940x^6 + 918855x^5 + 5157591x^4 - 11890401x^3 - 56759508x^2 + 62864118*x + 272110107
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			17.2
Root			$-4.30460 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	38.17
Dual form			38.4.e.a.9.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.347296 - 1.96962i) q^{2} +(2.93054 + 2.45902i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(14.2818 - 5.19813i) q^{5} +(5.86108 - 4.91803i) q^{6} +(-0.806634 - 1.39713i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-2.14719 - 12.1773i) q^{9} +O(q^{10})$	\(q+(0.347296 - 1.96962i) q^{2} +(2.93054 + 2.45902i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(14.2818 - 5.19813i) q^{5} +(5.86108 - 4.91803i) q^{6} +(-0.806634 - 1.39713i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-2.14719 - 12.1773i) q^{9} +(-5.27832 - 29.9349i) q^{10} +(-19.2603 + 33.3598i) q^{11} +(-7.65110 - 13.2521i) q^{12} +(-3.06062 + 2.56816i) q^{13} +(-3.03195 + 1.10354i) q^{14} +(54.6355 + 19.8857i) q^{15} +(12.2567 + 10.2846i) q^{16} +(-15.5204 + 88.0204i) q^{17} -24.7304 q^{18} +(-77.1453 + 30.1265i) q^{19} -60.7933 q^{20} +(1.07169 - 6.07787i) q^{21} +(59.0169 + 49.5211i) q^{22} +(-63.4335 - 23.0879i) q^{23} +(-28.7587 + 10.4673i) q^{24} +(81.1923 - 68.1284i) q^{25} +(3.99535 + 6.92015i) q^{26} +(75.2967 - 130.418i) q^{27} +(1.12056 + 6.35503i) q^{28} +(-46.2659 - 262.387i) q^{29} +(58.1419 - 100.705i) q^{30} +(95.4652 + 165.351i) q^{31} +(24.5134 - 20.5692i) q^{32} +(-138.475 + 50.4009i) q^{33} +(167.976 + 61.1383i) q^{34} +(-18.7826 - 15.7605i) q^{35} +(-8.58876 + 48.7093i) q^{36} +137.719 q^{37} +(32.5453 + 162.409i) q^{38} -15.2844 q^{39} +(-21.1133 + 119.739i) q^{40} +(-189.962 - 159.397i) q^{41} +(-11.5989 - 4.22164i) q^{42} +(260.732 - 94.8987i) q^{43} +(118.034 - 99.0422i) q^{44} +(-93.9650 - 162.752i) q^{45} +(-67.5045 + 116.921i) q^{46} +(64.1805 + 363.985i) q^{47} +(10.6288 + 60.2789i) q^{48} +(170.199 - 294.793i) q^{49} +(-105.989 - 183.578i) q^{50} +(-261.927 + 219.782i) q^{51} +(15.0176 - 5.46596i) q^{52} +(-383.283 - 139.504i) q^{53} +(-230.722 - 193.599i) q^{54} +(-101.662 + 576.554i) q^{55} +12.9061 q^{56} +(-300.159 - 101.414i) q^{57} -532.869 q^{58} +(-102.217 + 579.700i) q^{59} +(-178.157 - 149.492i) q^{60} +(757.876 + 275.844i) q^{61} +(358.832 - 130.604i) q^{62} +(-15.2813 + 12.8225i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(-30.3613 + 52.5873i) q^{65} +(51.1784 + 290.247i) q^{66} +(-35.5080 - 201.376i) q^{67} +(178.756 - 309.615i) q^{68} +(-129.121 - 223.644i) q^{69} +(-37.5652 + 31.5210i) q^{70} +(671.014 - 244.229i) q^{71} +(92.9558 + 33.8331i) q^{72} +(81.6202 + 68.4875i) q^{73} +(47.8293 - 271.253i) q^{74} +405.466 q^{75} +(331.187 - 7.69764i) q^{76} +62.1440 q^{77} +(-5.30822 + 30.1044i) q^{78} +(-393.010 - 329.775i) q^{79} +(228.508 + 83.1701i) q^{80} +(227.633 - 82.8518i) q^{81} +(-379.924 + 318.794i) q^{82} +(-439.020 - 760.404i) q^{83} +(-12.3433 + 21.3792i) q^{84} +(235.884 + 1337.76i) q^{85} +(-96.3626 - 546.500i) q^{86} +(509.629 - 882.704i) q^{87} +(-154.082 - 266.878i) q^{88} +(362.075 - 303.817i) q^{89} +(-353.193 + 128.552i) q^{90} +(6.05685 + 2.20451i) q^{91} +(206.846 + 173.564i) q^{92} +(-126.835 + 719.317i) q^{93} +739.201 q^{94} +(-945.168 + 831.271i) q^{95} +122.418 q^{96} +(285.092 - 1616.84i) q^{97} +(-521.519 - 437.606i) q^{98} +(447.589 + 162.909i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 9 q^{3} - 18 q^{6} + 21 q^{7} - 48 q^{8} - 27 q^{9}+O(q^{10}) $ 12 * q - 9 * q^3 - 18 * q^6 + 21 * q^7 - 48 * q^8 - 27 * q^9	\( 12 q - 9 q^{3} - 18 q^{6} + 21 q^{7} - 48 q^{8} - 27 q^{9} - 9 q^{11} + 36 q^{12} + 39 q^{13} - 138 q^{14} + 423 q^{15} + 69 q^{17} + 132 q^{18} - 462 q^{19} - 216 q^{20} - 279 q^{21} + 204 q^{22} - 66 q^{23} - 72 q^{24} + 342 q^{25} + 48 q^{26} + 189 q^{27} + 192 q^{28} + 159 q^{29} + 72 q^{31} - 1560 q^{33} + 408 q^{34} - 135 q^{35} - 108 q^{36} + 1116 q^{37} - 294 q^{38} - 1248 q^{39} + 147 q^{41} + 414 q^{42} - 117 q^{43} + 408 q^{44} + 1296 q^{45} + 528 q^{46} + 783 q^{47} + 288 q^{48} + 1413 q^{49} - 354 q^{50} - 2301 q^{51} - 348 q^{52} - 249 q^{53} - 540 q^{54} + 2187 q^{55} - 336 q^{56} - 2670 q^{57} - 1932 q^{58} - 4248 q^{59} + 324 q^{60} + 3114 q^{61} - 438 q^{62} + 363 q^{63} - 384 q^{64} + 495 q^{65} + 822 q^{66} + 3060 q^{67} + 408 q^{68} - 237 q^{69} - 270 q^{70} + 1686 q^{71} + 432 q^{72} + 1626 q^{73} + 90 q^{74} - 1854 q^{75} - 1416 q^{77} - 108 q^{78} - 327 q^{79} + 3483 q^{81} + 294 q^{82} + 927 q^{83} + 204 q^{84} - 3294 q^{85} + 1188 q^{86} + 2892 q^{87} - 72 q^{88} - 6366 q^{89} - 5076 q^{90} + 840 q^{91} - 156 q^{92} + 870 q^{93} + 3432 q^{94} + 513 q^{95} - 576 q^{96} - 8052 q^{97} + 378 q^{98} + 4494 q^{99}+O(q^{100}) \) 12 * q - 9 * q^3 - 18 * q^6 + 21 * q^7 - 48 * q^8 - 27 * q^9 - 9 * q^11 + 36 * q^12 + 39 * q^13 - 138 * q^14 + 423 * q^15 + 69 * q^17 + 132 * q^18 - 462 * q^19 - 216 * q^20 - 279 * q^21 + 204 * q^22 - 66 * q^23 - 72 * q^24 + 342 * q^25 + 48 * q^26 + 189 * q^27 + 192 * q^28 + 159 * q^29 + 72 * q^31 - 1560 * q^33 + 408 * q^34 - 135 * q^35 - 108 * q^36 + 1116 * q^37 - 294 * q^38 - 1248 * q^39 + 147 * q^41 + 414 * q^42 - 117 * q^43 + 408 * q^44 + 1296 * q^45 + 528 * q^46 + 783 * q^47 + 288 * q^48 + 1413 * q^49 - 354 * q^50 - 2301 * q^51 - 348 * q^52 - 249 * q^53 - 540 * q^54 + 2187 * q^55 - 336 * q^56 - 2670 * q^57 - 1932 * q^58 - 4248 * q^59 + 324 * q^60 + 3114 * q^61 - 438 * q^62 + 363 * q^63 - 384 * q^64 + 495 * q^65 + 822 * q^66 + 3060 * q^67 + 408 * q^68 - 237 * q^69 - 270 * q^70 + 1686 * q^71 + 432 * q^72 + 1626 * q^73 + 90 * q^74 - 1854 * q^75 - 1416 * q^77 - 108 * q^78 - 327 * q^79 + 3483 * q^81 + 294 * q^82 + 927 * q^83 + 204 * q^84 - 3294 * q^85 + 1188 * q^86 + 2892 * q^87 - 72 * q^88 - 6366 * q^89 - 5076 * q^90 + 840 * q^91 - 156 * q^92 + 870 * q^93 + 3432 * q^94 + 513 * q^95 - 576 * q^96 - 8052 * q^97 + 378 * q^98 + 4494 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	0.347296	−	1.96962i	0.122788	−	0.696364i
$2$	0.347296	−	1.96962i	0.122788	−	0.696364i
$3$	2.93054	+	2.45902i	0.563983	+	0.473238i	0.879643	−	0.475635i	$-0.157782\pi$
$3$	2.93054	+	2.45902i	0.563983	+	0.473238i	−0.315660	+	0.948872i	$0.602226\pi$
$4$	−3.75877	−	1.36808i	−0.469846	−	0.171010i
$5$	14.2818	−	5.19813i	1.27740	−	0.464935i	0.387828	−	0.921732i	$-0.373226\pi$
$5$	14.2818	−	5.19813i	1.27740	−	0.464935i	0.889571	+	0.456797i	$0.151003\pi$
$6$	5.86108	−	4.91803i	0.398796	−	0.334630i
$7$	−0.806634	−	1.39713i	−0.0435541	−	0.0754379i	0.843427	−	0.537245i	$-0.180535\pi$
$7$	−0.806634	−	1.39713i	−0.0435541	−	0.0754379i	−0.886981	+	0.461807i	$0.847201\pi$
$8$	−4.00000	+	6.92820i	−0.176777	+	0.306186i
$9$	−2.14719	−	12.1773i	−0.0795256	−	0.451012i
$10$	−5.27832	−	29.9349i	−0.166915	−	0.946623i
$11$	−19.2603	+	33.3598i	−0.527927	+	0.914396i	0.471543	+	0.881843i	$0.343697\pi$
$11$	−19.2603	+	33.3598i	−0.527927	+	0.914396i	−0.999470	+	0.0325530i	$0.989636\pi$
$12$	−7.65110	−	13.2521i	−0.184057	−	0.318796i
$13$	−3.06062	+	2.56816i	−0.0652971	+	0.0547908i	−0.674852	−	0.737953i	$-0.735793\pi$
$13$	−3.06062	+	2.56816i	−0.0652971	+	0.0547908i	0.609555	+	0.792744i	$0.291348\pi$
$14$	−3.03195	+	1.10354i	−0.0578802	+	0.0210667i
$15$	54.6355	+	19.8857i	0.940456	+	0.342298i
$16$	12.2567	+	10.2846i	0.191511	+	0.160697i
$17$	−15.5204	+	88.0204i	−0.221426	+	1.25577i	0.647975	+	0.761662i	$0.275616\pi$
$17$	−15.5204	+	88.0204i	−0.221426	+	1.25577i	−0.869401	+	0.494108i	$0.835495\pi$
$18$	−24.7304			−0.323833
$19$	−77.1453	+	30.1265i	−0.931492	+	0.363763i
$19$	−77.1453	+	30.1265i	−0.931492	+	0.363763i
$20$	−60.7933			−0.679690
$21$	1.07169	−	6.07787i	0.0111363	−	0.0631571i
$22$	59.0169	+	49.5211i	0.571930	+	0.479906i
$23$	−63.4335	−	23.0879i	−0.575078	−	0.209311i	0.0380759	−	0.999275i	$-0.487877\pi$
$23$	−63.4335	−	23.0879i	−0.575078	−	0.209311i	−0.613154	+	0.789964i	$0.710099\pi$
$24$	−28.7587	+	10.4673i	−0.244598	+	0.0890263i
$25$	81.1923	−	68.1284i	0.649538	−	0.545027i
$26$	3.99535	+	6.92015i	0.0301366	+	0.0521982i
$27$	75.2967	−	130.418i	0.536698	−	0.929589i
$28$	1.12056	+	6.35503i	0.00756309	+	0.0428924i
$29$	−46.2659	−	262.387i	−0.296254	−	1.68014i	−0.662062	−	0.749449i	$-0.730319\pi$
$29$	−46.2659	−	262.387i	−0.296254	−	1.68014i	0.365808	−	0.930690i	$-0.380793\pi$
$30$	58.1419	−	100.705i	0.353840	−	0.612870i
$31$	95.4652	+	165.351i	0.553098	+	0.957994i	0.998049	+	0.0624392i	$0.0198880\pi$
$31$	95.4652	+	165.351i	0.553098	+	0.957994i	−0.444950	+	0.895555i	$0.646779\pi$
$32$	24.5134	−	20.5692i	0.135419	−	0.113630i
$33$	−138.475	+	50.4009i	−0.730468	+	0.265869i
$34$	167.976	+	61.1383i	0.847284	+	0.308386i
$35$	−18.7826	−	15.7605i	−0.0907097	−	0.0761145i
$36$	−8.58876	+	48.7093i	−0.0397628	+	0.225506i
$37$	137.719			0.611915			0.305957	−	0.952045i	$-0.401023\pi$
$37$	137.719			0.611915			0.305957	+	0.952045i	$0.401023\pi$
$38$	32.5453	+	162.409i	0.138936	+	0.693323i
$39$	−15.2844			−0.0627555
$40$	−21.1133	+	119.739i	−0.0834576	+	0.473312i
$41$	−189.962	−	159.397i	−0.723587	−	0.607161i	0.204788	−	0.978806i	$-0.434349\pi$
$41$	−189.962	−	159.397i	−0.723587	−	0.607161i	−0.928375	+	0.371645i	$0.878794\pi$
$42$	−11.5989	−	4.22164i	−0.0426130	−	0.0155099i
$43$	260.732	−	94.8987i	0.924680	−	0.336556i	0.164581	−	0.986364i	$-0.447373\pi$
$43$	260.732	−	94.8987i	0.924680	−	0.336556i	0.760099	+	0.649807i	$0.225150\pi$
$44$	118.034	−	99.0422i	0.404415	−	0.339345i
$45$	−93.9650	−	162.752i	−0.311277	−	0.539148i
$46$	−67.5045	+	116.921i	−0.216369	+	0.374763i
$47$	64.1805	+	363.985i	0.199185	+	1.12963i	0.906332	+	0.422566i	$0.138871\pi$
$47$	64.1805	+	363.985i	0.199185	+	1.12963i	−0.707147	+	0.707066i	$0.750018\pi$
$48$	10.6288	+	60.2789i	0.0319611	+	0.181261i
$49$	170.199	−	294.793i	0.496206	−	0.859454i
$50$	−105.989	−	183.578i	−0.299782	−	0.519238i
$51$	−261.927	+	219.782i	−0.719158	+	0.603445i
$52$	15.0176	−	5.46596i	0.0400494	−	0.0145768i
$53$	−383.283	−	139.504i	−0.993358	−	0.361553i	−0.206338	−	0.978481i	$-0.566155\pi$
$53$	−383.283	−	139.504i	−0.993358	−	0.361553i	−0.787019	+	0.616928i	$0.788377\pi$
$54$	−230.722	−	193.599i	−0.581432	−	0.487880i
$55$	−101.662	+	576.554i	−0.249238	+	1.41350i
$56$	12.9061			0.0307974
$57$	−300.159	−	101.414i	−0.697491	−	0.235661i
$58$	−532.869			−1.20637
$59$	−102.217	+	579.700i	−0.225551	+	1.27916i	0.636079	+	0.771624i	$0.280555\pi$
$59$	−102.217	+	579.700i	−0.225551	+	1.27916i	−0.861630	+	0.507538i	$0.830556\pi$
$60$	−178.157	−	149.492i	−0.383333	−	0.321655i
$61$	757.876	+	275.844i	1.59076	+	0.578988i	0.977507	−	0.210902i	$-0.0676401\pi$
$61$	757.876	+	275.844i	1.59076	+	0.578988i	0.613249	+	0.789890i	$0.289862\pi$
$62$	358.832	−	130.604i	0.735027	−	0.267528i
$63$	−15.2813	+	12.8225i	−0.0305598	+	0.0256427i
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	−30.3613	+	52.5873i	−0.0579363	+	0.100349i
$66$	51.1784	+	290.247i	0.0954488	+	0.541317i
$67$	−35.5080	−	201.376i	−0.0647461	−	0.367194i	−0.999916	−	0.0129929i	$-0.995864\pi$
$67$	−35.5080	−	201.376i	−0.0647461	−	0.367194i	0.935169	−	0.354201i	$-0.115247\pi$
$68$	178.756	−	309.615i	0.318785	−	0.552153i
$69$	−129.121	−	223.644i	−0.225280	−	0.390196i
$70$	−37.5652	+	31.5210i	−0.0641415	+	0.0538211i
$71$	671.014	−	244.229i	1.12162	−	0.408235i	0.286375	−	0.958118i	$-0.407550\pi$
$71$	671.014	−	244.229i	1.12162	−	0.408235i	0.835242	+	0.549883i	$0.185328\pi$
$72$	92.9558	+	33.8331i	0.152152	+	0.0553788i
$73$	81.6202	+	68.4875i	0.130862	+	0.109806i	0.705870	−	0.708342i	$-0.250556\pi$
$73$	81.6202	+	68.4875i	0.130862	+	0.109806i	−0.575008	+	0.818148i	$0.695001\pi$
$74$	47.8293	−	271.253i	0.0751357	−	0.426116i
$75$	405.466			0.624256
$76$	331.187	−	7.69764i	0.499865	−	0.0116182i
$77$	62.1440			0.0919735
$78$	−5.30822	+	30.1044i	−0.00770561	+	0.0437007i
$79$	−393.010	−	329.775i	−0.559710	−	0.469653i	0.318503	−	0.947922i	$-0.396820\pi$
$79$	−393.010	−	329.775i	−0.559710	−	0.469653i	−0.878213	+	0.478269i	$0.841264\pi$
$80$	228.508	+	83.1701i	0.319350	+	0.116234i
$81$	227.633	−	82.8518i	0.312254	−	0.113651i
$82$	−379.924	+	318.794i	−0.511653	+	0.429328i
$83$	−439.020	−	760.404i	−0.580586	−	1.00561i	−0.995410	−	0.0957033i	$-0.969490\pi$
$83$	−439.020	−	760.404i	−0.580586	−	1.00561i	0.414823	−	0.909902i	$-0.363843\pi$
$84$	−12.3433	+	21.3792i	−0.0160329	+	0.0277697i
$85$	235.884	+	1337.76i	0.301002	+	1.70707i
$86$	−96.3626	−	546.500i	−0.120826	−	0.685239i
$87$	509.629	−	882.704i	0.628023	−	1.08777i
$88$	−154.082	−	266.878i	−0.186650	−	0.323288i
$89$	362.075	−	303.817i	0.431234	−	0.361848i	−0.401183	−	0.915998i	$-0.631401\pi$
$89$	362.075	−	303.817i	0.431234	−	0.361848i	0.832417	+	0.554149i	$0.186956\pi$
$90$	−353.193	+	128.552i	−0.413664	+	0.150562i
$91$	6.05685	+	2.20451i	0.00697726	+	0.00253952i
$92$	206.846	+	173.564i	0.234404	+	0.196688i
$93$	−126.835	+	719.317i	−0.141421	+	0.802039i
$94$	739.201			0.811093
$95$	−945.168	+	831.271i	−1.02076	+	0.897753i
$96$	122.418			0.130148
$97$	285.092	−	1616.84i	0.298419	−	1.69242i	−0.354551	−	0.935037i	$-0.615366\pi$
$97$	285.092	−	1616.84i	0.298419	−	1.69242i	0.652970	−	0.757384i	$-0.273523\pi$
$98$	−521.519	−	437.606i	−0.537565	−	0.451071i
$99$	447.589	+	162.909i	0.454387	+	0.165383i
$100$	−398.388	+	145.002i	−0.398388	+	0.145002i
$101$	−1242.95	+	1042.96i	−1.22454	+	1.02751i	−0.225964	+	0.974136i	$0.572553\pi$
$101$	−1242.95	+	1042.96i	−1.22454	+	1.02751i	−0.998575	+	0.0533740i	$0.983002\pi$
$102$	341.921	+	592.224i	0.331914	+	0.574891i
$103$	49.5297	−	85.7879i	0.0473816	−	0.0820673i	−0.841362	−	0.540472i	$-0.818246\pi$
$103$	49.5297	−	85.7879i	0.0473816	−	0.0820673i	0.888744	+	0.458405i	$0.151579\pi$
$104$	−5.55028	−	31.4772i	−0.00523317	−	0.0296788i
$105$	−16.2879	−	92.3734i	−0.0151385	−	0.0858545i
$106$	−407.881	+	706.471i	−0.373744	+	0.647344i
$107$	−850.648	−	1473.37i	−0.768554	−	1.33117i	−0.938347	−	0.345695i	$-0.887643\pi$
$107$	−850.648	−	1473.37i	−0.768554	−	1.33117i	0.169793	−	0.985480i	$-0.445690\pi$
$108$	−461.445	+	387.198i	−0.411135	+	0.344983i
$109$	−1142.28	+	415.758i	−1.00377	+	0.365343i	−0.791038	−	0.611768i	$-0.790459\pi$
$109$	−1142.28	+	415.758i	−1.00377	+	0.365343i	−0.212733	+	0.977110i	$0.568237\pi$
$110$	1100.28	+	400.470i	0.953707	+	0.347121i
$111$	403.591	+	338.653i	0.345109	+	0.289581i
$112$	4.48225	−	25.4201i	0.00378155	−	0.0214462i
$113$	1228.73			1.02291			0.511457	−	0.859309i	$-0.329106\pi$
$113$	1228.73			1.02291			0.511457	+	0.859309i	$0.329106\pi$
$114$	−303.992	+	555.977i	−0.249749	+	0.456772i
$115$	−1025.95			−0.831920
$116$	−185.064	+	1049.55i	−0.148127	+	0.840069i
$117$	37.8451	+	31.7558i	0.0299041	+	0.0250925i
$118$	1106.29	+	402.655i	0.863067	+	0.314131i
$119$	135.495	−	49.3162i	0.104377	−	0.0379900i
$120$	−356.314	+	298.983i	−0.271057	+	0.227444i
$121$	−76.4170	−	132.358i	−0.0574132	−	0.0994427i
$122$	806.515	−	1396.92i	0.598512	−	1.03665i
$123$	−164.731	−	934.238i	−0.120759	−	0.684857i
$124$	−132.619	−	752.119i	−0.0960445	−	0.544696i
$125$	−144.468	+	250.225i	−0.103373	+	0.179047i
$126$	19.9483	+	34.5515i	0.0141043	+	0.0244293i
$127$	−442.286	+	371.122i	−0.309028	+	0.259305i	−0.784090	−	0.620647i	$-0.786870\pi$
$127$	−442.286	+	371.122i	−0.309028	+	0.259305i	0.475062	+	0.879952i	$0.342426\pi$
$128$	−120.281	+	43.7786i	−0.0830579	+	0.0302306i
$129$	997.443	+	363.039i	0.680775	+	0.247782i
$130$	93.0325	+	78.0635i	0.0627653	+	0.0526663i
$131$	−459.283	+	2604.72i	−0.306319	+	1.73722i	0.310913	+	0.950438i	$0.399365\pi$
$131$	−459.283	+	2604.72i	−0.306319	+	1.73722i	−0.617232	+	0.786781i	$0.711746\pi$
$132$	589.449			0.388674
$133$	104.319	+	83.4810i	0.0680118	+	0.0544264i
$134$	−408.965			−0.263651
$135$	397.440	−	2254.00i	0.253379	−	1.43699i
$136$	−547.742	−	459.610i	−0.345356	−	0.289788i
$137$	−397.518	−	144.685i	−0.247899	−	0.0902280i	0.215082	−	0.976596i	$-0.430998\pi$
$137$	−397.518	−	144.685i	−0.247899	−	0.0902280i	−0.462981	+	0.886368i	$0.653220\pi$
$138$	−485.336	+	176.648i	−0.299380	+	0.108966i
$139$	1055.16	−	885.385i	0.643867	−	0.540269i	−0.261336	−	0.965248i	$-0.584163\pi$
$139$	1055.16	−	885.385i	0.643867	−	0.540269i	0.905203	+	0.424979i	$0.139719\pi$
$140$	49.0379	+	84.9361i	0.0296033	+	0.0512744i
$141$	−706.962	+	1224.49i	−0.422248	+	0.731355i
$142$	−247.997	−	1406.46i	−0.146559	−	0.831180i
$143$	−26.7250	−	151.565i	−0.0156284	−	0.0886329i
$144$	98.9214	−	171.337i	0.0572462	−	0.0991533i
$145$	−2024.68	−	3506.85i	−1.15959	−	2.00847i
$146$	163.240	−	136.975i	0.0925334	−	0.0776448i
$147$	1223.67	−	445.381i	0.686578	−	0.249894i
$148$	−517.654	−	188.411i	−0.287506	−	0.104644i
$149$	2633.00	+	2209.35i	1.44768	+	1.21475i	0.934252	+	0.356613i	$0.116068\pi$
$149$	2633.00	+	2209.35i	1.44768	+	1.21475i	0.513426	+	0.858134i	$0.328376\pi$
$150$	140.817	−	798.612i	0.0766510	−	0.434709i
$151$	968.182			0.521785			0.260892	−	0.965368i	$-0.415983\pi$
$151$	968.182			0.521785			0.260892	+	0.965368i	$0.415983\pi$
$152$	99.8586	−	654.984i	0.0532869	−	0.349515i
$153$	1105.18			0.583976
$154$	21.5824	−	122.400i	0.0112932	−	0.0640471i
$155$	2222.92	+	1865.25i	1.15193	+	0.966586i
$156$	57.4506	+	20.9103i	0.0294854	+	0.0107318i
$157$	1576.54	−	573.812i	0.801409	−	0.291689i	0.0913388	−	0.995820i	$-0.470885\pi$
$157$	1576.54	−	573.812i	0.801409	−	0.291689i	0.710070	+	0.704131i	$0.248663\pi$
$158$	−786.021	+	659.550i	−0.395775	+	0.332095i
$159$	−780.184	−	1351.32i	−0.389136	−	0.674004i
$160$	243.173	−	421.188i	0.120153	−	0.208112i
$161$	18.9108	+	107.248i	0.00925700	+	0.0524991i
$162$	−84.1299	−	477.124i	−0.0408017	−	0.231398i
$163$	437.165	−	757.192i	0.210070	−	0.363852i	−0.741666	−	0.670769i	$-0.765964\pi$
$163$	437.165	−	757.192i	0.210070	−	0.363852i	0.951736	+	0.306917i	$0.0992975\pi$
$164$	495.955	+	859.020i	0.236144	+	0.409013i
$165$	−1715.68	+	1439.63i	−0.809487	+	0.679241i
$166$	−1650.17	+	600.614i	−0.771556	+	0.280824i
$167$	−2527.16	−	919.810i	−1.17100	−	0.426210i	−0.317986	−	0.948095i	$-0.603007\pi$
$167$	−2527.16	−	919.810i	−1.17100	−	0.426210i	−0.853016	+	0.521885i	$0.825229\pi$
$168$	37.8219	+	31.7364i	0.0173692	+	0.0145745i
$169$	−378.733	+	2147.90i	−0.172386	+	0.977652i
$170$	2716.80			1.22570
$171$	532.506	+	874.736i	0.238139	+	0.391186i
$172$	−1109.86			−0.492012
$173$	−315.297	+	1788.14i	−0.138564	+	0.785837i	0.833747	+	0.552147i	$0.186191\pi$
$173$	−315.297	+	1788.14i	−0.138564	+	0.785837i	−0.972311	+	0.233690i	$0.924920\pi$
$174$	−1561.59	−	1310.33i	−0.680369	−	0.570897i
$175$	−160.677	−	58.4815i	−0.0694058	−	0.0252616i
$176$	−579.160	+	210.797i	−0.248044	+	0.0902808i
$177$	−1725.04	+	1447.48i	−0.732554	+	0.614686i
$178$	−472.655	−	818.662i	−0.199028	−	0.344727i
$179$	186.205	−	322.517i	0.0777521	−	0.134671i	−0.824528	−	0.565822i	$-0.808559\pi$
$179$	186.205	−	322.517i	0.0777521	−	0.134671i	0.902280	+	0.431151i	$0.141892\pi$
$180$	130.535	+	740.300i	0.0540527	+	0.306548i
$181$	373.294	+	2117.06i	0.153297	+	0.869389i	0.960326	+	0.278878i	$0.0899626\pi$
$181$	373.294	+	2117.06i	0.153297	+	0.869389i	−0.807030	+	0.590511i	$0.798926\pi$
$182$	6.44557	−	11.1641i	0.00262515	−	0.00454689i
$183$	1542.68	+	2672.00i	0.623160	+	1.07934i
$184$	413.691	−	347.128i	0.165749	−	0.139080i
$185$	1966.87	−	715.881i	0.781659	−	0.284501i
$186$	1372.73	+	499.632i	0.541147	+	0.196961i
$187$	−2637.41	−	2213.05i	−1.03137	−	0.865425i
$188$	256.722	−	1455.94i	0.0995924	−	0.564816i
$189$	−242.947			−0.0935017
$190$	1309.03	+	2150.32i	0.499826	+	0.821054i
$191$	−3291.72			−1.24702			−0.623509	−	0.781816i	$-0.714293\pi$
$191$	−3291.72			−1.24702			−0.623509	+	0.781816i	$0.714293\pi$
$192$	42.5152	−	241.115i	0.0159806	−	0.0906303i
$193$	−321.207	−	269.525i	−0.119798	−	0.100522i	0.580921	−	0.813960i	$-0.302693\pi$
$193$	−321.207	−	269.525i	−0.119798	−	0.100522i	−0.700718	+	0.713438i	$0.747137\pi$
$194$	−3085.53	−	1123.04i	−1.14190	−	0.415617i
$195$	−218.288	+	79.4504i	−0.0801638	+	0.0291772i
$196$	−1043.04	+	875.213i	−0.380116	+	0.318955i
$197$	−1017.65	−	1762.63i	−0.368044	−	0.637471i	0.621215	−	0.783640i	$-0.286639\pi$
$197$	−1017.65	−	1762.63i	−0.368044	−	0.637471i	−0.989260	+	0.146168i	$0.953306\pi$
$198$	476.314	−	825.000i	0.170960	−	0.296112i
$199$	−440.599	−	2498.76i	−0.156951	−	0.890114i	−0.956980	−	0.290153i	$-0.906294\pi$
$199$	−440.599	−	2498.76i	−0.156951	−	0.890114i	0.800029	−	0.599961i	$-0.204817\pi$
$200$	147.238	+	835.030i	0.0520566	+	0.295228i
$201$	391.129	−	677.454i	0.137254	−	0.237731i
$202$	1622.56	+	2810.35i	0.565163	+	0.978890i
$203$	−329.269	+	276.290i	−0.113843	+	0.0955257i
$204$	1285.20	−	467.775i	0.441089	−	0.160543i
$205$	−3541.55	−	1289.02i	−1.20660	−	0.439166i
$206$	−151.768	−	127.348i	−0.0513309	−	0.0430717i
$207$	−144.945	+	822.024i	−0.0486685	+	0.276013i
$208$	−63.9256			−0.0213098
$209$	480.826	−	3153.80i	0.159136	−	1.04379i
$210$	−187.597			−0.0616448
$211$	−230.987	+	1309.99i	−0.0753639	+	0.427410i	0.923659	+	0.383215i	$0.125183\pi$
$211$	−230.987	+	1309.99i	−0.0753639	+	0.427410i	−0.999023	+	0.0441946i	$0.985928\pi$
$212$	1249.82	+	1048.72i	0.404896	+	0.339748i
$213$	2567.00	+	934.311i	0.825764	+	0.300554i
$214$	−3197.39	+	1163.76i	−1.02135	+	0.371742i
$215$	3230.41	−	2710.64i	1.02471	−	0.859832i
$216$	602.374	+	1043.34i	0.189752	+	0.328659i
$217$	154.011	−	266.755i	0.0481794	−	0.0834492i
$218$	422.171	+	2394.25i	0.131161	+	0.743850i
$219$	70.7796	+	401.411i	0.0218394	+	0.123858i
$220$	1170.90	−	2028.05i	0.358826	−	0.621505i
$221$	−178.549	−	309.255i	−0.0543461	−	0.0941302i
$222$	807.182	−	677.306i	0.244029	−	0.204765i
$223$	2738.39	−	996.691i	0.822314	−	0.299298i	0.103613	−	0.994618i	$-0.466960\pi$
$223$	2738.39	−	996.691i	0.822314	−	0.299298i	0.718700	+	0.695320i	$0.244737\pi$
$224$	−48.5112	−	17.6566i	−0.0144700	−	0.00526667i
$225$	−1003.96	−	842.420i	−0.297469	−	0.249606i
$226$	426.734	−	2420.13i	0.125601	−	0.712321i
$227$	−808.460			−0.236385			−0.118192	−	0.992991i	$-0.537710\pi$
$227$	−808.460			−0.236385			−0.118192	+	0.992991i	$0.537710\pi$
$228$	989.485	+	791.835i	0.287413	+	0.230003i
$229$	4517.68			1.30365			0.651827	−	0.758368i	$-0.274003\pi$
$229$	4517.68			1.30365			0.651827	+	0.758368i	$0.274003\pi$
$230$	−356.310	+	2020.74i	−0.102150	+	0.579319i
$231$	182.115	+	152.813i	0.0518715	+	0.0435253i
$232$	2002.93	+	729.008i	0.566806	+	0.206301i
$233$	2974.86	−	1082.76i	0.836435	−	0.304437i	0.111938	−	0.993715i	$-0.464294\pi$
$233$	2974.86	−	1082.76i	0.836435	−	0.304437i	0.724497	+	0.689278i	$0.242072\pi$
$234$	75.6902	−	63.5116i	0.0211454	−	0.0177431i
$235$	2808.65	+	4864.73i	0.779644	+	1.35038i
$236$	1177.29	−	2039.12i	0.324724	−	0.562438i
$237$	−340.811	−	1932.84i	−0.0934096	−	0.529752i
$238$	−50.0770	−	284.001i	−0.0136387	−	0.0773489i
$239$	−2186.52	+	3787.17i	−0.591776	+	1.02499i	0.402217	+	0.915544i	$0.368240\pi$
$239$	−2186.52	+	3787.17i	−0.591776	+	1.02499i	−0.993993	+	0.109442i	$0.965094\pi$
$240$	465.135	+	805.638i	0.125101	+	0.216682i
$241$	−2169.35	+	1820.30i	−0.579836	+	0.486540i	−0.884893	−	0.465794i	$-0.845769\pi$
$241$	−2169.35	+	1820.30i	−0.579836	+	0.486540i	0.305057	+	0.952334i	$0.401324\pi$
$242$	−287.234	+	104.545i	−0.0762980	+	0.0277702i
$243$	−2949.99	−	1073.71i	−0.778773	−	0.283450i
$244$	−2471.31	−	2073.67i	−0.648398	−	0.544071i
$245$	898.363	−	5094.87i	0.234263	−	1.32857i
$246$	−1897.30			−0.491738
$247$	158.742	−	290.327i	0.0408929	−	0.0747898i
$248$	−1527.44			−0.391100
$249$	583.281	−	3307.95i	0.148450	−	0.841899i
$250$	442.674	+	371.448i	0.111989	+	0.0939697i
$251$	−1563.77	−	569.167i	−0.393245	−	0.143130i	0.137827	−	0.990456i	$-0.455988\pi$
$251$	−1563.77	−	569.167i	−0.393245	−	0.143130i	−0.531072	+	0.847327i	$0.678211\pi$
$252$	74.9812	−	27.2909i	0.0187435	−	0.00682209i
$253$	1991.95	−	1671.45i	0.494992	−	0.415348i
$254$	577.363	+	1000.02i	0.142626	+	0.247035i
$255$	−2598.31	+	4500.41i	−0.638088	+	1.10520i
$256$	44.4539	+	252.111i	0.0108530	+	0.0615505i
$257$	−787.154	−	4464.17i	−0.191056	−	1.08353i	−0.917925	−	0.396754i	$-0.870137\pi$
$257$	−787.154	−	4464.17i	−0.191056	−	1.08353i	0.726869	−	0.686776i	$-0.240975\pi$
$258$	1061.46	−	1838.50i	0.256137	−	0.443642i
$259$	−111.089	−	192.411i	−0.0266514	−	0.0461616i
$260$	186.065	−	156.127i	0.0443818	−	0.0372407i
$261$	−3095.83	+	1126.79i	−0.734203	+	0.267228i
$262$	4970.80	+	1809.22i	1.17213	+	0.426619i
$263$	−240.295	−	201.631i	−0.0563392	−	0.0472742i	0.614183	−	0.789163i	$-0.289486\pi$
$263$	−240.295	−	201.631i	−0.0563392	−	0.0472742i	−0.670522	+	0.741889i	$0.733930\pi$
$264$	204.714	−	1160.99i	0.0477244	−	0.270659i
$265$	−6199.11			−1.43701
$266$	200.655	−	176.475i	0.0462516	−	0.0406781i
$267$	1808.16			0.414449
$268$	−142.032	+	805.503i	−0.0323731	+	0.183597i
$269$	2179.68	+	1828.97i	0.494042	+	0.414550i	0.855472	−	0.517849i	$-0.173267\pi$
$269$	2179.68	+	1828.97i	0.494042	+	0.414550i	−0.361430	+	0.932399i	$0.617711\pi$
$270$	−4301.48	−	1565.61i	−0.969553	−	0.352889i
$271$	3800.92	−	1383.42i	0.851990	−	0.310099i	0.121139	−	0.992636i	$-0.461345\pi$
$271$	3800.92	−	1383.42i	0.851990	−	0.310099i	0.730851	+	0.682537i	$0.239123\pi$
$272$	−1095.48	+	919.220i	−0.244204	+	0.204911i
$273$	12.3289	+	21.3543i	0.00273326	+	0.00473414i
$274$	−423.030	+	732.709i	−0.0932706	+	0.161549i
$275$	708.963	+	4020.73i	0.155462	+	0.881670i
$276$	179.373	+	1017.27i	0.0391195	+	0.221857i
$277$	−3925.62	+	6799.37i	−0.851507	+	1.47485i	0.0283408	+	0.999598i	$0.490978\pi$
$277$	−3925.62	+	6799.37i	−0.851507	+	1.47485i	−0.879848	+	0.475255i	$0.842356\pi$
$278$	−1377.41	−	2385.75i	−0.297165	−	0.514704i
$279$	1808.55	−	1517.55i	0.388082	−	0.325639i
$280$	184.322	−	67.0878i	0.0393406	−	0.0143188i
$281$	−174.275	−	63.4310i	−0.0369978	−	0.0134661i	0.323455	−	0.946244i	$-0.395156\pi$
$281$	−174.275	−	63.4310i	−0.0369978	−	0.0134661i	−0.360453	+	0.932777i	$0.617378\pi$
$282$	2166.26	+	1817.71i	0.457443	+	0.383840i
$283$	−888.369	+	5038.19i	−0.186601	+	1.05827i	0.737280	+	0.675587i	$0.236110\pi$
$283$	−888.369	+	5038.19i	−0.186601	+	1.05827i	−0.923881	+	0.382679i	$0.875001\pi$
$284$	−2856.31			−0.596800
$285$	−4813.96	+	111.889i	−1.00054	+	0.0232552i
$286$	−307.806			−0.0636398
$287$	−69.4687	+	393.976i	−0.0142878	+	0.0810303i
$288$	−303.113	−	254.342i	−0.0620177	−	0.0520390i
$289$	−2890.00	−	1051.87i	−0.588235	−	0.214100i
$290$	−7610.31	+	2769.93i	−1.54101	+	0.560881i
$291$	4811.30	−	4037.16i	0.969221	−	0.813273i
$292$	−213.095	−	369.092i	−0.0427071	−	0.0739708i
$293$	−1789.16	+	3098.91i	−0.356737	+	0.617886i	−0.987414	−	0.158160i	$-0.949444\pi$
$293$	−1789.16	+	3098.91i	−0.356737	+	0.617886i	0.630677	+	0.776045i	$0.282777\pi$
$294$	−452.252	−	2564.85i	−0.0897138	−	0.508792i
$295$	1553.52	+	8810.47i	0.306609	+	1.73887i
$296$	−550.876	+	954.145i	−0.108172	+	0.187360i
$297$	2900.47	+	5023.76i	0.566675	+	0.981510i
$298$	5266.01	−	4418.71i	1.02366	−	0.858955i
$299$	253.439	−	92.2442i	0.0490192	−	0.0178415i
$300$	−1524.05	−	554.710i	−0.293304	−	0.106754i
$301$	−342.901	−	287.728i	−0.0656627	−	0.0550976i
$302$	336.246	−	1906.95i	0.0640688	−	0.363352i
$303$	−6207.18			−1.17687
$304$	−1255.39	−	424.157i	−0.236847	−	0.0800232i
$305$	12257.7			2.30122
$306$	383.824	−	2176.78i	0.0717052	−	0.406660i
$307$	576.540	+	483.775i	0.107182	+	0.0899364i	0.694804	−	0.719199i	$-0.255491\pi$
$307$	576.540	+	483.775i	0.107182	+	0.0899364i	−0.587622	+	0.809136i	$0.699936\pi$
$308$	−233.585	−	85.0179i	−0.0432134	−	0.0157284i
$309$	356.103	−	129.611i	0.0655598	−	0.0238618i
$310$	4445.85	−	3730.51i	0.814539	−	0.683480i
$311$	−196.211	−	339.847i	−0.0357752	−	0.0619645i	0.847583	−	0.530662i	$-0.178057\pi$
$311$	−196.211	−	339.847i	−0.0357752	−	0.0619645i	−0.883359	+	0.468698i	$0.844723\pi$
$312$	61.1376	−	105.893i	0.0110937	−	0.0192149i
$313$	−480.364	−	2724.28i	−0.0867468	−	0.491966i	−0.996966	−	0.0778387i	$-0.975198\pi$
$313$	−480.364	−	2724.28i	−0.0867468	−	0.491966i	0.910219	−	0.414127i	$-0.135913\pi$
$314$	−582.664	−	3304.45i	−0.104719	−	0.593888i
$315$	−151.591	+	262.563i	−0.0271148	+	0.0469642i
$316$	1026.08	+	1777.22i	0.182663	+	0.316381i
$317$	4275.39	−	3587.48i	0.757507	−	0.635624i	−0.179970	−	0.983672i	$-0.557600\pi$
$317$	4275.39	−	3587.48i	0.757507	−	0.635624i	0.937477	+	0.348049i	$0.113156\pi$
$318$	−2932.53	+	1067.36i	−0.517133	+	0.188221i
$319$	9644.27	+	3510.23i	1.69271	+	0.616097i
$320$	−745.126	−	625.235i	−0.130168	−	0.109224i
$321$	1130.17	−	6409.52i	0.196511	−	1.11447i
$322$	217.805			0.0376951
$323$	−1454.42	−	7257.93i	−0.250546	−	1.25029i
$324$	−968.970			−0.166147
$325$	−73.5336	+	417.030i	−0.0125505	+	0.0711774i
$326$	−1339.55	−	1124.02i	−0.227579	−	0.190962i
$327$	−4369.87	−	1590.50i	−0.739003	−	0.268975i
$328$	1864.18	−	678.507i	0.313818	−	0.114220i
$329$	456.765	−	383.271i	0.0765418	−	0.0642262i
$330$	2239.66	+	3879.20i	0.373604	+	0.647100i
$331$	2098.00	−	3633.85i	0.348389	−	0.603427i	−0.637575	−	0.770389i	$-0.720062\pi$
$331$	2098.00	−	3633.85i	0.348389	−	0.603427i	0.985963	+	0.166962i	$0.0533956\pi$
$332$	609.880	+	3458.80i	0.100818	+	0.571766i
$333$	−295.709	−	1677.05i	−0.0486629	−	0.275981i
$334$	−2689.34	+	4658.08i	−0.440582	+	0.763110i
$335$	−1553.89	−	2691.42i	−0.253428	−	0.438950i
$336$	75.6439	−	63.4728i	0.0122819	−	0.0103057i
$337$	−3666.16	+	1334.37i	−0.592607	+	0.215691i	−0.620876	−	0.783909i	$-0.713223\pi$
$337$	−3666.16	+	1334.37i	−0.592607	+	0.215691i	0.0282689	+	0.999600i	$0.491001\pi$
$338$	4099.01	+	1491.92i	0.659635	+	0.240088i
$339$	3600.85	+	3021.47i	0.576906	+	0.484082i
$340$	943.534	−	5351.05i	0.150501	−	0.853533i
$341$	−7354.74			−1.16798
$342$	1907.83	−	745.039i	0.301648	−	0.117799i
$343$	−1102.50			−0.173556
$344$	−385.450	+	2186.00i	−0.0604131	+	0.342620i
$345$	−3006.60	−	2522.84i	−0.469188	−	0.393696i
$346$	3412.45	+	1242.03i	0.530215	+	0.192982i
$347$	−11111.6	+	4044.28i	−1.71902	+	0.625672i	−0.997754	−	0.0669855i	$-0.978662\pi$
$347$	−11111.6	+	4044.28i	−1.71902	+	0.625672i	−0.721266	+	0.692658i	$0.756440\pi$
$348$	−3123.19	+	2620.67i	−0.481094	+	0.403685i
$349$	547.409	+	948.141i	0.0839603	+	0.145424i	0.904948	−	0.425523i	$-0.139910\pi$
$349$	547.409	+	948.141i	0.0839603	+	0.145424i	−0.820987	+	0.570946i	$0.806576\pi$
$350$	−170.989	+	296.161i	−0.0261135	+	0.0452299i
$351$	104.480	+	592.533i	0.0158880	+	0.0901056i
$352$	214.049	+	1213.93i	0.0324115	+	0.183815i
$353$	1515.19	−	2624.39i	0.228457	−	0.395700i	−0.728894	−	0.684627i	$-0.759965\pi$
$353$	1515.19	−	2624.39i	0.228457	−	0.395700i	0.957351	+	0.288927i	$0.0932985\pi$
$354$	2251.88	+	3900.37i	0.338097	+	0.585600i
$355$	8313.73	−	6976.04i	1.24295	−	1.04296i
$356$	−1776.60	+	646.630i	−0.264494	+	0.0962678i
$357$	518.343	+	188.662i	0.0768449	+	0.0279693i
$358$	−570.566	−	478.761i	−0.0842328	−	0.0706797i
$359$	502.821	−	2851.64i	0.0739216	−	0.419230i	−0.925280	−	0.379284i	$-0.876170\pi$
$359$	502.821	−	2851.64i	0.0739216	−	0.419230i	0.999202	−	0.0399461i	$-0.0127186\pi$
$360$	1503.44			0.220106
$361$	5043.79	−	4648.23i	0.735353	−	0.677684i
$362$	4299.43			0.624235
$363$	101.528	−	575.792i	0.0146799	−	0.0832540i
$364$	−19.7504	−	16.5725i	−0.00284396	−	0.00238636i
$365$	1521.69	+	553.849i	0.218216	+	0.0794240i
$366$	5798.58	−	2110.51i	0.828133	−	0.301416i
$367$	−2774.26	+	2327.88i	−0.394592	+	0.331102i	−0.818399	−	0.574651i	$-0.805138\pi$
$367$	−2774.26	+	2327.88i	−0.394592	+	0.331102i	0.423807	+	0.905753i	$0.360694\pi$
$368$	−540.036	−	935.369i	−0.0764981	−	0.132499i
$369$	−1533.14	+	2655.48i	−0.216293	+	0.374631i
$370$	−726.925	−	4122.60i	−0.102138	−	0.579253i
$371$	114.264	+	648.024i	0.0159900	+	0.0906840i
$372$	1460.83	−	2530.23i	0.203603	−	0.352651i
$373$	2835.16	+	4910.64i	0.393563	+	0.681671i	0.992917	−	0.118813i	$-0.0379089\pi$
$373$	2835.16	+	4910.64i	0.393563	+	0.681671i	−0.599353	+	0.800485i	$0.704576\pi$
$374$	−5274.83	+	4426.11i	−0.729291	+	0.611948i
$375$	−1038.68	+	378.047i	−0.143032	+	0.0520594i
$376$	−2778.49	−	1011.29i	−0.381089	−	0.138705i
$377$	815.454	+	684.247i	0.111401	+	0.0934762i
$378$	−84.3747	+	478.513i	−0.0114809	+	0.0651112i
$379$	−9524.46			−1.29087			−0.645433	−	0.763817i	$-0.723323\pi$
$379$	−9524.46			−1.29087			−0.645433	+	0.763817i	$0.723323\pi$
$380$	4689.92	−	1831.49i	0.633125	−	0.247246i
$381$	−2208.73			−0.296999
$382$	−1143.20	+	6483.42i	−0.153119	+	0.868378i
$383$	5597.33	+	4696.72i	0.746763	+	0.626608i	0.934645	−	0.355583i	$-0.115718\pi$
$383$	5597.33	+	4696.72i	0.746763	+	0.626608i	−0.187882	+	0.982192i	$0.560162\pi$
$384$	−460.139	−	167.477i	−0.0611495	−	0.0222566i
$385$	887.525	−	323.033i	0.117487	−	0.0427617i
$386$	−642.414	+	539.049i	−0.0847098	+	0.0710800i
$387$	−1715.45	−	2971.25i	−0.225327	−	0.390277i
$388$	−3283.56	+	5687.29i	−0.429632	+	0.744145i
$389$	43.6252	+	247.411i	0.00568608	+	0.0322473i	0.987519	−	0.157501i	$-0.0503438\pi$
$389$	43.6252	+	247.411i	0.00568608	+	0.0322473i	−0.981833	+	0.189749i	$0.939233\pi$
$390$	80.6760	+	457.536i	0.0104748	+	0.0594058i
$391$	3016.72	−	5225.10i	0.390184	−	0.675818i
$392$	1361.59	+	2358.34i	0.175435	+	0.303863i
$393$	−7751.00	+	6503.86i	−0.994876	+	0.834800i
$394$	−3825.12	+	1392.23i	−0.489104	+	0.178019i
$395$	−7327.09	−	2666.84i	−0.933331	−	0.339705i
$396$	−1459.51	−	1224.67i	−0.185210	−	0.155410i
$397$	−719.710	+	4081.68i	−0.0909854	+	0.516004i	0.904918	+	0.425585i	$0.139932\pi$
$397$	−719.710	+	4081.68i	−0.0909854	+	0.516004i	−0.995904	+	0.0904188i	$0.971179\pi$
$398$	−5074.62			−0.639115
$399$	100.429	+	501.165i	0.0126008	+	0.0628813i
$400$	1695.82			0.211978
$401$	−491.601	+	2788.01i	−0.0612204	+	0.347198i	0.938776	+	0.344528i	$0.111961\pi$
$401$	−491.601	+	2788.01i	−0.0612204	+	0.347198i	−0.999996	+	0.00267008i	$0.999150\pi$
$402$	−1198.49	−	1005.65i	−0.148694	−	0.124769i
$403$	−716.829	−	260.904i	−0.0886050	−	0.0322496i
$404$	6098.83	−	2219.79i	0.751059	−	0.273363i
$405$	2820.33	−	2366.54i	0.346033	−	0.290356i
$406$	429.830	+	744.488i	0.0525422	+	0.0910057i
$407$	−2652.51	+	4594.27i	−0.323046	+	0.559532i
$408$	−474.991	−	2693.81i	−0.0576362	−	0.326871i
$409$	1624.68	+	9213.99i	0.196418	+	1.11394i	0.910385	+	0.413763i	$0.135786\pi$
$409$	1624.68	+	9213.99i	0.196418	+	1.11394i	−0.713966	+	0.700180i	$0.753103\pi$
$410$	−3768.84	+	6527.83i	−0.453975	+	0.786308i
$411$	−809.160	−	1401.51i	−0.0971117	−	0.168202i
$412$	−303.536	+	254.697i	−0.0362964	+	0.0304563i
$413$	892.368	−	324.795i	0.106321	−	0.0386977i
$414$	1568.73	+	570.972i	0.186229	+	0.0677820i
$415$	−10222.7	−	8577.83i	−1.20918	−	1.01462i
$416$	−22.2011	+	125.909i	−0.00261659	+	0.0148394i
$417$	5269.36			0.618805
$418$	−6044.77	−	2042.34i	−0.707320	−	0.238982i
$419$	−3304.33			−0.385267			−0.192633	−	0.981271i	$-0.561703\pi$
$419$	−3304.33			−0.385267			−0.192633	+	0.981271i	$0.561703\pi$
$420$	−65.1517	+	369.494i	−0.00756923	+	0.0429273i
$421$	1201.15	+	1007.89i	0.139051	+	0.116678i	0.709660	−	0.704544i	$-0.248848\pi$
$421$	1201.15	+	1007.89i	0.139051	+	0.116678i	−0.570609	+	0.821222i	$0.693293\pi$
$422$	2499.96	+	909.910i	0.288379	+	0.104961i
$423$	4294.56	−	1563.09i	0.493638	−	0.179669i
$424$	2499.64	−	2097.45i	0.286305	−	0.240238i
$425$	4736.56	+	8203.96i	0.540604	+	0.936354i
$426$	2731.74	−	4731.52i	0.310689	−	0.538128i
$427$	−225.938	−	1281.36i	−0.0256063	−	0.145221i
$428$	1181.71	+	6701.80i	0.133458	+	0.756878i
$429$	294.382	−	509.885i	0.0331303	−	0.0573834i
$430$	−4217.00	−	7304.07i	−0.472935	−	0.819147i
$431$	7656.81	−	6424.82i	0.855720	−	0.718035i	−0.105321	−	0.994438i	$-0.533587\pi$
$431$	7656.81	−	6424.82i	0.855720	−	0.718035i	0.961042	+	0.276404i	$0.0891427\pi$
$432$	2264.18	−	824.096i	0.252166	−	0.0917808i
$433$	−8910.95	−	3243.32i	−0.988991	−	0.359963i	−0.203662	−	0.979041i	$-0.565284\pi$
$433$	−8910.95	−	3243.32i	−0.988991	−	0.359963i	−0.785329	+	0.619078i	$0.787506\pi$
$434$	−471.916	−	395.985i	−0.0521952	−	0.0437970i
$435$	2689.99	−	15255.7i	0.296494	−	1.68150i
$436$	4862.38			0.534095
$437$	5589.15	−	129.906i	0.611820	−	0.0142203i
$438$	815.206			0.0889317
$439$	1213.19	−	6880.33i	0.131896	−	0.748018i	−0.845075	−	0.534647i	$-0.820445\pi$
$439$	1213.19	−	6880.33i	0.131896	−	0.748018i	0.976971	−	0.213371i	$-0.0684444\pi$
$440$	−3587.83	−	3010.55i	−0.388735	−	0.326187i
$441$	−3955.24	−	1439.59i	−0.427085	−	0.155446i
$442$	−671.124	+	244.269i	−0.0722219	+	0.0262866i
$443$	−6666.92	+	5594.21i	−0.715022	+	0.599975i	−0.926003	−	0.377515i	$-0.876779\pi$
$443$	−6666.92	+	5594.21i	−0.715022	+	0.599975i	0.210981	+	0.977490i	$0.432334\pi$
$444$	−1053.70	−	1825.06i	−0.112627	−	0.195076i
$445$	3591.78	−	6221.15i	0.382622	−	0.662721i
$446$	−1012.07	−	5739.72i	−0.107450	−	0.609380i
$447$	2283.29	+	12949.2i	0.241602	+	1.37019i
$448$	−51.6245	+	89.4163i	−0.00544426	+	0.00942974i
$449$	6975.37	+	12081.7i	0.733159	+	1.26987i	0.955526	+	0.294905i	$0.0952881\pi$
$449$	6975.37	+	12081.7i	0.733159	+	1.26987i	−0.222368	+	0.974963i	$0.571379\pi$
$450$	−2007.91	+	1684.84i	−0.210342	+	0.176498i
$451$	8976.17	−	3267.06i	0.937187	−	0.341108i
$452$	−4618.52	−	1681.00i	−0.480613	−	0.174929i
$453$	2837.30	+	2380.77i	0.294278	+	0.246928i
$454$	−280.775	+	1592.36i	−0.0290252	+	0.164610i
$455$	97.9618			0.0100935
$456$	1903.26	−	1673.90i	0.195456	−	0.171903i
$457$	−7064.52			−0.723116			−0.361558	−	0.932350i	$-0.617755\pi$
$457$	−7064.52			−0.723116			−0.361558	+	0.932350i	$0.617755\pi$
$458$	1568.97	−	8898.09i	0.160073	−	0.907818i
$459$	10310.8	+	8651.78i	1.04851	+	0.879805i
$460$	3856.33	+	1403.59i	0.390874	+	0.142267i
$461$	−2970.49	+	1081.17i	−0.300107	+	0.109230i	−0.487685	−	0.873020i	$-0.662159\pi$
$461$	−2970.49	+	1081.17i	−0.300107	+	0.109230i	0.187578	+	0.982250i	$0.439936\pi$
$462$	364.231	−	305.626i	0.0366787	−	0.0307771i
$463$	−4387.70	−	7599.71i	−0.440418	−	0.762826i	0.557302	−	0.830310i	$-0.311836\pi$
$463$	−4387.70	−	7599.71i	−0.440418	−	0.762826i	−0.997720	+	0.0674833i	$0.978503\pi$
$464$	2131.48	−	3691.83i	0.213257	−	0.369372i
$465$	1927.68	+	10932.4i	0.192245	+	1.09028i
$466$	−1099.46	−	6235.36i	−0.109295	−	0.619845i
$467$	8634.59	−	14955.6i	0.855592	−	1.48193i	−0.0205032	−	0.999790i	$-0.506527\pi$
$467$	8634.59	−	14955.6i	0.855592	−	1.48193i	0.876095	−	0.482139i	$-0.160140\pi$
$468$	−98.8065	−	171.138i	−0.00975925	−	0.0169035i
$469$	−252.706	+	212.046i	−0.0248804	+	0.0208771i
$470$	10557.1	−	3842.46i	1.03609	−	0.377106i
$471$	6031.11	+	2195.15i	0.590019	+	0.214749i
$472$	−3607.41	−	3026.98i	−0.351790	−	0.295186i
$473$	−1855.97	+	10525.7i	−0.180418	+	1.02320i
$474$	−3925.31			−0.380370
$475$	−4211.13	+	7701.83i	−0.406779	+	0.743966i
$476$	−576.764			−0.0555377
$477$	−875.799	+	4966.90i	−0.0840672	+	0.476769i
$478$	6699.90	+	5621.88i	0.641101	+	0.537948i
$479$	2048.83	+	745.711i	0.195435	+	0.0711324i	0.437883	−	0.899032i	$-0.355728\pi$
$479$	2048.83	+	745.711i	0.195435	+	0.0711324i	−0.242449	+	0.970164i	$0.577951\pi$
$480$	1748.34	−	636.343i	0.166251	−	0.0605103i
$481$	−421.505	+	353.685i	−0.0399563	+	0.0335273i
$482$	2831.89	+	4904.98i	0.267612	+	0.463518i
$483$	−208.306	+	360.797i	−0.0196237	+	0.0339893i
$484$	106.157	+	602.049i	0.00996970	+	0.0565410i
$485$	−4332.92	−	24573.2i	−0.405665	−	2.30064i
$486$	−3139.31	+	5437.45i	−0.293008	+	0.507505i
$487$	−2412.17	−	4178.00i	−0.224447	−	0.388754i	0.731706	−	0.681620i	$-0.238724\pi$
$487$	−2412.17	−	4178.00i	−0.224447	−	0.388754i	−0.956153	+	0.292866i	$0.905391\pi$
$488$	−4942.61	+	4147.34i	−0.458487	+	0.384716i
$489$	3143.08	−	1143.99i	0.290664	−	0.105793i
$490$	−9722.94	−	3538.86i	−0.896404	−	0.326264i
$491$	8557.94	+	7180.97i	0.786588	+	0.660025i	0.944898	−	0.327364i	$-0.106160\pi$
$491$	8557.94	+	7180.97i	0.786588	+	0.660025i	−0.158311	+	0.987389i	$0.550605\pi$
$492$	−658.925	+	3736.95i	−0.0603794	+	0.342428i
$493$	23813.5			2.17547
$494$	−516.702	−	413.491i	−0.0470598	−	0.0376596i
$495$	7239.17			0.657326
$496$	−530.475	+	3008.47i	−0.0480223	+	0.272348i
$497$	−882.483	−	740.491i	−0.0796474	−	0.0668321i
$498$	−6312.82	−	2297.68i	−0.568041	−	0.206750i
$499$	−14519.0	+	5284.47i	−1.30252	+	0.474079i	−0.897817	−	0.440369i	$-0.854848\pi$
$499$	−14519.0	+	5284.47i	−1.30252	+	0.474079i	−0.404704	+	0.914448i	$0.632626\pi$
$500$	885.349	−	742.896i	0.0791880	−	0.0664466i
$501$	−5144.11	−	8909.86i	−0.458726	−	0.794537i
$502$	−1664.13	+	2882.37i	−0.147956	+	0.256267i
$503$	−1379.27	−	7822.23i	−0.122264	−	0.693392i	−0.982896	−	0.184164i	$-0.941042\pi$
$503$	−1379.27	−	7822.23i	−0.122264	−	0.693392i	0.860632	−	0.509228i	$-0.170069\pi$
$504$	−27.7119	−	157.162i	−0.00244918	−	0.0138900i
$505$	−12330.1	+	21356.3i	−1.08650	+	1.88187i
$506$	−2600.31	−	4503.87i	−0.228454	−	0.395695i
$507$	−6391.62	+	5363.20i	−0.559885	+	0.469799i
$508$	2170.18	−	789.880i	0.189539	−	0.0689867i
$509$	−5204.55	−	1894.30i	−0.453218	−	0.164958i	0.105317	−	0.994439i	$-0.466414\pi$
$509$	−5204.55	−	1894.30i	−0.453218	−	0.164958i	−0.558535	+	0.829481i	$0.688636\pi$
$510$	7961.69	+	6680.65i	0.691273	+	0.580047i
$511$	29.8484	−	169.278i	0.00258398	−	0.0146545i
$512$	512.000			0.0441942
$513$	−1879.76	+	12329.5i	−0.161780	+	1.06114i
$514$	−9066.07			−0.777991
$515$	261.434	−	1482.66i	0.0223692	−	0.126862i
$516$	−3252.49	−	2729.16i	−0.277486	−	0.232839i
$517$	−13378.6	−	4869.42i	−1.13809	−	0.414230i
$518$	−417.557	+	151.978i	−0.0354178	+	0.0128910i
$519$	−5321.06	+	4464.90i	−0.450036	+	0.377625i
$520$	−242.891	−	420.699i	−0.0204836	−	0.0354786i
$521$	9252.40	−	16025.6i	0.778033	−	1.34759i	−0.155042	−	0.987908i	$-0.549551\pi$
$521$	9252.40	−	16025.6i	0.778033	−	1.34759i	0.933074	−	0.359684i	$-0.117115\pi$
$522$	1144.17	+	6488.92i	0.0959369	+	0.544085i
$523$	67.8315	+	384.692i	0.00567126	+	0.0321633i	0.987512	−	0.157543i	$-0.0503574\pi$
$523$	67.8315	+	384.692i	0.00567126	+	0.0321633i	−0.981841	+	0.189707i	$0.939246\pi$
$524$	5289.81	−	9162.22i	0.441005	−	0.763843i
$525$	−327.063	−	566.489i	−0.0271889	−	0.0470926i
$526$	−480.590	+	403.263i	−0.0398379	+	0.0334279i
$527$	−16035.9	+	5836.58i	−1.32549	+	0.482439i
$528$	−2215.60	−	806.414i	−0.182617	−	0.0664672i
$529$	−5829.71	−	4891.71i	−0.479141	−	0.402047i
$530$	−2152.93	+	12209.9i	−0.176448	+	1.00068i
$531$	7278.68			0.594854
$532$	−277.901	−	456.502i	−0.0226476	−	0.0372028i
$533$	990.757			0.0805150
$534$	627.969	−	3561.39i	0.0508893	−	0.288607i
$535$	−19807.5	−	16620.5i	−1.60066	−	1.34311i
$536$	1537.20	+	559.497i	0.123875	+	0.0450869i
$537$	1338.76	−	487.267i	0.107582	−	0.0391567i
$538$	4359.35	−	3657.93i	0.349340	−	0.293131i
$539$	6556.15	+	11355.6i	0.523921	+	0.907458i
$540$	−4577.53	+	7928.52i	−0.364788	+	0.631832i
$541$	−2259.51	−	12814.3i	−0.179564	−	1.01836i	−0.932743	−	0.360541i	$-0.882592\pi$
$541$	−2259.51	−	12814.3i	−0.179564	−	1.01836i	0.753180	−	0.657815i	$-0.228519\pi$
$542$	−1404.76	−	7966.80i	−0.111328	−	0.631372i
$543$	−4111.92	+	7122.05i	−0.324971	+	0.562866i
$544$	1430.05	+	2476.92i	0.112708	+	0.195215i
$545$	−14152.7	+	11875.5i	−1.11236	+	0.933377i
$546$	46.3416	−	16.8670i	0.00363230	−	0.00132205i
$547$	22033.0	+	8019.34i	1.72223	+	0.626841i	0.998030	−	0.0627456i	$-0.0199857\pi$
$547$	22033.0	+	8019.34i	1.72223	+	0.626841i	0.724203	+	0.689587i	$0.242208\pi$
$548$	1296.24	+	1087.67i	0.101045	+	0.0847866i
$549$	1731.74	−	9821.20i	0.134625	−	0.763494i
$550$	8165.51			0.633052
$551$	11474.0	+	18848.1i	0.887130	+	1.45727i
$552$	2065.93			0.159297
$553$	−143.723	+	815.094i	−0.0110519	+	0.0626787i
$554$	12028.8	+	10093.4i	0.922481	+	0.774053i
$555$	7524.35	+	2738.64i	0.575479	+	0.209457i
$556$	−5177.38	+	1884.41i	−0.394910	+	0.143735i
$557$	2199.71	−	1845.78i	0.167334	−	0.140410i	−0.555275	−	0.831666i	$-0.687387\pi$
$557$	2199.71	−	1845.78i	0.167334	−	0.140410i	0.722609	+	0.691257i	$0.242943\pi$
$558$	−2360.89	−	4089.18i	−0.179112	−	0.310231i
$559$	−554.285	+	960.050i	−0.0419388	+	0.0726401i
$560$	−68.1227	−	386.343i	−0.00514056	−	0.0291535i
$561$	−2287.12	−	12970.9i	−0.172125	−	0.976170i
$562$	−185.460	+	321.226i	−0.0139202	+	0.0241105i
$563$	−9639.92	−	16696.8i	−0.721623	−	1.24989i	−0.960349	−	0.278801i	$-0.910063\pi$
$563$	−9639.92	−	16696.8i	−0.721623	−	1.24989i	0.238725	−	0.971087i	$-0.423270\pi$
$564$	4332.52	−	3635.41i	0.323461	−	0.271416i
$565$	17548.4	−	6387.11i	1.30667	−	0.475589i
$566$	9614.77	+	3499.49i	0.714027	+	0.259884i
$567$	−299.371	−	251.203i	−0.0221736	−	0.0186058i
$568$	−991.988	+	5625.84i	−0.0732797	+	0.415590i
$569$	10628.0			0.783037			0.391519	−	0.920170i	$-0.371950\pi$
$569$	10628.0			0.783037			0.391519	+	0.920170i	$0.371950\pi$
$570$	−1451.49	+	9520.51i	−0.106660	+	0.699597i
$571$	−23994.9			−1.75859			−0.879296	−	0.476276i	$-0.841986\pi$
$571$	−23994.9			−1.75859			−0.879296	+	0.476276i	$0.841986\pi$
$572$	−106.900	+	606.260i	−0.00781419	+	0.0443165i
$573$	−9646.51	−	8094.38i	−0.703296	−	0.590136i
$574$	751.856	+	273.653i	0.0546722	+	0.0198991i
$575$	−6723.25	+	2447.06i	−0.487615	+	0.177478i
$576$	−606.226	+	508.684i	−0.0438531	+	0.0367972i
$577$	3421.54	+	5926.28i	0.246864	+	0.427581i	0.962654	−	0.270734i	$-0.0872665\pi$
$577$	3421.54	+	5926.28i	0.246864	+	0.427581i	−0.715790	+	0.698316i	$0.753933\pi$
$578$	−3075.47	+	5326.87i	−0.221320	+	0.383337i
$579$	−278.545	−	1579.70i	−0.0199929	−	0.113386i
$580$	2812.66	+	15951.4i	0.201361	+	1.14197i
$581$	−708.256	+	1226.74i	−0.0505739	+	0.0875965i
$582$	−6280.70	−	10878.5i	−0.447326	−	0.774791i
$583$	12035.9	−	10099.4i	0.855022	−	0.717449i
$584$	−800.976	+	291.532i	−0.0567545	+	0.0206570i
$585$	705.565	+	256.805i	0.0498658	+	0.0181497i
$586$	5482.30	+	4600.20i	0.386471	+	0.324287i
$587$	−2520.10	+	14292.2i	−0.177199	+	1.00495i	0.758376	+	0.651817i	$0.225993\pi$
$587$	−2520.10	+	14292.2i	−0.177199	+	1.00495i	−0.935575	+	0.353128i	$0.885118\pi$
$588$	−5208.83			−0.365320
$589$	−12346.1	−	9879.98i	−0.863689	−	0.691167i
$590$	17892.8			1.24853
$591$	1352.05	−	7667.87i	0.0941049	−	0.533695i
$592$	1687.98	+	1416.38i	0.117189	+	0.0983328i
$593$	17822.2	+	6486.75i	1.23418	+	0.449205i	0.875028	−	0.484073i	$-0.160843\pi$
$593$	17822.2	+	6486.75i	1.23418	+	0.449205i	0.359154	+	0.933278i	$0.383065\pi$
$594$	10902.2	−	3968.08i	0.753069	−	0.274095i
$595$	1678.76	−	1408.64i	0.115668	−	0.0970568i
$596$	−6874.28	−	11906.6i	−0.472452	−	0.818312i
$597$	4853.30	−	8406.17i	0.332718	−	0.576284i
$598$	−93.6672	−	531.213i	−0.00640525	−	0.0363260i
$599$	−1075.07	−	6097.00i	−0.0733322	−	0.415888i	−0.999270	−	0.0382109i	$-0.987834\pi$
$599$	−1075.07	−	6097.00i	−0.0733322	−	0.415888i	0.925937	−	0.377677i	$-0.123277\pi$
$600$	−1621.86	+	2809.15i	−0.110354	+	0.191139i
$601$	1672.47	+	2896.80i	0.113513	+	0.196611i	0.917184	−	0.398463i	$-0.130456\pi$
$601$	1672.47	+	2896.80i	0.113513	+	0.196611i	−0.803671	+	0.595074i	$0.797123\pi$
$602$	−685.802	+	575.456i	−0.0464306	+	0.0389599i
$603$	−2375.98	+	864.785i	−0.160460	+	0.0584026i
$604$	−3639.17	−	1324.55i	−0.245159	−	0.0892305i
$605$	−1779.38	−	1493.08i	−0.119574	−	0.100334i
$606$	−2155.73	+	12225.8i	−0.144506	+	0.819534i
$607$	19504.6			1.30423			0.652113	−	0.758122i	$-0.273883\pi$
$607$	19504.6			1.30423			0.652113	+	0.758122i	$0.273883\pi$
$608$	−1271.42	+	2325.32i	−0.0848072	+	0.155106i
$609$	−1644.34			−0.109412
$610$	4257.05	−	24142.9i	0.282562	−	1.60249i
$611$	−1131.21	−	949.194i	−0.0748996	−	0.0628482i
$612$	−4154.11	−	1511.97i	−0.274379	−	0.0998658i
$613$	14556.2	−	5298.03i	0.959087	−	0.349079i	0.185411	−	0.982661i	$-0.440638\pi$
$613$	14556.2	−	5298.03i	0.959087	−	0.349079i	0.773676	+	0.633582i	$0.218416\pi$
$614$	1153.08	−	967.549i	0.0757891	−	0.0635946i
$615$	−7208.95	−	12486.3i	−0.472671	−	0.818690i
$616$	−248.576	+	430.546i	−0.0162588	+	0.0281610i
$617$	−1718.15	−	9744.13i	−0.112107	−	0.635792i	−0.988142	−	0.153544i	$-0.950931\pi$
$617$	−1718.15	−	9744.13i	−0.112107	−	0.635792i	0.876035	−	0.482248i	$-0.160180\pi$
$618$	−131.610	−	746.398i	−0.00856657	−	0.0485834i
$619$	11028.8	−	19102.4i	0.716130	−	1.24037i	−0.246392	−	0.969170i	$-0.579245\pi$
$619$	11028.8	−	19102.4i	0.716130	−	1.24037i	0.962522	−	0.271203i	$-0.0874215\pi$
$620$	−5803.64	−	10052.2i	−0.375935	−	0.651139i
$621$	−7787.40	+	6534.40i	−0.503217	+	0.422249i
$622$	−737.511	+	268.432i	−0.0475426	+	0.0173041i
$623$	−716.533	−	260.797i	−0.0460791	−	0.0167714i
$624$	−187.337	−	157.194i	−0.0120184	−	0.0100846i
$625$	−3063.15	+	17372.0i	−0.196041	+	1.11181i
$626$	−5532.61			−0.353239
$627$	9164.31	−	8059.96i	0.583712	−	0.513372i
$628$	−6710.86			−0.426421
$629$	−2137.45	+	12122.1i	−0.135494	+	0.768424i
$630$	464.501	+	389.762i	0.0293748	+	0.0246484i
$631$	7694.35	+	2800.51i	0.485431	+	0.176683i	0.573130	−	0.819465i	$-0.305729\pi$
$631$	7694.35	+	2800.51i	0.485431	+	0.176683i	−0.0876987	+	0.996147i	$0.527951\pi$
$632$	3856.79	−	1403.76i	0.242745	−	0.0883519i
$633$	−3898.20	+	3270.98i	−0.244770	+	0.205387i
$634$	−5581.12	−	9666.78i	−0.349613	−	0.605547i
$635$	−4387.48	+	7599.33i	−0.274192	+	0.474914i
$636$	1083.82	+	6146.65i	0.0675728	+	0.383224i
$637$	236.163	+	1339.35i	0.0146893	+	0.0833074i
$638$	10263.2	−	17776.4i	0.636872	−	1.10310i
$639$	−4414.86	−	7646.75i	−0.273316	−	0.473397i
$640$	−1490.25	+	1250.47i	−0.0920428	+	0.0772330i
$641$	−23626.9	+	8599.48i	−1.45586	+	0.529889i	−0.944221	−	0.329312i	$-0.893183\pi$
$641$	−23626.9	+	8599.48i	−1.45586	+	0.529889i	−0.511637	+	0.859201i	$0.670961\pi$
$642$	−12231.8	−	4452.00i	−0.751947	−	0.273686i
$643$	19692.2	+	16523.7i	1.20775	+	1.01342i	0.999374	+	0.0353759i	$0.0112628\pi$
$643$	19692.2	+	16523.7i	1.20775	+	1.01342i	0.208378	+	0.978048i	$0.433182\pi$
$644$	75.6431	−	428.993i	0.00462850	−	0.0262495i
$645$	16132.4			0.984823
$646$	−14800.5	+	344.001i	−0.901418	+	0.0209513i
$647$	−4723.46			−0.287014			−0.143507	−	0.989649i	$-0.545838\pi$
$647$	−4723.46			−0.287014			−0.143507	+	0.989649i	$0.545838\pi$
$648$	−336.520	+	1908.50i	−0.0204008	+	0.115699i
$649$	−17370.0	−	14575.1i	−1.05059	−	0.881546i
$650$	795.851	+	289.666i	0.0480244	+	0.0174794i
$651$	1107.29	−	403.020i	0.0666637	−	0.0242636i
$652$	−2679.10	+	2248.03i	−0.160923	+	0.135030i
$653$	5177.17	+	8967.12i	0.310258	+	0.537382i	0.978418	−	0.206635i	$-0.0662513\pi$
$653$	5177.17	+	8967.12i	0.310258	+	0.537382i	−0.668160	+	0.744017i	$0.732918\pi$
$654$	−4650.31	+	8054.58i	−0.278045	+	0.481589i
$655$	6980.33	+	39587.4i	0.416403	+	2.36154i
$656$	−688.974	−	3907.36i	−0.0410059	−	0.232556i
$657$	658.741	−	1140.97i	0.0391171	−	0.0677528i
$658$	−596.264	−	1032.76i	−0.0353264	−	0.0611872i
$659$	−23336.0	+	19581.2i	−1.37943	+	1.15748i	−0.410002	+	0.912084i	$0.634472\pi$
$659$	−23336.0	+	19581.2i	−1.37943	+	1.15748i	−0.969424	+	0.245392i	$0.921083\pi$
$660$	8418.37	−	3064.03i	0.496492	−	0.180708i
$661$	3139.98	+	1142.86i	0.184767	+	0.0672497i	0.432747	−	0.901516i	$-0.357544\pi$
$661$	3139.98	+	1142.86i	0.184767	+	0.0672497i	−0.247980	+	0.968765i	$0.579767\pi$
$662$	−6428.65	−	5394.28i	−0.377427	−	0.316699i
$663$	237.220	−	1345.34i	0.0138957	−	0.0788064i
$664$	7024.32			0.410537
$665$	1923.80	+	649.992i	0.112183	+	0.0379032i
$666$	−3405.84			−0.198159
$667$	−3123.16	+	17712.3i	−0.181303	+	1.02822i
$668$	8240.63	+	6914.71i	0.477305	+	0.400506i
$669$	10475.8	+	3812.89i	0.605410	+	0.220351i
$670$	−5840.73	+	2125.85i	−0.336787	+	0.122580i
$671$	−23799.0	+	19969.7i	−1.36923	+	1.14892i
$672$	−98.7461	−	171.033i	−0.00566847	−	0.00981808i
$673$	10759.0	−	18635.2i	0.616241	−	1.06736i	−0.373924	−	0.927459i	$-0.621988\pi$
$673$	10759.0	−	18635.2i	0.616241	−	1.06736i	0.990165	−	0.139902i	$-0.0446787\pi$
$674$	1354.96	+	7684.35i	0.0774348	+	0.439154i
$675$	−2771.64	−	15718.8i	−0.158045	−	0.896319i
$676$	4362.07	−	7555.33i	0.248184	−	0.429867i
$677$	299.227	+	518.276i	0.0169870	+	0.0294224i	0.874394	−	0.485217i	$-0.161259\pi$
$677$	299.227	+	518.276i	0.0169870	+	0.0294224i	−0.857407	+	0.514639i	$0.827926\pi$
$678$	7201.70	−	6042.94i	0.407934	−	0.342298i
$679$	−2488.89	+	905.884i	−0.140670	+	0.0511997i
$680$	−10211.8	−	3716.80i	−0.575890	−	0.209607i
$681$	−2369.22	−	1988.02i	−0.133317	−	0.111866i
$682$	−2554.28	+	14486.0i	−0.143414	+	0.813341i
$683$	−16817.3			−0.942159			−0.471080	−	0.882091i	$-0.656136\pi$
$683$	−16817.3			−0.942159			−0.471080	+	0.882091i	$0.656136\pi$
$684$	−804.858	−	4016.44i	−0.0449920	−	0.224521i
$685$	−6429.34			−0.358617
$686$	−382.895	+	2171.51i	−0.0213105	+	0.120858i
$687$	13239.2	+	11109.0i	0.735238	+	0.616938i
$688$	4171.71	+	1518.38i	0.231170	+	0.0841390i
$689$	1531.35	−	557.366i	0.0846731	−	0.0308185i
$690$	−6013.20	+	5045.68i	−0.331766	+	0.278385i
$691$	4977.75	+	8621.72i	0.274041	+	0.474654i	0.969893	−	0.243532i	$-0.0783061\pi$
$691$	4977.75	+	8621.72i	0.274041	+	0.474654i	−0.695851	+	0.718186i	$0.744973\pi$
$692$	3631.45	−	6289.86i	0.199490	−	0.345527i
$693$	−133.435	−	756.747i	−0.00731425	−	0.0414812i
$694$	4106.67	+	23290.1i	0.224621	+	1.27389i
$695$	10467.2	−	18129.7i	0.571285	−	0.989495i
$696$	4077.03	+	7061.63i	0.222040	+	0.384584i
$697$	16978.5	−	14246.6i	0.922676	−	0.774217i
$698$	2057.59	−	748.900i	0.111577	−	0.0406107i
$699$	11380.5	+	4142.15i	0.615806	+	0.224135i
$700$	523.939	+	439.637i	0.0282901	+	0.0237382i
$701$	4172.16	−	23661.5i	0.224794	−	1.27487i	−0.638285	−	0.769800i	$-0.720356\pi$
$701$	4172.16	−	23661.5i	0.224794	−	1.27487i	0.863079	−	0.505069i	$-0.168533\pi$
$702$	1203.35			0.0646972
$703$	−10624.4	+	4148.99i	−0.569994	+	0.222592i
$704$	2465.32			0.131982
$705$	−3731.57	+	21162.8i	−0.199346	+	1.13055i
$706$	−4642.81	−	3895.78i	−0.247499	−	0.207677i
$707$	2459.76	+	895.279i	0.130847	+	0.0476244i
$708$	8464.31	−	3080.76i	0.449305	−	0.163534i
$709$	−16021.0	+	13443.2i	−0.848635	+	0.712089i	−0.959489	−	0.281748i	$-0.909086\pi$
$709$	−16021.0	+	13443.2i	−0.848635	+	0.712089i	0.110854	+	0.993837i	$0.464641\pi$
$710$	−10852.8	−	18797.6i	−0.573660	−	0.993607i
$711$	−3171.91	+	5493.91i	−0.167308	+	0.289786i
$712$	656.605	+	3723.79i	0.0345609	+	0.196004i
$713$	−2238.09	−	12692.8i	−0.117556	−	0.666691i
$714$	551.610	−	955.416i	0.0289124	−	0.0500778i
$715$	−1169.54	−	2025.69i	−0.0611722	−	0.105953i
$716$	−1141.13	+	957.523i	−0.0595616	+	0.0499781i
$717$	−15720.4	+	5721.76i	−0.818814	+	0.298024i
$718$	−5442.00	−	1980.73i	−0.282860	−	0.102953i
$719$	−4943.23	−	4147.86i	−0.256400	−	0.215145i	0.505523	−	0.862813i	$-0.331300\pi$
$719$	−4943.23	−	4147.86i	−0.256400	−	0.215145i	−0.761922	+	0.647669i	$0.775744\pi$
$720$	522.139	−	2961.20i	0.0270264	−	0.153274i
$721$	−159.809			−0.00825466
$722$	−7403.55	−	11548.6i	−0.381622	−	0.595285i
$723$	−10833.5			−0.557266
$724$	1493.18	−	8468.22i	0.0766484	−	0.434695i
$725$	−21632.4	−	18151.8i	−1.10815	−	0.929848i
$726$	−1098.83	−	399.941i	−0.0561726	−	0.0204452i
$727$	16271.3	−	5922.25i	0.830079	−	0.302124i	0.108188	−	0.994130i	$-0.465495\pi$
$727$	16271.3	−	5922.25i	0.830079	−	0.302124i	0.721891	+	0.692006i	$0.243273\pi$
$728$	−39.5007	+	33.1451i	−0.00201098	+	0.00168741i
$729$	−9275.07	−	16064.9i	−0.471222	−	0.816181i
$730$	1619.35	−	2804.79i	0.0821023	−	0.142205i
$731$	4306.36	+	24422.6i	0.217889	+	1.23571i
$732$	−2143.07	−	12154.0i	−0.108211	−	0.613693i
$733$	−200.224	+	346.798i	−0.0100893	+	0.0174751i	−0.871026	−	0.491237i	$-0.836545\pi$
$733$	−200.224	+	346.798i	−0.0100893	+	0.0174751i	0.860937	+	0.508712i	$0.169878\pi$
$734$	3621.54	+	6272.69i	0.182117	+	0.315435i
$735$	15161.1	−	12721.6i	0.760849	−	0.638428i
$736$	−2029.87	+	738.813i	−0.101660	+	0.0370013i
$737$	7401.75	+	2694.02i	0.369942	+	0.134648i
$738$	4697.82	+	3941.94i	0.234322	+	0.196619i
$739$	2759.21	−	15648.2i	0.137347	−	0.778931i	−0.835850	−	0.548957i	$-0.815025\pi$
$739$	2759.21	−	15648.2i	0.137347	−	0.778931i	0.973197	−	0.229974i	$-0.0738640\pi$
$740$	−8372.39			−0.415912
$741$	1179.12	−	460.466i	0.0584562	−	0.0228281i
$742$	1316.04			0.0651124
$743$	4058.11	−	23014.7i	0.200374	−	1.13638i	−0.704182	−	0.710020i	$-0.748686\pi$
$743$	4058.11	−	23014.7i	0.200374	−	1.13638i	0.904556	−	0.426356i	$-0.140203\pi$
$744$	−4476.23	−	3756.00i	−0.220573	−	0.185083i
$745$	49088.4	+	17866.7i	2.41404	+	0.878639i
$746$	10656.7	−	3878.73i	0.523016	−	0.190362i
$747$	−8317.03	+	6978.82i	−0.407369	+	0.341823i
$748$	6885.80	+	11926.6i	0.336591	+	0.582992i
$749$	−1372.32	+	2376.93i	−0.0669474	+	0.115956i
$750$	383.879	+	2177.09i	0.0186897	+	0.105995i
$751$	5040.78	+	28587.7i	0.244928	+	1.38905i	0.820660	+	0.571416i	$0.193606\pi$
$751$	5040.78	+	28587.7i	0.244928	+	1.38905i	−0.575732	+	0.817638i	$0.695283\pi$
$752$	−2956.80	+	5121.33i	−0.143382	+	0.248346i
$753$	−3183.11	−	5513.31i	−0.154049	−	0.266821i
$754$	1630.91	−	1368.49i	0.0787721	−	0.0660977i
$755$	13827.3	−	5032.74i	0.666527	−	0.242596i
$756$	913.183	+	332.372i	0.0439314	+	0.0159897i
$757$	−23139.1	−	19416.0i	−1.11097	−	0.932215i	−0.112857	−	0.993611i	$-0.536000\pi$
$757$	−23139.1	−	19416.0i	−1.11097	−	0.932215i	−0.998113	+	0.0613960i	$0.980445\pi$
$758$	−3307.81	+	18759.5i	−0.158503	+	0.898914i
$759$	9947.61			0.475725
$760$	−1978.54	−	9873.40i	−0.0944331	−	0.471245i
$761$	−6718.85			−0.320050			−0.160025	−	0.987113i	$-0.551158\pi$
$761$	−6718.85			−0.320050			−0.160025	+	0.987113i	$0.551158\pi$
$762$	−767.084	+	4350.35i	−0.0364679	+	0.206820i
$763$	1502.27	+	1260.56i	0.0712791	+	0.0598102i
$764$	12372.8	+	4503.33i	0.585906	+	0.213253i
$765$	15783.9	−	5744.86i	0.745970	−	0.271511i
$766$	11194.7	−	9393.43i	0.528041	−	0.443079i
$767$	−1175.92	−	2036.75i	−0.0553584	−	0.0958836i
$768$	−489.670	+	848.134i	−0.0230071	+	0.0398495i
$769$	−5834.53	−	33089.3i	−0.273600	−	1.55166i	−0.743373	−	0.668877i	$-0.766775\pi$
$769$	−5834.53	−	33089.3i	−0.273600	−	1.55166i	0.469773	−	0.882787i	$-0.344336\pi$
$770$	−328.016	−	1860.27i	−0.0153518	−	0.0870643i
$771$	8670.68	−	15018.1i	0.405015	−	0.701507i
$772$	838.611	+	1452.52i	0.0390962	+	0.0677166i
$773$	−10041.6	+	8425.92i	−0.467234	+	0.392056i	−0.845785	−	0.533525i	$-0.820867\pi$
$773$	−10041.6	+	8425.92i	−0.467234	+	0.392056i	0.378550	+	0.925581i	$0.376423\pi$
$774$	−6447.99	+	2346.88i	−0.299442	+	0.108988i
$775$	19016.1	+	6921.30i	0.881392	+	0.320800i
$776$	10061.4	+	8442.52i	0.465442	+	0.390552i
$777$	147.592	−	837.038i	0.00681447	−	0.0386468i
$778$	502.455			0.0231541
$779$	19456.7	+	6573.83i	0.894878	+	0.302352i
$780$	929.189			0.0426543
$781$	−4776.49	+	27088.8i	−0.218843	+	1.24112i
$782$	−9243.75	−	7756.43i	−0.422706	−	0.354692i
$783$	−37703.6	−	13723.0i	−1.72084	−	0.626334i
$784$	5117.90	−	1862.76i	0.233141	−	0.0848562i
$785$	19532.9	−	16390.1i	0.888102	−	0.745206i
$786$	10118.2	+	17525.3i	0.459166	+	0.795299i
$787$	1782.70	−	3087.73i	0.0807451	−	0.139855i	−0.822825	−	0.568295i	$-0.807603\pi$
$787$	1782.70	−	3087.73i	0.0807451	−	0.139855i	0.903570	+	0.428440i	$0.140937\pi$
$788$	1413.71	+	8017.53i	0.0639102	+	0.362453i
$789$	−208.379	−	1181.78i	−0.00940241	−	0.0533237i
$790$	−7797.33	+	13505.4i	−0.351160	+	0.608227i
$791$	−991.136	−	1716.70i	−0.0445522	−	0.0771666i
$792$	−2919.02	+	2449.35i	−0.130963	+	0.109891i
$793$	−3027.98	+	1102.10i	−0.135595	+	0.0493525i
$794$	7789.38	+	2835.10i	0.348155	+	0.126718i
$795$	−18166.7	−	15243.7i	−0.810450	−	0.680048i
$796$	−1762.40	+	9995.05i	−0.0784755	+	0.445057i
$797$	5492.40			0.244104			0.122052	−	0.992524i	$-0.461053\pi$
$797$	5492.40			0.244104			0.122052	+	0.992524i	$0.461053\pi$
$798$	1021.98	−	23.7535i	0.0453355	−	0.00105372i
$799$	−33034.2			−1.46266
$800$	588.954	−	3340.12i	0.0260283	−	0.147614i
$801$	−4477.12	−	3756.75i	−0.197492	−	0.165716i
$802$	5320.57	+	1936.53i	0.234259	+	0.0852634i
$803$	−3856.76	+	1403.75i	−0.169492	+	0.0616900i
$804$	−2396.97	+	2011.30i	−0.105143	+	0.0882253i
$805$	827.570	+	1433.39i	0.0362335	+	0.0627583i
$806$	−762.834	+	1321.27i	−0.0333371	+	0.0577415i
$807$	1890.18	+	10719.7i	0.0824502	+	0.467598i
$808$	−2254.04	−	12783.3i	−0.0981395	−	0.556577i
$809$	−1529.51	+	2649.19i	−0.0664707	+	0.115131i	−0.897345	−	0.441329i	$-0.854507\pi$
$809$	−1529.51	+	2649.19i	−0.0664707	+	0.115131i	0.830875	+	0.556459i	$0.187841\pi$
$810$	−3681.68	−	6376.85i	−0.159705	−	0.276617i
$811$	20114.8	−	16878.3i	0.870932	−	0.730799i	−0.0933623	−	0.995632i	$-0.529761\pi$
$811$	20114.8	−	16878.3i	0.870932	−	0.730799i	0.964294	+	0.264834i	$0.0853170\pi$
$812$	1615.63	−	588.042i	0.0698246	−	0.0254141i
$813$	14540.6	+	5292.34i	0.627258	+	0.228303i
$814$	8127.75	+	6819.99i	0.349972	+	0.293662i
$815$	2307.50	−	13086.5i	0.0991756	−	0.562453i
$816$	−5470.73			−0.234698
$817$	−17255.3	+	15175.9i	−0.738905	+	0.649863i
$818$	18712.3			0.799828
$819$	13.8399	−	78.4898i	0.000590481	−	0.00334879i
$820$	11548.4	+	9690.26i	0.491814	+	0.412681i
$821$	−8189.50	−	2980.74i	−0.348131	−	0.126709i	0.162036	−	0.986785i	$-0.448194\pi$
$821$	−8189.50	−	2980.74i	−0.348131	−	0.126709i	−0.510167	+	0.860076i	$0.670416\pi$
$822$	−3041.45	+	1107.00i	−0.129054	+	0.0469719i
$823$	25509.6	−	21405.1i	1.08045	−	0.906603i	0.0844899	−	0.996424i	$-0.473074\pi$
$823$	25509.6	−	21405.1i	1.08045	−	0.906603i	0.995958	+	0.0898210i	$0.0286295\pi$
$824$	396.238	+	686.303i	0.0167519	+	0.0290152i
$825$	−7809.39	+	13526.3i	−0.329561	+	0.570817i
$826$	−329.806	−	1870.42i	−0.0138928	−	0.0787897i
$827$	−8183.52	−	46411.1i	−0.344098	−	1.95148i	−0.305395	−	0.952226i	$-0.598789\pi$
$827$	−8183.52	−	46411.1i	−0.344098	−	1.95148i	−0.0387026	−	0.999251i	$-0.512322\pi$
$828$	1669.41	−	2891.50i	0.0700676	−	0.121361i
$829$	3895.19	+	6746.68i	0.163191	+	0.282656i	0.936012	−	0.351969i	$-0.114488\pi$
$829$	3895.19	+	6746.68i	0.163191	+	0.282656i	−0.772820	+	0.634625i	$0.781155\pi$
$830$	−20445.3	+	17155.7i	−0.855020	+	0.717447i
$831$	−28223.9	+	10272.7i	−1.17819	+	0.428827i
$832$	240.282	+	87.4554i	0.0100123	+	0.00364420i
$833$	23306.2	+	19556.2i	0.969403	+	0.813426i
$834$	1830.03	−	10378.6i	0.0759818	−	0.430914i
$835$	−40873.5			−1.69400
$836$	−6121.96	+	11196.6i	−0.253268	+	0.463208i
$837$	28752.8			1.18739
$838$	−1147.58	+	6508.25i	−0.0473061	+	0.268286i
$839$	12692.0	+	10649.8i	0.522259	+	0.438227i	0.865418	−	0.501050i	$-0.167053\pi$
$839$	12692.0	+	10649.8i	0.522259	+	0.438227i	−0.343159	+	0.939277i	$0.611497\pi$
$840$	705.134	+	256.648i	0.0289636	+	0.0105419i
$841$	−43788.2	+	15937.6i	−1.79541	+	0.653475i
$842$	2402.30	−	2015.77i	0.0983240	−	0.0825036i
$843$	−354.743	−	614.433i	−0.0144935	−	0.0251034i
$844$	2660.40	−	4607.95i	0.108501	−	0.187929i
$845$	5756.11	+	32644.5i	0.234339	+	1.32900i
$846$	−1587.21	−	9001.49i	−0.0645027	−	0.365813i
$847$	−123.281	+	213.529i	−0.00500117	+	0.00866227i
$848$	−3263.05	−	5651.77i	−0.132139	−	0.228871i
$849$	−14992.4	+	12580.1i	−0.606051	+	0.508537i
$850$	17803.6	−	6479.99i	0.718423	−	0.261484i
$851$	−8735.99	−	3179.64i	−0.351899	−	0.128081i
$852$	−8370.54	−	7023.72i	−0.336585	−	0.282428i
$853$	−7211.29	+	40897.3i	−0.289461	+	1.64161i	0.399442	+	0.916759i	$0.369204\pi$
$853$	−7211.29	+	40897.3i	−0.289461	+	1.64161i	−0.688902	+	0.724854i	$0.741907\pi$
$854$	−2602.25			−0.104271
$855$	12152.1	+	9724.72i	0.486074	+	0.388981i
$856$	13610.4			0.543450
$857$	5777.75	−	32767.3i	0.230297	−	1.30608i	−0.621999	−	0.783018i	$-0.713679\pi$
$857$	5777.75	−	32767.3i	0.230297	−	1.30608i	0.852296	−	0.523060i	$-0.175210\pi$
$858$	−902.039	−	756.900i	−0.0358917	−	0.0301167i
$859$	−25454.8	−	9264.81i	−1.01107	−	0.367999i	−0.217226	−	0.976121i	$-0.569701\pi$
$859$	−25454.8	−	9264.81i	−1.01107	−	0.367999i	−0.793843	+	0.608123i	$0.791923\pi$
$860$	−15850.8	+	5769.20i	−0.628496	+	0.228754i
$861$	−1172.37	+	983.739i	−0.0464047	+	0.0389381i
$862$	−9995.25	−	17312.3i	−0.394942	−	0.684059i
$863$	−19758.7	+	34223.1i	−0.779368	+	1.34991i	0.152938	+	0.988236i	$0.451127\pi$
$863$	−19758.7	+	34223.1i	−0.779368	+	1.34991i	−0.932306	+	0.361670i	$0.882207\pi$
$864$	−836.809	−	4745.78i	−0.0329500	−	0.186869i
$865$	4791.99	+	27176.7i	0.188361	+	1.06825i
$866$	−9482.84	+	16424.8i	−0.372102	+	0.644499i
$867$	−5882.68	−	10189.1i	−0.230434	−	0.399123i
$868$	−943.833	+	791.970i	−0.0369076	+	0.0309691i
$869$	18570.7	−	6759.19i	0.724935	−	0.263855i
$870$	−29113.6	−	10596.5i	−1.13453	−	0.412936i
$871$	625.842	+	525.144i	0.0243466	+	0.0204292i
$872$	1688.69	−	9577.01i	0.0655804	−	0.371925i
$873$	−20300.9			−0.787034
$874$	1685.23	−	11053.6i	0.0652215	−	0.427796i
$875$	466.130			0.0180092
$876$	283.118	−	1605.64i	0.0109197	−	0.0619288i
$877$	−3730.15	−	3129.96i	−0.143624	−	0.120515i	0.568145	−	0.822928i	$-0.307661\pi$
$877$	−3730.15	−	3129.96i	−0.143624	−	0.120515i	−0.711769	+	0.702414i	$0.752106\pi$
$878$	−13130.3	−	4779.02i	−0.504698	−	0.183695i
$879$	−12863.5	+	4681.92i	−0.493600	+	0.179656i
$880$	−7175.67	+	6021.10i	−0.274877	+	0.230649i
$881$	13795.9	+	23895.2i	0.527577	+	0.913790i	0.999483	+	0.0321414i	$0.0102327\pi$
$881$	13795.9	+	23895.2i	0.527577	+	0.913790i	−0.471906	+	0.881649i	$0.656434\pi$
$882$	−4209.07	+	7290.33i	−0.160688	+	0.278320i
$883$	−5778.40	−	32771.0i	−0.220225	−	1.24896i	−0.871606	−	0.490208i	$-0.836921\pi$
$883$	−5778.40	−	32771.0i	−0.220225	−	1.24896i	0.651381	−	0.758751i	$-0.274190\pi$
$884$	248.037	+	1406.69i	0.00943710	+	0.0535205i
$885$	−17112.4	+	29639.6i	−0.649975	+	1.12579i
$886$	8703.04	+	15074.1i	0.330005	+	0.571586i
$887$	25970.6	−	21791.9i	0.983097	−	0.824916i	−0.00145677	−	0.999999i	$-0.500464\pi$
$887$	25970.6	−	21791.9i	0.983097	−	0.824916i	0.984554	+	0.175083i	$0.0560193\pi$
$888$	−3960.62	+	1441.55i	−0.149673	+	0.0544765i
$889$	875.268	+	318.572i	0.0330209	+	0.0120186i
$890$	−11005.9	−	9235.01i	−0.414514	−	0.347818i
$891$	−1620.37	+	9189.55i	−0.0609251	+	0.345524i
$892$	−11656.5			−0.437544
$893$	−15916.8	−	26146.2i	−0.596457	−	0.979787i
$894$	26297.9			0.983818
$895$	982.851	−	5574.02i	0.0367073	−	0.208178i
$896$	158.187	+	132.734i	0.00589805	+	0.00494905i
$897$	969.543	+	352.885i	0.0360893	+	0.0131354i
$898$	26218.8	−	9542.87i	0.974314	−	0.354621i
$899$	38969.0	−	32698.9i	1.44571	−	1.21309i
$900$	2621.15	+	4539.96i	0.0970795	+	0.168147i
$901$	18227.8	−	31571.6i	0.673982	−	1.16737i
$902$	−3317.46	−	18814.2i	−0.122460	−	0.694507i
$903$	−297.357	−	1686.40i	−0.0109584	−	0.0621481i
$904$	−4914.93	+	8512.90i	−0.180828	+	0.313202i
$905$	16336.0	+	28294.8i	0.600031	+	1.03928i
$906$	5674.59	−	4761.55i	0.208086	−	0.174605i
$907$	30016.1	−	10925.0i	1.09886	−	0.399954i	0.271966	−	0.962307i	$-0.412326\pi$
$907$	30016.1	−	10925.0i	1.09886	−	0.399954i	0.826897	+	0.562353i	$0.190104\pi$
$908$	3038.82	+	1106.04i	0.111065	+	0.0404242i
$909$	15369.3	+	12896.4i	0.560801	+	0.470568i
$910$	34.0218	−	192.947i	0.00123935	−	0.00702872i
$911$	21773.0			0.791847			0.395923	−	0.918284i	$-0.370425\pi$
$911$	21773.0			0.791847			0.395923	+	0.918284i	$0.370425\pi$
$912$	−2635.95	−	4330.02i	−0.0957074	−	0.157216i
$913$	33822.6			1.22603
$914$	−2453.48	+	13914.4i	−0.0887899	+	0.503552i
$915$	35921.6	+	30141.8i	1.29785	+	1.08902i
$916$	−16980.9	−	6180.55i	−0.612517	−	0.222938i
$917$	4009.61	−	1459.38i	0.144394	−	0.0525550i
$918$	20621.6	−	17303.6i	0.741409	−	0.622116i
$919$	−5496.75	−	9520.65i	−0.197303	−	0.341738i	0.750350	−	0.661040i	$-0.229885\pi$
$919$	−5496.75	−	9520.65i	−0.197303	−	0.341738i	−0.947653	+	0.319302i	$0.896551\pi$
$920$	4103.82	−	7108.02i	0.147064	−	0.254722i
$921$	499.965	+	2835.44i	0.0178875	+	0.101445i
$922$	1097.85	+	6226.20i	0.0392144	+	0.222396i
$923$	−1426.50	+	2470.77i	−0.0508708	+	0.0881108i
$924$	−475.469	−	823.537i	−0.0169284	−	0.0293208i
$925$	11181.7	−	9382.57i	0.397462	−	0.333510i
$926$	−16492.3	+	6002.72i	−0.585283	+	0.213026i
$927$	−1151.02	−	418.936i	−0.0407814	−	0.0148432i
$928$	−6531.23	−	5480.35i	−0.231032	−	0.193859i
$929$	6014.95	−	34112.5i	0.212427	−	1.20473i	−0.672890	−	0.739742i	$-0.734947\pi$
$929$	6014.95	−	34112.5i	0.212427	−	1.20473i	0.885317	−	0.464988i	$-0.153942\pi$
$930$	22202.1			0.782834
$931$	−4248.95	+	27869.4i	−0.149574	+	0.981076i
$932$	−12663.1			−0.445058
$933$	260.685	−	1478.42i	0.00914733	−	0.0518771i
$934$	−26457.9	−	22200.8i	−0.926906	−	0.777766i
$935$	−49170.6	−	17896.7i	−1.71984	−	0.625971i
$936$	−371.391	+	135.175i	−0.0129693	+	0.00472045i
$937$	−1354.71	+	1136.74i	−0.0472321	+	0.0396324i	−0.666098	−	0.745864i	$-0.732037\pi$
$937$	−1354.71	+	1136.74i	−0.0472321	+	0.0396324i	0.618866	+	0.785497i	$0.287592\pi$
$938$	329.885	+	571.377i	0.0114831	+	0.0198893i
$939$	5291.31	−	9164.82i	0.183893	−	0.318512i
$940$	−3901.74	−	22127.9i	−0.135384	−	0.767800i
$941$	4268.83	+	24209.8i	0.147885	+	0.838699i	0.965005	+	0.262231i	$0.0844582\pi$
$941$	4268.83	+	24209.8i	0.147885	+	0.838699i	−0.817120	+	0.576468i	$0.804431\pi$
$942$	6418.18	−	11116.6i	0.221991	−	0.384500i
$943$	8369.80	+	14496.9i	0.289033	+	0.500620i
$944$	−7214.83	+	6053.96i	−0.248753	+	0.208728i
$945$	−3469.71	+	1262.87i	−0.119439	+	0.0434722i
$946$	20087.1	+	7311.10i	0.690367	+	0.251273i
$947$	703.399	+	590.222i	0.0241366	+	0.0202530i	0.654776	−	0.755823i	$-0.272763\pi$
$947$	703.399	+	590.222i	0.0241366	+	0.0202530i	−0.630640	+	0.776076i	$0.717207\pi$
$948$	−1363.25	+	7731.35i	−0.0467048	+	0.264876i
$949$	−425.695			−0.0145613
$950$	13707.1	+	10969.1i	0.468124	+	0.374616i
$951$	21350.8			0.728022
$952$	−200.308	+	1136.00i	−0.00681935	+	0.0386744i
$953$	−7280.66	−	6109.20i	−0.247475	−	0.207656i	0.510609	−	0.859813i	$-0.329420\pi$
$953$	−7280.66	−	6109.20i	−0.247475	−	0.207656i	−0.758084	+	0.652157i	$0.773864\pi$
$954$	9478.72	+	3449.97i	0.321682	+	0.117083i
$955$	−47011.5	+	17110.8i	−1.59294	+	0.579782i
$956$	13399.8	−	11243.8i	0.453327	−	0.380386i
$957$	19631.2	+	34002.3i	0.663100	+	1.14852i
$958$	2180.31	−	3776.42i	0.0735311	−	0.127360i
$959$	118.508	+	672.091i	0.00399043	+	0.0226308i
$960$	−646.159	−	3664.55i	−0.0217236	−	0.123201i
$961$	−3331.69	+	5770.66i	−0.111836	+	0.193705i
$962$	550.235	+	953.036i	0.0184411	+	0.0319409i
$963$	−16115.2	+	13522.2i	−0.539256	+	0.452490i
$964$	10644.4	−	3874.26i	0.355637	−	0.129441i
$965$	−5988.42	−	2179.61i	−0.199766	−	0.0727088i
$966$	638.288	+	535.587i	0.0212594	+	0.0178387i
$967$	5068.67	−	28745.8i	0.168560	−	0.955950i	−0.776758	−	0.629799i	$-0.783137\pi$
$967$	5068.67	−	28745.8i	0.168560	−	0.955950i	0.945318	−	0.326151i	$-0.105752\pi$
$968$	1222.67			0.0405973
$969$	13585.1	−	24846.1i	0.450379	−	0.823707i
$970$	−49904.5			−1.65190
$971$	−5521.36	+	31313.2i	−0.182481	+	1.03490i	0.746669	+	0.665196i	$0.231652\pi$
$971$	−5521.36	+	31313.2i	−0.182481	+	1.03490i	−0.929150	+	0.369704i	$0.879459\pi$
$972$	9619.41	+	8071.64i	0.317431	+	0.266356i
$973$	−2088.13	−	760.015i	−0.0687998	−	0.0250411i
$974$	−9066.78	+	3300.04i	−0.298274	+	0.108563i
$975$	−1240.98	+	1041.30i	−0.0407621	+	0.0342035i
$976$	6452.12	+	11175.4i	0.211606	+	0.366512i
$977$	4949.16	−	8572.20i	0.162065	−	0.280705i	−0.773544	−	0.633743i	$-0.781518\pi$
$977$	4949.16	−	8572.20i	0.162065	−	0.280705i	0.935609	+	0.353037i	$0.114851\pi$
$978$	−1161.63	−	6587.95i	−0.0379805	−	0.215398i
$979$	3161.60	+	17930.3i	0.103213	+	0.585348i
$980$	−10346.9	+	17921.4i	−0.337266	+	0.584162i
$981$	7515.52	+	13017.3i	0.244599	+	0.423659i
$982$	17115.9	−	14361.9i	0.556202	−	0.466709i
$983$	14423.2	−	5249.61i	0.467984	−	0.170332i	−0.0972550	−	0.995259i	$-0.531006\pi$
$983$	14423.2	−	5249.61i	0.467984	−	0.170332i	0.565239	+	0.824927i	$0.308784\pi$
$984$	7131.52	+	2595.66i	0.231041	+	0.0840921i
$985$	−23696.2	−	19883.5i	−0.766522	−	0.643188i
$986$	8270.33	−	46903.4i	0.267121	−	1.51492i
$987$	2281.04			0.0735625
$988$	−993.867	+	874.101i	−0.0320032	+	0.0281466i
$989$	−18730.1			−0.602208
$990$	2514.14	−	14258.4i	0.0807116	−	0.457739i
$991$	9950.61	+	8349.55i	0.318962	+	0.267641i	0.788185	−	0.615439i	$-0.211021\pi$
$991$	9950.61	+	8349.55i	0.318962	+	0.267641i	−0.469222	+	0.883080i	$0.655466\pi$
$992$	5741.31	+	2089.66i	0.183757	+	0.0668820i
$993$	15084.0	−	5490.11i	0.482050	−	0.175452i
$994$	−1764.97	+	1480.98i	−0.0563192	+	0.0472574i
$995$	−19281.4	−	33396.4i	−0.614334	−	1.06406i
$996$	−6717.96	+	11635.9i	−0.213722	+	0.370177i
$997$	−7581.77	−	42998.4i	−0.240840	−	1.36587i	−0.829959	−	0.557824i	$-0.811637\pi$
$997$	−7581.77	−	42998.4i	−0.240840	−	1.36587i	0.589120	−	0.808046i	$-0.299475\pi$
$998$	5365.99	+	30432.1i	0.170198	+	0.965240i
$999$	10369.8	−	17961.0i	0.328414	−	0.568829i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.4.e.a.17.2	yes	12
19.3	odd	18		722.4.a.o.1.2		6
19.9	even	9	inner	38.4.e.a.9.2	✓	12
19.16	even	9		722.4.a.p.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.e.a.9.2	✓	12	19.9	even	9	inner
38.4.e.a.17.2	yes	12	1.1	even	1	trivial
722.4.a.o.1.2		6	19.3	odd	18
722.4.a.p.1.5		6	19.16	even	9

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.347296 - 1.96962i) q^{2} +(2.93054 + 2.45902i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(14.2818 - 5.19813i) q^{5} +(5.86108 - 4.91803i) q^{6} +(-0.806634 - 1.39713i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-2.14719 - 12.1773i) q^{9} +O(q^{10})\)	\(q+(0.347296 - 1.96962i) q^{2} +(2.93054 + 2.45902i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(14.2818 - 5.19813i) q^{5} +(5.86108 - 4.91803i) q^{6} +(-0.806634 - 1.39713i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-2.14719 - 12.1773i) q^{9} +(-5.27832 - 29.9349i) q^{10} +(-19.2603 + 33.3598i) q^{11} +(-7.65110 - 13.2521i) q^{12} +(-3.06062 + 2.56816i) q^{13} +(-3.03195 + 1.10354i) q^{14} +(54.6355 + 19.8857i) q^{15} +(12.2567 + 10.2846i) q^{16} +(-15.5204 + 88.0204i) q^{17} -24.7304 q^{18} +(-77.1453 + 30.1265i) q^{19} -60.7933 q^{20} +(1.07169 - 6.07787i) q^{21} +(59.0169 + 49.5211i) q^{22} +(-63.4335 - 23.0879i) q^{23} +(-28.7587 + 10.4673i) q^{24} +(81.1923 - 68.1284i) q^{25} +(3.99535 + 6.92015i) q^{26} +(75.2967 - 130.418i) q^{27} +(1.12056 + 6.35503i) q^{28} +(-46.2659 - 262.387i) q^{29} +(58.1419 - 100.705i) q^{30} +(95.4652 + 165.351i) q^{31} +(24.5134 - 20.5692i) q^{32} +(-138.475 + 50.4009i) q^{33} +(167.976 + 61.1383i) q^{34} +(-18.7826 - 15.7605i) q^{35} +(-8.58876 + 48.7093i) q^{36} +137.719 q^{37} +(32.5453 + 162.409i) q^{38} -15.2844 q^{39} +(-21.1133 + 119.739i) q^{40} +(-189.962 - 159.397i) q^{41} +(-11.5989 - 4.22164i) q^{42} +(260.732 - 94.8987i) q^{43} +(118.034 - 99.0422i) q^{44} +(-93.9650 - 162.752i) q^{45} +(-67.5045 + 116.921i) q^{46} +(64.1805 + 363.985i) q^{47} +(10.6288 + 60.2789i) q^{48} +(170.199 - 294.793i) q^{49} +(-105.989 - 183.578i) q^{50} +(-261.927 + 219.782i) q^{51} +(15.0176 - 5.46596i) q^{52} +(-383.283 - 139.504i) q^{53} +(-230.722 - 193.599i) q^{54} +(-101.662 + 576.554i) q^{55} +12.9061 q^{56} +(-300.159 - 101.414i) q^{57} -532.869 q^{58} +(-102.217 + 579.700i) q^{59} +(-178.157 - 149.492i) q^{60} +(757.876 + 275.844i) q^{61} +(358.832 - 130.604i) q^{62} +(-15.2813 + 12.8225i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(-30.3613 + 52.5873i) q^{65} +(51.1784 + 290.247i) q^{66} +(-35.5080 - 201.376i) q^{67} +(178.756 - 309.615i) q^{68} +(-129.121 - 223.644i) q^{69} +(-37.5652 + 31.5210i) q^{70} +(671.014 - 244.229i) q^{71} +(92.9558 + 33.8331i) q^{72} +(81.6202 + 68.4875i) q^{73} +(47.8293 - 271.253i) q^{74} +405.466 q^{75} +(331.187 - 7.69764i) q^{76} +62.1440 q^{77} +(-5.30822 + 30.1044i) q^{78} +(-393.010 - 329.775i) q^{79} +(228.508 + 83.1701i) q^{80} +(227.633 - 82.8518i) q^{81} +(-379.924 + 318.794i) q^{82} +(-439.020 - 760.404i) q^{83} +(-12.3433 + 21.3792i) q^{84} +(235.884 + 1337.76i) q^{85} +(-96.3626 - 546.500i) q^{86} +(509.629 - 882.704i) q^{87} +(-154.082 - 266.878i) q^{88} +(362.075 - 303.817i) q^{89} +(-353.193 + 128.552i) q^{90} +(6.05685 + 2.20451i) q^{91} +(206.846 + 173.564i) q^{92} +(-126.835 + 719.317i) q^{93} +739.201 q^{94} +(-945.168 + 831.271i) q^{95} +122.418 q^{96} +(285.092 - 1616.84i) q^{97} +(-521.519 - 437.606i) q^{98} +(447.589 + 162.909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 9 q^{3} - 18 q^{6} + 21 q^{7} - 48 q^{8} - 27 q^{9}+O(q^{10}) \) 12 * q - 9 * q^3 - 18 * q^6 + 21 * q^7 - 48 * q^8 - 27 * q^9	\( 12 q - 9 q^{3} - 18 q^{6} + 21 q^{7} - 48 q^{8} - 27 q^{9} - 9 q^{11} + 36 q^{12} + 39 q^{13} - 138 q^{14} + 423 q^{15} + 69 q^{17} + 132 q^{18} - 462 q^{19} - 216 q^{20} - 279 q^{21} + 204 q^{22} - 66 q^{23} - 72 q^{24} + 342 q^{25} + 48 q^{26} + 189 q^{27} + 192 q^{28} + 159 q^{29} + 72 q^{31} - 1560 q^{33} + 408 q^{34} - 135 q^{35} - 108 q^{36} + 1116 q^{37} - 294 q^{38} - 1248 q^{39} + 147 q^{41} + 414 q^{42} - 117 q^{43} + 408 q^{44} + 1296 q^{45} + 528 q^{46} + 783 q^{47} + 288 q^{48} + 1413 q^{49} - 354 q^{50} - 2301 q^{51} - 348 q^{52} - 249 q^{53} - 540 q^{54} + 2187 q^{55} - 336 q^{56} - 2670 q^{57} - 1932 q^{58} - 4248 q^{59} + 324 q^{60} + 3114 q^{61} - 438 q^{62} + 363 q^{63} - 384 q^{64} + 495 q^{65} + 822 q^{66} + 3060 q^{67} + 408 q^{68} - 237 q^{69} - 270 q^{70} + 1686 q^{71} + 432 q^{72} + 1626 q^{73} + 90 q^{74} - 1854 q^{75} - 1416 q^{77} - 108 q^{78} - 327 q^{79} + 3483 q^{81} + 294 q^{82} + 927 q^{83} + 204 q^{84} - 3294 q^{85} + 1188 q^{86} + 2892 q^{87} - 72 q^{88} - 6366 q^{89} - 5076 q^{90} + 840 q^{91} - 156 q^{92} + 870 q^{93} + 3432 q^{94} + 513 q^{95} - 576 q^{96} - 8052 q^{97} + 378 q^{98} + 4494 q^{99}+O(q^{100}) \) 12 * q - 9 * q^3 - 18 * q^6 + 21 * q^7 - 48 * q^8 - 27 * q^9 - 9 * q^11 + 36 * q^12 + 39 * q^13 - 138 * q^14 + 423 * q^15 + 69 * q^17 + 132 * q^18 - 462 * q^19 - 216 * q^20 - 279 * q^21 + 204 * q^22 - 66 * q^23 - 72 * q^24 + 342 * q^25 + 48 * q^26 + 189 * q^27 + 192 * q^28 + 159 * q^29 + 72 * q^31 - 1560 * q^33 + 408 * q^34 - 135 * q^35 - 108 * q^36 + 1116 * q^37 - 294 * q^38 - 1248 * q^39 + 147 * q^41 + 414 * q^42 - 117 * q^43 + 408 * q^44 + 1296 * q^45 + 528 * q^46 + 783 * q^47 + 288 * q^48 + 1413 * q^49 - 354 * q^50 - 2301 * q^51 - 348 * q^52 - 249 * q^53 - 540 * q^54 + 2187 * q^55 - 336 * q^56 - 2670 * q^57 - 1932 * q^58 - 4248 * q^59 + 324 * q^60 + 3114 * q^61 - 438 * q^62 + 363 * q^63 - 384 * q^64 + 495 * q^65 + 822 * q^66 + 3060 * q^67 + 408 * q^68 - 237 * q^69 - 270 * q^70 + 1686 * q^71 + 432 * q^72 + 1626 * q^73 + 90 * q^74 - 1854 * q^75 - 1416 * q^77 - 108 * q^78 - 327 * q^79 + 3483 * q^81 + 294 * q^82 + 927 * q^83 + 204 * q^84 - 3294 * q^85 + 1188 * q^86 + 2892 * q^87 - 72 * q^88 - 6366 * q^89 - 5076 * q^90 + 840 * q^91 - 156 * q^92 + 870 * q^93 + 3432 * q^94 + 513 * q^95 - 576 * q^96 - 8052 * q^97 + 378 * q^98 + 4494 * q^99

Introduction

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