LMFDB - Embedded newform 38.4.e.b.9.1

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:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 165 x^{16} - 56 x^{15} + 18435 x^{14} - 11748 x^{13} + 1092662 x^{12} - 1833567 x^{11} + \cdots + 3892796082289 $ x^18 + 165x^16 - 56x^15 + 18435x^14 - 11748x^13 + 1092662x^12 - 1833567x^11 + 46842546x^10 - 93643115x^9 + 1273086000x^8 - 3159018183x^7 + 24752942108x^6 - 51265274250x^5 + 247917053361x^4 - 421854393530x^3 + 1634375353605x^2 - 2066139456366x + 3892796082289
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			9.1
Root			$-3.03492 - 5.25663i$ of defining polynomial
Character	$\chi$	$=$	38.9
Dual form			38.4.e.b.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.347296 - 1.96962i) q^{2} +(-5.68185 + 4.76764i) q^{3} +(-3.75877 + 1.36808i) q^{4} +(18.4168 + 6.70318i) q^{5} +(11.3637 + 9.53528i) q^{6} +(-15.6039 + 27.0267i) q^{7} +(4.00000 + 6.92820i) q^{8} +(4.86455 - 27.5882i) q^{9} +O(q^{10})$	\(q+(-0.347296 - 1.96962i) q^{2} +(-5.68185 + 4.76764i) q^{3} +(-3.75877 + 1.36808i) q^{4} +(18.4168 + 6.70318i) q^{5} +(11.3637 + 9.53528i) q^{6} +(-15.6039 + 27.0267i) q^{7} +(4.00000 + 6.92820i) q^{8} +(4.86455 - 27.5882i) q^{9} +(6.80659 - 38.6021i) q^{10} +(-5.32996 - 9.23176i) q^{11} +(14.8343 - 25.6937i) q^{12} +(-13.5424 - 11.3634i) q^{13} +(58.6514 + 21.3474i) q^{14} +(-136.600 + 49.7184i) q^{15} +(12.2567 - 10.2846i) q^{16} +(4.26583 + 24.1927i) q^{17} -56.0276 q^{18} +(82.5804 - 6.28253i) q^{19} -78.3952 q^{20} +(-40.1947 - 227.955i) q^{21} +(-16.3319 + 13.7041i) q^{22} +(46.1683 - 16.8039i) q^{23} +(-55.7586 - 20.2945i) q^{24} +(198.492 + 166.554i) q^{25} +(-17.6783 + 30.6198i) q^{26} +(3.75981 + 6.51218i) q^{27} +(21.6767 - 122.935i) q^{28} +(-18.7077 + 106.096i) q^{29} +(145.367 + 251.783i) q^{30} +(147.979 - 256.307i) q^{31} +(-24.5134 - 20.5692i) q^{32} +(74.2977 + 27.0422i) q^{33} +(46.1688 - 16.8041i) q^{34} +(-468.539 + 393.151i) q^{35} +(19.4582 + 110.353i) q^{36} -68.5088 q^{37} +(-41.0541 - 160.470i) q^{38} +131.122 q^{39} +(27.2264 + 154.408i) q^{40} +(39.8090 - 33.4038i) q^{41} +(-435.025 + 158.336i) q^{42} +(273.596 + 99.5808i) q^{43} +(32.6639 + 27.4083i) q^{44} +(274.518 - 475.480i) q^{45} +(-49.1313 - 85.0979i) q^{46} +(-47.7251 + 270.662i) q^{47} +(-20.6075 + 116.871i) q^{48} +(-315.462 - 546.396i) q^{49} +(259.112 - 448.796i) q^{50} +(-139.580 - 117.121i) q^{51} +(66.4488 + 24.1854i) q^{52} +(318.864 - 116.057i) q^{53} +(11.5207 - 9.66703i) q^{54} +(-36.2788 - 205.747i) q^{55} -249.662 q^{56} +(-439.257 + 429.410i) q^{57} +215.466 q^{58} +(-19.1390 - 108.542i) q^{59} +(445.430 - 373.760i) q^{60} +(-401.475 + 146.125i) q^{61} +(-556.219 - 202.447i) q^{62} +(669.713 + 561.956i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(-173.237 - 300.055i) q^{65} +(27.4593 - 155.730i) q^{66} +(-122.381 + 694.059i) q^{67} +(-49.1319 - 85.0989i) q^{68} +(-182.207 + 315.591i) q^{69} +(937.078 + 786.302i) q^{70} +(-250.290 - 91.0981i) q^{71} +(210.595 - 76.6503i) q^{72} +(689.350 - 578.434i) q^{73} +(23.7928 + 134.936i) q^{74} -1921.87 q^{75} +(-301.806 + 136.591i) q^{76} +332.672 q^{77} +(-45.5384 - 258.261i) q^{78} +(372.250 - 312.355i) q^{79} +(294.669 - 107.251i) q^{80} +(658.348 + 239.619i) q^{81} +(-79.6181 - 66.8075i) q^{82} +(-91.6924 + 158.816i) q^{83} +(462.944 + 801.842i) q^{84} +(-83.6051 + 474.148i) q^{85} +(101.117 - 573.463i) q^{86} +(-399.535 - 692.015i) q^{87} +(42.6397 - 73.8541i) q^{88} +(303.016 + 254.261i) q^{89} +(-1031.85 - 375.563i) q^{90} +(518.429 - 188.693i) q^{91} +(-150.547 + 126.324i) q^{92} +(381.185 + 2161.81i) q^{93} +549.675 q^{94} +(1562.98 + 437.847i) q^{95} +237.348 q^{96} +(119.080 + 675.336i) q^{97} +(-966.631 + 811.100i) q^{98} +(-280.616 + 102.136i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 6 q^{3} - 12 q^{6} - 33 q^{7} + 72 q^{8} + 42 q^{9}+O(q^{10}) $ 18 * q + 6 * q^3 - 12 * q^6 - 33 * q^7 + 72 * q^8 + 42 * q^9	\( 18 q + 6 q^{3} - 12 q^{6} - 33 q^{7} + 72 q^{8} + 42 q^{9} - 75 q^{11} + 36 q^{12} + 99 q^{13} + 162 q^{14} - 183 q^{15} - 111 q^{17} - 408 q^{18} - 372 q^{19} + 24 q^{20} - 207 q^{21} - 180 q^{22} + 198 q^{23} - 48 q^{24} + 534 q^{25} + 180 q^{26} + 678 q^{27} + 216 q^{28} + 669 q^{29} - 42 q^{31} + 315 q^{33} - 48 q^{34} - 1995 q^{35} + 168 q^{36} - 1056 q^{37} - 180 q^{38} + 1812 q^{39} - 210 q^{41} - 342 q^{42} - 399 q^{43} + 360 q^{44} + 1494 q^{45} + 672 q^{46} + 1149 q^{47} - 192 q^{48} - 858 q^{49} + 1068 q^{50} + 2646 q^{51} - 468 q^{52} - 633 q^{53} - 2898 q^{54} - 3483 q^{55} - 528 q^{56} - 2814 q^{57} + 636 q^{58} + 51 q^{59} - 84 q^{60} - 4104 q^{61} - 1326 q^{62} + 1215 q^{63} - 576 q^{64} + 1755 q^{65} + 2340 q^{66} - 675 q^{67} - 948 q^{68} + 3693 q^{69} + 3990 q^{70} + 2964 q^{71} + 672 q^{72} - 2004 q^{73} - 486 q^{74} - 4446 q^{75} - 408 q^{76} + 5820 q^{77} + 4992 q^{78} + 543 q^{79} + 1722 q^{81} + 420 q^{82} + 381 q^{83} + 1092 q^{84} + 1266 q^{85} - 3396 q^{86} - 4506 q^{87} + 600 q^{88} + 4386 q^{89} - 2148 q^{90} - 1356 q^{91} - 2628 q^{92} - 8604 q^{93} - 3264 q^{94} + 921 q^{95} + 576 q^{96} + 7599 q^{97} - 954 q^{98} - 5055 q^{99}+O(q^{100}) \) 18 * q + 6 * q^3 - 12 * q^6 - 33 * q^7 + 72 * q^8 + 42 * q^9 - 75 * q^11 + 36 * q^12 + 99 * q^13 + 162 * q^14 - 183 * q^15 - 111 * q^17 - 408 * q^18 - 372 * q^19 + 24 * q^20 - 207 * q^21 - 180 * q^22 + 198 * q^23 - 48 * q^24 + 534 * q^25 + 180 * q^26 + 678 * q^27 + 216 * q^28 + 669 * q^29 - 42 * q^31 + 315 * q^33 - 48 * q^34 - 1995 * q^35 + 168 * q^36 - 1056 * q^37 - 180 * q^38 + 1812 * q^39 - 210 * q^41 - 342 * q^42 - 399 * q^43 + 360 * q^44 + 1494 * q^45 + 672 * q^46 + 1149 * q^47 - 192 * q^48 - 858 * q^49 + 1068 * q^50 + 2646 * q^51 - 468 * q^52 - 633 * q^53 - 2898 * q^54 - 3483 * q^55 - 528 * q^56 - 2814 * q^57 + 636 * q^58 + 51 * q^59 - 84 * q^60 - 4104 * q^61 - 1326 * q^62 + 1215 * q^63 - 576 * q^64 + 1755 * q^65 + 2340 * q^66 - 675 * q^67 - 948 * q^68 + 3693 * q^69 + 3990 * q^70 + 2964 * q^71 + 672 * q^72 - 2004 * q^73 - 486 * q^74 - 4446 * q^75 - 408 * q^76 + 5820 * q^77 + 4992 * q^78 + 543 * q^79 + 1722 * q^81 + 420 * q^82 + 381 * q^83 + 1092 * q^84 + 1266 * q^85 - 3396 * q^86 - 4506 * q^87 + 600 * q^88 + 4386 * q^89 - 2148 * q^90 - 1356 * q^91 - 2628 * q^92 - 8604 * q^93 - 3264 * q^94 + 921 * q^95 + 576 * q^96 + 7599 * q^97 - 954 * q^98 - 5055 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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
$3$	−5.68185	+	4.76764i	−1.09347	+	0.917533i	−0.996969	−	0.0778000i	$-0.975210\pi$
$3$	−5.68185	+	4.76764i	−1.09347	+	0.917533i	−0.0965038	+	0.995333i	$0.530766\pi$
$4$	−3.75877	+	1.36808i	−0.469846	+	0.171010i
$5$	18.4168	+	6.70318i	1.64725	+	0.599551i	0.988285	−	0.152621i	$-0.0487714\pi$
$5$	18.4168	+	6.70318i	1.64725	+	0.599551i	0.658967	+	0.752172i	$0.270994\pi$
$6$	11.3637	+	9.53528i	0.773202	+	0.648794i
$7$	−15.6039	+	27.0267i	−0.842530	+	1.45931i	0.0452188	+	0.998977i	$0.485601\pi$
$7$	−15.6039	+	27.0267i	−0.842530	+	1.45931i	−0.887749	+	0.460328i	$0.847732\pi$
$8$	4.00000	+	6.92820i	0.176777	+	0.306186i
$9$	4.86455	−	27.5882i	0.180168	−	1.02179i
$10$	6.80659	−	38.6021i	0.215243	−	1.22070i
$11$	−5.32996	−	9.23176i	−0.146095	−	0.253044i	0.783686	−	0.621157i	$-0.213337\pi$
$11$	−5.32996	−	9.23176i	−0.146095	−	0.253044i	−0.929781	+	0.368113i	$0.880004\pi$
$12$	14.8343	−	25.6937i	0.356857	−	0.618094i
$13$	−13.5424	−	11.3634i	−0.288922	−	0.242434i	0.486794	−	0.873517i	$-0.338166\pi$
$13$	−13.5424	−	11.3634i	−0.288922	−	0.242434i	−0.775715	+	0.631083i	$0.782611\pi$
$14$	58.6514	+	21.3474i	1.11966	+	0.407523i
$15$	−136.600	+	49.7184i	−2.35133	+	0.855815i
$16$	12.2567	−	10.2846i	0.191511	−	0.160697i
$17$	4.26583	+	24.1927i	0.0608597	+	0.345153i	0.999999	+	0.00161521i	$0.000514139\pi$
$17$	4.26583	+	24.1927i	0.0608597	+	0.345153i	−0.939139	+	0.343538i	$0.888375\pi$
$18$	−56.0276			−0.733658
$19$	82.5804	−	6.28253i	0.997119	−	0.0758585i
$19$	82.5804	−	6.28253i	0.997119	−	0.0758585i
$20$	−78.3952			−0.876484
$21$	−40.1947	−	227.955i	−0.417676	−	2.36876i
$22$	−16.3319	+	13.7041i	−0.158272	+	0.132806i
$23$	46.1683	−	16.8039i	0.418555	−	0.152342i	−0.124153	−	0.992263i	$-0.539621\pi$
$23$	46.1683	−	16.8039i	0.418555	−	0.152342i	0.542708	+	0.839922i	$0.317399\pi$
$24$	−55.7586	−	20.2945i	−0.474236	−	0.172608i
$25$	198.492	+	166.554i	1.58793	+	1.33243i
$26$	−17.6783	+	30.6198i	−0.133346	+	0.230963i
$27$	3.75981	+	6.51218i	0.0267991	+	0.0464174i
$28$	21.6767	−	122.935i	0.146304	−	0.829730i
$29$	−18.7077	+	106.096i	−0.119791	+	0.679366i	0.864476	+	0.502674i	$0.167651\pi$
$29$	−18.7077	+	106.096i	−0.119791	+	0.679366i	−0.984266	+	0.176691i	$0.943461\pi$
$30$	145.367	+	251.783i	0.884674	+	1.53230i
$31$	147.979	−	256.307i	0.857349	−	1.48497i	−0.0171001	−	0.999854i	$-0.505443\pi$
$31$	147.979	−	256.307i	0.857349	−	1.48497i	0.874449	−	0.485118i	$-0.161223\pi$
$32$	−24.5134	−	20.5692i	−0.135419	−	0.113630i
$33$	74.2977	+	27.0422i	0.391927	+	0.142650i
$34$	46.1688	−	16.8041i	0.232879	−	0.0847611i
$35$	−468.539	+	393.151i	−2.26279	+	1.89870i
$36$	19.4582	+	110.353i	0.0900842	+	0.510893i
$37$	−68.5088			−0.304399			−0.152200	−	0.988350i	$-0.548636\pi$
$37$	−68.5088			−0.304399			−0.152200	+	0.988350i	$0.548636\pi$
$38$	−41.0541	−	160.470i	−0.175259	−	0.685043i
$39$	131.122			0.538369
$40$	27.2264	+	154.408i	0.107622	+	0.610352i
$41$	39.8090	−	33.4038i	0.151637	−	0.127239i	−0.563813	−	0.825903i	$-0.690666\pi$
$41$	39.8090	−	33.4038i	0.151637	−	0.127239i	0.715450	+	0.698664i	$0.246222\pi$
$42$	−435.025	+	158.336i	−1.59823	+	0.581709i
$43$	273.596	+	99.5808i	0.970302	+	0.353161i	0.778063	−	0.628187i	$-0.216203\pi$
$43$	273.596	+	99.5808i	0.970302	+	0.353161i	0.192240	+	0.981348i	$0.438425\pi$
$44$	32.6639	+	27.4083i	0.111915	+	0.0939079i
$45$	274.518	−	475.480i	0.909395	−	1.57512i
$46$	−49.1313	−	85.0979i	−0.157479	−	0.272761i
$47$	−47.7251	+	270.662i	−0.148115	+	0.840003i	0.816698	+	0.577066i	$0.195802\pi$
$47$	−47.7251	+	270.662i	−0.148115	+	0.840003i	−0.964813	+	0.262938i	$0.915309\pi$
$48$	−20.6075	+	116.871i	−0.0619675	+	0.351435i
$49$	−315.462	−	546.396i	−0.919714	−	1.59299i
$50$	259.112	−	448.796i	0.732881	−	1.26939i
$51$	−139.580	−	117.121i	−0.383237	−	0.321574i
$52$	66.4488	+	24.1854i	0.177207	+	0.0644983i
$53$	318.864	−	116.057i	0.826402	−	0.300786i	0.106021	−	0.994364i	$-0.466189\pi$
$53$	318.864	−	116.057i	0.826402	−	0.300786i	0.720381	+	0.693578i	$0.243967\pi$
$54$	11.5207	−	9.66703i	0.0290328	−	0.0243614i
$55$	−36.2788	−	205.747i	−0.0889425	−	0.504418i
$56$	−249.662			−0.595759
$57$	−439.257	+	429.410i	−1.02072	+	0.997838i
$58$	215.466			0.487795
$59$	−19.1390	−	108.542i	−0.0422319	−	0.239509i	0.956384	−	0.292114i	$-0.0943587\pi$
$59$	−19.1390	−	108.542i	−0.0422319	−	0.239509i	−0.998615	+	0.0526051i	$0.983248\pi$
$60$	445.430	−	373.760i	0.958412	−	0.804203i
$61$	−401.475	+	146.125i	−0.842683	+	0.306711i	−0.727053	−	0.686581i	$-0.759111\pi$
$61$	−401.475	+	146.125i	−0.842683	+	0.306711i	−0.115629	+	0.993292i	$0.536888\pi$
$62$	−556.219	−	202.447i	−1.13935	−	0.414691i
$63$	669.713	+	561.956i	1.33930	+	1.12381i
$64$	−32.0000	+	55.4256i	−0.0625000	+	0.108253i
$65$	−173.237	−	300.055i	−0.330575	−	0.572573i
$66$	27.4593	−	155.730i	0.0512123	−	0.290439i
$67$	−122.381	+	694.059i	−0.223153	+	1.26556i	0.643031	+	0.765840i	$0.277676\pi$
$67$	−122.381	+	694.059i	−0.223153	+	1.26556i	−0.866184	+	0.499724i	$0.833435\pi$
$68$	−49.1319	−	85.0989i	−0.0876193	−	0.151761i
$69$	−182.207	+	315.591i	−0.317900	+	0.550619i
$70$	937.078	+	786.302i	1.60003	+	1.34259i
$71$	−250.290	−	91.0981i	−0.418365	−	0.152273i	0.124256	−	0.992250i	$-0.460346\pi$
$71$	−250.290	−	91.0981i	−0.418365	−	0.152273i	−0.542621	+	0.839978i	$0.682568\pi$
$72$	210.595	−	76.6503i	0.344706	−	0.125463i
$73$	689.350	−	578.434i	1.10524	−	0.927405i	0.107472	−	0.994208i	$-0.465725\pi$
$73$	689.350	−	578.434i	1.10524	−	0.927405i	0.997766	+	0.0668036i	$0.0212801\pi$
$74$	23.7928	+	134.936i	0.0373765	+	0.211973i
$75$	−1921.87			−2.95891
$76$	−301.806	+	136.591i	−0.455520	+	0.206159i
$77$	332.672			0.492357
$78$	−45.5384	−	258.261i	−0.0661052	−	0.374901i
$79$	372.250	−	312.355i	0.530144	−	0.444844i	−0.338007	−	0.941144i	$-0.609753\pi$
$79$	372.250	−	312.355i	0.530144	−	0.444844i	0.868151	+	0.496300i	$0.165308\pi$
$80$	294.669	−	107.251i	0.411813	−	0.149888i
$81$	658.348	+	239.619i	0.903083	+	0.328695i
$82$	−79.6181	−	66.8075i	−0.107224	−	0.0899714i
$83$	−91.6924	+	158.816i	−0.121260	+	0.210028i	−0.920265	−	0.391297i	$-0.872027\pi$
$83$	−91.6924	+	158.816i	−0.121260	+	0.210028i	0.799005	+	0.601324i	$0.205360\pi$
$84$	462.944	+	801.842i	0.601325	+	1.04153i
$85$	−83.6051	+	474.148i	−0.106685	+	0.605042i
$86$	101.117	−	573.463i	0.126788	−	0.719048i
$87$	−399.535	−	692.015i	−0.492353	−	0.852780i
$88$	42.6397	−	73.8541i	0.0516523	−	0.0894644i
$89$	303.016	+	254.261i	0.360895	+	0.302827i	0.805147	−	0.593075i	$-0.202086\pi$
$89$	303.016	+	254.261i	0.360895	+	0.302827i	−0.444252	+	0.895902i	$0.646531\pi$
$90$	−1031.85	−	375.563i	−1.20852	−	0.439865i
$91$	518.429	−	188.693i	0.597211	−	0.217367i
$92$	−150.547	+	126.324i	−0.170605	+	0.143154i
$93$	381.185	+	2161.81i	0.425022	+	2.41042i
$94$	549.675			0.603135
$95$	1562.98	+	437.847i	1.68799	+	0.472865i
$96$	237.348			0.252336
$97$	119.080	+	675.336i	0.124647	+	0.706907i	0.981517	+	0.191375i	$0.0612946\pi$
$97$	119.080	+	675.336i	0.124647	+	0.706907i	−0.856870	+	0.515532i	$0.827594\pi$
$98$	−966.631	+	811.100i	−0.996373	+	0.836056i
$99$	−280.616	+	102.136i	−0.284878	+	0.103687i
$100$	−973.944	−	354.487i	−0.973944	−	0.354487i
$101$	−124.465	−	104.438i	−0.122621	−	0.102891i	0.579415	−	0.815033i	$-0.303281\pi$
$101$	−124.465	−	104.438i	−0.122621	−	0.102891i	−0.702036	+	0.712141i	$0.747725\pi$
$102$	−182.209	+	315.595i	−0.176876	+	0.306358i
$103$	−816.307	−	1413.88i	−0.780904	−	1.35257i	−0.931416	−	0.363957i	$-0.881426\pi$
$103$	−816.307	−	1413.88i	−0.780904	−	1.35257i	0.150512	−	0.988608i	$-0.451908\pi$
$104$	24.5585	−	139.278i	0.0231554	−	0.131321i
$105$	787.767	−	4467.65i	0.732173	−	4.15236i
$106$	−339.328	−	587.733i	−0.310929	−	0.538544i
$107$	203.651	−	352.733i	0.183997	−	0.318692i	−0.759241	−	0.650809i	$-0.774430\pi$
$107$	203.651	−	352.733i	0.183997	−	0.318692i	0.943238	+	0.332118i	$0.107763\pi$
$108$	−23.0414	−	19.3341i	−0.0205293	−	0.0172261i
$109$	−879.071	−	319.956i	−0.772475	−	0.281158i	−0.0744437	−	0.997225i	$-0.523718\pi$
$109$	−879.071	−	319.956i	−0.772475	−	0.281158i	−0.698031	+	0.716067i	$0.745940\pi$
$110$	−392.644	+	142.911i	−0.340338	+	0.123873i
$111$	389.257	−	326.625i	0.332852	−	0.279296i
$112$	86.7067	+	491.738i	0.0731519	+	0.414865i
$113$	−1831.60			−1.52480			−0.762399	−	0.647107i	$-0.775978\pi$
$113$	−1831.60			−1.52480			−0.762399	+	0.647107i	$0.775978\pi$
$114$	998.325	+	716.035i	0.820191	+	0.588270i
$115$	962.914			0.780802
$116$	−74.8306	−	424.386i	−0.0598953	−	0.339683i
$117$	−379.374	+	318.333i	−0.299770	+	0.251537i
$118$	−207.140	+	75.3928i	−0.161600	+	0.0588175i
$119$	−720.413	−	262.209i	−0.554959	−	0.201989i
$120$	−890.859	−	747.520i	−0.677700	−	0.568657i
$121$	608.683	−	1054.27i	0.457313	−	0.792089i
$122$	427.241	+	740.003i	0.317054	+	0.549154i
$123$	−66.9320	+	379.590i	−0.0490655	+	0.278264i
$124$	−205.570	+	1165.85i	−0.148877	+	0.844324i
$125$	1314.22	+	2276.30i	0.940380	+	1.62879i
$126$	874.248	−	1514.24i	0.618129	−	1.07063i
$127$	720.622	+	604.674i	0.503503	+	0.422489i	0.858836	−	0.512251i	$-0.171188\pi$
$127$	720.622	+	604.674i	0.503503	+	0.422489i	−0.355333	+	0.934740i	$0.615633\pi$
$128$	120.281	+	43.7786i	0.0830579	+	0.0302306i
$129$	−2029.30	+	738.604i	−1.38504	+	0.504112i
$130$	−530.829	+	445.418i	−0.358129	+	0.300506i
$131$	−44.2608	−	251.015i	−0.0295197	−	0.167415i	0.966484	−	0.256727i	$-0.0826441\pi$
$131$	−44.2608	−	251.015i	−0.0295197	−	0.167415i	−0.996004	+	0.0893125i	$0.971533\pi$
$132$	−316.264			−0.208540
$133$	−1118.78	+	2329.91i	−0.729402	+	1.51901i
$134$	1409.53			0.908694
$135$	25.5915	+	145.136i	0.0163153	+	0.0925285i
$136$	−150.549	+	126.325i	−0.0949224	+	0.0796494i
$137$	2245.00	−	817.112i	1.40002	−	0.509566i	0.471837	−	0.881686i	$-0.343591\pi$
$137$	2245.00	−	817.112i	1.40002	−	0.509566i	0.928185	+	0.372119i	$0.121369\pi$
$138$	684.873	+	249.273i	0.422466	+	0.153765i
$139$	−723.441	−	607.039i	−0.441449	−	0.370420i	0.394802	−	0.918766i	$-0.370813\pi$
$139$	−723.441	−	607.039i	−0.441449	−	0.370420i	−0.836251	+	0.548346i	$0.815258\pi$
$140$	1223.27	−	2118.76i	0.738465	−	1.27906i
$141$	−1019.25	−	1765.40i	−0.608770	−	1.05442i
$142$	−92.5034	+	524.613i	−0.0546670	+	0.310032i
$143$	−32.7239	+	185.587i	−0.0191364	+	0.108528i
$144$	−224.111	−	388.171i	−0.129694	−	0.224636i
$145$	−1055.72	+	1828.56i	−0.604639	+	1.04727i
$146$	−1378.70	−	1156.87i	−0.781521	−	0.655774i
$147$	4397.43	+	1600.53i	2.46730	+	0.898025i
$148$	257.509	−	93.7255i	0.143021	−	0.0520553i
$149$	−2115.24	+	1774.90i	−1.16300	+	0.975874i	−0.999942	−	0.0107429i	$-0.996580\pi$
$149$	−2115.24	+	1774.90i	−1.16300	+	0.975874i	−0.163058	+	0.986616i	$0.552136\pi$
$150$	667.459	+	3785.35i	0.363319	+	2.06048i
$151$	1312.82			0.707522			0.353761	−	0.935336i	$-0.384903\pi$
$151$	1312.82			0.707522			0.353761	+	0.935336i	$0.384903\pi$
$152$	373.848	+	547.004i	0.199494	+	0.291894i
$153$	688.185			0.363637
$154$	−115.536	−	655.236i	−0.0604555	−	0.342860i
$155$	4443.38	−	3728.44i	2.30258	−	1.93210i
$156$	−492.859	+	179.386i	−0.252951	+	0.0920666i
$157$	−1994.19	−	725.827i	−1.01372	−	0.368964i	−0.218859	−	0.975756i	$-0.570233\pi$
$157$	−1994.19	−	725.827i	−1.01372	−	0.368964i	−0.794860	+	0.606793i	$0.792456\pi$
$158$	−744.500	−	624.710i	−0.374869	−	0.314552i
$159$	−1258.42	+	2179.65i	−0.627667	+	1.08715i
$160$	−313.581	−	543.138i	−0.154942	−	0.268367i
$161$	−266.251	+	1509.98i	−0.130332	+	0.739152i
$162$	243.316	−	1379.91i	0.118004	−	0.669235i
$163$	−1568.37	−	2716.50i	−0.753648	−	1.30536i	−0.946044	−	0.324039i	$-0.894959\pi$
$163$	−1568.37	−	2716.50i	−0.753648	−	1.30536i	0.192396	−	0.981317i	$-0.438374\pi$
$164$	−103.934	+	180.019i	−0.0494871	+	0.0857142i
$165$	1187.06	+	996.062i	0.560076	+	0.469960i
$166$	344.651	+	125.443i	0.161145	+	0.0586520i
$167$	−3056.49	+	1112.47i	−1.41628	+	0.515483i	−0.932966	−	0.359964i	$-0.882789\pi$
$167$	−3056.49	+	1112.47i	−1.41628	+	0.515483i	−0.483313	+	0.875448i	$0.660567\pi$
$168$	1418.54	−	1190.30i	0.651446	−	0.546628i
$169$	−327.236	−	1855.85i	−0.148947	−	0.844719i
$170$	962.925			0.434429
$171$	228.393	−	2308.81i	0.102138	−	1.03251i
$172$	−1164.62			−0.516287
$173$	588.410	+	3337.04i	0.258589	+	1.46653i	0.786688	+	0.617350i	$0.211794\pi$
$173$	588.410	+	3337.04i	0.258589	+	1.46653i	−0.528099	+	0.849183i	$0.677095\pi$
$174$	−1224.25	+	1027.27i	−0.533390	+	0.447568i
$175$	−7598.65	+	2765.68i	−3.28231	+	1.19466i
$176$	−160.273	−	58.3345i	−0.0686421	−	0.0249837i
$177$	626.236	+	525.474i	0.265937	+	0.223147i
$178$	395.559	−	685.129i	0.166564	−	0.288498i
$179$	269.992	+	467.640i	0.112738	+	0.195268i	0.916873	−	0.399178i	$-0.130705\pi$
$179$	269.992	+	467.640i	0.112738	+	0.195268i	−0.804135	+	0.594447i	$0.797371\pi$
$180$	−381.357	+	2162.78i	−0.157915	+	0.895580i
$181$	57.6507	−	326.954i	0.0236748	−	0.134267i	−0.970679	−	0.240378i	$-0.922729\pi$
$181$	57.6507	−	326.954i	0.0236748	−	0.134267i	0.994354	+	0.106111i	$0.0338399\pi$
$182$	−551.701	−	955.574i	−0.224697	−	0.389186i
$183$	1584.45	−	2744.35i	0.640033	−	1.10857i
$184$	301.094	+	252.648i	0.120636	+	0.101225i
$185$	−1261.71	−	459.227i	−0.501422	−	0.182503i
$186$	4125.55	−	1501.58i	1.62634	−	0.591941i
$187$	200.605	−	168.327i	0.0784474	−	0.0658252i
$188$	−190.900	−	1082.65i	−0.0740576	−	0.420002i
$189$	−234.670			−0.0903161
$190$	319.572	−	3230.54i	0.122022	−	1.23352i
$191$	1333.27			0.505089			0.252545	−	0.967585i	$-0.418733\pi$
$191$	1333.27			0.505089			0.252545	+	0.967585i	$0.418733\pi$
$192$	−82.4302	−	467.485i	−0.0309838	−	0.175718i
$193$	892.680	−	749.047i	0.332935	−	0.279366i	−0.460959	−	0.887421i	$-0.652495\pi$
$193$	892.680	−	749.047i	0.332935	−	0.279366i	0.793895	+	0.608055i	$0.208050\pi$
$194$	1288.80	−	469.083i	0.476960	−	0.173599i
$195$	2414.86	+	878.938i	0.886830	+	0.322780i
$196$	1933.26	+	1622.20i	0.704542	+	0.591181i
$197$	966.271	−	1673.63i	0.349462	−	0.605286i	−0.636692	−	0.771118i	$-0.719698\pi$
$197$	966.271	−	1673.63i	0.349462	−	0.605286i	0.986154	+	0.165833i	$0.0530311\pi$
$198$	298.625	+	517.234i	0.107184	+	0.185647i
$199$	581.159	−	3295.92i	0.207021	−	1.17408i	−0.687206	−	0.726463i	$-0.741163\pi$
$199$	581.159	−	3295.92i	0.207021	−	1.17408i	0.894227	−	0.447614i	$-0.147726\pi$
$200$	−359.955	+	2041.41i	−0.127263	+	0.721747i
$201$	−2613.67	−	4527.01i	−0.917185	−	1.58861i
$202$	−162.477	+	281.419i	−0.0565933	+	0.0980225i
$203$	−2575.52	−	2161.12i	−0.890475	−	0.747197i
$204$	684.881	+	249.276i	0.235055	+	0.0855531i
$205$	957.068	−	348.344i	0.326071	−	0.118680i
$206$	−2501.31	+	2098.85i	−0.845993	+	0.709872i
$207$	−239.002	−	1355.45i	−0.0802501	−	0.455121i
$208$	−282.853			−0.0942901
$209$	−498.149	−	728.877i	−0.164869	−	0.241232i
$210$	−9073.14			−2.98146
$211$	33.5028	+	190.004i	0.0109309	+	0.0619923i	0.989785	−	0.142566i	$-0.0455353\pi$
$211$	33.5028	+	190.004i	0.0109309	+	0.0619923i	−0.978854	+	0.204558i	$0.934424\pi$
$212$	−1039.76	+	872.463i	−0.336845	+	0.282646i
$213$	1856.43	−	675.686i	0.597186	−	0.217358i
$214$	−765.476	−	278.610i	−0.244518	−	0.0889973i
$215$	4371.27	+	3667.93i	1.38659	+	1.16349i
$216$	−30.0785	+	52.0974i	−0.00947491	+	0.0164110i
$217$	4618.09	+	7998.77i	1.44468	+	2.50227i
$218$	−324.892	+	1842.55i	−0.100938	+	0.572447i
$219$	−1159.02	+	6573.15i	−0.357623	+	2.02818i
$220$	417.843	+	723.725i	0.128050	+	0.221789i
$221$	217.142	−	376.102i	0.0660931	−	0.114477i
$222$	−778.513	−	653.250i	−0.235362	−	0.197492i
$223$	−999.068	−	363.631i	−0.300011	−	0.109195i	0.187629	−	0.982240i	$-0.439920\pi$
$223$	−999.068	−	363.631i	−0.300011	−	0.109195i	−0.487640	+	0.873045i	$0.662142\pi$
$224$	938.422	−	341.558i	0.279915	−	0.101881i
$225$	5560.51	−	4665.82i	1.64756	−	1.38247i
$226$	636.107	+	3607.54i	0.187227	+	1.06181i
$227$	−378.985			−0.110811			−0.0554056	−	0.998464i	$-0.517645\pi$
$227$	−378.985			−0.110811			−0.0554056	+	0.998464i	$0.517645\pi$
$228$	1063.60	−	2214.99i	0.308941	−	0.643384i
$229$	4575.31			1.32028			0.660141	−	0.751141i	$-0.270496\pi$
$229$	4575.31			1.32028			0.660141	+	0.751141i	$0.270496\pi$
$230$	−334.417	−	1896.57i	−0.0958729	−	0.543722i
$231$	−1890.19	+	1586.06i	−0.538379	+	0.451754i
$232$	−809.888	+	294.775i	−0.229189	+	0.0834178i
$233$	−3247.81	−	1182.11i	−0.913182	−	0.332371i	−0.157659	−	0.987494i	$-0.550395\pi$
$233$	−3247.81	−	1182.11i	−0.913182	−	0.332371i	−0.755523	+	0.655123i	$0.772617\pi$
$234$	758.748	+	636.665i	0.211970	+	0.177864i
$235$	−2693.24	+	4664.83i	−0.747608	+	1.29489i
$236$	220.434	+	381.802i	0.0608009	+	0.105310i
$237$	−625.874	+	3549.51i	−0.171540	+	0.972850i
$238$	−266.254	+	1510.00i	−0.0725154	+	0.411256i
$239$	3021.60	+	5233.56i	0.817786	+	1.41645i	0.907310	+	0.420463i	$0.138132\pi$
$239$	3021.60	+	5233.56i	0.817786	+	1.41645i	−0.0895236	+	0.995985i	$0.528534\pi$
$240$	−1162.93	+	2014.26i	−0.312779	+	0.541750i
$241$	−375.282	−	314.899i	−0.100307	−	0.0841678i	0.591255	−	0.806485i	$-0.298633\pi$
$241$	−375.282	−	314.899i	−0.100307	−	0.0841678i	−0.691562	+	0.722317i	$0.743077\pi$
$242$	−2287.90	−	832.727i	−0.607735	−	0.221197i
$243$	−5073.84	+	1846.73i	−1.33945	+	0.487521i
$244$	1309.14	−	1098.50i	0.343481	−	0.288214i
$245$	−2147.22	−	12177.5i	−0.559922	−	3.17547i
$246$	770.892			0.199798
$247$	−1189.73	−	853.315i	−0.306480	−	0.219818i
$248$	2367.66			0.606237
$249$	−236.194	−	1339.52i	−0.0601133	−	0.340919i
$250$	4027.01	−	3379.06i	1.01876	−	0.854842i
$251$	1636.06	−	595.478i	0.411423	−	0.149746i	−0.128012	−	0.991773i	$-0.540860\pi$
$251$	1636.06	−	595.478i	0.411423	−	0.149746i	0.539436	+	0.842027i	$0.318638\pi$
$252$	−3286.10	−	1196.04i	−0.821447	−	0.298982i
$253$	−401.205	−	336.651i	−0.0996978	−	0.0836564i
$254$	940.705	−	1629.35i	0.232382	−	0.402498i
$255$	−1785.53	−	3092.64i	−0.438488	−	0.759484i
$256$	44.4539	−	252.111i	0.0108530	−	0.0615505i
$257$	646.330	−	3665.52i	0.156875	−	0.889684i	−0.800176	−	0.599765i	$-0.795261\pi$
$257$	646.330	−	3665.52i	0.156875	−	0.889684i	0.957051	−	0.289919i	$-0.0936283\pi$
$258$	2159.53	+	3740.42i	0.521111	+	0.902591i
$259$	1069.00	−	1851.57i	0.256465	−	0.444211i
$260$	1061.66	+	890.836i	0.253235	+	0.212490i
$261$	2836.01	+	1032.22i	0.672584	+	0.244801i
$262$	−479.032	+	174.353i	−0.112957	+	0.0411129i
$263$	−921.683	+	773.384i	−0.216097	+	0.181327i	−0.744410	−	0.667723i	$-0.767269\pi$
$263$	−921.683	+	773.384i	−0.216097	+	0.181327i	0.528313	+	0.849050i	$0.322825\pi$
$264$	109.837	+	622.918i	0.0256061	+	0.145220i
$265$	6650.41			1.54163
$266$	4977.57	+	1394.40i	1.14735	+	0.321413i
$267$	−2933.92			−0.672482
$268$	−489.525	−	2776.24i	−0.111577	−	0.632782i
$269$	−4542.16	+	3811.32i	−1.02952	+	0.863868i	−0.990793	−	0.135382i	$-0.956774\pi$
$269$	−4542.16	+	3811.32i	−1.02952	+	0.863868i	−0.0387242	+	0.999250i	$0.512329\pi$
$270$	276.975	−	100.811i	0.0624302	−	0.0227227i
$271$	7954.73	+	2895.29i	1.78308	+	0.648989i	0.999620	+	0.0275503i	$0.00877064\pi$
$271$	7954.73	+	2895.29i	1.78308	+	0.648989i	0.783463	+	0.621439i	$0.213452\pi$
$272$	301.098	+	252.651i	0.0671203	+	0.0563206i
$273$	−2046.02	+	3543.81i	−0.453592	+	0.785645i
$274$	−2389.08	−	4138.00i	−0.526749	−	0.912357i
$275$	479.637	−	2720.15i	0.105175	−	0.596478i
$276$	253.119	−	1435.51i	0.0552028	−	0.313070i
$277$	379.159	+	656.722i	0.0822434	+	0.142450i	0.904213	−	0.427081i	$-0.140458\pi$
$277$	379.159	+	656.722i	0.0822434	+	0.142450i	−0.821970	+	0.569531i	$0.807125\pi$
$278$	−944.385	+	1635.72i	−0.203743	+	0.352893i
$279$	−6351.21	−	5329.30i	−1.36286	−	1.14357i
$280$	−4597.98	−	1673.53i	−0.981365	−	0.357188i
$281$	−134.082	+	48.8018i	−0.0284649	+	0.0103604i	−0.356213	−	0.934405i	$-0.615932\pi$
$281$	−134.082	+	48.8018i	−0.0284649	+	0.0103604i	0.327748	+	0.944765i	$0.393710\pi$
$282$	−3123.17	+	2620.65i	−0.659512	+	0.553396i
$283$	−124.854	−	708.082i	−0.0262254	−	0.148732i	0.968883	−	0.247518i	$-0.0796150\pi$
$283$	−124.854	−	708.082i	−0.0262254	−	0.148732i	−0.995109	+	0.0987865i	$0.968504\pi$
$284$	1065.41			0.222608
$285$	−10968.1	+	4963.96i	−2.27964	+	1.03172i
$286$	376.899			0.0779249
$287$	281.618	+	1597.14i	0.0579212	+	0.328488i
$288$	−686.715	+	576.222i	−0.140504	+	0.117897i
$289$	4049.62	−	1473.94i	0.824266	−	0.300008i
$290$	3968.21	+	1444.31i	0.803521	+	0.292458i
$291$	−3896.35	−	3269.43i	−0.784908	−	0.658616i
$292$	−1799.77	+	3117.29i	−0.360696	+	0.624744i
$293$	−2952.64	−	5114.12i	−0.588720	−	1.01969i	−0.994400	−	0.105678i	$-0.966299\pi$
$293$	−2952.64	−	5114.12i	−0.588720	−	1.01969i	0.405680	−	0.914015i	$-0.367035\pi$
$294$	1625.22	−	9217.10i	0.322398	−	1.82841i
$295$	375.100	−	2127.30i	0.0740312	−	0.419852i
$296$	−274.035	−	474.643i	−0.0538107	−	0.0932028i
$297$	40.0792	−	69.4193i	0.00783041	−	0.0135627i
$298$	4230.48	+	3549.79i	0.822366	+	0.690047i
$299$	−816.179	−	297.065i	−0.157862	−	0.0574572i
$300$	7223.87	−	2629.27i	1.39023	−	0.506004i
$301$	−6960.50	+	5840.55i	−1.33288	+	1.11842i
$302$	−455.938	−	2585.75i	−0.0868750	−	0.492693i
$303$	1205.11			0.228488
$304$	947.551	−	926.310i	0.178769	−	0.174762i
$305$	−8373.41			−1.57200
$306$	−239.004	−	1355.46i	−0.0446502	−	0.253224i
$307$	−1282.08	+	1075.79i	−0.238346	+	0.199996i	−0.754135	−	0.656720i	$-0.771943\pi$
$307$	−1282.08	+	1075.79i	−0.238346	+	0.199996i	0.515789	+	0.856716i	$0.327499\pi$
$308$	−1250.44	+	455.122i	−0.231332	+	0.0841980i
$309$	11379.0	+	4141.63i	2.09492	+	0.762488i
$310$	−8886.75	−	7456.87i	−1.62817	−	1.36620i
$311$	1740.29	−	3014.27i	0.317307	−	0.549593i	−0.662618	−	0.748958i	$-0.730555\pi$
$311$	1740.29	−	3014.27i	0.317307	−	0.549593i	0.979925	+	0.199365i	$0.0638879\pi$
$312$	524.490	+	908.443i	0.0951711	+	0.164841i
$313$	1447.80	−	8210.87i	0.261452	−	1.48277i	−0.517500	−	0.855683i	$-0.673137\pi$
$313$	1447.80	−	8210.87i	0.261452	−	1.48277i	0.778952	−	0.627083i	$-0.215751\pi$
$314$	−737.024	+	4179.87i	−0.132461	+	0.751222i
$315$	8567.10	+	14838.7i	1.53239	+	2.65417i
$316$	−971.876	+	1683.34i	−0.173014	+	0.299668i
$317$	6960.66	+	5840.68i	1.23328	+	1.03484i	0.998019	+	0.0629114i	$0.0200386\pi$
$317$	6960.66	+	5840.68i	1.23328	+	1.03484i	0.235260	+	0.971933i	$0.424406\pi$
$318$	4730.11	+	1721.62i	0.834124	+	0.303596i
$319$	1079.17	−	392.785i	0.189410	−	0.0689396i
$320$	−960.867	+	806.263i	−0.167857	+	0.140848i
$321$	524.592	+	2975.11i	0.0912146	+	0.517304i
$322$	3066.56			0.530722
$323$	504.266	+	1971.05i	0.0868671	+	0.339541i
$324$	−2802.40			−0.480521
$325$	−795.426	−	4511.09i	−0.135761	−	0.769938i
$326$	−4805.78	+	4032.53i	−0.816465	+	0.685095i
$327$	6520.19	−	2373.15i	1.10265	−	0.401332i
$328$	390.664	+	142.190i	0.0657647	+	0.0239364i
$329$	−6570.42	−	5513.23i	−1.10103	−	0.923874i
$330$	1549.60	−	2683.98i	0.258493	−	0.447722i
$331$	−1834.88	−	3178.11i	−0.304696	−	0.527748i	0.672498	−	0.740099i	$-0.265221\pi$
$331$	−1834.88	−	3178.11i	−0.304696	−	0.527748i	−0.977194	+	0.212351i	$0.931888\pi$
$332$	127.378	−	722.395i	0.0210565	−	0.119417i
$333$	−333.264	+	1890.03i	−0.0548431	+	0.311031i
$334$	3252.65	+	5633.76i	0.532866	+	0.922951i
$335$	−6906.28	+	11962.0i	−1.12636	+	1.95091i
$336$	−2837.08	−	2380.60i	−0.460642	−	0.386524i
$337$	6202.18	+	2257.41i	1.00253	+	0.364893i	0.790562	−	0.612383i	$-0.209789\pi$
$337$	6202.18	+	2257.41i	1.00253	+	0.364893i	0.211973	+	0.977275i	$0.432011\pi$
$338$	−3541.66	+	1289.06i	−0.569943	+	0.207442i
$339$	10406.9	−	8732.39i	1.66732	−	1.39905i
$340$	−334.420	−	1896.59i	−0.0533426	−	0.302521i
$341$	−3154.89			−0.501017
$342$	−4626.79	+	351.995i	−0.731544	+	0.0556542i
$343$	8985.46			1.41449
$344$	404.468	+	2293.85i	0.0633938	+	0.359524i
$345$	−5471.14	+	4590.83i	−0.853786	+	0.716411i
$346$	6368.33	−	2317.88i	0.989490	−	0.360145i
$347$	−10905.4	−	3969.25i	−1.68713	−	0.614066i	−0.692872	−	0.721061i	$-0.743655\pi$
$347$	−10905.4	−	3969.25i	−1.68713	−	0.614066i	−0.994260	+	0.106995i	$0.965877\pi$
$348$	2448.49	+	2054.53i	0.377164	+	0.316478i
$349$	−3037.69	+	5261.44i	−0.465914	+	0.806986i	−0.999242	−	0.0389220i	$-0.987608\pi$
$349$	−3037.69	+	5261.44i	−0.465914	+	0.806986i	0.533329	+	0.845908i	$0.320941\pi$
$350$	8086.32	+	14005.9i	1.23495	+	2.13899i
$351$	23.0838	−	130.915i	0.00351032	−	0.0199080i
$352$	−59.2344	+	335.935i	−0.00896933	+	0.0508676i
$353$	−5649.49	−	9785.21i	−0.851819	−	1.47539i	−0.879565	−	0.475779i	$-0.842166\pi$
$353$	−5649.49	−	9785.21i	−0.851819	−	1.47539i	0.0277455	−	0.999615i	$-0.491167\pi$
$354$	817.493	−	1415.94i	0.122738	−	0.212588i
$355$	−3998.90	−	3355.48i	−0.597858	−	0.501662i
$356$	−1486.82	−	541.157i	−0.221352	−	0.0805654i
$357$	5343.40	−	1944.84i	0.792164	−	0.288324i
$358$	827.303	−	694.190i	0.122135	−	0.102483i
$359$	1261.64	+	7155.13i	0.185479	+	1.05190i	0.925338	+	0.379142i	$0.123781\pi$
$359$	1261.64	+	7155.13i	0.185479	+	1.05190i	−0.739859	+	0.672762i	$0.765108\pi$
$360$	4392.29			0.643040
$361$	6780.06	−	1037.63i	0.988491	−	0.151280i
$362$	−663.995			−0.0964055
$363$	1567.93	+	8892.19i	0.226708	+	1.28573i
$364$	−1690.51	+	1418.51i	−0.243425	+	0.204258i
$365$	16573.0	−	6032.08i	2.37663	−	0.865023i
$366$	−5955.59	−	2167.66i	−0.850556	−	0.309577i
$367$	−4469.75	−	3750.57i	−0.635747	−	0.533455i	0.266962	−	0.963707i	$-0.413980\pi$
$367$	−4469.75	−	3750.57i	−0.635747	−	0.533455i	−0.902709	+	0.430252i	$0.858425\pi$
$368$	393.051	−	680.783i	0.0556771	−	0.0964356i
$369$	−727.897	−	1260.75i	−0.102691	−	0.177865i
$370$	−466.311	+	2644.58i	−0.0655199	+	0.371582i
$371$	−1838.87	+	10428.8i	−0.257330	+	1.45939i
$372$	−4390.32	−	7604.25i	−0.611901	−	1.05984i
$373$	−2359.87	+	4087.42i	−0.327586	+	0.567396i	−0.982032	−	0.188713i	$-0.939568\pi$
$373$	−2359.87	+	4087.42i	−0.327586	+	0.567396i	0.654446	+	0.756108i	$0.272902\pi$
$374$	−401.209	−	336.655i	−0.0554707	−	0.0465454i
$375$	−18319.8	−	6667.85i	−2.52274	−	0.918204i
$376$	−2066.10	+	752.000i	−0.283381	+	0.103142i
$377$	1458.96	−	1224.22i	0.199312	−	0.167242i
$378$	81.5001	+	462.210i	0.0110897	+	0.0628929i
$379$	−5361.54			−0.726659			−0.363329	−	0.931661i	$-0.618360\pi$
$379$	−5361.54			−0.726659			−0.363329	+	0.931661i	$0.618360\pi$
$380$	−6473.91	+	492.520i	−0.873959	+	0.0664888i
$381$	−6977.33			−0.938214
$382$	−463.040	−	2626.03i	−0.0620188	−	0.351726i
$383$	11050.1	−	9272.13i	1.47424	−	1.23703i	0.562154	−	0.827033i	$-0.309973\pi$
$383$	11050.1	−	9272.13i	1.47424	−	1.23703i	0.912085	−	0.410000i	$-0.134471\pi$
$384$	−892.137	+	324.711i	−0.118559	+	0.0431520i
$385$	6126.77	+	2229.96i	0.811036	+	0.295193i
$386$	−1785.36	−	1498.09i	−0.235421	−	0.197541i
$387$	4078.18	−	7063.61i	0.535673	−	0.927813i
$388$	−1371.51	−	2375.52i	−0.179453	−	0.310822i
$389$	1050.25	−	5956.28i	0.136889	−	0.776338i	−0.836636	−	0.547759i	$-0.815481\pi$
$389$	1050.25	−	5956.28i	0.136889	−	0.776338i	0.973525	−	0.228579i	$-0.0734078\pi$
$390$	892.497	−	5061.60i	0.115880	−	0.657190i
$391$	603.478	+	1045.25i	0.0780542	+	0.135194i
$392$	2523.70	−	4371.17i	0.325168	−	0.563208i
$393$	1448.23	+	1215.21i	0.185887	+	0.155978i
$394$	−3631.99	−	1321.94i	−0.464409	−	0.169031i
$395$	8949.44	−	3257.33i	1.13999	−	0.414922i
$396$	915.040	−	767.810i	0.116117	−	0.0974341i
$397$	−1684.43	−	9552.86i	−0.212945	−	1.20767i	−0.884438	−	0.466658i	$-0.845458\pi$
$397$	−1684.43	−	9552.86i	−0.212945	−	1.20767i	0.671493	−	0.741011i	$-0.265653\pi$
$398$	−6693.52			−0.843005
$399$	−4751.43	−	18572.1i	−0.596163	−	2.33025i
$400$	4145.80			0.518225
$401$	−544.410	−	3087.50i	−0.0677969	−	0.384495i	−0.999759	−	0.0219403i	$-0.993016\pi$
$401$	−544.410	−	3087.50i	−0.0677969	−	0.384495i	0.931962	−	0.362555i	$-0.118095\pi$
$402$	−8008.75	+	6720.14i	−0.993632	+	0.833757i
$403$	−4916.51	+	1789.46i	−0.607714	+	0.221190i
$404$	610.714	+	222.282i	0.0752084	+	0.0273736i
$405$	10518.5	+	8826.05i	1.29054	+	1.08289i
$406$	−3362.11	+	5823.34i	−0.410982	+	0.711842i
$407$	365.149	+	632.456i	0.0444711	+	0.0770263i
$408$	253.122	−	1435.52i	0.0307142	−	0.174189i
$409$	−724.190	+	4107.08i	−0.0875523	+	0.496534i	0.909224	+	0.416307i	$0.136676\pi$
$409$	−724.190	+	4107.08i	−0.0875523	+	0.496534i	−0.996777	+	0.0802272i	$0.974435\pi$
$410$	−1018.49	−	1764.08i	−0.122682	−	0.212492i
$411$	−8860.04	+	15346.0i	−1.06334	+	1.84176i
$412$	5002.62	+	4197.70i	0.598207	+	0.501955i
$413$	3232.19	+	1176.42i	0.385098	+	0.140164i
$414$	−2586.70	+	941.483i	−0.307076	+	0.111767i
$415$	−2753.25	+	2310.25i	−0.325667	+	0.273267i
$416$	98.2339	+	557.112i	0.0115777	+	0.0656603i
$417$	7004.63			0.822585
$418$	−1262.60	+	1234.30i	−0.147741	+	0.144429i
$419$	−4140.40			−0.482749			−0.241374	−	0.970432i	$-0.577598\pi$
$419$	−4140.40			−0.482749			−0.241374	+	0.970432i	$0.577598\pi$
$420$	3151.07	+	17870.6i	0.366087	+	2.07618i
$421$	−4842.50	+	4063.34i	−0.560591	+	0.470392i	−0.878509	−	0.477727i	$-0.841461\pi$
$421$	−4842.50	+	4063.34i	−0.560591	+	0.470392i	0.317917	+	0.948118i	$0.397017\pi$
$422$	362.599	−	131.975i	0.0418271	−	0.0152238i
$423$	7234.93	+	2633.30i	0.831618	+	0.302684i
$424$	2079.52	+	1744.93i	0.238185	+	0.199861i
$425$	−3182.67	+	5512.55i	−0.363252	+	0.629171i
$426$	−1975.57	−	3421.79i	−0.224688	−	0.389170i
$427$	2315.29	−	13130.7i	0.262400	−	1.48814i
$428$	−282.909	+	1604.45i	−0.0319507	+	0.181201i
$429$	−698.877	−	1210.49i	−0.0786530	−	0.136231i
$430$	5706.28	−	9883.57i	0.639957	−	1.10844i
$431$	9088.13	+	7625.85i	1.01568	+	0.852260i	0.989079	−	0.147386i	$-0.0470859\pi$
$431$	9088.13	+	7625.85i	1.01568	+	0.852260i	0.0266052	+	0.999646i	$0.491530\pi$
$432$	113.058	+	41.1498i	0.0125915	+	0.00458291i
$433$	−9133.10	+	3324.18i	−1.01365	+	0.368937i	−0.794832	−	0.606829i	$-0.792441\pi$
$433$	−9133.10	+	3324.18i	−1.01365	+	0.368937i	−0.218814	+	0.975767i	$0.570219\pi$
$434$	14150.7	−	11873.8i	1.56510	−	1.31327i
$435$	−2719.47	−	15422.9i	−0.299744	−	1.69993i
$436$	3741.95			0.411025
$437$	3707.03	−	1677.73i	0.405792	−	0.183654i
$438$	13349.1			1.45627
$439$	1303.05	+	7389.96i	0.141665	+	0.803425i	0.969984	+	0.243168i	$0.0781865\pi$
$439$	1303.05	+	7389.96i	0.141665	+	0.803425i	−0.828319	+	0.560257i	$0.810702\pi$
$440$	1280.34	−	1074.34i	0.138723	−	0.116402i
$441$	−16608.7	+	6045.06i	−1.79340	+	0.652744i
$442$	−816.188	−	297.068i	−0.0878328	−	0.0319685i
$443$	10815.3	+	9075.08i	1.15993	+	0.973296i	0.999905	−	0.0138167i	$-0.00439815\pi$
$443$	10815.3	+	9075.08i	1.15993	+	0.973296i	0.160025	+	0.987113i	$0.448843\pi$
$444$	−1016.28	+	1760.24i	−0.108627	+	0.188147i
$445$	3876.24	+	6713.85i	0.412925	+	0.715207i
$446$	−369.241	+	2094.07i	−0.0392019	+	0.222325i
$447$	3556.41	−	20169.4i	0.376314	−	2.13418i
$448$	−998.648	−	1729.71i	−0.105316	−	0.182413i
$449$	−4295.82	+	7440.58i	−0.451520	+	0.782055i	−0.998481	−	0.0551028i	$-0.982451\pi$
$449$	−4295.82	+	7440.58i	−0.451520	+	0.782055i	0.546961	+	0.837158i	$0.315785\pi$
$450$	−11121.0	−	9331.64i	−1.16500	−	0.977551i
$451$	−520.556	−	189.467i	−0.0543504	−	0.0197819i
$452$	6884.55	−	2505.77i	0.716421	−	0.260756i
$453$	−7459.25	+	6259.05i	−0.773656	+	0.649174i
$454$	131.620	+	746.455i	0.0136063	+	0.0771650i
$455$	10812.7			1.11408
$456$	−4732.07	−	1325.62i	−0.485964	−	0.136136i
$457$	−6055.71			−0.619856			−0.309928	−	0.950760i	$-0.600305\pi$
$457$	−6055.71			−0.619856			−0.309928	+	0.950760i	$0.600305\pi$
$458$	−1588.99	−	9011.60i	−0.162115	−	0.919398i
$459$	−141.509	+	118.740i	−0.0143901	+	0.0120747i
$460$	−3619.37	+	1317.34i	−0.366857	+	0.133525i
$461$	−16813.9	−	6119.75i	−1.69870	−	0.618276i	−0.703023	−	0.711167i	$-0.748167\pi$
$461$	−16813.9	−	6119.75i	−1.69870	−	0.618276i	−0.995676	+	0.0928908i	$0.970389\pi$
$462$	3780.39	+	3172.12i	0.380692	+	0.319438i
$463$	−1096.58	+	1899.33i	−0.110070	+	0.190646i	−0.915798	−	0.401639i	$-0.868441\pi$
$463$	−1096.58	+	1899.33i	−0.110070	+	0.190646i	0.805728	+	0.592285i	$0.201774\pi$
$464$	861.865	+	1492.79i	0.0862308	+	0.149356i
$465$	−7470.77	+	42368.8i	−0.745051	+	4.22539i
$466$	−1200.34	+	6807.48i	−0.119324	+	0.676718i
$467$	−1518.32	−	2629.80i	−0.150448	−	0.260584i	0.780944	−	0.624601i	$-0.214738\pi$
$467$	−1518.32	−	2629.80i	−0.150448	−	0.260584i	−0.931392	+	0.364017i	$0.881405\pi$
$468$	990.475	−	1715.55i	0.0978306	−	0.169448i
$469$	−16848.5	−	14137.6i	−1.65883	−	1.39192i
$470$	10123.3	+	3684.57i	0.993515	+	0.361610i
$471$	14791.2	−	5383.55i	1.44701	−	0.526669i
$472$	675.448	−	566.768i	0.0658687	−	0.0552704i
$473$	−538.949	−	3056.53i	−0.0523910	−	0.297124i
$474$	7208.53			0.698521
$475$	17437.9	+	12507.1i	1.68443	+	1.20814i
$476$	3066.59			0.295288
$477$	−1650.68	−	9361.45i	−0.158447	−	0.898598i
$478$	9258.71	−	7768.98i	0.885949	−	0.743400i
$479$	−15916.4	+	5793.08i	−1.51824	+	0.552594i	−0.960708	−	0.277561i	$-0.910474\pi$
$479$	−15916.4	+	5793.08i	−1.51824	+	0.552594i	−0.557532	+	0.830155i	$0.688252\pi$
$480$	4371.20	+	1590.99i	0.415661	+	0.151288i
$481$	927.772	+	778.493i	0.0879475	+	0.0737967i
$482$	−489.896	+	848.525i	−0.0462950	+	0.0801852i
$483$	−5686.26	−	9848.89i	−0.535681	−	0.927826i
$484$	−845.574	+	4795.49i	−0.0794115	+	0.450365i
$485$	−2333.82	+	13235.8i	−0.218502	+	1.23919i
$486$	5399.46	+	9352.15i	0.503960	+	0.872885i
$487$	−199.989	+	346.391i	−0.0186086	+	0.0322310i	−0.875180	−	0.483798i	$-0.839257\pi$
$487$	−199.989	+	346.391i	−0.0186086	+	0.0322310i	0.856571	+	0.516029i	$0.172590\pi$
$488$	−2618.28	−	2197.00i	−0.242877	−	0.203798i
$489$	21862.6	+	7957.33i	2.02180	+	0.735875i
$490$	−23239.2	+	8458.39i	−2.14253	+	0.779819i
$491$	950.463	−	797.533i	0.0873600	−	0.0733038i	−0.598062	−	0.801450i	$-0.704062\pi$
$491$	950.463	−	797.533i	0.0873600	−	0.0733038i	0.685422	+	0.728146i	$0.259618\pi$
$492$	−267.728	−	1518.36i	−0.0245327	−	0.139132i
$493$	−2646.56			−0.241775
$494$	−1267.51	+	2639.66i	−0.115442	+	0.240413i
$495$	−5852.69			−0.531432
$496$	−822.281	−	4663.39i	−0.0744385	−	0.422162i
$497$	6367.57	−	5343.03i	0.574698	−	0.482228i
$498$	−2556.32	+	930.424i	−0.230023	+	0.0837214i
$499$	−3304.33	−	1202.68i	−0.296437	−	0.107894i	0.189520	−	0.981877i	$-0.439307\pi$
$499$	−3304.33	−	1202.68i	−0.296437	−	0.107894i	−0.485957	+	0.873983i	$0.661529\pi$
$500$	−8054.01	−	6758.12i	−0.720373	−	0.604465i
$501$	12062.7	−	20893.2i	1.07569	−	1.86315i
$502$	−1741.06	−	3015.60i	−0.154795	−	0.268114i
$503$	−162.566	+	921.959i	−0.0144105	+	0.0817259i	−0.991165	−	0.132636i	$-0.957656\pi$
$503$	−162.566	+	921.959i	−0.0144105	+	0.0817259i	0.976754	+	0.214362i	$0.0687671\pi$
$504$	−1214.49	+	6887.73i	−0.107337	+	0.608738i
$505$	−1592.18	−	2757.73i	−0.140299	−	0.243005i
$506$	−523.736	+	907.137i	−0.0460136	+	0.0796979i
$507$	10707.3	+	8984.50i	0.937926	+	0.787014i
$508$	−3535.90	−	1286.96i	−0.308819	−	0.112401i
$509$	−5889.17	+	2143.48i	−0.512835	+	0.186657i	−0.585458	−	0.810703i	$-0.699085\pi$
$509$	−5889.17	+	2143.48i	−0.512835	+	0.186657i	0.0726229	+	0.997359i	$0.476863\pi$
$510$	−5471.20	+	4590.88i	−0.475037	+	0.398603i
$511$	4876.62	+	27656.7i	0.422170	+	2.39425i
$512$	−512.000			−0.0441942
$513$	351.400	+	514.157i	0.0302430	+	0.0442507i
$514$	−7444.13			−0.638807
$515$	−5556.26	−	31511.1i	−0.475414	−	2.69621i
$516$	6617.19	−	5552.48i	0.564546	−	0.473710i
$517$	2753.06	−	1002.03i	0.234196	−	0.0852405i
$518$	−4018.13	−	1462.48i	−0.340824	−	0.124050i
$519$	−19253.0	−	16155.2i	−1.62835	−	1.36635i
$520$	1385.90	−	2400.44i	0.116876	−	0.202435i
$521$	5350.36	+	9267.09i	0.449911	+	0.779268i	0.998380	−	0.0569027i	$-0.0181225\pi$
$521$	5350.36	+	9267.09i	0.449911	+	0.779268i	−0.548469	+	0.836171i	$0.684789\pi$
$522$	1048.15	−	5944.33i	0.0878853	−	0.498422i
$523$	359.383	−	2038.16i	0.0300472	−	0.170406i	−0.966091	−	0.258200i	$-0.916871\pi$
$523$	359.383	−	2038.16i	0.0300472	−	0.170406i	0.996139	+	0.0877939i	$0.0279817\pi$
$524$	509.775	+	882.957i	0.0424993	+	0.0736110i
$525$	29988.6	−	51941.8i	2.49297	−	4.31796i
$526$	1843.37	+	1546.77i	0.152803	+	0.128217i
$527$	6832.02	+	2486.65i	0.564720	+	0.205541i
$528$	1188.76	−	432.675i	0.0979816	−	0.0356624i
$529$	−7471.32	+	6269.18i	−0.614064	+	0.515261i
$530$	−2309.66	−	13098.8i	−0.189293	−	1.07354i
$531$	−3087.60			−0.252336
$532$	1017.73	−	10288.2i	0.0829402	−	0.838438i
$533$	−918.690			−0.0746583
$534$	1018.94	+	5778.68i	0.0825726	+	0.468292i
$535$	6115.04	−	5131.12i	0.494161	−	0.414650i
$536$	−5298.11	+	1928.35i	−0.426947	+	0.155396i
$537$	−3763.59	−	1369.84i	−0.302441	−	0.110080i
$538$	9084.32	+	7622.65i	0.727979	+	0.610847i
$539$	−3362.80	+	5824.54i	−0.268731	+	0.465456i
$540$	−294.751	−	510.523i	−0.0234890	−	0.0406841i
$541$	929.238	−	5269.97i	0.0738467	−	0.418805i	−0.925364	−	0.379080i	$-0.876241\pi$
$541$	929.238	−	5269.97i	0.0738467	−	0.418805i	0.999211	−	0.0397254i	$-0.0126483\pi$
$542$	2939.95	−	16673.3i	0.232992	−	1.32136i
$543$	1231.23	+	2132.56i	0.0973063	+	0.168539i
$544$	393.055	−	680.791i	0.0309781	−	0.0536557i
$545$	−14045.0	−	11785.1i	−1.10389	−	0.926276i
$546$	7690.52	+	2799.12i	0.602791	+	0.219398i
$547$	−10216.4	+	3718.46i	−0.798575	+	0.290658i	−0.708896	−	0.705313i	$-0.750806\pi$
$547$	−10216.4	+	3718.46i	−0.798575	+	0.290658i	−0.0896793	+	0.995971i	$0.528584\pi$
$548$	−7320.55	+	6142.67i	−0.570654	+	0.478836i
$549$	2078.33	+	11786.8i	0.161569	+	0.916301i
$550$	−5524.24			−0.428280
$551$	−878.333	+	8879.02i	−0.0679097	+	0.686495i
$552$	−2915.31			−0.224789
$553$	2633.38	+	14934.6i	0.202500	+	1.14844i
$554$	1161.81	−	974.874i	0.0890984	−	0.0747625i
$555$	9358.30	−	3406.14i	0.715744	−	0.260509i
$556$	3549.73	+	1292.00i	0.270759	+	0.0985482i
$557$	11543.9	+	9686.46i	0.878150	+	0.736855i	0.965798	−	0.259296i	$-0.0834906\pi$
$557$	11543.9	+	9686.46i	0.878150	+	0.736855i	−0.0876478	+	0.996152i	$0.527935\pi$
$558$	−8290.91	+	14360.3i	−0.629001	+	1.08946i
$559$	−2573.57	−	4457.55i	−0.194723	−	0.337270i
$560$	−1699.35	+	9637.47i	−0.128233	+	0.727246i
$561$	−337.282	+	1912.82i	−0.0253833	+	0.143956i
$562$	142.687	+	247.141i	0.0107097	+	0.0185498i
$563$	2770.15	−	4798.04i	0.207367	−	0.359171i	−0.743517	−	0.668717i	$-0.766844\pi$
$563$	2770.15	−	4798.04i	0.207367	−	0.359171i	0.950884	+	0.309546i	$0.100177\pi$
$564$	6246.35	+	5241.31i	0.466345	+	0.391310i
$565$	−33732.2	−	12277.5i	−2.51173	−	0.914193i
$566$	−1351.29	+	491.828i	−0.100351	+	0.0365249i
$567$	−16748.9	+	14054.0i	−1.24054	+	1.04094i
$568$	−370.014	−	2098.45i	−0.0273335	−	0.155016i
$569$	16337.3			1.20369			0.601843	−	0.798615i	$-0.294433\pi$
$569$	16337.3			1.20369			0.601843	+	0.798615i	$0.294433\pi$
$570$	13586.3	+	19879.0i	0.998363	+	1.46077i
$571$	232.989			0.0170758			0.00853789	−	0.999964i	$-0.497282\pi$
$571$	232.989			0.0170758			0.00853789	+	0.999964i	$0.497282\pi$
$572$	−130.896	−	742.346i	−0.00956822	−	0.0542641i
$573$	−7575.44	+	6356.55i	−0.552301	+	0.463436i
$574$	3047.94	−	1109.36i	0.221635	−	0.0806685i
$575$	11962.8	+	4354.10i	0.867622	+	0.315789i
$576$	1373.43	+	1152.44i	0.0993511	+	0.0833654i
$577$	2074.23	−	3592.68i	0.149656	−	0.259212i	−0.781444	−	0.623975i	$-0.785517\pi$
$577$	2074.23	−	3592.68i	0.149656	−	0.259212i	0.931100	+	0.364763i	$0.118850\pi$
$578$	−4309.52	−	7464.30i	−0.310125	−	0.537152i
$579$	−1500.89	+	8511.95i	−0.107728	+	0.610958i
$580$	1466.59	−	8317.44i	0.104995	−	0.595454i
$581$	−2861.51	−	4956.28i	−0.204330	−	0.353909i
$582$	−5086.33	+	8809.77i	−0.362259	+	0.627452i
$583$	−2770.94	−	2325.10i	−0.196845	−	0.165173i
$584$	6764.91	+	2462.22i	0.479339	+	0.174465i
$585$	−9120.71	+	3319.67i	−0.644607	+	0.234618i
$586$	−9047.41	+	7591.68i	−0.637790	+	0.535170i
$587$	3726.34	+	21133.1i	0.262015	+	1.48596i	0.777403	+	0.629002i	$0.216536\pi$
$587$	3726.34	+	21133.1i	0.262015	+	1.48596i	−0.515389	+	0.856957i	$0.672352\pi$
$588$	−18718.6			−1.31283
$589$	10609.9	−	22095.6i	0.742231	−	1.54573i
$590$	−4320.23			−0.301460
$591$	2489.06	+	14116.2i	0.173242	+	0.982506i
$592$	−839.692	+	704.585i	−0.0582958	+	0.0489160i
$593$	−2678.83	+	975.015i	−0.185508	+	0.0675195i	−0.433104	−	0.901344i	$-0.642582\pi$
$593$	−2678.83	+	975.015i	−0.185508	+	0.0675195i	0.247596	+	0.968863i	$0.420360\pi$
$594$	−150.649	−	54.8316i	−0.0104060	−	0.00378749i
$595$	−11510.1	−	9658.12i	−0.793055	−	0.665452i
$596$	5522.50	−	9565.24i	0.379547	−	0.657395i
$597$	12411.7	+	21497.7i	0.850881	+	1.47377i
$598$	−301.648	+	1710.73i	−0.0206276	+	0.116985i
$599$	3857.13	−	21874.9i	0.263102	−	1.49213i	−0.511283	−	0.859412i	$-0.670830\pi$
$599$	3857.13	−	21874.9i	0.263102	−	1.49213i	0.774385	−	0.632714i	$-0.218059\pi$
$600$	−7687.48	−	13315.1i	−0.523067	−	0.905979i
$601$	9843.95	−	17050.2i	0.668125	−	1.15723i	−0.310303	−	0.950638i	$-0.600430\pi$
$601$	9843.95	−	17050.2i	0.668125	−	1.15723i	0.978428	−	0.206589i	$-0.0662363\pi$
$602$	13921.0	+	11681.1i	0.942488	+	0.790841i
$603$	18552.5	+	6752.57i	1.25293	+	0.456030i
$604$	−4934.59	+	1796.04i	−0.332426	+	0.120993i
$605$	18277.0	−	15336.2i	1.22821	−	1.03059i
$606$	−418.532	−	2373.61i	−0.0280556	−	0.159111i
$607$	−15879.4			−1.06182			−0.530912	−	0.847427i	$-0.678150\pi$
$607$	−15879.4			−1.06182			−0.530912	+	0.847427i	$0.678150\pi$
$608$	−2153.56	−	1544.61i	−0.143648	−	0.103030i
$609$	24937.2			1.65929
$610$	2908.05	+	16492.4i	0.193022	+	1.09468i
$611$	3721.96	−	3123.09i	0.246439	−	0.206787i
$612$	−2586.73	+	941.493i	−0.170854	+	0.0621856i
$613$	16537.6	+	6019.21i	1.08964	+	0.396596i	0.823487	−	0.567335i	$-0.192025\pi$
$613$	16537.6	+	6019.21i	1.08964	+	0.396596i	0.266152	+	0.963931i	$0.414248\pi$
$614$	2564.16	+	2151.59i	0.168536	+	0.141419i
$615$	−3777.14	+	6542.19i	−0.247657	+	0.428954i
$616$	1330.69	+	2304.82i	0.0870373	+	0.150753i
$617$	−680.092	+	3857.00i	−0.0443752	+	0.251664i	−0.998923	−	0.0463927i	$-0.985227\pi$
$617$	−680.092	+	3857.00i	−0.0443752	+	0.251664i	0.954548	+	0.298057i	$0.0963385\pi$
$618$	4205.52	−	23850.7i	0.273739	−	1.55245i
$619$	1361.84	+	2358.78i	0.0884284	+	0.153162i	0.906847	−	0.421460i	$-0.138482\pi$
$619$	1361.84	+	2358.78i	0.0884284	+	0.153162i	−0.818419	+	0.574622i	$0.805149\pi$
$620$	−11600.8	+	20093.2i	−0.751453	+	1.30155i
$621$	283.014	+	237.477i	0.0182882	+	0.0153456i
$622$	−6541.34	−	2380.85i	−0.421678	−	0.153478i
$623$	−11600.1	+	4222.07i	−0.745981	+	0.271515i
$624$	1607.13	−	1348.54i	0.103104	−	0.0865143i
$625$	3321.06	+	18834.7i	0.212548	+	1.20542i
$626$	−16675.1			−1.06465
$627$	6305.43	+	1766.38i	0.401618	+	0.112508i
$628$	8488.70			0.539389
$629$	−292.247	−	1657.41i	−0.0185257	−	0.105064i
$630$	26251.1	−	22027.3i	1.66011	−	1.39300i
$631$	−5269.85	+	1918.07i	−0.332471	+	0.121010i	−0.502861	−	0.864367i	$-0.667719\pi$
$631$	−5269.85	+	1918.07i	−0.332471	+	0.121010i	0.170390	+	0.985377i	$0.445497\pi$
$632$	3653.06	+	1329.60i	0.229922	+	0.0836849i
$633$	−1096.23	−	919.843i	−0.0688327	−	0.0577575i
$634$	9086.49	−	15738.3i	0.569197	−	0.985878i
$635$	9218.34	+	15966.6i	0.576093	+	0.997822i
$636$	1748.18	−	9914.41i	0.108993	−	0.618132i
$637$	−1936.82	+	10984.2i	−0.120470	+	0.683220i
$638$	−1148.43	−	1989.13i	−0.0712643	−	0.123433i
$639$	−3730.78	+	6461.90i	−0.230966	+	0.400045i
$640$	1921.73	+	1612.53i	0.118692	+	0.0995948i
$641$	2171.26	+	790.273i	0.133790	+	0.0486956i	0.408047	−	0.912961i	$-0.366210\pi$
$641$	2171.26	+	790.273i	0.133790	+	0.0486956i	−0.274257	+	0.961656i	$0.588432\pi$
$642$	5677.64	−	2066.49i	0.349032	−	0.127037i
$643$	23503.6	−	19721.9i	1.44151	−	1.20957i	0.503020	−	0.864275i	$-0.332222\pi$
$643$	23503.6	−	19721.9i	1.44151	−	1.20957i	0.938493	−	0.345298i	$-0.112222\pi$
$644$	−1065.00	−	6039.94i	−0.0651662	−	0.369576i
$645$	−42324.2			−2.58374
$646$	3707.07	−	1677.75i	0.225778	−	0.102183i
$647$	−15228.6			−0.925348			−0.462674	−	0.886529i	$-0.653110\pi$
$647$	−15228.6			−0.925348			−0.462674	+	0.886529i	$0.653110\pi$
$648$	973.262	+	5519.64i	0.0590021	+	0.334617i
$649$	−900.028	+	755.213i	−0.0544363	+	0.0456775i
$650$	−8608.86	+	3133.37i	−0.519488	+	0.189078i
$651$	−64374.6	−	23430.4i	−3.87563	−	1.41062i
$652$	9611.56	+	8065.05i	0.577328	+	0.484435i
$653$	5403.74	−	9359.55i	0.323835	−	0.560899i	−0.657441	−	0.753506i	$-0.728361\pi$
$653$	5403.74	−	9359.55i	0.323835	−	0.560899i	0.981276	+	0.192607i	$0.0616942\pi$
$654$	−6938.64	−	12018.1i	−0.414866	−	0.718569i
$655$	867.458	−	4919.60i	0.0517471	−	0.293473i
$656$	144.384	−	818.840i	0.00859334	−	0.0487353i
$657$	−12604.6	−	21831.8i	−0.748480	−	1.29641i
$658$	−8577.07	+	14855.9i	−0.508159	+	0.880158i
$659$	24099.0	+	20221.5i	1.42453	+	1.19532i	0.948860	+	0.315696i	$0.102238\pi$
$659$	24099.0	+	20221.5i	1.42453	+	1.19532i	0.475668	+	0.879625i	$0.342206\pi$
$660$	−5824.58	−	2119.97i	−0.343517	−	0.125030i
$661$	22988.8	−	8367.25i	1.35274	−	0.492358i	0.438939	−	0.898517i	$-0.355354\pi$
$661$	22988.8	−	8367.25i	1.35274	−	0.492358i	0.913802	+	0.406159i	$0.133132\pi$
$662$	−5622.41	+	4717.76i	−0.330092	+	0.276980i
$663$	559.346	+	3172.21i	0.0327650	+	0.185820i
$664$	−1467.08			−0.0857435
$665$	−36222.2	+	35410.2i	−2.11223	+	2.06488i
$666$	3838.38			0.223325
$667$	919.132	+	5212.66i	0.0533567	+	0.302601i
$668$	9966.71	−	8363.06i	0.577281	−	0.484396i
$669$	7410.22	−	2697.10i	0.428245	−	0.155868i
$670$	25959.1	+	9448.35i	1.49685	+	0.544808i
$671$	3488.84	+	2927.48i	0.200723	+	0.168427i
$672$	−3703.55	+	6414.74i	−0.212601	+	0.368235i
$673$	−10620.6	−	18395.4i	−0.608310	−	1.05362i	−0.991519	−	0.129962i	$-0.958514\pi$
$673$	−10620.6	−	18395.4i	−0.608310	−	1.05362i	0.383209	−	0.923662i	$-0.374819\pi$
$674$	2292.23	−	12999.9i	0.130999	−	0.742934i
$675$	−338.341	+	1918.83i	−0.0192929	+	0.109416i
$676$	3768.95	+	6528.02i	0.214437	+	0.371417i
$677$	883.172	−	1529.70i	0.0501375	−	0.0868407i	−0.839867	−	0.542791i	$-0.817367\pi$
$677$	883.172	−	1529.70i	0.0501375	−	0.0868407i	0.890005	+	0.455951i	$0.150701\pi$
$678$	−20813.7	−	17464.8i	−1.17898	−	0.989279i
$679$	−20110.2	−	7319.52i	−1.13661	−	0.413693i
$680$	−3619.41	+	1317.36i	−0.204115	+	0.0742918i
$681$	2153.34	−	1806.87i	0.121169	−	0.101673i
$682$	1095.68	+	6213.92i	0.0615188	+	0.348890i
$683$	−24637.6			−1.38028			−0.690139	−	0.723677i	$-0.742451\pi$
$683$	−24637.6			−1.38028			−0.690139	+	0.723677i	$0.742451\pi$
$684$	2300.16	+	8990.74i	0.128580	+	0.502587i
$685$	46823.0			2.61170
$686$	−3120.62	−	17697.9i	−0.173682	−	0.984998i
$687$	−25996.2	+	21813.4i	−1.44369	+	1.21140i
$688$	4377.54	−	1593.29i	0.242576	−	0.0882903i
$689$	−5636.98	−	2051.69i	−0.311686	−	0.113445i
$690$	10942.3	+	9181.66i	0.603718	+	0.506579i
$691$	5000.72	−	8661.51i	0.275306	−	0.476844i	−0.694906	−	0.719100i	$-0.744554\pi$
$691$	5000.72	−	8661.51i	0.275306	−	0.476844i	0.970212	+	0.242256i	$0.0778875\pi$
$692$	−6777.03	−	11738.2i	−0.372289	−	0.644824i
$693$	1618.30	−	9177.83i	0.0887072	−	0.503084i
$694$	−4030.49	+	22858.0i	−0.220454	+	1.25026i
$695$	−9254.40	−	16029.1i	−0.505093	−	0.874846i
$696$	3196.28	−	5536.12i	0.174073	−	0.301503i
$697$	977.946	+	820.594i	0.0531454	+	0.0445943i
$698$	11418.0	+	4155.81i	0.619165	+	0.225358i
$699$	24089.5	−	8767.84i	1.30350	−	0.474435i
$700$	24777.9	−	20791.1i	1.33788	−	1.12262i
$701$	4603.14	+	26105.7i	0.248015	+	1.40656i	0.813386	+	0.581725i	$0.197622\pi$
$701$	4603.14	+	26105.7i	0.248015	+	1.40656i	−0.565371	+	0.824837i	$0.691267\pi$
$702$	−265.868			−0.0142942
$703$	−5657.48	+	430.408i	−0.303522	+	0.0230913i
$704$	682.235			0.0365237
$705$	−6937.64	−	39345.3i	−0.370619	−	2.10189i
$706$	−17311.1	+	14525.7i	−0.922819	+	0.774337i
$707$	4764.76	−	1734.23i	0.253461	−	0.0922523i
$708$	−3072.77	−	1118.40i	−0.163110	−	0.0593671i
$709$	5862.14	+	4918.92i	0.310518	+	0.260555i	0.784706	−	0.619868i	$-0.212814\pi$
$709$	5862.14	+	4918.92i	0.310518	+	0.260555i	−0.474188	+	0.880424i	$0.657258\pi$
$710$	−5220.19	+	9041.64i	−0.275930	+	0.477925i
$711$	−6806.49	−	11789.2i	−0.359020	−	0.621841i
$712$	−549.505	+	3116.40i	−0.0289236	+	0.164034i
$713$	2524.98	−	14319.9i	0.132625	−	0.752152i
$714$	−5686.32	−	9849.00i	−0.298047	−	0.516232i
$715$	−1846.69	+	3198.56i	−0.0965907	+	0.167300i
$716$	−1654.61	−	1388.38i	−0.0863625	−	0.0724667i
$717$	−42120.0	−	15330.4i	−2.19386	−	0.798501i
$718$	13654.7	−	4969.90i	0.709734	−	0.258322i
$719$	−6238.82	+	5234.99i	−0.323601	+	0.271533i	−0.790086	−	0.612996i	$-0.789964\pi$
$719$	−6238.82	+	5234.99i	−0.323601	+	0.271533i	0.466486	+	0.884529i	$0.345520\pi$
$720$	−1525.43	−	8651.13i	−0.0789574	−	0.447790i
$721$	50950.2			2.63174
$722$	−4398.42	−	12993.7i	−0.226720	−	0.669774i
$723$	3633.63			0.186910
$724$	230.603	+	1307.81i	0.0118374	+	0.0671333i
$725$	−21384.1	+	17943.4i	−1.09543	+	0.919175i
$726$	16969.7	−	6176.45i	0.867497	−	0.315743i
$727$	−23721.4	−	8633.90i	−1.21015	−	0.440459i	−0.343395	−	0.939191i	$-0.611577\pi$
$727$	−23721.4	−	8633.90i	−1.21015	−	0.440459i	−0.866756	+	0.498732i	$0.833799\pi$
$728$	3381.02	+	2837.01i	0.172128	+	0.144432i
$729$	10566.2	−	18301.2i	0.536817	−	0.929795i
$730$	−17636.6	−	30547.5i	−0.894192	−	1.54879i
$731$	−1242.02	+	7043.83i	−0.0628422	+	0.356396i
$732$	−2201.10	+	12483.0i	−0.111141	+	0.630309i
$733$	−520.155	−	900.935i	−0.0262106	−	0.0453981i	0.852623	−	0.522527i	$-0.175011\pi$
$733$	−520.155	−	900.935i	−0.0262106	−	0.0453981i	−0.878833	+	0.477129i	$0.841677\pi$
$734$	−5834.85	+	10106.3i	−0.293417	+	0.508213i
$735$	70258.0	+	58953.5i	3.52586	+	2.95855i
$736$	−1477.39	−	537.725i	−0.0739908	−	0.0269304i
$737$	7059.67	−	2569.51i	0.352845	−	0.128425i
$738$	−2230.41	+	1871.53i	−0.111250	+	0.0933497i
$739$	−1477.75	−	8380.76i	−0.0735590	−	0.417174i	−0.999244	−	0.0388784i	$-0.987622\pi$
$739$	−1477.75	−	8380.76i	−0.0735590	−	0.417174i	0.925685	−	0.378295i	$-0.123490\pi$
$740$	5370.75			0.266801
$741$	10828.2	−	823.781i	0.536818	−	0.0408399i
$742$	21179.3			1.04787
$743$	6059.23	+	34363.6i	0.299181	+	1.69674i	0.649705	+	0.760186i	$0.274892\pi$
$743$	6059.23	+	34363.6i	0.299181	+	1.69674i	−0.350524	+	0.936554i	$0.613997\pi$
$744$	−13452.7	+	11288.2i	−0.662904	+	0.556242i
$745$	−50853.5	+	18509.1i	−2.50084	+	0.910232i
$746$	8870.22	+	3228.50i	0.435338	+	0.158450i
$747$	3935.40	+	3302.20i	0.192756	+	0.161742i
$748$	−523.742	+	907.147i	−0.0256015	+	0.0443430i
$749$	6355.48	+	11008.0i	0.310046	+	0.537015i
$750$	−6770.72	+	38398.6i	−0.329642	+	1.86949i
$751$	−467.364	+	2650.55i	−0.0227089	+	0.128788i	−0.994055	−	0.108882i	$-0.965273\pi$
$751$	−467.364	+	2650.55i	−0.0227089	+	0.128788i	0.971346	+	0.237671i	$0.0763839\pi$
$752$	2198.70	+	3808.26i	0.106620	+	0.184672i
$753$	−6456.83	+	11183.6i	−0.312484	+	0.541237i
$754$	−2917.93	−	2448.43i	−0.140935	−	0.118258i
$755$	24178.0	+	8800.07i	1.16547	+	0.424195i
$756$	882.072	−	321.048i	0.0424347	−	0.0154450i
$757$	−13771.5	+	11555.7i	−0.661207	+	0.554818i	−0.910448	−	0.413623i	$-0.864263\pi$
$757$	−13771.5	+	11555.7i	−0.661207	+	0.554818i	0.249242	+	0.968441i	$0.419819\pi$
$758$	1862.04	+	10560.2i	0.0892249	+	0.506019i
$759$	3884.62			0.185774
$760$	3218.44	+	12580.1i	0.153612	+	0.600430i
$761$	1094.45			0.0521337			0.0260668	−	0.999660i	$-0.491702\pi$
$761$	1094.45			0.0521337			0.0260668	+	0.999660i	$0.491702\pi$
$762$	2423.20	+	13742.7i	0.115201	+	0.653339i
$763$	22364.3	−	18765.9i	1.06113	−	0.890393i
$764$	−5011.46	+	1824.02i	−0.237314	+	0.0863753i
$765$	12674.2	+	4613.03i	0.599002	+	0.218019i
$766$	−22100.2	−	18544.3i	−1.04244	−	0.874715i
$767$	−974.225	+	1687.41i	−0.0458634	+	0.0794378i
$768$	949.393	+	1644.40i	0.0446071	+	0.0772618i
$769$	1250.49	−	7091.89i	0.0586396	−	0.332562i	−0.941348	−	0.337436i	$-0.890440\pi$
$769$	1250.49	−	7091.89i	0.0586396	−	0.332562i	0.999988	+	0.00487410i	$0.00155148\pi$
$770$	2264.36	−	12841.8i	0.105977	−	0.601023i
$771$	13803.5	+	23908.4i	0.644775	+	1.11678i
$772$	−2330.62	+	4036.75i	−0.108654	+	0.188194i
$773$	−14583.6	−	12237.1i	−0.678572	−	0.569389i	0.237017	−	0.971506i	$-0.423830\pi$
$773$	−14583.6	−	12237.1i	−0.678572	−	0.569389i	−0.915589	+	0.402116i	$0.868275\pi$
$774$	−15328.9	−	5579.28i	−0.711870	−	0.259099i
$775$	72061.6	−	26228.3i	3.34004	−	1.21568i
$776$	−4202.54	+	3526.35i	−0.194410	+	0.163130i
$777$	2753.69	+	15616.9i	0.127140	+	0.721048i
$778$	−12096.3			−0.557422
$779$	3077.59	−	3008.60i	0.141548	−	0.138375i
$780$	−10279.4			−0.471872
$781$	493.039	+	2796.16i	0.0225894	+	0.128111i
$782$	1849.16	−	1551.63i	0.0845601	−	0.0709543i
$783$	−761.256	+	277.074i	−0.0347447	+	0.0126460i
$784$	−9485.99	−	3452.62i	−0.432124	−	0.157280i
$785$	−31861.4	−	26734.9i	−1.44864	−	1.21555i
$786$	1890.53	−	3274.50i	0.0857928	−	0.148598i
$787$	−3190.38	−	5525.90i	−0.144504	−	0.250289i	0.784684	−	0.619896i	$-0.212825\pi$
$787$	−3190.38	−	5525.90i	−0.144504	−	0.250289i	−0.929188	+	0.369608i	$0.879492\pi$
$788$	−1342.33	+	7612.73i	−0.0606834	+	0.344153i
$789$	1549.65	−	8788.51i	0.0699227	−	0.396552i
$790$	−9523.80	−	16495.7i	−0.428913	−	0.742900i
$791$	28580.0	−	49502.0i	1.28469	−	2.22514i
$792$	−1830.08	−	1535.62i	−0.0821074	−	0.0688963i
$793$	7097.41	+	2583.25i	0.317827	+	0.115679i
$794$	−18230.5	+	6635.35i	−0.814830	+	0.296574i
$795$	−37786.7	+	31706.8i	−1.68573	+	1.41449i
$796$	2324.64	+	13183.7i	0.103511	+	0.587038i
$797$	4678.55			0.207933			0.103967	−	0.994581i	$-0.466846\pi$
$797$	4678.55			0.207933			0.103967	+	0.994581i	$0.466846\pi$
$798$	−34929.8	+	15808.5i	−1.54950	+	0.701273i
$799$	−6751.64			−0.298944
$800$	−1439.82	−	8165.63i	−0.0636317	−	0.360873i
$801$	8488.64	−	7122.81i	0.374446	−	0.314197i
$802$	−5892.12	+	2144.56i	−0.259424	+	0.0944226i
$803$	−9014.17	−	3280.89i	−0.396143	−	0.144184i
$804$	16017.5	+	13440.3i	0.702604	+	0.589555i
$805$	−15025.2	+	26024.4i	−0.657849	+	1.13943i
$806$	5232.04	+	9062.16i	0.228649	+	0.396031i
$807$	7636.85	−	43310.7i	0.333123	−	1.88923i
$808$	225.711	−	1280.07i	0.00982733	−	0.0557336i
$809$	10986.6	+	19029.4i	0.477466	+	0.826995i	0.999666	−	0.0258279i	$-0.00822220\pi$
$809$	10986.6	+	19029.4i	0.477466	+	0.826995i	−0.522201	+	0.852823i	$0.674889\pi$
$810$	13730.9	−	23782.6i	0.595623	−	1.03165i
$811$	−31343.3	−	26300.2i	−1.35711	−	1.13875i	−0.976864	−	0.213860i	$-0.931396\pi$
$811$	−31343.3	−	26300.2i	−1.35711	−	1.13875i	−0.380242	−	0.924887i	$-0.624159\pi$
$812$	12637.4	+	4599.64i	0.546165	+	0.198788i
$813$	−59001.3	+	21474.7i	−2.54522	+	0.926385i
$814$	1118.88	−	938.853i	0.0481778	−	0.0404260i
$815$	−10675.3	−	60542.5i	−0.458821	−	2.60210i
$816$	−2915.34			−0.125070
$817$	23219.3	+	6504.55i	0.994297	+	0.278538i
$818$	8340.89			0.356519
$819$	−2683.78	−	15220.5i	−0.114504	−	0.649384i
$820$	−3120.84	+	2618.69i	−0.132908	+	0.111523i
$821$	22452.9	−	8172.17i	0.954458	−	0.347394i	0.182599	−	0.983187i	$-0.441549\pi$
$821$	22452.9	−	8172.17i	0.954458	−	0.347394i	0.771860	+	0.635793i	$0.219327\pi$
$822$	33302.9	+	12121.3i	1.41310	+	0.514327i
$823$	19108.2	+	16033.7i	0.809318	+	0.679099i	0.950445	−	0.310893i	$-0.100628\pi$
$823$	19108.2	+	16033.7i	0.809318	+	0.679099i	−0.141127	+	0.989992i	$0.545072\pi$
$824$	6530.45	−	11311.1i	0.276091	−	0.478204i
$825$	10243.5	+	17742.3i	0.432282	+	0.748734i
$826$	1194.57	−	6774.73i	0.0503200	−	0.285379i
$827$	−2405.47	+	13642.1i	−0.101144	+	0.573619i	0.891546	+	0.452930i	$0.149621\pi$
$827$	−2405.47	+	13642.1i	−0.101144	+	0.573619i	−0.992690	+	0.120688i	$0.961490\pi$
$828$	2752.71	+	4767.84i	0.115535	+	0.200113i
$829$	−11238.9	+	19466.3i	−0.470859	+	0.815551i	−0.999444	−	0.0333288i	$-0.989389\pi$
$829$	−11238.9	+	19466.3i	−0.470859	+	0.815551i	0.528586	+	0.848880i	$0.322722\pi$
$830$	5506.51	+	4620.51i	0.230282	+	0.193229i
$831$	−5285.33	−	1923.70i	−0.220633	−	0.0803039i
$832$	1063.18	−	386.966i	0.0443019	−	0.0161246i
$833$	11873.1	−	9962.71i	0.493852	−	0.414391i
$834$	−2432.68	−	13796.4i	−0.101003	−	0.572819i
$835$	−63748.1			−2.64203
$836$	2869.59	+	2058.17i	0.118716	+	0.0851476i
$837$	2225.49			0.0919046
$838$	1437.95	+	8154.99i	0.0592756	+	0.336169i
$839$	−8869.82	+	7442.66i	−0.364982	+	0.306256i	−0.806773	−	0.590862i	$-0.798788\pi$
$839$	−8869.82	+	7442.66i	−0.364982	+	0.306256i	0.441791	+	0.897118i	$0.354343\pi$
$840$	34103.8	−	12412.8i	1.40083	−	0.509859i
$841$	12011.7	+	4371.90i	0.492504	+	0.179257i
$842$	9685.00	+	8126.68i	0.396398	+	0.332617i
$843$	529.163	−	916.538i	0.0216196	−	0.0374463i
$844$	−385.869	−	668.345i	−0.0157372	−	0.0272576i
$845$	6413.43	−	36372.4i	0.261099	−	1.48077i
$846$	2673.92	−	15164.6i	0.108666	−	0.616275i
$847$	18995.6	+	32901.4i	0.770599	+	1.33472i
$848$	2714.62	−	4701.86i	0.109930	−	0.190404i
$849$	4085.28	+	3427.96i	0.165143	+	0.138571i
$850$	11962.9	+	4354.15i	0.482735	+	0.175701i
$851$	−3162.94	+	1151.21i	−0.127408	+	0.0463726i
$852$	−6053.51	+	5079.50i	−0.243415	+	0.204250i
$853$	510.760	+	2896.67i	0.0205019	+	0.116272i	0.993341	−	0.115209i	$-0.0367539\pi$
$853$	510.760	+	2896.67i	0.0205019	+	0.116272i	−0.972839	+	0.231481i	$0.925643\pi$
$854$	−26666.5			−1.06851
$855$	19682.6	−	40990.0i	0.787289	−	1.63957i
$856$	3258.41			0.130105
$857$	−6118.37	−	34699.0i	−0.243873	−	1.38307i	−0.823095	−	0.567904i	$-0.807755\pi$
$857$	−6118.37	−	34699.0i	−0.243873	−	1.38307i	0.579222	−	0.815170i	$-0.303357\pi$
$858$	−2141.48	+	1796.92i	−0.0852087	+	0.0714986i
$859$	6968.95	−	2536.49i	0.276807	−	0.100750i	−0.199886	−	0.979819i	$-0.564057\pi$
$859$	6968.95	−	2536.49i	0.276807	−	0.100750i	0.476694	+	0.879069i	$0.341835\pi$
$860$	−21448.6	−	7806.65i	−0.850455	−	0.309540i
$861$	−9214.68	−	7732.03i	−0.364733	−	0.306048i
$862$	11863.7	−	20548.6i	0.468770	−	0.811933i
$863$	−12216.5	−	21159.6i	−0.481871	−	0.834626i	0.517912	−	0.855434i	$-0.326709\pi$
$863$	−12216.5	−	21159.6i	−0.481871	−	0.834626i	−0.999783	+	0.0208082i	$0.993376\pi$
$864$	41.7846	−	236.972i	0.00164530	−	0.00933096i
$865$	−11532.1	+	65401.9i	−0.453299	+	2.57079i
$866$	9719.24	+	16834.2i	0.381378	+	0.660566i
$867$	−15982.1	+	27681.8i	−0.626045	+	1.08434i
$868$	−28301.3	−	23747.6i	−1.10669	−	0.928625i
$869$	−4867.66	−	1771.68i	−0.190016	−	0.0691603i
$870$	−29432.7	+	10712.6i	−1.14697	+	0.417462i
$871$	9544.21	−	8008.55i	0.371290	−	0.311549i
$872$	−1299.57	−	7370.21i	−0.0504689	−	0.286223i
$873$	19210.6			0.744765
$874$	−4591.92	−	6718.76i	−0.177716	−	0.260029i
$875$	−82027.8			−3.16919
$876$	−4636.09	−	26292.6i	−0.178812	−	1.01409i
$877$	29107.8	−	24424.3i	1.12075	−	0.940424i	0.122111	−	0.992516i	$-0.461034\pi$
$877$	29107.8	−	24424.3i	1.12075	−	0.940424i	0.998642	+	0.0520926i	$0.0165891\pi$
$878$	14102.8	−	5133.01i	0.542081	−	0.197301i
$879$	41158.7	+	14980.6i	1.57935	+	0.574837i
$880$	−2560.69	−	2148.67i	−0.0980919	−	0.0823088i
$881$	519.254	−	899.374i	0.0198571	−	0.0343935i	−0.855926	−	0.517098i	$-0.827012\pi$
$881$	519.254	−	899.374i	0.0198571	−	0.0343935i	0.875783	+	0.482705i	$0.160346\pi$
$882$	17674.6	+	30613.3i	0.674755	+	1.16871i
$883$	−4939.39	+	28012.7i	−0.188249	+	1.06761i	0.733461	+	0.679732i	$0.237904\pi$
$883$	−4939.39	+	28012.7i	−0.188249	+	1.06761i	−0.921710	+	0.387880i	$0.873207\pi$
$884$	−301.651	+	1710.75i	−0.0114769	+	0.0650890i
$885$	8010.93	+	13875.3i	0.304276	+	0.527022i
$886$	14118.3	−	24453.7i	0.535344	−	0.927242i
$887$	−20066.0	−	16837.4i	−0.759585	−	0.637368i	0.178434	−	0.983952i	$-0.442897\pi$
$887$	−20066.0	−	16837.4i	−0.759585	−	0.637368i	−0.938019	+	0.346584i	$0.887341\pi$
$888$	3819.95	+	1390.35i	0.144357	+	0.0525417i
$889$	−27586.8	+	10040.8i	−1.04076	+	0.378805i
$890$	11877.5	−	9966.40i	0.447342	−	0.375365i
$891$	−1296.86	−	7354.87i	−0.0487615	−	0.276540i
$892$	4252.74			0.159633
$893$	−2240.71	+	22651.3i	−0.0839671	+	0.848819i
$894$	−40961.1			−1.53237
$895$	1837.72	+	10422.2i	0.0686350	+	0.389248i
$896$	−3060.04	+	2567.67i	−0.114094	+	0.0957366i
$897$	6053.71	−	2203.37i	0.225337	−	0.0820160i
$898$	16147.0	+	5877.03i	0.600037	+	0.218395i
$899$	24424.9	+	20494.9i	0.906137	+	0.760339i
$900$	−14517.5	+	25145.0i	−0.537684	+	0.931295i
$901$	4167.95	+	7219.10i	0.154112	+	0.266929i
$902$	−192.390	+	1091.10i	−0.00710186	+	0.0402766i
$903$	11702.9	−	66370.3i	0.431282	−	2.44592i
$904$	−7326.39	−	12689.7i	−0.269549	−	0.466872i
$905$	3253.37	−	5635.01i	0.119498	−	0.206977i
$906$	14918.5	+	12518.1i	0.547057	+	0.459036i
$907$	17577.7	+	6397.75i	0.643503	+	0.234216i	0.643098	−	0.765784i	$-0.277649\pi$
$907$	17577.7	+	6397.75i	0.643503	+	0.234216i	0.000404879		1.00000i	$0.499871\pi$
$908$	1424.52	−	518.482i	0.0520642	−	0.0189498i
$909$	−3486.73	+	2925.72i	−0.127225	+	0.106755i
$910$	−3755.20	−	21296.8i	−0.136795	−	0.775805i
$911$	40711.6			1.48061			0.740306	−	0.672270i	$-0.234681\pi$
$911$	40711.6			1.48061			0.740306	+	0.672270i	$0.234681\pi$
$912$	−967.533	+	9780.74i	−0.0351296	+	0.355124i
$913$	1954.87			0.0708616
$914$	2103.13	+	11927.4i	0.0761108	+	0.431646i
$915$	47576.4	−	39921.4i	1.71894	−	1.44236i
$916$	−17197.5	+	6259.39i	−0.620330	+	0.225782i
$917$	7474.76	+	2720.59i	0.269180	+	0.0979736i
$918$	283.017	+	237.480i	0.0101753	+	0.00853812i
$919$	−18174.2	+	31478.6i	−0.652352	+	1.12991i	0.330198	+	0.943912i	$0.392884\pi$
$919$	−18174.2	+	31478.6i	−0.652352	+	1.12991i	−0.982551	+	0.185996i	$0.940449\pi$
$920$	3851.66	+	6671.27i	0.138028	+	0.239071i
$921$	2155.60	−	12225.0i	0.0771220	−	0.437381i
$922$	−6214.16	+	35242.2i	−0.221966	+	1.25883i
$923$	2354.34	+	4077.83i	0.0839588	+	0.145421i
$924$	4934.94	−	8547.57i	0.175701	−	0.304323i
$925$	−13598.4	−	11410.4i	−0.483366	−	0.405592i
$926$	4121.79	+	1500.21i	0.146275	+	0.0532396i
$927$	−42977.5	+	15642.5i	−1.52273	+	0.554227i
$928$	2640.91	−	2215.98i	0.0934181	−	0.0783871i
$929$	7862.12	+	44588.3i	0.277662	+	1.57470i	0.730378	+	0.683044i	$0.239344\pi$
$929$	7862.12	+	44588.3i	0.277662	+	1.57470i	−0.452716	+	0.891655i	$0.649545\pi$
$930$	86044.9			3.03390
$931$	−29483.7	−	43139.7i	−1.03791	−	1.51863i
$932$	13825.0			0.485894
$933$	4482.88	+	25423.7i	0.157302	+	0.892105i
$934$	−4652.39	+	3903.82i	−0.162988	+	0.136763i
$935$	4822.83	−	1755.37i	0.168688	−	0.0613975i
$936$	−3722.97	−	1355.05i	−0.130010	−	0.0473196i
$937$	−21725.3	−	18229.7i	−0.757454	−	0.635580i	0.180008	−	0.983665i	$-0.442387\pi$
$937$	−21725.3	−	18229.7i	−0.757454	−	0.635580i	−0.937463	+	0.348085i	$0.886832\pi$
$938$	−21994.2	+	38095.0i	−0.765602	+	1.32606i
$939$	30920.3	+	53555.5i	1.07460	+	1.86125i
$940$	3741.41	−	21218.6i	0.129821	−	0.736250i
$941$	−1809.22	+	10260.6i	−0.0626767	+	0.355457i	0.937299	+	0.348526i	$0.113318\pi$
$941$	−1809.22	+	10260.6i	−0.0626767	+	0.355457i	−0.999976	+	0.00693170i	$0.997794\pi$
$942$	−15740.4	−	27263.3i	−0.544428	−	0.942978i
$943$	1276.60	−	2211.14i	0.0440848	−	0.0763571i
$944$	−1350.90	−	1133.54i	−0.0465762	−	0.0390821i
$945$	−4321.88	−	1573.04i	−0.148773	−	0.0541491i
$946$	−5833.02	+	2123.05i	−0.200473	+	0.0729664i
$947$	−23057.6	+	19347.6i	−0.791206	+	0.663901i	−0.946044	−	0.324039i	$-0.894959\pi$
$947$	−23057.6	+	19347.6i	−0.791206	+	0.663901i	0.154838	+	0.987940i	$0.450515\pi$
$948$	−2503.50	−	14198.0i	−0.0857698	−	0.486425i
$949$	−15908.4			−0.544162
$950$	18578.1	−	38689.7i	0.634475	−	1.32132i
$951$	−67395.7			−2.29806
$952$	−1065.02	−	6040.00i	−0.0362577	−	0.205628i
$953$	−35079.4	+	29435.1i	−1.19237	+	1.00052i	−0.192559	+	0.981285i	$0.561679\pi$
$953$	−35079.4	+	29435.1i	−1.19237	+	1.00052i	−0.999815	+	0.0192354i	$0.993877\pi$
$954$	−17865.2	+	6502.40i	−0.606296	+	0.220674i
$955$	24554.6	+	8937.15i	0.832009	+	0.302827i
$956$	−18517.4	−	15538.0i	−0.626461	−	0.525663i
$957$	−4259.01	+	7376.83i	−0.143860	+	0.249173i
$958$	16937.8	+	29337.2i	0.571228	+	0.989396i
$959$	−12946.8	+	73425.0i	−0.435948	+	2.47238i
$960$	1615.53	−	9162.13i	0.0543136	−	0.308028i
$961$	−28900.1	−	50056.4i	−0.970094	−	1.68025i
$962$	1211.12	−	2097.72i	0.0405905	−	0.0703049i
$963$	−8740.62	−	7334.25i	−0.292484	−	0.245424i
$964$	1841.41	+	670.218i	0.0615226	+	0.0223924i
$965$	21461.3	−	7811.29i	0.715922	−	0.260574i
$966$	−17423.7	+	14620.2i	−0.580330	+	0.486955i
$967$	6596.51	+	37410.7i	0.219369	+	1.24410i	0.873163	+	0.487429i	$0.162065\pi$
$967$	6596.51	+	37410.7i	0.219369	+	1.24410i	−0.653794	+	0.756672i	$0.726824\pi$
$968$	9738.93			0.323369
$969$	−12262.4	−	8795.03i	−0.406527	−	0.291576i
$970$	26879.9			0.889754
$971$	−1718.38	−	9745.44i	−0.0567926	−	0.322087i	0.943155	−	0.332354i	$-0.107843\pi$
$971$	−1718.38	−	9745.44i	−0.0567926	−	0.322087i	−0.999947	+	0.0102673i	$0.996732\pi$
$972$	16544.9	−	13882.8i	0.545966	−	0.458119i
$973$	27694.8	−	10080.1i	0.912490	−	0.332119i
$974$	751.713	+	273.601i	0.0247294	+	0.00900076i
$975$	26026.7	+	21839.0i	0.854895	+	0.717342i
$976$	−3417.93	+	5920.03i	−0.112096	+	0.194155i
$977$	−8583.06	−	14866.3i	−0.281061	−	0.486811i	0.690586	−	0.723251i	$-0.257353\pi$
$977$	−8583.06	−	14866.3i	−0.281061	−	0.486811i	−0.971646	+	0.236439i	$0.924020\pi$
$978$	8080.08	−	45824.4i	0.264185	−	1.49827i
$979$	732.210	−	4152.57i	0.0239035	−	0.135564i
$980$	24730.7	+	42834.8i	0.806115	+	1.39623i
$981$	−13103.3	+	22695.6i	−0.426459	+	0.738648i
$982$	−1900.93	−	1595.07i	−0.0617729	−	0.0518336i
$983$	41323.9	+	15040.7i	1.34082	+	0.488019i	0.910071	−	0.414452i	$-0.136027\pi$
$983$	41323.9	+	15040.7i	1.34082	+	0.488019i	0.430751	+	0.902471i	$0.358249\pi$
$984$	−2897.61	+	1054.64i	−0.0938743	+	0.0341675i
$985$	29014.3	−	24345.9i	0.938551	−	0.787538i
$986$	919.142	+	5212.71i	0.0296871	+	0.168364i
$987$	63617.2			2.05163
$988$	5639.32	+	1579.77i	0.181590	+	0.0508697i
$989$	14304.8			0.459926
$990$	2032.62	+	11527.5i	0.0652533	+	0.370070i
$991$	−22990.7	+	19291.5i	−0.736957	+	0.618380i	−0.932018	−	0.362411i	$-0.881954\pi$
$991$	−22990.7	+	19291.5i	−0.736957	+	0.618380i	0.195062	+	0.980791i	$0.437509\pi$
$992$	−8899.50	+	3239.15i	−0.284838	+	0.103673i
$993$	25577.6	+	9309.49i	0.817403	+	0.297510i
$994$	−12735.1	−	10686.1i	−0.406373	−	0.340987i
$995$	32796.2	−	56804.7i	1.04493	−	1.80988i
$996$	2720.38	+	4711.83i	0.0865446	+	0.149900i
$997$	−7402.24	+	41980.2i	−0.235137	+	1.33353i	0.607189	+	0.794557i	$0.292297\pi$
$997$	−7402.24	+	41980.2i	−0.235137	+	1.33353i	−0.842326	+	0.538969i	$0.818814\pi$
$998$	−1221.23	+	6925.95i	−0.0387349	+	0.219676i
$999$	−257.580	−	446.141i	−0.00815762	−	0.0141294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.4.e.b.9.1	✓	18
19.6	even	9		722.4.a.t.1.3		9
19.13	odd	18		722.4.a.u.1.7		9
19.17	even	9	inner	38.4.e.b.17.1	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.e.b.9.1	✓	18	1.1	even	1	trivial
38.4.e.b.17.1	yes	18	19.17	even	9	inner
722.4.a.t.1.3		9	19.6	even	9
722.4.a.u.1.7		9	19.13	odd	18

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)

\(f(q)\)	\(=\)	\(q+(-0.347296 - 1.96962i) q^{2} +(-5.68185 + 4.76764i) q^{3} +(-3.75877 + 1.36808i) q^{4} +(18.4168 + 6.70318i) q^{5} +(11.3637 + 9.53528i) q^{6} +(-15.6039 + 27.0267i) q^{7} +(4.00000 + 6.92820i) q^{8} +(4.86455 - 27.5882i) q^{9} +O(q^{10})\)	\(q+(-0.347296 - 1.96962i) q^{2} +(-5.68185 + 4.76764i) q^{3} +(-3.75877 + 1.36808i) q^{4} +(18.4168 + 6.70318i) q^{5} +(11.3637 + 9.53528i) q^{6} +(-15.6039 + 27.0267i) q^{7} +(4.00000 + 6.92820i) q^{8} +(4.86455 - 27.5882i) q^{9} +(6.80659 - 38.6021i) q^{10} +(-5.32996 - 9.23176i) q^{11} +(14.8343 - 25.6937i) q^{12} +(-13.5424 - 11.3634i) q^{13} +(58.6514 + 21.3474i) q^{14} +(-136.600 + 49.7184i) q^{15} +(12.2567 - 10.2846i) q^{16} +(4.26583 + 24.1927i) q^{17} -56.0276 q^{18} +(82.5804 - 6.28253i) q^{19} -78.3952 q^{20} +(-40.1947 - 227.955i) q^{21} +(-16.3319 + 13.7041i) q^{22} +(46.1683 - 16.8039i) q^{23} +(-55.7586 - 20.2945i) q^{24} +(198.492 + 166.554i) q^{25} +(-17.6783 + 30.6198i) q^{26} +(3.75981 + 6.51218i) q^{27} +(21.6767 - 122.935i) q^{28} +(-18.7077 + 106.096i) q^{29} +(145.367 + 251.783i) q^{30} +(147.979 - 256.307i) q^{31} +(-24.5134 - 20.5692i) q^{32} +(74.2977 + 27.0422i) q^{33} +(46.1688 - 16.8041i) q^{34} +(-468.539 + 393.151i) q^{35} +(19.4582 + 110.353i) q^{36} -68.5088 q^{37} +(-41.0541 - 160.470i) q^{38} +131.122 q^{39} +(27.2264 + 154.408i) q^{40} +(39.8090 - 33.4038i) q^{41} +(-435.025 + 158.336i) q^{42} +(273.596 + 99.5808i) q^{43} +(32.6639 + 27.4083i) q^{44} +(274.518 - 475.480i) q^{45} +(-49.1313 - 85.0979i) q^{46} +(-47.7251 + 270.662i) q^{47} +(-20.6075 + 116.871i) q^{48} +(-315.462 - 546.396i) q^{49} +(259.112 - 448.796i) q^{50} +(-139.580 - 117.121i) q^{51} +(66.4488 + 24.1854i) q^{52} +(318.864 - 116.057i) q^{53} +(11.5207 - 9.66703i) q^{54} +(-36.2788 - 205.747i) q^{55} -249.662 q^{56} +(-439.257 + 429.410i) q^{57} +215.466 q^{58} +(-19.1390 - 108.542i) q^{59} +(445.430 - 373.760i) q^{60} +(-401.475 + 146.125i) q^{61} +(-556.219 - 202.447i) q^{62} +(669.713 + 561.956i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(-173.237 - 300.055i) q^{65} +(27.4593 - 155.730i) q^{66} +(-122.381 + 694.059i) q^{67} +(-49.1319 - 85.0989i) q^{68} +(-182.207 + 315.591i) q^{69} +(937.078 + 786.302i) q^{70} +(-250.290 - 91.0981i) q^{71} +(210.595 - 76.6503i) q^{72} +(689.350 - 578.434i) q^{73} +(23.7928 + 134.936i) q^{74} -1921.87 q^{75} +(-301.806 + 136.591i) q^{76} +332.672 q^{77} +(-45.5384 - 258.261i) q^{78} +(372.250 - 312.355i) q^{79} +(294.669 - 107.251i) q^{80} +(658.348 + 239.619i) q^{81} +(-79.6181 - 66.8075i) q^{82} +(-91.6924 + 158.816i) q^{83} +(462.944 + 801.842i) q^{84} +(-83.6051 + 474.148i) q^{85} +(101.117 - 573.463i) q^{86} +(-399.535 - 692.015i) q^{87} +(42.6397 - 73.8541i) q^{88} +(303.016 + 254.261i) q^{89} +(-1031.85 - 375.563i) q^{90} +(518.429 - 188.693i) q^{91} +(-150.547 + 126.324i) q^{92} +(381.185 + 2161.81i) q^{93} +549.675 q^{94} +(1562.98 + 437.847i) q^{95} +237.348 q^{96} +(119.080 + 675.336i) q^{97} +(-966.631 + 811.100i) q^{98} +(-280.616 + 102.136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 6 q^{3} - 12 q^{6} - 33 q^{7} + 72 q^{8} + 42 q^{9}+O(q^{10}) \) 18 * q + 6 * q^3 - 12 * q^6 - 33 * q^7 + 72 * q^8 + 42 * q^9	\( 18 q + 6 q^{3} - 12 q^{6} - 33 q^{7} + 72 q^{8} + 42 q^{9} - 75 q^{11} + 36 q^{12} + 99 q^{13} + 162 q^{14} - 183 q^{15} - 111 q^{17} - 408 q^{18} - 372 q^{19} + 24 q^{20} - 207 q^{21} - 180 q^{22} + 198 q^{23} - 48 q^{24} + 534 q^{25} + 180 q^{26} + 678 q^{27} + 216 q^{28} + 669 q^{29} - 42 q^{31} + 315 q^{33} - 48 q^{34} - 1995 q^{35} + 168 q^{36} - 1056 q^{37} - 180 q^{38} + 1812 q^{39} - 210 q^{41} - 342 q^{42} - 399 q^{43} + 360 q^{44} + 1494 q^{45} + 672 q^{46} + 1149 q^{47} - 192 q^{48} - 858 q^{49} + 1068 q^{50} + 2646 q^{51} - 468 q^{52} - 633 q^{53} - 2898 q^{54} - 3483 q^{55} - 528 q^{56} - 2814 q^{57} + 636 q^{58} + 51 q^{59} - 84 q^{60} - 4104 q^{61} - 1326 q^{62} + 1215 q^{63} - 576 q^{64} + 1755 q^{65} + 2340 q^{66} - 675 q^{67} - 948 q^{68} + 3693 q^{69} + 3990 q^{70} + 2964 q^{71} + 672 q^{72} - 2004 q^{73} - 486 q^{74} - 4446 q^{75} - 408 q^{76} + 5820 q^{77} + 4992 q^{78} + 543 q^{79} + 1722 q^{81} + 420 q^{82} + 381 q^{83} + 1092 q^{84} + 1266 q^{85} - 3396 q^{86} - 4506 q^{87} + 600 q^{88} + 4386 q^{89} - 2148 q^{90} - 1356 q^{91} - 2628 q^{92} - 8604 q^{93} - 3264 q^{94} + 921 q^{95} + 576 q^{96} + 7599 q^{97} - 954 q^{98} - 5055 q^{99}+O(q^{100}) \) 18 * q + 6 * q^3 - 12 * q^6 - 33 * q^7 + 72 * q^8 + 42 * q^9 - 75 * q^11 + 36 * q^12 + 99 * q^13 + 162 * q^14 - 183 * q^15 - 111 * q^17 - 408 * q^18 - 372 * q^19 + 24 * q^20 - 207 * q^21 - 180 * q^22 + 198 * q^23 - 48 * q^24 + 534 * q^25 + 180 * q^26 + 678 * q^27 + 216 * q^28 + 669 * q^29 - 42 * q^31 + 315 * q^33 - 48 * q^34 - 1995 * q^35 + 168 * q^36 - 1056 * q^37 - 180 * q^38 + 1812 * q^39 - 210 * q^41 - 342 * q^42 - 399 * q^43 + 360 * q^44 + 1494 * q^45 + 672 * q^46 + 1149 * q^47 - 192 * q^48 - 858 * q^49 + 1068 * q^50 + 2646 * q^51 - 468 * q^52 - 633 * q^53 - 2898 * q^54 - 3483 * q^55 - 528 * q^56 - 2814 * q^57 + 636 * q^58 + 51 * q^59 - 84 * q^60 - 4104 * q^61 - 1326 * q^62 + 1215 * q^63 - 576 * q^64 + 1755 * q^65 + 2340 * q^66 - 675 * q^67 - 948 * q^68 + 3693 * q^69 + 3990 * q^70 + 2964 * q^71 + 672 * q^72 - 2004 * q^73 - 486 * q^74 - 4446 * q^75 - 408 * q^76 + 5820 * q^77 + 4992 * q^78 + 543 * q^79 + 1722 * q^81 + 420 * q^82 + 381 * q^83 + 1092 * q^84 + 1266 * q^85 - 3396 * q^86 - 4506 * q^87 + 600 * q^88 + 4386 * q^89 - 2148 * q^90 - 1356 * q^91 - 2628 * q^92 - 8604 * q^93 - 3264 * q^94 + 921 * q^95 + 576 * q^96 + 7599 * q^97 - 954 * q^98 - 5055 * q^99

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