LMFDB - Embedded newform 27.4.e.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,4,Mod(4,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	27.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:	$1.59305157015$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			13.8
Character	$\chi$	$=$	27.13
Dual form			27.4.e.a.25.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.904728 + 5.13097i) q^{2} +(-4.65940 - 2.30000i) q^{3} +(-17.9907 + 6.54810i) q^{4} +(10.7601 + 9.02881i) q^{5} +(7.58576 - 25.9881i) q^{6} +(9.67890 + 3.52283i) q^{7} +(-29.0343 - 50.2889i) q^{8} +(16.4200 + 21.4333i) q^{9} +O(q^{10})$	\(q+(0.904728 + 5.13097i) q^{2} +(-4.65940 - 2.30000i) q^{3} +(-17.9907 + 6.54810i) q^{4} +(10.7601 + 9.02881i) q^{5} +(7.58576 - 25.9881i) q^{6} +(9.67890 + 3.52283i) q^{7} +(-29.0343 - 50.2889i) q^{8} +(16.4200 + 21.4333i) q^{9} +(-36.5916 + 63.3784i) q^{10} +(21.5580 - 18.0893i) q^{11} +(98.8867 + 10.8686i) q^{12} +(-1.35031 + 7.65800i) q^{13} +(-9.31876 + 52.8493i) q^{14} +(-29.3694 - 66.8172i) q^{15} +(114.433 - 96.0207i) q^{16} +(4.59856 - 7.96494i) q^{17} +(-95.1178 + 103.642i) q^{18} +(-46.7770 - 81.0201i) q^{19} +(-252.704 - 91.9768i) q^{20} +(-36.9953 - 38.6758i) q^{21} +(112.320 + 94.2475i) q^{22} +(144.583 - 52.6238i) q^{23} +(19.6177 + 301.095i) q^{24} +(12.5547 + 71.2013i) q^{25} -40.5146 q^{26} +(-27.2105 - 137.632i) q^{27} -197.199 q^{28} +(30.3142 + 171.920i) q^{29} +(316.265 - 211.145i) q^{30} +(-199.014 + 72.4350i) q^{31} +(240.345 + 201.673i) q^{32} +(-142.053 + 34.7018i) q^{33} +(45.0283 + 16.3890i) q^{34} +(72.3392 + 125.295i) q^{35} +(-435.754 - 278.081i) q^{36} +(51.0621 - 88.4422i) q^{37} +(373.391 - 313.312i) q^{38} +(23.9051 - 32.5759i) q^{39} +(141.636 - 803.260i) q^{40} +(7.73239 - 43.8526i) q^{41} +(164.974 - 224.813i) q^{42} +(-10.2238 + 8.57879i) q^{43} +(-269.394 + 466.604i) q^{44} +(-16.8363 + 378.877i) q^{45} +(400.819 + 694.239i) q^{46} +(329.686 + 119.996i) q^{47} +(-754.037 + 184.202i) q^{48} +(-181.482 - 152.282i) q^{49} +(-353.973 + 128.836i) q^{50} +(-39.7459 + 26.5351i) q^{51} +(-25.8522 - 146.615i) q^{52} -102.943 q^{53} +(681.568 - 264.136i) q^{54} +395.292 q^{55} +(-103.861 - 589.024i) q^{56} +(31.6059 + 485.092i) q^{57} +(-854.691 + 311.082i) q^{58} +(-484.566 - 406.599i) q^{59} +(965.902 + 1009.78i) q^{60} +(549.302 + 199.930i) q^{61} +(-551.715 - 955.598i) q^{62} +(83.4213 + 265.295i) q^{63} +(-219.804 + 380.712i) q^{64} +(-83.6722 + 70.2093i) q^{65} +(-306.573 - 697.473i) q^{66} +(128.102 - 726.503i) q^{67} +(-30.5763 + 173.407i) q^{68} +(-794.704 - 87.3458i) q^{69} +(-577.438 + 484.528i) q^{70} +(-476.973 + 826.141i) q^{71} +(601.113 - 1448.04i) q^{72} +(-489.146 - 847.225i) q^{73} +(499.991 + 181.982i) q^{74} +(105.266 - 360.631i) q^{75} +(1372.08 + 1151.31i) q^{76} +(272.384 - 99.1395i) q^{77} +(188.774 + 93.1838i) q^{78} +(30.7362 + 174.314i) q^{79} +2098.27 q^{80} +(-189.770 + 703.867i) q^{81} +232.002 q^{82} +(-141.179 - 800.664i) q^{83} +(918.826 + 453.558i) q^{84} +(121.395 - 44.1842i) q^{85} +(-53.2672 - 44.6965i) q^{86} +(254.172 - 870.768i) q^{87} +(-1535.61 - 558.918i) q^{88} +(402.317 + 696.834i) q^{89} +(-1959.24 + 256.394i) q^{90} +(-40.0474 + 69.3641i) q^{91} +(-2256.57 + 1893.48i) q^{92} +(1093.88 + 120.229i) q^{93} +(-317.419 + 1800.17i) q^{94} +(228.189 - 1294.13i) q^{95} +(-656.012 - 1492.47i) q^{96} +(-274.487 + 230.322i) q^{97} +(617.161 - 1068.95i) q^{98} +(741.695 + 165.033i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.904728	+	5.13097i	0.319870	+	1.81407i	0.543514	+	0.839400i	$0.317093\pi$
$2$	0.904728	+	5.13097i	0.319870	+	1.81407i	−0.223645	+	0.974671i	$0.571796\pi$
$3$	−4.65940	−	2.30000i	−0.896701	−	0.442636i
$3$	−4.65940	−	2.30000i	−0.896701	−	0.442636i
$4$	−17.9907	+	6.54810i	−2.24884	+	0.818512i
$5$	10.7601	+	9.02881i	0.962414	+	0.807562i	0.981344	−	0.192259i	$-0.0615814\pi$
$5$	10.7601	+	9.02881i	0.962414	+	0.807562i	−0.0189297	+	0.999821i	$0.506026\pi$
$6$	7.58576	−	25.9881i	0.516146	−	1.76827i
$7$	9.67890	+	3.52283i	0.522612	+	0.190215i	0.589836	−	0.807523i	$-0.299192\pi$
$7$	9.67890	+	3.52283i	0.522612	+	0.190215i	−0.0672248	+	0.997738i	$0.521414\pi$
$8$	−29.0343	−	50.2889i	−1.28315	−	2.22248i
$9$	16.4200	+	21.4333i	0.608147	+	0.793825i
$10$	−36.5916	+	63.3784i	−1.15713	+	2.00420i
$11$	21.5580	−	18.0893i	0.590908	−	0.495831i	−0.297601	−	0.954690i	$-0.596186\pi$
$11$	21.5580	−	18.0893i	0.590908	−	0.495831i	0.888509	+	0.458860i	$0.151742\pi$
$12$	98.8867	+	10.8686i	2.37884	+	0.261458i
$13$	−1.35031	+	7.65800i	−0.0288084	+	0.163381i	−0.995818	−	0.0913595i	$-0.970879\pi$
$13$	−1.35031	+	7.65800i	−0.0288084	+	0.163381i	0.967010	+	0.254740i	$0.0819899\pi$
$14$	−9.31876	+	52.8493i	−0.177896	+	1.00890i
$15$	−29.3694	−	66.8172i	−0.505542	−	1.15014i
$16$	114.433	−	96.0207i	1.78802	−	1.50032i
$17$	4.59856	−	7.96494i	0.0656068	−	0.113634i	−0.831356	−	0.555740i	$-0.812435\pi$
$17$	4.59856	−	7.96494i	0.0656068	−	0.113634i	0.896963	+	0.442106i	$0.145768\pi$
$18$	−95.1178	+	103.642i	−1.24553	+	1.35714i
$19$	−46.7770	−	81.0201i	−0.564809	−	0.978278i	−0.997067	−	0.0765282i	$-0.975616\pi$
$19$	−46.7770	−	81.0201i	−0.564809	−	0.978278i	0.432258	−	0.901750i	$-0.357717\pi$
$20$	−252.704	−	91.9768i	−2.82532	−	1.02833i
$21$	−36.9953	−	38.6758i	−0.384430	−	0.401893i
$22$	112.320	+	94.2475i	1.08849	+	0.913347i
$23$	144.583	−	52.6238i	1.31077	−	0.477080i	0.410278	−	0.911961i	$-0.365432\pi$
$23$	144.583	−	52.6238i	1.31077	−	0.477080i	0.900488	+	0.434881i	$0.143210\pi$
$24$	19.6177	+	301.095i	0.166852	+	2.56086i
$25$	12.5547	+	71.2013i	0.100438	+	0.569610i
$26$	−40.5146			−0.305599
$27$	−27.2105	−	137.632i	−0.193950	−	0.981011i
$28$	−197.199			−1.33096
$29$	30.3142	+	171.920i	0.194110	+	1.10085i	0.913680	+	0.406435i	$0.133228\pi$
$29$	30.3142	+	171.920i	0.194110	+	1.10085i	−0.719569	+	0.694420i	$0.755661\pi$
$30$	316.265	−	211.145i	1.92473	−	1.28498i
$31$	−199.014	+	72.4350i	−1.15303	+	0.419668i	−0.846602	−	0.532226i	$-0.821356\pi$
$31$	−199.014	+	72.4350i	−1.15303	+	0.419668i	−0.306427	+	0.951894i	$0.599133\pi$
$32$	240.345	+	201.673i	1.32773	+	1.11410i
$33$	−142.053	+	34.7018i	−0.749340	+	0.183055i
$34$	45.0283	+	16.3890i	0.227126	+	0.0826672i
$35$	72.3392	+	125.295i	0.349359	+	0.605107i
$36$	−435.754	−	278.081i	−2.01738	−	1.28741i
$37$	51.0621	−	88.4422i	0.226880	−	0.392968i	−0.730002	−	0.683445i	$-0.760481\pi$
$37$	51.0621	−	88.4422i	0.226880	−	0.392968i	0.956882	+	0.290478i	$0.0938142\pi$
$38$	373.391	−	313.312i	1.59400	−	1.33752i
$39$	23.9051	−	32.5759i	0.0981506	−	0.133752i
$40$	141.636	−	803.260i	0.559867	−	3.17516i
$41$	7.73239	−	43.8526i	0.0294536	−	0.167040i	−0.966533	−	0.256542i	$-0.917417\pi$
$41$	7.73239	−	43.8526i	0.0294536	−	0.167040i	0.995987	+	0.0895028i	$0.0285278\pi$
$42$	164.974	−	224.813i	0.606094	−	0.825937i
$43$	−10.2238	+	8.57879i	−0.0362585	+	0.0304245i	−0.660737	−	0.750618i	$-0.729756\pi$
$43$	−10.2238	+	8.57879i	−0.0362585	+	0.0304245i	0.624478	+	0.781042i	$0.285312\pi$
$44$	−269.394	+	466.604i	−0.923016	+	1.59871i
$45$	−16.8363	+	378.877i	−0.0557734	+	1.25510i
$46$	400.819	+	694.239i	1.28473	+	2.22522i
$47$	329.686	+	119.996i	1.02318	+	0.372409i	0.798482	−	0.602019i	$-0.205637\pi$
$47$	329.686	+	119.996i	1.02318	+	0.372409i	0.224703	+	0.974427i	$0.427859\pi$
$48$	−754.037	+	184.202i	−2.26741	+	0.553902i
$49$	−181.482	−	152.282i	−0.529103	−	0.443970i
$50$	−353.973	+	128.836i	−1.00119	+	0.364402i
$51$	−39.7459	+	26.5351i	−0.109128	+	0.0728561i
$52$	−25.8522	−	146.615i	−0.0689433	−	0.390997i
$53$	−102.943			−0.266798			−0.133399	−	0.991062i	$-0.542589\pi$
$53$	−102.943			−0.266798			−0.133399	+	0.991062i	$0.542589\pi$
$54$	681.568	−	264.136i	1.71759	−	0.665635i
$55$	395.292			0.969112
$56$	−103.861	−	589.024i	−0.247839	−	1.40557i
$57$	31.6059	+	485.092i	0.0734439	+	1.12723i
$58$	−854.691	+	311.082i	−1.93494	+	0.704260i
$59$	−484.566	−	406.599i	−1.06924	−	0.897199i	−0.0742564	−	0.997239i	$-0.523658\pi$
$59$	−484.566	−	406.599i	−1.06924	−	0.897199i	−0.994983	+	0.100041i	$0.968103\pi$
$60$	965.902	+	1009.78i	2.07829	+	2.17269i
$61$	549.302	+	199.930i	1.15297	+	0.419645i	0.846580	−	0.532262i	$-0.178658\pi$
$61$	549.302	+	199.930i	1.15297	+	0.419645i	0.306386	+	0.951907i	$0.400880\pi$
$62$	−551.715	−	955.598i	−1.13013	−	1.95744i
$63$	83.4213	+	265.295i	0.166827	+	0.530541i
$64$	−219.804	+	380.712i	−0.429306	+	0.743579i
$65$	−83.6722	+	70.2093i	−0.159665	+	0.133975i
$66$	−306.573	−	697.473i	−0.571765	−	1.30080i
$67$	128.102	−	726.503i	0.233585	−	1.32472i	−0.611990	−	0.790866i	$-0.709631\pi$
$67$	128.102	−	726.503i	0.233585	−	1.32472i	0.845574	−	0.533858i	$-0.179258\pi$
$68$	−30.5763	+	173.407i	−0.0545283	+	0.309246i
$69$	−794.704	−	87.3458i	−1.38654	−	0.152394i
$70$	−577.438	+	484.528i	−0.985957	+	0.827316i
$71$	−476.973	+	826.141i	−0.797272	+	1.38091i	0.124115	+	0.992268i	$0.460391\pi$
$71$	−476.973	+	826.141i	−0.797272	+	1.38091i	−0.921387	+	0.388647i	$0.872943\pi$
$72$	601.113	−	1448.04i	0.983915	−	2.37019i
$73$	−489.146	−	847.225i	−0.784249	−	1.35836i	−0.929447	−	0.368956i	$-0.879715\pi$
$73$	−489.146	−	847.225i	−0.784249	−	1.35836i	0.145198	−	0.989403i	$-0.453618\pi$
$74$	499.991	+	181.982i	0.785443	+	0.285878i
$75$	105.266	−	360.631i	0.162067	−	0.555228i
$76$	1372.08	+	1151.31i	2.07090	+	1.73769i
$77$	272.384	−	99.1395i	0.403130	−	0.146727i
$78$	188.774	+	93.1838i	0.274031	+	0.135269i
$79$	30.7362	+	174.314i	0.0437733	+	0.248251i	0.998841	−	0.0481379i	$-0.0153287\pi$
$79$	30.7362	+	174.314i	0.0437733	+	0.248251i	−0.955067	+	0.296389i	$0.904218\pi$
$80$	2098.27			2.93242
$81$	−189.770	+	703.867i	−0.260316	+	0.965524i
$82$	232.002			0.312443
$83$	−141.179	−	800.664i	−0.186703	−	1.05885i	−0.923747	−	0.383002i	$-0.874890\pi$
$83$	−141.179	−	800.664i	−0.186703	−	1.05885i	0.737044	−	0.675845i	$-0.236221\pi$
$84$	918.826	+	453.558i	1.19348	+	0.589133i
$85$	121.395	−	44.1842i	0.154908	−	0.0563817i
$86$	−53.2672	−	44.6965i	−0.0667901	−	0.0560436i
$87$	254.172	−	870.768i	0.313219	−	1.07306i
$88$	−1535.61	−	558.918i	−1.86019	−	0.677055i
$89$	402.317	+	696.834i	0.479163	+	0.829935i	0.999714	−	0.0238952i	$-0.00760680\pi$
$89$	402.317	+	696.834i	0.479163	+	0.829935i	−0.520551	+	0.853831i	$0.674273\pi$
$90$	−1959.24	+	256.394i	−2.29469	+	0.300293i
$91$	−40.0474	+	69.3641i	−0.0461330	+	0.0799048i
$92$	−2256.57	+	1893.48i	−2.55721	+	2.14575i
$93$	1093.88	+	120.229i	1.21968	+	0.134055i
$94$	−317.419	+	1800.17i	−0.348290	+	1.97525i
$95$	228.189	−	1294.13i	0.246439	−	1.39763i
$96$	−656.012	−	1492.47i	−0.697437	−	1.58671i
$97$	−274.487	+	230.322i	−0.287319	+	0.241090i	−0.775043	−	0.631909i	$-0.782272\pi$
$97$	−274.487	+	230.322i	−0.287319	+	0.241090i	0.487724	+	0.872998i	$0.337827\pi$
$98$	617.161	−	1068.95i	0.636150	−	1.10184i
$99$	741.695	+	165.033i	0.752961	+	0.167540i
$100$	−692.101	−	1198.75i	−0.692101	−	1.19875i
$101$	26.9311	+	9.80212i	0.0265321	+	0.00965690i	0.355252	−	0.934771i	$-0.384395\pi$
$101$	26.9311	+	9.80212i	0.0265321	+	0.00965690i	−0.328720	+	0.944427i	$0.606617\pi$
$102$	−172.110	−	179.928i	−0.167073	−	0.174662i
$103$	−216.998	−	182.083i	−0.207587	−	0.174186i	0.533067	−	0.846073i	$-0.321039\pi$
$103$	−216.998	−	182.083i	−0.207587	−	0.174186i	−0.740653	+	0.671887i	$0.765484\pi$
$104$	424.318	−	154.439i	0.400075	−	0.145615i
$105$	−48.8775	−	750.180i	−0.0454282	−	0.697239i
$106$	−93.1355	−	528.198i	−0.0853407	−	0.483991i
$107$	−934.375			−0.844201			−0.422100	−	0.906549i	$-0.638707\pi$
$107$	−934.375			−0.844201			−0.422100	+	0.906549i	$0.638707\pi$
$108$	1390.76	+	2297.93i	1.23913	+	2.04739i
$109$	−776.307			−0.682172			−0.341086	−	0.940032i	$-0.610795\pi$
$109$	−776.307			−0.682172			−0.341086	+	0.940032i	$0.610795\pi$
$110$	357.632	+	2028.23i	0.309989	+	1.75804i
$111$	−441.336	+	294.644i	−0.377385	+	0.251949i
$112$	1445.85	−	526.247i	1.21982	−	0.443979i
$113$	1001.91	+	840.702i	0.834086	+	0.699881i	0.956225	−	0.292632i	$-0.0945310\pi$
$113$	1001.91	+	840.702i	0.834086	+	0.699881i	−0.122139	+	0.992513i	$0.538975\pi$
$114$	−2460.40	+	601.045i	−2.02138	+	0.493798i
$115$	2030.86	+	739.172i	1.64677	+	0.599376i
$116$	−1671.13	−	2894.47i	−1.33759	−	2.31677i
$117$	−186.308	+	96.8024i	−0.147215	+	0.0764905i
$118$	1647.85	−	2854.15i	1.28556	−	2.22666i
$119$	72.5682	−	60.8919i	0.0559018	−	0.0469072i
$120$	−2507.44	+	3416.94i	−1.90748	+	2.59936i
$121$	−93.6013	+	530.839i	−0.0703240	+	0.398828i
$122$	−528.863	+	2999.33i	−0.392468	+	2.22579i
$123$	−136.889	+	186.542i	−0.100349	+	0.136747i
$124$	3106.09	−	2606.32i	2.24948	−	1.88754i
$125$	370.123	−	641.073i	0.264839	−	0.458714i
$126$	−1285.75	+	668.052i	−0.909075	+	0.472340i
$127$	932.325	+	1614.83i	0.651421	+	1.12829i	0.982778	+	0.184789i	$0.0591602\pi$
$127$	932.325	+	1614.83i	0.651421	+	1.12829i	−0.331357	+	0.943505i	$0.607506\pi$
$128$	206.324	+	75.0957i	0.142474	+	0.0518562i
$129$	67.3680	−	16.4572i	0.0459800	−	0.0112324i
$130$	−435.942	−	365.799i	−0.294113	−	0.246790i
$131$	−1181.96	+	430.198i	−0.788308	+	0.286921i	−0.704633	−	0.709572i	$-0.748888\pi$
$131$	−1181.96	+	430.198i	−0.788308	+	0.286921i	−0.0836754	+	0.996493i	$0.526666\pi$
$132$	2328.41	−	1554.49i	1.53532	−	1.02501i
$133$	−167.330	−	948.973i	−0.109093	−	0.618695i
$134$	3843.56			2.47786
$135$	949.866	−	1726.62i	0.605567	−	1.10077i
$136$	−534.064			−0.336733
$137$	152.507	+	864.910i	0.0951062	+	0.539374i	0.994715	+	0.102677i	$0.0327407\pi$
$137$	152.507	+	864.910i	0.0951062	+	0.539374i	−0.899609	+	0.436697i	$0.856148\pi$
$138$	−270.822	−	4156.62i	−0.167057	−	2.56402i
$139$	−783.968	+	285.341i	−0.478383	+	0.174117i	−0.569946	−	0.821682i	$-0.693036\pi$
$139$	−783.968	+	285.341i	−0.478383	+	0.174117i	0.0915630	+	0.995799i	$0.470814\pi$
$140$	−2121.88	−	1780.47i	−1.28094	−	1.07484i
$141$	−1260.15	−	1317.39i	−0.752650	−	0.786838i
$142$	−4670.43	−	1699.90i	−2.76010	−	1.00459i
$143$	109.418	+	189.517i	0.0639859	+	0.110827i
$144$	3937.02	+	876.018i	2.27837	+	0.506955i
$145$	−1226.05	+	2123.58i	−0.702194	+	1.21623i
$146$	3904.54	−	3276.30i	2.21330	−	1.85718i
$147$	495.350	+	1126.95i	0.277930	+	0.632309i
$148$	−339.518	+	1925.50i	−0.188569	+	1.06943i
$149$	360.811	−	2046.26i	0.198381	−	1.12507i	−0.709140	−	0.705068i	$-0.750917\pi$
$149$	360.811	−	2046.26i	0.198381	−	1.12507i	0.907521	−	0.420007i	$-0.137972\pi$
$150$	1945.62	+	213.843i	1.05906	+	0.116401i
$151$	−2621.46	+	2199.67i	−1.41279	+	1.18547i	−0.457718	+	0.889097i	$0.651333\pi$
$151$	−2621.46	+	2199.67i	−1.41279	+	1.18547i	−0.955072	+	0.296374i	$0.904222\pi$
$152$	−2716.27	+	4704.72i	−1.44947	+	2.51055i
$153$	246.223	−	32.2218i	0.130104	−	0.0170260i
$154$	755.115	+	1307.90i	0.395122	+	0.684372i
$155$	−2795.41	−	1017.45i	−1.44860	−	0.527247i
$156$	−216.760	+	742.598i	−0.111248	+	0.381124i
$157$	−1137.69	−	954.638i	−0.578330	−	0.485276i	0.306068	−	0.952010i	$-0.400986\pi$
$157$	−1137.69	−	954.638i	−0.578330	−	0.485276i	−0.884398	+	0.466733i	$0.845431\pi$
$158$	−866.590	+	315.413i	−0.436343	+	0.158816i
$159$	479.653	+	236.770i	0.239239	+	0.118095i
$160$	765.268	+	4340.05i	0.378124	+	2.14445i
$161$	1584.79			0.775769
$162$	−3783.21	−	336.896i	−1.83480	−	0.163389i
$163$	−170.439			−0.0819008			−0.0409504	−	0.999161i	$-0.513039\pi$
$163$	−170.439			−0.0819008			−0.0409504	+	0.999161i	$0.513039\pi$
$164$	148.039	+	839.573i	0.0704874	+	0.399754i
$165$	−1841.82	−	909.173i	−0.869004	−	0.428964i
$166$	3980.45	−	1448.77i	1.86110	−	0.677386i
$167$	1252.93	+	1051.33i	0.580565	+	0.487152i	0.885132	−	0.465339i	$-0.154068\pi$
$167$	1252.93	+	1051.33i	0.580565	+	0.487152i	−0.304568	+	0.952491i	$0.598512\pi$
$168$	−870.830	+	2983.38i	−0.399917	+	1.37008i
$169$	2007.68	+	730.737i	0.913829	+	0.332607i
$170$	336.537	+	582.899i	0.151831	+	0.262978i
$171$	968.449	−	2332.93i	0.433095	−	1.04330i
$172$	127.759	−	221.285i	0.0566368	−	0.0980979i
$173$	−561.615	+	471.251i	−0.246814	+	0.207101i	−0.757799	−	0.652488i	$-0.773725\pi$
$173$	−561.615	+	471.251i	−0.246814	+	0.207101i	0.510985	+	0.859590i	$0.329281\pi$
$174$	4697.84	+	516.339i	2.04679	+	0.224963i
$175$	−129.314	+	733.378i	−0.0558586	+	0.316790i
$176$	729.999	−	4140.03i	0.312646	−	1.77311i
$177$	1322.61	+	3009.01i	0.561656	+	1.27780i
$178$	−3211.44	+	2694.72i	−1.35229	+	1.13471i
$179$	−610.701	+	1057.77i	−0.255005	+	0.441682i	−0.964897	−	0.262629i	$-0.915411\pi$
$179$	−610.701	+	1057.77i	−0.255005	+	0.441682i	0.709892	+	0.704311i	$0.248744\pi$
$180$	−2178.03	−	6926.53i	−0.901892	−	2.86818i
$181$	−1606.89	−	2783.22i	−0.659886	−	1.14296i	−0.980645	−	0.195796i	$-0.937271\pi$
$181$	−1606.89	−	2783.22i	−0.659886	−	1.14296i	0.320758	−	0.947161i	$-0.396062\pi$
$182$	−392.137	−	142.726i	−0.159709	−	0.0581295i
$183$	−2099.58	−	2194.95i	−0.848116	−	0.886641i
$184$	−6844.26	−	5743.01i	−2.74220	−	2.30098i
$185$	1347.96	−	490.618i	0.535698	−	0.194978i
$186$	372.778	+	5721.46i	0.146954	+	2.25547i
$187$	−44.9445	−	254.893i	−0.0175758	−	0.0996772i
$188$	−6717.05			−2.60580
$189$	221.487	−	1427.99i	0.0852425	−	0.549580i
$190$	6846.57			2.61422
$191$	−84.7425	−	480.599i	−0.0321034	−	0.182067i	0.964540	−	0.263938i	$-0.0850216\pi$
$191$	−84.7425	−	480.599i	−0.0321034	−	0.182067i	−0.996643	+	0.0818710i	$0.973910\pi$
$192$	1899.80	−	1268.34i	0.714094	−	0.476742i
$193$	4468.07	−	1626.24i	1.66642	−	0.606526i	0.675065	−	0.737758i	$-0.264115\pi$
$193$	4468.07	−	1626.24i	1.66642	−	0.606526i	0.991352	+	0.131232i	$0.0418933\pi$
$194$	−1430.11	−	1200.01i	−0.529258	−	0.444100i
$195$	551.343	−	134.687i	0.202474	−	0.0494621i
$196$	4262.16	+	1551.30i	1.55327	+	0.565342i
$197$	178.060	+	308.410i	0.0643973	+	0.111539i	0.896426	−	0.443192i	$-0.146154\pi$
$197$	178.060	+	308.410i	0.0643973	+	0.111539i	−0.832029	+	0.554732i	$0.812821\pi$
$198$	−175.746	+	3954.92i	−0.0630794	+	1.41952i
$199$	−711.033	+	1231.55i	−0.253285	+	0.438703i	−0.964428	−	0.264344i	$-0.914845\pi$
$199$	−711.033	+	1231.55i	−0.253285	+	0.438703i	0.711143	+	0.703047i	$0.248178\pi$
$200$	3216.12	−	2698.64i	1.13707	−	0.954114i
$201$	−2267.84	+	3090.43i	−0.795826	+	1.08449i
$202$	−25.9290	+	147.051i	−0.00903148	+	0.0512201i
$203$	−312.238	+	1770.79i	−0.107955	+	0.612242i
$204$	541.304	−	737.647i	0.185779	−	0.253165i
$205$	479.138	−	402.045i	0.163241	−	0.136976i
$206$	737.937	−	1278.14i	0.249585	−	0.432294i
$207$	3501.94	+	2234.80i	1.17586	+	0.750384i
$208$	580.806	+	1005.99i	0.193614	+	0.335349i
$209$	−2474.02	−	900.468i	−0.818810	−	0.298023i
$210$	3804.93	−	929.498i	1.25031	−	0.305435i
$211$	2551.95	+	2141.34i	0.832624	+	0.698654i	0.955892	−	0.293719i	$-0.0948930\pi$
$211$	2551.95	+	2141.34i	0.832624	+	0.698654i	−0.123268	+	0.992373i	$0.539337\pi$
$212$	1852.02	−	674.081i	0.599988	−	0.218378i
$213$	4122.54	−	2752.28i	1.32616	−	0.885367i
$214$	−845.355	−	4794.25i	−0.270034	−	1.53144i
$215$	−187.466			−0.0594653
$216$	−6131.33	+	5364.44i	−1.93141	+	1.68983i
$217$	−2181.41			−0.682413
$218$	−702.346	−	3983.20i	−0.218206	−	1.23751i
$219$	330.502	+	5072.60i	0.101978	+	1.56518i
$220$	−7111.60	+	2588.41i	−2.17938	+	0.793230i
$221$	54.7860	+	45.9709i	0.0166756	+	0.0139925i
$222$	−1911.10	−	1997.91i	−0.577768	−	0.604012i
$223$	24.9464	+	9.07976i	0.00749119	+	0.00272657i	0.345763	−	0.938322i	$-0.387620\pi$
$223$	24.9464	+	9.07976i	0.00749119	+	0.00272657i	−0.338272	+	0.941048i	$0.609842\pi$
$224$	1615.81	+	2798.67i	0.481968	+	0.834794i
$225$	−1319.93	+	1438.21i	−0.391090	+	0.426136i
$226$	−3407.16	+	5901.37i	−1.00284	+	1.73696i
$227$	−1339.89	+	1124.30i	−0.391769	+	0.328733i	−0.817302	−	0.576210i	$-0.804531\pi$
$227$	−1339.89	+	1124.30i	−0.391769	+	0.328733i	0.425533	+	0.904943i	$0.360087\pi$
$228$	−3745.04	−	8520.21i	−1.08781	−	2.47484i
$229$	879.549	−	4988.17i	0.253809	−	1.43942i	−0.545303	−	0.838239i	$-0.683585\pi$
$229$	879.549	−	4988.17i	0.253809	−	1.43942i	0.799112	−	0.601183i	$-0.205304\pi$
$230$	−1955.29	+	11089.0i	−0.560558	+	3.17908i
$231$	−1497.16	−	164.553i	−0.426434	−	0.0468693i
$232$	7765.53	−	6516.05i	2.19755	−	1.84397i
$233$	1863.46	−	3227.61i	0.523947	−	0.907502i	−0.475665	−	0.879627i	$-0.657792\pi$
$233$	1863.46	−	3227.61i	0.523947	−	0.907502i	0.999611	−	0.0278757i	$-0.00887427\pi$
$234$	−665.248	−	868.360i	−0.185849	−	0.242592i
$235$	2464.04	+	4267.85i	0.683985	+	1.18470i
$236$	11380.2	+	4142.04i	3.13892	+	1.14247i
$237$	257.710	−	882.890i	0.0706332	−	0.241983i
$238$	378.089	+	317.254i	0.102974	+	0.0864056i
$239$	−1196.76	+	435.586i	−0.323901	+	0.117890i	−0.498853	−	0.866687i	$-0.666245\pi$
$239$	−1196.76	+	435.586i	−0.323901	+	0.117890i	0.174952	+	0.984577i	$0.444023\pi$
$240$	−9776.65	−	4826.02i	−2.62950	−	1.29799i
$241$	−1183.07	−	6709.50i	−0.316216	−	1.79335i	−0.565320	−	0.824872i	$-0.691247\pi$
$241$	−1183.07	−	6709.50i	−0.316216	−	1.79335i	0.249104	−	0.968477i	$-0.419864\pi$
$242$	−2808.40			−0.745996
$243$	2503.11	−	2843.12i	0.660801	−	0.750561i
$244$	−11191.5			−2.93633
$245$	−577.849	−	3277.14i	−0.150683	−	0.854567i
$246$	−1080.99	−	533.605i	−0.280168	−	0.138298i
$247$	683.615	−	248.816i	0.176103	−	0.0640962i
$248$	9420.90	+	7905.07i	2.41221	+	2.02408i
$249$	−1183.72	+	4055.32i	−0.301267	+	1.03211i
$250$	3624.18	+	1319.09i	0.916854	+	0.333707i
$251$	−1357.33	−	2350.96i	−0.341329	−	0.591199i	0.643351	−	0.765572i	$-0.277544\pi$
$251$	−1357.33	−	2350.96i	−0.341329	−	0.591199i	−0.984680	+	0.174372i	$0.944210\pi$
$252$	−3237.99	−	4226.61i	−0.809422	−	1.05655i
$253$	2164.99	−	3749.87i	0.537991	−	0.931828i
$254$	−7442.16	+	6244.72i	−1.83844	+	1.54263i
$255$	−667.252	−	73.3375i	−0.163862	−	0.0180101i
$256$	−809.345	+	4590.02i	−0.197594	+	1.12061i
$257$	−185.247	+	1050.59i	−0.0449626	+	0.254996i	−0.999001	−	0.0446889i	$-0.985770\pi$
$257$	−185.247	+	1050.59i	−0.0449626	+	0.254996i	0.954038	+	0.299685i	$0.0968815\pi$
$258$	145.391	+	330.774i	0.0350839	+	0.0798181i
$259$	805.792	−	676.140i	0.193318	−	0.162213i
$260$	1045.59	−	1811.01i	0.249402	−	0.431977i
$261$	−3187.06	+	3472.66i	−0.755838	+	0.823571i
$262$	−3276.69	−	5675.39i	−0.772650	−	1.33827i
$263$	−610.224	−	222.103i	−0.143072	−	0.0520741i	0.269491	−	0.963003i	$-0.413144\pi$
$263$	−610.224	−	222.103i	−0.143072	−	0.0520741i	−0.412564	+	0.910929i	$0.635367\pi$
$264$	5869.52	+	6136.14i	1.36835	+	1.43050i
$265$	−1107.68	−	929.454i	−0.256771	−	0.215456i
$266$	4717.76	−	1717.12i	1.08746	−	0.395803i
$267$	−271.834	−	4172.16i	−0.0623071	−	0.956299i
$268$	2452.56	+	13909.2i	0.559007	+	3.17029i
$269$	4175.34			0.946376			0.473188	−	0.880961i	$-0.343103\pi$
$269$	4175.34			0.946376			0.473188	+	0.880961i	$0.343103\pi$
$270$	9718.58	+	3311.62i	2.19057	+	0.746439i
$271$	−3407.60			−0.763826			−0.381913	−	0.924198i	$-0.624735\pi$
$271$	−3407.60			−0.763826			−0.381913	+	0.924198i	$0.624735\pi$
$272$	−238.572	−	1353.01i	−0.0531822	−	0.301611i
$273$	346.134	−	231.086i	0.0767363	−	0.0512306i
$274$	−4299.85	+	1565.02i	−0.948041	+	0.345059i
$275$	1558.64	+	1307.85i	0.341780	+	0.286787i
$276$	14869.3	−	3632.38i	3.24284	−	0.792187i
$277$	−39.1626	−	14.2540i	−0.00849478	−	0.00309185i	0.337769	−	0.941229i	$-0.390328\pi$
$277$	−39.1626	−	14.2540i	−0.00849478	−	0.00309185i	−0.346264	+	0.938137i	$0.612550\pi$
$278$	−2173.35	−	3764.36i	−0.468881	−	0.812126i
$279$	−4820.31	−	3076.13i	−1.03435	−	0.660083i
$280$	4200.64	−	7275.71i	0.896557	−	1.55288i
$281$	−2537.78	+	2129.45i	−0.538759	+	0.452072i	−0.871113	−	0.491082i	$-0.836601\pi$
$281$	−2537.78	+	2129.45i	−0.538759	+	0.452072i	0.332354	+	0.943155i	$0.392157\pi$
$282$	5619.39	−	7657.66i	1.18663	−	1.61705i
$283$	−155.695	+	882.992i	−0.0327036	+	0.185471i	−0.996784	−	0.0801408i	$-0.974463\pi$
$283$	−155.695	+	882.992i	−0.0327036	+	0.185471i	0.964080	+	0.265612i	$0.0855741\pi$
$284$	3171.45	−	17986.2i	0.662643	−	3.75804i
$285$	−4039.72	+	5505.01i	−0.839623	+	1.14417i
$286$	−873.414	+	732.882i	−0.180581	+	0.151525i
$287$	229.326	−	397.205i	0.0471662	−	0.0816943i
$288$	−376.065	+	8462.83i	−0.0769439	+	1.73152i
$289$	2414.21	+	4181.53i	0.491392	+	0.851115i
$290$	−12005.3	−	4369.57i	−2.43095	−	0.884792i
$291$	1808.69	−	441.841i	0.364355	−	0.0890074i
$292$	14347.8	+	12039.2i	2.87549	+	2.41282i
$293$	−2143.41	+	780.138i	−0.427370	+	0.155550i	−0.546745	−	0.837299i	$-0.684133\pi$
$293$	−2143.41	+	780.138i	−0.427370	+	0.155550i	0.119375	+	0.992849i	$0.461911\pi$
$294$	−5334.20	+	3561.21i	−1.05815	+	0.706442i
$295$	−1542.88	−	8750.12i	−0.304509	−	1.72695i
$296$	−5930.21			−1.16448
$297$	−3076.27	−	2474.86i	−0.601022	−	0.483521i
$298$	10825.7			2.10442
$299$	207.761	+	1178.27i	0.0401845	+	0.227897i
$300$	467.633	+	7177.31i	0.0899961	+	1.38127i
$301$	−129.177	+	47.0165i	−0.0247363	+	0.00900328i
$302$	−13658.1	−	11460.5i	−2.60244	−	2.18370i
$303$	−102.938	−	107.614i	−0.0195169	−	0.0204034i
$304$	−13132.4	−	4779.81i	−2.47762	−	0.901780i
$305$	4105.43	+	7110.81i	0.770742	+	1.33496i
$306$	388.094	+	1234.21i	0.0725027	+	0.230572i
$307$	209.089	−	362.153i	0.0388709	−	0.0673263i	−0.845935	−	0.533285i	$-0.820957\pi$
$307$	209.089	−	362.153i	0.0388709	−	0.0673263i	0.884806	+	0.465959i	$0.154291\pi$
$308$	−4251.21	+	3567.19i	−0.786478	+	0.659933i
$309$	592.288	+	1347.49i	0.109042	+	0.248078i
$310$	2691.40	−	15263.7i	0.493101	−	2.79651i
$311$	−368.887	+	2092.06i	−0.0672593	+	0.381447i	0.932533	+	0.361084i	$0.117593\pi$
$311$	−368.887	+	2092.06i	−0.0672593	+	0.381447i	−0.999793	+	0.0203628i	$0.993518\pi$
$312$	−2332.27	−	256.340i	−0.423202	−	0.0465141i
$313$	−7874.07	+	6607.13i	−1.42194	+	1.19315i	−0.471656	+	0.881783i	$0.656344\pi$
$313$	−7874.07	+	6607.13i	−1.42194	+	1.19315i	−0.950289	+	0.311371i	$0.899212\pi$
$314$	3868.91	−	6701.15i	0.695335	−	1.20436i
$315$	−1497.68	+	3607.80i	−0.267888	+	0.645323i
$316$	−1694.39	−	2934.77i	−0.301636	−	0.522448i
$317$	10318.9	+	3755.76i	1.82828	+	0.665440i	0.993357	+	0.115073i	$0.0367103\pi$
$317$	10318.9	+	3755.76i	1.82828	+	0.665440i	0.834923	+	0.550366i	$0.185512\pi$
$318$	−780.902	+	2675.29i	−0.137707	+	0.471771i
$319$	3763.43	+	3157.90i	0.660539	+	0.554258i
$320$	−5802.50	+	2111.94i	−1.01366	+	0.368940i
$321$	4353.62	+	2149.07i	0.756996	+	0.373674i
$322$	1433.80	+	8131.50i	0.248145	+	1.40730i
$323$	−860.427			−0.148221
$324$	−1194.88	−	13905.7i	−0.204884	−	2.38438i
$325$	−562.212			−0.0959566
$326$	−154.201	−	874.518i	−0.0261976	−	0.148574i
$327$	3617.12	+	1785.51i	0.611704	+	0.301954i
$328$	−2429.80	+	884.376i	−0.409035	+	0.148876i
$329$	2768.28	+	2322.86i	0.463891	+	0.389250i
$330$	2998.59	−	10272.9i	0.500203	−	1.71365i
$331$	1904.54	+	693.198i	0.316264	+	0.115111i	0.495274	−	0.868737i	$-0.335068\pi$
$331$	1904.54	+	693.198i	0.316264	+	0.115111i	−0.179011	+	0.983847i	$0.557290\pi$
$332$	7782.73	+	13480.1i	1.28655	+	2.22836i
$333$	2734.04	−	357.789i	0.449924	−	0.0588790i
$334$	−4260.78	+	7379.89i	−0.698022	+	1.20901i
$335$	7937.85	−	6660.65i	1.29460	−	1.08630i
$336$	−7947.16	−	873.472i	−1.29034	−	0.141821i
$337$	−533.497	+	3025.61i	−0.0862357	+	0.489067i	0.910847	+	0.412743i	$0.135429\pi$
$337$	−533.497	+	3025.61i	−0.0862357	+	0.489067i	−0.997083	+	0.0763238i	$0.975682\pi$
$338$	−1932.98	+	10962.5i	−0.311066	+	1.76414i
$339$	−2734.68	−	6221.56i	−0.438133	−	0.996781i
$340$	−1894.67	+	1589.81i	−0.302214	+	0.253587i
$341$	−2980.04	+	5161.58i	−0.473249	+	0.819692i
$342$	12846.4	+	2858.42i	2.03115	+	0.451946i
$343$	−2986.55	−	5172.86i	−0.470142	−	0.814309i
$344$	728.259	+	265.064i	0.114143	+	0.0415445i
$345$	−7762.48	−	8115.08i	−1.21136	−	1.26638i
$346$	−2926.08	−	2455.27i	−0.454645	−	0.381492i
$347$	−1927.29	+	701.477i	−0.298163	+	0.108522i	−0.486770	−	0.873530i	$-0.661825\pi$
$347$	−1927.29	+	701.477i	−0.298163	+	0.108522i	0.188607	+	0.982053i	$0.439603\pi$
$348$	1129.13	+	17330.1i	0.173931	+	2.66951i
$349$	1918.28	+	10879.1i	0.294222	+	1.66861i	0.670350	+	0.742046i	$0.266144\pi$
$349$	1918.28	+	10879.1i	0.294222	+	1.66861i	−0.376128	+	0.926568i	$0.622745\pi$
$350$	−3879.93			−0.592546
$351$	1090.73	−	22.5315i	0.165866	−	0.00342634i
$352$	8829.48			1.33697
$353$	939.716	+	5329.39i	0.141688	+	0.803555i	0.969967	+	0.243238i	$0.0782097\pi$
$353$	939.716	+	5329.39i	0.141688	+	0.803555i	−0.828278	+	0.560317i	$0.810679\pi$
$354$	−14242.5	+	9508.58i	−2.13837	+	1.42761i
$355$	−12591.4	+	4582.88i	−1.88248	+	0.685166i
$356$	−11800.9	−	9902.15i	−1.75688	−	1.47419i
$357$	−478.176	+	116.813i	−0.0708900	+	0.0173176i
$358$	−5979.88	−	2176.50i	−0.882811	−	0.321317i
$359$	−4847.03	−	8395.31i	−0.712581	−	1.23423i	−0.963885	−	0.266319i	$-0.914193\pi$
$359$	−4847.03	−	8395.31i	−0.712581	−	1.23423i	0.251304	−	0.967908i	$-0.419141\pi$
$360$	19542.2	−	10153.8i	2.86101	−	1.48653i
$361$	−946.669	+	1639.68i	−0.138019	+	0.239055i
$362$	12826.8	−	10763.0i	1.86233	−	1.56268i
$363$	1657.06	−	2258.11i	0.239595	−	0.326501i
$364$	266.279	−	1510.15i	0.0383430	−	0.217454i
$365$	2386.17	−	13532.7i	0.342186	−	1.94063i
$366$	9362.66	−	12758.7i	1.33714	−	1.82215i
$367$	3237.97	−	2716.98i	0.460546	−	0.386444i	−0.382786	−	0.923837i	$-0.625035\pi$
$367$	3237.97	−	2716.98i	0.460546	−	0.386444i	0.843332	+	0.537393i	$0.180591\pi$
$368$	11492.1	−	19904.8i	1.62790	−	2.81960i
$369$	1066.87	−	554.327i	0.150512	−	0.0782035i
$370$	3736.88	+	6472.47i	0.525058	+	0.909427i
$371$	−996.376	−	362.651i	−0.139432	−	0.0507491i
$372$	−20467.1	+	4999.85i	−2.85260	+	0.696856i
$373$	−6860.80	−	5756.89i	−0.952383	−	0.799144i	0.0273146	−	0.999627i	$-0.491304\pi$
$373$	−6860.80	−	5756.89i	−0.952383	−	0.799144i	−0.979697	+	0.200483i	$0.935749\pi$
$374$	1267.19	−	461.218i	0.175200	−	0.0637674i
$375$	−3199.02	+	2135.73i	−0.440525	+	0.294102i
$376$	−3537.75	−	20063.6i	−0.485227	−	2.75186i
$377$	−1357.50			−0.185450
$378$	7527.33	−	155.495i	1.02424	−	0.0211581i
$379$	11673.7			1.58216			0.791080	−	0.611713i	$-0.209519\pi$
$379$	11673.7			1.58216			0.791080	+	0.611713i	$0.209519\pi$
$380$	4368.77	+	24776.5i	0.589771	+	3.34476i
$381$	−629.946	−	9668.51i	−0.0847063	−	1.30009i
$382$	2389.27	−	869.622i	0.320014	−	0.116476i
$383$	8536.82	+	7163.25i	1.13893	+	0.955678i	0.999403	−	0.0345397i	$-0.0109965\pi$
$383$	8536.82	+	7163.25i	1.13893	+	0.955678i	0.139530	+	0.990218i	$0.455441\pi$
$384$	−788.624	−	824.447i	−0.104803	−	0.109563i
$385$	3825.99	+	1392.55i	0.506469	+	0.184340i
$386$	12386.6	+	21454.2i	1.63332	+	2.82899i
$387$	−351.746	−	78.2661i	−0.0462022	−	0.0102803i
$388$	3430.06	−	5941.04i	0.448802	−	0.777347i
$389$	773.936	−	649.410i	0.100874	−	0.0846437i	−0.590956	−	0.806704i	$-0.701249\pi$
$389$	773.936	−	649.410i	0.100874	−	0.0846437i	0.691830	+	0.722060i	$0.256805\pi$
$390$	1189.89	+	2707.07i	0.154493	+	0.351482i
$391$	245.727	−	1393.59i	0.0317825	−	0.180247i
$392$	−2388.87	+	13548.0i	−0.307796	+	1.74560i
$393$	6496.68	+	714.049i	0.833878	+	0.0916515i
$394$	−1421.34	+	1192.65i	−0.181742	+	0.152499i
$395$	−1243.12	+	2153.15i	−0.158350	+	0.274270i
$396$	−14424.3	+	1887.63i	−1.83042	+	0.239537i
$397$	−2473.26	−	4283.81i	−0.312668	−	0.541557i	0.666271	−	0.745710i	$-0.267889\pi$
$397$	−2473.26	−	4283.81i	−0.312668	−	0.541557i	−0.978939	+	0.204153i	$0.934556\pi$
$398$	−6962.31	−	2534.07i	−0.876857	−	0.319150i
$399$	−1402.99	+	4806.50i	−0.176033	+	0.603073i
$400$	8273.47	+	6942.26i	1.03418	+	0.867783i
$401$	−12908.4	+	4698.27i	−1.60752	+	0.585089i	−0.980947	−	0.194275i	$-0.937764\pi$
$401$	−12908.4	+	4698.27i	−1.60752	+	0.585089i	−0.626571	+	0.779364i	$0.715542\pi$
$402$	−17908.7	−	8840.21i	−2.22190	−	1.09679i
$403$	−285.977	−	1621.86i	−0.0353487	−	0.200472i
$404$	−548.696			−0.0675709
$405$	−8397.03	+	5860.29i	−1.03025	+	0.719013i
$406$	−9368.36			−1.14518
$407$	−499.061	−	2830.32i	−0.0607802	−	0.344702i
$408$	2488.42	+	1228.35i	0.301949	+	0.149050i
$409$	7172.22	−	2610.48i	0.867099	−	0.315598i	0.130107	−	0.991500i	$-0.458468\pi$
$409$	7172.22	−	2610.48i	0.867099	−	0.315598i	0.736992	+	0.675902i	$0.236246\pi$
$410$	2496.37	+	2094.70i	0.300700	+	0.252317i
$411$	1278.71	−	4380.72i	0.153465	−	0.525755i
$412$	5096.25	+	1854.88i	0.609403	+	0.221805i
$413$	−3257.69	−	5642.48i	−0.388136	−	0.672272i
$414$	−8298.38	+	19990.2i	−0.985129	+	2.37311i
$415$	5709.95	−	9889.92i	0.675398	−	1.16982i
$416$	−1868.95	+	1568.24i	−0.220271	+	0.184830i
$417$	4309.10	+	473.613i	0.506037	+	0.0556185i
$418$	2381.96	−	13508.8i	0.278721	−	1.58071i
$419$	1580.39	−	8962.85i	0.184265	−	1.04502i	−0.742630	−	0.669702i	$-0.766422\pi$
$419$	1580.39	−	8962.85i	0.184265	−	1.04502i	0.926896	−	0.375319i	$-0.122467\pi$
$420$	5791.59	+	13176.2i	0.672859	+	1.53080i
$421$	−3026.66	+	2539.67i	−0.350381	+	0.294004i	−0.800943	−	0.598741i	$-0.795668\pi$
$421$	−3026.66	+	2539.67i	−0.350381	+	0.294004i	0.450562	+	0.892745i	$0.351224\pi$
$422$	−8678.33	+	15031.3i	−1.00108	+	1.73392i
$423$	2841.53	+	9036.58i	0.326619	+	1.03871i
$424$	2988.88	+	5176.89i	0.342342	+	0.592953i
$425$	624.848	+	227.426i	0.0713166	+	0.0259571i
$426$	17851.6	+	18662.5i	2.03032	+	2.12254i
$427$	4612.32	+	3870.20i	0.522731	+	0.438623i
$428$	16810.1	−	6118.38i	1.89847	−	0.690988i
$429$	−73.9306	−	1134.70i	−0.00832029	−	0.127701i
$430$	−169.605	−	961.880i	−0.0190212	−	0.107874i
$431$	−8689.98			−0.971187			−0.485594	−	0.874185i	$-0.661397\pi$
$431$	−8689.98			−0.971187			−0.485594	+	0.874185i	$0.661397\pi$
$432$	−16329.3	−	13136.9i	−1.81862	−	1.46308i
$433$	−466.281			−0.0517507			−0.0258753	−	0.999665i	$-0.508237\pi$
$433$	−466.281			−0.0517507			−0.0258753	+	0.999665i	$0.508237\pi$
$434$	−1973.58	−	11192.7i	−0.218283	−	1.23795i
$435$	10596.9	−	7074.70i	1.16801	−	0.779783i
$436$	13966.3	−	5083.33i	1.53410	−	0.558366i
$437$	−11026.7	−	9252.53i	−1.20705	−	1.01283i
$438$	−25728.3	+	6285.11i	−2.80673	+	0.685649i
$439$	−3386.08	−	1232.43i	−0.368129	−	0.133988i	0.151330	−	0.988483i	$-0.451644\pi$
$439$	−3386.08	−	1232.43i	−0.368129	−	0.133988i	−0.519459	+	0.854495i	$0.673867\pi$
$440$	−11477.0	−	19878.8i	−1.24351	−	2.15383i
$441$	283.964	−	6390.22i	0.0306624	−	0.690014i
$442$	−186.309	+	322.696i	−0.0200493	+	0.0347265i
$443$	−592.851	+	497.461i	−0.0635828	+	0.0533523i	−0.674025	−	0.738708i	$-0.735436\pi$
$443$	−592.851	+	497.461i	−0.0635828	+	0.0533523i	0.610442	+	0.792061i	$0.290992\pi$
$444$	6010.61	−	8190.78i	0.642457	−	0.875489i
$445$	−1962.60	+	11130.5i	−0.209070	+	1.18570i
$446$	−24.0182	+	136.214i	−0.00254999	+	0.0144617i
$447$	−6387.56	+	8704.46i	−0.675887	+	0.921045i
$448$	−3468.65	+	2910.54i	−0.365800	+	0.306943i
$449$	4055.26	−	7023.92i	0.426235	−	0.738261i	−0.570300	−	0.821437i	$-0.693173\pi$
$449$	4055.26	−	7023.92i	0.426235	−	0.738261i	0.996535	+	0.0831759i	$0.0265063\pi$
$450$	−8573.58	−	5471.32i	−0.898139	−	0.573157i
$451$	−626.568	−	1085.25i	−0.0654190	−	0.113309i
$452$	−23530.1	−	8564.26i	−2.44859	−	0.891214i
$453$	17273.7	−	4219.75i	1.79158	−	0.437662i
$454$	−6980.98	−	5857.73i	−0.721660	−	0.605544i
$455$	−1057.19	+	384.786i	−0.108927	+	0.0396462i
$456$	23477.1	−	15673.7i	2.41100	−	1.60963i
$457$	1689.39	+	9580.99i	0.172924	+	0.980700i	0.940513	+	0.339758i	$0.110345\pi$
$457$	1689.39	+	9580.99i	0.172924	+	0.980700i	−0.767589	+	0.640942i	$0.778544\pi$
$458$	26389.9			2.69240
$459$	−1221.36	−	416.180i	−0.124201	−	0.0423216i
$460$	−41376.9			−4.19393
$461$	2113.75	+	11987.7i	0.213552	+	1.21111i	0.883402	+	0.468615i	$0.155247\pi$
$461$	2113.75	+	11987.7i	0.213552	+	1.21111i	−0.669851	+	0.742496i	$0.733642\pi$
$462$	−510.210	−	7830.78i	−0.0513790	−	0.788573i
$463$	−15186.9	+	5527.57i	−1.52439	+	0.554834i	−0.962241	−	0.272199i	$-0.912249\pi$
$463$	−15186.9	+	5527.57i	−1.52439	+	0.554834i	−0.562153	+	0.827033i	$0.690027\pi$
$464$	19976.8	+	16762.6i	1.99871	+	1.67712i
$465$	10684.8	+	11170.1i	1.06558	+	1.11399i
$466$	18246.7	+	6641.26i	1.81387	+	0.660194i
$467$	−708.341	−	1226.88i	−0.0701887	−	0.121570i	0.828795	−	0.559552i	$-0.189027\pi$
$467$	−708.341	−	1226.88i	−0.0701887	−	0.121570i	−0.898984	+	0.437982i	$0.855693\pi$
$468$	2717.95	−	2961.51i	0.268456	−	0.292512i
$469$	3799.24	−	6580.47i	0.374056	−	0.647885i
$470$	−19668.9	+	16504.2i	−1.93034	+	1.61975i
$471$	3105.29	+	7064.74i	0.303788	+	0.691138i
$472$	−6378.39	+	36173.6i	−0.622011	+	3.52760i
$473$	−65.2204	+	369.883i	−0.00634004	+	0.0359561i
$474$	4763.24	+	523.527i	0.461567	+	0.0507308i
$475$	5181.46	−	4347.76i	0.500509	−	0.419977i
$476$	−906.829	+	1570.67i	−0.0873203	+	0.151243i
$477$	−1690.32	−	2206.41i	−0.162253	−	0.211791i
$478$	−3317.73	−	5746.47i	−0.317467	−	0.549869i
$479$	8263.76	+	3007.76i	0.788269	+	0.286906i	0.704616	−	0.709589i	$-0.251119\pi$
$479$	8263.76	+	3007.76i	0.788269	+	0.286906i	0.0836525	+	0.996495i	$0.473341\pi$
$480$	6416.45	−	21982.1i	0.610145	−	2.09030i
$481$	608.340	+	510.458i	0.0576672	+	0.0483885i
$482$	33355.9	−	12140.5i	3.15211	−	1.14728i
$483$	−7384.16	−	3645.02i	−0.695633	−	0.343383i
$484$	−1792.03	−	10163.1i	−0.168297	−	0.954462i
$485$	−5033.06			−0.471215
$486$	16852.6	+	10271.1i	1.57294	+	0.958658i
$487$	15649.1			1.45612			0.728059	−	0.685514i	$-0.240423\pi$
$487$	15649.1			1.45612			0.728059	+	0.685514i	$0.240423\pi$
$488$	−5894.37	−	33428.6i	−0.546774	−	3.10091i
$489$	794.144	+	392.011i	0.0734405	+	0.0362522i
$490$	16292.1	−	5929.84i	1.50205	−	0.546700i
$491$	6074.50	+	5097.11i	0.558326	+	0.468491i	0.877749	−	0.479121i	$-0.159044\pi$
$491$	6074.50	+	5097.11i	0.558326	+	0.468491i	−0.319423	+	0.947612i	$0.603489\pi$
$492$	1241.25	−	4252.40i	0.113739	−	0.389660i
$493$	1508.74	+	549.135i	0.137830	+	0.0501659i
$494$	1895.15	+	3282.50i	0.172605	+	0.298960i
$495$	6490.68	+	8472.40i	0.589362	+	0.769305i
$496$	−15818.5	+	27398.4i	−1.43200	+	2.48029i
$497$	−7526.93	+	6315.85i	−0.679334	+	0.570029i
$498$	−21878.7	−	2404.68i	−1.96869	−	0.216378i
$499$	−1554.53	+	8816.20i	−0.139460	+	0.790917i	0.832190	+	0.554491i	$0.187087\pi$
$499$	−1554.53	+	8816.20i	−0.139460	+	0.790917i	−0.971650	+	0.236426i	$0.924024\pi$
$500$	−2460.99	+	13957.0i	−0.220118	+	1.24835i
$501$	−3419.81	−	7780.29i	−0.304962	−	0.693808i
$502$	10834.7	−	9091.37i	0.963297	−	0.808302i
$503$	−1203.74	+	2084.94i	−0.106704	+	0.184817i	−0.914433	−	0.404737i	$-0.867363\pi$
$503$	−1203.74	+	2084.94i	−0.106704	+	0.184817i	0.807729	+	0.589554i	$0.200696\pi$
$504$	10919.3	−	11897.8i	0.965051	−	1.05153i
$505$	201.280	+	348.628i	0.0177364	+	0.0307203i
$506$	21199.2	+	7715.87i	1.86249	+	0.677890i
$507$	−7673.89	−	8022.47i	−0.672208	−	0.702743i
$508$	−27347.3	−	22947.1i	−2.38847	−	2.00416i
$509$	−15330.5	+	5579.84i	−1.33499	+	0.485898i	−0.908232	−	0.418467i	$-0.862568\pi$
$509$	−15330.5	+	5579.84i	−1.33499	+	0.485898i	−0.426761	+	0.904364i	$0.640345\pi$
$510$	−227.389	−	3490.00i	−0.0197430	−	0.303019i
$511$	−1749.76	−	9923.39i	−0.151477	−	0.859070i
$512$	−22527.0			−1.94446
$513$	−9878.14	+	8642.61i	−0.850157	+	0.743821i
$514$	−5558.13			−0.476963
$515$	−690.931	−	3918.47i	−0.0591186	−	0.335278i
$516$	−1104.24	+	737.209i	−0.0942080	+	0.0628950i
$517$	9278.03	−	3376.93i	0.789260	−	0.287267i
$518$	4198.27	+	3522.77i	0.356103	+	0.298806i
$519$	3700.67	−	904.028i	0.312989	−	0.0764594i
$520$	5960.11	+	2169.30i	0.502631	+	0.182943i
$521$	−663.090	−	1148.51i	−0.0557591	−	0.0965776i	0.836799	−	0.547511i	$-0.184425\pi$
$521$	−663.090	−	1148.51i	−0.0557591	−	0.0965776i	−0.892558	+	0.450933i	$0.851091\pi$
$522$	−20701.5	−	13210.9i	−1.73579	−	1.10771i
$523$	−6244.91	+	10816.5i	−0.522124	+	0.904346i	0.477545	+	0.878608i	$0.341527\pi$
$523$	−6244.91	+	10816.5i	−0.522124	+	0.904346i	−0.999669	+	0.0257380i	$0.991806\pi$
$524$	18447.4	−	15479.2i	1.53793	−	1.29048i
$525$	2289.30	−	3119.68i	0.190311	−	0.259341i
$526$	587.518	−	3331.98i	0.0487016	−	0.276200i
$527$	−338.235	+	1918.23i	−0.0279578	+	0.158557i
$528$	−12923.4	+	17611.0i	−1.06519	+	1.45156i
$529$	8814.46	−	7396.21i	0.724457	−	0.607891i
$530$	3766.85	−	6524.37i	0.308720	−	0.534718i
$531$	758.197	−	17062.2i	0.0619641	−	1.39442i
$532$	9224.35	+	15977.0i	0.751741	+	1.30205i
$533$	325.382	+	118.429i	0.0264425	+	0.00962428i
$534$	21161.3	−	5169.44i	1.71486	−	0.418921i
$535$	−10054.0	−	8436.30i	−0.812471	−	0.681744i
$536$	−40254.4	+	14651.4i	−3.24389	+	1.18068i
$537$	5278.37	−	3523.93i	0.424168	−	0.283183i
$538$	3777.55	+	21423.5i	0.302717	+	1.71679i
$539$	−6667.08			−0.532785
$540$	−5782.76	+	37282.9i	−0.460834	+	2.97111i
$541$	−952.104			−0.0756639			−0.0378319	−	0.999284i	$-0.512045\pi$
$541$	−952.104			−0.0756639			−0.0378319	+	0.999284i	$0.512045\pi$
$542$	−3082.95	−	17484.3i	−0.244325	−	1.38564i
$543$	1085.73	+	16664.0i	0.0858071	+	1.31698i
$544$	2711.55	−	986.925i	0.213707	−	0.0777832i
$545$	−8353.16	−	7009.13i	−0.656532	−	0.550896i
$546$	1498.85	+	1566.93i	0.117481	+	0.122818i
$547$	−20935.7	−	7619.95i	−1.63646	−	0.595623i	−0.650045	−	0.759895i	$-0.725250\pi$
$547$	−20935.7	−	7619.95i	−1.63646	−	0.595623i	−0.986415	+	0.164273i	$0.947472\pi$
$548$	−8407.22	−	14561.7i	−0.655363	−	1.13512i
$549$	4734.37	+	15056.2i	0.368048	+	1.17046i
$550$	−5300.40	+	9180.57i	−0.410927	+	0.711747i
$551$	12511.0	−	10498.0i	0.967307	−	0.811667i
$552$	18681.2	+	42500.8i	1.44044	+	3.27709i
$553$	−316.585	+	1795.44i	−0.0243446	+	0.138065i
$554$	37.7054	−	213.838i	0.00289161	−	0.0163991i
$555$	−7409.11	−	814.335i	−0.566666	−	0.0622821i
$556$	12235.7	−	10267.0i	0.933292	−	0.783125i
$557$	593.031	−	1027.16i	0.0451123	−	0.0781368i	−0.842588	−	0.538559i	$-0.818969\pi$
$557$	593.031	−	1027.16i	0.0451123	−	0.0781368i	0.887700	+	0.460423i	$0.152302\pi$
$558$	11422.5	−	27515.9i	0.866579	−	2.08753i
$559$	−51.8910	−	89.8779i	−0.00392622	−	0.00680041i
$560$	20308.9	+	7391.84i	1.53251	+	0.557790i
$561$	−376.841	+	1291.02i	−0.0283605	+	0.0971603i
$562$	−13222.1	−	11094.7i	−0.992424	−	0.832742i
$563$	−8233.42	+	2996.72i	−0.616337	+	0.224328i	−0.631274	−	0.775560i	$-0.717467\pi$
$563$	−8233.42	+	2996.72i	−0.616337	+	0.224328i	0.0149370	+	0.999888i	$0.495245\pi$
$564$	31297.4	+	15449.2i	2.33663	+	1.15342i
$565$	3190.13	+	18092.1i	0.237539	+	1.34715i
$566$	−4671.46			−0.346919
$567$	−4316.37	+	6144.13i	−0.319701	+	0.455078i
$568$	55394.3			4.09207
$569$	−3624.70	−	20556.7i	−0.267057	−	1.51455i	−0.763114	−	0.646264i	$-0.776330\pi$
$569$	−3624.70	−	20556.7i	−0.267057	−	1.51455i	0.496057	−	0.868290i	$-0.334781\pi$
$570$	−31900.9	−	15747.1i	−2.34418	−	1.15715i
$571$	2011.89	−	732.266i	0.147451	−	0.0536679i	−0.267240	−	0.963630i	$-0.586112\pi$
$571$	2011.89	−	732.266i	0.147451	−	0.0536679i	0.414692	+	0.909962i	$0.363889\pi$
$572$	−3209.49	−	2693.08i	−0.234607	−	0.196859i
$573$	−710.530	+	2434.21i	−0.0518025	+	0.177470i
$574$	2245.52	+	817.304i	0.163286	+	0.0594313i
$575$	5562.08	+	9633.80i	0.403400	+	0.698709i
$576$	−11769.1	+	1540.15i	−0.851352	+	0.111412i
$577$	−6084.38	+	10538.5i	−0.438988	+	0.760350i	−0.997612	−	0.0690715i	$-0.977996\pi$
$577$	−6084.38	+	10538.5i	−0.438988	+	0.760350i	0.558624	+	0.829421i	$0.311330\pi$
$578$	−19271.1	+	16170.4i	−1.38680	+	1.16366i
$579$	−24558.9	−	2699.26i	−1.76275	−	0.193743i
$580$	8152.15	−	46233.2i	0.583620	−	3.30988i
$581$	1454.15	−	8246.90i	0.103835	−	0.588879i
$582$	3903.44	+	8880.58i	0.278012	+	0.632494i
$583$	−2219.25	+	1862.17i	−0.157653	+	0.132287i
$584$	−28404.0	+	49197.2i	−2.01261	+	3.48595i
$585$	−2878.71	−	640.535i	−0.203453	−	0.0452698i
$586$	−5942.07	−	10292.0i	−0.418881	−	0.725524i
$587$	6654.84	+	2422.16i	0.467930	+	0.170312i	0.565214	−	0.824944i	$-0.308794\pi$
$587$	6654.84	+	2422.16i	0.467930	+	0.170312i	−0.0972847	+	0.995257i	$0.531016\pi$
$588$	−16291.1	−	17031.1i	−1.14257	−	1.19447i
$589$	15177.9	+	12735.8i	1.06179	+	0.890950i
$590$	43500.7	−	15832.9i	3.03541	−	1.10480i
$591$	−120.310	−	1846.54i	−0.00837378	−	0.128522i
$592$	−2649.09	−	15023.7i	−0.183914	−	1.04303i
$593$	12714.8			0.880498			0.440249	−	0.897876i	$-0.354890\pi$
$593$	12714.8			0.880498			0.440249	+	0.897876i	$0.354890\pi$
$594$	9915.21	−	18023.3i	0.684892	−	1.24496i
$595$	1330.62			0.0916811
$596$	6907.85	+	39176.3i	0.474759	+	2.69249i
$597$	6145.55	−	4102.88i	0.421307	−	0.281272i
$598$	−5857.72	+	2132.03i	−0.400568	+	0.145795i
$599$	15146.2	+	12709.2i	1.03315	+	0.866916i	0.991222	−	0.132205i	$-0.0422056\pi$
$599$	15146.2	+	12709.2i	1.03315	+	0.866916i	0.0419278	+	0.999121i	$0.486650\pi$
$600$	−21192.1	+	5176.96i	−1.44194	+	0.352248i
$601$	−17664.7	−	6429.42i	−1.19893	−	0.436375i	−0.336080	−	0.941834i	$-0.609101\pi$
$601$	−17664.7	−	6429.42i	−1.19893	−	0.436375i	−0.862851	+	0.505459i	$0.831323\pi$
$602$	−358.110	−	620.265i	−0.0242450	−	0.0419935i
$603$	17674.8	−	9183.50i	1.19365	−	0.620201i
$604$	32758.4	−	56739.2i	2.20682	−	3.82233i
$605$	−5800.01	+	4866.79i	−0.389759	+	0.327046i
$606$	459.031	−	625.531i	0.0307704	−	0.0419315i
$607$	1337.17	−	7583.44i	0.0894133	−	0.507088i	−0.906903	−	0.421339i	$-0.861560\pi$
$607$	1337.17	−	7583.44i	0.0894133	−	0.507088i	0.996317	−	0.0857495i	$-0.0273285\pi$
$608$	5096.98	−	28906.4i	0.339983	−	1.92814i
$609$	5527.67	−	7532.67i	0.367804	−	0.501214i
$610$	−32771.1	+	27498.2i	−2.17518	+	1.82519i
$611$	−1364.11	+	2362.71i	−0.0903207	+	0.156440i
$612$	−4218.74	+	2191.99i	−0.278648	+	0.144781i
$613$	−4893.21	−	8475.28i	−0.322406	−	0.558423i	0.658578	−	0.752512i	$-0.271158\pi$
$613$	−4893.21	−	8475.28i	−0.322406	−	0.558423i	−0.980984	+	0.194089i	$0.937825\pi$
$614$	2047.37	+	745.180i	0.134568	+	0.0489789i
$615$	−3157.20	+	771.266i	−0.207009	+	0.0505698i
$616$	−12894.1	−	10819.4i	−0.843373	−	0.707674i
$617$	20934.3	−	7619.47i	1.36594	−	0.497161i	0.448053	−	0.894007i	$-0.352117\pi$
$617$	20934.3	−	7619.47i	1.36594	−	0.497161i	0.917885	+	0.396846i	$0.129895\pi$
$618$	−6378.08	+	4258.12i	−0.415152	+	0.277163i
$619$	2272.40	+	12887.4i	0.147554	+	0.836818i	0.965281	+	0.261213i	$0.0841223\pi$
$619$	2272.40	+	12887.4i	0.147554	+	0.836818i	−0.817728	+	0.575605i	$0.804767\pi$
$620$	56953.9			3.68923
$621$	−11176.9	−	18467.3i	−0.722244	−	1.19335i
$622$	−11068.0			−0.713486
$623$	1439.16	+	8161.88i	0.0925501	+	0.524878i
$624$	−392.434	−	6023.14i	−0.0251762	−	0.386408i
$625$	18263.1	−	6647.24i	1.16884	−	0.425423i
$626$	−41024.8	−	34423.9i	−2.61930	−	2.19785i
$627$	9456.34	+	9885.89i	0.602313	+	0.629672i
$628$	26719.0	+	9724.92i	1.69778	+	0.617941i
$629$	−469.624	−	813.413i	−0.0297697	−	0.0515627i
$630$	−19866.5	−	4420.45i	−1.25635	−	0.279548i
$631$	2430.50	−	4209.75i	0.153339	−	0.265590i	−0.779114	−	0.626882i	$-0.784331\pi$
$631$	2430.50	−	4209.75i	0.153339	−	0.265590i	0.932453	+	0.361292i	$0.117664\pi$
$632$	7873.64	−	6606.77i	0.495564	−	0.415828i
$633$	−6965.46	−	15846.9i	−0.437365	−	0.995034i
$634$	−9934.91	+	56343.7i	−0.622343	+	3.52948i
$635$	−4548.11	+	25793.6i	−0.284230	+	1.61195i
$636$	−10179.7	−	1118.85i	−0.634672	−	0.0697567i
$637$	1411.23	−	1184.16i	0.0877787	−	0.0736551i
$638$	−12798.2	+	22167.1i	−0.794177	+	1.37555i
$639$	−25538.8	+	3342.12i	−1.58106	+	0.206905i
$640$	1542.04	+	2670.90i	0.0952416	+	0.164963i
$641$	−17114.5	−	6229.18i	−1.05458	−	0.383834i	−0.244188	−	0.969728i	$-0.578521\pi$
$641$	−17114.5	−	6229.18i	−1.05458	−	0.383834i	−0.810388	+	0.585894i	$0.800744\pi$
$642$	−7087.95	+	24282.6i	−0.435730	+	1.49277i
$643$	−3185.24	−	2672.73i	−0.195355	−	0.163923i	0.539863	−	0.841753i	$-0.318476\pi$
$643$	−3185.24	−	2672.73i	−0.195355	−	0.163923i	−0.735218	+	0.677830i	$0.762920\pi$
$644$	−28511.5	+	10377.3i	−1.74458	+	0.634976i
$645$	873.477	+	431.172i	0.0533226	+	0.0263215i
$646$	−778.452	−	4414.82i	−0.0474114	−	0.268884i
$647$	20866.7			1.26793			0.633967	−	0.773360i	$-0.281426\pi$
$647$	20866.7			1.26793			0.633967	+	0.773360i	$0.281426\pi$
$648$	40906.5	−	10893.0i	2.47988	−	0.660364i
$649$	−17801.4			−1.07668
$650$	−508.649	−	2884.69i	−0.0306936	−	0.174072i
$651$	10164.1	+	5017.25i	0.611921	+	0.302061i
$652$	3066.33	−	1116.05i	0.184182	−	0.0670368i
$653$	7895.77	+	6625.34i	0.473178	+	0.397044i	0.847952	−	0.530073i	$-0.177835\pi$
$653$	7895.77	+	6625.34i	0.473178	+	0.397044i	−0.374774	+	0.927116i	$0.622280\pi$
$654$	−5888.88	+	20174.7i	−0.352100	+	1.20626i
$655$	−16602.2	−	6042.71i	−0.990385	−	0.360471i
$656$	−3325.91	−	5760.65i	−0.197950	−	0.342859i
$657$	10127.1	−	24395.4i	0.601361	−	1.44864i
$658$	−9413.98	+	16305.5i	−0.557743	+	0.966040i
$659$	16184.5	−	13580.4i	0.956691	−	0.802759i	−0.0237207	−	0.999719i	$-0.507551\pi$
$659$	16184.5	−	13580.4i	0.956691	−	0.802759i	0.980412	+	0.196960i	$0.0631068\pi$
$660$	39089.1	+	4296.28i	2.30537	+	0.253382i
$661$	3063.45	−	17373.7i	0.180264	−	1.02233i	−0.751627	−	0.659588i	$-0.770731\pi$
$661$	3063.45	−	17373.7i	0.180264	−	1.02233i	0.931891	−	0.362739i	$-0.118158\pi$
$662$	−1833.68	+	10399.3i	−0.107656	+	0.610545i
$663$	−149.536	−	340.205i	−0.00875945	−	0.0199283i
$664$	−36165.5	+	30346.4i	−2.11369	+	1.77360i
$665$	6767.61	−	11721.9i	0.394642	−	0.683540i
$666$	4309.36	+	13704.6i	0.250727	+	0.797360i
$667$	13430.0	+	23261.5i	0.779629	+	1.35036i
$668$	−29425.3	−	10709.9i	−1.70434	−	0.620328i
$669$	−95.3518	−	99.6831i	−0.00551048	−	0.00576079i
$670$	41357.2	+	34702.8i	2.38473	+	2.00102i
$671$	15458.5	−	5626.42i	0.889370	−	0.323704i
$672$	−1091.76	−	16756.5i	−0.0626718	−	0.961897i
$673$	−1387.28	−	7867.66i	−0.0794588	−	0.450633i	−0.998415	−	0.0562744i	$-0.982078\pi$
$673$	−1387.28	−	7867.66i	−0.0794588	−	0.450633i	0.918957	−	0.394359i	$-0.129033\pi$
$674$	−16007.0			−0.914787
$675$	9457.96	−	3665.35i	0.539314	−	0.209007i
$676$	−40904.7			−2.32730
$677$	4095.58	+	23227.2i	0.232505	+	1.31860i	0.847805	+	0.530308i	$0.177924\pi$
$677$	4095.58	+	23227.2i	0.232505	+	1.31860i	−0.615300	+	0.788293i	$0.710965\pi$
$678$	29448.5	−	19660.3i	1.66809	−	1.11364i
$679$	−3468.12	+	1262.29i	−0.196015	+	0.0713437i
$680$	−5746.60	−	4821.97i	−0.324076	−	0.271932i
$681$	8828.96	−	2156.81i	0.496808	−	0.121364i
$682$	−29180.0	−	10620.6i	−1.63836	−	0.596313i
$683$	5535.91	+	9588.48i	0.310140	+	0.537179i	0.978393	−	0.206756i	$-0.0662906\pi$
$683$	5535.91	+	9588.48i	0.310140	+	0.537179i	−0.668252	+	0.743935i	$0.732957\pi$
$684$	−2146.88	+	48312.6i	−0.120012	+	2.70070i
$685$	−6168.11	+	10683.5i	−0.344046	+	0.595905i
$686$	23839.7	−	20003.9i	1.32683	−	1.11334i
$687$	−15571.0	+	21218.9i	−0.864731	+	1.17839i
$688$	−346.199	+	1963.39i	−0.0191842	+	0.108799i
$689$	139.005	−	788.338i	0.00768604	−	0.0435897i
$690$	34615.3	−	47171.0i	1.90983	−	2.60256i
$691$	19995.6	−	16778.3i	1.10082	−	0.923699i	0.103342	−	0.994646i	$-0.467046\pi$
$691$	19995.6	−	16778.3i	1.10082	−	0.923699i	0.997480	+	0.0709466i	$0.0226020\pi$
$692$	7018.07	−	12155.7i	0.385531	−	0.667759i
$693$	6597.41	+	4210.20i	0.361638	+	0.230783i
$694$	−5342.93	−	9254.22i	−0.292240	−	0.506175i
$695$	−11011.9	−	4007.99i	−0.601013	−	0.218751i
$696$	−51169.6	+	12500.1i	−2.78675	+	0.680770i
$697$	−313.725	−	263.247i	−0.0170491	−	0.0143059i
$698$	−54084.9	+	19685.3i	−2.93287	+	1.06748i
$699$	−16106.1	+	10752.8i	−0.871517	+	0.581841i
$700$	−2475.77	−	14040.8i	−0.133679	−	0.758131i
$701$	18219.9			0.981678			0.490839	−	0.871250i	$-0.336690\pi$
$701$	18219.9			0.981678			0.490839	+	0.871250i	$0.336690\pi$
$702$	1102.42	+	5576.11i	0.0592710	+	0.299796i
$703$	−9554.12			−0.512575
$704$	2148.28	+	12183.5i	0.115009	+	0.652249i
$705$	−1664.88	−	25552.9i	−0.0889407	−	1.36508i
$706$	−26494.8	+	9643.30i	−1.41238	+	0.514066i
$707$	226.132	+	189.747i	0.0120291	+	0.0100936i
$708$	−43498.0	−	45473.8i	−2.30897	−	2.41386i
$709$	19001.5	+	6915.98i	1.00651	+	0.366340i	0.792092	−	0.610401i	$-0.208992\pi$
$709$	19001.5	+	6915.98i	1.00651	+	0.366340i	0.214419	+	0.976742i	$0.431214\pi$
$710$	−34906.4	−	60459.6i	−1.84509	−	3.19579i
$711$	−3231.43	+	3521.00i	−0.170447	+	0.185721i
$712$	23362.0	−	40464.2i	1.22967	−	2.12986i
$713$	−24962.1	+	20945.7i	−1.31114	+	1.10017i
$714$	−1031.98	−	2347.82i	−0.0540909	−	0.123060i
$715$	−533.767	+	3027.14i	−0.0279186	+	0.158334i
$716$	4060.62	−	23028.9i	0.211945	−	1.20200i
$717$	6578.05	+	722.993i	0.342624	+	0.0376578i
$718$	38690.8	−	32465.4i	2.01104	−	1.68746i
$719$	8055.41	−	13952.4i	0.417825	−	0.723694i	−0.577896	−	0.816111i	$-0.696126\pi$
$719$	8055.41	−	13952.4i	0.417825	−	0.723694i	0.995720	+	0.0924168i	$0.0294592\pi$
$720$	34453.4	+	44972.7i	1.78334	+	2.32782i
$721$	−1458.85	−	2526.81i	−0.0753545	−	0.130518i
$722$	−9269.62	−	3373.86i	−0.477811	−	0.173909i
$723$	−9919.51	+	33983.3i	−0.510250	+	1.74807i
$724$	47134.0	+	39550.1i	2.41950	+	2.03021i
$725$	−11860.4	+	4316.82i	−0.607562	+	0.221135i
$726$	13085.5	+	6459.34i	0.668935	+	0.330205i
$727$	−4290.68	−	24333.7i	−0.218889	−	1.24138i	−0.874029	−	0.485875i	$-0.838501\pi$
$727$	−4290.68	−	24333.7i	−0.218889	−	1.24138i	0.655139	−	0.755508i	$-0.272610\pi$
$728$	4650.99			0.236782
$729$	−18202.2	+	7490.07i	−0.924767	+	0.380535i
$730$	71594.4			3.62990
$731$	21.3148	+	120.882i	0.00107846	+	0.00611626i
$732$	52145.7	+	25740.5i	2.63301	+	1.29972i
$733$	−20250.8	+	7370.68i	−1.02044	+	0.371408i	−0.797432	−	0.603409i	$-0.793809\pi$
$733$	−20250.8	+	7370.68i	−1.02044	+	0.371408i	−0.223004	+	0.974817i	$0.571586\pi$
$734$	16870.2	+	14155.8i	0.848352	+	0.711852i
$735$	−4845.02	+	16598.6i	−0.243144	+	0.832989i
$736$	45362.5	+	16510.6i	2.27185	+	0.826887i
$737$	−10380.3	−	17979.2i	−0.518811	−	0.898608i
$738$	3809.46	+	4972.56i	0.190011	+	0.248025i
$739$	5521.39	−	9563.33i	0.274841	−	0.476039i	−0.695254	−	0.718764i	$-0.744708\pi$
$739$	5521.39	−	9563.33i	0.274841	−	0.476039i	0.970095	+	0.242725i	$0.0780414\pi$
$740$	−21038.2	+	17653.2i	−1.04511	+	0.876951i
$741$	−3757.51	−	412.988i	−0.186283	−	0.0204743i
$742$	959.302	−	5440.47i	0.0474624	−	0.269173i
$743$	2058.94	−	11676.8i	0.101662	−	0.576556i	−0.890839	−	0.454320i	$-0.849882\pi$
$743$	2058.94	−	11676.8i	0.101662	−	0.576556i	0.992501	−	0.122236i	$-0.0390065\pi$
$744$	−25714.0	−	58501.0i	−1.26710	−	2.88273i
$745$	22357.7	−	18760.3i	1.09949	−	0.922583i
$746$	23331.3	−	40411.0i	1.14507	−	1.98331i
$747$	14842.7	−	16172.8i	0.726996	−	0.792144i
$748$	2477.65	+	4291.42i	0.121112	+	0.209772i
$749$	−9043.73	−	3291.65i	−0.441189	−	0.160580i
$750$	−13852.6	−	14481.8i	−0.674433	−	0.705069i
$751$	−6621.63	−	5556.21i	−0.321740	−	0.269972i	0.467584	−	0.883949i	$-0.345124\pi$
$751$	−6621.63	−	5556.21i	−0.321740	−	0.269972i	−0.789324	+	0.613977i	$0.789569\pi$
$752$	49249.1	−	17925.2i	2.38820	−	0.869235i
$753$	917.106	+	14075.9i	0.0443841	+	0.681214i
$754$	−1228.17	−	6965.28i	−0.0593199	−	0.336420i
$755$	−48067.6			−2.31703
$756$	5365.86	+	27140.8i	0.258141	+	1.30569i
$757$	−16230.3			−0.779262			−0.389631	−	0.920971i	$-0.627397\pi$
$757$	−16230.3			−0.779262			−0.389631	+	0.920971i	$0.627397\pi$
$758$	10561.5	+	59897.4i	0.506085	+	2.87015i
$759$	−18712.3	+	12492.7i	−0.894878	+	0.597437i
$760$	−71705.5	+	26098.7i	−3.42241	+	1.24566i
$761$	12775.6	+	10720.0i	0.608561	+	0.510643i	0.894184	−	0.447699i	$-0.147756\pi$
$761$	12775.6	+	10720.0i	0.608561	+	0.510643i	−0.285624	+	0.958342i	$0.592201\pi$
$762$	49038.9	−	11979.6i	2.33135	−	0.569521i
$763$	−7513.80	−	2734.80i	−0.356511	−	0.129759i
$764$	4671.59	+	8091.42i	0.221220	+	0.383164i
$765$	2940.31	+	1876.39i	0.138964	+	0.0886811i
$766$	−29030.9	+	50282.9i	−1.36936	+	2.37180i
$767$	3768.05	−	3161.77i	0.177388	−	0.148846i
$768$	14328.1	−	19525.2i	0.673206	−	0.917391i
$769$	2432.62	−	13796.1i	0.114074	−	0.646943i	−0.873131	−	0.487485i	$-0.837914\pi$
$769$	2432.62	−	13796.1i	0.114074	−	0.646943i	0.987205	−	0.159458i	$-0.0509746\pi$
$770$	−3683.63	+	20890.9i	−0.172401	+	0.977735i
$771$	3279.50	−	4469.04i	0.153188	−	0.208753i
$772$	−69735.1	+	58514.7i	−3.25106	+	2.72796i
$773$	3460.13	−	5993.12i	0.160999	−	0.278858i	−0.774228	−	0.632906i	$-0.781862\pi$
$773$	3460.13	−	5993.12i	0.160999	−	0.278858i	0.935227	+	0.354048i	$0.115195\pi$
$774$	83.3468	−	1875.61i	0.00387059	−	0.0871024i
$775$	−7656.02	−	13260.6i	−0.354855	−	0.614626i
$776$	19552.2	+	7116.42i	0.904489	+	0.329207i
$777$	−5309.63	+	1297.08i	−0.245150	+	0.0598873i
$778$	4032.30	+	3383.50i	0.185816	+	0.155918i
$779$	−3914.64	+	1424.81i	−0.180047	+	0.0655317i
$780$	−9037.14	+	6033.36i	−0.414848	+	0.276960i
$781$	4661.75	+	26438.1i	0.213586	+	1.21130i
$782$	7372.77			0.337148
$783$	22836.9	−	8850.24i	1.04230	−	0.403936i
$784$	−35389.8			−1.61214
$785$	−3622.47	−	20544.0i	−0.164702	−	0.934074i
$786$	2213.96	+	33980.3i	0.100470	+	1.54203i
$787$	35308.6	−	12851.3i	1.59926	−	0.582082i	0.619981	−	0.784617i	$-0.287140\pi$
$787$	35308.6	−	12851.3i	1.59926	−	0.582082i	0.979275	+	0.202535i	$0.0649181\pi$
$788$	−5222.93	−	4382.56i	−0.236116	−	0.198125i
$789$	2332.44	+	2438.39i	0.105243	+	0.110024i
$790$	−12172.4	−	4430.40i	−0.548196	−	0.199527i
$791$	6735.73	+	11666.6i	0.302775	+	0.524422i
$792$	−13235.3	−	42090.6i	−0.593807	−	1.88842i
$793$	−2272.79	+	3936.59i	−0.101777	+	0.176283i
$794$	19742.4	−	16565.9i	0.882410	−	0.740430i
$795$	3023.37	+	6878.36i	0.134878	+	0.306856i
$796$	4727.74	−	26812.3i	0.210515	−	1.19389i
$797$	−1263.82	+	7167.48i	−0.0561692	+	0.318551i	−0.999927	−	0.0120864i	$-0.996153\pi$
$797$	−1263.82	+	7167.48i	−0.0561692	+	0.318551i	0.943758	+	0.330638i	$0.107264\pi$
$798$	−25931.3	−	2850.11i	−1.15032	−	0.126432i
$799$	2471.84	−	2074.12i	0.109446	−	0.0918363i
$800$	−11341.9	+	19644.8i	−0.501247	+	0.868185i
$801$	−8329.40	+	20065.0i	−0.367422	+	0.885094i
$802$	−35785.3	−	61981.9i	−1.57559	−	2.72900i
$803$	−25870.7	−	9416.18i	−1.13693	−	0.413810i
$804$	20563.7	−	70449.2i	0.902021	−	3.09024i
$805$	17052.5	+	14308.8i	0.746611	+	0.626481i
$806$	8062.95	−	2934.68i	0.352364	−	0.128250i
$807$	−19454.6	−	9603.31i	−0.848617	−	0.418900i
$808$	−288.988	−	1638.93i	−0.0125824	−	0.0713582i
$809$	14235.3			0.618647			0.309324	−	0.950957i	$-0.399897\pi$
$809$	14235.3			0.618647			0.309324	+	0.950957i	$0.399897\pi$
$810$	−37666.0	−	37782.9i	−1.63389	−	1.63896i
$811$	15402.3			0.666891			0.333445	−	0.942769i	$-0.391789\pi$
$811$	15402.3			0.666891			0.333445	+	0.942769i	$0.391789\pi$
$812$	−5977.91	−	33902.4i	−0.258354	−	1.46520i
$813$	15877.4	+	7837.50i	0.684924	+	0.338097i
$814$	14070.7	−	5121.33i	0.605871	−	0.220519i
$815$	−1833.95	−	1538.86i	−0.0788225	−	0.0661399i
$816$	−2000.33	+	6852.92i	−0.0858155	+	0.293995i
$817$	1173.29	+	427.043i	0.0502427	+	0.0182869i
$818$	19883.2	+	34438.7i	0.849876	+	1.47203i
$819$	−2144.28	+	280.609i	−0.0914860	+	0.0119723i
$820$	−5987.43	+	10370.5i	−0.254988	+	0.441652i
$821$	−21741.7	+	18243.5i	−0.924228	+	0.775520i	−0.974772	−	0.223202i	$-0.928349\pi$
$821$	−21741.7	+	18243.5i	−0.924228	+	0.775520i	0.0505439	+	0.998722i	$0.483905\pi$
$822$	23634.2	+	2597.64i	1.00284	+	0.110223i
$823$	1499.38	−	8503.41i	0.0635056	−	0.360158i	−0.936451	−	0.350799i	$-0.885910\pi$
$823$	1499.38	−	8503.41i	0.0635056	−	0.360158i	0.999956	−	0.00935864i	$-0.00297899\pi$
$824$	−2856.36	+	16199.2i	−0.120760	+	0.684863i
$825$	−4254.24	−	9678.67i	−0.179532	−	0.408446i
$826$	26004.1	−	21820.0i	1.09540	−	0.919146i
$827$	−15912.0	+	27560.3i	−0.669060	+	1.15885i	0.309107	+	0.951027i	$0.399970\pi$
$827$	−15912.0	+	27560.3i	−0.669060	+	1.15885i	−0.978167	+	0.207819i	$0.933363\pi$
$828$	−77636.3	−	17274.7i	−3.25851	−	0.725044i
$829$	966.465	+	1673.97i	0.0404906	+	0.0701318i	0.885561	−	0.464524i	$-0.153775\pi$
$829$	966.465	+	1673.97i	0.0404906	+	0.0701318i	−0.845070	+	0.534656i	$0.820441\pi$
$830$	55910.8	+	20349.9i	2.33818	+	0.851029i
$831$	149.690	+	156.489i	0.00624872	+	0.00653256i
$832$	−2618.69	−	2197.34i	−0.109119	−	0.0915615i
$833$	−2047.47	+	745.220i	−0.0851630	+	0.0309968i
$834$	1468.47	+	22538.3i	0.0609701	+	0.935778i
$835$	3989.37	+	22624.9i	0.165339	+	0.937683i
$836$	50405.8			2.08531
$837$	15384.6	+	25419.7i	0.635329	+	1.04974i
$838$	47417.9			1.95468
$839$	−2927.39	−	16602.1i	−0.120459	−	0.683155i	−0.983902	−	0.178709i	$-0.942808\pi$
$839$	−2927.39	−	16602.1i	−0.120459	−	0.683155i	0.863443	−	0.504446i	$-0.168303\pi$
$840$	−36306.6	+	24239.0i	−1.49131	+	0.995623i
$841$	−5719.47	+	2081.72i	−0.234510	+	0.0853547i
$842$	−15769.2	−	13232.0i	−0.645421	−	0.541572i
$843$	16722.3	−	4085.05i	0.683209	−	0.166900i
$844$	−59933.2	−	21813.9i	−2.44430	−	0.889651i
$845$	15005.2	+	25989.8i	0.610882	+	1.05808i
$846$	−43795.6	+	22755.4i	−1.77982	+	0.924761i
$847$	−2776.02	+	4808.20i	−0.112615	+	0.195055i
$848$	−11780.1	+	9884.67i	−0.477040	+	0.400284i
$849$	2756.33	−	3756.11i	0.111422	−	0.151837i
$850$	−601.598	+	3411.83i	−0.0242760	+	0.137676i
$851$	2728.54	−	15474.3i	0.109910	−	0.623328i
$852$	−56145.3	+	76510.3i	−2.25764	+	3.07653i
$853$	−25651.5	+	21524.2i	−1.02965	+	0.863979i	−0.990809	−	0.135267i	$-0.956811\pi$
$853$	−25651.5	+	21524.2i	−1.02965	+	0.863979i	−0.0388405	+	0.999245i	$0.512366\pi$
$854$	−15685.0	+	27167.2i	−0.628488	+	1.08857i
$855$	31484.2	−	16358.7i	1.25934	−	0.654332i
$856$	27128.9	+	46988.7i	1.08323	+	1.87622i
$857$	11423.9	+	4157.94i	0.455346	+	0.165732i	0.559503	−	0.828828i	$-0.310992\pi$
$857$	11423.9	+	4157.94i	0.455346	+	0.165732i	−0.104157	+	0.994561i	$0.533214\pi$
$858$	5755.21	−	1405.93i	0.228997	−	0.0559413i
$859$	3092.97	+	2595.31i	0.122853	+	0.103086i	0.702144	−	0.712035i	$-0.252226\pi$
$859$	3092.97	+	2595.31i	0.122853	+	0.103086i	−0.579291	+	0.815121i	$0.696671\pi$
$860$	3372.65	−	1227.54i	0.133728	−	0.0486731i
$861$	−1982.10	+	1323.28i	−0.0784549	+	0.0523779i
$862$	−7862.07	−	44588.0i	−0.310653	−	1.76180i
$863$	8105.02			0.319696			0.159848	−	0.987142i	$-0.448900\pi$
$863$	8105.02			0.319696			0.159848	+	0.987142i	$0.448900\pi$
$864$	21216.8	−	38566.7i	0.835428	−	1.51860i
$865$	−10297.9			−0.404784
$866$	−421.857	−	2392.47i	−0.0165535	−	0.0938794i
$867$	−1631.21	−	25036.1i	−0.0638972	−	0.980704i
$868$	39245.2	−	14284.1i	1.53464	−	0.558564i
$869$	3815.83	+	3201.86i	0.148956	+	0.124989i
$870$	45887.4	+	47971.7i	1.78819	+	1.86942i
$871$	5390.58	+	1962.01i	0.209705	+	0.0763263i
$872$	22539.5	+	39039.6i	0.875327	+	1.51611i
$873$	−9443.63	−	2101.28i	−0.366115	−	0.0814635i
$874$	37498.2	−	64948.8i	1.45125	−	2.51365i
$875$	5840.78	−	4901.00i	0.225662	−	0.189353i
$876$	−39161.8	−	89095.6i	−1.51045	−	3.43637i
$877$	3680.34	−	20872.3i	0.141706	−	0.803656i	−0.828247	−	0.560364i	$-0.810661\pi$
$877$	3680.34	−	20872.3i	0.141706	−	0.803656i	0.969953	−	0.243293i	$-0.0782275\pi$
$878$	3260.08	−	18488.9i	0.125310	−	0.710671i
$879$	11781.3	+	1294.88i	0.452075	+	0.0496876i
$880$	45234.4	−	37956.2i	1.73279	−	1.45398i
$881$	−14704.5	+	25469.0i	−0.562324	+	0.973974i	0.434969	+	0.900445i	$0.356759\pi$
$881$	−14704.5	+	25469.0i	−0.562324	+	0.973974i	−0.997293	+	0.0735285i	$0.976574\pi$
$882$	33044.9	−	4324.40i	1.26154	−	0.165091i
$883$	6465.24	+	11198.1i	0.246402	+	0.426780i	0.962525	−	0.271194i	$-0.0874185\pi$
$883$	6465.24	+	11198.1i	0.246402	+	0.426780i	−0.716123	+	0.697974i	$0.754085\pi$
$884$	−1286.66	−	468.307i	−0.0489538	−	0.0178177i
$885$	−12936.4	+	44318.9i	−0.491359	+	1.68335i
$886$	−3088.82	−	2591.83i	−0.117123	−	0.0982780i
$887$	11051.4	−	4022.38i	0.418342	−	0.152264i	−0.124268	−	0.992249i	$-0.539658\pi$
$887$	11051.4	−	4022.38i	0.418342	−	0.152264i	0.542610	+	0.839985i	$0.317436\pi$
$888$	27631.2	+	13639.5i	1.04419	+	0.515442i
$889$	3335.09	+	18914.3i	0.125822	+	0.713570i
$890$	−58885.7			−2.21781
$891$	8641.41	+	18606.8i	0.324914	+	0.699608i
$892$	−508.260			−0.0190782
$893$	−5699.64	−	32324.3i	−0.213585	−	1.21130i
$894$	−50441.3	−	24899.2i	−1.88704	−	0.931492i
$895$	−16121.6	+	5867.78i	−0.602107	+	0.219149i
$896$	1732.44	+	1453.69i	0.0645946	+	0.0542013i
$897$	1741.99	−	5967.90i	0.0648422	−	0.222143i
$898$	39708.4	+	14452.7i	1.47560	+	0.537073i
$899$	−18486.0	−	32018.7i	−0.685809	−	1.18786i
$900$	14329.0	−	34517.5i	0.530702	−	1.27843i
$901$	−473.390	+	819.936i	−0.0175038	+	0.0303174i
$902$	5001.50	−	4196.76i	0.184625	−	0.154919i
$903$	710.024	+	78.0387i	0.0261662	+	0.00287593i
$904$	13188.2	−	74794.1i	0.485214	−	2.75179i
$905$	7838.82	−	44456.1i	0.287924	−	1.63290i
$906$	37279.3	+	84812.8i	1.36702	+	3.11006i
$907$	−3676.90	+	3085.29i	−0.134608	+	0.112950i	−0.707606	−	0.706607i	$-0.750225\pi$
$907$	−3676.90	+	3085.29i	−0.134608	+	0.112950i	0.572998	+	0.819557i	$0.305780\pi$
$908$	16743.6	−	29000.7i	0.611954	−	1.05994i
$909$	232.116	+	738.172i	0.00846953	+	0.0269347i
$910$	−2930.79	−	5076.28i	−0.106764	−	0.184920i
$911$	12899.8	+	4695.14i	0.469143	+	0.170754i	0.565764	−	0.824567i	$-0.308581\pi$
$911$	12899.8	+	4695.14i	0.469143	+	0.170754i	−0.0966213	+	0.995321i	$0.530804\pi$
$912$	50195.6	+	52475.7i	1.82253	+	1.90531i
$913$	−17527.0	−	14706.9i	−0.635333	−	0.533108i
$914$	−47631.3	+	17336.4i	−1.72375	+	0.627392i
$915$	−2773.92	−	42574.6i	−0.100222	−	1.53822i
$916$	16839.3	+	95500.3i	0.607408	+	3.44478i
$917$	−12955.6			−0.466556
$918$	1030.41	−	6643.29i	0.0370462	−	0.238847i
$919$	−19834.0			−0.711931			−0.355965	−	0.934499i	$-0.615848\pi$
$919$	−19834.0			−0.711931			−0.355965	+	0.934499i	$0.615848\pi$
$920$	−21792.4	−	123591.i	−0.780952	−	4.42900i
$921$	−1807.18	+	1206.51i	−0.0646566	+	0.0431660i
$922$	−59596.0	+	21691.2i	−2.12873	+	0.774795i
$923$	−5682.53	−	4768.21i	−0.202646	−	0.170041i
$924$	28012.6	−	6843.14i	0.997346	−	0.243639i
$925$	6938.26	+	2525.32i	0.246626	+	0.0897644i
$926$	−42101.8	−	72922.5i	−1.49412	−	2.58788i
$927$	339.535	−	7640.77i	0.0120300	−	0.270718i
$928$	−27385.8	+	47433.7i	−0.968733	+	1.67789i
$929$	−15073.1	+	12647.8i	−0.532327	+	0.446675i	−0.868904	−	0.494980i	$-0.835175\pi$
$929$	−15073.1	+	12647.8i	−0.532327	+	0.446675i	0.336577	+	0.941656i	$0.390731\pi$
$930$	−47646.8	+	64929.3i	−1.68000	+	2.28937i
$931$	−3848.69	+	21827.0i	−0.135484	+	0.768369i
$932$	−12390.4	+	70269.3i	−0.435473	+	2.46969i
$933$	6530.54	−	8899.30i	0.229154	−	0.312272i
$934$	5654.24	−	4744.47i	0.198086	−	0.166214i
$935$	1817.77	−	3148.48i	0.0635803	−	0.110124i
$936$	10277.4	+	6558.63i	0.358897	+	0.229034i
$937$	10482.4	+	18156.1i	0.365470	+	0.633012i	0.988851	−	0.148905i	$-0.0475750\pi$
$937$	10482.4	+	18156.1i	0.365470	+	0.633012i	−0.623382	+	0.781918i	$0.714242\pi$
$938$	37201.4	+	13540.2i	1.29496	+	0.471326i
$939$	51884.8	−	12674.8i	1.80319	−	0.440498i
$940$	−72276.2	−	60647.0i	−2.50786	−	2.10435i
$941$	−542.100	+	197.308i	−0.0187800	+	0.00683535i	−0.351393	−	0.936228i	$-0.614292\pi$
$941$	−542.100	+	197.308i	−0.0187800	+	0.00683535i	0.332613	+	0.943063i	$0.392070\pi$
$942$	−33439.5	+	22324.8i	−1.15660	+	0.772167i
$943$	−1189.72	−	6747.24i	−0.0410844	−	0.233001i
$944$	−94492.3			−3.25791
$945$	15276.2	−	13365.5i	0.525858	−	0.460085i
$946$	−1956.87			−0.0672549
$947$	3625.41	+	20560.7i	0.124404	+	0.705528i	0.981660	+	0.190638i	$0.0610558\pi$
$947$	3625.41	+	20560.7i	0.124404	+	0.705528i	−0.857257	+	0.514889i	$0.827833\pi$
$948$	1144.85	+	17571.4i	0.0392226	+	0.601995i
$949$	7148.55	−	2601.86i	0.244522	−	0.0889989i
$950$	26996.0	+	22652.4i	0.921965	+	0.773621i
$951$	−39441.4	−	41233.0i	−1.34487	−	1.40596i
$952$	−5169.16	−	1881.42i	−0.175980	−	0.0640516i
$953$	17822.9	+	30870.1i	0.605812	+	1.04930i	0.991923	+	0.126845i	$0.0404851\pi$
$953$	17822.9	+	30870.1i	0.605812	+	1.04930i	−0.386110	+	0.922453i	$0.626182\pi$
$954$	9791.72	−	10669.2i	0.332305	−	0.362083i
$955$	3427.39	−	5936.42i	0.116134	−	0.201150i
$956$	18678.4	−	15673.1i	0.631907	−	0.530233i
$957$	−10272.2	−	23369.8i	−0.346972	−	0.789382i
$958$	−7956.27	+	45122.3i	−0.268325	+	1.52175i
$959$	−1570.83	+	8908.63i	−0.0528934	+	0.299974i
$960$	31893.6	+	3505.43i	1.07225	+	0.117851i
$961$	11538.3	−	9681.82i	0.387310	−	0.324991i
$962$	−2068.76	+	3583.20i	−0.0693342	+	0.120090i
$963$	−15342.4	−	20026.7i	−0.513398	−	0.670147i
$964$	65218.7	+	112962.i	2.17900	+	3.77413i
$965$	62760.0	+	22842.8i	2.09359	+	0.762005i
$966$	12021.8	−	41185.6i	0.400410	−	1.37177i
$967$	−26210.9	−	21993.6i	−0.871651	−	0.731402i	0.0927942	−	0.995685i	$-0.470420\pi$
$967$	−26210.9	−	21993.6i	−0.871651	−	0.731402i	−0.964445	+	0.264283i	$0.914865\pi$
$968$	29413.0	−	10705.4i	0.976621	−	0.355461i
$969$	4009.07	+	1978.99i	0.132910	+	0.0656080i
$970$	−4553.55	−	25824.4i	−0.150727	−	0.854817i
$971$	10036.0			0.331691			0.165845	−	0.986152i	$-0.446965\pi$
$971$	10036.0			0.331691			0.165845	+	0.986152i	$0.446965\pi$
$972$	−26415.8	+	67540.5i	−0.871694	+	2.22877i
$973$	−8593.15			−0.283128
$974$	14158.2	+	80295.2i	0.465768	+	2.64150i
$975$	2619.57	+	1293.09i	0.0860444	+	0.0424739i
$976$	82055.7	−	29865.8i	2.69113	−	0.979490i
$977$	−40261.8	−	33783.7i	−1.31841	−	1.10628i	−0.986639	−	0.162922i	$-0.947908\pi$
$977$	−40261.8	−	33783.7i	−1.31841	−	1.10628i	−0.331775	−	0.943359i	$-0.607647\pi$
$978$	−1292.91	+	4429.39i	−0.0422727	+	0.144822i
$979$	21278.4	+	7744.71i	0.694649	+	0.252831i
$980$	31855.0	+	55174.4i	1.03834	+	1.79845i
$981$	−12746.9	−	16638.8i	−0.414860	−	0.541525i
$982$	−20657.3	+	35779.5i	−0.671285	+	1.16270i
$983$	39084.2	−	32795.5i	1.26815	−	1.06410i	0.273386	−	0.961904i	$-0.411856\pi$
$983$	39084.2	−	32795.5i	1.26815	−	1.06410i	0.994764	−	0.102199i	$-0.0325880\pi$
$984$	13355.5	+	1467.90i	0.432680	+	0.0475558i
$985$	−868.621	+	4926.20i	−0.0280981	+	0.159352i
$986$	−1452.60	+	8238.10i	−0.0469170	+	0.266080i
$987$	−7555.91	−	17190.2i	−0.243675	−	0.554376i
$988$	−10669.5	+	8952.75i	−0.343564	+	0.288284i
$989$	−1026.74	+	1778.36i	−0.0330115	+	0.0571775i
$990$	−37599.3	+	40968.7i	−1.20705	+	1.31522i
$991$	7837.88	+	13575.6i	0.251240	+	0.435160i	0.963867	−	0.266383i	$-0.0858285\pi$
$991$	7837.88	+	13575.6i	0.251240	+	0.435160i	−0.712628	+	0.701542i	$0.752495\pi$
$992$	−62440.0	−	22726.3i	−1.99846	−	0.727380i
$993$	−7279.67	−	7610.34i	−0.232642	−	0.243209i
$994$	−39216.2	−	32906.3i	−1.25137	−	1.05003i
$995$	−18770.2	+	6831.79i	−0.598045	+	0.217671i
$996$	−5258.57	−	80709.4i	−0.167293	−	2.56765i
$997$	−2406.21	−	13646.3i	−0.0764346	−	0.433482i	−0.998878	−	0.0473508i	$-0.984922\pi$
$997$	−2406.21	−	13646.3i	−0.0764346	−	0.433482i	0.922444	−	0.386132i	$-0.126189\pi$
$998$	−46642.1			−1.47939
$999$	−13561.9	−	4621.23i	−0.429509	−	0.146356i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.4.e.a.13.8	✓	48
3.2	odd	2		81.4.e.a.10.1		48
9.2	odd	6		243.4.e.b.109.1		48
9.4	even	3		243.4.e.d.190.1		48
9.5	odd	6		243.4.e.a.190.8		48
9.7	even	3		243.4.e.c.109.8		48
27.2	odd	18		81.4.e.a.73.1		48
27.5	odd	18		729.4.a.c.1.3		24
27.7	even	9		243.4.e.c.136.8		48
27.11	odd	18		243.4.e.a.55.8		48
27.16	even	9		243.4.e.d.55.1		48
27.20	odd	18		243.4.e.b.136.1		48
27.22	even	9		729.4.a.d.1.22		24
27.25	even	9	inner	27.4.e.a.25.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.13.8	✓	48	1.1	even	1	trivial
27.4.e.a.25.8	yes	48	27.25	even	9	inner
81.4.e.a.10.1		48	3.2	odd	2
81.4.e.a.73.1		48	27.2	odd	18
243.4.e.a.55.8		48	27.11	odd	18
243.4.e.a.190.8		48	9.5	odd	6
243.4.e.b.109.1		48	9.2	odd	6
243.4.e.b.136.1		48	27.20	odd	18
243.4.e.c.109.8		48	9.7	even	3
243.4.e.c.136.8		48	27.7	even	9
243.4.e.d.55.1		48	27.16	even	9
243.4.e.d.190.1		48	9.4	even	3
729.4.a.c.1.3		24	27.5	odd	18
729.4.a.d.1.22		24	27.22	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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.904728 + 5.13097i) q^{2} +(-4.65940 - 2.30000i) q^{3} +(-17.9907 + 6.54810i) q^{4} +(10.7601 + 9.02881i) q^{5} +(7.58576 - 25.9881i) q^{6} +(9.67890 + 3.52283i) q^{7} +(-29.0343 - 50.2889i) q^{8} +(16.4200 + 21.4333i) q^{9} +O(q^{10})\)	\(q+(0.904728 + 5.13097i) q^{2} +(-4.65940 - 2.30000i) q^{3} +(-17.9907 + 6.54810i) q^{4} +(10.7601 + 9.02881i) q^{5} +(7.58576 - 25.9881i) q^{6} +(9.67890 + 3.52283i) q^{7} +(-29.0343 - 50.2889i) q^{8} +(16.4200 + 21.4333i) q^{9} +(-36.5916 + 63.3784i) q^{10} +(21.5580 - 18.0893i) q^{11} +(98.8867 + 10.8686i) q^{12} +(-1.35031 + 7.65800i) q^{13} +(-9.31876 + 52.8493i) q^{14} +(-29.3694 - 66.8172i) q^{15} +(114.433 - 96.0207i) q^{16} +(4.59856 - 7.96494i) q^{17} +(-95.1178 + 103.642i) q^{18} +(-46.7770 - 81.0201i) q^{19} +(-252.704 - 91.9768i) q^{20} +(-36.9953 - 38.6758i) q^{21} +(112.320 + 94.2475i) q^{22} +(144.583 - 52.6238i) q^{23} +(19.6177 + 301.095i) q^{24} +(12.5547 + 71.2013i) q^{25} -40.5146 q^{26} +(-27.2105 - 137.632i) q^{27} -197.199 q^{28} +(30.3142 + 171.920i) q^{29} +(316.265 - 211.145i) q^{30} +(-199.014 + 72.4350i) q^{31} +(240.345 + 201.673i) q^{32} +(-142.053 + 34.7018i) q^{33} +(45.0283 + 16.3890i) q^{34} +(72.3392 + 125.295i) q^{35} +(-435.754 - 278.081i) q^{36} +(51.0621 - 88.4422i) q^{37} +(373.391 - 313.312i) q^{38} +(23.9051 - 32.5759i) q^{39} +(141.636 - 803.260i) q^{40} +(7.73239 - 43.8526i) q^{41} +(164.974 - 224.813i) q^{42} +(-10.2238 + 8.57879i) q^{43} +(-269.394 + 466.604i) q^{44} +(-16.8363 + 378.877i) q^{45} +(400.819 + 694.239i) q^{46} +(329.686 + 119.996i) q^{47} +(-754.037 + 184.202i) q^{48} +(-181.482 - 152.282i) q^{49} +(-353.973 + 128.836i) q^{50} +(-39.7459 + 26.5351i) q^{51} +(-25.8522 - 146.615i) q^{52} -102.943 q^{53} +(681.568 - 264.136i) q^{54} +395.292 q^{55} +(-103.861 - 589.024i) q^{56} +(31.6059 + 485.092i) q^{57} +(-854.691 + 311.082i) q^{58} +(-484.566 - 406.599i) q^{59} +(965.902 + 1009.78i) q^{60} +(549.302 + 199.930i) q^{61} +(-551.715 - 955.598i) q^{62} +(83.4213 + 265.295i) q^{63} +(-219.804 + 380.712i) q^{64} +(-83.6722 + 70.2093i) q^{65} +(-306.573 - 697.473i) q^{66} +(128.102 - 726.503i) q^{67} +(-30.5763 + 173.407i) q^{68} +(-794.704 - 87.3458i) q^{69} +(-577.438 + 484.528i) q^{70} +(-476.973 + 826.141i) q^{71} +(601.113 - 1448.04i) q^{72} +(-489.146 - 847.225i) q^{73} +(499.991 + 181.982i) q^{74} +(105.266 - 360.631i) q^{75} +(1372.08 + 1151.31i) q^{76} +(272.384 - 99.1395i) q^{77} +(188.774 + 93.1838i) q^{78} +(30.7362 + 174.314i) q^{79} +2098.27 q^{80} +(-189.770 + 703.867i) q^{81} +232.002 q^{82} +(-141.179 - 800.664i) q^{83} +(918.826 + 453.558i) q^{84} +(121.395 - 44.1842i) q^{85} +(-53.2672 - 44.6965i) q^{86} +(254.172 - 870.768i) q^{87} +(-1535.61 - 558.918i) q^{88} +(402.317 + 696.834i) q^{89} +(-1959.24 + 256.394i) q^{90} +(-40.0474 + 69.3641i) q^{91} +(-2256.57 + 1893.48i) q^{92} +(1093.88 + 120.229i) q^{93} +(-317.419 + 1800.17i) q^{94} +(228.189 - 1294.13i) q^{95} +(-656.012 - 1492.47i) q^{96} +(-274.487 + 230.322i) q^{97} +(617.161 - 1068.95i) q^{98} +(741.695 + 165.033i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Introduction

L-functions

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