LMFDB - Embedded newform 27.4.e.a.22.5

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			22.5
Character	$\chi$	$=$	27.22
Dual form			27.4.e.a.16.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.644303 - 0.540635i) q^{2} +(0.739495 + 5.14326i) q^{3} +(-1.26634 + 7.18180i) q^{4} +(10.1642 - 3.69948i) q^{5} +(3.25709 + 2.91402i) q^{6} +(-4.63497 - 26.2862i) q^{7} +(6.43113 + 11.1390i) q^{8} +(-25.9063 + 7.60683i) q^{9} +O(q^{10})$	\(q+(0.644303 - 0.540635i) q^{2} +(0.739495 + 5.14326i) q^{3} +(-1.26634 + 7.18180i) q^{4} +(10.1642 - 3.69948i) q^{5} +(3.25709 + 2.91402i) q^{6} +(-4.63497 - 26.2862i) q^{7} +(6.43113 + 11.1390i) q^{8} +(-25.9063 + 7.60683i) q^{9} +(4.54878 - 7.87873i) q^{10} +(17.1115 + 6.22807i) q^{11} +(-37.8743 - 1.20224i) q^{12} +(-27.1242 - 22.7599i) q^{13} +(-17.1976 - 14.4305i) q^{14} +(26.5438 + 49.5416i) q^{15} +(-44.6566 - 16.2537i) q^{16} +(56.4726 - 97.8135i) q^{17} +(-12.5790 + 18.9070i) q^{18} +(9.33302 + 16.1653i) q^{19} +(13.6975 + 77.6823i) q^{20} +(131.769 - 43.2774i) q^{21} +(14.3921 - 5.23830i) q^{22} +(-24.1953 + 137.218i) q^{23} +(-52.5352 + 41.3143i) q^{24} +(-6.13000 + 5.14368i) q^{25} -29.7811 q^{26} +(-58.2815 - 127.618i) q^{27} +194.652 q^{28} +(61.6559 - 51.7354i) q^{29} +(43.8862 + 17.5693i) q^{30} +(-42.0656 + 238.566i) q^{31} +(-134.252 + 48.8638i) q^{32} +(-19.3787 + 92.6145i) q^{33} +(-16.4958 - 93.5526i) q^{34} +(-144.356 - 250.032i) q^{35} +(-21.8244 - 195.687i) q^{36} +(-16.7704 + 29.0472i) q^{37} +(14.7528 + 5.36958i) q^{38} +(97.0021 - 156.338i) q^{39} +(106.576 + 89.4281i) q^{40} +(-297.882 - 249.953i) q^{41} +(61.5022 - 99.1229i) q^{42} +(-79.2414 - 28.8415i) q^{43} +(-66.3978 + 115.004i) q^{44} +(-235.176 + 173.157i) q^{45} +(58.5958 + 101.491i) q^{46} +(80.1234 + 454.402i) q^{47} +(50.5735 - 241.700i) q^{48} +(-347.168 + 126.359i) q^{49} +(-1.16873 + 6.62818i) q^{50} +(544.842 + 218.121i) q^{51} +(197.806 - 165.979i) q^{52} +351.057 q^{53} +(-106.546 - 50.7155i) q^{54} +196.966 q^{55} +(262.995 - 220.679i) q^{56} +(-76.2405 + 59.9563i) q^{57} +(11.7551 - 66.6666i) q^{58} +(-47.3108 + 17.2197i) q^{59} +(-389.411 + 127.895i) q^{60} +(-24.6637 - 139.875i) q^{61} +(101.874 + 176.451i) q^{62} +(320.030 + 645.721i) q^{63} +(130.008 - 225.181i) q^{64} +(-359.897 - 130.992i) q^{65} +(37.5848 + 70.1486i) q^{66} +(-79.8993 - 67.0435i) q^{67} +(630.963 + 529.440i) q^{68} +(-723.641 - 22.9704i) q^{69} +(-228.185 - 83.0527i) q^{70} +(161.669 - 280.019i) q^{71} +(-251.340 - 239.651i) q^{72} +(-292.351 - 506.366i) q^{73} +(4.89869 + 27.7819i) q^{74} +(-30.9884 - 27.7245i) q^{75} +(-127.914 + 46.5571i) q^{76} +(84.4012 - 478.663i) q^{77} +(-22.0229 - 153.172i) q^{78} +(-486.977 + 408.622i) q^{79} -514.030 q^{80} +(613.272 - 394.130i) q^{81} -327.060 q^{82} +(740.364 - 621.240i) q^{83} +(143.944 + 1001.14i) q^{84} +(212.142 - 1203.12i) q^{85} +(-66.6483 + 24.2580i) q^{86} +(311.683 + 278.854i) q^{87} +(40.6714 + 230.659i) q^{88} +(233.107 + 403.753i) q^{89} +(-57.9100 + 238.710i) q^{90} +(-472.553 + 818.485i) q^{91} +(-954.833 - 347.531i) q^{92} +(-1258.11 - 39.9361i) q^{93} +(297.289 + 249.455i) q^{94} +(154.666 + 129.780i) q^{95} +(-350.598 - 654.360i) q^{96} +(1569.83 + 571.373i) q^{97} +(-155.367 + 269.104i) q^{98} +(-490.671 - 31.1820i) 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 $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	0.644303	−	0.540635i	0.227796	−	0.191143i	−0.521745	−	0.853101i	$-0.674719\pi$
$2$	0.644303	−	0.540635i	0.227796	−	0.191143i	0.749541	+	0.661958i	$0.230274\pi$
$3$	0.739495	+	5.14326i	0.142316	+	0.989821i
$3$	0.739495	+	5.14326i	0.142316	+	0.989821i
$4$	−1.26634	+	7.18180i	−0.158293	+	0.897725i
$5$	10.1642	−	3.69948i	0.909117	−	0.330892i	0.155217	−	0.987880i	$-0.450392\pi$
$5$	10.1642	−	3.69948i	0.909117	−	0.330892i	0.753900	+	0.656989i	$0.228170\pi$
$6$	3.25709	+	2.91402i	0.221617	+	0.198274i
$7$	−4.63497	−	26.2862i	−0.250265	−	1.41932i	−0.807941	−	0.589264i	$-0.799418\pi$
$7$	−4.63497	−	26.2862i	−0.250265	−	1.41932i	0.557676	−	0.830059i	$-0.311693\pi$
$8$	6.43113	+	11.1390i	0.284219	+	0.492281i
$9$	−25.9063	+	7.60683i	−0.959492	+	0.281735i
$10$	4.54878	−	7.87873i	0.143845	−	0.249147i
$11$	17.1115	+	6.22807i	0.469028	+	0.170712i	0.565712	−	0.824603i	$-0.308601\pi$
$11$	17.1115	+	6.22807i	0.469028	+	0.170712i	−0.0966840	+	0.995315i	$0.530824\pi$
$12$	−37.8743	−	1.20224i	−0.911115	−	0.0289214i
$13$	−27.1242	−	22.7599i	−0.578686	−	0.485575i	0.305830	−	0.952086i	$-0.401066\pi$
$13$	−27.1242	−	22.7599i	−0.578686	−	0.485575i	−0.884515	+	0.466511i	$0.845511\pi$
$14$	−17.1976	−	14.4305i	−0.328303	−	0.275479i
$15$	26.5438	+	49.5416i	0.456905	+	0.852772i
$16$	−44.6566	−	16.2537i	−0.697759	−	0.253963i
$17$	56.4726	−	97.8135i	0.805684	−	1.39549i	−0.110145	−	0.993916i	$-0.535131\pi$
$17$	56.4726	−	97.8135i	0.805684	−	1.39549i	0.915828	−	0.401570i	$-0.131535\pi$
$18$	−12.5790	+	18.9070i	−0.164717	+	0.247578i
$19$	9.33302	+	16.1653i	0.112692	+	0.195188i	0.916855	−	0.399221i	$-0.130719\pi$
$19$	9.33302	+	16.1653i	0.112692	+	0.195188i	−0.804163	+	0.594409i	$0.797386\pi$
$20$	13.6975	+	77.6823i	0.153143	+	0.868514i
$21$	131.769	−	43.2774i	1.36926	−	0.449710i
$22$	14.3921	−	5.23830i	0.139473	−	0.0507640i
$23$	−24.1953	+	137.218i	−0.219351	+	1.24400i	0.653845	+	0.756628i	$0.273155\pi$
$23$	−24.1953	+	137.218i	−0.219351	+	1.24400i	−0.873196	+	0.487370i	$0.837956\pi$
$24$	−52.5352	+	41.3143i	−0.446821	+	0.351385i
$25$	−6.13000	+	5.14368i	−0.0490400	+	0.0411494i
$26$	−29.7811			−0.224636
$27$	−58.2815	−	127.618i	−0.415418	−	0.909631i
$28$	194.652			1.31378
$29$	61.6559	−	51.7354i	0.394800	−	0.331277i	−0.423679	−	0.905812i	$-0.639262\pi$
$29$	61.6559	−	51.7354i	0.394800	−	0.331277i	0.818480	+	0.574535i	$0.194817\pi$
$30$	43.8862	+	17.5693i	0.267083	+	0.106923i
$31$	−42.0656	+	238.566i	−0.243716	+	1.38218i	0.579739	+	0.814802i	$0.303154\pi$
$31$	−42.0656	+	238.566i	−0.243716	+	1.38218i	−0.823456	+	0.567381i	$0.807957\pi$
$32$	−134.252	+	48.8638i	−0.741646	+	0.269937i
$33$	−19.3787	+	92.6145i	−0.102224	+	0.488549i
$34$	−16.4958	−	93.5526i	−0.0832063	−	0.471886i
$35$	−144.356	−	250.032i	−0.697162	−	1.20752i
$36$	−21.8244	−	195.687i	−0.101039	−	0.905957i
$37$	−16.7704	+	29.0472i	−0.0745145	+	0.129063i	−0.900875	−	0.434078i	$-0.857074\pi$
$37$	−16.7704	+	29.0472i	−0.0745145	+	0.129063i	0.826361	+	0.563141i	$0.190407\pi$
$38$	14.7528	+	5.36958i	0.0629795	+	0.0229227i
$39$	97.0021	−	156.338i	0.398276	−	0.641900i
$40$	106.576	+	89.4281i	0.421279	+	0.353495i
$41$	−297.882	−	249.953i	−1.13467	−	0.952099i	−0.135416	−	0.990789i	$-0.543237\pi$
$41$	−297.882	−	249.953i	−1.13467	−	0.952099i	−0.999251	+	0.0386895i	$0.987682\pi$
$42$	61.5022	−	99.1229i	0.225952	−	0.364166i
$43$	−79.2414	−	28.8415i	−0.281028	−	0.102286i	0.197661	−	0.980270i	$-0.436666\pi$
$43$	−79.2414	−	28.8415i	−0.281028	−	0.102286i	−0.478689	+	0.877985i	$0.658888\pi$
$44$	−66.3978	+	115.004i	−0.227496	+	0.394035i
$45$	−235.176	+	173.157i	−0.779067	+	0.573618i
$46$	58.5958	+	101.491i	0.187815	+	0.325305i
$47$	80.1234	+	454.402i	0.248664	+	1.41024i	0.811828	+	0.583897i	$0.198473\pi$
$47$	80.1234	+	454.402i	0.248664	+	1.41024i	−0.563164	+	0.826345i	$0.690416\pi$
$48$	50.5735	−	241.700i	0.152076	−	0.726800i
$49$	−347.168	+	126.359i	−1.01215	+	0.368393i
$50$	−1.16873	+	6.62818i	−0.00330566	+	0.0187473i
$51$	544.842	+	218.121i	1.49594	+	0.598883i
$52$	197.806	−	165.979i	0.527514	−	0.442637i
$53$	351.057			0.909838			0.454919	−	0.890533i	$-0.349668\pi$
$53$	351.057			0.909838			0.454919	+	0.890533i	$0.349668\pi$
$54$	−106.546	−	50.7155i	−0.268500	−	0.127806i
$55$	196.966			0.482888
$56$	262.995	−	220.679i	0.627575	−	0.526598i
$57$	−76.2405	+	59.9563i	−0.177163	+	0.139323i
$58$	11.7551	−	66.6666i	0.0266125	−	0.150927i
$59$	−47.3108	+	17.2197i	−0.104396	+	0.0379969i	−0.393690	−	0.919243i	$-0.628802\pi$
$59$	−47.3108	+	17.2197i	−0.104396	+	0.0379969i	0.289294	+	0.957240i	$0.406579\pi$
$60$	−389.411	+	127.895i	−0.837879	+	0.275187i
$61$	−24.6637	−	139.875i	−0.0517682	−	0.293592i	0.947921	−	0.318504i	$-0.103180\pi$
$61$	−24.6637	−	139.875i	−0.0517682	−	0.293592i	−0.999690	+	0.0249123i	$0.992069\pi$
$62$	101.874	+	176.451i	0.208677	+	0.361440i
$63$	320.030	+	645.721i	0.639999	+	1.29132i
$64$	130.008	−	225.181i	0.253923	−	0.439807i
$65$	−359.897	−	130.992i	−0.686766	−	0.249962i
$66$	37.5848	+	70.1486i	0.0700965	+	0.130829i
$67$	−79.8993	−	67.0435i	−0.145690	−	0.122249i	0.567030	−	0.823697i	$-0.308093\pi$
$67$	−79.8993	−	67.0435i	−0.145690	−	0.122249i	−0.712720	+	0.701449i	$0.752537\pi$
$68$	630.963	+	529.440i	1.12523	+	0.944178i
$69$	−723.641	−	22.9704i	−1.26255	−	0.0400770i
$70$	−228.185	−	83.0527i	−0.389620	−	0.141810i
$71$	161.669	−	280.019i	0.270234	−	0.468059i	−0.698688	−	0.715427i	$-0.746232\pi$
$71$	161.669	−	280.019i	0.270234	−	0.468059i	0.968922	+	0.247368i	$0.0795657\pi$
$72$	−251.340	−	239.651i	−0.411398	−	0.392266i
$73$	−292.351	−	506.366i	−0.468727	−	0.811859i	0.530634	−	0.847601i	$-0.321954\pi$
$73$	−292.351	−	506.366i	−0.468727	−	0.811859i	−0.999361	+	0.0357420i	$0.988621\pi$
$74$	4.89869	+	27.7819i	0.00769543	+	0.0436429i
$75$	−30.9884	−	27.7245i	−0.0477098	−	0.0426846i
$76$	−127.914	+	46.5571i	−0.193063	+	0.0702692i
$77$	84.4012	−	478.663i	0.124914	−	0.708425i
$78$	−22.0229	−	153.172i	−0.0319693	−	0.222350i
$79$	−486.977	+	408.622i	−0.693534	+	0.581944i	−0.919926	−	0.392092i	$-0.871751\pi$
$79$	−486.977	+	408.622i	−0.693534	+	0.581944i	0.226392	+	0.974036i	$0.427307\pi$
$80$	−514.030			−0.718379
$81$	613.272	−	394.130i	0.841251	−	0.540644i
$82$	−327.060			−0.440460
$83$	740.364	−	621.240i	0.979103	−	0.821565i	−0.00485076	−	0.999988i	$-0.501544\pi$
$83$	740.364	−	621.240i	0.979103	−	0.821565i	0.983954	+	0.178423i	$0.0570996\pi$
$84$	143.944	+	1001.14i	0.186971	+	1.30040i
$85$	212.142	−	1203.12i	0.270707	−	1.53525i
$86$	−66.6483	+	24.2580i	−0.0835682	+	0.0304163i
$87$	311.683	+	278.854i	0.384091	+	0.343636i
$88$	40.6714	+	230.659i	0.0492681	+	0.279413i
$89$	233.107	+	403.753i	0.277633	+	0.480874i	0.970796	−	0.239907i	$-0.0771169\pi$
$89$	233.107	+	403.753i	0.277633	+	0.480874i	−0.693163	+	0.720781i	$0.743784\pi$
$90$	−57.9100	+	238.710i	−0.0678250	+	0.279581i
$91$	−472.553	+	818.485i	−0.544363	+	0.942864i
$92$	−954.833	−	347.531i	−1.08205	−	0.393833i
$93$	−1258.11	−	39.9361i	−1.40280	−	0.0445288i
$94$	297.289	+	249.455i	0.326203	+	0.273717i
$95$	154.666	+	129.780i	0.167036	+	0.140160i
$96$	−350.598	−	654.360i	−0.372737	−	0.695681i
$97$	1569.83	+	571.373i	1.64322	+	0.598084i	0.987598	−	0.157004i	$-0.0501835\pi$
$97$	1569.83	+	571.373i	1.64322	+	0.598084i	0.655624	+	0.755088i	$0.272406\pi$
$98$	−155.367	+	269.104i	−0.160148	+	0.277384i
$99$	−490.671	−	31.1820i	−0.498124	−	0.0316557i
$100$	−29.1782	−	50.5381i	−0.0291782	−	0.0505381i
$101$	243.204	+	1379.28i	0.239601	+	1.35884i	0.832705	+	0.553717i	$0.186791\pi$
$101$	243.204	+	1379.28i	0.239601	+	1.35884i	−0.593104	+	0.805126i	$0.702098\pi$
$102$	468.967	−	154.024i	0.455242	−	0.149516i
$103$	1702.75	−	619.749i	1.62890	−	0.592871i	0.643851	−	0.765151i	$-0.277336\pi$
$103$	1702.75	−	619.749i	1.62890	−	0.592871i	0.985048	+	0.172280i	$0.0551134\pi$
$104$	79.0845	−	448.510i	0.0745661	−	0.422885i
$105$	1179.23	−	927.360i	1.09601	−	0.861915i
$106$	226.187	−	189.794i	0.207257	−	0.173909i
$107$	−501.812			−0.453384			−0.226692	−	0.973967i	$-0.572791\pi$
$107$	−501.812			−0.453384			−0.226692	+	0.973967i	$0.572791\pi$
$108$	990.328	−	256.958i	0.882356	−	0.228943i
$109$	−1311.94			−1.15286			−0.576428	−	0.817148i	$-0.695554\pi$
$109$	−1311.94			−1.15286			−0.576428	+	0.817148i	$0.695554\pi$
$110$	126.906	−	106.487i	0.110000	−	0.0923009i
$111$	−161.799	−	64.7743i	−0.138354	−	0.0553884i
$112$	−220.265	+	1249.19i	−0.185831	+	1.05390i
$113$	553.519	−	201.465i	0.460803	−	0.167719i	−0.101179	−	0.994868i	$-0.532261\pi$
$113$	553.519	−	201.465i	0.460803	−	0.167719i	0.561982	+	0.827150i	$0.310039\pi$
$114$	−16.7075	+	79.8483i	−0.0137264	+	0.0656007i
$115$	261.709	+	1484.23i	0.212213	+	1.20352i
$116$	293.476	+	508.315i	0.234901	+	0.406861i
$117$	875.820	+	383.296i	0.692048	+	0.302870i
$118$	−21.1729	+	36.6726i	−0.0165180	+	0.0286100i
$119$	−2832.89	−	1031.09i	−2.18228	−	0.794284i
$120$	−381.139	+	614.281i	−0.289943	+	0.467299i
$121$	−765.591	−	642.407i	−0.575200	−	0.482650i
$122$	−91.5119	−	76.7876i	−0.0679107	−	0.0569838i
$123$	1065.29	−	1716.92i	0.780927	−	1.25862i
$124$	−1660.06	−	604.213i	−1.20224	−	0.437580i
$125$	−719.312	+	1245.89i	−0.514698	+	0.891483i
$126$	555.295	+	243.021i	0.392616	+	0.171826i
$127$	480.719	+	832.630i	0.335881	+	0.581763i	0.983654	−	0.180071i	$-0.0576326\pi$
$127$	480.719	+	832.630i	0.335881	+	0.581763i	−0.647773	+	0.761834i	$0.724299\pi$
$128$	−236.446	−	1340.95i	−0.163274	−	0.925974i
$129$	89.7409	−	428.888i	0.0612499	−	0.292724i
$130$	−302.702	+	110.174i	−0.204221	+	0.0743303i
$131$	−99.7592	+	565.763i	−0.0665344	+	0.377335i	0.933299	+	0.359099i	$0.116916\pi$
$131$	−99.7592	+	565.763i	−0.0665344	+	0.377335i	−0.999834	+	0.0182359i	$0.994195\pi$
$132$	−640.598	−	256.456i	−0.422401	−	0.169103i
$133$	381.665	−	320.255i	0.248832	−	0.208794i
$134$	−87.7254			−0.0565547
$135$	−1064.51	−	1081.52i	−0.678653	−	0.689502i
$136$	1452.73			0.915961
$137$	180.781	−	151.693i	0.112738	−	0.0945987i	−0.584676	−	0.811267i	$-0.698778\pi$
$137$	180.781	−	151.693i	0.112738	−	0.0945987i	0.697414	+	0.716668i	$0.254334\pi$
$138$	−478.663	+	376.426i	−0.295265	+	0.232199i
$139$	101.240	−	574.163i	0.0617777	−	0.350359i	−0.938213	−	0.346058i	$-0.887520\pi$
$139$	101.240	−	574.163i	0.0617777	−	0.350359i	0.999991	−	0.00430070i	$-0.00136896\pi$
$140$	1978.49	−	720.110i	1.19438	−	0.434717i
$141$	−2277.86	+	748.124i	−1.36050	+	0.446833i
$142$	−47.2241	−	267.821i	−0.0279082	−	0.158275i
$143$	−322.386	−	558.388i	−0.188526	−	0.326537i
$144$	1280.53	+	81.3770i	0.741045	+	0.0470932i
$145$	435.291	−	753.946i	0.249303	−	0.431805i
$146$	−462.122	−	168.199i	−0.261955	−	0.0953439i
$147$	−906.624	−	1692.13i	−0.508688	−	0.949420i
$148$	−187.374	−	157.225i	−0.104068	−	0.0873233i
$149$	−243.212	−	204.079i	−0.133723	−	0.112207i	0.573473	−	0.819224i	$-0.305596\pi$
$149$	−243.212	−	204.079i	−0.133723	−	0.112207i	−0.707196	+	0.707018i	$0.750040\pi$
$150$	−34.9547	−	1.10956i	−0.0190270	−	0.000603970i
$151$	1368.57	+	498.120i	0.737568	+	0.268453i	0.683365	−	0.730077i	$-0.260516\pi$
$151$	1368.57	+	498.120i	0.737568	+	0.268453i	0.0542035	+	0.998530i	$0.482738\pi$
$152$	−120.044	+	207.922i	−0.0640581	+	0.110952i
$153$	−718.946	+	2963.56i	−0.379891	+	1.56595i
$154$	−204.402	−	354.034i	−0.106956	−	0.185253i
$155$	455.005	+	2580.46i	0.235786	+	1.33721i
$156$	999.950	+	894.627i	0.513205	+	0.459151i
$157$	352.082	−	128.148i	0.178976	−	0.0651419i	−0.250978	−	0.967993i	$-0.580752\pi$
$157$	352.082	−	128.148i	0.178976	−	0.0651419i	0.429954	+	0.902851i	$0.358530\pi$
$158$	−92.8455	+	526.553i	−0.0467493	+	0.265129i
$159$	259.605	+	1805.58i	0.129484	+	0.900577i
$160$	−1183.80	+	993.327i	−0.584923	+	0.490809i
$161$	3719.09			1.82053
$162$	182.053	−	585.495i	0.0882928	−	0.283956i
$163$	−2543.28			−1.22212			−0.611059	−	0.791585i	$-0.709256\pi$
$163$	−2543.28			−1.22212			−0.611059	+	0.791585i	$0.709256\pi$
$164$	2172.33	−	1822.80i	1.03433	−	0.867908i
$165$	145.655	+	1013.05i	0.0687227	+	0.477973i
$166$	141.156	−	800.533i	0.0659988	−	0.374298i
$167$	−2190.39	+	797.238i	−1.01496	+	0.369414i	−0.795334	−	0.606171i	$-0.792705\pi$
$167$	−2190.39	+	797.238i	−1.01496	+	0.369414i	−0.219622	+	0.975585i	$0.570483\pi$
$168$	1329.49	+	1189.46i	0.610552	+	0.546244i
$169$	−163.795	−	928.930i	−0.0745541	−	0.422817i
$170$	−513.764	−	889.865i	−0.231787	−	0.401468i
$171$	−364.751	−	347.787i	−0.163118	−	0.155532i
$172$	307.481	−	532.573i	0.136309	−	0.236095i
$173$	3603.90	+	1311.71i	1.58381	+	0.576461i	0.976029	−	0.217642i	$-0.0698364\pi$
$173$	3603.90	+	1311.71i	1.58381	+	0.576461i	0.607784	+	0.794102i	$0.292059\pi$
$174$	351.577	+	11.1600i	0.153178	+	0.00486230i
$175$	163.620	+	137.294i	0.0706773	+	0.0593053i
$176$	−662.911	−	556.249i	−0.283914	−	0.238232i
$177$	−123.552	−	230.598i	−0.0524673	−	0.0979254i
$178$	368.475	+	134.114i	0.155159	+	0.0564734i
$179$	813.490	−	1409.01i	0.339682	−	0.588347i	−0.644691	−	0.764444i	$-0.723014\pi$
$179$	813.490	−	1409.01i	0.339682	−	0.588347i	0.984373	+	0.176097i	$0.0563471\pi$
$180$	−945.767	−	1908.27i	−0.391630	−	0.790187i
$181$	−641.734	−	1111.52i	−0.263534	−	0.456455i	0.703644	−	0.710553i	$-0.251555\pi$
$181$	−641.734	−	1111.52i	−0.263534	−	0.456455i	−0.967179	+	0.254097i	$0.918222\pi$
$182$	138.034	+	782.831i	0.0562186	+	0.318831i
$183$	701.173	−	230.288i	0.283236	−	0.0930240i
$184$	−1684.08	+	612.956i	−0.674740	+	0.245585i
$185$	−62.9989	+	357.284i	−0.0250366	+	0.141990i
$186$	−832.197	+	654.449i	−0.328063	+	0.257992i
$187$	1575.52	−	1322.02i	0.616115	−	0.516982i
$188$	−3364.89			−1.30537
$189$	−3084.45	+	2123.50i	−1.18709	+	0.817260i
$190$	169.816			0.0648406
$191$	−161.401	+	135.431i	−0.0611443	+	0.0513061i	−0.672848	−	0.739781i	$-0.734929\pi$
$191$	−161.401	+	135.431i	−0.0611443	+	0.0513061i	0.611703	+	0.791087i	$0.290485\pi$
$192$	1254.31	+	502.147i	0.471468	+	0.188747i
$193$	−327.542	+	1857.58i	−0.122161	+	0.692807i	0.860793	+	0.508955i	$0.169968\pi$
$193$	−327.542	+	1857.58i	−0.122161	+	0.692807i	−0.982954	+	0.183852i	$0.941143\pi$
$194$	1320.35	−	480.569i	0.488638	−	0.177850i
$195$	407.583	−	1947.91i	0.149680	−	0.715349i
$196$	−467.848	−	2653.30i	−0.170499	−	0.966946i
$197$	−401.854	−	696.031i	−0.145334	−	0.251727i	0.784163	−	0.620555i	$-0.213092\pi$
$197$	−401.854	−	696.031i	−0.145334	−	0.251727i	−0.929498	+	0.368828i	$0.879759\pi$
$198$	−332.999	+	245.183i	−0.119521	+	0.0880021i
$199$	525.362	−	909.953i	0.187145	−	0.324145i	−0.757152	−	0.653239i	$-0.773410\pi$
$199$	525.362	−	909.953i	0.187145	−	0.324145i	0.944297	+	0.329094i	$0.106743\pi$
$200$	−96.7185	−	35.2027i	−0.0341952	−	0.0124460i
$201$	285.737	−	460.522i	0.100270	−	0.161605i
$202$	902.382	+	757.188i	0.314314	+	0.263740i
$203$	−1645.70	−	1380.91i	−0.568993	−	0.477442i
$204$	−2256.46	+	3636.72i	−0.774430	+	1.24815i
$205$	−3952.44	−	1438.57i	−1.34659	−	0.490118i
$206$	762.028	−	1319.87i	0.257733	−	0.446406i
$207$	−416.986	−	3738.86i	−0.140012	−	1.25541i
$208$	841.343	+	1457.25i	0.280465	+	0.485779i
$209$	59.0234	+	334.738i	0.0195346	+	0.110786i
$210$	258.420	−	1235.03i	0.0849174	−	0.405836i
$211$	−2545.31	+	926.418i	−0.830457	+	0.302262i	−0.722047	−	0.691844i	$-0.756798\pi$
$211$	−2545.31	+	926.418i	−0.830457	+	0.302262i	−0.108411	+	0.994106i	$0.534576\pi$
$212$	−444.559	+	2521.22i	−0.144021	+	0.816784i
$213$	1559.77	+	624.434i	0.501753	+	0.200871i
$214$	−323.319	+	271.297i	−0.103279	+	0.0866612i
$215$	−912.127			−0.289333
$216$	1046.72	−	1469.93i	0.329724	−	0.463036i
$217$	6465.96			2.02276
$218$	−845.289	+	709.281i	−0.262616	+	0.220361i
$219$	2388.18	−	1878.09i	0.736888	−	0.579496i
$220$	−249.427	+	1414.57i	−0.0764379	+	0.433501i
$221$	−3758.01	+	1367.80i	−1.14385	+	0.416327i
$222$	−139.267	+	45.7398i	−0.0421035	+	0.0138282i
$223$	11.0519	+	62.6785i	0.00331879	+	0.0188218i	0.986422	−	0.164229i	$-0.0525137\pi$
$223$	11.0519	+	62.6785i	0.00331879	+	0.0188218i	−0.983103	+	0.183051i	$0.941403\pi$
$224$	1906.70	+	3302.50i	0.568736	+	0.985079i
$225$	119.678	−	179.884i	0.0354603	−	0.0532988i
$226$	247.716	−	429.056i	0.0729106	−	0.126285i
$227$	−62.1838	−	22.6331i	−0.0181819	−	0.00661766i	0.332913	−	0.942957i	$-0.391968\pi$
$227$	−62.1838	−	22.6331i	−0.0181819	−	0.00661766i	−0.351095	+	0.936340i	$0.614191\pi$
$228$	−334.047	−	623.469i	−0.0970299	−	0.181098i
$229$	1881.94	+	1579.13i	0.543066	+	0.455686i	0.872585	−	0.488463i	$-0.162442\pi$
$229$	1881.94	+	1579.13i	0.543066	+	0.455686i	−0.329519	+	0.944149i	$0.606887\pi$
$230$	971.045	+	814.804i	0.278386	+	0.233594i
$231$	2524.30	+	80.1286i	0.718991	+	0.0228228i
$232$	972.800	+	354.070i	0.275291	+	0.100198i
$233$	1545.62	−	2677.09i	0.434579	−	0.752713i	−0.562682	−	0.826673i	$-0.690231\pi$
$233$	1545.62	−	2677.09i	0.434579	−	0.752713i	0.997261	+	0.0739605i	$0.0235639\pi$
$234$	771.517	−	226.540i	0.215537	−	0.0632879i
$235$	2495.44	+	4322.24i	0.692702	+	1.19979i
$236$	−63.7568	−	361.583i	−0.0175856	−	0.0997331i
$237$	−2461.77	−	2202.48i	−0.674721	−	0.603655i
$238$	−2382.69	+	867.227i	−0.648935	+	0.236193i
$239$	594.064	−	3369.10i	0.160781	−	0.911837i	−0.792527	−	0.609837i	$-0.791235\pi$
$239$	594.064	−	3369.10i	0.160781	−	0.911837i	0.953308	−	0.302000i	$-0.0976542\pi$
$240$	−380.123	−	2643.79i	−0.102237	−	0.711067i
$241$	−544.093	+	456.548i	−0.145428	+	0.122028i	−0.712599	−	0.701571i	$-0.752482\pi$
$241$	−544.093	+	456.548i	−0.145428	+	0.122028i	0.567171	+	0.823600i	$0.308038\pi$
$242$	−840.581			−0.223283
$243$	2480.62	+	2862.76i	0.654865	+	0.755746i
$244$	1035.78			0.271759
$245$	−3061.23	+	2568.68i	−0.798265	+	0.669824i
$246$	−241.859	−	1682.15i	−0.0626844	−	0.435976i
$247$	114.769	−	650.890i	0.0295652	−	0.167673i
$248$	−2927.92	+	1065.68i	−0.749691	+	0.272865i
$249$	3742.69	+	3348.48i	0.952544	+	0.852215i
$250$	210.114	+	1191.61i	0.0531550	+	0.301457i
$251$	−2536.71	−	4393.72i	−0.637912	−	1.10490i	−0.985890	−	0.167394i	$-0.946465\pi$
$251$	−2536.71	−	4393.72i	−0.637912	−	1.10490i	0.347978	−	0.937503i	$-0.386868\pi$
$252$	−5042.70	+	1480.68i	−1.26056	+	0.370136i
$253$	−1268.62	+	2197.32i	−0.315247	+	0.546024i
$254$	759.877	+	276.573i	0.187712	+	0.0683217i
$255$	6344.83	+	201.403i	1.55815	+	0.0494602i
$256$	716.166	+	600.935i	0.174845	+	0.146713i
$257$	1009.07	+	846.711i	0.244919	+	0.205511i	0.756981	−	0.653437i	$-0.226674\pi$
$257$	1009.07	+	846.711i	0.244919	+	0.205511i	−0.512062	+	0.858949i	$0.671118\pi$
$258$	−174.051	−	324.851i	−0.0419998	−	0.0783889i
$259$	841.271	+	306.198i	0.201830	+	0.0734602i
$260$	1396.51	−	2418.83i	0.333107	−	0.576959i
$261$	−1203.73	+	1809.28i	−0.285476	+	0.429086i
$262$	241.596	+	418.456i	0.0569688	+	0.0986729i
$263$	−688.981	−	3907.40i	−0.161538	−	0.916125i	−0.952563	−	0.304342i	$-0.901564\pi$
$263$	−688.981	−	3907.40i	−0.161538	−	0.916125i	0.791025	−	0.611783i	$-0.209548\pi$
$264$	−1156.26	+	379.755i	−0.269557	+	0.0885315i
$265$	3568.23	−	1298.73i	0.827149	−	0.301058i
$266$	72.7672	−	412.683i	0.0167731	−	0.0951249i
$267$	−1904.23	+	1497.50i	−0.436468	+	0.343243i
$268$	582.673	−	488.921i	0.132807	−	0.111439i
$269$	3723.56			0.843977			0.421988	−	0.906601i	$-0.361332\pi$
$269$	3723.56			0.843977			0.421988	+	0.906601i	$0.361332\pi$
$270$	−1270.57	−	121.321i	−0.286388	−	0.0273458i
$271$	−5380.04			−1.20596			−0.602978	−	0.797758i	$-0.706019\pi$
$271$	−5380.04			−1.20596			−0.602978	+	0.797758i	$0.706019\pi$
$272$	−4111.70	+	3450.13i	−0.916575	+	0.769098i
$273$	−4559.14	−	1825.20i	−1.01074	−	0.404637i
$274$	34.4671	−	195.473i	0.00759940	−	0.0430983i
$275$	−136.929	+	49.8379i	−0.0300258	+	0.0109285i
$276$	1081.35	−	5167.96i	0.235832	−	1.12708i
$277$	−177.469	−	1006.48i	−0.0384948	−	0.218315i	0.959492	−	0.281736i	$-0.0909101\pi$
$277$	−177.469	−	1006.48i	−0.0384948	−	0.218315i	−0.997987	+	0.0634206i	$0.979799\pi$
$278$	−245.183	−	424.670i	−0.0528961	−	0.0916187i
$279$	−724.967	−	6500.34i	−0.155565	−	1.39486i
$280$	1856.75	−	3215.98i	0.396293	−	0.686399i
$281$	6181.47	+	2249.87i	1.31230	+	0.477637i	0.900982	−	0.433856i	$-0.142847\pi$
$281$	6181.47	+	2249.87i	1.31230	+	0.477637i	0.411316	+	0.911493i	$0.365069\pi$
$282$	−1063.17	+	1713.51i	−0.224507	+	0.361837i
$283$	−5319.40	−	4463.51i	−1.11733	−	0.937554i	−0.118867	−	0.992910i	$-0.537926\pi$
$283$	−5319.40	−	4463.51i	−1.11733	−	0.937554i	−0.998467	+	0.0553558i	$0.982371\pi$
$284$	1806.31	+	1515.68i	0.377412	+	0.316686i
$285$	−553.119	+	891.460i	−0.114961	+	0.185283i
$286$	−509.598	−	185.479i	−0.105361	−	0.0383482i
$287$	−5189.64	+	8988.72i	−1.06737	+	1.84874i
$288$	3106.28	−	2287.12i	0.635553	−	0.467950i
$289$	−3921.82	−	6792.78i	−0.798253	−	1.38261i
$290$	−127.150	−	721.103i	−0.0257466	−	0.146016i
$291$	−1777.84	+	8496.60i	−0.358140	+	1.71161i
$292$	4006.84	−	1458.37i	0.803022	−	0.292276i
$293$	148.644	−	843.001i	0.0296378	−	0.168084i	−0.966396	−	0.257057i	$-0.917247\pi$
$293$	148.644	−	843.001i	0.0296378	−	0.168084i	0.996034	+	0.0889726i	$0.0283584\pi$
$294$	−1498.97	−	600.094i	−0.297352	−	0.119041i
$295$	−417.174	+	350.051i	−0.0823350	+	0.0690872i
$296$	−431.411			−0.0847137
$297$	−202.472	−	2546.71i	−0.0395576	−	0.497559i
$298$	−267.034			−0.0519090
$299$	3779.36	−	3171.26i	0.730989	−	0.613373i
$300$	238.354	−	187.444i	0.0458712	−	0.0360736i
$301$	−390.853	+	2216.64i	−0.0748451	+	0.424468i
$302$	1151.08	−	418.958i	0.219328	−	0.0798288i
$303$	−6914.13	+	2270.83i	−1.31091	+	0.430547i
$304$	−154.036	−	873.581i	−0.0290611	−	0.164814i
$305$	−768.150	−	1330.48i	−0.144210	−	0.249780i
$306$	1138.99	+	2298.12i	0.212783	+	0.429329i
$307$	−3310.94	+	5734.72i	−0.615522	+	1.06612i	0.374770	+	0.927118i	$0.377722\pi$
$307$	−3310.94	+	5734.72i	−0.615522	+	1.06612i	−0.990293	+	0.138998i	$0.955612\pi$
$308$	3330.78	+	1212.30i	0.616197	+	0.224278i
$309$	4446.70	+	8299.37i	0.818654	+	1.52794i
$310$	1688.25	+	1416.61i	0.309310	+	0.259542i
$311$	2458.09	+	2062.58i	0.448185	+	0.376072i	0.838762	−	0.544498i	$-0.183280\pi$
$311$	2458.09	+	2062.58i	0.448185	+	0.376072i	−0.390577	+	0.920570i	$0.627724\pi$
$312$	2365.29	+	75.0810i	0.429193	+	0.0136238i
$313$	−4008.38	−	1458.93i	−0.723857	−	0.263462i	−0.0462945	−	0.998928i	$-0.514741\pi$
$313$	−4008.38	−	1458.93i	−0.723857	−	0.263462i	−0.677562	+	0.735466i	$0.736963\pi$
$314$	157.567	−	272.914i	0.0283185	−	0.0490491i
$315$	5641.69	+	5379.32i	1.00912	+	0.962191i
$316$	−2317.96	−	4014.82i	−0.412644	−	0.714720i
$317$	−1656.77	−	9396.00i	−0.293544	−	1.66477i	−0.673063	−	0.739585i	$-0.735022\pi$
$317$	−1656.77	−	9396.00i	−0.293544	−	1.66477i	0.379519	−	0.925184i	$-0.376089\pi$
$318$	1143.42	+	1022.99i	0.201635	+	0.180397i
$319$	1377.24	−	501.273i	0.241725	−	0.0879808i
$320$	488.383	−	2769.76i	0.0853170	−	0.483857i
$321$	−371.088	−	2580.95i	−0.0645237	−	0.448769i
$322$	2396.22	−	2010.67i	0.414709	−	0.347982i
$323$	2108.24			0.363175
$324$	2053.95	+	4903.50i	0.352186	+	0.840792i
$325$	283.342			0.0483599
$326$	−1638.65	+	1374.99i	−0.278393	+	0.233600i
$327$	−970.175	−	6747.66i	−0.164070	−	1.14112i
$328$	868.517	−	4925.60i	0.146207	−	0.829180i
$329$	11573.1	−	4212.28i	1.93936	−	0.705868i
$330$	641.534	+	573.963i	0.107016	+	0.0957443i
$331$	1556.42	+	8826.91i	0.258455	+	1.46577i	0.787045	+	0.616896i	$0.211610\pi$
$331$	1556.42	+	8826.91i	0.258455	+	1.46577i	−0.528590	+	0.848878i	$0.677279\pi$
$332$	3524.06	+	6103.85i	0.582554	+	1.00901i
$333$	213.502	−	880.075i	0.0351346	−	0.144828i
$334$	−980.264	+	1697.87i	−0.160592	+	0.278153i
$335$	−1060.14	−	385.860i	−0.172901	−	0.0629307i
$336$	−6587.78	−	209.115i	−1.06962	−	0.0339529i
$337$	−2492.27	−	2091.26i	−0.402856	−	0.338037i	0.418740	−	0.908106i	$-0.362472\pi$
$337$	−2492.27	−	2091.26i	−0.402856	−	0.338037i	−0.821596	+	0.570070i	$0.806916\pi$
$338$	−607.746	−	509.959i	−0.0978018	−	0.0820654i
$339$	1445.51	+	2697.91i	0.231591	+	0.432244i
$340$	8371.91	+	3047.13i	1.33538	+	0.486040i
$341$	−2205.61	+	3820.23i	−0.350265	+	0.606677i
$342$	−423.036	−	26.8838i	−0.0668864	−	0.00425062i
$343$	352.972	+	611.365i	0.0555647	+	0.0962408i
$344$	−188.345	−	1068.16i	−0.0295200	−	0.167416i
$345$	−7440.24	+	2443.62i	−1.16107	+	0.381333i
$346$	3031.16	−	1103.25i	0.470972	−	0.171420i
$347$	−791.412	+	4488.32i	−0.122436	+	0.694368i	0.860362	+	0.509684i	$0.170238\pi$
$347$	−791.412	+	4488.32i	−0.122436	+	0.694368i	−0.982798	+	0.184685i	$0.940874\pi$
$348$	−2397.37	+	1885.32i	−0.369289	+	0.290413i
$349$	−3699.15	+	3103.95i	−0.567366	+	0.476077i	−0.880771	−	0.473543i	$-0.842975\pi$
$349$	−3699.15	+	3103.95i	−0.567366	+	0.476077i	0.313405	+	0.949620i	$0.398530\pi$
$350$	179.647			0.0274358
$351$	−1323.73	+	4788.02i	−0.201297	+	0.728107i
$352$	−2601.58			−0.393934
$353$	−9534.88	+	8000.71i	−1.43765	+	1.20633i	−0.496638	+	0.867958i	$0.665432\pi$
$353$	−9534.88	+	8000.71i	−1.43765	+	1.20633i	−0.941012	+	0.338374i	$0.890123\pi$
$354$	−204.274	−	81.7787i	−0.0306696	−	0.0122782i
$355$	607.318	−	3444.27i	0.0907975	−	0.514938i
$356$	−3194.87	+	1162.84i	−0.475639	+	0.173119i
$357$	3208.25	−	15332.8i	0.475626	−	2.27310i
$358$	−237.623	−	1347.63i	−0.0350804	−	0.198951i
$359$	1658.07	+	2871.86i	0.243759	+	0.422203i	0.961782	−	0.273816i	$-0.0882860\pi$
$359$	1658.07	+	2871.86i	0.243759	+	0.422203i	−0.718023	+	0.696019i	$0.754953\pi$
$360$	−3441.26	−	1506.04i	−0.503806	−	0.220487i
$361$	3255.29	−	5638.33i	0.474601	−	0.822033i
$362$	−1014.40	−	369.210i	−0.147280	−	0.0536056i
$363$	2737.92	−	4412.69i	0.395877	−	0.638034i
$364$	−5279.78	−	4430.26i	−0.760263	−	0.637936i
$365$	−4844.82	−	4065.28i	−0.694765	−	0.582977i
$366$	327.266	−	527.454i	0.0467390	−	0.0753291i
$367$	7220.79	+	2628.15i	1.02704	+	0.373810i	0.799951	−	0.600065i	$-0.204859\pi$
$367$	7220.79	+	2628.15i	1.02704	+	0.373810i	0.227084	+	0.973875i	$0.427081\pi$
$368$	3310.78	−	5734.43i	0.468984	−	0.812304i
$369$	9618.37	+	4209.41i	1.35694	+	0.593857i
$370$	152.570	+	264.259i	0.0214371	+	0.0371302i
$371$	−1627.14	−	9227.96i	−0.227700	−	1.29135i
$372$	1880.02	−	8984.94i	0.262028	−	1.25228i
$373$	−4188.24	+	1524.39i	−0.581390	+	0.211609i	−0.615938	−	0.787794i	$-0.711223\pi$
$373$	−4188.24	+	1524.39i	−0.581390	+	0.211609i	0.0345481	+	0.999403i	$0.489001\pi$
$374$	300.384	−	1703.56i	0.0415307	−	0.235532i
$375$	−6939.85	−	2778.29i	−0.955659	−	0.382587i
$376$	−4546.32	+	3814.82i	−0.623560	+	0.523229i
$377$	−2849.86			−0.389325
$378$	−839.282	+	3035.74i	−0.114201	+	0.413073i
$379$	−630.946			−0.0855132			−0.0427566	−	0.999086i	$-0.513614\pi$
$379$	−630.946			−0.0855132			−0.0427566	+	0.999086i	$0.513614\pi$
$380$	−1127.92	+	946.434i	−0.152265	+	0.127766i
$381$	−3926.94	+	3088.19i	−0.528040	+	0.415257i
$382$	−30.7722	+	174.518i	−0.00412158	+	0.0233746i
$383$	6755.15	−	2458.67i	0.901232	−	0.328022i	0.150486	−	0.988612i	$-0.451916\pi$
$383$	6755.15	−	2458.67i	0.901232	−	0.328022i	0.750746	+	0.660591i	$0.229694\pi$
$384$	6722.03	−	2207.74i	0.893313	−	0.293393i
$385$	−912.930	−	5177.49i	−0.120850	−	0.685374i
$386$	793.238	+	1373.93i	0.104598	+	0.181169i
$387$	2272.24	+	144.401i	0.298462	+	0.0189672i
$388$	−6091.44	+	10550.7i	−0.797025	+	1.38049i
$389$	−6510.52	−	2369.64i	−0.848577	−	0.308857i	−0.119117	−	0.992880i	$-0.538006\pi$
$389$	−6510.52	−	2369.64i	−0.848577	−	0.308857i	−0.729460	+	0.684023i	$0.760229\pi$
$390$	−790.502	−	1475.40i	−0.102638	−	0.191564i
$391$	12055.4	+	10115.7i	1.55925	+	1.30837i
$392$	−3640.20	−	3054.49i	−0.469025	−	0.393558i
$393$	−2983.64	−	94.7092i	−0.382963	−	0.0121563i
$394$	−635.214	−	231.199i	−0.0812224	−	0.0295625i
$395$	−3438.06	+	5954.89i	−0.437943	+	0.758540i
$396$	845.302	−	3484.41i	0.107268	−	0.442168i
$397$	1742.17	+	3017.52i	0.220244	+	0.381474i	0.954882	−	0.296985i	$-0.0959813\pi$
$397$	1742.17	+	3017.52i	0.220244	+	0.381474i	−0.734638	+	0.678459i	$0.762648\pi$
$398$	−153.460	−	870.314i	−0.0193273	−	0.109610i
$399$	1929.40	+	1726.18i	0.242082	+	0.216584i
$400$	357.348	−	130.064i	0.0446686	−	0.0162580i
$401$	−353.884	+	2006.98i	−0.0440702	+	0.249934i	−0.998882	−	0.0472772i	$-0.984946\pi$
$401$	−353.884	+	2006.98i	−0.0440702	+	0.249934i	0.954812	+	0.297212i	$0.0960567\pi$
$402$	−64.8725	−	451.195i	−0.00804863	−	0.0559790i
$403$	6570.74	−	5513.51i	0.812188	−	0.681507i
$404$	−10213.7			−1.25779
$405$	4775.37	−	6274.82i	0.585901	−	0.769872i
$406$	−1806.90			−0.220874
$407$	−467.875	+	392.593i	−0.0569820	+	0.0478136i
$408$	1074.29	+	7471.78i	0.130356	+	0.906638i
$409$	−949.794	+	5386.55i	−0.114827	+	0.651217i	0.872008	+	0.489491i	$0.162817\pi$
$409$	−949.794	+	5386.55i	−0.114827	+	0.651217i	−0.986836	+	0.161726i	$0.948294\pi$
$410$	−3324.31	+	1209.95i	−0.400429	+	0.145744i
$411$	913.884	+	817.627i	0.109680	+	0.0981279i
$412$	2294.65	+	13013.6i	0.274391	+	1.55615i
$413$	671.925	+	1163.81i	0.0800564	+	0.138662i
$414$	−2290.03	−	2183.53i	−0.271857	−	0.259214i
$415$	5226.98	−	9053.39i	0.618270	−	1.07088i
$416$	4753.63	+	1730.18i	0.560255	+	0.203916i
$417$	3027.94	+	96.1154i	0.355585	+	0.0112873i
$418$	219.000	+	183.763i	0.0256260	+	0.0215027i
$419$	5126.35	+	4301.52i	0.597706	+	0.501535i	0.890707	−	0.454577i	$-0.150210\pi$
$419$	5126.35	+	4301.52i	0.597706	+	0.501535i	−0.293002	+	0.956112i	$0.594654\pi$
$420$	5166.80	+	9643.35i	0.600271	+	1.12035i
$421$	−5783.44	−	2105.00i	−0.669519	−	0.243685i	−0.0151785	−	0.999885i	$-0.504832\pi$
$421$	−5783.44	−	2105.00i	−0.669519	−	0.243685i	−0.654341	+	0.756200i	$0.727054\pi$
$422$	−1139.10	+	1972.98i	−0.131399	+	0.227590i
$423$	−5532.26	−	11162.4i	−0.635905	−	1.28306i
$424$	2257.69	+	3910.44i	0.258593	+	0.447896i
$425$	156.944	+	890.074i	0.0179127	+	0.101588i
$426$	1342.55	−	440.938i	0.152692	−	0.0501491i
$427$	−3562.46	+	1296.63i	−0.403746	+	0.146951i
$428$	635.467	−	3603.92i	0.0717675	−	0.407014i
$429$	2633.53	−	2071.04i	0.296383	−	0.233079i
$430$	−587.687	+	493.128i	−0.0659088	+	0.0553040i
$431$	−1934.68			−0.216219			−0.108109	−	0.994139i	$-0.534480\pi$
$431$	−1934.68			−0.216219			−0.108109	+	0.994139i	$0.534480\pi$
$432$	528.399	+	6646.25i	0.0588486	+	0.740204i
$433$	7109.96			0.789106			0.394553	−	0.918873i	$-0.370899\pi$
$433$	7109.96			0.789106			0.394553	+	0.918873i	$0.370899\pi$
$434$	4166.04	−	3495.72i	0.460775	−	0.386636i
$435$	4199.64	+	1681.28i	0.462890	+	0.185313i
$436$	1661.37	−	9422.10i	0.182489	−	1.03495i
$437$	−2443.98	+	889.537i	−0.267532	+	0.0973738i
$438$	523.353	−	2501.20i	0.0570931	−	0.272858i
$439$	−951.221	−	5394.64i	−0.103415	−	0.586497i	−0.991841	−	0.127478i	$-0.959312\pi$
$439$	−951.221	−	5394.64i	−0.103415	−	0.586497i	0.888426	−	0.459019i	$-0.151799\pi$
$440$	1266.71	+	2194.01i	0.137246	+	0.237717i
$441$	8032.64	−	5914.33i	0.867362	−	0.638628i
$442$	−1681.81	+	2912.99i	−0.180986	+	0.313477i
$443$	12409.4	+	4516.66i	1.33090	+	0.484409i	0.906936	−	0.421269i	$-0.138415\pi$
$443$	12409.4	+	4516.66i	1.33090	+	0.484409i	0.423967	+	0.905678i	$0.360637\pi$
$444$	670.089	−	1079.98i	0.0716240	−	0.115436i
$445$	3863.03	+	3241.47i	0.411518	+	0.345304i
$446$	41.0070	+	34.4089i	0.00435367	+	0.00365316i
$447$	869.778	−	1401.82i	0.0920337	−	0.148330i
$448$	−6521.75	−	2373.72i	−0.687776	−	0.250330i
$449$	3190.47	−	5526.05i	0.335339	−	0.580825i	−0.648211	−	0.761461i	$-0.724482\pi$
$449$	3190.47	−	5526.05i	0.335339	−	0.580825i	0.983550	+	0.180636i	$0.0578157\pi$
$450$	−20.1421	−	180.602i	−0.00211002	−	0.0189192i
$451$	−3540.48	−	6132.30i	−0.369656	−	0.640263i
$452$	745.932	+	4230.39i	0.0776232	+	0.440223i
$453$	−1549.91	+	7407.28i	−0.160753	+	0.768266i
$454$	−52.3014	+	19.0362i	−0.00540667	+	0.00196787i
$455$	−1775.17	+	10067.5i	−0.182904	+	1.03730i
$456$	−1158.17	−	463.659i	−0.118939	−	0.0476159i
$457$	960.392	−	805.865i	0.0983047	−	0.0824875i	−0.592311	−	0.805710i	$-0.701784\pi$
$457$	960.392	−	805.865i	0.0983047	−	0.0824875i	0.690615	+	0.723222i	$0.257340\pi$
$458$	2066.28			0.210809
$459$	−15774.0	−	1506.19i	−1.60407	−	0.153165i
$460$	−10990.8			−1.11402
$461$	−4898.82	+	4110.60i	−0.494926	+	0.415292i	−0.855788	−	0.517327i	$-0.826927\pi$
$461$	−4898.82	+	4110.60i	−0.494926	+	0.415292i	0.360862	+	0.932619i	$0.382483\pi$
$462$	1669.74	−	1313.10i	0.168146	−	0.132231i
$463$	56.5577	−	320.755i	0.00567702	−	0.0321960i	−0.981838	−	0.189723i	$-0.939241\pi$
$463$	56.5577	−	320.755i	0.00567702	−	0.0321960i	0.987515	+	0.157527i	$0.0503521\pi$
$464$	−3594.23	+	1308.19i	−0.359608	+	0.130886i
$465$	−12935.5	+	4248.44i	−1.29004	+	0.423692i
$466$	−451.481	−	2560.47i	−0.0448808	−	0.254532i
$467$	−9230.26	−	15987.3i	−0.914615	−	1.58416i	−0.807464	−	0.589917i	$-0.799160\pi$
$467$	−9230.26	−	15987.3i	−0.914615	−	1.58416i	−0.107151	−	0.994243i	$-0.534173\pi$
$468$	−3861.85	+	5804.58i	−0.381440	+	0.573326i
$469$	−1391.99	+	2411.00i	−0.137049	+	0.237376i
$470$	3944.57	+	1435.71i	0.387127	+	0.140903i
$471$	919.459	+	1716.09i	0.0899500	+	0.167884i
$472$	−496.073	−	416.255i	−0.0483763	−	0.0405925i
$473$	−1176.31	−	987.043i	−0.114349	−	0.0959498i
$474$	−2776.86	−	88.1454i	−0.269083	−	0.00854146i
$475$	−140.360	−	51.0870i	−0.0135583	−	0.00493481i
$476$	10992.5	−	19039.6i	1.05849	−	1.83335i
$477$	−9094.59	+	2670.43i	−0.872983	+	0.256333i
$478$	−1438.70	−	2491.89i	−0.137666	−	0.238445i
$479$	1203.54	+	6825.63i	0.114804	+	0.651087i	0.986847	+	0.161657i	$0.0516840\pi$
$479$	1203.54	+	6825.63i	0.114804	+	0.651087i	−0.872043	+	0.489430i	$0.837205\pi$
$480$	−5984.36	−	5354.04i	−0.569057	−	0.509119i
$481$	1116.00	−	406.190i	0.105790	−	0.0385045i
$482$	−103.735	+	588.311i	−0.00980292	+	0.0555951i
$483$	2750.25	+	19128.3i	0.259090	+	1.80200i
$484$	5583.14	−	4684.81i	0.524337	−	0.439971i
$485$	18069.9			1.69178
$486$	3145.98	+	503.376i	0.293631	+	0.0469827i
$487$	10020.5			0.932391			0.466195	−	0.884682i	$-0.345624\pi$
$487$	10020.5			0.932391			0.466195	+	0.884682i	$0.345624\pi$
$488$	1399.45	−	1174.28i	0.129816	−	0.108929i
$489$	−1880.75	−	13080.8i	−0.173927	−	1.20968i
$490$	−583.645	+	3310.02i	−0.0538090	+	0.305166i
$491$	−5178.48	+	1884.81i	−0.475971	+	0.173239i	−0.568855	−	0.822438i	$-0.692614\pi$
$491$	−5178.48	+	1884.81i	−0.475971	+	0.173239i	0.0928844	+	0.995677i	$0.470391\pi$
$492$	10981.6	+	9824.92i	1.00628	+	0.900288i
$493$	−1578.55	−	8952.41i	−0.144208	−	0.817842i
$494$	−277.947	−	481.419i	−0.0253147	−	0.0438463i
$495$	−5102.65	+	1498.29i	−0.463328	+	0.136046i
$496$	5756.07	−	9969.81i	0.521079	−	0.902535i
$497$	−8109.97	−	2951.79i	−0.731956	−	0.266410i
$498$	4221.74	+	134.010i	0.379881	+	0.0120585i
$499$	−14672.9	−	12312.0i	−1.31633	−	1.10453i	−0.987070	−	0.160289i	$-0.948757\pi$
$499$	−14672.9	−	12312.0i	−1.31633	−	1.10453i	−0.329257	−	0.944241i	$-0.606798\pi$
$500$	−8036.80	−	6743.68i	−0.718833	−	0.603173i
$501$	−5720.19	−	10676.2i	−0.510098	−	0.952052i
$502$	−4009.81	−	1459.45i	−0.356507	−	0.129758i
$503$	−5797.94	+	10042.3i	−0.513951	+	0.890190i	0.485918	+	0.874005i	$0.338485\pi$
$503$	−5797.94	+	10042.3i	−0.513951	+	0.890190i	−0.999869	+	0.0161853i	$0.994848\pi$
$504$	−5134.56	+	7717.54i	−0.453793	+	0.682077i
$505$	7574.58	+	13119.6i	0.667455	+	1.15607i
$506$	370.569	+	2101.60i	0.0325569	+	0.184639i
$507$	4656.60	−	1529.38i	0.407903	−	0.133969i
$508$	−6588.53	+	2398.03i	−0.575431	+	0.209440i
$509$	1147.18	−	6505.98i	0.0998975	−	0.566547i	−0.893239	−	0.449583i	$-0.851573\pi$
$509$	1147.18	−	6505.98i	0.0998975	−	0.566547i	0.993136	−	0.116964i	$-0.0373163\pi$
$510$	4196.88	−	3300.47i	0.364394	−	0.286563i
$511$	−11955.4	+	10031.8i	−1.03498	+	0.868454i
$512$	11679.4			1.00813
$513$	1519.03	−	2133.19i	0.130735	−	0.183592i
$514$	1107.91			0.0950735
$515$	15014.4	−	12598.6i	1.28468	−	1.07798i
$516$	2966.54	+	1187.62i	0.253090	+	0.101322i
$517$	−1459.02	+	8274.51i	−0.124115	+	0.703893i
$518$	707.575	−	257.536i	0.0600175	−	0.0218446i
$519$	−4081.42	+	19505.8i	−0.345191	+	1.64973i
$520$	−855.422	−	4851.34i	−0.0721399	−	0.409125i
$521$	−2226.21	−	3855.91i	−0.187202	−	0.324243i	0.757114	−	0.653282i	$-0.226609\pi$
$521$	−2226.21	−	3855.91i	−0.187202	−	0.324243i	−0.944316	+	0.329039i	$0.893275\pi$
$522$	202.590	+	1816.50i	0.0169868	+	0.152311i
$523$	3394.82	−	5880.01i	0.283834	−	0.491615i	−0.688492	−	0.725244i	$-0.741727\pi$
$523$	3394.82	−	5880.01i	0.283834	−	0.491615i	0.972326	+	0.233629i	$0.0750602\pi$
$524$	−3936.86	−	1432.90i	−0.328211	−	0.119459i
$525$	−585.141	+	943.070i	−0.0486431	+	0.0783980i
$526$	−2556.39	−	2145.07i	−0.211909	−	0.177812i
$527$	20959.4	+	17587.0i	1.73246	+	1.45370i
$528$	2370.71	−	3820.87i	0.195402	−	0.314928i
$529$	−6810.18	−	2478.70i	−0.559725	−	0.203723i
$530$	1596.88	−	2765.88i	0.130876	−	0.226684i
$531$	1094.66	−	805.984i	0.0894617	−	0.0658696i
$532$	1816.69	+	3146.60i	0.148052	+	0.256433i
$533$	2390.92	+	13559.6i	0.194300	+	1.10193i
$534$	−417.297	+	1994.34i	−0.0338169	+	0.161617i
$535$	−5100.54	+	1856.45i	−0.412179	+	0.150021i
$536$	232.958	−	1321.17i	0.0187728	−	0.106466i
$537$	7848.46	+	3142.04i	0.630701	+	0.252494i
$538$	2399.10	−	2013.09i	0.192254	−	0.161320i
$539$	−6727.52			−0.537616
$540$	9115.32	−	6275.48i	0.726409	−	0.500100i
$541$	17202.4			1.36707			0.683537	−	0.729916i	$-0.260441\pi$
$541$	17202.4			1.36707			0.683537	+	0.729916i	$0.260441\pi$
$542$	−3466.38	+	2908.64i	−0.274712	+	0.230510i
$543$	5242.26	−	4122.57i	0.414304	−	0.325813i
$544$	−2802.04	+	15891.1i	−0.220839	+	1.25244i
$545$	−13334.9	+	4853.50i	−1.04808	+	0.381470i
$546$	−3924.23	+	1288.85i	−0.307585	+	0.101021i
$547$	−3992.83	−	22644.4i	−0.312104	−	1.77003i	−0.588019	−	0.808847i	$-0.700092\pi$
$547$	−3992.83	−	22644.4i	−0.312104	−	1.77003i	0.275915	−	0.961182i	$-0.411019\pi$
$548$	860.499	+	1490.43i	0.0670779	+	0.116182i
$549$	1702.95	+	3436.02i	0.132386	+	0.267114i
$550$	−61.2795	+	106.139i	−0.00475084	+	0.00822870i
$551$	1411.75	+	513.836i	0.109152	+	0.0397280i
$552$	−4397.96	−	8208.40i	−0.339112	−	0.632922i
$553$	12998.3	+	10906.8i	0.999533	+	0.838708i
$554$	−658.480	−	552.530i	−0.0504984	−	0.0423732i
$555$	−1884.19	−	59.8097i	−0.144107	−	0.00457438i
$556$	3995.32	+	1454.18i	0.304747	+	0.110919i
$557$	−9928.09	+	17195.9i	−0.755236	+	1.30811i	0.190021	+	0.981780i	$0.439144\pi$
$557$	−9928.09	+	17195.9i	−0.755236	+	1.30811i	−0.945257	+	0.326327i	$0.894189\pi$
$558$	−3981.41	−	3796.25i	−0.302055	−	0.288007i
$559$	1492.93	+	2585.84i	0.112959	+	0.195652i
$560$	2382.51	+	13511.9i	0.179785	+	1.01961i
$561$	7964.58	+	7125.69i	0.599402	+	0.536269i
$562$	5199.10	−	1892.32i	0.390233	−	0.142033i
$563$	925.723	−	5250.04i	0.0692976	−	0.393006i	−0.930355	−	0.366659i	$-0.880501\pi$
$563$	925.723	−	5250.04i	0.0692976	−	0.393006i	0.999653	−	0.0263470i	$-0.00838748\pi$
$564$	−2488.32	−	17306.5i	−0.185775	−	1.29208i
$565$	4880.79	−	4095.47i	0.363427	−	0.304952i
$566$	−5840.43			−0.433731
$567$	−13202.7	−	14293.8i	−0.977884	−	1.05870i
$568$	4158.86			0.307222
$569$	6662.49	−	5590.50i	0.490872	−	0.411891i	−0.363467	−	0.931607i	$-0.618407\pi$
$569$	6662.49	−	5590.50i	0.490872	−	0.411891i	0.854339	+	0.519717i	$0.173962\pi$
$570$	125.578	+	873.406i	0.00922785	+	0.0641806i
$571$	−542.707	+	3077.84i	−0.0397751	+	0.225576i	−0.998215	−	0.0597178i	$-0.980980\pi$
$571$	−542.707	+	3077.84i	−0.0397751	+	0.225576i	0.958440	+	0.285293i	$0.0920910\pi$
$572$	4418.48	−	1608.20i	0.322983	−	0.117556i
$573$	−815.914	−	729.976i	−0.0594857	−	0.0532202i
$574$	1515.91	+	8597.16i	0.110232	+	0.625154i
$575$	−557.490	−	965.600i	−0.0404329	−	0.0700318i
$576$	−1655.12	+	6822.56i	−0.119728	+	0.493530i
$577$	2717.27	−	4706.44i	0.196051	−	0.339570i	−0.751194	−	0.660082i	$-0.770522\pi$
$577$	2717.27	−	4706.44i	0.196051	−	0.339570i	0.947244	+	0.320512i	$0.103855\pi$
$578$	−6199.25	−	2256.34i	−0.446116	−	0.162373i
$579$	−9796.25	−	310.961i	−0.703141	−	0.0223197i
$580$	4863.46	+	4080.92i	0.348179	+	0.292157i
$581$	−19761.6	−	16582.0i	−1.41110	−	1.18405i
$582$	3448.09	+	6435.55i	0.245581	+	0.458354i
$583$	6007.11	+	2186.41i	0.426739	+	0.155320i
$584$	3760.29	−	6513.02i	0.266442	−	0.461491i
$585$	10320.0	+	655.836i	0.729369	+	0.0463512i
$586$	−359.984	−	623.510i	−0.0253768	−	0.0439539i
$587$	−1563.56	−	8867.40i	−0.109941	−	0.623504i	−0.989131	−	0.147034i	$-0.953027\pi$
$587$	−1563.56	−	8867.40i	−0.109941	−	0.623504i	0.879191	−	0.476470i	$-0.158084\pi$
$588$	13300.6	−	4368.37i	0.932839	−	0.306375i
$589$	−4249.08	+	1546.54i	−0.297250	+	0.108190i
$590$	−79.5371	+	451.078i	−0.00554999	+	0.0314755i
$591$	3282.70	−	2581.55i	0.228481	−	0.179680i
$592$	1221.03	−	1024.57i	0.0847705	−	0.0711309i
$593$	−6962.45			−0.482148			−0.241074	−	0.970507i	$-0.577500\pi$
$593$	−6962.45			−0.482148			−0.241074	+	0.970507i	$0.577500\pi$
$594$	−1507.29	−	1531.39i	−0.104116	−	0.105781i
$595$	−32608.7			−2.24677
$596$	1773.64	−	1488.26i	0.121898	−	0.102285i
$597$	5068.63	+	2029.17i	0.347479	+	0.139109i
$598$	720.561	−	4086.50i	0.0492741	−	0.279447i
$599$	−17588.5	+	6401.69i	−1.19974	+	0.436671i	−0.863135	−	0.504973i	$-0.831502\pi$
$599$	−17588.5	+	6401.69i	−1.19974	+	0.436671i	−0.336610	+	0.941644i	$0.609280\pi$
$600$	109.534	−	523.481i	0.00745282	−	0.0356184i
$601$	4956.51	+	28109.8i	0.336407	+	1.90786i	0.412880	+	0.910786i	$0.364523\pi$
$601$	4956.51	+	28109.8i	0.336407	+	1.90786i	−0.0764728	+	0.997072i	$0.524366\pi$
$602$	946.563	+	1639.50i	0.0640848	+	0.110998i
$603$	2579.88	+	1129.07i	0.174231	+	0.0762507i
$604$	−5310.48	+	9198.02i	−0.357749	+	0.619639i
$605$	−10158.2	−	3697.29i	−0.682629	−	0.248457i
$606$	−3227.11	+	5201.12i	−0.216324	+	0.348649i
$607$	−12502.6	−	10490.9i	−0.836019	−	0.701503i	0.120646	−	0.992696i	$-0.461504\pi$
$607$	−12502.6	−	10490.9i	−0.836019	−	0.701503i	−0.956664	+	0.291193i	$0.905948\pi$
$608$	−2042.88	−	1714.18i	−0.136266	−	0.114341i
$609$	5885.38	−	9485.45i	0.391605	−	0.631149i
$610$	−1214.22	−	441.941i	−0.0805942	−	0.0293339i
$611$	8168.88	−	14148.9i	0.540880	−	0.936832i
$612$	−20373.3	−	8916.21i	−1.34565	−	0.588916i
$613$	−1083.24	−	1876.22i	−0.0713728	−	0.123621i	0.828130	−	0.560536i	$-0.189405\pi$
$613$	−1083.24	−	1876.22i	−0.0713728	−	0.123621i	−0.899503	+	0.436914i	$0.856071\pi$
$614$	967.137	+	5484.91i	0.0635676	+	0.360510i
$615$	4476.14	−	21392.3i	0.293488	−	1.40263i
$616$	5874.65	−	2138.20i	0.384247	−	0.139855i
$617$	2009.48	−	11396.3i	0.131116	−	0.743595i	−0.846370	−	0.532595i	$-0.821217\pi$
$617$	2009.48	−	11396.3i	0.131116	−	0.743595i	0.977486	−	0.211000i	$-0.0676720\pi$
$618$	7351.96	+	2943.27i	0.478542	+	0.191579i
$619$	4431.85	−	3718.76i	0.287772	−	0.241469i	−0.487461	−	0.873145i	$-0.662077\pi$
$619$	4431.85	−	3718.76i	0.287772	−	0.241469i	0.775233	+	0.631675i	$0.217632\pi$
$620$	−19108.5			−1.23777
$621$	18921.6	−	4909.54i	1.22270	−	0.317251i
$622$	2698.86			0.173978
$623$	9532.70	−	7998.89i	0.613033	−	0.514396i
$624$	−6872.85	+	5404.88i	−0.440920	+	0.346744i
$625$	−2528.44	+	14339.5i	−0.161820	+	0.917727i
$626$	−3371.36	+	1227.08i	−0.215250	+	0.0783447i
$627$	−1678.00	+	551.110i	−0.106879	+	0.0351024i
$628$	474.472	+	2690.86i	0.0301489	+	0.170983i
$629$	1894.14	+	3280.74i	0.120070	+	0.207968i
$630$	6543.21	+	415.819i	0.413790	+	0.0262962i
$631$	−5539.27	+	9594.29i	−0.349469	+	0.605298i	−0.986155	−	0.165825i	$-0.946971\pi$
$631$	−5539.27	+	9594.29i	−0.349469	+	0.605298i	0.636686	+	0.771123i	$0.280305\pi$
$632$	−7683.47	−	2796.56i	−0.483595	−	0.176014i
$633$	−6647.06	−	12406.1i	−0.417372	−	0.778988i
$634$	−6147.26	−	5158.17i	−0.385077	−	0.323118i
$635$	7966.44	+	6684.64i	0.497856	+	0.417751i
$636$	−13296.1	−	422.054i	−0.828967	−	0.0263138i
$637$	12292.6	+	4474.13i	0.764599	+	0.278291i
$638$	616.352	−	1067.55i	0.0382470	−	0.0662458i
$639$	−2058.19	+	8484.05i	−0.127419	+	0.525233i
$640$	−7364.13	−	12755.0i	−0.454833	−	0.787793i
$641$	4569.84	+	25916.8i	0.281588	+	1.59696i	0.717226	+	0.696841i	$0.245412\pi$
$641$	4569.84	+	25916.8i	0.281588	+	1.59696i	−0.435638	+	0.900122i	$0.643477\pi$
$642$	−1634.45	−	1462.29i	−0.100477	−	0.0898943i
$643$	27197.0	−	9898.91i	1.66803	−	0.607115i	0.676440	−	0.736498i	$-0.263522\pi$
$643$	27197.0	−	9898.91i	1.66803	−	0.607115i	0.991595	+	0.129383i	$0.0412996\pi$
$644$	−4709.65	+	26709.8i	−0.288177	+	1.63433i
$645$	−674.514	−	4691.31i	−0.0411767	−	0.286388i
$646$	1358.35	−	1139.79i	0.0827298	−	0.0694185i
$647$	721.396			0.0438346			0.0219173	−	0.999760i	$-0.493023\pi$
$647$	721.396			0.0438346			0.0219173	+	0.999760i	$0.493023\pi$
$648$	8334.26	+	4296.57i	0.505248	+	0.260471i
$649$	−916.804			−0.0554510
$650$	182.558	−	153.184i	0.0110162	−	0.00924366i
$651$	4781.55	+	33256.1i	0.287870	+	2.00217i
$652$	3220.67	−	18265.3i	0.193453	−	1.09713i
$653$	27820.4	−	10125.8i	1.66722	−	0.606819i	0.675748	−	0.737133i	$-0.263821\pi$
$653$	27820.4	−	10125.8i	1.66722	−	0.606819i	0.991473	+	0.130314i	$0.0415986\pi$
$654$	−4273.11	−	3823.03i	−0.255492	−	0.228582i
$655$	1079.05	+	6119.60i	0.0643695	+	0.365058i
$656$	9239.75	+	16003.7i	0.549926	+	0.952500i
$657$	11425.6	+	10894.2i	0.678469	+	0.646916i
$658$	5179.31	−	8970.83i	0.306855	−	0.531488i
$659$	−15927.9	−	5797.29i	−0.941523	−	0.342686i	−0.174756	−	0.984612i	$-0.555914\pi$
$659$	−15927.9	−	5797.29i	−0.941523	−	0.342686i	−0.766767	+	0.641925i	$0.778136\pi$
$660$	−7459.95	−	236.800i	−0.439967	−	0.0139658i
$661$	13670.0	+	11470.5i	0.804389	+	0.674963i	0.949262	−	0.314488i	$-0.101833\pi$
$661$	13670.0	+	11470.5i	0.804389	+	0.674963i	−0.144872	+	0.989450i	$0.546277\pi$
$662$	5774.94	+	4845.75i	0.339048	+	0.284495i
$663$	−9814.00	−	18316.9i	−0.574878	−	1.07296i
$664$	11681.4	+	4251.68i	0.682720	+	0.248490i
$665$	2694.56	−	4667.11i	0.157129	−	0.272155i
$666$	−338.239	−	682.462i	−0.0196794	−	0.0397070i
$667$	5607.26	+	9712.06i	0.325508	+	0.563797i
$668$	−2951.81	−	16740.5i	−0.170971	−	0.969627i
$669$	−314.199	+	103.193i	−0.0181579	+	0.00596366i
$670$	−891.662	+	324.538i	−0.0514148	+	0.0187135i
$671$	449.117	−	2547.07i	0.0258390	−	0.146540i
$672$	−15575.6	+	12248.8i	−0.894112	+	0.703139i
$673$	−24248.6	+	20347.0i	−1.38888	+	1.16541i	−0.423087	+	0.906089i	$0.639054\pi$
$673$	−24248.6	+	20347.0i	−1.38888	+	1.16541i	−0.965792	+	0.259319i	$0.916502\pi$
$674$	−2736.39			−0.156382
$675$	1013.69	+	482.515i	0.0578029	+	0.0275141i
$676$	6878.81			0.391375
$677$	13542.1	−	11363.2i	0.768783	−	0.645085i	−0.171614	−	0.985164i	$-0.554898\pi$
$677$	13542.1	−	11363.2i	0.768783	−	0.645085i	0.940397	+	0.340079i	$0.110454\pi$
$678$	2389.93	+	956.782i	0.135376	+	0.0541961i
$679$	7743.10	−	43913.3i	0.437633	−	2.48194i
$680$	14765.9	−	5374.35i	0.832716	−	0.303084i
$681$	70.4231	−	336.565i	0.00396273	−	0.0189386i
$682$	644.266	+	3653.81i	0.0361733	+	0.205149i
$683$	3940.12	+	6824.48i	0.220738	+	0.382330i	0.955032	−	0.296501i	$-0.0958199\pi$
$683$	3940.12	+	6824.48i	0.220738	+	0.382330i	−0.734294	+	0.678832i	$0.762487\pi$
$684$	2959.64	−	2179.15i	0.165445	−	0.121815i
$685$	1276.31	−	2210.64i	0.0711904	−	0.123305i
$686$	557.946	+	203.076i	0.0310532	+	0.0113024i
$687$	−6730.22	+	10847.1i	−0.373761	+	0.602390i
$688$	3069.87	+	2575.93i	0.170113	+	0.142742i
$689$	−9522.16	−	7990.04i	−0.526510	−	0.441794i
$690$	−3472.67	+	5596.88i	−0.191597	+	0.308797i
$691$	−21426.4	−	7798.58i	−1.17959	−	0.429337i	−0.323535	−	0.946216i	$-0.604871\pi$
$691$	−21426.4	−	7798.58i	−1.17959	−	0.429337i	−0.856058	+	0.516879i	$0.827094\pi$
$692$	−13984.2	+	24221.4i	−0.768210	+	1.33058i
$693$	1454.59	+	13042.4i	0.0797334	+	0.714921i
$694$	1916.63	+	3319.71i	0.104833	+	0.181577i
$695$	−1095.07	−	6210.47i	−0.0597676	−	0.338959i
$696$	−1101.70	+	5265.20i	−0.0599995	+	0.286748i
$697$	−41270.9	+	15021.4i	−2.24282	+	0.816321i
$698$	−705.268	+	3999.77i	−0.0382447	+	0.216896i
$699$	14912.0	+	5969.83i	0.806899	+	0.323032i
$700$	−1193.22	+	1001.23i	−0.0644276	+	0.0540611i
$701$	31049.4			1.67293			0.836463	−	0.548024i	$-0.184620\pi$
$701$	31049.4			1.67293			0.836463	+	0.548024i	$0.184620\pi$
$702$	1735.69	+	3800.59i	0.0933180	+	0.204336i
$703$	−626.074			−0.0335887
$704$	3627.08	−	3043.48i	0.194177	−	0.162934i
$705$	−20385.0	+	16031.0i	−1.08900	+	0.856401i
$706$	−1817.89	+	10309.8i	−0.0969083	+	0.549594i
$707$	35128.7	−	12785.8i	1.86867	−	0.680141i
$708$	1812.57	−	595.306i	0.0962153	−	0.0316003i
$709$	−2231.86	−	12657.5i	−0.118222	−	0.670470i	−0.985104	−	0.171957i	$-0.944991\pi$
$709$	−2231.86	−	12657.5i	−0.118222	−	0.670470i	0.866882	−	0.498513i	$-0.166120\pi$
$710$	−1470.80	−	2547.49i	−0.0777437	−	0.134656i
$711$	9507.44	−	14290.2i	0.501487	−	0.753763i
$712$	−2998.28	+	5193.18i	−0.157817	+	0.273346i
$713$	−31717.8	−	11544.3i	−1.66597	−	0.606365i
$714$	−6222.36	−	11613.5i	−0.326143	−	0.608716i
$715$	−5342.55	−	4482.93i	−0.279441	−	0.234479i
$716$	9089.04	+	7626.61i	0.474404	+	0.398072i
$717$	17767.5	+	563.990i	0.925438	+	0.0293760i
$718$	2620.93	+	953.939i	0.136229	+	0.0495831i
$719$	−5713.43	+	9895.95i	−0.296349	+	0.513292i	−0.975298	−	0.220894i	$-0.929103\pi$
$719$	−5713.43	+	9895.95i	−0.296349	+	0.513292i	0.678949	+	0.734186i	$0.262436\pi$
$720$	13316.6	−	3910.14i	0.689279	−	0.202392i
$721$	−24183.0	−	41886.2i	−1.24913	−	2.16356i
$722$	−950.881	−	5392.72i	−0.0490140	−	0.277972i
$723$	−2750.50	−	2460.80i	−0.141483	−	0.126581i
$724$	8795.34	−	3201.24i	0.451487	−	0.164328i
$725$	−111.840	+	634.276i	−0.00572915	+	0.0324916i
$726$	−621.605	−	4323.33i	−0.0317768	−	0.221011i
$727$	25582.4	−	21466.2i	1.30509	−	1.09510i	0.315846	−	0.948811i	$-0.397712\pi$
$727$	25582.4	−	21466.2i	1.30509	−	1.09510i	0.989242	−	0.146288i	$-0.0467326\pi$
$728$	−12156.2			−0.618872
$729$	−12889.5	+	14875.5i	−0.654856	+	0.755754i
$730$	−5319.36			−0.269697
$731$	−7296.06	+	6122.12i	−0.369158	+	0.309760i
$732$	765.957	+	5327.31i	0.0386756	+	0.268993i
$733$	2783.30	−	15784.9i	0.140251	−	0.795400i	−0.830808	−	0.556559i	$-0.812121\pi$
$733$	2783.30	−	15784.9i	0.140251	−	0.795400i	0.971059	−	0.238841i	$-0.0767676\pi$
$734$	6073.25	−	2210.48i	0.305405	−	0.111158i
$735$	−15475.2	−	13845.2i	−0.776612	−	0.694813i
$736$	−3456.74	−	19604.1i	−0.173121	−	0.981817i
$737$	−949.645	−	1644.83i	−0.0474635	−	0.0822092i
$738$	8472.90	−	2487.89i	0.422618	−	0.124093i
$739$	−14887.0	+	25785.0i	−0.741038	+	1.28352i	0.210985	+	0.977489i	$0.432333\pi$
$739$	−14887.0	+	25785.0i	−0.741038	+	1.28352i	−0.952023	+	0.306027i	$0.901000\pi$
$740$	−2486.17	−	904.890i	−0.123504	−	0.0449519i
$741$	3432.57	+	108.959i	0.170173	+	0.00540179i
$742$	−6037.33	−	5065.92i	−0.298703	−	0.250641i
$743$	7095.90	+	5954.17i	0.350368	+	0.293994i	0.800938	−	0.598748i	$-0.204335\pi$
$743$	7095.90	+	5954.17i	0.350368	+	0.293994i	−0.450570	+	0.892741i	$0.648779\pi$
$744$	−7646.24	−	14271.0i	−0.376781	−	0.703227i
$745$	−3227.05	−	1174.55i	−0.158698	−	0.0577613i
$746$	−1874.35	+	3246.48i	−0.0919906	+	0.159332i
$747$	−14454.4	+	21725.8i	−0.707979	+	1.06413i
$748$	7499.31	+	12989.2i	0.366580	+	0.634936i
$749$	2325.89	+	13190.8i	0.113466	+	0.643497i
$750$	−5973.40	+	1961.86i	−0.290824	+	0.0955161i
$751$	14447.2	−	5258.35i	0.701978	−	0.255499i	0.0337229	−	0.999431i	$-0.489264\pi$
$751$	14447.2	−	5258.35i	0.701978	−	0.255499i	0.668255	+	0.743932i	$0.267041\pi$
$752$	3807.67	−	21594.3i	0.184643	−	1.04716i
$753$	20722.2	−	16296.1i	1.00286	−	0.788663i
$754$	−1836.18	+	1540.74i	−0.0886865	+	0.0744168i
$755$	15753.3			0.759365
$756$	−11344.6	−	24841.0i	−0.545766	−	1.19505i
$757$	−27010.0			−1.29682			−0.648411	−	0.761291i	$-0.724566\pi$
$757$	−27010.0			−1.29682			−0.648411	+	0.761291i	$0.724566\pi$
$758$	−406.521	+	341.111i	−0.0194795	+	0.0163453i
$759$	−12239.5	−	4899.95i	−0.585331	−	0.234331i
$760$	−450.950	+	2557.47i	−0.0215233	+	0.122065i
$761$	−20254.5	+	7372.04i	−0.964816	+	0.351164i	−0.775919	−	0.630833i	$-0.782713\pi$
$761$	−20254.5	+	7372.04i	−0.964816	+	0.351164i	−0.188897	+	0.981997i	$0.560491\pi$
$762$	−860.561	+	4112.77i	−0.0409118	+	0.195525i
$763$	6080.81	+	34486.0i	0.288519	+	1.63627i
$764$	−768.252	−	1330.65i	−0.0363801	−	0.0630121i
$765$	3656.10	+	32782.1i	0.172793	+	1.54933i
$766$	3023.12	−	5236.20i	0.142598	−	0.246986i
$767$	1675.19	+	609.719i	0.0788626	+	0.0287036i
$768$	−2561.16	+	4127.82i	−0.120336	+	0.193945i
$769$	7558.69	+	6342.49i	0.354451	+	0.297420i	0.802575	−	0.596552i	$-0.203463\pi$
$769$	7558.69	+	6342.49i	0.354451	+	0.297420i	−0.448123	+	0.893972i	$0.647907\pi$
$770$	−3387.33	−	2842.31i	−0.158534	−	0.133026i
$771$	−3608.66	+	5816.06i	−0.168564	+	0.271673i
$772$	−12926.0	−	4704.68i	−0.602613	−	0.219333i
$773$	−3806.71	+	6593.42i	−0.177125	+	0.306790i	−0.940895	−	0.338699i	$-0.890013\pi$
$773$	−3806.71	+	6593.42i	−0.177125	+	0.306790i	0.763769	+	0.645489i	$0.223346\pi$
$774$	1542.08	−	1135.42i	0.0716137	−	0.0527283i
$775$	−969.244	−	1678.78i	−0.0449242	−	0.0778110i
$776$	3731.26	+	21161.0i	0.172609	+	0.978913i
$777$	−952.739	+	4553.31i	−0.0439888	+	0.210231i
$778$	−5475.86	+	1993.05i	−0.252338	+	0.0918436i
$779$	1260.41	−	7148.16i	0.0579705	−	0.328767i
$780$	13473.4	+	5393.91i	0.618493	+	0.247606i
$781$	4510.38	−	3784.66i	0.206650	−	0.173400i
$782$	13236.2			0.605277
$783$	−10195.8	−	4853.16i	−0.465347	−	0.221504i
$784$	17557.1			0.799795
$785$	3104.57	−	2605.04i	0.141155	−	0.118443i
$786$	−1973.57	+	1552.04i	−0.0895610	+	0.0704317i
$787$	−565.306	+	3206.01i	−0.0256048	+	0.145212i	−0.994930	−	0.100570i	$-0.967934\pi$
$787$	−565.306	+	3206.01i	−0.0256048	+	0.145212i	0.969325	+	0.245782i	$0.0790446\pi$
$788$	5507.64	−	2004.62i	0.248987	−	0.0906237i
$789$	19587.3	−	6433.11i	0.883811	−	0.290272i
$790$	1004.27	+	5695.49i	0.0452282	+	0.256502i
$791$	−7861.29	−	13616.1i	−0.353369	−	0.612054i
$792$	−2808.23	−	5666.14i	−0.125993	−	0.254214i
$793$	−2514.55	+	4355.34i	−0.112603	+	0.195035i
$794$	2753.86	+	1002.32i	0.123087	+	0.0447999i
$795$	9318.39	+	17391.9i	0.415710	+	0.775884i
$796$	5869.81	+	4925.35i	0.261369	+	0.219315i
$797$	−15242.1	−	12789.6i	−0.677418	−	0.568421i	0.237833	−	0.971306i	$-0.423563\pi$
$797$	−15242.1	−	12789.6i	−0.677418	−	0.568421i	−0.915251	+	0.402885i	$0.868007\pi$
$798$	2176.35	+	69.0835i	0.0965437	+	0.00306457i
$799$	48971.4	+	17824.1i	2.16832	+	0.789203i
$800$	571.626	−	990.086i	0.0252626	−	0.0437560i
$801$	−9110.22	−	8686.54i	−0.401865	−	0.383176i
$802$	857.033	+	1484.42i	0.0377343	+	0.0653577i
$803$	−1848.87	−	10485.5i	−0.0812518	−	0.460802i
$804$	2945.53	+	2635.28i	0.129205	+	0.115596i
$805$	37801.7	−	13758.7i	1.65508	−	0.602398i
$806$	1252.76	−	7104.74i	0.0547475	−	0.310489i
$807$	2753.56	+	19151.3i	0.120111	+	0.835386i
$808$	−13799.8	+	11579.4i	−0.600834	+	0.504159i
$809$	−23559.5			−1.02387			−0.511933	−	0.859025i	$-0.671070\pi$
$809$	−23559.5			−1.02387			−0.511933	+	0.859025i	$0.671070\pi$
$810$	−315.598	−	6624.61i	−0.0136901	−	0.287364i
$811$	−6947.85			−0.300829			−0.150414	−	0.988623i	$-0.548061\pi$
$811$	−6947.85			−0.300829			−0.150414	+	0.988623i	$0.548061\pi$
$812$	12001.4	−	10070.4i	0.518679	−	0.435223i
$813$	−3978.51	−	27671.0i	−0.171627	−	1.19368i
$814$	−89.2036	+	505.899i	−0.00384101	+	0.0217835i
$815$	−25850.5	+	9408.83i	−1.11105	+	0.404389i
$816$	−20785.5	−	18596.2i	−0.891713	−	0.797791i
$817$	−273.331	−	1550.14i	−0.0117046	−	0.0663800i
$818$	2300.20	+	3984.06i	0.0983186	+	0.170293i
$819$	6016.01	−	24798.6i	0.256674	−	1.05804i
$820$	15336.7	−	26563.9i	0.653146	−	1.13128i
$821$	16081.2	+	5853.09i	0.683604	+	0.248811i	0.660394	−	0.750919i	$-0.270389\pi$
$821$	16081.2	+	5853.09i	0.683604	+	0.248811i	0.0232097	+	0.999731i	$0.492611\pi$
$822$	1030.86	+	32.7223i	0.0437412	+	0.00138847i
$823$	1262.17	+	1059.08i	0.0534586	+	0.0448571i	0.669125	−	0.743149i	$-0.266669\pi$
$823$	1262.17	+	1059.08i	0.0534586	+	0.0448571i	−0.615667	+	0.788007i	$0.711113\pi$
$824$	17854.0	+	14981.3i	0.754822	+	0.633371i
$825$	−357.588	−	667.405i	−0.0150904	−	0.0281649i
$826$	1062.12	+	386.580i	0.0447407	+	0.0162843i
$827$	1768.75	−	3063.57i	0.0743719	−	0.128816i	−0.826441	−	0.563023i	$-0.809638\pi$
$827$	1768.75	−	3063.57i	0.0743719	−	0.128816i	0.900813	+	0.434207i	$0.142971\pi$
$828$	27379.8	+	1739.98i	1.14917	+	0.0730295i
$829$	20425.4	+	35377.8i	0.855734	+	1.48217i	0.875962	+	0.482379i	$0.160227\pi$
$829$	20425.4	+	35377.8i	0.855734	+	1.48217i	−0.0202283	+	0.999795i	$0.506439\pi$
$830$	−1526.82	−	8659.01i	−0.0638513	−	0.362119i
$831$	5045.33	−	1657.05i	0.210615	−	0.0691727i
$832$	−8651.49	+	3148.89i	−0.360501	+	0.131211i
$833$	−7245.89	+	41093.5i	−0.301387	+	1.70925i
$834$	2002.88	−	1575.08i	0.0831581	−	0.0653964i
$835$	−19314.3	+	16206.6i	−0.800478	+	0.671681i
$836$	−2478.77			−0.102548
$837$	32896.8	−	8535.66i	1.35852	−	0.352492i
$838$	5628.48			0.232020
$839$	−24034.6	+	20167.4i	−0.988995	+	0.829865i	−0.985422	−	0.170129i	$-0.945582\pi$
$839$	−24034.6	+	20167.4i	−0.988995	+	0.829865i	−0.00357284	+	0.999994i	$0.501137\pi$
$840$	17913.7	+	7171.54i	0.735811	+	0.294573i
$841$	−3110.21	+	17638.9i	−0.127525	+	0.723231i
$842$	−4864.33	+	1770.47i	−0.199092	+	0.0724637i
$843$	−7000.51	+	33456.7i	−0.286015	+	1.36692i
$844$	−3430.10	−	19453.1i	−0.139892	−	0.793368i
$845$	−5101.41	−	8835.90i	−0.207685	−	0.359721i
$846$	−9599.23	−	4201.03i	−0.390104	−	0.170726i
$847$	−13338.0	+	23102.0i	−0.541084	+	0.937184i
$848$	−15677.0	−	5705.96i	−0.634847	−	0.231066i
$849$	19023.3	−	30659.8i	0.768997	−	1.23939i
$850$	582.324	+	488.628i	0.0234983	+	0.0197174i
$851$	−3580.04	−	3004.01i	−0.144209	−	0.121006i
$852$	−6459.76	+	10411.2i	−0.259751	+	0.418639i
$853$	−18591.9	−	6766.88i	−0.746275	−	0.271622i	−0.0592378	−	0.998244i	$-0.518867\pi$
$853$	−18591.9	−	6766.88i	−0.746275	−	0.271622i	−0.687038	+	0.726622i	$0.741089\pi$
$854$	−1594.30	+	2761.41i	−0.0638827	+	0.110648i
$855$	−4994.04	−	2185.61i	−0.199758	−	0.0874224i
$856$	−3227.22	−	5589.71i	−0.128860	−	0.223192i
$857$	−2118.58	−	12015.1i	−0.0844449	−	0.478911i	−0.997475	−	0.0710187i	$-0.977375\pi$
$857$	−2118.58	−	12015.1i	−0.0844449	−	0.478911i	0.913030	−	0.407892i	$-0.133736\pi$
$858$	577.120	−	2758.16i	0.0229633	−	0.109746i
$859$	−35218.5	+	12818.5i	−1.39888	+	0.509151i	−0.927846	−	0.372964i	$-0.878342\pi$
$859$	−35218.5	+	12818.5i	−1.39888	+	0.509151i	−0.471035	+	0.882115i	$0.656119\pi$
$860$	1155.07	−	6550.71i	0.0457994	−	0.259741i
$861$	−50069.0	−	20044.6i	−1.98182	−	0.793399i
$862$	−1246.52	+	1045.95i	−0.0492537	+	0.0413287i
$863$	−27228.3			−1.07400			−0.537000	−	0.843582i	$-0.680443\pi$
$863$	−27228.3			−1.07400			−0.537000	+	0.843582i	$0.680443\pi$
$864$	14060.3	+	14285.1i	0.553636	+	0.562487i
$865$	41483.6			1.63062
$866$	4580.97	−	3843.89i	0.179755	−	0.150832i
$867$	32036.9	−	25194.2i	1.25494	−	0.986896i
$868$	−8188.14	+	46437.2i	−0.320188	+	1.81588i
$869$	−10877.8	+	3959.20i	−0.424632	+	0.154553i
$870$	3614.80	−	1187.22i	0.140866	−	0.0462649i
$871$	641.303	+	3637.01i	0.0249480	+	0.141487i
$872$	−8437.27	−	14613.8i	−0.327663	−	0.567529i
$873$	−45014.9	−	2860.69i	−1.74516	−	0.110904i
$874$	−1093.75	+	1894.43i	−0.0423303	+	0.0733183i
$875$	36083.6	+	13133.4i	1.39411	+	0.507416i
$876$	10463.8	+	19529.8i	0.403584	+	0.753253i
$877$	−22347.5	−	18751.8i	−0.860459	−	0.722011i	0.101608	−	0.994825i	$-0.467601\pi$
$877$	−22347.5	−	18751.8i	−0.860459	−	0.722011i	−0.962067	+	0.272814i	$0.912046\pi$
$878$	−3529.41	−	2961.52i	−0.135662	−	0.113834i
$879$	4445.70	+	141.119i	0.170591	+	0.00541505i
$880$	−8795.82	−	3201.42i	−0.336940	−	0.122636i
$881$	21666.5	−	37527.4i	0.828560	−	1.43511i	−0.0706072	−	0.997504i	$-0.522494\pi$
$881$	21666.5	−	37527.4i	0.828560	−	1.43511i	0.899168	−	0.437604i	$-0.144173\pi$
$882$	1977.96	−	8153.35i	0.0755118	−	0.311267i
$883$	−17434.7	−	30197.8i	−0.664466	−	1.15089i	−0.979430	−	0.201786i	$-0.935326\pi$
$883$	−17434.7	−	30197.8i	−0.664466	−	1.15089i	0.314963	−	0.949104i	$-0.398008\pi$
$884$	−5064.35	−	28721.4i	−0.192684	−	1.09276i
$885$	−2108.90	−	1886.77i	−0.0801016	−	0.0716647i
$886$	10437.3	−	3798.87i	0.395765	−	0.144047i
$887$	1710.69	−	9701.83i	0.0647570	−	0.367255i	−0.935158	−	0.354230i	$-0.884743\pi$
$887$	1710.69	−	9701.83i	0.0647570	−	0.367255i	0.999915	−	0.0130248i	$-0.00414604\pi$
$888$	−319.026	−	2218.86i	−0.0120561	−	0.0838514i
$889$	19658.6	−	16495.5i	0.741650	−	0.622318i
$890$	4241.42			0.159744
$891$	12948.7	−	2924.64i	0.486865	−	0.109965i
$892$	−464.140			−0.0174221
$893$	−6597.74	+	5536.16i	−0.247240	+	0.207459i
$894$	−197.471	−	1373.43i	−0.00738748	−	0.0513806i
$895$	3055.92	−	17331.0i	0.114132	−	0.647274i
$896$	−34152.7	+	12430.6i	−1.27339	+	0.463478i
$897$	19105.4	+	17093.1i	0.711161	+	0.636256i
$898$	−931.946	−	5285.33i	−0.0346319	−	0.196407i
$899$	9748.71	+	16885.3i	0.361666	+	0.626424i
$900$	1140.33	+	1087.30i	0.0422346	+	0.0402704i
$901$	19825.1	−	34338.1i	0.733042	−	1.26967i
$902$	−5596.48	−	2036.95i	−0.206588	−	0.0751918i
$903$	−11689.8	−	371.067i	−0.430799	−	0.0136748i
$904$	5803.88	+	4870.03i	0.213533	+	0.179176i
$905$	−10634.8	−	8923.63i	−0.390621	−	0.327770i
$906$	3006.02	+	5610.47i	0.110230	+	0.205734i
$907$	−2358.31	−	858.355i	−0.0863356	−	0.0314236i	0.298491	−	0.954412i	$-0.403517\pi$
$907$	−2358.31	−	858.355i	−0.0863356	−	0.0314236i	−0.384827	+	0.922989i	$0.625739\pi$
$908$	241.292	−	417.930i	0.00881890	−	0.0152748i
$909$	−16792.4	−	33881.9i	−0.612728	−	1.23630i
$910$	4299.08	+	7446.23i	0.156608	+	0.271253i
$911$	6229.90	+	35331.5i	0.226570	+	1.28494i	0.859660	+	0.510866i	$0.170675\pi$
$911$	6229.90	+	35331.5i	0.226570	+	1.28494i	−0.633090	+	0.774078i	$0.718214\pi$
$912$	4379.15	−	1438.26i	0.159000	−	0.0522209i
$913$	16537.9	−	6019.29i	0.599478	−	0.218192i
$914$	183.106	−	1038.44i	0.00662647	−	0.0375806i
$915$	6274.94	−	4934.68i	0.226714	−	0.178290i
$916$	−13724.2	+	11516.0i	−0.495044	+	0.415392i
$917$	15334.1			0.552212
$918$	−10977.6	+	7557.55i	−0.394677	+	0.271717i
$919$	15985.1			0.573776			0.286888	−	0.957964i	$-0.407379\pi$
$919$	15985.1			0.573776			0.286888	+	0.957964i	$0.407379\pi$
$920$	−14849.8	+	12460.5i	−0.532156	+	0.446532i
$921$	−31943.6	−	12788.2i	−1.14286	−	0.457532i
$922$	−933.995	+	5296.95i	−0.0333617	+	0.189204i
$923$	−10758.4	+	3915.73i	−0.383658	+	0.139640i
$924$	−3772.11	+	18027.6i	−0.134300	+	0.641844i
$925$	−46.6069	−	264.321i	−0.00165668	−	0.00939548i
$926$	−136.971	−	237.240i	−0.00486084	−	0.00841922i
$927$	−39397.5	+	29007.9i	−1.39588	+	1.02777i
$928$	−5749.45	+	9958.34i	−0.203378	+	0.352261i
$929$	41945.8	+	15267.0i	1.48138	+	0.539177i	0.951163	−	0.308688i	$-0.0998899\pi$
$929$	41945.8	+	15267.0i	1.48138	+	0.539177i	0.530213	+	0.847865i	$0.322112\pi$
$930$	−6037.53	+	9730.67i	−0.212880	+	0.343098i
$931$	−5282.74	−	4432.75i	−0.185967	−	0.156045i
$932$	17269.0	+	14490.4i	0.606938	+	0.509281i
$933$	−8790.67	+	14167.9i	−0.308460	+	0.497144i
$934$	−14590.4	−	5310.46i	−0.511147	−	0.186042i
$935$	11123.2	−	19265.9i	0.389055	−	0.673864i
$936$	1362.96	+	12220.8i	0.0475958	+	0.426763i
$937$	5729.57	+	9923.90i	0.199762	+	0.345998i	0.948451	−	0.316923i	$-0.102650\pi$
$937$	5729.57	+	9923.90i	0.199762	+	0.345998i	−0.748689	+	0.662921i	$0.769317\pi$
$938$	406.605	+	2305.97i	0.0141536	+	0.0802693i
$939$	4539.49	−	21695.0i	0.157764	−	0.753983i
$940$	−34201.5	+	12448.3i	−1.18673	+	0.431936i
$941$	1458.38	−	8270.88i	0.0505226	−	0.286528i	−0.949070	−	0.315065i	$-0.897974\pi$
$941$	1458.38	−	8270.88i	0.0505226	−	0.286528i	0.999593	+	0.0285369i	$0.00908481\pi$
$942$	1520.19	+	608.589i	0.0525800	+	0.0210498i
$943$	41505.4	−	34827.2i	1.43330	−	1.20268i
$944$	2392.62			0.0824928
$945$	−23495.2	+	32994.7i	−0.808783	+	1.13578i
$946$	−1291.53			−0.0443883
$947$	−3896.91	+	3269.89i	−0.133720	+	0.112204i	−0.707194	−	0.707019i	$-0.750039\pi$
$947$	−3896.91	+	3269.89i	−0.133720	+	0.112204i	0.573475	+	0.819223i	$0.305595\pi$
$948$	18935.2	−	14890.8i	0.648719	−	0.510160i
$949$	−3595.08	+	20388.7i	−0.122973	+	0.697413i
$950$	−118.054	+	42.9682i	−0.00403177	+	0.00146744i
$951$	47100.9	−	15469.5i	1.60605	−	0.527479i
$952$	−6733.37	−	38186.8i	−0.229233	−	1.30004i
$953$	16612.3	+	28773.3i	0.564663	+	0.978025i	0.997081	+	0.0763519i	$0.0243272\pi$
$953$	16612.3	+	28773.3i	0.564663	+	0.978025i	−0.432418	+	0.901673i	$0.642339\pi$
$954$	−4415.95	+	6637.42i	−0.149865	+	0.225256i
$955$	−1139.49	+	1973.66i	−0.0386105	+	0.0668754i
$956$	23443.9	+	8532.89i	0.793128	+	0.288675i
$957$	3596.64	+	6712.79i	0.121487	+	0.226744i
$958$	4465.62	+	3747.10i	0.150603	+	0.126371i
$959$	−4825.35	−	4048.95i	−0.162480	−	0.136337i
$960$	14606.7	+	463.660i	0.491074	+	0.0155881i
$961$	−27149.7	−	9881.68i	−0.911339	−	0.331700i
$962$	499.441	−	865.056i	0.0167387	−	0.0289922i
$963$	13000.1	−	3817.20i	0.435018	−	0.127734i
$964$	−2589.83	−	4485.71i	−0.0865277	−	0.149870i
$965$	3542.88	+	20092.7i	0.118186	+	0.670265i
$966$	12113.4	+	10837.5i	0.403460	+	0.360964i
$967$	−7112.66	+	2588.80i	−0.236533	+	0.0860911i	−0.457567	−	0.889175i	$-0.651279\pi$
$967$	−7112.66	+	2588.80i	−0.236533	+	0.0860911i	0.221034	+	0.975266i	$0.429057\pi$
$968$	2232.19	−	12659.4i	0.0741169	−	0.420338i
$969$	1559.03	+	10843.2i	0.0516856	+	0.359479i
$970$	11642.5	−	9769.24i	0.385381	−	0.323373i
$971$	17710.5			0.585331			0.292665	−	0.956215i	$-0.405458\pi$
$971$	17710.5			0.585331			0.292665	+	0.956215i	$0.405458\pi$
$972$	−23701.1	+	14190.1i	−0.782112	+	0.468259i
$973$	−15561.8			−0.512733
$974$	6456.27	−	5417.46i	0.212395	−	0.178220i
$975$	209.530	+	1457.30i	0.00688238	+	0.0478676i
$976$	−1172.08	+	6647.19i	−0.0384399	+	0.218004i
$977$	22298.6	−	8116.03i	0.730190	−	0.265768i	0.0499450	−	0.998752i	$-0.484095\pi$
$977$	22298.6	−	8116.03i	0.730190	−	0.265768i	0.680245	+	0.732984i	$0.261873\pi$
$978$	−8283.69	−	7411.19i	−0.270842	−	0.242315i
$979$	1474.20	+	8360.63i	0.0481264	+	0.272938i
$980$	−14571.2	−	25238.0i	−0.474958	−	0.822651i
$981$	33987.6	−	9979.73i	1.10616	−	0.324799i
$982$	−2317.52	+	4014.06i	−0.0753106	+	0.130442i
$983$	39968.7	+	14547.4i	1.29685	+	0.472015i	0.895970	−	0.444114i	$-0.146482\pi$
$983$	39968.7	+	14547.4i	1.29685	+	0.472015i	0.400882	+	0.916130i	$0.368704\pi$
$984$	25975.9	+	824.550i	0.841547	+	0.0267131i
$985$	−6659.49	−	5587.97i	−0.215420	−	0.180759i
$986$	−5857.05	−	4914.65i	−0.189175	−	0.158737i
$987$	30223.1	+	56408.8i	0.974684	+	1.81916i
$988$	4529.22	+	1648.50i	0.145844	+	0.0530828i
$989$	5874.85	−	10175.5i	0.188887	−	0.327162i
$990$	−2477.63	+	3724.02i	−0.0795397	+	0.119553i
$991$	15829.8	+	27418.0i	0.507416	+	0.878870i	0.999963	+	0.00858430i	$0.00273250\pi$
$991$	15829.8	+	27418.0i	0.507416	+	0.878870i	−0.492547	+	0.870286i	$0.663934\pi$
$992$	−6009.84	−	34083.5i	−0.192351	−	1.09088i
$993$	−44248.2	+	14532.5i	−1.41407	+	0.464427i
$994$	−6821.12	+	2482.69i	−0.217659	+	0.0792213i
$995$	1973.55	−	11192.5i	0.0628800	−	0.356610i
$996$	−28787.7	+	22638.9i	−0.915836	+	0.720223i
$997$	−8438.56	+	7080.79i	−0.268056	+	0.224926i	−0.766901	−	0.641766i	$-0.778202\pi$
$997$	−8438.56	+	7080.79i	−0.268056	+	0.224926i	0.498845	+	0.866691i	$0.333758\pi$
$998$	−16110.1			−0.510977
$999$	4684.34	+	447.285i	0.148354	+	0.0141656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.4.e.a.22.5	yes	48
3.2	odd	2		81.4.e.a.37.4		48
9.2	odd	6		243.4.e.b.190.5		48
9.4	even	3		243.4.e.d.28.5		48
9.5	odd	6		243.4.e.a.28.4		48
9.7	even	3		243.4.e.c.190.4		48
27.2	odd	18		243.4.e.b.55.5		48
27.4	even	9		729.4.a.d.1.13		24
27.7	even	9		243.4.e.d.217.5		48
27.11	odd	18		81.4.e.a.46.4		48
27.16	even	9	inner	27.4.e.a.16.5	✓	48
27.20	odd	18		243.4.e.a.217.4		48
27.23	odd	18		729.4.a.c.1.12		24
27.25	even	9		243.4.e.c.55.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.16.5	✓	48	27.16	even	9	inner
27.4.e.a.22.5	yes	48	1.1	even	1	trivial
81.4.e.a.37.4		48	3.2	odd	2
81.4.e.a.46.4		48	27.11	odd	18
243.4.e.a.28.4		48	9.5	odd	6
243.4.e.a.217.4		48	27.20	odd	18
243.4.e.b.55.5		48	27.2	odd	18
243.4.e.b.190.5		48	9.2	odd	6
243.4.e.c.55.4		48	27.25	even	9
243.4.e.c.190.4		48	9.7	even	3
243.4.e.d.28.5		48	9.4	even	3
243.4.e.d.217.5		48	27.7	even	9
729.4.a.c.1.12		24	27.23	odd	18
729.4.a.d.1.13		24	27.4	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)

\(f(q)\)	\(=\)	\(q+(0.644303 - 0.540635i) q^{2} +(0.739495 + 5.14326i) q^{3} +(-1.26634 + 7.18180i) q^{4} +(10.1642 - 3.69948i) q^{5} +(3.25709 + 2.91402i) q^{6} +(-4.63497 - 26.2862i) q^{7} +(6.43113 + 11.1390i) q^{8} +(-25.9063 + 7.60683i) q^{9} +O(q^{10})\)	\(q+(0.644303 - 0.540635i) q^{2} +(0.739495 + 5.14326i) q^{3} +(-1.26634 + 7.18180i) q^{4} +(10.1642 - 3.69948i) q^{5} +(3.25709 + 2.91402i) q^{6} +(-4.63497 - 26.2862i) q^{7} +(6.43113 + 11.1390i) q^{8} +(-25.9063 + 7.60683i) q^{9} +(4.54878 - 7.87873i) q^{10} +(17.1115 + 6.22807i) q^{11} +(-37.8743 - 1.20224i) q^{12} +(-27.1242 - 22.7599i) q^{13} +(-17.1976 - 14.4305i) q^{14} +(26.5438 + 49.5416i) q^{15} +(-44.6566 - 16.2537i) q^{16} +(56.4726 - 97.8135i) q^{17} +(-12.5790 + 18.9070i) q^{18} +(9.33302 + 16.1653i) q^{19} +(13.6975 + 77.6823i) q^{20} +(131.769 - 43.2774i) q^{21} +(14.3921 - 5.23830i) q^{22} +(-24.1953 + 137.218i) q^{23} +(-52.5352 + 41.3143i) q^{24} +(-6.13000 + 5.14368i) q^{25} -29.7811 q^{26} +(-58.2815 - 127.618i) q^{27} +194.652 q^{28} +(61.6559 - 51.7354i) q^{29} +(43.8862 + 17.5693i) q^{30} +(-42.0656 + 238.566i) q^{31} +(-134.252 + 48.8638i) q^{32} +(-19.3787 + 92.6145i) q^{33} +(-16.4958 - 93.5526i) q^{34} +(-144.356 - 250.032i) q^{35} +(-21.8244 - 195.687i) q^{36} +(-16.7704 + 29.0472i) q^{37} +(14.7528 + 5.36958i) q^{38} +(97.0021 - 156.338i) q^{39} +(106.576 + 89.4281i) q^{40} +(-297.882 - 249.953i) q^{41} +(61.5022 - 99.1229i) q^{42} +(-79.2414 - 28.8415i) q^{43} +(-66.3978 + 115.004i) q^{44} +(-235.176 + 173.157i) q^{45} +(58.5958 + 101.491i) q^{46} +(80.1234 + 454.402i) q^{47} +(50.5735 - 241.700i) q^{48} +(-347.168 + 126.359i) q^{49} +(-1.16873 + 6.62818i) q^{50} +(544.842 + 218.121i) q^{51} +(197.806 - 165.979i) q^{52} +351.057 q^{53} +(-106.546 - 50.7155i) q^{54} +196.966 q^{55} +(262.995 - 220.679i) q^{56} +(-76.2405 + 59.9563i) q^{57} +(11.7551 - 66.6666i) q^{58} +(-47.3108 + 17.2197i) q^{59} +(-389.411 + 127.895i) q^{60} +(-24.6637 - 139.875i) q^{61} +(101.874 + 176.451i) q^{62} +(320.030 + 645.721i) q^{63} +(130.008 - 225.181i) q^{64} +(-359.897 - 130.992i) q^{65} +(37.5848 + 70.1486i) q^{66} +(-79.8993 - 67.0435i) q^{67} +(630.963 + 529.440i) q^{68} +(-723.641 - 22.9704i) q^{69} +(-228.185 - 83.0527i) q^{70} +(161.669 - 280.019i) q^{71} +(-251.340 - 239.651i) q^{72} +(-292.351 - 506.366i) q^{73} +(4.89869 + 27.7819i) q^{74} +(-30.9884 - 27.7245i) q^{75} +(-127.914 + 46.5571i) q^{76} +(84.4012 - 478.663i) q^{77} +(-22.0229 - 153.172i) q^{78} +(-486.977 + 408.622i) q^{79} -514.030 q^{80} +(613.272 - 394.130i) q^{81} -327.060 q^{82} +(740.364 - 621.240i) q^{83} +(143.944 + 1001.14i) q^{84} +(212.142 - 1203.12i) q^{85} +(-66.6483 + 24.2580i) q^{86} +(311.683 + 278.854i) q^{87} +(40.6714 + 230.659i) q^{88} +(233.107 + 403.753i) q^{89} +(-57.9100 + 238.710i) q^{90} +(-472.553 + 818.485i) q^{91} +(-954.833 - 347.531i) q^{92} +(-1258.11 - 39.9361i) q^{93} +(297.289 + 249.455i) q^{94} +(154.666 + 129.780i) q^{95} +(-350.598 - 654.360i) q^{96} +(1569.83 + 571.373i) q^{97} +(-155.367 + 269.104i) q^{98} +(-490.671 - 31.1820i) 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

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