LMFDB - Embedded newform 38.4.e.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.24207258022$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 135 x^{10} + 730 x^{9} + 7953 x^{8} - 36258 x^{7} - 262940 x^{6} + 918855 x^{5} + \cdots + 272110107 $ x^12 - 6x^11 - 135x^10 + 730x^9 + 7953x^8 - 36258x^7 - 262940x^6 + 918855x^5 + 5157591x^4 - 11890401x^3 - 56759508x^2 + 62864118*x + 272110107
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			5.2
Root			$-4.05412 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	38.5
Dual form			38.4.e.a.23.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87939 + 0.684040i) q^{2} +(0.0408138 - 0.231467i) q^{3} +(3.06418 - 2.57115i) q^{4} +(8.45426 + 7.09396i) q^{5} +(0.0816277 + 0.462933i) q^{6} +(9.26682 + 16.0506i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(25.3198 + 9.21565i) q^{9} +O(q^{10})$	\(q+(-1.87939 + 0.684040i) q^{2} +(0.0408138 - 0.231467i) q^{3} +(3.06418 - 2.57115i) q^{4} +(8.45426 + 7.09396i) q^{5} +(0.0816277 + 0.462933i) q^{6} +(9.26682 + 16.0506i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(25.3198 + 9.21565i) q^{9} +(-20.7414 - 7.54924i) q^{10} +(-6.98757 + 12.1028i) q^{11} +(-0.470075 - 0.814194i) q^{12} +(-9.37199 - 53.1512i) q^{13} +(-28.3952 - 23.8264i) q^{14} +(1.98707 - 1.66735i) q^{15} +(2.77837 - 15.7569i) q^{16} +(-7.65864 + 2.78752i) q^{17} -53.8895 q^{18} +(-31.6628 - 76.5275i) q^{19} +44.1450 q^{20} +(4.09339 - 1.48987i) q^{21} +(4.85351 - 27.5257i) q^{22} +(-93.7306 + 78.6493i) q^{23} +(1.44039 + 1.20863i) q^{24} +(-0.555893 - 3.15263i) q^{25} +(53.9711 + 93.4808i) q^{26} +(6.33952 - 10.9804i) q^{27} +(69.6637 + 25.3555i) q^{28} +(208.061 + 75.7281i) q^{29} +(-2.59393 + 4.49282i) q^{30} +(-23.1180 - 40.0415i) q^{31} +(5.55674 + 31.5138i) q^{32} +(2.51621 + 2.11135i) q^{33} +(12.4868 - 10.4776i) q^{34} +(-35.5183 + 201.434i) q^{35} +(101.279 - 36.8626i) q^{36} -99.6840 q^{37} +(111.855 + 122.166i) q^{38} -12.6852 q^{39} +(-82.9654 + 30.1969i) q^{40} +(55.1499 - 312.771i) q^{41} +(-6.67393 + 5.60009i) q^{42} +(-358.181 - 300.549i) q^{43} +(9.70703 + 55.0513i) q^{44} +(148.684 + 257.529i) q^{45} +(122.357 - 211.928i) q^{46} +(16.4020 + 5.96984i) q^{47} +(-3.53381 - 1.28620i) q^{48} +(-0.247862 + 0.429309i) q^{49} +(3.20126 + 5.54475i) q^{50} +(0.332639 + 1.88649i) q^{51} +(-165.377 - 138.768i) q^{52} +(33.9477 - 28.4855i) q^{53} +(-4.40338 + 24.9728i) q^{54} +(-144.932 + 52.7508i) q^{55} -148.269 q^{56} +(-19.0059 + 4.20551i) q^{57} -442.828 q^{58} +(-599.714 + 218.278i) q^{59} +(1.80173 - 10.2181i) q^{60} +(631.321 - 529.741i) q^{61} +(70.8376 + 59.4398i) q^{62} +(86.7172 + 491.798i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(297.819 - 515.838i) q^{65} +(-6.17318 - 2.24685i) q^{66} +(789.297 + 287.281i) q^{67} +(-16.3003 + 28.2330i) q^{68} +(14.3792 + 24.9055i) q^{69} +(-71.0366 - 402.869i) q^{70} +(-442.799 - 371.552i) q^{71} +(-165.127 + 138.558i) q^{72} +(-131.269 + 744.464i) q^{73} +(187.345 - 68.1878i) q^{74} -0.752416 q^{75} +(-293.784 - 153.084i) q^{76} -259.010 q^{77} +(23.8405 - 8.67721i) q^{78} +(58.9570 - 334.362i) q^{79} +(135.268 - 113.503i) q^{80} +(555.021 + 465.718i) q^{81} +(110.300 + 625.541i) q^{82} +(382.805 + 663.037i) q^{83} +(8.71220 - 15.0900i) q^{84} +(-84.5227 - 30.7637i) q^{85} +(878.748 + 319.838i) q^{86} +(26.0203 - 45.0685i) q^{87} +(-55.9006 - 96.8226i) q^{88} +(157.608 + 893.840i) q^{89} +(-455.596 - 382.290i) q^{90} +(766.260 - 642.969i) q^{91} +(-84.9880 + 481.991i) q^{92} +(-10.2118 + 3.71680i) q^{93} -34.9093 q^{94} +(275.198 - 871.598i) q^{95} +7.52120 q^{96} +(-1581.25 + 575.527i) q^{97} +(0.172163 - 0.976385i) q^{98} +(-288.459 + 242.046i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 9 q^{3} - 18 q^{6} + 21 q^{7} - 48 q^{8} - 27 q^{9}+O(q^{10}) $ 12 * q - 9 * q^3 - 18 * q^6 + 21 * q^7 - 48 * q^8 - 27 * q^9	\( 12 q - 9 q^{3} - 18 q^{6} + 21 q^{7} - 48 q^{8} - 27 q^{9} - 9 q^{11} + 36 q^{12} + 39 q^{13} - 138 q^{14} + 423 q^{15} + 69 q^{17} + 132 q^{18} - 462 q^{19} - 216 q^{20} - 279 q^{21} + 204 q^{22} - 66 q^{23} - 72 q^{24} + 342 q^{25} + 48 q^{26} + 189 q^{27} + 192 q^{28} + 159 q^{29} + 72 q^{31} - 1560 q^{33} + 408 q^{34} - 135 q^{35} - 108 q^{36} + 1116 q^{37} - 294 q^{38} - 1248 q^{39} + 147 q^{41} + 414 q^{42} - 117 q^{43} + 408 q^{44} + 1296 q^{45} + 528 q^{46} + 783 q^{47} + 288 q^{48} + 1413 q^{49} - 354 q^{50} - 2301 q^{51} - 348 q^{52} - 249 q^{53} - 540 q^{54} + 2187 q^{55} - 336 q^{56} - 2670 q^{57} - 1932 q^{58} - 4248 q^{59} + 324 q^{60} + 3114 q^{61} - 438 q^{62} + 363 q^{63} - 384 q^{64} + 495 q^{65} + 822 q^{66} + 3060 q^{67} + 408 q^{68} - 237 q^{69} - 270 q^{70} + 1686 q^{71} + 432 q^{72} + 1626 q^{73} + 90 q^{74} - 1854 q^{75} - 1416 q^{77} - 108 q^{78} - 327 q^{79} + 3483 q^{81} + 294 q^{82} + 927 q^{83} + 204 q^{84} - 3294 q^{85} + 1188 q^{86} + 2892 q^{87} - 72 q^{88} - 6366 q^{89} - 5076 q^{90} + 840 q^{91} - 156 q^{92} + 870 q^{93} + 3432 q^{94} + 513 q^{95} - 576 q^{96} - 8052 q^{97} + 378 q^{98} + 4494 q^{99}+O(q^{100}) \) 12 * q - 9 * q^3 - 18 * q^6 + 21 * q^7 - 48 * q^8 - 27 * q^9 - 9 * q^11 + 36 * q^12 + 39 * q^13 - 138 * q^14 + 423 * q^15 + 69 * q^17 + 132 * q^18 - 462 * q^19 - 216 * q^20 - 279 * q^21 + 204 * q^22 - 66 * q^23 - 72 * q^24 + 342 * q^25 + 48 * q^26 + 189 * q^27 + 192 * q^28 + 159 * q^29 + 72 * q^31 - 1560 * q^33 + 408 * q^34 - 135 * q^35 - 108 * q^36 + 1116 * q^37 - 294 * q^38 - 1248 * q^39 + 147 * q^41 + 414 * q^42 - 117 * q^43 + 408 * q^44 + 1296 * q^45 + 528 * q^46 + 783 * q^47 + 288 * q^48 + 1413 * q^49 - 354 * q^50 - 2301 * q^51 - 348 * q^52 - 249 * q^53 - 540 * q^54 + 2187 * q^55 - 336 * q^56 - 2670 * q^57 - 1932 * q^58 - 4248 * q^59 + 324 * q^60 + 3114 * q^61 - 438 * q^62 + 363 * q^63 - 384 * q^64 + 495 * q^65 + 822 * q^66 + 3060 * q^67 + 408 * q^68 - 237 * q^69 - 270 * q^70 + 1686 * q^71 + 432 * q^72 + 1626 * q^73 + 90 * q^74 - 1854 * q^75 - 1416 * q^77 - 108 * q^78 - 327 * q^79 + 3483 * q^81 + 294 * q^82 + 927 * q^83 + 204 * q^84 - 3294 * q^85 + 1188 * q^86 + 2892 * q^87 - 72 * q^88 - 6366 * q^89 - 5076 * q^90 + 840 * q^91 - 156 * q^92 + 870 * q^93 + 3432 * q^94 + 513 * q^95 - 576 * q^96 - 8052 * q^97 + 378 * q^98 + 4494 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−1.87939	+	0.684040i	−0.664463	+	0.241845i
$2$	−1.87939	+	0.684040i	−0.664463	+	0.241845i
$3$	0.0408138	−	0.231467i	0.00785462	−	0.0445458i	−0.980629	−	0.195877i	$-0.937245\pi$
$3$	0.0408138	−	0.231467i	0.00785462	−	0.0445458i	0.988483	+	0.151331i	$0.0483559\pi$
$4$	3.06418	−	2.57115i	0.383022	−	0.321394i
$5$	8.45426	+	7.09396i	0.756172	+	0.634503i	0.937127	−	0.348988i	$-0.113475\pi$
$5$	8.45426	+	7.09396i	0.756172	+	0.634503i	−0.180956	+	0.983491i	$0.557919\pi$
$6$	0.0816277	+	0.462933i	0.00555406	+	0.0314986i
$7$	9.26682	+	16.0506i	0.500361	+	0.866651i	1.00000		0.000417110i	$0.000132770\pi$
$7$	9.26682	+	16.0506i	0.500361	+	0.866651i	−0.499639	+	0.866234i	$0.666534\pi$
$8$	−4.00000	+	6.92820i	−0.176777	+	0.306186i
$9$	25.3198	+	9.21565i	0.937770	+	0.341320i
$10$	−20.7414	−	7.54924i	−0.655899	−	0.238728i
$11$	−6.98757	+	12.1028i	−0.191530	+	0.331740i	−0.945758	−	0.324873i	$-0.894678\pi$
$11$	−6.98757	+	12.1028i	−0.191530	+	0.331740i	0.754227	+	0.656613i	$0.228012\pi$
$12$	−0.470075	−	0.814194i	−0.0113082	−	0.0195865i
$13$	−9.37199	−	53.1512i	−0.199948	−	1.13396i	−0.905194	−	0.424998i	$-0.860275\pi$
$13$	−9.37199	−	53.1512i	−0.199948	−	1.13396i	0.705246	−	0.708962i	$-0.250836\pi$
$14$	−28.3952	−	23.8264i	−0.542067	−	0.454848i
$15$	1.98707	−	1.66735i	0.0342039	−	0.0287005i
$16$	2.77837	−	15.7569i	0.0434120	−	0.246202i
$17$	−7.65864	+	2.78752i	−0.109264	+	0.0397690i	−0.396074	−	0.918219i	$-0.629628\pi$
$17$	−7.65864	+	2.78752i	−0.109264	+	0.0397690i	0.286809	+	0.957988i	$0.407405\pi$
$18$	−53.8895			−0.705660
$19$	−31.6628	−	76.5275i	−0.382313	−	0.924033i
$19$	−31.6628	−	76.5275i	−0.382313	−	0.924033i
$20$	44.1450			0.493556
$21$	4.09339	−	1.48987i	0.0425358	−	0.0154818i
$22$	4.85351	−	27.5257i	0.0470351	−	0.266749i
$23$	−93.7306	+	78.6493i	−0.849747	+	0.713022i	−0.959734	−	0.280911i	$-0.909364\pi$
$23$	−93.7306	+	78.6493i	−0.849747	+	0.713022i	0.109987	+	0.993933i	$0.464919\pi$
$24$	1.44039	+	1.20863i	0.0122508	+	0.0102796i
$25$	−0.555893	−	3.15263i	−0.00444714	−	0.0252210i
$26$	53.9711	+	93.4808i	0.407100	+	0.705119i
$27$	6.33952	−	10.9804i	0.0451867	−	0.0782657i
$28$	69.6637	+	25.3555i	0.470186	+	0.171134i
$29$	208.061	+	75.7281i	1.33228	+	0.484909i	0.907372	−	0.420329i	$-0.138085\pi$
$29$	208.061	+	75.7281i	1.33228	+	0.484909i	0.424904	+	0.905238i	$0.360308\pi$
$30$	−2.59393	+	4.49282i	−0.0157862	+	0.0273424i
$31$	−23.1180	−	40.0415i	−0.133939	−	0.231989i	0.791253	−	0.611490i	$-0.209429\pi$
$31$	−23.1180	−	40.0415i	−0.133939	−	0.231989i	−0.925192	+	0.379500i	$0.876096\pi$
$32$	5.55674	+	31.5138i	0.0306970	+	0.174091i
$33$	2.51621	+	2.11135i	0.0132732	+	0.0111376i
$34$	12.4868	−	10.4776i	0.0629842	−	0.0528500i
$35$	−35.5183	+	201.434i	−0.171534	+	0.972818i
$36$	101.279	−	36.8626i	0.468885	−	0.170660i
$37$	−99.6840			−0.442917			−0.221459	−	0.975170i	$-0.571082\pi$
$37$	−99.6840			−0.442917			−0.221459	+	0.975170i	$0.571082\pi$
$38$	111.855	+	122.166i	0.477506	+	0.521525i
$39$	−12.6852			−0.0520837
$40$	−82.9654	+	30.1969i	−0.327950	+	0.119364i
$41$	55.1499	−	312.771i	0.210072	−	1.19138i	−0.679183	−	0.733969i	$-0.737666\pi$
$41$	55.1499	−	312.771i	0.210072	−	1.19138i	0.889255	−	0.457411i	$-0.151223\pi$
$42$	−6.67393	+	5.60009i	−0.0245193	+	0.0205741i
$43$	−358.181	−	300.549i	−1.27028	−	1.06589i	−0.994507	−	0.104669i	$-0.966622\pi$
$43$	−358.181	−	300.549i	−1.27028	−	1.06589i	−0.275773	−	0.961223i	$-0.588934\pi$
$44$	9.70703	+	55.0513i	0.0332589	+	0.188620i
$45$	148.684	+	257.529i	0.492546	+	0.853115i
$46$	122.357	−	211.928i	0.392185	−	0.679284i
$47$	16.4020	+	5.96984i	0.0509037	+	0.0185274i	0.367347	−	0.930084i	$-0.380266\pi$
$47$	16.4020	+	5.96984i	0.0509037	+	0.0185274i	−0.316443	+	0.948612i	$0.602489\pi$
$48$	−3.53381	−	1.28620i	−0.0106263	−	0.00386765i
$49$	−0.247862	+	0.429309i	−0.000722629	+	0.00125163i
$50$	3.20126	+	5.54475i	0.00905453	+	0.0156829i
$51$	0.332639	+	1.88649i	0.000913310	+	0.00517964i
$52$	−165.377	−	138.768i	−0.441032	−	0.370070i
$53$	33.9477	−	28.4855i	0.0879825	−	0.0738261i	−0.597736	−	0.801693i	$-0.703933\pi$
$53$	33.9477	−	28.4855i	0.0879825	−	0.0738261i	0.685718	+	0.727867i	$0.259488\pi$
$54$	−4.40338	+	24.9728i	−0.0110968	+	0.0629328i
$55$	−144.932	+	52.7508i	−0.355320	+	0.129326i
$56$	−148.269			−0.353809
$57$	−19.0059	+	4.20551i	−0.0441647	+	0.00977252i
$58$	−442.828			−1.00252
$59$	−599.714	+	218.278i	−1.32332	+	0.481650i	−0.904522	−	0.426427i	$-0.859772\pi$
$59$	−599.714	+	218.278i	−1.32332	+	0.481650i	−0.418802	+	0.908078i	$0.637550\pi$
$60$	1.80173	−	10.2181i	0.00387670	−	0.0219858i
$61$	631.321	−	529.741i	1.32512	−	1.11191i	0.339928	−	0.940451i	$-0.389597\pi$
$61$	631.321	−	529.741i	1.32512	−	1.11191i	0.985192	−	0.171456i	$-0.0548472\pi$
$62$	70.8376	+	59.4398i	0.145103	+	0.121756i
$63$	86.7172	+	491.798i	0.173418	+	0.983503i
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	297.819	−	515.838i	0.568307	−	0.984336i
$66$	−6.17318	−	2.24685i	−0.0115131	−	0.00419043i
$67$	789.297	+	287.281i	1.43922	+	0.523835i	0.939560	−	0.342385i	$-0.111235\pi$
$67$	789.297	+	287.281i	1.43922	+	0.523835i	0.499664	+	0.866219i	$0.333457\pi$
$68$	−16.3003	+	28.2330i	−0.0290692	+	0.0503493i
$69$	14.3792	+	24.9055i	0.0250877	+	0.0434532i
$70$	−71.0366	−	402.869i	−0.121293	−	0.687886i
$71$	−442.799	−	371.552i	−0.740149	−	0.621059i	0.192729	−	0.981252i	$-0.438266\pi$
$71$	−442.799	−	371.552i	−0.740149	−	0.621059i	−0.932878	+	0.360193i	$0.882711\pi$
$72$	−165.127	+	138.558i	−0.270283	+	0.226795i
$73$	−131.269	+	744.464i	−0.210464	+	1.19360i	0.678142	+	0.734931i	$0.262785\pi$
$73$	−131.269	+	744.464i	−0.210464	+	1.19360i	−0.888606	+	0.458671i	$0.848326\pi$
$74$	187.345	−	68.1878i	0.294302	−	0.107117i
$75$	−0.752416			−0.00115842
$76$	−293.784	−	153.084i	−0.443413	−	0.231052i
$77$	−259.010			−0.383337
$78$	23.8405	−	8.67721i	0.0346077	−	0.0125962i
$79$	58.9570	−	334.362i	0.0839643	−	0.476185i	−0.913611	−	0.406589i	$-0.866718\pi$
$79$	58.9570	−	334.362i	0.0839643	−	0.476185i	0.997575	−	0.0695958i	$-0.0221709\pi$
$80$	135.268	−	113.503i	0.189043	−	0.158626i
$81$	555.021	+	465.718i	0.761346	+	0.638845i
$82$	110.300	+	625.541i	0.148544	+	0.842433i
$83$	382.805	+	663.037i	0.506244	+	0.876841i	0.999974	+	0.00722548i	$0.00229996\pi$
$83$	382.805	+	663.037i	0.506244	+	0.876841i	−0.493730	+	0.869616i	$0.664367\pi$
$84$	8.71220	−	15.0900i	0.0113164	−	0.0196006i
$85$	−84.5227	−	30.7637i	−0.107856	−	0.0392564i
$86$	878.748	+	319.838i	1.10183	+	0.401035i
$87$	26.0203	−	45.0685i	0.0320652	−	0.0555385i
$88$	−55.9006	−	96.8226i	−0.0677161	−	0.117288i
$89$	157.608	+	893.840i	0.187713	+	1.06457i	0.922420	+	0.386188i	$0.126208\pi$
$89$	157.608	+	893.840i	0.187713	+	1.06457i	−0.734707	+	0.678384i	$0.762681\pi$
$90$	−455.596	−	382.290i	−0.533600	−	0.447744i
$91$	766.260	−	642.969i	0.882702	−	0.740675i
$92$	−84.9880	+	481.991i	−0.0963110	+	0.546207i
$93$	−10.2118	+	3.71680i	−0.0113862	+	0.00414424i
$94$	−34.9093			−0.0383044
$95$	275.198	−	871.598i	0.297207	−	0.941306i
$96$	7.52120			0.00799614
$97$	−1581.25	+	575.527i	−1.65517	+	0.602432i	−0.989592	−	0.143898i	$-0.954036\pi$
$97$	−1581.25	+	575.527i	−1.65517	+	0.602432i	−0.665576	+	0.746330i	$0.731814\pi$
$98$	0.172163	−	0.976385i	0.000177460	−	0.00100643i
$99$	−288.459	+	242.046i	−0.292841	+	0.245723i
$100$	−9.80923	−	8.23092i	−0.00980923	−	0.00823092i
$101$	−209.868	−	1190.22i	−0.206759	−	1.17259i	−0.894648	−	0.446771i	$-0.852574\pi$
$101$	−209.868	−	1190.22i	−0.206759	−	1.17259i	0.687889	−	0.725816i	$-0.258537\pi$
$102$	−1.91559	−	3.31790i	−0.00185953	−	0.00322080i
$103$	24.0814	−	41.7103i	0.0230370	−	0.0399013i	−0.854277	−	0.519818i	$-0.826000\pi$
$103$	24.0814	−	41.7103i	0.0230370	−	0.0399013i	0.877314	+	0.479917i	$0.159333\pi$
$104$	405.730	+	147.674i	0.382549	+	0.139237i
$105$	45.1757	+	16.4426i	0.0419876	+	0.0152822i
$106$	−44.3155	+	76.7568i	−0.0406066	+	0.0703328i
$107$	−436.087	−	755.325i	−0.394001	−	0.682430i	0.598972	−	0.800770i	$-0.295576\pi$
$107$	−436.087	−	755.325i	−0.394001	−	0.682430i	−0.992973	+	0.118340i	$0.962243\pi$
$108$	−8.80677	−	49.9457i	−0.00784659	−	0.0445002i
$109$	−432.221	−	362.677i	−0.379810	−	0.318698i	0.432818	−	0.901481i	$-0.357519\pi$
$109$	−432.221	−	362.677i	−0.379810	−	0.318698i	−0.812628	+	0.582783i	$0.801964\pi$
$110$	236.299	−	198.278i	0.204820	−	0.171864i
$111$	−4.06848	+	23.0735i	−0.00347895	+	0.0197301i
$112$	278.655	−	101.422i	0.235093	−	0.0855668i
$113$	−2333.39			−1.94254			−0.971270	−	0.237982i	$-0.923514\pi$
$113$	−2333.39			−1.94254			−0.971270	+	0.237982i	$0.923514\pi$
$114$	32.8426	−	20.9046i	0.0269824	−	0.0171745i
$115$	−1350.36			−1.09497
$116$	832.245	−	302.912i	0.666138	−	0.242454i
$117$	252.526	−	1432.15i	0.199539	−	1.13164i
$118$	977.782	−	820.457i	0.762815	−	0.640078i
$119$	−115.713	−	97.0944i	−0.0891374	−	0.0747952i
$120$	3.60345	+	20.4362i	0.00274124	+	0.0155463i
$121$	567.848	+	983.541i	0.426632	+	0.738949i
$122$	−824.130	+	1427.44i	−0.611584	+	1.05929i
$123$	−70.1451	−	25.5307i	−0.0514209	−	0.0187157i
$124$	−173.790	−	63.2546i	−0.125862	−	0.0458099i
$125$	707.430	−	1225.31i	0.506196	−	0.876757i
$126$	−499.384	−	864.959i	−0.353085	−	0.611561i
$127$	328.791	+	1864.67i	0.229729	+	1.30286i	0.853436	+	0.521197i	$0.174514\pi$
$127$	328.791	+	1864.67i	0.229729	+	1.30286i	−0.623708	+	0.781658i	$0.714374\pi$
$128$	98.0537	+	82.2768i	0.0677094	+	0.0568149i
$129$	−84.1859	+	70.6404i	−0.0574586	+	0.0482135i
$130$	−206.863	+	1173.18i	−0.139562	+	0.791497i
$131$	2141.57	−	779.468i	1.42832	−	0.519866i	0.491871	−	0.870668i	$-0.336313\pi$
$131$	2141.57	−	779.468i	1.42832	−	0.519866i	0.936450	+	0.350802i	$0.114091\pi$
$132$	13.1387			0.00866348
$133$	934.899	−	1217.37i	0.609519	−	0.793682i
$134$	−1679.91			−1.08300
$135$	131.490	−	47.8585i	0.0838287	−	0.0305112i
$136$	11.3221	−	64.2107i	0.00713868	−	0.0404855i
$137$	−1225.56	+	1028.37i	−0.764281	+	0.641308i	−0.939238	−	0.343268i	$-0.888466\pi$
$137$	−1225.56	+	1028.37i	−0.764281	+	0.641308i	0.174956	+	0.984576i	$0.444022\pi$
$138$	−44.0604	−	36.9711i	−0.0271788	−	0.0228057i
$139$	298.632	+	1693.63i	0.182228	+	1.03346i	0.929466	+	0.368908i	$0.120268\pi$
$139$	298.632	+	1693.63i	0.182228	+	1.03346i	−0.747238	+	0.664556i	$0.768621\pi$
$140$	409.084	+	708.554i	0.246956	+	0.427741i
$141$	2.05125	−	3.55286i	0.00122515	−	0.00212202i
$142$	1086.35	+	395.398i	0.642001	+	0.233669i
$143$	708.767	+	257.970i	0.414476	+	0.150857i
$144$	215.558	−	373.358i	0.124744	−	0.216063i
$145$	1221.79	+	2116.20i	0.699753	+	1.21201i
$146$	−262.538	−	1488.93i	−0.148821	−	0.844003i
$147$	0.0892546	+	0.0748935i	5.00789e−5	+	4.20212e-5i
$148$	−305.449	+	256.302i	−0.169647	+	0.142351i
$149$	−413.264	+	2343.74i	−0.227221	+	1.28863i	0.631173	+	0.775642i	$0.282574\pi$
$149$	−413.264	+	2343.74i	−0.227221	+	1.28863i	−0.858394	+	0.512991i	$0.828537\pi$
$150$	1.41408	−	0.514683i	0.000769728	−	0.000280158i
$151$	2143.06			1.15497			0.577483	−	0.816402i	$-0.304035\pi$
$151$	2143.06			1.15497			0.577483	+	0.816402i	$0.304035\pi$
$152$	656.850	+	86.7435i	0.350510	+	0.0462883i
$153$	−219.604			−0.116039
$154$	486.780	−	177.173i	0.254713	−	0.0927080i
$155$	88.6078	−	502.520i	0.0459171	−	0.260409i
$156$	−38.8698	+	32.6157i	−0.0199492	+	0.0167394i
$157$	634.917	+	532.758i	0.322751	+	0.270820i	0.789738	−	0.613444i	$-0.210216\pi$
$157$	634.917	+	532.758i	0.322751	+	0.270820i	−0.466988	+	0.884264i	$0.654661\pi$
$158$	117.914	+	668.723i	0.0593717	+	0.336714i
$159$	−5.20790	−	9.02036i	−0.00259757	−	0.00449912i
$160$	−176.580	+	305.845i	−0.0872492	+	0.151120i
$161$	−2130.95	−	775.604i	−1.04312	−	0.379665i
$162$	−1361.67	−	495.607i	−0.660387	−	0.240361i
$163$	1147.65	−	1987.79i	0.551477	−	0.955186i	−0.446691	−	0.894688i	$-0.647398\pi$
$163$	1147.65	−	1987.79i	0.551477	−	0.955186i	0.998168	−	0.0604981i	$-0.0192689\pi$
$164$	−635.191	−	1100.18i	−0.302440	−	0.523841i
$165$	6.29484	+	35.6998i	0.00297002	+	0.0168438i
$166$	−1172.98	−	984.249i	−0.548440	−	0.460196i
$167$	503.571	−	422.546i	0.233338	−	0.195794i	−0.518620	−	0.855005i	$-0.673554\pi$
$167$	503.571	−	422.546i	0.233338	−	0.195794i	0.751958	+	0.659211i	$0.229110\pi$
$168$	−6.05143	+	34.3194i	−0.00277904	+	0.0157607i
$169$	−672.711	+	244.847i	−0.306195	+	0.111446i
$170$	179.894			0.0811604
$171$	−96.4456	−	2229.45i	−0.0431309	−	0.997021i
$172$	−1870.29			−0.829117
$173$	154.152	−	56.1066i	0.0677453	−	0.0246573i	−0.307925	−	0.951411i	$-0.599635\pi$
$173$	154.152	−	56.1066i	0.0677453	−	0.0246573i	0.375670	+	0.926753i	$0.377412\pi$
$174$	−18.0735	+	102.500i	−0.00787443	+	0.0446581i
$175$	45.4502	−	38.1372i	0.0196326	−	0.0164737i
$176$	171.289	+	143.729i	0.0733603	+	0.0615566i
$177$	26.0475	+	147.723i	0.0110613	+	0.0627317i
$178$	−907.629	−	1572.06i	−0.382189	−	0.661971i
$179$	−283.414	+	490.888i	−0.118343	+	0.204976i	−0.919111	−	0.393998i	$-0.871092\pi$
$179$	−283.414	+	490.888i	−0.118343	+	0.204976i	0.800768	+	0.598974i	$0.204425\pi$
$180$	1117.74	+	406.825i	0.462842	+	0.168461i
$181$	−1099.80	−	400.296i	−0.451645	−	0.164385i	0.106175	−	0.994347i	$-0.466140\pi$
$181$	−1099.80	−	400.296i	−0.451645	−	0.164385i	−0.557820	+	0.829962i	$0.688362\pi$
$182$	−1000.28	+	1732.54i	−0.407394	+	0.705628i
$183$	−96.8508	−	167.750i	−0.0391225	−	0.0677621i
$184$	−169.976	−	963.982i	−0.0681022	−	0.386227i
$185$	−842.754	−	707.154i	−0.334922	−	0.281033i
$186$	16.6495	−	13.9706i	0.00656344	−	0.00550738i
$187$	19.7785	−	112.169i	0.00773446	−	0.0438643i
$188$	65.6079	−	23.8793i	0.0254519	−	0.00926372i
$189$	234.989			0.0904387
$190$	79.0059	+	1826.32i	0.0301668	+	0.697341i
$191$	1297.38			0.491493			0.245747	−	0.969334i	$-0.420967\pi$
$191$	1297.38			0.491493			0.245747	+	0.969334i	$0.420967\pi$
$192$	−14.1352	+	5.14480i	−0.00531314	+	0.00193382i
$193$	−343.453	+	1947.82i	−0.128095	+	0.726462i	0.851327	+	0.524636i	$0.175799\pi$
$193$	−343.453	+	1947.82i	−0.128095	+	0.726462i	−0.979421	+	0.201826i	$0.935313\pi$
$194$	2578.09	−	2163.27i	0.954103	−	0.800587i
$195$	−107.244	−	89.9886i	−0.0393842	−	0.0330473i
$196$	0.344326	+	1.95277i	0.000125483	+	0.000711651i
$197$	−1167.66	−	2022.45i	−0.422297	−	0.731439i	0.573867	−	0.818948i	$-0.305443\pi$
$197$	−1167.66	−	2022.45i	−0.422297	−	0.731439i	−0.996164	+	0.0875092i	$0.972109\pi$
$198$	376.557	−	652.215i	0.135155	−	0.234096i
$199$	−2447.67	−	890.879i	−0.871914	−	0.317351i	−0.132972	−	0.991120i	$-0.542452\pi$
$199$	−2447.67	−	890.879i	−0.871914	−	0.317351i	−0.738942	+	0.673769i	$0.764674\pi$
$200$	24.0656	+	8.75917i	0.00850848	+	0.00309683i
$201$	98.7102	−	170.971i	0.0346392	−	0.0599968i
$202$	1208.58	+	2093.32i	0.420968	+	0.729137i
$203$	712.584	+	4041.27i	0.246373	+	1.39725i
$204$	5.86971	+	4.92528i	0.00201452	+	0.00169038i
$205$	2685.03	−	2253.01i	0.914785	−	0.767596i
$206$	−16.7268	+	94.8623i	−0.00565733	+	0.0320843i
$207$	−3098.04	+	1127.60i	−1.04024	+	0.378615i
$208$	−863.538			−0.287863
$209$	1147.45	+	151.532i	0.379763	+	0.0501515i
$210$	−96.1500			−0.0315951
$211$	−4731.31	+	1722.05i	−1.54368	+	0.561854i	−0.966924	−	0.255063i	$-0.917904\pi$
$211$	−4731.31	+	1722.05i	−1.54368	+	0.561854i	−0.576756	+	0.816917i	$0.695682\pi$
$212$	30.7812	−	174.569i	0.00997200	−	0.0565540i
$213$	−104.074	+	87.3287i	−0.0334791	+	0.0280923i
$214$	1336.25	+	1121.25i	0.426842	+	0.358163i
$215$	−896.066	−	5081.84i	−0.284238	−	1.61199i
$216$	50.7162	+	87.8430i	0.0159759	+	0.0276711i
$217$	428.461	−	742.115i	0.134036	−	0.232157i
$218$	1060.40	+	385.953i	0.329445	+	0.119908i
$219$	166.961	+	60.7688i	0.0515168	+	0.0187506i
$220$	−308.466	+	534.279i	−0.0945308	+	0.163732i
$221$	219.937	+	380.941i	0.0669436	+	0.115950i
$222$	−8.13697	−	46.1470i	−0.00245999	−	0.0139513i
$223$	2869.68	+	2407.95i	0.861741	+	0.723087i	0.962342	−	0.271840i	$-0.0876322\pi$
$223$	2869.68	+	2407.95i	0.861741	+	0.723087i	−0.100601	+	0.994927i	$0.532077\pi$
$224$	−454.323	+	381.222i	−0.135517	+	0.113712i
$225$	14.9784	−	84.9468i	0.00443805	−	0.0251694i
$226$	4385.34	−	1596.13i	1.29075	−	0.469793i
$227$	1621.77			0.474187			0.237093	−	0.971487i	$-0.423805\pi$
$227$	1621.77			0.474187			0.237093	+	0.971487i	$0.423805\pi$
$228$	−47.4243	+	61.7534i	−0.0137752	+	0.0179374i
$229$	3975.70			1.14726			0.573628	−	0.819116i	$-0.305536\pi$
$229$	3975.70			1.14726			0.573628	+	0.819116i	$0.305536\pi$
$230$	2537.84	−	923.699i	0.727567	−	0.264813i
$231$	−10.5712	+	59.9522i	−0.00301097	+	0.0170760i
$232$	−1356.90	+	1138.58i	−0.383988	+	0.322204i
$233$	−1051.68	−	882.463i	−0.295698	−	0.248120i	0.482853	−	0.875702i	$-0.339601\pi$
$233$	−1051.68	−	882.463i	−0.295698	−	0.248120i	−0.778551	+	0.627581i	$0.784045\pi$
$234$	505.052	+	2864.29i	0.141095	+	0.800191i
$235$	96.3168	+	166.826i	0.0267362	+	0.0463085i
$236$	−1276.40	+	2210.80i	−0.352063	+	0.609791i
$237$	−74.9873	−	27.2932i	−0.0205525	−	0.00748051i
$238$	283.885	+	103.326i	0.0773174	+	0.0281412i
$239$	−2494.88	+	4321.27i	−0.675233	+	1.16954i	0.301168	+	0.953571i	$0.402624\pi$
$239$	−2494.88	+	4321.27i	−0.675233	+	1.16954i	−0.976401	+	0.215967i	$0.930710\pi$
$240$	−20.7515	−	35.9426i	−0.00558125	−	0.00966701i
$241$	−239.897	−	1360.52i	−0.0641209	−	0.363648i	−0.999938	−	0.0111609i	$-0.996447\pi$
$241$	−239.897	−	1360.52i	−0.0641209	−	0.363648i	0.935817	−	0.352487i	$-0.114664\pi$
$242$	−1739.99	−	1460.02i	−0.462192	−	0.387825i
$243$	392.694	−	329.509i	0.103668	−	0.0869878i
$244$	572.435	−	3246.44i	0.150190	−	0.851771i
$245$	−5.14099	+	1.87117i	−0.00134059	+	0.000487937i
$246$	149.294			0.0386936
$247$	−3770.79	+	2400.13i	−0.971374	+	0.618287i
$248$	369.888			0.0947093
$249$	169.095	−	61.5455i	0.0430359	−	0.0156638i
$250$	−491.376	+	2786.73i	−0.124309	+	0.704994i
$251$	268.214	−	225.058i	0.0674482	−	0.0565958i	−0.608440	−	0.793600i	$-0.708205\pi$
$251$	268.214	−	225.058i	0.0674482	−	0.0565958i	0.675889	+	0.737004i	$0.263760\pi$
$252$	1530.20	+	1283.99i	0.382515	+	0.320968i
$253$	−296.930	−	1683.97i	−0.0737858	−	0.418460i
$254$	−1893.43	−	3279.52i	−0.467735	−	0.810140i
$255$	−10.5705	+	18.3086i	−0.00259588	+	0.00449619i
$256$	−240.561	−	87.5572i	−0.0587308	−	0.0213763i
$257$	2359.48	+	858.780i	0.572686	+	0.208441i	0.612097	−	0.790782i	$-0.290326\pi$
$257$	2359.48	+	858.780i	0.572686	+	0.208441i	−0.0394114	+	0.999223i	$0.512548\pi$
$258$	109.897	−	190.347i	0.0265189	−	0.0459321i
$259$	−923.753	−	1599.99i	−0.221619	−	0.383855i
$260$	−413.726	−	2346.36i	−0.0986855	−	0.559673i
$261$	4570.18	+	3834.84i	1.08386	+	0.909466i
$262$	−3491.65	+	2929.84i	−0.823339	+	0.690864i
$263$	815.637	−	4625.71i	0.191233	−	1.08454i	−0.726448	−	0.687221i	$-0.758830\pi$
$263$	815.637	−	4625.71i	0.191233	−	1.08454i	0.917682	−	0.397317i	$-0.130059\pi$
$264$	−24.6927	+	8.98742i	−0.00575656	+	0.00209522i
$265$	489.077			0.113373
$266$	−924.302	+	2927.42i	−0.213055	+	0.674782i
$267$	213.327			0.0488966
$268$	3157.19	−	1149.12i	0.719612	−	0.261917i
$269$	−393.217	+	2230.05i	−0.0891259	+	0.505458i	0.907264	+	0.420562i	$0.138167\pi$
$269$	−393.217	+	2230.05i	−0.0891259	+	0.505458i	−0.996390	+	0.0848964i	$0.972944\pi$
$270$	−214.384	+	179.889i	−0.0483221	+	0.0405471i
$271$	−1781.25	−	1494.65i	−0.399274	−	0.335031i	0.420939	−	0.907089i	$-0.361701\pi$
$271$	−1781.25	−	1494.65i	−0.399274	−	0.335031i	−0.820213	+	0.572058i	$0.806145\pi$
$272$	22.6442	+	128.421i	0.00504781	+	0.0286275i
$273$	−117.552	−	203.606i	−0.0260607	−	0.0451384i
$274$	1599.85	−	2771.03i	0.352740	−	0.610963i
$275$	42.0400	+	15.3013i	0.00921858	+	0.00335529i
$276$	108.096	+	39.3438i	0.0235747	+	0.00858050i
$277$	3127.59	−	5417.15i	0.678407	−	1.17504i	−0.297053	−	0.954861i	$-0.596004\pi$
$277$	3127.59	−	5417.15i	0.678407	−	1.17504i	0.975460	−	0.220175i	$-0.0706629\pi$
$278$	−1719.75	−	2978.70i	−0.371022	−	0.642628i
$279$	−216.334	−	1226.89i	−0.0464214	−	0.263269i
$280$	−1253.50	−	1051.82i	−0.267540	−	0.224493i
$281$	−5454.65	+	4577.00i	−1.15800	+	0.971675i	−0.999876	−	0.0157444i	$-0.994988\pi$
$281$	−5454.65	+	4577.00i	−1.15800	+	0.971675i	−0.158121	+	0.987420i	$0.550544\pi$
$282$	−1.42478	+	8.08033i	−0.000300867	+	0.00170630i
$283$	−6279.63	+	2285.60i	−1.31903	+	0.480088i	−0.903147	−	0.429331i	$-0.858750\pi$
$283$	−6279.63	+	2285.60i	−1.31903	+	0.480088i	−0.415883	+	0.909418i	$0.636527\pi$
$284$	−2312.13			−0.483098
$285$	−190.514	−	99.2724i	−0.0395968	−	0.0206329i
$286$	−1508.51			−0.311888
$287$	5531.22	−	2013.20i	1.13762	−	0.414061i
$288$	−149.725	+	849.133i	−0.0306341	+	0.173735i
$289$	−3712.69	+	3115.32i	−0.755687	+	0.634097i
$290$	−3743.78	−	3141.41i	−0.758078	−	0.636103i
$291$	68.6786	+	389.495i	0.0138351	+	0.0784626i
$292$	1511.90	+	2618.68i	0.303004	+	0.524818i
$293$	1295.02	−	2243.04i	0.258211	−	0.447235i	−0.707552	−	0.706662i	$-0.750200\pi$
$293$	1295.02	−	2243.04i	0.258211	−	0.447235i	0.965763	+	0.259427i	$0.0835336\pi$
$294$	−0.218974	−	0.0797000i	−4.34382e−5	−	1.58102e-5i
$295$	−6618.59	−	2408.97i	−1.30627	−	0.475443i
$296$	398.736	−	690.631i	0.0782975	−	0.135615i
$297$	88.5957	+	153.452i	0.0173092	+	0.0299805i
$298$	−826.528	−	4687.47i	−0.160669	−	0.911201i
$299$	5058.75	+	4244.79i	0.978444	+	0.821012i
$300$	−2.30554	+	1.93458i	−0.000443701	+	0.000372309i
$301$	1504.80	−	8534.15i	0.288157	−	1.63422i
$302$	−4027.64	+	1465.94i	−0.767433	+	0.279323i
$303$	−284.062			−0.0538578
$304$	−1293.81	+	286.287i	−0.244096	+	0.0540122i
$305$	9095.31			1.70753
$306$	412.720	−	150.218i	0.0771035	−	0.0280634i
$307$	1333.22	−	7561.07i	0.247853	−	1.40565i	−0.565919	−	0.824461i	$-0.691478\pi$
$307$	1333.22	−	7561.07i	0.247853	−	1.40565i	0.813772	−	0.581185i	$-0.197411\pi$
$308$	−793.653	+	665.954i	−0.146827	+	0.123202i
$309$	−8.67168	−	7.27641i	−0.00159649	−	0.00133961i
$310$	177.216	+	1005.04i	0.0324683	+	0.184137i
$311$	2748.80	+	4761.07i	0.501191	+	0.868088i	0.999999	+	0.00137581i	$0.000437934\pi$
$311$	2748.80	+	4761.07i	0.501191	+	0.868088i	−0.498808	+	0.866712i	$0.666229\pi$
$312$	50.7410	−	87.8859i	0.00920718	−	0.0159473i
$313$	3427.01	+	1247.33i	0.618869	+	0.225250i	0.632380	−	0.774659i	$-0.282078\pi$
$313$	3427.01	+	1247.33i	0.618869	+	0.225250i	−0.0135102	+	0.999909i	$0.504301\pi$
$314$	−1557.68	−	566.950i	−0.279952	−	0.101894i
$315$	−2755.66	+	4772.95i	−0.492902	+	0.853731i
$316$	−679.040	−	1176.13i	−0.120883	−	0.209375i
$317$	596.154	+	3380.96i	0.105626	+	0.599033i	0.990969	+	0.134094i	$0.0428126\pi$
$317$	596.154	+	3380.96i	0.105626	+	0.599033i	−0.885343	+	0.464939i	$0.846076\pi$
$318$	15.9579	+	13.3903i	0.00281408	+	0.00236129i
$319$	−2370.37	+	1988.97i	−0.416035	+	0.349095i
$320$	122.651	−	695.589i	0.0214263	−	0.121514i
$321$	−192.631	+	70.1120i	−0.0334941	+	0.0121909i
$322$	4535.43			0.784936
$323$	455.816	+	497.836i	0.0785210	+	0.0857596i
$324$	2898.11			0.496933
$325$	−162.356	+	59.0928i	−0.0277104	+	0.0100858i
$326$	−797.148	+	4520.85i	−0.135429	+	0.768058i
$327$	−101.588	+	85.2426i	−0.0171799	+	0.0144157i
$328$	1946.34	+	1633.17i	0.327648	+	0.274929i
$329$	56.1748	+	318.583i	0.00941343	+	0.0533862i
$330$	−36.2506	−	62.7878i	−0.00604705	−	0.0104738i
$331$	−1193.15	+	2066.59i	−0.198131	+	0.343173i	−0.947922	−	0.318501i	$-0.896821\pi$
$331$	−1193.15	+	2066.59i	−0.198131	+	0.343173i	0.749791	+	0.661674i	$0.230154\pi$
$332$	2877.75	+	1047.42i	0.475714	+	0.173146i
$333$	−2523.98	−	918.653i	−0.415355	−	0.151177i
$334$	−657.365	+	1138.59i	−0.107693	+	0.186530i
$335$	4634.96	+	8027.99i	0.755925	+	1.30930i
$336$	−12.1029	−	68.6387i	−0.00196507	−	0.0111445i
$337$	1309.35	+	1098.67i	0.211646	+	0.177592i	0.742448	−	0.669904i	$-0.233665\pi$
$337$	1309.35	+	1098.67i	0.211646	+	0.177592i	−0.530802	+	0.847496i	$0.678109\pi$
$338$	1096.80	−	920.322i	0.176503	−	0.148103i
$339$	−95.2346	+	540.102i	−0.0152579	+	0.0865319i
$340$	−338.091	+	123.055i	−0.0539281	+	0.0196282i
$341$	646.154			0.102614
$342$	1706.30	+	4124.03i	0.269783	+	0.652053i
$343$	6347.85			0.999276
$344$	3514.99	−	1279.35i	0.550917	−	0.200518i
$345$	−55.1133	+	312.563i	−0.00860058	+	0.0487763i
$346$	−251.331	+	210.892i	−0.0390510	+	0.0327677i
$347$	−2323.51	−	1949.66i	−0.359460	−	0.301622i	0.445116	−	0.895473i	$-0.353163\pi$
$347$	−2323.51	−	1949.66i	−0.359460	−	0.301622i	−0.804575	+	0.593851i	$0.797607\pi$
$348$	−36.1470	−	205.000i	−0.00556806	−	0.0315780i
$349$	−1030.90	−	1785.57i	−0.158117	−	0.273866i	0.776073	−	0.630643i	$-0.217209\pi$
$349$	−1030.90	−	1785.57i	−0.158117	−	0.273866i	−0.934190	+	0.356777i	$0.883876\pi$
$350$	−59.3310	+	102.764i	−0.00906107	+	0.0156942i
$351$	−643.034	−	234.045i	−0.0977852	−	0.0355909i
$352$	−420.235	−	152.953i	−0.0636323	−	0.0231603i
$353$	−3674.57	+	6364.55i	−0.554045	+	0.959634i	0.443932	+	0.896060i	$0.353583\pi$
$353$	−3674.57	+	6364.55i	−0.554045	+	0.959634i	−0.997977	+	0.0635736i	$0.979750\pi$
$354$	−150.001	−	259.810i	−0.0225211	−	0.0390078i
$355$	−1107.76	−	6282.40i	−0.165616	−	0.939254i
$356$	2781.14	+	2333.65i	0.414045	+	0.347425i
$357$	−27.1968	+	22.8208i	−0.00403195	+	0.00338321i
$358$	196.857	−	1116.43i	0.0290621	−	0.164819i
$359$	−616.056	+	224.226i	−0.0905687	+	0.0329643i	−0.386907	−	0.922119i	$-0.626457\pi$
$359$	−616.056	+	224.226i	−0.0905687	+	0.0329643i	0.296338	+	0.955083i	$0.404234\pi$
$360$	−2378.95			−0.348283
$361$	−4853.93	+	4846.16i	−0.707673	+	0.706540i
$362$	2340.77			0.339857
$363$	250.833	−	91.2958i	0.0362681	−	0.0132005i
$364$	694.788	−	3940.34i	0.100046	−	0.567390i
$365$	−6390.98	+	5362.67i	−0.916491	+	0.769027i
$366$	296.768	+	249.018i	0.0423834	+	0.0355639i
$367$	−2136.09	−	12114.4i	−0.303823	−	1.72307i	−0.628992	−	0.777412i	$-0.716532\pi$
$367$	−2136.09	−	12114.4i	−0.303823	−	1.72307i	0.325169	−	0.945656i	$-0.394579\pi$
$368$	978.853	+	1695.42i	0.138658	+	0.240163i
$369$	4278.77	−	7411.04i	0.603642	−	1.04554i
$370$	2067.58	+	752.538i	0.290509	+	0.105737i
$371$	771.796	+	280.911i	0.108004	+	0.0393104i
$372$	−21.7344	+	37.6450i	−0.00302923	+	0.00524679i
$373$	−511.270	−	885.546i	−0.0709720	−	0.122927i	0.828356	−	0.560203i	$-0.189277\pi$
$373$	−511.270	−	885.546i	−0.0709720	−	0.122927i	−0.899328	+	0.437276i	$0.855943\pi$
$374$	39.5569	+	224.338i	0.00546909	+	0.0310167i
$375$	−254.744	−	213.756i	−0.0350799	−	0.0294355i
$376$	−106.968	+	89.7570i	−0.0146714	+	0.0123108i
$377$	2075.09	−	11768.4i	0.283482	−	1.60771i
$378$	−441.634	+	160.742i	−0.0600932	+	0.0218721i
$379$	1217.86			0.165058			0.0825292	−	0.996589i	$-0.473700\pi$
$379$	1217.86			0.165058			0.0825292	+	0.996589i	$0.473700\pi$
$380$	−1397.76	−	3378.31i	−0.188693	−	0.456062i
$381$	445.028			0.0598411
$382$	−2438.28	+	887.461i	−0.326579	+	0.118865i
$383$	−1784.08	+	10118.0i	−0.238021	+	1.34988i	0.598136	+	0.801394i	$0.295908\pi$
$383$	−1784.08	+	10118.0i	−0.238021	+	1.34988i	−0.836157	+	0.548490i	$0.815203\pi$
$384$	23.0463	−	19.3381i	0.00306270	−	0.00256991i
$385$	−2189.74	−	1837.41i	−0.289869	−	0.243229i
$386$	−686.906	−	3895.64i	−0.0905767	−	0.513686i
$387$	−6299.30	−	10910.7i	−0.827420	−	1.43313i
$388$	−3365.46	+	5829.14i	−0.440348	+	0.762706i
$389$	−13812.6	−	5027.38i	−1.80033	−	0.655265i	−0.998320	−	0.0579490i	$-0.981544\pi$
$389$	−13812.6	−	5027.38i	−1.80033	−	0.655265i	−0.802006	−	0.597316i	$-0.796234\pi$
$390$	263.109	+	95.7639i	0.0341617	+	0.0124338i
$391$	498.613	−	863.623i	0.0644909	−	0.111701i
$392$	−1.98289	−	3.43447i	−0.000255488	−	0.000442518i
$393$	−93.0153	−	527.516i	−0.0119389	−	0.0677090i
$394$	3577.92	+	3002.23i	0.457495	+	0.383884i
$395$	2870.39	−	2408.54i	0.365633	−	0.306802i
$396$	−261.554	+	1483.34i	−0.0331908	+	0.188234i
$397$	2178.71	−	792.986i	0.275432	−	0.100249i	−0.200611	−	0.979671i	$-0.564293\pi$
$397$	2178.71	−	792.986i	0.275432	−	0.100249i	0.476043	+	0.879422i	$0.342071\pi$
$398$	5209.51			0.656104
$399$	−243.625	−	266.084i	−0.0305677	−	0.0333856i
$400$	−51.2202			−0.00640252
$401$	−3690.36	+	1343.18i	−0.459571	+	0.167270i	−0.561422	−	0.827529i	$-0.689746\pi$
$401$	−3690.36	+	1343.18i	−0.459571	+	0.167270i	0.101851	+	0.994800i	$0.467523\pi$
$402$	−68.5634	+	388.842i	−0.00850654	+	0.0482430i
$403$	−1911.59	+	1604.02i	−0.236286	+	0.198268i
$404$	−3703.31	−	3107.44i	−0.456055	−	0.382676i
$405$	1388.50	+	7874.60i	0.170359	+	0.966153i
$406$	−4103.61	−	7107.66i	−0.501623	−	0.868836i
$407$	696.549	−	1206.46i	0.0848320	−	0.146933i
$408$	−14.4005	−	5.24137i	−0.00174738	−	0.000635996i
$409$	2465.59	+	897.403i	0.298083	+	0.108493i	0.486732	−	0.873551i	$-0.338189\pi$
$409$	2465.59	+	897.403i	0.298083	+	0.108493i	−0.188650	+	0.982044i	$0.560411\pi$
$410$	−3505.06	+	6070.95i	−0.422202	+	0.731275i
$411$	188.013	+	325.648i	0.0225644	+	0.0390828i
$412$	−33.4536	−	189.725i	−0.00400034	−	0.0226870i
$413$	−9060.93	−	7603.02i	−1.07956	−	0.905860i
$414$	5051.10	−	4238.37i	0.599632	−	0.503151i
$415$	−1467.23	+	8321.09i	−0.173551	+	0.984256i
$416$	1622.92	−	590.695i	0.191275	−	0.0696183i
$417$	404.207			0.0474678
$418$	−2260.15	+	500.113i	−0.264467	+	0.0585199i
$419$	4324.14			0.504172			0.252086	−	0.967705i	$-0.418883\pi$
$419$	4324.14			0.504172			0.252086	+	0.967705i	$0.418883\pi$
$420$	180.703	−	65.7705i	0.0209938	−	0.00764112i
$421$	−2157.09	+	12233.4i	−0.249715	+	1.41620i	0.559568	+	0.828785i	$0.310967\pi$
$421$	−2157.09	+	12233.4i	−0.249715	+	1.41620i	−0.809283	+	0.587419i	$0.800144\pi$
$422$	7713.99	−	6472.81i	0.889837	−	0.746662i
$423$	360.279	+	302.310i	0.0414122	+	0.0347490i
$424$	61.5625	+	349.138i	0.00705127	+	0.0399897i
$425$	13.0454	+	22.5953i	0.00148893	+	0.00257890i
$426$	135.859	−	235.315i	0.0154517	−	0.0267631i
$427$	14353.0	+	5224.06i	1.62667	+	0.592061i
$428$	−3278.30	−	1193.20i	−0.370240	−	0.134756i
$429$	88.6390	−	153.527i	0.00997560	−	0.0172782i
$430$	5160.24	+	8937.79i	0.578718	+	1.00237i
$431$	−1450.91	−	8228.49i	−0.162152	−	0.919612i	−0.951952	−	0.306247i	$-0.900927\pi$
$431$	−1450.91	−	8228.49i	−0.162152	−	0.919612i	0.789800	−	0.613365i	$-0.210184\pi$
$432$	−155.403	−	130.399i	−0.0173075	−	0.0145227i
$433$	3540.14	−	2970.53i	0.392906	−	0.329687i	−0.424838	−	0.905269i	$-0.639669\pi$
$433$	3540.14	−	2970.53i	0.392906	−	0.329687i	0.817744	+	0.575582i	$0.195224\pi$
$434$	−297.606	+	1687.81i	−0.0329160	+	0.186676i
$435$	539.697	−	196.434i	0.0594861	−	0.0216512i
$436$	−2256.90			−0.247903
$437$	8986.62	+	4682.71i	0.983726	+	0.512596i
$438$	−355.352			−0.0387657
$439$	8675.58	−	3157.65i	0.943196	−	0.343295i	0.175769	−	0.984431i	$-0.443759\pi$
$439$	8675.58	−	3157.65i	0.943196	−	0.343295i	0.767427	+	0.641136i	$0.221537\pi$
$440$	214.258	−	1215.12i	0.0232145	−	0.131656i
$441$	−10.2322	+	8.58581i	−0.00110487	+	0.000927093i
$442$	−673.925	−	565.490i	−0.0725234	−	0.0608543i
$443$	1008.67	+	5720.46i	0.108179	+	0.613516i	0.989903	+	0.141749i	$0.0452725\pi$
$443$	1008.67	+	5720.46i	0.108179	+	0.613516i	−0.881723	+	0.471767i	$0.843616\pi$
$444$	46.8589	+	81.1621i	0.00500862	+	0.00867518i
$445$	−5008.41	+	8674.82i	−0.533531	+	0.924103i
$446$	−7040.38	−	2562.49i	−0.747470	−	0.272057i
$447$	525.630	+	191.314i	0.0556185	+	0.0202435i
$448$	593.076	−	1027.24i	0.0625451	−	0.108331i
$449$	−3910.06	−	6772.41i	−0.410973	−	0.711826i	0.584023	−	0.811737i	$-0.301478\pi$
$449$	−3910.06	−	6772.41i	−0.410973	−	0.711826i	−0.994996	+	0.0999106i	$0.968144\pi$
$450$	29.9568	+	169.894i	0.00313817	+	0.0177975i
$451$	3400.04	+	2852.98i	0.354993	+	0.297875i
$452$	−7149.92	+	5999.50i	−0.744036	+	0.624320i
$453$	87.4666	−	496.048i	0.00907183	−	0.0514489i
$454$	−3047.92	+	1109.35i	−0.315080	+	0.114680i
$455$	11039.4			1.13743
$456$	46.8868	−	148.499i	0.00481508	−	0.0152502i
$457$	−9140.92			−0.935654			−0.467827	−	0.883820i	$-0.654963\pi$
$457$	−9140.92			−0.935654			−0.467827	+	0.883820i	$0.654963\pi$
$458$	−7471.87	+	2719.54i	−0.762309	+	0.277458i
$459$	−17.9441	+	101.766i	−0.00182475	+	0.0103487i
$460$	−4137.74	+	3471.97i	−0.419398	+	0.351916i
$461$	9792.35	+	8216.76i	0.989317	+	0.830136i	0.985469	−	0.169857i	$-0.0543306\pi$
$461$	9792.35	+	8216.76i	0.989317	+	0.830136i	0.00384843	+	0.999993i	$0.498775\pi$
$462$	−21.1424	−	119.904i	−0.00212908	−	0.0120746i
$463$	439.731	+	761.636i	0.0441383	+	0.0764498i	0.887251	−	0.461288i	$-0.152612\pi$
$463$	439.731	+	761.636i	0.0441383	+	0.0764498i	−0.843112	+	0.537738i	$0.819279\pi$
$464$	1771.31	−	3068.00i	0.177222	−	0.306958i
$465$	−112.700	−	41.0195i	−0.0112394	−	0.00409083i
$466$	2580.15	+	939.097i	0.256487	+	0.0933537i
$467$	4012.07	−	6949.11i	0.397552	−	0.688580i	−0.595872	−	0.803080i	$-0.703193\pi$
$467$	4012.07	−	6949.11i	0.397552	−	0.688580i	0.993423	+	0.114500i	$0.0365266\pi$
$468$	−2908.48	−	5037.63i	−0.287274	−	0.497574i
$469$	2703.25	+	15330.9i	0.266150	+	1.50941i
$470$	−295.132	−	247.645i	−0.0289647	−	0.0243043i
$471$	149.229	−	125.218i	0.0145990	−	0.0122500i
$472$	886.581	−	5028.05i	0.0864580	−	0.490328i
$473$	6140.31	−	2234.89i	0.596896	−	0.217252i
$474$	159.600			0.0154655
$475$	−223.662	+	142.362i	−0.0216048	+	0.0137516i
$476$	−604.208			−0.0581803
$477$	1122.06	−	408.396i	0.107706	−	0.0392017i
$478$	1732.93	−	9827.93i	0.165821	−	0.940416i
$479$	13205.1	−	11080.4i	1.25962	−	1.05695i	0.263898	−	0.964551i	$-0.414992\pi$
$479$	13205.1	−	11080.4i	1.25962	−	1.05695i	0.995722	−	0.0923959i	$-0.0294525\pi$
$480$	63.5861	+	53.3551i	0.00604645	+	0.00507358i
$481$	934.237	+	5298.32i	0.0885604	+	0.502251i
$482$	1381.51	+	2392.85i	0.130552	+	0.226123i
$483$	−266.499	+	461.589i	−0.0251058	+	0.0434846i
$484$	4268.82	+	1553.72i	0.400903	+	0.145917i
$485$	−17451.0	−	6351.66i	−1.63384	−	0.594668i
$486$	−512.625	+	887.893i	−0.0478460	+	0.0828717i
$487$	1115.87	+	1932.74i	0.103829	+	0.179837i	0.913259	−	0.407379i	$-0.133557\pi$
$487$	1115.87	+	1932.74i	0.103829	+	0.179837i	−0.809430	+	0.587216i	$0.800224\pi$
$488$	1144.87	+	6492.88i	0.106200	+	0.602293i
$489$	−413.266	−	346.772i	−0.0382179	−	0.0320686i
$490$	8.38194	−	7.03329i	0.000772771	−	0.000648432i
$491$	−1756.20	+	9959.88i	−0.161418	+	0.915444i	0.791264	+	0.611475i	$0.209423\pi$
$491$	−1756.20	+	9959.88i	−0.161418	+	0.915444i	−0.952682	+	0.303970i	$0.901688\pi$
$492$	−280.580	+	102.123i	−0.0257105	+	0.00935784i
$493$	−1804.56			−0.164855
$494$	5444.97	−	7090.15i	0.495913	−	0.645750i
$495$	−4155.77			−0.377350
$496$	−695.162	+	253.018i	−0.0629308	+	0.0229049i
$497$	1860.30	−	10550.3i	0.167899	−	0.952204i
$498$	−275.695	+	231.335i	−0.0248076	+	0.0208160i
$499$	1283.66	+	1077.12i	0.115159	+	0.0966303i	0.698549	−	0.715562i	$-0.253829\pi$
$499$	1283.66	+	1077.12i	0.115159	+	0.0966303i	−0.583389	+	0.812193i	$0.698274\pi$
$500$	−982.752	−	5573.46i	−0.0879000	−	0.498506i
$501$	−77.2527	−	133.806i	−0.00688901	−	0.0119321i
$502$	−350.128	+	606.440i	−0.0311295	+	0.0539178i
$503$	−13636.1	−	4963.14i	−1.20876	−	0.439951i	−0.342484	−	0.939524i	$-0.611268\pi$
$503$	−13636.1	−	4963.14i	−1.20876	−	0.439951i	−0.866272	+	0.499573i	$0.833490\pi$
$504$	−3754.14	−	1366.40i	−0.331791	−	0.120762i
$505$	6669.10	−	11551.2i	0.587665	−	1.01787i
$506$	1709.95	+	2961.72i	0.150230	+	0.260207i
$507$	29.2180	+	165.703i	0.00255940	+	0.0145151i
$508$	5801.82	+	4868.30i	0.506721	+	0.425189i
$509$	−10257.8	+	8607.34i	−0.893262	+	0.749536i	−0.968862	−	0.247602i	$-0.920357\pi$
$509$	−10257.8	+	8607.34i	−0.893262	+	0.749536i	0.0755995	+	0.997138i	$0.475913\pi$
$510$	7.34217	−	41.6395i	0.000637484	−	0.00361535i
$511$	−13165.5	+	4791.86i	−1.13974	+	0.414833i
$512$	512.000			0.0441942
$513$	−1041.03	−	137.478i	−0.0895955	−	0.0118320i
$514$	−5021.81			−0.430939
$515$	499.482	−	181.796i	0.0427375	−	0.0155552i
$516$	−76.3336	+	432.909i	−0.00651240	+	0.0369337i
$517$	−186.862	+	156.796i	−0.0158959	+	0.0133382i
$518$	2830.54	+	2375.11i	0.240091	+	0.201460i
$519$	−6.69529	−	37.9709i	−0.000566263	−	0.00321144i
$520$	2382.56	+	4126.71i	0.200927	+	0.348015i
$521$	2387.24	−	4134.82i	0.200743	−	0.347697i	−0.748025	−	0.663670i	$-0.768998\pi$
$521$	2387.24	−	4134.82i	0.200743	−	0.347697i	0.948768	+	0.315974i	$0.102331\pi$
$522$	−11212.3	−	4080.95i	−0.940134	−	0.342181i
$523$	10609.1	+	3861.39i	0.887004	+	0.322843i	0.745033	−	0.667028i	$-0.232434\pi$
$523$	10609.1	+	3861.39i	0.887004	+	0.322843i	0.141971	+	0.989871i	$0.454656\pi$
$524$	4558.03	−	7894.73i	0.379997	−	0.658174i
$525$	−6.97250	−	12.0767i	−0.000579629	−	0.00100395i
$526$	1631.27	+	9251.42i	0.135222	+	0.766884i
$527$	288.669	+	242.222i	0.0238608	+	0.0200215i
$528$	40.2594	−	33.7816i	0.00331830	−	0.00278439i
$529$	486.934	−	2761.54i	0.0400208	−	0.226969i
$530$	−919.164	+	334.548i	−0.0753320	+	0.0274186i
$531$	−17196.2			−1.40537
$532$	−265.356	−	6134.02i	−0.0216253	−	0.499894i
$533$	−17141.0			−1.39298
$534$	−400.923	+	145.924i	−0.0324900	+	0.0118254i
$535$	1671.46	−	9479.30i	0.135072	−	0.766030i
$536$	−5147.53	+	4319.29i	−0.414812	+	0.348069i
$537$	102.057	+	85.6360i	0.00820127	+	0.00688168i
$538$	−786.434	−	4460.09i	−0.0630215	−	0.357413i
$539$	−3.46390	−	5.99965i	−0.000276810	−	0.000479450i
$540$	279.858	−	484.728i	0.0223022	−	0.0386285i
$541$	16307.1	+	5935.30i	1.29593	+	0.471679i	0.895668	−	0.444723i	$-0.146698\pi$
$541$	16307.1	+	5935.30i	1.29593	+	0.471679i	0.400259	+	0.916402i	$0.368920\pi$
$542$	4370.06	+	1590.57i	0.346328	+	0.126053i
$543$	−137.542	+	238.230i	−0.0108702	+	0.0188277i
$544$	−130.402	−	225.864i	−0.0102775	−	0.0178012i
$545$	−1081.29	−	6132.32i	−0.0849863	−	0.481981i
$546$	360.200	+	302.243i	0.0282328	+	0.0236902i
$547$	1716.71	−	1440.49i	0.134189	−	0.112598i	−0.573223	−	0.819400i	$-0.694307\pi$
$547$	1716.71	−	1440.49i	0.134189	−	0.112598i	0.707412	+	0.706802i	$0.249863\pi$
$548$	−1111.25	+	6302.19i	−0.0866243	+	0.491271i
$549$	20866.8	−	7594.90i	1.62217	−	0.590423i
$550$	−89.4761			−0.00693686
$551$	−792.526	−	18320.2i	−0.0612754	−	1.41645i
$552$	−230.067			−0.0177397
$553$	5913.05	−	2152.17i	0.454699	−	0.165497i
$554$	−2172.40	+	12320.3i	−0.166600	+	0.944837i
$555$	−198.079	+	166.208i	−0.0151495	+	0.0127119i
$556$	5269.63	+	4421.75i	0.401946	+	0.337273i
$557$	234.400	+	1329.35i	0.0178310	+	0.101124i	0.992424	−	0.122857i	$-0.0392056\pi$
$557$	234.400	+	1329.35i	0.0178310	+	0.101124i	−0.974593	+	0.223981i	$0.928095\pi$
$558$	1245.82	+	2157.82i	0.0945155	+	0.163706i
$559$	−12617.7	+	21854.5i	−0.954690	+	1.65357i
$560$	3075.30	+	1119.32i	0.232063	+	0.0844640i
$561$	−25.1562	−	9.15611i	−0.00189322	−	0.000689075i
$562$	7120.54	−	12333.1i	0.534452	−	0.925698i
$563$	−8911.18	−	15434.6i	−0.667072	−	1.15540i	−0.978719	−	0.205204i	$-0.934214\pi$
$563$	−8911.18	−	15434.6i	−0.667072	−	1.15540i	0.311648	−	0.950198i	$-0.399119\pi$
$564$	−2.84956	−	16.1607i	−0.000212745	−	0.00120654i
$565$	−19727.1	−	16553.0i	−1.46889	−	1.23255i
$566$	10238.4	−	8591.05i	0.760340	−	0.638001i
$567$	−2331.77	+	13224.1i	−0.172708	+	0.979474i
$568$	4345.39	−	1581.59i	0.321001	−	0.116835i
$569$	−8579.20			−0.632090			−0.316045	−	0.948744i	$-0.602355\pi$
$569$	−8579.20			−0.632090			−0.316045	+	0.948744i	$0.602355\pi$
$570$	425.956	+	56.2517i	0.0313006	+	0.00413355i
$571$	−19827.3			−1.45314			−0.726572	−	0.687090i	$-0.758888\pi$
$571$	−19827.3			−1.45314			−0.726572	+	0.687090i	$0.758888\pi$
$572$	2835.07	−	1031.88i	0.207238	−	0.0754285i
$573$	52.9511	−	300.301i	0.00386050	−	0.0218940i
$574$	−9018.19	+	7567.16i	−0.655770	+	0.550256i
$575$	300.056	+	251.777i	0.0217621	+	0.0182606i
$576$	−299.450	−	1698.27i	−0.0216616	−	0.122849i
$577$	5655.66	+	9795.89i	0.408056	+	0.706773i	0.994672	−	0.103092i	$-0.0328735\pi$
$577$	5655.66	+	9795.89i	0.408056	+	0.706773i	−0.586616	+	0.809865i	$0.699540\pi$
$578$	4846.57	−	8394.51i	0.348773	−	0.604093i
$579$	436.838	+	158.996i	0.0313547	+	0.0114122i
$580$	9184.86	+	3343.02i	0.657553	+	0.239330i
$581$	−7094.77	+	12288.5i	−0.506610	+	0.877474i
$582$	−395.504	−	685.033i	−0.0281687	−	0.0487896i
$583$	107.543	+	609.907i	0.00763976	+	0.0433272i
$584$	−4632.72	−	3887.31i	−0.328259	−	0.275442i
$585$	12294.5	−	10316.3i	0.868915	−	0.729106i
$586$	−899.511	+	5101.38i	−0.0634104	+	0.359618i
$587$	2841.65	−	1034.28i	0.199808	−	0.0727242i	−0.240178	−	0.970729i	$-0.577206\pi$
$587$	2841.65	−	1034.28i	0.199808	−	0.0727242i	0.439986	+	0.898005i	$0.354983\pi$
$588$	0.466054			3.26867e−5
$589$	−2332.30	+	3036.99i	−0.163159	+	0.212457i
$590$	14086.7			0.982950
$591$	−515.786	+	187.731i	−0.0358995	+	0.0130664i
$592$	−276.959	+	1570.71i	−0.0192279	+	0.109047i
$593$	10073.3	−	8452.51i	0.697574	−	0.585334i	−0.223509	−	0.974702i	$-0.571751\pi$
$593$	10073.3	−	8452.51i	0.697574	−	0.585334i	0.921082	+	0.389368i	$0.127307\pi$
$594$	−271.473	−	227.793i	−0.0187520	−	0.0157348i
$595$	−289.480	−	1641.72i	−0.0199454	−	0.113116i
$596$	4759.79	+	8244.19i	0.327128	+	0.566603i
$597$	−306.108	+	530.194i	−0.0209852	+	0.0363474i
$598$	−12410.9	−	4517.21i	−0.848698	−	0.308901i
$599$	20547.7	+	7478.75i	1.40160	+	0.510140i	0.928652	−	0.370952i	$-0.120969\pi$
$599$	20547.7	+	7478.75i	1.40160	+	0.510140i	0.472945	+	0.881092i	$0.343191\pi$
$600$	3.00966	−	5.21289i	0.000204782	−	0.000354692i
$601$	4936.16	+	8549.68i	0.335025	+	0.580281i	0.983490	−	0.180964i	$-0.0579218\pi$
$601$	4936.16	+	8549.68i	0.335025	+	0.580281i	−0.648464	+	0.761245i	$0.724588\pi$
$602$	3009.60	+	17068.3i	0.203758	+	1.15557i
$603$	17337.4	+	14547.8i	1.17087	+	0.982473i
$604$	6566.73	−	5510.14i	0.442378	−	0.371199i
$605$	−2176.47	+	12343.4i	−0.146258	+	0.829472i
$606$	533.861	−	194.310i	0.0357865	−	0.0130252i
$607$	−2036.42			−0.136171			−0.0680854	−	0.997679i	$-0.521689\pi$
$607$	−2036.42			−0.136171			−0.0680854	+	0.997679i	$0.521689\pi$
$608$	2235.73	−	1423.06i	0.149130	−	0.0949223i
$609$	964.502			0.0641767
$610$	−17093.6	+	6221.56i	−1.13459	+	0.412956i
$611$	163.585	−	927.734i	0.0108313	−	0.0614274i
$612$	−672.906	+	564.635i	−0.0444454	+	0.0372941i
$613$	8305.63	+	6969.25i	0.547245	+	0.459193i	0.874007	−	0.485914i	$-0.161513\pi$
$613$	8305.63	+	6969.25i	0.547245	+	0.459193i	−0.326762	+	0.945107i	$0.605958\pi$
$614$	2666.44	+	15122.1i	0.175259	+	0.993942i
$615$	−411.911	−	713.450i	−0.0270079	−	0.0467790i
$616$	1036.04	−	1794.48i	0.0677650	−	0.117372i
$617$	9571.42	+	3483.71i	0.624524	+	0.227308i	0.634846	−	0.772639i	$-0.281064\pi$
$617$	9571.42	+	3483.71i	0.624524	+	0.227308i	−0.0103224	+	0.999947i	$0.503286\pi$
$618$	21.2748	+	7.74339i	0.00138479	+	0.000504021i
$619$	2752.31	−	4767.14i	0.178715	−	0.309544i	−0.762726	−	0.646722i	$-0.776139\pi$
$619$	2752.31	−	4767.14i	0.178715	−	0.309544i	0.941441	+	0.337178i	$0.109473\pi$
$620$	−1020.54	−	1767.63i	−0.0661065	−	0.114500i
$621$	269.392	+	1527.80i	0.0174079	+	0.0987252i
$622$	−8422.83	−	7067.59i	−0.542966	−	0.455602i
$623$	−12886.2	+	10812.8i	−0.828688	+	0.695352i
$624$	−35.2443	+	199.880i	−0.00226106	+	0.0128231i
$625$	14297.0	−	5203.70i	0.915011	−	0.333037i
$626$	−7293.90			−0.465691
$627$	81.9062	−	259.411i	0.00521693	−	0.0165229i
$628$	3315.30			0.210661
$629$	763.444	−	277.871i	0.0483951	−	0.0176144i
$630$	1914.06	−	10855.2i	0.121045	−	0.686479i
$631$	14640.2	−	12284.6i	0.923639	−	0.775025i	−0.0510254	−	0.998697i	$-0.516249\pi$
$631$	14640.2	−	12284.6i	0.923639	−	0.775025i	0.974664	+	0.223672i	$0.0718045\pi$
$632$	2080.70	+	1745.91i	0.130958	+	0.109887i
$633$	205.496	+	1165.42i	0.0129032	+	0.0731776i
$634$	−3433.12	−	5946.33i	−0.215057	−	0.372490i
$635$	−10448.2	+	18096.8i	−0.652952	+	1.13095i
$636$	−39.1506	−	14.2497i	−0.00244092	−	0.000888421i
$637$	25.1412	+	9.15067i	0.00156379	+	0.000569172i
$638$	3094.29	−	5359.47i	0.192013	−	0.332576i
$639$	−7787.48	−	13488.3i	−0.482109	−	0.835038i
$640$	245.302	+	1391.18i	0.0151507	+	0.0859237i
$641$	−19570.2	−	16421.3i	−1.20589	−	1.01186i	−0.999442	−	0.0334040i	$-0.989365\pi$
$641$	−19570.2	−	16421.3i	−1.20589	−	1.01186i	−0.206448	−	0.978458i	$-0.566190\pi$
$642$	314.069	−	263.535i	0.0193073	−	0.0162008i
$643$	−1731.70	+	9820.96i	−0.106208	+	0.602334i	0.884523	+	0.466496i	$0.154484\pi$
$643$	−1731.70	+	9820.96i	−0.106208	+	0.602334i	−0.990731	+	0.135838i	$0.956627\pi$
$644$	−8523.81	+	3102.41i	−0.521561	+	0.189833i
$645$	−1212.85			−0.0740401
$646$	−1197.19	−	623.829i	−0.0729148	−	0.0379942i
$647$	−18928.1			−1.15014			−0.575069	−	0.818105i	$-0.695025\pi$
$647$	−18928.1			−1.15014			−0.575069	+	0.818105i	$0.695025\pi$
$648$	−5446.67	+	1982.43i	−0.330194	+	0.120181i
$649$	1548.76	−	8783.46i	0.0936737	−	0.531250i
$650$	264.708	−	222.116i	0.0159734	−	0.0134032i
$651$	−154.288	−	129.463i	−0.00928882	−	0.00779424i
$652$	−1594.30	−	9041.70i	−0.0957630	−	0.543099i
$653$	7077.11	+	12257.9i	0.424118	+	0.734593i	0.996338	−	0.0855069i	$-0.0272510\pi$
$653$	7077.11	+	12257.9i	0.424118	+	0.734593i	−0.572220	+	0.820100i	$0.693918\pi$
$654$	132.614	−	229.694i	0.00792908	−	0.0137336i
$655$	23634.9	+	8602.41i	1.40991	+	0.513166i
$656$	−4775.08	−	1737.99i	−0.284200	−	0.103440i
$657$	−10184.4	+	17639.9i	−0.604767	+	1.04749i
$658$	−323.498	−	560.315i	−0.0191660	−	0.0331966i
$659$	−5614.83	−	31843.3i	−0.331901	−	1.88230i	−0.455915	−	0.890023i	$-0.650688\pi$
$659$	−5614.83	−	31843.3i	−0.331901	−	1.88230i	0.124014	−	0.992280i	$-0.460423\pi$
$660$	111.078	+	93.2056i	0.00655108	+	0.00549701i
$661$	14185.2	−	11902.8i	0.834705	−	0.700401i	−0.121661	−	0.992572i	$-0.538822\pi$
$661$	14185.2	−	11902.8i	0.834705	−	0.700401i	0.956366	+	0.292171i	$0.0943776\pi$
$662$	828.753	−	4700.09i	0.0486562	−	0.275943i
$663$	97.1517	−	35.3603i	0.00569089	−	0.00207131i
$664$	−6124.88			−0.357969
$665$	16539.9	−	3659.86i	0.964495	−	0.213418i
$666$	5371.92			0.312549
$667$	−25457.7	+	9265.83i	−1.47785	+	0.537893i
$668$	456.601	−	2589.51i	0.0264467	−	0.149987i
$669$	674.483	−	565.959i	0.0389791	−	0.0327074i
$670$	−14202.3	−	11917.2i	−0.818932	−	0.687166i
$671$	1999.96	+	11342.4i	0.115064	+	0.652559i
$672$	69.6976	+	120.720i	0.00400096	+	0.00692986i
$673$	16513.0	−	28601.3i	0.945806	−	1.63818i	0.191678	−	0.981458i	$-0.438607\pi$
$673$	16513.0	−	28601.3i	0.945806	−	1.63818i	0.754129	−	0.656727i	$-0.228059\pi$
$674$	−3212.30	−	1169.18i	−0.183580	−	0.0668178i
$675$	−38.1411	−	13.8822i	−0.00217489	−	0.000791596i
$676$	−1431.77	+	2479.89i	−0.0814615	+	0.141095i
$677$	5465.42	+	9466.39i	0.310271	+	0.537404i	0.978421	−	0.206622i	$-0.0662470\pi$
$677$	5465.42	+	9466.39i	0.310271	+	0.537404i	−0.668150	+	0.744026i	$0.732914\pi$
$678$	−190.469	−	1080.20i	−0.0107890	−	0.0611873i
$679$	−23890.7	−	20046.7i	−1.35028	−	1.13302i
$680$	551.228	−	462.535i	0.0310862	−	0.0260844i
$681$	66.1905	−	375.385i	0.00372456	−	0.0211230i
$682$	−1214.37	+	441.996i	−0.0681829	+	0.0248166i
$683$	16689.0			0.934972			0.467486	−	0.884000i	$-0.345160\pi$
$683$	16689.0			0.934972			0.467486	+	0.884000i	$0.345160\pi$
$684$	−6027.79	−	6583.47i	−0.336957	−	0.368019i
$685$	−17656.4			−0.984840
$686$	−11930.1	+	4342.19i	−0.663982	+	0.241670i
$687$	162.263	−	920.242i	0.00901126	−	0.0511054i
$688$	−5730.89	+	4808.79i	−0.317570	+	0.266473i
$689$	−1832.19	−	1537.39i	−0.101308	−	0.0850073i
$690$	−110.227	−	625.126i	−0.00608153	−	0.0344900i
$691$	−11592.8	−	20079.2i	−0.638219	−	1.10543i	−0.985823	−	0.167786i	$-0.946338\pi$
$691$	−11592.8	−	20079.2i	−0.638219	−	1.10543i	0.347605	−	0.937641i	$-0.386995\pi$
$692$	328.089	−	568.268i	0.0180232	−	0.0312172i
$693$	−6558.08	−	2386.95i	−0.359482	−	0.130841i
$694$	5700.41	+	2074.78i	0.311793	+	0.113484i
$695$	−9489.82	+	16436.8i	−0.517941	+	0.897101i
$696$	208.163	+	360.548i	0.0113368	+	0.0196358i
$697$	449.480	+	2549.13i	0.0244265	+	0.138530i
$698$	3158.86	+	2650.60i	0.171296	+	0.143734i
$699$	−247.184	+	207.412i	−0.0133753	+	0.0112232i
$700$	41.2109	−	233.719i	0.00222518	−	0.0126196i
$701$	765.089	−	278.470i	0.0412225	−	0.0150038i	−0.321327	−	0.946968i	$-0.604129\pi$
$701$	765.089	−	278.470i	0.0412225	−	0.0150038i	0.362549	+	0.931965i	$0.381907\pi$
$702$	1368.60			0.0735821
$703$	3156.28	+	7628.57i	0.169333	+	0.409270i
$704$	894.409			0.0478825
$705$	42.5456	−	15.4853i	0.00227285	−	0.000827251i
$706$	2552.33	−	14475.0i	0.136060	−	0.771634i
$707$	17158.9	−	14398.1i	0.912770	−	0.765905i
$708$	459.631	+	385.676i	0.0243983	+	0.0204726i
$709$	3036.16	+	17218.9i	0.160826	+	0.912088i	0.953265	+	0.302137i	$0.0977000\pi$
$709$	3036.16	+	17218.9i	0.160826	+	0.912088i	−0.792439	+	0.609951i	$0.791189\pi$
$710$	6379.31	+	11049.3i	0.337199	+	0.584046i
$711$	4574.14	−	7922.64i	0.241271	−	0.417893i
$712$	−6823.14	−	2483.42i	−0.359140	−	0.130716i
$713$	5316.10	+	1934.90i	0.279228	+	0.101631i
$714$	35.5029	−	61.4928i	0.00186087	−	0.00322312i
$715$	4162.07	+	7208.91i	0.217696	+	0.377060i
$716$	393.715	+	2232.87i	0.0205500	+	0.116545i
$717$	898.404	+	753.850i	0.0467943	+	0.0392651i
$718$	1004.43	−	842.814i	0.0522073	−	0.0438071i
$719$	−4348.35	+	24660.7i	−0.225544	+	1.27912i	0.636099	+	0.771607i	$0.280547\pi$
$719$	−4348.35	+	24660.7i	−0.225544	+	1.27912i	−0.861643	+	0.507515i	$0.830564\pi$
$720$	4470.97	−	1627.30i	0.231421	−	0.0842303i
$721$	892.633			0.0461074
$722$	5807.43	−	12428.1i	0.299349	−	0.640617i
$723$	−324.707			−0.0167026
$724$	−4399.21	+	1601.18i	−0.225822	+	0.0821927i
$725$	123.083	−	698.036i	0.00630507	−	0.0357578i
$726$	−408.962	+	343.160i	−0.0209063	+	0.0175425i
$727$	−22177.1	−	18608.8i	−1.13137	−	0.949329i	−0.132243	−	0.991217i	$-0.542218\pi$
$727$	−22177.1	−	18608.8i	−1.13137	−	0.949329i	−0.999122	+	0.0418888i	$0.986662\pi$
$728$	1389.58	+	7880.68i	0.0707433	+	0.401205i
$729$	9720.89	+	16837.1i	0.493872	+	0.855412i
$730$	8342.83	−	14450.2i	0.422989	−	0.732639i
$731$	3580.96	+	1303.36i	0.181186	+	0.0659462i
$732$	−728.080	−	264.999i	−0.0367631	−	0.0133807i
$733$	15781.1	−	27333.6i	0.795208	−	1.37734i	−0.127499	−	0.991839i	$-0.540695\pi$
$733$	15781.1	−	27333.6i	0.795208	−	1.37734i	0.922707	−	0.385502i	$-0.125972\pi$
$734$	12301.3	+	21306.4i	0.618594	+	1.07144i
$735$	0.223289	+	1.26634i	1.12057e−5	+	6.35504e-5i
$736$	−2999.38	−	2516.78i	−0.150215	−	0.126046i
$737$	−8992.18	+	7545.33i	−0.449432	+	0.377118i
$738$	−2972.00	+	16855.1i	−0.148240	+	0.840709i
$739$	−14618.3	+	5320.64i	−0.727665	+	0.264848i	−0.679176	−	0.733975i	$-0.737663\pi$
$739$	−14618.3	+	5320.64i	−0.727665	+	0.264848i	−0.0484889	+	0.998824i	$0.515441\pi$
$740$	−4400.55			−0.218605
$741$	401.651	+	970.770i	0.0199123	+	0.0481270i
$742$	−1642.66			−0.0812720
$743$	2523.72	−	918.561i	0.124612	−	0.0453549i	−0.278962	−	0.960302i	$-0.589990\pi$
$743$	2523.72	−	918.561i	0.124612	−	0.0453549i	0.403573	+	0.914947i	$0.367768\pi$
$744$	15.0965	−	85.6167i	0.000743906	−	0.00421890i
$745$	−20120.2	+	16882.9i	−0.989460	+	0.830256i
$746$	1566.62	+	1314.55i	0.0768876	+	0.0645163i
$747$	3582.22	+	20315.8i	0.175457	+	0.995067i
$748$	−227.799	−	394.560i	−0.0111352	−	0.0192868i
$749$	8082.28	−	13998.9i	0.394286	−	0.682923i
$750$	624.981	+	227.474i	0.0304281	+	0.0110749i
$751$	30036.0	+	10932.2i	1.45942	+	0.531187i	0.945207	−	0.326473i	$-0.105860\pi$
$751$	30036.0	+	10932.2i	1.45942	+	0.531187i	0.514218	+	0.857660i	$0.328082\pi$
$752$	139.637	−	241.858i	0.00677133	−	0.0117283i
$753$	−41.1466	−	71.2681i	−0.00199132	−	0.00344907i
$754$	4150.18	+	23536.9i	0.200452	+	1.13682i
$755$	18118.0	+	15202.8i	0.873353	+	0.732830i
$756$	720.047	−	604.191i	0.0346400	−	0.0290664i
$757$	567.601	−	3219.03i	0.0272521	−	0.154554i	−0.968145	−	0.250390i	$-0.919441\pi$
$757$	567.601	−	3219.03i	0.0272521	−	0.154554i	0.995397	+	0.0958356i	$0.0305523\pi$
$758$	−2288.82	+	833.063i	−0.109675	+	0.0399185i
$759$	−401.902			−0.0192202
$760$	4937.82	+	5393.02i	0.235676	+	0.257402i
$761$	21394.1			1.01910			0.509549	−	0.860441i	$-0.329812\pi$
$761$	21394.1			1.01910			0.509549	+	0.860441i	$0.329812\pi$
$762$	−836.379	+	304.417i	−0.0397622	+	0.0144723i
$763$	1815.86	−	10298.3i	0.0861581	−	0.488627i
$764$	3975.41	−	3335.76i	0.188253	−	0.157963i
$765$	−1856.59	−	1557.86i	−0.0877452	−	0.0736270i
$766$	−3568.15	−	20236.0i	−0.168306	−	0.954512i
$767$	17222.2	+	29829.8i	0.810768	+	1.40429i
$768$	−30.0848	+	52.1084i	−0.00141353	+	0.00244831i
$769$	−9587.85	−	3489.69i	−0.449605	−	0.163643i	0.107286	−	0.994228i	$-0.465784\pi$
$769$	−9587.85	−	3489.69i	−0.449605	−	0.163643i	−0.556892	+	0.830585i	$0.688006\pi$
$770$	5372.22	+	1955.33i	0.251430	+	0.0915132i
$771$	295.078	−	511.091i	0.0137834	−	0.0238735i
$772$	3955.74	+	6851.54i	0.184417	+	0.319420i
$773$	−2203.99	−	12499.4i	−0.102551	−	0.581596i	−0.992170	−	0.124893i	$-0.960141\pi$
$773$	−2203.99	−	12499.4i	−0.102551	−	0.581596i	0.889619	−	0.456703i	$-0.150970\pi$
$774$	19302.2	+	16196.5i	0.896386	+	0.752157i
$775$	−113.385	+	95.1412i	−0.00525536	+	0.00440977i
$776$	2337.62	−	13257.3i	0.108139	−	0.613286i
$777$	−408.046	+	148.517i	−0.0188398	+	0.00685714i
$778$	29398.1			1.35472
$779$	−25681.8	+	5682.72i	−1.18119	+	0.261367i
$780$	−559.990			−0.0257062
$781$	7590.92	−	2762.87i	0.347791	−	0.126585i
$782$	−346.333	+	1964.15i	−0.0158374	+	0.0898183i
$783$	2150.53	−	1804.51i	0.0981529	−	0.0823601i
$784$	6.07594	+	5.09832i	0.000276783	+	0.000232248i
$785$	1588.38	+	9008.15i	0.0722187	+	0.409573i
$786$	535.654	+	927.779i	0.0243081	+	0.0421028i
$787$	−1256.27	+	2175.92i	−0.0569009	+	0.0985553i	−0.893073	−	0.449912i	$-0.851455\pi$
$787$	−1256.27	+	2175.92i	−0.0569009	+	0.0985553i	0.836172	+	0.548468i	$0.184789\pi$
$788$	−8777.94	−	3194.91i	−0.396829	−	0.144434i
$789$	−1037.41	−	377.586i	−0.0468095	−	0.0170373i
$790$	−3747.02	+	6490.04i	−0.168751	+	0.292285i
$791$	−21623.1	−	37452.3i	−0.971971	−	1.68350i
$792$	−523.107	−	2966.69i	−0.0234694	−	0.133102i
$793$	−34073.1	−	28590.7i	−1.52581	−	1.28031i
$794$	−3552.20	+	2980.65i	−0.158769	+	0.133223i
$795$	19.9611	−	113.205i	0.000890500	−	0.00505028i
$796$	−9790.68	+	3563.52i	−0.435957	+	0.158675i
$797$	−39544.5			−1.75751			−0.878756	−	0.477272i	$-0.841626\pi$
$797$	−39544.5			−1.75751			−0.878756	+	0.477272i	$0.841626\pi$
$798$	639.877	+	333.425i	0.0283852	+	0.0147909i
$799$	−142.258			−0.00629878
$800$	96.2624	−	35.0367i	0.00425424	−	0.00154842i
$801$	−4246.71	+	24084.3i	−0.187329	+	1.06239i
$802$	6016.82	−	5048.72i	0.264915	−	0.222290i
$803$	−8092.86	−	6790.72i	−0.355655	−	0.298430i
$804$	−137.127	−	777.684i	−0.00601503	−	0.0341129i
$805$	−12513.5	−	21674.1i	−0.547880	−	0.948956i
$806$	2495.41	−	4322.18i	0.109053	−	0.188886i
$807$	500.133	+	182.033i	0.0218160	+	0.00794037i
$808$	9085.56	+	3306.87i	0.395580	+	0.143979i
$809$	9335.13	−	16168.9i	0.405693	−	0.702681i	−0.588709	−	0.808345i	$-0.700364\pi$
$809$	9335.13	−	16168.9i	0.405693	−	0.702681i	0.994402	+	0.105664i	$0.0336969\pi$
$810$	−7996.07	−	13849.6i	−0.346856	−	0.600772i
$811$	−700.869	−	3974.82i	−0.0303463	−	0.172102i	0.965868	−	0.259035i	$-0.0834045\pi$
$811$	−700.869	−	3974.82i	−0.0303463	−	0.172102i	−0.996214	+	0.0869329i	$0.972293\pi$
$812$	12574.2	+	10551.0i	0.543433	+	0.455994i
$813$	−418.661	+	351.298i	−0.0180604	+	0.0151544i
$814$	−483.818	+	2743.87i	−0.0208327	+	0.118148i
$815$	23803.8	−	8663.87i	1.02308	−	0.372371i
$816$	30.6495			0.00131488
$817$	−11659.3	+	36926.9i	−0.499274	+	1.58129i
$818$	−5247.66			−0.224303
$819$	25326.9	−	9218.24i	1.08058	−	0.393299i
$820$	2434.59	−	13807.3i	0.103682	−	0.588013i
$821$	−6521.75	+	5472.40i	−0.277236	+	0.232629i	−0.770794	−	0.637084i	$-0.780140\pi$
$821$	−6521.75	+	5472.40i	−0.277236	+	0.232629i	0.493558	+	0.869713i	$0.335696\pi$
$822$	−576.104	−	483.409i	−0.0244452	−	0.0205120i
$823$	−3691.22	−	20934.0i	−0.156340	−	0.886649i	−0.957550	−	0.288266i	$-0.906921\pi$
$823$	−3691.22	−	20934.0i	−0.156340	−	0.886649i	0.801210	−	0.598383i	$-0.204190\pi$
$824$	192.651	+	333.682i	0.00814482	+	0.0141072i
$825$	5.25756	−	9.10636i	0.000221872	−	0.000384294i
$826$	22229.8	+	8090.97i	0.936407	+	0.340824i
$827$	−27045.2	−	9843.65i	−1.13719	−	0.413902i	−0.296291	−	0.955098i	$-0.595750\pi$
$827$	−27045.2	−	9843.65i	−1.13719	−	0.413902i	−0.840897	+	0.541195i	$0.817972\pi$
$828$	−6593.74	+	11420.7i	−0.276749	+	0.479343i
$829$	7361.77	+	12751.0i	0.308426	+	0.534209i	0.978018	−	0.208520i	$-0.0668646\pi$
$829$	7361.77	+	12751.0i	0.308426	+	0.534209i	−0.669593	+	0.742729i	$0.733531\pi$
$830$	−2934.47	−	16642.2i	−0.122719	−	0.695974i
$831$	−1126.24	−	945.028i	−0.0470143	−	0.0394497i
$832$	−2646.03	+	2220.29i	−0.110258	+	0.0925175i
$833$	0.701577	−	3.97884i	2.91815e−5	−	0.000165497i
$834$	−759.660	+	276.494i	−0.0315406	+	0.0114798i
$835$	7254.84			0.300676
$836$	3905.59	−	2485.94i	0.161576	−	0.102844i
$837$	−586.228			−0.0242091
$838$	−8126.72	+	2957.88i	−0.335003	+	0.121931i
$839$	2233.84	−	12668.8i	0.0919200	−	0.521304i	−0.903728	−	0.428108i	$-0.859180\pi$
$839$	2233.84	−	12668.8i	0.0919200	−	0.521304i	0.995648	−	0.0931965i	$-0.0297085\pi$
$840$	−294.621	+	247.216i	−0.0121016	+	0.0101545i
$841$	18871.7	+	15835.2i	0.773779	+	0.649277i
$842$	−4314.17	−	24466.9i	−0.176575	−	1.00141i
$843$	836.797	+	1449.38i	0.0341884	+	0.0592161i
$844$	−10069.9	+	17441.6i	−0.410688	+	0.711332i
$845$	−7424.20	−	2702.19i	−0.302249	−	0.110010i
$846$	−883.895	−	321.712i	−0.0359207	−	0.0130741i
$847$	−10524.3	+	18228.6i	−0.426941	+	0.739483i
$848$	−354.524	−	614.054i	−0.0143566	−	0.0248664i
$849$	272.744	+	1546.81i	0.0110254	+	0.0625281i
$850$	−39.9734	−	33.5417i	−0.00161303	−	0.00135349i
$851$	9343.44	−	7840.07i	0.376368	−	0.315810i
$852$	−94.3670	+	535.182i	−0.00379455	+	0.0215200i
$853$	−5919.51	+	2154.53i	−0.237609	+	0.0864825i	−0.458080	−	0.888911i	$-0.651463\pi$
$853$	−5919.51	+	2154.53i	−0.237609	+	0.0864825i	0.220471	+	0.975393i	$0.429240\pi$
$854$	−30548.3			−1.22405
$855$	15000.3	−	19532.6i	0.599999	−	0.781286i
$856$	6977.40			0.278601
$857$	5716.13	−	2080.50i	0.227840	−	0.0829271i	−0.225577	−	0.974225i	$-0.572427\pi$
$857$	5716.13	−	2080.50i	0.227840	−	0.0829271i	0.453418	+	0.891298i	$0.350205\pi$
$858$	−61.5680	+	349.169i	−0.00244976	+	0.0138933i
$859$	−1580.81	+	1326.45i	−0.0627897	+	0.0526869i	−0.673642	−	0.739057i	$-0.735271\pi$
$859$	−1580.81	+	1326.45i	−0.0627897	+	0.0526869i	0.610853	+	0.791744i	$0.290827\pi$
$860$	−15811.9	−	13267.7i	−0.626954	−	0.526077i
$861$	−240.238	−	1362.46i	−0.00950906	−	0.0539286i
$862$	8355.43	+	14472.0i	0.330148	+	0.571832i
$863$	−10510.3	+	18204.3i	−0.414570	+	0.718056i	−0.995383	−	0.0959810i	$-0.969401\pi$
$863$	−10510.3	+	18204.3i	−0.414570	+	0.718056i	0.580814	+	0.814037i	$0.302735\pi$
$864$	381.261	+	138.768i	0.0150124	+	0.00546408i
$865$	1701.26	+	619.206i	0.0668722	+	0.0243395i
$866$	−4621.33	+	8004.37i	−0.181338	+	0.314087i
$867$	569.563	+	986.513i	0.0223107	+	0.0386433i
$868$	−595.211	−	3375.61i	−0.0232751	−	0.132000i
$869$	3634.76	+	3049.92i	0.141888	+	0.119058i
$870$	−879.929	+	738.348i	−0.0342901	+	0.0287728i
$871$	7872.03	−	44644.5i	0.306238	−	1.73676i
$872$	4241.58	−	1543.81i	0.164723	−	0.0599541i
$873$	−45340.7			−1.75779
$874$	−20092.5	−	2653.41i	−0.777618	−	0.102692i
$875$	26222.5			1.01312
$876$	667.844	−	243.075i	0.0257584	−	0.00937529i
$877$	−2396.94	+	13593.7i	−0.0922908	+	0.523407i	0.903253	+	0.429108i	$0.141172\pi$
$877$	−2396.94	+	13593.7i	−0.0922908	+	0.523407i	−0.995544	+	0.0942991i	$0.969939\pi$
$878$	−14144.8	+	11868.9i	−0.543695	+	0.456214i
$879$	−466.334	−	391.301i	−0.0178943	−	0.0150151i
$880$	428.517	+	2430.24i	0.0164151	+	0.0930947i
$881$	−6116.29	−	10593.7i	−0.233897	−	0.405121i	0.725055	−	0.688691i	$-0.241814\pi$
$881$	−6116.29	−	10593.7i	−0.233897	−	0.405121i	−0.958951	+	0.283570i	$0.908481\pi$
$882$	13.3571	−	23.1353i	0.000509930	−	0.000883225i
$883$	42610.0	+	15508.8i	1.62394	+	0.591066i	0.984127	−	0.177464i	$-0.0567894\pi$
$883$	42610.0	+	15508.8i	1.62394	+	0.591066i	0.639813	+	0.768530i	$0.279012\pi$
$884$	1653.38	+	601.782i	0.0629064	+	0.0228961i
$885$	−827.726	+	1433.66i	−0.0314392	+	0.0544543i
$886$	−5808.71	−	10061.0i	−0.220257	−	0.381496i
$887$	2486.03	+	14099.0i	0.0941066	+	0.533705i	0.995017	+	0.0997009i	$0.0317886\pi$
$887$	2486.03	+	14099.0i	0.0941066	+	0.533705i	−0.900911	+	0.434004i	$0.857100\pi$
$888$	−143.584	−	120.481i	−0.00542609	−	0.00455303i
$889$	−26882.2	+	22556.8i	−1.01417	+	0.850993i
$890$	3478.81	−	19729.3i	0.131022	−	0.743064i
$891$	−9514.75	+	3463.09i	−0.357751	+	0.130211i
$892$	14984.4			0.562462
$893$	−62.4768	−	1444.23i	−0.00234122	−	0.0541200i
$894$	−1118.73			−0.0418522
$895$	−5878.40	+	2139.56i	−0.219545	+	0.0799080i
$896$	−411.947	+	2336.26i	−0.0153596	+	0.0871084i
$897$	1189.00	−	997.685i	0.0442580	−	0.0371368i
$898$	11981.1	+	10053.3i	0.445228	+	0.373591i
$899$	−1777.69	−	10081.8i	−0.0659502	−	0.374022i
$900$	−172.514	−	298.804i	−0.00638942	−	0.0110668i
$901$	−180.589	+	312.790i	−0.00667736	+	0.0115655i
$902$	−8341.54	−	3036.07i	−0.307919	−	0.112073i
$903$	−1913.96	−	696.623i	−0.0705343	−	0.0256724i
$904$	9333.56	−	16166.2i	0.343396	−	0.594779i
$905$	−6458.34	−	11186.2i	−0.237218	−	0.410874i
$906$	174.933	+	992.096i	0.00641475	+	0.0363799i
$907$	31050.2	+	26054.2i	1.13672	+	0.953822i	0.999327	−	0.0366943i	$-0.0116828\pi$
$907$	31050.2	+	26054.2i	1.13672	+	0.953822i	0.137394	+	0.990516i	$0.456127\pi$
$908$	4969.38	−	4169.81i	0.181624	−	0.152401i
$909$	5654.84	−	32070.2i	0.206336	−	1.17019i
$910$	−20747.2	+	7551.36i	−0.755783	+	0.275083i
$911$	43801.4			1.59298			0.796491	−	0.604651i	$-0.206687\pi$
$911$	43801.4			1.59298			0.796491	+	0.604651i	$0.206687\pi$
$912$	13.4606	+	311.158i	0.000488735	+	0.0112977i
$913$	−10699.5			−0.387844
$914$	17179.3	−	6252.76i	0.621708	−	0.226283i
$915$	371.214	−	2105.26i	0.0134120	−	0.0760631i
$916$	12182.2	−	10222.1i	0.439424	−	0.368721i
$917$	32356.5	+	27150.3i	1.16522	+	0.977735i
$918$	−35.8883	−	203.532i	−0.00129029	−	0.00731762i
$919$	−1705.21	−	2953.50i	−0.0612074	−	0.106014i	0.833798	−	0.552070i	$-0.186162\pi$
$919$	−1705.21	−	2953.50i	−0.0612074	−	0.106014i	−0.895005	+	0.446055i	$0.852828\pi$
$920$	5401.43	−	9355.55i	0.193565	−	0.335265i
$921$	−1695.72	−	617.193i	−0.0606688	−	0.0220816i
$922$	−24024.2	−	8744.09i	−0.858129	−	0.312333i
$923$	−15598.5	+	27017.5i	−0.556265	+	0.963479i
$924$	121.754	+	210.884i	0.00433487	+	0.00750821i
$925$	55.4136	+	314.266i	0.00196972	+	0.0111708i
$926$	−1347.41	−	1130.61i	−0.0478172	−	0.0401234i
$927$	994.124	−	834.169i	0.0352226	−	0.0295552i
$928$	−1230.34	+	6977.61i	−0.0435215	+	0.246823i
$929$	14420.0	−	5248.45i	0.509262	−	0.185356i	−0.0745932	−	0.997214i	$-0.523766\pi$
$929$	14420.0	−	5248.45i	0.509262	−	0.185356i	0.583855	+	0.811858i	$0.301544\pi$
$930$	239.866			0.00845754
$931$	40.7020	+	5.37510i	0.00143282	+	0.000189218i
$932$	−5491.47			−0.193003
$933$	1214.22	−	441.939i	0.0426063	−	0.0155074i
$934$	−2786.76	+	15804.5i	−0.0976290	+	0.553681i
$935$	962.936	−	807.999i	0.0336806	−	0.0282614i
$936$	8912.09	+	7478.14i	0.311219	+	0.261144i
$937$	−690.765	−	3917.53i	−0.0240836	−	0.136585i	0.970395	−	0.241523i	$-0.0776468\pi$
$937$	−690.765	−	3917.53i	−0.0240836	−	0.136585i	−0.994479	+	0.104938i	$0.966536\pi$
$938$	−15567.4	−	26963.5i	−0.541890	−	0.938581i
$939$	428.585	−	742.331i	0.0148949	−	0.0257988i
$940$	724.065	+	263.538i	0.0251238	+	0.00914433i
$941$	1271.25	+	462.695i	0.0440398	+	0.0160292i	0.363946	−	0.931420i	$-0.381429\pi$
$941$	1271.25	+	462.695i	0.0440398	+	0.0160292i	−0.319906	+	0.947449i	$0.603651\pi$
$942$	−194.805	+	337.412i	−0.00673788	+	0.0116704i
$943$	19430.0	+	33653.7i	0.670972	+	1.16216i
$944$	1773.16	+	10056.1i	0.0611351	+	0.346714i
$945$	1986.65	+	1667.00i	0.0683872	+	0.0573837i
$946$	−10011.3	+	8400.44i	−0.344074	+	0.288712i
$947$	238.780	−	1354.19i	0.00819357	−	0.0464680i	−0.980437	−	0.196834i	$-0.936934\pi$
$947$	238.780	−	1354.19i	0.00819357	−	0.0464680i	0.988630	+	0.150366i	$0.0480452\pi$
$948$	−299.949	+	109.173i	−0.0102763	+	0.00374026i
$949$	40799.4			1.39558
$950$	322.965	−	420.547i	0.0110299	−	0.0143625i
$951$	806.911			0.0275141
$952$	1135.54	−	413.303i	0.0386587	−	0.0140706i
$953$	−7954.12	+	45110.1i	−0.270366	+	1.53332i	0.482939	+	0.875654i	$0.339569\pi$
$953$	−7954.12	+	45110.1i	−0.270366	+	1.53332i	−0.753306	+	0.657671i	$0.771542\pi$
$954$	−1829.42	+	1535.07i	−0.0620857	+	0.0520961i
$955$	10968.4	+	9203.57i	0.371653	+	0.311854i
$956$	3465.86	+	19655.9i	0.117253	+	0.664975i
$957$	363.637	+	629.839i	0.0122829	+	0.0212746i
$958$	−17238.1	+	29857.2i	−0.581354	+	1.00693i
$959$	−27862.9	−	10141.3i	−0.938207	−	0.341479i
$960$	−156.000	−	56.7793i	−0.00524466	−	0.00190890i
$961$	13826.6	−	23948.4i	0.464121	−	0.803880i
$962$	−5380.06	−	9318.53i	−0.180312	−	0.312309i
$963$	−4080.82	−	23143.5i	−0.136555	−	0.774443i
$964$	−4233.20	−	3552.08i	−0.141434	−	0.118677i
$965$	−16721.4	+	14030.9i	−0.557804	+	0.468053i
$966$	185.108	−	1049.80i	0.00616538	−	0.0349656i
$967$	−23050.7	+	8389.78i	−0.766558	+	0.279004i	−0.695556	−	0.718472i	$-0.744842\pi$
$967$	−23050.7	+	8389.78i	−0.766558	+	0.279004i	−0.0710017	+	0.997476i	$0.522620\pi$
$968$	−9085.56			−0.301675
$969$	133.836	−	85.1877i	0.00443698	−	0.00282417i
$970$	37142.0			1.22944
$971$	17330.5	−	6307.78i	0.572772	−	0.208472i	−0.0393636	−	0.999225i	$-0.512533\pi$
$971$	17330.5	−	6307.78i	0.572772	−	0.208472i	0.612135	+	0.790753i	$0.290311\pi$
$972$	356.066	−	2019.35i	0.0117498	−	0.0666365i
$973$	−24416.4	+	20487.8i	−0.804474	+	0.675033i
$974$	−3419.21	−	2869.06i	−0.112483	−	0.0943845i
$975$	7.05164	+	39.9918i	0.000231624	+	0.00131360i
$976$	−6593.04	−	11419.5i	−0.216228	−	0.374517i
$977$	7804.32	−	13517.5i	0.255560	−	0.442643i	−0.709487	−	0.704718i	$-0.751073\pi$
$977$	7804.32	−	13517.5i	0.255560	−	0.442643i	0.965048	+	0.262075i	$0.0844067\pi$
$978$	1013.89	+	369.027i	0.0331500	+	0.0120656i
$979$	−11919.3	−	4338.27i	−0.389114	−	0.141626i
$980$	−10.9419	+	18.9518i	−0.000356658	+	0.000617749i
$981$	−7601.45	−	13166.1i	−0.247396	−	0.428503i
$982$	−3512.39	−	19919.8i	−0.114139	−	0.647317i
$983$	35621.0	+	29889.6i	1.15578	+	0.969816i	0.999839	−	0.0179501i	$-0.00571399\pi$
$983$	35621.0	+	29889.6i	1.15578	+	0.969816i	0.155943	+	0.987766i	$0.450158\pi$
$984$	457.463	−	383.857i	0.0148205	−	0.0124359i
$985$	4475.47	−	25381.6i	0.144772	−	0.821042i
$986$	3391.46	−	1234.39i	0.109540	−	0.0398692i
$987$	76.0341			0.00245207
$988$	−5383.26	+	17049.7i	−0.173344	+	0.549011i
$989$	57210.5			1.83942
$990$	7810.30	−	2842.72i	0.250735	−	0.0912600i
$991$	614.763	−	3486.50i	0.0197060	−	0.111758i	−0.973368	−	0.229247i	$-0.926374\pi$
$991$	614.763	−	3486.50i	0.0197060	−	0.111758i	0.993074	+	0.117489i	$0.0374846\pi$
$992$	1133.40	−	951.037i	0.0362758	−	0.0304390i
$993$	429.651	+	360.520i	0.0137307	+	0.0115214i
$994$	3720.60	+	21100.6i	0.118723	+	0.673310i
$995$	−14373.4	−	24895.4i	−0.457956	−	0.793203i
$996$	359.894	−	623.354i	0.0114495	−	0.0198311i
$997$	−10730.1	−	3905.44i	−0.340848	−	0.124059i	0.165924	−	0.986139i	$-0.446939\pi$
$997$	−10730.1	−	3905.44i	−0.340848	−	0.124059i	−0.506772	+	0.862080i	$0.669162\pi$
$998$	−3149.29	−	1146.25i	−0.0998887	−	0.0363565i
$999$	−631.948	+	1094.57i	−0.0200140	+	0.0346652i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.4.e.a.5.2	✓	12
19.2	odd	18		722.4.a.o.1.3		6
19.4	even	9	inner	38.4.e.a.23.2	yes	12
19.17	even	9		722.4.a.p.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.e.a.5.2	✓	12	1.1	even	1	trivial
38.4.e.a.23.2	yes	12	19.4	even	9	inner
722.4.a.o.1.3		6	19.2	odd	18
722.4.a.p.1.4		6	19.17	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.87939 + 0.684040i) q^{2} +(0.0408138 - 0.231467i) q^{3} +(3.06418 - 2.57115i) q^{4} +(8.45426 + 7.09396i) q^{5} +(0.0816277 + 0.462933i) q^{6} +(9.26682 + 16.0506i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(25.3198 + 9.21565i) q^{9} +O(q^{10})\)	\(q+(-1.87939 + 0.684040i) q^{2} +(0.0408138 - 0.231467i) q^{3} +(3.06418 - 2.57115i) q^{4} +(8.45426 + 7.09396i) q^{5} +(0.0816277 + 0.462933i) q^{6} +(9.26682 + 16.0506i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(25.3198 + 9.21565i) q^{9} +(-20.7414 - 7.54924i) q^{10} +(-6.98757 + 12.1028i) q^{11} +(-0.470075 - 0.814194i) q^{12} +(-9.37199 - 53.1512i) q^{13} +(-28.3952 - 23.8264i) q^{14} +(1.98707 - 1.66735i) q^{15} +(2.77837 - 15.7569i) q^{16} +(-7.65864 + 2.78752i) q^{17} -53.8895 q^{18} +(-31.6628 - 76.5275i) q^{19} +44.1450 q^{20} +(4.09339 - 1.48987i) q^{21} +(4.85351 - 27.5257i) q^{22} +(-93.7306 + 78.6493i) q^{23} +(1.44039 + 1.20863i) q^{24} +(-0.555893 - 3.15263i) q^{25} +(53.9711 + 93.4808i) q^{26} +(6.33952 - 10.9804i) q^{27} +(69.6637 + 25.3555i) q^{28} +(208.061 + 75.7281i) q^{29} +(-2.59393 + 4.49282i) q^{30} +(-23.1180 - 40.0415i) q^{31} +(5.55674 + 31.5138i) q^{32} +(2.51621 + 2.11135i) q^{33} +(12.4868 - 10.4776i) q^{34} +(-35.5183 + 201.434i) q^{35} +(101.279 - 36.8626i) q^{36} -99.6840 q^{37} +(111.855 + 122.166i) q^{38} -12.6852 q^{39} +(-82.9654 + 30.1969i) q^{40} +(55.1499 - 312.771i) q^{41} +(-6.67393 + 5.60009i) q^{42} +(-358.181 - 300.549i) q^{43} +(9.70703 + 55.0513i) q^{44} +(148.684 + 257.529i) q^{45} +(122.357 - 211.928i) q^{46} +(16.4020 + 5.96984i) q^{47} +(-3.53381 - 1.28620i) q^{48} +(-0.247862 + 0.429309i) q^{49} +(3.20126 + 5.54475i) q^{50} +(0.332639 + 1.88649i) q^{51} +(-165.377 - 138.768i) q^{52} +(33.9477 - 28.4855i) q^{53} +(-4.40338 + 24.9728i) q^{54} +(-144.932 + 52.7508i) q^{55} -148.269 q^{56} +(-19.0059 + 4.20551i) q^{57} -442.828 q^{58} +(-599.714 + 218.278i) q^{59} +(1.80173 - 10.2181i) q^{60} +(631.321 - 529.741i) q^{61} +(70.8376 + 59.4398i) q^{62} +(86.7172 + 491.798i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(297.819 - 515.838i) q^{65} +(-6.17318 - 2.24685i) q^{66} +(789.297 + 287.281i) q^{67} +(-16.3003 + 28.2330i) q^{68} +(14.3792 + 24.9055i) q^{69} +(-71.0366 - 402.869i) q^{70} +(-442.799 - 371.552i) q^{71} +(-165.127 + 138.558i) q^{72} +(-131.269 + 744.464i) q^{73} +(187.345 - 68.1878i) q^{74} -0.752416 q^{75} +(-293.784 - 153.084i) q^{76} -259.010 q^{77} +(23.8405 - 8.67721i) q^{78} +(58.9570 - 334.362i) q^{79} +(135.268 - 113.503i) q^{80} +(555.021 + 465.718i) q^{81} +(110.300 + 625.541i) q^{82} +(382.805 + 663.037i) q^{83} +(8.71220 - 15.0900i) q^{84} +(-84.5227 - 30.7637i) q^{85} +(878.748 + 319.838i) q^{86} +(26.0203 - 45.0685i) q^{87} +(-55.9006 - 96.8226i) q^{88} +(157.608 + 893.840i) q^{89} +(-455.596 - 382.290i) q^{90} +(766.260 - 642.969i) q^{91} +(-84.9880 + 481.991i) q^{92} +(-10.2118 + 3.71680i) q^{93} -34.9093 q^{94} +(275.198 - 871.598i) q^{95} +7.52120 q^{96} +(-1581.25 + 575.527i) q^{97} +(0.172163 - 0.976385i) q^{98} +(-288.459 + 242.046i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 9 q^{3} - 18 q^{6} + 21 q^{7} - 48 q^{8} - 27 q^{9}+O(q^{10}) \) 12 * q - 9 * q^3 - 18 * q^6 + 21 * q^7 - 48 * q^8 - 27 * q^9	\( 12 q - 9 q^{3} - 18 q^{6} + 21 q^{7} - 48 q^{8} - 27 q^{9} - 9 q^{11} + 36 q^{12} + 39 q^{13} - 138 q^{14} + 423 q^{15} + 69 q^{17} + 132 q^{18} - 462 q^{19} - 216 q^{20} - 279 q^{21} + 204 q^{22} - 66 q^{23} - 72 q^{24} + 342 q^{25} + 48 q^{26} + 189 q^{27} + 192 q^{28} + 159 q^{29} + 72 q^{31} - 1560 q^{33} + 408 q^{34} - 135 q^{35} - 108 q^{36} + 1116 q^{37} - 294 q^{38} - 1248 q^{39} + 147 q^{41} + 414 q^{42} - 117 q^{43} + 408 q^{44} + 1296 q^{45} + 528 q^{46} + 783 q^{47} + 288 q^{48} + 1413 q^{49} - 354 q^{50} - 2301 q^{51} - 348 q^{52} - 249 q^{53} - 540 q^{54} + 2187 q^{55} - 336 q^{56} - 2670 q^{57} - 1932 q^{58} - 4248 q^{59} + 324 q^{60} + 3114 q^{61} - 438 q^{62} + 363 q^{63} - 384 q^{64} + 495 q^{65} + 822 q^{66} + 3060 q^{67} + 408 q^{68} - 237 q^{69} - 270 q^{70} + 1686 q^{71} + 432 q^{72} + 1626 q^{73} + 90 q^{74} - 1854 q^{75} - 1416 q^{77} - 108 q^{78} - 327 q^{79} + 3483 q^{81} + 294 q^{82} + 927 q^{83} + 204 q^{84} - 3294 q^{85} + 1188 q^{86} + 2892 q^{87} - 72 q^{88} - 6366 q^{89} - 5076 q^{90} + 840 q^{91} - 156 q^{92} + 870 q^{93} + 3432 q^{94} + 513 q^{95} - 576 q^{96} - 8052 q^{97} + 378 q^{98} + 4494 q^{99}+O(q^{100}) \) 12 * q - 9 * q^3 - 18 * q^6 + 21 * q^7 - 48 * q^8 - 27 * q^9 - 9 * q^11 + 36 * q^12 + 39 * q^13 - 138 * q^14 + 423 * q^15 + 69 * q^17 + 132 * q^18 - 462 * q^19 - 216 * q^20 - 279 * q^21 + 204 * q^22 - 66 * q^23 - 72 * q^24 + 342 * q^25 + 48 * q^26 + 189 * q^27 + 192 * q^28 + 159 * q^29 + 72 * q^31 - 1560 * q^33 + 408 * q^34 - 135 * q^35 - 108 * q^36 + 1116 * q^37 - 294 * q^38 - 1248 * q^39 + 147 * q^41 + 414 * q^42 - 117 * q^43 + 408 * q^44 + 1296 * q^45 + 528 * q^46 + 783 * q^47 + 288 * q^48 + 1413 * q^49 - 354 * q^50 - 2301 * q^51 - 348 * q^52 - 249 * q^53 - 540 * q^54 + 2187 * q^55 - 336 * q^56 - 2670 * q^57 - 1932 * q^58 - 4248 * q^59 + 324 * q^60 + 3114 * q^61 - 438 * q^62 + 363 * q^63 - 384 * q^64 + 495 * q^65 + 822 * q^66 + 3060 * q^67 + 408 * q^68 - 237 * q^69 - 270 * q^70 + 1686 * q^71 + 432 * q^72 + 1626 * q^73 + 90 * q^74 - 1854 * q^75 - 1416 * q^77 - 108 * q^78 - 327 * q^79 + 3483 * q^81 + 294 * q^82 + 927 * q^83 + 204 * q^84 - 3294 * q^85 + 1188 * q^86 + 2892 * q^87 - 72 * q^88 - 6366 * q^89 - 5076 * q^90 + 840 * q^91 - 156 * q^92 + 870 * q^93 + 3432 * q^94 + 513 * q^95 - 576 * q^96 - 8052 * q^97 + 378 * q^98 + 4494 * q^99

Introduction

L-functions

Modular forms

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