LMFDB - Embedded newform 50.3.f.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,3,Mod(3,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("50.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	50.f (of order $20$, degree $8$, 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:	$1.36240132180$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 30x^{14} + 351x^{12} + 2130x^{10} + 7341x^{8} + 14480x^{6} + 15196x^{4} + 6560x^{2} + 16 $ x^16 + 30x^14 + 351x^12 + 2130x^10 + 7341x^8 + 14480x^6 + 15196x^4 + 6560*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			17.1
Root			$-2.26402i$ of defining polynomial
Character	$\chi$	$=$	50.17
Dual form			50.3.f.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642040 + 1.26007i) q^{2} +(-0.711697 + 4.49348i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(-4.53886 - 2.09733i) q^{5} +(-5.20517 - 3.78178i) q^{6} +(3.58690 + 3.58690i) q^{7} +(2.79360 - 0.442463i) q^{8} +(-11.1253 - 3.61484i) q^{9} +O(q^{10})$	\(q+(-0.642040 + 1.26007i) q^{2} +(-0.711697 + 4.49348i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(-4.53886 - 2.09733i) q^{5} +(-5.20517 - 3.78178i) q^{6} +(3.58690 + 3.58690i) q^{7} +(2.79360 - 0.442463i) q^{8} +(-11.1253 - 3.61484i) q^{9} +(5.55691 - 4.37272i) q^{10} +(3.53728 + 10.8866i) q^{11} +(8.10725 - 4.13085i) q^{12} +(10.0537 + 19.7315i) q^{13} +(-6.82270 + 2.21683i) q^{14} +(12.6546 - 18.9026i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(-3.10698 - 19.6167i) q^{17} +(11.6979 - 11.6979i) q^{18} +(15.8404 - 21.8024i) q^{19} +(1.94220 + 9.80958i) q^{20} +(-18.6705 + 13.5649i) q^{21} +(-15.9890 - 2.53241i) q^{22} +(-0.476846 - 0.242965i) q^{23} +12.8679i q^{24} +(16.2024 + 19.0389i) q^{25} -31.3180 q^{26} +(5.57222 - 10.9361i) q^{27} +(1.58707 - 10.0204i) q^{28} +(-3.67470 - 5.05779i) q^{29} +(15.6939 + 28.0819i) q^{30} +(5.42369 + 3.94054i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-51.4362 + 8.14670i) q^{33} +(26.7133 + 8.67968i) q^{34} +(-8.75753 - 23.8034i) q^{35} +(7.22967 + 22.2506i) q^{36} +(-5.24626 + 2.67310i) q^{37} +(17.3025 + 33.9580i) q^{38} +(-95.8181 + 31.1332i) q^{39} +(-13.6078 - 3.85083i) q^{40} +(7.33457 - 22.5735i) q^{41} +(-5.10558 - 32.2354i) q^{42} +(44.7386 - 44.7386i) q^{43} +(13.4566 - 18.5214i) q^{44} +(42.9147 + 39.7407i) q^{45} +(0.612308 - 0.444868i) q^{46} +(-27.2676 - 4.31877i) q^{47} +(-16.2145 - 8.26170i) q^{48} -23.2682i q^{49} +(-34.3931 + 8.19249i) q^{50} +90.3585 q^{51} +(20.1074 - 39.4630i) q^{52} +(-13.6315 + 86.0658i) q^{53} +(10.2027 + 14.0428i) q^{54} +(6.77762 - 56.8316i) q^{55} +(11.6075 + 8.43332i) q^{56} +(86.6950 + 86.6950i) q^{57} +(8.73248 - 1.38309i) q^{58} +(20.7422 + 6.73954i) q^{59} +(-45.4614 + 1.74577i) q^{60} +(-21.3293 - 65.6449i) q^{61} +(-8.44760 + 4.30427i) q^{62} +(-26.9394 - 52.8715i) q^{63} +(7.60845 - 2.47214i) q^{64} +(-4.24886 - 110.644i) q^{65} +(22.7587 - 70.0439i) q^{66} +(14.4421 + 91.1840i) q^{67} +(-28.0880 + 28.0880i) q^{68} +(1.43113 - 1.96978i) q^{69} +(35.6167 + 4.24757i) q^{70} +(12.7283 - 9.24768i) q^{71} +(-32.6792 - 5.17587i) q^{72} +(-60.4466 - 30.7991i) q^{73} -8.32691i q^{74} +(-97.0823 + 59.2553i) q^{75} -53.8984 q^{76} +(-26.3614 + 51.7371i) q^{77} +(22.2889 - 140.727i) q^{78} +(71.8966 + 98.9571i) q^{79} +(13.5890 - 14.6744i) q^{80} +(-39.9985 - 29.0606i) q^{81} +(23.7352 + 23.7352i) q^{82} +(60.8973 - 9.64518i) q^{83} +(43.8969 + 14.2630i) q^{84} +(-27.0406 + 95.5539i) q^{85} +(27.6500 + 85.0979i) q^{86} +(25.3423 - 12.9126i) q^{87} +(14.6987 + 28.8478i) q^{88} +(75.7710 - 24.6195i) q^{89} +(-77.6291 + 28.5606i) q^{90} +(-34.7133 + 106.837i) q^{91} +(0.167440 + 1.05718i) q^{92} +(-21.5668 + 21.5668i) q^{93} +(22.9488 - 31.5864i) q^{94} +(-117.624 + 65.7354i) q^{95} +(20.8207 - 15.1271i) q^{96} +(-134.309 - 21.2725i) q^{97} +(29.3197 + 14.9391i) q^{98} -133.904i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} - 40 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 - 40 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} - 40 q^{9} + 10 q^{10} + 32 q^{11} + 4 q^{12} - 8 q^{13} - 30 q^{14} + 16 q^{16} - 62 q^{17} - 16 q^{18} + 30 q^{19} - 20 q^{20} - 68 q^{21} - 48 q^{22} - 18 q^{23} + 70 q^{25} - 56 q^{26} - 40 q^{27} + 44 q^{28} + 100 q^{29} + 120 q^{30} + 132 q^{31} - 64 q^{32} - 36 q^{33} + 100 q^{34} + 150 q^{35} + 48 q^{36} + 138 q^{37} + 20 q^{38} - 320 q^{39} - 88 q^{41} - 8 q^{42} - 78 q^{43} + 40 q^{44} - 20 q^{45} - 26 q^{46} - 22 q^{47} - 8 q^{48} - 20 q^{50} - 168 q^{51} - 16 q^{52} + 182 q^{53} + 80 q^{54} + 280 q^{55} + 48 q^{56} + 280 q^{57} - 120 q^{58} - 350 q^{59} - 140 q^{60} + 372 q^{61} - 158 q^{62} + 22 q^{63} - 910 q^{65} - 202 q^{66} - 112 q^{67} - 196 q^{68} - 30 q^{69} - 20 q^{70} + 122 q^{71} - 132 q^{72} - 248 q^{73} - 80 q^{75} + 40 q^{76} + 16 q^{77} + 438 q^{78} + 760 q^{79} + 80 q^{80} - 144 q^{81} + 352 q^{82} + 132 q^{83} - 20 q^{84} - 30 q^{85} + 264 q^{86} + 770 q^{87} + 116 q^{88} + 550 q^{89} - 140 q^{90} - 798 q^{91} + 384 q^{92} + 54 q^{93} + 190 q^{94} + 40 q^{95} - 16 q^{96} - 292 q^{97} - 24 q^{98}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 - 40 * q^9 + 10 * q^10 + 32 * q^11 + 4 * q^12 - 8 * q^13 - 30 * q^14 + 16 * q^16 - 62 * q^17 - 16 * q^18 + 30 * q^19 - 20 * q^20 - 68 * q^21 - 48 * q^22 - 18 * q^23 + 70 * q^25 - 56 * q^26 - 40 * q^27 + 44 * q^28 + 100 * q^29 + 120 * q^30 + 132 * q^31 - 64 * q^32 - 36 * q^33 + 100 * q^34 + 150 * q^35 + 48 * q^36 + 138 * q^37 + 20 * q^38 - 320 * q^39 - 88 * q^41 - 8 * q^42 - 78 * q^43 + 40 * q^44 - 20 * q^45 - 26 * q^46 - 22 * q^47 - 8 * q^48 - 20 * q^50 - 168 * q^51 - 16 * q^52 + 182 * q^53 + 80 * q^54 + 280 * q^55 + 48 * q^56 + 280 * q^57 - 120 * q^58 - 350 * q^59 - 140 * q^60 + 372 * q^61 - 158 * q^62 + 22 * q^63 - 910 * q^65 - 202 * q^66 - 112 * q^67 - 196 * q^68 - 30 * q^69 - 20 * q^70 + 122 * q^71 - 132 * q^72 - 248 * q^73 - 80 * q^75 + 40 * q^76 + 16 * q^77 + 438 * q^78 + 760 * q^79 + 80 * q^80 - 144 * q^81 + 352 * q^82 + 132 * q^83 - 20 * q^84 - 30 * q^85 + 264 * q^86 + 770 * q^87 + 116 * q^88 + 550 * q^89 - 140 * q^90 - 798 * q^91 + 384 * q^92 + 54 * q^93 + 190 * q^94 + 40 * q^95 - 16 * q^96 - 292 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{13}{20}\right)$

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 $

$2$	−0.642040	+	1.26007i	−0.321020	+	0.630037i
$2$	−0.642040	+	1.26007i	−0.321020	+	0.630037i
$3$	−0.711697	+	4.49348i	−0.237232	+	1.49783i	0.525323	+	0.850903i	$0.323945\pi$
$3$	−0.711697	+	4.49348i	−0.237232	+	1.49783i	−0.762555	+	0.646923i	$0.776055\pi$
$4$	−1.17557	−	1.61803i	−0.293893	−	0.404508i
$5$	−4.53886	−	2.09733i	−0.907771	−	0.419466i
$5$	−4.53886	−	2.09733i	−0.907771	−	0.419466i
$6$	−5.20517	−	3.78178i	−0.867529	−	0.630297i
$7$	3.58690	+	3.58690i	0.512415	+	0.512415i	0.915266	−	0.402851i	$-0.131981\pi$
$7$	3.58690	+	3.58690i	0.512415	+	0.512415i	−0.402851	+	0.915266i	$0.631981\pi$
$8$	2.79360	−	0.442463i	0.349201	−	0.0553079i
$9$	−11.1253	−	3.61484i	−1.23615	−	0.401648i
$10$	5.55691	−	4.37272i	0.555691	−	0.437272i
$11$	3.53728	+	10.8866i	0.321571	+	0.989692i	0.972965	+	0.230953i	$0.0741844\pi$
$11$	3.53728	+	10.8866i	0.321571	+	0.989692i	−0.651394	+	0.758739i	$0.725816\pi$
$12$	8.10725	−	4.13085i	0.675604	−	0.344238i
$13$	10.0537	+	19.7315i	0.773361	+	1.51781i	0.853541	+	0.521025i	$0.174450\pi$
$13$	10.0537	+	19.7315i	0.773361	+	1.51781i	−0.0801805	+	0.996780i	$0.525550\pi$
$14$	−6.82270	+	2.21683i	−0.487336	+	0.158345i
$15$	12.6546	−	18.9026i	0.843639	−	1.26017i
$16$	−1.23607	+	3.80423i	−0.0772542	+	0.237764i
$17$	−3.10698	−	19.6167i	−0.182764	−	1.15392i	−0.893032	−	0.449994i	$-0.851426\pi$
$17$	−3.10698	−	19.6167i	−0.182764	−	1.15392i	0.710268	−	0.703931i	$-0.248574\pi$
$18$	11.6979	−	11.6979i	0.649881	−	0.649881i
$19$	15.8404	−	21.8024i	0.833703	−	1.14749i	−0.153520	−	0.988146i	$-0.549061\pi$
$19$	15.8404	−	21.8024i	0.833703	−	1.14749i	0.987222	−	0.159348i	$-0.0509392\pi$
$20$	1.94220	+	9.80958i	0.0971098	+	0.490479i
$21$	−18.6705	+	13.5649i	−0.889070	+	0.645947i
$22$	−15.9890	−	2.53241i	−0.726773	−	0.115110i
$23$	−0.476846	−	0.242965i	−0.0207324	−	0.0105637i	0.443594	−	0.896228i	$-0.353703\pi$
$23$	−0.476846	−	0.242965i	−0.0207324	−	0.0105637i	−0.464326	+	0.885664i	$0.653703\pi$
$24$			12.8679i			0.536162i
$25$	16.2024	+	19.0389i	0.648097	+	0.761558i
$26$	−31.3180			−1.20454
$27$	5.57222	−	10.9361i	0.206378	−	0.405041i
$28$	1.58707	−	10.0204i	0.0566812	−	0.357871i
$29$	−3.67470	−	5.05779i	−0.126714	−	0.174406i	0.740947	−	0.671564i	$-0.234377\pi$
$29$	−3.67470	−	5.05779i	−0.126714	−	0.174406i	−0.867660	+	0.497157i	$0.834377\pi$
$30$	15.6939	+	28.0819i	0.523130	+	0.936064i
$31$	5.42369	+	3.94054i	0.174958	+	0.127114i	0.671818	−	0.740716i	$-0.265514\pi$
$31$	5.42369	+	3.94054i	0.174958	+	0.127114i	−0.496860	+	0.867831i	$0.665514\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−51.4362	+	8.14670i	−1.55867	+	0.246870i
$34$	26.7133	+	8.67968i	0.785686	+	0.255285i
$35$	−8.75753	−	23.8034i	−0.250215	−	0.680096i
$36$	7.22967	+	22.2506i	0.200824	+	0.618073i
$37$	−5.24626	+	2.67310i	−0.141791	+	0.0722460i	−0.523446	−	0.852059i	$-0.675354\pi$
$37$	−5.24626	+	2.67310i	−0.141791	+	0.0722460i	0.381656	+	0.924305i	$0.375354\pi$
$38$	17.3025	+	33.9580i	0.455328	+	0.893632i
$39$	−95.8181	+	31.1332i	−2.45688	+	0.798287i
$40$	−13.6078	−	3.85083i	−0.340194	−	0.0962707i
$41$	7.33457	−	22.5735i	0.178892	−	0.550573i	−0.820898	−	0.571075i	$-0.806526\pi$
$41$	7.33457	−	22.5735i	0.178892	−	0.550573i	0.999790	+	0.0205022i	$0.00652650\pi$
$42$	−5.10558	−	32.2354i	−0.121561	−	0.767508i
$43$	44.7386	−	44.7386i	1.04043	−	1.04043i	0.0412854	−	0.999147i	$-0.486855\pi$
$43$	44.7386	−	44.7386i	1.04043	−	1.04043i	0.999147	−	0.0412854i	$-0.0131453\pi$
$44$	13.4566	−	18.5214i	0.305832	−	0.420941i
$45$	42.9147	+	39.7407i	0.953661	+	0.883126i
$46$	0.612308	−	0.444868i	0.0133110	−	0.00967104i
$47$	−27.2676	−	4.31877i	−0.580162	−	0.0918886i	−0.140545	−	0.990074i	$-0.544886\pi$
$47$	−27.2676	−	4.31877i	−0.580162	−	0.0918886i	−0.439616	+	0.898186i	$0.644886\pi$
$48$	−16.2145	−	8.26170i	−0.337802	−	0.172119i
$49$		−	23.2682i		−	0.474862i
$50$	−34.3931	+	8.19249i	−0.687861	+	0.163850i
$51$	90.3585			1.77174
$52$	20.1074	−	39.4630i	0.386680	−	0.758903i
$53$	−13.6315	+	86.0658i	−0.257198	+	1.62388i	0.433788	+	0.901015i	$0.357177\pi$
$53$	−13.6315	+	86.0658i	−0.257198	+	1.62388i	−0.690986	+	0.722868i	$0.742823\pi$
$54$	10.2027	+	14.0428i	0.188939	+	0.260052i
$55$	6.77762	−	56.8316i	0.123230	−	1.03330i
$56$	11.6075	+	8.43332i	0.207276	+	0.150595i
$57$	86.6950	+	86.6950i	1.52096	+	1.52096i
$58$	8.73248	−	1.38309i	0.150560	−	0.0238464i
$59$	20.7422	+	6.73954i	0.351562	+	0.114229i	0.479474	−	0.877556i	$-0.340827\pi$
$59$	20.7422	+	6.73954i	0.351562	+	0.114229i	−0.127912	+	0.991786i	$0.540827\pi$
$60$	−45.4614	+	1.74577i	−0.757690	+	0.0290961i
$61$	−21.3293	−	65.6449i	−0.349661	−	1.07615i	−0.959041	−	0.283267i	$-0.908582\pi$
$61$	−21.3293	−	65.6449i	−0.349661	−	1.07615i	0.609380	−	0.792878i	$-0.291418\pi$
$62$	−8.44760	+	4.30427i	−0.136252	+	0.0694237i
$63$	−26.9394	−	52.8715i	−0.427609	−	0.839231i
$64$	7.60845	−	2.47214i	0.118882	−	0.0386271i
$65$	−4.24886	−	110.644i	−0.0653671	−	1.70222i
$66$	22.7587	−	70.0439i	0.344828	−	1.06127i
$67$	14.4421	+	91.1840i	0.215554	+	1.36096i	0.823653	+	0.567094i	$0.191932\pi$
$67$	14.4421	+	91.1840i	0.215554	+	1.36096i	−0.608099	+	0.793861i	$0.708068\pi$
$68$	−28.0880	+	28.0880i	−0.413060	+	0.413060i
$69$	1.43113	−	1.96978i	0.0207410	−	0.0285475i
$70$	35.6167	+	4.24757i	0.508809	+	0.0606796i
$71$	12.7283	−	9.24768i	0.179272	−	0.130249i	−0.494530	−	0.869161i	$-0.664660\pi$
$71$	12.7283	−	9.24768i	0.179272	−	0.130249i	0.673803	+	0.738911i	$0.264660\pi$
$72$	−32.6792	−	5.17587i	−0.453878	−	0.0718871i
$73$	−60.4466	−	30.7991i	−0.828036	−	0.421905i	−0.0120152	−	0.999928i	$-0.503825\pi$
$73$	−60.4466	−	30.7991i	−0.828036	−	0.421905i	−0.816021	+	0.578022i	$0.803825\pi$
$74$		−	8.32691i		−	0.112526i
$75$	−97.0823	+	59.2553i	−1.29443	+	0.790071i
$76$	−53.8984			−0.709190
$77$	−26.3614	+	51.7371i	−0.342356	+	0.671911i
$78$	22.2889	−	140.727i	0.285755	−	1.80419i
$79$	71.8966	+	98.9571i	0.910083	+	1.25262i	0.967138	+	0.254251i	$0.0818289\pi$
$79$	71.8966	+	98.9571i	0.910083	+	1.25262i	−0.0570551	+	0.998371i	$0.518171\pi$
$80$	13.5890	−	14.6744i	0.169863	−	0.183430i
$81$	−39.9985	−	29.0606i	−0.493809	−	0.358773i
$82$	23.7352	+	23.7352i	0.289453	+	0.289453i
$83$	60.8973	−	9.64518i	0.733702	−	0.116207i	0.221607	−	0.975136i	$-0.428870\pi$
$83$	60.8973	−	9.64518i	0.733702	−	0.116207i	0.512095	+	0.858929i	$0.328870\pi$
$84$	43.8969	+	14.2630i	0.522582	+	0.169797i
$85$	−27.0406	+	95.5539i	−0.318124	+	1.12416i
$86$	27.6500	+	85.0979i	0.321511	+	0.989510i
$87$	25.3423	−	12.9126i	0.291291	−	0.148420i
$88$	14.6987	+	28.8478i	0.167030	+	0.327816i
$89$	75.7710	−	24.6195i	0.851359	−	0.276623i	0.149344	−	0.988785i	$-0.452284\pi$
$89$	75.7710	−	24.6195i	0.851359	−	0.276623i	0.702015	+	0.712162i	$0.252284\pi$
$90$	−77.6291	+	28.5606i	−0.862546	+	0.317340i
$91$	−34.7133	+	106.837i	−0.381465	+	1.17403i
$92$	0.167440	+	1.05718i	0.00182000	+	0.0114910i
$93$	−21.5668	+	21.5668i	−0.231901	+	0.231901i
$94$	22.9488	−	31.5864i	0.244137	−	0.336025i
$95$	−117.624	+	65.7354i	−1.23815	+	0.691952i
$96$	20.8207	−	15.1271i	0.216882	−	0.157574i
$97$	−134.309	−	21.2725i	−1.38463	−	0.219304i	−0.580743	−	0.814087i	$-0.697238\pi$
$97$	−134.309	−	21.2725i	−1.38463	−	0.219304i	−0.803886	+	0.594783i	$0.797238\pi$
$98$	29.3197	+	14.9391i	0.299180	+	0.152440i
$99$		−	133.904i		−	1.35256i
$100$	11.7586	−	48.5977i	0.117586	−	0.485977i
$101$	60.2160			0.596198			0.298099	−	0.954535i	$-0.403648\pi$
$101$	60.2160			0.596198			0.298099	+	0.954535i	$0.403648\pi$
$102$	−58.0138	+	113.858i	−0.568762	+	1.11626i
$103$	11.2435	−	70.9888i	0.109160	−	0.689211i	−0.871041	−	0.491210i	$-0.836555\pi$
$103$	11.2435	−	70.9888i	0.109160	−	0.689211i	0.980202	−	0.198002i	$-0.0634452\pi$
$104$	36.8165	+	50.6735i	0.354005	+	0.487246i
$105$	113.193	−	22.4110i	1.07802	−	0.213438i
$106$	−99.6973	−	72.4343i	−0.940540	−	0.683342i
$107$	−9.22591	−	9.22591i	−0.0862234	−	0.0862234i	0.662680	−	0.748903i	$-0.269419\pi$
$107$	−9.22591	−	9.22591i	−0.0862234	−	0.0862234i	−0.748903	+	0.662680i	$0.769419\pi$
$108$	−24.2455	+	3.84011i	−0.224495	+	0.0355566i
$109$	4.89779	+	1.59139i	0.0449339	+	0.0145999i	0.331398	−	0.943491i	$-0.392480\pi$
$109$	4.89779	+	1.59139i	0.0449339	+	0.0145999i	−0.286464	+	0.958091i	$0.592480\pi$
$110$	67.2605	+	45.0284i	0.611459	+	0.409349i
$111$	−8.27778	−	25.4764i	−0.0745746	−	0.229517i
$112$	−18.0791	+	9.21174i	−0.161420	+	0.0822477i
$113$	−47.9858	−	94.1774i	−0.424653	−	0.833428i	−0.999881	−	0.0154352i	$-0.995087\pi$
$113$	−47.9858	−	94.1774i	−0.424653	−	0.833428i	0.575228	−	0.817993i	$-0.304913\pi$
$114$	−164.904	+	53.5804i	−1.44652	+	0.470004i
$115$	1.65476	+	2.10289i	0.0143892	+	0.0182860i
$116$	−3.86380	+	11.8916i	−0.0333087	+	0.102514i
$117$	−40.5245	−	255.861i	−0.346363	−	2.18685i
$118$	−21.8096	+	21.8096i	−0.184827	+	0.184827i
$119$	59.2189	−	81.5078i	0.497638	−	0.684939i
$120$	26.9882	−	58.4055i	0.224902	−	0.486713i
$121$	−8.11501	+	5.89590i	−0.0670662	+	0.0487265i
$122$	96.4116	+	15.2701i	0.790259	+	0.125165i
$123$	96.2135	+	49.0232i	0.782223	+	0.398563i
$124$		−	13.4081i		−	0.108130i
$125$	−33.6096	−	120.397i	−0.268877	−	0.963175i
$126$	83.9182			0.666017
$127$	−27.8658	+	54.6898i	−0.219416	+	0.430628i	−0.974308	−	0.225221i	$-0.927689\pi$
$127$	−27.8658	+	54.6898i	−0.219416	+	0.430628i	0.754892	+	0.655850i	$0.227689\pi$
$128$	−1.76985	+	11.1744i	−0.0138270	+	0.0873001i
$129$	169.192	+	232.872i	1.31156	+	1.80521i
$130$	142.148	+	65.6841i	1.09344	+	0.505262i
$131$	58.9504	+	42.8300i	0.450003	+	0.326947i	0.789597	−	0.613626i	$-0.210290\pi$
$131$	58.9504	+	42.8300i	0.450003	+	0.326947i	−0.339594	+	0.940572i	$0.610290\pi$
$132$	73.6486	+	73.6486i	0.557944	+	0.557944i
$133$	135.021	−	21.3852i	1.01519	−	0.160791i
$134$	−124.171	−	40.3456i	−0.926649	−	0.301087i
$135$	−48.2281	+	37.9506i	−0.357245	+	0.281115i
$136$	−17.3594	−	53.4266i	−0.127642	−	0.392843i
$137$	140.901	−	71.7926i	1.02847	−	0.524033i	0.143488	−	0.989652i	$-0.454168\pi$
$137$	140.901	−	71.7926i	1.02847	−	0.524033i	0.884985	+	0.465619i	$0.154168\pi$
$138$	1.56323	+	3.06800i	0.0113277	+	0.0222319i
$139$	−112.170	+	36.4463i	−0.806981	+	0.262204i	−0.683318	−	0.730120i	$-0.739464\pi$
$139$	−112.170	+	36.4463i	−0.806981	+	0.262204i	−0.123662	+	0.992324i	$0.539464\pi$
$140$	−28.2196	+	42.1525i	−0.201568	+	0.301089i
$141$	38.8126	−	119.453i	0.275266	−	0.847183i
$142$	3.48066	+	21.9760i	0.0245117	+	0.154761i
$143$	−179.246	+	179.246i	−1.25347	+	1.25347i
$144$	27.5033	−	37.8551i	0.190995	−	0.262882i
$145$	6.07108	+	30.6636i	0.0418695	+	0.211473i
$146$	77.6183	−	56.3930i	0.531632	−	0.386253i
$147$	104.555	+	16.5599i	0.711260	+	0.112653i
$148$	10.4925	+	5.34620i	0.0708954	+	0.0361230i
$149$		−	127.548i		−	0.856024i	−0.903773	−	0.428012i	$-0.859214\pi$
$149$		−	127.548i		−	0.856024i	0.903773	−	0.428012i	$-0.140786\pi$
$150$	−12.3354	−	160.375i	−0.0822357	−	1.06917i
$151$	−89.8058			−0.594741			−0.297370	−	0.954762i	$-0.596110\pi$
$151$	−89.8058			−0.594741			−0.297370	+	0.954762i	$0.596110\pi$
$152$	34.6049	−	67.9160i	0.227664	−	0.446816i
$153$	−36.3450	+	229.474i	−0.237549	+	1.49983i
$154$	−48.2675	−	66.4346i	−0.313426	−	0.431393i
$155$	−16.3528	−	29.2608i	−0.105502	−	0.188780i
$156$	163.016	+	118.438i	1.04497	+	0.759216i
$157$	−58.6460	−	58.6460i	−0.373541	−	0.373541i	0.495224	−	0.868765i	$-0.335086\pi$
$157$	−58.6460	−	58.6460i	−0.373541	−	0.373541i	−0.868765	+	0.495224i	$0.835086\pi$
$158$	−170.854	+	27.0606i	−1.08135	+	0.171269i
$159$	−377.033	−	122.506i	−2.37128	−	0.770475i
$160$	9.76611	+	26.5447i	0.0610382	+	0.165905i
$161$	−0.838909	−	2.58190i	−0.00521061	−	0.0160366i
$162$	62.2991	−	31.7430i	0.384563	−	0.195944i
$163$	−86.5547	−	169.873i	−0.531011	−	1.04217i	−0.988253	−	0.152825i	$-0.951163\pi$
$163$	−86.5547	−	169.873i	−0.531011	−	1.04217i	0.457243	−	0.889342i	$-0.348837\pi$
$164$	−45.1470	+	14.6691i	−0.275286	+	0.0894460i
$165$	250.548	+	70.9020i	1.51847	+	0.429709i
$166$	−26.9448	+	82.9276i	−0.162318	+	0.499564i
$167$	−20.9891	−	132.520i	−0.125683	−	0.793532i	−0.967333	−	0.253509i	$-0.918415\pi$
$167$	−20.9891	−	132.520i	−0.125683	−	0.793532i	0.841650	−	0.540024i	$-0.181585\pi$
$168$	−46.1559	+	46.1559i	−0.274738	+	0.274738i
$169$	−188.919	+	260.024i	−1.11786	+	1.53861i
$170$	−103.044	−	95.4224i	−0.606140	−	0.561309i
$171$	−255.041	+	185.298i	−1.49147	+	1.08362i
$172$	−124.982	−	19.7952i	−0.726639	−	0.115088i
$173$	111.098	+	56.6075i	0.642187	+	0.327211i	0.744580	−	0.667533i	$-0.232650\pi$
$173$	111.098	+	56.6075i	0.642187	+	0.327211i	−0.102393	+	0.994744i	$0.532650\pi$
$174$			40.2236i			0.231170i
$175$	−10.1743	+	126.407i	−0.0581389	+	0.722328i
$176$	−45.7875			−0.260156
$177$	−45.0461	+	88.4080i	−0.254498	+	0.499480i
$178$	−17.6256	+	111.284i	−0.0990203	+	0.625189i
$179$	103.351	+	142.251i	0.577381	+	0.794697i	0.993405	−	0.114656i	$-0.0365767\pi$
$179$	103.351	+	142.251i	0.577381	+	0.794697i	−0.416024	+	0.909354i	$0.636577\pi$
$180$	13.8525	−	116.155i	0.0769581	−	0.645308i
$181$	4.01656	+	2.91820i	0.0221909	+	0.0161227i	0.598825	−	0.800880i	$-0.295634\pi$
$181$	4.01656	+	2.91820i	0.0221909	+	0.0161227i	−0.576635	+	0.817002i	$0.695634\pi$
$182$	−112.335	−	112.335i	−0.617223	−	0.617223i
$183$	310.154	−	49.1235i	1.69483	−	0.268435i
$184$	−1.43962	−	0.467762i	−0.00782404	−	0.00254218i
$185$	29.4184	−	1.12970i	0.159018	−	0.00610648i
$186$	−13.3290	−	41.0224i	−0.0716613	−	0.220551i
$187$	202.569	−	103.214i	1.08326	−	0.551948i
$188$	25.0671	+	49.1969i	0.133336	+	0.261686i
$189$	59.2138	−	19.2397i	0.313300	−	0.101797i
$190$	−7.31232	−	190.419i	−0.0384859	−	1.00221i
$191$	−57.5605	+	177.153i	−0.301364	+	0.927503i	0.679645	+	0.733541i	$0.262134\pi$
$191$	−57.5605	+	177.153i	−0.301364	+	0.927503i	−0.981009	+	0.193962i	$0.937866\pi$
$192$	5.69358	+	35.9478i	0.0296540	+	0.187228i
$193$	149.932	−	149.932i	0.776850	−	0.776850i	−0.202444	−	0.979294i	$-0.564888\pi$
$193$	149.932	−	149.932i	0.776850	−	0.776850i	0.979294	+	0.202444i	$0.0648883\pi$
$194$	113.037	−	155.581i	0.582663	−	0.801966i
$195$	500.201	+	59.6530i	2.56513	+	0.305913i
$196$	−37.6488	+	27.3534i	−0.192086	+	0.139558i
$197$	−297.815	−	47.1692i	−1.51175	−	0.239437i	−0.655181	−	0.755472i	$-0.727408\pi$
$197$	−297.815	−	47.1692i	−1.51175	−	0.239437i	−0.856568	+	0.516034i	$0.827408\pi$
$198$	168.729	+	85.9715i	0.852165	+	0.434200i
$199$		−	137.629i		−	0.691604i	−0.938307	−	0.345802i	$-0.887607\pi$
$199$		−	137.629i		−	0.691604i	0.938307	−	0.345802i	$-0.112393\pi$
$200$	53.6872	+	46.0183i	0.268436	+	0.230091i
$201$	−420.012			−2.08961
$202$	−38.6610	+	75.8765i	−0.191391	+	0.375626i
$203$	4.96101	−	31.3226i	0.0244385	−	0.154298i
$204$	−106.223	−	146.203i	−0.520700	−	0.716682i
$205$	−80.6346	+	87.0748i	−0.393339	+	0.424755i
$206$	82.2323	+	59.7453i	0.399186	+	0.290026i
$207$	4.42679	+	4.42679i	0.0213854	+	0.0213854i
$208$	−87.4900	+	13.8571i	−0.420625	+	0.0666205i
$209$	293.386	+	95.3268i	1.40376	+	0.456109i
$210$	−44.4346	+	157.020i	−0.211594	+	0.747713i
$211$	34.9377	+	107.527i	0.165582	+	0.509608i	0.999079	−	0.0429161i	$-0.0136648\pi$
$211$	34.9377	+	107.527i	0.165582	+	0.509608i	−0.833497	+	0.552524i	$0.813665\pi$
$212$	155.282	−	79.1202i	0.732463	−	0.373208i
$213$	32.4955	+	63.7761i	0.152561	+	0.299418i
$214$	17.5487	−	5.70192i	0.0820034	−	0.0266445i
$215$	−296.894	+	109.231i	−1.38090	+	0.508049i
$216$	10.7278	−	33.0166i	0.0496655	−	0.152855i
$217$	5.31992	+	33.5886i	0.0245157	+	0.154786i
$218$	−5.14985	+	5.14985i	−0.0236231	+	0.0236231i
$219$	181.415	−	249.696i	0.828378	−	1.14016i
$220$	−99.9230	+	55.8431i	−0.454196	+	0.253832i
$221$	355.830	−	258.526i	1.61009	−	1.16980i
$222$	37.4168	+	5.92624i	0.168544	+	0.0266948i
$223$	−213.575	−	108.822i	−0.957738	−	0.487992i	−0.0960197	−	0.995379i	$-0.530611\pi$
$223$	−213.575	−	108.822i	−0.957738	−	0.487992i	−0.861718	+	0.507388i	$0.830611\pi$
$224$		−	28.6952i		−	0.128104i
$225$	−111.435	−	270.383i	−0.495265	−	1.20170i
$226$	149.479			0.661413
$227$	55.9856	−	109.878i	0.246633	−	0.484044i	−0.734190	−	0.678944i	$-0.762438\pi$
$227$	55.9856	−	109.878i	0.246633	−	0.484044i	0.980823	+	0.194900i	$0.0624381\pi$
$228$	38.3594	−	242.191i	0.168243	−	1.06224i
$229$	−150.862	−	207.644i	−0.658787	−	0.906742i	0.340654	−	0.940189i	$-0.389352\pi$
$229$	−150.862	−	207.644i	−0.658787	−	0.906742i	−0.999440	+	0.0334469i	$0.989352\pi$
$230$	−3.71221	+	0.734980i	−0.0161401	+	0.00319557i
$231$	−213.718	−	155.275i	−0.925187	−	0.672188i
$232$	−12.5035	−	12.5035i	−0.0538945	−	0.0538945i
$233$	10.2744	−	1.62731i	0.0440962	−	0.00698416i	−0.134347	−	0.990934i	$-0.542894\pi$
$233$	10.2744	−	1.62731i	0.0440962	−	0.00698416i	0.178444	+	0.983950i	$0.442894\pi$
$234$	348.423	+	113.209i	1.48899	+	0.483801i
$235$	114.706	+	76.7914i	0.488110	+	0.326772i
$236$	−13.4791	−	41.4843i	−0.0571147	−	0.175781i
$237$	−495.830	+	252.638i	−2.09211	+	1.06598i
$238$	64.6849	+	126.951i	0.271785	+	0.533409i
$239$	69.6575	−	22.6331i	0.291454	−	0.0946992i	−0.159641	−	0.987175i	$-0.551034\pi$
$239$	69.6575	−	22.6331i	0.291454	−	0.0946992i	0.451095	+	0.892476i	$0.351034\pi$
$240$	56.2678	+	71.5058i	0.234449	+	0.297941i
$241$	−20.2934	+	62.4568i	−0.0842052	+	0.259157i	−0.984290	−	0.176557i	$-0.943504\pi$
$241$	−20.2934	+	62.4568i	−0.0842052	+	0.259157i	0.900085	+	0.435714i	$0.143504\pi$
$242$	−2.21911	−	14.0109i	−0.00916988	−	0.0578964i
$243$	237.160	−	237.160i	0.975969	−	0.975969i
$244$	−81.1415	+	111.682i	−0.332547	+	0.457712i
$245$	−48.8011	+	105.611i	−0.199188	+	0.431066i
$246$	−123.546	+	89.7612i	−0.502218	+	0.364883i
$247$	589.447	+	93.3593i	2.38643	+	0.377973i
$248$	16.8952	+	8.60854i	0.0681258	+	0.0347118i
$249$			280.505i			1.12653i
$250$	173.288	+	34.9490i	0.693150	+	0.139796i
$251$	−47.1625			−0.187898			−0.0939492	−	0.995577i	$-0.529949\pi$
$251$	−47.1625			−0.187898			−0.0939492	+	0.995577i	$0.529949\pi$
$252$	−53.8788	+	105.743i	−0.213805	+	0.419615i
$253$	0.958333	−	6.05068i	0.00378788	−	0.0239157i
$254$	−51.0222	−	70.2260i	−0.200875	−	0.276480i
$255$	−410.124	−	189.512i	−1.60833	−	0.743183i
$256$	−12.9443	−	9.40456i	−0.0505636	−	0.0367366i
$257$	−85.1375	−	85.1375i	−0.331274	−	0.331274i	0.521796	−	0.853070i	$-0.325262\pi$
$257$	−85.1375	−	85.1375i	−0.331274	−	0.331274i	−0.853070	+	0.521796i	$0.825262\pi$
$258$	−402.064	+	63.6807i	−1.55839	+	0.246824i
$259$	−28.4060	−	9.22967i	−0.109676	−	0.0356358i
$260$	−174.031	+	136.945i	−0.669351	+	0.526711i
$261$	22.5991	+	69.5529i	0.0865866	+	0.266486i
$262$	−91.8175	+	46.7833i	−0.350448	+	0.178562i
$263$	157.397	+	308.908i	0.598467	+	1.17456i	0.969305	+	0.245860i	$0.0790702\pi$
$263$	157.397	+	308.908i	0.598467	+	1.17456i	−0.370839	+	0.928697i	$0.620930\pi$
$264$	−140.088	+	45.5173i	−0.530636	+	0.172414i
$265$	242.380	−	362.051i	0.914640	−	1.36623i
$266$	−59.7418	+	183.866i	−0.224593	+	0.691227i
$267$	56.7011	+	357.997i	0.212364	+	1.34081i
$268$	130.561	−	130.561i	0.487168	−	0.487168i
$269$	−114.651	+	157.804i	−0.426212	+	0.586631i	−0.967079	−	0.254478i	$-0.918097\pi$
$269$	−114.651	+	157.804i	−0.426212	+	0.586631i	0.540866	+	0.841109i	$0.318097\pi$
$270$	−16.8562	−	85.1367i	−0.0624304	−	0.315321i
$271$	295.640	−	214.795i	1.09092	−	0.792602i	0.111368	−	0.993779i	$-0.464477\pi$
$271$	295.640	−	214.795i	1.09092	−	0.792602i	0.979555	+	0.201177i	$0.0644768\pi$
$272$	78.4669	+	12.4279i	0.288481	+	0.0456909i
$273$	−455.362	−	232.019i	−1.66799	−	0.849885i
$274$			223.639i			0.816201i
$275$	−149.957	+	243.736i	−0.545299	+	0.886311i
$276$	−4.86956			−0.0176433
$277$	−46.0601	+	90.3980i	−0.166282	+	0.326346i	−0.959079	−	0.283139i	$-0.908624\pi$
$277$	−46.0601	+	90.3980i	−0.166282	+	0.326346i	0.792797	+	0.609486i	$0.208624\pi$
$278$	26.0927	−	164.743i	0.0938586	−	0.592600i
$279$	−46.0959	−	63.4456i	−0.165218	−	0.227404i
$280$	−34.9972	−	62.6223i	−0.124990	−	0.223651i
$281$	324.001	+	235.401i	1.15303	+	0.837725i	0.988881	−	0.148710i	$-0.0475121\pi$
$281$	324.001	+	235.401i	1.15303	+	0.837725i	0.164149	+	0.986436i	$0.447512\pi$
$282$	125.600	+	125.600i	0.445390	+	0.445390i
$283$	−246.358	+	39.0193i	−0.870523	+	0.137877i	−0.575687	−	0.817670i	$-0.695265\pi$
$283$	−246.358	+	39.0193i	−0.870523	+	0.137877i	−0.294837	+	0.955548i	$0.595265\pi$
$284$	−29.9261	−	9.72359i	−0.105374	−	0.0342380i
$285$	−211.668	−	575.324i	−0.742695	−	2.01868i
$286$	−110.780	−	340.947i	−0.387344	−	1.19212i
$287$	107.277	−	54.6606i	0.373789	−	0.190455i
$288$	30.0419	+	58.9606i	0.104312	+	0.204724i
$289$	−100.307	+	32.5918i	−0.347084	+	0.112774i
$290$	−42.5363	−	12.0372i	−0.146677	−	0.0415077i
$291$	191.175	−	588.375i	0.656957	−	2.02191i
$292$	21.2253	+	134.011i	0.0726894	+	0.458943i
$293$	−353.989	+	353.989i	−1.20815	+	1.20815i	−0.236529	+	0.971624i	$0.576010\pi$
$293$	−353.989	+	353.989i	−1.20815	+	1.20815i	−0.971624	+	0.236529i	$0.923990\pi$
$294$	−87.9953	+	121.115i	−0.299304	+	0.411956i
$295$	−80.0107	−	74.0930i	−0.271223	−	0.251163i
$296$	−13.4732	+	9.78887i	−0.0455176	+	0.0330705i
$297$	138.768	+	21.9786i	0.467231	+	0.0740021i
$298$	160.719	+	81.8906i	0.539326	+	0.274801i
$299$		−	11.8516i		−	0.0396374i
$300$	210.004	+	87.4237i	0.700014	+	0.291412i
$301$	320.946			1.06627
$302$	57.6589	−	113.162i	0.190923	−	0.374708i
$303$	−42.8555	+	270.579i	−0.141437	+	0.893000i
$304$	63.3614	+	87.2095i	0.208426	+	0.286873i
$305$	−40.8682	+	342.687i	−0.133994	+	1.12356i
$306$	−265.819	−	193.129i	−0.868688	−	0.631139i
$307$	−235.076	−	235.076i	−0.765718	−	0.765718i	0.211631	−	0.977350i	$-0.432122\pi$
$307$	−235.076	−	235.076i	−0.765718	−	0.765718i	−0.977350	+	0.211631i	$0.932122\pi$
$308$	114.702	−	18.1670i	0.372409	−	0.0589839i
$309$	310.985	+	101.045i	1.00642	+	0.327006i
$310$	47.3699	−	1.81906i	0.152806	−	0.00586793i
$311$	73.4853	+	226.164i	0.236287	+	0.727217i	0.996948	+	0.0780676i	$0.0248750\pi$
$311$	73.4853	+	226.164i	0.236287	+	0.727217i	−0.760661	+	0.649149i	$0.775125\pi$
$312$	−253.903	+	129.370i	−0.813791	+	0.414647i
$313$	−17.1378	−	33.6349i	−0.0547535	−	0.107460i	0.862008	−	0.506894i	$-0.169207\pi$
$313$	−17.1378	−	33.6349i	−0.0547535	−	0.107460i	−0.916762	+	0.399434i	$0.869207\pi$
$314$	111.551	−	36.2452i	0.355259	−	0.115431i
$315$	11.3851	+	296.477i	0.0361430	+	0.941197i
$316$	75.5965	−	232.662i	0.239230	−	0.736273i
$317$	30.3237	+	191.456i	0.0956583	+	0.603963i	0.988220	+	0.153038i	$0.0489058\pi$
$317$	30.3237	+	191.456i	0.0956583	+	0.603963i	−0.892562	+	0.450925i	$0.851094\pi$
$318$	396.436	−	396.436i	1.24665	−	1.24665i
$319$	42.0638	−	57.8958i	0.131861	−	0.181492i
$320$	−39.7185	−	4.73675i	−0.124120	−	0.0148024i
$321$	48.0225	−	34.8904i	0.149603	−	0.108693i
$322$	3.79199	+	0.600592i	0.0117764	+	0.00186519i
$323$	−476.907	−	242.996i	−1.47649	−	0.752310i
$324$			98.8817i			0.305191i
$325$	−212.772	+	511.109i	−0.654684	+	1.57264i
$326$	269.624			0.827068
$327$	−10.6366	+	20.8755i	−0.0325279	+	0.0638396i
$328$	10.5019	−	66.3067i	0.0320181	−	0.202155i
$329$	−82.3153	−	113.297i	−0.250199	−	0.344369i
$330$	−250.203	+	270.187i	−0.758192	+	0.818748i
$331$	206.636	+	150.130i	0.624279	+	0.453566i	0.854414	−	0.519593i	$-0.173917\pi$
$331$	206.636	+	150.130i	0.624279	+	0.453566i	−0.230134	+	0.973159i	$0.573917\pi$
$332$	−87.1953	−	87.1953i	−0.262636	−	0.262636i
$333$	68.0291	−	10.7748i	0.204292	−	0.0323566i
$334$	180.461	+	58.6352i	0.540301	+	0.175555i
$335$	125.692	−	444.161i	0.375200	−	1.32585i
$336$	−28.5259	−	87.7938i	−0.0848986	−	0.261291i
$337$	326.020	−	166.116i	0.967419	−	0.492925i	0.102444	−	0.994739i	$-0.467334\pi$
$337$	326.020	−	166.116i	0.967419	−	0.492925i	0.864975	+	0.501814i	$0.167334\pi$
$338$	−206.356	−	404.997i	−0.610522	−	1.19822i
$339$	457.335	−	148.597i	1.34907	−	0.438340i
$340$	186.397	−	68.5777i	0.548228	−	0.201699i
$341$	−23.7141	+	72.9845i	−0.0695428	+	0.214031i
$342$	−69.7429	−	440.339i	−0.203927	−	1.28754i
$343$	259.219	−	259.219i	0.755741	−	0.755741i
$344$	105.187	−	144.777i	0.305776	−	0.420864i
$345$	−10.6270	+	5.93900i	−0.0308028	+	0.0172145i
$346$	−142.659	+	103.648i	−0.412310	+	0.299560i
$347$	−452.474	−	71.6649i	−1.30396	−	0.206527i	−0.534471	−	0.845187i	$-0.679489\pi$
$347$	−452.474	−	71.6649i	−1.30396	−	0.206527i	−0.769489	+	0.638660i	$0.779489\pi$
$348$	−50.6846	−	25.8251i	−0.145646	−	0.0742101i
$349$			98.1992i			0.281373i	0.990054	+	0.140686i	$0.0449310\pi$
$349$			98.1992i			0.281373i	−0.990054	+	0.140686i	$0.955069\pi$
$350$	−152.750	−	93.9790i	−0.436430	−	0.268511i
$351$	271.807			0.774378
$352$	29.3974	−	57.6956i	0.0835152	−	0.163908i
$353$	22.0875	−	139.455i	0.0625710	−	0.395058i	−0.936449	−	0.350803i	$-0.885909\pi$
$353$	22.0875	−	139.455i	0.0625710	−	0.395058i	0.999020	−	0.0442546i	$-0.0140913\pi$
$354$	−82.4792	−	113.523i	−0.232992	−	0.320686i
$355$	−77.1675	+	15.2784i	−0.217373	+	0.0430377i
$356$	−128.909	−	93.6581i	−0.362105	−	0.263085i
$357$	324.108	+	324.108i	0.907864	+	0.907864i
$358$	−245.602	+	38.8996i	−0.686039	+	0.108658i
$359$	−419.653	−	136.354i	−1.16895	−	0.379815i	−0.340699	−	0.940172i	$-0.610664\pi$
$359$	−419.653	−	136.354i	−1.16895	−	0.379815i	−0.828251	+	0.560358i	$0.810664\pi$
$360$	137.471	+	92.0315i	0.381863	+	0.255643i
$361$	−112.872	−	347.383i	−0.312664	−	0.962281i
$362$	−6.25594	+	3.18756i	−0.0172816	+	0.00880541i
$363$	−20.7177	−	40.6607i	−0.0570735	−	0.112013i
$364$	213.673	−	69.4266i	0.587014	−	0.190732i
$365$	209.763	+	266.569i	0.574692	+	0.730326i
$366$	−137.232	+	422.356i	−0.374950	+	1.15398i
$367$	53.9032	+	340.331i	0.146875	+	0.927333i	0.945528	+	0.325541i	$0.105546\pi$
$367$	53.9032	+	340.331i	0.146875	+	0.927333i	−0.798653	+	0.601792i	$0.794454\pi$
$368$	1.51371	−	1.51371i	0.00411334	−	0.00411334i
$369$	−163.199	+	224.624i	−0.442274	+	0.608737i
$370$	−17.4643	+	37.7946i	−0.0472007	+	0.102148i
$371$	−357.605	+	259.815i	−0.963894	+	0.700310i
$372$	60.2490	+	9.54251i	0.161960	+	0.0256519i
$373$	316.871	+	161.454i	0.849520	+	0.432852i	0.823843	−	0.566818i	$-0.191826\pi$
$373$	316.871	+	161.454i	0.849520	+	0.432852i	0.0256771	+	0.999670i	$0.491826\pi$
$374$			321.520i			0.859679i
$375$	564.920	−	65.3378i	1.50645	−	0.174234i
$376$	−78.0858			−0.207675
$377$	62.8533	−	123.357i	0.166720	−	0.327206i
$378$	−13.7741	+	86.9663i	−0.0364395	+	0.230070i
$379$	−155.812	−	214.457i	−0.411115	−	0.565851i	0.552375	−	0.833596i	$-0.313722\pi$
$379$	−155.812	−	214.457i	−0.411115	−	0.565851i	−0.963490	+	0.267745i	$0.913722\pi$
$380$	244.637	+	113.043i	0.643782	+	0.297481i
$381$	−225.915	−	164.137i	−0.592954	−	0.430806i
$382$	−186.270	−	186.270i	−0.487617	−	0.487617i
$383$	380.286	−	60.2315i	0.992915	−	0.157262i	0.361221	−	0.932480i	$-0.382360\pi$
$383$	380.286	−	60.2315i	0.992915	−	0.157262i	0.631694	+	0.775218i	$0.282360\pi$
$384$	−48.9524	−	15.9056i	−0.127480	−	0.0414208i
$385$	228.160	−	179.539i	0.592624	−	0.466335i
$386$	92.6631	+	285.188i	0.240060	+	0.738828i
$387$	−659.454	+	336.009i	−1.70402	+	0.868239i
$388$	123.470	+	242.324i	0.318222	+	0.624546i
$389$	607.465	−	197.377i	1.56161	−	0.507397i	0.604370	−	0.796704i	$-0.293425\pi$
$389$	607.465	−	197.377i	1.56161	−	0.507397i	0.957236	+	0.289307i	$0.0934250\pi$
$390$	−396.316	+	591.991i	−1.01620	+	1.51792i
$391$	−3.28463	+	10.1090i	−0.00840059	+	0.0258543i
$392$	−10.2953	−	65.0022i	−0.0262636	−	0.165822i
$393$	−234.411	+	234.411i	−0.596464	+	0.596464i
$394$	250.645	−	344.984i	0.636156	−	0.875593i
$395$	−118.783	−	599.943i	−0.300715	−	1.51884i
$396$	−216.661	+	157.413i	−0.547123	+	0.397508i
$397$	−19.7208	−	3.12348i	−0.0496747	−	0.00786770i	0.131548	−	0.991310i	$-0.458005\pi$
$397$	−19.7208	−	3.12348i	−0.0496747	−	0.00786770i	−0.181222	+	0.983442i	$0.558005\pi$
$398$	173.423	+	88.3634i	0.435736	+	0.222019i
$399$			621.933i			1.55873i
$400$	−92.4557	+	38.1043i	−0.231139	+	0.0952607i
$401$	−546.371			−1.36252			−0.681261	−	0.732041i	$-0.738568\pi$
$401$	−546.371			−1.36252			−0.681261	+	0.732041i	$0.738568\pi$
$402$	269.664	−	529.246i	0.670806	−	1.31653i
$403$	−23.2246	+	146.634i	−0.0576293	+	0.363857i
$404$	−70.7881	−	97.4315i	−0.175218	−	0.241167i
$405$	120.598	+	215.792i	0.297772	+	0.532820i
$406$	36.2836	+	26.3616i	0.0893685	+	0.0649300i
$407$	−47.6585	−	47.6585i	−0.117097	−	0.117097i
$408$	252.426	−	39.9804i	0.618691	−	0.0979911i
$409$	−396.232	−	128.743i	−0.968782	−	0.314776i	−0.218458	−	0.975846i	$-0.570103\pi$
$409$	−396.232	−	128.743i	−0.968782	−	0.314776i	−0.750324	+	0.661070i	$0.770103\pi$
$410$	−57.9501	−	157.511i	−0.141342	−	0.384173i
$411$	222.320	+	684.229i	0.540924	+	1.66479i
$412$	−128.080	+	65.2599i	−0.310873	+	0.158398i
$413$	50.2261	+	98.5743i	0.121613	+	0.238679i
$414$	−8.42025	+	2.73591i	−0.0203388	+	0.00660847i
$415$	−296.633	−	83.9435i	−0.714779	−	0.202274i
$416$	38.7111	−	119.141i	0.0930556	−	0.286396i
$417$	−83.9396	−	529.974i	−0.201294	−	1.27092i
$418$	−308.484	+	308.484i	−0.738000	+	0.738000i
$419$	−245.790	+	338.302i	−0.586612	+	0.807402i	−0.994401	−	0.105674i	$-0.966300\pi$
$419$	−245.790	+	338.302i	−0.586612	+	0.807402i	0.407789	+	0.913076i	$0.366300\pi$
$420$	−169.328	−	156.804i	−0.403161	−	0.373342i
$421$	−240.021	+	174.386i	−0.570122	+	0.414218i	−0.835149	−	0.550023i	$-0.814619\pi$
$421$	−240.021	+	174.386i	−0.570122	+	0.414218i	0.265028	+	0.964241i	$0.414619\pi$
$422$	−157.924	−	25.0126i	−0.374227	−	0.0592717i
$423$	287.749	+	146.616i	0.680258	+	0.346609i
$424$			246.465i			0.581286i
$425$	323.141	−	376.992i	0.760332	−	0.887041i
$426$	−101.226			−0.237620
$427$	158.956	−	311.968i	0.372262	−	0.730605i
$428$	−4.08213	+	25.7735i	−0.00953768	+	0.0602185i
$429$	−677.870	−	933.008i	−1.58012	−	2.17484i
$430$	52.9789	−	444.238i	0.123207	−	1.03311i
$431$	−319.131	−	231.862i	−0.740442	−	0.537963i	0.152408	−	0.988318i	$-0.451297\pi$
$431$	−319.131	−	231.862i	−0.740442	−	0.537963i	−0.892850	+	0.450355i	$0.851297\pi$
$432$	34.7157	+	34.7157i	0.0803605	+	0.0803605i
$433$	−112.334	+	17.7920i	−0.259432	+	0.0410901i	−0.284796	−	0.958588i	$-0.591926\pi$
$433$	−112.334	+	17.7920i	−0.259432	+	0.0410901i	0.0253633	+	0.999678i	$0.491926\pi$
$434$	−45.7397	−	14.8617i	−0.105391	−	0.0342436i
$435$	−142.107	+	5.45707i	−0.326683	+	0.0125450i
$436$	−3.18278	−	9.79559i	−0.00729995	−	0.0224669i
$437$	−12.8506	+	6.54773i	−0.0294065	+	0.0149834i
$438$	198.160	+	388.911i	0.452420	+	0.887924i
$439$	−541.776	+	176.034i	−1.23411	+	0.400988i	−0.852203	−	0.523211i	$-0.824734\pi$
$439$	−541.776	+	176.034i	−1.23411	+	0.400988i	−0.381911	+	0.924199i	$0.624734\pi$
$440$	−6.21191	−	161.764i	−0.0141180	−	0.367645i
$441$	−84.1108	+	258.867i	−0.190728	+	0.586999i
$442$	97.3044	+	614.356i	0.220146	+	1.38995i
$443$	−277.860	+	277.860i	−0.627222	+	0.627222i	−0.947368	−	0.320146i	$-0.896268\pi$
$443$	−277.860	+	277.860i	−0.627222	+	0.627222i	0.320146	+	0.947368i	$0.396268\pi$
$444$	−31.4905	+	43.3430i	−0.0709246	+	0.0976194i
$445$	−395.549	−	47.1723i	−0.888874	−	0.106005i
$446$	274.248	−	199.253i	0.614905	−	0.446755i
$447$	573.132	+	90.7752i	1.28217	+	0.203077i
$448$	36.1581	+	18.4235i	0.0807101	+	0.0411238i
$449$		−	733.358i		−	1.63331i	−0.577124	−	0.816657i	$-0.695825\pi$
$449$		−	733.358i		−	1.63331i	0.577124	−	0.816657i	$-0.304175\pi$
$450$	412.248	+	33.1812i	0.916108	+	0.0737359i
$451$	271.693			0.602424
$452$	−95.9716	+	188.355i	−0.212327	+	0.416714i
$453$	63.9145	−	403.540i	0.141092	−	0.890818i
$454$	102.509	+	141.092i	0.225792	+	0.310775i
$455$	381.630	−	412.111i	0.838747	−	0.905737i
$456$	280.551	+	203.832i	0.615243	+	0.447000i
$457$	637.278	+	637.278i	1.39448	+	1.39448i	0.814948	+	0.579535i	$0.196766\pi$
$457$	637.278	+	637.278i	1.39448	+	1.39448i	0.579535	+	0.814948i	$0.303234\pi$
$458$	358.506	−	56.7818i	0.782764	−	0.123978i
$459$	−231.843	−	75.3304i	−0.505105	−	0.164119i
$460$	1.45726	−	5.14955i	0.00316795	−	0.0111947i
$461$	−199.771	−	614.831i	−0.433342	−	1.33369i	−0.894776	−	0.446515i	$-0.852665\pi$
$461$	−199.771	−	614.831i	−0.433342	−	1.33369i	0.461434	−	0.887175i	$-0.347335\pi$
$462$	332.874	−	169.608i	0.720507	−	0.367116i
$463$	−152.915	−	300.113i	−0.330271	−	0.648192i	0.664837	−	0.746988i	$-0.268501\pi$
$463$	−152.915	−	300.113i	−0.330271	−	0.648192i	−0.995108	+	0.0987958i	$0.968501\pi$
$464$	23.7831	−	7.72761i	0.0512568	−	0.0166543i
$465$	143.121	−	52.6559i	0.307787	−	0.113238i
$466$	−4.54606	+	13.9913i	−0.00975549	+	0.0300243i
$467$	88.2096	+	556.933i	0.188886	+	1.19258i	0.881824	+	0.471579i	$0.156316\pi$
$467$	88.2096	+	556.933i	0.188886	+	1.19258i	−0.692938	+	0.720997i	$0.743684\pi$
$468$	−366.353	+	366.353i	−0.782806	+	0.782806i
$469$	−275.266	+	378.871i	−0.586921	+	0.807827i
$470$	−170.409	+	95.2347i	−0.362571	+	0.202627i
$471$	305.263	−	221.786i	0.648116	−	0.470884i
$472$	60.9274	+	9.64996i	0.129084	+	0.0204448i
$473$	645.305	+	328.799i	1.36428	+	0.695136i
$474$		−	786.986i		−	1.66031i
$475$	671.746	−	51.6678i	1.41420	−	0.108774i
$476$	−201.498			−0.423316
$477$	462.768	−	908.234i	0.970164	−	1.90405i
$478$	−16.2035	+	102.305i	−0.0338986	+	0.214027i
$479$	478.041	+	657.967i	0.997998	+	1.37363i	0.926546	+	0.376182i	$0.122763\pi$
$479$	478.041	+	657.967i	0.997998	+	1.37363i	0.0714519	+	0.997444i	$0.477237\pi$
$480$	−126.229	+	24.9920i	−0.262976	+	0.0520666i
$481$	−105.489	−	76.6419i	−0.219311	−	0.159339i
$482$	−65.6710	−	65.6710i	−0.136247	−	0.136247i
$483$	12.1987	−	1.93209i	0.0252562	−	0.00400019i
$484$	19.0795	+	6.19932i	0.0394205	+	0.0128085i
$485$	564.994	+	378.243i	1.16494	+	0.779882i
$486$	146.573	+	451.106i	0.301591	+	0.928202i
$487$	−106.854	+	54.4449i	−0.219413	+	0.111796i	−0.560243	−	0.828329i	$-0.689292\pi$
$487$	−106.854	+	54.4449i	−0.219413	+	0.111796i	0.340830	+	0.940125i	$0.389292\pi$
$488$	−88.6311	−	173.948i	−0.181621	−	0.356452i
$489$	824.922	−	268.033i	1.68696	−	0.548126i
$490$	−101.746	−	129.300i	−0.207644	−	0.263877i
$491$	−47.2164	+	145.317i	−0.0961637	+	0.295962i	−0.987555	−	0.157273i	$-0.949730\pi$
$491$	−47.2164	+	145.317i	−0.0961637	+	0.295962i	0.891391	+	0.453234i	$0.149730\pi$
$492$	−33.7845	−	213.307i	−0.0686677	−	0.433551i
$493$	−87.8000	+	87.8000i	−0.178093	+	0.178093i
$494$	−496.088	+	682.806i	−1.00423	+	1.38220i
$495$	−280.840	+	607.770i	−0.567354	+	1.22782i
$496$	−21.6948	+	15.7622i	−0.0437395	+	0.0317786i
$497$	78.8259	+	12.4848i	0.158603	+	0.0251203i
$498$	−353.457	−	180.095i	−0.709753	−	0.361637i
$499$		−	424.984i		−	0.851671i	−0.904801	−	0.425836i	$-0.859980\pi$
$499$		−	424.984i		−	0.851671i	0.904801	−	0.425836i	$-0.140020\pi$
$500$	−155.296	+	195.916i	−0.310592	+	0.391833i
$501$	610.413			1.21839
$502$	30.2802	−	59.4282i	0.0603191	−	0.118383i
$503$	−93.9909	+	593.435i	−0.186861	+	1.17979i	0.698751	+	0.715365i	$0.253740\pi$
$503$	−93.9909	+	593.435i	−0.186861	+	1.17979i	−0.885611	+	0.464427i	$0.846260\pi$
$504$	−98.6518	−	135.782i	−0.195738	−	0.269410i
$505$	−273.312	−	126.293i	−0.541211	−	0.250084i
$506$	7.00901	+	5.09234i	0.0138518	+	0.0100639i
$507$	−1033.96	−	1033.96i	−2.03937	−	2.03937i
$508$	121.248	−	19.2038i	0.238678	−	0.0378028i
$509$	−103.142	−	33.5130i	−0.202637	−	0.0658408i	0.205940	−	0.978565i	$-0.433975\pi$
$509$	−103.142	−	33.5130i	−0.202637	−	0.0658408i	−0.408577	+	0.912724i	$0.633975\pi$
$510$	502.115	−	395.113i	0.984538	−	0.774731i
$511$	−106.343	−	327.290i	−0.208107	−	0.640489i
$512$	20.1612	−	10.2726i	0.0393773	−	0.0200637i
$513$	−150.167	−	294.719i	−0.292723	−	0.574501i
$514$	161.941	−	52.6179i	0.315061	−	0.102369i
$515$	−199.919	+	298.626i	−0.388193	+	0.579857i
$516$	177.899	−	547.516i	0.344765	−	1.06108i
$517$	−49.4363	−	312.129i	−0.0956215	−	0.603730i
$518$	29.8678	−	29.8678i	0.0576599	−	0.0576599i
$519$	−333.433	+	458.931i	−0.642452	+	0.884260i
$520$	−60.8257	−	307.216i	−0.116972	−	0.590800i
$521$	−161.044	+	117.005i	−0.309105	+	0.224578i	−0.731512	−	0.681828i	$-0.761185\pi$
$521$	−161.044	+	117.005i	−0.309105	+	0.224578i	0.422407	+	0.906406i	$0.361185\pi$
$522$	−102.151	−	16.1792i	−0.195692	−	0.0309946i
$523$	565.327	+	288.049i	1.08093	+	0.550762i	0.901399	−	0.432990i	$-0.142541\pi$
$523$	565.327	+	288.049i	1.08093	+	0.550762i	0.179533	+	0.983752i	$0.442541\pi$
$524$		−	145.734i		−	0.278117i
$525$	−560.768	−	135.682i	−1.06813	−	0.258442i
$526$	−490.302			−0.932134
$527$	60.4492	−	118.638i	0.114704	−	0.225120i
$528$	32.5868	−	205.745i	0.0617174	−	0.389668i
$529$	−310.770	−	427.738i	−0.587467	−	0.808579i
$530$	300.593	+	537.867i	0.567157	+	1.01484i
$531$	−206.401	−	149.959i	−0.388702	−	0.282409i
$532$	−193.329	−	193.329i	−0.363400	−	0.363400i
$533$	519.148	−	82.2249i	0.974011	−	0.154268i
$534$	−487.507	−	158.401i	−0.912934	−	0.296630i
$535$	22.5253	+	61.2248i	0.0421034	+	0.114439i
$536$	80.6912	+	248.342i	0.150543	+	0.463325i
$537$	−712.756	+	363.167i	−1.32729	+	0.676289i
$538$	−125.234	−	245.785i	−0.232777	−	0.456850i
$539$	253.312	−	82.3061i	0.469967	−	0.152702i
$540$	118.101	+	33.4211i	0.218705	+	0.0618909i
$541$	−287.608	+	885.166i	−0.531622	+	1.63617i	0.219214	+	0.975677i	$0.429651\pi$
$541$	−287.608	+	885.166i	−0.531622	+	1.63617i	−0.750836	+	0.660489i	$0.770349\pi$
$542$	80.8450	+	510.435i	0.149161	+	0.941762i
$543$	−15.9714	+	15.9714i	−0.0294133	+	0.0294133i
$544$	−66.0390	+	90.8948i	−0.121395	+	0.167086i
$545$	−18.8927	−	17.4954i	−0.0346655	−	0.0321016i
$546$	584.721	−	424.825i	1.07092	−	0.778067i
$547$	−674.591	−	106.845i	−1.23326	−	0.195328i	−0.494425	−	0.869220i	$-0.664621\pi$
$547$	−674.591	−	106.845i	−1.23326	−	0.195328i	−0.738830	+	0.673892i	$0.764621\pi$
$548$	−281.802	−	143.585i	−0.514237	−	0.262017i
$549$			807.422i			1.47071i
$550$	−210.846	−	345.445i	−0.383357	−	0.628082i
$551$	−168.480			−0.305772
$552$	3.12645	−	6.13601i	0.00566386	−	0.0111160i
$553$	−97.0637	+	612.836i	−0.175522	+	1.10820i
$554$	−84.3357	−	116.078i	−0.152231	−	0.209527i
$555$	−15.8607	+	132.995i	−0.0285778	+	0.239630i
$556$	190.836	+	138.650i	0.343229	+	0.249371i
$557$	18.5591	+	18.5591i	0.0333198	+	0.0333198i	0.723570	−	0.690251i	$-0.242500\pi$
$557$	18.5591	+	18.5591i	0.0333198	+	0.0333198i	−0.690251	+	0.723570i	$0.742500\pi$
$558$	109.542	−	17.3497i	0.196311	−	0.0310926i
$559$	1332.55	+	432.971i	2.38380	+	0.774545i
$560$	101.378	−	3.89304i	0.181033	−	0.00695186i
$561$	319.623	+	983.699i	0.569738	+	1.75347i
$562$	−504.644	+	257.129i	−0.897943	+	0.457525i
$563$	−428.520	−	841.019i	−0.761138	−	1.49382i	−0.866388	−	0.499371i	$-0.833565\pi$
$563$	−428.520	−	841.019i	−0.761138	−	1.49382i	0.105251	−	0.994446i	$-0.466435\pi$
$564$	−238.906	+	77.6251i	−0.423591	+	0.137633i
$565$	20.2796	+	528.100i	0.0358931	+	0.934690i
$566$	109.004	−	335.481i	0.192587	−	0.592723i
$567$	−39.2332	−	247.709i	−0.0691943	−	0.436876i
$568$	31.4662	−	31.4662i	0.0553982	−	0.0553982i
$569$	212.998	−	293.167i	0.374337	−	0.515231i	−0.579736	−	0.814804i	$-0.696844\pi$
$569$	212.998	−	293.167i	0.374337	−	0.515231i	0.954073	+	0.299573i	$0.0968443\pi$
$570$	860.850	+	102.663i	1.51026	+	0.180111i
$571$	−908.751	+	660.246i	−1.59151	+	1.15630i	−0.689758	+	0.724040i	$0.742283\pi$
$571$	−908.751	+	660.246i	−1.59151	+	1.15630i	−0.901750	+	0.432258i	$0.857717\pi$
$572$	500.743	+	79.3099i	0.875425	+	0.138654i
$573$	−755.067	−	384.726i	−1.31774	−	0.671424i
$574$			170.272i			0.296640i
$575$	−3.10026	−	13.0153i	−0.00539176	−	0.0226353i
$576$	−93.5828			−0.162470
$577$	42.7144	−	83.8317i	0.0740284	−	0.145289i	−0.851026	−	0.525124i	$-0.824019\pi$
$577$	42.7144	−	83.8317i	0.0740284	−	0.145289i	0.925054	+	0.379835i	$0.124019\pi$
$578$	23.3331	−	147.320i	0.0403688	−	0.254878i
$579$	567.010	+	780.423i	0.979292	+	1.34788i
$580$	42.4778	−	45.8704i	0.0732375	−	0.0790870i
$581$	253.029	+	183.836i	0.435506	+	0.316414i
$582$	618.654	+	618.654i	1.06298	+	1.06298i
$583$	−985.183	+	156.038i	−1.68985	+	0.267646i
$584$	−182.491	−	59.2951i	−0.312485	−	0.101533i
$585$	−352.691	+	1246.31i	−0.602890	+	2.13045i
$586$	−218.777	−	673.327i	−0.373340	−	1.14902i
$587$	349.794	−	178.229i	0.595901	−	0.303627i	−0.129905	−	0.991526i	$-0.541467\pi$
$587$	349.794	−	178.229i	0.595901	−	0.303627i	0.725806	+	0.687900i	$0.241467\pi$
$588$	−96.1176	−	188.641i	−0.163465	−	0.320819i
$589$	171.826	−	55.8298i	0.291726	−	0.0947875i
$590$	144.733	−	53.2488i	0.245309	−	0.0902521i
$591$	423.907	−	1304.65i	0.717271	−	2.20753i
$592$	−3.68435	−	23.2621i	−0.00622357	−	0.0392941i
$593$	730.554	−	730.554i	1.23196	−	1.23196i	0.268754	−	0.963209i	$-0.413388\pi$
$593$	730.554	−	730.554i	1.23196	−	1.23196i	0.963209	−	0.268754i	$-0.0866120\pi$
$594$	−116.789	+	160.746i	−0.196614	+	0.270616i
$595$	−439.735	+	245.751i	−0.739050	+	0.413026i
$596$	−206.376	+	149.941i	−0.346269	+	0.251579i
$597$	618.434	+	97.9503i	1.03590	+	0.164071i
$598$	14.9339	+	7.60918i	0.0249730	+	0.0127244i
$599$			287.501i			0.479968i	0.970777	+	0.239984i	$0.0771422\pi$
$599$			287.501i			0.479968i	−0.970777	+	0.239984i	$0.922858\pi$
$600$	−244.991	+	208.491i	−0.408319	+	0.347485i
$601$	481.352			0.800919			0.400459	−	0.916314i	$-0.368851\pi$
$601$	481.352			0.800919			0.400459	+	0.916314i	$0.368851\pi$
$602$	−206.060	+	404.416i	−0.342293	+	0.671787i
$603$	168.942	−	1066.66i	0.280169	−	1.76892i
$604$	105.573	+	145.309i	0.174790	+	0.240578i
$605$	49.1985	−	9.74080i	0.0813199	−	0.0161005i
$606$	−313.435	−	227.724i	−0.517219	−	0.375781i
$607$	−431.854	−	431.854i	−0.711456	−	0.711456i	0.255383	−	0.966840i	$-0.417798\pi$
$607$	−431.854	−	431.854i	−0.711456	−	0.711456i	−0.966840	+	0.255383i	$0.917798\pi$
$608$	−150.571	+	23.8481i	−0.247650	+	0.0392238i
$609$	137.217	+	44.5844i	0.225315	+	0.0732092i
$610$	−405.572	−	271.516i	−0.664872	−	0.445108i
$611$	−188.924	−	581.450i	−0.309205	−	0.951636i
$612$	414.022	−	210.955i	0.676507	−	0.344698i
$613$	−136.550	−	267.994i	−0.222757	−	0.437185i	0.752398	−	0.658709i	$-0.228897\pi$
$613$	−136.550	−	267.994i	−0.222757	−	0.437185i	−0.975155	+	0.221524i	$0.928897\pi$
$614$	447.140	−	145.285i	0.728242	−	0.236620i
$615$	−333.881	−	424.301i	−0.542897	−	0.689920i
$616$	−50.7515	+	156.197i	−0.0823888	+	0.253567i
$617$	6.55430	+	41.3822i	0.0106228	+	0.0670700i	0.992430	−	0.122809i	$-0.0391903\pi$
$617$	6.55430	+	41.3822i	0.0106228	+	0.0670700i	−0.981807	+	0.189879i	$0.939190\pi$
$618$	−326.988	+	326.988i	−0.529108	+	0.529108i
$619$	491.415	−	676.375i	0.793885	−	1.09269i	−0.199728	−	0.979851i	$-0.564006\pi$
$619$	491.415	−	676.375i	0.793885	−	1.09269i	0.993613	−	0.112838i	$-0.0359941\pi$
$620$	−28.1212	+	60.8575i	−0.0453568	+	0.0981572i
$621$	−5.31418	+	3.86098i	−0.00855746	+	0.00621736i
$622$	−332.164	−	52.6097i	−0.534026	−	0.0845814i
$623$	360.091	+	183.476i	0.577995	+	0.294503i
$624$		−	402.997i		−	0.645828i
$625$	−99.9627	+	616.954i	−0.159940	+	0.987127i
$626$	53.3856			0.0852805
$627$	−637.151	+	1250.48i	−1.01619	+	1.99438i
$628$	−25.9487	+	163.834i	−0.0413196	+	0.260882i
$629$	68.7376	+	94.6091i	0.109281	+	0.150412i
$630$	−380.893	−	176.004i	−0.604591	−	0.279371i
$631$	559.824	+	406.736i	0.887201	+	0.644589i	0.935147	−	0.354261i	$-0.115268\pi$
$631$	559.824	+	406.736i	0.887201	+	0.644589i	−0.0479460	+	0.998850i	$0.515268\pi$
$632$	244.635	+	244.635i	0.387081	+	0.387081i
$633$	−508.036	+	80.4651i	−0.802585	+	0.127117i
$634$	−260.718	−	84.7124i	−0.411227	−	0.133616i
$635$	241.182	−	189.785i	0.379813	−	0.298874i
$636$	245.011	+	754.066i	0.385237	+	1.18564i
$637$	459.116	−	233.932i	0.720748	−	0.367239i
$638$	45.9464	+	90.1748i	0.0720162	+	0.141340i
$639$	−175.036	+	56.8726i	−0.273921	+	0.0890025i
$640$	31.4695	−	47.0071i	0.0491712	−	0.0734486i
$641$	353.774	−	1088.81i	0.551910	−	1.69860i	−0.152057	−	0.988372i	$-0.548590\pi$
$641$	353.774	−	1088.81i	0.551910	−	1.69860i	0.703967	−	0.710233i	$-0.251410\pi$
$642$	13.1321	+	82.9128i	0.0204550	+	0.129148i
$643$	160.690	−	160.690i	0.249906	−	0.249906i	−0.571026	−	0.820932i	$-0.693454\pi$
$643$	160.690	−	160.690i	0.249906	−	0.249906i	0.820932	+	0.571026i	$0.193454\pi$
$644$	−3.19140	+	4.39258i	−0.00495559	+	0.00682078i
$645$	−279.527	−	1411.82i	−0.433375	−	2.18887i
$646$	612.386	−	444.925i	0.947966	−	0.688738i
$647$	197.406	+	31.2660i	0.305110	+	0.0483246i	0.307112	−	0.951673i	$-0.400637\pi$
$647$	197.406	+	31.2660i	0.305110	+	0.0483246i	−0.00200241	+	0.999998i	$0.500637\pi$
$648$	−124.598	−	63.4860i	−0.192281	−	0.0979722i
$649$			249.652i			0.384671i
$650$	−507.427	−	596.261i	−0.780657	−	0.917325i
$651$	−154.716			−0.237659
$652$	−173.109	+	339.746i	−0.265505	+	0.521083i
$653$	123.333	−	778.694i	0.188871	−	1.19249i	−0.692979	−	0.720958i	$-0.743702\pi$
$653$	123.333	−	778.694i	0.188871	−	1.19249i	0.881850	−	0.471529i	$-0.156298\pi$
$654$	−19.4756	−	26.8058i	−0.0297792	−	0.0409875i
$655$	−177.739	−	318.038i	−0.271357	−	0.485554i
$656$	76.8086	+	55.8047i	0.117086	+	0.0850682i
$657$	561.155	+	561.155i	0.854117	+	0.854117i
$658$	195.613	−	30.9820i	0.297284	−	0.0470851i
$659$	119.459	+	38.8147i	0.181274	+	0.0588994i	0.398247	−	0.917278i	$-0.369619\pi$
$659$	119.459	+	38.8147i	0.181274	+	0.0588994i	−0.216974	+	0.976177i	$0.569619\pi$
$660$	−179.815	−	488.745i	−0.272447	−	0.740523i
$661$	−358.442	−	1103.17i	−0.542272	−	1.66894i	−0.727390	−	0.686224i	$-0.759267\pi$
$661$	−358.442	−	1103.17i	−0.542272	−	1.66894i	0.185118	−	0.982716i	$-0.440733\pi$
$662$	−321.844	+	163.988i	−0.486169	+	0.247715i
$663$	908.437	+	1782.91i	1.37019	+	2.68915i
$664$	165.855	−	53.8897i	0.249782	−	0.0811591i
$665$	−657.692	−	186.119i	−0.989011	−	0.279878i
$666$	−30.1004	+	92.6395i	−0.0451958	+	0.139098i
$667$	0.523399	+	3.30461i	0.000784706	+	0.00495444i
$668$	−189.748	+	189.748i	−0.284053	+	0.284053i
$669$	640.991	−	882.248i	0.958133	−	1.31876i
$670$	478.976	+	443.550i	0.714890	+	0.662015i
$671$	639.203	−	464.408i	0.952612	−	0.692113i
$672$	128.941	+	20.4223i	0.191877	+	0.0303903i
$673$	210.697	+	107.355i	0.313071	+	0.159517i	0.603465	−	0.797390i	$-0.293786\pi$
$673$	210.697	+	107.355i	0.313071	+	0.159517i	−0.290394	+	0.956907i	$0.593786\pi$
$674$			517.462i			0.767748i
$675$	298.495	−	71.1021i	0.442215	−	0.105336i
$676$	642.816			0.950911
$677$	−349.807	+	686.535i	−0.516701	+	1.01408i	0.474317	+	0.880354i	$0.342695\pi$
$677$	−349.807	+	686.535i	−0.516701	+	1.01408i	−0.991018	+	0.133729i	$0.957305\pi$
$678$	−106.384	+	671.682i	−0.156908	+	0.990681i
$679$	−405.451	−	558.056i	−0.597130	−	0.821879i
$680$	−33.2615	+	278.904i	−0.0489140	+	0.410153i
$681$	453.890	+	329.770i	0.666504	+	0.484244i
$682$	−76.7404	−	76.7404i	−0.112523	−	0.112523i
$683$	−442.682	+	70.1140i	−0.648144	+	0.102656i	−0.471846	−	0.881681i	$-0.656412\pi$
$683$	−442.682	+	70.1140i	−0.648144	+	0.102656i	−0.176298	+	0.984337i	$0.556412\pi$
$684$	599.638	+	194.834i	0.876663	+	0.284845i
$685$	−790.101	+	30.3408i	−1.15343	+	0.0442931i
$686$	160.206	+	493.064i	0.233537	+	0.718753i
$687$	1040.41	−	530.116i	1.51443	−	0.771639i
$688$	114.896	+	225.496i	0.167000	+	0.327755i
$689$	−1835.25	+	596.309i	−2.66365	+	0.865471i
$690$	−0.660646	−	17.2038i	−0.000957458	−	0.0249331i
$691$	−316.495	+	974.071i	−0.458024	+	1.40965i	0.409523	+	0.912300i	$0.365695\pi$
$691$	−316.495	+	974.071i	−0.458024	+	1.40965i	−0.867547	+	0.497355i	$0.834305\pi$
$692$	−39.0112	−	246.307i	−0.0563746	−	0.355935i
$693$	480.300	−	480.300i	0.693074	−	0.693074i
$694$	380.809	−	524.139i	0.548717	−	0.755244i
$695$	585.565	+	69.8333i	0.842539	+	0.100480i
$696$	65.0831	−	47.2856i	0.0935102	−	0.0679391i
$697$	−465.606	−	73.7448i	−0.668015	−	0.105803i
$698$	−123.738	−	63.0477i	−0.177275	−	0.0903263i
$699$			47.3260i			0.0677054i
$700$	216.492	−	132.138i	0.309275	−	0.188769i
$701$	−1352.58			−1.92951			−0.964753	−	0.263156i	$-0.915237\pi$
$701$	−1352.58			−1.92951			−0.964753	+	0.263156i	$0.915237\pi$
$702$	−174.511	+	342.496i	−0.248591	+	0.487887i
$703$	−24.8226	+	156.724i	−0.0353095	+	0.222936i
$704$	53.8264	+	74.0857i	0.0764579	+	0.105235i
$705$	−426.696	+	460.776i	−0.605243	+	0.653583i
$706$	161.543	+	117.368i	0.228814	+	0.166243i
$707$	215.989	+	215.989i	0.305501	+	0.305501i
$708$	196.002	−	31.0437i	0.276839	−	0.0438470i
$709$	−131.683	−	42.7865i	−0.185731	−	0.0603477i	0.214675	−	0.976686i	$-0.431131\pi$
$709$	−131.683	−	42.7865i	−0.185731	−	0.0603477i	−0.400406	+	0.916338i	$0.631131\pi$
$710$	30.2927	−	107.046i	0.0426658	−	0.150769i
$711$	−442.159	−	1360.82i	−0.621883	−	1.91396i
$712$	200.781	−	102.303i	0.281996	−	0.143684i
$713$	−1.62885	−	3.19680i	−0.00228451	−	0.00448359i
$714$	−616.489	+	200.309i	−0.863430	+	0.280545i
$715$	1189.51	−	437.635i	1.66365	−	0.612077i
$716$	108.670	−	334.452i	0.151774	−	0.467111i
$717$	52.1263	+	329.112i	0.0727005	+	0.459013i
$718$	441.249	−	441.249i	0.614553	−	0.614553i
$719$	165.133	−	227.286i	0.229670	−	0.316114i	−0.678592	−	0.734515i	$-0.737410\pi$
$719$	165.133	−	227.286i	0.229670	−	0.316114i	0.908262	+	0.418402i	$0.137410\pi$
$720$	−204.228	+	114.135i	−0.283650	+	0.158521i
$721$	294.959	−	214.301i	0.409098	−	0.297227i
$722$	510.197	+	80.8072i	0.706644	+	0.111921i
$723$	−266.205	−	135.638i	−0.368196	−	0.187605i
$724$		−	9.92948i		−	0.0137147i
$725$	36.7559	−	151.911i	0.0506978	−	0.209532i
$726$	64.5371			0.0888940
$727$	−83.8826	+	164.629i	−0.115382	+	0.226449i	−0.941474	−	0.337085i	$-0.890559\pi$
$727$	−83.8826	+	164.629i	−0.115382	+	0.226449i	0.826092	+	0.563535i	$0.190559\pi$
$728$	−49.7040	+	313.818i	−0.0682747	+	0.431069i
$729$	635.343	+	874.475i	0.871527	+	1.19955i
$730$	−470.573	+	93.1686i	−0.644620	+	0.127628i
$731$	−1016.63	−	738.623i	−1.39073	−	1.01043i
$732$	−444.091	−	444.091i	−0.606682	−	0.606682i
$733$	91.4234	−	14.4800i	0.124725	−	0.0197545i	−0.0937599	−	0.995595i	$-0.529889\pi$
$733$	91.4234	−	14.4800i	0.124725	−	0.0197545i	0.218485	+	0.975840i	$0.429889\pi$
$734$	−463.450	−	150.584i	−0.631404	−	0.205155i
$735$	−439.830	−	294.450i	−0.598408	−	0.400612i
$736$	0.935524	+	2.87925i	0.00127109	+	0.00391202i
$737$	−941.600	+	479.769i	−1.27761	+	0.650975i
$738$	−178.263	−	349.860i	−0.241548	−	0.474065i
$739$	146.136	−	47.4824i	0.197748	−	0.0642523i	−0.208468	−	0.978029i	$-0.566848\pi$
$739$	146.136	−	47.4824i	0.197748	−	0.0642523i	0.406217	+	0.913777i	$0.366848\pi$
$740$	−36.4113	−	46.2719i	−0.0492044	−	0.0625296i
$741$	−839.015	+	2582.22i	−1.13227	+	3.48478i
$742$	−97.7897	−	617.420i	−0.131792	−	0.832102i
$743$	−379.385	+	379.385i	−0.510613	+	0.510613i	−0.914714	−	0.404101i	$-0.867584\pi$
$743$	−379.385	+	379.385i	−0.510613	+	0.510613i	0.404101	+	0.914714i	$0.367584\pi$
$744$	−50.7065	+	69.7916i	−0.0681539	+	0.0938058i
$745$	−267.509	+	578.920i	−0.359073	+	0.777074i
$746$	−406.887	+	295.621i	−0.545425	+	0.396275i
$747$	−712.368	−	112.828i	−0.953638	−	0.151041i
$748$	−405.139	−	206.429i	−0.541630	−	0.275974i
$749$		−	66.1849i		−	0.0883644i
$750$	−280.371	+	753.791i	−0.373828	+	1.00505i
$751$	1091.70			1.45366			0.726829	−	0.686819i	$-0.240993\pi$
$751$	1091.70			1.45366			0.726829	+	0.686819i	$0.240993\pi$
$752$	50.1342	−	98.3939i	0.0666678	−	0.130843i
$753$	33.5654	−	211.924i	0.0445756	−	0.281439i
$754$	115.084	+	158.400i	0.152631	+	0.210079i
$755$	407.616	+	188.352i	0.539888	+	0.249473i
$756$	−100.740	−	73.1922i	−0.133255	−	0.0968151i
$757$	167.215	+	167.215i	0.220892	+	0.220892i	0.808874	−	0.587982i	$-0.200077\pi$
$757$	167.215	+	167.215i	0.220892	+	0.220892i	−0.587982	+	0.808874i	$0.700077\pi$
$758$	370.270	−	58.6450i	0.488483	−	0.0773681i
$759$	26.5065	+	8.61250i	0.0349230	+	0.0113472i
$760$	−299.509	+	235.683i	−0.394091	+	0.310109i
$761$	274.175	+	843.824i	0.360283	+	1.10884i	0.952883	+	0.303339i	$0.0981015\pi$
$761$	274.175	+	843.824i	0.360283	+	1.10884i	−0.592600	+	0.805497i	$0.701899\pi$
$762$	351.871	−	179.287i	0.461774	−	0.235285i
$763$	11.8598	+	23.2761i	0.0155436	+	0.0305060i
$764$	354.306	−	115.121i	0.463751	−	0.150682i
$765$	646.246	−	965.320i	0.844767	−	1.26186i
$766$	−168.263	+	517.860i	−0.219664	+	0.676057i
$767$	75.5543	+	477.031i	0.0985062	+	0.621944i
$768$	51.4716	−	51.4716i	0.0670203	−	0.0670203i
$769$	259.529	−	357.212i	0.337489	−	0.464514i	−0.606217	−	0.795300i	$-0.707314\pi$
$769$	259.529	−	357.212i	0.337489	−	0.464514i	0.943706	+	0.330785i	$0.107314\pi$
$770$	79.7443	+	402.770i	0.103564	+	0.523078i
$771$	443.156	−	321.971i	0.574780	−	0.417602i
$772$	−418.851	−	66.3395i	−0.542553	−	0.0859320i
$773$	−674.908	−	343.883i	−0.873102	−	0.444868i	−0.0407854	−	0.999168i	$-0.512986\pi$
$773$	−674.908	−	343.883i	−0.873102	−	0.444868i	−0.832317	+	0.554300i	$0.812986\pi$
$774$		−	1046.69i		−	1.35231i
$775$	12.8532	+	167.108i	0.0165848	+	0.215623i
$776$	−384.618			−0.495642
$777$	61.6898	−	121.073i	0.0793948	−	0.155821i
$778$	−141.307	+	892.174i	−0.181628	+	1.14675i
$779$	−375.974	−	517.483i	−0.482636	−	0.664292i
$780$	−491.501	−	879.469i	−0.630130	−	1.12752i
$781$	145.700	+	105.857i	0.186555	+	0.135540i
$782$	−10.6293	−	10.6293i	−0.0135924	−	0.0135924i
$783$	−75.7886	+	12.0037i	−0.0967926	+	0.0153304i
$784$	88.5176	+	28.7611i	0.112905	+	0.0366851i
$785$	143.186	+	389.186i	0.182402	+	0.495778i
$786$	−144.874	−	445.875i	−0.184318	−	0.567271i
$787$	987.772	−	503.295i	1.25511	−	0.639511i	0.305276	−	0.952264i	$-0.401251\pi$
$787$	987.772	−	503.295i	1.25511	−	0.639511i	0.949834	+	0.312753i	$0.101251\pi$
$788$	273.781	+	537.325i	0.347437	+	0.681884i
$789$	−1500.09	+	487.409i	−1.90126	+	0.617756i
$790$	832.235	+	235.512i	1.05346	+	0.298117i
$791$	165.685	−	509.926i	0.209463	−	0.644660i
$792$	−59.2475	−	374.074i	−0.0748075	−	0.472316i
$793$	1080.83	−	1080.83i	1.36297	−	1.36297i
$794$	16.5974	−	22.8443i	0.0209035	−	0.0287712i
$795$	1454.37	+	1346.80i	1.82939	+	1.69408i
$796$	−222.689	+	161.793i	−0.279760	+	0.203257i
$797$	292.105	+	46.2648i	0.366505	+	0.0580487i	0.336971	−	0.941515i	$-0.390598\pi$
$797$	292.105	+	46.2648i	0.366505	+	0.0580487i	0.0295343	+	0.999564i	$0.490598\pi$
$798$	−783.682	−	399.306i	−0.982057	−	0.500383i
$799$			548.320i			0.686257i
$800$	11.3461	−	140.965i	0.0141826	−	0.176207i
$801$	−931.972			−1.16351
$802$	350.792	−	688.468i	0.437396	−	0.858439i
$803$	121.482	−	767.004i	0.151285	−	0.955173i
$804$	493.753	+	679.593i	0.614121	+	0.845265i
$805$	−1.60740	+	13.4783i	−0.00199677	+	0.0167433i
$806$	−169.859	−	123.410i	−0.210743	−	0.153114i
$807$	−627.491	−	627.491i	−0.777560	−	0.777560i
$808$	168.220	−	26.6434i	0.208193	−	0.0329745i
$809$	−173.388	−	56.3370i	−0.214323	−	0.0696378i	0.199887	−	0.979819i	$-0.435942\pi$
$809$	−173.388	−	56.3370i	−0.214323	−	0.0696378i	−0.414211	+	0.910181i	$0.635942\pi$
$810$	−349.342	+	13.4151i	−0.431287	+	0.0165619i
$811$	368.062	+	1132.78i	0.453837	+	1.39677i	0.872495	+	0.488622i	$0.162500\pi$
$811$	368.062	+	1132.78i	0.453837	+	1.39677i	−0.418659	+	0.908144i	$0.637500\pi$
$812$	−56.5130	+	28.7948i	−0.0695973	+	0.0354616i
$813$	754.771	+	1481.32i	0.928377	+	1.82204i
$814$	90.6519	−	29.4546i	0.111366	−	0.0361850i
$815$	36.5795	+	952.564i	0.0448828	+	1.16879i
$816$	−111.689	+	343.744i	−0.136874	+	0.421255i
$817$	−266.733	−	1684.08i	−0.326478	−	2.06130i
$818$	416.623	−	416.623i	0.509319	−	0.509319i
$819$	772.393	−	1063.11i	0.943093	−	1.29806i
$820$	235.682	+	28.1069i	0.287417	+	0.0342767i
$821$	388.310	−	282.124i	0.472972	−	0.343634i	−0.325626	−	0.945499i	$-0.605575\pi$
$821$	388.310	−	282.124i	0.472972	−	0.343634i	0.798598	+	0.601864i	$0.205575\pi$
$822$	−1004.92	−	159.163i	−1.22253	−	0.193629i
$823$	−156.554	−	79.7683i	−0.190224	−	0.0969238i	0.356285	−	0.934377i	$-0.384043\pi$
$823$	−156.554	−	79.7683i	−0.190224	−	0.0969238i	−0.546508	+	0.837454i	$0.684043\pi$
$824$		−	203.289i		−	0.246710i
$825$	−988.496	−	847.295i	−1.19818	−	1.02702i
$826$	−156.458			−0.189416
$827$	−73.1995	+	143.662i	−0.0885121	+	0.173715i	−0.931019	−	0.364971i	$-0.881079\pi$
$827$	−73.1995	+	143.662i	−0.0885121	+	0.173715i	0.842507	+	0.538686i	$0.181079\pi$
$828$	1.95869	−	12.3667i	0.00236557	−	0.0149356i
$829$	920.375	+	1266.79i	1.11022	+	1.52809i	0.821087	+	0.570803i	$0.193368\pi$
$829$	920.375	+	1266.79i	1.11022	+	1.52809i	0.289136	+	0.957288i	$0.406632\pi$
$830$	296.225	−	319.884i	0.356898	−	0.385403i
$831$	−373.420	−	271.306i	−0.449363	−	0.326481i
$832$	125.272	+	125.272i	0.150567	+	0.150567i
$833$	−456.446	+	72.2940i	−0.547955	+	0.0867875i
$834$	721.698	+	234.494i	0.865346	+	0.281168i
$835$	−182.671	+	645.510i	−0.218768	+	0.773066i
$836$	−190.654	−	586.772i	−0.228055	−	0.701880i
$837$	73.3162	−	37.3565i	0.0875940	−	0.0446314i
$838$	−268.478	−	526.917i	−0.320379	−	0.628779i
$839$	−1047.63	+	340.396i	−1.24867	+	0.405717i	−0.857443	−	0.514579i	$-0.827948\pi$
$839$	−1047.63	+	340.396i	−1.24867	+	0.405717i	−0.391224	+	0.920295i	$0.627948\pi$
$840$	306.299	−	112.691i	0.364642	−	0.134156i
$841$	247.805	−	762.667i	0.294656	−	0.906857i
$842$	−65.6356	−	414.407i	−0.0779520	−	0.492170i
$843$	−1288.36	+	1288.36i	−1.52830	+	1.52830i
$844$	132.911	−	182.936i	0.157477	−	0.216749i
$845$	1402.83	−	783.988i	1.66016	−	0.927797i
$846$	−369.493	+	268.452i	−0.436753	+	0.317319i
$847$	−50.2558	−	7.95974i	−0.0593339	−	0.00939757i
$848$	−310.564	−	158.240i	−0.366231	−	0.186604i
$849$		−	1134.77i		−	1.33660i
$850$	267.569	+	649.225i	0.314787	+	0.763795i
$851$	3.15113			0.00370285
$852$	64.9911	−	127.552i	0.0762806	−	0.149709i
$853$	69.4424	−	438.442i	0.0814096	−	0.514000i	−0.912961	−	0.408046i	$-0.866210\pi$
$853$	69.4424	−	438.442i	0.0814096	−	0.514000i	0.994371	−	0.105954i	$-0.0337897\pi$
$854$	291.047	+	400.592i	0.340804	+	0.469077i
$855$	1546.23	−	306.137i	1.80845	−	0.358055i
$856$	−29.8557	−	21.6914i	−0.0348781	−	0.0253404i
$857$	155.970	+	155.970i	0.181996	+	0.181996i	0.792225	−	0.610229i	$-0.208923\pi$
$857$	155.970	+	155.970i	0.181996	+	0.181996i	−0.610229	+	0.792225i	$0.708923\pi$
$858$	1610.88	−	255.138i	1.87748	−	0.297364i
$859$	391.117	+	127.082i	0.455316	+	0.147941i	0.527691	−	0.849436i	$-0.323058\pi$
$859$	391.117	+	127.082i	0.455316	+	0.147941i	−0.0723749	+	0.997377i	$0.523058\pi$
$860$	525.758	+	351.976i	0.611347	+	0.409274i
$861$	169.267	+	520.950i	0.196593	+	0.605053i
$862$	497.057	−	253.263i	0.576633	−	0.293809i
$863$	140.246	+	275.247i	0.162509	+	0.318943i	0.957874	−	0.287189i	$-0.0927206\pi$
$863$	140.246	+	275.247i	0.162509	+	0.318943i	−0.795365	+	0.606131i	$0.792721\pi$
$864$	−66.0333	+	21.4555i	−0.0764274	+	0.0248328i
$865$	−385.535	−	489.943i	−0.445705	−	0.566408i
$866$	49.7038	−	152.973i	0.0573947	−	0.176643i
$867$	−75.0621	−	473.924i	−0.0865769	−	0.546625i
$868$	48.0936	−	48.0936i	0.0554074	−	0.0554074i
$869$	−822.990	+	1132.75i	−0.947054	+	1.30351i
$870$	84.3620	−	182.569i	0.0969678	−	0.209849i
$871$	−1654.00	+	1201.70i	−1.89897	+	1.37968i
$872$	14.3866	+	2.27862i	0.0164984	+	0.00261309i
$873$	1417.33	+	722.168i	1.62352	+	0.827225i
$874$		−	20.3966i		−	0.0233371i
$875$	311.298	−	552.406i	0.355769	−	0.631321i
$876$	−617.282			−0.704660
$877$	160.555	−	315.106i	0.183073	−	0.359300i	−0.781171	−	0.624317i	$-0.785377\pi$
$877$	160.555	−	315.106i	0.183073	−	0.359300i	0.964244	+	0.265016i	$0.0853774\pi$
$878$	126.026	−	795.699i	0.143538	−	0.906263i
$879$	−1338.71	−	1842.57i	−1.52299	−	2.09622i
$880$	207.823	+	96.0313i	0.236162	+	0.109127i
$881$	1399.81	+	1017.02i	1.58889	+	1.15440i	0.905503	+	0.424340i	$0.139494\pi$
$881$	1399.81	+	1017.02i	1.58889	+	1.15440i	0.683387	+	0.730056i	$0.260506\pi$
$882$	−272.188	−	272.188i	−0.308604	−	0.308604i
$883$	−1262.49	+	199.959i	−1.42978	+	0.226454i	−0.822830	−	0.568288i	$-0.807606\pi$
$883$	−1262.49	+	199.959i	−1.42978	+	0.226454i	−0.606947	+	0.794742i	$0.707606\pi$
$884$	−836.607	−	271.830i	−0.946388	−	0.307500i
$885$	389.878	−	306.795i	0.440541	−	0.346661i
$886$	−171.727	−	528.520i	−0.193822	−	0.596524i
$887$	1492.83	−	760.633i	1.68301	−	0.857534i	0.692284	−	0.721625i	$-0.256605\pi$
$887$	1492.83	−	760.633i	1.68301	−	0.857534i	0.990721	−	0.135909i	$-0.0433954\pi$
$888$	−34.3972	−	67.5083i	−0.0387356	−	0.0760229i
$889$	−296.119	+	96.2150i	−0.333092	+	0.108228i
$890$	313.399	−	468.134i	0.352133	−	0.525993i
$891$	174.886	−	538.244i	0.196281	−	0.604090i
$892$	74.9951	+	473.500i	0.0840752	+	0.530830i
$893$	−526.088	+	526.088i	−0.589124	+	0.589124i
$894$	−482.357	+	663.907i	−0.539549	+	0.742626i
$895$	−170.750	−	862.418i	−0.190782	−	0.963595i
$896$	−46.4299	+	33.7333i	−0.0518191	+	0.0376487i
$897$	53.2548	+	8.43473i	0.0593699	+	0.00940327i
$898$	924.085	+	470.845i	1.02905	+	0.524326i
$899$		−	41.9122i		−	0.0466209i
$900$	−306.491	+	498.160i	−0.340545	+	0.553511i
$901$	1730.68			1.92085
$902$	−174.438	+	342.354i	−0.193390	+	0.379549i
$903$	−228.416	+	1442.16i	−0.252953	+	1.59708i
$904$	−175.723	−	241.862i	−0.194384	−	0.267547i
$905$	−12.1102	−	21.6693i	−0.0133814	−	0.0239440i
$906$	467.455	+	339.626i	0.515955	+	0.374863i
$907$	324.628	+	324.628i	0.357914	+	0.357914i	0.863044	−	0.505129i	$-0.168555\pi$
$907$	324.628	+	324.628i	0.357914	+	0.357914i	−0.505129	+	0.863044i	$0.668555\pi$
$908$	−243.601	+	38.5827i	−0.268283	+	0.0424919i
$909$	−669.922	−	217.671i	−0.736988	−	0.239462i
$910$	274.268	+	745.473i	0.301393	+	0.819201i
$911$	184.738	+	568.566i	0.202786	+	0.624112i	0.999797	+	0.0201467i	$0.00641332\pi$
$911$	184.738	+	568.566i	0.202786	+	0.624112i	−0.797011	+	0.603965i	$0.793587\pi$
$912$	−436.968	+	222.646i	−0.479132	+	0.244130i
$913$	320.414	+	628.848i	0.350946	+	0.688771i
$914$	−1212.18	+	393.860i	−1.32623	+	0.430919i
$915$	−1510.77	−	427.530i	−1.65112	−	0.467246i
$916$	−158.626	+	488.200i	−0.173172	+	0.532970i
$917$	57.8225	+	365.077i	0.0630561	+	0.398121i
$918$	243.774	−	243.774i	0.265549	−	0.265549i
$919$	−432.747	+	595.625i	−0.470889	+	0.648123i	−0.976722	−	0.214508i	$-0.931185\pi$
$919$	−432.747	+	595.625i	−0.470889	+	0.648123i	0.505833	+	0.862631i	$0.331185\pi$
$920$	5.55319	+	5.14247i	0.00603608	+	0.00558964i
$921$	1223.61	−	889.004i	1.32857	−	0.965260i
$922$	902.993	+	143.020i	0.979385	+	0.155119i
$923$	310.437	+	158.176i	0.336335	+	0.171371i
$924$			528.341i			0.571797i
$925$	−135.895	−	56.5725i	−0.146914	−	0.0611594i
$926$	476.342			0.514408
$927$	−381.701	+	749.130i	−0.411759	+	0.808122i
$928$	−5.53236	+	34.9299i	−0.00596159	+	0.0376400i
$929$	−469.300	−	645.936i	−0.505167	−	0.695303i	0.477928	−	0.878399i	$-0.341388\pi$
$929$	−469.300	−	645.936i	−0.505167	−	0.695303i	−0.983095	+	0.183096i	$0.941388\pi$
$930$	−25.5391	+	214.150i	−0.0274614	+	0.230269i
$931$	−507.303	−	368.577i	−0.544901	−	0.395894i
$932$	−14.7114	−	14.7114i	−0.0157847	−	0.0157847i
$933$	−1068.56	+	169.244i	−1.14530	+	0.181398i
$934$	−758.411	−	246.423i	−0.812003	−	0.263836i
$935$	−1135.91	+	43.6201i	−1.21487	+	0.0466526i
$936$	−226.419	−	696.845i	−0.241900	−	0.744493i
$937$	−1258.08	+	641.022i	−1.34266	+	0.684122i	−0.969831	−	0.243776i	$-0.921614\pi$
$937$	−1258.08	+	641.022i	−1.34266	+	0.684122i	−0.372833	+	0.927898i	$0.621614\pi$
$938$	−300.674	−	590.105i	−0.320548	−	0.629110i
$939$	163.335	−	53.0706i	0.173945	−	0.0565182i
$940$	−10.5938	−	275.872i	−0.0112700	−	0.293481i
$941$	−135.437	+	416.831i	−0.143928	+	0.442966i	−0.996872	−	0.0790378i	$-0.974815\pi$
$941$	−135.437	+	416.831i	−0.143928	+	0.442966i	0.852943	+	0.522004i	$0.174815\pi$
$942$	83.4764	+	527.049i	0.0886161	+	0.559500i
$943$	−8.98204	+	8.98204i	−0.00952496	+	0.00952496i
$944$	−51.2775	+	70.5774i	−0.0543194	+	0.0747642i
$945$	−309.115	−	36.8644i	−0.327105	−	0.0390099i
$946$	−828.622	+	602.029i	−0.875922	+	0.636395i
$947$	−941.730	−	149.155i	−0.994435	−	0.157503i	−0.362051	−	0.932158i	$-0.617923\pi$
$947$	−941.730	−	149.155i	−0.994435	−	0.157503i	−0.632384	+	0.774655i	$0.717923\pi$
$948$	991.661	+	505.276i	1.04606	+	0.532992i
$949$		−	1502.35i		−	1.58308i
$950$	−366.183	+	879.623i	−0.385455	+	0.925919i
$951$	−881.886			−0.927325
$952$	129.370	−	253.903i	0.135893	−	0.266705i
$953$	7.52363	−	47.5024i	0.00789468	−	0.0498451i	−0.983427	−	0.181307i	$-0.941967\pi$
$953$	7.52363	−	47.5024i	0.00789468	−	0.0498451i	0.991321	+	0.131462i	$0.0419672\pi$
$954$	847.326	+	1166.24i	0.888182	+	1.22248i
$955$	632.807	−	683.349i	0.662625	−	0.715548i
$956$	−118.508	−	86.1014i	−0.123963	−	0.0900642i
$957$	230.217	+	230.217i	0.240561	+	0.240561i
$958$	−1136.01	+	179.926i	−1.18581	+	0.187814i
$959$	762.911	+	247.885i	0.795528	+	0.258483i
$960$	49.5521	−	175.103i	0.0516167	−	0.182399i
$961$	−283.077	−	871.221i	−0.294565	−	0.906577i
$962$	164.302	−	83.7162i	0.170792	−	0.0870230i
$963$	69.2910	+	135.991i	0.0719533	+	0.141216i
$964$	124.914	−	40.5869i	0.129578	−	0.0421026i
$965$	−994.977	+	366.063i	−1.03106	+	0.379340i
$966$	−5.39750	+	16.6118i	−0.00558747	+	0.0171965i
$967$	−157.289	−	993.084i	−0.162657	−	1.02697i	−0.925046	−	0.379856i	$-0.875974\pi$
$967$	−157.289	−	993.084i	−0.162657	−	1.02697i	0.762389	−	0.647119i	$-0.224026\pi$
$968$	−20.0614	+	20.0614i	−0.0207246	+	0.0207246i
$969$	1431.31	−	1970.03i	1.47710	−	2.03306i
$970$	−839.362	+	469.087i	−0.865322	+	0.483595i
$971$	722.828	−	525.165i	0.744416	−	0.540850i	−0.149675	−	0.988735i	$-0.547823\pi$
$971$	722.828	−	525.165i	0.744416	−	0.540850i	0.894091	+	0.447885i	$0.147823\pi$
$972$	−662.533	−	104.935i	−0.681618	−	0.107958i
$973$	−533.074	−	271.615i	−0.547866	−	0.279152i
$974$		−	169.600i		−	0.174127i
$975$	−2145.23	−	1319.84i	−2.20024	−	1.35368i
$976$	276.092			0.282882
$977$	319.212	−	626.489i	0.326727	−	0.641237i	−0.667959	−	0.744198i	$-0.732832\pi$
$977$	319.212	−	626.489i	0.326727	−	0.641237i	0.994685	+	0.102961i	$0.0328317\pi$
$978$	−191.891	+	1211.55i	−0.196207	+	1.23880i
$979$	536.046	+	737.804i	0.547544	+	0.753630i
$980$	228.252	−	45.1915i	0.232910	−	0.0461137i
$981$	−48.7369	−	35.4094i	−0.0496809	−	0.0360953i
$982$	−152.795	−	152.795i	−0.155596	−	0.155596i
$983$	1496.27	−	236.985i	1.52214	−	0.241084i	0.661364	−	0.750065i	$-0.269978\pi$
$983$	1496.27	−	236.985i	1.52214	−	0.241084i	0.860777	+	0.508981i	$0.169978\pi$
$984$	290.473	+	94.3805i	0.295197	+	0.0959152i
$985$	1252.81	+	838.709i	1.27189	+	0.851481i
$986$	−54.2634	−	167.005i	−0.0550338	−	0.169377i
$987$	567.683	−	289.249i	0.575160	−	0.293058i
$988$	−541.878	−	1063.50i	−0.548460	−	1.07641i
$989$	−32.2034	+	10.4635i	−0.0325615	+	0.0105799i
$990$	−585.524	−	744.092i	−0.591439	−	0.751608i
$991$	349.037	−	1074.23i	0.352207	−	1.08398i	−0.605404	−	0.795918i	$-0.706989\pi$
$991$	349.037	−	1074.23i	0.352207	−	1.08398i	0.957611	−	0.288063i	$-0.0930114\pi$
$992$	−5.93260	−	37.4570i	−0.00598044	−	0.0377590i
$993$	−821.669	+	821.669i	−0.827461	+	0.827461i
$994$	−66.3411	+	91.3107i	−0.0667416	+	0.0918619i
$995$	−288.654	+	624.679i	−0.290104	+	0.627819i
$996$	453.867	−	329.753i	0.455689	−	0.331078i
$997$	1358.50	+	215.165i	1.36259	+	0.215813i	0.794554	−	0.607194i	$-0.207705\pi$
$997$	1358.50	+	215.165i	1.36259	+	0.215813i	0.568033	+	0.823006i	$0.307705\pi$
$998$	535.511	+	272.857i	0.536584	+	0.273403i
$999$			72.2687i			0.0723410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.3.f.a.17.1	yes	16
4.3	odd	2		400.3.bg.a.17.2		16
5.2	odd	4		250.3.f.c.143.2		16
5.3	odd	4		250.3.f.a.143.1		16
5.4	even	2		250.3.f.b.107.2		16
25.3	odd	20	inner	50.3.f.a.3.1	✓	16
25.4	even	10		250.3.f.c.7.2		16
25.21	even	5		250.3.f.a.7.1		16
25.22	odd	20		250.3.f.b.243.2		16
100.3	even	20		400.3.bg.a.353.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.a.3.1	✓	16	25.3	odd	20	inner
50.3.f.a.17.1	yes	16	1.1	even	1	trivial
250.3.f.a.7.1		16	25.21	even	5
250.3.f.a.143.1		16	5.3	odd	4
250.3.f.b.107.2		16	5.4	even	2
250.3.f.b.243.2		16	25.22	odd	20
250.3.f.c.7.2		16	25.4	even	10
250.3.f.c.143.2		16	5.2	odd	4
400.3.bg.a.17.2		16	4.3	odd	2
400.3.bg.a.353.2		16	100.3	even	20

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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	50.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642040 + 1.26007i) q^{2} +(-0.711697 + 4.49348i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(-4.53886 - 2.09733i) q^{5} +(-5.20517 - 3.78178i) q^{6} +(3.58690 + 3.58690i) q^{7} +(2.79360 - 0.442463i) q^{8} +(-11.1253 - 3.61484i) q^{9} +O(q^{10})\)	\(q+(-0.642040 + 1.26007i) q^{2} +(-0.711697 + 4.49348i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(-4.53886 - 2.09733i) q^{5} +(-5.20517 - 3.78178i) q^{6} +(3.58690 + 3.58690i) q^{7} +(2.79360 - 0.442463i) q^{8} +(-11.1253 - 3.61484i) q^{9} +(5.55691 - 4.37272i) q^{10} +(3.53728 + 10.8866i) q^{11} +(8.10725 - 4.13085i) q^{12} +(10.0537 + 19.7315i) q^{13} +(-6.82270 + 2.21683i) q^{14} +(12.6546 - 18.9026i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(-3.10698 - 19.6167i) q^{17} +(11.6979 - 11.6979i) q^{18} +(15.8404 - 21.8024i) q^{19} +(1.94220 + 9.80958i) q^{20} +(-18.6705 + 13.5649i) q^{21} +(-15.9890 - 2.53241i) q^{22} +(-0.476846 - 0.242965i) q^{23} +12.8679i q^{24} +(16.2024 + 19.0389i) q^{25} -31.3180 q^{26} +(5.57222 - 10.9361i) q^{27} +(1.58707 - 10.0204i) q^{28} +(-3.67470 - 5.05779i) q^{29} +(15.6939 + 28.0819i) q^{30} +(5.42369 + 3.94054i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-51.4362 + 8.14670i) q^{33} +(26.7133 + 8.67968i) q^{34} +(-8.75753 - 23.8034i) q^{35} +(7.22967 + 22.2506i) q^{36} +(-5.24626 + 2.67310i) q^{37} +(17.3025 + 33.9580i) q^{38} +(-95.8181 + 31.1332i) q^{39} +(-13.6078 - 3.85083i) q^{40} +(7.33457 - 22.5735i) q^{41} +(-5.10558 - 32.2354i) q^{42} +(44.7386 - 44.7386i) q^{43} +(13.4566 - 18.5214i) q^{44} +(42.9147 + 39.7407i) q^{45} +(0.612308 - 0.444868i) q^{46} +(-27.2676 - 4.31877i) q^{47} +(-16.2145 - 8.26170i) q^{48} -23.2682i q^{49} +(-34.3931 + 8.19249i) q^{50} +90.3585 q^{51} +(20.1074 - 39.4630i) q^{52} +(-13.6315 + 86.0658i) q^{53} +(10.2027 + 14.0428i) q^{54} +(6.77762 - 56.8316i) q^{55} +(11.6075 + 8.43332i) q^{56} +(86.6950 + 86.6950i) q^{57} +(8.73248 - 1.38309i) q^{58} +(20.7422 + 6.73954i) q^{59} +(-45.4614 + 1.74577i) q^{60} +(-21.3293 - 65.6449i) q^{61} +(-8.44760 + 4.30427i) q^{62} +(-26.9394 - 52.8715i) q^{63} +(7.60845 - 2.47214i) q^{64} +(-4.24886 - 110.644i) q^{65} +(22.7587 - 70.0439i) q^{66} +(14.4421 + 91.1840i) q^{67} +(-28.0880 + 28.0880i) q^{68} +(1.43113 - 1.96978i) q^{69} +(35.6167 + 4.24757i) q^{70} +(12.7283 - 9.24768i) q^{71} +(-32.6792 - 5.17587i) q^{72} +(-60.4466 - 30.7991i) q^{73} -8.32691i q^{74} +(-97.0823 + 59.2553i) q^{75} -53.8984 q^{76} +(-26.3614 + 51.7371i) q^{77} +(22.2889 - 140.727i) q^{78} +(71.8966 + 98.9571i) q^{79} +(13.5890 - 14.6744i) q^{80} +(-39.9985 - 29.0606i) q^{81} +(23.7352 + 23.7352i) q^{82} +(60.8973 - 9.64518i) q^{83} +(43.8969 + 14.2630i) q^{84} +(-27.0406 + 95.5539i) q^{85} +(27.6500 + 85.0979i) q^{86} +(25.3423 - 12.9126i) q^{87} +(14.6987 + 28.8478i) q^{88} +(75.7710 - 24.6195i) q^{89} +(-77.6291 + 28.5606i) q^{90} +(-34.7133 + 106.837i) q^{91} +(0.167440 + 1.05718i) q^{92} +(-21.5668 + 21.5668i) q^{93} +(22.9488 - 31.5864i) q^{94} +(-117.624 + 65.7354i) q^{95} +(20.8207 - 15.1271i) q^{96} +(-134.309 - 21.2725i) q^{97} +(29.3197 + 14.9391i) q^{98} -133.904i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} - 40 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 - 40 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} - 40 q^{9} + 10 q^{10} + 32 q^{11} + 4 q^{12} - 8 q^{13} - 30 q^{14} + 16 q^{16} - 62 q^{17} - 16 q^{18} + 30 q^{19} - 20 q^{20} - 68 q^{21} - 48 q^{22} - 18 q^{23} + 70 q^{25} - 56 q^{26} - 40 q^{27} + 44 q^{28} + 100 q^{29} + 120 q^{30} + 132 q^{31} - 64 q^{32} - 36 q^{33} + 100 q^{34} + 150 q^{35} + 48 q^{36} + 138 q^{37} + 20 q^{38} - 320 q^{39} - 88 q^{41} - 8 q^{42} - 78 q^{43} + 40 q^{44} - 20 q^{45} - 26 q^{46} - 22 q^{47} - 8 q^{48} - 20 q^{50} - 168 q^{51} - 16 q^{52} + 182 q^{53} + 80 q^{54} + 280 q^{55} + 48 q^{56} + 280 q^{57} - 120 q^{58} - 350 q^{59} - 140 q^{60} + 372 q^{61} - 158 q^{62} + 22 q^{63} - 910 q^{65} - 202 q^{66} - 112 q^{67} - 196 q^{68} - 30 q^{69} - 20 q^{70} + 122 q^{71} - 132 q^{72} - 248 q^{73} - 80 q^{75} + 40 q^{76} + 16 q^{77} + 438 q^{78} + 760 q^{79} + 80 q^{80} - 144 q^{81} + 352 q^{82} + 132 q^{83} - 20 q^{84} - 30 q^{85} + 264 q^{86} + 770 q^{87} + 116 q^{88} + 550 q^{89} - 140 q^{90} - 798 q^{91} + 384 q^{92} + 54 q^{93} + 190 q^{94} + 40 q^{95} - 16 q^{96} - 292 q^{97} - 24 q^{98}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 - 40 * q^9 + 10 * q^10 + 32 * q^11 + 4 * q^12 - 8 * q^13 - 30 * q^14 + 16 * q^16 - 62 * q^17 - 16 * q^18 + 30 * q^19 - 20 * q^20 - 68 * q^21 - 48 * q^22 - 18 * q^23 + 70 * q^25 - 56 * q^26 - 40 * q^27 + 44 * q^28 + 100 * q^29 + 120 * q^30 + 132 * q^31 - 64 * q^32 - 36 * q^33 + 100 * q^34 + 150 * q^35 + 48 * q^36 + 138 * q^37 + 20 * q^38 - 320 * q^39 - 88 * q^41 - 8 * q^42 - 78 * q^43 + 40 * q^44 - 20 * q^45 - 26 * q^46 - 22 * q^47 - 8 * q^48 - 20 * q^50 - 168 * q^51 - 16 * q^52 + 182 * q^53 + 80 * q^54 + 280 * q^55 + 48 * q^56 + 280 * q^57 - 120 * q^58 - 350 * q^59 - 140 * q^60 + 372 * q^61 - 158 * q^62 + 22 * q^63 - 910 * q^65 - 202 * q^66 - 112 * q^67 - 196 * q^68 - 30 * q^69 - 20 * q^70 + 122 * q^71 - 132 * q^72 - 248 * q^73 - 80 * q^75 + 40 * q^76 + 16 * q^77 + 438 * q^78 + 760 * q^79 + 80 * q^80 - 144 * q^81 + 352 * q^82 + 132 * q^83 - 20 * q^84 - 30 * q^85 + 264 * q^86 + 770 * q^87 + 116 * q^88 + 550 * q^89 - 140 * q^90 - 798 * q^91 + 384 * q^92 + 54 * q^93 + 190 * q^94 + 40 * q^95 - 16 * q^96 - 292 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

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Database

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