LMFDB - Embedded newform 50.3.f.a.37.1

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			37.1
Root			$0.0495271i$ of defining polynomial
Character	$\chi$	$=$	50.37
Dual form			50.3.f.a.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.221232 - 1.39680i) q^{2} +(-2.40328 - 1.22453i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-1.59895 - 4.73744i) q^{5} +(-1.17875 + 3.62781i) q^{6} +(-3.03568 - 3.03568i) q^{7} +(1.28408 + 2.52015i) q^{8} +(-1.01379 - 1.39536i) q^{9} +O(q^{10})$	\(q+(-0.221232 - 1.39680i) q^{2} +(-2.40328 - 1.22453i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-1.59895 - 4.73744i) q^{5} +(-1.17875 + 3.62781i) q^{6} +(-3.03568 - 3.03568i) q^{7} +(1.28408 + 2.52015i) q^{8} +(-1.01379 - 1.39536i) q^{9} +(-6.26353 + 3.28149i) q^{10} +(15.9782 + 11.6089i) q^{11} +(5.32811 + 0.843890i) q^{12} +(2.40210 - 15.1663i) q^{13} +(-3.56865 + 4.91183i) q^{14} +(-1.95842 + 13.3434i) q^{15} +(3.23607 - 2.35114i) q^{16} +(18.6060 - 9.48022i) q^{17} +(-1.72476 + 1.72476i) q^{18} +(-3.15850 - 1.02626i) q^{19} +(5.96929 + 8.02294i) q^{20} +(3.57830 + 11.0129i) q^{21} +(12.6804 - 24.8867i) q^{22} +(-16.3014 + 2.58189i) q^{23} -7.62902i q^{24} +(-19.8867 + 15.1499i) q^{25} -21.7157 q^{26} +(4.52526 + 28.5714i) q^{27} +(7.65035 + 3.89805i) q^{28} +(-6.49731 + 2.11110i) q^{29} +(19.0713 - 0.216458i) q^{30} +(7.69031 - 23.6683i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-24.1848 - 47.4652i) q^{33} +(-17.3582 - 23.8916i) q^{34} +(-9.52743 + 19.2353i) q^{35} +(2.79072 + 2.02758i) q^{36} +(-16.6649 - 2.63946i) q^{37} +(-0.734721 + 4.63885i) q^{38} +(-24.3445 + 33.5073i) q^{39} +(9.88586 - 10.1128i) q^{40} +(29.2279 - 21.2353i) q^{41} +(14.5912 - 7.43457i) q^{42} +(19.9893 - 19.9893i) q^{43} +(-37.5671 - 12.2063i) q^{44} +(-4.98944 + 7.03388i) q^{45} +(7.21279 + 22.1987i) q^{46} +(-12.1343 + 23.8149i) q^{47} +(-10.6562 + 1.68778i) q^{48} -30.5693i q^{49} +(25.5610 + 24.4261i) q^{50} -56.3243 q^{51} +(4.80420 + 30.3325i) q^{52} +(86.7430 + 44.1977i) q^{53} +(38.9074 - 12.6418i) q^{54} +(29.4479 - 94.2580i) q^{55} +(3.75230 - 11.5484i) q^{56} +(6.33408 + 6.33408i) q^{57} +(4.38621 + 8.60842i) q^{58} +(63.0774 + 86.8186i) q^{59} +(-4.52153 - 26.5910i) q^{60} +(65.0278 + 47.2455i) q^{61} +(-34.7613 - 5.50566i) q^{62} +(-1.15833 + 7.31340i) q^{63} +(-4.70228 + 6.47214i) q^{64} +(-75.6901 + 12.8703i) q^{65} +(-60.9491 + 44.2821i) q^{66} +(-55.4435 + 28.2499i) q^{67} +(-29.5316 + 29.5316i) q^{68} +(42.3386 + 13.7566i) q^{69} +(28.9756 + 9.05249i) q^{70} +(-30.4221 - 93.6296i) q^{71} +(2.21473 - 4.34665i) q^{72} +(-50.7302 + 8.03488i) q^{73} +23.8615i q^{74} +(66.3449 - 12.0576i) q^{75} +6.64209 q^{76} +(-13.2640 - 83.7456i) q^{77} +(52.1889 + 26.5916i) q^{78} +(35.6183 - 11.5731i) q^{79} +(-16.3127 - 11.5713i) q^{80} +(19.3143 - 59.4433i) q^{81} +(-36.1276 - 36.1276i) q^{82} +(-1.11819 - 2.19457i) q^{83} +(-13.6127 - 18.7362i) q^{84} +(-74.6621 - 72.9863i) q^{85} +(-32.3434 - 23.4989i) q^{86} +(18.2000 + 2.88259i) q^{87} +(-8.73874 + 55.1742i) q^{88} +(73.7197 - 101.466i) q^{89} +(10.9288 + 5.41314i) q^{90} +(-53.3319 + 38.7479i) q^{91} +(29.4115 - 14.9859i) q^{92} +(-47.4646 + 47.4646i) q^{93} +(35.9492 + 11.6806i) q^{94} +(0.188456 + 16.6042i) q^{95} +(4.71499 + 14.5113i) q^{96} +(-47.3640 + 92.9571i) q^{97} +(-42.6993 + 6.76290i) q^{98} -34.0643i 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 $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{9}{20}\right)$

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 $

$2$	−0.221232	−	1.39680i	−0.110616	−	0.698401i
$2$	−0.221232	−	1.39680i	−0.110616	−	0.698401i
$3$	−2.40328	−	1.22453i	−0.801094	−	0.408178i	0.00498387	−	0.999988i	$-0.498414\pi$
$3$	−2.40328	−	1.22453i	−0.801094	−	0.408178i	−0.806078	+	0.591810i	$0.798414\pi$
$4$	−1.90211	+	0.618034i	−0.475528	+	0.154508i
$5$	−1.59895	−	4.73744i	−0.319791	−	0.947488i
$5$	−1.59895	−	4.73744i	−0.319791	−	0.947488i
$6$	−1.17875	+	3.62781i	−0.196458	+	0.604636i
$7$	−3.03568	−	3.03568i	−0.433668	−	0.433668i	0.456206	−	0.889874i	$-0.349208\pi$
$7$	−3.03568	−	3.03568i	−0.433668	−	0.433668i	−0.889874	+	0.456206i	$0.849208\pi$
$8$	1.28408	+	2.52015i	0.160510	+	0.315018i
$9$	−1.01379	−	1.39536i	−0.112643	−	0.155040i
$10$	−6.26353	+	3.28149i	−0.626353	+	0.328149i
$11$	15.9782	+	11.6089i	1.45257	+	1.05535i	0.985223	+	0.171276i	$0.0547890\pi$
$11$	15.9782	+	11.6089i	1.45257	+	1.05535i	0.467344	+	0.884076i	$0.345211\pi$
$12$	5.32811	+	0.843890i	0.444010	+	0.0703242i
$13$	2.40210	−	15.1663i	0.184777	−	1.16664i	−0.704649	−	0.709556i	$-0.748896\pi$
$13$	2.40210	−	15.1663i	0.184777	−	1.16664i	0.889426	−	0.457079i	$-0.151104\pi$
$14$	−3.56865	+	4.91183i	−0.254904	+	0.350845i
$15$	−1.95842	+	13.3434i	−0.130561	+	0.889558i
$16$	3.23607	−	2.35114i	0.202254	−	0.146946i
$17$	18.6060	−	9.48022i	1.09447	−	0.557660i	0.188960	−	0.981985i	$-0.439488\pi$
$17$	18.6060	−	9.48022i	1.09447	−	0.557660i	0.905510	+	0.424325i	$0.139488\pi$
$18$	−1.72476	+	1.72476i	−0.0958200	+	0.0958200i
$19$	−3.15850	−	1.02626i	−0.166237	−	0.0540137i	0.224716	−	0.974424i	$-0.427855\pi$
$19$	−3.15850	−	1.02626i	−0.166237	−	0.0540137i	−0.390953	+	0.920411i	$0.627855\pi$
$20$	5.96929	+	8.02294i	0.298465	+	0.401147i
$21$	3.57830	+	11.0129i	0.170395	+	0.524423i
$22$	12.6804	−	24.8867i	0.576382	−	1.13121i
$23$	−16.3014	+	2.58189i	−0.708758	+	0.112256i	−0.500398	−	0.865796i	$-0.666813\pi$
$23$	−16.3014	+	2.58189i	−0.708758	+	0.112256i	−0.208361	+	0.978052i	$0.566813\pi$
$24$		−	7.62902i		−	0.317876i
$25$	−19.8867	+	15.1499i	−0.795468	+	0.605996i
$26$	−21.7157			−0.835219
$27$	4.52526	+	28.5714i	0.167602	+	1.05820i
$28$	7.65035	+	3.89805i	0.273227	+	0.139216i
$29$	−6.49731	+	2.11110i	−0.224045	+	0.0727967i	−0.418888	−	0.908038i	$-0.637580\pi$
$29$	−6.49731	+	2.11110i	−0.224045	+	0.0727967i	0.194843	+	0.980834i	$0.437580\pi$
$30$	19.0713	−	0.216458i	0.635711	−	0.00721525i
$31$	7.69031	−	23.6683i	0.248075	−	0.763495i	−0.747041	−	0.664778i	$-0.768526\pi$
$31$	7.69031	−	23.6683i	0.248075	−	0.763495i	0.995116	−	0.0987170i	$-0.0314739\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−24.1848	−	47.4652i	−0.732871	−	1.43834i
$34$	−17.3582	−	23.8916i	−0.510536	−	0.702693i
$35$	−9.52743	+	19.2353i	−0.272212	+	0.549579i
$36$	2.79072	+	2.02758i	0.0775200	+	0.0563216i
$37$	−16.6649	−	2.63946i	−0.450402	−	0.0713367i	−0.0728873	−	0.997340i	$-0.523221\pi$
$37$	−16.6649	−	2.63946i	−0.450402	−	0.0713367i	−0.377515	+	0.926003i	$0.623221\pi$
$38$	−0.734721	+	4.63885i	−0.0193348	+	0.122075i
$39$	−24.3445	+	33.5073i	−0.624218	+	0.859162i
$40$	9.88586	−	10.1128i	0.247147	−	0.252821i
$41$	29.2279	−	21.2353i	0.712875	−	0.517934i	−0.171225	−	0.985232i	$-0.554773\pi$
$41$	29.2279	−	21.2353i	0.712875	−	0.517934i	0.884100	+	0.467298i	$0.154773\pi$
$42$	14.5912	−	7.43457i	0.347409	−	0.177014i
$43$	19.9893	−	19.9893i	0.464868	−	0.464868i	−0.435379	−	0.900247i	$-0.643386\pi$
$43$	19.9893	−	19.9893i	0.464868	−	0.464868i	0.900247	+	0.435379i	$0.143386\pi$
$44$	−37.5671	−	12.2063i	−0.853797	−	0.277416i
$45$	−4.98944	+	7.03388i	−0.110876	+	0.156308i
$46$	7.21279	+	22.1987i	0.156800	+	0.482580i
$47$	−12.1343	+	23.8149i	−0.258177	+	0.506700i	−0.983317	−	0.181901i	$-0.941775\pi$
$47$	−12.1343	+	23.8149i	−0.258177	+	0.506700i	0.725140	+	0.688601i	$0.241775\pi$
$48$	−10.6562	+	1.68778i	−0.222005	+	0.0351621i
$49$		−	30.5693i		−	0.623864i
$50$	25.5610	+	24.4261i	0.511220	+	0.488523i
$51$	−56.3243			−1.10440
$52$	4.80420	+	30.3325i	0.0923884	+	0.583318i
$53$	86.7430	+	44.1977i	1.63666	+	0.833920i	0.997918	+	0.0644987i	$0.0205448\pi$
$53$	86.7430	+	44.1977i	1.63666	+	0.833920i	0.638742	+	0.769421i	$0.279455\pi$
$54$	38.9074	−	12.6418i	0.720508	−	0.234107i
$55$	29.4479	−	94.2580i	0.535416	−	1.71378i
$56$	3.75230	−	11.5484i	0.0670054	−	0.206221i
$57$	6.33408	+	6.33408i	0.111124	+	0.111124i
$58$	4.38621	+	8.60842i	0.0756243	+	0.148421i
$59$	63.0774	+	86.8186i	1.06911	+	1.47150i	0.870975	+	0.491327i	$0.163488\pi$
$59$	63.0774	+	86.8186i	1.06911	+	1.47150i	0.198134	+	0.980175i	$0.436512\pi$
$60$	−4.52153	−	26.5910i	−0.0753588	−	0.443183i
$61$	65.0278	+	47.2455i	1.06603	+	0.774516i	0.975194	−	0.221350i	$-0.0710464\pi$
$61$	65.0278	+	47.2455i	1.06603	+	0.774516i	0.0908350	+	0.995866i	$0.471046\pi$
$62$	−34.7613	−	5.50566i	−0.560667	−	0.0888009i
$63$	−1.15833	+	7.31340i	−0.0183862	+	0.116086i
$64$	−4.70228	+	6.47214i	−0.0734732	+	0.101127i
$65$	−75.6901	+	12.8703i	−1.16446	+	0.198005i
$66$	−60.9491	+	44.2821i	−0.923472	+	0.670941i
$67$	−55.4435	+	28.2499i	−0.827515	+	0.421640i	−0.815830	−	0.578292i	$-0.803720\pi$
$67$	−55.4435	+	28.2499i	−0.827515	+	0.421640i	−0.0116849	+	0.999932i	$0.503720\pi$
$68$	−29.5316	+	29.5316i	−0.434288	+	0.434288i
$69$	42.3386	+	13.7566i	0.613602	+	0.199371i
$70$	28.9756	+	9.05249i	0.413937	+	0.129321i
$71$	−30.4221	−	93.6296i	−0.428480	−	1.31873i	−0.899622	−	0.436669i	$-0.856158\pi$
$71$	−30.4221	−	93.6296i	−0.428480	−	1.31873i	0.471142	−	0.882057i	$-0.343842\pi$
$72$	2.21473	−	4.34665i	0.0307601	−	0.0603701i
$73$	−50.7302	+	8.03488i	−0.694934	+	0.110067i	−0.493902	−	0.869518i	$-0.664430\pi$
$73$	−50.7302	+	8.03488i	−0.694934	+	0.110067i	−0.201033	+	0.979585i	$0.564430\pi$
$74$			23.8615i			0.322453i
$75$	66.3449	−	12.0576i	0.884598	−	0.160767i
$76$	6.64209			0.0873960
$77$	−13.2640	−	83.7456i	−0.172260	−	1.08760i
$78$	52.1889	+	26.5916i	0.669088	+	0.340918i
$79$	35.6183	−	11.5731i	0.450864	−	0.146495i	−0.0747784	−	0.997200i	$-0.523825\pi$
$79$	35.6183	−	11.5731i	0.450864	−	0.146495i	0.525643	+	0.850706i	$0.323825\pi$
$80$	−16.3127	−	11.5713i	−0.203909	−	0.144641i
$81$	19.3143	−	59.4433i	0.238448	−	0.733868i
$82$	−36.1276	−	36.1276i	−0.440581	−	0.440581i
$83$	−1.11819	−	2.19457i	−0.0134721	−	0.0264406i	0.884172	−	0.467161i	$-0.154723\pi$
$83$	−1.11819	−	2.19457i	−0.0134721	−	0.0264406i	−0.897645	+	0.440720i	$0.854723\pi$
$84$	−13.6127	−	18.7362i	−0.162055	−	0.223050i
$85$	−74.6621	−	72.9863i	−0.878378	−	0.858663i
$86$	−32.3434	−	23.4989i	−0.376086	−	0.273242i
$87$	18.2000	+	2.88259i	0.209195	+	0.0331333i
$88$	−8.73874	+	55.1742i	−0.0993038	+	0.626980i
$89$	73.7197	−	101.466i	0.828311	−	1.14007i	−0.159924	−	0.987129i	$-0.551125\pi$
$89$	73.7197	−	101.466i	0.828311	−	1.14007i	0.988235	−	0.152943i	$-0.0488750\pi$
$90$	10.9288	+	5.41314i	0.121431	+	0.0601460i
$91$	−53.3319	+	38.7479i	−0.586064	+	0.425801i
$92$	29.4115	−	14.9859i	0.319690	−	0.162890i
$93$	−47.4646	+	47.4646i	−0.510373	+	0.510373i
$94$	35.9492	+	11.6806i	0.382439	+	0.124262i
$95$	0.188456	+	16.6042i	0.00198374	+	0.174781i
$96$	4.71499	+	14.5113i	0.0491145	+	0.151159i
$97$	−47.3640	+	92.9571i	−0.488289	+	0.958320i	0.507054	+	0.861915i	$0.330735\pi$
$97$	−47.3640	+	92.9571i	−0.488289	+	0.958320i	−0.995342	+	0.0964057i	$0.969265\pi$
$98$	−42.6993	+	6.76290i	−0.435707	+	0.0690092i
$99$		−	34.0643i		−	0.344084i
$100$	28.4636	−	41.1075i	0.284636	−	0.411075i
$101$	−153.672			−1.52150			−0.760751	−	0.649044i	$-0.775169\pi$
$101$	−153.672			−1.52150			−0.760751	+	0.649044i	$0.775169\pi$
$102$	12.4607	+	78.6739i	0.122164	+	0.771312i
$103$	23.5663	+	12.0076i	0.228799	+	0.116579i	0.564632	−	0.825343i	$-0.309018\pi$
$103$	23.5663	+	12.0076i	0.228799	+	0.116579i	−0.335834	+	0.941921i	$0.609018\pi$
$104$	41.3057	−	13.4210i	0.397170	−	0.129048i
$105$	46.4513	−	34.5611i	0.442393	−	0.329153i
$106$	42.5452	−	130.941i	0.401370	−	1.23529i
$107$	43.3886	+	43.3886i	0.405501	+	0.405501i	0.880166	−	0.474666i	$-0.157431\pi$
$107$	43.3886	+	43.3886i	0.405501	+	0.405501i	−0.474666	+	0.880166i	$0.657431\pi$
$108$	−26.2656	−	51.5492i	−0.243200	−	0.477308i
$109$	4.51121	+	6.20915i	0.0413873	+	0.0569647i	0.829209	−	0.558939i	$-0.188791\pi$
$109$	4.51121	+	6.20915i	0.0413873	+	0.0569647i	−0.787822	+	0.615903i	$0.788791\pi$
$110$	−138.175	−	20.2800i	−1.25613	−	0.184363i
$111$	36.8183	+	26.7501i	0.331696	+	0.240992i
$112$	−16.9610	−	2.68635i	−0.151437	−	0.0239853i
$113$	−21.3215	+	134.618i	−0.188685	+	1.19131i	0.693516	+	0.720441i	$0.256061\pi$
$113$	−21.3215	+	134.618i	−0.188685	+	1.19131i	−0.882202	+	0.470872i	$0.843939\pi$
$114$	7.44616	−	10.2488i	0.0653172	−	0.0899014i
$115$	38.2968	+	73.0988i	0.333016	+	0.635641i
$116$	11.0539	−	8.03112i	0.0952921	−	0.0692338i
$117$	−23.5976	+	12.0236i	−0.201689	+	0.102766i
$118$	107.314	−	107.314i	0.909438	−	0.909438i
$119$	−85.2607	−	27.7029i	−0.716476	−	0.232797i
$120$	−36.1420	+	12.1984i	−0.301184	+	0.101654i
$121$	83.1472	+	255.901i	0.687167	+	2.11488i
$122$	51.6064	−	101.283i	0.423003	−	0.830190i
$123$	−96.2461	+	15.2439i	−0.782488	+	0.123934i
$124$			49.7727i			0.401393i
$125$	103.570	+	69.9880i	0.828557	+	0.559904i
$126$	10.4716			0.0831082
$127$	−19.5250	−	123.276i	−0.153740	−	0.970677i	−0.937088	−	0.349093i	$-0.886490\pi$
$127$	−19.5250	−	123.276i	−0.153740	−	0.970677i	0.783348	−	0.621583i	$-0.213510\pi$
$128$	10.0806	+	5.13632i	0.0787546	+	0.0401275i
$129$	−72.5175	+	23.5624i	−0.562151	+	0.182654i
$130$	34.7224	+	102.877i	0.267095	+	0.791360i
$131$	52.6853	−	162.149i	0.402178	−	1.23778i	−0.521050	−	0.853526i	$-0.674460\pi$
$131$	52.6853	−	162.149i	0.402178	−	1.23778i	0.923229	−	0.384251i	$-0.125540\pi$
$132$	75.3373	+	75.3373i	0.570737	+	0.570737i
$133$	6.47280	+	12.7036i	0.0486677	+	0.0955157i
$134$	51.7253	+	71.1938i	0.386010	+	0.531297i
$135$	128.120	−	67.1225i	0.949034	−	0.497204i
$136$	47.7831	+	34.7165i	0.351346	+	0.255268i
$137$	116.319	+	18.4231i	0.849041	+	0.134475i	0.565768	−	0.824564i	$-0.308580\pi$
$137$	116.319	+	18.4231i	0.849041	+	0.134475i	0.283273	+	0.959039i	$0.408580\pi$
$138$	9.84866	−	62.1820i	0.0713671	−	0.450594i
$139$	−64.0359	+	88.1378i	−0.460690	+	0.634085i	−0.974652	−	0.223728i	$-0.928177\pi$
$139$	−64.0359	+	88.1378i	−0.460690	+	0.634085i	0.513962	+	0.857813i	$0.328177\pi$
$140$	6.23422	−	42.4759i	0.0445301	−	0.303399i
$141$	58.3243	−	42.3751i	0.413648	−	0.300533i
$142$	−124.052	+	63.2075i	−0.873603	+	0.445123i
$143$	214.444	−	214.444i	1.49961	−	1.49961i
$144$	−6.56138	−	2.13192i	−0.0455651	−	0.0148050i
$145$	20.3901	+	27.4051i	0.140622	+	0.189000i
$146$	22.4463	+	69.0825i	0.153742	+	0.473168i
$147$	−37.4331	+	73.4667i	−0.254647	+	0.499773i
$148$	33.3298	−	5.27892i	0.225201	−	0.0356684i
$149$			61.4078i			0.412133i	0.978538	+	0.206066i	$0.0660663\pi$
$149$			61.4078i			0.412133i	−0.978538	+	0.206066i	$0.933934\pi$
$150$	−31.5196	−	90.0031i	−0.210131	−	0.600021i
$151$	−168.345			−1.11487			−0.557433	−	0.830222i	$-0.688214\pi$
$151$	−168.345			−1.11487			−0.557433	+	0.830222i	$0.688214\pi$
$152$	−1.46944	−	9.27769i	−0.00966738	−	0.0610374i
$153$	−32.0909	−	16.3511i	−0.209744	−	0.106870i
$154$	−114.042	+	37.0543i	−0.740530	+	0.240613i
$155$	−124.424	+	1.41220i	−0.802735	+	0.00911096i
$156$	25.5973	−	78.7805i	0.164085	−	0.505003i
$157$	−84.0849	−	84.0849i	−0.535572	−	0.535572i	0.386653	−	0.922225i	$-0.373631\pi$
$157$	−84.0849	−	84.0849i	−0.535572	−	0.535572i	−0.922225	+	0.386653i	$0.873631\pi$
$158$	−24.0452	−	47.1913i	−0.152185	−	0.298679i
$159$	−154.346	−	212.439i	−0.970730	−	1.33610i
$160$	−12.5539	+	25.3456i	−0.0784622	+	0.158410i
$161$	57.3237	+	41.6481i	0.356048	+	0.258684i
$162$	−87.3034	−	13.8275i	−0.538910	−	0.0853550i
$163$	5.28541	−	33.3708i	0.0324258	−	0.204729i	−0.966157	−	0.257956i	$-0.916951\pi$
$163$	5.28541	−	33.3708i	0.0324258	−	0.204729i	0.998582	+	0.0532277i	$0.0169509\pi$
$164$	−42.4706	+	58.4557i	−0.258967	+	0.356437i
$165$	−186.193	+	190.469i	−1.12845	+	1.15435i
$166$	−2.81800	+	2.04740i	−0.0169759	+	0.0123337i
$167$	119.421	−	60.8479i	0.715095	−	0.364359i	−0.0582868	−	0.998300i	$-0.518564\pi$
$167$	119.421	−	60.8479i	0.715095	−	0.364359i	0.773381	+	0.633941i	$0.218564\pi$
$168$	−23.1592	+	23.1592i	−0.137853	+	0.137853i
$169$	−63.5167	−	20.6378i	−0.375839	−	0.122117i
$170$	−85.4298	+	120.435i	−0.502528	+	0.708442i
$171$	1.77005	+	5.44766i	0.0103512	+	0.0318577i
$172$	−25.6679	+	50.3760i	−0.149232	+	0.292884i
$173$	130.283	−	20.6348i	0.753082	−	0.119276i	0.231921	−	0.972735i	$-0.425499\pi$
$173$	130.283	−	20.6348i	0.753082	−	0.119276i	0.521161	+	0.853458i	$0.325499\pi$
$174$		−	26.0595i		−	0.149767i
$175$	106.360	+	14.3794i	0.607770	+	0.0821679i
$176$	79.0007			0.448868
$177$	−45.2805	−	285.890i	−0.255822	−	1.61520i
$178$	−158.038	−	80.5242i	−0.887852	−	0.452383i
$179$	−215.065	+	69.8787i	−1.20148	+	0.390384i	−0.840304	−	0.542115i	$-0.817624\pi$
$179$	−215.065	+	69.8787i	−1.20148	+	0.390384i	−0.361173	+	0.932499i	$0.617624\pi$
$180$	5.14329	−	16.4629i	0.0285739	−	0.0914604i
$181$	−18.7263	+	57.6336i	−0.103460	+	0.318418i	−0.989366	−	0.145447i	$-0.953538\pi$
$181$	−18.7263	+	57.6336i	−0.103460	+	0.318418i	0.885906	+	0.463865i	$0.153538\pi$
$182$	65.9218	+	65.9218i	0.362208	+	0.362208i
$183$	−98.4264	−	193.173i	−0.537849	−	1.05559i
$184$	−27.4391	−	37.7667i	−0.149125	−	0.205254i
$185$	14.1421	+	83.1693i	0.0764438	+	0.449564i
$186$	76.7994	+	55.7980i	0.412900	+	0.299989i
$187$	407.346	+	64.5172i	2.17832	+	0.345012i
$188$	8.36240	−	52.7981i	0.0444808	−	0.280841i
$189$	72.9963	−	100.471i	0.386224	−	0.531591i
$190$	23.1510	−	3.93660i	0.121848	−	0.0207190i
$191$	−144.737	+	105.158i	−0.757787	+	0.550565i	−0.898231	−	0.439524i	$-0.855147\pi$
$191$	−144.737	+	105.158i	−0.757787	+	0.550565i	0.140444	+	0.990089i	$0.455147\pi$
$192$	19.2262	−	9.79626i	0.100137	−	0.0510222i
$193$	−125.750	+	125.750i	−0.651554	+	0.651554i	−0.953367	−	0.301813i	$-0.902408\pi$
$193$	−125.750	+	125.750i	−0.651554	+	0.651554i	0.301813	+	0.953367i	$0.402408\pi$
$194$	140.321	+	45.5931i	0.723304	+	0.235016i
$195$	197.665	+	61.7539i	1.01367	+	0.316687i
$196$	18.8929	+	58.1463i	0.0963922	+	0.296665i
$197$	129.093	−	253.359i	0.655294	−	1.28609i	−0.289108	−	0.957296i	$-0.593359\pi$
$197$	129.093	−	253.359i	0.655294	−	1.28609i	0.944403	−	0.328791i	$-0.106641\pi$
$198$	−47.5811	+	7.53611i	−0.240309	+	0.0380612i
$199$		−	6.73587i		−	0.0338486i	−0.999857	−	0.0169243i	$-0.994613\pi$
$199$		−	6.73587i		−	0.0338486i	0.999857	−	0.0169243i	$-0.00538743\pi$
$200$	−63.7161	−	30.6637i	−0.318580	−	0.153319i
$201$	167.839			0.835021
$202$	33.9971	+	214.649i	0.168302	+	1.06262i
$203$	26.1324	+	13.3151i	0.128731	+	0.0655917i
$204$	107.135	−	34.8103i	0.525172	−	0.170639i
$205$	−147.335	−	104.511i	−0.718707	−	0.509810i
$206$	11.5587	−	35.5739i	0.0561100	−	0.172689i
$207$	20.1289	+	20.1289i	0.0972410	+	0.0972410i
$208$	−27.8847	−	54.7267i	−0.134061	−	0.263109i
$209$	−38.5536	−	53.0645i	−0.184467	−	0.253897i
$210$	−58.5515	−	57.2373i	−0.278816	−	0.272558i
$211$	150.905	+	109.639i	0.715189	+	0.519615i	0.884844	−	0.465888i	$-0.154265\pi$
$211$	150.905	+	109.639i	0.715189	+	0.519615i	−0.169654	+	0.985504i	$0.554265\pi$
$212$	−192.311	−	30.4590i	−0.907126	−	0.143675i
$213$	−41.5396	+	262.271i	−0.195022	+	1.23132i
$214$	51.0063	−	70.2042i	0.238347	−	0.328057i
$215$	−126.660	−	62.7362i	−0.589117	−	0.291796i
$216$	−66.1933	+	48.0922i	−0.306450	+	0.222649i
$217$	−95.1948	+	48.5042i	−0.438686	+	0.223521i
$218$	7.67493	−	7.67493i	0.0352061	−	0.0352061i
$219$	131.758	+	42.8107i	0.601634	+	0.195483i
$220$	2.24148	+	197.489i	0.0101886	+	0.897678i
$221$	−99.0861	−	304.956i	−0.448353	−	1.37989i
$222$	29.2192	−	57.3459i	0.131618	−	0.258315i
$223$	−108.214	+	17.1394i	−0.485265	+	0.0768585i	−0.394273	−	0.918993i	$-0.629004\pi$
$223$	−108.214	+	17.1394i	−0.485265	+	0.0768585i	−0.0909918	+	0.995852i	$0.529004\pi$
$224$			24.2854i			0.108417i
$225$	41.3005	+	12.3903i	0.183558	+	0.0550680i
$226$	192.752			0.852886
$227$	37.3191	+	235.624i	0.164401	+	1.03799i	0.922542	+	0.385898i	$0.126108\pi$
$227$	37.3191	+	235.624i	0.164401	+	1.03799i	−0.758140	+	0.652091i	$0.773892\pi$
$228$	−15.9628	−	8.13346i	−0.0700123	−	0.0356731i
$229$	337.031	−	109.508i	1.47175	−	0.478201i	0.540115	−	0.841591i	$-0.318381\pi$
$229$	337.031	−	109.508i	1.47175	−	0.478201i	0.931637	+	0.363390i	$0.118381\pi$
$230$	93.6321	−	69.6649i	0.407096	−	0.302891i
$231$	−70.6721	+	217.506i	−0.305940	+	0.941586i
$232$	−13.6634	−	13.6634i	−0.0588938	−	0.0588938i
$233$	137.042	+	268.960i	0.588162	+	1.15433i	0.972882	+	0.231300i	$0.0742979\pi$
$233$	137.042	+	268.960i	0.588162	+	1.15433i	−0.384720	+	0.923033i	$0.625702\pi$
$234$	22.0151	+	30.3012i	0.0940817	+	0.129492i
$235$	132.224	+	19.4066i	0.562655	+	0.0825813i
$236$	−173.637	−	126.155i	−0.735751	−	0.534555i
$237$	−99.7723	−	15.8024i	−0.420980	−	0.0666767i
$238$	−19.8331	+	125.221i	−0.0833322	+	0.526139i
$239$	−147.049	+	202.396i	−0.615269	+	0.846845i	−0.996998	−	0.0774294i	$-0.975329\pi$
$239$	−147.049	+	202.396i	−0.615269	+	0.846845i	0.381729	+	0.924274i	$0.375329\pi$
$240$	25.0346	+	47.7846i	0.104311	+	0.199102i
$241$	134.577	−	97.7760i	0.558411	−	0.405709i	−0.272466	−	0.962165i	$-0.587839\pi$
$241$	134.577	−	97.7760i	0.558411	−	0.405709i	0.830877	+	0.556456i	$0.187839\pi$
$242$	339.048	−	172.753i	1.40102	−	0.713857i
$243$	64.8857	−	64.8857i	0.267019	−	0.267019i
$244$	−152.890	−	49.6768i	−0.626596	−	0.203594i
$245$	−144.820	+	48.8789i	−0.591104	+	0.199506i
$246$	42.5854	+	131.064i	0.173111	+	0.532782i
$247$	−23.1516	+	45.4375i	−0.0937310	+	0.183957i
$248$	69.5227	−	11.0113i	0.280333	−	0.0444004i
$249$			6.64342i			0.0266804i
$250$	74.8466	−	160.150i	0.299386	−	0.640600i
$251$	−254.134			−1.01248			−0.506242	−	0.862391i	$-0.668966\pi$
$251$	−254.134			−1.01248			−0.506242	+	0.862391i	$0.668966\pi$
$252$	−2.31666	−	14.6268i	−0.00919309	−	0.0580429i
$253$	−290.441	−	147.987i	−1.14799	−	0.584929i
$254$	−167.873	+	54.5451i	−0.660915	+	0.214744i
$255$	90.0599	+	266.833i	0.353176	+	1.04640i
$256$	4.94427	−	15.2169i	0.0193136	−	0.0594410i
$257$	−208.034	−	208.034i	−0.809470	−	0.809470i	0.175083	−	0.984554i	$-0.443981\pi$
$257$	−208.034	−	208.034i	−0.809470	−	0.809470i	−0.984554	+	0.175083i	$0.943981\pi$
$258$	48.9551	+	96.0799i	0.189749	+	0.372403i
$259$	42.5767	+	58.6018i	0.164389	+	0.226262i
$260$	136.017	−	71.2599i	0.523142	−	0.274077i
$261$	9.53265	+	6.92588i	0.0365236	+	0.0265359i
$262$	−238.145	−	37.7185i	−0.908952	−	0.143964i
$263$	−5.12987	+	32.3887i	−0.0195052	+	0.123151i	−0.995520	−	0.0945547i	$-0.969857\pi$
$263$	−5.12987	+	32.3887i	−0.0195052	+	0.123151i	0.976014	+	0.217706i	$0.0698573\pi$
$264$	88.5643	−	121.898i	0.335471	−	0.461736i
$265$	70.6862	−	481.610i	0.266740	−	1.81740i
$266$	16.3124	−	11.8517i	0.0613249	−	0.0445551i
$267$	−301.418	+	153.580i	−1.12891	+	0.575207i
$268$	88.0004	−	88.0004i	0.328360	−	0.328360i
$269$	234.274	+	76.1202i	0.870906	+	0.282975i	0.710176	−	0.704024i	$-0.248615\pi$
$269$	234.274	+	76.1202i	0.870906	+	0.282975i	0.160730	+	0.986998i	$0.448615\pi$
$270$	−122.101	−	164.108i	−0.452226	−	0.607807i
$271$	−66.4989	−	204.663i	−0.245383	−	0.755213i	−0.995573	−	0.0939900i	$-0.970038\pi$
$271$	−66.4989	−	204.663i	−0.245383	−	0.755213i	0.750190	−	0.661223i	$-0.229962\pi$
$272$	37.9209	−	74.4240i	0.139415	−	0.273617i
$273$	175.619	−	27.8154i	0.643295	−	0.101888i
$274$		−	166.550i		−	0.607846i
$275$	−493.627	+	11.2067i	−1.79501	+	0.0407516i
$276$	−89.0348			−0.322590
$277$	18.3162	+	115.644i	0.0661234	+	0.417486i	0.998440	+	0.0558424i	$0.0177844\pi$
$277$	18.3162	+	115.644i	0.0661234	+	0.417486i	−0.932316	+	0.361644i	$0.882216\pi$
$278$	137.278	+	69.9465i	0.493805	+	0.251606i
$279$	−40.8222	+	13.2639i	−0.146316	+	0.0475410i
$280$	−60.7096	+	0.689048i	−0.216820	+	0.00246089i
$281$	−86.1504	+	265.144i	−0.306585	+	0.943571i	0.672496	+	0.740101i	$0.265222\pi$
$281$	−86.1504	+	265.144i	−0.306585	+	0.943571i	−0.979081	+	0.203471i	$0.934778\pi$
$282$	−72.0928	−	72.0928i	−0.255648	−	0.255648i
$283$	−31.0915	−	61.0205i	−0.109864	−	0.215620i	0.829528	−	0.558465i	$-0.188610\pi$
$283$	−31.0915	−	61.0205i	−0.109864	−	0.215620i	−0.939392	+	0.342845i	$0.888610\pi$
$284$	115.732	+	159.292i	0.407509	+	0.560888i
$285$	19.8794	−	40.1352i	0.0697524	−	0.140825i
$286$	−346.978	−	252.095i	−1.21321	−	0.881449i
$287$	−153.190	−	24.2629i	−0.533763	−	0.0845397i
$288$	−1.52629	+	9.63660i	−0.00529961	+	0.0334604i
$289$	86.4382	−	118.972i	0.299094	−	0.411668i
$290$	33.7685	−	34.5439i	0.116443	−	0.119117i
$291$	227.658	−	165.403i	0.782330	−	0.568396i
$292$	91.5288	−	46.6362i	0.313455	−	0.159713i
$293$	105.951	−	105.951i	0.361609	−	0.361609i	−0.502796	−	0.864405i	$-0.667695\pi$
$293$	105.951	−	105.951i	0.361609	−	0.361609i	0.864405	+	0.502796i	$0.167695\pi$
$294$	110.900	+	36.0335i	0.377210	+	0.122563i
$295$	310.440	−	437.645i	1.05234	−	1.48354i
$296$	−14.7472	−	45.3872i	−0.0498217	−	0.153335i
$297$	−259.376	+	509.053i	−0.873319	+	1.71398i
$298$	85.7745	−	13.5854i	0.287834	−	0.0455884i
$299$			253.434i			0.847605i
$300$	−118.743	+	63.9382i	−0.395811	+	0.213127i
$301$	−121.362			−0.403197
$302$	37.2432	+	235.144i	0.123322	+	0.778624i
$303$	369.316	+	188.176i	1.21887	+	0.621043i
$304$	−12.6340	+	4.10504i	−0.0415592	+	0.0135034i
$305$	119.846	−	383.609i	0.392938	−	1.25773i
$306$	−15.7398	+	48.4420i	−0.0514371	+	0.158307i
$307$	54.2997	+	54.2997i	0.176872	+	0.176872i	0.789991	−	0.613119i	$-0.210085\pi$
$307$	54.2997	+	54.2997i	0.176872	+	0.176872i	−0.613119	+	0.789991i	$0.710085\pi$
$308$	76.9872	+	151.096i	0.249958	+	0.490571i
$309$	−41.9327	−	57.7153i	−0.135704	−	0.186781i
$310$	29.4991	+	173.483i	0.0951583	+	0.559623i
$311$	−38.3357	−	27.8525i	−0.123266	−	0.0895579i	0.524444	−	0.851445i	$-0.324273\pi$
$311$	−38.3357	−	27.8525i	−0.123266	−	0.0895579i	−0.647710	+	0.761887i	$0.724273\pi$
$312$	−115.704	−	18.3257i	−0.370845	−	0.0587361i
$313$	23.0002	−	145.218i	0.0734832	−	0.463955i	−0.923318	−	0.384036i	$-0.874534\pi$
$313$	23.0002	−	145.218i	0.0734832	−	0.463955i	0.996801	−	0.0799187i	$-0.0254661\pi$
$314$	−98.8477	+	136.052i	−0.314802	+	0.433287i
$315$	36.4989	−	6.20628i	0.115870	−	0.0197025i
$316$	−60.5974	+	44.0266i	−0.191764	+	0.139325i
$317$	−60.5119	+	30.8324i	−0.190889	+	0.0972630i	−0.546823	−	0.837248i	$-0.684163\pi$
$317$	−60.5119	+	30.8324i	−0.190889	+	0.0972630i	0.355934	+	0.934511i	$0.384163\pi$
$318$	−262.589	+	262.589i	−0.825753	+	0.825753i
$319$	−128.323	−	41.6947i	−0.402267	−	0.130704i
$320$	38.1801	+	11.9281i	0.119313	+	0.0372754i
$321$	−51.1442	−	157.406i	−0.159328	−	0.490360i
$322$	45.4924	−	89.2838i	0.141281	−	0.277279i
$323$	−68.4962	+	10.8487i	−0.212063	+	0.0335874i
$324$			125.005i			0.385817i
$325$	181.997	+	337.998i	0.559992	+	1.03999i
$326$	−47.7817			−0.146570
$327$	−3.23840	−	20.4465i	−0.00990336	−	0.0625274i
$328$	91.0469	+	46.3907i	0.277582	+	0.141435i
$329$	109.130	−	35.4586i	0.331703	−	0.107777i
$330$	307.239	+	217.938i	0.931027	+	0.660418i
$331$	−10.7322	+	33.0304i	−0.0324236	+	0.0997897i	−0.965959	−	0.258697i	$-0.916707\pi$
$331$	−10.7322	+	33.0304i	−0.0324236	+	0.0997897i	0.933535	+	0.358486i	$0.116707\pi$
$332$	3.48324	+	3.48324i	0.0104917	+	0.0104917i
$333$	13.2117	+	25.9294i	0.0396747	+	0.0778660i
$334$	−111.412	−	153.346i	−0.333569	−	0.459119i
$335$	222.484	+	217.490i	0.664130	+	0.649224i
$336$	37.4724	+	27.2253i	0.111525	+	0.0810277i
$337$	134.926	+	21.3702i	0.400374	+	0.0634131i	0.353375	−	0.935482i	$-0.385034\pi$
$337$	134.926	+	21.3702i	0.400374	+	0.0634131i	0.0469995	+	0.998895i	$0.485034\pi$
$338$	−14.7751	+	93.2861i	−0.0437132	+	0.275994i
$339$	216.086	−	297.417i	0.637422	−	0.877336i
$340$	187.124	+	92.6845i	0.550364	+	0.272602i
$341$	397.640	−	288.903i	1.16610	−	0.847222i
$342$	7.21771	−	3.67761i	0.0211044	−	0.0107532i
$343$	−241.547	+	241.547i	−0.704218	+	0.704218i
$344$	76.0439	+	24.7082i	0.221058	+	0.0718260i
$345$	−2.52618	−	222.573i	−0.00732225	−	0.645138i
$346$	−57.6455	−	177.415i	−0.166606	−	0.512759i
$347$	−140.732	+	276.202i	−0.405567	+	0.795970i	−0.999966	−	0.00819994i	$-0.997390\pi$
$347$	−140.732	+	276.202i	−0.405567	+	0.795970i	0.594399	+	0.804170i	$0.297390\pi$
$348$	−36.4000	+	5.76519i	−0.104598	+	0.0165666i
$349$			134.320i			0.384872i	0.981310	+	0.192436i	$0.0616388\pi$
$349$			134.320i			0.384872i	−0.981310	+	0.192436i	$0.938361\pi$
$350$	−3.44502	−	151.745i	−0.00984291	−	0.433557i
$351$	444.191			1.26550
$352$	−17.4775	−	110.348i	−0.0496519	−	0.313490i
$353$	−407.275	−	207.517i	−1.15375	−	0.587866i	−0.230884	−	0.972981i	$-0.574162\pi$
$353$	−407.275	−	207.517i	−1.15375	−	0.587866i	−0.922869	+	0.385115i	$0.874162\pi$
$354$	−389.314	+	126.496i	−1.09976	+	0.357333i
$355$	−394.921	+	293.832i	−1.11245	+	0.827696i
$356$	−77.5134	+	238.562i	−0.217734	+	0.670118i
$357$	170.982	+	170.982i	0.478942	+	0.478942i
$358$	145.186	+	284.943i	0.405547	+	0.795931i
$359$	160.357	+	220.712i	0.446676	+	0.614797i	0.971679	−	0.236303i	$-0.0759359\pi$
$359$	160.357	+	220.712i	0.446676	+	0.614797i	−0.525003	+	0.851100i	$0.675936\pi$
$360$	−24.1332	−	3.54205i	−0.0670368	−	0.00983904i
$361$	−283.132	−	205.708i	−0.784300	−	0.569827i
$362$	84.6457	+	13.4066i	0.233828	+	0.0370347i
$363$	113.533	−	716.818i	0.312762	−	1.97470i
$364$	77.4957	−	106.664i	0.212900	−	0.293032i
$365$	119.180	+	227.484i	0.326521	+	0.623244i
$366$	−248.049	+	180.218i	−0.677730	+	0.492400i
$367$	131.060	−	66.7782i	0.357111	−	0.181957i	−0.266226	−	0.963911i	$-0.585777\pi$
$367$	131.060	−	66.7782i	0.357111	−	0.181957i	0.623337	+	0.781954i	$0.285777\pi$
$368$	−46.6822	+	46.6822i	−0.126854	+	0.126854i
$369$	−59.2618	−	19.2553i	−0.160601	−	0.0521824i
$370$	113.042	−	38.1534i	0.305520	−	0.103117i
$371$	−129.154	−	397.494i	−0.348123	−	1.07141i
$372$	60.9484	−	119.618i	0.163840	−	0.321553i
$373$	280.873	−	44.4859i	0.753011	−	0.119265i	0.231883	−	0.972744i	$-0.425511\pi$
$373$	280.873	−	44.4859i	0.753011	−	0.119265i	0.521128	+	0.853479i	$0.325511\pi$
$374$		−	583.254i		−	1.55950i
$375$	−163.204	−	295.025i	−0.435212	−	0.786734i
$376$	−75.5985			−0.201060
$377$	16.4104	+	103.611i	0.0435288	+	0.274830i
$378$	−156.487	−	79.7340i	−0.413986	−	0.210937i
$379$	664.737	−	215.986i	1.75392	−	0.569884i	0.757381	−	0.652974i	$-0.226479\pi$
$379$	664.737	−	215.986i	1.75392	−	0.569884i	0.996542	+	0.0830897i	$0.0264788\pi$
$380$	−10.6204	−	31.4665i	−0.0279484	−	0.0828066i
$381$	−104.031	+	320.176i	−0.273048	+	0.840356i
$382$	178.905	+	178.905i	0.468338	+	0.468338i
$383$	227.760	+	447.004i	0.594673	+	1.16711i	0.970653	+	0.240484i	$0.0773062\pi$
$383$	227.760	+	447.004i	0.594673	+	1.16711i	−0.375980	+	0.926628i	$0.622694\pi$
$384$	−17.9369	−	24.6880i	−0.0467107	−	0.0642917i
$385$	−375.531	+	196.743i	−0.975405	+	0.511020i
$386$	203.468	+	147.828i	0.527119	+	0.382974i
$387$	−48.1572	−	7.62736i	−0.124437	−	0.0197089i
$388$	32.6410	−	206.087i	0.0841264	−	0.531153i
$389$	−252.774	+	347.914i	−0.649805	+	0.894379i	−0.999091	−	0.0426369i	$-0.986424\pi$
$389$	−252.774	+	347.914i	−0.649805	+	0.894379i	0.349286	+	0.937016i	$0.386424\pi$
$390$	42.5283	−	289.760i	0.109047	−	0.742976i
$391$	−278.827	+	202.580i	−0.713114	+	0.518107i
$392$	77.0392	−	39.2534i	0.196529	−	0.100136i
$393$	−325.174	+	325.174i	−0.827415	+	0.827415i
$394$	−382.452	−	124.266i	−0.970691	−	0.315397i
$395$	−111.779	−	150.235i	−0.282984	−	0.380341i
$396$	21.0529	+	64.7942i	0.0531639	+	0.163622i
$397$	258.120	−	506.590i	0.650177	−	1.27604i	−0.296860	−	0.954921i	$-0.595940\pi$
$397$	258.120	−	506.590i	0.650177	−	1.27604i	0.947037	−	0.321123i	$-0.104060\pi$
$398$	−9.40868	+	1.49019i	−0.0236399	+	0.00374419i
$399$		−	38.4565i		−	0.0963821i
$400$	−28.7351	+	95.7825i	−0.0718378	+	0.239456i
$401$	596.762			1.48818			0.744092	−	0.668077i	$-0.232882\pi$
$401$	596.762			1.48818			0.744092	+	0.668077i	$0.232882\pi$
$402$	−37.1314	−	234.438i	−0.0923666	−	0.583180i
$403$	−340.487	−	173.487i	−0.844882	−	0.430489i
$404$	292.301	−	94.9743i	0.723517	−	0.235085i
$405$	−312.492	+	3.54675i	−0.771584	+	0.00875741i
$406$	12.8173	−	39.4475i	0.0315696	−	0.0971613i
$407$	−235.634	−	235.634i	−0.578954	−	0.578954i
$408$	−72.3248	−	141.945i	−0.177267	−	0.347905i
$409$	11.2451	+	15.4776i	0.0274942	+	0.0378425i	0.822543	−	0.568703i	$-0.192555\pi$
$409$	11.2451	+	15.4776i	0.0274942	+	0.0378425i	−0.795049	+	0.606546i	$0.792555\pi$
$410$	−113.386	+	228.919i	−0.276551	+	0.558339i
$411$	−256.987	−	186.712i	−0.625272	−	0.454287i
$412$	−52.2468	−	8.27508i	−0.126813	−	0.0200852i
$413$	72.0706	−	455.036i	0.174505	−	1.10178i
$414$	23.6629	−	32.5692i	0.0571568	−	0.0786696i
$415$	−8.60870	+	8.80636i	−0.0207439	+	0.0212201i
$416$	−70.2734	+	51.0566i	−0.168927	+	0.122732i
$417$	261.824	−	133.406i	0.627875	−	0.319918i
$418$	−65.5913	+	65.5913i	−0.156917	+	0.156917i
$419$	−427.833	−	139.011i	−1.02108	−	0.331769i	−0.249822	−	0.968292i	$-0.580372\pi$
$419$	−427.833	−	139.011i	−1.02108	−	0.331769i	−0.771258	+	0.636523i	$0.780372\pi$
$420$	−66.9957	+	94.4475i	−0.159514	+	0.224875i
$421$	222.954	+	686.182i	0.529582	+	1.62989i	0.755072	+	0.655641i	$0.227602\pi$
$421$	222.954	+	686.182i	0.529582	+	1.62989i	−0.225490	+	0.974245i	$0.572398\pi$
$422$	119.759	−	235.040i	0.283789	−	0.556967i
$423$	45.5320	−	7.21156i	0.107641	−	0.0170486i
$424$			275.358i			0.649430i
$425$	−226.387	+	470.409i	−0.532676	+	1.10685i
$426$	375.531			0.881527
$427$	−53.9814	−	340.825i	−0.126420	−	0.798186i
$428$	−109.346	−	55.7143i	−0.255480	−	0.130174i
$429$	−777.964	+	252.776i	−1.81344	+	0.589221i
$430$	−59.6088	+	190.799i	−0.138625	+	0.443717i
$431$	−81.0065	+	249.312i	−0.187950	+	0.578451i	−0.999987	−	0.00515539i	$-0.998359\pi$
$431$	−81.0065	+	249.312i	−0.187950	+	0.578451i	0.812037	+	0.583607i	$0.198359\pi$
$432$	81.8194	+	81.8194i	0.189397	+	0.189397i
$433$	−148.962	−	292.354i	−0.344023	−	0.675183i	0.652564	−	0.757734i	$-0.273693\pi$
$433$	−148.962	−	292.354i	−0.344023	−	0.675183i	−0.996587	+	0.0825505i	$0.973693\pi$
$434$	88.8108	+	122.238i	0.204633	+	0.281654i
$435$	−15.4448	−	90.8305i	−0.0355053	−	0.208806i
$436$	−12.4183	−	9.02242i	−0.0284823	−	0.0206936i
$437$	54.1378	+	8.57459i	0.123885	+	0.0196215i
$438$	30.6491	−	193.511i	0.0699751	−	0.441806i
$439$	−235.016	+	323.472i	−0.535344	+	0.736837i	−0.987933	−	0.154882i	$-0.950500\pi$
$439$	−235.016	+	323.472i	−0.535344	+	0.736837i	0.452589	+	0.891719i	$0.350500\pi$
$440$	275.357	−	46.8218i	0.625812	−	0.106413i
$441$	−42.6552	+	30.9908i	−0.0967239	+	0.0702740i
$442$	−404.042	+	205.870i	−0.914122	+	0.465768i
$443$	−123.250	+	123.250i	−0.278216	+	0.278216i	−0.832396	−	0.554181i	$-0.813032\pi$
$443$	−123.250	+	123.250i	−0.278216	+	0.278216i	0.554181	+	0.832396i	$0.313032\pi$
$444$	−86.5650	−	28.1267i	−0.194966	−	0.0633484i
$445$	−598.566	−	187.002i	−1.34509	−	0.420230i
$446$	47.8808	+	147.362i	0.107356	+	0.330408i
$447$	75.1959	−	147.580i	0.168223	−	0.330157i
$448$	33.9219	−	5.37271i	0.0757186	−	0.0119926i
$449$		−	330.000i		−	0.734966i	−0.930030	−	0.367483i	$-0.880220\pi$
$449$		−	330.000i		−	0.734966i	0.930030	−	0.367483i	$-0.119780\pi$
$450$	8.16983	−	60.4297i	0.0181552	−	0.134288i
$451$	713.527			1.58210
$452$	−42.6429	−	269.237i	−0.0943427	−	0.595657i
$453$	404.580	+	206.144i	0.893112	+	0.455063i
$454$	320.863	−	104.255i	0.706747	−	0.229636i
$455$	268.841	+	190.701i	0.590859	+	0.419122i
$456$	−7.82935	+	24.0963i	−0.0171696	+	0.0528427i
$457$	105.636	+	105.636i	0.231151	+	0.231151i	0.813173	−	0.582022i	$-0.197738\pi$
$457$	105.636	+	105.636i	0.231151	+	0.231151i	−0.582022	+	0.813173i	$0.697738\pi$
$458$	−227.523	−	446.539i	−0.496775	−	0.974977i
$459$	355.060	+	488.698i	0.773551	+	1.06470i
$460$	−118.022	−	115.373i	−0.256570	−	0.250812i
$461$	−81.4590	−	59.1834i	−0.176701	−	0.128381i	0.495919	−	0.868369i	$-0.334831\pi$
$461$	−81.4590	−	59.1834i	−0.176701	−	0.128381i	−0.672620	+	0.739988i	$0.734831\pi$
$462$	319.448	+	50.5956i	0.691446	+	0.109514i
$463$	−0.953017	+	6.01712i	−0.00205835	+	0.0129959i	−0.988696	−	0.149933i	$-0.952094\pi$
$463$	−0.953017	+	6.01712i	−0.00205835	+	0.0129959i	0.986638	+	0.162929i	$0.0520942\pi$
$464$	−16.0622	+	22.1078i	−0.0346169	+	0.0476461i
$465$	300.755	+	148.967i	0.646784	+	0.320360i
$466$	345.365	−	250.923i	0.741127	−	0.538461i
$467$	127.516	−	64.9728i	0.273054	−	0.139128i	−0.312102	−	0.950049i	$-0.601033\pi$
$467$	127.516	−	64.9728i	0.273054	−	0.139128i	0.585156	+	0.810921i	$0.301033\pi$
$468$	37.4544	−	37.4544i	0.0800307	−	0.0800307i
$469$	254.066	+	82.5511i	0.541719	+	0.176015i
$470$	−2.14495	−	188.984i	−0.00456373	−	0.402094i
$471$	99.1149	+	305.044i	0.210435	+	0.647652i
$472$	−137.799	+	270.446i	−0.291948	+	0.572980i
$473$	551.447	−	87.3407i	1.16585	−	0.184653i
$474$			142.858i			0.301389i
$475$	78.3599	−	27.4421i	0.164968	−	0.0577728i
$476$	179.297			0.376674
$477$	−26.2672	−	165.845i	−0.0550676	−	0.347683i
$478$	315.239	+	160.622i	0.659496	+	0.336030i
$479$	−189.361	+	61.5271i	−0.395326	+	0.128449i	−0.499932	−	0.866065i	$-0.666642\pi$
$479$	−189.361	+	61.5271i	−0.395326	+	0.128449i	0.104606	+	0.994514i	$0.466642\pi$
$480$	61.2072	−	45.5398i	0.127515	−	0.0948746i
$481$	−80.0614	+	246.404i	−0.166448	+	0.512274i
$482$	−166.346	−	166.346i	−0.345117	−	0.345117i
$483$	−86.7655	−	170.287i	−0.179639	−	0.352561i
$484$	−316.311	−	435.364i	−0.653534	−	0.899513i
$485$	516.111	+	75.7500i	1.06415	+	0.156186i
$486$	−104.987	−	76.2777i	−0.216023	−	0.156950i
$487$	371.062	+	58.7704i	0.761934	+	0.120678i	0.525296	−	0.850919i	$-0.323955\pi$
$487$	371.062	+	58.7704i	0.761934	+	0.120678i	0.236638	+	0.971598i	$0.423955\pi$
$488$	−35.5647	+	224.547i	−0.0728784	+	0.460136i
$489$	−53.5659	+	73.7272i	−0.109542	+	0.150771i
$490$	100.313	+	191.472i	0.204721	+	0.390759i
$491$	263.402	−	191.373i	0.536460	−	0.389761i	−0.286309	−	0.958137i	$-0.592428\pi$
$491$	263.402	−	191.373i	0.536460	−	0.389761i	0.822769	+	0.568376i	$0.192428\pi$
$492$	173.650	−	88.4789i	0.352946	−	0.179835i
$493$	−100.875	+	100.875i	−0.204615	+	0.204615i
$494$	68.5891	+	22.2859i	0.138844	+	0.0451132i
$495$	−161.378	+	54.4673i	−0.326016	+	0.110035i
$496$	−30.7612	−	94.6734i	−0.0620186	−	0.190874i
$497$	−191.877	+	376.581i	−0.386071	+	0.757708i
$498$	9.27954	−	1.46974i	0.0186336	−	0.00295128i
$499$		−	400.069i		−	0.801742i	−0.916134	−	0.400871i	$-0.868708\pi$
$499$		−	400.069i		−	0.801742i	0.916134	−	0.400871i	$-0.131292\pi$
$500$	−240.256	−	69.1156i	−0.480512	−	0.138231i
$501$	−361.512			−0.721581
$502$	56.2224	+	354.974i	0.111997	+	0.707120i
$503$	159.768	+	81.4059i	0.317630	+	0.161841i	0.605536	−	0.795818i	$-0.292959\pi$
$503$	159.768	+	81.4059i	0.317630	+	0.161841i	−0.287905	+	0.957659i	$0.592959\pi$
$504$	−19.9182	+	6.47183i	−0.0395203	+	0.0128409i
$505$	245.714	+	728.010i	0.486562	+	1.44160i
$506$	−142.454	+	438.428i	−0.281530	+	0.866459i
$507$	127.377	+	127.377i	0.251236	+	0.251236i
$508$	113.327	+	222.418i	0.223086	+	0.437830i
$509$	−274.861	−	378.313i	−0.540002	−	0.743248i	0.448612	−	0.893727i	$-0.351919\pi$
$509$	−274.861	−	378.313i	−0.540002	−	0.743248i	−0.988613	+	0.150478i	$0.951919\pi$
$510$	352.789	−	184.828i	0.691742	−	0.362407i
$511$	178.392	+	129.609i	0.349103	+	0.253638i
$512$	−22.3488	−	3.53971i	−0.0436501	−	0.00691349i
$513$	15.0286	−	94.8869i	0.0292955	−	0.184965i
$514$	−244.559	+	336.606i	−0.475795	+	0.654875i
$515$	19.2040	−	130.843i	0.0372893	−	0.254065i
$516$	123.374	−	89.6366i	0.239097	−	0.173714i
$517$	−470.349	+	239.655i	−0.909766	+	0.463549i
$518$	72.4358	−	72.4358i	0.139837	−	0.139837i
$519$	−338.375	−	109.945i	−0.651975	−	0.211839i
$520$	−129.627	−	174.224i	−0.249283	−	0.335045i
$521$	−14.5003	−	44.6274i	−0.0278317	−	0.0856571i	0.936176	−	0.351532i	$-0.114339\pi$
$521$	−14.5003	−	44.6274i	−0.0278317	−	0.0856571i	−0.964008	+	0.265875i	$0.914339\pi$
$522$	7.56516	−	14.8475i	0.0144926	−	0.0284434i
$523$	−901.048	+	142.712i	−1.72285	+	0.272872i	−0.937953	−	0.346761i	$-0.887281\pi$
$523$	−901.048	+	142.712i	−1.72285	+	0.272872i	−0.784892	+	0.619633i	$0.787281\pi$
$524$			340.987i			0.650738i
$525$	−238.004	−	164.799i	−0.453342	−	0.313902i
$526$	46.3755			0.0881664
$527$	−81.2954	−	513.279i	−0.154261	−	0.973964i
$528$	−189.861	−	96.7390i	−0.359585	−	0.183218i
$529$	−244.038	+	79.2928i	−0.461320	+	0.149892i
$530$	−688.352	+	7.81272i	−1.29878	+	0.0147410i
$531$	57.1961	−	176.032i	0.107714	−	0.331509i
$532$	−20.1633	−	20.1633i	−0.0379009	−	0.0379009i
$533$	−251.852	−	494.287i	−0.472517	−	0.927367i
$534$	281.204	+	387.045i	0.526600	+	0.724803i
$535$	136.174	−	274.927i	0.254532	−	0.513882i
$536$	−142.388	−	103.451i	−0.265649	−	0.193005i
$537$	602.429	+	95.4154i	1.12184	+	0.177682i
$538$	54.4960	−	344.074i	0.101294	−	0.639543i
$539$	354.875	−	488.444i	0.658396	−	0.906204i
$540$	−202.214	+	206.857i	−0.374470	+	0.383068i
$541$	−221.533	+	160.953i	−0.409487	+	0.297510i	−0.773394	−	0.633925i	$-0.781443\pi$
$541$	−221.533	+	160.953i	−0.409487	+	0.297510i	0.363907	+	0.931435i	$0.381443\pi$
$542$	−271.162	+	138.164i	−0.500298	+	0.254915i
$543$	115.579	−	115.579i	0.212852	−	0.212852i
$544$	−112.345	−	36.5031i	−0.206516	−	0.0671012i
$545$	22.2023	−	31.2997i	0.0407381	−	0.0574307i
$546$	−77.7052	−	239.152i	−0.142317	−	0.438007i
$547$	167.934	−	329.590i	0.307010	−	0.602541i	−0.685023	−	0.728522i	$-0.740208\pi$
$547$	167.934	−	329.590i	0.307010	−	0.602541i	0.992033	+	0.125981i	$0.0402077\pi$
$548$	−232.637	+	36.8461i	−0.424521	+	0.0672375i
$549$		−	138.634i		−	0.252521i
$550$	124.860	+	687.021i	0.227017	+	1.24913i
$551$	22.6883			0.0411766
$552$	19.6973	+	124.364i	0.0356835	+	0.225297i
$553$	−143.258	−	72.9935i	−0.259056	−	0.131995i
$554$	157.479	−	51.1681i	0.284259	−	0.0923613i
$555$	67.8561	−	217.197i	0.122263	−	0.391345i
$556$	67.3313	−	207.224i	0.121099	−	0.372706i
$557$	348.444	+	348.444i	0.625572	+	0.625572i	0.946951	−	0.321379i	$-0.104146\pi$
$557$	348.444	+	348.444i	0.625572	+	0.625572i	−0.321379	+	0.946951i	$0.604146\pi$
$558$	27.5583	+	54.0862i	0.0493876	+	0.0969286i
$559$	−255.147	−	351.179i	−0.456434	−	0.628228i
$560$	14.3934	+	84.6469i	0.0257024	+	0.151155i
$561$	−899.962	−	653.861i	−1.60421	−	1.16553i
$562$	389.412	+	61.6768i	0.692904	+	0.109745i
$563$	−2.82791	+	17.8547i	−0.00502292	+	0.0317135i	−0.990073	−	0.140558i	$-0.955110\pi$
$563$	−2.82791	+	17.8547i	−0.00502292	+	0.0317135i	0.985050	+	0.172271i	$0.0551105\pi$
$564$	−84.7502	+	116.649i	−0.150266	+	0.206824i
$565$	671.839	−	114.239i	1.18909	−	0.202194i
$566$	−78.3552	+	56.9284i	−0.138437	+	0.100580i
$567$	−239.083	+	121.819i	−0.421662	+	0.214848i
$568$	196.896	−	196.896i	0.346648	−	0.346648i
$569$	103.461	+	33.6166i	0.181830	+	0.0590801i	0.398517	−	0.917161i	$-0.369525\pi$
$569$	103.461	+	33.6166i	0.181830	+	0.0590801i	−0.216687	+	0.976241i	$0.569525\pi$
$570$	−60.4590	−	18.8884i	−0.106068	−	0.0331376i
$571$	−308.868	−	950.597i	−0.540924	−	1.66479i	−0.730489	−	0.682925i	$-0.760708\pi$
$571$	−308.868	−	950.597i	−0.540924	−	1.66479i	0.189564	−	0.981868i	$-0.439292\pi$
$572$	−275.364	+	540.431i	−0.481405	+	0.944810i
$573$	476.614	−	75.4882i	0.831787	−	0.131742i
$574$			219.344i			0.382132i
$575$	285.066	−	298.310i	0.495767	−	0.518801i
$576$	13.7981			0.0239550
$577$	36.5466	+	230.746i	0.0633389	+	0.399906i	0.998906	+	0.0467579i	$0.0148889\pi$
$577$	36.5466	+	230.746i	0.0633389	+	0.399906i	−0.935567	+	0.353148i	$0.885111\pi$
$578$	−185.303	−	94.4167i	−0.320594	−	0.163351i
$579$	456.198	−	148.228i	0.787906	−	0.256006i
$580$	−55.7216	−	39.5257i	−0.0960717	−	0.0681478i
$581$	−3.26754	+	10.0565i	−0.00562399	+	0.0173089i
$582$	−281.401	−	281.401i	−0.483506	−	0.483506i
$583$	872.914	+	1713.19i	1.49728	+	2.93858i
$584$	−85.3907	−	117.530i	−0.146217	−	0.201250i
$585$	94.6925	+	92.5672i	0.161868	+	0.158234i
$586$	−171.433	−	124.553i	−0.292547	−	0.212548i
$587$	−1054.05	−	166.945i	−1.79565	−	0.284403i	−0.832629	−	0.553831i	$-0.813165\pi$
$587$	−1054.05	−	166.945i	−1.79565	−	0.284403i	−0.963021	+	0.269428i	$0.913165\pi$
$588$	25.7972	−	162.877i	0.0438727	−	0.277001i
$589$	−48.5797	+	66.8643i	−0.0824783	+	0.113522i
$590$	−679.982	−	336.803i	−1.15251	−	0.570852i
$591$	−620.493	+	450.815i	−1.04990	+	0.762800i
$592$	−60.1345	+	30.6400i	−0.101578	+	0.0517568i
$593$	−167.596	+	167.596i	−0.282624	+	0.282624i	−0.834155	−	0.551531i	$-0.814044\pi$
$593$	−167.596	+	167.596i	−0.282624	+	0.282624i	0.551531	+	0.834155i	$0.314044\pi$
$594$	768.429	+	249.678i	1.29365	+	0.420333i
$595$	5.08717	+	448.213i	0.00854987	+	0.753299i
$596$	−37.9521	−	116.805i	−0.0636780	−	0.195981i
$597$	−8.24830	+	16.1882i	−0.0138162	+	0.0271159i
$598$	353.997	−	56.0676i	0.591968	−	0.0937585i
$599$		−	982.845i		−	1.64081i	−0.571783	−	0.820405i	$-0.693748\pi$
$599$		−	982.845i		−	1.64081i	0.571783	−	0.820405i	$-0.306252\pi$
$600$	115.579	+	151.716i	0.192631	+	0.252860i
$601$	−334.454			−0.556495			−0.278248	−	0.960509i	$-0.589754\pi$
$601$	−334.454			−0.556495			−0.278248	+	0.960509i	$0.589754\pi$
$602$	26.8492	+	169.519i	0.0446000	+	0.281593i
$603$	95.6267	+	48.7243i	0.158585	+	0.0808031i
$604$	320.211	−	104.043i	0.530150	−	0.172256i
$605$	1079.37	−	803.078i	1.78408	−	1.32740i
$606$	181.140	−	557.492i	0.298911	−	0.919954i
$607$	−311.482	−	311.482i	−0.513151	−	0.513151i	0.402340	−	0.915490i	$-0.368197\pi$
$607$	−311.482	−	311.482i	−0.513151	−	0.513151i	−0.915490	+	0.402340i	$0.868197\pi$
$608$	8.52897	+	16.7391i	0.0140279	+	0.0275313i
$609$	−46.4987	−	63.9999i	−0.0763525	−	0.105090i
$610$	−562.339	−	82.5349i	−0.921868	−	0.135303i
$611$	332.035	+	241.238i	0.543430	+	0.394825i
$612$	71.1460	+	11.2684i	0.116252	+	0.0184125i
$613$	−124.870	+	788.398i	−0.203703	+	1.28613i	0.647812	+	0.761800i	$0.275684\pi$
$613$	−124.870	+	788.398i	−0.203703	+	1.28613i	−0.851515	+	0.524330i	$0.824316\pi$
$614$	63.8332	−	87.8588i	0.103963	−	0.143093i
$615$	226.110	+	431.586i	0.367659	+	0.701766i
$616$	194.019	−	140.963i	0.314966	−	0.228836i
$617$	294.720	−	150.167i	0.477666	−	0.243383i	−0.198544	−	0.980092i	$-0.563621\pi$
$617$	294.720	−	150.167i	0.477666	−	0.243383i	0.676210	+	0.736709i	$0.263621\pi$
$618$	−71.3401	+	71.3401i	−0.115437	+	0.115437i
$619$	701.808	+	228.031i	1.13378	+	0.368386i	0.815010	−	0.579447i	$-0.196731\pi$
$619$	701.808	+	228.031i	1.13378	+	0.368386i	0.318767	+	0.947833i	$0.396731\pi$
$620$	235.795	−	79.5843i	0.380315	−	0.128362i
$621$	−147.537	−	454.071i	−0.237579	−	0.731193i
$622$	−30.4234	+	59.7092i	−0.0489122	+	0.0959956i
$623$	−531.808	+	84.2302i	−0.853625	+	0.135201i
$624$			165.669i			0.265496i
$625$	165.961	−	602.563i	0.265538	−	0.964100i
$626$	−207.929			−0.332155
$627$	27.6759	+	174.739i	0.0441402	+	0.278691i
$628$	211.906	+	107.972i	0.337430	+	0.171929i
$629$	−335.089	+	108.877i	−0.532733	+	0.173096i
$630$	−16.7437	−	49.6087i	−0.0265772	−	0.0787440i
$631$	−86.2411	+	265.423i	−0.136674	+	0.420638i	−0.995847	−	0.0910471i	$-0.970979\pi$
$631$	−86.2411	+	265.423i	−0.136674	+	0.420638i	0.859173	+	0.511685i	$0.170979\pi$
$632$	74.9025	+	74.9025i	0.118517	+	0.118517i
$633$	−228.411	−	448.281i	−0.360838	−	0.708185i
$634$	56.4539	+	77.7021i	0.0890440	+	0.122559i
$635$	−552.793	+	289.611i	−0.870540	+	0.456080i
$636$	424.878	+	308.692i	0.668048	+	0.485365i
$637$	−463.622	−	73.4305i	−0.727821	−	0.115276i
$638$	−29.8501	+	188.466i	−0.0467870	+	0.295402i
$639$	−99.8054	+	137.370i	−0.156190	+	0.214977i
$640$	8.21460	−	55.9689i	0.0128353	−	0.0874514i
$641$	−258.559	+	187.854i	−0.403369	+	0.293065i	−0.770912	−	0.636942i	$-0.780199\pi$
$641$	−258.559	+	187.854i	−0.403369	+	0.293065i	0.367543	+	0.930007i	$0.380199\pi$
$642$	−208.550	+	106.261i	−0.324844	+	0.165516i
$643$	331.237	−	331.237i	0.515144	−	0.515144i	−0.400954	−	0.916098i	$-0.631321\pi$
$643$	331.237	−	331.237i	0.515144	−	0.515144i	0.916098	+	0.400954i	$0.131321\pi$
$644$	−134.776	−	43.7914i	−0.209280	−	0.0679991i
$645$	227.578	+	305.872i	0.352833	+	0.474221i
$646$	30.3071	+	93.2756i	0.0469150	+	0.144390i
$647$	52.8755	−	103.774i	0.0817242	−	0.160393i	−0.846528	−	0.532344i	$-0.821311\pi$
$647$	52.8755	−	103.774i	0.0817242	−	0.160393i	0.928252	+	0.371951i	$0.121311\pi$
$648$	174.607	−	27.6550i	0.269455	−	0.0426775i
$649$			2119.47i			3.26574i
$650$	431.853	−	328.990i	0.664389	−	0.506139i
$651$	288.175			0.442665
$652$	10.5708	+	66.7416i	0.0162129	+	0.102364i
$653$	−143.296	−	73.0129i	−0.219442	−	0.111811i	0.340814	−	0.940131i	$-0.389297\pi$
$653$	−143.296	−	73.0129i	−0.219442	−	0.111811i	−0.560256	+	0.828319i	$0.689297\pi$
$654$	−27.8432	+	9.04681i	−0.0425737	+	0.0138330i
$655$	−852.412	+	9.67479i	−1.30139	+	0.0147707i
$656$	44.6562	−	137.438i	0.0680735	−	0.209509i
$657$	62.6413	+	62.6413i	0.0953444	+	0.0953444i
$658$	−73.6717	−	144.589i	−0.111963	−	0.219740i
$659$	406.460	+	559.444i	0.616783	+	0.848929i	0.997114	−	0.0759218i	$-0.0241899\pi$
$659$	406.460	+	559.444i	0.616783	+	0.848929i	−0.380331	+	0.924850i	$0.624190\pi$
$660$	236.445	−	477.367i	0.358250	−	0.723283i
$661$	109.891	+	79.8405i	0.166250	+	0.120787i	0.667799	−	0.744341i	$-0.267236\pi$
$661$	109.891	+	79.8405i	0.166250	+	0.120787i	−0.501549	+	0.865129i	$0.667236\pi$
$662$	48.5112	+	7.68343i	0.0732798	+	0.0116064i
$663$	−135.296	+	854.228i	−0.204067	+	1.28843i
$664$	4.09479	−	5.63600i	0.00616685	−	0.00848794i
$665$	49.8328	−	50.9770i	0.0749365	−	0.0766571i
$666$	33.2954	−	24.1905i	0.0499931	−	0.0363221i
$667$	100.465	−	51.1894i	0.150622	−	0.0767457i
$668$	−189.546	+	189.546i	−0.283751	+	0.283751i
$669$	281.057	+	91.3209i	0.420115	+	0.136504i
$670$	254.570	−	358.881i	0.379955	−	0.535644i
$671$	490.563	+	1509.80i	0.731093	+	2.25007i
$672$	29.7383	−	58.3647i	0.0442534	−	0.0868522i
$673$	808.411	−	128.040i	1.20120	−	0.190252i	0.476414	−	0.879221i	$-0.341936\pi$
$673$	808.411	−	128.040i	1.20120	−	0.190252i	0.724791	+	0.688969i	$0.241936\pi$
$674$		−	193.193i		−	0.286636i
$675$	−522.846	−	499.633i	−0.774587	−	0.740197i
$676$	133.571			0.197590
$677$	161.374	+	1018.88i	0.238367	+	1.50499i	0.758934	+	0.651168i	$0.225721\pi$
$677$	161.374	+	1018.88i	0.238367	+	1.50499i	−0.520567	+	0.853821i	$0.674279\pi$
$678$	−463.238	−	236.031i	−0.683242	−	0.348129i
$679$	425.969	−	138.406i	0.627348	−	0.203838i
$680$	88.0642	−	281.880i	0.129506	−	0.414529i
$681$	198.840	−	611.968i	0.291983	−	0.898631i
$682$	−491.510	−	491.510i	−0.720690	−	0.720690i
$683$	323.239	+	634.392i	0.473264	+	0.928832i	0.997033	+	0.0769723i	$0.0245253\pi$
$683$	323.239	+	634.392i	0.473264	+	0.928832i	−0.523770	+	0.851860i	$0.675475\pi$
$684$	−6.73368	−	9.26811i	−0.00984456	−	0.0135499i
$685$	−98.7100	−	580.510i	−0.144102	−	0.847460i
$686$	390.831	+	283.955i	0.569724	+	0.413929i
$687$	−944.077	−	149.527i	−1.37420	−	0.217652i
$688$	17.6891	−	111.684i	0.0257109	−	0.162332i
$689$	878.680	−	1209.40i	1.27530	−	1.75530i
$690$	−310.331	+	52.7687i	−0.449755	+	0.0764764i
$691$	−43.7044	+	31.7531i	−0.0632481	+	0.0459524i	−0.618960	−	0.785422i	$-0.712446\pi$
$691$	−43.7044	+	31.7531i	−0.0632481	+	0.0459524i	0.555712	+	0.831375i	$0.312446\pi$
$692$	−235.060	+	119.769i	−0.339682	+	0.173077i
$693$	−103.408	+	103.408i	−0.149218	+	0.149218i
$694$	416.933	+	135.470i	0.600769	+	0.195202i
$695$	519.938	+	162.438i	0.748112	+	0.233723i
$696$	16.1057	+	49.5681i	0.0231403	+	0.0712185i
$697$	342.498	−	672.190i	0.491389	−	0.964405i
$698$	187.619	−	29.7159i	0.268795	−	0.0425729i
$699$		−	814.198i		−	1.16480i
$700$	−211.195	+	38.3828i	−0.301708	+	0.0548325i
$701$	−743.065			−1.06001			−0.530003	−	0.847996i	$-0.677809\pi$
$701$	−743.065			−1.06001			−0.530003	+	0.847996i	$0.677809\pi$
$702$	−98.2691	−	620.447i	−0.139985	−	0.883828i
$703$	49.9273	+	25.4392i	0.0710204	+	0.0361867i
$704$	−150.268	+	48.8251i	−0.213449	+	0.0693539i
$705$	−294.007	−	208.552i	−0.417032	−	0.295819i
$706$	−199.758	+	614.792i	−0.282943	+	0.870810i
$707$	466.498	+	466.498i	0.659827	+	0.659827i
$708$	262.818	+	515.810i	0.371212	+	0.728545i
$709$	−415.044	−	571.258i	−0.585393	−	0.805724i	0.408881	−	0.912588i	$-0.365919\pi$
$709$	−415.044	−	571.258i	−0.585393	−	0.805724i	−0.994274	+	0.106864i	$0.965919\pi$
$710$	497.795	+	486.621i	0.701119	+	0.685382i
$711$	−52.2580	−	37.9677i	−0.0734993	−	0.0534004i
$712$	350.372	+	55.4935i	0.492096	+	0.0779403i
$713$	−64.2540	+	405.684i	−0.0901178	+	0.568981i
$714$	201.002	−	276.655i	0.281515	−	0.387472i
$715$	−1358.80	−	673.031i	−1.90043	−	0.941302i
$716$	365.890	−	265.834i	0.511019	−	0.371277i
$717$	601.241	−	306.348i	0.838551	−	0.427263i
$718$	272.815	−	272.815i	0.379965	−	0.379965i
$719$	−472.434	−	153.503i	−0.657072	−	0.213495i	−0.0385419	−	0.999257i	$-0.512271\pi$
$719$	−472.434	−	153.503i	−0.657072	−	0.213495i	−0.618530	+	0.785762i	$0.712271\pi$
$720$	0.391492	+	34.4930i	0.000543739	+	0.0479069i
$721$	−35.0884	−	107.991i	−0.0486662	−	0.149779i
$722$	−224.695	+	440.989i	−0.311212	+	0.610788i
$723$	−443.156	+	70.1891i	−0.612941	+	0.0970803i
$724$		−	121.199i		−	0.167402i
$725$	97.2270	−	140.417i	0.134106	−	0.193678i
$726$	−1026.37			−1.41373
$727$	4.08595	+	25.7977i	0.00562029	+	0.0354851i	0.990339	−	0.138667i	$-0.0442817\pi$
$727$	4.08595	+	25.7977i	0.00562029	+	0.0354851i	−0.984719	+	0.174152i	$0.944282\pi$
$728$	−166.133	−	84.6488i	−0.228204	−	0.116276i
$729$	−770.383	+	250.313i	−1.05677	+	0.343364i
$730$	291.384	−	216.798i	0.399156	−	0.296983i
$731$	182.418	−	561.424i	0.249546	−	0.768022i
$732$	306.606	+	306.606i	0.418860	+	0.418860i
$733$	−635.542	−	1247.32i	−0.867042	−	1.70167i	−0.698051	−	0.716048i	$-0.745949\pi$
$733$	−635.542	−	1247.32i	−0.867042	−	1.70167i	−0.168991	−	0.985618i	$-0.554051\pi$
$734$	−122.271	−	168.291i	−0.166581	−	0.229279i
$735$	407.898	+	59.8675i	0.554963	+	0.0814523i
$736$	75.5333	+	54.8782i	0.102627	+	0.0745627i
$737$	−1213.84	−	192.253i	−1.64700	−	0.260859i
$738$	−13.7853	+	87.0368i	−0.0186792	+	0.117936i
$739$	−611.917	+	842.232i	−0.828034	+	1.13969i	0.160252	+	0.987076i	$0.448769\pi$
$739$	−611.917	+	842.232i	−0.828034	+	1.13969i	−0.988286	+	0.152615i	$0.951231\pi$
$740$	−78.3013	−	149.457i	−0.105813	−	0.201969i
$741$	111.279	−	80.8492i	0.150175	−	0.109108i
$742$	−526.647	+	268.340i	−0.709767	+	0.361645i
$743$	273.617	−	273.617i	0.368259	−	0.368259i	−0.498583	−	0.866842i	$-0.666146\pi$
$743$	273.617	−	273.617i	0.368259	−	0.368259i	0.866842	+	0.498583i	$0.166146\pi$
$744$	−180.566	−	58.6695i	−0.242697	−	0.0788569i
$745$	290.916	−	98.1882i	0.390491	−	0.131796i
$746$	−124.276	−	382.482i	−0.166590	−	0.512711i
$747$	−1.92861	+	3.78510i	−0.00258180	+	0.00506707i
$748$	−814.691	+	129.034i	−1.08916	+	0.172506i
$749$		−	263.427i		−	0.351705i
$750$	−375.986	+	293.233i	−0.501315	+	0.390978i
$751$	−1071.26			−1.42645			−0.713225	−	0.700935i	$-0.752766\pi$
$751$	−1071.26			−1.42645			−0.713225	+	0.700935i	$0.752766\pi$
$752$	16.7248	+	105.596i	0.0222404	+	0.140420i
$753$	610.755	+	311.195i	0.811095	+	0.413274i
$754$	141.094	−	45.8441i	0.187127	−	0.0608012i
$755$	269.175	+	797.523i	0.356524	+	1.05632i
$756$	−76.7528	+	236.221i	−0.101525	+	0.312461i
$757$	−605.160	−	605.160i	−0.799418	−	0.799418i	0.183586	−	0.983004i	$-0.441230\pi$
$757$	−605.160	−	605.160i	−0.799418	−	0.799418i	−0.983004	+	0.183586i	$0.941230\pi$
$758$	−448.751	−	880.723i	−0.592019	−	1.16190i
$759$	516.796	+	711.309i	0.680891	+	0.937166i
$760$	−41.6029	+	21.7960i	−0.0547407	+	0.0286789i
$761$	676.103	+	491.218i	0.888440	+	0.645489i	0.935471	−	0.353404i	$-0.114976\pi$
$761$	676.103	+	491.218i	0.888440	+	0.645489i	−0.0470307	+	0.998893i	$0.514976\pi$
$762$	470.237	+	74.4782i	0.617109	+	0.0977405i
$763$	5.15439	−	32.5436i	0.00675543	−	0.0426521i
$764$	210.316	−	289.475i	0.275282	−	0.378894i
$765$	−26.1506	+	178.173i	−0.0341838	+	0.232906i
$766$	573.988	−	417.027i	0.749332	−	0.544422i
$767$	1468.23	−	748.102i	1.91425	−	0.975361i
$768$	−30.5161	+	30.5161i	−0.0397345	+	0.0397345i
$769$	−304.763	−	99.0236i	−0.396311	−	0.128769i	0.104080	−	0.994569i	$-0.466810\pi$
$769$	−304.763	−	99.0236i	−0.396311	−	0.128769i	−0.500391	+	0.865800i	$0.666810\pi$
$770$	357.890	+	481.017i	0.464792	+	0.624697i
$771$	245.220	+	754.708i	0.318054	+	0.978869i
$772$	161.473	−	316.908i	0.209162	−	0.410503i
$773$	−771.310	+	122.164i	−0.997814	+	0.158038i	−0.633917	−	0.773401i	$-0.718554\pi$
$773$	−771.310	+	122.164i	−0.997814	+	0.158038i	−0.363897	+	0.931439i	$0.618554\pi$
$774$			68.9536i			0.0890873i
$775$	205.638	+	587.193i	0.265340	+	0.757668i
$776$	−295.085			−0.380264
$777$	−30.5639	−	192.973i	−0.0393358	−	0.248357i
$778$	541.888	+	276.106i	0.696514	+	0.354892i
$779$	−114.109	+	37.0763i	−0.146482	+	0.0475948i
$780$	−414.147	+	4.70052i	−0.530957	+	0.00602631i
$781$	600.842	−	1849.20i	0.769324	−	2.36774i
$782$	344.650	+	344.650i	0.440728	+	0.440728i
$783$	−89.7192	−	176.084i	−0.114584	−	0.224884i
$784$	−71.8728	−	98.9244i	−0.0916745	−	0.126179i
$785$	−263.899	+	532.795i	−0.336177	+	0.678720i
$786$	526.143	+	382.265i	0.669393	+	0.486342i
$787$	1130.54	+	179.060i	1.43652	+	0.227523i	0.825639	−	0.564198i	$-0.190815\pi$
$787$	1130.54	+	179.060i	1.43652	+	0.227523i	0.610883	+	0.791721i	$0.290815\pi$
$788$	−88.9648	+	561.702i	−0.112900	+	0.712819i
$789$	51.9895	−	71.5575i	0.0658930	−	0.0906939i
$790$	−185.119	+	189.369i	−0.234328	+	0.239708i
$791$	473.383	−	343.933i	0.598462	−	0.434808i
$792$	85.8471	−	43.7413i	0.108393	−	0.0552289i
$793$	872.740	−	872.740i	1.10055	−	1.10055i
$794$	−764.710	−	248.469i	−0.963111	−	0.312934i
$795$	−759.626	+	1070.89i	−0.955504	+	1.34703i
$796$	4.16300	+	12.8124i	0.00522990	+	0.0160960i
$797$	−369.247	+	724.688i	−0.463296	+	0.909270i	0.534641	+	0.845079i	$0.320447\pi$
$797$	−369.247	+	724.688i	−0.463296	+	0.909270i	−0.997938	+	0.0641912i	$0.979553\pi$
$798$	−53.7161	+	8.50779i	−0.0673134	+	0.0106614i
$799$			558.136i			0.698543i
$800$	140.146	+	18.9472i	0.175183	+	0.0236840i
$801$	−216.318			−0.270060
$802$	−132.023	−	833.558i	−0.164617	−	1.03935i
$803$	−903.855	−	460.537i	−1.12560	−	0.573521i
$804$	−319.249	+	103.730i	−0.397076	+	0.129018i
$805$	105.648	−	338.161i	0.131239	−	0.420076i
$806$	−167.000	+	513.974i	−0.207197	+	0.637685i
$807$	−469.814	−	469.814i	−0.582174	−	0.582174i
$808$	−197.327	−	387.275i	−0.244216	−	0.479301i
$809$	100.488	+	138.310i	0.124213	+	0.170964i	0.866595	−	0.499013i	$-0.166304\pi$
$809$	100.488	+	138.310i	0.124213	+	0.170964i	−0.742382	+	0.669977i	$0.766304\pi$
$810$	74.0872	+	435.704i	0.0914657	+	0.537907i
$811$	285.260	+	207.253i	0.351738	+	0.255553i	0.749598	−	0.661894i	$-0.230247\pi$
$811$	285.260	+	207.253i	0.351738	+	0.255553i	−0.397860	+	0.917446i	$0.630247\pi$
$812$	−57.9359	−	9.17615i	−0.0713497	−	0.0113007i
$813$	−90.8005	+	573.292i	−0.111686	+	0.705156i
$814$	−277.005	+	381.264i	−0.340301	+	0.468384i
$815$	−166.543	+	28.3190i	−0.204348	+	0.0347473i
$816$	−182.269	+	132.426i	−0.223369	+	0.162287i
$817$	−83.6506	+	42.6221i	−0.102387	+	0.0521690i
$818$	19.1314	−	19.1314i	0.0233880	−	0.0233880i
$819$	108.134	+	35.1350i	0.132032	+	0.0428999i
$820$	344.839	+	107.734i	0.420535	+	0.131383i
$821$	−79.5914	−	244.957i	−0.0969445	−	0.298364i	0.890811	−	0.454374i	$-0.150137\pi$
$821$	−79.5914	−	244.957i	−0.0969445	−	0.298364i	−0.987756	+	0.156009i	$0.950137\pi$
$822$	−203.946	+	400.266i	−0.248109	+	0.486942i
$823$	707.978	−	112.133i	0.860240	−	0.136249i	0.289298	−	0.957239i	$-0.406578\pi$
$823$	707.978	−	112.133i	0.860240	−	0.136249i	0.570942	+	0.820990i	$0.306578\pi$
$824$			74.8092i			0.0907879i
$825$	1200.05	+	577.530i	1.45460	+	0.700037i
$826$	−651.540			−0.788789
$827$	210.601	+	1329.68i	0.254656	+	1.60784i	0.701125	+	0.713038i	$0.252681\pi$
$827$	210.601	+	1329.68i	0.254656	+	1.60784i	−0.446469	+	0.894799i	$0.647319\pi$
$828$	−50.7278	−	25.8471i	−0.0612654	−	0.0312163i
$829$	360.692	−	117.196i	0.435093	−	0.141370i	−0.0832774	−	0.996526i	$-0.526539\pi$
$829$	360.692	−	117.196i	0.435093	−	0.141370i	0.518371	+	0.855156i	$0.326539\pi$
$830$	14.2053	+	10.0764i	0.0171148	+	0.0121402i
$831$	97.5907	−	300.353i	0.117438	−	0.361436i
$832$	86.8627	+	86.8627i	0.104402	+	0.104402i
$833$	−289.804	−	568.772i	−0.347904	−	0.682800i
$834$	−244.265	−	336.202i	−0.292884	−	0.403120i
$835$	−479.212	−	468.456i	−0.573906	−	0.561025i
$836$	106.129	+	77.1072i	0.126948	+	0.0922335i
$837$	711.038	+	112.617i	0.849508	+	0.134549i
$838$	−99.5211	+	628.351i	−0.118760	+	0.749823i
$839$	236.136	−	325.013i	0.281449	−	0.387382i	−0.644764	−	0.764382i	$-0.723044\pi$
$839$	236.136	−	325.013i	0.281449	−	0.387382i	0.926213	+	0.377000i	$0.123044\pi$
$840$	146.746	+	72.6850i	0.174698	+	0.0865297i
$841$	−642.625	+	466.894i	−0.764120	+	0.555166i
$842$	909.137	−	463.228i	1.07973	−	0.550152i
$843$	531.720	−	531.720i	0.630748	−	0.630748i
$844$	−354.799	−	115.281i	−0.420378	−	0.136589i
$845$	3.78980	+	333.906i	0.00448497	+	0.395155i
$846$	−20.1463	−	62.0038i	−0.0238135	−	0.0732906i
$847$	524.424	−	1029.24i	0.619154	−	1.21516i
$848$	384.621	−	60.9180i	0.453563	−	0.0718373i
$849$			184.722i			0.217576i
$850$	707.153	+	212.149i	0.831944	+	0.249587i
$851$	278.476			0.327234
$852$	−83.0793	−	524.542i	−0.0975109	−	0.615660i
$853$	−163.158	−	83.1331i	−0.191275	−	0.0974596i	0.355730	−	0.934589i	$-0.384232\pi$
$853$	−163.158	−	83.1331i	−0.191275	−	0.0974596i	−0.547005	+	0.837129i	$0.684232\pi$
$854$	−464.123	+	150.803i	−0.543470	+	0.176584i
$855$	22.9777	−	17.0961i	0.0268745	−	0.0199954i
$856$	−53.6312	+	165.060i	−0.0626533	+	0.192827i
$857$	534.946	+	534.946i	0.624207	+	0.624207i	0.946604	−	0.322397i	$-0.104489\pi$
$857$	534.946	+	534.946i	0.624207	+	0.624207i	−0.322397	+	0.946604i	$0.604489\pi$
$858$	525.188	+	1030.74i	0.612108	+	1.20133i
$859$	−844.089	−	1161.79i	−0.982641	−	1.35249i	−0.935394	−	0.353606i	$-0.884955\pi$
$859$	−844.089	−	1161.79i	−0.982641	−	1.35249i	−0.0472468	−	0.998883i	$-0.515045\pi$
$860$	279.695	+	41.0511i	0.325227	+	0.0477338i
$861$	338.448	+	245.897i	0.393087	+	0.285594i
$862$	366.161	+	57.9943i	0.424781	+	0.0672787i
$863$	242.561	−	1531.47i	0.281068	−	1.77459i	−0.293327	−	0.956012i	$-0.594763\pi$
$863$	242.561	−	1531.47i	0.281068	−	1.77459i	0.574395	−	0.818578i	$-0.305237\pi$
$864$	96.1845	−	132.387i	0.111325	−	0.153225i
$865$	−306.073	−	584.214i	−0.353842	−	0.675392i
$866$	−375.406	+	272.748i	−0.433494	+	0.314952i
$867$	−353.420	+	180.077i	−0.407636	+	0.207701i
$868$	151.094	−	151.094i	0.174071	−	0.174071i
$869$	703.467	+	228.570i	0.809514	+	0.263027i
$870$	−123.455	+	41.6679i	−0.141903	+	0.0478942i
$871$	295.264	+	908.729i	0.338994	+	1.04332i
$872$	−9.85522	+	19.3420i	−0.0113019	+	0.0221811i
$873$	177.726	−	28.1490i	0.203580	−	0.0322440i
$874$		−	77.5168i		−	0.0886920i
$875$	−101.943	−	526.865i	−0.116506	−	0.602132i
$876$	−277.077			−0.316298
$877$	227.820	+	1438.40i	0.259772	+	1.64014i	0.680354	+	0.732884i	$0.261826\pi$
$877$	227.820	+	1438.40i	0.259772	+	1.64014i	−0.420582	+	0.907255i	$0.638174\pi$
$878$	503.819	+	256.708i	0.573825	+	0.292379i
$879$	−384.372	+	124.890i	−0.437283	+	0.142082i
$880$	−126.319	−	374.261i	−0.143544	−	0.425297i
$881$	−48.9623	+	150.691i	−0.0555759	+	0.171045i	−0.974991	−	0.222243i	$-0.928662\pi$
$881$	−48.9623	+	150.691i	−0.0555759	+	0.171045i	0.919416	+	0.393288i	$0.128662\pi$
$882$	52.7248	+	52.7248i	0.0597786	+	0.0597786i
$883$	−592.151	−	1162.16i	−0.670613	−	1.31615i	−0.935997	−	0.352009i	$-0.885499\pi$
$883$	−592.151	−	1162.16i	−0.670613	−	1.31615i	0.265384	−	0.964143i	$-0.414501\pi$
$884$	376.946	+	518.822i	0.426409	+	0.586902i
$885$	−1281.99	+	671.639i	−1.44857	+	0.758914i
$886$	199.422	+	144.889i	0.225081	+	0.163531i
$887$	−1001.95	−	158.693i	−1.12959	−	0.178909i	−0.436460	−	0.899724i	$-0.643768\pi$
$887$	−1001.95	−	158.693i	−1.12959	−	0.178909i	−0.693128	+	0.720814i	$0.743768\pi$
$888$	−20.1365	+	127.137i	−0.0226762	+	0.143172i
$889$	−314.954	+	433.498i	−0.354279	+	0.487624i
$890$	−128.784	+	877.449i	−0.144701	+	0.985897i
$891$	998.677	−	725.582i	1.12085	−	0.814345i
$892$	195.243	−	99.4812i	0.218882	−	0.111526i
$893$	62.7665	−	62.7665i	0.0702873	−	0.0702873i
$894$	−222.776	−	72.3843i	−0.249190	−	0.0809668i
$895$	674.924	+	907.123i	0.754106	+	1.01354i
$896$	−15.0092	−	46.1936i	−0.0167514	−	0.0515554i
$897$	310.338	−	609.073i	0.345973	−	0.679011i
$898$	−460.945	+	73.0064i	−0.513301	+	0.0812989i
$899$			170.016i			0.189116i
$900$	−86.2158	+	1.95733i	−0.0957953	+	0.00217482i
$901$	2032.94			2.25632
$902$	−157.855	−	996.657i	−0.175005	−	1.10494i
$903$	291.668	+	148.612i	0.322998	+	0.164576i
$904$	−366.637	+	119.127i	−0.405571	+	0.131778i
$905$	302.978	−	3.43878i	0.334783	−	0.00379975i
$906$	198.436	−	610.723i	0.219024	−	0.674088i
$907$	165.144	+	165.144i	0.182078	+	0.182078i	0.792261	−	0.610183i	$-0.208904\pi$
$907$	165.144	+	165.144i	0.182078	+	0.182078i	−0.610183	+	0.792261i	$0.708904\pi$
$908$	−216.608	−	425.118i	−0.238556	−	0.468192i
$909$	155.791	+	214.427i	0.171387	+	0.235894i
$910$	206.895	−	417.707i	0.227357	−	0.459018i
$911$	547.636	+	397.881i	0.601137	+	0.436752i	0.846282	−	0.532735i	$-0.178836\pi$
$911$	547.636	+	397.881i	0.601137	+	0.436752i	−0.245145	+	0.969486i	$0.578836\pi$
$912$	35.3898	+	5.60520i	0.0388046	+	0.00614605i
$913$	7.60977	−	48.0462i	0.00833491	−	0.0526245i
$914$	124.182	−	170.922i	0.135867	−	0.187005i
$915$	−757.765	+	775.164i	−0.828159	+	0.847174i
$916$	−573.392	+	416.593i	−0.625974	+	0.454796i
$917$	−652.167	+	332.296i	−0.711196	+	0.362373i
$918$	604.064	−	604.064i	0.658022	−	0.658022i
$919$	−1508.64	−	490.188i	−1.64161	−	0.533393i	−0.664716	−	0.747096i	$-0.731448\pi$
$919$	−1508.64	−	490.188i	−1.64161	−	0.533393i	−0.976899	+	0.213703i	$0.931448\pi$
$920$	−135.044	+	190.378i	−0.146786	+	0.206933i
$921$	−64.0057	−	196.989i	−0.0694959	−	0.213886i
$922$	−64.6462	+	126.875i	−0.0701152	+	0.137609i
$923$	−1493.09	+	236.482i	−1.61765	+	0.256210i
$924$		−	457.399i		−	0.495021i
$925$	371.397	−	199.981i	0.401510	−	0.216196i
$926$	8.61556			0.00930406
$927$	−7.13627	−	45.0566i	−0.00769824	−	0.0486048i
$928$	34.4337	+	17.5448i	0.0371052	+	0.0189061i
$929$	−1055.34	+	342.899i	−1.13599	+	0.369106i	−0.815850	−	0.578264i	$-0.803730\pi$
$929$	−1055.34	+	342.899i	−1.13599	+	0.369106i	−0.320141	+	0.947370i	$0.603730\pi$
$930$	141.541	−	453.051i	0.152195	−	0.487152i
$931$	−31.3721	+	96.5533i	−0.0336972	+	0.103709i
$932$	−426.895	−	426.895i	−0.458042	−	0.458042i
$933$	58.0251	+	113.881i	0.0621920	+	0.122059i
$934$	−118.965	−	163.741i	−0.127371	−	0.175312i
$935$	−345.680	−	2032.94i	−0.369712	−	2.17426i
$936$	−60.6024	−	44.0302i	−0.0647462	−	0.0470408i
$937$	−1045.94	−	165.660i	−1.11626	−	0.176799i	−0.429069	−	0.903272i	$-0.641158\pi$
$937$	−1045.94	−	165.660i	−1.11626	−	0.176799i	−0.687195	+	0.726473i	$0.741158\pi$
$938$	59.1000	−	373.143i	0.0630064	−	0.397807i
$939$	−233.100	+	320.835i	−0.248243	+	0.341677i
$940$	−263.499	+	44.8054i	−0.280318	+	0.0476653i
$941$	−1507.67	+	1095.38i	−1.60219	+	1.16406i	−0.719054	+	0.694954i	$0.755425\pi$
$941$	−1507.67	+	1095.38i	−1.60219	+	1.16406i	−0.883141	+	0.469108i	$0.844575\pi$
$942$	404.159	−	205.929i	0.429044	−	0.218609i
$943$	−421.629	+	421.629i	−0.447114	+	0.447114i
$944$	408.246	+	132.647i	0.432464	+	0.140516i
$945$	−592.692	−	185.167i	−0.627187	−	0.195944i
$946$	−243.995	−	750.940i	−0.257923	−	0.793806i
$947$	−68.9086	+	135.241i	−0.0727651	+	0.142810i	−0.924523	−	0.381126i	$-0.875537\pi$
$947$	−68.9086	+	135.241i	−0.0727651	+	0.142810i	0.851758	+	0.523935i	$0.175537\pi$
$948$	199.545	−	31.6048i	0.210490	−	0.0333384i
$949$			788.688i			0.831073i
$950$	−55.6669	−	103.382i	−0.0585967	−	0.108823i
$951$	183.182			0.192621
$952$	−39.6661	−	250.442i	−0.0416661	−	0.263069i
$953$	−391.244	−	199.349i	−0.410539	−	0.209180i	0.236509	−	0.971629i	$-0.423997\pi$
$953$	−391.244	−	199.349i	−0.410539	−	0.209180i	−0.647048	+	0.762449i	$0.723997\pi$
$954$	−225.841	+	73.3803i	−0.236731	+	0.0769186i
$955$	729.608	+	517.542i	0.763987	+	0.541929i
$956$	154.617	−	475.861i	0.161733	−	0.497763i
$957$	257.340	+	257.340i	0.268903	+	0.268903i
$958$	127.834	+	250.888i	0.133438	+	0.261887i
$959$	−297.179	−	409.032i	−0.309885	−	0.426520i
$960$	−77.1511	−	75.4194i	−0.0803657	−	0.0785619i
$961$	276.416	+	200.828i	0.287633	+	0.208978i
$962$	361.889	+	57.3177i	0.376184	+	0.0595818i
$963$	16.5558	−	104.530i	0.0171920	−	0.108546i
$964$	−195.552	+	269.154i	−0.202855	+	0.279206i
$965$	796.802	+	394.665i	0.825701	+	0.408979i
$966$	−218.662	+	158.867i	−0.226358	+	0.164459i
$967$	−878.028	+	447.377i	−0.907991	+	0.462645i	−0.844633	−	0.535346i	$-0.820181\pi$
$967$	−878.028	+	447.377i	−0.907991	+	0.462645i	−0.0633586	+	0.997991i	$0.520181\pi$
$968$	−538.140	+	538.140i	−0.555929	+	0.555929i
$969$	177.900	+	57.8033i	0.183592	+	0.0596526i
$970$	−8.37241	−	737.664i	−0.00863135	−	0.760478i
$971$	98.9422	+	304.513i	0.101897	+	0.313607i	0.988990	−	0.147984i	$-0.0472785\pi$
$971$	98.9422	+	304.513i	0.101897	+	0.313607i	−0.887092	+	0.461592i	$0.847279\pi$
$972$	−83.3184	+	163.522i	−0.0857185	+	0.168232i
$973$	461.950	−	73.1657i	0.474769	−	0.0751960i
$974$		−	531.302i		−	0.545484i
$975$	−23.5011	−	1035.17i	−0.0241037	−	1.06171i
$976$	321.515			0.329421
$977$	−195.642	−	1235.23i	−0.200248	−	1.26431i	−0.859009	−	0.511961i	$-0.828919\pi$
$977$	−195.642	−	1235.23i	−0.200248	−	1.26431i	0.658761	−	0.752352i	$-0.271081\pi$
$978$	114.833	+	58.5102i	0.117416	+	0.0598264i
$979$	2355.82	−	765.452i	2.40635	−	0.781872i
$980$	245.256	−	182.477i	0.250261	−	0.186201i
$981$	4.09059	−	12.5895i	0.00416981	−	0.0128334i
$982$	−325.583	−	325.583i	−0.331551	−	0.331551i
$983$	173.746	+	340.995i	0.176750	+	0.346892i	0.962337	−	0.271860i	$-0.0876386\pi$
$983$	173.746	+	340.995i	0.176750	+	0.346892i	−0.785586	+	0.618752i	$0.787639\pi$
$984$	−162.004	−	222.980i	−0.164639	−	0.226606i
$985$	−1406.69	−	206.461i	−1.42811	−	0.209605i
$986$	163.219	+	118.586i	0.165537	+	0.120270i
$987$	−305.691	−	48.4167i	−0.309717	−	0.0490544i
$988$	15.9550	−	100.736i	0.0161488	−	0.101959i
$989$	−274.244	+	377.465i	−0.277295	+	0.381663i
$990$	111.782	+	213.363i	0.112911	+	0.215518i
$991$	−166.968	+	121.309i	−0.168485	+	0.122411i	−0.668832	−	0.743413i	$-0.733206\pi$
$991$	−166.968	+	121.309i	−0.168485	+	0.122411i	0.500348	+	0.865825i	$0.333206\pi$
$992$	−125.435	+	63.9121i	−0.126446	+	0.0644276i
$993$	66.2394	−	66.2394i	0.0667063	−	0.0667063i
$994$	568.458	+	184.703i	0.571890	+	0.185818i
$995$	−31.9108	+	10.7703i	−0.0320712	+	0.0108245i
$996$	−4.10586	−	12.6365i	−0.00412235	−	0.0126873i
$997$	−325.309	+	638.454i	−0.326288	+	0.640376i	−0.994632	−	0.103477i	$-0.967003\pi$
$997$	−325.309	+	638.454i	−0.326288	+	0.640376i	0.668344	+	0.743852i	$0.267003\pi$
$998$	−558.818	+	88.5080i	−0.559938	+	0.0886854i
$999$		−	488.083i		−	0.488572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.3.f.a.37.1	yes	16
4.3	odd	2		400.3.bg.a.337.2		16
5.2	odd	4		250.3.f.c.43.1		16
5.3	odd	4		250.3.f.a.43.2		16
5.4	even	2		250.3.f.b.207.2		16
25.2	odd	20		250.3.f.b.93.2		16
25.11	even	5		250.3.f.a.157.2		16
25.14	even	10		250.3.f.c.157.1		16
25.23	odd	20	inner	50.3.f.a.23.1	✓	16
100.23	even	20		400.3.bg.a.273.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.a.23.1	✓	16	25.23	odd	20	inner
50.3.f.a.37.1	yes	16	1.1	even	1	trivial
250.3.f.a.43.2		16	5.3	odd	4
250.3.f.a.157.2		16	25.11	even	5
250.3.f.b.93.2		16	25.2	odd	20
250.3.f.b.207.2		16	5.4	even	2
250.3.f.c.43.1		16	5.2	odd	4
250.3.f.c.157.1		16	25.14	even	10
400.3.bg.a.273.2		16	100.23	even	20
400.3.bg.a.337.2		16	4.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.221232 - 1.39680i) q^{2} +(-2.40328 - 1.22453i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-1.59895 - 4.73744i) q^{5} +(-1.17875 + 3.62781i) q^{6} +(-3.03568 - 3.03568i) q^{7} +(1.28408 + 2.52015i) q^{8} +(-1.01379 - 1.39536i) q^{9} +O(q^{10})\)	\(q+(-0.221232 - 1.39680i) q^{2} +(-2.40328 - 1.22453i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-1.59895 - 4.73744i) q^{5} +(-1.17875 + 3.62781i) q^{6} +(-3.03568 - 3.03568i) q^{7} +(1.28408 + 2.52015i) q^{8} +(-1.01379 - 1.39536i) q^{9} +(-6.26353 + 3.28149i) q^{10} +(15.9782 + 11.6089i) q^{11} +(5.32811 + 0.843890i) q^{12} +(2.40210 - 15.1663i) q^{13} +(-3.56865 + 4.91183i) q^{14} +(-1.95842 + 13.3434i) q^{15} +(3.23607 - 2.35114i) q^{16} +(18.6060 - 9.48022i) q^{17} +(-1.72476 + 1.72476i) q^{18} +(-3.15850 - 1.02626i) q^{19} +(5.96929 + 8.02294i) q^{20} +(3.57830 + 11.0129i) q^{21} +(12.6804 - 24.8867i) q^{22} +(-16.3014 + 2.58189i) q^{23} -7.62902i q^{24} +(-19.8867 + 15.1499i) q^{25} -21.7157 q^{26} +(4.52526 + 28.5714i) q^{27} +(7.65035 + 3.89805i) q^{28} +(-6.49731 + 2.11110i) q^{29} +(19.0713 - 0.216458i) q^{30} +(7.69031 - 23.6683i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-24.1848 - 47.4652i) q^{33} +(-17.3582 - 23.8916i) q^{34} +(-9.52743 + 19.2353i) q^{35} +(2.79072 + 2.02758i) q^{36} +(-16.6649 - 2.63946i) q^{37} +(-0.734721 + 4.63885i) q^{38} +(-24.3445 + 33.5073i) q^{39} +(9.88586 - 10.1128i) q^{40} +(29.2279 - 21.2353i) q^{41} +(14.5912 - 7.43457i) q^{42} +(19.9893 - 19.9893i) q^{43} +(-37.5671 - 12.2063i) q^{44} +(-4.98944 + 7.03388i) q^{45} +(7.21279 + 22.1987i) q^{46} +(-12.1343 + 23.8149i) q^{47} +(-10.6562 + 1.68778i) q^{48} -30.5693i q^{49} +(25.5610 + 24.4261i) q^{50} -56.3243 q^{51} +(4.80420 + 30.3325i) q^{52} +(86.7430 + 44.1977i) q^{53} +(38.9074 - 12.6418i) q^{54} +(29.4479 - 94.2580i) q^{55} +(3.75230 - 11.5484i) q^{56} +(6.33408 + 6.33408i) q^{57} +(4.38621 + 8.60842i) q^{58} +(63.0774 + 86.8186i) q^{59} +(-4.52153 - 26.5910i) q^{60} +(65.0278 + 47.2455i) q^{61} +(-34.7613 - 5.50566i) q^{62} +(-1.15833 + 7.31340i) q^{63} +(-4.70228 + 6.47214i) q^{64} +(-75.6901 + 12.8703i) q^{65} +(-60.9491 + 44.2821i) q^{66} +(-55.4435 + 28.2499i) q^{67} +(-29.5316 + 29.5316i) q^{68} +(42.3386 + 13.7566i) q^{69} +(28.9756 + 9.05249i) q^{70} +(-30.4221 - 93.6296i) q^{71} +(2.21473 - 4.34665i) q^{72} +(-50.7302 + 8.03488i) q^{73} +23.8615i q^{74} +(66.3449 - 12.0576i) q^{75} +6.64209 q^{76} +(-13.2640 - 83.7456i) q^{77} +(52.1889 + 26.5916i) q^{78} +(35.6183 - 11.5731i) q^{79} +(-16.3127 - 11.5713i) q^{80} +(19.3143 - 59.4433i) q^{81} +(-36.1276 - 36.1276i) q^{82} +(-1.11819 - 2.19457i) q^{83} +(-13.6127 - 18.7362i) q^{84} +(-74.6621 - 72.9863i) q^{85} +(-32.3434 - 23.4989i) q^{86} +(18.2000 + 2.88259i) q^{87} +(-8.73874 + 55.1742i) q^{88} +(73.7197 - 101.466i) q^{89} +(10.9288 + 5.41314i) q^{90} +(-53.3319 + 38.7479i) q^{91} +(29.4115 - 14.9859i) q^{92} +(-47.4646 + 47.4646i) q^{93} +(35.9492 + 11.6806i) q^{94} +(0.188456 + 16.6042i) q^{95} +(4.71499 + 14.5113i) q^{96} +(-47.3640 + 92.9571i) q^{97} +(-42.6993 + 6.76290i) q^{98} -34.0643i 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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