LMFDB - Embedded newform 50.3.f.a.23.2

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			23.2
Root			$-1.56851i$ of defining polynomial
Character	$\chi$	$=$	50.23
Dual form			50.3.f.a.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.221232 + 1.39680i) q^{2} +(2.68205 - 1.36657i) q^{3} +(-1.90211 - 0.618034i) q^{4} +(4.84361 - 1.24072i) q^{5} +(1.31548 + 4.04862i) q^{6} +(-3.67488 + 3.67488i) q^{7} +(1.28408 - 2.52015i) q^{8} +(0.0358006 - 0.0492753i) q^{9} +O(q^{10})$	\(q+(-0.221232 + 1.39680i) q^{2} +(2.68205 - 1.36657i) q^{3} +(-1.90211 - 0.618034i) q^{4} +(4.84361 - 1.24072i) q^{5} +(1.31548 + 4.04862i) q^{6} +(-3.67488 + 3.67488i) q^{7} +(1.28408 - 2.52015i) q^{8} +(0.0358006 - 0.0492753i) q^{9} +(0.661483 + 7.04006i) q^{10} +(-4.26034 + 3.09532i) q^{11} +(-5.94615 + 0.941777i) q^{12} +(-1.52821 - 9.64872i) q^{13} +(-4.32008 - 5.94607i) q^{14} +(11.2953 - 9.94683i) q^{15} +(3.23607 + 2.35114i) q^{16} +(-19.6698 - 10.0223i) q^{17} +(0.0609076 + 0.0609076i) q^{18} +(11.5245 - 3.74453i) q^{19} +(-9.97991 - 0.633523i) q^{20} +(-4.83421 + 14.8782i) q^{21} +(-3.38103 - 6.63564i) q^{22} +(-39.5357 - 6.26183i) q^{23} -8.51395i q^{24} +(21.9212 - 12.0192i) q^{25} +13.8154 q^{26} +(-4.20932 + 26.5766i) q^{27} +(9.26123 - 4.71883i) q^{28} +(29.8865 + 9.71070i) q^{29} +(11.3949 + 17.9778i) q^{30} +(14.9177 + 45.9119i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-7.19647 + 14.1239i) q^{33} +(18.3507 - 25.2576i) q^{34} +(-13.2402 + 22.3592i) q^{35} +(-0.0985505 + 0.0716011i) q^{36} +(57.5307 - 9.11196i) q^{37} +(2.68079 + 16.9258i) q^{38} +(-17.2844 - 23.7899i) q^{39} +(3.09278 - 13.7998i) q^{40} +(-32.9907 - 23.9692i) q^{41} +(-19.7124 - 10.0440i) q^{42} +(-31.9512 - 31.9512i) q^{43} +(10.0167 - 3.25461i) q^{44} +(0.112267 - 0.283089i) q^{45} +(17.4931 - 53.8382i) q^{46} +(9.82058 + 19.2740i) q^{47} +(11.8923 + 1.88355i) q^{48} +21.9906i q^{49} +(11.9387 + 33.2786i) q^{50} -66.4516 q^{51} +(-3.05641 + 19.2974i) q^{52} +(67.5979 - 34.4429i) q^{53} +(-36.1910 - 11.7592i) q^{54} +(-16.7950 + 20.2784i) q^{55} +(4.54240 + 13.9801i) q^{56} +(25.7921 - 25.7921i) q^{57} +(-20.1758 + 39.5972i) q^{58} +(-16.7696 + 23.0813i) q^{59} +(-27.6324 + 11.9391i) q^{60} +(41.1195 - 29.8751i) q^{61} +(-67.4301 + 10.6799i) q^{62} +(0.0495178 + 0.312643i) q^{63} +(-4.70228 - 6.47214i) q^{64} +(-19.3734 - 44.8386i) q^{65} +(-18.1362 - 13.1767i) q^{66} +(10.9904 + 5.59988i) q^{67} +(31.2201 + 31.2201i) q^{68} +(-114.594 + 37.2338i) q^{69} +(-28.3022 - 23.4405i) q^{70} +(30.7061 - 94.5035i) q^{71} +(-0.0782101 - 0.153496i) q^{72} +(3.58842 + 0.568350i) q^{73} +82.3748i q^{74} +(42.3687 - 62.1929i) q^{75} -24.2351 q^{76} +(4.28131 - 27.0312i) q^{77} +(37.0537 - 18.8798i) q^{78} +(76.6046 + 24.8903i) q^{79} +(18.5914 + 7.37296i) q^{80} +(25.1986 + 77.5534i) q^{81} +(40.7788 - 40.7788i) q^{82} +(-32.5050 + 63.7946i) q^{83} +(18.3904 - 25.3123i) q^{84} +(-107.708 - 24.1392i) q^{85} +(51.6981 - 37.5609i) q^{86} +(93.4274 - 14.7974i) q^{87} +(2.33005 + 14.7113i) q^{88} +(32.5227 + 44.7637i) q^{89} +(0.370582 + 0.219443i) q^{90} +(41.0738 + 29.8419i) q^{91} +(71.3313 + 36.3451i) q^{92} +(102.752 + 102.752i) q^{93} +(-29.0946 + 9.45339i) q^{94} +(51.1742 - 32.4358i) q^{95} +(-5.26191 + 16.1945i) q^{96} +(-45.0519 - 88.4193i) q^{97} +(-30.7165 - 4.86501i) q^{98} +0.320744i 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 $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{11}{20}\right)$

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
$3$	2.68205	−	1.36657i	0.894016	−	0.455524i	0.0542846	−	0.998526i	$-0.482712\pi$
$3$	2.68205	−	1.36657i	0.894016	−	0.455524i	0.839732	+	0.543001i	$0.182712\pi$
$4$	−1.90211	−	0.618034i	−0.475528	−	0.154508i
$5$	4.84361	−	1.24072i	0.968723	−	0.248145i
$5$	4.84361	−	1.24072i	0.968723	−	0.248145i
$6$	1.31548	+	4.04862i	0.219246	+	0.674770i
$7$	−3.67488	+	3.67488i	−0.524982	+	0.524982i	−0.919072	−	0.394090i	$-0.871060\pi$
$7$	−3.67488	+	3.67488i	−0.524982	+	0.524982i	0.394090	+	0.919072i	$0.371060\pi$
$8$	1.28408	−	2.52015i	0.160510	−	0.315018i
$9$	0.0358006	−	0.0492753i	0.00397784	−	0.00547503i
$10$	0.661483	+	7.04006i	0.0661483	+	0.704006i
$11$	−4.26034	+	3.09532i	−0.387304	+	0.281393i	−0.764350	−	0.644802i	$-0.776940\pi$
$11$	−4.26034	+	3.09532i	−0.387304	+	0.281393i	0.377046	+	0.926195i	$0.376940\pi$
$12$	−5.94615	+	0.941777i	−0.495512	+	0.0784815i
$13$	−1.52821	−	9.64872i	−0.117554	−	0.742209i	−0.974097	−	0.226132i	$-0.927392\pi$
$13$	−1.52821	−	9.64872i	−0.117554	−	0.742209i	0.856542	−	0.516077i	$-0.172608\pi$
$14$	−4.32008	−	5.94607i	−0.308577	−	0.424720i
$15$	11.2953	−	9.94683i	0.753018	−	0.663122i
$16$	3.23607	+	2.35114i	0.202254	+	0.146946i
$17$	−19.6698	−	10.0223i	−1.15705	−	0.589546i	−0.233247	−	0.972418i	$-0.574935\pi$
$17$	−19.6698	−	10.0223i	−1.15705	−	0.589546i	−0.923801	+	0.382872i	$0.874935\pi$
$18$	0.0609076	+	0.0609076i	0.00338375	+	0.00338375i
$19$	11.5245	−	3.74453i	0.606552	−	0.197081i	0.0103913	−	0.999946i	$-0.496692\pi$
$19$	11.5245	−	3.74453i	0.606552	−	0.197081i	0.596160	+	0.802865i	$0.296692\pi$
$20$	−9.97991	−	0.633523i	−0.498996	−	0.0316762i
$21$	−4.83421	+	14.8782i	−0.230201	+	0.708485i
$22$	−3.38103	−	6.63564i	−0.153683	−	0.301620i
$23$	−39.5357	−	6.26183i	−1.71894	−	0.272254i	−0.782391	−	0.622787i	$-0.786000\pi$
$23$	−39.5357	−	6.26183i	−1.71894	−	0.272254i	−0.936550	+	0.350534i	$0.886000\pi$
$24$		−	8.51395i		−	0.354748i
$25$	21.9212	−	12.0192i	0.876848	−	0.480767i
$26$	13.8154			0.531363
$27$	−4.20932	+	26.5766i	−0.155901	+	0.984318i
$28$	9.26123	−	4.71883i	0.330758	−	0.168530i
$29$	29.8865	+	9.71070i	1.03057	+	0.334852i	0.775015	−	0.631943i	$-0.217742\pi$
$29$	29.8865	+	9.71070i	1.03057	+	0.334852i	0.255553	+	0.966795i	$0.417742\pi$
$30$	11.3949	+	17.9778i	0.379829	+	0.599261i
$31$	14.9177	+	45.9119i	0.481216	+	1.48103i	0.837388	+	0.546609i	$0.184082\pi$
$31$	14.9177	+	45.9119i	0.481216	+	1.48103i	−0.356172	+	0.934420i	$0.615918\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	−7.19647	+	14.1239i	−0.218075	+	0.427996i
$34$	18.3507	−	25.2576i	0.539727	−	0.742871i
$35$	−13.2402	+	22.3592i	−0.378291	+	0.638834i
$36$	−0.0985505	+	0.0716011i	−0.00273751	+	0.00198892i
$37$	57.5307	−	9.11196i	1.55488	−	0.246269i	0.680955	−	0.732325i	$-0.261565\pi$
$37$	57.5307	−	9.11196i	1.55488	−	0.246269i	0.873928	+	0.486056i	$0.161565\pi$
$38$	2.68079	+	16.9258i	0.0705471	+	0.445417i
$39$	−17.2844	−	23.7899i	−0.443190	−	0.609998i
$40$	3.09278	−	13.7998i	0.0773195	−	0.344995i
$41$	−32.9907	−	23.9692i	−0.804652	−	0.584614i	0.107623	−	0.994192i	$-0.465676\pi$
$41$	−32.9907	−	23.9692i	−0.804652	−	0.584614i	−0.912275	+	0.409578i	$0.865676\pi$
$42$	−19.7124	−	10.0440i	−0.469343	−	0.239142i
$43$	−31.9512	−	31.9512i	−0.743051	−	0.743051i	0.230113	−	0.973164i	$-0.426091\pi$
$43$	−31.9512	−	31.9512i	−0.743051	−	0.743051i	−0.973164	+	0.230113i	$0.926091\pi$
$44$	10.0167	−	3.25461i	0.227652	−	0.0739685i
$45$	0.112267	−	0.283089i	0.00249483	−	0.00629087i
$46$	17.4931	−	53.8382i	0.380284	−	1.17040i
$47$	9.82058	+	19.2740i	0.208949	+	0.410085i	0.971567	−	0.236764i	$-0.0760867\pi$
$47$	9.82058	+	19.2740i	0.208949	+	0.410085i	−0.762619	+	0.646848i	$0.776087\pi$
$48$	11.8923	+	1.88355i	0.247756	+	0.0392407i
$49$			21.9906i			0.448787i
$50$	11.9387	+	33.2786i	0.238775	+	0.665572i
$51$	−66.4516			−1.30297
$52$	−3.05641	+	19.2974i	−0.0587772	+	0.371104i
$53$	67.5979	−	34.4429i	1.27543	−	0.649865i	0.320658	−	0.947195i	$-0.396096\pi$
$53$	67.5979	−	34.4429i	1.27543	−	0.649865i	0.954775	+	0.297330i	$0.0960961\pi$
$54$	−36.1910	−	11.7592i	−0.670204	−	0.217762i
$55$	−16.7950	+	20.2784i	−0.305364	+	0.368699i
$56$	4.54240	+	13.9801i	0.0811142	+	0.249644i
$57$	25.7921	−	25.7921i	0.452492	−	0.452492i
$58$	−20.1758	+	39.5972i	−0.347858	+	0.682710i
$59$	−16.7696	+	23.0813i	−0.284230	+	0.391209i	−0.927129	−	0.374742i	$-0.877731\pi$
$59$	−16.7696	+	23.0813i	−0.284230	+	0.391209i	0.642899	+	0.765951i	$0.277731\pi$
$60$	−27.6324	+	11.9391i	−0.460540	+	0.198986i
$61$	41.1195	−	29.8751i	0.674090	−	0.489755i	−0.197302	−	0.980343i	$-0.563218\pi$
$61$	41.1195	−	29.8751i	0.674090	−	0.489755i	0.871392	+	0.490588i	$0.163218\pi$
$62$	−67.4301	+	10.6799i	−1.08758	+	0.172256i
$63$	0.0495178	+	0.312643i	0.000785997	+	0.00496259i
$64$	−4.70228	−	6.47214i	−0.0734732	−	0.101127i
$65$	−19.3734	−	44.8386i	−0.298053	−	0.689824i
$66$	−18.1362	−	13.1767i	−0.274790	−	0.199647i
$67$	10.9904	+	5.59988i	0.164036	+	0.0835803i	0.534081	−	0.845433i	$-0.320658\pi$
$67$	10.9904	+	5.59988i	0.164036	+	0.0835803i	−0.370045	+	0.929014i	$0.620658\pi$
$68$	31.2201	+	31.2201i	0.459119	+	0.459119i
$69$	−114.594	+	37.2338i	−1.66078	+	0.539620i
$70$	−28.3022	−	23.4405i	−0.404317	−	0.334864i
$71$	30.7061	−	94.5035i	0.432480	−	1.33104i	−0.463168	−	0.886271i	$-0.653287\pi$
$71$	30.7061	−	94.5035i	0.432480	−	1.33104i	0.895647	−	0.444765i	$-0.146713\pi$
$72$	−0.0782101	−	0.153496i	−0.00108625	−	0.00213189i
$73$	3.58842	+	0.568350i	0.0491565	+	0.00778562i	0.180964	−	0.983490i	$-0.442078\pi$
$73$	3.58842	+	0.568350i	0.0491565	+	0.00778562i	−0.131808	+	0.991275i	$0.542078\pi$
$74$			82.3748i			1.11317i
$75$	42.3687	−	62.1929i	0.564916	−	0.829239i
$76$	−24.2351			−0.318883
$77$	4.28131	−	27.0312i	0.0556015	−	0.351054i
$78$	37.0537	−	18.8798i	0.475047	−	0.242049i
$79$	76.6046	+	24.8903i	0.969678	+	0.315067i	0.750686	−	0.660659i	$-0.229723\pi$
$79$	76.6046	+	24.8903i	0.969678	+	0.315067i	0.218992	+	0.975727i	$0.429723\pi$
$80$	18.5914	+	7.37296i	0.232392	+	0.0921620i
$81$	25.1986	+	77.5534i	0.311094	+	0.957449i
$82$	40.7788	−	40.7788i	0.497302	−	0.497302i
$83$	−32.5050	+	63.7946i	−0.391626	+	0.768609i	−0.999680	−	0.0252861i	$-0.991950\pi$
$83$	−32.5050	+	63.7946i	−0.391626	+	0.768609i	0.608054	+	0.793896i	$0.291950\pi$
$84$	18.3904	−	25.3123i	0.218934	−	0.301337i
$85$	−107.708	−	24.1392i	−1.26715	−	0.283991i
$86$	51.6981	−	37.5609i	0.601141	−	0.436755i
$87$	93.4274	−	14.7974i	1.07388	−	0.170086i
$88$	2.33005	+	14.7113i	0.0264778	+	0.167174i
$89$	32.5227	+	44.7637i	0.365424	+	0.502963i	0.951650	−	0.307185i	$-0.0993869\pi$
$89$	32.5227	+	44.7637i	0.365424	+	0.502963i	−0.586226	+	0.810148i	$0.699387\pi$
$90$	0.370582	+	0.219443i	0.00411758	+	0.00243826i
$91$	41.0738	+	29.8419i	0.451360	+	0.327933i
$92$	71.3313	+	36.3451i	0.775340	+	0.395055i
$93$	102.752	+	102.752i	1.10486	+	1.10486i
$94$	−29.0946	+	9.45339i	−0.309517	+	0.100568i
$95$	51.1742	−	32.4358i	0.538676	−	0.341429i
$96$	−5.26191	+	16.1945i	−0.0548115	+	0.168693i
$97$	−45.0519	−	88.4193i	−0.464453	−	0.911540i	−0.997841	−	0.0656694i	$-0.979082\pi$
$97$	−45.0519	−	88.4193i	−0.464453	−	0.911540i	0.533389	−	0.845870i	$-0.320918\pi$
$98$	−30.7165	−	4.86501i	−0.313433	−	0.0496430i
$99$			0.320744i			0.00323984i
$100$	−49.1249	+	9.31377i	−0.491249	+	0.0931377i
$101$	−171.411			−1.69714			−0.848569	−	0.529084i	$-0.822536\pi$
$101$	−171.411			−1.69714			−0.848569	+	0.529084i	$0.822536\pi$
$102$	14.7012	−	92.8197i	0.144129	−	0.909997i
$103$	44.4884	−	22.6680i	0.431926	−	0.220077i	−0.224490	−	0.974476i	$-0.572072\pi$
$103$	44.4884	−	22.6680i	0.431926	−	0.220077i	0.656416	+	0.754399i	$0.272072\pi$
$104$	−26.2785	−	8.53841i	−0.252678	−	0.0821001i
$105$	−4.95537	+	78.0621i	−0.0471940	+	0.743449i
$106$	33.1551	+	102.041i	0.312784	+	0.962649i
$107$	−62.5710	+	62.5710i	−0.584775	+	0.584775i	−0.936212	−	0.351436i	$-0.885693\pi$
$107$	−62.5710	+	62.5710i	−0.584775	+	0.584775i	0.351436	+	0.936212i	$0.385693\pi$
$108$	24.4318	−	47.9502i	0.226221	−	0.443983i
$109$	−39.7773	+	54.7488i	−0.364930	+	0.502283i	−0.951514	−	0.307606i	$-0.900472\pi$
$109$	−39.7773	+	54.7488i	−0.364930	+	0.502283i	0.586584	+	0.809888i	$0.300472\pi$
$110$	−24.6094	−	27.9456i	−0.223722	−	0.254051i
$111$	141.848	−	103.059i	1.27791	−	0.928455i
$112$	−20.5323	+	3.25200i	−0.183324	+	0.0290357i
$113$	0.459791	+	2.90301i	0.00406895	+	0.0256903i	0.989639	−	0.143576i	$-0.0458602\pi$
$113$	0.459791	+	2.90301i	0.00406895	+	0.0256903i	−0.985570	+	0.169266i	$0.945860\pi$
$114$	30.3204	+	41.7324i	0.265968	+	0.366074i
$115$	−199.265	+	18.7229i	−1.73274	+	0.162808i
$116$	−50.8459	−	36.9417i	−0.438327	−	0.318463i
$117$	−0.530154	−	0.270127i	−0.00453123	−	0.00230878i
$118$	−28.5301	−	28.5301i	−0.241780	−	0.241780i
$119$	109.115	−	35.4535i	0.916931	−	0.297929i
$120$	−10.5634	−	41.2383i	−0.0880287	−	0.343652i
$121$	−28.8215	+	88.7036i	−0.238195	+	0.733087i
$122$	32.6326	+	64.0451i	0.267480	+	0.524960i
$123$	−121.238	−	19.2023i	−0.985677	−	0.156116i
$124$		−	96.5493i		−	0.778623i
$125$	91.2654	−	85.4144i	0.730124	−	0.683315i
$126$	−0.447655			−0.00355282
$127$	−2.95545	+	18.6600i	−0.0232713	+	0.146929i	−0.996588	−	0.0825366i	$-0.973698\pi$
$127$	−2.95545	+	18.6600i	−0.0232713	+	0.146929i	0.973317	+	0.229466i	$0.0736979\pi$
$128$	10.0806	−	5.13632i	0.0787546	−	0.0401275i
$129$	−129.358	−	42.0311i	−1.00278	−	0.325822i
$130$	66.9166	−	17.1411i	0.514743	−	0.131855i
$131$	−50.5498	−	155.576i	−0.385876	−	1.18761i	−0.935843	−	0.352418i	$-0.885359\pi$
$131$	−50.5498	−	155.576i	−0.385876	−	1.18761i	0.549966	−	0.835187i	$-0.314641\pi$
$132$	22.4175	−	22.4175i	0.169830	−	0.169830i
$133$	−28.5904	+	56.1117i	−0.214965	+	0.421893i
$134$	−10.2534	+	14.1125i	−0.0765176	+	0.105317i
$135$	12.5859	+	133.949i	0.0932287	+	0.992217i
$136$	−50.5152	+	36.7015i	−0.371435	+	0.269864i
$137$	−184.242	+	29.1811i	−1.34484	+	0.213001i	−0.787001	−	0.616951i	$-0.788368\pi$
$137$	−184.242	+	29.1811i	−1.34484	+	0.213001i	−0.557834	+	0.829952i	$0.688368\pi$
$138$	−26.6564	−	168.302i	−0.193163	−	1.21958i
$139$	−31.2476	−	43.0086i	−0.224803	−	0.309414i	0.681686	−	0.731645i	$-0.261247\pi$
$139$	−31.2476	−	43.0086i	−0.224803	−	0.309414i	−0.906488	+	0.422231i	$0.861247\pi$
$140$	39.0031	−	34.3468i	0.278593	−	0.245334i
$141$	52.6786	+	38.2732i	0.373607	+	0.271441i
$142$	125.210	+	63.7975i	0.881758	+	0.449278i
$143$	36.3765	+	36.3765i	0.254381	+	0.254381i
$144$	0.231706	−	0.0752859i	0.00160907	−	0.000522819i
$145$	156.807	+	9.95407i	1.08143	+	0.0686488i
$146$	−1.58775	+	4.88658i	−0.0108750	+	0.0334697i
$147$	30.0517	+	58.9798i	0.204433	+	0.401223i
$148$	−115.061	−	18.2239i	−0.777441	−	0.123135i
$149$		−	167.422i		−	1.12364i	−0.827260	−	0.561819i	$-0.810102\pi$
$149$		−	167.422i		−	1.12364i	0.827260	−	0.561819i	$-0.189898\pi$
$150$	77.4979	+	72.9397i	0.516653	+	0.486265i
$151$	−92.9621			−0.615643			−0.307822	−	0.951444i	$-0.599600\pi$
$151$	−92.9621			−0.615643			−0.307822	+	0.951444i	$0.599600\pi$
$152$	5.36158	−	33.8517i	0.0352735	−	0.222708i
$153$	−1.19804	+	0.610432i	−0.00783033	+	0.00398975i
$154$	36.8100	+	11.9603i	0.239026	+	0.0776643i
$155$	129.220	+	203.871i	0.833674	+	1.31530i
$156$	18.1739	+	55.9335i	0.116499	+	0.358548i
$157$	−84.9835	+	84.9835i	−0.541296	+	0.541296i	−0.923909	−	0.382613i	$-0.875024\pi$
$157$	−84.9835	+	84.9835i	−0.541296	+	0.541296i	0.382613	+	0.923909i	$0.375024\pi$
$158$	−51.7142	+	101.495i	−0.327305	+	0.642373i
$159$	134.232	−	184.755i	0.844228	−	1.16198i
$160$	−14.4116	+	24.3374i	−0.0900723	+	0.152108i
$161$	168.300	−	122.277i	1.04534	−	0.759486i
$162$	−113.901	+	18.0402i	−0.703096	+	0.111359i
$163$	−26.8126	−	169.288i	−0.164494	−	1.03858i	−0.922407	−	0.386220i	$-0.873781\pi$
$163$	−26.8126	−	169.288i	−0.164494	−	1.03858i	0.757913	−	0.652356i	$-0.226219\pi$
$164$	47.9383	+	65.9814i	0.292307	+	0.402326i
$165$	−17.3331	+	77.3394i	−0.105049	+	0.468724i
$166$	−81.9173	−	59.5164i	−0.493478	−	0.358532i
$167$	−55.1743	−	28.1127i	−0.330385	−	0.168340i	0.280927	−	0.959729i	$-0.409358\pi$
$167$	−55.1743	−	28.1127i	−0.330385	−	0.168340i	−0.611312	+	0.791390i	$0.709358\pi$
$168$	31.2877	+	31.2877i	0.186236	+	0.186236i
$169$	69.9663	−	22.7334i	0.414002	−	0.134517i
$170$	57.5462	−	145.106i	0.338507	−	0.853567i
$171$	0.228070	−	0.701928i	0.00133374	−	0.00410484i
$172$	41.0279	+	80.5218i	0.238534	+	0.468150i
$173$	43.3353	+	6.86365i	0.250493	+	0.0396742i	0.280418	−	0.959878i	$-0.409527\pi$
$173$	43.3353	+	6.86365i	0.250493	+	0.0396742i	−0.0299249	+	0.999552i	$0.509527\pi$
$174$			133.773i			0.768812i
$175$	−36.3888	+	124.727i	−0.207936	+	0.712724i
$176$	−21.0643			−0.119683
$177$	−13.4345	+	84.8220i	−0.0759011	+	0.479221i
$178$	−69.7211	+	35.5247i	−0.391692	+	0.199577i
$179$	61.4863	+	19.9781i	0.343499	+	0.111610i	0.475686	−	0.879615i	$-0.342200\pi$
$179$	61.4863	+	19.9781i	0.343499	+	0.111610i	−0.132187	+	0.991225i	$0.542200\pi$
$180$	−0.388504	+	0.469082i	−0.00215835	+	0.00260601i
$181$	109.779	+	337.866i	0.606515	+	1.86666i	0.486020	+	0.873948i	$0.338448\pi$
$181$	109.779	+	337.866i	0.606515	+	1.86666i	0.120495	+	0.992714i	$0.461552\pi$
$182$	−50.7700	+	50.7700i	−0.278956	+	0.278956i
$183$	69.4581	−	136.319i	0.379552	−	0.744913i
$184$	−66.5476	+	91.5950i	−0.361672	+	0.497799i
$185$	267.351	−	115.514i	1.44514	−	0.624402i
$186$	−166.256	+	120.792i	−0.893850	+	0.649420i
$187$	114.822	−	18.1861i	0.614023	−	0.0972517i
$188$	−6.76788	−	42.7307i	−0.0359994	−	0.227291i
$189$	−82.1969	−	113.134i	−0.434904	−	0.598595i
$190$	33.9850	+	78.6561i	0.178868	+	0.413979i
$191$	106.961	+	77.7115i	0.560004	+	0.406867i	0.831460	−	0.555584i	$-0.187505\pi$
$191$	106.961	+	77.7115i	0.560004	+	0.406867i	−0.271456	+	0.962451i	$0.587505\pi$
$192$	−21.4564	−	10.9326i	−0.111752	−	0.0569405i
$193$	47.0095	+	47.0095i	0.243573	+	0.243573i	0.818326	−	0.574754i	$-0.194902\pi$
$193$	47.0095	+	47.0095i	0.243573	+	0.243573i	−0.574754	+	0.818326i	$0.694902\pi$
$194$	133.471	−	43.3674i	0.687996	−	0.223543i
$195$	−113.236	−	93.7841i	−0.580696	−	0.480944i
$196$	13.5909	−	41.8286i	0.0693414	−	0.213411i
$197$	−112.759	−	221.303i	−0.572382	−	1.12336i	−0.977860	−	0.209259i	$-0.932895\pi$
$197$	−112.759	−	221.303i	−0.572382	−	1.12336i	0.405478	−	0.914105i	$-0.367105\pi$
$198$	−0.448016	−	0.0709587i	−0.00226270	−	0.000358377i
$199$		−	91.2618i		−	0.458602i	−0.973356	−	0.229301i	$-0.926356\pi$
$199$		−	91.2618i		−	0.458602i	0.973356	−	0.229301i	$-0.0736440\pi$
$200$	−2.14151	−	70.6782i	−0.0107075	−	0.353391i
$201$	37.1294			0.184723
$202$	37.9216	−	239.427i	0.187730	−	1.18528i
$203$	−145.515	+	74.1434i	−0.716821	+	0.365239i
$204$	126.398	+	41.0693i	0.619600	+	0.201320i
$205$	−189.533	−	75.1650i	−0.924553	−	0.366659i
$206$	21.8204	+	67.1564i	0.105924	+	0.326002i
$207$	−1.72395	+	1.72395i	−0.00832827	+	0.00832827i
$208$	17.7401	−	34.8169i	0.0852890	−	0.167389i
$209$	−37.5077	+	51.6249i	−0.179463	+	0.247009i
$210$	−107.941	−	24.1915i	−0.514005	−	0.115198i
$211$	−16.2872	+	11.8333i	−0.0771904	+	0.0560821i	−0.625711	−	0.780055i	$-0.715191\pi$
$211$	−16.2872	+	11.8333i	−0.0771904	+	0.0560821i	0.548521	+	0.836137i	$0.315191\pi$
$212$	−149.866	+	23.7364i	−0.706914	+	0.111964i
$213$	−46.7908	−	295.425i	−0.219675	−	1.38697i
$214$	−73.5566	−	101.242i	−0.343722	−	0.473093i
$215$	−194.402	−	115.117i	−0.904195	−	0.535427i
$216$	61.5718	+	44.7345i	0.285055	+	0.207104i
$217$	−223.541	−	113.900i	−1.03014	−	0.524885i
$218$	−67.6733	−	67.6733i	−0.310428	−	0.310428i
$219$	10.4010	−	3.37950i	0.0474932	−	0.0154315i
$220$	44.4788	−	28.1920i	0.202176	−	0.128145i
$221$	−66.6425	+	205.105i	−0.301550	+	0.928075i
$222$	112.571	+	220.933i	0.507077	+	0.995195i
$223$	125.432	+	19.8664i	0.562474	+	0.0890871i	0.431196	−	0.902259i	$-0.358092\pi$
$223$	125.432	+	19.8664i	0.562474	+	0.0890871i	0.131278	+	0.991346i	$0.458092\pi$
$224$		−	29.3990i		−	0.131246i
$225$	0.192544	−	1.51047i	0.000855752	−	0.00671318i
$226$	−4.15664			−0.0183922
$227$	−32.0573	+	202.402i	−0.141222	+	0.891638i	0.810737	+	0.585411i	$0.199067\pi$
$227$	−32.0573	+	202.402i	−0.141222	+	0.891638i	−0.951958	+	0.306227i	$0.900933\pi$
$228$	−64.9998	+	33.1190i	−0.285087	+	0.145259i
$229$	−248.816	−	80.8451i	−1.08653	−	0.353035i	−0.289626	−	0.957140i	$-0.593531\pi$
$229$	−248.816	−	80.8451i	−1.08653	−	0.353035i	−0.796905	+	0.604105i	$0.793531\pi$
$230$	17.9315	−	282.475i	0.0779630	−	1.22815i
$231$	−25.4573	−	78.3496i	−0.110205	−	0.339176i
$232$	62.8490	−	62.8490i	0.270901	−	0.270901i
$233$	−146.611	+	287.740i	−0.629231	+	1.23494i	0.327744	+	0.944767i	$0.393712\pi$
$233$	−146.611	+	287.740i	−0.629231	+	1.23494i	−0.956975	+	0.290169i	$0.906288\pi$
$234$	0.494600	−	0.680759i	0.00211368	−	0.00290923i
$235$	71.4808	+	81.1711i	0.304173	+	0.345409i
$236$	46.1626	−	33.5391i	0.195604	−	0.142115i
$237$	239.472	−	37.9286i	1.01043	−	0.160036i
$238$	25.3819	+	160.255i	0.106647	+	0.673341i
$239$	115.963	+	159.609i	0.485199	+	0.667819i	0.979494	−	0.201475i	$-0.0645736\pi$
$239$	115.963	+	159.609i	0.485199	+	0.667819i	−0.494295	+	0.869294i	$0.664574\pi$
$240$	59.9387	−	5.63183i	0.249745	−	0.0234660i
$241$	23.3359	+	16.9545i	0.0968295	+	0.0703508i	0.635147	−	0.772392i	$-0.280940\pi$
$241$	23.3359	+	16.9545i	0.0968295	+	0.0703508i	−0.538317	+	0.842742i	$0.680940\pi$
$242$	−117.525	−	59.8820i	−0.485641	−	0.247446i
$243$	2.32564	+	2.32564i	0.00957054	+	0.00957054i
$244$	−96.6777	+	31.4125i	−0.396220	+	0.128740i
$245$	27.2842	+	106.514i	0.111364	+	0.434750i
$246$	53.6435	−	165.098i	0.218063	−	0.671129i
$247$	−53.7417	−	105.474i	−0.217578	−	0.427020i
$248$	134.860	+	21.3598i	0.543791	+	0.0861281i
$249$			215.521i			0.865545i
$250$	99.1162	+	146.376i	0.396465	+	0.585505i
$251$	−129.059			−0.514179			−0.257090	−	0.966388i	$-0.582764\pi$
$251$	−129.059			−0.514179			−0.257090	+	0.966388i	$0.582764\pi$
$252$	0.0990356	−	0.625286i	0.000392998	−	0.00248129i
$253$	187.818	−	95.6980i	0.742363	−	0.378253i
$254$	−25.4105	−	8.25636i	−0.100041	−	0.0325054i
$255$	−321.866	+	82.4480i	−1.26222	+	0.323326i
$256$	4.94427	+	15.2169i	0.0193136	+	0.0594410i
$257$	75.3505	−	75.3505i	0.293193	−	0.293193i	−0.545148	−	0.838340i	$-0.683526\pi$
$257$	75.3505	−	75.3505i	0.293193	−	0.293193i	0.838340	+	0.545148i	$0.183526\pi$
$258$	87.3273	−	171.389i	0.338478	−	0.664300i
$259$	−177.933	+	244.903i	−0.686999	+	0.945573i
$260$	9.13868	+	97.2615i	0.0351488	+	0.374083i
$261$	1.54845	−	1.12501i	0.00593276	−	0.00431040i
$262$	228.493	−	36.1897i	0.872109	−	0.138129i
$263$	74.9246	+	473.055i	0.284884	+	1.79869i	0.550740	+	0.834677i	$0.314346\pi$
$263$	74.9246	+	473.055i	0.284884	+	1.79869i	−0.265855	+	0.964013i	$0.585654\pi$
$264$	26.3534	+	36.2723i	0.0998234	+	0.137395i
$265$	284.684	−	250.698i	1.07428	−	0.946031i
$266$	−72.0519	−	52.3488i	−0.270872	−	0.196800i
$267$	148.400	+	75.6138i	0.555807	+	0.283198i
$268$	−17.4440	−	17.4440i	−0.0650897	−	0.0650897i
$269$	84.1269	−	27.3345i	0.312739	−	0.101615i	−0.148442	−	0.988921i	$-0.547426\pi$
$269$	84.1269	−	27.3345i	0.312739	−	0.101615i	0.461181	+	0.887306i	$0.347426\pi$
$270$	−189.885	−	12.0539i	−0.703278	−	0.0446440i
$271$	121.101	−	372.711i	0.446867	−	1.37532i	−0.433555	−	0.901127i	$-0.642741\pi$
$271$	121.101	−	372.711i	0.446867	−	1.37532i	0.880423	−	0.474190i	$-0.157259\pi$
$272$	−40.0891	−	78.6793i	−0.147386	−	0.289262i
$273$	150.943	+	23.9070i	0.552905	+	0.0875715i
$274$		−	263.806i		−	0.962796i
$275$	−56.1887	+	119.059i	−0.204323	+	0.432942i
$276$	240.982			0.873124
$277$	−47.7028	+	301.184i	−0.172212	+	1.08731i	0.738497	+	0.674257i	$0.235536\pi$
$277$	−47.7028	+	301.184i	−0.172212	+	1.08731i	−0.910709	+	0.413048i	$0.864464\pi$
$278$	66.9875	−	34.1318i	0.240962	−	0.122776i
$279$	2.79638	+	0.908600i	0.0100229	+	0.00325663i
$280$	39.3470	+	62.0782i	0.140525	+	0.221708i
$281$	−145.169	−	446.783i	−0.516614	−	1.58997i	−0.780326	−	0.625373i	$-0.784947\pi$
$281$	−145.169	−	446.783i	−0.516614	−	1.58997i	0.263712	−	0.964601i	$-0.415053\pi$
$282$	−65.1143	+	65.1143i	−0.230902	+	0.230902i
$283$	184.728	−	362.549i	0.652748	−	1.28109i	−0.292976	−	0.956120i	$-0.594646\pi$
$283$	184.728	−	362.549i	0.652748	−	1.28109i	0.945724	−	0.324971i	$-0.105354\pi$
$284$	−116.813	+	160.779i	−0.411313	+	0.566123i
$285$	92.9260	−	156.928i	0.326056	−	0.550623i
$286$	−58.8585	+	42.7632i	−0.205799	+	0.149522i
$287$	209.321	−	33.1531i	0.729340	−	0.115516i
$288$	0.0538987	+	0.340303i	0.000187148	+	0.00118161i
$289$	116.586	+	160.467i	0.403412	+	0.555249i
$290$	−48.5945	+	216.826i	−0.167567	+	0.747676i
$291$	−241.663	−	175.578i	−0.830456	−	0.603362i
$292$	−6.47433	−	3.29883i	−0.0221724	−	0.0112974i
$293$	103.216	+	103.216i	0.352274	+	0.352274i	0.860955	−	0.508681i	$-0.169867\pi$
$293$	103.216	+	103.216i	0.352274	+	0.352274i	−0.508681	+	0.860955i	$0.669867\pi$
$294$	−89.0315	+	28.9281i	−0.302828	+	0.0983949i
$295$	−52.5878	+	132.603i	−0.178264	+	0.449503i
$296$	50.9104	−	156.686i	0.171995	−	0.529345i
$297$	−64.3299	−	126.255i	−0.216599	−	0.425100i
$298$	233.856	+	37.0391i	0.784751	+	0.124292i
$299$			391.038i			1.30782i
$300$	−119.027	+	92.1127i	−0.396758	+	0.307042i
$301$	234.834			0.780178
$302$	20.5662	−	129.850i	0.0680999	−	0.429966i
$303$	−459.733	+	234.246i	−1.51727	+	0.773088i
$304$	46.0979	+	14.9781i	0.151638	+	0.0492701i
$305$	162.100	−	195.721i	0.531477	−	0.641709i
$306$	−0.587609	−	1.80847i	−0.00192029	−	0.00591004i
$307$	169.339	−	169.339i	0.551592	−	0.551592i	−0.375308	−	0.926900i	$-0.622463\pi$
$307$	169.339	−	169.339i	0.551592	−	0.551592i	0.926900	+	0.375308i	$0.122463\pi$
$308$	−24.8497	+	48.7703i	−0.0806809	+	0.158345i
$309$	88.3427	−	121.593i	0.285899	−	0.393506i
$310$	−313.355	+	135.391i	−1.01082	+	0.436746i
$311$	−244.150	+	177.385i	−0.785047	+	0.570370i	−0.906490	−	0.422228i	$-0.861248\pi$
$311$	−244.150	+	177.385i	−0.785047	+	0.570370i	0.121442	+	0.992598i	$0.461248\pi$
$312$	−82.1486	+	13.0111i	−0.263297	+	0.0417021i
$313$	−1.92501	−	12.1540i	−0.00615018	−	0.0388307i	0.984422	−	0.175820i	$-0.0562575\pi$
$313$	−1.92501	−	12.1540i	−0.00615018	−	0.0388307i	−0.990573	+	0.136989i	$0.956258\pi$
$314$	−99.9041	−	137.506i	−0.318166	−	0.437918i
$315$	0.627749	+	1.45288i	0.00199285	+	0.00461233i
$316$	−130.327	−	94.6884i	−0.412429	−	0.299647i
$317$	166.319	+	84.7437i	0.524665	+	0.267330i	0.696200	−	0.717848i	$-0.254873\pi$
$317$	166.319	+	84.7437i	0.524665	+	0.267330i	−0.171535	+	0.985178i	$0.554873\pi$
$318$	228.370	+	228.370i	0.718144	+	0.718144i
$319$	−157.384	+	51.1373i	−0.493368	+	0.160305i
$320$	−30.8062	−	25.5143i	−0.0962693	−	0.0797322i
$321$	−82.3106	+	253.326i	−0.256419	+	0.789178i
$322$	133.564	+	262.134i	0.414794	+	0.814079i
$323$	−264.213	−	41.8473i	−0.817998	−	0.129558i
$324$		−	163.089i		−	0.503361i
$325$	−149.470	−	193.144i	−0.459907	−	0.594289i
$326$	242.393			0.743538
$327$	−31.8666	+	201.198i	−0.0974513	+	0.615283i
$328$	−102.768	+	52.3632i	−0.313319	+	0.159644i
$329$	−106.919	−	34.7400i	−0.324981	−	0.105593i
$330$	−104.193	−	41.3209i	−0.315737	−	0.125215i
$331$	−126.807	−	390.271i	−0.383102	−	1.17907i	−0.937848	−	0.347047i	$-0.887184\pi$
$331$	−126.807	−	390.271i	−0.383102	−	1.17907i	0.554745	−	0.832020i	$-0.312816\pi$
$332$	101.255	−	101.255i	0.304986	−	0.304986i
$333$	1.61064	−	3.16105i	0.00483674	−	0.00949265i
$334$	51.4742	−	70.8481i	0.154114	−	0.212120i
$335$	60.1811	+	13.4876i	0.179645	+	0.0402616i
$336$	−50.6246	+	36.7809i	−0.150668	+	0.109467i
$337$	395.546	−	62.6483i	1.17373	−	0.185900i	0.461038	−	0.887381i	$-0.347477\pi$
$337$	395.546	−	62.6483i	1.17373	−	0.185900i	0.712689	+	0.701481i	$0.247477\pi$
$338$	16.2753	+	102.758i	0.0481519	+	0.304019i
$339$	5.20035	+	7.15767i	0.0153403	+	0.0211141i
$340$	189.954	+	112.483i	0.558688	+	0.330832i
$341$	−205.667	−	149.426i	−0.603128	−	0.438198i
$342$	0.929998	+	0.473858i	0.00271929	+	0.00138555i
$343$	−260.882	−	260.882i	−0.760588	−	0.760588i
$344$	−121.550	+	39.4939i	−0.353342	+	0.114808i
$345$	−508.851	+	322.525i	−1.47493	+	0.934856i
$346$	−19.1743	+	59.0125i	−0.0554171	+	0.170556i
$347$	−5.00956	−	9.83181i	−0.0144368	−	0.0283337i	0.883676	−	0.468100i	$-0.155061\pi$
$347$	−5.00956	−	9.83181i	−0.0144368	−	0.0283337i	−0.898112	+	0.439766i	$0.855061\pi$
$348$	−186.855	−	29.5949i	−0.536939	−	0.0850428i
$349$		−	135.601i		−	0.388542i	−0.980948	−	0.194271i	$-0.937766\pi$
$349$		−	135.601i		−	0.388542i	0.980948	−	0.194271i	$-0.0622341\pi$
$350$	−166.168	−	78.4214i	−0.474766	−	0.224061i
$351$	262.863			0.748896
$352$	4.66009	−	29.4227i	0.0132389	−	0.0835871i
$353$	−29.4184	+	14.9894i	−0.0833381	+	0.0424629i	−0.495163	−	0.868800i	$-0.664892\pi$
$353$	−29.4184	+	14.9894i	−0.0833381	+	0.0424629i	0.411825	+	0.911263i	$0.364892\pi$
$354$	−115.507	−	37.5307i	−0.326292	−	0.106019i
$355$	31.4756	−	495.836i	0.0886637	−	1.39672i
$356$	−34.1964	−	105.246i	−0.0960574	−	0.295634i
$357$	244.201	−	244.201i	0.684038	−	0.684038i
$358$	−41.5082	+	81.4645i	−0.115945	+	0.227554i
$359$	325.869	−	448.521i	0.907714	−	1.24936i	−0.0602268	−	0.998185i	$-0.519182\pi$
$359$	325.869	−	448.521i	0.907714	−	1.24936i	0.967941	−	0.251177i	$-0.0808176\pi$
$360$	−0.569266	−	0.646438i	−0.00158129	−	0.00179566i
$361$	−173.263	+	125.883i	−0.479953	+	0.348706i
$362$	−496.218	+	78.5933i	−1.37077	+	0.217108i
$363$	43.9191	+	277.294i	0.120989	+	0.763896i
$364$	−59.6837	−	82.1476i	−0.163966	−	0.225680i
$365$	18.0861	−	1.69937i	0.0495510	−	0.00465581i
$366$	175.045	+	127.177i	0.478264	+	0.347479i
$367$	−186.096	−	94.8209i	−0.507075	−	0.258368i	0.181685	−	0.983357i	$-0.441845\pi$
$367$	−186.096	−	94.8209i	−0.507075	−	0.258368i	−0.688760	+	0.724989i	$0.741845\pi$
$368$	−113.218	−	113.218i	−0.307657	−	0.307657i
$369$	−2.36217	+	0.767516i	−0.00640155	+	0.00207999i
$370$	102.204	+	398.992i	0.276228	+	1.07836i
$371$	−121.841	+	374.987i	−0.328412	+	1.01075i
$372$	−131.942	−	258.950i	−0.354682	−	0.696102i
$373$	188.216	+	29.8104i	0.504600	+	0.0799208i	0.403544	−	0.914960i	$-0.367778\pi$
$373$	188.216	+	29.8104i	0.504600	+	0.0799208i	0.101055	+	0.994881i	$0.467778\pi$
$374$			164.407i			0.439592i
$375$	128.053	−	353.806i	0.341476	−	0.943484i
$376$	61.1836			0.162722
$377$	48.0231	−	303.206i	0.127382	−	0.804260i
$378$	176.211	−	89.7840i	0.466167	−	0.237524i
$379$	297.278	+	96.5916i	0.784375	+	0.254859i	0.673707	−	0.738998i	$-0.264701\pi$
$379$	297.278	+	96.5916i	0.784375	+	0.254859i	0.110668	+	0.993857i	$0.464701\pi$
$380$	−117.386	+	30.0691i	−0.308909	+	0.0791291i
$381$	17.5736	+	54.0858i	0.0461248	+	0.141958i
$382$	−132.211	+	132.211i	−0.346101	+	0.346101i
$383$	78.2257	−	153.527i	0.204245	−	0.400853i	−0.766049	−	0.642782i	$-0.777780\pi$
$383$	78.2257	−	153.527i	0.204245	−	0.400853i	0.970294	+	0.241929i	$0.0777802\pi$
$384$	20.0175	−	27.5517i	0.0521289	−	0.0717492i
$385$	−12.8011	−	136.240i	−0.0332497	−	0.353871i
$386$	−76.0630	+	55.2630i	−0.197054	+	0.143168i
$387$	−2.71828	+	0.430533i	−0.00702397	+	0.00111249i
$388$	31.0477	+	196.027i	0.0800197	+	0.505225i
$389$	233.516	+	321.408i	0.600299	+	0.826241i	0.995736	−	0.0922523i	$-0.0294066\pi$
$389$	233.516	+	321.408i	0.600299	+	0.826241i	−0.395436	+	0.918493i	$0.629407\pi$
$390$	156.049	−	137.420i	0.400126	−	0.352358i
$391$	714.902	+	519.406i	1.82839	+	1.32841i
$392$	55.4195	+	28.2376i	0.141376	+	0.0720348i
$393$	−348.183	−	348.183i	−0.885963	−	0.885963i
$394$	334.062	−	108.543i	0.847873	−	0.275491i
$395$	401.925	+	25.5141i	1.01753	+	0.0645927i
$396$	0.198231	−	0.610091i	0.000500582	−	0.00154063i
$397$	125.732	+	246.762i	0.316704	+	0.621567i	0.993401	−	0.114695i	$-0.0365891\pi$
$397$	125.732	+	246.762i	0.316704	+	0.621567i	−0.676697	+	0.736262i	$0.736589\pi$
$398$	127.475	+	20.1900i	0.320288	+	0.0507286i
$399$			189.565i			0.475101i
$400$	99.1973	+	12.6450i	0.247993	+	0.0316125i
$401$	129.386			0.322658			0.161329	−	0.986901i	$-0.448422\pi$
$401$	129.386			0.322658			0.161329	+	0.986901i	$0.448422\pi$
$402$	−8.21420	+	51.8624i	−0.0204333	+	0.129011i
$403$	420.194	−	214.099i	1.04266	−	0.531264i
$404$	326.043	+	105.938i	0.807037	+	0.262222i
$405$	218.275	+	344.374i	0.538950	+	0.850307i
$406$	−71.3713	−	219.658i	−0.175791	−	0.541030i
$407$	−216.896	+	216.896i	−0.532914	+	0.532914i
$408$	−85.3291	+	167.468i	−0.209140	+	0.410460i
$409$	−373.902	+	514.631i	−0.914185	+	1.25827i	0.0515322	+	0.998671i	$0.483590\pi$
$409$	−373.902	+	514.631i	−0.914185	+	1.25827i	−0.965717	+	0.259596i	$0.916410\pi$
$410$	146.922	−	248.112i	0.358345	−	0.605151i
$411$	−454.269	+	330.046i	−1.10528	+	0.803031i
$412$	−98.6316	+	15.6217i	−0.239397	+	0.0379168i
$413$	−23.1949	−	146.447i	−0.0561621	−	0.354593i
$414$	−2.02663	−	2.78941i	−0.00489523	−	0.00673771i
$415$	−78.2901	+	349.326i	−0.188651	+	0.841750i
$416$	44.7077	+	32.4820i	0.107470	+	0.0780818i
$417$	−142.582	−	72.6491i	−0.341923	−	0.174218i
$418$	−63.8119	−	63.8119i	−0.152660	−	0.152660i
$419$	−268.403	+	87.2095i	−0.640580	+	0.208137i	−0.611256	−	0.791433i	$-0.709336\pi$
$419$	−268.403	+	87.2095i	−0.640580	+	0.208137i	−0.0293242	+	0.999570i	$0.509336\pi$
$420$	57.6707	−	145.420i	0.137311	−	0.346239i
$421$	−112.020	+	344.764i	−0.266082	+	0.818916i	0.725360	+	0.688369i	$0.241673\pi$
$421$	−112.020	+	344.764i	−0.266082	+	0.818916i	−0.991442	+	0.130546i	$0.958327\pi$
$422$	−12.9256	−	25.3679i	−0.0306293	−	0.0601134i
$423$	1.30131	+	0.206108i	0.00307639	+	0.000487252i
$424$		−	214.584i		−	0.506095i
$425$	−551.646	+	16.7145i	−1.29799	+	0.0393283i
$426$	423.002			0.992963
$427$	−41.3219	+	260.896i	−0.0967726	+	0.610998i
$428$	157.688	−	80.3461i	0.368430	−	0.187724i
$429$	147.275	+	47.8525i	0.343298	+	0.111544i
$430$	203.803	−	246.074i	0.473961	−	0.572264i
$431$	−47.8537	−	147.279i	−0.111030	−	0.341714i	0.880069	−	0.474846i	$-0.157496\pi$
$431$	−47.8537	−	147.279i	−0.111030	−	0.341714i	−0.991098	+	0.133133i	$0.957496\pi$
$432$	−76.1069	+	76.1069i	−0.176173	+	0.176173i
$433$	−5.21724	+	10.2394i	−0.0120490	+	0.0236476i	−0.896953	−	0.442127i	$-0.854224\pi$
$433$	−5.21724	+	10.2394i	−0.0120490	+	0.0236476i	0.884904	+	0.465774i	$0.154224\pi$
$434$	208.550	−	287.045i	0.480530	−	0.661393i
$435$	434.167	−	187.591i	0.998084	−	0.431243i
$436$	109.498	−	79.5547i	0.251141	−	0.182465i
$437$	−479.075	+	75.8781i	−1.09628	+	0.173634i
$438$	2.41945	+	15.2758i	0.00552386	+	0.0348763i
$439$	−413.058	−	568.526i	−0.940907	−	1.29505i	−0.955450	−	0.295153i	$-0.904629\pi$
$439$	−413.058	−	568.526i	−0.940907	−	1.29505i	0.0145431	−	0.999894i	$-0.495371\pi$
$440$	29.5385	+	68.3651i	0.0671330	+	0.155375i
$441$	1.08359	+	0.787275i	0.00245712	+	0.00178520i
$442$	−271.747	−	138.462i	−0.614813	−	0.313263i
$443$	−414.720	−	414.720i	−0.936162	−	0.936162i	0.0619190	−	0.998081i	$-0.480278\pi$
$443$	−414.720	−	414.720i	−0.936162	−	0.936162i	−0.998081	+	0.0619190i	$0.980278\pi$
$444$	−333.504	+	108.362i	−0.751136	+	0.244059i
$445$	213.067	+	176.466i	0.478802	+	0.396554i
$446$	−55.4989	+	170.808i	−0.124437	+	0.382978i
$447$	−228.795	−	449.035i	−0.511845	−	1.00455i
$448$	41.0646	+	6.50399i	0.0916621	+	0.0145178i
$449$		−	284.407i		−	0.633423i	−0.948522	−	0.316711i	$-0.897421\pi$
$449$		−	284.407i		−	0.633423i	0.948522	−	0.316711i	$-0.102579\pi$
$450$	2.06723	+	0.603109i	0.00459384	+	0.00134024i
$451$	214.744			0.476151
$452$	0.919582	−	5.80601i	0.00203447	−	0.0128452i
$453$	−249.329	+	127.039i	−0.550395	+	0.280440i
$454$	−275.623	−	89.5554i	−0.607100	−	0.197259i
$455$	235.971	+	93.5813i	0.518618	+	0.205673i
$456$	−31.8807	−	98.1188i	−0.0699139	−	0.215173i
$457$	−518.518	+	518.518i	−1.13461	+	1.13461i	−0.145213	+	0.989400i	$0.546387\pi$
$457$	−518.518	+	518.518i	−1.13461	+	1.13461i	−0.989400	+	0.145213i	$0.953613\pi$
$458$	167.970	−	329.661i	0.366748	−	0.719783i
$459$	349.154	−	480.570i	0.760685	−	1.04699i
$460$	390.595	+	87.5393i	0.849120	+	0.190303i
$461$	21.7328	−	15.7898i	0.0471427	−	0.0342511i	−0.563964	−	0.825799i	$-0.690724\pi$
$461$	21.7328	−	15.7898i	0.0471427	−	0.0342511i	0.611107	+	0.791548i	$0.290724\pi$
$462$	115.071	−	18.2254i	0.249071	−	0.0394490i
$463$	60.6288	+	382.795i	0.130948	+	0.826772i	0.962491	+	0.271312i	$0.0874576\pi$
$463$	60.6288	+	382.795i	0.130948	+	0.826772i	−0.831544	+	0.555459i	$0.812542\pi$
$464$	73.8834	+	101.692i	0.159231	+	0.219163i
$465$	625.177	+	370.204i	1.34447	+	0.796138i
$466$	−369.481	−	268.444i	−0.792878	−	0.576059i
$467$	535.215	+	272.705i	1.14607	+	0.583952i	0.920680	−	0.390317i	$-0.127635\pi$
$467$	535.215	+	272.705i	1.14607	+	0.583952i	0.225389	+	0.974269i	$0.427635\pi$
$468$	0.841464	+	0.841464i	0.00179800	+	0.00179800i
$469$	−60.9672	+	19.8094i	−0.129994	+	0.0422376i
$470$	−129.194	+	81.8869i	−0.274880	+	0.174227i
$471$	−111.794	+	344.066i	−0.237354	+	0.730501i
$472$	36.6349	+	71.9000i	0.0776163	+	0.152330i
$473$	235.022	+	37.2239i	0.496876	+	0.0786974i
$474$			342.886i			0.723387i
$475$	207.624	−	220.599i	0.437104	−	0.464420i
$476$	−229.460			−0.482059
$477$	0.722863	−	4.56398i	0.00151544	−	0.00956809i
$478$	−248.596	+	126.666i	−0.520076	+	0.264992i
$479$	−339.002	−	110.148i	−0.707728	−	0.229955i	−0.0670335	−	0.997751i	$-0.521353\pi$
$479$	−339.002	−	110.148i	−0.707728	−	0.229955i	−0.640694	+	0.767796i	$0.721353\pi$
$480$	−5.39378	+	84.9684i	−0.0112370	+	0.177018i
$481$	−175.837	−	541.172i	−0.365566	−	1.12510i
$482$	−28.8448	+	28.8448i	−0.0598439	+	0.0598439i
$483$	284.289	−	557.948i	0.588589	−	1.15517i
$484$	109.644	−	150.912i	0.226536	−	0.311801i
$485$	−327.918	−	372.372i	−0.676120	−	0.767778i
$486$	−3.76296	+	2.73395i	−0.00774273	+	0.00562542i
$487$	−819.232	+	129.754i	−1.68220	+	0.266434i	−0.923106	−	0.384546i	$-0.874358\pi$
$487$	−819.232	+	129.754i	−1.68220	+	0.266434i	−0.759095	+	0.650980i	$0.774358\pi$
$488$	−22.4889	−	141.989i	−0.0460837	−	0.290961i
$489$	−303.257	−	417.397i	−0.620157	−	0.853573i
$490$	−154.815	+	14.5464i	−0.315949	+	0.0296865i
$491$	555.843	+	403.843i	1.13206	+	0.822492i	0.985994	−	0.166783i	$-0.0533379\pi$
$491$	555.843	+	403.843i	1.13206	+	0.822492i	0.146069	+	0.989274i	$0.453338\pi$
$492$	218.741	+	111.454i	0.444596	+	0.226533i
$493$	−490.538	−	490.538i	−0.995007	−	0.995007i
$494$	159.216	−	51.7323i	0.322299	−	0.104721i
$495$	0.397954	+	1.55356i	0.000803948	+	0.00313850i
$496$	−59.6707	+	183.648i	−0.120304	+	0.370257i
$497$	234.448	+	460.130i	0.471726	+	0.925814i
$498$	−301.040	−	47.6800i	−0.604497	−	0.0957430i
$499$		−	127.495i		−	0.255501i	−0.991806	−	0.127751i	$-0.959224\pi$
$499$		−	127.495i		−	0.255501i	0.991806	−	0.127751i	$-0.0407757\pi$
$500$	−226.386	+	106.063i	−0.452772	+	0.212125i
$501$	−186.398			−0.372052
$502$	28.5519	−	180.270i	0.0568764	−	0.359103i
$503$	113.602	−	57.8832i	0.225849	−	0.115076i	−0.337405	−	0.941360i	$-0.609549\pi$
$503$	113.602	−	57.8832i	0.225849	−	0.115076i	0.563254	+	0.826284i	$0.309549\pi$
$504$	0.851491	+	0.276666i	0.00168947	+	0.000548941i
$505$	−830.249	+	212.674i	−1.64406	+	0.421136i
$506$	92.1199	+	283.516i	0.182055	+	0.560308i
$507$	156.586	−	156.586i	0.308848	−	0.308848i
$508$	17.1541	−	33.6668i	0.0337679	−	0.0662733i
$509$	102.811	−	141.507i	0.201985	−	0.278009i	−0.695993	−	0.718049i	$-0.745036\pi$
$509$	102.811	−	141.507i	0.201985	−	0.278009i	0.897978	+	0.440039i	$0.145036\pi$
$510$	−43.9566	−	467.823i	−0.0861895	−	0.917300i
$511$	−15.2756	+	11.0984i	−0.0298936	+	0.0217190i
$512$	−22.3488	+	3.53971i	−0.0436501	+	0.00691349i
$513$	51.0066	+	322.043i	0.0994282	+	0.627765i
$514$	88.5798	+	121.920i	0.172334	+	0.237198i
$515$	187.360	−	164.993i	0.363806	−	0.320374i
$516$	220.078	+	159.896i	0.426507	+	0.309875i
$517$	−101.498	−	51.7159i	−0.196321	−	0.100031i
$518$	−302.717	−	302.717i	−0.584396	−	0.584396i
$519$	125.607	−	40.8123i	0.242018	−	0.0786363i
$520$	−137.877	−	8.75240i	−0.265148	−	0.0168315i
$521$	98.8513	−	304.233i	0.189734	−	0.583941i	−0.810264	−	0.586065i	$-0.800676\pi$
$521$	98.8513	−	304.233i	0.189734	−	0.583941i	0.999998	+	0.00212454i	$0.000676262\pi$
$522$	1.22886	+	2.41177i	0.00235413	+	0.00462024i
$523$	−84.6243	−	13.4032i	−0.161806	−	0.0256275i	0.0750060	−	0.997183i	$-0.476102\pi$
$523$	−84.6243	−	13.4032i	−0.161806	−	0.0256275i	−0.236812	+	0.971556i	$0.576102\pi$
$524$			327.165i			0.624361i
$525$	72.8516	+	384.251i	0.138765	+	0.731907i
$526$	−677.341			−1.28772
$527$	166.714	−	1052.59i	0.316345	−	1.99732i
$528$	−56.4955	+	28.7859i	−0.106999	+	0.0545187i
$529$	1020.75	+	331.661i	1.92958	+	0.626959i
$530$	287.195	+	453.110i	0.541877	+	0.854925i
$531$	0.536978	+	1.65265i	0.00101126	+	0.00311233i
$532$	89.0610	−	89.0610i	0.167408	−	0.167408i
$533$	−180.855	+	354.948i	−0.339315	+	0.665944i
$534$	−138.448	+	190.558i	−0.259267	+	0.356850i
$535$	−225.436	+	380.703i	−0.421376	+	0.711594i
$536$	28.2251	−	20.5067i	0.0526587	−	0.0382588i
$537$	192.211	−	30.4432i	0.357935	−	0.0566913i
$538$	19.5693	+	123.556i	0.0363742	+	0.229658i
$539$	−68.0679	−	93.6874i	−0.126285	−	0.173817i
$540$	58.8455	−	262.565i	0.108973	−	0.486232i
$541$	−316.524	−	229.968i	−0.585072	−	0.425080i	0.255477	−	0.966815i	$-0.417767\pi$
$541$	−316.524	−	229.968i	−0.585072	−	0.425080i	−0.840549	+	0.541736i	$0.817767\pi$
$542$	493.812	+	251.610i	0.911092	+	0.464225i
$543$	756.151	+	756.151i	1.39254	+	1.39254i
$544$	118.768	−	38.5902i	0.218324	−	0.0709379i
$545$	−124.738	+	314.535i	−0.228877	+	0.577128i
$546$	−66.7868	+	205.549i	−0.122320	+	0.376463i
$547$	253.958	+	498.421i	0.464275	+	0.911190i	0.997856	+	0.0654416i	$0.0208456\pi$
$547$	253.958	+	498.421i	0.464275	+	0.911190i	−0.533582	+	0.845748i	$0.679154\pi$
$548$	368.485	+	58.3623i	0.672418	+	0.106501i
$549$		−	3.09572i		−	0.00563883i
$550$	−153.871	−	104.824i	−0.279766	−	0.190589i
$551$	380.788			0.691085
$552$	−53.3129	+	336.604i	−0.0965813	+	0.609791i
$553$	−372.981	+	190.043i	−0.674469	+	0.343659i
$554$	−410.140	−	133.263i	−0.740326	−	0.240546i
$555$	559.189	−	675.170i	1.00755	−	1.21652i
$556$	32.8556	+	101.119i	0.0590929	+	0.181869i
$557$	−28.2545	+	28.2545i	−0.0507262	+	0.0507262i	−0.732015	−	0.681289i	$-0.761420\pi$
$557$	−28.2545	+	28.2545i	−0.0507262	+	0.0507262i	0.681289	+	0.732015i	$0.261420\pi$
$558$	−1.88778	+	3.70498i	−0.00338312	+	0.00663975i
$559$	−259.460	+	357.116i	−0.464150	+	0.638848i
$560$	−95.4157	+	41.2263i	−0.170385	+	0.0736184i
$561$	283.107	−	205.689i	0.504646	−	0.366647i
$562$	656.183	−	103.929i	1.16759	−	0.184927i
$563$	23.0534	+	145.553i	0.0409474	+	0.258532i	0.999667	−	0.0258231i	$-0.00822066\pi$
$563$	23.0534	+	145.553i	0.0409474	+	0.258532i	−0.958719	+	0.284355i	$0.908221\pi$
$564$	−76.5464	−	105.357i	−0.135721	−	0.186803i
$565$	5.82888	+	13.4906i	0.0103166	+	0.0238771i
$566$	465.541	+	338.235i	0.822511	+	0.597589i
$567$	−377.601	−	192.397i	−0.665963	−	0.339325i
$568$	−198.734	−	198.734i	−0.349883	−	0.349883i
$569$	899.114	−	292.140i	1.58017	−	0.513427i	0.618066	−	0.786126i	$-0.287916\pi$
$569$	899.114	−	292.140i	1.58017	−	0.513427i	0.962099	+	0.272699i	$0.0879164\pi$
$570$	198.639	+	164.517i	0.348489	+	0.288626i
$571$	135.460	−	416.903i	0.237233	−	0.730128i	−0.759585	−	0.650409i	$-0.774598\pi$
$571$	135.460	−	416.903i	0.237233	−	0.730128i	0.996817	−	0.0797190i	$-0.0254023\pi$
$572$	−46.7104	−	91.6743i	−0.0816615	−	0.160270i
$573$	393.072	+	62.2566i	0.685990	+	0.108650i
$574$			299.714i			0.522150i
$575$	−941.931	+	337.919i	−1.63814	+	0.587685i
$576$	−0.487260			−0.000845938
$577$	116.378	−	734.780i	0.201694	−	1.27345i	−0.654209	−	0.756314i	$-0.726998\pi$
$577$	116.378	−	734.780i	0.201694	−	1.27345i	0.855904	−	0.517135i	$-0.173002\pi$
$578$	−249.933	+	127.347i	−0.432410	+	0.220324i
$579$	190.324	+	61.8399i	0.328711	+	0.106805i
$580$	−292.112	−	115.846i	−0.503642	−	0.199734i
$581$	−114.985	−	353.889i	−0.197910	−	0.609103i
$582$	298.712	−	298.712i	0.513250	−	0.513250i
$583$	−181.379	+	355.976i	−0.311113	+	0.610593i
$584$	6.04015	−	8.31355i	0.0103427	−	0.0142355i
$585$	−2.90301	−	0.650616i	−0.00496241	−	0.00111216i
$586$	−167.007	+	121.338i	−0.284995	+	0.207061i
$587$	403.155	−	63.8535i	0.686806	−	0.108779i	0.196728	−	0.980458i	$-0.436968\pi$
$587$	403.155	−	63.8535i	0.686806	−	0.108779i	0.490078	+	0.871679i	$0.336968\pi$
$588$	−20.7102	−	130.759i	−0.0352215	−	0.222380i
$589$	343.837	+	473.251i	0.583764	+	0.803483i
$590$	−173.587	−	102.791i	−0.294215	−	0.174222i
$591$	−604.852	−	439.451i	−1.02344	−	0.743571i
$592$	207.597	+	105.776i	0.350670	+	0.178675i
$593$	270.505	+	270.505i	0.456163	+	0.456163i	0.897394	−	0.441231i	$-0.145458\pi$
$593$	270.505	+	270.505i	0.456163	+	0.456163i	−0.441231	+	0.897394i	$0.645458\pi$
$594$	190.584	−	61.9247i	0.320849	−	0.104250i
$595$	484.522	−	307.105i	0.814323	−	0.516142i
$596$	−103.473	+	318.456i	−0.173612	+	0.534322i
$597$	−124.716	−	244.769i	−0.208904	−	0.409998i
$598$	−546.202	−	86.5099i	−0.913382	−	0.144665i
$599$		−	588.933i		−	0.983193i	−0.870823	−	0.491596i	$-0.836414\pi$
$599$		−	588.933i		−	0.983193i	0.870823	−	0.491596i	$-0.163586\pi$
$600$	−102.331	−	186.636i	−0.170551	−	0.311060i
$601$	314.905			0.523969			0.261984	−	0.965072i	$-0.415623\pi$
$601$	314.905			0.523969			0.261984	+	0.965072i	$0.415623\pi$
$602$	−51.9526	+	328.016i	−0.0863000	+	0.544877i
$603$	0.669398	−	0.341075i	0.00111011	−	0.000565631i
$604$	176.824	+	57.4537i	0.292756	+	0.0951221i
$605$	−29.5439	+	465.406i	−0.0488328	+	0.769265i
$606$	−225.487	−	693.978i	−0.372091	−	1.14518i
$607$	−314.078	+	314.078i	−0.517426	+	0.517426i	−0.916792	−	0.399366i	$-0.869230\pi$
$607$	−314.078	+	314.078i	−0.517426	+	0.517426i	0.399366	+	0.916792i	$0.369230\pi$
$608$	−31.1198	+	61.0760i	−0.0511839	+	0.100454i
$609$	−288.955	+	397.713i	−0.474475	+	0.653059i
$610$	237.522	+	269.722i	0.389380	+	0.442167i
$611$	170.961	−	124.211i	0.279806	−	0.203291i
$612$	2.65608	−	0.420681i	0.00434000	−	0.000687388i
$613$	−14.9266	−	94.2428i	−0.0243501	−	0.153740i	0.972517	−	0.232830i	$-0.0747986\pi$
$613$	−14.9266	−	94.2428i	−0.0243501	−	0.153740i	−0.996867	+	0.0790898i	$0.974799\pi$
$614$	199.070	+	273.996i	0.324218	+	0.446247i
$615$	−611.056	+	57.4148i	−0.993588	+	0.0933574i
$616$	−62.6249	−	45.4997i	−0.101664	−	0.0738631i
$617$	522.597	+	266.276i	0.846997	+	0.431566i	0.822929	−	0.568144i	$-0.192338\pi$
$617$	522.597	+	266.276i	0.846997	+	0.431566i	0.0240674	+	0.999710i	$0.492338\pi$
$618$	150.298	+	150.298i	0.243200	+	0.243200i
$619$	−1124.35	+	365.323i	−1.81640	+	0.590183i	−0.816480	+	0.577374i	$0.804077\pi$
$619$	−1124.35	+	365.323i	−1.81640	+	0.590183i	−0.999918	+	0.0128089i	$0.995923\pi$
$620$	−119.791	−	467.648i	−0.193211	−	0.754270i
$621$	332.836	−	1024.36i	0.535968	−	1.64954i
$622$	−193.758	−	380.272i	−0.311508	−	0.611370i
$623$	−284.018	−	44.9841i	−0.455888	−	0.0722055i
$624$		−	117.624i		−	0.188500i
$625$	336.079	−	526.950i	0.537727	−	0.843119i
$626$	17.4026			0.0277997
$627$	−30.0483	+	189.718i	−0.0479240	+	0.302580i
$628$	214.171	−	109.125i	0.341036	−	0.173767i
$629$	−1222.94	−	397.357i	−1.94426	−	0.631729i
$630$	−2.16827	+	0.555417i	−0.00344170	+	0.000881614i
$631$	185.000	+	569.372i	0.293186	+	0.902333i	0.983825	+	0.179133i	$0.0573293\pi$
$631$	185.000	+	569.372i	0.293186	+	0.902333i	−0.690639	+	0.723200i	$0.742671\pi$
$632$	161.094	−	161.094i	0.254895	−	0.254895i
$633$	−27.5119	+	53.9952i	−0.0434627	+	0.0853004i
$634$	−155.165	+	213.567i	−0.244740	+	0.336856i
$635$	8.83681	+	94.0487i	0.0139162	+	0.148108i
$636$	−369.510	+	268.465i	−0.580990	+	0.422114i
$637$	212.181	−	33.6061i	0.333094	−	0.0527569i
$638$	−36.6102	−	231.148i	−0.0573828	−	0.362301i
$639$	−3.55739	−	4.89633i	−0.00556712	−	0.00766249i
$640$	42.4537	−	37.3856i	0.0663340	−	0.0584149i
$641$	−40.2224	−	29.2233i	−0.0627494	−	0.0455901i	0.555968	−	0.831203i	$-0.312348\pi$
$641$	−40.2224	−	29.2233i	−0.0627494	−	0.0455901i	−0.618718	+	0.785613i	$0.712348\pi$
$642$	−335.637	−	171.015i	−0.522799	−	0.266379i
$643$	734.030	+	734.030i	1.14157	+	1.14157i	0.988163	+	0.153408i	$0.0490249\pi$
$643$	734.030	+	734.030i	1.14157	+	1.14157i	0.153408	+	0.988163i	$0.450975\pi$
$644$	−395.697	+	128.570i	−0.614437	+	0.199643i
$645$	−678.711	−	43.0845i	−1.05227	−	0.0667976i
$646$	116.905	−	359.796i	0.180967	−	0.556959i
$647$	−66.8972	−	131.293i	−0.103396	−	0.202926i	0.833513	−	0.552500i	$-0.186326\pi$
$647$	−66.8972	−	131.293i	−0.103396	−	0.202926i	−0.936909	+	0.349574i	$0.886326\pi$
$648$	227.803	+	36.0804i	0.351548	+	0.0556797i
$649$		−	150.241i		−	0.231497i
$650$	302.851	−	166.050i	0.465925	−	0.255462i
$651$	−755.201			−1.16006
$652$	−53.6251	+	338.576i	−0.0822471	+	0.519288i
$653$	193.327	−	98.5048i	0.296059	−	0.150850i	−0.299652	−	0.954049i	$-0.596870\pi$
$653$	193.327	−	98.5048i	0.296059	−	0.150850i	0.595711	+	0.803199i	$0.296870\pi$
$654$	−273.983	−	89.0226i	−0.418935	−	0.136120i
$655$	−437.871	−	690.833i	−0.668505	−	1.05471i
$656$	−50.4053	−	155.132i	−0.0768374	−	0.236481i
$657$	0.156473	−	0.156473i	0.000238163	−	0.000238163i
$658$	72.1788	−	141.659i	0.109694	−	0.215287i
$659$	−590.438	+	812.668i	−0.895961	+	1.23318i	0.0757779	+	0.997125i	$0.475856\pi$
$659$	−590.438	+	812.668i	−0.895961	+	1.23318i	−0.971739	+	0.236059i	$0.924144\pi$
$660$	80.7679	−	136.396i	0.122376	−	0.206660i
$661$	422.492	−	306.958i	0.639170	−	0.464385i	−0.220395	−	0.975411i	$-0.570735\pi$
$661$	422.492	−	306.958i	0.639170	−	0.464385i	0.859565	+	0.511026i	$0.170735\pi$
$662$	573.185	−	90.7837i	0.865839	−	0.137135i
$663$	101.552	+	641.173i	0.153170	+	0.967078i
$664$	119.033	+	163.835i	0.179266	+	0.246739i
$665$	−68.8615	+	307.256i	−0.103551	+	0.462040i
$666$	4.05904	+	2.94906i	0.00609465	+	0.00442802i
$667$	−1120.77	−	571.063i	−1.68032	−	0.856166i
$668$	87.5731	+	87.5731i	0.131097	+	0.131097i
$669$	363.563	−	118.129i	0.543442	−	0.176575i
$670$	−32.1536	+	81.0772i	−0.0479904	+	0.121011i
$671$	−82.7103	+	254.556i	−0.123264	+	0.379368i
$672$	−40.1759	−	78.8496i	−0.0597855	−	0.117336i
$673$	498.398	+	78.9385i	0.740562	+	0.117293i	0.515306	−	0.857006i	$-0.327678\pi$
$673$	498.398	+	78.9385i	0.740562	+	0.117293i	0.225256	+	0.974300i	$0.427678\pi$
$674$			566.359i			0.840295i
$675$	227.155	+	633.184i	0.336526	+	0.938050i
$676$	−147.134			−0.217653
$677$	−107.904	+	681.279i	−0.159385	+	1.00632i	0.770224	+	0.637773i	$0.220144\pi$
$677$	−107.904	+	681.279i	−0.159385	+	1.00632i	−0.929609	+	0.368546i	$0.879856\pi$
$678$	−11.1483	+	5.68036i	−0.0164430	+	0.00837811i
$679$	490.490	+	159.370i	0.722372	+	0.234713i
$680$	−199.140	+	240.443i	−0.292853	+	0.353593i
$681$	190.618	+	586.660i	0.279908	+	0.861469i
$682$	254.218	−	254.218i	0.372753	−	0.372753i
$683$	438.216	−	860.046i	0.641604	−	1.25922i	−0.309662	−	0.950847i	$-0.600216\pi$
$683$	438.216	−	860.046i	0.641604	−	1.25922i	0.951266	−	0.308372i	$-0.0997841\pi$
$684$	−0.867631	+	1.19419i	−0.00126847	+	0.00174589i
$685$	−856.194	+	369.936i	−1.24992	+	0.540053i
$686$	422.115	−	306.685i	0.615328	−	0.447062i
$687$	−777.816	+	123.194i	−1.13219	+	0.179322i
$688$	−28.2745	−	178.518i	−0.0410966	−	0.259474i
$689$	−435.633	−	599.597i	−0.632269	−	0.870243i
$690$	−337.930	−	782.118i	−0.489754	−	1.13350i
$691$	−551.842	−	400.937i	−0.798614	−	0.580227i	0.111893	−	0.993720i	$-0.464308\pi$
$691$	−551.842	−	400.937i	−0.798614	−	0.580227i	−0.910507	+	0.413493i	$0.864308\pi$
$692$	−78.1868	−	39.8381i	−0.112987	−	0.0575696i
$693$	−1.17869	−	1.17869i	−0.00170086	−	0.00170086i
$694$	14.8414	−	4.82225i	0.0213852	−	0.00694849i
$695$	−204.713	−	169.548i	−0.294551	−	0.243953i
$696$	82.6764	−	254.452i	0.118788	−	0.365592i
$697$	408.696	+	802.111i	0.586365	+	1.15081i
$698$	189.408	+	29.9993i	0.271358	+	0.0429789i
$699$			972.087i			1.39068i
$700$	146.301	−	214.755i	0.209001	−	0.306793i
$701$	531.096			0.757627			0.378813	−	0.925473i	$-0.376332\pi$
$701$	531.096			0.757627			0.378813	+	0.925473i	$0.376332\pi$
$702$	−58.1536	+	367.167i	−0.0828398	+	0.523030i
$703$	628.891	−	320.436i	0.894582	−	0.455812i
$704$	40.0667	+	13.0184i	0.0569129	+	0.0184921i
$705$	302.641	+	120.021i	0.429278	+	0.170243i
$706$	−14.4290	−	44.4078i	−0.0204376	−	0.0629005i
$707$	629.914	−	629.914i	0.890968	−	0.890968i
$708$	77.9768	−	153.038i	0.110137	−	0.216156i
$709$	159.105	−	218.990i	0.224408	−	0.308872i	−0.681936	−	0.731412i	$-0.738862\pi$
$709$	159.105	−	218.990i	0.224408	−	0.308872i	0.906344	+	0.422541i	$0.138862\pi$
$710$	685.622	+	153.660i	0.965665	+	0.216422i
$711$	3.96896	−	2.88362i	0.00558223	−	0.00405573i
$712$	154.573	−	24.4819i	0.217097	−	0.0343848i
$713$	−302.288	−	1908.57i	−0.423966	−	2.67682i
$714$	287.076	+	395.126i	0.402067	+	0.553398i
$715$	221.327	+	131.061i	0.309549	+	0.183302i
$716$	−104.607	−	76.0013i	−0.146099	−	0.106147i
$717$	529.134	+	269.607i	0.737983	+	0.376021i
$718$	554.402	+	554.402i	0.772148	+	0.772148i
$719$	−682.256	+	221.678i	−0.948896	+	0.308315i	−0.742267	−	0.670104i	$-0.766249\pi$
$719$	−682.256	+	221.678i	−0.948896	+	0.308315i	−0.206629	+	0.978419i	$0.566249\pi$
$720$	1.02889	−	0.652139i	0.00142901	−	0.000905749i
$721$	−80.1874	+	246.791i	−0.111217	+	0.342290i
$722$	−137.502	−	269.863i	−0.190446	−	0.373772i
$723$	85.7577	+	13.5827i	0.118614	+	0.0187866i
$724$		−	710.506i		−	0.981362i
$725$	771.862	−	146.340i	1.06464	−	0.201849i
$726$	−397.041			−0.546889
$727$	107.712	−	680.065i	0.148159	−	0.935440i	−0.795844	−	0.605502i	$-0.792972\pi$
$727$	107.712	−	680.065i	0.148159	−	0.935440i	0.944003	−	0.329938i	$-0.107028\pi$
$728$	127.948	−	65.1927i	0.175753	−	0.0895504i
$729$	−688.565	−	223.728i	−0.944533	−	0.306898i
$730$	−1.62754	+	25.6387i	−0.00222950	+	0.0351215i
$731$	308.251	+	948.699i	0.421684	+	1.29781i
$732$	−216.367	+	216.367i	−0.295583	+	0.295583i
$733$	−537.730	+	1055.35i	−0.733602	+	1.43977i	0.158228	+	0.987403i	$0.449422\pi$
$733$	−537.730	+	1055.35i	−0.733602	+	1.43977i	−0.891830	+	0.452371i	$0.850578\pi$
$734$	173.616	−	238.963i	0.236535	−	0.325562i
$735$	218.736	+	248.390i	0.297601	+	0.337945i
$736$	183.190	−	133.095i	0.248899	−	0.180836i
$737$	−64.1563	+	10.1614i	−0.0870506	+	0.0137875i
$738$	−0.549481	−	3.46929i	−0.000744554	−	0.00470093i
$739$	210.697	+	289.999i	0.285111	+	0.392421i	0.927418	−	0.374026i	$-0.122023\pi$
$739$	210.697	+	289.999i	0.285111	+	0.392421i	−0.642308	+	0.766447i	$0.722023\pi$
$740$	−579.924	+	54.4896i	−0.783680	+	0.0736346i
$741$	−288.276	−	209.445i	−0.389036	−	0.282651i
$742$	−496.828	−	253.147i	−0.669580	−	0.341168i
$743$	551.973	+	551.973i	0.742898	+	0.742898i	0.973135	−	0.230237i	$-0.0739500\pi$
$743$	551.973	+	551.973i	0.742898	+	0.742898i	−0.230237	+	0.973135i	$0.573950\pi$
$744$	390.892	−	127.008i	0.525392	−	0.170710i
$745$	−207.725	−	810.929i	−0.278825	−	1.08849i
$746$	−83.2786	+	256.305i	−0.111634	+	0.343573i
$747$	1.97980	+	3.88557i	0.00265033	+	0.00520157i
$748$	−229.645	−	36.3721i	−0.307012	−	0.0486259i
$749$		−	459.881i		−	0.613993i
$750$	465.868	+	257.139i	0.621157	+	0.342851i
$751$	932.370			1.24150			0.620752	−	0.784007i	$-0.286827\pi$
$751$	932.370			1.24150			0.620752	+	0.784007i	$0.286827\pi$
$752$	−13.5358	+	85.4615i	−0.0179997	+	0.113646i
$753$	−346.143	+	176.368i	−0.459685	+	0.234221i
$754$	412.895	+	134.158i	0.547606	+	0.177928i
$755$	−450.273	+	115.340i	−0.596388	+	0.152769i
$756$	86.4270	+	265.995i	0.114321	+	0.351845i
$757$	406.532	−	406.532i	0.537031	−	0.537031i	−0.385625	−	0.922656i	$-0.626014\pi$
$757$	406.532	−	406.532i	0.537031	−	0.537031i	0.922656	+	0.385625i	$0.126014\pi$
$758$	−200.687	+	393.870i	−0.264758	+	0.519617i
$759$	372.958	−	513.333i	0.491381	−	0.676328i
$760$	−16.0311	−	170.617i	−0.0210936	−	0.224496i
$761$	−684.847	+	497.570i	−0.899930	+	0.653837i	−0.938448	−	0.345420i	$-0.887736\pi$
$761$	−684.847	+	497.570i	−0.899930	+	0.653837i	0.0385180	+	0.999258i	$0.487736\pi$
$762$	−79.4350	+	12.5813i	−0.104245	+	0.0165109i
$763$	−55.0183	−	347.372i	−0.0721079	−	0.455271i
$764$	−155.423	−	213.922i	−0.203433	−	0.280002i
$765$	−5.04547	+	4.44314i	−0.00659539	+	0.00580802i
$766$	197.140	+	143.231i	0.257363	+	0.186985i
$767$	248.332	+	126.532i	0.323771	+	0.164970i
$768$	34.0558	+	34.0558i	0.0443435	+	0.0443435i
$769$	1221.98	−	397.045i	1.58905	−	0.516314i	0.624682	−	0.780879i	$-0.285228\pi$
$769$	1221.98	−	397.045i	1.58905	−	0.516314i	0.964368	+	0.264565i	$0.0852284\pi$
$770$	193.133	+	12.2600i	0.250822	+	0.0159221i
$771$	99.1218	−	305.066i	0.128563	−	0.395675i
$772$	−60.3639	−	118.471i	−0.0781916	−	0.153460i
$773$	−785.770	−	124.454i	−1.01652	−	0.161001i	−0.374128	−	0.927377i	$-0.622058\pi$
$773$	−785.770	−	124.454i	−1.01652	−	0.161001i	−0.642392	+	0.766376i	$0.722058\pi$
$774$		−	3.89214i		−	0.00502861i
$775$	878.837	+	827.147i	1.13398	+	1.06729i
$776$	−280.680			−0.361701
$777$	−142.546	+	900.001i	−0.183457	+	1.15830i
$778$	−500.604	+	255.071i	−0.643450	+	0.327854i
$779$	−469.954	−	152.697i	−0.603279	−	0.196017i
$780$	157.425	+	248.371i	0.201827	+	0.318425i
$781$	161.700	+	497.663i	0.207043	+	0.637212i
$782$	−883.667	+	883.667i	−1.13001	+	1.13001i
$783$	−383.879	+	753.405i	−0.490267	+	0.962203i
$784$	−51.7029	+	71.1630i	−0.0659476	+	0.0907691i
$785$	−306.186	+	517.068i	−0.390046	+	0.658686i
$786$	563.373	−	409.314i	0.716759	−	0.520756i
$787$	774.249	−	122.629i	0.983798	−	0.155818i	0.356245	−	0.934392i	$-0.384057\pi$
$787$	774.249	−	122.629i	0.983798	−	0.155818i	0.627553	+	0.778574i	$0.284057\pi$
$788$	77.7084	+	490.632i	0.0986147	+	0.622629i
$789$	847.416	+	1166.37i	1.07404	+	1.47829i
$790$	−124.557	+	555.765i	−0.157667	+	0.703500i
$791$	−12.3579	−	8.97851i	−0.0156231	−	0.0113508i
$792$	0.808321	+	0.411860i	0.00102061	+	0.000520026i
$793$	−351.095	−	351.095i	−0.442743	−	0.442743i
$794$	−372.494	+	121.031i	−0.469136	+	0.152431i
$795$	420.940	−	1061.43i	0.529484	−	1.33513i
$796$	−56.4029	+	173.590i	−0.0708579	+	0.218078i
$797$	−108.193	−	212.340i	−0.135750	−	0.266424i	0.813117	−	0.582100i	$-0.197769\pi$
$797$	−108.193	−	212.340i	−0.135750	−	0.266424i	−0.948867	+	0.315676i	$0.897769\pi$
$798$	−264.785	−	41.9378i	−0.331811	−	0.0525537i
$799$		−	477.540i		−	0.597672i
$800$	−39.6082	+	135.762i	−0.0495102	+	0.169702i
$801$	3.37008			0.00420734
$802$	−28.6243	+	180.727i	−0.0356911	+	0.225345i
$803$	−17.0471	+	8.68595i	−0.0212293	+	0.0108169i
$804$	−70.6243	−	22.9472i	−0.0878412	−	0.0285413i
$805$	663.469	−	801.077i	0.824185	−	0.995127i
$806$	206.094	+	634.293i	0.255700	+	0.786964i
$807$	188.278	−	188.278i	0.233306	−	0.233306i
$808$	−220.105	+	431.981i	−0.272408	+	0.534630i
$809$	363.196	−	499.897i	0.448945	−	0.617919i	−0.523226	−	0.852194i	$-0.675272\pi$
$809$	363.196	−	499.897i	0.448945	−	0.617919i	0.972170	+	0.234275i	$0.0752715\pi$
$810$	−529.312	+	228.700i	−0.653472	+	0.282346i
$811$	−569.119	+	413.489i	−0.701750	+	0.509851i	−0.880502	−	0.474043i	$-0.842794\pi$
$811$	−569.119	+	413.489i	−0.701750	+	0.509851i	0.178752	+	0.983894i	$0.442794\pi$
$812$	322.609	−	51.0962i	0.397301	−	0.0629263i
$813$	−184.537	−	1165.12i	−0.226983	−	1.43311i
$814$	−254.976	−	350.945i	−0.313239	−	0.431136i
$815$	−339.909	−	786.698i	−0.417066	−	0.965274i
$816$	−215.042	−	156.237i	−0.263532	−	0.191467i
$817$	−487.863	−	248.579i	−0.597140	−	0.304258i
$818$	−636.120	−	636.120i	−0.777652	−	0.777652i
$819$	2.94093	−	0.955566i	0.00359088	−	0.00116675i
$820$	314.059	+	260.110i	0.382999	+	0.317208i
$821$	219.876	−	676.710i	0.267815	−	0.824251i	−0.723216	−	0.690622i	$-0.757337\pi$
$821$	219.876	−	676.710i	0.267815	−	0.824251i	0.991031	−	0.133629i	$-0.0426631\pi$
$822$	−360.510	−	707.541i	−0.438577	−	0.860755i
$823$	−851.080	−	134.798i	−1.03412	−	0.163788i	−0.383774	−	0.923427i	$-0.625376\pi$
$823$	−851.080	−	134.798i	−1.03412	−	0.163788i	−0.650345	+	0.759639i	$0.725376\pi$
$824$		−	141.225i		−	0.171389i
$825$	12.0018	+	396.108i	0.0145477	+	0.480131i
$826$	209.689			0.253861
$827$	8.65680	−	54.6569i	0.0104677	−	0.0660905i	−0.981902	−	0.189392i	$-0.939348\pi$
$827$	8.65680	−	54.6569i	0.0104677	−	0.0660905i	0.992369	+	0.123302i	$0.0393483\pi$
$828$	4.34461	−	2.21369i	0.00524712	−	0.00267354i
$829$	1421.51	+	461.876i	1.71473	+	0.557149i	0.991109	−	0.133051i	$-0.0424773\pi$
$829$	1421.51	+	461.876i	1.71473	+	0.557149i	0.723619	+	0.690200i	$0.242477\pi$
$830$	−470.619	−	186.638i	−0.567011	−	0.224865i
$831$	283.648	+	872.978i	0.341333	+	1.05052i
$832$	−55.2617	+	55.2617i	−0.0664204	+	0.0664204i
$833$	220.396	−	432.551i	0.264581	−	0.519268i
$834$	133.020	−	183.086i	0.159497	−	0.219528i
$835$	−302.123	−	67.7111i	−0.361824	−	0.0810911i
$836$	103.250	−	75.0154i	0.123505	−	0.0897314i
$837$	−1282.98	+	203.203i	−1.53283	+	0.242776i
$838$	−62.4351	−	394.200i	−0.0745049	−	0.470405i
$839$	−251.046	−	345.535i	−0.299221	−	0.411842i	0.632761	−	0.774347i	$-0.281922\pi$
$839$	−251.046	−	345.535i	−0.299221	−	0.411842i	−0.931982	+	0.362505i	$0.881922\pi$
$840$	190.365	+	112.726i	0.226625	+	0.134198i
$841$	118.520	+	86.1098i	0.140927	+	0.102390i
$842$	−456.784	−	232.743i	−0.542499	−	0.276417i
$843$	−999.910	−	999.910i	−1.18613	−	1.18613i
$844$	38.2934	−	12.4423i	0.0453714	−	0.0147421i
$845$	310.684	−	196.921i	0.367673	−	0.233042i
$846$	−0.575783	+	1.77208i	−0.000680595	+	0.00209466i
$847$	−220.059	−	431.890i	−0.259810	−	0.509906i
$848$	299.732	+	47.4728i	0.353457	+	0.0559821i
$849$		−	1224.82i		−	1.44266i
$850$	98.6947	−	774.238i	0.116111	−	0.910868i
$851$	−2331.57			−2.73980
$852$	−93.5815	+	590.850i	−0.109837	+	0.693486i
$853$	−836.385	+	426.159i	−0.980522	+	0.499601i	−0.869348	−	0.494200i	$-0.835461\pi$
$853$	−836.385	+	426.159i	−0.980522	+	0.499601i	−0.111174	+	0.993801i	$0.535461\pi$
$854$	−355.279	−	115.437i	−0.416017	−	0.135172i
$855$	0.233786	−	3.68284i	0.000273434	−	0.00430742i
$856$	77.3420	+	238.034i	0.0903528	+	0.278077i
$857$	144.940	−	144.940i	0.169125	−	0.169125i	−0.617470	−	0.786595i	$-0.711842\pi$
$857$	144.940	−	144.940i	0.169125	−	0.169125i	0.786595	+	0.617470i	$0.211842\pi$
$858$	−99.4224	+	195.127i	−0.115877	+	0.227421i
$859$	11.7976	−	16.2380i	0.0137341	−	0.0189034i	−0.802095	−	0.597197i	$-0.796281\pi$
$859$	11.7976	−	16.2380i	0.0137341	−	0.0189034i	0.815829	+	0.578293i	$0.196281\pi$
$860$	298.628	+	339.112i	0.347242	+	0.394316i
$861$	516.102	−	374.970i	0.599421	−	0.435505i
$862$	216.306	−	34.2595i	0.250935	−	0.0397442i
$863$	36.6064	+	231.124i	0.0424176	+	0.267814i	0.999778	−	0.0210831i	$-0.00671144\pi$
$863$	36.6064	+	231.124i	0.0424176	+	0.267814i	−0.957360	+	0.288897i	$0.906711\pi$
$864$	−89.4691	−	123.144i	−0.103552	−	0.142527i
$865$	218.416	−	20.5223i	0.252504	−	0.0237252i
$866$	−13.1482	−	9.55273i	−0.0151827	−	0.0110309i
$867$	531.979	+	271.057i	0.613586	+	0.312638i
$868$	354.807	+	354.807i	0.408763	+	0.408763i
$869$	−403.405	+	131.074i	−0.464218	+	0.150833i
$870$	165.976	+	647.946i	0.190776	+	0.744765i
$871$	37.2361	−	114.601i	0.0427510	−	0.131574i
$872$	86.8978	+	170.547i	0.0996534	+	0.195581i
$873$	−5.96977	−	0.945518i	−0.00683822	−	0.00108307i
$874$		−	685.960i		−	0.784852i
$875$	−21.5019	+	649.277i	−0.0245736	+	0.742030i
$876$	−21.8726			−0.0249687
$877$	72.5804	−	458.255i	0.0827599	−	0.522525i	−0.911127	−	0.412125i	$-0.864787\pi$
$877$	72.5804	−	458.255i	0.0827599	−	0.522525i	0.993887	−	0.110400i	$-0.0352133\pi$
$878$	885.500	−	451.185i	1.00854	−	0.513878i
$879$	417.883	+	135.779i	0.475408	+	0.154469i
$880$	−102.027	+	26.1350i	−0.115940	+	0.0296988i
$881$	362.325	+	1115.12i	0.411266	+	1.26575i	0.915548	+	0.402208i	$0.131757\pi$
$881$	362.325	+	1115.12i	0.411266	+	1.26575i	−0.504282	+	0.863539i	$0.668243\pi$
$882$	−1.33939	+	1.33939i	−0.00151859	+	0.00151859i
$883$	156.054	−	306.274i	0.176732	−	0.346856i	−0.785599	−	0.618736i	$-0.787645\pi$
$883$	156.054	−	306.274i	0.176732	−	0.346856i	0.962331	+	0.271879i	$0.0876452\pi$
$884$	253.523	−	348.945i	0.286791	−	0.394734i
$885$	40.1692	+	427.514i	0.0453889	+	0.483066i
$886$	671.031	−	487.532i	0.757371	−	0.550262i
$887$	−745.775	+	118.119i	−0.840784	+	0.133167i	−0.561949	−	0.827172i	$-0.689948\pi$
$887$	−745.775	+	118.119i	−0.840784	+	0.133167i	−0.278835	+	0.960339i	$0.589948\pi$
$888$	−77.5787	−	489.813i	−0.0873634	−	0.551591i
$889$	−57.7122	−	79.4341i	−0.0649181	−	0.0893521i
$890$	−293.626	+	258.572i	−0.329917	+	0.290531i
$891$	−347.407	−	252.406i	−0.389907	−	0.283284i
$892$	−226.307	−	115.309i	−0.253707	−	0.129270i
$893$	185.349	+	185.349i	0.207558	+	0.207558i
$894$	677.829	−	220.240i	0.758198	−	0.246353i
$895$	322.603	+	20.4788i	0.360451	+	0.0228814i
$896$	−18.1696	+	55.9202i	−0.0202786	+	0.0624110i
$897$	534.381	+	1048.78i	0.595743	+	1.16921i
$898$	397.260	+	62.9198i	0.442383	+	0.0700666i
$899$			1517.01i			1.68744i
$900$	−1.29976	+	2.75408i	−0.00144418	+	0.00306009i
$901$	−1674.84			−1.85886
$902$	−47.5082	+	299.955i	−0.0526698	+	0.332544i
$903$	629.835	−	320.917i	0.697492	−	0.355390i
$904$	7.90641	+	2.56895i	0.00874603	+	0.00284176i
$905$	950.926	+	1500.29i	1.05075	+	1.65777i
$906$	−122.289	−	376.368i	−0.134977	−	0.415418i
$907$	−845.222	+	845.222i	−0.931888	+	0.931888i	−0.997824	−	0.0659361i	$-0.978997\pi$
$907$	−845.222	+	845.222i	−0.931888	+	0.931888i	0.0659361	+	0.997824i	$0.478997\pi$
$908$	186.068	−	365.179i	0.204921	−	0.402179i
$909$	−6.13661	+	8.44632i	−0.00675095	+	0.00929188i
$910$	−182.919	+	308.902i	−0.201010	+	0.339453i
$911$	934.142	−	678.694i	1.02540	−	0.744999i	0.0580192	−	0.998315i	$-0.481522\pi$
$911$	934.142	−	678.694i	1.02540	−	0.744999i	0.967383	+	0.253317i	$0.0815215\pi$
$912$	144.106	−	22.8241i	0.158011	−	0.0250264i
$913$	−58.9824	−	372.400i	−0.0646028	−	0.407886i
$914$	−609.555	−	838.980i	−0.666909	−	0.917921i
$915$	167.294	−	746.456i	0.182835	−	0.815799i
$916$	423.310	+	307.553i	0.462129	+	0.335757i
$917$	757.488	+	385.959i	0.826050	+	0.420894i
$918$	594.017	+	594.017i	0.647077	+	0.647077i
$919$	433.958	−	141.001i	0.472207	−	0.153429i	−0.0632399	−	0.997998i	$-0.520143\pi$
$919$	433.958	−	141.001i	0.472207	−	0.153429i	0.535447	+	0.844569i	$0.320143\pi$
$920$	−208.687	+	526.218i	−0.226834	+	0.571976i
$921$	222.761	−	685.589i	0.241869	−	0.744396i
$922$	17.2472	+	33.8496i	0.0187063	+	0.0367132i
$923$	−958.763	−	151.853i	−1.03875	−	0.164521i
$924$			164.763i			0.178315i
$925$	1151.62	−	891.216i	1.24500	−	0.963477i
$926$	−548.102			−0.591903
$927$	0.475740	−	3.00370i	0.000513204	−	0.00324024i
$928$	−158.389	+	80.7031i	−0.170677	+	0.0869645i
$929$	−1072.55	−	348.494i	−1.15452	−	0.375128i	−0.331679	−	0.943392i	$-0.607615\pi$
$929$	−1072.55	−	348.494i	−1.15452	−	0.375128i	−0.822846	+	0.568265i	$0.807615\pi$
$930$	−655.411	+	791.348i	−0.704743	+	0.850912i
$931$	82.3444	+	253.430i	0.0884472	+	0.272213i
$932$	456.704	−	456.704i	0.490025	−	0.490025i
$933$	−412.412	+	809.404i	−0.442028	+	0.867528i
$934$	−499.322	+	687.258i	−0.534606	+	0.735822i
$935$	533.591	−	230.549i	0.570686	−	0.246577i
$936$	−1.36152	+	0.989201i	−0.00145461	+	0.00105684i
$937$	46.6891	−	7.39483i	0.0498283	−	0.00789203i	−0.131471	−	0.991320i	$-0.541970\pi$
$937$	46.6891	−	7.39483i	0.0498283	−	0.00789203i	0.181299	+	0.983428i	$0.441970\pi$
$938$	−14.1820	−	89.5416i	−0.0151194	−	0.0954601i
$939$	−21.7723	−	29.9670i	−0.0231867	−	0.0319137i
$940$	−85.7980	−	198.574i	−0.0912745	−	0.211249i
$941$	884.604	+	642.703i	0.940068	+	0.683000i	0.948437	−	0.316965i	$-0.102664\pi$
$941$	884.604	+	642.703i	0.940068	+	0.683000i	−0.00836874	+	0.999965i	$0.502664\pi$
$942$	−455.860	−	232.272i	−0.483927	−	0.246573i
$943$	1154.22	+	1154.22i	1.22399	+	1.22399i
$944$	−108.535	+	35.2651i	−0.114973	+	0.0373571i
$945$	−538.499	−	445.996i	−0.569840	−	0.471953i
$946$	−103.989	+	320.045i	−0.109925	+	0.338314i
$947$	311.570	+	611.490i	0.329007	+	0.645713i	0.994959	−	0.100282i	$-0.0319745\pi$
$947$	311.570	+	611.490i	0.329007	+	0.645713i	−0.665952	+	0.745995i	$0.731974\pi$
$948$	−478.943	−	75.8572i	−0.505214	−	0.0800181i
$949$		−	35.4922i		−	0.0373996i
$950$	262.201	+	338.814i	0.276001	+	0.356646i
$951$	561.884			0.590835
$952$	50.7639	−	320.510i	0.0533234	−	0.336671i
$953$	19.1893	−	9.77745i	0.0201357	−	0.0102597i	−0.443894	−	0.896079i	$-0.646403\pi$
$953$	19.1893	−	9.77745i	0.0201357	−	0.0102597i	0.464029	+	0.885820i	$0.346403\pi$
$954$	6.21506	+	2.01939i	0.00651473	+	0.00211677i
$955$	614.495	+	243.696i	0.643451	+	0.255179i
$956$	−121.930	−	375.263i	−0.127542	−	0.392534i
$957$	−352.230	+	352.230i	−0.368056	+	0.368056i
$958$	228.853	−	449.150i	0.238887	−	0.468841i
$959$	569.831	−	784.305i	0.594193	−	0.817837i
$960$	−117.491	−	26.3318i	−0.122386	−	0.0274289i
$961$	−1107.90	+	804.938i	−1.15286	+	0.837604i
$962$	794.811	−	125.886i	0.826207	−	0.130858i
$963$	0.843124	+	5.32328i	0.000875518	+	0.00552780i
$964$	−33.9091	−	46.6718i	−0.0351754	−	0.0484148i
$965$	286.022	+	169.370i	0.296396	+	0.175513i
$966$	716.449	+	520.531i	0.741665	+	0.538852i
$967$	568.539	+	289.685i	0.587941	+	0.299571i	0.722540	−	0.691329i	$-0.242975\pi$
$967$	568.539	+	289.685i	0.587941	+	0.299571i	−0.134599	+	0.990900i	$0.542975\pi$
$968$	186.537	+	186.537i	0.192703	+	0.192703i
$969$	−765.820	+	248.830i	−0.790320	+	0.256791i
$970$	592.676	−	375.656i	0.611006	−	0.387274i
$971$	−283.693	+	873.117i	−0.292166	+	0.899194i	0.691993	+	0.721904i	$0.256733\pi$
$971$	−283.693	+	873.117i	−0.292166	+	0.899194i	−0.984159	+	0.177290i	$0.943267\pi$
$972$	−2.98631	−	5.86096i	−0.00307233	−	0.00602979i
$973$	272.882	+	43.2203i	0.280455	+	0.0444196i
$974$		−	1173.01i		−	1.20432i
$975$	−664.830	−	313.760i	−0.681877	−	0.321805i
$976$	203.306			0.208305
$977$	27.7818	−	175.408i	0.0284359	−	0.179537i	−0.969383	−	0.245556i	$-0.921030\pi$
$977$	27.7818	−	175.408i	0.0284359	−	0.179537i	0.997818	+	0.0660185i	$0.0210296\pi$
$978$	650.111	−	331.248i	0.664735	−	0.338700i
$979$	−277.116	−	90.0405i	−0.283060	−	0.0919719i
$980$	13.9315	−	219.464i	0.0142159	−	0.223943i
$981$	1.27371	+	3.92008i	0.00129838	+	0.00399600i
$982$	−687.059	+	687.059i	−0.699653	+	0.699653i
$983$	780.215	−	1531.26i	0.793708	−	1.55774i	−0.0358752	−	0.999356i	$-0.511422\pi$
$983$	780.215	−	1531.26i	0.793708	−	1.55774i	0.829583	−	0.558383i	$-0.188578\pi$
$984$	−204.072	+	280.881i	−0.207390	+	0.285448i
$985$	−820.738	−	932.001i	−0.833236	−	0.946194i
$986$	793.708	−	576.662i	0.804977	−	0.584850i
$987$	−334.236	+	52.9379i	−0.338639	+	0.0536351i
$988$	37.0363	+	233.838i	0.0374861	+	0.236678i
$989$	1063.14	+	1463.29i	1.07496	+	1.47956i
$990$	−2.25805	+	0.212167i	−0.00228086	+	0.000214310i
$991$	−921.394	−	669.432i	−0.929762	−	0.675512i	0.0161727	−	0.999869i	$-0.494852\pi$
$991$	−921.394	−	669.432i	−0.929762	−	0.675512i	−0.945935	+	0.324358i	$0.894852\pi$
$992$	−243.318	−	123.977i	−0.245281	−	0.124977i
$993$	−873.436	−	873.436i	−0.879593	−	0.879593i
$994$	−694.578	+	225.682i	−0.698770	+	0.227044i
$995$	−113.231	−	442.037i	−0.113800	−	0.444258i
$996$	133.199	−	409.945i	0.133734	−	0.411591i
$997$	−355.368	−	697.449i	−0.356437	−	0.699547i	0.641264	−	0.767321i	$-0.278411\pi$
$997$	−355.368	−	697.449i	−0.356437	−	0.699547i	−0.997701	+	0.0677734i	$0.978411\pi$
$998$	178.086	+	28.2060i	0.178442	+	0.0282625i
$999$			1567.32i			1.56889i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.3.f.a.23.2	✓	16
4.3	odd	2		400.3.bg.a.273.1		16
5.2	odd	4		250.3.f.a.157.1		16
5.3	odd	4		250.3.f.c.157.2		16
5.4	even	2		250.3.f.b.93.1		16
25.9	even	10		250.3.f.c.43.2		16
25.12	odd	20	inner	50.3.f.a.37.2	yes	16
25.13	odd	20		250.3.f.b.207.1		16
25.16	even	5		250.3.f.a.43.1		16
100.87	even	20		400.3.bg.a.337.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.a.23.2	✓	16	1.1	even	1	trivial
50.3.f.a.37.2	yes	16	25.12	odd	20	inner
250.3.f.a.43.1		16	25.16	even	5
250.3.f.a.157.1		16	5.2	odd	4
250.3.f.b.93.1		16	5.4	even	2
250.3.f.b.207.1		16	25.13	odd	20
250.3.f.c.43.2		16	25.9	even	10
250.3.f.c.157.2		16	5.3	odd	4
400.3.bg.a.273.1		16	4.3	odd	2
400.3.bg.a.337.1		16	100.87	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)

\(f(q)\)	\(=\)	\(q+(-0.221232 + 1.39680i) q^{2} +(2.68205 - 1.36657i) q^{3} +(-1.90211 - 0.618034i) q^{4} +(4.84361 - 1.24072i) q^{5} +(1.31548 + 4.04862i) q^{6} +(-3.67488 + 3.67488i) q^{7} +(1.28408 - 2.52015i) q^{8} +(0.0358006 - 0.0492753i) q^{9} +O(q^{10})\)	\(q+(-0.221232 + 1.39680i) q^{2} +(2.68205 - 1.36657i) q^{3} +(-1.90211 - 0.618034i) q^{4} +(4.84361 - 1.24072i) q^{5} +(1.31548 + 4.04862i) q^{6} +(-3.67488 + 3.67488i) q^{7} +(1.28408 - 2.52015i) q^{8} +(0.0358006 - 0.0492753i) q^{9} +(0.661483 + 7.04006i) q^{10} +(-4.26034 + 3.09532i) q^{11} +(-5.94615 + 0.941777i) q^{12} +(-1.52821 - 9.64872i) q^{13} +(-4.32008 - 5.94607i) q^{14} +(11.2953 - 9.94683i) q^{15} +(3.23607 + 2.35114i) q^{16} +(-19.6698 - 10.0223i) q^{17} +(0.0609076 + 0.0609076i) q^{18} +(11.5245 - 3.74453i) q^{19} +(-9.97991 - 0.633523i) q^{20} +(-4.83421 + 14.8782i) q^{21} +(-3.38103 - 6.63564i) q^{22} +(-39.5357 - 6.26183i) q^{23} -8.51395i q^{24} +(21.9212 - 12.0192i) q^{25} +13.8154 q^{26} +(-4.20932 + 26.5766i) q^{27} +(9.26123 - 4.71883i) q^{28} +(29.8865 + 9.71070i) q^{29} +(11.3949 + 17.9778i) q^{30} +(14.9177 + 45.9119i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-7.19647 + 14.1239i) q^{33} +(18.3507 - 25.2576i) q^{34} +(-13.2402 + 22.3592i) q^{35} +(-0.0985505 + 0.0716011i) q^{36} +(57.5307 - 9.11196i) q^{37} +(2.68079 + 16.9258i) q^{38} +(-17.2844 - 23.7899i) q^{39} +(3.09278 - 13.7998i) q^{40} +(-32.9907 - 23.9692i) q^{41} +(-19.7124 - 10.0440i) q^{42} +(-31.9512 - 31.9512i) q^{43} +(10.0167 - 3.25461i) q^{44} +(0.112267 - 0.283089i) q^{45} +(17.4931 - 53.8382i) q^{46} +(9.82058 + 19.2740i) q^{47} +(11.8923 + 1.88355i) q^{48} +21.9906i q^{49} +(11.9387 + 33.2786i) q^{50} -66.4516 q^{51} +(-3.05641 + 19.2974i) q^{52} +(67.5979 - 34.4429i) q^{53} +(-36.1910 - 11.7592i) q^{54} +(-16.7950 + 20.2784i) q^{55} +(4.54240 + 13.9801i) q^{56} +(25.7921 - 25.7921i) q^{57} +(-20.1758 + 39.5972i) q^{58} +(-16.7696 + 23.0813i) q^{59} +(-27.6324 + 11.9391i) q^{60} +(41.1195 - 29.8751i) q^{61} +(-67.4301 + 10.6799i) q^{62} +(0.0495178 + 0.312643i) q^{63} +(-4.70228 - 6.47214i) q^{64} +(-19.3734 - 44.8386i) q^{65} +(-18.1362 - 13.1767i) q^{66} +(10.9904 + 5.59988i) q^{67} +(31.2201 + 31.2201i) q^{68} +(-114.594 + 37.2338i) q^{69} +(-28.3022 - 23.4405i) q^{70} +(30.7061 - 94.5035i) q^{71} +(-0.0782101 - 0.153496i) q^{72} +(3.58842 + 0.568350i) q^{73} +82.3748i q^{74} +(42.3687 - 62.1929i) q^{75} -24.2351 q^{76} +(4.28131 - 27.0312i) q^{77} +(37.0537 - 18.8798i) q^{78} +(76.6046 + 24.8903i) q^{79} +(18.5914 + 7.37296i) q^{80} +(25.1986 + 77.5534i) q^{81} +(40.7788 - 40.7788i) q^{82} +(-32.5050 + 63.7946i) q^{83} +(18.3904 - 25.3123i) q^{84} +(-107.708 - 24.1392i) q^{85} +(51.6981 - 37.5609i) q^{86} +(93.4274 - 14.7974i) q^{87} +(2.33005 + 14.7113i) q^{88} +(32.5227 + 44.7637i) q^{89} +(0.370582 + 0.219443i) q^{90} +(41.0738 + 29.8419i) q^{91} +(71.3313 + 36.3451i) q^{92} +(102.752 + 102.752i) q^{93} +(-29.0946 + 9.45339i) q^{94} +(51.1742 - 32.4358i) q^{95} +(-5.26191 + 16.1945i) q^{96} +(-45.0519 - 88.4193i) q^{97} +(-30.7165 - 4.86501i) q^{98} +0.320744i 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

Varieties

Fields

Representations

Groups

Database

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