LMFDB - Embedded newform 224.2.bd.a.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(37,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("224.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.bd (of order $24$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			109.3
Character	$\chi$	$=$	224.109
Dual form			224.2.bd.a.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32342 - 0.498548i) q^{2} +(0.615442 + 0.802059i) q^{3} +(1.50290 + 1.31958i) q^{4} +(-1.98693 - 1.52462i) q^{5} +(-0.414625 - 1.36829i) q^{6} +(2.32280 + 1.26674i) q^{7} +(-1.33110 - 2.49563i) q^{8} +(0.511927 - 1.91054i) q^{9} +O(q^{10})$	\(q+(-1.32342 - 0.498548i) q^{2} +(0.615442 + 0.802059i) q^{3} +(1.50290 + 1.31958i) q^{4} +(-1.98693 - 1.52462i) q^{5} +(-0.414625 - 1.36829i) q^{6} +(2.32280 + 1.26674i) q^{7} +(-1.33110 - 2.49563i) q^{8} +(0.511927 - 1.91054i) q^{9} +(1.86945 + 3.00830i) q^{10} +(2.73340 + 0.359859i) q^{11} +(-0.133434 + 2.01754i) q^{12} +(1.75735 + 0.727920i) q^{13} +(-2.44251 - 2.83445i) q^{14} -2.53195i q^{15} +(0.517417 + 3.96639i) q^{16} +(3.86322 + 2.23043i) q^{17} +(-1.62999 + 2.27323i) q^{18} +(0.560244 + 4.25547i) q^{19} +(-0.974292 - 4.91327i) q^{20} +(0.413547 + 2.64262i) q^{21} +(-3.43804 - 1.83898i) q^{22} +(1.95628 - 7.30092i) q^{23} +(1.18243 - 2.60354i) q^{24} +(0.329313 + 1.22901i) q^{25} +(-1.96282 - 1.83947i) q^{26} +(4.64948 - 1.92588i) q^{27} +(1.81937 + 4.96889i) q^{28} +(-2.62657 + 6.34110i) q^{29} +(-1.26230 + 3.35085i) q^{30} +(2.43479 - 4.21718i) q^{31} +(1.29268 - 5.50718i) q^{32} +(1.39362 + 2.41382i) q^{33} +(-4.00070 - 4.87780i) q^{34} +(-2.68393 - 6.05831i) q^{35} +(3.29048 - 2.19582i) q^{36} +(-5.03484 - 3.86337i) q^{37} +(1.38012 - 5.91110i) q^{38} +(0.497714 + 1.85749i) q^{39} +(-1.16010 + 6.98807i) q^{40} +(1.93503 + 1.93503i) q^{41} +(0.770176 - 3.70348i) q^{42} +(-1.24347 - 3.00201i) q^{43} +(3.63316 + 4.14777i) q^{44} +(-3.93001 + 3.01560i) q^{45} +(-6.22884 + 8.68691i) q^{46} +(-9.22259 + 5.32466i) q^{47} +(-2.86284 + 2.85608i) q^{48} +(3.79076 + 5.88474i) q^{49} +(0.176901 - 1.79068i) q^{50} +(0.588648 + 4.47123i) q^{51} +(1.68058 + 3.41296i) q^{52} +(-7.67508 - 1.01044i) q^{53} +(-7.11337 + 0.230763i) q^{54} +(-4.88242 - 4.88242i) q^{55} +(0.0694365 - 7.48299i) q^{56} +(-3.06834 + 3.06834i) q^{57} +(6.63741 - 7.08249i) q^{58} +(-0.407380 + 3.09436i) q^{59} +(3.34111 - 3.80527i) q^{60} +(-9.03144 + 1.18901i) q^{61} +(-5.32472 + 4.36725i) q^{62} +(3.60925 - 3.78931i) q^{63} +(-4.45635 + 6.64387i) q^{64} +(-2.38193 - 4.12563i) q^{65} +(-0.640944 - 3.88929i) q^{66} +(0.327236 + 0.426462i) q^{67} +(2.86280 + 8.44994i) q^{68} +(7.05974 - 2.92424i) q^{69} +(0.531622 + 9.35577i) q^{70} +(-5.00372 + 5.00372i) q^{71} +(-5.44942 + 1.26553i) q^{72} +(-10.0917 + 2.70405i) q^{73} +(4.73715 + 7.62298i) q^{74} +(-0.783068 + 1.02051i) q^{75} +(-4.77345 + 7.13484i) q^{76} +(5.89328 + 4.29837i) q^{77} +(0.267363 - 2.70639i) q^{78} +(14.4077 - 8.31826i) q^{79} +(5.01919 - 8.66981i) q^{80} +(-0.732671 - 0.423008i) q^{81} +(-1.59616 - 3.52557i) q^{82} +(-7.13629 - 2.95595i) q^{83} +(-2.86563 + 4.51730i) q^{84} +(-4.27537 - 10.3217i) q^{85} +(0.148996 + 4.59286i) q^{86} +(-6.70244 + 1.79591i) q^{87} +(-2.74035 - 7.30056i) q^{88} +(14.3769 + 3.85227i) q^{89} +(6.70449 - 2.03162i) q^{90} +(3.15989 + 3.91692i) q^{91} +(12.5742 - 8.39109i) q^{92} +(4.88090 - 0.642582i) q^{93} +(14.8600 - 2.44888i) q^{94} +(5.37483 - 9.30949i) q^{95} +(5.21265 - 2.35254i) q^{96} -0.0617316 q^{97} +(-2.08295 - 9.67788i) q^{98} +(2.08682 - 5.03804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{8}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.32342	−	0.498548i	−0.935802	−	0.352527i
$2$	−1.32342	−	0.498548i	−0.935802	−	0.352527i
$3$	0.615442	+	0.802059i	0.355325	+	0.463069i	0.936478	−	0.350725i	$-0.114065\pi$
$3$	0.615442	+	0.802059i	0.355325	+	0.463069i	−0.581153	+	0.813794i	$0.697398\pi$
$4$	1.50290	+	1.31958i	0.751450	+	0.659790i
$5$	−1.98693	−	1.52462i	−0.888582	−	0.681833i	0.0600567	−	0.998195i	$-0.480872\pi$
$5$	−1.98693	−	1.52462i	−0.888582	−	0.681833i	−0.948638	+	0.316362i	$0.897539\pi$
$6$	−0.414625	−	1.36829i	−0.169270	−	0.558603i
$7$	2.32280	+	1.26674i	0.877934	+	0.478782i
$7$	2.32280	+	1.26674i	0.877934	+	0.478782i
$8$	−1.33110	−	2.49563i	−0.470615	−	0.882339i
$9$	0.511927	−	1.91054i	0.170642	−	0.636845i
$10$	1.86945	+	3.00830i	0.591172	+	0.951309i
$11$	2.73340	+	0.359859i	0.824151	+	0.108501i	0.530793	−	0.847501i	$-0.321894\pi$
$11$	2.73340	+	0.359859i	0.824151	+	0.108501i	0.293357	+	0.956003i	$0.405227\pi$
$12$	−0.133434	+	2.01754i	−0.0385191	+	0.582413i
$13$	1.75735	+	0.727920i	0.487403	+	0.201889i	0.612831	−	0.790214i	$-0.290031\pi$
$13$	1.75735	+	0.727920i	0.487403	+	0.201889i	−0.125429	+	0.992103i	$0.540031\pi$
$14$	−2.44251	−	2.83445i	−0.652789	−	0.757540i
$15$		−	2.53195i		−	0.653747i
$16$	0.517417	+	3.96639i	0.129354	+	0.991598i
$17$	3.86322	+	2.23043i	0.936968	+	0.540959i	0.889009	−	0.457891i	$-0.151395\pi$
$17$	3.86322	+	2.23043i	0.936968	+	0.540959i	0.0479595	+	0.998849i	$0.484728\pi$
$18$	−1.62999	+	2.27323i	−0.384192	+	0.535805i
$19$	0.560244	+	4.25547i	0.128529	+	0.976273i	0.927216	+	0.374527i	$0.122195\pi$
$19$	0.560244	+	4.25547i	0.128529	+	0.976273i	−0.798687	+	0.601746i	$0.794472\pi$
$20$	−0.974292	−	4.91327i	−0.217858	−	1.09864i
$21$	0.413547	+	2.64262i	0.0902433	+	0.576667i
$22$	−3.43804	−	1.83898i	−0.732992	−	0.392071i
$23$	1.95628	−	7.30092i	0.407912	−	1.52235i	−0.390710	−	0.920514i	$-0.627770\pi$
$23$	1.95628	−	7.30092i	0.407912	−	1.52235i	0.798622	−	0.601833i	$-0.205563\pi$
$24$	1.18243	−	2.60354i	0.241362	−	0.531445i
$25$	0.329313	+	1.22901i	0.0658626	+	0.245802i
$26$	−1.96282	−	1.83947i	−0.384941	−	0.360750i
$27$	4.64948	−	1.92588i	0.894792	−	0.370635i
$28$	1.81937	+	4.96889i	0.343828	+	0.939033i
$29$	−2.62657	+	6.34110i	−0.487742	+	1.17751i	0.468112	+	0.883669i	$0.344935\pi$
$29$	−2.62657	+	6.34110i	−0.487742	+	1.17751i	−0.955853	+	0.293844i	$0.905065\pi$
$30$	−1.26230	+	3.35085i	−0.230463	+	0.611778i
$31$	2.43479	−	4.21718i	0.437301	−	0.757428i	−0.560179	−	0.828371i	$-0.689268\pi$
$31$	2.43479	−	4.21718i	0.437301	−	0.757428i	0.997480	+	0.0709438i	$0.0226011\pi$
$32$	1.29268	−	5.50718i	0.228515	−	0.973540i
$33$	1.39362	+	2.41382i	0.242598	+	0.420192i
$34$	−4.00070	−	4.87780i	−0.686114	−	0.836536i
$35$	−2.68393	−	6.05831i	−0.453667	−	1.02404i
$36$	3.29048	−	2.19582i	0.548413	−	0.365969i
$37$	−5.03484	−	3.86337i	−0.827722	−	0.635133i	0.105506	−	0.994419i	$-0.466354\pi$
$37$	−5.03484	−	3.86337i	−0.827722	−	0.635133i	−0.933228	+	0.359285i	$0.883020\pi$
$38$	1.38012	−	5.91110i	0.223885	−	0.958907i
$39$	0.497714	+	1.85749i	0.0796981	+	0.297437i
$40$	−1.16010	+	6.98807i	−0.183428	+	1.10491i
$41$	1.93503	+	1.93503i	0.302201	+	0.302201i	0.841874	−	0.539674i	$-0.181452\pi$
$41$	1.93503	+	1.93503i	0.302201	+	0.302201i	−0.539674	+	0.841874i	$0.681452\pi$
$42$	0.770176	−	3.70348i	0.118841	−	0.571460i
$43$	−1.24347	−	3.00201i	−0.189628	−	0.457802i	0.800260	−	0.599653i	$-0.204695\pi$
$43$	−1.24347	−	3.00201i	−0.189628	−	0.457802i	−0.989888	+	0.141851i	$0.954695\pi$
$44$	3.63316	+	4.14777i	0.547720	+	0.625300i
$45$	−3.93001	+	3.01560i	−0.585852	+	0.449540i
$46$	−6.22884	+	8.68691i	−0.918392	+	1.28082i
$47$	−9.22259	+	5.32466i	−1.34525	+	0.776682i	−0.987573	−	0.157162i	$-0.949765\pi$
$47$	−9.22259	+	5.32466i	−1.34525	+	0.776682i	−0.357680	+	0.933844i	$0.616432\pi$
$48$	−2.86284	+	2.85608i	−0.413216	+	0.412240i
$49$	3.79076	+	5.88474i	0.541536	+	0.840677i
$50$	0.176901	−	1.79068i	0.0250176	−	0.253241i
$51$	0.588648	+	4.47123i	0.0824273	+	0.626097i
$52$	1.68058	+	3.41296i	0.233054	+	0.473293i
$53$	−7.67508	−	1.01044i	−1.05425	−	0.138795i	−0.416578	−	0.909100i	$-0.636771\pi$
$53$	−7.67508	−	1.01044i	−1.05425	−	0.138795i	−0.637676	+	0.770305i	$0.720104\pi$
$54$	−7.11337	+	0.230763i	−0.968007	+	0.0314029i
$55$	−4.88242	−	4.88242i	−0.658345	−	0.658345i
$56$	0.0694365	−	7.48299i	0.00927884	−	0.999957i
$57$	−3.06834	+	3.06834i	−0.406412	+	0.406412i
$58$	6.63741	−	7.08249i	0.871534	−	0.929977i
$59$	−0.407380	+	3.09436i	−0.0530364	+	0.402851i	0.944250	+	0.329230i	$0.106789\pi$
$59$	−0.407380	+	3.09436i	−0.0530364	+	0.402851i	−0.997286	+	0.0736217i	$0.976544\pi$
$60$	3.34111	−	3.80527i	0.431336	−	0.491258i
$61$	−9.03144	+	1.18901i	−1.15636	+	0.152237i	−0.684212	−	0.729283i	$-0.739854\pi$
$61$	−9.03144	+	1.18901i	−1.15636	+	0.152237i	−0.472145	+	0.881521i	$0.656520\pi$
$62$	−5.32472	+	4.36725i	−0.676240	+	0.554642i
$63$	3.60925	−	3.78931i	0.454722	−	0.477408i
$64$	−4.45635	+	6.64387i	−0.557044	+	0.830483i
$65$	−2.38193	−	4.12563i	−0.295443	−	0.511722i
$66$	−0.640944	−	3.88929i	−0.0788948	−	0.478739i
$67$	0.327236	+	0.426462i	0.0399782	+	0.0521006i	0.812915	−	0.582383i	$-0.197880\pi$
$67$	0.327236	+	0.426462i	0.0399782	+	0.0521006i	−0.772936	+	0.634483i	$0.781213\pi$
$68$	2.86280	+	8.44994i	0.347165	+	1.02471i
$69$	7.05974	−	2.92424i	0.849893	−	0.352037i
$70$	0.531622	+	9.35577i	0.0635410	+	1.11823i
$71$	−5.00372	+	5.00372i	−0.593832	+	0.593832i	−0.938664	−	0.344832i	$-0.887936\pi$
$71$	−5.00372	+	5.00372i	−0.593832	+	0.593832i	0.344832	+	0.938664i	$0.387936\pi$
$72$	−5.44942	+	1.26553i	−0.642220	+	0.149145i
$73$	−10.0917	+	2.70405i	−1.18114	+	0.316485i	−0.795378	−	0.606114i	$-0.792728\pi$
$73$	−10.0917	+	2.70405i	−1.18114	+	0.316485i	−0.385761	+	0.922599i	$0.626061\pi$
$74$	4.73715	+	7.62298i	0.550682	+	0.886153i
$75$	−0.783068	+	1.02051i	−0.0904209	+	0.117839i
$76$	−4.77345	+	7.13484i	−0.547552	+	0.818422i
$77$	5.89328	+	4.29837i	0.671601	+	0.489845i
$78$	0.267363	−	2.70639i	0.0302729	−	0.306438i
$79$	14.4077	−	8.31826i	1.62099	−	0.935878i	0.634332	−	0.773061i	$-0.281275\pi$
$79$	14.4077	−	8.31826i	1.62099	−	0.935878i	0.986656	−	0.162817i	$-0.0520579\pi$
$80$	5.01919	−	8.66981i	0.561162	−	0.969314i
$81$	−0.732671	−	0.423008i	−0.0814079	−	0.0470009i
$82$	−1.59616	−	3.52557i	−0.176266	−	0.389334i
$83$	−7.13629	−	2.95595i	−0.783310	−	0.324457i	−0.0450593	−	0.998984i	$-0.514348\pi$
$83$	−7.13629	−	2.95595i	−0.783310	−	0.324457i	−0.738250	+	0.674527i	$0.764348\pi$
$84$	−2.86563	+	4.51730i	−0.312666	+	0.492878i
$85$	−4.27537	−	10.3217i	−0.463729	−	1.11954i
$86$	0.148996	+	4.59286i	0.0160666	+	0.495261i
$87$	−6.70244	+	1.79591i	−0.718577	+	0.192542i
$88$	−2.74035	−	7.30056i	−0.292122	−	0.778243i
$89$	14.3769	+	3.85227i	1.52395	+	0.408340i	0.921039	−	0.389471i	$-0.127342\pi$
$89$	14.3769	+	3.85227i	1.52395	+	0.408340i	0.602908	+	0.797811i	$0.294009\pi$
$90$	6.70449	−	2.03162i	0.706716	−	0.214152i
$91$	3.15989	+	3.91692i	0.331247	+	0.410604i
$92$	12.5742	−	8.39109i	1.31095	−	0.874832i
$93$	4.88090	−	0.642582i	0.506125	−	0.0666327i
$94$	14.8600	−	2.44888i	1.53269	−	0.252583i
$95$	5.37483	−	9.30949i	0.551446	−	0.955133i
$96$	5.21265	−	2.35254i	0.532014	−	0.240105i
$97$	−0.0617316			−0.00626790			−0.00313395	−	0.999995i	$-0.500998\pi$
$97$	−0.0617316			−0.00626790			−0.00313395	+	0.999995i	$0.500998\pi$
$98$	−2.08295	−	9.67788i	−0.210410	−	0.977613i
$99$	2.08682	−	5.03804i	0.209734	−	0.506342i
$100$	−1.12686	+	2.28164i	−0.112686	+	0.228164i
$101$	1.29231	−	9.81605i	0.128589	−	0.976733i	−0.798527	−	0.601959i	$-0.794387\pi$
$101$	1.29231	−	9.81605i	0.128589	−	0.976733i	0.927116	−	0.374774i	$-0.122280\pi$
$102$	1.45009	−	6.21080i	0.143580	−	0.614961i
$103$	0.976308	+	0.261601i	0.0961985	+	0.0257763i	0.306597	−	0.951839i	$-0.400810\pi$
$103$	0.976308	+	0.261601i	0.0961985	+	0.0257763i	−0.210399	+	0.977616i	$0.567476\pi$
$104$	−0.522594	−	5.35464i	−0.0512445	−	0.525066i
$105$	3.20732	−	5.88121i	0.313002	−	0.573947i
$106$	9.65363	+	5.16364i	0.937643	+	0.501537i
$107$	0.844989	−	1.10121i	0.0816882	−	0.106458i	−0.750722	−	0.660619i	$-0.770294\pi$
$107$	0.844989	−	1.10121i	0.0816882	−	0.106458i	0.832410	+	0.554161i	$0.186961\pi$
$108$	9.52905	+	3.24096i	0.916933	+	0.311861i
$109$	2.40341	−	1.84420i	0.230205	−	0.176643i	−0.487218	−	0.873280i	$-0.661988\pi$
$109$	2.40341	−	1.84420i	0.230205	−	0.176643i	0.717423	+	0.696638i	$0.245322\pi$
$110$	4.02739	+	8.89563i	0.383997	+	0.848165i
$111$		−	6.41591i		−	0.608971i
$112$	−3.82252	+	9.86855i	−0.361195	+	0.932490i
$113$		−	5.54816i		−	0.521927i	−0.965349	−	0.260964i	$-0.915960\pi$
$113$		−	5.54816i		−	0.521927i	0.965349	−	0.260964i	$-0.0840403\pi$
$114$	5.59044	−	2.53100i	0.523592	−	0.237050i
$115$	−15.0181	+	11.5238i	−1.40045	+	1.07460i
$116$	−12.3151	+	6.06407i	−1.14343	+	0.563035i
$117$	2.29035	−	2.98485i	0.211743	−	0.275949i
$118$	2.08182	−	3.89205i	0.191647	−	0.358292i
$119$	6.14810	+	10.0745i	0.563595	+	0.923529i
$120$	−6.31882	+	3.37028i	−0.576827	+	0.307663i
$121$	−3.28321	−	0.879735i	−0.298474	−	0.0799759i
$122$	12.5452	+	2.92904i	1.13579	+	0.265183i
$123$	−0.361110	+	2.74291i	−0.0325602	+	0.247319i
$124$	9.22415	−	3.12510i	0.828353	−	0.280642i
$125$	−3.57263	+	8.62510i	−0.319546	+	0.771453i
$126$	−6.66571	+	3.21548i	−0.593829	+	0.286457i
$127$	3.16121			0.280512			0.140256	−	0.990115i	$-0.455207\pi$
$127$	3.16121			0.280512			0.140256	+	0.990115i	$0.455207\pi$
$128$	9.20992	−	6.57095i	0.814050	−	0.580795i
$129$	1.64250	−	2.84490i	0.144614	−	0.250479i
$130$	1.09548	+	6.64747i	0.0960803	+	0.583021i
$131$	−6.09222	+	0.802056i	−0.532280	+	0.0700759i	−0.391875	−	0.920018i	$-0.628174\pi$
$131$	−6.09222	+	0.802056i	−0.532280	+	0.0700759i	−0.140404	+	0.990094i	$0.544840\pi$
$132$	−1.09076	+	5.46672i	−0.0949383	+	0.475817i
$133$	−4.08923	+	10.5943i	−0.354582	+	0.918640i
$134$	−0.220460	−	0.727533i	−0.0190448	−	0.0628493i
$135$	−12.1744	−	3.26213i	−1.04781	−	0.280759i
$136$	0.424003	−	12.6101i	0.0363579	−	1.08131i
$137$	−21.2605	+	5.69674i	−1.81641	+	0.486706i	−0.996334	−	0.0855493i	$-0.972735\pi$
$137$	−21.2605	+	5.69674i	−1.81641	+	0.486706i	−0.820076	+	0.572255i	$0.806069\pi$
$138$	−10.8009	+	0.350390i	−0.919434	+	0.0298272i
$139$	6.80964	+	16.4399i	0.577586	+	1.39442i	0.894973	+	0.446119i	$0.147194\pi$
$139$	6.80964	+	16.4399i	0.577586	+	1.39442i	−0.317388	+	0.948296i	$0.602806\pi$
$140$	3.96074	−	12.6467i	0.334744	−	1.06884i
$141$	−9.94666	−	4.12004i	−0.837660	−	0.346970i
$142$	9.11663	−	4.12744i	0.765050	−	0.346367i
$143$	4.54160	+	2.62210i	0.379788	+	0.219271i
$144$	7.84282	+	1.04196i	0.653568	+	0.0868299i
$145$	14.8866	−	8.59479i	1.23627	−	0.713758i
$146$	14.7036	+	1.45257i	1.21688	+	0.120215i
$147$	−2.38692	+	6.66212i	−0.196870	+	0.549483i
$148$	−2.46883	−	12.4501i	−0.202937	−	1.02339i
$149$	−13.3377	+	17.3820i	−1.09266	+	1.42399i	−0.196368	+	0.980530i	$0.562915\pi$
$149$	−13.3377	+	17.3820i	−1.09266	+	1.42399i	−0.896296	+	0.443456i	$0.853752\pi$
$150$	1.54511	−	0.960175i	0.126157	−	0.0783980i
$151$	3.71641	−	0.995808i	0.302437	−	0.0810377i	−0.104409	−	0.994534i	$-0.533295\pi$
$151$	3.71641	−	0.995808i	0.302437	−	0.0810377i	0.406846	+	0.913497i	$0.366628\pi$
$152$	9.87435	−	7.06262i	0.800916	−	0.572854i
$153$	6.23900	−	6.23900i	0.504393	−	0.504393i
$154$	−5.65636	−	8.62665i	−0.455802	−	0.695155i
$155$	−11.2674	+	4.66710i	−0.905017	+	0.374870i
$156$	−1.70310	+	3.44840i	−0.136357	+	0.276093i
$157$	5.23917	+	6.82782i	0.418131	+	0.544920i	0.954167	−	0.299276i	$-0.0967452\pi$
$157$	5.23917	+	6.82782i	0.418131	+	0.544920i	−0.536035	+	0.844196i	$0.680079\pi$
$158$	−23.2145	+	3.82568i	−1.84685	+	0.304355i
$159$	−3.91313	−	6.77774i	−0.310331	−	0.537509i
$160$	−10.9648	+	8.97152i	−0.866846	+	0.709261i
$161$	13.7924	−	14.4805i	1.08699	−	1.14122i
$162$	0.758745	+	0.925090i	0.0596126	+	0.0726820i
$163$	−6.47560	+	0.852529i	−0.507208	+	0.0667752i	−0.379788	−	0.925074i	$-0.624003\pi$
$163$	−6.47560	+	0.852529i	−0.507208	+	0.0667752i	−0.127420	+	0.991849i	$0.540670\pi$
$164$	0.354729	+	5.46158i	0.0276997	+	0.426478i
$165$	0.911145	−	6.92083i	0.0709325	−	0.538786i
$166$	7.97065	+	7.46975i	0.618643	+	0.579765i
$167$	0.219615	−	0.219615i	0.0169943	−	0.0169943i	−0.698559	−	0.715553i	$-0.746175\pi$
$167$	0.219615	−	0.219615i	0.0169943	−	0.0169943i	0.715553	+	0.698559i	$0.246175\pi$
$168$	6.04454	−	4.54965i	0.466346	−	0.351013i
$169$	−6.63396	−	6.63396i	−0.510305	−	0.510305i
$170$	0.512286	+	15.7914i	0.0392905	+	1.21115i
$171$	8.41704	+	1.10812i	0.643667	+	0.0847404i
$172$	2.09257	−	6.15258i	0.159557	−	0.469130i
$173$	−1.91962	−	14.5810i	−0.145946	−	1.10857i	−0.895001	−	0.446064i	$-0.852825\pi$
$173$	−1.91962	−	14.5810i	−0.145946	−	1.10857i	0.749055	−	0.662508i	$-0.230508\pi$
$174$	9.76552	+	0.964733i	0.740322	+	0.0731362i
$175$	−0.791909	+	3.27190i	−0.0598627	+	0.247332i
$176$	−0.0130349	+	11.0279i	−0.000982546	+	0.831262i
$177$	−2.73258	+	1.57766i	−0.205393	+	0.118584i
$178$	−17.1062	−	12.2658i	−1.28216	−	0.919357i
$179$	12.3641	−	9.48730i	0.924136	−	0.709114i	−0.0327853	−	0.999462i	$-0.510438\pi$
$179$	12.3641	−	9.48730i	0.924136	−	0.709114i	0.956921	+	0.290348i	$0.0937711\pi$
$180$	−9.88575	−	0.653814i	−0.736840	−	0.0487324i
$181$	2.81555	+	6.79735i	0.209279	+	0.505243i	0.993310	−	0.115478i	$-0.0368400\pi$
$181$	2.81555	+	6.79735i	0.209279	+	0.505243i	−0.784032	+	0.620721i	$0.786840\pi$
$182$	−2.22911	−	6.75910i	−0.165232	−	0.501018i
$183$	−6.51198	−	6.51198i	−0.481379	−	0.481379i
$184$	−20.8244	+	4.83611i	−1.53520	+	0.356523i
$185$	4.11368	+	15.3525i	0.302444	+	1.12874i
$186$	−6.77985	−	1.58295i	−0.497123	−	0.116068i
$187$	9.75708	+	7.48687i	0.713508	+	0.547494i
$188$	−20.8869	−	4.16751i	−1.52334	−	0.303947i
$189$	13.2394	+	1.41625i	0.963022	+	0.103017i
$190$	−11.7544	+	9.64078i	−0.852754	+	0.699416i
$191$	−3.10564	−	5.37912i	−0.224716	−	0.389219i	0.731518	−	0.681822i	$-0.238812\pi$
$191$	−3.10564	−	5.37912i	−0.224716	−	0.389219i	−0.956234	+	0.292602i	$0.905479\pi$
$192$	−8.07140	+	0.514657i	−0.582503	+	0.0371422i
$193$	5.46159	−	9.45975i	0.393134	−	0.680928i	−0.599727	−	0.800205i	$-0.704724\pi$
$193$	5.46159	−	9.45975i	0.393134	−	0.680928i	0.992861	+	0.119277i	$0.0380575\pi$
$194$	0.0816971	+	0.0307762i	0.00586551	+	0.00220960i
$195$	1.84306	−	4.44954i	0.131984	−	0.318638i
$196$	−2.06826	+	13.8464i	−0.147733	+	0.989027i
$197$	18.3910	−	7.61779i	1.31030	−	0.542745i	0.385330	−	0.922779i	$-0.374087\pi$
$197$	18.3910	−	7.61779i	1.31030	−	0.542745i	0.924973	+	0.380033i	$0.124087\pi$
$198$	−5.27345	+	5.62707i	−0.374768	+	0.399899i
$199$	5.45407	+	20.3549i	0.386629	+	1.44292i	0.835583	+	0.549364i	$0.185130\pi$
$199$	5.45407	+	20.3549i	0.386629	+	1.44292i	−0.448954	+	0.893555i	$0.648203\pi$
$200$	2.62881	−	2.45778i	0.185885	−	0.173791i
$201$	−0.140653	+	0.524925i	−0.00992092	+	0.0370254i
$202$	−6.60404	+	12.3465i	−0.464659	+	0.868697i
$203$	−14.1335	+	11.4019i	−0.991977	+	0.800257i
$204$	−5.01547	+	7.49658i	−0.351153	+	0.524866i
$205$	−0.894573	−	6.79496i	−0.0624797	−	0.474581i
$206$	−1.16165	−	0.832945i	−0.0809359	−	0.0580341i
$207$	−12.9472	−	7.47507i	−0.899893	−	0.519553i
$208$	−1.97793	+	7.34700i	−0.137145	+	0.509423i
$209$			11.8335i			0.818541i
$210$	−7.17670	+	6.18433i	−0.495239	+	0.426759i
$211$	8.48944	+	3.51644i	0.584437	+	0.242082i	0.655255	−	0.755407i	$-0.272561\pi$
$211$	8.48944	+	3.51644i	0.584437	+	0.242082i	−0.0708182	+	0.997489i	$0.522561\pi$
$212$	−10.2015	−	11.6465i	−0.700643	−	0.799883i
$213$	−7.09277	−	0.933781i	−0.485989	−	0.0639816i
$214$	−1.66728	+	1.03610i	−0.113973	+	0.0708264i
$215$	−2.10624	+	7.86060i	−0.143645	+	0.536089i
$216$	−10.9952	−	9.03985i	−0.748128	−	0.615084i
$217$	10.9976	−	6.71140i	0.746564	−	0.455600i
$218$	−4.10015	+	1.24245i	−0.277698	+	0.0841490i
$219$	−8.37963	−	6.42992i	−0.566243	−	0.434494i
$220$	−0.895045	−	13.7805i	−0.0603439	−	0.929083i
$221$	5.16547	+	6.73177i	0.347467	+	0.452828i
$222$	−3.19864	+	8.49097i	−0.214679	+	0.569877i
$223$	−0.596226			−0.0399262			−0.0199631	−	0.999801i	$-0.506355\pi$
$223$	−0.596226			−0.0399262			−0.0199631	+	0.999801i	$0.506355\pi$
$224$	9.97876	−	11.1546i	0.666734	−	0.745296i
$225$	2.51666			0.167777
$226$	−2.76603	+	7.34257i	−0.183993	+	0.488421i
$227$	−0.0449641	−	0.0585984i	−0.00298437	−	0.00388931i	0.791859	−	0.610704i	$-0.209114\pi$
$227$	−0.0449641	−	0.0585984i	−0.00298437	−	0.00388931i	−0.794843	+	0.606815i	$0.792447\pi$
$228$	−8.66034	+	0.562489i	−0.573545	+	0.0372517i
$229$	−17.2472	−	13.2343i	−1.13973	−	0.874545i	−0.146328	−	0.989236i	$-0.546745\pi$
$229$	−17.2472	−	13.2343i	−1.13973	−	0.874545i	−0.993401	+	0.114691i	$0.963412\pi$
$230$	25.6205	−	7.76364i	1.68937	−	0.511919i
$231$	0.179418	+	7.37216i	0.0118048	+	0.485052i
$232$	19.3213	−	1.88569i	1.26850	−	0.123801i
$233$	2.51633	−	9.39106i	0.164850	−	0.615229i	−0.833209	−	0.552958i	$-0.813499\pi$
$233$	2.51633	−	9.39106i	0.164850	−	0.615229i	0.998059	−	0.0622710i	$-0.0198343\pi$
$234$	−4.51920	+	2.80837i	−0.295429	+	0.183589i
$235$	26.4427	+	3.48125i	1.72493	+	0.227092i
$236$	−4.69551	+	4.11294i	−0.305652	+	0.267730i
$237$	15.5388	+	6.43639i	1.00935	+	0.418088i
$238$	−3.11391	−	16.3980i	−0.201845	−	1.06292i
$239$			22.1673i			1.43389i	0.697132	+	0.716943i	$0.254459\pi$
$239$			22.1673i			1.43389i	−0.697132	+	0.716943i	$0.745541\pi$
$240$	10.0427	−	1.31007i	0.648255	−	0.0845650i
$241$	−20.1593	−	11.6390i	−1.29858	−	0.749733i	−0.318418	−	0.947950i	$-0.603152\pi$
$241$	−20.1593	−	11.6390i	−1.29858	−	0.749733i	−0.980158	+	0.198217i	$0.936485\pi$
$242$	3.90649	+	2.80110i	0.251119	+	0.180062i
$243$	−2.08228	−	15.8165i	−0.133578	−	1.01463i
$244$	−15.1423	−	10.1307i	−0.969389	−	0.648554i
$245$	1.44006	−	17.4720i	0.0920019	−	1.11625i
$246$	1.84537	−	3.45000i	0.117657	−	0.219964i
$247$	−2.11310	+	7.88619i	−0.134453	+	0.501786i
$248$	−13.7655	−	0.462851i	−0.874108	−	0.0293911i
$249$	−2.02112	−	7.54294i	−0.128084	−	0.478014i
$250$	9.02813	−	9.63353i	0.570989	−	0.609278i
$251$	2.09630	−	0.868315i	0.132317	−	0.0548076i	−0.315542	−	0.948911i	$-0.602186\pi$
$251$	2.09630	−	0.868315i	0.132317	−	0.0548076i	0.447860	+	0.894104i	$0.352186\pi$
$252$	10.4246	−	0.932260i	0.656690	−	0.0587269i
$253$	7.97458	−	19.2523i	0.501358	−	1.21038i
$254$	−4.18362	−	1.57602i	−0.262504	−	0.0988881i
$255$	5.64734	−	9.78148i	0.353650	−	0.612540i
$256$	−15.4646	+	4.10456i	−0.966535	+	0.256535i
$257$	7.30609	+	12.6545i	0.455742	+	0.789368i	0.998731	−	0.0503723i	$-0.0160408\pi$
$257$	7.30609	+	12.6545i	0.455742	+	0.789368i	−0.542989	+	0.839740i	$0.682707\pi$
$258$	−3.59204	+	2.94614i	−0.223631	+	0.183419i
$259$	−6.80103	−	15.3516i	−0.422595	−	0.953903i
$260$	1.86429	−	9.34357i	0.115618	−	0.579463i
$261$	10.7703	+	8.26434i	0.666665	+	0.511550i
$262$	8.46245	+	1.97580i	0.522812	+	0.122066i
$263$	2.09985	+	7.83673i	0.129482	+	0.483234i	0.999960	−	0.00897424i	$-0.00285663\pi$
$263$	2.09985	+	7.83673i	0.129482	+	0.483234i	−0.870478	+	0.492208i	$0.836190\pi$
$264$	4.16896	−	6.69099i	0.256582	−	0.411802i
$265$	13.7093	+	13.7093i	0.842155	+	0.842155i
$266$	10.6935	−	11.9820i	0.655663	−	0.734666i
$267$	5.75838	+	13.9020i	0.352407	+	0.850786i
$268$	−0.0709481	+	1.07274i	−0.00433384	+	0.0655283i
$269$	−20.1204	+	15.4389i	−1.22676	+	0.941327i	−0.999472	−	0.0324996i	$-0.989653\pi$
$269$	−20.1204	+	15.4389i	−1.22676	+	0.941327i	−0.227290	+	0.973827i	$0.572987\pi$
$270$	14.4856	+	10.3867i	0.881565	+	0.632115i
$271$	−10.2505	+	5.91813i	−0.622673	+	0.359501i	−0.777909	−	0.628377i	$-0.783720\pi$
$271$	−10.2505	+	5.91813i	−0.622673	+	0.359501i	0.155236	+	0.987877i	$0.450386\pi$
$272$	−6.84787	+	16.4771i	−0.415213	+	0.999071i
$273$	−1.19687	+	4.94505i	−0.0724378	+	0.299288i
$274$	30.9768	+	3.06019i	1.87138	+	0.184873i
$275$	0.457872	+	3.47789i	0.0276107	+	0.209724i
$276$	14.4689	+	4.92105i	0.870923	+	0.296213i
$277$	0.620564	+	0.0816988i	0.0372861	+	0.00490881i	0.149146	−	0.988815i	$-0.452348\pi$
$277$	0.620564	+	0.0816988i	0.0372861	+	0.00490881i	−0.111860	+	0.993724i	$0.535681\pi$
$278$	−0.815948	−	25.1519i	−0.0489373	−	1.50851i
$279$	−6.81064	−	6.81064i	−0.407742	−	0.407742i
$280$	−11.5467	+	14.7623i	−0.690048	+	0.882217i
$281$	−20.5896	+	20.5896i	−1.22827	+	1.22827i	−0.263654	+	0.964617i	$0.584928\pi$
$281$	−20.5896	+	20.5896i	−1.22827	+	1.22827i	−0.964617	+	0.263654i	$0.915072\pi$
$282$	11.1096	+	10.4114i	0.661567	+	0.619993i
$283$	1.87974	−	14.2780i	0.111739	−	0.848740i	−0.840163	−	0.542335i	$-0.817541\pi$
$283$	1.87974	−	14.2780i	0.111739	−	0.848740i	0.951901	−	0.306405i	$-0.0991262\pi$
$284$	−14.1229	+	0.917281i	−0.838039	+	0.0544306i
$285$	10.7747	−	1.41851i	0.638235	−	0.0840253i
$286$	−4.70322	−	5.73435i	−0.278107	−	0.339079i
$287$	2.04350	+	6.94585i	0.120624	+	0.410001i
$288$	−9.85990	−	5.28897i	−0.581000	−	0.311656i
$289$	1.44964	+	2.51084i	0.0852728	+	0.147697i
$290$	−23.9862	+	3.95286i	−1.40852	+	0.232120i
$291$	−0.0379922	−	0.0495124i	−0.00222714	−	0.00290247i
$292$	−18.7350	−	9.25283i	−1.09638	−	0.541481i
$293$	11.1102	−	4.60199i	0.649064	−	0.268851i	−0.0337643	−	0.999430i	$-0.510750\pi$
$293$	11.1102	−	4.60199i	0.649064	−	0.268851i	0.682829	+	0.730579i	$0.260750\pi$
$294$	6.48030	−	7.62682i	0.377939	−	0.444805i
$295$	5.52717	−	5.52717i	0.321804	−	0.321804i
$296$	−2.93967	+	17.7076i	−0.170865	+	1.02923i
$297$	13.4019	−	3.59103i	0.777658	−	0.208373i
$298$	26.3171	−	16.3543i	1.52451	−	0.947376i
$299$	8.75236	−	11.4063i	0.506162	−	0.659643i
$300$	−2.52352	+	0.500409i	−0.145696	+	0.0288912i
$301$	0.914422	−	8.54820i	0.0527064	−	0.492710i
$302$	−5.41484	−	0.534931i	−0.311589	−	0.0307818i
$303$	8.66839	−	5.00470i	0.497986	−	0.287512i
$304$	−16.5890	+	4.42400i	−0.951445	+	0.253734i
$305$	19.7576	+	11.4071i	1.13132	+	0.653167i
$306$	−11.3673	+	5.14640i	−0.649824	+	0.294200i
$307$	−21.8728	−	9.06000i	−1.24835	−	0.517082i	−0.342032	−	0.939688i	$-0.611115\pi$
$307$	−21.8728	−	9.06000i	−1.24835	−	0.517082i	−0.906313	+	0.422607i	$0.861115\pi$
$308$	3.18496	+	14.2367i	0.181480	+	0.811210i
$309$	0.391041	+	0.944057i	0.0222456	+	0.0537055i
$310$	17.2383	−	0.559223i	0.979068	−	0.0317617i
$311$	15.1005	−	4.04616i	0.856270	−	0.229437i	0.196128	−	0.980578i	$-0.437163\pi$
$311$	15.1005	−	4.04616i	0.856270	−	0.229437i	0.660141	+	0.751141i	$0.270496\pi$
$312$	3.97311	−	3.71462i	0.224933	−	0.210299i
$313$	−18.8927	−	5.06229i	−1.06788	−	0.286138i	−0.318259	−	0.948004i	$-0.603098\pi$
$313$	−18.8927	−	5.06229i	−1.06788	−	0.286138i	−0.749622	+	0.661866i	$0.769765\pi$
$314$	−3.52965	−	11.6481i	−0.199190	−	0.657339i
$315$	−12.9486	+	2.02634i	−0.729570	+	0.114171i
$316$	32.6299	+	6.51054i	1.83557	+	0.366246i
$317$	8.87936	−	1.16899i	0.498715	−	0.0656570i	0.123027	−	0.992403i	$-0.460740\pi$
$317$	8.87936	−	1.16899i	0.498715	−	0.0656570i	0.375688	+	0.926746i	$0.377407\pi$
$318$	1.79970	+	10.9207i	0.100922	+	0.612402i
$319$	−9.46137	+	16.3876i	−0.529735	+	0.917528i
$320$	18.9838	−	6.40663i	1.06123	−	0.358142i
$321$	1.40328			0.0783233
$322$	−25.4724	+	12.2876i	−1.41952	+	0.684762i
$323$	−7.32719	+	17.6894i	−0.407696	+	0.984265i
$324$	−0.542939	−	1.60256i	−0.0301633	−	0.0890309i
$325$	−0.315903	+	2.39952i	−0.0175232	+	0.133102i
$326$	8.99499	+	2.10014i	0.498186	+	0.116316i
$327$	2.95832	+	0.792679i	0.163595	+	0.0438353i
$328$	2.25340	−	7.40484i	0.124423	−	0.408864i
$329$	−28.1671	+	0.685511i	−1.55290	+	0.0377934i
$330$	−4.65620	+	8.70495i	−0.256315	+	0.479191i
$331$	21.4900	−	28.0063i	1.18120	−	1.53937i	0.398249	−	0.917277i	$-0.369618\pi$
$331$	21.4900	−	28.0063i	1.18120	−	1.53937i	0.782947	−	0.622088i	$-0.213715\pi$
$332$	−6.82452	−	13.8594i	−0.374544	−	0.760633i
$333$	−9.95857	+	7.64148i	−0.545726	+	0.418750i
$334$	−0.400133	+	0.181155i	−0.0218943	+	0.00991238i
$335$		−	1.34626i		−	0.0735541i
$336$	−10.2677	+	3.00763i	−0.560149	+	0.164080i
$337$		−	5.43607i		−	0.296122i	−0.988978	−	0.148061i	$-0.952697\pi$
$337$		−	5.43607i		−	0.296122i	0.988978	−	0.148061i	$-0.0473031\pi$
$338$	5.47219	+	12.0869i	0.297648	+	0.657440i
$339$	4.44996	−	3.41457i	0.241688	−	0.185454i
$340$	7.19480	−	21.1541i	0.390193	−	1.14724i
$341$	8.17284	−	10.6510i	0.442584	−	0.576787i
$342$	−10.5869	−	5.66282i	−0.572472	−	0.306210i
$343$	1.35073	+	18.4709i	0.0729325	+	0.997337i
$344$	−5.83672	+	7.09922i	−0.314695	+	0.382764i
$345$	−18.4856	−	4.95320i	−0.995230	−	0.266671i
$346$	−4.72884	+	20.2538i	−0.254224	+	1.08885i
$347$	0.285258	−	2.16675i	0.0153134	−	0.116317i	−0.982081	−	0.188460i	$-0.939650\pi$
$347$	0.285258	−	2.16675i	0.0153134	−	0.116317i	0.997394	+	0.0721429i	$0.0229838\pi$
$348$	−12.4429	−	6.14533i	−0.667012	−	0.329424i
$349$	−7.42992	+	17.9374i	−0.397715	+	0.960168i	0.590492	+	0.807043i	$0.298934\pi$
$349$	−7.42992	+	17.9374i	−0.397715	+	0.960168i	−0.988207	+	0.153125i	$0.951066\pi$
$350$	2.67923	−	3.93530i	0.143211	−	0.210351i
$351$	9.57267			0.510951
$352$	5.51520	−	14.5881i	0.293961	−	0.777550i
$353$	−3.12699	+	5.41610i	−0.166433	+	0.288270i	−0.937163	−	0.348891i	$-0.886558\pi$
$353$	−3.12699	+	5.41610i	−0.166433	+	0.288270i	0.770730	+	0.637161i	$0.219892\pi$
$354$	4.40290	−	0.725585i	0.234011	−	0.0385644i
$355$	17.5708	−	2.31324i	0.932562	−	0.122774i
$356$	16.5236	+	24.7610i	0.875751	+	1.31233i
$357$	−4.29656	+	11.1314i	−0.227398	+	0.589137i
$358$	−21.0928	+	6.39163i	−1.11479	+	0.337808i
$359$	−0.638126	−	0.170985i	−0.0336790	−	0.00902426i	0.241940	−	0.970291i	$-0.422216\pi$
$359$	−0.638126	−	0.170985i	−0.0336790	−	0.00902426i	−0.275619	+	0.961267i	$0.588883\pi$
$360$	12.7571	+	5.79379i	0.672357	+	0.305360i
$361$	0.557410	−	0.149358i	0.0293374	−	0.00786092i
$362$	−0.337367	−	10.3995i	−0.0177316	−	0.546584i
$363$	−1.31503	−	3.17476i	−0.0690211	−	0.166632i
$364$	−0.419682	+	10.0565i	−0.0219973	+	0.527102i
$365$	24.1741	+	10.0132i	1.26533	+	0.524116i
$366$	5.37157	+	11.8646i	0.280777	+	0.620175i
$367$	−12.5156	−	7.22587i	−0.653307	−	0.377187i	0.136415	−	0.990652i	$-0.456442\pi$
$367$	−12.5156	−	7.22587i	−0.653307	−	0.377187i	−0.789722	+	0.613465i	$0.789775\pi$
$368$	29.9705	+	3.98174i	1.56232	+	0.207563i
$369$	4.68754	−	2.70635i	0.244023	−	0.140887i
$370$	2.20980	−	22.3687i	0.114882	−	1.16289i
$371$	−16.5477	−	12.0694i	−0.859112	−	0.626610i
$372$	8.18344	+	5.47500i	0.424292	+	0.283865i
$373$	5.33634	−	6.95446i	0.276305	−	0.360088i	−0.634501	−	0.772922i	$-0.718794\pi$
$373$	5.33634	−	6.95446i	0.276305	−	0.360088i	0.910806	+	0.412834i	$0.135461\pi$
$374$	−9.18018	−	14.7727i	−0.474696	−	0.763876i
$375$	−9.11659	+	2.44278i	−0.470779	+	0.126145i
$376$	25.5646	+	15.9285i	1.31839	+	0.821451i
$377$	−9.23163	+	9.23163i	−0.475453	+	0.475453i
$378$	−16.8152	−	8.47475i	−0.864881	−	0.435894i
$379$	14.1825	−	5.87456i	0.728504	−	0.301756i	0.0125667	−	0.999921i	$-0.496000\pi$
$379$	14.1825	−	5.87456i	0.728504	−	0.301756i	0.715937	+	0.698165i	$0.246000\pi$
$380$	20.3624	−	6.89870i	1.04457	−	0.353896i
$381$	1.94554	+	2.53548i	0.0996732	+	0.129897i
$382$	1.42832	+	8.66716i	0.0730794	+	0.443451i
$383$	12.2253	+	21.1749i	0.624685	+	1.08199i	0.988602	+	0.150555i	$0.0481061\pi$
$383$	12.2253	+	21.1749i	0.624685	+	1.08199i	−0.363916	+	0.931432i	$0.618561\pi$
$384$	10.9385	+	3.34287i	0.558201	+	0.170590i
$385$	−5.15612	−	17.5256i	−0.262780	−	0.893187i
$386$	−11.9441	+	9.79640i	−0.607941	+	0.498623i
$387$	−6.37201	+	0.838891i	−0.323907	+	0.0426432i
$388$	−0.0927765	−	0.0814598i	−0.00471001	−	0.00413550i
$389$	−1.51157	+	11.4816i	−0.0766399	+	0.582138i	0.909436	+	0.415843i	$0.136514\pi$
$389$	−1.51157	+	11.4816i	−0.0766399	+	0.582138i	−0.986076	+	0.166294i	$0.946820\pi$
$390$	−4.65746	+	4.96977i	−0.235839	+	0.251654i
$391$	23.8417	−	23.8417i	1.20573	−	1.20573i
$392$	9.64027	−	17.2935i	0.486907	−	0.873454i
$393$	−4.39270	−	4.39270i	−0.221582	−	0.221582i
$394$	−28.1369	+	0.912783i	−1.41752	+	0.0459854i
$395$	−41.3092	−	5.43846i	−2.07849	−	0.273639i
$396$	9.78438	−	4.81793i	0.491683	−	0.242110i
$397$	−0.399027	−	3.03091i	−0.0200266	−	0.152117i	0.978510	−	0.206200i	$-0.0661098\pi$
$397$	−0.399027	−	3.03091i	−0.0200266	−	0.152117i	−0.998536	+	0.0540829i	$0.982776\pi$
$398$	2.92983	−	29.6572i	0.146859	−	1.48658i
$399$	−11.0139	+	3.24035i	−0.551386	+	0.162220i
$400$	−4.70435	+	1.94210i	−0.235218	+	0.0971048i
$401$	−13.6175	+	7.86209i	−0.680027	+	0.392614i	−0.799865	−	0.600180i	$-0.795096\pi$
$401$	−13.6175	+	7.86209i	−0.680027	+	0.392614i	0.119838	+	0.992793i	$0.461762\pi$
$402$	0.447844	−	0.624576i	0.0223364	−	0.0311510i
$403$	7.34856	−	5.63875i	0.366058	−	0.280886i
$404$	14.8953	−	13.0472i	0.741067	−	0.649124i
$405$	0.810838	+	1.95753i	0.0402908	+	0.0972707i
$406$	24.3890	−	8.04333i	1.21041	−	0.399184i
$407$	−12.3719	−	12.3719i	−0.613255	−	0.613255i
$408$	10.3750	−	7.42070i	0.513638	−	0.367379i
$409$	−8.67608	−	32.3796i	−0.429004	−	1.60107i	−0.755020	−	0.655702i	$-0.772373\pi$
$409$	−8.67608	−	32.3796i	−0.429004	−	1.60107i	0.326015	−	0.945364i	$-0.394294\pi$
$410$	−2.20371	+	9.43860i	−0.108834	+	0.466139i
$411$	−17.6537	−	13.5462i	−0.870795	−	0.668184i
$412$	1.12209	+	1.68148i	0.0552814	+	0.0828404i
$413$	−4.86600	+	6.67152i	−0.239440	+	0.328284i
$414$	13.4080	+	16.3475i	0.658965	+	0.803435i
$415$	9.67259	+	16.7534i	0.474809	+	0.822393i
$416$	6.28047	−	8.73710i	0.307926	−	0.428371i
$417$	−8.99485	+	15.5795i	−0.440480	+	0.762933i
$418$	5.89957	−	15.6608i	0.288558	−	0.765992i
$419$	15.2889	−	36.9106i	0.746910	−	1.80320i	0.171785	−	0.985134i	$-0.445046\pi$
$419$	15.2889	−	36.9106i	0.746910	−	1.80320i	0.575125	−	0.818066i	$-0.304954\pi$
$420$	12.5810	−	4.60655i	0.613890	−	0.224777i
$421$	7.20302	−	2.98359i	0.351054	−	0.145411i	−0.200186	−	0.979758i	$-0.564155\pi$
$421$	7.20302	−	2.98359i	0.351054	−	0.145411i	0.551240	+	0.834347i	$0.314155\pi$
$422$	−9.48201	−	8.88613i	−0.461577	−	0.432570i
$423$	5.45167	+	20.3459i	0.265070	+	0.989253i
$424$	7.69460	+	20.4992i	0.373683	+	0.995527i
$425$	−1.46902	+	5.48245i	−0.0712579	+	0.265938i
$426$	8.92121	+	4.77187i	0.432234	+	0.231198i
$427$	−22.4843	−	8.67863i	−1.08809	−	0.419988i
$428$	2.72307	−	0.539980i	0.131625	−	0.0261009i
$429$	0.692016	+	5.25638i	0.0334108	+	0.253780i
$430$	6.70634	−	9.35285i	0.323408	−	0.451034i
$431$	2.14064	+	1.23590i	0.103111	+	0.0595311i	0.550669	−	0.834724i	$-0.314373\pi$
$431$	2.14064	+	1.23590i	0.103111	+	0.0595311i	−0.447558	+	0.894255i	$0.647706\pi$
$432$	10.0445	+	17.4452i	0.483266	+	0.839331i
$433$			12.7033i			0.610484i	0.952275	+	0.305242i	$0.0987373\pi$
$433$			12.7033i			0.610484i	−0.952275	+	0.305242i	$0.901263\pi$
$434$	−17.9004	+	3.39921i	−0.859247	+	0.163168i
$435$	16.0554	+	6.65035i	0.769796	+	0.318860i
$436$	6.04566	+	0.399842i	0.289535	+	0.0191490i
$437$	32.1649	+	4.23458i	1.53865	+	0.202568i
$438$	7.88418	+	12.6872i	0.376721	+	0.606216i
$439$	−3.63297	+	13.5584i	−0.173392	+	0.647109i	0.823427	+	0.567422i	$0.192059\pi$
$439$	−3.63297	+	13.5584i	−0.173392	+	0.647109i	−0.996820	+	0.0796878i	$0.974608\pi$
$440$	−5.68573	+	18.6837i	−0.271057	+	0.890711i
$441$	13.1836	−	4.22982i	0.627790	−	0.201420i
$442$	−3.47999	−	11.4842i	−0.165526	−	0.546249i
$443$	−5.66505	−	4.34695i	−0.269155	−	0.206530i	0.465362	−	0.885121i	$-0.345924\pi$
$443$	−5.66505	−	4.34695i	−0.269155	−	0.206530i	−0.734516	+	0.678591i	$0.762591\pi$
$444$	8.46631	−	9.64247i	0.401793	−	0.457612i
$445$	−22.6926	−	29.5735i	−1.07573	−	1.40192i
$446$	0.789060	+	0.297247i	0.0373631	+	0.0140751i
$447$	−22.1499			−1.04766
$448$	−18.7672	+	9.78732i	−0.886668	+	0.462407i
$449$	−18.8037			−0.887401			−0.443701	−	0.896175i	$-0.646335\pi$
$449$	−18.8037			−0.887401			−0.443701	+	0.896175i	$0.646335\pi$
$450$	−3.33060	−	1.25467i	−0.157006	−	0.0591459i
$451$	4.59287	+	5.98554i	0.216270	+	0.281848i
$452$	7.32125	−	8.33834i	0.344362	−	0.392202i
$453$	3.08593	+	2.36792i	0.144990	+	0.111254i
$454$	0.0302925	+	0.0999672i	0.00142170	+	0.00469170i
$455$	−0.306656	−	12.6003i	−0.0143763	−	0.590710i
$456$	11.7417	+	3.57318i	0.549857	+	0.167330i
$457$	−7.03868	+	26.2687i	−0.329256	+	1.22880i	0.580708	+	0.814112i	$0.302776\pi$
$457$	−7.03868	+	26.2687i	−0.329256	+	1.22880i	−0.909964	+	0.414687i	$0.863891\pi$
$458$	16.2275	+	26.1131i	0.758260	+	1.22019i
$459$	22.2575	+	2.93025i	1.03889	+	0.136772i
$460$	−37.7774	−	2.49848i	−1.76138	−	0.116492i
$461$	−15.7310	−	6.51599i	−0.732666	−	0.303480i	−0.0150187	−	0.999887i	$-0.504781\pi$
$461$	−15.7310	−	6.51599i	−0.732666	−	0.303480i	−0.717647	+	0.696407i	$0.754781\pi$
$462$	3.43793	−	9.84594i	0.159947	−	0.458074i
$463$		−	33.2552i		−	1.54550i	−0.634711	−	0.772749i	$-0.718881\pi$
$463$		−	33.2552i		−	1.54550i	0.634711	−	0.772749i	$-0.281119\pi$
$464$	−26.5103	−	7.13702i	−1.23071	−	0.331328i
$465$	−10.6777	−	6.16477i	−0.495166	−	0.285884i
$466$	−8.01206	+	11.1738i	−0.371152	+	0.517618i
$467$	1.78891	+	13.5881i	0.0827809	+	0.628783i	0.981667	+	0.190602i	$0.0610439\pi$
$467$	1.78891	+	13.5881i	0.0827809	+	0.628783i	−0.898887	+	0.438181i	$0.855623\pi$
$468$	7.38092	−	1.46362i	0.341183	−	0.0676560i
$469$	0.219887	+	1.40511i	0.0101534	+	0.0648818i
$470$	−33.2594	−	17.7901i	−1.53414	−	0.820598i
$471$	−2.25191	+	8.40425i	−0.103763	+	0.387247i
$472$	8.26465	−	3.10223i	0.380411	−	0.142792i
$473$	−2.31861	−	8.65316i	−0.106610	−	0.397873i
$474$	−17.3556	−	16.2649i	−0.797168	−	0.747072i
$475$	−5.04553	+	2.08993i	−0.231505	+	0.0958925i
$476$	−4.05415	+	23.2539i	−0.185822	+	1.06584i
$477$	−5.85957	+	14.1462i	−0.268291	+	0.647712i
$478$	11.0515	−	29.3368i	0.505483	−	1.34183i
$479$	9.18575	−	15.9102i	0.419708	−	0.726955i	−0.576202	−	0.817307i	$-0.695466\pi$
$479$	9.18575	−	15.9102i	0.419708	−	0.726955i	0.995910	+	0.0903522i	$0.0287993\pi$
$480$	−13.9439	−	3.27299i	−0.636449	−	0.149391i
$481$	−6.03577	−	10.4543i	−0.275207	−	0.476673i
$482$	20.8767	+	25.4537i	0.950909	+	1.15938i
$483$	20.1026	+	2.15042i	0.914699	+	0.0978477i
$484$	−3.77346	−	5.65462i	−0.171521	−	0.257028i
$485$	0.122656	+	0.0941176i	0.00556954	+	0.00427366i
$486$	−5.12954	+	21.9700i	−0.232681	+	0.996581i
$487$	0.709378	+	2.64743i	0.0321450	+	0.119967i	0.980134	−	0.198336i	$-0.0635538\pi$
$487$	0.709378	+	2.64743i	0.0321450	+	0.119967i	−0.947989	+	0.318303i	$0.896887\pi$
$488$	14.9891	+	20.9564i	0.678524	+	0.948654i
$489$	−4.66913	−	4.66913i	−0.211145	−	0.211145i
$490$	−10.6165	+	22.4050i	−0.479603	+	1.01215i
$491$	3.74307	+	9.03656i	0.168922	+	0.407814i	0.985558	−	0.169339i	$-0.0541634\pi$
$491$	3.74307	+	9.03656i	0.168922	+	0.407814i	−0.816636	+	0.577154i	$0.804163\pi$
$492$	−4.16220	+	3.64580i	−0.187646	+	0.164365i
$493$	−24.2904	+	18.6387i	−1.09398	+	0.839444i
$494$	6.72817	−	9.38329i	0.302715	−	0.422174i
$495$	−11.8275	+	6.82860i	−0.531606	+	0.306923i
$496$	17.9868	+	7.47529i	0.807631	+	0.335651i
$497$	−17.9610	+	5.28422i	−0.805661	+	0.237029i
$498$	−1.08571	+	10.9901i	−0.0486520	+	0.492480i
$499$	2.53888	+	19.2847i	0.113656	+	0.863303i	0.949375	+	0.314145i	$0.101718\pi$
$499$	2.53888	+	19.2847i	0.113656	+	0.863303i	−0.835719	+	0.549157i	$0.814949\pi$
$500$	−16.7508	+	8.24829i	−0.749120	+	0.368875i
$501$	0.311305	+	0.0409841i	0.0139081	+	0.00183103i
$502$	−3.20719	+	0.104044i	−0.143144	+	0.00464370i
$503$	−3.99722	−	3.99722i	−0.178227	−	0.178227i	0.612355	−	0.790583i	$-0.290222\pi$
$503$	−3.99722	−	3.99722i	−0.178227	−	0.178227i	−0.790583	+	0.612355i	$0.790222\pi$
$504$	−14.2610	−	3.96340i	−0.635235	−	0.176544i
$505$	−17.5335	+	17.5335i	−0.780231	+	0.780231i
$506$	−20.1520	+	21.5033i	−0.895864	+	0.955938i
$507$	1.23801	−	9.40364i	0.0549821	−	0.417630i
$508$	4.75099	+	4.17147i	0.210791	+	0.185079i
$509$	−16.2453	+	2.13874i	−0.720061	+	0.0947979i	−0.481647	−	0.876366i	$-0.659961\pi$
$509$	−16.2453	+	2.13874i	−0.720061	+	0.0947979i	−0.238415	+	0.971163i	$0.576628\pi$
$510$	−12.3504	+	10.1296i	−0.546883	+	0.448545i
$511$	−26.8662	−	6.50252i	−1.18849	−	0.287654i
$512$	22.5125	+	2.27775i	0.994921	+	0.100663i
$513$	10.8004	+	18.7068i	0.476847	+	0.825924i
$514$	−3.36017	−	20.3897i	−0.148211	−	0.899353i
$515$	−1.54101	−	2.00829i	−0.0679051	−	0.0884957i
$516$	6.22259	−	2.10818i	0.273934	−	0.0928076i
$517$	−27.1251	+	11.2356i	−1.19296	+	0.494141i
$518$	1.34712	+	23.7073i	0.0591890	+	1.04164i
$519$	10.5134	−	10.5134i	0.461487	−	0.461487i
$520$	−7.12546	+	11.4361i	−0.312472	+	0.501504i
$521$	17.1968	−	4.60788i	0.753408	−	0.201875i	0.138379	−	0.990379i	$-0.455811\pi$
$521$	17.1968	−	4.60788i	0.753408	−	0.201875i	0.615029	+	0.788504i	$0.289144\pi$
$522$	−10.1335	−	16.3067i	−0.443531	−	0.713726i
$523$	14.5053	−	18.9037i	0.634273	−	0.826601i	−0.360058	−	0.932930i	$-0.617243\pi$
$523$	14.5053	−	18.9037i	0.634273	−	0.826601i	0.994331	+	0.106329i	$0.0339096\pi$
$524$	−10.2144	−	6.83376i	−0.446217	−	0.298534i
$525$	−3.11163	+	1.37850i	−0.135803	+	0.0601628i
$526$	1.12800	−	11.4182i	0.0491832	−	0.497857i
$527$	18.8122	−	10.8613i	0.819474	−	0.473124i
$528$	−8.85308	+	6.77659i	−0.385281	+	0.294913i
$529$	−29.5578	−	17.0652i	−1.28512	−	0.741966i
$530$	−11.3085	−	24.9779i	−0.491208	−	1.08497i
$531$	5.70334	+	2.36240i	0.247504	+	0.102519i
$532$	−20.1257	+	10.5261i	−0.872560	+	0.456363i
$533$	1.99199	+	4.80908i	0.0862825	+	0.208304i
$534$	−0.689984	−	21.2690i	−0.0298585	−	0.920400i
$535$	−3.35787	+	0.899738i	−0.145173	+	0.0388991i
$536$	0.628709	−	1.38432i	0.0271561	−	0.0597937i
$537$	15.2188	+	4.07785i	0.656738	+	0.175972i
$538$	34.3248	−	10.4013i	1.47985	−	0.448430i
$539$	8.24397	+	17.4495i	0.355093	+	0.751602i
$540$	−13.9923	−	20.9678i	−0.602133	−	0.902309i
$541$	21.2167	−	2.79323i	0.912175	−	0.120090i	0.340193	−	0.940356i	$-0.389508\pi$
$541$	21.2167	−	2.79323i	0.912175	−	0.120090i	0.571983	+	0.820266i	$0.306174\pi$
$542$	16.5162	−	2.72182i	0.709432	−	0.116912i
$543$	−3.71907	+	6.44161i	−0.159600	+	0.276436i
$544$	17.2773	−	18.3922i	0.740756	−	0.788559i
$545$	−7.58712			−0.324997
$546$	4.04931	−	5.94770i	0.173294	−	0.254538i
$547$	−13.0284	+	31.4533i	−0.557054	+	1.34485i	0.355035	+	0.934853i	$0.384469\pi$
$547$	−13.0284	+	31.4533i	−0.557054	+	1.34485i	−0.912089	+	0.409993i	$0.865531\pi$
$548$	−39.4698	−	19.4933i	−1.68606	−	0.832714i
$549$	−2.35178	+	17.8636i	−0.100372	+	0.762399i
$550$	1.12793	−	4.83099i	0.0480953	−	0.205994i
$551$	−28.4559	−	7.62474i	−1.21226	−	0.324825i
$552$	−16.6950	−	13.7261i	−0.710589	−	0.584220i
$553$	44.0031	−	1.07091i	1.87120	−	0.0455399i
$554$	−0.780538	−	0.417503i	−0.0331619	−	0.0177380i
$555$	−9.78186	+	12.7480i	−0.415217	+	0.541121i
$556$	−11.4596	+	33.6934i	−0.485995	+	1.42892i
$557$	33.3326	−	25.5770i	1.41235	−	1.08373i	0.428735	−	0.903430i	$-0.358959\pi$
$557$	33.3326	−	25.5770i	1.41235	−	1.08373i	0.983611	−	0.180301i	$-0.0577073\pi$
$558$	5.61793	+	12.4088i	0.237826	+	0.525306i
$559$		−	6.18074i		−	0.261417i
$560$	22.6409	−	13.7802i	0.956753	−	0.582320i
$561$			12.4335i			0.524942i
$562$	37.5136	−	16.9838i	1.58242	−	0.716420i
$563$	15.4502	−	11.8553i	0.651148	−	0.499643i	−0.229565	−	0.973293i	$-0.573730\pi$
$563$	15.4502	−	11.8553i	0.651148	−	0.499643i	0.880713	+	0.473650i	$0.157064\pi$
$564$	−9.51211	−	19.3174i	−0.400532	−	0.813410i
$565$	−8.45887	+	11.0238i	−0.355867	+	0.463775i
$566$	−9.60596	+	17.9587i	−0.403769	+	0.754861i
$567$	−1.16601	−	1.91066i	−0.0489676	−	0.0802403i
$568$	19.1479	+	5.82698i	0.803427	+	0.244495i
$569$	3.96387	+	1.06212i	0.166174	+	0.0445262i	0.340947	−	0.940083i	$-0.389252\pi$
$569$	3.96387	+	1.06212i	0.166174	+	0.0445262i	−0.174773	+	0.984609i	$0.555919\pi$
$570$	−14.9666	−	3.49439i	−0.626883	−	0.146364i
$571$	0.297212	−	2.25755i	0.0124379	−	0.0944755i	−0.984100	−	0.177616i	$-0.943162\pi$
$571$	0.297212	−	2.25755i	0.0124379	−	0.0944755i	0.996538	+	0.0831402i	$0.0264949\pi$
$572$	3.36551	+	9.93376i	0.140719	+	0.415351i
$573$	2.40303	−	5.80144i	0.100388	−	0.242359i
$574$	0.758418	−	10.2111i	0.0316557	−	0.426203i
$575$	9.61715			0.401063
$576$	10.4120	+	11.9152i	0.433834	+	0.496466i
$577$	18.8541	−	32.6562i	0.784905	−	1.35950i	−0.144151	−	0.989556i	$-0.546045\pi$
$577$	18.8541	−	32.6562i	0.784905	−	1.35950i	0.929056	−	0.369939i	$-0.120622\pi$
$578$	−0.666707	−	4.04562i	−0.0277314	−	0.168276i
$579$	10.9486	−	1.44141i	0.455007	−	0.0599028i
$580$	33.7146	+	6.72697i	1.39992	+	0.279322i
$581$	−12.8317	−	15.9059i	−0.532350	−	0.659887i
$582$	0.0255955	+	0.0844668i	0.00106097	+	0.00350126i
$583$	−20.6154	−	5.52389i	−0.853804	−	0.228776i
$584$	20.1813	+	21.5857i	0.835109	+	0.893222i
$585$	−9.10154	+	2.43875i	−0.376303	+	0.100830i
$586$	−16.9978	+	0.551422i	−0.702173	+	0.0227790i
$587$	−11.6713	−	28.1769i	−0.481725	−	1.16299i	−0.958789	−	0.284118i	$-0.908299\pi$
$587$	−11.6713	−	28.1769i	−0.481725	−	1.16299i	0.477065	−	0.878868i	$-0.341701\pi$
$588$	−12.3785	+	6.86277i	−0.510481	+	0.283016i
$589$	19.3102	+	7.99853i	0.795662	+	0.329574i
$590$	−10.0704	+	4.55923i	−0.414590	+	0.187701i
$591$	17.4285	+	10.0623i	0.716913	+	0.413910i
$592$	12.7185	−	21.9691i	0.522728	−	0.902925i
$593$	3.98155	−	2.29875i	0.163503	−	0.0943983i	−0.416016	−	0.909357i	$-0.636574\pi$
$593$	3.98155	−	2.29875i	0.163503	−	0.0943983i	0.579519	+	0.814959i	$0.303241\pi$
$594$	−19.5267	−	1.92904i	−0.801191	−	0.0791495i
$595$	3.14402	−	29.3909i	0.128892	−	1.20491i
$596$	−42.9821	+	8.52326i	−1.76061	+	0.349126i
$597$	−12.9692	+	16.9017i	−0.530792	+	0.691742i
$598$	−17.2697	+	10.7319i	−0.706209	+	0.438860i
$599$	30.5811	−	8.19418i	1.24951	−	0.334805i	0.427362	−	0.904080i	$-0.359443\pi$
$599$	30.5811	−	8.19418i	1.24951	−	0.334805i	0.822147	+	0.569276i	$0.192776\pi$
$600$	3.58917	+	0.595843i	0.146527	+	0.0243252i
$601$	15.2570	−	15.2570i	0.622345	−	0.622345i	−0.323786	−	0.946130i	$-0.604956\pi$
$601$	15.2570	−	15.2570i	0.622345	−	0.622345i	0.946130	+	0.323786i	$0.104956\pi$
$602$	−5.47185	+	10.8570i	−0.223016	+	0.442499i
$603$	0.982292	−	0.406879i	0.0400020	−	0.0165694i
$604$	6.89944	+	3.40750i	0.280734	+	0.138649i
$605$	5.18225	+	6.75364i	0.210688	+	0.274575i
$606$	−13.9670	+	2.30173i	−0.567372	+	0.0935013i
$607$	14.6267	+	25.3342i	0.593681	+	1.02829i	0.993732	+	0.111792i	$0.0356591\pi$
$607$	14.6267	+	25.3342i	0.593681	+	1.02829i	−0.400051	+	0.916493i	$0.631008\pi$
$608$	24.1599	+	2.41559i	0.979812	+	0.0979649i
$609$	−17.8433	−	4.31869i	−0.723049	−	0.175002i
$610$	−20.4607	−	24.9465i	−0.828431	−	1.01005i
$611$	−20.0833	+	2.64402i	−0.812483	+	0.106965i
$612$	17.6095	−	1.14373i	0.711820	−	0.0462327i
$613$	−2.56083	+	19.4514i	−0.103431	+	0.785635i	0.858591	+	0.512662i	$0.171340\pi$
$613$	−2.56083	+	19.4514i	−0.103431	+	0.785635i	−0.962022	+	0.272973i	$0.911993\pi$
$614$	24.4301	+	22.8948i	0.985919	+	0.923961i
$615$	4.89940	−	4.89940i	0.197563	−	0.197563i
$616$	2.88262	−	20.4290i	0.116144	−	0.823108i
$617$	15.6760	+	15.6760i	0.631090	+	0.631090i	0.948342	−	0.317251i	$-0.102760\pi$
$617$	15.6760	+	15.6760i	0.631090	+	0.631090i	−0.317251	+	0.948342i	$0.602760\pi$
$618$	−0.0468556	−	1.44434i	−0.00188481	−	0.0580999i
$619$	−32.0547	−	4.22009i	−1.28839	−	0.169620i	−0.544975	−	0.838452i	$-0.683461\pi$
$619$	−32.0547	−	4.22009i	−1.28839	−	0.169620i	−0.743413	+	0.668833i	$0.766794\pi$
$620$	−23.0923	−	7.85401i	−0.927410	−	0.315425i
$621$	−4.96501	−	37.7130i	−0.199239	−	1.51337i
$622$	−22.0015	−	2.17353i	−0.882181	−	0.0871505i
$623$	28.5147	+	27.1598i	1.14242	+	1.08813i
$624$	−7.11003	+	2.93523i	−0.284629	+	0.117503i
$625$	25.7581	−	14.8715i	1.03032	−	0.594858i
$626$	22.4793	+	16.1185i	0.898454	+	0.644225i
$627$	−9.49118	+	7.28284i	−0.379041	+	0.290848i
$628$	−1.13591	+	17.1750i	−0.0453276	+	0.685359i
$629$	−10.8337	−	26.1549i	−0.431968	−	1.04286i
$630$	18.1467	+	3.77379i	0.722982	+	0.150351i
$631$	−6.11926	−	6.11926i	−0.243604	−	0.243604i	0.574735	−	0.818339i	$-0.305105\pi$
$631$	−6.11926	−	6.11926i	−0.243604	−	0.243604i	−0.818339	+	0.574735i	$0.805105\pi$
$632$	−39.9373	−	24.8838i	−1.58862	−	0.989823i
$633$	2.40436	+	8.97320i	0.0955648	+	0.356653i
$634$	−12.3340	−	2.87972i	−0.489844	−	0.114368i
$635$	−6.28111	−	4.81966i	−0.249258	−	0.191262i
$636$	3.06273	−	15.3499i	0.121445	−	0.608665i
$637$	2.37808	+	13.1009i	0.0942230	+	0.519078i
$638$	20.6914	−	16.9707i	0.819180	−	0.671878i
$639$	6.99824	+	12.1213i	0.276846	+	0.479512i
$640$	−28.3177	−	0.985667i	−1.11935	−	0.0389619i
$641$	−14.5697	+	25.2355i	−0.575470	+	0.996744i	0.420520	+	0.907283i	$0.361848\pi$
$641$	−14.5697	+	25.2355i	−0.575470	+	0.996744i	−0.995990	+	0.0894605i	$0.971486\pi$
$642$	−1.85713	−	0.699601i	−0.0732951	−	0.0276111i
$643$	−18.9545	+	45.7602i	−0.747493	+	1.80461i	−0.175246	+	0.984525i	$0.556072\pi$
$643$	−18.9545	+	45.7602i	−0.747493	+	1.80461i	−0.572246	+	0.820082i	$0.693928\pi$
$644$	39.8367	−	3.56254i	1.56979	−	0.140384i
$645$	−7.60094	+	3.14841i	−0.299287	+	0.123969i
$646$	18.5160	−	19.7576i	0.728502	−	0.777353i
$647$	−0.337357	−	1.25903i	−0.0132629	−	0.0494977i	0.958977	−	0.283483i	$-0.0914899\pi$
$647$	−0.337357	−	1.25903i	−0.0132629	−	0.0494977i	−0.972240	+	0.233985i	$0.924823\pi$
$648$	−0.0804134	+	2.39154i	−0.00315894	+	0.0939487i
$649$	−2.22707	+	8.31152i	−0.0874200	+	0.326256i
$650$	1.61435	−	3.01809i	0.0633201	−	0.118379i
$651$	12.1513	+	4.69023i	0.476247	+	0.183824i
$652$	−10.8572	−	7.26380i	−0.425199	−	0.284473i
$653$	−1.62201	−	12.3204i	−0.0634742	−	0.482135i	−0.993428	−	0.114458i	$-0.963487\pi$
$653$	−1.62201	−	12.3204i	−0.0634742	−	0.482135i	0.929954	−	0.367676i	$-0.119847\pi$
$654$	−3.51992	−	2.52391i	−0.137640	−	0.0986928i
$655$	13.3276	+	7.69472i	0.520754	+	0.300657i
$656$	−6.67387	+	8.67631i	−0.260571	+	0.338753i
$657$			20.6647i			0.806209i
$658$	37.6188	+	13.1354i	1.46653	+	0.512073i
$659$	20.4743	+	8.48071i	0.797564	+	0.330362i	0.743980	−	0.668202i	$-0.232936\pi$
$659$	20.4743	+	8.48071i	0.797564	+	0.330362i	0.0535834	+	0.998563i	$0.482936\pi$
$660$	10.5020	−	9.19899i	0.408788	−	0.358070i
$661$	32.1821	+	4.23686i	1.25174	+	0.164795i	0.727101	−	0.686530i	$-0.240867\pi$
$661$	32.1821	+	4.23686i	1.25174	+	0.164795i	0.524639	+	0.851325i	$0.324200\pi$
$662$	−42.4028	+	26.3504i	−1.64803	+	1.02414i
$663$	−2.22023	+	8.28602i	−0.0862267	+	0.321803i
$664$	2.12216	+	21.7442i	0.0823556	+	0.843839i
$665$	24.2773	−	14.8155i	0.941434	−	0.574522i
$666$	16.9890	−	5.14809i	0.658312	−	0.199484i
$667$	41.1576	+	31.5813i	1.59363	+	1.22283i
$668$	0.619860	−	0.0402599i	0.0239831	−	0.00155770i
$669$	−0.366942	−	0.478208i	−0.0141868	−	0.0184886i
$670$	−0.671176	+	1.78167i	−0.0259298	+	0.0688321i
$671$	−25.1144			−0.969531
$672$	15.0880	+	1.13858i	0.582031	+	0.0439215i
$673$	−13.5148			−0.520956			−0.260478	−	0.965480i	$-0.583880\pi$
$673$	−13.5148			−0.520956			−0.260478	+	0.965480i	$0.583880\pi$
$674$	−2.71014	+	7.19422i	−0.104391	+	0.277111i
$675$	3.89806	+	5.08005i	0.150036	+	0.195531i
$676$	−1.21614	−	18.7242i	−0.0467745	−	0.720162i
$677$	15.5249	+	11.9127i	0.596672	+	0.457843i	0.862415	−	0.506201i	$-0.168951\pi$
$677$	15.5249	+	11.9127i	0.596672	+	0.457843i	−0.265743	+	0.964044i	$0.585617\pi$
$678$	−7.59150	+	2.30041i	−0.291550	+	0.0883466i
$679$	−0.143390	−	0.0781977i	−0.00550280	−	0.00300095i
$680$	−20.0681	+	24.4089i	−0.769577	+	0.936039i
$681$	0.0193266	−	0.0721278i	0.000740596	−	0.00276394i
$682$	−16.1262	+	10.0213i	−0.617504	+	0.383735i
$683$	−14.6485	−	1.92851i	−0.560507	−	0.0737922i	−0.155051	−	0.987906i	$-0.549554\pi$
$683$	−14.6485	−	1.92851i	−0.560507	−	0.0737922i	−0.405457	+	0.914114i	$0.632887\pi$
$684$	11.1877	+	12.7724i	0.427773	+	0.488363i
$685$	50.9286	+	21.0953i	1.94588	+	0.806010i
$686$	7.42106	−	25.1183i	0.283337	−	0.959020i
$687$		−	21.9782i		−	0.838521i
$688$	11.2637	−	6.48539i	0.429426	−	0.247253i
$689$	−12.7523	−	7.36255i	−0.485824	−	0.280491i
$690$	21.9948	+	15.7711i	0.837330	+	0.600396i
$691$	−2.32732	−	17.6778i	−0.0885355	−	0.672494i	−0.976953	−	0.213457i	$-0.931528\pi$
$691$	−2.32732	−	17.6778i	−0.0885355	−	0.672494i	0.888417	−	0.459037i	$-0.151806\pi$
$692$	16.3558	−	24.4469i	0.621753	−	0.929330i
$693$	11.2291	−	9.05887i	0.426559	−	0.344118i
$694$	−1.45774	+	2.72531i	−0.0553352	+	0.103451i
$695$	11.5344	−	43.0471i	0.437526	−	1.63287i
$696$	13.4036	+	14.3363i	0.508060	+	0.543415i
$697$	3.15949	+	11.7914i	0.119674	+	0.446631i
$698$	18.7756	−	20.0346i	0.710667	−	0.758322i
$699$	9.08084	−	3.76141i	0.343469	−	0.142269i
$700$	−5.50769	+	3.87235i	−0.208171	+	0.146361i
$701$	15.9123	−	38.4156i	0.600998	−	1.45094i	−0.271558	−	0.962422i	$-0.587539\pi$
$701$	15.9123	−	38.4156i	0.600998	−	1.45094i	0.872556	−	0.488515i	$-0.162461\pi$
$702$	−12.6687	−	4.77243i	−0.478149	−	0.180124i
$703$	13.6197	−	23.5900i	0.513677	−	0.889715i
$704$	−14.5718	+	16.5567i	−0.549196	+	0.624003i
$705$	13.4818	+	23.3512i	0.507754	+	0.879455i
$706$	6.83851	−	5.60884i	0.257371	−	0.211092i
$707$	15.4361	−	21.1637i	0.580535	−	0.795941i
$708$	−6.18863	−	1.23480i	−0.232583	−	0.0464066i
$709$	32.5308	+	24.9617i	1.22172	+	0.937458i	0.999297	−	0.0374928i	$-0.0119371\pi$
$709$	32.5308	+	24.9617i	1.22172	+	0.937458i	0.222422	+	0.974951i	$0.428604\pi$
$710$	−24.4069	−	5.69849i	−0.915974	−	0.213861i
$711$	−8.51668	−	31.7847i	−0.319401	−	1.19202i
$712$	−9.52321	−	41.0071i	−0.356897	−	1.53681i
$713$	−26.0262	−	26.0262i	−0.974688	−	0.974688i
$714$	11.2357	−	12.5895i	0.420486	−	0.471151i
$715$	−5.02613	−	12.1342i	−0.187967	−	0.453792i
$716$	31.1013	+	2.05694i	1.16231	+	0.0768716i
$717$	−17.7795	+	13.6427i	−0.663988	+	0.509496i
$718$	0.759266	+	0.544422i	0.0283356	+	0.0203177i
$719$	−6.47984	+	3.74114i	−0.241657	+	0.139521i	−0.615938	−	0.787794i	$-0.711223\pi$
$719$	−6.47984	+	3.74114i	−0.241657	+	0.139521i	0.374281	+	0.927315i	$0.377890\pi$
$720$	−13.9945	−	14.0277i	−0.521545	−	0.522780i
$721$	1.93638	+	1.84437i	0.0721147	+	0.0686880i
$722$	−0.812151	−	0.0802322i	−0.0302251	−	0.00298593i
$723$	−3.07173	−	23.3321i	−0.114239	−	0.867730i
$724$	−4.73815	+	13.9311i	−0.176092	+	0.517745i
$725$	−8.65826	−	1.13988i	−0.321560	−	0.0423341i
$726$	0.157570	+	4.85715i	0.00584797	+	0.180266i
$727$	28.9723	+	28.9723i	1.07452	+	1.07452i	0.996990	+	0.0775341i	$0.0247047\pi$
$727$	28.9723	+	28.9723i	1.07452	+	1.07452i	0.0775341	+	0.996990i	$0.475295\pi$
$728$	5.56905	−	13.0997i	0.206403	−	0.485508i
$729$	9.60957	−	9.60957i	0.355910	−	0.355910i
$730$	−27.0005	−	25.3037i	−0.999332	−	0.936531i
$731$	1.89196	−	14.3709i	0.0699768	−	0.531526i
$732$	−1.19378	−	18.3799i	−0.0441232	−	0.679342i
$733$	−13.3661	+	1.75968i	−0.493689	+	0.0649954i	−0.373260	−	0.927727i	$-0.621760\pi$
$733$	−13.3661	+	1.75968i	−0.493689	+	0.0649954i	−0.120429	+	0.992722i	$0.538427\pi$
$734$	12.9610	+	15.8025i	0.478398	+	0.583281i
$735$	14.8999	−	9.59801i	0.549590	−	0.354028i
$736$	−37.6786	−	20.2113i	−1.38885	−	0.744998i
$737$	0.741000	+	1.28345i	0.0272951	+	0.0472765i
$738$	−7.55284	+	1.24469i	−0.278024	+	0.0458176i
$739$	15.5530	+	20.2691i	0.572127	+	0.745610i	0.986368	−	0.164557i	$-0.0526196\pi$
$739$	15.5530	+	20.2691i	0.572127	+	0.745610i	−0.414241	+	0.910167i	$0.635953\pi$
$740$	−14.0764	+	28.5016i	−0.517457	+	1.04774i
$741$	−7.62568	+	3.15866i	−0.280136	+	0.116036i
$742$	15.8824	+	24.2227i	0.583062	+	0.889243i
$743$	14.5232	−	14.5232i	0.532805	−	0.532805i	−0.388601	−	0.921406i	$-0.627042\pi$
$743$	14.5232	−	14.5232i	0.532805	−	0.532805i	0.921406	+	0.388601i	$0.127042\pi$
$744$	−8.10061	−	11.3256i	−0.296983	−	0.415216i
$745$	53.0020	−	14.2018i	1.94184	−	0.520315i
$746$	−10.5294	+	6.54327i	−0.385508	+	0.239566i
$747$	−9.30070	+	12.1209i	−0.340295	+	0.443481i
$748$	4.78439	+	24.1273i	0.174935	+	0.882180i
$749$	3.35768	−	1.48751i	0.122687	−	0.0543524i
$750$	13.2830	+	1.31222i	0.485025	+	0.0479155i
$751$	−33.9654	+	19.6099i	−1.23941	+	0.715576i	−0.968975	−	0.247160i	$-0.920503\pi$
$751$	−33.9654	+	19.6099i	−1.23941	+	0.715576i	−0.270440	+	0.962737i	$0.587169\pi$
$752$	−25.8916	−	33.8253i	−0.944171	−	1.23348i
$753$	1.98659	+	1.14696i	0.0723954	+	0.0417975i
$754$	16.8198	−	7.61495i	0.612540	−	0.277320i
$755$	−8.90247	−	3.68752i	−0.323994	−	0.134203i
$756$	18.0286	+	19.5989i	0.655693	+	0.712804i
$757$	7.67574	+	18.5309i	0.278979	+	0.673516i	0.999808	−	0.0195976i	$-0.00623851\pi$
$757$	7.67574	+	18.5309i	0.278979	+	0.673516i	−0.720829	+	0.693113i	$0.756239\pi$
$758$	−21.6981	+	0.703905i	−0.788112	+	0.0255670i
$759$	20.3494	−	5.45261i	0.738637	−	0.197917i
$760$	−30.3875	−	1.02175i	−1.10227	−	0.0370628i
$761$	41.6588	+	11.1624i	1.51013	+	0.404638i	0.916479	−	0.400083i	$-0.131019\pi$
$761$	41.6588	+	11.1624i	1.51013	+	0.404638i	0.593652	+	0.804722i	$0.297685\pi$
$762$	−1.31072	−	4.32546i	−0.0474823	−	0.156695i
$763$	7.91875	−	1.23921i	0.286678	−	0.0448626i
$764$	2.43072	−	12.1824i	0.0879403	−	0.440744i
$765$	−21.9086	+	2.88432i	−0.792107	+	0.104283i
$766$	−5.62259	−	34.1183i	−0.203153	−	1.23274i
$767$	−2.96836	+	5.14135i	−0.107181	+	0.185643i
$768$	−12.8096	−	9.87738i	−0.462228	−	0.356419i
$769$	−53.6881			−1.93604			−0.968022	−	0.250866i	$-0.919285\pi$
$769$	−53.6881			−1.93604			−0.968022	+	0.250866i	$0.919285\pi$
$770$	−1.91362	+	25.7644i	−0.0689621	+	0.928483i
$771$	−5.65320	+	13.6480i	−0.203595	+	0.491522i
$772$	20.6911	−	7.01006i	0.744690	−	0.252297i
$773$	3.76805	−	28.6212i	0.135527	−	1.02943i	−0.779603	−	0.626274i	$-0.784579\pi$
$773$	3.76805	−	28.6212i	0.135527	−	1.02943i	0.915131	−	0.403158i	$-0.132087\pi$
$774$	8.85110	+	2.06654i	0.318146	+	0.0742804i
$775$	5.98477	+	1.60361i	0.214979	+	0.0576035i
$776$	0.0821709	+	0.154059i	0.00294976	+	0.00553041i
$777$	8.12727	−	14.9029i	0.291564	−	0.534637i
$778$	7.72456	−	14.4414i	0.276939	−	0.517748i
$779$	−7.15038	+	9.31855i	−0.256189	+	0.333872i
$780$	8.64146	−	4.25515i	0.309414	−	0.152359i
$781$	−15.4778	+	11.8765i	−0.553838	+	0.424975i
$782$	−43.4389	+	19.6665i	−1.55337	+	0.703271i
$783$			34.5413i			1.23440i
$784$	−21.3798	+	18.0805i	−0.763564	+	0.645732i
$785$		−	21.5542i		−	0.769301i
$786$	3.62343	+	8.00338i	0.129244	+	0.285471i
$787$	23.3383	−	17.9081i	0.831922	−	0.638356i	−0.102417	−	0.994742i	$-0.532658\pi$
$787$	23.3383	−	17.9081i	0.831922	−	0.638356i	0.934339	+	0.356386i	$0.115991\pi$
$788$	37.6921	+	12.8196i	1.34273	+	0.456679i
$789$	−4.99319	+	6.50725i	−0.177762	+	0.231664i
$790$	51.9583	+	27.7920i	1.84859	+	0.988795i
$791$	7.02806	−	12.8872i	0.249889	−	0.458218i
$792$	−15.3508	+	1.49819i	−0.545469	+	0.0532358i
$793$	−16.7369	−	4.48465i	−0.594346	−	0.159255i
$794$	−0.982974	+	4.21012i	−0.0348844	+	0.149412i
$795$	−2.55839	+	19.4329i	−0.0907369	+	0.689215i
$796$	−18.6630	+	37.7884i	−0.661491	+	1.33938i
$797$	16.2376	−	39.2011i	0.575167	−	1.38858i	−0.321940	−	0.946760i	$-0.604335\pi$
$797$	16.2376	−	39.2011i	0.575167	−	1.38858i	0.897106	−	0.441815i	$-0.145665\pi$
$798$	16.1916	+	1.20261i	0.573175	+	0.0425719i
$799$	−47.5052			−1.68061
$800$	7.19408	−	0.224870i	0.254349	−	0.00795035i
$801$	14.7198	−	25.4955i	0.520099	−	0.900838i
$802$	21.9414	−	3.61588i	0.774777	−	0.127681i
$803$	−28.5576	+	3.75968i	−1.00778	+	0.132676i
$804$	−0.904068	+	0.603307i	−0.0318840	+	0.0212770i
$805$	−49.4817	+	7.74345i	−1.74400	+	0.272921i
$806$	−12.5364	+	3.79884i	−0.441577	+	0.133809i
$807$	−24.7659	−	6.63599i	−0.871799	−	0.233598i
$808$	−26.2174	+	9.84101i	−0.922326	+	0.346206i
$809$	24.8268	−	6.65231i	0.872863	−	0.233883i	0.205537	−	0.978649i	$-0.434106\pi$
$809$	24.8268	−	6.65231i	0.872863	−	0.233883i	0.667325	+	0.744766i	$0.267439\pi$
$810$	−0.0971566	−	2.99489i	−0.00341374	−	0.105230i
$811$	12.6529	+	30.5468i	0.444304	+	1.07264i	0.974423	+	0.224721i	$0.0721471\pi$
$811$	12.6529	+	30.5468i	0.444304	+	1.07264i	−0.530119	+	0.847923i	$0.677853\pi$
$812$	−36.2870	−	1.51435i	−1.27342	−	0.0531432i
$813$	−11.0553	−	4.57924i	−0.387725	−	0.160601i
$814$	10.2053	+	22.5413i	0.357696	+	0.790073i
$815$	14.1663	+	8.17894i	0.496225	+	0.286496i
$816$	−17.4301	+	4.64830i	−0.610175	+	0.162723i
$817$	12.0783	−	6.97342i	0.422567	−	0.243969i
$818$	−4.66064	+	47.1773i	−0.162955	+	1.64952i
$819$	9.10104	−	4.03191i	0.318016	−	0.140886i
$820$	7.62204	−	11.3926i	0.266173	−	0.397847i
$821$	−13.5352	+	17.6394i	−0.472380	+	0.615618i	−0.967397	−	0.253266i	$-0.918495\pi$
$821$	−13.5352	+	17.6394i	−0.472380	+	0.615618i	0.495017	+	0.868884i	$0.335162\pi$
$822$	16.6100	+	26.7286i	0.579339	+	0.932266i
$823$	−16.9189	+	4.53342i	−0.589757	+	0.158025i	−0.541342	−	0.840802i	$-0.682084\pi$
$823$	−16.9189	+	4.53342i	−0.589757	+	0.158025i	−0.0484149	+	0.998827i	$0.515417\pi$
$824$	−0.646704	−	2.78472i	−0.0225290	−	0.0970104i
$825$	−2.50768	+	2.50768i	−0.0873061	+	0.0873061i
$826$	9.76585	−	6.40331i	0.339798	−	0.222800i
$827$	−25.4205	+	10.5295i	−0.883957	+	0.366147i	−0.778030	−	0.628227i	$-0.783781\pi$
$827$	−25.4205	+	10.5295i	−0.883957	+	0.366147i	−0.105927	+	0.994374i	$0.533781\pi$
$828$	−9.59440	−	28.3192i	−0.333428	−	0.984159i
$829$	−23.8618	−	31.0974i	−0.828756	−	1.08006i	−0.995566	−	0.0940670i	$-0.970013\pi$
$829$	−23.8618	−	31.0974i	−0.828756	−	1.08006i	0.166810	−	0.985989i	$-0.446653\pi$
$830$	−4.44855	−	26.9941i	−0.154412	−	0.936980i
$831$	0.316394	+	0.548010i	0.0109756	+	0.0190103i
$832$	−12.6676	+	8.43176i	−0.439170	+	0.292319i
$833$	1.51901	+	31.1891i	0.0526306	+	1.08064i
$834$	19.6711	−	16.1340i	0.681156	−	0.558673i
$835$	−0.771191	+	0.101529i	−0.0266882	+	0.00351356i
$836$	−15.6153	+	17.7846i	−0.540065	+	0.615093i
$837$	3.19873	−	24.2968i	0.110564	−	0.839820i
$838$	−38.6353	+	41.2261i	−1.33464	+	1.42413i
$839$	−20.7786	+	20.7786i	−0.717357	+	0.717357i	−0.968063	−	0.250706i	$-0.919337\pi$
$839$	−20.7786	+	20.7786i	−0.717357	+	0.717357i	0.250706	+	0.968063i	$0.419337\pi$
$840$	−18.9466	−	0.175810i	−0.653719	−	0.00606601i
$841$	−12.8046	−	12.8046i	−0.441538	−	0.441538i
$842$	−11.0201	+	0.357501i	−0.379778	+	0.0123203i
$843$	−29.1857	−	3.84238i	−1.00521	−	0.132338i
$844$	8.11855	+	16.4874i	0.279452	+	0.567518i
$845$	3.06691	+	23.2955i	0.105505	+	0.801390i
$846$	2.92854	−	29.6442i	0.100685	−	1.01919i
$847$	−6.51184	−	6.20241i	−0.223750	−	0.213117i
$848$	0.0366007	−	30.9652i	0.00125687	−	1.06335i
$849$	12.6087	−	7.27962i	0.432729	−	0.249836i
$850$	4.67740	−	6.52323i	0.160433	−	0.223745i
$851$	−38.0557	+	29.2011i	−1.30453	+	1.00100i
$852$	−9.42753	−	10.7629i	−0.322982	−	0.368729i
$853$	−2.68024	−	6.47066i	−0.0917695	−	0.221551i	0.871330	−	0.490698i	$-0.163258\pi$
$853$	−2.68024	−	6.47066i	−0.0917695	−	0.221551i	−0.963099	+	0.269147i	$0.913258\pi$
$854$	25.4296	+	22.6950i	0.870183	+	0.776608i
$855$	−15.0346	−	15.0346i	−0.514172	−	0.514172i
$856$	−3.87298	−	0.642959i	−0.132376	−	0.0219759i
$857$	0.833516	+	3.11072i	0.0284724	+	0.106260i	0.978700	−	0.205297i	$-0.0658161\pi$
$857$	0.833516	+	3.11072i	0.0284724	+	0.106260i	−0.950227	+	0.311557i	$0.899149\pi$
$858$	1.70473	−	7.30142i	0.0581984	−	0.249266i
$859$	13.9113	+	10.6745i	0.474646	+	0.364209i	0.818209	−	0.574921i	$-0.194967\pi$
$859$	13.9113	+	10.6745i	0.474646	+	0.364209i	−0.343563	+	0.939130i	$0.611634\pi$
$860$	−13.5382	+	9.03435i	−0.461648	+	0.308069i
$861$	−4.31333	+	5.91378i	−0.146998	+	0.201541i
$862$	−2.21682	−	2.70283i	−0.0755051	−	0.0920587i
$863$	26.5199	+	45.9338i	0.902748	+	1.56361i	0.823911	+	0.566719i	$0.191787\pi$
$863$	26.5199	+	45.9338i	0.902748	+	1.56361i	0.0788371	+	0.996888i	$0.474879\pi$
$864$	−4.59588	−	28.0950i	−0.156355	−	0.955812i
$865$	−18.4164	+	31.8981i	−0.626175	+	1.08457i
$866$	6.33322	−	16.8119i	0.215212	−	0.571292i
$867$	−1.12168	+	2.70797i	−0.0380942	+	0.0919676i
$868$	25.3845	+	4.42561i	0.861606	+	0.150215i
$869$	42.3753	−	17.5524i	1.43748	−	0.595425i
$870$	−17.9325	−	16.8056i	−0.607970	−	0.569763i
$871$	0.264639	+	0.987647i	0.00896696	+	0.0334651i
$872$	−7.80163	−	3.54321i	−0.264196	−	0.119988i
$873$	−0.0316021	+	0.117941i	−0.00106957	+	0.00399168i
$874$	−40.4566	−	21.6399i	−1.36846	−	0.731980i
$875$	−19.2242	+	15.5088i	−0.649898	+	0.524292i
$876$	−4.10896	−	20.7211i	−0.138829	−	0.700102i
$877$	−5.19261	−	39.4418i	−0.175342	−	1.33186i	−0.822180	−	0.569228i	$-0.807242\pi$
$877$	−5.19261	−	39.4418i	−0.175342	−	1.33186i	0.646838	−	0.762628i	$-0.276091\pi$
$878$	11.5675	−	16.1324i	0.390384	−	0.544441i
$879$	10.5287	+	6.07877i	0.355126	+	0.205032i
$880$	16.8394	−	21.8918i	0.567654	−	0.737974i
$881$			7.86925i			0.265122i	0.991175	+	0.132561i	$0.0423200\pi$
$881$			7.86925i			0.265122i	−0.991175	+	0.132561i	$0.957680\pi$
$882$	−19.5563	−	0.974813i	−0.658493	−	0.0328237i
$883$	29.7770	+	12.3340i	1.00208	+	0.415073i	0.822558	−	0.568681i	$-0.192546\pi$
$883$	29.7770	+	12.3340i	1.00208	+	0.415073i	0.179518	+	0.983755i	$0.442546\pi$
$884$	−1.11993	+	16.9334i	−0.0376672	+	0.569533i
$885$	7.83477	+	1.03147i	0.263363	+	0.0346724i
$886$	5.33010	+	8.57715i	0.179068	+	0.288155i
$887$	−8.22929	+	30.7121i	−0.276313	+	1.03121i	0.678644	+	0.734467i	$0.262568\pi$
$887$	−8.22929	+	30.7121i	−0.276313	+	1.03121i	−0.954957	+	0.296746i	$0.904099\pi$
$888$	−16.0117	+	8.54022i	−0.537319	+	0.286591i
$889$	7.34285	+	4.00443i	0.246271	+	0.134304i
$890$	15.2881	+	50.4517i	0.512457	+	1.69114i
$891$	−1.85046	−	1.41991i	−0.0619927	−	0.0475687i
$892$	−0.896068	−	0.786768i	−0.0300026	−	0.0263429i
$893$	−27.8259	−	36.2634i	−0.931157	−	1.21351i
$894$	29.3137	+	11.0428i	0.980398	+	0.369326i
$895$	−39.0312			−1.30467
$896$	29.7164	−	3.59641i	0.992756	−	0.120148i
$897$	14.5351			0.485313
$898$	24.8852	+	9.37454i	0.830432	+	0.312832i
$899$	20.3464	+	26.5160i	0.678591	+	0.884357i
$900$	3.78228	+	3.32093i	0.126076	+	0.110698i
$901$	−27.3968	−	21.0223i	−0.912719	−	0.700354i
$902$	−3.09423	−	10.2112i	−0.103027	−	0.339995i
$903$	7.41894	−	4.52750i	0.246887	−	0.150666i
$904$	−13.8462	+	7.38516i	−0.460517	+	0.245627i
$905$	4.76910	−	17.7985i	0.158530	−	0.591643i
$906$	−2.90347	−	4.67224i	−0.0964614	−	0.155225i
$907$	−39.3447	−	5.17983i	−1.30642	−	0.171994i	−0.555018	−	0.831838i	$-0.687289\pi$
$907$	−39.3447	−	5.17983i	−1.30642	−	0.171994i	−0.751402	+	0.659844i	$0.770622\pi$
$908$	0.00974868	−	0.147401i	0.000323521	−	0.00489168i
$909$	−18.0923	−	7.49409i	−0.600085	−	0.248563i
$910$	−5.87601	+	16.8284i	−0.194788	+	0.557856i
$911$			7.15330i			0.236999i	0.992954	+	0.118500i	$0.0378085\pi$
$911$			7.15330i			0.236999i	−0.992954	+	0.118500i	$0.962192\pi$
$912$	−13.7579	−	10.5826i	−0.455569	−	0.350426i
$913$	−18.4426	−	10.6478i	−0.610361	−	0.352392i
$914$	22.4114	−	31.2555i	0.741302	−	1.03384i
$915$	3.01052	+	22.8672i	0.0995247	+	0.755965i
$916$	−8.45719	−	42.6489i	−0.279433	−	1.40916i
$917$	−15.1670	−	5.85423i	−0.500857	−	0.193324i
$918$	−27.9952	−	14.9744i	−0.923979	−	0.494228i
$919$	4.53725	−	16.9332i	0.149670	−	0.558576i	−0.849833	−	0.527052i	$-0.823297\pi$
$919$	4.53725	−	16.9332i	0.149670	−	0.558576i	0.999503	−	0.0315238i	$-0.0100360\pi$
$920$	48.7499	+	22.1404i	1.60724	+	0.729947i
$921$	−6.19476	−	23.1192i	−0.204124	−	0.761802i
$922$	17.5702	+	16.4661i	0.578645	+	0.542281i
$923$	−12.4356	+	5.15100i	−0.409323	+	0.169547i
$924$	−9.45850	+	11.3164i	−0.311162	+	0.372281i
$925$	3.09009	−	7.46013i	0.101601	−	0.245288i
$926$	−16.5793	+	44.0107i	−0.544829	+	1.44628i
$927$	0.999596	−	1.73135i	0.0328311	−	0.0568651i
$928$	31.5263	+	22.6620i	1.03490	+	0.743916i
$929$	16.9890	+	29.4258i	0.557391	+	0.965429i	0.997713	+	0.0675891i	$0.0215307\pi$
$929$	16.9890	+	29.4258i	0.557391	+	0.965429i	−0.440323	+	0.897840i	$0.645136\pi$
$930$	11.0577	+	13.4819i	0.362596	+	0.442090i
$931$	−22.9186	+	19.4283i	−0.751127	+	0.636738i
$932$	16.1740	−	10.7933i	0.529799	−	0.353547i
$933$	12.5387	+	9.62130i	0.410499	+	0.314987i
$934$	4.40684	−	18.8747i	0.144196	−	0.617599i
$935$	−7.97196	−	29.7517i	−0.260711	−	0.972986i
$936$	−10.4978	−	1.74275i	−0.343130	−	0.0569636i
$937$	6.26216	+	6.26216i	0.204576	+	0.204576i	0.801957	−	0.597381i	$-0.203792\pi$
$937$	6.26216	+	6.26216i	0.204576	+	0.204576i	−0.597381	+	0.801957i	$0.703792\pi$
$938$	0.409509	−	1.96917i	0.0133710	−	0.0642958i
$939$	−7.56712	−	18.2686i	−0.246944	−	0.596175i
$940$	35.1470	+	40.1253i	1.14637	+	1.30874i
$941$	10.7617	−	8.25774i	0.350821	−	0.269194i	−0.418285	−	0.908316i	$-0.637369\pi$
$941$	10.7617	−	8.25774i	0.350821	−	0.269194i	0.769106	+	0.639121i	$0.220702\pi$
$942$	7.17016	−	9.99970i	0.233616	−	0.325808i
$943$	17.9129	−	10.3420i	0.583326	−	0.336783i
$944$	−12.4842	−	0.0147563i	−0.406327	−	0.000480276i
$945$	−24.1464	−	22.9990i	−0.785483	−	0.748159i
$946$	−1.24551	+	12.6077i	−0.0404952	+	0.409913i
$947$	3.63223	+	27.5895i	0.118031	+	0.896538i	0.943333	+	0.331846i	$0.107672\pi$
$947$	3.63223	+	27.5895i	0.118031	+	0.896538i	−0.825302	+	0.564692i	$0.808995\pi$
$948$	14.8600	+	30.1780i	0.482629	+	0.980134i
$949$	−19.7030	−	2.59394i	−0.639585	−	0.0842029i
$950$	7.71931	−	0.250420i	0.250447	−	0.00812471i
$951$	6.40233	+	6.40233i	0.207610	+	0.207610i
$952$	16.9585	−	28.7536i	0.549629	−	0.931908i
$953$	−5.58095	+	5.58095i	−0.180785	+	0.180785i	−0.791698	−	0.610913i	$-0.790803\pi$
$953$	−5.58095	+	5.58095i	−0.180785	+	0.180785i	0.610913	+	0.791698i	$0.290803\pi$
$954$	14.8073	−	15.8002i	0.479403	−	0.511550i
$955$	−2.03046	+	15.4229i	−0.0657041	+	0.499072i
$956$	−29.2516	+	33.3153i	−0.946063	+	1.07749i
$957$	−18.9667	+	2.49702i	−0.613107	+	0.0807170i
$958$	−20.0886	+	16.4764i	−0.649034	+	0.532328i
$959$	−56.6001	−	13.6991i	−1.82771	−	0.442368i
$960$	16.8220	+	11.2833i	0.542926	+	0.364166i
$961$	3.64360	+	6.31091i	0.117536	+	0.203578i
$962$	2.77593	+	16.8445i	0.0894996	+	0.543090i
$963$	−1.67133	−	2.17812i	−0.0538579	−	0.0701890i
$964$	−14.9389	−	44.0941i	−0.481149	−	1.42017i
$965$	−25.2744	+	10.4690i	−0.813611	+	0.337009i
$966$	−25.5321	−	12.8680i	−0.821483	−	0.414022i
$967$	−27.8504	+	27.8504i	−0.895607	+	0.895607i	−0.995044	−	0.0994369i	$-0.968296\pi$
$967$	−27.8504	+	27.8504i	−0.895607	+	0.895607i	0.0994369	+	0.995044i	$0.468296\pi$
$968$	2.17479	+	9.36471i	0.0699005	+	0.300993i
$969$	−18.6974	+	5.00996i	−0.600647	+	0.160943i
$970$	−0.115404	−	0.185707i	−0.00370541	−	0.00596271i
$971$	14.1704	−	18.4672i	0.454750	−	0.592642i	−0.508562	−	0.861025i	$-0.669823\pi$
$971$	14.1704	−	18.4672i	0.454750	−	0.592642i	0.963312	+	0.268383i	$0.0864894\pi$
$972$	17.7417	−	26.5183i	0.569064	−	0.850576i
$973$	−5.00766	+	46.8126i	−0.160538	+	1.50074i
$974$	0.381065	−	3.85734i	0.0122101	−	0.123597i
$975$	−2.11898	+	1.22339i	−0.0678617	+	0.0391800i
$976$	−9.38911	−	35.2070i	−0.300538	−	1.12695i
$977$	52.9216	+	30.5543i	1.69311	+	0.977518i	0.951982	+	0.306155i	$0.0990427\pi$
$977$	52.9216	+	30.5543i	1.69311	+	0.977518i	0.741129	+	0.671363i	$0.234291\pi$
$978$	3.85145	+	8.50702i	0.123156	+	0.272025i
$979$	37.9115	+	15.7034i	1.21166	+	0.501884i
$980$	25.2200	−	24.3585i	0.805624	−	0.778102i
$981$	−2.29305	−	5.53590i	−0.0732113	−	0.176748i
$982$	−0.448504	−	13.8253i	−0.0143123	−	0.441183i
$983$	17.7684	−	4.76102i	0.566723	−	0.151853i	0.0359300	−	0.999354i	$-0.488561\pi$
$983$	17.7684	−	4.76102i	0.566723	−	0.151853i	0.530793	+	0.847501i	$0.321894\pi$
$984$	7.32595	−	2.74988i	0.233543	−	0.0876630i
$985$	−48.1559	−	12.9033i	−1.53437	−	0.411134i
$986$	41.4388	−	12.5569i	1.31968	−	0.399894i
$987$	−17.8850	−	22.1698i	−0.569287	−	0.705673i
$988$	−13.5822	+	9.06375i	−0.432108	+	0.288356i
$989$	−24.3500	+	3.20574i	−0.774285	+	0.101937i
$990$	19.0572	−	3.14056i	0.605676	−	0.0998137i
$991$	−10.8840	+	18.8517i	−0.345743	+	0.598845i	−0.985488	−	0.169742i	$-0.945706\pi$
$991$	−10.8840	+	18.8517i	−0.345743	+	0.598845i	0.639745	+	0.768587i	$0.279040\pi$
$992$	−20.0774	−	18.8603i	−0.637457	−	0.598814i
$993$	35.6885			1.13254
$994$	26.4044	+	1.96116i	0.837498	+	0.0622043i
$995$	20.1967	−	48.7591i	0.640278	−	1.54577i
$996$	6.91597	−	14.0033i	0.219141	−	0.443712i
$997$	−1.94386	+	14.7651i	−0.0615627	+	0.467615i	0.932700	+	0.360652i	$0.117446\pi$
$997$	−1.94386	+	14.7651i	−0.0615627	+	0.467615i	−0.994263	+	0.106963i	$0.965887\pi$
$998$	6.25434	−	26.7876i	0.197978	−	0.847947i
$999$	−30.8497	−	8.26616i	−0.976042	−	0.261530i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.109.3	yes	240
4.3	odd	2		896.2.bh.a.529.11		240
7.2	even	3	inner	224.2.bd.a.205.17	yes	240
28.23	odd	6		896.2.bh.a.401.20		240
32.5	even	8	inner	224.2.bd.a.165.17	yes	240
32.27	odd	8		896.2.bh.a.753.20		240
224.37	even	24	inner	224.2.bd.a.37.3	✓	240
224.219	odd	24		896.2.bh.a.625.11		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.3	✓	240	224.37	even	24	inner
224.2.bd.a.109.3	yes	240	1.1	even	1	trivial
224.2.bd.a.165.17	yes	240	32.5	even	8	inner
224.2.bd.a.205.17	yes	240	7.2	even	3	inner
896.2.bh.a.401.20		240	28.23	odd	6
896.2.bh.a.529.11		240	4.3	odd	2
896.2.bh.a.625.11		240	224.219	odd	24
896.2.bh.a.753.20		240	32.27	odd	8

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.bd (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32342 - 0.498548i) q^{2} +(0.615442 + 0.802059i) q^{3} +(1.50290 + 1.31958i) q^{4} +(-1.98693 - 1.52462i) q^{5} +(-0.414625 - 1.36829i) q^{6} +(2.32280 + 1.26674i) q^{7} +(-1.33110 - 2.49563i) q^{8} +(0.511927 - 1.91054i) q^{9} +O(q^{10})\)	\(q+(-1.32342 - 0.498548i) q^{2} +(0.615442 + 0.802059i) q^{3} +(1.50290 + 1.31958i) q^{4} +(-1.98693 - 1.52462i) q^{5} +(-0.414625 - 1.36829i) q^{6} +(2.32280 + 1.26674i) q^{7} +(-1.33110 - 2.49563i) q^{8} +(0.511927 - 1.91054i) q^{9} +(1.86945 + 3.00830i) q^{10} +(2.73340 + 0.359859i) q^{11} +(-0.133434 + 2.01754i) q^{12} +(1.75735 + 0.727920i) q^{13} +(-2.44251 - 2.83445i) q^{14} -2.53195i q^{15} +(0.517417 + 3.96639i) q^{16} +(3.86322 + 2.23043i) q^{17} +(-1.62999 + 2.27323i) q^{18} +(0.560244 + 4.25547i) q^{19} +(-0.974292 - 4.91327i) q^{20} +(0.413547 + 2.64262i) q^{21} +(-3.43804 - 1.83898i) q^{22} +(1.95628 - 7.30092i) q^{23} +(1.18243 - 2.60354i) q^{24} +(0.329313 + 1.22901i) q^{25} +(-1.96282 - 1.83947i) q^{26} +(4.64948 - 1.92588i) q^{27} +(1.81937 + 4.96889i) q^{28} +(-2.62657 + 6.34110i) q^{29} +(-1.26230 + 3.35085i) q^{30} +(2.43479 - 4.21718i) q^{31} +(1.29268 - 5.50718i) q^{32} +(1.39362 + 2.41382i) q^{33} +(-4.00070 - 4.87780i) q^{34} +(-2.68393 - 6.05831i) q^{35} +(3.29048 - 2.19582i) q^{36} +(-5.03484 - 3.86337i) q^{37} +(1.38012 - 5.91110i) q^{38} +(0.497714 + 1.85749i) q^{39} +(-1.16010 + 6.98807i) q^{40} +(1.93503 + 1.93503i) q^{41} +(0.770176 - 3.70348i) q^{42} +(-1.24347 - 3.00201i) q^{43} +(3.63316 + 4.14777i) q^{44} +(-3.93001 + 3.01560i) q^{45} +(-6.22884 + 8.68691i) q^{46} +(-9.22259 + 5.32466i) q^{47} +(-2.86284 + 2.85608i) q^{48} +(3.79076 + 5.88474i) q^{49} +(0.176901 - 1.79068i) q^{50} +(0.588648 + 4.47123i) q^{51} +(1.68058 + 3.41296i) q^{52} +(-7.67508 - 1.01044i) q^{53} +(-7.11337 + 0.230763i) q^{54} +(-4.88242 - 4.88242i) q^{55} +(0.0694365 - 7.48299i) q^{56} +(-3.06834 + 3.06834i) q^{57} +(6.63741 - 7.08249i) q^{58} +(-0.407380 + 3.09436i) q^{59} +(3.34111 - 3.80527i) q^{60} +(-9.03144 + 1.18901i) q^{61} +(-5.32472 + 4.36725i) q^{62} +(3.60925 - 3.78931i) q^{63} +(-4.45635 + 6.64387i) q^{64} +(-2.38193 - 4.12563i) q^{65} +(-0.640944 - 3.88929i) q^{66} +(0.327236 + 0.426462i) q^{67} +(2.86280 + 8.44994i) q^{68} +(7.05974 - 2.92424i) q^{69} +(0.531622 + 9.35577i) q^{70} +(-5.00372 + 5.00372i) q^{71} +(-5.44942 + 1.26553i) q^{72} +(-10.0917 + 2.70405i) q^{73} +(4.73715 + 7.62298i) q^{74} +(-0.783068 + 1.02051i) q^{75} +(-4.77345 + 7.13484i) q^{76} +(5.89328 + 4.29837i) q^{77} +(0.267363 - 2.70639i) q^{78} +(14.4077 - 8.31826i) q^{79} +(5.01919 - 8.66981i) q^{80} +(-0.732671 - 0.423008i) q^{81} +(-1.59616 - 3.52557i) q^{82} +(-7.13629 - 2.95595i) q^{83} +(-2.86563 + 4.51730i) q^{84} +(-4.27537 - 10.3217i) q^{85} +(0.148996 + 4.59286i) q^{86} +(-6.70244 + 1.79591i) q^{87} +(-2.74035 - 7.30056i) q^{88} +(14.3769 + 3.85227i) q^{89} +(6.70449 - 2.03162i) q^{90} +(3.15989 + 3.91692i) q^{91} +(12.5742 - 8.39109i) q^{92} +(4.88090 - 0.642582i) q^{93} +(14.8600 - 2.44888i) q^{94} +(5.37483 - 9.30949i) q^{95} +(5.21265 - 2.35254i) q^{96} -0.0617316 q^{97} +(-2.08295 - 9.67788i) q^{98} +(2.08682 - 5.03804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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