LMFDB - Embedded newform 160.2.u.a.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,2,Mod(43,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 6]))

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

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

chi := DirichletCharacter("160.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	160.u (of order $8$, degree $4$, 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:	$1.27760643234$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			43.2
Character	$\chi$	$=$	160.43
Dual form			160.2.u.a.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40216 - 0.184269i) q^{2} +(0.458849 - 1.10776i) q^{3} +(1.93209 + 0.516749i) q^{4} +(-0.222064 + 2.22501i) q^{5} +(-0.847505 + 1.46870i) q^{6} +4.27741i q^{7} +(-2.61387 - 1.08059i) q^{8} +(1.10473 + 1.10473i) q^{9} +O(q^{10})$	\(q+(-1.40216 - 0.184269i) q^{2} +(0.458849 - 1.10776i) q^{3} +(1.93209 + 0.516749i) q^{4} +(-0.222064 + 2.22501i) q^{5} +(-0.847505 + 1.46870i) q^{6} +4.27741i q^{7} +(-2.61387 - 1.08059i) q^{8} +(1.10473 + 1.10473i) q^{9} +(0.721371 - 3.07890i) q^{10} +(2.07866 - 5.01832i) q^{11} +(1.45897 - 1.90318i) q^{12} +(-0.690379 + 1.66672i) q^{13} +(0.788195 - 5.99760i) q^{14} +(2.36289 + 1.26694i) q^{15} +(3.46594 + 1.99681i) q^{16} +(1.37190 + 1.37190i) q^{17} +(-1.34544 - 1.75257i) q^{18} +(0.945045 + 2.28154i) q^{19} +(-1.57882 + 4.18418i) q^{20} +(4.73834 + 1.96269i) q^{21} +(-3.83933 + 6.65344i) q^{22} -4.98215i q^{23} +(-2.39641 + 2.39972i) q^{24} +(-4.90138 - 0.988190i) q^{25} +(1.27515 - 2.20979i) q^{26} +(5.05396 - 2.09342i) q^{27} +(-2.21035 + 8.26433i) q^{28} +(0.341673 + 0.824872i) q^{29} +(-3.07968 - 2.21186i) q^{30} -2.71175i q^{31} +(-4.49184 - 3.43851i) q^{32} +(-4.60531 - 4.60531i) q^{33} +(-1.67082 - 2.17641i) q^{34} +(-9.51729 - 0.949857i) q^{35} +(1.56357 + 2.70531i) q^{36} +(-1.72661 - 4.16841i) q^{37} +(-0.904684 - 3.37322i) q^{38} +(1.52955 + 1.52955i) q^{39} +(2.98477 - 5.57594i) q^{40} +(-7.66597 + 7.66597i) q^{41} +(-6.28224 - 3.62512i) q^{42} +(4.17851 - 1.73080i) q^{43} +(6.60936 - 8.62170i) q^{44} +(-2.70336 + 2.21272i) q^{45} +(-0.918058 + 6.98576i) q^{46} +(-2.80165 + 2.80165i) q^{47} +(3.80233 - 2.92319i) q^{48} -11.2962 q^{49} +(6.69041 + 2.28877i) q^{50} +(2.14923 - 0.890239i) q^{51} +(-2.19515 + 2.86350i) q^{52} +(-1.72165 - 4.15643i) q^{53} +(-7.47220 + 2.00401i) q^{54} +(10.7042 + 5.73943i) q^{55} +(4.62212 - 11.1806i) q^{56} +2.96103 q^{57} +(-0.327081 - 1.21956i) q^{58} +(3.28196 - 7.92336i) q^{59} +(3.91062 + 3.66886i) q^{60} +(5.01044 - 2.07539i) q^{61} +(-0.499693 + 3.80230i) q^{62} +(-4.72538 + 4.72538i) q^{63} +(5.66465 + 5.64904i) q^{64} +(-3.55517 - 1.90622i) q^{65} +(5.60874 + 7.30598i) q^{66} +(-8.26619 - 3.42397i) q^{67} +(1.94170 + 3.35955i) q^{68} +(-5.51903 - 2.28606i) q^{69} +(13.1697 + 3.08559i) q^{70} +(-4.04255 + 4.04255i) q^{71} +(-1.69386 - 4.08138i) q^{72} +15.9465 q^{73} +(1.65287 + 6.16293i) q^{74} +(-3.34367 + 4.97612i) q^{75} +(0.646927 + 4.89649i) q^{76} +(21.4654 + 8.89126i) q^{77} +(-1.86282 - 2.42652i) q^{78} -10.1034i q^{79} +(-5.21260 + 7.26835i) q^{80} -1.87217i q^{81} +(12.1615 - 9.33629i) q^{82} +(-4.63164 - 1.91849i) q^{83} +(8.14068 + 6.24062i) q^{84} +(-3.35714 + 2.74784i) q^{85} +(-6.17787 + 1.65688i) q^{86} +1.07054 q^{87} +(-10.8561 + 10.8711i) q^{88} +(-7.27190 + 7.27190i) q^{89} +(4.19827 - 2.60443i) q^{90} +(-7.12924 - 2.95303i) q^{91} +(2.57452 - 9.62596i) q^{92} +(-3.00397 - 1.24429i) q^{93} +(4.44461 - 3.41210i) q^{94} +(-5.28632 + 1.59609i) q^{95} +(-5.87013 + 3.39812i) q^{96} +(3.43179 - 3.43179i) q^{97} +(15.8391 + 2.08155i) q^{98} +(7.84024 - 3.24753i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8}+O(q^{10}) $ 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8	$ 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8} - 16 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} + 16 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} + 16 q^{19} + 24 q^{20} - 8 q^{21} - 20 q^{22} - 32 q^{24} - 4 q^{25} - 8 q^{26} - 16 q^{27} + 12 q^{28} + 8 q^{30} - 24 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 8 q^{36} - 4 q^{37} - 60 q^{38} + 16 q^{40} - 8 q^{41} + 60 q^{42} - 36 q^{43} + 16 q^{44} - 4 q^{45} - 8 q^{46} - 8 q^{47} - 24 q^{48} - 40 q^{49} - 12 q^{50} + 8 q^{51} - 56 q^{52} - 4 q^{53} - 56 q^{54} - 36 q^{55} + 40 q^{56} - 8 q^{57} - 36 q^{58} + 12 q^{60} - 40 q^{61} + 40 q^{62} + 56 q^{63} + 48 q^{64} - 8 q^{65} + 72 q^{66} + 20 q^{67} + 8 q^{68} + 24 q^{69} + 60 q^{70} + 24 q^{71} + 24 q^{72} - 8 q^{73} + 8 q^{75} + 56 q^{76} + 24 q^{77} + 32 q^{78} - 8 q^{80} + 84 q^{82} - 44 q^{83} + 56 q^{84} - 4 q^{85} + 24 q^{86} - 120 q^{87} + 104 q^{88} + 148 q^{90} - 8 q^{91} + 124 q^{92} + 8 q^{93} - 32 q^{94} + 24 q^{96} - 8 q^{97} - 16 q^{98}+O(q^{100}) $ 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8 - 16 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 + 16 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 + 16 * q^19 + 24 * q^20 - 8 * q^21 - 20 * q^22 - 32 * q^24 - 4 * q^25 - 8 * q^26 - 16 * q^27 + 12 * q^28 + 8 * q^30 - 24 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 8 * q^36 - 4 * q^37 - 60 * q^38 + 16 * q^40 - 8 * q^41 + 60 * q^42 - 36 * q^43 + 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 24 * q^48 - 40 * q^49 - 12 * q^50 + 8 * q^51 - 56 * q^52 - 4 * q^53 - 56 * q^54 - 36 * q^55 + 40 * q^56 - 8 * q^57 - 36 * q^58 + 12 * q^60 - 40 * q^61 + 40 * q^62 + 56 * q^63 + 48 * q^64 - 8 * q^65 + 72 * q^66 + 20 * q^67 + 8 * q^68 + 24 * q^69 + 60 * q^70 + 24 * q^71 + 24 * q^72 - 8 * q^73 + 8 * q^75 + 56 * q^76 + 24 * q^77 + 32 * q^78 - 8 * q^80 + 84 * q^82 - 44 * q^83 + 56 * q^84 - 4 * q^85 + 24 * q^86 - 120 * q^87 + 104 * q^88 + 148 * q^90 - 8 * q^91 + 124 * q^92 + 8 * q^93 - 32 * q^94 + 24 * q^96 - 8 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{8}\right)$

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 $

$2$	−1.40216	−	0.184269i	−0.991475	−	0.130298i
$2$	−1.40216	−	0.184269i	−0.991475	−	0.130298i
$3$	0.458849	−	1.10776i	0.264917	−	0.639566i	−0.734313	−	0.678811i	$-0.762495\pi$
$3$	0.458849	−	1.10776i	0.264917	−	0.639566i	0.999230	+	0.0392455i	$0.0124954\pi$
$4$	1.93209	+	0.516749i	0.966045	+	0.258375i
$5$	−0.222064	+	2.22501i	−0.0993100	+	0.995057i
$5$	−0.222064	+	2.22501i	−0.0993100	+	0.995057i
$6$	−0.847505	+	1.46870i	−0.345993	+	0.599595i
$7$			4.27741i			1.61671i	0.588697	+	0.808354i	$0.299641\pi$
$7$			4.27741i			1.61671i	−0.588697	+	0.808354i	$0.700359\pi$
$8$	−2.61387	−	1.08059i	−0.924143	−	0.382046i
$9$	1.10473	+	1.10473i	0.368243	+	0.368243i
$10$	0.721371	−	3.07890i	0.228117	−	0.973634i
$11$	2.07866	−	5.01832i	0.626738	−	1.51308i	−0.216914	−	0.976191i	$-0.569599\pi$
$11$	2.07866	−	5.01832i	0.626738	−	1.51308i	0.843653	−	0.536890i	$-0.180401\pi$
$12$	1.45897	−	1.90318i	0.421169	−	0.549401i
$13$	−0.690379	+	1.66672i	−0.191477	+	0.462265i	−0.990239	−	0.139382i	$-0.955489\pi$
$13$	−0.690379	+	1.66672i	−0.191477	+	0.462265i	0.798762	+	0.601647i	$0.205489\pi$
$14$	0.788195	−	5.99760i	0.210654	−	1.60292i
$15$	2.36289	+	1.26694i	0.610095	+	0.327122i
$16$	3.46594	+	1.99681i	0.866485	+	0.499203i
$17$	1.37190	+	1.37190i	0.332734	+	0.332734i	0.853624	−	0.520890i	$-0.174400\pi$
$17$	1.37190	+	1.37190i	0.332734	+	0.332734i	−0.520890	+	0.853624i	$0.674400\pi$
$18$	−1.34544	−	1.75257i	−0.317123	−	0.413085i
$19$	0.945045	+	2.28154i	0.216808	+	0.523421i	0.994441	−	0.105298i	$-0.0335796\pi$
$19$	0.945045	+	2.28154i	0.216808	+	0.523421i	−0.777633	+	0.628719i	$0.783580\pi$
$20$	−1.57882	+	4.18418i	−0.353035	+	0.935610i
$21$	4.73834	+	1.96269i	1.03399	+	0.428293i
$22$	−3.83933	+	6.65344i	−0.818547	+	1.41852i
$23$		−	4.98215i		−	1.03885i	−0.854516	−	0.519425i	$-0.826146\pi$
$23$		−	4.98215i		−	1.03885i	0.854516	−	0.519425i	$-0.173854\pi$
$24$	−2.39641	+	2.39972i	−0.489165	+	0.489840i
$25$	−4.90138	−	0.988190i	−0.980275	−	0.197638i
$26$	1.27515	−	2.20979i	0.250077	−	0.433375i
$27$	5.05396	−	2.09342i	0.972635	−	0.402879i
$28$	−2.21035	+	8.26433i	−0.417716	+	1.56181i
$29$	0.341673	+	0.824872i	0.0634471	+	0.153175i	0.952423	−	0.304779i	$-0.0985826\pi$
$29$	0.341673	+	0.824872i	0.0634471	+	0.153175i	−0.888976	+	0.457954i	$0.848583\pi$
$30$	−3.07968	−	2.21186i	−0.562271	−	0.403828i
$31$		−	2.71175i		−	0.487045i	−0.969895	−	0.243523i	$-0.921697\pi$
$31$		−	2.71175i		−	0.487045i	0.969895	−	0.243523i	$-0.0783030\pi$
$32$	−4.49184	−	3.43851i	−0.794053	−	0.607849i
$33$	−4.60531	−	4.60531i	−0.801681	−	0.801681i
$34$	−1.67082	−	2.17641i	−0.286543	−	0.373252i
$35$	−9.51729	−	0.949857i	−1.60872	−	0.160555i
$36$	1.56357	+	2.70531i	0.260595	+	0.450884i
$37$	−1.72661	−	4.16841i	−0.283853	−	0.685282i	0.716065	−	0.698033i	$-0.245941\pi$
$37$	−1.72661	−	4.16841i	−0.283853	−	0.685282i	−0.999919	+	0.0127508i	$0.995941\pi$
$38$	−0.904684	−	3.37322i	−0.146759	−	0.547209i
$39$	1.52955	+	1.52955i	0.244924	+	0.244924i
$40$	2.98477	−	5.57594i	0.471934	−	0.881634i
$41$	−7.66597	+	7.66597i	−1.19722	+	1.19722i	−0.222229	+	0.974994i	$0.571333\pi$
$41$	−7.66597	+	7.66597i	−1.19722	+	1.19722i	−0.974994	+	0.222229i	$0.928667\pi$
$42$	−6.28224	−	3.62512i	−0.969370	−	0.559369i
$43$	4.17851	−	1.73080i	0.637217	−	0.263944i	−0.0405987	−	0.999176i	$-0.512927\pi$
$43$	4.17851	−	1.73080i	0.637217	−	0.263944i	0.677816	+	0.735231i	$0.262927\pi$
$44$	6.60936	−	8.62170i	0.996399	−	1.29977i
$45$	−2.70336	+	2.21272i	−0.402993	+	0.329853i
$46$	−0.918058	+	6.98576i	−0.135360	+	1.02999i
$47$	−2.80165	+	2.80165i	−0.408663	+	0.408663i	−0.881272	−	0.472609i	$-0.843312\pi$
$47$	−2.80165	+	2.80165i	−0.408663	+	0.408663i	0.472609	+	0.881272i	$0.343312\pi$
$48$	3.80233	−	2.92319i	0.548820	−	0.421927i
$49$	−11.2962			−1.61374
$50$	6.69041	+	2.28877i	0.946166	+	0.323681i
$51$	2.14923	−	0.890239i	0.300952	−	0.124658i
$52$	−2.19515	+	2.86350i	−0.304413	+	0.397096i
$53$	−1.72165	−	4.15643i	−0.236487	−	0.570930i	0.760428	−	0.649423i	$-0.224989\pi$
$53$	−1.72165	−	4.15643i	−0.236487	−	0.570930i	−0.996915	+	0.0784926i	$0.974989\pi$
$54$	−7.47220	+	2.00401i	−1.01684	+	0.272712i
$55$	10.7042	+	5.73943i	1.44336	+	0.773904i
$56$	4.62212	−	11.1806i	0.617657	−	1.49407i
$57$	2.96103			0.392198
$58$	−0.327081	−	1.21956i	−0.0429478	−	0.160136i
$59$	3.28196	−	7.92336i	0.427275	−	1.03153i	−0.552873	−	0.833266i	$-0.686468\pi$
$59$	3.28196	−	7.92336i	0.427275	−	1.03153i	0.980148	−	0.198268i	$-0.0635316\pi$
$60$	3.91062	+	3.66886i	0.504859	+	0.473648i
$61$	5.01044	−	2.07539i	0.641521	−	0.265727i	−0.0381185	−	0.999273i	$-0.512136\pi$
$61$	5.01044	−	2.07539i	0.641521	−	0.265727i	0.679639	+	0.733547i	$0.262136\pi$
$62$	−0.499693	+	3.80230i	−0.0634611	+	0.482893i
$63$	−4.72538	+	4.72538i	−0.595342	+	0.595342i
$64$	5.66465	+	5.64904i	0.708082	+	0.706130i
$65$	−3.55517	−	1.90622i	−0.440965	−	0.236438i
$66$	5.60874	+	7.30598i	0.690389	+	0.899304i
$67$	−8.26619	−	3.42397i	−1.00988	−	0.418304i	−0.184466	−	0.982839i	$-0.559056\pi$
$67$	−8.26619	−	3.42397i	−1.00988	−	0.418304i	−0.825409	+	0.564535i	$0.809056\pi$
$68$	1.94170	+	3.35955i	0.235466	+	0.407406i
$69$	−5.51903	−	2.28606i	−0.664413	−	0.275209i
$70$	13.1697	+	3.08559i	1.57408	+	0.368799i
$71$	−4.04255	+	4.04255i	−0.479762	+	0.479762i	−0.905056	−	0.425293i	$-0.860171\pi$
$71$	−4.04255	+	4.04255i	−0.479762	+	0.479762i	0.425293	+	0.905056i	$0.360171\pi$
$72$	−1.69386	−	4.08138i	−0.199624	−	0.480996i
$73$	15.9465			1.86640			0.933200	−	0.359357i	$-0.117004\pi$
$73$	15.9465			1.86640			0.933200	+	0.359357i	$0.117004\pi$
$74$	1.65287	+	6.16293i	0.192142	+	0.716426i
$75$	−3.34367	+	4.97612i	−0.386094	+	0.574593i
$76$	0.646927	+	4.89649i	0.0742076	+	0.561666i
$77$	21.4654	+	8.89126i	2.44621	+	1.01325i
$78$	−1.86282	−	2.42652i	−0.210923	−	0.274749i
$79$		−	10.1034i		−	1.13672i	−0.822781	−	0.568359i	$-0.807579\pi$
$79$		−	10.1034i		−	1.13672i	0.822781	−	0.568359i	$-0.192421\pi$
$80$	−5.21260	+	7.26835i	−0.582786	+	0.812626i
$81$		−	1.87217i		−	0.208019i
$82$	12.1615	−	9.33629i	1.34301	−	1.03102i
$83$	−4.63164	−	1.91849i	−0.508389	−	0.210582i	0.113719	−	0.993513i	$-0.463724\pi$
$83$	−4.63164	−	1.91849i	−0.508389	−	0.210582i	−0.622108	+	0.782931i	$0.713724\pi$
$84$	8.14068	+	6.24062i	0.888221	+	0.680907i
$85$	−3.35714	+	2.74784i	−0.364133	+	0.298045i
$86$	−6.17787	+	1.65688i	−0.666177	+	0.178666i
$87$	1.07054			0.114774
$88$	−10.8561	+	10.8711i	−1.15726	+	1.15886i
$89$	−7.27190	+	7.27190i	−0.770820	+	0.770820i	−0.978250	−	0.207430i	$-0.933490\pi$
$89$	−7.27190	+	7.27190i	−0.770820	+	0.770820i	0.207430	+	0.978250i	$0.433490\pi$
$90$	4.19827	−	2.60443i	0.442537	−	0.274531i
$91$	−7.12924	−	2.95303i	−0.747348	−	0.309562i
$92$	2.57452	−	9.62596i	0.268413	−	1.00358i
$93$	−3.00397	−	1.24429i	−0.311497	−	0.129026i
$94$	4.44461	−	3.41210i	0.458427	−	0.351931i
$95$	−5.28632	+	1.59609i	−0.542365	+	0.163755i
$96$	−5.87013	+	3.39812i	−0.599117	+	0.346820i
$97$	3.43179	−	3.43179i	0.348446	−	0.348446i	−0.511085	−	0.859530i	$-0.670756\pi$
$97$	3.43179	−	3.43179i	0.348446	−	0.348446i	0.859530	+	0.511085i	$0.170756\pi$
$98$	15.8391	+	2.08155i	1.59999	+	0.210268i
$99$	7.84024	−	3.24753i	0.787974	−	0.326390i
$100$	−8.95925	−	4.44206i	−0.895925	−	0.444206i
$101$	4.79964	−	11.5873i	0.477582	−	1.15298i	−0.483158	−	0.875533i	$-0.660510\pi$
$101$	4.79964	−	11.5873i	0.477582	−	1.15298i	0.960740	−	0.277451i	$-0.0894896\pi$
$102$	−3.17760	+	0.852218i	−0.314629	+	0.0843822i
$103$	−2.36139			−0.232675			−0.116338	−	0.993210i	$-0.537115\pi$
$103$	−2.36139			−0.232675			−0.116338	+	0.993210i	$0.537115\pi$
$104$	3.60560	−	3.61058i	0.353558	−	0.354047i
$105$	−5.41922	+	10.1070i	−0.528861	+	0.986346i
$106$	1.64812	+	6.14522i	0.160080	+	0.596877i
$107$	0.696113	+	1.68056i	0.0672957	+	0.162466i	0.953949	−	0.299968i	$-0.0969761\pi$
$107$	0.696113	+	1.68056i	0.0672957	+	0.162466i	−0.886653	+	0.462434i	$0.846976\pi$
$108$	10.8465	−	1.43304i	1.04370	−	0.137895i
$109$	9.77735	−	4.04991i	0.936500	−	0.387911i	0.138359	−	0.990382i	$-0.455817\pi$
$109$	9.77735	−	4.04991i	0.936500	−	0.387911i	0.798141	+	0.602471i	$0.205817\pi$
$110$	−13.9514	−	10.0200i	−1.33022	−	0.955373i
$111$	−5.40985			−0.513481
$112$	−8.54118	+	14.8252i	−0.807065	+	1.40085i
$113$	10.3400	−	10.3400i	0.972709	−	0.972709i	−0.0269280	−	0.999637i	$-0.508572\pi$
$113$	10.3400	−	10.3400i	0.972709	−	0.972709i	0.999637	+	0.0269280i	$0.00857248\pi$
$114$	−4.15183	−	0.545628i	−0.388855	−	0.0511027i
$115$	11.0854	+	1.10636i	1.03371	+	0.103168i
$116$	0.233891	+	1.77029i	0.0217162	+	0.164367i
$117$	−2.60396	+	1.07860i	−0.240736	+	0.0997162i
$118$	−6.06186	+	10.5050i	−0.558040	+	0.967067i
$119$	−5.86816	+	5.86816i	−0.537933	+	0.537933i
$120$	−4.80725	−	5.86493i	−0.438840	−	0.535392i
$121$	−13.0845	−	13.0845i	−1.18950	−	1.18950i
$122$	−7.40785	+	1.98675i	−0.670675	+	0.179872i
$123$	4.97453	+	12.0096i	0.448539	+	1.08287i
$124$	1.40130	−	5.23935i	0.125840	−	0.470507i
$125$	3.28716	−	10.6862i	0.294012	−	0.955802i
$126$	7.49647	−	5.75498i	0.667838	−	0.512695i
$127$	−3.51939	−	3.51939i	−0.312296	−	0.312296i	0.533503	−	0.845798i	$-0.320875\pi$
$127$	−3.51939	−	3.51939i	−0.312296	−	0.312296i	−0.845798	+	0.533503i	$0.820875\pi$
$128$	−6.90179	−	8.96467i	−0.610038	−	0.792372i
$129$		−	5.42297i		−	0.477466i
$130$	4.63365	+	3.32793i	0.406398	+	0.291879i
$131$	0.478118	+	1.15428i	0.0417734	+	0.100850i	0.943389	−	0.331688i	$-0.107618\pi$
$131$	0.478118	+	1.15428i	0.0417734	+	0.100850i	−0.901616	+	0.432538i	$0.857618\pi$
$132$	−6.51807	−	11.2777i	−0.567325	−	0.981593i
$133$	−9.75908	+	4.04234i	−0.846219	+	0.350516i
$134$	10.9596	+	6.32415i	0.946762	+	0.546323i
$135$	3.53559	+	11.7100i	0.304295	+	1.00784i
$136$	−2.10351	−	5.06842i	−0.180374	−	0.434613i
$137$		−	5.57339i		−	0.476167i	−0.971245	−	0.238084i	$-0.923481\pi$
$137$		−	5.57339i		−	0.476167i	0.971245	−	0.238084i	$-0.0765192\pi$
$138$	7.31729	+	4.22240i	0.622889	+	0.359434i
$139$	−6.59735	−	2.73271i	−0.559580	−	0.231786i	0.0849227	−	0.996388i	$-0.472936\pi$
$139$	−6.59735	−	2.73271i	−0.559580	−	0.231786i	−0.644503	+	0.764602i	$0.722936\pi$
$140$	−17.8974	−	6.75326i	−1.51261	−	0.570755i
$141$	1.81802	+	4.38909i	0.153105	+	0.369628i
$142$	6.41321	−	4.92337i	0.538184	−	0.413160i
$143$	6.92908	+	6.92908i	0.579439	+	0.579439i
$144$	1.62299	+	6.03487i	0.135249	+	0.502906i
$145$	−1.91122	+	0.577053i	−0.158719	+	0.0479216i
$146$	−22.3595	−	2.93846i	−1.85049	−	0.243189i
$147$	−5.18326	+	12.5135i	−0.427508	+	1.03210i
$148$	−1.18195	−	8.94597i	−0.0971553	−	0.735354i
$149$	−7.77412	+	18.7684i	−0.636881	+	1.53757i	0.193933	+	0.981015i	$0.437876\pi$
$149$	−7.77412	+	18.7684i	−0.636881	+	1.53757i	−0.830813	+	0.556551i	$0.812124\pi$
$150$	5.60530	−	6.36116i	0.457671	−	0.519387i
$151$	−5.93512	−	5.93512i	−0.482993	−	0.482993i	0.423093	−	0.906086i	$-0.360944\pi$
$151$	−5.93512	−	5.93512i	−0.482993	−	0.482993i	−0.906086	+	0.423093i	$0.860944\pi$
$152$	−0.00481927	−	6.98486i	−0.000390895	−	0.566547i
$153$			3.03115i			0.245054i
$154$	−28.4595	−	16.4224i	−2.29333	−	1.32335i
$155$	6.03369	+	0.602182i	0.484637	+	0.0483684i
$156$	2.16483	+	3.74562i	0.173325	+	0.299889i
$157$	−1.69597	+	4.09445i	−0.135354	+	0.326772i	−0.976994	−	0.213265i	$-0.931590\pi$
$157$	−1.69597	+	4.09445i	−0.135354	+	0.326772i	0.841641	+	0.540038i	$0.181590\pi$
$158$	−1.86174	+	14.1665i	−0.148112	+	1.12703i
$159$	−5.39431			−0.427797
$160$	8.64821	−	9.23084i	0.683701	−	0.729762i
$161$	21.3107			1.67952
$162$	−0.344984	+	2.62508i	−0.0271045	+	0.206245i
$163$	−5.01273	+	12.1018i	−0.392628	+	0.947887i	0.596738	+	0.802436i	$0.296463\pi$
$163$	−5.01273	+	12.1018i	−0.392628	+	0.947887i	−0.989365	+	0.145451i	$0.953537\pi$
$164$	−18.7727	+	10.8500i	−1.46590	+	0.847239i
$165$	11.2695	−	9.22420i	0.877333	−	0.718103i
$166$	6.14077	+	3.54349i	0.476616	+	0.275028i
$167$			10.2726i			0.794921i	0.917619	+	0.397460i	$0.130108\pi$
$167$			10.2726i			0.794921i	−0.917619	+	0.397460i	$0.869892\pi$
$168$	−10.2646	−	10.2504i	−0.791928	−	0.790836i
$169$	6.89105	+	6.89105i	0.530081	+	0.530081i
$170$	5.21358	−	3.23429i	0.399863	−	0.248058i
$171$	−1.47647	+	3.56451i	−0.112908	+	0.272585i
$172$	8.96765	−	1.18481i	0.683777	−	0.0903409i
$173$	5.84807	−	14.1185i	0.444621	−	1.07341i	−0.529688	−	0.848193i	$-0.677691\pi$
$173$	5.84807	−	14.1185i	0.444621	−	1.07341i	0.974309	−	0.225217i	$-0.0723091\pi$
$174$	−1.50106	−	0.197267i	−0.113795	−	0.0149548i
$175$	4.22689	−	20.9652i	0.319523	−	1.58482i
$176$	17.2251	−	13.2425i	1.29839	−	0.998192i
$177$	−7.27126	−	7.27126i	−0.546541	−	0.546541i
$178$	11.5363	−	8.85636i	0.864685	−	0.663812i
$179$	−1.11617	−	2.69467i	−0.0834263	−	0.201409i	0.876662	−	0.481108i	$-0.159765\pi$
$179$	−1.11617	−	2.69467i	−0.0834263	−	0.201409i	−0.960088	+	0.279699i	$0.909765\pi$
$180$	−6.36656	+	2.87821i	−0.474535	+	0.214529i
$181$	−3.51290	−	1.45509i	−0.261112	−	0.108156i	0.248287	−	0.968686i	$-0.420132\pi$
$181$	−3.51290	−	1.45509i	−0.261112	−	0.108156i	−0.509399	+	0.860530i	$0.670132\pi$
$182$	9.45217	+	5.45431i	0.700641	+	0.404301i
$183$		−	6.50265i		−	0.480690i
$184$	−5.38366	+	13.0227i	−0.396888	+	0.960046i
$185$	9.65819	−	2.91608i	0.710084	−	0.214395i
$186$	3.98276	+	2.29822i	0.292030	+	0.168514i
$187$	9.73632	−	4.03291i	0.711990	−	0.294916i
$188$	−6.86079	+	3.96529i	−0.500375	+	0.289198i
$189$	8.95441	+	21.6178i	0.651337	+	1.57247i
$190$	7.70636	−	1.26386i	0.559078	−	0.0916903i
$191$			5.51937i			0.399367i	0.979860	+	0.199684i	$0.0639915\pi$
$191$			5.51937i			0.399367i	−0.979860	+	0.199684i	$0.936009\pi$
$192$	8.85701	−	3.68302i	0.639200	−	0.265799i
$193$	7.98212	+	7.98212i	0.574565	+	0.574565i	0.933401	−	0.358836i	$-0.116826\pi$
$193$	7.98212	+	7.98212i	0.574565	+	0.574565i	−0.358836	+	0.933401i	$0.616826\pi$
$194$	−5.44428	+	4.17954i	−0.390877	+	0.300073i
$195$	−3.74292	+	3.06361i	−0.268036	+	0.219390i
$196$	−21.8253	−	5.83731i	−1.55895	−	0.416951i
$197$	3.90256	+	9.42161i	0.278046	+	0.671262i	0.999781	−	0.0209069i	$-0.00665537\pi$
$197$	3.90256	+	9.42161i	0.278046	+	0.671262i	−0.721736	+	0.692169i	$0.756655\pi$
$198$	−11.5917	+	3.10884i	−0.823784	+	0.220935i
$199$	1.93098	+	1.93098i	0.136884	+	0.136884i	0.772229	−	0.635345i	$-0.219142\pi$
$199$	1.93098	+	1.93098i	0.136884	+	0.136884i	−0.635345	+	0.772229i	$0.719142\pi$
$200$	11.7437	+	7.87938i	0.830408	+	0.557156i
$201$	−7.58587	+	7.58587i	−0.535066	+	0.535066i
$202$	−8.86504	+	15.3629i	−0.623742	+	1.08093i
$203$	−3.52831	+	1.46147i	−0.247639	+	0.102575i
$204$	4.61253	−	0.609410i	0.322942	−	0.0426672i
$205$	−15.3546	−	18.7592i	−1.07241	−	1.31020i
$206$	3.31105	+	0.435133i	0.230691	+	0.0303171i
$207$	5.50393	−	5.50393i	0.382550	−	0.382550i
$208$	−5.72094	+	4.39820i	−0.396676	+	0.304960i
$209$	13.4139			0.927860
$210$	9.46101	−	13.1731i	0.652872	−	0.909027i
$211$	−21.1201	+	8.74824i	−1.45397	+	0.602254i	−0.963140	−	0.269002i	$-0.913306\pi$
$211$	−21.1201	+	8.74824i	−1.45397	+	0.602254i	−0.490830	+	0.871256i	$0.663306\pi$
$212$	−1.17855	−	8.92026i	−0.0809431	−	0.612646i
$213$	2.62325	+	6.33310i	0.179742	+	0.433937i
$214$	−0.666383	−	2.48469i	−0.0455530	−	0.169850i
$215$	2.92315	+	9.68160i	0.199357	+	0.660280i
$216$	−15.4725	+	0.0106754i	−1.05277	+	0.000726371i
$217$	11.5993			0.787409
$218$	−14.4557	+	3.87694i	−0.979060	+	0.262580i
$219$	7.31706	−	17.6649i	0.494441	−	1.19369i
$220$	17.7157	+	16.6205i	1.19439	+	1.12055i
$221$	−3.23370	+	1.33944i	−0.217522	+	0.0901006i
$222$	7.58547	+	0.996871i	0.509103	+	0.0669056i
$223$	14.3719	−	14.3719i	0.962414	−	0.962414i	−0.0369045	−	0.999319i	$-0.511750\pi$
$223$	14.3719	−	14.3719i	0.962414	−	0.962414i	0.999319	+	0.0369045i	$0.0117497\pi$
$224$	14.7079	−	19.2134i	0.982714	−	1.28375i
$225$	−4.32301	−	6.50638i	−0.288201	−	0.433759i
$226$	−16.4037	+	12.5930i	−1.09116	+	0.837675i
$227$	−0.483213	−	0.200153i	−0.0320720	−	0.0132846i	0.366590	−	0.930383i	$-0.380525\pi$
$227$	−0.483213	−	0.200153i	−0.0320720	−	0.0132846i	−0.398662	+	0.917098i	$0.630525\pi$
$228$	5.72098	+	1.53011i	0.378881	+	0.101334i
$229$	−8.71794	−	3.61109i	−0.576098	−	0.238628i	0.0755591	−	0.997141i	$-0.475926\pi$
$229$	−8.71794	−	3.61109i	−0.576098	−	0.238628i	−0.651657	+	0.758514i	$0.725926\pi$
$230$	−15.3395	−	3.59398i	−1.01146	−	0.236980i
$231$	19.6988	−	19.6988i	1.29608	−	1.29608i
$232$	−0.00174237	−	2.52532i	−0.000114392	−	0.165795i
$233$	−8.63392			−0.565627			−0.282814	−	0.959175i	$-0.591268\pi$
$233$	−8.63392			−0.565627			−0.282814	+	0.959175i	$0.591268\pi$
$234$	3.84991	−	1.03253i	0.251677	−	0.0674986i
$235$	−5.61157	−	6.85586i	−0.366058	−	0.447227i
$236$	10.4354	−	13.6127i	0.679289	−	0.886111i
$237$	−11.1921	−	4.63592i	−0.727006	−	0.301136i
$238$	9.30941	−	7.14676i	0.603439	−	0.463256i
$239$			23.0934i			1.49379i	0.664942	+	0.746895i	$0.268456\pi$
$239$			23.0934i			1.49379i	−0.664942	+	0.746895i	$0.731544\pi$
$240$	5.65979	+	9.10938i	0.365338	+	0.588008i
$241$			14.0069i			0.902266i	0.892457	+	0.451133i	$0.148980\pi$
$241$			14.0069i			0.902266i	−0.892457	+	0.451133i	$0.851020\pi$
$242$	15.9355	+	20.7577i	1.02437	+	1.33435i
$243$	13.0880	+	5.42121i	0.839594	+	0.347771i
$244$	10.7531	−	1.42070i	0.688395	−	0.0909510i
$245$	2.50848	−	25.1342i	0.160261	−	1.60577i
$246$	−4.76208	−	17.7560i	−0.303619	−	1.13208i
$247$	−4.45513			−0.283473
$248$	−2.93029	+	7.08817i	−0.186074	+	0.450099i
$249$	−4.25045	+	4.25045i	−0.269361	+	0.269361i
$250$	−6.57825	+	14.3780i	−0.416045	+	0.909344i
$251$	−9.23350	−	3.82464i	−0.582814	−	0.241409i	0.0717419	−	0.997423i	$-0.477144\pi$
$251$	−9.23350	−	3.82464i	−0.582814	−	0.241409i	−0.654556	+	0.756014i	$0.727144\pi$
$252$	−11.5717	+	6.68802i	−0.728948	+	0.421306i
$253$	−25.0020	−	10.3562i	−1.57186	−	0.651087i
$254$	4.28623	+	5.58326i	0.268942	+	0.350325i
$255$	1.50353	+	4.97975i	0.0941546	+	0.311844i
$256$	8.02548	+	13.8417i	0.501593	+	0.865104i
$257$	−0.769154	+	0.769154i	−0.0479785	+	0.0479785i	−0.730689	−	0.682710i	$-0.760801\pi$
$257$	−0.769154	+	0.769154i	−0.0479785	+	0.0479785i	0.682710	+	0.730689i	$0.260801\pi$
$258$	−0.999287	+	7.60385i	−0.0622129	+	0.473395i
$259$	17.8300	−	7.38542i	1.10790	−	0.458908i
$260$	−5.88387	−	5.52012i	−0.364902	−	0.342343i
$261$	−0.533804	+	1.28872i	−0.0330416	+	0.0797696i
$262$	−0.457699	−	1.70658i	−0.0282767	−	0.105433i
$263$	−11.4195			−0.704154			−0.352077	−	0.935971i	$-0.614525\pi$
$263$	−11.4195			−0.704154			−0.352077	+	0.935971i	$0.614525\pi$
$264$	7.06124	+	17.0141i	0.434589	+	1.04715i
$265$	9.63044	−	2.90770i	0.591593	−	0.178619i
$266$	14.4286	−	3.86970i	0.884677	−	0.237266i
$267$	4.71882	+	11.3922i	0.288787	+	0.697193i
$268$	−14.2017	−	10.8870i	−0.867506	−	0.665027i
$269$	−6.59730	+	2.73269i	−0.402244	+	0.166615i	−0.574628	−	0.818415i	$-0.694853\pi$
$269$	−6.59730	+	2.73269i	−0.402244	+	0.166615i	0.172384	+	0.985030i	$0.444853\pi$
$270$	−2.79965	−	17.0708i	−0.170381	−	1.03889i
$271$	2.55220			0.155035			0.0775176	−	0.996991i	$-0.475301\pi$
$271$	2.55220			0.155035			0.0775176	+	0.996991i	$0.475301\pi$
$272$	2.01549	+	7.49433i	0.122207	+	0.454411i
$273$	−6.54250	+	6.54250i	−0.395970	+	0.395970i
$274$	−1.02701	+	7.81477i	−0.0620437	+	0.472108i
$275$	−15.1473	+	22.5426i	−0.913418	+	1.35937i
$276$	−9.48194	−	7.26882i	−0.570746	−	0.437532i
$277$	−9.71609	+	4.02454i	−0.583784	+	0.241811i	−0.654974	−	0.755652i	$-0.727320\pi$
$277$	−9.71609	+	4.02454i	−0.583784	+	0.241811i	0.0711901	+	0.997463i	$0.477320\pi$
$278$	8.74697	+	5.04739i	0.524609	+	0.302722i
$279$	2.99575	−	2.99575i	0.179351	−	0.179351i
$280$	23.8506	+	12.7671i	1.42534	+	0.762979i
$281$	18.4753	+	18.4753i	1.10215	+	1.10215i	0.994151	+	0.107995i	$0.0344430\pi$
$281$	18.4753	+	18.4753i	1.10215	+	1.10215i	0.107995	+	0.994151i	$0.465557\pi$
$282$	−1.74038	−	6.48920i	−0.103638	−	0.386426i
$283$	7.42585	+	17.9276i	0.441421	+	1.06568i	0.975450	+	0.220219i	$0.0706772\pi$
$283$	7.42585	+	17.9276i	0.441421	+	1.06568i	−0.534029	+	0.845466i	$0.679323\pi$
$284$	−9.89955	+	5.72158i	−0.587430	+	0.339513i
$285$	−0.657539	+	6.58834i	−0.0389492	+	0.390260i
$286$	−8.43884	−	10.9925i	−0.498999	−	0.649999i
$287$	−32.7905	−	32.7905i	−1.93556	−	1.93556i
$288$	−1.16364	−	8.76090i	−0.0685684	−	0.516241i
$289$		−	13.2358i		−	0.778576i
$290$	2.78617	−	0.456939i	0.163610	−	0.0268324i
$291$	−2.22693	−	5.37628i	−0.130545	−	0.315163i
$292$	30.8101	+	8.24036i	1.80303	+	0.482231i
$293$	−29.6293	+	12.2729i	−1.73096	+	0.716989i	−0.731586	+	0.681750i	$0.761219\pi$
$293$	−29.6293	+	12.2729i	−1.73096	+	0.716989i	−0.999379	+	0.0352392i	$0.988781\pi$
$294$	9.57359	−	16.5908i	0.558343	−	0.967593i
$295$	16.9008	+	9.06191i	0.984002	+	0.527605i
$296$	0.00880489	+	12.7614i	0.000511774	+	0.741744i
$297$		−	29.7139i		−	1.72417i
$298$	14.3590	−	24.8837i	0.831793	−	1.44147i
$299$	8.30386	+	3.43957i	0.480224	+	0.198915i
$300$	−9.03168	+	7.88647i	−0.521444	+	0.455325i
$301$	7.40332	+	17.8732i	0.426720	+	1.03019i
$302$	7.22831	+	9.41563i	0.415943	+	0.541809i
$303$	−10.6337	−	10.6337i	−0.610890	−	0.610890i
$304$	−1.28034	+	9.79476i	−0.0734325	+	0.561768i
$305$	3.50514	+	11.6092i	0.200704	+	0.664738i
$306$	0.558549	−	4.25015i	0.0319301	−	0.242965i
$307$	10.3266	−	24.9307i	0.589372	−	1.42287i	−0.294732	−	0.955580i	$-0.595230\pi$
$307$	10.3266	−	24.9307i	0.589372	−	1.42287i	0.884104	−	0.467290i	$-0.154770\pi$
$308$	36.8785	+	28.2709i	2.10135	+	1.61089i
$309$	−1.08352	+	2.61586i	−0.0616395	+	0.148811i
$310$	−8.34921	−	1.95618i	−0.474203	−	0.111103i
$311$	11.3391	+	11.3391i	0.642981	+	0.642981i	0.951287	−	0.308306i	$-0.0997622\pi$
$311$	11.3391	+	11.3391i	0.642981	+	0.642981i	−0.308306	+	0.951287i	$0.599762\pi$
$312$	−2.34523	−	5.65086i	−0.132773	−	0.319917i
$313$			11.6305i			0.657395i	0.944435	+	0.328697i	$0.106610\pi$
$313$			11.6305i			0.657395i	−0.944435	+	0.328697i	$0.893390\pi$
$314$	3.13250	−	5.42854i	0.176777	−	0.306350i
$315$	−9.46470	−	11.5634i	−0.533275	−	0.651522i
$316$	5.22091	−	19.5206i	0.293699	−	1.09812i
$317$	−1.87861	+	4.53537i	−0.105513	+	0.254732i	−0.967815	−	0.251664i	$-0.919022\pi$
$317$	−1.87861	+	4.53537i	−0.105513	+	0.254732i	0.862301	+	0.506395i	$0.169022\pi$
$318$	7.56367	+	0.994006i	0.424150	+	0.0557411i
$319$	4.84969			0.271530
$320$	−13.8271	+	11.3495i	−0.772959	+	0.634456i
$321$	2.18107			0.121736
$322$	−29.8809	−	3.92691i	−1.66520	−	0.218838i
$323$	−1.83353	+	4.42654i	−0.102021	+	0.246299i
$324$	0.967443	−	3.61720i	0.0537468	−	0.200956i
$325$	5.03084	−	7.48700i	0.279061	−	0.415304i
$326$	9.25864	−	16.0449i	0.512788	−	0.888647i
$327$		−	12.6893i		−	0.701717i
$328$	28.3216	−	11.7541i	1.56380	−	0.649012i
$329$	−11.9838	−	11.9838i	−0.660688	−	0.660688i
$330$	−17.5014	+	10.8571i	−0.963421	+	0.597666i
$331$	1.49595	−	3.61154i	0.0822248	−	0.198508i	−0.877420	−	0.479723i	$-0.840737\pi$
$331$	1.49595	−	3.61154i	0.0822248	−	0.198508i	0.959645	+	0.281215i	$0.0907373\pi$
$332$	−7.95737	−	6.10009i	−0.436717	−	0.334786i
$333$	2.69753	−	6.51241i	0.147824	−	0.356878i
$334$	1.89293	−	14.4039i	0.103577	−	0.788144i
$335$	9.45400	−	17.6320i	0.516527	−	0.963342i
$336$	12.5037	+	16.2641i	0.682132	+	0.887281i
$337$	5.89977	+	5.89977i	0.321381	+	0.321381i	0.849297	−	0.527916i	$-0.177026\pi$
$337$	5.89977	+	5.89977i	0.321381	+	0.321381i	−0.527916	+	0.849297i	$0.677026\pi$
$338$	−8.39253	−	10.9321i	−0.456493	−	0.594630i
$339$	−6.70977	−	16.1988i	−0.364425	−	0.879799i
$340$	−7.90624	+	3.57428i	−0.428776	+	0.193842i
$341$	−13.6084	−	5.63680i	−0.736938	−	0.305250i
$342$	2.72707	−	4.72593i	0.147463	−	0.255549i
$343$		−	18.3766i		−	0.992244i
$344$	−12.7924	+	0.00882623i	−0.689719	+	0.000475878i
$345$	6.31208	−	11.7723i	0.339831	−	0.633797i
$346$	−10.8015	+	18.7187i	−0.580694	+	1.00633i
$347$	−9.91142	+	4.10545i	−0.532073	+	0.220392i	−0.632511	−	0.774551i	$-0.717976\pi$
$347$	−9.91142	+	4.10545i	−0.532073	+	0.220392i	0.100438	+	0.994943i	$0.467976\pi$
$348$	2.06837	+	0.553199i	0.110876	+	0.0296546i
$349$	−7.95529	−	19.2058i	−0.425837	−	1.02806i	−0.980594	−	0.196049i	$-0.937189\pi$
$349$	−7.95529	−	19.2058i	−0.425837	−	1.02806i	0.554757	−	0.832012i	$-0.312811\pi$
$350$	−9.79001	+	28.6176i	−0.523298	+	1.52967i
$351$			9.86880i			0.526757i
$352$	−26.5925	+	15.3940i	−1.41739	+	0.820504i
$353$	−1.32025	−	1.32025i	−0.0702698	−	0.0702698i	0.671098	−	0.741368i	$-0.265823\pi$
$353$	−1.32025	−	1.32025i	−0.0702698	−	0.0702698i	−0.741368	+	0.671098i	$0.765823\pi$
$354$	8.85558	+	11.5353i	0.470669	+	0.613095i
$355$	−8.09702	−	9.89243i	−0.429745	−	0.525036i
$356$	−17.8077	+	10.2922i	−0.943807	+	0.545486i
$357$	3.80791	+	9.19312i	0.201536	+	0.486551i
$358$	1.06850	+	3.98402i	0.0564719	+	0.210562i
$359$	−21.4154	−	21.4154i	−1.13026	−	1.13026i	−0.990133	−	0.140130i	$-0.955248\pi$
$359$	−21.4154	−	21.4154i	−1.13026	−	1.13026i	−0.140130	−	0.990133i	$-0.544752\pi$
$360$	9.45728	−	2.86254i	0.498442	−	0.150869i
$361$	9.12271	−	9.12271i	0.480143	−	0.480143i
$362$	4.65751	+	2.68759i	0.244793	+	0.141256i
$363$	−20.4984	+	8.49070i	−1.07589	+	0.445646i
$364$	−12.2484	−	9.38955i	−0.641989	−	0.492146i
$365$	−3.54115	+	35.4813i	−0.185352	+	1.85717i
$366$	−1.19824	+	9.11774i	−0.0626330	+	0.476592i
$367$	−17.5064	+	17.5064i	−0.913826	+	0.913826i	−0.996571	−	0.0827444i	$-0.973631\pi$
$367$	−17.5064	+	17.5064i	−0.913826	+	0.913826i	0.0827444	+	0.996571i	$0.473631\pi$
$368$	9.94842	−	17.2678i	0.518597	−	0.900148i
$369$	−16.9377			−0.881739
$370$	−14.0796	+	2.30910i	−0.731966	+	0.120044i
$371$	17.7788	−	7.36420i	0.923027	−	0.382330i
$372$	−5.16096	−	3.95637i	−0.267583	−	0.205128i
$373$	2.92892	+	7.07104i	0.151654	+	0.366125i	0.981388	−	0.192033i	$-0.0615082\pi$
$373$	2.92892	+	7.07104i	0.151654	+	0.366125i	−0.829735	+	0.558158i	$0.811508\pi$
$374$	−14.3950	+	3.86067i	−0.744347	+	0.199631i
$375$	−10.3294	−	8.54473i	−0.533409	−	0.441248i
$376$	10.3506	−	4.29572i	0.533791	−	0.221535i
$377$	−1.61071			−0.0829560
$378$	−8.57198	−	31.9616i	−0.440895	−	1.64393i
$379$	−8.32972	+	20.1097i	−0.427869	+	1.03297i	0.552093	+	0.833783i	$0.313829\pi$
$379$	−8.32972	+	20.1097i	−0.427869	+	1.03297i	−0.979962	+	0.199185i	$0.936171\pi$
$380$	−11.0384	+	0.352087i	−0.566259	+	0.0180617i
$381$	−5.51352	+	2.28377i	−0.282466	+	0.117001i
$382$	1.01705	−	7.73902i	0.0520368	−	0.395963i
$383$	17.9145	−	17.9145i	0.915387	−	0.915387i	−0.0813024	−	0.996689i	$-0.525908\pi$
$383$	17.9145	−	17.9145i	0.915387	−	0.915387i	0.996689	+	0.0813024i	$0.0259080\pi$
$384$	−13.0976	+	3.53210i	−0.668383	+	0.180247i
$385$	−24.5499	+	45.7864i	−1.25118	+	2.33349i
$386$	−9.72132	−	12.6630i	−0.494802	−	0.644532i
$387$	6.52819	+	2.70407i	0.331847	+	0.137455i
$388$	8.40390	−	4.85715i	0.426644	−	0.246585i
$389$	33.4343	+	13.8490i	1.69519	+	0.702170i	0.999863	−	0.0165255i	$-0.00526047\pi$
$389$	33.4343	+	13.8490i	1.69519	+	0.702170i	0.695325	+	0.718696i	$0.255260\pi$
$390$	5.81270	−	3.60595i	0.294337	−	0.182595i
$391$	6.83500	−	6.83500i	0.345661	−	0.345661i
$392$	29.5268	+	12.2066i	1.49133	+	0.616524i
$393$	1.49805			0.0755666
$394$	−3.73589	−	13.9297i	−0.188211	−	0.701768i
$395$	22.4801	+	2.24359i	1.13110	+	0.112887i
$396$	16.8262	−	2.22309i	0.845549	−	0.111714i
$397$	−24.0480	−	9.96101i	−1.20693	−	0.499929i	−0.313701	−	0.949522i	$-0.601569\pi$
$397$	−24.0480	−	9.96101i	−1.20693	−	0.499929i	−0.893233	+	0.449593i	$0.851569\pi$
$398$	−2.35172	−	3.06336i	−0.117881	−	0.153553i
$399$			12.6655i			0.634070i
$400$	−15.0146	−	13.2121i	−0.750732	−	0.660607i
$401$			5.98554i			0.298904i	0.988769	+	0.149452i	$0.0477509\pi$
$401$			5.98554i			0.298904i	−0.988769	+	0.149452i	$0.952249\pi$
$402$	12.0344	−	9.23874i	0.600223	−	0.460786i
$403$	4.51973	+	1.87214i	0.225144	+	0.0932577i
$404$	15.2611	−	19.9076i	0.759267	−	0.990439i
$405$	4.16560	+	0.415741i	0.206991	+	0.0206584i
$406$	5.21655	−	1.39906i	0.258893	−	0.0694340i
$407$	−24.5074			−1.21479
$408$	−6.57979	+	0.00453979i	−0.325748	+	0.000224753i
$409$	−9.42306	+	9.42306i	−0.465940	+	0.465940i	−0.900596	−	0.434656i	$-0.856870\pi$
$409$	−9.42306	+	9.42306i	−0.465940	+	0.465940i	0.434656	+	0.900596i	$0.356870\pi$
$410$	18.0728	+	29.1328i	0.892550	+	1.43876i
$411$	−6.17398	−	2.55735i	−0.304540	−	0.126145i
$412$	−4.56242	−	1.22025i	−0.224775	−	0.0601174i
$413$	33.8914	+	14.0383i	1.66769	+	0.690779i
$414$	−8.73158	+	6.70317i	−0.429134	+	0.329443i
$415$	5.29719	−	9.87944i	0.260029	−	0.484963i
$416$	8.83211	−	5.11277i	0.433030	−	0.250674i
$417$	−6.05438	+	6.05438i	−0.296484	+	0.296484i
$418$	−18.8084	−	2.47178i	−0.919950	−	0.120899i
$419$	5.22597	−	2.16467i	0.255306	−	0.105751i	−0.251360	−	0.967894i	$-0.580878\pi$
$419$	5.22597	−	2.16467i	0.255306	−	0.105751i	0.506666	+	0.862143i	$0.330878\pi$
$420$	−15.6932	+	16.7273i	−0.765751	+	0.816210i
$421$	7.29565	−	17.6133i	0.355568	−	0.858418i	−0.640344	−	0.768089i	$-0.721208\pi$
$421$	7.29565	−	17.6133i	0.355568	−	0.858418i	0.995912	−	0.0903294i	$-0.0287920\pi$
$422$	31.2258	−	8.37462i	1.52005	−	0.407670i
$423$	−6.19013			−0.300975
$424$	0.00877959	+	12.7248i	0.000426375	+	0.617970i
$425$	−5.36849	−	8.07988i	−0.260410	−	0.391932i
$426$	−2.51122	−	9.36338i	−0.121669	−	0.453657i
$427$	8.87729	+	21.4317i	0.429602	+	1.03715i
$428$	0.476521	+	3.60672i	0.0230335	+	0.174337i
$429$	10.8552	−	4.49636i	0.524092	−	0.217086i
$430$	−2.31469	−	14.1138i	−0.111624	−	0.680627i
$431$	−7.67300			−0.369596			−0.184798	−	0.982777i	$-0.559163\pi$
$431$	−7.67300			−0.369596			−0.184798	+	0.982777i	$0.559163\pi$
$432$	21.6969	+	2.83615i	1.04389	+	0.136454i
$433$	6.69752	−	6.69752i	0.321862	−	0.321862i	−0.527619	−	0.849481i	$-0.676915\pi$
$433$	6.69752	−	6.69752i	0.321862	−	0.321862i	0.849481	+	0.527619i	$0.176915\pi$
$434$	−16.2640	−	2.13739i	−0.780697	−	0.102598i
$435$	−0.237727	+	2.38196i	−0.0113982	+	0.114206i
$436$	20.9835	−	2.77235i	1.00493	−	0.132771i
$437$	11.3670	−	4.70836i	0.543756	−	0.225231i
$438$	−13.5148	+	23.4207i	−0.645761	+	1.11908i
$439$	13.8728	−	13.8728i	0.662111	−	0.662111i	−0.293767	−	0.955877i	$-0.594909\pi$
$439$	13.8728	−	13.8728i	0.662111	−	0.662111i	0.955877	+	0.293767i	$0.0949088\pi$
$440$	−21.7775	−	26.5690i	−1.03820	−	1.26663i
$441$	−12.4793	−	12.4793i	−0.594250	−	0.594250i
$442$	4.78097	−	1.28224i	0.227408	−	0.0609897i
$443$	3.41887	+	8.25387i	0.162435	+	0.392153i	0.984051	−	0.177889i	$-0.0569268\pi$
$443$	3.41887	+	8.25387i	0.162435	+	0.392153i	−0.821615	+	0.570042i	$0.806927\pi$
$444$	−10.4523	−	2.79554i	−0.496045	−	0.132670i
$445$	−14.5653	−	17.7949i	−0.690459	−	0.843559i
$446$	−22.8000	+	17.5034i	−1.07961	+	0.828809i
$447$	17.2237	+	17.2237i	0.814654	+	0.814654i
$448$	−24.1633	+	24.2300i	−1.14161	+	1.14476i
$449$		−	36.5109i		−	1.72305i	−0.507711	−	0.861527i	$-0.669508\pi$
$449$		−	36.5109i		−	1.72305i	0.507711	−	0.861527i	$-0.330492\pi$
$450$	4.86262	+	9.91957i	0.229226	+	0.467613i
$451$	22.5354	+	54.4052i	1.06115	+	2.56184i
$452$	25.3211	−	14.6347i	1.19100	−	0.688357i
$453$	−9.29802	+	3.85137i	−0.436859	+	0.180953i
$454$	0.640658	+	0.369688i	0.0300676	+	0.0173503i
$455$	8.15368	−	15.2069i	0.382250	−	0.712911i
$456$	−7.73976	−	3.19966i	−0.362448	−	0.149838i
$457$			29.8236i			1.39509i	0.716541	+	0.697545i	$0.245724\pi$
$457$			29.8236i			1.39509i	−0.716541	+	0.697545i	$0.754276\pi$
$458$	11.5585	+	6.66977i	0.540094	+	0.311658i
$459$	9.80547	+	4.06156i	0.457680	+	0.189577i
$460$	20.8462	+	7.86593i	0.971958	+	0.366751i
$461$	1.86042	+	4.49145i	0.0866483	+	0.209187i	0.961264	−	0.275629i	$-0.0888862\pi$
$461$	1.86042	+	4.49145i	0.0866483	+	0.209187i	−0.874616	+	0.484817i	$0.838886\pi$
$462$	−31.2506	+	23.9909i	−1.45391	+	1.11616i
$463$	17.9914	+	17.9914i	0.836130	+	0.836130i	0.988347	−	0.152217i	$-0.0486412\pi$
$463$	17.9914	+	17.9914i	0.836130	+	0.836130i	−0.152217	+	0.988347i	$0.548641\pi$
$464$	−0.462896	+	3.54121i	−0.0214894	+	0.164397i
$465$	3.43563	−	6.40757i	0.159323	−	0.297144i
$466$	12.1061	+	1.59097i	0.560805	+	0.0737002i
$467$	1.26855	−	3.06256i	0.0587017	−	0.141718i	−0.891807	−	0.452415i	$-0.850562\pi$
$467$	1.26855	−	3.06256i	0.0587017	−	0.141718i	0.950509	+	0.310697i	$0.100562\pi$
$468$	−5.58845	+	0.738348i	−0.258326	+	0.0341302i
$469$	14.6457	−	35.3579i	0.676276	−	1.63267i
$470$	6.60497	+	10.6470i	0.304665	+	0.491111i
$471$	3.75747	+	3.75747i	0.173135	+	0.173135i
$472$	−17.1405	+	17.1642i	−0.788957	+	0.790046i
$473$		−	24.5669i		−	1.12958i
$474$	14.8388	+	8.56266i	0.681570	+	0.393296i
$475$	−2.37742	−	12.1166i	−0.109084	−	0.555946i
$476$	−14.3702	+	8.30544i	−0.658656	+	0.380679i
$477$	2.68978	−	6.49370i	0.123156	−	0.297326i
$478$	4.25542	−	32.3806i	0.194638	−	1.48106i
$479$	24.5851			1.12332			0.561661	−	0.827367i	$-0.310162\pi$
$479$	24.5851			1.12332			0.561661	+	0.827367i	$0.310162\pi$
$480$	−6.25733	−	13.8157i	−0.285607	−	0.630598i
$481$	8.13959			0.371134
$482$	2.58105	−	19.6399i	0.117564	−	0.894574i
$483$	9.77839	−	23.6071i	0.444932	−	1.07416i
$484$	−18.5191	−	32.0419i	−0.841776	−	1.45645i
$485$	6.87371	+	8.39786i	0.312119	+	0.381327i
$486$	−17.3524	−	10.0131i	−0.787122	−	0.454204i
$487$		−	7.39975i		−	0.335315i	−0.985845	−	0.167657i	$-0.946380\pi$
$487$		−	7.39975i		−	0.335315i	0.985845	−	0.167657i	$-0.0536202\pi$
$488$	−15.3393	+	0.0105835i	−0.694377	+	0.000479092i
$489$	11.1058	+	11.1058i	0.502222	+	0.502222i
$490$	−8.14875	+	34.7799i	−0.368123	+	1.57119i
$491$	12.8940	−	31.1288i	0.581896	−	1.40482i	−0.309196	−	0.950998i	$-0.600060\pi$
$491$	12.8940	−	31.1288i	0.581896	−	1.40482i	0.891092	−	0.453823i	$-0.149940\pi$
$492$	3.40530	+	25.7742i	0.153523	+	1.16199i
$493$	−0.662899	+	1.60038i	−0.0298555	+	0.0720774i
$494$	6.24679	+	0.820945i	0.281057	+	0.0369360i
$495$	5.48478	+	18.1658i	0.246522	+	0.816492i
$496$	5.41486	−	9.39877i	0.243134	−	0.422017i
$497$	−17.2916	−	17.2916i	−0.775635	−	0.775635i
$498$	6.74303	−	5.17657i	0.302162	−	0.231968i
$499$	−0.282367	−	0.681694i	−0.0126405	−	0.0305168i	0.917433	−	0.397890i	$-0.130257\pi$
$499$	−0.282367	−	0.681694i	−0.0126405	−	0.0305168i	−0.930074	+	0.367373i	$0.880257\pi$
$500$	11.8732	−	18.9480i	0.530984	−	0.847382i
$501$	11.3796	+	4.71360i	0.508404	+	0.210588i
$502$	12.2421	+	7.06420i	0.546390	+	0.315291i
$503$			22.8015i			1.01667i	0.861160	+	0.508333i	$0.169738\pi$
$503$			22.8015i			1.01667i	−0.861160	+	0.508333i	$0.830262\pi$
$504$	17.4577	−	7.24534i	0.777629	−	0.322733i
$505$	24.7162	+	13.2524i	1.09986	+	0.589723i
$506$	33.1484	+	19.1281i	1.47363	+	0.850347i
$507$	10.7956	−	4.47168i	0.479449	−	0.198594i
$508$	−4.98114	−	8.61843i	−0.221002	−	0.382381i
$509$	14.3610	+	34.6704i	0.636538	+	1.53674i	0.831262	+	0.555881i	$0.187619\pi$
$509$	14.3610	+	34.6704i	0.636538	+	1.53674i	−0.194724	+	0.980858i	$0.562381\pi$
$510$	−1.19057	−	7.25945i	−0.0527192	−	0.321454i
$511$			68.2098i			3.01742i
$512$	−8.70239	−	20.8870i	−0.384595	−	0.923085i
$513$	9.55244	+	9.55244i	0.421751	+	0.421751i
$514$	1.22021	−	0.936743i	0.0538210	−	0.0413180i
$515$	0.524380	−	5.25413i	0.0231070	−	0.231525i
$516$	2.80232	−	10.4777i	0.123365	−	0.461253i
$517$	8.23591	+	19.8832i	0.362215	+	0.874464i
$518$	−26.3613	+	7.07000i	−1.15825	+	0.310638i
$519$	−12.9565	−	12.9565i	−0.568729	−	0.568729i
$520$	7.23292	+	8.82430i	0.317185	+	0.386971i
$521$	−22.8457	+	22.8457i	−1.00089	+	1.00089i	−0.000890154		1.00000i	$0.500283\pi$
$521$	−22.8457	+	22.8457i	−1.00089	+	1.00089i	−1.00000		0.000890154i	$0.999717\pi$
$522$	0.985948	−	1.70862i	0.0431538	−	0.0747843i
$523$	−9.44993	+	3.91429i	−0.413217	+	0.171160i	−0.579600	−	0.814901i	$-0.696791\pi$
$523$	−9.44993	+	3.91429i	−0.413217	+	0.171160i	0.166383	+	0.986061i	$0.446791\pi$
$524$	0.327294	+	2.47724i	0.0142979	+	0.108219i
$525$	−21.2849	−	14.3022i	−0.928948	−	0.624201i
$526$	16.0119	+	2.10426i	0.698151	+	0.0917500i
$527$	3.72024	−	3.72024i	0.162056	−	0.162056i
$528$	−6.76578	−	25.1576i	−0.294443	−	1.09485i
$529$	−1.82182			−0.0792094
$530$	−14.0392	+	2.30246i	−0.609823	+	0.100013i
$531$	12.3789	−	5.12749i	0.537197	−	0.222514i
$532$	−20.9443	+	2.76717i	−0.908050	+	0.119972i
$533$	−7.48462	−	18.0695i	−0.324195	−	0.782675i
$534$	−4.51728	−	16.8432i	−0.195482	−	0.728878i
$535$	−3.89386	+	1.17567i	−0.168346	+	0.0508285i
$536$	17.9069	+	17.8822i	0.773459	+	0.772392i
$537$	−3.49720			−0.150915
$538$	9.75400	−	2.61598i	0.420525	−	0.112783i
$539$	−23.4809	+	56.6880i	−1.01139	+	2.44172i
$540$	0.779927	+	24.4518i	0.0335627	+	1.05224i
$541$	−17.9708	+	7.44376i	−0.772626	+	0.320032i	−0.733936	−	0.679219i	$-0.762319\pi$
$541$	−17.9708	+	7.44376i	−0.772626	+	0.320032i	−0.0386904	+	0.999251i	$0.512319\pi$
$542$	−3.57859	−	0.470293i	−0.153714	−	0.0202008i
$543$	−3.22378	+	3.22378i	−0.138346	+	0.138346i
$544$	−1.44506	−	10.8796i	−0.0619564	−	0.466460i
$545$	6.83991	+	22.6541i	0.292990	+	0.970394i
$546$	10.3792	−	7.96803i	0.444188	−	0.341000i
$547$	−18.4765	−	7.65320i	−0.789996	−	0.327227i	−0.0490543	−	0.998796i	$-0.515621\pi$
$547$	−18.4765	−	7.65320i	−0.789996	−	0.327227i	−0.740942	+	0.671569i	$0.765621\pi$
$548$	2.88005	−	10.7683i	0.123030	−	0.459999i
$549$	7.82793	+	3.24243i	0.334088	+	0.138384i
$550$	25.3928	−	28.8170i	1.08275	−	1.22876i
$551$	−1.55908	+	1.55908i	−0.0664191	+	0.0664191i
$552$	11.9557	+	11.9393i	0.508870	+	0.508169i
$553$	43.2162			1.83774
$554$	14.3651	−	3.85266i	0.610314	−	0.163684i
$555$	1.20133	−	12.0370i	0.0509937	−	0.510942i
$556$	−11.3346	−	8.68903i	−0.480692	−	0.368497i
$557$	−35.0496	−	14.5180i	−1.48510	−	0.615148i	−0.514856	−	0.857277i	$-0.672154\pi$
$557$	−35.0496	−	14.5180i	−1.48510	−	0.615148i	−0.970244	+	0.242128i	$0.922154\pi$
$558$	−4.75254	+	3.64849i	−0.201191	+	0.154453i
$559$			8.15932i			0.345103i
$560$	−31.0897	−	22.2964i	−1.31378	−	0.942194i
$561$		−	12.6360i		−	0.533493i
$562$	−22.5009	−	29.3098i	−0.949143	−	1.23636i
$563$	−34.4540	−	14.2713i	−1.45206	−	0.601464i	−0.489374	−	0.872074i	$-0.662775\pi$
$563$	−34.4540	−	14.2713i	−1.45206	−	0.601464i	−0.962689	+	0.270610i	$0.912775\pi$
$564$	1.24452	+	9.41958i	0.0524037	+	0.396636i
$565$	20.7106	+	25.3029i	0.871301	+	1.06450i
$566$	−7.10870	−	26.5057i	−0.298801	−	1.11412i
$567$	8.00803			0.336306
$568$	14.9350	−	6.19837i	0.626660	−	0.260078i
$569$	10.8079	−	10.8079i	0.453091	−	0.453091i	−0.443288	−	0.896379i	$-0.646188\pi$
$569$	10.8079	−	10.8079i	0.453091	−	0.453091i	0.896379	+	0.443288i	$0.146188\pi$
$570$	2.13600	−	9.11673i	0.0894673	−	0.381858i
$571$	−41.2263	−	17.0765i	−1.72527	−	0.714630i	−0.999648	−	0.0265351i	$-0.991553\pi$
$571$	−41.2263	−	17.0765i	−1.72527	−	0.714630i	−0.725621	−	0.688095i	$-0.758447\pi$
$572$	9.80701	+	16.9682i	0.410051	+	0.709476i
$573$	6.11414	+	2.53256i	0.255422	+	0.105799i
$574$	39.9351	+	52.0197i	1.66686	+	2.17126i
$575$	−4.92331	+	24.4194i	−0.205316	+	1.01836i
$576$	0.0172470	+	12.4986i	0.000718627	+	0.520774i
$577$	−11.9571	+	11.9571i	−0.497781	+	0.497781i	−0.910747	−	0.412965i	$-0.864493\pi$
$577$	−11.9571	+	11.9571i	−0.497781	+	0.497781i	0.412965	+	0.910747i	$0.364493\pi$
$578$	−2.43895	+	18.5587i	−0.101447	+	0.771939i
$579$	12.5049	−	5.17968i	0.519684	−	0.215260i
$580$	−3.99085	+	0.127294i	−0.165711	+	0.00528560i
$581$	8.20616	−	19.8114i	0.340449	−	0.821916i
$582$	2.13182	+	7.94874i	0.0883667	+	0.329486i
$583$	−24.4370			−1.01208
$584$	−41.6822	−	17.2316i	−1.72482	−	0.713051i
$585$	−1.82164	−	6.03336i	−0.0753157	−	0.249449i
$586$	43.8065	−	11.7487i	1.80963	−	0.485335i
$587$	−9.50105	−	22.9376i	−0.392150	−	0.946735i	−0.989471	−	0.144732i	$-0.953768\pi$
$587$	−9.50105	−	22.9376i	−0.392150	−	0.946735i	0.597321	−	0.802003i	$-0.296232\pi$
$588$	−16.4809	+	21.4987i	−0.679659	+	0.886593i
$589$	6.18697	−	2.56273i	0.254930	−	0.105595i
$590$	−22.0277	−	15.8205i	−0.906867	−	0.651320i
$591$	12.2276			0.502975
$592$	2.33920	−	17.8952i	0.0961405	−	0.735487i
$593$	8.61838	−	8.61838i	0.353914	−	0.353914i	−0.507649	−	0.861564i	$-0.669485\pi$
$593$	8.61838	−	8.61838i	0.353914	−	0.353914i	0.861564	+	0.507649i	$0.169485\pi$
$594$	−5.47536	+	41.6635i	−0.224657	+	1.70948i
$595$	−11.7536	−	14.3598i	−0.481852	−	0.588696i
$596$	−24.7188	+	32.2449i	−1.01252	+	1.32080i
$597$	3.02510	−	1.25304i	0.123809	−	0.0512834i
$598$	−11.0095	−	6.35296i	−0.450212	−	0.259792i
$599$	−23.4236	+	23.4236i	−0.957064	+	0.957064i	−0.999115	−	0.0420512i	$-0.986611\pi$
$599$	−23.4236	+	23.4236i	−0.957064	+	0.957064i	0.0420512	+	0.999115i	$0.486611\pi$
$600$	14.1171	−	9.39380i	0.576327	−	0.383500i
$601$	−12.9452	−	12.9452i	−0.528045	−	0.528045i	0.391944	−	0.919989i	$-0.371803\pi$
$601$	−12.9452	−	12.9452i	−0.528045	−	0.528045i	−0.919989	+	0.391944i	$0.871803\pi$
$602$	−7.08714	−	26.4252i	−0.288850	−	1.07701i
$603$	−5.34935	−	12.9145i	−0.217842	−	0.525918i
$604$	−8.40021	−	14.5342i	−0.341800	−	0.591386i
$605$	32.0189	−	26.2077i	1.30175	−	1.06549i
$606$	12.9506	+	16.8696i	0.526084	+	0.685279i
$607$	26.2383	+	26.2383i	1.06498	+	1.06498i	0.997737	+	0.0672422i	$0.0214200\pi$
$607$	26.2383	+	26.2383i	1.06498	+	1.06498i	0.0672422	+	0.997737i	$0.478580\pi$
$608$	3.60011	−	13.4979i	0.146004	−	0.547411i
$609$			4.57912i			0.185555i
$610$	−2.77554	−	16.9238i	−0.112378	−	0.685223i
$611$	−2.73537	−	6.60377i	−0.110661	−	0.267160i
$612$	−1.56635	+	5.85646i	−0.0633158	+	0.236733i
$613$	−15.9398	+	6.60248i	−0.643802	+	0.266672i	−0.680605	−	0.732651i	$-0.738283\pi$
$613$	−15.9398	+	6.60248i	−0.643802	+	0.266672i	0.0368022	+	0.999323i	$0.488283\pi$
$614$	−19.0735	+	33.0539i	−0.769745	+	1.33395i
$615$	−27.8262	+	8.40151i	−1.12206	+	0.338782i
$616$	−46.5000	−	46.4359i	−1.87354	−	1.87095i
$617$		−	37.8944i		−	1.52557i	−0.646651	−	0.762786i	$-0.723831\pi$
$617$		−	37.8944i		−	1.52557i	0.646651	−	0.762786i	$-0.276169\pi$
$618$	2.00129	−	3.46818i	0.0805038	−	0.139511i
$619$	−21.8403	−	9.04654i	−0.877835	−	0.363611i	−0.102178	−	0.994766i	$-0.532581\pi$
$619$	−21.8403	−	9.04654i	−0.877835	−	0.363611i	−0.775657	+	0.631155i	$0.782581\pi$
$620$	11.3464	+	4.28137i	0.455684	+	0.171944i
$621$	−10.4297	−	25.1796i	−0.418531	−	1.01042i
$622$	−13.8097	−	17.9886i	−0.553720	−	0.721278i
$623$	−31.1049	−	31.1049i	−1.24619	−	1.24619i
$624$	2.24710	+	8.35554i	0.0899560	+	0.334489i
$625$	23.0470	+	9.68698i	0.921878	+	0.387479i
$626$	2.14315	−	16.3078i	0.0856573	−	0.651790i
$627$	6.15497	−	14.8594i	0.245806	−	0.593428i
$628$	−5.39258	+	7.03444i	−0.215187	+	0.280705i
$629$	3.34989	−	8.08736i	0.133569	−	0.322464i
$630$	11.1402	+	17.9577i	0.443837	+	0.715453i
$631$	−18.4261	−	18.4261i	−0.733533	−	0.733533i	0.237785	−	0.971318i	$-0.423579\pi$
$631$	−18.4261	−	18.4261i	−0.733533	−	0.733533i	−0.971318	+	0.237785i	$0.923579\pi$
$632$	−10.9176	+	26.4089i	−0.434278	+	1.05049i
$633$			27.4102i			1.08946i
$634$	3.46984	−	6.01313i	0.137805	−	0.238812i
$635$	8.61223	−	7.04917i	0.341766	−	0.279738i
$636$	−10.4223	−	2.78751i	−0.413271	−	0.110532i
$637$	7.79866	−	18.8276i	0.308994	−	0.745978i
$638$	−6.80003	−	0.893650i	−0.269216	−	0.0353799i
$639$	−8.93185			−0.353339
$640$	21.4792	−	13.3659i	0.849038	−	0.528332i
$641$	−6.19657			−0.244750			−0.122375	−	0.992484i	$-0.539051\pi$
$641$	−6.19657			−0.244750			−0.122375	+	0.992484i	$0.539051\pi$
$642$	−3.05821	−	0.401905i	−0.120698	−	0.0158619i
$643$	−5.32387	+	12.8530i	−0.209953	+	0.506871i	−0.993415	−	0.114568i	$-0.963452\pi$
$643$	−5.32387	+	12.8530i	−0.209953	+	0.506871i	0.783462	+	0.621439i	$0.213452\pi$
$644$	41.1741	+	11.0123i	1.62249	+	0.433945i
$645$	12.0662	+	1.20425i	0.475105	+	0.0474171i
$646$	3.38658	−	5.86884i	0.133243	−	0.230907i
$647$			23.2595i			0.914426i	0.889357	+	0.457213i	$0.151152\pi$
$647$			23.2595i			0.914426i	−0.889357	+	0.457213i	$0.848848\pi$
$648$	−2.02305	+	4.89361i	−0.0794728	+	0.192239i
$649$	−32.9399	−	32.9399i	−1.29300	−	1.29300i
$650$	−8.43366	+	9.57092i	−0.330795	+	0.375402i
$651$	5.32232	−	12.8492i	0.208598	−	0.503600i
$652$	−15.9387	+	20.7915i	−0.624206	+	0.814256i
$653$	−6.24907	+	15.0866i	−0.244545	+	0.590384i	−0.997724	−	0.0674318i	$-0.978519\pi$
$653$	−6.24907	+	15.0866i	−0.244545	+	0.590384i	0.753179	+	0.657816i	$0.228519\pi$
$654$	−2.33824	+	17.7923i	−0.0914325	+	0.695735i
$655$	−2.67446	+	0.807496i	−0.104500	+	0.0315515i
$656$	−41.8773	+	11.2623i	−1.63503	+	0.439719i
$657$	17.6166	+	17.6166i	0.687289	+	0.687289i
$658$	14.5949	+	19.0114i	0.568969	+	0.741142i
$659$	−2.29846	−	5.54898i	−0.0895355	−	0.216158i	0.872768	−	0.488135i	$-0.162323\pi$
$659$	−2.29846	−	5.54898i	−0.0895355	−	0.216158i	−0.962304	+	0.271977i	$0.912323\pi$
$660$	26.5404	−	11.9984i	1.03308	−	0.467039i
$661$	4.71180	+	1.95169i	0.183268	+	0.0759119i	0.472430	−	0.881368i	$-0.343377\pi$
$661$	4.71180	+	1.95169i	0.183268	+	0.0759119i	−0.289163	+	0.957280i	$0.593377\pi$
$662$	−2.76305	+	4.78829i	−0.107389	+	0.186102i
$663$			4.19676i			0.162989i
$664$	10.0334	+	10.0196i	0.389372	+	0.388835i
$665$	−6.82713	−	22.6117i	−0.264745	−	0.876846i
$666$	−4.98240	+	8.63435i	−0.193064	+	0.334574i
$667$	4.10963	−	1.70227i	0.159126	−	0.0659120i
$668$	−5.30838	+	19.8477i	−0.205387	+	0.767929i
$669$	−9.32609	−	22.5152i	−0.360567	−	0.870487i
$670$	−16.5050	+	22.9808i	−0.637645	+	0.887827i
$671$		−	29.4580i		−	1.13721i
$672$	−14.5352	−	25.1089i	−0.560706	−	0.968597i
$673$	−29.4134	−	29.4134i	−1.13380	−	1.13380i	−0.989540	−	0.144262i	$-0.953919\pi$
$673$	−29.4134	−	29.4134i	−1.13380	−	1.13380i	−0.144262	−	0.989540i	$-0.546081\pi$
$674$	−7.18526	−	9.35956i	−0.276766	−	0.360517i
$675$	−26.8401	+	5.26636i	−1.03307	+	0.202702i
$676$	9.75318	+	16.8751i	0.375122	+	0.649041i
$677$	3.58925	+	8.66522i	0.137946	+	0.333031i	0.977723	−	0.209901i	$-0.0673141\pi$
$677$	3.58925	+	8.66522i	0.137946	+	0.333031i	−0.839777	+	0.542932i	$0.817314\pi$
$678$	6.42320	+	23.9497i	0.246682	+	0.919782i
$679$	14.6792	+	14.6792i	0.563335	+	0.563335i
$680$	11.7444	−	3.55482i	0.450378	−	0.136321i
$681$	−0.443444	+	0.443444i	−0.0169928	+	0.0169928i
$682$	18.0425	+	10.4113i	0.690882	+	0.398669i
$683$	−12.9219	+	5.35244i	−0.494444	+	0.204805i	−0.615950	−	0.787785i	$-0.711228\pi$
$683$	−12.9219	+	5.35244i	−0.494444	+	0.204805i	0.121506	+	0.992591i	$0.461228\pi$
$684$	−4.69462	+	6.12398i	−0.179503	+	0.234156i
$685$	12.4009	+	1.23765i	0.473813	+	0.0472881i
$686$	−3.38625	+	25.7669i	−0.129288	+	0.983785i
$687$	−8.00045	+	8.00045i	−0.305236	+	0.305236i
$688$	17.9386	+	2.34487i	0.683901	+	0.0893973i
$689$	8.11621			0.309203
$690$	−11.0198	+	15.3434i	−0.419517	+	0.584115i
$691$	28.0793	−	11.6308i	1.06819	−	0.442458i	0.221836	−	0.975084i	$-0.428795\pi$
$691$	28.0793	−	11.6308i	1.06819	−	0.442458i	0.846350	+	0.532626i	$0.178795\pi$
$692$	18.5947	−	24.2562i	0.706866	−	0.922083i
$693$	13.8910	+	33.5359i	0.527676	+	1.27392i
$694$	14.6539	−	3.93011i	0.556254	−	0.149185i
$695$	7.54536	−	14.0724i	0.286212	−	0.533795i
$696$	−2.79825	−	1.15681i	−0.106067	−	0.0438488i
$697$	−21.0338			−0.796714
$698$	7.61553	+	28.3954i	0.288252	+	1.07478i
$699$	−3.96167	+	9.56432i	−0.149844	+	0.361756i
$700$	19.0005	−	38.3223i	0.718150	−	1.44845i
$701$	12.5265	−	5.18864i	0.473119	−	0.195972i	−0.133367	−	0.991067i	$-0.542579\pi$
$701$	12.5265	−	5.18864i	0.473119	−	0.195972i	0.606485	+	0.795095i	$0.292579\pi$
$702$	1.81852	−	13.8376i	0.0686355	−	0.522267i
$703$	7.87867	−	7.87867i	0.297150	−	0.297150i
$704$	40.1236	−	16.6846i	1.51221	−	0.628826i
$705$	−10.1695	+	3.07046i	−0.383006	+	0.115640i
$706$	1.60792	+	2.09448i	0.0605148	+	0.0788268i
$707$	49.5638	+	20.5300i	1.86404	+	0.772110i
$708$	−10.2913	−	17.8061i	−0.386771	−	0.669196i
$709$	−19.5852	−	8.11244i	−0.735536	−	0.304669i	−0.0167112	−	0.999860i	$-0.505320\pi$
$709$	−19.5852	−	8.11244i	−0.735536	−	0.304669i	−0.718825	+	0.695191i	$0.755320\pi$
$710$	9.53043	+	15.3628i	0.357671	+	0.576555i
$711$	11.1615	−	11.1615i	0.418589	−	0.418589i
$712$	26.8657	−	11.1499i	1.00684	−	0.417859i
$713$	−13.5104			−0.505967
$714$	−3.64528	−	13.5919i	−0.136421	−	0.508663i
$715$	−16.9560	+	13.8786i	−0.634118	+	0.519030i
$716$	−0.764068	−	5.78312i	−0.0285546	−	0.216125i
$717$	25.5820	+	10.5964i	0.955377	+	0.395730i
$718$	26.0816	+	33.9740i	0.973356	+	1.26790i
$719$			6.73697i			0.251246i	0.992078	+	0.125623i	$0.0400930\pi$
$719$			6.73697i			0.251246i	−0.992078	+	0.125623i	$0.959907\pi$
$720$	−13.7881	+	2.27105i	−0.513851	+	0.0846370i
$721$		−	10.1006i		−	0.376168i
$722$	−14.4725	+	11.1104i	−0.538611	+	0.413488i
$723$	15.5163	+	6.42708i	0.577059	+	0.239026i
$724$	−6.03532	−	4.62666i	−0.224301	−	0.171948i
$725$	−0.859537	−	4.38064i	−0.0319224	−	0.162693i
$726$	30.3065	−	8.12808i	1.12478	−	0.301661i
$727$	52.5921			1.95053			0.975266	−	0.221036i	$-0.0709438\pi$
$727$	52.5921			1.95053			0.975266	+	0.221036i	$0.0709438\pi$
$728$	15.4439	+	15.4226i	0.572390	+	0.571601i
$729$	15.9823	−	15.9823i	0.591936	−	0.591936i
$730$	11.5034	−	49.0978i	0.425758	−	1.81719i
$731$	8.10697	+	3.35801i	0.299847	+	0.124201i
$732$	3.36024	−	12.5637i	0.124198	−	0.464368i
$733$	7.83141	+	3.24388i	0.289260	+	0.119815i	0.522595	−	0.852581i	$-0.324964\pi$
$733$	7.83141	+	3.24388i	0.289260	+	0.119815i	−0.233335	+	0.972396i	$0.574964\pi$
$734$	27.7726	−	21.3208i	1.02511	−	0.786966i
$735$	−26.6917	−	14.3116i	−0.984537	−	0.527892i
$736$	−17.1312	+	22.3790i	−0.631464	+	0.824902i
$737$	−34.3651	+	34.3651i	−1.26586	+	1.26586i
$738$	23.7493	+	3.12109i	0.874222	+	0.114889i
$739$	−15.8294	+	6.55676i	−0.582295	+	0.241194i	−0.654332	−	0.756207i	$-0.727050\pi$
$739$	−15.8294	+	6.55676i	−0.582295	+	0.241194i	0.0720369	+	0.997402i	$0.477050\pi$
$740$	20.1674	−	0.643269i	0.741367	−	0.0236470i
$741$	−2.04423	+	4.93522i	−0.0750968	+	0.181300i
$742$	−26.2856	+	7.04969i	−0.964975	+	0.258802i
$743$	−6.91946			−0.253850			−0.126925	−	0.991912i	$-0.540511\pi$
$743$	−6.91946			−0.253850			−0.126925	+	0.991912i	$0.540511\pi$
$744$	6.50744	+	6.49846i	0.238574	+	0.238245i
$745$	−40.0336	−	21.4653i	−1.46672	−	0.786428i
$746$	−2.80383	−	10.4544i	−0.102656	−	0.382764i
$747$	−2.99730	−	7.23613i	−0.109666	−	0.264756i
$748$	20.8954	−	2.76072i	0.764013	−	0.100942i
$749$	−7.18846	+	2.97756i	−0.262660	+	0.108798i
$750$	12.9089	+	13.8845i	0.471368	+	0.506989i
$751$	−50.8320			−1.85489			−0.927443	−	0.373963i	$-0.877999\pi$
$751$	−50.8320			−1.85489			−0.927443	+	0.373963i	$0.877999\pi$
$752$	−15.3047	+	4.11598i	−0.558106	+	0.150094i
$753$	−8.47357	+	8.47357i	−0.308794	+	0.308794i
$754$	2.25848	+	0.296806i	0.0822488	+	0.0108090i
$755$	14.5237	−	11.8878i	0.528572	−	0.432640i
$756$	6.12970	+	46.3948i	0.222935	+	1.68736i
$757$	35.4084	−	14.6666i	1.28694	−	0.533068i	0.368868	−	0.929482i	$-0.379745\pi$
$757$	35.4084	−	14.6666i	1.28694	−	0.533068i	0.918072	+	0.396413i	$0.129745\pi$
$758$	15.3852	−	26.6621i	0.558815	−	0.968411i
$759$	−22.9443	+	22.9443i	−0.832826	+	0.832826i
$760$	15.5425	+	1.54036i	0.563785	+	0.0558748i
$761$	−21.0295	−	21.0295i	−0.762318	−	0.762318i	0.214423	−	0.976741i	$-0.431213\pi$
$761$	−21.0295	−	21.0295i	−0.762318	−	0.762318i	−0.976741	+	0.214423i	$0.931213\pi$
$762$	8.15165	−	2.18624i	0.295303	−	0.0791990i
$763$	17.3231	+	41.8217i	0.627139	+	1.51405i
$764$	−2.85213	+	10.6639i	−0.103186	+	0.385807i
$765$	−6.74435	−	0.673109i	−0.243843	−	0.0243363i
$766$	−28.4200	+	21.8178i	−1.02686	+	0.788310i
$767$	10.9402	+	10.9402i	0.395029	+	0.395029i
$768$	19.0157	−	2.53907i	0.686171	−	0.0916208i
$769$			37.8557i			1.36511i	0.730833	+	0.682556i	$0.239132\pi$
$769$			37.8557i			1.36511i	−0.730833	+	0.682556i	$0.760868\pi$
$770$	42.8598	−	59.6759i	1.54456	−	2.15057i
$771$	0.499113	+	1.20496i	0.0179751	+	0.0433957i
$772$	11.2974	+	19.5469i	0.406603	+	0.703509i
$773$	44.8508	−	18.5778i	1.61317	−	0.668197i	0.619971	−	0.784625i	$-0.287144\pi$
$773$	44.8508	−	18.5778i	1.61317	−	0.668197i	0.993199	+	0.116428i	$0.0371443\pi$
$774$	−8.65528	−	4.99447i	−0.311108	−	0.179523i
$775$	−2.67973	+	13.2913i	−0.0962587	+	0.477438i
$776$	−12.6786	+	5.26191i	−0.455136	+	0.188891i
$777$		−	23.1401i		−	0.830148i
$778$	−44.3283	−	25.5793i	−1.58925	−	0.917064i
$779$	−24.7349	−	10.2455i	−0.886220	−	0.367085i
$780$	−8.81478	+	3.98501i	−0.315620	+	0.142686i
$781$	11.8837	+	28.6899i	0.425233	+	1.02660i
$782$	−10.8432	+	8.32426i	−0.387753	+	0.297675i
$783$	3.45360	+	3.45360i	0.123422	+	0.123422i
$784$	−39.1520	−	22.5564i	−1.39828	−	0.805586i
$785$	−8.73358	−	4.68280i	−0.311715	−	0.167136i
$786$	−2.10050	−	0.276045i	−0.0749224	−	0.00984619i
$787$	−9.67228	+	23.3509i	−0.344779	+	0.832371i	0.652439	+	0.757841i	$0.273746\pi$
$787$	−9.67228	+	23.3509i	−0.344779	+	0.832371i	−0.997219	+	0.0745302i	$0.976254\pi$
$788$	2.67148	+	20.2200i	0.0951676	+	0.720309i
$789$	−5.23981	+	12.6500i	−0.186542	+	0.450353i
$790$	−31.1073	−	7.28827i	−1.10675	−	0.259305i
$791$	44.2286	+	44.2286i	1.57259	+	1.57259i
$792$	−24.0026	+	0.0165609i	−0.852897	+	0.000588464i
$793$			9.78380i			0.347433i
$794$	31.8836	+	18.3982i	1.13151	+	0.652928i
$795$	1.19788	−	12.0024i	0.0424845	−	0.425682i
$796$	2.73300	+	4.72867i	0.0968686	+	0.167603i
$797$	−5.45903	+	13.1793i	−0.193369	+	0.466834i	−0.990592	−	0.136852i	$-0.956302\pi$
$797$	−5.45903	+	13.1793i	−0.193369	+	0.466834i	0.797223	+	0.603685i	$0.206302\pi$
$798$	2.33387	−	17.7591i	0.0826182	−	0.628665i
$799$	−7.68715			−0.271952
$800$	18.6183	+	21.2922i	0.658256	+	0.752794i
$801$	−16.0670			−0.567699
$802$	1.10295	−	8.39267i	0.0389466	−	0.296356i
$803$	33.1473	−	80.0248i	1.16974	−	2.82401i
$804$	−18.5766	+	10.7366i	−0.655145	+	0.378650i
$805$	−4.73233	+	47.4166i	−0.166793	+	1.67121i
$806$	−5.99240	−	3.45788i	−0.211073	−	0.121799i
$807$			8.56211i			0.301401i
$808$	−25.0668	+	25.1014i	−0.881847	+	0.883064i
$809$	26.1235	+	26.1235i	0.918453	+	0.918453i	0.996917	−	0.0784643i	$-0.0250017\pi$
$809$	26.1235	+	26.1235i	0.918453	+	0.918453i	−0.0784643	+	0.996917i	$0.525002\pi$
$810$	−5.76422	−	1.35053i	−0.202534	−	0.0474527i
$811$	−6.41066	+	15.4767i	−0.225109	+	0.543460i	−0.995570	−	0.0940267i	$-0.970026\pi$
$811$	−6.41066	+	15.4767i	−0.225109	+	0.543460i	0.770461	+	0.637487i	$0.220026\pi$
$812$	−7.57223	+	1.00045i	−0.265733	+	0.0351088i
$813$	1.17108	−	2.82723i	0.0410714	−	0.0991552i
$814$	34.3633	+	4.51597i	1.20443	+	0.158285i
$815$	−25.8136	−	13.8408i	−0.904209	−	0.484821i
$816$	9.22673	+	1.20609i	0.323000	+	0.0422215i
$817$	7.89777	+	7.89777i	0.276308	+	0.276308i
$818$	14.9490	−	11.4762i	0.522679	−	0.401257i
$819$	−4.61359	−	11.1382i	−0.161212	−	0.389200i
$820$	−19.9726	−	44.1790i	−0.697472	−	1.54280i
$821$	−27.9685	−	11.5849i	−0.976106	−	0.404316i	−0.163124	−	0.986606i	$-0.552157\pi$
$821$	−27.9685	−	11.5849i	−0.976106	−	0.404316i	−0.812982	+	0.582289i	$0.802157\pi$
$822$	8.18566	+	4.72348i	0.285508	+	0.164750i
$823$		−	29.7741i		−	1.03786i	−0.854817	−	0.518929i	$-0.826331\pi$
$823$		−	29.7741i		−	1.03786i	0.854817	−	0.518929i	$-0.173669\pi$
$824$	6.17238	+	2.55170i	0.215025	+	0.0888926i
$825$	18.0214	+	27.1232i	0.627425	+	0.944310i
$826$	−44.9343	−	25.9290i	−1.56346	−	0.902187i
$827$	21.0410	−	8.71545i	0.731666	−	0.303066i	0.0144294	−	0.999896i	$-0.495407\pi$
$827$	21.0410	−	8.71545i	0.731666	−	0.303066i	0.717236	+	0.696830i	$0.245407\pi$
$828$	13.4782	−	7.78993i	0.468401	−	0.270719i
$829$	0.840704	+	2.02964i	0.0291989	+	0.0704923i	0.937806	−	0.347159i	$-0.112853\pi$
$829$	0.840704	+	2.02964i	0.0291989	+	0.0704923i	−0.908608	+	0.417651i	$0.862853\pi$
$830$	−9.24797	+	12.8764i	−0.321002	+	0.446947i
$831$			12.6098i			0.437428i
$832$	−13.3261	+	5.54142i	−0.462001	+	0.192114i
$833$	−15.4972	−	15.4972i	−0.536947	−	0.536947i
$834$	9.60484	−	7.37356i	0.332588	−	0.255325i
$835$	−22.8568	−	2.28118i	−0.790991	−	0.0789436i
$836$	25.9169	+	6.93164i	0.896355	+	0.239736i
$837$	−5.67683	−	13.7051i	−0.196220	−	0.473717i
$838$	−7.72652	+	2.07222i	−0.266908	+	0.0715836i
$839$	−1.61923	−	1.61923i	−0.0559021	−	0.0559021i	0.678603	−	0.734505i	$-0.262586\pi$
$839$	−1.61923	−	1.61923i	−0.0559021	−	0.0559021i	−0.734505	+	0.678603i	$0.762586\pi$
$840$	25.0867	−	20.5625i	0.865573	−	0.709475i
$841$	19.9424	−	19.9424i	0.687670	−	0.687670i
$842$	−13.4752	+	23.3522i	−0.464387	+	0.804770i
$843$	28.9436	−	11.9889i	0.996872	−	0.412918i
$844$	−45.3266	+	5.98857i	−1.56021	+	0.206135i
$845$	−16.8629	+	13.8024i	−0.580103	+	0.474818i
$846$	8.67954	+	1.14065i	0.298409	+	0.0392164i
$847$	55.9679	−	55.9679i	1.92308	−	1.92308i
$848$	2.33248	−	17.8438i	0.0800976	−	0.612757i
$849$	23.2668			0.798515
$850$	6.03859	+	12.3185i	0.207122	+	0.422521i
$851$	−20.7676	+	8.60224i	−0.711906	+	0.294881i
$852$	1.79574	+	13.5917i	0.0615210	+	0.465643i
$853$	−4.82343	−	11.6448i	−0.165151	−	0.398710i	0.819539	−	0.573023i	$-0.194230\pi$
$853$	−4.82343	−	11.6448i	−0.165151	−	0.398710i	−0.984690	+	0.174313i	$0.944230\pi$
$854$	−8.49815	−	31.6864i	−0.290801	−	1.08429i
$855$	−7.60321	−	4.07671i	−0.260024	−	0.139420i
$856$	−0.00354984	−	5.14499i	−0.000121331	−	0.175852i
$857$	19.0312			0.650095			0.325047	−	0.945698i	$-0.394620\pi$
$857$	19.0312			0.650095			0.325047	+	0.945698i	$0.394620\pi$
$858$	−16.0492	+	4.30432i	−0.547910	+	0.146947i
$859$	3.86867	−	9.33980i	0.131997	−	0.318670i	−0.844037	−	0.536284i	$-0.819828\pi$
$859$	3.86867	−	9.33980i	0.131997	−	0.318670i	0.976035	+	0.217614i	$0.0698275\pi$
$860$	0.644828	+	20.2163i	0.0219885	+	0.689369i
$861$	−51.3699	+	21.2781i	−1.75068	+	0.725156i
$862$	10.7588	+	1.41390i	0.366445	+	0.0481576i
$863$	3.68547	−	3.68547i	0.125455	−	0.125455i	−0.641592	−	0.767046i	$-0.721726\pi$
$863$	3.68547	−	3.68547i	0.125455	−	0.125455i	0.767046	+	0.641592i	$0.221726\pi$
$864$	−29.8998	−	7.97480i	−1.01721	−	0.271308i
$865$	30.1152	+	16.1473i	1.02395	+	0.549023i
$866$	−10.6251	+	8.15683i	−0.361056	+	0.277180i
$867$	−14.6621	−	6.07324i	−0.497951	−	0.206258i
$868$	22.4108	+	5.99391i	0.760673	+	0.203447i
$869$	−50.7019	−	21.0014i	−1.71994	−	0.712424i
$870$	0.772254	−	3.29607i	0.0261818	−	0.111747i
$871$	11.4136	−	11.4136i	0.386735	−	0.386735i
$872$	−29.9330	+	0.0206526i	−1.01366	+	0.000699385i
$873$	7.58241			0.256626
$874$	−16.8059	+	4.50727i	−0.568468	+	0.152461i
$875$	45.7092	+	14.0605i	1.54525	+	0.475332i
$876$	23.2656	−	30.3491i	0.786070	−	1.02540i
$877$	−5.54243	−	2.29575i	−0.187155	−	0.0775220i	0.287138	−	0.957889i	$-0.407296\pi$
$877$	−5.54243	−	2.29575i	−0.187155	−	0.0775220i	−0.474293	+	0.880367i	$0.657296\pi$
$878$	−22.0081	+	16.8955i	−0.742738	+	0.570194i
$879$			38.4536i			1.29701i
$880$	25.6397	+	41.2669i	0.864314	+	1.39111i
$881$		−	17.7304i		−	0.597352i	−0.954355	−	0.298676i	$-0.903455\pi$
$881$		−	17.7304i		−	0.597352i	0.954355	−	0.298676i	$-0.0965449\pi$
$882$	15.1983	+	19.7974i	0.511755	+	0.666614i
$883$	38.8643	+	16.0981i	1.30789	+	0.541745i	0.924267	−	0.381746i	$-0.124677\pi$
$883$	38.8643	+	16.0981i	1.30789	+	0.541745i	0.383621	+	0.923491i	$0.374677\pi$
$884$	−6.93995	+	0.916909i	−0.233416	+	0.0308390i
$885$	17.7933	−	14.5640i	0.598116	−	0.489562i
$886$	−3.27285	−	12.2032i	−0.109954	−	0.409975i
$887$	−33.9047			−1.13841			−0.569204	−	0.822197i	$-0.692748\pi$
$887$	−33.9047			−1.13841			−0.569204	+	0.822197i	$0.692748\pi$
$888$	14.1407	+	5.84583i	0.474530	+	0.196173i
$889$	15.0539	−	15.0539i	0.504891	−	0.504891i
$890$	17.1437	+	27.6352i	0.574659	+	0.926333i
$891$	−9.39515	−	3.89160i	−0.314749	−	0.130373i
$892$	35.1945	−	20.3411i	1.17840	−	0.681072i
$893$	−9.03976	−	3.74439i	−0.302504	−	0.125301i
$894$	−20.9766	−	27.3242i	−0.701561	−	0.913857i
$895$	6.24353	−	1.88510i	0.208698	−	0.0630120i
$896$	38.3455	−	29.5218i	1.28103	−	0.986253i
$897$	7.62044	−	7.62044i	0.254439	−	0.254439i
$898$	−6.72784	+	51.1940i	−0.224511	+	1.70837i
$899$	2.23685	−	0.926532i	0.0746030	−	0.0309016i
$900$	−4.99028	−	14.8048i	−0.166343	−	0.493494i
$901$	3.34027	−	8.06412i	0.111281	−	0.268655i
$902$	−21.5729	−	80.4372i	−0.718300	−	2.67827i
$903$	23.1962			0.771922
$904$	−38.2009	+	15.8542i	−1.27054	+	0.527303i
$905$	4.01769	−	7.49313i	0.133552	−	0.249080i
$906$	13.7470	−	3.68688i	0.456713	−	0.122488i
$907$	−4.44973	−	10.7426i	−0.147751	−	0.356702i	0.832626	−	0.553836i	$-0.186837\pi$
$907$	−4.44973	−	10.7426i	−0.147751	−	0.356702i	−0.980377	+	0.197134i	$0.936837\pi$
$908$	−0.830182	−	0.636414i	−0.0275505	−	0.0211202i
$909$	18.1032	−	7.49859i	0.600445	−	0.248712i
$910$	−14.2349	+	19.8200i	−0.471883	+	0.657027i
$911$	−4.95485			−0.164161			−0.0820807	−	0.996626i	$-0.526157\pi$
$911$	−4.95485			−0.164161			−0.0820807	+	0.996626i	$0.526157\pi$
$912$	10.2628	+	5.91263i	0.339834	+	0.195787i
$913$	−19.2552	+	19.2552i	−0.637253	+	0.637253i
$914$	5.49558	−	41.8174i	0.181778	−	1.38320i
$915$	14.4685	+	1.44400i	0.478314	+	0.0477373i
$916$	−14.9778	−	11.4819i	−0.494881	−	0.379374i
$917$	−4.93732	+	2.04511i	−0.163045	+	0.0675354i
$918$	−13.0004	−	7.50179i	−0.429077	−	0.247596i
$919$	3.72103	−	3.72103i	0.122746	−	0.122746i	−0.643066	−	0.765811i	$-0.722338\pi$
$919$	3.72103	−	3.72103i	0.122746	−	0.122746i	0.765811	+	0.643066i	$0.222338\pi$
$920$	−27.7802	−	14.8706i	−0.915885	−	0.490269i
$921$	−22.8789	−	22.8789i	−0.753884	−	0.753884i
$922$	−1.78096	−	6.64053i	−0.0586529	−	0.218694i
$923$	−3.94691	−	9.52869i	−0.129914	−	0.313641i
$924$	48.2391	−	27.8804i	1.58695	−	0.917199i
$925$	4.34359	+	22.1372i	0.142816	+	0.727865i
$926$	−21.9115	−	28.5420i	−0.720056	−	0.937948i
$927$	−2.60870	−	2.60870i	−0.0856810	−	0.0856810i
$928$	1.30159	−	4.88004i	0.0427268	−	0.160195i
$929$			15.5528i			0.510270i	0.966905	+	0.255135i	$0.0821200\pi$
$929$			15.5528i			0.510270i	−0.966905	+	0.255135i	$0.917880\pi$
$930$	−5.99801	+	8.35134i	−0.196682	+	0.273851i
$931$	−10.6754	−	25.7728i	−0.349873	−	0.844668i
$932$	−16.6815	−	4.46158i	−0.546421	−	0.146144i
$933$	17.7639	−	7.35806i	0.581565	−	0.240892i
$934$	−2.34305	+	4.06044i	−0.0766669	+	0.132862i
$935$	6.81121	+	22.5590i	0.222750	+	0.737758i
$936$	7.97193	−	0.00550032i	0.260571	−	0.000179783i
$937$			51.6312i			1.68672i	0.537350	+	0.843359i	$0.319425\pi$
$937$			51.6312i			1.68672i	−0.537350	+	0.843359i	$0.680575\pi$
$938$	−27.0509	+	46.8785i	−0.883245	+	1.53064i
$939$	12.8838	+	5.33665i	0.420447	+	0.174155i
$940$	−7.29929	−	16.1459i	−0.238076	−	0.526621i
$941$	4.35878	+	10.5230i	0.142092	+	0.343041i	0.978864	−	0.204510i	$-0.0655601\pi$
$941$	4.35878	+	10.5230i	0.142092	+	0.343041i	−0.836772	+	0.547551i	$0.815560\pi$
$942$	−4.57617	−	5.96095i	−0.149100	−	0.194218i
$943$	38.1930	+	38.1930i	1.24374	+	1.24374i
$944$	27.1966	−	20.9084i	0.885172	−	0.680511i
$945$	−50.0885	+	15.1231i	−1.62938	+	0.491956i
$946$	−4.52692	+	34.4466i	−0.147183	+	1.11996i
$947$	−4.14900	+	10.0166i	−0.134824	+	0.325495i	−0.976844	−	0.213952i	$-0.931366\pi$
$947$	−4.14900	+	10.0166i	−0.134824	+	0.325495i	0.842020	+	0.539446i	$0.181366\pi$
$948$	−19.2285	−	14.7405i	−0.624514	−	0.478750i
$949$	−11.0091	+	26.5784i	−0.357372	+	0.862772i
$950$	1.10081	+	17.4274i	0.0357149	+	0.565420i
$951$	4.16210	+	4.16210i	0.134965	+	0.134965i
$952$	21.6797	−	8.99755i	0.702643	−	0.291612i
$953$			50.9623i			1.65083i	0.564526	+	0.825415i	$0.309059\pi$
$953$			50.9623i			1.65083i	−0.564526	+	0.825415i	$0.690941\pi$
$954$	−4.96808	+	8.60954i	−0.160848	+	0.278744i
$955$	−12.2807	−	1.22565i	−0.397393	−	0.0396612i
$956$	−11.9335	+	44.6186i	−0.385958	+	1.44307i
$957$	2.22528	−	5.37229i	0.0719330	−	0.173662i
$958$	−34.4722	−	4.53029i	−1.11375	−	0.146367i
$959$	23.8397			0.769823
$960$	6.22795	+	20.5248i	0.201006	+	0.662436i
$961$	23.6464			0.762787
$962$	−11.4130	−	1.49988i	−0.367970	−	0.0483580i
$963$	−1.08755	+	2.62559i	−0.0350459	+	0.0846083i
$964$	−7.23808	+	27.0627i	−0.233123	+	0.871630i
$965$	−19.5329	+	15.9878i	−0.628785	+	0.514665i
$966$	−18.0609	+	31.2990i	−0.581100	+	1.00703i
$967$		−	38.8525i		−	1.24941i	−0.780860	−	0.624706i	$-0.785219\pi$
$967$		−	38.8525i		−	1.24941i	0.780860	−	0.624706i	$-0.214781\pi$
$968$	20.0623	+	48.3403i	0.644827	+	1.55372i
$969$	4.06223	+	4.06223i	0.130498	+	0.130498i
$970$	−8.09055	−	13.0417i	−0.259772	−	0.418745i
$971$	−13.0201	+	31.4332i	−0.417833	+	1.00874i	0.565141	+	0.824995i	$0.308822\pi$
$971$	−13.0201	+	31.4332i	−0.417833	+	1.00874i	−0.982974	+	0.183744i	$0.941178\pi$
$972$	22.4857	+	17.2375i	0.721230	+	0.552892i
$973$	11.6889	−	28.2196i	0.374730	−	0.904678i
$974$	−1.36355	+	10.3756i	−0.0436909	+	0.332456i
$975$	−5.98540	−	9.00837i	−0.191686	−	0.288499i
$976$	21.5100	+	2.81172i	0.688519	+	0.0900010i
$977$	−18.5646	−	18.5646i	−0.593935	−	0.593935i	0.344757	−	0.938692i	$-0.387961\pi$
$977$	−18.5646	−	18.5646i	−0.593935	−	0.593935i	−0.938692	+	0.344757i	$0.887961\pi$
$978$	−13.5256	−	17.6186i	−0.432502	−	0.563379i
$979$	21.3769	+	51.6085i	0.683210	+	1.64941i
$980$	17.8347	−	47.2653i	0.569708	−	1.50983i
$981$	15.2754	+	6.32727i	0.487706	+	0.202014i
$982$	−23.8154	+	41.2714i	−0.759981	+	1.31702i
$983$			1.22454i			0.0390566i	0.999809	+	0.0195283i	$0.00621645\pi$
$983$			1.22454i			0.0390566i	−0.999809	+	0.0195283i	$0.993784\pi$
$984$	−0.0253677	−	36.7670i	−0.000808693	−	1.17209i
$985$	−21.8298	+	6.59105i	−0.695556	+	0.210008i
$986$	1.22439	−	2.12183i	0.0389925	−	0.0675729i
$987$	−18.7739	+	7.77642i	−0.597581	+	0.247526i
$988$	−8.60771	−	2.30219i	−0.273848	−	0.0732423i
$989$	−8.62309	−	20.8180i	−0.274198	−	0.661973i
$990$	−4.34311	−	26.4820i	−0.138033	−	0.841653i
$991$		−	51.7983i		−	1.64543i	−0.568457	−	0.822713i	$-0.692459\pi$
$991$		−	51.7983i		−	1.64543i	0.568457	−	0.822713i	$-0.307541\pi$
$992$	−9.32439	+	12.1808i	−0.296050	+	0.386739i
$993$	−3.31430	−	3.31430i	−0.105176	−	0.105176i
$994$	21.0593	+	27.4319i	0.667959	+	0.870087i
$995$	−4.72527	+	3.86766i	−0.149801	+	0.122613i
$996$	−10.4087	+	6.01584i	−0.329811	+	0.190619i
$997$	11.6429	+	28.1085i	0.368735	+	0.890205i	0.993958	+	0.109759i	$0.0350079\pi$
$997$	11.6429	+	28.1085i	0.368735	+	0.890205i	−0.625223	+	0.780446i	$0.714992\pi$
$998$	0.270308	+	1.00787i	0.00855644	+	0.0319037i
$999$	−17.4525	−	17.4525i	−0.552171	−	0.552171i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.2.u.a.43.2	✓	88
4.3	odd	2		640.2.u.a.463.9		88
5.2	odd	4		160.2.ba.a.107.13	yes	88
5.3	odd	4		800.2.bb.b.107.10		88
5.4	even	2		800.2.v.b.43.21		88
20.7	even	4		640.2.ba.a.207.14		88
32.3	odd	8		160.2.ba.a.3.13	yes	88
32.29	even	8		640.2.ba.a.303.14		88
160.3	even	8		800.2.v.b.707.21		88
160.67	even	8	inner	160.2.u.a.67.2	yes	88
160.99	odd	8		800.2.bb.b.643.10		88
160.157	odd	8		640.2.u.a.47.9		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.u.a.43.2	✓	88	1.1	even	1	trivial
160.2.u.a.67.2	yes	88	160.67	even	8	inner
160.2.ba.a.3.13	yes	88	32.3	odd	8
160.2.ba.a.107.13	yes	88	5.2	odd	4
640.2.u.a.47.9		88	160.157	odd	8
640.2.u.a.463.9		88	4.3	odd	2
640.2.ba.a.207.14		88	20.7	even	4
640.2.ba.a.303.14		88	32.29	even	8
800.2.v.b.43.21		88	5.4	even	2
800.2.v.b.707.21		88	160.3	even	8
800.2.bb.b.107.10		88	5.3	odd	4
800.2.bb.b.643.10		88	160.99	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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	160.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40216 - 0.184269i) q^{2} +(0.458849 - 1.10776i) q^{3} +(1.93209 + 0.516749i) q^{4} +(-0.222064 + 2.22501i) q^{5} +(-0.847505 + 1.46870i) q^{6} +4.27741i q^{7} +(-2.61387 - 1.08059i) q^{8} +(1.10473 + 1.10473i) q^{9} +O(q^{10})\)	\(q+(-1.40216 - 0.184269i) q^{2} +(0.458849 - 1.10776i) q^{3} +(1.93209 + 0.516749i) q^{4} +(-0.222064 + 2.22501i) q^{5} +(-0.847505 + 1.46870i) q^{6} +4.27741i q^{7} +(-2.61387 - 1.08059i) q^{8} +(1.10473 + 1.10473i) q^{9} +(0.721371 - 3.07890i) q^{10} +(2.07866 - 5.01832i) q^{11} +(1.45897 - 1.90318i) q^{12} +(-0.690379 + 1.66672i) q^{13} +(0.788195 - 5.99760i) q^{14} +(2.36289 + 1.26694i) q^{15} +(3.46594 + 1.99681i) q^{16} +(1.37190 + 1.37190i) q^{17} +(-1.34544 - 1.75257i) q^{18} +(0.945045 + 2.28154i) q^{19} +(-1.57882 + 4.18418i) q^{20} +(4.73834 + 1.96269i) q^{21} +(-3.83933 + 6.65344i) q^{22} -4.98215i q^{23} +(-2.39641 + 2.39972i) q^{24} +(-4.90138 - 0.988190i) q^{25} +(1.27515 - 2.20979i) q^{26} +(5.05396 - 2.09342i) q^{27} +(-2.21035 + 8.26433i) q^{28} +(0.341673 + 0.824872i) q^{29} +(-3.07968 - 2.21186i) q^{30} -2.71175i q^{31} +(-4.49184 - 3.43851i) q^{32} +(-4.60531 - 4.60531i) q^{33} +(-1.67082 - 2.17641i) q^{34} +(-9.51729 - 0.949857i) q^{35} +(1.56357 + 2.70531i) q^{36} +(-1.72661 - 4.16841i) q^{37} +(-0.904684 - 3.37322i) q^{38} +(1.52955 + 1.52955i) q^{39} +(2.98477 - 5.57594i) q^{40} +(-7.66597 + 7.66597i) q^{41} +(-6.28224 - 3.62512i) q^{42} +(4.17851 - 1.73080i) q^{43} +(6.60936 - 8.62170i) q^{44} +(-2.70336 + 2.21272i) q^{45} +(-0.918058 + 6.98576i) q^{46} +(-2.80165 + 2.80165i) q^{47} +(3.80233 - 2.92319i) q^{48} -11.2962 q^{49} +(6.69041 + 2.28877i) q^{50} +(2.14923 - 0.890239i) q^{51} +(-2.19515 + 2.86350i) q^{52} +(-1.72165 - 4.15643i) q^{53} +(-7.47220 + 2.00401i) q^{54} +(10.7042 + 5.73943i) q^{55} +(4.62212 - 11.1806i) q^{56} +2.96103 q^{57} +(-0.327081 - 1.21956i) q^{58} +(3.28196 - 7.92336i) q^{59} +(3.91062 + 3.66886i) q^{60} +(5.01044 - 2.07539i) q^{61} +(-0.499693 + 3.80230i) q^{62} +(-4.72538 + 4.72538i) q^{63} +(5.66465 + 5.64904i) q^{64} +(-3.55517 - 1.90622i) q^{65} +(5.60874 + 7.30598i) q^{66} +(-8.26619 - 3.42397i) q^{67} +(1.94170 + 3.35955i) q^{68} +(-5.51903 - 2.28606i) q^{69} +(13.1697 + 3.08559i) q^{70} +(-4.04255 + 4.04255i) q^{71} +(-1.69386 - 4.08138i) q^{72} +15.9465 q^{73} +(1.65287 + 6.16293i) q^{74} +(-3.34367 + 4.97612i) q^{75} +(0.646927 + 4.89649i) q^{76} +(21.4654 + 8.89126i) q^{77} +(-1.86282 - 2.42652i) q^{78} -10.1034i q^{79} +(-5.21260 + 7.26835i) q^{80} -1.87217i q^{81} +(12.1615 - 9.33629i) q^{82} +(-4.63164 - 1.91849i) q^{83} +(8.14068 + 6.24062i) q^{84} +(-3.35714 + 2.74784i) q^{85} +(-6.17787 + 1.65688i) q^{86} +1.07054 q^{87} +(-10.8561 + 10.8711i) q^{88} +(-7.27190 + 7.27190i) q^{89} +(4.19827 - 2.60443i) q^{90} +(-7.12924 - 2.95303i) q^{91} +(2.57452 - 9.62596i) q^{92} +(-3.00397 - 1.24429i) q^{93} +(4.44461 - 3.41210i) q^{94} +(-5.28632 + 1.59609i) q^{95} +(-5.87013 + 3.39812i) q^{96} +(3.43179 - 3.43179i) q^{97} +(15.8391 + 2.08155i) q^{98} +(7.84024 - 3.24753i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8}+O(q^{10}) \) 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8	\( 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8} - 16 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} + 16 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} + 16 q^{19} + 24 q^{20} - 8 q^{21} - 20 q^{22} - 32 q^{24} - 4 q^{25} - 8 q^{26} - 16 q^{27} + 12 q^{28} + 8 q^{30} - 24 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 8 q^{36} - 4 q^{37} - 60 q^{38} + 16 q^{40} - 8 q^{41} + 60 q^{42} - 36 q^{43} + 16 q^{44} - 4 q^{45} - 8 q^{46} - 8 q^{47} - 24 q^{48} - 40 q^{49} - 12 q^{50} + 8 q^{51} - 56 q^{52} - 4 q^{53} - 56 q^{54} - 36 q^{55} + 40 q^{56} - 8 q^{57} - 36 q^{58} + 12 q^{60} - 40 q^{61} + 40 q^{62} + 56 q^{63} + 48 q^{64} - 8 q^{65} + 72 q^{66} + 20 q^{67} + 8 q^{68} + 24 q^{69} + 60 q^{70} + 24 q^{71} + 24 q^{72} - 8 q^{73} + 8 q^{75} + 56 q^{76} + 24 q^{77} + 32 q^{78} - 8 q^{80} + 84 q^{82} - 44 q^{83} + 56 q^{84} - 4 q^{85} + 24 q^{86} - 120 q^{87} + 104 q^{88} + 148 q^{90} - 8 q^{91} + 124 q^{92} + 8 q^{93} - 32 q^{94} + 24 q^{96} - 8 q^{97} - 16 q^{98}+O(q^{100}) \) 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8 - 16 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 + 16 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 + 16 * q^19 + 24 * q^20 - 8 * q^21 - 20 * q^22 - 32 * q^24 - 4 * q^25 - 8 * q^26 - 16 * q^27 + 12 * q^28 + 8 * q^30 - 24 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 8 * q^36 - 4 * q^37 - 60 * q^38 + 16 * q^40 - 8 * q^41 + 60 * q^42 - 36 * q^43 + 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 24 * q^48 - 40 * q^49 - 12 * q^50 + 8 * q^51 - 56 * q^52 - 4 * q^53 - 56 * q^54 - 36 * q^55 + 40 * q^56 - 8 * q^57 - 36 * q^58 + 12 * q^60 - 40 * q^61 + 40 * q^62 + 56 * q^63 + 48 * q^64 - 8 * q^65 + 72 * q^66 + 20 * q^67 + 8 * q^68 + 24 * q^69 + 60 * q^70 + 24 * q^71 + 24 * q^72 - 8 * q^73 + 8 * q^75 + 56 * q^76 + 24 * q^77 + 32 * q^78 - 8 * q^80 + 84 * q^82 - 44 * q^83 + 56 * q^84 - 4 * q^85 + 24 * q^86 - 120 * q^87 + 104 * q^88 + 148 * q^90 - 8 * q^91 + 124 * q^92 + 8 * q^93 - 32 * q^94 + 24 * q^96 - 8 * q^97 - 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more