LMFDB - Embedded newform 680.2.t.a.523.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(523,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.523"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.t (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$208$
Relative dimension:	$104$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			523.5
Character	$\chi$	$=$	680.523
Dual form			680.2.t.a.667.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40194 + 0.185930i) q^{2} -2.65957i q^{3} +(1.93086 - 0.521326i) q^{4} +(-0.163750 - 2.23006i) q^{5} +(0.494495 + 3.72855i) q^{6} +1.56006 q^{7} +(-2.61002 + 1.08987i) q^{8} -4.07332 q^{9} +(0.644204 + 3.09597i) q^{10} +(-0.688367 + 0.688367i) q^{11} +(-1.38650 - 5.13526i) q^{12} +(3.75034 - 3.75034i) q^{13} +(-2.18710 + 0.290062i) q^{14} +(-5.93101 + 0.435505i) q^{15} +(3.45644 - 2.01321i) q^{16} +(-3.32461 - 2.43864i) q^{17} +(5.71054 - 0.757354i) q^{18} +0.733580 q^{19} +(-1.47877 - 4.22057i) q^{20} -4.14908i q^{21} +(0.837059 - 1.09304i) q^{22} -6.29519i q^{23} +(2.89859 + 6.94152i) q^{24} +(-4.94637 + 0.730347i) q^{25} +(-4.56044 + 5.95505i) q^{26} +2.85457i q^{27} +(3.01225 - 0.813298i) q^{28} +(1.95429 + 1.95429i) q^{29} +(8.23394 - 1.71331i) q^{30} +(1.99098 - 1.99098i) q^{31} +(-4.47140 + 3.46506i) q^{32} +(1.83076 + 1.83076i) q^{33} +(5.11432 + 2.80067i) q^{34} +(-0.255460 - 3.47903i) q^{35} +(-7.86501 + 2.12353i) q^{36} +10.8829i q^{37} +(-1.02843 + 0.136395i) q^{38} +(-9.97430 - 9.97430i) q^{39} +(2.85787 + 5.64203i) q^{40} +(-6.99271 + 6.99271i) q^{41} +(0.771441 + 5.81676i) q^{42} +(4.24516 - 4.24516i) q^{43} +(-0.970276 + 1.68800i) q^{44} +(0.667007 + 9.08376i) q^{45} +(1.17047 + 8.82546i) q^{46} +(4.16348 + 4.16348i) q^{47} +(-5.35428 - 9.19265i) q^{48} -4.56622 q^{49} +(6.79871 - 1.94358i) q^{50} +(-6.48573 + 8.84204i) q^{51} +(5.28623 - 9.19653i) q^{52} +(2.59977 + 2.59977i) q^{53} +(-0.530751 - 4.00193i) q^{54} +(1.64782 + 1.42238i) q^{55} +(-4.07177 + 1.70026i) q^{56} -1.95101i q^{57} +(-3.10315 - 2.37643i) q^{58} +3.14644 q^{59} +(-11.2249 + 3.93289i) q^{60} +(-2.66983 - 2.66983i) q^{61} +(-2.42104 + 3.16141i) q^{62} -6.35461 q^{63} +(5.62436 - 5.68916i) q^{64} +(-8.97762 - 7.74938i) q^{65} +(-2.90701 - 2.22622i) q^{66} +(-1.58165 + 1.58165i) q^{67} +(-7.69068 - 2.97546i) q^{68} -16.7425 q^{69} +(1.00500 + 4.82988i) q^{70} +(-1.38270 + 1.38270i) q^{71} +(10.6314 - 4.43939i) q^{72} +0.0700142i q^{73} +(-2.02346 - 15.2571i) q^{74} +(1.94241 + 13.1552i) q^{75} +(1.41644 - 0.382434i) q^{76} +(-1.07389 + 1.07389i) q^{77} +(15.8379 + 12.1288i) q^{78} +(-5.15461 + 5.15461i) q^{79} +(-5.05559 - 7.37842i) q^{80} -4.62803 q^{81} +(8.50318 - 11.1035i) q^{82} +(12.0334 - 12.0334i) q^{83} +(-2.16302 - 8.01130i) q^{84} +(-4.89391 + 7.81343i) q^{85} +(-5.16215 + 6.74076i) q^{86} +(5.19756 - 5.19756i) q^{87} +(1.04642 - 2.54688i) q^{88} +12.5002i q^{89} +(-2.62405 - 12.6109i) q^{90} +(5.85075 - 5.85075i) q^{91} +(-3.28184 - 12.1551i) q^{92} +(-5.29515 - 5.29515i) q^{93} +(-6.61106 - 5.06282i) q^{94} +(-0.120124 - 1.63593i) q^{95} +(9.21557 + 11.8920i) q^{96} +0.402052 q^{97} +(6.40156 - 0.848999i) q^{98} +(2.80394 - 2.80394i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 208 q - 8 q^{6} - 192 q^{9} + 2 q^{10} - 8 q^{11} + 8 q^{12} - 16 q^{14} - 16 q^{16} - 12 q^{18} - 10 q^{20} + 4 q^{22} + 16 q^{24} + 12 q^{28} - 24 q^{30} + 20 q^{32} - 8 q^{33} - 4 q^{34} - 8 q^{35} - 12 q^{38}+ \cdots + 24 q^{99}+O(q^{100}) $ 208 * q - 8 * q^6 - 192 * q^9 + 2 * q^10 - 8 * q^11 + 8 * q^12 - 16 * q^14 - 16 * q^16 - 12 * q^18 - 10 * q^20 + 4 * q^22 + 16 * q^24 + 12 * q^28 - 24 * q^30 + 20 * q^32 - 8 * q^33 - 4 * q^34 - 8 * q^35 - 12 * q^38 - 42 * q^40 - 8 * q^41 - 32 * q^42 + 8 * q^44 - 16 * q^46 + 160 * q^49 + 16 * q^50 - 8 * q^51 - 20 * q^52 + 36 * q^54 + 4 * q^56 - 56 * q^58 - 64 * q^59 + 32 * q^60 - 48 * q^65 - 8 * q^67 - 56 * q^68 - 28 * q^70 - 56 * q^72 + 8 * q^74 + 8 * q^75 - 12 * q^78 + 6 * q^80 + 128 * q^81 + 44 * q^82 + 8 * q^86 - 82 * q^90 + 24 * q^91 + 64 * q^94 - 48 * q^96 - 16 * q^97 - 40 * q^98 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

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 $

$2$	−1.40194	+	0.185930i	−0.991320	+	0.131473i
$2$	−1.40194	+	0.185930i	−0.991320	+	0.131473i
$3$		−	2.65957i		−	1.53550i	−0.640747	−	0.767752i	$-0.721375\pi$
$3$		−	2.65957i		−	1.53550i	0.640747	−	0.767752i	$-0.278625\pi$
$4$	1.93086	−	0.521326i	0.965430	−	0.260663i
$5$	−0.163750	−	2.23006i	−0.0732313	−	0.997315i
$5$	−0.163750	−	2.23006i	−0.0732313	−	0.997315i
$6$	0.494495	+	3.72855i	0.201877	+	1.52218i
$7$	1.56006			0.589646			0.294823	−	0.955552i	$-0.404739\pi$
$7$	1.56006			0.589646			0.294823	+	0.955552i	$0.404739\pi$
$8$	−2.61002	+	1.08987i	−0.922780	+	0.385328i
$9$	−4.07332			−1.35777
$10$	0.644204	+	3.09597i	0.203715	+	0.979030i
$11$	−0.688367	+	0.688367i	−0.207550	+	0.207550i	−0.803225	−	0.595675i	$-0.796885\pi$
$11$	−0.688367	+	0.688367i	−0.207550	+	0.207550i	0.595675	+	0.803225i	$0.296885\pi$
$12$	−1.38650	−	5.13526i	−0.400249	−	1.48242i
$13$	3.75034	−	3.75034i	1.04016	−	1.04016i	0.0409983	−	0.999159i	$-0.486946\pi$
$13$	3.75034	−	3.75034i	1.04016	−	1.04016i	0.999159	−	0.0409983i	$-0.0130538\pi$
$14$	−2.18710	+	0.290062i	−0.584528	+	0.0775223i
$15$	−5.93101	+	0.435505i	−1.53138	+	0.112447i
$16$	3.45644	−	2.01321i	0.864110	−	0.503303i
$17$	−3.32461	−	2.43864i	−0.806337	−	0.591457i
$17$	−3.32461	−	2.43864i	−0.806337	−	0.591457i
$18$	5.71054	−	0.757354i	1.34599	−	0.178510i
$19$	0.733580			0.168295			0.0841474	−	0.996453i	$-0.473183\pi$
$19$	0.733580			0.168295			0.0841474	+	0.996453i	$0.473183\pi$
$20$	−1.47877	−	4.22057i	−0.330663	−	0.943749i
$21$		−	4.14908i		−	0.905404i
$22$	0.837059	−	1.09304i	0.178462	−	0.233036i
$23$		−	6.29519i		−	1.31264i	−0.754484	−	0.656319i	$-0.772113\pi$
$23$		−	6.29519i		−	1.31264i	0.754484	−	0.656319i	$-0.227887\pi$
$24$	2.89859	+	6.94152i	0.591672	+	1.41693i
$25$	−4.94637	+	0.730347i	−0.989274	+	0.146069i
$26$	−4.56044	+	5.95505i	−0.894377	+	1.16788i
$27$			2.85457i			0.549362i
$28$	3.01225	−	0.813298i	0.569262	−	0.153699i
$29$	1.95429	+	1.95429i	0.362902	+	0.362902i	0.864880	−	0.501978i	$-0.167394\pi$
$29$	1.95429	+	1.95429i	0.362902	+	0.362902i	−0.501978	+	0.864880i	$0.667394\pi$
$30$	8.23394	−	1.71331i	1.50330	−	0.312806i
$31$	1.99098	−	1.99098i	0.357590	−	0.357590i	−0.505334	−	0.862924i	$-0.668631\pi$
$31$	1.99098	−	1.99098i	0.357590	−	0.357590i	0.862924	+	0.505334i	$0.168631\pi$
$32$	−4.47140	+	3.46506i	−0.790439	+	0.612541i
$33$	1.83076	+	1.83076i	0.318694	+	0.318694i
$34$	5.11432	+	2.80067i	0.877098	+	0.480311i
$35$	−0.255460	−	3.47903i	−0.0431806	−	0.588063i
$36$	−7.86501	+	2.12353i	−1.31083	+	0.353921i
$37$			10.8829i			1.78913i	0.446935	+	0.894567i	$0.352516\pi$
$37$			10.8829i			1.78913i	−0.446935	+	0.894567i	$0.647484\pi$
$38$	−1.02843	+	0.136395i	−0.166834	+	0.0221262i
$39$	−9.97430	−	9.97430i	−1.59717	−	1.59717i
$40$	2.85787	+	5.64203i	0.451870	+	0.892084i
$41$	−6.99271	+	6.99271i	−1.09208	+	1.09208i	−0.0967703	+	0.995307i	$0.530851\pi$
$41$	−6.99271	+	6.99271i	−1.09208	+	1.09208i	−0.995307	+	0.0967703i	$0.969149\pi$
$42$	0.771441	+	5.81676i	0.119036	+	0.897545i
$43$	4.24516	−	4.24516i	0.647381	−	0.647381i	−0.304978	−	0.952359i	$-0.598649\pi$
$43$	4.24516	−	4.24516i	0.647381	−	0.647381i	0.952359	+	0.304978i	$0.0986492\pi$
$44$	−0.970276	+	1.68800i	−0.146275	+	0.254476i
$45$	0.667007	+	9.08376i	0.0994315	+	1.35413i
$46$	1.17047	+	8.82546i	0.172576	+	1.30124i
$47$	4.16348	+	4.16348i	0.607306	+	0.607306i	0.942241	−	0.334935i	$-0.108714\pi$
$47$	4.16348	+	4.16348i	0.607306	+	0.607306i	−0.334935	+	0.942241i	$0.608714\pi$
$48$	−5.35428	−	9.19265i	−0.772824	−	1.32684i
$49$	−4.56622			−0.652317
$50$	6.79871	−	1.94358i	0.961483	−	0.274864i
$51$	−6.48573	+	8.84204i	−0.908184	+	1.23813i
$52$	5.28623	−	9.19653i	0.733069	−	1.27533i
$53$	2.59977	+	2.59977i	0.357107	+	0.357107i	0.862745	−	0.505639i	$-0.168743\pi$
$53$	2.59977	+	2.59977i	0.357107	+	0.357107i	−0.505639	+	0.862745i	$0.668743\pi$
$54$	−0.530751	−	4.00193i	−0.0722260	−	0.544593i
$55$	1.64782	+	1.42238i	0.222192	+	0.191794i
$56$	−4.07177	+	1.70026i	−0.544114	+	0.227207i
$57$		−	1.95101i		−	0.258417i
$58$	−3.10315	−	2.37643i	−0.407463	−	0.312040i
$59$	3.14644			0.409632			0.204816	−	0.978800i	$-0.434340\pi$
$59$	3.14644			0.409632			0.204816	+	0.978800i	$0.434340\pi$
$60$	−11.2249	+	3.93289i	−1.44913	+	0.507734i
$61$	−2.66983	−	2.66983i	−0.341837	−	0.341837i	0.515220	−	0.857058i	$-0.327710\pi$
$61$	−2.66983	−	2.66983i	−0.341837	−	0.341837i	−0.857058	+	0.515220i	$0.827710\pi$
$62$	−2.42104	+	3.16141i	−0.307473	+	0.401500i
$63$	−6.35461			−0.800606
$64$	5.62436	−	5.68916i	0.703045	−	0.711145i
$65$	−8.97762	−	7.74938i	−1.11354	−	0.961193i
$66$	−2.90701	−	2.22622i	−0.357828	−	0.274029i
$67$	−1.58165	+	1.58165i	−0.193229	+	0.193229i	−0.797090	−	0.603861i	$-0.793628\pi$
$67$	−1.58165	+	1.58165i	−0.193229	+	0.193229i	0.603861	+	0.797090i	$0.293628\pi$
$68$	−7.69068	−	2.97546i	−0.932632	−	0.360828i
$69$	−16.7425			−2.01556
$70$	1.00500	+	4.82988i	0.120120	+	0.577281i
$71$	−1.38270	+	1.38270i	−0.164096	+	0.164096i	−0.784378	−	0.620283i	$-0.787018\pi$
$71$	−1.38270	+	1.38270i	−0.164096	+	0.164096i	0.620283	+	0.784378i	$0.287018\pi$
$72$	10.6314	−	4.43939i	1.25293	−	0.523188i
$73$			0.0700142i			0.00819454i	0.999992	+	0.00409727i	$0.00130421\pi$
$73$			0.0700142i			0.00819454i	−0.999992	+	0.00409727i	$0.998696\pi$
$74$	−2.02346	−	15.2571i	−0.235222	−	1.77360i
$75$	1.94241	+	13.1552i	0.224290	+	1.51903i
$76$	1.41644	−	0.382434i	0.162477	−	0.0438682i
$77$	−1.07389	+	1.07389i	−0.122381	+	0.122381i
$78$	15.8379	+	12.1288i	1.79329	+	1.37332i
$79$	−5.15461	+	5.15461i	−0.579939	+	0.579939i	−0.934886	−	0.354947i	$-0.884499\pi$
$79$	−5.15461	+	5.15461i	−0.579939	+	0.579939i	0.354947	+	0.934886i	$0.384499\pi$
$80$	−5.05559	−	7.37842i	−0.565232	−	0.824932i
$81$	−4.62803			−0.514226
$82$	8.50318	−	11.1035i	0.939019	−	1.22618i
$83$	12.0334	−	12.0334i	1.32084	−	1.32084i	0.407740	−	0.913098i	$-0.366317\pi$
$83$	12.0334	−	12.0334i	1.32084	−	1.32084i	0.913098	−	0.407740i	$-0.133683\pi$
$84$	−2.16302	−	8.01130i	−0.236005	−	0.874104i
$85$	−4.89391	+	7.81343i	−0.530819	+	0.847485i
$86$	−5.16215	+	6.74076i	−0.556649	+	0.726875i
$87$	5.19756	−	5.19756i	0.557237	−	0.557237i
$88$	1.04642	−	2.54688i	0.111548	−	0.271498i
$89$			12.5002i			1.32502i	0.749052	+	0.662511i	$0.230509\pi$
$89$			12.5002i			1.32502i	−0.749052	+	0.662511i	$0.769491\pi$
$90$	−2.62405	−	12.6109i	−0.276599	−	1.32930i
$91$	5.85075	−	5.85075i	0.613325	−	0.613325i
$92$	−3.28184	−	12.1551i	−0.342156	−	1.26726i
$93$	−5.29515	−	5.29515i	−0.549081	−	0.549081i
$94$	−6.61106	−	5.06282i	−0.681879	−	0.522190i
$95$	−0.120124	−	1.63593i	−0.0123244	−	0.167843i
$96$	9.21557	+	11.8920i	0.940560	+	1.21372i
$97$	0.402052			0.0408222			0.0204111	−	0.999792i	$-0.493502\pi$
$97$	0.402052			0.0408222			0.0204111	+	0.999792i	$0.493502\pi$
$98$	6.40156	−	0.848999i	0.646655	−	0.0857619i
$99$	2.80394	−	2.80394i	0.281806	−	0.281806i
$100$	−9.17000	+	3.98887i	−0.917000	+	0.398887i
$101$		−	8.00189i		−	0.796218i	−0.917338	−	0.398109i	$-0.869667\pi$
$101$		−	8.00189i		−	0.796218i	0.917338	−	0.398109i	$-0.130333\pi$
$102$	7.44859	−	13.6019i	0.737520	−	1.34679i
$103$	9.61710	−	9.61710i	0.947601	−	0.947601i	−0.0510929	−	0.998694i	$-0.516270\pi$
$103$	9.61710	−	9.61710i	0.947601	−	0.947601i	0.998694	+	0.0510929i	$0.0162705\pi$
$104$	−5.70106	+	13.8758i	−0.559035	+	1.36064i
$105$	−9.25272	+	0.679413i	−0.902973	+	0.0663039i
$106$	−4.12810	−	3.16135i	−0.400957	−	0.307057i
$107$	−15.4263			−1.49131			−0.745656	−	0.666331i	$-0.767864\pi$
$107$	−15.4263			−1.49131			−0.745656	+	0.666331i	$0.767864\pi$
$108$	1.48816	+	5.51177i	0.143198	+	0.530370i
$109$	13.1411	−	13.1411i	1.25869	−	1.25869i	0.306970	−	0.951719i	$-0.400685\pi$
$109$	13.1411	−	13.1411i	1.25869	−	1.25869i	0.951719	−	0.306970i	$-0.0993153\pi$
$110$	−2.57461	−	1.68771i	−0.245479	−	0.160917i
$111$	28.9438			2.74722
$112$	5.39224	−	3.14073i	0.509519	−	0.296771i
$113$	0.0244697			0.00230192			0.00115096	−	0.999999i	$-0.499634\pi$
$113$	0.0244697			0.00230192			0.00115096	+	0.999999i	$0.499634\pi$
$114$	0.362752	+	2.73519i	0.0339748	+	0.256174i
$115$	−14.0387	+	1.03084i	−1.30911	+	0.0961262i
$116$	4.79227	+	2.75463i	0.444951	+	0.255761i
$117$	−15.2763	+	15.2763i	−1.41230	+	1.41230i
$118$	−4.41112	+	0.585020i	−0.406076	+	0.0538554i
$119$	−5.18659	−	3.80441i	−0.475453	−	0.348750i
$120$	15.0054	−	7.60072i	1.36980	−	0.693848i
$121$			10.0523i			0.913846i
$122$	4.23934	+	3.24654i	0.383812	+	0.293928i
$123$	18.5976	+	18.5976i	1.67689	+	1.67689i
$124$	2.80635	−	4.88225i	0.252018	−	0.438439i
$125$	2.43869	+	10.9111i	0.218123	+	0.975921i
$126$	8.90877	−	1.18152i	0.793656	−	0.105258i
$127$	−1.24030	+	1.24030i	−0.110058	+	0.110058i	−0.759992	−	0.649933i	$-0.774797\pi$
$127$	−1.24030	+	1.24030i	−0.110058	+	0.110058i	0.649933	+	0.759992i	$0.274797\pi$
$128$	−6.82722	+	9.02159i	−0.603446	+	0.797404i
$129$	−11.2903	−	11.2903i	−0.994056	−	0.994056i
$130$	14.0269	+	9.19494i	1.23024	+	0.806450i
$131$	5.84673	+	5.84673i	0.510832	+	0.510832i	0.914781	−	0.403950i	$-0.132363\pi$
$131$	5.84673	+	5.84673i	0.510832	+	0.510832i	−0.403950	+	0.914781i	$0.632363\pi$
$132$	4.48936	+	2.58052i	0.390749	+	0.224605i
$133$	1.14443			0.0992344
$134$	1.92330	−	2.51145i	0.166148	−	0.216956i
$135$	6.36587	−	0.467436i	0.547887	−	0.0402305i
$136$	11.3351	+	2.74148i	0.971976	+	0.235080i
$137$	7.33896	−	7.33896i	0.627010	−	0.627010i	−0.320305	−	0.947315i	$-0.603785\pi$
$137$	7.33896	−	7.33896i	0.627010	−	0.627010i	0.947315	+	0.320305i	$0.103785\pi$
$138$	23.4719	−	3.11294i	1.99806	−	0.264991i
$139$	1.32051	−	1.32051i	0.112004	−	0.112004i	−0.648884	−	0.760888i	$-0.724764\pi$
$139$	1.32051	−	1.32051i	0.112004	−	0.112004i	0.760888	+	0.648884i	$0.224764\pi$
$140$	−2.30696	−	6.58434i	−0.194974	−	0.556478i
$141$	11.0731	−	11.0731i	0.932521	−	0.932521i
$142$	1.68137	−	2.19554i	0.141097	−	0.184246i
$143$			5.16322i			0.431770i
$144$	−14.0792	+	8.20046i	−1.17326	+	0.683372i
$145$	4.03817	−	4.67820i	0.335352	−	0.388503i
$146$	−0.0130178	−	0.0981555i	−0.00107736	−	0.00812341i
$147$			12.1442i			1.00164i
$148$	5.67352	+	21.0133i	0.466360	+	1.72728i
$149$	−5.06444			−0.414895			−0.207448	−	0.978246i	$-0.566516\pi$
$149$	−5.06444			−0.414895			−0.207448	+	0.978246i	$0.566516\pi$
$150$	−5.16909	−	18.0817i	−0.422055	−	1.47636i
$151$	5.34921			0.435312			0.217656	−	0.976026i	$-0.430159\pi$
$151$	5.34921			0.435312			0.217656	+	0.976026i	$0.430159\pi$
$152$	−1.91465	+	0.799508i	−0.155299	+	0.0648487i
$153$	13.5422	+	9.93335i	1.09482	+	0.803064i
$154$	1.30586	−	1.70520i	0.105229	−	0.137409i
$155$	−4.76603	−	4.11399i	−0.382817	−	0.330443i
$156$	−24.4588	−	14.0591i	−1.95827	−	1.12563i
$157$	4.02349	+	4.02349i	0.321109	+	0.321109i	0.849193	−	0.528083i	$-0.177089\pi$
$157$	4.02349	+	4.02349i	0.321109	+	0.321109i	−0.528083	+	0.849193i	$0.677089\pi$
$158$	6.26805	−	8.18484i	0.498659	−	0.651151i
$159$	6.91429	−	6.91429i	0.548339	−	0.548339i
$160$	8.45949	+	9.40410i	0.668781	+	0.743459i
$161$		−	9.82085i		−	0.773992i
$162$	6.48821	−	0.860491i	0.509762	−	0.0676066i
$163$	−25.1622			−1.97086			−0.985428	−	0.170095i	$-0.945593\pi$
$163$	−25.1622			−1.97086			−0.985428	+	0.170095i	$0.945593\pi$
$164$	−9.85646	+	17.1474i	−0.769660	+	1.33899i
$165$	3.78293	−	4.38250i	0.294500	−	0.341177i
$166$	−14.6327	+	19.1075i	−1.13572	+	1.48303i
$167$		−	12.8815i		−	0.996799i	−0.866947	−	0.498399i	$-0.833921\pi$
$167$		−	12.8815i		−	0.996799i	0.866947	−	0.498399i	$-0.166079\pi$
$168$	4.52197	+	10.8292i	0.348877	+	0.835489i
$169$		−	15.1301i		−	1.16386i
$170$	5.40821	−	11.8639i	0.414791	−	0.909917i
$171$	−2.98811			−0.228506
$172$	5.98370	−	10.4099i	0.456253	−	0.793749i
$173$	−3.56937			−0.271374			−0.135687	−	0.990752i	$-0.543324\pi$
$173$	−3.56937			−0.271374			−0.135687	+	0.990752i	$0.543324\pi$
$174$	−6.32028	+	8.25305i	−0.479139	+	0.625662i
$175$	−7.71662	+	1.13938i	−0.583322	+	0.0861292i
$176$	−0.993469	+	3.76513i	−0.0748855	+	0.283807i
$177$		−	8.36819i		−	0.628992i
$178$	−2.32417	−	17.5246i	−0.174204	−	1.31352i
$179$	22.2424			1.66247			0.831236	−	0.555919i	$-0.187634\pi$
$179$	22.2424			1.66247			0.831236	+	0.555919i	$0.187634\pi$
$180$	6.02349	+	17.1917i	0.448965	+	1.28140i
$181$	6.72654	+	6.72654i	0.499979	+	0.499979i	0.911431	−	0.411452i	$-0.134978\pi$
$181$	6.72654	+	6.72654i	0.499979	+	0.499979i	−0.411452	+	0.911431i	$0.634978\pi$
$182$	−7.11455	+	9.29022i	−0.527366	+	0.688637i
$183$	−7.10061	+	7.10061i	−0.524892	+	0.524892i
$184$	6.86095	+	16.4305i	0.505796	+	1.21128i
$185$	24.2695	−	1.78207i	1.78433	−	0.131021i
$186$	8.40800	+	6.43894i	0.616504	+	0.472126i
$187$	3.96723	−	0.609875i	0.290113	−	0.0445985i
$188$	10.2096	+	5.86857i	0.744613	+	0.428009i
$189$			4.45329i			0.323929i
$190$	0.472575	+	2.27114i	0.0342842	+	0.164766i
$191$		−	17.9549i		−	1.29917i	−0.760289	−	0.649585i	$-0.774943\pi$
$191$		−	17.9549i		−	1.29917i	0.760289	−	0.649585i	$-0.225057\pi$
$192$	−15.1307	−	14.9584i	−1.09197	−	1.07953i
$193$	1.98214			0.142677			0.0713387	−	0.997452i	$-0.477273\pi$
$193$	1.98214			0.142677			0.0713387	+	0.997452i	$0.477273\pi$
$194$	−0.563653	+	0.0747537i	−0.0404679	+	0.00536701i
$195$	−20.6100	+	23.8766i	−1.47592	+	1.70984i
$196$	−8.81673	+	2.38049i	−0.629767	+	0.170035i
$197$	−9.47788			−0.675271			−0.337636	−	0.941277i	$-0.609627\pi$
$197$	−9.47788			−0.675271			−0.337636	+	0.941277i	$0.609627\pi$
$198$	−3.40961	+	4.45228i	−0.242310	+	0.316410i
$199$	16.2177	+	16.2177i	1.14964	+	1.14964i	0.986623	+	0.163016i	$0.0521222\pi$
$199$	16.2177	+	16.2177i	1.14964	+	1.14964i	0.163016	+	0.986623i	$0.447878\pi$
$200$	12.1141	−	7.29713i	0.856598	−	0.515985i
$201$	4.20651	+	4.20651i	0.296704	+	0.296704i
$202$	1.48779	+	11.2182i	0.104681	+	0.789306i
$203$	3.04880	+	3.04880i	0.213984	+	0.213984i
$204$	−7.91345	+	20.4539i	−0.554053	+	1.43206i
$205$	16.7392	+	14.4491i	1.16912	+	1.00917i
$206$	−11.6945	+	15.2707i	−0.814792	+	1.06396i
$207$			25.6423i			1.78226i
$208$	5.41259	−	20.5131i	0.375296	−	1.42233i
$209$	−0.504972	+	0.504972i	−0.0349296	+	0.0349296i
$210$	12.8454	−	2.67286i	0.886418	−	0.184445i
$211$	18.5867	−	18.5867i	1.27956	−	1.27956i	0.338648	−	0.940913i	$-0.390030\pi$
$211$	18.5867	−	18.5867i	1.27956	−	1.27956i	0.940913	−	0.338648i	$-0.109970\pi$
$212$	6.37513	+	3.66447i	0.437846	+	0.251677i
$213$	3.67738	+	3.67738i	0.251970	+	0.251970i
$214$	21.6267	−	2.86821i	1.47837	−	0.196067i
$215$	−10.1621	−	8.77184i	−0.693052	−	0.598234i
$216$	−3.11111	−	7.45047i	−0.211684	−	0.506940i
$217$	3.10604	−	3.10604i	0.210852	−	0.210852i
$218$	−15.9797	+	20.8663i	−1.08228	+	1.41325i
$219$	0.186208			0.0125828
$220$	3.92324	+	1.88737i	0.264505	+	0.127246i
$221$	−21.6142	+	3.32271i	−1.45393	+	0.223509i
$222$	−40.5774	+	5.38153i	−2.72337	+	0.361184i
$223$	6.11183	+	6.11183i	0.409279	+	0.409279i	0.881487	−	0.472208i	$-0.156543\pi$
$223$	6.11183	+	6.11183i	0.409279	+	0.409279i	−0.472208	+	0.881487i	$0.656543\pi$
$224$	−6.97563	+	5.40569i	−0.466079	+	0.361183i
$225$	20.1481	−	2.97494i	1.34321	−	0.198329i
$226$	−0.0343050	+	0.00454966i	−0.00228194	+	0.000302639i
$227$		−	22.9409i		−	1.52264i	−0.648376	−	0.761321i	$-0.724551\pi$
$227$		−	22.9409i		−	1.52264i	0.648376	−	0.761321i	$-0.275449\pi$
$228$	−1.01711	−	3.76712i	−0.0673598	−	0.249484i
$229$		−	11.5448i		−	0.762902i	−0.924389	−	0.381451i	$-0.875425\pi$
$229$		−	11.5448i		−	0.762902i	0.924389	−	0.381451i	$-0.124575\pi$
$230$	19.4897	−	4.05539i	1.28511	−	0.267404i
$231$	2.85609	+	2.85609i	0.187917	+	0.187917i
$232$	−7.23064	−	2.97080i	−0.474715	−	0.195042i
$233$		−	17.9481i		−	1.17582i	−0.808927	−	0.587909i	$-0.799951\pi$
$233$		−	17.9481i		−	1.17582i	0.808927	−	0.587909i	$-0.200049\pi$
$234$	18.5761	−	24.2568i	1.21436	−	1.58572i
$235$	8.60306	−	9.96660i	0.561202	−	0.650149i
$236$	6.07534	−	1.64032i	0.395471	−	0.106776i
$237$	13.7091	+	13.7091i	0.890499	+	0.890499i
$238$	7.97863	+	4.36921i	0.517178	+	0.283214i
$239$	7.76907			0.502539			0.251270	−	0.967917i	$-0.419152\pi$
$239$	7.76907			0.502539			0.251270	+	0.967917i	$0.419152\pi$
$240$	−19.6234	+	13.4457i	−1.26669	+	0.867916i
$241$	0.186182	+	0.186182i	0.0119931	+	0.0119931i	0.713078	−	0.701085i	$-0.247301\pi$
$241$	0.186182	+	0.186182i	0.0119931	+	0.0119931i	−0.701085	+	0.713078i	$0.747301\pi$
$242$	−1.86903	−	14.0927i	−0.120146	−	0.905913i
$243$			20.8723i			1.33896i
$244$	−6.54693	−	3.76322i	−0.419124	−	0.240916i
$245$	0.747719	+	10.1830i	0.0477700	+	0.650566i
$246$	−29.5305	−	22.6148i	−1.88280	−	1.44187i
$247$	2.75118	−	2.75118i	0.175053	−	0.175053i
$248$	−3.02657	+	7.36639i	−0.192188	+	0.467766i
$249$	−32.0037	−	32.0037i	−2.02815	−	2.02815i
$250$	−5.44760	−	14.8433i	−0.344537	−	0.938773i
$251$	13.1663			0.831051			0.415525	−	0.909582i	$-0.363598\pi$
$251$	13.1663			0.831051			0.415525	+	0.909582i	$0.363598\pi$
$252$	−12.2699	+	3.31282i	−0.772929	+	0.208688i
$253$	4.33340	+	4.33340i	0.272438	+	0.272438i
$254$	1.50821	−	1.96943i	0.0946335	−	0.123573i
$255$	20.7804	+	13.0157i	1.30132	+	0.815075i
$256$	7.89394	−	13.9171i	0.493372	−	0.869819i
$257$	7.70026	+	7.70026i	0.480329	+	0.480329i	0.905237	−	0.424908i	$-0.139693\pi$
$257$	7.70026	+	7.70026i	0.480329	+	0.480329i	−0.424908	+	0.905237i	$0.639693\pi$
$258$	17.9275	+	13.7291i	1.11612	+	0.854737i
$259$			16.9779i			1.05496i
$260$	−21.3745	−	10.2827i	−1.32559	−	0.637706i
$261$	−7.96043	−	7.96043i	−0.492738	−	0.492738i
$262$	−9.28384	−	7.10967i	−0.573558	−	0.439237i
$263$	−7.89126	−	7.89126i	−0.486596	−	0.486596i	0.420634	−	0.907230i	$-0.361807\pi$
$263$	−7.89126	−	7.89126i	−0.486596	−	0.486596i	−0.907230	+	0.420634i	$0.861807\pi$
$264$	−6.77361	−	2.78302i	−0.416887	−	0.171283i
$265$	5.37195	−	6.22338i	0.329996	−	0.382299i
$266$	−1.60442	+	0.212784i	−0.0983730	+	0.0130466i
$267$	33.2453			2.03458
$268$	−2.22939	+	3.87850i	−0.136182	+	0.236917i
$269$	−9.50734	−	9.50734i	−0.579673	−	0.579673i	0.355140	−	0.934813i	$-0.384433\pi$
$269$	−9.50734	−	9.50734i	−0.579673	−	0.579673i	−0.934813	+	0.355140i	$0.884433\pi$
$270$	−8.83764	+	1.83892i	−0.537842	+	0.111913i
$271$			26.3491i			1.60059i	0.599604	+	0.800297i	$0.295325\pi$
$271$			26.3491i			1.60059i	−0.599604	+	0.800297i	$0.704675\pi$
$272$	−16.4008	−	1.73585i	−0.994446	−	0.105251i
$273$	−15.5605	−	15.5605i	−0.941763	−	0.941763i
$274$	−8.92423	+	11.6533i	−0.539133	+	0.704002i
$275$	2.90217	−	3.90766i	0.175008	−	0.235641i
$276$	−32.3274	+	8.72830i	−1.94588	+	0.525382i
$277$		−	27.3216i		−	1.64160i	−0.571219	−	0.820798i	$-0.693529\pi$
$277$		−	27.3216i		−	1.64160i	0.571219	−	0.820798i	$-0.306471\pi$
$278$	−1.60575	+	2.09679i	−0.0963063	+	0.125757i
$279$	−8.10989	+	8.10989i	−0.485526	+	0.485526i
$280$	4.45845	+	8.80190i	0.266443	+	0.526014i
$281$		−	30.9007i		−	1.84338i	−0.387925	−	0.921691i	$-0.626808\pi$
$281$		−	30.9007i		−	1.84338i	0.387925	−	0.921691i	$-0.373192\pi$
$282$	−13.4649	+	17.5826i	−0.801825	+	1.04703i
$283$	−16.5664			−0.984771			−0.492386	−	0.870377i	$-0.663875\pi$
$283$	−16.5664			−0.984771			−0.492386	+	0.870377i	$0.663875\pi$
$284$	−1.94896	+	3.39063i	−0.115649	+	0.201197i
$285$	−4.35087	+	0.319478i	−0.257723	+	0.0189242i
$286$	−0.959999	−	7.23851i	−0.0567660	−	0.428022i
$287$	−10.9090	+	10.9090i	−0.643939	+	0.643939i
$288$	18.2134	−	14.1143i	1.07324	−	0.831692i
$289$	5.10609	+	16.2150i	0.300358	+	0.953826i
$290$	−4.79144	+	7.30936i	−0.281363	+	0.429221i
$291$		−	1.06929i		−	0.0626827i
$292$	0.0365002	+	0.135188i	0.00213601	+	0.00791125i
$293$	−15.6912	+	15.6912i	−0.916687	+	0.916687i	−0.996787	−	0.0800995i	$-0.974476\pi$
$293$	−15.6912	+	15.6912i	−0.916687	+	0.916687i	0.0800995	+	0.996787i	$0.474476\pi$
$294$	−2.25797	−	17.0254i	−0.131688	−	0.992942i
$295$	−0.515231	−	7.01677i	−0.0299979	−	0.408532i
$296$	−11.8609	−	28.4045i	−0.689403	−	1.65098i
$297$	−1.96499	−	1.96499i	−0.114020	−	0.114020i
$298$	7.10004	−	0.941634i	0.411294	−	0.0545474i
$299$	−23.6091	−	23.6091i	−1.36535	−	1.36535i
$300$	10.6087	+	24.3883i	0.612492	+	1.40806i
$301$	6.62270	−	6.62270i	0.381726	−	0.381726i
$302$	−7.49925	+	0.994580i	−0.431534	+	0.0572316i
$303$	−21.2816			−1.22260
$304$	2.53557	−	1.47685i	0.145425	−	0.0847033i
$305$	−5.51671	+	6.39109i	−0.315886	+	0.365953i
$306$	−20.8322	−	11.4080i	−1.19090	−	0.652154i
$307$	4.71420	−	4.71420i	0.269053	−	0.269053i	−0.559665	−	0.828719i	$-0.689070\pi$
$307$	4.71420	−	4.71420i	0.269053	−	0.269053i	0.828719	+	0.559665i	$0.189070\pi$
$308$	−1.51369	+	2.63338i	−0.0862503	+	0.150051i
$309$	−25.5774	−	25.5774i	−1.45505	−	1.45505i
$310$	7.44659	+	4.88140i	0.422938	+	0.277245i
$311$	18.2827	−	18.2827i	1.03672	−	1.03672i	0.0374182	−	0.999300i	$-0.488087\pi$
$311$	18.2827	−	18.2827i	1.03672	−	1.03672i	0.999300	−	0.0374182i	$-0.0119134\pi$
$312$	36.9038	+	15.1624i	2.08927	+	0.858400i
$313$	−27.1445			−1.53430			−0.767148	−	0.641471i	$-0.778325\pi$
$313$	−27.1445			−1.53430			−0.767148	+	0.641471i	$0.778325\pi$
$314$	−6.38877	−	4.89259i	−0.360539	−	0.276105i
$315$	1.04057	+	14.1712i	0.0586294	+	0.798456i
$316$	−7.26560	+	12.6401i	−0.408722	+	0.711059i
$317$	18.8982			1.06143			0.530714	−	0.847551i	$-0.321924\pi$
$317$	18.8982			1.06143			0.530714	+	0.847551i	$0.321924\pi$
$318$	−8.40782	+	10.9790i	−0.471487	+	0.615670i
$319$	−2.69053			−0.150641
$320$	−13.6082	−	11.6111i	−0.760721	−	0.649079i
$321$			41.0272i			2.28992i
$322$	1.82599	+	13.7682i	0.101759	+	0.767273i
$323$	−2.43887	−	1.78894i	−0.135702	−	0.0995391i
$324$	−8.93608	+	2.41271i	−0.496449	+	0.134039i
$325$	−15.8115	+	21.2896i	−0.877066	+	1.18094i
$326$	35.2758	−	4.67842i	1.95375	−	0.259114i
$327$	−34.9497	−	34.9497i	−1.93272	−	1.93272i
$328$	10.6299	−	25.8722i	0.586939	−	1.42855i
$329$	6.49527	+	6.49527i	0.358096	+	0.358096i
$330$	−4.48859	+	6.84735i	−0.247089	+	0.376934i
$331$		−	7.46399i		−	0.410258i	−0.978735	−	0.205129i	$-0.934239\pi$
$331$		−	7.46399i		−	0.410258i	0.978735	−	0.205129i	$-0.0657614\pi$
$332$	16.9615	−	29.5081i	0.930883	−	1.61947i
$333$		−	44.3294i		−	2.42924i
$334$	2.39506	+	18.0590i	0.131052	+	0.988147i
$335$	3.78618	+	3.26818i	0.206861	+	0.178560i
$336$	−8.35299	−	14.3411i	−0.455693	−	0.782369i
$337$	−19.4043			−1.05702			−0.528510	−	0.848927i	$-0.677249\pi$
$337$	−19.4043			−1.05702			−0.528510	+	0.848927i	$0.677249\pi$
$338$	2.81315	+	21.2115i	0.153015	+	1.15375i
$339$		−	0.0650790i		−	0.00353461i
$340$	−5.37612	+	17.6380i	−0.291561	+	0.956552i
$341$			2.74105i			0.148436i
$342$	4.18914	−	0.555579i	0.226523	−	0.0300423i
$343$	−18.0440			−0.974283
$344$	−6.45326	+	15.7066i	−0.347936	+	0.846844i
$345$	2.74159	+	37.3369i	0.147602	+	2.01015i
$346$	5.00403	−	0.663654i	0.269018	−	0.0356782i
$347$			3.20787i			0.172207i	0.996286	+	0.0861036i	$0.0274416\pi$
$347$			3.20787i			0.172207i	−0.996286	+	0.0861036i	$0.972558\pi$
$348$	7.32614	−	12.7454i	0.392723	−	0.683225i
$349$		−	0.963390i		−	0.0515691i	−0.999668	−	0.0257845i	$-0.991792\pi$
$349$		−	0.963390i		−	0.0515691i	0.999668	−	0.0257845i	$-0.00820839\pi$
$350$	10.6064	−	3.03210i	0.566935	−	0.162072i
$351$	10.7056	+	10.7056i	0.571423	+	0.571423i
$352$	0.692730	−	5.46319i	0.0369226	−	0.291189i
$353$	21.0087	+	21.0087i	1.11818	+	1.11818i	0.992008	+	0.126174i	$0.0402698\pi$
$353$	21.0087	+	21.0087i	1.11818	+	1.11818i	0.126174	+	0.992008i	$0.459730\pi$
$354$	1.55590	+	11.7317i	0.0826952	+	0.623532i
$355$	3.30992	+	2.85709i	0.175672	+	0.151638i
$356$	6.51669	+	24.1362i	0.345384	+	1.27922i
$357$	−10.1181	+	13.7941i	−0.535507	+	0.730061i
$358$	−31.1824	+	4.13553i	−1.64804	+	0.218570i
$359$			13.5395i			0.714585i	0.933992	+	0.357293i	$0.116300\pi$
$359$			13.5395i			0.714585i	−0.933992	+	0.357293i	$0.883700\pi$
$360$	−11.6410	−	22.9818i	−0.613536	−	1.21125i
$361$	−18.4619			−0.971677
$362$	−10.6809	−	8.17952i	−0.561373	−	0.429906i
$363$	26.7348			1.40321
$364$	8.24683	−	14.3471i	0.432251	−	0.751993i
$365$	0.156136	−	0.0114648i	0.00817254	−	0.000600097i
$366$	8.63440	−	11.2748i	0.451327	−	0.589345i
$367$	6.80340			0.355134			0.177567	−	0.984109i	$-0.443177\pi$
$367$	6.80340			0.355134			0.177567	+	0.984109i	$0.443177\pi$
$368$	−12.6736	−	21.7589i	−0.660655	−	1.13426i
$369$	28.4835	−	28.4835i	1.48279	−	1.48279i
$370$	−33.6930	+	7.01079i	−1.75162	+	0.364474i
$371$	4.05580	+	4.05580i	0.210567	+	0.210567i
$372$	−12.9847	−	7.46369i	−0.673224	−	0.386974i
$373$	6.39548	−	6.39548i	0.331145	−	0.331145i	−0.521876	−	0.853021i	$-0.674768\pi$
$373$	6.39548	−	6.39548i	0.331145	−	0.331145i	0.853021	+	0.521876i	$0.174768\pi$
$374$	−5.44841	+	1.59264i	−0.281731	+	0.0823532i
$375$	29.0189	−	6.48587i	1.49853	−	0.334929i
$376$	−15.4044	−	6.32909i	−0.794422	−	0.326398i
$377$	14.6585			0.754950
$378$	−0.828002	−	6.24324i	−0.0425878	−	0.321117i
$379$	16.6735	−	16.6735i	0.856458	−	0.856458i	−0.134461	−	0.990919i	$-0.542930\pi$
$379$	16.6735	−	16.6735i	0.856458	−	0.856458i	0.990919	+	0.134461i	$0.0429303\pi$
$380$	−1.08479	−	3.09613i	−0.0556488	−	0.158828i
$381$	3.29866	+	3.29866i	0.168995	+	0.168995i
$382$	3.33836	+	25.1716i	0.170805	+	1.28789i
$383$	−11.7394	−	11.7394i	−0.599853	−	0.599853i	0.340420	−	0.940273i	$-0.389431\pi$
$383$	−11.7394	−	11.7394i	−0.599853	−	0.599853i	−0.940273	+	0.340420i	$0.889431\pi$
$384$	23.9936	+	18.1575i	1.22442	+	0.926594i
$385$	2.57070	+	2.21900i	0.131015	+	0.113091i
$386$	−2.77883	+	0.368540i	−0.141439	+	0.0187582i
$387$	−17.2919	+	17.2919i	−0.878997	+	0.878997i
$388$	0.776307	−	0.209600i	0.0394110	−	0.0106408i
$389$			29.6087i			1.50122i	0.660746	+	0.750609i	$0.270240\pi$
$389$			29.6087i			1.50122i	−0.660746	+	0.750609i	$0.729760\pi$
$390$	24.4546	−	37.3056i	1.23831	−	1.88904i
$391$	−15.3517	+	20.9291i	−0.776368	+	1.05843i
$392$	11.9179	−	4.97659i	0.601945	−	0.251356i
$393$	15.5498	−	15.5498i	0.784384	−	0.784384i
$394$	13.2874	−	1.76223i	0.669410	−	0.0887797i
$395$	12.3392	+	10.6510i	0.620852	+	0.535912i
$396$	3.95225	−	6.87577i	0.198608	−	0.345521i
$397$	26.2663			1.31827			0.659135	−	0.752025i	$-0.270923\pi$
$397$	26.2663			1.31827			0.659135	+	0.752025i	$0.270923\pi$
$398$	−25.7515	−	19.7208i	−1.29081	−	0.988514i
$399$		−	3.04368i		−	0.152375i
$400$	−15.6265	+	12.4825i	−0.781324	+	0.624125i
$401$	−5.49471	+	5.49471i	−0.274393	+	0.274393i	−0.830866	−	0.556473i	$-0.812154\pi$
$401$	−5.49471	+	5.49471i	−0.274393	+	0.274393i	0.556473	+	0.830866i	$0.312154\pi$
$402$	−6.67938	−	5.11515i	−0.333137	−	0.255120i
$403$		−	14.9337i		−	0.743900i
$404$	−4.17159	−	15.4505i	−0.207544	−	0.768692i
$405$	0.757841	+	10.3208i	0.0376574	+	0.512845i
$406$	−4.84109	−	3.70736i	−0.240259	−	0.183993i
$407$	−7.49141	−	7.49141i	−0.371335	−	0.371335i
$408$	7.29117	−	30.1465i	0.360967	−	1.49247i
$409$			8.49228i			0.419916i	0.977710	+	0.209958i	$0.0673328\pi$
$409$			8.49228i			0.419916i	−0.977710	+	0.209958i	$0.932667\pi$
$410$	−26.1539	−	17.1444i	−1.29165	−	0.846704i
$411$	−19.5185	−	19.5185i	−0.962776	−	0.962776i
$412$	13.5556	−	23.5829i	0.667838	−	1.16185i
$413$	4.90863			0.241538
$414$	−4.76768	−	35.9489i	−0.234319	−	1.76679i
$415$	−28.8057	−	24.8648i	−1.41402	−	1.22056i
$416$	−3.77411	+	29.7644i	−0.185041	+	1.45932i
$417$	−3.51198	−	3.51198i	−0.171982	−	0.171982i
$418$	0.614050	−	0.801829i	0.0300342	−	0.0392187i
$419$	19.5738	+	19.5738i	0.956244	+	0.956244i	0.999082	−	0.0428376i	$-0.0136398\pi$
$419$	19.5738	+	19.5738i	0.956244	+	0.956244i	−0.0428376	+	0.999082i	$0.513640\pi$
$420$	−17.5115	+	6.13553i	−0.854474	+	0.299383i
$421$		−	26.2340i		−	1.27857i	−0.768972	−	0.639283i	$-0.779231\pi$
$421$		−	26.2340i		−	1.27857i	0.768972	−	0.639283i	$-0.220769\pi$
$422$	−22.6016	+	29.5132i	−1.10023	+	1.43668i
$423$	−16.9592	−	16.9592i	−0.824584	−	0.824584i
$424$	−9.61887	−	3.95203i	−0.467134	−	0.191928i
$425$	18.2258	+	9.63429i	0.884082	+	0.467332i
$426$	−5.83919	−	4.47172i	−0.282910	−	0.216656i
$427$	−4.16509	−	4.16509i	−0.201563	−	0.201563i
$428$	−29.7859	+	8.04210i	−1.43976	+	0.388730i
$429$	13.7320			0.662985
$430$	15.8776	+	10.4081i	0.765687	+	0.501924i
$431$	11.7262	+	11.7262i	0.564831	+	0.564831i	0.930676	−	0.365845i	$-0.119220\pi$
$431$	11.7262	+	11.7262i	0.564831	+	0.564831i	−0.365845	+	0.930676i	$0.619220\pi$
$432$	5.74685	+	9.86664i	0.276496	+	0.474709i
$433$	4.53366	−	4.53366i	0.217874	−	0.217874i	−0.589728	−	0.807602i	$-0.700765\pi$
$433$	4.53366	−	4.53366i	0.217874	−	0.217874i	0.807602	+	0.589728i	$0.200765\pi$
$434$	−3.77697	+	4.93198i	−0.181300	+	0.236743i
$435$	−12.4420	−	10.7398i	−0.596548	−	0.514934i
$436$	18.5228	−	32.2244i	0.887083	−	1.54327i
$437$		−	4.61802i		−	0.220910i
$438$	−0.261052	+	0.0346217i	−0.0124735	+	0.00165429i
$439$	−5.76725	−	5.76725i	−0.275256	−	0.275256i	0.555956	−	0.831212i	$-0.312352\pi$
$439$	−5.76725	−	5.76725i	−0.275256	−	0.275256i	−0.831212	+	0.555956i	$0.812352\pi$
$440$	−5.85105	−	1.91652i	−0.278938	−	0.0913667i
$441$	18.5997			0.885699
$442$	29.6839	−	8.67695i	1.41192	−	0.412721i
$443$	11.2633	+	11.2633i	0.535137	+	0.535137i	0.922097	−	0.386960i	$-0.126475\pi$
$443$	11.2633	+	11.2633i	0.535137	+	0.535137i	−0.386960	+	0.922097i	$0.626475\pi$
$444$	55.8864	−	15.0891i	2.65225	−	0.716098i
$445$	27.8763	−	2.04692i	1.32146	−	0.0970331i
$446$	−9.70478	−	7.43203i	−0.459535	−	0.351917i
$447$			13.4692i			0.637074i
$448$	8.77432	−	8.87542i	0.414548	−	0.419324i
$449$	17.7617	+	17.7617i	0.838228	+	0.838228i	0.988626	−	0.150398i	$-0.0480555\pi$
$449$	17.7617	+	17.7617i	0.838228	+	0.838228i	−0.150398	+	0.988626i	$0.548055\pi$
$450$	−27.6933	+	7.91683i	−1.30548	+	0.373203i
$451$		−	9.62709i		−	0.453322i
$452$	0.0472476	−	0.0127567i	0.00222234	−	0.000600024i
$453$		−	14.2266i		−	0.668424i
$454$	4.26541	+	32.1617i	0.200186	+	1.50942i
$455$	−14.0056	−	12.0895i	−0.656593	−	0.566764i
$456$	2.12635	+	5.09216i	0.0995754	+	0.238462i
$457$	18.3075	+	18.3075i	0.856388	+	0.856388i	0.990911	−	0.134523i	$-0.0429501\pi$
$457$	18.3075	+	18.3075i	0.856388	+	0.856388i	−0.134523	+	0.990911i	$0.542950\pi$
$458$	2.14653	+	16.1851i	0.100301	+	0.756279i
$459$	6.96126	−	9.49033i	0.324924	−	0.442971i
$460$	−26.5693	+	9.30912i	−1.23880	+	0.434040i
$461$	17.8234			0.830117			0.415059	−	0.909795i	$-0.363761\pi$
$461$	17.8234			0.830117			0.415059	+	0.909795i	$0.363761\pi$
$462$	−4.53510	−	3.47303i	−0.210992	−	0.161580i
$463$	−10.0048	+	10.0048i	−0.464964	+	0.464964i	−0.900278	−	0.435314i	$-0.856637\pi$
$463$	−10.0048	+	10.0048i	−0.464964	+	0.464964i	0.435314	+	0.900278i	$0.356637\pi$
$464$	10.6893	+	2.82048i	0.496237	+	0.130937i
$465$	−10.9414	+	12.6756i	−0.507397	+	0.587817i
$466$	3.33709	+	25.1621i	0.154588	+	1.16561i
$467$	2.80145	+	2.80145i	0.129636	+	0.129636i	0.768948	−	0.639312i	$-0.220781\pi$
$467$	2.80145	+	2.80145i	0.129636	+	0.129636i	−0.639312	+	0.768948i	$0.720781\pi$
$468$	−21.5325	+	37.4604i	−0.995341	+	1.73161i
$469$	−2.46746	+	2.46746i	−0.113937	+	0.113937i
$470$	−10.2079	+	15.5721i	−0.470853	+	0.718288i
$471$	10.7008	−	10.7008i	0.493065	−	0.493065i
$472$	−8.21227	+	3.42922i	−0.378000	+	0.157843i
$473$			5.84446i			0.268728i
$474$	−21.7682	−	16.6703i	−0.999845	−	0.765693i
$475$	−3.62856	+	0.535768i	−0.166490	+	0.0245827i
$476$	−11.9979	−	4.64189i	−0.549923	−	0.212761i
$477$	−10.5897	−	10.5897i	−0.484870	−	0.484870i
$478$	−10.8918	+	1.44451i	−0.498177	+	0.0660702i
$479$	−0.127353	−	0.127353i	−0.00581889	−	0.00581889i	0.704191	−	0.710010i	$-0.251310\pi$
$479$	−0.127353	−	0.127353i	−0.00581889	−	0.00581889i	−0.710010	+	0.704191i	$0.751310\pi$
$480$	25.0109	−	22.4986i	1.14158	−	1.02692i
$481$	40.8145	+	40.8145i	1.86098	+	1.86098i
$482$	−0.295633	−	0.226399i	−0.0134657	−	0.0103122i
$483$	−26.1193			−1.18847
$484$	5.24052	+	19.4096i	0.238206	+	0.882254i
$485$	−0.0658362	−	0.896603i	−0.00298947	−	0.0407126i
$486$	−3.88079	−	29.2616i	−0.176036	−	1.32733i
$487$	10.3466			0.468849			0.234424	−	0.972134i	$-0.424679\pi$
$487$	10.3466			0.468849			0.234424	+	0.972134i	$0.424679\pi$
$488$	9.87808	+	4.05853i	0.447160	+	0.183721i
$489$			66.9207i			3.02626i
$490$	−2.94158	−	14.1369i	−0.132887	−	0.638638i
$491$			13.1680i			0.594266i	0.954836	+	0.297133i	$0.0960304\pi$
$491$			13.1680i			0.594266i	−0.954836	+	0.297133i	$0.903970\pi$
$492$	45.6048	+	26.2139i	2.05602	+	1.18182i
$493$	−1.73145	−	11.2630i	−0.0779805	−	0.507262i
$494$	−3.34545	+	4.36850i	−0.150519	+	0.196548i
$495$	−6.71210	−	5.79381i	−0.301687	−	0.260413i
$496$	2.87343	−	10.8900i	0.129021	−	0.488974i
$497$	−2.15709	+	2.15709i	−0.0967585	+	0.0967585i
$498$	50.8177	+	38.9167i	2.27719	+	1.74390i
$499$	−18.5416	−	18.5416i	−0.830036	−	0.830036i	0.157485	−	0.987521i	$-0.449661\pi$
$499$	−18.5416	−	18.5416i	−0.830036	−	0.830036i	−0.987521	+	0.157485i	$0.949661\pi$
$500$	10.3970	+	19.7965i	0.464969	+	0.885327i
$501$	−34.2592			−1.53059
$502$	−18.4584	+	2.44802i	−0.823837	+	0.109260i
$503$			40.0463i			1.78558i	0.450475	+	0.892789i	$0.351255\pi$
$503$			40.0463i			1.78558i	−0.450475	+	0.892789i	$0.648745\pi$
$504$	16.5856	−	6.92571i	0.738783	−	0.308496i
$505$	−17.8447	+	1.31031i	−0.794080	+	0.0583081i
$506$	−6.88087	−	5.26944i	−0.305892	−	0.234255i
$507$	−40.2396			−1.78710
$508$	−1.74824	+	3.04144i	−0.0775656	+	0.134942i
$509$	10.6206			0.470751			0.235375	−	0.971905i	$-0.424368\pi$
$509$	10.6206			0.470751			0.235375	+	0.971905i	$0.424368\pi$
$510$	−31.5528	−	14.3835i	−1.39718	−	0.636913i
$511$			0.109226i			0.00483188i
$512$	−8.47921	+	20.9786i	−0.374732	+	0.927133i
$513$			2.09405i			0.0924547i
$514$	−12.2270	−	9.36357i	−0.539310	−	0.413010i
$515$	−23.0216	−	19.8719i	−1.01445	−	0.875663i
$516$	−27.6859	−	15.9141i	−1.21881	−	0.700578i
$517$	−5.73200			−0.252093
$518$	−3.15671	−	23.8020i	−0.138698	−	1.04580i
$519$			9.49299i			0.416696i
$520$	31.8776	+	10.4416i	1.39792	+	0.457892i
$521$	−24.9222	+	24.9222i	−1.09186	+	1.09186i	−0.0965310	+	0.995330i	$0.530775\pi$
$521$	−24.9222	+	24.9222i	−1.09186	+	1.09186i	−0.995330	+	0.0965310i	$0.969225\pi$
$522$	12.6401	+	9.67995i	0.553243	+	0.423680i
$523$	4.25787	+	4.25787i	0.186183	+	0.186183i	0.794044	−	0.607860i	$-0.207972\pi$
$523$	4.25787	+	4.25787i	0.186183	+	0.186183i	−0.607860	+	0.794044i	$0.707972\pi$
$524$	14.3373	+	8.24117i	0.626327	+	0.360017i
$525$	3.03027	+	20.5229i	0.132252	+	0.895693i
$526$	12.5303	+	9.59583i	0.546346	+	0.418398i
$527$	−11.4745	+	1.76395i	−0.499837	+	0.0768391i
$528$	10.0136	+	2.64220i	0.435787	+	0.114987i
$529$	−16.6294			−0.723017
$530$	−6.37403	+	9.72360i	−0.276870	+	0.422366i
$531$	−12.8165			−0.556188
$532$	2.20973	−	0.596619i	0.0958038	−	0.0258667i
$533$			52.4501i			2.27186i
$534$	−46.6078	+	6.18131i	−2.01692	+	0.267491i
$535$	2.52605	+	34.4015i	0.109211	+	1.48731i
$536$	2.40433	−	5.85192i	0.103851	−	0.252765i
$537$		−	59.1552i		−	2.55273i
$538$	15.0964	+	11.5610i	0.650852	+	0.498430i
$539$	3.14323	−	3.14323i	0.135389	−	0.135389i
$540$	12.0479	−	4.22124i	0.518460	−	0.181653i
$541$	−9.28608	+	9.28608i	−0.399240	+	0.399240i	−0.877965	−	0.478725i	$-0.841099\pi$
$541$	−9.28608	+	9.28608i	−0.399240	+	0.399240i	0.478725	+	0.877965i	$0.341099\pi$
$542$	−4.89910	−	36.9398i	−0.210434	−	1.58670i
$543$	17.8897	−	17.8897i	0.767721	−	0.767721i
$544$	23.3157	−	0.615855i	0.999651	−	0.0264046i
$545$	−31.4574	−	27.1536i	−1.34749	−	1.16313i
$546$	24.7080	+	18.9217i	1.05740	+	0.809772i
$547$	−26.0796			−1.11509			−0.557543	−	0.830148i	$-0.688256\pi$
$547$	−26.0796			−1.11509			−0.557543	+	0.830148i	$0.688256\pi$
$548$	10.3445	−	17.9965i	0.441896	−	0.768772i
$549$	10.8751	+	10.8751i	0.464137	+	0.464137i
$550$	−3.34211	+	6.01790i	−0.142508	+	0.256604i
$551$	1.43363	+	1.43363i	0.0610745	+	0.0610745i
$552$	43.6982	−	18.2472i	1.85992	−	0.776651i
$553$	−8.04149	+	8.04149i	−0.341959	+	0.341959i
$554$	5.07991	+	38.3032i	0.215825	+	1.62735i
$555$	−4.73955	−	64.5465i	−0.201183	−	2.73984i
$556$	1.86130	−	3.23813i	0.0789367	−	0.137327i
$557$	23.9084	+	23.9084i	1.01303	+	1.01303i	0.999914	+	0.0131183i	$0.00417579\pi$
$557$	23.9084	+	23.9084i	1.01303	+	1.01303i	0.0131183	+	0.999914i	$0.495824\pi$
$558$	9.86169	−	12.8774i	0.417478	−	0.545145i
$559$		−	31.8416i		−	1.34676i
$560$	−7.88701	−	11.5108i	−0.333287	−	0.486418i
$561$	−1.62201	−	10.5511i	−0.0684811	−	0.445469i
$562$	5.74538	+	43.3209i	0.242354	+	1.82738i
$563$	22.2136	−	22.2136i	0.936190	−	0.936190i	−0.0618929	−	0.998083i	$-0.519714\pi$
$563$	22.2136	−	22.2136i	0.936190	−	0.936190i	0.998083	+	0.0618929i	$0.0197137\pi$
$564$	15.6079	−	27.1532i	0.657210	−	1.14336i
$565$	−0.00400692	−	0.0545691i	−0.000168572	−	0.00229574i
$566$	23.2251	−	3.08020i	0.976223	−	0.129470i
$567$	−7.21999			−0.303211
$568$	2.10190	−	5.11582i	0.0881937	−	0.214655i
$569$	33.4221			1.40113			0.700564	−	0.713590i	$-0.252932\pi$
$569$	33.4221			1.40113			0.700564	+	0.713590i	$0.252932\pi$
$570$	6.04025	−	1.25685i	0.252998	−	0.0526435i
$571$	−18.0889	+	18.0889i	−0.756995	+	0.756995i	−0.975774	−	0.218779i	$-0.929793\pi$
$571$	−18.0889	+	18.0889i	−0.756995	+	0.756995i	0.218779	+	0.975774i	$0.429793\pi$
$572$	2.69172	+	9.96945i	0.112546	+	0.416844i
$573$	−47.7523			−1.99488
$574$	13.2655	−	17.3221i	0.553689	−	0.723010i
$575$	4.59767	+	31.1383i	0.191736	+	1.29856i
$576$	−22.9098	+	23.1738i	−0.954575	+	0.965574i
$577$	−8.71178	+	8.71178i	−0.362676	+	0.362676i	−0.864797	−	0.502121i	$-0.832553\pi$
$577$	−8.71178	+	8.71178i	−0.362676	+	0.362676i	0.502121	+	0.864797i	$0.332553\pi$
$578$	−10.1733	−	21.7831i	−0.423153	−	0.906058i
$579$		−	5.27164i		−	0.219082i
$580$	5.35827	−	11.1381i	0.222490	−	0.462486i
$581$	18.7728	−	18.7728i	0.778827	−	0.778827i
$582$	0.198813	+	1.49907i	0.00824106	+	0.0621386i
$583$	−3.57920			−0.148235
$584$	−0.0763065	−	0.182738i	−0.00315758	−	0.00756176i
$585$	36.5687	+	31.5657i	1.51193	+	1.30508i
$586$	19.0806	−	24.9155i	0.788211	−	1.02925i
$587$	15.5812	+	15.5812i	0.643104	+	0.643104i	0.951317	−	0.308214i	$-0.0997312\pi$
$587$	15.5812	+	15.5812i	0.643104	+	0.643104i	−0.308214	+	0.951317i	$0.599731\pi$
$588$	6.33108	+	23.4487i	0.261089	+	0.967009i
$589$	1.46054	−	1.46054i	0.0601806	−	0.0601806i
$590$	2.02695	+	9.74128i	0.0834483	+	0.401042i
$591$			25.2071i			1.03688i
$592$	21.9095	+	37.6160i	0.900477	+	1.54601i
$593$	−22.7622	+	22.7622i	−0.934733	+	0.934733i	−0.997997	−	0.0632634i	$-0.979849\pi$
$593$	−22.7622	+	22.7622i	−0.934733	+	0.934733i	0.0632634	+	0.997997i	$0.479849\pi$
$594$	3.12014	+	2.38944i	0.128021	+	0.0980400i
$595$	−7.63478	+	12.1894i	−0.312996	+	0.499716i
$596$	−9.77873	+	2.64022i	−0.400552	+	0.108148i
$597$	43.1320	−	43.1320i	1.76528	−	1.76528i
$598$	37.4882	+	28.7089i	1.53300	+	1.17399i
$599$	11.8993			0.486193			0.243097	−	0.970002i	$-0.421837\pi$
$599$	11.8993			0.486193			0.243097	+	0.970002i	$0.421837\pi$
$600$	−19.4072	−	32.2184i	−0.792297	−	1.31531i
$601$	7.45499	−	7.45499i	0.304096	−	0.304096i	−0.538518	−	0.842614i	$-0.681016\pi$
$601$	7.45499	−	7.45499i	0.304096	−	0.304096i	0.842614	+	0.538518i	$0.181016\pi$
$602$	−8.05325	+	10.5160i	−0.328226	+	0.428599i
$603$	6.44256	−	6.44256i	0.262361	−	0.262361i
$604$	10.3286	−	2.78868i	0.420263	−	0.113470i
$605$	22.4173	−	1.64607i	0.911392	−	0.0669221i
$606$	29.8355	−	3.95689i	1.21198	−	0.160738i
$607$			3.15126i			0.127906i	0.997953	+	0.0639529i	$0.0203707\pi$
$607$			3.15126i			0.127906i	−0.997953	+	0.0639529i	$0.979629\pi$
$608$	−3.28013	+	2.54190i	−0.133027	+	0.103088i
$609$	8.10850	−	8.10850i	0.328573	−	0.328573i
$610$	6.54579	−	9.98563i	0.265031	−	0.404306i
$611$	31.2289			1.26339
$612$	31.3266	+	12.1200i	1.26630	+	0.489922i
$613$	0.0507432	−	0.0507432i	0.00204950	−	0.00204950i	−0.706081	−	0.708131i	$-0.749539\pi$
$613$	0.0507432	−	0.0507432i	0.00204950	−	0.00204950i	0.708131	+	0.706081i	$0.249539\pi$
$614$	−5.73250	+	7.48552i	−0.231345	+	0.302091i
$615$	38.4285	−	44.5192i	1.54959	−	1.79519i
$616$	1.63247	−	3.97328i	0.0657741	−	0.160088i
$617$	−36.6115			−1.47392			−0.736962	−	0.675934i	$-0.763740\pi$
$617$	−36.6115			−1.47392			−0.736962	+	0.675934i	$0.763740\pi$
$618$	40.6135	+	31.1023i	1.63371	+	1.25112i
$619$	−15.2125	−	15.2125i	−0.611443	−	0.611443i	0.331879	−	0.943322i	$-0.392317\pi$
$619$	−15.2125	−	15.2125i	−0.611443	−	0.611443i	−0.943322	+	0.331879i	$0.892317\pi$
$620$	−11.3473	−	5.45887i	−0.455717	−	0.219234i
$621$	17.9700			0.721113
$622$	−22.2319	+	29.0305i	−0.891419	+	1.16402i
$623$			19.5011i			0.781295i
$624$	−54.5560	−	14.3952i	−2.18399	−	0.576268i
$625$	23.9332	−	7.22513i	0.957327	−	0.289005i
$626$	38.0548	−	5.04698i	1.52098	−	0.201718i
$627$	1.34301	+	1.34301i	0.0536346	+	0.0536346i
$628$	9.86634	+	5.67125i	0.393710	+	0.226307i
$629$	26.5394	−	36.1813i	1.05819	−	1.44264i
$630$	−4.09367	−	19.6737i	−0.163096	−	0.783817i
$631$	−7.21444			−0.287202			−0.143601	−	0.989636i	$-0.545868\pi$
$631$	−7.21444			−0.287202			−0.143601	+	0.989636i	$0.545868\pi$
$632$	7.83575	−	19.0715i	0.311689	−	0.758623i
$633$	−49.4326	−	49.4326i	−1.96477	−	1.96477i
$634$	−26.4941	+	3.51375i	−1.05221	+	0.139549i
$635$	2.96904	+	2.56284i	0.117823	+	0.101703i
$636$	9.74592	−	16.9551i	0.386451	−	0.672314i
$637$	−17.1249	+	17.1249i	−0.678513	+	0.678513i
$638$	3.77196	−	0.500251i	0.149333	−	0.0198051i
$639$	5.63216	−	5.63216i	0.222805	−	0.222805i
$640$	21.2367	+	13.7478i	0.839454	+	0.543431i
$641$	−21.1951	−	21.1951i	−0.837157	−	0.837157i	0.151327	−	0.988484i	$-0.451645\pi$
$641$	−21.1951	−	21.1951i	−0.837157	−	0.837157i	−0.988484	+	0.151327i	$0.951645\pi$
$642$	−7.62821	−	57.5176i	−0.301061	−	2.27004i
$643$			15.3198i			0.604153i	0.953284	+	0.302077i	$0.0976799\pi$
$643$			15.3198i			0.604153i	−0.953284	+	0.302077i	$0.902320\pi$
$644$	−5.11986	−	18.9627i	−0.201751	−	0.747235i
$645$	−23.3293	+	27.0269i	−0.918591	+	1.06418i
$646$	3.75176	+	2.05452i	0.147611	+	0.0808339i
$647$	−30.7513	−	30.7513i	−1.20896	−	1.20896i	−0.971365	−	0.237594i	$-0.923641\pi$
$647$	−30.7513	−	30.7513i	−1.20896	−	1.20896i	−0.237594	−	0.971365i	$-0.576359\pi$
$648$	12.0792	−	5.04396i	0.474517	−	0.198145i
$649$	−2.16591	+	2.16591i	−0.0850193	+	0.0850193i
$650$	18.2084	−	32.7866i	0.714192	−	1.28600i
$651$	−8.26073	−	8.26073i	−0.323764	−	0.323764i
$652$	−48.5847	+	13.1177i	−1.90272	+	0.513729i
$653$			7.20109i			0.281801i	0.990024	+	0.140900i	$0.0449997\pi$
$653$			7.20109i			0.281801i	−0.990024	+	0.140900i	$0.955000\pi$
$654$	55.4955	+	42.4991i	2.17005	+	1.66185i
$655$	12.0812	−	13.9960i	0.472051	−	0.546869i
$656$	−10.0921	+	38.2477i	−0.394028	+	1.49332i
$657$		−	0.285190i		−	0.0111263i
$658$	−10.3136	−	7.89829i	−0.402067	−	0.307908i
$659$			26.5931i			1.03592i	0.855405	+	0.517960i	$0.173308\pi$
$659$			26.5931i			1.03592i	−0.855405	+	0.517960i	$0.826692\pi$
$660$	5.01959	−	10.4341i	0.195387	−	0.406148i
$661$	40.2944			1.56727			0.783635	−	0.621221i	$-0.213363\pi$
$661$	40.2944			1.56727			0.783635	+	0.621221i	$0.213363\pi$
$662$	1.38778	+	10.4641i	0.0539377	+	0.406697i
$663$	8.83697	+	57.4844i	0.343200	+	2.23251i
$664$	−18.2925	+	44.5222i	−0.709887	+	1.72780i
$665$	−0.187400	−	2.55214i	−0.00726706	−	0.0989679i
$666$	8.24218	+	62.1471i	0.319378	+	2.40815i
$667$	12.3026	−	12.3026i	0.476359	−	0.476359i
$668$	−6.71545	−	24.8723i	−0.259828	−	0.962340i
$669$	16.2549	−	16.2549i	0.628449	−	0.628449i
$670$	−5.91564	−	3.87783i	−0.228541	−	0.149814i
$671$	3.67565			0.141897
$672$	14.3768	+	18.5522i	0.554598	+	0.715666i
$673$	25.2208			0.972191			0.486096	−	0.873906i	$-0.338421\pi$
$673$	25.2208			0.972191			0.486096	+	0.873906i	$0.338421\pi$
$674$	27.2037	−	3.60785i	1.04785	−	0.138969i
$675$	−2.08482	−	14.1198i	−0.0802449	−	0.543470i
$676$	−7.88772	−	29.2141i	−0.303374	−	1.12362i
$677$			1.33997i			0.0514991i	0.999668	+	0.0257496i	$0.00819724\pi$
$677$			1.33997i			0.0514991i	−0.999668	+	0.0257496i	$0.991803\pi$
$678$	0.0121002	+	0.0912367i	0.000464704	+	0.00350392i
$679$	0.627225			0.0240707
$680$	4.25756	−	25.7269i	0.163270	−	0.986581i
$681$	−61.0130			−2.33802
$682$	−0.509644	−	3.84278i	−0.0195153	−	0.147147i
$683$		−	4.86709i		−	0.186234i	−0.995655	−	0.0931169i	$-0.970317\pi$
$683$		−	4.86709i		−	0.186234i	0.995655	−	0.0931169i	$-0.0296830\pi$
$684$	−5.76961	+	1.55778i	−0.220607	+	0.0595630i
$685$	−17.5681	−	15.1646i	−0.671243	−	0.579410i
$686$	25.2965	−	3.35492i	0.965826	−	0.128091i
$687$	−30.7042			−1.17144
$688$	6.12673	−	23.2196i	0.233579	−	0.885238i
$689$	19.5001			0.742894
$690$	−10.7856	−	51.8342i	−0.410600	−	1.97329i
$691$	−0.721793	+	0.721793i	−0.0274583	+	0.0274583i	−0.720703	−	0.693244i	$-0.756181\pi$
$691$	−0.721793	+	0.721793i	−0.0274583	+	0.0274583i	0.693244	+	0.720703i	$0.256181\pi$
$692$	−6.89195	+	1.86080i	−0.261993	+	0.0707371i
$693$	4.37430	−	4.37430i	0.166166	−	0.166166i
$694$	−0.596440	−	4.49723i	−0.0226405	−	0.170713i
$695$	−3.16105	−	2.72858i	−0.119905	−	0.103501i
$696$	−7.90104	+	19.2304i	−0.299488	+	0.728926i
$697$	40.3007	−	6.19536i	1.52650	−	0.234666i
$698$	0.179123	+	1.35061i	0.00677992	+	0.0511215i
$699$	−47.7342			−1.80547
$700$	−14.3057	+	6.22286i	−0.540706	+	0.235202i
$701$		−	0.0837431i		−	0.00316293i	−0.999999	−	0.00158147i	$-0.999497\pi$
$701$		−	0.0837431i		−	0.00316293i	0.999999	−	0.00158147i	$-0.000503397\pi$
$702$	−16.9991	−	13.0181i	−0.641589	−	0.491336i
$703$			7.98346i			0.301102i
$704$	0.0446083	+	7.78785i	0.00168124	+	0.293516i
$705$	−26.5069	−	22.8804i	−0.998307	−	0.861727i
$706$	−33.3591	−	25.5468i	−1.25549	−	0.961466i
$707$		−	12.4834i		−	0.469487i
$708$	−4.36255	−	16.1578i	−0.163955	−	0.607248i
$709$	12.3924	+	12.3924i	0.465405	+	0.465405i	0.900422	−	0.435017i	$-0.143258\pi$
$709$	12.3924	+	12.3924i	0.465405	+	0.465405i	−0.435017	+	0.900422i	$0.643258\pi$
$710$	−5.17152	−	3.39004i	−0.194084	−	0.127226i
$711$	20.9964	−	20.9964i	0.787426	−	0.787426i
$712$	−13.6237	−	32.6258i	−0.510568	−	1.22270i
$713$	−12.5336	−	12.5336i	−0.469386	−	0.469386i
$714$	11.6202	−	21.2197i	0.434876	−	0.794128i
$715$	11.5143	−	0.845478i	0.430611	−	0.0316191i
$716$	42.9469	−	11.5955i	1.60500	−	0.433345i
$717$		−	20.6624i		−	0.771651i
$718$	−2.51740	−	18.9815i	−0.0939484	−	0.708383i
$719$	7.40991	+	7.40991i	0.276343	+	0.276343i	0.831647	−	0.555304i	$-0.187398\pi$
$719$	7.40991	+	7.40991i	0.276343	+	0.276343i	−0.555304	+	0.831647i	$0.687398\pi$
$720$	20.5930	+	30.0546i	0.767457	+	1.12007i
$721$	15.0032	−	15.0032i	0.558749	−	0.558749i
$722$	25.8824	−	3.43262i	0.963243	−	0.127749i
$723$	0.495165	−	0.495165i	0.0184154	−	0.0184154i
$724$	16.4947	+	9.48128i	0.613021	+	0.352369i
$725$	−11.0939	−	8.23932i	−0.412018	−	0.306001i
$726$	−37.4805	+	4.97081i	−1.39103	+	0.184484i
$727$	−25.2505	−	25.2505i	−0.936491	−	0.936491i	0.0616094	−	0.998100i	$-0.480377\pi$
$727$	−25.2505	−	25.2505i	−0.936491	−	0.936491i	−0.998100	+	0.0616094i	$0.980377\pi$
$728$	−8.89398	+	21.6471i	−0.329633	+	0.802295i
$729$	41.6272			1.54175
$730$	−0.216761	+	0.0451034i	−0.00802270	+	0.00166935i
$731$	−24.4659	+	3.76110i	−0.904905	+	0.139109i
$732$	−10.0086	+	17.4120i	−0.369927	+	0.643567i
$733$	−27.6165	−	27.6165i	−1.02004	−	1.02004i	−0.999795	−	0.0202450i	$-0.993555\pi$
$733$	−27.6165	−	27.6165i	−1.02004	−	1.02004i	−0.0202450	−	0.999795i	$-0.506445\pi$
$734$	−9.53794	+	1.26496i	−0.352052	+	0.0466904i
$735$	27.0823	−	1.98861i	0.998947	−	0.0733511i
$736$	21.8132	+	28.1483i	0.804045	+	1.03756i
$737$		−	2.17751i		−	0.0802096i
$738$	−34.6362	+	45.2281i	−1.27498	+	1.66487i
$739$	−17.0736			−0.628062			−0.314031	−	0.949413i	$-0.601680\pi$
$739$	−17.0736			−0.628062			−0.314031	+	0.949413i	$0.601680\pi$
$740$	45.9320	−	16.0932i	1.68849	−	0.591599i
$741$	−7.31695	−	7.31695i	−0.268795	−	0.268795i
$742$	−6.44007	−	4.93188i	−0.236422	−	0.181055i
$743$	38.4115			1.40918			0.704590	−	0.709614i	$-0.251131\pi$
$743$	38.4115			1.40918			0.704590	+	0.709614i	$0.251131\pi$
$744$	19.5914	+	8.04939i	0.718257	+	0.295105i
$745$	0.829304	+	11.2940i	0.0303833	+	0.413781i
$746$	−7.77695	+	10.1552i	−0.284734	+	0.371807i
$747$	−49.0159	+	49.0159i	−1.79340	+	1.79340i
$748$	7.34222	−	3.24580i	0.268458	−	0.118678i
$749$	−24.0658			−0.879347
$750$	−39.4768	+	14.4883i	−1.44149	+	0.529037i
$751$	−24.5915	+	24.5915i	−0.897358	+	0.897358i	−0.995202	−	0.0978437i	$-0.968805\pi$
$751$	−24.5915	+	24.5915i	−0.897358	+	0.897358i	0.0978437	+	0.995202i	$0.468805\pi$
$752$	22.7728	+	6.00884i	0.830438	+	0.219120i
$753$		−	35.0168i		−	1.27608i
$754$	−20.5503	+	2.72546i	−0.748397	+	0.0992553i
$755$	−0.875933	−	11.9291i	−0.0318785	−	0.434143i
$756$	2.32161	+	8.59868i	0.0844363	+	0.312731i
$757$	12.3415	−	12.3415i	0.448561	−	0.448561i	−0.446315	−	0.894876i	$-0.647264\pi$
$757$	12.3415	−	12.3415i	0.448561	−	0.448561i	0.894876	+	0.446315i	$0.147264\pi$
$758$	−20.2750	+	26.4752i	−0.736423	+	0.961624i
$759$	11.5250	−	11.5250i	0.418330	−	0.418330i
$760$	2.09648	+	4.13888i	0.0760473	+	0.150133i
$761$	−18.3851			−0.666458			−0.333229	−	0.942846i	$-0.608138\pi$
$761$	−18.3851			−0.666458			−0.333229	+	0.942846i	$0.608138\pi$
$762$	−5.23783	−	4.01119i	−0.189747	−	0.145310i
$763$	20.5009	−	20.5009i	0.742182	−	0.742182i
$764$	−9.36034	−	34.6684i	−0.338645	−	1.25426i
$765$	19.9345	−	31.8266i	0.720732	−	1.15069i
$766$	18.6406	+	14.2752i	0.673511	+	0.515782i
$767$	11.8002	−	11.8002i	0.426082	−	0.426082i
$768$	−37.0135	−	20.9945i	−1.33561	−	0.757574i
$769$			8.21402i			0.296205i	0.988972	+	0.148103i	$0.0473166\pi$
$769$			8.21402i			0.296205i	−0.988972	+	0.148103i	$0.952683\pi$
$770$	−4.01654	−	2.63293i	−0.144746	−	0.0948840i
$771$	20.4794	−	20.4794i	0.737547	−	0.737547i
$772$	3.82723	−	1.03334i	0.137745	−	0.0371907i
$773$	−27.2399	−	27.2399i	−0.979750	−	0.979750i	0.0200488	−	0.999799i	$-0.493618\pi$
$773$	−27.2399	−	27.2399i	−0.979750	−	0.979750i	−0.999799	+	0.0200488i	$0.993618\pi$
$774$	21.0271	−	27.4573i	0.755803	−	0.986931i
$775$	−8.39401	+	11.3022i	−0.301522	+	0.405988i
$776$	−1.04936	+	0.438186i	−0.0376699	+	0.0157299i
$777$	45.1539			1.61989
$778$	−5.50515	−	41.5095i	−0.197369	−	1.48819i
$779$	−5.12971	+	5.12971i	−0.183791	+	0.183791i
$780$	−27.3476	+	56.8469i	−0.979201	+	2.03545i
$781$		−	1.90360i		−	0.0681163i
$782$	17.6308	−	32.1956i	0.630475	−	1.15131i
$783$	−5.57864	+	5.57864i	−0.199364	+	0.199364i
$784$	−15.7829	+	9.19278i	−0.563674	+	0.328313i
$785$	8.31379	−	9.63149i	0.296732	−	0.343762i
$786$	−18.9087	+	24.6910i	−0.674450	+	0.880700i
$787$	−5.98782			−0.213443			−0.106721	−	0.994289i	$-0.534035\pi$
$787$	−5.98782			−0.213443			−0.106721	+	0.994289i	$0.534035\pi$
$788$	−18.3005	+	4.94106i	−0.651927	+	0.176018i
$789$	−20.9874	+	20.9874i	−0.747170	+	0.747170i
$790$	−19.2791	−	12.6379i	−0.685920	−	0.449635i
$791$	0.0381742			0.00135732
$792$	−4.26239	+	10.3743i	−0.151457	+	0.368633i
$793$	−20.0256			−0.711129
$794$	−36.8238	+	4.88371i	−1.30683	+	0.173316i
$795$	−16.5515	−	14.2871i	−0.587022	−	0.506711i
$796$	39.7687	+	22.8593i	1.40956	+	0.810228i
$797$	−11.0798	+	11.0798i	−0.392465	+	0.392465i	−0.875565	−	0.483100i	$-0.839511\pi$
$797$	−11.0798	+	11.0798i	−0.392465	+	0.392465i	0.483100	+	0.875565i	$0.339511\pi$
$798$	0.565913	+	4.26706i	0.0200331	+	0.151052i
$799$	−3.68874	−	23.9952i	−0.130498	−	0.848888i
$800$	19.5865	−	20.4051i	0.692487	−	0.721430i
$801$		−	50.9175i		−	1.79908i
$802$	6.68161	−	8.72488i	0.235936	−	0.308086i
$803$	−0.0481954	−	0.0481954i	−0.00170078	−	0.00170078i
$804$	10.3151	+	5.92922i	0.363787	+	0.209107i
$805$	−21.9011	+	1.60817i	−0.771914	+	0.0566804i
$806$	2.77663	+	20.9361i	0.0978025	+	0.737443i
$807$	−25.2855	+	25.2855i	−0.890090	+	0.890090i
$808$	8.72103	+	20.8851i	0.306805	+	0.734734i
$809$	10.5755	+	10.5755i	0.371815	+	0.371815i	0.868138	−	0.496323i	$-0.165317\pi$
$809$	10.5755	+	10.5755i	0.371815	+	0.371815i	−0.496323	+	0.868138i	$0.665317\pi$
$810$	−2.98140	−	14.3282i	−0.104756	−	0.503442i
$811$	18.0270	+	18.0270i	0.633012	+	0.633012i	0.948822	−	0.315810i	$-0.102276\pi$
$811$	18.0270	+	18.0270i	0.633012	+	0.633012i	−0.315810	+	0.948822i	$0.602276\pi$
$812$	7.47622	+	4.29739i	0.262364	+	0.150809i
$813$	70.0773			2.45772
$814$	11.8954	+	9.10961i	0.416932	+	0.319292i
$815$	4.12031	+	56.1133i	0.144328	+	1.96556i
$816$	−4.61662	+	43.6191i	−0.161614	+	1.52698i
$817$	3.11417	−	3.11417i	0.108951	−	0.108951i
$818$	−1.57897	−	11.9057i	−0.0552075	−	0.416271i
$819$	−23.8320	+	23.8320i	−0.832756	+	0.832756i
$820$	39.8538	+	19.1726i	1.39176	+	0.669538i
$821$	4.78068	−	4.78068i	0.166847	−	0.166847i	−0.618745	−	0.785592i	$-0.712359\pi$
$821$	4.78068	−	4.78068i	0.166847	−	0.166847i	0.785592	+	0.618745i	$0.212359\pi$
$822$	30.9928	+	23.7346i	1.08100	+	0.827841i
$823$			18.0502i			0.629189i	0.949226	+	0.314594i	$0.101868\pi$
$823$			18.0502i			0.629189i	−0.949226	+	0.314594i	$0.898132\pi$
$824$	−14.6194	+	35.5822i	−0.509290	+	1.23956i
$825$	−10.3927	−	7.71853i	−0.361828	−	0.268725i
$826$	−6.88160	+	0.912664i	−0.239441	+	0.0317556i
$827$			24.0381i			0.835888i	0.908473	+	0.417944i	$0.137249\pi$
$827$			24.0381i			0.835888i	−0.908473	+	0.417944i	$0.862751\pi$
$828$	13.3680	+	49.5117i	0.464570	+	1.72065i
$829$	−54.5041			−1.89301			−0.946504	−	0.322693i	$-0.895412\pi$
$829$	−54.5041			−1.89301			−0.946504	+	0.322693i	$0.895412\pi$
$830$	45.0070	+	29.5030i	1.56222	+	1.02407i
$831$	−72.6637			−2.52068
$832$	−0.243034	−	42.4296i	−0.00842568	−	1.47098i
$833$	15.1809	+	11.1354i	0.525988	+	0.385817i
$834$	5.57656	+	4.27060i	0.193101	+	0.147879i
$835$	−28.7265	+	2.10934i	−0.994123	+	0.0729969i
$836$	−0.711775	+	1.23828i	−0.0246173	+	0.0428270i
$837$	5.68338	+	5.68338i	0.196446	+	0.196446i
$838$	−31.0807	−	23.8019i	−1.07366	−	0.822224i
$839$	26.2491	−	26.2491i	0.906220	−	0.906220i	−0.0897444	−	0.995965i	$-0.528605\pi$
$839$	26.2491	−	26.2491i	0.906220	−	0.906220i	0.995965	+	0.0897444i	$0.0286050\pi$
$840$	23.4093	−	11.8576i	0.807697	−	0.409125i
$841$		−	21.3615i		−	0.736604i
$842$	4.87769	+	36.7784i	0.168096	+	1.26747i
$843$	−82.1827			−2.83052
$844$	26.1986	−	45.5780i	0.901792	−	1.56886i
$845$	−33.7411	+	2.47756i	−1.16073	+	0.0852306i
$846$	26.9289	+	20.6225i	0.925836	+	0.709016i
$847$			15.6822i			0.538846i
$848$	14.2199	+	3.75206i	0.488312	+	0.128846i
$849$			44.0596i			1.51212i
$850$	−27.3428	−	10.1179i	−0.937849	−	0.347043i
$851$	68.5097			2.34848
$852$	9.01762	+	5.18339i	0.308938	+	0.177580i
$853$	12.8401			0.439637			0.219818	−	0.975541i	$-0.429454\pi$
$853$	12.8401			0.439637			0.219818	+	0.975541i	$0.429454\pi$
$854$	6.61362	+	5.06479i	0.226313	+	0.173313i
$855$	0.489303	+	6.66367i	0.0167338	+	0.227893i
$856$	40.2628	−	16.8126i	1.37615	−	0.574644i
$857$			15.6507i			0.534616i	0.963611	+	0.267308i	$0.0861341\pi$
$857$			15.6507i			0.534616i	−0.963611	+	0.267308i	$0.913866\pi$
$858$	−19.2513	+	2.55319i	−0.657230	+	0.0871644i
$859$	−45.3264			−1.54652			−0.773259	−	0.634091i	$-0.781375\pi$
$859$	−45.3264			−1.54652			−0.773259	+	0.634091i	$0.781375\pi$
$860$	−24.1946	−	11.6394i	−0.825030	−	0.396901i
$861$	29.0133	+	29.0133i	0.988771	+	0.988771i
$862$	−18.6196	−	14.2591i	−0.634187	−	0.485668i
$863$	6.78897	−	6.78897i	0.231099	−	0.231099i	−0.582052	−	0.813151i	$-0.697750\pi$
$863$	6.78897	−	6.78897i	0.231099	−	0.231099i	0.813151	+	0.582052i	$0.197750\pi$
$864$	−9.89124	−	12.7639i	−0.336507	−	0.434237i
$865$	0.584484	+	7.95992i	0.0198731	+	0.270645i
$866$	−5.51296	+	7.19885i	−0.187338	+	0.244627i
$867$	43.1251	−	13.5800i	1.46460	−	0.461201i
$868$	4.37807	−	7.61658i	0.148601	−	0.258524i
$869$		−	7.09653i		−	0.240733i
$870$	19.4398	+	12.7432i	0.659070	+	0.432034i
$871$			11.8635i			0.401978i
$872$	−19.9764	+	48.6206i	−0.676485	+	1.64650i
$873$	−1.63769			−0.0554273
$874$	0.858631	+	6.47418i	0.0290436	+	0.218993i
$875$	3.80449	+	17.0220i	0.128615	+	0.575448i
$876$	0.359541	−	0.0970748i	0.0121478	−	0.00327986i
$877$	23.4361			0.791379			0.395690	−	0.918384i	$-0.370506\pi$
$877$	23.4361			0.791379			0.395690	+	0.918384i	$0.370506\pi$
$878$	9.15763	+	7.01302i	0.309055	+	0.236678i
$879$	41.7318	+	41.7318i	1.40758	+	1.40758i
$880$	8.55915	+	1.59896i	0.288529	+	0.0539009i
$881$	22.5078	+	22.5078i	0.758308	+	0.758308i	0.976014	−	0.217706i	$-0.0698575\pi$
$881$	22.5078	+	22.5078i	0.758308	+	0.758308i	−0.217706	+	0.976014i	$0.569858\pi$
$882$	−26.0756	+	3.45824i	−0.878011	+	0.116445i
$883$	−39.3128	−	39.3128i	−1.32298	−	1.32298i	−0.911351	−	0.411630i	$-0.864960\pi$
$883$	−39.3128	−	39.3128i	−1.32298	−	1.32298i	−0.411630	−	0.911351i	$-0.635040\pi$
$884$	−40.0017	+	17.6837i	−1.34540	+	0.594767i
$885$	−18.6616	+	1.37029i	−0.627303	+	0.0460619i
$886$	−17.8847	−	13.6963i	−0.600847	−	0.460136i
$887$			8.40522i			0.282220i	0.989994	+	0.141110i	$0.0450671\pi$
$887$			8.40522i			0.282220i	−0.989994	+	0.141110i	$0.954933\pi$
$888$	−75.5437	+	31.5450i	−2.53508	+	1.05858i
$889$	−1.93493	+	1.93493i	−0.0648956	+	0.0648956i
$890$	−38.7003	+	8.05271i	−1.29724	+	0.269927i
$891$	3.18578	−	3.18578i	0.106728	−	0.106728i
$892$	14.9873	+	8.61484i	0.501813	+	0.288446i
$893$	3.05425	+	3.05425i	0.102206	+	0.102206i
$894$	−2.50434	−	18.8831i	−0.0837577	−	0.631544i
$895$	−3.64219	−	49.6019i	−0.121745	−	1.65801i
$896$	−10.6508	+	14.0742i	−0.355820	+	0.470186i
$897$	−62.7901	+	62.7901i	−2.09650	+	2.09650i
$898$	−28.2033	−	21.5984i	−0.941156	−	0.720748i
$899$	7.78188			0.259540
$900$	37.3523	−	16.2479i	1.24508	−	0.541598i
$901$	−2.30333	−	14.9832i	−0.0767351	−	0.499161i
$902$	1.78997	+	13.4966i	0.0595994	+	0.449387i
$903$	−17.6135	−	17.6135i	−0.586142	−	0.586142i
$904$	−0.0638664	+	0.0266689i	−0.00212416	+	0.000886993i
$905$	13.8991	−	16.1021i	0.462023	−	0.535251i
$906$	2.64516	+	19.9448i	0.0878794	+	0.662622i
$907$			52.1542i			1.73175i	0.500259	+	0.865876i	$0.333238\pi$
$907$			52.1542i			1.73175i	−0.500259	+	0.865876i	$0.666762\pi$
$908$	−11.9597	−	44.2957i	−0.396896	−	1.47000i
$909$			32.5942i			1.08108i
$910$	21.8828	+	14.3446i	0.725407	+	0.475520i
$911$	9.82346	+	9.82346i	0.325466	+	0.325466i	0.850859	−	0.525394i	$-0.176082\pi$
$911$	9.82346	+	9.82346i	0.325466	+	0.325466i	−0.525394	+	0.850859i	$0.676082\pi$
$912$	−3.92780	−	6.74354i	−0.130062	−	0.223301i
$913$			16.5668i			0.548281i
$914$	−29.0699	−	22.2620i	−0.961546	−	0.736363i
$915$	16.9975	+	14.6721i	0.561922	+	0.485045i
$916$	−6.01860	−	22.2914i	−0.198860	−	0.736528i
$917$	9.12124	+	9.12124i	0.301210	+	0.301210i
$918$	−7.99471	+	14.5992i	−0.263865	+	0.481844i
$919$	−31.0471			−1.02415			−0.512075	−	0.858940i	$-0.671123\pi$
$919$	−31.0471			−1.02415			−0.512075	+	0.858940i	$0.671123\pi$
$920$	35.5177	−	17.9909i	1.17098	−	0.593141i
$921$	−12.5377	−	12.5377i	−0.413133	−	0.413133i
$922$	−24.9873	+	3.31391i	−0.822912	+	0.109138i
$923$			10.3712i			0.341371i
$924$	7.00366	+	4.02576i	0.230404	+	0.132438i
$925$	−7.94827	−	53.8307i	−0.261337	−	1.76994i
$926$	12.1660	−	15.8864i	0.399798	−	0.522058i
$927$	−39.1735	+	39.1735i	−1.28663	+	1.28663i
$928$	−15.5101	−	1.96667i	−0.509144	−	0.0645592i
$929$	3.29196	+	3.29196i	0.108006	+	0.108006i	0.759044	−	0.651039i	$-0.225666\pi$
$929$	3.29196	+	3.29196i	0.108006	+	0.108006i	−0.651039	+	0.759044i	$0.725666\pi$
$930$	12.9824	−	19.8047i	0.425711	−	0.649423i
$931$	−3.34969			−0.109782
$932$	−9.35680	−	34.6552i	−0.306492	−	1.13517i
$933$	−48.6242	−	48.6242i	−1.59188	−	1.59188i
$934$	−4.44834	−	3.40659i	−0.145554	−	0.111467i
$935$	−2.00969	−	8.74731i	−0.0657240	−	0.286068i
$936$	23.2222	−	56.5207i	0.759042	−	1.84744i
$937$	22.2487	+	22.2487i	0.726832	+	0.726832i	0.969987	−	0.243155i	$-0.0781825\pi$
$937$	22.2487	+	22.2487i	0.726832	+	0.726832i	−0.243155	+	0.969987i	$0.578183\pi$
$938$	3.00045	−	3.91801i	0.0979683	−	0.127927i
$939$			72.1926i			2.35592i
$940$	11.4155	−	23.7291i	0.372331	−	0.773958i
$941$	−38.7948	−	38.7948i	−1.26468	−	1.26468i	−0.948801	−	0.315875i	$-0.897702\pi$
$941$	−38.7948	−	38.7948i	−1.26468	−	1.26468i	−0.315875	−	0.948801i	$-0.602298\pi$
$942$	−13.0122	+	16.9914i	−0.423960	+	0.553609i
$943$	44.0204	+	44.0204i	1.43350	+	1.43350i
$944$	10.8755	−	6.33446i	0.353967	−	0.206169i
$945$	9.93112	−	0.729227i	0.323059	−	0.0237218i
$946$	−1.08666	−	8.19357i	−0.0353304	−	0.266396i
$947$	4.62835			0.150401			0.0752006	−	0.997168i	$-0.476040\pi$
$947$	4.62835			0.150401			0.0752006	+	0.997168i	$0.476040\pi$
$948$	33.6171	+	19.3234i	1.09183	+	0.627594i
$949$	0.262577	+	0.262577i	0.00852361	+	0.00852361i
$950$	4.98740	−	1.42577i	0.161813	−	0.0462582i
$951$		−	50.2611i		−	1.62983i
$952$	17.6834	+	4.27687i	0.573122	+	0.138614i
$953$	−11.7624	−	11.7624i	−0.381021	−	0.381021i	0.490449	−	0.871470i	$-0.336833\pi$
$953$	−11.7624	−	11.7624i	−0.381021	−	0.381021i	−0.871470	+	0.490449i	$0.836833\pi$
$954$	16.8151	+	12.8772i	0.544408	+	0.416914i
$955$	−40.0405	+	2.94012i	−1.29568	+	0.0951399i
$956$	15.0010	−	4.05021i	0.485166	−	0.130993i
$957$			7.15566i			0.231310i
$958$	0.202219	+	0.154862i	0.00653341	+	0.00500336i
$959$	11.4492	−	11.4492i	0.369714	−	0.369714i
$960$	−30.8805	+	36.1919i	−0.996664	+	1.16809i
$961$			23.0720i			0.744259i
$962$	−64.8080	−	49.6307i	−2.08949	−	1.60016i
$963$	62.8361			2.02486
$964$	0.456553	+	0.262430i	0.0147046	+	0.00845231i
$965$	−0.324575	−	4.42029i	−0.0104485	−	0.142294i
$966$	36.6176	−	4.85636i	1.17815	−	0.156251i
$967$	6.58343	−	6.58343i	0.211709	−	0.211709i	−0.593284	−	0.804993i	$-0.702169\pi$
$967$	6.58343	−	6.58343i	0.211709	−	0.211709i	0.804993	+	0.593284i	$0.202169\pi$
$968$	−10.9557	−	26.2367i	−0.352130	−	0.843278i
$969$	−4.75780	+	6.48634i	−0.152843	+	0.208371i
$970$	0.259004	+	1.24474i	0.00831611	+	0.0399662i
$971$			17.9459i			0.575912i	0.957644	+	0.287956i	$0.0929757\pi$
$971$			17.9459i			0.575912i	−0.957644	+	0.287956i	$0.907024\pi$
$972$	10.8813	+	40.3014i	0.349016	+	1.29267i
$973$	2.06007	−	2.06007i	0.0660427	−	0.0660427i
$974$	−14.5053	+	1.92375i	−0.464779	+	0.0616408i
$975$	56.6213	+	42.0519i	1.81333	+	1.34674i
$976$	−14.6031	−	3.85317i	−0.467433	−	0.123337i
$977$	−2.49628	−	2.49628i	−0.0798631	−	0.0798631i	0.666047	−	0.745910i	$-0.267985\pi$
$977$	−2.49628	−	2.49628i	−0.0798631	−	0.0798631i	−0.745910	+	0.666047i	$0.767985\pi$
$978$	−12.4426	−	93.8186i	−0.397870	−	2.99999i
$979$	−8.60475	−	8.60475i	−0.275009	−	0.275009i
$980$	6.75238	+	19.2721i	0.215697	+	0.615624i
$981$	−53.5279	+	53.5279i	−1.70901	+	1.70901i
$982$	−2.44834	−	18.4608i	−0.0781296	−	0.589107i
$983$	30.1790			0.962560			0.481280	−	0.876567i	$-0.340172\pi$
$983$	30.1790			0.962560			0.481280	+	0.876567i	$0.340172\pi$
$984$	−68.8090	−	28.2710i	−2.19355	−	0.901247i
$985$	1.55200	+	21.1363i	0.0494510	+	0.673458i
$986$	4.52152	+	15.4682i	0.143995	+	0.492606i
$987$	17.2746	−	17.2746i	0.549857	−	0.549857i
$988$	3.87788	−	6.74639i	0.123372	−	0.214631i
$989$	−26.7241	−	26.7241i	−0.849777	−	0.849777i
$990$	10.4872	+	6.87458i	0.333305	+	0.218489i
$991$	−12.8847	+	12.8847i	−0.409297	+	0.409297i	−0.881493	−	0.472197i	$-0.843461\pi$
$991$	−12.8847	+	12.8847i	−0.409297	+	0.409297i	0.472197	+	0.881493i	$0.343461\pi$
$992$	−2.00360	+	15.8013i	−0.0636143	+	0.501692i
$993$	−19.8510			−0.629953
$994$	2.62303	−	3.42517i	0.0831975	−	0.108640i
$995$	33.5108	−	38.8221i	1.06236	−	1.23074i
$996$	−78.4790	−	45.1103i	−2.48670	−	1.42938i
$997$	36.5622			1.15794			0.578969	−	0.815350i	$-0.303455\pi$
$997$	36.5622			1.15794			0.578969	+	0.815350i	$0.303455\pi$
$998$	29.4416	+	22.5467i	0.931958	+	0.713704i
$999$	−31.0659			−0.982882

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.t.a.523.5	✓	208
5.2	odd	4		680.2.bl.a.387.49	yes	208
8.3	odd	2	inner	680.2.t.a.523.56	yes	208
17.4	even	4		680.2.bl.a.123.100	yes	208
40.27	even	4		680.2.bl.a.387.100	yes	208
85.72	odd	4	inner	680.2.t.a.667.56	yes	208
136.123	odd	4		680.2.bl.a.123.49	yes	208
680.667	even	4	inner	680.2.t.a.667.5	yes	208

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.t.a.523.5	✓	208	1.1	even	1	trivial
680.2.t.a.523.56	yes	208	8.3	odd	2	inner
680.2.t.a.667.5	yes	208	680.667	even	4	inner
680.2.t.a.667.56	yes	208	85.72	odd	4	inner
680.2.bl.a.123.49	yes	208	136.123	odd	4
680.2.bl.a.123.100	yes	208	17.4	even	4
680.2.bl.a.387.49	yes	208	5.2	odd	4
680.2.bl.a.387.100	yes	208	40.27	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40194 + 0.185930i) q^{2} -2.65957i q^{3} +(1.93086 - 0.521326i) q^{4} +(-0.163750 - 2.23006i) q^{5} +(0.494495 + 3.72855i) q^{6} +1.56006 q^{7} +(-2.61002 + 1.08987i) q^{8} -4.07332 q^{9} +(0.644204 + 3.09597i) q^{10} +(-0.688367 + 0.688367i) q^{11} +(-1.38650 - 5.13526i) q^{12} +(3.75034 - 3.75034i) q^{13} +(-2.18710 + 0.290062i) q^{14} +(-5.93101 + 0.435505i) q^{15} +(3.45644 - 2.01321i) q^{16} +(-3.32461 - 2.43864i) q^{17} +(5.71054 - 0.757354i) q^{18} +0.733580 q^{19} +(-1.47877 - 4.22057i) q^{20} -4.14908i q^{21} +(0.837059 - 1.09304i) q^{22} -6.29519i q^{23} +(2.89859 + 6.94152i) q^{24} +(-4.94637 + 0.730347i) q^{25} +(-4.56044 + 5.95505i) q^{26} +2.85457i q^{27} +(3.01225 - 0.813298i) q^{28} +(1.95429 + 1.95429i) q^{29} +(8.23394 - 1.71331i) q^{30} +(1.99098 - 1.99098i) q^{31} +(-4.47140 + 3.46506i) q^{32} +(1.83076 + 1.83076i) q^{33} +(5.11432 + 2.80067i) q^{34} +(-0.255460 - 3.47903i) q^{35} +(-7.86501 + 2.12353i) q^{36} +10.8829i q^{37} +(-1.02843 + 0.136395i) q^{38} +(-9.97430 - 9.97430i) q^{39} +(2.85787 + 5.64203i) q^{40} +(-6.99271 + 6.99271i) q^{41} +(0.771441 + 5.81676i) q^{42} +(4.24516 - 4.24516i) q^{43} +(-0.970276 + 1.68800i) q^{44} +(0.667007 + 9.08376i) q^{45} +(1.17047 + 8.82546i) q^{46} +(4.16348 + 4.16348i) q^{47} +(-5.35428 - 9.19265i) q^{48} -4.56622 q^{49} +(6.79871 - 1.94358i) q^{50} +(-6.48573 + 8.84204i) q^{51} +(5.28623 - 9.19653i) q^{52} +(2.59977 + 2.59977i) q^{53} +(-0.530751 - 4.00193i) q^{54} +(1.64782 + 1.42238i) q^{55} +(-4.07177 + 1.70026i) q^{56} -1.95101i q^{57} +(-3.10315 - 2.37643i) q^{58} +3.14644 q^{59} +(-11.2249 + 3.93289i) q^{60} +(-2.66983 - 2.66983i) q^{61} +(-2.42104 + 3.16141i) q^{62} -6.35461 q^{63} +(5.62436 - 5.68916i) q^{64} +(-8.97762 - 7.74938i) q^{65} +(-2.90701 - 2.22622i) q^{66} +(-1.58165 + 1.58165i) q^{67} +(-7.69068 - 2.97546i) q^{68} -16.7425 q^{69} +(1.00500 + 4.82988i) q^{70} +(-1.38270 + 1.38270i) q^{71} +(10.6314 - 4.43939i) q^{72} +0.0700142i q^{73} +(-2.02346 - 15.2571i) q^{74} +(1.94241 + 13.1552i) q^{75} +(1.41644 - 0.382434i) q^{76} +(-1.07389 + 1.07389i) q^{77} +(15.8379 + 12.1288i) q^{78} +(-5.15461 + 5.15461i) q^{79} +(-5.05559 - 7.37842i) q^{80} -4.62803 q^{81} +(8.50318 - 11.1035i) q^{82} +(12.0334 - 12.0334i) q^{83} +(-2.16302 - 8.01130i) q^{84} +(-4.89391 + 7.81343i) q^{85} +(-5.16215 + 6.74076i) q^{86} +(5.19756 - 5.19756i) q^{87} +(1.04642 - 2.54688i) q^{88} +12.5002i q^{89} +(-2.62405 - 12.6109i) q^{90} +(5.85075 - 5.85075i) q^{91} +(-3.28184 - 12.1551i) q^{92} +(-5.29515 - 5.29515i) q^{93} +(-6.61106 - 5.06282i) q^{94} +(-0.120124 - 1.63593i) q^{95} +(9.21557 + 11.8920i) q^{96} +0.402052 q^{97} +(6.40156 - 0.848999i) q^{98} +(2.80394 - 2.80394i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 208 q - 8 q^{6} - 192 q^{9} + 2 q^{10} - 8 q^{11} + 8 q^{12} - 16 q^{14} - 16 q^{16} - 12 q^{18} - 10 q^{20} + 4 q^{22} + 16 q^{24} + 12 q^{28} - 24 q^{30} + 20 q^{32} - 8 q^{33} - 4 q^{34} - 8 q^{35} - 12 q^{38}+ \cdots + 24 q^{99}+O(q^{100}) \) 208 * q - 8 * q^6 - 192 * q^9 + 2 * q^10 - 8 * q^11 + 8 * q^12 - 16 * q^14 - 16 * q^16 - 12 * q^18 - 10 * q^20 + 4 * q^22 + 16 * q^24 + 12 * q^28 - 24 * q^30 + 20 * q^32 - 8 * q^33 - 4 * q^34 - 8 * q^35 - 12 * q^38 - 42 * q^40 - 8 * q^41 - 32 * q^42 + 8 * q^44 - 16 * q^46 + 160 * q^49 + 16 * q^50 - 8 * q^51 - 20 * q^52 + 36 * q^54 + 4 * q^56 - 56 * q^58 - 64 * q^59 + 32 * q^60 - 48 * q^65 - 8 * q^67 - 56 * q^68 - 28 * q^70 - 56 * q^72 + 8 * q^74 + 8 * q^75 - 12 * q^78 + 6 * q^80 + 128 * q^81 + 44 * q^82 + 8 * q^86 - 82 * q^90 + 24 * q^91 + 64 * q^94 - 48 * q^96 - 16 * q^97 - 40 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

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