LMFDB - Embedded newform 680.2.bl.a.123.49

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(123,680)] 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, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.123"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.bl (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			123.49
Character	$\chi$	$=$	680.123
Dual form			680.2.bl.a.387.49

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.185930 + 1.40194i) q^{2} -2.65957 q^{3} +(-1.93086 - 0.521326i) q^{4} +(2.23006 - 0.163750i) q^{5} +(0.494495 - 3.72855i) q^{6} -1.56006i q^{7} +(1.08987 - 2.61002i) q^{8} +4.07332 q^{9} +(-0.185069 + 3.15686i) q^{10} +(-0.688367 - 0.688367i) q^{11} +(5.13526 + 1.38650i) 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} +(2.43864 + 3.32461i) q^{17} +(-0.757354 + 5.71054i) q^{18} -0.733580 q^{19} +(-4.39131 - 0.846411i) q^{20} +4.14908i q^{21} +(1.09304 - 0.837059i) q^{22} -6.29519 q^{23} +(-2.89859 + 6.94152i) q^{24} +(4.94637 - 0.730347i) q^{25} +(-4.56044 - 5.95505i) q^{26} -2.85457 q^{27} +(-0.813298 + 3.01225i) q^{28} +(-1.95429 + 1.95429i) q^{29} +(0.492204 - 8.39589i) q^{30} +(1.99098 + 1.99098i) q^{31} +(-3.46506 + 4.47140i) 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} -10.8829 q^{37} +(0.136395 - 1.02843i) q^{38} +(9.97430 - 9.97430i) q^{39} +(2.00309 - 5.99897i) q^{40} +(-6.99271 - 6.99271i) q^{41} +(-5.81676 - 0.771441i) q^{42} +(-4.24516 + 4.24516i) q^{43} +(0.970276 + 1.68800i) q^{44} +(9.08376 - 0.667007i) q^{45} +(1.17047 - 8.82546i) q^{46} +(-4.16348 - 4.16348i) q^{47} +(-9.19265 - 5.35428i) q^{48} +4.56622 q^{49} +(0.104220 + 7.07030i) q^{50} +(-6.48573 - 8.84204i) q^{51} +(9.19653 - 5.28623i) 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} +1.95101 q^{57} +(-2.37643 - 3.10315i) q^{58} -3.14644 q^{59} +(11.6790 + 2.25109i) q^{60} +(-2.66983 + 2.66983i) q^{61} +(-3.16141 + 2.42104i) q^{62} -6.35461i q^{63} +(-5.62436 - 5.68916i) q^{64} +(-7.74938 + 8.97762i) q^{65} +(-2.90701 + 2.22622i) q^{66} +(-1.58165 + 1.58165i) q^{67} +(-2.97546 - 7.69068i) q^{68} +16.7425 q^{69} +(4.92488 + 0.288718i) q^{70} +(-1.38270 - 1.38270i) q^{71} +(4.43939 - 10.6314i) q^{72} +0.0700142 q^{73} +(2.02346 - 15.2571i) q^{74} +(-13.1552 + 1.94241i) q^{75} +(1.41644 + 0.382434i) q^{76} +(-1.07389 + 1.07389i) q^{77} +(12.1288 + 15.8379i) q^{78} +(5.15461 + 5.15461i) q^{79} +(8.03775 + 3.92360i) q^{80} -4.62803 q^{81} +(11.1035 - 8.50318i) q^{82} +(-12.0334 + 12.0334i) q^{83} +(2.16302 - 8.01130i) q^{84} +(5.98272 + 7.01477i) q^{85} +(-5.16215 - 6.74076i) q^{86} +(5.19756 - 5.19756i) q^{87} +(-2.54688 + 1.04642i) q^{88} +12.5002i q^{89} +(-0.753845 + 12.8589i) q^{90} +(5.85075 + 5.85075i) q^{91} +(12.1551 + 3.28184i) q^{92} +(-5.29515 - 5.29515i) q^{93} +(6.61106 - 5.06282i) q^{94} +(-1.63593 + 0.120124i) q^{95} +(9.21557 - 11.8920i) q^{96} -0.402052i q^{97} +(-0.848999 + 6.40156i) q^{98} +(-2.80394 - 2.80394i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 208 q - 8 q^{3} - 8 q^{6} + 192 q^{9} - 6 q^{10} - 8 q^{11} + 16 q^{14} - 16 q^{16} - 12 q^{18} - 10 q^{20} - 16 q^{24} - 32 q^{27} - 24 q^{30} - 20 q^{32} - 8 q^{33} + 4 q^{34} - 8 q^{35} - 12 q^{38} + 38 q^{40}+ \cdots - 24 q^{99}+O(q^{100}) $ 208 * q - 8 * q^3 - 8 * q^6 + 192 * q^9 - 6 * q^10 - 8 * q^11 + 16 * q^14 - 16 * q^16 - 12 * q^18 - 10 * q^20 - 16 * q^24 - 32 * q^27 - 24 * q^30 - 20 * q^32 - 8 * q^33 + 4 * q^34 - 8 * q^35 - 12 * q^38 + 38 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^44 - 16 * q^46 + 68 * q^48 - 160 * q^49 + 16 * q^50 - 8 * q^51 - 20 * q^52 - 36 * q^54 + 4 * q^56 - 32 * q^57 + 64 * q^59 - 32 * q^60 - 72 * q^62 + 32 * q^65 - 8 * q^67 - 28 * q^68 + 28 * q^70 - 56 * q^72 + 32 * q^73 - 8 * q^74 - 16 * q^75 - 10 * q^80 + 128 * q^81 + 8 * q^86 - 16 * q^88 - 118 * q^90 + 24 * q^91 - 56 * q^92 - 64 * q^94 - 48 * q^96 - 40 * q^98 - 24 * q^99

Character values

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

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

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 $

$2$	−0.185930	+	1.40194i	−0.131473	+	0.991320i
$2$	−0.185930	+	1.40194i	−0.131473	+	0.991320i
$3$	−2.65957			−1.53550			−0.767752	−	0.640747i	$-0.778625\pi$
$3$	−2.65957			−1.53550			−0.767752	+	0.640747i	$0.778625\pi$
$4$	−1.93086	−	0.521326i	−0.965430	−	0.260663i
$5$	2.23006	−	0.163750i	0.997315	−	0.0732313i
$5$	2.23006	−	0.163750i	0.997315	−	0.0732313i
$6$	0.494495	−	3.72855i	0.201877	−	1.52218i
$7$		−	1.56006i		−	0.589646i	−0.955552	−	0.294823i	$-0.904739\pi$
$7$		−	1.56006i		−	0.589646i	0.955552	−	0.294823i	$-0.0952607\pi$
$8$	1.08987	−	2.61002i	0.385328	−	0.922780i
$9$	4.07332			1.35777
$10$	−0.185069	+	3.15686i	−0.0585240	+	0.998286i
$11$	−0.688367	−	0.688367i	−0.207550	−	0.207550i	0.595675	−	0.803225i	$-0.296885\pi$
$11$	−0.688367	−	0.688367i	−0.207550	−	0.207550i	−0.803225	+	0.595675i	$0.796885\pi$
$12$	5.13526	+	1.38650i	1.48242	+	0.400249i
$13$	−3.75034	+	3.75034i	−1.04016	+	1.04016i	−0.0409983	+	0.999159i	$0.513054\pi$
$13$	−3.75034	+	3.75034i	−1.04016	+	1.04016i	−0.999159	+	0.0409983i	$0.986946\pi$
$14$	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
$17$	2.43864	+	3.32461i	0.591457	+	0.806337i
$17$	2.43864	+	3.32461i	0.591457	+	0.806337i
$18$	−0.757354	+	5.71054i	−0.178510	+	1.34599i
$19$	−0.733580			−0.168295			−0.0841474	−	0.996453i	$-0.526817\pi$
$19$	−0.733580			−0.168295			−0.0841474	+	0.996453i	$0.526817\pi$
$20$	−4.39131	−	0.846411i	−0.981926	−	0.189263i
$21$			4.14908i			0.905404i
$22$	1.09304	−	0.837059i	0.233036	−	0.178462i
$23$	−6.29519			−1.31264			−0.656319	−	0.754484i	$-0.727887\pi$
$23$	−6.29519			−1.31264			−0.656319	+	0.754484i	$0.727887\pi$
$24$	−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
$27$	−2.85457			−0.549362
$28$	−0.813298	+	3.01225i	−0.153699	+	0.569262i
$29$	−1.95429	+	1.95429i	−0.362902	+	0.362902i	−0.864880	−	0.501978i	$-0.832606\pi$
$29$	−1.95429	+	1.95429i	−0.362902	+	0.362902i	0.501978	+	0.864880i	$0.332606\pi$
$30$	0.492204	−	8.39589i	0.0898638	−	1.53287i
$31$	1.99098	+	1.99098i	0.357590	+	0.357590i	0.862924	−	0.505334i	$-0.168631\pi$
$31$	1.99098	+	1.99098i	0.357590	+	0.357590i	−0.505334	+	0.862924i	$0.668631\pi$
$32$	−3.46506	+	4.47140i	−0.612541	+	0.790439i
$33$	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
$37$	−10.8829			−1.78913			−0.894567	−	0.446935i	$-0.852516\pi$
$37$	−10.8829			−1.78913			−0.894567	+	0.446935i	$0.852516\pi$
$38$	0.136395	−	1.02843i	0.0221262	−	0.166834i
$39$	9.97430	−	9.97430i	1.59717	−	1.59717i
$40$	2.00309	−	5.99897i	0.316717	−	0.948520i
$41$	−6.99271	−	6.99271i	−1.09208	−	1.09208i	−0.995307	−	0.0967703i	$-0.969149\pi$
$41$	−6.99271	−	6.99271i	−1.09208	−	1.09208i	−0.0967703	−	0.995307i	$-0.530851\pi$
$42$	−5.81676	−	0.771441i	−0.897545	−	0.119036i
$43$	−4.24516	+	4.24516i	−0.647381	+	0.647381i	−0.952359	−	0.304978i	$-0.901351\pi$
$43$	−4.24516	+	4.24516i	−0.647381	+	0.647381i	0.304978	+	0.952359i	$0.401351\pi$
$44$	0.970276	+	1.68800i	0.146275	+	0.254476i
$45$	9.08376	−	0.667007i	1.35413	−	0.0994315i
$46$	1.17047	−	8.82546i	0.172576	−	1.30124i
$47$	−4.16348	−	4.16348i	−0.607306	−	0.607306i	0.334935	−	0.942241i	$-0.391286\pi$
$47$	−4.16348	−	4.16348i	−0.607306	−	0.607306i	−0.942241	+	0.334935i	$0.891286\pi$
$48$	−9.19265	−	5.35428i	−1.32684	−	0.772824i
$49$	4.56622			0.652317
$50$	0.104220	+	7.07030i	0.0147390	+	0.999891i
$51$	−6.48573	−	8.84204i	−0.908184	−	1.23813i
$52$	9.19653	−	5.28623i	1.27533	−	0.733069i
$53$	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
$57$	1.95101			0.258417
$58$	−2.37643	−	3.10315i	−0.312040	−	0.407463i
$59$	−3.14644			−0.409632			−0.204816	−	0.978800i	$-0.565660\pi$
$59$	−3.14644			−0.409632			−0.204816	+	0.978800i	$0.565660\pi$
$60$	11.6790	+	2.25109i	1.50775	+	0.290614i
$61$	−2.66983	+	2.66983i	−0.341837	+	0.341837i	−0.857058	−	0.515220i	$-0.827710\pi$
$61$	−2.66983	+	2.66983i	−0.341837	+	0.341837i	0.515220	+	0.857058i	$0.327710\pi$
$62$	−3.16141	+	2.42104i	−0.401500	+	0.307473i
$63$		−	6.35461i		−	0.800606i
$64$	−5.62436	−	5.68916i	−0.703045	−	0.711145i
$65$	−7.74938	+	8.97762i	−0.961193	+	1.11354i
$66$	−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	$0.293628\pi$
$68$	−2.97546	−	7.69068i	−0.360828	−	0.932632i
$69$	16.7425			2.01556
$70$	4.92488	+	0.288718i	0.588636	+	0.0345084i
$71$	−1.38270	−	1.38270i	−0.164096	−	0.164096i	0.620283	−	0.784378i	$-0.287018\pi$
$71$	−1.38270	−	1.38270i	−0.164096	−	0.164096i	−0.784378	+	0.620283i	$0.787018\pi$
$72$	4.43939	−	10.6314i	0.523188	−	1.25293i
$73$	0.0700142			0.00819454			0.00409727	−	0.999992i	$-0.498696\pi$
$73$	0.0700142			0.00819454			0.00409727	+	0.999992i	$0.498696\pi$
$74$	2.02346	−	15.2571i	0.235222	−	1.77360i
$75$	−13.1552	+	1.94241i	−1.51903	+	0.224290i
$76$	1.41644	+	0.382434i	0.162477	+	0.0438682i
$77$	−1.07389	+	1.07389i	−0.122381	+	0.122381i
$78$	12.1288	+	15.8379i	1.37332	+	1.79329i
$79$	5.15461	+	5.15461i	0.579939	+	0.579939i	0.934886	−	0.354947i	$-0.115501\pi$
$79$	5.15461	+	5.15461i	0.579939	+	0.579939i	−0.354947	+	0.934886i	$0.615501\pi$
$80$	8.03775	+	3.92360i	0.898647	+	0.438672i
$81$	−4.62803			−0.514226
$82$	11.1035	−	8.50318i	1.22618	−	0.939019i
$83$	−12.0334	+	12.0334i	−1.32084	+	1.32084i	−0.407740	+	0.913098i	$0.633683\pi$
$83$	−12.0334	+	12.0334i	−1.32084	+	1.32084i	−0.913098	+	0.407740i	$0.866317\pi$
$84$	2.16302	−	8.01130i	0.236005	−	0.874104i
$85$	5.98272	+	7.01477i	0.648918	+	0.760859i
$86$	−5.16215	−	6.74076i	−0.556649	−	0.726875i
$87$	5.19756	−	5.19756i	0.557237	−	0.557237i
$88$	−2.54688	+	1.04642i	−0.271498	+	0.111548i
$89$			12.5002i			1.32502i	0.749052	+	0.662511i	$0.230509\pi$
$89$			12.5002i			1.32502i	−0.749052	+	0.662511i	$0.769491\pi$
$90$	−0.753845	+	12.8589i	−0.0794623	+	1.35545i
$91$	5.85075	+	5.85075i	0.613325	+	0.613325i
$92$	12.1551	+	3.28184i	1.26726	+	0.342156i
$93$	−5.29515	−	5.29515i	−0.549081	−	0.549081i
$94$	6.61106	−	5.06282i	0.681879	−	0.522190i
$95$	−1.63593	+	0.120124i	−0.167843	+	0.0123244i
$96$	9.21557	−	11.8920i	0.940560	−	1.21372i
$97$		−	0.402052i		−	0.0408222i	−0.999792	−	0.0204111i	$-0.993502\pi$
$97$		−	0.402052i		−	0.0408222i	0.999792	−	0.0204111i	$-0.00649751\pi$
$98$	−0.848999	+	6.40156i	−0.0857619	+	0.646655i
$99$	−2.80394	−	2.80394i	−0.281806	−	0.281806i
$100$	−9.93150	−	1.16847i	−0.993150	−	0.116847i
$101$			8.00189i			0.796218i	0.917338	+	0.398109i	$0.130333\pi$
$101$			8.00189i			0.796218i	−0.917338	+	0.398109i	$0.869667\pi$
$102$	13.6019	−	7.44859i	1.34679	−	0.737520i
$103$	−9.61710	+	9.61710i	−0.947601	+	0.947601i	−0.998694	−	0.0510929i	$-0.983730\pi$
$103$	−9.61710	+	9.61710i	−0.947601	+	0.947601i	0.0510929	+	0.998694i	$0.483730\pi$
$104$	5.70106	+	13.8758i	0.559035	+	1.36064i
$105$	0.679413	+	9.25272i	0.0663039	+	0.902973i
$106$	−4.12810	+	3.16135i	−0.400957	+	0.307057i
$107$			15.4263i			1.49131i	0.666331	+	0.745656i	$0.267864\pi$
$107$			15.4263i			1.49131i	−0.666331	+	0.745656i	$0.732136\pi$
$108$	5.51177	+	1.48816i	0.530370	+	0.143198i
$109$	−13.1411	−	13.1411i	−1.25869	−	1.25869i	−0.951719	−	0.306970i	$-0.900685\pi$
$109$	−13.1411	−	13.1411i	−1.25869	−	1.25869i	−0.306970	−	0.951719i	$-0.599315\pi$
$110$	2.30047	−	2.04568i	0.219341	−	0.195048i
$111$	28.9438			2.74722
$112$	3.14073	−	5.39224i	0.296771	−	0.509519i
$113$			0.0244697i			0.00230192i	0.999999	+	0.00115096i	$0.000366362\pi$
$113$			0.0244697i			0.00230192i	−0.999999	+	0.00115096i	$0.999634\pi$
$114$	−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
$118$	0.585020	−	4.41112i	0.0538554	−	0.406076i
$119$	5.18659	−	3.80441i	0.475453	−	0.348750i
$120$	−5.32737	+	15.9547i	−0.486320	+	1.45646i
$121$		−	10.0523i		−	0.913846i
$122$	−3.24654	−	4.23934i	−0.293928	−	0.383812i
$123$	18.5976	+	18.5976i	1.67689	+	1.67689i
$124$	−2.80635	−	4.88225i	−0.252018	−	0.438439i
$125$	10.9111	−	2.43869i	0.975921	−	0.218123i
$126$	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	$0.274797\pi$
$128$	9.02159	−	6.82722i	0.797404	−	0.603446i
$129$	11.2903	−	11.2903i	0.994056	−	0.994056i
$130$	−11.1452	−	12.5334i	−0.977501	−	1.09925i
$131$	5.84673	−	5.84673i	0.510832	−	0.510832i	−0.403950	−	0.914781i	$-0.632363\pi$
$131$	5.84673	−	5.84673i	0.510832	−	0.510832i	0.914781	+	0.403950i	$0.132363\pi$
$132$	−2.58052	−	4.48936i	−0.224605	−	0.390749i
$133$			1.14443i			0.0992344i
$134$	−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	$0.103785\pi$
$138$	−3.11294	+	23.4719i	−0.264991	+	1.99806i
$139$	−1.32051	−	1.32051i	−0.112004	−	0.112004i	0.648884	−	0.760888i	$-0.275236\pi$
$139$	−1.32051	−	1.32051i	−0.112004	−	0.112004i	−0.760888	+	0.648884i	$0.775236\pi$
$140$	−1.32045	+	6.85069i	−0.111598	+	0.578989i
$141$	11.0731	+	11.0731i	0.932521	+	0.932521i
$142$	2.19554	−	1.68137i	0.184246	−	0.141097i
$143$	5.16322			0.431770
$144$	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
$147$	−12.1442			−1.00164
$148$	21.0133	+	5.67352i	1.72728	+	0.466360i
$149$	5.06444			0.414895			0.207448	−	0.978246i	$-0.433484\pi$
$149$	5.06444			0.414895			0.207448	+	0.978246i	$0.433484\pi$
$150$	−0.277181	−	18.8040i	−0.0226317	−	1.53534i
$151$	5.34921			0.435312			0.217656	−	0.976026i	$-0.430159\pi$
$151$	5.34921			0.435312			0.217656	+	0.976026i	$0.430159\pi$
$152$	−0.799508	+	1.91465i	−0.0648487	+	0.155299i
$153$	9.93335	+	13.5422i	0.803064	+	1.09482i
$154$	−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	0.528083	−	0.849193i	$-0.322911\pi$
$157$	−4.02349	−	4.02349i	−0.321109	−	0.321109i	−0.849193	+	0.528083i	$0.822911\pi$
$158$	−8.18484	+	6.26805i	−0.651151	+	0.498659i
$159$	−6.91429	−	6.91429i	−0.548339	−	0.548339i
$160$	−6.99511	+	10.5389i	−0.553012	+	0.833173i
$161$			9.82085i			0.773992i
$162$	0.860491	−	6.48821i	0.0676066	−	0.509762i
$163$		−	25.1622i		−	1.97086i	−0.170095	−	0.985428i	$-0.554407\pi$
$163$		−	25.1622i		−	1.97086i	0.170095	−	0.985428i	$-0.445593\pi$
$164$	9.85646	+	17.1474i	0.769660	+	1.33899i
$165$	4.38250	+	3.78293i	0.341177	+	0.294500i
$166$	−14.6327	−	19.1075i	−1.13572	−	1.48303i
$167$	12.8815			0.996799			0.498399	−	0.866947i	$-0.333921\pi$
$167$	12.8815			0.996799			0.498399	+	0.866947i	$0.333921\pi$
$168$	10.8292	+	4.52197i	0.835489	+	0.348877i
$169$		−	15.1301i		−	1.16386i
$170$	−10.9466	+	7.08315i	−0.839569	+	0.543253i
$171$	−2.98811			−0.228506
$172$	10.4099	−	5.98370i	0.793749	−	0.456253i
$173$		−	3.56937i		−	0.271374i	−0.990752	−	0.135687i	$-0.956676\pi$
$173$		−	3.56937i		−	0.271374i	0.990752	−	0.135687i	$-0.0433241\pi$
$174$	6.32028	+	8.25305i	0.479139	+	0.625662i
$175$	−1.13938	−	7.71662i	−0.0861292	−	0.583322i
$176$	−0.993469	−	3.76513i	−0.0748855	−	0.283807i
$177$	8.36819			0.628992
$178$	−17.5246	−	2.32417i	−1.31352	−	0.174204i
$179$	−22.2424			−1.66247			−0.831236	−	0.555919i	$-0.812366\pi$
$179$	−22.2424			−1.66247			−0.831236	+	0.555919i	$0.812366\pi$
$180$	−17.8872	−	3.44770i	−1.33323	−	0.256977i
$181$	6.72654	−	6.72654i	0.499979	−	0.499979i	−0.411452	−	0.911431i	$-0.634978\pi$
$181$	6.72654	−	6.72654i	0.499979	−	0.499979i	0.911431	+	0.411452i	$0.134978\pi$
$182$	−9.29022	+	7.11455i	−0.688637	+	0.527366i
$183$	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
$187$	0.609875	−	3.96723i	0.0445985	−	0.290113i
$188$	5.86857	+	10.2096i	0.428009	+	0.744613i
$189$			4.45329i			0.323929i
$190$	0.135763	−	2.31581i	0.00984928	−	0.168006i
$191$			17.9549i			1.29917i	0.760289	+	0.649585i	$0.225057\pi$
$191$			17.9549i			1.29917i	−0.760289	+	0.649585i	$0.774943\pi$
$192$	14.9584	+	15.1307i	1.07953	+	1.09197i
$193$			1.98214i			0.142677i	0.997452	+	0.0713387i	$0.0227271\pi$
$193$			1.98214i			0.142677i	−0.997452	+	0.0713387i	$0.977273\pi$
$194$	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
$197$			9.47788i			0.675271i	0.941277	+	0.337636i	$0.109627\pi$
$197$			9.47788i			0.675271i	−0.941277	+	0.337636i	$0.890373\pi$
$198$	4.45228	−	3.40961i	0.316410	−	0.242310i
$199$	−16.2177	+	16.2177i	−1.14964	+	1.14964i	−0.163016	+	0.986623i	$0.552122\pi$
$199$	−16.2177	+	16.2177i	−1.14964	+	1.14964i	−0.986623	+	0.163016i	$0.947878\pi$
$200$	3.48469	−	13.7061i	0.246405	−	0.969167i
$201$	4.20651	−	4.20651i	0.296704	−	0.296704i
$202$	−11.2182	−	1.48779i	−0.789306	−	0.104681i
$203$	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
$207$	−25.6423			−1.78226
$208$	−20.5131	+	5.41259i	−1.42233	+	0.375296i
$209$	0.504972	+	0.504972i	0.0349296	+	0.0349296i
$210$	−13.0981	−	0.767867i	−0.903852	−	0.0529878i
$211$	18.5867	+	18.5867i	1.27956	+	1.27956i	0.940913	+	0.338648i	$0.109970\pi$
$211$	18.5867	+	18.5867i	1.27956	+	1.27956i	0.338648	+	0.940913i	$0.390030\pi$
$212$	−3.66447	−	6.37513i	−0.251677	−	0.437846i
$213$	3.67738	+	3.67738i	0.251970	+	0.251970i
$214$	−21.6267	−	2.86821i	−1.47837	−	0.196067i
$215$	−8.77184	+	10.1621i	−0.598234	+	0.693052i
$216$	−3.11111	+	7.45047i	−0.211684	+	0.506940i
$217$	3.10604	−	3.10604i	0.210852	−	0.210852i
$218$	20.8663	−	15.9797i	1.41325	−	1.08228i
$219$	−0.186208			−0.0125828
$220$	2.44019	+	3.60547i	0.164518	+	0.243081i
$221$	−21.6142	−	3.32271i	−1.45393	−	0.223509i
$222$	−5.38153	+	40.5774i	−0.361184	+	2.72337i
$223$	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
$227$	22.9409			1.52264			0.761321	−	0.648376i	$-0.224551\pi$
$227$	22.9409			1.52264			0.761321	+	0.648376i	$0.224551\pi$
$228$	−3.76712	−	1.01711i	−0.249484	−	0.0673598i
$229$		−	11.5448i		−	0.762902i	−0.924389	−	0.381451i	$-0.875425\pi$
$229$		−	11.5448i		−	0.762902i	0.924389	−	0.381451i	$-0.124575\pi$
$230$	1.16504	−	19.8730i	0.0768208	−	1.31039i
$231$	2.85609	−	2.85609i	0.187917	−	0.187917i
$232$	2.97080	+	7.23064i	0.195042	+	0.474715i
$233$	−17.9481			−1.17582			−0.587909	−	0.808927i	$-0.700049\pi$
$233$	−17.9481			−1.17582			−0.587909	+	0.808927i	$0.700049\pi$
$234$	−18.5761	−	24.2568i	−1.21436	−	1.58572i
$235$	−9.96660	−	8.60306i	−0.650149	−	0.561202i
$236$	6.07534	+	1.64032i	0.395471	+	0.106776i
$237$	−13.7091	−	13.7091i	−0.890499	−	0.890499i
$238$	4.36921	+	7.97863i	0.283214	+	0.517178i
$239$	−7.76907			−0.502539			−0.251270	−	0.967917i	$-0.580848\pi$
$239$	−7.76907			−0.502539			−0.251270	+	0.967917i	$0.580848\pi$
$240$	−21.3770	−	10.4351i	−1.37988	−	0.673583i
$241$	0.186182	−	0.186182i	0.0119931	−	0.0119931i	−0.701085	−	0.713078i	$-0.747301\pi$
$241$	0.186182	−	0.186182i	0.0119931	−	0.0119931i	0.713078	+	0.701085i	$0.247301\pi$
$242$	14.0927	+	1.86903i	0.905913	+	0.120146i
$243$	20.8723			1.33896
$244$	6.54693	−	3.76322i	0.419124	−	0.240916i
$245$	10.1830	−	0.747719i	0.650566	−	0.0477700i
$246$	−29.5305	+	22.6148i	−1.88280	+	1.44187i
$247$	2.75118	−	2.75118i	0.175053	−	0.175053i
$248$	7.36639	−	3.02657i	0.467766	−	0.192188i
$249$	32.0037	−	32.0037i	2.02815	−	2.02815i
$250$	1.39018	+	15.7502i	0.0879227	+	0.996127i
$251$	13.1663			0.831051			0.415525	−	0.909582i	$-0.363598\pi$
$251$	13.1663			0.831051			0.415525	+	0.909582i	$0.363598\pi$
$252$	−3.31282	+	12.2699i	−0.208688	+	0.772929i
$253$	4.33340	+	4.33340i	0.272438	+	0.272438i
$254$	−1.50821	−	1.96943i	−0.0946335	−	0.123573i
$255$	−15.9115	−	18.6563i	−0.996416	−	1.16830i
$256$	7.89394	+	13.9171i	0.493372	+	0.869819i
$257$	−7.70026	−	7.70026i	−0.480329	−	0.480329i	0.424908	−	0.905237i	$-0.360307\pi$
$257$	−7.70026	−	7.70026i	−0.480329	−	0.480329i	−0.905237	+	0.424908i	$0.860307\pi$
$258$	13.7291	+	17.9275i	0.854737	+	1.11612i
$259$			16.9779i			1.05496i
$260$	19.6432	−	13.2946i	1.21822	−	0.824495i
$261$	−7.96043	+	7.96043i	−0.492738	+	0.492738i
$262$	7.10967	+	9.28384i	0.439237	+	0.573558i
$263$	−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
$265$	6.22338	+	5.37195i	0.382299	+	0.329996i
$266$	−1.60442	−	0.212784i	−0.0983730	−	0.0130466i
$267$		−	33.2453i		−	2.03458i
$268$	3.87850	−	2.22939i	0.236917	−	0.136182i
$269$	9.50734	−	9.50734i	0.579673	−	0.579673i	−0.355140	−	0.934813i	$-0.615567\pi$
$269$	9.50734	−	9.50734i	0.579673	−	0.579673i	0.934813	+	0.355140i	$0.115567\pi$
$270$	0.528292	−	9.01147i	0.0321508	−	0.548420i
$271$		−	26.3491i		−	1.60059i	−0.599604	−	0.800297i	$-0.704675\pi$
$271$		−	26.3491i		−	1.60059i	0.599604	−	0.800297i	$-0.295325\pi$
$272$	1.73585	+	16.4008i	0.105251	+	0.994446i
$273$	−15.5605	−	15.5605i	−0.941763	−	0.941763i
$274$	8.92423	+	11.6533i	0.539133	+	0.704002i
$275$	−3.90766	−	2.90217i	−0.235641	−	0.175008i
$276$	−32.3274	−	8.72830i	−1.94588	−	0.525382i
$277$	27.3216			1.64160			0.820798	−	0.571219i	$-0.193529\pi$
$277$	27.3216			1.64160			0.820798	+	0.571219i	$0.193529\pi$
$278$	2.09679	−	1.60575i	0.125757	−	0.0963063i
$279$	8.10989	+	8.10989i	0.485526	+	0.485526i
$280$	−9.35873	−	3.12494i	−0.559291	−	0.186751i
$281$			30.9007i			1.84338i	0.387925	+	0.921691i	$0.373192\pi$
$281$			30.9007i			1.84338i	−0.387925	+	0.921691i	$0.626808\pi$
$282$	−17.5826	+	13.4649i	−1.04703	+	0.801825i
$283$		−	16.5664i		−	0.984771i	−0.870377	−	0.492386i	$-0.836125\pi$
$283$		−	16.5664i		−	0.984771i	0.870377	−	0.492386i	$-0.163875\pi$
$284$	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
$288$	−14.1143	+	18.2134i	−0.831692	+	1.07324i
$289$	−5.10609	+	16.2150i	−0.300358	+	0.953826i
$290$	−5.80773	−	6.53108i	−0.341041	−	0.383518i
$291$			1.06929i			0.0626827i
$292$	−0.135188	−	0.0365002i	−0.00791125	−	0.00213601i
$293$	15.6912	−	15.6912i	0.916687	−	0.916687i	−0.0800995	−	0.996787i	$-0.525524\pi$
$293$	15.6912	−	15.6912i	0.916687	−	0.916687i	0.996787	+	0.0800995i	$0.0255238\pi$
$294$	2.25797	−	17.0254i	0.131688	−	0.992942i
$295$	−7.01677	+	0.515231i	−0.408532	+	0.0299979i
$296$	−11.8609	+	28.4045i	−0.689403	+	1.65098i
$297$	1.96499	+	1.96499i	0.114020	+	0.114020i
$298$	−0.941634	+	7.10004i	−0.0545474	+	0.411294i
$299$	23.6091	−	23.6091i	1.36535	−	1.36535i
$300$	26.4135	+	3.10764i	1.52499	+	0.179420i
$301$	6.62270	+	6.62270i	0.381726	+	0.381726i
$302$	−0.994580	+	7.49925i	−0.0572316	+	0.431534i
$303$		−	21.2816i		−	1.22260i
$304$	−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	$0.189070\pi$
$308$	2.63338	−	1.51369i	0.150051	−	0.0862503i
$309$	25.5774	−	25.5774i	1.45505	−	1.45505i
$310$	−6.65370	+	5.91677i	−0.377905	+	0.336050i
$311$	18.2827	+	18.2827i	1.03672	+	1.03672i	0.999300	+	0.0374182i	$0.0119134\pi$
$311$	18.2827	+	18.2827i	1.03672	+	1.03672i	0.0374182	+	0.999300i	$0.488087\pi$
$312$	−15.1624	−	36.9038i	−0.858400	−	2.08927i
$313$		−	27.1445i		−	1.53430i	−0.641471	−	0.767148i	$-0.721675\pi$
$313$		−	27.1445i		−	1.53430i	0.641471	−	0.767148i	$-0.278325\pi$
$314$	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
$317$		−	18.8982i		−	1.06143i	−0.847551	−	0.530714i	$-0.821924\pi$
$317$		−	18.8982i		−	1.06143i	0.847551	−	0.530714i	$-0.178076\pi$
$318$	10.9790	−	8.40782i	0.615670	−	0.471487i
$319$	2.69053			0.150641
$320$	−13.4743	−	11.7662i	−0.753235	−	0.657751i
$321$		−	41.0272i		−	2.28992i
$322$	−13.7682	−	1.82599i	−0.767273	−	0.101759i
$323$	−1.78894	−	2.43887i	−0.0995391	−	0.135702i
$324$	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
$328$	−25.8722	+	10.6299i	−1.42855	+	0.586939i
$329$	−6.49527	+	6.49527i	−0.358096	+	0.358096i
$330$	−6.11827	+	5.44063i	−0.336799	+	0.299497i
$331$			7.46399i			0.410258i	0.978735	+	0.205129i	$0.0657614\pi$
$331$			7.46399i			0.410258i	−0.978735	+	0.205129i	$0.934239\pi$
$332$	29.5081	−	16.9615i	1.61947	−	0.930883i
$333$	−44.3294			−2.42924
$334$	−2.39506	+	18.0590i	−0.131052	+	0.988147i
$335$	−3.26818	+	3.78618i	−0.178560	+	0.206861i
$336$	−8.35299	+	14.3411i	−0.455693	+	0.782369i
$337$			19.4043i			1.05702i	0.848927	+	0.528510i	$0.177249\pi$
$337$			19.4043i			1.05702i	−0.848927	+	0.528510i	$0.822751\pi$
$338$	21.2115	+	2.81315i	1.15375	+	0.153015i
$339$		−	0.0650790i		−	0.00353461i
$340$	−7.89482	−	16.6635i	−0.428157	−	0.903704i
$341$		−	2.74105i		−	0.148436i
$342$	0.555579	−	4.18914i	0.0300423	−	0.226523i
$343$		−	18.0440i		−	0.974283i
$344$	6.45326	+	15.7066i	0.347936	+	0.846844i
$345$	37.3369	−	2.74159i	2.01015	−	0.147602i
$346$	5.00403	+	0.663654i	0.269018	+	0.0356782i
$347$	−3.20787			−0.172207			−0.0861036	−	0.996286i	$-0.527442\pi$
$347$	−3.20787			−0.172207			−0.0861036	+	0.996286i	$0.527442\pi$
$348$	−12.7454	+	7.32614i	−0.683225	+	0.392723i
$349$		−	0.963390i		−	0.0515691i	−0.999668	−	0.0257845i	$-0.991792\pi$
$349$		−	0.963390i		−	0.0515691i	0.999668	−	0.0257845i	$-0.00820839\pi$
$350$	11.0301	−	0.162589i	0.589582	−	0.00869077i
$351$	10.7056	−	10.7056i	0.571423	−	0.571423i
$352$	5.46319	−	0.692730i	0.291189	−	0.0369226i
$353$	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
$357$	−13.7941	+	10.1181i	−0.730061	+	0.535507i
$358$	4.13553	−	31.1824i	0.218570	−	1.64804i
$359$			13.5395i			0.714585i	0.933992	+	0.357293i	$0.116300\pi$
$359$			13.5395i			0.714585i	−0.933992	+	0.357293i	$0.883700\pi$
$360$	8.15924	−	24.4357i	0.430030	−	1.28788i
$361$	−18.4619			−0.971677
$362$	8.17952	+	10.6809i	0.429906	+	0.561373i
$363$			26.7348i			1.40321i
$364$	−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
$367$		−	6.80340i		−	0.355134i	−0.984109	−	0.177567i	$-0.943177\pi$
$367$		−	6.80340i		−	0.355134i	0.984109	−	0.177567i	$-0.0568227\pi$
$368$	−21.7589	−	12.6736i	−1.13426	−	0.660655i
$369$	−28.4835	−	28.4835i	−1.48279	−	1.48279i
$370$	2.01408	−	34.3557i	0.104707	−	1.78607i
$371$	4.05580	−	4.05580i	0.210567	−	0.210567i
$372$	7.46369	+	12.9847i	0.386974	+	0.673224i
$373$	−6.39548	+	6.39548i	−0.331145	+	0.331145i	−0.853021	−	0.521876i	$-0.825232\pi$
$373$	−6.39548	+	6.39548i	−0.331145	+	0.331145i	0.521876	+	0.853021i	$0.325232\pi$
$374$	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
$377$		−	14.6585i		−	0.754950i
$378$	−6.24324	−	0.828002i	−0.321117	−	0.0425878i
$379$	−16.6735	−	16.6735i	−0.856458	−	0.856458i	0.134461	−	0.990919i	$-0.457070\pi$
$379$	−16.6735	−	16.6735i	−0.856458	−	0.856458i	−0.990919	+	0.134461i	$0.957070\pi$
$380$	3.22138	+	0.620910i	0.165253	+	0.0318520i
$381$	3.29866	−	3.29866i	0.168995	−	0.168995i
$382$	−25.1716	−	3.33836i	−1.28789	−	0.170805i
$383$	−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
$385$	−2.21900	+	2.57070i	−0.113091	+	0.131015i
$386$	−2.77883	−	0.368540i	−0.141439	−	0.0187582i
$387$	−17.2919	+	17.2919i	−0.878997	+	0.878997i
$388$	−0.209600	+	0.776307i	−0.0106408	+	0.0394110i
$389$			29.6087i			1.50122i	0.660746	+	0.750609i	$0.270240\pi$
$389$			29.6087i			1.50122i	−0.660746	+	0.750609i	$0.729760\pi$
$390$	29.6415	+	33.3334i	1.50096	+	1.68790i
$391$	−15.3517	−	20.9291i	−0.776368	−	1.05843i
$392$	4.97659	−	11.9179i	0.251356	−	0.601945i
$393$	−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
$397$		−	26.2663i		−	1.31827i	−0.752025	−	0.659135i	$-0.770923\pi$
$397$		−	26.2663i		−	1.31827i	0.752025	−	0.659135i	$-0.229077\pi$
$398$	−19.7208	−	25.7515i	−0.988514	−	1.29081i
$399$		−	3.04368i		−	0.152375i
$400$	18.5672	+	7.43370i	0.928359	+	0.371685i
$401$	−5.49471	−	5.49471i	−0.274393	−	0.274393i	0.556473	−	0.830866i	$-0.312154\pi$
$401$	−5.49471	−	5.49471i	−0.274393	−	0.274393i	−0.830866	+	0.556473i	$0.812154\pi$
$402$	5.11515	+	6.67938i	0.255120	+	0.333137i
$403$	−14.9337			−0.743900
$404$	4.17159	−	15.4505i	0.207544	−	0.768692i
$405$	−10.3208	+	0.757841i	−0.512845	+	0.0376574i
$406$	−4.84109	+	3.70736i	−0.240259	+	0.183993i
$407$	7.49141	+	7.49141i	0.371335	+	0.371335i
$408$	−30.1465	+	7.29117i	−1.49247	+	0.360967i
$409$			8.49228i			0.419916i	0.977710	+	0.209958i	$0.0673328\pi$
$409$			8.49228i			0.419916i	−0.977710	+	0.209958i	$0.932667\pi$
$410$	23.3691	−	20.7808i	1.15412	−	1.02629i
$411$	−19.5185	+	19.5185i	−0.962776	+	0.962776i
$412$	23.5829	−	13.5556i	1.16185	−	0.667838i
$413$			4.90863i			0.241538i
$414$	4.76768	−	35.9489i	0.234319	−	1.76679i
$415$	−24.8648	+	28.8057i	−1.22056	+	1.41402i
$416$	−3.77411	−	29.7644i	−0.185041	−	1.45932i
$417$	3.51198	+	3.51198i	0.171982	+	0.171982i
$418$	−0.801829	+	0.614050i	−0.0392187	+	0.0300342i
$419$	−19.5738	+	19.5738i	−0.956244	+	0.956244i	−0.999082	−	0.0428376i	$-0.986360\pi$
$419$	−19.5738	+	19.5738i	−0.956244	+	0.956244i	0.0428376	+	0.999082i	$0.486360\pi$
$420$	3.51183	−	18.2199i	0.171360	−	0.889040i
$421$			26.2340i			1.27857i	0.768972	+	0.639283i	$0.220769\pi$
$421$			26.2340i			1.27857i	−0.768972	+	0.639283i	$0.779231\pi$
$422$	−29.5132	+	22.6016i	−1.43668	+	1.10023i
$423$	−16.9592	−	16.9592i	−0.824584	−	0.824584i
$424$	9.61887	−	3.95203i	0.467134	−	0.191928i
$425$	14.4905	+	14.6637i	0.702894	+	0.711295i
$426$	−5.83919	+	4.47172i	−0.282910	+	0.216656i
$427$	4.16509	+	4.16509i	0.201563	+	0.201563i
$428$	8.04210	−	29.7859i	0.388730	−	1.43976i
$429$	−13.7320			−0.662985
$430$	−12.6157	−	14.1870i	−0.608384	−	0.684159i
$431$	11.7262	−	11.7262i	0.564831	−	0.564831i	−0.365845	−	0.930676i	$-0.619220\pi$
$431$	11.7262	−	11.7262i	0.564831	−	0.564831i	0.930676	+	0.365845i	$0.119220\pi$
$432$	−9.86664	−	5.74685i	−0.474709	−	0.276496i
$433$	−4.53366	+	4.53366i	−0.217874	+	0.217874i	−0.807602	−	0.589728i	$-0.799235\pi$
$433$	−4.53366	+	4.53366i	−0.217874	+	0.217874i	0.589728	+	0.807602i	$0.299235\pi$
$434$	3.77697	+	4.93198i	0.181300	+	0.236743i
$435$	10.7398	−	12.4420i	0.514934	−	0.596548i
$436$	18.5228	+	32.2244i	0.887083	+	1.54327i
$437$	4.61802			0.220910
$438$	0.0346217	−	0.261052i	0.00165429	−	0.0124735i
$439$	5.76725	−	5.76725i	0.275256	−	0.275256i	−0.555956	−	0.831212i	$-0.687648\pi$
$439$	5.76725	−	5.76725i	0.275256	−	0.275256i	0.831212	+	0.555956i	$0.187648\pi$
$440$	−5.50835	+	2.75063i	−0.262600	+	0.131131i
$441$	18.5997			0.885699
$442$	8.67695	−	29.6839i	0.412721	−	1.41192i
$443$	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
$445$	2.04692	+	27.8763i	0.0970331	+	1.32146i
$446$	−9.70478	+	7.43203i	−0.459535	+	0.351917i
$447$	−13.4692			−0.637074
$448$	−8.87542	+	8.77432i	−0.419324	+	0.414548i
$449$	−17.7617	+	17.7617i	−0.838228	+	0.838228i	−0.988626	−	0.150398i	$-0.951945\pi$
$449$	−17.7617	+	17.7617i	−0.838228	+	0.838228i	0.150398	+	0.988626i	$0.451945\pi$
$450$	0.424522	+	28.7996i	0.0200121	+	1.35763i
$451$			9.62709i			0.453322i
$452$	0.0127567	−	0.0472476i	0.000600024	−	0.00222234i
$453$	−14.2266			−0.668424
$454$	−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	0.134523	−	0.990911i	$-0.457050\pi$
$457$	−18.3075	−	18.3075i	−0.856388	−	0.856388i	−0.990911	+	0.134523i	$0.957050\pi$
$458$	16.1851	+	2.14653i	0.756279	+	0.100301i
$459$	−6.96126	−	9.49033i	−0.324924	−	0.442971i
$460$	27.6441	+	5.32832i	1.28891	+	0.248434i
$461$	17.8234			0.830117			0.415059	−	0.909795i	$-0.363761\pi$
$461$	17.8234			0.830117			0.415059	+	0.909795i	$0.363761\pi$
$462$	3.47303	+	4.53510i	0.161580	+	0.210992i
$463$	10.0048	−	10.0048i	0.464964	−	0.464964i	−0.435314	−	0.900278i	$-0.643363\pi$
$463$	10.0048	−	10.0048i	0.464964	−	0.464964i	0.900278	+	0.435314i	$0.143363\pi$
$464$	−10.6893	+	2.82048i	−0.496237	+	0.130937i
$465$	−12.6756	−	10.9414i	−0.587817	−	0.507397i
$466$	3.33709	−	25.1621i	0.154588	−	1.16561i
$467$	−2.80145	−	2.80145i	−0.129636	−	0.129636i	0.639312	−	0.768948i	$-0.279219\pi$
$467$	−2.80145	−	2.80145i	−0.129636	−	0.129636i	−0.768948	+	0.639312i	$0.779219\pi$
$468$	37.4604	−	21.5325i	1.73161	−	0.995341i
$469$	2.46746	+	2.46746i	0.113937	+	0.113937i
$470$	13.9140	−	12.3730i	0.641807	−	0.570723i
$471$	10.7008	+	10.7008i	0.493065	+	0.493065i
$472$	−3.42922	+	8.21227i	−0.157843	+	0.378000i
$473$	5.84446			0.268728
$474$	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
$478$	1.44451	−	10.8918i	0.0660702	−	0.498177i
$479$	0.127353	−	0.127353i	0.00581889	−	0.00581889i	−0.704191	−	0.710010i	$-0.748690\pi$
$479$	0.127353	−	0.127353i	0.00581889	−	0.00581889i	0.710010	+	0.704191i	$0.248690\pi$
$480$	18.6040	−	28.0290i	0.849152	−	1.27934i
$481$	40.8145	−	40.8145i	1.86098	−	1.86098i
$482$	0.226399	+	0.295633i	0.0103122	+	0.0134657i
$483$		−	26.1193i		−	1.18847i
$484$	−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
$487$		−	10.3466i		−	0.468849i	−0.972134	−	0.234424i	$-0.924679\pi$
$487$		−	10.3466i		−	0.468849i	0.972134	−	0.234424i	$-0.0753205\pi$
$488$	4.05853	+	9.87808i	0.183721	+	0.447160i
$489$			66.9207i			3.02626i
$490$	−0.845066	+	14.4149i	−0.0381762	+	0.651199i
$491$		−	13.1680i		−	0.594266i	−0.954836	−	0.297133i	$-0.903970\pi$
$491$		−	13.1680i		−	0.594266i	0.954836	−	0.297133i	$-0.0960304\pi$
$492$	−26.2139	−	45.6048i	−1.18182	−	2.05602i
$493$	−11.2630	−	1.73145i	−0.507262	−	0.0779805i
$494$	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
$498$	38.9167	+	50.8177i	1.74390	+	2.27719i
$499$	18.5416	−	18.5416i	0.830036	−	0.830036i	−0.157485	−	0.987521i	$-0.550339\pi$
$499$	18.5416	−	18.5416i	0.830036	−	0.830036i	0.987521	+	0.157485i	$0.0503386\pi$
$500$	−22.3392	−	0.979485i	−0.999040	−	0.0438039i
$501$	−34.2592			−1.53059
$502$	−2.44802	+	18.4584i	−0.109260	+	0.823837i
$503$	40.0463			1.78558			0.892789	−	0.450475i	$-0.148745\pi$
$503$	40.0463			1.78558			0.892789	+	0.450475i	$0.148745\pi$
$504$	−16.5856	−	6.92571i	−0.738783	−	0.308496i
$505$	1.31031	+	17.8447i	0.0583081	+	0.794080i
$506$	−6.88087	+	5.26944i	−0.305892	+	0.234255i
$507$			40.2396i			1.78710i
$508$	3.04144	−	1.74824i	0.134942	−	0.0775656i
$509$	−10.6206			−0.470751			−0.235375	−	0.971905i	$-0.575632\pi$
$509$	−10.6206			−0.470751			−0.235375	+	0.971905i	$0.575632\pi$
$510$	29.1134	−	18.8381i	1.28916	−	0.834167i
$511$		−	0.109226i		−	0.00483188i
$512$	−20.9786	+	8.47921i	−0.927133	+	0.374732i
$513$	2.09405			0.0924547
$514$	12.2270	−	9.36357i	0.539310	−	0.413010i
$515$	−19.8719	+	23.0216i	−0.875663	+	1.01445i
$516$	−27.6859	+	15.9141i	−1.21881	+	0.700578i
$517$			5.73200i			0.252093i
$518$	−23.8020	−	3.15671i	−1.04580	−	0.138698i
$519$			9.49299i			0.416696i
$520$	14.9859	+	30.0105i	0.657175	+	1.31605i
$521$	−24.9222	−	24.9222i	−1.09186	−	1.09186i	−0.995330	−	0.0965310i	$-0.969225\pi$
$521$	−24.9222	−	24.9222i	−1.09186	−	1.09186i	−0.0965310	−	0.995330i	$-0.530775\pi$
$522$	−9.67995	−	12.6401i	−0.423680	−	0.553243i
$523$	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
$527$	−1.76395	+	11.4745i	−0.0768391	+	0.499837i
$528$	2.64220	+	10.0136i	0.114987	+	0.435787i
$529$	16.6294			0.723017
$530$	−8.68826	+	7.72598i	−0.377394	+	0.335595i
$531$	−12.8165			−0.556188
$532$	0.596619	−	2.20973i	0.0258667	−	0.0958038i
$533$	52.4501			2.27186
$534$	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
$537$	59.1552			2.55273
$538$	11.5610	+	15.0964i	0.498430	+	0.650852i
$539$	−3.14323	−	3.14323i	−0.135389	−	0.135389i
$540$	12.5353	+	2.41614i	0.539433	+	0.103974i
$541$	−9.28608	−	9.28608i	−0.399240	−	0.399240i	0.478725	−	0.877965i	$-0.341099\pi$
$541$	−9.28608	−	9.28608i	−0.399240	−	0.399240i	−0.877965	+	0.478725i	$0.841099\pi$
$542$	36.9398	+	4.89910i	1.58670	+	0.210434i
$543$	−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
$547$			26.0796i			1.11509i	0.830148	+	0.557543i	$0.188256\pi$
$547$			26.0796i			1.11509i	−0.830148	+	0.557543i	$0.811744\pi$
$548$	−17.9965	+	10.3445i	−0.768772	+	0.441896i
$549$	−10.8751	+	10.8751i	−0.464137	+	0.464137i
$550$	4.79522	−	4.93870i	0.204469	−	0.210587i
$551$	1.43363	−	1.43363i	0.0610745	−	0.0610745i
$552$	18.2472	−	43.6982i	0.776651	−	1.85992i
$553$	8.04149	−	8.04149i	0.341959	−	0.341959i
$554$	−5.07991	+	38.3032i	−0.215825	+	1.62735i
$555$	64.5465	−	4.73955i	2.73984	−	0.201183i
$556$	1.86130	+	3.23813i	0.0789367	+	0.137327i
$557$	−23.9084	−	23.9084i	−1.01303	−	1.01303i	−0.999914	−	0.0131183i	$-0.995824\pi$
$557$	−23.9084	−	23.9084i	−1.01303	−	1.01303i	−0.0131183	−	0.999914i	$-0.504176\pi$
$558$	−12.8774	+	9.86169i	−0.545145	+	0.417478i
$559$		−	31.8416i		−	1.34676i
$560$	6.12104	−	12.5393i	0.258661	−	0.529884i
$561$	−1.62201	+	10.5511i	−0.0684811	+	0.445469i
$562$	−43.3209	−	5.74538i	−1.82738	−	0.242354i
$563$	−22.2136	+	22.2136i	−0.936190	+	0.936190i	−0.998083	−	0.0618929i	$-0.980286\pi$
$563$	−22.2136	+	22.2136i	−0.936190	+	0.936190i	0.0618929	+	0.998083i	$0.480286\pi$
$564$	−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
$567$			7.21999i			0.303211i
$568$	−5.11582	+	2.10190i	−0.214655	+	0.0881937i
$569$	−33.4221			−1.40113			−0.700564	−	0.713590i	$-0.747068\pi$
$569$	−33.4221			−1.40113			−0.700564	+	0.713590i	$0.747068\pi$
$570$	−0.361071	+	6.15905i	−0.0151236	+	0.257974i
$571$	−18.0889	−	18.0889i	−0.756995	−	0.756995i	0.218779	−	0.975774i	$-0.429793\pi$
$571$	−18.0889	−	18.0889i	−0.756995	−	0.756995i	−0.975774	+	0.218779i	$0.929793\pi$
$572$	−9.96945	−	2.69172i	−0.416844	−	0.112546i
$573$		−	47.7523i		−	1.99488i
$574$	−13.2655	−	17.3221i	−0.553689	−	0.723010i
$575$	−31.1383	+	4.59767i	−1.29856	+	0.191736i
$576$	−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	$0.332553\pi$
$578$	−21.7831	−	10.1733i	−0.906058	−	0.423153i
$579$		−	5.27164i		−	0.219082i
$580$	10.2360	−	6.92774i	0.425027	−	0.287659i
$581$	18.7728	+	18.7728i	0.778827	+	0.778827i
$582$	−1.49907	−	0.198813i	−0.0621386	−	0.00824106i
$583$		−	3.57920i		−	0.148235i
$584$	0.0763065	−	0.182738i	0.00315758	−	0.00756176i
$585$	−31.5657	+	36.5687i	−1.30508	+	1.51193i
$586$	19.0806	+	24.9155i	0.788211	+	1.02925i
$587$	−15.5812	−	15.5812i	−0.643104	−	0.643104i	0.308214	−	0.951317i	$-0.400269\pi$
$587$	−15.5812	−	15.5812i	−0.643104	−	0.643104i	−0.951317	+	0.308214i	$0.900269\pi$
$588$	23.4487	+	6.33108i	0.967009	+	0.261089i
$589$	−1.46054	−	1.46054i	−0.0601806	−	0.0601806i
$590$	0.582309	−	9.93288i	0.0239733	−	0.408930i
$591$		−	25.2071i		−	1.03688i
$592$	−37.6160	−	21.9095i	−1.54601	−	0.900477i
$593$	22.7622	−	22.7622i	0.934733	−	0.934733i	−0.0632634	−	0.997997i	$-0.520151\pi$
$593$	22.7622	−	22.7622i	0.934733	−	0.934733i	0.997997	+	0.0632634i	$0.0201508\pi$
$594$	−3.12014	+	2.38944i	−0.128021	+	0.0980400i
$595$	10.9434	−	9.33339i	0.448637	−	0.382632i
$596$	−9.77873	−	2.64022i	−0.400552	−	0.108148i
$597$	43.1320	−	43.1320i	1.76528	−	1.76528i
$598$	28.7089	+	37.4882i	1.17399	+	1.53300i
$599$	−11.8993			−0.486193			−0.243097	−	0.970002i	$-0.578163\pi$
$599$	−11.8993			−0.486193			−0.243097	+	0.970002i	$0.578163\pi$
$600$	−9.26779	+	36.4523i	−0.378356	+	1.48816i
$601$	7.45499	+	7.45499i	0.304096	+	0.304096i	0.842614	−	0.538518i	$-0.181016\pi$
$601$	7.45499	+	7.45499i	0.304096	+	0.304096i	−0.538518	+	0.842614i	$0.681016\pi$
$602$	−10.5160	+	8.05325i	−0.428599	+	0.328226i
$603$	−6.44256	+	6.44256i	−0.262361	+	0.262361i
$604$	−10.3286	−	2.78868i	−0.420263	−	0.113470i
$605$	−1.64607	−	22.4173i	−0.0669221	−	0.911392i
$606$	29.8355	+	3.95689i	1.21198	+	0.160738i
$607$	−3.15126			−0.127906			−0.0639529	−	0.997953i	$-0.520371\pi$
$607$	−3.15126			−0.127906			−0.0639529	+	0.997953i	$0.520371\pi$
$608$	2.54190	−	3.28013i	0.103088	−	0.133027i
$609$	−8.10850	−	8.10850i	−0.328573	−	0.328573i
$610$	−7.93418	−	8.92239i	−0.321246	−	0.361257i
$611$	31.2289			1.26339
$612$	−12.1200	−	31.3266i	−0.489922	−	1.26630i
$613$	−0.0507432	+	0.0507432i	−0.00204950	+	0.00204950i	−0.708131	−	0.706081i	$-0.750461\pi$
$613$	−0.0507432	+	0.0507432i	−0.00204950	+	0.00204950i	0.706081	+	0.708131i	$0.250461\pi$
$614$	5.73250	+	7.48552i	0.231345	+	0.302091i
$615$	44.5192	+	38.4285i	1.79519	+	1.54959i
$616$	1.63247	+	3.97328i	0.0657741	+	0.160088i
$617$			36.6115i			1.47392i	0.675934	+	0.736962i	$0.263740\pi$
$617$			36.6115i			1.47392i	−0.675934	+	0.736962i	$0.736260\pi$
$618$	31.1023	+	40.6135i	1.25112	+	1.63371i
$619$	15.2125	−	15.2125i	0.611443	−	0.611443i	−0.331879	−	0.943322i	$-0.607683\pi$
$619$	15.2125	−	15.2125i	0.611443	−	0.611443i	0.943322	+	0.331879i	$0.107683\pi$
$620$	−7.05781	−	10.4282i	−0.283449	−	0.418806i
$621$	17.9700			0.721113
$622$	−29.0305	+	22.2319i	−1.16402	+	0.891419i
$623$	19.5011			0.781295
$624$	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
$628$	5.67125	+	9.86634i	0.226307	+	0.393710i
$629$	−26.5394	−	36.1813i	−1.05819	−	1.44264i
$630$	20.0606	+	1.17604i	0.799233	+	0.0468546i
$631$	−7.21444			−0.287202			−0.143601	−	0.989636i	$-0.545868\pi$
$631$	−7.21444			−0.287202			−0.143601	+	0.989636i	$0.545868\pi$
$632$	19.0715	−	7.83575i	0.758623	−	0.311689i
$633$	−49.4326	−	49.4326i	−1.96477	−	1.96477i
$634$	26.4941	+	3.51375i	1.05221	+	0.139549i
$635$	−2.56284	+	2.96904i	−0.101703	+	0.117823i
$636$	9.74592	+	16.9551i	0.386451	+	0.672314i
$637$	−17.1249	+	17.1249i	−0.678513	+	0.678513i
$638$	−0.500251	+	3.77196i	−0.0198051	+	0.149333i
$639$	−5.63216	−	5.63216i	−0.222805	−	0.222805i
$640$	19.0008	−	16.7024i	0.751071	−	0.660221i
$641$	−21.1951	+	21.1951i	−0.837157	+	0.837157i	−0.988484	−	0.151327i	$-0.951645\pi$
$641$	−21.1951	+	21.1951i	−0.837157	+	0.837157i	0.151327	+	0.988484i	$0.451645\pi$
$642$	57.5176	+	7.62821i	2.27004	+	0.301061i
$643$	15.3198			0.604153			0.302077	−	0.953284i	$-0.402320\pi$
$643$	15.3198			0.604153			0.302077	+	0.953284i	$0.402320\pi$
$644$	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	$0.0763587\pi$
$647$	30.7513	+	30.7513i	1.20896	+	1.20896i	0.237594	+	0.971365i	$0.423641\pi$
$648$	−5.04396	+	12.0792i	−0.198145	+	0.474517i
$649$	2.16591	+	2.16591i	0.0850193	+	0.0850193i
$650$	−26.9069	−	26.1252i	−1.05538	−	1.02471i
$651$	−8.26073	+	8.26073i	−0.323764	+	0.323764i
$652$	−13.1177	+	48.5847i	−0.513729	+	1.90272i
$653$	7.20109			0.281801			0.140900	−	0.990024i	$-0.455000\pi$
$653$	7.20109			0.281801			0.140900	+	0.990024i	$0.455000\pi$
$654$	−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
$657$	0.285190			0.0111263
$658$	−7.89829	−	10.3136i	−0.307908	−	0.402067i
$659$			26.5931i			1.03592i	0.855405	+	0.517960i	$0.173308\pi$
$659$			26.5931i			1.03592i	−0.855405	+	0.517960i	$0.826692\pi$
$660$	−6.48986	−	9.58901i	−0.252617	−	0.373252i
$661$	40.2944			1.56727			0.783635	−	0.621221i	$-0.213363\pi$
$661$	40.2944			1.56727			0.783635	+	0.621221i	$0.213363\pi$
$662$	−10.4641	−	1.38778i	−0.406697	−	0.0539377i
$663$	57.4844	+	8.83697i	2.23251	+	0.343200i
$664$	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
$668$	−24.8723	−	6.71545i	−0.962340	−	0.259828i
$669$	−16.2549	−	16.2549i	−0.628449	−	0.628449i
$670$	−4.70033	−	5.28576i	−0.181589	−	0.204207i
$671$	3.67565			0.141897
$672$	−18.5522	−	14.3768i	−0.715666	−	0.554598i
$673$			25.2208i			0.972191i	0.873906	+	0.486096i	$0.161579\pi$
$673$			25.2208i			0.972191i	−0.873906	+	0.486096i	$0.838421\pi$
$674$	−27.2037	−	3.60785i	−1.04785	−	0.138969i
$675$	−14.1198	+	2.08482i	−0.543470	+	0.0802449i
$676$	−7.88772	+	29.2141i	−0.303374	+	1.12362i
$677$	−1.33997			−0.0514991			−0.0257496	−	0.999668i	$-0.508197\pi$
$677$	−1.33997			−0.0514991			−0.0257496	+	0.999668i	$0.508197\pi$
$678$	0.0912367	+	0.0121002i	0.00350392	+	0.000464704i
$679$	−0.627225			−0.0240707
$680$	24.8291	−	7.96980i	0.952151	−	0.305628i
$681$	−61.0130			−2.33802
$682$	3.84278	+	0.509644i	0.147147	+	0.0195153i
$683$	−4.86709			−0.186234			−0.0931169	−	0.995655i	$-0.529683\pi$
$683$	−4.86709			−0.186234			−0.0931169	+	0.995655i	$0.529683\pi$
$684$	5.76961	+	1.55778i	0.220607	+	0.0595630i
$685$	15.1646	−	17.5681i	0.579410	−	0.671243i
$686$	25.2965	+	3.35492i	0.965826	+	0.128091i
$687$			30.7042i			1.17144i
$688$	−23.2196	+	6.12673i	−0.885238	+	0.233579i
$689$	−19.5001			−0.742894
$690$	−3.09852	+	52.8537i	−0.117959	+	2.01211i
$691$	−0.721793	−	0.721793i	−0.0274583	−	0.0274583i	0.693244	−	0.720703i	$-0.256181\pi$
$691$	−0.721793	−	0.721793i	−0.0274583	−	0.0274583i	−0.720703	+	0.693244i	$0.756181\pi$
$692$	−1.86080	+	6.89195i	−0.0707371	+	0.261993i
$693$	−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
$697$	6.19536	−	40.3007i	0.234666	−	1.52650i
$698$	1.35061	+	0.179123i	0.0511215	+	0.00677992i
$699$	47.7342			1.80547
$700$	−1.82289	+	15.4937i	−0.0688986	+	0.585607i
$701$			0.0837431i			0.00316293i	0.999999	+	0.00158147i	$0.000503397\pi$
$701$			0.0837431i			0.00316293i	−0.999999	+	0.00158147i	$0.999497\pi$
$702$	13.0181	+	16.9991i	0.491336	+	0.641589i
$703$	7.98346			0.301102
$704$	−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
$707$	12.4834			0.469487
$708$	−16.1578	−	4.36255i	−0.607248	−	0.163955i
$709$	−12.3924	+	12.3924i	−0.465405	+	0.465405i	−0.900422	−	0.435017i	$-0.856742\pi$
$709$	−12.3924	+	12.3924i	−0.465405	+	0.465405i	0.435017	+	0.900422i	$0.356742\pi$
$710$	4.62087	−	4.10908i	0.173418	−	0.154211i
$711$	20.9964	+	20.9964i	0.787426	+	0.787426i
$712$	32.6258	+	13.6237i	1.22270	+	0.510568i
$713$	−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
$717$	20.6624			0.771651
$718$	−18.9815	−	2.51740i	−0.708383	−	0.0939484i
$719$	−7.40991	+	7.40991i	−0.276343	+	0.276343i	−0.831647	−	0.555304i	$-0.812602\pi$
$719$	−7.40991	+	7.40991i	−0.276343	+	0.276343i	0.555304	+	0.831647i	$0.312602\pi$
$720$	32.7403	+	15.9821i	1.22016	+	0.595617i
$721$	15.0032	+	15.0032i	0.558749	+	0.558749i
$722$	3.43262	−	25.8824i	0.127749	−	0.963243i
$723$	−0.495165	+	0.495165i	−0.0184154	+	0.0184154i
$724$	−16.4947	+	9.48128i	−0.613021	+	0.352369i
$725$	−8.23932	+	11.0939i	−0.306001	+	0.412018i
$726$	−37.4805	−	4.97081i	−1.39103	−	0.184484i
$727$	25.2505	+	25.2505i	0.936491	+	0.936491i	0.998100	−	0.0616094i	$-0.0196233\pi$
$727$	25.2505	+	25.2505i	0.936491	+	0.936491i	−0.0616094	+	0.998100i	$0.519623\pi$
$728$	21.6471	−	8.89398i	0.802295	−	0.329633i
$729$	−41.6272			−1.54175
$730$	−0.0129575	+	0.221025i	−0.000479577	+	0.00818049i
$731$	−24.4659	−	3.76110i	−0.904905	−	0.139109i
$732$	−17.4120	+	10.0086i	−0.643567	+	0.369927i
$733$	−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
$737$	2.17751			0.0802096
$738$	45.2281	−	34.6362i	1.66487	−	1.27498i
$739$	17.0736			0.628062			0.314031	−	0.949413i	$-0.398320\pi$
$739$	17.0736			0.628062			0.314031	+	0.949413i	$0.398320\pi$
$740$	47.7900	+	9.21138i	1.75680	+	0.338617i
$741$	−7.31695	+	7.31695i	−0.268795	+	0.268795i
$742$	4.93188	+	6.44007i	0.181055	+	0.236422i
$743$			38.4115i			1.40918i	0.709614	+	0.704590i	$0.248869\pi$
$743$			38.4115i			1.40918i	−0.709614	+	0.704590i	$0.751131\pi$
$744$	−19.5914	+	8.04939i	−0.718257	+	0.295105i
$745$	11.2940	−	0.829304i	0.413781	−	0.0303833i
$746$	−7.77695	−	10.1552i	−0.284734	−	0.371807i
$747$	−49.0159	+	49.0159i	−1.79340	+	1.79340i
$748$	−3.24580	+	7.34222i	−0.118678	+	0.268458i
$749$	24.0658			0.879347
$750$	−3.69728	−	41.8887i	−0.135006	−	1.52956i
$751$	−24.5915	−	24.5915i	−0.897358	−	0.897358i	0.0978437	−	0.995202i	$-0.468805\pi$
$751$	−24.5915	−	24.5915i	−0.897358	−	0.897358i	−0.995202	+	0.0978437i	$0.968805\pi$
$752$	−6.00884	−	22.7728i	−0.219120	−	0.830438i
$753$	−35.0168			−1.27608
$754$	20.5503	+	2.72546i	0.748397	+	0.0992553i
$755$	11.9291	−	0.875933i	0.434143	−	0.0318785i
$756$	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	$0.147264\pi$
$758$	26.4752	−	20.2750i	0.961624	−	0.736423i
$759$	−11.5250	−	11.5250i	−0.418330	−	0.418330i
$760$	−1.46943	+	4.40072i	−0.0533018	+	0.159631i
$761$	−18.3851			−0.666458			−0.333229	−	0.942846i	$-0.608138\pi$
$761$	−18.3851			−0.666458			−0.333229	+	0.942846i	$0.608138\pi$
$762$	4.01119	+	5.23783i	0.145310	+	0.189747i
$763$	−20.5009	+	20.5009i	−0.742182	+	0.742182i
$764$	9.36034	−	34.6684i	0.338645	−	1.25426i
$765$	24.3695	+	28.5734i	0.881083	+	1.03307i
$766$	18.6406	−	14.2752i	0.673511	−	0.515782i
$767$	11.8002	−	11.8002i	0.426082	−	0.426082i
$768$	−20.9945	−	37.0135i	−0.757574	−	1.33561i
$769$			8.21402i			0.296205i	0.988972	+	0.148103i	$0.0473166\pi$
$769$			8.21402i			0.296205i	−0.988972	+	0.148103i	$0.952683\pi$
$770$	−3.19138	−	3.58887i	−0.115009	−	0.129334i
$771$	20.4794	+	20.4794i	0.737547	+	0.737547i
$772$	1.03334	−	3.82723i	0.0371907	−	0.137745i
$773$	−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
$775$	11.3022	+	8.39401i	0.405988	+	0.301522i
$776$	−1.04936	−	0.438186i	−0.0376699	−	0.0157299i
$777$		−	45.1539i		−	1.61989i
$778$	−41.5095	−	5.50515i	−1.48819	−	0.197369i
$779$	5.12971	+	5.12971i	0.183791	+	0.183791i
$780$	−52.2426	+	35.3579i	−1.87058	+	1.26601i
$781$			1.90360i			0.0681163i
$782$	32.1956	−	17.6308i	1.15131	−	0.630475i
$783$	5.57864	−	5.57864i	0.199364	−	0.199364i
$784$	15.7829	+	9.19278i	0.563674	+	0.328313i
$785$	−9.63149	−	8.31379i	−0.343762	−	0.296732i
$786$	−18.9087	−	24.6910i	−0.674450	−	0.880700i
$787$			5.98782i			0.213443i	0.994289	+	0.106721i	$0.0340353\pi$
$787$			5.98782i			0.213443i	−0.994289	+	0.106721i	$0.965965\pi$
$788$	4.94106	−	18.3005i	0.176018	−	0.651927i
$789$	20.9874	+	20.9874i	0.747170	+	0.747170i
$790$	−17.2263	+	15.3184i	−0.612885	+	0.545005i
$791$	0.0381742			0.00135732
$792$	−10.3743	+	4.26239i	−0.368633	+	0.151457i
$793$		−	20.0256i		−	0.711129i
$794$	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	$0.339511\pi$
$798$	4.26706	+	0.565913i	0.151052	+	0.0200331i
$799$	3.68874	−	23.9952i	0.130498	−	0.848888i
$800$	−13.8738	+	24.6479i	−0.490513	+	0.871434i
$801$			50.9175i			1.79908i
$802$	8.72488	−	6.68161i	0.308086	−	0.235936i
$803$	−0.0481954	−	0.0481954i	−0.00170078	−	0.00170078i
$804$	−10.3151	+	5.92922i	−0.363787	+	0.209107i
$805$	1.60817	+	21.9011i	0.0566804	+	0.771914i
$806$	2.77663	−	20.9361i	0.0978025	−	0.737443i
$807$	−25.2855	+	25.2855i	−0.890090	+	0.890090i
$808$	20.8851	+	8.72103i	0.734734	+	0.306805i
$809$	−10.5755	+	10.5755i	−0.371815	+	0.371815i	−0.868138	−	0.496323i	$-0.834683\pi$
$809$	−10.5755	+	10.5755i	−0.371815	+	0.371815i	0.496323	+	0.868138i	$0.334683\pi$
$810$	0.856505	−	14.6100i	0.0300945	−	0.513344i
$811$	18.0270	−	18.0270i	0.633012	−	0.633012i	−0.315810	−	0.948822i	$-0.602276\pi$
$811$	18.0270	−	18.0270i	0.633012	−	0.633012i	0.948822	+	0.315810i	$0.102276\pi$
$812$	−4.29739	−	7.47622i	−0.150809	−	0.262364i
$813$			70.0773i			2.45772i
$814$	−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
$818$	−11.9057	−	1.57897i	−0.416271	−	0.0552075i
$819$	23.8320	+	23.8320i	0.832756	+	0.832756i
$820$	24.7884	+	36.6258i	0.865649	+	1.27903i
$821$	4.78068	+	4.78068i	0.166847	+	0.166847i	0.785592	−	0.618745i	$-0.212359\pi$
$821$	4.78068	+	4.78068i	0.166847	+	0.166847i	−0.618745	+	0.785592i	$0.712359\pi$
$822$	−23.7346	−	30.9928i	−0.827841	−	1.08100i
$823$	18.0502			0.629189			0.314594	−	0.949226i	$-0.398132\pi$
$823$	18.0502			0.629189			0.314594	+	0.949226i	$0.398132\pi$
$824$	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
$827$	−24.0381			−0.835888			−0.417944	−	0.908473i	$-0.637249\pi$
$827$	−24.0381			−0.835888			−0.417944	+	0.908473i	$0.637249\pi$
$828$	49.5117	+	13.3680i	1.72065	+	0.464570i
$829$	54.5041			1.89301			0.946504	−	0.322693i	$-0.104588\pi$
$829$	54.5041			1.89301			0.946504	+	0.322693i	$0.104588\pi$
$830$	−35.7607	−	40.2148i	−1.24127	−	1.39587i
$831$	−72.6637			−2.52068
$832$	42.4296	+	0.243034i	1.47098	+	0.00842568i
$833$	11.1354	+	15.1809i	0.385817	+	0.525988i
$834$	−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
$838$	−23.8019	−	31.0807i	−0.822224	−	1.07366i
$839$	−26.2491	−	26.2491i	−0.906220	−	0.906220i	0.0897444	−	0.995965i	$-0.471395\pi$
$839$	−26.2491	−	26.2491i	−0.906220	−	0.906220i	−0.995965	+	0.0897444i	$0.971395\pi$
$840$	24.8902	+	8.31100i	0.858794	+	0.286757i
$841$			21.3615i			0.736604i
$842$	−36.7784	−	4.87769i	−1.26747	−	0.168096i
$843$		−	82.1827i		−	2.83052i
$844$	−26.1986	−	45.5780i	−0.901792	−	1.56886i
$845$	−2.47756	−	33.7411i	−0.0852306	−	1.16073i
$846$	26.9289	−	20.6225i	0.925836	−	0.709016i
$847$	−15.6822			−0.538846
$848$	3.75206	+	14.2199i	0.128846	+	0.488312i
$849$			44.0596i			1.51212i
$850$	−23.2518	+	17.5884i	−0.797532	+	0.603277i
$851$	68.5097			2.34848
$852$	−5.18339	−	9.01762i	−0.177580	−	0.308938i
$853$			12.8401i			0.439637i	0.975541	+	0.219818i	$0.0705465\pi$
$853$			12.8401i			0.439637i	−0.975541	+	0.219818i	$0.929454\pi$
$854$	−6.61362	+	5.06479i	−0.226313	+	0.173313i
$855$	−6.66367	+	0.489303i	−0.227893	+	0.0167338i
$856$	40.2628	+	16.8126i	1.37615	+	0.574644i
$857$	−15.6507			−0.534616			−0.267308	−	0.963611i	$-0.586134\pi$
$857$	−15.6507			−0.534616			−0.267308	+	0.963611i	$0.586134\pi$
$858$	2.55319	−	19.2513i	0.0871644	−	0.657230i
$859$	45.3264			1.54652			0.773259	−	0.634091i	$-0.218625\pi$
$859$	45.3264			1.54652			0.773259	+	0.634091i	$0.218625\pi$
$860$	22.2350	−	15.0487i	0.758206	−	0.513155i
$861$	29.0133	−	29.0133i	0.988771	−	0.988771i
$862$	14.2591	+	18.6196i	0.485668	+	0.634187i
$863$	−6.78897	+	6.78897i	−0.231099	+	0.231099i	−0.813151	−	0.582052i	$-0.802250\pi$
$863$	−6.78897	+	6.78897i	−0.231099	+	0.231099i	0.582052	+	0.813151i	$0.302250\pi$
$864$	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
$867$	13.5800	−	43.1251i	0.461201	−	1.46460i
$868$	−7.61658	+	4.37807i	−0.258524	+	0.148601i
$869$		−	7.09653i		−	0.240733i
$870$	15.4461	+	17.3699i	0.523670	+	0.588894i
$871$		−	11.8635i		−	0.401978i
$872$	−48.6206	+	19.9764i	−1.64650	+	0.676485i
$873$		−	1.63769i		−	0.0554273i
$874$	−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
$877$		−	23.4361i		−	0.791379i	−0.918384	−	0.395690i	$-0.870506\pi$
$877$		−	23.4361i		−	0.791379i	0.918384	−	0.395690i	$-0.129494\pi$
$878$	7.01302	+	9.15763i	0.236678	+	0.309055i
$879$	−41.7318	+	41.7318i	−1.40758	+	1.40758i
$880$	−2.83204	−	8.23379i	−0.0954680	−	0.277561i
$881$	22.5078	−	22.5078i	0.758308	−	0.758308i	−0.217706	−	0.976014i	$-0.569858\pi$
$881$	22.5078	−	22.5078i	0.758308	−	0.758308i	0.976014	+	0.217706i	$0.0698575\pi$
$882$	−3.45824	+	26.0756i	−0.116445	+	0.878011i
$883$	−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
$887$	−8.40522			−0.282220			−0.141110	−	0.989994i	$-0.545067\pi$
$887$	−8.40522			−0.282220			−0.141110	+	0.989994i	$0.545067\pi$
$888$	31.5450	−	75.5437i	1.05858	−	2.53508i
$889$	1.93493	+	1.93493i	0.0648956	+	0.0648956i
$890$	−39.4615	−	2.31341i	−1.32275	−	0.0775456i
$891$	3.18578	+	3.18578i	0.106728	+	0.106728i
$892$	−8.61484	−	14.9873i	−0.288446	−	0.501813i
$893$	3.05425	+	3.05425i	0.102206	+	0.102206i
$894$	2.50434	−	18.8831i	0.0837577	−	0.631544i
$895$	−49.6019	+	3.64219i	−1.65801	+	0.121745i
$896$	−10.6508	−	14.0742i	−0.355820	−	0.470186i
$897$	−62.7901	+	62.7901i	−2.09650	+	2.09650i
$898$	−21.5984	−	28.2033i	−0.720748	−	0.941156i
$899$	−7.78188			−0.259540
$900$	−40.4542	−	4.75956i	−1.34847	−	0.158652i
$901$	−2.30333	+	14.9832i	−0.0767351	+	0.499161i
$902$	−13.4966	−	1.78997i	−0.449387	−	0.0595994i
$903$	−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
$907$	−52.1542			−1.73175			−0.865876	−	0.500259i	$-0.833238\pi$
$907$	−52.1542			−1.73175			−0.865876	+	0.500259i	$0.833238\pi$
$908$	−44.2957	−	11.9597i	−1.47000	−	0.396896i
$909$			32.5942i			1.08108i
$910$	−19.5528	+	17.3872i	−0.648168	+	0.576380i
$911$	9.82346	−	9.82346i	0.325466	−	0.325466i	−0.525394	−	0.850859i	$-0.676082\pi$
$911$	9.82346	−	9.82346i	0.325466	−	0.325466i	0.850859	+	0.525394i	$0.176082\pi$
$912$	6.74354	+	3.92780i	0.223301	+	0.130062i
$913$	16.5668			0.548281
$914$	29.0699	−	22.2620i	0.961546	−	0.736363i
$915$	14.6721	−	16.9975i	0.485045	−	0.561922i
$916$	−6.01860	+	22.2914i	−0.198860	+	0.736528i
$917$	−9.12124	−	9.12124i	−0.301210	−	0.301210i
$918$	14.5992	−	7.99471i	0.481844	−	0.263865i
$919$	31.0471			1.02415			0.512075	−	0.858940i	$-0.328877\pi$
$919$	31.0471			1.02415			0.512075	+	0.858940i	$0.328877\pi$
$920$	−12.6098	+	37.7646i	−0.415734	+	1.24506i
$921$	−12.5377	+	12.5377i	−0.413133	+	0.413133i
$922$	−3.31391	+	24.9873i	−0.109138	+	0.822912i
$923$	10.3712			0.341371
$924$	−7.00366	+	4.02576i	−0.230404	+	0.132438i
$925$	−53.8307	+	7.94827i	−1.76994	+	0.261337i
$926$	12.1660	+	15.8864i	0.399798	+	0.522058i
$927$	−39.1735	+	39.1735i	−1.28663	+	1.28663i
$928$	−1.96667	−	15.5101i	−0.0645592	−	0.509144i
$929$	−3.29196	+	3.29196i	−0.108006	+	0.108006i	−0.759044	−	0.651039i	$-0.774334\pi$
$929$	−3.29196	+	3.29196i	−0.108006	+	0.108006i	0.651039	+	0.759044i	$0.274334\pi$
$930$	17.6960	−	15.7361i	0.580274	−	0.516006i
$931$	−3.34969			−0.109782
$932$	34.6552	+	9.35680i	1.13517	+	0.306492i
$933$	−48.6242	−	48.6242i	−1.59188	−	1.59188i
$934$	4.44834	−	3.40659i	0.145554	−	0.111467i
$935$	0.710426	−	8.94704i	0.0232334	−	0.292600i
$936$	23.2222	+	56.5207i	0.759042	+	1.84744i
$937$	−22.2487	−	22.2487i	−0.726832	−	0.726832i	0.243155	−	0.969987i	$-0.421817\pi$
$937$	−22.2487	−	22.2487i	−0.726832	−	0.726832i	−0.969987	+	0.243155i	$0.921817\pi$
$938$	−3.91801	+	3.00045i	−0.127927	+	0.0979683i
$939$			72.1926i			2.35592i
$940$	14.7591	+	21.8071i	0.481389	+	0.711270i
$941$	−38.7948	+	38.7948i	−1.26468	+	1.26468i	−0.315875	+	0.948801i	$0.602298\pi$
$941$	−38.7948	+	38.7948i	−1.26468	+	1.26468i	−0.948801	+	0.315875i	$0.897702\pi$
$942$	−16.9914	+	13.0122i	−0.553609	+	0.423960i
$943$	44.0204	+	44.0204i	1.43350	+	1.43350i
$944$	−10.8755	−	6.33446i	−0.353967	−	0.206169i
$945$	0.729227	+	9.93112i	0.0237218	+	0.323059i
$946$	−1.08666	+	8.19357i	−0.0353304	+	0.266396i
$947$		−	4.62835i		−	0.150401i	−0.997168	−	0.0752006i	$-0.976040\pi$
$947$		−	4.62835i		−	0.150401i	0.997168	−	0.0752006i	$-0.0239597\pi$
$948$	19.3234	+	33.6171i	0.627594	+	1.09183i
$949$	−0.262577	+	0.262577i	−0.00852361	+	0.00852361i
$950$	−0.0764538	−	5.18663i	−0.00248049	−	0.168276i
$951$			50.2611i			1.62983i
$952$	−4.27687	−	17.6834i	−0.138614	−	0.573122i
$953$	−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
$955$	2.94012	+	40.0405i	0.0951399	+	1.29568i
$956$	15.0010	+	4.05021i	0.485166	+	0.130993i
$957$	−7.15566			−0.231310
$958$	0.154862	+	0.202219i	0.00500336	+	0.00653341i
$959$	−11.4492	−	11.4492i	−0.369714	−	0.369714i
$960$	35.8358	+	31.2931i	1.15660	+	1.00998i
$961$		−	23.0720i		−	0.744259i
$962$	49.6307	+	64.8080i	1.60016	+	2.08949i
$963$			62.8361i			2.02486i
$964$	−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	$0.202169\pi$
$968$	−26.2367	−	10.9557i	−0.843278	−	0.352130i
$969$	4.75780	+	6.48634i	0.152843	+	0.208371i
$970$	1.26922	+	0.0744075i	0.0407523	+	0.00238908i
$971$		−	17.9459i		−	0.575912i	−0.957644	−	0.287956i	$-0.907024\pi$
$971$		−	17.9459i		−	0.575912i	0.957644	−	0.287956i	$-0.0929757\pi$
$972$	−40.3014	−	10.8813i	−1.29267	−	0.349016i
$973$	−2.06007	+	2.06007i	−0.0660427	+	0.0660427i
$974$	14.5053	+	1.92375i	0.464779	+	0.0616408i
$975$	42.0519	−	56.6213i	1.34674	−	1.81333i
$976$	−14.6031	+	3.85317i	−0.467433	+	0.123337i
$977$	2.49628	+	2.49628i	0.0798631	+	0.0798631i	0.745910	−	0.666047i	$-0.232015\pi$
$977$	2.49628	+	2.49628i	0.0798631	+	0.0798631i	−0.666047	+	0.745910i	$0.732015\pi$
$978$	−93.8186	−	12.4426i	−2.99999	−	0.397870i
$979$	8.60475	−	8.60475i	0.275009	−	0.275009i
$980$	−20.0517	−	3.86490i	−0.640528	−	0.123460i
$981$	−53.5279	−	53.5279i	−1.70901	−	1.70901i
$982$	18.4608	+	2.44834i	0.589107	+	0.0781296i
$983$			30.1790i			0.962560i	0.876567	+	0.481280i	$0.159828\pi$
$983$			30.1790i			0.962560i	−0.876567	+	0.481280i	$0.840172\pi$
$984$	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
$988$	−6.74639	+	3.87788i	−0.214631	+	0.123372i
$989$	26.7241	−	26.7241i	0.849777	−	0.849777i
$990$	9.37055	−	8.33271i	0.297816	−	0.264831i
$991$	−12.8847	−	12.8847i	−0.409297	−	0.409297i	0.472197	−	0.881493i	$-0.343461\pi$
$991$	−12.8847	−	12.8847i	−0.409297	−	0.409297i	−0.881493	+	0.472197i	$0.843461\pi$
$992$	−15.8013	+	2.00360i	−0.501692	+	0.0636143i
$993$		−	19.8510i		−	0.629953i
$994$	−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
$997$		−	36.5622i		−	1.15794i	−0.815350	−	0.578969i	$-0.803455\pi$
$997$		−	36.5622i		−	1.15794i	0.815350	−	0.578969i	$-0.196545\pi$
$998$	22.5467	+	29.4416i	0.713704	+	0.931958i
$999$	31.0659			0.982882

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.t.a.523.5	✓	208	136.115	odd	4
680.2.t.a.523.56	yes	208	17.13	even	4
680.2.t.a.667.5	yes	208	5.2	odd	4
680.2.t.a.667.56	yes	208	40.27	even	4
680.2.bl.a.123.49	yes	208	1.1	even	1	trivial
680.2.bl.a.123.100	yes	208	8.3	odd	2	inner
680.2.bl.a.387.49	yes	208	680.387	even	4	inner
680.2.bl.a.387.100	yes	208	85.47	odd	4	inner

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.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.185930 + 1.40194i) q^{2} -2.65957 q^{3} +(-1.93086 - 0.521326i) q^{4} +(2.23006 - 0.163750i) q^{5} +(0.494495 - 3.72855i) q^{6} -1.56006i q^{7} +(1.08987 - 2.61002i) q^{8} +4.07332 q^{9} +(-0.185069 + 3.15686i) q^{10} +(-0.688367 - 0.688367i) q^{11} +(5.13526 + 1.38650i) 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} +(2.43864 + 3.32461i) q^{17} +(-0.757354 + 5.71054i) q^{18} -0.733580 q^{19} +(-4.39131 - 0.846411i) q^{20} +4.14908i q^{21} +(1.09304 - 0.837059i) q^{22} -6.29519 q^{23} +(-2.89859 + 6.94152i) q^{24} +(4.94637 - 0.730347i) q^{25} +(-4.56044 - 5.95505i) q^{26} -2.85457 q^{27} +(-0.813298 + 3.01225i) q^{28} +(-1.95429 + 1.95429i) q^{29} +(0.492204 - 8.39589i) q^{30} +(1.99098 + 1.99098i) q^{31} +(-3.46506 + 4.47140i) 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} -10.8829 q^{37} +(0.136395 - 1.02843i) q^{38} +(9.97430 - 9.97430i) q^{39} +(2.00309 - 5.99897i) q^{40} +(-6.99271 - 6.99271i) q^{41} +(-5.81676 - 0.771441i) q^{42} +(-4.24516 + 4.24516i) q^{43} +(0.970276 + 1.68800i) q^{44} +(9.08376 - 0.667007i) q^{45} +(1.17047 - 8.82546i) q^{46} +(-4.16348 - 4.16348i) q^{47} +(-9.19265 - 5.35428i) q^{48} +4.56622 q^{49} +(0.104220 + 7.07030i) q^{50} +(-6.48573 - 8.84204i) q^{51} +(9.19653 - 5.28623i) 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} +1.95101 q^{57} +(-2.37643 - 3.10315i) q^{58} -3.14644 q^{59} +(11.6790 + 2.25109i) q^{60} +(-2.66983 + 2.66983i) q^{61} +(-3.16141 + 2.42104i) q^{62} -6.35461i q^{63} +(-5.62436 - 5.68916i) q^{64} +(-7.74938 + 8.97762i) q^{65} +(-2.90701 + 2.22622i) q^{66} +(-1.58165 + 1.58165i) q^{67} +(-2.97546 - 7.69068i) q^{68} +16.7425 q^{69} +(4.92488 + 0.288718i) q^{70} +(-1.38270 - 1.38270i) q^{71} +(4.43939 - 10.6314i) q^{72} +0.0700142 q^{73} +(2.02346 - 15.2571i) q^{74} +(-13.1552 + 1.94241i) q^{75} +(1.41644 + 0.382434i) q^{76} +(-1.07389 + 1.07389i) q^{77} +(12.1288 + 15.8379i) q^{78} +(5.15461 + 5.15461i) q^{79} +(8.03775 + 3.92360i) q^{80} -4.62803 q^{81} +(11.1035 - 8.50318i) q^{82} +(-12.0334 + 12.0334i) q^{83} +(2.16302 - 8.01130i) q^{84} +(5.98272 + 7.01477i) q^{85} +(-5.16215 - 6.74076i) q^{86} +(5.19756 - 5.19756i) q^{87} +(-2.54688 + 1.04642i) q^{88} +12.5002i q^{89} +(-0.753845 + 12.8589i) q^{90} +(5.85075 + 5.85075i) q^{91} +(12.1551 + 3.28184i) q^{92} +(-5.29515 - 5.29515i) q^{93} +(6.61106 - 5.06282i) q^{94} +(-1.63593 + 0.120124i) q^{95} +(9.21557 - 11.8920i) q^{96} -0.402052i q^{97} +(-0.848999 + 6.40156i) q^{98} +(-2.80394 - 2.80394i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 208 q - 8 q^{3} - 8 q^{6} + 192 q^{9} - 6 q^{10} - 8 q^{11} + 16 q^{14} - 16 q^{16} - 12 q^{18} - 10 q^{20} - 16 q^{24} - 32 q^{27} - 24 q^{30} - 20 q^{32} - 8 q^{33} + 4 q^{34} - 8 q^{35} - 12 q^{38} + 38 q^{40}+ \cdots - 24 q^{99}+O(q^{100}) \) 208 * q - 8 * q^3 - 8 * q^6 + 192 * q^9 - 6 * q^10 - 8 * q^11 + 16 * q^14 - 16 * q^16 - 12 * q^18 - 10 * q^20 - 16 * q^24 - 32 * q^27 - 24 * q^30 - 20 * q^32 - 8 * q^33 + 4 * q^34 - 8 * q^35 - 12 * q^38 + 38 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^44 - 16 * q^46 + 68 * q^48 - 160 * q^49 + 16 * q^50 - 8 * q^51 - 20 * q^52 - 36 * q^54 + 4 * q^56 - 32 * q^57 + 64 * q^59 - 32 * q^60 - 72 * q^62 + 32 * q^65 - 8 * q^67 - 28 * q^68 + 28 * q^70 - 56 * q^72 + 32 * q^73 - 8 * q^74 - 16 * q^75 - 10 * q^80 + 128 * q^81 + 8 * q^86 - 16 * q^88 - 118 * q^90 + 24 * q^91 - 56 * q^92 - 64 * q^94 - 48 * q^96 - 40 * q^98 - 24 * q^99

Introduction

L-functions

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