LMFDB - Embedded newform 680.2.ba.b.21.70

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(21,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.21"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 0, 3])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [140] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$70$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.70
Character	$\chi$	$=$	680.21
Dual form			680.2.ba.b.421.70

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40821 + 0.130188i) q^{2} +(-1.50733 - 1.50733i) q^{3} +(1.96610 + 0.366665i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.92640 - 2.31888i) q^{6} +(-3.09613 - 3.09613i) q^{7} +(2.72095 + 0.772304i) q^{8} +1.54411i q^{9} +(0.903697 + 1.08781i) q^{10} +(-0.701775 + 0.701775i) q^{11} +(-2.41089 - 3.51626i) q^{12} -2.89436i q^{13} +(-3.95692 - 4.76308i) q^{14} -2.13169i q^{15} +(3.73111 + 1.44180i) q^{16} +(-0.250472 - 4.11549i) q^{17} +(-0.201025 + 2.17443i) q^{18} +0.884823 q^{19} +(1.13097 + 1.64952i) q^{20} +9.33381i q^{21} +(-1.07961 + 0.896882i) q^{22} +(-5.80970 - 5.80970i) q^{23} +(-2.93725 - 5.26549i) q^{24} +1.00000i q^{25} +(0.376812 - 4.07586i) q^{26} +(-2.19451 + 2.19451i) q^{27} +(-4.95207 - 7.22255i) q^{28} +(1.66327 + 1.66327i) q^{29} +(0.277522 - 3.00187i) q^{30} +(5.09308 - 5.09308i) q^{31} +(5.06648 + 2.51610i) q^{32} +2.11562 q^{33} +(0.183072 - 5.82808i) q^{34} -4.37859i q^{35} +(-0.566170 + 3.03588i) q^{36} +(4.33804 + 4.33804i) q^{37} +(1.24601 + 0.115194i) q^{38} +(-4.36276 + 4.36276i) q^{39} +(1.37790 + 2.47010i) q^{40} +(-1.87963 - 1.87963i) q^{41} +(-1.21515 + 13.1439i) q^{42} -6.65956 q^{43} +(-1.63708 + 1.12244i) q^{44} +(-1.09185 + 1.09185i) q^{45} +(-7.42492 - 8.93763i) q^{46} +2.34610 q^{47} +(-3.45076 - 7.79731i) q^{48} +12.1721i q^{49} +(-0.130188 + 1.40821i) q^{50} +(-5.82587 + 6.58096i) q^{51} +(1.06126 - 5.69060i) q^{52} +5.44693 q^{53} +(-3.37603 + 2.80463i) q^{54} -0.992459 q^{55} +(-6.03325 - 10.8156i) q^{56} +(-1.33372 - 1.33372i) q^{57} +(2.12569 + 2.55876i) q^{58} -2.64592 q^{59} +(0.781616 - 4.19112i) q^{60} +(3.01194 - 3.01194i) q^{61} +(7.83517 - 6.50905i) q^{62} +(4.78076 - 4.78076i) q^{63} +(6.80709 + 4.20280i) q^{64} +(2.04662 - 2.04662i) q^{65} +(2.97923 + 0.275429i) q^{66} +5.12442i q^{67} +(1.01655 - 8.18331i) q^{68} +17.5143i q^{69} +(0.570042 - 6.16597i) q^{70} +(5.55550 - 5.55550i) q^{71} +(-1.19252 + 4.20144i) q^{72} +(-1.24434 + 1.24434i) q^{73} +(5.54410 + 6.67362i) q^{74} +(1.50733 - 1.50733i) q^{75} +(1.73965 + 0.324433i) q^{76} +4.34557 q^{77} +(-6.71166 + 5.57570i) q^{78} +(6.96053 + 6.96053i) q^{79} +(1.61879 + 3.65780i) q^{80} +11.2481 q^{81} +(-2.40220 - 2.89162i) q^{82} +16.7947 q^{83} +(-3.42238 + 18.3512i) q^{84} +(2.73298 - 3.08720i) q^{85} +(-9.37804 - 0.866997i) q^{86} -5.01420i q^{87} +(-2.45147 + 1.36751i) q^{88} -9.48330 q^{89} +(-1.67970 + 1.39541i) q^{90} +(-8.96131 + 8.96131i) q^{91} +(-9.29225 - 13.5527i) q^{92} -15.3539 q^{93} +(3.30380 + 0.305435i) q^{94} +(0.625664 + 0.625664i) q^{95} +(-3.84427 - 11.4295i) q^{96} +(-4.16899 + 4.16899i) q^{97} +(-1.58466 + 17.1408i) q^{98} +(-1.08362 - 1.08362i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 8 q^{4} - 4 q^{6} - 12 q^{7} + 20 q^{12} + 28 q^{14} - 24 q^{16} - 16 q^{17} - 8 q^{20} + 40 q^{22} + 4 q^{23} + 48 q^{24} - 20 q^{28} + 28 q^{31} - 8 q^{34} - 56 q^{38} + 24 q^{40} + 44 q^{41}+ \cdots + 176 q^{98}+O(q^{100}) $ 140 * q - 8 * q^4 - 4 * q^6 - 12 * q^7 + 20 * q^12 + 28 * q^14 - 24 * q^16 - 16 * q^17 - 8 * q^20 + 40 * q^22 + 4 * q^23 + 48 * q^24 - 20 * q^28 + 28 * q^31 - 8 * q^34 - 56 * q^38 + 24 * q^40 + 44 * q^41 + 28 * q^44 - 40 * q^46 - 120 * q^47 + 32 * q^48 - 48 * q^52 - 4 * q^54 + 16 * q^55 + 16 * q^56 - 16 * q^57 - 52 * q^58 - 72 * q^62 + 44 * q^63 - 104 * q^64 + 8 * q^68 + 12 * q^71 - 104 * q^72 + 36 * q^73 + 20 * q^74 + 28 * q^78 - 44 * q^79 - 76 * q^81 - 44 * q^82 + 48 * q^84 + 120 * q^86 + 28 * q^88 + 24 * q^89 + 28 * q^90 - 72 * q^92 + 8 * q^95 - 116 * q^96 + 12 * q^97 + 176 * q^98

Character values

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

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

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 $

$2$	1.40821	+	0.130188i	0.995754	+	0.0920571i
$2$	1.40821	+	0.130188i	0.995754	+	0.0920571i
$3$	−1.50733	−	1.50733i	−0.870259	−	0.870259i	0.122241	−	0.992500i	$-0.460992\pi$
$3$	−1.50733	−	1.50733i	−0.870259	−	0.870259i	−0.992500	+	0.122241i	$0.960992\pi$
$4$	1.96610	+	0.366665i	0.983051	+	0.183332i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$	−1.92640	−	2.31888i	−0.786450	−	0.946678i
$7$	−3.09613	−	3.09613i	−1.17023	−	1.17023i	−0.982155	−	0.188073i	$-0.939776\pi$
$7$	−3.09613	−	3.09613i	−1.17023	−	1.17023i	−0.188073	−	0.982155i	$-0.560224\pi$
$8$	2.72095	+	0.772304i	0.962000	+	0.273051i
$9$			1.54411i			0.514703i
$10$	0.903697	+	1.08781i	0.285774	+	0.343996i
$11$	−0.701775	+	0.701775i	−0.211593	+	0.211593i	−0.804944	−	0.593351i	$-0.797805\pi$
$11$	−0.701775	+	0.701775i	−0.211593	+	0.211593i	0.593351	+	0.804944i	$0.297805\pi$
$12$	−2.41089	−	3.51626i	−0.695963	−	1.01506i
$13$		−	2.89436i		−	0.802750i	−0.915914	−	0.401375i	$-0.868532\pi$
$13$		−	2.89436i		−	0.802750i	0.915914	−	0.401375i	$-0.131468\pi$
$14$	−3.95692	−	4.76308i	−1.05753	−	1.27299i
$15$		−	2.13169i		−	0.550400i
$16$	3.73111	+	1.44180i	0.932778	+	0.360450i
$17$	−0.250472	−	4.11549i	−0.0607485	−	0.998153i
$17$	−0.250472	−	4.11549i	−0.0607485	−	0.998153i
$18$	−0.201025	+	2.17443i	−0.0473821	+	0.512517i
$19$	0.884823			0.202992			0.101496	−	0.994836i	$-0.467637\pi$
$19$	0.884823			0.202992			0.101496	+	0.994836i	$0.467637\pi$
$20$	1.13097	+	1.64952i	0.252893	+	0.368843i
$21$			9.33381i			2.03680i
$22$	−1.07961	+	0.896882i	−0.230173	+	0.191216i
$23$	−5.80970	−	5.80970i	−1.21141	−	1.21141i	−0.970564	−	0.240842i	$-0.922576\pi$
$23$	−5.80970	−	5.80970i	−1.21141	−	1.21141i	−0.240842	−	0.970564i	$-0.577424\pi$
$24$	−2.93725	−	5.26549i	−0.599564	−	1.07481i
$25$			1.00000i			0.200000i
$26$	0.376812	−	4.07586i	0.0738989	−	0.799342i
$27$	−2.19451	+	2.19451i	−0.422334	+	0.422334i
$28$	−4.95207	−	7.22255i	−0.935853	−	1.36493i
$29$	1.66327	+	1.66327i	0.308861	+	0.308861i	0.844468	−	0.535607i	$-0.179917\pi$
$29$	1.66327	+	1.66327i	0.308861	+	0.308861i	−0.535607	+	0.844468i	$0.679917\pi$
$30$	0.277522	−	3.00187i	0.0506683	−	0.548063i
$31$	5.09308	−	5.09308i	0.914744	−	0.914744i	−0.0818971	−	0.996641i	$-0.526098\pi$
$31$	5.09308	−	5.09308i	0.914744	−	0.914744i	0.996641	+	0.0818971i	$0.0260979\pi$
$32$	5.06648	+	2.51610i	0.895636	+	0.444789i
$33$	2.11562			0.368282
$34$	0.183072	−	5.82808i	0.0313966	−	0.999507i
$35$		−	4.37859i		−	0.740117i
$36$	−0.566170	+	3.03588i	−0.0943617	+	0.505979i
$37$	4.33804	+	4.33804i	0.713169	+	0.713169i	0.967197	−	0.254028i	$-0.0817555\pi$
$37$	4.33804	+	4.33804i	0.713169	+	0.713169i	−0.254028	+	0.967197i	$0.581756\pi$
$38$	1.24601	+	0.115194i	0.202130	+	0.0186869i
$39$	−4.36276	+	4.36276i	−0.698601	+	0.698601i
$40$	1.37790	+	2.47010i	0.217865	+	0.390557i
$41$	−1.87963	−	1.87963i	−0.293549	−	0.293549i	0.544932	−	0.838481i	$-0.316556\pi$
$41$	−1.87963	−	1.87963i	−0.293549	−	0.293549i	−0.838481	+	0.544932i	$0.816556\pi$
$42$	−1.21515	+	13.1439i	−0.187502	+	2.02815i
$43$	−6.65956			−1.01557			−0.507786	−	0.861483i	$-0.669536\pi$
$43$	−6.65956			−1.01557			−0.507786	+	0.861483i	$0.669536\pi$
$44$	−1.63708	+	1.12244i	−0.246799	+	0.169215i
$45$	−1.09185	+	1.09185i	−0.162763	+	0.162763i
$46$	−7.42492	−	8.93763i	−1.09474	−	1.31778i
$47$	2.34610			0.342214			0.171107	−	0.985252i	$-0.445266\pi$
$47$	2.34610			0.342214			0.171107	+	0.985252i	$0.445266\pi$
$48$	−3.45076	−	7.79731i	−0.498074	−	1.12544i
$49$			12.1721i			1.73887i
$50$	−0.130188	+	1.40821i	−0.0184114	+	0.199151i
$51$	−5.82587	+	6.58096i	−0.815785	+	0.921519i
$52$	1.06126	−	5.69060i	0.147170	−	0.789145i
$53$	5.44693			0.748193			0.374097	−	0.927390i	$-0.377953\pi$
$53$	5.44693			0.748193			0.374097	+	0.927390i	$0.377953\pi$
$54$	−3.37603	+	2.80463i	−0.459420	+	0.381662i
$55$	−0.992459			−0.133823
$56$	−6.03325	−	10.8156i	−0.806227	−	1.44529i
$57$	−1.33372	−	1.33372i	−0.176656	−	0.176656i
$58$	2.12569	+	2.55876i	0.279117	+	0.335982i
$59$	−2.64592			−0.344469			−0.172235	−	0.985056i	$-0.555099\pi$
$59$	−2.64592			−0.344469			−0.172235	+	0.985056i	$0.555099\pi$
$60$	0.781616	−	4.19112i	0.100906	−	0.541072i
$61$	3.01194	−	3.01194i	0.385639	−	0.385639i	−0.487490	−	0.873129i	$-0.662087\pi$
$61$	3.01194	−	3.01194i	0.385639	−	0.385639i	0.873129	+	0.487490i	$0.162087\pi$
$62$	7.83517	−	6.50905i	0.995068	−	0.826651i
$63$	4.78076	−	4.78076i	0.602320	−	0.602320i
$64$	6.80709	+	4.20280i	0.850887	+	0.525350i
$65$	2.04662	−	2.04662i	0.253852	−	0.253852i
$66$	2.97923	+	0.275429i	0.366718	+	0.0339030i
$67$			5.12442i			0.626048i	0.949745	+	0.313024i	$0.101342\pi$
$67$			5.12442i			0.626048i	−0.949745	+	0.313024i	$0.898658\pi$
$68$	1.01655	−	8.18331i	0.123275	−	0.992373i
$69$			17.5143i			2.10848i
$70$	0.570042	−	6.16597i	0.0681330	−	0.736974i
$71$	5.55550	−	5.55550i	0.659317	−	0.659317i	−0.295901	−	0.955218i	$-0.595620\pi$
$71$	5.55550	−	5.55550i	0.659317	−	0.659317i	0.955218	+	0.295901i	$0.0956200\pi$
$72$	−1.19252	+	4.20144i	−0.140540	+	0.495144i
$73$	−1.24434	+	1.24434i	−0.145639	+	0.145639i	−0.776167	−	0.630528i	$-0.782838\pi$
$73$	−1.24434	+	1.24434i	−0.145639	+	0.145639i	0.630528	+	0.776167i	$0.282838\pi$
$74$	5.54410	+	6.67362i	0.644488	+	0.775793i
$75$	1.50733	−	1.50733i	0.174052	−	0.174052i
$76$	1.73965	+	0.324433i	0.199552	+	0.0372151i
$77$	4.34557			0.495224
$78$	−6.71166	+	5.57570i	−0.759946	+	0.631323i
$79$	6.96053	+	6.96053i	0.783120	+	0.783120i	0.980356	−	0.197236i	$-0.0631964\pi$
$79$	6.96053	+	6.96053i	0.783120	+	0.783120i	−0.197236	+	0.980356i	$0.563196\pi$
$80$	1.61879	+	3.65780i	0.180986	+	0.408955i
$81$	11.2481			1.24978
$82$	−2.40220	−	2.89162i	−0.265279	−	0.319326i
$83$	16.7947			1.84346			0.921731	−	0.387831i	$-0.126775\pi$
$83$	16.7947			1.84346			0.921731	+	0.387831i	$0.126775\pi$
$84$	−3.42238	+	18.3512i	−0.373412	+	2.00228i
$85$	2.73298	−	3.08720i	0.296433	−	0.334854i
$86$	−9.37804	−	0.866997i	−1.01126	−	0.0934907i
$87$		−	5.01420i		−	0.537578i
$88$	−2.45147	+	1.36751i	−0.261328	+	0.145777i
$89$	−9.48330			−1.00523			−0.502614	−	0.864511i	$-0.667628\pi$
$89$	−9.48330			−1.00523			−0.502614	+	0.864511i	$0.667628\pi$
$90$	−1.67970	+	1.39541i	−0.177056	+	0.147089i
$91$	−8.96131	+	8.96131i	−0.939401	+	0.939401i
$92$	−9.29225	−	13.5527i	−0.968784	−	1.41296i
$93$	−15.3539			−1.59213
$94$	3.30380	+	0.305435i	0.340761	+	0.0315032i
$95$	0.625664	+	0.625664i	0.0641918	+	0.0641918i
$96$	−3.84427	−	11.4295i	−0.392354	−	1.16652i
$97$	−4.16899	+	4.16899i	−0.423296	+	0.423296i	−0.886337	−	0.463041i	$-0.846758\pi$
$97$	−4.16899	+	4.16899i	−0.423296	+	0.423296i	0.463041	+	0.886337i	$0.346758\pi$
$98$	−1.58466	+	17.1408i	−0.160075	+	1.73148i
$99$	−1.08362	−	1.08362i	−0.108908	−	0.108908i
$100$	−0.366665	+	1.96610i	−0.0366665	+	0.196610i
$101$		−	9.87617i		−	0.982716i	−0.870958	−	0.491358i	$-0.836501\pi$
$101$		−	9.87617i		−	0.982716i	0.870958	−	0.491358i	$-0.163499\pi$
$102$	−9.06081	+	8.50891i	−0.897154	+	0.842507i
$103$	17.4902			1.72336			0.861681	−	0.507451i	$-0.169412\pi$
$103$	17.4902			1.72336			0.861681	+	0.507451i	$0.169412\pi$
$104$	2.23532	−	7.87539i	0.219192	−	0.772246i
$105$	−6.60000	+	6.60000i	−0.644094	+	0.644094i
$106$	7.67041	+	0.709127i	0.745016	+	0.0688765i
$107$	−1.88541	−	1.88541i	−0.182269	−	0.182269i	0.610075	−	0.792344i	$-0.291139\pi$
$107$	−1.88541	−	1.88541i	−0.182269	−	0.182269i	−0.792344	+	0.610075i	$0.791139\pi$
$108$	−5.11929	+	3.50999i	−0.492604	+	0.337749i
$109$	−8.77529	+	8.77529i	−0.840521	+	0.840521i	−0.988927	−	0.148406i	$-0.952586\pi$
$109$	−8.77529	+	8.77529i	−0.840521	+	0.840521i	0.148406	+	0.988927i	$0.452586\pi$
$110$	−1.39759	−	0.129207i	−0.133255	−	0.0123194i
$111$		−	13.0777i		−	1.24128i
$112$	−7.08801	−	16.0160i	−0.669754	−	1.51337i
$113$	−1.39014	−	1.39014i	−0.130773	−	0.130773i	0.638691	−	0.769464i	$-0.279476\pi$
$113$	−1.39014	−	1.39014i	−0.130773	−	0.130773i	−0.769464	+	0.638691i	$0.779476\pi$
$114$	−1.70452	−	2.05179i	−0.159643	−	0.192168i
$115$		−	8.21616i		−	0.766161i
$116$	2.66029	+	3.88001i	0.247002	+	0.360250i
$117$	4.46920			0.413178
$118$	−3.72601	−	0.344468i	−0.343007	−	0.0317109i
$119$	−11.9666	+	13.5176i	−1.09698	+	1.23916i
$120$	1.64631	−	5.80022i	0.150287	−	0.529485i
$121$			10.0150i			0.910457i
$122$	4.63356	−	3.84932i	0.419502	−	0.348501i
$123$			5.66646i			0.510927i
$124$	11.8810	−	8.14606i	1.06694	−	0.731537i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	7.35471	−	6.10991i	0.655210	−	0.544314i
$127$			16.6950i			1.48144i	0.671812	+	0.740722i	$0.265516\pi$
$127$			16.6950i			1.48144i	−0.671812	+	0.740722i	$0.734484\pi$
$128$	9.03865	+	6.80462i	0.798911	+	0.601449i
$129$	10.0382	+	10.0382i	0.883812	+	0.883812i
$130$	3.14851	−	2.61562i	0.276143	−	0.229405i
$131$	10.1007	+	10.1007i	0.882502	+	0.882502i	0.993788	−	0.111286i	$-0.0354970\pi$
$131$	10.1007	+	10.1007i	0.882502	+	0.882502i	−0.111286	+	0.993788i	$0.535497\pi$
$132$	4.15952	+	0.775723i	0.362040	+	0.0675180i
$133$	−2.73953	−	2.73953i	−0.237547	−	0.237547i
$134$	−0.667141	+	7.21626i	−0.0576322	+	0.623390i
$135$	−3.10351			−0.267108
$136$	2.49689	−	11.3915i	0.214106	−	0.976810i
$137$	13.3365			1.13941			0.569706	−	0.821849i	$-0.307057\pi$
$137$	13.3365			1.13941			0.569706	+	0.821849i	$0.307057\pi$
$138$	−2.28016	+	24.6638i	−0.194100	+	2.09952i
$139$	11.5971	+	11.5971i	0.983657	+	0.983657i	0.999869	−	0.0162120i	$-0.00516067\pi$
$139$	11.5971	+	11.5971i	0.983657	+	0.983657i	−0.0162120	+	0.999869i	$0.505161\pi$
$140$	1.60548	−	8.60876i	0.135687	−	0.727573i
$141$	−3.53636	−	3.53636i	−0.297815	−	0.297815i
$142$	8.54657	−	7.10005i	0.717212	−	0.595823i
$143$	2.03119	+	2.03119i	0.169856	+	0.169856i
$144$	−2.22630	+	5.76125i	−0.185525	+	0.480104i
$145$			2.35221i			0.195341i
$146$	−1.91429	+	1.59029i	−0.158427	+	0.131613i
$147$	18.3474	−	18.3474i	1.51326	−	1.51326i
$148$	6.93842	+	10.1196i	0.570334	+	0.831828i
$149$			1.10281i			0.0903460i	0.998979	+	0.0451730i	$0.0143839\pi$
$149$			1.10281i			0.0903460i	−0.998979	+	0.0451730i	$0.985616\pi$
$150$	2.31888	−	1.92640i	0.189336	−	0.157290i
$151$		−	20.2137i		−	1.64497i	−0.568790	−	0.822483i	$-0.692588\pi$
$151$		−	20.2137i		−	1.64497i	0.568790	−	0.822483i	$-0.307412\pi$
$152$	2.40755	+	0.683352i	0.195278	+	0.0554272i
$153$	6.35477	−	0.386757i	0.513752	−	0.0312674i
$154$	6.11947	+	0.565743i	0.493121	+	0.0455889i
$155$	7.20270			0.578535
$156$	−10.1773	+	6.97796i	−0.814837	+	0.558684i
$157$		−	7.57056i		−	0.604197i	−0.953277	−	0.302098i	$-0.902313\pi$
$157$		−	7.57056i		−	0.604197i	0.953277	−	0.302098i	$-0.0976871\pi$
$158$	8.89569	+	10.7081i	0.707703	+	0.851887i
$159$	−8.21034	−	8.21034i	−0.651122	−	0.651122i
$160$	1.80339	+	5.36170i	0.142570	+	0.423879i
$161$			35.9752i			2.83524i
$162$	15.8396	+	1.46437i	1.24448	+	0.115051i
$163$	−0.412441	+	0.412441i	−0.0323049	+	0.0323049i	−0.723075	−	0.690770i	$-0.757272\pi$
$163$	−0.412441	+	0.412441i	−0.0323049	+	0.0323049i	0.690770	+	0.723075i	$0.257272\pi$
$164$	−3.00635	−	4.38474i	−0.234757	−	0.342391i
$165$	1.49597	+	1.49597i	0.116461	+	0.116461i
$166$	23.6505	+	2.18648i	1.83563	+	0.169704i
$167$	−11.6584	+	11.6584i	−0.902157	+	0.902157i	−0.995623	−	0.0934653i	$-0.970206\pi$
$167$	−11.6584	+	11.6584i	−0.902157	+	0.902157i	0.0934653	+	0.995623i	$0.470206\pi$
$168$	−7.20854	+	25.3968i	−0.556151	+	1.95940i
$169$	4.62269			0.355592
$170$	4.25052	−	3.99162i	0.326000	−	0.306143i
$171$			1.36626i			0.104481i
$172$	−13.0934	−	2.44183i	−0.998360	−	0.186187i
$173$	−8.50994	−	8.50994i	−0.646999	−	0.646999i	0.305268	−	0.952267i	$-0.401254\pi$
$173$	−8.50994	−	8.50994i	−0.646999	−	0.646999i	−0.952267	+	0.305268i	$0.901254\pi$
$174$	0.652790	−	7.06103i	0.0494879	−	0.535296i
$175$	3.09613	−	3.09613i	0.234046	−	0.234046i
$176$	−3.63022	+	1.60658i	−0.273638	+	0.121101i
$177$	3.98828	+	3.98828i	0.299778	+	0.299778i
$178$	−13.3545	−	1.23462i	−1.00096	−	0.0925384i
$179$	−21.6505			−1.61824			−0.809118	−	0.587646i	$-0.800055\pi$
$179$	−21.6505			−1.61824			−0.809118	+	0.587646i	$0.800055\pi$
$180$	−2.54703	+	1.74635i	−0.189844	+	0.130165i
$181$	16.7132	−	16.7132i	1.24228	−	1.24228i	0.283228	−	0.959053i	$-0.408595\pi$
$181$	16.7132	−	16.7132i	1.24228	−	1.24228i	0.959053	−	0.283228i	$-0.0914054\pi$
$182$	−13.7861	+	11.4527i	−1.02189	+	0.848933i
$183$	−9.07999			−0.671212
$184$	−11.3210	−	20.2947i	−0.834597	−	1.49615i
$185$			6.13491i			0.451048i
$186$	−21.6215	−	1.99890i	−1.58537	−	0.146567i
$187$	3.06392	+	2.71237i	0.224056	+	0.198348i
$188$	4.61267	+	0.860233i	0.336414	+	0.0627389i
$189$	13.5890			0.988455
$190$	0.799611	+	0.962520i	0.0580099	+	0.0698285i
$191$	−15.5196			−1.12296			−0.561481	−	0.827490i	$-0.689768\pi$
$191$	−15.5196			−1.12296			−0.561481	+	0.827490i	$0.689768\pi$
$192$	−3.92554	−	16.5956i	−0.283302	−	1.19768i
$193$	−3.44015	−	3.44015i	−0.247627	−	0.247627i	0.572369	−	0.819996i	$-0.306025\pi$
$193$	−3.44015	−	3.44015i	−0.247627	−	0.247627i	−0.819996	+	0.572369i	$0.806025\pi$
$194$	−6.41355	+	5.32805i	−0.460466	+	0.382532i
$195$	−6.16988			−0.441834
$196$	−4.46307	+	23.9315i	−0.318791	+	1.70939i
$197$	7.48294	−	7.48294i	0.533138	−	0.533138i	−0.388367	−	0.921505i	$-0.626961\pi$
$197$	7.48294	−	7.48294i	0.533138	−	0.533138i	0.921505	+	0.388367i	$0.126961\pi$
$198$	−1.38488	−	1.66703i	−0.0984194	−	0.118471i
$199$	16.9768	−	16.9768i	1.20345	−	1.20345i	0.230344	−	0.973109i	$-0.426015\pi$
$199$	16.9768	−	16.9768i	1.20345	−	1.20345i	0.973109	−	0.230344i	$-0.0739851\pi$
$200$	−0.772304	+	2.72095i	−0.0546102	+	0.192400i
$201$	7.72422	−	7.72422i	0.544824	−	0.544824i
$202$	1.28576	−	13.9077i	0.0904660	−	0.978543i
$203$		−	10.2994i		−	0.722875i
$204$	−13.8673	+	10.8027i	−0.970903	+	0.756340i
$205$		−	2.65820i		−	0.185657i
$206$	24.6299	+	2.27702i	1.71604	+	0.158648i
$207$	8.97081	−	8.97081i	0.623515	−	0.623515i
$208$	4.17309	−	10.7992i	0.289352	−	0.748788i
$209$	−0.620946	+	0.620946i	−0.0429517	+	0.0429517i
$210$	−10.1534	+	8.43493i	−0.700652	+	0.582065i
$211$	−5.71809	+	5.71809i	−0.393650	+	0.393650i	−0.875986	−	0.482336i	$-0.839788\pi$
$211$	−5.71809	+	5.71809i	−0.393650	+	0.393650i	0.482336	+	0.875986i	$0.339788\pi$
$212$	10.7092	+	1.99720i	0.735512	+	0.137168i
$213$	−16.7480			−1.14755
$214$	−2.40959	−	2.90050i	−0.164716	−	0.198274i
$215$	−4.70902	−	4.70902i	−0.321152	−	0.321152i
$216$	−7.66598	+	4.27632i	−0.521604	+	0.290967i
$217$	−31.5377			−2.14092
$218$	−13.4999	+	11.2150i	−0.914327	+	0.759576i
$219$	3.75127			0.253487
$220$	−1.95128	−	0.363900i	−0.131555	−	0.0245341i
$221$	−11.9117	+	0.724956i	−0.801268	+	0.0487658i
$222$	1.70257	−	18.4162i	0.114269	−	1.23601i
$223$		−	10.7899i		−	0.722543i	−0.932461	−	0.361272i	$-0.882343\pi$
$223$		−	10.7899i		−	0.722543i	0.932461	−	0.361272i	$-0.117657\pi$
$224$	−7.89630	−	23.4767i	−0.527594	−	1.56860i
$225$	−1.54411			−0.102941
$226$	−1.77662	−	2.13858i	−0.118179	−	0.142256i
$227$	−10.5732	+	10.5732i	−0.701765	+	0.701765i	−0.964789	−	0.263024i	$-0.915280\pi$
$227$	−10.5732	+	10.5732i	−0.701765	+	0.701765i	0.263024	+	0.964789i	$0.415280\pi$
$228$	−2.13321	−	3.11126i	−0.141275	−	0.206048i
$229$	3.38246			0.223519			0.111760	−	0.993735i	$-0.464351\pi$
$229$	3.38246			0.223519			0.111760	+	0.993735i	$0.464351\pi$
$230$	1.06965	−	11.5701i	0.0705306	−	0.762907i
$231$	−6.55023	−	6.55023i	−0.430973	−	0.430973i
$232$	3.24111	+	5.81021i	0.212789	+	0.381459i
$233$	−0.513828	+	0.513828i	−0.0336620	+	0.0336620i	−0.723737	−	0.690075i	$-0.757577\pi$
$233$	−0.513828	+	0.513828i	−0.0336620	+	0.0336620i	0.690075	+	0.723737i	$0.257577\pi$
$234$	6.29357	+	0.581838i	0.411423	+	0.0380360i
$235$	1.65894	+	1.65894i	0.108218	+	0.108218i
$236$	−5.20215	−	0.970166i	−0.338631	−	0.0631524i
$237$		−	20.9837i		−	1.36304i
$238$	−18.6113	+	17.4777i	−1.20639	+	1.13291i
$239$	−23.2662			−1.50497			−0.752484	−	0.658611i	$-0.771144\pi$
$239$	−23.2662			−1.50497			−0.752484	+	0.658611i	$0.771144\pi$
$240$	3.07348	−	7.95358i	0.198392	−	0.513402i
$241$	−7.83919	+	7.83919i	−0.504967	+	0.504967i	−0.912977	−	0.408010i	$-0.866223\pi$
$241$	−7.83919	+	7.83919i	−0.504967	+	0.504967i	0.408010	+	0.912977i	$0.366223\pi$
$242$	−1.30384	+	14.1032i	−0.0838140	+	0.906591i
$243$	−10.3710	−	10.3710i	−0.665302	−	0.665302i
$244$	7.02615	−	4.81740i	0.449803	−	0.308403i
$245$	−8.60695	+	8.60695i	−0.549878	+	0.549878i
$246$	−0.737707	+	7.97956i	−0.0470345	+	0.508758i
$247$		−	2.56099i		−	0.162952i
$248$	17.7914	−	9.92458i	1.12975	−	0.630212i
$249$	−25.3153	−	25.3153i	−1.60429	−	1.60429i
$250$	−1.08781	+	0.903697i	−0.0687992	+	0.0571548i
$251$		−	3.73407i		−	0.235692i	−0.993032	−	0.117846i	$-0.962401\pi$
$251$		−	3.73407i		−	0.235692i	0.993032	−	0.117846i	$-0.0375990\pi$
$252$	11.1524	−	7.64653i	0.702536	−	0.481686i
$253$	8.15420			0.512650
$254$	−2.17350	+	23.5101i	−0.136377	+	1.47515i
$255$	−8.77296	+	0.533930i	−0.549384	+	0.0334360i
$256$	11.8424	+	10.7590i	0.740151	+	0.672440i
$257$		−	9.81088i		−	0.611986i	−0.952034	−	0.305993i	$-0.901012\pi$
$257$		−	9.81088i		−	0.611986i	0.952034	−	0.305993i	$-0.0989884\pi$
$258$	12.8290	+	15.4427i	0.798698	+	0.961420i
$259$		−	26.8623i		−	1.66914i
$260$	4.77429	−	3.27344i	0.296089	−	0.203010i
$261$	−2.56827	+	2.56827i	−0.158972	+	0.158972i
$262$	12.9089	+	15.5389i	0.797514	+	0.959996i
$263$		−	4.41679i		−	0.272351i	−0.990685	−	0.136175i	$-0.956519\pi$
$263$		−	4.41679i		−	0.272351i	0.990685	−	0.136175i	$-0.0434811\pi$
$264$	5.75648	+	1.63390i	0.354287	+	0.100560i
$265$	3.85156	+	3.85156i	0.236599	+	0.236599i
$266$	−3.50117	−	4.21448i	−0.214671	−	0.258406i
$267$	14.2945	+	14.2945i	0.874809	+	0.874809i
$268$	−1.87895	+	10.0751i	−0.114775	+	0.615437i
$269$	−17.4973	−	17.4973i	−1.06683	−	1.06683i	−0.997601	−	0.0692289i	$-0.977946\pi$
$269$	−17.4973	−	17.4973i	−1.06683	−	1.06683i	−0.0692289	−	0.997601i	$-0.522054\pi$
$270$	−4.37039	−	0.404041i	−0.265973	−	0.0245892i
$271$	6.48958			0.394214			0.197107	−	0.980382i	$-0.436845\pi$
$271$	6.48958			0.394214			0.197107	+	0.980382i	$0.436845\pi$
$272$	4.99918	−	15.7165i	0.303120	−	0.952952i
$273$	27.0154			1.63504
$274$	18.7805	+	1.73625i	1.13457	+	0.104891i
$275$	−0.701775	−	0.701775i	−0.0423186	−	0.0423186i
$276$	−6.42188	+	34.4349i	−0.386552	+	2.07274i
$277$	−17.8871	−	17.8871i	−1.07473	−	1.07473i	−0.996972	−	0.0777597i	$-0.975223\pi$
$277$	−17.8871	−	17.8871i	−1.07473	−	1.07473i	−0.0777597	−	0.996972i	$-0.524777\pi$
$278$	14.8214	+	17.8410i	0.888927	+	1.07003i
$279$	7.86427	+	7.86427i	0.470821	+	0.470821i
$280$	3.38160	−	11.9139i	0.202090	−	0.711992i
$281$		−	23.8795i		−	1.42453i	−0.701911	−	0.712265i	$-0.747670\pi$
$281$		−	23.8795i		−	1.42453i	0.701911	−	0.712265i	$-0.252330\pi$
$282$	−4.51954	−	5.44032i	−0.269134	−	0.323966i
$283$	15.2752	−	15.2752i	0.908019	−	0.908019i	−0.0880930	−	0.996112i	$-0.528077\pi$
$283$	15.2752	−	15.2752i	0.908019	−	0.908019i	0.996112	+	0.0880930i	$0.0280773\pi$
$284$	12.9597	−	8.88568i	0.769016	−	0.527268i
$285$		−	1.88617i		−	0.111727i
$286$	2.59590	+	3.12477i	0.153499	+	0.184772i
$287$			11.6392i			0.687038i
$288$	−3.88514	+	7.82320i	−0.228934	+	0.460986i
$289$	−16.8745	+	2.06163i	−0.992619	+	0.121273i
$290$	−0.306231	+	3.31241i	−0.0179825	+	0.194511i
$291$	12.5681			0.736755
$292$	−2.90275	+	1.99024i	−0.169871	+	0.116470i
$293$			28.0994i			1.64158i	0.571227	+	0.820792i	$0.306468\pi$
$293$			28.0994i			1.64158i	−0.571227	+	0.820792i	$0.693532\pi$
$294$	28.2255	−	23.4483i	1.64615	−	1.36753i
$295$	−1.87095	−	1.87095i	−0.108931	−	0.108931i
$296$	8.45328	+	15.1538i	0.491337	+	0.880799i
$297$		−	3.08011i		−	0.178726i
$298$	−0.143574	+	1.55299i	−0.00831699	+	0.0899624i
$299$	−16.8154	+	16.8154i	−0.972457	+	0.972457i
$300$	3.51626	−	2.41089i	0.203011	−	0.139193i
$301$	20.6189	+	20.6189i	1.18845	+	1.18845i
$302$	2.63159	−	28.4651i	0.151431	−	1.63798i
$303$	−14.8867	+	14.8867i	−0.855218	+	0.855218i
$304$	3.30137	+	1.27574i	0.189347	+	0.0731686i
$305$	4.25952			0.243900
$306$	8.99919	+	0.282683i	0.514449	+	0.0161599i
$307$		−	19.0700i		−	1.08838i	−0.838962	−	0.544190i	$-0.816837\pi$
$307$		−	19.0700i		−	1.08838i	0.838962	−	0.544190i	$-0.183163\pi$
$308$	8.54384	+	1.59337i	0.486831	+	0.0907906i
$309$	−26.3636	−	26.3636i	−1.49977	−	1.49977i
$310$	10.1429	+	0.937708i	0.576078	+	0.0532582i
$311$	19.3595	−	19.3595i	1.09778	−	1.09778i	0.103106	−	0.994670i	$-0.467122\pi$
$311$	19.3595	−	19.3595i	1.09778	−	1.09778i	0.994670	−	0.103106i	$-0.0328780\pi$
$312$	−15.2402	+	8.50146i	−0.862808	+	0.481300i
$313$	9.00050	+	9.00050i	0.508738	+	0.508738i	0.914139	−	0.405401i	$-0.132868\pi$
$313$	9.00050	+	9.00050i	0.508738	+	0.508738i	−0.405401	+	0.914139i	$0.632868\pi$
$314$	0.985599	−	10.6609i	0.0556206	−	0.601631i
$315$	6.76102			0.380940
$316$	11.1329	+	16.2373i	0.626276	+	0.913419i
$317$	−7.70969	+	7.70969i	−0.433019	+	0.433019i	−0.889654	−	0.456635i	$-0.849055\pi$
$317$	−7.70969	+	7.70969i	−0.433019	+	0.433019i	0.456635	+	0.889654i	$0.349055\pi$
$318$	−10.4930	−	12.6308i	−0.588417	−	0.708298i
$319$	−2.33448			−0.130706
$320$	1.84152	+	7.78517i	0.102944	+	0.435204i
$321$			5.68387i			0.317243i
$322$	−4.68355	+	50.6606i	−0.261004	+	2.82320i
$323$	−0.221624	−	3.64148i	−0.0123315	−	0.202617i
$324$	22.1148	+	4.12427i	1.22860	+	0.229126i
$325$	2.89436			0.160550
$326$	−0.634498	+	0.527108i	−0.0351416	+	0.0291938i
$327$	26.4546			1.46294
$328$	−3.66273	−	6.56602i	−0.202240	−	0.362548i
$329$	−7.26384	−	7.26384i	−0.400468	−	0.400468i
$330$	1.91188	+	2.30139i	0.105245	+	0.126687i
$331$	−20.5596			−1.13006			−0.565028	−	0.825072i	$-0.691135\pi$
$331$	−20.5596			−1.13006			−0.565028	+	0.825072i	$0.691135\pi$
$332$	33.0202	+	6.15804i	1.81222	+	0.337966i
$333$	−6.69840	+	6.69840i	−0.367070	+	0.367070i
$334$	−17.9353	+	14.8997i	−0.981376	+	0.815276i
$335$	−3.62352	+	3.62352i	−0.197974	+	0.197974i
$336$	−13.4575	+	34.8255i	−0.734166	+	1.89989i
$337$	21.2587	−	21.2587i	1.15803	−	1.15803i	0.173134	−	0.984898i	$-0.444611\pi$
$337$	21.2587	−	21.2587i	1.15803	−	1.15803i	0.984898	−	0.173134i	$-0.0553894\pi$
$338$	6.50972	+	0.601821i	0.354082	+	0.0327348i
$339$			4.19079i			0.227613i
$340$	6.50529	−	5.06767i	0.352799	−	0.274833i
$341$			7.14839i			0.387107i
$342$	−0.177872	+	1.92398i	−0.00961819	+	0.104037i
$343$	16.0134	−	16.0134i	0.864641	−	0.864641i
$344$	−18.1203	−	5.14320i	−0.976981	−	0.277303i
$345$	−12.3845	+	12.3845i	−0.666759	+	0.666759i
$346$	−10.8759	−	13.0917i	−0.584691	−	0.703812i
$347$	−10.0308	+	10.0308i	−0.538480	+	0.538480i	−0.923082	−	0.384602i	$-0.874339\pi$
$347$	−10.0308	+	10.0308i	−0.538480	+	0.538480i	0.384602	+	0.923082i	$0.374339\pi$
$348$	1.83853	−	9.85842i	0.0985555	−	0.528467i
$349$	9.40176			0.503265			0.251632	−	0.967823i	$-0.419033\pi$
$349$	9.40176			0.503265			0.251632	+	0.967823i	$0.419033\pi$
$350$	4.76308	−	3.95692i	0.254597	−	0.211506i
$351$	6.35171	+	6.35171i	0.339029	+	0.339029i
$352$	−5.32127	+	1.78979i	−0.283624	+	0.0953961i
$353$	−0.901361			−0.0479746			−0.0239873	−	0.999712i	$-0.507636\pi$
$353$	−0.901361			−0.0479746			−0.0239873	+	0.999712i	$0.507636\pi$
$354$	5.09711	+	6.13556i	0.270908	+	0.326101i
$355$	7.85667			0.416989
$356$	−18.6451	−	3.47719i	−0.988190	−	0.184291i
$357$	38.4132	−	2.33786i	2.03304	−	0.123733i
$358$	−30.4885	−	2.81865i	−1.61136	−	0.148970i
$359$			25.4840i			1.34500i	0.740099	+	0.672498i	$0.234778\pi$
$359$			25.4840i			1.34500i	−0.740099	+	0.672498i	$0.765222\pi$
$360$	−3.81410	+	2.12762i	−0.201021	+	0.112136i
$361$	−18.2171			−0.958794
$362$	25.7115	−	21.3598i	1.35137	−	1.12264i
$363$	15.0960	−	15.0960i	0.792334	−	0.792334i
$364$	−20.9047	+	14.3331i	−1.09570	+	0.751256i
$365$	−1.75976			−0.0921101
$366$	−12.7865	−	1.18211i	−0.668362	−	0.0617898i
$367$	1.89572	+	1.89572i	0.0989560	+	0.0989560i	0.754852	−	0.655896i	$-0.227709\pi$
$367$	1.89572	+	1.89572i	0.0989560	+	0.0989560i	−0.655896	+	0.754852i	$0.727709\pi$
$368$	−13.3002	−	30.0531i	−0.693322	−	1.56663i
$369$	2.90235	−	2.90235i	0.151090	−	0.151090i
$370$	−0.798694	+	8.63923i	−0.0415221	+	0.449132i
$371$	−16.8644	−	16.8644i	−0.875557	−	0.875557i
$372$	−30.1874	−	5.62975i	−1.56514	−	0.291889i
$373$			30.3588i			1.57192i	0.618277	+	0.785960i	$0.287831\pi$
$373$			30.3588i			1.57192i	−0.618277	+	0.785960i	$0.712169\pi$
$374$	3.96152	+	4.21847i	0.204845	+	0.218132i
$375$	2.13169			0.110080
$376$	6.38361	+	1.81190i	0.329210	+	0.0934418i
$377$	4.81409	−	4.81409i	0.247938	−	0.247938i
$378$	19.1362	+	1.76913i	0.984257	+	0.0909943i
$379$	27.0355	+	27.0355i	1.38872	+	1.38872i	0.828021	+	0.560696i	$0.189467\pi$
$379$	27.0355	+	27.0355i	1.38872	+	1.38872i	0.560696	+	0.828021i	$0.310533\pi$
$380$	1.00071	+	1.45953i	0.0513354	+	0.0748722i
$381$	25.1650	−	25.1650i	1.28924	−	1.28924i
$382$	−21.8549	−	2.02048i	−1.11819	−	0.103377i
$383$		−	23.5356i		−	1.20261i	−0.799019	−	0.601306i	$-0.794647\pi$
$383$		−	23.5356i		−	1.20261i	0.799019	−	0.601306i	$-0.205353\pi$
$384$	−3.36743	−	23.8811i	−0.171843	−	1.21868i
$385$	3.07278	+	3.07278i	0.156604	+	0.156604i
$386$	−4.39658	−	5.29231i	−0.223780	−	0.269372i
$387$		−	10.2831i		−	0.522718i
$388$	−9.72527	+	6.66803i	−0.493726	+	0.338518i
$389$	26.2333			1.33008			0.665041	−	0.746807i	$-0.268414\pi$
$389$	26.2333			1.33008			0.665041	+	0.746807i	$0.268414\pi$
$390$	−8.68847	−	0.803247i	−0.439958	−	0.0406740i
$391$	−22.4546	+	25.3649i	−1.13558	+	1.28276i
$392$	−9.40054	+	33.1195i	−0.474799	+	1.67279i
$393$		−	30.4503i		−	1.53601i
$394$	11.5117	−	9.56335i	0.579953	−	0.481795i
$395$			9.84367i			0.495289i
$396$	−1.73318	−	2.52782i	−0.0870954	−	0.127028i
$397$	−11.5277	+	11.5277i	−0.578558	+	0.578558i	−0.934506	−	0.355948i	$-0.884158\pi$
$397$	−11.5277	+	11.5277i	−0.578558	+	0.578558i	0.355948	+	0.934506i	$0.384158\pi$
$398$	26.1171	−	21.6967i	1.30913	−	1.08756i
$399$			8.25876i			0.413455i
$400$	−1.44180	+	3.73111i	−0.0720901	+	0.186556i
$401$	11.1375	+	11.1375i	0.556178	+	0.556178i	0.928217	−	0.372039i	$-0.121341\pi$
$401$	11.1375	+	11.1375i	0.556178	+	0.556178i	−0.372039	+	0.928217i	$0.621341\pi$
$402$	11.8829	−	9.87170i	0.592666	−	0.492356i
$403$	−14.7412	−	14.7412i	−0.734311	−	0.734311i
$404$	3.62124	−	19.4176i	0.180164	−	0.966060i
$405$	7.95358	+	7.95358i	0.395216	+	0.395216i
$406$	1.34086	−	14.5037i	0.0665458	−	0.719806i
$407$	−6.08865			−0.301803
$408$	−20.9344	+	13.4071i	−1.03641	+	0.663750i
$409$	−6.53271			−0.323022			−0.161511	−	0.986871i	$-0.551637\pi$
$409$	−6.53271			−0.323022			−0.161511	+	0.986871i	$0.551637\pi$
$410$	0.346067	−	3.74330i	0.0170910	−	0.184868i
$411$	−20.1025	−	20.1025i	−0.991583	−	0.991583i
$412$	34.3875	+	6.41305i	1.69415	+	0.315948i
$413$	8.19212	+	8.19212i	0.403108	+	0.403108i
$414$	13.8007	−	11.4649i	0.678266	−	0.563468i
$415$	11.8757	+	11.8757i	0.582954	+	0.582954i
$416$	7.28250	−	14.6642i	0.357054	−	0.718972i
$417$		−	34.9615i		−	1.71207i
$418$	−0.955262	+	0.793582i	−0.0467234	+	0.0388153i
$419$	−7.82113	+	7.82113i	−0.382087	+	0.382087i	−0.871854	−	0.489766i	$-0.837082\pi$
$419$	−7.82113	+	7.82113i	−0.382087	+	0.382087i	0.489766	+	0.871854i	$0.337082\pi$
$420$	−15.3963	+	10.5563i	−0.751260	+	0.515094i
$421$		−	33.8784i		−	1.65113i	−0.564305	−	0.825566i	$-0.690856\pi$
$421$		−	33.8784i		−	1.65113i	0.564305	−	0.825566i	$-0.309144\pi$
$422$	−8.79670	+	7.30784i	−0.428217	+	0.355740i
$423$			3.62264i			0.176139i
$424$	14.8208	+	4.20669i	0.719762	+	0.204295i
$425$	4.11549	−	0.250472i	0.199631	−	0.0121497i
$426$	−23.5847	−	2.18040i	−1.14268	−	0.105640i
$427$	−18.6507			−0.902571
$428$	−3.01559	−	4.39821i	−0.145764	−	0.212596i
$429$		−	6.12335i		−	0.295638i
$430$	−6.01822	−	7.24434i	−0.290224	−	0.349353i
$431$	25.1392	+	25.1392i	1.21091	+	1.21091i	0.970727	+	0.240186i	$0.0772086\pi$
$431$	25.1392	+	25.1392i	1.21091	+	1.21091i	0.240186	+	0.970727i	$0.422791\pi$
$432$	−11.3520	+	5.02393i	−0.546175	+	0.241714i
$433$		−	9.12065i		−	0.438310i	−0.975690	−	0.219155i	$-0.929670\pi$
$433$		−	9.12065i		−	0.438310i	0.975690	−	0.219155i	$-0.0703301\pi$
$434$	−44.4116	−	4.10584i	−2.13183	−	0.197087i
$435$	3.54557	−	3.54557i	0.169997	−	0.169997i
$436$	−20.4707	+	14.0355i	−0.980369	+	0.672180i
$437$	−5.14056	−	5.14056i	−0.245906	−	0.245906i
$438$	5.28256	+	0.488371i	0.252411	+	0.0233353i
$439$	−17.2748	+	17.2748i	−0.824482	+	0.824482i	−0.986747	−	0.162265i	$-0.948120\pi$
$439$	−17.2748	+	17.2748i	−0.824482	+	0.824482i	0.162265	+	0.986747i	$0.448120\pi$
$440$	−2.70043	−	0.766481i	−0.128738	−	0.0365405i
$441$	−18.7950			−0.894999
$442$	−16.8685	−	0.529876i	−0.802355	−	0.0252036i
$443$			5.15762i			0.245046i	0.992466	+	0.122523i	$0.0390985\pi$
$443$			5.15762i			0.245046i	−0.992466	+	0.122523i	$0.960901\pi$
$444$	4.79515	−	25.7122i	0.227568	−	1.22025i
$445$	−6.70571	−	6.70571i	−0.317881	−	0.317881i
$446$	1.40472	−	15.1944i	0.0665153	−	0.719475i
$447$	1.66231	−	1.66231i	0.0786244	−	0.0786244i
$448$	−8.06324	−	34.0881i	−0.380952	−	1.61051i
$449$	27.0200	+	27.0200i	1.27515	+	1.27515i	0.943347	+	0.331807i	$0.107658\pi$
$449$	27.0200	+	27.0200i	1.27515	+	1.27515i	0.331807	+	0.943347i	$0.392342\pi$
$450$	−2.17443	−	0.201025i	−0.102503	−	0.00947641i
$451$	2.63815			0.124226
$452$	−2.22343	−	3.24286i	−0.104582	−	0.152531i
$453$	−30.4687	+	30.4687i	−1.43155	+	1.43155i
$454$	−16.2657	+	13.5127i	−0.763388	+	0.634183i
$455$	−12.6732			−0.594129
$456$	−2.59895	−	4.65903i	−0.121707	−	0.218179i
$457$		−	15.2841i		−	0.714960i	−0.933921	−	0.357480i	$-0.883636\pi$
$457$		−	15.2841i		−	0.714960i	0.933921	−	0.357480i	$-0.116364\pi$
$458$	4.76320	+	0.440357i	0.222570	+	0.0205765i
$459$	9.58117	+	8.48184i	0.447210	+	0.395898i
$460$	3.01258	−	16.1538i	0.140462	−	0.753175i
$461$	−21.8561			−1.01794			−0.508971	−	0.860784i	$-0.669974\pi$
$461$	−21.8561			−1.01794			−0.508971	+	0.860784i	$0.669974\pi$
$462$	−8.37132	−	10.0769i	−0.389469	−	0.468818i
$463$	31.1063			1.44563			0.722816	−	0.691040i	$-0.242847\pi$
$463$	31.1063			1.44563			0.722816	+	0.691040i	$0.242847\pi$
$464$	3.80774	+	8.60394i	0.176770	+	0.399428i
$465$	−10.8569	−	10.8569i	−0.503475	−	0.503475i
$466$	−0.790471	+	0.656682i	−0.0366179	+	0.0304202i
$467$	−36.6639			−1.69661			−0.848303	−	0.529512i	$-0.822375\pi$
$467$	−36.6639			−1.69661			−0.848303	+	0.529512i	$0.822375\pi$
$468$	8.78691	+	1.63870i	0.406175	+	0.0757489i
$469$	15.8659	−	15.8659i	0.732619	−	0.732619i
$470$	2.12016	+	2.55211i	0.0977959	+	0.117720i
$471$	−11.4114	+	11.4114i	−0.525808	+	0.525808i
$472$	−7.19940	−	2.04346i	−0.331379	−	0.0940576i
$473$	4.67351	−	4.67351i	0.214888	−	0.214888i
$474$	2.73183	−	29.5494i	0.125477	−	1.35725i
$475$			0.884823i			0.0405984i
$476$	−28.4840	+	22.1892i	−1.30556	+	1.01704i
$477$			8.41065i			0.385097i
$478$	−32.7637	−	3.02899i	−1.49858	−	0.138543i
$479$	16.4540	−	16.4540i	0.751801	−	0.751801i	−0.223015	−	0.974815i	$-0.571590\pi$
$479$	16.4540	−	16.4540i	0.751801	−	0.751801i	0.974815	+	0.223015i	$0.0715897\pi$
$480$	5.36356	−	10.8002i	0.244812	−	0.492958i
$481$	12.5558	−	12.5558i	0.572497	−	0.572497i
$482$	−12.0598	+	10.0186i	−0.549308	+	0.456337i
$483$	54.2266	−	54.2266i	2.46740	−	2.46740i
$484$	−3.67216	+	19.6906i	−0.166916	+	0.895025i
$485$	−5.89584			−0.267716
$486$	−13.2544	−	15.9548i	−0.601231	−	0.723723i
$487$	16.7415	+	16.7415i	0.758628	+	0.758628i	0.976073	−	0.217445i	$-0.0697722\pi$
$487$	16.7415	+	16.7415i	0.758628	+	0.758628i	−0.217445	+	0.976073i	$0.569772\pi$
$488$	10.5215	−	5.86919i	0.476284	−	0.265686i
$489$	1.24337			0.0562272
$490$	−13.2409	+	10.9999i	−0.598163	+	0.496923i
$491$	−9.93950			−0.448563			−0.224282	−	0.974524i	$-0.572004\pi$
$491$	−9.93950			−0.448563			−0.224282	+	0.974524i	$0.572004\pi$
$492$	−2.07769	+	11.1408i	−0.0936696	+	0.502268i
$493$	6.42856	−	7.26176i	0.289528	−	0.327053i
$494$	0.333412	−	3.60641i	0.0150009	−	0.162260i
$495$		−	1.53247i		−	0.0688792i
$496$	26.3461	−	11.6596i	1.18297	−	0.523534i
$497$	−34.4011			−1.54310
$498$	−32.3534	−	38.9449i	−1.44979	−	1.74516i
$499$	7.00062	−	7.00062i	0.313391	−	0.313391i	−0.532831	−	0.846222i	$-0.678872\pi$
$499$	7.00062	−	7.00062i	0.313391	−	0.313391i	0.846222	+	0.532831i	$0.178872\pi$
$500$	−1.64952	+	1.13097i	−0.0737686	+	0.0505786i
$501$	35.1463			1.57022
$502$	0.486132	−	5.25835i	0.0216971	−	0.234691i
$503$	9.21563	+	9.21563i	0.410904	+	0.410904i	0.882054	−	0.471149i	$-0.156161\pi$
$503$	9.21563	+	9.21563i	0.410904	+	0.410904i	−0.471149	+	0.882054i	$0.656161\pi$
$504$	16.7004	−	9.31600i	0.743895	−	0.414967i
$505$	6.98351	−	6.98351i	0.310762	−	0.310762i
$506$	11.4828	+	1.06158i	0.510474	+	0.0471931i
$507$	−6.96794	−	6.96794i	−0.309457	−	0.309457i
$508$	−6.12148	+	32.8241i	−0.271597	+	1.45633i
$509$			9.64590i			0.427547i	0.976883	+	0.213773i	$0.0685754\pi$
$509$			9.64590i			0.427547i	−0.976883	+	0.213773i	$0.931425\pi$
$510$	−12.4237	−	0.390253i	−0.550129	−	0.0172807i
$511$	7.70527			0.340861
$512$	15.2759	+	16.6927i	0.675105	+	0.737721i
$513$	−1.94176	+	1.94176i	−0.0857306	+	0.0857306i
$514$	1.27726	−	13.8158i	0.0563376	−	0.609387i
$515$	12.3674	+	12.3674i	0.544975	+	0.544975i
$516$	16.0554	+	23.4167i	0.706801	+	1.03086i
$517$	−1.64643	+	1.64643i	−0.0724101	+	0.0724101i
$518$	3.49716	−	37.8277i	0.153656	−	1.66205i
$519$			25.6546i			1.12611i
$520$	7.14935	−	3.98813i	0.313520	−	0.174891i
$521$	5.27565	+	5.27565i	0.231130	+	0.231130i	0.813164	−	0.582034i	$-0.197743\pi$
$521$	5.27565	+	5.27565i	0.231130	+	0.231130i	−0.582034	+	0.813164i	$0.697743\pi$
$522$	−3.95101	+	3.28229i	−0.172931	+	0.143662i
$523$			13.5809i			0.593851i	0.954901	+	0.296926i	$0.0959613\pi$
$523$			13.5809i			0.593851i	−0.954901	+	0.296926i	$0.904039\pi$
$524$	16.1554	+	23.5626i	0.705754	+	1.02934i
$525$	−9.33381			−0.407361
$526$	0.575015	−	6.21976i	0.0250718	−	0.271194i
$527$	−22.2362	−	19.6848i	−0.968623	−	0.857485i
$528$	7.89361	+	3.05030i	0.343525	+	0.132747i
$529$			44.5053i			1.93501i
$530$	4.92237	+	5.92523i	0.213814	+	0.257375i
$531$		−	4.08559i		−	0.177299i
$532$	−4.38170	−	6.39068i	−0.189971	−	0.277071i
$533$	−5.44032	+	5.44032i	−0.235646	+	0.235646i
$534$	18.2687	+	21.9906i	0.790562	+	0.951627i
$535$		−	2.66637i		−	0.115277i
$536$	−3.95761	+	13.9433i	−0.170943	+	0.602258i
$537$	32.6346	+	32.6346i	1.40829	+	1.40829i
$538$	−22.3619	−	26.9178i	−0.964090	−	1.16051i
$539$	−8.54205	−	8.54205i	−0.367932	−	0.367932i
$540$	−6.10182	−	1.13795i	−0.262580	−	0.0489695i
$541$	7.01594	+	7.01594i	0.301639	+	0.301639i	0.841655	−	0.540016i	$-0.181582\pi$
$541$	7.01594	+	7.01594i	0.301639	+	0.301639i	−0.540016	+	0.841655i	$0.681582\pi$
$542$	9.13868	+	0.844868i	0.392540	+	0.0362902i
$543$	−50.3847			−2.16221
$544$	9.08599	−	21.4813i	0.389559	−	0.921002i
$545$	−12.4101			−0.531592
$546$	38.0433	+	3.51709i	1.62810	+	0.150517i
$547$	14.2910	+	14.2910i	0.611040	+	0.611040i	0.943217	−	0.332177i	$-0.107783\pi$
$547$	14.2910	+	14.2910i	0.611040	+	0.611040i	−0.332177	+	0.943217i	$0.607783\pi$
$548$	26.2208	+	4.89001i	1.12010	+	0.208891i
$549$	4.65076	+	4.65076i	0.198490	+	0.198490i
$550$	−0.896882	−	1.07961i	−0.0382432	−	0.0460346i
$551$	1.47170	+	1.47170i	0.0626964	+	0.0626964i
$552$	−13.5264	+	47.6555i	−0.575721	+	2.02835i
$553$		−	43.1014i		−	1.83286i
$554$	−22.8601	−	27.5175i	−0.971232	−	1.16910i
$555$	9.24736	−	9.24736i	0.392528	−	0.392528i
$556$	18.5489	+	27.0534i	0.786648	+	1.14732i
$557$		−	0.412029i		−	0.0174582i	−0.999962	−	0.00872911i	$-0.997221\pi$
$557$		−	0.412029i		−	0.0174582i	0.999962	−	0.00872911i	$-0.00277860\pi$
$558$	10.0507	+	12.0984i	0.425480	+	0.512164i
$559$			19.2751i			0.815251i
$560$	6.31306	−	16.3370i	0.266775	−	0.690365i
$561$	−0.529904	−	8.70680i	−0.0223725	−	0.367602i
$562$	3.10883	−	33.6273i	0.131138	−	1.41848i
$563$	−39.9825			−1.68506			−0.842531	−	0.538648i	$-0.818935\pi$
$563$	−39.9825			−1.68506			−0.842531	+	0.538648i	$0.818935\pi$
$564$	−5.65618	−	8.24950i	−0.238168	−	0.347366i
$565$		−	1.96595i		−	0.0827080i
$566$	23.4994	−	19.5221i	0.987753	−	0.820574i
$567$	−34.8255	−	34.8255i	−1.46253	−	1.46253i
$568$	19.4068	−	10.8257i	0.814290	−	0.454236i
$569$		−	17.6654i		−	0.740573i	−0.928918	−	0.370287i	$-0.879259\pi$
$569$		−	17.6654i		−	0.740573i	0.928918	−	0.370287i	$-0.120741\pi$
$570$	0.245557	−	2.65612i	0.0102853	−	0.111253i
$571$	−20.3803	+	20.3803i	−0.852889	+	0.852889i	−0.990488	−	0.137599i	$-0.956061\pi$
$571$	−20.3803	+	20.3803i	−0.852889	+	0.852889i	0.137599	+	0.990488i	$0.456061\pi$
$572$	3.24876	+	4.73829i	0.135837	+	0.198118i
$573$	23.3933	+	23.3933i	0.977268	+	0.977268i
$574$	−1.51528	+	16.3904i	−0.0632468	+	0.684121i
$575$	5.80970	−	5.80970i	0.242281	−	0.242281i
$576$	−6.48957	+	10.5109i	−0.270399	+	0.437954i
$577$	35.3577			1.47196			0.735979	−	0.677004i	$-0.236722\pi$
$577$	35.3577			1.47196			0.735979	+	0.677004i	$0.236722\pi$
$578$	−24.0313	+	0.706341i	−0.999568	+	0.0293799i
$579$			10.3709i			0.431000i
$580$	−0.862475	+	4.62469i	−0.0358123	+	0.192030i
$581$	−51.9987	−	51.9987i	−2.15727	−	2.15727i
$582$	17.6985	+	1.63622i	0.733627	+	0.0678236i
$583$	−3.82252	+	3.82252i	−0.158313	+	0.158313i
$584$	−4.34679	+	2.42477i	−0.179871	+	0.100338i
$585$	3.16020	+	3.16020i	0.130658	+	0.130658i
$586$	−3.65822	+	39.5698i	−0.151120	+	1.63461i
$587$	10.6133			0.438056			0.219028	−	0.975719i	$-0.429711\pi$
$587$	10.6133			0.438056			0.219028	+	0.975719i	$0.429711\pi$
$588$	42.8001	−	29.3454i	1.76505	−	1.21019i
$589$	4.50647	−	4.50647i	0.185686	−	0.185686i
$590$	−2.39111	−	2.87826i	−0.0984404	−	0.118496i
$591$	−22.5586			−0.927936
$592$	9.93112	+	22.4403i	0.408167	+	0.922290i
$593$			20.2462i			0.831412i	0.909499	+	0.415706i	$0.136465\pi$
$593$			20.2462i			0.831412i	−0.909499	+	0.415706i	$0.863535\pi$
$594$	0.400994	−	4.33743i	0.0164530	−	0.177967i
$595$	−18.0201	+	1.09672i	−0.738750	+	0.0449610i
$596$	−0.404363	+	2.16824i	−0.0165633	+	0.0888147i
$597$	−51.1794			−2.09463
$598$	−25.8687	+	21.4904i	−1.05785	+	0.878806i
$599$	−39.0195			−1.59429			−0.797146	−	0.603787i	$-0.793658\pi$
$599$	−39.0195			−1.59429			−0.797146	+	0.603787i	$0.793658\pi$
$600$	5.26549	−	2.93725i	0.214963	−	0.119913i
$601$	−21.0592	−	21.0592i	−0.859021	−	0.859021i	0.132202	−	0.991223i	$-0.457795\pi$
$601$	−21.0592	−	21.0592i	−0.859021	−	0.859021i	−0.991223	+	0.132202i	$0.957795\pi$
$602$	26.3513	+	31.7200i	1.07400	+	1.29281i
$603$	−7.91267			−0.322229
$604$	7.41164	−	39.7421i	0.301575	−	1.61708i
$605$	−7.08169	+	7.08169i	−0.287912	+	0.287912i
$606$	−22.9016	+	19.0255i	−0.930315	+	0.772857i
$607$	−9.13377	+	9.13377i	−0.370728	+	0.370728i	−0.867742	−	0.497014i	$-0.834430\pi$
$607$	−9.13377	+	9.13377i	−0.370728	+	0.370728i	0.497014	+	0.867742i	$0.334430\pi$
$608$	4.48294	+	2.22631i	0.181807	+	0.0902886i
$609$	−15.5246	+	15.5246i	−0.629089	+	0.629089i
$610$	5.99830	+	0.554541i	0.242864	+	0.0224527i
$611$		−	6.79046i		−	0.274712i
$612$	12.6359	+	1.56967i	0.510777	+	0.0634500i
$613$			26.8697i			1.08526i	0.839972	+	0.542629i	$0.182571\pi$
$613$			26.8697i			1.08526i	−0.839972	+	0.542629i	$0.817429\pi$
$614$	2.48269	−	26.8545i	0.100193	−	1.08376i
$615$	−4.00679	+	4.00679i	−0.161569	+	0.161569i
$616$	11.8241	+	3.35611i	0.476405	+	0.135221i
$617$	−9.66232	+	9.66232i	−0.388991	+	0.388991i	−0.874327	−	0.485337i	$-0.838697\pi$
$617$	−9.66232	+	9.66232i	−0.388991	+	0.388991i	0.485337	+	0.874327i	$0.338697\pi$
$618$	−33.6932	−	40.5577i	−1.35534	−	1.63147i
$619$	−7.13126	+	7.13126i	−0.286629	+	0.286629i	−0.835746	−	0.549116i	$-0.814964\pi$
$619$	−7.13126	+	7.13126i	−0.286629	+	0.286629i	0.549116	+	0.835746i	$0.314964\pi$
$620$	14.1612	+	2.64098i	0.568729	+	0.106064i
$621$	25.4989			1.02324
$622$	29.7826	−	24.7418i	1.19417	−	0.992057i
$623$	29.3615	+	29.3615i	1.17635	+	1.17635i
$624$	−22.5682	+	9.98773i	−0.903451	+	0.399829i
$625$	−1.00000			−0.0400000
$626$	11.5028	+	13.8463i	0.459745	+	0.553411i
$627$	1.87195			0.0747583
$628$	2.77586	−	14.8845i	0.110769	−	0.593956i
$629$	16.7666	−	18.9397i	0.668528	−	0.755176i
$630$	9.52093	+	0.880207i	0.379323	+	0.0350683i
$631$		−	17.1466i		−	0.682597i	−0.939955	−	0.341298i	$-0.889133\pi$
$631$		−	17.1466i		−	0.682597i	0.939955	−	0.341298i	$-0.110867\pi$
$632$	13.5636	+	24.3149i	0.539530	+	0.967193i
$633$	17.2381			0.685155
$634$	−11.8606	+	9.85313i	−0.471043	+	0.391318i
$635$	−11.8052	+	11.8052i	−0.468474	+	0.468474i
$636$	−13.1319	−	19.1528i	−0.520715	−	0.759458i
$637$	35.2303			1.39588
$638$	−3.28743	−	0.303922i	−0.130151	−	0.0120324i
$639$	8.57830	+	8.57830i	0.339352	+	0.339352i
$640$	1.57970	+	11.2029i	0.0624431	+	0.442833i
$641$	19.7569	−	19.7569i	0.780349	−	0.780349i	−0.199541	−	0.979890i	$-0.563945\pi$
$641$	19.7569	−	19.7569i	0.780349	−	0.780349i	0.979890	+	0.199541i	$0.0639450\pi$
$642$	−0.739975	+	8.00408i	−0.0292045	+	0.315896i
$643$	8.40557	+	8.40557i	0.331483	+	0.331483i	0.853150	−	0.521666i	$-0.174689\pi$
$643$	8.40557	+	8.40557i	0.331483	+	0.331483i	−0.521666	+	0.853150i	$0.674689\pi$
$644$	−13.1908	+	70.7309i	−0.519792	+	2.78719i
$645$			14.1961i			0.558972i
$646$	0.161986	−	5.15681i	0.00637326	−	0.202892i
$647$	14.5808			0.573229			0.286614	−	0.958046i	$-0.407470\pi$
$647$	14.5808			0.573229			0.286614	+	0.958046i	$0.407470\pi$
$648$	30.6053	+	8.68692i	1.20229	+	0.341254i
$649$	1.85684	−	1.85684i	0.0728873	−	0.0728873i
$650$	4.07586	+	0.376812i	0.159868	+	0.0147798i
$651$	47.5378	+	47.5378i	1.86315	+	1.86315i
$652$	−0.962128	+	0.659673i	−0.0376798	+	0.0258348i
$653$	−10.3318	+	10.3318i	−0.404313	+	0.404313i	−0.879750	−	0.475437i	$-0.842290\pi$
$653$	−10.3318	+	10.3318i	−0.404313	+	0.404313i	0.475437	+	0.879750i	$0.342290\pi$
$654$	37.2536	+	3.44408i	1.45673	+	0.134674i
$655$			14.2845i			0.558144i
$656$	−4.30306	−	9.72317i	−0.168006	−	0.379626i
$657$	−1.92139	−	1.92139i	−0.0749607	−	0.0749607i
$658$	−9.28333	−	11.1747i	−0.361902	−	0.435634i
$659$		−	26.6812i		−	1.03935i	−0.854364	−	0.519675i	$-0.826053\pi$
$659$		−	26.6812i		−	1.03935i	0.854364	−	0.519675i	$-0.173947\pi$
$660$	2.39271	+	3.48974i	0.0931359	+	0.135838i
$661$	26.3670			1.02556			0.512779	−	0.858521i	$-0.328616\pi$
$661$	26.3670			1.02556			0.512779	+	0.858521i	$0.328616\pi$
$662$	−28.9522	−	2.67662i	−1.12526	−	0.104030i
$663$	19.0477	+	16.8622i	0.739750	+	0.654872i
$664$	45.6976	+	12.9706i	1.77341	+	0.503359i
$665$		−	3.87428i		−	0.150238i
$666$	−10.3048	+	8.56069i	−0.399303	+	0.331720i
$667$		−	19.3262i		−	0.748312i
$668$	−27.1964	+	18.6469i	−1.05226	+	0.721472i
$669$	−16.2639	+	16.2639i	−0.628800	+	0.628800i
$670$	−5.57440	+	4.63093i	−0.215358	+	0.178908i
$671$			4.22740i			0.163197i
$672$	−23.4848	+	47.2895i	−0.905947	+	1.82423i
$673$	4.30861	+	4.30861i	0.166085	+	0.166085i	0.785256	−	0.619171i	$-0.212531\pi$
$673$	4.30861	+	4.30861i	0.166085	+	0.166085i	−0.619171	+	0.785256i	$0.712531\pi$
$674$	32.7042	−	27.1690i	1.25972	−	1.04651i
$675$	−2.19451	−	2.19451i	−0.0844669	−	0.0844669i
$676$	9.08869	+	1.69498i	0.349565	+	0.0651915i
$677$	−10.8363	−	10.8363i	−0.416473	−	0.416473i	0.467513	−	0.883986i	$-0.345150\pi$
$677$	−10.8363	−	10.8363i	−0.416473	−	0.416473i	−0.883986	+	0.467513i	$0.845150\pi$
$678$	−0.545593	+	5.90151i	−0.0209534	+	0.226646i
$679$	25.8155			0.990706
$680$	9.82055	−	6.28942i	0.376601	−	0.241188i
$681$	31.8746			1.22144
$682$	−0.930637	+	10.0664i	−0.0356359	+	0.385463i
$683$	36.2238	+	36.2238i	1.38607	+	1.38607i	0.833409	+	0.552657i	$0.186386\pi$
$683$	36.2238	+	36.2238i	1.38607	+	1.38607i	0.552657	+	0.833409i	$0.313614\pi$
$684$	−0.500960	+	2.68621i	−0.0191547	+	0.102710i
$685$	9.43030	+	9.43030i	0.360313	+	0.360313i
$686$	24.6349	−	20.4654i	0.940566	−	0.781374i
$687$	−5.09849	−	5.09849i	−0.194520	−	0.194520i
$688$	−24.8476	−	9.60176i	−0.947305	−	0.366064i
$689$		−	15.7654i		−	0.600612i
$690$	−19.0523	+	15.8276i	−0.725307	+	0.602548i
$691$	−8.12118	+	8.12118i	−0.308944	+	0.308944i	−0.844500	−	0.535556i	$-0.820102\pi$
$691$	−8.12118	+	8.12118i	−0.308944	+	0.308944i	0.535556	+	0.844500i	$0.320102\pi$
$692$	−13.6111	−	19.8517i	−0.517417	−	0.754649i
$693$			6.71004i			0.254893i
$694$	−15.4313	+	12.8195i	−0.585764	+	0.486622i
$695$			16.4008i			0.622119i
$696$	3.87249	−	13.6434i	0.146786	−	0.517150i
$697$	−7.26481	+	8.20640i	−0.275174	+	0.310839i
$698$	13.2396	+	1.22400i	0.501128	+	0.0463291i
$699$	1.54902			0.0585893
$700$	7.22255	−	4.95207i	0.272987	−	0.187171i
$701$			39.5912i			1.49534i	0.664071	+	0.747669i	$0.268827\pi$
$701$			39.5912i			1.49534i	−0.664071	+	0.747669i	$0.731173\pi$
$702$	8.11761	+	9.77145i	0.306379	+	0.368799i
$703$	3.83839	+	3.83839i	0.144768	+	0.144768i
$704$	−7.72646	+	1.82763i	−0.291202	+	0.0688814i
$705$		−	5.00116i		−	0.188355i
$706$	−1.26930	−	0.117347i	−0.0477709	−	0.00441641i
$707$	−30.5779	+	30.5779i	−1.15000	+	1.15000i
$708$	6.37901	+	9.30374i	0.239738	+	0.349656i
$709$	4.50038	+	4.50038i	0.169015	+	0.169015i	0.786547	−	0.617531i	$-0.211867\pi$
$709$	4.50038	+	4.50038i	0.169015	+	0.169015i	−0.617531	+	0.786547i	$0.711867\pi$
$710$	11.0638	+	1.02285i	0.415218	+	0.0383868i
$711$	−10.7478	+	10.7478i	−0.403074	+	0.403074i
$712$	−25.8035	−	7.32399i	−0.967029	−	0.274478i
$713$	−59.1785			−2.21625
$714$	54.3981	+	1.70876i	2.03580	+	0.0639487i
$715$			2.87253i			0.107427i
$716$	−42.5671	−	7.93849i	−1.59081	−	0.296675i
$717$	35.0700	+	35.0700i	1.30971	+	1.30971i
$718$	−3.31772	+	35.8868i	−0.123816	+	1.33928i
$719$	−8.59852	+	8.59852i	−0.320671	+	0.320671i	−0.849024	−	0.528354i	$-0.822810\pi$
$719$	−8.59852	+	8.59852i	−0.320671	+	0.320671i	0.528354	+	0.849024i	$0.322810\pi$
$720$	−5.64805	+	2.49959i	−0.210490	+	0.0931541i
$721$	−54.1520	−	54.1520i	−2.01673	−	2.01673i
$722$	−25.6535	−	2.37165i	−0.954723	−	0.0882638i
$723$	23.6326			0.878904
$724$	38.9879	−	26.7317i	1.44898	−	0.993475i
$725$	−1.66327	+	1.66327i	−0.0617722	+	0.0617722i
$726$	23.2236	−	19.2930i	0.861909	−	0.716029i
$727$	26.4711			0.981760			0.490880	−	0.871227i	$-0.336675\pi$
$727$	26.4711			0.981760			0.490880	+	0.871227i	$0.336675\pi$
$728$	−31.3041	+	17.4624i	−1.16021	+	0.647199i
$729$		−	2.47896i		−	0.0918135i
$730$	−2.47811	−	0.229100i	−0.0917189	−	0.00847939i
$731$	1.66803	+	27.4073i	0.0616945	+	1.01370i
$732$	−17.8522	−	3.32931i	−0.659836	−	0.123055i
$733$	−36.5266			−1.34914			−0.674570	−	0.738211i	$-0.735671\pi$
$733$	−36.5266			−1.34914			−0.674570	+	0.738211i	$0.735671\pi$
$734$	2.42277	+	2.91637i	0.0894262	+	0.107645i
$735$	25.9471			0.957072
$736$	−14.8169	−	44.0526i	−0.546159	−	1.62380i
$737$	−3.59619	−	3.59619i	−0.132467	−	0.132467i
$738$	4.46497	−	3.70927i	0.164358	−	0.136540i
$739$	49.3647			1.81591			0.907954	−	0.419070i	$-0.137644\pi$
$739$	49.3647			1.81591			0.907954	+	0.419070i	$0.137644\pi$
$740$	−2.24946	+	12.0619i	−0.0826917	+	0.443403i
$741$	−3.86027	+	3.86027i	−0.141811	+	0.141811i
$742$	−21.5531	−	25.9442i	−0.791237	−	0.952440i
$743$	15.9999	−	15.9999i	0.586980	−	0.586980i	−0.349832	−	0.936812i	$-0.613761\pi$
$743$	15.9999	−	15.9999i	0.586980	−	0.586980i	0.936812	+	0.349832i	$0.113761\pi$
$744$	−41.7772	−	11.8579i	−1.53163	−	0.434732i
$745$	−0.779807	+	0.779807i	−0.0285699	+	0.0285699i
$746$	−3.95237	+	42.7515i	−0.144706	+	1.56525i
$747$			25.9329i			0.948835i
$748$	5.02945	+	6.45623i	0.183895	+	0.236063i
$749$			11.6749i			0.426593i
$750$	3.00187	+	0.277522i	0.109613	+	0.0101337i
$751$	13.3306	−	13.3306i	0.486439	−	0.486439i	−0.420741	−	0.907181i	$-0.638230\pi$
$751$	13.3306	−	13.3306i	0.486439	−	0.486439i	0.907181	+	0.420741i	$0.138230\pi$
$752$	8.75357	+	3.38261i	0.319210	+	0.123351i
$753$	−5.62849	+	5.62849i	−0.205113	+	0.205113i
$754$	7.40598	−	6.15250i	0.269710	−	0.224061i
$755$	14.2932	−	14.2932i	0.520184	−	0.520184i
$756$	26.7174	+	4.98261i	0.971701	+	0.181216i
$757$	14.4656			0.525761			0.262881	−	0.964828i	$-0.415327\pi$
$757$	14.4656			0.525761			0.262881	+	0.964828i	$0.415327\pi$
$758$	34.5518	+	41.5913i	1.25498	+	1.51066i
$759$	−12.2911	−	12.2911i	−0.446139	−	0.446139i
$760$	1.21919	+	2.18560i	0.0442248	+	0.0792801i
$761$	42.9408			1.55660			0.778302	−	0.627890i	$-0.216081\pi$
$761$	42.9408			1.55660			0.778302	+	0.627890i	$0.216081\pi$
$762$	38.7137	−	32.1613i	1.40245	−	1.16508i
$763$	54.3389			1.96720
$764$	−30.5132	−	5.69051i	−1.10393	−	0.205875i
$765$	4.76698	+	4.22002i	0.172350	+	0.152575i
$766$	3.06406	−	33.1430i	0.110709	−	1.19750i
$767$			7.65824i			0.276523i
$768$	−1.63300	−	34.0679i	−0.0589259	−	1.22932i
$769$	9.17266			0.330774			0.165387	−	0.986229i	$-0.447113\pi$
$769$	9.17266			0.330774			0.165387	+	0.986229i	$0.447113\pi$
$770$	3.92708	+	4.72716i	0.141522	+	0.170355i
$771$	−14.7883	+	14.7883i	−0.532586	+	0.532586i
$772$	−5.50230	−	8.02506i	−0.198032	−	0.288828i
$773$	9.44541			0.339728			0.169864	−	0.985468i	$-0.445667\pi$
$773$	9.44541			0.339728			0.169864	+	0.985468i	$0.445667\pi$
$774$	1.33874	−	14.4807i	0.0481199	−	0.520499i
$775$	5.09308	+	5.09308i	0.182949	+	0.182949i
$776$	−14.5633	+	8.12386i	−0.522792	+	0.291630i
$777$	−40.4904	+	40.4904i	−1.45258	+	1.45258i
$778$	36.9420	+	3.41527i	1.32443	+	0.122443i
$779$	−1.66314	−	1.66314i	−0.0595881	−	0.0595881i
$780$	−12.1306	−	2.26228i	−0.434345	−	0.0810025i
$781$			7.79743i			0.279014i
$782$	−34.9230	+	32.7958i	−1.24884	+	1.17278i
$783$	−7.30012			−0.260885
$784$	−17.5497	+	45.4153i	−0.626775	+	1.62198i
$785$	5.35320	−	5.35320i	0.191064	−	0.191064i
$786$	3.96427	−	42.8803i	0.141401	−	1.52949i
$787$	13.3322	+	13.3322i	0.475243	+	0.475243i	0.903606	−	0.428364i	$-0.140910\pi$
$787$	13.3322	+	13.3322i	0.475243	+	0.475243i	−0.428364	+	0.903606i	$0.640910\pi$
$788$	17.4560	−	11.9685i	0.621843	−	0.426360i
$789$	−6.65757	+	6.65757i	−0.237016	+	0.237016i
$790$	−1.28153	+	13.8619i	−0.0455949	+	0.493186i
$791$			8.60808i			0.306068i
$792$	−2.11158	−	3.78534i	−0.0750317	−	0.134506i
$793$	−8.71762	−	8.71762i	−0.309572	−	0.309572i
$794$	−17.7341	+	14.7326i	−0.629361	+	0.522841i
$795$		−	11.6112i		−	0.411806i
$796$	39.6029	−	27.1533i	1.40369	−	0.962424i
$797$	6.04966			0.214290			0.107145	−	0.994243i	$-0.465829\pi$
$797$	6.04966			0.214290			0.107145	+	0.994243i	$0.465829\pi$
$798$	−1.07520	+	11.6301i	−0.0380615	+	0.411700i
$799$	−0.587633	−	9.65536i	−0.0207890	−	0.341582i
$800$	−2.51610	+	5.06648i	−0.0889577	+	0.179127i
$801$		−	14.6432i		−	0.517394i
$802$	14.2339	+	17.1338i	0.502616	+	0.605016i
$803$		−	1.74649i		−	0.0616323i
$804$	18.0188	−	12.3544i	0.635474	−	0.435706i
$805$	−25.4383	+	25.4383i	−0.896583	+	0.896583i
$806$	−18.8395	−	22.6778i	−0.663594	−	0.798791i
$807$			52.7486i			1.85684i
$808$	7.62741	−	26.8725i	0.268331	−	0.945372i
$809$	−5.30400	−	5.30400i	−0.186479	−	0.186479i	0.607693	−	0.794172i	$-0.292095\pi$
$809$	−5.30400	−	5.30400i	−0.186479	−	0.186479i	−0.794172	+	0.607693i	$0.792095\pi$
$810$	10.1648	+	12.2358i	0.357156	+	0.429921i
$811$	14.5428	+	14.5428i	0.510667	+	0.510667i	0.914731	−	0.404064i	$-0.132403\pi$
$811$	14.5428	+	14.5428i	0.510667	+	0.510667i	−0.404064	+	0.914731i	$0.632403\pi$
$812$	3.77642	−	20.2496i	0.132526	−	0.710623i
$813$	−9.78196	−	9.78196i	−0.343068	−	0.343068i
$814$	−8.57409	−	0.792672i	−0.300522	−	0.0277831i
$815$	−0.583279			−0.0204314
$816$	−31.2254	+	16.1546i	−1.09311	+	0.565523i
$817$	−5.89253			−0.206153
$818$	−9.19941	−	0.850483i	−0.321650	−	0.0297364i
$819$	−13.8372	−	13.8372i	−0.483512	−	0.483512i
$820$	0.974668	−	5.22629i	0.0340369	−	0.182510i
$821$	−21.4559	−	21.4559i	−0.748815	−	0.748815i	0.225442	−	0.974257i	$-0.427618\pi$
$821$	−21.4559	−	21.4559i	−0.748815	−	0.748815i	−0.974257	+	0.225442i	$0.927618\pi$
$822$	−25.6914	−	30.9256i	−0.896090	−	1.07865i
$823$	−9.88466	−	9.88466i	−0.344558	−	0.344558i	0.513520	−	0.858078i	$-0.328341\pi$
$823$	−9.88466	−	9.88466i	−0.344558	−	0.344558i	−0.858078	+	0.513520i	$0.828341\pi$
$824$	47.5899	+	13.5078i	1.65787	+	0.470565i
$825$			2.11562i			0.0736563i
$826$	10.4697	+	12.6027i	0.364287	+	0.438505i
$827$	−33.5090	+	33.5090i	−1.16522	+	1.16522i	−0.181905	+	0.983316i	$0.558226\pi$
$827$	−33.5090	+	33.5090i	−1.16522	+	1.16522i	−0.983316	+	0.181905i	$0.941774\pi$
$828$	20.9268	−	14.3482i	0.727257	−	0.498636i
$829$		−	39.0084i		−	1.35482i	−0.735606	−	0.677410i	$-0.763102\pi$
$829$		−	39.0084i		−	1.35482i	0.735606	−	0.677410i	$-0.236898\pi$
$830$	15.1773	+	18.2695i	0.526813	+	0.634143i
$831$			53.9237i			1.87059i
$832$	12.1644	−	19.7022i	0.421725	−	0.683049i
$833$	50.0940	−	3.04876i	1.73565	−	0.105633i
$834$	4.55158	−	49.2331i	0.157608	−	1.70480i
$835$	−16.4875			−0.570574
$836$	−1.44852	+	0.993164i	−0.0500982	+	0.0343493i
$837$			22.3537i			0.772655i
$838$	−12.0320	+	9.99556i	−0.415639	+	0.345291i
$839$	8.39531	+	8.39531i	0.289838	+	0.289838i	0.837016	−	0.547178i	$-0.184298\pi$
$839$	8.39531	+	8.39531i	0.289838	+	0.289838i	−0.547178	+	0.837016i	$0.684298\pi$
$840$	−23.0554	+	12.8610i	−0.795488	+	0.443748i
$841$		−	23.4671i		−	0.809210i
$842$	4.41058	−	47.7079i	0.151998	−	1.64412i
$843$	−35.9943	+	35.9943i	−1.23971	+	1.23971i
$844$	−13.3390	+	9.14573i	−0.459147	+	0.314809i
$845$	3.26874	+	3.26874i	0.112448	+	0.112448i
$846$	−0.471625	+	5.10143i	−0.0162148	+	0.175391i
$847$	31.0078	−	31.0078i	1.06544	−	1.06544i
$848$	20.3231	+	7.85339i	0.697899	+	0.269686i
$849$	−46.0498			−1.58042
$850$	5.82808	+	0.183072i	0.199901	+	0.00627932i
$851$		−	50.4054i		−	1.72787i
$852$	−32.9283	−	6.14090i	−1.12810	−	0.210384i
$853$	−32.9919	−	32.9919i	−1.12962	−	1.12962i	−0.990239	−	0.139383i	$-0.955488\pi$
$853$	−32.9919	−	32.9919i	−1.12962	−	1.12962i	−0.139383	−	0.990239i	$-0.544512\pi$
$854$	−26.2641	−	2.42811i	−0.898739	−	0.0830881i
$855$	−0.966093	+	0.966093i	−0.0330397	+	0.0330397i
$856$	−3.67398	−	6.58620i	−0.125574	−	0.225112i
$857$	8.97068	+	8.97068i	0.306433	+	0.306433i	0.843524	−	0.537091i	$-0.180477\pi$
$857$	8.97068	+	8.97068i	0.306433	+	0.306433i	−0.537091	+	0.843524i	$0.680477\pi$
$858$	0.797190	−	8.62296i	0.0272156	−	0.294383i
$859$	−15.4863			−0.528387			−0.264193	−	0.964470i	$-0.585106\pi$
$859$	−15.4863			−0.528387			−0.264193	+	0.964470i	$0.585106\pi$
$860$	−7.53178	−	10.9850i	−0.256831	−	0.374587i
$861$	17.5441	−	17.5441i	0.597901	−	0.597901i
$862$	32.1284	+	38.6741i	1.09430	+	1.31724i
$863$	−45.5571			−1.55078			−0.775391	−	0.631482i	$-0.782447\pi$
$863$	−45.5571			−1.55078			−0.775391	+	0.631482i	$0.782447\pi$
$864$	−16.6401	+	5.59683i	−0.566107	+	0.190408i
$865$		−	12.0349i		−	0.409198i
$866$	1.18740	−	12.8438i	0.0403496	−	0.436449i
$867$	28.5431	+	22.3280i	0.969375	+	0.758298i
$868$	−62.0063	−	11.5638i	−2.10463	−	0.392499i
$869$	−9.76944			−0.331406
$870$	5.45450	−	4.53131i	0.184925	−	0.153626i
$871$	14.8319			0.502560
$872$	−30.6543	+	17.0999i	−1.03809	+	0.579076i
$873$	−6.43737	−	6.43737i	−0.217872	−	0.217872i
$874$	−6.56973	−	7.90821i	−0.222225	−	0.267499i
$875$	4.37859			0.148023
$876$	7.37537	+	1.37546i	0.249191	+	0.0464724i
$877$	−17.7481	+	17.7481i	−0.599311	+	0.599311i	−0.940129	−	0.340818i	$-0.889296\pi$
$877$	−17.7481	+	17.7481i	−0.599311	+	0.599311i	0.340818	+	0.940129i	$0.389296\pi$
$878$	−26.5755	+	22.0776i	−0.896880	+	0.745081i
$879$	42.3552	−	42.3552i	1.42860	−	1.42860i
$880$	−3.70298	−	1.43093i	−0.124827	−	0.0482366i
$881$	−10.2814	+	10.2814i	−0.346389	+	0.346389i	−0.858763	−	0.512374i	$-0.828766\pi$
$881$	−10.2814	+	10.2814i	−0.346389	+	0.346389i	0.512374	+	0.858763i	$0.328766\pi$
$882$	−26.4673	−	2.44689i	−0.891199	−	0.0823911i
$883$		−	48.7290i		−	1.63986i	−0.572462	−	0.819931i	$-0.694011\pi$
$883$		−	48.7290i		−	1.63986i	0.572462	−	0.819931i	$-0.305989\pi$
$884$	−23.6854	−	2.94226i	−0.796627	−	0.0989591i
$885$			5.64028i			0.189596i
$886$	−0.671463	+	7.26301i	−0.0225582	+	0.244005i
$887$	−15.2064	+	15.2064i	−0.510581	+	0.510581i	−0.914705	−	0.404123i	$-0.867577\pi$
$887$	−15.2064	+	15.2064i	−0.510581	+	0.510581i	0.404123	+	0.914705i	$0.367577\pi$
$888$	10.1000	−	35.5838i	0.338934	−	1.19411i
$889$	51.6900	−	51.6900i	1.73363	−	1.73363i
$890$	−8.57003	−	10.3160i	−0.287268	−	0.345794i
$891$	−7.89360	+	7.89360i	−0.264446	+	0.264446i
$892$	3.95627	−	21.2140i	0.132466	−	0.710297i
$893$	2.07588			0.0694668
$894$	2.55729	−	2.12446i	0.0855285	−	0.0710526i
$895$	−15.3092	−	15.3092i	−0.511731	−	0.511731i
$896$	−6.91686	−	49.0528i	−0.231076	−	1.63874i
$897$	50.6927			1.69258
$898$	34.5321	+	41.5675i	1.15235	+	1.38713i
$899$	16.9423			0.565057
$900$	−3.03588	−	0.566170i	−0.101196	−	0.0188723i
$901$	−1.36431	−	22.4168i	−0.0454516	−	0.746811i
$902$	3.71507	+	0.343457i	0.123698	+	0.0114359i
$903$		−	62.1590i		−	2.06852i
$904$	−2.70887	−	4.85609i	−0.0900958	−	0.161511i
$905$	23.6360			0.785687
$906$	−46.8730	+	38.9397i	−1.55725	+	1.29368i
$907$	−16.4947	+	16.4947i	−0.547696	+	0.547696i	−0.925774	−	0.378078i	$-0.876585\pi$
$907$	−16.4947	+	16.4947i	−0.547696	+	0.547696i	0.378078	+	0.925774i	$0.376585\pi$
$908$	−24.6647	+	16.9111i	−0.818527	+	0.561215i
$909$	15.2499			0.505807
$910$	−17.8465	−	1.64991i	−0.591606	−	0.0546938i
$911$	14.8103	+	14.8103i	0.490688	+	0.490688i	0.908523	−	0.417835i	$-0.137211\pi$
$911$	14.8103	+	14.8103i	0.490688	+	0.490688i	−0.417835	+	0.908523i	$0.637211\pi$
$912$	−3.05331	−	6.89923i	−0.101105	−	0.228456i
$913$	−11.7861	+	11.7861i	−0.390064	+	0.390064i
$914$	1.98981	−	21.5232i	0.0658172	−	0.711924i
$915$	−6.42052	−	6.42052i	−0.212256	−	0.212256i
$916$	6.65025	+	1.24023i	0.219731	+	0.0409783i
$917$		−	62.5462i		−	2.06546i
$918$	12.3880	+	13.1915i	0.408866	+	0.435386i
$919$	4.60055			0.151758			0.0758790	−	0.997117i	$-0.475824\pi$
$919$	4.60055			0.151758			0.0758790	+	0.997117i	$0.475824\pi$
$920$	6.34537	−	22.3557i	0.209201	−	0.737046i
$921$	−28.7448	+	28.7448i	−0.947174	+	0.947174i
$922$	−30.7780	−	2.84542i	−1.01362	−	0.0937088i
$923$	−16.0796	−	16.0796i	−0.529267	−	0.529267i
$924$	−10.4767	−	15.2802i	−0.344657	−	0.502680i
$925$	−4.33804	+	4.33804i	−0.142634	+	0.142634i
$926$	43.8042	+	4.04968i	1.43949	+	0.133081i
$927$			27.0068i			0.887019i
$928$	4.24196	+	12.6119i	0.139249	+	0.414005i
$929$	−17.1776	−	17.1776i	−0.563577	−	0.563577i	0.366744	−	0.930322i	$-0.380472\pi$
$929$	−17.1776	−	17.1776i	−0.563577	−	0.563577i	−0.930322	+	0.366744i	$0.880472\pi$
$930$	−13.8753	−	16.7022i	−0.454989	−	0.547686i
$931$			10.7701i			0.352976i
$932$	−1.19864	+	0.821835i	−0.0392628	+	0.0269201i
$933$	−58.3624			−1.91070
$934$	−51.6305	−	4.77322i	−1.68940	−	0.156185i
$935$	0.248584	+	4.08446i	0.00812955	+	0.133576i
$936$	12.1605	+	3.45158i	0.397477	+	0.112819i
$937$			37.4944i			1.22489i	0.790514	+	0.612444i	$0.209813\pi$
$937$			37.4944i			1.22489i	−0.790514	+	0.612444i	$0.790187\pi$
$938$	24.4080	−	20.2769i	0.796951	−	0.662065i
$939$		−	27.1335i		−	0.885468i
$940$	2.65338	+	3.86993i	0.0865436	+	0.126223i
$941$	19.6760	−	19.6760i	0.641418	−	0.641418i	−0.309486	−	0.950904i	$-0.600157\pi$
$941$	19.6760	−	19.6760i	0.641418	−	0.641418i	0.950904	+	0.309486i	$0.100157\pi$
$942$	−17.5552	+	14.5839i	−0.571979	+	0.475171i
$943$			21.8402i			0.711214i
$944$	−9.87223	−	3.81489i	−0.321314	−	0.124164i
$945$	9.60888	+	9.60888i	0.312577	+	0.312577i
$946$	7.18971	−	5.97284i	0.233758	−	0.194194i
$947$	−17.7346	−	17.7346i	−0.576297	−	0.576297i	0.357584	−	0.933881i	$-0.383601\pi$
$947$	−17.7346	−	17.7346i	−0.576297	−	0.576297i	−0.933881	+	0.357584i	$0.883601\pi$
$948$	7.69397	−	41.2560i	0.249889	−	1.33993i
$949$	3.60156	+	3.60156i	0.116912	+	0.116912i
$950$	−0.115194	+	1.24601i	−0.00373738	+	0.0404261i
$951$	23.2421			0.753678
$952$	−43.0002	+	27.5388i	−1.39364	+	0.892537i
$953$	0.964814			0.0312534			0.0156267	−	0.999878i	$-0.495026\pi$
$953$	0.964814			0.0312534			0.0156267	+	0.999878i	$0.495026\pi$
$954$	−1.09497	+	11.8440i	−0.0354509	+	0.383462i
$955$	−10.9740	−	10.9740i	−0.355112	−	0.355112i
$956$	−45.7438	−	8.53091i	−1.47946	−	0.275909i
$957$	3.51884	+	3.51884i	0.113748	+	0.113748i
$958$	25.3127	−	21.0285i	0.817817	−	0.679400i
$959$	−41.2914	−	41.2914i	−1.33337	−	1.33337i
$960$	8.95906	−	14.5106i	0.289153	−	0.468328i
$961$		−	20.8789i		−	0.673512i
$962$	19.3158	−	16.0466i	0.622768	−	0.517363i
$963$	2.91127	−	2.91127i	0.0938145	−	0.0938145i
$964$	−18.2870	+	12.5383i	−0.588985	+	0.403831i
$965$		−	4.86510i		−	0.156613i
$966$	83.4221	−	69.3027i	2.68406	−	2.22978i
$967$			28.7887i			0.925783i	0.886415	+	0.462892i	$0.153188\pi$
$967$			28.7887i			0.925783i	−0.886415	+	0.462892i	$0.846812\pi$
$968$	−7.73465	+	27.2503i	−0.248601	+	0.875859i
$969$	−5.15486	+	5.82298i	−0.165598	+	0.187061i
$970$	−8.30257	−	0.767570i	−0.266579	−	0.0246452i
$971$	17.9776			0.576928			0.288464	−	0.957491i	$-0.406855\pi$
$971$	17.9776			0.576928			0.288464	+	0.957491i	$0.406855\pi$
$972$	−16.5878	−	24.1932i	−0.532054	−	0.775997i
$973$		−	71.8125i		−	2.30220i
$974$	21.3959	+	25.7550i	0.685569	+	0.825244i
$975$	−4.36276	−	4.36276i	−0.139720	−	0.139720i
$976$	15.5805	−	6.89527i	0.498720	−	0.220712i
$977$		−	6.40440i		−	0.204895i	−0.994738	−	0.102447i	$-0.967333\pi$
$977$		−	6.40440i		−	0.204895i	0.994738	−	0.102447i	$-0.0326673\pi$
$978$	1.75093	+	0.161873i	0.0559885	+	0.00517612i
$979$	6.65514	−	6.65514i	0.212699	−	0.212699i
$980$	−20.0780	+	13.7663i	−0.641368	+	0.439747i
$981$	−13.5500	−	13.5500i	−0.432618	−	0.432618i
$982$	−13.9969	−	1.29401i	−0.446659	−	0.0412935i
$983$	−17.7660	+	17.7660i	−0.566649	+	0.566649i	−0.931188	−	0.364539i	$-0.881226\pi$
$983$	−17.7660	+	17.7660i	−0.566649	+	0.566649i	0.364539	+	0.931188i	$0.381226\pi$
$984$	−4.37623	+	15.4181i	−0.139509	+	0.491512i
$985$	10.5825			0.337186
$986$	9.99815	−	9.38915i	0.318406	−	0.299012i
$987$			21.8981i			0.697023i
$988$	0.939026	−	5.03517i	0.0298744	−	0.160190i
$989$	38.6900	+	38.6900i	1.23027	+	1.23027i
$990$	0.199509	−	2.15803i	0.00634082	−	0.0685867i
$991$	−0.511129	+	0.511129i	−0.0162365	+	0.0162365i	−0.715178	−	0.698942i	$-0.753655\pi$
$991$	−0.511129	+	0.511129i	−0.0162365	+	0.0162365i	0.698942	+	0.715178i	$0.253655\pi$
$992$	38.6187	−	12.9893i	1.22614	−	0.412409i
$993$	30.9901	+	30.9901i	0.983442	+	0.983442i
$994$	−48.4440	−	4.47863i	−1.53655	−	0.142054i
$995$	24.0088			0.761131
$996$	−40.4902	−	59.0546i	−1.28298	−	1.87122i
$997$	−41.6071	+	41.6071i	−1.31771	+	1.31771i	−0.402123	+	0.915586i	$0.631728\pi$
$997$	−41.6071	+	41.6071i	−1.31771	+	1.31771i	−0.915586	+	0.402123i	$0.868272\pi$
$998$	10.7697	−	8.94694i	0.340910	−	0.283210i
$999$	−19.0398			−0.602391

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.ba.b.21.70	yes	140
8.5	even	2	inner	680.2.ba.b.21.1	✓	140
17.13	even	4	inner	680.2.ba.b.421.1	yes	140
136.13	even	4	inner	680.2.ba.b.421.70	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.ba.b.21.1	✓	140	8.5	even	2	inner
680.2.ba.b.21.70	yes	140	1.1	even	1	trivial
680.2.ba.b.421.1	yes	140	17.13	even	4	inner
680.2.ba.b.421.70	yes	140	136.13	even	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.ba (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40821 + 0.130188i) q^{2} +(-1.50733 - 1.50733i) q^{3} +(1.96610 + 0.366665i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.92640 - 2.31888i) q^{6} +(-3.09613 - 3.09613i) q^{7} +(2.72095 + 0.772304i) q^{8} +1.54411i q^{9} +(0.903697 + 1.08781i) q^{10} +(-0.701775 + 0.701775i) q^{11} +(-2.41089 - 3.51626i) q^{12} -2.89436i q^{13} +(-3.95692 - 4.76308i) q^{14} -2.13169i q^{15} +(3.73111 + 1.44180i) q^{16} +(-0.250472 - 4.11549i) q^{17} +(-0.201025 + 2.17443i) q^{18} +0.884823 q^{19} +(1.13097 + 1.64952i) q^{20} +9.33381i q^{21} +(-1.07961 + 0.896882i) q^{22} +(-5.80970 - 5.80970i) q^{23} +(-2.93725 - 5.26549i) q^{24} +1.00000i q^{25} +(0.376812 - 4.07586i) q^{26} +(-2.19451 + 2.19451i) q^{27} +(-4.95207 - 7.22255i) q^{28} +(1.66327 + 1.66327i) q^{29} +(0.277522 - 3.00187i) q^{30} +(5.09308 - 5.09308i) q^{31} +(5.06648 + 2.51610i) q^{32} +2.11562 q^{33} +(0.183072 - 5.82808i) q^{34} -4.37859i q^{35} +(-0.566170 + 3.03588i) q^{36} +(4.33804 + 4.33804i) q^{37} +(1.24601 + 0.115194i) q^{38} +(-4.36276 + 4.36276i) q^{39} +(1.37790 + 2.47010i) q^{40} +(-1.87963 - 1.87963i) q^{41} +(-1.21515 + 13.1439i) q^{42} -6.65956 q^{43} +(-1.63708 + 1.12244i) q^{44} +(-1.09185 + 1.09185i) q^{45} +(-7.42492 - 8.93763i) q^{46} +2.34610 q^{47} +(-3.45076 - 7.79731i) q^{48} +12.1721i q^{49} +(-0.130188 + 1.40821i) q^{50} +(-5.82587 + 6.58096i) q^{51} +(1.06126 - 5.69060i) q^{52} +5.44693 q^{53} +(-3.37603 + 2.80463i) q^{54} -0.992459 q^{55} +(-6.03325 - 10.8156i) q^{56} +(-1.33372 - 1.33372i) q^{57} +(2.12569 + 2.55876i) q^{58} -2.64592 q^{59} +(0.781616 - 4.19112i) q^{60} +(3.01194 - 3.01194i) q^{61} +(7.83517 - 6.50905i) q^{62} +(4.78076 - 4.78076i) q^{63} +(6.80709 + 4.20280i) q^{64} +(2.04662 - 2.04662i) q^{65} +(2.97923 + 0.275429i) q^{66} +5.12442i q^{67} +(1.01655 - 8.18331i) q^{68} +17.5143i q^{69} +(0.570042 - 6.16597i) q^{70} +(5.55550 - 5.55550i) q^{71} +(-1.19252 + 4.20144i) q^{72} +(-1.24434 + 1.24434i) q^{73} +(5.54410 + 6.67362i) q^{74} +(1.50733 - 1.50733i) q^{75} +(1.73965 + 0.324433i) q^{76} +4.34557 q^{77} +(-6.71166 + 5.57570i) q^{78} +(6.96053 + 6.96053i) q^{79} +(1.61879 + 3.65780i) q^{80} +11.2481 q^{81} +(-2.40220 - 2.89162i) q^{82} +16.7947 q^{83} +(-3.42238 + 18.3512i) q^{84} +(2.73298 - 3.08720i) q^{85} +(-9.37804 - 0.866997i) q^{86} -5.01420i q^{87} +(-2.45147 + 1.36751i) q^{88} -9.48330 q^{89} +(-1.67970 + 1.39541i) q^{90} +(-8.96131 + 8.96131i) q^{91} +(-9.29225 - 13.5527i) q^{92} -15.3539 q^{93} +(3.30380 + 0.305435i) q^{94} +(0.625664 + 0.625664i) q^{95} +(-3.84427 - 11.4295i) q^{96} +(-4.16899 + 4.16899i) q^{97} +(-1.58466 + 17.1408i) q^{98} +(-1.08362 - 1.08362i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 8 q^{4} - 4 q^{6} - 12 q^{7} + 20 q^{12} + 28 q^{14} - 24 q^{16} - 16 q^{17} - 8 q^{20} + 40 q^{22} + 4 q^{23} + 48 q^{24} - 20 q^{28} + 28 q^{31} - 8 q^{34} - 56 q^{38} + 24 q^{40} + 44 q^{41}+ \cdots + 176 q^{98}+O(q^{100}) \) 140 * q - 8 * q^4 - 4 * q^6 - 12 * q^7 + 20 * q^12 + 28 * q^14 - 24 * q^16 - 16 * q^17 - 8 * q^20 + 40 * q^22 + 4 * q^23 + 48 * q^24 - 20 * q^28 + 28 * q^31 - 8 * q^34 - 56 * q^38 + 24 * q^40 + 44 * q^41 + 28 * q^44 - 40 * q^46 - 120 * q^47 + 32 * q^48 - 48 * q^52 - 4 * q^54 + 16 * q^55 + 16 * q^56 - 16 * q^57 - 52 * q^58 - 72 * q^62 + 44 * q^63 - 104 * q^64 + 8 * q^68 + 12 * q^71 - 104 * q^72 + 36 * q^73 + 20 * q^74 + 28 * q^78 - 44 * q^79 - 76 * q^81 - 44 * q^82 + 48 * q^84 + 120 * q^86 + 28 * q^88 + 24 * q^89 + 28 * q^90 - 72 * q^92 + 8 * q^95 - 116 * q^96 + 12 * q^97 + 176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more