LMFDB - Embedded newform 680.2.ba.b.21.1

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)

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")

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);

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			21.1
Character	$\chi$	$=$	680.21
Dual form			680.2.ba.b.421.1

$q$-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} +(-2.31888 - 1.92640i) q^{6} +(-3.09613 - 3.09613i) q^{7} +(-2.72095 + 0.772304i) q^{8} +1.54411i q^{9} +(1.08781 + 0.903697i) q^{10} +(0.701775 - 0.701775i) q^{11} +(3.51626 + 2.41089i) q^{12} +2.89436i q^{13} +(4.76308 + 3.95692i) 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} +(-1.64952 - 1.13097i) q^{20} -9.33381i q^{21} +(-0.896882 + 1.07961i) q^{22} +(-5.80970 - 5.80970i) q^{23} +(-5.26549 - 2.93725i) q^{24} +1.00000i q^{25} +(-0.376812 - 4.07586i) q^{26} +(2.19451 - 2.19451i) q^{27} +(-7.22255 - 4.95207i) 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} +(0.888506 + 5.76286i) 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} +(2.47010 + 1.37790i) q^{40} +(-1.87963 - 1.87963i) q^{41} +(1.21515 + 13.1439i) q^{42} +6.65956 q^{43} +(1.12244 - 1.63708i) q^{44} +(1.09185 - 1.09185i) q^{45} +(8.93763 + 7.42492i) q^{46} +2.34610 q^{47} +(7.79731 + 3.45076i) 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} +(-2.80463 + 3.37603i) q^{54} -0.992459 q^{55} +(10.8156 + 6.03325i) q^{56} +(-1.33372 - 1.33372i) q^{57} +(2.55876 + 2.12569i) q^{58} +2.64592 q^{59} +(-0.781616 - 4.19112i) q^{60} +(-3.01194 + 3.01194i) q^{61} +(-6.50905 + 7.83517i) 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} +(-2.00146 - 7.99963i) 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} +(6.67362 + 5.54410i) q^{74} +(-1.50733 + 1.50733i) q^{75} +(-1.73965 + 0.324433i) q^{76} -4.34557 q^{77} +(5.57570 - 6.71166i) q^{78} +(6.96053 + 6.96053i) q^{79} +(-3.65780 - 1.61879i) q^{80} +11.2481 q^{81} +(2.89162 + 2.40220i) 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} +(-1.36751 + 2.45147i) q^{88} -9.48330 q^{89} +(-1.39541 + 1.67970i) q^{90} +(8.96131 - 8.96131i) q^{91} +(-13.5527 - 9.29225i) q^{92} +15.3539 q^{93} +(-3.30380 + 0.305435i) q^{94} +(0.625664 + 0.625664i) q^{95} +(-11.4295 - 3.84427i) 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	0.992500	−	0.122241i	$-0.0390081\pi$
$3$	1.50733	+	1.50733i	0.870259	+	0.870259i	−0.122241	+	0.992500i	$0.539008\pi$
$4$	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
$6$	−2.31888	−	1.92640i	−0.946678	−	0.786450i
$7$	−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
$10$	1.08781	+	0.903697i	0.343996	+	0.285774i
$11$	0.701775	−	0.701775i	0.211593	−	0.211593i	−0.593351	−	0.804944i	$-0.702195\pi$
$11$	0.701775	−	0.701775i	0.211593	−	0.211593i	0.804944	+	0.593351i	$0.202195\pi$
$12$	3.51626	+	2.41089i	1.01506	+	0.695963i
$13$			2.89436i			0.802750i	0.915914	+	0.401375i	$0.131468\pi$
$13$			2.89436i			0.802750i	−0.915914	+	0.401375i	$0.868532\pi$
$14$	4.76308	+	3.95692i	1.27299	+	1.05753i
$15$		−	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	$-0.532363\pi$
$19$	−0.884823			−0.202992			−0.101496	+	0.994836i	$0.532363\pi$
$20$	−1.64952	−	1.13097i	−0.368843	−	0.252893i
$21$		−	9.33381i		−	2.03680i
$22$	−0.896882	+	1.07961i	−0.191216	+	0.230173i
$23$	−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	$-0.577424\pi$
$24$	−5.26549	−	2.93725i	−1.07481	−	0.599564i
$25$			1.00000i			0.200000i
$26$	−0.376812	−	4.07586i	−0.0738989	−	0.799342i
$27$	2.19451	−	2.19451i	0.422334	−	0.422334i
$28$	−7.22255	−	4.95207i	−1.36493	−	0.935853i
$29$	−1.66327	−	1.66327i	−0.308861	−	0.308861i	0.535607	−	0.844468i	$-0.320083\pi$
$29$	−1.66327	−	1.66327i	−0.308861	−	0.308861i	−0.844468	+	0.535607i	$0.820083\pi$
$30$	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
$34$	0.888506	+	5.76286i	0.152378	+	0.988322i
$35$			4.37859i			0.740117i
$36$	0.566170	+	3.03588i	0.0943617	+	0.505979i
$37$	−4.33804	−	4.33804i	−0.713169	−	0.713169i	0.254028	−	0.967197i	$-0.418244\pi$
$37$	−4.33804	−	4.33804i	−0.713169	−	0.713169i	−0.967197	+	0.254028i	$0.918244\pi$
$38$	1.24601	−	0.115194i	0.202130	−	0.0186869i
$39$	−4.36276	+	4.36276i	−0.698601	+	0.698601i
$40$	2.47010	+	1.37790i	0.390557	+	0.217865i
$41$	−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	$-0.330464\pi$
$43$	6.65956			1.01557			0.507786	+	0.861483i	$0.330464\pi$
$44$	1.12244	−	1.63708i	0.169215	−	0.246799i
$45$	1.09185	−	1.09185i	0.162763	−	0.162763i
$46$	8.93763	+	7.42492i	1.31778	+	1.09474i
$47$	2.34610			0.342214			0.171107	−	0.985252i	$-0.445266\pi$
$47$	2.34610			0.342214			0.171107	+	0.985252i	$0.445266\pi$
$48$	7.79731	+	3.45076i	1.12544	+	0.498074i
$49$			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	$-0.622047\pi$
$53$	−5.44693			−0.748193			−0.374097	+	0.927390i	$0.622047\pi$
$54$	−2.80463	+	3.37603i	−0.381662	+	0.459420i
$55$	−0.992459			−0.133823
$56$	10.8156	+	6.03325i	1.44529	+	0.806227i
$57$	−1.33372	−	1.33372i	−0.176656	−	0.176656i
$58$	2.55876	+	2.12569i	0.335982	+	0.279117i
$59$	2.64592			0.344469			0.172235	−	0.985056i	$-0.444901\pi$
$59$	2.64592			0.344469			0.172235	+	0.985056i	$0.444901\pi$
$60$	−0.781616	−	4.19112i	−0.100906	−	0.541072i
$61$	−3.01194	+	3.01194i	−0.385639	+	0.385639i	−0.873129	−	0.487490i	$-0.837913\pi$
$61$	−3.01194	+	3.01194i	−0.385639	+	0.385639i	0.487490	+	0.873129i	$0.337913\pi$
$62$	−6.50905	+	7.83517i	−0.826651	+	0.995068i
$63$	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	$-0.898658\pi$
$67$		−	5.12442i		−	0.626048i	0.949745	−	0.313024i	$-0.101342\pi$
$68$	−2.00146	−	7.99963i	−0.242713	−	0.970098i
$69$		−	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	$0.282838\pi$
$74$	6.67362	+	5.54410i	0.775793	+	0.644488i
$75$	−1.50733	+	1.50733i	−0.174052	+	0.174052i
$76$	−1.73965	+	0.324433i	−0.199552	+	0.0372151i
$77$	−4.34557			−0.495224
$78$	5.57570	−	6.71166i	0.631323	−	0.759946i
$79$	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	$0.563196\pi$
$80$	−3.65780	−	1.61879i	−0.408955	−	0.180986i
$81$	11.2481			1.24978
$82$	2.89162	+	2.40220i	0.319326	+	0.265279i
$83$	−16.7947			−1.84346			−0.921731	−	0.387831i	$-0.873225\pi$
$83$	−16.7947			−1.84346			−0.921731	+	0.387831i	$0.873225\pi$
$84$	−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
$88$	−1.36751	+	2.45147i	−0.145777	+	0.261328i
$89$	−9.48330			−1.00523			−0.502614	−	0.864511i	$-0.667628\pi$
$89$	−9.48330			−1.00523			−0.502614	+	0.864511i	$0.667628\pi$
$90$	−1.39541	+	1.67970i	−0.147089	+	0.177056i
$91$	8.96131	−	8.96131i	0.939401	−	0.939401i
$92$	−13.5527	−	9.29225i	−1.41296	−	0.968784i
$93$	15.3539			1.59213
$94$	−3.30380	+	0.305435i	−0.340761	+	0.0315032i
$95$	0.625664	+	0.625664i	0.0641918	+	0.0641918i
$96$	−11.4295	−	3.84427i	−1.16652	−	0.392354i
$97$	−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	$0.163499\pi$
$101$			9.87617i			0.982716i	−0.870958	+	0.491358i	$0.836501\pi$
$102$	−7.34728	+	10.0258i	−0.727489	+	0.992705i
$103$	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	0.792344	−	0.610075i	$-0.208861\pi$
$107$	1.88541	+	1.88541i	0.182269	+	0.182269i	−0.610075	+	0.792344i	$0.708861\pi$
$108$	3.50999	−	5.11929i	0.337749	−	0.492604i
$109$	8.77529	−	8.77529i	0.840521	−	0.840521i	−0.148406	−	0.988927i	$-0.547414\pi$
$109$	8.77529	−	8.77529i	0.840521	−	0.840521i	0.988927	+	0.148406i	$0.0474142\pi$
$110$	1.39759	−	0.129207i	0.133255	−	0.0123194i
$111$		−	13.0777i		−	1.24128i
$112$	−16.0160	−	7.08801i	−1.51337	−	0.669754i
$113$	−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	$0.779476\pi$
$114$	2.05179	+	1.70452i	0.192168	+	0.159643i
$115$			8.21616i			0.766161i
$116$	−3.88001	−	2.66029i	−0.360250	−	0.247002i
$117$	−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
$122$	3.84932	−	4.63356i	0.348501	−	0.419502i
$123$		−	5.66646i		−	0.510927i
$124$	8.14606	−	11.8810i	0.731537	−	1.06694i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	−6.10991	+	7.35471i	−0.544314	+	0.655210i
$127$			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
$130$	−2.61562	+	3.14851i	−0.229405	+	0.276143i
$131$	−10.1007	−	10.1007i	−0.882502	−	0.882502i	0.111286	−	0.993788i	$-0.464503\pi$
$131$	−10.1007	−	10.1007i	−0.882502	−	0.882502i	−0.993788	+	0.111286i	$0.964503\pi$
$132$	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
$136$	3.85993	+	11.0046i	0.330986	+	0.943635i
$137$	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	0.0162120	−	0.999869i	$-0.494839\pi$
$139$	−11.5971	−	11.5971i	−0.983657	−	0.983657i	−0.999869	+	0.0162120i	$0.994839\pi$
$140$	1.60548	+	8.60876i	0.135687	+	0.727573i
$141$	3.53636	+	3.53636i	0.297815	+	0.297815i
$142$	−7.10005	+	8.54657i	−0.595823	+	0.717212i
$143$	2.03119	+	2.03119i	0.169856	+	0.169856i
$144$	2.22630	+	5.76125i	0.185525	+	0.480104i
$145$			2.35221i			0.195341i
$146$	1.59029	−	1.91429i	0.131613	−	0.158427i
$147$	−18.3474	+	18.3474i	−1.51326	+	1.51326i
$148$	−10.1196	−	6.93842i	−0.831828	−	0.570334i
$149$		−	1.10281i		−	0.0903460i	−0.998979	−	0.0451730i	$-0.985616\pi$
$149$		−	1.10281i		−	0.0903460i	0.998979	−	0.0451730i	$-0.0143839\pi$
$150$	1.92640	−	2.31888i	0.157290	−	0.189336i
$151$		−	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
$156$	−6.97796	+	10.1773i	−0.558684	+	0.814837i
$157$			7.57056i			0.604197i	0.953277	+	0.302098i	$0.0976871\pi$
$157$			7.57056i			0.604197i	−0.953277	+	0.302098i	$0.902313\pi$
$158$	−10.7081	−	8.89569i	−0.851887	−	0.707703i
$159$	−8.21034	−	8.21034i	−0.651122	−	0.651122i
$160$	5.36170	+	1.80339i	0.423879	+	0.142570i
$161$			35.9752i			2.83524i
$162$	−15.8396	+	1.46437i	−1.24448	+	0.115051i
$163$	0.412441	−	0.412441i	0.0323049	−	0.0323049i	−0.690770	−	0.723075i	$-0.742728\pi$
$163$	0.412441	−	0.412441i	0.0323049	−	0.0323049i	0.723075	+	0.690770i	$0.242728\pi$
$164$	−4.38474	−	3.00635i	−0.342391	−	0.234757i
$165$	−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
$170$	3.44669	−	4.70323i	0.264349	−	0.360721i
$171$		−	1.36626i		−	0.104481i
$172$	13.0934	−	2.44183i	0.998360	−	0.186187i
$173$	8.50994	+	8.50994i	0.646999	+	0.646999i	0.952267	−	0.305268i	$-0.0987459\pi$
$173$	8.50994	+	8.50994i	0.646999	+	0.646999i	−0.305268	+	0.952267i	$0.598746\pi$
$174$	0.652790	+	7.06103i	0.0494879	+	0.535296i
$175$	3.09613	−	3.09613i	0.234046	−	0.234046i
$176$	1.60658	−	3.63022i	0.121101	−	0.273638i
$177$	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	$-0.199945\pi$
$179$	21.6505			1.61824			0.809118	+	0.587646i	$0.199945\pi$
$180$	1.74635	−	2.54703i	0.130165	−	0.189844i
$181$	−16.7132	+	16.7132i	−1.24228	+	1.24228i	−0.283228	+	0.959053i	$0.591405\pi$
$181$	−16.7132	+	16.7132i	−1.24228	+	1.24228i	−0.959053	+	0.283228i	$0.908595\pi$
$182$	−11.4527	+	13.7861i	−0.848933	+	1.02189i
$183$	−9.07999			−0.671212
$184$	20.2947	+	11.3210i	1.49615	+	0.834597i
$185$			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
$190$	−0.962520	−	0.799611i	−0.0698285	−	0.0580099i
$191$	−15.5196			−1.12296			−0.561481	−	0.827490i	$-0.689768\pi$
$191$	−15.5196			−1.12296			−0.561481	+	0.827490i	$0.689768\pi$
$192$	16.5956	+	3.92554i	1.19768	+	0.283302i
$193$	−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	$0.806025\pi$
$194$	5.32805	−	6.41355i	0.382532	−	0.460466i
$195$	6.16988			0.441834
$196$	4.46307	+	23.9315i	0.318791	+	1.70939i
$197$	−7.48294	+	7.48294i	−0.533138	+	0.533138i	−0.921505	−	0.388367i	$-0.873039\pi$
$197$	−7.48294	+	7.48294i	−0.533138	+	0.533138i	0.388367	+	0.921505i	$0.373039\pi$
$198$	−1.66703	−	1.38488i	−0.118471	−	0.0984194i
$199$	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
$204$	9.04125	−	15.0750i	0.633014	−	1.05546i
$205$			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
$210$	8.43493	−	10.1534i	0.582065	−	0.700652i
$211$	5.71809	−	5.71809i	0.393650	−	0.393650i	−0.482336	−	0.875986i	$-0.660212\pi$
$211$	5.71809	−	5.71809i	0.393650	−	0.393650i	0.875986	+	0.482336i	$0.160212\pi$
$212$	−10.7092	+	1.99720i	−0.735512	+	0.137168i
$213$	16.7480			1.14755
$214$	−2.90050	−	2.40959i	−0.198274	−	0.164716i
$215$	−4.70902	−	4.70902i	−0.321152	−	0.321152i
$216$	−4.27632	+	7.66598i	−0.290967	+	0.521604i
$217$	−31.5377			−2.14092
$218$	−11.2150	+	13.4999i	−0.759576	+	0.914327i
$219$	−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	$-0.117657\pi$
$224$	23.4767	+	7.89630i	1.56860	+	0.527594i
$225$	−1.54411			−0.102941
$226$	2.13858	+	1.77662i	0.142256	+	0.118179i
$227$	10.5732	−	10.5732i	0.701765	−	0.701765i	−0.263024	−	0.964789i	$-0.584720\pi$
$227$	10.5732	−	10.5732i	0.701765	−	0.701765i	0.964789	+	0.263024i	$0.0847198\pi$
$228$	−3.11126	−	2.13321i	−0.206048	−	0.141275i
$229$	−3.38246			−0.223519			−0.111760	−	0.993735i	$-0.535649\pi$
$229$	−3.38246			−0.223519			−0.111760	+	0.993735i	$0.535649\pi$
$230$	−1.06965	−	11.5701i	−0.0705306	−	0.762907i
$231$	−6.55023	−	6.55023i	−0.430973	−	0.430973i
$232$	5.81021	+	3.24111i	0.381459	+	0.212789i
$233$	−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
$238$	15.0916	−	20.5935i	0.978246	−	1.33488i
$239$	−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
$244$	−4.81740	+	7.02615i	−0.308403	+	0.449803i
$245$	8.60695	−	8.60695i	0.549878	−	0.549878i
$246$	0.737707	+	7.97956i	0.0470345	+	0.508758i
$247$		−	2.56099i		−	0.162952i
$248$	−9.92458	+	17.7914i	−0.630212	+	1.12975i
$249$	−25.3153	−	25.3153i	−1.60429	−	1.60429i
$250$	−0.903697	+	1.08781i	−0.0571548	+	0.0687992i
$251$			3.73407i			0.235692i	0.993032	+	0.117846i	$0.0375990\pi$
$251$			3.73407i			0.235692i	−0.993032	+	0.117846i	$0.962401\pi$
$252$	7.64653	−	11.1524i	0.481686	−	0.702536i
$253$	−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	$-0.0989884\pi$
$258$	−15.4427	−	12.8290i	−0.961420	−	0.798698i
$259$			26.8623i			1.66914i
$260$	3.27344	−	4.77429i	0.203010	−	0.296089i
$261$	2.56827	−	2.56827i	0.158972	−	0.158972i
$262$	15.5389	+	12.9089i	0.959996	+	0.797514i
$263$		−	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
$266$	−4.21448	−	3.50117i	−0.258406	−	0.214671i
$267$	−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	$0.0220539\pi$
$269$	17.4973	+	17.4973i	1.06683	+	1.06683i	0.0692289	+	0.997601i	$0.477946\pi$
$270$	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	$0.436845\pi$
$272$	−6.86826	−	14.9942i	−0.416449	−	0.909159i
$273$	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	$0.0247767\pi$
$277$	17.8871	+	17.8871i	1.07473	+	1.07473i	0.0777597	+	0.996972i	$0.475223\pi$
$278$	17.8410	+	14.8214i	1.07003	+	0.888927i
$279$	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	$-0.252330\pi$
$282$	−5.44032	−	4.51954i	−0.323966	−	0.269134i
$283$	−15.2752	+	15.2752i	−0.908019	+	0.908019i	−0.996112	−	0.0880930i	$-0.971923\pi$
$283$	−15.2752	+	15.2752i	−0.908019	+	0.908019i	0.0880930	+	0.996112i	$0.471923\pi$
$284$	8.88568	−	12.9597i	0.527268	−	0.769016i
$285$			1.88617i			0.111727i
$286$	−3.12477	−	2.59590i	−0.184772	−	0.153499i
$287$			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
$292$	−1.99024	+	2.90275i	−0.116470	+	0.169871i
$293$		−	28.0994i		−	1.64158i	−0.571227	−	0.820792i	$-0.693532\pi$
$293$		−	28.0994i		−	1.64158i	0.571227	−	0.820792i	$-0.306468\pi$
$294$	23.4483	−	28.2255i	1.36753	−	1.64615i
$295$	−1.87095	−	1.87095i	−0.108931	−	0.108931i
$296$	15.1538	+	8.45328i	0.880799	+	0.491337i
$297$		−	3.08011i		−	0.178726i
$298$	0.143574	+	1.55299i	0.00831699	+	0.0899624i
$299$	16.8154	−	16.8154i	0.972457	−	0.972457i
$300$	−2.41089	+	3.51626i	−0.139193	+	0.203011i
$301$	−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
$306$	−8.89848	+	1.37195i	−0.508692	+	0.0784292i
$307$			19.0700i			1.08838i	0.838962	+	0.544190i	$0.183163\pi$
$307$			19.0700i			1.08838i	−0.838962	+	0.544190i	$0.816837\pi$
$308$	−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	$-0.0328780\pi$
$312$	8.50146	−	15.2402i	0.481300	−	0.862808i
$313$	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
$316$	16.2373	+	11.1329i	0.913419	+	0.626276i
$317$	7.70969	−	7.70969i	0.433019	−	0.433019i	−0.456635	−	0.889654i	$-0.650945\pi$
$317$	7.70969	−	7.70969i	0.433019	−	0.433019i	0.889654	+	0.456635i	$0.150945\pi$
$318$	12.6308	+	10.4930i	0.708298	+	0.588417i
$319$	−2.33448			−0.130706
$320$	−7.78517	−	1.84152i	−0.435204	−	0.102944i
$321$			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
$326$	−0.527108	+	0.634498i	−0.0291938	+	0.0351416i
$327$	26.4546			1.46294
$328$	6.56602	+	3.66273i	0.362548	+	0.202240i
$329$	−7.26384	−	7.26384i	−0.400468	−	0.400468i
$330$	2.30139	+	1.91188i	0.126687	+	0.105245i
$331$	20.5596			1.13006			0.565028	−	0.825072i	$-0.308865\pi$
$331$	20.5596			1.13006			0.565028	+	0.825072i	$0.308865\pi$
$332$	−33.0202	+	6.15804i	−1.81222	+	0.337966i
$333$	6.69840	−	6.69840i	0.367070	−	0.367070i
$334$	14.8997	−	17.9353i	0.815276	−	0.981376i
$335$	−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
$340$	−4.24135	+	7.07184i	−0.230020	+	0.383524i
$341$		−	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
$346$	−13.0917	−	10.8759i	−0.703812	−	0.584691i
$347$	10.0308	−	10.0308i	0.538480	−	0.538480i	−0.384602	−	0.923082i	$-0.625661\pi$
$347$	10.0308	−	10.0308i	0.538480	−	0.538480i	0.923082	+	0.384602i	$0.125661\pi$
$348$	−1.83853	−	9.85842i	−0.0985555	−	0.528467i
$349$	−9.40176			−0.503265			−0.251632	−	0.967823i	$-0.580967\pi$
$349$	−9.40176			−0.503265			−0.251632	+	0.967823i	$0.580967\pi$
$350$	−3.95692	+	4.76308i	−0.211506	+	0.254597i
$351$	6.35171	+	6.35171i	0.339029	+	0.339029i
$352$	−1.78979	+	5.32127i	−0.0953961	+	0.283624i
$353$	−0.901361			−0.0479746			−0.0239873	−	0.999712i	$-0.507636\pi$
$353$	−0.901361			−0.0479746			−0.0239873	+	0.999712i	$0.507636\pi$
$354$	−6.13556	−	5.09711i	−0.326101	−	0.270908i
$355$	−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	$0.765222\pi$
$360$	−2.12762	+	3.81410i	−0.112136	+	0.201021i
$361$	−18.2171			−0.958794
$362$	21.3598	−	25.7115i	1.12264	−	1.35137i
$363$	−15.0960	+	15.0960i	−0.792334	+	0.792334i
$364$	14.3331	−	20.9047i	0.751256	−	1.09570i
$365$	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	$0.727709\pi$
$368$	−30.0531	−	13.3002i	−1.56663	−	0.693322i
$369$	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	$-0.712169\pi$
$373$		−	30.3588i		−	1.57192i	0.618277	−	0.785960i	$-0.287831\pi$
$374$	4.66776	+	3.42070i	0.241364	+	0.176880i
$375$	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	$-0.810533\pi$
$379$	−27.0355	−	27.0355i	−1.38872	−	1.38872i	−0.560696	−	0.828021i	$-0.689467\pi$
$380$	1.45953	+	1.00071i	0.0748722	+	0.0513354i
$381$	−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	$-0.205353\pi$
$384$	−23.8811	−	3.36743i	−1.21868	−	0.171843i
$385$	3.07278	+	3.07278i	0.156604	+	0.156604i
$386$	5.29231	+	4.39658i	0.269372	+	0.223780i
$387$			10.2831i			0.522718i
$388$	−6.66803	+	9.72527i	−0.338518	+	0.493726i
$389$	−26.2333			−1.33008			−0.665041	−	0.746807i	$-0.731586\pi$
$389$	−26.2333			−1.33008			−0.665041	+	0.746807i	$0.731586\pi$
$390$	−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
$394$	9.56335	−	11.5117i	0.481795	−	0.579953i
$395$		−	9.84367i		−	0.495289i
$396$	2.52782	+	1.73318i	0.127028	+	0.0870954i
$397$	11.5277	−	11.5277i	0.578558	−	0.578558i	−0.355948	−	0.934506i	$-0.615842\pi$
$397$	11.5277	−	11.5277i	0.578558	−	0.578558i	0.934506	+	0.355948i	$0.115842\pi$
$398$	−21.6967	+	26.1171i	−1.08756	+	1.30913i
$399$			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	$0.621341\pi$
$402$	−9.87170	+	11.8829i	−0.492356	+	0.592666i
$403$	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
$408$	−10.7694	+	22.4058i	−0.533164	+	1.10925i
$409$	−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
$414$	−11.4649	+	13.8007i	−0.563468	+	0.678266i
$415$	11.8757	+	11.8757i	0.582954	+	0.582954i
$416$	−7.28250	−	14.6642i	−0.357054	−	0.718972i
$417$		−	34.9615i		−	1.71207i
$418$	0.793582	−	0.955262i	0.0388153	−	0.0467234i
$419$	7.82113	−	7.82113i	0.382087	−	0.382087i	−0.489766	−	0.871854i	$-0.662918\pi$
$419$	7.82113	−	7.82113i	0.382087	−	0.382087i	0.871854	+	0.489766i	$0.162918\pi$
$420$	−10.5563	+	15.3963i	−0.515094	+	0.751260i
$421$			33.8784i			1.65113i	0.564305	+	0.825566i	$0.309144\pi$
$421$			33.8784i			1.65113i	−0.564305	+	0.825566i	$0.690856\pi$
$422$	−7.30784	+	8.79670i	−0.355740	+	0.428217i
$423$			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
$428$	4.39821	+	3.01559i	0.212596	+	0.145764i
$429$			6.12335i			0.295638i
$430$	7.24434	+	6.01822i	0.349353	+	0.290224i
$431$	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	$0.422791\pi$
$432$	5.02393	−	11.3520i	0.241714	−	0.546175i
$433$		−	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
$436$	14.0355	−	20.4707i	0.672180	−	0.980369i
$437$	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
$442$	−16.6798	+	2.57166i	−0.793376	+	0.122321i
$443$		−	5.15762i		−	0.245046i	−0.992466	−	0.122523i	$-0.960901\pi$
$443$		−	5.15762i		−	0.245046i	0.992466	−	0.122523i	$-0.0390985\pi$
$444$	−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
$448$	−34.0881	−	8.06324i	−1.61051	−	0.380952i
$449$	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
$452$	−3.24286	−	2.22343i	−0.152531	−	0.104582i
$453$	30.4687	−	30.4687i	1.43155	−	1.43155i
$454$	−13.5127	+	16.2657i	−0.634183	+	0.763388i
$455$	−12.6732			−0.594129
$456$	4.65903	+	2.59895i	0.218179	+	0.121707i
$457$		−	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	$-0.330026\pi$
$461$	21.8561			1.01794			0.508971	+	0.860784i	$0.330026\pi$
$462$	10.0769	+	8.37132i	0.468818	+	0.389469i
$463$	31.1063			1.44563			0.722816	−	0.691040i	$-0.242847\pi$
$463$	31.1063			1.44563			0.722816	+	0.691040i	$0.242847\pi$
$464$	−8.60394	−	3.80774i	−0.399428	−	0.176770i
$465$	−10.8569	−	10.8569i	−0.503475	−	0.503475i
$466$	0.656682	−	0.790471i	0.0304202	−	0.0366179i
$467$	36.6639			1.69661			0.848303	−	0.529512i	$-0.177625\pi$
$467$	36.6639			1.69661			0.848303	+	0.529512i	$0.177625\pi$
$468$	−8.78691	+	1.63870i	−0.406175	+	0.0757489i
$469$	−15.8659	+	15.8659i	−0.732619	+	0.732619i
$470$	2.55211	+	2.12016i	0.117720	+	0.0977959i
$471$	−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
$476$	−18.5711	+	30.9647i	−0.851207	+	1.41926i
$477$		−	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
$482$	10.0186	−	12.0598i	0.456337	−	0.549308i
$483$	−54.2266	+	54.2266i	−2.46740	+	2.46740i
$484$	3.67216	+	19.6906i	0.166916	+	0.895025i
$485$	5.89584			0.267716
$486$	−15.9548	−	13.2544i	−0.723723	−	0.601231i
$487$	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	$0.569772\pi$
$488$	5.86919	−	10.5215i	0.265686	−	0.476284i
$489$	1.24337			0.0562272
$490$	−10.9999	+	13.2409i	−0.496923	+	0.598163i
$491$	9.93950			0.448563			0.224282	−	0.974524i	$-0.427996\pi$
$491$	9.93950			0.448563			0.224282	+	0.974524i	$0.427996\pi$
$492$	−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
$496$	11.6596	−	26.3461i	0.523534	−	1.18297i
$497$	−34.4011			−1.54310
$498$	38.9449	+	32.3534i	1.74516	+	1.44979i
$499$	−7.00062	+	7.00062i	−0.313391	+	0.313391i	−0.846222	−	0.532831i	$-0.821128\pi$
$499$	−7.00062	+	7.00062i	−0.313391	+	0.313391i	0.532831	+	0.846222i	$0.321128\pi$
$500$	1.13097	−	1.64952i	0.0505786	−	0.0737686i
$501$	−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	$0.656161\pi$
$504$	−9.31600	+	16.7004i	−0.414967	+	0.743895i
$505$	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	$-0.931425\pi$
$509$		−	9.64590i		−	0.427547i	0.976883	−	0.213773i	$-0.0685754\pi$
$510$	12.2846	−	1.89402i	0.543973	−	0.0838687i
$511$	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
$516$	23.4167	+	16.0554i	1.03086	+	0.706801i
$517$	1.64643	−	1.64643i	0.0724101	−	0.0724101i
$518$	−3.49716	−	37.8277i	−0.153656	−	1.66205i
$519$			25.6546i			1.12611i
$520$	−3.98813	+	7.14935i	−0.174891	+	0.313520i
$521$	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	$0.697743\pi$
$522$	−3.28229	+	3.95101i	−0.143662	+	0.172931i
$523$		−	13.5809i		−	0.593851i	−0.954901	−	0.296926i	$-0.904039\pi$
$523$		−	13.5809i		−	0.593851i	0.954901	−	0.296926i	$-0.0959613\pi$
$524$	−23.5626	−	16.1554i	−1.02934	−	0.705754i
$525$	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
$530$	−5.92523	−	4.92237i	−0.257375	−	0.213814i
$531$			4.08559i			0.177299i
$532$	6.39068	+	4.38170i	0.277071	+	0.189971i
$533$	5.44032	−	5.44032i	0.235646	−	0.235646i
$534$	21.9906	+	18.2687i	0.951627	+	0.790562i
$535$		−	2.66637i		−	0.115277i
$536$	3.95761	+	13.9433i	0.170943	+	0.602258i
$537$	32.6346	+	32.6346i	1.40829	+	1.40829i
$538$	−26.9178	−	22.3619i	−1.16051	−	0.964090i
$539$	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	0.540016	−	0.841655i	$-0.318418\pi$
$541$	−7.01594	−	7.01594i	−0.301639	−	0.301639i	−0.841655	+	0.540016i	$0.818418\pi$
$542$	−9.13868	+	0.844868i	−0.392540	+	0.0362902i
$543$	−50.3847			−2.16221
$544$	11.6240	+	20.2208i	0.498376	+	0.866961i
$545$	−12.4101			−0.531592
$546$	−38.0433	+	3.51709i	−1.62810	+	0.150517i
$547$	−14.2910	−	14.2910i	−0.611040	−	0.611040i	0.332177	−	0.943217i	$-0.392217\pi$
$547$	−14.2910	−	14.2910i	−0.611040	−	0.611040i	−0.943217	+	0.332177i	$0.892217\pi$
$548$	26.2208	−	4.89001i	1.12010	−	0.208891i
$549$	−4.65076	−	4.65076i	−0.198490	−	0.198490i
$550$	−1.07961	−	0.896882i	−0.0460346	−	0.0382432i
$551$	1.47170	+	1.47170i	0.0626964	+	0.0626964i
$552$	13.5264	+	47.6555i	0.575721	+	2.02835i
$553$		−	43.1014i		−	1.83286i
$554$	−27.5175	−	22.8601i	−1.16910	−	0.971232i
$555$	−9.24736	+	9.24736i	−0.392528	+	0.392528i
$556$	−27.0534	−	18.5489i	−1.14732	−	0.786648i
$557$			0.412029i			0.0174582i	0.999962	+	0.00872911i	$0.00277860\pi$
$557$			0.412029i			0.0174582i	−0.999962	+	0.00872911i	$0.997221\pi$
$558$	−12.0984	−	10.0507i	−0.512164	−	0.425480i
$559$			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	$-0.181065\pi$
$563$	39.9825			1.68506			0.842531	+	0.538648i	$0.181065\pi$
$564$	8.24950	+	5.65618i	0.347366	+	0.238168i
$565$			1.96595i			0.0827080i
$566$	19.5221	−	23.4994i	0.820574	−	0.987753i
$567$	−34.8255	−	34.8255i	−1.46253	−	1.46253i
$568$	−10.8257	+	19.4068i	−0.454236	+	0.814290i
$569$		−	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	−0.137599	−	0.990488i	$-0.543939\pi$
$571$	20.3803	−	20.3803i	0.852889	−	0.852889i	0.990488	+	0.137599i	$0.0439385\pi$
$572$	4.73829	+	3.24876i	0.198118	+	0.135837i
$573$	−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	$0.236722\pi$
$578$	23.4945	−	5.10008i	0.977240	−	0.212135i
$579$		−	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
$584$	2.42477	−	4.34679i	0.100338	−	0.179871i
$585$	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	$-0.570289\pi$
$587$	−10.6133			−0.438056			−0.219028	+	0.975719i	$0.570289\pi$
$588$	−29.3454	+	42.8001i	−1.21019	+	1.76505i
$589$	−4.50647	+	4.50647i	−0.185686	+	0.185686i
$590$	2.87826	+	2.39111i	0.118496	+	0.0984404i
$591$	−22.5586			−0.927936
$592$	−22.4403	−	9.93112i	−0.922290	−	0.408167i
$593$			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
$598$	−21.4904	+	25.8687i	−0.878806	+	1.05785i
$599$	−39.0195			−1.59429			−0.797146	−	0.603787i	$-0.793658\pi$
$599$	−39.0195			−1.59429			−0.797146	+	0.603787i	$0.793658\pi$
$600$	2.93725	−	5.26549i	0.119913	−	0.214963i
$601$	−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	$0.957795\pi$
$602$	31.7200	+	26.3513i	1.29281	+	1.07400i
$603$	7.91267			0.322229
$604$	−7.41164	−	39.7421i	−0.301575	−	1.61708i
$605$	7.08169	−	7.08169i	0.287912	−	0.287912i
$606$	19.0255	−	22.9016i	0.772857	−	0.930315i
$607$	−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
$612$	12.3523	−	3.09047i	0.499312	−	0.124925i
$613$		−	26.8697i		−	1.08526i	−0.839972	−	0.542629i	$-0.817429\pi$
$613$		−	26.8697i		−	1.08526i	0.839972	−	0.542629i	$-0.182571\pi$
$614$	−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	$0.338697\pi$
$618$	−40.5577	−	33.6932i	−1.63147	−	1.35534i
$619$	7.13126	−	7.13126i	0.286629	−	0.286629i	−0.549116	−	0.835746i	$-0.685036\pi$
$619$	7.13126	−	7.13126i	0.286629	−	0.286629i	0.835746	+	0.549116i	$0.185036\pi$
$620$	−14.1612	+	2.64098i	−0.568729	+	0.106064i
$621$	−25.4989			−1.02324
$622$	−24.7418	+	29.7826i	−0.992057	+	1.19417i
$623$	29.3615	+	29.3615i	1.17635	+	1.17635i
$624$	−9.98773	+	22.5682i	−0.399829	+	0.903451i
$625$	−1.00000			−0.0400000
$626$	−13.8463	−	11.5028i	−0.553411	−	0.459745i
$627$	−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	$-0.110867\pi$
$632$	−24.3149	−	13.5636i	−0.967193	−	0.539530i
$633$	17.2381			0.685155
$634$	−9.85313	+	11.8606i	−0.391318	+	0.471043i
$635$	11.8052	−	11.8052i	0.468474	−	0.468474i
$636$	−19.1528	−	13.1319i	−0.759458	−	0.520715i
$637$	−35.2303			−1.39588
$638$	3.28743	−	0.303922i	0.130151	−	0.0120324i
$639$	8.57830	+	8.57830i	0.339352	+	0.339352i
$640$	11.2029	+	1.57970i	0.442833	+	0.0624431i
$641$	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	0.521666	−	0.853150i	$-0.325311\pi$
$643$	−8.40557	−	8.40557i	−0.331483	−	0.331483i	−0.853150	+	0.521666i	$0.825311\pi$
$644$	13.1908	+	70.7309i	0.519792	+	2.78719i
$645$		−	14.1961i		−	0.558972i
$646$	−0.786171	−	5.09911i	−0.0309315	−	0.200622i
$647$	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
$652$	0.659673	−	0.962128i	0.0258348	−	0.0376798i
$653$	10.3318	−	10.3318i	0.404313	−	0.404313i	−0.475437	−	0.879750i	$-0.657710\pi$
$653$	10.3318	−	10.3318i	0.404313	−	0.404313i	0.879750	+	0.475437i	$0.157710\pi$
$654$	−37.2536	+	3.44408i	−1.45673	+	0.134674i
$655$			14.2845i			0.558144i
$656$	−9.72317	−	4.30306i	−0.379626	−	0.168006i
$657$	−1.92139	−	1.92139i	−0.0749607	−	0.0749607i
$658$	11.1747	+	9.28333i	0.435634	+	0.361902i
$659$			26.6812i			1.03935i	0.854364	+	0.519675i	$0.173947\pi$
$659$			26.6812i			1.03935i	−0.854364	+	0.519675i	$0.826053\pi$
$660$	−3.48974	−	2.39271i	−0.135838	−	0.0931359i
$661$	−26.3670			−1.02556			−0.512779	−	0.858521i	$-0.671384\pi$
$661$	−26.3670			−1.02556			−0.512779	+	0.858521i	$0.671384\pi$
$662$	−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
$666$	−8.56069	+	10.3048i	−0.331720	+	0.399303i
$667$			19.3262i			0.748312i
$668$	−18.6469	+	27.1964i	−0.721472	+	1.05226i
$669$	16.2639	−	16.2639i	0.628800	−	0.628800i
$670$	4.63093	−	5.57440i	0.178908	−	0.215358i
$671$			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	$0.712531\pi$
$674$	−27.1690	+	32.7042i	−1.04651	+	1.25972i
$675$	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	0.883986	−	0.467513i	$-0.154850\pi$
$677$	10.8363	+	10.8363i	0.416473	+	0.416473i	−0.467513	+	0.883986i	$0.654850\pi$
$678$	0.545593	+	5.90151i	0.0209534	+	0.226646i
$679$	25.8155			0.990706
$680$	5.05203	−	10.5108i	0.193737	−	0.403071i
$681$	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	$-0.813614\pi$
$683$	−36.2238	−	36.2238i	−1.38607	−	1.38607i	−0.552657	−	0.833409i	$-0.686386\pi$
$684$	−0.500960	−	2.68621i	−0.0191547	−	0.102710i
$685$	−9.43030	−	9.43030i	−0.360313	−	0.360313i
$686$	−20.4654	+	24.6349i	−0.781374	+	0.940566i
$687$	−5.09849	−	5.09849i	−0.194520	−	0.194520i
$688$	24.8476	−	9.60176i	0.947305	−	0.366064i
$689$		−	15.7654i		−	0.600612i
$690$	15.8276	−	19.0523i	0.602548	−	0.725307i
$691$	8.12118	−	8.12118i	0.308944	−	0.308944i	−0.535556	−	0.844500i	$-0.679898\pi$
$691$	8.12118	−	8.12118i	0.308944	−	0.308944i	0.844500	+	0.535556i	$0.179898\pi$
$692$	19.8517	+	13.6111i	0.754649	+	0.517417i
$693$		−	6.71004i		−	0.254893i
$694$	−12.8195	+	15.4313i	−0.486622	+	0.585764i
$695$			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
$700$	4.95207	−	7.22255i	0.187171	−	0.272987i
$701$		−	39.5912i		−	1.49534i	−0.664071	−	0.747669i	$-0.731173\pi$
$701$		−	39.5912i		−	1.49534i	0.664071	−	0.747669i	$-0.268827\pi$
$702$	−9.77145	−	8.11761i	−0.368799	−	0.306379i
$703$	3.83839	+	3.83839i	0.144768	+	0.144768i
$704$	1.82763	−	7.72646i	0.0688814	−	0.291202i
$705$		−	5.00116i		−	0.188355i
$706$	1.26930	−	0.117347i	0.0477709	−	0.00441641i
$707$	30.5779	−	30.5779i	1.15000	−	1.15000i
$708$	9.30374	+	6.37901i	0.349656	+	0.239738i
$709$	−4.50038	−	4.50038i	−0.169015	−	0.169015i	0.617531	−	0.786547i	$-0.288133\pi$
$709$	−4.50038	−	4.50038i	−0.169015	−	0.169015i	−0.786547	+	0.617531i	$0.788133\pi$
$710$	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
$714$	53.7894	−	8.29315i	2.01302	−	0.310363i
$715$		−	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	$0.322810\pi$
$720$	2.49959	−	5.64805i	0.0931541	−	0.210490i
$721$	−54.1520	−	54.1520i	−2.01673	−	2.01673i
$722$	25.6535	−	2.37165i	0.954723	−	0.0882638i
$723$	−23.6326			−0.878904
$724$	−26.7317	+	38.9879i	−0.993475	+	1.44898i
$725$	1.66327	−	1.66327i	0.0617722	−	0.0617722i
$726$	19.2930	−	23.2236i	0.716029	−	0.861909i
$727$	26.4711			0.981760			0.490880	−	0.871227i	$-0.336675\pi$
$727$	26.4711			0.981760			0.490880	+	0.871227i	$0.336675\pi$
$728$	−17.4624	+	31.3041i	−0.647199	+	1.16021i
$729$		−	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	$-0.264329\pi$
$733$	36.5266			1.34914			0.674570	+	0.738211i	$0.264329\pi$
$734$	−2.91637	−	2.42277i	−0.107645	−	0.0894262i
$735$	25.9471			0.957072
$736$	44.0526	+	14.8169i	1.62380	+	0.546159i
$737$	−3.59619	−	3.59619i	−0.132467	−	0.132467i
$738$	−3.70927	+	4.46497i	−0.136540	+	0.164358i
$739$	−49.3647			−1.81591			−0.907954	−	0.419070i	$-0.862356\pi$
$739$	−49.3647			−1.81591			−0.907954	+	0.419070i	$0.862356\pi$
$740$	2.24946	+	12.0619i	0.0826917	+	0.443403i
$741$	3.86027	−	3.86027i	0.141811	−	0.141811i
$742$	−25.9442	−	21.5531i	−0.952440	−	0.791237i
$743$	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
$748$	−7.01852	−	4.20937i	−0.256622	−	0.153910i
$749$		−	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
$754$	−6.15250	+	7.40598i	−0.224061	+	0.269710i
$755$	−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	$-0.584673\pi$
$757$	−14.4656			−0.525761			−0.262881	+	0.964828i	$0.584673\pi$
$758$	41.5913	+	34.5518i	1.51066	+	1.25498i
$759$	−12.2911	−	12.2911i	−0.446139	−	0.446139i
$760$	−2.18560	−	1.21919i	−0.0792801	−	0.0442248i
$761$	42.9408			1.55660			0.778302	−	0.627890i	$-0.216081\pi$
$761$	42.9408			1.55660			0.778302	+	0.627890i	$0.216081\pi$
$762$	32.1613	−	38.7137i	1.16508	−	1.40245i
$763$	−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
$768$	34.0679	+	1.63300i	1.22932	+	0.0589259i
$769$	9.17266			0.330774			0.165387	−	0.986229i	$-0.447113\pi$
$769$	9.17266			0.330774			0.165387	+	0.986229i	$0.447113\pi$
$770$	−4.72716	−	3.92708i	−0.170355	−	0.141522i
$771$	14.7883	−	14.7883i	0.532586	−	0.532586i
$772$	−8.02506	−	5.50230i	−0.288828	−	0.198032i
$773$	−9.44541			−0.339728			−0.169864	−	0.985468i	$-0.554333\pi$
$773$	−9.44541			−0.339728			−0.169864	+	0.985468i	$0.554333\pi$
$774$	−1.33874	−	14.4807i	−0.0481199	−	0.520499i
$775$	5.09308	+	5.09308i	0.182949	+	0.182949i
$776$	8.12386	−	14.5633i	0.291630	−	0.522792i
$777$	−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
$782$	28.3185	−	38.6425i	1.01267	−	1.38185i
$783$	−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	0.428364	−	0.903606i	$-0.359090\pi$
$787$	−13.3322	−	13.3322i	−0.475243	−	0.475243i	−0.903606	+	0.428364i	$0.859090\pi$
$788$	−11.9685	+	17.4560i	−0.426360	+	0.621843i
$789$	6.65757	−	6.65757i	0.237016	−	0.237016i
$790$	1.28153	+	13.8619i	0.0455949	+	0.493186i
$791$			8.60808i			0.306068i
$792$	−3.78534	−	2.11158i	−0.134506	−	0.0750317i
$793$	−8.71762	−	8.71762i	−0.309572	−	0.309572i
$794$	−14.7326	+	17.7341i	−0.522841	+	0.629361i
$795$			11.6112i			0.411806i
$796$	27.1533	−	39.6029i	0.962424	−	1.40369i
$797$	−6.04966			−0.214290			−0.107145	−	0.994243i	$-0.534171\pi$
$797$	−6.04966			−0.214290			−0.107145	+	0.994243i	$0.534171\pi$
$798$	−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
$802$	−17.1338	−	14.2339i	−0.605016	−	0.502616i
$803$			1.74649i			0.0616323i
$804$	12.3544	−	18.0188i	0.435706	−	0.635474i
$805$	25.4383	−	25.4383i	0.896583	−	0.896583i
$806$	−22.6778	−	18.8395i	−0.798791	−	0.663594i
$807$			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	$0.792095\pi$
$810$	12.2358	+	10.1648i	0.429921	+	0.357156i
$811$	−14.5428	−	14.5428i	−0.510667	−	0.510667i	0.404064	−	0.914731i	$-0.367597\pi$
$811$	−14.5428	−	14.5428i	−0.510667	−	0.510667i	−0.914731	+	0.404064i	$0.867597\pi$
$812$	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
$816$	12.2486	−	32.9541i	0.428785	−	1.15362i
$817$	−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	0.974257	−	0.225442i	$-0.0723825\pi$
$821$	21.4559	+	21.4559i	0.748815	+	0.748815i	−0.225442	+	0.974257i	$0.572382\pi$
$822$	−30.9256	−	25.6914i	−1.07865	−	0.896090i
$823$	−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
$826$	12.6027	+	10.4697i	0.438505	+	0.364287i
$827$	33.5090	−	33.5090i	1.16522	−	1.16522i	0.181905	−	0.983316i	$-0.441774\pi$
$827$	33.5090	−	33.5090i	1.16522	−	1.16522i	0.983316	−	0.181905i	$-0.0582264\pi$
$828$	14.3482	−	20.9268i	0.498636	−	0.727257i
$829$			39.0084i			1.35482i	0.735606	+	0.677410i	$0.236898\pi$
$829$			39.0084i			1.35482i	−0.735606	+	0.677410i	$0.763102\pi$
$830$	−18.2695	−	15.1773i	−0.634143	−	0.526813i
$831$			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
$836$	−0.993164	+	1.44852i	−0.0343493	+	0.0500982i
$837$		−	22.3537i		−	0.772655i
$838$	−9.99556	+	12.0320i	−0.345291	+	0.415639i
$839$	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	$0.684298\pi$
$840$	12.8610	−	23.0554i	0.443748	−	0.795488i
$841$		−	23.4671i		−	0.809210i
$842$	−4.41058	−	47.7079i	−0.151998	−	1.64412i
$843$	35.9943	−	35.9943i	1.23971	−	1.23971i
$844$	9.14573	−	13.3390i	0.314809	−	0.459147i
$845$	−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
$850$	−5.76286	+	0.888506i	−0.197664	+	0.0304755i
$851$			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	$0.0445119\pi$
$853$	32.9919	+	32.9919i	1.12962	+	1.12962i	0.139383	+	0.990239i	$0.455488\pi$
$854$	−26.2641	+	2.42811i	−0.898739	+	0.0830881i
$855$	−0.966093	+	0.966093i	−0.0330397	+	0.0330397i
$856$	−6.58620	−	3.67398i	−0.225112	−	0.125574i
$857$	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	$-0.414894\pi$
$859$	15.4863			0.528387			0.264193	+	0.964470i	$0.414894\pi$
$860$	−10.9850	−	7.53178i	−0.374587	−	0.256831i
$861$	−17.5441	+	17.5441i	−0.597901	+	0.597901i
$862$	−38.6741	−	32.1284i	−1.31724	−	1.09430i
$863$	−45.5571			−1.55078			−0.775391	−	0.631482i	$-0.782447\pi$
$863$	−45.5571			−1.55078			−0.775391	+	0.631482i	$0.782447\pi$
$864$	−5.59683	+	16.6401i	−0.190408	+	0.566107i
$865$		−	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
$870$	4.53131	−	5.45450i	0.153626	−	0.184925i
$871$	14.8319			0.502560
$872$	−17.0999	+	30.6543i	−0.579076	+	1.03809i
$873$	−6.43737	−	6.43737i	−0.217872	−	0.217872i
$874$	−7.90821	−	6.56973i	−0.267499	−	0.222225i
$875$	−4.37859			−0.148023
$876$	−7.37537	+	1.37546i	−0.249191	+	0.0464724i
$877$	17.7481	−	17.7481i	0.599311	−	0.599311i	−0.340818	−	0.940129i	$-0.610704\pi$
$877$	17.7481	−	17.7481i	0.599311	−	0.599311i	0.940129	+	0.340818i	$0.110704\pi$
$878$	22.0776	−	26.5755i	0.745081	−	0.896880i
$879$	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	$0.305989\pi$
$883$			48.7290i			1.63986i	−0.572462	+	0.819931i	$0.694011\pi$
$884$	23.1538	−	5.79294i	0.778747	−	0.194838i
$885$		−	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
$890$	−10.3160	−	8.57003i	−0.345794	−	0.287268i
$891$	7.89360	−	7.89360i	0.264446	−	0.264446i
$892$	−3.95627	−	21.2140i	−0.132466	−	0.710297i
$893$	−2.07588			−0.0694668
$894$	−2.12446	+	2.55729i	−0.0710526	+	0.0855285i
$895$	−15.3092	−	15.3092i	−0.511731	−	0.511731i
$896$	49.0528	+	6.91686i	1.63874	+	0.231076i
$897$	50.6927			1.69258
$898$	−41.5675	−	34.5321i	−1.38713	−	1.15235i
$899$	−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
$904$	4.85609	+	2.70887i	0.161511	+	0.0900958i
$905$	23.6360			0.785687
$906$	−38.9397	+	46.8730i	−1.29368	+	1.55725i
$907$	16.4947	−	16.4947i	0.547696	−	0.547696i	−0.378078	−	0.925774i	$-0.623415\pi$
$907$	16.4947	−	16.4947i	0.547696	−	0.547696i	0.925774	+	0.378078i	$0.123415\pi$
$908$	16.9111	−	24.6647i	0.561215	−	0.818527i
$909$	−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	$0.637211\pi$
$912$	−6.89923	−	3.05331i	−0.228456	−	0.101105i
$913$	−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
$918$	14.5965	+	10.6968i	0.481757	+	0.353048i
$919$	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
$924$	−15.2802	−	10.4767i	−0.502680	−	0.344657i
$925$	4.33804	−	4.33804i	0.142634	−	0.142634i
$926$	−43.8042	+	4.04968i	−1.43949	+	0.133081i
$927$			27.0068i			0.887019i
$928$	12.6119	+	4.24196i	0.414005	+	0.139249i
$929$	−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	$0.880472\pi$
$930$	16.7022	+	13.8753i	0.547686	+	0.454989i
$931$		−	10.7701i		−	0.352976i
$932$	−0.821835	+	1.19864i	−0.0269201	+	0.0392628i
$933$	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	$0.790187\pi$
$938$	20.2769	−	24.4080i	0.662065	−	0.796951i
$939$			27.1335i			0.885468i
$940$	−3.86993	−	2.65338i	−0.126223	−	0.0865436i
$941$	−19.6760	+	19.6760i	−0.641418	+	0.641418i	−0.950904	−	0.309486i	$-0.899843\pi$
$941$	−19.6760	+	19.6760i	−0.641418	+	0.641418i	0.309486	+	0.950904i	$0.399843\pi$
$942$	14.5839	−	17.5552i	0.475171	−	0.571979i
$943$			21.8402i			0.711214i
$944$	9.87223	−	3.81489i	0.321314	−	0.124164i
$945$	9.60888	+	9.60888i	0.312577	+	0.312577i
$946$	−5.97284	+	7.18971i	−0.194194	+	0.233758i
$947$	17.7346	+	17.7346i	0.576297	+	0.576297i	0.933881	−	0.357584i	$-0.116399\pi$
$947$	17.7346	+	17.7346i	0.576297	+	0.576297i	−0.357584	+	0.933881i	$0.616399\pi$
$948$	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
$952$	22.1208	−	46.0225i	0.716939	−	1.49160i
$953$	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
$958$	−21.0285	+	25.3127i	−0.679400	+	0.817817i
$959$	−41.2914	−	41.2914i	−1.33337	−	1.33337i
$960$	−8.95906	−	14.5106i	−0.289153	−	0.468328i
$961$		−	20.8789i		−	0.673512i
$962$	−16.0466	+	19.3158i	−0.517363	+	0.622768i
$963$	−2.91127	+	2.91127i	−0.0938145	+	0.0938145i
$964$	−12.5383	+	18.2870i	−0.403831	+	0.588985i
$965$			4.86510i			0.156613i
$966$	69.3027	−	83.4221i	2.22978	−	2.68406i
$967$			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	$-0.593145\pi$
$971$	−17.9776			−0.576928			−0.288464	+	0.957491i	$0.593145\pi$
$972$	24.1932	+	16.5878i	0.775997	+	0.532054i
$973$			71.8125i			2.30220i
$974$	−25.7550	−	21.3959i	−0.825244	−	0.685569i
$975$	−4.36276	−	4.36276i	−0.139720	−	0.139720i
$976$	−6.89527	+	15.5805i	−0.220712	+	0.498720i
$977$		−	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
$980$	13.7663	−	20.0780i	0.439747	−	0.641368i
$981$	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
$986$	8.10735	−	11.0630i	0.258191	−	0.352318i
$987$		−	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	$0.253655\pi$
$992$	−12.9893	+	38.6187i	−0.412409	+	1.22614i
$993$	30.9901	+	30.9901i	0.983442	+	0.983442i
$994$	48.4440	−	4.47863i	1.53655	−	0.142054i
$995$	−24.0088			−0.761131
$996$	−59.0546	−	40.4902i	−1.87122	−	1.28298i
$997$	41.6071	−	41.6071i	1.31771	−	1.31771i	0.402123	−	0.915586i	$-0.368272\pi$
$997$	41.6071	−	41.6071i	1.31771	−	1.31771i	0.915586	−	0.402123i	$-0.131728\pi$
$998$	8.94694	−	10.7697i	0.283210	−	0.340910i
$999$	−19.0398			−0.602391

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.ba.b.21.1	✓	140	1.1	even	1	trivial
680.2.ba.b.21.70	yes	140	8.5	even	2	inner
680.2.ba.b.421.1	yes	140	136.13	even	4	inner
680.2.ba.b.421.70	yes	140	17.13	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} +(-2.31888 - 1.92640i) q^{6} +(-3.09613 - 3.09613i) q^{7} +(-2.72095 + 0.772304i) q^{8} +1.54411i q^{9} +(1.08781 + 0.903697i) q^{10} +(0.701775 - 0.701775i) q^{11} +(3.51626 + 2.41089i) q^{12} +2.89436i q^{13} +(4.76308 + 3.95692i) 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} +(-1.64952 - 1.13097i) q^{20} -9.33381i q^{21} +(-0.896882 + 1.07961i) q^{22} +(-5.80970 - 5.80970i) q^{23} +(-5.26549 - 2.93725i) q^{24} +1.00000i q^{25} +(-0.376812 - 4.07586i) q^{26} +(2.19451 - 2.19451i) q^{27} +(-7.22255 - 4.95207i) 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} +(0.888506 + 5.76286i) 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} +(2.47010 + 1.37790i) q^{40} +(-1.87963 - 1.87963i) q^{41} +(1.21515 + 13.1439i) q^{42} +6.65956 q^{43} +(1.12244 - 1.63708i) q^{44} +(1.09185 - 1.09185i) q^{45} +(8.93763 + 7.42492i) q^{46} +2.34610 q^{47} +(7.79731 + 3.45076i) 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} +(-2.80463 + 3.37603i) q^{54} -0.992459 q^{55} +(10.8156 + 6.03325i) q^{56} +(-1.33372 - 1.33372i) q^{57} +(2.55876 + 2.12569i) q^{58} +2.64592 q^{59} +(-0.781616 - 4.19112i) q^{60} +(-3.01194 + 3.01194i) q^{61} +(-6.50905 + 7.83517i) 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} +(-2.00146 - 7.99963i) 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} +(6.67362 + 5.54410i) q^{74} +(-1.50733 + 1.50733i) q^{75} +(-1.73965 + 0.324433i) q^{76} -4.34557 q^{77} +(5.57570 - 6.71166i) q^{78} +(6.96053 + 6.96053i) q^{79} +(-3.65780 - 1.61879i) q^{80} +11.2481 q^{81} +(2.89162 + 2.40220i) 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} +(-1.36751 + 2.45147i) q^{88} -9.48330 q^{89} +(-1.39541 + 1.67970i) q^{90} +(8.96131 - 8.96131i) q^{91} +(-13.5527 - 9.29225i) q^{92} +15.3539 q^{93} +(-3.30380 + 0.305435i) q^{94} +(0.625664 + 0.625664i) q^{95} +(-11.4295 - 3.84427i) 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

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