LMFDB - Embedded newform 840.2.bj.b.517.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(13,840)] 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("840.13"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.bj (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [184] 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:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			517.25
Character	$\chi$	$=$	840.517
Dual form			840.2.bj.b.13.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.772078 - 1.18486i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-0.807792 + 1.82961i) q^{4} +(-0.563926 + 2.16379i) q^{5} +(1.38376 + 0.291882i) q^{6} +(-0.271325 + 2.63180i) q^{7} +(2.79151 - 0.455480i) q^{8} -1.00000i q^{9} +(2.99919 - 1.00244i) q^{10} +5.15070i q^{11} +(-0.722534 - 1.86492i) q^{12} +(-1.67208 + 1.67208i) q^{13} +(3.32780 - 1.71047i) q^{14} +(-1.13127 - 1.92879i) q^{15} +(-2.69494 - 2.95589i) q^{16} +(-3.33200 + 3.33200i) q^{17} +(-1.18486 + 0.772078i) q^{18} -2.52629i q^{19} +(-3.50336 - 2.77966i) q^{20} +(-1.66911 - 2.05282i) q^{21} +(6.10286 - 3.97674i) q^{22} +(5.67473 - 5.67473i) q^{23} +(-1.65182 + 2.29597i) q^{24} +(-4.36397 - 2.44044i) q^{25} +(3.27216 + 0.690207i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-4.59600 - 2.62237i) q^{28} +5.90326 q^{29} +(-1.41191 + 2.82958i) q^{30} -9.01760i q^{31} +(-1.42161 + 5.47531i) q^{32} +(-3.64209 - 3.64209i) q^{33} +(6.52053 + 1.37540i) q^{34} +(-5.54166 - 2.07123i) q^{35} +(1.82961 + 0.807792i) q^{36} +(-7.00111 + 7.00111i) q^{37} +(-2.99331 + 1.95050i) q^{38} -2.36468i q^{39} +(-0.588643 + 6.29710i) q^{40} +2.60560i q^{41} +(-1.14362 + 3.56260i) q^{42} +(-4.96630 - 4.96630i) q^{43} +(-9.42377 - 4.16069i) q^{44} +(2.16379 + 0.563926i) q^{45} +(-11.1051 - 2.34243i) q^{46} +(-2.51054 + 2.51054i) q^{47} +(3.99574 + 0.184515i) q^{48} +(-6.85277 - 1.42814i) q^{49} +(0.477751 + 7.05491i) q^{50} -4.71216i q^{51} +(-1.70856 - 4.40995i) q^{52} +(-0.853301 - 0.853301i) q^{53} +(0.291882 - 1.38376i) q^{54} +(-11.1450 - 2.90461i) q^{55} +(0.441327 + 7.47029i) q^{56} +(1.78636 + 1.78636i) q^{57} +(-4.55778 - 6.99454i) q^{58} +9.72563i q^{59} +(4.44276 - 0.511733i) q^{60} +9.15780 q^{61} +(-10.6846 + 6.96229i) q^{62} +(2.63180 + 0.271325i) q^{63} +(7.58508 - 2.54295i) q^{64} +(-2.67510 - 4.56096i) q^{65} +(-1.50340 + 7.12735i) q^{66} +(-2.91136 + 2.91136i) q^{67} +(-3.40470 - 8.78783i) q^{68} +8.02527i q^{69} +(1.82447 + 8.16525i) q^{70} -5.38495 q^{71} +(-0.455480 - 2.79151i) q^{72} +(7.42430 + 7.42430i) q^{73} +(13.7007 + 2.88994i) q^{74} +(4.81144 - 1.36015i) q^{75} +(4.62213 + 2.04072i) q^{76} +(-13.5556 - 1.39751i) q^{77} +(-2.80182 + 1.82572i) q^{78} -8.61557i q^{79} +(7.91567 - 4.16439i) q^{80} -1.00000 q^{81} +(3.08728 - 2.01173i) q^{82} +(0.922710 - 0.922710i) q^{83} +(5.10415 - 1.39557i) q^{84} +(-5.33075 - 9.08876i) q^{85} +(-2.05001 + 9.71875i) q^{86} +(-4.17424 + 4.17424i) q^{87} +(2.34604 + 14.3782i) q^{88} +6.30249 q^{89} +(-1.00244 - 2.99919i) q^{90} +(-3.94691 - 4.85426i) q^{91} +(5.79854 + 14.9665i) q^{92} +(6.37641 + 6.37641i) q^{93} +(4.91298 + 1.03631i) q^{94} +(5.46637 + 1.42464i) q^{95} +(-2.86640 - 4.87686i) q^{96} +(-3.84469 + 3.84469i) q^{97} +(3.59871 + 9.22222i) q^{98} +5.15070 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 8 q^{2} + 4 q^{7} + 8 q^{8} - 16 q^{15} + 64 q^{16} + 8 q^{18} + 16 q^{23} - 32 q^{25} - 4 q^{28} + 24 q^{30} - 32 q^{32} - 16 q^{36} - 20 q^{42} - 80 q^{46} + 80 q^{50} + 56 q^{58} - 56 q^{60}+ \cdots + 48 q^{98}+O(q^{100}) $ 184 * q + 8 * q^2 + 4 * q^7 + 8 * q^8 - 16 * q^15 + 64 * q^16 + 8 * q^18 + 16 * q^23 - 32 * q^25 - 4 * q^28 + 24 * q^30 - 32 * q^32 - 16 * q^36 - 20 * q^42 - 80 * q^46 + 80 * q^50 + 56 * q^58 - 56 * q^60 + 4 * q^63 + 32 * q^65 - 44 * q^70 + 32 * q^71 - 8 * q^72 + 8 * q^78 - 184 * q^81 - 16 * q^86 - 64 * q^88 + 104 * q^92 - 96 * q^95 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.772078	−	1.18486i	−0.545941	−	0.837823i
$2$	−0.772078	−	1.18486i	−0.545941	−	0.837823i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−0.807792	+	1.82961i	−0.403896	+	0.914805i
$5$	−0.563926	+	2.16379i	−0.252195	+	0.967676i
$5$	−0.563926	+	2.16379i	−0.252195	+	0.967676i
$6$	1.38376	+	0.291882i	0.564920	+	0.119160i
$7$	−0.271325	+	2.63180i	−0.102551	+	0.994728i
$7$	−0.271325	+	2.63180i	−0.102551	+	0.994728i
$8$	2.79151	−	0.455480i	0.986948	−	0.161036i
$9$		−	1.00000i		−	0.333333i
$10$	2.99919	−	1.00244i	0.948426	−	0.316999i
$11$			5.15070i			1.55299i	0.630121	+	0.776497i	$0.283005\pi$
$11$			5.15070i			1.55299i	−0.630121	+	0.776497i	$0.716995\pi$
$12$	−0.722534	−	1.86492i	−0.208578	−	0.538357i
$13$	−1.67208	+	1.67208i	−0.463752	+	0.463752i	−0.899883	−	0.436131i	$-0.856348\pi$
$13$	−1.67208	+	1.67208i	−0.463752	+	0.463752i	0.436131	+	0.899883i	$0.356348\pi$
$14$	3.32780	−	1.71047i	0.889393	−	0.457143i
$15$	−1.13127	−	1.92879i	−0.292094	−	0.498011i
$16$	−2.69494	−	2.95589i	−0.673736	−	0.738972i
$17$	−3.33200	+	3.33200i	−0.808129	+	0.808129i	−0.984351	−	0.176221i	$-0.943613\pi$
$17$	−3.33200	+	3.33200i	−0.808129	+	0.808129i	0.176221	+	0.984351i	$0.443613\pi$
$18$	−1.18486	+	0.772078i	−0.279274	+	0.181980i
$19$		−	2.52629i		−	0.579571i	−0.957092	−	0.289786i	$-0.906416\pi$
$19$		−	2.52629i		−	0.579571i	0.957092	−	0.289786i	$-0.0935841\pi$
$20$	−3.50336	−	2.77966i	−0.783374	−	0.621550i
$21$	−1.66911	−	2.05282i	−0.364230	−	0.447962i
$22$	6.10286	−	3.97674i	1.30113	−	0.847843i
$23$	5.67473	−	5.67473i	1.18326	−	1.18326i	0.204368	−	0.978894i	$-0.434486\pi$
$23$	5.67473	−	5.67473i	1.18326	−	1.18326i	0.978894	−	0.204368i	$-0.0655139\pi$
$24$	−1.65182	+	2.29597i	−0.337177	+	0.468663i
$25$	−4.36397	−	2.44044i	−0.872795	−	0.488087i
$26$	3.27216	+	0.690207i	0.641723	+	0.135361i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−4.59600	−	2.62237i	−0.868562	−	0.495581i
$29$	5.90326			1.09621			0.548104	−	0.836410i	$-0.315350\pi$
$29$	5.90326			1.09621			0.548104	+	0.836410i	$0.315350\pi$
$30$	−1.41191	+	2.82958i	−0.257779	+	0.516608i
$31$		−	9.01760i		−	1.61961i	−0.586700	−	0.809805i	$-0.699573\pi$
$31$		−	9.01760i		−	1.61961i	0.586700	−	0.809805i	$-0.300427\pi$
$32$	−1.42161	+	5.47531i	−0.251308	+	0.967907i
$33$	−3.64209	−	3.64209i	−0.634007	−	0.634007i
$34$	6.52053	+	1.37540i	1.11826	+	0.235878i
$35$	−5.54166	−	2.07123i	−0.936712	−	0.350102i
$36$	1.82961	+	0.807792i	0.304935	+	0.134632i
$37$	−7.00111	+	7.00111i	−1.15098	+	1.15098i	−0.164618	+	0.986357i	$0.552639\pi$
$37$	−7.00111	+	7.00111i	−1.15098	+	1.15098i	−0.986357	+	0.164618i	$0.947361\pi$
$38$	−2.99331	+	1.95050i	−0.485579	+	0.316412i
$39$		−	2.36468i		−	0.378652i
$40$	−0.588643	+	6.29710i	−0.0930727	+	0.995659i
$41$			2.60560i			0.406927i	0.979083	+	0.203464i	$0.0652198\pi$
$41$			2.60560i			0.406927i	−0.979083	+	0.203464i	$0.934780\pi$
$42$	−1.14362	+	3.56260i	−0.176465	+	0.549721i
$43$	−4.96630	−	4.96630i	−0.757354	−	0.757354i	0.218486	−	0.975840i	$-0.429888\pi$
$43$	−4.96630	−	4.96630i	−0.757354	−	0.757354i	−0.975840	+	0.218486i	$0.929888\pi$
$44$	−9.42377	−	4.16069i	−1.42069	−	0.627248i
$45$	2.16379	+	0.563926i	0.322559	+	0.0840651i
$46$	−11.1051	−	2.34243i	−1.63736	−	0.345373i
$47$	−2.51054	+	2.51054i	−0.366201	+	0.366201i	−0.866090	−	0.499889i	$-0.833374\pi$
$47$	−2.51054	+	2.51054i	−0.366201	+	0.366201i	0.499889	+	0.866090i	$0.333374\pi$
$48$	3.99574	+	0.184515i	0.576736	+	0.0266324i
$49$	−6.85277	−	1.42814i	−0.978967	−	0.204021i
$50$	0.477751	+	7.05491i	0.0675642	+	0.997715i
$51$		−	4.71216i		−	0.659835i
$52$	−1.70856	−	4.40995i	−0.236935	−	0.611550i
$53$	−0.853301	−	0.853301i	−0.117210	−	0.117210i	0.646069	−	0.763279i	$-0.276412\pi$
$53$	−0.853301	−	0.853301i	−0.117210	−	0.117210i	−0.763279	+	0.646069i	$0.776412\pi$
$54$	0.291882	−	1.38376i	0.0397201	−	0.188307i
$55$	−11.1450	−	2.90461i	−1.50280	−	0.391658i
$56$	0.441327	+	7.47029i	0.0589748	+	0.998259i
$57$	1.78636	+	1.78636i	0.236609	+	0.236609i
$58$	−4.55778	−	6.99454i	−0.598465	−	0.918429i
$59$			9.72563i			1.26617i	0.774082	+	0.633085i	$0.218212\pi$
$59$			9.72563i			1.26617i	−0.774082	+	0.633085i	$0.781788\pi$
$60$	4.44276	−	0.511733i	0.573558	−	0.0660645i
$61$	9.15780			1.17254			0.586268	−	0.810117i	$-0.300597\pi$
$61$	9.15780			1.17254			0.586268	+	0.810117i	$0.300597\pi$
$62$	−10.6846	+	6.96229i	−1.35695	+	0.884212i
$63$	2.63180	+	0.271325i	0.331576	+	0.0341837i
$64$	7.58508	−	2.54295i	0.948135	−	0.317869i
$65$	−2.67510	−	4.56096i	−0.331806	−	0.565718i
$66$	−1.50340	+	7.12735i	−0.185055	+	0.877316i
$67$	−2.91136	+	2.91136i	−0.355679	+	0.355679i	−0.862217	−	0.506539i	$-0.830925\pi$
$67$	−2.91136	+	2.91136i	−0.355679	+	0.355679i	0.506539	+	0.862217i	$0.330925\pi$
$68$	−3.40470	−	8.78783i	−0.412881	−	1.06568i
$69$			8.02527i			0.966129i
$70$	1.82447	+	8.16525i	0.218066	+	0.975934i
$71$	−5.38495			−0.639076			−0.319538	−	0.947573i	$-0.603528\pi$
$71$	−5.38495			−0.639076			−0.319538	+	0.947573i	$0.603528\pi$
$72$	−0.455480	−	2.79151i	−0.0536788	−	0.328983i
$73$	7.42430	+	7.42430i	0.868949	+	0.868949i	0.992356	−	0.123407i	$-0.0393821\pi$
$73$	7.42430	+	7.42430i	0.868949	+	0.868949i	−0.123407	+	0.992356i	$0.539382\pi$
$74$	13.7007	+	2.88994i	1.59268	+	0.335949i
$75$	4.81144	−	1.36015i	0.555578	−	0.157056i
$76$	4.62213	+	2.04072i	0.530195	+	0.234087i
$77$	−13.5556	−	1.39751i	−1.54481	−	0.159261i
$78$	−2.80182	+	1.82572i	−0.317243	+	0.206722i
$79$		−	8.61557i		−	0.969328i	−0.874700	−	0.484664i	$-0.838942\pi$
$79$		−	8.61557i		−	0.969328i	0.874700	−	0.484664i	$-0.161058\pi$
$80$	7.91567	−	4.16439i	0.884999	−	0.465593i
$81$	−1.00000			−0.111111
$82$	3.08728	−	2.01173i	0.340933	−	0.222158i
$83$	0.922710	−	0.922710i	0.101281	−	0.101281i	−0.654651	−	0.755931i	$-0.727184\pi$
$83$	0.922710	−	0.922710i	0.101281	−	0.101281i	0.755931	+	0.654651i	$0.227184\pi$
$84$	5.10415	−	1.39557i	0.556909	−	0.152269i
$85$	−5.33075	−	9.08876i	−0.578201	−	0.985814i
$86$	−2.05001	+	9.71875i	−0.221058	+	1.04800i
$87$	−4.17424	+	4.17424i	−0.447525	+	0.447525i
$88$	2.34604	+	14.3782i	0.250089	+	1.53272i
$89$	6.30249			0.668063			0.334031	−	0.942562i	$-0.391591\pi$
$89$	6.30249			0.668063			0.334031	+	0.942562i	$0.391591\pi$
$90$	−1.00244	−	2.99919i	−0.105666	−	0.316142i
$91$	−3.94691	−	4.85426i	−0.413749	−	0.508865i
$92$	5.79854	+	14.9665i	0.604539	+	1.56037i
$93$	6.37641	+	6.37641i	0.661203	+	0.661203i
$94$	4.91298	+	1.03631i	0.506735	+	0.106887i
$95$	5.46637	+	1.42464i	0.560838	+	0.146165i
$96$	−2.86640	−	4.87686i	−0.292551	−	0.497742i
$97$	−3.84469	+	3.84469i	−0.390370	+	0.390370i	−0.874819	−	0.484450i	$-0.839020\pi$
$97$	−3.84469	+	3.84469i	−0.390370	+	0.390370i	0.484450	+	0.874819i	$0.339020\pi$
$98$	3.59871	+	9.22222i	0.363525	+	0.931584i
$99$	5.15070			0.517665
$100$	7.99023	−	6.01301i	0.799023	−	0.601301i
$101$	4.35024			0.432865			0.216433	−	0.976298i	$-0.430558\pi$
$101$	4.35024			0.432865			0.216433	+	0.976298i	$0.430558\pi$
$102$	−5.58326	+	3.63816i	−0.552825	+	0.360231i
$103$	−13.6171	−	13.6171i	−1.34174	−	1.34174i	−0.894332	−	0.447405i	$-0.852348\pi$
$103$	−13.6171	−	13.6171i	−1.34174	−	1.34174i	−0.447405	−	0.894332i	$-0.647652\pi$
$104$	−3.90603	+	5.42923i	−0.383018	+	0.532380i
$105$	5.38313	−	2.45396i	0.525339	−	0.239482i
$106$	−0.352228	+	1.66986i	−0.0342115	+	0.162191i
$107$	−4.07905	+	4.07905i	−0.394337	+	0.394337i	−0.876230	−	0.481893i	$-0.839949\pi$
$107$	−4.07905	+	4.07905i	−0.394337	+	0.394337i	0.481893	+	0.876230i	$0.339949\pi$
$108$	−1.86492	+	0.722534i	−0.179452	+	0.0695259i
$109$	3.19824			0.306336			0.153168	−	0.988200i	$-0.451052\pi$
$109$	3.19824			0.306336			0.153168	+	0.988200i	$0.451052\pi$
$110$	5.16326	+	15.4479i	0.492298	+	1.47290i
$111$		−	9.90106i		−	0.939767i
$112$	8.51052	−	6.29056i	0.804168	−	0.594402i
$113$	−6.82664	+	6.82664i	−0.642196	+	0.642196i	−0.951095	−	0.308899i	$-0.900039\pi$
$113$	−6.82664	+	6.82664i	−0.642196	+	0.642196i	0.308899	+	0.951095i	$0.400039\pi$
$114$	0.737379	−	3.49580i	0.0690619	−	0.327411i
$115$	9.07879	+	15.4790i	0.846601	+	1.44343i
$116$	−4.76861	+	10.8007i	−0.442754	+	1.00282i
$117$	1.67208	+	1.67208i	0.154584	+	0.154584i
$118$	11.5235	−	7.50894i	1.06083	−	0.691254i
$119$	−7.86512	−	9.67323i	−0.720994	−	0.886743i
$120$	−4.03649	−	4.86896i	−0.368479	−	0.444473i
$121$	−15.5297			−1.41179
$122$	−7.07053	−	10.8507i	−0.640136	−	0.982378i
$123$	−1.84244	−	1.84244i	−0.166127	−	0.166127i
$124$	16.4987	+	7.28435i	1.48163	+	0.654154i
$125$	7.74155	−	8.06650i	0.692425	−	0.721490i
$126$	−1.71047	−	3.32780i	−0.152381	−	0.296464i
$127$	7.05588	+	7.05588i	0.626108	+	0.626108i	0.947087	−	0.320978i	$-0.104012\pi$
$127$	7.05588	+	7.05588i	0.626108	+	0.626108i	−0.320978	+	0.947087i	$0.604012\pi$
$128$	−8.86932	−	7.02390i	−0.783944	−	0.620831i
$129$	7.02341			0.618377
$130$	−3.33872	+	6.69104i	−0.292825	+	0.586843i
$131$	0.394051			0.0344284			0.0172142	−	0.999852i	$-0.494520\pi$
$131$	0.394051			0.0344284			0.0172142	+	0.999852i	$0.494520\pi$
$132$	9.60566	−	3.72156i	0.836066	−	0.323920i
$133$	6.64870	+	0.685445i	0.576516	+	0.0594356i
$134$	5.69735	+	1.20176i	0.492176	+	0.103816i
$135$	−1.92879	+	1.13127i	−0.166004	+	0.0973646i
$136$	−7.78366	+	10.8190i	−0.667444	+	0.927720i
$137$	4.18798	+	4.18798i	0.357803	+	0.357803i	0.863003	−	0.505199i	$-0.168581\pi$
$137$	4.18798	+	4.18798i	0.357803	+	0.357803i	−0.505199	+	0.863003i	$0.668581\pi$
$138$	9.50884	−	6.19614i	0.809446	−	0.527450i
$139$		−	13.6587i		−	1.15851i	−0.815146	−	0.579256i	$-0.803343\pi$
$139$		−	13.6587i		−	1.15851i	0.815146	−	0.579256i	$-0.196657\pi$
$140$	8.26605	−	8.46595i	0.698609	−	0.715504i
$141$		−	3.55045i		−	0.299002i
$142$	4.15760	+	6.38042i	0.348898	+	0.535433i
$143$	−8.61238	−	8.61238i	−0.720203	−	0.720203i
$144$	−2.95589	+	2.69494i	−0.246324	+	0.224579i
$145$	−3.32900	+	12.7734i	−0.276459	+	1.06077i
$146$	3.06463	−	14.5289i	0.253631	−	1.20242i
$147$	5.85549	−	3.83579i	0.482953	−	0.316370i
$148$	−7.15386	−	18.4647i	−0.588044	−	1.51779i
$149$	−13.5533			−1.11033			−0.555167	−	0.831739i	$-0.687345\pi$
$149$	−13.5533			−1.11033			−0.555167	+	0.831739i	$0.687345\pi$
$150$	−5.32640	−	4.65075i	−0.434898	−	0.379732i
$151$	19.0617			1.55122			0.775611	−	0.631211i	$-0.217442\pi$
$151$	19.0617			1.55122			0.775611	+	0.631211i	$0.217442\pi$
$152$	−1.15068	−	7.05218i	−0.0933321	−	0.572007i
$153$	3.33200	+	3.33200i	0.269376	+	0.269376i
$154$	8.81013	+	17.1405i	0.709941	+	1.38122i
$155$	19.5122	+	5.08526i	1.56726	+	0.408458i
$156$	4.32644	+	1.91017i	0.346392	+	0.152936i
$157$	−8.80830	−	8.80830i	−0.702979	−	0.702979i	0.262070	−	0.965049i	$-0.415595\pi$
$157$	−8.80830	−	8.80830i	−0.702979	−	0.702979i	−0.965049	+	0.262070i	$0.915595\pi$
$158$	−10.2083	+	6.65189i	−0.812126	+	0.529196i
$159$	1.20675			0.0957015
$160$	−11.0457	−	6.16374i	−0.873242	−	0.487286i
$161$	13.3951	+	16.4744i	1.05568	+	1.29837i
$162$	0.772078	+	1.18486i	0.0606602	+	0.0930915i
$163$	−10.2447	−	10.2447i	−0.802423	−	0.802423i	0.181051	−	0.983474i	$-0.442050\pi$
$163$	−10.2447	−	10.2447i	−0.802423	−	0.802423i	−0.983474	+	0.181051i	$0.942050\pi$
$164$	−4.76724	−	2.10479i	−0.372259	−	0.164356i
$165$	9.93459	−	5.82685i	0.773407	−	0.453620i
$166$	−1.80569	−	0.380879i	−0.140148	−	0.0295620i
$167$	4.71450	−	4.71450i	0.364819	−	0.364819i	−0.500765	−	0.865584i	$-0.666948\pi$
$167$	4.71450	−	4.71450i	0.364819	−	0.364819i	0.865584	+	0.500765i	$0.166948\pi$
$168$	−5.59436	−	4.97023i	−0.431614	−	0.383461i
$169$			7.40829i			0.569869i
$170$	−6.65316	+	13.3334i	−0.510274	+	1.02263i
$171$	−2.52629			−0.193190
$172$	13.0981	−	5.07465i	0.998723	−	0.386939i
$173$	−9.83536	+	9.83536i	−0.747769	+	0.747769i	−0.974060	−	0.226291i	$-0.927340\pi$
$173$	−9.83536	+	9.83536i	−0.747769	+	0.747769i	0.226291	+	0.974060i	$0.427340\pi$
$174$	8.16872	+	1.72306i	0.619269	+	0.130624i
$175$	7.60680	−	10.8230i	0.575020	−	0.818140i
$176$	15.2249	−	13.8808i	1.14762	−	1.04631i
$177$	−6.87706	−	6.87706i	−0.516912	−	0.516912i
$178$	−4.86601	−	7.46758i	−0.364723	−	0.559719i
$179$	7.39824			0.552971			0.276485	−	0.961018i	$-0.410830\pi$
$179$	7.39824			0.552971			0.276485	+	0.961018i	$0.410830\pi$
$180$	−2.77966	+	3.50336i	−0.207183	+	0.261125i
$181$	−18.6048			−1.38289			−0.691444	−	0.722430i	$-0.743025\pi$
$181$	−18.6048			−1.38289			−0.691444	+	0.722430i	$0.743025\pi$
$182$	−2.70431	+	8.42441i	−0.200456	+	0.624459i
$183$	−6.47554	+	6.47554i	−0.478686	+	0.478686i
$184$	13.2563	−	18.4258i	0.977270	−	1.35837i
$185$	−11.2008	−	19.0970i	−0.823501	−	1.40404i
$186$	2.63208	−	12.4782i	0.192993	−	0.914949i
$187$	−17.1621	−	17.1621i	−1.25502	−	1.25502i
$188$	−2.56532	−	6.62132i	−0.187095	−	0.482909i
$189$	−2.05282	+	1.66911i	−0.149321	+	0.121410i
$190$	−2.53246	−	7.57682i	−0.183724	−	0.549681i
$191$	16.4410			1.18963			0.594815	−	0.803863i	$-0.297225\pi$
$191$	16.4410			1.18963			0.594815	+	0.803863i	$0.297225\pi$
$192$	−3.56532	+	7.16160i	−0.257305	+	0.516844i
$193$	−11.7512	+	11.7512i	−0.845868	+	0.845868i	−0.989615	−	0.143747i	$-0.954085\pi$
$193$	−11.7512	+	11.7512i	−0.845868	+	0.845868i	0.143747	+	0.989615i	$0.454085\pi$
$194$	7.52383	+	1.58703i	0.540180	+	0.113942i
$195$	5.11667	+	1.33350i	0.366412	+	0.0954942i
$196$	8.14856	−	11.3842i	0.582040	−	0.813160i
$197$	−4.65177	+	4.65177i	−0.331425	+	0.331425i	−0.853127	−	0.521703i	$-0.825297\pi$
$197$	−4.65177	+	4.65177i	−0.331425	+	0.331425i	0.521703	+	0.853127i	$0.325297\pi$
$198$	−3.97674	−	6.10286i	−0.282614	−	0.433711i
$199$	14.9107			1.05699			0.528495	−	0.848936i	$-0.322757\pi$
$199$	14.9107			1.05699			0.528495	+	0.848936i	$0.322757\pi$
$200$	−13.2937	−	4.82480i	−0.940003	−	0.341165i
$201$		−	4.11728i		−	0.290410i
$202$	−3.35873	−	5.15443i	−0.236319	−	0.362665i
$203$	−1.60170	+	15.5362i	−0.112417	+	1.09043i
$204$	8.62142	+	3.80645i	0.603620	+	0.266505i
$205$	−5.63798	−	1.46937i	−0.393774	−	0.102625i
$206$	−5.62093	+	26.6479i	−0.391629	+	1.85665i
$207$	−5.67473	−	5.67473i	−0.394421	−	0.394421i
$208$	9.44865	+	0.436319i	0.655146	+	0.0302533i
$209$	13.0122			0.900071
$210$	−7.06380	−	4.48361i	−0.487448	−	0.309398i
$211$			15.6001i			1.07396i	0.843596	+	0.536978i	$0.180434\pi$
$211$			15.6001i			1.07396i	−0.843596	+	0.536978i	$0.819566\pi$
$212$	2.25050	−	0.871918i	0.154565	−	0.0598836i
$213$	3.80774	−	3.80774i	0.260902	−	0.260902i
$214$	7.98246	+	1.68377i	0.545670	+	0.115100i
$215$	13.5467	−	7.94540i	0.923874	−	0.541872i
$216$	2.29597	+	1.65182i	0.156221	+	0.112392i
$217$	23.7325	+	2.44670i	1.61107	+	0.166093i
$218$	−2.46929	−	3.78948i	−0.167242	−	0.256656i
$219$	−10.4996			−0.709494
$220$	14.3172	−	18.0447i	0.965263	−	1.21658i
$221$		−	11.1428i		−	0.749543i
$222$	−11.7314	+	7.64439i	−0.787359	+	0.513058i
$223$	9.90113	+	9.90113i	0.663028	+	0.663028i	0.956093	−	0.293064i	$-0.0946750\pi$
$223$	9.90113	+	9.90113i	0.663028	+	0.663028i	−0.293064	+	0.956093i	$0.594675\pi$
$224$	−14.0242	−	5.22698i	−0.937032	−	0.349242i
$225$	−2.44044	+	4.36397i	−0.162696	+	0.290932i
$226$	13.3593	+	2.81792i	0.888648	+	0.187445i
$227$	2.46872	+	2.46872i	0.163855	+	0.163855i	0.784272	−	0.620417i	$-0.213037\pi$
$227$	2.46872	+	2.46872i	0.163855	+	0.163855i	−0.620417	+	0.784272i	$0.713037\pi$
$228$	−4.71135	+	1.82533i	−0.312017	+	0.120886i
$229$		−	2.05866i		−	0.136040i	−0.997684	−	0.0680200i	$-0.978332\pi$
$229$		−	2.05866i		−	0.136040i	0.997684	−	0.0680200i	$-0.0216682\pi$
$230$	11.3310	−	22.7081i	0.747143	−	1.49733i
$231$	10.5735	−	8.59708i	0.695682	−	0.565646i
$232$	16.4790	−	2.68882i	1.08190	−	0.176529i
$233$	5.02721	−	5.02721i	0.329343	−	0.329343i	−0.522993	−	0.852337i	$-0.675185\pi$
$233$	5.02721	−	5.02721i	0.329343	−	0.329343i	0.852337	+	0.522993i	$0.175185\pi$
$234$	0.690207	−	3.27216i	0.0451203	−	0.213908i
$235$	−4.01653	−	6.84805i	−0.262010	−	0.446718i
$236$	−17.7941	−	7.85629i	−1.15830	−	0.511401i
$237$	6.09213	+	6.09213i	0.395726	+	0.395726i
$238$	−5.38895	+	16.7876i	−0.349314	+	1.08818i
$239$			21.3479i			1.38088i	0.723390	+	0.690439i	$0.242583\pi$
$239$			21.3479i			1.38088i	−0.723390	+	0.690439i	$0.757417\pi$
$240$	−2.65255	+	8.54189i	−0.171222	+	0.551377i
$241$			3.80737i			0.245254i	0.992453	+	0.122627i	$0.0391319\pi$
$241$			3.80737i			0.245254i	−0.992453	+	0.122627i	$0.960868\pi$
$242$	11.9901	+	18.4005i	0.770754	+	1.18283i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−7.39760	+	16.7552i	−0.473583	+	1.07264i
$245$	6.95466	−	14.0226i	0.444317	−	0.895870i
$246$	−0.760529	+	3.60554i	−0.0484895	+	0.229881i
$247$	4.22417	+	4.22417i	0.268777	+	0.268777i
$248$	−4.10734	−	25.1727i	−0.260816	−	1.59847i
$249$			1.30491i			0.0826952i
$250$	−15.5348	−	2.94469i	−0.982505	−	0.186239i
$251$	−21.1664			−1.33601			−0.668006	−	0.744156i	$-0.732852\pi$
$251$	−21.1664			−1.33601			−0.668006	+	0.744156i	$0.732852\pi$
$252$	−2.62237	+	4.59600i	−0.165194	+	0.289521i
$253$	29.2288	+	29.2288i	1.83760	+	1.83760i
$254$	2.91255	−	13.8079i	0.182750	−	0.866386i
$255$	10.1961	+	2.65731i	0.638507	+	0.166407i
$256$	−1.47455	+	15.9319i	−0.0921593	+	0.995744i
$257$	−0.402214	+	0.402214i	−0.0250894	+	0.0250894i	−0.719540	−	0.694451i	$-0.755647\pi$
$257$	−0.402214	+	0.402214i	−0.0250894	+	0.0250894i	0.694451	+	0.719540i	$0.255647\pi$
$258$	−5.42262	−	8.32176i	−0.337597	−	0.518090i
$259$	−16.5260	−	20.3251i	−1.02687	−	1.26294i
$260$	10.5057	−	1.21008i	0.651536	−	0.0750463i
$261$		−	5.90326i		−	0.365403i
$262$	−0.304238	−	0.466896i	−0.0187959	−	0.0288449i
$263$	9.04566	−	9.04566i	0.557780	−	0.557780i	−0.370895	−	0.928675i	$-0.620949\pi$
$263$	9.04566	−	9.04566i	0.557780	−	0.557780i	0.928675	+	0.370895i	$0.120949\pi$
$264$	−11.8258	−	8.50804i	−0.727830	−	0.523634i
$265$	2.32756	−	1.36517i	0.142981	−	0.0838615i
$266$	−4.32116	−	8.40701i	−0.264947	−	0.515467i
$267$	−4.45654	+	4.45654i	−0.272736	+	0.272736i
$268$	−2.97488	−	7.67842i	−0.181719	−	0.469034i
$269$		−	20.2813i		−	1.23657i	−0.785954	−	0.618285i	$-0.787828\pi$
$269$		−	20.2813i		−	1.23657i	0.785954	−	0.618285i	$-0.212172\pi$
$270$	2.82958	+	1.41191i	0.172203	+	0.0859262i
$271$			0.243465i			0.0147894i	0.999973	+	0.00739472i	$0.00235383\pi$
$271$			0.243465i			0.0147894i	−0.999973	+	0.00739472i	$0.997646\pi$
$272$	18.8286	+	0.869465i	1.14165	+	0.0527190i
$273$	6.22337	+	0.641595i	0.376655	+	0.0388311i
$274$	1.72873	−	8.19562i	0.104436	−	0.495116i
$275$	12.5699	−	22.4775i	0.757996	−	1.35544i
$276$	−14.6831	−	6.48275i	−0.883820	−	0.390216i
$277$	−4.00984	+	4.00984i	−0.240928	+	0.240928i	−0.817234	−	0.576306i	$-0.804494\pi$
$277$	−4.00984	+	4.00984i	−0.240928	+	0.240928i	0.576306	+	0.817234i	$0.304494\pi$
$278$	−16.1836	+	10.5455i	−0.970629	+	0.632480i
$279$	−9.01760			−0.539870
$280$	−16.4130	−	3.25775i	−0.980865	−	0.194688i
$281$	−25.3458			−1.51201			−0.756003	−	0.654568i	$-0.772850\pi$
$281$	−25.3458			−1.51201			−0.756003	+	0.654568i	$0.772850\pi$
$282$	−4.20679	+	2.74122i	−0.250510	+	0.163237i
$283$	−1.39809	+	1.39809i	−0.0831081	+	0.0831081i	−0.747439	−	0.664331i	$-0.768717\pi$
$283$	−1.39809	+	1.39809i	−0.0831081	+	0.0831081i	0.664331	+	0.747439i	$0.268717\pi$
$284$	4.34992	−	9.85236i	0.258120	−	0.584630i
$285$	−4.87268	+	2.85793i	−0.288633	+	0.169289i
$286$	−3.55505	+	16.8539i	−0.210214	+	0.996592i
$287$	−6.85743	−	0.706964i	−0.404782	−	0.0417308i
$288$	5.47531	+	1.42161i	0.322636	+	0.0837692i
$289$		−	5.20448i		−	0.306146i
$290$	17.7050	−	5.91767i	1.03967	−	0.347497i
$291$		−	5.43722i		−	0.318735i
$292$	−19.5809	+	7.58629i	−1.14588	+	0.443954i
$293$	6.54622	−	6.54622i	0.382434	−	0.382434i	−0.489544	−	0.871978i	$-0.662837\pi$
$293$	6.54622	−	6.54622i	0.382434	−	0.382434i	0.871978	+	0.489544i	$0.162837\pi$
$294$	−9.06577	−	3.97642i	−0.528726	−	0.231909i
$295$	−21.0442	−	5.48454i	−1.22524	−	0.319322i
$296$	−16.3548	+	22.7325i	−0.950604	+	1.32130i
$297$	−3.64209	+	3.64209i	−0.211336	+	0.211336i
$298$	10.4642	+	16.0588i	0.606177	+	0.930263i
$299$			18.9772i			1.09748i
$300$	−1.39811	+	9.90178i	−0.0807197	+	0.571680i
$301$	14.4178	−	11.7228i	0.831028	−	0.675693i
$302$	−14.7171	−	22.5855i	−0.846877	−	1.29965i
$303$	−3.07609	+	3.07609i	−0.176717	+	0.176717i
$304$	−7.46744	+	6.80822i	−0.428287	+	0.390478i
$305$	−5.16432	+	19.8156i	−0.295708	+	1.13464i
$306$	1.37540	−	6.52053i	0.0786261	−	0.372754i
$307$	−3.66001	−	3.66001i	−0.208888	−	0.208888i	0.594907	−	0.803795i	$-0.297189\pi$
$307$	−3.66001	−	3.66001i	−0.208888	−	0.208888i	−0.803795	+	0.594907i	$0.797189\pi$
$308$	13.5070	−	23.6726i	0.769634	−	1.34887i
$309$	19.2575			1.09552
$310$	−9.03961	−	27.0455i	−0.513415	−	1.53608i
$311$		−	1.88622i		−	0.106957i	−0.998569	−	0.0534787i	$-0.982969\pi$
$311$		−	1.88622i		−	0.106957i	0.998569	−	0.0534787i	$-0.0170309\pi$
$312$	−1.07706	−	6.60103i	−0.0609767	−	0.373710i
$313$	20.7950	+	20.7950i	1.17541	+	1.17541i	0.980902	+	0.194504i	$0.0623097\pi$
$313$	20.7950	+	20.7950i	1.17541	+	1.17541i	0.194504	+	0.980902i	$0.437690\pi$
$314$	−3.63592	+	17.2373i	−0.205187	+	0.972758i
$315$	−2.07123	+	5.54166i	−0.116701	+	0.312237i
$316$	15.7631	+	6.95959i	0.886746	+	0.391508i
$317$	2.65202	−	2.65202i	0.148952	−	0.148952i	−0.628698	−	0.777650i	$-0.716412\pi$
$317$	2.65202	−	2.65202i	0.148952	−	0.148952i	0.777650	+	0.628698i	$0.216412\pi$
$318$	−0.931705	−	1.42983i	−0.0522474	−	0.0801809i
$319$			30.4059i			1.70240i
$320$	1.22500	+	17.8466i	0.0684795	+	0.997653i
$321$		−	5.76865i		−	0.321975i
$322$	9.17790	−	28.5908i	0.511465	−	1.59331i
$323$	8.41762	+	8.41762i	0.468369	+	0.468369i
$324$	0.807792	−	1.82961i	0.0448773	−	0.101645i
$325$	11.3775	−	3.21631i	0.631111	−	0.178409i
$326$	−4.22882	+	20.0482i	−0.234213	+	1.11036i
$327$	−2.26150	+	2.26150i	−0.125061	+	0.125061i
$328$	1.18680	+	7.27357i	0.0655301	+	0.401616i
$329$	−5.92609	−	7.28843i	−0.326716	−	0.401824i
$330$	−14.5743	−	7.27233i	−0.802288	−	0.400329i
$331$			32.7208i			1.79850i	0.437435	+	0.899250i	$0.355887\pi$
$331$			32.7208i			1.79850i	−0.437435	+	0.899250i	$0.644113\pi$
$332$	0.942842	+	2.43356i	0.0517452	+	0.133559i
$333$	7.00111	+	7.00111i	0.383658	+	0.383658i
$334$	−9.22599	−	1.94607i	−0.504824	−	0.106484i
$335$	−4.65777	−	7.94135i	−0.254481	−	0.433882i
$336$	−1.56975	+	10.4659i	−0.0856369	+	0.570964i
$337$	4.90379	+	4.90379i	0.267126	+	0.267126i	0.827941	−	0.560815i	$-0.189512\pi$
$337$	4.90379	+	4.90379i	0.267126	+	0.267126i	−0.560815	+	0.827941i	$0.689512\pi$
$338$	8.77780	−	5.71978i	0.477449	−	0.311115i
$339$		−	9.65432i		−	0.524351i
$340$	20.9350	−	2.41137i	1.13536	−	0.130775i
$341$	46.4469			2.51524
$342$	1.95050	+	2.99331i	0.105471	+	0.161860i
$343$	5.61792	−	17.6476i	0.303339	−	0.952883i
$344$	−16.1255	−	11.6014i	−0.869431	−	0.625507i
$345$	−17.3650	−	4.52566i	−0.934901	−	0.243653i
$346$	19.2472	+	4.05987i	1.03474	+	0.218260i
$347$	8.26679	−	8.26679i	0.443784	−	0.443784i	−0.449497	−	0.893282i	$-0.648397\pi$
$347$	8.26679	−	8.26679i	0.443784	−	0.443784i	0.893282	+	0.449497i	$0.148397\pi$
$348$	−4.26531	−	11.0091i	−0.228645	−	0.590152i
$349$			31.5705i			1.68993i	0.534823	+	0.844964i	$0.320378\pi$
$349$			31.5705i			1.68993i	−0.534823	+	0.844964i	$0.679622\pi$
$350$	−18.6968	−	0.656824i	−0.999383	−	0.0351087i
$351$	−2.36468			−0.126217
$352$	−28.2017	−	7.32228i	−1.50315	−	0.390279i
$353$	15.1489	+	15.1489i	0.806293	+	0.806293i	0.984071	−	0.177777i	$-0.0568907\pi$
$353$	15.1489	+	15.1489i	0.806293	+	0.806293i	−0.177777	+	0.984071i	$0.556891\pi$
$354$	−2.83874	+	13.4580i	−0.150877	+	0.715284i
$355$	3.03671	−	11.6519i	0.161172	−	0.618419i
$356$	−5.09110	+	11.5311i	−0.269828	+	0.611147i
$357$	12.4015	+	1.27853i	0.656356	+	0.0676667i
$358$	−5.71202	−	8.76589i	−0.301890	−	0.463292i
$359$		−	0.0423478i		−	0.00223503i	−0.999999	−	0.00111752i	$-0.999644\pi$
$359$		−	0.0423478i		−	0.00223503i	0.999999	−	0.00111752i	$-0.000355716\pi$
$360$	6.29710	+	0.588643i	0.331886	+	0.0310242i
$361$	12.6178			0.664097
$362$	14.3644	+	22.0442i	0.754975	+	1.15862i
$363$	10.9811	−	10.9811i	0.576360	−	0.576360i
$364$	12.0697	−	3.30007i	0.632624	−	0.172971i
$365$	−20.2514	+	11.8779i	−1.06001	+	0.621716i
$366$	12.6722	+	2.67300i	0.662389	+	0.139720i
$367$	−12.7442	+	12.7442i	−0.665240	+	0.665240i	−0.956610	−	0.291370i	$-0.905889\pi$
$367$	−12.7442	+	12.7442i	−0.665240	+	0.665240i	0.291370	+	0.956610i	$0.405889\pi$
$368$	−32.0669	−	1.48078i	−1.67160	−	0.0771911i
$369$	2.60560			0.135642
$370$	−13.9794	+	28.0158i	−0.726756	+	1.45647i
$371$	2.47724	−	2.01420i	0.128612	−	0.104572i
$372$	−16.8172	+	6.51553i	−0.871929	+	0.337814i
$373$	−1.83933	−	1.83933i	−0.0952370	−	0.0952370i	0.657883	−	0.753120i	$-0.271452\pi$
$373$	−1.83933	−	1.83933i	−0.0952370	−	0.0952370i	−0.753120	+	0.657883i	$0.771452\pi$
$374$	−7.08424	+	33.5852i	−0.366318	+	1.73665i
$375$	0.229776	+	11.1780i	0.0118656	+	0.577228i
$376$	−5.86471	+	8.15172i	−0.302449	+	0.420393i
$377$	−9.87073	+	9.87073i	−0.508368	+	0.508368i
$378$	3.56260	+	1.14362i	0.183240	+	0.0588217i
$379$	−19.0430			−0.978174			−0.489087	−	0.872235i	$-0.662670\pi$
$379$	−19.0430			−0.978174			−0.489087	+	0.872235i	$0.662670\pi$
$380$	−7.02223	+	8.85051i	−0.360233	+	0.454021i
$381$	−9.97852			−0.511215
$382$	−12.6937	−	19.4803i	−0.649468	−	0.996699i
$383$	20.2953	+	20.2953i	1.03704	+	1.03704i	0.999287	+	0.0377566i	$0.0120211\pi$
$383$	20.2953	+	20.2953i	1.03704	+	1.03704i	0.0377566	+	0.999287i	$0.487979\pi$
$384$	11.2382	−	1.30490i	0.573497	−	0.0665906i
$385$	10.6683	−	28.5434i	0.543706	−	1.45471i
$386$	22.9963	+	4.85069i	1.17048	+	0.246894i
$387$	−4.96630	+	4.96630i	−0.252451	+	0.252451i
$388$	−3.92858	−	10.1400i	−0.199443	−	0.514781i
$389$	3.47313			0.176095			0.0880473	−	0.996116i	$-0.471937\pi$
$389$	3.47313			0.176095			0.0880473	+	0.996116i	$0.471937\pi$
$390$	−2.37045	−	7.09211i	−0.120032	−	0.359123i
$391$			37.8164i			1.91246i
$392$	−19.7801	−	0.865387i	−0.999044	−	0.0437086i
$393$	−0.278636	+	0.278636i	−0.0140553	+	0.0140553i
$394$	9.10322	+	1.92017i	0.458614	+	0.0967368i
$395$	18.6423	+	4.85855i	0.937996	+	0.244460i
$396$	−4.16069	+	9.42377i	−0.209083	+	0.473562i
$397$	−11.3545	−	11.3545i	−0.569865	−	0.569865i	0.362225	−	0.932091i	$-0.382017\pi$
$397$	−11.3545	−	11.3545i	−0.569865	−	0.569865i	−0.932091	+	0.362225i	$0.882017\pi$
$398$	−11.5122	−	17.6671i	−0.577055	−	0.885571i
$399$	−5.18603	+	4.21666i	−0.259626	+	0.211097i
$400$	4.54702	+	19.4763i	0.227351	+	0.973813i
$401$	−38.2876			−1.91199			−0.955995	−	0.293382i	$-0.905219\pi$
$401$	−38.2876			−1.91199			−0.955995	+	0.293382i	$0.905219\pi$
$402$	−4.87840	+	3.17886i	−0.243313	+	0.158547i
$403$	15.0782	+	15.0782i	0.751097	+	0.751097i
$404$	−3.51409	+	7.95925i	−0.174833	+	0.395987i
$405$	0.563926	−	2.16379i	0.0280217	−	0.107520i
$406$	19.6449	−	10.0974i	0.974960	−	0.501124i
$407$	−36.0606	−	36.0606i	−1.78746	−	1.78746i
$408$	−2.14630	−	13.1541i	−0.106257	−	0.651223i
$409$	−15.9114			−0.786770			−0.393385	−	0.919374i	$-0.628696\pi$
$409$	−15.9114			−0.786770			−0.393385	+	0.919374i	$0.628696\pi$
$410$	2.61196	+	7.81469i	0.128996	+	0.385940i
$411$	−5.92270			−0.292145
$412$	35.9139	−	13.9142i	1.76935	−	0.685505i
$413$	−25.5959	−	2.63880i	−1.25949	−	0.129847i
$414$	−2.34243	+	11.1051i	−0.115124	+	0.545785i
$415$	1.47621	+	2.51689i	0.0724643	+	0.123549i
$416$	−6.77811	−	11.5322i	−0.332324	−	0.565413i
$417$	9.65813	+	9.65813i	0.472961	+	0.472961i
$418$	−10.0464	−	15.4176i	−0.491386	−	0.754100i
$419$		−	2.36583i		−	0.115578i	−0.998329	−	0.0577891i	$-0.981595\pi$
$419$		−	2.36583i		−	0.115578i	0.998329	−	0.0577891i	$-0.0184051\pi$
$420$	0.141350	+	11.8313i	0.00689720	+	0.577309i
$421$		−	8.02564i		−	0.391146i	−0.980689	−	0.195573i	$-0.937343\pi$
$421$		−	8.02564i		−	0.391146i	0.980689	−	0.195573i	$-0.0626566\pi$
$422$	18.4840	−	12.0445i	0.899785	−	0.586317i
$423$	2.51054	+	2.51054i	0.122067	+	0.122067i
$424$	−2.77066	−	1.99334i	−0.134555	−	0.0968051i
$425$	22.6723	−	6.40924i	1.09977	−	0.310894i
$426$	−7.45151	−	1.57177i	−0.361027	−	0.0761525i
$427$	−2.48474	+	24.1015i	−0.120245	+	1.16635i
$428$	−4.16805	−	10.7581i	−0.201470	−	0.520012i
$429$	12.1797			0.588044
$430$	−19.8733	−	9.91644i	−0.958374	−	0.478213i
$431$	−9.31639			−0.448755			−0.224377	−	0.974502i	$-0.572035\pi$
$431$	−9.31639			−0.448755			−0.224377	+	0.974502i	$0.572035\pi$
$432$	0.184515	−	3.99574i	0.00887748	−	0.192245i
$433$	0.642368	+	0.642368i	0.0308702	+	0.0308702i	0.722373	−	0.691503i	$-0.243051\pi$
$433$	0.642368	+	0.642368i	0.0308702	+	0.0308702i	−0.691503	+	0.722373i	$0.743051\pi$
$434$	−15.4244	−	30.0088i	−0.740394	−	1.44047i
$435$	−6.67821	−	11.3861i	−0.320196	−	0.545923i
$436$	−2.58352	+	5.85154i	−0.123728	+	0.280238i
$437$	−14.3360	−	14.3360i	−0.685785	−	0.685785i
$438$	8.10647	+	12.4405i	0.387342	+	0.594431i
$439$	−28.3583			−1.35347			−0.676733	−	0.736229i	$-0.736605\pi$
$439$	−28.3583			−1.35347			−0.676733	+	0.736229i	$0.736605\pi$
$440$	−32.4345	−	3.03192i	−1.54625	−	0.144541i
$441$	−1.42814	+	6.85277i	−0.0680069	+	0.326322i
$442$	−13.2026	+	8.60307i	−0.627984	+	0.409206i
$443$	14.7490	+	14.7490i	0.700747	+	0.700747i	0.964571	−	0.263824i	$-0.0849839\pi$
$443$	14.7490	+	14.7490i	0.700747	+	0.700747i	−0.263824	+	0.964571i	$0.584984\pi$
$444$	18.1151	+	7.99800i	0.859704	+	0.379568i
$445$	−3.55414	+	13.6373i	−0.168482	+	0.646469i
$446$	4.08702	−	19.3759i	0.193526	−	0.917475i
$447$	9.58366	−	9.58366i	0.453292	−	0.453292i
$448$	4.63454	+	20.6524i	0.218961	+	0.975734i
$449$			30.5161i			1.44014i	0.693899	+	0.720072i	$0.255891\pi$
$449$			30.5161i			1.44014i	−0.693899	+	0.720072i	$0.744109\pi$
$450$	7.05491	−	0.477751i	0.332572	−	0.0225214i
$451$	−13.4207			−0.631955
$452$	−6.97558	−	18.0046i	−0.328104	−	0.846864i
$453$	−13.4787	+	13.4787i	−0.633284	+	0.633284i
$454$	1.01905	−	4.83113i	0.0478262	−	0.226736i
$455$	12.7294	−	5.80284i	0.596762	−	0.272041i
$456$	5.80029	+	4.17299i	0.271624	+	0.195418i
$457$	−3.48416	−	3.48416i	−0.162982	−	0.162982i	0.620904	−	0.783886i	$-0.286766\pi$
$457$	−3.48416	−	3.48416i	−0.162982	−	0.162982i	−0.783886	+	0.620904i	$0.786766\pi$
$458$	−2.43923	+	1.58945i	−0.113978	+	0.0742699i
$459$	−4.71216			−0.219945
$460$	−35.6544	+	4.10680i	−1.66239	+	0.191480i
$461$	4.86218			0.226454			0.113227	−	0.993569i	$-0.463881\pi$
$461$	4.86218			0.226454			0.113227	+	0.993569i	$0.463881\pi$
$462$	−18.3499	−	5.89046i	−0.853713	−	0.274049i
$463$	−23.6863	+	23.6863i	−1.10080	+	1.10080i	−0.106482	+	0.994315i	$0.533959\pi$
$463$	−23.6863	+	23.6863i	−1.10080	+	1.10080i	−0.994315	+	0.106482i	$0.966041\pi$
$464$	−15.9090	−	17.4494i	−0.738555	−	0.810067i
$465$	−17.3930	+	10.2014i	−0.806583	+	0.473078i
$466$	−9.83794	−	2.07515i	−0.455734	−	0.0961294i
$467$	24.7511	+	24.7511i	1.14535	+	1.14535i	0.987457	+	0.157888i	$0.0504685\pi$
$467$	24.7511	+	24.7511i	1.14535	+	1.14535i	0.157888	+	0.987457i	$0.449531\pi$
$468$	−4.40995	+	1.70856i	−0.203850	+	0.0789783i
$469$	−6.87219	−	8.45203i	−0.317328	−	0.390279i
$470$	−5.01292	+	10.0463i	−0.231229	+	0.463399i
$471$	12.4568			0.573980
$472$	4.42983	+	27.1492i	0.203899	+	1.24964i
$473$	25.5799	−	25.5799i	1.17617	−	1.17617i
$474$	2.51473	−	11.9219i	0.115505	−	0.547592i
$475$	−6.16526	+	11.0247i	−0.282881	+	0.505847i
$476$	24.0516	−	6.57614i	1.10240	−	0.301417i
$477$	−0.853301	+	0.853301i	−0.0390700	+	0.0390700i
$478$	25.2943	−	16.4822i	1.15693	−	0.753879i
$479$	30.3198			1.38535			0.692674	−	0.721251i	$-0.256432\pi$
$479$	30.3198			1.38535			0.692674	+	0.721251i	$0.256432\pi$
$480$	12.1689	−	3.45210i	0.555433	−	0.157566i
$481$		−	23.4128i		−	1.06753i
$482$	4.51121	−	2.93959i	0.205480	−	0.133894i
$483$	−21.1209	−	2.17745i	−0.961036	−	0.0990776i
$484$	12.5447	−	28.4133i	0.570216	−	1.29151i
$485$	−6.15099	−	10.4872i	−0.279302	−	0.476201i
$486$	−1.38376	−	0.291882i	−0.0627688	−	0.0132400i
$487$	13.6193	+	13.6193i	0.617151	+	0.617151i	0.944800	−	0.327649i	$-0.106256\pi$
$487$	13.6193	+	13.6193i	0.617151	+	0.617151i	−0.327649	+	0.944800i	$0.606256\pi$
$488$	25.5641	−	4.17119i	1.15723	−	0.188821i
$489$	14.4881			0.655176
$490$	−21.9843	+	2.58622i	−0.993152	+	0.116833i
$491$			19.0990i			0.861924i	0.902370	+	0.430962i	$0.141826\pi$
$491$			19.0990i			0.861924i	−0.902370	+	0.430962i	$0.858174\pi$
$492$	4.85926	−	1.88264i	0.219072	−	0.0848759i
$493$	−19.6697	+	19.6697i	−0.885878	+	0.885878i
$494$	1.74367	−	8.26644i	0.0784512	−	0.371925i
$495$	−2.90461	+	11.1450i	−0.130553	+	0.500932i
$496$	−26.6550	+	24.3019i	−1.19685	+	1.09119i
$497$	1.46107	−	14.1721i	0.0655379	−	0.635707i
$498$	1.54614	−	1.00749i	0.0692840	−	0.0451468i
$499$	−22.6234			−1.01276			−0.506381	−	0.862310i	$-0.669017\pi$
$499$	−22.6234			−1.01276			−0.506381	+	0.862310i	$0.669017\pi$
$500$	8.50499	+	20.6801i	0.380355	+	0.924841i
$501$			6.66731i			0.297874i
$502$	16.3421	+	25.0793i	0.729385	+	1.11934i
$503$	−15.1983	−	15.1983i	−0.677658	−	0.677658i	0.281812	−	0.959470i	$-0.409065\pi$
$503$	−15.1983	−	15.1983i	−0.677658	−	0.677658i	−0.959470	+	0.281812i	$0.909065\pi$
$504$	7.47029	−	0.441327i	0.332753	−	0.0196583i
$505$	−2.45322	+	9.41301i	−0.109167	+	0.418874i
$506$	12.0652	−	57.1990i	0.536362	−	2.54280i
$507$	−5.23845	−	5.23845i	−0.232648	−	0.232648i
$508$	−18.6092	+	7.20983i	−0.825649	+	0.319884i
$509$			18.4978i			0.819899i	0.912108	+	0.409949i	$0.134454\pi$
$509$			18.4978i			0.819899i	−0.912108	+	0.409949i	$0.865546\pi$
$510$	−4.72366	−	14.1327i	−0.209167	−	0.625804i
$511$	−21.5537	+	17.5249i	−0.953479	+	0.775256i
$512$	20.0156	−	10.5535i	0.884571	−	0.466405i
$513$	1.78636	−	1.78636i	0.0788697	−	0.0788697i
$514$	0.787108	+	0.166027i	0.0347178	+	0.00732314i
$515$	37.1437	−	21.7856i	1.63675	−	0.959987i
$516$	−5.67345	+	12.8501i	−0.249760	+	0.565694i
$517$	−12.9311	−	12.9311i	−0.568707	−	0.568707i
$518$	−11.3231	+	35.2735i	−0.497509	+	1.54983i
$519$		−	13.9093i		−	0.610551i
$520$	−9.54500	−	11.5135i	−0.418576	−	0.504901i
$521$			2.65824i			0.116459i	0.998303	+	0.0582297i	$0.0185456\pi$
$521$			2.65824i			0.116459i	−0.998303	+	0.0582297i	$0.981454\pi$
$522$	−6.99454	+	4.55778i	−0.306143	+	0.199488i
$523$	18.8753	−	18.8753i	0.825358	−	0.825358i	−0.161513	−	0.986871i	$-0.551637\pi$
$523$	18.8753	−	18.8753i	0.825358	−	0.825358i	0.986871	+	0.161513i	$0.0516373\pi$
$524$	−0.318311	+	0.720959i	−0.0139055	+	0.0314953i
$525$	2.27418	+	13.0318i	0.0992532	+	0.568755i
$526$	−17.7018	−	3.73390i	−0.771836	−	0.162806i
$527$	30.0467	+	30.0467i	1.30885	+	1.30885i
$528$	−0.950381	+	20.5809i	−0.0413600	+	0.895667i
$529$		−	41.4050i		−	1.80022i
$530$	−3.41459	−	1.70382i	−0.148320	−	0.0740094i
$531$	9.72563			0.422057
$532$	−6.62487	+	11.6108i	−0.287224	+	0.503394i
$533$	−4.35678	−	4.35678i	−0.188713	−	0.188713i
$534$	8.72117	+	1.83958i	0.377402	+	0.0796066i
$535$	−6.52593	−	11.1265i	−0.282141	−	0.481040i
$536$	−6.80102	+	9.45315i	−0.293759	+	0.408314i
$537$	−5.23135	+	5.23135i	−0.225749	+	0.225749i
$538$	−24.0305	+	15.6587i	−1.03603	+	0.675095i
$539$	7.35594	−	35.2965i	0.316843	−	1.52033i
$540$	−0.511733	−	4.44276i	−0.0220215	−	0.191186i
$541$			3.87240i			0.166487i	0.996529	+	0.0832437i	$0.0265280\pi$
$541$			3.87240i			0.166487i	−0.996529	+	0.0832437i	$0.973472\pi$
$542$	0.288472	−	0.187974i	0.0123909	−	0.00807417i
$543$	13.1556	−	13.1556i	0.564561	−	0.564561i
$544$	−13.5069	−	22.9806i	−0.579105	−	0.985283i
$545$	−1.80357	+	6.92033i	−0.0772566	+	0.296434i
$546$	−4.04472	−	7.86919i	−0.173098	−	0.336770i
$547$	1.97663	−	1.97663i	0.0845148	−	0.0845148i	−0.663586	−	0.748100i	$-0.730966\pi$
$547$	1.97663	−	1.97663i	0.0845148	−	0.0845148i	0.748100	+	0.663586i	$0.230966\pi$
$548$	−11.0454	+	4.27935i	−0.471836	+	0.182805i
$549$		−	9.15780i		−	0.390845i
$550$	−36.3377	+	2.46075i	−1.54944	+	0.104927i
$551$		−	14.9134i		−	0.635331i
$552$	3.65535	+	22.4026i	0.155582	+	0.953520i
$553$	22.6745	+	2.33762i	0.964217	+	0.0994056i
$554$	7.84702	+	1.65520i	0.333388	+	0.0703226i
$555$	21.4238	+	5.58347i	0.909391	+	0.237005i
$556$	24.9900	+	11.0334i	1.05981	+	0.467918i
$557$	−12.7754	+	12.7754i	−0.541313	+	0.541313i	−0.923914	−	0.382601i	$-0.875028\pi$
$557$	−12.7754	+	12.7754i	−0.541313	+	0.541313i	0.382601	+	0.923914i	$0.375028\pi$
$558$	6.96229	+	10.6846i	0.294737	+	0.452316i
$559$	16.6081			0.702448
$560$	8.81214	+	21.9624i	0.372381	+	0.928080i
$561$	24.2709			1.02472
$562$	19.5690	+	30.0313i	0.825467	+	1.26679i
$563$	−5.99693	+	5.99693i	−0.252741	+	0.252741i	−0.822093	−	0.569353i	$-0.807194\pi$
$563$	−5.99693	+	5.99693i	−0.252741	+	0.252741i	0.569353	+	0.822093i	$0.307194\pi$
$564$	6.49593	+	2.86802i	0.273528	+	0.120766i
$565$	−10.9217	−	18.6211i	−0.459479	−	0.783397i
$566$	2.73598	+	0.577110i	0.115002	+	0.0242577i
$567$	0.271325	−	2.63180i	0.0113946	−	0.110525i
$568$	−15.0322	+	2.45274i	−0.630735	+	0.102915i
$569$			4.03460i			0.169139i	0.996418	+	0.0845696i	$0.0269515\pi$
$569$			4.03460i			0.169139i	−0.996418	+	0.0845696i	$0.973048\pi$
$570$	7.14834	+	3.56690i	0.299411	+	0.149401i
$571$		−	43.2162i		−	1.80854i	−0.426959	−	0.904271i	$-0.640415\pi$
$571$		−	43.2162i		−	1.80854i	0.426959	−	0.904271i	$-0.359585\pi$
$572$	22.7143	−	8.80029i	0.949733	−	0.367958i
$573$	−11.6255	+	11.6255i	−0.485664	+	0.485664i
$574$	4.45682	+	8.67094i	0.186024	+	0.361918i
$575$	−38.6132	+	10.9156i	−1.61028	+	0.455210i
$576$	−2.54295	−	7.58508i	−0.105956	−	0.316045i
$577$	20.3564	−	20.3564i	0.847448	−	0.847448i	−0.142366	−	0.989814i	$-0.545471\pi$
$577$	20.3564	−	20.3564i	0.847448	−	0.847448i	0.989814	+	0.142366i	$0.0454710\pi$
$578$	−6.16659	+	4.01826i	−0.256496	+	0.167138i
$579$		−	16.6187i		−	0.690648i
$580$	−20.6812	−	16.4090i	−0.858741	−	0.681348i
$581$	2.17804	+	2.67874i	0.0903602	+	0.111133i
$582$	−6.44235	+	4.19796i	−0.267044	+	0.174011i
$583$	4.39509	−	4.39509i	0.182026	−	0.182026i
$584$	24.1067	+	17.3434i	0.997540	+	0.717675i
$585$	−4.56096	+	2.67510i	−0.188573	+	0.110602i
$586$	−12.8105	−	2.70217i	−0.529199	−	0.111626i
$587$	3.65791	+	3.65791i	0.150978	+	0.150978i	0.778555	−	0.627577i	$-0.215953\pi$
$587$	3.65791	+	3.65791i	0.150978	+	0.150978i	−0.627577	+	0.778555i	$0.715953\pi$
$588$	2.28798	+	13.8118i	0.0943546	+	0.569588i
$589$	−22.7811			−0.938679
$590$	9.74936	+	29.1690i	0.401375	+	1.20087i
$591$		−	6.57859i		−	0.270607i
$592$	39.5621	+	1.82689i	1.62599	+	0.0750849i
$593$	−32.9811	−	32.9811i	−1.35437	−	1.35437i	−0.880706	−	0.473664i	$-0.842931\pi$
$593$	−32.9811	−	32.9811i	−1.35437	−	1.35437i	−0.473664	−	0.880706i	$-0.657069\pi$
$594$	7.12735	+	1.50340i	0.292439	+	0.0616851i
$595$	25.3662	−	11.5635i	1.03991	−	0.474056i
$596$	10.9483	−	24.7973i	0.448459	−	1.01574i
$597$	−10.5434	+	10.5434i	−0.431514	+	0.431514i
$598$	22.4853	−	14.6519i	0.919494	−	0.599160i
$599$			3.98653i			0.162885i	0.996678	+	0.0814427i	$0.0259528\pi$
$599$			3.98653i			0.162885i	−0.996678	+	0.0814427i	$0.974047\pi$
$600$	12.8117	−	5.98838i	0.523035	−	0.244475i
$601$			5.37345i			0.219188i	0.993976	+	0.109594i	$0.0349550\pi$
$601$			5.37345i			0.219188i	−0.993976	+	0.109594i	$0.965045\pi$
$602$	−25.0216	−	8.03214i	−1.01980	−	0.327366i
$603$	2.91136	+	2.91136i	0.118560	+	0.118560i
$604$	−15.3979	+	34.8756i	−0.626533	+	1.41907i
$605$	8.75759	−	33.6030i	0.356047	−	1.36615i
$606$	6.01971	+	1.26976i	0.244534	+	0.0515804i
$607$	18.2522	−	18.2522i	0.740835	−	0.740835i	−0.231904	−	0.972739i	$-0.574495\pi$
$607$	18.2522	−	18.2522i	0.740835	−	0.740835i	0.972739	+	0.231904i	$0.0744954\pi$
$608$	13.8322	+	3.59140i	0.560971	+	0.145651i
$609$	−9.85319	−	12.1183i	−0.399271	−	0.491060i
$610$	27.4659	−	9.18015i	1.11206	−	0.371693i
$611$		−	8.39567i		−	0.339652i
$612$	−8.78783	+	3.40470i	−0.355227	+	0.137627i
$613$	11.6742	+	11.6742i	0.471517	+	0.471517i	0.902405	−	0.430888i	$-0.141800\pi$
$613$	11.6742	+	11.6742i	0.471517	+	0.471517i	−0.430888	+	0.902405i	$0.641800\pi$
$614$	−1.51079	+	7.16241i	−0.0609706	+	0.289052i
$615$	5.02565	−	2.94765i	0.202654	−	0.118861i
$616$	−38.4772	+	2.27314i	−1.55029	+	0.0915875i
$617$	9.71546	+	9.71546i	0.391130	+	0.391130i	0.875090	−	0.483960i	$-0.160802\pi$
$617$	9.71546	+	9.71546i	0.391130	+	0.391130i	−0.483960	+	0.875090i	$0.660802\pi$
$618$	−14.8683	−	22.8175i	−0.598091	−	0.917855i
$619$			28.1022i			1.12952i	0.825254	+	0.564762i	$0.191032\pi$
$619$			28.1022i			1.12952i	−0.825254	+	0.564762i	$0.808968\pi$
$620$	−25.0658	+	31.5919i	−1.00667	+	1.26876i
$621$	8.02527			0.322043
$622$	−2.23490	+	1.45630i	−0.0896115	+	0.0583925i
$623$	−1.71002	+	16.5869i	−0.0685105	+	0.664541i
$624$	−6.98973	+	6.37268i	−0.279813	+	0.255111i
$625$	13.0886	+	21.3000i	0.523542	+	0.852000i
$626$	8.58385	−	40.6946i	0.343080	−	1.62648i
$627$	−9.20100	+	9.20100i	−0.367452	+	0.367452i
$628$	23.2310	−	9.00048i	0.927019	−	0.359158i
$629$		−	46.6554i		−	1.86027i
$630$	8.16525	−	1.82447i	0.325311	−	0.0726887i
$631$	−44.7908			−1.78309			−0.891546	−	0.452930i	$-0.850379\pi$
$631$	−44.7908			−1.78309			−0.891546	+	0.452930i	$0.850379\pi$
$632$	−3.92422	−	24.0505i	−0.156097	−	0.956677i
$633$	−11.0309	−	11.0309i	−0.438440	−	0.438440i
$634$	−5.18985	−	1.09471i	−0.206115	−	0.0434765i
$635$	−19.2464	+	11.2885i	−0.763772	+	0.447968i
$636$	−0.974803	+	2.20788i	−0.0386534	+	0.0875482i
$637$	13.8464	−	9.07040i	0.548612	−	0.359383i
$638$	36.0268	−	23.4757i	1.42631	−	0.929413i
$639$			5.38495i			0.213025i
$640$	20.1999	−	15.2304i	0.798471	−	0.602034i
$641$	16.2466			0.641702			0.320851	−	0.947130i	$-0.396031\pi$
$641$	16.2466			0.641702			0.320851	+	0.947130i	$0.396031\pi$
$642$	−6.83505	+	4.45385i	−0.269758	+	0.175779i
$643$	16.7741	−	16.7741i	0.661505	−	0.661505i	−0.294230	−	0.955735i	$-0.595063\pi$
$643$	16.7741	−	16.7741i	0.661505	−	0.661505i	0.955735	+	0.294230i	$0.0950632\pi$
$644$	−40.9622	+	11.1998i	−1.61414	+	0.441335i
$645$	−3.96068	+	15.1972i	−0.155952	+	0.598388i
$646$	3.47465	−	16.4728i	0.136708	−	0.648112i
$647$	−28.5330	+	28.5330i	−1.12175	+	1.12175i	−0.130269	+	0.991479i	$0.541584\pi$
$647$	−28.5330	+	28.5330i	−1.12175	+	1.12175i	−0.991479	+	0.130269i	$0.958416\pi$
$648$	−2.79151	+	0.455480i	−0.109661	+	0.0178929i
$649$	−50.0938			−1.96635
$650$	−12.5952	−	10.9975i	−0.494025	−	0.431359i
$651$	−18.5115	+	15.0514i	−0.725524	+	0.589910i
$652$	27.0193	−	10.4682i	1.05816	−	0.409965i
$653$	15.8054	+	15.8054i	0.618513	+	0.618513i	0.945150	−	0.326637i	$-0.105915\pi$
$653$	15.8054	+	15.8054i	0.618513	+	0.618513i	−0.326637	+	0.945150i	$0.605915\pi$
$654$	4.42562	+	0.933510i	0.173055	+	0.0365031i
$655$	−0.222216	+	0.852643i	−0.00868268	+	0.0333155i
$656$	7.70187	−	7.02196i	0.300708	−	0.274161i
$657$	7.42430	−	7.42430i	0.289650	−	0.289650i
$658$	−4.06038	+	12.6488i	−0.158290	+	0.493102i
$659$	−7.74091			−0.301543			−0.150771	−	0.988569i	$-0.548176\pi$
$659$	−7.74091			−0.301543			−0.150771	+	0.988569i	$0.548176\pi$
$660$	2.63578	+	22.8833i	0.102598	+	0.890732i
$661$	19.8958			0.773856			0.386928	−	0.922110i	$-0.373536\pi$
$661$	19.8958			0.773856			0.386928	+	0.922110i	$0.373536\pi$
$662$	38.7697	−	25.2630i	1.50683	−	0.981876i
$663$	7.87912	+	7.87912i	0.306000	+	0.306000i
$664$	2.15548	−	2.99603i	0.0836488	−	0.116269i
$665$	−5.23254	+	13.9999i	−0.202909	+	0.542891i
$666$	2.88994	−	13.7007i	0.111983	−	0.530893i
$667$	33.4994	−	33.4994i	1.29710	−	1.29710i
$668$	4.81736	+	12.4340i	0.186389	+	0.481087i
$669$	−14.0023			−0.541360
$670$	−5.81324	+	11.6502i	−0.224585	+	0.450085i
$671$			47.1690i			1.82094i
$672$	13.6127	−	6.22058i	0.525120	−	0.239964i
$673$	−5.16500	+	5.16500i	−0.199096	+	0.199096i	−0.799612	−	0.600516i	$-0.794962\pi$
$673$	−5.16500	+	5.16500i	−0.199096	+	0.199096i	0.600516	+	0.799612i	$0.294962\pi$
$674$	2.02420	−	9.59641i	0.0779693	−	0.369640i
$675$	−1.36015	−	4.81144i	−0.0523521	−	0.185193i
$676$	−13.5543	−	5.98436i	−0.521319	−	0.230168i
$677$	3.01547	+	3.01547i	0.115894	+	0.115894i	0.762675	−	0.646781i	$-0.223885\pi$
$677$	3.01547	+	3.01547i	0.115894	+	0.115894i	−0.646781	+	0.762675i	$0.723885\pi$
$678$	−11.4390	+	7.45389i	−0.439313	+	0.286265i
$679$	−9.07531	−	11.1616i	−0.348279	−	0.428344i
$680$	−19.0206	−	22.9433i	−0.729407	−	0.879836i
$681$	−3.49129			−0.133787
$682$	−35.8607	−	55.0332i	−1.37318	−	2.10733i
$683$	−28.6172	−	28.6172i	−1.09501	−	1.09501i	−0.994985	−	0.100023i	$-0.968108\pi$
$683$	−28.6172	−	28.6172i	−1.09501	−	1.09501i	−0.100023	−	0.994985i	$-0.531892\pi$
$684$	2.04072	−	4.62213i	0.0780289	−	0.176732i
$685$	−11.4236	+	6.70020i	−0.436474	+	0.256001i
$686$	−25.2475	+	6.96889i	−0.963953	+	0.266074i
$687$	1.45569	+	1.45569i	0.0555381	+	0.0555381i
$688$	−1.29592	+	28.0637i	−0.0494066	+	1.06992i
$689$	2.85358			0.108713
$690$	8.04486	+	24.0693i	0.306262	+	0.916302i
$691$	11.9509			0.454635			0.227318	−	0.973821i	$-0.427004\pi$
$691$	11.9509			0.454635			0.227318	+	0.973821i	$0.427004\pi$
$692$	−10.0499	−	25.9398i	−0.382042	−	0.986083i
$693$	−1.39751	+	13.5556i	−0.0530870	+	0.514935i
$694$	−16.1776	−	3.41239i	−0.614093	−	0.129533i
$695$	29.5545	+	7.70247i	1.12107	+	0.292171i
$696$	−9.75115	+	13.5537i	−0.369616	+	0.513752i
$697$	−8.68188	−	8.68188i	−0.328850	−	0.328850i
$698$	37.4066	−	24.3748i	1.41586	−	0.922602i
$699$			7.10955i			0.268908i
$700$	13.6571	+	22.6602i	0.516190	+	0.856474i
$701$		−	39.7823i		−	1.50256i	−0.659985	−	0.751279i	$-0.729437\pi$
$701$		−	39.7823i		−	1.50256i	0.659985	−	0.751279i	$-0.270563\pi$
$702$	1.82572	+	2.80182i	0.0689072	+	0.105748i
$703$	17.6869	+	17.6869i	0.667072	+	0.667072i
$704$	13.0980	+	39.0684i	0.493649	+	1.47245i
$705$	7.68242	+	2.00219i	0.289337	+	0.0754068i
$706$	6.25320	−	29.6454i	0.235342	−	1.11572i
$707$	−1.18033	+	11.4490i	−0.0443908	+	0.430583i
$708$	18.1376	−	7.02710i	0.681652	−	0.264095i
$709$	51.7991			1.94536			0.972679	−	0.232155i	$-0.0745776\pi$
$709$	51.7991			1.94536			0.972679	+	0.232155i	$0.0745776\pi$
$710$	−16.1505	+	5.39809i	−0.606116	+	0.202587i
$711$	−8.61557			−0.323109
$712$	17.5935	−	2.87066i	0.659344	−	0.107582i
$713$	−51.1724	−	51.1724i	−1.91642	−	1.91642i
$714$	−8.06003	−	15.6812i	−0.301639	−	0.586852i
$715$	23.4921	−	13.7786i	0.878556	−	0.515292i
$716$	−5.97624	+	13.5359i	−0.223343	+	0.505860i
$717$	−15.0952	−	15.0952i	−0.563741	−	0.563741i
$718$	−0.0501763	+	0.0326958i	−0.00187256	+	0.00122020i
$719$	30.1055			1.12275			0.561373	−	0.827563i	$-0.310273\pi$
$719$	30.1055			1.12275			0.561373	+	0.827563i	$0.310273\pi$
$720$	−4.16439	−	7.91567i	−0.155198	−	0.295000i
$721$	39.5323	−	32.1429i	1.47226	−	1.19707i
$722$	−9.74195	−	14.9504i	−0.362558	−	0.556396i
$723$	−2.69222	−	2.69222i	−0.100125	−	0.100125i
$724$	15.0288	−	34.0396i	0.558542	−	1.26507i
$725$	−25.7617	−	14.4065i	−0.956765	−	0.535045i
$726$	−21.4894	−	4.53283i	−0.797547	−	0.168229i
$727$	30.2698	−	30.2698i	1.12265	−	1.12265i	0.131303	−	0.991342i	$-0.458084\pi$
$727$	30.2698	−	30.2698i	1.12265	−	1.12265i	0.991342	−	0.131303i	$-0.0419162\pi$
$728$	−13.2289	−	11.7530i	−0.490294	−	0.435595i
$729$			1.00000i			0.0370370i
$730$	29.7093	+	14.8244i	1.09959	+	0.548677i
$731$	33.0954			1.22408
$732$	−6.61683	−	17.0786i	−0.244565	−	0.631243i
$733$	−7.20460	+	7.20460i	−0.266108	+	0.266108i	−0.827530	−	0.561422i	$-0.810255\pi$
$733$	−7.20460	+	7.20460i	−0.266108	+	0.266108i	0.561422	+	0.827530i	$0.310255\pi$
$734$	24.9396	+	5.26058i	0.920536	+	0.194172i
$735$	4.99777	+	14.8331i	0.184346	+	0.547129i
$736$	23.0036	+	39.1381i	0.847925	+	1.44265i
$737$	−14.9955	−	14.9955i	−0.552367	−	0.552367i
$738$	−2.01173	−	3.08728i	−0.0740528	−	0.113644i
$739$	−26.1241			−0.960992			−0.480496	−	0.876997i	$-0.659543\pi$
$739$	−26.1241			−0.960992			−0.480496	+	0.876997i	$0.659543\pi$
$740$	43.9881	−	5.06670i	1.61703	−	0.186256i
$741$	−5.97387			−0.219456
$742$	−4.29917	−	1.38007i	−0.157827	−	0.0506639i
$743$	−0.603340	+	0.603340i	−0.0221344	+	0.0221344i	−0.718087	−	0.695953i	$-0.754982\pi$
$743$	−0.603340	+	0.603340i	−0.0221344	+	0.0221344i	0.695953	+	0.718087i	$0.254982\pi$
$744$	20.7041	+	14.8955i	0.759051	+	0.546095i
$745$	7.64308	−	29.3266i	0.280021	−	1.07444i
$746$	−0.759246	+	3.59946i	−0.0277980	+	0.131786i
$747$	−0.922710	−	0.922710i	−0.0337602	−	0.0337602i
$748$	45.2634	−	17.5366i	1.65500	−	0.641201i
$749$	−9.62851	−	11.8420i	−0.351818	−	0.432698i
$750$	13.0669	−	8.90252i	0.477137	−	0.325074i
$751$	6.27365			0.228929			0.114464	−	0.993427i	$-0.463485\pi$
$751$	6.27365			0.228929			0.114464	+	0.993427i	$0.463485\pi$
$752$	14.1867	+	0.655110i	0.517335	+	0.0238894i
$753$	14.9669	−	14.9669i	0.545425	−	0.545425i
$754$	19.3164	+	4.07447i	0.703462	+	0.148384i
$755$	−10.7494	+	41.2456i	−0.391211	+	1.50108i
$756$	−1.39557	−	5.10415i	−0.0507563	−	0.185636i
$757$	−14.3084	+	14.3084i	−0.520049	+	0.520049i	−0.917586	−	0.397537i	$-0.869865\pi$
$757$	−14.3084	+	14.3084i	−0.520049	+	0.520049i	0.397537	+	0.917586i	$0.369865\pi$
$758$	14.7027	+	22.5633i	0.534025	+	0.819537i
$759$	−41.3358			−1.50039
$760$	15.9083	+	1.48709i	0.577056	+	0.0539423i
$761$		−	11.5121i		−	0.417314i	−0.977989	−	0.208657i	$-0.933091\pi$
$761$		−	11.5121i		−	0.417314i	0.977989	−	0.208657i	$-0.0669093\pi$
$762$	7.70420	+	11.8232i	0.279094	+	0.428308i
$763$	−0.867762	+	8.41715i	−0.0314151	+	0.304721i
$764$	−13.2809	+	30.0806i	−0.480486	+	1.08828i
$765$	−9.08876	+	5.33075i	−0.328605	+	0.192734i
$766$	8.37758	−	39.7167i	0.302694	−	1.43502i
$767$	−16.2620	−	16.2620i	−0.587188	−	0.587188i
$768$	−10.2229	−	12.3082i	−0.368887	−	0.444135i
$769$	−5.61832			−0.202602			−0.101301	−	0.994856i	$-0.532300\pi$
$769$	−5.61832			−0.202602			−0.101301	+	0.994856i	$0.532300\pi$
$770$	−42.0567	+	9.39730i	−1.51562	+	0.338655i
$771$		−	0.568816i		−	0.0204854i
$772$	−12.0076	−	30.9926i	−0.432162	−	1.11545i
$773$	−34.9945	+	34.9945i	−1.25866	+	1.25866i	−0.306932	+	0.951731i	$0.599302\pi$
$773$	−34.9945	+	34.9945i	−1.25866	+	1.25866i	−0.951731	+	0.306932i	$0.900698\pi$
$774$	9.71875	+	2.05001i	0.349333	+	0.0736859i
$775$	−22.0069	+	39.3526i	−0.790510	+	1.41359i
$776$	−8.98133	+	12.4837i	−0.322411	+	0.448138i
$777$	26.0576	+	2.68640i	0.934813	+	0.0963741i
$778$	−2.68152	−	4.11517i	−0.0961373	−	0.147536i
$779$	6.58252			0.235843
$780$	−6.57300	+	8.28432i	−0.235351	+	0.296626i
$781$		−	27.7363i		−	0.992481i
$782$	44.8072	−	29.1972i	1.60230	−	1.04409i
$783$	4.17424	+	4.17424i	0.149175	+	0.149175i
$784$	14.2464	+	24.1048i	0.508800	+	0.860885i
$785$	24.0265	−	14.0921i	0.857544	−	0.502968i
$786$	0.545274	+	0.115016i	0.0194493	+	0.00410250i
$787$	−26.4339	−	26.4339i	−0.942267	−	0.942267i	0.0561548	−	0.998422i	$-0.482116\pi$
$787$	−26.4339	−	26.4339i	−0.942267	−	0.942267i	−0.998422	+	0.0561548i	$0.982116\pi$
$788$	−4.75326	−	12.2686i	−0.169328	−	0.437050i
$789$			12.7925i			0.455425i
$790$	−8.63660	−	25.8397i	−0.307276	−	0.919336i
$791$	−16.1141	−	19.8186i	−0.572952	−	0.704668i
$792$	14.3782	−	2.34604i	0.510908	−	0.0833628i
$793$	−15.3126	+	15.3126i	−0.543766	+	0.543766i
$794$	−4.68694	+	22.2200i	−0.166333	+	0.788559i
$795$	−0.680518	+	2.61115i	−0.0241355	+	0.0926081i
$796$	−12.0447	+	27.2807i	−0.426914	+	0.966940i
$797$	23.3643	+	23.3643i	0.827607	+	0.827607i	0.987185	−	0.159579i	$-0.0510135\pi$
$797$	23.3643	+	23.3643i	0.827607	+	0.827607i	−0.159579	+	0.987185i	$0.551014\pi$
$798$	9.00017	+	2.88913i	0.318603	+	0.102274i
$799$		−	16.7303i		−	0.591875i
$800$	19.5660	−	20.4248i	0.691763	−	0.722125i
$801$		−	6.30249i		−	0.222688i
$802$	29.5610	+	45.3655i	1.04383	+	1.60191i
$803$	−38.2403	+	38.2403i	−1.34947	+	1.34947i
$804$	7.53301	+	3.32590i	0.265669	+	0.117296i
$805$	−43.2011	+	19.6937i	−1.52264	+	0.694113i
$806$	6.22401	−	29.5070i	0.219232	−	1.03934i
$807$	14.3410	+	14.3410i	0.504828	+	0.504828i
$808$	12.1438	−	1.98145i	0.427216	−	0.0697071i
$809$			22.7738i			0.800684i	0.916366	+	0.400342i	$0.131109\pi$
$809$			22.7738i			0.800684i	−0.916366	+	0.400342i	$0.868891\pi$
$810$	−2.99919	+	1.00244i	−0.105381	+	0.0352222i
$811$	−7.72619			−0.271303			−0.135652	−	0.990757i	$-0.543313\pi$
$811$	−7.72619			−0.271303			−0.135652	+	0.990757i	$0.543313\pi$
$812$	−27.1314	−	15.4805i	−0.952124	−	0.543260i
$813$	−0.172156	−	0.172156i	−0.00603776	−	0.00603776i
$814$	−14.8852	+	70.5684i	−0.521726	+	2.47342i
$815$	27.9445	−	16.3901i	0.978853	−	0.574119i
$816$	−13.9286	+	12.6990i	−0.487599	+	0.444555i
$817$	−12.5463	+	12.5463i	−0.438941	+	0.438941i
$818$	12.2849	+	18.8528i	0.429530	+	0.659174i
$819$	−4.85426	+	3.94691i	−0.169622	+	0.137916i
$820$	7.24269	−	9.12836i	0.252926	−	0.318776i
$821$		−	6.24353i		−	0.217901i	−0.994047	−	0.108950i	$-0.965251\pi$
$821$		−	6.24353i		−	0.217901i	0.994047	−	0.108950i	$-0.0347489\pi$
$822$	4.57278	+	7.01758i	0.159494	+	0.244766i
$823$	24.9458	−	24.9458i	0.869557	−	0.869557i	−0.122866	−	0.992423i	$-0.539209\pi$
$823$	24.9458	−	24.9458i	0.869557	−	0.869557i	0.992423	+	0.122866i	$0.0392086\pi$
$824$	−44.2147	−	31.8101i	−1.54029	−	1.10816i
$825$	7.00571	+	24.7823i	0.243908	+	0.862809i
$826$	16.6354	+	32.3650i	0.578821	+	1.12612i
$827$	4.19002	−	4.19002i	0.145701	−	0.145701i	−0.630493	−	0.776195i	$-0.717147\pi$
$827$	4.19002	−	4.19002i	0.145701	−	0.145701i	0.776195	+	0.630493i	$0.217147\pi$
$828$	14.9665	−	5.79854i	0.520123	−	0.201513i
$829$			40.2043i			1.39635i	0.715926	+	0.698176i	$0.246005\pi$
$829$			40.2043i			1.39635i	−0.715926	+	0.698176i	$0.753995\pi$
$830$	1.84242	−	3.69234i	0.0639512	−	0.128163i
$831$		−	5.67077i		−	0.196717i
$832$	−8.43083	+	16.9349i	−0.292287	+	0.587112i
$833$	27.5920	−	18.0749i	0.956007	−	0.626256i
$834$	3.98672	−	18.9004i	0.138049	−	0.654466i
$835$	7.54256	+	12.8598i	0.261021	+	0.445032i
$836$	−10.5111	+	23.8072i	−0.363535	+	0.823389i
$837$	6.37641	−	6.37641i	0.220401	−	0.220401i
$838$	−2.80318	+	1.82660i	−0.0968341	+	0.0630989i
$839$	−19.9254			−0.687903			−0.343951	−	0.938987i	$-0.611766\pi$
$839$	−19.9254			−0.687903			−0.343951	+	0.938987i	$0.611766\pi$
$840$	13.9093	−	9.30218i	0.479918	−	0.320956i
$841$	5.84849			0.201672
$842$	−9.50927	+	6.19642i	−0.327711	+	0.213543i
$843$	17.9222	−	17.9222i	0.617274	−	0.617274i
$844$	−28.5421	−	12.6016i	−0.982460	−	0.433766i
$845$	−16.0300	−	4.17773i	−0.551448	−	0.143718i
$846$	1.03631	−	4.91298i	0.0356291	−	0.168912i
$847$	4.21358	−	40.8710i	0.144780	−	1.40435i
$848$	−0.222663	+	4.82186i	−0.00764629	+	0.165583i
$849$		−	1.97720i		−	0.0678575i
$850$	−25.0988	−	21.9151i	−0.860883	−	0.751682i
$851$			79.4588i			2.72381i
$852$	3.89081	+	10.0425i	0.133297	+	0.344051i
$853$	6.36836	−	6.36836i	0.218048	−	0.218048i	−0.589627	−	0.807676i	$-0.700725\pi$
$853$	6.36836	−	6.36836i	0.218048	−	0.218048i	0.807676	+	0.589627i	$0.200725\pi$
$854$	30.4754	−	15.6642i	1.04285	−	0.536017i
$855$	1.42464	−	5.46637i	0.0487218	−	0.186946i
$856$	−9.52880	+	13.2447i	−0.325688	+	0.452693i
$857$	−24.7215	+	24.7215i	−0.844472	+	0.844472i	−0.989437	−	0.144965i	$-0.953693\pi$
$857$	−24.7215	+	24.7215i	−0.844472	+	0.844472i	0.144965	+	0.989437i	$0.453693\pi$
$858$	−9.40371	−	14.4313i	−0.321037	−	0.492677i
$859$		−	40.1782i		−	1.37086i	−0.728137	−	0.685431i	$-0.759614\pi$
$859$		−	40.1782i		−	1.37086i	0.728137	−	0.685431i	$-0.240386\pi$
$860$	3.59411	+	31.2033i	0.122558	+	1.06402i
$861$	5.34884	−	4.34904i	0.182288	−	0.148215i
$862$	7.19298	+	11.0386i	0.244994	+	0.375977i
$863$	−3.84231	+	3.84231i	−0.130794	+	0.130794i	−0.769473	−	0.638679i	$-0.779481\pi$
$863$	−3.84231	+	3.84231i	−0.130794	+	0.130794i	0.638679	+	0.769473i	$0.279481\pi$
$864$	−4.87686	+	2.86640i	−0.165914	+	0.0975169i
$865$	−15.7352	−	26.8281i	−0.535014	−	0.912182i
$866$	0.265159	−	1.25707i	0.00901046	−	0.0427171i
$867$	3.68012	+	3.68012i	0.124984	+	0.124984i
$868$	−23.6475	+	41.4449i	−0.802647	+	1.40673i
$869$	44.3762			1.50536
$870$	−8.33489	+	16.7037i	−0.282579	+	0.566309i
$871$		−	9.73604i		−	0.329893i
$872$	8.92794	−	1.45674i	0.302338	−	0.0493313i
$873$	3.84469	+	3.84469i	0.130123	+	0.130123i
$874$	−5.91767	+	28.0547i	−0.200168	+	0.948965i
$875$	19.1290	+	22.5629i	0.646677	+	0.762764i
$876$	8.48145	−	19.2101i	0.286562	−	0.649048i
$877$	11.5497	−	11.5497i	0.390006	−	0.390006i	−0.484684	−	0.874689i	$-0.661065\pi$
$877$	11.5497	−	11.5497i	0.390006	−	0.390006i	0.874689	+	0.484684i	$0.161065\pi$
$878$	21.8948	+	33.6006i	0.738913	+	1.13396i
$879$			9.25775i			0.312256i
$880$	21.4495	+	40.7712i	0.723063	+	1.37440i
$881$		−	11.8310i		−	0.398598i	−0.979939	−	0.199299i	$-0.936134\pi$
$881$		−	11.8310i		−	0.398598i	0.979939	−	0.199299i	$-0.0638665\pi$
$882$	9.22222	−	3.59871i	0.310528	−	0.121175i
$883$	23.5185	+	23.5185i	0.791462	+	0.791462i	0.981732	−	0.190270i	$-0.0609364\pi$
$883$	23.5185	+	23.5185i	0.791462	+	0.791462i	−0.190270	+	0.981732i	$0.560936\pi$
$884$	20.3869	+	9.00103i	0.685685	+	0.302737i
$885$	18.7587	−	11.0024i	0.630566	−	0.369840i
$886$	6.08815	−	28.8629i	0.204535	−	0.969668i
$887$	−9.76299	+	9.76299i	−0.327809	+	0.327809i	−0.851753	−	0.523944i	$-0.824460\pi$
$887$	−9.76299	+	9.76299i	−0.327809	+	0.327809i	0.523944	+	0.851753i	$0.324460\pi$
$888$	−4.50973	−	27.6389i	−0.151337	−	0.927502i
$889$	−20.4841	+	16.6552i	−0.687015	+	0.558599i
$890$	18.9023	−	6.31787i	0.633608	−	0.211776i
$891$		−	5.15070i		−	0.172555i
$892$	−26.1132	+	10.1171i	−0.874336	+	0.338747i
$893$	6.34237	+	6.34237i	0.212239	+	0.212239i
$894$	−18.7546	−	3.95598i	−0.627249	−	0.132308i
$895$	−4.17206	+	16.0082i	−0.139457	+	0.535097i
$896$	20.8920	−	21.4365i	0.697952	−	0.716144i
$897$	−13.4189	−	13.4189i	−0.448044	−	0.448044i
$898$	36.1573	−	23.5608i	1.20659	−	0.786234i
$899$		−	53.2333i		−	1.77543i
$900$	−6.01301	−	7.99023i	−0.200434	−	0.266341i
$901$	5.68640			0.189442
$902$	10.3618	+	15.9016i	0.345010	+	0.529467i
$903$	−1.90562	+	18.4842i	−0.0634152	+	0.615116i
$904$	−15.9472	+	22.1660i	−0.530397	+	0.737231i
$905$	10.4918	−	40.2570i	0.348758	−	1.33819i
$906$	26.3770	+	5.56378i	0.876316	+	0.184844i
$907$	2.13567	−	2.13567i	0.0709137	−	0.0709137i	−0.670760	−	0.741674i	$-0.734032\pi$
$907$	2.13567	−	2.13567i	0.0709137	−	0.0709137i	0.741674	+	0.670760i	$0.234032\pi$
$908$	−6.51100	+	2.52258i	−0.216075	+	0.0837148i
$909$		−	4.35024i		−	0.144288i
$910$	−16.7036	−	10.6023i	−0.553720	−	0.351463i
$911$	−11.0958			−0.367620			−0.183810	−	0.982962i	$-0.558843\pi$
$911$	−11.0958			−0.367620			−0.183810	+	0.982962i	$0.558843\pi$
$912$	0.466139	−	10.0944i	0.0154354	−	0.334260i
$913$	4.75260	+	4.75260i	0.157288	+	0.157288i
$914$	−1.43820	+	6.81829i	−0.0475716	+	0.225529i
$915$	−10.3600	−	17.6634i	−0.342491	−	0.583935i
$916$	3.76654	+	1.66297i	0.124450	+	0.0549460i
$917$	−0.106916	+	1.03706i	−0.00353067	+	0.0342469i
$918$	3.63816	+	5.58326i	0.120077	+	0.184275i
$919$			27.5278i			0.908059i	0.890987	+	0.454029i	$0.150014\pi$
$919$			27.5278i			0.908059i	−0.890987	+	0.454029i	$0.849986\pi$
$920$	32.3939	+	39.0747i	1.06800	+	1.28826i
$921$	5.17603			0.170556
$922$	−3.75398	−	5.76100i	−0.123631	−	0.189729i
$923$	9.00408	−	9.00408i	0.296373	−	0.296373i
$924$	7.18815	+	26.2900i	0.236473	+	0.864876i
$925$	47.6384	−	13.4669i	1.56634	−	0.442789i
$926$	46.3527	+	9.77732i	1.52324	+	0.321303i
$927$	−13.6171	+	13.6171i	−0.447245	+	0.447245i
$928$	−8.39214	+	32.3222i	−0.275485	+	1.06103i
$929$	56.6438			1.85842			0.929211	−	0.369551i	$-0.120488\pi$
$929$	56.6438			1.85842			0.929211	+	0.369551i	$0.120488\pi$
$930$	25.5160	+	12.7321i	0.836703	+	0.417501i
$931$	−3.60791	+	17.3121i	−0.118245	+	0.567381i
$932$	5.13689	+	13.2588i	0.168264	+	0.434305i
$933$	1.33376	+	1.33376i	0.0436652	+	0.0436652i
$934$	10.2169	−	48.4364i	0.334306	−	1.58489i
$935$	46.8134	−	27.4571i	1.53096	−	0.897943i
$936$	5.42923	+	3.90603i	0.177460	+	0.127673i
$937$	9.19223	−	9.19223i	0.300297	−	0.300297i	−0.540833	−	0.841130i	$-0.681891\pi$
$937$	9.19223	−	9.19223i	0.300297	−	0.300297i	0.841130	+	0.540833i	$0.181891\pi$
$938$	−4.70862	+	14.6682i	−0.153742	+	0.478934i
$939$	−29.4086			−0.959715
$940$	15.7738	−	1.81688i	0.514484	−	0.0592601i
$941$	−17.9694			−0.585785			−0.292892	−	0.956145i	$-0.594618\pi$
$941$	−17.9694			−0.585785			−0.292892	+	0.956145i	$0.594618\pi$
$942$	−9.61763	−	14.7596i	−0.313359	−	0.480894i
$943$	14.7861	+	14.7861i	0.481501	+	0.481501i
$944$	28.7479	−	26.2100i	0.935664	−	0.853064i
$945$	−2.45396	−	5.38313i	−0.0798275	−	0.175113i
$946$	−50.0583	−	10.5590i	−1.62754	−	0.343301i
$947$	22.2454	−	22.2454i	0.722879	−	0.722879i	−0.246312	−	0.969191i	$-0.579219\pi$
$947$	22.2454	−	22.2454i	0.722879	−	0.722879i	0.969191	+	0.246312i	$0.0792188\pi$
$948$	−16.0674	+	6.22505i	−0.521845	+	0.202180i
$949$	−24.8281			−0.805953
$950$	17.8228	−	1.20694i	0.578247	−	0.0391583i
$951$			3.75053i			0.121619i
$952$	−26.3615	−	23.4205i	−0.854382	−	0.759063i
$953$	36.8379	−	36.8379i	1.19330	−	1.19330i	0.217160	−	0.976136i	$-0.430321\pi$
$953$	36.8379	−	36.8379i	1.19330	−	1.19330i	0.976136	−	0.217160i	$-0.0696793\pi$
$954$	1.66986	+	0.352228i	0.0540636	+	0.0114038i
$955$	−9.27151	+	35.5749i	−0.300019	+	1.15118i
$956$	−39.0583	−	17.2446i	−1.26323	−	0.557731i
$957$	−21.5002	−	21.5002i	−0.695003	−	0.695003i
$958$	−23.4093	−	35.9248i	−0.756319	−	1.16068i
$959$	−12.1582	+	9.88563i	−0.392610	+	0.319224i
$960$	−13.4856	−	11.7532i	−0.435247	−	0.379333i
$961$	−50.3172			−1.62313
$962$	−27.7410	+	18.0765i	−0.894405	+	0.582811i
$963$	4.07905	+	4.07905i	0.131446	+	0.131446i
$964$	−6.96600	−	3.07556i	−0.224360	−	0.0990572i
$965$	−18.8003	−	32.0539i	−0.605202	−	1.03185i
$966$	13.7270	+	26.7065i	0.441660	+	0.859269i
$967$	9.12506	+	9.12506i	0.293442	+	0.293442i	0.838438	−	0.544996i	$-0.183469\pi$
$967$	9.12506	+	9.12506i	0.293442	+	0.293442i	−0.544996	+	0.838438i	$0.683469\pi$
$968$	−43.3513	+	7.07345i	−1.39336	+	0.227349i
$969$	−11.9043			−0.382421
$970$	−7.67688	+	15.3850i	−0.246490	+	0.493983i
$971$	−8.32961			−0.267310			−0.133655	−	0.991028i	$-0.542671\pi$
$971$	−8.32961			−0.267310			−0.133655	+	0.991028i	$0.542671\pi$
$972$	0.722534	+	1.86492i	0.0231753	+	0.0598175i
$973$	35.9469	+	3.70593i	1.15240	+	0.118807i
$974$	5.62183	−	26.6522i	0.180135	−	0.853991i
$975$	−5.77085	+	10.3194i	−0.184815	+	0.330485i
$976$	−24.6798	−	27.0694i	−0.789980	−	0.866471i
$977$	−19.3851	−	19.3851i	−0.620186	−	0.620186i	0.325393	−	0.945579i	$-0.394503\pi$
$977$	−19.3851	−	19.3851i	−0.620186	−	0.620186i	−0.945579	+	0.325393i	$0.894503\pi$
$978$	−11.1860	−	17.1664i	−0.357688	−	0.548922i
$979$			32.4622i			1.03750i
$980$	20.0379	+	24.0516i	0.640088	+	0.768301i
$981$		−	3.19824i		−	0.102112i
$982$	22.6296	−	14.7459i	0.722140	−	0.470560i
$983$	−7.23192	−	7.23192i	−0.230663	−	0.230663i	0.582307	−	0.812969i	$-0.302150\pi$
$983$	−7.23192	−	7.23192i	−0.230663	−	0.230663i	−0.812969	+	0.582307i	$0.802150\pi$
$984$	−5.98239	−	4.30400i	−0.190712	−	0.137206i
$985$	−7.44219	−	12.6887i	−0.237128	−	0.404295i
$986$	38.4924	+	8.11932i	1.22585	+	0.258572i
$987$	9.34407	+	0.963323i	0.297425	+	0.0306629i
$988$	−11.1408	+	4.31633i	−0.354437	+	0.137321i
$989$	−56.3648			−1.79230
$990$	15.4479	−	5.16326i	0.490966	−	0.164099i
$991$	29.2147			0.928036			0.464018	−	0.885826i	$-0.346407\pi$
$991$	29.2147			0.928036			0.464018	+	0.885826i	$0.346407\pi$
$992$	49.3742	+	12.8195i	1.56763	+	0.407020i
$993$	−23.1371	−	23.1371i	−0.734235	−	0.734235i
$994$	−17.9201	+	9.21082i	−0.568390	+	0.292150i
$995$	−8.40852	+	32.2636i	−0.266568	+	1.02282i
$996$	−2.38747	−	1.05409i	−0.0756500	−	0.0334003i
$997$	32.9468	+	32.9468i	1.04344	+	1.04344i	0.999013	+	0.0444243i	$0.0141453\pi$
$997$	32.9468	+	32.9468i	1.04344	+	1.04344i	0.0444243	+	0.999013i	$0.485855\pi$
$998$	17.4670	+	26.8056i	0.552909	+	0.848516i
$999$	−9.90106			−0.313256

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bj.b.517.25	yes	184
5.3	odd	4	inner	840.2.bj.b.13.17	✓	184
7.6	odd	2	inner	840.2.bj.b.517.26	yes	184
8.5	even	2	inner	840.2.bj.b.517.18	yes	184
35.13	even	4	inner	840.2.bj.b.13.18	yes	184
40.13	odd	4	inner	840.2.bj.b.13.26	yes	184
56.13	odd	2	inner	840.2.bj.b.517.17	yes	184
280.13	even	4	inner	840.2.bj.b.13.25	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bj.b.13.17	✓	184	5.3	odd	4	inner
840.2.bj.b.13.18	yes	184	35.13	even	4	inner
840.2.bj.b.13.25	yes	184	280.13	even	4	inner
840.2.bj.b.13.26	yes	184	40.13	odd	4	inner
840.2.bj.b.517.17	yes	184	56.13	odd	2	inner
840.2.bj.b.517.18	yes	184	8.5	even	2	inner
840.2.bj.b.517.25	yes	184	1.1	even	1	trivial
840.2.bj.b.517.26	yes	184	7.6	odd	2	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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.bj (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.772078 - 1.18486i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-0.807792 + 1.82961i) q^{4} +(-0.563926 + 2.16379i) q^{5} +(1.38376 + 0.291882i) q^{6} +(-0.271325 + 2.63180i) q^{7} +(2.79151 - 0.455480i) q^{8} -1.00000i q^{9} +(2.99919 - 1.00244i) q^{10} +5.15070i q^{11} +(-0.722534 - 1.86492i) q^{12} +(-1.67208 + 1.67208i) q^{13} +(3.32780 - 1.71047i) q^{14} +(-1.13127 - 1.92879i) q^{15} +(-2.69494 - 2.95589i) q^{16} +(-3.33200 + 3.33200i) q^{17} +(-1.18486 + 0.772078i) q^{18} -2.52629i q^{19} +(-3.50336 - 2.77966i) q^{20} +(-1.66911 - 2.05282i) q^{21} +(6.10286 - 3.97674i) q^{22} +(5.67473 - 5.67473i) q^{23} +(-1.65182 + 2.29597i) q^{24} +(-4.36397 - 2.44044i) q^{25} +(3.27216 + 0.690207i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-4.59600 - 2.62237i) q^{28} +5.90326 q^{29} +(-1.41191 + 2.82958i) q^{30} -9.01760i q^{31} +(-1.42161 + 5.47531i) q^{32} +(-3.64209 - 3.64209i) q^{33} +(6.52053 + 1.37540i) q^{34} +(-5.54166 - 2.07123i) q^{35} +(1.82961 + 0.807792i) q^{36} +(-7.00111 + 7.00111i) q^{37} +(-2.99331 + 1.95050i) q^{38} -2.36468i q^{39} +(-0.588643 + 6.29710i) q^{40} +2.60560i q^{41} +(-1.14362 + 3.56260i) q^{42} +(-4.96630 - 4.96630i) q^{43} +(-9.42377 - 4.16069i) q^{44} +(2.16379 + 0.563926i) q^{45} +(-11.1051 - 2.34243i) q^{46} +(-2.51054 + 2.51054i) q^{47} +(3.99574 + 0.184515i) q^{48} +(-6.85277 - 1.42814i) q^{49} +(0.477751 + 7.05491i) q^{50} -4.71216i q^{51} +(-1.70856 - 4.40995i) q^{52} +(-0.853301 - 0.853301i) q^{53} +(0.291882 - 1.38376i) q^{54} +(-11.1450 - 2.90461i) q^{55} +(0.441327 + 7.47029i) q^{56} +(1.78636 + 1.78636i) q^{57} +(-4.55778 - 6.99454i) q^{58} +9.72563i q^{59} +(4.44276 - 0.511733i) q^{60} +9.15780 q^{61} +(-10.6846 + 6.96229i) q^{62} +(2.63180 + 0.271325i) q^{63} +(7.58508 - 2.54295i) q^{64} +(-2.67510 - 4.56096i) q^{65} +(-1.50340 + 7.12735i) q^{66} +(-2.91136 + 2.91136i) q^{67} +(-3.40470 - 8.78783i) q^{68} +8.02527i q^{69} +(1.82447 + 8.16525i) q^{70} -5.38495 q^{71} +(-0.455480 - 2.79151i) q^{72} +(7.42430 + 7.42430i) q^{73} +(13.7007 + 2.88994i) q^{74} +(4.81144 - 1.36015i) q^{75} +(4.62213 + 2.04072i) q^{76} +(-13.5556 - 1.39751i) q^{77} +(-2.80182 + 1.82572i) q^{78} -8.61557i q^{79} +(7.91567 - 4.16439i) q^{80} -1.00000 q^{81} +(3.08728 - 2.01173i) q^{82} +(0.922710 - 0.922710i) q^{83} +(5.10415 - 1.39557i) q^{84} +(-5.33075 - 9.08876i) q^{85} +(-2.05001 + 9.71875i) q^{86} +(-4.17424 + 4.17424i) q^{87} +(2.34604 + 14.3782i) q^{88} +6.30249 q^{89} +(-1.00244 - 2.99919i) q^{90} +(-3.94691 - 4.85426i) q^{91} +(5.79854 + 14.9665i) q^{92} +(6.37641 + 6.37641i) q^{93} +(4.91298 + 1.03631i) q^{94} +(5.46637 + 1.42464i) q^{95} +(-2.86640 - 4.87686i) q^{96} +(-3.84469 + 3.84469i) q^{97} +(3.59871 + 9.22222i) q^{98} +5.15070 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 8 q^{2} + 4 q^{7} + 8 q^{8} - 16 q^{15} + 64 q^{16} + 8 q^{18} + 16 q^{23} - 32 q^{25} - 4 q^{28} + 24 q^{30} - 32 q^{32} - 16 q^{36} - 20 q^{42} - 80 q^{46} + 80 q^{50} + 56 q^{58} - 56 q^{60}+ \cdots + 48 q^{98}+O(q^{100}) \) 184 * q + 8 * q^2 + 4 * q^7 + 8 * q^8 - 16 * q^15 + 64 * q^16 + 8 * q^18 + 16 * q^23 - 32 * q^25 - 4 * q^28 + 24 * q^30 - 32 * q^32 - 16 * q^36 - 20 * q^42 - 80 * q^46 + 80 * q^50 + 56 * q^58 - 56 * q^60 + 4 * q^63 + 32 * q^65 - 44 * q^70 + 32 * q^71 - 8 * q^72 + 8 * q^78 - 184 * q^81 - 16 * q^86 - 64 * q^88 + 104 * q^92 - 96 * q^95 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more