LMFDB - Embedded newform 840.2.bj.b.13.17

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)

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")

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);

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			13.17
Character	$\chi$	$=$	840.13
Dual form			840.2.bj.b.517.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.18486 + 0.772078i) 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} +(2.63180 + 0.271325i) q^{7} +(0.455480 + 2.79151i) q^{8} +1.00000i q^{9} +(2.33879 + 2.12840i) q^{10} +5.15070i q^{11} +(-1.86492 + 0.722534i) 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} +(-0.772078 - 1.18486i) q^{18} +2.52629i q^{19} +(-4.41443 - 0.716127i) q^{20} +(-1.66911 - 2.05282i) q^{21} +(-3.97674 - 6.10286i) 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} +(2.62237 - 4.59600i) q^{28} -5.90326 q^{29} +(-0.148770 - 3.15878i) q^{30} -9.01760i q^{31} +(5.47531 + 1.42161i) q^{32} +(3.64209 - 3.64209i) q^{33} +(-6.52053 - 1.37540i) q^{34} +(-0.897053 - 5.84767i) q^{35} +(1.82961 + 0.807792i) q^{36} +(7.00111 + 7.00111i) q^{37} +(-1.95050 - 2.99331i) q^{38} +2.36468i q^{39} +(5.78339 - 2.55977i) q^{40} +2.60560i q^{41} +(3.56260 + 1.14362i) 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} +(-0.184515 + 3.99574i) q^{48} +(6.85277 + 1.42814i) q^{49} +(3.28650 - 6.26090i) q^{50} -4.71216i q^{51} +(-4.40995 + 1.70856i) 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} +(6.99454 - 4.55778i) q^{58} -9.72563i q^{59} +(2.61509 + 3.62785i) q^{60} +9.15780 q^{61} +(6.96229 + 10.6846i) q^{62} +(-0.271325 + 2.63180i) 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} +(8.78783 - 3.40470i) q^{68} -8.02527i q^{69} +(5.57774 + 6.23609i) q^{70} -5.38495 q^{71} +(-2.79151 + 0.455480i) 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} +(-1.39751 + 13.5556i) q^{77} +(-1.82572 - 2.80182i) q^{78} +8.61557i q^{79} +(-4.87617 + 7.49820i) q^{80} -1.00000 q^{81} +(-2.01173 - 3.08728i) 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} +(-14.3782 + 2.34604i) q^{88} -6.30249 q^{89} +(-2.12840 + 2.33879i) q^{90} +(-3.94691 - 4.85426i) q^{91} +(14.9665 - 5.79854i) 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} +(-9.22222 + 3.59871i) 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 $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−1.18486	+	0.772078i	−0.837823	+	0.545941i
$2$	−1.18486	+	0.772078i	−0.837823	+	0.545941i
$3$	−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
$7$	2.63180	+	0.271325i	0.994728	+	0.102551i
$7$	2.63180	+	0.271325i	0.994728	+	0.102551i
$8$	0.455480	+	2.79151i	0.161036	+	0.986948i
$9$			1.00000i			0.333333i
$10$	2.33879	+	2.12840i	0.739590	+	0.673058i
$11$			5.15070i			1.55299i	0.630121	+	0.776497i	$0.283005\pi$
$11$			5.15070i			1.55299i	−0.630121	+	0.776497i	$0.716995\pi$
$12$	−1.86492	+	0.722534i	−0.538357	+	0.208578i
$13$	−1.67208	−	1.67208i	−0.463752	−	0.463752i	0.436131	−	0.899883i	$-0.356348\pi$
$13$	−1.67208	−	1.67208i	−0.463752	−	0.463752i	−0.899883	+	0.436131i	$0.856348\pi$
$14$	−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	$-0.0563874\pi$
$17$	3.33200	+	3.33200i	0.808129	+	0.808129i	−0.176221	+	0.984351i	$0.556387\pi$
$18$	−0.772078	−	1.18486i	−0.181980	−	0.279274i
$19$			2.52629i			0.579571i	0.957092	+	0.289786i	$0.0935841\pi$
$19$			2.52629i			0.579571i	−0.957092	+	0.289786i	$0.906416\pi$
$20$	−4.41443	−	0.716127i	−0.987096	−	0.160131i
$21$	−1.66911	−	2.05282i	−0.364230	−	0.447962i
$22$	−3.97674	−	6.10286i	−0.847843	−	1.30113i
$23$	5.67473	+	5.67473i	1.18326	+	1.18326i	0.978894	+	0.204368i	$0.0655139\pi$
$23$	5.67473	+	5.67473i	1.18326	+	1.18326i	0.204368	+	0.978894i	$0.434486\pi$
$24$	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
$28$	2.62237	−	4.59600i	0.495581	−	0.868562i
$29$	−5.90326			−1.09621			−0.548104	−	0.836410i	$-0.684650\pi$
$29$	−5.90326			−1.09621			−0.548104	+	0.836410i	$0.684650\pi$
$30$	−0.148770	−	3.15878i	−0.0271615	−	0.576711i
$31$		−	9.01760i		−	1.61961i	−0.586700	−	0.809805i	$-0.699573\pi$
$31$		−	9.01760i		−	1.61961i	0.586700	−	0.809805i	$-0.300427\pi$
$32$	5.47531	+	1.42161i	0.967907	+	0.251308i
$33$	3.64209	−	3.64209i	0.634007	−	0.634007i
$34$	−6.52053	−	1.37540i	−1.11826	−	0.235878i
$35$	−0.897053	−	5.84767i	−0.151630	−	0.988437i
$36$	1.82961	+	0.807792i	0.304935	+	0.134632i
$37$	7.00111	+	7.00111i	1.15098	+	1.15098i	0.986357	+	0.164618i	$0.0526391\pi$
$37$	7.00111	+	7.00111i	1.15098	+	1.15098i	0.164618	+	0.986357i	$0.447361\pi$
$38$	−1.95050	−	2.99331i	−0.316412	−	0.485579i
$39$			2.36468i			0.378652i
$40$	5.78339	−	2.55977i	0.914434	−	0.404735i
$41$			2.60560i			0.406927i	0.979083	+	0.203464i	$0.0652198\pi$
$41$			2.60560i			0.406927i	−0.979083	+	0.203464i	$0.934780\pi$
$42$	3.56260	+	1.14362i	0.549721	+	0.176465i
$43$	4.96630	−	4.96630i	0.757354	−	0.757354i	−0.218486	−	0.975840i	$-0.570112\pi$
$43$	4.96630	−	4.96630i	0.757354	−	0.757354i	0.975840	+	0.218486i	$0.0701119\pi$
$44$	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	$-0.166626\pi$
$47$	2.51054	+	2.51054i	0.366201	+	0.366201i	−0.499889	+	0.866090i	$0.666626\pi$
$48$	−0.184515	+	3.99574i	−0.0266324	+	0.576736i
$49$	6.85277	+	1.42814i	0.978967	+	0.204021i
$50$	3.28650	−	6.26090i	0.464781	−	0.885426i
$51$		−	4.71216i		−	0.659835i
$52$	−4.40995	+	1.70856i	−0.611550	+	0.236935i
$53$	0.853301	−	0.853301i	0.117210	−	0.117210i	−0.646069	−	0.763279i	$-0.723588\pi$
$53$	0.853301	−	0.853301i	0.117210	−	0.117210i	0.763279	+	0.646069i	$0.223588\pi$
$54$	−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
$58$	6.99454	−	4.55778i	0.918429	−	0.598465i
$59$		−	9.72563i		−	1.26617i	−0.774082	−	0.633085i	$-0.781788\pi$
$59$		−	9.72563i		−	1.26617i	0.774082	−	0.633085i	$-0.218212\pi$
$60$	2.61509	+	3.62785i	0.337607	+	0.468353i
$61$	9.15780			1.17254			0.586268	−	0.810117i	$-0.300597\pi$
$61$	9.15780			1.17254			0.586268	+	0.810117i	$0.300597\pi$
$62$	6.96229	+	10.6846i	0.884212	+	1.35695i
$63$	−0.271325	+	2.63180i	−0.0341837	+	0.331576i
$64$	−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	$-0.169075\pi$
$67$	2.91136	+	2.91136i	0.355679	+	0.355679i	−0.506539	+	0.862217i	$0.669075\pi$
$68$	8.78783	−	3.40470i	1.06568	−	0.412881i
$69$		−	8.02527i		−	0.966129i
$70$	5.57774	+	6.23609i	0.666668	+	0.745355i
$71$	−5.38495			−0.639076			−0.319538	−	0.947573i	$-0.603528\pi$
$71$	−5.38495			−0.639076			−0.319538	+	0.947573i	$0.603528\pi$
$72$	−2.79151	+	0.455480i	−0.328983	+	0.0536788i
$73$	−7.42430	+	7.42430i	−0.868949	+	0.868949i	−0.992356	−	0.123407i	$-0.960618\pi$
$73$	−7.42430	+	7.42430i	−0.868949	+	0.868949i	0.123407	+	0.992356i	$0.460618\pi$
$74$	−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
$77$	−1.39751	+	13.5556i	−0.159261	+	1.54481i
$78$	−1.82572	−	2.80182i	−0.206722	−	0.317243i
$79$			8.61557i			0.969328i	0.874700	+	0.484664i	$0.161058\pi$
$79$			8.61557i			0.969328i	−0.874700	+	0.484664i	$0.838942\pi$
$80$	−4.87617	+	7.49820i	−0.545173	+	0.838324i
$81$	−1.00000			−0.111111
$82$	−2.01173	−	3.08728i	−0.222158	−	0.340933i
$83$	0.922710	+	0.922710i	0.101281	+	0.101281i	0.755931	−	0.654651i	$-0.227184\pi$
$83$	0.922710	+	0.922710i	0.101281	+	0.101281i	−0.654651	+	0.755931i	$0.727184\pi$
$84$	−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
$88$	−14.3782	+	2.34604i	−1.53272	+	0.250089i
$89$	−6.30249			−0.668063			−0.334031	−	0.942562i	$-0.608409\pi$
$89$	−6.30249			−0.668063			−0.334031	+	0.942562i	$0.608409\pi$
$90$	−2.12840	+	2.33879i	−0.224353	+	0.246530i
$91$	−3.94691	−	4.85426i	−0.413749	−	0.508865i
$92$	14.9665	−	5.79854i	1.56037	−	0.604539i
$93$	−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	$-0.160980\pi$
$97$	3.84469	+	3.84469i	0.390370	+	0.390370i	−0.484450	+	0.874819i	$0.660980\pi$
$98$	−9.22222	+	3.59871i	−0.931584	+	0.363525i
$99$	−5.15070			−0.517665
$100$	0.939861	+	9.95574i	0.0939861	+	0.995574i
$101$	4.35024			0.432865			0.216433	−	0.976298i	$-0.430558\pi$
$101$	4.35024			0.432865			0.216433	+	0.976298i	$0.430558\pi$
$102$	3.63816	+	5.58326i	0.360231	+	0.552825i
$103$	13.6171	−	13.6171i	1.34174	−	1.34174i	0.447405	−	0.894332i	$-0.352348\pi$
$103$	13.6171	−	13.6171i	1.34174	−	1.34174i	0.894332	−	0.447405i	$-0.147652\pi$
$104$	3.90603	−	5.42923i	0.383018	−	0.532380i
$105$	−3.50062	+	4.76924i	−0.341625	+	0.465430i
$106$	−0.352228	+	1.66986i	−0.0342115	+	0.162191i
$107$	4.07905	+	4.07905i	0.394337	+	0.394337i	0.876230	−	0.481893i	$-0.160051\pi$
$107$	4.07905	+	4.07905i	0.394337	+	0.394337i	−0.481893	+	0.876230i	$0.660051\pi$
$108$	−0.722534	−	1.86492i	−0.0695259	−	0.179452i
$109$	−3.19824			−0.306336			−0.153168	−	0.988200i	$-0.548948\pi$
$109$	−3.19824			−0.306336			−0.153168	+	0.988200i	$0.548948\pi$
$110$	−10.9627	+	12.0464i	−1.04525	+	1.14858i
$111$		−	9.90106i		−	0.939767i
$112$	−6.29056	−	8.51052i	−0.594402	−	0.804168i
$113$	−6.82664	−	6.82664i	−0.642196	−	0.642196i	0.308899	−	0.951095i	$-0.400039\pi$
$113$	−6.82664	−	6.82664i	−0.642196	−	0.642196i	−0.951095	+	0.308899i	$0.900039\pi$
$114$	−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
$118$	7.50894	+	11.5235i	0.691254	+	1.06083i
$119$	7.86512	+	9.67323i	0.720994	+	0.886743i
$120$	−5.89950	−	2.27944i	−0.538549	−	0.208084i
$121$	−15.5297			−1.41179
$122$	−10.8507	+	7.07053i	−0.982378	+	0.640136i
$123$	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	−0.320978	−	0.947087i	$-0.604012\pi$
$127$	7.05588	−	7.05588i	0.626108	−	0.626108i	0.947087	+	0.320978i	$0.104012\pi$
$128$	7.02390	−	8.86932i	0.620831	−	0.783944i
$129$	−7.02341			−0.618377
$130$	−0.351793	−	7.46949i	−0.0308543	−	0.655118i
$131$	0.394051			0.0344284			0.0172142	−	0.999852i	$-0.494520\pi$
$131$	0.394051			0.0344284			0.0172142	+	0.999852i	$0.494520\pi$
$132$	−3.72156	−	9.60566i	−0.323920	−	0.836066i
$133$	−0.685445	+	6.64870i	−0.0594356	+	0.576516i
$134$	−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	−0.505199	−	0.863003i	$-0.668581\pi$
$137$	4.18798	−	4.18798i	0.357803	−	0.357803i	0.863003	+	0.505199i	$0.168581\pi$
$138$	6.19614	+	9.50884i	0.527450	+	0.809446i
$139$			13.6587i			1.15851i	0.815146	+	0.579256i	$0.196657\pi$
$139$			13.6587i			1.15851i	−0.815146	+	0.579256i	$0.803343\pi$
$140$	−11.4236	−	3.08245i	−0.965470	−	0.260514i
$141$		−	3.55045i		−	0.299002i
$142$	6.38042	−	4.15760i	0.535433	−	0.348898i
$143$	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
$147$	−3.83579	−	5.85549i	−0.316370	−	0.482953i
$148$	18.4647	−	7.15386i	1.51779	−	0.588044i
$149$	13.5533			1.11033			0.555167	−	0.831739i	$-0.312655\pi$
$149$	13.5533			1.11033			0.555167	+	0.831739i	$0.312655\pi$
$150$	−6.75103	+	2.10322i	−0.551220	+	0.171727i
$151$	19.0617			1.55122			0.775611	−	0.631211i	$-0.217442\pi$
$151$	19.0617			1.55122			0.775611	+	0.631211i	$0.217442\pi$
$152$	−7.05218	+	1.15068i	−0.572007	+	0.0933321i
$153$	−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	−0.965049	−	0.262070i	$-0.915595\pi$
$157$	−8.80830	+	8.80830i	−0.702979	+	0.702979i	0.262070	+	0.965049i	$0.415595\pi$
$158$	−6.65189	−	10.2083i	−0.529196	−	0.812126i
$159$	−1.20675			−0.0957015
$160$	−0.0116041	−	12.6491i	−0.000917388	−	1.00000i
$161$	13.3951	+	16.4744i	1.05568	+	1.29837i
$162$	1.18486	−	0.772078i	0.0930915	−	0.0606602i
$163$	10.2447	−	10.2447i	0.802423	−	0.802423i	−0.181051	−	0.983474i	$-0.557950\pi$
$163$	10.2447	−	10.2447i	0.802423	−	0.802423i	0.983474	+	0.181051i	$0.0579498\pi$
$164$	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	$-0.333052\pi$
$167$	−4.71450	−	4.71450i	−0.364819	−	0.364819i	−0.865584	+	0.500765i	$0.833052\pi$
$168$	4.97023	−	5.59436i	0.383461	−	0.431614i
$169$		−	7.40829i		−	0.569869i
$170$	0.701027	+	14.8847i	0.0537663	+	1.14160i
$171$	−2.52629			−0.193190
$172$	−5.07465	−	13.0981i	−0.386939	−	0.998723i
$173$	−9.83536	−	9.83536i	−0.747769	−	0.747769i	0.226291	−	0.974060i	$-0.427340\pi$
$173$	−9.83536	−	9.83536i	−0.747769	−	0.747769i	−0.974060	+	0.226291i	$0.927340\pi$
$174$	−8.16872	−	1.72306i	−0.619269	−	0.130624i
$175$	−12.1473	+	5.23869i	−0.918247	+	0.396008i
$176$	15.2249	−	13.8808i	1.14762	−	1.04631i
$177$	−6.87706	+	6.87706i	−0.516912	+	0.516912i
$178$	7.46758	−	4.86601i	0.559719	−	0.364723i
$179$	−7.39824			−0.552971			−0.276485	−	0.961018i	$-0.589170\pi$
$179$	−7.39824			−0.552971			−0.276485	+	0.961018i	$0.589170\pi$
$180$	0.716127	−	4.41443i	0.0533770	−	0.329032i
$181$	−18.6048			−1.38289			−0.691444	−	0.722430i	$-0.743025\pi$
$181$	−18.6048			−1.38289			−0.691444	+	0.722430i	$0.743025\pi$
$182$	8.42441	+	2.70431i	0.624459	+	0.200456i
$183$	−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
$188$	6.62132	−	2.56532i	0.482909	−	0.187095i
$189$	2.05282	−	1.66911i	0.149321	−	0.121410i
$190$	−5.37695	+	5.90847i	−0.390085	+	0.428645i
$191$	16.4410			1.18963			0.594815	−	0.803863i	$-0.297225\pi$
$191$	16.4410			1.18963			0.594815	+	0.803863i	$0.297225\pi$
$192$	7.16160	+	3.56532i	0.516844	+	0.257305i
$193$	−11.7512	−	11.7512i	−0.845868	−	0.845868i	0.143747	−	0.989615i	$-0.454085\pi$
$193$	−11.7512	−	11.7512i	−0.845868	−	0.845868i	−0.989615	+	0.143747i	$0.954085\pi$
$194$	−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	$-0.174703\pi$
$197$	4.65177	+	4.65177i	0.331425	+	0.331425i	−0.521703	+	0.853127i	$0.674703\pi$
$198$	6.10286	−	3.97674i	0.433711	−	0.282614i
$199$	−14.9107			−1.05699			−0.528495	−	0.848936i	$-0.677243\pi$
$199$	−14.9107			−1.05699			−0.528495	+	0.848936i	$0.677243\pi$
$200$	−8.80021	−	11.0705i	−0.622269	−	0.782804i
$201$		−	4.11728i		−	0.290410i
$202$	−5.15443	+	3.35873i	−0.362665	+	0.236319i
$203$	−15.5362	−	1.60170i	−1.09043	−	0.112417i
$204$	−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
$208$	−0.436319	+	9.44865i	−0.0302533	+	0.655146i
$209$	−13.0122			−0.900071
$210$	0.465521	−	8.35364i	0.0321240	−	0.576456i
$211$			15.6001i			1.07396i	0.843596	+	0.536978i	$0.180434\pi$
$211$			15.6001i			1.07396i	−0.843596	+	0.536978i	$0.819566\pi$
$212$	−0.871918	−	2.25050i	−0.0598836	−	0.154565i
$213$	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
$217$	2.44670	−	23.7325i	0.166093	−	1.61107i
$218$	3.78948	−	2.46929i	0.256656	−	0.167242i
$219$	10.4996			0.709494
$220$	3.68856	−	22.7374i	0.248682	−	1.53295i
$221$		−	11.1428i		−	0.749543i
$222$	7.64439	+	11.7314i	0.513058	+	0.787359i
$223$	−9.90113	+	9.90113i	−0.663028	+	0.663028i	−0.956093	−	0.293064i	$-0.905325\pi$
$223$	−9.90113	+	9.90113i	−0.663028	+	0.663028i	0.293064	+	0.956093i	$0.405325\pi$
$224$	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	−0.620417	−	0.784272i	$-0.713037\pi$
$227$	2.46872	−	2.46872i	0.163855	−	0.163855i	0.784272	+	0.620417i	$0.213037\pi$
$228$	−1.82533	−	4.71135i	−0.120886	−	0.312017i
$229$			2.05866i			0.136040i	0.997684	+	0.0680200i	$0.0216682\pi$
$229$			2.05866i			0.136040i	−0.997684	+	0.0680200i	$0.978332\pi$
$230$	1.19392	+	25.3500i	0.0787246	+	1.67153i
$231$	10.5735	−	8.59708i	0.695682	−	0.565646i
$232$	−2.68882	−	16.4790i	−0.176529	−	1.08190i
$233$	5.02721	+	5.02721i	0.329343	+	0.329343i	0.852337	−	0.522993i	$-0.175185\pi$
$233$	5.02721	+	5.02721i	0.329343	+	0.329343i	−0.522993	+	0.852337i	$0.675185\pi$
$234$	−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
$238$	−16.7876	−	5.38895i	−1.08818	−	0.349314i
$239$		−	21.3479i		−	1.38088i	−0.723390	−	0.690439i	$-0.757417\pi$
$239$		−	21.3479i		−	1.38088i	0.723390	−	0.690439i	$-0.242583\pi$
$240$	8.75000	−	1.85405i	0.564810	−	0.119679i
$241$			3.80737i			0.245254i	0.992453	+	0.122627i	$0.0391319\pi$
$241$			3.80737i			0.245254i	−0.992453	+	0.122627i	$0.960868\pi$
$242$	18.4005	−	11.9901i	1.18283	−	0.770754i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	7.39760	−	16.7552i	0.473583	−	1.07264i
$245$	−0.774248	−	15.6333i	−0.0494649	−	0.998776i
$246$	−0.760529	+	3.60554i	−0.0484895	+	0.229881i
$247$	4.22417	−	4.22417i	0.268777	−	0.268777i
$248$	25.1727	−	4.10734i	1.59847	−	0.260816i
$249$		−	1.30491i		−	0.0826952i
$250$	−15.4006	−	3.58061i	−0.974021	−	0.226457i
$251$	−21.1664			−1.33601			−0.668006	−	0.744156i	$-0.732852\pi$
$251$	−21.1664			−1.33601			−0.668006	+	0.744156i	$0.732852\pi$
$252$	4.59600	+	2.62237i	0.289521	+	0.165194i
$253$	−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	$-0.244353\pi$
$257$	0.402214	+	0.402214i	0.0250894	+	0.0250894i	−0.694451	+	0.719540i	$0.744353\pi$
$258$	8.32176	−	5.42262i	0.518090	−	0.337597i
$259$	16.5260	+	20.3251i	1.02687	+	1.26294i
$260$	6.18385	+	8.57870i	0.383506	+	0.532028i
$261$		−	5.90326i		−	0.365403i
$262$	−0.466896	+	0.304238i	−0.0288449	+	0.0187959i
$263$	9.04566	+	9.04566i	0.557780	+	0.557780i	0.928675	−	0.370895i	$-0.120949\pi$
$263$	9.04566	+	9.04566i	0.557780	+	0.557780i	−0.370895	+	0.928675i	$0.620949\pi$
$264$	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
$268$	7.67842	−	2.97488i	0.469034	−	0.181719i
$269$			20.2813i			1.23657i	0.785954	+	0.618285i	$0.212172\pi$
$269$			20.2813i			1.23657i	−0.785954	+	0.618285i	$0.787828\pi$
$270$	3.15878	−	0.148770i	0.192237	−	0.00905384i
$271$			0.243465i			0.0147894i	0.999973	+	0.00739472i	$0.00235383\pi$
$271$			0.243465i			0.0147894i	−0.999973	+	0.00739472i	$0.997646\pi$
$272$	0.869465	−	18.8286i	0.0527190	−	1.14165i
$273$	−0.641595	+	6.22337i	−0.0388311	+	0.376655i
$274$	−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	$-0.195506\pi$
$277$	4.00984	+	4.00984i	0.240928	+	0.240928i	−0.576306	+	0.817234i	$0.695506\pi$
$278$	−10.5455	−	16.1836i	−0.632480	−	0.970629i
$279$	9.01760			0.539870
$280$	15.9153	−	5.16763i	0.951119	−	0.308825i
$281$	−25.3458			−1.51201			−0.756003	−	0.654568i	$-0.772850\pi$
$281$	−25.3458			−1.51201			−0.756003	+	0.654568i	$0.772850\pi$
$282$	2.74122	+	4.20679i	0.163237	+	0.250510i
$283$	−1.39809	−	1.39809i	−0.0831081	−	0.0831081i	0.664331	−	0.747439i	$-0.268717\pi$
$283$	−1.39809	−	1.39809i	−0.0831081	−	0.0831081i	−0.747439	+	0.664331i	$0.768717\pi$
$284$	−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
$287$	−0.706964	+	6.85743i	−0.0417308	+	0.404782i
$288$	−1.42161	+	5.47531i	−0.0837692	+	0.322636i
$289$			5.20448i			0.306146i
$290$	−13.8065	−	12.5645i	−0.810744	−	0.737811i
$291$		−	5.43722i		−	0.318735i
$292$	7.58629	+	19.5809i	0.443954	+	1.14588i
$293$	6.54622	+	6.54622i	0.382434	+	0.382434i	0.871978	−	0.489544i	$-0.162837\pi$
$293$	6.54622	+	6.54622i	0.382434	+	0.382434i	−0.489544	+	0.871978i	$0.662837\pi$
$294$	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
$298$	−16.0588	+	10.4642i	−0.930263	+	0.606177i
$299$		−	18.9772i		−	1.09748i
$300$	6.37519	−	7.70435i	0.368072	−	0.444811i
$301$	14.4178	−	11.7228i	0.831028	−	0.675693i
$302$	−22.5855	+	14.7171i	−1.29965	+	0.846877i
$303$	−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	−0.803795	−	0.594907i	$-0.797189\pi$
$307$	−3.66001	+	3.66001i	−0.208888	+	0.208888i	0.594907	+	0.803795i	$0.297189\pi$
$308$	23.6726	+	13.5070i	1.34887	+	0.769634i
$309$	−19.2575			−1.09552
$310$	19.1930	−	21.0903i	1.09009	−	1.19785i
$311$		−	1.88622i		−	0.106957i	−0.998569	−	0.0534787i	$-0.982969\pi$
$311$		−	1.88622i		−	0.106957i	0.998569	−	0.0534787i	$-0.0170309\pi$
$312$	−6.60103	+	1.07706i	−0.373710	+	0.0609767i
$313$	−20.7950	+	20.7950i	−1.17541	+	1.17541i	−0.194504	+	0.980902i	$0.562310\pi$
$313$	−20.7950	+	20.7950i	−1.17541	+	1.17541i	−0.980902	+	0.194504i	$0.937690\pi$
$314$	3.63592	−	17.2373i	0.205187	−	0.972758i
$315$	5.84767	−	0.897053i	0.329479	−	0.0505432i
$316$	15.7631	+	6.95959i	0.886746	+	0.391508i
$317$	−2.65202	−	2.65202i	−0.148952	−	0.148952i	0.628698	−	0.777650i	$-0.283588\pi$
$317$	−2.65202	−	2.65202i	−0.148952	−	0.148952i	−0.777650	+	0.628698i	$0.783588\pi$
$318$	1.42983	−	0.931705i	0.0801809	−	0.0522474i
$319$		−	30.4059i		−	1.70240i
$320$	9.77984	+	14.9785i	0.546710	+	0.837322i
$321$		−	5.76865i		−	0.321975i
$322$	−28.5908	−	9.17790i	−1.59331	−	0.511465i
$323$	−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
$328$	−7.27357	+	1.18680i	−0.401616	+	0.0655301i
$329$	5.92609	+	7.28843i	0.326716	+	0.401824i
$330$	16.2699	−	0.766268i	0.895628	−	0.0421817i
$331$			32.7208i			1.79850i	0.437435	+	0.899250i	$0.355887\pi$
$331$			32.7208i			1.79850i	−0.437435	+	0.899250i	$0.644113\pi$
$332$	2.43356	−	0.942842i	0.133559	−	0.0517452i
$333$	−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	−0.560815	−	0.827941i	$-0.689512\pi$
$337$	4.90379	−	4.90379i	0.267126	−	0.267126i	0.827941	+	0.560815i	$0.189512\pi$
$338$	5.71978	+	8.77780i	0.311115	+	0.477449i
$339$			9.65432i			0.524351i
$340$	−12.3227	−	17.0950i	−0.668295	−	0.927108i
$341$	46.4469			2.51524
$342$	2.99331	−	1.95050i	0.161860	−	0.105471i
$343$	17.6476	+	5.61792i	0.952883	+	0.303339i
$344$	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	$-0.351603\pi$
$347$	−8.26679	−	8.26679i	−0.443784	−	0.443784i	−0.893282	+	0.449497i	$0.851603\pi$
$348$	11.0091	−	4.26531i	0.590152	−	0.228645i
$349$		−	31.5705i		−	1.68993i	−0.534823	−	0.844964i	$-0.679622\pi$
$349$		−	31.5705i		−	1.68993i	0.534823	−	0.844964i	$-0.320378\pi$
$350$	10.3482	−	15.5858i	0.553132	−	0.833094i
$351$	−2.36468			−0.126217
$352$	−7.32228	+	28.2017i	−0.390279	+	1.50315i
$353$	−15.1489	+	15.1489i	−0.806293	+	0.806293i	−0.984071	−	0.177777i	$-0.943109\pi$
$353$	−15.1489	+	15.1489i	−0.806293	+	0.806293i	0.177777	+	0.984071i	$0.443109\pi$
$354$	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
$357$	1.27853	−	12.4015i	0.0676667	−	0.656356i
$358$	8.76589	−	5.71202i	0.463292	−	0.301890i
$359$			0.0423478i			0.00223503i	0.999999	+	0.00111752i	$0.000355716\pi$
$359$			0.0423478i			0.00223503i	−0.999999	+	0.00111752i	$0.999644\pi$
$360$	2.55977	+	5.78339i	0.134912	+	0.304811i
$361$	12.6178			0.664097
$362$	22.0442	−	14.3644i	1.15862	−	0.754975i
$363$	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	$-0.0941112\pi$
$367$	12.7442	+	12.7442i	0.665240	+	0.665240i	−0.291370	+	0.956610i	$0.594111\pi$
$368$	1.48078	−	32.0669i	0.0771911	−	1.67160i
$369$	−2.60560			−0.135642
$370$	1.47298	+	31.2752i	0.0765765	+	1.62592i
$371$	2.47724	−	2.01420i	0.128612	−	0.104572i
$372$	6.51553	+	16.8172i	0.337814	+	0.871929i
$373$	1.83933	−	1.83933i	0.0952370	−	0.0952370i	−0.657883	−	0.753120i	$-0.728548\pi$
$373$	1.83933	−	1.83933i	0.0952370	−	0.0952370i	0.753120	+	0.657883i	$0.228548\pi$
$374$	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
$378$	−1.14362	+	3.56260i	−0.0588217	+	0.183240i
$379$	19.0430			0.978174			0.489087	−	0.872235i	$-0.337330\pi$
$379$	19.0430			0.978174			0.489087	+	0.872235i	$0.337330\pi$
$380$	1.80915	−	11.1521i	0.0928073	−	0.572093i
$381$	−9.97852			−0.511215
$382$	−19.4803	+	12.6937i	−0.996699	+	0.649468i
$383$	−20.2953	+	20.2953i	−1.03704	+	1.03704i	−0.0377566	+	0.999287i	$0.512021\pi$
$383$	−20.2953	+	20.2953i	−1.03704	+	1.03704i	−0.999287	+	0.0377566i	$0.987979\pi$
$384$	−11.2382	+	1.30490i	−0.573497	+	0.0665906i
$385$	30.1196	−	4.62045i	1.53504	−	0.235480i
$386$	22.9963	+	4.85069i	1.17048	+	0.246894i
$387$	4.96630	+	4.96630i	0.252451	+	0.252451i
$388$	10.1400	−	3.92858i	0.514781	−	0.199443i
$389$	−3.47313			−0.176095			−0.0880473	−	0.996116i	$-0.528063\pi$
$389$	−3.47313			−0.176095			−0.0880473	+	0.996116i	$0.528063\pi$
$390$	−5.03297	+	5.53048i	−0.254855	+	0.280047i
$391$			37.8164i			1.91246i
$392$	−0.865387	+	19.7801i	−0.0437086	+	0.999044i
$393$	−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	−0.932091	−	0.362225i	$-0.882017\pi$
$397$	−11.3545	+	11.3545i	−0.569865	+	0.569865i	0.362225	+	0.932091i	$0.382017\pi$
$398$	17.6671	−	11.5122i	0.885571	−	0.577055i
$399$	5.18603	−	4.21666i	0.259626	−	0.211097i
$400$	18.9743	+	6.32258i	0.948716	+	0.316129i
$401$	−38.2876			−1.91199			−0.955995	−	0.293382i	$-0.905219\pi$
$401$	−38.2876			−1.91199			−0.955995	+	0.293382i	$0.905219\pi$
$402$	3.17886	+	4.87840i	0.158547	+	0.243313i
$403$	−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
$408$	13.1541	−	2.14630i	0.651223	−	0.106257i
$409$	15.9114			0.786770			0.393385	−	0.919374i	$-0.371304\pi$
$409$	15.9114			0.786770			0.393385	+	0.919374i	$0.371304\pi$
$410$	−5.54576	+	6.09396i	−0.273885	+	0.300959i
$411$	−5.92270			−0.292145
$412$	−13.9142	−	35.9139i	−0.685505	−	1.76935i
$413$	2.63880	−	25.5959i	0.129847	−	1.25949i
$414$	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
$418$	15.4176	−	10.0464i	0.754100	−	0.491386i
$419$			2.36583i			0.115578i	0.998329	+	0.0577891i	$0.0184051\pi$
$419$			2.36583i			0.115578i	−0.998329	+	0.0577891i	$0.981595\pi$
$420$	5.89808	+	10.2573i	0.287797	+	0.500506i
$421$		−	8.02564i		−	0.391146i	−0.980689	−	0.195573i	$-0.937343\pi$
$421$		−	8.02564i		−	0.391146i	0.980689	−	0.195573i	$-0.0626566\pi$
$422$	−12.0445	−	18.4840i	−0.586317	−	0.899785i
$423$	−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
$427$	24.1015	+	2.48474i	1.16635	+	0.120245i
$428$	10.7581	−	4.16805i	0.520012	−	0.201470i
$429$	−12.1797			−0.588044
$430$	22.1854	−	1.04487i	1.06987	−	0.0503881i
$431$	−9.31639			−0.448755			−0.224377	−	0.974502i	$-0.572035\pi$
$431$	−9.31639			−0.448755			−0.224377	+	0.974502i	$0.572035\pi$
$432$	−3.99574	−	0.184515i	−0.192245	−	0.00887748i
$433$	−0.642368	+	0.642368i	−0.0308702	+	0.0308702i	−0.722373	−	0.691503i	$-0.756949\pi$
$433$	−0.642368	+	0.642368i	−0.0308702	+	0.0308702i	0.691503	+	0.722373i	$0.256949\pi$
$434$	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
$438$	−12.4405	+	8.10647i	−0.594431	+	0.387342i
$439$	28.3583			1.35347			0.676733	−	0.736229i	$-0.263395\pi$
$439$	28.3583			1.35347			0.676733	+	0.736229i	$0.263395\pi$
$440$	13.1846	+	29.7885i	0.628551	+	1.42011i
$441$	−1.42814	+	6.85277i	−0.0680069	+	0.326322i
$442$	8.60307	+	13.2026i	0.409206	+	0.627984i
$443$	−14.7490	+	14.7490i	−0.700747	+	0.700747i	−0.964571	−	0.263824i	$-0.915016\pi$
$443$	−14.7490	+	14.7490i	−0.700747	+	0.700747i	0.263824	+	0.964571i	$0.415016\pi$
$444$	−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
$448$	−20.6524	+	4.63454i	−0.975734	+	0.218961i
$449$		−	30.5161i		−	1.44014i	−0.693899	−	0.720072i	$-0.744109\pi$
$449$		−	30.5161i		−	1.44014i	0.693899	−	0.720072i	$-0.255891\pi$
$450$	6.26090	+	3.28650i	0.295142	+	0.154927i
$451$	−13.4207			−0.631955
$452$	−18.0046	+	6.97558i	−0.846864	+	0.328104i
$453$	−13.4787	−	13.4787i	−0.633284	−	0.633284i
$454$	−1.01905	+	4.83113i	−0.0478262	+	0.226736i
$455$	−8.27784	+	11.2777i	−0.388071	+	0.528708i
$456$	5.80029	+	4.17299i	0.271624	+	0.195418i
$457$	−3.48416	+	3.48416i	−0.162982	+	0.162982i	−0.783886	−	0.620904i	$-0.786766\pi$
$457$	−3.48416	+	3.48416i	−0.162982	+	0.162982i	0.620904	+	0.783886i	$0.286766\pi$
$458$	−1.58945	−	2.43923i	−0.0742699	−	0.113978i
$459$	4.71216			0.219945
$460$	−20.9868	−	29.1145i	−0.978516	−	1.35747i
$461$	4.86218			0.226454			0.113227	−	0.993569i	$-0.463881\pi$
$461$	4.86218			0.226454			0.113227	+	0.993569i	$0.463881\pi$
$462$	−5.89046	+	18.3499i	−0.274049	+	0.853713i
$463$	−23.6863	−	23.6863i	−1.10080	−	1.10080i	−0.994315	−	0.106482i	$-0.966041\pi$
$463$	−23.6863	−	23.6863i	−1.10080	−	1.10080i	−0.106482	−	0.994315i	$-0.533959\pi$
$464$	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	0.157888	−	0.987457i	$-0.449531\pi$
$467$	24.7511	−	24.7511i	1.14535	−	1.14535i	0.987457	−	0.157888i	$-0.0504685\pi$
$468$	−1.70856	−	4.40995i	−0.0789783	−	0.203850i
$469$	6.87219	+	8.45203i	0.317328	+	0.390279i
$470$	0.528199	+	11.2151i	0.0243640	+	0.517312i
$471$	12.4568			0.573980
$472$	27.1492	−	4.42983i	1.24964	−	0.203899i
$473$	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
$478$	16.4822	+	25.2943i	0.753879	+	1.15693i
$479$	−30.3198			−1.38535			−0.692674	−	0.721251i	$-0.743568\pi$
$479$	−30.3198			−1.38535			−0.692674	+	0.721251i	$0.743568\pi$
$480$	−8.93606	+	8.95247i	−0.407874	+	0.408623i
$481$		−	23.4128i		−	1.06753i
$482$	−2.93959	−	4.51121i	−0.133894	−	0.205480i
$483$	2.17745	−	21.1209i	0.0990776	−	0.961036i
$484$	−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	−0.327649	−	0.944800i	$-0.606256\pi$
$487$	13.6193	−	13.6193i	0.617151	−	0.617151i	0.944800	+	0.327649i	$0.106256\pi$
$488$	4.17119	+	25.5641i	0.188821	+	1.15723i
$489$	−14.4881			−0.655176
$490$	12.9875	+	17.9255i	0.586716	+	0.809793i
$491$			19.0990i			0.861924i	0.902370	+	0.430962i	$0.141826\pi$
$491$			19.0990i			0.861924i	−0.902370	+	0.430962i	$0.858174\pi$
$492$	−1.88264	−	4.85926i	−0.0848759	−	0.219072i
$493$	−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
$497$	−14.1721	−	1.46107i	−0.635707	−	0.0655379i
$498$	1.00749	+	1.54614i	0.0451468	+	0.0692840i
$499$	22.6234			1.01276			0.506381	−	0.862310i	$-0.330983\pi$
$499$	22.6234			1.01276			0.506381	+	0.862310i	$0.330983\pi$
$500$	21.0121	−	7.64796i	0.939690	−	0.342027i
$501$			6.66731i			0.297874i
$502$	25.0793	−	16.3421i	1.11934	−	0.729385i
$503$	15.1983	−	15.1983i	0.677658	−	0.677658i	−0.281812	−	0.959470i	$-0.590935\pi$
$503$	15.1983	−	15.1983i	0.677658	−	0.677658i	0.959470	+	0.281812i	$0.0909354\pi$
$504$	−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
$508$	−7.20983	−	18.6092i	−0.319884	−	0.825649i
$509$		−	18.4978i		−	0.819899i	−0.912108	−	0.409949i	$-0.865546\pi$
$509$		−	18.4978i		−	0.819899i	0.912108	−	0.409949i	$-0.134454\pi$
$510$	10.0293	−	11.0208i	0.444107	−	0.488007i
$511$	−21.5537	+	17.5249i	−0.953479	+	0.775256i
$512$	−10.5535	−	20.0156i	−0.466405	−	0.884571i
$513$	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
$518$	−35.2735	−	11.3231i	−1.54983	−	0.497509i
$519$			13.9093i			0.610551i
$520$	−13.9504	−	5.39015i	−0.611767	−	0.236374i
$521$			2.65824i			0.116459i	0.998303	+	0.0582297i	$0.0185456\pi$
$521$			2.65824i			0.116459i	−0.998303	+	0.0582297i	$0.981454\pi$
$522$	4.55778	+	6.99454i	0.199488	+	0.306143i
$523$	18.8753	+	18.8753i	0.825358	+	0.825358i	0.986871	−	0.161513i	$-0.0516373\pi$
$523$	18.8753	+	18.8753i	0.825358	+	0.825358i	−0.161513	+	0.986871i	$0.551637\pi$
$524$	0.318311	−	0.720959i	0.0139055	−	0.0314953i
$525$	12.2937	+	4.88510i	0.536542	+	0.213203i
$526$	−17.7018	−	3.73390i	−0.771836	−	0.162806i
$527$	30.0467	−	30.0467i	1.30885	−	1.30885i
$528$	−20.5809	−	0.950381i	−0.895667	−	0.0413600i
$529$			41.4050i			1.80022i
$530$	3.81185	−	0.179528i	0.165576	−	0.00779819i
$531$	9.72563			0.422057
$532$	11.6108	+	6.62487i	0.503394	+	0.287224i
$533$	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
$538$	−15.6587	−	24.0305i	−0.675095	−	1.03603i
$539$	−7.35594	+	35.2965i	−0.316843	+	1.52033i
$540$	−3.62785	+	2.61509i	−0.156118	+	0.112536i
$541$			3.87240i			0.166487i	0.996529	+	0.0832437i	$0.0265280\pi$
$541$			3.87240i			0.166487i	−0.996529	+	0.0832437i	$0.973472\pi$
$542$	−0.187974	−	0.288472i	−0.00807417	−	0.0123909i
$543$	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	$-0.269034\pi$
$547$	−1.97663	−	1.97663i	−0.0845148	−	0.0845148i	−0.748100	+	0.663586i	$0.769034\pi$
$548$	−4.27935	−	11.0454i	−0.182805	−	0.471836i
$549$			9.15780i			0.390845i
$550$	32.2480	+	16.9278i	1.37506	+	0.721802i
$551$		−	14.9134i		−	0.635331i
$552$	22.4026	−	3.65535i	0.953520	−	0.155582i
$553$	−2.33762	+	22.6745i	−0.0994056	+	0.964217i
$554$	−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	$-0.124972\pi$
$557$	12.7754	+	12.7754i	0.541313	+	0.541313i	−0.382601	+	0.923914i	$0.624972\pi$
$558$	−10.6846	+	6.96229i	−0.452316	+	0.294737i
$559$	−16.6081			−0.702448
$560$	−14.8676	+	18.4107i	−0.628269	+	0.777996i
$561$	24.2709			1.02472
$562$	30.0313	−	19.5690i	1.26679	−	0.825467i
$563$	−5.99693	−	5.99693i	−0.252741	−	0.252741i	0.569353	−	0.822093i	$-0.307194\pi$
$563$	−5.99693	−	5.99693i	−0.252741	−	0.252741i	−0.822093	+	0.569353i	$0.807194\pi$
$564$	−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
$567$	−2.63180	−	0.271325i	−0.110525	−	0.0113946i
$568$	−2.45274	−	15.0322i	−0.102915	−	0.630735i
$569$		−	4.03460i		−	0.169139i	−0.996418	−	0.0845696i	$-0.973048\pi$
$569$		−	4.03460i		−	0.169139i	0.996418	−	0.0845696i	$-0.0269515\pi$
$570$	7.98000	−	0.375836i	0.334245	−	0.0157420i
$571$		−	43.2162i		−	1.80854i	−0.426959	−	0.904271i	$-0.640415\pi$
$571$		−	43.2162i		−	1.80854i	0.426959	−	0.904271i	$-0.359585\pi$
$572$	−8.80029	−	22.7143i	−0.367958	−	0.949733i
$573$	−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	$-0.454529\pi$
$577$	−20.3564	−	20.3564i	−0.847448	−	0.847448i	−0.989814	+	0.142366i	$0.954529\pi$
$578$	−4.01826	−	6.16659i	−0.167138	−	0.256496i
$579$			16.6187i			0.690648i
$580$	26.0595	+	4.22749i	1.08206	+	0.175537i
$581$	2.17804	+	2.67874i	0.0903602	+	0.111133i
$582$	4.19796	+	6.44235i	0.174011	+	0.267044i
$583$	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	−0.627577	−	0.778555i	$-0.715953\pi$
$587$	3.65791	−	3.65791i	0.150978	−	0.150978i	0.778555	+	0.627577i	$0.215953\pi$
$588$	−13.8118	+	2.28798i	−0.569588	+	0.0943546i
$589$	22.7811			0.938679
$590$	20.7000	−	22.7462i	0.852205	−	0.936446i
$591$		−	6.57859i		−	0.270607i
$592$	1.82689	−	39.5621i	0.0750849	−	1.62599i
$593$	32.9811	−	32.9811i	1.35437	−	1.35437i	0.473664	−	0.880706i	$-0.342931\pi$
$593$	32.9811	−	32.9811i	1.35437	−	1.35437i	0.880706	−	0.473664i	$-0.157069\pi$
$594$	−7.12735	−	1.50340i	−0.292439	−	0.0616851i
$595$	16.4955	−	22.4734i	0.676249	−	0.921322i
$596$	10.9483	−	24.7973i	0.448459	−	1.01574i
$597$	10.5434	+	10.5434i	0.431514	+	0.431514i
$598$	14.6519	+	22.4853i	0.599160	+	0.919494i
$599$		−	3.98653i		−	0.162885i	−0.996678	−	0.0814427i	$-0.974047\pi$
$599$		−	3.98653i		−	0.162885i	0.996678	−	0.0814427i	$-0.0259528\pi$
$600$	−1.60535	+	14.0507i	−0.0655383	+	0.573618i
$601$			5.37345i			0.219188i	0.993976	+	0.109594i	$0.0349550\pi$
$601$			5.37345i			0.219188i	−0.993976	+	0.109594i	$0.965045\pi$
$602$	−8.03214	+	25.0216i	−0.327366	+	1.01980i
$603$	−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	$-0.425505\pi$
$607$	−18.2522	−	18.2522i	−0.740835	−	0.740835i	−0.972739	+	0.231904i	$0.925505\pi$
$608$	−3.59140	+	13.8322i	−0.145651	+	0.560971i
$609$	9.85319	+	12.1183i	0.399271	+	0.491060i
$610$	21.4182	+	19.4914i	0.867196	+	0.789185i
$611$		−	8.39567i		−	0.339652i
$612$	3.40470	+	8.78783i	0.137627	+	0.355227i
$613$	−11.6742	+	11.6742i	−0.471517	+	0.471517i	−0.902405	−	0.430888i	$-0.858200\pi$
$613$	−11.6742	+	11.6742i	−0.471517	+	0.471517i	0.430888	+	0.902405i	$0.358200\pi$
$614$	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	−0.483960	−	0.875090i	$-0.660802\pi$
$617$	9.71546	−	9.71546i	0.391130	−	0.391130i	0.875090	+	0.483960i	$0.160802\pi$
$618$	22.8175	−	14.8683i	0.917855	−	0.598091i
$619$		−	28.1022i		−	1.12952i	−0.825254	−	0.564762i	$-0.808968\pi$
$619$		−	28.1022i		−	1.12952i	0.825254	−	0.564762i	$-0.191032\pi$
$620$	−6.45775	+	39.8075i	−0.259350	+	1.59871i
$621$	8.02527			0.322043
$622$	1.45630	+	2.23490i	0.0583925	+	0.0896115i
$623$	−16.5869	−	1.71002i	−0.664541	−	0.0685105i
$624$	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
$628$	9.00048	+	23.2310i	0.359158	+	0.927019i
$629$			46.6554i			1.86027i
$630$	−6.23609	+	5.57774i	−0.248452	+	0.222223i
$631$	−44.7908			−1.78309			−0.891546	−	0.452930i	$-0.850379\pi$
$631$	−44.7908			−1.78309			−0.891546	+	0.452930i	$0.850379\pi$
$632$	−24.0505	+	3.92422i	−0.956677	+	0.156097i
$633$	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
$637$	−9.07040	−	13.8464i	−0.359383	−	0.548612i
$638$	23.4757	+	36.0268i	0.929413	+	1.42631i
$639$		−	5.38495i		−	0.213025i
$640$	−23.1523	−	10.1966i	−0.915175	−	0.403057i
$641$	16.2466			0.641702			0.320851	−	0.947130i	$-0.396031\pi$
$641$	16.2466			0.641702			0.320851	+	0.947130i	$0.396031\pi$
$642$	4.45385	+	6.83505i	0.175779	+	0.269758i
$643$	16.7741	+	16.7741i	0.661505	+	0.661505i	0.955735	−	0.294230i	$-0.0950632\pi$
$643$	16.7741	+	16.7741i	0.661505	+	0.661505i	−0.294230	+	0.955735i	$0.595063\pi$
$644$	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	0.991479	+	0.130269i	$0.0415840\pi$
$647$	28.5330	+	28.5330i	1.12175	+	1.12175i	0.130269	+	0.991479i	$0.458416\pi$
$648$	−0.455480	−	2.79151i	−0.0178929	−	0.109661i
$649$	50.0938			1.96635
$650$	−15.9640	+	4.97345i	−0.626161	+	0.195075i
$651$	−18.5115	+	15.0514i	−0.725524	+	0.589910i
$652$	−10.4682	−	27.0193i	−0.409965	−	1.05816i
$653$	−15.8054	+	15.8054i	−0.618513	+	0.618513i	−0.945150	−	0.326637i	$-0.894085\pi$
$653$	−15.8054	+	15.8054i	−0.618513	+	0.618513i	0.326637	+	0.945150i	$0.394085\pi$
$654$	−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
$658$	−12.6488	−	4.06038i	−0.493102	−	0.158290i
$659$	7.74091			0.301543			0.150771	−	0.988569i	$-0.451824\pi$
$659$	7.74091			0.301543			0.150771	+	0.988569i	$0.451824\pi$
$660$	−18.6860	+	13.4695i	−0.727350	+	0.524301i
$661$	19.8958			0.773856			0.386928	−	0.922110i	$-0.373536\pi$
$661$	19.8958			0.773856			0.386928	+	0.922110i	$0.373536\pi$
$662$	−25.2630	−	38.7697i	−0.981876	−	1.50683i
$663$	−7.87912	+	7.87912i	−0.306000	+	0.306000i
$664$	−2.15548	+	2.99603i	−0.0836488	+	0.116269i
$665$	14.7729	−	2.26622i	0.572870	−	0.0878802i
$666$	2.88994	−	13.7007i	0.111983	−	0.530893i
$667$	−33.4994	−	33.4994i	−1.29710	−	1.29710i
$668$	−12.4340	+	4.81736i	−0.481087	+	0.186389i
$669$	14.0023			0.541360
$670$	0.612527	+	13.0056i	0.0236640	+	0.502449i
$671$			47.1690i			1.82094i
$672$	−6.22058	−	13.6127i	−0.239964	−	0.525120i
$673$	−5.16500	−	5.16500i	−0.199096	−	0.199096i	0.600516	−	0.799612i	$-0.294962\pi$
$673$	−5.16500	−	5.16500i	−0.199096	−	0.199096i	−0.799612	+	0.600516i	$0.794962\pi$
$674$	−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	−0.646781	−	0.762675i	$-0.723885\pi$
$677$	3.01547	−	3.01547i	0.115894	−	0.115894i	0.762675	+	0.646781i	$0.223885\pi$
$678$	−7.45389	−	11.4390i	−0.286265	−	0.439313i
$679$	9.07531	+	11.1616i	0.348279	+	0.428344i
$680$	27.7994	+	10.7411i	1.06606	+	0.411903i
$681$	−3.49129			−0.133787
$682$	−55.0332	+	35.8607i	−2.10733	+	1.37318i
$683$	28.6172	−	28.6172i	1.09501	−	1.09501i	0.100023	−	0.994985i	$-0.468108\pi$
$683$	28.6172	−	28.6172i	1.09501	−	1.09501i	0.994985	−	0.100023i	$-0.0318916\pi$
$684$	−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
$688$	−28.0637	−	1.29592i	−1.06992	−	0.0494066i
$689$	−2.85358			−0.108713
$690$	17.0810	−	18.7694i	0.650261	−	0.714539i
$691$	11.9509			0.454635			0.227318	−	0.973821i	$-0.427004\pi$
$691$	11.9509			0.454635			0.227318	+	0.973821i	$0.427004\pi$
$692$	−25.9398	+	10.0499i	−0.986083	+	0.382042i
$693$	−13.5556	−	1.39751i	−0.514935	−	0.0530870i
$694$	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
$698$	24.3748	+	37.4066i	0.922602	+	1.41586i
$699$		−	7.10955i		−	0.268908i
$700$	−0.227707	+	26.4565i	−0.00860652	+	0.999963i
$701$		−	39.7823i		−	1.50256i	−0.659985	−	0.751279i	$-0.729437\pi$
$701$		−	39.7823i		−	1.50256i	0.659985	−	0.751279i	$-0.270563\pi$
$702$	2.80182	−	1.82572i	0.105748	−	0.0689072i
$703$	−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
$707$	11.4490	+	1.18033i	0.430583	+	0.0443908i
$708$	7.02710	+	18.1376i	0.264095	+	0.681652i
$709$	−51.7991			−1.94536			−0.972679	−	0.232155i	$-0.925422\pi$
$709$	−51.7991			−1.94536			−0.972679	+	0.232155i	$0.925422\pi$
$710$	−12.5943	−	11.4613i	−0.472654	−	0.430135i
$711$	−8.61557			−0.323109
$712$	−2.87066	−	17.5935i	−0.107582	−	0.659344i
$713$	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
$718$	−0.0326958	−	0.0501763i	−0.00122020	−	0.00187256i
$719$	−30.1055			−1.12275			−0.561373	−	0.827563i	$-0.689727\pi$
$719$	−30.1055			−1.12275			−0.561373	+	0.827563i	$0.689727\pi$
$720$	−7.49820	−	4.87617i	−0.279441	−	0.181724i
$721$	39.5323	−	32.1429i	1.47226	−	1.19707i
$722$	−14.9504	+	9.74195i	−0.556396	+	0.362558i
$723$	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	−0.991342	−	0.131303i	$-0.958084\pi$
$727$	−30.2698	−	30.2698i	−1.12265	−	1.12265i	−0.131303	−	0.991342i	$-0.541916\pi$
$728$	11.7530	−	13.2289i	0.435595	−	0.490294i
$729$		−	1.00000i		−	0.0370370i
$730$	−33.1657	+	1.56202i	−1.22752	+	0.0578128i
$731$	33.0954			1.22408
$732$	−17.0786	+	6.61683i	−0.631243	+	0.244565i
$733$	−7.20460	−	7.20460i	−0.266108	−	0.266108i	0.561422	−	0.827530i	$-0.310255\pi$
$733$	−7.20460	−	7.20460i	−0.266108	−	0.266108i	−0.827530	+	0.561422i	$0.810255\pi$
$734$	−24.9396	−	5.26058i	−0.920536	−	0.194172i
$735$	−10.5069	+	11.6019i	−0.387555	+	0.427942i
$736$	23.0036	+	39.1381i	0.847925	+	1.44265i
$737$	−14.9955	+	14.9955i	−0.552367	+	0.552367i
$738$	3.08728	−	2.01173i	0.113644	−	0.0740528i
$739$	26.1241			0.960992			0.480496	−	0.876997i	$-0.340457\pi$
$739$	26.1241			0.960992			0.480496	+	0.876997i	$0.340457\pi$
$740$	−25.8922	−	35.9196i	−0.951816	−	1.32043i
$741$	−5.97387			−0.219456
$742$	−1.38007	+	4.29917i	−0.0506639	+	0.157827i
$743$	−0.603340	−	0.603340i	−0.0221344	−	0.0221344i	0.695953	−	0.718087i	$-0.254982\pi$
$743$	−0.603340	−	0.603340i	−0.0221344	−	0.0221344i	−0.718087	+	0.695953i	$0.754982\pi$
$744$	−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
$748$	17.5366	+	45.2634i	0.641201	+	1.65500i
$749$	9.62851	+	11.8420i	0.351818	+	0.432698i
$750$	8.35802	+	13.4218i	0.305192	+	0.490093i
$751$	6.27365			0.228929			0.114464	−	0.993427i	$-0.463485\pi$
$751$	6.27365			0.228929			0.114464	+	0.993427i	$0.463485\pi$
$752$	0.655110	−	14.1867i	0.0238894	−	0.517335i
$753$	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	$-0.130135\pi$
$757$	14.3084	+	14.3084i	0.520049	+	0.520049i	−0.397537	+	0.917586i	$0.630135\pi$
$758$	−22.5633	+	14.7027i	−0.819537	+	0.534025i
$759$	41.3358			1.50039
$760$	6.46673	+	14.6105i	0.234573	+	0.529980i
$761$		−	11.5121i		−	0.417314i	−0.977989	−	0.208657i	$-0.933091\pi$
$761$		−	11.5121i		−	0.417314i	0.977989	−	0.208657i	$-0.0669093\pi$
$762$	11.8232	−	7.70420i	0.428308	−	0.279094i
$763$	−8.41715	−	0.867762i	−0.304721	−	0.0314151i
$764$	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
$768$	12.3082	−	10.2229i	0.444135	−	0.368887i
$769$	5.61832			0.202602			0.101301	−	0.994856i	$-0.467700\pi$
$769$	5.61832			0.202602			0.101301	+	0.994856i	$0.467700\pi$
$770$	−32.1202	+	28.7293i	−1.15753	+	1.03533i
$771$		−	0.568816i		−	0.0204854i
$772$	−30.9926	+	12.0076i	−1.11545	+	0.432162i
$773$	−34.9945	−	34.9945i	−1.25866	−	1.25866i	−0.951731	−	0.306932i	$-0.900698\pi$
$773$	−34.9945	−	34.9945i	−1.25866	−	1.25866i	−0.306932	−	0.951731i	$-0.599302\pi$
$774$	−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
$777$	2.68640	−	26.0576i	0.0963741	−	0.934813i
$778$	4.11517	−	2.68152i	0.147536	−	0.0961373i
$779$	−6.58252			−0.235843
$780$	1.69341	−	10.4387i	0.0606339	−	0.373766i
$781$		−	27.7363i		−	0.992481i
$782$	−29.1972	−	44.8072i	−1.04409	−	1.60230i
$783$	−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	−0.998422	−	0.0561548i	$-0.982116\pi$
$787$	−26.4339	+	26.4339i	−0.942267	+	0.942267i	0.0561548	+	0.998422i	$0.482116\pi$
$788$	12.2686	−	4.75326i	0.437050	−	0.169328i
$789$		−	12.7925i		−	0.455425i
$790$	−18.3374	+	20.1500i	−0.652414	+	0.716905i
$791$	−16.1141	−	19.8186i	−0.572952	−	0.704668i
$792$	−2.34604	−	14.3782i	−0.0833628	−	0.510908i
$793$	−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	−0.159579	−	0.987185i	$-0.551014\pi$
$797$	23.3643	−	23.3643i	0.827607	−	0.827607i	0.987185	+	0.159579i	$0.0510135\pi$
$798$	−2.88913	+	9.00017i	−0.102274	+	0.318603i
$799$			16.7303i			0.591875i
$800$	−27.3635	+	7.15827i	−0.967445	+	0.253083i
$801$		−	6.30249i		−	0.222688i
$802$	45.3655	−	29.5610i	1.60191	−	1.04383i
$803$	−38.2403	−	38.2403i	−1.34947	−	1.34947i
$804$	−7.53301	−	3.32590i	−0.265669	−	0.117296i
$805$	28.0934	−	38.2745i	0.990163	−	1.34900i
$806$	6.22401	−	29.5070i	0.219232	−	1.03934i
$807$	14.3410	−	14.3410i	0.504828	−	0.504828i
$808$	1.98145	+	12.1438i	0.0697071	+	0.427216i
$809$		−	22.7738i		−	0.800684i	−0.916366	−	0.400342i	$-0.868891\pi$
$809$		−	22.7738i		−	0.800684i	0.916366	−	0.400342i	$-0.131109\pi$
$810$	−2.33879	−	2.12840i	−0.0821766	−	0.0747842i
$811$	−7.72619			−0.271303			−0.135652	−	0.990757i	$-0.543313\pi$
$811$	−7.72619			−0.271303			−0.135652	+	0.990757i	$0.543313\pi$
$812$	−15.4805	+	27.1314i	−0.543260	+	0.952124i
$813$	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
$818$	−18.8528	+	12.2849i	−0.659174	+	0.429530i
$819$	4.85426	−	3.94691i	0.169622	−	0.137916i
$820$	1.86594	−	11.5022i	0.0651616	−	0.401676i
$821$		−	6.24353i		−	0.217901i	−0.994047	−	0.108950i	$-0.965251\pi$
$821$		−	6.24353i		−	0.217901i	0.994047	−	0.108950i	$-0.0347489\pi$
$822$	7.01758	−	4.57278i	0.244766	−	0.159494i
$823$	24.9458	+	24.9458i	0.869557	+	0.869557i	0.992423	−	0.122866i	$-0.0392086\pi$
$823$	24.9458	+	24.9458i	0.869557	+	0.869557i	−0.122866	+	0.992423i	$0.539209\pi$
$824$	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	$-0.282853\pi$
$827$	−4.19002	−	4.19002i	−0.145701	−	0.145701i	−0.776195	+	0.630493i	$0.782853\pi$
$828$	5.79854	+	14.9665i	0.201513	+	0.520123i
$829$		−	40.2043i		−	1.39635i	−0.715926	−	0.698176i	$-0.753995\pi$
$829$		−	40.2043i		−	1.39635i	0.715926	−	0.698176i	$-0.246005\pi$
$830$	0.194131	+	4.12191i	0.00673838	+	0.143074i
$831$		−	5.67077i		−	0.196717i
$832$	16.9349	+	8.43083i	0.587112	+	0.292287i
$833$	18.0749	+	27.5920i	0.626256	+	0.956007i
$834$	−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
$838$	−1.82660	−	2.80318i	−0.0630989	−	0.0968341i
$839$	19.9254			0.687903			0.343951	−	0.938987i	$-0.388234\pi$
$839$	19.9254			0.687903			0.343951	+	0.938987i	$0.388234\pi$
$840$	−14.9079	−	7.59972i	−0.514370	−	0.262215i
$841$	5.84849			0.201672
$842$	6.19642	+	9.50927i	0.213543	+	0.327711i
$843$	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
$847$	−40.8710	−	4.21358i	−1.40435	−	0.144780i
$848$	−4.82186	−	0.222663i	−0.165583	−	0.00764629i
$849$			1.97720i			0.0678575i
$850$	31.8120	−	9.91073i	1.09114	−	0.339935i
$851$			79.4588i			2.72381i
$852$	10.0425	−	3.89081i	0.344051	−	0.133297i
$853$	6.36836	+	6.36836i	0.218048	+	0.218048i	0.807676	−	0.589627i	$-0.200725\pi$
$853$	6.36836	+	6.36836i	0.218048	+	0.218048i	−0.589627	+	0.807676i	$0.700725\pi$
$854$	−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	$-0.0463070\pi$
$857$	24.7215	+	24.7215i	0.844472	+	0.844472i	−0.144965	+	0.989437i	$0.546307\pi$
$858$	14.4313	−	9.40371i	0.492677	−	0.321037i
$859$			40.1782i			1.37086i	0.728137	+	0.685431i	$0.240386\pi$
$859$			40.1782i			1.37086i	−0.728137	+	0.685431i	$0.759614\pi$
$860$	−25.4799	+	18.3669i	−0.868856	+	0.626305i
$861$	5.34884	−	4.34904i	0.182288	−	0.148215i
$862$	11.0386	−	7.19298i	0.375977	−	0.244994i
$863$	−3.84231	−	3.84231i	−0.130794	−	0.130794i	0.638679	−	0.769473i	$-0.279481\pi$
$863$	−3.84231	−	3.84231i	−0.130794	−	0.130794i	−0.769473	+	0.638679i	$0.779481\pi$
$864$	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
$868$	−41.4449	−	23.6475i	−1.40673	−	0.802647i
$869$	−44.3762			−1.50536
$870$	0.878227	+	18.6471i	0.0297747	+	0.632195i
$871$		−	9.73604i		−	0.329893i
$872$	−1.45674	−	8.92794i	−0.0493313	−	0.302338i
$873$	−3.84469	+	3.84469i	−0.130123	+	0.130123i
$874$	5.91767	−	28.0547i	0.200168	−	0.948965i
$875$	18.1856	+	23.3299i	0.614785	+	0.788695i
$876$	8.48145	−	19.2101i	0.286562	−	0.649048i
$877$	−11.5497	−	11.5497i	−0.390006	−	0.390006i	0.484684	−	0.874689i	$-0.338935\pi$
$877$	−11.5497	−	11.5497i	−0.390006	−	0.390006i	−0.874689	+	0.484684i	$0.838935\pi$
$878$	−33.6006	+	21.8948i	−1.13396	+	0.738913i
$879$		−	9.25775i		−	0.312256i
$880$	−38.6209	−	25.1157i	−1.30191	−	0.846649i
$881$		−	11.8310i		−	0.398598i	−0.979939	−	0.199299i	$-0.936134\pi$
$881$		−	11.8310i		−	0.398598i	0.979939	−	0.199299i	$-0.0638665\pi$
$882$	−3.59871	−	9.22222i	−0.121175	−	0.310528i
$883$	−23.5185	+	23.5185i	−0.791462	+	0.791462i	−0.981732	−	0.190270i	$-0.939064\pi$
$883$	−23.5185	+	23.5185i	−0.791462	+	0.791462i	0.190270	+	0.981732i	$0.439064\pi$
$884$	−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	$-0.175540\pi$
$887$	9.76299	+	9.76299i	0.327809	+	0.327809i	−0.523944	+	0.851753i	$0.675540\pi$
$888$	27.6389	−	4.50973i	0.927502	−	0.151337i
$889$	20.4841	−	16.6552i	0.687015	−	0.558599i
$890$	−14.7402	−	13.4142i	−0.494093	−	0.449645i
$891$		−	5.15070i		−	0.172555i
$892$	10.1171	+	26.1132i	0.338747	+	0.874336i
$893$	−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
$898$	23.5608	+	36.1573i	0.786234	+	1.20659i
$899$			53.2333i			1.77543i
$900$	−9.95574	+	0.939861i	−0.331858	+	0.0313287i
$901$	5.68640			0.189442
$902$	15.9016	−	10.3618i	0.529467	−	0.345010i
$903$	−18.4842	−	1.90562i	−0.615116	−	0.0634152i
$904$	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	$-0.265968\pi$
$907$	−2.13567	−	2.13567i	−0.0709137	−	0.0709137i	−0.741674	+	0.670760i	$0.765968\pi$
$908$	−2.52258	−	6.51100i	−0.0837148	−	0.216075i
$909$			4.35024i			0.144288i
$910$	1.10081	−	19.7537i	0.0364914	−	0.654828i
$911$	−11.0958			−0.367620			−0.183810	−	0.982962i	$-0.558843\pi$
$911$	−11.0958			−0.367620			−0.183810	+	0.982962i	$0.558843\pi$
$912$	−10.0944	−	0.466139i	−0.334260	−	0.0154354i
$913$	−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
$917$	1.03706	+	0.106916i	0.0342469	+	0.00353067i
$918$	−5.58326	+	3.63816i	−0.184275	+	0.120077i
$919$		−	27.5278i		−	0.908059i	−0.890987	−	0.454029i	$-0.849986\pi$
$919$		−	27.5278i		−	0.908059i	0.890987	−	0.454029i	$-0.150014\pi$
$920$	47.3451	+	18.2932i	1.56092	+	0.603108i
$921$	5.17603			0.170556
$922$	−5.76100	+	3.75398i	−0.189729	+	0.123631i
$923$	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
$928$	−32.3222	−	8.39214i	−1.06103	−	0.275485i
$929$	−56.6438			−1.85842			−0.929211	−	0.369551i	$-0.879512\pi$
$929$	−56.6438			−1.85842			−0.929211	+	0.369551i	$0.879512\pi$
$930$	−28.4846	+	1.34155i	−0.934047	+	0.0439910i
$931$	−3.60791	+	17.3121i	−0.118245	+	0.567381i
$932$	13.2588	−	5.13689i	0.434305	−	0.168264i
$933$	−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	$-0.318109\pi$
$937$	−9.19223	−	9.19223i	−0.300297	−	0.300297i	−0.841130	+	0.540833i	$0.818109\pi$
$938$	−14.6682	−	4.70862i	−0.478934	−	0.153742i
$939$	29.4086			0.959715
$940$	−9.28475	−	12.8805i	−0.302835	−	0.420115i
$941$	−17.9694			−0.585785			−0.292892	−	0.956145i	$-0.594618\pi$
$941$	−17.9694			−0.585785			−0.292892	+	0.956145i	$0.594618\pi$
$942$	−14.7596	+	9.61763i	−0.480894	+	0.313359i
$943$	−14.7861	+	14.7861i	−0.481501	+	0.481501i
$944$	−28.7479	+	26.2100i	−0.935664	+	0.853064i
$945$	−4.76924	−	3.50062i	−0.155143	−	0.113875i
$946$	−50.0583	−	10.5590i	−1.62754	−	0.343301i
$947$	−22.2454	−	22.2454i	−0.722879	−	0.722879i	0.246312	−	0.969191i	$-0.420781\pi$
$947$	−22.2454	−	22.2454i	−0.722879	−	0.722879i	−0.969191	+	0.246312i	$0.920781\pi$
$948$	−6.22505	−	16.0674i	−0.202180	−	0.521845i
$949$	24.8281			0.805953
$950$	15.8169	+	8.30266i	0.513167	+	0.269374i
$951$			3.75053i			0.121619i
$952$	−23.4205	+	26.3615i	−0.759063	+	0.854382i
$953$	36.8379	+	36.8379i	1.19330	+	1.19330i	0.976136	+	0.217160i	$0.0696793\pi$
$953$	36.8379	+	36.8379i	1.19330	+	1.19330i	0.217160	+	0.976136i	$0.430321\pi$
$954$	−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
$958$	35.9248	−	23.4093i	1.16068	−	0.756319i
$959$	12.1582	−	9.88563i	0.392610	−	0.319224i
$960$	3.67599	−	17.5068i	0.118642	−	0.565029i
$961$	−50.3172			−1.62313
$962$	18.0765	+	27.7410i	0.582811	+	0.894405i
$963$	−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	−0.544996	−	0.838438i	$-0.683469\pi$
$967$	9.12506	−	9.12506i	0.293442	−	0.293442i	0.838438	+	0.544996i	$0.183469\pi$
$968$	−7.07345	−	43.3513i	−0.227349	−	1.39336i
$969$	11.9043			0.382421
$970$	0.808894	+	17.1750i	0.0259720	+	0.551455i
$971$	−8.32961			−0.267310			−0.133655	−	0.991028i	$-0.542671\pi$
$971$	−8.32961			−0.267310			−0.133655	+	0.991028i	$0.542671\pi$
$972$	1.86492	−	0.722534i	0.0598175	−	0.0231753i
$973$	−3.70593	+	35.9469i	−0.118807	+	1.15240i
$974$	−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	−0.945579	−	0.325393i	$-0.894503\pi$
$977$	−19.3851	+	19.3851i	−0.620186	+	0.620186i	0.325393	+	0.945579i	$0.394503\pi$
$978$	17.1664	−	11.1860i	0.548922	−	0.357688i
$979$		−	32.4622i		−	1.03750i
$980$	−29.2283	−	11.2119i	−0.933664	−	0.358151i
$981$		−	3.19824i		−	0.102112i
$982$	−14.7459	−	22.6296i	−0.470560	−	0.722140i
$983$	7.23192	−	7.23192i	0.230663	−	0.230663i	−0.582307	−	0.812969i	$-0.697850\pi$
$983$	7.23192	−	7.23192i	0.230663	−	0.230663i	0.812969	+	0.582307i	$0.197850\pi$
$984$	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
$987$	0.963323	−	9.34407i	0.0306629	−	0.297425i
$988$	−4.31633	−	11.1408i	−0.137321	−	0.354437i
$989$	56.3648			1.79230
$990$	−12.0464	−	10.9627i	−0.382859	−	0.348418i
$991$	29.2147			0.928036			0.464018	−	0.885826i	$-0.346407\pi$
$991$	29.2147			0.928036			0.464018	+	0.885826i	$0.346407\pi$
$992$	12.8195	−	49.3742i	0.407020	−	1.56763i
$993$	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	0.0444243	−	0.999013i	$-0.485855\pi$
$997$	32.9468	−	32.9468i	1.04344	−	1.04344i	0.999013	−	0.0444243i	$-0.0141453\pi$
$998$	−26.8056	+	17.4670i	−0.848516	+	0.552909i
$999$	9.90106			0.313256

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bj.b.13.17	✓	184	1.1	even	1	trivial
840.2.bj.b.13.18	yes	184	7.6	odd	2	inner
840.2.bj.b.13.25	yes	184	56.13	odd	2	inner
840.2.bj.b.13.26	yes	184	8.5	even	2	inner
840.2.bj.b.517.17	yes	184	280.237	even	4	inner
840.2.bj.b.517.18	yes	184	40.37	odd	4	inner
840.2.bj.b.517.25	yes	184	5.2	odd	4	inner
840.2.bj.b.517.26	yes	184	35.27	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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.bj (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18486 + 0.772078i) 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} +(2.63180 + 0.271325i) q^{7} +(0.455480 + 2.79151i) q^{8} +1.00000i q^{9} +(2.33879 + 2.12840i) q^{10} +5.15070i q^{11} +(-1.86492 + 0.722534i) 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} +(-0.772078 - 1.18486i) q^{18} +2.52629i q^{19} +(-4.41443 - 0.716127i) q^{20} +(-1.66911 - 2.05282i) q^{21} +(-3.97674 - 6.10286i) 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} +(2.62237 - 4.59600i) q^{28} -5.90326 q^{29} +(-0.148770 - 3.15878i) q^{30} -9.01760i q^{31} +(5.47531 + 1.42161i) q^{32} +(3.64209 - 3.64209i) q^{33} +(-6.52053 - 1.37540i) q^{34} +(-0.897053 - 5.84767i) q^{35} +(1.82961 + 0.807792i) q^{36} +(7.00111 + 7.00111i) q^{37} +(-1.95050 - 2.99331i) q^{38} +2.36468i q^{39} +(5.78339 - 2.55977i) q^{40} +2.60560i q^{41} +(3.56260 + 1.14362i) 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} +(-0.184515 + 3.99574i) q^{48} +(6.85277 + 1.42814i) q^{49} +(3.28650 - 6.26090i) q^{50} -4.71216i q^{51} +(-4.40995 + 1.70856i) 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} +(6.99454 - 4.55778i) q^{58} -9.72563i q^{59} +(2.61509 + 3.62785i) q^{60} +9.15780 q^{61} +(6.96229 + 10.6846i) q^{62} +(-0.271325 + 2.63180i) 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} +(8.78783 - 3.40470i) q^{68} -8.02527i q^{69} +(5.57774 + 6.23609i) q^{70} -5.38495 q^{71} +(-2.79151 + 0.455480i) 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} +(-1.39751 + 13.5556i) q^{77} +(-1.82572 - 2.80182i) q^{78} +8.61557i q^{79} +(-4.87617 + 7.49820i) q^{80} -1.00000 q^{81} +(-2.01173 - 3.08728i) 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} +(-14.3782 + 2.34604i) q^{88} -6.30249 q^{89} +(-2.12840 + 2.33879i) q^{90} +(-3.94691 - 4.85426i) q^{91} +(14.9665 - 5.79854i) 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} +(-9.22222 + 3.59871i) 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

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