LMFDB - Embedded newform 195.2.v.a.4.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,2,Mod(4,195)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("195.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.v (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.15
Character	$\chi$	$=$	195.4
Dual form			195.2.v.a.49.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30511 - 2.26052i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-2.40664 - 4.16842i) q^{4} +(-2.09035 - 0.794006i) q^{5} +(2.26052 - 1.30511i) q^{6} +(-0.372536 - 0.645251i) q^{7} -7.34329 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.30511 - 2.26052i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-2.40664 - 4.16842i) q^{4} +(-2.09035 - 0.794006i) q^{5} +(2.26052 - 1.30511i) q^{6} +(-0.372536 - 0.645251i) q^{7} -7.34329 q^{8} +(0.500000 + 0.866025i) q^{9} +(-4.52301 + 3.68901i) q^{10} +(4.61946 + 2.66705i) q^{11} -4.81328i q^{12} +(3.57858 - 0.440198i) q^{13} -1.94480 q^{14} +(-1.41329 - 1.73280i) q^{15} +(-4.77054 + 8.26282i) q^{16} +(-1.74020 + 1.00470i) q^{17} +2.61023 q^{18} +(3.92063 - 2.26358i) q^{19} +(1.72096 + 10.6243i) q^{20} -0.745071i q^{21} +(12.0578 - 6.96160i) q^{22} +(-4.28015 - 2.47114i) q^{23} +(-6.35947 - 3.67164i) q^{24} +(3.73911 + 3.31950i) q^{25} +(3.67537 - 8.66396i) q^{26} +1.00000i q^{27} +(-1.79312 + 3.10577i) q^{28} +(-4.47447 + 7.75001i) q^{29} +(-5.76154 + 0.933271i) q^{30} +4.43329i q^{31} +(5.10890 + 8.84888i) q^{32} +(2.66705 + 4.61946i) q^{33} +5.24500i q^{34} +(0.266396 + 1.64459i) q^{35} +(2.40664 - 4.16842i) q^{36} +(-1.60563 + 2.78103i) q^{37} -11.8169i q^{38} +(3.31924 + 1.40807i) q^{39} +(15.3500 + 5.83062i) q^{40} +(-5.22633 - 3.01742i) q^{41} +(-1.68425 - 0.972402i) q^{42} +(-2.84358 + 1.64174i) q^{43} -25.6745i q^{44} +(-0.357544 - 2.20730i) q^{45} +(-11.1721 + 6.45024i) q^{46} -3.07882 q^{47} +(-8.26282 + 4.77054i) q^{48} +(3.22243 - 5.58142i) q^{49} +(12.3838 - 4.12001i) q^{50} -2.00941 q^{51} +(-10.4473 - 13.8576i) q^{52} +2.14507i q^{53} +(2.26052 + 1.30511i) q^{54} +(-7.53863 - 9.24294i) q^{55} +(2.73564 + 4.73826i) q^{56} +4.52716 q^{57} +(11.6794 + 20.2293i) q^{58} +(5.56056 - 3.21039i) q^{59} +(-3.82177 + 10.0614i) q^{60} +(-2.57340 - 4.45726i) q^{61} +(10.0215 + 5.78594i) q^{62} +(0.372536 - 0.645251i) q^{63} +7.58861 q^{64} +(-7.82999 - 1.92125i) q^{65} +13.9232 q^{66} +(-2.90415 + 5.03014i) q^{67} +(8.37605 + 4.83591i) q^{68} +(-2.47114 - 4.28015i) q^{69} +(4.06532 + 1.54419i) q^{70} +(-3.29251 + 1.90093i) q^{71} +(-3.67164 - 6.35947i) q^{72} +16.0480 q^{73} +(4.19105 + 7.25912i) q^{74} +(1.57841 + 4.74432i) q^{75} +(-18.8711 - 10.8952i) q^{76} -3.97428i q^{77} +(7.51495 - 5.66553i) q^{78} -11.4449 q^{79} +(16.5328 - 13.4843i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-13.6419 + 7.87615i) q^{82} +11.1517 q^{83} +(-3.10577 + 1.79312i) q^{84} +(4.43536 - 0.718451i) q^{85} +8.57064i q^{86} +(-7.75001 + 4.47447i) q^{87} +(-33.9220 - 19.5849i) q^{88} +(-2.30838 - 1.33274i) q^{89} +(-5.45628 - 2.07254i) q^{90} +(-1.61719 - 2.14509i) q^{91} +23.7886i q^{92} +(-2.21664 + 3.83934i) q^{93} +(-4.01821 + 6.95974i) q^{94} +(-9.99278 + 1.61866i) q^{95} +10.2178i q^{96} +(0.570099 + 0.987440i) q^{97} +(-8.41128 - 14.5688i) q^{98} +5.33410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 20 q^{4} + 16 q^{9}+O(q^{10}) $ 32 * q - 20 * q^4 + 16 * q^9	$ 32 q - 20 q^{4} + 16 q^{9} + 2 q^{10} - 12 q^{11} + 8 q^{14} - 6 q^{15} - 28 q^{16} - 30 q^{20} - 4 q^{25} + 52 q^{26} - 24 q^{29} + 4 q^{30} - 2 q^{35} + 20 q^{36} + 4 q^{40} - 36 q^{41} + 12 q^{45} - 48 q^{46} - 28 q^{49} + 54 q^{50} - 40 q^{51} + 24 q^{55} - 56 q^{56} + 84 q^{59} - 32 q^{61} + 136 q^{64} + 20 q^{65} + 8 q^{66} - 24 q^{69} + 12 q^{71} + 40 q^{74} - 16 q^{75} + 48 q^{76} - 104 q^{79} + 66 q^{80} - 16 q^{81} - 48 q^{84} - 54 q^{85} - 48 q^{89} + 4 q^{90} + 12 q^{91} - 8 q^{94} + 12 q^{95}+O(q^{100}) $ 32 * q - 20 * q^4 + 16 * q^9 + 2 * q^10 - 12 * q^11 + 8 * q^14 - 6 * q^15 - 28 * q^16 - 30 * q^20 - 4 * q^25 + 52 * q^26 - 24 * q^29 + 4 * q^30 - 2 * q^35 + 20 * q^36 + 4 * q^40 - 36 * q^41 + 12 * q^45 - 48 * q^46 - 28 * q^49 + 54 * q^50 - 40 * q^51 + 24 * q^55 - 56 * q^56 + 84 * q^59 - 32 * q^61 + 136 * q^64 + 20 * q^65 + 8 * q^66 - 24 * q^69 + 12 * q^71 + 40 * q^74 - 16 * q^75 + 48 * q^76 - 104 * q^79 + 66 * q^80 - 16 * q^81 - 48 * q^84 - 54 * q^85 - 48 * q^89 + 4 * q^90 + 12 * q^91 - 8 * q^94 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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 $

$2$	1.30511	−	2.26052i	0.922854	−	1.59843i	0.127878	−	0.991790i	$-0.459184\pi$
$2$	1.30511	−	2.26052i	0.922854	−	1.59843i	0.794977	−	0.606640i	$-0.207483\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−2.40664	−	4.16842i	−1.20332	−	2.08421i
$5$	−2.09035	−	0.794006i	−0.934832	−	0.355090i
$5$	−2.09035	−	0.794006i	−0.934832	−	0.355090i
$6$	2.26052	−	1.30511i	0.922854	−	0.532810i
$7$	−0.372536	−	0.645251i	−0.140805	−	0.243882i	0.786995	−	0.616960i	$-0.211636\pi$
$7$	−0.372536	−	0.645251i	−0.140805	−	0.243882i	−0.927800	+	0.373078i	$0.878302\pi$
$8$	−7.34329			−2.59624
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−4.52301	+	3.68901i	−1.43030	+	1.16657i
$11$	4.61946	+	2.66705i	1.39282	+	0.804145i	0.993627	−	0.112721i	$-0.0359567\pi$
$11$	4.61946	+	2.66705i	1.39282	+	0.804145i	0.399194	+	0.916867i	$0.369290\pi$
$12$		−	4.81328i		−	1.38947i
$13$	3.57858	−	0.440198i	0.992519	−	0.122089i
$13$	3.57858	−	0.440198i	0.992519	−	0.122089i
$14$	−1.94480			−0.519771
$15$	−1.41329	−	1.73280i	−0.364910	−	0.447408i
$16$	−4.77054	+	8.26282i	−1.19264	+	2.06571i
$17$	−1.74020	+	1.00470i	−0.422060	+	0.243676i	−0.695958	−	0.718082i	$-0.745020\pi$
$17$	−1.74020	+	1.00470i	−0.422060	+	0.243676i	0.273899	+	0.961759i	$0.411687\pi$
$18$	2.61023			0.615236
$19$	3.92063	−	2.26358i	0.899455	−	0.519300i	0.0224314	−	0.999748i	$-0.492859\pi$
$19$	3.92063	−	2.26358i	0.899455	−	0.519300i	0.877023	+	0.480448i	$0.159526\pi$
$20$	1.72096	+	10.6243i	0.384818	+	2.37567i
$21$		−	0.745071i		−	0.162588i
$22$	12.0578	−	6.96160i	2.57074	−	1.48422i
$23$	−4.28015	−	2.47114i	−0.892472	−	0.515269i	−0.0177217	−	0.999843i	$-0.505641\pi$
$23$	−4.28015	−	2.47114i	−0.892472	−	0.515269i	−0.874750	+	0.484574i	$0.838975\pi$
$24$	−6.35947	−	3.67164i	−1.29812	−	0.749471i
$25$	3.73911	+	3.31950i	0.747822	+	0.663900i
$26$	3.67537	−	8.66396i	0.720800	−	1.69914i
$27$			1.00000i			0.192450i
$28$	−1.79312	+	3.10577i	−0.338867	+	0.586936i
$29$	−4.47447	+	7.75001i	−0.830889	+	1.43914i	0.0664460	+	0.997790i	$0.478834\pi$
$29$	−4.47447	+	7.75001i	−0.830889	+	1.43914i	−0.897335	+	0.441351i	$0.854499\pi$
$30$	−5.76154	+	0.933271i	−1.05191	+	0.170391i
$31$			4.43329i			0.796242i	0.917333	+	0.398121i	$0.130338\pi$
$31$			4.43329i			0.796242i	−0.917333	+	0.398121i	$0.869662\pi$
$32$	5.10890	+	8.84888i	0.903135	+	1.56428i
$33$	2.66705	+	4.61946i	0.464273	+	0.804145i
$34$			5.24500i			0.899510i
$35$	0.266396	+	1.64459i	0.0450291	+	0.277987i
$36$	2.40664	−	4.16842i	0.401106	−	0.694737i
$37$	−1.60563	+	2.78103i	−0.263964	+	0.457199i	−0.967292	−	0.253667i	$-0.918363\pi$
$37$	−1.60563	+	2.78103i	−0.263964	+	0.457199i	0.703328	+	0.710866i	$0.251697\pi$
$38$		−	11.8169i		−	1.91695i
$39$	3.31924	+	1.40807i	0.531504	+	0.225471i
$40$	15.3500	+	5.83062i	2.42705	+	0.921902i
$41$	−5.22633	−	3.01742i	−0.816215	−	0.471242i	0.0328945	−	0.999459i	$-0.489527\pi$
$41$	−5.22633	−	3.01742i	−0.816215	−	0.471242i	−0.849109	+	0.528217i	$0.822861\pi$
$42$	−1.68425	−	0.972402i	−0.259885	−	0.150045i
$43$	−2.84358	+	1.64174i	−0.433642	+	0.250363i	−0.700897	−	0.713262i	$-0.747217\pi$
$43$	−2.84358	+	1.64174i	−0.433642	+	0.250363i	0.267255	+	0.963626i	$0.413883\pi$
$44$		−	25.6745i		−	3.87057i
$45$	−0.357544	−	2.20730i	−0.0532996	−	0.329044i
$46$	−11.1721	+	6.45024i	−1.64724	+	0.951036i
$47$	−3.07882			−0.449092			−0.224546	−	0.974463i	$-0.572090\pi$
$47$	−3.07882			−0.449092			−0.224546	+	0.974463i	$0.572090\pi$
$48$	−8.26282	+	4.77054i	−1.19264	+	0.688568i
$49$	3.22243	−	5.58142i	0.460348	−	0.797346i
$50$	12.3838	−	4.12001i	1.75133	−	0.582658i
$51$	−2.00941			−0.281373
$52$	−10.4473	−	13.8576i	−1.44878	−	1.92171i
$53$			2.14507i			0.294648i	0.989088	+	0.147324i	$0.0470660\pi$
$53$			2.14507i			0.294648i	−0.989088	+	0.147324i	$0.952934\pi$
$54$	2.26052	+	1.30511i	0.307618	+	0.177603i
$55$	−7.53863	−	9.24294i	−1.01651	−	1.24632i
$56$	2.73564	+	4.73826i	0.365565	+	0.633177i
$57$	4.52716			0.599636
$58$	11.6794	+	20.2293i	1.53358	+	2.65623i
$59$	5.56056	−	3.21039i	0.723924	−	0.417958i	−0.0922713	−	0.995734i	$-0.529413\pi$
$59$	5.56056	−	3.21039i	0.723924	−	0.417958i	0.816195	+	0.577776i	$0.196079\pi$
$60$	−3.82177	+	10.0614i	−0.493389	+	1.29892i
$61$	−2.57340	−	4.45726i	−0.329490	−	0.570694i	0.652920	−	0.757426i	$-0.273544\pi$
$61$	−2.57340	−	4.45726i	−0.329490	−	0.570694i	−0.982411	+	0.186732i	$0.940210\pi$
$62$	10.0215	+	5.78594i	1.27274	+	0.734815i
$63$	0.372536	−	0.645251i	0.0469351	−	0.0812940i
$64$	7.58861			0.948576
$65$	−7.82999	−	1.92125i	−0.971191	−	0.238301i
$66$	13.9232			1.71383
$67$	−2.90415	+	5.03014i	−0.354799	+	0.614529i	−0.987083	−	0.160207i	$-0.948784\pi$
$67$	−2.90415	+	5.03014i	−0.354799	+	0.614529i	0.632285	+	0.774736i	$0.282117\pi$
$68$	8.37605	+	4.83591i	1.01574	+	0.586441i
$69$	−2.47114	−	4.28015i	−0.297491	−	0.515269i
$70$	4.06532	+	1.54419i	0.485898	+	0.184566i
$71$	−3.29251	+	1.90093i	−0.390749	+	0.225599i	−0.682485	−	0.730900i	$-0.739101\pi$
$71$	−3.29251	+	1.90093i	−0.390749	+	0.225599i	0.291736	+	0.956499i	$0.405767\pi$
$72$	−3.67164	−	6.35947i	−0.432707	−	0.749471i
$73$	16.0480			1.87828			0.939140	−	0.343535i	$-0.111624\pi$
$73$	16.0480			1.87828			0.939140	+	0.343535i	$0.111624\pi$
$74$	4.19105	+	7.25912i	0.487200	+	0.843856i
$75$	1.57841	+	4.74432i	0.182259	+	0.547827i
$76$	−18.8711	−	10.8952i	−2.16466	−	1.24977i
$77$		−	3.97428i		−	0.452912i
$78$	7.51495	−	5.66553i	0.850900	−	0.641495i
$79$	−11.4449			−1.28765			−0.643824	−	0.765173i	$-0.722653\pi$
$79$	−11.4449			−1.28765			−0.643824	+	0.765173i	$0.722653\pi$
$80$	16.5328	−	13.4843i	1.84843	−	1.50759i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−13.6419	+	7.87615i	−1.50649	+	0.869775i
$83$	11.1517			1.22406			0.612030	−	0.790834i	$-0.290353\pi$
$83$	11.1517			1.22406			0.612030	+	0.790834i	$0.290353\pi$
$84$	−3.10577	+	1.79312i	−0.338867	+	0.195645i
$85$	4.43536	−	0.718451i	0.481082	−	0.0779270i
$86$			8.57064i			0.924196i
$87$	−7.75001	+	4.47447i	−0.830889	+	0.479714i
$88$	−33.9220	−	19.5849i	−3.61610	−	2.08776i
$89$	−2.30838	−	1.33274i	−0.244688	−	0.141271i	0.372642	−	0.927975i	$-0.378452\pi$
$89$	−2.30838	−	1.33274i	−0.244688	−	0.141271i	−0.617329	+	0.786705i	$0.711785\pi$
$90$	−5.45628	−	2.07254i	−0.575142	−	0.218464i
$91$	−1.61719	−	2.14509i	−0.169527	−	0.224867i
$92$			23.7886i			2.48013i
$93$	−2.21664	+	3.83934i	−0.229855	+	0.398121i
$94$	−4.01821	+	6.95974i	−0.414446	+	0.717842i
$95$	−9.99278	+	1.61866i	−1.02524	+	0.166071i
$96$			10.2178i			1.04285i
$97$	0.570099	+	0.987440i	0.0578847	+	0.100259i	0.893516	−	0.449032i	$-0.148231\pi$
$97$	0.570099	+	0.987440i	0.0578847	+	0.100259i	−0.835631	+	0.549291i	$0.814898\pi$
$98$	−8.41128	−	14.5688i	−0.849668	−	1.47167i
$99$			5.33410i			0.536097i
$100$	4.83838	−	23.5750i	0.483838	−	2.35750i
$101$	−1.98838	+	3.44398i	−0.197852	+	0.342689i	−0.947832	−	0.318771i	$-0.896730\pi$
$101$	−1.98838	+	3.44398i	−0.197852	+	0.342689i	0.749980	+	0.661461i	$0.230063\pi$
$102$	−2.62250	+	4.54230i	−0.259666	+	0.449755i
$103$		−	2.40384i		−	0.236857i	−0.992963	−	0.118429i	$-0.962214\pi$
$103$		−	2.40384i		−	0.236857i	0.992963	−	0.118429i	$-0.0377857\pi$
$104$	−26.2785	+	3.23250i	−2.57682	+	0.316973i
$105$	−0.591591	+	1.55746i	−0.0577334	+	0.151992i
$106$	4.84898	+	2.79956i	0.470975	+	0.271917i
$107$	−14.2637	−	8.23517i	−1.37893	−	0.796124i	−0.386896	−	0.922123i	$-0.626453\pi$
$107$	−14.2637	−	8.23517i	−1.37893	−	0.796124i	−0.992030	+	0.125999i	$0.959786\pi$
$108$	4.16842	−	2.40664i	0.401106	−	0.231579i
$109$			3.18571i			0.305136i	0.988293	+	0.152568i	$0.0487542\pi$
$109$			3.18571i			0.305136i	−0.988293	+	0.152568i	$0.951246\pi$
$110$	−30.7326	+	4.97816i	−2.93024	+	0.474649i
$111$	−2.78103	+	1.60563i	−0.263964	+	0.152400i
$112$	7.10879			0.671717
$113$	4.55664	−	2.63078i	0.428653	−	0.247483i	−0.270120	−	0.962827i	$-0.587063\pi$
$113$	4.55664	−	2.63078i	0.428653	−	0.247483i	0.698773	+	0.715344i	$0.253730\pi$
$114$	5.90845	−	10.2337i	0.553377	−	0.958477i
$115$	6.98489	+	8.56401i	0.651344	+	0.798598i
$116$	43.0737			3.99930
$117$	2.17051	+	2.87904i	0.200664	+	0.266167i
$118$		−	16.7597i		−	1.54286i
$119$	1.29657	+	0.748575i	0.118856	+	0.0686218i
$120$	10.3782	+	12.7245i	0.947396	+	1.16158i
$121$	8.72629	+	15.1144i	0.793299	+	1.37403i
$122$	−13.4343			−1.21629
$123$	−3.01742	−	5.22633i	−0.272072	−	0.471242i
$124$	18.4798	−	10.6693i	1.65954	−	0.958133i
$125$	−5.18033	−	9.90778i	−0.463343	−	0.886179i
$126$	−0.972402	−	1.68425i	−0.0866285	−	0.150045i
$127$	5.24794	+	3.02990i	0.465679	+	0.268860i	0.714429	−	0.699708i	$-0.246686\pi$
$127$	5.24794	+	3.02990i	0.465679	+	0.268860i	−0.248750	+	0.968568i	$0.580020\pi$
$128$	−0.313817	+	0.543547i	−0.0277378	+	0.0480433i
$129$	−3.28349			−0.289095
$130$	−14.5620	+	15.1924i	−1.27718	+	1.33246i
$131$	−19.2543			−1.68225			−0.841127	−	0.540837i	$-0.818108\pi$
$131$	−19.2543			−1.68225			−0.841127	+	0.540837i	$0.818108\pi$
$132$	12.8372	−	22.2348i	1.11734	−	1.93529i
$133$	−2.92115	−	1.68653i	−0.253296	−	0.146240i
$134$	7.58049	+	13.1298i	0.654855	+	1.13424i
$135$	0.794006	−	2.09035i	0.0683372	−	0.179908i
$136$	12.7788	−	7.37782i	1.09577	−	0.632643i
$137$	7.48201	+	12.9592i	0.639231	+	1.10718i	0.985602	+	0.169083i	$0.0540806\pi$
$137$	7.48201	+	12.9592i	0.639231	+	1.10718i	−0.346371	+	0.938098i	$0.612586\pi$
$138$	−12.9005			−1.09816
$139$	−5.83686	−	10.1097i	−0.495076	−	0.857496i	0.504908	−	0.863173i	$-0.331526\pi$
$139$	−5.83686	−	10.1097i	−0.495076	−	0.857496i	−0.999984	+	0.00567680i	$0.998193\pi$
$140$	6.21424	−	5.06839i	0.525199	−	0.428358i
$141$	−2.66634	−	1.53941i	−0.224546	−	0.129642i
$142$			9.92371i			0.832780i
$143$	17.7051	+	7.51076i	1.48058	+	0.628081i
$144$	−9.54108			−0.795090
$145$	15.5068	−	12.6475i	1.28777	−	1.05031i
$146$	20.9445	−	36.2769i	1.73338	−	3.00230i
$147$	5.58142	−	3.22243i	0.460348	−	0.265782i
$148$	15.4567			1.27053
$149$	11.5523	−	6.66971i	0.946399	−	0.546404i	0.0544385	−	0.998517i	$-0.482663\pi$
$149$	11.5523	−	6.66971i	0.946399	−	0.546404i	0.891960	+	0.452113i	$0.149330\pi$
$150$	12.7847	+	2.62384i	1.04386	+	0.214236i
$151$			2.44431i			0.198915i	0.995042	+	0.0994574i	$0.0317107\pi$
$151$			2.44431i			0.198915i	−0.995042	+	0.0994574i	$0.968289\pi$
$152$	−28.7903	+	16.6221i	−2.33520	+	1.34823i
$153$	−1.74020	−	1.00470i	−0.140687	−	0.0812254i
$154$	−8.98395	−	5.18689i	−0.723947	−	0.417971i
$155$	3.52006	−	9.26711i	0.282738	−	0.744352i
$156$	−2.11880	−	17.2247i	−0.169639	−	1.37908i
$157$		−	19.7353i		−	1.57505i	−0.616284	−	0.787524i	$-0.711363\pi$
$157$		−	19.7353i		−	1.57505i	0.616284	−	0.787524i	$-0.288637\pi$
$158$	−14.9368	+	25.8714i	−1.18831	+	2.05822i
$159$	−1.07254	+	1.85769i	−0.0850576	+	0.147324i
$160$	−3.65332	−	22.5537i	−0.288820	−	1.78303i
$161$			3.68236i			0.290210i
$162$	1.30511	+	2.26052i	0.102539	+	0.177603i
$163$	−3.76607	−	6.52302i	−0.294981	−	0.510922i	0.679999	−	0.733213i	$-0.261980\pi$
$163$	−3.76607	−	6.52302i	−0.294981	−	0.510922i	−0.974981	+	0.222290i	$0.928647\pi$
$164$			29.0474i			2.26822i
$165$	−1.90718	−	11.7739i	−0.148473	−	0.916600i
$166$	14.5543	−	25.2087i	1.12963	−	1.95658i
$167$	−5.55821	+	9.62710i	−0.430107	+	0.744968i	−0.996882	−	0.0789052i	$-0.974858\pi$
$167$	−5.55821	+	9.62710i	−0.430107	+	0.744968i	0.566775	+	0.823873i	$0.308191\pi$
$168$			5.47127i			0.422118i
$169$	12.6125	−	3.15057i	0.970189	−	0.242351i
$170$	4.16456	−	10.9639i	0.319407	−	0.840891i
$171$	3.92063	+	2.26358i	0.299818	+	0.173100i
$172$	13.6869	+	7.90216i	1.04362	+	0.602534i
$173$	9.22179	−	5.32420i	0.701120	−	0.404792i	−0.106645	−	0.994297i	$-0.534011\pi$
$173$	9.22179	−	5.32420i	0.701120	−	0.404792i	0.807764	+	0.589506i	$0.200677\pi$
$174$			23.3588i			1.77082i
$175$	0.748958	−	3.64929i	0.0566159	−	0.275861i
$176$	−44.0747	+	25.4465i	−3.32225	+	1.91810i
$177$	6.42079			0.482616
$178$	−6.02539	+	3.47876i	−0.451622	+	0.260744i
$179$	−8.51246	+	14.7440i	−0.636251	+	1.10202i	0.349997	+	0.936751i	$0.386182\pi$
$179$	−8.51246	+	14.7440i	−0.636251	+	1.10202i	−0.986249	+	0.165269i	$0.947151\pi$
$180$	−8.34046	+	6.80256i	−0.621661	+	0.507033i
$181$	2.25248			0.167426			0.0837129	−	0.996490i	$-0.473322\pi$
$181$	2.25248			0.167426			0.0837129	+	0.996490i	$0.473322\pi$
$182$	−6.95964	+	0.856100i	−0.515883	+	0.0634583i
$183$		−	5.14680i		−	0.380463i
$184$	31.4303	+	18.1463i	2.31708	+	1.33776i
$185$	5.56448	−	4.53844i	0.409109	−	0.333673i
$186$	5.78594	+	10.0215i	0.424246	+	0.734815i
$187$	−10.7184			−0.783804
$188$	7.40961	+	12.8338i	0.540401	+	0.936002i
$189$	0.645251	−	0.372536i	0.0469351	−	0.0270980i
$190$	−9.38269	+	24.7014i	−0.680692	+	1.79203i
$191$	5.44970	+	9.43916i	0.394327	+	0.682994i	0.993015	−	0.117988i	$-0.0376445\pi$
$191$	5.44970	+	9.43916i	0.394327	+	0.682994i	−0.598688	+	0.800982i	$0.704311\pi$
$192$	6.57193	+	3.79430i	0.474288	+	0.273830i
$193$	−7.53493	+	13.0509i	−0.542376	+	0.939423i	0.456391	+	0.889779i	$0.349142\pi$
$193$	−7.53493	+	13.0509i	−0.542376	+	0.939423i	−0.998767	+	0.0496434i	$0.984192\pi$
$194$	2.97617			0.213677
$195$	−5.82035	−	5.57885i	−0.416804	−	0.399509i
$196$	−31.0209			−2.21578
$197$	9.92251	−	17.1863i	0.706949	−	1.22447i	−0.259034	−	0.965868i	$-0.583404\pi$
$197$	9.92251	−	17.1863i	0.706949	−	1.22447i	0.965983	−	0.258604i	$-0.0832625\pi$
$198$	12.0578	+	6.96160i	0.856913	+	0.494739i
$199$	−9.77008	−	16.9223i	−0.692582	−	1.19959i	−0.970989	−	0.239124i	$-0.923140\pi$
$199$	−9.77008	−	16.9223i	−0.692582	−	1.19959i	0.278407	−	0.960463i	$-0.410194\pi$
$200$	−27.4573	−	24.3760i	−1.94153	−	1.72365i
$201$	−5.03014	+	2.90415i	−0.354799	+	0.204843i
$202$	5.19013	+	8.98957i	0.365176	+	0.632504i
$203$	6.66760			0.467974
$204$	4.83591	+	8.37605i	0.338582	+	0.586441i
$205$	8.52899	+	10.4572i	0.595690	+	0.730362i
$206$	−5.43393	−	3.13728i	−0.378600	−	0.218585i
$207$		−	4.94229i		−	0.343513i
$208$	−13.4345	+	31.6691i	−0.931514	+	2.19586i
$209$	24.1483			1.67037
$210$	2.74857	+	3.36996i	0.189670	+	0.232550i
$211$	−4.99214	+	8.64665i	−0.343673	+	0.595260i	−0.985112	−	0.171915i	$-0.945005\pi$
$211$	−4.99214	+	8.64665i	−0.343673	+	0.595260i	0.641438	+	0.767175i	$0.278338\pi$
$212$	8.94156	−	5.16241i	0.614109	−	0.354556i
$213$	−3.80186			−0.260499
$214$	−37.2316	+	21.4956i	−2.54510	+	1.46941i
$215$	7.24763	−	1.17399i	0.494284	−	0.0800655i
$216$		−	7.34329i		−	0.499647i
$217$	2.86058	−	1.65156i	0.194189	−	0.112115i
$218$	7.20136	+	4.15771i	0.487738	+	0.281596i
$219$	13.8980	+	8.02401i	0.939140	+	0.542213i
$220$	−20.3857	+	53.6686i	−1.37440	+	3.61834i
$221$	−5.78516	+	4.36144i	−0.389152	+	0.293382i
$222$			8.38211i			0.562570i
$223$	−3.38822	+	5.86857i	−0.226892	+	0.392989i	−0.956885	−	0.290466i	$-0.906190\pi$
$223$	−3.38822	+	5.86857i	−0.226892	+	0.392989i	0.729993	+	0.683454i	$0.239523\pi$
$224$	3.80650	−	6.59305i	0.254332	−	0.440516i
$225$	−1.00522	+	4.89791i	−0.0670144	+	0.326527i
$226$		−	13.7339i		−	0.913563i
$227$	−7.16627	−	12.4124i	−0.475642	−	0.823837i	0.523968	−	0.851738i	$-0.324451\pi$
$227$	−7.16627	−	12.4124i	−0.475642	−	0.823837i	−0.999611	+	0.0279011i	$0.991118\pi$
$228$	−10.8952	−	18.8711i	−0.721554	−	1.24977i
$229$		−	23.0736i		−	1.52475i	−0.647137	−	0.762374i	$-0.724034\pi$
$229$		−	23.0736i		−	1.52475i	0.647137	−	0.762374i	$-0.275966\pi$
$230$	28.4752	−	4.61249i	1.87760	−	0.304139i
$231$	1.98714	−	3.44183i	0.130744	−	0.226456i
$232$	32.8573	−	56.9106i	2.15719	−	3.73636i
$233$		−	2.70544i		−	0.177240i	−0.996066	−	0.0886198i	$-0.971754\pi$
$233$		−	2.70544i		−	0.177240i	0.996066	−	0.0886198i	$-0.0282456\pi$
$234$	9.34090	−	1.14902i	0.610634	−	0.0751136i
$235$	6.43580	+	2.44460i	0.419826	+	0.159468i
$236$	−26.7645	−	15.4525i	−1.74222	−	1.00587i
$237$	−9.91155	−	5.72243i	−0.643824	−	0.371712i
$238$	3.38434	−	1.95395i	0.219374	−	0.126656i
$239$		−	5.93661i		−	0.384007i	−0.981394	−	0.192004i	$-0.938501\pi$
$239$		−	5.93661i		−	0.384007i	0.981394	−	0.192004i	$-0.0614986\pi$
$240$	21.0600	−	3.41136i	1.35942	−	0.220202i
$241$	−1.89302	+	1.09293i	−0.121940	+	0.0704021i	−0.559729	−	0.828675i	$-0.689095\pi$
$241$	−1.89302	+	1.09293i	−0.121940	+	0.0704021i	0.437789	+	0.899078i	$0.355762\pi$
$242$	45.5552			2.92840
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−12.3865	+	21.4540i	−0.792964	+	1.37345i
$245$	−11.1677	+	9.10848i	−0.713478	+	0.581919i
$246$	−15.7523			−1.00433
$247$	13.0339	−	9.82625i	0.829325	−	0.625229i
$248$		−	32.5549i		−	2.06724i
$249$	9.65767	+	5.57586i	0.612030	+	0.353356i
$250$	−29.1577	−	1.22052i	−1.84409	−	0.0771924i
$251$	1.84213	+	3.19067i	0.116274	+	0.201393i	0.918288	−	0.395912i	$-0.129571\pi$
$251$	1.84213	+	3.19067i	0.116274	+	0.201393i	−0.802014	+	0.597305i	$0.796238\pi$
$252$	−3.58624			−0.225912
$253$	−13.1813	−	22.8307i	−0.828702	−	1.43535i
$254$	13.6983	−	7.90872i	0.859508	−	0.496237i
$255$	4.20036	+	1.59548i	0.263037	+	0.0999129i
$256$	8.40774	+	14.5626i	0.525484	+	0.910165i
$257$	22.5840	+	13.0389i	1.40875	+	0.813344i	0.995268	−	0.0971673i	$-0.0309782\pi$
$257$	22.5840	+	13.0389i	1.40875	+	0.813344i	0.413485	+	0.910511i	$0.364312\pi$
$258$	−4.28532	+	7.42239i	−0.266792	+	0.462098i
$259$	2.39262			0.148670
$260$	10.8354	+	37.2625i	0.671983	+	2.31092i
$261$	−8.94894			−0.553926
$262$	−25.1290	+	43.5247i	−1.55248	+	2.68897i
$263$	−0.844103	−	0.487343i	−0.0520496	−	0.0300509i	0.473749	−	0.880660i	$-0.342900\pi$
$263$	−0.844103	−	0.487343i	−0.0520496	−	0.0300509i	−0.525799	+	0.850609i	$0.676234\pi$
$264$	−19.5849	−	33.9220i	−1.20537	−	2.08776i
$265$	1.70320	−	4.48394i	0.104627	−	0.275447i
$266$	−7.62486	+	4.40222i	−0.467510	+	0.269917i
$267$	−1.33274	−	2.30838i	−0.0815626	−	0.141271i
$268$	27.9570			1.70774
$269$	−0.575856	−	0.997411i	−0.0351105	−	0.0608132i	0.847936	−	0.530098i	$-0.177845\pi$
$269$	−0.575856	−	0.997411i	−0.0351105	−	0.0608132i	−0.883047	+	0.469285i	$0.844512\pi$
$270$	−3.68901	−	4.52301i	−0.224506	−	0.275262i
$271$	3.89046	+	2.24616i	0.236329	+	0.136445i	0.613488	−	0.789704i	$-0.289766\pi$
$271$	3.89046	+	2.24616i	0.236329	+	0.136445i	−0.377159	+	0.926148i	$0.623099\pi$
$272$		−	19.1719i		−	1.16247i
$273$	−0.327979	−	2.66630i	−0.0198502	−	0.161372i
$274$	39.0595			2.35967
$275$	8.41941	+	25.3067i	0.507709	+	1.52605i
$276$	−11.8943	+	20.6015i	−0.715953	+	1.24007i
$277$	−5.81040	+	3.35463i	−0.349113	+	0.201560i	−0.664294	−	0.747471i	$-0.731268\pi$
$277$	−5.81040	+	3.35463i	−0.349113	+	0.201560i	0.315182	+	0.949031i	$0.397935\pi$
$278$	−30.4710			−1.82753
$279$	−3.83934	+	2.21664i	−0.229855	+	0.132707i
$280$	−1.95622	−	12.0767i	−0.116907	−	0.721723i
$281$		−	30.5476i		−	1.82232i	−0.412054	−	0.911160i	$-0.635188\pi$
$281$		−	30.5476i		−	1.82232i	0.412054	−	0.911160i	$-0.364812\pi$
$282$	−6.95974	+	4.01821i	−0.414446	+	0.239281i
$283$	−10.3971	−	6.00278i	−0.618045	−	0.356828i	0.158063	−	0.987429i	$-0.449475\pi$
$283$	−10.3971	−	6.00278i	−0.618045	−	0.356828i	−0.776107	+	0.630601i	$0.782809\pi$
$284$	15.8478	+	9.14970i	0.940391	+	0.542935i
$285$	−9.46333	−	3.59459i	−0.560559	−	0.212925i
$286$	40.0854	−	30.2205i	2.37030	−	1.78697i
$287$			4.49639i			0.265413i
$288$	−5.10890	+	8.84888i	−0.301045	+	0.521425i
$289$	−6.48114	+	11.2257i	−0.381244	+	0.660334i
$290$	−8.35179	−	51.5597i	−0.490434	−	3.02769i
$291$			1.14020i			0.0668396i
$292$	−38.6218	−	66.8949i	−2.26017	−	3.91473i
$293$	−0.328488	−	0.568959i	−0.0191905	−	0.0332389i	0.856271	−	0.516527i	$-0.172776\pi$
$293$	−0.328488	−	0.568959i	−0.0191905	−	0.0332389i	−0.875461	+	0.483288i	$0.839442\pi$
$294$		−	16.8226i		−	0.981112i
$295$	−14.1726	+	2.29572i	−0.825160	+	0.133662i
$296$	11.7906	−	20.4219i	0.685315	−	1.18700i
$297$	−2.66705	+	4.61946i	−0.154758	+	0.268048i
$298$		−	34.8189i		−	2.01700i
$299$	−16.4046	−	6.95907i	−0.948704	−	0.402453i
$300$	15.9777	−	17.9974i	0.922471	−	1.03908i
$301$	2.11867	+	1.22322i	0.122118	+	0.0705050i
$302$	5.52541	+	3.19009i	0.317951	+	0.183569i
$303$	−3.44398	+	1.98838i	−0.197852	+	0.114230i
$304$			43.1940i			2.47734i
$305$	1.84021	+	11.3605i	0.105370	+	0.650502i
$306$	−4.54230	+	2.62250i	−0.259666	+	0.149918i
$307$	−1.96322			−0.112047			−0.0560233	−	0.998429i	$-0.517842\pi$
$307$	−1.96322			−0.112047			−0.0560233	+	0.998429i	$0.517842\pi$
$308$	−16.5665	+	9.56466i	−0.943963	+	0.544997i
$309$	1.20192	−	2.08179i	0.0683748	−	0.118429i
$310$	−16.3544	−	20.0518i	−0.928869	−	1.13887i
$311$	16.8994			0.958277			0.479139	−	0.877739i	$-0.340949\pi$
$311$	16.8994			0.958277			0.479139	+	0.877739i	$0.340949\pi$
$312$	−24.3741	−	10.3398i	−1.37991	−	0.585378i
$313$			24.4222i			1.38042i	0.723608	+	0.690211i	$0.242482\pi$
$313$			24.4222i			1.38042i	−0.723608	+	0.690211i	$0.757518\pi$
$314$	−44.6120	−	25.7568i	−2.51760	−	1.45354i
$315$	−1.29106	+	1.05300i	−0.0727431	+	0.0593300i
$316$	27.5437	+	47.7070i	1.54945	+	2.68373i
$317$	6.24200			0.350586			0.175293	−	0.984516i	$-0.443913\pi$
$317$	6.24200			0.350586			0.175293	+	0.984516i	$0.443913\pi$
$318$	2.79956	+	4.84898i	0.156992	+	0.271917i
$319$	−41.3393	+	23.8673i	−2.31456	+	1.33631i
$320$	−15.8628	−	6.02540i	−0.886759	−	0.336830i
$321$	−8.23517	−	14.2637i	−0.459642	−	0.796124i
$322$	8.32405	+	4.80589i	0.463881	+	0.267822i
$323$	−4.54845	+	7.87814i	−0.253082	+	0.438351i
$324$	4.81328			0.267404
$325$	14.8419	+	10.2331i	0.823282	+	0.567632i
$326$	−19.6606			−1.08890
$327$	−1.59285	+	2.75890i	−0.0880850	+	0.152568i
$328$	38.3784	+	22.1578i	2.11909	+	1.22346i
$329$	1.14697	+	1.98661i	0.0632345	+	0.109525i
$330$	−29.1043	−	11.0551i	−1.60214	−	0.608563i
$331$	11.1115	−	6.41522i	0.610742	−	0.352612i	−0.162514	−	0.986706i	$-0.551960\pi$
$331$	11.1115	−	6.41522i	0.610742	−	0.352612i	0.773256	+	0.634094i	$0.218627\pi$
$332$	−26.8382	−	46.4851i	−1.47294	−	2.55120i
$333$	−3.21126			−0.175976
$334$	14.5082	+	25.1289i	0.793852	+	1.37499i
$335$	10.0646	−	8.20882i	0.549891	−	0.448496i
$336$	6.15639	+	3.55439i	0.335859	+	0.193908i
$337$		−	6.39946i		−	0.348601i	−0.984693	−	0.174301i	$-0.944234\pi$
$337$		−	6.39946i		−	0.348601i	0.984693	−	0.174301i	$-0.0557664\pi$
$338$	9.33874	−	32.6226i	0.507961	−	1.77443i
$339$	5.26156			0.285769
$340$	−13.6691	−	16.7594i	−0.741311	−	0.908905i
$341$	−11.8238	+	20.4794i	−0.640294	+	1.10902i
$342$	10.2337	−	5.90845i	0.553377	−	0.319492i
$343$	−10.0174			−0.540888
$344$	20.8812	−	12.0558i	1.12584	−	0.650005i
$345$	1.76709	+	10.9091i	0.0951367	+	0.587326i
$346$		−	27.7947i		−	1.49425i
$347$	15.0295	−	8.67730i	0.806827	−	0.465822i	−0.0390257	−	0.999238i	$-0.512425\pi$
$347$	15.0295	−	8.67730i	0.806827	−	0.465822i	0.845853	+	0.533416i	$0.179092\pi$
$348$	37.3030	+	21.5369i	1.99965	+	1.15450i
$349$	18.5622	+	10.7169i	0.993614	+	0.573663i	0.906353	−	0.422522i	$-0.138855\pi$
$349$	18.5622	+	10.7169i	0.993614	+	0.573663i	0.0872616	+	0.996185i	$0.472188\pi$
$350$	−7.27183	−	6.45578i	−0.388696	−	0.345076i
$351$	0.440198	+	3.57858i	0.0234960	+	0.191010i
$352$			54.5028i			2.90501i
$353$	−6.82103	+	11.8144i	−0.363047	+	0.628816i	−0.988461	−	0.151477i	$-0.951597\pi$
$353$	−6.82103	+	11.8144i	−0.363047	+	0.628816i	0.625414	+	0.780293i	$0.284930\pi$
$354$	8.37985	−	14.5143i	0.445384	−	0.771428i
$355$	8.39184	−	1.35933i	0.445392	−	0.0721459i
$356$			12.8297i			0.679974i
$357$	0.748575	+	1.29657i	0.0396188	+	0.0686218i
$358$	22.2194	+	38.4852i	1.17433	+	2.03401i
$359$		−	13.8964i		−	0.733422i	−0.930335	−	0.366711i	$-0.880484\pi$
$359$		−	13.8964i		−	0.733422i	0.930335	−	0.366711i	$-0.119516\pi$
$360$	2.62555	+	16.2088i	0.138379	+	0.854280i
$361$	0.747568	−	1.29483i	0.0393457	−	0.0681488i
$362$	2.93975	−	5.09179i	0.154510	−	0.267619i
$363$			17.4526i			0.916023i
$364$	−5.04966	+	11.9036i	−0.264674	+	0.623917i
$365$	−33.5460	−	12.7422i	−1.75588	−	0.666959i
$366$	−11.6345	−	6.71716i	−0.608143	−	0.351112i
$367$	14.8707	+	8.58561i	0.776245	+	0.448165i	0.835098	−	0.550102i	$-0.185411\pi$
$367$	14.8707	+	8.58561i	0.776245	+	0.448165i	−0.0588530	+	0.998267i	$0.518744\pi$
$368$	40.8372	−	23.5774i	2.12879	−	1.22906i
$369$		−	6.03484i		−	0.314161i
$370$	−2.99698	−	18.5018i	−0.155805	−	0.961863i
$371$	1.38411	−	0.799116i	0.0718594	−	0.0414880i
$372$	21.3386			1.10636
$373$	−10.7364	+	6.19865i	−0.555908	+	0.320954i	−0.751502	−	0.659731i	$-0.770670\pi$
$373$	−10.7364	+	6.19865i	−0.555908	+	0.320954i	0.195593	+	0.980685i	$0.437337\pi$
$374$	−13.9887	+	24.2291i	−0.723337	+	1.25286i
$375$	0.467591	−	11.1706i	0.0241463	−	0.576845i
$376$	22.6087			1.16595
$377$	−12.6007	+	29.7037i	−0.648969	+	1.52982i
$378$		−	1.94480i		−	0.100030i
$379$	−29.4483	−	17.0020i	−1.51266	−	0.873334i	−0.999890	−	0.0148065i	$-0.995287\pi$
$379$	−29.4483	−	17.0020i	−1.51266	−	0.873334i	−0.512768	−	0.858527i	$-0.671380\pi$
$380$	30.7963	+	37.7586i	1.57981	+	1.93697i
$381$	3.02990	+	5.24794i	0.155226	+	0.268860i
$382$	28.4499			1.45562
$383$	−8.20981	−	14.2198i	−0.419502	−	0.726598i	0.576388	−	0.817176i	$-0.304462\pi$
$383$	−8.20981	−	14.2198i	−0.419502	−	0.726598i	−0.995889	+	0.0905781i	$0.971129\pi$
$384$	−0.543547	+	0.313817i	−0.0277378	+	0.0160144i
$385$	−3.15561	+	8.30763i	−0.160825	+	0.423396i
$386$	19.6679	+	34.0657i	1.00107	+	1.73390i
$387$	−2.84358	−	1.64174i	−0.144547	−	0.0834545i
$388$	2.74404	−	4.75282i	0.139308	−	0.241288i
$389$	19.2459			0.975804			0.487902	−	0.872898i	$-0.337762\pi$
$389$	19.2459			0.975804			0.487902	+	0.872898i	$0.337762\pi$
$390$	−20.2073	+	5.87601i	−1.02324	+	0.297543i
$391$	9.93106			0.502235
$392$	−23.6633	+	40.9860i	−1.19518	+	2.07010i
$393$	−16.6747	−	9.62714i	−0.841127	−	0.485625i
$394$	−25.9000	−	44.8601i	−1.30482	−	2.26002i
$395$	23.9238	+	9.08730i	1.20373	+	0.457232i
$396$	22.2348	−	12.8372i	1.11734	−	0.645096i
$397$	4.55470	+	7.88897i	0.228594	+	0.395936i	0.957392	−	0.288793i	$-0.0932539\pi$
$397$	4.55470	+	7.88897i	0.228594	+	0.395936i	−0.728798	+	0.684729i	$0.759921\pi$
$398$	−51.0042			−2.55661
$399$	−1.68653	−	2.92115i	−0.0844320	−	0.146240i
$400$	−45.2660	+	15.0598i	−2.26330	+	0.752989i
$401$	−18.4340	−	10.6429i	−0.920552	−	0.531481i	−0.0367407	−	0.999325i	$-0.511698\pi$
$401$	−18.4340	−	10.6429i	−0.920552	−	0.531481i	−0.883811	+	0.467844i	$0.845031\pi$
$402$			15.1610i			0.756161i
$403$	1.95153	+	15.8649i	0.0972124	+	0.790285i
$404$	19.1413			0.952315
$405$	1.73280	−	1.41329i	0.0861037	−	0.0702270i
$406$	8.70197	−	15.0723i	0.431872	−	0.748024i
$407$	−14.8343	+	8.56458i	−0.735308	+	0.424531i
$408$	14.7556			0.730513
$409$	−12.5325	+	7.23564i	−0.619692	+	0.357779i	−0.776749	−	0.629810i	$-0.783133\pi$
$409$	−12.5325	+	7.23564i	−0.619692	+	0.357779i	0.157057	+	0.987590i	$0.449799\pi$
$410$	34.7700	−	5.63214i	1.71717	−	0.278152i
$411$			14.9640i			0.738120i
$412$	−10.0202	+	5.78517i	−0.493660	+	0.285015i
$413$	−4.14302	−	2.39197i	−0.203865	−	0.117701i
$414$	−11.1721	−	6.45024i	−0.549081	−	0.317012i
$415$	−23.3110	−	8.85454i	−1.14429	−	0.434652i
$416$	22.1779	+	29.4175i	1.08736	+	1.44231i
$417$		−	11.6737i		−	0.571664i
$418$	31.5162	−	54.5877i	1.54151	−	2.66997i
$419$	−18.2030	+	31.5285i	−0.889274	+	1.54027i	−0.0485386	+	0.998821i	$0.515456\pi$
$419$	−18.2030	+	31.5285i	−0.889274	+	1.54027i	−0.840735	+	0.541446i	$0.817877\pi$
$420$	7.91589	−	1.28224i	0.386256	−	0.0625668i
$421$			18.3140i			0.892569i	0.894891	+	0.446285i	$0.147253\pi$
$421$			18.3140i			0.892569i	−0.894891	+	0.446285i	$0.852747\pi$
$422$	13.0306	+	22.5697i	0.634321	+	1.09868i
$423$	−1.53941	−	2.66634i	−0.0748487	−	0.129642i
$424$		−	15.7519i		−	0.764979i
$425$	−9.84189	−	2.01989i	−0.477402	−	0.0979789i
$426$	−4.96186	+	8.59419i	−0.240403	+	0.416390i
$427$	−1.91737	+	3.32098i	−0.0927880	+	0.160713i
$428$			79.2763i			3.83196i
$429$	11.5777	+	15.3571i	0.558978	+	0.741447i
$430$	6.80514	−	17.9156i	0.328173	−	0.863968i
$431$	12.6403	+	7.29788i	0.608862	+	0.351526i	0.772520	−	0.634991i	$-0.218996\pi$
$431$	12.6403	+	7.29788i	0.608862	+	0.351526i	−0.163658	+	0.986517i	$0.552329\pi$
$432$	−8.26282	−	4.77054i	−0.397545	−	0.229523i
$433$	−14.7643	+	8.52419i	−0.709528	+	0.409646i	−0.810886	−	0.585204i	$-0.801015\pi$
$433$	−14.7643	+	8.52419i	−0.709528	+	0.409646i	0.101358	+	0.994850i	$0.467681\pi$
$434$		−	8.62188i		−	0.413863i
$435$	19.7530	−	3.19964i	0.947083	−	0.153411i
$436$	13.2794	−	7.66685i	0.635967	−	0.367175i
$437$	−22.3745			−1.07032
$438$	36.2769	−	20.9445i	1.73338	−	1.00077i
$439$	2.74229	−	4.74979i	0.130883	−	0.226695i	−0.793134	−	0.609047i	$-0.791552\pi$
$439$	2.74229	−	4.74979i	0.130883	−	0.226695i	0.924017	+	0.382351i	$0.124886\pi$
$440$	55.3583	+	67.8736i	2.63911	+	3.23575i
$441$	6.44487			0.306899
$442$	2.30884	+	18.7697i	0.109820	+	0.892781i
$443$		−	30.2136i		−	1.43549i	−0.696305	−	0.717746i	$-0.745174\pi$
$443$		−	30.2136i		−	1.43549i	0.696305	−	0.717746i	$-0.254826\pi$
$444$	13.3859	+	7.72834i	0.635266	+	0.366771i
$445$	3.76711	+	4.61877i	0.178578	+	0.218950i
$446$	8.84403	+	15.3183i	0.418777	+	0.725343i
$447$	13.3394			0.630933
$448$	−2.82703	−	4.89655i	−0.133564	−	0.231340i
$449$	13.3302	−	7.69620i	0.629092	−	0.363206i	−0.151309	−	0.988487i	$-0.548349\pi$
$449$	13.3302	−	7.69620i	0.629092	−	0.363206i	0.780400	+	0.625280i	$0.215015\pi$
$450$	9.75991	+	8.66464i	0.460087	+	0.408455i
$451$	−16.0952	−	27.8777i	−0.757894	−	1.31271i
$452$	−21.9324	−	12.6627i	−1.03161	−	0.595602i
$453$	−1.22215	+	2.11683i	−0.0574217	+	0.0994574i
$454$	−37.4112			−1.75579
$455$	1.67727	+	5.76804i	0.0786315	+	0.270410i
$456$	−33.2442			−1.55680
$457$	−3.74141	+	6.48031i	−0.175016	+	0.303136i	−0.940167	−	0.340715i	$-0.889331\pi$
$457$	−3.74141	+	6.48031i	−0.175016	+	0.303136i	0.765151	+	0.643851i	$0.222664\pi$
$458$	−52.1584	−	30.1137i	−2.43720	−	1.40712i
$459$	−1.00470	−	1.74020i	−0.0468955	−	0.0812254i
$460$	18.8883	−	49.7264i	0.880671	−	2.31851i
$461$	1.29561	−	0.748018i	0.0603424	−	0.0348387i	−0.469525	−	0.882919i	$-0.655575\pi$
$461$	1.29561	−	0.748018i	0.0603424	−	0.0348387i	0.529868	+	0.848080i	$0.322242\pi$
$462$	−5.18689	−	8.98395i	−0.241316	−	0.417971i
$463$	−2.35856			−0.109611			−0.0548057	−	0.998497i	$-0.517454\pi$
$463$	−2.35856			−0.109611			−0.0548057	+	0.998497i	$0.517454\pi$
$464$	−42.6913	−	73.9435i	−1.98189	−	3.43274i
$465$	7.68202	−	6.26552i	0.356245	−	0.290557i
$466$	−6.11572	−	3.53091i	−0.283305	−	0.163566i
$467$			0.629544i			0.0291318i	0.999894	+	0.0145659i	$0.00463664\pi$
$467$			0.629544i			0.0291318i	−0.999894	+	0.0145659i	$0.995363\pi$
$468$	6.77741	−	15.9764i	0.313286	−	0.738510i
$469$	4.32760			0.199830
$470$	13.9255	−	11.3578i	0.642337	−	0.523896i
$471$	9.86764	−	17.0913i	0.454677	−	0.787524i
$472$	−40.8328	+	23.5748i	−1.87948	+	1.08512i
$473$	−17.5144			−0.805314
$474$	−25.8714	+	14.9368i	−1.18831	+	0.686072i
$475$	22.1736	+	4.55077i	1.01739	+	0.208804i
$476$		−	7.20620i		−	0.330296i
$477$	−1.85769	+	1.07254i	−0.0850576	+	0.0491080i
$478$	−13.4198	−	7.74795i	−0.613809	−	0.354383i
$479$	25.2015	+	14.5501i	1.15148	+	0.664810i	0.949249	−	0.314527i	$-0.101846\pi$
$479$	25.2015	+	14.5501i	1.15148	+	0.664810i	0.202236	+	0.979337i	$0.435179\pi$
$480$	8.11300	−	21.3588i	0.370306	−	0.974890i
$481$	−4.52167	+	10.6589i	−0.206170	+	0.486006i
$482$			5.70561i			0.259884i
$483$	−1.84118	+	3.18901i	−0.0837765	+	0.145105i
$484$	42.0021	−	72.7497i	1.90918	−	3.30680i
$485$	−0.407671	−	2.51675i	−0.0185114	−	0.114280i
$486$			2.61023i			0.118402i
$487$	2.03036	+	3.51669i	0.0920044	+	0.159356i	0.908354	−	0.418201i	$-0.137339\pi$
$487$	2.03036	+	3.51669i	0.0920044	+	0.159356i	−0.816350	+	0.577557i	$0.804006\pi$
$488$	18.8972	+	32.7310i	0.855437	+	1.48166i
$489$		−	7.53213i		−	0.340615i
$490$	6.01481	+	37.1324i	0.271721	+	1.67747i
$491$	17.4621	−	30.2453i	0.788054	−	1.36495i	−0.139104	−	0.990278i	$-0.544422\pi$
$491$	17.4621	−	30.2453i	0.788054	−	1.36495i	0.927158	−	0.374672i	$-0.122245\pi$
$492$	−14.5237	+	25.1558i	−0.654778	+	1.13411i
$493$		−	17.9821i		−	0.809871i
$494$	−5.20178	−	42.2877i	−0.234039	−	1.90261i
$495$	4.23531	−	11.1501i	0.190363	−	0.501160i
$496$	−36.6315	−	21.1492i	−1.64480	−	0.949626i
$497$	2.45315	+	1.41633i	0.110039	+	0.0635310i
$498$	25.2087	−	14.5543i	1.12963	−	0.652192i
$499$		−	27.9581i		−	1.25158i	−0.779993	−	0.625788i	$-0.784778\pi$
$499$		−	27.9581i		−	1.25158i	0.779993	−	0.625788i	$-0.215222\pi$
$500$	−28.8326	+	45.4383i	−1.28943	+	2.03206i
$501$	−9.62710	+	5.55821i	−0.430107	+	0.248323i
$502$	9.61677			0.429218
$503$	15.8300	−	9.13948i	0.705827	−	0.407509i	−0.103687	−	0.994610i	$-0.533064\pi$
$503$	15.8300	−	9.13948i	0.705827	−	0.407509i	0.809514	+	0.587101i	$0.199731\pi$
$504$	−2.73564	+	4.73826i	−0.121855	+	0.211059i
$505$	6.89096	−	5.62033i	0.306644	−	0.250102i
$506$	−68.8124			−3.05908
$507$	12.4980	+	3.57775i	0.555055	+	0.158894i
$508$		−	29.1675i		−	1.29410i
$509$	−5.96939	−	3.44643i	−0.264588	−	0.152760i	0.361837	−	0.932241i	$-0.382150\pi$
$509$	−5.96939	−	3.44643i	−0.264588	−	0.152760i	−0.626426	+	0.779481i	$0.715483\pi$
$510$	9.08856	−	7.41271i	0.402448	−	0.328240i
$511$	−5.97846	−	10.3550i	−0.264472	−	0.458078i
$512$	42.6369			1.88430
$513$	2.26358	+	3.92063i	0.0999394	+	0.173100i
$514$	58.9494	−	34.0344i	2.60015	−	1.50120i
$515$	−1.90866	+	5.02486i	−0.0841057	+	0.221422i
$516$	7.90216	+	13.6869i	0.347873	+	0.602534i
$517$	−14.2225	−	8.21136i	−0.625504	−	0.361135i
$518$	3.12264	−	5.40856i	0.137201	−	0.237639i
$519$	10.6484			0.467413
$520$	57.4979	+	14.1083i	2.52145	+	0.618688i
$521$	2.12968			0.0933030			0.0466515	−	0.998911i	$-0.485145\pi$
$521$	2.12968			0.0933030			0.0466515	+	0.998911i	$0.485145\pi$
$522$	−11.6794	+	20.2293i	−0.511193	+	0.885412i
$523$	9.86249	+	5.69411i	0.431256	+	0.248986i	0.699882	−	0.714259i	$-0.253236\pi$
$523$	9.86249	+	5.69411i	0.431256	+	0.248986i	−0.268625	+	0.963245i	$0.586569\pi$
$524$	46.3381	+	80.2600i	2.02429	+	3.50617i
$525$	2.47326	−	2.78590i	0.107942	−	0.121587i
$526$	−2.20330	+	1.27208i	−0.0960685	+	0.0554652i
$527$	−4.45414	−	7.71479i	−0.194025	−	0.336061i
$528$	−50.8931			−2.21484
$529$	0.713097	+	1.23512i	0.0310042	+	0.0537009i
$530$	−7.91319	−	9.70217i	−0.343727	−	0.421436i
$531$	5.56056	+	3.21039i	0.241308	+	0.139319i
$532$			16.2354i			0.703896i
$533$	−20.0311	−	8.49746i	−0.867642	−	0.368066i
$534$	−6.95752			−0.301081
$535$	23.2774	+	28.5399i	1.00637	+	1.23389i
$536$	21.3260	−	36.9378i	0.921144	−	1.59547i
$537$	−14.7440	+	8.51246i	−0.636251	+	0.367340i
$538$	−3.00623			−0.129608
$539$	29.7718	−	17.1888i	1.28236	−	0.740373i
$540$	−10.6243	+	1.72096i	−0.457199	+	0.0740583i
$541$			38.8425i			1.66997i	0.550272	+	0.834985i	$0.314524\pi$
$541$			38.8425i			1.66997i	−0.550272	+	0.834985i	$0.685476\pi$
$542$	10.1550	−	5.86299i	0.436194	−	0.251837i
$543$	1.95071	+	1.12624i	0.0837129	+	0.0483317i
$544$	−17.7810	−	10.2659i	−0.762353	−	0.440145i
$545$	2.52947	−	6.65924i	0.108351	−	0.285250i
$546$	−6.45527	−	2.73841i	−0.276260	−	0.117193i
$547$			40.1704i			1.71756i	0.512344	+	0.858781i	$0.328777\pi$
$547$			40.1704i			1.71756i	−0.512344	+	0.858781i	$0.671223\pi$
$548$	36.0130	−	62.3763i	1.53840	−	2.66458i
$549$	2.57340	−	4.45726i	0.109830	−	0.190231i
$550$	68.1946	+	13.9958i	2.90783	+	0.596784i
$551$			40.5133i			1.72592i
$552$	18.1463	+	31.4303i	0.772359	+	1.33776i
$553$	4.26362	+	7.38481i	0.181308	+	0.314034i
$554$			17.5127i			0.744043i
$555$	7.08820	−	1.14817i	0.300877	−	0.0487370i
$556$	−28.0944	+	48.6609i	−1.19147	+	2.06368i
$557$	6.40745	−	11.0980i	0.271492	−	0.470239i	−0.697752	−	0.716340i	$-0.745816\pi$
$557$	6.40745	−	11.0980i	0.271492	−	0.470239i	0.969244	+	0.246101i	$0.0791495\pi$
$558$			11.5719i			0.489877i
$559$	−9.45329	+	7.12685i	−0.399832	+	0.301433i
$560$	−14.8598	−	5.64442i	−0.627943	−	0.238520i
$561$	−9.28237	−	5.35918i	−0.391902	−	0.226265i
$562$	−69.0536	−	39.8681i	−2.91285	−	1.68173i
$563$	−7.71441	+	4.45392i	−0.325124	+	0.187710i	−0.653674	−	0.756776i	$-0.726773\pi$
$563$	−7.71441	+	4.45392i	−0.325124	+	0.187710i	0.328550	+	0.944486i	$0.393440\pi$
$564$			14.8192i			0.624001i
$565$	−11.6138	+	1.88124i	−0.488597	+	0.0791444i
$566$	−27.1388	+	15.6686i	−1.14073	+	0.658601i
$567$	0.745071			0.0312901
$568$	24.1778	−	13.9591i	1.01448	−	0.585710i
$569$	−7.58581	+	13.1390i	−0.318014	+	0.550816i	−0.980074	−	0.198635i	$-0.936349\pi$
$569$	−7.58581	+	13.1390i	−0.318014	+	0.550816i	0.662060	+	0.749451i	$0.269683\pi$
$570$	−20.4764	+	16.7007i	−0.857660	+	0.699516i
$571$	−18.3704			−0.768777			−0.384389	−	0.923171i	$-0.625588\pi$
$571$	−18.3704			−0.768777			−0.384389	+	0.923171i	$0.625588\pi$
$572$	−11.3019	−	91.8782i	−0.472555	−	3.84162i
$573$			10.8994i			0.455329i
$574$	10.1642	+	5.86829i	0.424245	+	0.244938i
$575$	−7.80097	−	23.4478i	−0.325323	−	0.977841i
$576$	3.79430	+	6.57193i	0.158096	+	0.273830i
$577$	4.25878			0.177295			0.0886477	−	0.996063i	$-0.471745\pi$
$577$	4.25878			0.177295			0.0886477	+	0.996063i	$0.471745\pi$
$578$	16.9172	+	29.3015i	0.703665	+	1.21878i
$579$	−13.0509	+	7.53493i	−0.542376	+	0.313141i
$580$	−90.0391	−	34.2008i	−3.73867	−	1.42011i
$581$	−4.15441	−	7.19566i	−0.172354	−	0.298526i
$582$	2.57744	+	1.48809i	0.106838	+	0.0616832i
$583$	−5.72101	+	9.90908i	−0.236940	+	0.410392i
$584$	−117.845			−4.87647
$585$	−2.25115	−	7.74160i	−0.0930735	−	0.320076i
$586$	−1.71486			−0.0708401
$587$	2.01772	−	3.49480i	0.0832803	−	0.144246i	−0.821377	−	0.570386i	$-0.806794\pi$
$587$	2.01772	−	3.49480i	0.0832803	−	0.144246i	0.904657	+	0.426140i	$0.140127\pi$
$588$	−26.8649	−	15.5105i	−1.10789	−	0.639641i
$589$	10.0351	+	17.3813i	0.413489	+	0.716183i
$590$	−13.3073	+	35.0336i	−0.547853	+	1.44231i
$591$	17.1863	−	9.92251i	0.706949	−	0.408157i
$592$	−15.3194	−	26.5341i	−0.629625	−	1.09054i
$593$	10.3515			0.425086			0.212543	−	0.977152i	$-0.431825\pi$
$593$	10.3515			0.425086			0.212543	+	0.977152i	$0.431825\pi$
$594$	6.96160	+	12.0578i	0.285638	+	0.494739i
$595$	−2.11591	−	2.59427i	−0.0867438	−	0.106355i
$596$	−55.6043	−	32.1031i	−2.27764	−	1.31500i
$597$		−	19.5402i		−	0.799725i
$598$	−37.1410	+	28.0007i	−1.51881	+	1.14503i
$599$	−19.7440			−0.806716			−0.403358	−	0.915042i	$-0.632157\pi$
$599$	−19.7440			−0.806716			−0.403358	+	0.915042i	$0.632157\pi$
$600$	−11.5907	−	34.8389i	−0.473190	−	1.42229i
$601$	17.6108	−	30.5028i	0.718360	−	1.24424i	−0.243290	−	0.969954i	$-0.578227\pi$
$601$	17.6108	−	30.5028i	0.718360	−	1.24424i	0.961649	−	0.274282i	$-0.0884400\pi$
$602$	5.53021	−	3.19287i	0.225395	−	0.130132i
$603$	−5.80830			−0.236532
$604$	10.1889	−	5.88256i	0.414580	−	0.239358i
$605$	−6.24007	−	38.5230i	−0.253695	−	1.56618i
$606$			10.3803i			0.421669i
$607$	16.3612	−	9.44615i	0.664081	−	0.383407i	−0.129749	−	0.991547i	$-0.541417\pi$
$607$	16.3612	−	9.44615i	0.664081	−	0.383407i	0.793830	+	0.608140i	$0.208084\pi$
$608$	40.0602	+	23.1288i	1.62466	+	0.937997i
$609$	5.77431	+	3.33380i	0.233987	+	0.135092i
$610$	28.0824	+	10.6669i	1.13702	+	0.431892i
$611$	−11.0178	+	1.35529i	−0.445732	+	0.0548292i
$612$			9.67183i			0.390960i
$613$	22.4608	−	38.9032i	0.907182	−	1.57128i	0.0892202	−	0.996012i	$-0.471563\pi$
$613$	22.4608	−	38.9032i	0.907182	−	1.57128i	0.817962	−	0.575273i	$-0.195104\pi$
$614$	−2.56222	+	4.43789i	−0.103403	+	0.179099i
$615$	2.15772	+	13.3207i	0.0870078	+	0.537142i
$616$			29.1843i			1.17587i
$617$	−1.35336	−	2.34409i	−0.0544843	−	0.0943697i	0.837497	−	0.546442i	$-0.184018\pi$
$617$	−1.35336	−	2.34409i	−0.0544843	−	0.0943697i	−0.891981	+	0.452072i	$0.850685\pi$
$618$	−3.13728	−	5.43393i	−0.126200	−	0.218585i
$619$		−	0.161111i		−	0.00647558i	−0.999995	−	0.00323779i	$-0.998969\pi$
$619$		−	0.161111i		−	0.00647558i	0.999995	−	0.00323779i	$-0.00103062\pi$
$620$	−47.1007	+	7.62951i	−1.89161	+	0.306408i
$621$	2.47114	−	4.28015i	0.0991636	−	0.171756i
$622$	22.0556	−	38.2015i	0.884350	−	1.53174i
$623$			1.98598i			0.0795665i
$624$	−27.4692	+	20.7090i	−1.09965	+	0.829025i
$625$	2.96186	+	24.8239i	0.118474	+	0.992957i
$626$	55.2068	+	31.8737i	2.20651	+	1.27393i
$627$	20.9130	+	12.0741i	0.835186	+	0.482195i
$628$	−82.2650	+	47.4957i	−3.28273	+	1.89528i
$629$		−	6.45272i		−	0.257287i
$630$	0.695354	+	4.29276i	0.0277036	+	0.171028i
$631$	−9.61284	+	5.54997i	−0.382681	+	0.220941i	−0.678984	−	0.734153i	$-0.737579\pi$
$631$	−9.61284	+	5.54997i	−0.382681	+	0.220941i	0.296303	+	0.955094i	$0.404246\pi$
$632$	84.0430			3.34305
$633$	−8.64665	+	4.99214i	−0.343673	+	0.198420i
$634$	8.14651	−	14.1102i	0.323539	−	0.560387i
$635$	−8.56426	−	10.5004i	−0.339862	−	0.416697i
$636$	10.3248			0.409406
$637$	9.07480	−	21.3921i	0.359557	−	0.847584i
$638$			124.598i			4.93288i
$639$	−3.29251	−	1.90093i	−0.130250	−	0.0751996i
$640$	1.08757	−	0.887030i	0.0429899	−	0.0350629i
$641$	−0.356239	−	0.617025i	−0.0140706	−	0.0243710i	0.858904	−	0.512136i	$-0.171146\pi$
$641$	−0.356239	−	0.617025i	−0.0140706	−	0.0243710i	−0.872975	+	0.487765i	$0.837812\pi$
$642$	−42.9913			−1.69673
$643$	−8.51460	−	14.7477i	−0.335783	−	0.581593i	0.647852	−	0.761766i	$-0.275668\pi$
$643$	−8.51460	−	14.7477i	−0.335783	−	0.581593i	−0.983635	+	0.180173i	$0.942334\pi$
$644$	15.3496	−	8.86210i	0.604859	−	0.349216i
$645$	6.86363	+	2.60711i	0.270255	+	0.102655i
$646$	11.8725	+	20.5637i	0.467116	+	0.809069i
$647$	−27.6148	−	15.9434i	−1.08565	−	0.626800i	−0.153235	−	0.988190i	$-0.548969\pi$
$647$	−27.6148	−	15.9434i	−1.08565	−	0.626800i	−0.932415	+	0.361390i	$0.882302\pi$
$648$	3.67164	−	6.35947i	0.144236	−	0.249824i
$649$	34.2491			1.34439
$650$	42.5026	−	20.1951i	1.66709	−	0.792117i
$651$	3.30312			0.129459
$652$	−18.1271	+	31.3971i	−0.709913	+	1.22961i
$653$	33.7363	+	19.4777i	1.32020	+	0.762220i	0.983761	−	0.179484i	$-0.0574430\pi$
$653$	33.7363	+	19.4777i	1.32020	+	0.762220i	0.336442	+	0.941704i	$0.390776\pi$
$654$	4.15771	+	7.20136i	0.162579	+	0.281596i
$655$	40.2482	+	15.2880i	1.57263	+	0.597353i
$656$	49.8648	−	28.7895i	1.94689	−	1.12404i
$657$	8.02401	+	13.8980i	0.313047	+	0.542213i
$658$	5.98770			0.233425
$659$	16.7491	+	29.0103i	0.652453	+	1.13008i	0.982526	+	0.186126i	$0.0595932\pi$
$659$	16.7491	+	29.0103i	0.652453	+	1.13008i	−0.330073	+	0.943955i	$0.607073\pi$
$660$	−44.4888	+	36.2855i	−1.73173	+	1.41241i
$661$	0.216191	+	0.124818i	0.00840886	+	0.00485486i	0.504199	−	0.863588i	$-0.331788\pi$
$661$	0.216191	+	0.124818i	0.00840886	+	0.00485486i	−0.495790	+	0.868443i	$0.665121\pi$
$662$		−	33.4903i		−	1.30164i
$663$	−7.19082	+	0.884537i	−0.279268	+	0.0343526i
$664$	−81.8903			−3.17796
$665$	4.76711	+	5.84484i	0.184861	+	0.226653i
$666$	−4.19105	+	7.25912i	−0.162400	+	0.281285i
$667$	38.3028	−	22.1141i	1.48309	−	0.856262i
$668$	53.5064			2.07023
$669$	−5.86857	+	3.38822i	−0.226892	+	0.130996i
$670$	−5.42072	−	33.4648i	−0.209421	−	1.29286i
$671$		−	27.4535i		−	1.05983i
$672$	6.59305	−	3.80650i	0.254332	−	0.146839i
$673$	11.3249	+	6.53842i	0.436542	+	0.252038i	0.702130	−	0.712049i	$-0.252233\pi$
$673$	11.3249	+	6.53842i	0.436542	+	0.252038i	−0.265588	+	0.964087i	$0.585566\pi$
$674$	−14.4661	−	8.35202i	−0.557214	−	0.321708i
$675$	−3.31950	+	3.73911i	−0.127768	+	0.143918i
$676$	−43.4865	−	44.9917i	−1.67256	−	1.73045i
$677$		−	5.68622i		−	0.218539i	−0.994012	−	0.109270i	$-0.965149\pi$
$677$		−	5.68622i		−	0.218539i	0.994012	−	0.109270i	$-0.0348512\pi$
$678$	6.86693	−	11.8939i	0.263723	−	0.456781i
$679$	0.424764	−	0.735713i	0.0163010	−	0.0282341i
$680$	−32.5701	+	5.27580i	−1.24901	+	0.202318i
$681$		−	14.3325i		−	0.549224i
$682$	30.8628	+	53.4559i	1.18180	+	2.04693i
$683$	−7.00400	−	12.1313i	−0.268001	−	0.464191i	0.700345	−	0.713805i	$-0.253030\pi$
$683$	−7.00400	−	12.1313i	−0.268001	−	0.464191i	−0.968345	+	0.249614i	$0.919696\pi$
$684$		−	21.7905i		−	0.833179i
$685$	−5.35030	−	33.0300i	−0.204424	−	1.26201i
$686$	−13.0738	+	22.6445i	−0.499161	+	0.864572i
$687$	11.5368	−	19.9823i	0.440157	−	0.762374i
$688$		−	31.3280i		−	1.19437i
$689$	0.944257	+	7.67631i	0.0359733	+	0.292444i
$690$	26.9665	+	10.2431i	1.02660	+	0.389947i
$691$	14.7089	+	8.49220i	0.559554	+	0.323059i	0.752966	−	0.658059i	$-0.228622\pi$
$691$	14.7089	+	8.49220i	0.559554	+	0.323059i	−0.193412	+	0.981118i	$0.561956\pi$
$692$	−44.3870	−	25.6269i	−1.68734	−	0.974187i
$693$	3.44183	−	1.98714i	0.130744	−	0.0754853i
$694$		−	45.2994i		−	1.71954i
$695$	4.17387	+	25.7674i	0.158324	+	0.977412i
$696$	56.9106	−	32.8573i	2.15719	−	1.24545i
$697$	12.1264			0.459322
$698$	48.4516	−	27.9736i	1.83392	−	1.05882i
$699$	1.35272	−	2.34298i	0.0511647	−	0.0886198i
$700$	−17.0143	+	5.66056i	−0.643079	+	0.213949i
$701$	22.6599			0.855853			0.427926	−	0.903814i	$-0.359244\pi$
$701$	22.6599			0.855853			0.427926	+	0.903814i	$0.359244\pi$
$702$	8.66396	+	3.67537i	0.327000	+	0.138718i
$703$			14.5379i			0.548306i
$704$	35.0553	+	20.2392i	1.32120	+	0.762793i
$705$	4.35127	+	5.33499i	0.163878	+	0.200927i
$706$	17.8044	+	30.8382i	0.670079	+	1.16061i
$707$	2.96298			0.111434
$708$	−15.4525	−	26.7645i	−0.580741	−	1.00587i
$709$	−14.7593	+	8.52129i	−0.554298	+	0.320024i	−0.750854	−	0.660469i	$-0.770358\pi$
$709$	−14.7593	+	8.52129i	−0.554298	+	0.320024i	0.196556	+	0.980493i	$0.437024\pi$
$710$	7.87949	−	20.7440i	0.295712	−	0.778509i
$711$	−5.72243	−	9.91155i	−0.214608	−	0.371712i
$712$	16.9511	+	9.78672i	0.635269	+	0.366773i
$713$	10.9553	−	18.9751i	0.410279	−	0.710624i
$714$	3.90790			0.146250
$715$	−31.0463	−	29.7581i	−1.16107	−	1.11289i
$716$	81.9457			3.06245
$717$	2.96831	−	5.14126i	0.110853	−	0.192004i
$718$	−31.4130	−	18.1363i	−1.17232	−	0.676841i
$719$	−25.1819	−	43.6164i	−0.939127	−	1.62662i	−0.767103	−	0.641524i	$-0.778303\pi$
$719$	−25.1819	−	43.6164i	−0.939127	−	1.62662i	−0.172024	−	0.985093i	$-0.555031\pi$
$720$	19.9442	+	7.57568i	0.743276	+	0.282329i
$721$	−1.55108	+	0.895516i	−0.0577652	+	0.0333507i
$722$	−1.95132	−	3.37979i	−0.0726207	−	0.125783i
$723$	−2.18587			−0.0812934
$724$	−5.42092	−	9.38930i	−0.201467	−	0.348951i
$725$	−42.4567	+	14.1251i	−1.57680	+	0.524594i
$726$	39.4519	+	22.7776i	1.46420	+	0.845356i
$727$			36.6222i			1.35824i	0.734026	+	0.679122i	$0.237639\pi$
$727$			36.6222i			1.35824i	−0.734026	+	0.679122i	$0.762361\pi$
$728$	11.8755	+	15.7520i	0.440134	+	0.583809i
$729$	−1.00000			−0.0370370
$730$	−72.5854	+	59.2013i	−2.68650	+	2.19114i
$731$	3.29893	−	5.71391i	0.122015	−	0.211337i
$732$	−21.4540	+	12.3865i	−0.792964	+	0.457818i
$733$	−47.6527			−1.76009			−0.880046	−	0.474888i	$-0.842489\pi$
$733$	−47.6527			−1.76009			−0.880046	+	0.474888i	$0.842489\pi$
$734$	38.8159	−	22.4104i	1.43272	−	0.827182i
$735$	−14.2257	+	2.30433i	−0.524724	+	0.0849963i
$736$		−	50.4993i		−	1.86143i
$737$	−26.8312	+	15.4910i	−0.988341	+	0.570619i
$738$	−13.6419	−	7.87615i	−0.502165	−	0.289925i
$739$	−12.5068	−	7.22081i	−0.460070	−	0.265622i	0.252004	−	0.967726i	$-0.418911\pi$
$739$	−12.5068	−	7.22081i	−0.460070	−	0.265622i	−0.712074	+	0.702105i	$0.752244\pi$
$740$	−32.3098	−	12.2727i	−1.18773	−	0.451153i
$741$	16.2008	−	1.99285i	0.595151	−	0.0732090i
$742$		−	4.17174i		−	0.153150i
$743$	3.79209	−	6.56809i	0.139118	−	0.240960i	−0.788045	−	0.615618i	$-0.788907\pi$
$743$	3.79209	−	6.56809i	0.139118	−	0.240960i	0.927163	+	0.374658i	$0.122240\pi$
$744$	16.2775	−	28.1934i	0.596760	−	1.03362i
$745$	−29.4441	+	4.76943i	−1.07875	+	0.174738i
$746$			32.3597i			1.18477i
$747$	5.57586	+	9.65767i	0.204010	+	0.353356i
$748$	25.7952	+	44.6786i	0.943167	+	1.63361i
$749$			12.2716i			0.448394i
$750$	−24.6410	−	15.6358i	−0.899763	−	0.570940i
$751$	7.21396	−	12.4949i	0.263241	−	0.455947i	−0.703860	−	0.710338i	$-0.748542\pi$
$751$	7.21396	−	12.4949i	0.263241	−	0.455947i	0.967101	+	0.254392i	$0.0818752\pi$
$752$	14.6876	−	25.4397i	0.535603	−	0.927692i
$753$			3.68427i			0.134262i
$754$	50.7005	+	67.2508i	1.84640	+	2.44913i
$755$	1.94079	−	5.10945i	0.0706327	−	0.185952i
$756$	−3.10577	−	1.79312i	−0.112956	−	0.0652151i
$757$	−30.7052	−	17.7277i	−1.11600	−	0.644323i	−0.175623	−	0.984457i	$-0.556194\pi$
$757$	−30.7052	−	17.7277i	−1.11600	−	0.644323i	−0.940377	+	0.340134i	$0.889527\pi$
$758$	−76.8667	+	44.3790i	−2.79193	+	1.61192i
$759$		−	26.3626i		−	0.956903i
$760$	73.3799	−	11.8863i	2.66177	−	0.431161i
$761$	36.6928	−	21.1846i	1.33011	−	0.767941i	0.344797	−	0.938677i	$-0.387948\pi$
$761$	36.6928	−	21.1846i	1.33011	−	0.767941i	0.985317	+	0.170736i	$0.0546146\pi$
$762$	15.8174			0.573005
$763$	2.05558	−	1.18679i	0.0744170	−	0.0429647i
$764$	26.2309	−	45.4333i	0.949002	−	1.64372i
$765$	2.83987	+	3.48190i	0.102676	+	0.125889i
$766$	−42.8589			−1.54856
$767$	18.4857	−	13.9364i	0.667480	−	0.503214i
$768$			16.8155i			0.606776i
$769$	12.5717	+	7.25829i	0.453348	+	0.261741i	0.709243	−	0.704964i	$-0.249037\pi$
$769$	12.5717	+	7.25829i	0.453348	+	0.261741i	−0.255895	+	0.966705i	$0.582370\pi$
$770$	14.6612	+	17.9757i	0.528352	+	0.647800i
$771$	13.0389	+	22.5840i	0.469584	+	0.813344i
$772$	72.5354			2.61061
$773$	−19.2871	−	33.4063i	−0.693710	−	1.20154i	−0.970614	−	0.240644i	$-0.922641\pi$
$773$	−19.2871	−	33.4063i	−0.693710	−	1.20154i	0.276903	−	0.960898i	$-0.410692\pi$
$774$	−7.42239	+	4.28532i	−0.266792	+	0.154033i
$775$	−14.7163	+	16.5765i	−0.528625	+	0.595447i
$776$	−4.18640	−	7.25106i	−0.150283	−	0.260298i
$777$	2.07207	+	1.19631i	0.0743350	+	0.0429173i
$778$	25.1180	−	43.5057i	0.900525	−	1.55975i
$779$	−27.3207			−0.978864
$780$	−9.24749	+	37.6879i	−0.331113	+	1.34944i
$781$	−20.2795			−0.725657
$782$	12.9611	−	22.4494i	0.463490	−	0.802788i
$783$	−7.75001	−	4.47447i	−0.276963	−	0.159905i
$784$	30.7455	+	53.2528i	1.09805	+	1.90189i
$785$	−15.6699	+	41.2536i	−0.559284	+	1.47240i
$786$	−43.5247	+	25.1290i	−1.55248	+	0.896322i
$787$	−6.97122	−	12.0745i	−0.248497	−	0.430410i	0.714612	−	0.699521i	$-0.246603\pi$
$787$	−6.97122	−	12.0745i	−0.248497	−	0.430410i	−0.963109	+	0.269111i	$0.913270\pi$
$788$	−95.5196			−3.40274
$789$	−0.487343	−	0.844103i	−0.0173499	−	0.0300509i
$790$	51.7652	−	42.2202i	1.84172	−	1.50213i
$791$	−3.39503	−	1.96012i	−0.120713	−	0.0696938i
$792$		−	39.1698i		−	1.39184i
$793$	−11.1712	−	14.8179i	−0.396701	−	0.526198i
$794$	23.7776			0.843835
$795$	3.71699	−	3.03161i	0.131828	−	0.107520i
$796$	−47.0261	+	81.4516i	−1.66680	+	2.88697i
$797$	−15.9352	+	9.20020i	−0.564455	+	0.325888i	−0.754931	−	0.655804i	$-0.772330\pi$
$797$	−15.9352	+	9.20020i	−0.564455	+	0.325888i	0.190477	+	0.981692i	$0.438997\pi$
$798$	−8.80443			−0.311674
$799$	5.35775	−	3.09330i	0.189544	−	0.109433i
$800$	−10.2711	+	50.0459i	−0.363138	+	1.76939i
$801$		−	2.66549i		−	0.0941804i
$802$	−48.1170	+	27.7804i	−1.69907	+	0.980958i
$803$	74.1333	+	42.8009i	2.61611	+	1.51041i
$804$	24.2115	+	13.9785i	0.853872	+	0.492983i
$805$	2.92381	−	7.69741i	0.103051	−	0.271298i
$806$	38.4098	+	16.2940i	1.35293	+	0.573931i
$807$		−	1.15171i		−	0.0405421i
$808$	14.6013	−	25.2902i	0.513671	−	0.889705i
$809$	−25.4168	+	44.0232i	−0.893607	+	1.54777i	−0.0580875	+	0.998311i	$0.518500\pi$
$809$	−25.4168	+	44.0232i	−0.893607	+	1.54777i	−0.835519	+	0.549461i	$0.814833\pi$
$810$	−0.933271	−	5.76154i	−0.0327918	−	0.202440i
$811$		−	18.7352i		−	0.657881i	−0.944351	−	0.328940i	$-0.893309\pi$
$811$		−	18.7352i		−	0.657881i	0.944351	−	0.328940i	$-0.106691\pi$
$812$	−16.0465	−	27.7934i	−0.563122	−	0.975356i
$813$	2.24616	+	3.89046i	0.0787763	+	0.136445i
$814$			44.7110i			1.56712i
$815$	2.69307	+	16.6257i	0.0943342	+	0.582371i
$816$	9.58595	−	16.6034i	0.335575	−	0.581234i
$817$	−7.43242	+	12.8733i	−0.260028	+	0.450381i
$818$			37.7733i			1.32071i
$819$	1.04911	−	2.47307i	0.0366589	−	0.0864161i
$820$	23.0638	−	60.7191i	0.805422	−	2.12040i
$821$	−9.21876	−	5.32246i	−0.321737	−	0.185755i	0.330430	−	0.943831i	$-0.392806\pi$
$821$	−9.21876	−	5.32246i	−0.321737	−	0.185755i	−0.652167	+	0.758076i	$0.726140\pi$
$822$	33.8265	+	19.5297i	1.17983	+	0.681177i
$823$	33.5434	−	19.3663i	1.16925	−	0.675066i	0.215745	−	0.976450i	$-0.430782\pi$
$823$	33.5434	−	19.3663i	1.16925	−	0.675066i	0.953503	+	0.301384i	$0.0974486\pi$
$824$			17.6521i			0.614939i
$825$	−5.36192	+	26.1259i	−0.186678	+	0.909588i
$826$	−10.8142	+	6.24359i	−0.376275	+	0.217242i
$827$	−18.1501			−0.631142			−0.315571	−	0.948902i	$-0.602196\pi$
$827$	−18.1501			−0.631142			−0.315571	+	0.948902i	$0.602196\pi$
$828$	−20.6015	+	11.8943i	−0.715953	+	0.413355i
$829$	−18.8859	+	32.7114i	−0.655936	+	1.13611i	0.325723	+	0.945465i	$0.394392\pi$
$829$	−18.8859	+	32.7114i	−0.655936	+	1.13611i	−0.981658	+	0.190648i	$0.938941\pi$
$830$	−50.4393	+	41.1388i	−1.75077	+	1.42795i
$831$	−6.70927			−0.232742
$832$	27.1564	−	3.34049i	0.941480	−	0.115811i
$833$			12.9504i			0.448703i
$834$	−26.3887	−	15.2355i	−0.913765	−	0.527563i
$835$	19.2626	−	15.7107i	0.666609	−	0.543692i
$836$	−58.1162	−	100.660i	−2.00999	−	3.48141i
$837$	−4.43329			−0.153237
$838$	47.5139	+	82.2965i	1.64134	+	2.84288i
$839$	−6.06895	+	3.50391i	−0.209523	+	0.120968i	−0.601090	−	0.799181i	$-0.705267\pi$
$839$	−6.06895	+	3.50391i	−0.209523	+	0.120968i	0.391566	+	0.920150i	$0.371933\pi$
$840$	4.34423	−	11.4369i	0.149890	−	0.394609i
$841$	−25.5418	−	44.2397i	−0.880751	−	1.52551i
$842$	41.3992	+	23.9018i	1.42671	+	0.823711i
$843$	15.2738	−	26.4550i	0.526058	−	0.911160i
$844$	48.0572			1.65420
$845$	−28.8660	−	3.42858i	−0.993020	−	0.117947i
$846$	−8.03641			−0.276298
$847$	6.50171	−	11.2613i	0.223401	−	0.386943i
$848$	−17.7243	−	10.2332i	−0.608656	−	0.351408i
$849$	−6.00278	−	10.3971i	−0.206015	−	0.356828i
$850$	−17.4108	+	19.6116i	−0.597185	+	0.672673i
$851$	13.7447	−	7.93548i	0.471161	−	0.272025i
$852$	9.14970	+	15.8478i	0.313464	+	0.542935i
$853$	−1.17550			−0.0402483			−0.0201242	−	0.999797i	$-0.506406\pi$
$853$	−1.17550			−0.0402483			−0.0201242	+	0.999797i	$0.506406\pi$
$854$	5.00476	+	8.66850i	0.171259	+	0.296630i
$855$	−6.39819	−	7.84467i	−0.218813	−	0.268282i
$856$	104.743	+	60.4732i	3.58003	+	2.06693i
$857$		−	12.8574i		−	0.439200i	−0.975590	−	0.219600i	$-0.929525\pi$
$857$		−	12.8574i		−	0.439200i	0.975590	−	0.219600i	$-0.0704752\pi$
$858$	49.8252	−	6.12897i	1.70101	−	0.209239i
$859$	−0.0582206			−0.00198646			−0.000993230	−	1.00000i	$-0.500316\pi$
$859$	−0.0582206			−0.00198646			−0.000993230		1.00000i	$0.500316\pi$
$860$	−22.3361	−	27.3858i	−0.761655	−	0.933848i
$861$	−2.24819	+	3.89399i	−0.0766182	+	0.132707i
$862$	32.9940	−	19.0491i	1.12378	−	0.648815i
$863$	27.6526			0.941305			0.470652	−	0.882319i	$-0.344019\pi$
$863$	27.6526			0.941305			0.470652	+	0.882319i	$0.344019\pi$
$864$	−8.84888	+	5.10890i	−0.301045	+	0.173808i
$865$	−23.5042	+	3.80728i	−0.799167	+	0.129451i
$866$			44.5001i			1.51217i
$867$	−11.2257	+	6.48114i	−0.381244	+	0.220111i
$868$	−13.7688	−	7.94941i	−0.467343	−	0.269820i
$869$	−52.8691	−	30.5240i	−1.79346	−	1.03546i
$870$	18.5470	−	48.8279i	0.628802	−	1.65542i
$871$	−8.17848	+	19.2791i	−0.277117	+	0.653249i
$872$		−	23.3936i		−	0.792206i
$873$	−0.570099	+	0.987440i	−0.0192949	+	0.0334198i
$874$	−29.2012	+	50.5780i	−0.987747	+	1.71083i
$875$	−4.46315	+	7.03362i	−0.150882	+	0.237780i
$876$		−	77.2436i		−	2.60982i
$877$	28.1798	+	48.8088i	0.951564	+	1.64816i	0.742043	+	0.670353i	$0.233857\pi$
$877$	28.1798	+	48.8088i	0.951564	+	1.64816i	0.209521	+	0.977804i	$0.432810\pi$
$878$	−7.15801	−	12.3980i	−0.241571	−	0.418413i
$879$		−	0.656977i		−	0.0221593i
$880$	112.336	−	18.1965i	3.78685	−	0.613405i
$881$	−24.0337	+	41.6277i	−0.809717	+	1.40247i	0.103342	+	0.994646i	$0.467046\pi$
$881$	−24.0337	+	41.6277i	−0.809717	+	1.40247i	−0.913060	+	0.407826i	$0.866287\pi$
$882$	8.41128	−	14.5688i	0.283223	−	0.490556i
$883$			12.7367i			0.428624i	0.976765	+	0.214312i	$0.0687510\pi$
$883$			12.7367i			0.428624i	−0.976765	+	0.214312i	$0.931249\pi$
$884$	32.1031	+	13.6186i	1.07974	+	0.458042i
$885$	−13.4217	−	5.09815i	−0.451165	−	0.171372i
$886$	−68.2985	−	39.4322i	−2.29453	−	1.32475i
$887$	39.4122	+	22.7546i	1.32333	+	0.764026i	0.984259	−	0.176734i	$-0.0565531\pi$
$887$	39.4122	+	22.7546i	1.32333	+	0.764026i	0.339074	+	0.940760i	$0.389886\pi$
$888$	20.4219	−	11.7906i	0.685315	−	0.395667i
$889$		−	4.51498i		−	0.151428i
$890$	15.3573	−	2.48762i	0.514779	−	0.0833853i
$891$	−4.61946	+	2.66705i	−0.154758	+	0.0893495i
$892$	32.6169			1.09210
$893$	−12.0709	+	6.96915i	−0.403938	+	0.233214i
$894$	17.4094	−	30.1540i	0.582259	−	1.00850i
$895$	29.5008	−	24.0612i	0.986105	−	0.804276i
$896$	0.467633			0.0156225
$897$	−10.7273	−	14.2290i	−0.358174	−	0.475094i
$898$		−	40.1777i		−	1.34075i
$899$	−34.3580	−	19.8366i	−1.14590	−	0.661588i
$900$	22.8357	−	7.59734i	0.761192	−	0.253245i
$901$	−2.15516	−	3.73284i	−0.0717988	−	0.124359i
$902$	−84.0243			−2.79770
$903$	1.22322	+	2.11867i	0.0407061	+	0.0705050i
$904$	−33.4608	+	19.3186i	−1.11289	+	0.642526i
$905$	−4.70848	−	1.78849i	−0.156515	−	0.0594513i
$906$	3.19009	+	5.52541i	0.105984	+	0.183569i
$907$	−50.4853	−	29.1477i	−1.67634	−	0.967833i	−0.963965	−	0.266031i	$-0.914288\pi$
$907$	−50.4853	−	29.1477i	−1.67634	−	0.967833i	−0.712372	−	0.701802i	$-0.752379\pi$
$908$	−34.4933	+	59.7441i	−1.14470	+	1.98268i
$909$	−3.97677			−0.131901
$910$	15.2278	+	3.73645i	0.504797	+	0.123862i
$911$	−18.3550			−0.608129			−0.304065	−	0.952651i	$-0.598344\pi$
$911$	−18.3550			−0.608129			−0.304065	+	0.952651i	$0.598344\pi$
$912$	−21.5970	+	37.4071i	−0.715148	+	1.23867i
$913$	51.5150	+	29.7422i	1.70490	+	0.984322i
$914$	9.76593	+	16.9151i	0.323028	+	0.559501i
$915$	−4.08659	+	10.7586i	−0.135099	+	0.355669i
$916$	−96.1806	+	55.5299i	−3.17790	+	1.83476i
$917$	7.17291	+	12.4238i	0.236870	+	0.410271i
$918$	−5.24500			−0.173111
$919$	18.3478	+	31.7793i	0.605237	+	1.04830i	0.992014	+	0.126128i	$0.0402551\pi$
$919$	18.3478	+	31.7793i	0.605237	+	1.04830i	−0.386777	+	0.922173i	$0.626412\pi$
$920$	−51.2921	−	62.8880i	−1.69105	−	2.07336i
$921$	−1.70020	−	0.981608i	−0.0560233	−	0.0323451i
$922$		−	3.90499i		−	0.128604i
$923$	−10.9457	+	8.25198i	−0.360282	+	0.271617i
$924$	−19.1293			−0.629309
$925$	−15.2353	+	5.06869i	−0.500932	+	0.166658i
$926$	−3.07818	+	5.33157i	−0.101155	+	0.175206i
$927$	2.08179	−	1.20192i	0.0683748	−	0.0394762i
$928$	−91.4386			−3.00162
$929$	47.1734	−	27.2356i	1.54771	−	0.893571i	0.549394	−	0.835564i	$-0.314859\pi$
$929$	47.1734	−	27.2356i	1.54771	−	0.893571i	0.998316	−	0.0580072i	$-0.0184746\pi$
$930$	−4.13746	−	25.5426i	−0.135673	−	0.837574i
$931$		−	29.1769i		−	0.956235i
$932$	−11.2774	+	6.51103i	−0.369405	+	0.213276i
$933$	14.6353	+	8.44970i	0.479139	+	0.276631i
$934$	1.42310	+	0.821626i	0.0465652	+	0.0268844i
$935$	22.4051	+	8.51045i	0.732725	+	0.278321i
$936$	−15.9387	−	21.1416i	−0.520973	−	0.691036i
$937$		−	15.4559i		−	0.504923i	−0.967607	−	0.252461i	$-0.918760\pi$
$937$		−	15.4559i		−	0.504923i	0.967607	−	0.252461i	$-0.0812401\pi$
$938$	5.64801	−	9.78264i	0.184414	−	0.319414i
$939$	−12.2111	+	21.1502i	−0.398494	+	0.690211i
$940$	−5.29852	−	32.7104i	−0.172819	−	1.06690i
$941$		−	27.3267i		−	0.890824i	−0.895326	−	0.445412i	$-0.853057\pi$
$941$		−	27.3267i		−	0.890824i	0.895326	−	0.445412i	$-0.146943\pi$
$942$	−25.7568	−	44.6120i	−0.839201	−	1.45354i
$943$	14.9130	+	25.8300i	0.485633	+	0.841140i
$944$			61.2613i			1.99388i
$945$	−1.64459	+	0.266396i	−0.0534987	+	0.00866586i
$946$	−22.8583	+	39.5917i	−0.743188	+	1.28724i
$947$	10.4804	−	18.1525i	0.340566	−	0.589877i	−0.643972	−	0.765049i	$-0.722715\pi$
$947$	10.4804	−	18.1525i	0.340566	−	0.589877i	0.984538	+	0.175172i	$0.0560481\pi$
$948$			55.0873i			1.78915i
$949$	57.4291	−	7.06431i	1.86423	−	0.229317i
$950$	39.2262	−	44.1847i	1.27267	−	1.43354i
$951$	5.40573	+	3.12100i	0.175293	+	0.101205i
$952$	−9.52109	−	5.49700i	−0.308580	−	0.178159i
$953$	50.3289	−	29.0574i	1.63031	−	0.941261i	0.646316	−	0.763070i	$-0.276309\pi$
$953$	50.3289	−	29.0574i	1.63031	−	0.941261i	0.983996	−	0.178191i	$-0.0570245\pi$
$954$			5.59912i			0.181278i
$955$	−3.89702	−	24.0582i	−0.126105	−	0.778506i
$956$	−24.7463	+	14.2873i	−0.800352	+	0.462084i
$957$	−47.7345			−1.54304
$958$	65.7815	−	37.9790i	2.12530	−	1.22704i
$959$	5.57463	−	9.65554i	0.180014	−	0.311794i
$960$	−10.7249	−	13.1496i	−0.346145	−	0.424400i
$961$	11.3460			0.365999
$962$	18.1935	+	24.1324i	0.586581	+	0.778061i
$963$		−	16.4703i		−	0.530749i
$964$	9.11162	+	5.26060i	0.293466	+	0.169432i
$965$	26.1131	−	21.2981i	0.840610	−	0.685610i
$966$	4.80589	+	8.32405i	0.154627	+	0.267822i
$967$	−14.7540			−0.474458			−0.237229	−	0.971454i	$-0.576239\pi$
$967$	−14.7540			−0.474458			−0.237229	+	0.971454i	$0.576239\pi$
$968$	−64.0797	−	110.989i	−2.05960	−	3.56733i
$969$	−7.87814	+	4.54845i	−0.253082	+	0.146117i
$970$	−6.22123	−	2.36310i	−0.199752	−	0.0758746i
$971$	7.83816	+	13.5761i	0.251538	+	0.435677i	0.963950	−	0.266085i	$-0.0857302\pi$
$971$	7.83816	+	13.5761i	0.251538	+	0.435677i	−0.712411	+	0.701762i	$0.752397\pi$
$972$	4.16842	+	2.40664i	0.133702	+	0.0771930i
$973$	−4.34887	+	7.53247i	−0.139419	+	0.241480i
$974$	10.5994			0.339627
$975$	7.73692	+	16.2831i	0.247780	+	0.521477i
$976$	49.1061			1.57185
$977$	−20.7767	+	35.9863i	−0.664706	+	1.15130i	0.314660	+	0.949205i	$0.398110\pi$
$977$	−20.7767	+	35.9863i	−0.664706	+	1.15130i	−0.979365	+	0.202099i	$0.935224\pi$
$978$	−17.0266	−	9.83028i	−0.544449	−	0.314338i
$979$	−7.10898	−	12.3131i	−0.227204	−	0.393529i
$980$	64.8446	+	24.6308i	2.07138	+	0.786803i
$981$	−2.75890	+	1.59285i	−0.0880850	+	0.0508559i
$982$	−45.5800	−	78.9470i	−1.45452	−	2.51930i
$983$	−12.4586			−0.397368			−0.198684	−	0.980064i	$-0.563667\pi$
$983$	−12.4586			−0.397368			−0.198684	+	0.980064i	$0.563667\pi$
$984$	22.1578	+	38.3784i	0.706365	+	1.22346i
$985$	−34.3875	+	28.0468i	−1.09568	+	0.893645i
$986$	−40.6488	−	23.4686i	−1.29452	−	0.747393i
$987$			2.29394i			0.0730169i
$988$	−72.3277	−	30.6824i	−2.30105	−	0.976137i
$989$	16.2279			0.516018
$990$	−19.6775	−	24.1262i	−0.625393	−	0.766780i
$991$	3.53197	−	6.11755i	0.112197	−	0.194330i	−0.804459	−	0.594008i	$-0.797545\pi$
$991$	3.53197	−	6.11755i	0.112197	−	0.194330i	0.916656	+	0.399678i	$0.130878\pi$
$992$	−39.2296	+	22.6492i	−1.24554	+	0.719114i
$993$	12.8304			0.407162
$994$	6.40328	−	3.69694i	0.203100	−	0.117260i
$995$	6.98647	+	43.1309i	0.221486	+	1.36734i
$996$		−	53.6763i		−	1.70080i
$997$	14.7515	−	8.51678i	0.467185	−	0.269729i	−0.247876	−	0.968792i	$-0.579733\pi$
$997$	14.7515	−	8.51678i	0.467185	−	0.269729i	0.715060	+	0.699063i	$0.246399\pi$
$998$	−63.1998	−	36.4884i	−2.00056	−	1.15502i
$999$	−2.78103	−	1.60563i	−0.0879879	−	0.0507999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.v.a.4.15	yes	32
3.2	odd	2		585.2.bf.c.199.2		32
5.2	odd	4		975.2.bc.n.901.8		16
5.3	odd	4		975.2.bc.m.901.1		16
5.4	even	2	inner	195.2.v.a.4.2	✓	32
13.10	even	6	inner	195.2.v.a.49.2	yes	32
15.14	odd	2		585.2.bf.c.199.15		32
39.23	odd	6		585.2.bf.c.244.15		32
65.23	odd	12		975.2.bc.m.751.1		16
65.49	even	6	inner	195.2.v.a.49.15	yes	32
65.62	odd	12		975.2.bc.n.751.8		16
195.179	odd	6		585.2.bf.c.244.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.v.a.4.2	✓	32	5.4	even	2	inner
195.2.v.a.4.15	yes	32	1.1	even	1	trivial
195.2.v.a.49.2	yes	32	13.10	even	6	inner
195.2.v.a.49.15	yes	32	65.49	even	6	inner
585.2.bf.c.199.2		32	3.2	odd	2
585.2.bf.c.199.15		32	15.14	odd	2
585.2.bf.c.244.2		32	195.179	odd	6
585.2.bf.c.244.15		32	39.23	odd	6
975.2.bc.m.751.1		16	65.23	odd	12
975.2.bc.m.901.1		16	5.3	odd	4
975.2.bc.n.751.8		16	65.62	odd	12
975.2.bc.n.901.8		16	5.2	odd	4

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30511 - 2.26052i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-2.40664 - 4.16842i) q^{4} +(-2.09035 - 0.794006i) q^{5} +(2.26052 - 1.30511i) q^{6} +(-0.372536 - 0.645251i) q^{7} -7.34329 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.30511 - 2.26052i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-2.40664 - 4.16842i) q^{4} +(-2.09035 - 0.794006i) q^{5} +(2.26052 - 1.30511i) q^{6} +(-0.372536 - 0.645251i) q^{7} -7.34329 q^{8} +(0.500000 + 0.866025i) q^{9} +(-4.52301 + 3.68901i) q^{10} +(4.61946 + 2.66705i) q^{11} -4.81328i q^{12} +(3.57858 - 0.440198i) q^{13} -1.94480 q^{14} +(-1.41329 - 1.73280i) q^{15} +(-4.77054 + 8.26282i) q^{16} +(-1.74020 + 1.00470i) q^{17} +2.61023 q^{18} +(3.92063 - 2.26358i) q^{19} +(1.72096 + 10.6243i) q^{20} -0.745071i q^{21} +(12.0578 - 6.96160i) q^{22} +(-4.28015 - 2.47114i) q^{23} +(-6.35947 - 3.67164i) q^{24} +(3.73911 + 3.31950i) q^{25} +(3.67537 - 8.66396i) q^{26} +1.00000i q^{27} +(-1.79312 + 3.10577i) q^{28} +(-4.47447 + 7.75001i) q^{29} +(-5.76154 + 0.933271i) q^{30} +4.43329i q^{31} +(5.10890 + 8.84888i) q^{32} +(2.66705 + 4.61946i) q^{33} +5.24500i q^{34} +(0.266396 + 1.64459i) q^{35} +(2.40664 - 4.16842i) q^{36} +(-1.60563 + 2.78103i) q^{37} -11.8169i q^{38} +(3.31924 + 1.40807i) q^{39} +(15.3500 + 5.83062i) q^{40} +(-5.22633 - 3.01742i) q^{41} +(-1.68425 - 0.972402i) q^{42} +(-2.84358 + 1.64174i) q^{43} -25.6745i q^{44} +(-0.357544 - 2.20730i) q^{45} +(-11.1721 + 6.45024i) q^{46} -3.07882 q^{47} +(-8.26282 + 4.77054i) q^{48} +(3.22243 - 5.58142i) q^{49} +(12.3838 - 4.12001i) q^{50} -2.00941 q^{51} +(-10.4473 - 13.8576i) q^{52} +2.14507i q^{53} +(2.26052 + 1.30511i) q^{54} +(-7.53863 - 9.24294i) q^{55} +(2.73564 + 4.73826i) q^{56} +4.52716 q^{57} +(11.6794 + 20.2293i) q^{58} +(5.56056 - 3.21039i) q^{59} +(-3.82177 + 10.0614i) q^{60} +(-2.57340 - 4.45726i) q^{61} +(10.0215 + 5.78594i) q^{62} +(0.372536 - 0.645251i) q^{63} +7.58861 q^{64} +(-7.82999 - 1.92125i) q^{65} +13.9232 q^{66} +(-2.90415 + 5.03014i) q^{67} +(8.37605 + 4.83591i) q^{68} +(-2.47114 - 4.28015i) q^{69} +(4.06532 + 1.54419i) q^{70} +(-3.29251 + 1.90093i) q^{71} +(-3.67164 - 6.35947i) q^{72} +16.0480 q^{73} +(4.19105 + 7.25912i) q^{74} +(1.57841 + 4.74432i) q^{75} +(-18.8711 - 10.8952i) q^{76} -3.97428i q^{77} +(7.51495 - 5.66553i) q^{78} -11.4449 q^{79} +(16.5328 - 13.4843i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-13.6419 + 7.87615i) q^{82} +11.1517 q^{83} +(-3.10577 + 1.79312i) q^{84} +(4.43536 - 0.718451i) q^{85} +8.57064i q^{86} +(-7.75001 + 4.47447i) q^{87} +(-33.9220 - 19.5849i) q^{88} +(-2.30838 - 1.33274i) q^{89} +(-5.45628 - 2.07254i) q^{90} +(-1.61719 - 2.14509i) q^{91} +23.7886i q^{92} +(-2.21664 + 3.83934i) q^{93} +(-4.01821 + 6.95974i) q^{94} +(-9.99278 + 1.61866i) q^{95} +10.2178i q^{96} +(0.570099 + 0.987440i) q^{97} +(-8.41128 - 14.5688i) q^{98} +5.33410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 20 q^{4} + 16 q^{9}+O(q^{10}) \) 32 * q - 20 * q^4 + 16 * q^9	\( 32 q - 20 q^{4} + 16 q^{9} + 2 q^{10} - 12 q^{11} + 8 q^{14} - 6 q^{15} - 28 q^{16} - 30 q^{20} - 4 q^{25} + 52 q^{26} - 24 q^{29} + 4 q^{30} - 2 q^{35} + 20 q^{36} + 4 q^{40} - 36 q^{41} + 12 q^{45} - 48 q^{46} - 28 q^{49} + 54 q^{50} - 40 q^{51} + 24 q^{55} - 56 q^{56} + 84 q^{59} - 32 q^{61} + 136 q^{64} + 20 q^{65} + 8 q^{66} - 24 q^{69} + 12 q^{71} + 40 q^{74} - 16 q^{75} + 48 q^{76} - 104 q^{79} + 66 q^{80} - 16 q^{81} - 48 q^{84} - 54 q^{85} - 48 q^{89} + 4 q^{90} + 12 q^{91} - 8 q^{94} + 12 q^{95}+O(q^{100}) \) 32 * q - 20 * q^4 + 16 * q^9 + 2 * q^10 - 12 * q^11 + 8 * q^14 - 6 * q^15 - 28 * q^16 - 30 * q^20 - 4 * q^25 + 52 * q^26 - 24 * q^29 + 4 * q^30 - 2 * q^35 + 20 * q^36 + 4 * q^40 - 36 * q^41 + 12 * q^45 - 48 * q^46 - 28 * q^49 + 54 * q^50 - 40 * q^51 + 24 * q^55 - 56 * q^56 + 84 * q^59 - 32 * q^61 + 136 * q^64 + 20 * q^65 + 8 * q^66 - 24 * q^69 + 12 * q^71 + 40 * q^74 - 16 * q^75 + 48 * q^76 - 104 * q^79 + 66 * q^80 - 16 * q^81 - 48 * q^84 - 54 * q^85 - 48 * q^89 + 4 * q^90 + 12 * q^91 - 8 * q^94 + 12 * q^95

Introduction

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