LMFDB - Embedded newform 195.2.v.a.4.2

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			4.2
Character	$\chi$	$=$	195.4
Dual form			195.2.v.a.49.2

$q$-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} +(-0.933271 + 5.76154i) q^{10} +(4.61946 + 2.66705i) q^{11} +4.81328i q^{12} +(-3.57858 + 0.440198i) q^{13} -1.94480 q^{14} +(-2.20730 - 0.357544i) q^{15} +(-4.77054 + 8.26282i) q^{16} +(1.74020 - 1.00470i) q^{17} -2.61023 q^{18} +(3.92063 - 2.26358i) q^{19} +(-8.34046 - 6.80256i) 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} +(3.68901 - 4.52301i) q^{30} +4.43329i q^{31} +(-5.10890 - 8.84888i) q^{32} +(-2.66705 - 4.61946i) q^{33} +5.24500i q^{34} +(1.29106 + 1.05300i) 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} +(1.73280 + 1.41329i) q^{45} +(-11.1721 + 6.45024i) q^{46} +3.07882 q^{47} +(8.26282 - 4.77054i) q^{48} +(3.22243 - 5.58142i) q^{49} +(2.62384 + 12.7847i) q^{50} -2.00941 q^{51} +(10.4473 + 13.8576i) q^{52} -2.14507i q^{53} +(2.26052 + 1.30511i) q^{54} +(11.7739 + 1.90718i) 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} +(-7.13095 + 3.76158i) 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} +(-4.89791 + 1.00522i) q^{75} +(-18.8711 - 10.8952i) q^{76} +3.97428i q^{77} +(-7.51495 + 5.66553i) q^{78} -11.4449 q^{79} +(-3.41136 + 21.0600i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(13.6419 - 7.87615i) q^{82} -11.1517 q^{83} +(-3.10577 + 1.79312i) q^{84} +(2.83987 - 3.48190i) 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} +(6.39819 - 7.84467i) 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	$0.540816\pi$
$2$	−1.30511	+	2.26052i	−0.922854	+	1.59843i	−0.794977	+	0.606640i	$0.792517\pi$
$3$	−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	0.927800	−	0.373078i	$-0.121698\pi$
$7$	0.372536	+	0.645251i	0.140805	+	0.243882i	−0.786995	+	0.616960i	$0.788364\pi$
$8$	7.34329			2.59624
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.933271	+	5.76154i	−0.295126	+	1.82196i
$11$	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
$15$	−2.20730	−	0.357544i	−0.569922	−	0.0923175i
$16$	−4.77054	+	8.26282i	−1.19264	+	2.06571i
$17$	1.74020	−	1.00470i	0.422060	−	0.243676i	−0.273899	−	0.961759i	$-0.588313\pi$
$17$	1.74020	−	1.00470i	0.422060	−	0.243676i	0.695958	+	0.718082i	$0.254980\pi$
$18$	−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	$0.159526\pi$
$20$	−8.34046	−	6.80256i	−1.86498	−	1.52110i
$21$		−	0.745071i		−	0.162588i
$22$	−12.0578	+	6.96160i	−2.57074	+	1.48422i
$23$	4.28015	+	2.47114i	0.892472	+	0.515269i	0.874750	−	0.484574i	$-0.161025\pi$
$23$	4.28015	+	2.47114i	0.892472	+	0.515269i	0.0177217	+	0.999843i	$0.494359\pi$
$24$	−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	$0.854499\pi$
$30$	3.68901	−	4.52301i	0.673518	−	0.825785i
$31$			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
$35$	1.29106	+	1.05300i	0.218229	+	0.177990i
$36$	2.40664	−	4.16842i	0.401106	−	0.694737i
$37$	1.60563	−	2.78103i	0.263964	−	0.457199i	−0.703328	−	0.710866i	$-0.748303\pi$
$37$	1.60563	−	2.78103i	0.263964	−	0.457199i	0.967292	+	0.253667i	$0.0816367\pi$
$38$			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	−0.267255	−	0.963626i	$-0.586117\pi$
$43$	2.84358	−	1.64174i	0.433642	−	0.250363i	0.700897	+	0.713262i	$0.252783\pi$
$44$		−	25.6745i		−	3.87057i
$45$	1.73280	+	1.41329i	0.258311	+	0.210681i
$46$	−11.1721	+	6.45024i	−1.64724	+	0.951036i
$47$	3.07882			0.449092			0.224546	−	0.974463i	$-0.427910\pi$
$47$	3.07882			0.449092			0.224546	+	0.974463i	$0.427910\pi$
$48$	8.26282	−	4.77054i	1.19264	−	0.688568i
$49$	3.22243	−	5.58142i	0.460348	−	0.797346i
$50$	2.62384	+	12.7847i	0.371067	+	1.80802i
$51$	−2.00941			−0.281373
$52$	10.4473	+	13.8576i	1.44878	+	1.92171i
$53$		−	2.14507i		−	0.294648i	−0.989088	−	0.147324i	$-0.952934\pi$
$53$		−	2.14507i		−	0.294648i	0.989088	−	0.147324i	$-0.0470660\pi$
$54$	2.26052	+	1.30511i	0.307618	+	0.177603i
$55$	11.7739	+	1.90718i	1.58760	+	0.257163i
$56$	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
$65$	−7.13095	+	3.76158i	−0.884486	+	0.466567i
$66$	13.9232			1.71383
$67$	2.90415	−	5.03014i	0.354799	−	0.614529i	−0.632285	−	0.774736i	$-0.717883\pi$
$67$	2.90415	−	5.03014i	0.354799	−	0.614529i	0.987083	+	0.160207i	$0.0512161\pi$
$68$	−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	$-0.888376\pi$
$73$	−16.0480			−1.87828			−0.939140	+	0.343535i	$0.888376\pi$
$74$	4.19105	+	7.25912i	0.487200	+	0.843856i
$75$	−4.89791	+	1.00522i	−0.565562	+	0.116072i
$76$	−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	$0.722653\pi$
$80$	−3.41136	+	21.0600i	−0.381402	+	2.35458i
$81$	−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	$-0.709647\pi$
$83$	−11.1517			−1.22406			−0.612030	+	0.790834i	$0.709647\pi$
$84$	−3.10577	+	1.79312i	−0.338867	+	0.195645i
$85$	2.83987	−	3.48190i	0.308028	−	0.377666i
$86$			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
$95$	6.39819	−	7.84467i	0.656440	−	0.804846i
$96$			10.2178i			1.04285i
$97$	−0.570099	−	0.987440i	−0.0578847	−	0.100259i	0.835631	−	0.549291i	$-0.185102\pi$
$97$	−0.570099	−	0.987440i	−0.0578847	−	0.100259i	−0.893516	+	0.449032i	$0.851769\pi$
$98$	8.41128	+	14.5688i	0.849668	+	1.47167i
$99$			5.33410i			0.536097i
$100$	−22.8357	−	7.59734i	−2.28357	−	0.759734i
$101$	−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	$0.0377857\pi$
$103$			2.40384i			0.236857i	−0.992963	+	0.118429i	$0.962214\pi$
$104$	−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	0.992030	−	0.125999i	$-0.0402137\pi$
$107$	14.2637	+	8.23517i	1.37893	+	0.796124i	0.386896	+	0.922123i	$0.373547\pi$
$108$	−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	$0.951246\pi$
$110$	−19.6775	+	24.1262i	−1.87618	+	2.30034i
$111$	−2.78103	+	1.60563i	−0.263964	+	0.152400i
$112$	−7.10879			−0.671717
$113$	−4.55664	+	2.63078i	−0.428653	+	0.247483i	−0.698773	−	0.715344i	$-0.746270\pi$
$113$	−4.55664	+	2.63078i	−0.428653	+	0.247483i	0.270120	+	0.962827i	$0.412937\pi$
$114$	5.90845	−	10.2337i	0.553377	−	0.958477i
$115$	10.9091	+	1.76709i	1.01728	+	0.164782i
$116$	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
$120$	−16.2088	−	2.62555i	−1.47966	−	0.239679i
$121$	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	0.248750	−	0.968568i	$-0.419980\pi$
$127$	−5.24794	−	3.02990i	−0.465679	−	0.268860i	−0.714429	+	0.699708i	$0.753314\pi$
$128$	0.313817	−	0.543547i	0.0277378	−	0.0480433i
$129$	−3.28349			−0.289095
$130$	0.803562	−	21.0290i	0.0704771	−	1.84436i
$131$	−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	$-0.945919\pi$
$137$	−7.48201	−	12.9592i	−0.639231	−	1.10718i	0.346371	−	0.938098i	$-0.387414\pi$
$138$	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	$0.998193\pi$
$140$	1.28224	−	7.91589i	0.108369	−	0.669015i
$141$	−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
$145$	−3.19964	+	19.7530i	−0.265716	+	1.64040i
$146$	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	$0.149330\pi$
$150$	4.12001	−	12.3838i	0.336398	−	1.01113i
$151$			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	$0.288637\pi$
$157$			19.7353i			1.57505i	−0.616284	+	0.787524i	$0.711363\pi$
$158$	14.9368	−	25.8714i	1.18831	−	2.05822i
$159$	−1.07254	+	1.85769i	−0.0850576	+	0.147324i
$160$	−17.7054	−	14.4407i	−1.39974	−	1.14164i
$161$			3.68236i			0.290210i
$162$	−1.30511	−	2.26052i	−0.102539	−	0.177603i
$163$	3.76607	+	6.52302i	0.294981	+	0.510922i	0.974981	−	0.222290i	$-0.0713533\pi$
$163$	3.76607	+	6.52302i	0.294981	+	0.510922i	−0.679999	+	0.733213i	$0.738020\pi$
$164$			29.0474i			2.26822i
$165$	−9.24294	−	7.53863i	−0.719562	−	0.586882i
$166$	14.5543	−	25.2087i	1.12963	−	1.95658i
$167$	5.55821	−	9.62710i	0.430107	−	0.744968i	−0.566775	−	0.823873i	$-0.691809\pi$
$167$	5.55821	−	9.62710i	0.430107	−	0.744968i	0.996882	+	0.0789052i	$0.0251424\pi$
$168$		−	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	−0.807764	−	0.589506i	$-0.799323\pi$
$173$	−9.22179	+	5.32420i	−0.701120	+	0.404792i	0.106645	+	0.994297i	$0.465989\pi$
$174$			23.3588i			1.77082i
$175$	3.53486	+	1.17603i	0.267210	+	0.0888995i
$176$	−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	$0.947151\pi$
$180$	1.72096	−	10.6243i	0.128273	−	0.791891i
$181$	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
$185$	1.14817	−	7.08820i	0.0844149	−	0.521135i
$186$	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	$-0.650858\pi$
$193$	7.53493	−	13.0509i	0.542376	−	0.939423i	0.998767	−	0.0496434i	$-0.0158085\pi$
$194$	2.97617			0.213677
$195$	8.05638	+	0.307852i	0.576929	+	0.0220457i
$196$	−31.0209			−2.21578
$197$	−9.92251	+	17.1863i	−0.706949	+	1.22447i	0.259034	+	0.965868i	$0.416596\pi$
$197$	−9.92251	+	17.1863i	−0.706949	+	1.22447i	−0.965983	+	0.258604i	$0.916738\pi$
$198$	−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
$205$	−13.3207	−	2.15772i	−0.930357	−	0.150702i
$206$	−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
$210$	4.29276	+	0.695354i	0.296229	+	0.0479840i
$211$	−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
$215$	4.64052	−	5.68964i	0.316481	−	0.388030i
$216$		−	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	−0.729993	−	0.683454i	$-0.760477\pi$
$223$	3.38822	−	5.86857i	0.226892	−	0.392989i	0.956885	+	0.290466i	$0.0938102\pi$
$224$	3.80650	−	6.59305i	0.254332	−	0.440516i
$225$	4.74432	+	1.57841i	0.316288	+	0.105228i
$226$		−	13.7339i		−	0.913563i
$227$	7.16627	+	12.4124i	0.475642	+	0.823837i	0.999611	−	0.0279011i	$-0.00888233\pi$
$227$	7.16627	+	12.4124i	0.475642	+	0.823837i	−0.523968	+	0.851738i	$0.675549\pi$
$228$	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	$-0.275966\pi$
$230$	−18.2321	+	22.3540i	−1.20219	+	1.47398i
$231$	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	$0.0282456\pi$
$233$			2.70544i			0.177240i	−0.996066	+	0.0886198i	$0.971754\pi$
$234$	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	$-0.0614986\pi$
$240$	13.4843	−	16.5328i	0.870410	−	1.06719i
$241$	−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
$245$	2.30433	−	14.2257i	0.147218	−	0.908849i
$246$	−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
$250$	15.6358	+	24.6410i	0.988897	+	1.55844i
$251$	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	−0.413485	−	0.910511i	$-0.635688\pi$
$257$	−22.5840	−	13.0389i	−1.40875	−	0.813344i	−0.995268	+	0.0971673i	$0.969022\pi$
$258$	4.28532	−	7.42239i	0.266792	−	0.462098i
$259$	2.39262			0.148670
$260$	32.8415	+	20.6720i	2.03674	+	1.28203i
$261$	−8.94894			−0.553926
$262$	25.1290	−	43.5247i	1.55248	−	2.68897i
$263$	0.844103	+	0.487343i	0.0520496	+	0.0300509i	0.525799	−	0.850609i	$-0.323766\pi$
$263$	0.844103	+	0.487343i	0.0520496	+	0.0300509i	−0.473749	+	0.880660i	$0.657100\pi$
$264$	−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	$0.844512\pi$
$270$	5.76154	+	0.933271i	0.350636	+	0.0567971i
$271$	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
$275$	26.1259	−	5.36192i	1.57545	−	0.323336i
$276$	−11.8943	+	20.6015i	−0.715953	+	1.24007i
$277$	5.81040	−	3.35463i	0.349113	−	0.201560i	−0.315182	−	0.949031i	$-0.602065\pi$
$277$	5.81040	−	3.35463i	0.349113	−	0.201560i	0.664294	+	0.747471i	$0.268732\pi$
$278$	30.4710			1.82753
$279$	−3.83934	+	2.21664i	−0.229855	+	0.132707i
$280$	9.48064	+	7.73250i	0.566577	+	0.462105i
$281$		−	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	0.776107	−	0.630601i	$-0.217191\pi$
$283$	10.3971	+	6.00278i	0.618045	+	0.356828i	−0.158063	+	0.987429i	$0.550525\pi$
$284$	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
$290$	−40.4761	−	33.0127i	−2.37684	−	1.93857i
$291$			1.14020i			0.0668396i
$292$	38.6218	+	66.8949i	2.26017	+	3.91473i
$293$	0.328488	+	0.568959i	0.0191905	+	0.0332389i	0.875461	−	0.483288i	$-0.160558\pi$
$293$	0.328488	+	0.568959i	0.0191905	+	0.0332389i	−0.856271	+	0.516527i	$0.827224\pi$
$294$		−	16.8226i		−	0.981112i
$295$	9.07444	−	11.1260i	0.528334	−	0.647779i
$296$	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
$305$	−8.91840	−	7.27393i	−0.510666	−	0.416504i
$306$	−4.54230	+	2.62250i	−0.259666	+	0.149918i
$307$	1.96322			0.112047			0.0560233	−	0.998429i	$-0.482158\pi$
$307$	1.96322			0.112047			0.0560233	+	0.998429i	$0.482158\pi$
$308$	16.5665	−	9.56466i	0.943963	−	0.544997i
$309$	1.20192	−	2.08179i	0.0683748	−	0.118429i
$310$	−25.5426	−	4.13746i	−1.45072	−	0.234992i
$311$	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	$-0.757518\pi$
$313$		−	24.4222i		−	1.38042i	0.723608	−	0.690211i	$-0.242482\pi$
$314$	−44.6120	−	25.7568i	−2.51760	−	1.45354i
$315$	−0.266396	+	1.64459i	−0.0150097	+	0.0926624i
$316$	27.5437	+	47.7070i	1.54945	+	2.68373i
$317$	−6.24200			−0.350586			−0.175293	−	0.984516i	$-0.556087\pi$
$317$	−6.24200			−0.350586			−0.175293	+	0.984516i	$0.556087\pi$
$318$	−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
$325$	−11.9195	+	13.5250i	−0.661172	+	0.750234i
$326$	−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
$335$	2.07673	−	12.8207i	0.113464	−	0.700467i
$336$	6.15639	+	3.55439i	0.335859	+	0.193908i
$337$			6.39946i			0.348601i	0.984693	+	0.174301i	$0.0557664\pi$
$337$			6.39946i			0.348601i	−0.984693	+	0.174301i	$0.944234\pi$
$338$	−9.33874	+	32.6226i	−0.507961	+	1.77443i
$339$	5.26156			0.285769
$340$	−21.3486	−	3.45811i	−1.15779	−	0.187542i
$341$	−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
$345$	−8.56401	−	6.98489i	−0.461071	−	0.376054i
$346$		−	27.7947i		−	1.49425i
$347$	−15.0295	+	8.67730i	−0.806827	+	0.465822i	−0.845853	−	0.533416i	$-0.820908\pi$
$347$	−15.0295	+	8.67730i	−0.806827	+	0.465822i	0.0390257	+	0.999238i	$0.487575\pi$
$348$	−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	−0.625414	−	0.780293i	$-0.715070\pi$
$353$	6.82103	−	11.8144i	0.363047	−	0.628816i	0.988461	+	0.151477i	$0.0484031\pi$
$354$	8.37985	−	14.5143i	0.445384	−	0.771428i
$355$	−5.37314	+	6.58788i	−0.285176	+	0.349648i
$356$			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	$-0.119516\pi$
$360$	12.7245	+	10.3782i	0.670639	+	0.546979i
$361$	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	0.0588530	−	0.998267i	$-0.481256\pi$
$367$	−14.8707	−	8.58561i	−0.776245	−	0.448165i	−0.835098	+	0.550102i	$0.814589\pi$
$368$	−40.8372	+	23.5774i	−2.12879	+	1.22906i
$369$		−	6.03484i		−	0.314161i
$370$	14.5245	+	11.8464i	0.755095	+	0.615863i
$371$	1.38411	−	0.799116i	0.0718594	−	0.0414880i
$372$	−21.3386			−1.10636
$373$	10.7364	−	6.19865i	0.555908	−	0.320954i	−0.195593	−	0.980685i	$-0.562663\pi$
$373$	10.7364	−	6.19865i	0.555908	−	0.320954i	0.751502	+	0.659731i	$0.229330\pi$
$374$	−13.9887	+	24.2291i	−0.723337	+	1.25286i
$375$	−9.44019	+	5.99022i	−0.487489	+	0.309334i
$376$	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	$-0.671380\pi$
$380$	−48.0980	−	7.79105i	−2.46738	−	0.399673i
$381$	3.02990	+	5.24794i	0.155226	+	0.268860i
$382$	−28.4499			−1.45562
$383$	8.20981	+	14.2198i	0.419502	+	0.726598i	0.995889	−	0.0905781i	$-0.0288715\pi$
$383$	8.20981	+	14.2198i	0.419502	+	0.726598i	−0.576388	+	0.817176i	$0.695538\pi$
$384$	−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	$0.337762\pi$
$390$	−11.2104	+	17.8098i	−0.567660	+	0.901836i
$391$	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	0.728798	−	0.684729i	$-0.240079\pi$
$397$	−4.55470	−	7.88897i	−0.228594	−	0.395936i	−0.957392	+	0.288793i	$0.906746\pi$
$398$	51.0042			2.55661
$399$	−1.68653	−	2.92115i	−0.0844320	−	0.146240i
$400$	9.59085	+	46.7314i	0.479543	+	2.33657i
$401$	−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
$405$	−0.357544	+	2.20730i	−0.0177665	+	0.109681i
$406$	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	$0.449799\pi$
$410$	22.2626	−	27.2956i	1.09947	−	1.34804i
$411$			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	$0.817877\pi$
$420$	−5.06839	+	6.21424i	−0.247312	+	0.303224i
$421$			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
$425$	3.17167	−	9.53327i	0.153849	−	0.462432i
$426$	−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	−0.101358	−	0.994850i	$-0.532319\pi$
$433$	14.7643	−	8.52419i	0.709528	−	0.409646i	0.810886	+	0.585204i	$0.198985\pi$
$434$		−	8.62188i		−	0.413863i
$435$	12.6475	−	15.5068i	0.606399	−	0.743492i
$436$	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	$0.124886\pi$
$440$	86.4594	+	14.0049i	4.12179	+	0.667659i
$441$	6.44487			0.306899
$442$	−2.30884	−	18.7697i	−0.109820	−	0.892781i
$443$			30.2136i			1.43549i	0.696305	+	0.717746i	$0.254826\pi$
$443$			30.2136i			1.43549i	−0.696305	+	0.717746i	$0.745174\pi$
$444$	13.3859	+	7.72834i	0.635266	+	0.366771i
$445$	−5.88352	−	0.953030i	−0.278906	−	0.0451779i
$446$	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
$455$	−5.08370	−	3.19993i	−0.238327	−	0.150015i
$456$	−33.2442			−1.55680
$457$	3.74141	−	6.48031i	0.175016	−	0.303136i	−0.765151	−	0.643851i	$-0.777336\pi$
$457$	3.74141	−	6.48031i	0.175016	−	0.303136i	0.940167	+	0.340715i	$0.110669\pi$
$458$	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	$-0.482546\pi$
$463$	2.35856			0.109611			0.0548057	+	0.998497i	$0.482546\pi$
$464$	−42.6913	−	73.9435i	−1.98189	−	3.43274i
$465$	1.58510	−	9.78558i	0.0735071	−	0.453796i
$466$	−6.11572	−	3.53091i	−0.283305	−	0.163566i
$467$		−	0.629544i		−	0.0291318i	−0.999894	−	0.0145659i	$-0.995363\pi$
$467$		−	0.629544i		−	0.0291318i	0.999894	−	0.0145659i	$-0.00463664\pi$
$468$	−6.77741	+	15.9764i	−0.313286	+	0.738510i
$469$	4.32760			0.199830
$470$	−2.87337	+	17.7388i	−0.132539	+	0.818228i
$471$	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
$475$	7.14572	−	21.4783i	0.327868	−	0.985492i
$476$		−	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
$485$	−1.97574	−	1.61143i	−0.0897136	−	0.0731713i
$486$			2.61023i			0.118402i
$487$	−2.03036	−	3.51669i	−0.0920044	−	0.159356i	0.816350	−	0.577557i	$-0.195994\pi$
$487$	−2.03036	−	3.51669i	−0.0920044	−	0.159356i	−0.908354	+	0.418201i	$0.862661\pi$
$488$	−18.8972	−	32.7310i	−0.855437	−	1.48166i
$489$		−	7.53213i		−	0.340615i
$490$	29.1502	+	23.7752i	1.31687	+	1.07405i
$491$	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	$-0.215222\pi$
$500$	−53.7670	+	2.25065i	−2.40453	+	0.100652i
$501$	−9.62710	+	5.55821i	−0.430107	+	0.248323i
$502$	−9.61677			−0.429218
$503$	−15.8300	+	9.13948i	−0.705827	+	0.407509i	−0.809514	−	0.587101i	$-0.800269\pi$
$503$	−15.8300	+	9.13948i	−0.705827	+	0.407509i	0.103687	+	0.994610i	$0.466936\pi$
$504$	−2.73564	+	4.73826i	−0.121855	+	0.211059i
$505$	−1.42187	+	8.77791i	−0.0632724	+	0.390612i
$506$	−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	$0.715483\pi$
$510$	1.87532	−	11.5773i	0.0830406	−	0.512650i
$511$	−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
$520$	−52.3647	+	27.6224i	−2.29634	+	1.21132i
$521$	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	0.268625	−	0.963245i	$-0.413431\pi$
$523$	−9.86249	−	5.69411i	−0.431256	−	0.248986i	−0.699882	+	0.714259i	$0.746764\pi$
$524$	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
$530$	12.3589	+	2.00193i	0.536837	+	0.0869584i
$531$	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
$535$	36.3549	+	5.88887i	1.57176	+	0.254598i
$536$	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
$540$	−6.80256	+	8.34046i	−0.292736	+	0.358916i
$541$			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	$-0.671223\pi$
$547$		−	40.1704i		−	1.71756i	0.512344	−	0.858781i	$-0.328777\pi$
$548$	−36.0130	+	62.3763i	−1.53840	+	2.66458i
$549$	2.57340	−	4.45726i	0.109830	−	0.190231i
$550$	−21.9766	+	66.0561i	−0.937083	+	2.81664i
$551$			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
$555$	−4.53844	+	5.56448i	−0.192646	+	0.236199i
$556$	−28.0944	+	48.6609i	−1.19147	+	2.06368i
$557$	−6.40745	+	11.0980i	−0.271492	+	0.470239i	−0.969244	−	0.246101i	$-0.920851\pi$
$557$	−6.40745	+	11.0980i	−0.271492	+	0.470239i	0.697752	+	0.716340i	$0.254184\pi$
$558$		−	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	−0.328550	−	0.944486i	$-0.606560\pi$
$563$	7.71441	−	4.45392i	0.325124	−	0.187710i	0.653674	+	0.756776i	$0.273227\pi$
$564$			14.8192i			0.624001i
$565$	−7.43612	+	9.11725i	−0.312840	+	0.383566i
$566$	−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	$0.269683\pi$
$570$	4.22506	−	26.0834i	0.176968	−	1.09251i
$571$	−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
$575$	24.2069	−	4.96807i	1.00950	−	0.207183i
$576$	3.79430	+	6.57193i	0.158096	+	0.273830i
$577$	−4.25878			−0.177295			−0.0886477	−	0.996063i	$-0.528255\pi$
$577$	−4.25878			−0.177295			−0.0886477	+	0.996063i	$0.528255\pi$
$578$	−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
$585$	−6.82310	−	4.29480i	−0.282101	−	0.177568i
$586$	−1.71486			−0.0708401
$587$	−2.01772	+	3.49480i	−0.0832803	+	0.144246i	−0.904657	−	0.426140i	$-0.859873\pi$
$587$	−2.01772	+	3.49480i	−0.0832803	+	0.144246i	0.821377	+	0.570386i	$0.193206\pi$
$588$	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	$-0.568175\pi$
$593$	−10.3515			−0.425086			−0.212543	+	0.977152i	$0.568175\pi$
$594$	6.96160	+	12.0578i	0.285638	+	0.494739i
$595$	3.30466	+	0.535298i	0.135478	+	0.0219451i
$596$	−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	$0.632157\pi$
$600$	−35.9668	+	7.38159i	−1.46834	+	0.301352i
$601$	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
$605$	30.2419	+	24.6656i	1.22951	+	1.00280i
$606$			10.3803i			0.421669i
$607$	−16.3612	+	9.44615i	−0.664081	+	0.383407i	−0.793830	−	0.608140i	$-0.791916\pi$
$607$	−16.3612	+	9.44615i	−0.664081	+	0.383407i	0.129749	+	0.991547i	$0.458583\pi$
$608$	−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	$0.528437\pi$
$613$	−22.4608	+	38.9032i	−0.907182	+	1.57128i	−0.817962	+	0.575273i	$0.804896\pi$
$614$	−2.56222	+	4.43789i	−0.103403	+	0.179099i
$615$	10.4572	+	8.52899i	0.421675	+	0.343922i
$616$			29.1843i			1.17587i
$617$	1.35336	+	2.34409i	0.0544843	+	0.0943697i	0.891981	−	0.452072i	$-0.149315\pi$
$617$	1.35336	+	2.34409i	0.0544843	+	0.0943697i	−0.837497	+	0.546442i	$0.815982\pi$
$618$	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	$-0.00103062\pi$
$620$	30.1577	−	36.9757i	1.21116	−	1.48498i
$621$	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
$630$	−3.36996	−	2.74857i	−0.134263	−	0.109506i
$631$	−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
$635$	−13.3758	−	2.16665i	−0.530801	−	0.0859807i
$636$	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
$640$	0.224407	−	1.38538i	0.00887047	−	0.0547618i
$641$	−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	0.983635	−	0.180173i	$-0.0576658\pi$
$643$	8.51460	+	14.7477i	0.335783	+	0.581593i	−0.647852	+	0.761766i	$0.724332\pi$
$644$	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	0.932415	−	0.361390i	$-0.117698\pi$
$647$	27.6148	+	15.9434i	1.08565	+	0.626800i	0.153235	+	0.988190i	$0.451031\pi$
$648$	−3.67164	+	6.35947i	−0.144236	+	0.249824i
$649$	34.2491			1.34439
$650$	−15.0174	−	44.5959i	−0.589031	−	1.74919i
$651$	3.30312			0.129459
$652$	18.1271	−	31.3971i	0.709913	−	1.22961i
$653$	−33.7363	−	19.4777i	−1.32020	−	0.762220i	−0.336442	−	0.941704i	$-0.609224\pi$
$653$	−33.7363	−	19.4777i	−1.32020	−	0.762220i	−0.983761	+	0.179484i	$0.942557\pi$
$654$	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	$0.607073\pi$
$660$	−9.17976	+	56.6712i	−0.357322	+	2.20592i
$661$	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
$665$	7.44533	+	1.20602i	0.288718	+	0.0467673i
$666$	−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
$670$	26.2710	+	21.4269i	1.01494	+	0.827793i
$671$		−	27.4535i		−	1.05983i
$672$	−6.59305	+	3.80650i	−0.254332	+	0.146839i
$673$	−11.3249	−	6.53842i	−0.436542	−	0.252038i	0.265588	−	0.964087i	$-0.414434\pi$
$673$	−11.3249	−	6.53842i	−0.436542	−	0.252038i	−0.702130	+	0.712049i	$0.747767\pi$
$674$	−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	$0.0348512\pi$
$677$			5.68622i			0.218539i	−0.994012	+	0.109270i	$0.965149\pi$
$678$	−6.86693	+	11.8939i	−0.263723	+	0.456781i
$679$	0.424764	−	0.735713i	0.0163010	−	0.0282341i
$680$	20.8540	−	25.5686i	0.799715	−	0.980512i
$681$		−	14.3325i		−	0.549224i
$682$	−30.8628	−	53.4559i	−1.18180	−	2.04693i
$683$	7.00400	+	12.1313i	0.268001	+	0.464191i	0.968345	−	0.249614i	$-0.0803037\pi$
$683$	7.00400	+	12.1313i	0.268001	+	0.464191i	−0.700345	+	0.713805i	$0.746970\pi$
$684$		−	21.7905i		−	0.833179i
$685$	−25.9297	−	21.1485i	−0.990723	−	0.808043i
$686$	−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
$695$	−20.2283	−	16.4984i	−0.767301	−	0.625818i
$696$	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
$700$	−3.60494	−	17.5651i	−0.136254	−	0.663897i
$701$	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
$705$	−6.79587	−	1.10081i	−0.255947	−	0.0414591i
$706$	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
$715$	−42.9735	−	1.64211i	−1.60712	−	0.0614115i
$716$	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
$725$	8.99562	+	43.8311i	0.334089	+	1.62785i
$726$	39.4519	+	22.7776i	1.46420	+	0.845356i
$727$		−	36.6222i		−	1.35824i	−0.734026	−	0.679122i	$-0.762361\pi$
$727$		−	36.6222i		−	1.35824i	0.734026	−	0.679122i	$-0.237639\pi$
$728$	−11.8755	−	15.7520i	−0.440134	−	0.583809i
$729$	−1.00000			−0.0370370
$730$	14.9772	−	92.4614i	0.554330	−	3.42215i
$731$	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	$-0.157511\pi$
$733$	47.6527			1.76009			0.880046	+	0.474888i	$0.157511\pi$
$734$	38.8159	−	22.4104i	1.43272	−	0.827182i
$735$	−9.10848	+	11.1677i	−0.335971	+	0.411926i
$736$		−	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	−0.927163	−	0.374658i	$-0.877760\pi$
$743$	−3.79209	+	6.56809i	−0.139118	+	0.240960i	0.788045	+	0.615618i	$0.211093\pi$
$744$	16.2775	−	28.1934i	0.596760	−	1.03362i
$745$	18.8525	−	23.1146i	0.690701	−	0.846853i
$746$			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
$750$	−1.22052	−	29.1577i	−0.0445670	−	1.06469i
$751$	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	0.940377	−	0.340134i	$-0.110473\pi$
$757$	30.7052	+	17.7277i	1.11600	+	0.644323i	0.175623	+	0.984457i	$0.443806\pi$
$758$	76.8667	−	44.3790i	2.79193	−	1.61192i
$759$		−	26.3626i		−	0.956903i
$760$	46.9837	−	57.6057i	1.70428	−	2.08958i
$761$	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
$765$	4.43536	+	0.718451i	0.160361	+	0.0259757i
$766$	−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	$0.582370\pi$
$770$	−22.8980	−	3.70908i	−0.825187	−	0.133666i
$771$	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	$0.0773585\pi$
$773$	19.2871	+	33.4063i	0.693710	+	1.20154i	−0.276903	+	0.960898i	$0.589308\pi$
$774$	−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
$780$	−18.1055	−	34.3233i	−0.648282	−	1.22897i
$781$	−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	0.963109	−	0.269111i	$-0.0867300\pi$
$787$	6.97122	+	12.0745i	0.248497	+	0.430410i	−0.714612	+	0.699521i	$0.753397\pi$
$788$	95.5196			3.40274
$789$	−0.487343	−	0.844103i	−0.0173499	−	0.0300509i
$790$	10.6812	−	65.9401i	0.380019	−	2.34604i
$791$	−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
$795$	−0.766958	+	4.73481i	−0.0272012	+	0.167926i
$796$	−47.0261	+	81.4516i	−1.66680	+	2.88697i
$797$	15.9352	−	9.20020i	0.564455	−	0.325888i	−0.190477	−	0.981692i	$-0.561003\pi$
$797$	15.9352	−	9.20020i	0.564455	−	0.325888i	0.754931	+	0.655804i	$0.227670\pi$
$798$	8.80443			0.311674
$799$	5.35775	−	3.09330i	0.189544	−	0.109433i
$800$	−48.4766	−	16.1279i	−1.71391	−	0.570208i
$801$		−	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	$0.814833\pi$
$810$	−4.52301	−	3.68901i	−0.158922	−	0.129619i
$811$		−	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
$815$	13.0517	+	10.6451i	0.457181	+	0.372882i
$816$	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	−0.953503	−	0.301384i	$-0.902551\pi$
$823$	−33.5434	+	19.3663i	−1.16925	+	0.675066i	−0.215745	+	0.976450i	$0.569218\pi$
$824$			17.6521i			0.614939i
$825$	−25.3067	−	8.41941i	−0.881066	−	0.293126i
$826$	−10.8142	+	6.24359i	−0.376275	+	0.217242i
$827$	18.1501			0.631142			0.315571	−	0.948902i	$-0.397804\pi$
$827$	18.1501			0.631142			0.315571	+	0.948902i	$0.397804\pi$
$828$	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	$0.938941\pi$
$830$	10.4076	−	64.2511i	0.361252	−	2.23019i
$831$	−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
$835$	3.97461	−	24.5372i	0.137547	−	0.849146i
$836$	−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
$845$	23.8628	−	16.6001i	0.820907	−	0.571062i
$846$	−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	$-0.493594\pi$
$853$	1.17550			0.0402483			0.0201242	+	0.999797i	$0.493594\pi$
$854$	5.00476	+	8.66850i	0.171259	+	0.296630i
$855$	9.99278	+	1.61866i	0.341746	+	0.0553570i
$856$	104.743	+	60.4732i	3.58003	+	2.06693i
$857$			12.8574i			0.439200i	0.975590	+	0.219600i	$0.0704752\pi$
$857$			12.8574i			0.439200i	−0.975590	+	0.219600i	$0.929525\pi$
$858$	−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	$0.500316\pi$
$860$	−34.8848	−	5.65075i	−1.18956	−	0.192689i
$861$	−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	$-0.655981\pi$
$863$	−27.6526			−0.941305			−0.470652	+	0.882319i	$0.655981\pi$
$864$	−8.84888	+	5.10890i	−0.301045	+	0.173808i
$865$	−15.0493	+	18.4516i	−0.511691	+	0.627373i
$866$			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
$875$	8.32286	−	0.348389i	0.281364	−	0.0117777i
$876$		−	77.2436i		−	2.60982i
$877$	−28.1798	−	48.8088i	−0.951564	−	1.64816i	−0.742043	−	0.670353i	$-0.766143\pi$
$877$	−28.1798	−	48.8088i	−0.951564	−	1.64816i	−0.209521	−	0.977804i	$-0.567190\pi$
$878$	7.15801	+	12.3980i	0.241571	+	0.418413i
$879$		−	0.656977i		−	0.0221593i
$880$	−71.9267	+	88.1877i	−2.42465	+	2.97281i
$881$	−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	$-0.931249\pi$
$883$		−	12.7367i		−	0.428624i	0.976765	−	0.214312i	$-0.0687510\pi$
$884$	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	−0.339074	−	0.940760i	$-0.610114\pi$
$887$	−39.4122	−	22.7546i	−1.32333	−	0.764026i	−0.984259	+	0.176734i	$0.943447\pi$
$888$	−20.4219	+	11.7906i	−0.685315	+	0.395667i
$889$		−	4.51498i		−	0.151428i
$890$	9.83300	−	12.0560i	0.329603	−	0.404119i
$891$	−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
$895$	−6.08716	+	37.5791i	−0.203471	+	1.25613i
$896$	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
$900$	−4.83838	−	23.5750i	−0.161279	−	0.785834i
$901$	−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	$0.0857123\pi$
$907$	50.4853	+	29.1477i	1.67634	+	0.967833i	0.712372	+	0.701802i	$0.247621\pi$
$908$	34.4933	−	59.7441i	1.14470	−	1.98268i
$909$	−3.97677			−0.131901
$910$	13.8683	−	7.31554i	0.459730	−	0.242508i
$911$	−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	$0.626412\pi$
$920$	80.1086	+	12.9762i	2.64110	+	0.427813i
$921$	−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
$925$	−3.22801	−	15.7285i	−0.106136	−	0.517149i
$926$	−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	$-0.0184746\pi$
$930$	20.0518	+	16.3544i	0.657524	+	0.536283i
$931$		−	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	$0.0812401\pi$
$937$			15.4559i			0.504923i	−0.967607	+	0.252461i	$0.918760\pi$
$938$	−5.64801	+	9.78264i	−0.184414	+	0.319414i
$939$	−12.2111	+	21.1502i	−0.398494	+	0.690211i
$940$	−25.6788	−	20.9439i	−0.837550	−	0.683113i
$941$		−	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
$945$	1.05300	−	1.29106i	0.0342542	−	0.0419983i
$946$	−22.8583	+	39.5917i	−0.743188	+	1.28724i
$947$	−10.4804	+	18.1525i	−0.340566	+	0.589877i	−0.984538	−	0.175172i	$-0.943952\pi$
$947$	−10.4804	+	18.1525i	−0.340566	+	0.589877i	0.643972	+	0.765049i	$0.277285\pi$
$948$		−	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	$0.723691\pi$
$953$	−50.3289	+	29.0574i	−1.63031	+	0.941261i	−0.983996	+	0.178191i	$0.942976\pi$
$954$			5.59912i			0.181278i
$955$	18.8865	+	15.4040i	0.611154	+	0.498463i
$956$	−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
$960$	−16.7503	−	2.71326i	−0.540614	−	0.0875702i
$961$	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
$965$	5.38814	−	33.2637i	0.173450	−	1.07079i
$966$	4.80589	+	8.32405i	0.154627	+	0.267822i
$967$	14.7540			0.474458			0.237229	−	0.971454i	$-0.423761\pi$
$967$	14.7540			0.474458			0.237229	+	0.971454i	$0.423761\pi$
$968$	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
$975$	17.0851	−	5.75330i	0.547160	−	0.184253i
$976$	49.1061			1.57185
$977$	20.7767	−	35.9863i	0.664706	−	1.15130i	−0.314660	−	0.949205i	$-0.601890\pi$
$977$	20.7767	−	35.9863i	0.664706	−	1.15130i	0.979365	−	0.202099i	$-0.0647763\pi$
$978$	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	$-0.436333\pi$
$983$	12.4586			0.397368			0.198684	+	0.980064i	$0.436333\pi$
$984$	22.1578	+	38.3784i	0.706365	+	1.22346i
$985$	−7.09547	+	43.8038i	−0.226080	+	1.39571i
$986$	−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
$990$	−30.7326	−	4.97816i	−0.976747	−	0.158216i
$991$	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
$995$	−33.8592	−	27.6159i	−1.07341	−	0.875484i
$996$		−	53.6763i		−	1.70080i
$997$	−14.7515	+	8.51678i	−0.467185	+	0.269729i	−0.715060	−	0.699063i	$-0.753601\pi$
$997$	−14.7515	+	8.51678i	−0.467185	+	0.269729i	0.247876	+	0.968792i	$0.420267\pi$
$998$	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.4.2	✓	32
3.2	odd	2		585.2.bf.c.199.15		32
5.2	odd	4		975.2.bc.m.901.1		16
5.3	odd	4		975.2.bc.n.901.8		16
5.4	even	2	inner	195.2.v.a.4.15	yes	32
13.10	even	6	inner	195.2.v.a.49.15	yes	32
15.14	odd	2		585.2.bf.c.199.2		32
39.23	odd	6		585.2.bf.c.244.2		32
65.23	odd	12		975.2.bc.n.751.8		16
65.49	even	6	inner	195.2.v.a.49.2	yes	32
65.62	odd	12		975.2.bc.m.751.1		16
195.179	odd	6		585.2.bf.c.244.15		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.v.a.4.2	✓	32	1.1	even	1	trivial
195.2.v.a.4.15	yes	32	5.4	even	2	inner
195.2.v.a.49.2	yes	32	65.49	even	6	inner
195.2.v.a.49.15	yes	32	13.10	even	6	inner
585.2.bf.c.199.2		32	15.14	odd	2
585.2.bf.c.199.15		32	3.2	odd	2
585.2.bf.c.244.2		32	39.23	odd	6
585.2.bf.c.244.15		32	195.179	odd	6
975.2.bc.m.751.1		16	65.62	odd	12
975.2.bc.m.901.1		16	5.2	odd	4
975.2.bc.n.751.8		16	65.23	odd	12
975.2.bc.n.901.8		16	5.3	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} +(-0.933271 + 5.76154i) q^{10} +(4.61946 + 2.66705i) q^{11} +4.81328i q^{12} +(-3.57858 + 0.440198i) q^{13} -1.94480 q^{14} +(-2.20730 - 0.357544i) q^{15} +(-4.77054 + 8.26282i) q^{16} +(1.74020 - 1.00470i) q^{17} -2.61023 q^{18} +(3.92063 - 2.26358i) q^{19} +(-8.34046 - 6.80256i) 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} +(3.68901 - 4.52301i) q^{30} +4.43329i q^{31} +(-5.10890 - 8.84888i) q^{32} +(-2.66705 - 4.61946i) q^{33} +5.24500i q^{34} +(1.29106 + 1.05300i) 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} +(1.73280 + 1.41329i) q^{45} +(-11.1721 + 6.45024i) q^{46} +3.07882 q^{47} +(8.26282 - 4.77054i) q^{48} +(3.22243 - 5.58142i) q^{49} +(2.62384 + 12.7847i) q^{50} -2.00941 q^{51} +(10.4473 + 13.8576i) q^{52} -2.14507i q^{53} +(2.26052 + 1.30511i) q^{54} +(11.7739 + 1.90718i) 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} +(-7.13095 + 3.76158i) 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} +(-4.89791 + 1.00522i) q^{75} +(-18.8711 - 10.8952i) q^{76} +3.97428i q^{77} +(-7.51495 + 5.66553i) q^{78} -11.4449 q^{79} +(-3.41136 + 21.0600i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(13.6419 - 7.87615i) q^{82} -11.1517 q^{83} +(-3.10577 + 1.79312i) q^{84} +(2.83987 - 3.48190i) 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} +(6.39819 - 7.84467i) 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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