LMFDB - Embedded newform 195.2.v.a.4.5

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			4.5
Character	$\chi$	$=$	195.4
Dual form			195.2.v.a.49.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.733363 + 1.27022i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.0756426 - 0.131017i) q^{4} +(0.387771 - 2.20219i) q^{5} +(1.27022 - 0.733363i) q^{6} +(-2.16559 - 3.75091i) q^{7} -2.71156 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.733363 + 1.27022i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.0756426 - 0.131017i) q^{4} +(0.387771 - 2.20219i) q^{5} +(1.27022 - 0.733363i) q^{6} +(-2.16559 - 3.75091i) q^{7} -2.71156 q^{8} +(0.500000 + 0.866025i) q^{9} +(2.51289 + 2.10756i) q^{10} +(-5.05511 - 2.91857i) q^{11} +0.151285i q^{12} +(3.21192 + 1.63816i) q^{13} +6.35265 q^{14} +(-1.43691 + 1.71327i) q^{15} +(2.13984 - 3.70631i) q^{16} +(2.49317 - 1.43943i) q^{17} -1.46673 q^{18} +(2.89056 - 1.66887i) q^{19} +(-0.317856 + 0.115775i) q^{20} +4.33118i q^{21} +(7.41446 - 4.28074i) q^{22} +(-1.07921 - 0.623084i) q^{23} +(2.34828 + 1.35578i) q^{24} +(-4.69927 - 1.70789i) q^{25} +(-4.43633 + 2.87849i) q^{26} -1.00000i q^{27} +(-0.327622 + 0.567457i) q^{28} +(-2.86622 + 4.96444i) q^{29} +(-1.12245 - 3.08164i) q^{30} +0.880021i q^{31} +(0.427003 + 0.739591i) q^{32} +(2.91857 + 5.05511i) q^{33} +4.22250i q^{34} +(-9.09997 + 3.31454i) q^{35} +(0.0756426 - 0.131017i) q^{36} +(-0.0960639 + 0.166388i) q^{37} +4.89554i q^{38} +(-1.96253 - 3.02465i) q^{39} +(-1.05146 + 5.97136i) q^{40} +(0.198375 + 0.114532i) q^{41} +(-5.50156 - 3.17633i) q^{42} +(4.27940 - 2.47071i) q^{43} +0.883072i q^{44} +(2.10104 - 0.765275i) q^{45} +(1.58291 - 0.913893i) q^{46} -0.0904255 q^{47} +(-3.70631 + 2.13984i) q^{48} +(-5.87956 + 10.1837i) q^{49} +(5.61567 - 4.71661i) q^{50} -2.87886 q^{51} +(-0.0283319 - 0.544730i) q^{52} -4.46001i q^{53} +(1.27022 + 0.733363i) q^{54} +(-8.38746 + 10.0006i) q^{55} +(5.87212 + 10.1708i) q^{56} -3.33774 q^{57} +(-4.20396 - 7.28147i) q^{58} +(6.48915 - 3.74651i) q^{59} +(0.333158 + 0.0586640i) q^{60} +(-6.78634 - 11.7543i) q^{61} +(-1.11782 - 0.645375i) q^{62} +(2.16559 - 3.75091i) q^{63} +7.30677 q^{64} +(4.85302 - 6.43803i) q^{65} -8.56148 q^{66} +(-3.73475 + 6.46878i) q^{67} +(-0.377179 - 0.217765i) q^{68} +(0.623084 + 1.07921i) q^{69} +(2.46337 - 13.9897i) q^{70} +(3.08252 - 1.77969i) q^{71} +(-1.35578 - 2.34828i) q^{72} -8.62359 q^{73} +(-0.140899 - 0.244045i) q^{74} +(3.21574 + 3.82871i) q^{75} +(-0.437299 - 0.252475i) q^{76} +25.2817i q^{77} +(5.28122 - 0.274681i) q^{78} +6.75912 q^{79} +(-7.33223 - 6.14954i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.290961 + 0.167987i) q^{82} +9.36059 q^{83} +(0.567457 - 0.327622i) q^{84} +(-2.20312 - 6.04859i) q^{85} +7.24771i q^{86} +(4.96444 - 2.86622i) q^{87} +(13.7072 + 7.91387i) q^{88} +(13.1729 + 7.60535i) q^{89} +(-0.568754 + 3.23001i) q^{90} +(-0.811121 - 15.5952i) q^{91} +0.188527i q^{92} +(0.440010 - 0.762120i) q^{93} +(0.0663147 - 0.114860i) q^{94} +(-2.55428 - 7.01270i) q^{95} -0.854006i q^{96} +(-0.762993 - 1.32154i) q^{97} +(-8.62370 - 14.9367i) q^{98} -5.83714i 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 $

$2$	−0.733363	+	1.27022i	−0.518566	+	0.898183i	0.481201	+	0.876610i	$0.340201\pi$
$2$	−0.733363	+	1.27022i	−0.518566	+	0.898183i	−0.999767	+	0.0215725i	$0.993133\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.0756426	−	0.131017i	−0.0378213	−	0.0655084i
$5$	0.387771	−	2.20219i	0.173416	−	0.984849i
$5$	0.387771	−	2.20219i	0.173416	−	0.984849i
$6$	1.27022	−	0.733363i	0.518566	−	0.299394i
$7$	−2.16559	−	3.75091i	−0.818516	−	1.41771i	−0.906775	−	0.421614i	$-0.861464\pi$
$7$	−2.16559	−	3.75091i	−0.818516	−	1.41771i	0.0882594	−	0.996098i	$-0.471870\pi$
$8$	−2.71156			−0.958681
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	2.51289	+	2.10756i	0.794646	+	0.666469i
$11$	−5.05511	−	2.91857i	−1.52417	−	0.879982i	−0.999590	−	0.0286221i	$-0.990888\pi$
$11$	−5.05511	−	2.91857i	−1.52417	−	0.879982i	−0.524583	−	0.851360i	$-0.675779\pi$
$12$			0.151285i			0.0436723i
$13$	3.21192	+	1.63816i	0.890827	+	0.454343i
$13$	3.21192	+	1.63816i	0.890827	+	0.454343i
$14$	6.35265			1.69782
$15$	−1.43691	+	1.71327i	−0.371010	+	0.442363i
$16$	2.13984	−	3.70631i	0.534960	−	0.926579i
$17$	2.49317	−	1.43943i	0.604682	−	0.349113i	−0.166199	−	0.986092i	$-0.553149\pi$
$17$	2.49317	−	1.43943i	0.604682	−	0.349113i	0.770881	+	0.636979i	$0.219816\pi$
$18$	−1.46673			−0.345711
$19$	2.89056	−	1.66887i	0.663141	−	0.382864i	−0.130332	−	0.991470i	$-0.541604\pi$
$19$	2.89056	−	1.66887i	0.663141	−	0.382864i	0.793473	+	0.608606i	$0.208271\pi$
$20$	−0.317856	+	0.115775i	−0.0710747	+	0.0258880i
$21$			4.33118i			0.945141i
$22$	7.41446	−	4.28074i	1.58077	−	0.912657i
$23$	−1.07921	−	0.623084i	−0.225031	−	0.129922i	0.383246	−	0.923646i	$-0.374806\pi$
$23$	−1.07921	−	0.623084i	−0.225031	−	0.129922i	−0.608278	+	0.793724i	$0.708139\pi$
$24$	2.34828	+	1.35578i	0.479340	+	0.276747i
$25$	−4.69927	−	1.70789i	−0.939853	−	0.341578i
$26$	−4.43633	+	2.87849i	−0.870035	+	0.564518i
$27$		−	1.00000i		−	0.192450i
$28$	−0.327622	+	0.567457i	−0.0619147	+	0.107239i
$29$	−2.86622	+	4.96444i	−0.532243	+	0.921873i	0.467048	+	0.884232i	$0.345318\pi$
$29$	−2.86622	+	4.96444i	−0.532243	+	0.921873i	−0.999291	+	0.0376406i	$0.988016\pi$
$30$	−1.12245	−	3.08164i	−0.204930	−	0.562629i
$31$			0.880021i			0.158056i	0.996872	+	0.0790282i	$0.0251817\pi$
$31$			0.880021i			0.158056i	−0.996872	+	0.0790282i	$0.974818\pi$
$32$	0.427003	+	0.739591i	0.0754842	+	0.130742i
$33$	2.91857	+	5.05511i	0.508058	+	0.879982i
$34$			4.22250i			0.724153i
$35$	−9.09997	+	3.31454i	−1.53818	+	0.560260i
$36$	0.0756426	−	0.131017i	0.0126071	−	0.0218361i
$37$	−0.0960639	+	0.166388i	−0.0157928	+	0.0273539i	−0.873814	−	0.486261i	$-0.838361\pi$
$37$	−0.0960639	+	0.166388i	−0.0157928	+	0.0273539i	0.858021	+	0.513615i	$0.171694\pi$
$38$			4.89554i			0.794162i
$39$	−1.96253	−	3.02465i	−0.314256	−	0.484331i
$40$	−1.05146	+	5.97136i	−0.166251	+	0.944155i
$41$	0.198375	+	0.114532i	0.0309809	+	0.0178868i	0.515410	−	0.856943i	$-0.327639\pi$
$41$	0.198375	+	0.114532i	0.0309809	+	0.0178868i	−0.484430	+	0.874830i	$0.660973\pi$
$42$	−5.50156	−	3.17633i	−0.848909	−	0.490118i
$43$	4.27940	−	2.47071i	0.652602	−	0.376780i	−0.136850	−	0.990592i	$-0.543698\pi$
$43$	4.27940	−	2.47071i	0.652602	−	0.376780i	0.789452	+	0.613812i	$0.210365\pi$
$44$			0.883072i			0.133128i
$45$	2.10104	−	0.765275i	0.313204	−	0.114080i
$46$	1.58291	−	0.913893i	0.233387	−	0.134746i
$47$	−0.0904255			−0.0131899			−0.00659495	−	0.999978i	$-0.502099\pi$
$47$	−0.0904255			−0.0131899			−0.00659495	+	0.999978i	$0.502099\pi$
$48$	−3.70631	+	2.13984i	−0.534960	+	0.308860i
$49$	−5.87956	+	10.1837i	−0.839937	+	1.45481i
$50$	5.61567	−	4.71661i	0.794175	−	0.667029i
$51$	−2.87886			−0.403121
$52$	−0.0283319	−	0.544730i	−0.00392893	−	0.0755405i
$53$		−	4.46001i		−	0.612630i	−0.951930	−	0.306315i	$-0.900904\pi$
$53$		−	4.46001i		−	0.612630i	0.951930	−	0.306315i	$-0.0990961\pi$
$54$	1.27022	+	0.733363i	0.172855	+	0.0997981i
$55$	−8.38746	+	10.0006i	−1.13097	+	1.34848i
$56$	5.87212	+	10.1708i	0.784695	+	1.35913i
$57$	−3.33774			−0.442094
$58$	−4.20396	−	7.28147i	−0.552007	−	0.956103i
$59$	6.48915	−	3.74651i	0.844815	−	0.487754i	−0.0140831	−	0.999901i	$-0.504483\pi$
$59$	6.48915	−	3.74651i	0.844815	−	0.487754i	0.858898	+	0.512147i	$0.171150\pi$
$60$	0.333158	+	0.0586640i	0.0430106	+	0.00757349i
$61$	−6.78634	−	11.7543i	−0.868902	−	1.50498i	−0.863120	−	0.504999i	$-0.831493\pi$
$61$	−6.78634	−	11.7543i	−0.868902	−	1.50498i	−0.00578155	−	0.999983i	$-0.501840\pi$
$62$	−1.11782	−	0.645375i	−0.141963	−	0.0819627i
$63$	2.16559	−	3.75091i	0.272839	−	0.472570i
$64$	7.30677			0.913347
$65$	4.85302	−	6.43803i	0.601943	−	0.798539i
$66$	−8.56148			−1.05385
$67$	−3.73475	+	6.46878i	−0.456273	+	0.790287i	−0.998760	−	0.0497763i	$-0.984149\pi$
$67$	−3.73475	+	6.46878i	−0.456273	+	0.790287i	0.542488	+	0.840064i	$0.317482\pi$
$68$	−0.377179	−	0.217765i	−0.0457397	−	0.0264078i
$69$	0.623084	+	1.07921i	0.0750105	+	0.129922i
$70$	2.46337	−	13.9897i	0.294430	−	1.67209i
$71$	3.08252	−	1.77969i	0.365828	−	0.211211i	−0.305806	−	0.952094i	$-0.598926\pi$
$71$	3.08252	−	1.77969i	0.365828	−	0.211211i	0.671634	+	0.740883i	$0.265593\pi$
$72$	−1.35578	−	2.34828i	−0.159780	−	0.276747i
$73$	−8.62359			−1.00931			−0.504657	−	0.863320i	$-0.668381\pi$
$73$	−8.62359			−1.00931			−0.504657	+	0.863320i	$0.668381\pi$
$74$	−0.140899	−	0.244045i	−0.0163792	−	0.0283696i
$75$	3.21574	+	3.82871i	0.371322	+	0.442101i
$76$	−0.437299	−	0.252475i	−0.0501617	−	0.0289609i
$77$			25.2817i			2.88112i
$78$	5.28122	−	0.274681i	0.597980	−	0.0311015i
$79$	6.75912			0.760460			0.380230	−	0.924892i	$-0.375845\pi$
$79$	6.75912			0.760460			0.380230	+	0.924892i	$0.375845\pi$
$80$	−7.33223	−	6.14954i	−0.819769	−	0.687539i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.290961	+	0.167987i	−0.0321313	+	0.0185510i
$83$	9.36059			1.02746			0.513729	−	0.857953i	$-0.328264\pi$
$83$	9.36059			1.02746			0.513729	+	0.857953i	$0.328264\pi$
$84$	0.567457	−	0.327622i	0.0619147	−	0.0357464i
$85$	−2.20312	−	6.04859i	−0.238962	−	0.656062i
$86$			7.24771i			0.781541i
$87$	4.96444	−	2.86622i	0.532243	−	0.307291i
$88$	13.7072	+	7.91387i	1.46119	+	0.843621i
$89$	13.1729	+	7.60535i	1.39632	+	0.806166i	0.994005	−	0.109335i	$-0.0348722\pi$
$89$	13.1729	+	7.60535i	1.39632	+	0.806166i	0.402315	+	0.915501i	$0.368205\pi$
$90$	−0.568754	+	3.23001i	−0.0599519	+	0.340473i
$91$	−0.811121	−	15.5952i	−0.0850286	−	1.63482i
$92$			0.188527i			0.0196553i
$93$	0.440010	−	0.762120i	0.0456269	−	0.0790282i
$94$	0.0663147	−	0.114860i	0.00683984	−	0.0118469i
$95$	−2.55428	−	7.01270i	−0.262064	−	0.719488i
$96$		−	0.854006i		−	0.0871616i
$97$	−0.762993	−	1.32154i	−0.0774702	−	0.134182i	0.824688	−	0.565588i	$-0.191351\pi$
$97$	−0.762993	−	1.32154i	−0.0774702	−	0.134182i	−0.902158	+	0.431406i	$0.858018\pi$
$98$	−8.62370	−	14.9367i	−0.871125	−	1.50883i
$99$		−	5.83714i		−	0.586654i
$100$	0.131703	+	0.744872i	0.0131703	+	0.0744872i
$101$	8.70020	−	15.0692i	0.865703	−	1.49944i	−0.000645396	−	1.00000i	$-0.500205\pi$
$101$	8.70020	−	15.0692i	0.865703	−	1.49944i	0.866348	−	0.499441i	$-0.166461\pi$
$102$	2.11125	−	3.65679i	0.209045	−	0.362077i
$103$			9.01269i			0.888046i	0.896015	+	0.444023i	$0.146449\pi$
$103$			9.01269i			0.888046i	−0.896015	+	0.444023i	$0.853551\pi$
$104$	−8.70931	−	4.44196i	−0.854018	−	0.435570i
$105$	9.53807	+	1.67951i	0.930821	+	0.163903i
$106$	5.66521	+	3.27081i	0.550254	+	0.317689i
$107$	2.57834	+	1.48861i	0.249258	+	0.143909i	0.619424	−	0.785056i	$-0.287366\pi$
$107$	2.57834	+	1.48861i	0.249258	+	0.143909i	−0.370167	+	0.928965i	$0.620699\pi$
$108$	−0.131017	+	0.0756426i	−0.0126071	+	0.00727871i
$109$		−	1.50275i		−	0.143938i	−0.997407	−	0.0719689i	$-0.977072\pi$
$109$		−	1.50275i		−	0.143938i	0.997407	−	0.0719689i	$-0.0229282\pi$
$110$	−6.55189	−	17.9880i	−0.624698	−	1.71509i
$111$	0.166388	−	0.0960639i	0.0157928	−	0.00911798i
$112$	−18.5361			−1.75149
$113$	13.2825	−	7.66865i	1.24951	−	0.721406i	0.278500	−	0.960436i	$-0.410163\pi$
$113$	13.2825	−	7.66865i	1.24951	−	0.721406i	0.971012	+	0.239030i	$0.0768296\pi$
$114$	2.44777	−	4.23966i	0.229255	−	0.397081i
$115$	−1.79063	+	2.13502i	−0.166978	+	0.199091i
$116$	0.867233			0.0805205
$117$	0.187275	+	3.60068i	0.0173136	+	0.332883i
$118$			10.9902i			1.01173i
$119$	−10.7984	−	6.23444i	−0.989884	−	0.571510i
$120$	3.89627	−	4.64562i	0.355680	−	0.424085i
$121$	11.5361	+	19.9811i	1.04874	+	1.81646i
$122$	19.9074			1.80233
$123$	−0.114532	−	0.198375i	−0.0103270	−	0.0178868i
$124$	0.115297	−	0.0665670i	0.0103540	−	0.00597790i
$125$	−5.58333	+	9.68640i	−0.499389	+	0.866378i
$126$	3.17633	+	5.50156i	0.282970	+	0.490118i
$127$	−3.45359	−	1.99393i	−0.306457	−	0.176933i	0.338883	−	0.940829i	$-0.389951\pi$
$127$	−3.45359	−	1.99393i	−0.306457	−	0.176933i	−0.645340	+	0.763896i	$0.723284\pi$
$128$	−6.21252	+	10.7604i	−0.549115	+	0.951094i
$129$	−4.94142			−0.435068
$130$	4.61870	+	10.8858i	0.405087	+	0.954750i
$131$	−13.1554			−1.14939			−0.574697	−	0.818366i	$-0.694880\pi$
$131$	−13.1554			−1.14939			−0.574697	+	0.818366i	$0.694880\pi$
$132$	0.441536	−	0.764763i	0.0384308	−	0.0665641i
$133$	−12.5196	−	7.22817i	−1.08558	−	0.626761i
$134$	−5.47786	−	9.48793i	−0.473215	−	0.819632i
$135$	−2.20219	−	0.387771i	−0.189534	−	0.0333740i
$136$	−6.76037	+	3.90310i	−0.579697	+	0.334688i
$137$	5.60578	+	9.70950i	0.478934	+	0.829539i	0.999708	−	0.0241559i	$-0.00768982\pi$
$137$	5.60578	+	9.70950i	0.478934	+	0.829539i	−0.520774	+	0.853695i	$0.674356\pi$
$138$	−1.82779			−0.155591
$139$	2.96644	+	5.13802i	0.251610	+	0.435801i	0.963969	−	0.266014i	$-0.0857066\pi$
$139$	2.96644	+	5.13802i	0.251610	+	0.435801i	−0.712359	+	0.701815i	$0.752373\pi$
$140$	1.12261	+	0.941528i	0.0948775	+	0.0795736i
$141$	0.0783107	+	0.0452127i	0.00659495	+	0.00380760i
$142$			5.22065i			0.438107i
$143$	−11.4555	−	17.6553i	−0.957960	−	1.47641i
$144$	4.27968			0.356640
$145$	9.82119	+	8.23702i	0.815605	+	0.684047i
$146$	6.32422	−	10.9539i	0.523396	−	0.906549i
$147$	10.1837	−	5.87956i	0.839937	−	0.484938i
$148$	0.0290661			0.00238922
$149$	−3.69486	+	2.13323i	−0.302695	+	0.174761i	−0.643653	−	0.765318i	$-0.722582\pi$
$149$	−3.69486	+	2.13323i	−0.302695	+	0.174761i	0.340958	+	0.940078i	$0.389249\pi$
$150$	−7.22162	+	1.27687i	−0.589642	+	0.104256i
$151$		−	14.1907i		−	1.15483i	−0.816452	−	0.577413i	$-0.804062\pi$
$151$		−	14.1907i		−	1.15483i	0.816452	−	0.577413i	$-0.195938\pi$
$152$	−7.83793	+	4.52523i	−0.635740	+	0.367045i
$153$	2.49317	+	1.43943i	0.201561	+	0.116371i
$154$	−32.1134	−	18.5407i	−2.58777	−	1.49405i
$155$	1.93797	+	0.341246i	0.155662	+	0.0274096i
$156$	−0.247829	+	0.485916i	−0.0198422	+	0.0389044i
$157$		−	20.9096i		−	1.66877i	−0.551185	−	0.834383i	$-0.685824\pi$
$157$		−	20.9096i		−	1.66877i	0.551185	−	0.834383i	$-0.314176\pi$
$158$	−4.95689	+	8.58558i	−0.394349	+	0.683032i
$159$	−2.23001	+	3.86249i	−0.176851	+	0.306315i
$160$	1.79430	−	0.653549i	0.141852	−	0.0516676i
$161$			5.39737i			0.425373i
$162$	−0.733363	−	1.27022i	−0.0576184	−	0.0997981i
$163$	−3.44348	−	5.96428i	−0.269714	−	0.467159i	0.699074	−	0.715049i	$-0.253596\pi$
$163$	−3.44348	−	5.96428i	−0.269714	−	0.467159i	−0.968788	+	0.247891i	$0.920263\pi$
$164$		−	0.0346539i		−	0.00270601i
$165$	12.2640	−	4.46701i	0.954754	−	0.347757i
$166$	−6.86471	+	11.8900i	−0.532805	+	0.922845i
$167$	−4.09004	+	7.08416i	−0.316497	+	0.548188i	−0.979755	−	0.200203i	$-0.935840\pi$
$167$	−4.09004	+	7.08416i	−0.316497	+	0.548188i	0.663258	+	0.748391i	$0.269173\pi$
$168$		−	11.7442i		−	0.906088i
$169$	7.63288	+	10.5233i	0.587145	+	0.809482i
$170$	9.29875	+	1.63736i	0.713181	+	0.125580i
$171$	2.89056	+	1.66887i	0.221047	+	0.127621i
$172$	−0.647409	−	0.373782i	−0.0493645	−	0.0285006i
$173$	−7.18337	+	4.14732i	−0.546141	+	0.315315i	−0.747564	−	0.664189i	$-0.768777\pi$
$173$	−7.18337	+	4.14732i	−0.546141	+	0.315315i	0.201423	+	0.979504i	$0.435443\pi$
$174$			8.40791i			0.637402i
$175$	3.77054	+	21.3251i	0.285026	+	1.61203i
$176$	−21.6343	+	12.4906i	−1.63074	+	0.941511i
$177$	−7.49302			−0.563210
$178$	−19.3210	+	11.1550i	−1.44817	+	0.836100i
$179$	−1.49417	+	2.58798i	−0.111680	+	0.193435i	−0.916448	−	0.400155i	$-0.868956\pi$
$179$	−1.49417	+	2.58798i	−0.111680	+	0.193435i	0.804768	+	0.593590i	$0.202290\pi$
$180$	−0.259192	−	0.217384i	−0.0193190	−	0.0162028i
$181$	18.9713			1.41013			0.705063	−	0.709145i	$-0.250919\pi$
$181$	18.9713			1.41013			0.705063	+	0.709145i	$0.250919\pi$
$182$	20.4042	+	10.4066i	1.51246	+	0.771392i
$183$			13.5727i			1.00332i
$184$	2.92635	+	1.68953i	0.215733	+	0.124554i
$185$	0.329166	+	0.276071i	0.0242008	+	0.0202971i
$186$	0.645375	+	1.11782i	0.0473212	+	0.0819627i
$187$	−16.8043			−1.22885
$188$	0.00684001	+	0.0118473i	0.000498859	+	0.000864050i
$189$	−3.75091	+	2.16559i	−0.272839	+	0.157523i
$190$	10.7809	+	1.89835i	0.782129	+	0.137721i
$191$	7.97149	+	13.8070i	0.576797	+	0.999042i	0.995844	+	0.0910770i	$0.0290309\pi$
$191$	7.97149	+	13.8070i	0.576797	+	0.999042i	−0.419047	+	0.907965i	$0.637636\pi$
$192$	−6.32785	−	3.65339i	−0.456673	−	0.263660i
$193$	9.66985	−	16.7487i	0.696051	−	1.20560i	−0.273774	−	0.961794i	$-0.588272\pi$
$193$	9.66985	−	16.7487i	0.696051	−	1.20560i	0.969825	−	0.243802i	$-0.0783947\pi$
$194$	2.23820			0.160694
$195$	−7.42185	+	3.14898i	−0.531490	+	0.225503i
$196$	1.77898			0.127070
$197$	7.32341	−	12.6845i	0.521771	−	0.903735i	−0.477908	−	0.878410i	$-0.658605\pi$
$197$	7.32341	−	12.6845i	0.521771	−	0.903735i	0.999679	−	0.0253246i	$-0.00806192\pi$
$198$	7.41446	+	4.28074i	0.526923	+	0.304219i
$199$	−7.56087	−	13.0958i	−0.535976	−	0.928338i	−0.999115	−	0.0420522i	$-0.986610\pi$
$199$	−7.56087	−	13.0958i	−0.535976	−	0.928338i	0.463139	−	0.886285i	$-0.346723\pi$
$200$	12.7423	+	4.63104i	0.901019	+	0.327464i
$201$	6.46878	−	3.73475i	0.456273	−	0.263429i
$202$	12.7608	+	22.1024i	0.897848	+	1.55512i
$203$	24.8282			1.74260
$204$	0.217765	+	0.377179i	0.0152466	+	0.0264078i
$205$	0.329144	−	0.392446i	0.0229884	−	0.0274096i
$206$	−11.4481	−	6.60957i	−0.797628	−	0.460511i
$207$		−	1.24617i		−	0.0866146i
$208$	12.9445	−	8.39899i	0.897542	−	0.582365i
$209$	−19.4828			−1.34765
$210$	−9.12822	+	10.8838i	−0.629907	+	0.751052i
$211$	0.677150	−	1.17286i	0.0466169	−	0.0807429i	−0.841775	−	0.539828i	$-0.818489\pi$
$211$	0.677150	−	1.17286i	0.0466169	−	0.0807429i	0.888392	+	0.459085i	$0.151823\pi$
$212$	−0.584337	+	0.337367i	−0.0401324	+	0.0231705i
$213$	−3.55939			−0.243885
$214$	−3.78172	+	2.18338i	−0.258513	+	0.149253i
$215$	−3.78155	−	10.3821i	−0.257899	−	0.708054i
$216$			2.71156i			0.184498i
$217$	3.30088	−	1.90576i	0.224078	−	0.129372i
$218$	1.90883	+	1.10206i	0.129282	+	0.0746412i
$219$	7.46825	+	4.31179i	0.504657	+	0.291364i
$220$	1.94469	+	0.342430i	0.131111	+	0.0230866i
$221$	10.3659	−	0.539139i	0.697284	−	0.0362664i
$222$			0.281799i			0.0189131i
$223$	−9.94117	+	17.2186i	−0.665710	+	1.15304i	0.313382	+	0.949627i	$0.398538\pi$
$223$	−9.94117	+	17.2186i	−0.665710	+	1.15304i	−0.979092	+	0.203417i	$0.934795\pi$
$224$	1.84943	−	3.20330i	0.123570	−	0.214030i
$225$	−0.870558	−	4.92363i	−0.0580372	−	0.328242i
$226$			22.4956i			1.49639i
$227$	−7.13414	−	12.3567i	−0.473510	−	0.820143i	0.526030	−	0.850466i	$-0.323680\pi$
$227$	−7.13414	−	12.3567i	−0.473510	−	0.820143i	−0.999540	+	0.0303227i	$0.990346\pi$
$228$	0.252475	+	0.437299i	0.0167206	+	0.0289609i
$229$		−	20.1823i		−	1.33369i	−0.745198	−	0.666844i	$-0.767645\pi$
$229$		−	20.1823i		−	1.33369i	0.745198	−	0.666844i	$-0.232355\pi$
$230$	−1.39876	−	3.84024i	−0.0922314	−	0.253218i
$231$	12.6408	−	21.8946i	0.831707	−	1.44056i
$232$	7.77192	−	13.4614i	0.510251	−	0.883781i
$233$			14.4799i			0.948609i	0.880361	+	0.474304i	$0.157300\pi$
$233$			14.4799i			0.948609i	−0.880361	+	0.474304i	$0.842700\pi$
$234$	−4.71101	−	2.40273i	−0.307968	−	0.157071i
$235$	−0.0350644	+	0.199134i	−0.00228735	+	0.0129901i
$236$	−0.981712	−	0.566791i	−0.0639040	−	0.0368950i
$237$	−5.85357	−	3.37956i	−0.380230	−	0.219526i
$238$	15.8382	−	9.14421i	1.02664	−	0.592731i
$239$		−	0.961764i		−	0.0622113i	−0.999516	−	0.0311057i	$-0.990097\pi$
$239$		−	0.961764i		−	0.0622113i	0.999516	−	0.0311057i	$-0.00990284\pi$
$240$	3.27513	+	8.99177i	0.211409	+	0.580416i
$241$	−19.0818	+	11.0169i	−1.22917	+	0.709661i	−0.966856	−	0.255322i	$-0.917819\pi$
$241$	−19.0818	+	11.0169i	−1.22917	+	0.709661i	−0.262313	+	0.964983i	$0.584485\pi$
$242$	−33.8406			−2.17535
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−1.02667	+	1.77825i	−0.0657260	+	0.113841i
$245$	20.1465	+	16.8968i	1.28711	+	1.07950i
$246$	0.335973			0.0214209
$247$	12.0181	−	0.625074i	0.764695	−	0.0397725i
$248$		−	2.38623i		−	0.151526i
$249$	−8.10651	−	4.68029i	−0.513729	−	0.296602i
$250$	−8.20927	−	14.1957i	−0.519200	−	0.897816i
$251$	−2.76328	−	4.78614i	−0.174417	−	0.302098i	0.765543	−	0.643385i	$-0.222471\pi$
$251$	−2.76328	−	4.78614i	−0.174417	−	0.302098i	−0.939959	+	0.341287i	$0.889137\pi$
$252$	−0.655243			−0.0412764
$253$	3.63702	+	6.29951i	0.228658	+	0.396047i
$254$	5.06548	−	2.92455i	0.317836	−	0.183503i
$255$	−1.11634	+	6.33980i	−0.0699079	+	0.397013i
$256$	−1.80530	−	3.12686i	−0.112831	−	0.195429i
$257$	−5.62684	−	3.24866i	−0.350993	−	0.202646i	0.314130	−	0.949380i	$-0.398287\pi$
$257$	−5.62684	−	3.24866i	−0.350993	−	0.202646i	−0.665122	+	0.746734i	$0.731621\pi$
$258$	3.62386	−	6.27671i	0.225612	−	0.390771i
$259$	0.832140			0.0517067
$260$	−1.21058	−	0.148838i	−0.0750773	−	0.00923056i
$261$	−5.73244			−0.354829
$262$	9.64770	−	16.7103i	0.596037	−	1.03237i
$263$	−15.7767	−	9.10870i	−0.972835	−	0.561666i	−0.0727356	−	0.997351i	$-0.523173\pi$
$263$	−15.7767	−	9.10870i	−0.972835	−	0.561666i	−0.900099	+	0.435685i	$0.856506\pi$
$264$	−7.91387	−	13.7072i	−0.487065	−	0.843621i
$265$	−9.82179	−	1.72946i	−0.603348	−	0.106240i
$266$	18.3627	−	10.6017i	1.12589	−	0.650034i
$267$	−7.60535	−	13.1729i	−0.465440	−	0.806166i
$268$	1.13003			0.0690273
$269$	2.00971	+	3.48092i	0.122534	+	0.212235i	0.920766	−	0.390114i	$-0.127565\pi$
$269$	2.00971	+	3.48092i	0.122534	+	0.212235i	−0.798232	+	0.602350i	$0.794231\pi$
$270$	2.10756	−	2.51289i	0.128262	−	0.152930i
$271$	−2.85930	−	1.65082i	−0.173690	−	0.100280i	0.410635	−	0.911800i	$-0.365307\pi$
$271$	−2.85930	−	1.65082i	−0.173690	−	0.100280i	−0.584325	+	0.811520i	$0.698641\pi$
$272$		−	12.3206i		−	0.747047i
$273$	−7.09515	+	13.9114i	−0.429418	+	0.841957i
$274$	−16.4443			−0.993436
$275$	18.7707	+	22.3487i	1.13192	+	1.34768i
$276$	0.0942633	−	0.163269i	0.00567398	−	0.00982763i
$277$	13.4191	−	7.74754i	0.806277	−	0.465505i	−0.0393840	−	0.999224i	$-0.512540\pi$
$277$	13.4191	−	7.74754i	0.806277	−	0.465505i	0.845661	+	0.533720i	$0.179206\pi$
$278$	−8.70191			−0.521906
$279$	−0.762120	+	0.440010i	−0.0456269	+	0.0263427i
$280$	24.6751	−	8.98757i	1.47462	−	0.537110i
$281$		−	12.0808i		−	0.720678i	−0.932822	−	0.360339i	$-0.882661\pi$
$281$		−	12.0808i		−	0.720678i	0.932822	−	0.360339i	$-0.117339\pi$
$282$	−0.114860	+	0.0663147i	−0.00683984	+	0.00394898i
$283$	3.82453	+	2.20809i	0.227345	+	0.131257i	0.609346	−	0.792904i	$-0.291432\pi$
$283$	3.82453	+	2.20809i	0.227345	+	0.131257i	−0.382002	+	0.924162i	$0.624765\pi$
$284$	−0.466340	−	0.269241i	−0.0276722	−	0.0159765i
$285$	−1.29428	+	7.35032i	−0.0766663	+	0.435395i
$286$	30.8272	−	1.60335i	1.82285	−	0.0948081i
$287$		−	0.992115i		−	0.0585627i
$288$	−0.427003	+	0.739591i	−0.0251614	+	0.0435808i
$289$	−4.35608	+	7.54494i	−0.256240	+	0.443820i
$290$	−17.6653	+	6.43436i	−1.03734	+	0.377839i
$291$			1.52599i			0.0894549i
$292$	0.652310	+	1.12983i	0.0381736	+	0.0661186i
$293$	2.87502	+	4.97968i	0.167960	+	0.290916i	0.937703	−	0.347439i	$-0.112949\pi$
$293$	2.87502	+	4.97968i	0.167960	+	0.290916i	−0.769742	+	0.638355i	$0.779615\pi$
$294$			17.2474i			1.00589i
$295$	−5.73422	−	15.7431i	−0.333859	−	0.916599i
$296$	0.260483	−	0.451169i	0.0151403	−	0.0262237i
$297$	−2.91857	+	5.05511i	−0.169353	+	0.293327i
$298$		−	6.25772i		−	0.362500i
$299$	−2.44564	−	3.76922i	−0.141435	−	0.217979i
$300$	0.258378	−	0.710929i	0.0149175	−	0.0410455i
$301$	−18.5348	−	10.7011i	−1.06833	−	0.616801i
$302$	18.0254	+	10.4070i	1.03724	+	0.598853i
$303$	−15.0692	+	8.70020i	−0.865703	+	0.499814i
$304$		−	14.2844i		−	0.819269i
$305$	−28.5167	+	10.3868i	−1.63286	+	0.594748i
$306$	−3.65679	+	2.11125i	−0.209045	+	0.120692i
$307$	−11.0611			−0.631290			−0.315645	−	0.948877i	$-0.602221\pi$
$307$	−11.0611			−0.631290			−0.315645	+	0.948877i	$0.602221\pi$
$308$	3.31233	−	1.91237i	0.188737	−	0.108968i
$309$	4.50634	−	7.80522i	0.256357	−	0.444023i
$310$	−1.85470	+	2.21140i	−0.105340	+	0.125599i
$311$	21.9430			1.24427			0.622136	−	0.782909i	$-0.286265\pi$
$311$	21.9430			1.24427			0.622136	+	0.782909i	$0.286265\pi$
$312$	5.32151	+	8.20151i	0.301271	+	0.464319i
$313$			18.5304i			1.04740i	0.851903	+	0.523699i	$0.175448\pi$
$313$			18.5304i			1.04740i	−0.851903	+	0.523699i	$0.824552\pi$
$314$	26.5598	+	15.3343i	1.49886	+	0.865366i
$315$	−7.42046	−	6.22353i	−0.418096	−	0.350656i
$316$	−0.511277	−	0.885558i	−0.0287616	−	0.0498165i
$317$	4.17176			0.234309			0.117155	−	0.993114i	$-0.462623\pi$
$317$	4.17176			0.234309			0.117155	+	0.993114i	$0.462623\pi$
$318$	−3.27081	−	5.66521i	−0.183418	−	0.317689i
$319$	28.9781	−	16.7305i	1.62246	−	0.936729i
$320$	2.83335	−	16.0909i	0.158389	−	0.899508i
$321$	−1.48861	−	2.57834i	−0.0830858	−	0.143909i
$322$	−6.85586	−	3.95823i	−0.382062	−	0.220584i
$323$	4.80444	−	8.32153i	0.267326	−	0.463023i
$324$	0.151285			0.00840473
$325$	−12.2959	−	13.1837i	−0.682053	−	0.731303i
$326$	10.1013			0.559458
$327$	−0.751377	+	1.30142i	−0.0415512	+	0.0719689i
$328$	−0.537905	−	0.310559i	−0.0297008	−	0.0171478i
$329$	0.195824	+	0.339178i	0.0107962	+	0.0186995i
$330$	−3.31989	+	18.8540i	−0.182754	+	1.03788i
$331$	−27.0983	+	15.6452i	−1.48946	+	0.859939i	−0.999927	−	0.0120465i	$-0.996165\pi$
$331$	−27.0983	+	15.6452i	−1.48946	+	0.859939i	−0.489531	+	0.871986i	$0.662832\pi$
$332$	−0.708059	−	1.22639i	−0.0388598	−	0.0673071i
$333$	−0.192128			−0.0105285
$334$	−5.99897	−	10.3905i	−0.328249	−	0.568544i
$335$	12.7972	+	10.7330i	0.699188	+	0.586408i
$336$	16.0527	+	9.26804i	0.875747	+	0.505613i
$337$		−	21.2476i		−	1.15743i	−0.815529	−	0.578716i	$-0.803554\pi$
$337$		−	21.2476i		−	1.15743i	0.815529	−	0.578716i	$-0.196446\pi$
$338$	−18.9646	+	1.97808i	−1.03154	+	0.107593i
$339$	−15.3373			−0.833008
$340$	−0.625818	+	0.746177i	−0.0339397	+	0.0404671i
$341$	2.56840	−	4.44860i	0.139087	−	0.240905i
$342$	−4.23966	+	2.44777i	−0.229255	+	0.132360i
$343$	20.6126			1.11298
$344$	−11.6038	+	6.69948i	−0.625637	+	0.361212i
$345$	2.61824	−	0.953660i	0.140961	−	0.0513433i
$346$		−	12.1660i		−	0.654046i
$347$	7.22712	−	4.17258i	0.387972	−	0.223996i	−0.293309	−	0.956018i	$-0.594757\pi$
$347$	7.22712	−	4.17258i	0.387972	−	0.223996i	0.681281	+	0.732022i	$0.261423\pi$
$348$	−0.751045	−	0.433616i	−0.0402603	−	0.0232443i
$349$	9.46216	+	5.46298i	0.506498	+	0.292427i	0.731393	−	0.681956i	$-0.238871\pi$
$349$	9.46216	+	5.46298i	0.506498	+	0.292427i	−0.224895	+	0.974383i	$0.572204\pi$
$350$	−29.8528	−	10.8496i	−1.59570	−	0.579937i
$351$	1.63816	−	3.21192i	0.0874384	−	0.171440i
$352$		−	4.98495i		−	0.265699i
$353$	3.29579	−	5.70847i	0.175417	−	0.303831i	−0.764888	−	0.644163i	$-0.777206\pi$
$353$	3.29579	−	5.70847i	0.175417	−	0.303831i	0.940306	+	0.340332i	$0.110539\pi$
$354$	5.49510	−	9.51780i	0.292061	−	0.505865i
$355$	−2.72391	−	7.47841i	−0.144570	−	0.396913i
$356$		−	2.30115i		−	0.121961i
$357$	6.23444	+	10.7984i	0.329961	+	0.571510i
$358$	−2.19154	−	3.79586i	−0.115827	−	0.200618i
$359$		−	4.55712i		−	0.240516i	−0.992743	−	0.120258i	$-0.961628\pi$
$359$		−	4.55712i		−	0.240516i	0.992743	−	0.120258i	$-0.0383721\pi$
$360$	−5.69708	+	2.07509i	−0.300263	+	0.109367i
$361$	−3.92976	+	6.80655i	−0.206830	+	0.358239i
$362$	−13.9129	+	24.0978i	−0.731243	+	1.26655i
$363$		−	23.0722i		−	1.21098i
$364$	−1.98188	+	1.28593i	−0.103879	+	0.0674012i
$365$	−3.34398	+	18.9908i	−0.175032	+	0.994022i
$366$	−17.2403	−	9.95370i	−0.901166	−	0.520288i
$367$	32.3010	+	18.6490i	1.68610	+	0.973469i	0.957459	+	0.288570i	$0.0931798\pi$
$367$	32.3010	+	18.6490i	1.68610	+	0.973469i	0.728638	+	0.684899i	$0.240153\pi$
$368$	−4.61869	+	2.66660i	−0.240766	+	0.139006i
$369$			0.229063i			0.0119246i
$370$	−0.592070	+	0.215654i	−0.0307802	+	0.0112113i
$371$	−16.7291	+	9.65856i	−0.868533	+	0.501448i
$372$	−0.133134			−0.00690268
$373$	18.5388	−	10.7034i	0.959902	−	0.554200i	0.0637593	−	0.997965i	$-0.479691\pi$
$373$	18.5388	−	10.7034i	0.959902	−	0.554200i	0.896143	+	0.443766i	$0.146358\pi$
$374$	12.3237	−	21.3452i	0.637241	−	1.10373i
$375$	9.67851	−	5.59700i	0.499796	−	0.289028i
$376$	0.245194			0.0126449
$377$	−17.3386	+	11.2501i	−0.892983	+	0.579408i
$378$		−	6.35265i		−	0.326745i
$379$	21.1680	+	12.2214i	1.08733	+	0.627769i	0.932864	−	0.360230i	$-0.117302\pi$
$379$	21.1680	+	12.2214i	1.08733	+	0.627769i	0.154464	+	0.987998i	$0.450635\pi$
$380$	−0.725569	+	0.865113i	−0.0372209	+	0.0443794i
$381$	1.99393	+	3.45359i	0.102152	+	0.176933i
$382$	−23.3840			−1.19643
$383$	18.4418	+	31.9421i	0.942331	+	1.63217i	0.761008	+	0.648742i	$0.224705\pi$
$383$	18.4418	+	31.9421i	0.942331	+	1.63217i	0.181323	+	0.983424i	$0.441962\pi$
$384$	10.7604	−	6.21252i	0.549115	−	0.317031i
$385$	55.6751	+	9.80351i	2.83746	+	0.499633i
$386$	14.1830	+	24.5657i	0.721897	+	1.25036i
$387$	4.27940	+	2.47071i	0.217534	+	0.125593i
$388$	−0.115429	+	0.199930i	−0.00586004	+	0.0101499i
$389$	−32.2245			−1.63384			−0.816922	−	0.576748i	$-0.804322\pi$
$389$	−32.2245			−1.63384			−0.816922	+	0.576748i	$0.804322\pi$
$390$	1.44300	−	11.7367i	0.0730693	−	0.594313i
$391$	−3.58754			−0.181430
$392$	15.9428	−	27.6137i	0.805231	−	1.39470i
$393$	11.3929	+	6.57771i	0.574697	+	0.331802i
$394$	10.7414	+	18.6047i	0.541146	+	0.937292i
$395$	2.62099	−	14.8849i	0.131876	−	0.748938i
$396$	−0.764763	+	0.441536i	−0.0384308	+	0.0221880i
$397$	0.00651172	+	0.0112786i	0.000326814	+	0.000566058i	0.866189	−	0.499717i	$-0.166563\pi$
$397$	0.00651172	+	0.0112786i	0.000326814	+	0.000566058i	−0.865862	+	0.500283i	$0.833229\pi$
$398$	22.1795			1.11176
$399$	7.22817	+	12.5196i	0.361861	+	0.626761i
$400$	−16.3857	+	13.7623i	−0.819283	+	0.688117i
$401$	8.22918	+	4.75112i	0.410946	+	0.237260i	0.691196	−	0.722667i	$-0.257084\pi$
$401$	8.22918	+	4.75112i	0.410946	+	0.237260i	−0.280250	+	0.959927i	$0.590417\pi$
$402$			10.9557i			0.546421i
$403$	−1.44161	+	2.82656i	−0.0718118	+	0.140801i
$404$	−2.63242			−0.130968
$405$	1.71327	+	1.43691i	0.0851329	+	0.0714008i
$406$	−18.2081	+	31.5373i	−0.903653	+	1.56517i
$407$	0.971227	−	0.560738i	0.0481419	−	0.0277948i
$408$	7.80620			0.386465
$409$	−21.7452	+	12.5546i	−1.07523	+	0.620785i	−0.929606	−	0.368554i	$-0.879853\pi$
$409$	−21.7452	+	12.5546i	−1.07523	+	0.620785i	−0.145626	+	0.989340i	$0.546519\pi$
$410$	0.257112	+	0.705892i	0.0126978	+	0.0348615i
$411$		−	11.2116i		−	0.553026i
$412$	1.18081	−	0.681743i	0.0581745	−	0.0335871i
$413$	−28.1057	−	16.2268i	−1.38299	−	0.798469i
$414$	1.58291	+	0.913893i	0.0777957	+	0.0449154i
$415$	3.62976	−	20.6138i	0.178178	−	1.01189i
$416$	0.159934	+	3.07501i	0.00784141	+	0.150765i
$417$		−	5.93288i		−	0.290534i
$418$	14.2880	−	24.7475i	0.698848	−	1.21044i
$419$	−4.23799	+	7.34042i	−0.207039	+	0.358603i	−0.950781	−	0.309865i	$-0.899716\pi$
$419$	−4.23799	+	7.34042i	−0.207039	+	0.358603i	0.743741	+	0.668468i	$0.233050\pi$
$420$	−0.501441	−	1.37669i	−0.0244678	−	0.0671756i
$421$		−	7.41306i		−	0.361290i	−0.983548	−	0.180645i	$-0.942181\pi$
$421$		−	7.41306i		−	0.361290i	0.983548	−	0.180645i	$-0.0578185\pi$
$422$	0.993193	+	1.72026i	0.0483479	+	0.0837410i
$423$	−0.0452127	−	0.0783107i	−0.00219832	−	0.00380760i
$424$			12.0936i			0.587317i
$425$	−14.1745	+	2.50622i	−0.687562	+	0.121569i
$426$	2.61032	−	4.52121i	0.126471	−	0.219054i
$427$	−29.3929	+	50.9099i	−1.42242	+	2.46370i
$428$		−	0.450408i		−	0.0217713i
$429$	1.09315	+	21.0177i	0.0527778	+	1.01474i
$430$	15.9608	+	2.81045i	0.769700	+	0.135532i
$431$	−28.6049	−	16.5150i	−1.37785	−	0.795502i	−0.385949	−	0.922520i	$-0.626126\pi$
$431$	−28.6049	−	16.5150i	−1.37785	−	0.795502i	−0.991900	+	0.127018i	$0.959459\pi$
$432$	−3.70631	−	2.13984i	−0.178320	−	0.102953i
$433$	−24.0157	+	13.8655i	−1.15412	+	0.666333i	−0.949888	−	0.312590i	$-0.898804\pi$
$433$	−24.0157	+	13.8655i	−1.15412	+	0.666333i	−0.204234	+	0.978922i	$0.565470\pi$
$434$			5.59047i			0.268351i
$435$	−4.38689	−	12.0441i	−0.210335	−	0.577468i
$436$	−0.196886	+	0.113672i	−0.00942913	+	0.00544391i
$437$	−4.15938			−0.198970
$438$	−10.9539	+	6.32422i	−0.523396	+	0.302183i
$439$	−11.8882	+	20.5909i	−0.567392	+	0.982751i	0.429431	+	0.903100i	$0.358714\pi$
$439$	−11.8882	+	20.5909i	−0.567392	+	0.982751i	−0.996823	+	0.0796518i	$0.974619\pi$
$440$	22.7431	−	27.1171i	1.08423	−	1.29276i
$441$	−11.7591			−0.559958
$442$	−6.91712	+	13.5623i	−0.329014	+	0.645095i
$443$		−	29.2262i		−	1.38858i	−0.719696	−	0.694289i	$-0.755719\pi$
$443$		−	29.2262i		−	1.38858i	0.719696	−	0.694289i	$-0.244281\pi$
$444$	−0.0251720	−	0.0145330i	−0.00119461	−	0.000689708i
$445$	21.8565	−	26.0600i	1.03610	−	1.23536i
$446$	−14.5810	−	25.2550i	−0.690429	−	1.19586i
$447$	4.26646			0.201796
$448$	−15.8235	−	27.4071i	−0.747589	−	1.29486i
$449$	−5.40940	+	3.12312i	−0.255286	+	0.147389i	−0.622182	−	0.782873i	$-0.713754\pi$
$449$	−5.40940	+	3.12312i	−0.255286	+	0.147389i	0.366897	+	0.930262i	$0.380420\pi$
$450$	6.89254	+	2.50501i	0.324917	+	0.118087i
$451$	−0.668537	−	1.15794i	−0.0314802	−	0.0545253i
$452$	−2.00944	−	1.16015i	−0.0945163	−	0.0545690i
$453$	−7.09537	+	12.2895i	−0.333369	+	0.577413i
$454$	20.9277			0.982184
$455$	−34.6581	−	4.26113i	−1.62480	−	0.199765i
$456$	9.05046			0.423827
$457$	2.78464	−	4.82314i	0.130260	−	0.225617i	−0.793517	−	0.608548i	$-0.791752\pi$
$457$	2.78464	−	4.82314i	0.130260	−	0.225617i	0.923777	+	0.382931i	$0.125085\pi$
$458$	25.6361	+	14.8010i	1.19789	+	0.691605i
$459$	−1.43943	−	2.49317i	−0.0671869	−	0.116371i
$460$	0.415171	+	0.0731051i	0.0193575	+	0.00340854i
$461$	18.7277	−	10.8125i	0.872238	−	0.503587i	0.00414673	−	0.999991i	$-0.498680\pi$
$461$	18.7277	−	10.8125i	0.872238	−	0.503587i	0.868091	+	0.496405i	$0.165347\pi$
$462$	18.5407	+	32.1134i	0.862590	+	1.49405i
$463$	−28.2921			−1.31485			−0.657423	−	0.753522i	$-0.728354\pi$
$463$	−28.2921			−1.31485			−0.657423	+	0.753522i	$0.728354\pi$
$464$	12.2665	+	21.2462i	0.569458	+	0.986331i
$465$	−1.50771	−	1.26451i	−0.0699183	−	0.0586404i
$466$	−18.3927	−	10.6190i	−0.852024	−	0.491916i
$467$			10.8308i			0.501188i	0.968092	+	0.250594i	$0.0806259\pi$
$467$			10.8308i			0.501188i	−0.968092	+	0.250594i	$0.919374\pi$
$468$	0.457584	−	0.296901i	0.0211518	−	0.0137243i
$469$	32.3518			1.49387
$470$	−0.227229	−	0.190577i	−0.0104813	−	0.00879066i
$471$	−10.4548	+	18.1082i	−0.481731	+	0.834383i
$472$	−17.5957	+	10.1589i	−0.809908	+	0.467600i
$473$	−28.8438			−1.32624
$474$	8.58558	−	4.95689i	0.394349	−	0.227677i
$475$	−16.4338	+	2.90569i	−0.754033	+	0.133322i
$476$			1.88635i			0.0864609i
$477$	3.86249	−	2.23001i	0.176851	−	0.102105i
$478$	1.22165	+	0.705322i	0.0558771	+	0.0322607i
$479$	−0.240119	−	0.138633i	−0.0109713	−	0.00633429i	0.494504	−	0.869175i	$-0.335350\pi$
$479$	−0.240119	−	0.138633i	−0.0109713	−	0.00633429i	−0.505476	+	0.862841i	$0.668683\pi$
$480$	−1.88068	−	0.331159i	−0.0858410	−	0.0151153i
$481$	−0.581119	+	0.377056i	−0.0264967	+	0.0171923i
$482$		−	32.3175i		−	1.47202i
$483$	2.69869	−	4.67426i	0.122795	−	0.212686i
$484$	1.74524	−	3.02284i	0.0793290	−	0.137402i
$485$	−3.20615	+	1.16780i	−0.145584	+	0.0530270i
$486$			1.46673i			0.0665320i
$487$	20.2599	+	35.0911i	0.918063	+	1.59013i	0.802354	+	0.596848i	$0.203581\pi$
$487$	20.2599	+	35.0911i	0.918063	+	1.59013i	0.115709	+	0.993283i	$0.463086\pi$
$488$	18.4016	+	31.8724i	0.832999	+	1.44280i
$489$			6.88696i			0.311439i
$490$	−36.2374	+	13.1990i	−1.63704	+	0.596270i
$491$	−3.24278	+	5.61666i	−0.146345	+	0.253476i	−0.929874	−	0.367879i	$-0.880084\pi$
$491$	−3.24278	+	5.61666i	−0.146345	+	0.253476i	0.783529	+	0.621355i	$0.213418\pi$
$492$	−0.0173269	+	0.0300111i	−0.000781159	+	0.00135301i
$493$			16.5029i			0.743253i
$494$	−8.01967	+	15.7241i	−0.360822	+	0.707461i
$495$	−12.8545	−	2.26347i	−0.577766	−	0.101736i
$496$	3.26163	+	1.88310i	0.146452	+	0.0845539i
$497$	−13.3510	−	7.70818i	−0.598872	−	0.345759i
$498$	11.8900	−	6.86471i	0.532805	−	0.307615i
$499$		−	7.13608i		−	0.319455i	−0.987161	−	0.159727i	$-0.948938\pi$
$499$		−	7.13608i		−	0.319455i	0.987161	−	0.159727i	$-0.0510615\pi$
$500$	1.69142	−	0.00119402i	0.0756426	−	5.33982e-5i
$501$	7.08416	−	4.09004i	0.316497	−	0.182729i
$502$	8.10594			0.361786
$503$	−14.6107	+	8.43552i	−0.651461	+	0.376121i	−0.789016	−	0.614373i	$-0.789409\pi$
$503$	−14.6107	+	8.43552i	−0.651461	+	0.376121i	0.137555	+	0.990494i	$0.456076\pi$
$504$	−5.87212	+	10.1708i	−0.261565	+	0.453044i
$505$	−29.8115	−	25.0029i	−1.32660	−	1.11261i
$506$	−10.6690			−0.474297
$507$	−1.34864	−	12.9299i	−0.0598950	−	0.574235i
$508$			0.603305i			0.0267673i
$509$	−3.37840	−	1.95052i	−0.149745	−	0.0864552i	0.423255	−	0.906010i	$-0.360887\pi$
$509$	−3.37840	−	1.95052i	−0.149745	−	0.0864552i	−0.573000	+	0.819555i	$0.694221\pi$
$510$	−7.23427	−	6.06737i	−0.320339	−	0.268668i
$511$	18.6752	+	32.3463i	0.826140	+	1.43092i
$512$	−19.5543			−0.864188
$513$	−1.66887	−	2.89056i	−0.0736823	−	0.127621i
$514$	8.25304	−	4.76489i	0.364026	−	0.210170i
$515$	19.8476	+	3.49486i	0.874591	+	0.154002i
$516$	0.373782	+	0.647409i	0.0164548	+	0.0285006i
$517$	0.457111	+	0.263913i	0.0201037	+	0.0116069i
$518$	−0.610261	+	1.05700i	−0.0268133	+	0.0464420i
$519$	8.29464			0.364094
$520$	−13.1592	+	17.4571i	−0.577071	+	0.765544i
$521$	−1.26123			−0.0552557			−0.0276278	−	0.999618i	$-0.508795\pi$
$521$	−1.26123			−0.0552557			−0.0276278	+	0.999618i	$0.508795\pi$
$522$	4.20396	−	7.28147i	0.184002	−	0.318701i
$523$	−6.06931	−	3.50412i	−0.265392	−	0.153224i	0.361399	−	0.932411i	$-0.382299\pi$
$523$	−6.06931	−	3.50412i	−0.265392	−	0.153224i	−0.626792	+	0.779187i	$0.715632\pi$
$524$	0.995110	+	1.72358i	0.0434716	+	0.0752950i
$525$	7.39718	−	20.3534i	0.322839	−	0.888294i
$526$	23.1401	−	13.3600i	1.00896	−	0.582522i
$527$	1.26673	+	2.19404i	0.0551796	+	0.0955739i
$528$	24.9811			1.08716
$529$	−10.7235	−	18.5737i	−0.466241	−	0.807552i
$530$	9.39974	−	11.2075i	0.408299	−	0.486824i
$531$	6.48915	+	3.74651i	0.281605	+	0.162585i
$532$			2.18703i			0.0948197i
$533$	0.449543	+	0.692836i	0.0194719	+	0.0300100i
$534$	22.3099			0.965446
$535$	4.27799	−	5.10075i	0.184954	−	0.220525i
$536$	10.1270	−	17.5405i	0.437420	−	0.757633i
$537$	2.58798	−	1.49417i	0.111680	−	0.0644783i
$538$	−5.89539			−0.254168
$539$	59.4436	−	34.3198i	2.56042	−	1.47826i
$540$	0.115775	+	0.317856i	0.00498215	+	0.0136783i
$541$		−	18.1982i		−	0.782400i	−0.920306	−	0.391200i	$-0.872060\pi$
$541$		−	18.1982i		−	0.782400i	0.920306	−	0.391200i	$-0.127940\pi$
$542$	4.19381	−	2.42130i	0.180140	−	0.104004i
$543$	−16.4296	−	9.48565i	−0.705063	−	0.407068i
$544$	2.12918	+	1.22928i	0.0912879	+	0.0527051i
$545$	−3.30935	−	0.582724i	−0.141757	−	0.0249612i
$546$	−12.4673	−	19.2145i	−0.533549	−	0.822306i
$547$		−	32.3587i		−	1.38356i	−0.722110	−	0.691779i	$-0.756827\pi$
$547$		−	32.3587i		−	1.38356i	0.722110	−	0.691779i	$-0.243173\pi$
$548$	0.848072	−	1.46890i	0.0362278	−	0.0627485i
$549$	6.78634	−	11.7543i	0.289634	−	0.501661i
$550$	−42.1536	+	7.45327i	−1.79743	+	0.317808i
$551$			19.1334i			0.815108i
$552$	−1.68953	−	2.92635i	−0.0719111	−	0.124554i
$553$	−14.6375	−	25.3529i	−0.622449	−	1.07811i
$554$			22.7270i			0.965579i
$555$	−0.147031	−	0.403667i	−0.00624110	−	0.0171347i
$556$	0.448778	−	0.777307i	0.0190324	−	0.0329651i
$557$	15.3762	−	26.6324i	0.651513	−	1.12845i	−0.331243	−	0.943545i	$-0.607468\pi$
$557$	15.3762	−	26.6324i	0.651513	−	1.12845i	0.982756	−	0.184907i	$-0.0591985\pi$
$558$		−	1.29075i		−	0.0546418i
$559$	17.7925	−	0.925405i	0.752543	−	0.0391405i
$560$	−7.18775	+	40.8199i	−0.303738	+	1.72496i
$561$	14.5530	+	8.40216i	0.614427	+	0.354739i
$562$	15.3452	+	8.85958i	0.647300	+	0.373719i
$563$	12.9112	−	7.45428i	0.544142	−	0.314160i	−0.202614	−	0.979259i	$-0.564944\pi$
$563$	12.9112	−	7.45428i	0.544142	−	0.314160i	0.746756	+	0.665098i	$0.231610\pi$
$564$		−	0.0136800i		−	0.000576033i
$565$	−11.7372	−	32.2242i	−0.493790	−	1.35568i
$566$	−5.60953	+	3.23867i	−0.235786	+	0.136131i
$567$	4.33118			0.181892
$568$	−8.35844	+	4.82575i	−0.350712	+	0.202484i
$569$	−6.19394	+	10.7282i	−0.259664	+	0.449751i	−0.966152	−	0.257974i	$-0.916945\pi$
$569$	−6.19394	+	10.7282i	−0.259664	+	0.449751i	0.706488	+	0.707725i	$0.250278\pi$
$570$	−8.38737	−	7.03447i	−0.351308	−	0.294642i
$571$	9.04382			0.378472			0.189236	−	0.981932i	$-0.439399\pi$
$571$	9.04382			0.378472			0.189236	+	0.981932i	$0.439399\pi$
$572$	−1.44661	+	2.83636i	−0.0604859	+	0.118594i
$573$		−	15.9430i		−	0.666028i
$574$	1.26021	+	0.727580i	0.0526000	+	0.0303686i
$575$	4.00735	+	4.77121i	0.167118	+	0.198973i
$576$	3.65339	+	6.32785i	0.152224	+	0.263660i
$577$	22.8578			0.951582			0.475791	−	0.879558i	$-0.342162\pi$
$577$	22.8578			0.951582			0.475791	+	0.879558i	$0.342162\pi$
$578$	−6.38917	−	11.0664i	−0.265754	−	0.460300i
$579$	−16.7487	+	9.66985i	−0.696051	+	0.401865i
$580$	0.336288	−	1.90981i	0.0139636	−	0.0793005i
$581$	−20.2712	−	35.1107i	−0.840991	−	1.45664i
$582$	−1.93834	−	1.11910i	−0.0803468	−	0.0463883i
$583$	−13.0169	+	22.5459i	−0.539103	+	0.933754i
$584$	23.3834			0.967610
$585$	8.00201	+	0.983826i	0.330842	+	0.0406762i
$586$	−8.43373			−0.348394
$587$	−3.00951	+	5.21262i	−0.124216	+	0.215148i	−0.921426	−	0.388554i	$-0.872975\pi$
$587$	−3.00951	+	5.21262i	−0.124216	+	0.215148i	0.797210	+	0.603702i	$0.206308\pi$
$588$	−1.54064	−	0.889490i	−0.0635350	−	0.0366819i
$589$	1.46864	+	2.54376i	0.0605142	+	0.104814i
$590$	24.2025	+	4.26168i	0.996402	+	0.175451i
$591$	−12.6845	+	7.32341i	−0.521771	+	0.301245i
$592$	0.411123	+	0.712086i	0.0168971	+	0.0292666i
$593$	39.3501			1.61592			0.807958	−	0.589240i	$-0.200573\pi$
$593$	39.3501			1.61592			0.807958	+	0.589240i	$0.200573\pi$
$594$	−4.28074	−	7.41446i	−0.175641	−	0.304219i
$595$	−17.9167	+	21.3625i	−0.734513	+	0.875777i
$596$	0.558977	+	0.322726i	0.0228966	+	0.0132194i
$597$			15.1217i			0.618892i
$598$	6.58128	−	0.342298i	0.269129	−	0.0139976i
$599$	26.4292			1.07987			0.539934	−	0.841708i	$-0.318449\pi$
$599$	26.4292			1.07987			0.539934	+	0.841708i	$0.318449\pi$
$600$	−8.71967	−	10.3818i	−0.355979	−	0.423834i
$601$	−3.43793	+	5.95467i	−0.140236	+	0.242896i	−0.927585	−	0.373611i	$-0.878119\pi$
$601$	−3.43793	+	5.95467i	−0.140236	+	0.242896i	0.787349	+	0.616507i	$0.211453\pi$
$602$	27.1855	−	15.6956i	1.10800	−	0.639704i
$603$	−7.46950			−0.304182
$604$	−1.85922	+	1.07342i	−0.0756508	+	0.0436770i
$605$	48.4755	−	17.6566i	1.97081	−	0.717841i
$606$		−	25.5216i		−	1.03675i
$607$	21.6546	−	12.5023i	0.878932	−	0.507452i	0.00862576	−	0.999963i	$-0.497254\pi$
$607$	21.6546	−	12.5023i	0.878932	−	0.507452i	0.870306	+	0.492511i	$0.163921\pi$
$608$	2.46856	+	1.42522i	0.100113	+	0.0578004i
$609$	−21.5019	−	12.4141i	−0.871300	−	0.503045i
$610$	7.71951	−	43.8398i	0.312554	−	1.77502i
$611$	−0.290439	−	0.148131i	−0.0117499	−	0.00599274i
$612$		−	0.435529i		−	0.0176052i
$613$	−12.8941	+	22.3333i	−0.520788	+	0.902032i	0.478919	+	0.877859i	$0.341029\pi$
$613$	−12.8941	+	22.3333i	−0.520788	+	0.902032i	−0.999708	+	0.0241730i	$0.992305\pi$
$614$	8.11180	−	14.0500i	0.327365	−	0.567014i
$615$	−0.481271	+	0.175296i	−0.0194067	+	0.00706863i
$616$		−	68.5528i		−	2.76207i
$617$	14.3243	+	24.8105i	0.576675	+	0.998831i	0.995857	+	0.0909289i	$0.0289836\pi$
$617$	14.3243	+	24.8105i	0.576675	+	0.998831i	−0.419182	+	0.907902i	$0.637683\pi$
$618$	6.60957	+	11.4481i	0.265876	+	0.460511i
$619$		−	5.82443i		−	0.234103i	−0.993126	−	0.117052i	$-0.962656\pi$
$619$		−	5.82443i		−	0.234103i	0.993126	−	0.117052i	$-0.0373443\pi$
$620$	−0.101884	−	0.279720i	−0.00409176	−	0.0112338i
$621$	−0.623084	+	1.07921i	−0.0250035	+	0.0433073i
$622$	−16.0922	+	27.8725i	−0.645237	+	1.11758i
$623$		−	65.8803i		−	2.63944i
$624$	−15.4098	+	0.801477i	−0.616885	+	0.0320848i
$625$	19.1662	+	16.0517i	0.766649	+	0.642066i
$626$	−23.5377	−	13.5895i	−0.940755	−	0.543145i
$627$	16.8726	+	9.74141i	0.673827	+	0.389034i
$628$	−2.73951	+	1.58166i	−0.109318	+	0.0631149i
$629$			0.553109i			0.0220539i
$630$	13.3472	−	4.86153i	0.531764	−	0.193688i
$631$	16.0642	−	9.27464i	0.639504	−	0.369218i	−0.144920	−	0.989443i	$-0.546292\pi$
$631$	16.0642	−	9.27464i	0.639504	−	0.369218i	0.784423	+	0.620226i	$0.212959\pi$
$632$	−18.3277			−0.729038
$633$	−1.17286	+	0.677150i	−0.0466169	+	0.0269143i
$634$	−3.05941	+	5.29906i	−0.121505	+	0.210452i
$635$	−5.73022	+	6.83228i	−0.227397	+	0.271131i
$636$	0.674734			0.0267549
$637$	−35.5672	+	23.0776i	−1.40922	+	0.914367i
$638$			49.0782i			1.94302i
$639$	3.08252	+	1.77969i	0.121943	+	0.0704036i
$640$	21.2874	+	17.8537i	0.841459	+	0.705730i
$641$	4.02727	+	6.97544i	0.159068	+	0.275513i	0.934533	−	0.355877i	$-0.115818\pi$
$641$	4.02727	+	6.97544i	0.159068	+	0.275513i	−0.775465	+	0.631390i	$0.782485\pi$
$642$	4.36675			0.172342
$643$	7.94510	+	13.7613i	0.313324	+	0.542693i	0.979080	−	0.203477i	$-0.0652241\pi$
$643$	7.94510	+	13.7613i	0.313324	+	0.542693i	−0.665756	+	0.746170i	$0.731891\pi$
$644$	0.707147	−	0.408271i	0.0278655	−	0.0160881i
$645$	−1.91614	+	10.8819i	−0.0754480	+	0.428476i
$646$	7.04680	+	12.2054i	0.277253	+	0.480215i
$647$	−38.0278	−	21.9553i	−1.49503	−	0.863153i	−0.495042	−	0.868869i	$-0.664847\pi$
$647$	−38.0278	−	21.9553i	−1.49503	−	0.863153i	−0.999984	+	0.00571557i	$0.998181\pi$
$648$	1.35578	−	2.34828i	0.0532600	−	0.0922491i
$649$	−43.7378			−1.71686
$650$	25.7636	−	5.95003i	1.01053	−	0.233380i
$651$	−3.81153			−0.149386
$652$	−0.520947	+	0.902307i	−0.0204019	+	0.0353371i
$653$	9.60449	+	5.54515i	0.375853	+	0.216999i	0.676012	−	0.736890i	$-0.263707\pi$
$653$	9.60449	+	5.54515i	0.375853	+	0.216999i	−0.300160	+	0.953889i	$0.597040\pi$
$654$	−1.10206	−	1.90883i	−0.0430941	−	0.0746412i
$655$	−5.10129	+	28.9707i	−0.199324	+	1.13198i
$656$	0.848981	−	0.490159i	0.0331471	−	0.0191375i
$657$	−4.31179	−	7.46825i	−0.168219	−	0.291364i
$658$	−0.574442			−0.0223941
$659$	−3.38804	−	5.86826i	−0.131979	−	0.228595i	0.792460	−	0.609924i	$-0.208800\pi$
$659$	−3.38804	−	5.86826i	−0.131979	−	0.228595i	−0.924440	+	0.381329i	$0.875467\pi$
$660$	−1.51294	−	1.26890i	−0.0588910	−	0.0493918i
$661$	−5.43456	−	3.13765i	−0.211380	−	0.122040i	0.390573	−	0.920572i	$-0.372277\pi$
$661$	−5.43456	−	3.13765i	−0.211380	−	0.122040i	−0.601953	+	0.798532i	$0.705610\pi$
$662$		−	45.8945i		−	1.78374i
$663$	−9.24668	−	4.71603i	−0.359111	−	0.183155i
$664$	−25.3818			−0.985004
$665$	−20.7725	+	24.7675i	−0.805523	+	0.960444i
$666$	0.140899	−	0.244045i	0.00545974	−	0.00945655i
$667$	6.18652	−	3.57179i	0.239543	−	0.138300i
$668$	1.23752			0.0478813
$669$	17.2186	−	9.94117i	0.665710	−	0.384348i
$670$	−23.0184	+	8.38413i	−0.889277	+	0.323907i
$671$			79.2256i			3.05847i
$672$	−3.20330	+	1.84943i	−0.123570	+	0.0713432i
$673$	20.9339	+	12.0862i	0.806943	+	0.465889i	0.845893	−	0.533352i	$-0.179068\pi$
$673$	20.9339	+	12.0862i	0.806943	+	0.465889i	−0.0389502	+	0.999241i	$0.512401\pi$
$674$	26.9892	+	15.5822i	1.03958	+	0.600204i
$675$	−1.70789	+	4.69927i	−0.0657367	+	0.180875i
$676$	0.801354	−	1.79604i	0.0308213	−	0.0690786i
$677$		−	43.4583i		−	1.67024i	−0.550069	−	0.835119i	$-0.685399\pi$
$677$		−	43.4583i		−	1.67024i	0.550069	−	0.835119i	$-0.314601\pi$
$678$	11.2478	−	19.4818i	0.431969	−	0.748193i
$679$	−3.30466	+	5.72384i	−0.126821	+	0.219661i
$680$	5.97389	+	16.4011i	0.229088	+	0.628954i
$681$			14.2683i			0.546762i
$682$	3.76714	+	6.52488i	0.144251	+	0.249851i
$683$	0.385375	+	0.667489i	0.0147460	+	0.0255408i	0.873304	−	0.487175i	$-0.161973\pi$
$683$	0.385375	+	0.667489i	0.0147460	+	0.0255408i	−0.858558	+	0.512716i	$0.828639\pi$
$684$		−	0.504950i		−	0.0193072i
$685$	23.5559	−	8.57993i	0.900025	−	0.327822i
$686$	−15.1165	+	26.1826i	−0.577151	+	0.999655i
$687$	−10.0912	+	17.4784i	−0.385002	+	0.666844i
$688$		−	21.1477i		−	0.806250i
$689$	7.30620	−	14.3252i	0.278344	−	0.545747i
$690$	−0.708762	+	4.02513i	−0.0269821	+	0.153234i
$691$	21.5384	+	12.4352i	0.819360	+	0.473058i	0.850196	−	0.526467i	$-0.176484\pi$
$691$	21.5384	+	12.4352i	0.819360	+	0.473058i	−0.0308357	+	0.999524i	$0.509817\pi$
$692$	1.08674	+	0.627428i	0.0413115	+	0.0238512i
$693$	−21.8946	+	12.6408i	−0.831707	+	0.480186i
$694$			12.2401i			0.464626i
$695$	12.4652	−	4.54028i	0.472832	−	0.172223i
$696$	−13.4614	+	7.77192i	−0.510251	+	0.294594i
$697$	0.659442			0.0249781
$698$	−13.8784	+	8.01270i	−0.525305	+	0.303285i
$699$	7.23994	−	12.5399i	0.273840	−	0.474304i
$700$	2.50874	−	2.10709i	0.0948213	−	0.0796406i
$701$	−0.800213			−0.0302236			−0.0151118	−	0.999886i	$-0.504810\pi$
$701$	−0.800213			−0.0302236			−0.0151118	+	0.999886i	$0.504810\pi$
$702$	2.87849	+	4.43633i	0.108642	+	0.167438i
$703$			0.641272i			0.0241860i
$704$	−36.9365	−	21.3253i	−1.39210	−	0.803728i
$705$	0.129934	−	0.154923i	0.00489358	−	0.00583473i
$706$	4.83402	+	8.37276i	0.181931	+	0.315113i
$707$	−75.3643			−2.83437
$708$	0.566791	+	0.981712i	0.0213013	+	0.0368950i
$709$	−14.9035	+	8.60456i	−0.559714	+	0.323151i	−0.753031	−	0.657985i	$-0.771409\pi$
$709$	−14.9035	+	8.60456i	−0.559714	+	0.323151i	0.193317	+	0.981136i	$0.438076\pi$
$710$	11.4969	+	2.02442i	0.431469	+	0.0759750i
$711$	3.37956	+	5.85357i	0.126743	+	0.219526i
$712$	−35.7190	−	20.6224i	−1.33863	−	0.772856i
$713$	0.548326	−	0.949729i	0.0205350	−	0.0355676i
$714$	−18.2884			−0.684427
$715$	−43.3224	+	18.3811i	−1.62017	+	0.687412i
$716$	0.452092			0.0168955
$717$	−0.480882	+	0.832912i	−0.0179589	+	0.0311057i
$718$	5.78855	+	3.34202i	0.216027	+	0.124723i
$719$	13.8942	+	24.0654i	0.518165	+	0.897489i	0.999777	+	0.0211041i	$0.00671814\pi$
$719$	13.8942	+	24.0654i	0.518165	+	0.897489i	−0.481612	+	0.876385i	$0.659949\pi$
$720$	1.65954	−	9.42467i	0.0618473	−	0.351237i
$721$	33.8058	−	19.5178i	1.25899	−	0.726880i
$722$	−5.76388	−	9.98334i	−0.214510	−	0.371541i
$723$	22.0338			0.819446
$724$	−1.43504	−	2.48556i	−0.0533328	−	0.0923751i
$725$	21.9478	−	18.4340i	0.815122	−	0.684623i
$726$	29.3068	+	16.9203i	1.08768	+	0.627971i
$727$			1.86277i			0.0690862i	0.999403	+	0.0345431i	$0.0109976\pi$
$727$			1.86277i			0.0690862i	−0.999403	+	0.0345431i	$0.989002\pi$
$728$	2.19940	+	42.2873i	0.0815153	+	1.56727i
$729$	−1.00000			−0.0370370
$730$	−21.6701	−	18.1747i	−0.802048	−	0.672676i
$731$	7.11284	−	12.3198i	0.263078	−	0.455664i
$732$	1.77825	−	1.02667i	0.0657260	−	0.0379469i
$733$	36.8157			1.35982			0.679909	−	0.733296i	$-0.262019\pi$
$733$	36.8157			1.35982			0.679909	+	0.733296i	$0.262019\pi$
$734$	−47.3767	+	27.3529i	−1.74871	+	1.00962i
$735$	−8.99896	−	24.7063i	−0.331931	−	0.911307i
$736$		−	1.06423i		−	0.0392282i
$737$	37.7592	−	21.8003i	1.39088	−	0.803023i
$738$	−0.290961	−	0.167987i	−0.0107104	−	0.00618367i
$739$	38.9201	+	22.4705i	1.43170	+	0.826592i	0.997250	−	0.0741051i	$-0.0236100\pi$
$739$	38.9201	+	22.4705i	1.43170	+	0.826592i	0.434448	+	0.900697i	$0.356943\pi$
$740$	0.0112710	−	0.0640090i	0.000414330	−	0.00235302i
$741$	−10.7205	−	5.46774i	−0.393829	−	0.200862i
$742$		−	28.3329i		−	1.04013i
$743$	1.44671	−	2.50578i	0.0530748	−	0.0919282i	−0.838267	−	0.545259i	$-0.816431\pi$
$743$	1.44671	−	2.50578i	0.0530748	−	0.0919282i	0.891342	+	0.453331i	$0.149765\pi$
$744$	−1.19311	+	2.06653i	−0.0437417	+	0.0757628i
$745$	3.26501	+	8.96398i	0.119621	+	0.328415i
$746$			31.3978i			1.14956i
$747$	4.68029	+	8.10651i	0.171243	+	0.296602i
$748$	1.27112	+	2.20165i	0.0464768	+	0.0805002i
$749$		−	12.8948i		−	0.471167i
$750$	0.0115762	+	16.3985i	0.000422701	+	0.598788i
$751$	11.6251	−	20.1352i	0.424205	−	0.734745i	−0.572141	−	0.820155i	$-0.693887\pi$
$751$	11.6251	−	20.1352i	0.424205	−	0.734745i	0.996346	+	0.0854107i	$0.0272202\pi$
$752$	−0.193496	+	0.335145i	−0.00705608	+	0.0122215i
$753$			5.52656i			0.201399i
$754$	−1.57459	−	30.2742i	−0.0573432	−	1.10252i
$755$	−31.2507	−	5.50275i	−1.13733	−	0.200266i
$756$	0.567457	+	0.327622i	0.0206382	+	0.0119155i
$757$	−16.4183	−	9.47909i	−0.596732	−	0.344524i	0.171023	−	0.985267i	$-0.445293\pi$
$757$	−16.4183	−	9.47909i	−0.596732	−	0.344524i	−0.767755	+	0.640744i	$0.778626\pi$
$758$	−31.0477	+	17.9254i	−1.12770	+	0.651079i
$759$		−	7.27405i		−	0.264031i
$760$	6.92609	+	19.0154i	0.251236	+	0.689759i
$761$	13.0019	−	7.50663i	0.471317	−	0.272115i	−0.245474	−	0.969403i	$-0.578943\pi$
$761$	13.0019	−	7.50663i	0.471317	−	0.272115i	0.716791	+	0.697288i	$0.245610\pi$
$762$	−5.84911			−0.211891
$763$	−5.63670	+	3.25435i	−0.204062	+	0.117815i
$764$	1.20597	−	2.08880i	0.0436304	−	0.0755701i
$765$	4.13668	−	4.93226i	0.149562	−	0.178326i
$766$	−54.0981			−1.95464
$767$	26.9800	−	1.40326i	0.974191	−	0.0506686i
$768$			3.61059i			0.130286i
$769$	−31.6388	−	18.2667i	−1.14093	−	0.658714i	−0.194266	−	0.980949i	$-0.562232\pi$
$769$	−31.6388	−	18.2667i	−1.14093	−	0.658714i	−0.946660	+	0.322235i	$0.895566\pi$
$770$	−53.2827	+	63.5301i	−1.92017	+	2.28947i
$771$	3.24866	+	5.62684i	0.116998	+	0.202646i
$772$	−2.92581			−0.105302
$773$	9.00188	+	15.5917i	0.323775	+	0.560795i	0.981264	−	0.192670i	$-0.0617146\pi$
$773$	9.00188	+	15.5917i	0.323775	+	0.560795i	−0.657489	+	0.753464i	$0.728381\pi$
$774$	−6.27671	+	3.62386i	−0.225612	+	0.130257i
$775$	1.50298	−	4.13545i	0.0539886	−	0.148550i
$776$	2.06890	+	3.58344i	0.0742692	+	0.128638i
$777$	−0.720654	−	0.416070i	−0.0258533	−	0.0149264i
$778$	23.6322	−	40.9322i	0.847256	−	1.46749i
$779$	0.764553			0.0273930
$780$	0.973978	+	0.734190i	0.0348740	+	0.0262882i
$781$	−20.7766			−0.743447
$782$	2.63097	−	4.55698i	0.0940834	−	0.162957i
$783$	4.96444	+	2.86622i	0.177414	+	0.102430i
$784$	25.1626	+	43.5830i	0.898666	+	1.55654i
$785$	−46.0469	−	8.10813i	−1.64348	−	0.289392i
$786$	−16.7103	+	9.64770i	−0.596037	+	0.344122i
$787$	23.2165	+	40.2121i	0.827577	+	1.43341i	0.899933	+	0.436027i	$0.143615\pi$
$787$	23.2165	+	40.2121i	0.827577	+	1.43341i	−0.0723560	+	0.997379i	$0.523052\pi$
$788$	−2.21585			−0.0789363
$789$	9.10870	+	15.7767i	0.324278	+	0.561666i
$790$	16.9849	+	14.2452i	0.604297	+	0.506823i
$791$	−57.5289	−	33.2143i	−2.04549	−	1.18096i
$792$			15.8277i			0.562414i
$793$	−2.54182	−	48.8709i	−0.0902628	−	1.73546i
$794$	−0.0191018			−0.000677898
$795$	7.64119	+	6.40866i	0.271005	+	0.227292i
$796$	−1.14385	+	1.98120i	−0.0405426	+	0.0702218i
$797$	2.85435	−	1.64796i	0.101106	−	0.0583738i	−0.448594	−	0.893736i	$-0.648075\pi$
$797$	2.85435	−	1.64796i	0.101106	−	0.0583738i	0.549701	+	0.835362i	$0.314742\pi$
$798$	−21.2035			−0.750595
$799$	−0.225446	+	0.130161i	−0.00797570	+	0.00460477i
$800$	−0.743462	−	4.20481i	−0.0262854	−	0.148662i
$801$			15.2107i			0.537444i
$802$	−12.0700	+	6.96859i	−0.426205	+	0.246069i
$803$	43.5932	+	25.1685i	1.53837	+	0.888178i
$804$	−0.978630	−	0.565013i	−0.0345136	−	0.0199265i
$805$	11.8860	+	2.09294i	0.418928	+	0.0737666i
$806$	−2.53313	−	3.90406i	−0.0892257	−	0.137515i
$807$		−	4.01942i		−	0.141490i
$808$	−23.5911	+	40.8610i	−0.829932	+	1.43748i
$809$	−17.1861	+	29.7671i	−0.604230	+	1.04656i	0.387943	+	0.921683i	$0.373186\pi$
$809$	−17.1861	+	29.7671i	−0.604230	+	1.04656i	−0.992173	+	0.124873i	$0.960147\pi$
$810$	−3.08164	+	1.12245i	−0.108278	+	0.0394388i
$811$			12.3546i			0.433827i	0.976191	+	0.216914i	$0.0695990\pi$
$811$			12.3546i			0.433827i	−0.976191	+	0.216914i	$0.930401\pi$
$812$	−1.87807	−	3.25291i	−0.0659073	−	0.114155i
$813$	1.65082	+	2.85930i	0.0578967	+	0.100280i
$814$			1.64490i			0.0576537i
$815$	−14.4698	+	5.27042i	−0.506853	+	0.184615i
$816$	−6.16031	+	10.6700i	−0.215654	+	0.373524i
$817$	8.24658	−	14.2835i	0.288511	−	0.499716i
$818$		−	36.8283i		−	1.28767i
$819$	13.1003	−	8.50006i	0.457761	−	0.297016i
$820$	−0.0763144	−	0.0134378i	−0.00266501	−	0.000469267i
$821$	27.7068	+	15.9965i	0.966975	+	0.558283i	0.898313	−	0.439357i	$-0.144794\pi$
$821$	27.7068	+	15.9965i	0.966975	+	0.558283i	0.0686622	+	0.997640i	$0.478127\pi$
$822$	14.2412	+	8.22215i	0.496718	+	0.286780i
$823$	25.0960	−	14.4892i	0.874790	−	0.505060i	0.00585284	−	0.999983i	$-0.498137\pi$
$823$	25.0960	−	14.4892i	0.874790	−	0.505060i	0.868937	+	0.494923i	$0.164804\pi$
$824$		−	24.4384i		−	0.851353i
$825$	−5.08157	−	28.7399i	−0.176917	−	1.00060i
$826$	41.2233	−	23.8003i	1.43434	−	0.828118i
$827$	−9.51866			−0.330996			−0.165498	−	0.986210i	$-0.552923\pi$
$827$	−9.51866			−0.330996			−0.165498	+	0.986210i	$0.552923\pi$
$828$	−0.163269	+	0.0942633i	−0.00567398	+	0.00327588i
$829$	−8.58075	+	14.8623i	−0.298022	+	0.516189i	−0.975683	−	0.219185i	$-0.929660\pi$
$829$	−8.58075	+	14.8623i	−0.298022	+	0.516189i	0.677662	+	0.735374i	$0.262993\pi$
$830$	23.5221	+	19.7280i	0.816465	+	0.684768i
$831$	−15.4951			−0.537518
$832$	23.4688	+	11.9696i	0.813634	+	0.414973i
$833$			33.8529i			1.17293i
$834$	7.53607	+	4.35095i	0.260953	+	0.150661i
$835$	14.0146	+	11.7541i	0.484997	+	0.406766i
$836$	1.47373	+	2.55258i	0.0509700	+	0.0882827i
$837$	0.880021			0.0304180
$838$	−6.21597	−	10.7664i	−0.214727	−	0.371918i
$839$	−5.65008	+	3.26207i	−0.195062	+	0.112619i	−0.594350	−	0.804206i	$-0.702591\pi$
$839$	−5.65008	+	3.26207i	−0.195062	+	0.112619i	0.399288	+	0.916826i	$0.369257\pi$
$840$	−25.8630	−	4.55408i	−0.892360	−	0.157131i
$841$	−1.93042	−	3.34358i	−0.0665661	−	0.115296i
$842$	9.41623	+	5.43646i	0.324505	+	0.187353i
$843$	−6.04038	+	10.4622i	−0.208042	+	0.360339i
$844$	−0.204885			−0.00705245
$845$	26.1340	−	12.7284i	0.899038	−	0.437871i
$846$	0.132629			0.00455989
$847$	49.9649	−	86.5417i	1.71681	−	2.97361i
$848$	−16.5302	−	9.54372i	−0.567650	−	0.327733i
$849$	−2.20809	−	3.82453i	−0.0757815	−	0.131257i
$850$	7.21157	−	19.8427i	0.247355	−	0.680598i
$851$	0.207347	−	0.119712i	0.00710775	−	0.00410366i
$852$	0.269241	+	0.466340i	0.00922406	+	0.0159765i
$853$	17.3445			0.593864			0.296932	−	0.954899i	$-0.404037\pi$
$853$	17.3445			0.593864			0.296932	+	0.954899i	$0.404037\pi$
$854$	−43.1113	−	74.6709i	−1.47524	−	2.55519i
$855$	4.79604	−	5.71843i	0.164021	−	0.195566i
$856$	−6.99132	−	4.03644i	−0.238958	−	0.137963i
$857$			25.7013i			0.877938i	0.898502	+	0.438969i	$0.144656\pi$
$857$			25.7013i			0.877938i	−0.898502	+	0.438969i	$0.855344\pi$
$858$	−27.4988	−	14.0251i	−0.938794	−	0.478807i
$859$	30.2057			1.03060			0.515302	−	0.857009i	$-0.327680\pi$
$859$	30.2057			1.03060			0.515302	+	0.857009i	$0.327680\pi$
$860$	−1.07419	+	1.28078i	−0.0366294	+	0.0436741i
$861$	−0.496057	+	0.859197i	−0.0169056	+	0.0292813i
$862$	41.9556	−	24.2230i	1.42901	−	0.825040i
$863$	−0.739245			−0.0251642			−0.0125821	−	0.999921i	$-0.504005\pi$
$863$	−0.739245			−0.0251642			−0.0125821	+	0.999921i	$0.504005\pi$
$864$	0.739591	−	0.427003i	0.0251614	−	0.0145269i
$865$	6.34768	+	17.4273i	0.215828	+	0.592547i
$866$		−	40.6737i		−	1.38215i
$867$	7.54494	−	4.35608i	0.256240	−	0.147940i
$868$	−0.499374	−	0.288314i	−0.0169499	−	0.00978601i
$869$	−34.1681	−	19.7270i	−1.15907	−	0.669191i
$870$	18.5158	+	3.26034i	0.627745	+	0.110536i
$871$	−22.5926	+	14.6591i	−0.765521	+	0.496705i
$872$			4.07480i			0.137990i
$873$	0.762993	−	1.32154i	0.0258234	−	0.0447274i
$874$	3.05033	−	5.28333i	0.103179	−	0.178711i
$875$	48.4240	−	0.0341839i	1.63703	−	0.00115563i
$876$		−	1.30462i		−	0.0440791i
$877$	−14.8630	−	25.7435i	−0.501888	−	0.869295i	−0.999998	−	0.00218091i	$-0.999306\pi$
$877$	−14.8630	−	25.7435i	−0.501888	−	0.869295i	0.498110	−	0.867114i	$-0.334028\pi$
$878$	−17.4367	−	30.2013i	−0.588460	−	1.01924i
$879$		−	5.75004i		−	0.193944i
$880$	19.1174	+	52.4862i	0.644448	+	1.76931i
$881$	−4.97132	+	8.61058i	−0.167488	+	0.290098i	−0.937536	−	0.347888i	$-0.886899\pi$
$881$	−4.97132	+	8.61058i	−0.167488	+	0.290098i	0.770048	+	0.637986i	$0.220232\pi$
$882$	8.62370	−	14.9367i	0.290375	−	0.502945i
$883$			57.2873i			1.92787i	0.266134	+	0.963936i	$0.414254\pi$
$883$			57.2873i			1.92787i	−0.266134	+	0.963936i	$0.585746\pi$
$884$	−0.854738	−	1.31732i	−0.0287479	−	0.0443063i
$885$	−2.90558	+	16.5010i	−0.0976699	+	0.554677i
$886$	37.1238	+	21.4334i	1.24720	+	0.720070i
$887$	−29.7572	−	17.1804i	−0.999150	−	0.576860i	−0.0911536	−	0.995837i	$-0.529055\pi$
$887$	−29.7572	−	17.1804i	−0.999150	−	0.576860i	−0.907997	+	0.418977i	$0.862389\pi$
$888$	−0.451169	+	0.260483i	−0.0151403	+	0.00874123i
$889$			17.2722i			0.579290i
$890$	17.0732	+	46.8740i	0.572296	+	1.57122i
$891$	5.05511	−	2.91857i	0.169353	−	0.0977757i
$892$	3.00790			0.100712
$893$	−0.261381	+	0.150908i	−0.00874677	+	0.00504995i
$894$	−3.12886	+	5.41935i	−0.104645	+	0.181250i
$895$	5.11983	+	4.29399i	0.171137	+	0.143532i
$896$	53.8151			1.79784
$897$	0.233376	+	4.48705i	0.00779219	+	0.149818i
$898$		−	9.16152i		−	0.305724i
$899$	−4.36881	−	2.52233i	−0.145708	−	0.0841245i
$900$	−0.579227	+	0.486494i	−0.0193076	+	0.0162165i
$901$	−6.41988	−	11.1196i	−0.213877	−	0.370446i
$902$	1.96112			0.0652982
$903$	10.7011	+	18.5348i	0.356110	+	0.616801i
$904$	−36.0162	+	20.7940i	−1.19788	+	0.691598i
$905$	7.35652	−	41.7784i	0.244539	−	1.38876i
$906$	−10.4070	−	18.0254i	−0.345748	−	0.598853i
$907$	11.5628	+	6.67576i	0.383935	+	0.221665i	0.679529	−	0.733649i	$-0.262184\pi$
$907$	11.5628	+	6.67576i	0.383935	+	0.221665i	−0.295594	+	0.955314i	$0.595517\pi$
$908$	−1.07929	+	1.86939i	−0.0358175	+	0.0620377i
$909$	17.4004			0.577135
$910$	30.8296	−	40.8986i	1.02199	−	1.35577i
$911$	53.6004			1.77586			0.887930	−	0.459980i	$-0.152143\pi$
$911$	53.6004			1.77586			0.887930	+	0.459980i	$0.152143\pi$
$912$	−7.14222	+	12.3707i	−0.236503	+	0.409635i
$913$	−47.3188	−	27.3195i	−1.56602	−	0.904144i
$914$	4.08430	+	7.07422i	0.135097	+	0.233994i
$915$	29.8896	+	5.26309i	0.988120	+	0.173992i
$916$	−2.64423	+	1.52664i	−0.0873677	+	0.0504418i
$917$	28.4892	+	49.3448i	0.940798	+	1.62951i
$918$	4.22250			0.139363
$919$	−16.0713	−	27.8363i	−0.530143	−	0.918234i	−0.999382	−	0.0351627i	$-0.988805\pi$
$919$	−16.0713	−	27.8363i	−0.530143	−	0.918234i	0.469239	−	0.883071i	$-0.344528\pi$
$920$	4.85541	−	5.78922i	0.160078	−	0.190865i
$921$	9.57919	+	5.53055i	0.315645	+	0.182238i
$922$			31.7179i			1.04457i
$923$	12.8162	−	0.666584i	0.421852	−	0.0219409i
$924$	−3.82474			−0.125825
$925$	0.735601	−	0.617833i	0.0241864	−	0.0203142i
$926$	20.7484	−	35.9373i	0.681835	−	1.18097i
$927$	−7.80522	+	4.50634i	−0.256357	+	0.148008i
$928$	−4.89554			−0.160704
$929$	−18.4385	+	10.6455i	−0.604947	+	0.349266i	−0.770985	−	0.636853i	$-0.780236\pi$
$929$	−18.4385	+	10.6455i	−0.604947	+	0.349266i	0.166038	+	0.986119i	$0.446903\pi$
$930$	2.71191	−	0.987778i	0.0889271	−	0.0323905i
$931$			39.2488i			1.28633i
$932$	1.89711	−	1.09530i	0.0621418	−	0.0358776i
$933$	−19.0032	−	10.9715i	−0.622136	−	0.359191i
$934$	−13.7575	−	7.94288i	−0.450158	−	0.259899i
$935$	−6.51623	+	37.0063i	−0.213103	+	1.21023i
$936$	−0.507807	−	9.76347i	−0.0165982	−	0.319129i
$937$			46.7261i			1.52648i	0.646118	+	0.763238i	$0.276391\pi$
$937$			46.7261i			1.52648i	−0.646118	+	0.763238i	$0.723609\pi$
$938$	−23.7256	+	41.0939i	−0.774668	+	1.34176i
$939$	9.26518	−	16.0478i	0.302358	−	0.523699i
$940$	0.0287422	−	0.0104690i	0.000937469	−	0.000341460i
$941$			21.1046i			0.687990i	0.938972	+	0.343995i	$0.111780\pi$
$941$			21.1046i			0.687990i	−0.938972	+	0.343995i	$0.888220\pi$
$942$	−15.3343	−	26.5598i	−0.499619	−	0.865366i
$943$	−0.142726	−	0.247208i	−0.00464779	−	0.00805020i
$944$		−	32.0678i		−	1.04372i
$945$	3.31454	+	9.09997i	0.107822	+	0.296022i
$946$	21.1530	−	36.6380i	0.687742	−	1.19120i
$947$	−4.84229	+	8.38709i	−0.157353	+	0.272544i	−0.933913	−	0.357499i	$-0.883629\pi$
$947$	−4.84229	+	8.38709i	−0.157353	+	0.272544i	0.776560	+	0.630043i	$0.216963\pi$
$948$			1.02255i			0.0332110i
$949$	−27.6983	−	14.1268i	−0.899124	−	0.458575i
$950$	8.36105	−	23.0055i	0.271268	−	0.746396i
$951$	−3.61285	−	2.08588i	−0.117155	−	0.0676392i
$952$	29.2804	+	16.9050i	0.948982	+	0.547895i
$953$	−9.69531	+	5.59759i	−0.314062	+	0.181324i	−0.648743	−	0.761008i	$-0.724705\pi$
$953$	−9.69531	+	5.59759i	−0.314062	+	0.181324i	0.334681	+	0.942332i	$0.391371\pi$
$954$			6.54162i			0.211793i
$955$	33.4968	−	12.2008i	1.08393	−	0.394807i
$956$	−0.126007	+	0.0727503i	−0.00407537	+	0.00235291i
$957$	−33.4610			−1.08164
$958$	0.352188	−	0.203336i	0.0113787	−	0.00656949i
$959$	24.2797	−	42.0536i	0.784031	−	1.35798i
$960$	−10.4992	+	12.5184i	−0.338860	+	0.404031i
$961$	30.2256			0.975018
$962$	−0.0527739	−	1.01467i	−0.00170150	−	0.0327142i
$963$			2.97721i			0.0959393i
$964$	2.88680	+	1.66669i	0.0929775	+	0.0536806i
$965$	−33.1341	−	27.7895i	−1.06662	−	0.894575i
$966$	3.95823	+	6.85586i	0.127354	+	0.220584i
$967$	−6.57485			−0.211433			−0.105717	−	0.994396i	$-0.533714\pi$
$967$	−6.57485			−0.211433			−0.105717	+	0.994396i	$0.533714\pi$
$968$	−31.2808	−	54.1799i	−1.00540	−	1.74141i
$969$	−8.32153	+	4.80444i	−0.267326	+	0.154341i
$970$	0.867910	−	4.92894i	0.0278669	−	0.158259i
$971$	24.9896	+	43.2833i	0.801955	+	1.38903i	0.918328	+	0.395821i	$0.129540\pi$
$971$	24.9896	+	43.2833i	0.801955	+	1.38903i	−0.116373	+	0.993206i	$0.537127\pi$
$972$	−0.131017	−	0.0756426i	−0.00420237	−	0.00242624i
$973$	12.8482	−	22.2537i	0.411894	−	0.713421i
$974$	−59.4314			−1.90430
$975$	4.05668	+	17.5654i	0.129918	+	0.562543i
$976$	−58.0868			−1.85931
$977$	−19.6354	+	34.0095i	−0.628191	+	1.08806i	0.359723	+	0.933059i	$0.382871\pi$
$977$	−19.6354	+	34.0095i	−0.628191	+	1.08806i	−0.987915	+	0.155000i	$0.950462\pi$
$978$	−8.74797	−	5.05064i	−0.279729	−	0.161502i
$979$	−44.3935	−	76.8918i	−1.41882	−	2.45747i
$980$	0.689837	−	3.91765i	0.0220360	−	0.125145i
$981$	1.30142	−	0.751377i	0.0415512	−	0.0239896i
$982$	−4.75627	−	8.23811i	−0.151779	−	0.262889i
$983$	−37.5931			−1.19903			−0.599516	−	0.800363i	$-0.704640\pi$
$983$	−37.5931			−1.19903			−0.599516	+	0.800363i	$0.704640\pi$
$984$	0.310559	+	0.537905i	0.00990027	+	0.0171478i
$985$	−25.0939	−	21.0462i	−0.799558	−	0.670588i
$986$	−20.9623	−	12.1026i	−0.667577	−	0.385426i
$987$		−	0.391649i		−	0.0124663i
$988$	−0.990978	−	1.52729i	−0.0315272	−	0.0485897i
$989$	−6.15784			−0.195808
$990$	12.3021	−	14.6681i	0.390987	−	0.466183i
$991$	23.4774	−	40.6640i	0.745783	−	1.29173i	−0.204045	−	0.978961i	$-0.565409\pi$
$991$	23.4774	−	40.6640i	0.745783	−	1.29173i	0.949828	−	0.312772i	$-0.101258\pi$
$992$	−0.650855	+	0.375772i	−0.0206647	+	0.0119308i
$993$	31.2904			0.992972
$994$	19.5822	−	11.3058i	0.621109	−	0.358598i
$995$	−31.7713	+	11.5723i	−1.00722	+	0.366866i
$996$			1.41612i			0.0448714i
$997$	−41.4451	+	23.9283i	−1.31258	+	0.757818i	−0.982523	−	0.186143i	$-0.940401\pi$
$997$	−41.4451	+	23.9283i	−1.31258	+	0.757818i	−0.330057	+	0.943961i	$0.607068\pi$
$998$	9.06441	+	5.23334i	0.286929	+	0.165658i
$999$	0.166388	+	0.0960639i	0.00526427	+	0.00303933i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.v.a.4.5	✓	32
3.2	odd	2		585.2.bf.c.199.12		32
5.2	odd	4		975.2.bc.m.901.3		16
5.3	odd	4		975.2.bc.n.901.6		16
5.4	even	2	inner	195.2.v.a.4.12	yes	32
13.10	even	6	inner	195.2.v.a.49.12	yes	32
15.14	odd	2		585.2.bf.c.199.5		32
39.23	odd	6		585.2.bf.c.244.5		32
65.23	odd	12		975.2.bc.n.751.6		16
65.49	even	6	inner	195.2.v.a.49.5	yes	32
65.62	odd	12		975.2.bc.m.751.3		16
195.179	odd	6		585.2.bf.c.244.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.v.a.4.5	✓	32	1.1	even	1	trivial
195.2.v.a.4.12	yes	32	5.4	even	2	inner
195.2.v.a.49.5	yes	32	65.49	even	6	inner
195.2.v.a.49.12	yes	32	13.10	even	6	inner
585.2.bf.c.199.5		32	15.14	odd	2
585.2.bf.c.199.12		32	3.2	odd	2
585.2.bf.c.244.5		32	39.23	odd	6
585.2.bf.c.244.12		32	195.179	odd	6
975.2.bc.m.751.3		16	65.62	odd	12
975.2.bc.m.901.3		16	5.2	odd	4
975.2.bc.n.751.6		16	65.23	odd	12
975.2.bc.n.901.6		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)

\(f(q)\)	\(=\)	\(q+(-0.733363 + 1.27022i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.0756426 - 0.131017i) q^{4} +(0.387771 - 2.20219i) q^{5} +(1.27022 - 0.733363i) q^{6} +(-2.16559 - 3.75091i) q^{7} -2.71156 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.733363 + 1.27022i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.0756426 - 0.131017i) q^{4} +(0.387771 - 2.20219i) q^{5} +(1.27022 - 0.733363i) q^{6} +(-2.16559 - 3.75091i) q^{7} -2.71156 q^{8} +(0.500000 + 0.866025i) q^{9} +(2.51289 + 2.10756i) q^{10} +(-5.05511 - 2.91857i) q^{11} +0.151285i q^{12} +(3.21192 + 1.63816i) q^{13} +6.35265 q^{14} +(-1.43691 + 1.71327i) q^{15} +(2.13984 - 3.70631i) q^{16} +(2.49317 - 1.43943i) q^{17} -1.46673 q^{18} +(2.89056 - 1.66887i) q^{19} +(-0.317856 + 0.115775i) q^{20} +4.33118i q^{21} +(7.41446 - 4.28074i) q^{22} +(-1.07921 - 0.623084i) q^{23} +(2.34828 + 1.35578i) q^{24} +(-4.69927 - 1.70789i) q^{25} +(-4.43633 + 2.87849i) q^{26} -1.00000i q^{27} +(-0.327622 + 0.567457i) q^{28} +(-2.86622 + 4.96444i) q^{29} +(-1.12245 - 3.08164i) q^{30} +0.880021i q^{31} +(0.427003 + 0.739591i) q^{32} +(2.91857 + 5.05511i) q^{33} +4.22250i q^{34} +(-9.09997 + 3.31454i) q^{35} +(0.0756426 - 0.131017i) q^{36} +(-0.0960639 + 0.166388i) q^{37} +4.89554i q^{38} +(-1.96253 - 3.02465i) q^{39} +(-1.05146 + 5.97136i) q^{40} +(0.198375 + 0.114532i) q^{41} +(-5.50156 - 3.17633i) q^{42} +(4.27940 - 2.47071i) q^{43} +0.883072i q^{44} +(2.10104 - 0.765275i) q^{45} +(1.58291 - 0.913893i) q^{46} -0.0904255 q^{47} +(-3.70631 + 2.13984i) q^{48} +(-5.87956 + 10.1837i) q^{49} +(5.61567 - 4.71661i) q^{50} -2.87886 q^{51} +(-0.0283319 - 0.544730i) q^{52} -4.46001i q^{53} +(1.27022 + 0.733363i) q^{54} +(-8.38746 + 10.0006i) q^{55} +(5.87212 + 10.1708i) q^{56} -3.33774 q^{57} +(-4.20396 - 7.28147i) q^{58} +(6.48915 - 3.74651i) q^{59} +(0.333158 + 0.0586640i) q^{60} +(-6.78634 - 11.7543i) q^{61} +(-1.11782 - 0.645375i) q^{62} +(2.16559 - 3.75091i) q^{63} +7.30677 q^{64} +(4.85302 - 6.43803i) q^{65} -8.56148 q^{66} +(-3.73475 + 6.46878i) q^{67} +(-0.377179 - 0.217765i) q^{68} +(0.623084 + 1.07921i) q^{69} +(2.46337 - 13.9897i) q^{70} +(3.08252 - 1.77969i) q^{71} +(-1.35578 - 2.34828i) q^{72} -8.62359 q^{73} +(-0.140899 - 0.244045i) q^{74} +(3.21574 + 3.82871i) q^{75} +(-0.437299 - 0.252475i) q^{76} +25.2817i q^{77} +(5.28122 - 0.274681i) q^{78} +6.75912 q^{79} +(-7.33223 - 6.14954i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.290961 + 0.167987i) q^{82} +9.36059 q^{83} +(0.567457 - 0.327622i) q^{84} +(-2.20312 - 6.04859i) q^{85} +7.24771i q^{86} +(4.96444 - 2.86622i) q^{87} +(13.7072 + 7.91387i) q^{88} +(13.1729 + 7.60535i) q^{89} +(-0.568754 + 3.23001i) q^{90} +(-0.811121 - 15.5952i) q^{91} +0.188527i q^{92} +(0.440010 - 0.762120i) q^{93} +(0.0663147 - 0.114860i) q^{94} +(-2.55428 - 7.01270i) q^{95} -0.854006i q^{96} +(-0.762993 - 1.32154i) q^{97} +(-8.62370 - 14.9367i) q^{98} -5.83714i 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more