LMFDB - Embedded newform 192.2.s.a.107.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [192,2,Mod(11,192)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("192.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(192, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 5, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.s (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			107.20
Character	$\chi$	$=$	192.107
Dual form			192.2.s.a.131.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.486023 - 1.32807i) q^{2} +(1.18349 + 1.26466i) q^{3} +(-1.52756 - 1.29095i) q^{4} +(-1.96325 - 2.93821i) q^{5} +(2.25476 - 0.957103i) q^{6} +(1.41332 - 3.41205i) q^{7} +(-2.45691 + 1.40129i) q^{8} +(-0.198726 + 2.99341i) q^{9} +(-4.85635 + 1.17930i) q^{10} +(1.35426 + 0.269378i) q^{11} +(-0.175237 - 3.45967i) q^{12} +(3.69962 + 2.47201i) q^{13} +(-3.84455 - 3.53533i) q^{14} +(1.39236 - 5.96017i) q^{15} +(0.666898 + 3.94401i) q^{16} +(-1.07694 - 1.07694i) q^{17} +(3.87889 + 1.71879i) q^{18} +(2.55792 + 1.70915i) q^{19} +(-0.794095 + 7.02276i) q^{20} +(5.98772 - 2.25075i) q^{21} +(1.01595 - 1.66763i) q^{22} +(-0.348914 - 0.842354i) q^{23} +(-4.67986 - 1.44875i) q^{24} +(-2.86532 + 6.91750i) q^{25} +(5.08112 - 3.71192i) q^{26} +(-4.02083 + 3.29134i) q^{27} +(-6.56372 + 3.38760i) q^{28} +(1.64436 + 8.26676i) q^{29} +(-7.23884 - 4.74594i) q^{30} -7.50303 q^{31} +(5.56207 + 1.03119i) q^{32} +(1.26207 + 2.03148i) q^{33} +(-1.95367 + 0.906837i) q^{34} +(-12.8000 + 2.54608i) q^{35} +(4.16791 - 4.31608i) q^{36} +(-1.83441 - 2.74539i) q^{37} +(3.51308 - 2.56642i) q^{38} +(1.25220 + 7.60435i) q^{39} +(8.94080 + 4.46784i) q^{40} +(9.24158 - 3.82799i) q^{41} +(-0.0789866 - 9.04605i) q^{42} +(-2.87193 - 0.571263i) q^{43} +(-1.72096 - 2.15977i) q^{44} +(9.18543 - 5.29292i) q^{45} +(-1.28829 + 0.0539808i) q^{46} +(3.91043 - 3.91043i) q^{47} +(-4.19857 + 5.51108i) q^{48} +(-4.69487 - 4.69487i) q^{49} +(7.79434 + 7.16743i) q^{50} +(0.0874195 - 2.63650i) q^{51} +(-2.46017 - 8.55218i) q^{52} +(-0.750588 + 3.77346i) q^{53} +(2.41692 + 6.93963i) q^{54} +(-1.86725 - 4.50795i) q^{55} +(1.30887 + 10.3636i) q^{56} +(0.865771 + 5.25765i) q^{57} +(11.7781 + 1.83400i) q^{58} +(1.97738 - 1.32124i) q^{59} +(-9.82120 + 7.30708i) q^{60} +(2.15485 + 10.8331i) q^{61} +(-3.64665 + 9.96458i) q^{62} +(9.93280 + 4.90870i) q^{63} +(4.07280 - 6.88566i) q^{64} -15.7235i q^{65} +(3.31135 - 0.688778i) q^{66} +(1.15899 - 0.230537i) q^{67} +(0.254818 + 3.03536i) q^{68} +(0.652356 - 1.43817i) q^{69} +(-2.83972 + 18.2368i) q^{70} +(-7.50045 - 3.10679i) q^{71} +(-3.70637 - 7.63301i) q^{72} +(-3.51016 + 1.45396i) q^{73} +(-4.53765 + 1.10191i) q^{74} +(-12.1393 + 4.56310i) q^{75} +(-1.70096 - 5.91297i) q^{76} +(2.83313 - 4.24007i) q^{77} +(10.7077 + 2.03288i) q^{78} +(8.03113 - 8.03113i) q^{79} +(10.2791 - 9.70258i) q^{80} +(-8.92102 - 1.18974i) q^{81} +(-0.592231 - 14.1340i) q^{82} +(2.45014 - 3.66690i) q^{83} +(-12.0522 - 4.29169i) q^{84} +(-1.04997 + 5.27857i) q^{85} +(-2.15450 + 3.53649i) q^{86} +(-8.50856 + 11.8631i) q^{87} +(-3.70476 + 1.23586i) q^{88} +(0.100607 + 0.0416728i) q^{89} +(-2.56506 - 14.7714i) q^{90} +(13.6634 - 9.12957i) q^{91} +(-0.554448 + 1.73718i) q^{92} +(-8.87972 - 9.48878i) q^{93} +(-3.29278 - 7.09391i) q^{94} -10.8712i q^{95} +(5.27852 + 8.25453i) q^{96} +12.5267i q^{97} +(-8.51695 + 3.95332i) q^{98} +(-1.07549 + 4.00031i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{16}\right)$

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 $

$2$	0.486023	−	1.32807i	0.343670	−	0.939090i
$2$	0.486023	−	1.32807i	0.343670	−	0.939090i
$3$	1.18349	+	1.26466i	0.683285	+	0.730151i
$3$	1.18349	+	1.26466i	0.683285	+	0.730151i
$4$	−1.52756	−	1.29095i	−0.763782	−	0.645475i
$5$	−1.96325	−	2.93821i	−0.877993	−	1.31401i	−0.948591	−	0.316504i	$-0.897491\pi$
$5$	−1.96325	−	2.93821i	−0.877993	−	1.31401i	0.0705987	−	0.997505i	$-0.477509\pi$
$6$	2.25476	−	0.957103i	0.920503	−	0.390735i
$7$	1.41332	−	3.41205i	0.534184	−	1.28963i	−0.394546	−	0.918876i	$-0.629098\pi$
$7$	1.41332	−	3.41205i	0.534184	−	1.28963i	0.928730	−	0.370757i	$-0.120902\pi$
$8$	−2.45691	+	1.40129i	−0.868648	+	0.495429i
$9$	−0.198726	+	2.99341i	−0.0662420	+	0.997804i
$10$	−4.85635	+	1.17930i	−1.53571	+	0.372929i
$11$	1.35426	+	0.269378i	0.408324	+	0.0812206i	0.394979	−	0.918690i	$-0.370752\pi$
$11$	1.35426	+	0.269378i	0.408324	+	0.0812206i	0.0133450	+	0.999911i	$0.495752\pi$
$12$	−0.175237	−	3.45967i	−0.0505864	−	0.998720i
$13$	3.69962	+	2.47201i	1.02609	+	0.685612i	0.950244	−	0.311507i	$-0.100834\pi$
$13$	3.69962	+	2.47201i	1.02609	+	0.685612i	0.0758473	+	0.997119i	$0.475834\pi$
$14$	−3.84455	−	3.53533i	−1.02750	−	0.944856i
$15$	1.39236	−	5.96017i	0.359506	−	1.53891i
$16$	0.666898	+	3.94401i	0.166724	+	0.986004i
$17$	−1.07694	−	1.07694i	−0.261196	−	0.261196i	0.564344	−	0.825540i	$-0.309129\pi$
$17$	−1.07694	−	1.07694i	−0.261196	−	0.261196i	−0.825540	+	0.564344i	$0.809129\pi$
$18$	3.87889	+	1.71879i	0.914262	+	0.405123i
$19$	2.55792	+	1.70915i	0.586827	+	0.392105i	0.813242	−	0.581926i	$-0.197701\pi$
$19$	2.55792	+	1.70915i	0.586827	+	0.392105i	−0.226415	+	0.974031i	$0.572701\pi$
$20$	−0.794095	+	7.02276i	−0.177565	+	1.57034i
$21$	5.98772	−	2.25075i	1.30663	−	0.491153i
$22$	1.01595	−	1.66763i	0.216602	−	0.355540i
$23$	−0.348914	−	0.842354i	−0.0727537	−	0.175643i	0.883319	−	0.468772i	$-0.155303\pi$
$23$	−0.348914	−	0.842354i	−0.0727537	−	0.175643i	−0.956073	+	0.293129i	$0.905303\pi$
$24$	−4.67986	−	1.44875i	−0.955273	−	0.295725i
$25$	−2.86532	+	6.91750i	−0.573065	+	1.38350i
$26$	5.08112	−	3.71192i	0.996489	−	0.727968i
$27$	−4.02083	+	3.29134i	−0.773810	+	0.633418i
$28$	−6.56372	+	3.38760i	−1.24043	+	0.640196i
$29$	1.64436	+	8.26676i	0.305350	+	1.53510i	0.763255	+	0.646097i	$0.223600\pi$
$29$	1.64436	+	8.26676i	0.305350	+	1.53510i	−0.457905	+	0.889001i	$0.651400\pi$
$30$	−7.23884	−	4.74594i	−1.32162	−	0.866486i
$31$	−7.50303			−1.34758			−0.673792	−	0.738921i	$-0.735336\pi$
$31$	−7.50303			−1.34758			−0.673792	+	0.738921i	$0.735336\pi$
$32$	5.56207	+	1.03119i	0.983245	+	0.182291i
$33$	1.26207	+	2.03148i	0.219698	+	0.353635i
$34$	−1.95367	+	0.906837i	−0.335052	+	0.155521i
$35$	−12.8000	+	2.54608i	−2.16360	+	0.430367i
$36$	4.16791	−	4.31608i	0.694652	−	0.719346i
$37$	−1.83441	−	2.74539i	−0.301576	−	0.451340i	0.649471	−	0.760386i	$-0.274990\pi$
$37$	−1.83441	−	2.74539i	−0.301576	−	0.451340i	−0.951047	+	0.309046i	$0.899990\pi$
$38$	3.51308	−	2.56642i	0.569897	−	0.416329i
$39$	1.25220	+	7.60435i	0.200512	+	1.21767i
$40$	8.94080	+	4.46784i	1.41367	+	0.706428i
$41$	9.24158	−	3.82799i	1.44329	−	0.597831i	0.482698	−	0.875787i	$-0.339657\pi$
$41$	9.24158	−	3.82799i	1.44329	−	0.597831i	0.960594	+	0.277956i	$0.0896569\pi$
$42$	−0.0789866	−	9.04605i	−0.0121879	−	1.39584i
$43$	−2.87193	−	0.571263i	−0.437966	−	0.0871168i	−0.0288173	−	0.999585i	$-0.509174\pi$
$43$	−2.87193	−	0.571263i	−0.437966	−	0.0871168i	−0.409148	+	0.912468i	$0.634174\pi$
$44$	−1.72096	−	2.15977i	−0.259444	−	0.325597i
$45$	9.18543	−	5.29292i	1.36928	−	0.789022i
$46$	−1.28829	+	0.0539808i	−0.189948	+	0.00795903i
$47$	3.91043	−	3.91043i	0.570395	−	0.570395i	−0.361844	−	0.932239i	$-0.617853\pi$
$47$	3.91043	−	3.91043i	0.570395	−	0.570395i	0.932239	+	0.361844i	$0.117853\pi$
$48$	−4.19857	+	5.51108i	−0.606011	+	0.795456i
$49$	−4.69487	−	4.69487i	−0.670696	−	0.670696i
$50$	7.79434	+	7.16743i	1.10229	+	1.01363i
$51$	0.0874195	−	2.63650i	0.0122412	−	0.369184i
$52$	−2.46017	−	8.55218i	−0.341164	−	1.18597i
$53$	−0.750588	+	3.77346i	−0.103101	+	0.518325i	0.894375	+	0.447319i	$0.147621\pi$
$53$	−0.750588	+	3.77346i	−0.103101	+	0.518325i	−0.997476	+	0.0710061i	$0.977379\pi$
$54$	2.41692	+	6.93963i	0.328901	+	0.944364i
$55$	−1.86725	−	4.50795i	−0.251780	−	0.607852i
$56$	1.30887	+	10.3636i	0.174905	+	1.38489i
$57$	0.865771	+	5.25765i	0.114674	+	0.696392i
$58$	11.7781	+	1.83400i	1.54654	+	0.240816i
$59$	1.97738	−	1.32124i	0.257433	−	0.172011i	−0.420156	−	0.907452i	$-0.638025\pi$
$59$	1.97738	−	1.32124i	0.257433	−	0.172011i	0.677589	+	0.735440i	$0.263025\pi$
$60$	−9.82120	+	7.30708i	−1.26791	+	0.943339i
$61$	2.15485	+	10.8331i	0.275900	+	1.38704i	0.831469	+	0.555572i	$0.187501\pi$
$61$	2.15485	+	10.8331i	0.275900	+	1.38704i	−0.555569	+	0.831471i	$0.687499\pi$
$62$	−3.64665	+	9.96458i	−0.463124	+	1.26550i
$63$	9.93280	+	4.90870i	1.25142	+	0.618438i
$64$	4.07280	−	6.88566i	0.509100	−	0.860708i
$65$		−	15.7235i		−	1.95025i
$66$	3.31135	−	0.688778i	0.407599	−	0.0847827i
$67$	1.15899	−	0.230537i	0.141593	−	0.0281646i	−0.123785	−	0.992309i	$-0.539503\pi$
$67$	1.15899	−	0.230537i	0.141593	−	0.0281646i	0.265378	+	0.964144i	$0.414503\pi$
$68$	0.254818	+	3.03536i	0.0309012	+	0.368092i
$69$	0.652356	−	1.43817i	0.0785344	−	0.173135i
$70$	−2.83972	+	18.2368i	−0.339412	+	2.17972i
$71$	−7.50045	−	3.10679i	−0.890139	−	0.368708i	−0.109719	−	0.993963i	$-0.534995\pi$
$71$	−7.50045	−	3.10679i	−0.890139	−	0.368708i	−0.780421	+	0.625255i	$0.784995\pi$
$72$	−3.70637	−	7.63301i	−0.436800	−	0.899559i
$73$	−3.51016	+	1.45396i	−0.410833	+	0.170173i	−0.578521	−	0.815667i	$-0.696370\pi$
$73$	−3.51016	+	1.45396i	−0.410833	+	0.170173i	0.167688	+	0.985840i	$0.446370\pi$
$74$	−4.53765	+	1.10191i	−0.527491	+	0.128095i
$75$	−12.1393	+	4.56310i	−1.40173	+	0.526902i
$76$	−1.70096	−	5.91297i	−0.195113	−	0.678265i
$77$	2.83313	−	4.24007i	0.322865	−	0.483201i
$78$	10.7077	+	2.03288i	1.21241	+	0.230178i
$79$	8.03113	−	8.03113i	0.903573	−	0.903573i	−0.0921705	−	0.995743i	$-0.529380\pi$
$79$	8.03113	−	8.03113i	0.903573	−	0.903573i	0.995743	+	0.0921705i	$0.0293805\pi$
$80$	10.2791	−	9.70258i	1.14923	−	1.08478i
$81$	−8.92102	−	1.18974i	−0.991224	−	0.132193i
$82$	−0.592231	−	14.1340i	−0.0654009	−	1.56084i
$83$	2.45014	−	3.66690i	0.268938	−	0.402494i	−0.672278	−	0.740298i	$-0.734684\pi$
$83$	2.45014	−	3.66690i	0.268938	−	0.402494i	0.941216	+	0.337804i	$0.109684\pi$
$84$	−12.0522	−	4.29169i	−1.31500	−	0.468262i
$85$	−1.04997	+	5.27857i	−0.113886	+	0.572542i
$86$	−2.15450	+	3.53649i	−0.232326	+	0.381350i
$87$	−8.50856	+	11.8631i	−0.912213	+	1.27186i
$88$	−3.70476	+	1.23586i	−0.394929	+	0.131743i
$89$	0.100607	+	0.0416728i	0.0106643	+	0.00441731i	0.388009	−	0.921655i	$-0.373163\pi$
$89$	0.100607	+	0.0416728i	0.0106643	+	0.00441731i	−0.377345	+	0.926073i	$0.623163\pi$
$90$	−2.56506	−	14.7714i	−0.270381	−	1.55704i
$91$	13.6634	−	9.12957i	1.43231	−	0.957039i
$92$	−0.554448	+	1.73718i	−0.0578052	+	0.181114i
$93$	−8.87972	−	9.48878i	−0.920784	−	0.983940i
$94$	−3.29278	−	7.09391i	−0.339625	−	0.731681i
$95$		−	10.8712i		−	1.11536i
$96$	5.27852	+	8.25453i	0.538737	+	0.842474i
$97$			12.5267i			1.27189i	0.771735	+	0.635945i	$0.219389\pi$
$97$			12.5267i			1.27189i	−0.771735	+	0.635945i	$0.780611\pi$
$98$	−8.51695	+	3.95332i	−0.860342	+	0.399346i
$99$	−1.07549	+	4.00031i	−0.108090	+	0.402047i
$100$	13.3071	−	6.86793i	1.33071	−	0.686793i
$101$	−7.14638	+	4.77506i	−0.711091	+	0.475136i	−0.857760	−	0.514050i	$-0.828145\pi$
$101$	−7.14638	+	4.77506i	−0.711091	+	0.475136i	0.146669	+	0.989186i	$0.453145\pi$
$102$	−3.45898	−	1.39750i	−0.342490	−	0.138373i
$103$	−15.7808	−	6.53662i	−1.55493	−	0.644072i	−0.570729	−	0.821139i	$-0.693339\pi$
$103$	−15.7808	−	6.53662i	−1.55493	−	0.644072i	−0.984199	+	0.177066i	$0.943339\pi$
$104$	−12.5536	−	0.889270i	−1.23098	−	0.0872001i
$105$	−18.3686	−	13.1744i	−1.79259	−	1.28569i
$106$	4.64663	+	2.83083i	0.451321	+	0.274954i
$107$	0.485556	−	2.44105i	0.0469404	−	0.235986i	−0.950192	−	0.311666i	$-0.899113\pi$
$107$	0.485556	−	2.44105i	0.0469404	−	0.235986i	0.997132	+	0.0756806i	$0.0241130\pi$
$108$	10.3910	+	0.162970i	0.999877	+	0.0156818i
$109$	1.80331	−	2.69885i	0.172726	−	0.258503i	−0.734999	−	0.678068i	$-0.762817\pi$
$109$	1.80331	−	2.69885i	0.172726	−	0.258503i	0.907725	+	0.419565i	$0.137817\pi$
$110$	−6.89442	+	0.288884i	−0.657357	+	0.0275440i
$111$	1.30099	−	5.56904i	0.123484	−	0.528590i
$112$	14.3997	+	3.29866i	1.36064	+	0.311694i
$113$	−7.35380	+	7.35380i	−0.691788	+	0.691788i	−0.962625	−	0.270837i	$-0.912699\pi$
$113$	−7.35380	+	7.35380i	−0.691788	+	0.691788i	0.270837	+	0.962625i	$0.412699\pi$
$114$	7.40333	+	1.40553i	0.693385	+	0.131640i
$115$	−1.79001	+	2.67894i	−0.166919	+	0.249812i
$116$	8.16010	−	14.7508i	0.757647	−	1.36958i
$117$	−8.13495	+	10.5832i	−0.752077	+	0.978421i
$118$	−0.793657	−	3.26827i	−0.0730621	−	0.300868i
$119$	−5.19662	+	2.15251i	−0.476373	+	0.197320i
$120$	4.93101	+	16.5947i	0.450137	+	1.51488i
$121$	−8.40123	−	3.47990i	−0.763748	−	0.316355i
$122$	15.4345	+	2.40336i	1.39738	+	0.217590i
$123$	15.7784	+	7.15708i	1.42269	+	0.645332i
$124$	11.4613	+	9.68603i	1.02926	+	0.869831i
$125$	8.62114	−	1.71485i	0.771099	−	0.153381i
$126$	11.3467	−	10.8058i	1.01084	−	0.962654i
$127$		−	3.48281i		−	0.309050i	−0.987989	−	0.154525i	$-0.950615\pi$
$127$		−	3.48281i		−	0.309050i	0.987989	−	0.154525i	$-0.0493846\pi$
$128$	−7.16520	−	8.75557i	−0.633320	−	0.773890i
$129$	−2.67644	−	4.30810i	−0.235647	−	0.379307i
$130$	−20.8819	−	7.64196i	−1.83147	−	0.670245i
$131$	1.52866	+	7.68509i	0.133560	+	0.671449i	0.988316	+	0.152420i	$0.0487066\pi$
$131$	1.52866	+	7.68509i	0.133560	+	0.671449i	−0.854756	+	0.519030i	$0.826293\pi$
$132$	0.694644	−	4.73248i	0.0604610	−	0.411909i
$133$	9.44684	−	6.31218i	0.819145	−	0.547335i
$134$	0.257125	−	1.65127i	0.0222122	−	0.142648i
$135$	17.5646	+	5.35235i	1.51172	+	0.460657i
$136$	4.15504	+	1.13684i	0.356291	+	0.0974832i
$137$	1.50317	+	3.62897i	0.128424	+	0.310044i	0.974993	−	0.222236i	$-0.0713355\pi$
$137$	1.50317	+	3.62897i	0.128424	+	0.310044i	−0.846569	+	0.532280i	$0.821335\pi$
$138$	−1.59294	−	1.56536i	−0.135600	−	0.133252i
$139$	−4.01465	+	20.1830i	−0.340518	+	1.71190i	0.308581	+	0.951198i	$0.400146\pi$
$139$	−4.01465	+	20.1830i	−0.340518	+	1.71190i	−0.649100	+	0.760703i	$0.724854\pi$
$140$	22.8397	+	12.6349i	1.93031	+	1.06784i
$141$	9.57330	+	0.317426i	0.806218	+	0.0267321i
$142$	−7.77143	+	8.45118i	−0.652164	+	0.709207i
$143$	4.34433	+	4.34433i	0.363291	+	0.363291i
$144$	−11.9386	+	1.21252i	−0.994882	+	0.101043i
$145$	21.0612	−	21.0612i	1.74904	−	1.74904i
$146$	0.224943	+	5.36841i	0.0186164	+	0.444293i
$147$	0.381102	−	11.4937i	0.0314328	−	0.947986i
$148$	−0.741983	+	6.56189i	−0.0609906	+	0.539384i
$149$	−20.3831	−	4.05445i	−1.66985	−	0.332153i	−0.732557	−	0.680705i	$-0.761673\pi$
$149$	−20.3831	−	4.05445i	−1.66985	−	0.332153i	−0.937289	+	0.348552i	$0.886673\pi$
$150$	0.160135	+	18.3397i	0.0130750	+	1.49743i
$151$	−2.14039	+	0.886580i	−0.174183	+	0.0721488i	−0.468071	−	0.883691i	$-0.655051\pi$
$151$	−2.14039	+	0.886580i	−0.174183	+	0.0721488i	0.293888	+	0.955840i	$0.405051\pi$
$152$	−8.67957	−	0.614841i	−0.704006	−	0.0498702i
$153$	3.43773	−	3.00970i	0.277924	−	0.243320i
$154$	−4.25417	−	5.82337i	−0.342811	−	0.469261i
$155$	14.7303	+	22.0455i	1.18317	+	1.77074i
$156$	7.90402	−	13.2327i	0.632828	−	1.05946i
$157$	1.80242	−	0.358524i	0.143849	−	0.0286133i	−0.122641	−	0.992451i	$-0.539136\pi$
$157$	1.80242	−	0.358524i	0.143849	−	0.0286133i	0.266489	+	0.963838i	$0.414136\pi$
$158$	−6.76262	−	14.5693i	−0.538005	−	1.15907i
$159$	−5.66045	+	3.51660i	−0.448903	+	0.278884i
$160$	−7.88988	−	18.3670i	−0.623750	−	1.45204i
$161$	−3.36728			−0.265379
$162$	−5.91588	+	11.2695i	−0.464795	+	0.885418i
$163$	−2.11463	−	10.6309i	−0.165630	−	0.832679i	−0.970847	−	0.239699i	$-0.922951\pi$
$163$	−2.11463	−	10.6309i	−0.165630	−	0.832679i	0.805217	−	0.592980i	$-0.202049\pi$
$164$	−19.0588	−	6.08292i	−1.48824	−	0.474996i
$165$	3.49115	−	7.69653i	0.271786	−	0.599174i
$166$	−3.67908	−	5.03617i	−0.285552	−	0.390882i
$167$	5.11061	−	12.3381i	0.395471	−	0.954751i	−0.593255	−	0.805014i	$-0.702158\pi$
$167$	5.11061	−	12.3381i	0.395471	−	0.954751i	0.988726	−	0.149736i	$-0.0478425\pi$
$168$	−11.5573	+	13.9204i	−0.891668	+	1.07398i
$169$	2.60150	+	6.28058i	0.200115	+	0.483121i
$170$	6.50002	+	3.95995i	0.498529	+	0.303714i
$171$	−5.62450	+	7.31725i	−0.430116	+	0.559564i
$172$	3.64959	+	4.58016i	0.278278	+	0.349234i
$173$	−2.34005	−	1.56357i	−0.177911	−	0.118876i	0.463426	−	0.886136i	$-0.346620\pi$
$173$	−2.34005	−	1.56357i	−0.177911	−	0.118876i	−0.641337	+	0.767259i	$0.721620\pi$
$174$	11.6198	+	17.0658i	0.880893	+	1.29375i
$175$	19.5532	+	19.5532i	1.47809	+	1.47809i
$176$	−0.159282	+	5.52085i	−0.0120063	+	0.416150i
$177$	4.01113	+	0.937041i	0.301495	+	0.0704323i
$178$	0.104242	−	0.113360i	0.00781326	−	0.00849666i
$179$	−5.84520	−	3.90564i	−0.436891	−	0.291921i	0.317609	−	0.948222i	$-0.397120\pi$
$179$	−5.84520	−	3.90564i	−0.436891	−	0.291921i	−0.754499	+	0.656301i	$0.772120\pi$
$180$	−20.8642	−	3.77266i	−1.55513	−	0.281197i
$181$	25.4769	+	5.06767i	1.89368	+	0.376677i	0.997722	−	0.0674565i	$-0.0214884\pi$
$181$	25.4769	+	5.06767i	1.89368	+	0.376677i	0.895961	+	0.444133i	$0.146488\pi$
$182$	−5.48403	−	22.5831i	−0.406504	−	1.67397i
$183$	−11.1500	+	15.5460i	−0.824232	+	1.14919i
$184$	2.03763	+	1.58066i	0.150216	+	0.116528i
$185$	−4.46513	+	10.7798i	−0.328283	+	0.792546i
$186$	−16.9175	+	7.18117i	−1.24045	+	0.526549i
$187$	−1.16835	−	1.74855i	−0.0854379	−	0.127867i
$188$	−11.0216	+	0.925260i	−0.803833	+	0.0674815i
$189$	5.54749	+	18.3710i	0.403521	+	1.33629i
$190$	−14.4378	−	5.28365i	−1.04742	−	0.383316i
$191$	−5.07582			−0.367273			−0.183637	−	0.982994i	$-0.558787\pi$
$191$	−5.07582			−0.367273			−0.183637	+	0.982994i	$0.558787\pi$
$192$	13.5281	−	2.99838i	0.976307	−	0.216389i
$193$	−10.3233			−0.743087			−0.371544	−	0.928416i	$-0.621171\pi$
$193$	−10.3233			−0.743087			−0.371544	+	0.928416i	$0.621171\pi$
$194$	16.6363	+	6.08825i	1.19442	+	0.437111i
$195$	19.8848	−	18.6085i	1.42398	−	1.33258i
$196$	1.11087	+	13.2326i	0.0793478	+	0.945182i
$197$	2.22569	+	3.33097i	0.158574	+	0.237322i	0.902246	−	0.431223i	$-0.141918\pi$
$197$	2.22569	+	3.33097i	0.158574	+	0.237322i	−0.743672	+	0.668545i	$0.766918\pi$
$198$	4.79000	+	3.37257i	0.340411	+	0.239678i
$199$	4.93691	−	11.9188i	0.349968	−	0.844898i	−0.646655	−	0.762783i	$-0.723832\pi$
$199$	4.93691	−	11.9188i	0.349968	−	0.844898i	0.996623	−	0.0821152i	$-0.0261675\pi$
$200$	−2.65356	−	21.0108i	−0.187635	−	1.48569i
$201$	1.66320	+	1.19289i	0.117313	+	0.0841398i
$202$	2.86833	+	11.8117i	0.201815	+	0.831069i
$203$	30.5306	+	6.07291i	2.14283	+	0.426235i
$204$	−3.53713	+	3.91456i	−0.247648	+	0.274074i
$205$	−29.3910	−	19.6384i	−2.05275	−	1.37161i
$206$	−16.3509	+	17.7811i	−1.13922	+	1.23887i
$207$	2.59085	−	0.877047i	0.180077	−	0.0609590i
$208$	−7.28237	+	16.2399i	−0.504942	+	1.12604i
$209$	3.00367	+	3.00367i	0.207768	+	0.207768i
$210$	−26.4242	+	17.9918i	−1.82344	+	1.24155i
$211$	−11.8550	−	7.92128i	−0.816134	−	0.545323i	0.0759927	−	0.997108i	$-0.475787\pi$
$211$	−11.8550	−	7.92128i	−0.816134	−	0.545323i	−0.892127	+	0.451785i	$0.850787\pi$
$212$	6.01792	−	4.79523i	0.413312	−	0.329338i
$213$	−4.94764	−	13.1623i	−0.339007	−	0.901869i
$214$	−3.00591	−	1.83126i	−0.205480	−	0.125183i
$215$	3.95983	+	9.55988i	0.270058	+	0.651978i
$216$	5.26672	−	13.7208i	0.358355	−	0.933586i
$217$	−10.6042	+	25.6007i	−0.719857	+	1.73789i
$218$	−2.70782	−	3.70664i	−0.183397	−	0.251045i
$219$	−5.99299	−	2.71842i	−0.404968	−	0.183694i
$220$	−2.96719	+	9.29671i	−0.200048	+	0.626784i
$221$	−1.32206	−	6.64647i	−0.0889317	−	0.447090i
$222$	−6.76379	−	4.43449i	−0.453956	−	0.297623i
$223$	15.0068			1.00493			0.502464	−	0.864598i	$-0.332427\pi$
$223$	15.0068			1.00493			0.502464	+	0.864598i	$0.332427\pi$
$224$	11.3795	−	17.5207i	0.760322	−	1.17065i
$225$	−20.1375	−	9.95177i	−1.34250	−	0.663452i
$226$	6.19228	+	13.3405i	0.411904	+	0.887398i
$227$	14.3174	−	2.84791i	0.950278	−	0.189022i	0.304470	−	0.952522i	$-0.401521\pi$
$227$	14.3174	−	2.84791i	0.950278	−	0.189022i	0.645808	+	0.763500i	$0.276521\pi$
$228$	5.46484	−	9.14905i	0.361918	−	0.605911i
$229$	−9.15707	−	13.7045i	−0.605116	−	0.905620i	0.394797	−	0.918768i	$-0.370815\pi$
$229$	−9.15707	−	13.7045i	−0.605116	−	0.905620i	−0.999914	+	0.0131478i	$0.995815\pi$
$230$	2.68784	+	3.67929i	0.177231	+	0.242605i
$231$	8.71521	−	1.43512i	0.573419	−	0.0944242i
$232$	−15.6241	−	18.0064i	−1.02577	−	1.18218i
$233$	14.9724	−	6.20176i	0.980873	−	0.406291i	0.166124	−	0.986105i	$-0.446875\pi$
$233$	14.9724	−	6.20176i	0.980873	−	0.406291i	0.814749	+	0.579814i	$0.196875\pi$
$234$	10.1016	+	15.9475i	0.660359	+	1.04252i
$235$	−19.1668	−	3.81252i	−1.25031	−	0.248702i
$236$	−4.72624	−	0.534417i	−0.307652	−	0.0347876i
$237$	19.6614	+	0.651920i	1.27714	+	0.0423467i
$238$	0.333016	+	7.94767i	0.0215863	+	0.515171i
$239$	−13.3330	+	13.3330i	−0.862438	+	0.862438i	−0.991621	−	0.129182i	$-0.958765\pi$
$239$	−13.3330	+	13.3330i	−0.862438	+	0.862438i	0.129182	+	0.991621i	$0.458765\pi$
$240$	24.4356	+	1.51666i	1.57731	+	0.0979000i
$241$	12.8148	+	12.8148i	0.825476	+	0.825476i	0.986887	−	0.161411i	$-0.0516046\pi$
$241$	12.8148	+	12.8148i	0.825476	+	0.825476i	−0.161411	+	0.986887i	$0.551605\pi$
$242$	−8.70476	+	9.46614i	−0.559563	+	0.608507i
$243$	−9.05328	−	12.6901i	−0.580768	−	0.814069i
$244$	10.6934	−	19.3301i	0.684574	−	1.23748i
$245$	−4.57732	+	23.0117i	−0.292434	+	1.47017i
$246$	17.1738	−	17.4763i	1.09496	−	1.11425i
$247$	5.23831	+	12.6464i	0.333306	+	0.804671i
$248$	18.4343	−	10.5139i	1.17058	−	0.667633i
$249$	7.53708	−	1.24112i	0.477643	−	0.0786529i
$250$	1.91262	−	12.2830i	0.120965	−	0.776844i
$251$	−15.4290	+	10.3094i	−0.973872	+	0.650721i	−0.937268	−	0.348609i	$-0.886654\pi$
$251$	−15.4290	+	10.3094i	−0.973872	+	0.650721i	−0.0366041	+	0.999330i	$0.511654\pi$
$252$	−8.83610	−	20.3211i	−0.556622	−	1.28011i
$253$	−0.245608	−	1.23475i	−0.0154412	−	0.0776283i
$254$	−4.62543	−	1.69273i	−0.290225	−	0.106211i
$255$	−7.91822	+	4.91925i	−0.495858	+	0.308056i
$256$	−15.1105	+	5.26051i	−0.944406	+	0.328782i
$257$			7.36483i			0.459405i	0.973261	+	0.229703i	$0.0737754\pi$
$257$			7.36483i			0.459405i	−0.973261	+	0.229703i	$0.926225\pi$
$258$	−7.02228	+	1.46067i	−0.437188	+	0.0909374i
$259$	−11.9600	+	2.37900i	−0.743160	+	0.147824i
$260$	−20.2982	+	24.0186i	−1.25884	+	1.48957i
$261$	−25.0726	+	3.27943i	−1.55195	+	0.202991i
$262$	10.9493	+	1.70496i	0.676452	+	0.105333i
$263$	21.2218	+	8.79034i	1.30859	+	0.542036i	0.924473	−	0.381248i	$-0.124506\pi$
$263$	21.2218	+	8.79034i	1.30859	+	0.542036i	0.384118	+	0.923284i	$0.374506\pi$
$264$	−5.94747	−	3.22263i	−0.366042	−	0.198339i
$265$	12.5608	−	5.20286i	0.771605	−	0.319609i
$266$	−3.79166	−	15.6140i	−0.232482	−	0.957354i
$267$	0.0663650	+	0.176553i	0.00406147	+	0.0108048i
$268$	−2.06804	−	1.14403i	−0.126326	−	0.0698831i
$269$	−3.20130	+	4.79109i	−0.195187	+	0.292118i	−0.916134	−	0.400872i	$-0.868707\pi$
$269$	−3.20130	+	4.79109i	−0.195187	+	0.292118i	0.720947	+	0.692990i	$0.243707\pi$
$270$	15.6451	−	20.7257i	0.952130	−	1.26132i
$271$	−11.1155	+	11.1155i	−0.675220	+	0.675220i	−0.958915	−	0.283695i	$-0.908440\pi$
$271$	−11.1155	+	11.1155i	−0.675220	+	0.675220i	0.283695	+	0.958915i	$0.408440\pi$
$272$	3.52925	−	4.96567i	0.213992	−	0.301088i
$273$	27.7162	+	6.47479i	1.67746	+	0.391872i
$274$	5.55012	−	0.232556i	0.335295	−	0.0140492i
$275$	−5.74381	+	8.59621i	−0.346364	+	0.518371i
$276$	−2.85312	+	1.35474i	−0.171738	+	0.0815457i
$277$	−0.155896	+	0.783742i	−0.00936688	+	0.0470905i	−0.985186	−	0.171489i	$-0.945142\pi$
$277$	−0.155896	+	0.783742i	−0.00936688	+	0.0470905i	0.975819	+	0.218579i	$0.0701422\pi$
$278$	24.8533	+	15.1412i	1.49060	+	0.908107i
$279$	1.49105	−	22.4596i	0.0892666	−	1.34462i
$280$	27.8807	−	24.1920i	1.66619	−	1.44575i
$281$	2.65178	+	1.09840i	0.158192	+	0.0655253i	0.460374	−	0.887725i	$-0.347715\pi$
$281$	2.65178	+	1.09840i	0.158192	+	0.0655253i	−0.302182	+	0.953250i	$0.597715\pi$
$282$	5.07441	−	12.5598i	0.302177	−	0.747924i
$283$	25.0238	−	16.7204i	1.48751	−	0.993922i	0.495384	−	0.868674i	$-0.335027\pi$
$283$	25.0238	−	16.7204i	1.48751	−	0.993922i	0.992125	−	0.125248i	$-0.0399727\pi$
$284$	7.44670	+	14.4285i	0.441880	+	0.856175i
$285$	13.7484	−	12.8659i	0.814382	−	0.762110i
$286$	7.88104	−	3.65815i	0.466016	−	0.216311i
$287$		−	36.9429i		−	2.18067i
$288$	−4.19211	+	16.4446i	−0.247023	+	0.969010i
$289$		−	14.6804i		−	0.863554i
$290$	−17.7346	−	38.2071i	−1.04141	−	2.24360i
$291$	−15.8420	+	14.8251i	−0.928672	+	0.869064i
$292$	7.23898	+	2.31043i	0.423629	+	0.135208i
$293$	8.66794	−	5.79173i	0.506386	−	0.338356i	−0.275992	−	0.961160i	$-0.589006\pi$
$293$	8.66794	−	5.79173i	0.506386	−	0.338356i	0.782378	+	0.622803i	$0.214006\pi$
$294$	−15.0793	−	6.09235i	−0.879442	−	0.355313i
$295$	−7.76419	−	3.21603i	−0.452049	−	0.187245i
$296$	8.35406	+	4.17464i	0.485570	+	0.242646i
$297$	−6.33185	+	3.37419i	−0.367411	+	0.195790i
$298$	−15.2913	+	25.0997i	−0.885798	+	1.45399i
$299$	0.791455	−	3.97891i	0.0457710	−	0.230106i
$300$	24.4344	+	8.70086i	1.41072	+	0.502344i
$301$	−6.00813	+	8.99180i	−0.346303	+	0.518279i
$302$	0.137163	+	3.27350i	0.00789286	+	0.188369i
$303$	−14.4965	−	3.38652i	−0.832799	−	0.194551i
$304$	−5.03503	+	11.2283i	−0.288779	+	0.643987i
$305$	27.5996	−	27.5996i	1.58035	−	1.58035i
$306$	−2.32629	−	6.02835i	−0.132985	−	0.344618i
$307$	−1.97934	+	2.96229i	−0.112967	+	0.169067i	−0.883645	−	0.468158i	$-0.844918\pi$
$307$	−1.97934	+	2.96229i	−0.112967	+	0.169067i	0.770678	+	0.637225i	$0.219918\pi$
$308$	−9.80150	+	2.81955i	−0.558492	+	0.160659i
$309$	−10.4097	−	27.6933i	−0.592189	−	1.57542i
$310$	36.4373	−	8.84835i	2.06950	−	0.502553i
$311$	−14.8552	+	6.15323i	−0.842362	+	0.348918i	−0.761785	−	0.647830i	$-0.775677\pi$
$311$	−14.8552	+	6.15323i	−0.842362	+	0.348918i	−0.0805778	+	0.996748i	$0.525677\pi$
$312$	−13.7324	−	16.9285i	−0.777445	−	0.958388i
$313$	19.4086	+	8.03931i	1.09704	+	0.454409i	0.856456	−	0.516220i	$-0.172661\pi$
$313$	19.4086	+	8.03931i	1.09704	+	0.454409i	0.240583	+	0.970629i	$0.422661\pi$
$314$	0.399872	−	2.56800i	0.0225661	−	0.144921i
$315$	−5.07778	−	38.8217i	−0.286100	−	2.18736i
$316$	−22.6358	+	1.90027i	−1.27337	+	0.106899i
$317$	−26.5384	+	5.27881i	−1.49054	+	0.296488i	−0.872095	−	0.489337i	$-0.837239\pi$
$317$	−26.5384	+	5.27881i	−1.49054	+	0.296488i	−0.618449	+	0.785825i	$0.712239\pi$
$318$	1.91919	+	9.22665i	0.107623	+	0.517405i
$319$			11.6383i			0.651618i
$320$	−28.2275	+	1.55154i	−1.57796	+	0.0867337i
$321$	3.66175	−	2.27489i	0.204379	−	0.126972i
$322$	−1.63658	+	4.47200i	−0.0912028	+	0.249215i
$323$	−0.914075	−	4.59536i	−0.0508605	−	0.255693i
$324$	12.0915	+	13.3340i	0.671751	+	0.740777i
$325$	−27.7007	+	18.5090i	−1.53656	+	1.02670i
$326$	−15.1464	−	2.35850i	−0.838883	−	0.130625i
$327$	5.54732	−	0.913471i	0.306767	−	0.0505150i
$328$	−17.3416	+	22.3551i	−0.957530	+	1.23435i
$329$	−7.81591	−	18.8693i	−0.430905	−	1.04030i
$330$	−8.52478	−	8.37720i	−0.469274	−	0.461150i
$331$	0.802821	−	4.03605i	0.0441270	−	0.221841i	−0.952429	−	0.304759i	$-0.901424\pi$
$331$	0.802821	−	4.03605i	0.0441270	−	0.221841i	0.996556	+	0.0829179i	$0.0264239\pi$
$332$	−8.47652	+	2.43840i	−0.465210	+	0.133825i
$333$	8.58263	−	4.94557i	0.470325	−	0.271016i
$334$	−13.9020	−	12.7839i	−0.760686	−	0.699502i
$335$	−2.95275	−	2.95275i	−0.161326	−	0.161326i
$336$	12.8702	+	22.1146i	0.702125	+	1.20645i
$337$	4.18438	−	4.18438i	0.227938	−	0.227938i	−0.583893	−	0.811831i	$-0.698471\pi$
$337$	4.18438	−	4.18438i	0.227938	−	0.227938i	0.811831	+	0.583893i	$0.198471\pi$
$338$	9.60547	−	0.402480i	0.522468	−	0.0218920i
$339$	−18.0032	−	0.596938i	−0.977798	−	0.0324212i
$340$	8.41827	−	6.70789i	0.456545	−	0.363786i
$341$	−10.1610	−	2.02115i	−0.550250	−	0.109452i
$342$	6.98421	+	11.0261i	0.377663	+	0.596224i
$343$	1.22987	−	0.509431i	0.0664070	−	0.0275067i
$344$	7.85658	−	2.62086i	0.423598	−	0.141307i
$345$	−5.50639	+	0.906731i	−0.296454	+	0.0488168i
$346$	−3.21386	+	2.34783i	−0.172778	+	0.126220i
$347$	−4.27956	−	6.40482i	−0.229739	−	0.343829i	0.698634	−	0.715480i	$-0.253792\pi$
$347$	−4.27956	−	6.40482i	−0.229739	−	0.343829i	−0.928373	+	0.371651i	$0.878792\pi$
$348$	28.3121	−	7.13758i	1.51769	−	0.382614i
$349$	−29.3368	+	5.83546i	−1.57036	+	0.312365i	−0.902089	−	0.431550i	$-0.857967\pi$
$349$	−29.3368	+	5.83546i	−1.57036	+	0.312365i	−0.668275	+	0.743915i	$0.732967\pi$
$350$	35.4715	−	16.4648i	1.89603	−	0.880082i
$351$	−23.0118	+	2.23717i	−1.22828	+	0.119411i
$352$	7.25469	+	2.89480i	0.386676	+	0.154293i
$353$	34.8629			1.85556			0.927782	−	0.373122i	$-0.121713\pi$
$353$	34.8629			1.85556			0.927782	+	0.373122i	$0.121713\pi$
$354$	3.19396	−	4.87165i	0.169757	−	0.258925i
$355$	5.59686	+	28.1373i	0.297050	+	1.49337i
$356$	−0.0998860	−	0.193536i	−0.00529395	−	0.0102574i
$357$	−8.87232	−	4.02449i	−0.469573	−	0.212999i
$358$	−8.02788	+	5.86463i	−0.424287	+	0.309955i
$359$	−6.91509	+	16.6945i	−0.364965	+	0.881103i	0.629594	+	0.776924i	$0.283221\pi$
$359$	−6.91509	+	16.6945i	−0.364965	+	0.881103i	−0.994559	+	0.104178i	$0.966779\pi$
$360$	−15.1509	+	25.8756i	−0.798520	+	1.36376i
$361$	−3.64922	−	8.81000i	−0.192064	−	0.463684i
$362$	19.1126	−	31.3722i	1.00454	−	1.64889i
$363$	−5.54184	−	14.7431i	−0.290871	−	0.773812i
$364$	−32.6575	−	3.69273i	−1.71172	−	0.193551i
$365$	11.1634	+	7.45912i	0.584317	+	0.390428i
$366$	15.2271	+	22.3638i	0.795933	+	1.16897i
$367$	13.6204	+	13.6204i	0.710979	+	0.710979i	0.966740	−	0.255761i	$-0.0823260\pi$
$367$	13.6204	+	13.6204i	0.710979	+	0.710979i	−0.255761	+	0.966740i	$0.582326\pi$
$368$	3.08957	−	1.93789i	0.161055	−	0.101019i
$369$	9.62220	+	28.4246i	0.500912	+	1.47972i
$370$	12.1462	+	11.1693i	0.631451	+	0.580662i
$371$	11.8144	+	7.89414i	0.613374	+	0.409843i
$372$	1.31481	+	25.9580i	0.0681695	+	1.34586i
$373$	9.51416	+	1.89248i	0.492625	+	0.0979891i	0.435150	−	0.900358i	$-0.356695\pi$
$373$	9.51416	+	1.89248i	0.492625	+	0.0979891i	0.0574743	+	0.998347i	$0.481695\pi$
$374$	−2.89005	+	0.701813i	−0.149441	+	0.0362899i
$375$	12.3717	+	8.87331i	0.638872	+	0.458216i
$376$	−4.12794	+	15.0872i	−0.212882	+	0.778063i
$377$	−14.3520	+	34.6488i	−0.739165	+	1.78450i
$378$	27.0942	+	1.56125i	1.39358	+	0.0803018i
$379$	−8.54045	−	12.7817i	−0.438693	−	0.656551i	0.544575	−	0.838712i	$-0.316691\pi$
$379$	−8.54045	−	12.7817i	−0.438693	−	0.656551i	−0.983269	+	0.182161i	$0.941691\pi$
$380$	−14.0342	+	16.6064i	−0.719937	+	0.851892i
$381$	4.40457	−	4.12186i	0.225653	−	0.211169i
$382$	−2.46696	+	6.74106i	−0.126221	+	0.344903i
$383$	0.474263			0.0242337			0.0121169	−	0.999927i	$-0.496143\pi$
$383$	0.474263			0.0242337			0.0121169	+	0.999927i	$0.496143\pi$
$384$	2.59290	−	19.4236i	0.132319	−	0.991207i
$385$	−18.0204			−0.918403
$386$	−5.01736	+	13.7101i	−0.255377	+	0.697826i
$387$	2.28075	−	8.48335i	0.115937	−	0.431233i
$388$	16.1713	−	19.1353i	0.820973	−	0.971446i
$389$	3.08095	+	4.61097i	0.156210	+	0.233785i	0.901317	−	0.433160i	$-0.142601\pi$
$389$	3.08095	+	4.61097i	0.156210	+	0.233785i	−0.745107	+	0.666945i	$0.767601\pi$
$390$	−15.0490	−	35.4527i	−0.762034	−	1.79522i
$391$	−0.531404	+	1.28292i	−0.0268742	+	0.0648802i
$392$	18.1137	+	4.95601i	0.914881	+	0.250316i
$393$	−7.90987	+	11.0284i	−0.399000	+	0.556310i
$394$	5.50552	−	1.33695i	0.277364	−	0.0673543i
$395$	−39.3643	−	7.83004i	−1.98063	−	0.393972i
$396$	6.80707	−	4.72233i	0.342068	−	0.237306i
$397$	18.6371	+	12.4529i	0.935369	+	0.624994i	0.927036	−	0.374972i	$-0.122348\pi$
$397$	18.6371	+	12.4529i	0.935369	+	0.624994i	0.00833284	+	0.999965i	$0.497348\pi$
$398$	−13.4295	−	12.3494i	−0.673162	−	0.619018i
$399$	19.1630	+	4.47667i	0.959348	+	0.224114i
$400$	−29.1936	−	6.68761i	−1.45968	−	0.334380i
$401$	−1.22748	−	1.22748i	−0.0612974	−	0.0612974i	0.675794	−	0.737091i	$-0.263801\pi$
$401$	−1.22748	−	1.22748i	−0.0612974	−	0.0612974i	−0.737091	+	0.675794i	$0.763801\pi$
$402$	2.39259	−	1.62908i	0.119332	−	0.0812509i
$403$	−27.7584	−	18.5476i	−1.38274	−	0.923920i
$404$	17.0809	+	1.93141i	0.849807	+	0.0960915i
$405$	14.0185	+	28.5476i	0.696585	+	1.41854i
$406$	22.9039	−	37.5953i	1.13670	−	1.86582i
$407$	−1.74472	−	4.21212i	−0.0864823	−	0.208787i
$408$	3.47971	+	6.60014i	0.172271	+	0.326755i
$409$	8.06274	−	19.4652i	0.398677	−	0.962491i	−0.589303	−	0.807912i	$-0.700598\pi$
$409$	8.06274	−	19.4652i	0.398677	−	0.962491i	0.987980	−	0.154580i	$-0.0494023\pi$
$410$	−40.3660	+	29.4887i	−1.99353	+	1.45634i
$411$	−2.81043	+	6.19583i	−0.138628	+	0.305618i
$412$	15.6677	+	30.3573i	0.771893	+	1.49560i
$413$	−1.71348	−	8.61426i	−0.0843150	−	0.423880i
$414$	0.0944298	−	3.86711i	0.00464097	−	0.190058i
$415$	−15.5844			−0.765006
$416$	18.0285	+	17.5645i	0.883918	+	0.861171i
$417$	−30.2759	+	18.8091i	−1.48262	+	0.921087i
$418$	5.44895	−	2.52924i	0.266517	−	0.123709i
$419$	7.02653	−	1.39766i	0.343269	−	0.0682804i	−0.0204456	−	0.999791i	$-0.506508\pi$
$419$	7.02653	−	1.39766i	0.343269	−	0.0682804i	0.363714	+	0.931511i	$0.381508\pi$
$420$	11.0516	+	43.8376i	0.539264	+	2.13906i
$421$	4.50708	+	6.74533i	0.219662	+	0.328747i	0.924891	−	0.380232i	$-0.124156\pi$
$421$	4.50708	+	6.74533i	0.219662	+	0.328747i	−0.705229	+	0.708979i	$0.749156\pi$
$422$	−16.2819	+	11.8944i	−0.792589	+	0.579012i
$423$	10.9284	+	12.4826i	0.531358	+	0.606927i
$424$	−3.44357	−	10.3228i	−0.167235	−	0.501321i
$425$	10.5355	−	4.36394i	0.511046	−	0.211682i
$426$	−19.8852	+	0.173630i	−0.963443	+	0.00841241i
$427$	40.0087	+	7.95823i	1.93616	+	0.385126i
$428$	−3.89299	+	3.10203i	−0.188175	+	0.149942i
$429$	−0.352647	+	10.6356i	−0.0170260	+	0.513489i
$430$	14.6208	−	0.612628i	0.705078	−	0.0295436i
$431$	−8.97176	+	8.97176i	−0.432154	+	0.432154i	−0.889361	−	0.457206i	$-0.848850\pi$
$431$	−8.97176	+	8.97176i	−0.432154	+	0.432154i	0.457206	+	0.889361i	$0.348850\pi$
$432$	−15.6626	−	13.6632i	−0.753565	−	0.657373i
$433$	−15.2633	−	15.2633i	−0.733509	−	0.733509i	0.237804	−	0.971313i	$-0.423572\pi$
$433$	−15.2633	−	15.2633i	−0.733509	−	0.733509i	−0.971313	+	0.237804i	$0.923572\pi$
$434$	28.8458	+	26.5257i	1.38464	+	1.27327i
$435$	51.5609	+	1.70962i	2.47215	+	0.0819702i
$436$	−6.23875	+	1.79467i	−0.298782	+	0.0859493i
$437$	0.547212	−	2.75102i	0.0261767	−	0.131599i
$438$	−6.52300	+	6.63791i	−0.311681	+	0.317172i
$439$	−2.80587	−	6.77397i	−0.133917	−	0.323304i	0.842669	−	0.538432i	$-0.180983\pi$
$439$	−2.80587	−	6.77397i	−0.133917	−	0.323304i	−0.976586	+	0.215128i	$0.930983\pi$
$440$	10.9046	+	8.45906i	0.519856	+	0.403270i
$441$	14.9867	−	13.1207i	0.713651	−	0.624794i
$442$	−9.46956	−	1.47454i	−0.450421	−	0.0701366i
$443$	2.06022	−	1.37659i	0.0978839	−	0.0654040i	−0.505665	−	0.862730i	$-0.668753\pi$
$443$	2.06022	−	1.37659i	0.0978839	−	0.0654040i	0.603549	+	0.797326i	$0.293753\pi$
$444$	−9.17669	+	6.82755i	−0.435506	+	0.324021i
$445$	−0.0750733	−	0.377419i	−0.00355881	−	0.0178914i
$446$	7.29364	−	19.9301i	0.345364	−	0.943718i
$447$	−18.9956	−	30.5760i	−0.898460	−	1.44620i
$448$	−17.7381	−	23.6282i	−0.838045	−	1.11633i
$449$			12.7302i			0.600774i	0.953817	+	0.300387i	$0.0971158\pi$
$449$			12.7302i			0.600774i	−0.953817	+	0.300387i	$0.902884\pi$
$450$	−23.0040	+	21.9073i	−1.08442	+	1.03272i
$451$	13.5466	−	2.69459i	0.637886	−	0.126883i
$452$	20.7268	−	1.74001i	0.974906	−	0.0818431i
$453$	−3.65434	−	1.65761i	−0.171696	−	0.0778815i
$454$	3.17635	−	20.3987i	0.149074	−	0.957358i
$455$	−53.6492	−	22.2222i	−2.51511	−	1.04179i
$456$	−9.49458	−	11.7044i	−0.444625	−	0.548107i
$457$	−24.7432	+	10.2490i	−1.15744	+	0.479426i	−0.877021	−	0.480453i	$-0.840472\pi$
$457$	−24.7432	+	10.2490i	−1.15744	+	0.479426i	−0.280416	+	0.959879i	$0.590472\pi$
$458$	−22.6512	+	5.50055i	−1.05842	+	0.257024i
$459$	7.87475	+	0.785623i	0.367562	+	0.0366698i
$460$	6.19272	−	1.78143i	0.288737	−	0.0830598i
$461$	10.5730	−	15.8236i	0.492432	−	0.736976i	−0.499142	−	0.866520i	$-0.666351\pi$
$461$	10.5730	−	15.8236i	0.492432	−	0.736976i	0.991574	+	0.129544i	$0.0413513\pi$
$462$	2.32984	−	12.2719i	0.108394	−	0.570943i
$463$	0.428275	−	0.428275i	0.0199036	−	0.0199036i	−0.697085	−	0.716989i	$-0.745520\pi$
$463$	0.428275	−	0.428275i	0.0199036	−	0.0199036i	0.716989	+	0.697085i	$0.245520\pi$
$464$	−31.5076	+	11.9985i	−1.46270	+	0.557015i
$465$	−10.4469	+	44.7194i	−0.484464	+	2.07381i
$466$	−0.959479	−	22.8986i	−0.0444470	−	1.06076i
$467$	19.1176	−	28.6115i	0.884657	−	1.32398i	−0.0607716	−	0.998152i	$-0.519356\pi$
$467$	19.1176	−	28.6115i	0.884657	−	1.32398i	0.945428	−	0.325831i	$-0.105644\pi$
$468$	26.0891	−	5.66475i	1.20597	−	0.261853i
$469$	0.851414	−	4.28035i	0.0393146	−	0.197648i
$470$	−14.3788	+	23.6020i	−0.663247	+	1.08868i
$471$	2.58655	+	1.85514i	0.119182	+	0.0854804i
$472$	−3.00680	+	6.01705i	−0.138399	+	0.276957i
$473$	−3.73545	−	1.54727i	−0.171756	−	0.0711437i
$474$	10.4217	−	25.7949i	0.478683	−	1.18480i
$475$	−19.1523	+	12.7971i	−0.878767	+	0.587173i
$476$	10.7169	+	3.42048i	0.491211	+	0.156777i
$477$	−11.1464	−	2.99670i	−0.510357	−	0.137210i
$478$	11.2270	+	24.1873i	0.513513	+	1.10630i
$479$			1.62319i			0.0741654i	0.999312	+	0.0370827i	$0.0118065\pi$
$479$			1.62319i			0.0741654i	−0.999312	+	0.0370827i	$0.988194\pi$
$480$	13.8905	−	31.7151i	0.634011	−	1.44759i
$481$		−	14.6916i		−	0.669880i
$482$	23.2474	−	10.7907i	1.05889	−	0.491505i
$483$	−3.98513	−	4.25846i	−0.181330	−	0.193767i
$484$	8.34103	+	16.1613i	0.379138	+	0.734606i
$485$	36.8060	−	24.5930i	1.67127	−	1.11671i
$486$	−21.2535	+	5.85575i	−0.964077	+	0.265622i
$487$	−17.8470	−	7.39248i	−0.808726	−	0.334985i	−0.0602804	−	0.998181i	$-0.519199\pi$
$487$	−17.8470	−	7.39248i	−0.808726	−	0.334985i	−0.748446	+	0.663196i	$0.769199\pi$
$488$	−20.4746	−	23.5965i	−0.926841	−	1.06816i
$489$	10.9419	−	15.2558i	0.494809	−	0.689893i
$490$	28.3366	+	17.2633i	1.28012	+	0.779874i
$491$	4.82274	−	24.2456i	0.217647	−	1.09419i	−0.705196	−	0.709012i	$-0.749141\pi$
$491$	4.82274	−	24.2456i	0.217647	−	1.09419i	0.922844	−	0.385175i	$-0.125859\pi$
$492$	−14.8630	−	31.3020i	−0.670077	−	1.41120i
$493$	7.13191	−	10.6737i	0.321205	−	0.480717i
$494$	19.3413	−	0.810423i	0.870206	−	0.0364626i
$495$	13.8652	−	4.69361i	0.623195	−	0.210962i
$496$	−5.00375	−	29.5921i	−0.224675	−	1.32872i
$497$	−21.2010	+	21.2010i	−0.950996	+	0.950996i
$498$	2.01489	−	10.6130i	0.0902895	−	0.475581i
$499$	7.36807	−	11.0271i	0.329840	−	0.493640i	−0.629071	−	0.777348i	$-0.716565\pi$
$499$	7.36807	−	11.0271i	0.329840	−	0.493640i	0.958911	+	0.283708i	$0.0915645\pi$
$500$	−15.3831	−	8.50992i	−0.687954	−	0.380575i
$501$	21.6518	−	8.13878i	0.967332	−	0.363614i
$502$	6.19272	+	25.5015i	0.276395	+	1.13819i
$503$	22.2212	−	9.20431i	0.990793	−	0.410400i	0.172380	−	0.985031i	$-0.444854\pi$
$503$	22.2212	−	9.20431i	0.990793	−	0.410400i	0.818413	+	0.574631i	$0.194854\pi$
$504$	−31.2825	+	1.85847i	−1.39343	+	0.0827827i
$505$	28.0603	+	11.6229i	1.24867	+	0.517214i
$506$	−1.75921	−	0.273933i	−0.0782066	−	0.0121778i
$507$	−4.86395	+	10.7230i	−0.216016	+	0.476224i
$508$	−4.49613	+	5.32021i	−0.199484	+	0.236046i
$509$	−11.6720	+	2.32171i	−0.517354	+	0.102908i	−0.446860	−	0.894604i	$-0.647458\pi$
$509$	−11.6720	+	2.32171i	−0.517354	+	0.102908i	−0.0704946	+	0.997512i	$0.522458\pi$
$510$	2.68469	+	12.9069i	0.118880	+	0.571525i
$511$			14.0318i			0.620728i
$512$	−0.357706	+	22.6246i	−0.0158085	+	0.999875i
$513$	−15.9103	+	1.54678i	−0.702459	+	0.0682919i
$514$	9.78104	+	3.57948i	0.431423	+	0.157884i
$515$	11.7757	+	59.2004i	0.518899	+	2.60868i
$516$	−1.47311	+	10.0360i	−0.0648501	+	0.441812i
$517$	6.34911	−	4.24234i	0.279234	−	0.186578i
$518$	−2.65336	+	17.0400i	−0.116582	+	0.748697i
$519$	−0.792030	−	4.80983i	−0.0347662	−	0.211128i
$520$	22.0331	+	38.6311i	0.966214	+	1.69409i
$521$	3.86481	+	9.33049i	0.169321	+	0.408776i	0.985648	−	0.168813i	$-0.0539935\pi$
$521$	3.86481	+	9.33049i	0.169321	+	0.408776i	−0.816327	+	0.577589i	$0.803993\pi$
$522$	−7.83053	+	34.8921i	−0.342733	+	1.52719i
$523$	4.79573	−	24.1098i	0.209703	−	1.05425i	−0.722240	−	0.691642i	$-0.756888\pi$
$523$	4.79573	−	24.1098i	0.209703	−	1.05425i	0.931943	−	0.362604i	$-0.118112\pi$
$524$	7.58594	−	13.7129i	0.331393	−	0.599050i
$525$	−1.58722	+	47.8692i	−0.0692718	+	2.08918i
$526$	21.9885	−	23.9118i	0.958744	−	1.04260i
$527$	8.08030	+	8.08030i	0.351983	+	0.351983i
$528$	−7.17051	+	6.33241i	−0.312056	+	0.275583i
$529$	15.6756	−	15.6756i	0.681549	−	0.681549i
$530$	−0.804939	−	19.2104i	−0.0349643	−	0.834447i
$531$	3.56207	+	6.18168i	0.154581	+	0.268262i
$532$	−22.5794	−	2.55315i	−0.978939	−	0.110693i
$533$	43.6532	+	8.68316i	1.89083	+	0.376109i
$534$	0.266730	−	0.00232898i	0.0115425	−	0.000100785i
$535$	−8.12560	+	3.36573i	−0.351300	+	0.145513i
$536$	−2.52448	+	2.19048i	−0.109041	+	0.0946144i
$537$	−1.97841	−	12.0145i	−0.0853745	−	0.518462i
$538$	4.80702	+	6.58015i	0.207245	+	0.283691i
$539$	−5.09336	−	7.62275i	−0.219387	−	0.328335i
$540$	−19.9214	−	30.8510i	−0.857279	−	1.32762i
$541$	−2.98380	+	0.593515i	−0.128284	+	0.0255172i	−0.258815	−	0.965927i	$-0.583332\pi$
$541$	−2.98380	+	0.593515i	−0.128284	+	0.0255172i	0.130531	+	0.991444i	$0.458332\pi$
$542$	9.35984	+	20.1646i	0.402039	+	0.866145i
$543$	23.7427	+	38.2171i	1.01889	+	1.64005i
$544$	−4.87948	−	7.10054i	−0.209206	−	0.304433i
$545$	−11.4701			−0.491327
$546$	22.0697	−	33.6622i	0.944496	−	1.44061i
$547$	5.92667	+	29.7954i	0.253406	+	1.27396i	0.872490	+	0.488633i	$0.162504\pi$
$547$	5.92667	+	29.7954i	0.253406	+	1.27396i	−0.619084	+	0.785325i	$0.712496\pi$
$548$	2.38863	−	7.48400i	0.102037	−	0.319701i
$549$	−32.8563	+	4.29751i	−1.40227	+	0.183413i
$550$	8.62479	+	11.8062i	0.367762	+	0.503416i
$551$	−9.92296	+	23.9561i	−0.422732	+	1.02057i
$552$	0.412511	+	4.44759i	0.0175576	+	0.189302i
$553$	−16.0521	−	38.7532i	−0.682604	−	1.64795i
$554$	0.965098	+	0.587958i	0.0410031	+	0.0249799i
$555$	−18.9172	+	7.11085i	−0.802990	+	0.301839i
$556$	32.1879	−	25.6481i	1.36507	−	1.08772i
$557$	−27.1192	−	18.1205i	−1.14908	−	0.767790i	−0.172939	−	0.984933i	$-0.555326\pi$
$557$	−27.1192	−	18.1205i	−1.14908	−	0.767790i	−0.976140	+	0.217143i	$0.930326\pi$
$558$	−29.1034	−	12.8961i	−1.23205	−	0.545937i
$559$	−9.21290	−	9.21290i	−0.389664	−	0.389664i
$560$	−18.5781	−	48.7855i	−0.785068	−	2.06156i
$561$	0.828604	−	3.54695i	0.0349837	−	0.149752i
$562$	2.74759	−	2.98791i	0.115900	−	0.126038i
$563$	−34.3209	−	22.9325i	−1.44645	−	0.966489i	−0.997331	−	0.0730192i	$-0.976737\pi$
$563$	−34.3209	−	22.9325i	−1.44645	−	0.966489i	−0.449123	−	0.893470i	$-0.648263\pi$
$564$	−14.2140	−	12.8435i	−0.598519	−	0.540811i
$565$	36.0444	+	7.16968i	1.51640	+	0.301631i
$566$	−10.0437	−	41.3599i	−0.422170	−	1.73849i
$567$	−16.6677	+	28.7575i	−0.699976	+	1.20770i
$568$	22.7814	−	2.87718i	0.955886	−	0.120724i
$569$	7.91757	−	19.1147i	0.331922	−	0.801330i	−0.666518	−	0.745489i	$-0.732216\pi$
$569$	7.91757	−	19.1147i	0.331922	−	0.801330i	0.998440	−	0.0558410i	$-0.0177840\pi$
$570$	−10.4048	−	24.5120i	−0.435811	−	1.02669i
$571$	11.8416	+	17.7222i	0.495556	+	0.741651i	0.991975	−	0.126431i	$-0.0403523\pi$
$571$	11.8416	+	17.7222i	0.495556	+	0.741651i	−0.496420	+	0.868083i	$0.665352\pi$
$572$	−1.02793	−	12.2446i	−0.0429798	−	0.511971i
$573$	−6.00715	−	6.41918i	−0.250952	−	0.268165i
$574$	−49.0629	−	17.9551i	−2.04785	−	0.749431i
$575$	6.82674			0.284695
$576$	19.8022	+	13.5599i	0.825093	+	0.564996i
$577$	25.7108			1.07036			0.535178	−	0.844739i	$-0.320245\pi$
$577$	25.7108			1.07036			0.535178	+	0.844739i	$0.320245\pi$
$578$	−19.4967	−	7.13502i	−0.810955	−	0.296778i
$579$	−12.2175	−	13.0555i	−0.507741	−	0.542566i
$580$	−59.3613	+	4.98336i	−2.46484	+	0.206923i
$581$	−9.04880	−	13.5425i	−0.375408	−	0.561837i
$582$	11.9893	+	28.2446i	0.496972	+	1.17078i
$583$	−2.03298	+	4.90804i	−0.0841973	+	0.203270i
$584$	6.58674	−	8.49098i	0.272561	−	0.351359i
$585$	47.0668	+	3.12466i	1.94597	+	0.129189i
$586$	−3.47903	−	14.3266i	−0.143717	−	0.591825i
$587$	−27.2847	−	5.42726i	−1.12616	−	0.224007i	−0.403344	−	0.915049i	$-0.632152\pi$
$587$	−27.2847	−	5.42726i	−1.12616	−	0.224007i	−0.722815	+	0.691042i	$0.757152\pi$
$588$	−15.4200	+	17.0654i	−0.635909	+	0.703765i
$589$	−19.1921	−	12.8238i	−0.790798	−	0.528395i
$590$	−8.04471	+	8.74836i	−0.331196	+	0.360164i
$591$	−1.57848	+	6.75689i	−0.0649300	+	0.277941i
$592$	9.60450	−	9.06584i	0.394743	−	0.372604i
$593$	−24.6273	−	24.6273i	−1.01132	−	1.01132i	−0.999935	−	0.0113851i	$-0.996376\pi$
$593$	−24.6273	−	24.6273i	−1.01132	−	1.01132i	−0.0113851	−	0.999935i	$-0.503624\pi$
$594$	1.40374	+	10.0491i	0.0575963	+	0.412320i
$595$	16.5268	+	11.0429i	0.677533	+	0.452713i
$596$	25.9023	+	32.5069i	1.06100	+	1.33154i
$597$	20.9159	−	7.86216i	0.856032	−	0.321777i
$598$	−4.89963	−	2.98495i	−0.200361	−	0.122064i
$599$	−13.3132	−	32.1409i	−0.543963	−	1.31324i	−0.921906	−	0.387414i	$-0.873368\pi$
$599$	−13.3132	−	32.1409i	−0.543963	−	1.31324i	0.377943	−	0.925829i	$-0.376632\pi$
$600$	23.4311	−	28.2218i	0.956569	−	1.15215i
$601$	7.28047	−	17.5766i	0.296977	−	0.716965i	−0.703007	−	0.711183i	$-0.748160\pi$
$601$	7.28047	−	17.5766i	0.296977	−	0.716965i	0.999983	−	0.00578169i	$-0.00184038\pi$
$602$	9.02169	+	12.3495i	0.367697	+	0.503327i
$603$	0.459771	+	3.51514i	0.0187233	+	0.143148i
$604$	4.41411	+	1.40883i	0.179608	+	0.0573246i
$605$	6.26903	+	31.5165i	0.254872	+	1.28133i
$606$	−11.5432	+	17.6064i	−0.468909	+	0.715213i
$607$	−10.4645			−0.424739			−0.212370	−	0.977189i	$-0.568118\pi$
$607$	−10.4645			−0.424739			−0.212370	+	0.977189i	$0.568118\pi$
$608$	12.4649	+	12.1441i	0.505517	+	0.492508i
$609$	28.4523	+	45.7980i	1.15295	+	1.85583i
$610$	−23.2403	−	50.0683i	−0.940971	−	2.02721i
$611$	24.1338	−	4.80050i	0.976347	−	0.194208i
$612$	−9.13673	+	0.159569i	−0.369330	+	0.00645019i
$613$	4.61631	+	6.90880i	0.186451	+	0.279044i	0.912906	−	0.408171i	$-0.133833\pi$
$613$	4.61631	+	6.90880i	0.186451	+	0.279044i	−0.726455	+	0.687215i	$0.758833\pi$
$614$	2.97213	+	4.06845i	0.119946	+	0.164189i
$615$	−9.94787	−	60.4113i	−0.401137	−	2.43602i
$616$	−1.01918	+	14.3875i	−0.0410638	+	0.579688i
$617$	1.58520	−	0.656613i	0.0638179	−	0.0264343i	−0.350546	−	0.936545i	$-0.614004\pi$
$617$	1.58520	−	0.656613i	0.0638179	−	0.0264343i	0.414364	+	0.910111i	$0.364004\pi$
$618$	−41.8382	+	0.365315i	−1.68298	+	0.0146951i
$619$	24.9444	+	4.96175i	1.00260	+	0.199430i	0.668982	−	0.743279i	$-0.266730\pi$
$619$	24.9444	+	4.96175i	1.00260	+	0.199430i	0.333618	+	0.942708i	$0.391730\pi$
$620$	5.95812	−	52.6920i	0.239284	−	2.11616i
$621$	4.17540	+	2.23857i	0.167553	+	0.0898307i
$622$	0.951971	+	22.7195i	0.0381706	+	0.910967i
$623$	0.284379	−	0.284379i	0.0113934	−	0.0113934i
$624$	−29.1566	+	10.0100i	−1.16720	+	0.400721i
$625$	4.50806	+	4.50806i	0.180322	+	0.180322i
$626$	20.1098	−	21.8688i	0.803750	−	0.874052i
$627$	−0.243820	+	7.35342i	−0.00973724	+	0.293667i
$628$	−3.21615	−	1.77917i	−0.128338	−	0.0709965i
$629$	−0.981069	+	4.93217i	−0.0391178	+	0.196658i
$630$	−54.0260	−	12.1246i	−2.15245	−	0.483055i
$631$	11.2810	+	27.2347i	0.449089	+	1.08420i	0.972664	+	0.232217i	$0.0745980\pi$
$631$	11.2810	+	27.2347i	0.449089	+	1.08420i	−0.523575	+	0.851980i	$0.675402\pi$
$632$	−8.47784	+	30.9857i	−0.337230	+	1.23254i
$633$	−4.01254	−	24.3673i	−0.159484	−	0.968513i
$634$	−5.88761	+	37.8106i	−0.233827	+	1.50165i
$635$	−10.2332	+	6.83763i	−0.406094	+	0.271343i
$636$	13.1864	+	1.93554i	0.522877	+	0.0767490i
$637$	−5.76349	−	28.9750i	−0.228358	−	1.14803i
$638$	15.4565	+	5.65646i	0.611928	+	0.223942i
$639$	10.7904	−	21.8345i	0.426862	−	0.863760i
$640$	−11.6586	+	38.2422i	−0.460848	+	1.51166i
$641$			7.35273i			0.290415i	0.989401	+	0.145208i	$0.0463850\pi$
$641$			7.35273i			0.290415i	−0.989401	+	0.145208i	$0.953615\pi$
$642$	−1.24153	−	5.96872i	−0.0489991	−	0.235567i
$643$	−4.59538	+	0.914079i	−0.181224	+	0.0360477i	−0.284868	−	0.958567i	$-0.591950\pi$
$643$	−4.59538	+	0.914079i	−0.181224	+	0.0360477i	0.103644	+	0.994614i	$0.466950\pi$
$644$	5.14373	+	4.34699i	0.202691	+	0.171295i
$645$	−7.40359	+	16.3218i	−0.291516	+	0.642671i
$646$	−6.54725	−	1.01949i	−0.257598	−	0.0401115i
$647$	34.8538	+	14.4369i	1.37024	+	0.567574i	0.941855	−	0.336021i	$-0.109081\pi$
$647$	34.8538	+	14.4369i	1.37024	+	0.567574i	0.428389	+	0.903594i	$0.359081\pi$
$648$	23.5853	−	9.57782i	0.926517	−	0.376252i
$649$	3.03380	−	1.25664i	0.119087	−	0.0493274i
$650$	11.1182	+	45.7845i	0.436091	+	1.79581i
$651$	−44.9260	+	16.8874i	−1.76079	+	0.661870i
$652$	−10.4938	+	18.9693i	−0.410968	+	0.742895i
$653$	−2.26295	+	3.38674i	−0.0885561	+	0.132534i	−0.873103	−	0.487536i	$-0.837896\pi$
$653$	−2.26295	+	3.38674i	−0.0885561	+	0.132534i	0.784547	+	0.620070i	$0.212896\pi$
$654$	1.48297	−	7.81122i	0.0579886	−	0.305443i
$655$	19.5793	−	19.5793i	0.765026	−	0.765026i
$656$	21.2608	+	33.8960i	0.830096	+	1.32342i
$657$	−3.65473	−	10.7963i	−0.142585	−	0.421204i
$658$	−28.8585	+	1.20920i	−1.12502	+	0.0471397i
$659$	11.4690	−	17.1646i	0.446770	−	0.668639i	−0.537911	−	0.843001i	$-0.680787\pi$
$659$	11.4690	−	17.1646i	0.446770	−	0.668639i	0.984681	+	0.174363i	$0.0557865\pi$
$660$	−15.2688	+	7.25003i	−0.594337	+	0.282207i
$661$	−0.162121	+	0.815036i	−0.00630577	+	0.0317012i	−0.983810	−	0.179214i	$-0.942644\pi$
$661$	−0.162121	+	0.815036i	−0.00630577	+	0.0317012i	0.977504	+	0.210915i	$0.0676445\pi$
$662$	−4.96999	−	3.02782i	−0.193164	−	0.117680i
$663$	6.84087	−	9.53795i	0.265677	−	0.370423i
$664$	−0.881404	+	12.4426i	−0.0342051	+	0.482866i
$665$	−37.0931	−	15.3644i	−1.43841	−	0.595808i
$666$	−2.39673	−	13.8020i	−0.0928713	−	0.534818i
$667$	6.38980	−	4.26952i	0.247414	−	0.165317i
$668$	−23.7346	+	12.2497i	−0.918321	+	0.473955i
$669$	17.7603	+	18.9784i	0.686652	+	0.733749i
$670$	−5.35658	+	2.48637i	−0.206943	+	0.0960567i
$671$			15.2513i			0.588771i
$672$	35.6251	−	6.34431i	1.37427	−	0.244737i
$673$		−	24.8299i		−	0.957121i	−0.878055	−	0.478560i	$-0.841159\pi$
$673$		−	24.8299i		−	0.957121i	0.878055	−	0.478560i	$-0.158841\pi$
$674$	−3.52346	−	7.59087i	−0.135719	−	0.292390i
$675$	−11.2468	−	37.2449i	−0.432891	−	1.43356i
$676$	4.13396	−	12.9524i	0.158998	−	0.498169i
$677$	9.22007	−	6.16065i	0.354356	−	0.236773i	−0.365632	−	0.930759i	$-0.619147\pi$
$677$	9.22007	−	6.16065i	0.354356	−	0.236773i	0.719988	+	0.693986i	$0.244147\pi$
$678$	−9.54274	+	23.6194i	−0.366487	+	0.907099i
$679$	42.7416	+	17.7041i	1.64027	+	0.679423i
$680$	−4.81710	−	14.4403i	−0.184727	−	0.553759i
$681$	20.5460	+	14.7362i	0.787326	+	0.564691i
$682$	−7.62273	+	12.5123i	−0.291890	+	0.479119i
$683$	−2.21498	+	11.1355i	−0.0847538	+	0.426086i	0.914990	+	0.403475i	$0.132198\pi$
$683$	−2.21498	+	11.1355i	−0.0847538	+	0.426086i	−0.999744	+	0.0226109i	$0.992802\pi$
$684$	18.0380	−	3.91661i	0.689700	−	0.149755i
$685$	7.71159	−	11.5412i	0.294645	−	0.440967i
$686$	−0.0788144	−	1.88096i	−0.00300915	−	0.0718154i
$687$	6.49430	−	27.7997i	0.247773	−	1.06062i
$688$	0.337784	−	11.7079i	0.0128779	−	0.446360i
$689$	−12.1049	+	12.1049i	−0.461161	+	0.461161i
$690$	−1.47203	+	7.75359i	−0.0560391	+	0.295174i
$691$	−21.0411	+	31.4903i	−0.800442	+	1.19795i	0.176471	+	0.984306i	$0.443532\pi$
$691$	−21.0411	+	31.4903i	−0.800442	+	1.19795i	−0.976912	+	0.213640i	$0.931468\pi$
$692$	1.55608	+	5.40934i	0.0591534	+	0.205632i
$693$	12.1293	+	9.32332i	0.460753	+	0.354164i
$694$	−10.5860	+	2.57069i	−0.401841	+	0.0975820i
$695$	67.1838	−	27.8284i	2.54843	−	1.05559i
$696$	4.28109	−	41.0696i	0.162274	−	1.55674i
$697$	−14.0751	−	5.83010i	−0.533133	−	0.220831i
$698$	−6.50845	+	41.7976i	−0.246349	+	1.58206i
$699$	25.5627	+	11.5953i	0.966870	+	0.438573i
$700$	−4.62656	−	55.1111i	−0.174867	−	2.08300i
$701$	−22.0599	+	4.38799i	−0.833192	+	0.165732i	−0.593213	−	0.805046i	$-0.702141\pi$
$701$	−22.0599	+	4.38799i	−0.833192	+	0.165732i	−0.239979	+	0.970778i	$0.577141\pi$
$702$	−8.21314	+	31.6487i	−0.309985	+	1.19450i
$703$		−	10.1578i		−	0.383108i
$704$	7.37046	−	8.22783i	0.277785	−	0.310098i
$705$	−17.8621	−	28.7516i	−0.672727	−	1.08285i
$706$	16.9442	−	46.3005i	0.637702	−	1.74254i
$707$	6.19263	+	31.1325i	0.232898	+	1.17086i
$708$	−4.91757	−	6.60955i	−0.184814	−	0.248402i
$709$	34.9257	−	23.3366i	1.31166	−	0.876426i	0.314324	−	0.949316i	$-0.398222\pi$
$709$	34.9257	−	23.3366i	1.31166	−	0.876426i	0.997340	+	0.0728900i	$0.0232222\pi$
$710$	40.0886	+	6.24234i	1.50450	+	0.234271i
$711$	22.4445	+	25.6365i	0.841734	+	0.961443i
$712$	−0.305578	+	0.0385929i	−0.0114520	+	0.00144633i
$713$	2.61792	+	6.32021i	0.0980417	+	0.236694i
$714$	−9.65697	+	9.82710i	−0.361403	+	0.367770i
$715$	4.23556	−	21.2936i	0.158401	−	0.796335i
$716$	3.88693	+	13.5120i	0.145261	+	0.504966i
$717$	−32.6410	−	1.08229i	−1.21900	−	0.0404189i
$718$	18.8107	+	17.2977i	0.702008	+	0.645544i
$719$	25.4632	+	25.4632i	0.949618	+	0.949618i	0.998790	−	0.0491720i	$-0.0156583\pi$
$719$	25.4632	+	25.4632i	0.949618	+	0.949618i	−0.0491720	+	0.998790i	$0.515658\pi$
$720$	27.0011	+	32.6976i	1.00627	+	1.21857i
$721$	−44.6065	+	44.6065i	−1.66123	+	1.66123i
$722$	−13.4739	+	0.564573i	−0.501448	+	0.0210112i
$723$	−1.04023	+	31.3726i	−0.0386867	+	1.16676i
$724$	−32.3755	−	40.6306i	−1.20322	−	1.51002i
$725$	−61.8969	−	12.3121i	−2.29879	−	0.457259i
$726$	−22.2734	+	0.194483i	−0.826644	+	0.00721793i
$727$	−9.12297	+	3.77886i	−0.338352	+	0.140150i	−0.545389	−	0.838183i	$-0.683618\pi$
$727$	−9.12297	+	3.77886i	−0.338352	+	0.140150i	0.207037	+	0.978333i	$0.433618\pi$
$728$	−20.7765	+	41.5768i	−0.770028	+	1.54094i
$729$	5.33421	−	26.4678i	0.197563	−	0.980290i
$730$	15.3319	−	11.2005i	0.567460	−	0.414548i
$731$	2.47768	+	3.70811i	0.0916402	+	0.137149i
$732$	37.1015	−	9.35342i	1.37131	−	0.345712i
$733$	−12.7770	+	2.54150i	−0.471928	+	0.0938724i	−0.425324	−	0.905041i	$-0.639840\pi$
$733$	−12.7770	+	2.54150i	−0.471928	+	0.0938724i	−0.0466042	+	0.998913i	$0.514840\pi$
$734$	24.7087	−	11.4691i	0.912016	−	0.423331i
$735$	−34.5192	+	21.4453i	−1.27326	+	0.791022i
$736$	−1.07206	−	5.04503i	−0.0395166	−	0.185962i
$737$	1.63167			0.0601033
$738$	42.4265	+	1.03600i	1.56174	+	0.0381357i
$739$	3.73646	+	18.7844i	0.137448	+	0.690997i	0.986640	+	0.162914i	$0.0520892\pi$
$739$	3.73646	+	18.7844i	0.137448	+	0.690997i	−0.849192	+	0.528083i	$0.822911\pi$
$740$	20.7369	−	10.7025i	0.762305	−	0.393433i
$741$	−9.79392	+	21.5915i	−0.359789	+	0.793184i
$742$	16.2261	−	11.8537i	0.595678	−	0.435163i
$743$	15.5455	−	37.5302i	0.570310	−	1.37685i	−0.330982	−	0.943637i	$-0.607380\pi$
$743$	15.5455	−	37.5302i	0.570310	−	1.37685i	0.901292	−	0.433213i	$-0.142620\pi$
$744$	35.1132	+	10.8700i	1.28731	+	0.398514i
$745$	28.1043	+	67.8497i	1.02966	+	2.48582i
$746$	7.13746	−	11.7157i	0.261321	−	0.428943i
$747$	10.4896	+	8.06299i	0.383795	+	0.295009i
$748$	−0.472572	+	4.17930i	−0.0172790	+	0.152810i
$749$	−7.64275	−	5.10672i	−0.279260	−	0.186596i
$750$	17.7973	−	12.1179i	0.649867	−	0.442483i
$751$	−15.2299	−	15.2299i	−0.555747	−	0.555747i	0.372346	−	0.928094i	$-0.378553\pi$
$751$	−15.2299	−	15.2299i	−0.555747	−	0.555747i	−0.928094	+	0.372346i	$0.878553\pi$
$752$	18.0307	+	12.8149i	0.657511	+	0.467313i
$753$	−31.2979	−	7.31151i	−1.14056	−	0.266446i
$754$	39.0407	+	35.9006i	1.42178	+	1.30742i
$755$	6.80709	+	4.54835i	0.247735	+	0.165531i
$756$	15.2419	−	35.2244i	0.554342	−	1.28110i
$757$	−47.7615	−	9.50036i	−1.73592	−	0.345296i	−0.777116	−	0.629357i	$-0.783318\pi$
$757$	−47.7615	−	9.50036i	−1.73592	−	0.345296i	−0.958806	+	0.284061i	$0.908318\pi$
$758$	−21.1259	+	5.13015i	−0.767326	+	0.186336i
$759$	1.27087	−	1.77192i	0.0461296	−	0.0643167i
$760$	15.2336	+	26.7095i	0.552583	+	0.968856i
$761$	18.9859	−	45.8359i	0.688237	−	1.66155i	−0.0600660	−	0.998194i	$-0.519131\pi$
$761$	18.9859	−	45.8359i	0.688237	−	1.66155i	0.748303	−	0.663357i	$-0.230869\pi$
$762$	−3.33341	−	7.85291i	−0.120757	−	0.284481i
$763$	−6.65995	−	9.96732i	−0.241106	−	0.360841i
$764$	7.75363	+	6.55262i	0.280517	+	0.237066i
$765$	−15.5923	−	4.19199i	−0.563740	−	0.151562i
$766$	0.230503	−	0.629857i	0.00832841	−	0.0227577i
$767$	10.5817			0.382083
$768$	−24.5358	−	12.8839i	−0.885359	−	0.464908i
$769$	−33.7659			−1.21763			−0.608816	−	0.793312i	$-0.708355\pi$
$769$	−33.7659			−1.21763			−0.608816	+	0.793312i	$0.708355\pi$
$770$	−8.75832	+	23.9324i	−0.315628	+	0.862464i
$771$	−9.31400	+	8.71617i	−0.335436	+	0.313905i
$772$	15.7695	+	13.3269i	0.567556	+	0.479644i
$773$	6.58543	+	9.85580i	0.236862	+	0.354488i	0.930789	−	0.365556i	$-0.119121\pi$
$773$	6.58543	+	9.85580i	0.236862	+	0.354488i	−0.693928	+	0.720045i	$0.744121\pi$
$774$	−10.1580	−	7.15211i	−0.365122	−	0.257077i
$775$	21.4986	−	51.9022i	0.772252	−	1.86438i
$776$	−17.5534	−	30.7768i	−0.630131	−	1.10482i
$777$	−17.1631	−	12.3098i	−0.615724	−	0.441613i
$778$	7.62113	−	1.85069i	0.273231	−	0.0663506i
$779$	30.1818	+	6.00353i	1.08138	+	0.215099i
$780$	−54.3979	+	2.75533i	−1.94776	+	0.0986565i
$781$	−9.32062	−	6.22784i	−0.333518	−	0.222850i
$782$	1.44554	+	1.32927i	0.0516925	+	0.0475347i
$783$	−33.8204	−	27.8271i	−1.20864	−	0.994460i
$784$	15.3856	−	21.6476i	0.549487	−	0.773130i
$785$	−4.59202	−	4.59202i	−0.163896	−	0.163896i
$786$	10.8022	+	15.8650i	0.385301	+	0.565885i
$787$	18.4705	+	12.3416i	0.658403	+	0.439931i	0.839371	−	0.543558i	$-0.182923\pi$
$787$	18.4705	+	12.3416i	0.658403	+	0.439931i	−0.180969	+	0.983489i	$0.557923\pi$
$788$	0.900245	−	7.96152i	0.0320699	−	0.283617i
$789$	13.9989	+	37.2415i	0.498372	+	1.32583i
$790$	−29.5308	+	48.4731i	−1.05066	+	1.72460i
$791$	14.6983	+	35.4848i	0.522611	+	1.26169i
$792$	−2.96321	−	11.3355i	−0.105293	−	0.402788i
$793$	−18.8075	+	45.4054i	−0.667875	+	1.61239i
$794$	25.5965	−	18.6990i	0.908384	−	0.663604i
$795$	21.4454	+	9.72765i	0.760590	+	0.345004i
$796$	−22.9280	+	11.8333i	−0.812660	+	0.419422i
$797$	6.18293	+	31.0837i	0.219011	+	1.10104i	0.921211	+	0.389062i	$0.127201\pi$
$797$	6.18293	+	31.0837i	0.219011	+	1.10104i	−0.702201	+	0.711979i	$0.747799\pi$
$798$	15.2590	−	23.2741i	0.540162	−	0.823893i
$799$	−8.42259			−0.297970
$800$	−23.0704	+	35.5209i	−0.815662	+	1.25585i
$801$	−0.144737	+	0.292877i	−0.00511403	+	0.0103483i
$802$	−2.22677	+	1.03360i	−0.0786299	+	0.0364977i
$803$	−5.14532	+	1.02347i	−0.181575	+	0.0361174i
$804$	−1.00068	−	3.96931i	−0.0352912	−	0.139987i
$805$	6.61082	+	9.89379i	0.233001	+	0.348710i
$806$	−38.1238	+	27.8507i	−1.34285	+	0.980998i
$807$	−9.84779	+	1.62163i	−0.346659	+	0.0570839i
$808$	10.8668	−	21.7460i	0.382292	−	0.765022i
$809$	−42.0193	+	17.4049i	−1.47732	+	0.611925i	−0.968515	−	0.248957i	$-0.919912\pi$
$809$	−42.0193	+	17.4049i	−1.47732	+	0.611925i	−0.508804	+	0.860882i	$0.669912\pi$
$810$	44.7266	−	4.74281i	1.57153	−	0.166645i
$811$	−45.9109	−	9.13225i	−1.61215	−	0.320677i	−0.694937	−	0.719071i	$-0.744568\pi$
$811$	−45.9109	−	9.13225i	−1.61215	−	0.320677i	−0.917214	+	0.398394i	$0.869568\pi$
$812$	−38.7976	−	48.6902i	−1.36153	−	1.70869i
$813$	−27.2124	−	0.902292i	−0.954380	−	0.0316448i
$814$	−6.44197	+	0.269926i	−0.225791	+	0.00946091i
$815$	−27.0844	+	27.0844i	−0.948726	+	0.948726i
$816$	10.4567	−	1.41349i	0.366057	−	0.0494821i
$817$	−6.36980	−	6.36980i	−0.222851	−	0.222851i
$818$	−21.9325	−	20.1685i	−0.766853	−	0.705173i
$819$	24.6133	+	42.7143i	0.860058	+	1.49256i
$820$	19.5444	+	67.9412i	0.682518	+	2.37261i
$821$	6.81834	−	34.2781i	0.237962	−	1.19631i	−0.658288	−	0.752766i	$-0.728719\pi$
$821$	6.81834	−	34.2781i	0.237962	−	1.19631i	0.896250	−	0.443549i	$-0.146281\pi$
$822$	6.86259	+	6.74378i	0.239360	+	0.235216i
$823$	−3.45114	−	8.33178i	−0.120299	−	0.290428i	0.852246	−	0.523141i	$-0.175240\pi$
$823$	−3.45114	−	8.33178i	−0.120299	−	0.290428i	−0.972545	+	0.232713i	$0.925240\pi$
$824$	47.9316	−	6.05353i	1.66978	−	0.210885i
$825$	−17.6690	+	2.90953i	−0.615155	+	0.101297i
$826$	−12.2732	−	1.91110i	−0.427038	−	0.0664956i
$827$	−1.42295	+	0.950787i	−0.0494809	+	0.0330621i	−0.580065	−	0.814570i	$-0.696973\pi$
$827$	−1.42295	+	0.950787i	−0.0494809	+	0.0330621i	0.530584	+	0.847633i	$0.321973\pi$
$828$	−5.08991	−	2.00491i	−0.176887	−	0.0696755i
$829$	0.820323	+	4.12404i	0.0284910	+	0.143234i	0.992413	−	0.122953i	$-0.0392363\pi$
$829$	0.820323	+	4.12404i	0.0284910	+	0.143234i	−0.963922	+	0.266187i	$0.914236\pi$
$830$	−7.57436	+	20.6972i	−0.262910	+	0.718410i
$831$	−1.17567	+	0.730392i	−0.0407834	+	0.0253370i
$832$	32.0892	−	15.4064i	1.11249	−	0.534120i
$833$			10.1122i			0.350366i
$834$	10.2651	+	49.3503i	0.355452	+	1.70886i
$835$	−46.2854	+	9.20673i	−1.60177	+	0.318612i
$836$	−0.710708	−	8.46588i	−0.0245804	−	0.292799i
$837$	30.1684	−	24.6950i	1.04277	−	0.853584i
$838$	1.55886	−	10.0111i	0.0538498	−	0.345826i
$839$	−51.5648	−	21.3589i	−1.78022	−	0.737390i	−0.992630	−	0.121185i	$-0.961331\pi$
$839$	−51.5648	−	21.3589i	−1.78022	−	0.737390i	−0.787586	−	0.616205i	$-0.788669\pi$
$840$	63.5910	+	6.62872i	2.19410	+	0.228713i
$841$	−38.8429	+	16.0892i	−1.33941	+	0.554801i
$842$	11.1488	−	2.70736i	0.384214	−	0.0933017i
$843$	1.74924	+	4.65354i	0.0602469	+	0.160277i
$844$	7.88334	+	27.4045i	0.271356	+	0.943302i
$845$	13.3463	−	19.9741i	0.459126	−	0.687131i
$846$	21.8893	−	8.44691i	0.752571	−	0.290411i
$847$	−23.7472	+	23.7472i	−0.815964	+	0.815964i
$848$	−15.3831	−	0.443818i	−0.528259	−	0.0152408i
$849$	50.7608	+	11.8583i	1.74211	+	0.406975i
$850$	−0.675149	−	16.1129i	−0.0231574	−	0.552668i
$851$	−1.67254	+	2.50313i	−0.0573339	+	0.0858063i
$852$	−9.43409	+	26.4935i	−0.323207	+	0.907651i
$853$	1.80310	−	9.06478i	0.0617368	−	0.310372i	−0.937562	−	0.347819i	$-0.886922\pi$
$853$	1.80310	−	9.06478i	0.0617368	−	0.310372i	0.999299	+	0.0374467i	$0.0119224\pi$
$854$	30.0143	−	49.2667i	1.02707	−	1.68587i
$855$	32.5419	+	2.16039i	1.11291	+	0.0738837i
$856$	2.22765	+	6.67785i	0.0761394	+	0.228244i
$857$	−1.10169	−	0.456333i	−0.0376329	−	0.0155880i	0.363788	−	0.931482i	$-0.381483\pi$
$857$	−1.10169	−	0.456333i	−0.0376329	−	0.0155880i	−0.401420	+	0.915894i	$0.631483\pi$
$858$	13.9534	+	5.63747i	0.476362	+	0.192460i
$859$	−35.2780	+	23.5720i	−1.20367	+	0.804266i	−0.985172	−	0.171571i	$-0.945116\pi$
$859$	−35.2780	+	23.5720i	−1.20367	+	0.804266i	−0.218498	+	0.975837i	$0.570116\pi$
$860$	6.29243	−	19.7153i	0.214570	−	0.672285i
$861$	46.7202	−	43.7214i	1.59222	−	1.49002i
$862$	7.55468	+	16.2756i	0.257313	+	0.554351i
$863$			0.341243i			0.0116161i	0.999983	+	0.00580803i	$0.00184876\pi$
$863$			0.341243i			0.0116161i	−0.999983	+	0.00580803i	$0.998151\pi$
$864$	−25.7582	+	14.1604i	−0.876311	+	0.481746i
$865$			9.94525i			0.338149i
$866$	−27.6892	+	12.8525i	−0.940917	+	0.436746i
$867$	18.5657	−	17.3740i	0.630525	−	0.590054i
$868$	49.2478	−	25.4173i	1.67158	−	0.862718i
$869$	13.0396	−	8.71280i	0.442339	−	0.295561i
$870$	27.3303	−	67.6457i	0.926583	−	2.29341i
$871$	4.85771	+	2.01213i	0.164597	+	0.0681784i
$872$	−0.648716	+	9.15778i	−0.0219683	+	0.310122i
$873$	−37.4974	−	2.48937i	−1.26910	−	0.0842525i
$874$	−3.38760	−	2.06380i	−0.114587	−	0.0698090i
$875$	6.33325	−	31.8394i	0.214103	−	1.07637i
$876$	5.64531	+	11.8892i	0.190738	+	0.401699i
$877$	25.7297	−	38.5072i	0.868829	−	1.30029i	−0.0839003	−	0.996474i	$-0.526738\pi$
$877$	25.7297	−	38.5072i	0.868829	−	1.30029i	0.952729	−	0.303820i	$-0.0982623\pi$
$878$	−10.3601	+	0.434098i	−0.349635	+	0.0146501i
$879$	17.5829	+	4.10756i	0.593058	+	0.138545i
$880$	16.5342	−	10.3708i	0.557366	−	0.349600i
$881$	−22.1495	+	22.1495i	−0.746235	+	0.746235i	−0.973770	−	0.227535i	$-0.926933\pi$
$881$	−22.1495	+	22.1495i	−0.746235	+	0.746235i	0.227535	+	0.973770i	$0.426933\pi$
$882$	−10.1414	−	26.2804i	−0.341478	−	0.884906i
$883$	−27.6724	+	41.4147i	−0.931251	+	1.39372i	−0.0120494	+	0.999927i	$0.503836\pi$
$883$	−27.6724	+	41.4147i	−0.931251	+	1.39372i	−0.919201	+	0.393788i	$0.871164\pi$
$884$	−6.56072	+	11.8596i	−0.220661	+	0.398882i
$885$	−5.12162	−	13.6252i	−0.172161	−	0.458006i
$886$	−0.826905	−	3.40518i	−0.0277804	−	0.114399i
$887$	−0.0137020	+	0.00567556i	−0.000460069	+	0.000190567i	−0.382913	−	0.923784i	$-0.625079\pi$
$887$	−0.0137020	+	0.00567556i	−0.000460069	+	0.000190567i	0.382453	+	0.923975i	$0.375079\pi$
$888$	4.60741	+	15.5057i	0.154615	+	0.520336i
$889$	−11.8835	−	4.92232i	−0.398561	−	0.165089i
$890$	−0.537728	−	0.0837314i	−0.0180247	−	0.00280668i
$891$	−11.7609	−	4.01434i	−0.394003	−	0.134485i
$892$	−22.9238	−	19.3730i	−0.767545	−	0.648655i
$893$	16.6861	−	3.31907i	0.558378	−	0.111068i
$894$	−49.8395	+	10.3669i	−1.66688	+	0.346720i
$895$			24.8422i			0.830383i
$896$	−40.0011	+	12.0736i	−1.33634	+	0.403351i
$897$	5.96864	−	3.70806i	0.199287	−	0.123809i
$898$	16.9066	+	6.18716i	0.564181	+	0.206468i
$899$	−12.3377	−	62.0257i	−0.411485	−	2.06867i
$900$	17.9141	+	41.1985i	0.597136	+	1.37328i
$901$	4.87212	−	3.25545i	0.162314	−	0.108455i
$902$	3.00536	−	19.3006i	0.100068	−	0.642639i
$903$	−18.4821	+	3.04343i	−0.615046	+	0.101279i
$904$	7.76284	−	28.3724i	0.258188	−	0.943652i
$905$	−35.1277	−	84.8057i	−1.16768	−	2.81904i
$906$	−3.97753	+	4.04760i	−0.132145	+	0.134473i
$907$	0.607801	−	3.05562i	0.0201817	−	0.101460i	−0.969382	−	0.245559i	$-0.921028\pi$
$907$	0.607801	−	3.05562i	0.0201817	−	0.101460i	0.989563	+	0.144099i	$0.0460284\pi$
$908$	−25.5472	−	14.1327i	−0.847814	−	0.469009i
$909$	−12.8735	−	22.3410i	−0.426988	−	0.741003i
$910$	−55.5875	+	60.4496i	−1.84271	+	2.00389i
$911$	−22.9549	−	22.9549i	−0.760529	−	0.760529i	0.215889	−	0.976418i	$-0.430735\pi$
$911$	−22.9549	−	22.9549i	−0.760529	−	0.760529i	−0.976418	+	0.215889i	$0.930735\pi$
$912$	−20.1588	+	6.92092i	−0.667526	+	0.229175i
$913$	4.30590	−	4.30590i	0.142505	−	0.142505i
$914$	1.58562	+	37.8420i	0.0524478	+	1.25170i
$915$	67.5678	+	2.24037i	2.23372	+	0.0740644i
$916$	−3.70385	+	32.7558i	−0.122379	+	1.08228i
$917$	28.3824	+	5.64561i	0.937269	+	0.186434i
$918$	4.87068	−	10.0764i	0.160756	−	0.332572i
$919$	23.5333	−	9.74781i	0.776292	−	0.321551i	0.0408739	−	0.999164i	$-0.486986\pi$
$919$	23.5333	−	9.74781i	0.776292	−	0.321551i	0.735418	+	0.677614i	$0.236986\pi$
$920$	0.643930	−	9.09022i	0.0212297	−	0.299696i
$921$	−6.08880	+	1.00264i	−0.200633	+	0.0330380i
$922$	−15.8762	−	21.7323i	−0.522853	−	0.715715i
$923$	−20.0688	−	30.0351i	−0.660573	−	0.988618i
$924$	−15.1657	−	9.05865i	−0.498915	−	0.298008i
$925$	24.2474	−	4.82312i	0.797251	−	0.158583i
$926$	−0.360629	−	0.776932i	−0.0118510	−	0.0255316i
$927$	22.7028	−	45.9394i	0.745659	−	1.50885i
$928$	0.621430	+	47.6760i	0.0203995	+	1.56504i
$929$	29.0039			0.951588			0.475794	−	0.879557i	$-0.342161\pi$
$929$	29.0039			0.951588			0.475794	+	0.879557i	$0.342161\pi$
$930$	54.3132	+	35.6089i	1.78100	+	1.16766i
$931$	−3.98487	−	20.0333i	−0.130599	−	0.656566i
$932$	−30.8774	−	9.85501i	−1.01142	−	0.322811i
$933$	−25.3627	−	11.5045i	−0.830337	−	0.376641i
$934$	−28.7066	−	39.2954i	−0.939309	−	1.28579i
$935$	−2.84387	+	6.86570i	−0.0930043	+	0.224532i
$936$	5.15668	−	37.4014i	0.168551	−	1.22250i
$937$	−3.33957	−	8.06243i	−0.109099	−	0.263388i	0.859896	−	0.510470i	$-0.170528\pi$
$937$	−3.33957	−	8.06243i	−0.109099	−	0.263388i	−0.968995	+	0.247082i	$0.920528\pi$
$938$	−5.27081	−	3.21109i	−0.172098	−	0.104846i
$939$	12.8028	+	34.0597i	0.417804	+	1.11150i
$940$	24.3568	+	30.5673i	0.794431	+	0.996995i
$941$	15.0978	+	10.0880i	0.492174	+	0.328860i	0.776767	−	0.629788i	$-0.216858\pi$
$941$	15.0978	+	10.0880i	0.492174	+	0.328860i	−0.284593	+	0.958649i	$0.591858\pi$
$942$	3.72089	−	2.53349i	0.121233	−	0.0825455i
$943$	−6.44904	−	6.44904i	−0.210010	−	0.210010i
$944$	6.52972	+	6.91769i	0.212524	+	0.225152i
$945$	43.0868	−	52.3666i	1.40161	−	1.70348i
$946$	−3.87041	+	4.20894i	−0.125838	+	0.136844i
$947$	−32.9455	−	22.0135i	−1.07059	−	0.715343i	−0.110170	−	0.993913i	$-0.535140\pi$
$947$	−32.9455	−	22.0135i	−1.07059	−	0.715343i	−0.960416	+	0.278570i	$0.910140\pi$
$948$	−29.1924	−	26.3777i	−0.948124	−	0.856707i
$949$	−16.5805	−	3.29806i	−0.538225	−	0.107060i
$950$	7.68711	+	31.6554i	0.249403	+	1.02704i
$951$	−38.0837	−	27.3146i	−1.23495	−	0.885737i
$952$	9.75134	−	12.5705i	0.316043	−	0.407411i
$953$	−17.0882	+	41.2546i	−0.553542	+	1.33637i	0.361260	+	0.932465i	$0.382347\pi$
$953$	−17.0882	+	41.2546i	−0.553542	+	1.33637i	−0.914802	+	0.403903i	$0.867653\pi$
$954$	−9.39723	+	13.3467i	−0.304247	+	0.432116i
$955$	9.96510	+	14.9138i	0.322463	+	0.482600i
$956$	37.5792	−	3.15476i	1.21540	−	0.102032i
$957$	−14.7184	+	13.7737i	−0.475779	+	0.445241i
$958$	2.15571	+	0.788907i	0.0696480	+	0.0254884i
$959$	14.5067			0.468445
$960$	−35.3689	−	33.8619i	−1.14153	−	1.09289i
$961$	25.2954			0.815982
$962$	−19.5115	−	7.14046i	−0.629077	−	0.230218i
$963$	7.21058	+	1.93857i	0.232358	+	0.0624695i
$964$	−3.03216	−	36.1188i	−0.0976593	−	1.16331i
$965$	20.2672	+	30.3320i	0.652425	+	0.976423i
$966$	−7.59242	+	3.22283i	−0.244282	+	0.103693i
$967$	−10.5437	+	25.4548i	−0.339063	+	0.818570i	0.658743	+	0.752368i	$0.271088\pi$
$967$	−10.5437	+	25.4548i	−0.339063	+	0.818570i	−0.997806	+	0.0662026i	$0.978912\pi$
$968$	25.5174	−	3.22272i	0.820160	−	0.103582i
$969$	4.72978	−	6.59454i	0.151942	−	0.211847i
$970$	−14.7727	−	60.8338i	−0.474324	−	1.95326i
$971$	23.0007	+	4.57513i	0.738129	+	0.146823i	0.549815	−	0.835286i	$-0.314698\pi$
$971$	23.0007	+	4.57513i	0.738129	+	0.146823i	0.188313	+	0.982109i	$0.439698\pi$
$972$	−2.55280	+	31.0722i	−0.0818812	+	0.996642i
$973$	63.1915	+	42.2232i	2.02583	+	1.35361i
$974$	−18.4918	+	20.1093i	−0.592516	+	0.644342i
$975$	−56.1911	−	13.1268i	−1.79955	−	0.420395i
$976$	−41.2890	+	15.7233i	−1.32163	+	0.503292i
$977$	24.3302	+	24.3302i	0.778392	+	0.778392i	0.979557	−	0.201166i	$-0.0644729\pi$
$977$	24.3302	+	24.3302i	0.778392	+	0.778392i	−0.201166	+	0.979557i	$0.564473\pi$
$978$	−14.9429	−	21.9463i	−0.477821	−	0.701766i
$979$	0.125022	+	0.0835369i	0.00399572	+	0.00266985i
$980$	36.6991	−	29.2428i	1.17231	−	0.934127i
$981$	7.72040	+	5.93439i	0.246493	+	0.189470i
$982$	−29.8559	−	18.1889i	−0.952741	−	0.580430i
$983$	3.51432	+	8.48432i	0.112089	+	0.270608i	0.969963	−	0.243253i	$-0.0782147\pi$
$983$	3.51432	+	8.48432i	0.112089	+	0.270608i	−0.857873	+	0.513861i	$0.828215\pi$
$984$	−48.7951	+	4.52571i	−1.55553	+	0.144274i
$985$	5.41753	−	13.0791i	0.172617	−	0.416734i
$986$	−10.7091	−	14.6594i	−0.341048	−	0.466849i
$987$	14.6132	−	32.2160i	0.465143	−	1.02545i
$988$	8.32402	−	26.0806i	0.264822	−	0.829733i
$989$	0.520853	+	2.61851i	0.0165622	+	0.0832636i
$990$	0.505351	−	20.6952i	0.0160611	−	0.657738i
$991$	38.7994			1.23250			0.616252	−	0.787549i	$-0.288650\pi$
$991$	38.7994			1.23250			0.616252	+	0.787549i	$0.288650\pi$
$992$	−41.7324	−	7.73707i	−1.32500	−	0.245652i
$993$	6.05436	−	3.76131i	0.192129	−	0.119362i
$994$	17.8523	+	38.4607i	0.566242	+	1.21990i
$995$	−44.7122	+	8.89382i	−1.41747	+	0.281953i
$996$	−13.1156	−	7.83410i	−0.415583	−	0.248233i
$997$	20.7514	+	31.0566i	0.657203	+	0.983574i	0.999040	+	0.0438142i	$0.0139510\pi$
$997$	20.7514	+	31.0566i	0.657203	+	0.983574i	−0.341837	+	0.939759i	$0.611049\pi$
$998$	−11.0637	−	15.1448i	−0.350217	−	0.479399i
$999$	16.4119	+	5.00110i	0.519249	+	0.158228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.s.a.107.20	yes	240
3.2	odd	2	inner	192.2.s.a.107.11	✓	240
4.3	odd	2		768.2.s.a.335.8		240
12.11	even	2		768.2.s.a.335.11		240
64.3	odd	16	inner	192.2.s.a.131.11	yes	240
64.61	even	16		768.2.s.a.431.11		240
192.125	odd	16		768.2.s.a.431.8		240
192.131	even	16	inner	192.2.s.a.131.20	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.107.11	✓	240	3.2	odd	2	inner
192.2.s.a.107.20	yes	240	1.1	even	1	trivial
192.2.s.a.131.11	yes	240	64.3	odd	16	inner
192.2.s.a.131.20	yes	240	192.131	even	16	inner
768.2.s.a.335.8		240	4.3	odd	2
768.2.s.a.335.11		240	12.11	even	2
768.2.s.a.431.8		240	192.125	odd	16
768.2.s.a.431.11		240	64.61	even	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.486023 - 1.32807i) q^{2} +(1.18349 + 1.26466i) q^{3} +(-1.52756 - 1.29095i) q^{4} +(-1.96325 - 2.93821i) q^{5} +(2.25476 - 0.957103i) q^{6} +(1.41332 - 3.41205i) q^{7} +(-2.45691 + 1.40129i) q^{8} +(-0.198726 + 2.99341i) q^{9} +(-4.85635 + 1.17930i) q^{10} +(1.35426 + 0.269378i) q^{11} +(-0.175237 - 3.45967i) q^{12} +(3.69962 + 2.47201i) q^{13} +(-3.84455 - 3.53533i) q^{14} +(1.39236 - 5.96017i) q^{15} +(0.666898 + 3.94401i) q^{16} +(-1.07694 - 1.07694i) q^{17} +(3.87889 + 1.71879i) q^{18} +(2.55792 + 1.70915i) q^{19} +(-0.794095 + 7.02276i) q^{20} +(5.98772 - 2.25075i) q^{21} +(1.01595 - 1.66763i) q^{22} +(-0.348914 - 0.842354i) q^{23} +(-4.67986 - 1.44875i) q^{24} +(-2.86532 + 6.91750i) q^{25} +(5.08112 - 3.71192i) q^{26} +(-4.02083 + 3.29134i) q^{27} +(-6.56372 + 3.38760i) q^{28} +(1.64436 + 8.26676i) q^{29} +(-7.23884 - 4.74594i) q^{30} -7.50303 q^{31} +(5.56207 + 1.03119i) q^{32} +(1.26207 + 2.03148i) q^{33} +(-1.95367 + 0.906837i) q^{34} +(-12.8000 + 2.54608i) q^{35} +(4.16791 - 4.31608i) q^{36} +(-1.83441 - 2.74539i) q^{37} +(3.51308 - 2.56642i) q^{38} +(1.25220 + 7.60435i) q^{39} +(8.94080 + 4.46784i) q^{40} +(9.24158 - 3.82799i) q^{41} +(-0.0789866 - 9.04605i) q^{42} +(-2.87193 - 0.571263i) q^{43} +(-1.72096 - 2.15977i) q^{44} +(9.18543 - 5.29292i) q^{45} +(-1.28829 + 0.0539808i) q^{46} +(3.91043 - 3.91043i) q^{47} +(-4.19857 + 5.51108i) q^{48} +(-4.69487 - 4.69487i) q^{49} +(7.79434 + 7.16743i) q^{50} +(0.0874195 - 2.63650i) q^{51} +(-2.46017 - 8.55218i) q^{52} +(-0.750588 + 3.77346i) q^{53} +(2.41692 + 6.93963i) q^{54} +(-1.86725 - 4.50795i) q^{55} +(1.30887 + 10.3636i) q^{56} +(0.865771 + 5.25765i) q^{57} +(11.7781 + 1.83400i) q^{58} +(1.97738 - 1.32124i) q^{59} +(-9.82120 + 7.30708i) q^{60} +(2.15485 + 10.8331i) q^{61} +(-3.64665 + 9.96458i) q^{62} +(9.93280 + 4.90870i) q^{63} +(4.07280 - 6.88566i) q^{64} -15.7235i q^{65} +(3.31135 - 0.688778i) q^{66} +(1.15899 - 0.230537i) q^{67} +(0.254818 + 3.03536i) q^{68} +(0.652356 - 1.43817i) q^{69} +(-2.83972 + 18.2368i) q^{70} +(-7.50045 - 3.10679i) q^{71} +(-3.70637 - 7.63301i) q^{72} +(-3.51016 + 1.45396i) q^{73} +(-4.53765 + 1.10191i) q^{74} +(-12.1393 + 4.56310i) q^{75} +(-1.70096 - 5.91297i) q^{76} +(2.83313 - 4.24007i) q^{77} +(10.7077 + 2.03288i) q^{78} +(8.03113 - 8.03113i) q^{79} +(10.2791 - 9.70258i) q^{80} +(-8.92102 - 1.18974i) q^{81} +(-0.592231 - 14.1340i) q^{82} +(2.45014 - 3.66690i) q^{83} +(-12.0522 - 4.29169i) q^{84} +(-1.04997 + 5.27857i) q^{85} +(-2.15450 + 3.53649i) q^{86} +(-8.50856 + 11.8631i) q^{87} +(-3.70476 + 1.23586i) q^{88} +(0.100607 + 0.0416728i) q^{89} +(-2.56506 - 14.7714i) q^{90} +(13.6634 - 9.12957i) q^{91} +(-0.554448 + 1.73718i) q^{92} +(-8.87972 - 9.48878i) q^{93} +(-3.29278 - 7.09391i) q^{94} -10.8712i q^{95} +(5.27852 + 8.25453i) q^{96} +12.5267i q^{97} +(-8.51695 + 3.95332i) q^{98} +(-1.07549 + 4.00031i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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