LMFDB - Embedded newform 520.2.ca.b.101.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(101,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 5]))

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

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

chi := DirichletCharacter("520.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.ca (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:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.7
Character	$\chi$	$=$	520.101
Dual form			520.2.ca.b.381.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.13415 - 0.844810i) q^{2} +(-1.79930 + 1.03883i) q^{3} +(0.572591 + 1.91628i) q^{4} +1.00000 q^{5} +(2.91828 + 0.341882i) q^{6} +(3.65440 + 2.10987i) q^{7} +(0.969491 - 2.65708i) q^{8} +(0.658316 - 1.14024i) q^{9} +(-1.13415 - 0.844810i) q^{10} +(-2.34007 - 4.05312i) q^{11} +(-3.02095 - 2.85314i) q^{12} +(3.60058 + 0.189253i) q^{13} +(-2.36220 - 5.48017i) q^{14} +(-1.79930 + 1.03883i) q^{15} +(-3.34428 + 2.19449i) q^{16} +(1.44020 - 2.49450i) q^{17} +(-1.70991 + 0.737048i) q^{18} +(-3.09741 + 5.36488i) q^{19} +(0.572591 + 1.91628i) q^{20} -8.76713 q^{21} +(-0.770127 + 6.57376i) q^{22} +(3.36550 + 5.82921i) q^{23} +(1.01584 + 5.78802i) q^{24} +1.00000 q^{25} +(-3.92372 - 3.25645i) q^{26} -3.49745i q^{27} +(-1.95062 + 8.21095i) q^{28} +(4.64674 - 2.68280i) q^{29} +(2.91828 + 0.341882i) q^{30} -0.540960i q^{31} +(5.64684 + 0.336395i) q^{32} +(8.42096 + 4.86185i) q^{33} +(-3.74078 + 1.61244i) q^{34} +(3.65440 + 2.10987i) q^{35} +(2.56196 + 0.608630i) q^{36} +(-0.815399 - 1.41231i) q^{37} +(8.04524 - 3.46785i) q^{38} +(-6.67512 + 3.39985i) q^{39} +(0.969491 - 2.65708i) q^{40} +(1.36715 - 0.789323i) q^{41} +(9.94324 + 7.40656i) q^{42} +(4.99574 + 2.88429i) q^{43} +(6.42702 - 6.80501i) q^{44} +(0.658316 - 1.14024i) q^{45} +(1.10760 - 9.45440i) q^{46} +4.24596i q^{47} +(3.73766 - 7.42267i) q^{48} +(5.40307 + 9.35839i) q^{49} +(-1.13415 - 0.844810i) q^{50} +5.98446i q^{51} +(1.69900 + 7.00810i) q^{52} +10.7922i q^{53} +(-2.95468 + 3.96663i) q^{54} +(-2.34007 - 4.05312i) q^{55} +(9.14899 - 7.66453i) q^{56} -12.8707i q^{57} +(-7.53655 - 0.882920i) q^{58} +(-6.90961 + 11.9678i) q^{59} +(-3.02095 - 2.85314i) q^{60} +(6.45691 + 3.72790i) q^{61} +(-0.457008 + 0.613529i) q^{62} +(4.81150 - 2.77792i) q^{63} +(-6.12018 - 5.15203i) q^{64} +(3.60058 + 0.189253i) q^{65} +(-5.44330 - 12.6282i) q^{66} +(5.52888 + 9.57630i) q^{67} +(5.60481 + 1.33150i) q^{68} +(-12.1111 - 6.99233i) q^{69} +(-2.36220 - 5.48017i) q^{70} +(-8.93003 - 5.15576i) q^{71} +(-2.39147 - 2.85465i) q^{72} -8.13434i q^{73} +(-0.268351 + 2.29063i) q^{74} +(-1.79930 + 1.03883i) q^{75} +(-12.0542 - 2.86364i) q^{76} -19.7489i q^{77} +(10.4428 + 1.78327i) q^{78} +1.61033 q^{79} +(-3.34428 + 2.19449i) q^{80} +(5.60819 + 9.71367i) q^{81} +(-2.21738 - 0.259770i) q^{82} +3.34719 q^{83} +(-5.01998 - 16.8003i) q^{84} +(1.44020 - 2.49450i) q^{85} +(-3.22924 - 7.49168i) q^{86} +(-5.57391 + 9.65430i) q^{87} +(-13.0381 + 2.28830i) q^{88} +(-2.76408 + 1.59584i) q^{89} +(-1.70991 + 0.737048i) q^{90} +(12.7586 + 8.28835i) q^{91} +(-9.24336 + 9.78700i) q^{92} +(0.561963 + 0.973348i) q^{93} +(3.58703 - 4.81556i) q^{94} +(-3.09741 + 5.36488i) q^{95} +(-10.5098 + 5.26081i) q^{96} +(-12.2894 - 7.09529i) q^{97} +(1.77817 - 15.1784i) q^{98} -6.16202 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9} - 8 q^{11} + 6 q^{12} - 4 q^{14} + 14 q^{16} + 18 q^{18} - 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 22 q^{24} + 56 q^{25} - 37 q^{26} - 12 q^{28} - 13 q^{30}+ \cdots - 48 q^{99}+O(q^{100}) $ 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9 - 8 * q^11 + 6 * q^12 - 4 * q^14 + 14 * q^16 + 18 * q^18 - 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 22 * q^24 + 56 * q^25 - 37 * q^26 - 12 * q^28 - 13 * q^30 - 30 * q^32 - 16 * q^34 + 15 * q^36 + 4 * q^37 - 24 * q^39 - 61 * q^42 + 24 * q^44 + 28 * q^45 - 19 * q^46 - 51 * q^48 + 20 * q^49 - 64 * q^52 - 5 * q^54 - 8 * q^55 - 23 * q^56 - q^58 - 16 * q^59 + 6 * q^60 + 10 * q^62 - 30 * q^64 + 14 * q^66 - 36 * q^67 - 51 * q^68 - 4 * q^70 - 81 * q^72 + 70 * q^74 - 60 * q^76 + 143 * q^78 + 14 * q^80 - 28 * q^81 + 21 * q^82 + 40 * q^83 + 31 * q^84 - 28 * q^86 - 36 * q^87 - 19 * q^88 + 18 * q^90 + 16 * q^91 - 18 * q^92 + 43 * q^94 - 16 * q^95 - 48 * q^96 + 24 * q^97 + 56 * q^98 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.13415	−	0.844810i	−0.801965	−	0.597371i
$2$	−1.13415	−	0.844810i	−0.801965	−	0.597371i
$3$	−1.79930	+	1.03883i	−1.03883	+	0.599766i	−0.919500	−	0.393089i	$-0.871406\pi$
$3$	−1.79930	+	1.03883i	−1.03883	+	0.599766i	−0.119325	+	0.992855i	$0.538073\pi$
$4$	0.572591	+	1.91628i	0.286296	+	0.958141i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	2.91828	+	0.341882i	1.19138	+	0.139573i
$7$	3.65440	+	2.10987i	1.38123	+	0.797454i	0.992305	−	0.123815i	$-0.0395128\pi$
$7$	3.65440	+	2.10987i	1.38123	+	0.797454i	0.388926	+	0.921269i	$0.372846\pi$
$8$	0.969491	−	2.65708i	0.342767	−	0.939421i
$9$	0.658316	−	1.14024i	0.219439	−	0.380079i
$10$	−1.13415	−	0.844810i	−0.358650	−	0.267152i
$11$	−2.34007	−	4.05312i	−0.705557	−	1.22206i	−0.966490	−	0.256704i	$-0.917363\pi$
$11$	−2.34007	−	4.05312i	−0.705557	−	1.22206i	0.260933	−	0.965357i	$-0.415970\pi$
$12$	−3.02095	−	2.85314i	−0.872072	−	0.823631i
$13$	3.60058	+	0.189253i	0.998621	+	0.0524894i
$13$	3.60058	+	0.189253i	0.998621	+	0.0524894i
$14$	−2.36220	−	5.48017i	−0.631323	−	1.46464i
$15$	−1.79930	+	1.03883i	−0.464577	+	0.268224i
$16$	−3.34428	+	2.19449i	−0.836069	+	0.548624i
$17$	1.44020	−	2.49450i	0.349300	−	0.605005i	−0.636826	−	0.771008i	$-0.719753\pi$
$17$	1.44020	−	2.49450i	0.349300	−	0.605005i	0.986125	+	0.166003i	$0.0530862\pi$
$18$	−1.70991	+	0.737048i	−0.403031	+	0.173724i
$19$	−3.09741	+	5.36488i	−0.710596	+	1.23079i	0.254038	+	0.967194i	$0.418241\pi$
$19$	−3.09741	+	5.36488i	−0.710596	+	1.23079i	−0.964634	+	0.263594i	$0.915092\pi$
$20$	0.572591	+	1.91628i	0.128035	+	0.428494i
$21$	−8.76713			−1.91314
$22$	−0.770127	+	6.57376i	−0.164192	+	1.40153i
$23$	3.36550	+	5.82921i	0.701754	+	1.21547i	0.967850	+	0.251528i	$0.0809329\pi$
$23$	3.36550	+	5.82921i	0.701754	+	1.21547i	−0.266096	+	0.963947i	$0.585734\pi$
$24$	1.01584	+	5.78802i	0.207358	+	1.18147i
$25$	1.00000			0.200000
$26$	−3.92372	−	3.25645i	−0.769504	−	0.638642i
$27$		−	3.49745i		−	0.673084i
$28$	−1.95062	+	8.21095i	−0.368633	+	1.55172i
$29$	4.64674	−	2.68280i	0.862878	−	0.498183i	−0.00209727	−	0.999998i	$-0.500668\pi$
$29$	4.64674	−	2.68280i	0.862878	−	0.498183i	0.864975	+	0.501815i	$0.167334\pi$
$30$	2.91828	+	0.341882i	0.532803	+	0.0624188i
$31$		−	0.540960i		−	0.0971592i	−0.998819	−	0.0485796i	$-0.984531\pi$
$31$		−	0.540960i		−	0.0971592i	0.998819	−	0.0485796i	$-0.0154695\pi$
$32$	5.64684	+	0.336395i	0.998230	+	0.0594668i
$33$	8.42096	+	4.86185i	1.46590	+	0.846339i
$34$	−3.74078	+	1.61244i	−0.641538	+	0.276531i
$35$	3.65440	+	2.10987i	0.617706	+	0.356632i
$36$	2.56196	+	0.608630i	0.426994	+	0.101438i
$37$	−0.815399	−	1.41231i	−0.134051	−	0.232183i	0.791184	−	0.611579i	$-0.209465\pi$
$37$	−0.815399	−	1.41231i	−0.134051	−	0.232183i	−0.925234	+	0.379396i	$0.876132\pi$
$38$	8.04524	−	3.46785i	1.30511	−	0.562559i
$39$	−6.67512	+	3.39985i	−1.06887	+	0.544412i
$40$	0.969491	−	2.65708i	0.153290	−	0.420122i
$41$	1.36715	−	0.789323i	0.213513	−	0.123272i	−0.389430	−	0.921056i	$-0.627328\pi$
$41$	1.36715	−	0.789323i	0.213513	−	0.123272i	0.602943	+	0.797784i	$0.293995\pi$
$42$	9.94324	+	7.40656i	1.53427	+	1.14286i
$43$	4.99574	+	2.88429i	0.761844	+	0.439851i	0.829957	−	0.557827i	$-0.188365\pi$
$43$	4.99574	+	2.88429i	0.761844	+	0.439851i	−0.0681136	+	0.997678i	$0.521698\pi$
$44$	6.42702	−	6.80501i	0.968909	−	1.02589i
$45$	0.658316	−	1.14024i	0.0981360	−	0.169977i
$46$	1.10760	−	9.45440i	0.163307	−	1.39398i
$47$			4.24596i			0.619338i	0.950844	+	0.309669i	$0.100218\pi$
$47$			4.24596i			0.619338i	−0.950844	+	0.309669i	$0.899782\pi$
$48$	3.73766	−	7.42267i	0.539484	−	1.07137i
$49$	5.40307	+	9.35839i	0.771867	+	1.33691i
$50$	−1.13415	−	0.844810i	−0.160393	−	0.119474i
$51$			5.98446i			0.837992i
$52$	1.69900	+	7.00810i	0.235609	+	0.971848i
$53$			10.7922i			1.48242i	0.671274	+	0.741209i	$0.265747\pi$
$53$			10.7922i			1.48242i	−0.671274	+	0.741209i	$0.734253\pi$
$54$	−2.95468	+	3.96663i	−0.402081	+	0.539790i
$55$	−2.34007	−	4.05312i	−0.315535	−	0.546522i
$56$	9.14899	−	7.66453i	1.22259	−	1.02422i
$57$		−	12.8707i		−	1.70476i
$58$	−7.53655	−	0.882920i	−0.989597	−	0.115933i
$59$	−6.90961	+	11.9678i	−0.899554	+	1.55807i	−0.0714891	+	0.997441i	$0.522775\pi$
$59$	−6.90961	+	11.9678i	−0.899554	+	1.55807i	−0.828065	+	0.560632i	$0.810558\pi$
$60$	−3.02095	−	2.85314i	−0.390002	−	0.368339i
$61$	6.45691	+	3.72790i	0.826723	+	0.477309i	0.852729	−	0.522353i	$-0.174946\pi$
$61$	6.45691	+	3.72790i	0.826723	+	0.477309i	−0.0260064	+	0.999662i	$0.508279\pi$
$62$	−0.457008	+	0.613529i	−0.0580401	+	0.0779183i
$63$	4.81150	−	2.77792i	0.606192	−	0.349985i
$64$	−6.12018	−	5.15203i	−0.765022	−	0.644004i
$65$	3.60058	+	0.189253i	0.446597	+	0.0234740i
$66$	−5.44330	−	12.6282i	−0.670024	−	1.55442i
$67$	5.52888	+	9.57630i	0.675460	+	1.16993i	0.976334	+	0.216268i	$0.0693884\pi$
$67$	5.52888	+	9.57630i	0.675460	+	1.16993i	−0.300874	+	0.953664i	$0.597278\pi$
$68$	5.60481	+	1.33150i	0.679683	+	0.161468i
$69$	−12.1111	−	6.99233i	−1.45800	−	0.841777i
$70$	−2.36220	−	5.48017i	−0.282336	−	0.655006i
$71$	−8.93003	−	5.15576i	−1.05980	−	0.611876i	−0.134423	−	0.990924i	$-0.542918\pi$
$71$	−8.93003	−	5.15576i	−1.05980	−	0.611876i	−0.925377	+	0.379048i	$0.876251\pi$
$72$	−2.39147	−	2.85465i	−0.281838	−	0.336424i
$73$		−	8.13434i		−	0.952052i	−0.879431	−	0.476026i	$-0.842077\pi$
$73$		−	8.13434i		−	0.952052i	0.879431	−	0.476026i	$-0.157923\pi$
$74$	−0.268351	+	2.29063i	−0.0311952	+	0.266281i
$75$	−1.79930	+	1.03883i	−0.207765	+	0.119953i
$76$	−12.0542	−	2.86364i	−1.38271	−	0.328482i
$77$		−	19.7489i		−	2.25060i
$78$	10.4428	+	1.78327i	1.18242	+	0.201915i
$79$	1.61033			0.181177			0.0905884	−	0.995888i	$-0.471125\pi$
$79$	1.61033			0.181177			0.0905884	+	0.995888i	$0.471125\pi$
$80$	−3.34428	+	2.19449i	−0.373902	+	0.245352i
$81$	5.60819	+	9.71367i	0.623132	+	1.07930i
$82$	−2.21738	−	0.259770i	−0.244869	−	0.0286868i
$83$	3.34719			0.367402			0.183701	−	0.982982i	$-0.441192\pi$
$83$	3.34719			0.367402			0.183701	+	0.982982i	$0.441192\pi$
$84$	−5.01998	−	16.8003i	−0.547725	−	1.83306i
$85$	1.44020	−	2.49450i	0.156212	−	0.270566i
$86$	−3.22924	−	7.49168i	−0.348218	−	0.807848i
$87$	−5.57391	+	9.65430i	−0.597586	+	1.03505i
$88$	−13.0381	+	2.28830i	−1.38987	+	0.243933i
$89$	−2.76408	+	1.59584i	−0.292992	+	0.169159i	−0.639290	−	0.768965i	$-0.720772\pi$
$89$	−2.76408	+	1.59584i	−0.292992	+	0.169159i	0.346299	+	0.938124i	$0.387438\pi$
$90$	−1.70991	+	0.737048i	−0.180241	+	0.0776917i
$91$	12.7586	+	8.28835i	1.33747	+	0.868855i
$92$	−9.24336	+	9.78700i	−0.963687	+	1.02036i
$93$	0.561963	+	0.973348i	0.0582728	+	0.100931i
$94$	3.58703	−	4.81556i	0.369974	−	0.496687i
$95$	−3.09741	+	5.36488i	−0.317788	+	0.550425i
$96$	−10.5098	+	5.26081i	−1.07265	+	0.536929i
$97$	−12.2894	−	7.09529i	−1.24780	−	0.720417i	−0.277129	−	0.960833i	$-0.589383\pi$
$97$	−12.2894	−	7.09529i	−1.24780	−	0.720417i	−0.970670	+	0.240415i	$0.922716\pi$
$98$	1.77817	−	15.1784i	0.179623	−	1.53325i
$99$	−6.16202			−0.619307
$100$	0.572591	+	1.91628i	0.0572591	+	0.191628i
$101$	4.98479	−	2.87797i	0.496005	−	0.286369i	−0.231057	−	0.972940i	$-0.574218\pi$
$101$	4.98479	−	2.87797i	0.496005	−	0.286369i	0.727062	+	0.686571i	$0.240885\pi$
$102$	5.05573	−	6.78728i	0.500592	−	0.672040i
$103$	6.54307			0.644708			0.322354	−	0.946619i	$-0.395526\pi$
$103$	6.54307			0.644708			0.322354	+	0.946619i	$0.395526\pi$
$104$	3.99359	−	9.38356i	0.391604	−	0.920134i
$105$	−8.76713			−0.855584
$106$	9.11734	−	12.2399i	0.885554	−	1.18885i
$107$	−6.67483	+	3.85372i	−0.645280	+	0.372553i	−0.786646	−	0.617405i	$-0.788184\pi$
$107$	−6.67483	+	3.85372i	−0.645280	+	0.372553i	0.141365	+	0.989957i	$0.454851\pi$
$108$	6.70210	−	2.00261i	0.644910	−	0.192701i
$109$	−2.58204			−0.247314			−0.123657	−	0.992325i	$-0.539462\pi$
$109$	−2.58204			−0.247314			−0.123657	+	0.992325i	$0.539462\pi$
$110$	−0.770127	+	6.57376i	−0.0734287	+	0.626783i
$111$	2.93429	+	1.69411i	0.278511	+	0.160798i
$112$	−16.8514	+	0.963571i	−1.59231	+	0.0910489i
$113$	−1.34722	+	2.33345i	−0.126736	+	0.219513i	−0.922410	−	0.386212i	$-0.873783\pi$
$113$	−1.34722	+	2.33345i	−0.126736	+	0.219513i	0.795674	+	0.605725i	$0.207117\pi$
$114$	−10.8733	+	14.5973i	−1.01838	+	1.36716i
$115$	3.36550	+	5.82921i	0.313834	+	0.543577i
$116$	7.80168	+	7.36832i	0.724368	+	0.684131i
$117$	2.58612	−	3.98093i	0.239086	−	0.368037i
$118$	17.9470	−	7.73596i	1.65216	−	0.712153i
$119$	10.5261	−	6.07725i	0.964927	−	0.557101i
$120$	1.01584	+	5.78802i	0.0927333	+	0.528371i
$121$	−5.45184	+	9.44287i	−0.495622	+	0.858443i
$122$	−4.17374	−	9.68286i	−0.377872	−	0.876645i
$123$	−1.63994	+	2.84046i	−0.147868	+	0.256115i
$124$	1.03663	−	0.309749i	0.0930922	−	0.0278163i
$125$	1.00000			0.0894427
$126$	−7.80377	−	0.914225i	−0.695215	−	0.0814457i
$127$	−9.44785	−	16.3642i	−0.838361	−	1.45208i	−0.891264	−	0.453484i	$-0.850181\pi$
$127$	−9.44785	−	16.3642i	−0.838361	−	1.45208i	0.0529034	−	0.998600i	$-0.483152\pi$
$128$	2.58871	+	11.0136i	0.228811	+	0.973471i
$129$	−11.9851			−1.05523
$130$	−3.92372	−	3.25645i	−0.344133	−	0.285609i
$131$		−	15.2492i		−	1.33233i	−0.745804	−	0.666166i	$-0.767934\pi$
$131$		−	15.2492i		−	1.33233i	0.745804	−	0.666166i	$-0.232066\pi$
$132$	−4.49490	+	18.9208i	−0.391231	+	1.64684i
$133$	−22.6384	+	13.0703i	−1.96299	+	1.13334i
$134$	1.81958	−	15.5318i	0.157188	−	1.34174i
$135$		−	3.49745i		−	0.301012i
$136$	−5.23183	−	6.24512i	−0.448626	−	0.535515i
$137$	11.2331	+	6.48544i	0.959709	+	0.554089i	0.896084	−	0.443885i	$-0.146400\pi$
$137$	11.2331	+	6.48544i	0.959709	+	0.554089i	0.0636258	+	0.997974i	$0.479734\pi$
$138$	7.82857	+	18.1619i	0.666412	+	1.54604i
$139$	−3.38486	−	1.95425i	−0.287100	−	0.165758i	0.349533	−	0.936924i	$-0.386340\pi$
$139$	−3.38486	−	1.95425i	−0.287100	−	0.165758i	−0.636634	+	0.771166i	$0.719674\pi$
$140$	−1.95062	+	8.21095i	−0.164858	+	0.693952i
$141$	−4.41082	−	7.63976i	−0.371458	−	0.643384i
$142$	5.77236	+	13.3916i	0.484406	+	1.12380i
$143$	−7.65854	−	15.0364i	−0.640439	−	1.25741i
$144$	0.300651	+	5.25794i	0.0250543	+	0.438162i
$145$	4.64674	−	2.68280i	0.385891	−	0.222794i
$146$	−6.87197	+	9.22556i	−0.568728	+	0.763513i
$147$	−19.4435	−	11.2257i	−1.60367	−	0.925879i
$148$	2.23950	−	2.37121i	0.184086	−	0.194913i
$149$	7.20590	−	12.4810i	0.590331	−	1.02248i	−0.403857	−	0.914822i	$-0.632331\pi$
$149$	7.20590	−	12.4810i	0.590331	−	1.02248i	0.994188	−	0.107661i	$-0.0343360\pi$
$150$	2.91828	+	0.341882i	0.238277	+	0.0279145i
$151$		−	6.40908i		−	0.521564i	−0.965398	−	0.260782i	$-0.916020\pi$
$151$		−	6.40908i		−	0.521564i	0.965398	−	0.260782i	$-0.0839804\pi$
$152$	11.2520	+	13.4313i	0.912659	+	1.08942i
$153$	−1.89621	−	3.28434i	−0.153300	−	0.265523i
$154$	−16.6841	+	22.3982i	−1.34444	+	1.80490i
$155$		−	0.540960i		−	0.0434509i
$156$	−10.3372	−	10.8447i	−0.827638	−	0.868270i
$157$			11.0979i			0.885705i	0.896594	+	0.442853i	$0.146034\pi$
$157$			11.0979i			0.885705i	−0.896594	+	0.442853i	$0.853966\pi$
$158$	−1.82636	−	1.36043i	−0.145297	−	0.108230i
$159$	−11.2112	−	19.4183i	−0.889104	−	1.53997i
$160$	5.64684	+	0.336395i	0.446422	+	0.0265944i
$161$			28.4030i			2.23847i
$162$	1.84568	−	15.7546i	0.145010	−	1.23780i
$163$	0.589705	−	1.02140i	0.0461893	−	0.0800021i	−0.842006	−	0.539467i	$-0.818626\pi$
$163$	0.589705	−	1.02140i	0.0461893	−	0.0800021i	0.888196	+	0.459465i	$0.151959\pi$
$164$	2.29538	+	2.16788i	0.179239	+	0.169283i
$165$	8.42096	+	4.86185i	0.655571	+	0.378494i
$166$	−3.79622	−	2.82774i	−0.294644	−	0.219475i
$167$	13.8124	−	7.97461i	1.06884	−	0.617094i	0.140974	−	0.990013i	$-0.454977\pi$
$167$	13.8124	−	7.97461i	1.06884	−	0.617094i	0.927864	+	0.372920i	$0.121643\pi$
$168$	−8.49965	+	23.2950i	−0.655762	+	1.79725i
$169$	12.9284	+	1.36284i	0.994490	+	0.104834i
$170$	−3.74078	+	1.61244i	−0.286905	+	0.123668i
$171$	4.07816	+	7.06358i	0.311865	+	0.540165i
$172$	−2.66660	+	11.2248i	−0.203326	+	0.855881i
$173$	−15.7961	−	9.11987i	−1.20095	−	0.693371i	−0.240187	−	0.970727i	$-0.577209\pi$
$173$	−15.7961	−	9.11987i	−1.20095	−	0.693371i	−0.960767	+	0.277356i	$0.910542\pi$
$174$	14.4777	−	6.24052i	1.09755	−	0.473093i
$175$	3.65440	+	2.10987i	0.276246	+	0.159491i
$176$	16.7204	+	8.41949i	1.26035	+	0.634643i
$177$		−	28.7115i		−	2.15809i
$178$	4.48306	+	0.525199i	0.336020	+	0.0393653i
$179$	14.8849	−	8.59378i	1.11255	−	0.642329i	0.173059	−	0.984912i	$-0.444635\pi$
$179$	14.8849	−	8.59378i	1.11255	−	0.642329i	0.939488	+	0.342582i	$0.111302\pi$
$180$	2.56196	+	0.608630i	0.190958	+	0.0453646i
$181$			4.06663i			0.302270i	0.988513	+	0.151135i	$0.0482929\pi$
$181$			4.06663i			0.302270i	−0.988513	+	0.151135i	$0.951707\pi$
$182$	−7.46814	−	20.1789i	−0.553575	−	1.49576i
$183$	−15.4906			−1.14509
$184$	18.7515	−	3.29104i	1.38238	−	0.242618i
$185$	−0.815399	−	1.41231i	−0.0599493	−	0.103835i
$186$	0.184944	−	1.57867i	0.0135608	−	0.115754i
$187$	−13.4807			−0.985803
$188$	−8.13647	+	2.43120i	−0.593413	+	0.177314i
$189$	7.37915	−	12.7811i	0.536754	−	0.929685i
$190$	8.04524	−	3.46785i	0.583663	−	0.251584i
$191$	−12.9380	+	22.4093i	−0.936160	+	1.62148i	−0.163608	+	0.986525i	$0.552313\pi$
$191$	−12.9380	+	22.4093i	−0.936160	+	1.62148i	−0.772552	+	0.634951i	$0.781020\pi$
$192$	16.3641	+	2.91225i	1.18098	+	0.210174i
$193$	−6.08089	+	3.51080i	−0.437712	+	0.252713i	−0.702627	−	0.711559i	$-0.747990\pi$
$193$	−6.08089	+	3.51080i	−0.437712	+	0.252713i	0.264915	+	0.964272i	$0.414656\pi$
$194$	7.94385	+	18.4293i	0.570335	+	1.32315i
$195$	−6.67512	+	3.39985i	−0.478015	+	0.243468i
$196$	−14.8396	+	15.7123i	−1.05997	+	1.12231i
$197$	−1.16170	−	2.01213i	−0.0827678	−	0.143358i	0.821670	−	0.569963i	$-0.193043\pi$
$197$	−1.16170	−	2.01213i	−0.0827678	−	0.143358i	−0.904438	+	0.426605i	$0.859709\pi$
$198$	6.98866	+	5.20574i	0.496662	+	0.369956i
$199$	−0.401539	+	0.695486i	−0.0284643	+	0.0493017i	−0.879907	−	0.475147i	$-0.842395\pi$
$199$	−0.401539	+	0.695486i	−0.0284643	+	0.0493017i	0.851442	+	0.524448i	$0.175728\pi$
$200$	0.969491	−	2.65708i	0.0685533	−	0.187884i
$201$	−19.8962	−	11.4871i	−1.40337	−	0.810236i
$202$	−8.08484	−	0.947153i	−0.568847	−	0.0666414i
$203$	22.6414			1.58911
$204$	−11.4679	+	3.42665i	−0.802915	+	0.239914i
$205$	1.36715	−	0.789323i	0.0954858	−	0.0551287i
$206$	−7.42082	−	5.52765i	−0.517033	−	0.385130i
$207$	8.86225			0.615969
$208$	−12.4567	+	7.26854i	−0.863714	+	0.503983i
$209$	28.9927			2.00546
$210$	9.94324	+	7.40656i	0.686149	+	0.511101i
$211$	9.32232	−	5.38225i	0.641775	−	0.370529i	−0.143523	−	0.989647i	$-0.545843\pi$
$211$	9.32232	−	5.38225i	0.641775	−	0.370529i	0.785298	+	0.619118i	$0.212510\pi$
$212$	−20.6808	+	6.17950i	−1.42037	+	0.424410i
$213$	21.4237			1.46793
$214$	10.8259	+	1.26827i	0.740045	+	0.0866975i
$215$	4.99574	+	2.88429i	0.340707	+	0.196707i
$216$	−9.29301	−	3.39074i	−0.632309	−	0.230711i
$217$	1.14135	−	1.97688i	0.0774800	−	0.134199i
$218$	2.92841	+	2.18133i	0.198337	+	0.147738i
$219$	8.45016	+	14.6361i	0.571009	+	0.989016i
$220$	6.42702	−	6.80501i	0.433309	−	0.458794i
$221$	5.65764	−	8.70908i	0.380574	−	0.585836i
$222$	−1.89672	−	4.40030i	−0.127300	−	0.295329i
$223$	22.4020	−	12.9338i	1.50015	−	0.866111i	0.500148	−	0.865940i	$-0.333279\pi$
$223$	22.4020	−	12.9338i	1.50015	−	0.866111i	1.00000		0.000171297i	$-5.45256e-5\pi$
$224$	19.9260	+	13.1434i	1.33137	+	0.878181i
$225$	0.658316	−	1.14024i	0.0438878	−	0.0760158i
$226$	3.49928	−	1.50834i	0.232768	−	0.100333i
$227$	10.2245	−	17.7093i	0.678622	−	1.17541i	−0.296774	−	0.954948i	$-0.595911\pi$
$227$	10.2245	−	17.7093i	0.678622	−	1.17541i	0.975396	−	0.220460i	$-0.0707560\pi$
$228$	24.6639	−	7.36965i	1.63341	−	0.488067i
$229$	−9.71044			−0.641684			−0.320842	−	0.947133i	$-0.603966\pi$
$229$	−9.71044			−0.641684			−0.320842	+	0.947133i	$0.603966\pi$
$230$	1.10760	−	9.45440i	0.0730329	−	0.623405i
$231$	20.5157	+	35.5342i	1.34983	+	2.33798i
$232$	−2.62344	−	14.9477i	−0.172237	−	0.981365i
$233$	11.4878			0.752592			0.376296	−	0.926499i	$-0.377198\pi$
$233$	11.4878			0.752592			0.376296	+	0.926499i	$0.377198\pi$
$234$	−6.29617	+	2.33019i	−0.411594	+	0.152330i
$235$			4.24596i			0.276976i
$236$	−26.8900	−	6.38810i	−1.75039	−	0.415830i
$237$	−2.89747	+	1.67286i	−0.188211	+	0.108664i
$238$	−17.0723	−	2.00005i	−1.10663	−	0.129644i
$239$		−	22.5813i		−	1.46066i	−0.683092	−	0.730332i	$-0.739365\pi$
$239$		−	22.5813i		−	1.46066i	0.683092	−	0.730332i	$-0.260635\pi$
$240$	3.73766	−	7.42267i	0.241265	−	0.479131i
$241$	−10.8755	−	6.27899i	−0.700555	−	0.404465i	0.106999	−	0.994259i	$-0.465876\pi$
$241$	−10.8755	−	6.27899i	−0.700555	−	0.404465i	−0.807554	+	0.589794i	$0.799209\pi$
$242$	14.1606	−	6.10386i	0.910281	−	0.392371i
$243$	−11.0950	−	6.40568i	−0.711743	−	0.410925i
$244$	−3.44654	+	14.5078i	−0.220642	+	0.928769i
$245$	5.40307	+	9.35839i	0.345189	+	0.597886i
$246$	4.25958	−	1.83607i	0.271581	−	0.117063i
$247$	−12.1678	+	18.7305i	−0.774219	+	1.19179i
$248$	−1.43737	−	0.524455i	−0.0912734	−	0.0333029i
$249$	−6.02260	+	3.47715i	−0.381667	+	0.220355i
$250$	−1.13415	−	0.844810i	−0.0717299	−	0.0534305i
$251$	−14.4105	−	8.31990i	−0.909582	−	0.525147i	−0.0292854	−	0.999571i	$-0.509323\pi$
$251$	−14.4105	−	8.31990i	−0.909582	−	0.525147i	−0.880297	+	0.474424i	$0.842657\pi$
$252$	8.07830	+	7.62958i	0.508885	+	0.480618i
$253$	15.7510	−	27.2815i	0.990256	−	1.71517i
$254$	−3.10933	+	26.5410i	−0.195097	+	1.66533i
$255$			5.98446i			0.374761i
$256$	6.36839	−	14.6780i	0.398024	−	0.917375i
$257$	−2.81728	−	4.87967i	−0.175737	−	0.304386i	0.764679	−	0.644411i	$-0.222898\pi$
$257$	−2.81728	−	4.87967i	−0.175737	−	0.304386i	−0.940416	+	0.340026i	$0.889564\pi$
$258$	13.5929	+	10.1251i	0.846258	+	0.630364i
$259$		−	6.88153i		−	0.427598i
$260$	1.69900	+	7.00810i	0.105367	+	0.434624i
$261$		−	7.06451i		−	0.437282i
$262$	−12.8827	+	17.2949i	−0.795896	+	1.06848i
$263$	−1.87968	−	3.25571i	−0.115906	−	0.200755i	0.802235	−	0.597008i	$-0.203644\pi$
$263$	−1.87968	−	3.25571i	−0.115906	−	0.200755i	−0.918142	+	0.396252i	$0.870311\pi$
$264$	21.0824	−	17.6617i	1.29753	−	1.08700i
$265$			10.7922i			0.662958i
$266$	36.7172	+	4.30148i	2.25127	+	0.263741i
$267$	3.31560	−	5.74279i	0.202912	−	0.351453i
$268$	−15.1851	+	16.0782i	−0.927578	+	0.982133i
$269$	−12.5502	−	7.24587i	−0.765200	−	0.441788i	0.0659599	−	0.997822i	$-0.478989\pi$
$269$	−12.5502	−	7.24587i	−0.765200	−	0.441788i	−0.831159	+	0.556034i	$0.812322\pi$
$270$	−2.95468	+	3.96663i	−0.179816	+	0.241401i
$271$	−13.9302	+	8.04262i	−0.846201	+	0.488554i	−0.859367	−	0.511359i	$-0.829142\pi$
$271$	−13.9302	+	8.04262i	−0.846201	+	0.488554i	0.0131665	+	0.999913i	$0.495809\pi$
$272$	0.657735	+	11.5028i	0.0398811	+	0.697460i
$273$	−31.5668	−	1.65921i	−1.91051	−	0.100420i
$274$	−7.26106	−	16.8453i	−0.438657	−	1.01766i
$275$	−2.34007	−	4.05312i	−0.141111	−	0.244412i
$276$	6.46458	−	27.2120i	0.389122	−	1.63797i
$277$	13.6436	+	7.87715i	0.819766	+	0.473292i	0.850336	−	0.526240i	$-0.176399\pi$
$277$	13.6436	+	7.87715i	0.819766	+	0.473292i	−0.0305697	+	0.999533i	$0.509732\pi$
$278$	2.18797	+	5.07598i	0.131226	+	0.304437i
$279$	−0.616822	−	0.356123i	−0.0369282	−	0.0213205i
$280$	9.14899	−	7.66453i	0.546757	−	0.458044i
$281$		−	5.80257i		−	0.346152i	−0.984908	−	0.173076i	$-0.944629\pi$
$281$		−	5.80257i		−	0.346152i	0.984908	−	0.173076i	$-0.0553707\pi$
$282$	−1.45162	+	12.3909i	−0.0864426	+	0.737869i
$283$	4.16933	−	2.40717i	0.247841	−	0.143091i	−0.370934	−	0.928659i	$-0.620962\pi$
$283$	4.16933	−	2.40717i	0.247841	−	0.143091i	0.618775	+	0.785568i	$0.287629\pi$
$284$	4.76663	−	20.0646i	0.282847	−	1.19062i
$285$		−	12.8707i		−	0.762394i
$286$	−4.01701	+	23.5236i	−0.237531	+	1.39098i
$287$	6.66147			0.393214
$288$	4.10098	−	6.21729i	0.241653	−	0.366357i
$289$	4.35165	+	7.53729i	0.255980	+	0.443370i
$290$	−7.53655	−	0.882920i	−0.442561	−	0.0518468i
$291$	29.4831			1.72833
$292$	15.5877	−	4.65765i	0.912201	−	0.272568i
$293$	−6.81988	+	11.8124i	−0.398422	+	0.690087i	−0.993531	−	0.113558i	$-0.963775\pi$
$293$	−6.81988	+	11.8124i	−0.398422	+	0.690087i	0.595110	+	0.803645i	$0.297109\pi$
$294$	12.5682	+	29.1577i	0.732994	+	1.70051i
$295$	−6.90961	+	11.9678i	−0.402293	+	0.696792i
$296$	−4.54315	+	0.797359i	−0.264065	+	0.0463456i
$297$	−14.1756	+	8.18427i	−0.822550	+	0.474900i
$298$	−18.7166	+	8.06769i	−1.08423	+	0.467349i
$299$	11.0145	+	21.6255i	0.636988	+	1.25063i
$300$	−3.02095	−	2.85314i	−0.174414	−	0.164726i
$301$	12.1709	+	21.0807i	0.701522	+	1.21507i
$302$	−5.41446	+	7.26886i	−0.311567	+	0.418276i
$303$	−5.97942	+	10.3567i	−0.343509	+	0.594974i
$304$	−1.41458	−	24.7389i	−0.0811318	−	1.41887i
$305$	6.45691	+	3.72790i	0.369722	+	0.213459i
$306$	−0.624052	+	5.32687i	−0.0356747	+	0.304517i
$307$	−19.0421			−1.08679			−0.543396	−	0.839476i	$-0.682862\pi$
$307$	−19.0421			−1.08679			−0.543396	+	0.839476i	$0.682862\pi$
$308$	37.8445	−	11.3081i	2.15639	−	0.644337i
$309$	−11.7729	+	6.79711i	−0.669739	+	0.386674i
$310$	−0.457008	+	0.613529i	−0.0259563	+	0.0348461i
$311$	−23.9649			−1.35893			−0.679463	−	0.733710i	$-0.737787\pi$
$311$	−23.9649			−1.35893			−0.679463	+	0.733710i	$0.737787\pi$
$312$	2.56222	+	21.0325i	0.145057	+	1.19073i
$313$	−3.59532			−0.203219			−0.101610	−	0.994824i	$-0.532399\pi$
$313$	−3.59532			−0.203219			−0.101610	+	0.994824i	$0.532399\pi$
$314$	9.37558	−	12.5866i	0.529095	−	0.710305i
$315$	4.81150	−	2.77792i	0.271097	−	0.156518i
$316$	0.922064	+	3.08586i	0.0518701	+	0.173593i
$317$	−6.01208			−0.337672			−0.168836	−	0.985644i	$-0.554001\pi$
$317$	−6.01208			−0.337672			−0.168836	+	0.985644i	$0.554001\pi$
$318$	−3.68965	+	31.4946i	−0.206905	+	1.76613i
$319$	−21.7474	−	12.5559i	−1.21762	−	0.702993i
$320$	−6.12018	−	5.15203i	−0.342128	−	0.288007i
$321$	8.00668	−	13.8680i	0.446889	−	0.774035i
$322$	23.9951	−	32.2132i	1.33720	−	1.79517i
$323$	8.92179	+	15.4530i	0.496421	+	0.859827i
$324$	−15.4029	+	16.3088i	−0.855718	+	0.906046i
$325$	3.60058	+	0.189253i	0.199724	+	0.0104979i
$326$	−1.53170	+	0.660231i	−0.0848331	+	0.0365668i
$327$	4.64585	−	2.68228i	0.256916	−	0.148331i
$328$	−0.771860	−	4.39787i	−0.0426189	−	0.242832i
$329$	−8.95842	+	15.5164i	−0.493893	+	0.855449i
$330$	−5.44330	−	12.6282i	−0.299644	−	0.695158i
$331$	10.7523	−	18.6235i	0.590999	−	1.02364i	−0.403099	−	0.915156i	$-0.632067\pi$
$331$	10.7523	−	18.6235i	0.590999	−	1.02364i	0.994098	−	0.108484i	$-0.0345996\pi$
$332$	1.91657	+	6.41416i	0.105186	+	0.352023i
$333$	−2.14716			−0.117664
$334$	−22.4024	−	2.62448i	−1.22580	−	0.143605i
$335$	5.52888	+	9.57630i	0.302075	+	0.523209i
$336$	29.3197	−	19.2394i	1.59952	−	1.04960i
$337$	24.9010			1.35644			0.678222	−	0.734857i	$-0.262751\pi$
$337$	24.9010			1.35644			0.678222	+	0.734857i	$0.262751\pi$
$338$	−13.5114	−	12.4677i	−0.734921	−	0.678153i
$339$		−	5.59811i		−	0.304047i
$340$	5.60481	+	1.33150i	0.303963	+	0.0722107i
$341$	−2.19257	+	1.26588i	−0.118734	+	0.0685514i
$342$	1.34214	−	11.4564i	0.0725746	−	0.619492i
$343$			16.0609i			0.867206i
$344$	12.5071	−	10.4778i	0.674339	−	0.564926i
$345$	−12.1111	−	6.99233i	−0.652038	−	0.376454i
$346$	10.2106	+	23.6880i	0.548923	+	1.27347i
$347$	−18.2812	−	10.5547i	−0.981387	−	0.566604i	−0.0786982	−	0.996898i	$-0.525076\pi$
$347$	−18.2812	−	10.5547i	−0.981387	−	0.566604i	−0.902689	+	0.430295i	$0.858410\pi$
$348$	−21.6919	−	5.15322i	−1.16281	−	0.276242i
$349$	0.206890	+	0.358345i	0.0110746	+	0.0191818i	0.871510	−	0.490378i	$-0.163141\pi$
$349$	0.206890	+	0.358345i	0.0110746	+	0.0191818i	−0.860435	+	0.509560i	$0.829808\pi$
$350$	−2.36220	−	5.48017i	−0.126265	−	0.292928i
$351$	0.661903	−	12.5928i	0.0353298	−	0.672157i
$352$	−11.8506	−	23.6745i	−0.631637	−	1.26186i
$353$	0.692167	−	0.399623i	0.0368403	−	0.0212698i	−0.481467	−	0.876464i	$-0.659896\pi$
$353$	0.692167	−	0.399623i	0.0368403	−	0.0212698i	0.518307	+	0.855195i	$0.326562\pi$
$354$	−24.2558	+	32.5631i	−1.28918	+	1.73071i
$355$	−8.93003	−	5.15576i	−0.473957	−	0.273639i
$356$	−4.64077	−	4.38299i	−0.245960	−	0.232298i
$357$	−12.6264	+	21.8696i	−0.668261	+	1.15746i
$358$	−24.1418	−	2.82825i	−1.27593	−	0.149478i
$359$			21.7606i			1.14848i	0.818687	+	0.574239i	$0.194702\pi$
$359$			21.7606i			1.14848i	−0.818687	+	0.574239i	$0.805298\pi$
$360$	−2.39147	−	2.85465i	−0.126042	−	0.150453i
$361$	−9.68795	−	16.7800i	−0.509892	−	0.883159i
$362$	3.43553	−	4.61217i	0.180568	−	0.242410i
$363$		−	22.6541i		−	1.18903i
$364$	−8.57733	+	29.1950i	−0.449574	+	1.53023i
$365$		−	8.13434i		−	0.425771i
$366$	17.5686	+	13.0866i	0.918326	+	0.684046i
$367$	10.9820	+	19.0214i	0.573256	+	0.992909i	0.996229	+	0.0867661i	$0.0276533\pi$
$367$	10.9820	+	19.0214i	0.573256	+	0.992909i	−0.422973	+	0.906142i	$0.639013\pi$
$368$	−24.0473	−	12.1089i	−1.25355	−	0.631222i
$369$		−	2.07850i		−	0.108202i
$370$	−0.268351	+	2.29063i	−0.0139509	+	0.119084i
$371$	−22.7700	+	39.4389i	−1.18216	+	2.04756i
$372$	−1.54343	+	1.63421i	−0.0800233	+	0.0847298i
$373$	28.5612	+	16.4898i	1.47884	+	0.853811i	0.999714	−	0.0239335i	$-0.00761900\pi$
$373$	28.5612	+	16.4898i	1.47884	+	0.853811i	0.479130	+	0.877744i	$0.340952\pi$
$374$	15.2891	+	11.3886i	0.790580	+	0.588890i
$375$	−1.79930	+	1.03883i	−0.0929154	+	0.0536447i
$376$	11.2819	+	4.11642i	0.581818	+	0.212288i
$377$	17.2387	−	8.78021i	0.887837	−	0.452204i
$378$	−19.1666	+	8.26166i	−0.985825	+	0.424934i
$379$	−16.1032	−	27.8915i	−0.827164	−	1.43269i	−0.900254	−	0.435364i	$-0.856620\pi$
$379$	−16.1032	−	27.8915i	−0.827164	−	1.43269i	0.0730906	−	0.997325i	$-0.476714\pi$
$380$	−12.0542	−	2.86364i	−0.618366	−	0.146901i
$381$	33.9990	+	19.6293i	1.74182	+	1.00564i
$382$	33.6052	−	14.4853i	1.71939	−	0.741133i
$383$	−20.5285	−	11.8521i	−1.04896	−	0.605616i	−0.126600	−	0.991954i	$-0.540407\pi$
$383$	−20.5285	−	11.8521i	−1.04896	−	0.605616i	−0.922357	+	0.386338i	$0.873740\pi$
$384$	−16.0990	−	17.1275i	−0.821550	−	0.874033i
$385$		−	19.7489i		−	1.00650i
$386$	9.86260	+	1.15542i	0.501993	+	0.0588094i
$387$	6.57756	−	3.79756i	0.334356	−	0.193041i
$388$	6.55977	−	27.6127i	0.333022	−	1.40182i
$389$			3.45599i			0.175226i	0.996155	+	0.0876129i	$0.0279238\pi$
$389$			3.45599i			0.175226i	−0.996155	+	0.0876129i	$0.972076\pi$
$390$	10.4428	+	1.78327i	0.528793	+	0.0902993i
$391$	19.3879			0.980490
$392$	30.1042	−	5.28353i	1.52049	−	0.266859i
$393$	15.8413	+	27.4379i	0.799088	+	1.38406i
$394$	−0.382321	+	3.26347i	−0.0192610	+	0.164411i
$395$	1.61033			0.0810247
$396$	−3.52832	−	11.8082i	−0.177305	−	0.593383i
$397$	7.49043	−	12.9738i	0.375934	−	0.651137i	−0.614532	−	0.788892i	$-0.710655\pi$
$397$	7.49043	−	12.9738i	0.375934	−	0.651137i	0.990466	+	0.137755i	$0.0439886\pi$
$398$	1.04296	−	0.449561i	0.0522788	−	0.0225345i
$399$	27.1554	−	47.0346i	1.35947	−	2.35467i
$400$	−3.34428	+	2.19449i	−0.167214	+	0.109725i
$401$	−10.9989	+	6.35022i	−0.549259	+	0.317115i	−0.748823	−	0.662770i	$-0.769381\pi$
$401$	−10.9989	+	6.35022i	−0.549259	+	0.317115i	0.199564	+	0.979885i	$0.436047\pi$
$402$	12.8609	+	29.8366i	0.641442	+	1.48811i
$403$	0.102378	−	1.94777i	0.00509982	−	0.0970253i
$404$	8.36925	+	7.90437i	0.416386	+	0.393257i
$405$	5.60819	+	9.71367i	0.278673	+	0.482676i
$406$	−25.6787	−	19.1276i	−1.27441	−	0.949289i
$407$	−3.81618	+	6.60982i	−0.189161	+	0.327637i
$408$	15.9012	+	5.80188i	0.787227	+	0.287236i
$409$	14.9268	+	8.61798i	0.738082	+	0.426132i	0.821372	−	0.570394i	$-0.193209\pi$
$409$	14.9268	+	8.61798i	0.738082	+	0.426132i	−0.0832895	+	0.996525i	$0.526543\pi$
$410$	−2.21738	−	0.259770i	−0.109509	−	0.0128291i
$411$	−26.9490			−1.32929
$412$	3.74651	+	12.5384i	0.184577	+	0.617721i
$413$	−50.5009	+	29.1567i	−2.48498	+	1.43471i
$414$	−10.0511	−	7.48692i	−0.493985	−	0.367962i
$415$	3.34719			0.164307
$416$	20.2683	+	2.27990i	0.993733	+	0.111781i
$417$	8.12051			0.397663
$418$	−32.8820	−	24.4933i	−1.60831	−	1.19801i
$419$	4.33703	−	2.50399i	0.211878	−	0.122328i	−0.390306	−	0.920685i	$-0.627631\pi$
$419$	4.33703	−	2.50399i	0.211878	−	0.122328i	0.602184	+	0.798357i	$0.294297\pi$
$420$	−5.01998	−	16.8003i	−0.244950	−	0.819771i
$421$	−1.07321			−0.0523052			−0.0261526	−	0.999658i	$-0.508326\pi$
$421$	−1.07321			−0.0523052			−0.0261526	+	0.999658i	$0.508326\pi$
$422$	−15.1199	−	1.77132i	−0.736025	−	0.0862265i
$423$	4.84141	+	2.79519i	0.235397	+	0.135907i
$424$	28.6757	+	10.4629i	1.39261	+	0.508124i
$425$	1.44020	−	2.49450i	0.0698599	−	0.121001i
$426$	−24.2977	−	18.0990i	−1.17723	−	0.876899i
$427$	15.7307	+	27.2464i	0.761264	+	1.31855i
$428$	−11.2068	−	10.5843i	−0.541699	−	0.511609i
$429$	29.4002	+	19.0992i	1.41946	+	0.922116i
$430$	−3.22924	−	7.49168i	−0.155728	−	0.361281i
$431$	28.2850	−	16.3303i	1.36244	−	0.786605i	0.372491	−	0.928036i	$-0.378504\pi$
$431$	28.2850	−	16.3303i	1.36244	−	0.786605i	0.989948	+	0.141431i	$0.0451703\pi$
$432$	7.67513	+	11.6964i	0.369270	+	0.562745i
$433$	−15.1418	+	26.2263i	−0.727666	+	1.26036i	0.230201	+	0.973143i	$0.426062\pi$
$433$	−15.1418	+	26.2263i	−0.727666	+	1.26036i	−0.957867	+	0.287212i	$0.907272\pi$
$434$	−2.96455	+	1.27785i	−0.142303	+	0.0613389i
$435$	−5.57391	+	9.65430i	−0.267249	+	0.462888i
$436$	−1.47845	−	4.94791i	−0.0708050	−	0.236962i
$437$	−41.6973			−1.99465
$438$	2.78098	−	23.7383i	0.132881	−	1.13426i
$439$	−5.00307	−	8.66557i	−0.238784	−	0.413585i	0.721582	−	0.692329i	$-0.243415\pi$
$439$	−5.00307	−	8.66557i	−0.238784	−	0.413585i	−0.960366	+	0.278744i	$0.910082\pi$
$440$	−13.0381	+	2.28830i	−0.621569	+	0.109090i
$441$	14.2277			0.677510
$442$	−13.7741	+	5.09776i	−0.655169	+	0.242476i
$443$		−	37.3244i		−	1.77333i	−0.462408	−	0.886667i	$-0.653015\pi$
$443$		−	37.3244i		−	1.77333i	0.462408	−	0.886667i	$-0.346985\pi$
$444$	−1.56625	+	6.59297i	−0.0743310	+	0.312889i
$445$	−2.76408	+	1.59584i	−0.131030	+	0.0756502i
$446$	−36.3338	−	4.25657i	−1.72046	−	0.201554i
$447$			29.9427i			1.41624i
$448$	−11.4954	−	31.7403i	−0.543109	−	1.49959i
$449$	−28.4869	−	16.4469i	−1.34438	−	0.776179i	−0.356934	−	0.934130i	$-0.616178\pi$
$449$	−28.4869	−	16.4469i	−1.34438	−	0.776179i	−0.987447	+	0.157951i	$0.949511\pi$
$450$	−1.70991	+	0.737048i	−0.0806061	+	0.0347448i
$451$	−6.39844	−	3.69414i	−0.301291	−	0.173950i
$452$	−5.24296	−	1.24554i	−0.246608	−	0.0585852i
$453$	6.65792	+	11.5319i	0.312816	+	0.541814i
$454$	−26.5571	+	11.4473i	−1.24639	+	0.537247i
$455$	12.7586	+	8.28835i	0.598135	+	0.388564i
$456$	−34.1985	−	12.4780i	−1.60149	−	0.584337i
$457$	9.78982	−	5.65215i	0.457948	−	0.264397i	−0.253233	−	0.967405i	$-0.581494\pi$
$457$	9.78982	−	5.65215i	0.457948	−	0.264397i	0.711181	+	0.703009i	$0.248161\pi$
$458$	11.0131	+	8.20348i	0.514608	+	0.383323i
$459$	−8.72438	−	5.03702i	−0.407219	−	0.235108i
$460$	−9.24336	+	9.78700i	−0.430974	+	0.456321i
$461$	−9.91141	+	17.1671i	−0.461620	+	0.799550i	−0.999042	−	0.0437640i	$-0.986065\pi$
$461$	−9.91141	+	17.1671i	−0.461620	+	0.799550i	0.537422	+	0.843314i	$0.319398\pi$
$462$	6.75180	−	57.6330i	0.314122	−	2.68133i
$463$		−	20.3842i		−	0.947334i	−0.880704	−	0.473667i	$-0.842930\pi$
$463$		−	20.3842i		−	0.947334i	0.880704	−	0.473667i	$-0.157070\pi$
$464$	−9.65260	+	19.1693i	−0.448111	+	0.889910i
$465$	0.561963	+	0.973348i	0.0260604	+	0.0451379i
$466$	−13.0289	−	9.70503i	−0.603553	−	0.449577i
$467$			4.30726i			0.199316i	0.995022	+	0.0996582i	$0.0317749\pi$
$467$			4.30726i			0.199316i	−0.995022	+	0.0996582i	$0.968225\pi$
$468$	9.10937	+	2.67628i	0.421081	+	0.123711i
$469$			46.6608i			2.15460i
$470$	3.58703	−	4.81556i	0.165458	−	0.222125i
$471$	−11.5287	−	19.9684i	−0.531216	−	0.920093i
$472$	25.1006	+	29.9621i	1.15535	+	1.37912i
$473$		−	26.9978i		−	1.24136i
$474$	4.69941	+	0.550544i	0.215851	+	0.0252873i
$475$	−3.09741	+	5.36488i	−0.142119	+	0.246158i
$476$	17.6729	+	16.6912i	0.810036	+	0.765041i
$477$	12.3056	+	7.10466i	0.563436	+	0.325300i
$478$	−19.0769	+	25.6106i	−0.872559	+	1.17140i
$479$	−0.320478	+	0.185028i	−0.0146430	+	0.00845416i	−0.507304	−	0.861767i	$-0.669358\pi$
$479$	−0.320478	+	0.185028i	−0.0146430	+	0.00845416i	0.492661	+	0.870222i	$0.336024\pi$
$480$	−10.5098	+	5.26081i	−0.479705	+	0.240122i
$481$	−2.66863	−	5.23946i	−0.121679	−	0.238899i
$482$	7.02993	+	16.3091i	0.320204	+	0.742858i
$483$	−29.5057	−	51.1054i	−1.34256	−	2.32538i
$484$	−21.2169	−	5.04037i	−0.964404	−	0.229108i
$485$	−12.2894	−	7.09529i	−0.558033	−	0.322180i
$486$	7.17177	+	16.6381i	0.325318	+	0.754722i
$487$	−13.0866	−	7.55556i	−0.593011	−	0.342375i	0.173276	−	0.984873i	$-0.444565\pi$
$487$	−13.0866	−	7.55556i	−0.593011	−	0.342375i	−0.766287	+	0.642498i	$0.777898\pi$
$488$	16.1653	−	13.5424i	0.731767	−	0.613035i
$489$			2.45040i			0.110811i
$490$	1.77817	−	15.1784i	0.0803297	−	0.685689i
$491$	18.7732	−	10.8387i	0.847222	−	0.489144i	−0.0124909	−	0.999922i	$-0.503976\pi$
$491$	18.7732	−	10.8387i	0.847222	−	0.489144i	0.859712	+	0.510778i	$0.170643\pi$
$492$	−6.38213	−	1.51616i	−0.287729	−	0.0683540i
$493$		−	15.4550i		−	0.696060i
$494$	29.6238	−	10.9637i	1.33284	−	0.493280i
$495$	−6.16202			−0.276962
$496$	1.18713	+	1.80912i	0.0533038	+	0.0812318i
$497$	−21.7559	−	37.6824i	−0.975886	−	1.69028i
$498$	9.76806	+	1.14434i	0.437717	+	0.0512793i
$499$	−0.654941			−0.0293192			−0.0146596	−	0.999893i	$-0.504666\pi$
$499$	−0.654941			−0.0293192			−0.0146596	+	0.999893i	$0.504666\pi$
$500$	0.572591	+	1.91628i	0.0256071	+	0.0856988i
$501$	−16.5684	+	28.6974i	−0.740224	+	1.28210i
$502$	9.31492	+	21.6101i	0.415745	+	0.964508i
$503$	−4.58330	+	7.93851i	−0.204359	+	0.353961i	−0.949928	−	0.312468i	$-0.898844\pi$
$503$	−4.58330	+	7.93851i	−0.204359	+	0.353961i	0.745569	+	0.666428i	$0.232178\pi$
$504$	−2.71646	−	15.4777i	−0.121001	−	0.689432i
$505$	4.98479	−	2.87797i	0.221820	−	0.128068i
$506$	−40.9117	+	17.6347i	−1.81875	+	0.783959i
$507$	−24.6777	+	10.9782i	−1.09598	+	0.487557i
$508$	25.9486	−	27.4747i	1.15128	−	1.21899i
$509$	−14.9502	−	25.8945i	−0.662656	−	1.14775i	−0.979915	−	0.199415i	$-0.936096\pi$
$509$	−14.9502	−	25.8945i	−0.662656	−	1.14775i	0.317260	−	0.948339i	$-0.397237\pi$
$510$	5.05573	−	6.78728i	0.223872	−	0.300546i
$511$	17.1624	−	29.7261i	0.759218	−	1.31500i
$512$	−19.6228	+	11.2670i	−0.867215	+	0.497934i
$513$	18.7634	+	10.8330i	0.828424	+	0.478291i
$514$	−0.927179	+	7.91435i	−0.0408961	+	0.349087i
$515$	6.54307			0.288322
$516$	−6.86257	−	22.9669i	−0.302108	−	1.01106i
$517$	17.2094	−	9.93585i	0.756868	−	0.436978i
$518$	−5.81359	+	7.80469i	−0.255434	+	0.342918i
$519$	37.8958			1.66344
$520$	3.99359	−	9.38356i	0.175131	−	0.411496i
$521$	−15.0167			−0.657892			−0.328946	−	0.944349i	$-0.606693\pi$
$521$	−15.0167			−0.657892			−0.328946	+	0.944349i	$0.606693\pi$
$522$	−5.96817	+	8.01222i	−0.261220	+	0.350685i
$523$	−30.6671	+	17.7057i	−1.34098	+	0.774214i	−0.986951	−	0.161021i	$-0.948521\pi$
$523$	−30.6671	+	17.7057i	−1.34098	+	0.774214i	−0.354028	+	0.935235i	$0.615188\pi$
$524$	29.2218	−	8.73158i	1.27656	−	0.381441i
$525$	−8.76713			−0.382629
$526$	−0.618612	+	5.28043i	−0.0269728	+	0.230238i
$527$	−1.34942	−	0.779089i	−0.0587818	−	0.0339377i
$528$	−38.8313	+	2.22039i	−1.68992	+	0.0966302i
$529$	−11.1531	+	19.3178i	−0.484918	+	0.839903i
$530$	9.11734	−	12.2399i	0.396032	−	0.531669i
$531$	9.09742	+	15.7572i	0.394794	+	0.683804i
$532$	−38.0088	−	35.8976i	−1.64789	−	1.55636i
$533$	5.07191	−	2.58329i	0.219689	−	0.111895i
$534$	−8.61196	+	3.71213i	−0.372676	+	0.160640i
$535$	−6.67483	+	3.85372i	−0.288578	+	0.166611i
$536$	30.8052	−	5.40656i	1.33058	−	0.233528i
$537$	−17.8549	+	30.9255i	−0.770494	+	1.33454i
$538$	8.11243	+	18.8204i	0.349752	+	0.811407i
$539$	25.2871	−	43.7986i	1.08919	−	1.88654i
$540$	6.70210	−	2.00261i	0.288412	−	0.0861786i
$541$	−8.30501			−0.357060			−0.178530	−	0.983934i	$-0.557134\pi$
$541$	−8.30501			−0.357060			−0.178530	+	0.983934i	$0.557134\pi$
$542$	22.5934	+	2.64686i	0.970471	+	0.113692i
$543$	−4.22452	−	7.31709i	−0.181292	−	0.314006i
$544$	8.97171	−	13.6016i	0.384659	−	0.583162i
$545$	−2.58204			−0.110602
$546$	34.3997	+	28.5497i	1.47217	+	1.22181i
$547$		−	32.6250i		−	1.39494i	−0.716613	−	0.697471i	$-0.754308\pi$
$547$		−	32.6250i		−	1.39494i	0.716613	−	0.697471i	$-0.245692\pi$
$548$	−5.99595	+	25.2393i	−0.256134	+	1.07817i
$549$	8.50138	−	4.90828i	0.362830	−	0.209480i
$550$	−0.770127	+	6.57376i	−0.0328383	+	0.280306i
$551$			33.2389i			1.41603i
$552$	−30.3207	+	25.4011i	−1.29054	+	1.08114i
$553$	5.88480	+	3.39759i	0.250247	+	0.144480i
$554$	−8.81922	−	20.4601i	−0.374693	−	0.869268i
$555$	2.93429	+	1.69411i	0.124554	+	0.0719112i
$556$	1.80676	−	7.60535i	0.0766235	−	0.322539i
$557$	1.73486	+	3.00486i	0.0735082	+	0.127320i	0.900437	−	0.434987i	$-0.143247\pi$
$557$	1.73486	+	3.00486i	0.0735082	+	0.127320i	−0.826928	+	0.562307i	$0.809914\pi$
$558$	0.398713	+	0.924994i	0.0168789	+	0.0391581i
$559$	17.4417	+	11.3306i	0.737706	+	0.479233i
$560$	−16.8514	+	0.963571i	−0.712102	+	0.0407183i
$561$	24.2557	−	14.0041i	1.02408	−	0.591252i
$562$	−4.90207	+	6.58098i	−0.206781	+	0.277602i
$563$	32.2772	+	18.6353i	1.36032	+	0.785383i	0.989667	−	0.143387i	$-0.0457993\pi$
$563$	32.2772	+	18.6353i	1.36032	+	0.785383i	0.370657	+	0.928770i	$0.379133\pi$
$564$	12.1143	−	12.8268i	0.510106	−	0.540107i
$565$	−1.34722	+	2.33345i	−0.0566780	+	0.0981691i
$566$	−6.76225	−	0.792209i	−0.284238	−	0.0332990i
$567$			47.3301i			1.98768i
$568$	−22.3569	+	18.7294i	−0.938073	+	0.785867i
$569$	−8.01421	−	13.8810i	−0.335973	−	0.581923i	0.647698	−	0.761897i	$-0.275732\pi$
$569$	−8.01421	−	13.8810i	−0.335973	−	0.581923i	−0.983671	+	0.179975i	$0.942398\pi$
$570$	−10.8733	+	14.5973i	−0.455432	+	0.611413i
$571$		−	2.29368i		−	0.0959874i	−0.998848	−	0.0479937i	$-0.984717\pi$
$571$		−	2.29368i		−	0.0959874i	0.998848	−	0.0479937i	$-0.0152827\pi$
$572$	24.4289	−	23.2857i	1.02142	−	0.973623i
$573$		−	53.7613i		−	2.24591i
$574$	−7.55510	−	5.62767i	−0.315344	−	0.234895i
$575$	3.36550	+	5.82921i	0.140351	+	0.243095i
$576$	−9.90355	+	3.58679i	−0.412648	+	0.149449i
$577$		−	29.9365i		−	1.24627i	−0.782112	−	0.623137i	$-0.785858\pi$
$577$		−	29.9365i		−	1.24627i	0.782112	−	0.623137i	$-0.214142\pi$
$578$	1.43215	−	12.2247i	0.0595695	−	0.508482i
$579$	7.29422	−	12.6340i	0.303138	−	0.525050i
$580$	7.80168	+	7.36832i	0.323947	+	0.305953i
$581$	12.2320	+	7.06213i	0.507467	+	0.292986i
$582$	−33.4382	−	24.9076i	−1.38606	−	1.03245i
$583$	43.7419	−	25.2544i	1.81161	−	1.04593i
$584$	−21.6136	−	7.88616i	−0.894377	−	0.326332i
$585$	2.58612	−	3.98093i	0.106923	−	0.164591i
$586$	17.7140	−	7.63551i	0.731758	−	0.315420i
$587$	14.6690	+	25.4074i	0.605453	+	1.04867i	0.991980	+	0.126397i	$0.0403412\pi$
$587$	14.6690	+	25.4074i	0.605453	+	1.04867i	−0.386527	+	0.922278i	$0.626325\pi$
$588$	10.3784	−	43.6869i	0.427999	−	1.80162i
$589$	2.90218	+	1.67558i	0.119582	+	0.0690409i
$590$	17.9470	−	7.73596i	0.738868	−	0.318484i
$591$	4.18049	+	2.41361i	0.171963	+	0.0992826i
$592$	5.82623	+	2.93378i	0.239457	+	0.120578i
$593$		−	5.23547i		−	0.214995i	−0.994205	−	0.107497i	$-0.965716\pi$
$593$		−	5.23547i		−	0.214995i	0.994205	−	0.107497i	$-0.0342838\pi$
$594$	22.9914	+	2.69348i	0.943348	+	0.110515i
$595$	10.5261	−	6.07725i	0.431529	−	0.249143i
$596$	28.0431	+	6.66204i	1.14869	+	0.272888i
$597$		−	1.66852i		−	0.0682878i
$598$	5.77728	−	33.8317i	0.236250	−	1.38348i
$599$	−28.6604			−1.17103			−0.585516	−	0.810661i	$-0.699108\pi$
$599$	−28.6604			−1.17103			−0.585516	+	0.810661i	$0.699108\pi$
$600$	1.01584	+	5.78802i	0.0414716	+	0.236295i
$601$	20.1120	+	34.8349i	0.820384	+	1.42095i	0.905397	+	0.424567i	$0.139574\pi$
$601$	20.1120	+	34.8349i	0.820384	+	1.42095i	−0.0850125	+	0.996380i	$0.527093\pi$
$602$	4.00551	−	34.1908i	0.163252	−	1.39351i
$603$	14.5590			0.592889
$604$	12.2816	−	3.66979i	0.499732	−	0.149322i
$605$	−5.45184	+	9.44287i	−0.221649	+	0.383907i
$606$	15.5310	−	6.69453i	0.630902	−	0.271947i
$607$	19.3563	−	33.5261i	0.785647	−	1.36078i	−0.142965	−	0.989728i	$-0.545663\pi$
$607$	19.3563	−	33.5261i	0.785647	−	1.36078i	0.928612	−	0.371053i	$-0.121003\pi$
$608$	−19.2953	+	29.2527i	−0.782529	+	1.18635i
$609$	−40.7386	+	23.5204i	−1.65081	+	0.953095i
$610$	−4.17374	−	9.68286i	−0.168990	−	0.392048i
$611$	−0.803562	+	15.2879i	−0.0325086	+	0.618484i
$612$	5.20796	−	5.51426i	0.210519	−	0.222901i
$613$	0.213542	+	0.369866i	0.00862488	+	0.0149387i	0.870306	−	0.492512i	$-0.163921\pi$
$613$	0.213542	+	0.369866i	0.00862488	+	0.0149387i	−0.861681	+	0.507451i	$0.830588\pi$
$614$	21.5966	+	16.0870i	0.871569	+	0.649218i
$615$	−1.63994	+	2.84046i	−0.0661287	+	0.114538i
$616$	−52.4745	−	19.1464i	−2.11426	−	0.771430i
$617$	8.43751	+	4.87140i	0.339681	+	0.196115i	0.660131	−	0.751150i	$-0.270501\pi$
$617$	8.43751	+	4.87140i	0.339681	+	0.196115i	−0.320450	+	0.947266i	$0.603834\pi$
$618$	19.0945	+	2.23696i	0.768095	+	0.0899836i
$619$	13.2781			0.533693			0.266846	−	0.963739i	$-0.414018\pi$
$619$	13.2781			0.533693			0.266846	+	0.963739i	$0.414018\pi$
$620$	1.03663	−	0.309749i	0.0416321	−	0.0124398i
$621$	20.3874	−	11.7707i	0.818117	−	0.472340i
$622$	27.1798	+	20.2458i	1.08981	+	0.811783i
$623$	−13.4680			−0.539586
$624$	14.8625	−	26.0186i	0.594976	−	1.04158i
$625$	1.00000			0.0400000
$626$	4.07763	+	3.03736i	0.162975	+	0.121397i
$627$	−52.1664	+	30.1183i	−2.08333	+	1.20281i
$628$	−21.2666	+	6.35454i	−0.848631	+	0.253574i
$629$	−4.69735			−0.187296
$630$	−7.80377	−	0.914225i	−0.310910	−	0.0364236i
$631$	2.49100	+	1.43818i	0.0991651	+	0.0572530i	0.548762	−	0.835978i	$-0.315099\pi$
$631$	2.49100	+	1.43818i	0.0991651	+	0.0572530i	−0.449597	+	0.893231i	$0.648433\pi$
$632$	1.56120	−	4.27879i	0.0621014	−	0.170201i
$633$	−11.1824	+	19.3685i	−0.444462	+	0.769830i
$634$	6.81860	+	5.07906i	0.270801	+	0.201715i
$635$	−9.44785	−	16.3642i	−0.374926	−	0.649392i
$636$	30.7916	−	32.6026i	1.22097	−	1.29278i
$637$	17.6831	+	34.7182i	0.700629	+	1.37558i
$638$	14.0575	+	32.6126i	0.556540	+	1.29115i
$639$	−11.7576	+	6.78824i	−0.465123	+	0.268539i
$640$	2.58871	+	11.0136i	0.102328	+	0.435349i
$641$	−5.38877	+	9.33363i	−0.212844	+	0.368656i	−0.952603	−	0.304215i	$-0.901606\pi$
$641$	−5.38877	+	9.33363i	−0.212844	+	0.368656i	0.739760	+	0.672871i	$0.234939\pi$
$642$	−20.7966	+	8.96423i	−0.820775	+	0.353790i
$643$	−23.0476	+	39.9196i	−0.908907	+	1.57427i	−0.0933229	+	0.995636i	$0.529749\pi$
$643$	−23.0476	+	39.9196i	−0.908907	+	1.57427i	−0.815585	+	0.578638i	$0.803584\pi$
$644$	−54.4281	+	16.2633i	−2.14477	+	0.640864i
$645$	−11.9851			−0.471913
$646$	2.93620	−	25.0632i	0.115523	−	0.986099i
$647$	16.5893	+	28.7336i	0.652194	+	1.12963i	0.982589	+	0.185790i	$0.0594845\pi$
$647$	16.5893	+	28.7336i	0.652194	+	1.12963i	−0.330396	+	0.943843i	$0.607182\pi$
$648$	31.2471	−	5.48411i	1.22750	−	0.215436i
$649$	64.6758			2.53875
$650$	−3.92372	−	3.25645i	−0.153901	−	0.127728i
$651$			4.74266i			0.185880i
$652$	2.29495	+	0.545197i	0.0898771	+	0.0213516i
$653$	−5.63062	+	3.25084i	−0.220343	+	0.127215i	−0.606109	−	0.795381i	$-0.707271\pi$
$653$	−5.63062	+	3.25084i	−0.220343	+	0.127215i	0.385766	+	0.922597i	$0.373937\pi$
$654$	−7.53511	−	0.882751i	−0.294646	−	0.0345183i
$655$		−	15.2492i		−	0.595837i
$656$	−2.83996	+	5.63992i	−0.110882	+	0.220202i
$657$	−9.27508	−	5.35497i	−0.361855	−	0.208917i
$658$	23.2686	−	10.0298i	0.907105	−	0.391002i
$659$	26.2456	+	15.1529i	1.02239	+	0.590274i	0.914794	−	0.403921i	$-0.132353\pi$
$659$	26.2456	+	15.1529i	1.02239	+	0.590274i	0.107591	+	0.994195i	$0.465686\pi$
$660$	−4.49490	+	18.9208i	−0.174964	+	0.736491i
$661$	−24.0994	−	41.7415i	−0.937360	−	1.62355i	−0.770371	−	0.637596i	$-0.779929\pi$
$661$	−24.0994	−	41.7415i	−0.937360	−	1.62355i	−0.166989	−	0.985959i	$-0.553404\pi$
$662$	−27.9280	+	12.0382i	−1.08545	+	0.467878i
$663$	−1.13258	+	21.5475i	−0.0439857	+	0.836837i
$664$	3.24507	−	8.89376i	0.125933	−	0.345145i
$665$	−22.6384	+	13.0703i	−0.877878	+	0.506843i
$666$	2.43520	+	1.81395i	0.0943623	+	0.0702890i
$667$	31.2772	+	18.0579i	1.21106	+	0.699204i
$668$	23.1905	+	21.9023i	0.897266	+	0.847426i
$669$	−26.8719	+	46.5435i	−1.03893	+	1.79948i
$670$	1.81958	−	15.5318i	0.0702965	−	0.600046i
$671$		−	34.8942i		−	1.34707i
$672$	−49.5066	−	2.94922i	−1.90976	−	0.113769i
$673$	−13.1217	−	22.7275i	−0.505805	−	0.876080i	−0.999977	−	0.00671639i	$-0.997862\pi$
$673$	−13.1217	−	22.7275i	−0.505805	−	0.876080i	0.494172	−	0.869364i	$-0.335471\pi$
$674$	−28.2415	−	21.0366i	−1.08782	−	0.810301i
$675$		−	3.49745i		−	0.134617i
$676$	4.79108	+	25.5548i	0.184272	+	0.982875i
$677$		−	12.0617i		−	0.463567i	−0.972767	−	0.231784i	$-0.925544\pi$
$677$		−	12.0617i		−	0.463567i	0.972767	−	0.231784i	$-0.0744562\pi$
$678$	−4.72934	+	6.34909i	−0.181629	+	0.243835i
$679$	−29.9402	−	51.8580i	−1.14900	−	1.99013i
$680$	−5.23183	−	6.24512i	−0.200631	−	0.239489i
$681$			42.4858i			1.62806i
$682$	3.55614	+	0.416608i	0.136172	+	0.0159527i
$683$	−20.3899	+	35.3163i	−0.780198	+	1.35134i	0.151629	+	0.988438i	$0.451548\pi$
$683$	−20.3899	+	35.3163i	−0.780198	+	1.35134i	−0.931826	+	0.362904i	$0.881785\pi$
$684$	−11.2007	+	11.8594i	−0.428269	+	0.453457i
$685$	11.2331	+	6.48544i	0.429195	+	0.247796i
$686$	13.5684	−	18.2154i	0.518044	−	0.695469i
$687$	17.4720	−	10.0875i	0.666598	−	0.384860i
$688$	−23.0367	+	1.31725i	−0.878267	+	0.0502197i
$689$	−2.04245	+	38.8581i	−0.0778112	+	1.48038i
$690$	7.82857	+	18.1619i	0.298029	+	0.691411i
$691$	10.2243	+	17.7090i	0.388950	+	0.673681i	0.992309	−	0.123789i	$-0.0395045\pi$
$691$	10.2243	+	17.7090i	0.388950	+	0.673681i	−0.603358	+	0.797470i	$0.706171\pi$
$692$	8.43155	−	35.4917i	0.320520	−	1.34919i
$693$	−22.5185	−	13.0010i	−0.855406	−	0.493869i
$694$	11.8169	+	27.4147i	0.448565	+	1.04065i
$695$	−3.38486	−	1.95425i	−0.128395	−	0.0741290i
$696$	20.2484	+	24.1701i	0.767514	+	0.916165i
$697$		−	4.54713i		−	0.172235i
$698$	0.0680885	−	0.581200i	0.00257719	−	0.0219987i
$699$	−20.6700	+	11.9338i	−0.781812	+	0.451379i
$700$	−1.95062	+	8.21095i	−0.0737267	+	0.310345i
$701$			0.845844i			0.0319471i	0.999872	+	0.0159735i	$0.00508475\pi$
$701$			0.845844i			0.0319471i	−0.999872	+	0.0159735i	$0.994915\pi$
$702$	−11.3893	+	13.7230i	−0.429860	+	0.517941i
$703$	10.1025			0.381024
$704$	−6.56016	+	36.8619i	−0.247246	+	1.38929i
$705$	−4.41082	−	7.63976i	−0.166121	−	0.287730i
$706$	−1.12263	−	0.131518i	−0.0422506	−	0.00494973i
$707$	24.2885			0.913464
$708$	55.0193	−	16.4400i	2.06775	−	0.617852i
$709$	−8.32789	+	14.4243i	−0.312760	+	0.541717i	−0.978959	−	0.204058i	$-0.934587\pi$
$709$	−8.32789	+	14.4243i	−0.312760	+	0.541717i	0.666199	+	0.745774i	$0.267920\pi$
$710$	5.77236	+	13.3916i	0.216633	+	0.502577i
$711$	1.06011	−	1.83616i	0.0397572	−	0.0688615i
$712$	1.56053	+	8.89154i	0.0584835	+	0.333225i
$713$	3.15337	−	1.82060i	0.118095	−	0.0681819i
$714$	32.7959	−	14.1365i	1.22736	−	0.529044i
$715$	−7.65854	−	15.0364i	−0.286413	−	0.562331i
$716$	24.9910	+	23.6029i	0.933959	+	0.882081i
$717$	23.4581	+	40.6306i	0.876057	+	1.51738i
$718$	18.3836	−	24.6797i	0.686068	−	0.921040i
$719$	9.33227	−	16.1640i	0.348035	−	0.602814i	−0.637865	−	0.770148i	$-0.720182\pi$
$719$	9.33227	−	16.1640i	0.348035	−	0.602814i	0.985900	+	0.167334i	$0.0535157\pi$
$720$	0.300651	+	5.25794i	0.0112046	+	0.195952i
$721$	23.9110	+	13.8050i	0.890491	+	0.514125i
$722$	−3.18835	+	27.2155i	−0.118658	+	1.01286i
$723$	26.0911			0.970338
$724$	−7.79282	+	2.32852i	−0.289618	+	0.0865387i
$725$	4.64674	−	2.68280i	0.172576	−	0.0996365i
$726$	−19.1384	+	25.6931i	−0.710292	+	0.953560i
$727$	18.7035			0.693676			0.346838	−	0.937925i	$-0.387255\pi$
$727$	18.7035			0.693676			0.346838	+	0.937925i	$0.387255\pi$
$728$	34.3922	−	25.8653i	1.27466	−	0.958632i
$729$	−7.03158			−0.260429
$730$	−6.87197	+	9.22556i	−0.254343	+	0.341453i
$731$	14.3897	−	8.30791i	0.532223	−	0.307279i
$732$	−8.86976	−	29.6843i	−0.327836	−	1.09716i
$733$	4.81485			0.177840			0.0889202	−	0.996039i	$-0.471658\pi$
$733$	4.81485			0.177840			0.0889202	+	0.996039i	$0.471658\pi$
$734$	3.61423	−	30.8508i	0.133404	−	1.13872i
$735$	−19.4435	−	11.2257i	−0.717183	−	0.414066i
$736$	17.0435	+	34.0488i	0.628232	+	1.25505i
$737$	25.8759	−	44.8184i	0.953152	−	1.65091i
$738$	−1.75594	+	2.35733i	−0.0646369	+	0.0867745i
$739$	−6.93504	−	12.0118i	−0.255110	−	0.441863i	0.709816	−	0.704387i	$-0.248778\pi$
$739$	−6.93504	−	12.0118i	−0.255110	−	0.441863i	−0.964925	+	0.262525i	$0.915445\pi$
$740$	2.23950	−	2.37121i	0.0823257	−	0.0871676i
$741$	2.43582	−	46.3420i	0.0894820	−	1.70241i
$742$	59.1430	−	25.4932i	2.17121	−	0.935885i
$743$	−1.73048	+	0.999093i	−0.0634851	+	0.0366532i	−0.531407	−	0.847117i	$-0.678336\pi$
$743$	−1.73048	+	0.999093i	−0.0634851	+	0.0366532i	0.467921	+	0.883770i	$0.345003\pi$
$744$	3.13108	−	0.549530i	0.114791	−	0.0201467i
$745$	7.20590	−	12.4810i	0.264004	−	0.457268i
$746$	−18.4619	−	42.8307i	−0.675939	−	1.56814i
$747$	2.20351	−	3.81659i	0.0806223	−	0.139642i
$748$	−7.71891	−	25.8328i	−0.282231	−	0.944539i
$749$	−32.5233			−1.18838
$750$	2.91828	+	0.341882i	0.106561	+	0.0124838i
$751$	−8.93720	−	15.4797i	−0.326123	−	0.564862i	0.655616	−	0.755095i	$-0.272409\pi$
$751$	−8.93720	−	15.4797i	−0.326123	−	0.564862i	−0.981739	+	0.190233i	$0.939076\pi$
$752$	−9.31774	−	14.1997i	−0.339783	−	0.517809i
$753$	34.5717			1.25986
$754$	−26.9689	−	4.60534i	−0.982148	−	0.167717i
$755$		−	6.40908i		−	0.233250i
$756$	28.7174	+	6.82221i	1.04444	+	0.248121i
$757$	29.8138	−	17.2130i	1.08360	−	0.625617i	0.151734	−	0.988421i	$-0.451514\pi$
$757$	29.8138	−	17.2130i	1.08360	−	0.625617i	0.931865	+	0.362805i	$0.118181\pi$
$758$	−5.29962	+	45.2372i	−0.192491	+	1.64309i
$759$			65.4501i			2.37569i
$760$	11.2520	+	13.4313i	0.408153	+	0.487204i
$761$	−18.4679	−	10.6624i	−0.669460	−	0.386513i	0.126412	−	0.991978i	$-0.459654\pi$
$761$	−18.4679	−	10.6624i	−0.669460	−	0.386513i	−0.795872	+	0.605465i	$0.792987\pi$
$762$	−21.9769	−	50.9853i	−0.796139	−	1.84700i
$763$	−9.43578	−	5.44775i	−0.341598	−	0.197222i
$764$	−50.3507	−	11.9615i	−1.82162	−	0.432752i
$765$	−1.89621	−	3.28434i	−0.0685577	−	0.118745i
$766$	13.2696	+	30.7848i	0.479450	+	1.11230i
$767$	−27.1435	+	41.7833i	−0.980096	+	1.50871i
$768$	3.78924	+	33.0257i	0.136732	+	1.19171i
$769$	−36.5662	+	21.1115i	−1.31861	+	0.761301i	−0.983505	−	0.180880i	$-0.942105\pi$
$769$	−36.5662	+	21.1115i	−1.31861	+	0.761301i	−0.335106	+	0.942180i	$0.608772\pi$
$770$	−16.6841	+	22.3982i	−0.601253	+	0.807177i
$771$	10.1383	+	5.85333i	0.365120	+	0.210802i
$772$	−10.2096	−	9.64245i	−0.367450	−	0.347039i
$773$	7.02255	−	12.1634i	0.252583	−	0.437487i	−0.711653	−	0.702531i	$-0.752053\pi$
$773$	7.02255	−	12.1634i	0.252583	−	0.437487i	0.964236	+	0.265044i	$0.0853864\pi$
$774$	−10.6682	−	1.24979i	−0.383459	−	0.0449229i
$775$		−	0.540960i		−	0.0194318i
$776$	−30.7672	+	25.7751i	−1.10448	+	0.925274i
$777$	7.14871	+	12.3819i	0.256459	+	0.444199i
$778$	2.91966	−	3.91961i	0.104675	−	0.140525i
$779$			9.77945i			0.350385i
$780$	−10.3372	−	10.8447i	−0.370131	−	0.388302i
$781$			48.2593i			1.72685i
$782$	−21.9888	−	16.3791i	−0.786319	−	0.585716i
$783$	−9.38294	−	16.2517i	−0.335319	−	0.580789i
$784$	−38.6063	−	19.4401i	−1.37880	−	0.694288i
$785$			11.0979i			0.396100i
$786$	5.21344	−	44.5016i	0.185957	−	1.58732i
$787$	15.4322	−	26.7293i	0.550098	−	0.952798i	−0.448169	−	0.893949i	$-0.647924\pi$
$787$	15.4322	−	26.7293i	0.550098	−	0.952798i	0.998267	−	0.0588488i	$-0.0187430\pi$
$788$	3.19062	−	3.37827i	0.113661	−	0.120346i
$789$	6.76422	+	3.90532i	0.240813	+	0.139033i
$790$	−1.82636	−	1.36043i	−0.0649790	−	0.0484018i
$791$	−9.84655	+	5.68491i	−0.350103	+	0.202132i
$792$	−5.97402	+	16.3730i	−0.212278	+	0.581789i
$793$	22.5431	+	14.6446i	0.800530	+	0.520045i
$794$	−19.4557	+	8.38625i	−0.690456	+	0.297617i
$795$	−11.2112	−	19.4183i	−0.397620	−	0.688697i
$796$	−1.56267	−	0.371233i	−0.0553872	−	0.0131580i
$797$	−2.69913	−	1.55834i	−0.0956081	−	0.0551994i	0.451434	−	0.892305i	$-0.350913\pi$
$797$	−2.69913	−	1.55834i	−0.0956081	−	0.0551994i	−0.547042	+	0.837105i	$0.684246\pi$
$798$	−70.5336	+	30.4031i	−2.49686	+	1.07626i
$799$	10.5915	+	6.11503i	0.374702	+	0.216334i
$800$	5.64684	+	0.336395i	0.199646	+	0.0118934i
$801$			4.20228i			0.148480i
$802$	17.8391	+	2.08988i	0.629921	+	0.0737964i
$803$	−32.9694	+	19.0349i	−1.16347	+	0.671727i
$804$	10.6201	−	44.7042i	0.374542	−	1.57659i
$805$			28.4030i			1.00107i
$806$	−1.76161	+	2.12257i	−0.0620500	+	0.0747644i
$807$	30.1088			1.05988
$808$	−2.81430	−	16.0352i	−0.0990067	−	0.564115i
$809$	4.88111	+	8.45433i	0.171611	+	0.297238i	0.938983	−	0.343963i	$-0.111770\pi$
$809$	4.88111	+	8.45433i	0.171611	+	0.297238i	−0.767372	+	0.641202i	$0.778436\pi$
$810$	1.84568	−	15.7546i	0.0648506	−	0.553560i
$811$	−9.76800			−0.343001			−0.171501	−	0.985184i	$-0.554862\pi$
$811$	−9.76800			−0.343001			−0.171501	+	0.985184i	$0.554862\pi$
$812$	12.9642	+	43.3872i	0.454956	+	1.52259i
$813$	16.7097	−	28.9421i	0.586036	−	1.01504i
$814$	9.91216	−	4.27258i	0.347421	−	0.149754i
$815$	0.589705	−	1.02140i	0.0206565	−	0.0357780i
$816$	−13.1329	−	20.0137i	−0.459742	−	0.700620i
$817$	−30.9478	+	17.8677i	−1.08273	+	0.625112i
$818$	−9.64865	−	22.3844i	−0.337357	−	0.782652i
$819$	17.8499	−	9.09153i	0.623726	−	0.317684i
$820$	2.29538	+	2.16788i	0.0801583	+	0.0757057i
$821$	−19.3717	−	33.5527i	−0.676076	−	1.17100i	−0.976153	−	0.217083i	$-0.930346\pi$
$821$	−19.3717	−	33.5527i	−0.676076	−	1.17100i	0.300077	−	0.953915i	$-0.402988\pi$
$822$	30.5642	+	22.7668i	1.06605	+	0.794082i
$823$	−12.3185	+	21.3362i	−0.429395	+	0.743734i	−0.996820	−	0.0796917i	$-0.974606\pi$
$823$	−12.3185	+	21.3362i	−0.429395	+	0.743734i	0.567425	+	0.823425i	$0.307940\pi$
$824$	6.34344	−	17.3855i	0.220984	−	0.605652i
$825$	8.42096	+	4.86185i	0.293180	+	0.169268i
$826$	81.9074	+	9.59559i	2.84992	+	0.333873i
$827$	−28.5420			−0.992501			−0.496251	−	0.868179i	$-0.665290\pi$
$827$	−28.5420			−0.992501			−0.496251	+	0.868179i	$0.665290\pi$
$828$	5.07445	+	16.9826i	0.176349	+	0.590185i
$829$	−3.02183	+	1.74465i	−0.104952	+	0.0605943i	−0.551557	−	0.834137i	$-0.685966\pi$
$829$	−3.02183	+	1.74465i	−0.104952	+	0.0605943i	0.446605	+	0.894731i	$0.352633\pi$
$830$	−3.79622	−	2.82774i	−0.131769	−	0.0981523i
$831$	−32.7319			−1.13546
$832$	−21.0612	−	19.7086i	−0.730164	−	0.683272i
$833$	31.1260			1.07845
$834$	−9.20987	−	6.86029i	−0.318912	−	0.237552i
$835$	13.8124	−	7.97461i	0.477999	−	0.275973i
$836$	16.6009	+	55.5581i	0.574156	+	1.92152i
$837$	−1.89198			−0.0653963
$838$	−7.03424	−	0.824073i	−0.242994	−	0.0284671i
$839$	28.9185	+	16.6961i	0.998379	+	0.576414i	0.907768	−	0.419472i	$-0.137785\pi$
$839$	28.9185	+	16.6961i	0.998379	+	0.576414i	0.0906106	+	0.995886i	$0.471118\pi$
$840$	−8.49965	+	23.2950i	−0.293266	+	0.803753i
$841$	−0.105217	+	0.182242i	−0.00362818	+	0.00628419i
$842$	1.21718	+	0.906661i	0.0419469	+	0.0312456i
$843$	6.02786	+	10.4406i	0.207610	+	0.359592i
$844$	15.6518	+	14.7824i	0.538757	+	0.508830i
$845$	12.9284	+	1.36284i	0.444749	+	0.0468832i
$846$	−3.12948	−	7.26023i	−0.107594	−	0.249612i
$847$	−39.8464	+	23.0053i	−1.36914	+	0.790472i
$848$	−23.6834	−	36.0920i	−0.813290	−	1.23940i
$849$	−5.00125	+	8.66242i	−0.171642	+	0.297293i
$850$	−3.74078	+	1.61244i	−0.128308	+	0.0553062i
$851$	5.48845	−	9.50627i	0.188142	−	0.325871i
$852$	12.2670	+	41.0539i	0.420262	+	1.40648i
$853$	−11.7700			−0.402999			−0.201499	−	0.979489i	$-0.564581\pi$
$853$	−11.7700			−0.402999			−0.201499	+	0.979489i	$0.564581\pi$
$854$	5.17706	−	44.1910i	0.177155	−	1.51219i
$855$	4.07816	+	7.06358i	0.139470	+	0.241569i
$856$	3.76846	+	21.4717i	0.128803	+	0.733888i
$857$	−38.7207			−1.32267			−0.661337	−	0.750089i	$-0.730011\pi$
$857$	−38.7207			−1.32267			−0.661337	+	0.750089i	$0.730011\pi$
$858$	−17.2091	−	46.4989i	−0.587509	−	1.58745i
$859$			5.85717i			0.199844i	0.994995	+	0.0999221i	$0.0318593\pi$
$859$			5.85717i			0.199844i	−0.994995	+	0.0999221i	$0.968141\pi$
$860$	−2.66660	+	11.2248i	−0.0909304	+	0.382762i
$861$	−11.9860	+	6.92010i	−0.408481	+	0.235836i
$862$	−45.8754	−	5.37439i	−1.56252	−	0.183052i
$863$		−	2.78447i		−	0.0947846i	−0.998876	−	0.0473923i	$-0.984909\pi$
$863$		−	2.78447i		−	0.0947846i	0.998876	−	0.0473923i	$-0.0150911\pi$
$864$	1.17652	−	19.7495i	0.0400262	−	0.671893i
$865$	−15.7961	−	9.11987i	−0.537083	−	0.310085i
$866$	39.3293	−	16.9526i	1.33646	−	0.576074i
$867$	−15.6598	−	9.04122i	−0.531836	−	0.307056i
$868$	4.44179	+	1.05521i	0.150764	+	0.0358161i
$869$	−3.76829	−	6.52688i	−0.127831	−	0.221409i
$870$	14.4777	−	6.24052i	0.490840	−	0.211574i
$871$	18.0948	+	35.5266i	0.613120	+	1.20377i
$872$	−2.50326	+	6.86068i	−0.0847710	+	0.232332i
$873$	−16.1806	+	9.34189i	−0.547631	+	0.316175i
$874$	47.2910	+	35.2263i	1.59964	+	1.19155i
$875$	3.65440	+	2.10987i	0.123541	+	0.0713265i
$876$	−23.2084	+	24.5734i	−0.784140	+	0.830258i
$877$	10.9554	−	18.9752i	0.369936	−	0.640748i	−0.619619	−	0.784903i	$-0.712713\pi$
$877$	10.9554	−	18.9752i	0.369936	−	0.640748i	0.989555	+	0.144155i	$0.0460462\pi$
$878$	−1.64653	+	14.0547i	−0.0555678	+	0.474323i
$879$		−	28.3387i		−	0.955840i
$880$	16.7204	+	8.41949i	0.563644	+	0.283821i
$881$	21.1391	+	36.6141i	0.712196	+	1.23356i	0.964031	+	0.265789i	$0.0856324\pi$
$881$	21.1391	+	36.6141i	0.712196	+	1.23356i	−0.251836	+	0.967770i	$0.581034\pi$
$882$	−16.1364	−	12.0197i	−0.543340	−	0.404725i
$883$			1.53603i			0.0516914i	0.999666	+	0.0258457i	$0.00822786\pi$
$883$			1.53603i			0.0516914i	−0.999666	+	0.0258457i	$0.991772\pi$
$884$	19.9286	+	5.85490i	0.670271	+	0.196922i
$885$		−	28.7115i		−	0.965126i
$886$	−31.5320	+	42.3314i	−1.05934	+	1.42215i
$887$	−14.2355	−	24.6565i	−0.477980	−	0.827885i	0.521701	−	0.853128i	$-0.325297\pi$
$887$	−14.2355	−	24.6565i	−0.477980	−	0.827885i	−0.999681	+	0.0252427i	$0.991964\pi$
$888$	7.34617	−	6.15423i	0.246521	−	0.206522i
$889$		−	79.7348i		−	2.67422i
$890$	4.48306	+	0.525199i	0.150273	+	0.0176047i
$891$	26.2471	−	45.4613i	0.879311	−	1.52301i
$892$	37.6120	+	35.5228i	1.25934	+	1.18939i
$893$	−22.7791	−	13.1515i	−0.762273	−	0.440099i
$894$	25.2959	−	33.9595i	0.846021	−	1.13578i
$895$	14.8849	−	8.59378i	0.497546	−	0.287258i
$896$	−13.7770	+	45.7097i	−0.460257	+	1.52706i
$897$	−42.2835	−	27.4685i	−1.41181	−	0.917146i
$898$	18.4139	+	42.7193i	0.614480	+	1.42556i
$899$	−1.45128	−	2.51370i	−0.0484030	−	0.0838365i
$900$	2.56196	+	0.608630i	0.0853988	+	0.0202877i
$901$	26.9210	+	15.5429i	0.896870	+	0.517808i
$902$	4.13594	+	9.59518i	0.137712	+	0.319485i
$903$	−43.7983	−	25.2870i	−1.45752	−	0.841498i
$904$	4.89406	+	5.84194i	0.162774	+	0.194300i
$905$			4.06663i			0.135179i
$906$	2.19115	−	18.7035i	0.0727961	−	0.621383i
$907$	39.0468	−	22.5437i	1.29653	−	0.748552i	0.316726	−	0.948517i	$-0.397416\pi$
$907$	39.0468	−	22.5437i	1.29653	−	0.748552i	0.979803	+	0.199965i	$0.0640830\pi$
$908$	39.7905	+	9.45278i	1.32049	+	0.313702i
$909$		−	7.57846i		−	0.251362i
$910$	−7.46814	−	20.1789i	−0.247566	−	0.668923i
$911$	0.112762			0.00373596			0.00186798	−	0.999998i	$-0.499405\pi$
$911$	0.112762			0.00373596			0.00186798	+	0.999998i	$0.499405\pi$
$912$	28.2447	+	43.0432i	0.935274	+	1.42530i
$913$	−7.83266	−	13.5666i	−0.259223	−	0.448988i
$914$	−15.8781	−	1.86015i	−0.525201	−	0.0615282i
$915$	−15.4906			−0.512102
$916$	−5.56012	−	18.6079i	−0.183711	−	0.614824i
$917$	32.1738	−	55.7267i	1.06247	−	1.84026i
$918$	5.63942	+	13.0832i	0.186129	+	0.431809i
$919$	−7.83986	+	13.5790i	−0.258613	+	0.447931i	−0.965871	−	0.259025i	$-0.916599\pi$
$919$	−7.83986	+	13.5790i	−0.258613	+	0.447931i	0.707258	+	0.706956i	$0.249932\pi$
$920$	18.7515	−	3.29104i	0.618219	−	0.108502i
$921$	34.2625	−	19.7815i	1.12899	−	0.651821i
$922$	25.7439	−	11.0968i	0.847831	−	0.365452i
$923$	−31.1776	−	20.2538i	−1.02622	−	0.666661i
$924$	−56.3465	+	59.6604i	−1.85366	+	1.96268i
$925$	−0.815399	−	1.41231i	−0.0268102	−	0.0464366i
$926$	−17.2208	+	23.1187i	−0.565910	+	0.759729i
$927$	4.30741	−	7.46065i	0.141474	−	0.245040i
$928$	27.1419	−	13.5862i	0.890976	−	0.445988i
$929$	−10.9875	−	6.34364i	−0.360488	−	0.208128i	0.308807	−	0.951125i	$-0.400070\pi$
$929$	−10.9875	−	6.34364i	−0.360488	−	0.208128i	−0.669295	+	0.742997i	$0.733404\pi$
$930$	0.184944	−	1.57867i	0.00606456	−	0.0517668i
$931$	−66.9422			−2.19394
$932$	6.57783	+	22.0139i	0.215464	+	0.721090i
$933$	43.1200	−	24.8954i	1.41169	−	0.815037i
$934$	3.63882	−	4.88508i	0.119066	−	0.159845i
$935$	−13.4807			−0.440865
$936$	−8.07044	−	10.7310i	−0.263791	−	0.350754i
$937$	−53.4048			−1.74466			−0.872330	−	0.488918i	$-0.837392\pi$
$937$	−53.4048			−1.74466			−0.872330	+	0.488918i	$0.837392\pi$
$938$	39.4195	−	52.9203i	1.28709	−	1.72791i
$939$	6.46905	−	3.73491i	0.211109	−	0.121884i
$940$	−8.13647	+	2.43120i	−0.265382	+	0.0792971i
$941$	−12.0724			−0.393550			−0.196775	−	0.980449i	$-0.563047\pi$
$941$	−12.0724			−0.393550			−0.196775	+	0.980449i	$0.563047\pi$
$942$	−3.79416	+	32.3867i	−0.123620	+	1.05522i
$943$	9.20226	+	5.31293i	0.299667	+	0.173013i
$944$	−3.15560	−	55.1867i	−0.102706	−	1.79617i
$945$	7.37915	−	12.7811i	0.240044	−	0.415768i
$946$	−22.8080	+	30.6195i	−0.741552	+	0.995527i
$947$	2.15077	+	3.72525i	0.0698907	+	0.121054i	0.898853	−	0.438250i	$-0.144402\pi$
$947$	2.15077	+	3.72525i	0.0698907	+	0.121054i	−0.828962	+	0.559304i	$0.811068\pi$
$948$	−4.86473	−	4.59451i	−0.157999	−	0.149223i
$949$	1.53945	−	29.2883i	0.0499726	−	0.950740i
$950$	8.04524	−	3.46785i	0.261022	−	0.112512i
$951$	10.8175	−	6.24550i	0.350782	−	0.202524i
$952$	−5.94280	−	33.8606i	−0.192607	−	1.09743i
$953$	−10.4800	+	18.1519i	−0.339480	+	0.587997i	−0.984335	−	0.176308i	$-0.943585\pi$
$953$	−10.4800	+	18.1519i	−0.339480	+	0.587997i	0.644855	+	0.764305i	$0.276918\pi$
$954$	−7.95434	−	18.4537i	−0.257531	−	0.597460i
$955$	−12.9380	+	22.4093i	−0.418664	+	0.725147i
$956$	43.2722	−	12.9299i	1.39952	−	0.418182i
$957$	52.1734			1.68652
$958$	0.519784	+	0.0608936i	0.0167935	+	0.00196738i
$959$	27.3668	+	47.4007i	0.883721	+	1.53065i
$960$	16.3641	+	2.91225i	0.528149	+	0.0939925i
$961$	30.7074			0.990560
$962$	−1.39973	+	8.19682i	−0.0451291	+	0.264276i
$963$			10.1479i			0.327010i
$964$	5.80508	−	24.4359i	0.186969	−	0.787027i
$965$	−6.08089	+	3.51080i	−0.195751	+	0.113017i
$966$	−9.71047	+	82.8880i	−0.312429	+	2.66688i
$967$		−	37.5679i		−	1.20810i	−0.796945	−	0.604051i	$-0.793552\pi$
$967$		−	37.5679i		−	1.20810i	0.796945	−	0.604051i	$-0.206448\pi$
$968$	19.8050	+	23.6408i	0.636556	+	0.759843i
$969$	−32.1059	−	18.5364i	−1.03139	−	0.595474i
$970$	7.94385	+	18.4293i	0.255062	+	0.591730i
$971$	44.8001	+	25.8654i	1.43770	+	0.830059i	0.997690	−	0.0679322i	$-0.0216402\pi$
$971$	44.8001	+	25.8654i	1.43770	+	0.830059i	0.440014	+	0.897991i	$0.354973\pi$
$972$	5.92221	−	24.9289i	0.189955	−	0.799596i
$973$	−8.24642	−	14.2832i	−0.264368	−	0.457899i
$974$	8.45917	+	19.6248i	0.271049	+	0.628821i
$975$	−6.67512	+	3.39985i	−0.213775	+	0.108882i
$976$	−29.7746	+	1.70252i	−0.953061	+	0.0544964i
$977$	48.0706	−	27.7536i	1.53791	−	0.887915i	0.538953	−	0.842336i	$-0.318820\pi$
$977$	48.0706	−	27.7536i	1.53791	−	0.887915i	0.998961	−	0.0455794i	$-0.0145134\pi$
$978$	2.07012	−	2.77912i	0.0661953	−	0.0888666i
$979$	12.9363	+	7.46876i	0.413445	+	0.238703i
$980$	−14.8396	+	15.7123i	−0.474033	+	0.501912i
$981$	−1.69980	+	2.94413i	−0.0542703	+	0.0939990i
$982$	−30.4482	−	3.56706i	−0.971642	−	0.113830i
$983$		−	27.4922i		−	0.876866i	−0.898764	−	0.438433i	$-0.855534\pi$
$983$		−	27.4922i		−	0.876866i	0.898764	−	0.438433i	$-0.144466\pi$
$984$	5.95742	+	7.11125i	0.189916	+	0.226698i
$985$	−1.16170	−	2.01213i	−0.0370149	−	0.0641116i
$986$	−13.0566	+	17.5283i	−0.415806	+	0.558216i
$987$		−	37.2249i		−	1.18488i
$988$	−42.8601	−	12.5920i	−1.36356	−	0.400606i
$989$			38.8283i			1.23467i
$990$	6.98866	+	5.20574i	0.222114	+	0.165449i
$991$	−28.2271	−	48.8907i	−0.896662	−	1.55306i	−0.831734	−	0.555174i	$-0.812652\pi$
$991$	−28.2271	−	48.8907i	−0.896662	−	1.55306i	−0.0649278	−	0.997890i	$-0.520682\pi$
$992$	0.181976	−	3.05471i	0.00577775	−	0.0969873i
$993$			44.6790i			1.41784i
$994$	−7.15997	+	61.1171i	−0.227100	+	1.93852i
$995$	−0.401539	+	0.695486i	−0.0127296	+	0.0220484i
$996$	−10.1117	−	9.55001i	−0.320401	−	0.302604i
$997$	−0.633066	−	0.365501i	−0.0200494	−	0.0115755i	0.489942	−	0.871755i	$-0.337018\pi$
$997$	−0.633066	−	0.365501i	−0.0200494	−	0.0115755i	−0.509991	+	0.860180i	$0.670351\pi$
$998$	0.742801	+	0.553301i	0.0235130	+	0.0175144i
$999$	−4.93949	+	2.85182i	−0.156279	+	0.0902275i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	520.2.ca.b.101.7	yes	56
8.5	even	2		520.2.ca.a.101.16	✓	56
13.4	even	6		520.2.ca.a.381.16	yes	56
104.69	even	6	inner	520.2.ca.b.381.7	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.ca.a.101.16	✓	56	8.5	even	2
520.2.ca.a.381.16	yes	56	13.4	even	6
520.2.ca.b.101.7	yes	56	1.1	even	1	trivial
520.2.ca.b.381.7	yes	56	104.69	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.ca (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13415 - 0.844810i) q^{2} +(-1.79930 + 1.03883i) q^{3} +(0.572591 + 1.91628i) q^{4} +1.00000 q^{5} +(2.91828 + 0.341882i) q^{6} +(3.65440 + 2.10987i) q^{7} +(0.969491 - 2.65708i) q^{8} +(0.658316 - 1.14024i) q^{9} +(-1.13415 - 0.844810i) q^{10} +(-2.34007 - 4.05312i) q^{11} +(-3.02095 - 2.85314i) q^{12} +(3.60058 + 0.189253i) q^{13} +(-2.36220 - 5.48017i) q^{14} +(-1.79930 + 1.03883i) q^{15} +(-3.34428 + 2.19449i) q^{16} +(1.44020 - 2.49450i) q^{17} +(-1.70991 + 0.737048i) q^{18} +(-3.09741 + 5.36488i) q^{19} +(0.572591 + 1.91628i) q^{20} -8.76713 q^{21} +(-0.770127 + 6.57376i) q^{22} +(3.36550 + 5.82921i) q^{23} +(1.01584 + 5.78802i) q^{24} +1.00000 q^{25} +(-3.92372 - 3.25645i) q^{26} -3.49745i q^{27} +(-1.95062 + 8.21095i) q^{28} +(4.64674 - 2.68280i) q^{29} +(2.91828 + 0.341882i) q^{30} -0.540960i q^{31} +(5.64684 + 0.336395i) q^{32} +(8.42096 + 4.86185i) q^{33} +(-3.74078 + 1.61244i) q^{34} +(3.65440 + 2.10987i) q^{35} +(2.56196 + 0.608630i) q^{36} +(-0.815399 - 1.41231i) q^{37} +(8.04524 - 3.46785i) q^{38} +(-6.67512 + 3.39985i) q^{39} +(0.969491 - 2.65708i) q^{40} +(1.36715 - 0.789323i) q^{41} +(9.94324 + 7.40656i) q^{42} +(4.99574 + 2.88429i) q^{43} +(6.42702 - 6.80501i) q^{44} +(0.658316 - 1.14024i) q^{45} +(1.10760 - 9.45440i) q^{46} +4.24596i q^{47} +(3.73766 - 7.42267i) q^{48} +(5.40307 + 9.35839i) q^{49} +(-1.13415 - 0.844810i) q^{50} +5.98446i q^{51} +(1.69900 + 7.00810i) q^{52} +10.7922i q^{53} +(-2.95468 + 3.96663i) q^{54} +(-2.34007 - 4.05312i) q^{55} +(9.14899 - 7.66453i) q^{56} -12.8707i q^{57} +(-7.53655 - 0.882920i) q^{58} +(-6.90961 + 11.9678i) q^{59} +(-3.02095 - 2.85314i) q^{60} +(6.45691 + 3.72790i) q^{61} +(-0.457008 + 0.613529i) q^{62} +(4.81150 - 2.77792i) q^{63} +(-6.12018 - 5.15203i) q^{64} +(3.60058 + 0.189253i) q^{65} +(-5.44330 - 12.6282i) q^{66} +(5.52888 + 9.57630i) q^{67} +(5.60481 + 1.33150i) q^{68} +(-12.1111 - 6.99233i) q^{69} +(-2.36220 - 5.48017i) q^{70} +(-8.93003 - 5.15576i) q^{71} +(-2.39147 - 2.85465i) q^{72} -8.13434i q^{73} +(-0.268351 + 2.29063i) q^{74} +(-1.79930 + 1.03883i) q^{75} +(-12.0542 - 2.86364i) q^{76} -19.7489i q^{77} +(10.4428 + 1.78327i) q^{78} +1.61033 q^{79} +(-3.34428 + 2.19449i) q^{80} +(5.60819 + 9.71367i) q^{81} +(-2.21738 - 0.259770i) q^{82} +3.34719 q^{83} +(-5.01998 - 16.8003i) q^{84} +(1.44020 - 2.49450i) q^{85} +(-3.22924 - 7.49168i) q^{86} +(-5.57391 + 9.65430i) q^{87} +(-13.0381 + 2.28830i) q^{88} +(-2.76408 + 1.59584i) q^{89} +(-1.70991 + 0.737048i) q^{90} +(12.7586 + 8.28835i) q^{91} +(-9.24336 + 9.78700i) q^{92} +(0.561963 + 0.973348i) q^{93} +(3.58703 - 4.81556i) q^{94} +(-3.09741 + 5.36488i) q^{95} +(-10.5098 + 5.26081i) q^{96} +(-12.2894 - 7.09529i) q^{97} +(1.77817 - 15.1784i) q^{98} -6.16202 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9} - 8 q^{11} + 6 q^{12} - 4 q^{14} + 14 q^{16} + 18 q^{18} - 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 22 q^{24} + 56 q^{25} - 37 q^{26} - 12 q^{28} - 13 q^{30}+ \cdots - 48 q^{99}+O(q^{100}) \) 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9 - 8 * q^11 + 6 * q^12 - 4 * q^14 + 14 * q^16 + 18 * q^18 - 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 22 * q^24 + 56 * q^25 - 37 * q^26 - 12 * q^28 - 13 * q^30 - 30 * q^32 - 16 * q^34 + 15 * q^36 + 4 * q^37 - 24 * q^39 - 61 * q^42 + 24 * q^44 + 28 * q^45 - 19 * q^46 - 51 * q^48 + 20 * q^49 - 64 * q^52 - 5 * q^54 - 8 * q^55 - 23 * q^56 - q^58 - 16 * q^59 + 6 * q^60 + 10 * q^62 - 30 * q^64 + 14 * q^66 - 36 * q^67 - 51 * q^68 - 4 * q^70 - 81 * q^72 + 70 * q^74 - 60 * q^76 + 143 * q^78 + 14 * q^80 - 28 * q^81 + 21 * q^82 + 40 * q^83 + 31 * q^84 - 28 * q^86 - 36 * q^87 - 19 * q^88 + 18 * q^90 + 16 * q^91 - 18 * q^92 + 43 * q^94 - 16 * q^95 - 48 * q^96 + 24 * q^97 + 56 * q^98 - 48 * q^99

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