LMFDB - Embedded newform 672.2.bs.a.155.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(155,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1, 4, 0]))

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

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

chi := DirichletCharacter("672.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bs (of order $8$, degree $4$, 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			155.17
Character	$\chi$	$=$	672.155
Dual form			672.2.bs.a.659.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.651302 - 1.25531i) q^{2} +(-0.203847 + 1.72001i) q^{3} +(-1.15161 + 1.63517i) q^{4} +(-0.577425 + 1.39403i) q^{5} +(2.29192 - 0.864357i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.80270 + 0.380642i) q^{8} +(-2.91689 - 0.701238i) q^{9} +O(q^{10})$	\(q+(-0.651302 - 1.25531i) q^{2} +(-0.203847 + 1.72001i) q^{3} +(-1.15161 + 1.63517i) q^{4} +(-0.577425 + 1.39403i) q^{5} +(2.29192 - 0.864357i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.80270 + 0.380642i) q^{8} +(-2.91689 - 0.701238i) q^{9} +(2.12602 - 0.183084i) q^{10} +(-1.24272 + 3.00020i) q^{11} +(-2.57777 - 2.31411i) q^{12} +(-4.25613 + 1.76295i) q^{13} +(1.34818 + 0.427099i) q^{14} +(-2.28004 - 1.27735i) q^{15} +(-1.34758 - 3.76617i) q^{16} +2.41041 q^{17} +(1.01951 + 4.11833i) q^{18} +(-2.94021 - 7.09830i) q^{19} +(-1.61451 - 2.54957i) q^{20} +(-1.07209 - 1.36037i) q^{21} +(4.57557 - 0.394030i) q^{22} +(4.69526 - 4.69526i) q^{23} +(-1.22603 + 4.74308i) q^{24} +(1.92564 + 1.92564i) q^{25} +(4.98507 + 4.19455i) q^{26} +(1.80074 - 4.87415i) q^{27} +(-0.341929 - 1.97055i) q^{28} +(0.656417 - 0.271897i) q^{29} +(-0.118474 + 3.69410i) q^{30} -3.19582i q^{31} +(-3.85004 + 4.14454i) q^{32} +(-4.90706 - 2.74908i) q^{33} +(-1.56991 - 3.02582i) q^{34} +(-0.577425 - 1.39403i) q^{35} +(4.50577 - 3.96207i) q^{36} +(-11.1041 - 4.59946i) q^{37} +(-6.99561 + 8.31402i) q^{38} +(-2.16469 - 7.67997i) q^{39} +(-2.14897 + 3.68724i) q^{40} +(3.84257 + 3.84257i) q^{41} +(-1.00944 + 2.23182i) q^{42} +(-7.68932 - 3.18502i) q^{43} +(-3.47471 - 5.48713i) q^{44} +(2.66183 - 3.66132i) q^{45} +(-8.95205 - 2.83598i) q^{46} +12.6172i q^{47} +(6.75256 - 1.55013i) q^{48} -1.00000i q^{49} +(1.16311 - 3.67145i) q^{50} +(-0.491354 + 4.14594i) q^{51} +(2.01869 - 8.98973i) q^{52} +(-5.89794 - 2.44301i) q^{53} +(-7.29140 + 0.914058i) q^{54} +(-3.46478 - 3.46478i) q^{55} +(-2.25096 + 1.71265i) q^{56} +(12.8085 - 3.61024i) q^{57} +(-0.768840 - 0.646921i) q^{58} +(-8.68463 - 3.59729i) q^{59} +(4.71440 - 2.25725i) q^{60} +(4.25913 + 10.2824i) q^{61} +(-4.01175 + 2.08144i) q^{62} +(2.55840 - 1.56671i) q^{63} +(7.71022 + 2.13365i) q^{64} -6.95113i q^{65} +(-0.254977 + 7.95036i) q^{66} +(3.17732 - 1.31609i) q^{67} +(-2.77586 + 3.94144i) q^{68} +(7.11880 + 9.03303i) q^{69} +(-1.37386 + 1.63278i) q^{70} +(-7.70510 - 7.70510i) q^{71} +(-7.90825 - 3.07565i) q^{72} +(-6.27972 + 6.27972i) q^{73} +(1.45835 + 16.9347i) q^{74} +(-3.70466 + 2.91959i) q^{75} +(14.9929 + 3.36674i) q^{76} +(-1.24272 - 3.00020i) q^{77} +(-8.23088 + 7.71934i) q^{78} -8.05290 q^{79} +(6.02827 + 0.296120i) q^{80} +(8.01653 + 4.09087i) q^{81} +(2.32095 - 7.32630i) q^{82} +(6.21303 - 2.57352i) q^{83} +(3.45908 - 0.186431i) q^{84} +(-1.39183 + 3.36018i) q^{85} +(1.00987 + 11.7269i) q^{86} +(0.333858 + 1.18447i) q^{87} +(-4.62497 + 7.93561i) q^{88} +(0.514120 - 0.514120i) q^{89} +(-6.32975 - 0.956805i) q^{90} +(1.76295 - 4.25613i) q^{91} +(2.27044 + 13.0847i) q^{92} +(5.49686 + 0.651457i) q^{93} +(15.8386 - 8.21763i) q^{94} +11.5930 q^{95} +(-6.34385 - 7.46696i) q^{96} +12.7671 q^{97} +(-1.25531 + 0.651302i) q^{98} +(5.72874 - 7.87981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 16 q^{4}+O(q^{10}) $ 192 * q - 16 * q^4	$ 192 q - 16 q^{4} + 8 q^{10} + 16 q^{16} + 16 q^{22} + 24 q^{27} - 84 q^{30} + 40 q^{36} + 32 q^{37} + 24 q^{39} - 96 q^{46} - 72 q^{48} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 28 q^{60} - 16 q^{61} - 64 q^{64} - 12 q^{66} - 32 q^{67} + 56 q^{69} - 24 q^{70} + 60 q^{72} + 80 q^{75} - 56 q^{76} + 100 q^{78} - 32 q^{79} - 120 q^{82} - 56 q^{87} + 40 q^{88} + 60 q^{90} - 80 q^{93} + 216 q^{94} + 96 q^{96} - 64 q^{99}+O(q^{100}) $ 192 * q - 16 * q^4 + 8 * q^10 + 16 * q^16 + 16 * q^22 + 24 * q^27 - 84 * q^30 + 40 * q^36 + 32 * q^37 + 24 * q^39 - 96 * q^46 - 72 * q^48 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 28 * q^60 - 16 * q^61 - 64 * q^64 - 12 * q^66 - 32 * q^67 + 56 * q^69 - 24 * q^70 + 60 * q^72 + 80 * q^75 - 56 * q^76 + 100 * q^78 - 32 * q^79 - 120 * q^82 - 56 * q^87 + 40 * q^88 + 60 * q^90 - 80 * q^93 + 216 * q^94 + 96 * q^96 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$e\left(\frac{1}{8}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.651302	−	1.25531i	−0.460540	−	0.887639i
$2$	−0.651302	−	1.25531i	−0.460540	−	0.887639i
$3$	−0.203847	+	1.72001i	−0.117691	+	0.993050i
$3$	−0.203847	+	1.72001i	−0.117691	+	0.993050i
$4$	−1.15161	+	1.63517i	−0.575806	+	0.817586i
$5$	−0.577425	+	1.39403i	−0.258232	+	0.623428i	−0.998822	−	0.0485298i	$-0.984546\pi$
$5$	−0.577425	+	1.39403i	−0.258232	+	0.623428i	0.740589	+	0.671958i	$0.234546\pi$
$6$	2.29192	−	0.864357i	0.935672	−	0.352872i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	2.80270	+	0.380642i	0.990903	+	0.134577i
$9$	−2.91689	−	0.701238i	−0.972298	−	0.233746i
$10$	2.12602	−	0.183084i	0.672305	−	0.0578963i
$11$	−1.24272	+	3.00020i	−0.374695	+	0.904593i	0.618246	+	0.785985i	$0.287843\pi$
$11$	−1.24272	+	3.00020i	−0.374695	+	0.904593i	−0.992941	+	0.118609i	$0.962157\pi$
$12$	−2.57777	−	2.31411i	−0.744137	−	0.668027i
$13$	−4.25613	+	1.76295i	−1.18044	+	0.488953i	−0.884630	−	0.466294i	$-0.845589\pi$
$13$	−4.25613	+	1.76295i	−1.18044	+	0.488953i	−0.295808	+	0.955248i	$0.595589\pi$
$14$	1.34818	+	0.427099i	0.360316	+	0.114147i
$15$	−2.28004	−	1.27735i	−0.588704	−	0.329809i
$16$	−1.34758	−	3.76617i	−0.336894	−	0.941542i
$17$	2.41041			0.584611			0.292305	−	0.956325i	$-0.405578\pi$
$17$	2.41041			0.584611			0.292305	+	0.956325i	$0.405578\pi$
$18$	1.01951	+	4.11833i	0.240300	+	0.970699i
$19$	−2.94021	−	7.09830i	−0.674531	−	1.62846i	−0.773822	−	0.633403i	$-0.781657\pi$
$19$	−2.94021	−	7.09830i	−0.674531	−	1.62846i	0.0992909	−	0.995058i	$-0.468343\pi$
$20$	−1.61451	−	2.54957i	−0.361014	−	0.570101i
$21$	−1.07209	−	1.36037i	−0.233950	−	0.296858i
$22$	4.57557	−	0.394030i	0.975514	−	0.0840075i
$23$	4.69526	−	4.69526i	0.979030	−	0.979030i	−0.0207544	−	0.999785i	$-0.506607\pi$
$23$	4.69526	−	4.69526i	0.979030	−	0.979030i	0.999785	+	0.0207544i	$0.00660679\pi$
$24$	−1.22603	+	4.74308i	−0.250262	+	0.968178i
$25$	1.92564	+	1.92564i	0.385128	+	0.385128i
$26$	4.98507	+	4.19455i	0.977652	+	0.822620i
$27$	1.80074	−	4.87415i	0.346552	−	0.938031i
$28$	−0.341929	−	1.97055i	−0.0646184	−	0.372400i
$29$	0.656417	−	0.271897i	0.121894	−	0.0504900i	−0.320903	−	0.947112i	$-0.603986\pi$
$29$	0.656417	−	0.271897i	0.121894	−	0.0504900i	0.442797	+	0.896622i	$0.353986\pi$
$30$	−0.118474	+	3.69410i	−0.0216302	+	0.674447i
$31$		−	3.19582i		−	0.573987i	−0.957933	−	0.286993i	$-0.907344\pi$
$31$		−	3.19582i		−	0.573987i	0.957933	−	0.286993i	$-0.0926557\pi$
$32$	−3.85004	+	4.14454i	−0.680597	+	0.732658i
$33$	−4.90706	−	2.74908i	−0.854209	−	0.478553i
$34$	−1.56991	−	3.02582i	−0.269237	−	0.518923i
$35$	−0.577425	−	1.39403i	−0.0976026	−	0.235634i
$36$	4.50577	−	3.96207i	0.750962	−	0.660345i
$37$	−11.1041	−	4.59946i	−1.82550	−	0.756146i	−0.971972	−	0.235098i	$-0.924459\pi$
$37$	−11.1041	−	4.59946i	−1.82550	−	0.756146i	−0.853527	−	0.521049i	$-0.825541\pi$
$38$	−6.99561	+	8.31402i	−1.13484	+	1.34871i
$39$	−2.16469	−	7.67997i	−0.346628	−	1.22978i
$40$	−2.14897	+	3.68724i	−0.339782	+	0.583005i
$41$	3.84257	+	3.84257i	0.600109	+	0.600109i	0.940341	−	0.340232i	$-0.110506\pi$
$41$	3.84257	+	3.84257i	0.600109	+	0.600109i	−0.340232	+	0.940341i	$0.610506\pi$
$42$	−1.00944	+	2.23182i	−0.155760	+	0.344378i
$43$	−7.68932	−	3.18502i	−1.17261	−	0.485711i	−0.290556	−	0.956858i	$-0.593840\pi$
$43$	−7.68932	−	3.18502i	−1.17261	−	0.485711i	−0.882055	+	0.471147i	$0.843840\pi$
$44$	−3.47471	−	5.48713i	−0.523832	−	0.827216i
$45$	2.66183	−	3.66132i	0.396802	−	0.545797i
$46$	−8.95205	−	2.83598i	−1.31991	−	0.418143i
$47$			12.6172i			1.84041i	0.391433	+	0.920207i	$0.371979\pi$
$47$			12.6172i			1.84041i	−0.391433	+	0.920207i	$0.628021\pi$
$48$	6.75256	−	1.55013i	0.974648	−	0.223742i
$49$		−	1.00000i		−	0.142857i
$50$	1.16311	−	3.67145i	0.164488	−	0.519222i
$51$	−0.491354	+	4.14594i	−0.0688033	+	0.580548i
$52$	2.01869	−	8.98973i	0.279942	−	1.24665i
$53$	−5.89794	−	2.44301i	−0.810144	−	0.335573i	−0.0611327	−	0.998130i	$-0.519471\pi$
$53$	−5.89794	−	2.44301i	−0.810144	−	0.335573i	−0.749012	+	0.662557i	$0.769471\pi$
$54$	−7.29140	+	0.914058i	−0.992234	+	0.124387i
$55$	−3.46478	−	3.46478i	−0.467191	−	0.467191i
$56$	−2.25096	+	1.71265i	−0.300797	+	0.228863i
$57$	12.8085	−	3.61024i	1.69653	−	0.478188i
$58$	−0.768840	−	0.646921i	−0.100954	−	0.0849448i
$59$	−8.68463	−	3.59729i	−1.13064	−	0.468328i	−0.262644	−	0.964893i	$-0.584594\pi$
$59$	−8.68463	−	3.59729i	−1.13064	−	0.468328i	−0.867999	+	0.496565i	$0.834594\pi$
$60$	4.71440	−	2.25725i	0.608627	−	0.291410i
$61$	4.25913	+	10.2824i	0.545325	+	1.31653i	0.920921	+	0.389748i	$0.127438\pi$
$61$	4.25913	+	10.2824i	0.545325	+	1.31653i	−0.375596	+	0.926783i	$0.622562\pi$
$62$	−4.01175	+	2.08144i	−0.509493	+	0.264344i
$63$	2.55840	−	1.56671i	0.322329	−	0.197386i
$64$	7.71022	+	2.13365i	0.963778	+	0.266706i
$65$		−	6.95113i		−	0.862181i
$66$	−0.254977	+	7.95036i	−0.0313855	+	0.978622i
$67$	3.17732	−	1.31609i	0.388171	−	0.160786i	−0.180058	−	0.983656i	$-0.557629\pi$
$67$	3.17732	−	1.31609i	0.388171	−	0.160786i	0.568229	+	0.822870i	$0.307629\pi$
$68$	−2.77586	+	3.94144i	−0.336623	+	0.477970i
$69$	7.11880	+	9.03303i	0.857003	+	1.08745i
$70$	−1.37386	+	1.63278i	−0.164208	+	0.195155i
$71$	−7.70510	−	7.70510i	−0.914427	−	0.914427i	0.0821898	−	0.996617i	$-0.473809\pi$
$71$	−7.70510	−	7.70510i	−0.914427	−	0.914427i	−0.996617	+	0.0821898i	$0.973809\pi$
$72$	−7.90825	−	3.07565i	−0.931996	−	0.362469i
$73$	−6.27972	+	6.27972i	−0.734985	+	0.734985i	−0.971603	−	0.236618i	$-0.923961\pi$
$73$	−6.27972	+	6.27972i	−0.734985	+	0.734985i	0.236618	+	0.971603i	$0.423961\pi$
$74$	1.45835	+	16.9347i	0.169530	+	1.96862i
$75$	−3.70466	+	2.91959i	−0.427778	+	0.337126i
$76$	14.9929	+	3.36674i	1.71981	+	0.386191i
$77$	−1.24272	−	3.00020i	−0.141621	−	0.341904i
$78$	−8.23088	+	7.71934i	−0.931964	+	0.874043i
$79$	−8.05290			−0.906022			−0.453011	−	0.891505i	$-0.649650\pi$
$79$	−8.05290			−0.906022			−0.453011	+	0.891505i	$0.649650\pi$
$80$	6.02827	+	0.296120i	0.673981	+	0.0331073i
$81$	8.01653	+	4.09087i	0.890726	+	0.454541i
$82$	2.32095	−	7.32630i	0.256306	−	0.809055i
$83$	6.21303	−	2.57352i	0.681969	−	0.282481i	−0.0146808	−	0.999892i	$-0.504673\pi$
$83$	6.21303	−	2.57352i	0.681969	−	0.282481i	0.696650	+	0.717412i	$0.254673\pi$
$84$	3.45908	−	0.186431i	0.377417	−	0.0203413i
$85$	−1.39183	+	3.36018i	−0.150965	+	0.364463i
$86$	1.00987	+	11.7269i	0.108898	+	1.26454i
$87$	0.333858	+	1.18447i	0.0357933	+	0.126989i
$88$	−4.62497	+	7.93561i	−0.493024	+	0.845939i
$89$	0.514120	−	0.514120i	0.0544966	−	0.0544966i	−0.679333	−	0.733830i	$-0.737731\pi$
$89$	0.514120	−	0.514120i	0.0544966	−	0.0544966i	0.733830	+	0.679333i	$0.237731\pi$
$90$	−6.32975	−	0.956805i	−0.667214	−	0.100856i
$91$	1.76295	−	4.25613i	0.184807	−	0.446163i
$92$	2.27044	+	13.0847i	0.236710	+	1.36417i
$93$	5.49686	+	0.651457i	0.569998	+	0.0675530i
$94$	15.8386	−	8.21763i	1.63362	−	0.847583i
$95$	11.5930			1.18941
$96$	−6.34385	−	7.46696i	−0.647467	−	0.762094i
$97$	12.7671			1.29630			0.648149	−	0.761513i	$-0.275543\pi$
$97$	12.7671			1.29630			0.648149	+	0.761513i	$0.275543\pi$
$98$	−1.25531	+	0.651302i	−0.126806	+	0.0657914i
$99$	5.72874	−	7.87981i	0.575760	−	0.791951i
$100$	−5.36635	+	0.931163i	−0.536635	+	0.0931163i
$101$	−1.73944	+	4.19938i	−0.173081	+	0.417854i	−0.986486	−	0.163843i	$-0.947611\pi$
$101$	−1.73944	+	4.19938i	−0.173081	+	0.417854i	0.813406	+	0.581697i	$0.197611\pi$
$102$	5.52447	−	2.08346i	0.547004	−	0.206293i
$103$	−7.46610	+	7.46610i	−0.735656	+	0.735656i	−0.971734	−	0.236078i	$-0.924138\pi$
$103$	−7.46610	+	7.46610i	−0.735656	+	0.735656i	0.236078	+	0.971734i	$0.424138\pi$
$104$	−12.5997	+	3.32094i	−1.23550	+	0.325645i
$105$	2.51545	−	0.709011i	0.245483	−	0.0691924i
$106$	0.774604	+	8.99488i	0.0752362	+	0.873660i
$107$	2.11964	−	5.11726i	0.204913	−	0.494704i	−0.787695	−	0.616065i	$-0.788726\pi$
$107$	2.11964	−	5.11726i	0.204913	−	0.494704i	0.992608	+	0.121361i	$0.0387259\pi$
$108$	5.89633	+	8.55765i	0.567374	+	0.823460i
$109$	−4.15820	+	1.72238i	−0.398283	+	0.164974i	−0.572829	−	0.819675i	$-0.694154\pi$
$109$	−4.15820	+	1.72238i	−0.398283	+	0.164974i	0.174546	+	0.984649i	$0.444154\pi$
$110$	−2.09276	+	6.60599i	−0.199537	+	0.629856i
$111$	10.1747	−	18.1616i	0.965736	−	1.72382i
$112$	3.61597	+	1.71020i	0.341677	+	0.161599i
$113$	−4.36837			−0.410941			−0.205471	−	0.978663i	$-0.565873\pi$
$113$	−4.36837			−0.410941			−0.205471	+	0.978663i	$0.565873\pi$
$114$	−12.8742	−	13.7273i	−1.20578	−	1.28568i
$115$	3.83416	+	9.25649i	0.357538	+	0.863172i
$116$	−0.311340	+	1.38647i	−0.0289072	+	0.128731i
$117$	13.6509	−	2.15777i	1.26203	−	0.199486i
$118$	1.14059	+	13.2448i	0.105000	+	1.21929i
$119$	−1.70442	+	1.70442i	−0.156244	+	0.156244i
$120$	−5.90405	−	4.44789i	−0.538964	−	0.406035i
$121$	0.321350	+	0.321350i	0.0292136	+	0.0292136i
$122$	10.1337	−	12.0435i	0.917461	−	1.09037i
$123$	−7.39258	+	5.82599i	−0.666566	+	0.525311i
$124$	5.22572	+	3.68035i	0.469284	+	0.330505i
$125$	−10.7664	+	4.45961i	−0.962980	+	0.398879i
$126$	−3.63300	−	2.19120i	−0.323653	−	0.195207i
$127$			2.78908i			0.247491i	0.992314	+	0.123745i	$0.0394906\pi$
$127$			2.78908i			0.247491i	−0.992314	+	0.123745i	$0.960509\pi$
$128$	−2.34329	−	11.0684i	−0.207120	−	0.978316i
$129$	7.04572	−	12.5765i	0.620341	−	1.10730i
$130$	−8.72583	+	4.52728i	−0.765306	+	0.397069i
$131$	5.08810	+	12.2838i	0.444549	+	1.07324i	0.974334	+	0.225105i	$0.0722726\pi$
$131$	5.08810	+	12.2838i	0.444549	+	1.07324i	−0.529785	+	0.848132i	$0.677727\pi$
$132$	10.1462	−	4.85801i	0.883117	−	0.422835i
$133$	7.09830	+	2.94021i	0.615501	+	0.254949i
$134$	−3.72149	−	3.13135i	−0.321488	−	0.270508i
$135$	5.75491	+	5.32473i	0.495304	+	0.458280i
$136$	6.75566	+	0.917503i	0.579293	+	0.0786752i
$137$	1.91645	+	1.91645i	0.163734	+	0.163734i	0.784219	−	0.620485i	$-0.213064\pi$
$137$	1.91645	+	1.91645i	0.163734	+	0.163734i	−0.620485	+	0.784219i	$0.713064\pi$
$138$	6.70278	−	14.8195i	0.570578	−	1.26152i
$139$	−12.8010	−	5.30235i	−1.08577	−	0.449739i	−0.233238	−	0.972420i	$-0.574932\pi$
$139$	−12.8010	−	5.30235i	−1.08577	−	0.449739i	−0.852529	+	0.522681i	$0.824932\pi$
$140$	2.94444	+	0.661190i	0.248851	+	0.0558807i
$141$	−21.7018	−	2.57198i	−1.82762	−	0.216600i
$142$	−4.65395	+	14.6906i	−0.390551	+	1.23281i
$143$		−	14.9601i		−	1.25102i
$144$	1.28976	+	11.9305i	0.107480	+	0.994207i
$145$			1.07206i			0.0890300i
$146$	11.9730	+	3.79301i	0.990892	+	0.313912i
$147$	1.72001	+	0.203847i	0.141864	+	0.0168130i
$148$	20.3085	−	12.8603i	1.66935	−	1.05711i
$149$	−6.69853	−	2.77462i	−0.548765	−	0.227306i	0.0910345	−	0.995848i	$-0.470983\pi$
$149$	−6.69853	−	2.77462i	−0.548765	−	0.227306i	−0.639800	+	0.768542i	$0.720983\pi$
$150$	6.07785	+	2.74897i	0.496255	+	0.224453i
$151$	−14.4608	−	14.4608i	−1.17680	−	1.17680i	−0.980554	−	0.196249i	$-0.937124\pi$
$151$	−14.4608	−	14.4608i	−1.17680	−	1.17680i	−0.196249	−	0.980554i	$-0.562876\pi$
$152$	−5.53862	−	21.0136i	−0.449241	−	1.70442i
$153$	−7.03091	−	1.69027i	−0.568416	−	0.136650i
$154$	−2.95679	+	3.51404i	−0.238265	+	0.283169i
$155$	4.45506	+	1.84535i	0.357839	+	0.148222i
$156$	15.0510	+	5.30470i	1.20504	+	0.424716i
$157$	6.43132	+	15.5266i	0.513275	+	1.23916i	0.941967	+	0.335705i	$0.108975\pi$
$157$	6.43132	+	15.5266i	0.513275	+	1.23916i	−0.428692	+	0.903451i	$0.641025\pi$
$158$	5.24487	+	10.1089i	0.417259	+	0.804220i
$159$	5.40428	−	9.64654i	0.428587	−	0.765020i
$160$	−3.55450	−	7.76022i	−0.281008	−	0.613499i
$161$			6.64011i			0.523314i
$162$	−0.0858651	−	12.7276i	−0.00674620	−	0.999977i
$163$	23.0026	−	9.52797i	1.80170	−	0.746289i	0.815939	−	0.578139i	$-0.196221\pi$
$163$	23.0026	−	9.52797i	1.80170	−	0.746289i	0.985761	−	0.168150i	$-0.0537793\pi$
$164$	−10.7084	+	1.85812i	−0.836188	+	0.145094i
$165$	6.66575	−	5.25318i	0.518928	−	0.408960i
$166$	−7.27713	−	6.12315i	−0.564815	−	0.475249i
$167$	−3.23505	−	3.23505i	−0.250336	−	0.250336i	0.570772	−	0.821108i	$-0.306644\pi$
$167$	−3.23505	−	3.23505i	−0.250336	−	0.250336i	−0.821108	+	0.570772i	$0.806644\pi$
$168$	−2.48693	−	4.22080i	−0.191871	−	0.325642i
$169$	5.81425	−	5.81425i	0.447250	−	0.447250i
$170$	5.12457	−	0.441308i	0.393037	−	0.0338468i
$171$	3.59869	+	22.7668i	0.275199	+	1.74102i
$172$	14.0632	−	8.90545i	1.07231	−	0.679035i
$173$	4.52338	+	10.9204i	0.343906	+	0.830262i	0.997313	+	0.0732557i	$0.0233389\pi$
$173$	4.52338	+	10.9204i	0.343906	+	0.830262i	−0.653407	+	0.757007i	$0.726661\pi$
$174$	1.26944	−	1.19054i	0.0962358	−	0.0902549i
$175$	−2.72327			−0.205860
$176$	12.9739	+	0.637304i	0.977946	+	0.0480386i
$177$	7.95772	−	14.2044i	0.598139	−	1.06767i
$178$	−0.980228	−	0.310534i	−0.0734712	−	0.0232755i
$179$	−9.25503	+	3.83356i	−0.691753	+	0.286534i	−0.700730	−	0.713426i	$-0.747142\pi$
$179$	−9.25503	+	3.83356i	−0.691753	+	0.286534i	0.00897721	+	0.999960i	$0.497142\pi$
$180$	2.92149	+	8.56897i	0.217755	+	0.638693i
$181$	−0.220743	+	0.532921i	−0.0164077	+	0.0396117i	−0.931871	−	0.362790i	$-0.881824\pi$
$181$	−0.220743	+	0.532921i	−0.0164077	+	0.0396117i	0.915463	+	0.402401i	$0.131824\pi$
$182$	−6.49097	+	0.558977i	−0.481143	+	0.0414341i
$183$	−18.5541	+	5.22972i	−1.37156	+	0.386592i
$184$	14.9466	−	11.3722i	1.10188	−	0.838369i
$185$	12.8235	−	12.8235i	0.942806	−	0.942806i
$186$	−2.76233	−	7.32456i	−0.202544	−	0.537063i
$187$	−2.99547	+	7.23171i	−0.219051	+	0.528835i
$188$	−20.6314	−	14.5302i	−1.50470	−	1.05972i
$189$	2.17323	+	4.71986i	0.158079	+	0.343319i
$190$	−7.55052	−	14.5528i	−0.547773	−	1.05577i
$191$	−2.32165			−0.167989			−0.0839943	−	0.996466i	$-0.526768\pi$
$191$	−2.32165			−0.167989			−0.0839943	+	0.996466i	$0.526768\pi$
$192$	−5.24160	+	12.8268i	−0.378280	+	0.925691i
$193$	−3.05203			−0.219690			−0.109845	−	0.993949i	$-0.535035\pi$
$193$	−3.05203			−0.219690			−0.109845	+	0.993949i	$0.535035\pi$
$194$	−8.31520	−	16.0266i	−0.596997	−	1.15064i
$195$	11.9560	+	1.41696i	0.856189	+	0.101471i
$196$	1.63517	+	1.15161i	0.116798	+	0.0822580i
$197$	−2.68175	+	6.47432i	−0.191067	+	0.461276i	−0.990162	−	0.139929i	$-0.955313\pi$
$197$	−2.68175	+	6.47432i	−0.191067	+	0.461276i	0.799095	+	0.601205i	$0.205313\pi$
$198$	−13.6228	−	2.05922i	−0.968127	−	0.146342i
$199$	−3.37319	+	3.37319i	−0.239119	+	0.239119i	−0.816485	−	0.577366i	$-0.804080\pi$
$199$	−3.37319	+	3.37319i	−0.239119	+	0.239119i	0.577366	+	0.816485i	$0.304080\pi$
$200$	4.66401	+	6.12997i	0.329795	+	0.433454i
$201$	1.61600	+	5.73331i	0.113984	+	0.404396i
$202$	6.40443	−	0.551524i	0.450614	−	0.0388051i
$203$	−0.271897	+	0.656417i	−0.0190834	+	0.0460714i
$204$	−6.21348	−	5.57797i	−0.435031	−	0.390536i
$205$	−7.57545	+	3.13786i	−0.529093	+	0.219157i
$206$	14.2350	+	4.50959i	0.991796	+	0.314198i
$207$	−16.9881	+	10.4031i	−1.18075	+	0.723065i
$208$	12.3750	+	13.6536i	0.858053	+	0.946706i
$209$	24.9502			1.72584
$210$	−2.52835	−	2.69589i	−0.174473	−	0.186034i
$211$	−1.48202	−	3.57792i	−0.102027	−	0.246314i	0.864621	−	0.502425i	$-0.167559\pi$
$211$	−1.48202	−	3.57792i	−0.102027	−	0.246314i	−0.966647	+	0.256111i	$0.917559\pi$
$212$	10.7869	−	6.83075i	0.740846	−	0.469138i
$213$	14.8235	−	11.6822i	1.01569	−	0.800452i
$214$	−7.80427	+	0.672073i	−0.533489	+	0.0459420i
$215$	8.88001	−	8.88001i	0.605612	−	0.605612i
$216$	6.90222	−	12.9753i	0.469637	−	0.882860i
$217$	2.25979	+	2.25979i	0.153404	+	0.153404i
$218$	4.87037	+	4.09805i	0.329863	+	0.277555i
$219$	−9.52110	−	12.0813i	−0.643376	−	0.816378i
$220$	9.65559	−	1.67543i	0.650980	−	0.112957i
$221$	−10.2590	+	4.24943i	−0.690096	+	0.285847i
$222$	−29.4252	−	0.943698i	−1.97489	−	0.0633369i
$223$			16.6837i			1.11722i	0.829429	+	0.558612i	$0.188666\pi$
$223$			16.6837i			1.11722i	−0.829429	+	0.558612i	$0.811334\pi$
$224$	−0.208247	−	5.65302i	−0.0139141	−	0.377708i
$225$	−4.26656	−	6.96722i	−0.284437	−	0.464481i
$226$	2.84512	+	5.48366i	0.189255	+	0.364768i
$227$	−0.485009	−	1.17091i	−0.0321911	−	0.0777163i	0.906966	−	0.421203i	$-0.138392\pi$
$227$	−0.485009	−	1.17091i	−0.0321911	−	0.0777163i	−0.939158	+	0.343487i	$0.888392\pi$
$228$	−8.84709	+	25.1017i	−0.585913	+	1.66240i
$229$	−6.19512	−	2.56610i	−0.409385	−	0.169573i	0.168480	−	0.985705i	$-0.446114\pi$
$229$	−6.19512	−	2.56610i	−0.409385	−	0.169573i	−0.577865	+	0.816132i	$0.696114\pi$
$230$	9.12258	−	10.8418i	0.601525	−	0.714889i
$231$	5.41370	−	1.52592i	0.356196	−	0.100398i
$232$	1.94323	−	0.512185i	0.127580	−	0.0336266i
$233$	17.6694	+	17.6694i	1.15756	+	1.15756i	0.984998	+	0.172564i	$0.0552051\pi$
$233$	17.6694	+	17.6694i	1.15756	+	1.15756i	0.172564	+	0.984998i	$0.444795\pi$
$234$	−11.5995	−	15.7308i	−0.758285	−	1.02835i
$235$	−17.5888	−	7.28551i	−1.14737	−	0.475254i
$236$	15.8835	−	10.0582i	1.03393	−	0.654732i
$237$	1.64156	−	13.8511i	0.106630	−	0.899725i
$238$	3.24967	+	1.02949i	0.210645	+	0.0667316i
$239$		−	0.978603i		−	0.0633005i	−0.999499	−	0.0316503i	$-0.989924\pi$
$239$		−	0.978603i		−	0.0633005i	0.999499	−	0.0316503i	$-0.0100763\pi$
$240$	−1.73817	+	10.3083i	−0.112199	+	0.665401i
$241$		−	19.7050i		−	1.26931i	−0.772795	−	0.634656i	$-0.781142\pi$
$241$		−	19.7050i		−	1.26931i	0.772795	−	0.634656i	$-0.218858\pi$
$242$	0.194099	−	0.612690i	0.0124771	−	0.0393852i
$243$	−8.67049	+	12.9546i	−0.556212	+	0.831040i
$244$	−21.7184	−	4.87698i	−1.39038	−	0.312217i
$245$	1.39403	+	0.577425i	0.0890611	+	0.0368903i
$246$	12.1282	+	5.48551i	0.773267	+	0.349743i
$247$	25.0278	+	25.0278i	1.59248	+	1.59248i
$248$	1.21646	−	8.95692i	0.0772454	−	0.568765i
$249$	3.15999	+	11.2111i	0.200256	+	0.710475i
$250$	12.6104	+	10.6107i	0.797552	+	0.671079i
$251$	13.9861	+	5.79325i	0.882797	+	0.365667i	0.777581	−	0.628783i	$-0.216447\pi$
$251$	13.9861	+	5.79325i	0.882797	+	0.365667i	0.105216	+	0.994449i	$0.466447\pi$
$252$	−0.384458	+	5.98767i	−0.0242186	+	0.377188i
$253$	8.25181	+	19.9216i	0.518787	+	1.25246i
$254$	3.50116	−	1.81653i	0.219682	−	0.113979i
$255$	−5.49584	−	3.07893i	−0.344163	−	0.192810i
$256$	−12.3681	+	10.1504i	−0.773004	+	0.634401i
$257$			12.0086i			0.749076i	0.927212	+	0.374538i	$0.122199\pi$
$257$			12.0086i			0.749076i	−0.927212	+	0.374538i	$0.877801\pi$
$258$	−20.3763	−	0.653490i	−1.26857	−	0.0406845i
$259$	11.1041	−	4.59946i	0.689974	−	0.285796i
$260$	11.3663	+	8.00500i	0.704907	+	0.496449i
$261$	−2.10536	+	0.332790i	−0.130319	+	0.0205992i
$262$	12.1061	−	14.3876i	0.747914	−	0.888868i
$263$	−17.2926	−	17.2926i	−1.06631	−	1.06631i	−0.997639	−	0.0686709i	$-0.978124\pi$
$263$	−17.2926	−	17.2926i	−1.06631	−	1.06631i	−0.0686709	−	0.997639i	$-0.521876\pi$
$264$	−12.7066	−	9.57267i	−0.782036	−	0.589157i
$265$	6.81124	−	6.81124i	0.418411	−	0.418411i
$266$	−0.932253	−	10.8255i	−0.0571601	−	0.663756i
$267$	0.779492	+	0.989095i	0.0477041	+	0.0605316i
$268$	−1.50701	+	6.71108i	−0.0920551	+	0.409945i
$269$	−8.27518	−	19.9781i	−0.504547	−	1.21808i	−0.946983	−	0.321284i	$-0.895886\pi$
$269$	−8.27518	−	19.9781i	−0.504547	−	1.21808i	0.442436	−	0.896800i	$-0.354114\pi$
$270$	2.93602	−	10.6922i	0.178680	−	0.650707i
$271$	0.0608473			0.00369621			0.00184811	−	0.999998i	$-0.499412\pi$
$271$	0.0608473			0.00369621			0.00184811	+	0.999998i	$0.499412\pi$
$272$	−3.24822	−	9.07802i	−0.196952	−	0.550436i
$273$	6.96123	+	3.89989i	0.421313	+	0.236032i
$274$	1.15756	−	3.65394i	0.0699306	−	0.220742i
$275$	−8.17034	+	3.38427i	−0.492690	+	0.204079i
$276$	−22.9687	+	1.23792i	−1.38255	+	0.0745142i
$277$	−1.43023	+	3.45288i	−0.0859342	+	0.207464i	−0.961005	−	0.276532i	$-0.910815\pi$
$277$	−1.43023	+	3.45288i	−0.0859342	+	0.207464i	0.875071	+	0.483995i	$0.160815\pi$
$278$	1.68121	+	19.5227i	0.100833	+	1.17089i
$279$	−2.24103	+	9.32187i	−0.134167	+	0.558086i
$280$	−1.08772	−	4.12683i	−0.0650039	−	0.246625i
$281$	−16.4777	+	16.4777i	−0.982978	+	0.982978i	−0.999858	−	0.0168797i	$-0.994627\pi$
$281$	−16.4777	+	16.4777i	−0.982978	+	0.982978i	0.0168797	+	0.999858i	$0.494627\pi$
$282$	10.9058	+	28.9177i	0.649431	+	1.72202i
$283$	−1.00432	+	2.42465i	−0.0597008	+	0.144130i	−0.950915	−	0.309452i	$-0.899854\pi$
$283$	−1.00432	+	2.42465i	−0.0597008	+	0.144130i	0.891214	+	0.453583i	$0.149854\pi$
$284$	21.4725	−	3.72588i	1.27416	−	0.221090i
$285$	−2.36319	+	19.9401i	−0.139983	+	1.18115i
$286$	−18.7795	+	9.74352i	−1.11046	+	0.576146i
$287$	−5.43422			−0.320772
$288$	14.1365	−	9.38940i	0.832998	−	0.553275i
$289$	−11.1899			−0.658230
$290$	1.34577	−	0.698236i	0.0790265	−	0.0410019i
$291$	−2.60252	+	21.9595i	−0.152562	+	1.28729i
$292$	−3.03662	−	17.5002i	−0.177705	−	1.02412i
$293$	−5.78597	+	13.9686i	−0.338020	+	0.816052i	0.659886	+	0.751366i	$0.270605\pi$
$293$	−5.78597	+	13.9686i	−0.338020	+	0.816052i	−0.997906	+	0.0646860i	$0.979395\pi$
$294$	−0.864357	−	2.29192i	−0.0504103	−	0.133667i
$295$	10.0294	−	10.0294i	0.583937	−	0.583937i
$296$	−29.3706	−	17.1176i	−1.70713	−	0.994938i
$297$	12.3856	+	11.4598i	0.718685	+	0.664964i
$298$	0.879749	+	10.2159i	0.0509625	+	0.591789i
$299$	−11.7061	+	28.2611i	−0.676984	+	1.63438i
$300$	−0.507702	−	9.42001i	−0.0293122	−	0.543864i
$301$	7.68932	−	3.18502i	0.443205	−	0.183582i
$302$	−8.73446	+	27.5711i	−0.502612	+	1.58654i
$303$	−6.86841	−	3.84789i	−0.394580	−	0.221056i
$304$	−22.7712	+	20.6388i	−1.30602	+	1.18372i
$305$	−16.7933			−0.961583
$306$	2.45743	+	9.92686i	0.140482	+	0.567481i
$307$	0.838906	+	2.02530i	0.0478789	+	0.115590i	0.946009	−	0.324139i	$-0.105075\pi$
$307$	0.838906	+	2.02530i	0.0478789	+	0.115590i	−0.898131	+	0.439729i	$0.855075\pi$
$308$	6.33697	+	1.42300i	0.361083	+	0.0810829i
$309$	−11.3198	−	14.3637i	−0.643964	−	0.817124i
$310$	−0.585104	−	6.79437i	−0.0332317	−	0.385894i
$311$	−20.5437	+	20.5437i	−1.16492	+	1.16492i	−0.181541	+	0.983383i	$0.558108\pi$
$311$	−20.5437	+	20.5437i	−1.16492	+	1.16492i	−0.983383	+	0.181541i	$0.941892\pi$
$312$	−3.14367	−	22.3486i	−0.177975	−	1.26524i
$313$	−17.2334	−	17.2334i	−0.974092	−	0.974092i	0.0255807	−	0.999673i	$-0.491857\pi$
$313$	−17.2334	−	17.2334i	−0.974092	−	0.974092i	−0.999673	+	0.0255807i	$0.991857\pi$
$314$	15.3020	−	18.1858i	0.863540	−	1.02628i
$315$	0.706743	+	4.47114i	0.0398204	+	0.251920i
$316$	9.27382	−	13.1679i	0.521693	−	0.740751i
$317$	11.7604	−	4.87131i	0.660528	−	0.273600i	−0.0271324	−	0.999632i	$-0.508638\pi$
$317$	11.7604	−	4.87131i	0.660528	−	0.273600i	0.687661	+	0.726032i	$0.258638\pi$
$318$	−15.6292	−	0.501246i	−0.876443	−	0.0281085i
$319$			2.30727i			0.129182i
$320$	−7.42644	+	9.51624i	−0.415150	+	0.531974i
$321$	8.36967	+	4.68894i	0.467149	+	0.261711i
$322$	8.33540	−	4.32471i	0.464514	−	0.241007i
$323$	−7.08712	−	17.1098i	−0.394338	−	0.952016i
$324$	−15.9212	+	8.39731i	−0.884512	+	0.466517i
$325$	−11.5906	−	4.80097i	−0.642929	−	0.266310i
$326$	−26.9422	−	22.6698i	−1.49219	−	1.25556i
$327$	−2.11489	−	7.50326i	−0.116954	−	0.414931i
$328$	9.30693	+	12.2322i	0.513889	+	0.675411i
$329$	−8.92173	−	8.92173i	−0.491871	−	0.491871i
$330$	−10.9358	−	4.94618i	−0.601995	−	0.272278i
$331$	0.246462	+	0.102088i	0.0135468	+	0.00561126i	0.389447	−	0.921049i	$-0.372666\pi$
$331$	0.246462	+	0.102088i	0.0135468	+	0.00561126i	−0.375900	+	0.926660i	$0.622666\pi$
$332$	−2.94685	+	13.1231i	−0.161730	+	0.720222i
$333$	29.1641	+	21.2027i	1.59818	+	1.16190i
$334$	−1.95400	+	6.16799i	−0.106918	+	0.337498i
$335$			5.18921i			0.283517i
$336$	−3.67867	+	5.87089i	−0.200688	+	0.320283i
$337$		−	16.5414i		−	0.901066i	−0.892760	−	0.450533i	$-0.851234\pi$
$337$		−	16.5414i		−	0.901066i	0.892760	−	0.450533i	$-0.148766\pi$
$338$	−11.0855	−	3.51186i	−0.602973	−	0.191020i
$339$	0.890476	−	7.51365i	0.0483640	−	0.408085i
$340$	−3.89162	−	6.14551i	−0.211053	−	0.333287i
$341$	9.58810	+	3.97152i	0.519225	+	0.215070i
$342$	26.2355	−	19.3455i	1.41866	−	1.04609i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−20.3385	−	11.8535i	−1.09658	−	0.639099i
$345$	−16.7029	+	4.70791i	−0.899252	+	0.253465i
$346$	10.7624	−	12.7907i	0.578591	−	0.687633i
$347$	22.8075	+	9.44716i	1.22437	+	0.507150i	0.898796	−	0.438367i	$-0.144443\pi$
$347$	22.8075	+	9.44716i	1.22437	+	0.507150i	0.325573	+	0.945517i	$0.394443\pi$
$348$	−2.32129	−	0.818137i	−0.124434	−	0.0438567i
$349$	−5.10630	−	12.3277i	−0.273334	−	0.659887i	0.726288	−	0.687391i	$-0.241244\pi$
$349$	−5.10630	−	12.3277i	−0.273334	−	0.659887i	−0.999622	+	0.0275041i	$0.991244\pi$
$350$	1.77367	+	3.41855i	0.0948066	+	0.182729i
$351$	0.928699	+	23.9196i	0.0495703	+	1.27673i
$352$	−7.64992	−	16.7014i	−0.407742	−	0.890187i
$353$		−	2.62740i		−	0.139843i	−0.997553	−	0.0699213i	$-0.977725\pi$
$353$		−	2.62740i		−	0.139843i	0.997553	−	0.0699213i	$-0.0222748\pi$
$354$	−23.0138	−	0.738078i	−1.22317	−	0.0392284i
$355$	15.1902	−	6.29200i	0.806214	−	0.333945i
$356$	0.248608	+	1.43274i	0.0131762	+	0.0759352i
$357$	−2.58418	−	3.27906i	−0.136769	−	0.173546i
$358$	10.8401	+	9.12114i	0.572918	+	0.482067i
$359$	5.75937	+	5.75937i	0.303968	+	0.303968i	0.842564	−	0.538596i	$-0.181045\pi$
$359$	5.75937	+	5.75937i	0.303968	+	0.303968i	−0.538596	+	0.842564i	$0.681045\pi$
$360$	8.85396	−	9.24836i	0.466645	−	0.487431i
$361$	−28.3060	+	28.3060i	−1.48979	+	1.48979i
$362$	0.812753	−	0.0699911i	0.0427173	−	0.00367865i
$363$	−0.618233	+	0.487220i	−0.0324488	+	0.0255724i
$364$	4.92927	+	7.78413i	0.258364	+	0.407999i
$365$	−5.12803	−	12.3802i	−0.268413	−	0.648007i
$366$	18.6493	+	19.8851i	0.974813	+	1.03941i
$367$	−14.8464			−0.774976			−0.387488	−	0.921875i	$-0.626657\pi$
$367$	−14.8464			−0.774976			−0.387488	+	0.921875i	$0.626657\pi$
$368$	−24.0104	−	11.3559i	−1.25163	−	0.591969i
$369$	−8.51382	−	13.9029i	−0.443212	−	0.723758i
$370$	−24.4495	−	7.74554i	−1.27107	−	0.402672i
$371$	5.89794	−	2.44301i	0.306206	−	0.126835i
$372$	−7.39549	+	8.23808i	−0.383438	+	0.427125i
$373$	−0.299489	+	0.723032i	−0.0155070	+	0.0374372i	−0.931443	−	0.363886i	$-0.881450\pi$
$373$	−0.299489	+	0.723032i	−0.0155070	+	0.0374372i	0.915936	+	0.401323i	$0.131450\pi$
$374$	11.0290	−	0.949775i	0.570296	−	0.0491117i
$375$	−5.47588	−	19.4275i	−0.282773	−	1.00323i
$376$	−4.80264	+	35.3623i	−0.247677	+	1.82367i
$377$	−2.31445	+	2.31445i	−0.119200	+	0.119200i
$378$	4.50946	−	5.80213i	0.231942	−	0.298430i
$379$	−5.49836	+	13.2742i	−0.282432	+	0.681851i	−0.999891	−	0.0147495i	$-0.995305\pi$
$379$	−5.49836	+	13.2742i	−0.282432	+	0.681851i	0.717459	+	0.696600i	$0.245305\pi$
$380$	−13.3506	+	18.9565i	−0.684872	+	0.972449i
$381$	−4.79725	−	0.568544i	−0.245771	−	0.0291274i
$382$	1.51209	+	2.91439i	0.0773655	+	0.149113i
$383$	12.9466			0.661538			0.330769	−	0.943712i	$-0.392692\pi$
$383$	12.9466			0.661538			0.330769	+	0.943712i	$0.392692\pi$
$384$	19.5154	−	1.77424i	0.995893	−	0.0905415i
$385$	4.89994			0.249724
$386$	1.98779	+	3.83125i	0.101176	+	0.195005i
$387$	20.1955	+	14.6824i	1.02659	+	0.746349i
$388$	−14.7027	+	20.8763i	−0.746417	+	1.05984i
$389$	−6.43565	+	15.5370i	−0.326300	+	0.787759i	0.672561	+	0.740042i	$0.265194\pi$
$389$	−6.43565	+	15.5370i	−0.326300	+	0.787759i	−0.998861	+	0.0477166i	$0.984806\pi$
$390$	−6.00825	−	15.9314i	−0.304240	−	0.806718i
$391$	11.3175	−	11.3175i	0.572352	−	0.572352i
$392$	0.380642	−	2.80270i	0.0192253	−	0.141558i
$393$	−22.1654	+	6.24760i	−1.11810	+	0.315150i
$394$	9.87392	−	0.850303i	0.497441	−	0.0428377i
$395$	4.64994	−	11.2260i	0.233964	−	0.564839i
$396$	6.28756	+	18.4420i	0.315962	+	0.926744i
$397$	−4.12683	+	1.70939i	−0.207120	+	0.0857918i	−0.483831	−	0.875161i	$-0.660755\pi$
$397$	−4.12683	+	1.70939i	−0.207120	+	0.0857918i	0.276712	+	0.960953i	$0.410755\pi$
$398$	6.43136	+	2.03744i	0.322375	+	0.102127i
$399$	−6.50417	+	11.6098i	−0.325616	+	0.581218i
$400$	4.65734	−	9.84724i	0.232867	−	0.492362i
$401$	−25.6063			−1.27872			−0.639358	−	0.768909i	$-0.720800\pi$
$401$	−25.6063			−1.27872			−0.639358	+	0.768909i	$0.720800\pi$
$402$	6.14458	−	5.76270i	0.306464	−	0.287417i
$403$	5.63406	+	13.6018i	0.280653	+	0.677555i
$404$	−4.86355	−	7.68034i	−0.241971	−	0.382111i
$405$	−10.3317	+	8.81309i	−0.513388	+	0.437926i
$406$	1.00109	−	0.0862103i	0.0496835	−	0.00427855i
$407$	27.5986	−	27.5986i	1.36801	−	1.36801i
$408$	−2.95523	+	11.4328i	−0.146306	+	0.566007i
$409$	4.32590	+	4.32590i	0.213902	+	0.213902i	0.805923	−	0.592021i	$-0.201670\pi$
$409$	4.32590	+	4.32590i	0.213902	+	0.213902i	−0.592021	+	0.805923i	$0.701670\pi$
$410$	8.87289	+	7.46586i	0.438201	+	0.368713i
$411$	−3.68699	+	2.90566i	−0.181866	+	0.143326i
$412$	−3.61031	−	20.8064i	−0.177867	−	1.02506i
$413$	8.68463	−	3.59729i	0.427343	−	0.177011i
$414$	24.1235	+	14.5498i	1.18560	+	0.715083i
$415$			10.1472i			0.498104i
$416$	9.07964	−	24.4271i	0.445166	−	1.19764i
$417$	11.7295	−	20.9370i	0.574398	−	1.02529i
$418$	−16.2501	−	31.3202i	−0.794818	−	1.53192i
$419$	6.15209	+	14.8525i	0.300549	+	0.725590i	0.999941	+	0.0108517i	$0.00345429\pi$
$419$	6.15209	+	14.8525i	0.300549	+	0.725590i	−0.699392	+	0.714738i	$0.746546\pi$
$420$	−1.73747	+	4.92970i	−0.0847799	+	0.240545i
$421$	−4.58456	−	1.89899i	−0.223438	−	0.0925511i	0.268156	−	0.963375i	$-0.413586\pi$
$421$	−4.58456	−	1.89899i	−0.223438	−	0.0925511i	−0.491594	+	0.870824i	$0.663586\pi$
$422$	−3.52616	+	4.19070i	−0.171651	+	0.204000i
$423$	8.84768	−	36.8031i	0.430189	−	1.78943i
$424$	−15.6002	−	9.09201i	−0.757614	−	0.441547i
$425$	4.64159	+	4.64159i	0.225150	+	0.225150i
$426$	−24.3194	−	10.9995i	−1.17828	−	0.532927i
$427$	−10.2824	−	4.25913i	−0.497602	−	0.206114i
$428$	5.92660	+	9.35907i	0.286473	+	0.452388i
$429$	25.7315	+	3.04956i	1.24233	+	0.147234i
$430$	−16.9307	−	5.36361i	−0.816473	−	0.258656i
$431$		−	30.9381i		−	1.49024i	−0.666932	−	0.745119i	$-0.732393\pi$
$431$		−	30.9381i		−	1.49024i	0.666932	−	0.745119i	$-0.267607\pi$
$432$	−20.7835	−	0.213583i	−0.999947	−	0.0102760i
$433$			8.47997i			0.407521i	0.979021	+	0.203761i	$0.0653164\pi$
$433$			8.47997i			0.407521i	−0.979021	+	0.203761i	$0.934684\pi$
$434$	1.36493	−	4.30854i	0.0655189	−	0.206817i
$435$	−1.84396	−	0.218536i	−0.0884113	−	0.0104780i
$436$	1.97224	−	8.78289i	0.0944533	−	0.420624i
$437$	−47.1335	−	19.5233i	−2.25470	−	0.933927i
$438$	−8.96468	+	19.8205i	−0.428349	+	0.947061i
$439$	−10.3738	−	10.3738i	−0.495117	−	0.495117i	0.414797	−	0.909914i	$-0.363853\pi$
$439$	−10.3738	−	10.3738i	−0.495117	−	0.495117i	−0.909914	+	0.414797i	$0.863853\pi$
$440$	−8.39189	−	11.0296i	−0.400067	−	0.525814i
$441$	−0.701238	+	2.91689i	−0.0333923	+	0.138900i
$442$	12.0161	+	10.1106i	0.571546	+	0.480912i
$443$	32.5495	+	13.4824i	1.54647	+	0.640570i	0.982674	−	0.185343i	$-0.0593395\pi$
$443$	32.5495	+	13.4824i	1.54647	+	0.640570i	0.563798	+	0.825912i	$0.309339\pi$
$444$	17.9800	+	37.5524i	0.853295	+	1.78216i
$445$	0.419832	+	1.01356i	0.0199019	+	0.0480475i
$446$	20.9432	−	10.8661i	0.991691	−	0.514526i
$447$	6.13786	−	10.9560i	0.290311	−	0.518199i
$448$	−6.96067	+	3.94324i	−0.328861	+	0.186300i
$449$			22.8908i			1.08028i	0.841575	+	0.540141i	$0.181629\pi$
$449$			22.8908i			1.08028i	−0.841575	+	0.540141i	$0.818371\pi$
$450$	−5.96722	+	9.89362i	−0.281297	+	0.466390i
$451$	−16.3037	+	6.75323i	−0.767713	+	0.317997i
$452$	5.03066	−	7.14303i	0.236623	−	0.335980i
$453$	27.8206	−	21.9250i	1.30712	−	1.03013i
$454$	−1.15397	+	1.37145i	−0.0541587	+	0.0643656i
$455$	4.91519	+	4.91519i	0.230428	+	0.230428i
$456$	37.2726	−	5.24296i	1.74545	−	0.245524i
$457$	3.86130	−	3.86130i	0.180624	−	0.180624i	−0.611004	−	0.791628i	$-0.709234\pi$
$457$	3.86130	−	3.86130i	0.180624	−	0.180624i	0.791628	+	0.611004i	$0.209234\pi$
$458$	0.813635	+	9.44811i	0.0380186	+	0.441481i
$459$	4.34052	−	11.7487i	0.202598	−	0.548383i
$460$	−19.5514	−	4.39037i	−0.911590	−	0.204702i
$461$	0.723239	+	1.74605i	0.0336846	+	0.0813218i	0.939827	−	0.341652i	$-0.110986\pi$
$461$	0.723239	+	1.74605i	0.0336846	+	0.0813218i	−0.906142	+	0.422974i	$0.860986\pi$
$462$	−5.44146	−	5.80205i	−0.253160	−	0.269936i
$463$	−0.115422			−0.00536413			−0.00268206	−	0.999996i	$-0.500854\pi$
$463$	−0.115422			−0.00536413			−0.00268206	+	0.999996i	$0.500854\pi$
$464$	−1.90858	−	2.10578i	−0.0886037	−	0.0977582i
$465$	−4.08217	+	7.28660i	−0.189306	+	0.337908i
$466$	10.6725	−	33.6887i	0.494394	−	1.56060i
$467$	17.9711	−	7.44388i	0.831604	−	0.344461i	0.0740662	−	0.997253i	$-0.476402\pi$
$467$	17.9711	−	7.44388i	0.831604	−	0.344461i	0.757537	+	0.652792i	$0.226402\pi$
$468$	−12.1922	+	24.8065i	−0.563586	+	1.14668i
$469$	−1.31609	+	3.17732i	−0.0607713	+	0.146715i
$470$	2.31002	+	26.8244i	0.106553	+	1.23732i
$471$	−28.0169	+	7.89692i	−1.29095	+	0.363871i
$472$	−22.9711	−	13.3879i	−1.05733	−	0.616226i
$473$	19.1114	−	19.1114i	0.878742	−	0.878742i
$474$	−18.4566	+	6.96058i	−0.847739	+	0.319710i
$475$	8.00699	−	19.3306i	0.367386	−	0.886948i
$476$	−0.824189	−	4.74985i	−0.0377766	−	0.217709i
$477$	15.4905	+	11.2618i	0.709263	+	0.515644i
$478$	−1.22845	+	0.637366i	−0.0561880	+	0.0291524i
$479$	−8.49070			−0.387950			−0.193975	−	0.981006i	$-0.562138\pi$
$479$	−8.49070			−0.387950			−0.193975	+	0.981006i	$0.562138\pi$
$480$	14.0723	−	4.53189i	0.642307	−	0.206852i
$481$	55.3690			2.52461
$482$	−24.7359	+	12.8339i	−1.12669	+	0.584568i
$483$	−11.4211	−	1.35356i	−0.519677	−	0.0615892i
$484$	−0.895534	+	0.155392i	−0.0407061	+	0.00706328i
$485$	−7.37202	+	17.7976i	−0.334746	+	0.808149i
$486$	21.9092	+	2.44679i	0.993822	+	0.110989i
$487$	−5.21945	+	5.21945i	−0.236516	+	0.236516i	−0.815406	−	0.578890i	$-0.803486\pi$
$487$	−5.21945	+	5.21945i	−0.236516	+	0.236516i	0.578890	+	0.815406i	$0.303486\pi$
$488$	8.02312	+	30.4398i	0.363190	+	1.37794i
$489$	11.6993	+	41.5070i	0.529058	+	1.87701i
$490$	−0.183084	−	2.12602i	−0.00827090	−	0.0960436i
$491$	8.13962	−	19.6508i	0.367336	−	0.886827i	−0.626849	−	0.779141i	$-0.715656\pi$
$491$	8.13962	−	19.6508i	0.367336	−	0.886827i	0.994185	−	0.107686i	$-0.0343443\pi$
$492$	−1.01311	−	18.7974i	−0.0456744	−	0.847453i
$493$	1.58224	−	0.655383i	0.0712603	−	0.0295170i
$494$	15.1171	−	47.7184i	0.680148	−	2.14695i
$495$	7.67675	+	12.5360i	0.345044	+	0.563452i
$496$	−12.0360	+	4.30662i	−0.540433	+	0.193373i
$497$	10.8967			0.488782
$498$	12.0153	−	11.2686i	0.538419	−	0.504957i
$499$	15.8593	+	38.2878i	0.709961	+	1.71400i	0.700099	+	0.714045i	$0.253139\pi$
$499$	15.8593	+	38.2878i	0.709961	+	1.71400i	0.00986131	+	0.999951i	$0.496861\pi$
$500$	5.10655	−	22.7407i	0.228372	−	1.01700i
$501$	6.22379	−	4.90488i	0.278058	−	0.219134i
$502$	−1.83687	−	21.3301i	−0.0819833	−	0.952009i
$503$	18.4548	−	18.4548i	0.822860	−	0.822860i	−0.163657	−	0.986517i	$-0.552329\pi$
$503$	18.4548	−	18.4548i	0.822860	−	0.822860i	0.986517	+	0.163657i	$0.0523292\pi$
$504$	7.76679	−	3.41717i	0.345960	−	0.152213i
$505$	−4.84965	−	4.84965i	−0.215807	−	0.215807i
$506$	19.6334	−	23.3336i	0.872812	−	1.03730i
$507$	8.81538	+	11.1858i	0.391505	+	0.496779i
$508$	−4.56062	−	3.21194i	−0.202345	−	0.142507i
$509$	21.3451	−	8.84143i	0.946105	−	0.391890i	0.144340	−	0.989528i	$-0.453894\pi$
$509$	21.3451	−	8.84143i	0.946105	−	0.391890i	0.801766	+	0.597639i	$0.203894\pi$
$510$	−0.285571	+	8.90430i	−0.0126453	+	0.394289i
$511$		−	8.88086i		−	0.392866i
$512$	20.7973	+	8.91479i	0.919118	+	0.393982i
$513$	−39.8927	+	1.54887i	−1.76131	+	0.0683842i
$514$	15.0745	−	7.82122i	0.664909	−	0.344979i
$515$	−6.09683	−	14.7191i	−0.268658	−	0.648599i
$516$	12.4508	+	26.0042i	0.548115	+	1.14477i
$517$	−37.8542	−	15.6797i	−1.66483	−	0.689593i
$518$	−13.0059	−	10.9434i	−0.571444	−	0.480827i
$519$	−19.7053	+	5.55418i	−0.864967	+	0.243802i
$520$	2.64589	−	19.4819i	0.116030	−	0.854338i
$521$	−3.26838	−	3.26838i	−0.143190	−	0.143190i	0.631878	−	0.775068i	$-0.282284\pi$
$521$	−3.26838	−	3.26838i	−0.143190	−	0.143190i	−0.775068	+	0.631878i	$0.782284\pi$
$522$	1.78898	+	2.42614i	0.0783015	+	0.106189i
$523$	−7.75530	−	3.21235i	−0.339116	−	0.140466i	0.206626	−	0.978420i	$-0.433752\pi$
$523$	−7.75530	−	3.21235i	−0.339116	−	0.140466i	−0.545741	+	0.837954i	$0.683752\pi$
$524$	−25.9456	−	5.82621i	−1.13344	−	0.254519i
$525$	0.555129	−	4.68406i	0.0242278	−	0.204429i
$526$	−10.4449	+	32.9704i	−0.455420	+	1.43758i
$527$		−	7.70325i		−	0.335559i
$528$	−3.74086	+	22.1854i	−0.162800	+	0.965496i
$529$		−	21.0910i		−	0.917000i
$530$	−12.9864	−	4.11405i	−0.564093	−	0.178703i
$531$	22.8096	+	16.5829i	0.989852	+	0.719637i
$532$	−12.9822	+	8.22096i	−0.562852	+	0.356424i
$533$	−23.1287	−	9.58024i	−1.00182	−	0.414966i
$534$	0.733938	−	1.62270i	0.0317606	−	0.0702213i
$535$	5.90966	+	5.90966i	0.255497	+	0.255497i
$536$	9.40602	−	2.47918i	0.406278	−	0.107084i
$537$	−4.70717	−	16.7002i	−0.203129	−	0.720668i
$538$	−19.6890	+	23.3997i	−0.848855	+	1.00883i
$539$	3.00020	+	1.24272i	0.129228	+	0.0535278i
$540$	−15.3343	+	3.27824i	−0.659882	+	0.141073i
$541$	−8.02742	−	19.3799i	−0.345126	−	0.833207i	−0.997181	−	0.0750358i	$-0.976093\pi$
$541$	−8.02742	−	19.3799i	−0.345126	−	0.833207i	0.652055	−	0.758172i	$-0.273907\pi$
$542$	−0.0396300	−	0.0763823i	−0.00170225	−	0.00328090i
$543$	−0.871634	−	0.488316i	−0.0374054	−	0.0209556i
$544$	−9.28017	+	9.99005i	−0.397884	+	0.428320i
$545$		−	6.79119i		−	0.290903i
$546$	0.361714	−	11.2785i	0.0154799	−	0.482676i
$547$	−1.69275	+	0.701161i	−0.0723769	+	0.0299795i	−0.418578	−	0.908181i	$-0.637471\pi$
$547$	−1.69275	+	0.701161i	−0.0723769	+	0.0299795i	0.346201	+	0.938160i	$0.387471\pi$
$548$	−5.34075	+	0.926721i	−0.228145	+	0.0395875i
$549$	−5.21298	−	32.9794i	−0.222485	−	1.40753i
$550$	9.56966	+	8.05214i	0.408052	+	0.343345i
$551$	−3.86001	−	3.86001i	−0.164442	−	0.164442i
$552$	16.5135	+	28.0266i	0.702862	+	1.19289i
$553$	5.69426	−	5.69426i	0.242144	−	0.242144i
$554$	5.26595	−	0.453483i	0.223729	−	0.0192666i
$555$	19.4426	+	24.6707i	0.825294	+	1.04721i
$556$	23.4120	−	14.8256i	0.992891	−	0.628745i
$557$	−2.00137	−	4.83173i	−0.0848007	−	0.204727i	0.875791	−	0.482691i	$-0.160341\pi$
$557$	−2.00137	−	4.83173i	−0.0848007	−	0.204727i	−0.960592	+	0.277964i	$0.910341\pi$
$558$	13.1614	−	3.25816i	0.557168	−	0.137929i
$559$	38.3417			1.62168
$560$	−4.47202	+	4.05324i	−0.188977	+	0.171281i
$561$	−11.8280	−	6.62641i	−0.499380	−	0.279767i
$562$	31.4166	+	9.95270i	1.32523	+	0.419829i
$563$	30.1426	−	12.4855i	1.27036	−	0.526199i	0.357285	−	0.933995i	$-0.383703\pi$
$563$	30.1426	−	12.4855i	1.27036	−	0.526199i	0.913073	+	0.407796i	$0.133703\pi$
$564$	29.1977	−	32.5243i	1.22945	−	1.36952i
$565$	2.52240	−	6.08962i	0.106118	−	0.256192i
$566$	3.69781	−	0.318441i	0.155430	−	0.0133851i
$567$	−8.56123	+	2.77586i	−0.359538	+	0.116575i
$568$	−18.6622	−	24.5279i	−0.783048	−	1.02917i
$569$	−22.0058	+	22.0058i	−0.922533	+	0.922533i	−0.997208	−	0.0746750i	$-0.976208\pi$
$569$	−22.0058	+	22.0058i	−0.922533	+	0.922533i	0.0746750	+	0.997208i	$0.476208\pi$
$570$	26.5702	−	10.0205i	1.11290	−	0.419711i
$571$	15.3220	−	36.9906i	0.641207	−	1.54801i	−0.183846	−	0.982955i	$-0.558855\pi$
$571$	15.3220	−	36.9906i	0.641207	−	1.54801i	0.825053	−	0.565055i	$-0.191145\pi$
$572$	24.4623	+	17.2282i	1.02282	+	0.720347i
$573$	0.473260	−	3.99327i	0.0197707	−	0.166821i
$574$	3.53932	+	6.82164i	0.147728	+	0.284730i
$575$	18.0828			0.754104
$576$	−20.9937	−	11.6303i	−0.874738	−	0.484596i
$577$	1.66169			0.0691771			0.0345885	−	0.999402i	$-0.488988\pi$
$577$	1.66169			0.0691771			0.0345885	+	0.999402i	$0.488988\pi$
$578$	7.28801	+	14.0468i	0.303141	+	0.584271i
$579$	0.622145	−	5.24953i	0.0258555	−	0.218163i
$580$	−1.75301	−	1.23460i	−0.0727897	−	0.0512640i
$581$	−2.57352	+	6.21303i	−0.106768	+	0.257760i
$582$	29.2610	−	11.0353i	1.21291	−	0.457428i
$583$	14.6590	−	14.6590i	0.607114	−	0.607114i
$584$	−19.9905	+	15.2098i	−0.827211	+	0.629387i
$585$	−4.87439	+	20.2757i	−0.201531	+	0.838297i
$586$	21.3033	−	1.83456i	0.880031	−	0.0757848i
$587$	−11.6291	+	28.0751i	−0.479984	+	1.15878i	0.479632	+	0.877470i	$0.340770\pi$
$587$	−11.6291	+	28.0751i	−0.479984	+	1.15878i	−0.959616	+	0.281314i	$0.909230\pi$
$588$	−2.31411	+	2.57777i	−0.0954324	+	0.106305i
$589$	−22.6849	+	9.39639i	−0.934715	+	0.387172i
$590$	−19.1223	−	6.05788i	−0.787252	−	0.249399i
$591$	−10.5893	−	5.93242i	−0.435584	−	0.244027i
$592$	−2.35874	+	48.0180i	−0.0969435	+	1.97353i
$593$	−11.7539			−0.482675			−0.241338	−	0.970441i	$-0.577586\pi$
$593$	−11.7539			−0.482675			−0.241338	+	0.970441i	$0.577586\pi$
$594$	6.31883	−	23.0116i	0.259265	−	0.944176i
$595$	−1.39183	−	3.36018i	−0.0570596	−	0.137754i
$596$	12.2511	−	7.75796i	0.501824	−	0.317779i
$597$	−5.11431	−	6.48954i	−0.209315	−	0.265599i
$598$	43.1008	−	3.71167i	1.76252	−	0.151781i
$599$	8.03416	−	8.03416i	0.328267	−	0.328267i	−0.523660	−	0.851927i	$-0.675434\pi$
$599$	8.03416	−	8.03416i	0.328267	−	0.328267i	0.851927	+	0.523660i	$0.175434\pi$
$600$	−11.4944	+	6.77259i	−0.469256	+	0.276490i
$601$	−3.33987	−	3.33987i	−0.136236	−	0.136236i	0.635700	−	0.771936i	$-0.280712\pi$
$601$	−3.33987	−	3.33987i	−0.136236	−	0.136236i	−0.771936	+	0.635700i	$0.780712\pi$
$602$	−9.00626	−	7.57808i	−0.367068	−	0.308860i
$603$	−10.1908	+	1.61083i	−0.415001	+	0.0655982i
$604$	40.2991	−	6.99266i	1.63975	−	0.284527i
$605$	−0.633526	+	0.262415i	−0.0257565	+	0.0106687i
$606$	−0.356891	+	11.1281i	−0.0144977	+	0.452049i
$607$			8.22852i			0.333985i	0.985958	+	0.166993i	$0.0534056\pi$
$607$			8.22852i			0.333985i	−0.985958	+	0.166993i	$0.946594\pi$
$608$	40.7391	+	15.1429i	1.65219	+	0.614125i
$609$	−1.07362	−	0.601474i	−0.0435053	−	0.0243730i
$610$	10.9375	+	21.0809i	0.442847	+	0.853539i
$611$	−22.2435	−	53.7006i	−0.899876	−	2.17249i
$612$	10.8608	−	9.55022i	0.439021	−	0.386045i
$613$	10.3513	+	4.28766i	0.418086	+	0.173177i	0.581802	−	0.813331i	$-0.302348\pi$
$613$	10.3513	+	4.28766i	0.418086	+	0.173177i	−0.163716	+	0.986508i	$0.552348\pi$
$614$	1.99600	−	2.37217i	0.0805519	−	0.0957329i
$615$	−3.85292	−	13.6695i	−0.155365	−	0.551208i
$616$	−2.34098	−	8.88168i	−0.0943206	−	0.357853i
$617$	−10.0775	−	10.0775i	−0.405705	−	0.405705i	0.474533	−	0.880238i	$-0.342617\pi$
$617$	−10.0775	−	10.0775i	−0.405705	−	0.405705i	−0.880238	+	0.474533i	$0.842617\pi$
$618$	−10.6583	+	23.5650i	−0.428740	+	0.947925i
$619$	−27.9068	−	11.5594i	−1.12167	−	0.464610i	−0.256727	−	0.966484i	$-0.582644\pi$
$619$	−27.9068	−	11.5594i	−1.12167	−	0.464610i	−0.864941	+	0.501874i	$0.832644\pi$
$620$	−8.14797	+	5.15967i	−0.327230	+	0.207217i
$621$	−14.4305	−	31.3404i	−0.579076	−	1.25765i
$622$	39.1688	+	12.4086i	1.57053	+	0.497538i
$623$			0.727076i			0.0291297i
$624$	−26.0070	+	18.5020i	−1.04111	+	0.740671i
$625$		−	3.96747i		−	0.158699i
$626$	−10.4092	+	32.8575i	−0.416034	+	1.31325i
$627$	−5.08600	+	42.9146i	−0.203115	+	1.71385i
$628$	−32.7950	−	7.36429i	−1.30866	−	0.293867i
$629$	−26.7654	−	11.0866i	−1.06721	−	0.442051i
$630$	5.15237	−	3.79924i	0.205275	−	0.151365i
$631$	3.58893	+	3.58893i	0.142873	+	0.142873i	0.774926	−	0.632053i	$-0.217787\pi$
$631$	3.58893	+	3.58893i	0.142873	+	0.142873i	−0.632053	+	0.774926i	$0.717787\pi$
$632$	−22.5698	−	3.06527i	−0.897780	−	0.121930i
$633$	6.45618	−	1.81975i	0.256610	−	0.0723287i
$634$	−13.7746	−	11.5902i	−0.547058	−	0.460307i
$635$	−3.88805	−	1.61048i	−0.154293	−	0.0639101i
$636$	9.55012	+	19.9460i	0.378687	+	0.790910i
$637$	1.76295	+	4.25613i	0.0698504	+	0.168634i
$638$	2.89634	−	1.50273i	0.114667	−	0.0594937i
$639$	17.0718	+	27.8781i	0.675352	+	1.10284i
$640$	16.7827	+	3.12455i	0.663394	+	0.123509i
$641$		−	26.1158i		−	1.03151i	−0.856736	−	0.515756i	$-0.827511\pi$
$641$		−	26.1158i		−	1.03151i	0.856736	−	0.515756i	$-0.172489\pi$
$642$	0.434899	−	13.5605i	0.0171641	−	0.535188i
$643$	−18.9931	+	7.86718i	−0.749013	+	0.310251i	−0.724339	−	0.689444i	$-0.757855\pi$
$643$	−18.9931	+	7.86718i	−0.749013	+	0.310251i	−0.0246743	+	0.999696i	$0.507855\pi$
$644$	−10.8577	−	7.64683i	−0.427854	−	0.301327i
$645$	13.4636	+	17.0839i	0.530128	+	0.672678i
$646$	−16.8623	+	20.0402i	−0.663439	+	0.788471i
$647$	14.3609	+	14.3609i	0.564584	+	0.564584i	0.930606	−	0.366022i	$-0.119281\pi$
$647$	14.3609	+	14.3609i	0.564584	+	0.564584i	−0.366022	+	0.930606i	$0.619281\pi$
$648$	20.9108	+	14.5169i	0.821452	+	0.570278i
$649$	21.5852	−	21.5852i	0.847292	−	0.847292i
$650$	1.52224	+	17.6767i	0.0597073	+	0.693336i
$651$	−4.34751	+	3.42622i	−0.170393	+	0.134284i
$652$	−10.9102	+	48.5857i	−0.427275	+	1.90276i
$653$	17.3268	+	41.8306i	0.678051	+	1.63696i	0.767563	+	0.640973i	$0.221469\pi$
$653$	17.3268	+	41.8306i	0.678051	+	1.63696i	−0.0895124	+	0.995986i	$0.528531\pi$
$654$	−8.04150	+	7.54173i	−0.314448	+	0.294905i
$655$	−20.0619			−0.783883
$656$	9.29362	−	19.6500i	0.362855	−	0.767202i
$657$	22.7208	−	13.9137i	0.886424	−	0.542825i
$658$	−5.38881	+	17.0103i	−0.210078	+	0.663130i
$659$	5.34798	−	2.21521i	0.208328	−	0.0862921i	−0.276080	−	0.961135i	$-0.589035\pi$
$659$	5.34798	−	2.21521i	0.208328	−	0.0862921i	0.484407	+	0.874843i	$0.339035\pi$
$660$	0.913500	+	16.9493i	0.0355580	+	0.659750i
$661$	−9.07706	+	21.9140i	−0.353057	+	0.852354i	0.643183	+	0.765713i	$0.277614\pi$
$661$	−9.07706	+	21.9140i	−0.353057	+	0.852354i	−0.996240	+	0.0866417i	$0.972386\pi$
$662$	−0.0323690	−	0.375876i	−0.00125806	−	0.0146088i
$663$	−5.21780	−	18.5119i	−0.202643	−	0.718942i
$664$	18.3928	−	4.84787i	0.713780	−	0.188134i
$665$	−8.19747	+	8.19747i	−0.317884	+	0.317884i
$666$	7.62140	−	50.4194i	0.295323	−	1.95371i
$667$	1.80542	−	4.35868i	0.0699063	−	0.168769i
$668$	9.01540	−	1.56434i	0.348816	−	0.0605262i
$669$	−28.6962	−	3.40092i	−1.10946	−	0.131487i
$670$	6.51407	−	3.37974i	0.251661	−	0.130571i
$671$	−36.1423			−1.39526
$672$	9.76572	+	0.794160i	0.376721	+	0.0306354i
$673$	28.8991			1.11398			0.556990	−	0.830520i	$-0.311956\pi$
$673$	28.8991			1.11398			0.556990	+	0.830520i	$0.311956\pi$
$674$	−20.7646	+	10.7734i	−0.799822	+	0.414977i
$675$	12.8534	−	5.91829i	0.494729	−	0.227795i
$676$	2.81154	+	16.2031i	0.108136	+	0.623195i
$677$	−12.7981	+	30.8974i	−0.491872	+	1.18748i	0.461894	+	0.886935i	$0.347170\pi$
$677$	−12.7981	+	30.8974i	−0.491872	+	1.18748i	−0.953766	+	0.300549i	$0.902830\pi$
$678$	−10.0119	+	3.77583i	−0.384506	+	0.145010i
$679$	−9.02767	+	9.02767i	−0.346450	+	0.346450i
$680$	−5.17991	+	8.88778i	−0.198640	+	0.340831i
$681$	2.11286	−	0.595534i	0.0809648	−	0.0228209i
$682$	−1.25925	−	14.6227i	−0.0482192	−	0.559932i
$683$	−19.0288	+	45.9396i	−0.728118	+	1.75783i	−0.0793475	+	0.996847i	$0.525284\pi$
$683$	−19.0288	+	45.9396i	−0.728118	+	1.75783i	−0.648770	+	0.760984i	$0.724716\pi$
$684$	−41.3719	−	20.3340i	−1.58189	−	0.777491i
$685$	−3.77820	+	1.56498i	−0.144358	+	0.0597949i
$686$	0.427099	−	1.34818i	0.0163067	−	0.0514737i
$687$	5.67659	−	10.1326i	0.216575	−	0.386583i
$688$	−1.63337	+	33.2513i	−0.0622717	+	1.26770i
$689$	29.4093			1.12040
$690$	16.7885	+	17.9010i	0.639127	+	0.681481i
$691$	−9.72882	−	23.4875i	−0.370102	−	0.893505i	−0.993732	−	0.111786i	$-0.964343\pi$
$691$	−9.72882	−	23.4875i	−0.370102	−	0.893505i	0.623631	−	0.781719i	$-0.285657\pi$
$692$	−23.0659	−	5.17956i	−0.876834	−	0.196897i
$693$	1.52104	+	9.62270i	0.0577794	+	0.365536i
$694$	−2.99541	−	34.7834i	−0.113704	−	1.32036i
$695$	14.7832	−	14.7832i	0.560760	−	0.560760i
$696$	0.484844	+	3.44679i	0.0183779	+	0.130650i
$697$	9.26219	+	9.26219i	0.350830	+	0.350830i
$698$	−12.1494	+	14.4391i	−0.459860	+	0.546526i
$699$	−33.9935	+	26.7898i	−1.28575	+	1.01328i
$700$	3.13615	−	4.45301i	0.118535	−	0.168308i
$701$	23.8340	−	9.87237i	0.900198	−	0.372874i	0.115902	−	0.993261i	$-0.463024\pi$
$701$	23.8340	−	9.87237i	0.900198	−	0.372874i	0.784296	+	0.620386i	$0.213024\pi$
$702$	29.4217	−	16.7447i	1.11045	−	0.631987i
$703$			92.3434i			3.48280i
$704$	−15.9830	+	20.4807i	−0.602383	+	0.771894i
$705$	16.1166	−	28.7678i	0.606986	−	1.08346i
$706$	−3.29821	+	1.71123i	−0.124130	+	0.0644030i
$707$	−1.73944	−	4.19938i	−0.0654184	−	0.157934i
$708$	14.0624	+	29.3702i	0.528498	+	1.10380i
$709$	−19.1954	−	7.95098i	−0.720897	−	0.298605i	−0.00809180	−	0.999967i	$-0.502576\pi$
$709$	−19.1954	−	7.95098i	−0.720897	−	0.298605i	−0.712805	+	0.701362i	$0.752576\pi$
$710$	−17.7918	−	14.9705i	−0.667716	−	0.561832i
$711$	23.4894	+	5.64699i	0.880923	+	0.211779i
$712$	1.63662	−	1.24523i	0.0613349	−	0.0466669i
$713$	−15.0052	−	15.0052i	−0.561950	−	0.561950i
$714$	−2.43316	+	5.37961i	−0.0910588	+	0.201327i
$715$	20.8548	+	8.63832i	0.779923	+	0.323055i
$716$	4.38968	−	19.5483i	0.164050	−	0.730556i
$717$	1.68321	+	0.199485i	0.0628606	+	0.00744989i
$718$	3.47872	−	10.9809i	0.129825	−	0.409803i
$719$		−	7.21269i		−	0.268988i	−0.990914	−	0.134494i	$-0.957059\pi$
$719$		−	7.21269i		−	0.268988i	0.990914	−	0.134494i	$-0.0429409\pi$
$720$	−17.3762	−	5.09100i	−0.647571	−	0.189730i
$721$		−	10.5587i		−	0.393225i
$722$	53.9686	+	17.0971i	2.00850	+	0.636288i
$723$	33.8929	+	4.01680i	1.26049	+	0.149386i
$724$	−0.617208	−	0.974672i	−0.0229383	−	0.0362234i
$725$	1.78760	+	0.740448i	0.0663898	+	0.0274995i
$726$	1.01427	+	0.458747i	0.0376431	+	0.0170257i
$727$	12.3061	+	12.3061i	0.456409	+	0.456409i	0.897475	−	0.441066i	$-0.145399\pi$
$727$	12.3061	+	12.3061i	0.456409	+	0.456409i	−0.441066	+	0.897475i	$0.645399\pi$
$728$	6.56106	−	11.2576i	0.243169	−	0.417234i
$729$	−20.5147	−	17.5541i	−0.759804	−	0.650153i
$730$	−12.2011	+	14.5005i	−0.451582	+	0.536687i
$731$	−18.5344	−	7.67721i	−0.685521	−	0.283952i
$732$	12.8157	−	36.3618i	0.473682	−	1.34397i
$733$	6.64683	+	16.0469i	0.245506	+	0.592704i	0.997812	−	0.0661094i	$-0.0210586\pi$
$733$	6.64683	+	16.0469i	0.245506	+	0.592704i	−0.752306	+	0.658814i	$0.771059\pi$
$734$	9.66948	+	18.6368i	0.356907	+	0.687899i
$735$	−1.27735	+	2.28004i	−0.0471156	+	0.0841005i
$736$	1.38279	+	37.5367i	0.0509701	+	1.38362i
$737$			11.1681i			0.411383i
$738$	−11.9074	+	19.7425i	−0.438319	+	0.726732i
$739$	−3.04746	+	1.26230i	−0.112102	+	0.0464344i	−0.438030	−	0.898960i	$-0.644324\pi$
$739$	−3.04746	+	1.26230i	−0.112102	+	0.0464344i	0.325927	+	0.945395i	$0.394324\pi$
$740$	6.20095	+	35.7365i	0.227952	+	1.31370i
$741$	−48.1500	+	37.9464i	−1.76884	+	1.39399i
$742$	−6.90807	−	5.81261i	−0.253603	−	0.213388i
$743$	−9.98615	−	9.98615i	−0.366356	−	0.366356i	0.499790	−	0.866146i	$-0.333410\pi$
$743$	−9.98615	−	9.98615i	−0.366356	−	0.366356i	−0.866146	+	0.499790i	$0.833410\pi$
$744$	15.1581	+	3.91817i	0.555721	+	0.143647i
$745$	7.73580	−	7.73580i	0.283418	−	0.283418i
$746$	1.10269	−	0.0949591i	0.0403723	−	0.00347670i
$747$	−19.9274	+	3.14988i	−0.729105	+	0.115248i
$748$	−8.37547	−	13.2262i	−0.306238	−	0.483599i
$749$	2.11964	+	5.11726i	0.0774499	+	0.186980i
$750$	−20.8211	+	19.5271i	−0.760280	+	0.713029i
$751$	18.0083			0.657131			0.328566	−	0.944481i	$-0.393435\pi$
$751$	18.0083			0.657131			0.328566	+	0.944481i	$0.393435\pi$
$752$	47.5187	−	17.0027i	1.73283	−	0.620025i
$753$	−12.8155	+	22.8754i	−0.467022	+	0.833626i
$754$	4.41277	+	1.39795i	0.160704	+	0.0509104i
$755$	28.5088	−	11.8087i	1.03754	−	0.429763i
$756$	−10.2205	−	1.88184i	−0.371716	−	0.0684418i
$757$	5.65649	−	13.6560i	0.205589	−	0.496335i	−0.787131	−	0.616786i	$-0.788434\pi$
$757$	5.65649	−	13.6560i	0.205589	−	0.496335i	0.992719	+	0.120452i	$0.0384342\pi$
$758$	20.2444	−	1.74337i	0.735309	−	0.0633219i
$759$	−35.9476	+	10.1323i	−1.30481	+	0.367778i
$760$	32.4916	+	4.41277i	1.17859	+	0.160068i
$761$	16.8369	−	16.8369i	0.610336	−	0.610336i	−0.332698	−	0.943034i	$-0.607959\pi$
$761$	16.8369	−	16.8369i	0.610336	−	0.610336i	0.943034	+	0.332698i	$0.107959\pi$
$762$	2.41076	+	6.39233i	0.0873325	+	0.231570i
$763$	1.72238	−	4.15820i	0.0623545	−	0.150537i
$764$	2.67364	−	3.79630i	0.0967289	−	0.137345i
$765$	6.41611	−	8.82528i	0.231975	−	0.319079i
$766$	−8.43212	−	16.2520i	−0.304665	−	0.587207i
$767$	43.3047			1.56364
$768$	−14.9377	−	23.3424i	−0.539016	−	0.842295i
$769$	22.6717			0.817562			0.408781	−	0.912632i	$-0.365954\pi$
$769$	22.6717			0.817562			0.408781	+	0.912632i	$0.365954\pi$
$770$	−3.19134	−	6.15094i	−0.115008	−	0.221665i
$771$	−20.6550	−	2.44791i	−0.743870	−	0.0881594i
$772$	3.51475	−	4.99059i	0.126499	−	0.179615i
$773$	16.4379	−	39.6847i	0.591231	−	1.42736i	−0.291084	−	0.956698i	$-0.594016\pi$
$773$	16.4379	−	39.6847i	0.591231	−	1.42736i	0.882315	−	0.470660i	$-0.155984\pi$
$774$	5.27765	−	34.9143i	0.189701	−	1.25497i
$775$	6.15401	−	6.15401i	0.221058	−	0.221058i
$776$	35.7822	+	4.85967i	1.28451	+	0.174452i
$777$	5.64760	+	20.0367i	0.202607	+	0.718814i
$778$	23.6954	−	2.04055i	0.849520	−	0.0731573i
$779$	15.9778	−	38.5737i	0.572463	−	1.38205i
$780$	−16.0857	+	17.9184i	−0.575960	+	0.641581i
$781$	32.6921	−	13.5415i	1.16982	−	0.484554i
$782$	−21.5781	−	6.83589i	−0.771632	−	0.244451i
$783$	−0.143232	−	3.68909i	−0.00511869	−	0.131837i
$784$	−3.76617	+	1.34758i	−0.134506	+	0.0481278i
$785$	−25.3581			−0.905069
$786$	22.2791	+	23.7554i	0.794668	+	0.847328i
$787$	−18.3786	−	44.3698i	−0.655125	−	1.58161i	−0.805243	−	0.592945i	$-0.797965\pi$
$787$	−18.3786	−	44.3698i	−0.655125	−	1.58161i	0.150118	−	0.988668i	$-0.452035\pi$
$788$	−7.49829	−	11.8410i	−0.267116	−	0.421820i
$789$	33.2686	−	26.2185i	1.18439	−	0.933405i
$790$	−17.1206	+	1.47436i	−0.609123	+	0.0524553i
$791$	3.08890	−	3.08890i	0.109829	−	0.109829i
$792$	19.0553	−	19.9041i	0.677101	−	0.707262i
$793$	−36.2548	−	36.2548i	−1.28744	−	1.28744i
$794$	4.83363	+	4.06713i	0.171539	+	0.144337i
$795$	10.3270	+	13.1039i	0.366260	+	0.464746i
$796$	−1.63114	−	9.40034i	−0.0578141	−	0.333186i
$797$	−2.68428	+	1.11187i	−0.0950821	+	0.0393843i	−0.429718	−	0.902963i	$-0.641387\pi$
$797$	−2.68428	+	1.11187i	−0.0950821	+	0.0393843i	0.334635	+	0.942348i	$0.391387\pi$
$798$	18.8101	+	0.603261i	0.665871	+	0.0213552i
$799$			30.4127i			1.07593i
$800$	−15.3947	+	0.567114i	−0.544284	+	0.0200505i
$801$	−1.86015	+	1.13911i	−0.0657253	+	0.0402486i
$802$	16.6774	+	32.1438i	0.588900	+	1.13504i
$803$	−11.0364	−	26.6443i	−0.389468	−	0.940258i
$804$	−11.2360	−	3.96010i	−0.396262	−	0.139662i
$805$	−9.25649	−	3.83416i	−0.326248	−	0.135137i
$806$	13.4050	−	15.9314i	0.472173	−	0.561159i
$807$	36.0494	−	10.1610i	1.26900	−	0.357683i
$808$	−6.47358	+	11.1075i	−0.227740	+	0.390760i
$809$	−35.8302	−	35.8302i	−1.25972	−	1.25972i	−0.951225	−	0.308499i	$-0.900173\pi$
$809$	−35.8302	−	35.8302i	−1.25972	−	1.25972i	−0.308499	−	0.951225i	$-0.599827\pi$
$810$	17.7922	+	7.22956i	0.625156	+	0.254021i
$811$	2.13586	+	0.884701i	0.0750001	+	0.0310660i	0.419868	−	0.907585i	$-0.362076\pi$
$811$	2.13586	+	0.884701i	0.0750001	+	0.0310660i	−0.344868	+	0.938651i	$0.612076\pi$
$812$	−0.760235	−	1.20054i	−0.0266790	−	0.0421306i
$813$	−0.0124035	+	0.104658i	−0.000435010	+	0.00367052i
$814$	−52.6198	−	16.6698i	−1.84432	−	0.584276i
$815$			37.5679i			1.31595i
$816$	16.2765	−	3.73646i	0.569790	−	0.130802i
$817$			63.9457i			2.23718i
$818$	2.61289	−	8.24782i	0.0913574	−	0.288378i
$819$	−8.12688	+	11.1784i	−0.283976	+	0.390606i
$820$	3.59305	−	16.0008i	0.125475	−	0.558771i
$821$	15.8043	+	6.54636i	0.551575	+	0.228470i	0.641023	−	0.767522i	$-0.278510\pi$
$821$	15.8043	+	6.54636i	0.551575	+	0.228470i	−0.0894483	+	0.995991i	$0.528510\pi$
$822$	6.04886	+	2.73586i	0.210978	+	0.0954239i
$823$	23.2382	+	23.2382i	0.810033	+	0.810033i	0.984638	−	0.174606i	$-0.0558651\pi$
$823$	23.2382	+	23.2382i	0.810033	+	0.810033i	−0.174606	+	0.984638i	$0.555865\pi$
$824$	−23.7671	+	18.0833i	−0.827967	+	0.629962i
$825$	−4.15549	−	14.7430i	−0.144676	−	0.513284i
$826$	−10.1720	−	8.55899i	−0.353930	−	0.297806i
$827$	−44.5536	−	18.4547i	−1.54928	−	0.641732i	−0.566094	−	0.824341i	$-0.691546\pi$
$827$	−44.5536	−	18.4547i	−1.54928	−	0.641732i	−0.983186	+	0.182608i	$0.941546\pi$
$828$	2.55284	−	39.7588i	0.0887173	−	1.38171i
$829$	2.08869	+	5.04254i	0.0725432	+	0.175135i	0.955992	−	0.293393i	$-0.0947845\pi$
$829$	2.08869	+	5.04254i	0.0725432	+	0.175135i	−0.883449	+	0.468528i	$0.844785\pi$
$830$	12.7378	−	6.60886i	0.442137	−	0.229397i
$831$	−5.64745	−	3.16387i	−0.195908	−	0.109754i
$832$	−36.5772	+	4.51164i	−1.26809	+	0.156413i
$833$		−	2.41041i		−	0.0835158i
$834$	−33.9219	−	1.08791i	−1.17462	−	0.0376714i
$835$	6.37775	−	2.64175i	0.220711	−	0.0914216i
$836$	−28.7329	+	40.7978i	−0.993749	+	1.41102i
$837$	−15.5769	−	5.75483i	−0.538417	−	0.198916i
$838$	14.6376	−	17.3962i	0.505647	−	0.600942i
$839$	9.57161	+	9.57161i	0.330449	+	0.330449i	0.852757	−	0.522308i	$-0.174929\pi$
$839$	9.57161	+	9.57161i	0.330449	+	0.330449i	−0.522308	+	0.852757i	$0.674929\pi$
$840$	7.31993	−	1.02966i	0.252562	−	0.0355266i
$841$	−20.1491	+	20.1491i	−0.694798	+	0.694798i
$842$	0.602112	+	6.99187i	0.0207502	+	0.240956i
$843$	−24.9830	−	31.7008i	−0.860459	−	1.09183i
$844$	7.55723	+	1.69701i	0.260131	+	0.0584136i
$845$	4.74793	+	11.4625i	0.163334	+	0.394323i
$846$	−51.9619	+	12.8633i	−1.78649	+	0.442251i
$847$	−0.454458			−0.0156154
$848$	−1.25285	+	25.5048i	−0.0430229	+	0.875838i
$849$	−3.96570	−	2.22171i	−0.136103	−	0.0762487i
$850$	2.80356	−	8.84971i	0.0961615	−	0.303543i
$851$	−73.7322	+	30.5409i	−2.52751	+	1.04693i
$852$	2.03148	+	37.6924i	0.0695972	+	1.29132i
$853$	14.3935	−	34.7489i	0.492823	−	1.18978i	−0.460455	−	0.887683i	$-0.652314\pi$
$853$	14.3935	−	34.7489i	0.492823	−	1.18978i	0.953277	−	0.302096i	$-0.0976864\pi$
$854$	1.35044	+	15.6816i	0.0462112	+	0.536615i
$855$	−33.8155	−	8.12943i	−1.15646	−	0.278021i
$856$	7.88854	−	13.5353i	0.269625	−	0.462627i
$857$	−24.3573	+	24.3573i	−0.832029	+	0.832029i	−0.987794	−	0.155765i	$-0.950216\pi$
$857$	−24.3573	+	24.3573i	−0.832029	+	0.832029i	0.155765	+	0.987794i	$0.450216\pi$
$858$	−12.9308	−	34.2873i	−0.441452	−	1.17055i
$859$	−16.8229	+	40.6142i	−0.573991	+	1.38574i	0.324140	+	0.946009i	$0.394925\pi$
$859$	−16.8229	+	40.6142i	−0.573991	+	1.38574i	−0.898131	+	0.439728i	$0.855075\pi$
$860$	4.29402	+	24.7467i	0.146425	+	0.843855i
$861$	1.10775	−	9.34693i	0.0377519	−	0.318543i
$862$	−38.8370	+	20.1501i	−1.32279	+	0.686314i
$863$	1.31939			0.0449125			0.0224563	−	0.999748i	$-0.492851\pi$
$863$	1.31939			0.0449125			0.0224563	+	0.999748i	$0.492851\pi$
$864$	13.2682	+	26.2289i	0.451394	+	0.892325i
$865$	−17.8352			−0.606416
$866$	10.6450	−	5.52302i	0.361732	−	0.187680i
$867$	2.28102	−	19.2468i	0.0774677	−	0.653656i
$868$	−6.29754	+	1.09274i	−0.213752	+	0.0370901i
$869$	10.0075	−	24.1603i	0.339482	−	0.819581i
$870$	0.926645	+	2.45708i	0.0314162	+	0.0833028i
$871$	−11.2029	+	11.2029i	−0.379595	+	0.379595i
$872$	−12.3098	+	3.24453i	−0.416862	+	0.109874i
$873$	−37.2401	−	8.95274i	−1.26039	−	0.303004i
$874$	6.19026	+	71.8827i	0.209389	+	2.43147i
$875$	4.45961	−	10.7664i	0.150762	−	0.363972i
$876$	30.7196	−	1.65567i	1.03792	−	0.0559399i
$877$	−4.72811	+	1.95845i	−0.159657	+	0.0661320i	−0.461081	−	0.887358i	$-0.652538\pi$
$877$	−4.72811	+	1.95845i	−0.159657	+	0.0661320i	0.301424	+	0.953490i	$0.402538\pi$
$878$	−6.26590	+	19.7789i	−0.211464	+	0.667506i
$879$	−22.8467	−	12.7994i	−0.770599	−	0.431712i
$880$	−8.37988	+	17.7180i	−0.282486	+	0.597274i
$881$	4.33982			0.146212			0.0731060	−	0.997324i	$-0.476709\pi$
$881$	4.33982			0.146212			0.0731060	+	0.997324i	$0.476709\pi$
$882$	4.11833	−	1.01951i	0.138671	−	0.0343285i
$883$	−11.4648	−	27.6785i	−0.385822	−	0.931456i	−0.990815	−	0.135226i	$-0.956824\pi$
$883$	−11.4648	−	27.6785i	−0.385822	−	0.931456i	0.604993	−	0.796231i	$-0.293176\pi$
$884$	4.86587	−	21.6690i	0.163657	−	0.728806i
$885$	15.2063	+	19.2953i	0.511155	+	0.648603i
$886$	−4.27488	−	49.6409i	−0.143617	−	1.66772i
$887$	−9.15922	+	9.15922i	−0.307536	+	0.307536i	−0.843953	−	0.536417i	$-0.819778\pi$
$887$	−9.15922	+	9.15922i	−0.307536	+	0.307536i	0.536417	+	0.843953i	$0.319778\pi$
$888$	35.4295	−	47.0285i	1.18894	−	1.57817i
$889$	−1.97217	−	1.97217i	−0.0661446	−	0.0661446i
$890$	0.998900	−	1.18716i	0.0334832	−	0.0397935i
$891$	−22.2357	+	18.9674i	−0.744925	+	0.635430i
$892$	−27.2807	−	19.2132i	−0.913427	−	0.643304i
$893$	89.5609	−	37.0974i	2.99704	−	1.24142i
$894$	−17.7507	−	0.569286i	−0.593674	−	0.0190398i
$895$		−	15.1154i		−	0.505251i
$896$	9.48348	+	6.16957i	0.316821	+	0.206111i
$897$	−46.2233	−	25.8957i	−1.54335	−	0.864631i
$898$	28.7350	−	14.9088i	0.958900	−	0.497513i
$899$	−0.868934	−	2.09779i	−0.0289806	−	0.0699653i
$900$	16.3060	+	1.04698i	0.543534	+	0.0348994i
$901$	−14.2165	−	5.88865i	−0.473619	−	0.196179i
$902$	19.0961	+	16.0679i	0.635829	+	0.535002i
$903$	3.91084	+	13.8750i	0.130145	+	0.461731i
$904$	−12.2432	−	1.66278i	−0.407203	−	0.0553033i
$905$	−0.615444	−	0.615444i	−0.0204581	−	0.0204581i
$906$	−45.6423	−	20.6437i	−1.51636	−	0.685840i
$907$	45.1492	+	18.7014i	1.49915	+	0.620970i	0.973286	−	0.229595i	$-0.0737403\pi$
$907$	45.1492	+	18.7014i	1.49915	+	0.620970i	0.525869	+	0.850566i	$0.323740\pi$
$908$	2.47319	+	0.555367i	0.0820756	+	0.0184305i
$909$	8.01852	−	11.0294i	0.265958	−	0.365822i
$910$	2.96882	−	9.37136i	0.0984155	−	0.310658i
$911$			54.4120i			1.80275i	0.433039	+	0.901375i	$0.357441\pi$
$911$			54.4120i			1.80275i	−0.433039	+	0.901375i	$0.642559\pi$
$912$	−30.8573	−	43.3740i	−1.02179	−	1.43626i
$913$			21.8385i			0.722749i
$914$	−7.36201	−	2.33226i	−0.243513	−	0.0771444i
$915$	3.42326	−	28.8848i	0.113170	−	0.954901i
$916$	11.3304	−	7.17494i	0.374367	−	0.237067i
$917$	−12.2838	−	5.08810i	−0.405645	−	0.168024i
$918$	−17.5753	+	2.20326i	−0.580071	+	0.0727183i
$919$	−12.0655	−	12.0655i	−0.398003	−	0.398003i	0.479525	−	0.877528i	$-0.340809\pi$
$919$	−12.0655	−	12.0655i	−0.398003	−	0.398003i	−0.877528	+	0.479525i	$0.840809\pi$
$920$	7.22260	+	27.4026i	0.238122	+	0.903436i
$921$	−3.65455	+	1.03008i	−0.120421	+	0.0339423i
$922$	1.72079	−	2.04510i	0.0566713	−	0.0673517i
$923$	46.3775	+	19.2102i	1.52654	+	0.632312i
$924$	−3.73935	+	10.6096i	−0.123016	+	0.349030i
$925$	−12.5256	−	30.2394i	−0.411838	−	0.994264i
$926$	0.0751747	+	0.144891i	0.00247039	+	0.00476141i
$927$	27.0133	−	16.5423i	0.887233	−	0.543320i
$928$	−1.40034	+	3.76736i	−0.0459684	+	0.123670i
$929$		−	0.469624i		−	0.0154079i	−0.999970	−	0.00770394i	$-0.997548\pi$
$929$		−	0.469624i		−	0.0154079i	0.999970	−	0.00770394i	$-0.00245226\pi$
$930$	11.8057	+	0.378621i	0.387123	+	0.0124155i
$931$	−7.09830	+	2.94021i	−0.232637	+	0.0963616i
$932$	−49.2409	+	8.54423i	−1.61294	+	0.279875i
$933$	−31.1476	−	39.5231i	−1.01973	−	1.29393i
$934$	−21.0490	−	17.7111i	−0.688744	−	0.579526i
$935$	−8.35154	−	8.35154i	−0.273125	−	0.273125i
$936$	39.0807	−	0.851466i	1.27739	−	0.0278310i
$937$	9.25513	−	9.25513i	0.302352	−	0.302352i	−0.539581	−	0.841933i	$-0.681417\pi$
$937$	9.25513	−	9.25513i	0.302352	−	0.302352i	0.841933	+	0.539581i	$0.181417\pi$
$938$	4.84569	−	0.417292i	0.158217	−	0.0136251i
$939$	33.1547	−	26.1288i	1.08196	−	0.852681i
$940$	32.1685	−	20.3706i	1.04922	−	0.664416i
$941$	14.2190	+	34.3276i	0.463525	+	1.11905i	0.966940	+	0.255004i	$0.0820768\pi$
$941$	14.2190	+	34.3276i	0.463525	+	1.11905i	−0.503415	+	0.864045i	$0.667923\pi$
$942$	28.1606	+	30.0267i	0.917521	+	0.978323i
$943$	36.0838			1.17505
$944$	−1.84480	+	37.5554i	−0.0600430	+	1.22233i
$945$	−7.83449	+	0.304181i	−0.254856	+	0.00989500i
$946$	−36.4380	−	11.5435i	−1.18470	−	0.375310i
$947$	−4.87579	+	2.01962i	−0.158442	+	0.0656288i	−0.460495	−	0.887662i	$-0.652328\pi$
$947$	−4.87579	+	2.01962i	−0.158442	+	0.0656288i	0.302053	+	0.953291i	$0.402328\pi$
$948$	20.7585	+	18.6353i	0.674204	+	0.605247i
$949$	15.6565	−	37.7981i	0.508231	−	1.22698i
$950$	−29.4808	+	2.53877i	−0.956485	+	0.0823687i
$951$	5.98140	+	21.2210i	0.193960	+	0.688138i
$952$	−5.42574	+	4.12820i	−0.175849	+	0.133796i
$953$	27.9288	−	27.9288i	0.904703	−	0.904703i	−0.0911359	−	0.995838i	$-0.529050\pi$
$953$	27.9288	−	27.9288i	0.904703	−	0.904703i	0.995838	+	0.0911359i	$0.0290498\pi$
$954$	4.04811	−	26.7803i	0.131062	−	0.867044i
$955$	1.34058	−	3.23644i	0.0433801	−	0.104729i
$956$	1.60018	+	1.12697i	0.0517537	+	0.0364488i
$957$	−3.96854	−	0.470329i	−0.128285	−	0.0152036i
$958$	5.53000	+	10.6585i	0.178666	+	0.344359i
$959$	−2.71028			−0.0875194
$960$	−14.8542	−	14.7134i	−0.479418	−	0.474874i
$961$	20.7867			0.670539
$962$	−36.0619	−	69.5053i	−1.16268	−	2.24094i
$963$	−9.77117	+	13.4401i	−0.314871	+	0.433102i
$964$	32.2211	+	22.6925i	1.03777	+	0.730877i
$965$	1.76232	−	4.25461i	0.0567310	−	0.136961i
$966$	5.73942	+	15.2186i	0.184663	+	0.489650i
$967$	7.83222	−	7.83222i	0.251867	−	0.251867i	−0.569869	−	0.821736i	$-0.693006\pi$
$967$	7.83222	−	7.83222i	0.251867	−	0.251867i	0.821736	+	0.569869i	$0.193006\pi$
$968$	0.778328	+	1.02297i	0.0250164	+	0.0328794i
$969$	30.8738	−	8.70217i	0.991810	−	0.279554i
$970$	27.1430	−	2.33745i	0.871508	−	0.0750509i
$971$	−0.407943	+	0.984861i	−0.0130915	+	0.0316057i	−0.930290	−	0.366825i	$-0.880445\pi$
$971$	−0.407943	+	0.984861i	−0.0130915	+	0.0316057i	0.917199	+	0.398430i	$0.130445\pi$
$972$	−11.1980	−	29.0965i	−0.359176	−	0.933270i
$973$	12.8010	−	5.30235i	0.410381	−	0.169985i
$974$	9.95148	+	3.15260i	0.318866	+	0.101016i
$975$	10.6204	−	18.9573i	0.340126	−	0.607119i
$976$	32.9859	−	29.8970i	1.05585	−	0.956979i
$977$	−32.1300			−1.02793			−0.513965	−	0.857811i	$-0.671824\pi$
$977$	−32.1300			−1.02793			−0.513965	+	0.857811i	$0.671824\pi$
$978$	44.4844	−	41.7198i	1.42245	−	1.33405i
$979$	0.903553	+	2.18137i	0.0288777	+	0.0697169i
$980$	−2.54957	+	1.61451i	−0.0814430	+	0.0515735i
$981$	13.3368	−	2.10812i	0.425812	−	0.0673071i
$982$	−29.9692	+	2.58083i	−0.956355	+	0.0823576i
$983$	7.64708	−	7.64708i	0.243904	−	0.243904i	−0.574559	−	0.818463i	$-0.694826\pi$
$983$	7.64708	−	7.64708i	0.243904	−	0.243904i	0.818463	+	0.574559i	$0.194826\pi$
$984$	−22.9368	+	13.5146i	−0.731197	+	0.430828i
$985$	−7.47687	−	7.47687i	−0.238233	−	0.238233i
$986$	−1.85322	−	1.55935i	−0.0590186	−	0.0496597i
$987$	17.1642	−	13.5268i	0.546341	−	0.430564i
$988$	−69.7472	+	12.1025i	−2.21895	+	0.385031i
$989$	−51.0579	+	21.1489i	−1.62355	+	0.672495i
$990$	10.7367	−	17.8014i	0.341235	−	0.565767i
$991$			1.94449i			0.0617688i	0.999523	+	0.0308844i	$0.00983237\pi$
$991$			1.94449i			0.0617688i	−0.999523	+	0.0308844i	$0.990168\pi$
$992$	13.2452	+	12.3040i	0.420536	+	0.390653i
$993$	−0.225833	+	0.403107i	−0.00716659	+	0.0127922i
$994$	−7.09701	−	13.6787i	−0.225103	−	0.433862i
$995$	−2.75455	−	6.65008i	−0.0873252	−	0.210822i
$996$	−21.9712	−	7.74372i	−0.696183	−	0.245369i
$997$	26.1725	+	10.8410i	0.828891	+	0.343338i	0.756464	−	0.654036i	$-0.226925\pi$
$997$	26.1725	+	10.8410i	0.828891	+	0.343338i	0.0724275	+	0.997374i	$0.476925\pi$
$998$	37.7339	−	44.8453i	1.19445	−	1.41955i
$999$	−42.4140	+	45.8405i	−1.34192	+	1.45033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bs.a.155.17	✓	192
3.2	odd	2	inner	672.2.bs.a.155.32	yes	192
32.19	odd	8	inner	672.2.bs.a.659.32	yes	192
96.83	even	8	inner	672.2.bs.a.659.17	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bs.a.155.17	✓	192	1.1	even	1	trivial
672.2.bs.a.155.32	yes	192	3.2	odd	2	inner
672.2.bs.a.659.17	yes	192	96.83	even	8	inner
672.2.bs.a.659.32	yes	192	32.19	odd	8	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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bs (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.651302 - 1.25531i) q^{2} +(-0.203847 + 1.72001i) q^{3} +(-1.15161 + 1.63517i) q^{4} +(-0.577425 + 1.39403i) q^{5} +(2.29192 - 0.864357i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.80270 + 0.380642i) q^{8} +(-2.91689 - 0.701238i) q^{9} +O(q^{10})\)	\(q+(-0.651302 - 1.25531i) q^{2} +(-0.203847 + 1.72001i) q^{3} +(-1.15161 + 1.63517i) q^{4} +(-0.577425 + 1.39403i) q^{5} +(2.29192 - 0.864357i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.80270 + 0.380642i) q^{8} +(-2.91689 - 0.701238i) q^{9} +(2.12602 - 0.183084i) q^{10} +(-1.24272 + 3.00020i) q^{11} +(-2.57777 - 2.31411i) q^{12} +(-4.25613 + 1.76295i) q^{13} +(1.34818 + 0.427099i) q^{14} +(-2.28004 - 1.27735i) q^{15} +(-1.34758 - 3.76617i) q^{16} +2.41041 q^{17} +(1.01951 + 4.11833i) q^{18} +(-2.94021 - 7.09830i) q^{19} +(-1.61451 - 2.54957i) q^{20} +(-1.07209 - 1.36037i) q^{21} +(4.57557 - 0.394030i) q^{22} +(4.69526 - 4.69526i) q^{23} +(-1.22603 + 4.74308i) q^{24} +(1.92564 + 1.92564i) q^{25} +(4.98507 + 4.19455i) q^{26} +(1.80074 - 4.87415i) q^{27} +(-0.341929 - 1.97055i) q^{28} +(0.656417 - 0.271897i) q^{29} +(-0.118474 + 3.69410i) q^{30} -3.19582i q^{31} +(-3.85004 + 4.14454i) q^{32} +(-4.90706 - 2.74908i) q^{33} +(-1.56991 - 3.02582i) q^{34} +(-0.577425 - 1.39403i) q^{35} +(4.50577 - 3.96207i) q^{36} +(-11.1041 - 4.59946i) q^{37} +(-6.99561 + 8.31402i) q^{38} +(-2.16469 - 7.67997i) q^{39} +(-2.14897 + 3.68724i) q^{40} +(3.84257 + 3.84257i) q^{41} +(-1.00944 + 2.23182i) q^{42} +(-7.68932 - 3.18502i) q^{43} +(-3.47471 - 5.48713i) q^{44} +(2.66183 - 3.66132i) q^{45} +(-8.95205 - 2.83598i) q^{46} +12.6172i q^{47} +(6.75256 - 1.55013i) q^{48} -1.00000i q^{49} +(1.16311 - 3.67145i) q^{50} +(-0.491354 + 4.14594i) q^{51} +(2.01869 - 8.98973i) q^{52} +(-5.89794 - 2.44301i) q^{53} +(-7.29140 + 0.914058i) q^{54} +(-3.46478 - 3.46478i) q^{55} +(-2.25096 + 1.71265i) q^{56} +(12.8085 - 3.61024i) q^{57} +(-0.768840 - 0.646921i) q^{58} +(-8.68463 - 3.59729i) q^{59} +(4.71440 - 2.25725i) q^{60} +(4.25913 + 10.2824i) q^{61} +(-4.01175 + 2.08144i) q^{62} +(2.55840 - 1.56671i) q^{63} +(7.71022 + 2.13365i) q^{64} -6.95113i q^{65} +(-0.254977 + 7.95036i) q^{66} +(3.17732 - 1.31609i) q^{67} +(-2.77586 + 3.94144i) q^{68} +(7.11880 + 9.03303i) q^{69} +(-1.37386 + 1.63278i) q^{70} +(-7.70510 - 7.70510i) q^{71} +(-7.90825 - 3.07565i) q^{72} +(-6.27972 + 6.27972i) q^{73} +(1.45835 + 16.9347i) q^{74} +(-3.70466 + 2.91959i) q^{75} +(14.9929 + 3.36674i) q^{76} +(-1.24272 - 3.00020i) q^{77} +(-8.23088 + 7.71934i) q^{78} -8.05290 q^{79} +(6.02827 + 0.296120i) q^{80} +(8.01653 + 4.09087i) q^{81} +(2.32095 - 7.32630i) q^{82} +(6.21303 - 2.57352i) q^{83} +(3.45908 - 0.186431i) q^{84} +(-1.39183 + 3.36018i) q^{85} +(1.00987 + 11.7269i) q^{86} +(0.333858 + 1.18447i) q^{87} +(-4.62497 + 7.93561i) q^{88} +(0.514120 - 0.514120i) q^{89} +(-6.32975 - 0.956805i) q^{90} +(1.76295 - 4.25613i) q^{91} +(2.27044 + 13.0847i) q^{92} +(5.49686 + 0.651457i) q^{93} +(15.8386 - 8.21763i) q^{94} +11.5930 q^{95} +(-6.34385 - 7.46696i) q^{96} +12.7671 q^{97} +(-1.25531 + 0.651302i) q^{98} +(5.72874 - 7.87981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 16 q^{4}+O(q^{10}) \) 192 * q - 16 * q^4	\( 192 q - 16 q^{4} + 8 q^{10} + 16 q^{16} + 16 q^{22} + 24 q^{27} - 84 q^{30} + 40 q^{36} + 32 q^{37} + 24 q^{39} - 96 q^{46} - 72 q^{48} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 28 q^{60} - 16 q^{61} - 64 q^{64} - 12 q^{66} - 32 q^{67} + 56 q^{69} - 24 q^{70} + 60 q^{72} + 80 q^{75} - 56 q^{76} + 100 q^{78} - 32 q^{79} - 120 q^{82} - 56 q^{87} + 40 q^{88} + 60 q^{90} - 80 q^{93} + 216 q^{94} + 96 q^{96} - 64 q^{99}+O(q^{100}) \) 192 * q - 16 * q^4 + 8 * q^10 + 16 * q^16 + 16 * q^22 + 24 * q^27 - 84 * q^30 + 40 * q^36 + 32 * q^37 + 24 * q^39 - 96 * q^46 - 72 * q^48 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 28 * q^60 - 16 * q^61 - 64 * q^64 - 12 * q^66 - 32 * q^67 + 56 * q^69 - 24 * q^70 + 60 * q^72 + 80 * q^75 - 56 * q^76 + 100 * q^78 - 32 * q^79 - 120 * q^82 - 56 * q^87 + 40 * q^88 + 60 * q^90 - 80 * q^93 + 216 * q^94 + 96 * q^96 - 64 * q^99

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