LMFDB - Embedded newform 819.2.fy.a.50.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(50,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 0, 7]))

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

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

chi := DirichletCharacter("819.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fy (of order $12$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$84$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			50.7
Character	$\chi$	$=$	819.50
Dual form			819.2.fy.a.344.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.634582 - 2.36829i) q^{2} +(-1.61523 - 0.625330i) q^{3} +(-3.47406 + 2.00575i) q^{4} +(0.0143461 + 0.0535404i) q^{5} +(-0.455971 + 4.22216i) q^{6} +(0.707107 - 0.707107i) q^{7} +(3.48736 + 3.48736i) q^{8} +(2.21792 + 2.02010i) q^{9} +O(q^{10})$	\(q+(-0.634582 - 2.36829i) q^{2} +(-1.61523 - 0.625330i) q^{3} +(-3.47406 + 2.00575i) q^{4} +(0.0143461 + 0.0535404i) q^{5} +(-0.455971 + 4.22216i) q^{6} +(0.707107 - 0.707107i) q^{7} +(3.48736 + 3.48736i) q^{8} +(2.21792 + 2.02010i) q^{9} +(0.117696 - 0.0679516i) q^{10} +(-0.319064 + 0.0854928i) q^{11} +(6.86566 - 1.06731i) q^{12} +(2.89365 + 2.15100i) q^{13} +(-2.12335 - 1.22592i) q^{14} +(0.0103082 - 0.0954510i) q^{15} +(2.03457 - 3.52398i) q^{16} +(-0.503320 + 0.871775i) q^{17} +(3.37674 - 6.53461i) q^{18} +(7.38411 - 1.97857i) q^{19} +(-0.157228 - 0.157228i) q^{20} +(-1.58431 + 0.699963i) q^{21} +(0.404944 + 0.701384i) q^{22} +1.09412 q^{23} +(-3.45213 - 7.81364i) q^{24} +(4.32747 - 2.49846i) q^{25} +(3.25793 - 8.21799i) q^{26} +(-2.31922 - 4.64986i) q^{27} +(-1.03825 + 3.87481i) q^{28} +(-2.65181 - 1.53102i) q^{29} +(-0.232597 + 0.0361587i) q^{30} +(-0.661047 + 0.177127i) q^{31} +(-0.109276 - 0.0292805i) q^{32} +(0.568822 + 0.0614298i) q^{33} +(2.38402 + 0.638795i) q^{34} +(0.0480030 + 0.0277146i) q^{35} +(-11.7570 - 2.56936i) q^{36} +(2.16071 + 0.578959i) q^{37} +(-9.37165 - 16.2322i) q^{38} +(-3.32882 - 5.28384i) q^{39} +(-0.136685 + 0.236745i) q^{40} +(-5.88173 + 5.88173i) q^{41} +(2.66309 + 3.30793i) q^{42} +6.51701i q^{43} +(0.936970 - 0.936970i) q^{44} +(-0.0763386 + 0.147729i) q^{45} +(-0.694310 - 2.59120i) q^{46} +(3.15023 - 11.7568i) q^{47} +(-5.48995 + 4.41976i) q^{48} -1.00000i q^{49} +(-8.66322 - 8.66322i) q^{50} +(1.35812 - 1.09337i) q^{51} +(-14.3671 - 1.66876i) q^{52} +4.55847i q^{53} +(-9.54050 + 8.44331i) q^{54} +(-0.00915464 - 0.0158563i) q^{55} +4.93187 q^{56} +(-13.1643 - 1.42167i) q^{57} +(-1.94312 + 7.25181i) q^{58} +(0.887600 - 3.31257i) q^{59} +(0.155640 + 0.352279i) q^{60} -3.92879 q^{61} +(0.838977 + 1.45315i) q^{62} +(2.99674 - 0.139881i) q^{63} -7.86091i q^{64} +(-0.0736527 + 0.185786i) q^{65} +(-0.215480 - 1.38612i) q^{66} +(4.31681 + 4.31681i) q^{67} -4.03814i q^{68} +(-1.76726 - 0.684187i) q^{69} +(0.0351743 - 0.131272i) q^{70} +(0.139180 + 0.519426i) q^{71} +(0.689873 + 14.7795i) q^{72} +(0.387627 - 0.387627i) q^{73} -5.48458i q^{74} +(-8.55221 + 1.32949i) q^{75} +(-21.6844 + 21.6844i) q^{76} +(-0.165159 + 0.286065i) q^{77} +(-10.4013 + 11.2366i) q^{78} +(-3.02197 - 5.23421i) q^{79} +(0.217864 + 0.0583764i) q^{80} +(0.838370 + 8.96087i) q^{81} +(17.6621 + 10.1972i) q^{82} +(8.99705 + 2.41075i) q^{83} +(4.10005 - 5.60946i) q^{84} +(-0.0538959 - 0.0144414i) q^{85} +(15.4342 - 4.13558i) q^{86} +(3.32588 + 4.13121i) q^{87} +(-1.41083 - 0.814546i) q^{88} +(3.58584 - 13.3825i) q^{89} +(0.398309 + 0.0870457i) q^{90} +(3.56710 - 0.525134i) q^{91} +(-3.80105 + 2.19453i) q^{92} +(1.17850 + 0.127272i) q^{93} -29.8427 q^{94} +(0.211867 + 0.366964i) q^{95} +(0.158196 + 0.115629i) q^{96} +(5.78668 + 5.78668i) q^{97} +(-2.36829 + 0.634582i) q^{98} +(-0.880363 - 0.454925i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) $ 336 * q - 12 * q^6 + 36 * q^8	$ 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) $ 336 * q - 12 * q^6 + 36 * q^8 - 12 * q^11 + 4 * q^15 + 168 * q^16 - 4 * q^18 - 4 * q^21 + 8 * q^24 - 96 * q^26 + 24 * q^27 - 120 * q^30 - 72 * q^32 + 36 * q^33 + 72 * q^38 + 8 * q^39 - 48 * q^41 - 76 * q^45 + 24 * q^48 - 24 * q^50 - 36 * q^52 + 72 * q^54 + 32 * q^57 + 36 * q^58 - 72 * q^59 + 4 * q^60 + 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 48 * q^71 - 176 * q^72 - 60 * q^75 - 124 * q^78 - 12 * q^79 - 96 * q^80 - 20 * q^81 - 156 * q^83 - 12 * q^84 - 108 * q^85 - 24 * q^87 + 60 * q^89 - 72 * q^92 + 20 * q^93 + 96 * q^94 + 88 * q^96 - 96 * q^97 + 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$1$

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 $

$2$	−0.634582	−	2.36829i	−0.448717	−	1.67464i	−0.705931	−	0.708281i	$-0.749471\pi$
$2$	−0.634582	−	2.36829i	−0.448717	−	1.67464i	0.257214	−	0.966355i	$-0.417196\pi$
$3$	−1.61523	−	0.625330i	−0.932552	−	0.361035i
$3$	−1.61523	−	0.625330i	−0.932552	−	0.361035i
$4$	−3.47406	+	2.00575i	−1.73703	+	1.00288i
$5$	0.0143461	+	0.0535404i	0.00641578	+	0.0239440i	0.969060	−	0.246827i	$-0.0793880\pi$
$5$	0.0143461	+	0.0535404i	0.00641578	+	0.0239440i	−0.962644	+	0.270771i	$0.912721\pi$
$6$	−0.455971	+	4.22216i	−0.186149	+	1.72369i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	3.48736	+	3.48736i	1.23297	+	1.23297i
$9$	2.21792	+	2.02010i	0.739308	+	0.673368i
$10$	0.117696	−	0.0679516i	0.0372186	−	0.0214882i
$11$	−0.319064	+	0.0854928i	−0.0962013	+	0.0257771i	−0.306599	−	0.951839i	$-0.599191\pi$
$11$	−0.319064	+	0.0854928i	−0.0962013	+	0.0257771i	0.210397	+	0.977616i	$0.432524\pi$
$12$	6.86566	−	1.06731i	1.98195	−	0.308105i
$13$	2.89365	+	2.15100i	0.802554	+	0.596579i
$13$	2.89365	+	2.15100i	0.802554	+	0.596579i
$14$	−2.12335	−	1.22592i	−0.567490	−	0.327640i
$15$	0.0103082	−	0.0954510i	0.00266157	−	0.0246454i
$16$	2.03457	−	3.52398i	0.508643	−	0.880996i
$17$	−0.503320	+	0.871775i	−0.122073	+	0.211437i	−0.920585	−	0.390542i	$-0.872288\pi$
$17$	−0.503320	+	0.871775i	−0.122073	+	0.211437i	0.798512	+	0.601979i	$0.205621\pi$
$18$	3.37674	−	6.53461i	0.795905	−	1.54022i
$19$	7.38411	−	1.97857i	1.69403	−	0.453914i	0.722606	−	0.691260i	$-0.242944\pi$
$19$	7.38411	−	1.97857i	1.69403	−	0.453914i	0.971425	+	0.237346i	$0.0762775\pi$
$20$	−0.157228	−	0.157228i	−0.0351573	−	0.0351573i
$21$	−1.58431	+	0.699963i	−0.345726	+	0.152745i
$22$	0.404944	+	0.701384i	0.0863344	+	0.149535i
$23$	1.09412			0.228140			0.114070	−	0.993473i	$-0.463611\pi$
$23$	1.09412			0.228140			0.114070	+	0.993473i	$0.463611\pi$
$24$	−3.45213	−	7.81364i	−0.704663	−	1.59495i
$25$	4.32747	−	2.49846i	0.865493	−	0.499693i
$26$	3.25793	−	8.21799i	0.638933	−	1.61168i
$27$	−2.31922	−	4.64986i	−0.446334	−	0.894866i
$28$	−1.03825	+	3.87481i	−0.196211	+	0.732271i
$29$	−2.65181	−	1.53102i	−0.492428	−	0.284304i	0.233153	−	0.972440i	$-0.425096\pi$
$29$	−2.65181	−	1.53102i	−0.492428	−	0.284304i	−0.725581	+	0.688136i	$0.758429\pi$
$30$	−0.232597	+	0.0361587i	−0.0424663	+	0.00660164i
$31$	−0.661047	+	0.177127i	−0.118728	+	0.0318129i	−0.317694	−	0.948193i	$-0.602908\pi$
$31$	−0.661047	+	0.177127i	−0.118728	+	0.0318129i	0.198966	+	0.980006i	$0.436242\pi$
$32$	−0.109276	−	0.0292805i	−0.0193175	−	0.00517612i
$33$	0.568822	+	0.0614298i	0.0990192	+	0.0106935i
$34$	2.38402	+	0.638795i	0.408855	+	0.109552i
$35$	0.0480030	+	0.0277146i	0.00811399	+	0.00468462i
$36$	−11.7570	−	2.56936i	−1.95950	−	0.428227i
$37$	2.16071	+	0.578959i	0.355218	+	0.0951803i	0.432015	−	0.901866i	$-0.357803\pi$
$37$	2.16071	+	0.578959i	0.355218	+	0.0951803i	−0.0767972	+	0.997047i	$0.524469\pi$
$38$	−9.37165	−	16.2322i	−1.52028	−	2.63321i
$39$	−3.32882	−	5.28384i	−0.533038	−	0.846091i
$40$	−0.136685	+	0.236745i	−0.0216118	+	0.0374327i
$41$	−5.88173	+	5.88173i	−0.918571	+	0.918571i	−0.996926	−	0.0783543i	$-0.975033\pi$
$41$	−5.88173	+	5.88173i	−0.918571	+	0.918571i	0.0783543	+	0.996926i	$0.475033\pi$
$42$	2.66309	+	3.30793i	0.410924	+	0.510425i
$43$			6.51701i			0.993835i	0.867798	+	0.496918i	$0.165535\pi$
$43$			6.51701i			0.993835i	−0.867798	+	0.496918i	$0.834465\pi$
$44$	0.936970	−	0.936970i	0.141253	−	0.141253i
$45$	−0.0763386	+	0.147729i	−0.0113799	+	0.0220222i
$46$	−0.694310	−	2.59120i	−0.102370	−	0.382051i
$47$	3.15023	−	11.7568i	0.459509	−	1.71491i	−0.214974	−	0.976620i	$-0.568967\pi$
$47$	3.15023	−	11.7568i	0.459509	−	1.71491i	0.674483	−	0.738290i	$-0.264367\pi$
$48$	−5.48995	+	4.41976i	−0.792407	+	0.637937i
$49$		−	1.00000i		−	0.142857i
$50$	−8.66322	−	8.66322i	−1.22516	−	1.22516i
$51$	1.35812	−	1.09337i	0.190175	−	0.153103i
$52$	−14.3671	−	1.66876i	−1.99236	−	0.231415i
$53$			4.55847i			0.626155i	0.949728	+	0.313077i	$0.101360\pi$
$53$			4.55847i			0.626155i	−0.949728	+	0.313077i	$0.898640\pi$
$54$	−9.54050	+	8.44331i	−1.29830	+	1.14899i
$55$	−0.00915464	−	0.0158563i	−0.00123441	−	0.00213806i
$56$	4.93187			0.659049
$57$	−13.1643	−	1.42167i	−1.74365	−	0.188305i
$58$	−1.94312	+	7.25181i	−0.255144	+	0.952210i
$59$	0.887600	−	3.31257i	0.115556	−	0.431260i	−0.883772	−	0.467917i	$-0.845004\pi$
$59$	0.887600	−	3.31257i	0.115556	−	0.431260i	0.999328	+	0.0366577i	$0.0116711\pi$
$60$	0.155640	+	0.352279i	0.0200930	+	0.0454790i
$61$	−3.92879			−0.503030			−0.251515	−	0.967853i	$-0.580929\pi$
$61$	−3.92879			−0.503030			−0.251515	+	0.967853i	$0.580929\pi$
$62$	0.838977	+	1.45315i	0.106550	+	0.184550i
$63$	2.99674	−	0.139881i	0.377553	−	0.0176233i
$64$		−	7.86091i		−	0.982614i
$65$	−0.0736527	+	0.185786i	−0.00913549	+	0.0230439i
$66$	−0.215480	−	1.38612i	−0.0265238	−	0.170619i
$67$	4.31681	+	4.31681i	0.527382	+	0.527382i	0.919791	−	0.392409i	$-0.128358\pi$
$67$	4.31681	+	4.31681i	0.527382	+	0.527382i	−0.392409	+	0.919791i	$0.628358\pi$
$68$		−	4.03814i		−	0.489696i
$69$	−1.76726	−	0.684187i	−0.212753	−	0.0823665i
$70$	0.0351743	−	0.131272i	0.00420413	−	0.0156900i
$71$	0.139180	+	0.519426i	0.0165176	+	0.0616445i	0.973693	−	0.227865i	$-0.0731745\pi$
$71$	0.139180	+	0.519426i	0.0165176	+	0.0616445i	−0.957175	+	0.289510i	$0.906508\pi$
$72$	0.689873	+	14.7795i	0.0813023	+	1.74178i
$73$	0.387627	−	0.387627i	0.0453683	−	0.0453683i	−0.684059	−	0.729427i	$-0.739787\pi$
$73$	0.387627	−	0.387627i	0.0453683	−	0.0453683i	0.729427	+	0.684059i	$0.239787\pi$
$74$		−	5.48458i		−	0.637569i
$75$	−8.55221	+	1.32949i	−0.987524	+	0.153517i
$76$	−21.6844	+	21.6844i	−2.48737	+	2.48737i
$77$	−0.165159	+	0.286065i	−0.0188217	+	0.0326001i
$78$	−10.4013	+	11.2366i	−1.17771	+	1.27230i
$79$	−3.02197	−	5.23421i	−0.339998	−	0.588895i	0.644434	−	0.764660i	$-0.277093\pi$
$79$	−3.02197	−	5.23421i	−0.339998	−	0.588895i	−0.984432	+	0.175766i	$0.943760\pi$
$80$	0.217864	+	0.0583764i	0.0243579	+	0.00652668i
$81$	0.838370	+	8.96087i	0.0931523	+	0.995652i
$82$	17.6621	+	10.1972i	1.95045	+	1.12609i
$83$	8.99705	+	2.41075i	0.987555	+	0.264615i	0.716223	−	0.697871i	$-0.245869\pi$
$83$	8.99705	+	2.41075i	0.987555	+	0.264615i	0.271332	+	0.962486i	$0.412536\pi$
$84$	4.10005	−	5.60946i	0.447353	−	0.612042i
$85$	−0.0538959	−	0.0144414i	−0.00584583	−	0.00156639i
$86$	15.4342	−	4.13558i	1.66431	−	0.445951i
$87$	3.32588	+	4.13121i	0.356572	+	0.442912i
$88$	−1.41083	−	0.814546i	−0.150395	−	0.0868309i
$89$	3.58584	−	13.3825i	0.380098	−	1.41854i	−0.465653	−	0.884967i	$-0.654181\pi$
$89$	3.58584	−	13.3825i	0.380098	−	1.41854i	0.845751	−	0.533577i	$-0.179153\pi$
$90$	0.398309	+	0.0870457i	0.0419854	+	0.00917543i
$91$	3.56710	−	0.525134i	0.373934	−	0.0550490i
$92$	−3.80105	+	2.19453i	−0.396286	+	0.228796i
$93$	1.17850	+	0.127272i	0.122205	+	0.0131975i
$94$	−29.8427			−3.07804
$95$	0.211867	+	0.366964i	0.0217370	+	0.0376497i
$96$	0.158196	+	0.115629i	0.0161459	+	0.0118013i
$97$	5.78668	+	5.78668i	0.587548	+	0.587548i	0.936967	−	0.349418i	$-0.113621\pi$
$97$	5.78668	+	5.78668i	0.587548	+	0.587548i	−0.349418	+	0.936967i	$0.613621\pi$
$98$	−2.36829	+	0.634582i	−0.239234	+	0.0641025i
$99$	−0.880363	−	0.454925i	−0.0884798	−	0.0457216i
$100$	−10.0226	+	17.3596i	−1.00226	+	1.73596i
$101$	7.37418	−	12.7725i	0.733758	−	1.27091i	−0.221508	−	0.975159i	$-0.571098\pi$
$101$	7.37418	−	12.7725i	0.733758	−	1.27091i	0.955266	−	0.295748i	$-0.0955689\pi$
$102$	−3.45127	−	2.52260i	−0.341727	−	0.249774i
$103$	5.46568	+	3.15561i	0.538550	+	0.310932i	0.744491	−	0.667633i	$-0.232692\pi$
$103$	5.46568	+	3.15561i	0.538550	+	0.310932i	−0.205941	+	0.978564i	$0.566026\pi$
$104$	2.58990	+	17.5925i	0.253960	+	1.72509i
$105$	−0.0602051	−	0.0747831i	−0.00587541	−	0.00729808i
$106$	10.7958	−	2.89273i	1.04858	−	0.280966i
$107$	13.5313	−	7.81230i	1.30812	−	0.755243i	0.326337	−	0.945253i	$-0.394185\pi$
$107$	13.5313	−	7.81230i	1.30812	−	0.755243i	0.981782	+	0.190010i	$0.0608521\pi$
$108$	17.3836	+	11.5021i	1.67274	+	1.10679i
$109$	−3.49541	−	3.49541i	−0.334800	−	0.334800i	0.519606	−	0.854406i	$-0.326079\pi$
$109$	−3.49541	−	3.49541i	−0.334800	−	0.334800i	−0.854406	+	0.519606i	$0.826079\pi$
$110$	−0.0317430	+	0.0317430i	−0.00302658	+	0.00302658i
$111$	−3.12799	−	2.28631i	−0.296896	−	0.217007i
$112$	−1.05317	−	3.93049i	−0.0995154	−	0.371397i
$113$	−4.63614	+	2.67668i	−0.436131	+	0.251800i	−0.701955	−	0.712221i	$-0.747689\pi$
$113$	−4.63614	+	2.67668i	−0.436131	+	0.251800i	0.265824	+	0.964022i	$0.414356\pi$
$114$	4.98688	+	32.0790i	0.467064	+	3.00448i
$115$	0.0156964	+	0.0585797i	0.00146370	+	0.00546258i
$116$	12.2834			1.14048
$117$	2.07266	+	10.6162i	0.191617	+	0.981470i
$118$	−8.40839			−0.774055
$119$	0.260537	+	0.972339i	0.0238834	+	0.0891342i
$120$	0.368821	−	0.296924i	0.0336686	−	0.0271053i
$121$	−9.43179	+	5.44544i	−0.857435	+	0.495040i
$122$	2.49314	+	9.30453i	0.225718	+	0.842393i
$123$	13.1784	−	5.82231i	1.18825	−	0.524980i
$124$	1.94125	−	1.94125i	0.174329	−	0.174329i
$125$	0.391823	+	0.391823i	0.0350457	+	0.0350457i
$126$	−2.23295	−	7.00838i	−0.198927	−	0.624356i
$127$	14.6838	−	8.47770i	1.30298	−	0.752275i	0.322064	−	0.946718i	$-0.395623\pi$
$127$	14.6838	−	8.47770i	1.30298	−	0.752275i	0.980914	+	0.194443i	$0.0622900\pi$
$128$	−18.8355	+	5.04695i	−1.66484	+	0.446092i
$129$	4.07529	−	10.5265i	0.358809	−	0.926804i
$130$	0.486733	+	0.0565349i	0.0426893	+	0.00495844i
$131$	−18.8309	−	10.8720i	−1.64526	−	0.949891i	−0.978920	−	0.204242i	$-0.934527\pi$
$131$	−18.8309	−	10.8720i	−1.64526	−	0.949891i	−0.666339	−	0.745649i	$-0.732140\pi$
$132$	−2.09934	+	0.927504i	−0.182724	+	0.0807289i
$133$	3.82230	−	6.62041i	0.331435	−	0.574063i
$134$	7.48410	−	12.9628i	0.646528	−	1.11982i
$135$	0.215684	−	0.190879i	0.0185631	−	0.0164283i
$136$	−4.79545	+	1.28494i	−0.411207	+	0.110183i
$137$	5.66863	+	5.66863i	0.484304	+	0.484304i	0.906503	−	0.422199i	$-0.138742\pi$
$137$	5.66863	+	5.66863i	0.484304	+	0.484304i	−0.422199	+	0.906503i	$0.638742\pi$
$138$	−0.498887	+	4.61955i	−0.0424681	+	0.393242i
$139$	−10.5267	−	18.2328i	−0.892862	−	1.54648i	−0.836428	−	0.548076i	$-0.815360\pi$
$139$	−10.5267	−	18.2328i	−0.892862	−	1.54648i	−0.0564338	−	0.998406i	$-0.517973\pi$
$140$	−0.222354			−0.0187923
$141$	−12.4402	+	17.0200i	−1.04766	+	1.43334i
$142$	1.14183	−	0.659237i	0.0958204	−	0.0553219i
$143$	−1.10715	−	0.438919i	−0.0925848	−	0.0367042i
$144$	11.6313	−	3.70588i	0.969278	−	0.308823i
$145$	0.0439284	−	0.163943i	0.00364806	−	0.0136147i
$146$	−1.16399	−	0.672032i	−0.0963328	−	0.0556178i
$147$	−0.625330	+	1.61523i	−0.0515764	+	0.133222i
$148$	−8.66768	+	2.32250i	−0.712479	+	0.190908i
$149$	3.99549	+	1.07059i	0.327323	+	0.0877060i	0.418739	−	0.908107i	$-0.362472\pi$
$149$	3.99549	+	1.07059i	0.327323	+	0.0877060i	−0.0914152	+	0.995813i	$0.529139\pi$
$150$	8.57571	+	19.4105i	0.700203	+	1.58486i
$151$	15.6570	+	4.19529i	1.27415	+	0.341408i	0.831620	−	0.555345i	$-0.187414\pi$
$151$	15.6570	+	4.19529i	1.27415	+	0.341408i	0.442531	+	0.896753i	$0.354081\pi$
$152$	32.6510	+	18.8511i	2.64835	+	1.52903i
$153$	−2.87740	+	0.916774i	−0.232624	+	0.0741167i
$154$	0.782292	+	0.209614i	0.0630389	+	0.0168912i
$155$	−0.0189669	−	0.0328516i	−0.00152346	−	0.00263871i
$156$	22.1626	+	11.6796i	1.77443	+	0.935117i
$157$	6.94289	−	12.0254i	0.554103	−	0.959734i	−0.443870	−	0.896091i	$-0.646395\pi$
$157$	6.94289	−	12.0254i	0.554103	−	0.959734i	0.997973	−	0.0636427i	$-0.0202718\pi$
$158$	−10.4784	+	10.4784i	−0.833621	+	0.833621i
$159$	2.85055	−	7.36297i	0.226064	−	0.583922i
$160$		−	0.00627077i		−	0.000495748i
$161$	0.773660	−	0.773660i	0.0609730	−	0.0609730i
$162$	20.6899	−	7.67191i	1.62555	−	0.602762i
$163$	0.715221	+	2.66924i	0.0560204	+	0.209071i	0.988263	−	0.152763i	$-0.0488172\pi$
$163$	0.715221	+	2.66924i	0.0560204	+	0.209071i	−0.932242	+	0.361834i	$0.882151\pi$
$164$	8.63621	−	32.2308i	0.674374	−	2.51680i
$165$	0.00487140	+	0.0313362i	0.000379238	+	0.00243952i
$166$		−	22.8375i		−	1.77253i
$167$	−4.34776	−	4.34776i	−0.336440	−	0.336440i	0.518586	−	0.855026i	$-0.326459\pi$
$167$	−4.34776	−	4.34776i	−0.336440	−	0.336440i	−0.855026	+	0.518586i	$0.826459\pi$
$168$	−7.96610	−	3.08405i	−0.614598	−	0.237940i
$169$	3.74642	+	12.4485i	0.288186	+	0.957574i
$170$			0.136805i			0.0104925i
$171$	20.3743	+	10.5284i	1.55806	+	0.805123i
$172$	−13.0715	−	22.6405i	−0.996693	−	1.72632i
$173$	5.75168			0.437292			0.218646	−	0.975804i	$-0.429836\pi$
$173$	5.75168			0.437292			0.218646	+	0.975804i	$0.429836\pi$
$174$	7.67336	−	10.4982i	0.581716	−	0.795870i
$175$	1.29330	−	4.82666i	0.0977643	−	0.364861i
$176$	−0.347883	+	1.29832i	−0.0262227	+	0.0978643i
$177$	−3.50513	+	4.79551i	−0.263461	+	0.360453i
$178$	−33.9692			−2.54610
$179$	−5.05561	−	8.75657i	−0.377874	−	0.654496i	0.612879	−	0.790177i	$-0.290011\pi$
$179$	−5.05561	−	8.75657i	−0.377874	−	0.654496i	−0.990753	+	0.135680i	$0.956678\pi$
$180$	−0.0311030	−	0.666337i	−0.00231828	−	0.0496658i
$181$		−	10.5071i		−	0.780984i	−0.920606	−	0.390492i	$-0.872305\pi$
$181$		−	10.5071i		−	0.780984i	0.920606	−	0.390492i	$-0.127695\pi$
$182$	−3.50729	−	8.11470i	−0.259978	−	0.601502i
$183$	6.34590	+	2.45679i	0.469102	+	0.181611i
$184$	3.81560	+	3.81560i	0.281290	+	0.281290i
$185$			0.123991i			0.00911599i
$186$	−0.446440	−	2.87181i	−0.0327345	−	0.210571i
$187$	0.0860605	−	0.321182i	0.00629336	−	0.0234872i
$188$	12.6372	+	47.1626i	0.921660	+	3.43968i
$189$	−4.92789	−	1.64801i	−0.358451	−	0.119875i
$190$	0.734630	−	0.734630i	0.0532957	−	0.0532957i
$191$			22.7638i			1.64713i	0.567223	+	0.823564i	$0.308018\pi$
$191$			22.7638i			1.64713i	−0.567223	+	0.823564i	$0.691982\pi$
$192$	−4.91567	+	12.6972i	−0.354758	+	0.916339i
$193$	−12.9666	+	12.9666i	−0.933356	+	0.933356i	−0.997914	−	0.0645576i	$-0.979436\pi$
$193$	−12.9666	+	12.9666i	−0.933356	+	0.933356i	0.0645576	+	0.997914i	$0.479436\pi$
$194$	10.0324	−	17.3767i	0.720286	−	1.24757i
$195$	0.235143	−	0.254029i	0.0168390	−	0.0181914i
$196$	2.00575	+	3.47406i	0.143268	+	0.248147i
$197$	−5.99648	−	1.60675i	−0.427232	−	0.114476i	0.0387948	−	0.999247i	$-0.487648\pi$
$197$	−5.99648	−	1.60675i	−0.427232	−	0.114476i	−0.466026	+	0.884771i	$0.654315\pi$
$198$	−0.518732	+	2.37364i	−0.0368647	+	0.168688i
$199$	−3.11534	−	1.79864i	−0.220841	−	0.127503i	0.385499	−	0.922708i	$-0.374029\pi$
$199$	−3.11534	−	1.79864i	−0.220841	−	0.127503i	−0.606340	+	0.795206i	$0.707363\pi$
$200$	23.8045	+	6.37839i	1.68323	+	0.451021i
$201$	−4.27320	−	9.67206i	−0.301408	−	0.682215i
$202$	−34.9284	−	9.35904i	−2.45756	−	0.658500i
$203$	−2.95771	+	0.792515i	−0.207590	+	0.0556237i
$204$	−2.52517	+	6.52251i	−0.176797	+	0.456667i
$205$	−0.399290	−	0.230530i	−0.0278876	−	0.0161009i
$206$	4.00499	−	14.9468i	0.279041	−	1.04139i
$207$	2.42668	+	2.21024i	0.168666	+	0.153622i
$208$	13.4674	−	5.82081i	0.933798	−	0.403601i
$209$	−2.18685	+	1.26258i	−0.151267	+	0.0873343i
$210$	−0.138903	+	0.190039i	−0.00958523	+	0.0131140i
$211$	28.0931			1.93401			0.967006	−	0.254754i	$-0.0819945\pi$
$211$	28.0931			1.93401			0.967006	+	0.254754i	$0.0819945\pi$
$212$	−9.14316	−	15.8364i	−0.627955	−	1.08765i
$213$	0.100006	−	0.926025i	0.00685228	−	0.0634502i
$214$	−27.0885	−	27.0885i	−1.85173	−	1.85173i
$215$	−0.348924	+	0.0934938i	−0.0237964	+	0.00637622i
$216$	8.12779	−	24.3037i	0.553026	−	1.65366i
$217$	−0.342183	+	0.592678i	−0.0232289	+	0.0402336i
$218$	−6.06003	+	10.4963i	−0.410437	+	0.710898i
$219$	−0.868500	+	0.383711i	−0.0586878	+	0.0259288i
$220$	0.0636076	+	0.0367239i	0.00428842	+	0.00247592i
$221$	−3.33162	+	1.43997i	−0.224109	+	0.0968631i
$222$	−3.42967	+	8.85885i	−0.230185	+	0.594567i
$223$	15.0913	−	4.04371i	1.01059	−	0.270787i	0.284714	−	0.958612i	$-0.408101\pi$
$223$	15.0913	−	4.04371i	1.01059	−	0.270787i	0.725876	+	0.687826i	$0.241435\pi$
$224$	−0.0979746	+	0.0565657i	−0.00654620	+	0.00377945i
$225$	14.6451	+	3.20052i	0.976343	+	0.213368i
$226$	9.28116	+	9.28116i	0.617373	+	0.617373i
$227$	4.80557	−	4.80557i	0.318957	−	0.318957i	−0.529410	−	0.848366i	$-0.677587\pi$
$227$	4.80557	−	4.80557i	0.318957	−	0.318957i	0.848366	+	0.529410i	$0.177587\pi$
$228$	48.5851	−	21.4653i	3.21762	−	1.42157i
$229$	−4.90660	−	18.3117i	−0.324238	−	1.21007i	−0.915076	−	0.403281i	$-0.867870\pi$
$229$	−4.90660	−	18.3117i	−0.324238	−	1.21007i	0.590839	−	0.806790i	$-0.298797\pi$
$230$	0.128773	−	0.0743472i	0.00849105	−	0.00490231i
$231$	0.445655	−	0.358780i	0.0293220	−	0.0236060i
$232$	−3.90859	−	14.5870i	−0.256611	−	0.957686i
$233$	−8.19018			−0.536557			−0.268278	−	0.963341i	$-0.586455\pi$
$233$	−8.19018			−0.536557			−0.268278	+	0.963341i	$0.586455\pi$
$234$	23.8270	−	11.6455i	1.55762	−	0.761291i
$235$	0.674659			0.0440099
$236$	3.56061	+	13.2884i	0.231776	+	0.865000i
$237$	1.60806	+	10.3442i	0.104455	+	0.671926i
$238$	2.13745	−	1.23406i	0.138550	−	0.0799921i
$239$	4.62206	+	17.2497i	0.298976	+	1.11579i	0.938008	+	0.346613i	$0.112668\pi$
$239$	4.62206	+	17.2497i	0.298976	+	1.11579i	−0.639032	+	0.769180i	$0.720665\pi$
$240$	−0.315395	−	0.230528i	−0.0203587	−	0.0148805i
$241$	−4.13372	+	4.13372i	−0.266277	+	0.266277i	−0.827598	−	0.561321i	$-0.810293\pi$
$241$	−4.13372	+	4.13372i	−0.266277	+	0.266277i	0.561321	+	0.827598i	$0.310293\pi$
$242$	18.8816	+	18.8816i	1.21376	+	1.21376i
$243$	4.24934	−	14.9981i	0.272596	−	0.962129i
$244$	13.6489	−	7.88018i	0.873780	−	0.504477i
$245$	0.0535404	−	0.0143461i	0.00342057	−	0.000916539i
$246$	−22.1517	−	27.5155i	−1.41234	−	1.75432i
$247$	25.6229	+	10.1579i	1.63035	+	0.646333i
$248$	−2.92302	−	1.68760i	−0.185612	−	0.107163i
$249$	−13.0248	−	9.52005i	−0.825412	−	0.603309i
$250$	0.679307	−	1.17659i	0.0429631	−	0.0744143i
$251$	5.81262	−	10.0678i	0.366889	−	0.635471i	−0.622188	−	0.782868i	$-0.713756\pi$
$251$	5.81262	−	10.0678i	0.366889	−	0.635471i	0.989077	+	0.147397i	$0.0470894\pi$
$252$	−10.1303	+	6.49666i	−0.638148	+	0.409251i
$253$	−0.349094	+	0.0935395i	−0.0219474	+	0.00588078i
$254$	−29.3958	−	29.3958i	−1.84445	−	1.84445i
$255$	0.0780235	+	0.0570288i	0.00488602	+	0.00357128i
$256$	16.0444	+	27.7897i	1.00278	+	1.73686i
$257$	5.94902			0.371089			0.185545	−	0.982636i	$-0.440595\pi$
$257$	5.94902			0.371089			0.185545	+	0.982636i	$0.440595\pi$
$258$	−27.5158	−	2.97157i	−1.71306	−	0.185002i
$259$	1.93724	−	1.11846i	0.120374	−	0.0694979i
$260$	−0.116766	−	0.793160i	−0.00724150	−	0.0491897i
$261$	−2.78869	−	8.75261i	−0.172615	−	0.541773i
$262$	−13.7984	+	51.4961i	−0.852465	+	3.18144i
$263$	2.21023	+	1.27607i	0.136288	+	0.0786861i	0.566594	−	0.823997i	$-0.308261\pi$
$263$	2.21023	+	1.27607i	0.136288	+	0.0786861i	−0.430306	+	0.902683i	$0.641594\pi$
$264$	1.76946	+	2.19792i	0.108903	+	0.135272i
$265$	−0.244063	+	0.0653964i	−0.0149926	+	0.00401727i
$266$	−18.1046	−	4.85112i	−1.11007	−	0.297441i
$267$	−14.1604	+	19.3735i	−0.866605	+	1.18564i
$268$	−23.6553	−	6.33842i	−1.44498	−	0.387181i
$269$	23.3026	+	13.4537i	1.42078	+	0.820289i	0.996366	−	0.0851781i	$-0.0271459\pi$
$269$	23.3026	+	13.4537i	1.42078	+	0.820289i	0.424416	+	0.905467i	$0.360479\pi$
$270$	−0.588927	−	0.389673i	−0.0358410	−	0.0237148i
$271$	6.75270	+	1.80938i	0.410197	+	0.109912i	0.458016	−	0.888944i	$-0.348560\pi$
$271$	6.75270	+	1.80938i	0.410197	+	0.109912i	−0.0478187	+	0.998856i	$0.515227\pi$
$272$	2.04808	+	3.54738i	0.124183	+	0.215092i
$273$	−6.09007	−	1.38241i	−0.368588	−	0.0836671i
$274$	9.82777	−	17.0222i	0.593717	−	1.02835i
$275$	−1.16714	+	1.16714i	−0.0703810	+	0.0703810i
$276$	7.51186	−	1.16776i	0.452161	−	0.0702912i
$277$			15.3039i			0.919524i	0.888042	+	0.459762i	$0.152065\pi$
$277$			15.3039i			0.919524i	−0.888042	+	0.459762i	$0.847935\pi$
$278$	−36.5005	+	36.5005i	−2.18915	+	2.18915i
$279$	−1.82397	−	0.942528i	−0.109198	−	0.0564277i
$280$	0.0707532	+	0.264055i	0.00422831	+	0.0157803i
$281$	−4.22776	+	15.7782i	−0.252207	+	0.941249i	0.717416	+	0.696645i	$0.245325\pi$
$281$	−4.22776	+	15.7782i	−0.252207	+	0.941249i	−0.969623	+	0.244604i	$0.921342\pi$
$282$	48.2028	+	18.6615i	2.87043	+	1.11128i
$283$			6.43592i			0.382576i	0.981534	+	0.191288i	$0.0612664\pi$
$283$			6.43592i			0.382576i	−0.981534	+	0.191288i	$0.938734\pi$
$284$	−1.52536	−	1.52536i	−0.0905134	−	0.0905134i
$285$	−0.112739	−	0.725217i	−0.00667810	−	0.0429581i
$286$	−0.336908	+	2.90059i	−0.0199218	+	0.171516i
$287$			8.31802i			0.490997i
$288$	−0.183217	−	0.285692i	−0.0107962	−	0.0168345i
$289$	7.99334	+	13.8449i	0.470196	+	0.814404i
$290$	−0.416141			−0.0244367
$291$	−5.72822	−	12.9654i	−0.335794	−	0.760045i
$292$	−0.569157	+	2.12412i	−0.0333074	+	0.124305i
$293$	−2.81446	+	10.5037i	−0.164423	+	0.613634i	0.833691	+	0.552232i	$0.186224\pi$
$293$	−2.81446	+	10.5037i	−0.164423	+	0.613634i	−0.998113	+	0.0614016i	$0.980443\pi$
$294$	4.22216	+	0.455971i	0.246241	+	0.0265927i
$295$	0.190090			0.0110675
$296$	5.51612	+	9.55420i	0.320618	+	0.555327i
$297$	1.13751	+	1.28532i	0.0660050	+	0.0745821i
$298$		−	10.1419i		−	0.587503i
$299$	3.16600	+	2.35345i	0.183095	+	0.136104i
$300$	27.0443	−	21.7723i	1.56140	−	1.25703i
$301$	4.60822	+	4.60822i	0.265614	+	0.265614i
$302$		−	39.7427i		−	2.28693i
$303$	−19.8980	+	16.0191i	−1.14311	+	0.920275i
$304$	8.05108	−	30.0470i	0.461761	−	1.72332i
$305$	−0.0563629	−	0.210349i	−0.00322733	−	0.0120446i
$306$	3.99713	+	6.23276i	0.228501	+	0.356303i
$307$	−17.0261	+	17.0261i	−0.971730	+	0.971730i	−0.999611	−	0.0278810i	$-0.991124\pi$
$307$	−17.0261	+	17.0261i	−0.971730	+	0.971730i	0.0278810	+	0.999611i	$0.491124\pi$
$308$		−	1.32508i		−	0.0755032i
$309$	−6.85502	−	8.51489i	−0.389969	−	0.484395i
$310$	−0.0657662	+	0.0657662i	−0.00373527	+	0.00373527i
$311$	−7.64433	+	13.2404i	−0.433470	+	0.750792i	−0.997169	−	0.0751880i	$-0.976044\pi$
$311$	−7.64433	+	13.2404i	−0.433470	+	0.750792i	0.563699	+	0.825980i	$0.309378\pi$
$312$	6.81786	−	30.0355i	0.385985	−	1.70042i
$313$	−1.68382	−	2.91645i	−0.0951749	−	0.164848i	0.814507	−	0.580154i	$-0.197008\pi$
$313$	−1.68382	−	2.91645i	−0.0951749	−	0.164848i	−0.909682	+	0.415306i	$0.863674\pi$
$314$	−32.8856	−	8.81166i	−1.85584	−	0.497271i
$315$	0.0504808	+	0.158440i	0.00284427	+	0.00892707i
$316$	20.9970	+	12.1226i	1.18118	+	0.681952i
$317$	−15.5867	−	4.17643i	−0.875434	−	0.234572i	−0.206998	−	0.978341i	$-0.566369\pi$
$317$	−15.5867	−	4.17643i	−0.875434	−	0.234572i	−0.668436	+	0.743770i	$0.733036\pi$
$318$	−19.2466	−	2.07853i	−1.07929	−	0.116558i
$319$	0.976987	+	0.261783i	0.0547007	+	0.0146570i
$320$	0.420876	−	0.112774i	0.0235277	−	0.00630423i
$321$	−26.7414	+	4.15711i	−1.49256	+	0.232027i
$322$	−2.32321	−	1.34130i	−0.129467	−	0.0747479i
$323$	−1.99170	+	7.43314i	−0.110821	+	0.413591i
$324$	−20.8858	−	29.4491i	−1.16032	−	1.63606i
$325$	17.8964	+	2.07869i	0.992712	+	0.115305i
$326$	5.86768	−	3.38770i	0.324981	−	0.187628i
$327$	3.46010	+	7.83167i	0.191344	+	0.433092i
$328$	−41.0234			−2.26514
$329$	−6.08578	−	10.5409i	−0.335520	−	0.581138i
$330$	0.0711220	−	0.0314223i	0.00391514	−	0.00172974i
$331$	−8.14964	−	8.14964i	−0.447945	−	0.447945i	0.446726	−	0.894671i	$-0.352590\pi$
$331$	−8.14964	−	8.14964i	−0.447945	−	0.447945i	−0.894671	+	0.446726i	$0.852590\pi$
$332$	−36.0917	+	9.67074i	−1.98079	+	0.530751i
$333$	3.62272	+	5.64893i	0.198524	+	0.309560i
$334$	−7.53776	+	13.0558i	−0.412448	+	0.714380i
$335$	−0.169194	+	0.293053i	−0.00924407	+	0.0160112i
$336$	−0.756743	+	7.00722i	−0.0412837	+	0.382275i
$337$	19.0047	+	10.9724i	1.03525	+	0.597703i	0.918485	−	0.395457i	$-0.129414\pi$
$337$	19.0047	+	10.9724i	1.03525	+	0.597703i	0.116767	+	0.993159i	$0.462747\pi$
$338$	27.1042	−	16.7722i	1.47427	−	0.912287i
$339$	9.16223	−	1.42432i	0.497624	−	0.0773586i
$340$	0.216203	−	0.0579315i	0.0117253	−	0.00314178i
$341$	0.195773	−	0.113030i	0.0106017	−	0.00612089i
$342$	12.0051	−	54.9334i	0.649159	−	2.97046i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−22.7272	+	22.7272i	−1.22537	+	1.22537i
$345$	0.0112784	−	0.104435i	0.000607210	−	0.00562259i
$346$	−3.64991	−	13.6217i	−0.196220	−	0.732305i
$347$	−0.755301	+	0.436073i	−0.0405467	+	0.0234096i	−0.520136	−	0.854083i	$-0.674119\pi$
$347$	−0.755301	+	0.436073i	−0.0405467	+	0.0234096i	0.479590	+	0.877493i	$0.340786\pi$
$348$	−19.8405	−	7.68118i	−1.06356	−	0.411754i
$349$	1.89181	+	7.06034i	0.101266	+	0.377932i	0.997895	−	0.0648522i	$-0.0206576\pi$
$349$	1.89181	+	7.06034i	0.101266	+	0.377932i	−0.896628	+	0.442784i	$0.853991\pi$
$350$	−12.2516			−0.654878
$351$	3.29083	−	18.4437i	0.175652	−	0.984452i
$352$	0.0373694			0.00199180
$353$	6.67913	+	24.9268i	0.355494	+	1.32672i	0.879862	+	0.475230i	$0.157635\pi$
$353$	6.67913	+	24.9268i	0.355494	+	1.32672i	−0.524368	+	0.851492i	$0.675698\pi$
$354$	13.5815	+	5.25802i	0.721846	+	0.279461i
$355$	−0.0258136	+	0.0149035i	−0.00137004	+	0.000790995i
$356$	14.3846	+	53.6840i	0.762382	+	2.84525i
$357$	0.187206	−	1.73347i	0.00990798	−	0.0917450i
$358$	−17.5299	+	17.5299i	−0.926484	+	0.926484i
$359$	−12.5636	−	12.5636i	−0.663082	−	0.663082i	0.293023	−	0.956105i	$-0.405339\pi$
$359$	−12.5636	−	12.5636i	−0.663082	−	0.663082i	−0.956105	+	0.293023i	$0.905339\pi$
$360$	−0.781405	+	0.248965i	−0.0411837	+	0.0131216i
$361$	34.1559	−	19.7199i	1.79768	−	1.03789i
$362$	−24.8838	+	6.66760i	−1.30786	+	0.350441i
$363$	18.6397	−	2.89765i	0.978330	−	0.152087i
$364$	−11.3391	+	8.97907i	−0.594328	+	0.470631i
$365$	0.0263146	+	0.0151928i	0.00137737	+	0.000795225i
$366$	1.79141	−	16.5880i	0.0936387	−	0.867068i
$367$	−17.2580	+	29.8918i	−0.900862	+	1.56034i	−0.0744844	+	0.997222i	$0.523731\pi$
$367$	−17.2580	+	29.8918i	−0.900862	+	1.56034i	−0.826378	+	0.563116i	$0.809602\pi$
$368$	2.22607	−	3.85567i	0.116042	−	0.200990i
$369$	−24.9269	+	1.16353i	−1.29764	+	0.0605709i
$370$	0.293647	−	0.0786824i	0.0152660	−	0.00409050i
$371$	3.22333	+	3.22333i	0.167347	+	0.167347i
$372$	−4.34947	+	1.92163i	−0.225510	+	0.0996321i
$373$	−12.4066	−	21.4889i	−0.642392	−	1.11266i	−0.984897	−	0.173139i	$-0.944609\pi$
$373$	−12.4066	−	21.4889i	−0.642392	−	1.11266i	0.342506	−	0.939516i	$-0.388724\pi$
$374$	−0.815265			−0.0421564
$375$	−0.387864	−	0.877901i	−0.0200292	−	0.0453346i
$376$	51.9863	−	30.0143i	2.68099	−	1.54787i
$377$	−4.38018	−	10.1343i	−0.225591	−	0.521942i
$378$	−0.775827	+	12.7165i	−0.0399042	+	0.654065i
$379$	−1.79453	+	6.69726i	−0.0921786	+	0.344015i	−0.996577	−	0.0826748i	$-0.973654\pi$
$379$	−1.79453	+	6.69726i	−0.0921786	+	0.344015i	0.904398	+	0.426690i	$0.140320\pi$
$380$	−1.47208	−	0.849903i	−0.0755159	−	0.0435991i
$381$	−29.0191	+	4.51119i	−1.48669	+	0.231115i
$382$	53.9113	−	14.4455i	2.75834	−	0.739095i
$383$	−8.79046	−	2.35540i	−0.449171	−	0.120355i	0.0271403	−	0.999632i	$-0.491360\pi$
$383$	−8.79046	−	2.35540i	−0.449171	−	0.120355i	−0.476312	+	0.879277i	$0.658027\pi$
$384$	33.5796	+	3.62642i	1.71360	+	0.185060i
$385$	−0.0176854	−	0.00473879i	−0.000901332	−	0.000241511i
$386$	38.9371	+	22.4803i	1.98184	+	1.14422i
$387$	−13.1650	+	14.4542i	−0.669216	+	0.734750i
$388$	−31.7099	−	8.49665i	−1.60983	−	0.431352i
$389$	7.63087	+	13.2170i	0.386900	+	0.670131i	0.992031	−	0.125995i	$-0.0402124\pi$
$389$	7.63087	+	13.2170i	0.386900	+	0.670131i	−0.605131	+	0.796126i	$0.706879\pi$
$390$	−0.750832	−	0.395686i	−0.0380199	−	0.0200363i
$391$	−0.550693	+	0.953828i	−0.0278497	+	0.0482371i
$392$	3.48736	−	3.48736i	0.176138	−	0.176138i
$393$	23.6175	+	29.3363i	1.19135	+	1.47982i
$394$			15.2210i			0.766825i
$395$	0.236888	−	0.236888i	0.0119191	−	0.0119191i
$396$	3.97090	−	0.185352i	0.199545	−	0.00931430i
$397$	−4.33989	−	16.1967i	−0.217813	−	0.812889i	−0.985157	−	0.171654i	$-0.945089\pi$
$397$	−4.33989	−	16.1967i	−0.217813	−	0.812889i	0.767344	−	0.641235i	$-0.221578\pi$
$398$	−2.28277	+	8.51943i	−0.114425	+	0.427041i
$399$	−10.3138	+	8.30328i	−0.516337	+	0.415684i
$400$		−	20.3332i		−	1.01666i
$401$	−20.9253	−	20.9253i	−1.04496	−	1.04496i	−0.998941	−	0.0460202i	$-0.985346\pi$
$401$	−20.9253	−	20.9253i	−1.04496	−	1.04496i	−0.0460202	−	0.998941i	$-0.514654\pi$
$402$	−20.1946	+	16.2579i	−1.00721	+	0.810871i
$403$	−2.29384	−	0.909367i	−0.114264	−	0.0452988i
$404$			59.1631i			2.94347i
$405$	−0.467741	+	0.173440i	−0.0232422	+	0.00861832i
$406$	3.75381	+	6.50180i	0.186299	+	0.322679i
$407$	−0.738899			−0.0366259
$408$	8.54926	+	0.923276i	0.423252	+	0.0457090i
$409$	−2.02072	+	7.54143i	−0.0999181	+	0.372900i	−0.997719	−	0.0675017i	$-0.978497\pi$
$409$	−2.02072	+	7.54143i	−0.0999181	+	0.372900i	0.897801	+	0.440401i	$0.145164\pi$
$410$	−0.292581	+	1.09193i	−0.0144495	+	0.0539264i
$411$	−5.61137	−	12.7009i	−0.276788	−	0.626489i
$412$	−25.3175			−1.24730
$413$	−1.71471	−	2.96997i	−0.0843754	−	0.146143i
$414$	3.69456	−	7.14966i	0.181578	−	0.351386i
$415$			0.516291i			0.0253437i
$416$	−0.253225	−	0.319781i	−0.0124154	−	0.0156786i
$417$	5.60150	+	36.0327i	0.274307	+	1.76453i
$418$	4.37789	+	4.37789i	0.214129	+	0.214129i
$419$			18.9131i			0.923964i	0.886889	+	0.461982i	$0.152862\pi$
$419$			18.9131i			0.923964i	−0.886889	+	0.461982i	$0.847138\pi$
$420$	0.359152	+	0.139045i	0.0175248	+	0.00678469i
$421$	0.0113599	−	0.0423958i	0.000553649	−	0.00206625i	−0.965648	−	0.259852i	$-0.916326\pi$
$421$	0.0113599	−	0.0423958i	0.000553649	−	0.00206625i	0.966202	+	0.257786i	$0.0829929\pi$
$422$	−17.8274	−	66.5328i	−0.867824	−	3.23876i
$423$	30.7370	−	19.7120i	1.49448	−	0.958428i
$424$	−15.8970	+	15.8970i	−0.772029	+	0.772029i
$425$			5.03010i			0.243996i
$426$	−2.25656	+	0.350796i	−0.109331	+	0.0169961i
$427$	−2.77808	+	2.77808i	−0.134441	+	0.134441i
$428$	−31.3390	+	54.2808i	−1.51483	+	2.62376i
$429$	1.51384	+	1.40129i	0.0730887	+	0.0676549i
$430$	0.442841	+	0.767024i	0.0213557	+	0.0369892i
$431$	−10.0690	−	2.69799i	−0.485008	−	0.129957i	0.00802561	−	0.999968i	$-0.497445\pi$
$431$	−10.0690	−	2.69799i	−0.485008	−	0.129957i	−0.493034	+	0.870010i	$0.664112\pi$
$432$	−21.1047	−	1.28759i	−1.01540	−	0.0619491i
$433$	−21.7570	−	12.5614i	−1.04557	−	0.603662i	−0.124167	−	0.992261i	$-0.539626\pi$
$433$	−21.7570	−	12.5614i	−1.04557	−	0.603662i	−0.921407	+	0.388599i	$0.872959\pi$
$434$	1.62078	+	0.434286i	0.0777999	+	0.0208464i
$435$	−0.173473	+	0.237336i	−0.00831739	+	0.0113794i
$436$	19.1542	+	5.13235i	0.917320	+	0.245795i
$437$	8.07911	−	2.16479i	0.386476	−	0.103556i
$438$	1.45987	+	1.81337i	0.0697554	+	0.0866460i
$439$	−25.3935	−	14.6609i	−1.21196	−	0.699728i	−0.248777	−	0.968561i	$-0.580029\pi$
$439$	−25.3935	−	14.6609i	−1.21196	−	0.699728i	−0.963187	+	0.268833i	$0.913362\pi$
$440$	0.0233711	−	0.0872222i	0.00111417	−	0.00415816i
$441$	2.02010	−	2.21792i	0.0961954	−	0.105615i
$442$	5.52446	+	6.97646i	0.262772	+	0.331837i
$443$	20.1516	−	11.6346i	0.957433	−	0.552774i	0.0620512	−	0.998073i	$-0.480236\pi$
$443$	20.1516	−	11.6346i	0.957433	−	0.552774i	0.895382	+	0.445299i	$0.146902\pi$
$444$	15.4526	+	1.66880i	0.733348	+	0.0791977i
$445$	0.767949			0.0364043
$446$	−19.1534	−	33.1746i	−0.906939	−	1.57086i
$447$	−5.78416	−	4.22775i	−0.273581	−	0.199966i
$448$	−5.55850	−	5.55850i	−0.262615	−	0.262615i
$449$	−32.9617	+	8.83206i	−1.55556	+	0.416811i	−0.931254	−	0.364371i	$-0.881284\pi$
$449$	−32.9617	+	8.83206i	−1.55556	+	0.416811i	−0.624304	+	0.781181i	$0.714618\pi$
$450$	−1.71377	−	36.7150i	−0.0807878	−	1.73076i
$451$	1.37380	−	2.37949i	0.0646897	−	0.112046i
$452$	10.7375	−	18.5979i	0.505049	−	0.874770i
$453$	−22.6662	−	16.5672i	−1.06495	−	0.778394i
$454$	−14.4305	−	8.33146i	−0.677258	−	0.391015i
$455$	0.0792900	+	0.183451i	0.00371717	+	0.00860030i
$456$	−40.9507	−	50.8665i	−1.91769	−	2.38204i
$457$	11.2353	−	3.01048i	0.525564	−	0.140824i	0.0137248	−	0.999906i	$-0.495631\pi$
$457$	11.2353	−	3.01048i	0.525564	−	0.140824i	0.511839	+	0.859081i	$0.328964\pi$
$458$	−40.2538	+	23.2405i	−1.88094	+	1.08596i
$459$	5.22094	+	0.318528i	0.243693	+	0.0148676i
$460$	−0.172027	−	0.172027i	−0.00802078	−	0.00802078i
$461$	−11.9871	+	11.9871i	−0.558294	+	0.558294i	−0.928822	−	0.370527i	$-0.879177\pi$
$461$	−11.9871	+	11.9871i	−0.558294	+	0.558294i	0.370527	+	0.928822i	$0.379177\pi$
$462$	−1.13250	−	0.827766i	−0.0526887	−	0.0385112i
$463$	−1.89985	−	7.09036i	−0.0882937	−	0.329517i	0.907624	−	0.419785i	$-0.137894\pi$
$463$	−1.89985	−	7.09036i	−0.0882937	−	0.329517i	−0.995918	+	0.0902678i	$0.971228\pi$
$464$	−10.7906	+	6.22995i	−0.500941	+	0.289218i
$465$	0.0100927	+	0.0649235i	0.000468040	+	0.00301075i
$466$	5.19734	+	19.3967i	0.240762	+	0.898537i
$467$	32.5833			1.50778			0.753889	−	0.657002i	$-0.228176\pi$
$467$	32.5833			1.50778			0.753889	+	0.657002i	$0.228176\pi$
$468$	−28.4940	−	32.7242i	−1.31714	−	1.51268i
$469$	6.10489			0.281898
$470$	−0.428127	−	1.59779i	−0.0197480	−	0.0737006i
$471$	−18.7342	+	15.0822i	−0.863227	+	0.694952i
$472$	14.6475	−	8.45674i	0.674206	−	0.389253i
$473$	−0.557158	−	2.07934i	−0.0256182	−	0.0956082i
$474$	23.4776	−	10.3726i	1.07836	−	0.476429i
$475$	27.0111	−	27.0111i	1.23935	−	1.23935i
$476$	−2.85539	−	2.85539i	−0.130877	−	0.130877i
$477$	−9.20858	+	10.1103i	−0.421632	+	0.462921i
$478$	37.9194	−	21.8928i	1.73439	−	1.00135i
$479$	37.0506	−	9.92768i	1.69289	−	0.453607i	0.721754	−	0.692150i	$-0.243336\pi$
$479$	37.0506	−	9.92768i	1.69289	−	0.453607i	0.971132	+	0.238543i	$0.0766697\pi$
$480$	−0.00392130	+	0.0101287i	−0.000178982	+	0.000462311i
$481$	5.00698	+	6.32298i	0.228299	+	0.288303i
$482$	12.4131	+	7.16668i	0.565399	+	0.326433i
$483$	−1.73343	+	0.765845i	−0.0788739	+	0.0348471i
$484$	21.8444	−	37.8356i	0.992928	−	1.71980i
$485$	−0.226805	+	0.392838i	−0.0102987	+	0.0178378i
$486$	−38.2164	−	0.546162i	−1.73353	−	0.0247744i
$487$	−15.2121	+	4.07606i	−0.689325	+	0.184704i	−0.586444	−	0.809990i	$-0.699473\pi$
$487$	−15.2121	+	4.07606i	−0.689325	+	0.184704i	−0.102881	+	0.994694i	$0.532806\pi$
$488$	−13.7011	−	13.7011i	−0.620221	−	0.620221i
$489$	0.513913	−	4.75868i	0.0232399	−	0.215195i
$490$	−0.0679516	−	0.117696i	−0.00306974	−	0.00531694i
$491$	9.02238			0.407174			0.203587	−	0.979057i	$-0.434740\pi$
$491$	9.02238			0.407174			0.203587	+	0.979057i	$0.434740\pi$
$492$	−34.1043	+	46.6596i	−1.53754	+	2.10358i
$493$	2.66941	−	1.54119i	0.120224	−	0.0694116i
$494$	7.79710	−	67.1286i	0.350808	−	3.02026i
$495$	0.0117271	−	0.0536614i	0.000527093	−	0.00241190i
$496$	−0.720755	+	2.68990i	−0.0323629	+	0.120780i
$497$	0.465705	+	0.268875i	0.0208897	+	0.0120607i
$498$	−14.2810	+	36.8877i	−0.639946	+	1.65298i
$499$	−3.68483	+	0.987348i	−0.164956	+	0.0441998i	−0.340352	−	0.940298i	$-0.610546\pi$
$499$	−3.68483	+	0.987348i	−0.164956	+	0.0441998i	0.175396	+	0.984498i	$0.443879\pi$
$500$	−2.14711	−	0.575318i	−0.0960219	−	0.0257290i
$501$	4.30384	+	9.74141i	0.192281	+	0.435214i
$502$	−27.5320	−	7.37717i	−1.22881	−	0.329259i
$503$	−20.5870	−	11.8859i	−0.917930	−	0.529967i	−0.0349562	−	0.999389i	$-0.511129\pi$
$503$	−20.5870	−	11.8859i	−0.917930	−	0.529967i	−0.882974	+	0.469421i	$0.844463\pi$
$504$	10.9385	+	9.96289i	0.487240	+	0.443783i
$505$	0.789633	+	0.211582i	0.0351382	+	0.00941526i
$506$	0.443058	+	0.767399i	0.0196963	+	0.0341150i
$507$	1.73309	−	22.4499i	0.0769692	−	0.997033i
$508$	−34.0083	+	58.9042i	−1.50888	+	2.61345i
$509$	−10.1482	+	10.1482i	−0.449810	+	0.449810i	−0.895291	−	0.445481i	$-0.853033\pi$
$509$	−10.1482	+	10.1482i	−0.449810	+	0.449810i	0.445481	+	0.895291i	$0.353033\pi$
$510$	0.0855486	−	0.220972i	0.00378816	−	0.00978480i
$511$		−	0.548187i		−	0.0242504i
$512$	28.0557	−	28.0557i	1.23990	−	1.23990i
$513$	−26.3254	−	29.7464i	−1.16230	−	1.31333i
$514$	−3.77514	−	14.0890i	−0.166514	−	0.621439i
$515$	−0.0905415	+	0.337906i	−0.00398974	+	0.0148899i
$516$	6.95566	+	44.7436i	0.306206	+	1.96973i
$517$			4.02050i			0.176821i
$518$	−3.87818	−	3.87818i	−0.170398	−	0.170398i
$519$	−9.29027	−	3.59670i	−0.407798	−	0.157878i
$520$	−0.904755	+	0.391048i	−0.0396761	+	0.0171486i
$521$		−	17.7981i		−	0.779749i	−0.920868	−	0.389875i	$-0.872518\pi$
$521$		−	17.7981i		−	0.779749i	0.920868	−	0.389875i	$-0.127482\pi$
$522$	−18.9591	+	12.1587i	−0.829817	+	0.532171i
$523$	−21.9680	−	38.0497i	−0.960594	−	1.66380i	−0.721014	−	0.692920i	$-0.756324\pi$
$523$	−21.9680	−	38.0497i	−0.960594	−	1.66380i	−0.239580	−	0.970877i	$-0.577010\pi$
$524$	87.2261			3.81049
$525$	−5.10723	+	6.98742i	−0.222898	+	0.304956i
$526$	1.61955	−	6.04423i	0.0706156	−	0.263541i
$527$	0.178303	−	0.665436i	0.00776700	−	0.0289868i
$528$	1.37379	−	1.87954i	0.0597864	−	0.0817963i
$529$	−21.8029			−0.947952
$530$	0.309755	+	0.536512i	0.0134549	+	0.0233046i
$531$	8.66036	−	5.55398i	0.375828	−	0.241022i
$532$			30.6663i			1.32955i
$533$	−29.6712	+	4.36808i	−1.28520	+	0.189202i
$534$	54.8681	+	21.2420i	2.37437	+	0.919231i
$535$	0.612395	+	0.612395i	0.0264761	+	0.0264761i
$536$			30.1086i			1.30049i
$537$	2.69021	+	17.3053i	0.116091	+	0.746778i
$538$	17.0750	−	63.7248i	0.736156	−	2.74737i
$539$	0.0854928	+	0.319064i	0.00368244	+	0.0137430i
$540$	−0.366442	+	1.09574i	−0.0157692	+	0.0471529i
$541$	−0.0188884	+	0.0188884i	−0.000812075	+	0.000812075i	−0.707513	−	0.706701i	$-0.750183\pi$
$541$	−0.0188884	+	0.0188884i	−0.000812075	+	0.000812075i	0.706701	+	0.707513i	$0.250183\pi$
$542$		−	17.1406i		−	0.736250i
$543$	−6.57039	+	16.9713i	−0.281962	+	0.728309i
$544$	0.0805271	−	0.0805271i	0.00345257	−	0.00345257i
$545$	0.137000	−	0.237291i	0.00586844	−	0.0101644i
$546$	0.590703	+	15.3003i	0.0252798	+	0.654793i
$547$	5.13792	+	8.89914i	0.219682	+	0.380500i	0.954711	−	0.297536i	$-0.0961648\pi$
$547$	5.13792	+	8.89914i	0.219682	+	0.380500i	−0.735029	+	0.678036i	$0.762831\pi$
$548$	−31.0631	−	8.32332i	−1.32695	−	0.355555i
$549$	−8.71376	−	7.93657i	−0.371894	−	0.338724i
$550$	3.50476	+	2.02348i	0.149444	+	0.0862813i
$551$	−22.6105	−	6.05846i	−0.963238	−	0.258099i
$552$	−3.77705	−	8.54907i	−0.160762	−	0.363872i
$553$	−5.83800	−	1.56429i	−0.248257	−	0.0665203i
$554$	36.2442	−	9.71160i	1.53987	−	0.412606i
$555$	0.0775353	−	0.200274i	0.00329119	−	0.00850114i
$556$	73.1408	+	42.2278i	3.10186	+	1.79086i
$557$	−8.78859	+	32.7995i	−0.372385	+	1.38976i	0.484744	+	0.874656i	$0.338913\pi$
$557$	−8.78859	+	32.7995i	−0.372385	+	1.38976i	−0.857129	+	0.515102i	$0.827754\pi$
$558$	−1.07473	+	4.91780i	−0.0454968	+	0.208187i
$559$	−14.0181	+	18.8580i	−0.592902	+	0.797607i
$560$	0.195331	−	0.112775i	0.00825425	−	0.00476560i
$561$	−0.339852	+	0.464966i	−0.0143486	+	0.0196309i
$562$	40.0503			1.68942
$563$	−18.9143	−	32.7605i	−0.797142	−	1.38069i	−0.921470	−	0.388450i	$-0.873011\pi$
$563$	−18.9143	−	32.7605i	−0.797142	−	1.38069i	0.124327	−	0.992241i	$-0.460323\pi$
$564$	9.08027	−	84.0807i	0.382348	−	3.54044i
$565$	−0.209821	−	0.209821i	−0.00882723	−	0.00882723i
$566$	15.2421	−	4.08412i	0.640675	−	0.171668i
$567$	6.92911	+	5.74347i	0.290995	+	0.241203i
$568$	−1.32606	+	2.29680i	−0.0556401	+	0.0963714i
$569$	1.47007	−	2.54623i	0.0616284	−	0.106743i	−0.833565	−	0.552421i	$-0.813704\pi$
$569$	1.47007	−	2.54623i	0.0616284	−	0.106743i	0.895193	+	0.445678i	$0.147037\pi$
$570$	−1.64598	+	0.727209i	−0.0689426	+	0.0304594i
$571$	33.6007	+	19.3994i	1.40615	+	0.811839i	0.995014	−	0.0997363i	$-0.0317999\pi$
$571$	33.6007	+	19.3994i	1.40615	+	0.811839i	0.411133	+	0.911575i	$0.365133\pi$
$572$	4.72668	−	0.695842i	0.197632	−	0.0290946i
$573$	14.2349	−	36.7687i	0.594671	−	1.53603i
$574$	19.6995	−	5.27846i	0.822241	−	0.220319i
$575$	4.73477	−	2.73362i	0.197454	−	0.114000i
$576$	15.8799	−	17.4349i	0.661660	−	0.726454i
$577$	−29.4316	−	29.4316i	−1.22525	−	1.22525i	−0.965740	−	0.259512i	$-0.916438\pi$
$577$	−29.4316	−	29.4316i	−1.22525	−	1.22525i	−0.259512	−	0.965740i	$-0.583562\pi$
$578$	27.7163	−	27.7163i	1.15284	−	1.15284i
$579$	29.0524	−	12.8356i	1.20738	−	0.533430i
$580$	0.176219	+	0.657658i	0.00731709	+	0.0273078i
$581$	8.06654	−	4.65722i	0.334656	−	0.193214i
$582$	−27.0708	+	21.7937i	−1.12212	+	0.903378i
$583$	−0.389717	−	1.45444i	−0.0161404	−	0.0602369i
$584$	2.70359			0.111875
$585$	−0.538662	+	0.263272i	−0.0222709	+	0.0108850i
$586$	26.6619			1.10139
$587$	2.13175	+	7.95581i	0.0879869	+	0.328371i	0.995863	−	0.0908670i	$-0.0289638\pi$
$587$	2.13175	+	7.95581i	0.0879869	+	0.328371i	−0.907876	+	0.419238i	$0.862297\pi$
$588$	−1.06731	−	6.86566i	−0.0440150	−	0.283135i
$589$	−4.53079	+	2.61585i	−0.186688	+	0.107784i
$590$	−0.120628	−	0.450188i	−0.00496616	−	0.0185340i
$591$	8.68093	+	6.34505i	0.357086	+	0.261001i
$592$	6.43636	−	6.43636i	0.264533	−	0.264533i
$593$	31.3936	+	31.3936i	1.28918	+	1.28918i	0.935285	+	0.353896i	$0.115143\pi$
$593$	31.3936	+	31.3936i	1.28918	+	1.28918i	0.353896	+	0.935285i	$0.384857\pi$
$594$	2.32218	−	3.50960i	0.0952803	−	0.144001i
$595$	−0.0483217	+	0.0278986i	−0.00198100	+	0.00114373i
$596$	−16.0279	+	4.29467i	−0.656529	+	0.175916i
$597$	3.90724	+	4.85334i	0.159913	+	0.198634i
$598$	3.56457	−	8.99148i	0.145766	−	0.367689i
$599$	−10.9350	−	6.31331i	−0.446791	−	0.257955i	0.259683	−	0.965694i	$-0.416382\pi$
$599$	−10.9350	−	6.31331i	−0.446791	−	0.257955i	−0.706474	+	0.707739i	$0.749715\pi$
$600$	−34.4611	−	25.1882i	−1.40687	−	1.02831i
$601$	−10.5258	+	18.2312i	−0.429356	+	0.743667i	−0.996816	−	0.0797344i	$-0.974593\pi$
$601$	−10.5258	+	18.2312i	−0.429356	+	0.743667i	0.567460	+	0.823401i	$0.307926\pi$
$602$	7.98933	−	13.8379i	0.325621	−	0.563992i
$603$	0.853955	+	18.2948i	0.0347757	+	0.745020i
$604$	−62.8082	+	16.8294i	−2.55563	+	0.684779i
$605$	−0.426861	−	0.426861i	−0.0173544	−	0.0173544i
$606$	50.5649	+	36.9588i	2.05406	+	1.50135i
$607$	23.2906	+	40.3405i	0.945337	+	1.63737i	0.755075	+	0.655638i	$0.227600\pi$
$607$	23.2906	+	40.3405i	0.945337	+	1.63737i	0.190261	+	0.981733i	$0.439066\pi$
$608$	−0.864843			−0.0350740
$609$	5.27295	+	0.569451i	0.213671	+	0.0230753i
$610$	−0.462402	+	0.266968i	−0.0187221	+	0.0108092i
$611$	34.4046	−	27.2440i	1.39186	−	1.10217i
$612$	8.15745	−	8.95628i	0.329745	−	0.362036i
$613$	6.70700	−	25.0309i	0.270893	−	1.01099i	−0.687650	−	0.726042i	$-0.741358\pi$
$613$	6.70700	−	25.0309i	0.270893	−	1.01099i	0.958544	−	0.284946i	$-0.0919755\pi$
$614$	51.1272	+	29.5183i	2.06333	+	1.19126i
$615$	0.500787	+	0.622047i	0.0201937	+	0.0250834i
$616$	−1.57358	+	0.421640i	−0.0634014	+	0.0169884i
$617$	27.4733	+	7.36146i	1.10603	+	0.296361i	0.765220	−	0.643769i	$-0.222630\pi$
$617$	27.4733	+	7.36146i	1.10603	+	0.296361i	0.340815	+	0.940130i	$0.389297\pi$
$618$	−15.8157	+	21.6381i	−0.636200	+	0.870412i
$619$	26.4858	+	7.09686i	1.06456	+	0.285247i	0.748254	−	0.663412i	$-0.230892\pi$
$619$	26.4858	+	7.09686i	1.06456	+	0.285247i	0.316301	+	0.948659i	$0.397559\pi$
$620$	0.131784	+	0.0760858i	0.00529259	+	0.00305568i
$621$	−2.53751	−	5.08751i	−0.101827	−	0.204155i
$622$	36.2080	+	9.70190i	1.45181	+	0.389011i
$623$	−6.92730	−	11.9984i	−0.277537	−	0.480707i
$624$	−25.3929	+	0.980350i	−1.01653	+	0.0392454i
$625$	12.4770	−	21.6107i	0.499078	−	0.864429i
$626$	−5.83849	+	5.83849i	−0.233353	+	0.233353i
$627$	4.32179	−	0.671848i	0.172595	−	0.0268310i
$628$			55.7028i			2.22278i
$629$	−1.59225	+	1.59225i	−0.0634871	+	0.0634871i
$630$	0.343198	−	0.220096i	0.0136733	−	0.00876885i
$631$	−10.9175	−	40.7446i	−0.434618	−	1.62202i	−0.741979	−	0.670423i	$-0.766113\pi$
$631$	−10.9175	−	40.7446i	−0.434618	−	1.62202i	0.307361	−	0.951593i	$-0.400554\pi$
$632$	7.71487	−	28.7923i	0.306881	−	1.14530i
$633$	−45.3768	−	17.5675i	−1.80357	−	0.698245i
$634$			39.5640i			1.57129i
$635$	0.664555	+	0.664555i	0.0263721	+	0.0263721i
$636$	4.86530	+	31.2969i	0.192922	+	1.24100i
$637$	2.15100	−	2.89365i	0.0852256	−	0.114651i
$638$		−	2.47991i		−	0.0981807i
$639$	−0.740604	+	1.43320i	−0.0292978	+	0.0566967i
$640$	−0.540432	−	0.936056i	−0.0213625	−	0.0370009i
$641$	−12.7331			−0.502927			−0.251464	−	0.967867i	$-0.580912\pi$
$641$	−12.7331			−0.502927			−0.251464	+	0.967867i	$0.580912\pi$
$642$	26.8149	+	60.6934i	1.05830	+	2.39538i
$643$	−8.46266	+	31.5831i	−0.333735	+	1.24551i	0.571500	+	0.820602i	$0.306362\pi$
$643$	−8.46266	+	31.5831i	−0.333735	+	1.24551i	−0.905234	+	0.424913i	$0.860305\pi$
$644$	−1.13597	+	4.23952i	−0.0447637	+	0.167060i
$645$	0.622056	+	0.0671788i	0.0244934	+	0.00264516i
$646$	18.8677			0.742341
$647$	12.6079	+	21.8375i	0.495667	+	0.858521i	0.999988	−	0.00499569i	$-0.00159019\pi$
$647$	12.6079	+	21.8375i	0.495667	+	0.858521i	−0.504320	+	0.863517i	$0.668257\pi$
$648$	−28.3261	+	34.1735i	−1.11275	+	1.34246i
$649$			1.13280i			0.0444664i
$650$	−6.43376	−	43.7029i	−0.252353	−	1.71417i
$651$	0.923323	−	0.743333i	0.0361879	−	0.0291335i
$652$	−7.83856	−	7.83856i	−0.306982	−	0.306982i
$653$		−	0.344590i		−	0.0134849i	−0.999977	−	0.00674243i	$-0.997854\pi$
$653$		−	0.344590i		−	0.0134849i	0.999977	−	0.00674243i	$-0.00214620\pi$
$654$	16.3520	−	13.1644i	0.639413	−	0.514767i
$655$	0.311942	−	1.16418i	0.0121886	−	0.0454884i
$656$	8.76031	+	32.6939i	0.342033	+	1.27648i
$657$	1.64277	−	0.0766806i	0.0640906	−	0.00299160i
$658$	−21.1020	+	21.1020i	−0.822640	+	0.822640i
$659$		−	42.7070i		−	1.66363i	−0.555053	−	0.831815i	$-0.687302\pi$
$659$		−	42.7070i		−	1.66363i	0.555053	−	0.831815i	$-0.312698\pi$
$660$	−0.0797762	−	0.0990932i	−0.00310529	−	0.00385720i
$661$	−30.9080	+	30.9080i	−1.20218	+	1.20218i	−0.228678	+	0.973502i	$0.573440\pi$
$661$	−30.9080	+	30.9080i	−1.20218	+	1.20218i	−0.973502	+	0.228678i	$0.926560\pi$
$662$	−14.1291	+	24.4723i	−0.549144	+	0.951145i
$663$	6.28178	−	0.242522i	0.243964	−	0.00941879i
$664$	22.9688	+	39.7832i	0.891363	+	1.54389i
$665$	0.409295	+	0.109670i	0.0158718	+	0.00425283i
$666$	11.0794	−	12.1644i	0.429319	−	0.471360i
$667$	−2.90140	−	1.67512i	−0.112343	−	0.0648610i
$668$	23.8249	+	6.38387i	0.921814	+	0.246999i
$669$	−26.9046	−	2.90556i	−1.04019	−	0.112335i
$670$	0.801403	+	0.214735i	0.0309609	+	0.00829595i
$671$	1.25354	−	0.335884i	0.0483922	−	0.0129666i
$672$	0.193624	−	0.0300999i	0.00746919	−	0.00116113i
$673$	13.3675	+	7.71776i	0.515281	+	0.297498i	0.735002	−	0.678065i	$-0.237181\pi$
$673$	13.3675	+	7.71776i	0.515281	+	0.297498i	−0.219721	+	0.975563i	$0.570515\pi$
$674$	13.9257	−	51.9715i	0.536399	−	2.00187i
$675$	−21.6539	−	14.3276i	−0.833458	−	0.551471i
$676$	−37.9838	−	35.7324i	−1.46092	−	1.37432i
$677$	21.9763	−	12.6880i	0.844616	−	0.487639i	−0.0142146	−	0.999899i	$-0.504525\pi$
$677$	21.9763	−	12.6880i	0.844616	−	0.487639i	0.858831	+	0.512260i	$0.171191\pi$
$678$	−9.18740	−	20.7950i	−0.352840	−	0.798626i
$679$	8.18360			0.314058
$680$	−0.137592	−	0.238317i	−0.00527642	−	0.00913903i
$681$	−10.7672	+	4.75702i	−0.412598	+	0.182289i
$682$	−0.391921	−	0.391921i	−0.0150074	−	0.0150074i
$683$	−6.00867	+	1.61002i	−0.229915	+	0.0616056i	−0.371937	−	0.928258i	$-0.621306\pi$
$683$	−6.00867	+	1.61002i	−0.229915	+	0.0616056i	0.142022	+	0.989864i	$0.454640\pi$
$684$	−91.8989	+	4.28962i	−3.51384	+	0.164018i
$685$	−0.222178	+	0.384824i	−0.00848899	+	0.0147034i
$686$	−1.22592	+	2.12335i	−0.0468058	+	0.0810700i
$687$	−3.52558	+	32.6458i	−0.134509	+	1.24552i
$688$	22.9659	+	13.2593i	0.875565	+	0.505508i
$689$	−9.80527	+	13.1906i	−0.373551	+	0.502523i
$690$	−0.254490	+	0.0395619i	−0.00968826	+	0.00150610i
$691$	30.7648	−	8.24342i	1.17035	−	0.313594i	0.379258	−	0.925291i	$-0.376179\pi$
$691$	30.7648	−	8.24342i	1.17035	−	0.313594i	0.791092	+	0.611697i	$0.209513\pi$
$692$	−19.9817	+	11.5364i	−0.759590	+	0.438549i
$693$	−0.944191	+	0.300830i	−0.0358668	+	0.0114276i
$694$	1.51205	+	1.51205i	0.0573966	+	0.0573966i
$695$	0.825172	−	0.825172i	0.0313006	−	0.0313006i
$696$	−2.80846	+	26.0056i	−0.106455	+	0.985738i
$697$	−2.16715	−	8.08793i	−0.0820868	−	0.306352i
$698$	15.5204	−	8.96073i	0.587458	−	0.339169i
$699$	13.2290	+	5.12157i	0.500367	+	0.193716i
$700$	5.18808	+	19.3622i	0.196091	+	0.731821i
$701$	24.3784			0.920761			0.460380	−	0.887722i	$-0.347713\pi$
$701$	24.3784			0.920761			0.460380	+	0.887722i	$0.347713\pi$
$702$	−45.7684	+	3.91040i	−1.72742	+	0.147589i
$703$	17.1004			0.644954
$704$	0.672052	+	2.50813i	0.0253289	+	0.0945287i
$705$	−1.08973	−	0.421885i	−0.0410415	−	0.0158891i
$706$	54.7956	−	31.6362i	2.06226	−	1.19065i
$707$	−3.81716	−	14.2458i	−0.143559	−	0.535769i
$708$	2.55843	−	23.6903i	0.0961517	−	0.890337i
$709$	−14.7958	+	14.7958i	−0.555668	+	0.555668i	−0.928071	−	0.372403i	$-0.878534\pi$
$709$	−14.7958	+	14.7958i	−0.555668	+	0.555668i	0.372403	+	0.928071i	$0.378534\pi$
$710$	0.0516766	+	0.0516766i	0.00193939	+	0.00193939i
$711$	3.87114	−	17.7138i	0.145179	−	0.664318i
$712$	59.1748	−	34.1646i	2.21767	−	1.28037i
$713$	−0.723265	+	0.193798i	−0.0270865	+	0.00725780i
$714$	−4.22416	+	0.656672i	−0.158085	+	0.0245753i
$715$	0.00761655	−	0.0655742i	0.000284843	−	0.00245234i
$716$	35.1270	+	20.2806i	1.31276	+	0.757921i
$717$	3.32112	−	30.7526i	0.124029	−	1.14848i
$718$	−21.7817	+	37.7269i	−0.812884	+	1.40796i
$719$	−10.0910	+	17.4780i	−0.376329	+	0.651821i	−0.990525	−	0.137332i	$-0.956147\pi$
$719$	−10.0910	+	17.4780i	−0.376329	+	0.651821i	0.614196	+	0.789154i	$0.289480\pi$
$720$	0.365279	+	0.569582i	0.0136131	+	0.0212271i
$721$	6.09617	−	1.63347i	0.227033	−	0.0608334i
$722$	−68.3772	−	68.3772i	−2.54474	−	2.54474i
$723$	9.26185	−	4.09196i	0.344452	−	0.152182i
$724$	21.0746	+	36.5022i	0.783230	+	1.35659i
$725$	−15.3008			−0.568258
$726$	−18.6909	−	42.3054i	−0.693684	−	1.57010i
$727$	−16.1860	+	9.34496i	−0.600304	+	0.346585i	−0.769161	−	0.639055i	$-0.779326\pi$
$727$	−16.1860	+	9.34496i	−0.600304	+	0.346585i	0.168857	+	0.985640i	$0.445992\pi$
$728$	14.2711	+	10.6085i	0.528923	+	0.393175i
$729$	−16.2424	+	21.5681i	−0.601571	+	0.798819i
$730$	0.0192821	−	0.0719618i	0.000713662	−	0.00266342i
$731$	−5.68137	−	3.28014i	−0.210133	−	0.121320i
$732$	−26.9738	+	4.19323i	−0.996979	+	0.154986i
$733$	36.2670	−	9.71770i	1.33955	−	0.358932i	0.483283	−	0.875464i	$-0.339444\pi$
$733$	36.2670	−	9.71770i	1.33955	−	0.358932i	0.856268	+	0.516532i	$0.172777\pi$
$734$	81.7441	+	21.9033i	3.01723	+	0.808465i
$735$	−0.0954510	−	0.0103082i	−0.00352076	−	0.000380224i
$736$	−0.119562	−	0.0320365i	−0.00440710	−	0.00118088i
$737$	−1.74639	−	1.00828i	−0.0643292	−	0.0371405i
$738$	18.5737	+	58.2959i	0.683709	+	2.14590i
$739$	−26.4064	−	7.07557i	−0.971375	−	0.260279i	−0.261966	−	0.965077i	$-0.584371\pi$
$739$	−26.4064	−	7.07557i	−0.971375	−	0.260279i	−0.709408	+	0.704798i	$0.751038\pi$
$740$	−0.248695	−	0.430752i	−0.00914220	−	0.0158348i
$741$	−35.0348	−	32.4302i	−1.28704	−	1.19135i
$742$	5.58832	−	9.67925i	0.205154	−	0.355336i
$743$	11.0112	−	11.0112i	0.403964	−	0.403964i	−0.475664	−	0.879627i	$-0.657792\pi$
$743$	11.0112	−	11.0112i	0.403964	−	0.403964i	0.879627	+	0.475664i	$0.157792\pi$
$744$	3.66603	+	4.55372i	0.134403	+	0.166947i
$745$			0.229279i			0.00840013i
$746$	−43.0191	+	43.0191i	−1.57504	+	1.57504i
$747$	15.0848	+	23.5218i	0.551924	+	0.860619i
$748$	0.345232	+	1.28842i	0.0126229	+	0.0471094i
$749$	4.04394	−	15.0922i	0.147762	−	0.551457i
$750$	−1.83300	+	1.47568i	−0.0669315	+	0.0538841i
$751$		−	28.0479i		−	1.02348i	−0.859140	−	0.511741i	$-0.829001\pi$
$751$		−	28.0479i		−	1.02348i	0.859140	−	0.511741i	$-0.170999\pi$
$752$	−35.0215	−	35.0215i	−1.27710	−	1.27710i
$753$	−15.6844	+	12.6269i	−0.571571	+	0.460150i
$754$	−21.2213	+	16.8046i	−0.772835	+	0.611986i
$755$			0.898470i			0.0326987i
$756$	20.4253	−	4.15881i	0.742860	−	0.151255i
$757$	1.54232	+	2.67138i	0.0560566	+	0.0970928i	0.892692	−	0.450667i	$-0.148814\pi$
$757$	1.54232	+	2.67138i	0.0560566	+	0.0970928i	−0.836635	+	0.547760i	$0.815481\pi$
$758$	16.9998			0.617462
$759$	0.622360	+	0.0672116i	0.0225902	+	0.00243963i
$760$	−0.540880	+	2.01859i	−0.0196198	+	0.0732220i
$761$	−12.1678	+	45.4109i	−0.441083	+	1.64614i	0.284992	+	0.958530i	$0.408009\pi$
$761$	−12.1678	+	45.4109i	−0.441083	+	1.64614i	−0.726076	+	0.687615i	$0.758658\pi$
$762$	29.0988	+	65.8629i	1.05414	+	2.38596i
$763$	−4.94326			−0.178958
$764$	−45.6585	−	79.0828i	−1.65186	−	2.86111i
$765$	−0.0903639	−	0.140905i	−0.00326711	−	0.00509443i
$766$			22.3131i			0.806204i
$767$	9.69373	−	7.67619i	0.350020	−	0.277171i
$768$	−8.53762	−	54.9198i	−0.308075	−	1.98175i
$769$	−14.0525	−	14.0525i	−0.506745	−	0.506745i	0.406781	−	0.913526i	$-0.366651\pi$
$769$	−14.0525	−	14.0525i	−0.506745	−	0.506745i	−0.913526	+	0.406781i	$0.866651\pi$
$770$			0.0448914i			0.00161777i
$771$	−9.60902	−	3.72010i	−0.346060	−	0.133976i
$772$	19.0390	−	71.0546i	0.685229	−	2.55731i
$773$	5.32003	+	19.8546i	0.191348	+	0.714122i	0.993182	+	0.116574i	$0.0371913\pi$
$773$	5.32003	+	19.8546i	0.191348	+	0.714122i	−0.801834	+	0.597547i	$0.796142\pi$
$774$	42.5862	+	22.0063i	1.53073	+	0.790999i
$775$	−2.41811	+	2.41811i	−0.0868612	+	0.0868612i
$776$			40.3605i			1.44886i
$777$	−3.82849	+	0.595161i	−0.137346	+	0.0213513i
$778$	26.4594	−	26.4594i	0.948616	−	0.948616i
$779$	−31.7939	+	55.0687i	−1.13914	+	1.97304i
$780$	−0.307384	+	1.35415i	−0.0110061	+	0.0484864i
$781$	−0.0888144	−	0.153831i	−0.00317803	−	0.00550451i
$782$	2.60840	+	0.698919i	0.0932763	+	0.0249933i
$783$	−0.968913	+	15.8813i	−0.0346261	+	0.567552i
$784$	−3.52398	−	2.03457i	−0.125857	−	0.0726633i
$785$	0.743450	+	0.199207i	0.0265349	+	0.00711000i
$786$	54.4896	−	74.5495i	1.94358	−	2.65909i
$787$	−29.5357	−	7.91406i	−1.05283	−	0.282106i	−0.309411	−	0.950929i	$-0.600132\pi$
$787$	−29.5357	−	7.91406i	−1.05283	−	0.282106i	−0.743422	+	0.668823i	$0.766798\pi$
$788$	24.0549	−	6.44549i	0.856920	−	0.229611i
$789$	−2.77205	−	3.44327i	−0.0986876	−	0.122584i
$790$	−0.711345	−	0.410695i	−0.0253085	−	0.0146119i
$791$	−1.38555	+	5.17094i	−0.0492644	+	0.183857i
$792$	−1.48366	−	4.65663i	−0.0527195	−	0.165466i
$793$	−11.3686	−	8.45083i	−0.403709	−	0.300098i
$794$	−35.6045	+	20.5563i	−1.26356	+	0.729515i
$795$	0.435111	+	0.0469897i	0.0154318	+	0.00166655i
$796$	14.4305			0.511477
$797$	−12.6969	−	21.9917i	−0.449748	−	0.778986i	0.548621	−	0.836071i	$-0.315153\pi$
$797$	−12.6969	−	21.9917i	−0.449748	−	0.778986i	−0.998369	+	0.0570846i	$0.981820\pi$
$798$	26.2096	+	19.1570i	0.927808	+	0.678152i
$799$	8.66374	+	8.66374i	0.306501	+	0.306501i
$800$	−0.546047	+	0.146313i	−0.0193057	+	0.00517294i
$801$	34.9872	−	22.4377i	1.23621	−	0.792796i
$802$	−36.2784	+	62.8361i	−1.28104	+	2.21882i
$803$	−0.0905382	+	0.156817i	−0.00319502	+	0.00553395i
$804$	34.2451	+	25.0304i	1.20773	+	0.882754i
$805$	0.0525211	+	0.0303231i	0.00185113	+	0.00106875i
$806$	−0.698018	+	6.00955i	−0.0245866	+	0.211677i
$807$	−29.2259	−	36.3027i	−1.02880	−	1.27791i
$808$	70.2586	−	18.8257i	2.47169	−	0.662287i
$809$	−13.1718	+	7.60477i	−0.463098	+	0.267370i	−0.713346	−	0.700812i	$-0.752821\pi$
$809$	−13.1718	+	7.60477i	−0.463098	+	0.267370i	0.250248	+	0.968182i	$0.419488\pi$
$810$	0.707577	+	0.997686i	0.0248617	+	0.0350551i
$811$	−22.1094	−	22.1094i	−0.776365	−	0.776365i	0.202846	−	0.979211i	$-0.434981\pi$
$811$	−22.1094	−	22.1094i	−0.776365	−	0.776365i	−0.979211	+	0.202846i	$0.934981\pi$
$812$	8.68567	−	8.68567i	0.304807	−	0.304807i
$813$	−9.77568	−	7.14523i	−0.342848	−	0.250594i
$814$	0.468892	+	1.74993i	0.0164347	+	0.0613350i
$815$	−0.132652	+	0.0765864i	−0.00464658	+	0.00268271i
$816$	−1.08983	−	7.01056i	−0.0381518	−	0.245419i
$817$	12.8943	+	48.1224i	0.451116	+	1.68359i
$818$	19.1426			0.669306
$819$	8.97239	+	6.04121i	0.313521	+	0.211097i
$820$	1.84954			0.0645889
$821$	13.1465	+	49.0633i	0.458815	+	1.71232i	0.676623	+	0.736330i	$0.263443\pi$
$821$	13.1465	+	49.0633i	0.458815	+	1.71232i	−0.217808	+	0.975992i	$0.569891\pi$
$822$	−26.5186	+	21.3491i	−0.924942	+	0.744636i
$823$	24.4925	−	14.1408i	0.853755	−	0.492916i	−0.00816075	−	0.999967i	$-0.502598\pi$
$823$	24.4925	−	14.1408i	0.853755	−	0.492916i	0.861916	+	0.507051i	$0.169264\pi$
$824$	8.05605	+	30.0656i	0.280646	+	1.04738i
$825$	2.61504	−	1.15535i	0.0910439	−	0.0402240i
$826$	−5.94563	+	5.94563i	−0.206875	+	0.206875i
$827$	−5.64422	−	5.64422i	−0.196269	−	0.196269i	0.602130	−	0.798398i	$-0.294319\pi$
$827$	−5.64422	−	5.64422i	−0.196269	−	0.196269i	−0.798398	+	0.602130i	$0.794319\pi$
$828$	−12.8636	−	2.81119i	−0.447041	−	0.0976957i
$829$	3.36035	−	1.94010i	0.116710	−	0.0673824i	−0.440509	−	0.897748i	$-0.645202\pi$
$829$	3.36035	−	1.94010i	0.116710	−	0.0673824i	0.557218	+	0.830366i	$0.311869\pi$
$830$	1.22273	−	0.327629i	0.0424415	−	0.0113722i
$831$	9.57001	−	24.7193i	0.331980	−	0.857504i
$832$	16.9088	−	22.7467i	0.586207	−	0.788601i
$833$	0.871775	+	0.503320i	0.0302052	+	0.0174390i
$834$	81.7814	−	36.1317i	2.83186	−	1.25114i
$835$	0.170407	−	0.295154i	0.00589719	−	0.0102142i
$836$	5.06483	−	8.77254i	0.175171	−	0.303405i
$837$	2.35673	+	2.66298i	0.0814605	+	0.0920460i
$838$	44.7917	−	12.0019i	1.54730	−	0.414599i
$839$	−9.52706	−	9.52706i	−0.328911	−	0.328911i	0.523261	−	0.852172i	$-0.324715\pi$
$839$	−9.52706	−	9.52706i	−0.328911	−	0.328911i	−0.852172	+	0.523261i	$0.824715\pi$
$840$	0.0508388	−	0.470753i	0.00175411	−	0.0162425i
$841$	−9.81195	−	16.9948i	−0.338343	−	0.586027i
$842$	−0.107614			−0.00370864
$843$	16.6954	−	22.8417i	0.575020	−	0.786709i
$844$	−97.5973	+	56.3479i	−3.35944	+	1.93957i
$845$	−0.612750	+	0.379172i	−0.0210792	+	0.0130439i
$846$	−66.1888	−	60.2853i	−2.27562	−	2.07265i
$847$	−2.81877	+	10.5198i	−0.0968541	+	0.361464i
$848$	16.0640	+	9.27455i	0.551640	+	0.318489i
$849$	4.02458	−	10.3955i	0.138123	−	0.356772i
$850$	11.9128	−	3.19201i	0.408604	−	0.109485i
$851$	2.36407	+	0.633452i	0.0810394	+	0.0217144i
$852$	1.50995	+	3.41765i	0.0517300	+	0.117087i
$853$	−3.00750	−	0.805858i	−0.102975	−	0.0275921i	0.206964	−	0.978349i	$-0.433642\pi$
$853$	−3.00750	−	0.805858i	−0.102975	−	0.0275921i	−0.309939	+	0.950757i	$0.600308\pi$
$854$	8.34221	+	4.81638i	0.285465	+	0.164813i
$855$	−0.271400	+	1.24189i	−0.00928170	+	0.0424717i
$856$	74.4328	+	19.9442i	2.54406	+	0.681679i
$857$	17.8333	+	30.8882i	0.609174	+	1.05512i	0.991377	+	0.131042i	$0.0418323\pi$
$857$	17.8333	+	30.8882i	0.609174	+	1.05512i	−0.382203	+	0.924079i	$0.624834\pi$
$858$	2.35801	−	4.47444i	0.0805012	−	0.152755i
$859$	14.1270	−	24.4687i	0.482007	−	0.834861i	−0.517780	−	0.855514i	$-0.673241\pi$
$859$	14.1270	−	24.4687i	0.482007	−	0.834861i	0.999787	+	0.0206532i	$0.00657458\pi$
$860$	1.02466	−	1.02466i	0.0349405	−	0.0349405i
$861$	5.20151	−	13.4355i	0.177267	−	0.457880i
$862$			25.5585i			0.870526i
$863$	−17.7006	+	17.7006i	−0.602535	+	0.602535i	−0.940984	−	0.338450i	$-0.890098\pi$
$863$	−17.7006	+	17.7006i	−0.602535	+	0.602535i	0.338450	+	0.940984i	$0.390098\pi$
$864$	0.117286	+	0.576028i	0.00399014	+	0.0195969i
$865$	0.0825142	+	0.307947i	0.00280557	+	0.0104705i
$866$	−15.9425	+	59.4981i	−0.541747	+	2.02183i
$867$	−4.25345	−	27.3611i	−0.144455	−	0.929232i
$868$		−	2.74534i		−	0.0931828i
$869$	1.41169	+	1.41169i	0.0478883	+	0.0478883i
$870$	0.672163	+	0.260226i	0.0227885	+	0.00882248i
$871$	3.20589	+	21.7768i	0.108627	+	0.737878i
$872$		−	24.3795i		−	0.825595i
$873$	1.14473	+	24.5241i	0.0387431	+	0.830015i
$874$	−10.2537	−	17.7600i	−0.346837	−	0.600740i
$875$	0.554121			0.0187327
$876$	2.24760	−	3.07503i	0.0759392	−	0.103896i
$877$	3.74962	−	13.9938i	0.126616	−	0.472536i	−0.873276	−	0.487225i	$-0.838009\pi$
$877$	3.74962	−	13.9938i	0.126616	−	0.472536i	0.999892	+	0.0146888i	$0.00467577\pi$
$878$	−18.6071	+	69.4427i	−0.627960	+	2.34358i
$879$	11.1143	−	15.2059i	0.374876	−	0.512883i
$880$	−0.0745032			−0.00251150
$881$	−10.2550	−	17.7622i	−0.345500	−	0.598423i	0.639945	−	0.768421i	$-0.278957\pi$
$881$	−10.2550	−	17.7622i	−0.345500	−	0.598423i	−0.985444	+	0.169998i	$0.945624\pi$
$882$	−6.53461	−	3.37674i	−0.220032	−	0.113701i
$883$			37.3389i			1.25656i	0.777989	+	0.628278i	$0.216240\pi$
$883$			37.3389i			1.25656i	−0.777989	+	0.628278i	$0.783760\pi$
$884$	8.68602	−	11.6850i	0.292143	−	0.393007i
$885$	−0.307039	−	0.118869i	−0.0103210	−	0.00399574i
$886$	−40.3419	−	40.3419i	−1.35531	−	1.35531i
$887$		−	24.0715i		−	0.808241i	−0.914706	−	0.404121i	$-0.867578\pi$
$887$		−	24.0715i		−	0.808241i	0.914706	−	0.404121i	$-0.132422\pi$
$888$	−2.93526	−	18.8816i	−0.0985009	−	0.633626i
$889$	4.38838	−	16.3777i	0.147182	−	0.549289i
$890$	−0.487326	−	1.81873i	−0.0163352	−	0.0609639i
$891$	−1.03358	−	2.78741i	−0.0346263	−	0.0933818i
$892$	−44.3176	+	44.3176i	−1.48386	+	1.48386i
$893$		−	93.0467i		−	3.11369i
$894$	−6.34202	+	16.3814i	−0.212109	+	0.547877i
$895$	0.396302	−	0.396302i	0.0132469	−	0.0132469i
$896$	−9.74997	+	16.8874i	−0.325724	+	0.564170i
$897$	−3.64213	−	5.78116i	−0.121607	−	0.193027i
$898$	41.8338	+	72.4583i	1.39601	+	2.41796i
$899$	2.02415	+	0.542370i	0.0675093	+	0.0180891i
$900$	−57.2976	+	18.2557i	−1.90992	+	0.608523i
$901$	−3.97396	−	2.29437i	−0.132392	−	0.0764365i
$902$	−6.50712	−	1.74358i	−0.216663	−	0.0580547i
$903$	−4.56167	−	10.3250i	−0.151803	−	0.343594i
$904$	−25.5024	−	6.83335i	−0.848198	−	0.227274i
$905$	0.562553	−	0.150736i	0.0186999	−	0.00501062i
$906$	−24.8523	+	64.1935i	−0.825663	+	2.13269i
$907$	−4.03563	−	2.32997i	−0.134001	−	0.0773655i	0.431501	−	0.902113i	$-0.357984\pi$
$907$	−4.03563	−	2.32997i	−0.134001	−	0.0773655i	−0.565502	+	0.824747i	$0.691318\pi$
$908$	−7.05607	+	26.3336i	−0.234164	+	0.873912i
$909$	42.1570	−	13.4317i	1.39826	−	0.445502i
$910$	0.384149	−	0.304196i	0.0127344	−	0.0100840i
$911$	−12.0775	+	6.97294i	−0.400145	+	0.231024i	−0.686547	−	0.727086i	$-0.740874\pi$
$911$	−12.0775	+	6.97294i	−0.400145	+	0.231024i	0.286401	+	0.958110i	$0.407541\pi$
$912$	−31.7936	+	43.4982i	−1.05279	+	1.44037i
$913$	−3.07673			−0.101825
$914$	−14.2594	−	24.6980i	−0.471659	−	0.816937i
$915$	−0.0404988	+	0.375007i	−0.00133885	+	0.0123974i
$916$	53.7746	+	53.7746i	1.77676	+	1.77676i
$917$	−21.0031	+	5.62776i	−0.693583	+	0.185845i
$918$	−2.55875	−	12.5669i	−0.0844514	−	0.414768i
$919$	−8.29249	+	14.3630i	−0.273544	+	0.473792i	−0.969767	−	0.244034i	$-0.921529\pi$
$919$	−8.29249	+	14.3630i	−0.273544	+	0.473792i	0.696223	+	0.717826i	$0.254863\pi$
$920$	−0.149550	+	0.259028i	−0.00493051	+	0.00853989i
$921$	38.1480	−	16.8541i	1.25702	−	0.555361i
$922$	35.9957	+	20.7821i	1.18546	+	0.684423i
$923$	−0.714547	+	1.80241i	−0.0235196	+	0.0593271i
$924$	−0.828610	+	2.14030i	−0.0272593	+	0.0704107i
$925$	10.7969	−	2.89302i	0.355000	−	0.0951218i
$926$	−15.5864	+	8.99882i	−0.512202	+	0.295720i
$927$	5.74780	+	18.0401i	0.188783	+	0.592516i
$928$	0.244951	+	0.244951i	0.00804091	+	0.00804091i
$929$	−6.37357	+	6.37357i	−0.209110	+	0.209110i	−0.803889	−	0.594779i	$-0.797240\pi$
$929$	−6.37357	+	6.37357i	−0.209110	+	0.209110i	0.594779	+	0.803889i	$0.297240\pi$
$930$	0.147353	−	0.0651018i	0.00483190	−	0.00213477i
$931$	−1.97857	−	7.38411i	−0.0648449	−	0.242004i
$932$	28.4532	−	16.4275i	0.932016	−	0.538100i
$933$	20.6269	−	16.6060i	0.675296	−	0.543655i
$934$	−20.6768	−	77.1669i	−0.676566	−	2.52498i
$935$	0.0184308			0.000602753
$936$	−29.7945	+	44.2507i	−0.973863	+	1.44638i
$937$	16.5690			0.541285			0.270643	−	0.962680i	$-0.412764\pi$
$937$	16.5690			0.541285			0.270643	+	0.962680i	$0.412764\pi$
$938$	−3.87405	−	14.4582i	−0.126492	−	0.472076i
$939$	0.895998	+	5.76368i	0.0292398	+	0.188091i
$940$	−2.34381	+	1.35320i	−0.0764466	+	0.0441365i
$941$	3.45290	+	12.8864i	0.112561	+	0.420085i	0.999093	−	0.0425835i	$-0.0135588\pi$
$941$	3.45290	+	12.8864i	0.112561	+	0.420085i	−0.886532	+	0.462668i	$0.846892\pi$
$942$	47.6075	+	34.7972i	1.55114	+	1.13375i
$943$	−6.43532	+	6.43532i	−0.209563	+	0.209563i
$944$	−9.86755	−	9.86755i	−0.321161	−	0.321161i
$945$	0.0175393	−	0.287484i	0.000570552	−	0.00935184i
$946$	−4.57093	+	2.63903i	−0.148614	+	0.0858021i
$947$	−20.4815	+	5.48801i	−0.665560	+	0.178336i	−0.575754	−	0.817623i	$-0.695291\pi$
$947$	−20.4815	+	5.48801i	−0.665560	+	0.178336i	−0.0898061	+	0.995959i	$0.528625\pi$
$948$	−26.3344	−	32.7109i	−0.855300	−	1.06240i
$949$	1.95544	−	0.287872i	0.0634762	−	0.00934471i
$950$	−81.1110	−	46.8294i	−2.63159	−	1.51935i
$951$	22.5644	+	16.4927i	0.731699	+	0.534812i
$952$	−2.48231	+	4.29949i	−0.0804521	+	0.139347i
$953$	−24.9724	+	43.2536i	−0.808937	+	1.40112i	0.104664	+	0.994508i	$0.466623\pi$
$953$	−24.9724	+	43.2536i	−0.808937	+	1.40112i	−0.913601	+	0.406612i	$0.866710\pi$
$954$	29.7879	+	15.3928i	0.964417	+	0.498360i
$955$	−1.21878	+	0.326571i	−0.0394388	+	0.0105676i
$956$	−50.6560	−	50.6560i	−1.63833	−	1.63833i
$957$	−1.41436	−	1.03378i	−0.0457196	−	0.0334173i
$958$	−47.0233	−	81.4467i	−1.51925	−	2.63142i
$959$	8.01666			0.258871
$960$	−0.750332	−	0.0810319i	−0.0242169	−	0.00261529i
$961$	−26.4412	+	15.2658i	−0.852941	+	0.492446i
$962$	11.7973	−	15.8705i	0.380361	−	0.511684i
$963$	45.7930	+	10.0075i	1.47566	+	0.322488i
$964$	6.06960	−	22.6520i	0.195489	−	0.729573i
$965$	−0.880257	−	0.508217i	−0.0283365	−	0.0163601i
$966$	2.91375	+	3.61928i	0.0937483	+	0.116448i
$967$	−23.6907	+	6.34789i	−0.761840	+	0.204134i	−0.618764	−	0.785577i	$-0.712366\pi$
$967$	−23.6907	+	6.34789i	−0.761840	+	0.204134i	−0.143076	+	0.989712i	$0.545699\pi$
$968$	−51.8823	−	13.9018i	−1.66756	−	0.446821i
$969$	7.86522	−	10.7607i	0.252667	−	0.345685i
$970$	1.07428	+	0.287853i	0.0344931	+	0.00924239i
$971$	16.8712	+	9.74060i	0.541423	+	0.312591i	0.745655	−	0.666332i	$-0.232137\pi$
$971$	16.8712	+	9.74060i	0.541423	+	0.312591i	−0.204233	+	0.978922i	$0.565470\pi$
$972$	15.3200	+	60.6275i	0.491388	+	1.94463i
$973$	−20.3360	−	5.44902i	−0.651942	−	0.174687i
$974$	19.3066	+	33.4401i	0.618624	+	1.07149i
$975$	−27.6068	−	14.5487i	−0.884126	−	0.465931i
$976$	−7.99342	+	13.8450i	−0.255863	+	0.443168i
$977$	27.5948	−	27.5948i	0.882835	−	0.882835i	−0.110987	−	0.993822i	$-0.535401\pi$
$977$	27.5948	−	27.5948i	0.882835	−	0.882835i	0.993822	+	0.110987i	$0.0354013\pi$
$978$	−11.5961	+	1.80268i	−0.370801	+	0.0576433i
$979$			4.57644i			0.146264i
$980$	−0.157228	+	0.157228i	−0.00502247	+	0.00502247i
$981$	−0.691465	−	14.8136i	−0.0220768	−	0.472963i
$982$	−5.72544	−	21.3676i	−0.182706	−	0.681868i
$983$	−8.12713	+	30.3309i	−0.259215	+	0.967404i	0.706481	+	0.707732i	$0.250281\pi$
$983$	−8.12713	+	30.3309i	−0.259215	+	0.967404i	−0.965697	+	0.259673i	$0.916385\pi$
$984$	66.2622	+	25.6532i	2.11236	+	0.817794i
$985$		−	0.344105i		−	0.0109641i
$986$	−5.34394	−	5.34394i	−0.170186	−	0.170186i
$987$	3.23839	+	20.8316i	0.103079	+	0.663076i
$988$	−109.390	+	16.1039i	−3.48016	+	0.512334i
$989$			7.13040i			0.226734i
$990$	−0.134528	+	0.00627943i	−0.00427557	+	0.000199573i
$991$	−9.28984	−	16.0905i	−0.295101	−	0.511131i	0.679907	−	0.733298i	$-0.262020\pi$
$991$	−9.28984	−	16.0905i	−0.295101	−	0.511131i	−0.975008	+	0.222168i	$0.928687\pi$
$992$	0.0774232			0.00245819
$993$	8.06731	+	18.2597i	0.256008	+	0.579455i
$994$	0.341246	−	1.27355i	0.0108237	−	0.0403945i
$995$	0.0516071	−	0.192600i	0.00163606	−	0.00610584i
$996$	64.3437	+	6.94879i	2.03881	+	0.220181i
$997$	20.5972			0.652321			0.326160	−	0.945314i	$-0.394245\pi$
$997$	20.5972			0.652321			0.326160	+	0.945314i	$0.394245\pi$
$998$	4.67666	+	8.10020i	0.148037	+	0.256408i
$999$	−2.31907	−	11.3897i	−0.0733722	−	0.360355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fy.a.50.7	yes	336
9.2	odd	6		819.2.ew.a.596.78	✓	336
13.6	odd	12		819.2.ew.a.617.78	yes	336
117.110	even	12	inner	819.2.fy.a.344.7	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.ew.a.596.78	✓	336	9.2	odd	6
819.2.ew.a.617.78	yes	336	13.6	odd	12
819.2.fy.a.50.7	yes	336	1.1	even	1	trivial
819.2.fy.a.344.7	yes	336	117.110	even	12	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fy (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.634582 - 2.36829i) q^{2} +(-1.61523 - 0.625330i) q^{3} +(-3.47406 + 2.00575i) q^{4} +(0.0143461 + 0.0535404i) q^{5} +(-0.455971 + 4.22216i) q^{6} +(0.707107 - 0.707107i) q^{7} +(3.48736 + 3.48736i) q^{8} +(2.21792 + 2.02010i) q^{9} +O(q^{10})\)	\(q+(-0.634582 - 2.36829i) q^{2} +(-1.61523 - 0.625330i) q^{3} +(-3.47406 + 2.00575i) q^{4} +(0.0143461 + 0.0535404i) q^{5} +(-0.455971 + 4.22216i) q^{6} +(0.707107 - 0.707107i) q^{7} +(3.48736 + 3.48736i) q^{8} +(2.21792 + 2.02010i) q^{9} +(0.117696 - 0.0679516i) q^{10} +(-0.319064 + 0.0854928i) q^{11} +(6.86566 - 1.06731i) q^{12} +(2.89365 + 2.15100i) q^{13} +(-2.12335 - 1.22592i) q^{14} +(0.0103082 - 0.0954510i) q^{15} +(2.03457 - 3.52398i) q^{16} +(-0.503320 + 0.871775i) q^{17} +(3.37674 - 6.53461i) q^{18} +(7.38411 - 1.97857i) q^{19} +(-0.157228 - 0.157228i) q^{20} +(-1.58431 + 0.699963i) q^{21} +(0.404944 + 0.701384i) q^{22} +1.09412 q^{23} +(-3.45213 - 7.81364i) q^{24} +(4.32747 - 2.49846i) q^{25} +(3.25793 - 8.21799i) q^{26} +(-2.31922 - 4.64986i) q^{27} +(-1.03825 + 3.87481i) q^{28} +(-2.65181 - 1.53102i) q^{29} +(-0.232597 + 0.0361587i) q^{30} +(-0.661047 + 0.177127i) q^{31} +(-0.109276 - 0.0292805i) q^{32} +(0.568822 + 0.0614298i) q^{33} +(2.38402 + 0.638795i) q^{34} +(0.0480030 + 0.0277146i) q^{35} +(-11.7570 - 2.56936i) q^{36} +(2.16071 + 0.578959i) q^{37} +(-9.37165 - 16.2322i) q^{38} +(-3.32882 - 5.28384i) q^{39} +(-0.136685 + 0.236745i) q^{40} +(-5.88173 + 5.88173i) q^{41} +(2.66309 + 3.30793i) q^{42} +6.51701i q^{43} +(0.936970 - 0.936970i) q^{44} +(-0.0763386 + 0.147729i) q^{45} +(-0.694310 - 2.59120i) q^{46} +(3.15023 - 11.7568i) q^{47} +(-5.48995 + 4.41976i) q^{48} -1.00000i q^{49} +(-8.66322 - 8.66322i) q^{50} +(1.35812 - 1.09337i) q^{51} +(-14.3671 - 1.66876i) q^{52} +4.55847i q^{53} +(-9.54050 + 8.44331i) q^{54} +(-0.00915464 - 0.0158563i) q^{55} +4.93187 q^{56} +(-13.1643 - 1.42167i) q^{57} +(-1.94312 + 7.25181i) q^{58} +(0.887600 - 3.31257i) q^{59} +(0.155640 + 0.352279i) q^{60} -3.92879 q^{61} +(0.838977 + 1.45315i) q^{62} +(2.99674 - 0.139881i) q^{63} -7.86091i q^{64} +(-0.0736527 + 0.185786i) q^{65} +(-0.215480 - 1.38612i) q^{66} +(4.31681 + 4.31681i) q^{67} -4.03814i q^{68} +(-1.76726 - 0.684187i) q^{69} +(0.0351743 - 0.131272i) q^{70} +(0.139180 + 0.519426i) q^{71} +(0.689873 + 14.7795i) q^{72} +(0.387627 - 0.387627i) q^{73} -5.48458i q^{74} +(-8.55221 + 1.32949i) q^{75} +(-21.6844 + 21.6844i) q^{76} +(-0.165159 + 0.286065i) q^{77} +(-10.4013 + 11.2366i) q^{78} +(-3.02197 - 5.23421i) q^{79} +(0.217864 + 0.0583764i) q^{80} +(0.838370 + 8.96087i) q^{81} +(17.6621 + 10.1972i) q^{82} +(8.99705 + 2.41075i) q^{83} +(4.10005 - 5.60946i) q^{84} +(-0.0538959 - 0.0144414i) q^{85} +(15.4342 - 4.13558i) q^{86} +(3.32588 + 4.13121i) q^{87} +(-1.41083 - 0.814546i) q^{88} +(3.58584 - 13.3825i) q^{89} +(0.398309 + 0.0870457i) q^{90} +(3.56710 - 0.525134i) q^{91} +(-3.80105 + 2.19453i) q^{92} +(1.17850 + 0.127272i) q^{93} -29.8427 q^{94} +(0.211867 + 0.366964i) q^{95} +(0.158196 + 0.115629i) q^{96} +(5.78668 + 5.78668i) q^{97} +(-2.36829 + 0.634582i) q^{98} +(-0.880363 - 0.454925i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) \) 336 * q - 12 * q^6 + 36 * q^8	\( 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) \) 336 * q - 12 * q^6 + 36 * q^8 - 12 * q^11 + 4 * q^15 + 168 * q^16 - 4 * q^18 - 4 * q^21 + 8 * q^24 - 96 * q^26 + 24 * q^27 - 120 * q^30 - 72 * q^32 + 36 * q^33 + 72 * q^38 + 8 * q^39 - 48 * q^41 - 76 * q^45 + 24 * q^48 - 24 * q^50 - 36 * q^52 + 72 * q^54 + 32 * q^57 + 36 * q^58 - 72 * q^59 + 4 * q^60 + 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 48 * q^71 - 176 * q^72 - 60 * q^75 - 124 * q^78 - 12 * q^79 - 96 * q^80 - 20 * q^81 - 156 * q^83 - 12 * q^84 - 108 * q^85 - 24 * q^87 + 60 * q^89 - 72 * q^92 + 20 * q^93 + 96 * q^94 + 88 * q^96 - 96 * q^97 + 108 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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