LMFDB - Embedded newform 252.2.bi.c.139.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(139,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("252.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			139.15
Character	$\chi$	$=$	252.139
Dual form			252.2.bi.c.223.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.608631 - 1.27655i) q^{2} +(-0.420223 + 1.68030i) q^{3} +(-1.25914 + 1.55389i) q^{4} +(-2.25662 - 1.30286i) q^{5} +(2.40074 - 0.486250i) q^{6} +(1.96158 - 1.77545i) q^{7} +(2.74996 + 0.661599i) q^{8} +(-2.64683 - 1.41220i) q^{9} +O(q^{10})$	\(q+(-0.608631 - 1.27655i) q^{2} +(-0.420223 + 1.68030i) q^{3} +(-1.25914 + 1.55389i) q^{4} +(-2.25662 - 1.30286i) q^{5} +(2.40074 - 0.486250i) q^{6} +(1.96158 - 1.77545i) q^{7} +(2.74996 + 0.661599i) q^{8} +(-2.64683 - 1.41220i) q^{9} +(-0.289711 + 3.67364i) q^{10} +(3.80655 - 2.19771i) q^{11} +(-2.08189 - 2.76871i) q^{12} +(2.58681 + 1.49349i) q^{13} +(-3.46032 - 1.42345i) q^{14} +(3.13748 - 3.24431i) q^{15} +(-0.829151 - 3.91312i) q^{16} -6.35108i q^{17} +(-0.191800 + 4.23830i) q^{18} +4.43265 q^{19} +(4.86590 - 1.86606i) q^{20} +(2.15898 + 4.04213i) q^{21} +(-5.12227 - 3.52164i) q^{22} +(-1.50500 - 0.868910i) q^{23} +(-2.26728 + 4.34275i) q^{24} +(0.894893 + 1.55000i) q^{25} +(0.332101 - 4.21116i) q^{26} +(3.48518 - 3.85402i) q^{27} +(0.288954 + 5.28361i) q^{28} +(0.886455 + 1.53538i) q^{29} +(-6.05108 - 2.03055i) q^{30} +(-1.41210 + 2.44584i) q^{31} +(-4.49063 + 3.44010i) q^{32} +(2.09322 + 7.31968i) q^{33} +(-8.10745 + 3.86547i) q^{34} +(-6.73970 + 1.45084i) q^{35} +(5.52712 - 2.33472i) q^{36} -4.47624 q^{37} +(-2.69785 - 5.65848i) q^{38} +(-3.59656 + 3.71902i) q^{39} +(-5.34365 - 5.07579i) q^{40} +(-6.88823 - 3.97692i) q^{41} +(3.84593 - 5.21621i) q^{42} +(0.939597 - 0.542477i) q^{43} +(-1.37796 + 8.68218i) q^{44} +(4.13298 + 6.63525i) q^{45} +(-0.193215 + 2.45004i) q^{46} +(4.58720 + 7.94527i) q^{47} +(6.92365 + 0.251158i) q^{48} +(0.695583 - 6.96535i) q^{49} +(1.43399 - 2.08575i) q^{50} +(10.6717 + 2.66887i) q^{51} +(-5.57787 + 2.13910i) q^{52} +4.31655 q^{53} +(-7.04103 - 2.10331i) q^{54} -11.4533 q^{55} +(6.56890 - 3.58463i) q^{56} +(-1.86270 + 7.44819i) q^{57} +(1.42046 - 2.06608i) q^{58} +(4.10217 - 7.10516i) q^{59} +(1.09079 + 8.96034i) q^{60} +(3.57562 - 2.06438i) q^{61} +(3.98167 + 0.314003i) q^{62} +(-7.69925 + 1.92915i) q^{63} +(7.12457 + 3.63874i) q^{64} +(-3.89163 - 6.74050i) q^{65} +(8.06991 - 7.12708i) q^{66} +(3.92432 + 2.26571i) q^{67} +(9.86889 + 7.99688i) q^{68} +(2.09246 - 2.16371i) q^{69} +(5.95406 + 7.72050i) q^{70} +11.8806i q^{71} +(-6.34436 - 5.63464i) q^{72} -7.69032i q^{73} +(2.72438 + 5.71412i) q^{74} +(-2.98052 + 0.852344i) q^{75} +(-5.58131 + 6.88786i) q^{76} +(3.56493 - 11.0693i) q^{77} +(6.93647 + 2.32766i) q^{78} +(-11.7375 + 6.77665i) q^{79} +(-3.22717 + 9.91070i) q^{80} +(5.01137 + 7.47571i) q^{81} +(-0.884330 + 11.2136i) q^{82} +(0.518194 + 0.897538i) q^{83} +(-8.99948 - 1.73476i) q^{84} +(-8.27458 + 14.3320i) q^{85} +(-1.26436 - 0.869270i) q^{86} +(-2.95242 + 0.844307i) q^{87} +(11.9219 - 3.52522i) q^{88} -0.167616i q^{89} +(5.95474 - 9.31436i) q^{90} +(7.72584 - 1.66313i) q^{91} +(3.24519 - 1.24452i) q^{92} +(-3.51634 - 3.40056i) q^{93} +(7.35058 - 10.6915i) q^{94} +(-10.0028 - 5.77513i) q^{95} +(-3.89333 - 8.99122i) q^{96} +(5.35479 - 3.09159i) q^{97} +(-9.31494 + 3.35139i) q^{98} +(-13.1789 + 0.441344i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9}+O(q^{10}) $ 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9	$ 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44} + 24 q^{46} - 24 q^{49} - 12 q^{50} - 48 q^{53} + 32 q^{56} + 72 q^{57} - 14 q^{58} + 56 q^{60} - 8 q^{64} - 40 q^{65} - 22 q^{70} - 100 q^{72} + 64 q^{74} - 12 q^{77} - 24 q^{78} - 104 q^{81} + 62 q^{84} + 40 q^{85} - 52 q^{86} + 6 q^{88} + 30 q^{92} + 48 q^{93} + 20 q^{98}+O(q^{100}) $ 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$

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 $

$2$	−0.608631	−	1.27655i	−0.430367	−	0.902654i
$2$	−0.608631	−	1.27655i	−0.430367	−	0.902654i
$3$	−0.420223	+	1.68030i	−0.242616	+	0.970122i
$3$	−0.420223	+	1.68030i	−0.242616	+	0.970122i
$4$	−1.25914	+	1.55389i	−0.629568	+	0.776945i
$5$	−2.25662	−	1.30286i	−1.00919	−	0.582657i	−0.0982368	−	0.995163i	$-0.531320\pi$
$5$	−2.25662	−	1.30286i	−1.00919	−	0.582657i	−0.910955	+	0.412506i	$0.864654\pi$
$6$	2.40074	−	0.486250i	0.980099	−	0.198511i
$7$	1.96158	−	1.77545i	0.741407	−	0.671056i
$7$	1.96158	−	1.77545i	0.741407	−	0.671056i
$8$	2.74996	+	0.661599i	0.972258	+	0.233910i
$9$	−2.64683	−	1.41220i	−0.882275	−	0.470734i
$10$	−0.289711	+	3.67364i	−0.0916147	+	1.16171i
$11$	3.80655	−	2.19771i	1.14772	−	0.662636i	0.199388	−	0.979921i	$-0.436105\pi$
$11$	3.80655	−	2.19771i	1.14772	−	0.662636i	0.948330	+	0.317285i	$0.102771\pi$
$12$	−2.08189	−	2.76871i	−0.600989	−	0.799257i
$13$	2.58681	+	1.49349i	0.717451	+	0.414221i	0.813814	−	0.581126i	$-0.197388\pi$
$13$	2.58681	+	1.49349i	0.717451	+	0.414221i	−0.0963626	+	0.995346i	$0.530721\pi$
$14$	−3.46032	−	1.42345i	−0.924808	−	0.380434i
$15$	3.13748	−	3.24431i	0.810095	−	0.837678i
$16$	−0.829151	−	3.91312i	−0.207288	−	0.978280i
$17$		−	6.35108i		−	1.54036i	−0.637824	−	0.770182i	$-0.720165\pi$
$17$		−	6.35108i		−	1.54036i	0.637824	−	0.770182i	$-0.279835\pi$
$18$	−0.191800	+	4.23830i	−0.0452077	+	0.998978i
$19$	4.43265			1.01692			0.508460	−	0.861086i	$-0.330215\pi$
$19$	4.43265			1.01692			0.508460	+	0.861086i	$0.330215\pi$
$20$	4.86590	−	1.86606i	1.08805	−	0.417264i
$21$	2.15898	+	4.04213i	0.471129	+	0.882064i
$22$	−5.12227	−	3.52164i	−1.09207	−	0.750816i
$23$	−1.50500	−	0.868910i	−0.313813	−	0.181180i	0.334818	−	0.942283i	$-0.391325\pi$
$23$	−1.50500	−	0.868910i	−0.313813	−	0.181180i	−0.648632	+	0.761102i	$0.724658\pi$
$24$	−2.26728	+	4.34275i	−0.462807	+	0.886459i
$25$	0.894893	+	1.55000i	0.178979	+	0.310000i
$26$	0.332101	−	4.21116i	0.0651304	−	0.825877i
$27$	3.48518	−	3.85402i	0.670724	−	0.741707i
$28$	0.288954	+	5.28361i	0.0546071	+	0.998508i
$29$	0.886455	+	1.53538i	0.164611	+	0.285114i	0.936517	−	0.350622i	$-0.114030\pi$
$29$	0.886455	+	1.53538i	0.164611	+	0.285114i	−0.771906	+	0.635736i	$0.780697\pi$
$30$	−6.05108	−	2.03055i	−1.10477	−	0.370726i
$31$	−1.41210	+	2.44584i	−0.253621	+	0.439285i	−0.964520	−	0.264009i	$-0.914955\pi$
$31$	−1.41210	+	2.44584i	−0.253621	+	0.439285i	0.710899	+	0.703294i	$0.248288\pi$
$32$	−4.49063	+	3.44010i	−0.793838	+	0.608129i
$33$	2.09322	+	7.31968i	0.364383	+	1.27419i
$34$	−8.10745	+	3.86547i	−1.39042	+	0.662922i
$35$	−6.73970	+	1.45084i	−1.13922	+	0.245238i
$36$	5.52712	−	2.33472i	0.921187	−	0.389120i
$37$	−4.47624			−0.735889			−0.367944	−	0.929848i	$-0.619938\pi$
$37$	−4.47624			−0.735889			−0.367944	+	0.929848i	$0.619938\pi$
$38$	−2.69785	−	5.65848i	−0.437649	−	0.917927i
$39$	−3.59656	+	3.71902i	−0.575910	+	0.595519i
$40$	−5.34365	−	5.07579i	−0.844905	−	0.802554i
$41$	−6.88823	−	3.97692i	−1.07576	−	0.621091i	−0.146011	−	0.989283i	$-0.546644\pi$
$41$	−6.88823	−	3.97692i	−1.07576	−	0.621091i	−0.929750	+	0.368192i	$0.879977\pi$
$42$	3.84593	−	5.21621i	0.593440	−	0.804878i
$43$	0.939597	−	0.542477i	0.143287	−	0.0827269i	−0.426643	−	0.904420i	$-0.640304\pi$
$43$	0.939597	−	0.542477i	0.143287	−	0.0827269i	0.569930	+	0.821693i	$0.306970\pi$
$44$	−1.37796	+	8.68218i	−0.207735	+	1.30889i
$45$	4.13298	+	6.63525i	0.616108	+	0.989125i
$46$	−0.193215	+	2.45004i	−0.0284881	+	0.361239i
$47$	4.58720	+	7.94527i	0.669112	+	1.15894i	0.978153	+	0.207887i	$0.0666588\pi$
$47$	4.58720	+	7.94527i	0.669112	+	1.15894i	−0.309041	+	0.951049i	$0.600008\pi$
$48$	6.92365	+	0.251158i	0.999343	+	0.0362516i
$49$	0.695583	−	6.96535i	0.0993690	−	0.995051i
$50$	1.43399	−	2.08575i	0.202796	−	0.294970i
$51$	10.6717	+	2.66887i	1.49434	+	0.373717i
$52$	−5.57787	+	2.13910i	−0.773511	+	0.296640i
$53$	4.31655			0.592923			0.296462	−	0.955045i	$-0.404193\pi$
$53$	4.31655			0.592923			0.296462	+	0.955045i	$0.404193\pi$
$54$	−7.04103	−	2.10331i	−0.958163	−	0.286225i
$55$	−11.4533			−1.54436
$56$	6.56890	−	3.58463i	0.877806	−	0.479016i
$57$	−1.86270	+	7.44819i	−0.246721	+	0.986537i
$58$	1.42046	−	2.06608i	0.186516	−	0.271290i
$59$	4.10217	−	7.10516i	0.534056	−	0.925013i	−0.465152	−	0.885231i	$-0.654000\pi$
$59$	4.10217	−	7.10516i	0.534056	−	0.925013i	0.999208	−	0.0397821i	$-0.0126664\pi$
$60$	1.09079	+	8.96034i	0.140820	+	1.15677i
$61$	3.57562	−	2.06438i	0.457811	−	0.264317i	−0.253313	−	0.967384i	$-0.581520\pi$
$61$	3.57562	−	2.06438i	0.457811	−	0.264317i	0.711123	+	0.703067i	$0.248187\pi$
$62$	3.98167	+	0.314003i	0.505673	+	0.0398784i
$63$	−7.69925	+	1.92915i	−0.970014	+	0.243050i
$64$	7.12457	+	3.63874i	0.890572	+	0.454843i
$65$	−3.89163	−	6.74050i	−0.482697	−	0.836056i
$66$	8.06991	−	7.12708i	0.993337	−	0.877283i
$67$	3.92432	+	2.26571i	0.479433	+	0.276801i	0.720180	−	0.693787i	$-0.244059\pi$
$67$	3.92432	+	2.26571i	0.479433	+	0.276801i	−0.240747	+	0.970588i	$0.577393\pi$
$68$	9.86889	+	7.99688i	1.19678	+	0.969764i
$69$	2.09246	−	2.16371i	0.251903	−	0.260480i
$70$	5.95406	+	7.72050i	0.711646	+	0.922777i
$71$			11.8806i			1.40996i	0.709226	+	0.704981i	$0.249045\pi$
$71$			11.8806i			1.40996i	−0.709226	+	0.704981i	$0.750955\pi$
$72$	−6.34436	−	5.63464i	−0.747690	−	0.664048i
$73$		−	7.69032i		−	0.900084i	−0.893007	−	0.450042i	$-0.851409\pi$
$73$		−	7.69032i		−	0.900084i	0.893007	−	0.450042i	$-0.148591\pi$
$74$	2.72438	+	5.71412i	0.316702	+	0.664253i
$75$	−2.98052	+	0.852344i	−0.344161	+	0.0984203i
$76$	−5.58131	+	6.88786i	−0.640221	+	0.790091i
$77$	3.56493	−	11.0693i	0.406261	−	1.26147i
$78$	6.93647	+	2.32766i	0.785400	+	0.263555i
$79$	−11.7375	+	6.77665i	−1.32057	+	0.762432i	−0.983820	−	0.179161i	$-0.942662\pi$
$79$	−11.7375	+	6.77665i	−1.32057	+	0.762432i	−0.336752	+	0.941593i	$0.609328\pi$
$80$	−3.22717	+	9.91070i	−0.360809	+	1.10805i
$81$	5.01137	+	7.47571i	0.556819	+	0.830634i
$82$	−0.884330	+	11.2136i	−0.0976579	+	1.23834i
$83$	0.518194	+	0.897538i	0.0568792	+	0.0985176i	0.893063	−	0.449932i	$-0.148552\pi$
$83$	0.518194	+	0.897538i	0.0568792	+	0.0985176i	−0.836184	+	0.548449i	$0.815218\pi$
$84$	−8.99948	−	1.73476i	−0.981923	−	0.189278i
$85$	−8.27458	+	14.3320i	−0.897504	+	1.55452i
$86$	−1.26436	−	0.869270i	−0.136340	−	0.0937358i
$87$	−2.95242	+	0.844307i	−0.316532	+	0.0905193i
$88$	11.9219	−	3.52522i	1.27088	−	0.375790i
$89$		−	0.167616i		−	0.0177672i	−0.999961	−	0.00888361i	$-0.997172\pi$
$89$		−	0.167616i		−	0.0177672i	0.999961	−	0.00888361i	$-0.00282778\pi$
$90$	5.95474	−	9.31436i	0.627685	−	0.981819i
$91$	7.72584	−	1.66313i	0.809889	−	0.174343i
$92$	3.24519	−	1.24452i	0.338334	−	0.129751i
$93$	−3.51634	−	3.40056i	−0.364628	−	0.352621i
$94$	7.35058	−	10.6915i	0.758154	−	1.10274i
$95$	−10.0028	−	5.77513i	−1.02627	−	0.592516i
$96$	−3.89333	−	8.99122i	−0.397362	−	0.917662i
$97$	5.35479	−	3.09159i	0.543696	−	0.313903i	−0.202879	−	0.979204i	$-0.565030\pi$
$97$	5.35479	−	3.09159i	0.543696	−	0.313903i	0.746576	+	0.665300i	$0.231697\pi$
$98$	−9.31494	+	3.35139i	−0.940952	+	0.338541i
$99$	−13.1789	+	0.441344i	−1.32453	+	0.0443567i
$100$	−3.53532	−	0.561096i	−0.353532	−	0.0561096i
$101$	−12.6134	+	7.28234i	−1.25508	+	0.724620i	−0.972114	−	0.234510i	$-0.924651\pi$
$101$	−12.6134	+	7.28234i	−1.25508	+	0.724620i	−0.282965	+	0.959130i	$0.591318\pi$
$102$	−3.08822	−	15.2473i	−0.305779	−	1.50971i
$103$	8.96940	−	15.5355i	0.883781	−	1.53075i	0.0366767	−	0.999327i	$-0.488323\pi$
$103$	8.96940	−	15.5355i	0.883781	−	1.53075i	0.847104	−	0.531427i	$-0.178344\pi$
$104$	6.12553	+	5.81848i	0.600657	+	0.570549i
$105$	0.394319	−	11.9344i	0.0384816	−	1.16468i
$106$	−2.62718	−	5.51027i	−0.255175	−	0.535204i
$107$		−	10.4277i		−	1.00808i	−0.863679	−	0.504042i	$-0.831846\pi$
$107$		−	10.4277i		−	1.00808i	0.863679	−	0.504042i	$-0.168154\pi$
$108$	1.60041	+	10.2683i	0.154000	+	0.988071i
$109$	10.8402			1.03830			0.519149	−	0.854684i	$-0.326249\pi$
$109$	10.8402			1.03830			0.519149	+	0.854684i	$0.326249\pi$
$110$	6.97081	+	14.6206i	0.664641	+	1.39402i
$111$	1.88102	−	7.52143i	0.178538	−	0.713902i
$112$	−8.57398	−	6.20378i	−0.810165	−	0.586202i
$113$	−6.45034	+	11.1723i	−0.606797	+	1.05100i	0.384968	+	0.922930i	$0.374212\pi$
$113$	−6.45034	+	11.1723i	−0.606797	+	1.05100i	−0.991765	+	0.128073i	$0.959121\pi$
$114$	10.6417	−	2.15538i	0.996682	−	0.201870i
$115$	2.26414	+	3.92160i	0.211132	+	0.365691i
$116$	−3.50199	−	0.555805i	−0.325151	−	0.0516052i
$117$	−4.73771	−	7.60611i	−0.438002	−	0.703185i
$118$	−11.5668	−	0.912180i	−1.06481	−	0.0839729i
$119$	−11.2760	−	12.4582i	−1.03367	−	1.14204i
$120$	10.7744	−	6.84598i	0.983563	−	0.624949i
$121$	4.15989	−	7.20514i	0.378172	−	0.655013i
$122$	−4.81151	−	3.30799i	−0.435614	−	0.299491i
$123$	9.57702	−	9.90311i	0.863531	−	0.892933i
$124$	−2.02253	−	5.27390i	−0.181629	−	0.473610i
$125$			8.36492i			0.748182i
$126$	7.14865	+	8.65430i	0.636852	+	0.770986i
$127$		−	12.1610i		−	1.07911i	−0.841949	−	0.539557i	$-0.818592\pi$
$127$		−	12.1610i		−	1.07911i	0.841949	−	0.539557i	$-0.181408\pi$
$128$	0.308780	−	11.3095i	0.0272925	−	0.999627i
$129$	0.516684	+	1.80677i	0.0454915	+	0.159077i
$130$	−6.23599	+	9.07032i	−0.546932	+	0.795520i
$131$	−7.69288	+	13.3245i	−0.672130	+	1.16416i	0.305169	+	0.952298i	$0.401287\pi$
$131$	−7.69288	+	13.3245i	−0.672130	+	1.16416i	−0.977299	+	0.211865i	$0.932046\pi$
$132$	−14.0096	−	5.96384i	−1.21938	−	0.519086i
$133$	8.69500	−	7.86994i	0.753952	−	0.682410i
$134$	0.503815	−	6.38856i	0.0435230	−	0.551888i
$135$	−12.8860	+	4.15637i	−1.10905	+	0.357723i
$136$	4.20187	−	17.4652i	0.360307	−	1.49763i
$137$	2.13470	+	3.69741i	0.182380	+	0.315891i	0.942690	−	0.333669i	$-0.108287\pi$
$137$	2.13470	+	3.69741i	0.182380	+	0.315891i	−0.760311	+	0.649560i	$0.774953\pi$
$138$	−4.03561	−	1.35422i	−0.343534	−	0.115279i
$139$	−10.7224	+	18.5717i	−0.909459	+	1.57523i	−0.0946405	+	0.995512i	$0.530170\pi$
$139$	−10.7224	+	18.5717i	−0.909459	+	1.57523i	−0.814818	+	0.579717i	$0.803163\pi$
$140$	6.23175	−	12.2996i	0.526679	−	1.03950i
$141$	−15.2781	+	4.36910i	−1.28665	+	0.367945i
$142$	15.1661	−	7.23088i	1.27271	−	0.606802i
$143$	13.1291			1.09791
$144$	−3.33150	+	11.5283i	−0.277625	+	0.960690i
$145$		−	4.61971i		−	0.383646i
$146$	−9.81704	+	4.68057i	−0.812464	+	0.387367i
$147$	11.4116	+	4.09579i	0.941212	+	0.337815i
$148$	5.63619	−	6.95558i	0.463292	−	0.571745i
$149$	−5.22512	+	9.05017i	−0.428058	+	0.741419i	−0.996701	−	0.0811663i	$-0.974136\pi$
$149$	−5.22512	+	9.05017i	−0.428058	+	0.741419i	0.568642	+	0.822585i	$0.307469\pi$
$150$	2.90209	+	3.28601i	0.236955	+	0.268301i
$151$	−10.5519	+	6.09213i	−0.858700	+	0.495771i	−0.863577	−	0.504217i	$-0.831781\pi$
$151$	−10.5519	+	6.09213i	−0.858700	+	0.495771i	0.00487656	+	0.999988i	$0.498448\pi$
$152$	12.1896	+	2.93264i	0.988709	+	0.237868i
$153$	−8.96901	+	16.8102i	−0.725102	+	1.35903i
$154$	−16.3002	+	2.18634i	−1.31351	+	0.176180i
$155$	6.37317	−	3.67955i	0.511905	−	0.295549i
$156$	−1.25039	−	10.2714i	−0.100111	−	0.822370i
$157$	13.1637	+	7.60005i	1.05057	+	0.606550i	0.922810	−	0.385255i	$-0.125886\pi$
$157$	13.1637	+	7.60005i	1.05057	+	0.606550i	0.127765	+	0.991805i	$0.459220\pi$
$158$	15.7945	+	10.8590i	1.25654	+	0.863893i
$159$	−1.81391	+	7.25310i	−0.143853	+	0.575208i
$160$	14.6156	−	1.91233i	1.15547	−	0.151183i
$161$	−4.49487	+	0.967604i	−0.354245	+	0.0762579i
$162$	6.49300	−	10.9472i	0.510138	−	0.860092i
$163$		−	3.98564i		−	0.312179i	−0.987743	−	0.156090i	$-0.950111\pi$
$163$		−	3.98564i		−	0.312179i	0.987743	−	0.156090i	$-0.0498889\pi$
$164$	14.8529	−	5.69607i	1.15982	−	0.444788i
$165$	4.81292	−	19.2449i	0.374685	−	1.49822i
$166$	0.830359	−	1.20777i	0.0644484	−	0.0937410i
$167$	1.70062	−	2.94557i	0.131598	−	0.227935i	−0.792695	−	0.609619i	$-0.791322\pi$
$167$	1.70062	−	2.94557i	0.131598	−	0.227935i	0.924293	+	0.381684i	$0.124656\pi$
$168$	3.26286	+	12.5441i	0.251735	+	0.967796i
$169$	−2.03895	−	3.53157i	−0.156842	−	0.271659i
$170$	23.3316	+	1.83998i	1.78945	+	0.141120i
$171$	−11.7325	−	6.25980i	−0.897203	−	0.478699i
$172$	−0.340132	+	2.14308i	−0.0259348	+	0.163409i
$173$	5.09957	−	2.94424i	0.387713	−	0.223846i	−0.293456	−	0.955973i	$-0.594805\pi$
$173$	5.09957	−	2.94424i	0.387713	−	0.223846i	0.681169	+	0.732127i	$0.261472\pi$
$174$	2.87473	+	3.25502i	0.217933	+	0.246763i
$175$	4.50734	+	1.45161i	0.340723	+	0.109732i
$176$	−11.7561	−	13.0733i	−0.886151	−	0.985434i
$177$	10.2150	+	9.87863i	0.767805	+	0.742523i
$178$	−0.213969	+	0.102016i	−0.0160376	+	0.00764642i
$179$			14.2559i			1.06553i	0.846262	+	0.532767i	$0.178848\pi$
$179$			14.2559i			1.06553i	−0.846262	+	0.532767i	$0.821152\pi$
$180$	−15.5144	−	1.93249i	−1.15638	−	0.144039i
$181$			4.24221i			0.315321i	0.987493	+	0.157660i	$0.0503951\pi$
$181$			4.24221i			0.315321i	−0.987493	+	0.157660i	$0.949605\pi$
$182$	−6.82525	−	8.85016i	−0.505921	−	0.656017i
$183$	1.96623	+	6.87561i	0.145348	+	0.508260i
$184$	−3.56381	−	3.38517i	−0.262728	−	0.249558i
$185$	10.1012	+	5.83191i	0.742653	+	0.428771i
$186$	−2.20081	+	6.55846i	−0.161371	+	0.480889i
$187$	−13.9579	−	24.1757i	−1.02070	−	1.76790i
$188$	−18.1220	−	2.87616i	−1.32168	−	0.209766i
$189$	−0.00615392	−	13.7477i	−0.000447632	−	1.00000i
$190$	−1.28419	+	16.2840i	−0.0931649	+	1.18136i
$191$	2.00820	−	1.15943i	0.145308	−	0.0838937i	−0.425583	−	0.904919i	$-0.639931\pi$
$191$	2.00820	−	1.15943i	0.145308	−	0.0838937i	0.570891	+	0.821026i	$0.306598\pi$
$192$	−9.10809	+	10.4424i	−0.657320	+	0.753612i
$193$	0.803389	−	1.39151i	0.0578292	−	0.100163i	−0.835662	−	0.549245i	$-0.814915\pi$
$193$	0.803389	−	1.39151i	0.0578292	−	0.100163i	0.893491	+	0.449082i	$0.148249\pi$
$194$	−7.20564	−	4.95399i	−0.517335	−	0.355676i
$195$	12.9614	−	3.70660i	0.928187	−	0.265435i
$196$	9.94756	+	9.85119i	0.710540	+	0.703656i
$197$	−9.41145			−0.670538			−0.335269	−	0.942122i	$-0.608827\pi$
$197$	−9.41145			−0.670538			−0.335269	+	0.942122i	$0.608827\pi$
$198$	8.58448	+	16.5548i	0.610072	+	1.17650i
$199$	4.61701			0.327291			0.163646	−	0.986519i	$-0.447675\pi$
$199$	4.61701			0.327291			0.163646	+	0.986519i	$0.447675\pi$
$200$	1.43544	+	4.85450i	0.101501	+	0.343265i
$201$	−5.45617	+	5.64194i	−0.384848	+	0.397952i
$202$	16.9731	+	11.6693i	1.19423	+	0.821049i
$203$	4.46484	+	1.43793i	0.313371	+	0.100923i
$204$	−17.5843	+	13.2222i	−1.23115	+	0.925742i
$205$	10.3628	+	17.9488i	0.723766	+	1.25360i
$206$	−25.2908	−	1.99448i	−1.76209	−	0.138962i
$207$	2.75639	+	4.42521i	0.191582	+	0.307573i
$208$	3.69937	−	11.3608i	0.256505	−	0.787731i
$209$	16.8731	−	9.74170i	1.16714	−	0.673847i
$210$	−15.4748	+	6.76028i	−1.06786	+	0.466504i
$211$	22.3255	+	12.8897i	1.53695	+	0.887360i	0.999015	+	0.0443764i	$0.0141301\pi$
$211$	22.3255	+	12.8897i	1.53695	+	0.887360i	0.537938	+	0.842984i	$0.319203\pi$
$212$	−5.43512	+	6.70744i	−0.373286	+	0.460669i
$213$	−19.9629	−	4.99248i	−1.36784	−	0.342079i
$214$	−13.3114	+	6.34663i	−0.909952	+	0.433847i
$215$	−2.82709			−0.192806
$216$	12.1339	−	8.29263i	0.825610	−	0.564242i
$217$	1.57250	+	7.30481i	0.106748	+	0.495883i
$218$	−6.59766	−	13.8379i	−0.446850	−	0.937224i
$219$	12.9221	+	3.23165i	0.873192	+	0.218375i
$220$	14.4212	−	17.7971i	0.972278	−	1.19988i
$221$	9.48531	−	16.4290i	0.638051	−	1.10514i
$222$	−10.7463	+	2.17657i	−0.721244	+	0.146082i
$223$	4.03030	+	6.98069i	0.269889	+	0.467461i	0.968833	−	0.247715i	$-0.0796797\pi$
$223$	4.03030	+	6.98069i	0.269889	+	0.467461i	−0.698944	+	0.715176i	$0.746346\pi$
$224$	−2.70102	+	14.7209i	−0.180469	+	0.983581i
$225$	−0.179712	−	5.36635i	−0.0119808	−	0.357757i
$226$	18.1878	+	1.43433i	1.20984	+	0.0954103i
$227$	6.15006	+	10.6522i	0.408194	+	0.707013i	0.994687	−	0.102941i	$-0.0328253\pi$
$227$	6.15006	+	10.6522i	0.408194	+	0.707013i	−0.586493	+	0.809954i	$0.699492\pi$
$228$	−9.22828	−	12.2727i	−0.611158	−	0.812781i
$229$	−5.55114	−	3.20495i	−0.366830	−	0.211789i	0.305243	−	0.952275i	$-0.401262\pi$
$229$	−5.55114	−	3.20495i	−0.366830	−	0.211789i	−0.672072	+	0.740485i	$0.734596\pi$
$230$	3.62808	−	5.27708i	0.239228	−	0.347961i
$231$	17.1017	+	10.6417i	1.12521	+	0.700175i
$232$	1.42191	+	4.80873i	0.0933528	+	0.315708i
$233$	14.6005			0.956512			0.478256	−	0.878220i	$-0.341269\pi$
$233$	14.6005			0.956512			0.478256	+	0.878220i	$0.341269\pi$
$234$	−6.82603	+	10.6772i	−0.446231	+	0.697992i
$235$		−	23.9059i		−	1.55945i
$236$	5.87545	+	15.3207i	0.382459	+	0.997291i
$237$	−6.45445	−	22.5702i	−0.419261	−	1.46609i
$238$	−9.04047	+	21.9768i	−0.586007	+	1.42454i
$239$	−6.30063	−	3.63767i	−0.407554	−	0.235302i	0.282184	−	0.959360i	$-0.408941\pi$
$239$	−6.30063	−	3.63767i	−0.407554	−	0.235302i	−0.689738	+	0.724059i	$0.742274\pi$
$240$	−15.2968	−	9.58732i	−0.987406	−	0.618859i
$241$	−9.84681	+	5.68506i	−0.634289	+	0.366207i	−0.782411	−	0.622762i	$-0.786010\pi$
$241$	−9.84681	+	5.68506i	−0.634289	+	0.366207i	0.148122	+	0.988969i	$0.452677\pi$
$242$	−11.7295	−	0.925015i	−0.754002	−	0.0594622i
$243$	−14.6673	+	5.27915i	−0.940910	+	0.338658i
$244$	−1.29436	+	8.15546i	−0.0828631	+	0.522100i
$245$	−10.6446	+	14.8119i	−0.680056	+	0.946299i
$246$	−18.4706	−	6.19816i	−1.17765	−	0.395180i
$247$	11.4664	+	6.62014i	0.729591	+	0.421229i
$248$	−5.50139	+	5.79171i	−0.349339	+	0.367774i
$249$	−1.72589	+	0.493556i	−0.109374	+	0.0312778i
$250$	10.6782	−	5.09115i	0.675349	−	0.321993i
$251$	10.0975			0.637350			0.318675	−	0.947864i	$-0.396762\pi$
$251$	10.0975			0.637350			0.318675	+	0.947864i	$0.396762\pi$
$252$	6.69671	−	14.3928i	0.421853	−	0.906664i
$253$	−7.63846			−0.480226
$254$	−15.5241	+	7.40157i	−0.974067	+	0.464416i
$255$	−20.6049	−	19.9264i	−1.29033	−	1.24784i
$256$	−14.6250	+	6.48914i	−0.914063	+	0.405571i
$257$	5.68144	+	3.28018i	0.354398	+	0.204612i	0.666621	−	0.745397i	$-0.267740\pi$
$257$	5.68144	+	3.28018i	0.354398	+	0.204612i	−0.312222	+	0.950009i	$0.601073\pi$
$258$	1.99195	−	1.75923i	0.124013	−	0.109525i
$259$	−8.78049	+	7.94732i	−0.545593	+	0.493822i
$260$	15.3741	+	2.44004i	0.953461	+	0.151325i
$261$	−0.178017	−	5.31575i	−0.0110190	−	0.329037i
$262$	21.6914	+	1.71063i	1.34010	+	0.105683i
$263$	8.64854	−	4.99324i	0.533292	−	0.307896i	−0.209064	−	0.977902i	$-0.567042\pi$
$263$	8.64854	−	4.99324i	0.533292	−	0.307896i	0.742356	+	0.670006i	$0.233708\pi$
$264$	0.913585	+	21.5137i	0.0562273	+	1.32408i
$265$	−9.74081	−	5.62386i	−0.598373	−	0.345471i
$266$	−15.3384	−	6.30967i	−0.940456	−	0.386871i
$267$	0.281645	+	0.0704359i	0.0172364	+	0.00431061i
$268$	−8.46192	+	3.24513i	−0.516894	+	0.198228i
$269$			2.53470i			0.154543i	0.997010	+	0.0772716i	$0.0246209\pi$
$269$			2.53470i			0.154543i	−0.997010	+	0.0772716i	$0.975379\pi$
$270$	13.1486	+	13.9199i	0.800199	+	0.847136i
$271$	10.4463			0.634569			0.317285	−	0.948330i	$-0.397229\pi$
$271$	10.4463			0.634569			0.317285	+	0.948330i	$0.397229\pi$
$272$	−24.8526	+	5.26601i	−1.50691	+	0.319299i
$273$	−0.452016	+	13.6806i	−0.0273572	+	0.827990i
$274$	3.42066	−	4.97540i	0.206650	−	0.300575i
$275$	6.81291	+	3.93344i	0.410834	+	0.237195i
$276$	0.727473	+	5.97587i	0.0437887	+	0.359705i
$277$	−10.3949	−	18.0044i	−0.624567	−	1.08178i	−0.988624	−	0.150405i	$-0.951942\pi$
$277$	−10.3949	−	18.0044i	−0.624567	−	1.08178i	0.364057	−	0.931377i	$-0.381391\pi$
$278$	30.2335	+	2.38428i	1.81329	+	0.143000i
$279$	7.19161	−	4.47952i	0.430550	−	0.268182i
$280$	−19.4938	−	0.469208i	−1.16498	−	0.0280406i
$281$	−4.47362	−	7.74854i	−0.266874	−	0.462239i	0.701179	−	0.712985i	$-0.252657\pi$
$281$	−4.47362	−	7.74854i	−0.266874	−	0.462239i	−0.968053	+	0.250746i	$0.919324\pi$
$282$	14.8761	+	16.8440i	0.885857	+	1.00305i
$283$	−11.3594	+	19.6750i	−0.675243	+	1.16956i	0.301154	+	0.953575i	$0.402628\pi$
$283$	−11.3594	+	19.6750i	−0.675243	+	1.16956i	−0.976398	+	0.215980i	$0.930705\pi$
$284$	−18.4611	−	14.9592i	−1.09546	−	0.887668i
$285$	13.9074	−	14.3809i	0.823802	−	0.851851i
$286$	−7.99077	−	16.7599i	−0.472504	−	0.991032i
$287$	−20.5726	+	4.42864i	−1.21436	+	0.261414i
$288$	16.7440	−	2.76366i	0.986651	−	0.162850i
$289$	−23.3363			−1.37272
$290$	−5.89727	+	2.81170i	−0.346300	+	0.165109i
$291$	2.94460	+	10.2968i	0.172615	+	0.603610i
$292$	11.9499	+	9.68316i	0.699316	+	0.566664i
$293$	5.14713	+	2.97170i	0.300699	+	0.173608i	0.642757	−	0.766070i	$-0.277791\pi$
$293$	5.14713	+	2.97170i	0.300699	+	0.173608i	−0.342058	+	0.939679i	$0.611124\pi$
$294$	−1.71699	−	17.0602i	−0.100137	−	0.994974i
$295$	−18.5141	+	10.6891i	−1.07793	+	0.622344i
$296$	−12.3095	−	2.96147i	−0.715474	−	0.172132i
$297$	4.79648	−	22.3300i	0.278320	−	1.29572i
$298$	14.7331	+	1.16188i	0.853467	+	0.0673062i
$299$	−2.59542	−	4.49540i	−0.150097	−	0.259976i
$300$	2.42843	−	5.70462i	0.140206	−	0.329357i
$301$	0.879956	−	2.73231i	0.0507198	−	0.157488i
$302$	14.1991	+	9.76210i	0.817066	+	0.561746i
$303$	−6.93610	−	24.2545i	−0.398468	−	1.39338i
$304$	−3.67534	−	17.3455i	−0.210795	−	0.994833i
$305$	−10.7584			−0.616025
$306$	26.9178	+	1.21814i	1.53879	+	0.0696362i
$307$	10.0769			0.575121			0.287560	−	0.957763i	$-0.407156\pi$
$307$	10.0769			0.575121			0.287560	+	0.957763i	$0.407156\pi$
$308$	12.7118	+	19.4773i	0.724320	+	1.10982i
$309$	22.3351	+	21.5996i	1.27060	+	1.22876i
$310$	−8.57602	−	5.89615i	−0.487085	−	0.334879i
$311$	0.0398807	−	0.0690754i	0.00226143	−	0.00391691i	−0.864892	−	0.501957i	$-0.832613\pi$
$311$	0.0398807	−	0.0690754i	0.00226143	−	0.00391691i	0.867154	+	0.498040i	$0.165947\pi$
$312$	−12.3509	+	7.84767i	−0.699231	+	0.444287i
$313$	−20.6585	+	11.9272i	−1.16769	+	0.674164i	−0.953134	−	0.302548i	$-0.902163\pi$
$313$	−20.6585	+	11.9272i	−1.16769	+	0.674164i	−0.214553	+	0.976712i	$0.568829\pi$
$314$	1.68999	−	21.4296i	0.0953715	−	1.20934i
$315$	19.8877	+	5.67769i	1.12054	+	0.319901i
$316$	4.24894	−	26.7715i	0.239022	−	1.50602i
$317$	1.98299	+	3.43465i	0.111376	+	0.192909i	0.916325	−	0.400435i	$-0.131141\pi$
$317$	1.98299	+	3.43465i	0.111376	+	0.192909i	−0.804949	+	0.593344i	$0.797808\pi$
$318$	10.3629	−	2.09892i	0.581123	−	0.117702i
$319$	6.74867	+	3.89635i	0.377853	+	0.218154i
$320$	−11.3367	−	17.4936i	−0.633740	−	0.977921i
$321$	17.5217	+	4.38196i	0.977966	+	0.244577i
$322$	3.97091	+	5.14899i	0.221290	+	0.286942i
$323$		−	28.1521i		−	1.56643i
$324$	−17.9264	−	1.62581i	−0.995913	−	0.0903229i
$325$			5.34607i			0.296547i
$326$	−5.08785	+	2.42578i	−0.281790	+	0.134352i
$327$	−4.55528	+	18.2147i	−0.251908	+	1.00728i
$328$	−16.3112	−	15.4936i	−0.900638	−	0.855492i
$329$	23.1046	+	7.44094i	1.27380	+	0.410232i
$330$	−27.4963	+	5.56915i	−1.51362	+	0.306572i
$331$	17.2122	−	9.93744i	0.946066	−	0.546211i	0.0542091	−	0.998530i	$-0.482736\pi$
$331$	17.2122	−	9.93744i	0.946066	−	0.546211i	0.891857	+	0.452318i	$0.149403\pi$
$332$	−2.04715	−	0.324906i	−0.112352	−	0.0178315i
$333$	11.8478	+	6.32135i	0.649256	+	0.346408i
$334$	−4.79520	−	0.378160i	−0.262382	−	0.0206920i
$335$	−5.90381	−	10.2257i	−0.322560	−	0.558690i
$336$	14.0272	−	11.7999i	0.765247	−	0.643737i
$337$	0.692953	−	1.20023i	0.0377475	−	0.0653807i	−0.846534	−	0.532334i	$-0.821315\pi$
$337$	0.692953	−	1.20023i	0.0377475	−	0.0653807i	0.884282	+	0.466953i	$0.154648\pi$
$338$	−3.26724	+	4.75224i	−0.177714	+	0.258488i
$339$	−16.0623	−	15.5334i	−0.872383	−	0.843657i
$340$	−11.8515	−	30.9037i	−0.642739	−	1.67599i
$341$			12.4136i			0.672234i
$342$	−0.850182	+	18.7869i	−0.0459726	+	1.01588i
$343$	−11.0022	−	14.8981i	−0.594061	−	0.804420i
$344$	2.94276	−	0.870154i	0.158663	−	0.0469156i
$345$	−7.54091	+	2.15649i	−0.405989	+	0.116101i
$346$	−6.86221	−	4.71787i	−0.368914	−	0.253635i
$347$	11.3727	+	6.56605i	0.610520	+	0.352484i	0.773169	−	0.634200i	$-0.218671\pi$
$347$	11.3727	+	6.56605i	0.610520	+	0.352484i	−0.162649	+	0.986684i	$0.552004\pi$
$348$	2.40554	−	5.65083i	0.128950	−	0.302916i
$349$	−23.7743	+	13.7261i	−1.27261	+	0.734740i	−0.975478	−	0.220097i	$-0.929362\pi$
$349$	−23.7743	+	13.7261i	−1.27261	+	0.734740i	−0.297129	+	0.954837i	$0.596029\pi$
$350$	−0.890260	−	6.63733i	−0.0475864	−	0.354780i
$351$	14.7715	−	4.76452i	0.788442	−	0.254311i
$352$	−9.53346	+	22.9640i	−0.508135	+	1.22399i
$353$	26.7734	−	15.4576i	1.42501	−	0.822727i	0.428285	−	0.903644i	$-0.359118\pi$
$353$	26.7734	−	15.4576i	1.42501	−	0.822727i	0.996721	+	0.0809166i	$0.0257848\pi$
$354$	6.39336	−	19.0523i	0.339803	−	1.01262i
$355$	15.4787	−	26.8099i	0.821525	−	1.42292i
$356$	0.260456	+	0.211051i	0.0138042	+	0.0111857i
$357$	25.6719	−	13.7119i	1.35870	−	0.725710i
$358$	18.1983	−	8.67657i	0.961808	−	0.458571i
$359$			11.1419i			0.588045i	0.955799	+	0.294022i	$0.0949940\pi$
$359$			11.1419i			0.588045i	−0.955799	+	0.294022i	$0.905006\pi$
$360$	6.97566	+	20.9811i	0.367650	+	1.10580i
$361$	0.648409			0.0341268
$362$	5.41537	−	2.58194i	0.284625	−	0.135704i
$363$	10.3587	+	10.0176i	0.543692	+	0.525789i
$364$	−7.14357	+	14.0992i	−0.374425	+	0.739000i
$365$	−10.0194	+	17.3541i	−0.524440	+	0.908357i
$366$	7.58032	−	6.69469i	0.396230	−	0.349937i
$367$	11.9986	+	20.7821i	0.626319	+	1.08482i	0.988284	+	0.152625i	$0.0487727\pi$
$367$	11.9986	+	20.7821i	0.626319	+	1.08482i	−0.361965	+	0.932192i	$0.617894\pi$
$368$	−2.15228	+	6.60969i	−0.112195	+	0.344554i
$369$	12.6157	+	20.2538i	0.656749	+	1.05437i
$370$	1.29682	−	16.4441i	0.0674182	−	0.854887i
$371$	8.46724	−	7.66379i	0.439597	−	0.397884i
$372$	9.71165	−	1.18225i	0.503525	−	0.0612967i
$373$	9.88561	−	17.1224i	0.511857	−	0.886563i	−0.488048	−	0.872817i	$-0.662291\pi$
$373$	9.88561	−	17.1224i	0.511857	−	0.886563i	0.999906	−	0.0137464i	$-0.00437575\pi$
$374$	−22.3662	+	32.5319i	−1.15653	+	1.68219i
$375$	−14.0556	−	3.51513i	−0.725828	−	0.181521i
$376$	7.35805	+	24.8841i	0.379463	+	1.28330i
$377$			5.29566i			0.272740i
$378$	−17.5459	+	8.37515i	−0.902461	+	0.430771i
$379$			5.89248i			0.302676i	0.988482	+	0.151338i	$0.0483582\pi$
$379$			5.89248i			0.302676i	−0.988482	+	0.151338i	$0.951642\pi$
$380$	21.5688	−	8.27161i	1.10646	−	0.424325i
$381$	20.4342	+	5.11033i	1.04687	+	0.261810i
$382$	−2.70232	−	1.85789i	−0.138263	−	0.0950579i
$383$	−0.975897	+	1.69030i	−0.0498660	+	0.0863704i	−0.889881	−	0.456193i	$-0.849213\pi$
$383$	−0.975897	+	1.69030i	−0.0498660	+	0.0863704i	0.840015	+	0.542563i	$0.182546\pi$
$384$	18.8736	+	5.27135i	0.963139	+	0.269003i
$385$	−22.4665	+	20.3346i	−1.14500	+	1.03635i
$386$	−2.26529	−	0.178646i	−0.115300	−	0.00909283i
$387$	−3.25304	+	0.108940i	−0.165361	+	0.00553773i
$388$	−1.93842	+	12.2135i	−0.0984083	+	0.620046i
$389$	−2.26752	−	3.92746i	−0.114968	−	0.199130i	0.802799	−	0.596250i	$-0.203343\pi$
$389$	−2.26752	−	3.92746i	−0.114968	−	0.199130i	−0.917767	+	0.397120i	$0.870010\pi$
$390$	−12.6204	−	14.2899i	−0.639057	−	0.723597i
$391$	−5.51852	+	9.55836i	−0.279084	+	0.483387i
$392$	6.52109	−	18.6943i	0.329365	−	0.944203i
$393$	−19.1564	−	18.5256i	−0.966312	−	0.934493i
$394$	5.72810	+	12.0141i	0.288578	+	0.605264i
$395$	35.3161			1.77695
$396$	15.9082	−	21.0343i	0.799418	−	1.05701i
$397$			24.8829i			1.24883i	0.781091	+	0.624417i	$0.214664\pi$
$397$			24.8829i			1.24883i	−0.781091	+	0.624417i	$0.785336\pi$
$398$	−2.81005	−	5.89382i	−0.140855	−	0.295431i
$399$	9.57003	+	17.9173i	0.479101	+	0.896989i
$400$	5.32333	−	4.78701i	0.266167	−	0.239350i
$401$	−6.88532	+	11.9257i	−0.343836	+	0.595542i	−0.985142	−	0.171744i	$-0.945060\pi$
$401$	−6.88532	+	11.9257i	−0.343836	+	0.595542i	0.641305	+	0.767286i	$0.278393\pi$
$402$	10.5230	+	3.53118i	0.524839	+	0.176119i
$403$	−7.30568	+	4.21794i	−0.363922	+	0.210110i
$404$	4.56601	−	28.7693i	0.227168	−	1.43133i
$405$	−1.56896	−	23.3990i	−0.0779623	−	1.16270i
$406$	−0.881865	−	6.57474i	−0.0437662	−	0.326299i
$407$	−17.0390	+	9.83748i	−0.844593	+	0.487626i
$408$	27.5811	+	14.3997i	1.36547	+	0.712891i
$409$	−31.0609	−	17.9330i	−1.53586	−	0.886730i	−0.999075	−	0.0430132i	$-0.986304\pi$
$409$	−31.0609	−	17.9330i	−1.53586	−	0.886730i	−0.536788	−	0.843717i	$-0.680362\pi$
$410$	16.6054	−	24.1527i	0.820081	−	1.19282i
$411$	−7.10981	+	2.03320i	−0.350701	+	0.100290i
$412$	12.8467	+	33.4987i	0.632911	+	1.65036i
$413$	−4.56811	−	21.2205i	−0.224782	−	1.04419i
$414$	3.97136	−	6.21197i	0.195182	−	0.305302i
$415$		−	2.70054i		−	0.132564i
$416$	−16.7542	+	2.19214i	−0.821440	+	0.107479i
$417$	−26.7002	−	25.8210i	−1.30752	−	1.26446i
$418$	−22.7052	−	15.6102i	−1.11055	−	0.763520i
$419$	5.05240	−	8.75102i	0.246826	−	0.427515i	−0.715817	−	0.698287i	$-0.753946\pi$
$419$	5.05240	−	8.75102i	0.246826	−	0.427515i	0.962643	+	0.270772i	$0.0872791\pi$
$420$	18.0483	+	15.6398i	0.880665	+	0.763143i
$421$	−5.04296	−	8.73465i	−0.245779	−	0.425701i	0.716572	−	0.697514i	$-0.245710\pi$
$421$	−5.04296	−	8.73465i	−0.245779	−	0.425701i	−0.962350	+	0.271812i	$0.912377\pi$
$422$	2.86621	−	36.3446i	0.139525	−	1.76923i
$423$	−0.921200	−	27.5078i	−0.0447903	−	1.33747i
$424$	11.8703	+	2.85582i	0.576474	+	0.138691i
$425$	9.84418	−	5.68354i	0.477513	−	0.275692i
$426$	5.77692	+	28.5221i	0.279893	+	1.38190i
$427$	3.34865	−	10.3978i	0.162053	−	0.503183i
$428$	16.2035	+	13.1299i	0.783227	+	0.634658i
$429$	−5.51714	+	22.0608i	−0.266370	+	1.06511i
$430$	1.72065	+	3.60890i	0.0829773	+	0.174037i
$431$		−	19.4883i		−	0.938719i	−0.883007	−	0.469359i	$-0.844485\pi$
$431$		−	19.4883i		−	0.938719i	0.883007	−	0.469359i	$-0.155515\pi$
$432$	−17.9710	−	10.4424i	−0.864630	−	0.502408i
$433$		−	4.11856i		−	0.197925i	−0.995091	−	0.0989626i	$-0.968448\pi$
$433$		−	4.11856i		−	0.197925i	0.995091	−	0.0989626i	$-0.0315524\pi$
$434$	8.36786	−	6.45330i	0.401670	−	0.309768i
$435$	7.76250	+	1.94131i	0.372184	+	0.0930786i
$436$	−13.6492	+	16.8444i	−0.653680	+	0.806701i
$437$	−6.67112	−	3.85158i	−0.319123	−	0.184246i
$438$	−3.73942	−	18.4625i	−0.178676	−	0.882171i
$439$	−3.51549	−	6.08901i	−0.167785	−	0.290613i	0.769856	−	0.638218i	$-0.220328\pi$
$439$	−3.51549	−	6.08901i	−0.167785	−	0.290613i	−0.937641	+	0.347605i	$0.886995\pi$
$440$	−31.4960	−	7.57746i	−1.50151	−	0.361241i
$441$	−11.6776	+	17.4538i	−0.556075	+	0.831132i
$442$	−26.7455	−	2.10920i	−1.27215	−	0.100325i
$443$	−28.1700	+	16.2640i	−1.33840	+	0.772724i	−0.986570	−	0.163341i	$-0.947773\pi$
$443$	−28.1700	+	16.2640i	−1.33840	+	0.772724i	−0.351827	+	0.936065i	$0.614439\pi$
$444$	9.31902	+	12.3934i	0.442261	+	0.588164i
$445$	−0.218380	+	0.378245i	−0.0103522	+	0.0179305i
$446$	6.45820	−	9.39353i	0.305804	−	0.444796i
$447$	−13.0113	−	12.5829i	−0.615413	−	0.595149i
$448$	20.4358	−	5.51162i	0.965501	−	0.260400i
$449$	38.6596			1.82446			0.912229	−	0.409680i	$-0.134360\pi$
$449$	38.6596			1.82446			0.912229	+	0.409680i	$0.134360\pi$
$450$	−6.74101	+	3.49554i	−0.317774	+	0.164781i
$451$	−34.9605			−1.64623
$452$	−9.23870	−	24.0906i	−0.434552	−	1.13313i
$453$	−5.80248	−	20.2904i	−0.272624	−	0.953326i
$454$	9.85493	−	14.3341i	0.462515	−	0.672733i
$455$	−19.6011	−	6.31264i	−0.918915	−	0.295941i
$456$	−10.0501	+	19.2499i	−0.470638	+	0.901458i
$457$	11.4098	+	19.7623i	0.533727	+	0.924442i	0.999224	+	0.0393927i	$0.0125423\pi$
$457$	11.4098	+	19.7623i	0.533727	+	0.924442i	−0.465497	+	0.885050i	$0.654124\pi$
$458$	−0.712670	+	9.03691i	−0.0333009	+	0.422267i
$459$	−24.4772	−	22.1347i	−1.14250	−	1.03316i
$460$	−8.94460	−	1.41961i	−0.417044	−	0.0661896i
$461$	−11.1596	+	6.44301i	−0.519755	+	0.300081i	−0.736835	−	0.676073i	$-0.763680\pi$
$461$	−11.1596	+	6.44301i	−0.519755	+	0.300081i	0.217079	+	0.976154i	$0.430347\pi$
$462$	3.17602	−	28.3080i	0.147762	−	1.31701i
$463$	−24.8595	−	14.3527i	−1.15532	−	0.667025i	−0.205143	−	0.978732i	$-0.565766\pi$
$463$	−24.8595	−	14.3527i	−1.15532	−	0.667025i	−0.950178	+	0.311707i	$0.899099\pi$
$464$	5.27314	−	4.74187i	0.244799	−	0.220136i
$465$	3.50460	+	12.2551i	0.162522	+	0.568315i
$466$	−8.88634	−	18.6382i	−0.411652	−	0.863400i
$467$	−25.4161			−1.17612			−0.588058	−	0.808819i	$-0.700107\pi$
$467$	−25.4161			−1.17612			−0.588058	+	0.808819i	$0.700107\pi$
$468$	17.7845	+	2.21525i	0.822088	+	0.102400i
$469$	11.7205	−	2.52306i	0.541203	−	0.116504i
$470$	−30.5170	+	14.5499i	−1.40765	+	0.671137i
$471$	−18.3020	+	18.9252i	−0.843314	+	0.872028i
$472$	15.9816	−	16.8249i	0.735611	−	0.774430i
$473$	2.38442	−	4.12993i	0.109636	−	0.189894i
$474$	−24.8836	+	21.9763i	−1.14294	+	1.00941i
$475$	3.96675	+	6.87061i	0.182007	+	0.315245i
$476$	33.5566	−	1.83517i	1.53807	−	0.0841148i
$477$	−11.4251	−	6.09584i	−0.523121	−	0.279109i
$478$	−0.808893	+	10.2570i	−0.0369979	+	0.469146i
$479$	15.7078	+	27.2068i	0.717709	+	1.24311i	0.961905	+	0.273383i	$0.0881426\pi$
$479$	15.7078	+	27.2068i	0.717709	+	1.24311i	−0.244196	+	0.969726i	$0.578524\pi$
$480$	−2.92852	+	25.3622i	−0.133668	+	1.15762i
$481$	−11.5792	−	6.68523i	−0.527964	−	0.304820i
$482$	13.2503	+	9.10980i	0.603535	+	0.414940i
$483$	0.262981	−	7.95935i	0.0119661	−	0.362163i
$484$	5.95813	+	15.5363i	0.270824	+	0.706194i
$485$	−16.1116			−0.731592
$486$	15.6661	+	15.5105i	0.710627	+	0.703569i
$487$			27.8663i			1.26274i	0.775481	+	0.631371i	$0.217507\pi$
$487$			27.8663i			1.26274i	−0.775481	+	0.631371i	$0.782493\pi$
$488$	11.1986	−	3.31135i	0.506937	−	0.149898i
$489$	6.69708	+	1.67486i	0.302852	+	0.0757397i
$490$	25.3867	+	4.57326i	1.14685	+	0.206599i
$491$	24.8087	+	14.3233i	1.11960	+	0.646403i	0.941300	−	0.337572i	$-0.109606\pi$
$491$	24.8087	+	14.3233i	1.11960	+	0.646403i	0.178304	+	0.983976i	$0.442939\pi$
$492$	3.32958	+	27.3510i	0.150109	+	1.23308i
$493$	9.75136	−	5.62995i	0.439179	−	0.253560i
$494$	1.47209	−	18.6666i	0.0662325	−	0.839851i
$495$	30.3148	+	16.1743i	1.36255	+	0.726982i
$496$	10.7417	+	3.49776i	0.482316	+	0.157054i
$497$	21.0933	+	23.3046i	0.946163	+	1.04536i
$498$	1.68048	+	1.90279i	0.0753040	+	0.0852659i
$499$	−21.5390	−	12.4355i	−0.964218	−	0.556691i	−0.0667492	−	0.997770i	$-0.521263\pi$
$499$	−21.5390	−	12.4355i	−0.964218	−	0.556691i	−0.897469	+	0.441078i	$0.854596\pi$
$500$	−12.9982	−	10.5326i	−0.581296	−	0.471031i
$501$	4.23480	+	4.09535i	0.189197	+	0.182967i
$502$	−6.14567	−	12.8899i	−0.274294	−	0.575306i
$503$	−26.2058			−1.16846			−0.584229	−	0.811589i	$-0.698603\pi$
$503$	−26.2058			−1.16846			−0.584229	+	0.811589i	$0.698603\pi$
$504$	−22.4490	+	0.211278i	−0.999956	+	0.00941106i
$505$	37.9515			1.68882
$506$	4.64900	+	9.75084i	0.206673	+	0.433478i
$507$	6.79091	−	1.94201i	0.301595	−	0.0862476i
$508$	18.8969	+	15.3124i	0.838413	+	0.679376i
$509$	−4.29958	−	2.48236i	−0.190575	−	0.110029i	0.401677	−	0.915782i	$-0.368428\pi$
$509$	−4.29958	−	2.48236i	−0.190575	−	0.110029i	−0.592252	+	0.805753i	$0.701761\pi$
$510$	−12.8962	+	38.4309i	−0.571053	+	1.70175i
$511$	−13.6537	−	15.0852i	−0.604006	−	0.667329i
$512$	17.1849	+	14.7200i	0.759473	+	0.650538i
$513$	15.4486	−	17.0836i	0.682072	−	0.754257i
$514$	0.729398	−	9.24903i	0.0321724	−	0.407957i
$515$	−40.4811	+	23.3718i	−1.78381	+	1.02988i
$516$	−3.45809	−	1.47210i	−0.152234	−	0.0648054i
$517$	34.9228	+	20.1627i	1.53590	+	0.886755i
$518$	15.4892	+	6.37171i	0.680556	+	0.279957i
$519$	2.80425	+	9.80604i	0.123093	+	0.430438i
$520$	−6.24233	−	21.1108i	−0.273744	−	0.925770i
$521$		−	13.6674i		−	0.598781i	−0.954131	−	0.299391i	$-0.903217\pi$
$521$		−	13.6674i		−	0.598781i	0.954131	−	0.299391i	$-0.0967834\pi$
$522$	−6.67745	+	3.46258i	−0.292264	+	0.151553i
$523$	27.0038			1.18079			0.590397	−	0.807113i	$-0.298971\pi$
$523$	27.0038			1.18079			0.590397	+	0.807113i	$0.298971\pi$
$524$	−11.0184	−	28.7312i	−0.481339	−	1.25513i
$525$	−4.33324	+	6.96370i	−0.189118	+	0.303921i
$526$	−11.6379	−	8.00121i	−0.507435	−	0.348870i
$527$	15.5337	+	8.96839i	0.676659	+	0.390669i
$528$	26.9072	−	14.2602i	1.17099	−	0.620593i
$529$	−9.98999	−	17.3032i	−0.434347	−	0.752312i
$530$	−1.25055	+	15.8574i	−0.0543205	+	0.688803i
$531$	−20.8916	+	13.0130i	−0.906620	+	0.564717i
$532$	1.28083	+	23.4204i	0.0555311	+	1.01540i
$533$	−11.8790	−	20.5751i	−0.514537	−	0.891205i
$534$	−0.0815031	−	0.402402i	−0.00352698	−	0.0174136i
$535$	−13.5859	+	23.5314i	−0.587368	+	1.01735i
$536$	9.29275	+	8.82694i	0.401386	+	0.381266i
$537$	−23.9542	−	5.99064i	−1.03370	−	0.258515i
$538$	3.23566	−	1.54270i	0.139499	−	0.0665103i
$539$	−12.6601	−	28.0427i	−0.545308	−	1.20788i
$540$	9.76668	−	25.2569i	0.420291	−	1.08688i
$541$	−30.2237			−1.29942			−0.649710	−	0.760182i	$-0.725110\pi$
$541$	−30.2237			−1.29942			−0.649710	+	0.760182i	$0.725110\pi$
$542$	−6.35796	−	13.3352i	−0.273098	−	0.572796i
$543$	−7.12818	−	1.78267i	−0.305900	−	0.0765018i
$544$	21.8483	+	28.5204i	0.936740	+	1.22280i
$545$	−24.4621	−	14.1232i	−1.04784	−	0.604972i
$546$	17.7391	−	7.74944i	0.759162	−	0.331645i
$547$	−5.08073	+	2.93336i	−0.217236	+	0.125421i	−0.604670	−	0.796476i	$-0.706695\pi$
$547$	−5.08073	+	2.93336i	−0.217236	+	0.125421i	0.387434	+	0.921898i	$0.373362\pi$
$548$	−8.43324	−	1.33845i	−0.360250	−	0.0571758i
$549$	−12.3794	+	0.414568i	−0.528338	+	0.0176934i
$550$	0.874660	−	11.0910i	0.0372956	−	0.472922i
$551$	3.92935	+	6.80583i	0.167396	+	0.289938i
$552$	7.18570	−	4.56575i	0.305844	−	0.194331i
$553$	−10.9925	+	34.1322i	−0.467447	+	1.45145i
$554$	−16.6568	+	24.2276i	−0.707681	+	1.02933i
$555$	−14.0441	+	14.5223i	−0.596139	+	0.616438i
$556$	−15.3574	−	40.0456i	−0.651300	−	1.69831i
$557$	−26.6804			−1.13049			−0.565243	−	0.824925i	$-0.691217\pi$
$557$	−26.6804			−1.13049			−0.565243	+	0.824925i	$0.691217\pi$
$558$	−10.0954	−	6.45403i	−0.427370	−	0.273221i
$559$	3.24074			0.137069
$560$	11.2656	+	25.1703i	0.476057	+	1.06364i
$561$	46.4879	−	13.2942i	1.96272	−	0.561282i
$562$	−7.16858	+	10.4268i	−0.302388	+	0.439827i
$563$	16.4713	−	28.5292i	0.694184	−	1.20236i	−0.276271	−	0.961080i	$-0.589099\pi$
$563$	16.4713	−	28.5292i	0.694184	−	1.20236i	0.970455	−	0.241282i	$-0.0775679\pi$
$564$	12.4481	−	29.2418i	0.524159	−	1.23130i
$565$	29.1119	−	16.8078i	1.22475	−	0.707109i
$566$	32.0297	+	2.52593i	1.34631	+	0.106173i
$567$	23.1029	+	5.76677i	0.970231	+	0.242182i
$568$	−7.86016	+	32.6711i	−0.329805	+	1.37085i
$569$	0.320991	+	0.555972i	0.0134566	+	0.0233076i	0.872675	−	0.488301i	$-0.162383\pi$
$569$	0.320991	+	0.555972i	0.0134566	+	0.0233076i	−0.859219	+	0.511609i	$0.829050\pi$
$570$	−26.8223	−	9.00072i	−1.12346	−	0.376999i
$571$	11.6295	+	6.71428i	0.486679	+	0.280984i	0.723196	−	0.690643i	$-0.242673\pi$
$571$	11.6295	+	6.71428i	0.486679	+	0.280984i	−0.236517	+	0.971627i	$0.576006\pi$
$572$	−16.5313	+	20.4012i	−0.691209	+	0.853015i
$573$	1.10431	+	3.86160i	0.0461331	+	0.161321i
$574$	18.1745	+	23.5665i	0.758589	+	0.983646i
$575$		−	3.11033i		−	0.129710i
$576$	−13.7189	−	19.6925i	−0.571620	−	0.820519i
$577$			24.9083i			1.03695i	0.855094	+	0.518473i	$0.173499\pi$
$577$			24.9083i			1.03695i	−0.855094	+	0.518473i	$0.826501\pi$
$578$	14.2032	+	29.7898i	0.590774	+	1.23909i
$579$	2.00055	+	1.93468i	0.0831402	+	0.0804025i
$580$	7.17852	+	5.81684i	0.298072	+	0.241531i
$581$	2.61001	+	0.840567i	0.108281	+	0.0348726i
$582$	11.3522	−	10.0259i	0.470563	−	0.415586i
$583$	16.4312	−	9.48653i	0.680509	−	0.392892i
$584$	5.08790	−	21.1481i	0.210539	−	0.875114i
$585$	0.781515	+	23.3367i	0.0323117	+	0.964854i
$586$	0.660803	−	8.37922i	0.0272975	−	0.346142i
$587$	−12.8056	−	22.1799i	−0.528542	−	0.915462i	−0.999446	−	0.0332777i	$-0.989405\pi$
$587$	−12.8056	−	22.1799i	−0.528542	−	0.915462i	0.470904	−	0.882185i	$-0.343928\pi$
$588$	−20.7332	+	12.5752i	−0.855021	+	0.518593i
$589$	−6.25937	+	10.8415i	−0.257913	+	0.446718i
$590$	24.9134	+	17.1283i	1.02567	+	0.705162i
$591$	3.95491	−	15.8141i	0.162683	−	0.650504i
$592$	3.71148	+	17.5160i	0.152541	+	0.719905i
$593$		−	16.0701i		−	0.659921i	−0.943995	−	0.329960i	$-0.892965\pi$
$593$		−	16.0701i		−	0.659921i	0.943995	−	0.329960i	$-0.107035\pi$
$594$	−31.4245	+	7.46779i	−1.28936	+	0.306407i
$595$	9.21444	+	42.8044i	0.377755	+	1.75481i
$596$	−7.48384	−	19.5147i	−0.306550	−	0.799351i
$597$	−1.94017	+	7.75796i	−0.0794060	+	0.317512i
$598$	−4.15893	+	6.04922i	−0.170071	+	0.247371i
$599$	13.6480	+	7.87965i	0.557640	+	0.321954i	0.752198	−	0.658937i	$-0.228994\pi$
$599$	13.6480	+	7.87965i	0.557640	+	0.321954i	−0.194557	+	0.980891i	$0.562327\pi$
$600$	−8.76023	+	0.372005i	−0.357635	+	0.0151871i
$601$	29.4617	−	17.0097i	1.20177	−	0.693840i	0.240818	−	0.970570i	$-0.422584\pi$
$601$	29.4617	−	17.0097i	1.20177	−	0.693840i	0.960948	+	0.276730i	$0.0892508\pi$
$602$	−4.02349	+	0.539668i	−0.163985	+	0.0219952i
$603$	−7.18736	−	11.5389i	−0.292692	−	0.469899i
$604$	3.81975	−	24.0673i	0.155424	−	0.979285i
$605$	−18.7746	+	10.8395i	−0.763295	+	0.440689i
$606$	−26.7404	+	23.6163i	−1.08626	+	0.959346i
$607$	8.74550	−	15.1477i	0.354969	−	0.614824i	−0.632144	−	0.774851i	$-0.717825\pi$
$607$	8.74550	−	15.1477i	0.354969	−	0.614824i	0.987113	+	0.160027i	$0.0511581\pi$
$608$	−19.9054	+	15.2488i	−0.807270	+	0.618419i
$609$	−4.29238	+	6.89803i	−0.173936	+	0.279522i
$610$	6.54791	+	13.7336i	0.265117	+	0.556057i
$611$			27.4038i			1.10864i
$612$	−14.8280	−	35.1032i	−0.599387	−	1.41896i
$613$	4.11918			0.166372			0.0831860	−	0.996534i	$-0.473490\pi$
$613$	4.11918			0.166372			0.0831860	+	0.996534i	$0.473490\pi$
$614$	−6.13313	−	12.8637i	−0.247513	−	0.519135i
$615$	−34.5141	+	9.87005i	−1.39174	+	0.397999i
$616$	17.1269	−	28.0816i	0.690061	−	1.13144i
$617$	14.7264	−	25.5069i	0.592863	−	1.02687i	−0.400982	−	0.916086i	$-0.631331\pi$
$617$	14.7264	−	25.5069i	0.592863	−	1.02687i	0.993845	−	0.110783i	$-0.0353358\pi$
$618$	13.9791	−	41.6580i	0.562322	−	1.67573i
$619$	−4.03999	−	6.99747i	−0.162381	−	0.281252i	0.773341	−	0.633990i	$-0.218584\pi$
$619$	−4.03999	−	6.99747i	−0.162381	−	0.281252i	−0.935722	+	0.352738i	$0.885251\pi$
$620$	−2.30707	+	14.5363i	−0.0926541	+	0.583790i
$621$	−8.59399	+	2.77198i	−0.344865	+	0.111236i
$622$	−0.112450	−	0.00886808i	−0.00450885	−	0.000355578i
$623$	−0.297592	−	0.328791i	−0.0119228	−	0.0131727i
$624$	17.5350	+	10.9901i	0.701964	+	0.439957i
$625$	15.3728	−	26.6265i	0.614912	−	1.06506i
$626$	27.7990	+	19.1122i	1.11107	+	0.763879i
$627$	9.27852	+	32.4456i	0.370548	+	1.29575i
$628$	−28.3845	+	10.8854i	−1.13266	+	0.434375i
$629$			28.4290i			1.13354i
$630$	−4.85645	−	28.8432i	−0.193485	−	1.14914i
$631$			1.61516i			0.0642986i	0.999483	+	0.0321493i	$0.0102352\pi$
$631$			1.61516i			0.0642986i	−0.999483	+	0.0321493i	$0.989765\pi$
$632$	−36.7611	+	10.8700i	−1.46228	+	0.432386i
$633$	−31.0402	+	32.0971i	−1.23374	+	1.27575i
$634$	3.17757	−	4.62182i	0.126197	−	0.183556i
$635$	−15.8441	+	27.4428i	−0.628754	+	1.08903i
$636$	−8.98656	−	11.9513i	−0.356340	−	0.473898i
$637$	12.2021	−	16.9792i	0.483463	−	0.672740i
$638$	0.866413	−	10.9864i	0.0343016	−	0.434957i
$639$	16.7777	−	31.4458i	0.663717	−	1.24397i
$640$	−15.4315	+	25.1189i	−0.609983	+	0.992914i
$641$	15.1794	+	26.2915i	0.599551	+	1.03845i	0.992887	+	0.119058i	$0.0379875\pi$
$641$	15.1794	+	26.2915i	0.599551	+	1.03845i	−0.393336	+	0.919395i	$0.628679\pi$
$642$	−5.07048	−	25.0342i	−0.200116	−	0.988023i
$643$	7.27667	−	12.6036i	0.286964	−	0.497036i	−0.686120	−	0.727489i	$-0.740687\pi$
$643$	7.27667	−	12.6036i	0.286964	−	0.497036i	0.973084	+	0.230453i	$0.0740207\pi$
$644$	4.15610	−	8.20288i	0.163773	−	0.323239i
$645$	1.18801	−	4.75036i	0.0467777	−	0.187045i
$646$	−35.9375	+	17.1343i	−1.41394	+	0.674139i
$647$	40.4385			1.58980			0.794900	−	0.606740i	$-0.207523\pi$
$647$	40.4385			1.58980			0.794900	+	0.606740i	$0.207523\pi$
$648$	8.83516	+	23.8734i	0.347078	+	0.937836i
$649$		−	36.0615i		−	1.41554i
$650$	6.82450	−	3.25378i	0.267679	−	0.127624i
$651$	−12.9351	−	0.427383i	−0.506966	−	0.0167504i
$652$	6.19325	+	5.01846i	0.242546	+	0.196538i
$653$	15.9077	−	27.5529i	0.622515	−	1.07823i	−0.366501	−	0.930418i	$-0.619444\pi$
$653$	15.9077	−	27.5529i	0.622515	−	1.07823i	0.989016	−	0.147810i	$-0.0472224\pi$
$654$	26.0244	−	5.27103i	1.01764	−	0.206113i
$655$	34.7198	−	20.0455i	1.35662	−	0.783243i
$656$	−9.85079	+	30.2519i	−0.384609	+	1.18114i
$657$	−10.8603	+	20.3549i	−0.423700	+	0.794122i
$658$	−4.56345	−	34.0228i	−0.177902	−	1.32635i
$659$	−2.88773	+	1.66723i	−0.112490	+	0.0649460i	−0.555189	−	0.831724i	$-0.687354\pi$
$659$	−2.88773	+	1.66723i	−0.112490	+	0.0649460i	0.442699	+	0.896670i	$0.354021\pi$
$660$	23.8444	+	31.7107i	0.928141	+	1.23434i
$661$	26.0572	+	15.0442i	1.01351	+	0.585150i	0.912217	−	0.409707i	$-0.134369\pi$
$661$	26.0572	+	15.0442i	1.01351	+	0.585150i	0.101292	+	0.994857i	$0.467702\pi$
$662$	−23.1615	−	15.9239i	−0.900195	−	0.618898i
$663$	23.6198	+	22.8420i	0.917316	+	0.887111i
$664$	0.831203	+	2.81103i	0.0322569	+	0.109089i
$665$	−29.8747	+	6.43109i	−1.15849	+	0.249387i
$666$	0.858541	−	18.9716i	0.0332678	−	0.735136i
$667$		−	3.08100i		−	0.119297i
$668$	2.43577	+	6.35145i	0.0942428	+	0.245745i
$669$	−13.4233	+	3.83868i	−0.518974	+	0.148412i
$670$	−9.46033	+	13.7602i	−0.365484	+	0.531601i
$671$	9.07384	−	15.7164i	0.350292	−	0.606723i
$672$	−23.6005	−	10.7246i	−0.910409	−	0.413709i
$673$	−15.0593	−	26.0835i	−0.580493	−	1.00544i	−0.995421	−	0.0955891i	$-0.969527\pi$
$673$	−15.0593	−	26.0835i	−0.580493	−	1.00544i	0.414928	−	0.909854i	$-0.363807\pi$
$674$	−1.95390	−	0.154089i	−0.0752614	−	0.00593528i
$675$	9.09260	+	1.95309i	0.349974	+	0.0751746i
$676$	8.05499	+	1.27842i	0.309807	+	0.0491699i
$677$	−28.3970	+	16.3950i	−1.09138	+	0.630111i	−0.933945	−	0.357418i	$-0.883657\pi$
$677$	−28.3970	+	16.3950i	−1.09138	+	0.630111i	−0.157439	+	0.987529i	$0.550324\pi$
$678$	−10.0531	+	29.9583i	−0.386085	+	1.15054i
$679$	5.01489	−	15.5715i	0.192454	−	0.597581i
$680$	−32.2368	+	33.9380i	−1.23622	+	1.30146i
$681$	−20.4833	+	5.85765i	−0.784923	+	0.224466i
$682$	15.8465	−	7.55530i	0.606795	−	0.289307i
$683$		−	35.6698i		−	1.36487i	−0.730948	−	0.682433i	$-0.760922\pi$
$683$		−	35.6698i		−	1.36487i	0.730948	−	0.682433i	$-0.239078\pi$
$684$	24.4998	−	10.3490i	0.936774	−	0.395704i
$685$		−	11.1249i		−	0.425059i
$686$	−12.3218	+	23.1122i	−0.470448	+	0.882428i
$687$	7.71800	−	7.98079i	0.294460	−	0.304486i
$688$	−2.90184	−	3.22696i	−0.110632	−	0.123027i
$689$	11.1661	+	6.44673i	0.425393	+	0.245601i
$690$	7.34249	+	8.31381i	0.279524	+	0.316501i
$691$	7.74976	+	13.4230i	0.294815	+	0.510634i	0.974942	−	0.222460i	$-0.0714087\pi$
$691$	7.74976	+	13.4230i	0.294815	+	0.510634i	−0.680127	+	0.733094i	$0.738075\pi$
$692$	−1.84603	+	11.6314i	−0.0701755	+	0.442158i
$693$	−25.0679	+	24.2641i	−0.952249	+	0.921719i
$694$	1.46006	−	18.5141i	0.0554232	−	0.702786i
$695$	48.3926	−	27.9395i	1.83564	−	1.05980i
$696$	−8.67763	+	0.368498i	−0.328925	+	0.0139679i
$697$	−25.2578	+	43.7477i	−0.956706	+	1.65706i
$698$	31.9917	+	21.9948i	1.21090	+	0.832516i
$699$	−6.13548	+	24.5333i	−0.232065	+	0.927934i
$700$	−7.93101	+	5.17614i	−0.299764	+	0.195640i
$701$	30.0954			1.13669			0.568344	−	0.822791i	$-0.307584\pi$
$701$	30.0954			1.13669			0.568344	+	0.822791i	$0.307584\pi$
$702$	−15.0725	−	15.9566i	−0.568875	−	0.602243i
$703$	−19.8416			−0.748340
$704$	35.1170	−	1.80672i	1.32352	−	0.0680933i
$705$	40.1692	+	10.0458i	1.51286	+	0.378348i
$706$	−36.0275	−	24.7695i	−1.35591	−	0.932212i
$707$	−11.8127	+	36.6793i	−0.444264	+	1.37947i
$708$	−28.2124	+	3.43443i	−1.06029	+	0.129074i
$709$	9.74971	+	16.8870i	0.366158	+	0.634204i	0.988961	−	0.148174i	$-0.0473396\pi$
$709$	9.74971	+	16.8870i	0.366158	+	0.634204i	−0.622803	+	0.782379i	$0.714006\pi$
$710$	−43.6449	−	3.44193i	−1.63796	−	0.129173i
$711$	40.6371	−	1.36088i	1.52401	−	0.0510371i
$712$	0.110894	−	0.460936i	0.00415594	−	0.0172743i
$713$	4.25042	−	2.45398i	0.159180	−	0.0919023i
$714$	−33.1286	−	24.4258i	−1.23981	−	0.914114i
$715$	−29.6274	−	17.1054i	−1.10800	−	0.639705i
$716$	−22.1521	−	17.9501i	−0.827861	−	0.670826i
$717$	8.76006	−	9.05833i	0.327150	−	0.338290i
$718$	14.2231	−	6.78128i	0.530801	−	0.253075i
$719$	−8.18208			−0.305140			−0.152570	−	0.988293i	$-0.548755\pi$
$719$	−8.18208			−0.305140			−0.152570	+	0.988293i	$0.548755\pi$
$720$	22.5377	−	21.6745i	0.839929	−	0.807760i
$721$	−9.98818	−	46.3987i	−0.371979	−	1.72798i
$722$	−0.394642	−	0.827723i	−0.0146870	−	0.0308047i
$723$	−5.41476	−	18.9346i	−0.201377	−	0.704185i
$724$	−6.59192	−	5.34152i	−0.244987	−	0.198516i
$725$	−1.58656	+	2.74801i	−0.0589235	+	0.102059i
$726$	6.48332	−	19.3204i	0.240619	−	0.717048i
$727$	1.20415	+	2.08565i	0.0446595	+	0.0773525i	0.887491	−	0.460825i	$-0.152446\pi$
$727$	1.20415	+	2.08565i	0.0446595	+	0.0773525i	−0.842832	+	0.538177i	$0.819113\pi$
$728$	22.3461	+	0.537862i	0.828201	+	0.0199345i
$729$	−2.70701	−	26.8640i	−0.100260	−	0.994961i
$730$	28.2515	+	2.22797i	1.04563	+	0.0824609i
$731$	−3.44532	−	5.96746i	−0.127430	−	0.220715i
$732$	−13.1597	−	5.60203i	−0.486397	−	0.207057i
$733$	19.7132	+	11.3814i	0.728123	+	0.420382i	0.817735	−	0.575595i	$-0.195229\pi$
$733$	19.7132	+	11.3814i	0.728123	+	0.420382i	−0.0896122	+	0.995977i	$0.528563\pi$
$734$	19.2266	−	27.9653i	0.709667	−	1.03222i
$735$	−20.4154	−	24.1104i	−0.753033	−	0.889324i
$736$	9.74751	−	1.27538i	0.359298	−	0.0470111i
$737$	19.9175			0.733671
$738$	18.1766	−	28.4316i	0.669089	−	1.04658i
$739$		−	12.2257i		−	0.449729i	−0.974390	−	0.224865i	$-0.927806\pi$
$739$		−	12.2257i		−	0.449729i	0.974390	−	0.224865i	$-0.0721940\pi$
$740$	−21.7809	+	8.35294i	−0.800682	+	0.307060i
$741$	−15.9423	+	16.4851i	−0.585654	+	0.605595i
$742$	−14.9366	−	6.14440i	−0.548340	−	0.225568i
$743$	−9.48896	−	5.47845i	−0.348116	−	0.200985i	0.315739	−	0.948846i	$-0.397748\pi$
$743$	−9.48896	−	5.47845i	−0.348116	−	0.200985i	−0.663855	+	0.747861i	$0.731081\pi$
$744$	−7.42000	−	11.6778i	−0.272031	−	0.428129i
$745$	23.5822	−	13.6152i	0.863986	−	0.498822i
$746$	−27.8742	−	2.19822i	−1.02055	−	0.0804825i
$747$	−0.104063	−	3.10742i	−0.00380748	−	0.113695i
$748$	55.1413	+	8.75155i	2.01617	+	0.319988i
$749$	−18.5138	−	20.4548i	−0.676481	−	0.747401i
$750$	4.06745	+	20.0820i	0.148522	+	0.733292i
$751$	23.5744	+	13.6107i	0.860242	+	0.496661i	0.864093	−	0.503332i	$-0.167893\pi$
$751$	23.5744	+	13.6107i	0.860242	+	0.496661i	−0.00385154	+	0.999993i	$0.501226\pi$
$752$	27.2873	−	24.5381i	0.995065	−	0.894813i
$753$	−4.24321	+	16.9669i	−0.154631	+	0.618307i
$754$	6.76015	−	3.22310i	0.246190	−	0.117378i
$755$	31.7488			1.15546
$756$	21.3702	+	17.3007i	0.777227	+	0.629220i
$757$	24.4479			0.888572			0.444286	−	0.895885i	$-0.353457\pi$
$757$	24.4479			0.888572			0.444286	+	0.895885i	$0.353457\pi$
$758$	7.52202	−	3.58635i	0.273212	−	0.130262i
$759$	3.20986	−	12.8349i	0.116510	−	0.465878i
$760$	−23.6865	−	22.4992i	−0.859201	−	0.816133i
$761$	8.85621	+	5.11313i	0.321037	+	0.185351i	0.651855	−	0.758344i	$-0.273991\pi$
$761$	8.85621	+	5.11313i	0.321037	+	0.185351i	−0.330818	+	0.943695i	$0.607324\pi$
$762$	−5.91329	−	29.1954i	−0.214216	−	1.05764i
$763$	21.2638	−	19.2461i	0.769802	−	0.696756i
$764$	−0.726962	+	4.58041i	−0.0263006	+	0.165713i
$765$	42.1410	−	26.2489i	1.52361	−	0.949031i
$766$	2.75171	+	0.217006i	0.0994233	+	0.00784073i
$767$	21.2230	−	12.2531i	0.766319	−	0.442434i
$768$	−4.75794	−	27.3013i	−0.171687	−	0.985151i
$769$	−43.5864	−	25.1646i	−1.57177	−	0.907459i	−0.995953	−	0.0898782i	$-0.971352\pi$
$769$	−43.5864	−	25.1646i	−1.57177	−	0.907459i	−0.575813	−	0.817581i	$-0.695314\pi$
$770$	39.6319	+	16.3032i	1.42823	+	0.587526i
$771$	−7.89916	+	8.16812i	−0.284481	+	0.294168i
$772$	1.15068	+	3.00048i	0.0414138	+	0.107990i
$773$			2.39611i			0.0861820i	0.999071	+	0.0430910i	$0.0137205\pi$
$773$			2.39611i			0.0861820i	−0.999071	+	0.0430910i	$0.986279\pi$
$774$	2.11897	+	4.08634i	0.0761647	+	0.146881i
$775$	−5.05473			−0.181571
$776$	16.7709	−	4.95903i	0.602039	−	0.178019i
$777$	−9.66412	−	18.0935i	−0.346698	−	0.649101i
$778$	−3.63350	+	5.28497i	−0.130267	+	0.189475i
$779$	−30.5331	−	17.6283i	−1.09396	−	0.631600i
$780$	−10.5606	+	24.8077i	−0.378128	+	0.888260i
$781$	26.1101	+	45.2239i	0.934291	+	1.61824i
$782$	15.5604	+	1.22713i	0.556439	+	0.0438820i
$783$	9.00687	+	1.93468i	0.321879	+	0.0691397i
$784$	−27.8330	+	3.05343i	−0.994036	+	0.109051i
$785$	−19.8036	−	34.3009i	−0.706821	−	1.22425i
$786$	−11.9896	+	35.7292i	−0.427655	+	1.27442i
$787$	−26.4412	+	45.7975i	−0.942527	+	1.63251i	−0.181899	+	0.983317i	$0.558224\pi$
$787$	−26.4412	+	45.7975i	−0.942527	+	1.63251i	−0.760628	+	0.649188i	$0.775109\pi$
$788$	11.8503	−	14.6244i	0.422150	−	0.520972i
$789$	4.75583	+	16.6304i	0.169312	+	0.592059i
$790$	−21.4945	−	45.0826i	−0.764740	−	1.60397i
$791$	7.18299	+	33.3676i	0.255398	+	1.18642i
$792$	−36.5334	−	7.50546i	−1.29816	−	0.266695i
$793$	12.3326			0.437943
$794$	31.7641	−	15.1445i	1.12727	−	0.537458i
$795$	13.5431	−	14.0042i	0.480324	−	0.496679i
$796$	−5.81344	+	7.17432i	−0.206052	+	0.254287i
$797$	−10.7235	−	6.19123i	−0.379847	−	0.219305i	0.297905	−	0.954596i	$-0.403712\pi$
$797$	−10.7235	−	6.19123i	−0.379847	−	0.219305i	−0.677752	+	0.735291i	$0.737046\pi$
$798$	17.0477	−	23.1216i	0.603482	−	0.818497i
$799$	50.4611	−	29.1337i	1.78518	−	1.03068i
$800$	−9.35078	−	3.88196i	−0.330600	−	0.137248i
$801$	−0.236707	+	0.443649i	−0.00836363	+	0.0156756i
$802$	19.4143	+	1.53106i	0.685544	+	0.0540635i
$803$	−16.9011	−	29.2736i	−0.596428	−	1.03304i
$804$	−1.89691	−	15.5823i	−0.0668988	−	0.549544i
$805$	11.4039	+	3.67268i	0.401934	+	0.129445i
$806$	9.83085	+	6.75887i	0.346277	+	0.238071i
$807$	−4.25906	−	1.06514i	−0.149926	−	0.0374946i
$808$	−39.5043	+	11.6812i	−1.38976	+	0.410942i
$809$	−22.4198			−0.788239			−0.394119	−	0.919059i	$-0.628950\pi$
$809$	−22.4198			−0.788239			−0.394119	+	0.919059i	$0.628950\pi$
$810$	−28.9149	+	16.2442i	−1.01597	+	0.570762i
$811$	−4.09813			−0.143905			−0.0719525	−	0.997408i	$-0.522923\pi$
$811$	−4.09813			−0.143905			−0.0719525	+	0.997408i	$0.522923\pi$
$812$	−7.85623	+	5.12733i	−0.275699	+	0.179934i
$813$	−4.38979	+	17.5530i	−0.153957	+	0.615610i
$814$	22.9285	+	15.7637i	0.803643	+	0.552517i
$815$	−5.19273	+	8.99408i	−0.181894	+	0.315049i
$816$	1.59513	−	43.9727i	0.0558406	−	1.53935i
$817$	4.16491	−	2.40461i	0.145712	−	0.0841267i
$818$	−3.98768	+	50.5652i	−0.139426	+	1.76797i
$819$	−22.7976	−	6.50844i	−0.796614	−	0.227423i
$820$	−40.9386	−	6.49742i	−1.42964	−	0.226900i
$821$	−2.75549	−	4.77265i	−0.0961674	−	0.166567i	0.813928	−	0.580966i	$-0.197325\pi$
$821$	−2.75549	−	4.77265i	−0.0961674	−	0.166567i	−0.910095	+	0.414399i	$0.863992\pi$
$822$	6.92273	+	7.83852i	0.241458	+	0.273400i
$823$	−42.9452	−	24.7944i	−1.49697	−	0.864278i	−0.496980	−	0.867762i	$-0.665558\pi$
$823$	−42.9452	−	24.7944i	−1.49697	−	0.864278i	−0.999994	+	0.00348342i	$0.998891\pi$
$824$	34.9437	−	36.7878i	1.21732	−	1.28156i
$825$	−9.47230	+	9.79483i	−0.329783	+	0.341012i
$826$	−24.3086	+	18.7469i	−0.845806	+	0.652286i
$827$			4.41558i			0.153545i	0.997049	+	0.0767723i	$0.0244615\pi$
$827$			4.41558i			0.153545i	−0.997049	+	0.0767723i	$0.975539\pi$
$828$	−10.3470	−	1.28882i	−0.359582	−	0.0447897i
$829$		−	6.00543i		−	0.208577i	−0.994547	−	0.104289i	$-0.966743\pi$
$829$		−	6.00543i		−	0.208577i	0.994547	−	0.104289i	$-0.0332566\pi$
$830$	−3.44736	+	1.64363i	−0.119660	+	0.0570513i
$831$	34.6210	−	9.90063i	1.20099	−	0.343449i
$832$	12.9955	+	20.0532i	0.450537	+	0.695221i
$833$	−44.2376	−	4.41771i	−1.53274	−	0.153064i
$834$	−16.7111	+	49.7995i	−0.578659	+	1.72442i
$835$	−7.67533	+	4.43135i	−0.265616	+	0.153353i
$836$	−6.10802	+	38.4851i	−0.211250	+	1.33104i
$837$	4.50487	+	13.9665i	0.155711	+	0.482752i
$838$	−14.2461	−	1.12348i	−0.492124	−	0.0388099i
$839$	13.2905	+	23.0198i	0.458839	+	0.794732i	0.998900	−	0.0468940i	$-0.0149323\pi$
$839$	13.2905	+	23.0198i	0.458839	+	0.794732i	−0.540061	+	0.841626i	$0.681599\pi$
$840$	8.98015	−	32.5583i	0.309845	−	1.12337i
$841$	12.9284	−	22.3926i	0.445807	−	0.772160i
$842$	−8.08088	+	11.7537i	−0.278486	+	0.405061i
$843$	14.8998	−	4.26092i	0.513176	−	0.146754i
$844$	−48.1400	+	18.4616i	−1.65705	+	0.635475i
$845$			10.6259i			0.365541i
$846$	−34.5543	+	17.9181i	−1.18800	+	0.616035i
$847$	−4.63238	−	21.5191i	−0.159171	−	0.739405i
$848$	−3.57907	−	16.8912i	−0.122906	−	0.580045i
$849$	−28.2864	−	27.3550i	−0.970788	−	0.938821i
$850$	−13.2468	−	9.10736i	−0.454361	−	0.312380i
$851$	6.73672	+	3.88945i	0.230932	+	0.133328i
$852$	32.8938	−	24.7340i	1.12692	−	0.847372i
$853$	19.9843	−	11.5380i	0.684250	−	0.395052i	−0.117204	−	0.993108i	$-0.537393\pi$
$853$	19.9843	−	11.5380i	0.684250	−	0.395052i	0.801454	+	0.598056i	$0.204060\pi$
$854$	−15.3113	+	2.05370i	−0.523942	+	0.0702760i
$855$	18.3201	+	29.4118i	0.626533	+	1.00586i
$856$	6.89896	−	28.6758i	0.235802	−	0.980119i
$857$	−32.3152	+	18.6572i	−1.10387	+	0.637318i	−0.937234	−	0.348701i	$-0.886623\pi$
$857$	−32.3152	+	18.6572i	−1.10387	+	0.637318i	−0.166633	+	0.986019i	$0.553289\pi$
$858$	31.5195	−	6.38402i	1.07606	−	0.217947i
$859$	−3.22640	+	5.58830i	−0.110084	+	0.190670i	−0.915804	−	0.401626i	$-0.868445\pi$
$859$	−3.22640	+	5.58830i	−0.110084	+	0.190670i	0.805720	+	0.592296i	$0.201778\pi$
$860$	3.55969	−	4.39298i	0.121384	−	0.149799i
$861$	1.20364	−	36.4292i	0.0410200	−	1.24150i
$862$	−24.8777	+	11.8612i	−0.847338	+	0.403994i
$863$		−	28.0729i		−	0.955612i	−0.878465	−	0.477806i	$-0.841432\pi$
$863$		−	28.0729i		−	0.955612i	0.878465	−	0.477806i	$-0.158568\pi$
$864$	−2.39244	+	29.2964i	−0.0813924	+	0.996682i
$865$	−15.3437			−0.521702
$866$	−5.25753	+	2.50668i	−0.178658	+	0.0851805i
$867$	9.80643	−	39.2120i	0.333044	−	1.33171i
$868$	−13.3309	−	6.75427i	−0.452479	−	0.229255i
$869$	−29.7863	+	51.5913i	−1.01043	+	1.75012i
$870$	−2.24633	−	11.0907i	−0.0761579	−	0.376011i
$871$	6.76765	+	11.7219i	0.229313	+	0.397182i
$872$	29.8100	+	7.17183i	1.00949	+	0.242869i
$873$	−18.5391	+	0.620851i	−0.627455	+	0.0210126i
$874$	−0.856457	+	10.8602i	−0.0289701	+	0.367351i
$875$	14.8515	+	16.4085i	0.502071	+	0.554707i
$876$	−21.2923	+	16.0104i	−0.719399	+	0.540940i
$877$	14.9954	−	25.9728i	0.506360	−	0.877041i	−0.493613	−	0.869682i	$-0.664324\pi$
$877$	14.9954	−	25.9728i	0.506360	−	0.877041i	0.999973	−	0.00735913i	$-0.00234250\pi$
$878$	−5.63326	+	8.19365i	−0.190113	+	0.276522i
$879$	−7.15629	+	7.39996i	−0.241376	+	0.249594i
$880$	9.49649	+	44.8180i	0.320127	+	1.51081i
$881$		−	38.3766i		−	1.29294i	−0.762939	−	0.646471i	$-0.776244\pi$
$881$		−	38.3766i		−	1.29294i	0.762939	−	0.646471i	$-0.223756\pi$
$882$	29.3879	+	4.28405i	0.989541	+	0.144251i
$883$			37.0722i			1.24758i	0.781593	+	0.623789i	$0.214407\pi$
$883$			37.0722i			1.24758i	−0.781593	+	0.623789i	$0.785593\pi$
$884$	13.5856	+	35.4255i	0.456934	+	1.19149i
$885$	−10.1809	−	35.6010i	−0.342226	−	1.19672i
$886$	37.9068	+	26.0615i	1.27350	+	0.875554i
$887$	12.2145	−	21.1562i	0.410123	−	0.710355i	−0.584779	−	0.811192i	$-0.698819\pi$
$887$	12.2145	−	21.1562i	0.410123	−	0.710355i	0.994903	+	0.100838i	$0.0321523\pi$
$888$	10.1489	−	19.4392i	0.340574	−	0.652335i
$889$	−21.5912	−	23.8548i	−0.724146	−	0.800063i
$890$	0.615759	+	0.0485601i	0.0206403	+	0.00162774i
$891$	35.5055	+	17.4431i	1.18948	+	0.584366i
$892$	−15.9219	−	2.52699i	−0.533105	−	0.0846098i
$893$	20.3335	+	35.2186i	0.680434	+	1.17855i
$894$	−8.14351	+	24.2678i	−0.272360	+	0.811638i
$895$	18.5734	−	32.1701i	0.620841	−	1.07533i
$896$	−19.4737	−	22.7327i	−0.650571	−	0.759446i
$897$	8.64429	−	2.47202i	0.288624	−	0.0825384i
$898$	−23.5294	−	49.3507i	−0.785187	−	1.64685i
$899$	−5.00706			−0.166995
$900$	8.56500	+	6.47771i	0.285500	+	0.215924i
$901$		−	27.4147i		−	0.913318i
$902$	21.2781	+	44.6287i	0.708482	+	1.48597i
$903$	4.22133	+	2.62677i	0.140477	+	0.0874135i
$904$	−25.1298	+	26.4559i	−0.835803	+	0.879910i
$905$	5.52700	−	9.57305i	0.183724	−	0.318219i
$906$	−22.3701	+	19.7565i	−0.743195	+	0.656366i
$907$	−17.3676	+	10.0272i	−0.576683	+	0.332948i	−0.759814	−	0.650140i	$-0.774710\pi$
$907$	−17.3676	+	10.0272i	−0.576683	+	0.332948i	0.183131	+	0.983089i	$0.441377\pi$
$908$	−24.2962	−	3.85608i	−0.806296	−	0.127968i
$909$	43.6696	−	1.46244i	1.44843	−	0.0485060i
$910$	3.87148	+	28.8638i	0.128338	+	0.956826i
$911$	12.8106	−	7.39618i	0.424433	−	0.245046i	−0.272539	−	0.962145i	$-0.587864\pi$
$911$	12.8106	−	7.39618i	0.424433	−	0.245046i	0.696972	+	0.717098i	$0.254530\pi$
$912$	30.6901	+	1.11330i	1.01625	+	0.0368649i
$913$	3.94506	+	2.27768i	0.130563	+	0.0753803i
$914$	18.2831	−	26.5931i	0.604753	−	0.879620i
$915$	4.52093	−	18.0774i	0.149457	−	0.597620i
$916$	11.9698	−	4.59039i	0.395493	−	0.151671i
$917$	8.56667	+	39.7953i	0.282896	+	1.31416i
$918$	−13.3583	+	44.7182i	−0.440890	+	1.47592i
$919$			47.6023i			1.57026i	0.619333	+	0.785128i	$0.287403\pi$
$919$			47.6023i			1.57026i	−0.619333	+	0.785128i	$0.712597\pi$
$920$	3.63176	+	12.2822i	0.119736	+	0.404932i
$921$	−4.23455	+	16.9323i	−0.139533	+	0.557937i
$922$	15.0169	+	10.3243i	0.494555	+	0.340014i
$923$	−17.7435	+	30.7327i	−0.584036	+	1.01158i
$924$	−38.0695	+	13.1748i	−1.25239	+	0.433419i
$925$	−4.00575	−	6.93817i	−0.131708	−	0.228126i
$926$	−3.19153	+	40.4698i	−0.104880	+	1.32992i
$927$	−45.6796	+	28.4530i	−1.50032	+	0.934520i
$928$	−9.26261	−	3.84535i	−0.304060	−	0.126230i
$929$	−2.22951	+	1.28721i	−0.0731477	+	0.0422318i	−0.536128	−	0.844137i	$-0.680113\pi$
$929$	−2.22951	+	1.28721i	−0.0731477	+	0.0422318i	0.462980	+	0.886369i	$0.346780\pi$
$930$	13.5111	−	11.9326i	0.443048	−	0.391285i
$931$	3.08328	−	30.8750i	0.101050	−	1.01189i
$932$	−18.3841	+	22.6876i	−0.602190	+	0.743158i
$933$	0.0993087	+	0.0960386i	0.00325122	+	0.00314416i
$934$	15.4690	+	32.4448i	0.506162	+	1.06163i
$935$			72.7406i			2.37887i
$936$	−7.99633	−	24.0510i	−0.261368	−	0.786131i
$937$			10.0050i			0.326849i	0.986556	+	0.163424i	$0.0522539\pi$
$937$			10.0050i			0.326849i	−0.986556	+	0.163424i	$0.947746\pi$
$938$	−10.3543	−	13.4262i	−0.338079	−	0.438380i
$939$	−11.3601	−	39.7246i	−0.370723	−	1.29636i
$940$	37.1472	+	30.1008i	1.21161	+	0.981781i
$941$	−34.5062	−	19.9222i	−1.12487	−	0.649445i	−0.182231	−	0.983256i	$-0.558332\pi$
$941$	−34.5062	−	19.9222i	−1.12487	−	0.649445i	−0.942640	+	0.333811i	$0.891665\pi$
$942$	35.2981	+	11.8449i	1.15007	+	0.385928i
$943$	6.91117	+	11.9705i	0.225059	+	0.389813i
$944$	−31.2047	−	10.1610i	−1.01563	−	0.330713i
$945$	−17.8975	+	31.0314i	−0.582205	+	1.00945i
$946$	−6.72327	−	0.530212i	−0.218593	−	0.0172387i
$947$	−26.3058	+	15.1877i	−0.854824	+	0.493533i	−0.862276	−	0.506439i	$-0.830961\pi$
$947$	−26.3058	+	15.1877i	−0.854824	+	0.493533i	0.00745153	+	0.999972i	$0.497628\pi$
$948$	43.1987	+	18.3895i	1.40303	+	0.597263i
$949$	11.4854	−	19.8934i	0.372833	−	0.645766i
$950$	6.35636	−	9.24540i	0.206228	−	0.299961i
$951$	−6.60454	+	1.88871i	−0.214167	+	0.0612457i
$952$	−22.7663	−	41.7196i	−0.737860	−	1.35214i
$953$	27.5080			0.891073			0.445536	−	0.895264i	$-0.353013\pi$
$953$	27.5080			0.891073			0.445536	+	0.895264i	$0.353013\pi$
$954$	−0.827913	+	18.2948i	−0.0268047	+	0.592317i
$955$	−6.04232			−0.195525
$956$	13.5859	−	5.21017i	0.439400	−	0.168509i
$957$	−9.38298	+	9.70247i	−0.303309	+	0.313636i
$958$	25.1704	−	36.6106i	0.813218	−	1.18284i
$959$	10.7519	+	3.46271i	0.347198	+	0.111817i
$960$	34.1584	−	11.6979i	1.10246	−	0.377547i
$961$	11.5119	+	19.9392i	0.371352	+	0.643201i
$962$	−1.48656	+	18.8502i	−0.0479287	+	0.607754i
$963$	−14.7260	+	27.6003i	−0.474540	+	0.889408i
$964$	3.56452	−	22.4591i	0.114805	−	0.723360i
$965$	−3.62589	+	2.09341i	−0.116721	+	0.0673892i
$966$	−10.3205	+	4.50860i	−0.332057	+	0.145062i
$967$	51.9168	+	29.9742i	1.66953	+	0.963905i	0.967889	+	0.251377i	$0.0808835\pi$
$967$	51.9168	+	29.9742i	1.66953	+	0.963905i	0.701644	+	0.712528i	$0.252450\pi$
$968$	16.2064	−	17.0617i	0.520895	−	0.548383i
$969$	47.3041	+	11.8302i	1.51963	+	0.380040i
$970$	9.80605	+	20.5672i	0.314853	+	0.660374i
$971$	−30.8420			−0.989768			−0.494884	−	0.868959i	$-0.664789\pi$
$971$	−30.8420			−0.989768			−0.494884	+	0.868959i	$0.664789\pi$
$972$	10.2649	−	29.4386i	0.329248	−	0.944243i
$973$	11.9402	+	55.4668i	0.382787	+	1.77818i
$974$	35.5726	−	16.9603i	1.13982	−	0.543443i
$975$	−8.98301	−	2.24654i	−0.287686	−	0.0719469i
$976$	−11.0429	−	12.2801i	−0.353475	−	0.393077i
$977$	−6.22072	+	10.7746i	−0.199018	+	0.344710i	−0.948210	−	0.317643i	$-0.897109\pi$
$977$	−6.22072	+	10.7746i	−0.199018	+	0.344710i	0.749192	+	0.662353i	$0.230442\pi$
$978$	−1.93802	−	9.56849i	−0.0619710	−	0.305967i
$979$	−0.368371	−	0.638037i	−0.0117732	−	0.0203918i
$980$	−9.61315	−	35.1907i	−0.307081	−	1.12413i
$981$	−28.6920	−	15.3085i	−0.916065	−	0.488762i
$982$	3.18501	−	40.3871i	0.101638	−	1.28880i
$983$	−0.588026	−	1.01849i	−0.0187551	−	0.0324848i	0.856496	−	0.516154i	$-0.172637\pi$
$983$	−0.588026	−	1.01849i	−0.0187551	−	0.0324848i	−0.875251	+	0.483670i	$0.839304\pi$
$984$	32.8883	−	20.8970i	1.04844	−	0.666173i
$985$	21.2381	+	12.2618i	0.676702	+	0.390694i
$986$	−13.1219	−	9.02149i	−0.417885	−	0.287303i
$987$	−22.2121	+	35.6958i	−0.707018	+	1.13621i
$988$	−24.7248	+	9.48190i	−0.786599	+	0.301659i
$989$	−1.88545			−0.0599539
$990$	2.19673	−	48.5424i	0.0698168	−	1.54278i
$991$			7.08869i			0.225180i	0.993642	+	0.112590i	$0.0359146\pi$
$991$			7.08869i			0.225180i	−0.993642	+	0.112590i	$0.964085\pi$
$992$	−2.07268	−	15.8411i	−0.0658076	−	0.502956i
$993$	9.46496	+	33.0976i	0.300361	+	1.05032i
$994$	16.9114	−	41.1105i	0.536397	−	1.30394i
$995$	−10.4188	−	6.01532i	−0.330299	−	0.190698i
$996$	1.40620	−	3.30330i	0.0445572	−	0.104669i
$997$	22.9923	−	13.2746i	0.728173	−	0.420411i	−0.0895805	−	0.995980i	$-0.528553\pi$
$997$	22.9923	−	13.2746i	0.728173	−	0.420411i	0.817753	+	0.575569i	$0.195219\pi$
$998$	−2.76523	+	35.0642i	−0.0875320	+	1.10994i
$999$	−15.6005	+	17.2515i	−0.493578	+	0.545814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bi.c.139.15	yes	80
3.2	odd	2		756.2.bi.c.307.26		80
4.3	odd	2	inner	252.2.bi.c.139.14	yes	80
7.6	odd	2	inner	252.2.bi.c.139.16	yes	80
9.2	odd	6		756.2.bi.c.559.27		80
9.7	even	3	inner	252.2.bi.c.223.13	yes	80
12.11	even	2		756.2.bi.c.307.28		80
21.20	even	2		756.2.bi.c.307.25		80
28.27	even	2	inner	252.2.bi.c.139.13	✓	80
36.7	odd	6	inner	252.2.bi.c.223.16	yes	80
36.11	even	6		756.2.bi.c.559.25		80
63.20	even	6		756.2.bi.c.559.28		80
63.34	odd	6	inner	252.2.bi.c.223.14	yes	80
84.83	odd	2		756.2.bi.c.307.27		80
252.83	odd	6		756.2.bi.c.559.26		80
252.223	even	6	inner	252.2.bi.c.223.15	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.13	✓	80	28.27	even	2	inner
252.2.bi.c.139.14	yes	80	4.3	odd	2	inner
252.2.bi.c.139.15	yes	80	1.1	even	1	trivial
252.2.bi.c.139.16	yes	80	7.6	odd	2	inner
252.2.bi.c.223.13	yes	80	9.7	even	3	inner
252.2.bi.c.223.14	yes	80	63.34	odd	6	inner
252.2.bi.c.223.15	yes	80	252.223	even	6	inner
252.2.bi.c.223.16	yes	80	36.7	odd	6	inner
756.2.bi.c.307.25		80	21.20	even	2
756.2.bi.c.307.26		80	3.2	odd	2
756.2.bi.c.307.27		80	84.83	odd	2
756.2.bi.c.307.28		80	12.11	even	2
756.2.bi.c.559.25		80	36.11	even	6
756.2.bi.c.559.26		80	252.83	odd	6
756.2.bi.c.559.27		80	9.2	odd	6
756.2.bi.c.559.28		80	63.20	even	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.608631 - 1.27655i) q^{2} +(-0.420223 + 1.68030i) q^{3} +(-1.25914 + 1.55389i) q^{4} +(-2.25662 - 1.30286i) q^{5} +(2.40074 - 0.486250i) q^{6} +(1.96158 - 1.77545i) q^{7} +(2.74996 + 0.661599i) q^{8} +(-2.64683 - 1.41220i) q^{9} +O(q^{10})\)	\(q+(-0.608631 - 1.27655i) q^{2} +(-0.420223 + 1.68030i) q^{3} +(-1.25914 + 1.55389i) q^{4} +(-2.25662 - 1.30286i) q^{5} +(2.40074 - 0.486250i) q^{6} +(1.96158 - 1.77545i) q^{7} +(2.74996 + 0.661599i) q^{8} +(-2.64683 - 1.41220i) q^{9} +(-0.289711 + 3.67364i) q^{10} +(3.80655 - 2.19771i) q^{11} +(-2.08189 - 2.76871i) q^{12} +(2.58681 + 1.49349i) q^{13} +(-3.46032 - 1.42345i) q^{14} +(3.13748 - 3.24431i) q^{15} +(-0.829151 - 3.91312i) q^{16} -6.35108i q^{17} +(-0.191800 + 4.23830i) q^{18} +4.43265 q^{19} +(4.86590 - 1.86606i) q^{20} +(2.15898 + 4.04213i) q^{21} +(-5.12227 - 3.52164i) q^{22} +(-1.50500 - 0.868910i) q^{23} +(-2.26728 + 4.34275i) q^{24} +(0.894893 + 1.55000i) q^{25} +(0.332101 - 4.21116i) q^{26} +(3.48518 - 3.85402i) q^{27} +(0.288954 + 5.28361i) q^{28} +(0.886455 + 1.53538i) q^{29} +(-6.05108 - 2.03055i) q^{30} +(-1.41210 + 2.44584i) q^{31} +(-4.49063 + 3.44010i) q^{32} +(2.09322 + 7.31968i) q^{33} +(-8.10745 + 3.86547i) q^{34} +(-6.73970 + 1.45084i) q^{35} +(5.52712 - 2.33472i) q^{36} -4.47624 q^{37} +(-2.69785 - 5.65848i) q^{38} +(-3.59656 + 3.71902i) q^{39} +(-5.34365 - 5.07579i) q^{40} +(-6.88823 - 3.97692i) q^{41} +(3.84593 - 5.21621i) q^{42} +(0.939597 - 0.542477i) q^{43} +(-1.37796 + 8.68218i) q^{44} +(4.13298 + 6.63525i) q^{45} +(-0.193215 + 2.45004i) q^{46} +(4.58720 + 7.94527i) q^{47} +(6.92365 + 0.251158i) q^{48} +(0.695583 - 6.96535i) q^{49} +(1.43399 - 2.08575i) q^{50} +(10.6717 + 2.66887i) q^{51} +(-5.57787 + 2.13910i) q^{52} +4.31655 q^{53} +(-7.04103 - 2.10331i) q^{54} -11.4533 q^{55} +(6.56890 - 3.58463i) q^{56} +(-1.86270 + 7.44819i) q^{57} +(1.42046 - 2.06608i) q^{58} +(4.10217 - 7.10516i) q^{59} +(1.09079 + 8.96034i) q^{60} +(3.57562 - 2.06438i) q^{61} +(3.98167 + 0.314003i) q^{62} +(-7.69925 + 1.92915i) q^{63} +(7.12457 + 3.63874i) q^{64} +(-3.89163 - 6.74050i) q^{65} +(8.06991 - 7.12708i) q^{66} +(3.92432 + 2.26571i) q^{67} +(9.86889 + 7.99688i) q^{68} +(2.09246 - 2.16371i) q^{69} +(5.95406 + 7.72050i) q^{70} +11.8806i q^{71} +(-6.34436 - 5.63464i) q^{72} -7.69032i q^{73} +(2.72438 + 5.71412i) q^{74} +(-2.98052 + 0.852344i) q^{75} +(-5.58131 + 6.88786i) q^{76} +(3.56493 - 11.0693i) q^{77} +(6.93647 + 2.32766i) q^{78} +(-11.7375 + 6.77665i) q^{79} +(-3.22717 + 9.91070i) q^{80} +(5.01137 + 7.47571i) q^{81} +(-0.884330 + 11.2136i) q^{82} +(0.518194 + 0.897538i) q^{83} +(-8.99948 - 1.73476i) q^{84} +(-8.27458 + 14.3320i) q^{85} +(-1.26436 - 0.869270i) q^{86} +(-2.95242 + 0.844307i) q^{87} +(11.9219 - 3.52522i) q^{88} -0.167616i q^{89} +(5.95474 - 9.31436i) q^{90} +(7.72584 - 1.66313i) q^{91} +(3.24519 - 1.24452i) q^{92} +(-3.51634 - 3.40056i) q^{93} +(7.35058 - 10.6915i) q^{94} +(-10.0028 - 5.77513i) q^{95} +(-3.89333 - 8.99122i) q^{96} +(5.35479 - 3.09159i) q^{97} +(-9.31494 + 3.35139i) q^{98} +(-13.1789 + 0.441344i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9}+O(q^{10}) \) 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9	\( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44} + 24 q^{46} - 24 q^{49} - 12 q^{50} - 48 q^{53} + 32 q^{56} + 72 q^{57} - 14 q^{58} + 56 q^{60} - 8 q^{64} - 40 q^{65} - 22 q^{70} - 100 q^{72} + 64 q^{74} - 12 q^{77} - 24 q^{78} - 104 q^{81} + 62 q^{84} + 40 q^{85} - 52 q^{86} + 6 q^{88} + 30 q^{92} + 48 q^{93} + 20 q^{98}+O(q^{100}) \) 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

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