LMFDB - Embedded newform 252.2.bi.c.139.14

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			139.14
Character	$\chi$	$=$	252.139
Dual form			252.2.bi.c.223.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.801205 - 1.16536i) q^{2} +(0.420223 - 1.68030i) q^{3} +(-0.716141 + 1.86739i) q^{4} +(-2.25662 - 1.30286i) q^{5} +(-2.29485 + 0.856554i) q^{6} +(-1.96158 + 1.77545i) q^{7} +(2.74996 - 0.661599i) q^{8} +(-2.64683 - 1.41220i) q^{9} +O(q^{10})$	\(q+(-0.801205 - 1.16536i) q^{2} +(0.420223 - 1.68030i) q^{3} +(-0.716141 + 1.86739i) q^{4} +(-2.25662 - 1.30286i) q^{5} +(-2.29485 + 0.856554i) 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} +(2.83684 + 1.98805i) q^{12} +(2.58681 + 1.49349i) q^{13} +(3.64067 + 0.863454i) q^{14} +(-3.13748 + 3.24431i) q^{15} +(-2.97429 - 2.67463i) q^{16} -6.35108i q^{17} +(0.474923 + 4.21598i) q^{18} -4.43265 q^{19} +(4.04901 - 3.28096i) q^{20} +(2.15898 + 4.04213i) q^{21} +(5.61096 + 2.67519i) q^{22} +(1.50500 + 0.868910i) q^{23} +(0.0439117 - 4.89878i) q^{24} +(0.894893 + 1.55000i) q^{25} +(-0.332101 - 4.21116i) q^{26} +(-3.48518 + 3.85402i) q^{27} +(-1.91068 - 4.93450i) q^{28} +(0.886455 + 1.53538i) q^{29} +(6.29457 + 1.05695i) q^{30} +(1.41210 - 2.44584i) q^{31} +(-0.733897 + 5.60905i) q^{32} +(2.09322 + 7.31968i) q^{33} +(-7.40132 + 5.08852i) q^{34} +(6.73970 - 1.45084i) q^{35} +(4.53263 - 3.93132i) q^{36} -4.47624 q^{37} +(3.55146 + 5.16565i) q^{38} +(3.59656 - 3.71902i) q^{39} +(-7.06759 - 2.08984i) q^{40} +(-6.88823 - 3.97692i) q^{41} +(2.98075 - 5.75457i) 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} +(-5.74404 + 3.87376i) q^{48} +(0.695583 - 6.96535i) q^{49} +(1.08932 - 2.28474i) q^{50} +(-10.6717 - 2.66887i) q^{51} +(-4.64145 + 3.76102i) q^{52} +4.31655 q^{53} +(7.28368 + 0.973636i) q^{54} +11.4533 q^{55} +(-4.21963 + 6.18019i) q^{56} +(-1.86270 + 7.44819i) q^{57} +(1.07905 - 2.26320i) q^{58} +(-4.10217 + 7.10516i) q^{59} +(-3.81151 - 8.18228i) 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} +(6.85299 - 8.30393i) q^{66} +(-3.92432 - 2.26571i) q^{67} +(11.8599 + 4.54827i) q^{68} +(2.09246 - 2.16371i) q^{69} +(-7.09064 - 6.69177i) q^{70} -11.8806i q^{71} +(-8.21298 - 2.13237i) q^{72} -7.69032i q^{73} +(3.58638 + 5.21644i) q^{74} +(2.98052 - 0.852344i) q^{75} +(3.17440 - 8.27749i) q^{76} +(3.56493 - 11.0693i) q^{77} +(-7.21558 - 1.21160i) 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} +(-9.09436 + 1.13693i) q^{84} +(-8.27458 + 14.3320i) q^{85} +(1.38499 + 0.660336i) q^{86} +(2.95242 - 0.844307i) q^{87} +(-9.01386 + 8.56204i) q^{88} -0.167616i q^{89} +(4.42111 - 10.1326i) q^{90} +(-7.72584 + 1.66313i) q^{91} +(-2.70038 + 2.18815i) q^{92} +(-3.51634 - 3.40056i) q^{93} +(-5.58383 + 11.7115i) q^{94} +(10.0028 + 5.77513i) q^{95} +(9.11649 + 3.59022i) q^{96} +(5.35479 - 3.09159i) q^{97} +(-8.67447 + 4.77007i) 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 $

$2$	−0.801205	−	1.16536i	−0.566538	−	0.824036i
$2$	−0.801205	−	1.16536i	−0.566538	−	0.824036i
$3$	0.420223	−	1.68030i	0.242616	−	0.970122i
$3$	0.420223	−	1.68030i	0.242616	−	0.970122i
$4$	−0.716141	+	1.86739i	−0.358070	+	0.933695i
$5$	−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	$0.864654\pi$
$6$	−2.29485	+	0.856554i	−0.936867	+	0.349687i
$7$	−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	−0.948330	−	0.317285i	$-0.897229\pi$
$11$	−3.80655	+	2.19771i	−1.14772	+	0.662636i	−0.199388	+	0.979921i	$0.563895\pi$
$12$	2.83684	+	1.98805i	0.818925	+	0.573901i
$13$	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	$0.530721\pi$
$14$	3.64067	+	0.863454i	0.973009	+	0.230768i
$15$	−3.13748	+	3.24431i	−0.810095	+	0.837678i
$16$	−2.97429	−	2.67463i	−0.743571	−	0.668657i
$17$		−	6.35108i		−	1.54036i	−0.637824	−	0.770182i	$-0.720165\pi$
$17$		−	6.35108i		−	1.54036i	0.637824	−	0.770182i	$-0.279835\pi$
$18$	0.474923	+	4.21598i	0.111940	+	0.993715i
$19$	−4.43265			−1.01692			−0.508460	−	0.861086i	$-0.669785\pi$
$19$	−4.43265			−1.01692			−0.508460	+	0.861086i	$0.669785\pi$
$20$	4.04901	−	3.28096i	0.905385	−	0.733645i
$21$	2.15898	+	4.04213i	0.471129	+	0.882064i
$22$	5.61096	+	2.67519i	1.19626	+	0.570353i
$23$	1.50500	+	0.868910i	0.313813	+	0.181180i	0.648632	−	0.761102i	$-0.275342\pi$
$23$	1.50500	+	0.868910i	0.313813	+	0.181180i	−0.334818	+	0.942283i	$0.608675\pi$
$24$	0.0439117	−	4.89878i	0.00896345	−	0.999960i
$25$	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
$28$	−1.91068	−	4.93450i	−0.361085	−	0.932533i
$29$	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	$0.780697\pi$
$30$	6.29457	+	1.05695i	1.14923	+	0.192971i
$31$	1.41210	−	2.44584i	0.253621	−	0.439285i	−0.710899	−	0.703294i	$-0.751712\pi$
$31$	1.41210	−	2.44584i	0.253621	−	0.439285i	0.964520	+	0.264009i	$0.0850450\pi$
$32$	−0.733897	+	5.60905i	−0.129736	+	0.991549i
$33$	2.09322	+	7.31968i	0.364383	+	1.27419i
$34$	−7.40132	+	5.08852i	−1.26932	+	0.872674i
$35$	6.73970	−	1.45084i	1.13922	−	0.245238i
$36$	4.53263	−	3.93132i	0.755438	−	0.655220i
$37$	−4.47624			−0.735889			−0.367944	−	0.929848i	$-0.619938\pi$
$37$	−4.47624			−0.735889			−0.367944	+	0.929848i	$0.619938\pi$
$38$	3.55146	+	5.16565i	0.576124	+	0.837979i
$39$	3.59656	−	3.71902i	0.575910	−	0.595519i
$40$	−7.06759	−	2.08984i	−1.11748	−	0.330433i
$41$	−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	$0.879977\pi$
$42$	2.98075	−	5.75457i	0.459940	−	0.887950i
$43$	−0.939597	+	0.542477i	−0.143287	+	0.0827269i	−0.569930	−	0.821693i	$-0.693030\pi$
$43$	−0.939597	+	0.542477i	−0.143287	+	0.0827269i	0.426643	+	0.904420i	$0.359696\pi$
$44$	−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	$-0.933341\pi$
$47$	−4.58720	−	7.94527i	−0.669112	−	1.15894i	0.309041	−	0.951049i	$-0.399992\pi$
$48$	−5.74404	+	3.87376i	−0.829081	+	0.559129i
$49$	0.695583	−	6.96535i	0.0993690	−	0.995051i
$50$	1.08932	−	2.28474i	0.154053	−	0.323111i
$51$	−10.6717	−	2.66887i	−1.49434	−	0.373717i
$52$	−4.64145	+	3.76102i	−0.643654	+	0.521560i
$53$	4.31655			0.592923			0.296462	−	0.955045i	$-0.404193\pi$
$53$	4.31655			0.592923			0.296462	+	0.955045i	$0.404193\pi$
$54$	7.28368	+	0.973636i	0.991184	+	0.132495i
$55$	11.4533			1.54436
$56$	−4.21963	+	6.18019i	−0.563872	+	0.825862i
$57$	−1.86270	+	7.44819i	−0.246721	+	0.986537i
$58$	1.07905	−	2.26320i	0.141686	−	0.297173i
$59$	−4.10217	+	7.10516i	−0.534056	+	0.925013i	0.465152	+	0.885231i	$0.346000\pi$
$59$	−4.10217	+	7.10516i	−0.534056	+	0.925013i	−0.999208	+	0.0397821i	$0.987334\pi$
$60$	−3.81151	−	8.18228i	−0.492064	−	1.05633i
$61$	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
$66$	6.85299	−	8.30393i	0.843544	−	1.02214i
$67$	−3.92432	−	2.26571i	−0.479433	−	0.276801i	0.240747	−	0.970588i	$-0.422607\pi$
$67$	−3.92432	−	2.26571i	−0.479433	−	0.276801i	−0.720180	+	0.693787i	$0.755941\pi$
$68$	11.8599	+	4.54827i	1.43823	+	0.551559i
$69$	2.09246	−	2.16371i	0.251903	−	0.260480i
$70$	−7.09064	−	6.69177i	−0.847494	−	0.799820i
$71$		−	11.8806i		−	1.40996i	−0.709226	−	0.704981i	$-0.750955\pi$
$71$		−	11.8806i		−	1.40996i	0.709226	−	0.704981i	$-0.249045\pi$
$72$	−8.21298	−	2.13237i	−0.967909	−	0.251302i
$73$		−	7.69032i		−	0.900084i	−0.893007	−	0.450042i	$-0.851409\pi$
$73$		−	7.69032i		−	0.900084i	0.893007	−	0.450042i	$-0.148591\pi$
$74$	3.58638	+	5.21644i	0.416909	+	0.606399i
$75$	2.98052	−	0.852344i	0.344161	−	0.0984203i
$76$	3.17440	−	8.27749i	0.364129	−	0.949493i
$77$	3.56493	−	11.0693i	0.406261	−	1.26147i
$78$	−7.21558	−	1.21160i	−0.817004	−	0.137186i
$79$	11.7375	−	6.77665i	1.32057	−	0.762432i	0.336752	−	0.941593i	$-0.390672\pi$
$79$	11.7375	−	6.77665i	1.32057	−	0.762432i	0.983820	+	0.179161i	$0.0573383\pi$
$80$	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	0.836184	−	0.548449i	$-0.184782\pi$
$83$	−0.518194	−	0.897538i	−0.0568792	−	0.0985176i	−0.893063	+	0.449932i	$0.851448\pi$
$84$	−9.09436	+	1.13693i	−0.992276	+	0.124050i
$85$	−8.27458	+	14.3320i	−0.897504	+	1.55452i
$86$	1.38499	+	0.660336i	0.149348	+	0.0712059i
$87$	2.95242	−	0.844307i	0.316532	−	0.0905193i
$88$	−9.01386	+	8.56204i	−0.960881	+	0.912716i
$89$		−	0.167616i		−	0.0177672i	−0.999961	−	0.00888361i	$-0.997172\pi$
$89$		−	0.167616i		−	0.0177672i	0.999961	−	0.00888361i	$-0.00282778\pi$
$90$	4.42111	−	10.1326i	0.466026	−	1.06807i
$91$	−7.72584	+	1.66313i	−0.809889	+	0.174343i
$92$	−2.70038	+	2.18815i	−0.281534	+	0.228131i
$93$	−3.51634	−	3.40056i	−0.364628	−	0.352621i
$94$	−5.58383	+	11.7115i	−0.575928	+	1.20795i
$95$	10.0028	+	5.77513i	1.02627	+	0.592516i
$96$	9.11649	+	3.59022i	0.930448	+	0.366425i
$97$	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	$0.231697\pi$
$98$	−8.67447	+	4.77007i	−0.876254	+	0.481850i
$99$	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	$0.591318\pi$
$102$	5.44005	+	14.5748i	0.538645	+	1.44312i
$103$	−8.96940	+	15.5355i	−0.883781	+	1.53075i	−0.0366767	+	0.999327i	$0.511677\pi$
$103$	−8.96940	+	15.5355i	−0.883781	+	1.53075i	−0.847104	+	0.531427i	$0.821656\pi$
$104$	8.10171	+	2.39562i	0.794438	+	0.234910i
$105$	0.394319	−	11.9344i	0.0384816	−	1.16468i
$106$	−3.45844	−	5.03034i	−0.335913	−	0.488590i
$107$			10.4277i			1.00808i	0.863679	+	0.504042i	$0.168154\pi$
$107$			10.4277i			1.00808i	−0.863679	+	0.504042i	$0.831846\pi$
$108$	−4.70108	−	9.26821i	−0.452362	−	0.891834i
$109$	10.8402			1.03830			0.519149	−	0.854684i	$-0.326249\pi$
$109$	10.8402			1.03830			0.519149	+	0.854684i	$0.326249\pi$
$110$	−9.17641	−	13.3472i	−0.874936	−	1.27261i
$111$	−1.88102	+	7.52143i	−0.178538	+	0.713902i
$112$	10.5830	−	0.0341931i	0.999995	−	0.00323095i
$113$	−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	$0.959121\pi$
$114$	10.1723	−	3.79681i	0.952719	−	0.355604i
$115$	−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
$120$	−6.48152	+	10.9975i	−0.591680	+	1.00393i
$121$	4.15989	−	7.20514i	0.378172	−	0.655013i
$122$	−5.27056	−	2.51290i	−0.477174	−	0.227507i
$123$	−9.57702	+	9.90311i	−0.863531	+	0.892933i
$124$	3.55606	+	4.38851i	0.319344	+	0.394100i
$125$			8.36492i			0.748182i
$126$	−8.41683	−	7.42677i	−0.749831	−	0.661629i
$127$			12.1610i			1.07911i	0.841949	+	0.539557i	$0.181408\pi$
$127$			12.1610i			1.07911i	−0.841949	+	0.539557i	$0.818592\pi$
$128$	−9.94870	−	5.38734i	−0.879349	−	0.476178i
$129$	0.516684	+	1.80677i	0.0454915	+	0.159077i
$130$	−4.73713	+	9.93568i	−0.415474	+	0.871417i
$131$	7.69288	−	13.3245i	0.672130	−	1.16416i	−0.305169	−	0.952298i	$-0.598713\pi$
$131$	7.69288	−	13.3245i	0.672130	−	1.16416i	0.977299	−	0.211865i	$-0.0679537\pi$
$132$	−15.1677	−	1.33306i	−1.32018	−	0.116028i
$133$	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	$0.774953\pi$
$138$	−4.19800	−	0.704903i	−0.357358	−	0.0600053i
$139$	10.7224	−	18.5717i	0.909459	−	1.57523i	0.0946405	−	0.995512i	$-0.469830\pi$
$139$	10.7224	−	18.5717i	0.909459	−	1.57523i	0.814818	−	0.579717i	$-0.196837\pi$
$140$	−2.11728	+	13.6247i	−0.178943	+	1.15149i
$141$	−15.2781	+	4.36910i	−1.28665	+	0.367945i
$142$	−13.8452	+	9.51876i	−1.16186	+	0.798797i
$143$	−13.1291			−1.09791
$144$	4.09530	+	11.2796i	0.341275	+	0.939963i
$145$		−	4.61971i		−	0.383646i
$146$	−8.96201	+	6.16152i	−0.741701	+	0.509931i
$147$	−11.4116	−	4.09579i	−0.941212	−	0.337815i
$148$	3.20561	−	8.35888i	0.263500	−	0.687095i
$149$	−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	$0.307469\pi$
$150$	−3.38130	−	2.79049i	−0.276082	−	0.227842i
$151$	10.5519	−	6.09213i	0.858700	−	0.495771i	−0.00487656	−	0.999988i	$-0.501552\pi$
$151$	10.5519	−	6.09213i	0.858700	−	0.495771i	0.863577	+	0.504217i	$0.168219\pi$
$152$	−12.1896	+	2.93264i	−0.988709	+	0.237868i
$153$	−8.96901	+	16.8102i	−0.725102	+	1.35903i
$154$	−15.7560	+	4.71436i	−1.26966	+	0.379894i
$155$	−6.37317	+	3.67955i	−0.511905	+	0.295549i
$156$	4.36921	+	9.37951i	0.349817	+	0.750962i
$157$	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	$0.459220\pi$
$158$	−17.3014	−	8.24896i	−1.37643	−	0.656252i
$159$	1.81391	−	7.25310i	0.143853	−	0.575208i
$160$	8.96393	−	11.7013i	0.708661	−	0.925071i
$161$	−4.49487	+	0.967604i	−0.354245	+	0.0762579i
$162$	4.69677	−	11.8296i	0.369013	−	0.929424i
$163$			3.98564i			0.312179i	0.987743	+	0.156090i	$0.0498889\pi$
$163$			3.98564i			0.312179i	−0.987743	+	0.156090i	$0.950111\pi$
$164$	12.3594	−	10.0150i	0.965107	−	0.782038i
$165$	4.81292	−	19.2449i	0.374685	−	1.49822i
$166$	−0.630778	+	1.32300i	−0.0489579	+	0.102684i
$167$	−1.70062	+	2.94557i	−0.131598	+	0.227935i	−0.924293	−	0.381684i	$-0.875344\pi$
$167$	−1.70062	+	2.94557i	−0.131598	+	0.227935i	0.792695	+	0.609619i	$0.208678\pi$
$168$	8.61139	+	9.68731i	0.664383	+	0.747392i
$169$	−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	$0.261472\pi$
$174$	−3.34942	−	2.76417i	−0.253919	−	0.209551i
$175$	−4.50734	−	1.45161i	−0.340723	−	0.109732i
$176$	17.1998	+	3.64447i	1.29649	+	0.274713i
$177$	10.2150	+	9.87863i	0.767805	+	0.742523i
$178$	−0.195333	+	0.134294i	−0.0146408	+	0.0100658i
$179$		−	14.2559i		−	1.06553i	−0.846262	−	0.532767i	$-0.821152\pi$
$179$		−	14.2559i		−	1.06553i	0.846262	−	0.532767i	$-0.178848\pi$
$180$	−15.3504	+	2.96611i	−1.14415	+	0.221081i
$181$			4.24221i			0.315321i	0.987493	+	0.157660i	$0.0503951\pi$
$181$			4.24221i			0.315321i	−0.987493	+	0.157660i	$0.949605\pi$
$182$	8.12814	+	7.67090i	0.602498	+	0.568605i
$183$	−1.96623	−	6.87561i	−0.145348	−	0.508260i
$184$	4.71355	+	1.39377i	0.347488	+	0.102750i
$185$	10.1012	+	5.83191i	0.742653	+	0.428771i
$186$	−1.14557	+	6.82236i	−0.0839972	+	0.500240i
$187$	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	−0.570891	−	0.821026i	$-0.693402\pi$
$191$	−2.00820	+	1.15943i	−0.145308	+	0.0838937i	0.425583	+	0.904919i	$0.360069\pi$
$192$	−3.12027	−	13.5005i	−0.225186	−	0.974316i
$193$	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	$0.148249\pi$
$194$	−7.89311	−	3.76327i	−0.566692	−	0.270187i
$195$	−12.9614	+	3.70660i	−0.928187	+	0.265435i
$196$	12.5089	+	6.28710i	0.893492	+	0.449078i
$197$	−9.41145			−0.670538			−0.335269	−	0.942122i	$-0.608827\pi$
$197$	−9.41145			−0.670538			−0.335269	+	0.942122i	$0.608827\pi$
$198$	−11.0733	−	15.0046i	−0.786947	−	1.06633i
$199$	−4.61701			−0.327291			−0.163646	−	0.986519i	$-0.552325\pi$
$199$	−4.61701			−0.327291			−0.163646	+	0.986519i	$0.552325\pi$
$200$	3.48640	+	3.67038i	0.246526	+	0.259535i
$201$	−5.45617	+	5.64194i	−0.384848	+	0.397952i
$202$	18.5925	+	8.86452i	1.30816	+	0.623705i
$203$	−4.46484	−	1.43793i	−0.313371	−	0.100923i
$204$	12.6263	−	18.0170i	0.884017	−	1.26144i
$205$	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
$210$	−14.2238	+	9.10238i	−0.981538	+	0.628124i
$211$	−22.3255	−	12.8897i	−1.53695	−	0.887360i	−0.999015	−	0.0443764i	$-0.985870\pi$
$211$	−22.3255	−	12.8897i	−1.53695	−	0.887360i	−0.537938	−	0.842984i	$-0.680797\pi$
$212$	−3.09125	+	8.06067i	−0.212308	+	0.553609i
$213$	−19.9629	−	4.99248i	−1.36784	−	0.342079i
$214$	12.1521	−	8.35473i	0.830698	−	0.571118i
$215$	2.82709			0.192806
$216$	−7.03430	+	12.9042i	−0.478623	+	0.878020i
$217$	1.57250	+	7.30481i	0.106748	+	0.495883i
$218$	−8.68519	−	12.6327i	−0.588235	−	0.855595i
$219$	−12.9221	−	3.23165i	−0.873192	−	0.218375i
$220$	−8.20214	+	21.3877i	−0.552988	+	1.44196i
$221$	9.48531	−	16.4290i	0.638051	−	1.10514i
$222$	10.2723	−	3.83414i	0.689430	−	0.257331i
$223$	−4.03030	−	6.98069i	−0.269889	−	0.467461i	0.698944	−	0.715176i	$-0.253654\pi$
$223$	−4.03030	−	6.98069i	−0.269889	−	0.467461i	−0.968833	+	0.247715i	$0.920320\pi$
$224$	−8.51896	−	12.3056i	−0.569197	−	0.822201i
$225$	−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	0.586493	−	0.809954i	$-0.300508\pi$
$227$	−6.15006	−	10.6522i	−0.408194	−	0.707013i	−0.994687	+	0.102941i	$0.967175\pi$
$228$	−12.5747	−	8.81234i	−0.832781	−	0.583612i
$229$	−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	$0.734596\pi$
$230$	−2.75605	+	5.78055i	−0.181728	+	0.381158i
$231$	−17.1017	−	10.6417i	−1.12521	−	0.700175i
$232$	3.45352	+	3.63577i	0.226735	+	0.238700i
$233$	14.6005			0.956512			0.478256	−	0.878220i	$-0.341269\pi$
$233$	14.6005			0.956512			0.478256	+	0.878220i	$0.341269\pi$
$234$	−5.06800	+	11.6152i	−0.331306	+	0.759310i
$235$			23.9059i			1.55945i
$236$	−10.3304	−	12.7486i	−0.672450	−	0.829865i
$237$	−6.45445	−	22.5702i	−0.419261	−	1.46609i
$238$	5.48387	−	23.1222i	0.355467	−	1.49879i
$239$	6.30063	+	3.63767i	0.407554	+	0.235302i	0.689738	−	0.724059i	$-0.257726\pi$
$239$	6.30063	+	3.63767i	0.407554	+	0.235302i	−0.282184	+	0.959360i	$0.591059\pi$
$240$	18.0091	−	1.25792i	1.16248	−	0.0811981i
$241$	−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
$246$	19.2139	+	3.22628i	1.22503	+	0.205700i
$247$	−11.4664	−	6.62014i	−0.729591	−	0.421229i
$248$	2.26507	−	7.66020i	0.143832	−	0.486423i
$249$	−1.72589	+	0.493556i	−0.109374	+	0.0312778i
$250$	9.74817	−	6.70202i	0.616528	−	0.423873i
$251$	−10.0975			−0.637350			−0.318675	−	0.947864i	$-0.603238\pi$
$251$	−10.0975			−0.637350			−0.318675	+	0.947864i	$0.603238\pi$
$252$	−1.91127	+	15.7590i	−0.120399	+	0.992726i
$253$	−7.63846			−0.480226
$254$	14.1720	−	9.74346i	0.889229	−	0.611359i
$255$	20.6049	+	19.9264i	1.29033	+	1.24784i
$256$	1.69275	+	15.9102i	0.105797	+	0.994388i
$257$	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	$0.601073\pi$
$258$	1.69157	−	2.04972i	0.105313	−	0.127610i
$259$	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	−0.742356	−	0.670006i	$-0.766292\pi$
$263$	−8.64854	+	4.99324i	−0.533292	+	0.307896i	0.209064	+	0.977902i	$0.432958\pi$
$264$	10.5990	+	18.7440i	0.652321	+	1.15361i
$265$	−9.74081	−	5.62386i	−0.598373	−	0.345471i
$266$	−16.1378	−	3.82739i	−0.989472	−	0.234673i
$267$	−0.281645	−	0.0704359i	−0.0172364	−	0.00431061i
$268$	7.04133	−	5.70568i	0.430118	−	0.348530i
$269$			2.53470i			0.154543i	0.997010	+	0.0772716i	$0.0246209\pi$
$269$			2.53470i			0.154543i	−0.997010	+	0.0772716i	$0.975379\pi$
$270$	−15.1680	−	11.6868i	−0.923095	−	0.711233i
$271$	−10.4463			−0.634569			−0.317285	−	0.948330i	$-0.602771\pi$
$271$	−10.4463			−0.634569			−0.317285	+	0.948330i	$0.602771\pi$
$272$	−16.9868	+	18.8899i	−1.02997	+	1.14537i
$273$	−0.452016	+	13.6806i	−0.0273572	+	0.827990i
$274$	2.59849	−	5.45008i	0.156980	−	0.329251i
$275$	−6.81291	−	3.93344i	−0.410834	−	0.237195i
$276$	2.54199	+	5.45697i	0.153010	+	0.328471i
$277$	−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
$280$	17.5740	−	8.44874i	1.05025	−	0.504909i
$281$	−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	$0.919324\pi$
$282$	17.3325	+	14.3040i	1.03213	+	0.851789i
$283$	11.3594	−	19.6750i	0.675243	−	1.16956i	−0.301154	−	0.953575i	$-0.597372\pi$
$283$	11.3594	−	19.6750i	0.675243	−	1.16956i	0.976398	−	0.215980i	$-0.0692947\pi$
$284$	22.1856	+	8.50815i	1.31647	+	0.504866i
$285$	13.9074	−	14.3809i	0.823802	−	0.851851i
$286$	10.5191	+	15.3001i	0.622007	+	0.904717i
$287$	20.5726	−	4.42864i	1.21436	−	0.261414i
$288$	9.86360	−	13.8098i	0.581218	−	0.813748i
$289$	−23.3363			−1.37272
$290$	−5.38364	+	3.70133i	−0.316138	+	0.217350i
$291$	−2.94460	−	10.2968i	−0.172615	−	0.603610i
$292$	14.3608	+	5.50735i	0.840403	+	0.322293i
$293$	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	$0.611124\pi$
$294$	4.36995	+	16.5802i	0.254861	+	0.966978i
$295$	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
$300$	−0.542814	+	6.17619i	−0.0313394	+	0.356583i
$301$	0.879956	−	2.73231i	0.0507198	−	0.157488i
$302$	−15.5538	−	7.41572i	−0.895019	−	0.426727i
$303$	6.93610	+	24.2545i	0.398468	+	1.39338i
$304$	13.1840	+	11.8557i	0.756153	+	0.679970i
$305$	−10.7584			−0.616025
$306$	26.7760	−	3.01627i	1.53068	−	0.172429i
$307$	−10.0769			−0.575121			−0.287560	−	0.957763i	$-0.592844\pi$
$307$	−10.0769			−0.575121			−0.287560	+	0.957763i	$0.592844\pi$
$308$	18.1177	+	14.5843i	1.03235	+	0.831017i
$309$	22.3351	+	21.5996i	1.27060	+	1.22876i
$310$	9.39422	+	4.47898i	0.533556	+	0.254389i
$311$	−0.0398807	+	0.0690754i	−0.00226143	+	0.00391691i	−0.867154	−	0.498040i	$-0.834053\pi$
$311$	−0.0398807	+	0.0690754i	−0.00226143	+	0.00391691i	0.864892	+	0.501957i	$0.167387\pi$
$312$	7.42989	−	12.6066i	0.420635	−	0.713710i
$313$	−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	$0.797808\pi$
$318$	−9.90580	+	3.69735i	−0.555490	+	0.207337i
$319$	−6.74867	−	3.89635i	−0.377853	−	0.218154i
$320$	−20.8182	−	1.07107i	−1.16377	−	0.0598746i
$321$	17.5217	+	4.38196i	0.977966	+	0.244577i
$322$	4.72892	+	4.46291i	0.263533	+	0.248708i
$323$			28.1521i			1.56643i
$324$	−17.5489	+	4.00452i	−0.974939	+	0.222474i
$325$			5.34607i			0.296547i
$326$	4.64472	−	3.19332i	0.257247	−	0.176861i
$327$	4.55528	−	18.2147i	0.251908	−	1.00728i
$328$	−21.5735	−	6.37914i	−1.19120	−	0.352229i
$329$	23.1046	+	7.44094i	1.27380	+	0.410232i
$330$	−26.2835	+	9.81034i	−1.44686	+	0.540041i
$331$	−17.2122	+	9.93744i	−0.946066	+	0.546211i	−0.891857	−	0.452318i	$-0.850597\pi$
$331$	−17.2122	+	9.93744i	−0.946066	+	0.546211i	−0.0542091	+	0.998530i	$0.517264\pi$
$332$	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
$336$	4.38974	−	17.7969i	0.239480	−	0.970901i
$337$	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	$0.154648\pi$
$338$	−2.48194	+	5.20563i	−0.135000	+	0.283149i
$339$	16.0623	+	15.5334i	0.872383	+	0.843657i
$340$	−20.8376	−	25.7156i	−1.13008	−	1.39462i
$341$			12.4136i			0.672234i
$342$	−2.10517	−	18.6880i	−0.113834	−	1.01053i
$343$	11.0022	+	14.8981i	0.594061	+	0.804420i
$344$	−2.22495	+	2.11343i	−0.119961	+	0.113948i
$345$	−7.54091	+	2.15649i	−0.405989	+	0.116101i
$346$	−7.51690	−	3.58391i	−0.404111	−	0.192672i
$347$	−11.3727	−	6.56605i	−0.610520	−	0.352484i	0.162649	−	0.986684i	$-0.447996\pi$
$347$	−11.3727	−	6.56605i	−0.610520	−	0.352484i	−0.773169	+	0.634200i	$0.781329\pi$
$348$	−0.537695	+	6.11796i	−0.0288235	+	0.327957i
$349$	−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	$0.596029\pi$
$350$	1.91965	+	6.41573i	0.102610	+	0.342935i
$351$	−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	$0.0257848\pi$
$354$	3.32788	−	19.8190i	0.176875	−	1.05337i
$355$	−15.4787	+	26.8099i	−0.821525	+	1.42292i
$356$	0.313003	+	0.120036i	0.0165891	+	0.00636191i
$357$	25.6719	−	13.7119i	1.35870	−	0.725710i
$358$	−16.6133	+	11.4219i	−0.878038	+	0.603665i
$359$		−	11.1419i		−	0.588045i	−0.955799	−	0.294022i	$-0.905006\pi$
$359$		−	11.1419i		−	0.588045i	0.955799	−	0.294022i	$-0.0949940\pi$
$360$	15.7554	+	15.5123i	0.830383	+	0.817571i
$361$	0.648409			0.0341268
$362$	4.94371	−	3.39888i	0.259836	−	0.178641i
$363$	−10.3587	−	10.0176i	−0.543692	−	0.525789i
$364$	2.42708	−	15.6182i	0.127213	−	0.818616i
$365$	−10.0194	+	17.3541i	−0.524440	+	0.908357i
$366$	−6.43723	+	7.80015i	−0.336479	+	0.407720i
$367$	−11.9986	−	20.7821i	−0.626319	−	1.08482i	−0.988284	−	0.152625i	$-0.951227\pi$
$367$	−11.9986	−	20.7821i	−0.626319	−	1.08482i	0.361965	−	0.932192i	$-0.382106\pi$
$368$	−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
$372$	8.86836	−	4.13110i	0.459803	−	0.214188i
$373$	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	$-0.00437575\pi$
$374$	16.9904	−	35.6357i	0.878552	−	1.84268i
$375$	14.0556	+	3.51513i	0.725828	+	0.181521i
$376$	−17.8712	−	18.8143i	−0.921637	−	0.970273i
$377$			5.29566i			0.272740i
$378$	−16.0162	+	11.0219i	−0.823782	+	0.566906i
$379$		−	5.89248i		−	0.302676i	−0.988482	−	0.151338i	$-0.951642\pi$
$379$		−	5.89248i		−	0.302676i	0.988482	−	0.151338i	$-0.0483582\pi$
$380$	−17.9478	+	14.5434i	−0.920705	+	0.746058i
$381$	20.4342	+	5.11033i	1.04687	+	0.261810i
$382$	2.96014	+	1.41134i	0.151454	+	0.0722102i
$383$	0.975897	−	1.69030i	0.0498660	−	0.0863704i	−0.840015	−	0.542563i	$-0.817454\pi$
$383$	0.975897	−	1.69030i	0.0498660	−	0.0863704i	0.889881	+	0.456193i	$0.150787\pi$
$384$	−13.2330	+	14.4529i	−0.675295	+	0.737548i
$385$	−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	$0.870010\pi$
$390$	14.7043	+	12.1350i	0.744581	+	0.614480i
$391$	5.51852	−	9.55836i	0.279084	−	0.483387i
$392$	−2.69544	−	19.6147i	−0.136140	−	0.990690i
$393$	−19.1564	−	18.5256i	−0.966312	−	0.934493i
$394$	7.54051	+	10.9678i	0.379885	+	0.552548i
$395$	−35.3161			−1.77695
$396$	−8.61378	+	24.9262i	−0.432859	+	1.25259i
$397$			24.8829i			1.24883i	0.781091	+	0.624417i	$0.214664\pi$
$397$			24.8829i			1.24883i	−0.781091	+	0.624417i	$0.785336\pi$
$398$	3.69917	+	5.38049i	0.185423	+	0.269700i
$399$	−9.57003	−	17.9173i	−0.479101	−	0.896989i
$400$	1.48400	−	7.00365i	0.0742002	−	0.350182i
$401$	−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	$0.278393\pi$
$402$	10.9464	+	1.83806i	0.545958	+	0.0916740i
$403$	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
$406$	1.90155	+	6.35524i	0.0943724	+	0.315405i
$407$	17.0390	−	9.83748i	0.844593	−	0.487626i
$408$	−31.1126	−	0.278887i	−1.54030	−	0.0138070i
$409$	−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	$-0.680362\pi$
$410$	12.6142	−	26.4570i	0.622970	−	1.30662i
$411$	7.10981	−	2.03320i	0.350701	−	0.100290i
$412$	−22.5874	−	27.8749i	−1.11280	−	1.37330i
$413$	−4.56811	−	21.2205i	−0.224782	−	1.04419i
$414$	−2.94855	+	6.75769i	−0.144913	+	0.332122i
$415$			2.70054i			0.132564i
$416$	−10.2755	+	13.4135i	−0.503799	+	0.657649i
$417$	−26.7002	−	25.8210i	−1.30752	−	1.26446i
$418$	−24.8714	−	11.8582i	−1.21650	−	0.580004i
$419$	−5.05240	+	8.75102i	−0.246826	+	0.427515i	−0.962643	−	0.270772i	$-0.912721\pi$
$419$	−5.05240	+	8.75102i	−0.246826	+	0.427515i	0.715817	+	0.698287i	$0.246054\pi$
$420$	22.0038	+	9.28306i	1.07368	+	0.452967i
$421$	−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
$426$	10.1763	+	27.2640i	0.493045	+	1.32095i
$427$	−3.34865	+	10.3978i	−0.162053	+	0.503183i
$428$	−19.4726	−	7.46771i	−0.941243	−	0.360965i
$429$	−5.51714	+	22.0608i	−0.266370	+	1.06511i
$430$	−2.26508	−	3.29458i	−0.109232	−	0.158879i
$431$			19.4883i			0.938719i	0.883007	+	0.469359i	$0.155515\pi$
$431$			19.4883i			0.938719i	−0.883007	+	0.469359i	$0.844485\pi$
$432$	20.6740	−	2.14141i	0.994678	−	0.103029i
$433$		−	4.11856i		−	0.197925i	−0.995091	−	0.0989626i	$-0.968448\pi$
$433$		−	4.11856i		−	0.197925i	0.995091	−	0.0989626i	$-0.0315524\pi$
$434$	7.25287	−	7.68518i	0.348149	−	0.368901i
$435$	−7.76250	−	1.94131i	−0.372184	−	0.0930786i
$436$	−7.76307	+	20.2428i	−0.371784	+	0.969454i
$437$	−6.67112	−	3.85158i	−0.319123	−	0.184246i
$438$	6.58718	+	17.6481i	0.314747	+	0.843259i
$439$	3.51549	+	6.08901i	0.167785	+	0.290613i	0.937641	−	0.347605i	$-0.113005\pi$
$439$	3.51549	+	6.08901i	0.167785	+	0.290613i	−0.769856	+	0.638218i	$0.779672\pi$
$440$	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	0.351827	−	0.936065i	$-0.385561\pi$
$443$	28.1700	−	16.2640i	1.33840	−	0.772724i	0.986570	+	0.163341i	$0.0522272\pi$
$444$	−12.6984	−	8.89899i	−0.602637	−	0.422327i
$445$	−0.218380	+	0.378245i	−0.0103522	+	0.0179305i
$446$	−4.90593	+	10.2897i	−0.232303	+	0.487233i
$447$	13.0113	+	12.5829i	0.615413	+	0.595149i
$448$	−7.51503	+	19.7870i	−0.355052	+	0.934847i
$449$	38.6596			1.82446			0.912229	−	0.409680i	$-0.134360\pi$
$449$	38.6596			1.82446			0.912229	+	0.409680i	$0.134360\pi$
$450$	−6.10976	+	4.50898i	−0.288017	+	0.212555i
$451$	34.9605			1.64623
$452$	−16.2437	−	20.0462i	−0.764040	−	0.942896i
$453$	−5.80248	−	20.2904i	−0.272624	−	0.953326i
$454$	−7.48624	+	15.7017i	−0.351347	+	0.736916i
$455$	19.6011	+	6.31264i	0.918915	+	0.295941i
$456$	−0.194646	+	21.7146i	−0.00911511	+	1.01688i
$457$	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	$0.430347\pi$
$462$	1.30051	+	28.4559i	0.0605050	+	1.32389i
$463$	24.8595	+	14.3527i	1.15532	+	0.667025i	0.950178	−	0.311707i	$-0.100901\pi$
$463$	24.8595	+	14.3527i	1.15532	+	0.667025i	0.205143	+	0.978732i	$0.434234\pi$
$464$	1.47001	−	6.93761i	0.0682435	−	0.322070i
$465$	3.50460	+	12.2551i	0.162522	+	0.568315i
$466$	−11.6980	−	17.0149i	−0.541900	−	0.788201i
$467$	25.4161			1.17612			0.588058	−	0.808819i	$-0.299893\pi$
$467$	25.4161			1.17612			0.588058	+	0.808819i	$0.299893\pi$
$468$	17.5964	−	3.40011i	0.813396	−	0.157170i
$469$	11.7205	−	2.52306i	0.541203	−	0.116504i
$470$	27.8591	−	19.1536i	1.28504	−	0.883488i
$471$	18.3020	−	18.9252i	0.843314	−	0.872028i
$472$	−6.58003	+	22.2529i	−0.302871	+	1.02427i
$473$	2.38442	−	4.12993i	0.109636	−	0.189894i
$474$	−21.1312	+	25.6052i	−0.970587	+	1.17608i
$475$	−3.96675	−	6.87061i	−0.182007	−	0.315245i
$476$	−31.3394	+	12.1349i	−1.43644	+	0.556203i
$477$	−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	$-0.911857\pi$
$479$	−15.7078	−	27.2068i	−0.717709	−	1.24311i	0.244196	−	0.969726i	$-0.421476\pi$
$480$	−15.8949	−	19.9793i	−0.725500	−	0.911925i
$481$	−11.5792	−	6.68523i	−0.527964	−	0.304820i
$482$	14.5145	+	6.92021i	0.661116	+	0.315207i
$483$	−0.262981	+	7.95935i	−0.0119661	+	0.362163i
$484$	10.4757	+	12.9280i	0.476170	+	0.587637i
$485$	−16.1116			−0.731592
$486$	−17.9037	−	12.8631i	−0.812127	−	0.583481i
$487$		−	27.8663i		−	1.26274i	−0.775481	−	0.631371i	$-0.782493\pi$
$487$		−	27.8663i		−	1.26274i	0.775481	−	0.631371i	$-0.217507\pi$
$488$	8.46701	−	8.04260i	0.383284	−	0.364071i
$489$	6.69708	+	1.67486i	0.302852	+	0.0757397i
$490$	25.7897	+	0.537382i	1.16506	+	0.0242764i
$491$	−24.8087	−	14.3233i	−1.11960	−	0.646403i	−0.178304	−	0.983976i	$-0.557061\pi$
$491$	−24.8087	−	14.3233i	−1.11960	−	0.646403i	−0.941300	+	0.337572i	$0.890394\pi$
$492$	−11.6345	−	24.9760i	−0.524522	−	1.12601i
$493$	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
$498$	1.95796	+	1.61585i	0.0877385	+	0.0724080i
$499$	21.5390	+	12.4355i	0.964218	+	0.556691i	0.897469	−	0.441078i	$-0.145404\pi$
$499$	21.5390	+	12.4355i	0.964218	+	0.556691i	0.0667492	+	0.997770i	$0.478737\pi$
$500$	−15.6206	−	5.99046i	−0.698573	−	0.267902i
$501$	4.23480	+	4.09535i	0.189197	+	0.182967i
$502$	8.09019	+	11.7673i	0.361083	+	0.525199i
$503$	26.2058			1.16846			0.584229	−	0.811589i	$-0.301397\pi$
$503$	26.2058			1.16846			0.584229	+	0.811589i	$0.301397\pi$
$504$	19.8963	−	10.3989i	0.886252	−	0.463204i
$505$	37.9515			1.68882
$506$	6.11997	+	8.90158i	0.272066	+	0.395723i
$507$	−6.79091	+	1.94201i	−0.301595	+	0.0862476i
$508$	−22.7093	−	8.70899i	−1.00756	−	0.386399i
$509$	−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	$0.701761\pi$
$510$	6.71275	−	39.9773i	0.297246	−	1.77023i
$511$	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
$516$	−3.74396	−	0.329049i	−0.164819	−	0.0144856i
$517$	34.9228	+	20.1627i	1.53590	+	0.886755i
$518$	−16.2965	−	3.86503i	−0.716026	−	0.169819i
$519$	−2.80425	−	9.80604i	−0.123093	−	0.430438i
$520$	−15.1613	−	15.9614i	−0.664869	−	0.699955i
$521$		−	13.6674i		−	0.598781i	−0.954131	−	0.299391i	$-0.903217\pi$
$521$		−	13.6674i		−	0.598781i	0.954131	−	0.299391i	$-0.0967834\pi$
$522$	−6.05215	+	4.46646i	−0.264895	+	0.195492i
$523$	−27.0038			−1.18079			−0.590397	−	0.807113i	$-0.701029\pi$
$523$	−27.0038			−1.18079			−0.590397	+	0.807113i	$0.701029\pi$
$524$	19.3728	+	23.9078i	0.846303	+	1.04442i
$525$	−4.33324	+	6.96370i	−0.189118	+	0.303921i
$526$	12.7482	+	6.07808i	0.555847	+	0.265017i
$527$	−15.5337	−	8.96839i	−0.676659	−	0.390669i
$528$	13.3516	−	27.3694i	0.581053	−	1.19110i
$529$	−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
$532$	8.46939	+	21.8729i	0.367195	+	0.948312i
$533$	−11.8790	−	20.5751i	−0.514537	−	0.891205i
$534$	0.143572	+	0.384652i	0.00621296	+	0.0166455i
$535$	13.5859	−	23.5314i	0.587368	−	1.01735i
$536$	−12.2907	−	3.63429i	−0.530879	−	0.156977i
$537$	−23.9542	−	5.99064i	−1.03370	−	0.258515i
$538$	2.95384	−	2.03081i	0.127349	−	0.0875546i
$539$	12.6601	+	28.0427i	0.545308	+	1.20788i
$540$	−1.46663	+	27.0397i	−0.0631136	+	1.16360i
$541$	−30.2237			−1.29942			−0.649710	−	0.760182i	$-0.725110\pi$
$541$	−30.2237			−1.29942			−0.649710	+	0.760182i	$0.725110\pi$
$542$	8.36965	+	12.1738i	0.359507	+	0.522908i
$543$	7.12818	+	1.78267i	0.305900	+	0.0765018i
$544$	35.6235	+	4.66104i	1.52735	+	0.199840i
$545$	−24.4621	−	14.1232i	−1.04784	−	0.604972i
$546$	16.3051	−	10.4342i	0.697792	−	0.446544i
$547$	5.08073	−	2.93336i	0.217236	−	0.125421i	−0.387434	−	0.921898i	$-0.626638\pi$
$547$	5.08073	−	2.93336i	0.217236	−	0.125421i	0.604670	+	0.796476i	$0.293305\pi$
$548$	−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
$552$	4.32269	−	7.33449i	0.183986	−	0.312177i
$553$	−10.9925	+	34.1322i	−0.467447	+	1.45145i
$554$	−12.6533	+	26.5390i	−0.537586	+	1.12754i
$555$	14.0441	−	14.5223i	0.596139	−	0.616438i
$556$	27.0018	+	33.3227i	1.14513	+	1.41320i
$557$	−26.6804			−1.13049			−0.565243	−	0.824925i	$-0.691217\pi$
$557$	−26.6804			−1.13049			−0.565243	+	0.824925i	$0.691217\pi$
$558$	10.9822	+	4.79181i	0.464915	+	0.202854i
$559$	−3.24074			−0.137069
$560$	−23.9263	−	13.7110i	−1.01107	−	0.579393i
$561$	46.4879	−	13.2942i	1.96272	−	0.561282i
$562$	−5.44557	+	11.4216i	−0.229708	+	0.481790i
$563$	−16.4713	+	28.5292i	−0.694184	+	1.20236i	0.276271	+	0.961080i	$0.410901\pi$
$563$	−16.4713	+	28.5292i	−0.694184	+	1.20236i	−0.970455	+	0.241282i	$0.922432\pi$
$564$	2.78245	−	31.6590i	0.117162	−	1.33309i
$565$	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	$0.829050\pi$
$570$	−27.9016	−	4.68507i	−1.16867	−	0.196236i
$571$	−11.6295	−	6.71428i	−0.486679	−	0.280984i	0.236517	−	0.971627i	$-0.423994\pi$
$571$	−11.6295	−	6.71428i	−0.486679	−	0.280984i	−0.723196	+	0.690643i	$0.757327\pi$
$572$	9.40227	−	24.5171i	0.393129	−	1.02511i
$573$	1.10431	+	3.86160i	0.0461331	+	0.161321i
$574$	−21.6439	−	20.4263i	−0.903397	−	0.852578i
$575$			3.11033i			0.129710i
$576$	−23.9961	−	0.430228i	−0.999839	−	0.0179262i
$577$			24.9083i			1.03695i	0.855094	+	0.518473i	$0.173499\pi$
$577$			24.9083i			1.03695i	−0.855094	+	0.518473i	$0.826501\pi$
$578$	18.6971	+	27.1952i	0.777698	+	1.13117i
$579$	−2.00055	−	1.93468i	−0.0831402	−	0.0804025i
$580$	8.62680	+	3.30836i	0.358208	+	0.137372i
$581$	2.61001	+	0.840567i	0.108281	+	0.0348726i
$582$	−9.64030	+	11.6814i	−0.399603	+	0.484209i
$583$	−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	$0.0105946\pi$
$587$	12.8056	+	22.1799i	0.528542	+	0.915462i	−0.470904	+	0.882185i	$0.656072\pi$
$588$	15.8207	−	18.3767i	0.652436	−	0.757844i
$589$	−6.25937	+	10.8415i	−0.257913	+	0.446718i
$590$	−27.2902	−	13.0114i	−1.12352	−	0.535673i
$591$	−3.95491	+	15.8141i	−0.162683	+	0.650504i
$592$	13.3136	+	11.9723i	0.547186	+	0.492057i
$593$		−	16.0701i		−	0.659921i	−0.943995	−	0.329960i	$-0.892965\pi$
$593$		−	16.0701i		−	0.659921i	0.943995	−	0.329960i	$-0.107035\pi$
$594$	−29.8655	+	12.3013i	−1.22540	+	0.504726i
$595$	−9.21444	−	42.8044i	−0.377755	−	1.75481i
$596$	−13.1583	−	16.2385i	−0.538984	−	0.665156i
$597$	−1.94017	+	7.75796i	−0.0794060	+	0.317512i
$598$	3.15931	−	6.62635i	0.129194	−	0.270972i
$599$	−13.6480	−	7.87965i	−0.557640	−	0.321954i	0.194557	−	0.980891i	$-0.437673\pi$
$599$	−13.6480	−	7.87965i	−0.557640	−	0.321954i	−0.752198	+	0.658937i	$0.771006\pi$
$600$	7.63241	−	4.31582i	0.311592	−	0.176193i
$601$	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	$0.0892508\pi$
$602$	−3.88916	+	1.16368i	−0.158510	+	0.0474279i
$603$	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
$606$	22.7081	−	27.5159i	0.922451	−	1.11776i
$607$	−8.74550	+	15.1477i	−0.354969	+	0.614824i	−0.987113	−	0.160027i	$-0.948842\pi$
$607$	−8.74550	+	15.1477i	−0.354969	+	0.614824i	0.632144	+	0.774851i	$0.282175\pi$
$608$	3.25311	−	24.8630i	0.131931	−	1.00833i
$609$	−4.29238	+	6.89803i	−0.173936	+	0.279522i
$610$	8.61970	+	12.5375i	0.349001	+	0.507627i
$611$		−	27.4038i		−	1.10864i
$612$	−24.9681	−	28.7871i	−1.00928	−	1.16365i
$613$	4.11918			0.166372			0.0831860	−	0.996534i	$-0.473490\pi$
$613$	4.11918			0.166372			0.0831860	+	0.996534i	$0.473490\pi$
$614$	8.07369	+	11.7433i	0.325827	+	0.473920i
$615$	34.5141	−	9.87005i	1.39174	−	0.397999i
$616$	2.47997	−	32.7987i	0.0999210	−	1.32150i
$617$	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	$-0.0353358\pi$
$618$	7.27643	−	43.3342i	0.292701	−	1.74316i
$619$	4.03999	+	6.99747i	0.162381	+	0.281252i	0.935722	−	0.352738i	$-0.114749\pi$
$619$	4.03999	+	6.99747i	0.162381	+	0.281252i	−0.773341	+	0.633990i	$0.781416\pi$
$620$	−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
$624$	−20.6442	+	1.44197i	−0.826428	+	0.0577251i
$625$	15.3728	−	26.6265i	0.614912	−	1.06506i
$626$	30.4512	+	14.5185i	1.21707	+	0.580276i
$627$	−9.27852	−	32.4456i	−0.370548	−	1.29575i
$628$	−23.6193	+	19.1390i	−0.942512	+	0.763729i
$629$			28.4290i			1.13354i
$630$	9.31756	+	27.7254i	0.371221	+	1.10461i
$631$		−	1.61516i		−	0.0642986i	−0.999483	−	0.0321493i	$-0.989765\pi$
$631$		−	1.61516i		−	0.0642986i	0.999483	−	0.0321493i	$-0.0102352\pi$
$632$	27.7942	−	26.4010i	1.10560	−	1.05018i
$633$	−31.0402	+	32.0971i	−1.23374	+	1.27575i
$634$	2.41382	−	5.06277i	0.0958652	−	0.201068i
$635$	15.8441	−	27.4428i	0.628754	−	1.08903i
$636$	12.2453	+	8.58152i	0.485559	+	0.340279i
$637$	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	$0.628679\pi$
$642$	−8.93190	−	23.9300i	−0.352514	−	0.944441i
$643$	−7.27667	+	12.6036i	−0.286964	+	0.497036i	−0.973084	−	0.230453i	$-0.925979\pi$
$643$	−7.27667	+	12.6036i	−0.286964	+	0.497036i	0.686120	+	0.727489i	$0.259313\pi$
$644$	1.41207	−	9.08661i	0.0556432	−	0.358063i
$645$	1.18801	−	4.75036i	0.0467777	−	0.187045i
$646$	32.8075	−	22.5556i	1.29079	−	0.887440i
$647$	−40.4385			−1.58980			−0.794900	−	0.606740i	$-0.792477\pi$
$647$	−40.4385			−1.58980			−0.794900	+	0.606740i	$0.792477\pi$
$648$	18.7270	+	17.2424i	0.735666	+	0.677345i
$649$		−	36.0615i		−	1.41554i
$650$	6.23011	−	4.28330i	0.244365	−	0.168005i
$651$	12.9351	+	0.427383i	0.506966	+	0.0167504i
$652$	−7.44274	−	2.85428i	−0.291480	−	0.111782i
$653$	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	$-0.0472224\pi$
$654$	−24.8765	+	9.28518i	−0.972747	+	0.363079i
$655$	−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
$658$	−9.84009	−	32.8869i	−0.383607	−	1.28206i
$659$	2.88773	−	1.66723i	0.112490	−	0.0649460i	−0.442699	−	0.896670i	$-0.645979\pi$
$659$	2.88773	−	1.66723i	0.112490	−	0.0649460i	0.555189	+	0.831724i	$0.312646\pi$
$660$	32.4910	+	22.7697i	1.26471	+	0.886308i
$661$	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	$0.467702\pi$
$662$	25.3712	+	12.0965i	0.986079	+	0.470143i
$663$	−23.6198	−	22.8420i	−0.917316	−	0.887111i
$664$	−2.01882	−	2.12536i	−0.0783455	−	0.0824799i
$665$	−29.8747	+	6.43109i	−1.15849	+	0.249387i
$666$	−2.12587	−	18.8717i	−0.0823756	−	0.731264i
$667$			3.08100i			0.119297i
$668$	−4.28263	−	5.28517i	−0.165700	−	0.204489i
$669$	−13.4233	+	3.83868i	−0.518974	+	0.148412i
$670$	7.18648	−	15.0730i	0.277638	−	0.582319i
$671$	−9.07384	+	15.7164i	−0.350292	+	0.606723i
$672$	−24.2569	+	9.14334i	−0.935732	+	0.352712i
$673$	−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	$0.550324\pi$
$678$	5.23284	−	31.1638i	0.200966	−	1.19684i
$679$	−5.01489	+	15.5715i	−0.192454	+	0.597581i
$680$	−13.2727	+	44.8869i	−0.508987	+	1.72133i
$681$	−20.4833	+	5.85765i	−0.784923	+	0.224466i
$682$	14.4663	−	9.94584i	0.553945	−	0.380846i
$683$			35.6698i			1.36487i	0.730948	+	0.682433i	$0.239078\pi$
$683$			35.6698i			1.36487i	−0.730948	+	0.682433i	$0.760922\pi$
$684$	−20.0916	+	17.4262i	−0.768221	+	0.666306i
$685$		−	11.1249i		−	0.425059i
$686$	8.54665	−	24.7579i	0.326313	−	0.945262i
$687$	−7.71800	+	7.98079i	−0.294460	+	0.304486i
$688$	4.24555	+	0.899591i	0.161860	+	0.0342966i
$689$	11.1661	+	6.44673i	0.425393	+	0.245601i
$690$	8.55491	+	7.06011i	0.325680	+	0.268774i
$691$	−7.74976	−	13.4230i	−0.294815	−	0.510634i	0.680127	−	0.733094i	$-0.261925\pi$
$691$	−7.74976	−	13.4230i	−0.294815	−	0.510634i	−0.974942	+	0.222460i	$0.928591\pi$
$692$	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
$696$	7.56044	−	4.27513i	0.286578	−	0.162048i
$697$	−25.2578	+	43.7477i	−0.956706	+	1.65706i
$698$	35.0439	+	16.7082i	1.32643	+	0.632416i
$699$	6.13548	−	24.5333i	0.232065	−	0.927934i
$700$	5.93862	−	7.37741i	0.224459	−	0.278840i
$701$	30.0954			1.13669			0.568344	−	0.822791i	$-0.307584\pi$
$701$	30.0954			1.13669			0.568344	+	0.822791i	$0.307584\pi$
$702$	17.3874	+	13.3967i	0.656244	+	0.505628i
$703$	19.8416			0.748340
$704$	−19.1231	+	29.5088i	−0.720731	+	1.11216i
$705$	40.1692	+	10.0458i	1.51286	+	0.378348i
$706$	−39.4648	−	18.8160i	−1.48528	−	0.708150i
$707$	11.8127	−	36.6793i	0.444264	−	1.37947i
$708$	−25.7626	+	12.0009i	−0.968218	+	0.451020i
$709$	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
$714$	−36.5478	−	18.9310i	−1.36777	−	0.708476i
$715$	29.6274	+	17.1054i	1.10800	+	0.639705i
$716$	26.6213	+	10.2092i	0.994883	+	0.381536i
$717$	8.76006	−	9.05833i	0.327150	−	0.338290i
$718$	−12.9843	+	8.92691i	−0.484570	+	0.333149i
$719$	8.18208			0.305140			0.152570	−	0.988293i	$-0.451245\pi$
$719$	8.18208			0.305140			0.152570	+	0.988293i	$0.451245\pi$
$720$	5.45415	−	30.7893i	0.203264	−	1.14745i
$721$	−9.98818	−	46.3987i	−0.371979	−	1.72798i
$722$	−0.519508	−	0.755631i	−0.0193341	−	0.0281217i
$723$	5.41476	+	18.9346i	0.201377	+	0.704185i
$724$	−7.92185	−	3.03802i	−0.294413	−	0.112907i
$725$	−1.58656	+	2.74801i	−0.0589235	+	0.102059i
$726$	−3.37471	+	20.0978i	−0.125247	+	0.745901i
$727$	−1.20415	−	2.08565i	−0.0446595	−	0.0773525i	0.842832	−	0.538177i	$-0.180887\pi$
$727$	−1.20415	−	2.08565i	−0.0446595	−	0.0773525i	−0.887491	+	0.460825i	$0.847554\pi$
$728$	−20.1454	+	9.68495i	−0.746640	+	0.358948i
$729$	−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
$732$	14.2475	+	1.25219i	0.526604	+	0.0462822i
$733$	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	$0.528563\pi$
$734$	−14.6054	+	30.6334i	−0.539095	+	1.13070i
$735$	20.4154	+	24.1104i	0.753033	+	0.889324i
$736$	−5.97827	+	7.80390i	−0.220362	+	0.287656i
$737$	19.9175			0.733671
$738$	13.4952	−	30.9293i	0.496766	−	1.13852i
$739$			12.2257i			0.449729i	0.974390	+	0.224865i	$0.0721940\pi$
$739$			12.2257i			0.449729i	−0.974390	+	0.224865i	$0.927806\pi$
$740$	−18.1243	+	14.6863i	−0.666263	+	0.539881i
$741$	−15.9423	+	16.4851i	−0.585654	+	0.605595i
$742$	15.7151	+	3.72714i	0.576919	+	0.136828i
$743$	9.48896	+	5.47845i	0.348116	+	0.200985i	0.663855	−	0.747861i	$-0.268919\pi$
$743$	9.48896	+	5.47845i	0.348116	+	0.200985i	−0.315739	+	0.948846i	$0.602252\pi$
$744$	−11.9196	−	7.02499i	−0.436994	−	0.257549i
$745$	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
$750$	−7.16501	−	19.1962i	−0.261629	−	0.700946i
$751$	−23.5744	−	13.6107i	−0.860242	−	0.496661i	0.00385154	−	0.999993i	$-0.498774\pi$
$751$	−23.5744	−	13.6107i	−0.860242	−	0.496661i	−0.864093	+	0.503332i	$0.832107\pi$
$752$	−7.60697	+	35.9005i	−0.277398	+	1.30916i
$753$	−4.24321	+	16.9669i	−0.154631	+	0.618307i
$754$	6.17136	−	4.24291i	0.224748	−	0.154518i
$755$	−31.7488			−1.15546
$756$	25.6768	+	9.83381i	0.933855	+	0.357652i
$757$	24.4479			0.888572			0.444286	−	0.895885i	$-0.353457\pi$
$757$	24.4479			0.888572			0.444286	+	0.895885i	$0.353457\pi$
$758$	−6.86688	+	4.72108i	−0.249416	+	0.171478i
$759$	−3.20986	+	12.8349i	−0.116510	+	0.465878i
$760$	31.3282	+	9.26353i	1.13639	+	0.336024i
$761$	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	$0.607324\pi$
$762$	−10.4166	−	27.9076i	−0.377352	−	1.01099i
$763$	−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
$768$	27.4453	+	3.84150i	0.990346	+	0.138618i
$769$	−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	$-0.695314\pi$
$770$	41.6975	+	9.88937i	1.50267	+	0.356388i
$771$	7.89916	−	8.16812i	0.284481	−	0.294168i
$772$	2.02315	+	2.49676i	0.0728148	+	0.0898602i
$773$			2.39611i			0.0861820i	0.999071	+	0.0430910i	$0.0137205\pi$
$773$			2.39611i			0.0861820i	−0.999071	+	0.0430910i	$0.986279\pi$
$774$	−2.73330	−	3.70368i	−0.0982466	−	0.133126i
$775$	5.05473			0.181571
$776$	12.6801	−	12.0445i	0.455188	−	0.432371i
$777$	−9.66412	−	18.0935i	−0.346698	−	0.649101i
$778$	−2.76017	+	5.78919i	−0.0989568	+	0.207552i
$779$	30.5331	+	17.6283i	1.09396	+	0.631600i
$780$	2.36054	−	26.8585i	0.0845208	−	0.961687i
$781$	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
$784$	−20.6986	+	18.8565i	−0.739235	+	0.673447i
$785$	−19.8036	−	34.3009i	−0.706821	−	1.22425i
$786$	−6.24085	+	37.1669i	−0.222604	+	1.32570i
$787$	26.4412	−	45.7975i	0.942527	−	1.63251i	0.181899	−	0.983317i	$-0.441776\pi$
$787$	26.4412	−	45.7975i	0.942527	−	1.63251i	0.760628	−	0.649188i	$-0.224891\pi$
$788$	6.73992	−	17.5748i	0.240100	−	0.626078i
$789$	4.75583	+	16.6304i	0.169312	+	0.592059i
$790$	28.2955	+	41.1561i	1.00671	+	1.46427i
$791$	−7.18299	−	33.3676i	−0.255398	−	1.18642i
$792$	35.9495	−	9.93281i	1.27741	−	0.352947i
$793$	12.3326			0.437943
$794$	28.9976	−	19.9363i	1.02908	−	0.707512i
$795$	−13.5431	+	14.0042i	−0.480324	+	0.496679i
$796$	3.30643	−	8.62175i	0.117193	−	0.305590i
$797$	−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	$0.737046\pi$
$798$	−13.2126	+	25.5080i	−0.467723	+	0.902974i
$799$	−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
$804$	−6.62833	−	14.2292i	−0.233763	−	0.501826i
$805$	11.4039	+	3.67268i	0.401934	+	0.129445i
$806$	−10.7688	−	5.13434i	−0.379314	−	0.180849i
$807$	4.25906	+	1.06514i	0.149926	+	0.0374946i
$808$	−29.8683	+	28.3712i	−1.05076	+	0.998094i
$809$	−22.4198			−0.788239			−0.394119	−	0.919059i	$-0.628950\pi$
$809$	−22.4198			−0.788239			−0.394119	+	0.919059i	$0.628950\pi$
$810$	−26.0112	+	20.5758i	−0.913941	+	0.722959i
$811$	4.09813			0.143905			0.0719525	−	0.997408i	$-0.477077\pi$
$811$	4.09813			0.143905			0.0719525	+	0.997408i	$0.477077\pi$
$812$	5.88262	−	7.30784i	0.206440	−	0.256455i
$813$	−4.38979	+	17.5530i	−0.153957	+	0.615610i
$814$	−25.1160	−	11.9748i	−0.880315	−	0.419716i
$815$	5.19273	−	8.99408i	0.181894	−	0.315049i
$816$	24.6026	+	36.4809i	0.861262	+	1.27709i
$817$	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	$0.863992\pi$
$822$	−8.06583	−	6.65649i	−0.281328	−	0.232172i
$823$	42.9452	+	24.7944i	1.49697	+	0.864278i	0.999994	−	0.00348342i	$-0.00110881\pi$
$823$	42.9452	+	24.7944i	1.49697	+	0.864278i	0.496980	+	0.867762i	$0.334442\pi$
$824$	−14.3873	+	48.6560i	−0.501204	+	1.69501i
$825$	−9.47230	+	9.79483i	−0.329783	+	0.341012i
$826$	−21.0696	+	22.3255i	−0.733105	+	0.776803i
$827$		−	4.41558i		−	0.153545i	−0.997049	−	0.0767723i	$-0.975539\pi$
$827$		−	4.41558i		−	0.153545i	0.997049	−	0.0767723i	$-0.0244615\pi$
$828$	10.2376	−	1.97817i	0.355780	−	0.0687462i
$829$		−	6.00543i		−	0.208577i	−0.994547	−	0.104289i	$-0.966743\pi$
$829$		−	6.00543i		−	0.208577i	0.994547	−	0.104289i	$-0.0332566\pi$
$830$	3.14711	−	2.16369i	0.109238	−	0.0751026i
$831$	−34.6210	+	9.90063i	−1.20099	+	0.343449i
$832$	23.8643	+	1.22779i	0.827347	+	0.0425659i
$833$	−44.2376	−	4.41771i	−1.53274	−	0.153064i
$834$	−8.69851	+	51.8034i	−0.301205	+	1.79380i
$835$	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	0.540061	−	0.841626i	$-0.318401\pi$
$839$	−13.2905	−	23.0198i	−0.458839	−	0.794732i	−0.998900	+	0.0468940i	$0.985068\pi$
$840$	−6.81142	−	33.0800i	−0.235016	−	1.14137i
$841$	12.9284	−	22.3926i	0.445807	−	0.772160i
$842$	−6.13860	+	12.8751i	−0.211550	+	0.443706i
$843$	−14.8998	+	4.26092i	−0.513176	+	0.146754i
$844$	40.0582	−	32.4597i	1.37886	−	1.11731i
$845$			10.6259i			0.365541i
$846$	31.3185	−	23.1129i	1.07675	−	0.794638i
$847$	4.63238	+	21.5191i	0.159171	+	0.739405i
$848$	−12.8386	−	11.5451i	−0.440881	−	0.396462i
$849$	−28.2864	−	27.3550i	−0.970788	−	0.938821i
$850$	−14.5106	−	6.91836i	−0.497709	−	0.237298i
$851$	−6.73672	−	3.88945i	−0.230932	−	0.133328i
$852$	23.6192	−	33.7032i	0.809179	−	1.15465i
$853$	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	$0.204060\pi$
$854$	14.8001	−	4.42835i	0.506450	−	0.151535i
$855$	−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	$0.553289\pi$
$858$	30.1292	−	11.2458i	1.02859	−	0.383924i
$859$	3.22640	−	5.58830i	0.110084	−	0.190670i	−0.805720	−	0.592296i	$-0.798222\pi$
$859$	3.22640	−	5.58830i	0.110084	−	0.190670i	0.915804	+	0.401626i	$0.131555\pi$
$860$	−2.02459	+	5.27927i	−0.0690380	+	0.180022i
$861$	1.20364	−	36.4292i	0.0410200	−	1.24150i
$862$	22.7109	−	15.6141i	0.773538	−	0.531819i
$863$			28.0729i			0.955612i	0.878465	+	0.477806i	$0.158568\pi$
$863$			28.0729i			0.955612i	−0.878465	+	0.477806i	$0.841432\pi$
$864$	−19.0596	−	22.3770i	−0.648422	−	0.761281i
$865$	−15.3437			−0.521702
$866$	−4.79961	+	3.29981i	−0.163098	+	0.112132i
$867$	−9.80643	+	39.2120i	−0.333044	+	1.33171i
$868$	−14.7671	−	2.29481i	−0.501227	−	0.0778909i
$869$	−29.7863	+	51.5913i	−1.01043	+	1.75012i
$870$	3.95703	+	10.6015i	0.134156	+	0.359425i
$871$	−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
$876$	15.2888	−	21.8162i	0.516559	−	0.737101i
$877$	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	$-0.00234250\pi$
$878$	4.27928	−	8.97537i	0.144419	−	0.302904i
$879$	7.15629	−	7.39996i	0.241376	−	0.249594i
$880$	−34.0653	−	30.6332i	−1.14834	−	1.03264i
$881$		−	38.3766i		−	1.29294i	−0.762939	−	0.646471i	$-0.776244\pi$
$881$		−	38.3766i		−	1.29294i	0.762939	−	0.646471i	$-0.223756\pi$
$882$	29.6961	−	0.375443i	0.999920	−	0.0126418i
$883$		−	37.0722i		−	1.24758i	−0.781593	−	0.623789i	$-0.785593\pi$
$883$		−	37.0722i		−	1.24758i	0.781593	−	0.623789i	$-0.214407\pi$
$884$	23.8866	+	29.4783i	0.803393	+	0.991461i
$885$	−10.1809	−	35.6010i	−0.342226	−	1.19672i
$886$	−41.5233	−	19.7975i	−1.39500	−	0.665110i
$887$	−12.2145	+	21.1562i	−0.410123	+	0.710355i	−0.994903	−	0.100838i	$-0.967848\pi$
$887$	−12.2145	+	21.1562i	−0.410123	+	0.710355i	0.584779	+	0.811192i	$0.301181\pi$
$888$	−0.196559	+	21.9281i	−0.00659610	+	0.735859i
$889$	−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
$894$	4.23888	−	25.2443i	0.141769	−	0.844297i
$895$	−18.5734	+	32.1701i	−0.620841	+	1.07533i
$896$	29.0801	−	7.09569i	0.971497	−	0.237050i
$897$	8.64429	−	2.47202i	0.288624	−	0.0825384i
$898$	−30.9743	−	45.0524i	−1.03362	−	1.50342i
$899$	5.00706			0.166995
$900$	10.1498	+	3.50747i	0.338325	+	0.116916i
$901$		−	27.4147i		−	0.913318i
$902$	−28.0106	−	40.7417i	−0.932650	−	1.35655i
$903$	−4.22133	−	2.62677i	−0.140477	−	0.0874135i
$904$	−10.3466	+	34.9910i	−0.344123	+	1.16378i
$905$	5.52700	−	9.57305i	0.183724	−	0.318219i
$906$	−18.9967	+	23.0188i	−0.631123	+	0.764747i
$907$	17.3676	−	10.0272i	0.576683	−	0.332948i	−0.183131	−	0.983089i	$-0.558623\pi$
$907$	17.3676	−	10.0272i	0.576683	−	0.332948i	0.759814	+	0.650140i	$0.225290\pi$
$908$	24.2962	−	3.85608i	0.806296	−	0.127968i
$909$	43.6696	−	1.46244i	1.44843	−	0.0485060i
$910$	−8.34801	−	27.9002i	−0.276734	−	0.924881i
$911$	−12.8106	+	7.39618i	−0.424433	+	0.245046i	−0.696972	−	0.717098i	$-0.745470\pi$
$911$	−12.8106	+	7.39618i	−0.424433	+	0.245046i	0.272539	+	0.962145i	$0.412136\pi$
$912$	25.4613	−	17.1710i	0.843109	−	0.568589i
$913$	3.94506	+	2.27768i	0.130563	+	0.0753803i
$914$	13.8887	−	29.1302i	0.459397	−	0.963542i
$915$	−4.52093	+	18.0774i	−0.149457	+	0.597620i
$916$	9.96029	−	8.07094i	0.329097	−	0.266671i
$917$	8.56667	+	39.7953i	0.282896	+	1.31416i
$918$	6.18365	−	46.2593i	0.204091	−	1.52678i
$919$		−	47.6023i		−	1.57026i	−0.619333	−	0.785128i	$-0.712597\pi$
$919$		−	47.6023i		−	1.57026i	0.619333	−	0.785128i	$-0.287403\pi$
$920$	−8.82082	−	9.28630i	−0.290814	−	0.306160i
$921$	−4.23455	+	16.9323i	−0.139533	+	0.557937i
$922$	16.4496	+	7.84283i	0.541739	+	0.258290i
$923$	17.7435	−	30.7327i	0.584036	−	1.01158i
$924$	32.1195	−	24.3146i	1.05665	−	0.799891i
$925$	−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	$0.346780\pi$
$930$	11.4737	−	13.9030i	0.376237	−	0.455896i
$931$	−3.08328	+	30.8750i	−0.101050	+	1.01189i
$932$	−10.4560	+	27.2649i	−0.342499	+	0.893091i
$933$	0.0993087	+	0.0960386i	0.00325122	+	0.00314416i
$934$	−20.3635	−	29.6190i	−0.666314	−	0.969162i
$935$		−	72.7406i		−	2.37887i
$936$	−18.0607	−	17.7821i	−0.590333	−	0.581225i
$937$			10.0050i			0.326849i	0.986556	+	0.163424i	$0.0522539\pi$
$937$			10.0050i			0.326849i	−0.986556	+	0.163424i	$0.947746\pi$
$938$	−12.3308	−	11.6372i	−0.402615	−	0.379967i
$939$	11.3601	+	39.7246i	0.370723	+	1.29636i
$940$	−44.6417	−	17.1200i	−1.45605	−	0.558393i
$941$	−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	$0.891665\pi$
$942$	−36.7184	−	6.16554i	−1.19635	−	0.200884i
$943$	−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	−0.00745153	−	0.999972i	$-0.502372\pi$
$947$	26.3058	−	15.1877i	0.854824	−	0.493533i	0.862276	+	0.506439i	$0.169039\pi$
$948$	46.7697	+	4.11050i	1.51901	+	0.133503i
$949$	11.4854	−	19.8934i	0.372833	−	0.645766i
$950$	−4.82857	+	10.1275i	−0.156660	+	0.328579i
$951$	6.60454	−	1.88871i	0.214167	−	0.0612457i
$952$	39.2509	+	26.7992i	1.27213	+	0.868569i
$953$	27.5080			0.891073			0.445536	−	0.895264i	$-0.353013\pi$
$953$	27.5080			0.891073			0.445536	+	0.895264i	$0.353013\pi$
$954$	2.05002	+	18.1985i	0.0663720	+	0.589197i
$955$	6.04232			0.195525
$956$	−11.3051	+	9.16065i	−0.365633	+	0.296277i
$957$	−9.38298	+	9.70247i	−0.303309	+	0.313636i
$958$	−19.1206	+	40.1035i	−0.617757	+	1.29569i
$959$	−10.7519	−	3.46271i	−0.347198	−	0.111817i
$960$	−10.5480	+	34.5308i	−0.340436	+	1.11448i
$961$	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
$966$	9.48623	−	6.07060i	0.305214	−	0.195318i
$967$	−51.9168	−	29.9742i	−1.66953	−	0.963905i	−0.967889	−	0.251377i	$-0.919117\pi$
$967$	−51.9168	−	29.9742i	−1.66953	−	0.963905i	−0.701644	−	0.712528i	$-0.747550\pi$
$968$	6.67262	−	22.5660i	0.214466	−	0.725300i
$969$	47.3041	+	11.8302i	1.51963	+	0.380040i
$970$	12.9087	+	18.7759i	0.414474	+	0.602858i
$971$	30.8420			0.989768			0.494884	−	0.868959i	$-0.335211\pi$
$971$	30.8420			0.989768			0.494884	+	0.868959i	$0.335211\pi$
$972$	−0.645642	+	31.1702i	−0.0207090	+	0.999786i
$973$	11.9402	+	55.4668i	0.382787	+	1.77818i
$974$	−32.4743	+	22.3266i	−1.04054	+	0.715391i
$975$	8.98301	+	2.24654i	0.287686	+	0.0719469i
$976$	−16.1564	−	3.42337i	−0.517152	−	0.109579i
$977$	−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	$0.230442\pi$
$978$	−3.41392	−	9.14643i	−0.109165	−	0.292470i
$979$	0.368371	+	0.638037i	0.0117732	+	0.0203918i
$980$	−20.0366	−	30.4849i	−0.640046	−	0.973806i
$981$	−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	0.875251	−	0.483670i	$-0.160696\pi$
$983$	0.588026	+	1.01849i	0.0187551	+	0.0324848i	−0.856496	+	0.516154i	$0.827363\pi$
$984$	−19.7846	+	33.5693i	−0.630708	+	1.07015i
$985$	21.2381	+	12.2618i	0.676702	+	0.390694i
$986$	−14.3738	−	6.85312i	−0.457754	−	0.218248i
$987$	22.2121	−	35.6958i	0.707018	−	1.13621i
$988$	20.5739	−	16.6713i	0.654544	−	0.530385i
$989$	−1.88545			−0.0599539
$990$	5.43941	+	48.2867i	0.172876	+	1.53465i
$991$		−	7.08869i		−	0.225180i	−0.993642	−	0.112590i	$-0.964085\pi$
$991$		−	7.08869i		−	0.225180i	0.993642	−	0.112590i	$-0.0359146\pi$
$992$	12.6825	+	9.71555i	0.402669	+	0.308469i
$993$	9.46496	+	33.0976i	0.300361	+	1.05032i
$994$	10.2583	−	43.2531i	0.325374	−	1.37191i
$995$	10.4188	+	6.01532i	0.330299	+	0.190698i
$996$	0.314320	−	3.57637i	0.00995961	−	0.113322i
$997$	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.139.14	yes	80
3.2	odd	2		756.2.bi.c.307.28		80
4.3	odd	2	inner	252.2.bi.c.139.15	yes	80
7.6	odd	2	inner	252.2.bi.c.139.13	✓	80
9.2	odd	6		756.2.bi.c.559.25		80
9.7	even	3	inner	252.2.bi.c.223.16	yes	80
12.11	even	2		756.2.bi.c.307.26		80
21.20	even	2		756.2.bi.c.307.27		80
28.27	even	2	inner	252.2.bi.c.139.16	yes	80
36.7	odd	6	inner	252.2.bi.c.223.13	yes	80
36.11	even	6		756.2.bi.c.559.27		80
63.20	even	6		756.2.bi.c.559.26		80
63.34	odd	6	inner	252.2.bi.c.223.15	yes	80
84.83	odd	2		756.2.bi.c.307.25		80
252.83	odd	6		756.2.bi.c.559.28		80
252.223	even	6	inner	252.2.bi.c.223.14	yes	80

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

\(f(q)\)	\(=\)	\(q+(-0.801205 - 1.16536i) q^{2} +(0.420223 - 1.68030i) q^{3} +(-0.716141 + 1.86739i) q^{4} +(-2.25662 - 1.30286i) q^{5} +(-2.29485 + 0.856554i) q^{6} +(-1.96158 + 1.77545i) q^{7} +(2.74996 - 0.661599i) q^{8} +(-2.64683 - 1.41220i) q^{9} +O(q^{10})\)	\(q+(-0.801205 - 1.16536i) q^{2} +(0.420223 - 1.68030i) q^{3} +(-0.716141 + 1.86739i) q^{4} +(-2.25662 - 1.30286i) q^{5} +(-2.29485 + 0.856554i) 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} +(2.83684 + 1.98805i) q^{12} +(2.58681 + 1.49349i) q^{13} +(3.64067 + 0.863454i) q^{14} +(-3.13748 + 3.24431i) q^{15} +(-2.97429 - 2.67463i) q^{16} -6.35108i q^{17} +(0.474923 + 4.21598i) q^{18} -4.43265 q^{19} +(4.04901 - 3.28096i) q^{20} +(2.15898 + 4.04213i) q^{21} +(5.61096 + 2.67519i) q^{22} +(1.50500 + 0.868910i) q^{23} +(0.0439117 - 4.89878i) q^{24} +(0.894893 + 1.55000i) q^{25} +(-0.332101 - 4.21116i) q^{26} +(-3.48518 + 3.85402i) q^{27} +(-1.91068 - 4.93450i) q^{28} +(0.886455 + 1.53538i) q^{29} +(6.29457 + 1.05695i) q^{30} +(1.41210 - 2.44584i) q^{31} +(-0.733897 + 5.60905i) q^{32} +(2.09322 + 7.31968i) q^{33} +(-7.40132 + 5.08852i) q^{34} +(6.73970 - 1.45084i) q^{35} +(4.53263 - 3.93132i) q^{36} -4.47624 q^{37} +(3.55146 + 5.16565i) q^{38} +(3.59656 - 3.71902i) q^{39} +(-7.06759 - 2.08984i) q^{40} +(-6.88823 - 3.97692i) q^{41} +(2.98075 - 5.75457i) 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} +(-5.74404 + 3.87376i) q^{48} +(0.695583 - 6.96535i) q^{49} +(1.08932 - 2.28474i) q^{50} +(-10.6717 - 2.66887i) q^{51} +(-4.64145 + 3.76102i) q^{52} +4.31655 q^{53} +(7.28368 + 0.973636i) q^{54} +11.4533 q^{55} +(-4.21963 + 6.18019i) q^{56} +(-1.86270 + 7.44819i) q^{57} +(1.07905 - 2.26320i) q^{58} +(-4.10217 + 7.10516i) q^{59} +(-3.81151 - 8.18228i) 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} +(6.85299 - 8.30393i) q^{66} +(-3.92432 - 2.26571i) q^{67} +(11.8599 + 4.54827i) q^{68} +(2.09246 - 2.16371i) q^{69} +(-7.09064 - 6.69177i) q^{70} -11.8806i q^{71} +(-8.21298 - 2.13237i) q^{72} -7.69032i q^{73} +(3.58638 + 5.21644i) q^{74} +(2.98052 - 0.852344i) q^{75} +(3.17440 - 8.27749i) q^{76} +(3.56493 - 11.0693i) q^{77} +(-7.21558 - 1.21160i) 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} +(-9.09436 + 1.13693i) q^{84} +(-8.27458 + 14.3320i) q^{85} +(1.38499 + 0.660336i) q^{86} +(2.95242 - 0.844307i) q^{87} +(-9.01386 + 8.56204i) q^{88} -0.167616i q^{89} +(4.42111 - 10.1326i) q^{90} +(-7.72584 + 1.66313i) q^{91} +(-2.70038 + 2.18815i) q^{92} +(-3.51634 - 3.40056i) q^{93} +(-5.58383 + 11.7115i) q^{94} +(10.0028 + 5.77513i) q^{95} +(9.11649 + 3.59022i) q^{96} +(5.35479 - 3.09159i) q^{97} +(-8.67447 + 4.77007i) 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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